diff --git a/.gitattributes b/.gitattributes
index 0995f3ba28f945bb7cdb29489fe724313ac00e63..d424d6fbf704c45ff2e95f88109db7f742655332 100644
--- a/.gitattributes
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diff --git a/venv/lib/python3.12/site-packages/scipy-1.18.0.dist-info/INSTALLER b/venv/lib/python3.12/site-packages/scipy-1.18.0.dist-info/INSTALLER
new file mode 100644
index 0000000000000000000000000000000000000000..a1b589e38a32041e49332e5e81c2d363dc418d68
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy-1.18.0.dist-info/INSTALLER
@@ -0,0 +1 @@
+pip
diff --git a/venv/lib/python3.12/site-packages/scipy-1.18.0.dist-info/LICENSE.txt b/venv/lib/python3.12/site-packages/scipy-1.18.0.dist-info/LICENSE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..99828059c9523a0c94c7850a92843c0dfc9db548
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy-1.18.0.dist-info/LICENSE.txt
@@ -0,0 +1,937 @@
+Copyright (c) 2001-2002 Enthought, Inc. 2003, SciPy Developers.
+All rights reserved.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions
+are met:
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+1. Redistributions of source code must retain the above copyright
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+2. Redistributions in binary form must reproduce the above
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+3. Neither the name of the copyright holder nor the names of its
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+OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
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+DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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+
+----
+
+
+----
+
+This binary distribution of SciPy can also bundle the following software
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+
+Name: OpenBLAS
+Files: scipy.libs/libscipy_openblas*.so
+Description: bundled as a dynamically linked library
+Availability: https://github.com/OpenMathLib/OpenBLAS/
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+        distribution.
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+        derived from this software without specific prior written 
+        permission.
+  
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+
+
+Name: LAPACK
+Files: scipy.libs/libscipy_openblas*.so
+Description: bundled in OpenBLAS
+Availability: https://github.com/OpenMathLib/OpenBLAS/
+License: BSD-3-Clause-Open-MPI
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+Files: scipy.libs/libgfortran*.so
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+License: GPL-3.0-or-later WITH GCC-exception-3.1
+  Copyright (C) 2002-2017 Free Software Foundation, Inc.
+  
+  Libgfortran is free software; you can redistribute it and/or modify
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+  any later version.
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+  see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
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+
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+GCC RUNTIME LIBRARY EXCEPTION
+
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+
+----
+
+                    GNU GENERAL PUBLIC LICENSE
+                       Version 3, 29 June 2007
+
+ Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>
+ Everyone is permitted to copy and distribute verbatim copies
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+Files: scipy.libs/libquadmath*.so
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+License: LGPL-2.1-or-later
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diff --git a/venv/lib/python3.12/site-packages/scipy-1.18.0.dist-info/METADATA b/venv/lib/python3.12/site-packages/scipy-1.18.0.dist-info/METADATA
new file mode 100644
index 0000000000000000000000000000000000000000..102405d833b43b23254d3dc1d5bf061193150280
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy-1.18.0.dist-info/METADATA
@@ -0,0 +1,1091 @@
+Metadata-Version: 2.1
+Name: scipy
+Version: 1.18.0
+Summary: Fundamental algorithms for scientific computing in Python
+Maintainer-Email: SciPy Developers <scipy-dev@python.org>
+License: Copyright (c) 2001-2002 Enthought, Inc. 2003, SciPy Developers.
+         All rights reserved.
+         
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+         
+             c) Convey individual copies of the object code with a copy of the
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+             only if you received the object code with such an offer, in accord
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+         
+             d) Convey the object code by offering access from a designated
+             place (gratis or for a charge), and offer equivalent access to the
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+         
+             e) Convey the object code using peer-to-peer transmission, provided
+             you inform other peers where the object code and Corresponding
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+             charge under subsection 6d.
+         
+           A separable portion of the object code, whose source code is excluded
+         from the Corresponding Source as a System Library, need not be
+         included in conveying the object code work.
+         
+           A "User Product" is either (1) a "consumer product", which means any
+         tangible personal property which is normally used for personal, family,
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+           "Installation Information" for a User Product means any methods,
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+           If you convey an object code work under this section in, or with, or
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+         modified object code on the User Product (for example, the work has
+         been installed in ROM).
+         
+           The requirement to provide Installation Information does not include a
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+         the User Product in which it has been modified or installed.  Access to a
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+           Corresponding Source conveyed, and Installation Information provided,
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+         documented (and with an implementation available to the public in
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+         unpacking, reading or copying.
+         
+           7. Additional Terms.
+         
+           "Additional permissions" are terms that supplement the terms of this
+         License by making exceptions from one or more of its conditions.
+         Additional permissions that are applicable to the entire Program shall
+         be treated as though they were included in this License, to the extent
+         that they are valid under applicable law.  If additional permissions
+         apply only to part of the Program, that part may be used separately
+         under those permissions, but the entire Program remains governed by
+         this License without regard to the additional permissions.
+         
+           When you convey a copy of a covered work, you may at your option
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+           Notwithstanding any other provision of this License, for material you
+         add to a covered work, you may (if authorized by the copyright holders of
+         that material) supplement the terms of this License with terms:
+         
+             a) Disclaiming warranty or limiting liability differently from the
+             terms of sections 15 and 16 of this License; or
+         
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+         
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+             e) Declining to grant rights under trademark law for use of some
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+           All other non-permissive additional terms are considered "further
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+         received it, or any part of it, contains a notice stating that it is
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+           You may not propagate or modify a covered work except as expressly
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+           However, if you cease all violation of this License, then your
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+           Moreover, your license from a particular copyright holder is
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+           Termination of your rights under this section does not terminate the
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+         
+           9. Acceptance Not Required for Having Copies.
+         
+           You are not required to accept this License in order to receive or
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+         occurring solely as a consequence of using peer-to-peer transmission
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+         nothing other than this License grants you permission to propagate or
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+         not accept this License.  Therefore, by modifying or propagating a
+         covered work, you indicate your acceptance of this License to do so.
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+           10. Automatic Licensing of Downstream Recipients.
+         
+           Each time you convey a covered work, the recipient automatically
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+         propagate that work, subject to this License.  You are not responsible
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+           An "entity transaction" is a transaction transferring control of an
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+         any patent claim is infringed by making, using, selling, offering for
+         sale, or importing the Program or any portion of it.
+         
+           11. Patents.
+         
+           A "contributor" is a copyright holder who authorizes use under this
+         License of the Program or a work on which the Program is based.  The
+         work thus licensed is called the contributor's "contributor version".
+         
+           A contributor's "essential patent claims" are all patent claims
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+         hereafter acquired, that would be infringed by some manner, permitted
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+         consequence of further modification of the contributor version.  For
+         purposes of this definition, "control" includes the right to grant
+         patent sublicenses in a manner consistent with the requirements of
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+         
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+         patent license under the contributor's essential patent claims, to
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+         
+           In the following three paragraphs, a "patent license" is any express
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+         
+           If you convey a covered work, knowingly relying on a patent license,
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+         available, or (2) arrange to deprive yourself of the benefit of the
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+         consistent with the requirements of this License, to extend the patent
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+         actual knowledge that, but for the patent license, your conveying the
+         covered work in a country, or your recipient's use of the covered work
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+         
+           If, pursuant to or in connection with a single transaction or
+         arrangement, you convey, or propagate by procuring conveyance of, a
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+         
+           A patent license is "discriminatory" if it does not include within
+         the scope of its coverage, prohibits the exercise of, or is
+         conditioned on the non-exercise of one or more of the rights that are
+         specifically granted under this License.  You may not convey a covered
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+         in the business of distributing software, under which you make payment
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+         for and in connection with specific products or compilations that
+         contain the covered work, unless you entered into that arrangement,
+         or that patent license was granted, prior to 28 March 2007.
+         
+           Nothing in this License shall be construed as excluding or limiting
+         any implied license or other defenses to infringement that may
+         otherwise be available to you under applicable patent law.
+         
+           12. No Surrender of Others' Freedom.
+         
+           If conditions are imposed on you (whether by court order, agreement or
+         otherwise) that contradict the conditions of this License, they do not
+         excuse you from the conditions of this License.  If you cannot convey a
+         covered work so as to satisfy simultaneously your obligations under this
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+         not convey it at all.  For example, if you agree to terms that obligate you
+         to collect a royalty for further conveying from those to whom you convey
+         the Program, the only way you could satisfy both those terms and this
+         License would be to refrain entirely from conveying the Program.
+         
+           13. Use with the GNU Affero General Public License.
+         
+           Notwithstanding any other provision of this License, you have
+         permission to link or combine any covered work with a work licensed
+         under version 3 of the GNU Affero General Public License into a single
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+         License will continue to apply to the part which is the covered work,
+         but the special requirements of the GNU Affero General Public License,
+         section 13, concerning interaction through a network will apply to the
+         combination as such.
+         
+           14. Revised Versions of this License.
+         
+           The Free Software Foundation may publish revised and/or new versions of
+         the GNU General Public License from time to time.  Such new versions will
+         be similar in spirit to the present version, but may differ in detail to
+         address new problems or concerns.
+         
+           Each version is given a distinguishing version number.  If the
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+         Public License "or any later version" applies to it, you have the
+         option of following the terms and conditions either of that numbered
+         version or of any later version published by the Free Software
+         Foundation.  If the Program does not specify a version number of the
+         GNU General Public License, you may choose any version ever published
+         by the Free Software Foundation.
+         
+           If the Program specifies that a proxy can decide which future
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+         permissions.  However, no additional obligations are imposed on any
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+         later version.
+         
+           15. Disclaimer of Warranty.
+         
+           THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY
+         APPLICABLE LAW.  EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT
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+           16. Limitation of Liability.
+         
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+         
+           17. Interpretation of Sections 15 and 16.
+         
+           If the disclaimer of warranty and limitation of liability provided
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+         copy of the Program in return for a fee.
+         
+                              END OF TERMS AND CONDITIONS
+         
+                     How to Apply These Terms to Your New Programs
+         
+           If you develop a new program, and you want it to be of the greatest
+         possible use to the public, the best way to achieve this is to make it
+         free software which everyone can redistribute and change under these terms.
+         
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+         the "copyright" line and a pointer to where the full notice is found.
+         
+             <one line to give the program's name and a brief idea of what it does.>
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+         
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+             (at your option) any later version.
+         
+             This program is distributed in the hope that it will be useful,
+             but WITHOUT ANY WARRANTY; without even the implied warranty of
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+         
+             You should have received a copy of the GNU General Public License
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+         
+         Also add information on how to contact you by electronic and paper mail.
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+         
+             <program>  Copyright (C) <year>  <name of author>
+             This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
+             This is free software, and you are welcome to redistribute it
+             under certain conditions; type `show c' for details.
+         
+         The hypothetical commands `show w' and `show c' should show the appropriate
+         parts of the General Public License.  Of course, your program's commands
+         might be different; for a GUI interface, you would use an "about box".
+         
+           You should also get your employer (if you work as a programmer) or school,
+         if any, to sign a "copyright disclaimer" for the program, if necessary.
+         For more information on this, and how to apply and follow the GNU GPL, see
+         <http://www.gnu.org/licenses/>.
+         
+           The GNU General Public License does not permit incorporating your program
+         into proprietary programs.  If your program is a subroutine library, you
+         may consider it more useful to permit linking proprietary applications with
+         the library.  If this is what you want to do, use the GNU Lesser General
+         Public License instead of this License.  But first, please read
+         <http://www.gnu.org/philosophy/why-not-lgpl.html>.
+         
+         
+         Name: libquadmath
+         Files: scipy.libs/libquadmath*.so
+         Description: dynamically linked to files compiled with gcc
+         Availability: https://gcc.gnu.org/git/?p=gcc.git;a=tree;f=libquadmath
+         License: LGPL-2.1-or-later
+         
+             GCC Quad-Precision Math Library
+             Copyright (C) 2010-2019 Free Software Foundation, Inc.
+             Written by Francois-Xavier Coudert  <fxcoudert@gcc.gnu.org>
+         
+             This file is part of the libquadmath library.
+             Libquadmath is free software; you can redistribute it and/or
+             modify it under the terms of the GNU Library General Public
+             License as published by the Free Software Foundation; either
+             version 2.1 of the License, or (at your option) any later version.
+         
+             Libquadmath is distributed in the hope that it will be useful,
+             but WITHOUT ANY WARRANTY; without even the implied warranty of
+             MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+             Lesser General Public License for more details.
+             https://www.gnu.org/licenses/old-licenses/lgpl-2.1.html
+         
+Classifier: Development Status :: 5 - Production/Stable
+Classifier: Intended Audience :: Science/Research
+Classifier: Intended Audience :: Developers
+Classifier: License :: OSI Approved :: BSD License
+Classifier: Programming Language :: C
+Classifier: Programming Language :: Python
+Classifier: Programming Language :: Python :: 3
+Classifier: Programming Language :: Python :: 3.12
+Classifier: Programming Language :: Python :: 3.13
+Classifier: Programming Language :: Python :: 3.14
+Classifier: Topic :: Software Development :: Libraries
+Classifier: Topic :: Scientific/Engineering
+Classifier: Operating System :: Microsoft :: Windows
+Classifier: Operating System :: POSIX :: Linux
+Classifier: Operating System :: POSIX
+Classifier: Operating System :: Unix
+Classifier: Operating System :: MacOS
+Project-URL: homepage, https://scipy.org/
+Project-URL: documentation, https://docs.scipy.org/doc/scipy/
+Project-URL: source, https://github.com/scipy/scipy
+Project-URL: download, https://github.com/scipy/scipy/releases
+Project-URL: tracker, https://github.com/scipy/scipy/issues
+Requires-Python: >=3.12
+Requires-Dist: numpy<2.8,>=2.0.0
+Provides-Extra: test
+Requires-Dist: pytest>=8.0.0; extra == "test"
+Requires-Dist: pytest-cov; extra == "test"
+Requires-Dist: pytest-timeout; extra == "test"
+Requires-Dist: pytest-xdist; extra == "test"
+Requires-Dist: asv; extra == "test"
+Requires-Dist: mpmath; extra == "test"
+Requires-Dist: gmpy2; extra == "test"
+Requires-Dist: threadpoolctl; extra == "test"
+Requires-Dist: scikit-umfpack; extra == "test"
+Requires-Dist: pooch; extra == "test"
+Requires-Dist: hypothesis>=6.30; extra == "test"
+Requires-Dist: array-api-strict>=2.3.1; extra == "test"
+Requires-Dist: Cython; extra == "test"
+Requires-Dist: meson; extra == "test"
+Requires-Dist: ninja; sys_platform != "emscripten" and extra == "test"
+Requires-Dist: scipy-doctest>=2.0.0; extra == "test"
+Provides-Extra: doc
+Requires-Dist: sphinx<8.2.0,>=5.0.0; extra == "doc"
+Requires-Dist: intersphinx_registry; extra == "doc"
+Requires-Dist: pydata-sphinx-theme>=0.15.2; extra == "doc"
+Requires-Dist: sphinx-copybutton; extra == "doc"
+Requires-Dist: sphinx-design>=0.4.0; extra == "doc"
+Requires-Dist: matplotlib>=3.5; extra == "doc"
+Requires-Dist: numpydoc; extra == "doc"
+Requires-Dist: jupytext; extra == "doc"
+Requires-Dist: myst-nb>=1.2.0; extra == "doc"
+Requires-Dist: pooch; extra == "doc"
+Requires-Dist: jupyterlite-sphinx>=0.19.1; extra == "doc"
+Requires-Dist: jupyterlite-pyodide-kernel; extra == "doc"
+Requires-Dist: linkify-it-py; extra == "doc"
+Requires-Dist: tabulate; extra == "doc"
+Provides-Extra: dev
+Requires-Dist: click<8.3.0; extra == "dev"
+Requires-Dist: spin; extra == "dev"
+Requires-Dist: mypy==1.19.1; extra == "dev"
+Requires-Dist: pyrefly==0.63.0; extra == "dev"
+Requires-Dist: typing_extensions; extra == "dev"
+Requires-Dist: types-psutil; extra == "dev"
+Requires-Dist: pycodestyle; extra == "dev"
+Requires-Dist: ruff>=0.12.0; extra == "dev"
+Requires-Dist: cython-lint>=0.12.2; extra == "dev"
+Description-Content-Type: text/x-rst
+
+.. image:: https://raw.githubusercontent.com/scipy/scipy/main/doc/source/_static/logo.svg
+  :target: https://scipy.org
+  :width: 110
+  :height: 110
+  :align: left
+
+.. image:: https://img.shields.io/badge/powered%20by-NumFOCUS-orange.svg?style=flat&colorA=E1523D&colorB=007D8A
+  :target: https://numfocus.org
+
+.. image:: https://img.shields.io/pypi/dm/scipy.svg?label=Pypi%20downloads
+  :target: https://pypi.org/project/scipy/
+
+.. image:: https://img.shields.io/conda/dn/conda-forge/scipy.svg?label=Conda%20downloads
+  :target: https://anaconda.org/conda-forge/scipy
+
+.. image:: https://img.shields.io/badge/stackoverflow-Ask%20questions-blue.svg
+  :target: https://stackoverflow.com/questions/tagged/scipy
+
+.. image:: https://img.shields.io/badge/DOI-10.1038%2Fs41592--019--0686--2-blue.svg
+  :target: https://www.nature.com/articles/s41592-019-0686-2
+
+.. image:: https://insights.linuxfoundation.org/api/badge/health-score?project=scipy
+  :target: https://insights.linuxfoundation.org/project/scipy
+
+SciPy (pronounced "Sigh Pie") is an open-source software for mathematics,
+science, and engineering. It includes modules for statistics, optimization,
+integration, linear algebra, Fourier transforms, signal and image processing,
+ODE solvers, and more.
+
+- **Website:** https://scipy.org
+- **Documentation:** https://docs.scipy.org/doc/scipy/
+- **Development version of the documentation:** https://scipy.github.io/devdocs
+- **SciPy development forum:** https://discuss.scientific-python.org/c/contributor/scipy
+- **Stack Overflow:** https://stackoverflow.com/questions/tagged/scipy
+- **Source code:** https://github.com/scipy/scipy
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+- **Bug reports:** https://github.com/scipy/scipy/issues
+- **Code of Conduct:** https://docs.scipy.org/doc/scipy/dev/conduct/code_of_conduct.html
+- **Report a security vulnerability:** via Tidelift, as explained in
+  `our docs on Security <https://scipy.github.io/devdocs/tutorial/security.html>`__
+- **Citing in your work:** https://www.scipy.org/citing-scipy/
+
+SciPy is built to work with
+NumPy arrays, and provides many user-friendly and efficient numerical routines,
+such as routines for numerical integration and optimization. Together, they
+run on all popular operating systems, are quick to install, and are free of
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+
+For the installation instructions, see `our install
+guide <https://scipy.org/install/>`__.
+
+
+Call for Contributions
+----------------------
+
+We appreciate and welcome contributions. Small improvements or fixes are always appreciated; issues labeled as "good
+first issue" may be a good starting point. Have a look at `our contributing
+guide <https://scipy.github.io/devdocs/dev/index.html>`__.
+
+Writing code isn’t the only way to contribute to SciPy. You can also:
+
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+If you’re unsure where to start or how your skills fit in, reach out! You can
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+
+If you are new to contributing to open source, `this
+guide <https://opensource.guide/how-to-contribute/>`__ helps explain why, what,
+and how to get involved.
diff --git a/venv/lib/python3.12/site-packages/scipy-1.18.0.dist-info/RECORD b/venv/lib/python3.12/site-packages/scipy-1.18.0.dist-info/RECORD
new file mode 100644
index 0000000000000000000000000000000000000000..6b0cb7916e784e416c5871793bec4dea4a0b0a7f
--- /dev/null
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diff --git a/venv/lib/python3.12/site-packages/scipy/signal/_arraytools.py b/venv/lib/python3.12/site-packages/scipy/signal/_arraytools.py
new file mode 100644
index 0000000000000000000000000000000000000000..87ce75d8d892a64021da7abc5d149556c22cf983
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/_arraytools.py
@@ -0,0 +1,264 @@
+"""
+Functions for acting on a axis of an array.
+"""
+import numpy as np
+
+
+def axis_slice(a, start=None, stop=None, step=None, axis=-1):
+    """Take a slice along axis 'axis' from 'a'.
+
+    Parameters
+    ----------
+    a : numpy.ndarray
+        The array to be sliced.
+    start, stop, step : int or None
+        The slice parameters.
+    axis : int, optional
+        The axis of `a` to be sliced.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.signal._arraytools import axis_slice
+    >>> a = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
+    >>> axis_slice(a, start=0, stop=1, axis=1)
+    array([[1],
+           [4],
+           [7]])
+    >>> axis_slice(a, start=1, axis=0)
+    array([[4, 5, 6],
+           [7, 8, 9]])
+
+    Notes
+    -----
+    The keyword arguments start, stop and step are used by calling
+    slice(start, stop, step). This implies axis_slice() does not
+    handle its arguments the exactly the same as indexing. To select
+    a single index k, for example, use
+        axis_slice(a, start=k, stop=k+1)
+    In this case, the length of the axis 'axis' in the result will
+    be 1; the trivial dimension is not removed. (Use numpy.squeeze()
+    to remove trivial axes.)
+    """
+    a_slice = [slice(None)] * a.ndim
+    a_slice[axis] = slice(start, stop, step)
+    b = a[tuple(a_slice)]
+    return b
+
+
+def axis_reverse(a, axis=-1):
+    """Reverse the 1-D slices of `a` along axis `axis`.
+
+    Returns axis_slice(a, step=-1, axis=axis).
+    """
+    return axis_slice(a, step=-1, axis=axis)
+
+
+def odd_ext(x, n, axis=-1):
+    """
+    Odd extension at the boundaries of an array
+
+    Generate a new ndarray by making an odd extension of `x` along an axis.
+
+    Parameters
+    ----------
+    x : ndarray
+        The array to be extended.
+    n : int
+        The number of elements by which to extend `x` at each end of the axis.
+    axis : int, optional
+        The axis along which to extend `x`. Default is -1.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.signal._arraytools import odd_ext
+    >>> a = np.array([[1, 2, 3, 4, 5], [0, 1, 4, 9, 16]])
+    >>> odd_ext(a, 2)
+    array([[-1,  0,  1,  2,  3,  4,  5,  6,  7],
+           [-4, -1,  0,  1,  4,  9, 16, 23, 28]])
+
+    Odd extension is a "180 degree rotation" at the endpoints of the original
+    array:
+
+    >>> t = np.linspace(0, 1.5, 100)
+    >>> a = 0.9 * np.sin(2 * np.pi * t**2)
+    >>> b = odd_ext(a, 40)
+    >>> import matplotlib.pyplot as plt
+    >>> plt.plot(np.arange(-40, 140), b, 'b', lw=1, label='odd extension')
+    >>> plt.plot(np.arange(100), a, 'r', lw=2, label='original')
+    >>> plt.legend(loc='best')
+    >>> plt.show()
+    """
+    if n < 1:
+        return x
+    if n > x.shape[axis] - 1:
+        raise ValueError(("The extension length n (%d) is too big. " +
+                         "It must not exceed x.shape[axis]-1, which is %d.")
+                         % (n, x.shape[axis] - 1))
+    left_end = axis_slice(x, start=0, stop=1, axis=axis)
+    left_ext = axis_slice(x, start=n, stop=0, step=-1, axis=axis)
+    right_end = axis_slice(x, start=-1, axis=axis)
+    right_ext = axis_slice(x, start=-2, stop=-(n + 2), step=-1, axis=axis)
+    ext = np.concatenate((2 * left_end - left_ext,
+                          x,
+                          2 * right_end - right_ext),
+                         axis=axis)
+    return ext
+
+
+def even_ext(x, n, axis=-1):
+    """
+    Even extension at the boundaries of an array
+
+    Generate a new ndarray by making an even extension of `x` along an axis.
+
+    Parameters
+    ----------
+    x : ndarray
+        The array to be extended.
+    n : int
+        The number of elements by which to extend `x` at each end of the axis.
+    axis : int, optional
+        The axis along which to extend `x`. Default is -1.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.signal._arraytools import even_ext
+    >>> a = np.array([[1, 2, 3, 4, 5], [0, 1, 4, 9, 16]])
+    >>> even_ext(a, 2)
+    array([[ 3,  2,  1,  2,  3,  4,  5,  4,  3],
+           [ 4,  1,  0,  1,  4,  9, 16,  9,  4]])
+
+    Even extension is a "mirror image" at the boundaries of the original array:
+
+    >>> t = np.linspace(0, 1.5, 100)
+    >>> a = 0.9 * np.sin(2 * np.pi * t**2)
+    >>> b = even_ext(a, 40)
+    >>> import matplotlib.pyplot as plt
+    >>> plt.plot(np.arange(-40, 140), b, 'b', lw=1, label='even extension')
+    >>> plt.plot(np.arange(100), a, 'r', lw=2, label='original')
+    >>> plt.legend(loc='best')
+    >>> plt.show()
+    """
+    if n < 1:
+        return x
+    if n > x.shape[axis] - 1:
+        raise ValueError(("The extension length n (%d) is too big. " +
+                         "It must not exceed x.shape[axis]-1, which is %d.")
+                         % (n, x.shape[axis] - 1))
+    left_ext = axis_slice(x, start=n, stop=0, step=-1, axis=axis)
+    right_ext = axis_slice(x, start=-2, stop=-(n + 2), step=-1, axis=axis)
+    ext = np.concatenate((left_ext,
+                          x,
+                          right_ext),
+                         axis=axis)
+    return ext
+
+
+def const_ext(x, n, axis=-1):
+    """
+    Constant extension at the boundaries of an array
+
+    Generate a new ndarray that is a constant extension of `x` along an axis.
+
+    The extension repeats the values at the first and last element of
+    the axis.
+
+    Parameters
+    ----------
+    x : ndarray
+        The array to be extended.
+    n : int
+        The number of elements by which to extend `x` at each end of the axis.
+    axis : int, optional
+        The axis along which to extend `x`. Default is -1.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.signal._arraytools import const_ext
+    >>> a = np.array([[1, 2, 3, 4, 5], [0, 1, 4, 9, 16]])
+    >>> const_ext(a, 2)
+    array([[ 1,  1,  1,  2,  3,  4,  5,  5,  5],
+           [ 0,  0,  0,  1,  4,  9, 16, 16, 16]])
+
+    Constant extension continues with the same values as the endpoints of the
+    array:
+
+    >>> t = np.linspace(0, 1.5, 100)
+    >>> a = 0.9 * np.sin(2 * np.pi * t**2)
+    >>> b = const_ext(a, 40)
+    >>> import matplotlib.pyplot as plt
+    >>> plt.plot(np.arange(-40, 140), b, 'b', lw=1, label='constant extension')
+    >>> plt.plot(np.arange(100), a, 'r', lw=2, label='original')
+    >>> plt.legend(loc='best')
+    >>> plt.show()
+    """
+    if n < 1:
+        return x
+    left_end = axis_slice(x, start=0, stop=1, axis=axis)
+    ones_shape = [1] * x.ndim
+    ones_shape[axis] = n
+    ones = np.ones(ones_shape, dtype=x.dtype)
+    left_ext = ones * left_end
+    right_end = axis_slice(x, start=-1, axis=axis)
+    right_ext = ones * right_end
+    ext = np.concatenate((left_ext,
+                          x,
+                          right_ext),
+                         axis=axis)
+    return ext
+
+
+def zero_ext(x, n, axis=-1):
+    """
+    Zero padding at the boundaries of an array
+
+    Generate a new ndarray that is a zero-padded extension of `x` along
+    an axis.
+
+    Parameters
+    ----------
+    x : ndarray
+        The array to be extended.
+    n : int
+        The number of elements by which to extend `x` at each end of the
+        axis.
+    axis : int, optional
+        The axis along which to extend `x`. Default is -1.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.signal._arraytools import zero_ext
+    >>> a = np.array([[1, 2, 3, 4, 5], [0, 1, 4, 9, 16]])
+    >>> zero_ext(a, 2)
+    array([[ 0,  0,  1,  2,  3,  4,  5,  0,  0],
+           [ 0,  0,  0,  1,  4,  9, 16,  0,  0]])
+    """
+    if n < 1:
+        return x
+    zeros_shape = list(x.shape)
+    zeros_shape[axis] = n
+    zeros = np.zeros(zeros_shape, dtype=x.dtype)
+    ext = np.concatenate((zeros, x, zeros), axis=axis)
+    return ext
+
+
+def _validate_fs(fs, allow_none=True):
+    """
+    Check if the given sampling frequency is a scalar and raises an exception
+    otherwise. If allow_none is False, also raises an exception for none
+    sampling rates. Returns the sampling frequency as float or none if the
+    input is none.
+    """
+    if fs is None:
+        if not allow_none:
+            raise ValueError("Sampling frequency can not be none.")
+    else:  # should be float
+        if not np.isscalar(fs):
+            raise ValueError("Sampling frequency fs must be a single scalar.")
+        fs = float(fs)
+    return fs
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/_czt.py b/venv/lib/python3.12/site-packages/scipy/signal/_czt.py
new file mode 100644
index 0000000000000000000000000000000000000000..24b3892dfd5e48dc0679bea1cba0d6cdb24a5ec0
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/_czt.py
@@ -0,0 +1,580 @@
+# This program is public domain
+# Authors: Paul Kienzle, Nadav Horesh
+"""
+Chirp z-transform.
+
+We provide two interfaces to the chirp z-transform: an object interface
+which precalculates part of the transform and can be applied efficiently
+to many different data sets, and a functional interface which is applied
+only to the given data set.
+
+Transforms
+----------
+
+CZT : callable (x, axis=-1) -> array
+   Define a chirp z-transform that can be applied to different signals.
+ZoomFFT : callable (x, axis=-1) -> array
+   Define a Fourier transform on a range of frequencies.
+
+Functions
+---------
+
+czt : array
+   Compute the chirp z-transform for a signal.
+zoom_fft : array
+   Compute the Fourier transform on a range of frequencies.
+"""
+
+import cmath
+import numbers
+import numpy as np
+from numpy import pi, arange
+from scipy.fft import fft, ifft, next_fast_len
+
+__all__ = ['czt', 'zoom_fft', 'CZT', 'ZoomFFT', 'czt_points']
+
+
+def _validate_sizes(n, m):
+    if n < 1 or not isinstance(n, numbers.Integral):
+        raise ValueError('Invalid number of CZT data '
+                         f'points ({n}) specified. '
+                         'n must be positive and integer type.')
+
+    if m is None:
+        m = n
+    elif m < 1 or not isinstance(m, numbers.Integral):
+        raise ValueError('Invalid number of CZT output '
+                         f'points ({m}) specified. '
+                         'm must be positive and integer type.')
+
+    return m
+
+
+def czt_points(m, w=None, a=1+0j):
+    """
+    Return the points at which the chirp z-transform is computed.
+
+    Parameters
+    ----------
+    m : int
+        The number of points desired.
+    w : complex, optional
+        The ratio between points in each step.
+        Defaults to equally spaced points around the entire unit circle.
+    a : complex, optional
+        The starting point in the complex plane.  Default is 1+0j.
+
+    Returns
+    -------
+    out : ndarray
+        The points in the Z plane at which `CZT` samples the z-transform,
+        when called with arguments `m`, `w`, and `a`, as complex numbers.
+
+    See Also
+    --------
+    CZT : Class that creates a callable chirp z-transform function.
+    czt : Convenience function for quickly calculating CZT.
+
+    Examples
+    --------
+    Plot the points of a 16-point FFT:
+
+    >>> import numpy as np
+    >>> from scipy.signal import czt_points
+    >>> points = czt_points(16)
+    >>> import matplotlib.pyplot as plt
+    >>> plt.plot(points.real, points.imag, 'o')
+    >>> plt.gca().add_patch(plt.Circle((0,0), radius=1, fill=False, alpha=.3))
+    >>> plt.axis('equal')
+    >>> plt.show()
+
+    and a 91-point logarithmic spiral that crosses the unit circle:
+
+    >>> m, w, a = 91, 0.995*np.exp(-1j*np.pi*.05), 0.8*np.exp(1j*np.pi/6)
+    >>> points = czt_points(m, w, a)
+    >>> plt.plot(points.real, points.imag, 'o')
+    >>> plt.gca().add_patch(plt.Circle((0,0), radius=1, fill=False, alpha=.3))
+    >>> plt.axis('equal')
+    >>> plt.show()
+    """
+    m = _validate_sizes(1, m)
+
+    k = arange(m)
+
+    a = 1.0 * a  # at least float
+
+    if w is None:
+        # Nothing specified, default to FFT
+        return a * np.exp(2j * pi * k / m)
+    else:
+        # w specified
+        w = 1.0 * w  # at least float
+        return a * w**-k
+
+
+class CZT:
+    """
+    Create a callable chirp z-transform function.
+
+    Transform to compute the frequency response around a spiral.
+    Objects of this class are callables which can compute the
+    chirp z-transform on their inputs.  This object precalculates the constant
+    chirps used in the given transform.
+
+    Parameters
+    ----------
+    n : int
+        The size of the signal.
+    m : int, optional
+        The number of output points desired.  Default is `n`.
+    w : complex, optional
+        The ratio between points in each step.  This must be precise or the
+        accumulated error will degrade the tail of the output sequence.
+        Defaults to equally spaced points around the entire unit circle.
+    a : complex, optional
+        The starting point in the complex plane.  Default is 1+0j.
+
+    Returns
+    -------
+    f : CZT
+        Callable object ``f(x, axis=-1)`` for computing the chirp z-transform
+        on `x`.
+
+    See Also
+    --------
+    czt : Convenience function for quickly calculating CZT.
+    ZoomFFT : Class that creates a callable partial FFT function.
+
+    Notes
+    -----
+    The defaults are chosen such that ``f(x)`` is equivalent to
+    ``fft.fft(x)`` and, if ``m > len(x)``, that ``f(x, m)`` is equivalent to
+    ``fft.fft(x, m)``.
+
+    If `w` does not lie on the unit circle, then the transform will be
+    around a spiral with exponentially-increasing radius.  Regardless,
+    angle will increase linearly.
+
+    For transforms that do lie on the unit circle, accuracy is better when
+    using `ZoomFFT`, since any numerical error in `w` is
+    accumulated for long data lengths, drifting away from the unit circle.
+
+    The chirp z-transform can be faster than an equivalent FFT with
+    zero padding.  Try it with your own array sizes to see.
+
+    However, the chirp z-transform is considerably less precise than the
+    equivalent zero-padded FFT.
+
+    As this CZT is implemented using the Bluestein algorithm, it can compute
+    large prime-length Fourier transforms in O(N log N) time, rather than the
+    O(N**2) time required by the direct DFT calculation.  (`scipy.fft` also
+    uses Bluestein's algorithm'.)
+
+    (The name "chirp z-transform" comes from the use of a chirp in the
+    Bluestein algorithm.  It does not decompose signals into chirps, like
+    other transforms with "chirp" in the name.)
+
+    References
+    ----------
+    .. [1] Leo I. Bluestein, "A linear filtering approach to the computation
+           of the discrete Fourier transform," Northeast Electronics Research
+           and Engineering Meeting Record 10, 218-219 (1968).
+    .. [2] Rabiner, Schafer, and Rader, "The chirp z-transform algorithm and
+           its application," Bell Syst. Tech. J. 48, 1249-1292 (1969).
+
+    Examples
+    --------
+    Compute multiple prime-length FFTs:
+
+    >>> from scipy.signal import CZT
+    >>> import numpy as np
+    >>> a = np.random.rand(7)
+    >>> b = np.random.rand(7)
+    >>> c = np.random.rand(7)
+    >>> czt_7 = CZT(n=7)
+    >>> A = czt_7(a)
+    >>> B = czt_7(b)
+    >>> C = czt_7(c)
+
+    Display the points at which the FFT is calculated:
+
+    >>> czt_7.points()
+    array([ 1.00000000+0.j        ,  0.62348980+0.78183148j,
+           -0.22252093+0.97492791j, -0.90096887+0.43388374j,
+           -0.90096887-0.43388374j, -0.22252093-0.97492791j,
+            0.62348980-0.78183148j])
+    >>> import matplotlib.pyplot as plt
+    >>> plt.plot(czt_7.points().real, czt_7.points().imag, 'o')
+    >>> plt.gca().add_patch(plt.Circle((0,0), radius=1, fill=False, alpha=.3))
+    >>> plt.axis('equal')
+    >>> plt.show()
+    """
+
+    def __init__(self, n, m=None, w=None, a=1+0j):
+        m = _validate_sizes(n, m)
+
+        k = arange(max(m, n), dtype=np.min_scalar_type(-max(m, n)**2))
+
+        if w is None:
+            # Nothing specified, default to FFT-like
+            w = cmath.exp(-2j*pi/m)
+            wk2 = np.exp(-(1j * pi * ((k**2) % (2*m))) / m)
+        else:
+            # w specified
+            wk2 = w**(k**2/2.)
+
+        a = 1.0 * a  # at least float
+
+        self.w, self.a = w, a
+        self.m, self.n = m, n
+
+        nfft = next_fast_len(n + m - 1)
+        self._Awk2 = a**-k[:n] * wk2[:n]
+        self._nfft = nfft
+        self._Fwk2 = fft(1/np.hstack((wk2[n-1:0:-1], wk2[:m])), nfft)
+        self._wk2 = wk2[:m]
+        self._yidx = slice(n-1, n+m-1)
+
+    def __call__(self, x, *, axis=-1):
+        """
+        Calculate the chirp z-transform of a signal.
+
+        Parameters
+        ----------
+        x : array
+            The signal to transform.
+        axis : int, optional
+            Axis over which to compute the FFT. If not given, the last axis is
+            used.
+
+        Returns
+        -------
+        out : ndarray
+            An array of the same dimensions as `x`, but with the length of the
+            transformed axis set to `m`.
+        """
+        x = np.asarray(x)
+        if x.shape[axis] != self.n:
+            raise ValueError(f"CZT defined for length {self.n}, not "
+                             f"{x.shape[axis]}")
+        # Calculate transpose coordinates, to allow operation on any given axis
+        trnsp = np.arange(x.ndim)
+        trnsp[[axis, -1]] = [-1, axis]
+        x = x.transpose(*trnsp)
+        y = ifft(self._Fwk2 * fft(x*self._Awk2, self._nfft))
+        y = y[..., self._yidx] * self._wk2
+        return y.transpose(*trnsp)
+
+    def points(self):
+        """
+        Return the points at which the chirp z-transform is computed.
+
+        Returns
+        -------
+        ndarray
+            The points in the Z plane at which `CZT` samples the z-transform.
+        """
+        return czt_points(self.m, self.w, self.a)
+
+
+class ZoomFFT(CZT):
+    """
+    Create a callable zoom FFT transform function.
+
+    This is a specialization of the chirp z-transform (`CZT`) for a set of
+    equally-spaced frequencies around the unit circle, used to calculate a
+    section of the FFT more efficiently than calculating the entire FFT and
+    truncating.
+
+    Parameters
+    ----------
+    n : int
+        The size of the signal.
+    fn : array_like
+        A length-2 sequence [`f1`, `f2`] giving the frequency range, or a
+        scalar, for which the range [0, `fn`] is assumed.
+    m : int, optional
+        The number of points to evaluate.  Default is `n`.
+    fs : float, optional
+        The sampling frequency.  If ``fs=10`` represented 10 kHz, for example,
+        then `f1` and `f2` would also be given in kHz.
+        The default sampling frequency is 2, so `f1` and `f2` should be
+        in the range [0, 1] to keep the transform below the Nyquist
+        frequency.
+    endpoint : bool, optional
+        If True, `f2` is the last sample. Otherwise, it is not included.
+        Default is False.
+
+    Returns
+    -------
+    f : ZoomFFT
+        Callable object ``f(x, axis=-1)`` for computing the zoom FFT on `x`.
+
+    See Also
+    --------
+    zoom_fft : Convenience function for calculating a zoom FFT.
+
+    Notes
+    -----
+    The defaults are chosen such that ``f(x, 2)`` is equivalent to
+    ``fft.fft(x)`` and, if ``m > len(x)``, that ``f(x, 2, m)`` is equivalent to
+    ``fft.fft(x, m)``.
+
+    Sampling frequency is 1/dt, the time step between samples in the
+    signal `x`.  The unit circle corresponds to frequencies from 0 up
+    to the sampling frequency.  The default sampling frequency of 2
+    means that `f1`, `f2` values up to the Nyquist frequency are in the
+    range [0, 1). For `f1`, `f2` values expressed in radians, a sampling
+    frequency of 2*pi should be used.
+
+    Remember that a zoom FFT can only interpolate the points of the existing
+    FFT.  It cannot help to resolve two separate nearby frequencies.
+    Frequency resolution can only be increased by increasing acquisition
+    time.
+
+    These functions are implemented using Bluestein's algorithm (as is
+    `scipy.fft`). [2]_
+
+    References
+    ----------
+    .. [1] Steve Alan Shilling, "A study of the chirp z-transform and its
+           applications", pg 29 (1970)
+           https://krex.k-state.edu/dspace/bitstream/handle/2097/7844/LD2668R41972S43.pdf
+    .. [2] Leo I. Bluestein, "A linear filtering approach to the computation
+           of the discrete Fourier transform," Northeast Electronics Research
+           and Engineering Meeting Record 10, 218-219 (1968).
+
+    Examples
+    --------
+    To plot the transform results use something like the following:
+
+    >>> import numpy as np
+    >>> from scipy.signal import ZoomFFT
+    >>> t = np.linspace(0, 1, 1021)
+    >>> x = np.cos(2*np.pi*15*t) + np.sin(2*np.pi*17*t)
+    >>> f1, f2 = 5, 27
+    >>> transform = ZoomFFT(len(x), [f1, f2], len(x), fs=1021)
+    >>> X = transform(x)
+    >>> f = np.linspace(f1, f2, len(x))
+    >>> import matplotlib.pyplot as plt
+    >>> plt.plot(f, 20*np.log10(np.abs(X)))
+    >>> plt.show()
+    """
+
+    def __init__(self, n, fn, m=None, *, fs=2, endpoint=False):
+        m = _validate_sizes(n, m)
+
+        k = arange(max(m, n), dtype=np.min_scalar_type(-max(m, n)**2))
+
+        if np.size(fn) == 2:
+            f1, f2 = fn
+        elif np.size(fn) == 1:
+            f1, f2 = 0.0, fn
+        else:
+            raise ValueError('fn must be a scalar or 2-length sequence')
+
+        self.f1, self.f2, self.fs = f1, f2, fs
+
+        if endpoint:
+            scale = ((f2 - f1) * m) / (fs * (m - 1))
+        else:
+            scale = (f2 - f1) / fs
+        a = cmath.exp(2j * pi * f1/fs)
+        wk2 = np.exp(-(1j * pi * scale * k**2) / m)
+
+        self.w = cmath.exp(-2j*pi/m * scale)
+        self.a = a
+        self.m, self.n = m, n
+
+        ak = np.exp(-2j * pi * f1/fs * k[:n])
+        self._Awk2 = ak * wk2[:n]
+
+        nfft = next_fast_len(n + m - 1)
+        self._nfft = nfft
+        self._Fwk2 = fft(1/np.hstack((wk2[n-1:0:-1], wk2[:m])), nfft)
+        self._wk2 = wk2[:m]
+        self._yidx = slice(n-1, n+m-1)
+
+
+def czt(x, m=None, w=None, a=1+0j, *, axis=-1):
+    """
+    Compute the frequency response around a spiral in the Z plane.
+
+    Parameters
+    ----------
+    x : array
+        The signal to transform.
+    m : int, optional
+        The number of output points desired.  Default is the length of the
+        input data.
+    w : complex, optional
+        The ratio between points in each step.  This must be precise or the
+        accumulated error will degrade the tail of the output sequence.
+        Defaults to equally spaced points around the entire unit circle.
+    a : complex, optional
+        The starting point in the complex plane.  Default is 1+0j.
+    axis : int, optional
+        Axis over which to compute the FFT. If not given, the last axis is
+        used.
+
+    Returns
+    -------
+    out : ndarray
+        An array of the same dimensions as `x`, but with the length of the
+        transformed axis set to `m`.
+
+    See Also
+    --------
+    CZT : Class that creates a callable chirp z-transform function.
+    zoom_fft : Convenience function for partial FFT calculations.
+
+    Notes
+    -----
+    The defaults are chosen such that ``signal.czt(x)`` is equivalent to
+    ``fft.fft(x)`` and, if ``m > len(x)``, that ``signal.czt(x, m)`` is
+    equivalent to ``fft.fft(x, m)``.
+
+    If the transform needs to be repeated, use `CZT` to construct a
+    specialized transform function which can be reused without
+    recomputing constants.
+
+    An example application is in system identification, repeatedly evaluating
+    small slices of the z-transform of a system, around where a pole is
+    expected to exist, to refine the estimate of the pole's true location. [1]_
+
+    References
+    ----------
+    .. [1] Steve Alan Shilling, "A study of the chirp z-transform and its
+           applications", pg 20 (1970)
+           https://krex.k-state.edu/dspace/bitstream/handle/2097/7844/LD2668R41972S43.pdf
+
+    Examples
+    --------
+    Generate a sinusoid:
+
+    >>> import numpy as np
+    >>> f1, f2, fs = 8, 10, 200  # Hz
+    >>> t = np.linspace(0, 1, fs, endpoint=False)
+    >>> x = np.sin(2*np.pi*t*f2)
+    >>> import matplotlib.pyplot as plt
+    >>> plt.plot(t, x)
+    >>> plt.axis([0, 1, -1.1, 1.1])
+    >>> plt.show()
+
+    Its discrete Fourier transform has all of its energy in a single frequency
+    bin:
+
+    >>> from scipy.fft import rfft, rfftfreq
+    >>> from scipy.signal import czt, czt_points
+    >>> plt.plot(rfftfreq(fs, 1/fs), abs(rfft(x)))
+    >>> plt.margins(0, 0.1)
+    >>> plt.show()
+
+    However, if the sinusoid is logarithmically-decaying:
+
+    >>> x = np.exp(-t*f1) * np.sin(2*np.pi*t*f2)
+    >>> plt.plot(t, x)
+    >>> plt.axis([0, 1, -1.1, 1.1])
+    >>> plt.show()
+
+    the DFT will have spectral leakage:
+
+    >>> plt.plot(rfftfreq(fs, 1/fs), abs(rfft(x)))
+    >>> plt.margins(0, 0.1)
+    >>> plt.show()
+
+    While the DFT always samples the z-transform around the unit circle, the
+    chirp z-transform allows us to sample the Z-transform along any
+    logarithmic spiral, such as a circle with radius smaller than unity:
+
+    >>> M = fs // 2  # Just positive frequencies, like rfft
+    >>> a = np.exp(-f1/fs)  # Starting point of the circle, radius < 1
+    >>> w = np.exp(-1j*np.pi/M)  # "Step size" of circle
+    >>> points = czt_points(M + 1, w, a)  # M + 1 to include Nyquist
+    >>> plt.plot(points.real, points.imag, '.')
+    >>> plt.gca().add_patch(plt.Circle((0,0), radius=1, fill=False, alpha=.3))
+    >>> plt.axis('equal'); plt.axis([-1.05, 1.05, -0.05, 1.05])
+    >>> plt.show()
+
+    With the correct radius, this transforms the decaying sinusoid (and others
+    with the same decay rate) without spectral leakage:
+
+    >>> z_vals = czt(x, M + 1, w, a)  # Include Nyquist for comparison to rfft
+    >>> freqs = np.angle(points)*fs/(2*np.pi)  # angle = omega, radius = sigma
+    >>> plt.plot(freqs, abs(z_vals))
+    >>> plt.margins(0, 0.1)
+    >>> plt.show()
+    """
+    x = np.asarray(x)
+    transform = CZT(x.shape[axis], m=m, w=w, a=a)
+    return transform(x, axis=axis)
+
+
+def zoom_fft(x, fn, m=None, *, fs=2, endpoint=False, axis=-1):
+    """
+    Compute the DFT of `x` only for frequencies in range `fn`.
+
+    Parameters
+    ----------
+    x : array
+        The signal to transform.
+    fn : array_like
+        A length-2 sequence [`f1`, `f2`] giving the frequency range, or a
+        scalar, for which the range [0, `fn`] is assumed.
+    m : int, optional
+        The number of points to evaluate.  The default is the length of `x`.
+    fs : float, optional
+        The sampling frequency.  If ``fs=10`` represented 10 kHz, for example,
+        then `f1` and `f2` would also be given in kHz.
+        The default sampling frequency is 2, so `f1` and `f2` should be
+        in the range [0, 1] to keep the transform below the Nyquist
+        frequency.
+    endpoint : bool, optional
+        If True, `f2` is the last sample. Otherwise, it is not included.
+        Default is False.
+    axis : int, optional
+        Axis over which to compute the FFT. If not given, the last axis is
+        used.
+
+    Returns
+    -------
+    out : ndarray
+        The transformed signal.  The Fourier transform will be calculated
+        at the points f1, f1+df, f1+2df, ..., f2, where df=(f2-f1)/m.
+
+    See Also
+    --------
+    ZoomFFT : Class that creates a callable partial FFT function.
+
+    Notes
+    -----
+    The defaults are chosen such that ``signal.zoom_fft(x, 2)`` is equivalent
+    to ``fft.fft(x)`` and, if ``m > len(x)``, that ``signal.zoom_fft(x, 2, m)``
+    is equivalent to ``fft.fft(x, m)``.
+
+    To graph the magnitude of the resulting transform, use::
+
+        plot(linspace(f1, f2, m, endpoint=False), abs(zoom_fft(x, [f1, f2], m)))
+
+    If the transform needs to be repeated, use `ZoomFFT` to construct
+    a specialized transform function which can be reused without
+    recomputing constants.
+
+    Examples
+    --------
+    To plot the transform results use something like the following:
+
+    >>> import numpy as np
+    >>> from scipy.signal import zoom_fft
+    >>> t = np.linspace(0, 1, 1021)
+    >>> x = np.cos(2*np.pi*15*t) + np.sin(2*np.pi*17*t)
+    >>> f1, f2 = 5, 27
+    >>> X = zoom_fft(x, [f1, f2], len(x), fs=1021)
+    >>> f = np.linspace(f1, f2, len(x))
+    >>> import matplotlib.pyplot as plt
+    >>> plt.plot(f, 20*np.log10(np.abs(X)))
+    >>> plt.show()
+    """
+    x = np.asarray(x)
+    transform = ZoomFFT(x.shape[axis], fn, m=m, fs=fs, endpoint=endpoint)
+    return transform(x, axis=axis)
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/_delegators.py b/venv/lib/python3.12/site-packages/scipy/signal/_delegators.py
new file mode 100644
index 0000000000000000000000000000000000000000..42b2c22500c322a5e4fd839b447642f7e5bf796c
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/_delegators.py
@@ -0,0 +1,573 @@
+"""Delegators for alternative backends in scipy.signal.
+
+The signature of `func_signature` must match the signature of signal.func.
+The job of a `func_signature` is to know which arguments of `signal.func`
+are arrays.
+
+* signatures are generated by
+
+--------------
+ import inspect
+ from scipy import signal
+
+ names = [x for x in dir(signal) if not x.startswith('_')]
+ objs = [getattr(signal, name) for name in names]
+ funcs = [obj for obj in objs if inspect.isroutine(obj)]
+
+ for func in funcs:
+     try:
+        sig = inspect.signature(func)
+     except ValueError:
+         sig = "( FIXME )"
+     print(f"def {func.__name__}_signature{sig}:\n\treturn array_namespace(...
+ )\n\n")
+---------------
+
+* which arguments to delegate on: manually trawled the documentation for
+  array-like and array arguments
+
+"""
+import numpy as np
+from scipy._lib._array_api import array_namespace, np_compat, is_jax
+
+
+def _skip_if_lti(arg):
+    """Handle `system` arg overloads.
+
+    ATM, only pass tuples through. Consider updating when cupyx.lti class
+    is supported.
+    """
+    if isinstance(arg, tuple):
+        return arg
+    else:
+        return (None,)
+
+
+def _skip_if_str_or_tuple(window):
+    """Handle `window` being a str or a tuple or an array-like.
+    """
+    if isinstance(window, str) or isinstance(window, tuple) or callable(window):
+        return None
+    else:
+        return window
+
+
+def _skip_if_poly1d(arg):
+    return None if isinstance(arg, np.poly1d) else arg
+
+
+###################
+
+def abcd_normalize_signature(A=None, B=None, C=None, D=None):
+    return array_namespace(A, B, C, D)
+
+def argrelextrema_signature(data, *args, **kwds):
+    return array_namespace(data)
+
+argrelmax_signature = argrelextrema_signature
+argrelmin_signature = argrelextrema_signature
+
+
+def band_stop_obj_signature(wp, ind, passb, stopb, gpass, gstop, type):
+    return array_namespace(passb, stopb)
+
+
+def bessel_signature(N, Wn, *args, **kwds):
+    return array_namespace(Wn)
+
+butter_signature = bessel_signature
+
+
+def cheby2_signature(N, rs, Wn, *args, **kwds):
+    return array_namespace(Wn)
+
+
+def cheby1_signature(N, rp, Wn, *args, **kwds):
+    return array_namespace(Wn)
+
+
+def ellip_signature(N, rp, rs, Wn, *args, **kwds):
+    return array_namespace(Wn)
+
+
+########################## XXX: no arrays in, arrays out
+def besselap_signature(N, norm='phase', *, xp=None, device=None):
+    return np if xp is None else xp
+
+
+def buttap_signature(N, *, xp=None, device=None):
+    return np if xp is None else xp
+
+
+def cheb1ap_signature(N, rp, *, xp=None, device=None):
+    return np if xp is None else xp
+
+
+def cheb2ap_signature(N, rs, *, xp=None, device=None):
+    return np if xp is None else xp
+
+def ellipap_signature(N, rp, rs, *, xp=None, device=None):
+    return np if xp is None else xp
+
+def correlation_lags_signature(in1_len, in2_len, mode='full'):
+    return np
+
+
+def czt_points_signature(m, w=None, a=(1+0j)):
+    return np
+
+
+def gammatone_signature(
+    freq, ftype, order=None, numtaps=None, fs=None, *, xp=None, device=None
+    ):
+    return np_compat if xp is None else xp
+
+
+def iircomb_signature(
+    w0, Q, ftype='notch', fs=2.0, *, pass_zero=False, xp=None, device=None
+):
+    return np_compat if xp is None else xp
+
+
+def iirnotch_signature(w0, Q, fs=2.0, *, xp=None, device=None):
+    return np if xp is None else xp
+
+iirpeak_signature = iirnotch_signature
+
+
+def savgol_coeffs_signature(
+    window_length, polyorder, deriv=0, delta=1.0, pos=None, use='conv',
+    *, xp=None, device=None
+):
+    return np if xp is None else xp
+
+
+
+def unit_impulse_signature(shape, idx=None, dtype=float):
+    return np
+############################
+
+
+def buttord_signature(wp, ws, gpass, gstop, analog=False, fs=None):
+    return array_namespace(wp, ws)
+
+cheb1ord_signature = buttord_signature
+cheb2ord_signature = buttord_signature
+ellipord_signature = buttord_signature
+
+
+########### NB: scalars in, scalars out
+def kaiser_atten_signature(numtaps, width):
+    return np
+
+def kaiser_beta_signature(a):
+    return np
+
+def kaiserord_signature(ripple, width):
+    return np
+
+def get_window_signature(window, Nx, fftbins=True, *, xp=None, device=None):
+    return np if xp is None else xp
+#################################
+
+
+def bode_signature(system, w=None, n=100):
+    return array_namespace(*_skip_if_lti(system), w)
+
+dbode_signature = bode_signature
+
+
+def freqresp_signature(system, w=None, n=10000):
+    return array_namespace(*_skip_if_lti(system), w)
+
+dfreqresp_signature = freqresp_signature
+
+
+def impulse_signature(system, X0=None, T=None, N=None):
+    return array_namespace(*_skip_if_lti(system), X0, T)
+
+
+def dimpulse_signature(system, x0=None, t=None, n=None):
+    return array_namespace(*_skip_if_lti(system), x0, t)
+
+
+def lsim_signature(system, U, T, X0=None, interp=True):
+    return array_namespace(*_skip_if_lti(system), U, T, X0)
+
+
+def dlsim_signature(system, u, t=None, x0=None):
+    return array_namespace(*_skip_if_lti(system), u, t, x0)
+
+
+def step_signature(system, X0=None, T=None, N=None):
+    return array_namespace(*_skip_if_lti(system), X0, T)
+
+def dstep_signature(system, x0=None, t=None, n=None):
+    return array_namespace(*_skip_if_lti(system), x0, t)
+
+
+def cont2discrete_signature(system, dt, method='zoh', alpha=None):
+    return array_namespace(*_skip_if_lti(system))
+
+
+def bilinear_signature(b, a, fs=1.0):
+    return array_namespace(b, a)
+
+
+def bilinear_zpk_signature(z, p, k, fs):
+    return array_namespace(z, p)
+
+
+def chirp_signature(t,*args, **kwds):
+    return array_namespace(t)
+
+
+############## XXX: array-likes in, str out
+def choose_conv_method_signature(in1, in2, *args, **kwds):
+    return array_namespace(in1, in2)
+############################################
+
+
+def convolve_signature(in1, in2, *args, **kwds):
+    return array_namespace(in1, in2)
+
+fftconvolve_signature = convolve_signature
+oaconvolve_signature = convolve_signature
+correlate_signature = convolve_signature
+correlate_signature = convolve_signature
+convolve2d_signature = convolve_signature
+correlate2d_signature = convolve_signature
+
+
+def coherence_signature(x, y, fs=1.0, window='hann_periodic', *args, **kwds):
+    return array_namespace(x, y, _skip_if_str_or_tuple(window))
+
+
+def csd_signature(x, y, fs=1.0, window='hann_periodic', *args, **kwds):
+    return array_namespace(x, y, _skip_if_str_or_tuple(window))
+
+
+def periodogram_signature(x, fs=1.0, window='boxcar', *args, **kwds):
+    return array_namespace(x, _skip_if_str_or_tuple(window))
+
+
+def welch_signature(x, fs=1.0, window='hann_periodic', *args, **kwds):
+    return array_namespace(x, _skip_if_str_or_tuple(window))
+
+
+def spectrogram_signature(x, fs=1.0, window=('tukey_periodic', 0.25), *args, **kwds):
+    return array_namespace(x, _skip_if_str_or_tuple(window))
+
+
+def stft_signature(x, fs=1.0, window='hann_periodic', *args, **kwds):
+    return array_namespace(x, _skip_if_str_or_tuple(window))
+
+
+def istft_signature(Zxx, fs=1.0, window='hann_periodic', *args, **kwds):
+    return array_namespace(Zxx, _skip_if_str_or_tuple(window))
+
+
+def resample_signature(x, num, t=None, axis=0, window=None, domain='time'):
+    return array_namespace(x, t, _skip_if_str_or_tuple(window))
+
+
+def resample_poly_signature(x, up, down, axis=0, window=('kaiser', 5.0), *args, **kwds):
+    return array_namespace(x, _skip_if_str_or_tuple(window))
+
+
+def check_COLA_signature(window, nperseg, noverlap, tol=1e-10):
+    return array_namespace(_skip_if_str_or_tuple(window))
+
+
+def check_NOLA_signature(window, nperseg, noverlap, tol=1e-10):
+    return array_namespace(_skip_if_str_or_tuple(window))
+
+
+def czt_signature(x, *args, **kwds):
+    return array_namespace(x)
+
+decimate_signature = czt_signature
+gauss_spline_signature = czt_signature
+
+
+def deconvolve_signature(signal, divisor):
+    return array_namespace(signal, divisor)
+
+
+def detrend_signature(data, axis=1, type='linear', bp=0, *args, **kwds):
+    xp = array_namespace(data)
+    # JAX doesn't accept JAX arrays for bp, only ints, lists and NumPy
+    # arrays.
+    return xp if is_jax(xp) else array_namespace(data, bp)
+
+
+def filtfilt_signature(b, a, x, *args, **kwds):
+    return array_namespace(b, a, x)
+
+
+def lfilter_signature(b, a, x, axis=-1, zi=None):
+    return array_namespace(b, a, x, zi)
+
+
+def envelope_signature(z, *args, **kwds):
+    return array_namespace(z)
+
+
+def find_peaks_signature(
+    x, height=None, threshold=None, distance=None, prominence=None, width=None,
+    wlen=None, rel_height=0.5, plateau_size=None
+):
+    # TODO: fix me - `prominence` is not necessarily an array.
+    # return array_namespace(x, height, threshold, prominence, width, plateau_size)
+    # See https://github.com/scipy/scipy/pull/22644#issuecomment-3568443768. For now:
+    return np_compat
+
+def find_peaks_cwt_signature(
+    vector, widths, wavelet=None, max_distances=None, *args, **kwds
+):
+    return array_namespace(vector, widths, max_distances)
+
+
+def findfreqs_signature(num, den, N, kind='ba'):
+    return array_namespace(num, den)
+
+
+def firls_signature(numtaps, bands, desired, *, weight=None, fs=None):
+    return array_namespace(bands, desired, weight)
+
+
+def firwin_signature(numtaps, cutoff, *args, **kwds):
+    if isinstance(cutoff, int | float):
+        xp = np_compat
+    else:
+        xp = array_namespace(cutoff)
+    return xp
+
+
+def firwin2_signature(numtaps, freq, gain, *args, **kwds):
+    return array_namespace(freq, gain)
+
+
+def freqs_zpk_signature(z, p, k, worN=200, *args, **kwds):
+    return array_namespace(z, p, worN)
+
+freqz_zpk_signature = freqs_zpk_signature
+
+
+def freqs_signature(b, a, worN=200, *args, **kwds):
+    return array_namespace(b, a, worN)
+
+
+def freqz_signature(b, a=1, worN=512, *args, **kwds):
+    # differs from freqs: `a` has a default value
+    return array_namespace(b, a, worN)
+
+
+def freqz_sos_signature(sos, worN=512, *args, **kwds):
+    return array_namespace(sos, worN)
+
+sosfreqz_signature = freqz_sos_signature
+
+
+def gausspulse_signature(t, *args, **kwds):
+    arr_t = None if isinstance(t, str) else t
+    return array_namespace(arr_t)
+
+
+def group_delay_signature(system, w=512, whole=False, fs=6.283185307179586):
+    return array_namespace(*system, w)
+
+
+def hilbert_signature(x, *args, **kwds):
+    return array_namespace(x)
+
+hilbert2_signature = hilbert_signature
+
+
+def iirdesign_signature(wp, ws, *args, **kwds):
+    return array_namespace(wp, ws)
+
+
+def iirfilter_signature(N, Wn, *args, **kwds):
+    return array_namespace(Wn)
+
+
+def invres_signature(r, p, k, tol=0.001, rtype='avg'):
+    return array_namespace(r, p, k)
+
+invresz_signature = invres_signature
+
+
+############################### XXX: excluded, blacklisted on CuPy (mismatched API)
+def lfilter_zi_signature(b, a):
+    return array_namespace(b, a)
+
+def sosfilt_zi_signature(sos):
+    return array_namespace(sos)
+
+# needs to be blacklisted on CuPy (is not implemented)
+def remez_signature(numtaps, bands, desired, *, weight=None, **kwds):
+    return array_namespace(bands, desired, weight)
+#############################################
+
+def lfiltic_signature(b, a, y, x=None):
+    return array_namespace(b, a, y, x)
+
+
+def lombscargle_signature(
+    x, y, freqs, precenter=False, normalize=False, *,
+    weights=None, floating_mean=False
+):
+    return array_namespace(x, y, freqs, weights)
+
+
+def lp2bp_signature(b, a, *args, **kwds):
+    return array_namespace(b, a)
+
+lp2bs_signature = lp2bp_signature
+lp2hp_signature = lp2bp_signature
+lp2lp_signature = lp2bp_signature
+
+tf2zpk_signature = lp2bp_signature
+tf2sos_signature = lp2bp_signature
+
+normalize_signature = lp2bp_signature
+residue_signature = lp2bp_signature
+residuez_signature = residue_signature
+
+
+def lp2bp_zpk_signature(z, p, k, *args, **kwds):
+    return array_namespace(z, p)
+
+lp2bs_zpk_signature = lp2bp_zpk_signature
+lp2hp_zpk_signature = lp2bs_zpk_signature
+lp2lp_zpk_signature = lp2bs_zpk_signature
+
+
+def zpk2sos_signature(z, p, k, *args, **kwds):
+    return array_namespace(z, p)
+
+zpk2ss_signature = zpk2sos_signature
+zpk2tf_signature = zpk2sos_signature
+
+
+def max_len_seq_signature(nbits, state=None, length=None, taps=None):
+    return array_namespace(state, taps)
+
+
+def medfilt_signature(volume, kernel_size=None):
+    return array_namespace(volume)
+
+
+def medfilt2d_signature(input, kernel_size=3):
+    return array_namespace(input)
+
+
+def minimum_phase_signature(h, *args, **kwds):
+    return array_namespace(h)
+
+
+def order_filter_signature(a, domain, rank):
+    return array_namespace(a, domain)
+
+
+def peak_prominences_signature(x, peaks, *args, **kwds):
+    return array_namespace(x, peaks)
+
+
+peak_widths_signature = peak_prominences_signature
+
+
+def place_poles_signature(A, B, poles, method='YT', rtol=0.001, maxiter=30):
+    return array_namespace(A, B, poles)
+
+
+def savgol_filter_signature(x, *args, **kwds):
+    return array_namespace(x)
+
+
+def sawtooth_signature(t, width=1):
+    return array_namespace(t)
+
+
+def sepfir2d_signature(input, hrow, hcol):
+    return array_namespace(input, hrow, hcol)
+
+
+def sos2tf_signature(sos):
+    return array_namespace(sos)
+
+
+sos2zpk_signature = sos2tf_signature
+
+
+def sosfilt_signature(sos, x, axis=-1, zi=None):
+    return array_namespace(sos, x, zi)
+
+
+def sosfiltfilt_signature(sos, x, *args, **kwds):
+    return array_namespace(sos, x)
+
+
+def spline_filter_signature(Iin, lmbda=5.0):
+    return array_namespace(Iin)
+
+
+def square_signature(t, duty=0.5):
+    return array_namespace(t, duty)
+
+
+def ss2tf_signature(A, B, C, D, input=0):
+    return array_namespace(A, B, C, D)
+
+ss2zpk_signature = ss2tf_signature
+
+
+def sweep_poly_signature(t, poly, phi=0):
+    return array_namespace(t, _skip_if_poly1d(poly))
+
+
+def symiirorder1_signature(signal, c0, z1, precision=-1.0):
+    return array_namespace(signal)
+
+
+def symiirorder2_signature(input, r, omega, precision=-1.0):
+    return array_namespace(input, r, omega)
+
+
+def cspline1d_signature(signal, *args, **kwds):
+    return array_namespace(signal)
+
+qspline1d_signature = cspline1d_signature
+cspline2d_signature = cspline1d_signature
+qspline2d_signature = qspline1d_signature
+
+
+def cspline1d_eval_signature(cj, newx, *args, **kwds):
+    return array_namespace(cj, newx)
+
+qspline1d_eval_signature = cspline1d_eval_signature
+
+
+def tf2ss_signature(num, den):
+    return array_namespace(num, den)
+
+
+def unique_roots_signature(p, tol=0.001, rtype='min'):
+    return array_namespace(p)
+
+
+def upfirdn_signature(h, x, up=1, down=1, axis=-1, mode='constant', cval=0):
+    return array_namespace(h, x)
+
+
+def vectorstrength_signature(events, period):
+    return array_namespace(events, period)
+
+
+def wiener_signature(im, mysize=None, noise=None):
+    return array_namespace(im)
+
+
+def zoom_fft_signature(x, fn, m=None, *, fs=2, endpoint=False, axis=-1):
+    return array_namespace(x, fn)
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/_filter_design.py b/venv/lib/python3.12/site-packages/scipy/signal/_filter_design.py
new file mode 100644
index 0000000000000000000000000000000000000000..88710c15393ef7b1409862b6a0fc0d57e42afeff
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/_filter_design.py
@@ -0,0 +1,6097 @@
+"""Filter design."""
+import math
+import cmath
+import operator
+import warnings
+import builtins
+
+from math import pi
+
+import numpy as np
+from numpy.polynomial.polynomial import polyval as npp_polyval
+
+from scipy import special, optimize, fft as sp_fft
+from scipy.special import comb
+from scipy._lib import doccer
+from scipy._lib._util import float_factorial
+from scipy.signal._arraytools import _validate_fs
+from scipy.signal import _polyutils as _pu
+
+import scipy._external.array_api_extra as xpx
+from scipy._lib._array_api import (
+    array_namespace, xp_promote, xp_size, xp_default_dtype, is_jax, xp_float_to_complex,
+    xp_result_type,
+)
+from scipy._external.array_api_compat import numpy as np_compat
+
+
+__all__ = ['findfreqs', 'freqs', 'freqz', 'tf2zpk', 'zpk2tf', 'normalize',
+           'lp2lp', 'lp2hp', 'lp2bp', 'lp2bs', 'bilinear', 'iirdesign',
+           'iirfilter', 'butter', 'cheby1', 'cheby2', 'ellip', 'bessel',
+           'band_stop_obj', 'buttord', 'cheb1ord', 'cheb2ord', 'ellipord',
+           'buttap', 'cheb1ap', 'cheb2ap', 'ellipap', 'besselap',
+           'BadCoefficients', 'freqs_zpk', 'freqz_zpk',
+           'tf2sos', 'sos2tf', 'zpk2sos', 'sos2zpk', 'group_delay',
+           'sosfreqz', 'freqz_sos', 'iirnotch', 'iirpeak', 'bilinear_zpk',
+           'lp2lp_zpk', 'lp2hp_zpk', 'lp2bp_zpk', 'lp2bs_zpk',
+           'gammatone', 'iircomb']
+
+
+class BadCoefficients(UserWarning):
+    """Warning about badly conditioned filter coefficients."""
+    pass
+
+
+abs = np.absolute
+
+
+def _is_int_type(x):
+    """
+    Check if input is of a scalar integer type (so ``5`` and ``array(5)`` will
+    pass, while ``5.0`` and ``array([5])`` will fail.
+    """
+    if np.ndim(x) != 0:
+        # Older versions of NumPy did not raise for np.array([1]).__index__()
+        # This is safe to remove when support for those versions is dropped
+        return False
+    try:
+        operator.index(x)
+    except TypeError:
+        return False
+    else:
+        return True
+
+
+def _real_dtype_for_complex(dtyp, *, xp):
+    if xp.isdtype(dtyp, 'real floating'):
+        return dtyp
+    if dtyp == xp.complex64:
+        return xp.float32
+    elif dtyp == xp.complex128:
+        return xp.float64
+    else:
+        raise ValueError(f"Unknown dtype {dtyp}.")
+
+
+# https://github.com/numpy/numpy/blob/v2.2.0/numpy/_core/function_base.py#L195-L302
+def _logspace(start, stop, num=50, endpoint=True, base=10.0, dtype=None, *, xp):
+    if not isinstance(base, float | int) and xp.asarray(base).ndim > 0:
+        # If base is non-scalar, broadcast it with the others, since it
+        # may influence how axis is interpreted.
+        start, stop, base = map(xp.asarray, (start, stop, base))
+        ndmax = xp.broadcast_arrays(start, stop, base).ndim
+        start, stop, base = (
+            xpx.atleast_nd(a, ndim=ndmax)
+            for a in (start, stop, base)
+        )
+        base = xp.expand_dims(base)
+    try:
+        result_dt = xp.result_type(start, stop, base)
+    except ValueError:
+        # all of start, stop and base are python scalars
+        result_dt = xp_default_dtype(xp)
+    y = xp.linspace(start, stop, num=num, endpoint=endpoint, dtype=result_dt)
+
+    yp = xp.pow(base, y)
+    if dtype is None:
+        return yp
+    return xp.astype(yp, dtype, copy=False)
+
+
+def findfreqs(num, den, N, kind='ba'):
+    """
+    Find array of frequencies for computing the response of an analog filter.
+
+    Parameters
+    ----------
+    num, den : array_like, 1-D
+        The polynomial coefficients of the numerator and denominator of the
+        transfer function of the filter or LTI system, where the coefficients
+        are ordered from highest to lowest degree. Or, the roots  of the
+        transfer function numerator and denominator (i.e., zeroes and poles).
+    N : int
+        The length of the array to be computed.
+    kind : str {'ba', 'zp'}, optional
+        Specifies whether the numerator and denominator are specified by their
+        polynomial coefficients ('ba'), or their roots ('zp').
+
+    Returns
+    -------
+    w : (N,) ndarray
+        A 1-D array of frequencies, logarithmically spaced.
+
+    Examples
+    --------
+    Find a set of nine frequencies that span the "interesting part" of the
+    frequency response for the filter with the transfer function
+
+        H(s) = s / (s^2 + 8s + 25)
+
+    >>> from scipy import signal
+    >>> signal.findfreqs([1, 0], [1, 8, 25], N=9)
+    array([  1.00000000e-02,   3.16227766e-02,   1.00000000e-01,
+             3.16227766e-01,   1.00000000e+00,   3.16227766e+00,
+             1.00000000e+01,   3.16227766e+01,   1.00000000e+02])
+    """
+    xp = array_namespace(num, den)
+    num, den = map(xp.asarray, (num, den))
+
+    if kind == 'ba':
+        ep = xpx.atleast_nd(_pu.polyroots(den, xp=xp), ndim=1, xp=xp)
+        tz = xpx.atleast_nd(_pu.polyroots(num, xp=xp), ndim=1, xp=xp)
+    elif kind == 'zp':
+        ep = xpx.atleast_nd(den, ndim=1, xp=xp)
+        tz = xpx.atleast_nd(num, ndim=1, xp=xp)
+    else:
+        raise ValueError("input must be one of {'ba', 'zp'}")
+
+    ep = xp_float_to_complex(ep, xp=xp)
+    tz = xp_float_to_complex(tz, xp=xp)
+
+    if ep.shape[0] == 0:
+        ep = xp.asarray([-1000], dtype=ep.dtype)
+
+    ez = xp.concat((
+        ep[xp.imag(ep) >= 0],
+        tz[(xp.abs(tz) < 1e5) & (xp.imag(tz) >= 0)]
+    ))
+
+    integ = xp.astype(xp.abs(ez) < 1e-10, ez.dtype) # XXX True->1, False->0
+    hfreq = xp.round(
+        xp.log10(xp.max(3*xp.abs(xp.real(ez) + integ) + 1.5*xp.imag(ez))) + 0.5
+    )
+
+    # the fudge factor is for backwards compatibility: round(-1.5) can be -1 or -2
+    # depending on the floating-point jitter in -1.5
+    fudge = 1e-14 if is_jax(xp) else 0
+    lfreq = xp.round(
+        xp.log10(0.1*xp.min(xp.abs(xp.real(ez + integ)) + 2*xp.imag(ez))) - 0.5 - fudge
+    )
+
+    w = _logspace(lfreq, hfreq, N, xp=xp)
+    return w
+
+
+def freqs(b, a, worN=200, plot=None):
+    """
+    Compute frequency response of analog filter.
+
+    Given the M-order numerator `b` and N-order denominator `a` of an analog
+    filter, compute its frequency response::
+
+             b[0]*(jw)**M + b[1]*(jw)**(M-1) + ... + b[M]
+     H(w) = ----------------------------------------------
+             a[0]*(jw)**N + a[1]*(jw)**(N-1) + ... + a[N]
+
+    Parameters
+    ----------
+    b : array_like
+        Numerator of a linear filter.
+    a : array_like
+        Denominator of a linear filter.
+    worN : {None, int, array_like}, optional
+        If None, then compute at 200 frequencies around the interesting parts
+        of the response curve (determined by pole-zero locations). If a single
+        integer, then compute at that many frequencies. Otherwise, compute the
+        response at the angular frequencies (e.g., rad/s) given in `worN`.
+    plot : callable, optional
+        A callable that takes two arguments. If given, the return parameters
+        `w` and `h` are passed to plot. Useful for plotting the frequency
+        response inside `freqs`.
+
+    Returns
+    -------
+    w : ndarray
+        The angular frequencies at which `h` was computed.
+    h : ndarray
+        The frequency response.
+
+    See Also
+    --------
+    freqz : Compute the frequency response of a digital filter.
+
+    Notes
+    -----
+    Using Matplotlib's "plot" function as the callable for `plot` produces
+    unexpected results, this plots the real part of the complex transfer
+    function, not the magnitude. Try ``lambda w, h: plot(w, abs(h))``.
+
+    Examples
+    --------
+    >>> from scipy.signal import freqs, iirfilter
+    >>> import numpy as np
+
+    >>> b, a = iirfilter(4, [1, 10], 1, 60, analog=True, ftype='cheby1')
+
+    >>> w, h = freqs(b, a, worN=np.logspace(-1, 2, 1000))
+
+    >>> import matplotlib.pyplot as plt
+    >>> plt.semilogx(w, 20 * np.log10(abs(h)))
+    >>> plt.xlabel('Frequency [rad/s]')
+    >>> plt.ylabel('Amplitude response [dB]')
+    >>> plt.grid(True)
+    >>> plt.show()
+
+    """
+    xp = array_namespace(b, a, worN)
+
+    if worN is None:
+        # For backwards compatibility
+        w = findfreqs(b, a, 200)
+    elif _is_int_type(worN):
+        w = findfreqs(b, a, worN)
+    else:
+        w = xpx.atleast_nd(xp.asarray(worN), ndim=1, xp=xp)
+
+    s = 1j * w
+    h = _pu.polyval(b, s, xp=xp) / _pu.polyval(a, s, xp=xp)
+    if plot is not None:
+        plot(w, h)
+
+    return w, h
+
+
+def freqs_zpk(z, p, k, worN=200):
+    """
+    Compute frequency response of analog filter.
+
+    Given the zeros `z`, poles `p`, and gain `k` of a filter, compute its
+    frequency response::
+
+                (jw-z[0]) * (jw-z[1]) * ... * (jw-z[-1])
+     H(w) = k * ----------------------------------------
+                (jw-p[0]) * (jw-p[1]) * ... * (jw-p[-1])
+
+    Parameters
+    ----------
+    z : array_like
+        Zeroes of a linear filter
+    p : array_like
+        Poles of a linear filter
+    k : scalar
+        Gain of a linear filter
+    worN : {None, int, array_like}, optional
+        If None, then compute at 200 frequencies around the interesting parts
+        of the response curve (determined by pole-zero locations). If a single
+        integer, then compute at that many frequencies. Otherwise, compute the
+        response at the angular frequencies (e.g., rad/s) given in `worN`.
+
+    Returns
+    -------
+    w : ndarray
+        The angular frequencies at which `h` was computed.
+    h : ndarray
+        The frequency response.
+
+    See Also
+    --------
+    freqs : Compute the frequency response of an analog filter in TF form
+    freqz : Compute the frequency response of a digital filter in TF form
+    freqz_zpk : Compute the frequency response of a digital filter in ZPK form
+
+    Notes
+    -----
+    .. versionadded:: 0.19.0
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.signal import freqs_zpk, iirfilter
+
+    >>> z, p, k = iirfilter(4, [1, 10], 1, 60, analog=True, ftype='cheby1',
+    ...                     output='zpk')
+
+    >>> w, h = freqs_zpk(z, p, k, worN=np.logspace(-1, 2, 1000))
+
+    >>> import matplotlib.pyplot as plt
+    >>> plt.semilogx(w, 20 * np.log10(abs(h)))
+    >>> plt.xlabel('Frequency [rad/s]')
+    >>> plt.ylabel('Amplitude response [dB]')
+    >>> plt.grid(True)
+    >>> plt.show()
+
+    """
+    xp = array_namespace(z, p)
+    z, p = map(xp.asarray, (z, p))
+
+    # NB: k is documented to be a scalar; for backwards compat we keep allowing it
+    # to be a size-1 array, but it does not influence the namespace calculation.
+    k = xp.asarray(k, dtype=xp_default_dtype(xp))
+    if xp_size(k) > 1:
+        raise ValueError('k must be a single scalar gain')
+
+    if worN is None:
+        # For backwards compatibility
+        w = findfreqs(z, p, 200, kind='zp')
+    elif _is_int_type(worN):
+        w = findfreqs(z, p, worN, kind='zp')
+    else:
+        w = worN
+
+    w = xpx.atleast_nd(xp.asarray(w), ndim=1, xp=xp)
+    s = 1j * w
+    num = _pu.npp_polyvalfromroots(s, z, xp=xp)
+    den = _pu.npp_polyvalfromroots(s, p, xp=xp)
+    h = k * num/den
+    return w, h
+
+
+def freqz(b, a=1, worN=512, whole=False, plot=None, fs=2*pi,
+          include_nyquist=False):
+    """
+    Compute the frequency response of a digital filter.
+
+    Given the M-order numerator `b` and N-order denominator `a` of a digital
+    filter, compute its frequency response::
+
+                 jw                 -jw              -jwM
+        jw    B(e  )    b[0] + b[1]e    + ... + b[M]e
+     H(e  ) = ------ = -----------------------------------
+                 jw                 -jw              -jwN
+              A(e  )    a[0] + a[1]e    + ... + a[N]e
+
+    Parameters
+    ----------
+    b : array_like
+        Numerator of a linear filter. If `b` has dimension greater than 1,
+        it is assumed that the coefficients are stored in the first dimension,
+        and ``b.shape[1:]``, ``a.shape[1:]``, and the shape of the frequencies
+        array must be compatible for broadcasting.
+    a : array_like
+        Denominator of a linear filter. If `b` has dimension greater than 1,
+        it is assumed that the coefficients are stored in the first dimension,
+        and ``b.shape[1:]``, ``a.shape[1:]``, and the shape of the frequencies
+        array must be compatible for broadcasting.
+    worN : {None, int, array_like}, optional
+        If a single integer, then compute at that many frequencies (default is
+        N=512). This is a convenient alternative to::
+
+            np.linspace(0, fs if whole else fs/2, N, endpoint=include_nyquist)
+
+        Using a number that is fast for FFT computations can result in
+        faster computations (see Notes).
+
+        If an array_like, compute the response at the frequencies given.
+        These are in the same units as `fs`.
+    whole : bool, optional
+        Normally, frequencies are computed from 0 to the Nyquist frequency,
+        fs/2 (upper-half of unit-circle). If `whole` is True, compute
+        frequencies from 0 to fs. Ignored if worN is array_like.
+    plot : callable
+        A callable that takes two arguments. If given, the return parameters
+        `w` and `h` are passed to plot. Useful for plotting the frequency
+        response inside `freqz`.
+    fs : float, optional
+        The sampling frequency of the digital system. Defaults to 2*pi
+        radians/sample (so w is from 0 to pi).
+
+        .. versionadded:: 1.2.0
+    include_nyquist : bool, optional
+        If `whole` is False and `worN` is an integer, setting `include_nyquist`
+        to True will include the last frequency (Nyquist frequency) and is
+        otherwise ignored.
+
+        .. versionadded:: 1.5.0
+
+    Returns
+    -------
+    w : ndarray
+        The frequencies at which `h` was computed, in the same units as `fs`.
+        By default, `w` is normalized to the range [0, pi) (radians/sample).
+    h : ndarray
+        The frequency response, as complex numbers.
+
+    See Also
+    --------
+    freqz_zpk
+    freqz_sos
+
+    Notes
+    -----
+    Using Matplotlib's :func:`matplotlib.pyplot.plot` function as the callable
+    for `plot` produces unexpected results, as this plots the real part of the
+    complex transfer function, not the magnitude.
+    Try ``lambda w, h: plot(w, np.abs(h))``.
+
+    A direct computation via (R)FFT is used to compute the frequency response
+    when the following conditions are met:
+
+    1. An integer value is given for `worN`.
+    2. `worN` is fast to compute via FFT (i.e.,
+       `next_fast_len(worN) <scipy.fft.next_fast_len>` equals `worN`).
+    3. The denominator coefficients are a single value (``a.shape[0] == 1``).
+    4. `worN` is at least as long as the numerator coefficients
+       (``worN >= b.shape[0]``).
+    5. If ``b.ndim > 1``, then ``b.shape[-1] == 1``.
+
+    For long FIR filters, the FFT approach can have lower error and be much
+    faster than the equivalent direct polynomial calculation.
+
+    Examples
+    --------
+    >>> from scipy import signal
+    >>> import numpy as np
+    >>> taps, f_c = 80, 1.0  # number of taps and cut-off frequency
+    >>> b = signal.firwin(taps, f_c, window=('kaiser', 8), fs=2*np.pi)
+    >>> w, h = signal.freqz(b)
+
+    >>> import matplotlib.pyplot as plt
+    >>> fig, ax1 = plt.subplots(tight_layout=True)
+    >>> ax1.set_title(f"Frequency Response of {taps} tap FIR Filter" +
+    ...               f"($f_c={f_c}$ rad/sample)")
+    >>> ax1.axvline(f_c, color='black', linestyle=':', linewidth=0.8)
+    >>> ax1.plot(w, 20 * np.log10(abs(h)), 'C0')
+    >>> ax1.set_ylabel("Amplitude in dB", color='C0')
+    >>> ax1.set(xlabel="Frequency in rad/sample", xlim=(0, np.pi))
+
+    >>> ax2 = ax1.twinx()
+    >>> phase = np.unwrap(np.angle(h))
+    >>> ax2.plot(w, phase, 'C1')
+    >>> ax2.set_ylabel('Phase [rad]', color='C1')
+    >>> ax2.grid(True)
+    >>> ax2.axis('tight')
+    >>> plt.show()
+
+    Broadcasting Examples
+
+    Suppose we have two FIR filters whose coefficients are stored in the
+    rows of an array with shape (2, 25). For this demonstration, we'll
+    use random data:
+
+    >>> rng = np.random.default_rng()
+    >>> b = rng.random((2, 25))
+
+    To compute the frequency response for these two filters with one call
+    to `freqz`, we must pass in ``b.T``, because `freqz` expects the first
+    axis to hold the coefficients. We must then extend the shape with a
+    trivial dimension of length 1 to allow broadcasting with the array
+    of frequencies.  That is, we pass in ``b.T[..., np.newaxis]``, which has
+    shape (25, 2, 1):
+
+    >>> w, h = signal.freqz(b.T[..., np.newaxis], worN=1024)
+    >>> w.shape
+    (1024,)
+    >>> h.shape
+    (2, 1024)
+
+    Now, suppose we have two transfer functions, with the same numerator
+    coefficients ``b = [0.5, 0.5]``. The coefficients for the two denominators
+    are stored in the first dimension of the 2-D array  `a`::
+
+        a = [   1      1  ]
+            [ -0.25, -0.5 ]
+
+    >>> b = np.array([0.5, 0.5])
+    >>> a = np.array([[1, 1], [-0.25, -0.5]])
+
+    Only `a` is more than 1-D. To make it compatible for
+    broadcasting with the frequencies, we extend it with a trivial dimension
+    in the call to `freqz`:
+
+    >>> w, h = signal.freqz(b, a[..., np.newaxis], worN=1024)
+    >>> w.shape
+    (1024,)
+    >>> h.shape
+    (2, 1024)
+
+    """
+    xp = array_namespace(b, a)
+
+    b, a = map(xp.asarray, (b, a))
+    if xp.isdtype(a.dtype, 'integral'):
+        a = xp.astype(a, xp_default_dtype(xp))
+    res_dtype = xp.result_type(b, a)
+    real_dtype = _real_dtype_for_complex(res_dtype, xp=xp)
+
+    b = xpx.atleast_nd(b, ndim=1, xp=xp)
+    a = xpx.atleast_nd(a, ndim=1, xp=xp)
+
+    fs = _validate_fs(fs, allow_none=False)
+
+    if worN is None:
+        # For backwards compatibility
+        worN = 512
+
+    h = None
+
+    if _is_int_type(worN):
+        N = operator.index(worN)
+        del worN
+        if N < 0:
+            raise ValueError(f'worN must be nonnegative, got {N}')
+        lastpoint = 2 * pi if whole else pi
+        # if include_nyquist is true and whole is false, w should
+        # include end point
+        w = xp.linspace(0, lastpoint, N,
+                        endpoint=include_nyquist and not whole, dtype=real_dtype)
+        n_fft = N if whole else 2 * (N - 1) if include_nyquist else 2 * N
+        if (xp_size(a) == 1 and (b.ndim == 1 or (b.shape[-1] == 1))
+                and n_fft >= b.shape[0]
+                and n_fft > 0):  # TODO: review threshold acc. to benchmark?
+
+            if (xp.isdtype(b.dtype, "real floating") and
+                xp.isdtype(a.dtype, "real floating")
+            ):
+                fft_func = sp_fft.rfft
+            else:
+                fft_func = sp_fft.fft
+
+            h = fft_func(b, n=n_fft, axis=0)
+            h = h[:min(N, h.shape[0]), ...]
+            h /= a
+
+            if fft_func is sp_fft.rfft and whole:
+                # exclude DC and maybe Nyquist (no need to use axis_reverse
+                # here because we can build reversal with the truncation)
+                stop = None if n_fft % 2 == 1 else -1
+                h_flipped = xp.flip(h[1:stop, ...], axis=0)
+                h = xp.concat((h, xp.conj(h_flipped)))
+            if b.ndim > 1:
+                # Last axis of h has length 1, so drop it.
+                h = h[..., 0]
+                # Move the first axis of h to the end.
+                h = xp.moveaxis(h, 0, -1)
+    else:
+        if isinstance(worN, complex):
+            # backwards compat
+            worN = worN.real
+        w = xpx.atleast_nd(xp.asarray(worN, dtype=res_dtype), ndim=1, xp=xp)
+        if xp.isdtype(w.dtype, 'integral'):
+            w = xp.astype(w, xp_default_dtype(xp))
+        del worN
+        w = 2 * pi * w / fs
+
+    if h is None:  # still need to compute using freqs w
+        zm1 = xp.exp(-1j * w)
+        h = (_pu.npp_polyval(zm1, b, tensor=False, xp=xp) /
+             _pu.npp_polyval(zm1, a, tensor=False, xp=xp))
+
+    w = w * (fs / (2 * pi))
+
+    if plot is not None:
+        plot(w, h)
+
+    return w, h
+
+
+def freqz_zpk(z, p, k, worN=512, whole=False, fs=2*pi):
+    r"""
+    Compute the frequency response of a digital filter in ZPK form.
+
+    Given the Zeros, Poles and Gain of a digital filter, compute its frequency
+    response:
+
+    :math:`H(z)=k \prod_i (z - Z[i]) / \prod_j (z - P[j])`
+
+    where :math:`k` is the `gain`, :math:`Z` are the `zeros` and :math:`P` are
+    the `poles`.
+
+    Parameters
+    ----------
+    z : array_like
+        Zeroes of a linear filter
+    p : array_like
+        Poles of a linear filter
+    k : scalar
+        Gain of a linear filter
+    worN : {None, int, array_like}, optional
+        If a single integer, then compute at that many frequencies (default is
+        N=512).
+
+        If an array_like, compute the response at the frequencies given.
+        These are in the same units as `fs`.
+    whole : bool, optional
+        Normally, frequencies are computed from 0 to the Nyquist frequency,
+        fs/2 (upper-half of unit-circle). If `whole` is True, compute
+        frequencies from 0 to fs. Ignored if w is array_like.
+    fs : float, optional
+        The sampling frequency of the digital system. Defaults to 2*pi
+        radians/sample (so w is from 0 to pi).
+
+        .. versionadded:: 1.2.0
+
+    Returns
+    -------
+    w : ndarray
+        The frequencies at which `h` was computed, in the same units as `fs`.
+        By default, `w` is normalized to the range [0, pi) (radians/sample).
+    h : ndarray
+        The frequency response, as complex numbers.
+
+    See Also
+    --------
+    freqs : Compute the frequency response of an analog filter in TF form
+    freqs_zpk : Compute the frequency response of an analog filter in ZPK form
+    freqz : Compute the frequency response of a digital filter in TF form
+
+    Notes
+    -----
+    .. versionadded:: 0.19.0
+
+    Examples
+    --------
+    Design a 4th-order digital Butterworth filter with cut-off of 100 Hz in a
+    system with sample rate of 1000 Hz, and plot the frequency response:
+
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> z, p, k = signal.butter(4, 100, output='zpk', fs=1000)
+    >>> w, h = signal.freqz_zpk(z, p, k, fs=1000)
+
+    >>> import matplotlib.pyplot as plt
+    >>> fig = plt.figure()
+    >>> ax1 = fig.add_subplot(1, 1, 1)
+    >>> ax1.set_title('Digital filter frequency response')
+
+    >>> ax1.plot(w, 20 * np.log10(abs(h)), 'b')
+    >>> ax1.set_ylabel('Amplitude [dB]', color='b')
+    >>> ax1.set_xlabel('Frequency [Hz]')
+    >>> ax1.grid(True)
+
+    >>> ax2 = ax1.twinx()
+    >>> phase = np.unwrap(np.angle(h))
+    >>> ax2.plot(w, phase, 'g')
+    >>> ax2.set_ylabel('Phase [rad]', color='g')
+
+    >>> plt.axis('tight')
+    >>> plt.show()
+
+    """
+    xp = array_namespace(z, p)
+    z, p = map(xp.asarray, (z, p))
+
+    z = xpx.atleast_nd(z, ndim=1, xp=xp)
+    p = xpx.atleast_nd(p, ndim=1, xp=xp)
+    res_dtype = xp.result_type(z, p)
+    res_dtype = xp.float64 if res_dtype in (xp.float64, xp.complex128) else xp.float32
+
+    fs = _validate_fs(fs, allow_none=False)
+
+    if whole:
+        lastpoint = 2 * pi
+    else:
+        lastpoint = pi
+
+    if worN is None:
+        # For backwards compatibility
+        w = xp.linspace(0, lastpoint, 512, endpoint=False, dtype=res_dtype)
+    elif _is_int_type(worN):
+        w = xp.linspace(0, lastpoint, worN, endpoint=False, dtype=res_dtype)
+    else:
+        w = xp.asarray(worN)
+        if xp.isdtype(w.dtype, 'integral'):
+            w = xp.astype(w, xp_default_dtype(xp))
+        w = xpx.atleast_nd(w, ndim=1, xp=xp)
+        w = 2 * pi * w / fs
+
+    zm1 = xp.exp(1j * w)
+    func = _pu.npp_polyvalfromroots
+    h = xp.asarray(k, dtype=res_dtype) * func(zm1, z, xp=xp) / func(zm1, p, xp=xp)
+
+    w = w*(fs/(2*pi))
+
+    return w, h
+
+
+def group_delay(system, w=512, whole=False, fs=2*pi):
+    r"""Compute the group delay of a digital filter.
+
+    The group delay measures by how many samples amplitude envelopes of
+    various spectral components of a signal are delayed by a filter.
+    It is formally defined as the derivative of continuous (unwrapped) phase::
+
+               d        jw
+     D(w) = - -- arg H(e)
+              dw
+
+    Parameters
+    ----------
+    system : tuple of array_like (b, a)
+        Numerator and denominator coefficients of a filter transfer function.
+    w : {None, int, array_like}, optional
+        If a single integer, then compute at that many frequencies (default is
+        N=512).
+
+        If an array_like, compute the delay at the frequencies given. These
+        are in the same units as `fs`.
+    whole : bool, optional
+        Normally, frequencies are computed from 0 to the Nyquist frequency,
+        fs/2 (upper-half of unit-circle). If `whole` is True, compute
+        frequencies from 0 to fs. Ignored if w is array_like.
+    fs : float, optional
+        The sampling frequency of the digital system. Defaults to 2*pi
+        radians/sample (so w is from 0 to pi).
+
+        .. versionadded:: 1.2.0
+
+    Returns
+    -------
+    w : ndarray
+        The frequencies at which group delay was computed, in the same units
+        as `fs`.  By default, `w` is normalized to the range [0, pi)
+        (radians/sample).
+    gd : ndarray
+        The group delay.
+
+    See Also
+    --------
+    freqz : Frequency response of a digital filter
+
+    Notes
+    -----
+    The similar function in MATLAB is called `grpdelay`.
+
+    If the transfer function :math:`H(z)` has zeros or poles on the unit
+    circle, the group delay at corresponding frequencies is undefined.
+    When such a case arises the warning is raised and the group delay
+    is set to 0 at those frequencies.
+
+    For the details of numerical computation of the group delay refer to [1]_ or [2]_.
+
+    .. versionadded:: 0.16.0
+
+    References
+    ----------
+    .. [1] Richard G. Lyons, "Understanding Digital Signal Processing,
+           3rd edition", p. 830.
+    .. [2] Julius O. Smith III, "Numerical Computation of Group Delay",
+           in "Introduction to Digital Filters with Audio Applications",
+           online book, 2007,
+           https://ccrma.stanford.edu/~jos/fp/Numerical_Computation_Group_Delay.html
+
+    Examples
+    --------
+    >>> from scipy import signal
+    >>> b, a = signal.iirdesign(0.1, 0.3, 5, 50, ftype='cheby1')
+    >>> w, gd = signal.group_delay((b, a))
+
+    >>> import matplotlib.pyplot as plt
+    >>> plt.title('Digital filter group delay')
+    >>> plt.plot(w, gd)
+    >>> plt.ylabel('Group delay [samples]')
+    >>> plt.xlabel('Frequency [rad/sample]')
+    >>> plt.show()
+
+    """
+    xp = array_namespace(*system, w)
+    b, a = map(np.atleast_1d, system)
+
+    if w is None:
+        # For backwards compatibility
+        w = 512
+
+    fs = _validate_fs(fs, allow_none=False)
+
+    if _is_int_type(w):
+        if whole:
+            w = np.linspace(0, 2 * pi, w, endpoint=False)
+        else:
+            w = np.linspace(0, pi, w, endpoint=False)
+    else:
+        w = np.atleast_1d(w)
+        w = 2*pi*w/fs
+
+    c = np.convolve(b, np.conjugate(a[::-1]))
+    cr = c * np.arange(c.size)
+    z = np.exp(-1j * w)
+    num = np.polyval(cr[::-1], z)
+    den = np.polyval(c[::-1], z)
+    gd = np.real(num / den) - a.size + 1
+    singular = ~np.isfinite(gd)
+    near_singular = np.absolute(den) < 10 * EPSILON
+
+    if np.any(singular):
+        gd[singular] = 0
+        warnings.warn(
+            "The group delay is singular at frequencies "
+            f"[{', '.join(f'{ws:.3f}' for ws in w[singular])}], setting to 0",
+            stacklevel=2
+        )
+
+    elif np.any(near_singular):
+        warnings.warn(
+            "The filter's denominator is extremely small at frequencies "
+            f"[{', '.join(f'{ws:.3f}' for ws in w[near_singular])}], "
+            "around which a singularity may be present",
+            stacklevel=2
+        )
+
+    w = w * (fs / (2 * xp.pi))
+
+    return xp.asarray(w), xp.asarray(gd)
+
+
+def _validate_sos(sos, xp=None):
+    """Helper to validate a SOS input"""
+    if xp is None:
+        xp = np    # backcompat, cf sosfilt, sosfiltfilt
+
+    sos = xp.asarray(sos)
+    sos = xpx.atleast_nd(sos, ndim=2, xp=xp)
+    if sos.ndim != 2:
+        raise ValueError('sos array must be 2D')
+    n_sections, m = sos.shape
+    if m != 6:
+        raise ValueError('sos array must be shape (n_sections, 6)')
+    if not xp.all(sos[:, 3] == 1):
+        raise ValueError('sos[:, 3] should be all ones')
+    return sos, n_sections
+
+
+def freqz_sos(sos, worN=512, whole=False, fs=2*pi):
+    r"""
+    Compute the frequency response of a digital filter in SOS format.
+
+    Given `sos`, an array with shape (n, 6) of second order sections of
+    a digital filter, compute the frequency response of the system function::
+
+               B0(z)   B1(z)         B{n-1}(z)
+        H(z) = ----- * ----- * ... * ---------
+               A0(z)   A1(z)         A{n-1}(z)
+
+    for z = exp(omega*1j), where B{k}(z) and A{k}(z) are numerator and
+    denominator of the transfer function of the k-th second order section.
+
+    Parameters
+    ----------
+    sos : array_like
+        Array of second-order filter coefficients, must have shape
+        ``(n_sections, 6)``. Each row corresponds to a second-order
+        section, with the first three columns providing the numerator
+        coefficients and the last three providing the denominator
+        coefficients.
+    worN : {None, int, array_like}, optional
+        If a single integer, then compute at that many frequencies (default is
+        N=512).  Using a number that is fast for FFT computations can result
+        in faster computations (see Notes of `freqz`).
+
+        If an array_like, compute the response at the frequencies given (must
+        be 1-D). These are in the same units as `fs`.
+    whole : bool, optional
+        Normally, frequencies are computed from 0 to the Nyquist frequency,
+        fs/2 (upper-half of unit-circle). If `whole` is True, compute
+        frequencies from 0 to fs.
+    fs : float, optional
+        The sampling frequency of the digital system. Defaults to 2*pi
+        radians/sample (so w is from 0 to pi).
+
+        .. versionadded:: 1.2.0
+
+    Returns
+    -------
+    w : ndarray
+        The frequencies at which `h` was computed, in the same units as `fs`.
+        By default, `w` is normalized to the range [0, pi) (radians/sample).
+    h : ndarray
+        The frequency response, as complex numbers.
+
+    See Also
+    --------
+    freqz, sosfilt, sosfreqz
+
+    Notes
+    -----
+    This function used to be called ``sosfreqz`` in older versions (≥ 0.19.0)
+
+    .. versionadded:: 1.15.0
+
+    Examples
+    --------
+    Design a 15th-order bandpass filter in SOS format.
+
+    >>> from scipy import signal
+    >>> import numpy as np
+    >>> sos = signal.ellip(15, 0.5, 60, (0.2, 0.4), btype='bandpass',
+    ...                    output='sos')
+
+    Compute the frequency response at 1500 points from DC to Nyquist.
+
+    >>> w, h = signal.freqz_sos(sos, worN=1500)
+
+    Plot the response.
+
+    >>> import matplotlib.pyplot as plt
+    >>> plt.subplot(2, 1, 1)
+    >>> db = 20*np.log10(np.maximum(np.abs(h), 1e-5))
+    >>> plt.plot(w/np.pi, db)
+    >>> plt.ylim(-75, 5)
+    >>> plt.grid(True)
+    >>> plt.yticks([0, -20, -40, -60])
+    >>> plt.ylabel('Gain [dB]')
+    >>> plt.title('Frequency Response')
+    >>> plt.subplot(2, 1, 2)
+    >>> plt.plot(w/np.pi, np.angle(h))
+    >>> plt.grid(True)
+    >>> plt.yticks([-np.pi, -0.5*np.pi, 0, 0.5*np.pi, np.pi],
+    ...            [r'$-\pi$', r'$-\pi/2$', '0', r'$\pi/2$', r'$\pi$'])
+    >>> plt.ylabel('Phase [rad]')
+    >>> plt.xlabel('Normalized frequency (1.0 = Nyquist)')
+    >>> plt.show()
+
+    If the same filter is implemented as a single transfer function,
+    numerical error corrupts the frequency response:
+
+    >>> b, a = signal.ellip(15, 0.5, 60, (0.2, 0.4), btype='bandpass',
+    ...                    output='ba')
+    >>> w, h = signal.freqz(b, a, worN=1500)
+    >>> plt.subplot(2, 1, 1)
+    >>> db = 20*np.log10(np.maximum(np.abs(h), 1e-5))
+    >>> plt.plot(w/np.pi, db)
+    >>> plt.ylim(-75, 5)
+    >>> plt.grid(True)
+    >>> plt.yticks([0, -20, -40, -60])
+    >>> plt.ylabel('Gain [dB]')
+    >>> plt.title('Frequency Response')
+    >>> plt.subplot(2, 1, 2)
+    >>> plt.plot(w/np.pi, np.angle(h))
+    >>> plt.grid(True)
+    >>> plt.yticks([-np.pi, -0.5*np.pi, 0, 0.5*np.pi, np.pi],
+    ...            [r'$-\pi$', r'$-\pi/2$', '0', r'$\pi/2$', r'$\pi$'])
+    >>> plt.ylabel('Phase [rad]')
+    >>> plt.xlabel('Normalized frequency (1.0 = Nyquist)')
+    >>> plt.show()
+
+    """
+    xp = array_namespace(sos)
+
+    fs = _validate_fs(fs, allow_none=False)
+
+    sos, n_sections = _validate_sos(sos, xp)
+    if n_sections == 0:
+        raise ValueError('Cannot compute frequencies with no sections')
+    h = 1.
+    for j in range(sos.shape[0]):
+        row = sos[j, :]
+        w, rowh = freqz(row[:3], row[3:], worN=worN, whole=whole, fs=fs)
+        h *= rowh
+    return w, h
+
+
+def sosfreqz(*args, **kwargs):
+    """
+    Compute the frequency response of a digital filter in SOS format (legacy).
+
+   .. legacy:: function
+
+        This function is an alias, provided for backward compatibility.
+        New code should use the function :func:`scipy.signal.freqz_sos`.
+        This function became obsolete from version 1.15.0.
+
+    """  # numpydoc ignore=RT01
+    return freqz_sos(*args, **kwargs)
+
+
+def _cplxreal(z, tol=None):
+    """
+    Split into complex and real parts, combining conjugate pairs.
+
+    The 1-D input vector `z` is split up into its complex (`zc`) and real (`zr`)
+    elements. Every complex element must be part of a complex-conjugate pair,
+    which are combined into a single number (with positive imaginary part) in
+    the output. Two complex numbers are considered a conjugate pair if their
+    real and imaginary parts differ in magnitude by less than ``tol * abs(z)``.
+
+    Parameters
+    ----------
+    z : array_like
+        Vector of complex numbers to be sorted and split
+    tol : float, optional
+        Relative tolerance for testing realness and conjugate equality.
+        Default is ``100 * spacing(1)`` of `z`'s data type (i.e., 2e-14 for
+        float64)
+
+    Returns
+    -------
+    zc : ndarray
+        Complex elements of `z`, with each pair represented by a single value
+        having positive imaginary part, sorted first by real part, and then
+        by magnitude of imaginary part. The pairs are averaged when combined
+        to reduce error.
+    zr : ndarray
+        Real elements of `z` (those having imaginary part less than
+        `tol` times their magnitude), sorted by value.
+
+    Raises
+    ------
+    ValueError
+        If there are any complex numbers in `z` for which a conjugate
+        cannot be found.
+
+    See Also
+    --------
+    _cplxpair
+
+    Examples
+    --------
+    >>> from scipy.signal._filter_design import _cplxreal
+    >>> a = [4, 3, 1, 2-2j, 2+2j, 2-1j, 2+1j, 2-1j, 2+1j, 1+1j, 1-1j]
+    >>> zc, zr = _cplxreal(a)
+    >>> print(zc)
+    [ 1.+1.j  2.+1.j  2.+1.j  2.+2.j]
+    >>> print(zr)
+    [ 1.  3.  4.]
+    """
+
+    z = np.atleast_1d(z)
+    if z.size == 0:
+        return z, z
+    elif z.ndim != 1:
+        raise ValueError('_cplxreal only accepts 1-D input')
+
+    if tol is None:
+        # Get tolerance from dtype of input
+        tol = 100 * np.finfo((1.0 * z).dtype).eps
+
+    # Sort by real part, magnitude of imaginary part (speed up further sorting)
+    z = z[np.lexsort((abs(z.imag), z.real))]
+
+    # Split reals from conjugate pairs
+    real_indices = abs(z.imag) <= tol * abs(z)
+    zr = z[real_indices].real
+
+    if len(zr) == len(z):
+        # Input is entirely real
+        return np.array([]), zr
+
+    # Split positive and negative halves of conjugates
+    z = z[~real_indices]
+    zp = z[z.imag > 0]
+    zn = z[z.imag < 0]
+
+    if len(zp) != len(zn):
+        raise ValueError('Array contains complex value with no matching '
+                         'conjugate.')
+
+    # Find runs of (approximately) the same real part
+    same_real = np.diff(zp.real) <= tol * abs(zp[:-1])
+    diffs = np.diff(np.concatenate(([0], same_real, [0])))
+    run_starts = np.nonzero(diffs > 0)[0]
+    run_stops = np.nonzero(diffs < 0)[0]
+
+    # Sort each run by their imaginary parts
+    for i in range(len(run_starts)):
+        start = run_starts[i]
+        stop = run_stops[i] + 1
+        for chunk in (zp[start:stop], zn[start:stop]):
+            chunk[...] = chunk[np.lexsort([abs(chunk.imag)])]
+
+    # Check that negatives match positives
+    if any(abs(zp - zn.conj()) > tol * abs(zn)):
+        raise ValueError('Array contains complex value with no matching '
+                         'conjugate.')
+
+    # Average out numerical inaccuracy in real vs imag parts of pairs
+    zc = (zp + zn.conj()) / 2
+
+    return zc, zr
+
+
+def _cplxpair(z, tol=None):
+    """
+    Sort into pairs of complex conjugates.
+
+    Complex conjugates in `z` are sorted by increasing real part. In each
+    pair, the number with negative imaginary part appears first.
+
+    If pairs have identical real parts, they are sorted by increasing
+    imaginary magnitude.
+
+    Two complex numbers are considered a conjugate pair if their real and
+    imaginary parts differ in magnitude by less than ``tol * abs(z)``.  The
+    pairs are forced to be exact complex conjugates by averaging the positive
+    and negative values.
+
+    Purely real numbers are also sorted, but placed after the complex
+    conjugate pairs. A number is considered real if its imaginary part is
+    smaller than `tol` times the magnitude of the number.
+
+    Parameters
+    ----------
+    z : array_like
+        1-D input array to be sorted.
+    tol : float, optional
+        Relative tolerance for testing realness and conjugate equality.
+        Default is ``100 * spacing(1)`` of `z`'s data type (i.e., 2e-14 for
+        float64)
+
+    Returns
+    -------
+    y : ndarray
+        Complex conjugate pairs followed by real numbers.
+
+    Raises
+    ------
+    ValueError
+        If there are any complex numbers in `z` for which a conjugate
+        cannot be found.
+
+    See Also
+    --------
+    _cplxreal
+
+    Examples
+    --------
+    >>> from scipy.signal._filter_design import _cplxpair
+    >>> a = [4, 3, 1, 2-2j, 2+2j, 2-1j, 2+1j, 2-1j, 2+1j, 1+1j, 1-1j]
+    >>> z = _cplxpair(a)
+    >>> print(z)
+    [ 1.-1.j  1.+1.j  2.-1.j  2.+1.j  2.-1.j  2.+1.j  2.-2.j  2.+2.j  1.+0.j
+      3.+0.j  4.+0.j]
+    """
+
+    z = np.atleast_1d(z)
+    if z.size == 0 or np.isrealobj(z):
+        return np.sort(z)
+
+    if z.ndim != 1:
+        raise ValueError('z must be 1-D')
+
+    zc, zr = _cplxreal(z, tol)
+
+    # Interleave complex values and their conjugates, with negative imaginary
+    # parts first in each pair
+    zc = np.dstack((zc.conj(), zc)).flatten()
+    z = np.append(zc, zr)
+    return z
+
+
+def tf2zpk(b, a):
+    r"""Return zero, pole, gain (z, p, k) representation from a numerator,
+    denominator representation of a linear filter.
+
+    Parameters
+    ----------
+    b : array_like, shape (M,)
+        Numerator polynomial coefficients. Must be 1-D.
+    a : array_like, shape (N,)
+        Denominator polynomial coefficients. Must be 1-D.
+
+    Returns
+    -------
+    z : ndarray
+        Zeros of the transfer function.
+    p : ndarray
+        Poles of the transfer function.
+    k : float
+        System gain.
+
+    Notes
+    -----
+    If some values of `b` are too close to 0, they are removed. In that case,
+    a BadCoefficients warning is emitted.
+
+    The `b` and `a` arrays are interpreted as coefficients for positive,
+    descending powers of the transfer function variable. So the inputs
+    :math:`b = [b_0, b_1, ..., b_M]` and :math:`a =[a_0, a_1, ..., a_N]`
+    can represent an analog filter of the form:
+
+    .. math::
+
+        H(s) = \frac
+        {b_0 s^M + b_1 s^{(M-1)} + \cdots + b_M}
+        {a_0 s^N + a_1 s^{(N-1)} + \cdots + a_N}
+
+    or a discrete-time filter of the form:
+
+    .. math::
+
+        H(z) = \frac
+        {b_0 z^M + b_1 z^{(M-1)} + \cdots + b_M}
+        {a_0 z^N + a_1 z^{(N-1)} + \cdots + a_N}
+
+    This "positive powers" form is found more commonly in controls
+    engineering. If `M` and `N` are equal (which is true for all filters
+    generated by the bilinear transform), then this happens to be equivalent
+    to the "negative powers" discrete-time form preferred in DSP:
+
+    .. math::
+
+        H(z) = \frac
+        {b_0 + b_1 z^{-1} + \cdots + b_M z^{-M}}
+        {a_0 + a_1 z^{-1} + \cdots + a_N z^{-N}}
+
+    Although this is true for common filters, remember that this is not true
+    in the general case. If `M` and `N` are not equal, the discrete-time
+    transfer function coefficients must first be converted to the "positive
+    powers" form before finding the poles and zeros.
+
+    Examples
+    --------
+    Find the zeroes, poles and gain of
+    a filter with the transfer function
+
+    .. math::
+
+        H(s) = \frac{3s^2}{s^2 + 5s + 13}
+
+    >>> from scipy.signal import tf2zpk
+    >>> tf2zpk([3, 0, 0], [1, 5, 13])
+    (   array([ 0.               ,  0.              ]),
+        array([ -2.5+2.59807621j ,  -2.5-2.59807621j]),
+        3.0)
+    """
+    xp = array_namespace(b, a)
+    b, a = normalize(b, a)
+
+    a, b = xp_promote(a, b, xp=xp, force_floating=True)
+
+    k = b[0]
+    b = b / b[0]
+    z = _pu.polyroots(b, xp=xp)
+    p = _pu.polyroots(a, xp=xp)
+    return z, p, k
+
+
+def zpk2tf(z, p, k):
+    r"""
+    Return polynomial transfer function representation from zeros and poles.
+
+    Parameters
+    ----------
+    z : array_like
+        Zeros of the transfer function.
+    p : array_like
+        Poles of the transfer function.
+    k : float
+        System gain.
+
+    Returns
+    -------
+    b : ndarray
+        Numerator polynomial coefficients.
+    a : ndarray
+        Denominator polynomial coefficients.
+
+    Examples
+    --------
+    Find the polynomial representation of a transfer function H(s)
+    using its 'zpk' (Zero-Pole-Gain) representation.
+
+    .. math::
+
+        H(z) = 5 \frac
+        { (s - 2)(s - 6) }
+        { (s - 1)(s - 8) }
+
+    >>> from scipy.signal import zpk2tf
+    >>> z   = [2,   6]
+    >>> p   = [1,   8]
+    >>> k   = 5
+    >>> zpk2tf(z, p, k)
+    (   array([  5., -40.,  60.]), array([ 1., -9.,  8.]))
+    """
+    xp = array_namespace(z, p)
+    z, p = map(xp.asarray, (z, p))
+    k = xp.asarray(k, dtype=xp.result_type(xp.real(z), xp.real(p), k))
+    if xp.isdtype(k.dtype, "integral"):
+        k = xp.astype(k, xp.float64)
+
+    z = xpx.atleast_nd(z, ndim=1, xp=xp)
+    k = xpx.atleast_nd(k, ndim=1, xp=xp)
+
+    if z.ndim > 1:
+        temp = _pu.poly(z[0, ...], xp=xp)
+        result_dtype = xp_result_type(temp, k, force_floating=True, xp=xp)
+        b = xp.empty((z.shape[0], z.shape[1] + 1), dtype=result_dtype)
+        if k.shape[0] == 1:
+            k = [k[0]] * z.shape[0]
+        for i in range(z.shape[0]):
+            k_i = xp.asarray(k[i], dtype=result_dtype)
+            poly_i = xp.asarray(_pu.poly(z[i, ...], xp=xp), dtype=result_dtype)
+            b_i = k_i * poly_i
+            b = xpx.at(b)[i, ...].set(b_i)
+    else:
+        # Use xp.multiply to work around torch type promotion
+        # non-compliance for operations between 0d and higher
+        # dimensional arrays.
+        b = xp.multiply(k, _pu.poly(z, xp=xp))
+
+    a = _pu.poly(p, xp=xp)
+    a = xpx.atleast_nd(xp.asarray(a), ndim=1, xp=xp)
+
+    return b, a
+
+
+def tf2sos(b, a, pairing=None, *, analog=False):
+    r"""
+    Return second-order sections from transfer function representation.
+
+    Parameters
+    ----------
+    b : array_like, shape (M,)
+        Numerator polynomial coefficients. Must be 1-D.
+    a : array_like, shape (N,)
+        Denominator polynomial coefficients. Must be 1-D.
+    pairing : {None, 'nearest', 'keep_odd', 'minimal'}, optional
+        The method to use to combine pairs of poles and zeros into sections.
+        See `zpk2sos` for information and restrictions on `pairing` and
+        `analog` arguments.
+    analog : bool, optional
+        If True, system is analog, otherwise discrete.
+
+        .. versionadded:: 1.8.0
+
+    Returns
+    -------
+    sos : ndarray
+        Array of second-order filter coefficients, with shape
+        ``(n_sections, 6)``. See `sosfilt` for the SOS filter format
+        specification.
+
+    See Also
+    --------
+    zpk2sos, sosfilt
+
+    Notes
+    -----
+    It is generally discouraged to convert from TF to SOS format, since doing
+    so usually will not improve numerical precision errors. Instead, consider
+    designing filters in ZPK format and converting directly to SOS. TF is
+    converted to SOS by first converting to ZPK format, then converting
+    ZPK to SOS.
+
+    .. versionadded:: 0.16.0
+
+    Examples
+    --------
+    Find the 'sos' (second-order sections) of the transfer function H(s)
+    using its polynomial representation.
+
+    .. math::
+
+        H(s) = \frac{s^2 - 3.5s - 2}{s^4 + 3s^3 - 15s^2 - 19s + 30}
+
+    >>> from scipy.signal import tf2sos
+    >>> tf2sos([1, -3.5, -2], [1, 3, -15, -19, 30], analog=True)
+    array([[  0. ,   0. ,   1. ,   1. ,   2. , -15. ],
+           [  1. ,  -3.5,  -2. ,   1. ,   1. ,  -2. ]])
+    """
+    return zpk2sos(*tf2zpk(b, a), pairing=pairing, analog=analog)
+
+
+def sos2tf(sos):
+    r"""
+    Return a single transfer function from a series of second-order sections.
+
+    Parameters
+    ----------
+    sos : array_like
+        Array of second-order filter coefficients, must have shape
+        ``(n_sections, 6)``. See `sosfilt` for the SOS filter format
+        specification.
+
+    Returns
+    -------
+    b : ndarray
+        Numerator polynomial coefficients.
+    a : ndarray
+        Denominator polynomial coefficients.
+
+    Notes
+    -----
+    .. versionadded:: 0.16.0
+
+    Examples
+    --------
+    Find the polynomial representation of an elliptic filter
+    using its 'sos' (second-order sections) format.
+
+    >>> from scipy.signal import sos2tf
+    >>> from scipy import signal
+    >>> sos = signal.ellip(1, 0.001, 50, 0.1, output='sos')
+    >>> sos2tf(sos)
+    (   array([0.91256522, 0.91256522, 0.        ]),
+        array([1.        , 0.82513043, 0.        ]))
+    """
+    xp = array_namespace(sos)
+    sos = xp.asarray(sos)
+
+    result_type = sos.dtype
+    if xp.isdtype(result_type, 'integral'):
+        result_type = xp_default_dtype(xp)
+
+    b = xp.asarray([1], dtype=result_type)
+    a = xp.asarray([1], dtype=result_type)
+
+    n_sections = sos.shape[0]
+    for section in range(n_sections):
+        b = _pu.polymul(b, sos[section, :3], xp=xp)
+        a = _pu.polymul(a, sos[section, 3:], xp=xp)
+    return b, a
+
+
+def sos2zpk(sos):
+    """
+    Return zeros, poles, and gain of a series of second-order sections.
+
+    Parameters
+    ----------
+    sos : array_like
+        Array of second-order filter coefficients, must have shape
+        ``(n_sections, 6)``. See `sosfilt` for the SOS filter format
+        specification.
+
+    Returns
+    -------
+    z : ndarray
+        Zeros of the transfer function.
+    p : ndarray
+        Poles of the transfer function.
+    k : float
+        System gain.
+
+    Notes
+    -----
+    The number of zeros and poles returned will be ``n_sections * 2``
+    even if some of these are (effectively) zero.
+
+    .. versionadded:: 0.16.0
+    """
+    xp = array_namespace(sos)
+    sos = xp.asarray(sos)
+
+    n_sections = sos.shape[0]
+    z = xp.zeros(n_sections*2, dtype=xp.complex128)
+    p = xp.zeros(n_sections*2, dtype=xp.complex128)
+    k = 1.
+    for section in range(n_sections):
+        zpk = tf2zpk(sos[section, :3], sos[section, 3:])
+        z = xpx.at(z, slice(2*section, 2*section + zpk[0].shape[0])).set(zpk[0])
+        p = xpx.at(p, slice(2*section, 2*section + zpk[1].shape[0])).set(zpk[1])
+        k *= zpk[2]
+    return z, p, k
+
+
+def _nearest_real_complex_idx(fro, to, which):
+    """Get the next closest real or complex element based on distance"""
+    assert which in ('real', 'complex', 'any')
+    order = np.argsort(np.abs(fro - to))
+    if which == 'any':
+        return order[0]
+    else:
+        mask = np.isreal(fro[order])
+        if which == 'complex':
+            mask = ~mask
+        return order[np.nonzero(mask)[0][0]]
+
+
+def _single_zpksos(z, p, k):
+    """Create one second-order section from up to two zeros and poles"""
+    sos = np.zeros(6)
+    b, a = zpk2tf(z, p, k)
+    sos[3-len(b):3] = b
+    sos[6-len(a):6] = a
+    return sos
+
+
+def zpk2sos(z, p, k, pairing=None, *, analog=False):
+    """Return second-order sections from zeros, poles, and gain of a system.
+
+    Parameters
+    ----------
+    z : array_like
+        Zeros of the transfer function.
+    p : array_like
+        Poles of the transfer function.
+    k : float
+        System gain.
+    pairing : {None, 'nearest', 'keep_odd', 'minimal'}, optional
+        The method to use to combine pairs of poles and zeros into sections.
+        If analog is False and pairing is None, pairing is set to 'nearest';
+        if analog is True, pairing must be 'minimal', and is set to that if
+        it is None.
+    analog : bool, optional
+        If True, system is analog, otherwise discrete.
+
+        .. versionadded:: 1.8.0
+
+    Returns
+    -------
+    sos : ndarray
+        Array of second-order filter coefficients, with shape
+        ``(n_sections, 6)``. See `sosfilt` for the SOS filter format
+        specification.
+
+    See Also
+    --------
+    sosfilt
+
+    Notes
+    -----
+    The algorithm used to convert ZPK to SOS format is designed to
+    minimize errors due to numerical precision issues. The pairing
+    algorithm attempts to minimize the peak gain of each biquadratic
+    section. This is done by pairing poles with the nearest zeros, starting
+    with the poles closest to the unit circle for discrete-time systems, and
+    poles closest to the imaginary axis for continuous-time systems.
+
+    ``pairing='minimal'`` outputs may not be suitable for `sosfilt`,
+    and ``analog=True`` outputs will never be suitable for `sosfilt`.
+
+    *Algorithms*
+
+    The steps in the ``pairing='nearest'``, ``pairing='keep_odd'``,
+    and ``pairing='minimal'`` algorithms are mostly shared. The
+    ``'nearest'`` algorithm attempts to minimize the peak gain, while
+    ``'keep_odd'`` minimizes peak gain under the constraint that
+    odd-order systems should retain one section as first order.
+    ``'minimal'`` is similar to ``'keep_odd'``, but no additional
+    poles or zeros are introduced
+
+    The algorithm steps are as follows:
+
+    As a pre-processing step for ``pairing='nearest'``,
+    ``pairing='keep_odd'``, add poles or zeros to the origin as
+    necessary to obtain the same number of poles and zeros for
+    pairing.  If ``pairing == 'nearest'`` and there are an odd number
+    of poles, add an additional pole and a zero at the origin.
+
+    The following steps are then iterated over until no more poles or
+    zeros remain:
+
+    1. Take the (next remaining) pole (complex or real) closest to the
+       unit circle (or imaginary axis, for ``analog=True``) to
+       begin a new filter section.
+    2. If the pole is real and there are no other remaining real poles [#]_,
+       add the closest real zero to the section and leave it as a first
+       order section. Note that after this step we are guaranteed to be
+       left with an even number of real poles, complex poles, real zeros,
+       and complex zeros for subsequent pairing iterations.
+    3. Else:
+
+       1. If the pole is complex and the zero is the only remaining real
+          zero*, then pair the pole with the *next* closest zero
+          (guaranteed to be complex). This is necessary to ensure that
+          there will be a real zero remaining to eventually create a
+          first-order section (thus keeping the odd order).
+       2. Else pair the pole with the closest remaining zero (complex or real).
+       3. Proceed to complete the second-order section by adding another
+          pole and zero to the current pole and zero in the section:
+
+          1. If the current pole and zero are both complex, add their conjugates.
+          2. Else if the pole is complex and the zero is real, add the
+             conjugate pole and the next closest real zero.
+          3. Else if the pole is real and the zero is complex, add the
+             conjugate zero and the real pole closest to those zeros.
+          4. Else (we must have a real pole and real zero) add the next
+             real pole closest to the unit circle, and then add the real
+             zero closest to that pole.
+
+    .. [#] This conditional can only be met for specific odd-order inputs
+           with the ``pairing = 'keep_odd'`` or ``'minimal'`` methods.
+
+    .. versionadded:: 0.16.0
+
+    Examples
+    --------
+
+    Design a 6th order low-pass elliptic digital filter for a system with a
+    sampling rate of 8000 Hz that has a pass-band corner frequency of
+    1000 Hz. The ripple in the pass-band should not exceed 0.087 dB, and
+    the attenuation in the stop-band should be at least 90 dB.
+
+    In the following call to `ellip`, we could use ``output='sos'``,
+    but for this example, we'll use ``output='zpk'``, and then convert
+    to SOS format with `zpk2sos`:
+
+    >>> from scipy import signal
+    >>> import numpy as np
+    >>> z, p, k = signal.ellip(6, 0.087, 90, 1000/(0.5*8000), output='zpk')
+
+    Now convert to SOS format.
+
+    >>> sos = signal.zpk2sos(z, p, k)
+
+    The coefficients of the numerators of the sections:
+
+    >>> sos[:, :3]
+    array([[0.0014152 , 0.00248677, 0.0014152 ],
+           [1.        , 0.72976874, 1.        ],
+           [1.        , 0.17607852, 1.        ]])
+
+    The symmetry in the coefficients occurs because all the zeros are on the
+    unit circle.
+
+    The coefficients of the denominators of the sections:
+
+    >>> sos[:, 3:]
+    array([[ 1.        , -1.32544025,  0.46989976],
+           [ 1.        , -1.26118294,  0.62625924],
+           [ 1.        , -1.2570723 ,  0.8619958 ]])
+
+    The next example shows the effect of the `pairing` option.  We have a
+    system with three poles and three zeros, so the SOS array will have
+    shape (2, 6). The means there is, in effect, an extra pole and an extra
+    zero at the origin in the SOS representation.
+
+    >>> z1 = np.array([-1, -0.5-0.5j, -0.5+0.5j])
+    >>> p1 = np.array([0.75, 0.8+0.1j, 0.8-0.1j])
+
+    With ``pairing='nearest'`` (the default), we obtain
+
+    >>> signal.zpk2sos(z1, p1, 1)
+    array([[ 1.  ,  1.  ,  0.5 ,  1.  , -0.75,  0.  ],
+           [ 1.  ,  1.  ,  0.  ,  1.  , -1.6 ,  0.65]])
+
+    The first section has the zeros {-0.5-0.05j, -0.5+0.5j} and the poles
+    {0, 0.75}, and the second section has the zeros {-1, 0} and poles
+    {0.8+0.1j, 0.8-0.1j}. Note that the extra pole and zero at the origin
+    have been assigned to different sections.
+
+    With ``pairing='keep_odd'``, we obtain:
+
+    >>> signal.zpk2sos(z1, p1, 1, pairing='keep_odd')
+    array([[ 1.  ,  1.  ,  0.  ,  1.  , -0.75,  0.  ],
+           [ 1.  ,  1.  ,  0.5 ,  1.  , -1.6 ,  0.65]])
+
+    The extra pole and zero at the origin are in the same section.
+    The first section is, in effect, a first-order section.
+
+    With ``pairing='minimal'``, the first-order section doesn't have
+    the extra pole and zero at the origin:
+
+    >>> signal.zpk2sos(z1, p1, 1, pairing='minimal')
+    array([[ 0.  ,  1.  ,  1.  ,  0.  ,  1.  , -0.75],
+           [ 1.  ,  1.  ,  0.5 ,  1.  , -1.6 ,  0.65]])
+
+    """
+    # TODO in the near future:
+    # 1. Add SOS capability to `filtfilt`, `freqz`, etc. somehow (#3259).
+    # 2. Make `decimate` use `sosfilt` instead of `lfilter`.
+    # 3. Make sosfilt automatically simplify sections to first order
+    #    when possible. Note this might make `sosfiltfilt` a bit harder (ICs).
+    # 4. Further optimizations of the section ordering / pole-zero pairing.
+    # See the wiki for other potential issues.
+
+    xp = array_namespace(z, p)
+
+    # convert to numpy, convert back on exit   XXX
+    z, p = map(np.asarray, (z, p))
+    k = np.asarray(k)
+
+    if pairing is None:
+        pairing = 'minimal' if analog else 'nearest'
+
+    valid_pairings = ['nearest', 'keep_odd', 'minimal']
+    if pairing not in valid_pairings:
+        raise ValueError(f'pairing must be one of {valid_pairings}, not {pairing}')
+
+    if analog and pairing != 'minimal':
+        raise ValueError('for analog zpk2sos conversion, '
+                         'pairing must be "minimal"')
+
+    if len(z) == len(p) == 0:
+        if not analog:
+            return xp.asarray(np.asarray([[k, 0., 0., 1., 0., 0.]]))
+        else:
+            return xp.asarray(np.asarray([[0., 0., k, 0., 0., 1.]]))
+
+    if pairing != 'minimal':
+        # ensure we have the same number of poles and zeros, and make copies
+        p = np.concatenate((p, np.zeros(max(len(z) - len(p), 0))))
+        z = np.concatenate((z, np.zeros(max(len(p) - len(z), 0))))
+        n_sections = (max(len(p), len(z)) + 1) // 2
+
+        if len(p) % 2 == 1 and pairing == 'nearest':
+            p = np.concatenate((p, [0.]))
+            z = np.concatenate((z, [0.]))
+        assert len(p) == len(z)
+    else:
+        if len(p) < len(z):
+            raise ValueError('for analog zpk2sos conversion, '
+                             'must have len(p)>=len(z)')
+
+        n_sections = (len(p) + 1) // 2
+
+    # Ensure we have complex conjugate pairs
+    # (note that _cplxreal only gives us one element of each complex pair):
+    z = np.concatenate(_cplxreal(z))
+    p = np.concatenate(_cplxreal(p))
+    if not np.isreal(k):
+        raise ValueError('k must be real')
+    k = k.real
+
+    if not analog:
+        # digital: "worst" is the closest to the unit circle
+        def idx_worst(p):
+            return np.argmin(np.abs(1 - np.abs(p)))
+    else:
+        # analog: "worst" is the closest to the imaginary axis
+        def idx_worst(p):
+            return np.argmin(np.abs(np.real(p)))
+
+    sos = np.zeros((n_sections, 6))
+
+    # Construct the system, reversing order so the "worst" are last
+    for si in range(n_sections-1, -1, -1):
+        # Select the next "worst" pole
+        p1_idx = idx_worst(p)
+        p1 = p[p1_idx]
+        p = np.delete(p, p1_idx)
+
+        # Pair that pole with a zero
+
+        if np.isreal(p1) and np.isreal(p).sum() == 0:
+            # Special case (1): last remaining real pole
+            if pairing != 'minimal':
+                z1_idx = _nearest_real_complex_idx(z, p1, 'real')
+                z1 = z[z1_idx]
+                z = np.delete(z, z1_idx)
+                sos[si] = _single_zpksos([z1, 0], [p1, 0], 1)
+            elif len(z) > 0:
+                z1_idx = _nearest_real_complex_idx(z, p1, 'real')
+                z1 = z[z1_idx]
+                z = np.delete(z, z1_idx)
+                sos[si] = _single_zpksos([z1], [p1], 1)
+            else:
+                sos[si] = _single_zpksos([], [p1], 1)
+
+        elif (len(p) + 1 == len(z)
+              and not np.isreal(p1)
+              and np.isreal(p).sum() == 1
+              and np.isreal(z).sum() == 1):
+
+            # Special case (2): there's one real pole and one real zero
+            # left, and an equal number of poles and zeros to pair up.
+            # We *must* pair with a complex zero
+
+            z1_idx = _nearest_real_complex_idx(z, p1, 'complex')
+            z1 = z[z1_idx]
+            z = np.delete(z, z1_idx)
+            sos[si] = _single_zpksos([z1, z1.conj()], [p1, p1.conj()], 1)
+
+        else:
+            if np.isreal(p1):
+                prealidx = np.flatnonzero(np.isreal(p))
+                p2_idx = prealidx[idx_worst(p[prealidx])]
+                p2 = p[p2_idx]
+                p = np.delete(p, p2_idx)
+            else:
+                p2 = p1.conj()
+
+            # find closest zero
+            if len(z) > 0:
+                z1_idx = _nearest_real_complex_idx(z, p1, 'any')
+                z1 = z[z1_idx]
+                z = np.delete(z, z1_idx)
+
+                if not np.isreal(z1):
+                    sos[si] = _single_zpksos([z1, z1.conj()], [p1, p2], 1)
+                else:
+                    if len(z) > 0:
+                        z2_idx = _nearest_real_complex_idx(z, p1, 'real')
+                        z2 = z[z2_idx]
+                        assert np.isreal(z2)
+                        z = np.delete(z, z2_idx)
+                        sos[si] = _single_zpksos([z1, z2], [p1, p2], 1)
+                    else:
+                        sos[si] = _single_zpksos([z1], [p1, p2], 1)
+            else:
+                # no more zeros
+                sos[si] = _single_zpksos([], [p1, p2], 1)
+
+    assert len(p) == len(z) == 0  # we've consumed all poles and zeros
+    del p, z
+
+    # put gain in first sos
+    sos[0][:3] *= k
+    return xp.asarray(sos)
+
+
+def _align_nums(nums, xp):
+    """Aligns the shapes of multiple numerators.
+
+    Given an array of numerator coefficient arrays [[a_1, a_2,...,
+    a_n],..., [b_1, b_2,..., b_m]], this function pads shorter numerator
+    arrays with zero's so that all numerators have the same length. Such
+    alignment is necessary for functions like 'tf2ss', which needs the
+    alignment when dealing with SIMO transfer functions.
+
+    Parameters
+    ----------
+    nums: array_like
+        Numerator or list of numerators. Not necessarily with same length.
+
+    Returns
+    -------
+    nums: array
+        The numerator. If `nums` input was a list of numerators then a 2-D
+        array with padded zeros for shorter numerators is returned. Otherwise
+        returns ``np.asarray(nums)``.
+    """
+    try:
+        # The statement can throw a ValueError if one
+        # of the numerators is a single digit and another
+        # is array-like e.g. if nums = [5, [1, 2, 3]]
+        nums = xp.asarray(nums)
+
+        if not xp.isdtype(nums.dtype, "numeric"):
+            raise ValueError("dtype of numerator is non-numeric")
+
+        return nums
+
+    except ValueError:
+        nums = [xpx.atleast_nd(xp.asarray(num), ndim=1) for num in nums]
+        max_width = max(xp_size(num) for num in nums)
+
+        # pre-allocate
+        aligned_nums = xp.zeros((len(nums), max_width))
+
+        # Create numerators with padded zeros
+        for index, num in enumerate(nums):
+            aligned_nums[index, -num.size:] = num
+
+        return aligned_nums
+
+
+def normalize(b, a):
+    """Normalize numerator/denominator of a continuous-time transfer function.
+
+    If values of `b` are too close to 0, they are removed. In that case, a
+    BadCoefficients warning is emitted.
+
+    Parameters
+    ----------
+    b : array_like
+        Numerator of the transfer function. Can be a 2-D array to normalize
+        multiple transfer functions.
+    a : array_like
+        Denominator of the transfer function. At most 1-D.
+
+    Returns
+    -------
+    num : array
+        The numerator of the normalized transfer function. At least a 1-D
+        array. A 2-D array if the input `num` is a 2-D array.
+    den : 1-D array
+        The denominator of the normalized transfer function.
+
+    Notes
+    -----
+    Coefficients for both the numerator and denominator should be specified in
+    descending exponent order (e.g., ``s^2 + 3s + 5`` would be represented as
+    ``[1, 3, 5]``).
+
+    Examples
+    --------
+    >>> from scipy.signal import normalize
+
+    Normalize the coefficients of the transfer function
+    ``(3*s^2 - 2*s + 5) / (2*s^2 + 3*s + 1)``:
+
+    >>> b = [3, -2, 5]
+    >>> a = [2, 3, 1]
+    >>> normalize(b, a)
+    (array([ 1.5, -1. ,  2.5]), array([1. , 1.5, 0.5]))
+
+    A warning is generated if, for example, the first coefficient of
+    `b` is 0.  In the following example, the result is as expected:
+
+    >>> import warnings
+    >>> with warnings.catch_warnings(record=True, action='always') as w:
+    ...     num, den = normalize([0, 3, 6], [2, -5, 4])
+
+    >>> num
+    array([1.5, 3. ])
+    >>> den
+    array([ 1. , -2.5,  2. ])
+
+    >>> print(w[0].message)
+    Badly conditioned filter coefficients (numerator): the results may be meaningless
+
+    """
+    try:
+        xp = array_namespace(b, a)
+    except TypeError:
+        # object arrays, test_ltisys.py::TestSS2TF::test_simo_round_trip
+        xp = np_compat
+
+    den = xp.asarray(a)
+    den = xpx.atleast_nd(den, ndim=1, xp=xp)
+
+    num = xp.asarray(b)
+    num = xpx.atleast_nd(_align_nums(num, xp), ndim=2, xp=xp)
+
+    if den.ndim != 1:
+        raise ValueError("Denominator polynomial must be rank-1 array.")
+    if num.ndim > 2:
+        raise ValueError("Numerator polynomial must be rank-1 or"
+                         " rank-2 array.")
+    if xp.all(den == 0):
+        raise ValueError("Denominator must have at least on nonzero element.")
+
+    # Trim leading zeros in denominator, leave at least one.
+    den = _pu._trim_zeros(den, 'f')
+
+    # Normalize transfer function
+    num, den = num / den[0], den / den[0]
+
+    # Count numerator columns that are all zero
+    leading_zeros = 0
+    for j in range(num.shape[-1]):
+        col = num[:, j]
+        if xp.all(xp.abs(col) <= 1e-14):
+            leading_zeros += 1
+        else:
+            break
+
+    # Trim leading zeros of numerator
+    if leading_zeros > 0:
+        warnings.warn("Badly conditioned filter coefficients (numerator): the "
+                      "results may be meaningless",
+                      BadCoefficients, stacklevel=2)
+        # Make sure at least one column remains
+        if leading_zeros == num.shape[1]:
+            leading_zeros -= 1
+        num = num[:, leading_zeros:]
+
+    # Squeeze first dimension if singular
+    if num.shape[0] == 1:
+        num = num[0, :]
+
+    return num, den
+
+
+def lp2lp(b, a, wo=1.0):
+    r"""
+    Transform a lowpass filter prototype to a different frequency.
+
+    Return an analog low-pass filter with cutoff frequency `wo`
+    from an analog low-pass filter prototype with unity cutoff frequency, in
+    transfer function ('ba') representation.
+
+    Parameters
+    ----------
+    b : array_like, shape (M,)
+        Numerator polynomial coefficients. Must be 1-D.
+    a : array_like, shape (N,)
+        Denominator polynomial coefficients. Must be 1-D.
+    wo : float
+        Desired cutoff, as angular frequency (e.g. rad/s).
+        Defaults to no change.
+
+    Returns
+    -------
+    b : array_like
+        Numerator polynomial coefficients of the transformed low-pass filter.
+    a : array_like
+        Denominator polynomial coefficients of the transformed low-pass filter.
+
+    See Also
+    --------
+    lp2hp, lp2bp, lp2bs, bilinear
+    lp2lp_zpk
+
+    Notes
+    -----
+    This is derived from the s-plane substitution
+
+    .. math:: s \rightarrow \frac{s}{\omega_0}
+
+    Examples
+    --------
+
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+
+    >>> lp = signal.lti([1.0], [1.0, 1.0])
+    >>> lp2 = signal.lti(*signal.lp2lp(lp.num, lp.den, 2))
+    >>> w, mag_lp, p_lp = lp.bode()
+    >>> w, mag_lp2, p_lp2 = lp2.bode(w)
+
+    >>> plt.plot(w, mag_lp, label='Lowpass')
+    >>> plt.plot(w, mag_lp2, label='Transformed Lowpass')
+    >>> plt.semilogx()
+    >>> plt.grid(True)
+    >>> plt.xlabel('Frequency [rad/s]')
+    >>> plt.ylabel('Amplitude [dB]')
+    >>> plt.legend()
+
+    """
+    xp = array_namespace(a, b)
+    a, b = map(xp.asarray, (a, b))
+    a, b = xp_promote(a, b, force_floating=True, xp=xp)
+    a = xpx.atleast_nd(a, ndim=1, xp=xp)
+    b = xpx.atleast_nd(b, ndim=1, xp=xp)
+
+    try:
+        wo = float(wo)
+    except TypeError:
+        wo = float(wo[0])
+    d = a.shape[0]
+    n = b.shape[0]
+    M = max((d, n))
+    pwo = wo ** xp.arange(M - 1, -1, -1, dtype=xp.float64)
+    start1 = max((n - d, 0))
+    start2 = max((d - n, 0))
+    b = b * pwo[start1] / pwo[start2:]
+    a = a * pwo[start1] / pwo[start1:]
+    return normalize(b, a)
+
+
+def _resize(a, new_shape, xp):
+    # https://github.com/numpy/numpy/blob/v2.2.4/numpy/_core/fromnumeric.py#L1535
+    a = xp.reshape(a, (-1,))
+
+    new_size = 1
+    for dim_length in new_shape:
+        new_size *= dim_length
+        if dim_length < 0:
+            raise ValueError(
+                'all elements of `new_shape` must be non-negative'
+            )
+
+    if xp_size(a) == 0 or new_size == 0:
+        # First case must zero fill. The second would have repeats == 0.
+        return xp.zeros_like(a, shape=new_shape)
+
+    repeats = -(-new_size // xp_size(a))  # ceil division
+    a = xp.concat((a,) * repeats)[:new_size]
+
+    return xp.reshape(a, new_shape)
+
+
+def lp2hp(b, a, wo=1.0):
+    r"""
+    Transform a lowpass filter prototype to a highpass filter.
+
+    Return an analog high-pass filter with cutoff frequency `wo`
+    from an analog low-pass filter prototype with unity cutoff frequency, in
+    transfer function ('ba') representation.
+
+    Parameters
+    ----------
+    b : array_like, shape (M,)
+        Numerator polynomial coefficients. Must be 1-D.
+    a : array_like, shape (N,)
+        Denominator polynomial coefficients. Must be 1-D.
+    wo : float
+        Desired cutoff, as angular frequency (e.g., rad/s).
+        Defaults to no change.
+
+    Returns
+    -------
+    b : array_like
+        Numerator polynomial coefficients of the transformed high-pass filter.
+    a : array_like
+        Denominator polynomial coefficients of the transformed high-pass filter.
+
+    See Also
+    --------
+    lp2lp, lp2bp, lp2bs, bilinear
+    lp2hp_zpk
+
+    Notes
+    -----
+    This is derived from the s-plane substitution
+
+    .. math:: s \rightarrow \frac{\omega_0}{s}
+
+    This maintains symmetry of the lowpass and highpass responses on a
+    logarithmic scale.
+
+    Examples
+    --------
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+
+    >>> lp = signal.lti([1.0], [1.0, 1.0])
+    >>> hp = signal.lti(*signal.lp2hp(lp.num, lp.den))
+    >>> w, mag_lp, p_lp = lp.bode()
+    >>> w, mag_hp, p_hp = hp.bode(w)
+
+    >>> plt.plot(w, mag_lp, label='Lowpass')
+    >>> plt.plot(w, mag_hp, label='Highpass')
+    >>> plt.semilogx()
+    >>> plt.grid(True)
+    >>> plt.xlabel('Frequency [rad/s]')
+    >>> plt.ylabel('Amplitude [dB]')
+    >>> plt.legend()
+
+    """
+    xp = array_namespace(a, b)
+
+    a, b = map(xp.asarray, (a, b))
+    a, b = xp_promote(a, b, force_floating=True, xp=xp)
+    a = xpx.atleast_nd(a, ndim=1, xp=xp)
+    b = xpx.atleast_nd(b, ndim=1, xp=xp)
+
+    try:
+        wo = float(wo)
+    except TypeError:
+        wo = float(wo[0])
+    d = a.shape[0]
+    n = b.shape[0]
+    if wo != 1:
+        pwo = wo ** xp.arange(max((d, n)), dtype=b.dtype)
+    else:
+        pwo = xp.ones(max((d, n)), dtype=b.dtype)
+    if d >= n:
+        outa = xp.flip(a) * pwo
+        outb = _resize(b, (d,), xp=xp)
+        outb = xpx.at(outb)[n:].set(0.0)
+        outb = xpx.at(outb)[:n].set(xp.flip(b) * pwo[:n])
+    else:
+        outb = xp.flip(b) * pwo
+        outa = _resize(a, (n,), xp=xp)
+        outa = xpx.at(outa)[d:].set(0.0)
+        outa = xpx.at(outa)[:d].set(xp.flip(a) * pwo[:d])
+
+    return normalize(outb, outa)
+
+
+def lp2bp(b, a, wo=1.0, bw=1.0):
+    r"""
+    Transform a lowpass filter prototype to a bandpass filter.
+
+    Return an analog band-pass filter with center frequency `wo` and
+    bandwidth `bw` from an analog low-pass filter prototype with unity
+    cutoff frequency, in transfer function ('ba') representation.
+
+    Parameters
+    ----------
+    b : array_like, shape (M,)
+        Numerator polynomial coefficients. Must be 1-D.
+    a : array_like, shape (N,)
+        Denominator polynomial coefficients. Must be 1-D.
+    wo : float
+        Desired passband center, as angular frequency (e.g., rad/s).
+        Defaults to no change.
+    bw : float
+        Desired passband width, as angular frequency (e.g., rad/s).
+        Defaults to 1.
+
+    Returns
+    -------
+    b : array_like
+        Numerator polynomial coefficients of the transformed band-pass filter.
+    a : array_like
+        Denominator polynomial coefficients of the transformed band-pass filter.
+
+    See Also
+    --------
+    lp2lp, lp2hp, lp2bs, bilinear
+    lp2bp_zpk
+
+    Notes
+    -----
+    This is derived from the s-plane substitution
+
+    .. math:: s \rightarrow \frac{s^2 + {\omega_0}^2}{s \cdot \mathrm{BW}}
+
+    This is the "wideband" transformation, producing a passband with
+    geometric (log frequency) symmetry about `wo`.
+
+    Examples
+    --------
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+
+    >>> lp = signal.lti([1.0], [1.0, 1.0])
+    >>> bp = signal.lti(*signal.lp2bp(lp.num, lp.den))
+    >>> w, mag_lp, p_lp = lp.bode()
+    >>> w, mag_bp, p_bp = bp.bode(w)
+
+    >>> plt.plot(w, mag_lp, label='Lowpass')
+    >>> plt.plot(w, mag_bp, label='Bandpass')
+    >>> plt.semilogx()
+    >>> plt.grid(True)
+    >>> plt.xlabel('Frequency [rad/s]')
+    >>> plt.ylabel('Amplitude [dB]')
+    >>> plt.legend()
+    """
+    xp = array_namespace(a, b)
+
+    a, b = map(xp.asarray, (a, b))
+    a, b = xp_promote(a, b, force_floating=True, xp=xp)
+    a = xpx.atleast_nd(a, ndim=1, xp=xp)
+    b = xpx.atleast_nd(b, ndim=1, xp=xp)
+
+    D = a.shape[0] - 1
+    N = b.shape[0] - 1
+    ma = max([N, D])
+    Np = N + ma
+    Dp = D + ma
+    bprime = xp.empty(Np + 1, dtype=b.dtype)
+    aprime = xp.empty(Dp + 1, dtype=a.dtype)
+    wosq = wo * wo
+    for j in range(Np + 1):
+        val = 0.0
+        for i in range(0, N + 1):
+            for k in range(0, i + 1):
+                if ma - i + 2 * k == j:
+                    val += comb(i, k) * b[N - i] * (wosq) ** (i - k) / bw ** i
+        bprime = xpx.at(bprime, Np - j).set(val, xp=xp)
+    for j in range(Dp + 1):
+        val = 0.0
+        for i in range(0, D + 1):
+            for k in range(0, i + 1):
+                if ma - i + 2 * k == j:
+                    val += comb(i, k) * a[D - i] * (wosq) ** (i - k) / bw ** i
+        aprime = xpx.at(aprime, Dp - j).set(val, xp=xp)
+
+    return normalize(bprime, aprime)
+
+
+def lp2bs(b, a, wo=1.0, bw=1.0):
+    r"""
+    Transform a lowpass filter prototype to a bandstop filter.
+
+    Return an analog band-stop filter with center frequency `wo` and
+    bandwidth `bw` from an analog low-pass filter prototype with unity
+    cutoff frequency, in transfer function ('ba') representation.
+
+    Parameters
+    ----------
+    b : array_like, shape (M,)
+        Numerator polynomial coefficients. Must be 1-D.
+    a : array_like, shape (N,)
+        Denominator polynomial coefficients. Must be 1-D.
+    wo : float
+        Desired stopband center, as angular frequency (e.g., rad/s).
+        Defaults to no change.
+    bw : float
+        Desired stopband width, as angular frequency (e.g., rad/s).
+        Defaults to 1.
+
+    Returns
+    -------
+    b : array_like
+        Numerator polynomial coefficients of the transformed band-stop filter.
+    a : array_like
+        Denominator polynomial coefficients of the transformed band-stop filter.
+
+    See Also
+    --------
+    lp2lp, lp2hp, lp2bp, bilinear
+    lp2bs_zpk
+
+    Notes
+    -----
+    This is derived from the s-plane substitution
+
+    .. math:: s \rightarrow \frac{s \cdot \mathrm{BW}}{s^2 + {\omega_0}^2}
+
+    This is the "wideband" transformation, producing a stopband with
+    geometric (log frequency) symmetry about `wo`.
+
+    Examples
+    --------
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+
+    >>> lp = signal.lti([1.0], [1.0, 1.5])
+    >>> bs = signal.lti(*signal.lp2bs(lp.num, lp.den))
+    >>> w, mag_lp, p_lp = lp.bode()
+    >>> w, mag_bs, p_bs = bs.bode(w)
+    >>> plt.plot(w, mag_lp, label='Lowpass')
+    >>> plt.plot(w, mag_bs, label='Bandstop')
+    >>> plt.semilogx()
+    >>> plt.grid(True)
+    >>> plt.xlabel('Frequency [rad/s]')
+    >>> plt.ylabel('Amplitude [dB]')
+    >>> plt.legend()
+    """
+    xp = array_namespace(a, b)
+
+    a, b = map(xp.asarray, (a, b))
+    a, b = xp_promote(a, b, force_floating=True, xp=xp)
+    a = xpx.atleast_nd(a, ndim=1, xp=xp)
+    b = xpx.atleast_nd(b, ndim=1, xp=xp)
+
+    D = a.shape[0] - 1
+    N = b.shape[0] - 1
+    M = max([N, D])
+    Np = M + M
+    Dp = M + M
+    bprime = xp.empty(Np + 1, dtype=b.dtype)
+    aprime = xp.empty(Dp + 1, dtype=a.dtype)
+    wosq = wo * wo
+    for j in range(Np + 1):
+        val = 0.0
+        for i in range(0, N + 1):
+            for k in range(0, M - i + 1):
+                if i + 2 * k == j:
+                    val += (comb(M - i, k) * b[N - i] *
+                            (wosq) ** (M - i - k) * bw ** i)
+        bprime = xpx.at(bprime, Np - j).set(val, xp=xp)
+    for j in range(Dp + 1):
+        val = 0.0
+        for i in range(0, D + 1):
+            for k in range(0, M - i + 1):
+                if i + 2 * k == j:
+                    val += (comb(M - i, k) * a[D - i] *
+                            (wosq) ** (M - i - k) * bw ** i)
+        aprime = xpx.at(aprime, Dp - j).set(val, xp=xp)
+
+    return normalize(bprime, aprime)
+
+
+def bilinear(b, a, fs=1.0):
+    r"""Calculate a digital IIR filter from an analog transfer function by utilizing
+    the bilinear transform.
+
+    Parameters
+    ----------
+    b : array_like
+        Coefficients of the numerator polynomial of the analog transfer function in
+        form of a complex- or real-valued 1d array.
+    a : array_like
+        Coefficients of the denominator polynomial of the analog transfer function in
+        form of a complex- or real-valued 1d array.
+    fs : float
+        Sample rate, as ordinary frequency (e.g., hertz). No pre-warping is
+        done in this function.
+
+    Returns
+    -------
+    beta : ndarray
+        Coefficients of the numerator polynomial of the digital transfer function in
+        form of a complex- or real-valued 1d array.
+    alpha : ndarray
+        Coefficients of the denominator polynomial of the digital transfer function in
+        form of a complex- or real-valued 1d array.
+
+    Notes
+    -----
+    The parameters :math:`b = [b_0, \ldots, b_Q]` and :math:`a = [a_0, \ldots, a_P]`
+    are 1d arrays of length :math:`Q+1` and :math:`P+1`. They define the analog
+    transfer function
+
+    .. math::
+
+        H_a(s) = \frac{b_0 s^Q + b_1 s^{Q-1} + \cdots + b_Q}{
+                       a_0 s^P + a_1 s^{P-1} + \cdots + a_P}\ .
+
+    The bilinear transform [1]_ is applied by substituting
+
+    .. math::
+
+        s = \kappa \frac{z-1}{z+1}\ , \qquad \kappa := 2 f_s\ ,
+
+    into :math:`H_a(s)`, with :math:`f_s`  being the sampling rate.
+    This results in the digital transfer function in the :math:`z`-domain
+
+    .. math::
+
+        H_d(z) = \frac{b_0 \left(\kappa \frac{z-1}{z+1}\right)^Q +
+                       b_1 \left(\kappa \frac{z-1}{z+1}\right)^{Q-1} +
+                       \cdots + b_Q}{
+                       a_0 \left(\kappa \frac{z-1}{z+1}\right)^P +
+                       a_1 \left(\kappa \frac{z-1}{z+1}\right)^{P-1} +
+                       \cdots + a_P}\ .
+
+    This expression can be simplified by multiplying numerator and denominator by
+    :math:`(z+1)^N`, with :math:`N=\max(P, Q)`. This allows :math:`H_d(z)` to be
+    reformulated as
+
+    .. math::
+
+       & & \frac{b_0 \big(\kappa (z-1)\big)^Q     (z+1)^{N-Q} +
+                b_1 \big(\kappa (z-1)\big)^{Q-1} (z+1)^{N-Q+1} +
+                \cdots + b_Q(z+1)^N}{
+                a_0 \big(\kappa (z-1)\big)^P     (z+1)^{N-P} +
+                a_1 \big(\kappa (z-1)\big)^{P-1} (z+1)^{N-P+1} +
+                \cdots + a_P(z+1)^N}\\
+        &=:& \frac{\beta_0 + \beta_1  z^{-1} + \cdots + \beta_N  z^{-N}}{
+                 \alpha_0 + \alpha_1 z^{-1} + \cdots + \alpha_N z^{-N}}\ .
+
+
+    This is the equation implemented to perform the bilinear transform. Note that for
+    large :math:`f_s`, :math:`\kappa^Q` or :math:`\kappa^P` can cause a numeric
+    overflow for sufficiently large :math:`P` or :math:`Q`.
+
+    References
+    ----------
+    .. [1] "Bilinear Transform", Wikipedia,
+           https://en.wikipedia.org/wiki/Bilinear_transform
+
+    See Also
+    --------
+    lp2lp, lp2hp, lp2bp, lp2bs, bilinear_zpk
+
+    Examples
+    --------
+    The following example shows the frequency response of an analog bandpass filter and
+    the corresponding digital filter derived by utilitzing the bilinear transform:
+
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+    >>> import numpy as np
+    ...
+    >>> fs = 100  # sampling frequency
+    >>> om_c = 2 * np.pi * np.array([7, 13])  # corner frequencies
+    >>> bb_s, aa_s = signal.butter(4, om_c, btype='bandpass', analog=True, output='ba')
+    >>> bb_z, aa_z = signal.bilinear(bb_s, aa_s, fs)
+    ...
+    >>> w_z, H_z = signal.freqz(bb_z, aa_z)  # frequency response of digitial filter
+    >>> w_s, H_s = signal.freqs(bb_s, aa_s, worN=w_z*fs)  # analog filter response
+    ...
+    >>> f_z, f_s = w_z * fs / (2*np.pi), w_s / (2*np.pi)
+    >>> Hz_dB, Hs_dB = (20*np.log10(np.abs(H_).clip(1e-10)) for H_ in (H_z, H_s))
+    >>> fg0, ax0 = plt.subplots()
+    >>> ax0.set_title("Frequency Response of 4-th order Bandpass Filter")
+    >>> ax0.set(xlabel='Frequency $f$ in Hertz', ylabel='Magnitude in dB',
+    ...         xlim=[f_z[1], fs/2], ylim=[-200, 2])
+    >>> ax0.semilogx(f_z, Hz_dB, alpha=.5, label=r'$|H_z(e^{j 2 \pi f})|$')
+    >>> ax0.semilogx(f_s, Hs_dB, alpha=.5, label=r'$|H_s(j 2 \pi f)|$')
+    >>> ax0.legend()
+    >>> ax0.grid(which='both', axis='x')
+    >>> ax0.grid(which='major', axis='y')
+    >>> plt.show()
+
+    The difference in the higher frequencies shown in the plot is caused by an effect
+    called "frequency warping". [1]_ describes a method called "pre-warping" to
+    reduce those deviations.
+    """
+    xp = array_namespace(b, a)
+
+    b, a = map(np.asarray, (b, a))
+    b, a = np.atleast_1d(b), np.atleast_1d(a)  # convert scalars, if needed
+    if not a.ndim == 1:
+        raise ValueError(f"Parameter a is not a 1d array since {a.shape=}")
+    if not b.ndim == 1:
+        raise ValueError(f"Parameter b is not a 1d array since {b.shape=}")
+    b, a = np.trim_zeros(b, 'f'), np.trim_zeros(a, 'f')  # remove leading zeros
+    fs = _validate_fs(fs, allow_none=False)
+
+    # Splitting the factor fs*2 between numerator and denominator reduces the chance of
+    # numeric overflow for large fs and large N:
+    fac = np.sqrt(fs*2)
+    zp1 = np.polynomial.Polynomial((+1, 1)) / fac  # Polynomial (z + 1) / fac
+    zm1 = np.polynomial.Polynomial((-1, 1)) * fac  # Polynomial (z - 1) * fac
+    # Note that NumPy's Polynomial coefficient order is backward compared to a and b.
+
+    N = max(len(a), len(b)) - 1
+    numerator   = sum(b_ * zp1**(N-q) * zm1**q for q, b_ in enumerate(b[::-1]))
+    denominator = sum(a_ * zp1**(N-p) * zm1**p for p, a_ in enumerate(a[::-1]))
+
+    return normalize(
+        xp.asarray(numerator.coef[::-1].copy()),
+        xp.asarray(denominator.coef[::-1].copy())
+    )
+
+
+def _validate_gpass_gstop(gpass, gstop):
+
+    if gpass <= 0.0:
+        raise ValueError("gpass should be larger than 0.0")
+    elif gstop <= 0.0:
+        raise ValueError("gstop should be larger than 0.0")
+    elif gpass > gstop:
+        raise ValueError("gpass should be smaller than gstop")
+
+
+def iirdesign(wp, ws, gpass, gstop, analog=False, ftype='ellip', output='ba',
+              fs=None):
+    """Complete IIR digital and analog filter design.
+
+    Given passband and stopband frequencies and gains, construct an analog or
+    digital IIR filter of minimum order for a given basic type. Return the
+    output in numerator, denominator ('ba'), pole-zero ('zpk') or second order
+    sections ('sos') form.
+
+    Parameters
+    ----------
+    wp, ws : float or array like, shape (2,)
+        Passband and stopband edge frequencies. Possible values are scalars
+        (for lowpass and highpass filters) or ranges (for bandpass and bandstop
+        filters).
+        For digital filters, these are in the same units as `fs`. By default,
+        `fs` is 2 half-cycles/sample, so these are normalized from 0 to 1,
+        where 1 is the Nyquist frequency. For example:
+
+        - Lowpass:   wp = 0.2,          ws = 0.3
+        - Highpass:  wp = 0.3,          ws = 0.2
+        - Bandpass:  wp = [0.2, 0.5],   ws = [0.1, 0.6]
+        - Bandstop:  wp = [0.1, 0.6],   ws = [0.2, 0.5]
+
+        For analog filters, `wp` and `ws` are angular frequencies (e.g., rad/s).
+        Note, that for bandpass and bandstop filters passband must lie strictly
+        inside stopband or vice versa. Also note that the cutoff at the band edges
+        for IIR filters is defined as half-power, so -3dB, not half-amplitude (-6dB)
+        like for `scipy.signal.firwin`.
+    gpass : float
+        The maximum loss in the passband (dB).
+    gstop : float
+        The minimum attenuation in the stopband (dB).
+    analog : bool, optional
+        When True, return an analog filter, otherwise a digital filter is
+        returned.
+    ftype : str, optional
+        The type of IIR filter to design:
+
+        - Butterworth   : 'butter'
+        - Chebyshev I   : 'cheby1'
+        - Chebyshev II  : 'cheby2'
+        - Cauer/elliptic: 'ellip'
+
+    output : {'ba', 'zpk', 'sos'}, optional
+        Filter form of the output:
+
+        - second-order sections (recommended): 'sos'
+        - numerator/denominator (default)    : 'ba'
+        - pole-zero                          : 'zpk'
+
+        In general the second-order sections ('sos') form  is
+        recommended because inferring the coefficients for the
+        numerator/denominator form ('ba') suffers from numerical
+        instabilities. For reasons of backward compatibility the default
+        form is the numerator/denominator form ('ba'), where the 'b'
+        and the 'a' in 'ba' refer to the commonly used names of the
+        coefficients used.
+
+        Note: Using the second-order sections form ('sos') is sometimes
+        associated with additional computational costs: for
+        data-intense use cases it is therefore recommended to also
+        investigate the numerator/denominator form ('ba').
+
+    fs : float, optional
+        The sampling frequency of the digital system.
+
+        .. versionadded:: 1.2.0
+
+    Returns
+    -------
+    b, a : ndarray, ndarray
+        Numerator (`b`) and denominator (`a`) polynomials of the IIR filter.
+        Only returned if ``output='ba'``.
+    z, p, k : ndarray, ndarray, float
+        Zeros, poles, and system gain of the IIR filter transfer
+        function.  Only returned if ``output='zpk'``.
+    sos : ndarray
+        Second-order sections representation of the IIR filter.
+        Only returned if ``output='sos'``.
+
+    See Also
+    --------
+    butter : Filter design using order and critical points
+    cheby1, cheby2, ellip, bessel
+    buttord : Find order and critical points from passband and stopband spec
+    cheb1ord, cheb2ord, ellipord
+    iirfilter : General filter design using order and critical frequencies
+
+    Notes
+    -----
+    The ``'sos'`` output parameter was added in 0.16.0.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+    >>> import matplotlib.ticker
+
+    >>> wp = 0.2
+    >>> ws = 0.3
+    >>> gpass = 1
+    >>> gstop = 40
+
+    >>> system = signal.iirdesign(wp, ws, gpass, gstop)
+    >>> w, h = signal.freqz(*system)
+
+    >>> fig, ax1 = plt.subplots()
+    >>> ax1.set_title('Digital filter frequency response')
+    >>> ax1.plot(w, 20 * np.log10(abs(h)), 'b')
+    >>> ax1.set_ylabel('Amplitude [dB]', color='b')
+    >>> ax1.set_xlabel('Frequency [rad/sample]')
+    >>> ax1.grid(True)
+    >>> ax1.set_ylim([-120, 20])
+    >>> ax2 = ax1.twinx()
+    >>> phase = np.unwrap(np.angle(h))
+    >>> ax2.plot(w, phase, 'g')
+    >>> ax2.set_ylabel('Phase [rad]', color='g')
+    >>> ax2.grid(True)
+    >>> ax2.axis('tight')
+    >>> ax2.set_ylim([-6, 1])
+    >>> nticks = 8
+    >>> ax1.yaxis.set_major_locator(matplotlib.ticker.LinearLocator(nticks))
+    >>> ax2.yaxis.set_major_locator(matplotlib.ticker.LinearLocator(nticks))
+
+    """
+    xp = array_namespace(wp, ws)
+    wp, ws = map(xp.asarray, (wp, ws))
+
+    try:
+        ordfunc = filter_dict[ftype][1]
+    except KeyError as e:
+        raise ValueError(f"Invalid IIR filter type: {ftype}") from e
+    except IndexError as e:
+        raise ValueError(f"{ftype} does not have order selection. "
+                         "Use iirfilter function.") from e
+
+    _validate_gpass_gstop(gpass, gstop)
+
+    wp = xpx.atleast_nd(wp, ndim=1, xp=xp)
+    ws = xpx.atleast_nd(ws, ndim=1, xp=xp)
+
+    fs = _validate_fs(fs, allow_none=True)
+
+    if wp.shape[0] != ws.shape[0] or wp.shape not in [(1,), (2,)]:
+        raise ValueError("wp and ws must have one or two elements each, and "
+                         f"the same shape, got {wp.shape} and {ws.shape}")
+
+    if xp.any(wp <= 0) or xp.any(ws <= 0):
+        raise ValueError("Values for wp, ws must be greater than 0")
+
+    if not analog:
+        if fs is None:
+            if xp.any(wp >= 1) or xp.any(ws >= 1):
+                raise ValueError("Values for wp, ws must be less than 1")
+        elif xp.any(wp >= fs/2) or xp.any(ws >= fs/2):
+            raise ValueError("Values for wp, ws must be less than fs/2 "
+                             f"(fs={fs} -> fs/2={fs/2})")
+
+    if wp.shape[0] == 2:
+        if not ((ws[0] < wp[0] and wp[1] < ws[1]) or
+               (wp[0] < ws[0] and ws[1] < wp[1])):
+            raise ValueError("Passband must lie strictly inside stopband "
+                             "or vice versa")
+
+    band_type = 2 * (wp.shape[0] - 1)
+    band_type += 1
+    if wp[0] >= ws[0]:
+        band_type += 1
+
+    btype = {1: 'lowpass', 2: 'highpass',
+             3: 'bandstop', 4: 'bandpass'}[band_type]
+
+    N, Wn = ordfunc(wp, ws, gpass, gstop, analog=analog, fs=fs)
+    return iirfilter(N, Wn, rp=gpass, rs=gstop, analog=analog, btype=btype,
+                     ftype=ftype, output=output, fs=fs)
+
+
+def iirfilter(N, Wn, rp=None, rs=None, btype='band', analog=False,
+              ftype='butter', output='ba', fs=None):
+    """
+    IIR digital and analog filter design given order and critical points.
+
+    Design an Nth-order digital or analog filter and return the filter
+    coefficients.
+
+    Parameters
+    ----------
+    N : int
+        The order of the filter.
+    Wn : array_like
+        A scalar or length-2 sequence giving the critical frequencies.
+
+        For digital filters, `Wn` are in the same units as `fs`. By default,
+        `fs` is 2 half-cycles/sample, so these are normalized from 0 to 1,
+        where 1 is the Nyquist frequency. (`Wn` is thus in
+        half-cycles / sample.)
+
+        For analog filters, `Wn` is an angular frequency (e.g., rad/s).
+
+        When Wn is a length-2 sequence, ``Wn[0]`` must be less than ``Wn[1]``.
+    rp : float, optional
+        For Chebyshev and elliptic filters, provides the maximum ripple
+        in the passband. (dB)
+    rs : float, optional
+        For Chebyshev and elliptic filters, provides the minimum attenuation
+        in the stop band. (dB)
+    btype : {'bandpass', 'lowpass', 'highpass', 'bandstop'}, optional
+        The type of filter.  Default is 'bandpass'.
+    analog : bool, optional
+        When True, return an analog filter, otherwise a digital filter is
+        returned.
+    ftype : str, optional
+        The type of IIR filter to design:
+
+        - Butterworth   : 'butter'
+        - Chebyshev I   : 'cheby1'
+        - Chebyshev II  : 'cheby2'
+        - Cauer/elliptic: 'ellip'
+        - Bessel/Thomson: 'bessel'
+
+    output : {'ba', 'zpk', 'sos'}, optional
+        Filter form of the output:
+
+        - second-order sections (recommended): 'sos'
+        - numerator/denominator (default)    : 'ba'
+        - pole-zero                          : 'zpk'
+
+        In general the second-order sections ('sos') form  is
+        recommended because inferring the coefficients for the
+        numerator/denominator form ('ba') suffers from numerical
+        instabilities. For reasons of backward compatibility the default
+        form is the numerator/denominator form ('ba'), where the 'b'
+        and the 'a' in 'ba' refer to the commonly used names of the
+        coefficients used.
+
+        Note: Using the second-order sections form ('sos') is sometimes
+        associated with additional computational costs: for
+        data-intense use cases it is therefore recommended to also
+        investigate the numerator/denominator form ('ba').
+
+    fs : float, optional
+        The sampling frequency of the digital system.
+
+        .. versionadded:: 1.2.0
+
+    Returns
+    -------
+    b, a : ndarray, ndarray
+        Numerator (`b`) and denominator (`a`) polynomials of the IIR filter.
+        Only returned if ``output='ba'``.
+    z, p, k : ndarray, ndarray, float
+        Zeros, poles, and system gain of the IIR filter transfer
+        function.  Only returned if ``output='zpk'``.
+    sos : ndarray
+        Second-order sections representation of the IIR filter.
+        Only returned if ``output='sos'``.
+
+    See Also
+    --------
+    butter : Filter design using order and critical points
+    cheby1, cheby2, ellip, bessel
+    buttord : Find order and critical points from passband and stopband spec
+    cheb1ord, cheb2ord, ellipord
+    iirdesign : General filter design using passband and stopband spec
+
+    Notes
+    -----
+    The ``'sos'`` output parameter was added in 0.16.0.
+
+    The current behavior is for ``ndarray`` outputs to have 64 bit precision
+    (``float64`` or ``complex128``) regardless of the dtype of `Wn` but
+    outputs may respect the dtype of `Wn` in a future version.
+
+    Examples
+    --------
+    Generate a 17th-order Chebyshev II analog bandpass filter from 50 Hz to
+    200 Hz and plot the frequency response:
+
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+
+    >>> b, a = signal.iirfilter(17, [2*np.pi*50, 2*np.pi*200], rs=60,
+    ...                         btype='band', analog=True, ftype='cheby2')
+    >>> w, h = signal.freqs(b, a, 1000)
+    >>> fig = plt.figure()
+    >>> ax = fig.add_subplot(1, 1, 1)
+    >>> ax.semilogx(w / (2*np.pi), 20 * np.log10(np.maximum(abs(h), 1e-5)))
+    >>> ax.set_title('Chebyshev Type II bandpass frequency response')
+    >>> ax.set_xlabel('Frequency [Hz]')
+    >>> ax.set_ylabel('Amplitude [dB]')
+    >>> ax.axis((10, 1000, -100, 10))
+    >>> ax.grid(which='both', axis='both')
+    >>> plt.show()
+
+    Create a digital filter with the same properties, in a system with
+    sampling rate of 2000 Hz, and plot the frequency response. (Second-order
+    sections implementation is required to ensure stability of a filter of
+    this order):
+
+    >>> sos = signal.iirfilter(17, [50, 200], rs=60, btype='band',
+    ...                        analog=False, ftype='cheby2', fs=2000,
+    ...                        output='sos')
+    >>> w, h = signal.freqz_sos(sos, 2000, fs=2000)
+    >>> fig = plt.figure()
+    >>> ax = fig.add_subplot(1, 1, 1)
+    >>> ax.semilogx(w, 20 * np.log10(np.maximum(abs(h), 1e-5)))
+    >>> ax.set_title('Chebyshev Type II bandpass frequency response')
+    >>> ax.set_xlabel('Frequency [Hz]')
+    >>> ax.set_ylabel('Amplitude [dB]')
+    >>> ax.axis((10, 1000, -100, 10))
+    >>> ax.grid(which='both', axis='both')
+    >>> plt.show()
+
+    """
+    xp = array_namespace(Wn)
+    # For now, outputs will have float64 base dtype regardless of
+    # the dtype of Wn, so cast to float64 here to ensure 64 bit
+    # precision for all calculations.
+    Wn = xp.asarray(Wn, dtype=xp.float64)
+
+    fs = _validate_fs(fs, allow_none=True)
+    ftype, btype, output = (x.lower() for x in (ftype, btype, output))
+    if fs is not None:
+        if analog:
+            raise ValueError("fs cannot be specified for an analog filter")
+        Wn = Wn / (fs/2)
+
+    if xp.any(Wn <= 0):
+        raise ValueError("filter critical frequencies must be greater than 0")
+
+    if xp_size(Wn) > 1 and not Wn[0] < Wn[1]:
+        raise ValueError("Wn[0] must be less than Wn[1]")
+
+    try:
+        btype = band_dict[btype]
+    except KeyError as e:
+        raise ValueError(f"'{btype}' is an invalid bandtype for filter.") from e
+
+    try:
+        typefunc = filter_dict[ftype][0]
+    except KeyError as e:
+        raise ValueError(f"'{ftype}' is not a valid basic IIR filter.") from e
+
+    if output not in ['ba', 'zpk', 'sos']:
+        raise ValueError(f"'{output}' is not a valid output form.")
+
+    if rp is not None and rp < 0:
+        raise ValueError("passband ripple (rp) must be positive")
+
+    if rs is not None and rs < 0:
+        raise ValueError("stopband attenuation (rs) must be positive")
+
+    # Get analog lowpass prototype
+    if typefunc == buttap:
+        z, p, k = typefunc(N, xp=xp)
+    elif typefunc == besselap:
+        z, p, k = typefunc(N, norm=bessel_norms[ftype], xp=xp)
+    elif typefunc == cheb1ap:
+        if rp is None:
+            raise ValueError("passband ripple (rp) must be provided to "
+                             "design a Chebyshev I filter.")
+        z, p, k = typefunc(N, rp, xp=xp)
+    elif typefunc == cheb2ap:
+        if rs is None:
+            raise ValueError("stopband attenuation (rs) must be provided to "
+                             "design a Chebyshev II filter.")
+        z, p, k = typefunc(N, rs, xp=xp)
+    elif typefunc == ellipap:
+        if rs is None or rp is None:
+            raise ValueError("Both rp and rs must be provided to design an "
+                             "elliptic filter.")
+        z, p, k = typefunc(N, rp, rs, xp=xp)
+    else:
+        raise NotImplementedError(f"'{ftype}' not implemented in iirfilter.")
+
+    # Pre-warp frequencies for digital filter design
+    if not analog:
+        if xp.any(Wn <= 0) or xp.any(Wn >= 1):
+            if fs is not None:
+                raise ValueError("Digital filter critical frequencies must "
+                                 f"be 0 < Wn < fs/2 (fs={fs} -> fs/2={fs/2})")
+            raise ValueError("Digital filter critical frequencies "
+                             "must be 0 < Wn < 1")
+        fs = 2.0
+        warped = 2 * fs * xp.tan(xp.pi * Wn / fs)
+    else:
+        warped = Wn
+
+    # transform to lowpass, bandpass, highpass, or bandstop
+    if btype in ('lowpass', 'highpass'):
+        if xp_size(Wn) != 1:
+            raise ValueError('Must specify a single critical frequency Wn '
+                             'for lowpass or highpass filter')
+
+        if btype == 'lowpass':
+            z, p, k = lp2lp_zpk(z, p, k, wo=warped)
+        elif btype == 'highpass':
+            z, p, k = lp2hp_zpk(z, p, k, wo=warped)
+    elif btype in ('bandpass', 'bandstop'):
+        try:
+            bw = warped[1] - warped[0]
+            wo = xp.sqrt(warped[0] * warped[1])
+        except IndexError as e:
+            raise ValueError('Wn must specify start and stop frequencies for '
+                             'bandpass or bandstop filter') from e
+
+        if btype == 'bandpass':
+            z, p, k = lp2bp_zpk(z, p, k, wo=wo, bw=bw)
+        elif btype == 'bandstop':
+            z, p, k = lp2bs_zpk(z, p, k, wo=wo, bw=bw)
+    else:
+        raise NotImplementedError(f"'{btype}' not implemented in iirfilter.")
+
+    # Find discrete equivalent if necessary
+    if not analog:
+        z, p, k = bilinear_zpk(z, p, k, fs=fs)
+
+    # Transform to proper out type (pole-zero, state-space, numer-denom)
+    if output == 'zpk':
+        return z, p, k
+    elif output == 'ba':
+        return zpk2tf(z, p, k)
+    elif output == 'sos':
+        return zpk2sos(z, p, k, analog=analog)
+
+
+def _relative_degree(z, p):
+    """
+    Return relative degree of transfer function from zeros and poles
+    """
+    degree = p.shape[0] - z.shape[0]
+    if degree < 0:
+        raise ValueError("Improper transfer function. "
+                         "Must have at least as many poles as zeros.")
+    else:
+        return degree
+
+
+def bilinear_zpk(z, p, k, fs):
+    r"""
+    Return a digital IIR filter from an analog one using a bilinear transform.
+
+    Transform a set of poles and zeros from the analog s-plane to the digital
+    z-plane using Tustin's method, which substitutes ``2*fs*(z-1) / (z+1)`` for
+    ``s``, maintaining the shape of the frequency response.
+
+    Parameters
+    ----------
+    z : array_like
+        Zeros of the analog filter transfer function.
+    p : array_like
+        Poles of the analog filter transfer function.
+    k : float
+        System gain of the analog filter transfer function.
+    fs : float
+        Sample rate, as ordinary frequency (e.g., hertz). No prewarping is
+        done in this function.
+
+    Returns
+    -------
+    z : ndarray
+        Zeros of the transformed digital filter transfer function.
+    p : ndarray
+        Poles of the transformed digital filter transfer function.
+    k : float
+        System gain of the transformed digital filter.
+
+    See Also
+    --------
+    lp2lp_zpk, lp2hp_zpk, lp2bp_zpk, lp2bs_zpk
+    bilinear
+
+    Notes
+    -----
+    .. versionadded:: 1.1.0
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+
+    >>> fs = 100
+    >>> bf = 2 * np.pi * np.array([7, 13])
+    >>> filts = signal.lti(*signal.butter(4, bf, btype='bandpass', analog=True,
+    ...                                   output='zpk'))
+    >>> filtz = signal.lti(*signal.bilinear_zpk(filts.zeros, filts.poles,
+    ...                                         filts.gain, fs))
+    >>> wz, hz = signal.freqz_zpk(filtz.zeros, filtz.poles, filtz.gain)
+    >>> ws, hs = signal.freqs_zpk(filts.zeros, filts.poles, filts.gain,
+    ...                           worN=fs*wz)
+    >>> plt.semilogx(wz*fs/(2*np.pi), 20*np.log10(np.abs(hz).clip(1e-15)),
+    ...              label=r'$|H_z(e^{j \omega})|$')
+    >>> plt.semilogx(wz*fs/(2*np.pi), 20*np.log10(np.abs(hs).clip(1e-15)),
+    ...              label=r'$|H(j \omega)|$')
+    >>> plt.legend()
+    >>> plt.xlabel('Frequency [Hz]')
+    >>> plt.ylabel('Amplitude [dB]')
+    >>> plt.grid(True)
+    """
+    xp = array_namespace(z, p)
+
+    z, p = map(xp.asarray, (z, p))
+    z = xpx.atleast_nd(z, ndim=1, xp=xp)
+    p = xpx.atleast_nd(p, ndim=1, xp=xp)
+
+    fs = _validate_fs(fs, allow_none=False)
+
+    degree = _relative_degree(z, p)
+
+    fs2 = 2.0*fs
+
+    # Bilinear transform the poles and zeros
+    z_z = (fs2 + z) / (fs2 - z)
+    p_z = (fs2 + p) / (fs2 - p)
+
+    # Any zeros that were at infinity get moved to the Nyquist frequency
+    z_z = xp.concat((z_z, -xp.ones(degree)))
+
+    # Compensate for gain change
+    k_z = k * xp.real(xp.prod(fs2 - z) / xp.prod(fs2 - p))
+
+    return z_z, p_z, k_z
+
+
+def lp2lp_zpk(z, p, k, wo=1.0):
+    r"""
+    Transform a lowpass filter prototype to a different frequency.
+
+    Return an analog low-pass filter with cutoff frequency `wo`
+    from an analog low-pass filter prototype with unity cutoff frequency,
+    using zeros, poles, and gain ('zpk') representation.
+
+    Parameters
+    ----------
+    z : array_like
+        Zeros of the analog filter transfer function.
+    p : array_like
+        Poles of the analog filter transfer function.
+    k : float
+        System gain of the analog filter transfer function.
+    wo : float
+        Desired cutoff, as angular frequency (e.g., rad/s).
+        Defaults to no change.
+
+    Returns
+    -------
+    z : ndarray
+        Zeros of the transformed low-pass filter transfer function.
+    p : ndarray
+        Poles of the transformed low-pass filter transfer function.
+    k : float
+        System gain of the transformed low-pass filter.
+
+    See Also
+    --------
+    lp2hp_zpk, lp2bp_zpk, lp2bs_zpk, bilinear
+    lp2lp
+
+    Notes
+    -----
+    This is derived from the s-plane substitution
+
+    .. math:: s \rightarrow \frac{s}{\omega_0}
+
+    .. versionadded:: 1.1.0
+
+    Examples
+    --------
+    Use the 'zpk' (Zero-Pole-Gain) representation of a lowpass filter to
+    transform it to a new 'zpk' representation associated with a cutoff frequency wo.
+
+    >>> from scipy.signal import lp2lp_zpk
+    >>> z   = [7,   2]
+    >>> p   = [5,   13]
+    >>> k   = 0.8
+    >>> wo  = 0.4
+    >>> lp2lp_zpk(z, p, k, wo)
+    (   array([2.8, 0.8]), array([2. , 5.2]), 0.8)
+    """
+    xp = array_namespace(z, p)
+
+    z, p = map(xp.asarray, (z, p))
+    z = xpx.atleast_nd(z, ndim=1, xp=xp)
+    p = xpx.atleast_nd(p, ndim=1, xp=xp)
+
+    wo = float(wo)  # Avoid int wraparound
+
+    degree = _relative_degree(z, p)
+
+    # Scale all points radially from origin to shift cutoff frequency
+    z_lp = wo * z
+    p_lp = wo * p
+
+    # Each shifted pole decreases gain by wo, each shifted zero increases it.
+    # Cancel out the net change to keep overall gain the same
+    k_lp = k * wo**degree
+
+    return z_lp, p_lp, k_lp
+
+
+def lp2hp_zpk(z, p, k, wo=1.0):
+    r"""
+    Transform a lowpass filter prototype to a highpass filter.
+
+    Return an analog high-pass filter with cutoff frequency `wo`
+    from an analog low-pass filter prototype with unity cutoff frequency,
+    using zeros, poles, and gain ('zpk') representation.
+
+    Parameters
+    ----------
+    z : array_like
+        Zeros of the analog filter transfer function.
+    p : array_like
+        Poles of the analog filter transfer function.
+    k : float
+        System gain of the analog filter transfer function.
+    wo : float
+        Desired cutoff, as angular frequency (e.g., rad/s).
+        Defaults to no change.
+
+    Returns
+    -------
+    z : ndarray
+        Zeros of the transformed high-pass filter transfer function.
+    p : ndarray
+        Poles of the transformed high-pass filter transfer function.
+    k : float
+        System gain of the transformed high-pass filter.
+
+    See Also
+    --------
+    lp2lp_zpk, lp2bp_zpk, lp2bs_zpk, bilinear
+    lp2hp
+
+    Notes
+    -----
+    This is derived from the s-plane substitution
+
+    .. math:: s \rightarrow \frac{\omega_0}{s}
+
+    This maintains symmetry of the lowpass and highpass responses on a
+    logarithmic scale.
+
+    .. versionadded:: 1.1.0
+
+    Examples
+    --------
+    Use the 'zpk' (Zero-Pole-Gain) representation of a lowpass filter to
+    transform it to a highpass filter with a cutoff frequency wo.
+
+    >>> from scipy.signal import lp2hp_zpk
+    >>> z   = [ -2 + 3j ,  -0.5 - 0.8j ]
+    >>> p   = [ -1      ,  -4          ]
+    >>> k   = 10
+    >>> wo  = 0.6
+    >>> lp2hp_zpk(z, p, k, wo)
+    (   array([-0.09230769-0.13846154j, -0.33707865+0.53932584j]),
+        array([-0.6 , -0.15]),
+        8.5)
+    """
+    xp = array_namespace(z, p)
+
+    z, p = map(xp.asarray, (z, p))
+    # XXX: no xp_promote here since that breaks TestButter
+    z = xpx.atleast_nd(z, ndim=1, xp=xp)
+    p = xpx.atleast_nd(p, ndim=1, xp=xp)
+
+    wo = float(wo)
+
+    degree = _relative_degree(z, p)
+
+    # Invert positions radially about unit circle to convert LPF to HPF
+    # Scale all points radially from origin to shift cutoff frequency
+    z_hp = wo / z
+    p_hp = wo / p
+
+    # If lowpass had zeros at infinity, inverting moves them to origin.
+    z_hp = xp.concat((z_hp, xp.zeros(degree)))
+
+    # Cancel out gain change caused by inversion
+    k_hp = k * xp.real(xp.prod(-z) / xp.prod(-p))
+
+    return z_hp, p_hp, k_hp
+
+
+def lp2bp_zpk(z, p, k, wo=1.0, bw=1.0):
+    r"""
+    Transform a lowpass filter prototype to a bandpass filter.
+
+    Return an analog band-pass filter with center frequency `wo` and
+    bandwidth `bw` from an analog low-pass filter prototype with unity
+    cutoff frequency, using zeros, poles, and gain ('zpk') representation.
+
+    Parameters
+    ----------
+    z : array_like
+        Zeros of the analog filter transfer function.
+    p : array_like
+        Poles of the analog filter transfer function.
+    k : float
+        System gain of the analog filter transfer function.
+    wo : float
+        Desired passband center, as angular frequency (e.g., rad/s).
+        Defaults to no change.
+    bw : float
+        Desired passband width, as angular frequency (e.g., rad/s).
+        Defaults to 1.
+
+    Returns
+    -------
+    z : ndarray
+        Zeros of the transformed band-pass filter transfer function.
+    p : ndarray
+        Poles of the transformed band-pass filter transfer function.
+    k : float
+        System gain of the transformed band-pass filter.
+
+    See Also
+    --------
+    lp2lp_zpk, lp2hp_zpk, lp2bs_zpk, bilinear
+    lp2bp
+
+    Notes
+    -----
+    This is derived from the s-plane substitution
+
+    .. math:: s \rightarrow \frac{s^2 + {\omega_0}^2}{s \cdot \mathrm{BW}}
+
+    This is the "wideband" transformation, producing a passband with
+    geometric (log frequency) symmetry about `wo`.
+
+    .. versionadded:: 1.1.0
+
+    Examples
+    --------
+    Use the 'zpk' (Zero-Pole-Gain) representation of a lowpass filter to
+    transform it to a bandpass filter with a center frequency wo and
+    bandwidth bw.
+
+    >>> from scipy.signal import lp2bp_zpk
+    >>> z   = [ 5 + 2j ,  5 - 2j ]
+    >>> p   = [ 7      ,  -16    ]
+    >>> k   = 0.8
+    >>> wo  = 0.62
+    >>> bw  = 15
+    >>> lp2bp_zpk(z, p, k, wo, bw)
+    (   array([7.49955815e+01+3.00017676e+01j, 7.49955815e+01-3.00017676e+01j,
+               4.41850748e-03-1.76761126e-03j, 4.41850748e-03+1.76761126e-03j]),
+        array([1.04996339e+02+0.j, -1.60167736e-03+0.j,  3.66108003e-03+0.j,
+               -2.39998398e+02+0.j]), 0.8)
+    """
+    xp = array_namespace(z, p)
+
+    z, p = map(xp.asarray, (z, p))
+    z, p = xp_promote(z, p, force_floating=True, xp=xp)
+    z = xpx.atleast_nd(z, ndim=1, xp=xp)
+    p = xpx.atleast_nd(p, ndim=1, xp=xp)
+
+    wo = float(wo)
+    bw = float(bw)
+
+    degree = _relative_degree(z, p)
+
+    # Scale poles and zeros to desired bandwidth
+    z_lp = z * bw/2
+    p_lp = p * bw/2
+
+    # Square root needs to produce complex result, not NaN
+    z_lp = xp.astype(z_lp, xp.complex128)
+    p_lp = xp.astype(p_lp, xp.complex128)
+
+    # Duplicate poles and zeros and shift from baseband to +wo and -wo
+    z_bp = xp.concat((z_lp + xp.sqrt(z_lp**2 - wo**2),
+                      z_lp - xp.sqrt(z_lp**2 - wo**2)))
+    p_bp = xp.concat((p_lp + xp.sqrt(p_lp**2 - wo**2),
+                      p_lp - xp.sqrt(p_lp**2 - wo**2)))
+
+    # Move degree zeros to origin, leaving degree zeros at infinity for BPF
+    z_bp = xp.concat((z_bp, xp.zeros(degree)))
+
+    # Cancel out gain change from frequency scaling
+    k_bp = k * bw**degree
+
+    return z_bp, p_bp, k_bp
+
+
+def lp2bs_zpk(z, p, k, wo=1.0, bw=1.0):
+    r"""
+    Transform a lowpass filter prototype to a bandstop filter.
+
+    Return an analog band-stop filter with center frequency `wo` and
+    stopband width `bw` from an analog low-pass filter prototype with unity
+    cutoff frequency, using zeros, poles, and gain ('zpk') representation.
+
+    Parameters
+    ----------
+    z : array_like
+        Zeros of the analog filter transfer function.
+    p : array_like
+        Poles of the analog filter transfer function.
+    k : float
+        System gain of the analog filter transfer function.
+    wo : float
+        Desired stopband center, as angular frequency (e.g., rad/s).
+        Defaults to no change.
+    bw : float
+        Desired stopband width, as angular frequency (e.g., rad/s).
+        Defaults to 1.
+
+    Returns
+    -------
+    z : ndarray
+        Zeros of the transformed band-stop filter transfer function.
+    p : ndarray
+        Poles of the transformed band-stop filter transfer function.
+    k : float
+        System gain of the transformed band-stop filter.
+
+    See Also
+    --------
+    lp2lp_zpk, lp2hp_zpk, lp2bp_zpk, bilinear
+    lp2bs
+
+    Notes
+    -----
+    This is derived from the s-plane substitution
+
+    .. math:: s \rightarrow \frac{s \cdot \mathrm{BW}}{s^2 + {\omega_0}^2}
+
+    This is the "wideband" transformation, producing a stopband with
+    geometric (log frequency) symmetry about `wo`.
+
+    .. versionadded:: 1.1.0
+
+    Examples
+    --------
+    Transform a low-pass filter represented in 'zpk' (Zero-Pole-Gain) form
+    into a bandstop filter represented in 'zpk' form, with a center frequency wo and
+    bandwidth bw.
+
+    >>> from scipy.signal import lp2bs_zpk
+    >>> z   = [             ]
+    >>> p   = [ 0.7 ,    -1 ]
+    >>> k   = 9
+    >>> wo  = 0.5
+    >>> bw  = 10
+    >>> lp2bs_zpk(z, p, k, wo, bw)
+    (   array([0.+0.5j, 0.+0.5j, 0.-0.5j, 0.-0.5j]),
+        array([14.2681928 +0.j, -0.02506281+0.j,  0.01752149+0.j, -9.97493719+0.j]),
+        -12.857142857142858)
+    """
+    xp = array_namespace(z, p)
+
+    z, p = map(xp.asarray, (z, p))
+    z, p = xp_promote(z, p, force_floating=True, xp=xp)
+    z = xpx.atleast_nd(z, ndim=1, xp=xp)
+    p = xpx.atleast_nd(p, ndim=1, xp=xp)
+
+    wo = float(wo)
+    bw = float(bw)
+
+    degree = _relative_degree(z, p)
+
+    # Invert to a highpass filter with desired bandwidth
+    z_hp = (bw/2) / z
+    p_hp = (bw/2) / p
+
+    # Square root needs to produce complex result, not NaN
+    z_hp = xp.astype(z_hp, xp.complex128)
+    p_hp = xp.astype(p_hp, xp.complex128)
+
+    # Duplicate poles and zeros and shift from baseband to +wo and -wo
+    z_bs = xp.concat((z_hp + xp.sqrt(z_hp**2 - wo**2),
+                      z_hp - xp.sqrt(z_hp**2 - wo**2)))
+    p_bs = xp.concat((p_hp + xp.sqrt(p_hp**2 - wo**2),
+                      p_hp - xp.sqrt(p_hp**2 - wo**2)))
+
+    # Move any zeros that were at infinity to the center of the stopband
+    z_bs = xp.concat((z_bs, xp.full(degree, +1j*wo)))
+    z_bs = xp.concat((z_bs, xp.full(degree, -1j*wo)))
+
+    # Cancel out gain change caused by inversion
+    k_bs = k * xp.real(xp.prod(-z) / xp.prod(-p))
+
+    return z_bs, p_bs, k_bs
+
+
+def butter(N, Wn, btype='low', analog=False, output='ba', fs=None):
+    """
+    Butterworth digital and analog filter design.
+
+    Design an Nth-order digital or analog Butterworth filter and return
+    the filter coefficients.
+
+    Parameters
+    ----------
+    N : int
+        The order of the filter. For 'bandpass' and 'bandstop' filters,
+        the resulting order of the final second-order sections ('sos')
+        matrix is ``2*N``, with `N` the number of biquad sections
+        of the desired system.
+    Wn : array_like
+        The critical frequency or frequencies. For lowpass and highpass
+        filters, Wn is a scalar; for bandpass and bandstop filters,
+        Wn is a length-2 sequence.
+
+        For a Butterworth filter, this is the point at which the gain
+        drops to 1/sqrt(2) that of the passband (the "-3 dB point").
+
+        For digital filters, if `fs` is not specified, `Wn` units are
+        normalized from 0 to 1, where 1 is the Nyquist frequency (`Wn` is
+        thus in half cycles / sample and defined as 2*critical frequencies
+        / `fs`). If `fs` is specified, `Wn` is in the same units as `fs`.
+
+        For analog filters, `Wn` is an angular frequency (e.g. rad/s).
+    btype : {'lowpass', 'highpass', 'bandpass', 'bandstop'}, optional
+        The type of filter.  Default is 'lowpass'.
+    analog : bool, optional
+        When True, return an analog filter, otherwise a digital filter is
+        returned.
+    output : {'ba', 'zpk', 'sos'}, optional
+        Type of output:  numerator/denominator ('ba'), pole-zero ('zpk'), or
+        second-order sections ('sos'). Default is 'ba' for backwards
+        compatibility, but 'sos' should be used for general-purpose filtering.
+    fs : float, optional
+        The sampling frequency of the digital system.
+
+        .. versionadded:: 1.2.0
+
+    Returns
+    -------
+    b, a : ndarray, ndarray
+        Numerator (`b`) and denominator (`a`) polynomials of the IIR filter.
+        Only returned if ``output='ba'``.
+    z, p, k : ndarray, ndarray, float
+        Zeros, poles, and system gain of the IIR filter transfer
+        function.  Only returned if ``output='zpk'``.
+
+    sos : ndarray
+        Second-order sections representation of the IIR filter.
+        Only returned if ``output='sos'``.
+
+    See Also
+    --------
+    buttord, buttap
+
+    Notes
+    -----
+    The Butterworth filter has maximally flat frequency response in the
+    passband.
+
+    The ``'sos'`` output parameter was added in 0.16.0.
+
+    If the transfer function form ``[b, a]`` is requested, numerical
+    problems can occur since the conversion between roots and
+    the polynomial coefficients is a numerically sensitive operation,
+    even for N >= 4. It is recommended to work with the SOS
+    representation.
+
+    .. warning::
+        Designing high-order and narrowband IIR filters in TF form can
+        result in unstable or incorrect filtering due to floating point
+        numerical precision issues. Consider inspecting output filter
+        characteristics `freqz` or designing the filters with second-order
+        sections via ``output='sos'``.
+
+    The current behavior is for ``ndarray`` outputs to have 64 bit precision
+    (``float64`` or ``complex128``) regardless of the dtype of `Wn` but
+    outputs may respect the dtype of `Wn` in a future version.
+
+    Examples
+    --------
+    Design an analog filter and plot its frequency response, showing the
+    critical points:
+
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+    >>> import numpy as np
+
+    >>> b, a = signal.butter(4, 100, 'low', analog=True)
+    >>> w, h = signal.freqs(b, a)
+    >>> plt.semilogx(w, 20 * np.log10(abs(h)))
+    >>> plt.title('Butterworth filter frequency response')
+    >>> plt.xlabel('Frequency [rad/s]')
+    >>> plt.ylabel('Amplitude [dB]')
+    >>> plt.margins(0, 0.1)
+    >>> plt.grid(which='both', axis='both')
+    >>> plt.axvline(100, color='green') # cutoff frequency
+    >>> plt.show()
+
+    Generate a signal made up of 10 Hz and 20 Hz, sampled at 1 kHz
+
+    >>> t = np.linspace(0, 1, 1000, False)  # 1 second
+    >>> sig = np.sin(2*np.pi*10*t) + np.sin(2*np.pi*20*t)
+    >>> fig, (ax1, ax2) = plt.subplots(2, 1, sharex=True)
+    >>> ax1.plot(t, sig)
+    >>> ax1.set_title('10 Hz and 20 Hz sinusoids')
+    >>> ax1.axis([0, 1, -2, 2])
+
+    Design a digital high-pass filter at 15 Hz to remove the 10 Hz tone, and
+    apply it to the signal. (It's recommended to use second-order sections
+    format when filtering, to avoid numerical error with transfer function
+    (``ba``) format):
+
+    >>> sos = signal.butter(10, 15, 'hp', fs=1000, output='sos')
+    >>> filtered = signal.sosfilt(sos, sig)
+    >>> ax2.plot(t, filtered)
+    >>> ax2.set_title('After 15 Hz high-pass filter')
+    >>> ax2.axis([0, 1, -2, 2])
+    >>> ax2.set_xlabel('Time [s]')
+    >>> plt.tight_layout()
+    >>> plt.show()
+    """
+    return iirfilter(N, Wn, btype=btype, analog=analog,
+                     output=output, ftype='butter', fs=fs)
+
+
+def cheby1(N, rp, Wn, btype='low', analog=False, output='ba', fs=None):
+    """
+    Chebyshev type I digital and analog filter design.
+
+    Design an Nth-order digital or analog Chebyshev type I filter and
+    return the filter coefficients.
+
+    Parameters
+    ----------
+    N : int
+        The order of the filter.
+    rp : float
+        The maximum ripple allowed below unity gain in the passband.
+        Specified in decibels, as a positive number.
+    Wn : array_like
+        A scalar or length-2 sequence giving the critical frequencies.
+        For Type I filters, this is the point in the transition band at which
+        the gain first drops below -`rp`.
+
+        For digital filters, `Wn` are in the same units as `fs`. By default,
+        `fs` is 2 half-cycles/sample, so these are normalized from 0 to 1,
+        where 1 is the Nyquist frequency. (`Wn` is thus in
+        half-cycles / sample.)
+
+        For analog filters, `Wn` is an angular frequency (e.g., rad/s).
+    btype : {'lowpass', 'highpass', 'bandpass', 'bandstop'}, optional
+        The type of filter.  Default is 'lowpass'.
+    analog : bool, optional
+        When True, return an analog filter, otherwise a digital filter is
+        returned.
+    output : {'ba', 'zpk', 'sos'}, optional
+        Type of output:  numerator/denominator ('ba'), pole-zero ('zpk'), or
+        second-order sections ('sos'). Default is 'ba' for backwards
+        compatibility, but 'sos' should be used for general-purpose filtering.
+    fs : float, optional
+        The sampling frequency of the digital system.
+
+        .. versionadded:: 1.2.0
+
+    Returns
+    -------
+    b, a : ndarray, ndarray
+        Numerator (`b`) and denominator (`a`) polynomials of the IIR filter.
+        Only returned if ``output='ba'``.
+    z, p, k : ndarray, ndarray, float
+        Zeros, poles, and system gain of the IIR filter transfer
+        function.  Only returned if ``output='zpk'``.
+    sos : ndarray
+        Second-order sections representation of the IIR filter.
+        Only returned if ``output='sos'``.
+
+    See Also
+    --------
+    cheb1ord, cheb1ap
+
+    Notes
+    -----
+    The Chebyshev type I filter maximizes the rate of cutoff between the
+    frequency response's passband and stopband, at the expense of ripple in
+    the passband and increased ringing in the step response.
+
+    Type I filters roll off faster than Type II (`cheby2`), but Type II
+    filters do not have any ripple in the passband.
+
+    The equiripple passband has N maxima or minima (for example, a
+    5th-order filter has 3 maxima and 2 minima). Consequently, the DC gain is
+    unity for odd-order filters, or -rp dB for even-order filters.
+
+    The ``'sos'`` output parameter was added in 0.16.0.
+
+    The current behavior is for ``ndarray`` outputs to have 64 bit precision
+    (``float64`` or ``complex128``) regardless of the dtype of `Wn` but
+    outputs may respect the dtype of `Wn` in a future version.
+
+    Examples
+    --------
+    Design an analog filter and plot its frequency response, showing the
+    critical points:
+
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+    >>> import numpy as np
+
+    >>> b, a = signal.cheby1(4, 5, 100, 'low', analog=True)
+    >>> w, h = signal.freqs(b, a)
+    >>> plt.semilogx(w, 20 * np.log10(abs(h)))
+    >>> plt.title('Chebyshev Type I frequency response (rp=5)')
+    >>> plt.xlabel('Frequency [rad/s]')
+    >>> plt.ylabel('Amplitude [dB]')
+    >>> plt.margins(0, 0.1)
+    >>> plt.grid(which='both', axis='both')
+    >>> plt.axvline(100, color='green') # cutoff frequency
+    >>> plt.axhline(-5, color='green') # rp
+    >>> plt.show()
+
+    Generate a signal made up of 10 Hz and 20 Hz, sampled at 1 kHz
+
+    >>> t = np.linspace(0, 1, 1000, False)  # 1 second
+    >>> sig = np.sin(2*np.pi*10*t) + np.sin(2*np.pi*20*t)
+    >>> fig, (ax1, ax2) = plt.subplots(2, 1, sharex=True)
+    >>> ax1.plot(t, sig)
+    >>> ax1.set_title('10 Hz and 20 Hz sinusoids')
+    >>> ax1.axis([0, 1, -2, 2])
+
+    Design a digital high-pass filter at 15 Hz to remove the 10 Hz tone, and
+    apply it to the signal. (It's recommended to use second-order sections
+    format when filtering, to avoid numerical error with transfer function
+    (``ba``) format):
+
+    >>> sos = signal.cheby1(10, 1, 15, 'hp', fs=1000, output='sos')
+    >>> filtered = signal.sosfilt(sos, sig)
+    >>> ax2.plot(t, filtered)
+    >>> ax2.set_title('After 15 Hz high-pass filter')
+    >>> ax2.axis([0, 1, -2, 2])
+    >>> ax2.set_xlabel('Time [s]')
+    >>> plt.tight_layout()
+    >>> plt.show()
+    """
+    return iirfilter(N, Wn, rp=rp, btype=btype, analog=analog,
+                     output=output, ftype='cheby1', fs=fs)
+
+
+def cheby2(N, rs, Wn, btype='low', analog=False, output='ba', fs=None):
+    """
+    Chebyshev type II digital and analog filter design.
+
+    Design an Nth-order digital or analog Chebyshev type II filter and
+    return the filter coefficients.
+
+    Parameters
+    ----------
+    N : int
+        The order of the filter.
+    rs : float
+        The minimum attenuation required in the stop band.
+        Specified in decibels, as a positive number.
+    Wn : array_like
+        A scalar or length-2 sequence giving the critical frequencies.
+        For Type II filters, this is the point in the transition band at which
+        the gain first reaches -`rs`.
+
+        For digital filters, `Wn` are in the same units as `fs`. By default,
+        `fs` is 2 half-cycles/sample, so these are normalized from 0 to 1,
+        where 1 is the Nyquist frequency. (`Wn` is thus in
+        half-cycles / sample.)
+
+        For analog filters, `Wn` is an angular frequency (e.g., rad/s).
+    btype : {'lowpass', 'highpass', 'bandpass', 'bandstop'}, optional
+        The type of filter.  Default is 'lowpass'.
+    analog : bool, optional
+        When True, return an analog filter, otherwise a digital filter is
+        returned.
+    output : {'ba', 'zpk', 'sos'}, optional
+        Type of output:  numerator/denominator ('ba'), pole-zero ('zpk'), or
+        second-order sections ('sos'). Default is 'ba' for backwards
+        compatibility, but 'sos' should be used for general-purpose filtering.
+    fs : float, optional
+        The sampling frequency of the digital system.
+
+        .. versionadded:: 1.2.0
+
+    Returns
+    -------
+    b, a : ndarray, ndarray
+        Numerator (`b`) and denominator (`a`) polynomials of the IIR filter.
+        Only returned if ``output='ba'``.
+    z, p, k : ndarray, ndarray, float
+        Zeros, poles, and system gain of the IIR filter transfer
+        function.  Only returned if ``output='zpk'``.
+    sos : ndarray
+        Second-order sections representation of the IIR filter.
+        Only returned if ``output='sos'``.
+
+    See Also
+    --------
+    cheb2ord, cheb2ap
+
+    Notes
+    -----
+    The Chebyshev type II filter maximizes the rate of cutoff between the
+    frequency response's passband and stopband, at the expense of ripple in
+    the stopband and increased ringing in the step response.
+
+    Type II filters do not roll off as fast as Type I (`cheby1`).
+
+    The ``'sos'`` output parameter was added in 0.16.0.
+
+    The current behavior is for ``ndarray`` outputs to have 64 bit precision
+    (``float64`` or ``complex128``) regardless of the dtype of `Wn` but
+    outputs may respect the dtype of `Wn` in a future version.
+
+    Examples
+    --------
+    Design an analog filter and plot its frequency response, showing the
+    critical points:
+
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+    >>> import numpy as np
+
+    >>> b, a = signal.cheby2(4, 40, 100, 'low', analog=True)
+    >>> w, h = signal.freqs(b, a)
+    >>> plt.semilogx(w, 20 * np.log10(abs(h)))
+    >>> plt.title('Chebyshev Type II frequency response (rs=40)')
+    >>> plt.xlabel('Frequency [rad/s]')
+    >>> plt.ylabel('Amplitude [dB]')
+    >>> plt.margins(0, 0.1)
+    >>> plt.grid(which='both', axis='both')
+    >>> plt.axvline(100, color='green') # cutoff frequency
+    >>> plt.axhline(-40, color='green') # rs
+    >>> plt.show()
+
+    Generate a signal made up of 10 Hz and 20 Hz, sampled at 1 kHz
+
+    >>> t = np.linspace(0, 1, 1000, False)  # 1 second
+    >>> sig = np.sin(2*np.pi*10*t) + np.sin(2*np.pi*20*t)
+    >>> fig, (ax1, ax2) = plt.subplots(2, 1, sharex=True)
+    >>> ax1.plot(t, sig)
+    >>> ax1.set_title('10 Hz and 20 Hz sinusoids')
+    >>> ax1.axis([0, 1, -2, 2])
+
+    Design a digital high-pass filter at 17 Hz to remove the 10 Hz tone, and
+    apply it to the signal. (It's recommended to use second-order sections
+    format when filtering, to avoid numerical error with transfer function
+    (``ba``) format):
+
+    >>> sos = signal.cheby2(12, 20, 17, 'hp', fs=1000, output='sos')
+    >>> filtered = signal.sosfilt(sos, sig)
+    >>> ax2.plot(t, filtered)
+    >>> ax2.set_title('After 17 Hz high-pass filter')
+    >>> ax2.axis([0, 1, -2, 2])
+    >>> ax2.set_xlabel('Time [s]')
+    >>> plt.show()
+    """
+    return iirfilter(N, Wn, rs=rs, btype=btype, analog=analog,
+                     output=output, ftype='cheby2', fs=fs)
+
+
+def ellip(N, rp, rs, Wn, btype='low', analog=False, output='ba', fs=None):
+    """
+    Elliptic (Cauer) digital and analog filter design.
+
+    Design an Nth-order digital or analog elliptic filter and return
+    the filter coefficients.
+
+    Parameters
+    ----------
+    N : int
+        The order of the filter.
+    rp : float
+        The maximum ripple allowed below unity gain in the passband.
+        Specified in decibels, as a positive number.
+    rs : float
+        The minimum attenuation required in the stop band.
+        Specified in decibels, as a positive number.
+    Wn : array_like
+        A scalar or length-2 sequence giving the critical frequencies.
+        For elliptic filters, this is the point in the transition band at
+        which the gain first drops below -`rp`.
+
+        For digital filters, `Wn` are in the same units as `fs`. By default,
+        `fs` is 2 half-cycles/sample, so these are normalized from 0 to 1,
+        where 1 is the Nyquist frequency. (`Wn` is thus in
+        half-cycles / sample.)
+
+        For analog filters, `Wn` is an angular frequency (e.g., rad/s).
+    btype : {'lowpass', 'highpass', 'bandpass', 'bandstop'}, optional
+        The type of filter. Default is 'lowpass'.
+    analog : bool, optional
+        When True, return an analog filter, otherwise a digital filter is
+        returned.
+    output : {'ba', 'zpk', 'sos'}, optional
+        Type of output:  numerator/denominator ('ba'), pole-zero ('zpk'), or
+        second-order sections ('sos'). Default is 'ba' for backwards
+        compatibility, but 'sos' should be used for general-purpose filtering.
+    fs : float, optional
+        The sampling frequency of the digital system.
+
+        .. versionadded:: 1.2.0
+
+    Returns
+    -------
+    b, a : ndarray, ndarray
+        Numerator (`b`) and denominator (`a`) polynomials of the IIR filter.
+        Only returned if ``output='ba'``.
+    z, p, k : ndarray, ndarray, float
+        Zeros, poles, and system gain of the IIR filter transfer
+        function.  Only returned if ``output='zpk'``.
+    sos : ndarray
+        Second-order sections representation of the IIR filter.
+        Only returned if ``output='sos'``.
+
+    See Also
+    --------
+    ellipord, ellipap
+
+    Notes
+    -----
+    Also known as Cauer or Zolotarev filters, the elliptical filter maximizes
+    the rate of transition between the frequency response's passband and
+    stopband, at the expense of ripple in both, and increased ringing in the
+    step response.
+
+    As `rp` approaches 0, the elliptical filter becomes a Chebyshev
+    type II filter (`cheby2`). As `rs` approaches 0, it becomes a Chebyshev
+    type I filter (`cheby1`). As both approach 0, it becomes a Butterworth
+    filter (`butter`).
+
+    The equiripple passband has N maxima or minima (for example, a
+    5th-order filter has 3 maxima and 2 minima). Consequently, the DC gain is
+    unity for odd-order filters, or -rp dB for even-order filters.
+
+    The ``'sos'`` output parameter was added in 0.16.0.
+
+    The current behavior is for ``ndarray`` outputs to have 64 bit precision
+    (``float64`` or ``complex128``) regardless of the dtype of `Wn` but
+    outputs may respect the dtype of `Wn` in a future version.
+
+    Examples
+    --------
+    Design an analog filter and plot its frequency response, showing the
+    critical points:
+
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+    >>> import numpy as np
+
+    >>> b, a = signal.ellip(4, 5, 40, 100, 'low', analog=True)
+    >>> w, h = signal.freqs(b, a)
+    >>> plt.semilogx(w, 20 * np.log10(abs(h)))
+    >>> plt.title('Elliptic filter frequency response (rp=5, rs=40)')
+    >>> plt.xlabel('Frequency [rad/s]')
+    >>> plt.ylabel('Amplitude [dB]')
+    >>> plt.margins(0, 0.1)
+    >>> plt.grid(which='both', axis='both')
+    >>> plt.axvline(100, color='green') # cutoff frequency
+    >>> plt.axhline(-40, color='green') # rs
+    >>> plt.axhline(-5, color='green') # rp
+    >>> plt.show()
+
+    Generate a signal made up of 10 Hz and 20 Hz, sampled at 1 kHz
+
+    >>> t = np.linspace(0, 1, 1000, False)  # 1 second
+    >>> sig = np.sin(2*np.pi*10*t) + np.sin(2*np.pi*20*t)
+    >>> fig, (ax1, ax2) = plt.subplots(2, 1, sharex=True)
+    >>> ax1.plot(t, sig)
+    >>> ax1.set_title('10 Hz and 20 Hz sinusoids')
+    >>> ax1.axis([0, 1, -2, 2])
+
+    Design a digital high-pass filter at 17 Hz to remove the 10 Hz tone, and
+    apply it to the signal. (It's recommended to use second-order sections
+    format when filtering, to avoid numerical error with transfer function
+    (``ba``) format):
+
+    >>> sos = signal.ellip(8, 1, 100, 17, 'hp', fs=1000, output='sos')
+    >>> filtered = signal.sosfilt(sos, sig)
+    >>> ax2.plot(t, filtered)
+    >>> ax2.set_title('After 17 Hz high-pass filter')
+    >>> ax2.axis([0, 1, -2, 2])
+    >>> ax2.set_xlabel('Time [s]')
+    >>> plt.tight_layout()
+    >>> plt.show()
+    """
+    return iirfilter(N, Wn, rs=rs, rp=rp, btype=btype, analog=analog,
+                     output=output, ftype='elliptic', fs=fs)
+
+
+def bessel(N, Wn, btype='low', analog=False, output='ba', norm='phase',
+           fs=None):
+    """
+    Bessel/Thomson digital and analog filter design.
+
+    Design an Nth-order digital or analog Bessel filter and return the
+    filter coefficients.
+
+    Parameters
+    ----------
+    N : int
+        The order of the filter.
+    Wn : array_like
+        A scalar or length-2 sequence giving the critical frequencies (defined
+        by the `norm` parameter).
+        For analog filters, `Wn` is an angular frequency (e.g., rad/s).
+
+        For digital filters, `Wn` are in the same units as `fs`.  By default,
+        `fs` is 2 half-cycles/sample, so these are normalized from 0 to 1,
+        where 1 is the Nyquist frequency. (`Wn` is thus in
+        half-cycles / sample.)
+    btype : {'lowpass', 'highpass', 'bandpass', 'bandstop'}, optional
+        The type of filter.  Default is 'lowpass'.
+    analog : bool, optional
+        When True, return an analog filter, otherwise a digital filter is
+        returned. (See Notes.)
+    output : {'ba', 'zpk', 'sos'}, optional
+        Type of output:  numerator/denominator ('ba'), pole-zero ('zpk'), or
+        second-order sections ('sos'). Default is 'ba'.
+    norm : {'phase', 'delay', 'mag'}, optional
+        Critical frequency normalization:
+
+        ``phase``
+            The filter is normalized such that the phase response reaches its
+            midpoint at angular (e.g. rad/s) frequency `Wn`. This happens for
+            both low-pass and high-pass filters, so this is the
+            "phase-matched" case.
+
+            The magnitude response asymptotes are the same as a Butterworth
+            filter of the same order with a cutoff of `Wn`.
+
+            This is the default, and matches MATLAB's implementation.
+
+        ``delay``
+            The filter is normalized such that the group delay in the passband
+            is 1/`Wn` (e.g., seconds). This is the "natural" type obtained by
+            solving Bessel polynomials.
+
+        ``mag``
+            The filter is normalized such that the gain magnitude is -3 dB at
+            angular frequency `Wn`.
+
+        .. versionadded:: 0.18.0
+    fs : float, optional
+        The sampling frequency of the digital system.
+
+        .. versionadded:: 1.2.0
+
+    Returns
+    -------
+    b, a : ndarray, ndarray
+        Numerator (`b`) and denominator (`a`) polynomials of the IIR filter.
+        Only returned if ``output='ba'``.
+    z, p, k : ndarray, ndarray, float
+        Zeros, poles, and system gain of the IIR filter transfer
+        function.  Only returned if ``output='zpk'``.
+    sos : ndarray
+        Second-order sections representation of the IIR filter.
+        Only returned if ``output='sos'``.
+
+    Notes
+    -----
+    Also known as a Thomson filter, the analog Bessel filter has maximally
+    flat group delay and maximally linear phase response, with very little
+    ringing in the step response. [1]_
+
+    The Bessel is inherently an analog filter. This function generates digital
+    Bessel filters using the bilinear transform, which does not preserve the
+    phase response of the analog filter. As such, it is only approximately
+    correct at frequencies below about fs/4. To get maximally-flat group
+    delay at higher frequencies, the analog Bessel filter must be transformed
+    using phase-preserving techniques.
+
+    See `besselap` for implementation details and references.
+
+    The ``'sos'`` output parameter was added in 0.16.0.
+
+    The current behavior is for ``ndarray`` outputs to have 64 bit precision
+    (``float64`` or ``complex128``) regardless of the dtype of `Wn` but
+    outputs may respect the dtype of `Wn` in a future version.
+
+    References
+    ----------
+    .. [1] Thomson, W.E., "Delay Networks having Maximally Flat Frequency
+           Characteristics", Proceedings of the Institution of Electrical
+           Engineers, Part III, November 1949, Vol. 96, No. 44, pp. 487-490.
+
+    Examples
+    --------
+    Plot the phase-normalized frequency response, showing the relationship
+    to the Butterworth's cutoff frequency (green):
+
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+    >>> import numpy as np
+
+    >>> b, a = signal.butter(4, 100, 'low', analog=True)
+    >>> w, h = signal.freqs(b, a)
+    >>> plt.semilogx(w, 20 * np.log10(np.abs(h)), color='silver', ls='dashed')
+    >>> b, a = signal.bessel(4, 100, 'low', analog=True, norm='phase')
+    >>> w, h = signal.freqs(b, a)
+    >>> plt.semilogx(w, 20 * np.log10(np.abs(h)))
+    >>> plt.title('Bessel filter magnitude response (with Butterworth)')
+    >>> plt.xlabel('Frequency [rad/s]')
+    >>> plt.ylabel('Amplitude [dB]')
+    >>> plt.margins(0, 0.1)
+    >>> plt.grid(which='both', axis='both')
+    >>> plt.axvline(100, color='green')  # cutoff frequency
+    >>> plt.show()
+
+    and the phase midpoint:
+
+    >>> plt.figure()
+    >>> plt.semilogx(w, np.unwrap(np.angle(h)))
+    >>> plt.axvline(100, color='green')  # cutoff frequency
+    >>> plt.axhline(-np.pi, color='red')  # phase midpoint
+    >>> plt.title('Bessel filter phase response')
+    >>> plt.xlabel('Frequency [rad/s]')
+    >>> plt.ylabel('Phase [rad]')
+    >>> plt.margins(0, 0.1)
+    >>> plt.grid(which='both', axis='both')
+    >>> plt.show()
+
+    Plot the magnitude-normalized frequency response, showing the -3 dB cutoff:
+
+    >>> b, a = signal.bessel(3, 10, 'low', analog=True, norm='mag')
+    >>> w, h = signal.freqs(b, a)
+    >>> plt.semilogx(w, 20 * np.log10(np.abs(h)))
+    >>> plt.axhline(-3, color='red')  # -3 dB magnitude
+    >>> plt.axvline(10, color='green')  # cutoff frequency
+    >>> plt.title('Amplitude-normalized Bessel filter frequency response')
+    >>> plt.xlabel('Frequency [rad/s]')
+    >>> plt.ylabel('Amplitude [dB]')
+    >>> plt.margins(0, 0.1)
+    >>> plt.grid(which='both', axis='both')
+    >>> plt.show()
+
+    Plot the delay-normalized filter, showing the maximally-flat group delay
+    at 0.1 seconds:
+
+    >>> b, a = signal.bessel(5, 1/0.1, 'low', analog=True, norm='delay')
+    >>> w, h = signal.freqs(b, a)
+    >>> plt.figure()
+    >>> plt.semilogx(w[1:], -np.diff(np.unwrap(np.angle(h)))/np.diff(w))
+    >>> plt.axhline(0.1, color='red')  # 0.1 seconds group delay
+    >>> plt.title('Bessel filter group delay')
+    >>> plt.xlabel('Frequency [rad/s]')
+    >>> plt.ylabel('Group delay [s]')
+    >>> plt.margins(0, 0.1)
+    >>> plt.grid(which='both', axis='both')
+    >>> plt.show()
+
+    """
+    return iirfilter(N, Wn, btype=btype, analog=analog,
+                     output=output, ftype='bessel_'+norm, fs=fs)
+
+
+def maxflat():
+    pass
+
+
+def yulewalk():
+    pass
+
+
+def band_stop_obj(wp, ind, passb, stopb, gpass, gstop, type):
+    """
+    Band Stop Objective Function for order minimization.
+
+    Returns the non-integer order for an analog band stop filter.
+
+    Parameters
+    ----------
+    wp : scalar
+        Edge of passband `passb`.
+    ind : int, {0, 1}
+        Index specifying which `passb` edge to vary (0 or 1).
+    passb : ndarray
+        Two element sequence of fixed passband edges.
+    stopb : ndarray
+        Two element sequence of fixed stopband edges.
+    gpass : float
+        Amount of ripple in the passband in dB.
+    gstop : float
+        Amount of attenuation in stopband in dB.
+    type : {'butter', 'cheby', 'ellip'}
+        Type of filter.
+
+    Returns
+    -------
+    n : scalar
+        Filter order (possibly non-integer).
+
+    Notes
+    -----
+    Band-stop filters are used in applications where certain frequency
+    components need to be blocked while others are allowed; for instance,
+    removing noise at specific frequencies while allowing the desired signal
+    to pass through. The order of a filter often determines its complexity and
+    accuracy. Determining the right order can be a challenge. This function
+    aims to provide an appropriate order for an analog band stop filter.
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> from scipy.signal import band_stop_obj
+    >>> wp = 2
+    >>> ind = 1
+    >>> passb = np.array([1, 3])
+    >>> stopb = np.array([0.5, 4])
+    >>> gstop = 30
+    >>> gpass = 3
+    >>> filter_type = 'butter'
+    >>> band_stop_obj(wp, ind, passb, stopb, gpass, gstop, filter_type)
+    np.float64(-2.758504160760643)
+
+    """
+
+    _validate_gpass_gstop(gpass, gstop)
+
+    passbC = passb.copy()
+    passbC[ind] = wp
+    nat = (stopb * (passbC[0] - passbC[1]) /
+           (stopb ** 2 - passbC[0] * passbC[1]))
+    nat = min(abs(nat))
+
+    if type == 'butter':
+        GSTOP = 10 ** (0.1 * abs(gstop))
+        GPASS = 10 ** (0.1 * abs(gpass))
+        n = (np.log10((GSTOP - 1.0) / (GPASS - 1.0)) / (2 * np.log10(nat)))
+    elif type == 'cheby':
+        GSTOP = 10 ** (0.1 * abs(gstop))
+        GPASS = 10 ** (0.1 * abs(gpass))
+        n = np.arccosh(np.sqrt((GSTOP - 1.0) / (GPASS - 1.0))) / np.arccosh(nat)
+    elif type == 'ellip':
+        GSTOP = 10 ** (0.1 * gstop)
+        GPASS = 10 ** (0.1 * gpass)
+        arg1 = np.sqrt((GPASS - 1.0) / (GSTOP - 1.0))
+        arg0 = 1.0 / nat
+        d0 = special.ellipk([arg0 ** 2, 1 - arg0 ** 2])
+        d1 = special.ellipk([arg1 ** 2, 1 - arg1 ** 2])
+        n = (d0[0] * d1[1] / (d0[1] * d1[0]))
+    else:
+        raise ValueError(f"Incorrect type: {type}")
+    return n
+
+
+def _pre_warp(wp, ws, analog, *, xp):
+    # Pre-warp frequencies for digital filter design
+    if not analog:
+        passb = xp.tan(xp.pi * wp / 2.0)
+        stopb = xp.tan(xp.pi * ws / 2.0)
+    else:
+        passb, stopb = wp, ws
+    return passb, stopb
+
+
+def _validate_wp_ws(wp, ws, fs, analog, *, xp):
+    wp = xpx.atleast_nd(wp, ndim=1, xp=xp)
+    ws = xpx.atleast_nd(ws, ndim=1, xp=xp)
+    wp, ws = xp_promote(wp, ws, force_floating=True, xp=xp)
+
+    if fs is not None:
+        if analog:
+            raise ValueError("fs cannot be specified for an analog filter")
+        wp = 2 * wp / fs
+        ws = 2 * ws / fs
+
+    filter_type = 2 * (wp.shape[0] - 1) + 1
+    if wp[0] >= ws[0]:
+        filter_type += 1
+
+    return wp, ws, filter_type
+
+
+def _find_nat_freq(stopb, passb, gpass, gstop, filter_type, filter_kind, *, xp):
+    if filter_type == 1:            # low
+        nat = stopb / passb
+    elif filter_type == 2:          # high
+        nat = passb / stopb
+    elif filter_type == 3:          # stop
+
+        passb, stopb = np.asarray(passb), np.asarray(stopb)    # XXX fminbound array API
+        wp0 = optimize.fminbound(band_stop_obj, passb[0], stopb[0] - 1e-12,
+                                 args=(0, passb, stopb, gpass, gstop,
+                                       filter_kind),
+                                 disp=0)
+        wp1 = optimize.fminbound(band_stop_obj, stopb[1] + 1e-12, passb[1],
+                                 args=(1, passb, stopb, gpass, gstop,
+                                       filter_kind),
+                                 disp=0)
+        passb = [float(wp0), float(wp1)]
+        passb, stopb = xp.asarray(passb), xp.asarray(stopb)
+        nat = ((stopb * (passb[0] - passb[1])) /
+               (stopb ** 2 - passb[0] * passb[1]))
+    elif filter_type == 4:          # pass
+        nat = ((stopb ** 2 - passb[0] * passb[1]) /
+               (stopb * (passb[0] - passb[1])))
+    else:
+        raise ValueError(f"should not happen: {filter_type =}.")
+
+    nat = xp.min(xp.abs(nat))
+    return nat, passb
+
+
+def _postprocess_wn(WN, analog, fs, *, xp):
+    wn = WN if analog else xp.atan(WN) * 2.0 / xp.pi
+    if wn.shape[0] == 1:
+        wn = wn[0]
+    if fs is not None:
+        wn = wn * fs / 2
+    return wn
+
+
+def buttord(wp, ws, gpass, gstop, analog=False, fs=None):
+    """Butterworth filter order selection.
+
+    Return the order of the lowest order digital or analog Butterworth filter
+    that loses no more than `gpass` dB in the passband and has at least
+    `gstop` dB attenuation in the stopband.
+
+    Parameters
+    ----------
+    wp, ws : float or array-like
+        Passband and stopband edge frequencies.
+
+        For digital filters, these are in the same units as `fs`. By default,
+        `fs` is 2 half-cycles/sample, so these are normalized from 0 to 1,
+        where 1 is the Nyquist frequency. (`wp` and `ws` are thus in
+        half-cycles / sample.) For example:
+
+        - Lowpass:   wp = 0.2,          ws = 0.3
+        - Highpass:  wp = 0.3,          ws = 0.2
+        - Bandpass:  wp = [0.2, 0.5],   ws = [0.1, 0.6]
+        - Bandstop:  wp = [0.1, 0.6],   ws = [0.2, 0.5]
+
+        For analog filters, `wp` and `ws` are angular frequencies (e.g., rad/s).
+    gpass : float
+        The maximum loss in the passband (dB).
+    gstop : float
+        The minimum attenuation in the stopband (dB).
+    analog : bool, optional
+        When True, return an analog filter, otherwise a digital filter is
+        returned.
+    fs : float, optional
+        The sampling frequency of the digital system.
+
+        .. versionadded:: 1.2.0
+
+    Returns
+    -------
+    ord : int
+        The lowest order for a Butterworth filter which meets specs.
+    wn : ndarray or float
+        The Butterworth natural frequency (i.e. the "3dB frequency"). Should
+        be used with `butter` to give filter results. If `fs` is specified,
+        this is in the same units, and `fs` must also be passed to `butter`.
+
+    See Also
+    --------
+    butter : Filter design using order and critical points
+    cheb1ord : Find order and critical points from passband and stopband spec
+    cheb2ord, ellipord
+    iirfilter : General filter design using order and critical frequencies
+    iirdesign : General filter design using passband and stopband spec
+
+    Examples
+    --------
+    Design an analog bandpass filter with passband within 3 dB from 20 to
+    50 rad/s, while rejecting at least -40 dB below 14 and above 60 rad/s.
+    Plot its frequency response, showing the passband and stopband
+    constraints in gray.
+
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+    >>> import numpy as np
+
+    >>> N, Wn = signal.buttord([20, 50], [14, 60], 3, 40, True)
+    >>> b, a = signal.butter(N, Wn, 'band', True)
+    >>> w, h = signal.freqs(b, a, np.logspace(1, 2, 500))
+    >>> plt.semilogx(w, 20 * np.log10(abs(h)))
+    >>> plt.title('Butterworth bandpass filter fit to constraints')
+    >>> plt.xlabel('Frequency [rad/s]')
+    >>> plt.ylabel('Amplitude [dB]')
+    >>> plt.grid(which='both', axis='both')
+    >>> plt.fill([1,  14,  14,   1], [-40, -40, 99, 99], '0.9', lw=0) # stop
+    >>> plt.fill([20, 20,  50,  50], [-99, -3, -3, -99], '0.9', lw=0) # pass
+    >>> plt.fill([60, 60, 1e9, 1e9], [99, -40, -40, 99], '0.9', lw=0) # stop
+    >>> plt.axis([10, 100, -60, 3])
+    >>> plt.show()
+
+    """
+    xp = array_namespace(wp, ws)
+    wp, ws = map(xp.asarray, (wp, ws))
+
+    _validate_gpass_gstop(gpass, gstop)
+    fs = _validate_fs(fs, allow_none=True)
+    wp, ws, filter_type = _validate_wp_ws(wp, ws, fs, analog, xp=xp)
+    passb, stopb = _pre_warp(wp, ws, analog, xp=xp)
+    nat, passb = _find_nat_freq(
+        stopb, passb, gpass, gstop, filter_type, 'butter', xp=xp
+    )
+
+    GSTOP = 10 ** (0.1 * builtins.abs(gstop))
+    GPASS = 10 ** (0.1 * builtins.abs(gpass))
+    ord = int(
+        math.ceil(math.log10((GSTOP - 1.0) / (GPASS - 1.0)) / (2 * math.log10(nat)))
+    )
+
+    # Find the Butterworth natural frequency WN (or the "3dB" frequency")
+    # to give exactly gpass at passb.
+    try:
+        W0 = (GPASS - 1.0) ** (-1.0 / (2.0 * ord))
+    except ZeroDivisionError:
+        W0 = 1.0
+        warnings.warn("Order is zero...check input parameters.",
+                      RuntimeWarning, stacklevel=2)
+
+    # now convert this frequency back from lowpass prototype
+    # to the original analog filter
+
+    if filter_type == 1:  # low
+        WN = W0 * passb
+    elif filter_type == 2:  # high
+        WN = passb / W0
+    elif filter_type == 3:  # stop
+        discr = xp.sqrt((passb[1] - passb[0]) ** 2 +
+                     4 * W0 ** 2 * passb[0] * passb[1])
+        WN0 = ((passb[1] - passb[0]) + discr) / (2 * W0)
+        WN1 = ((passb[1] - passb[0]) - discr) / (2 * W0)
+        WN = xp.asarray([float(WN0), float(WN1)])
+        WN = xp.sort(xp.abs(WN))
+
+    elif filter_type == 4:  # pass
+        W0 = xp.asarray([-W0, W0], dtype=xp.float64)
+        WN = (-W0 * (passb[1] - passb[0]) / 2.0 +
+              xp.sqrt(W0 ** 2 / 4.0 * (passb[1] - passb[0]) ** 2 +
+                   passb[0] * passb[1]))
+        WN = xp.sort(xp.abs(WN))
+    else:
+        raise ValueError(f"Bad type: {filter_type}")
+
+    wn = _postprocess_wn(WN, analog, fs, xp=xp)
+
+    return ord, wn
+
+
+def cheb1ord(wp, ws, gpass, gstop, analog=False, fs=None):
+    """Chebyshev type I filter order selection.
+
+    Return the order of the lowest order digital or analog Chebyshev Type I
+    filter that loses no more than `gpass` dB in the passband and has at
+    least `gstop` dB attenuation in the stopband.
+
+    Parameters
+    ----------
+    wp, ws : float
+        Passband and stopband edge frequencies.
+
+        For digital filters, these are in the same units as `fs`. By default,
+        `fs` is 2 half-cycles/sample, so these are normalized from 0 to 1,
+        where 1 is the Nyquist frequency. (`wp` and `ws` are thus in
+        half-cycles / sample.)  For example:
+
+        - Lowpass:   wp = 0.2,          ws = 0.3
+        - Highpass:  wp = 0.3,          ws = 0.2
+        - Bandpass:  wp = [0.2, 0.5],   ws = [0.1, 0.6]
+        - Bandstop:  wp = [0.1, 0.6],   ws = [0.2, 0.5]
+
+        For analog filters, `wp` and `ws` are angular frequencies (e.g., rad/s).
+    gpass : float
+        The maximum loss in the passband (dB).
+    gstop : float
+        The minimum attenuation in the stopband (dB).
+    analog : bool, optional
+        When True, return an analog filter, otherwise a digital filter is
+        returned.
+    fs : float, optional
+        The sampling frequency of the digital system.
+
+        .. versionadded:: 1.2.0
+
+    Returns
+    -------
+    ord : int
+        The lowest order for a Chebyshev type I filter that meets specs.
+    wn : ndarray or float
+        The Chebyshev natural frequency (the "3dB frequency") for use with
+        `cheby1` to give filter results. If `fs` is specified,
+        this is in the same units, and `fs` must also be passed to `cheby1`.
+
+    See Also
+    --------
+    cheby1 : Filter design using order and critical points
+    buttord : Find order and critical points from passband and stopband spec
+    cheb2ord, ellipord
+    iirfilter : General filter design using order and critical frequencies
+    iirdesign : General filter design using passband and stopband spec
+
+    Examples
+    --------
+    Design a digital lowpass filter such that the passband is within 3 dB up
+    to 0.2*(fs/2), while rejecting at least -40 dB above 0.3*(fs/2). Plot its
+    frequency response, showing the passband and stopband constraints in gray.
+
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+    >>> import numpy as np
+
+    >>> N, Wn = signal.cheb1ord(0.2, 0.3, 3, 40)
+    >>> b, a = signal.cheby1(N, 3, Wn, 'low')
+    >>> w, h = signal.freqz(b, a)
+    >>> plt.semilogx(w / np.pi, 20 * np.log10(abs(h)))
+    >>> plt.title('Chebyshev I lowpass filter fit to constraints')
+    >>> plt.xlabel('Normalized frequency')
+    >>> plt.ylabel('Amplitude [dB]')
+    >>> plt.grid(which='both', axis='both')
+    >>> plt.fill([.01, 0.2, 0.2, .01], [-3, -3, -99, -99], '0.9', lw=0) # stop
+    >>> plt.fill([0.3, 0.3,   2,   2], [ 9, -40, -40,  9], '0.9', lw=0) # pass
+    >>> plt.axis([0.08, 1, -60, 3])
+    >>> plt.show()
+
+    """
+    xp = array_namespace(wp, ws)
+    wp, ws = map(xp.asarray, (wp, ws))
+
+    fs = _validate_fs(fs, allow_none=True)
+    _validate_gpass_gstop(gpass, gstop)
+    wp, ws, filter_type = _validate_wp_ws(wp, ws, fs, analog, xp=xp)
+    passb, stopb = _pre_warp(wp, ws, analog, xp=xp)
+    nat, passb = _find_nat_freq(stopb, passb, gpass, gstop, filter_type, 'cheby', xp=xp)
+
+    GSTOP = 10 ** (0.1 * builtins.abs(gstop))
+    GPASS = 10 ** (0.1 * builtins.abs(gpass))
+    v_pass_stop = math.acosh(math.sqrt((GSTOP - 1.0) / (GPASS - 1.0)))
+    ord = int(xp.ceil(v_pass_stop / xp.acosh(nat)))
+
+    # Natural frequencies are just the passband edges
+    wn = _postprocess_wn(passb, analog, fs, xp=xp)
+
+    return ord, wn
+
+
+def cheb2ord(wp, ws, gpass, gstop, analog=False, fs=None):
+    """Chebyshev type II filter order selection.
+
+    Return the order of the lowest order digital or analog Chebyshev Type II
+    filter that loses no more than `gpass` dB in the passband and has at least
+    `gstop` dB attenuation in the stopband.
+
+    Parameters
+    ----------
+    wp, ws : float
+        Passband and stopband edge frequencies.
+
+        For digital filters, these are in the same units as `fs`. By default,
+        `fs` is 2 half-cycles/sample, so these are normalized from 0 to 1,
+        where 1 is the Nyquist frequency. (`wp` and `ws` are thus in
+        half-cycles / sample.)  For example:
+
+        - Lowpass:   wp = 0.2,          ws = 0.3
+        - Highpass:  wp = 0.3,          ws = 0.2
+        - Bandpass:  wp = [0.2, 0.5],   ws = [0.1, 0.6]
+        - Bandstop:  wp = [0.1, 0.6],   ws = [0.2, 0.5]
+
+        For analog filters, `wp` and `ws` are angular frequencies (e.g., rad/s).
+    gpass : float
+        The maximum loss in the passband (dB).
+    gstop : float
+        The minimum attenuation in the stopband (dB).
+    analog : bool, optional
+        When True, return an analog filter, otherwise a digital filter is
+        returned.
+    fs : float, optional
+        The sampling frequency of the digital system.
+
+        .. versionadded:: 1.2.0
+
+    Returns
+    -------
+    ord : int
+        The lowest order for a Chebyshev type II filter that meets specs.
+    wn : ndarray or float
+        The Chebyshev natural frequency (the "3dB frequency") for use with
+        `cheby2` to give filter results. If `fs` is specified,
+        this is in the same units, and `fs` must also be passed to `cheby2`.
+
+    See Also
+    --------
+    cheby2 : Filter design using order and critical points
+    buttord : Find order and critical points from passband and stopband spec
+    cheb1ord, ellipord
+    iirfilter : General filter design using order and critical frequencies
+    iirdesign : General filter design using passband and stopband spec
+
+    Examples
+    --------
+    Design a digital bandstop filter which rejects -60 dB from 0.2*(fs/2) to
+    0.5*(fs/2), while staying within 3 dB below 0.1*(fs/2) or above
+    0.6*(fs/2). Plot its frequency response, showing the passband and
+    stopband constraints in gray.
+
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+    >>> import numpy as np
+
+    >>> N, Wn = signal.cheb2ord([0.1, 0.6], [0.2, 0.5], 3, 60)
+    >>> b, a = signal.cheby2(N, 60, Wn, 'stop')
+    >>> w, h = signal.freqz(b, a)
+    >>> plt.semilogx(w / np.pi, 20 * np.log10(abs(h)))
+    >>> plt.title('Chebyshev II bandstop filter fit to constraints')
+    >>> plt.xlabel('Normalized frequency')
+    >>> plt.ylabel('Amplitude [dB]')
+    >>> plt.grid(which='both', axis='both')
+    >>> plt.fill([.01, .1, .1, .01], [-3,  -3, -99, -99], '0.9', lw=0) # stop
+    >>> plt.fill([.2,  .2, .5,  .5], [ 9, -60, -60,   9], '0.9', lw=0) # pass
+    >>> plt.fill([.6,  .6,  2,   2], [-99, -3,  -3, -99], '0.9', lw=0) # stop
+    >>> plt.axis([0.06, 1, -80, 3])
+    >>> plt.show()
+
+    """
+    xp = array_namespace(wp, ws)
+    wp, ws = map(xp.asarray, (wp, ws))
+
+    fs = _validate_fs(fs, allow_none=True)
+    _validate_gpass_gstop(gpass, gstop)
+    wp, ws, filter_type = _validate_wp_ws(wp, ws, fs, analog, xp=xp)
+    passb, stopb = _pre_warp(wp, ws, analog, xp=xp)
+    nat, passb = _find_nat_freq(stopb, passb, gpass, gstop, filter_type, 'cheby', xp=xp)
+
+    GSTOP = 10 ** (0.1 * builtins.abs(gstop))
+    GPASS = 10 ** (0.1 * builtins.abs(gpass))
+    v_pass_stop = math.acosh(math.sqrt((GSTOP - 1.0) / (GPASS - 1.0)))
+    ord = int(xp.ceil(v_pass_stop / xp.acosh(nat)))
+
+    # Find frequency where analog response is -gpass dB.
+    # Then convert back from low-pass prototype to the original filter.
+
+    new_freq = math.cosh(1.0 / ord * v_pass_stop)
+    new_freq = 1.0 / new_freq
+
+    if filter_type == 1:
+        nat = passb / new_freq
+    elif filter_type == 2:
+        nat = passb * new_freq
+    elif filter_type == 3:
+        nat0 = (new_freq / 2.0 * (passb[0] - passb[1]) +
+                  math.sqrt(new_freq ** 2 * (passb[1] - passb[0]) ** 2 / 4.0 +
+                       passb[1] * passb[0]))
+        nat1 = passb[1] * passb[0] / nat0
+        nat = xp.asarray([float(nat0), float(nat1)])
+    elif filter_type == 4:
+        nat0 = (1.0 / (2.0 * new_freq) * (passb[0] - passb[1]) +
+                  math.sqrt((passb[1] - passb[0]) ** 2 / (4.0 * new_freq ** 2) +
+                       passb[1] * passb[0]))
+        nat1 = passb[0] * passb[1] / nat0
+        nat = xp.asarray([float(nat0), float(nat1)])
+
+    wn = _postprocess_wn(nat, analog, fs, xp=xp)
+
+    return ord, wn
+
+
+_POW10_LOG10 = math.log(10)
+
+
+def _pow10m1(x):
+    """10 ** x - 1 for x near 0"""
+    return math.expm1(_POW10_LOG10 * x)
+
+
+def ellipord(wp, ws, gpass, gstop, analog=False, fs=None):
+    """Elliptic (Cauer) filter order selection.
+
+    Return the order of the lowest order digital or analog elliptic filter
+    that loses no more than `gpass` dB in the passband and has at least
+    `gstop` dB attenuation in the stopband.
+
+    Parameters
+    ----------
+    wp, ws : float
+        Passband and stopband edge frequencies.
+
+        For digital filters, these are in the same units as `fs`. By default,
+        `fs` is 2 half-cycles/sample, so these are normalized from 0 to 1,
+        where 1 is the Nyquist frequency. (`wp` and `ws` are thus in
+        half-cycles / sample.) For example:
+
+        - Lowpass:   wp = 0.2,          ws = 0.3
+        - Highpass:  wp = 0.3,          ws = 0.2
+        - Bandpass:  wp = [0.2, 0.5],   ws = [0.1, 0.6]
+        - Bandstop:  wp = [0.1, 0.6],   ws = [0.2, 0.5]
+
+        For analog filters, `wp` and `ws` are angular frequencies (e.g., rad/s).
+    gpass : float
+        The maximum loss in the passband (dB).
+    gstop : float
+        The minimum attenuation in the stopband (dB).
+    analog : bool, optional
+        When True, return an analog filter, otherwise a digital filter is
+        returned.
+    fs : float, optional
+        The sampling frequency of the digital system.
+
+        .. versionadded:: 1.2.0
+
+    Returns
+    -------
+    ord : int
+        The lowest order for an Elliptic (Cauer) filter that meets specs.
+    wn : ndarray or float
+        The Chebyshev natural frequency (the "3dB frequency") for use with
+        `ellip` to give filter results. If `fs` is specified,
+        this is in the same units, and `fs` must also be passed to `ellip`.
+
+    See Also
+    --------
+    ellip : Filter design using order and critical points
+    buttord : Find order and critical points from passband and stopband spec
+    cheb1ord, cheb2ord
+    iirfilter : General filter design using order and critical frequencies
+    iirdesign : General filter design using passband and stopband spec
+
+    Examples
+    --------
+    Design an analog highpass filter such that the passband is within 3 dB
+    above 30 rad/s, while rejecting -60 dB at 10 rad/s. Plot its
+    frequency response, showing the passband and stopband constraints in gray.
+
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+    >>> import numpy as np
+
+    >>> N, Wn = signal.ellipord(30, 10, 3, 60, True)
+    >>> b, a = signal.ellip(N, 3, 60, Wn, 'high', True)
+    >>> w, h = signal.freqs(b, a, np.logspace(0, 3, 500))
+    >>> plt.semilogx(w, 20 * np.log10(abs(h)))
+    >>> plt.title('Elliptical highpass filter fit to constraints')
+    >>> plt.xlabel('Frequency [rad/s]')
+    >>> plt.ylabel('Amplitude [dB]')
+    >>> plt.grid(which='both', axis='both')
+    >>> plt.fill([.1, 10,  10,  .1], [1e4, 1e4, -60, -60], '0.9', lw=0) # stop
+    >>> plt.fill([30, 30, 1e9, 1e9], [-99,  -3,  -3, -99], '0.9', lw=0) # pass
+    >>> plt.axis([1, 300, -80, 3])
+    >>> plt.show()
+
+    """
+    xp = array_namespace(wp, ws)
+    wp, ws = map(xp.asarray, (wp, ws))
+
+    fs = _validate_fs(fs, allow_none=True)
+    _validate_gpass_gstop(gpass, gstop)
+    wp, ws, filter_type = _validate_wp_ws(wp, ws, fs, analog, xp=xp)
+    passb, stopb = _pre_warp(wp, ws, analog, xp=xp)
+    nat, passb = _find_nat_freq(stopb, passb, gpass, gstop, filter_type, 'ellip', xp=xp)
+
+    arg1_sq = _pow10m1(0.1 * gpass) / _pow10m1(0.1 * gstop)
+    arg0 = 1.0 / nat
+    arg0 = np.asarray(arg0)
+    d0 = special.ellipk(arg0 ** 2), special.ellipkm1(arg0 ** 2)
+    d1 = special.ellipk(arg1_sq), special.ellipkm1(arg1_sq)
+    ord = int(np.ceil(d0[0] * d1[1] / (d0[1] * d1[0])))
+
+    wn = _postprocess_wn(passb, analog, fs, xp=xp)
+
+    return ord, wn
+
+
+def buttap(N, *, xp=None, device=None):
+    """Return (z,p,k) for analog prototype of Nth-order Butterworth filter.
+
+    The filter will have an angular (e.g., rad/s) cutoff frequency of 1.
+
+    Parameters
+    ----------
+    N : int
+        The order of the filter
+    %(xp_device_snippet)s
+
+    Returns
+    -------
+    z : ndarray[float64]
+        Zeros of the transfer function. Is always an empty array.
+    p : ndarray[complex128]
+        Poles of the transfer function.
+    k : float
+        Gain of the transfer function.
+
+    See Also
+    --------
+    butter : Filter design function using this prototype
+
+    """
+    if xp is None:
+        xp = np_compat
+    if abs(int(N)) != N:
+        raise ValueError("Filter order must be a nonnegative integer")
+    z = xp.asarray([], device=device, dtype=xp.float64)
+    m = xp.arange(-N+1, N, 2, device=device, dtype=xp.float64)
+    # Middle value is 0 to ensure an exactly real pole
+    p = -xp.exp(1j * xp.pi * m / (2 * N))
+    k = 1.0
+    return z, p, k
+
+
+def cheb1ap(N, rp, *, xp=None, device=None):
+    """
+    Return (z,p,k) for Nth-order Chebyshev type I analog lowpass filter.
+
+    The returned filter prototype has `rp` decibels of ripple in the passband.
+
+    The filter's angular (e.g. rad/s) cutoff frequency is normalized to 1,
+    defined as the point at which the gain first drops below ``-rp``.
+
+    Parameters
+    ----------
+    N : int
+        The order of the filter
+    rp : float
+        The ripple intensity
+    %(xp_device_snippet)s
+
+    Returns
+    -------
+    z : ndarray[float64]
+        Zeros of the transfer function. Is always an empty array.
+    p : ndarray[complex128]
+        Poles of the transfer function.
+    k : float
+        Gain of the transfer function.
+
+    See Also
+    --------
+    cheby1 : Filter design function using this prototype
+
+    """
+    if xp is None:
+        xp = np_compat
+    if abs(int(N)) != N:
+        raise ValueError("Filter order must be a nonnegative integer")
+    elif N == 0:
+        # Avoid divide-by-zero error
+        # Even order filters have DC gain of -rp dB
+        return (
+            xp.asarray([], device=device, dtype=xp.float64),
+            xp.asarray([], device=device, dtype=xp.complex128), 10**(-rp/20)
+        )
+    z = xp.asarray([], device=device, dtype=xp.float64)
+
+    # Ripple factor (epsilon)
+    eps = math.sqrt(10 ** (0.1 * rp) - 1.0)
+    mu = 1.0 / N * math.asinh(1 / eps)
+
+    # Arrange poles in an ellipse on the left half of the S-plane
+    m = xp.arange(-N+1, N, 2, dtype=xp.float64, device=device)
+    theta = xp.pi * m / (2*N)
+    p = -xp.sinh(mu + 1j*theta)
+
+    k = xp.real(xp.prod(-p, axis=0))
+    if N % 2 == 0:
+        k = k / math.sqrt(1 + eps * eps)
+
+    return z, p, k
+
+
+def cheb2ap(N, rs, *, xp=None, device=None):
+    """
+    Return (z,p,k) for Nth-order Chebyshev type II analog lowpass filter.
+
+    The returned filter prototype has attenuation of at least ``rs`` decibels
+    in the stopband.
+
+    The filter's angular (e.g. rad/s) cutoff frequency is normalized to 1,
+    defined as the point at which the attenuation first reaches ``rs``.
+
+    Parameters
+    ----------
+    N : int
+        The order of the filter
+    rs : float
+        The attenuation in the stopband
+    %(xp_device_snippet)s
+
+    Returns
+    -------
+    z : ndarray[complex128]
+        Zeros of the transfer function.
+    p : ndarray[complex128]
+        Poles of the transfer function.
+    k : float
+        Gain of the transfer function.
+
+    See Also
+    --------
+    cheby2 : Filter design function using this prototype
+
+    """
+    if xp is None:
+        xp = np_compat
+    if abs(int(N)) != N:
+        raise ValueError("Filter order must be a nonnegative integer")
+    elif N == 0:
+        # Avoid divide-by-zero warning
+        return (
+            xp.asarray([], device=device, dtype=xp.complex128),
+            xp.asarray([], device=device, dtype=xp.complex128),
+            1.0
+        )
+
+    # Ripple factor (epsilon)
+    de = 1.0 / math.sqrt(10 ** (0.1 * rs) - 1)
+    mu = math.asinh(1.0 / de) / N
+
+    if N % 2:
+        m = xp.concat(
+            (xp.arange(-N + 1, 0, 2, dtype=xp.float64, device=device),
+             xp.arange(2, N, 2, dtype=xp.float64, device=device)
+            )
+        )
+    else:
+        m = xp.arange(-N+1, N, 2, dtype=xp.float64, device=device)
+
+    z = 1j / xp.sin(m * xp.pi / (2 * N))
+
+    # Poles around the unit circle like Butterworth
+    m1 = xp.arange(-N+1, N, 2, dtype=xp.float64, device=device)
+    theta1 = xp.pi * m1 / (2 * N)
+    p = -1 / xp.sinh(mu + 1j*theta1)
+
+    k = xp.real(xp.prod(-p, axis=0) / xp.prod(-z, axis=0))
+    return z, p, k
+
+
+EPSILON = 2e-16
+
+# number of terms in solving degree equation
+_ELLIPDEG_MMAX = 7
+
+
+def _ellipdeg(n, m1):
+    """Solve degree equation using nomes
+
+    Given n, m1, solve
+       n * K(m) / K'(m) = K1(m1) / K1'(m1)
+    for m
+
+    See [1], Eq. (49)
+
+    References
+    ----------
+    .. [1] Orfanidis, "Lecture Notes on Elliptic Filter Design",
+           https://www.ece.rutgers.edu/~orfanidi/ece521/notes.pdf
+    """
+    K1 = special.ellipk(m1)
+    K1p = special.ellipkm1(m1)
+
+    q1 = np.exp(-np.pi * K1p / K1)
+    q = q1 ** (1/n)
+
+    mnum = np.arange(_ELLIPDEG_MMAX + 1)
+    mden = np.arange(1, _ELLIPDEG_MMAX + 2)
+
+    num = np.sum(q ** (mnum * (mnum+1)))
+    den = 1 + 2 * np.sum(q ** (mden**2))
+
+    return 16 * q * (num / den) ** 4
+
+
+# Maximum number of iterations in Landen transformation recursion
+# sequence.  10 is conservative; unit tests pass with 4, Orfanidis
+# (see _arc_jac_cn [1]) suggests 5.
+_ARC_JAC_SN_MAXITER = 10
+
+
+def _arc_jac_sn(w, m):
+    """Inverse Jacobian elliptic sn
+
+    Solve for z in w = sn(z, m)
+
+    Parameters
+    ----------
+    w : complex scalar
+        argument
+
+    m : scalar
+        modulus; in interval [0, 1]
+
+
+    See [1], Eq. (56)
+
+    References
+    ----------
+    .. [1] Orfanidis, "Lecture Notes on Elliptic Filter Design",
+           https://www.ece.rutgers.edu/~orfanidi/ece521/notes.pdf
+
+    """
+
+    def _complement(kx):
+        # (1-k**2) ** 0.5; the expression below
+        # works for small kx
+        return ((1 - kx) * (1 + kx)) ** 0.5
+
+    k = m ** 0.5
+
+    if k > 1:
+        return np.nan
+    elif k == 1:
+        return np.arctanh(w)
+
+    ks = [k]
+    niter = 0
+    while ks[-1] != 0:
+        k_ = ks[-1]
+        k_p = _complement(k_)
+        ks.append((1 - k_p) / (1 + k_p))
+        niter += 1
+        if niter > _ARC_JAC_SN_MAXITER:
+            raise ValueError('Landen transformation not converging')
+
+    K = np.prod(1 + np.array(ks[1:])) * np.pi/2
+
+    wns = [w]
+
+    for kn, knext in zip(ks[:-1], ks[1:]):
+        wn = wns[-1]
+        wnext = (2 * wn /
+                 ((1 + knext) * (1 + _complement(kn * wn))))
+        wns.append(wnext)
+
+    u = 2 / np.pi * np.arcsin(wns[-1])
+
+    z = K * u
+    return z
+
+
+def _arc_jac_sc1(w, m):
+    """Real inverse Jacobian sc, with complementary modulus
+
+    Solve for z in w = sc(z, 1-m)
+
+    w - real scalar
+
+    m - modulus
+
+    From [1], sc(z, m) = -i * sn(i * z, 1 - m)
+
+    References
+    ----------
+    # noqa: E501
+    .. [1] https://functions.wolfram.com/EllipticFunctions/JacobiSC/introductions/JacobiPQs/ShowAll.html,
+       "Representations through other Jacobi functions"
+
+    """
+
+    zcomplex = _arc_jac_sn(1j * w, m)
+    if abs(zcomplex.real) > 1e-14:
+        raise ValueError
+
+    return zcomplex.imag
+
+
+def ellipap(N, rp, rs, *, xp=None, device=None):
+    """Return (z,p,k) of Nth-order elliptic analog lowpass filter.
+
+    The filter is a normalized prototype that has `rp` decibels of ripple
+    in the passband and a stopband `rs` decibels down.
+
+    The filter's angular (e.g., rad/s) cutoff frequency is normalized to 1,
+    defined as the point at which the gain first drops below ``-rp``.
+
+    Parameters
+    ----------
+    N : int
+        The order of the filter
+    rp : float
+        The passband ripple intensity
+    rs : float
+        The stopband attenuation
+    %(xp_device_snippet)s
+
+    Returns
+    -------
+    z : ndarray[complex128]
+        Zeros of the transfer function.
+    p : ndarray[complex128]
+        Poles of the transfer function.
+    k : float
+        Gain of the transfer function.
+
+    See Also
+    --------
+    ellip : Filter design function using this prototype
+
+    References
+    ----------
+    .. [1] Lutovac, Tosic, and Evans, "Filter Design for Signal Processing",
+           Chapters 5 and 12.
+
+    .. [2] Orfanidis, "Lecture Notes on Elliptic Filter Design",
+           https://www.ece.rutgers.edu/~orfanidi/ece521/notes.pdf
+
+    """
+    if xp is None:
+        xp = np_compat
+
+    if abs(int(N)) != N:
+        raise ValueError("Filter order must be a nonnegative integer")
+    elif N == 0:
+        # Avoid divide-by-zero warning
+        # Even order filters have DC gain of -rp dB
+        return (
+            xp.asarray([], device=device, dtype=xp.complex128),
+            xp.asarray([], device=device, dtype=xp.complex128),
+            10**(-rp/20)
+        )
+    elif N == 1:
+        p = -math.sqrt(1.0 / _pow10m1(0.1 * rp))
+        k = -p
+        z = []
+        return (
+            xp.asarray(z, device=device, dtype=xp.complex128),
+            xp.asarray(p, device=device, dtype=xp.complex128), k
+        )
+
+    eps_sq = _pow10m1(0.1 * rp)
+
+    eps = math.sqrt(eps_sq)
+    ck1_sq = eps_sq / _pow10m1(0.1 * rs)
+    if ck1_sq == 0:
+        raise ValueError("Cannot design a filter with given rp and rs"
+                         " specifications.")
+
+    # do computations with numpy, xp.asarray the return values
+
+    val = special.ellipk(ck1_sq), special.ellipkm1(ck1_sq)
+
+    m = _ellipdeg(N, ck1_sq)
+
+    capk = special.ellipk(m)
+
+    j = np.arange(1 - N % 2, N, 2)
+    jj = len(j)
+
+    [s, c, d, phi] = special.ellipj(j * capk / N, m * np.ones(jj))
+    snew = np.compress(abs(s) > EPSILON, s, axis=-1)
+    z = 1.0 / (np.sqrt(m) * snew)
+    z = 1j * z
+    z = np.concatenate((z, np.conjugate(z)))
+
+    r = _arc_jac_sc1(1. / eps, ck1_sq)
+    v0 = capk * r / (N * val[0])
+
+    [sv, cv, dv, phi] = special.ellipj(v0, 1 - m)
+    p = -(c * d * sv * cv + 1j * s * dv) / (1 - (d * sv) ** 2.0)
+
+    if N % 2:
+        newp = np.compress(
+            abs(p.imag) > EPSILON * np.sqrt(np.sum(p * np.conjugate(p), axis=0).real),
+            p, axis=-1
+        )
+        p = np.concatenate((p, np.conjugate(newp)))
+    else:
+        p = np.concatenate((p, np.conjugate(p)))
+
+    k = (np.prod(-p, axis=0) / np.prod(-z, axis=0)).real
+    if N % 2 == 0:
+        k = k / np.sqrt(1 + eps_sq)
+
+    return (
+        xp.asarray(z, device=device, dtype=xp.complex128),
+        xp.asarray(p, device=device, dtype=xp.complex128), float(k)
+    )
+
+
+# TODO: Make this a real public function scipy.misc.ff
+def _falling_factorial(x, n):
+    r"""
+    Return the factorial of `x` to the `n` falling.
+
+    This is defined as:
+
+    .. math::   x^\underline n = (x)_n = x (x-1) \cdots (x-n+1)
+
+    This can more efficiently calculate ratios of factorials, since:
+
+    n!/m! == falling_factorial(n, n-m)
+
+    where n >= m
+
+    skipping the factors that cancel out
+
+    the usual factorial n! == ff(n, n)
+    """
+    val = 1
+    for k in range(x - n + 1, x + 1):
+        val *= k
+    return val
+
+
+def _bessel_poly(n, reverse=False):
+    """
+    Return the coefficients of Bessel polynomial of degree `n`
+
+    If `reverse` is true, a reverse Bessel polynomial is output.
+
+    Output is a list of coefficients:
+    [1]                   = 1
+    [1,  1]               = 1*s   +  1
+    [1,  3,  3]           = 1*s^2 +  3*s   +  3
+    [1,  6, 15, 15]       = 1*s^3 +  6*s^2 + 15*s   +  15
+    [1, 10, 45, 105, 105] = 1*s^4 + 10*s^3 + 45*s^2 + 105*s + 105
+    etc.
+
+    Output is a Python list of arbitrary precision long ints, so n is only
+    limited by your hardware's memory.
+
+    Sequence is http://oeis.org/A001498, and output can be confirmed to
+    match http://oeis.org/A001498/b001498.txt :
+
+    .. code_block:: python
+
+        from scipy.signal._filter_design import _bessel_poly
+        i = 0
+        for n in range(51):
+            for x in _bessel_poly(n, reverse=True):
+                print(i, x)
+                i += 1
+
+    """
+    if abs(int(n)) != n:
+        raise ValueError("Polynomial order must be a nonnegative integer")
+    else:
+        n = int(n)  # np.int32 doesn't work, for instance
+
+    out = []
+    for k in range(n + 1):
+        num = _falling_factorial(2*n - k, n)
+        den = 2**(n - k) * math.factorial(k)
+        out.append(num // den)
+
+    if reverse:
+        return out[::-1]
+    else:
+        return out
+
+
+def _campos_zeros(n):
+    """
+    Return approximate zero locations of Bessel polynomials y_n(x) for order
+    `n` using polynomial fit (Campos-Calderon 2011)
+    """
+    if n == 1:
+        return np.asarray([-1+0j])
+
+    s = npp_polyval(n, [0, 0, 2, 0, -3, 1])
+    b3 = npp_polyval(n, [16, -8]) / s
+    b2 = npp_polyval(n, [-24, -12, 12]) / s
+    b1 = npp_polyval(n, [8, 24, -12, -2]) / s
+    b0 = npp_polyval(n, [0, -6, 0, 5, -1]) / s
+
+    r = npp_polyval(n, [0, 0, 2, 1])
+    a1 = npp_polyval(n, [-6, -6]) / r
+    a2 = 6 / r
+
+    k = np.arange(1, n+1)
+    x = npp_polyval(k, [0, a1, a2])
+    y = npp_polyval(k, [b0, b1, b2, b3])
+
+    return x + 1j*y
+
+
+def _aberth(f, fp, x0, tol=1e-15, maxiter=50):
+    """
+    Given a function `f`, its first derivative `fp`, and a set of initial
+    guesses `x0`, simultaneously find the roots of the polynomial using the
+    Aberth-Ehrlich method.
+
+    ``len(x0)`` should equal the number of roots of `f`.
+
+    (This is not a complete implementation of Bini's algorithm.)
+    """
+
+    N = len(x0)
+
+    x = np.array(x0, complex)
+    beta = np.empty_like(x0)
+
+    for iteration in range(maxiter):
+        alpha = -f(x) / fp(x)  # Newton's method
+
+        # Model "repulsion" between zeros
+        for k in range(N):
+            beta[k] = np.sum(1/(x[k] - x[k+1:]))
+            beta[k] += np.sum(1/(x[k] - x[:k]))
+
+        x += alpha / (1 + alpha * beta)
+
+        if not all(np.isfinite(x)):
+            raise RuntimeError('Root-finding calculation failed')
+
+        # Mekwi: The iterative process can be stopped when |hn| has become
+        # less than the largest error one is willing to permit in the root.
+        if all(abs(alpha) <= tol):
+            break
+    else:
+        raise Exception('Zeros failed to converge')
+
+    return x
+
+
+def _bessel_zeros(N):
+    """
+    Find zeros of ordinary Bessel polynomial of order `N`, by root-finding of
+    modified Bessel function of the second kind
+    """
+    if N == 0:
+        return np.asarray([])
+
+    # Generate starting points
+    x0 = _campos_zeros(N)
+
+    # Zeros are the same for exp(1/x)*K_{N+0.5}(1/x) and Nth-order ordinary
+    # Bessel polynomial y_N(x)
+    def f(x):
+        return special.kve(N+0.5, 1/x)
+
+    # First derivative of above
+    def fp(x):
+        return (special.kve(N-0.5, 1/x)/(2*x**2) -
+                special.kve(N+0.5, 1/x)/(x**2) +
+                special.kve(N+1.5, 1/x)/(2*x**2))
+
+    # Starting points converge to true zeros
+    x = _aberth(f, fp, x0)
+
+    # Improve precision using Newton's method on each
+    for i in range(len(x)):
+        x[i] = optimize.newton(f, x[i], fp, tol=1e-15)
+
+    # Average complex conjugates to make them exactly symmetrical
+    x = np.mean((x, x[::-1].conj()), 0)
+
+    # Zeros should sum to -1
+    if abs(np.sum(x) + 1) > 1e-15:
+        raise RuntimeError('Generated zeros are inaccurate')
+
+    return x
+
+
+def _norm_factor(p, k):
+    """
+    Numerically find frequency shift to apply to delay-normalized filter such
+    that -3 dB point is at 1 rad/sec.
+
+    `p` is an array_like of polynomial poles
+    `k` is a float gain
+
+    First 10 values are listed in "Bessel Scale Factors" table,
+    "Bessel Filters Polynomials, Poles and Circuit Elements 2003, C. Bond."
+    """
+    p = np.asarray(p, dtype=np.complex128)
+
+    def G(w):
+        """
+        Gain of filter
+        """
+        return np.abs(k / np.prod(1j*w - p))
+
+    def cutoff(w):
+        """
+        When gain = -3 dB, return 0
+        """
+        return G(w) - 1/math.sqrt(2)
+
+    return optimize.newton(cutoff, 1.5)
+
+
+def besselap(N, norm='phase', *, xp=None, device=None):
+    """
+    Return (z,p,k) for analog prototype of an Nth-order Bessel filter.
+
+    Parameters
+    ----------
+    N : int
+        The order of the filter.
+    norm : {'phase', 'delay', 'mag'}, optional
+        Frequency normalization:
+
+        ``phase``
+            The filter is normalized such that the phase response reaches its
+            midpoint at an angular (e.g., rad/s) cutoff frequency of 1. This
+            happens for both low-pass and high-pass filters, so this is the
+            "phase-matched" case. [6]_
+
+            The magnitude response asymptotes are the same as a Butterworth
+            filter of the same order with a cutoff of `Wn`.
+
+            This is the default, and matches MATLAB's implementation.
+
+        ``delay``
+            The filter is normalized such that the group delay in the passband
+            is 1 (e.g., 1 second). This is the "natural" type obtained by
+            solving Bessel polynomials
+
+        ``mag``
+            The filter is normalized such that the gain magnitude is -3 dB at
+            angular frequency 1. This is called "frequency normalization" by
+            Bond. [1]_
+
+        .. versionadded:: 0.18.0
+
+    %(xp_device_snippet)s
+
+    Returns
+    -------
+    z : ndarray[float64]
+        Zeros of the transfer function. Is always an empty array.
+    p : ndarray[complex128]
+        Poles of the transfer function.
+    k : float
+        Gain of the transfer function. For phase-normalized, this is always 1.
+
+    See Also
+    --------
+    bessel : Filter design function using this prototype
+
+    Notes
+    -----
+    To find the pole locations, approximate starting points are generated [2]_
+    for the zeros of the ordinary Bessel polynomial [3]_, then the
+    Aberth-Ehrlich method [4]_ [5]_ is used on the Kv(x) Bessel function to
+    calculate more accurate zeros, and these locations are then inverted about
+    the unit circle.
+
+    References
+    ----------
+    .. [1] C.R. Bond, "Bessel Filter Constants",
+           http://www.crbond.com/papers/bsf.pdf
+    .. [2] Campos and Calderon, "Approximate closed-form formulas for the
+           zeros of the Bessel Polynomials", :arXiv:`1105.0957`.
+    .. [3] Thomson, W.E., "Delay Networks having Maximally Flat Frequency
+           Characteristics", Proceedings of the Institution of Electrical
+           Engineers, Part III, November 1949, Vol. 96, No. 44, pp. 487-490.
+    .. [4] Aberth, "Iteration Methods for Finding all Zeros of a Polynomial
+           Simultaneously", Mathematics of Computation, Vol. 27, No. 122,
+           April 1973
+    .. [5] Ehrlich, "A modified Newton method for polynomials", Communications
+           of the ACM, Vol. 10, Issue 2, pp. 107-108, Feb. 1967,
+           :doi:`10.1145/363067.363115`.
+    .. [6] Miller and Bohn, "A Bessel Filter Crossover, and Its Relation to
+           Others", RaneNote 147, 1998,
+           https://www.ranecommercial.com/legacy/note147.html
+
+    """
+    if xp is None:
+        xp = np_compat
+
+    if abs(int(N)) != N:
+        raise ValueError("Filter order must be a nonnegative integer")
+
+    N = int(N)  # calculation below doesn't always fit in np.int64
+    if N == 0:
+        p = []
+        k = 1
+    else:
+        # Find roots of reverse Bessel polynomial
+        p = 1/_bessel_zeros(N)
+
+        a_last = _falling_factorial(2*N, N) // 2**N
+
+        # Shift them to a different normalization if required
+        if norm in ('delay', 'mag'):
+            # Normalized for group delay of 1
+            k = a_last
+            if norm == 'mag':
+                # -3 dB magnitude point is at 1 rad/sec
+                norm_factor = _norm_factor(p, k)
+                p /= norm_factor
+                k = norm_factor**-N * a_last
+        elif norm == 'phase':
+            # Phase-matched (1/2 max phase shift at 1 rad/sec)
+            # Asymptotes are same as Butterworth filter
+            p *= 10**(-math.log10(a_last)/N)
+            k = 1
+        else:
+            raise ValueError('normalization not understood')
+
+    z = xp.asarray([], device=device, dtype=xp.float64)
+    return (
+        z,
+        xp.asarray(p, device=device, dtype=xp.complex128),
+        float(k)
+    )
+
+
+def iirnotch(w0, Q, fs=2.0, *, xp=None, device=None):
+    """
+    Design second-order IIR notch digital filter.
+
+    A notch filter is a band-stop filter with a narrow bandwidth
+    (high quality factor). It rejects a narrow frequency band and
+    leaves the rest of the spectrum little changed.
+
+    Parameters
+    ----------
+    w0 : float
+        Frequency to remove from a signal. If `fs` is specified, this is in
+        the same units as `fs`. By default, it is a normalized scalar that must
+        satisfy  ``0 < w0 < 1``, with ``w0 = 1`` corresponding to half of the
+        sampling frequency.
+    Q : float
+        Quality factor. Dimensionless parameter that characterizes
+        notch filter -3 dB bandwidth ``bw`` relative to its center
+        frequency, ``Q = w0/bw``.
+    fs : float, optional
+        The sampling frequency of the digital system.
+
+        .. versionadded:: 1.2.0
+
+    %(xp_device_snippet)s
+
+    Returns
+    -------
+    b, a : ndarray, ndarray
+        Numerator (``b``) and denominator (``a``) polynomials
+        of the IIR filter.
+
+    See Also
+    --------
+    iirpeak
+
+    Notes
+    -----
+    .. versionadded:: 0.19.0
+
+    References
+    ----------
+    .. [1] Sophocles J. Orfanidis, "Introduction To Signal Processing",
+           Prentice-Hall, 1996
+
+    Examples
+    --------
+    Design and plot filter to remove the 60 Hz component from a
+    signal sampled at 200 Hz, using a quality factor Q = 30
+
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+    >>> import numpy as np
+
+    >>> fs = 200.0  # Sample frequency (Hz)
+    >>> f0 = 60.0  # Frequency to be removed from signal (Hz)
+    >>> Q = 30.0  # Quality factor
+    >>> # Design notch filter
+    >>> b, a = signal.iirnotch(f0, Q, fs)
+
+    >>> # Frequency response
+    >>> freq, h = signal.freqz(b, a, fs=fs)
+    >>> # Plot
+    >>> fig, ax = plt.subplots(2, 1, figsize=(8, 6))
+    >>> ax[0].plot(freq, 20*np.log10(abs(h)), color='blue')
+    >>> ax[0].set_title("Frequency Response")
+    >>> ax[0].set_ylabel("Amplitude [dB]", color='blue')
+    >>> ax[0].set_xlim([0, 100])
+    >>> ax[0].set_ylim([-25, 10])
+    >>> ax[0].grid(True)
+    >>> ax[1].plot(freq, np.unwrap(np.angle(h))*180/np.pi, color='green')
+    >>> ax[1].set_ylabel("Phase [deg]", color='green')
+    >>> ax[1].set_xlabel("Frequency [Hz]")
+    >>> ax[1].set_xlim([0, 100])
+    >>> ax[1].set_yticks([-90, -60, -30, 0, 30, 60, 90])
+    >>> ax[1].set_ylim([-90, 90])
+    >>> ax[1].grid(True)
+    >>> plt.show()
+    """
+
+    return _design_notch_peak_filter(w0, Q, "notch", fs, xp=xp, device=device)
+
+
+def iirpeak(w0, Q, fs=2.0, *, xp=None, device=None):
+    """
+    Design second-order IIR peak (resonant) digital filter.
+
+    A peak filter is a band-pass filter with a narrow bandwidth
+    (high quality factor). It rejects components outside a narrow
+    frequency band.
+
+    Parameters
+    ----------
+    w0 : float
+        Frequency to be retained in a signal. If `fs` is specified, this is in
+        the same units as `fs`. By default, it is a normalized scalar that must
+        satisfy  ``0 < w0 < 1``, with ``w0 = 1`` corresponding to half of the
+        sampling frequency.
+    Q : float
+        Quality factor. Dimensionless parameter that characterizes
+        peak filter -3 dB bandwidth ``bw`` relative to its center
+        frequency, ``Q = w0/bw``.
+    fs : float, optional
+        The sampling frequency of the digital system.
+
+        .. versionadded:: 1.2.0
+
+    %(xp_device_snippet)s
+
+    Returns
+    -------
+    b, a : ndarray, ndarray
+        Numerator (``b``) and denominator (``a``) polynomials
+        of the IIR filter.
+
+    See Also
+    --------
+    iirnotch
+
+    Notes
+    -----
+    .. versionadded:: 0.19.0
+
+    References
+    ----------
+    .. [1] Sophocles J. Orfanidis, "Introduction To Signal Processing",
+           Prentice-Hall, 1996
+
+    Examples
+    --------
+    Design and plot filter to remove the frequencies other than the 300 Hz
+    component from a signal sampled at 1000 Hz, using a quality factor Q = 30
+
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+
+    >>> fs = 1000.0  # Sample frequency (Hz)
+    >>> f0 = 300.0  # Frequency to be retained (Hz)
+    >>> Q = 30.0  # Quality factor
+    >>> # Design peak filter
+    >>> b, a = signal.iirpeak(f0, Q, fs)
+
+    >>> # Frequency response
+    >>> freq, h = signal.freqz(b, a, fs=fs)
+    >>> # Plot
+    >>> fig, ax = plt.subplots(2, 1, figsize=(8, 6))
+    >>> ax[0].plot(freq, 20*np.log10(np.maximum(abs(h), 1e-5)), color='blue')
+    >>> ax[0].set_title("Frequency Response")
+    >>> ax[0].set_ylabel("Amplitude [dB]", color='blue')
+    >>> ax[0].set_xlim([0, 500])
+    >>> ax[0].set_ylim([-50, 10])
+    >>> ax[0].grid(True)
+    >>> ax[1].plot(freq, np.unwrap(np.angle(h))*180/np.pi, color='green')
+    >>> ax[1].set_ylabel("Phase [deg]", color='green')
+    >>> ax[1].set_xlabel("Frequency [Hz]")
+    >>> ax[1].set_xlim([0, 500])
+    >>> ax[1].set_yticks([-90, -60, -30, 0, 30, 60, 90])
+    >>> ax[1].set_ylim([-90, 90])
+    >>> ax[1].grid(True)
+    >>> plt.show()
+    """
+
+    return _design_notch_peak_filter(w0, Q, "peak", fs, xp=xp, device=device)
+
+
+def _design_notch_peak_filter(w0, Q, ftype, fs=2.0, *, xp=None, device=None):
+    """
+    Design notch or peak digital filter.
+
+    Parameters
+    ----------
+    w0 : float
+        Normalized frequency to remove from a signal. If `fs` is specified,
+        this is in the same units as `fs`. By default, it is a normalized
+        scalar that must satisfy  ``0 < w0 < 1``, with ``w0 = 1``
+        corresponding to half of the sampling frequency.
+    Q : float
+        Quality factor. Dimensionless parameter that characterizes
+        notch filter -3 dB bandwidth ``bw`` relative to its center
+        frequency, ``Q = w0/bw``.
+    ftype : str
+        The type of IIR filter to design:
+
+            - notch filter : ``notch``
+            - peak filter  : ``peak``
+    fs : float, optional
+        The sampling frequency of the digital system.
+
+        .. versionadded:: 1.2.0:
+
+    Returns
+    -------
+    b, a : ndarray, ndarray
+        Numerator (``b``) and denominator (``a``) polynomials
+        of the IIR filter.
+    """
+    if xp is None:
+        xp = np_compat
+
+    fs = _validate_fs(fs, allow_none=False)
+
+    # Guarantee that the inputs are floats
+    w0 = float(w0)
+    Q = float(Q)
+    w0 = 2 * w0 / fs
+
+    # Checks if w0 is within the range
+    if w0 > 1.0 or w0 < 0.0:
+        raise ValueError("w0 should be such that 0 < w0 < 1")
+
+    # Get bandwidth
+    bw = w0/Q
+
+    # Normalize inputs
+    bw = bw * xp.pi
+    w0 = w0 * xp.pi
+
+    if ftype not in ("notch", "peak"):
+        raise ValueError("Unknown ftype.")
+
+    # Compute beta according to Eqs. 11.3.4 (p.575) and 11.3.19 (p.579) from
+    # reference [1]. Due to assuming a -3 dB attenuation value, i.e, assuming
+    # gb = 1 / np.sqrt(2), the following terms simplify to:
+    #   (np.sqrt(1.0 - gb**2.0) / gb) = 1
+    #   (gb / np.sqrt(1.0 - gb**2.0)) = 1
+    beta = math.tan(bw / 2.0)
+
+    # Compute gain: formula 11.3.6 (p.575) from reference [1]
+    gain = 1.0 / (1.0 + beta)
+
+    # Compute numerator b and denominator a
+    # formulas 11.3.7 (p.575) and 11.3.21 (p.579)
+    # from reference [1]
+    if ftype == "notch":
+        b = gain * xp.asarray([1.0, -2.0*math.cos(w0), 1.0], device=device)
+    else:
+        b = (1.0 - gain) * xp.asarray([1.0, 0.0, -1.0], device=device)
+    a = xp.asarray([1.0, -2.0 * gain * math.cos(w0), (2.0*gain - 1.0)], device=device)
+
+    return b, a
+
+
+def iircomb(w0, Q, ftype='notch', fs=2.0, *, pass_zero=False, xp=None, device=None):
+    """
+    Design IIR notching or peaking digital comb filter.
+
+    A notching comb filter consists of regularly-spaced band-stop filters with
+    a narrow bandwidth (high quality factor). Each rejects a narrow frequency
+    band and leaves the rest of the spectrum little changed.
+
+    A peaking comb filter consists of regularly-spaced band-pass filters with
+    a narrow bandwidth (high quality factor). Each rejects components outside
+    a narrow frequency band.
+
+    Parameters
+    ----------
+    w0 : float
+        The fundamental frequency of the comb filter (the spacing between its
+        peaks). This must evenly divide the sampling frequency. If `fs` is
+        specified, this is in the same units as `fs`. By default, it is
+        a normalized scalar that must satisfy  ``0 < w0 < 1``, with
+        ``w0 = 1`` corresponding to half of the sampling frequency.
+    Q : float
+        Quality factor. Dimensionless parameter that characterizes
+        notch filter -3 dB bandwidth ``bw`` relative to its center
+        frequency, ``Q = w0/bw``.
+    ftype : {'notch', 'peak'}
+        The type of comb filter generated by the function. If 'notch', then
+        the Q factor applies to the notches. If 'peak', then the `Q` factor
+        applies to the peaks.  Default is 'notch'.
+    fs : float, optional
+        The sampling frequency of the signal. Default is 2.0.
+    pass_zero : bool, optional
+        If False (default), the notches (nulls) of the filter are centered on
+        frequencies ``[0, w0, 2*w0, ...]``, and the peaks are centered on the
+        midpoints ``[w0/2, 3*w0/2, 5*w0/2, ...]``.  If True, the peaks are centered
+        on ``[0, w0, 2*w0, ...]`` (passing zero frequency) and vice versa.
+
+        .. versionadded:: 1.9.0
+
+    %(xp_device_snippet)s
+
+    Returns
+    -------
+    b, a : ndarray, ndarray
+        Numerator (``b``) and denominator (``a``) polynomials
+        of the IIR filter.
+
+    Raises
+    ------
+    ValueError
+        If `w0` is less than or equal to 0 or greater than or equal to
+        ``fs/2``, if `fs` is not divisible by `w0`, if `ftype`
+        is not 'notch' or 'peak'
+
+    See Also
+    --------
+    iirnotch
+    iirpeak
+
+    Notes
+    -----
+    For implementation details, see [1]_. The TF implementation of the
+    comb filter is numerically stable even at higher orders due to the
+    use of a single repeated pole, which won't suffer from precision loss.
+
+    References
+    ----------
+    .. [1] Sophocles J. Orfanidis, "Introduction To Signal Processing",
+           Prentice-Hall, 1996, ch. 11, "Digital Filter Design"
+
+    Examples
+    --------
+    Design and plot notching comb filter at 20 Hz for a
+    signal sampled at 200 Hz, using quality factor Q = 30
+
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+    >>> import numpy as np
+
+    >>> fs = 200.0  # Sample frequency (Hz)
+    >>> f0 = 20.0  # Frequency to be removed from signal (Hz)
+    >>> Q = 30.0  # Quality factor
+    >>> # Design notching comb filter
+    >>> b, a = signal.iircomb(f0, Q, ftype='notch', fs=fs)
+
+    >>> # Frequency response
+    >>> freq, h = signal.freqz(b, a, fs=fs)
+    >>> response = abs(h)
+    >>> # To avoid divide by zero when graphing
+    >>> response[response == 0] = 1e-20
+    >>> # Plot
+    >>> fig, ax = plt.subplots(2, 1, figsize=(8, 6), sharex=True)
+    >>> ax[0].plot(freq, 20*np.log10(abs(response)), color='blue')
+    >>> ax[0].set_title("Frequency Response")
+    >>> ax[0].set_ylabel("Amplitude [dB]", color='blue')
+    >>> ax[0].set_xlim([0, 100])
+    >>> ax[0].set_ylim([-30, 10])
+    >>> ax[0].grid(True)
+    >>> ax[1].plot(freq, np.mod(np.angle(h, deg=True) + 180, 360) - 180, color='green')
+    >>> ax[1].set_ylabel("Phase [deg]", color='green')
+    >>> ax[1].set_xlabel("Frequency [Hz]")
+    >>> ax[1].set_xlim([0, 100])
+    >>> ax[1].set_yticks([-90, -60, -30, 0, 30, 60, 90])
+    >>> ax[1].set_ylim([-90, 90])
+    >>> ax[1].grid(True)
+    >>> plt.show()
+
+    Design and plot peaking comb filter at 250 Hz for a
+    signal sampled at 1000 Hz, using quality factor Q = 30
+
+    >>> fs = 1000.0  # Sample frequency (Hz)
+    >>> f0 = 250.0  # Frequency to be retained (Hz)
+    >>> Q = 30.0  # Quality factor
+    >>> # Design peaking filter
+    >>> b, a = signal.iircomb(f0, Q, ftype='peak', fs=fs, pass_zero=True)
+
+    >>> # Frequency response
+    >>> freq, h = signal.freqz(b, a, fs=fs)
+    >>> response = abs(h)
+    >>> # To avoid divide by zero when graphing
+    >>> response[response == 0] = 1e-20
+    >>> # Plot
+    >>> fig, ax = plt.subplots(2, 1, figsize=(8, 6), sharex=True)
+    >>> ax[0].plot(freq, 20*np.log10(np.maximum(abs(h), 1e-5)), color='blue')
+    >>> ax[0].set_title("Frequency Response")
+    >>> ax[0].set_ylabel("Amplitude [dB]", color='blue')
+    >>> ax[0].set_xlim([0, 500])
+    >>> ax[0].set_ylim([-80, 10])
+    >>> ax[0].grid(True)
+    >>> ax[1].plot(freq, np.mod(np.angle(h)*180/np.pi + 180, 360) - 180, color='green')
+    >>> ax[1].set_ylabel("Phase [deg]", color='green')
+    >>> ax[1].set_xlabel("Frequency [Hz]")
+    >>> ax[1].set_xlim([0, 500])
+    >>> ax[1].set_yticks([-90, -60, -30, 0, 30, 60, 90])
+    >>> ax[1].set_ylim([-90, 90])
+    >>> ax[1].grid(True)
+    >>> plt.show()
+    """
+    if xp is None:
+        xp = np_compat
+
+    # Convert w0, Q, and fs to float
+    w0 = float(w0)
+    Q = float(Q)
+    fs = _validate_fs(fs, allow_none=False)
+
+    # Check for invalid cutoff frequency or filter type
+    ftype = ftype.lower()
+    if not 0 < w0 < fs / 2:
+        raise ValueError(f"w0 must be between 0 and {fs / 2}"
+                         f" (Nyquist), but given {w0}.")
+    if ftype not in ('notch', 'peak'):
+        raise ValueError('ftype must be either notch or peak.')
+
+    # Compute the order of the filter
+    N = round(fs / w0)
+
+    # Check for cutoff frequency divisibility
+    if abs(w0 - fs/N)/fs > 1e-14:
+        raise ValueError('fs must be divisible by w0.')
+
+    # Compute frequency in radians and filter bandwidth
+    # Eq. 11.3.1 (p. 574) from reference [1]
+    w0 = (2 * xp.pi * w0) / fs
+    w_delta = w0 / Q
+
+    # Define base gain values depending on notch or peak filter
+    # Compute -3dB attenuation
+    # Eqs. 11.4.1 and 11.4.2 (p. 582) from reference [1]
+    if ftype == 'notch':
+        G0, G = 1, 0
+    elif ftype == 'peak':
+        G0, G = 0, 1
+
+    # Compute beta according to Eq. 11.5.3 (p. 591) from reference [1]. Due to
+    # assuming a -3 dB attenuation value, i.e, assuming GB = 1 / np.sqrt(2),
+    # the following term simplifies to:
+    #   np.sqrt((GB**2 - G0**2) / (G**2 - GB**2)) = 1
+    beta = math.tan(N * w_delta / 4)
+
+    # Compute filter coefficients
+    # Eq 11.5.1 (p. 590) variables a, b, c from reference [1]
+    ax = (1 - beta) / (1 + beta)
+    bx = (G0 + G * beta) / (1 + beta)
+    cx = (G0 - G * beta) / (1 + beta)
+
+    # Last coefficients are negative to get peaking comb that passes zero or
+    # notching comb that doesn't.
+    negative_coef = ((ftype == 'peak' and pass_zero) or
+                     (ftype == 'notch' and not pass_zero))
+
+    # Compute numerator coefficients
+    # Eq 11.5.1 (p. 590) or Eq 11.5.4 (p. 591) from reference [1]
+    # b - cz^-N or b + cz^-N
+    b = xp.zeros(N + 1, device=device)
+    sgn = -1. if negative_coef else 1
+    xpx.at(b, 0).set(bx)
+    xpx.at(b, -1).set(sgn * cx)
+
+    # Compute denominator coefficients
+    # Eq 11.5.1 (p. 590) or Eq 11.5.4 (p. 591) from reference [1]
+    # 1 - az^-N or 1 + az^-N
+    a = xp.zeros(N + 1, device=device)
+    xpx.at(a, 0).set(1.)
+    xpx.at(a, -1).set(sgn * ax)
+
+    return b, a
+
+
+def _hz_to_erb(hz):
+    """
+    Utility for converting from frequency (Hz) to the
+    Equivalent Rectangular Bandwidth (ERB) scale
+    ERB = frequency / EarQ + minBW
+    """
+    EarQ = 9.26449
+    minBW = 24.7
+    return hz / EarQ + minBW
+
+
+def gammatone(freq, ftype, order=None, numtaps=None, fs=None, *, xp=None, device=None):
+    """
+    Gammatone filter design.
+
+    This function computes the coefficients of an FIR or IIR gammatone
+    digital filter [1]_.
+
+    Parameters
+    ----------
+    freq : float
+        Center frequency of the filter (expressed in the same units
+        as `fs`).
+    ftype : {'fir', 'iir'}
+        The type of filter the function generates. If 'fir', the function
+        will generate an Nth order FIR gammatone filter. If 'iir', the
+        function will generate an 8th order digital IIR filter, modeled as
+        as 4th order gammatone filter.
+    order : int, optional
+        The order of the filter. Only used when ``ftype='fir'``.
+        Default is 4 to model the human auditory system. Must be between
+        0 and 24.
+    numtaps : int, optional
+        Length of the filter. Only used when ``ftype='fir'``.
+        Default is ``fs*0.015`` if `fs` is greater than 1000,
+        15 if `fs` is less than or equal to 1000.
+    fs : float, optional
+        The sampling frequency of the signal. `freq` must be between
+        0 and ``fs/2``. Default is 2.
+    %(xp_device_snippet)s
+
+    Returns
+    -------
+    b, a : ndarray, ndarray
+        Numerator (``b``) and denominator (``a``) polynomials of the filter.
+
+    Raises
+    ------
+    ValueError
+        If `freq` is less than or equal to 0 or greater than or equal to
+        ``fs/2``, if `ftype` is not 'fir' or 'iir', if `order` is less than
+        or equal to 0 or greater than 24 when ``ftype='fir'``
+
+    See Also
+    --------
+    firwin
+    iirfilter
+
+    References
+    ----------
+    .. [1] Slaney, Malcolm, "An Efficient Implementation of the
+        Patterson-Holdsworth Auditory Filter Bank", Apple Computer
+        Technical Report 35, 1993, pp.3-8, 34-39.
+
+    Examples
+    --------
+    16-sample 4th order FIR Gammatone filter centered at 440 Hz
+
+    >>> from scipy import signal
+    >>> signal.gammatone(440, 'fir', numtaps=16, fs=16000)
+    (array([ 0.00000000e+00,  2.22196719e-07,  1.64942101e-06,  4.99298227e-06,
+        1.01993969e-05,  1.63125770e-05,  2.14648940e-05,  2.29947263e-05,
+        1.76776931e-05,  2.04980537e-06, -2.72062858e-05, -7.28455299e-05,
+       -1.36651076e-04, -2.19066855e-04, -3.18905076e-04, -4.33156712e-04]),
+       [1.0])
+
+    IIR Gammatone filter centered at 440 Hz
+
+    >>> import matplotlib.pyplot as plt
+    >>> import numpy as np
+
+    >>> fc, fs = 440, 16000
+    >>> b, a = signal.gammatone(fc, 'iir', fs=fs)
+    >>> w, h = signal.freqz(b, a)
+    >>> plt.plot(w * fs / (2 * np.pi), 20 * np.log10(abs(h)))
+    >>> plt.xscale('log')
+    >>> plt.title('Gammatone filter frequency response')
+    >>> plt.xlabel('Frequency [Hz]')
+    >>> plt.ylabel('Amplitude [dB]')
+    >>> plt.margins(0, 0.1)
+    >>> plt.grid(which='both', axis='both')
+    >>> plt.axvline(fc, color='green') # cutoff frequency
+    >>> plt.show()
+    """
+    if xp is None:
+        xp = np_compat
+
+    # Converts freq to float
+    freq = float(freq)
+
+    # Set sampling rate if not passed
+    if fs is None:
+        fs = 2
+    fs = _validate_fs(fs, allow_none=False)
+
+    # Check for invalid cutoff frequency or filter type
+    ftype = ftype.lower()
+    filter_types = ['fir', 'iir']
+    if not 0 < freq < fs / 2:
+        raise ValueError(f"The frequency must be between 0 and {fs / 2}"
+                         f" (Nyquist), but given {freq}.")
+    if ftype not in filter_types:
+        raise ValueError('ftype must be either fir or iir.')
+
+    # Calculate FIR gammatone filter
+    if ftype == 'fir':
+        # Set order and numtaps if not passed
+        if order is None:
+            order = 4
+        order = operator.index(order)
+
+        if numtaps is None:
+            numtaps = max(int(fs * 0.015), 15)
+        numtaps = operator.index(numtaps)
+
+        # Check for invalid order
+        if not 0 < order <= 24:
+            raise ValueError("Invalid order: order must be > 0 and <= 24.")
+
+        # Gammatone impulse response settings
+        t = xp.arange(numtaps, device=device, dtype=xp_default_dtype(xp)) / fs
+        bw = 1.019 * _hz_to_erb(freq)
+
+        # Calculate the FIR gammatone filter
+        b = (t ** (order - 1)) * xp.exp(-2 * xp.pi * bw * t)
+        b = b * xp.cos(2 * xp.pi * freq * t)
+
+        # Scale the FIR filter so the frequency response is 1 at cutoff
+        scale_factor = 2 * (2 * xp.pi * bw) ** (order)
+        scale_factor /= float_factorial(order - 1)
+        scale_factor /= fs
+        b = b * scale_factor
+        a = xp.asarray([1.0], device=device)
+
+    # Calculate IIR gammatone filter
+    elif ftype == 'iir':
+        # Raise warning if order and/or numtaps is passed
+        if order is not None:
+            warnings.warn('order is not used for IIR gammatone filter.', stacklevel=2)
+        if numtaps is not None:
+            warnings.warn('numtaps is not used for IIR gammatone filter.', stacklevel=2)
+
+        # Gammatone impulse response settings
+        T = 1./fs
+        bw = 2 * math.pi * 1.019 * _hz_to_erb(freq)
+        fr = 2 * freq * math.pi * T
+        bwT = bw * T
+
+        # Calculate the gain to normalize the volume at the center frequency
+        g1 = -2 * cmath.exp(2j * fr) * T
+        g2 = 2 * cmath.exp(-(bwT) + 1j * fr) * T
+        g3 = math.sqrt(3 + 2 ** (3 / 2)) * math.sin(fr)
+        g4 = math.sqrt(3 - 2 ** (3 / 2)) * math.sin(fr)
+        g5 = cmath.exp(2j * fr)
+
+        g = g1 + g2 * (math.cos(fr) - g4)
+        g *= (g1 + g2 * (math.cos(fr) + g4))
+        g *= (g1 + g2 * (math.cos(fr) - g3))
+        g *= (g1 + g2 * (math.cos(fr) + g3))
+        g /= ((-2 / math.exp(2 * bwT) - 2 * g5 + 2 * (1 + g5) / math.exp(bwT)) ** 4)
+        g = math.hypot(g.real, g.imag)
+
+        # Create empty filter coefficient lists
+        b = [None] * 5  #np.empty(5)
+        a = [None] * 9  # np.empty(9)
+
+        # Calculate the numerator coefficients
+        b[0] = (T ** 4) / g
+        b[1] = -4 * T ** 4 * math.cos(fr) / math.exp(bw * T) / g
+        b[2] = 6 * T ** 4 * math.cos(2 * fr) / math.exp(2 * bw * T) / g
+        b[3] = -4 * T ** 4 * math.cos(3 * fr) / math.exp(3 * bw * T) / g
+        b[4] = T ** 4 * math.cos(4 * fr) / math.exp(4 * bw * T) / g
+
+        # Calculate the denominator coefficients
+        a[0] = 1
+        a[1] = -8 * math.cos(fr) / math.exp(bw * T)
+        a[2] = 4 * (4 + 3 * math.cos(2 * fr)) / math.exp(2 * bw * T)
+        a[3] = -8 * (6 * math.cos(fr) + math.cos(3 * fr))
+        a[3] /= math.exp(3 * bw * T)
+        a[4] = 2 * (18 + 16 * math.cos(2 * fr) + math.cos(4 * fr))
+        a[4] /= math.exp(4 * bw * T)
+        a[5] = -8 * (6 * math.cos(fr) + math.cos(3 * fr))
+        a[5] /= math.exp(5 * bw * T)
+        a[6] = 4 * (4 + 3 * math.cos(2 * fr)) / math.exp(6 * bw * T)
+        a[7] = -8 * math.cos(fr) / math.exp(7 * bw * T)
+        a[8] = math.exp(-8 * bw * T)
+
+    return xp.asarray(b, device=device), xp.asarray(a, device=device)
+
+
+filter_dict = {'butter': [buttap, buttord],
+               'butterworth': [buttap, buttord],
+
+               'cauer': [ellipap, ellipord],
+               'elliptic': [ellipap, ellipord],
+               'ellip': [ellipap, ellipord],
+
+               'bessel': [besselap],
+               'bessel_phase': [besselap],
+               'bessel_delay': [besselap],
+               'bessel_mag': [besselap],
+
+               'cheby1': [cheb1ap, cheb1ord],
+               'chebyshev1': [cheb1ap, cheb1ord],
+               'chebyshevi': [cheb1ap, cheb1ord],
+
+               'cheby2': [cheb2ap, cheb2ord],
+               'chebyshev2': [cheb2ap, cheb2ord],
+               'chebyshevii': [cheb2ap, cheb2ord],
+               }
+
+band_dict = {'band': 'bandpass',
+             'bandpass': 'bandpass',
+             'pass': 'bandpass',
+             'bp': 'bandpass',
+
+             'bs': 'bandstop',
+             'bandstop': 'bandstop',
+             'bands': 'bandstop',
+             'stop': 'bandstop',
+
+             'l': 'lowpass',
+             'low': 'lowpass',
+             'lowpass': 'lowpass',
+             'lp': 'lowpass',
+
+             'high': 'highpass',
+             'highpass': 'highpass',
+             'h': 'highpass',
+             'hp': 'highpass',
+             }
+
+bessel_norms = {'bessel': 'phase',
+                'bessel_phase': 'phase',
+                'bessel_delay': 'delay',
+                'bessel_mag': 'mag'}
+
+
+########## complete the docstrings, on import
+_xp_device_snippet = {'xp_device_snippet':
+"""\
+xp : array_namespace, optional
+    Optional array namespace.
+    Should be compatible with the array API standard, or supported by array-api-compat.
+    Default: ``numpy``
+device : any
+    optional device specification for output. Should match one of the
+    supported device specification in ``xp``.
+"""
+}
+
+
+_names = ["buttap", "cheb1ap", "cheb2ap", "ellipap", "besselap",
+          "iirnotch", "iirpeak", "iircomb", "gammatone",
+]
+for name in _names:
+    window = vars()[name]
+    window.__doc__ = doccer.docformat(window.__doc__, _xp_device_snippet)
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/_fir_filter_design.py b/venv/lib/python3.12/site-packages/scipy/signal/_fir_filter_design.py
new file mode 100644
index 0000000000000000000000000000000000000000..23d229c323d85bec7d796a66009a416251e68d1d
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/_fir_filter_design.py
@@ -0,0 +1,1553 @@
+"""Functions for FIR filter design."""
+
+from math import ceil, log, log2
+import warnings
+from typing import Literal
+
+import numpy as np
+from scipy.fft import irfft, fft, ifft
+from scipy.linalg import (toeplitz, hankel, solve, LinAlgError, LinAlgWarning,
+                          lstsq)
+from scipy.signal._arraytools import _validate_fs
+from .windows import get_window
+from . import _sigtools
+
+from scipy._lib._array_api import array_namespace, xp_size, xp_default_dtype
+import scipy._external.array_api_extra as xpx
+
+
+__all__ = ['kaiser_beta', 'kaiser_atten', 'kaiserord',
+           'firwin', 'firwin2', 'firwin_2d', 'remez', 'firls', 'minimum_phase']
+
+
+# Some notes on function parameters:
+#
+# `cutoff` and `width` are given as numbers between 0 and 1.  These are
+# relative frequencies, expressed as a fraction of the Nyquist frequency.
+# For example, if the Nyquist frequency is 2 KHz, then width=0.15 is a width
+# of 300 Hz.
+#
+# The `order` of a FIR filter is one less than the number of taps.
+# This is a potential source of confusion, so in the following code,
+# we will always use the number of taps as the parameterization of
+# the 'size' of the filter. The "number of taps" means the number
+# of coefficients, which is the same as the length of the impulse
+# response of the filter.
+
+
+def kaiser_beta(a):
+    """Compute the Kaiser parameter `beta`, given the attenuation `a`.
+
+    Parameters
+    ----------
+    a : float
+        The desired attenuation in the stopband and maximum ripple in
+        the passband, in dB.  This should be a *positive* number.
+
+    Returns
+    -------
+    beta : float
+        The `beta` parameter to be used in the formula for a Kaiser window.
+
+    References
+    ----------
+    Oppenheim, Schafer, "Discrete-Time Signal Processing", p.475-476.
+
+    Examples
+    --------
+    Suppose we want to design a lowpass filter, with 65 dB attenuation
+    in the stop band.  The Kaiser window parameter to be used in the
+    window method is computed by ``kaiser_beta(65)``:
+
+    >>> from scipy.signal import kaiser_beta
+    >>> kaiser_beta(65)
+    6.20426
+
+    """
+    if a > 50:
+        beta = 0.1102 * (a - 8.7)
+    elif a > 21:
+        beta = 0.5842 * (a - 21) ** 0.4 + 0.07886 * (a - 21)
+    else:
+        beta = 0.0
+    return beta
+
+
+def kaiser_atten(numtaps, width):
+    """Compute the attenuation of a Kaiser FIR filter.
+
+    Given the number of taps `N` and the transition width `width`, compute the
+    attenuation `a` in dB, given by Kaiser's formula:
+
+        a = 2.285 * (N - 1) * pi * width + 7.95
+
+    Parameters
+    ----------
+    numtaps : int
+        The number of taps in the FIR filter.
+    width : float
+        The desired width of the transition region between passband and
+        stopband (or, in general, at any discontinuity) for the filter,
+        expressed as a fraction of the Nyquist frequency.
+
+    Returns
+    -------
+    a : float
+        The attenuation of the ripple, in dB.
+
+    See Also
+    --------
+    kaiserord, kaiser_beta
+
+    Examples
+    --------
+    Suppose we want to design a FIR filter using the Kaiser window method
+    that will have 211 taps and a transition width of 9 Hz for a signal that
+    is sampled at 480 Hz. Expressed as a fraction of the Nyquist frequency,
+    the width is 9/(0.5*480) = 0.0375. The approximate attenuation (in dB)
+    is computed as follows:
+
+    >>> from scipy.signal import kaiser_atten
+    >>> kaiser_atten(211, 0.0375)
+    64.48099630593983
+
+    """
+    a = 2.285 * (numtaps - 1) * np.pi * width + 7.95
+    return a
+
+
+def kaiserord(ripple, width):
+    """
+    Determine the filter window parameters for the Kaiser window method.
+
+    The parameters returned by this function are generally used to create
+    a finite impulse response filter using the window method, with either
+    `firwin` or `firwin2`.
+
+    Parameters
+    ----------
+    ripple : float
+        Upper bound for the deviation (in dB) of the magnitude of the
+        filter's frequency response from that of the desired filter (not
+        including frequencies in any transition intervals). That is, if w
+        is the frequency expressed as a fraction of the Nyquist frequency,
+        A(w) is the actual frequency response of the filter and D(w) is the
+        desired frequency response, the design requirement is that::
+
+            abs(A(w) - D(w))) < 10**(-ripple/20)
+
+        for 0 <= w <= 1 and w not in a transition interval.
+    width : float
+        Width of transition region, normalized so that 1 corresponds to pi
+        radians / sample. That is, the frequency is expressed as a fraction
+        of the Nyquist frequency.
+
+    Returns
+    -------
+    numtaps : int
+        The length of the Kaiser window.
+    beta : float
+        The beta parameter for the Kaiser window.
+
+    See Also
+    --------
+    kaiser_beta, kaiser_atten
+
+    Notes
+    -----
+    There are several ways to obtain the Kaiser window:
+
+    - ``signal.windows.kaiser(numtaps, beta, sym=True)``
+    - ``signal.get_window(beta, numtaps)``
+    - ``signal.get_window(('kaiser', beta), numtaps)``
+
+    The empirical equations discovered by Kaiser are used.
+
+    References
+    ----------
+    Oppenheim, Schafer, "Discrete-Time Signal Processing", pp.475-476.
+
+    Examples
+    --------
+    We will use the Kaiser window method to design a lowpass FIR filter
+    for a signal that is sampled at 1000 Hz.
+
+    We want at least 65 dB rejection in the stop band, and in the pass
+    band the gain should vary no more than 0.5%.
+
+    We want a cutoff frequency of 175 Hz, with a transition between the
+    pass band and the stop band of 24 Hz. That is, in the band [0, 163],
+    the gain varies no more than 0.5%, and in the band [187, 500], the
+    signal is attenuated by at least 65 dB.
+
+    >>> import numpy as np
+    >>> from scipy.signal import kaiserord, firwin, freqz
+    >>> import matplotlib.pyplot as plt
+    >>> fs = 1000.0
+    >>> cutoff = 175
+    >>> width = 24
+
+    The Kaiser method accepts just a single parameter to control the pass
+    band ripple and the stop band rejection, so we use the more restrictive
+    of the two. In this case, the pass band ripple is 0.005, or 46.02 dB,
+    so we will use 65 dB as the design parameter.
+
+    Use `kaiserord` to determine the length of the filter and the
+    parameter for the Kaiser window.
+
+    >>> numtaps, beta = kaiserord(65, width/(0.5*fs))
+    >>> numtaps
+    167
+    >>> beta
+    6.20426
+
+    Use `firwin` to create the FIR filter.
+
+    >>> taps = firwin(numtaps, cutoff, window=('kaiser', beta),
+    ...               scale=False, fs=fs)
+
+    Compute the frequency response of the filter.  ``w`` is the array of
+    frequencies, and ``h`` is the corresponding complex array of frequency
+    responses.
+
+    >>> w, h = freqz(taps, worN=8000)
+    >>> w *= 0.5*fs/np.pi  # Convert w to Hz.
+
+    Compute the deviation of the magnitude of the filter's response from
+    that of the ideal lowpass filter. Values in the transition region are
+    set to ``nan``, so they won't appear in the plot.
+
+    >>> ideal = w < cutoff  # The "ideal" frequency response.
+    >>> deviation = np.abs(np.abs(h) - ideal)
+    >>> deviation[(w > cutoff - 0.5*width) & (w < cutoff + 0.5*width)] = np.nan
+
+    Plot the deviation. A close look at the left end of the stop band shows
+    that the requirement for 65 dB attenuation is violated in the first lobe
+    by about 0.125 dB. This is not unusual for the Kaiser window method.
+
+    >>> plt.plot(w, 20*np.log10(np.abs(deviation)))
+    >>> plt.xlim(0, 0.5*fs)
+    >>> plt.ylim(-90, -60)
+    >>> plt.grid(alpha=0.25)
+    >>> plt.axhline(-65, color='r', ls='--', alpha=0.3)
+    >>> plt.xlabel('Frequency (Hz)')
+    >>> plt.ylabel('Deviation from ideal (dB)')
+    >>> plt.title('Lowpass Filter Frequency Response')
+    >>> plt.show()
+
+    """
+    A = abs(ripple)  # in case somebody is confused as to what's meant
+    if A < 8:
+        # Formula for N is not valid in this range.
+        raise ValueError("Requested maximum ripple attenuation "
+                         f"{A:f} is too small for the Kaiser formula.")
+    beta = kaiser_beta(A)
+
+    # Kaiser's formula (as given in Oppenheim and Schafer) is for the filter
+    # order, so we have to add 1 to get the number of taps.
+    numtaps = (A - 7.95) / 2.285 / (np.pi * width) + 1
+
+    return int(ceil(numtaps)), beta
+
+
+def firwin(numtaps, cutoff, *, width=None, window='hamming', pass_zero=True,
+           scale=True, fs=None):
+    r"""FIR filter design using the window method.
+
+    This function computes the coefficients of a finite impulse response
+    filter. The filter will have linear phase; it will be Type I if
+    `numtaps` is odd and Type II if `numtaps` is even.
+
+    Type II filters always have zero response at the Nyquist frequency, so a
+    ValueError exception is raised if firwin is called with `numtaps` even and
+    having a passband whose right end is at the Nyquist frequency.
+
+    Parameters
+    ----------
+    numtaps : int
+        Length of the filter (number of coefficients, i.e., the filter
+        order + 1).  `numtaps` must be odd if a passband includes the
+        Nyquist frequency.
+    cutoff : float or 1-D array_like
+        Cutoff frequency of filter (expressed in the same units as `fs`)
+        or an array of cutoff frequencies (that is, band edges). In the
+        former case, as a float, the cutoff frequency should correspond
+        with the half-amplitude point, where the attenuation will be -6 dB.
+        In the latter case, the frequencies in `cutoff` should be positive
+        and monotonically increasing between 0 and `fs/2`. The values 0
+        and `fs/2` must not be included in `cutoff`. It should be noted
+        that this is different from the behavior of `~scipy.signal.iirdesign`,
+        where the cutoff is the half-power point (-3 dB).
+    width : float or None, optional
+        If not ``None``, then a `~scipy.signal.windows.kaiser` window is calculated
+        where `width` specifies the approximate width of the transition region
+        (expressed in the same unit as `fs`). This is achieved by utilizing
+        `~scipy.signal.kaiser_atten` to calculate an attenuation which is passed to
+        `~scipy.signal.kaiser_beta` for determining the β parameter for the kaiser
+        window. In this case, the `window` argument is ignored.
+    window : str or tuple of str and parameter values, optional
+        Desired window to use. Default is ``'hamming'``. The window will be symmetric,
+        unless a suffix ``'_periodic'`` is appended to the window name (e.g.,
+        ``'hamming_perodic'``) Consult `~scipy.signal.get_window` for a list of windows
+        and required parameters.
+    pass_zero : {True, False, 'bandpass', 'lowpass', 'highpass', 'bandstop'}, optional
+        Toggles the zero frequency bin (or DC gain) to be in the passband (``True``) or
+        in the stopband (``False``).  ``'bandstop'``, ``'lowpass'`` are synonyms for
+        ``True`` and ``'bandpass'``, ``'highpass'`` are synonyms for ``False``.
+        ``'lowpass'``, ``'highpass'`` additionally require `cutoff` to be a scalar
+        value or a length-one array. Default: ``True``.
+
+        .. versionadded:: 1.3.0
+           Support for string arguments.
+    scale : bool, optional
+        Set to ``True`` to scale the coefficients so that the frequency response is
+        exactly unity at a certain frequency. That frequency is either:
+
+        - 0 (DC) if the first passband starts at 0 (i.e., `pass_zero` is ``True``)
+        - `fs/2` (the Nyquist frequency) if the first passband ends at `fs/2`
+          (i.e., the filter is a single band highpass filter); center of first
+          passband otherwise
+
+    fs : float, optional
+        The sampling frequency of the signal. Each frequency in `cutoff`
+        must be between 0 and ``fs/2``.  Default is 2.
+
+    Returns
+    -------
+    h : ndarray
+        FIR filter coefficients as 1d array with `numtaps` entries.
+
+    Raises
+    ------
+    ValueError
+        If any value in `cutoff` is less than or equal to 0 or greater
+        than or equal to ``fs/2``, if the values in `cutoff` are not strictly
+        monotonically increasing, or if `numtaps` is even but a passband
+        includes the Nyquist frequency.
+
+    See Also
+    --------
+    firwin2:  Window method FIR filter design specifying gain-frequency pairs.
+    firwin_2d: 2D FIR filter design using the window method.
+    firls: FIR filter design using least-squares error minimization.
+    minimum_phase: Convert a FIR filter to minimum phase
+    remez: Calculate the minimax optimal filter using the Remez exchange algorithm.
+
+    Examples
+    --------
+    The following example calculates frequency responses of a 30 Hz low-pass filter
+    with various numbers of taps. The transition region width is 20 Hz. The upper plot
+    shows the gain and the lower plot the phase. The vertical dashed line marks the
+    corner frequency and the gray background the transition region.
+
+    >>> import matplotlib.pyplot as plt
+    >>> import numpy as np
+    >>> import scipy.signal as signal
+    ...
+    >>> fs = 200  # sampling frequency and number of taps
+    >>> f_c, width = 30, 20  # corner frequency (-6 dB gain)
+    >>> taps = [20, 40, 60]  # number of taps
+    ...
+    >>> fg, (ax0, ax1) = plt.subplots(2, 1, sharex='all', layout="constrained",
+    ...                               figsize=(5, 4))
+    >>> ax0.set_title(rf"Response of ${f_c}\,$Hz low-pass Filter with " +
+    ...               rf"${width}\,$Hz transition region")
+    >>> ax0.set(ylabel="Gain in dB", xlim=(0, fs/2))
+    >>> ax1.set(xlabel=rf"Frequency $f\,$ in hertz (sampling frequency $f_S={fs}\,$Hz)",
+    ...         ylabel="Phase in Degrees")
+    ...
+    >>> for n in taps:  # calculate filter and plot response:
+    ...     bb = signal.firwin(n, f_c, width=width, fs=fs)
+    ...     f, H = signal.freqz(bb, fs=fs)  # calculate frequency response
+    ...     H_dB, H_ph = 20 * np.log10(abs(H)), np.rad2deg(np.unwrap(np.angle(H)))
+    ...     H_ph[H_dB<-150] = np.nan
+    ...     ax0.plot(f, H_dB, alpha=.5, label=rf"{n} taps")
+    ...     ax1.plot(f, H_ph, alpha=.5, label=rf"{n} taps")
+    >>> for ax_ in (ax0, ax1):
+    ...     ax_.axvspan(f_c-width/2, f_c+width/2,color='gray', alpha=.25)
+    ...     ax_.axvline(f_c, color='gray', linestyle='--', alpha=.5)
+    ...     ax_.grid()
+    ...     ax_.legend()
+    >>> plt.show()
+
+    The plots show that with increasing number of taps, the suppression in the stopband
+    increases and the (negative) slope of the phase steepens, which signifies a longer
+    signal delay in the filter. Note that the plots contain numeric artifacts caused by
+    the limited frequency resolution: The phase jumps are not real---in reality the
+    phase is a straight line with a constant negative slope. Furthermore, the gains
+    contain zero values (i.e., -∞ dB), which are also not depicted.
+
+    The second example determines the frequency responses of a 30 Hz low-pass filter
+    with 40 taps. This time the width of the transition region varies:
+
+    >>> import matplotlib.pyplot as plt
+    >>> import numpy as np
+    >>> import scipy.signal as signal
+    ...
+    >>> fs = 200  # sampling frequency and number of taps
+    >>> n, f_c = 40, 30  # number of taps and corner frequency (-6 dB gain)
+    >>> widths = (2, 10, 25)  # width of transition region
+    ...
+    >>> fg, ax = plt.subplots(1, 1, layout="constrained",)
+    >>> ax.set(title=rf"Response of {n}-tap ${f_c}\,$Hz low-pass Filter",
+    ...        xlabel=rf"Frequency $f\,$ in hertz (sampling frequency $f_S={fs}\,$Hz)",
+    ...        ylabel="Gain in dB", xlim=(0, fs/2))
+    >>> ax.axvline(f_c, color='gray', linestyle='--', alpha=.7)  # mark corner frequency
+    ...
+    >>> for width in widths:  # calculate filter and plot response:
+    ...     bb = signal.firwin(n, f_c, width=width, fs=fs)
+    ...     f, H = signal.freqz(bb, fs=fs)  # calculate frequency response
+    ...     H_dB= 20 * np.log10(abs(H))  # convert to dB
+    ...     ax.plot(f, H_dB, alpha=.5, label=rf"width$={width}\,$Hz")
+    ...
+    >>> ax.grid()
+    >>> ax.legend()
+    >>> plt.show()
+
+    It can be seen in the plot above that with increasing width of the transition
+    region the suppression in the stopband increases. Since the phase does not vary, it
+    is not depicted.
+
+    Instead of defining a transition region width, a window function can also be
+    specified. The plot below depicts the response of an 80 tap band-pass filter having
+    a passband ranging form 40 Hz to 60 Hz (denoted by a gray background) with
+    different windows:
+
+    >>> import matplotlib.pyplot as plt
+    >>> import numpy as np
+    >>> import scipy.signal as signal
+    ...
+    >>> fs, n = 200, 80  # sampling frequency and number of taps
+    >>> cutoff = [40, 60]  # corner frequencies (-6 dB gain)
+    >>> windows = ('boxcar', 'hamming', 'hann', 'blackman')
+    ...
+    >>> fg, ax = plt.subplots(1, 1, layout="constrained")  # set up plotting
+    >>> ax.set(title=rf"Response of {n}-tap Filter with ${cutoff}\,$Hz passband",
+    ...        xlabel=rf"Frequency $f\,$ in hertz (sampling frequency $f_S={fs}\,$Hz)",
+    ...        ylabel="Gain in dB", xlim=(0, fs/2))
+    >>> ax.axvspan(*cutoff, color='gray', alpha=.25)  # mark passband
+    ...
+    >>> for win in windows:  # calculate filter and plot response:
+    ...     bb = signal.firwin(n, cutoff, window=win, pass_zero=False, fs=fs)
+    ...     f, H = signal.freqz(bb, fs=fs)  # calculate frequency response
+    ...     H_dB = 20 * np.log10(abs(H))  # convert to dB
+    ...     ax.plot(f, H_dB, alpha=.5, label=win)
+    ...
+    >>> ax.grid()
+    >>> ax.legend()
+    >>> plt.show()
+
+    The plot shows that the choice of window mainly influences the balance of the
+    suppression in the stopband against the width of the transition region. Note that
+    utilizing the `~scipy.signal.windows.boxcar` window corresponds to just truncating
+    the ideal infinite impulse response to the length of `numtaps` samples.
+
+    The last example illustrates  how to use the `cutoff` and `pass_zero` parameters to
+    create a low-pass, a high-pass, a band-stop and a band-pass filter. The desired
+    ideal frequency gain is drawn as a gray dashed line whereas the response of the FIR
+    filter is depicted as a blue continuous line:
+
+    >>> from itertools import product
+    >>> import matplotlib.pyplot as plt
+    >>> import numpy as np
+    >>> import scipy.signal as signal
+    ...
+    >>> cutoffs = [0.5, (.25, .75)]  # cutoff parameters
+    >>> fg, axx = plt.subplots(4, 1, sharex='all', layout="constrained",
+    ...                        figsize=(5, 4))
+    >>> for ax, (cutoff, pass_zero) in zip(axx, product(cutoffs, (True, False))):
+    ...     ax.set(title=f"firwin(41, {cutoff=}, {pass_zero=}, fs=2)", ylabel="Gain")
+    ...     ax.set_yticks([0.5], minor=True)  # mark gain of 0.5 (= -6 dB)
+    ...     ax.grid(which='minor', axis='y')
+    ...
+    ...     bb = signal.firwin(41, cutoff, pass_zero=pass_zero, fs=2)
+    ...     ff, HH = signal.freqz(bb, fs=2)
+    ...     ax.plot(ff, abs(HH), 'C0-', label="FIR Response")
+    ...
+    ...     f_d = np.hstack(([0], np.atleast_1d(cutoff), [1]))
+    ...     H_d = np.tile([1, 0] if pass_zero else [0, 1], 2)[:len(f_d)]
+    ...     H_d[-1] = H_d[-2] # account for symmetry at Nyquist frequency
+    ...     ax.step(f_d, H_d, 'k--', where='post', alpha=.3, label="Desired Response")
+    >>> axx[-1].set(xlabel=r"Frequency $f\,$ in hertz (sampling frequency $f_S=2\,$Hz)",
+    ...             xlim=(0, 1))
+    >>> plt.show()
+    """
+    # NB: scipy's version of array_namespace returns `np_compat` for int or floats
+    xp = array_namespace(cutoff)
+
+    # The major enhancements to this function added in November 2010 were
+    # developed by Tom Krauss (see ticket #902).
+    fs = _validate_fs(fs, allow_none=True)
+    fs = 2 if fs is None else fs
+
+    nyq = 0.5 * fs
+
+    cutoff = xp.asarray(cutoff, dtype=xp_default_dtype(xp))
+    cutoff = xpx.atleast_nd(cutoff, ndim=1, xp=xp) / float(nyq)
+
+    # Check for invalid input.
+    if cutoff.ndim > 1:
+        raise ValueError("The cutoff argument must be at most "
+                         "one-dimensional.")
+    if xp_size(cutoff) == 0:
+        raise ValueError("At least one cutoff frequency must be given.")
+    if xp.min(cutoff) <= 0 or xp.max(cutoff) >= 1:
+        raise ValueError("Invalid cutoff frequency: frequencies must be "
+                         "greater than 0 and less than fs/2.")
+    if xp.any(cutoff[1:] - cutoff[:-1] <= 0):
+        raise ValueError("Invalid cutoff frequencies: the frequencies "
+                         "must be strictly increasing.")
+
+    if width is not None:
+        # A width was given.  Find the beta parameter of the Kaiser window
+        # and set `window`.  This overrides the value of `window` passed in.
+        atten = kaiser_atten(numtaps, float(width) / nyq)
+        beta = kaiser_beta(atten)
+        window = ('kaiser', beta)
+
+    if pass_zero in ('bandstop', 'lowpass'):
+        if pass_zero == 'lowpass':
+            if xp_size(cutoff) != 1:
+                raise ValueError('cutoff must have one element if '
+                                 f'pass_zero=="lowpass", got {cutoff.shape}')
+        elif xp_size(cutoff) <= 1:
+            raise ValueError('cutoff must have at least two elements if '
+                             f'pass_zero=="bandstop", got {cutoff.shape}')
+        pass_zero = True
+    elif pass_zero in ('bandpass', 'highpass'):
+        if pass_zero == 'highpass':
+            if xp_size(cutoff) != 1:
+                raise ValueError('cutoff must have one element if '
+                                 f'pass_zero=="highpass", got {cutoff.shape}')
+        elif xp_size(cutoff) <= 1:
+            raise ValueError('cutoff must have at least two elements if '
+                             f'pass_zero=="bandpass", got {cutoff.shape}')
+        pass_zero = False
+    elif not (pass_zero is True or pass_zero is False):
+        raise ValueError(f"Parameter {pass_zero=} not in (True, False, 'bandpass', " +
+                         "'lowpass', 'highpass', 'bandstop')")
+
+    pass_nyquist = (xp_size(cutoff) % 2 == 0) == pass_zero
+    if pass_nyquist and numtaps % 2 == 0:
+        raise ValueError("A filter with an even number of coefficients must "
+                         "have zero response at the Nyquist frequency.")
+
+    # Insert 0 and/or 1 at the ends of cutoff so that the length of cutoff
+    # is even, and each pair in cutoff corresponds to passband.
+    cutoff = xp.concat((xp.zeros(int(pass_zero)), cutoff, xp.ones(int(pass_nyquist))))
+
+
+    # `bands` is a 2-D array; each row gives the left and right edges of
+    # a passband.
+    bands = xp.reshape(cutoff, (-1, 2))
+
+    # Build up the coefficients.
+    alpha = 0.5 * (numtaps - 1)
+    m = xp.arange(0, numtaps, dtype=cutoff.dtype) - alpha
+    h = 0
+    for j in range(bands.shape[0]):
+        left, right = bands[j, 0], bands[j, 1]
+        h += right * xpx.sinc(right * m, xp=xp)
+        h -= left * xpx.sinc(left * m, xp=xp)
+
+    # Get and apply the window function.
+    win = get_window(window, numtaps, fftbins=False, xp=xp)
+    h *= win
+
+    # Now handle scaling if desired.
+    if scale:
+        # Get the first passband.
+        left, right = bands[0, ...]
+        if left == 0:
+            scale_frequency = 0.0
+        elif right == 1:
+            scale_frequency = 1.0
+        else:
+            scale_frequency = 0.5 * (left + right)
+        c = xp.cos(xp.pi * m * scale_frequency)
+        s = xp.sum(h * c)
+        h /= s
+
+    return h
+
+
+# Original version of firwin2 from scipy ticket #457, submitted by "tash".
+#
+# Rewritten by Warren Weckesser, 2010.
+def firwin2(numtaps, freq, gain, *, nfreqs=None, window='hamming',
+            antisymmetric=False, fs=None):
+    """
+    FIR filter design using the window method.
+
+    From the given frequencies `freq` and corresponding gains `gain`,
+    this function constructs an FIR filter with linear phase and
+    (approximately) the given frequency response.
+
+    Parameters
+    ----------
+    numtaps : int
+        The number of taps in the FIR filter.  `numtaps` must be less than
+        `nfreqs`.
+    freq : array_like, 1-D
+        The frequency sampling points. Typically 0.0 to 1.0 with 1.0 being
+        Nyquist.  The Nyquist frequency is half `fs`.
+        The values in `freq` must be nondecreasing. A value can be repeated
+        once to implement a discontinuity. The first value in `freq` must
+        be 0, and the last value must be ``fs/2``. Values 0 and ``fs/2`` must
+        not be repeated.
+    gain : array_like
+        The filter gains at the frequency sampling points. Certain
+        constraints to gain values, depending on the filter type, are applied,
+        see Notes for details.
+    nfreqs : int, optional
+        The size of the interpolation mesh used to construct the filter.
+        For most efficient behavior, this should be a power of 2 plus 1
+        (e.g, 129, 257, etc). The default is one more than the smallest
+        power of 2 that is not less than `numtaps`. `nfreqs` must be greater
+        than `numtaps`.
+    window : str or (str, float) or float, or None, optional
+        Desired window to use. Default is ``'hamming'``. The window will be symmetric,
+        unless a suffix ``'_periodic'`` is appended to the window name (e.g.,
+        ``'hamming_perodic'``) Consult `~scipy.signal.get_window` for a list of windows
+        and required parameters. If ``None``, no window function is applied.
+    antisymmetric : bool, optional
+        Whether resulting impulse response is symmetric/antisymmetric.
+        See Notes for more details.
+    fs : float, optional
+        The sampling frequency of the signal. Each frequency in `cutoff`
+        must be between 0 and ``fs/2``. Default is 2.
+
+    Returns
+    -------
+    taps : ndarray
+        The filter coefficients of the FIR filter, as a 1-D array of length
+        `numtaps`.
+
+    See Also
+    --------
+    firls
+    firwin
+    minimum_phase
+    remez
+
+    Notes
+    -----
+    From the given set of frequencies and gains, the desired response is
+    constructed in the frequency domain. The inverse FFT is applied to the
+    desired response to create the associated convolution kernel, and the
+    first `numtaps` coefficients of this kernel, scaled by `window`, are
+    returned.
+
+    The FIR filter will have linear phase. The type of filter is determined by
+    the value of 'numtaps` and `antisymmetric` flag.
+    There are four possible combinations:
+
+       - odd  `numtaps`, `antisymmetric` is False, type I filter is produced
+       - even `numtaps`, `antisymmetric` is False, type II filter is produced
+       - odd  `numtaps`, `antisymmetric` is True, type III filter is produced
+       - even `numtaps`, `antisymmetric` is True, type IV filter is produced
+
+    Magnitude response of all but type I filters are subjects to following
+    constraints:
+
+       - type II  -- zero at the Nyquist frequency
+       - type III -- zero at zero and Nyquist frequencies
+       - type IV  -- zero at zero frequency
+
+    .. versionadded:: 0.9.0
+
+    References
+    ----------
+    .. [1] Oppenheim, A. V. and Schafer, R. W., "Discrete-Time Signal
+       Processing", Prentice-Hall, Englewood Cliffs, New Jersey (1989).
+       (See, for example, Section 7.4.)
+
+    .. [2] Smith, Steven W., "The Scientist and Engineer's Guide to Digital
+       Signal Processing", Ch. 17. http://www.dspguide.com/ch17/1.htm
+
+    Examples
+    --------
+    A lowpass FIR filter with a response that is 1 on [0.0, 0.5], and
+    that decreases linearly on [0.5, 1.0] from 1 to 0:
+
+    >>> from scipy import signal
+    >>> taps = signal.firwin2(150, [0.0, 0.5, 1.0], [1.0, 1.0, 0.0])
+    >>> print(taps[72:78])
+    [-0.02286961 -0.06362756  0.57310236  0.57310236 -0.06362756 -0.02286961]
+
+    """
+    xp = array_namespace(freq, gain)
+    freq, gain = xp.asarray(freq), xp.asarray(gain)
+
+    fs = _validate_fs(fs, allow_none=True)
+    fs = 2 if fs is None else fs
+    nyq = 0.5 * fs
+
+    if freq.shape[0] != gain.shape[0]:
+        raise ValueError('freq and gain must be of same length.')
+
+    if nfreqs is not None and numtaps >= nfreqs:
+        raise ValueError(
+            f'ntaps must be less than nfreqs, but firwin2 was called with '
+            f'ntaps={numtaps} and nfreqs={nfreqs}'
+        )
+
+    if freq[0] != 0 or freq[-1] != nyq:
+        raise ValueError('freq must start with 0 and end with fs/2.')
+    d = freq[1:] - freq[:-1]
+    if xp.any(d < 0):
+        raise ValueError('The values in freq must be nondecreasing.')
+    d2 = d[:-1] + d[1:]
+    if xp.any(d2 == 0):
+        raise ValueError('A value in freq must not occur more than twice.')
+    if freq[1] == 0:
+        raise ValueError('Value 0 must not be repeated in freq')
+    if freq[-2] == nyq:
+        raise ValueError('Value fs/2 must not be repeated in freq')
+
+    if antisymmetric:
+        if numtaps % 2 == 0:
+            ftype = 4
+        else:
+            ftype = 3
+    else:
+        if numtaps % 2 == 0:
+            ftype = 2
+        else:
+            ftype = 1
+
+    if ftype == 2 and gain[-1] != 0.0:
+        raise ValueError("A Type II filter must have zero gain at the "
+                         "Nyquist frequency.")
+    elif ftype == 3 and (gain[0] != 0.0 or gain[-1] != 0.0):
+        raise ValueError("A Type III filter must have zero gain at zero "
+                         "and Nyquist frequencies.")
+    elif ftype == 4 and gain[0] != 0.0:
+        raise ValueError("A Type IV filter must have zero gain at zero "
+                         "frequency.")
+
+    if nfreqs is None:
+        nfreqs = 1 + 2 ** int(ceil(log(numtaps, 2)))
+
+    if xp.any(d == 0):
+        # Tweak any repeated values in freq so that interp works.
+        freq = xp.asarray(freq, copy=True)
+        eps = xp.finfo(xp_default_dtype(xp)).eps * nyq
+        for k in range(freq.shape[0] - 1):
+            if freq[k] == freq[k + 1]:
+                freq[k] = freq[k] - eps
+                freq[k + 1] = freq[k + 1] + eps
+        # Check if freq is strictly increasing after tweak
+        d = freq[1:] - freq[:-1]
+        if xp.any(d <= 0):
+            raise ValueError("freq cannot contain numbers that are too close "
+                             "(within eps * (fs/2): "
+                             f"{eps}) to a repeated value")
+
+    # Linearly interpolate the desired response on a uniform mesh `x`.
+    x = np.linspace(0.0, nyq, nfreqs)
+    fx = np.interp(x, np.asarray(freq), np.asarray(gain))  # XXX array-api-extra#193
+    x = xp.asarray(x)
+    fx = xp.asarray(fx)
+
+    # Adjust the phases of the coefficients so that the first `ntaps` of the
+    # inverse FFT are the desired filter coefficients.
+    shift = xp.exp(-(numtaps - 1) / 2. * 1j * xp.pi * x / nyq)
+    if ftype > 2:
+        shift *= 1j
+
+    fx2 = fx * shift
+
+    # Use irfft to compute the inverse FFT.
+    out_full = irfft(fx2)
+
+    if window is not None:
+        # Create the window to apply to the filter coefficients.
+        wind = get_window(window, numtaps, fftbins=False, xp=xp)
+    else:
+        wind = 1
+
+    # Keep only the first `numtaps` coefficients in `out`, and multiply by
+    # the window.
+    out = out_full[:numtaps] * wind
+
+    if ftype == 3:
+        out[xp_size(out) // 2] = 0.0
+
+    return out
+
+
+def remez(numtaps, bands, desired, *, weight=None, type='bandpass',
+          maxiter=25, grid_density=16, fs=None):
+    """
+    Calculate the minimax optimal filter using the Remez exchange algorithm.
+
+    Calculate the filter-coefficients for the finite impulse response
+    (FIR) filter whose transfer function minimizes the maximum error
+    between the desired gain and the realized gain in the specified
+    frequency bands using the Remez exchange algorithm.
+
+    Parameters
+    ----------
+    numtaps : int
+        The desired number of taps in the filter. The number of taps is
+        the number of terms in the filter, or the filter order plus one.
+    bands : array_like
+        A monotonic sequence containing the band edges.
+        All elements must be non-negative and less than half the sampling
+        frequency as given by `fs`.
+    desired : array_like
+        A sequence half the size of bands containing the desired gain
+        in each of the specified bands.
+    weight : array_like, optional
+        A relative weighting to give to each band region. The length of
+        `weight` has to be half the length of `bands`.
+    type : {'bandpass', 'differentiator', 'hilbert'}, optional
+        The type of filter:
+
+        * 'bandpass' : flat response in bands. This is the default.
+        * 'differentiator' : frequency proportional response in bands.
+        * 'hilbert' : filter with odd symmetry, that is, type III
+          (for even order) or type IV (for odd order) linear phase filters.
+
+    maxiter : int, optional
+        Maximum number of iterations of the algorithm. Default is 25.
+    grid_density : int, optional
+        Grid density. The dense grid used in `remez` is of size
+        ``(numtaps + 1) * grid_density``. Default is 16.
+    fs : float, optional
+        The sampling frequency of the signal.  Default is 1.
+
+    Returns
+    -------
+    out : ndarray
+        A rank-1 array containing the coefficients of the optimal
+        (in a minimax sense) filter.
+
+    See Also
+    --------
+    firls
+    firwin
+    firwin2
+    minimum_phase
+
+    References
+    ----------
+    .. [1] J. H. McClellan and T. W. Parks, "A unified approach to the
+           design of optimum FIR linear phase digital filters",
+           IEEE Trans. Circuit Theory, vol. CT-20, pp. 697-701, 1973.
+    .. [2] J. H. McClellan, T. W. Parks and L. R. Rabiner, "A Computer
+           Program for Designing Optimum FIR Linear Phase Digital
+           Filters", IEEE Trans. Audio Electroacoust., vol. AU-21,
+           pp. 506-525, 1973.
+
+    Examples
+    --------
+    In these examples, `remez` is used to design low-pass, high-pass,
+    band-pass and band-stop filters.  The parameters that define each filter
+    are the filter order, the band boundaries, the transition widths of the
+    boundaries, the desired gains in each band, and the sampling frequency.
+
+    We'll use a sample frequency of 22050 Hz in all the examples.  In each
+    example, the desired gain in each band is either 0 (for a stop band)
+    or 1 (for a pass band).
+
+    `freqz` is used to compute the frequency response of each filter, and
+    the utility function ``plot_response`` defined below is used to plot
+    the response.
+
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+
+    >>> fs = 22050   # Sample rate, Hz
+
+    >>> def plot_response(w, h, title):
+    ...     "Utility function to plot response functions"
+    ...     fig = plt.figure()
+    ...     ax = fig.add_subplot(111)
+    ...     ax.plot(w, 20*np.log10(np.abs(h)))
+    ...     ax.set_ylim(-40, 5)
+    ...     ax.grid(True)
+    ...     ax.set_xlabel('Frequency (Hz)')
+    ...     ax.set_ylabel('Gain (dB)')
+    ...     ax.set_title(title)
+
+    The first example is a low-pass filter, with cutoff frequency 8 kHz.
+    The filter length is 325, and the transition width from pass to stop
+    is 100 Hz.
+
+    >>> cutoff = 8000.0    # Desired cutoff frequency, Hz
+    >>> trans_width = 100  # Width of transition from pass to stop, Hz
+    >>> numtaps = 325      # Size of the FIR filter.
+    >>> taps = signal.remez(numtaps, [0, cutoff, cutoff + trans_width, 0.5*fs],
+    ...                     [1, 0], fs=fs)
+    >>> w, h = signal.freqz(taps, [1], worN=2000, fs=fs)
+    >>> plot_response(w, h, "Low-pass Filter")
+    >>> plt.show()
+
+    This example shows a high-pass filter:
+
+    >>> cutoff = 2000.0    # Desired cutoff frequency, Hz
+    >>> trans_width = 250  # Width of transition from pass to stop, Hz
+    >>> numtaps = 125      # Size of the FIR filter.
+    >>> taps = signal.remez(numtaps, [0, cutoff - trans_width, cutoff, 0.5*fs],
+    ...                     [0, 1], fs=fs)
+    >>> w, h = signal.freqz(taps, [1], worN=2000, fs=fs)
+    >>> plot_response(w, h, "High-pass Filter")
+    >>> plt.show()
+
+    This example shows a band-pass filter with a pass-band from 2 kHz to
+    5 kHz.  The transition width is 260 Hz and the length of the filter
+    is 63, which is smaller than in the other examples:
+
+    >>> band = [2000, 5000]  # Desired pass band, Hz
+    >>> trans_width = 260    # Width of transition from pass to stop, Hz
+    >>> numtaps = 63         # Size of the FIR filter.
+    >>> edges = [0, band[0] - trans_width, band[0], band[1],
+    ...          band[1] + trans_width, 0.5*fs]
+    >>> taps = signal.remez(numtaps, edges, [0, 1, 0], fs=fs)
+    >>> w, h = signal.freqz(taps, [1], worN=2000, fs=fs)
+    >>> plot_response(w, h, "Band-pass Filter")
+    >>> plt.show()
+
+    The low order leads to higher ripple and less steep transitions.
+
+    The next example shows a band-stop filter.
+
+    >>> band = [6000, 8000]  # Desired stop band, Hz
+    >>> trans_width = 200    # Width of transition from pass to stop, Hz
+    >>> numtaps = 175        # Size of the FIR filter.
+    >>> edges = [0, band[0] - trans_width, band[0], band[1],
+    ...          band[1] + trans_width, 0.5*fs]
+    >>> taps = signal.remez(numtaps, edges, [1, 0, 1], fs=fs)
+    >>> w, h = signal.freqz(taps, [1], worN=2000, fs=fs)
+    >>> plot_response(w, h, "Band-stop Filter")
+    >>> plt.show()
+
+    """
+    xp = array_namespace(bands, desired, weight)
+    bands = np.asarray(bands)
+    desired = np.asarray(desired)
+    if weight is not None:
+        weight = np.asarray(weight)
+
+    fs = _validate_fs(fs, allow_none=True)
+    fs = 1.0 if fs is None else fs
+
+    # Convert type
+    try:
+        tnum = {'bandpass': 1, 'differentiator': 2, 'hilbert': 3}[type]
+    except KeyError as e:
+        raise ValueError("Type must be 'bandpass', 'differentiator', "
+                         "or 'hilbert'") from e
+
+    # Convert weight
+    if weight is None:
+        weight = [1] * len(desired)
+
+    bands = np.asarray(bands).copy()
+    result = _sigtools._remez(numtaps, bands, desired, weight, tnum, fs,
+                              maxiter, grid_density)
+    return xp.asarray(result)
+
+
+def firls(numtaps, bands, desired, *, weight=None, fs=None):
+    """
+    FIR filter design using least-squares error minimization.
+
+    Calculate the filter coefficients for the linear-phase finite
+    impulse response (FIR) filter which has the best approximation
+    to the desired frequency response described by `bands` and
+    `desired` in the least squares sense (i.e., the integral of the
+    weighted mean-squared error within the specified bands is
+    minimized).
+
+    Parameters
+    ----------
+    numtaps : int
+        The number of taps in the FIR filter. `numtaps` must be odd.
+    bands : array_like
+        A monotonic nondecreasing sequence containing the band edges in
+        Hz. All elements must be non-negative and less than or equal to
+        the Nyquist frequency given by `nyq`. The bands are specified as
+        frequency pairs, thus, if using a 1D array, its length must be
+        even, e.g., `np.array([0, 1, 2, 3, 4, 5])`. Alternatively, the
+        bands can be specified as an nx2 sized 2D array, where n is the
+        number of bands, e.g, `np.array([[0, 1], [2, 3], [4, 5]])`.
+    desired : array_like
+        A sequence the same size as `bands` containing the desired gain
+        at the start and end point of each band.
+    weight : array_like, optional
+        A relative weighting to give to each band region when solving
+        the least squares problem. `weight` has to be half the size of
+        `bands`.
+    fs : float, optional
+        The sampling frequency of the signal. Each frequency in `bands`
+        must be between 0 and ``fs/2`` (inclusive). Default is 2.
+
+    Returns
+    -------
+    coeffs : ndarray
+        Coefficients of the optimal (in a least squares sense) FIR filter.
+
+    See Also
+    --------
+    firwin
+    firwin2
+    minimum_phase
+    remez
+
+    Notes
+    -----
+    This implementation follows the algorithm given in [1]_.
+    As noted there, least squares design has multiple advantages:
+
+    1. Optimal in a least-squares sense.
+    2. Simple, non-iterative method.
+    3. The general solution can obtained by solving a linear
+       system of equations.
+    4. Allows the use of a frequency dependent weighting function.
+
+    This function constructs a Type I linear phase FIR filter, which
+    contains an odd number of `coeffs` satisfying for :math:`n < numtaps`:
+
+    .. math:: coeffs(n) = coeffs(numtaps - 1 - n)
+
+    The odd number of coefficients and filter symmetry avoid boundary
+    conditions that could otherwise occur at the Nyquist and 0 frequencies
+    (e.g., for Type II, III, or IV variants).
+
+    .. versionadded:: 0.18
+
+    References
+    ----------
+    .. [1] Ivan Selesnick, Linear-Phase Fir Filter Design By Least Squares.
+           OpenStax CNX. Aug 9, 2005.
+           https://eeweb.engineering.nyu.edu/iselesni/EL713/firls/firls.pdf
+
+    Examples
+    --------
+    We want to construct a band-pass filter. Note that the behavior in the
+    frequency ranges between our stop bands and pass bands is unspecified,
+    and thus may overshoot depending on the parameters of our filter:
+
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+    >>> fig, axs = plt.subplots(2)
+    >>> fs = 10.0  # Hz
+    >>> desired = (0, 0, 1, 1, 0, 0)
+    >>> for bi, bands in enumerate(((0, 1, 2, 3, 4, 5), (0, 1, 2, 4, 4.5, 5))):
+    ...     fir_firls = signal.firls(73, bands, desired, fs=fs)
+    ...     fir_remez = signal.remez(73, bands, desired[::2], fs=fs)
+    ...     fir_firwin2 = signal.firwin2(73, bands, desired, fs=fs)
+    ...     hs = list()
+    ...     ax = axs[bi]
+    ...     for fir in (fir_firls, fir_remez, fir_firwin2):
+    ...         freq, response = signal.freqz(fir)
+    ...         hs.append(ax.semilogy(0.5*fs*freq/np.pi, np.abs(response))[0])
+    ...     for band, gains in zip(zip(bands[::2], bands[1::2]),
+    ...                            zip(desired[::2], desired[1::2])):
+    ...         ax.semilogy(band, np.maximum(gains, 1e-7), 'k--', linewidth=2)
+    ...     if bi == 0:
+    ...         ax.legend(hs, ('firls', 'remez', 'firwin2'),
+    ...                   loc='lower center', frameon=False)
+    ...     else:
+    ...         ax.set_xlabel('Frequency (Hz)')
+    ...     ax.grid(True)
+    ...     ax.set(title='Band-pass %d-%d Hz' % bands[2:4], ylabel='Magnitude')
+    ...
+    >>> fig.tight_layout()
+    >>> plt.show()
+
+    """
+    xp = array_namespace(bands, desired)
+    bands = np.asarray(bands)
+    desired = np.asarray(desired)
+
+    fs = _validate_fs(fs, allow_none=True)
+    fs = 2 if fs is None else fs
+    nyq = 0.5 * fs
+
+    numtaps = int(numtaps)
+    if numtaps % 2 == 0 or numtaps < 1:
+        raise ValueError("numtaps must be odd and >= 1")
+    M = (numtaps-1) // 2
+
+    # normalize bands 0->1 and make it 2 columns
+    nyq = float(nyq)
+    if nyq <= 0:
+        raise ValueError(f'nyq must be positive, got {nyq} <= 0.')
+    bands = np.asarray(bands).flatten() / nyq
+    if len(bands) % 2 != 0:
+        raise ValueError("bands must contain frequency pairs.")
+    if (bands < 0).any() or (bands > 1).any():
+        raise ValueError("bands must be between 0 and 1 relative to Nyquist")
+    bands = bands.reshape((-1, 2))
+
+    # check remaining params
+    desired = np.asarray(desired).flatten()
+    if bands.size != desired.size:
+        raise ValueError(
+            f"desired must have one entry per frequency, got {desired.size} "
+            f"gains for {bands.size} frequencies."
+        )
+    desired = desired.reshape((-1, 2))
+    if (np.diff(bands) <= 0).any() or (np.diff(bands[:, 0]) < 0).any():
+        raise ValueError("bands must be monotonically nondecreasing and have "
+                         "width > 0.")
+    if (bands[:-1, 1] > bands[1:, 0]).any():
+        raise ValueError("bands must not overlap.")
+    if (desired < 0).any():
+        raise ValueError("desired must be non-negative.")
+    if weight is None:
+        weight = np.ones(len(desired))
+    weight = np.asarray(weight).flatten()
+    if len(weight) != len(desired):
+        raise ValueError("weight must be the same size as the number of "
+                         f"band pairs ({len(bands)}).")
+    if (weight < 0).any():
+        raise ValueError("weight must be non-negative.")
+
+    # Set up the linear matrix equation to be solved, Qa = b
+
+    # We can express Q(k,n) = 0.5 Q1(k,n) + 0.5 Q2(k,n)
+    # where Q1(k,n)=q(k-n) and Q2(k,n)=q(k+n), i.e. a Toeplitz plus Hankel.
+
+    # We omit the factor of 0.5 above, instead adding it during coefficient
+    # calculation.
+
+    # We also omit the 1/π from both Q and b equations, as they cancel
+    # during solving.
+
+    # We have that:
+    #     q(n) = 1/π ∫W(ω)cos(nω)dω (over 0->π)
+    # Using our normalization ω=πf and with a constant weight W over each
+    # interval f1->f2 we get:
+    #     q(n) = W∫cos(πnf)df (0->1) = Wf sin(πnf)/πnf
+    # integrated over each f1->f2 pair (i.e., value at f2 - value at f1).
+    n = np.arange(numtaps)[:, np.newaxis, np.newaxis]
+    q = np.dot(np.diff(np.sinc(bands * n) * bands, axis=2)[:, :, 0], weight)
+
+    # Now we assemble our sum of Toeplitz and Hankel
+    Q1 = toeplitz(q[:M+1])
+    Q2 = hankel(q[:M+1], q[M:])
+    Q = Q1 + Q2
+
+    # Now for b(n) we have that:
+    #     b(n) = 1/π ∫ W(ω)D(ω)cos(nω)dω (over 0->π)
+    # Using our normalization ω=πf and with a constant weight W over each
+    # interval and a linear term for D(ω) we get (over each f1->f2 interval):
+    #     b(n) = W ∫ (mf+c)cos(πnf)df
+    #          = f(mf+c)sin(πnf)/πnf + mf**2 cos(nπf)/(πnf)**2
+    # integrated over each f1->f2 pair (i.e., value at f2 - value at f1).
+    n = n[:M + 1]  # only need this many coefficients here
+    # Choose m and c such that we are at the start and end weights
+    m = (np.diff(desired, axis=1) / np.diff(bands, axis=1))
+    c = desired[:, [0]] - bands[:, [0]] * m
+    b = bands * (m*bands + c) * np.sinc(bands * n)
+    # Use L'Hospital's rule here for cos(nπf)/(πnf)**2 @ n=0
+    b[0] -= m * bands * bands / 2.
+    b[1:] += m * np.cos(n[1:] * np.pi * bands) / (np.pi * n[1:]) ** 2
+    b = np.dot(np.diff(b, axis=2)[:, :, 0], weight)
+
+    # Now we can solve the equation
+    try:  # try the fast way
+        with warnings.catch_warnings(record=True) as w:
+            warnings.simplefilter('always')
+            a = solve(Q, b, assume_a="pos", check_finite=False)
+        for ww in w:
+            if (ww.category == LinAlgWarning and
+                    str(ww.message).startswith('Ill-conditioned matrix')):
+                raise LinAlgError(str(ww.message))
+    except LinAlgError:  # in case Q is rank deficient
+        # This is faster than pinvh, even though we don't explicitly use
+        # the symmetry here. gelsy was faster than gelsd and gelss in
+        # some non-exhaustive tests.
+        a = lstsq(Q, b, lapack_driver='gelsy')[0]
+
+    # make coefficients symmetric (linear phase)
+    coeffs = np.hstack((a[:0:-1], 2 * a[0], a[1:]))
+    return xp.asarray(coeffs)
+
+
+def _dhtm(mag, xp):
+    """Compute the modified 1-D discrete Hilbert transform
+
+    Parameters
+    ----------
+    mag : ndarray
+        The magnitude spectrum. Should be 1-D with an even length, and
+        preferably a fast length for FFT/IFFT.
+    """
+    # Adapted based on code by Niranjan Damera-Venkata,
+    # Brian L. Evans and Shawn R. McCaslin (see refs for `minimum_phase`)
+    sig = xp.zeros(mag.shape[0])
+    # Leave Nyquist and DC at 0, knowing np.abs(fftfreq(N)[midpt]) == 0.5
+    midpt = mag.shape[0] // 2
+    sig = xpx.at(sig)[1:midpt].set(1.0)
+    sig = xpx.at(sig)[midpt+1:].set(-1.0)
+    # eventually if we want to support complex filters, we will need a
+    # np.abs() on the mag inside the log, and should remove the .real
+    recon = xp.real(ifft(mag * xp.exp(fft(sig * ifft(xp.log(mag))))))
+    return recon
+
+
+def minimum_phase(h,
+                  method: Literal['homomorphic', 'hilbert'] = 'homomorphic',
+                  n_fft: int | None = None, *, half: bool = True):
+    """Convert a linear-phase FIR filter to minimum phase.
+
+    Parameters
+    ----------
+    h : array
+        Linear-phase FIR filter coefficients.
+    method : {'hilbert', 'homomorphic'}
+        The provided methods are:
+
+        - 'homomorphic' (default):
+          This method [4]_ [5]_ works best with filters with an
+          odd number of taps, and the resulting minimum phase filter
+          will have a magnitude response that approximates the square
+          root of the original filter's magnitude response using half
+          the number of taps when ``half=True`` (default), or the
+          original magnitude spectrum using the same number of taps
+          when ``half=False``.
+        - 'hilbert'
+          This method [1]_ is designed to be used with equiripple
+          filters (e.g., from `remez`) with unity or zero gain
+          regions.
+
+    n_fft : int
+        The number of points to use for the FFT. Should be at least a
+        few times larger than the signal length (see Notes).
+    half : bool
+        If ``True``, create a filter that is half the length of the original, with a
+        magnitude spectrum that is the square root of the original. If ``False``,
+        create a filter that is the same length as the original, with a magnitude
+        spectrum that is designed to match the original (only supported when
+        ``method='homomorphic'``).
+
+        .. versionadded:: 1.14.0
+
+    Returns
+    -------
+    h_minimum : array
+        The minimum-phase version of the filter, with length
+        ``(len(h) + 1) // 2`` when ``half is True`` or ``len(h)`` otherwise.
+
+    See Also
+    --------
+    firwin
+    firwin2
+    remez
+
+    Notes
+    -----
+    Both the Hilbert [1]_ or homomorphic [4]_ [5]_ methods require selection
+    of an FFT length to estimate the complex cepstrum of the filter.
+
+    In the case of the Hilbert method, the deviation from the ideal
+    spectrum ``epsilon`` is related to the number of stopband zeros
+    ``n_stop`` and FFT length ``n_fft`` as::
+
+        epsilon = 2. * n_stop / n_fft
+
+    For example, with 100 stopband zeros and a FFT length of 2048,
+    ``epsilon = 0.0976``. If we conservatively assume that the number of
+    stopband zeros is one less than the filter length, we can take the FFT
+    length to be the next power of 2 that satisfies ``epsilon=0.01`` as::
+
+        n_fft = 2 ** int(np.ceil(np.log2(2 * (len(h) - 1) / 0.01)))
+
+    This gives reasonable results for both the Hilbert and homomorphic
+    methods, and gives the value used when ``n_fft=None``.
+
+    Alternative implementations exist for creating minimum-phase filters,
+    including zero inversion [2]_ and spectral factorization [3]_ [4]_.
+    For more information, see `this DSPGuru page
+    <http://dspguru.com/dsp/howtos/how-to-design-minimum-phase-fir-filters>`__.
+
+    References
+    ----------
+    .. [1] N. Damera-Venkata and B. L. Evans, "Optimal design of real and
+           complex minimum phase digital FIR filters," Acoustics, Speech,
+           and Signal Processing, 1999. Proceedings., 1999 IEEE International
+           Conference on, Phoenix, AZ, 1999, pp. 1145-1148 vol.3.
+           :doi:`10.1109/ICASSP.1999.756179`
+    .. [2] X. Chen and T. W. Parks, "Design of optimal minimum phase FIR
+           filters by direct factorization," Signal Processing,
+           vol. 10, no. 4, pp. 369-383, Jun. 1986.
+    .. [3] T. Saramaki, "Finite Impulse Response Filter Design," in
+           Handbook for Digital Signal Processing, chapter 4,
+           New York: Wiley-Interscience, 1993.
+    .. [4] J. S. Lim, Advanced Topics in Signal Processing.
+           Englewood Cliffs, N.J.: Prentice Hall, 1988.
+    .. [5] A. V. Oppenheim, R. W. Schafer, and J. R. Buck,
+           "Discrete-Time Signal Processing," 3rd edition.
+           Upper Saddle River, N.J.: Pearson, 2009.
+
+    Examples
+    --------
+    Create an optimal linear-phase low-pass filter `h` with a transition band of
+    [0.2, 0.3] (assuming a Nyquist frequency of 1):
+
+    >>> import numpy as np
+    >>> from scipy.signal import remez, minimum_phase, freqz, group_delay
+    >>> import matplotlib.pyplot as plt
+    >>> freq = [0, 0.2, 0.3, 1.0]
+    >>> desired = [1, 0]
+    >>> h_linear = remez(151, freq, desired, fs=2)
+
+    Convert it to minimum phase:
+
+    >>> h_hil = minimum_phase(h_linear, method='hilbert')
+    >>> h_hom = minimum_phase(h_linear, method='homomorphic')
+    >>> h_hom_full = minimum_phase(h_linear, method='homomorphic', half=False)
+
+    Compare the impulse and frequency response of the four filters:
+
+    >>> fig0, ax0 = plt.subplots(figsize=(6, 3), tight_layout=True)
+    >>> fig1, axs = plt.subplots(3, sharex='all', figsize=(6, 6), tight_layout=True)
+    >>> ax0.set_title("Impulse response")
+    >>> ax0.set(xlabel='Samples', ylabel='Amplitude', xlim=(0, len(h_linear) - 1))
+    >>> axs[0].set_title("Frequency Response")
+    >>> axs[0].set(xlim=(0, .65), ylabel="Magnitude / dB")
+    >>> axs[1].set(ylabel="Phase / rad")
+    >>> axs[2].set(ylabel="Group Delay / samples", ylim=(-31, 81),
+    ...             xlabel='Normalized Frequency (Nyqist frequency: 1)')
+    >>> for h, lb in ((h_linear,   f'Linear ({len(h_linear)})'),
+    ...               (h_hil,      f'Min-Hilbert ({len(h_hil)})'),
+    ...               (h_hom,      f'Min-Homomorphic ({len(h_hom)})'),
+    ...               (h_hom_full, f'Min-Homom. Full ({len(h_hom_full)})')):
+    ...     w_H, H = freqz(h, fs=2)
+    ...     w_gd, gd = group_delay((h, 1), fs=2)
+    ...
+    ...     alpha = 1.0 if lb == 'linear' else 0.5  # full opacity for 'linear' line
+    ...     ax0.plot(h, '.-', alpha=alpha, label=lb)
+    ...     axs[0].plot(w_H, 20 * np.log10(np.abs(H)), alpha=alpha)
+    ...     axs[1].plot(w_H, np.unwrap(np.angle(H)), alpha=alpha, label=lb)
+    ...     axs[2].plot(w_gd, gd, alpha=alpha)
+    >>> ax0.grid(True)
+    >>> ax0.legend(title='Filter Phase (Order)')
+    >>> axs[1].legend(title='Filter Phase (Order)', loc='lower right')
+    >>> for ax_ in axs:  # shade transition band:
+    ...     ax_.axvspan(freq[1], freq[2], color='y', alpha=.25)
+    ...     ax_.grid(True)
+    >>> plt.show()
+
+    The impulse response and group delay plot depict the 75 sample delay of the linear
+    phase filter `h`. The phase should also be linear in the stop band--due to the small
+    magnitude, numeric noise dominates there. Furthermore, the plots show that the
+    minimum phase filters clearly show a reduced (negative) phase slope in the pass and
+    transition band. The plots also illustrate that the filter with parameters
+    ``method='homomorphic', half=False`` has same order and magnitude response as the
+    linear filter `h` whereas the other minimum phase filters have only half the order
+    and the square root  of the magnitude response.
+    """
+    xp = array_namespace(h)
+
+    h = xp.asarray(h)
+    if xp.isdtype(h.dtype, "complex floating"):
+        raise ValueError('Complex filters not supported')
+    if h.ndim != 1 or h.shape[0] <= 2:
+        raise ValueError('h must be 1-D and at least 2 samples long')
+    n_half = h.shape[0] // 2
+
+    if not xp.any(xp.flip(h[-n_half:]) - h[:n_half] <= 1e-8 + 1e-6*abs(h[:n_half])):
+        warnings.warn('h does not appear to by symmetric, conversion may fail',
+                      RuntimeWarning, stacklevel=2)
+    if not isinstance(method, str) or method not in \
+            ('homomorphic', 'hilbert',):
+        raise ValueError(f'method must be "homomorphic" or "hilbert", got {method!r}')
+    if method == "hilbert" and not half:
+        raise ValueError("`half=False` is only supported when `method='homomorphic'`")
+    if n_fft is None:
+        n_fft = 2 ** int(ceil(log2(2 * (h.shape[0] - 1) / 0.01)))
+    n_fft = int(n_fft)
+    if n_fft < h.shape[0]:
+        raise ValueError(f'n_fft must be at least len(h)=={len(h)}')
+
+    if method == 'hilbert':
+        w = xp.arange(n_fft, dtype=xp.float64) * (2 * xp.pi / n_fft * n_half)
+        H = xp.real(fft(h, n_fft) * xp.exp(1j * w))
+        dp = max(H) - 1
+        ds = 0 - min(H)
+        S = 4. / (xp.sqrt(1+dp+ds) + xp.sqrt(1-dp+ds)) ** 2
+        H += ds
+        H *= S
+        H = xp.sqrt(H)
+        H += 1e-10  # ensure that the log does not explode
+        h_minimum = _dhtm(H, xp)
+    else:  # method == 'homomorphic'
+        # zero-pad; calculate the DFT
+        h_temp = xp.abs(fft(h, n_fft))
+        # take 0.25*log(|H|**2) = 0.5*log(|H|)
+        h_temp += 1e-7 * xp.min(h_temp[h_temp > 0])  # don't let log blow up
+        h_temp = xp.log(h_temp)
+        if half:  # halving of magnitude spectrum optional
+            h_temp *= 0.5
+        # IDFT
+        h_temp = xp.real(ifft(h_temp))
+        # multiply pointwise by the homomorphic filter
+        # lmin[n] = 2u[n] - d[n]
+        # i.e., double the positive frequencies and zero out the negative ones;
+        # Oppenheim+Shafer 3rd ed p991 eq13.42b and p1004 fig13.7
+        win = xp.zeros(n_fft, dtype=h_temp.dtype)
+        win = xpx.at(win)[0].set(1)
+        stop = n_fft // 2
+        win = xpx.at(win)[1:stop].set(2)
+        # Nyquist freq: odd use 2, even use 1
+        win = xpx.at(win)[stop].set(1 + (n_fft % 2))
+        h_temp *= win
+        h_temp = ifft(xp.exp(fft(h_temp)))
+        h_minimum = xp.real(h_temp)
+    n_out = (n_half + h.shape[0] % 2) if half else h.shape[0]
+    return h_minimum[:n_out]
+
+
+def firwin_2d(hsize, window, *, fc=None, fs=2, circular=False,
+              pass_zero=True, scale=True):
+    """
+    2D FIR filter design using the window method.
+
+    This function computes the coefficients of a 2D finite impulse response
+    filter. The filter is separable with linear phase; it will be designed
+    as a product of two 1D filters with dimensions defined by `hsize`.
+    Additionally, it can create approximately circularly symmetric 2-D windows.
+
+    Parameters
+    ----------
+    hsize : tuple or list of length 2
+        Lengths of the filter in each dimension. `hsize[0]` specifies the
+        number of coefficients in the row direction and `hsize[1]` specifies
+        the number of coefficients in the column direction.
+    window : tuple or list of length 2 or str
+        Desired window to use for each 1D filter or a single window type for creating
+        circularly symmetric 2-D windows. Each element should be a string or tuple of
+        string and parameter values. The generated windows will be symmetric, unless a
+        suffix ``'_periodic'`` is appended to the window name (e.g.,
+        ``'hamming_perodic'``). Consult `~scipy.signal.get_window` for a list of windows
+        and required parameters.
+    fc : float or 1-D array_like, optional
+        Cutoff frequency of the filter in the same units as `fs`. This defines
+        the frequency at which the filter's gain drops to approximately -6 dB
+        (half power) in a low-pass or high-pass filter. For multi-band filters,
+        `fc` can be an array of cutoff frequencies (i.e., band edges) in the
+        range [0, fs/2], with each band specified in pairs. Required if
+        `circular` is False.
+    fs : float, optional
+        The sampling frequency of the signal. Default is 2.
+    circular : bool, optional
+        Whether to create a circularly symmetric 2-D window. Default is ``False``.
+    pass_zero : {True, False, 'bandpass', 'lowpass', 'highpass', 'bandstop'}, optional
+        This parameter is directly passed to `firwin` for each scalar frequency axis.
+        Hence, if ``True``, the DC gain, i.e., the gain at frequency (0, 0), is 1.
+        If ``False``, the DC gain is 0 at frequency (0, 0) if `circular` is ``True``.
+        If `circular` is ``False`` the frequencies (0, f1) and (f0, 0) will
+        have gain 0.
+        It can also be a string argument for the desired filter type
+        (equivalent to ``btype`` in IIR design functions).
+    scale : bool, optional
+        This parameter is directly passed to `firwin` for each scalar frequency axis.
+        Set to ``True`` to scale the coefficients so that the frequency
+        response is exactly unity at a certain frequency on one frequency axis.
+        That frequency is either:
+
+        - 0 (DC) if the first passband starts at 0 (i.e. pass_zero is ``True``)
+        - `fs`/2 (the Nyquist frequency) if the first passband ends at `fs`/2
+          (i.e., the filter is a single band highpass filter);
+          center of first passband otherwise
+
+    Returns
+    -------
+    filter_2d : (hsize[0], hsize[1]) ndarray
+        Coefficients of 2D FIR filter.
+
+    Raises
+    ------
+    ValueError
+        - If `hsize` and `window` are not 2-element tuples or lists.
+        - If `cutoff` is None when `circular` is True.
+        - If `cutoff` is outside the range [0, `fs`/2] and `circular` is ``False``.
+        - If any of the elements in `window` are not recognized.
+    RuntimeError
+        If `firwin` fails to converge when designing the filter.
+
+    See Also
+    --------
+    firwin: FIR filter design using the window method for 1d arrays.
+    get_window: Return a window of a given length and type.
+
+    Examples
+    --------
+    Generate a 5x5 low-pass filter with cutoff frequency 0.1:
+
+    >>> import numpy as np
+    >>> from scipy.signal import get_window
+    >>> from scipy.signal import firwin_2d
+    >>> hsize = (5, 5)
+    >>> window = (("kaiser", 5.0), ("kaiser", 5.0))
+    >>> fc = 0.1
+    >>> filter_2d = firwin_2d(hsize, window, fc=fc)
+    >>> filter_2d
+    array([[0.00025366, 0.00401662, 0.00738617, 0.00401662, 0.00025366],
+           [0.00401662, 0.06360159, 0.11695714, 0.06360159, 0.00401662],
+           [0.00738617, 0.11695714, 0.21507283, 0.11695714, 0.00738617],
+           [0.00401662, 0.06360159, 0.11695714, 0.06360159, 0.00401662],
+           [0.00025366, 0.00401662, 0.00738617, 0.00401662, 0.00025366]])
+
+    Generate a circularly symmetric 5x5 low-pass filter with Hamming window:
+
+    >>> filter_2d = firwin_2d((5, 5), 'hamming', fc=fc, circular=True)
+    >>> filter_2d
+    array([[-0.00020354, -0.00020354, -0.00020354, -0.00020354, -0.00020354],
+           [-0.00020354,  0.01506844,  0.09907658,  0.01506844, -0.00020354],
+           [-0.00020354,  0.09907658, -0.00020354,  0.09907658, -0.00020354],
+           [-0.00020354,  0.01506844,  0.09907658,  0.01506844, -0.00020354],
+           [-0.00020354, -0.00020354, -0.00020354, -0.00020354, -0.00020354]])
+
+    Generate Plots comparing the product of two 1d filters with a circular
+    symmetric filter:
+
+    >>> import matplotlib.pyplot as plt
+    >>> hsize, fc = (50, 50), 0.05
+    >>> window = (("kaiser", 5.0), ("kaiser", 5.0))
+    >>> filter0_2d = firwin_2d(hsize, window, fc=fc)
+    >>> filter1_2d = firwin_2d((50, 50), 'hamming', fc=fc, circular=True)
+    ...
+    >>> fg, (ax0, ax1) = plt.subplots(1, 2, tight_layout=True, figsize=(6.5, 3.5))
+    >>> ax0.set_title("Product of 2 Windows")
+    >>> im0 = ax0.imshow(filter0_2d, cmap='viridis', origin='lower', aspect='equal')
+    >>> fg.colorbar(im0, ax=ax0, shrink=0.7)
+    >>> ax1.set_title("Circular Window")
+    >>> im1 = ax1.imshow(filter1_2d, cmap='plasma', origin='lower', aspect='equal')
+    >>> fg.colorbar(im1, ax=ax1, shrink=0.7)
+    >>> plt.show()
+    """
+    if len(hsize) != 2:
+            raise ValueError("hsize must be a 2-element tuple or list")
+
+    if circular:
+        if fc is None:
+            raise ValueError("Cutoff frequency `fc` must be "
+                             "provided when `circular` is True")
+
+        n_r = max(hsize[0], hsize[1]) * 8  # oversample 1d window by factor 8
+
+        win_r = firwin(n_r, cutoff=fc, window=window, fs=fs)
+
+        f1, f2 = np.meshgrid(np.linspace(-1, 1, hsize[0]), np.linspace(-1, 1, hsize[1]))
+        r = np.sqrt(f1**2 + f2**2)
+
+        win_2d = np.interp(r, np.linspace(0, 1, n_r), win_r)
+        return win_2d
+
+    if len(window) != 2:
+        raise ValueError("window must be a 2-element tuple or list")
+
+    row_filter = firwin(hsize[0], cutoff=fc, window=window[0], fs=fs)
+    col_filter = firwin(hsize[1], cutoff=fc, window=window[1], fs=fs)
+
+    return np.outer(row_filter, col_filter)
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/_lti_conversion.py b/venv/lib/python3.12/site-packages/scipy/signal/_lti_conversion.py
new file mode 100644
index 0000000000000000000000000000000000000000..22074ba4b47a822f00301a2114aaec3a94bce7b8
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/_lti_conversion.py
@@ -0,0 +1,583 @@
+"""
+ltisys -- a collection of functions to convert linear time invariant systems
+from one representation to another.
+"""
+
+import numpy as np
+from numpy import (r_, eye, atleast_2d, poly, dot,
+                   asarray, zeros, array, outer)
+from scipy import linalg
+
+from scipy._lib._array_api import (array_namespace, xp_size, xp_promote,
+                                   xp_result_type)
+import scipy._external.array_api_extra as xpx
+from ._filter_design import tf2zpk, zpk2tf, normalize
+
+
+__all__ = ['tf2ss', 'abcd_normalize', 'ss2tf', 'zpk2ss', 'ss2zpk',
+           'cont2discrete']
+
+
+def tf2ss(num, den):
+    r"""Transfer function to state-space representation.
+
+    Parameters
+    ----------
+    num, den : array_like
+        Sequences representing the coefficients of the numerator and
+        denominator polynomials, in order of descending degree. The
+        denominator needs to be at least as long as the numerator.
+
+    Returns
+    -------
+    A, B, C, D : ndarray
+        State space representation of the system, in controller canonical
+        form.
+
+    Examples
+    --------
+    Convert the transfer function:
+
+    .. math:: H(s) = \frac{s^2 + 3s + 3}{s^2 + 2s + 1}
+
+    >>> num = [1, 3, 3]
+    >>> den = [1, 2, 1]
+
+    to the state-space representation:
+
+    .. math::
+
+        \dot{\textbf{x}}(t) =
+        \begin{bmatrix} -2 & -1 \\ 1 & 0 \end{bmatrix} \textbf{x}(t) +
+        \begin{bmatrix} 1 \\ 0 \end{bmatrix} \textbf{u}(t) \\
+
+        \textbf{y}(t) = \begin{bmatrix} 1 & 2 \end{bmatrix} \textbf{x}(t) +
+        \begin{bmatrix} 1 \end{bmatrix} \textbf{u}(t)
+
+    >>> from scipy.signal import tf2ss
+    >>> A, B, C, D = tf2ss(num, den)
+    >>> A
+    array([[-2., -1.],
+           [ 1.,  0.]])
+    >>> B
+    array([[ 1.],
+           [ 0.]])
+    >>> C
+    array([[ 1.,  2.]])
+    >>> D
+    array([[ 1.]])
+    """
+    # Controller canonical state-space representation.
+    #  if M+1 = len(num) and K+1 = len(den) then we must have M <= K
+    #  states are found by asserting that X(s) = U(s) / D(s)
+    #  then Y(s) = N(s) * X(s)
+    #
+    #   A, B, C, and D follow quite naturally.
+    #
+    num, den = normalize(num, den)   # Strips zeros, checks arrays
+    nn = len(num.shape)
+    if nn == 1:
+        num = asarray([num], num.dtype)
+    M = num.shape[1]
+    K = len(den)
+    if M > K:
+        msg = "Improper transfer function. `num` is longer than `den`."
+        raise ValueError(msg)
+    if M == 0 or K == 0:  # Null system
+        return (array([], float), array([], float), array([], float),
+                array([], float))
+
+    # pad numerator to have same number of columns has denominator
+    num = np.hstack((np.zeros((num.shape[0], K - M), dtype=num.dtype), num))
+
+    if num.shape[-1] > 0:
+        D = atleast_2d(num[:, 0])
+
+    else:
+        # We don't assign it an empty array because this system
+        # is not 'null'. It just doesn't have a non-zero D
+        # matrix. Thus, it should have a non-zero shape so that
+        # it can be operated on by functions like 'ss2tf'
+        D = array([[0]], float)
+
+    if K == 1:
+        D = D.reshape(num.shape)
+
+        return (zeros((1, 1)), zeros((1, D.shape[1])),
+                zeros((D.shape[0], 1)), D)
+
+    frow = -array([den[1:]])
+    A = r_[frow, eye(K - 2, K - 1)]
+    B = eye(K - 1, 1)
+    C = num[:, 1:] - outer(num[:, 0], den[1:])
+    D = D.reshape((C.shape[0], B.shape[1]))
+
+    return A, B, C, D
+
+
+def abcd_normalize(A=None, B=None, C=None, D=None):
+    r"""Check state-space matrices compatibility and ensure they are 2d arrays.
+
+    First, the input matrices are converted into two-dimensional arrays with
+    appropriate dtype as needed. Then the dimensions n, q, p are determined by
+    investigating the array shapes. If an input is ``None``, or has size zero, it is
+    set to an array of zeros of compatible shape. Finally, it is verified that all
+    parameter shapes are compatible with each other. If that fails, a ``ValueError`` is
+    raised. Note that the dimensions n, q, p are allowed to be zero.
+
+    Parameters
+    ----------
+    A : array_like, optional
+        Two-dimensional array of shape (n, n).
+    B : array_like, optional
+        Two-dimensional array of shape (n, p).
+    C : array_like, optional
+        Two-dimensional array of shape (q, n).
+    D : array_like, optional
+        Two-dimensional array of shape (q, p).
+
+    Returns
+    -------
+    A, B, C, D : array
+        State-space matrices as two-dimensional arrays with identical dtype.
+        The result dtype is determined based on the standard
+        `dtype promotion rules <https://numpy.org/doc/2.3/reference/arrays.promotion.html>`_
+        except for when the inputs are all of integer dtype, in which case the returned
+        arrays will have the default floating point dtype of ``float64``.
+
+    Raises
+    ------
+    ValueError
+        If the dimensions n, q, or p could not be determined or if the shapes are
+        incompatible with each other.
+
+    Notes
+    -----
+    If a matrix is not modified, the original matrix (not a copy) is returned.
+
+    The :ref:`tutorial_signal_state_space_representation` section of the
+    :ref:`user_guide` presents the corresponding definitions of continuous-time and
+    disrcete time state space systems.
+
+    See Also
+    --------
+    StateSpace: Linear Time Invariant system in state-space form.
+    dlti: Discrete-time linear time invariant system base class.
+    tf2ss: Transfer function to state-space representation.
+    ss2tf: State-space to transfer function.
+    ss2zpk: State-space representation to zero-pole-gain representation.
+    cont2discrete: Transform a continuous to a discrete state-space system.
+
+    Examples
+    --------
+    The following example demonstrates that the passed lists are converted into
+    two-dimensional arrays:
+
+    >>> from scipy.signal import abcd_normalize
+    >>> AA, BB, CC, DD = abcd_normalize(A=[[1, 2], [3, 4]], B=[[-1], [5]],
+    ...                                 C=[[4, 5]], D=2.5)
+    >>> AA.shape, BB.shape, CC.shape, DD.shape
+    ((2, 2), (2, 1), (1, 2), (1, 1))
+
+    In the following, the missing parameter C is assumed to be an array of zeros
+    with shape (1, 2):
+
+    >>> from scipy.signal import abcd_normalize
+    >>> AA, BB, CC, DD = abcd_normalize(A=[[1, 2], [3, 4]], B=[[-1], [5]], D=2.5)
+    >>> AA.shape, BB.shape, CC.shape, DD.shape
+    ((2, 2), (2, 1), (1, 2), (1, 1))
+    >>> CC
+    array([[0., 0.]])
+
+    """
+    if A is None and B is None and C is None:
+        raise ValueError("Dimension n is undefined for parameters A = B = C = None!")
+    if B is None and D is None:
+        raise ValueError("Dimension p is undefined for parameters B = D = None!")
+    if C is None and D is None:
+        raise ValueError("Dimension q is undefined for parameters C = D = None!")
+
+    xp = array_namespace(A, B, C, D)
+    A, B, C, D = xp_promote(A, B, C, D, xp=xp, force_floating=True)
+    dtype = xp_result_type(A, B, C, D, xp=xp)
+
+    # convert inputs into 2d arrays (zero-size 2d array if None):
+    A, B, C, D = (
+        xpx.atleast_nd(xp.asarray(M_), ndim=2, xp=xp)
+        if M_ is not None else xp.zeros((0, 0), dtype=dtype)
+        for M_ in (A, B, C, D)
+    )
+
+    n = A.shape[0] or B.shape[0] or C.shape[1] # try finding non-zero dimensions
+    p = B.shape[1] or D.shape[1]
+    q = C.shape[0] or D.shape[0]
+
+    # Create zero matrices as needed:
+    A = xp.zeros((n, n), dtype=dtype) if xp_size(A) == 0 else A
+    B = xp.zeros((n, p), dtype=dtype) if xp_size(B) == 0 else B
+    C = xp.zeros((q, n), dtype=dtype) if xp_size(C) == 0 else C
+    D = xp.zeros((q, p), dtype=dtype) if xp_size(D) == 0 else D
+
+    if A.shape != (n, n):
+        raise ValueError(f"Parameter A has shape {A.shape} but should be ({n}, {n})!")
+    if B.shape != (n, p):
+        raise ValueError(f"Parameter B has shape {B.shape} but should be ({n}, {p})!")
+    if C.shape != (q, n):
+        raise ValueError(f"Parameter C has shape {C.shape} but should be ({q}, {n})!")
+    if D.shape != (q, p):
+        raise ValueError(f"Parameter D has shape {D.shape} but should be ({q}, {p})!")
+
+    return A, B, C, D
+
+
+def ss2tf(A, B, C, D, input=0):
+    r"""State-space to transfer function.
+
+    A, B, C, D defines a linear state-space system with `p` inputs,
+    `q` outputs, and `n` state variables.
+
+    Parameters
+    ----------
+    A : array_like
+        State (or system) matrix of shape ``(n, n)``
+    B : array_like
+        Input matrix of shape ``(n, p)``
+    C : array_like
+        Output matrix of shape ``(q, n)``
+    D : array_like
+        Feedthrough (or feedforward) matrix of shape ``(q, p)``
+    input : int, optional
+        For multiple-input systems, the index of the input to use.
+
+    Returns
+    -------
+    num : 2-D ndarray
+        Numerator(s) of the resulting transfer function(s). `num` has one row
+        for each of the system's outputs. Each row is a sequence representation
+        of the numerator polynomial.
+    den : 1-D ndarray
+        Denominator of the resulting transfer function(s). `den` is a sequence
+        representation of the denominator polynomial.
+
+    Notes
+    -----
+    Before calculating `num` and `den`, the function `abcd_normalize` is called to
+    convert the parameters `A`, `B`, `C`, `D` into two-dimesional arrays of the
+    same dtype. The resulting dtype will be based on NumPy's dtype promotion rules,
+    except in the case where each of `A`, `B`, `C`, and `D` has integer dtype, in which
+    case the resulting dtype will be the default floating point dtype of ``float64``.
+
+    The :ref:`tutorial_signal_state_space_representation` section of the
+    :ref:`user_guide` presents the corresponding definitions of continuous-time and
+    disrcete time state space systems.
+
+    Examples
+    --------
+    Convert the state-space representation:
+
+    .. math::
+
+        \dot{\textbf{x}}(t) =
+        \begin{bmatrix} -2 & -1 \\ 1 & 0 \end{bmatrix} \textbf{x}(t) +
+        \begin{bmatrix} 1 \\ 0 \end{bmatrix} \textbf{u}(t) \\
+
+        \textbf{y}(t) = \begin{bmatrix} 1 & 2 \end{bmatrix} \textbf{x}(t) +
+        \begin{bmatrix} 1 \end{bmatrix} \textbf{u}(t)
+
+    >>> A = [[-2, -1], [1, 0]]
+    >>> B = [[1], [0]]  # 2-D column vector
+    >>> C = [[1, 2]]    # 2-D row vector
+    >>> D = 1
+
+    to the transfer function:
+
+    .. math:: H(s) = \frac{s^2 + 3s + 3}{s^2 + 2s + 1}
+
+    >>> from scipy.signal import ss2tf
+    >>> ss2tf(A, B, C, D)
+    (array([[1., 3., 3.]]), array([ 1.,  2.,  1.]))
+    """
+    # transfer function is C (sI - A)**(-1) B + D
+
+    # Check consistency and make them all floating point 2d arrays:
+    A, B, C, D = abcd_normalize(A, B, C, D)
+
+    nout, nin = D.shape
+    if input >= nin:
+        raise ValueError("System does not have the input specified.")
+
+    # make SIMO from possibly MIMO system.
+    B = B[:, input:input + 1]
+    D = D[:, input:input + 1]
+
+    try:
+        den = poly(A)
+    except ValueError:
+        den = 1
+
+    if (B.size == 0) and (C.size == 0):
+        num = np.ravel(D)
+        if (D.size == 0) and (A.size == 0):
+            den = []
+        return num, den
+
+    num_states = A.shape[0]
+    type_test = A[:, 0] + B[:, 0] + C[0, :] + D + 0.0
+    num = np.empty((nout, num_states + 1), type_test.dtype)
+    for k in range(nout):
+        Ck = atleast_2d(C[k, :])
+        num[k] = poly(A - dot(B, Ck)) + (D[k] - 1) * den
+
+    return num, den
+
+
+def zpk2ss(z, p, k):
+    """Zero-pole-gain representation to state-space representation.
+
+    Parameters
+    ----------
+    z, p : sequence
+        Zeros and poles.
+    k : float
+        System gain.
+
+    Returns
+    -------
+    A, B, C, D : ndarray
+        State space representation of the system, in controller canonical
+        form.
+
+    """
+    return tf2ss(*zpk2tf(z, p, k))
+
+
+def ss2zpk(A, B, C, D, input=0):
+    """State-space representation to zero-pole-gain representation.
+
+    A, B, C, D defines a linear state-space system with `p` inputs,
+    `q` outputs, and `n` state variables.
+
+    Parameters
+    ----------
+    A : array_like
+        State (or system) matrix of shape ``(n, n)``
+    B : array_like
+        Input matrix of shape ``(n, p)``
+    C : array_like
+        Output matrix of shape ``(q, n)``
+    D : array_like
+        Feedthrough (or feedforward) matrix of shape ``(q, p)``
+    input : int, optional
+        For multiple-input systems, the index of the input to use.
+
+    Returns
+    -------
+    z, p : sequence
+        Zeros and poles.
+    k : float
+        System gain.
+
+    """
+    return tf2zpk(*ss2tf(A, B, C, D, input=input))
+
+
+def cont2discrete(system, dt, method="zoh", alpha=None):
+    """
+    Transform a continuous to a discrete state-space system.
+
+    Parameters
+    ----------
+    system : a tuple describing the system or an instance of `lti`
+        The following gives the number of elements in the tuple and
+        the interpretation:
+
+        * 1: (instance of `lti`)
+        * 2: (num, den)
+        * 3: (zeros, poles, gain)
+        * 4: (A, B, C, D)
+
+    dt : float
+        The discretization time step.
+    method : str, optional
+        Which method to use:
+
+        * gbt: generalized bilinear transformation
+        * bilinear: Tustin's approximation ("gbt" with alpha=0.5)
+        * euler: Euler (or forward differencing) method ("gbt" with alpha=0)
+        * backward_diff: Backwards differencing ("gbt" with alpha=1.0)
+        * zoh: zero-order hold (default)
+        * foh: first-order hold (*versionadded: 1.3.0*)
+        * impulse: equivalent impulse response (*versionadded: 1.3.0*)
+
+    alpha : float within [0, 1], optional
+        The generalized bilinear transformation weighting parameter, which
+        should only be specified with method="gbt", and is ignored otherwise
+
+    Returns
+    -------
+    sysd : tuple containing the discrete system
+        Based on the input type, the output will be of the form
+
+        * (num, den, dt)   for transfer function input
+        * (zeros, poles, gain, dt)   for zeros-poles-gain input
+        * (A, B, C, D, dt) for state-space system input
+
+    Notes
+    -----
+    By default, the routine uses a Zero-Order Hold (zoh) method to perform
+    the transformation. Alternatively, a generalized bilinear transformation
+    may be used, which includes the common Tustin's bilinear approximation,
+    an Euler's method technique, or a backwards differencing technique.
+
+    The Zero-Order Hold (zoh) method is based on [1]_, the generalized bilinear
+    approximation is based on [2]_ and [3]_, the First-Order Hold (foh) method
+    is based on [4]_.
+
+    References
+    ----------
+    .. [1] https://en.wikipedia.org/wiki/Discretization#Discretization_of_linear_state_space_models
+
+    .. [2] http://techteach.no/publications/discretetime_signals_systems/discrete.pdf
+
+    .. [3] G. Zhang, X. Chen, and T. Chen, Digital redesign via the generalized
+        bilinear transformation, Int. J. Control, vol. 82, no. 4, pp. 741-754,
+        2009.
+        (https://www.mypolyuweb.hk/~magzhang/Research/ZCC09_IJC.pdf)
+
+    .. [4] G. F. Franklin, J. D. Powell, and M. L. Workman, Digital control
+        of dynamic systems, 3rd ed. Menlo Park, Calif: Addison-Wesley,
+        pp. 204-206, 1998.
+
+    Examples
+    --------
+    We can transform a continuous state-space system to a discrete one:
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.signal import cont2discrete, lti, dlti, dstep
+
+    Define a continuous state-space system.
+
+    >>> A = np.array([[0, 1],[-10., -3]])
+    >>> B = np.array([[0],[10.]])
+    >>> C = np.array([[1., 0]])
+    >>> D = np.array([[0.]])
+    >>> l_system = lti(A, B, C, D)
+    >>> t, x = l_system.step(T=np.linspace(0, 5, 100))
+    >>> fig, ax = plt.subplots()
+    >>> ax.plot(t, x, label='Continuous', linewidth=3)
+
+    Transform it to a discrete state-space system using several methods.
+
+    >>> dt = 0.1
+    >>> for method in ['zoh', 'bilinear', 'euler', 'backward_diff', 'foh', 'impulse']:
+    ...    d_system = cont2discrete((A, B, C, D), dt, method=method)
+    ...    s, x_d = dstep(d_system)
+    ...    ax.step(s, np.squeeze(x_d), label=method, where='post')
+    >>> ax.axis([t[0], t[-1], x[0], 1.4])
+    >>> ax.legend(loc='best')
+    >>> fig.tight_layout()
+    >>> plt.show()
+
+    """
+    if hasattr(system, 'to_discrete') and callable(system.to_discrete):
+        return system.to_discrete(dt=dt, method=method, alpha=alpha)
+
+    if len(system) == 2:
+        sysd = cont2discrete(tf2ss(system[0], system[1]), dt, method=method,
+                             alpha=alpha)
+        return ss2tf(sysd[0], sysd[1], sysd[2], sysd[3]) + (dt,)
+    elif len(system) == 3:
+        sysd = cont2discrete(zpk2ss(system[0], system[1], system[2]), dt,
+                             method=method, alpha=alpha)
+        return ss2zpk(sysd[0], sysd[1], sysd[2], sysd[3]) + (dt,)
+    elif len(system) == 4:
+        a, b, c, d = system
+    else:
+        raise ValueError("First argument must either be a tuple of 2 (tf), "
+                         "3 (zpk), or 4 (ss) arrays.")
+
+    if method == 'gbt':
+        if alpha is None:
+            raise ValueError("Alpha parameter must be specified for the "
+                             "generalized bilinear transform (gbt) method")
+        elif alpha < 0 or alpha > 1:
+            raise ValueError("Alpha parameter must be within the interval "
+                             "[0,1] for the gbt method")
+
+    if method == 'gbt':
+        # This parameter is used repeatedly - compute once here
+        ima = np.eye(a.shape[0]) - alpha*dt*a
+        ad = linalg.solve(ima, np.eye(a.shape[0]) + (1.0-alpha)*dt*a)
+        bd = linalg.solve(ima, dt*b)
+
+        # Similarly solve for the output equation matrices
+        cd = linalg.solve(ima.transpose(), c.transpose())
+        cd = cd.transpose()
+        dd = d + alpha*np.dot(c, bd)
+
+    elif method == 'bilinear' or method == 'tustin':
+        return cont2discrete(system, dt, method="gbt", alpha=0.5)
+
+    elif method == 'euler' or method == 'forward_diff':
+        return cont2discrete(system, dt, method="gbt", alpha=0.0)
+
+    elif method == 'backward_diff':
+        return cont2discrete(system, dt, method="gbt", alpha=1.0)
+
+    elif method == 'zoh':
+        # Build an exponential matrix
+        em_upper = np.hstack((a, b))
+
+        # Need to stack zeros under the a and b matrices
+        em_lower = np.hstack((np.zeros((b.shape[1], a.shape[0])),
+                              np.zeros((b.shape[1], b.shape[1]))))
+
+        em = np.vstack((em_upper, em_lower))
+        ms = linalg.expm(dt * em)
+
+        # Dispose of the lower rows
+        ms = ms[:a.shape[0], :]
+
+        ad = ms[:, 0:a.shape[1]]
+        bd = ms[:, a.shape[1]:]
+
+        cd = c
+        dd = d
+
+    elif method == 'foh':
+        # Size parameters for convenience
+        n = a.shape[0]
+        m = b.shape[1]
+
+        # Build an exponential matrix similar to 'zoh' method
+        em_upper = linalg.block_diag(np.block([a, b]) * dt, np.eye(m))
+        em_lower = zeros((m, n + 2 * m))
+        em = np.block([[em_upper], [em_lower]])
+
+        ms = linalg.expm(em)
+
+        # Get the three blocks from upper rows
+        ms11 = ms[:n, 0:n]
+        ms12 = ms[:n, n:n + m]
+        ms13 = ms[:n, n + m:]
+
+        ad = ms11
+        bd = ms12 - ms13 + ms11 @ ms13
+        cd = c
+        dd = d + c @ ms13
+
+    elif method == 'impulse':
+        if not np.allclose(d, 0):
+            raise ValueError("Impulse method is only applicable "
+                             "to strictly proper systems")
+
+        ad = linalg.expm(a * dt)
+        bd = ad @ b * dt
+        cd = c
+        dd = c @ b * dt
+
+    else:
+        raise ValueError(f"Unknown transformation method '{method}'")
+
+    return ad, bd, cd, dd, dt
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/_ltisys.py b/venv/lib/python3.12/site-packages/scipy/signal/_ltisys.py
new file mode 100644
index 0000000000000000000000000000000000000000..d7c7f4e17c90be6c13c79e4e9db8af595e42c588
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/_ltisys.py
@@ -0,0 +1,3851 @@
+"""
+ltisys -- a collection of classes and functions for modeling linear
+time invariant systems.
+"""
+#
+# Author: Travis Oliphant 2001
+#
+# Feb 2010: Warren Weckesser
+#   Rewrote lsim2 and added impulse2.
+# Apr 2011: Jeffrey Armstrong <jeff@approximatrix.com>
+#   Added dlsim, dstep, dimpulse, cont2discrete
+# Aug 2013: Juan Luis Cano
+#   Rewrote abcd_normalize.
+# Jan 2015: Irvin Probst irvin DOT probst AT ensta-bretagne DOT fr
+#   Added pole placement
+# Mar 2015: Clancy Rowley
+#   Rewrote lsim
+# May 2015: Felix Berkenkamp
+#   Split lti class into subclasses
+#   Merged discrete systems and added dlti
+
+import warnings
+from types import GenericAlias
+
+# np.linalg.qr fails on some tests with LinAlgError: zgeqrf returns -7
+# use scipy's qr until this is solved
+
+from scipy.linalg import qr as s_qr
+from scipy import linalg
+from scipy.interpolate import make_interp_spline
+from ._filter_design import (tf2zpk, zpk2tf, normalize, freqs, freqz, freqs_zpk,
+                            freqz_zpk)
+from ._lti_conversion import (tf2ss, abcd_normalize, ss2tf, zpk2ss, ss2zpk,
+                              cont2discrete)
+
+import numpy as np
+from numpy import (real, atleast_1d, squeeze, asarray, zeros,
+                   dot, transpose, ones, linspace)
+import copy
+
+__all__ = ['lti', 'dlti', 'TransferFunction', 'ZerosPolesGain', 'StateSpace',
+           'lsim', 'impulse', 'step', 'bode',
+           'freqresp', 'place_poles', 'dlsim', 'dstep', 'dimpulse',
+           'dfreqresp', 'dbode']
+
+
+class LinearTimeInvariant:
+    # generic type compatibility with scipy-stubs
+    __class_getitem__: classmethod = classmethod(GenericAlias)
+
+    def __new__(cls, *system, **kwargs):
+        """Create a new object, don't allow direct instances."""
+        if cls is LinearTimeInvariant:
+            raise NotImplementedError('The LinearTimeInvariant class is not '
+                                      'meant to be used directly, use `lti` '
+                                      'or `dlti` instead.')
+        return super().__new__(cls)
+
+    def __init__(self):
+        """
+        Initialize the `lti` baseclass.
+
+        The heavy lifting is done by the subclasses.
+        """
+        super().__init__()
+
+        self.inputs = None
+        self.outputs = None
+        self._dt = None
+
+    @property
+    def dt(self):
+        """Return the sampling time of the system, `None` for `lti` systems."""
+        return self._dt
+
+    @property
+    def _dt_dict(self):
+        if self.dt is None:
+            return {}
+        else:
+            return {'dt': self.dt}
+
+    @property
+    def zeros(self):
+        """Zeros of the system."""
+        return self.to_zpk().zeros
+
+    @property
+    def poles(self):
+        """Poles of the system."""
+        return self.to_zpk().poles
+
+    def _as_ss(self):
+        """Convert to `StateSpace` system, without copying.
+
+        Returns
+        -------
+        sys: StateSpace
+            The `StateSpace` system. If the class is already an instance of
+            `StateSpace` then this instance is returned.
+        """
+        if isinstance(self, StateSpace):
+            return self
+        else:
+            return self.to_ss()
+
+    def _as_zpk(self):
+        """Convert to `ZerosPolesGain` system, without copying.
+
+        Returns
+        -------
+        sys: ZerosPolesGain
+            The `ZerosPolesGain` system. If the class is already an instance of
+            `ZerosPolesGain` then this instance is returned.
+        """
+        if isinstance(self, ZerosPolesGain):
+            return self
+        else:
+            return self.to_zpk()
+
+    def _as_tf(self):
+        """Convert to `TransferFunction` system, without copying.
+
+        Returns
+        -------
+        sys: ZerosPolesGain
+            The `TransferFunction` system. If the class is already an instance of
+            `TransferFunction` then this instance is returned.
+        """
+        if isinstance(self, TransferFunction):
+            return self
+        else:
+            return self.to_tf()
+
+
+class lti(LinearTimeInvariant):
+    r"""
+    Continuous-time linear time invariant system base class.
+
+    Parameters
+    ----------
+    *system : arguments
+        The `lti` class can be instantiated with either 2, 3 or 4 arguments.
+        The following gives the number of arguments and the corresponding
+        continuous-time subclass that is created:
+
+        * 2: `TransferFunction`:  (numerator, denominator)
+        * 3: `ZerosPolesGain`: (zeros, poles, gain)
+        * 4: `StateSpace`:  (A, B, C, D)
+
+        Each argument can be an array or a sequence.
+
+    See Also
+    --------
+    ZerosPolesGain, StateSpace, TransferFunction, dlti
+
+    Notes
+    -----
+    `lti` instances do not exist directly. Instead, `lti` creates an instance
+    of one of its subclasses: `StateSpace`, `TransferFunction` or
+    `ZerosPolesGain`.
+
+    If (numerator, denominator) is passed in for ``*system``, coefficients for
+    both the numerator and denominator should be specified in descending
+    exponent order (e.g., ``s^2 + 3s + 5`` would be represented as ``[1, 3,
+    5]``).
+
+    Changing the value of properties that are not directly part of the current
+    system representation (such as the `zeros` of a `StateSpace` system) is
+    very inefficient and may lead to numerical inaccuracies. It is better to
+    convert to the specific system representation first. For example, call
+    ``sys = sys.to_zpk()`` before accessing/changing the zeros, poles or gain.
+
+    Examples
+    --------
+    >>> from scipy import signal
+
+    >>> signal.lti(1, 2, 3, 4)
+    StateSpaceContinuous(
+    array([[1.]]),
+    array([[2.]]),
+    array([[3.]]),
+    array([[4.]]),
+    dt: None
+    )
+
+    Construct the transfer function
+    :math:`H(s) = \frac{5(s - 1)(s - 2)}{(s - 3)(s - 4)}`:
+
+    >>> signal.lti([1, 2], [3, 4], 5)
+    ZerosPolesGainContinuous(
+    array([1, 2]),
+    array([3, 4]),
+    5,
+    dt: None
+    )
+
+    Construct the transfer function :math:`H(s) = \frac{3s + 4}{1s + 2}`:
+
+    >>> signal.lti([3, 4], [1, 2])
+    TransferFunctionContinuous(
+    array([3., 4.]),
+    array([1., 2.]),
+    dt: None
+    )
+
+    """
+    def __new__(cls, *system):
+        """Create an instance of the appropriate subclass."""
+        if cls is lti:
+            N = len(system)
+            if N == 2:
+                return TransferFunctionContinuous.__new__(
+                    TransferFunctionContinuous, *system)
+            elif N == 3:
+                return ZerosPolesGainContinuous.__new__(
+                    ZerosPolesGainContinuous, *system)
+            elif N == 4:
+                return StateSpaceContinuous.__new__(StateSpaceContinuous,
+                                                    *system)
+            else:
+                raise ValueError("`system` needs to be an instance of `lti` "
+                                 "or have 2, 3 or 4 arguments.")
+        # __new__ was called from a subclass, let it call its own functions
+        return super().__new__(cls)
+
+    def __init__(self, *system):
+        """
+        Initialize the `lti` baseclass.
+
+        The heavy lifting is done by the subclasses.
+        """
+        super().__init__(*system)
+
+    def impulse(self, X0=None, T=None, N=None):
+        """
+        Return the impulse response of a continuous-time system.
+
+        Parameters
+        ----------
+        X0 : array_like, optional
+            Initial state-vector.  Defaults to zero.
+        T : array_like, optional
+            Time points.  Computed if not given.
+        N : int, optional
+            The number of time points to compute (if `T` is not given).
+
+        Returns
+        -------
+        T : ndarray
+            A 1-D array of time points.
+        yout : ndarray
+            A 1-D array containing the impulse response of the system (except for
+            singularities at zero).
+
+        See Also
+        --------
+        impulse : Impulse response of continuous-time LTI systems.
+        """
+        return impulse(self, X0=X0, T=T, N=N)
+
+    def step(self, X0=None, T=None, N=None):
+        """
+        Return the step response of a continuous-time system.
+
+        Parameters
+        ----------
+        X0 : array_like, optional
+            Initial state-vector (default is zero).
+        T : array_like, optional
+            Time points (computed if not given).
+        N : int, optional
+            Number of time points to compute if `T` is not given.
+
+        Returns
+        -------
+        T : 1D ndarray
+            Output time points.
+        yout : 1D ndarray
+            Step response of system.
+
+        See Also
+        --------
+        step : Step response of continuous-time LTI systems.
+        """
+        return step(self, X0=X0, T=T, N=N)
+
+    def output(self, U, T, X0=None):
+        """
+        Return the response of a continuous-time system to input `U`.
+
+        Parameters
+        ----------
+        U : array_like
+            An input array describing the input at each time `T`
+            (interpolation is assumed between given times).  If there are
+            multiple inputs, then each column of the 2D array
+            represents an input.  If U = 0 or None, a zero input is used.
+        T : array_like
+            The time steps at which the input is defined and at which the
+            output is desired.  Must be nonnegative, increasing, and equally spaced.
+        X0 : array_like, optional
+            The initial conditions on the state vector (zero by default).
+
+        Returns
+        -------
+        T : 1D ndarray
+            Time values for the output.
+        yout : 1D ndarray
+            System response.
+        xout : ndarray
+            Time evolution of the state vector.
+
+        See Also
+        --------
+        lsim : Simulate output of continuous-time LTI systems.
+        """
+        return lsim(self, U, T, X0=X0)
+
+    def bode(self, w=None, n=100):
+        """
+        Calculate Bode magnitude and phase data of a continuous-time system.
+
+        Parameters
+        ----------
+        w : array_like, optional
+            Array of frequencies (in rad/s). Magnitude and phase data is calculated
+            for every value in this array. If not given a reasonable set will be
+            calculated.
+        n : int, optional
+            Number of frequency points to compute if `w` is not given. The `n`
+            frequencies are logarithmically spaced in an interval chosen to
+            include the influence of the poles and zeros of the system.
+            Defaults to 100.
+
+        Returns
+        -------
+        w : 1D ndarray
+            Frequency array [rad/s]
+        mag : 1D ndarray
+            Magnitude array [dB]
+        phase : 1D ndarray
+            Phase array [deg]
+
+        See Also
+        --------
+        bode : Bode plot data for continuous-time LTI systems.
+
+        Examples
+        --------
+        >>> from scipy import signal
+        >>> import matplotlib.pyplot as plt
+
+        >>> sys = signal.TransferFunction([1], [1, 1])
+        >>> w, mag, phase = sys.bode()
+
+        >>> plt.figure()
+        >>> plt.semilogx(w, mag)    # Bode magnitude plot
+        >>> plt.figure()
+        >>> plt.semilogx(w, phase)  # Bode phase plot
+        >>> plt.show()
+
+        """
+        return bode(self, w=w, n=n)
+
+    def freqresp(self, w=None, n=10000):
+        """
+        Calculate the frequency response of a continuous-time system.
+
+        Parameters
+        ----------
+        w : array_like, optional
+            Array of frequencies (in rad/s). Magnitude and phase data is
+            calculated for every value in this array. If not given, a reasonable
+            set will be calculated.
+        n : int, optional
+            Number of frequency points to compute if `w` is not given. The `n`
+            frequencies are logarithmically spaced in an interval chosen to
+            include the influence of the poles and zeros of the system.
+            Defaults to 10000.
+
+        Returns
+        -------
+        w : 1D ndarray
+            Frequency array [rad/s]
+        H : 1D ndarray
+            Array of complex magnitude values
+
+        See Also
+        --------
+        freqresp : Frequency response of continuous-time LTI systems.
+        """
+        return freqresp(self, w=w, n=n)
+
+    def to_discrete(self, dt, method='zoh', alpha=None):
+        """Return a discretized version of the current system.
+
+        Parameters
+        ----------
+        dt : float
+            The discretization time step.
+        method : str, optional
+            Which method to use:
+
+            * gbt: generalized bilinear transformation
+            * bilinear: Tustin's approximation ("gbt" with alpha=0.5)
+            * euler: Euler (or forward differencing) method ("gbt" with alpha=0)
+            * backward_diff: Backwards differencing ("gbt" with alpha=1.0)
+            * zoh: zero-order hold (default)
+            * foh: first-order hold
+            * impulse: equivalent impulse response
+
+        alpha : float within [0, 1], optional
+            The generalized bilinear transformation weighting parameter, which
+            should only be specified with method="gbt", and is ignored otherwise
+
+        Returns
+        -------
+        sys: dlti
+            Discrete version of the current system.
+
+        See Also
+        --------
+        cont2discrete
+        """
+        raise NotImplementedError('to_discrete is not implemented for this '
+                                  'system class.')
+
+
+class dlti(LinearTimeInvariant):
+    r"""
+    Discrete-time linear time invariant system base class.
+
+    Parameters
+    ----------
+    *system : arguments
+        The `dlti` class can be instantiated with either 2, 3 or 4 arguments.
+        The following gives the number of arguments and the corresponding
+        discrete-time subclass that is created:
+
+        * 2: `TransferFunction`:  (numerator, denominator)
+        * 3: `ZerosPolesGain`: (zeros, poles, gain)
+        * 4: `StateSpace`:  (A, B, C, D)
+
+        Each argument can be an array or a sequence.
+    dt : float, optional
+        Sampling time [s] of the discrete-time systems. Defaults to ``True``
+        (unspecified sampling time). Must be specified as a keyword argument,
+        for example, ``dt=0.1``.
+
+    See Also
+    --------
+    ZerosPolesGain, StateSpace, TransferFunction, lti
+
+    Notes
+    -----
+    `dlti` instances do not exist directly. Instead, `dlti` creates an instance
+    of one of its subclasses: `StateSpace`, `TransferFunction` or
+    `ZerosPolesGain`.
+
+    Changing the value of properties that are not directly part of the current
+    system representation (such as the `zeros` of a `StateSpace` system) is
+    very inefficient and may lead to numerical inaccuracies.  It is better to
+    convert to the specific system representation first. For example, call
+    ``sys = sys.to_zpk()`` before accessing/changing the zeros, poles or gain.
+
+    If (numerator, denominator) is passed in for ``*system``, coefficients for
+    both the numerator and denominator should be specified in descending
+    exponent order (e.g., ``z^2 + 3z + 5`` would be represented as ``[1, 3,
+    5]``).
+
+    .. versionadded:: 0.18.0
+
+    Examples
+    --------
+    >>> from scipy import signal
+
+    >>> signal.dlti(1, 2, 3, 4)
+    StateSpaceDiscrete(
+    array([[1.]]),
+    array([[2.]]),
+    array([[3.]]),
+    array([[4.]]),
+    dt: True
+    )
+
+    >>> signal.dlti(1, 2, 3, 4, dt=0.1)
+    StateSpaceDiscrete(
+    array([[1.]]),
+    array([[2.]]),
+    array([[3.]]),
+    array([[4.]]),
+    dt: 0.1
+    )
+
+    Construct the transfer function
+    :math:`H(z) = \frac{5(z - 1)(z - 2)}{(z - 3)(z - 4)}` with a sampling time
+    of 0.1 seconds:
+
+    >>> signal.dlti([1, 2], [3, 4], 5, dt=0.1)
+    ZerosPolesGainDiscrete(
+    array([1, 2]),
+    array([3, 4]),
+    5,
+    dt: 0.1
+    )
+
+    Construct the transfer function :math:`H(z) = \frac{3z + 4}{1z + 2}` with
+    a sampling time of 0.1 seconds:
+
+    >>> signal.dlti([3, 4], [1, 2], dt=0.1)
+    TransferFunctionDiscrete(
+    array([3., 4.]),
+    array([1., 2.]),
+    dt: 0.1
+    )
+
+    """
+    def __new__(cls, *system, dt=None):
+        """Create an instance of the appropriate subclass."""
+        if cls is dlti:
+            N = len(system)
+            if N == 2:
+                return TransferFunctionDiscrete.__new__(
+                    TransferFunctionDiscrete, *system, dt=dt)
+            elif N == 3:
+                return ZerosPolesGainDiscrete.__new__(ZerosPolesGainDiscrete,
+                                                      *system, dt=dt)
+            elif N == 4:
+                return StateSpaceDiscrete.__new__(StateSpaceDiscrete, *system,
+                                                  dt=dt)
+            else:
+                raise ValueError("`system` needs to be an instance of `dlti` "
+                                 "or have 2, 3 or 4 arguments.")
+        # __new__ was called from a subclass, let it call its own functions
+        return super().__new__(cls)
+
+    def __init__(self, *system, **kwargs):
+        """
+        Initialize the `lti` baseclass.
+
+        The heavy lifting is done by the subclasses.
+        """
+        dt = kwargs.pop('dt', True)
+        super().__init__(*system, **kwargs)
+
+        self.dt = dt
+
+    @property
+    def dt(self):
+        """Return the sampling time of the system."""
+        return self._dt
+
+    @dt.setter
+    def dt(self, dt):
+        self._dt = dt
+
+    def impulse(self, x0=None, t=None, n=None):
+        """
+        Return the impulse response of the discrete-time `dlti` system.
+
+        Parameters
+        ----------
+        x0 : array_like, optional
+            Initial state-vector.  Defaults to zero.
+        t : array_like, optional
+            Time points. Computed if not given.
+        n : int, optional
+            The number of time points to compute (if `t` is not given).
+
+        Returns
+        -------
+        tout : ndarray
+            Time values for the output, as a 1-D array.
+        yout : tuple of ndarray
+            Impulse response of system.  Each element of the tuple represents
+            the output of the system based on an impulse in each input.
+
+        See Also
+        --------
+        dimpulse : Impulse response of discrete-time LTI systems.
+        """
+        return dimpulse(self, x0=x0, t=t, n=n)
+
+    def step(self, x0=None, t=None, n=None):
+        """
+        Return the step response of the discrete-time `dlti` system.
+
+        Parameters
+        ----------
+        x0 : array_like, optional
+            Initial state-vector. Defaults to zero.
+        t : array_like, optional
+            Time points. Computed if not given.
+        n : int, optional
+            The number of time points to compute (if `t` is not given).
+
+        Returns
+        -------
+        tout : ndarray
+            Output time points, as a 1-D array.
+        yout : tuple of ndarray
+            Step response of system.  Each element of the tuple represents
+            the output of the system based on a step response to each input.
+
+        See Also
+        --------
+        dstep : Step response of discrete-time LTI systems.
+        """
+        return dstep(self, x0=x0, t=t, n=n)
+
+    def output(self, u, t, x0=None):
+        """
+        Return the response of the discrete-time system to input `u`.
+
+        Parameters
+        ----------
+        u : array_like
+            An input array describing the input at each time `t` (interpolation is
+            assumed between given times).  If there are multiple inputs, then each
+            column of the 2D array represents an input.
+        t : array_like, optional
+            The time steps at which the input is defined.  If `t` is given, it
+            must be the same length as `u`, and the final value in `t` determines
+            the number of steps returned in the output.
+        x0 : array_like, optional
+            The initial conditions on the state vector (zero by default).
+
+        Returns
+        -------
+        tout : ndarray
+            Time values for the output, as a 1-D array.
+        yout : ndarray
+            System response, as a 1-D array.
+        xout : ndarray, optional
+            Time-evolution of the state-vector.  Only generated if the input is a
+            `StateSpace` system.
+
+        See Also
+        --------
+        dlsim : Simulate output of discrete-time LTI systems.
+        """
+        return dlsim(self, u, t, x0=x0)
+
+    def bode(self, w=None, n=100):
+        r"""
+        Calculate Bode magnitude and phase data of a discrete-time system.
+
+        Parameters
+        ----------
+        w : array_like, optional
+            Array of frequencies normalized to the Nyquist frequency being π, i.e.,
+            having unit radiant / sample. Magnitude and phase data is calculated for
+            every value in this array. If not given, a reasonable set will be
+            calculated.
+        n : int, optional
+            Number of frequency points to compute if `w` is not given. The `n`
+            frequencies are logarithmically spaced in an interval chosen to
+            include the influence of the poles and zeros of the system.
+            Defaults to 100.
+
+        Returns
+        -------
+        w : 1D ndarray
+            Array of frequencies normalized to the Nyquist frequency being ``np.pi/dt``
+            with ``dt`` being the sampling interval of the `system` parameter.
+            The unit is rad/s assuming ``dt`` is in seconds.
+        mag : 1D ndarray
+            Magnitude array in dB
+        phase : 1D ndarray
+            Phase array in degrees
+
+        See Also
+        --------
+        dbode : Bode plot data for discrete-time LTI systems.
+
+        Examples
+        --------
+        >>> from scipy import signal
+        >>> import matplotlib.pyplot as plt
+
+        Construct the transfer function :math:`H(z) = \frac{1}{z^2 + 2z + 3}`
+        with sampling time 0.5s:
+
+        >>> sys = signal.TransferFunction([1], [1, 2, 3], dt=0.5)
+
+        Equivalent: signal.dbode(sys)
+
+        >>> w, mag, phase = sys.bode()
+
+        >>> plt.figure()
+        >>> plt.semilogx(w, mag)    # Bode magnitude plot
+        >>> plt.figure()
+        >>> plt.semilogx(w, phase)  # Bode phase plot
+        >>> plt.show()
+
+        """
+        return dbode(self, w=w, n=n)
+
+    def freqresp(self, w=None, n=10000, whole=False):
+        """
+        Calculate the frequency response of a discrete-time system.
+
+        Parameters
+        ----------
+        w : array_like, optional
+            Array of frequencies (in radians/sample). Magnitude and phase data is
+            calculated for every value in this array. If not given a reasonable
+            set will be calculated.
+        n : int, optional
+            Number of frequency points to compute if `w` is not given. The `n`
+            frequencies are logarithmically spaced in an interval chosen to
+            include the influence of the poles and zeros of the system.
+        whole : bool, optional
+            Normally, if `w` is not given, frequencies are computed from 0 to the
+            Nyquist frequency, pi radians/sample (upper-half of unit-circle). If
+            `whole` is True, compute frequencies from 0 to 2*pi radians/sample.
+
+        Returns
+        -------
+        w : 1D ndarray
+            Frequency array [radians/sample]
+        H : 1D ndarray
+            Array of complex magnitude values
+
+        See Also
+        --------
+        dfreqresp : Frequency response of discrete-time LTI systems.
+        """
+        return dfreqresp(self, w=w, n=n, whole=whole)
+
+
+class TransferFunction(LinearTimeInvariant):
+    r"""Linear Time Invariant system class in transfer function form.
+
+    Represents the system as the continuous-time transfer function
+    :math:`H(s)=\sum_{i=0}^N b[N-i] s^i / \sum_{j=0}^M a[M-j] s^j` or the
+    discrete-time transfer function
+    :math:`H(z)=\sum_{i=0}^N b[N-i] z^i / \sum_{j=0}^M a[M-j] z^j`, where
+    :math:`b` are elements of the numerator `num`, :math:`a` are elements of
+    the denominator `den`, and ``N == len(b) - 1``, ``M == len(a) - 1``.
+    `TransferFunction` systems inherit additional
+    functionality from the `lti`, respectively the `dlti` classes, depending on
+    which system representation is used.
+
+    Parameters
+    ----------
+    *system : arguments
+        The `TransferFunction` class can be instantiated with 1 or 2
+        arguments. The following gives the number of input arguments and their
+        interpretation:
+
+        * 1: `lti` or `dlti` system: (`StateSpace`, `TransferFunction` or
+          `ZerosPolesGain`)
+        * 2: array_like: (numerator, denominator)
+    dt : float, optional
+        Sampling time [s] of the discrete-time systems. Defaults to `None`
+        (continuous-time). Must be specified as a keyword argument, for
+        example, ``dt=0.1``.
+
+    See Also
+    --------
+    ZerosPolesGain, StateSpace, lti, dlti
+    tf2ss, tf2zpk, tf2sos
+
+    Notes
+    -----
+    Changing the value of properties that are not part of the
+    `TransferFunction` system representation (such as the `A`, `B`, `C`, `D`
+    state-space matrices) is very inefficient and may lead to numerical
+    inaccuracies.  It is better to convert to the specific system
+    representation first. For example, call ``sys = sys.to_ss()`` before
+    accessing/changing the A, B, C, D system matrices.
+
+    If (numerator, denominator) is passed in for ``*system``, coefficients
+    for both the numerator and denominator should be specified in descending
+    exponent order (e.g. ``s^2 + 3s + 5`` or ``z^2 + 3z + 5`` would be
+    represented as ``[1, 3, 5]``)
+
+    Examples
+    --------
+    Construct the transfer function
+    :math:`H(s) = \frac{s^2 + 3s + 3}{s^2 + 2s + 1}`:
+
+    >>> from scipy import signal
+
+    >>> num = [1, 3, 3]
+    >>> den = [1, 2, 1]
+
+    >>> signal.TransferFunction(num, den)
+    TransferFunctionContinuous(
+    array([1., 3., 3.]),
+    array([1., 2., 1.]),
+    dt: None
+    )
+
+    Construct the transfer function
+    :math:`H(z) = \frac{z^2 + 3z + 3}{z^2 + 2z + 1}` with a sampling time of
+    0.1 seconds:
+
+    >>> signal.TransferFunction(num, den, dt=0.1)
+    TransferFunctionDiscrete(
+    array([1., 3., 3.]),
+    array([1., 2., 1.]),
+    dt: 0.1
+    )
+
+    """
+    def __new__(cls, *system, dt=None):
+        """Handle object conversion if input is an instance of lti."""
+        if len(system) == 1 and isinstance(system[0], LinearTimeInvariant):
+            return system[0].to_tf()
+
+        # Choose whether to inherit from `lti` or from `dlti`
+        if cls is TransferFunction:
+            if dt is None:
+                return TransferFunctionContinuous.__new__(
+                    TransferFunctionContinuous, *system)
+            else:
+                return TransferFunctionDiscrete.__new__(
+                    TransferFunctionDiscrete, *system, dt=dt)
+
+        # No special conversion needed
+        return super().__new__(cls)
+
+    def __init__(self, *system, **kwargs):
+        """Initialize the state space LTI system."""
+        # Conversion of lti instances is handled in __new__
+        if isinstance(system[0], LinearTimeInvariant):
+            return
+
+        # Remove system arguments, not needed by parents anymore
+        super().__init__(**kwargs)
+
+        self._num = None
+        self._den = None
+
+        self.num, self.den = normalize(*system)
+
+    def __repr__(self):
+        """Return representation of the system's transfer function"""
+        return (
+            f'{self.__class__.__name__}(\n'
+            f'{repr(self.num)},\n'
+            f'{repr(self.den)},\n'
+            f'dt: {repr(self.dt)}\n)'
+        )
+
+    @property
+    def num(self):
+        """Numerator of the `TransferFunction` system."""
+        return self._num
+
+    @num.setter
+    def num(self, num):
+        self._num = atleast_1d(num)
+
+        # Update dimensions
+        if len(self.num.shape) > 1:
+            self.outputs, self.inputs = self.num.shape
+        else:
+            self.outputs = 1
+            self.inputs = 1
+
+    @property
+    def den(self):
+        """Denominator of the `TransferFunction` system."""
+        return self._den
+
+    @den.setter
+    def den(self, den):
+        self._den = atleast_1d(den)
+
+    def _copy(self, system):
+        """
+        Copy the parameters of another `TransferFunction` object
+
+        Parameters
+        ----------
+        system : `TransferFunction`
+            The `StateSpace` system that is to be copied
+
+        """
+        self.num = system.num
+        self.den = system.den
+
+    def to_tf(self):
+        """
+        Return a copy of the current `TransferFunction` system.
+
+        Returns
+        -------
+        sys : instance of `TransferFunction`
+            The current system (copy)
+
+        """
+        return copy.deepcopy(self)
+
+    def to_zpk(self):
+        """
+        Convert system representation to `ZerosPolesGain`.
+
+        Returns
+        -------
+        sys : instance of `ZerosPolesGain`
+            Zeros, poles, gain representation of the current system
+
+        """
+        return ZerosPolesGain(*tf2zpk(self.num, self.den),
+                              **self._dt_dict)
+
+    def to_ss(self):
+        """
+        Convert system representation to `StateSpace`.
+
+        Returns
+        -------
+        sys : instance of `StateSpace`
+            State space model of the current system
+
+        """
+        return StateSpace(*tf2ss(self.num, self.den),
+                          **self._dt_dict)
+
+    @staticmethod
+    def _z_to_zinv(num, den):
+        """Change a transfer function from the variable `z` to `z**-1`.
+
+        Parameters
+        ----------
+        num, den: 1d array_like
+            Sequences representing the coefficients of the numerator and
+            denominator polynomials, in order of descending degree of 'z'.
+            That is, ``5z**2 + 3z + 2`` is presented as ``[5, 3, 2]``.
+
+        Returns
+        -------
+        num, den: 1d array_like
+            Sequences representing the coefficients of the numerator and
+            denominator polynomials, in order of ascending degree of 'z**-1'.
+            That is, ``5 + 3 z**-1 + 2 z**-2`` is presented as ``[5, 3, 2]``.
+        """
+        diff = len(num) - len(den)
+        if diff > 0:
+            den = np.hstack((np.zeros(diff), den))
+        elif diff < 0:
+            num = np.hstack((np.zeros(-diff), num))
+        return num, den
+
+    @staticmethod
+    def _zinv_to_z(num, den):
+        """Change a transfer function from the variable `z` to `z**-1`.
+
+        Parameters
+        ----------
+        num, den: 1d array_like
+            Sequences representing the coefficients of the numerator and
+            denominator polynomials, in order of ascending degree of 'z**-1'.
+            That is, ``5 + 3 z**-1 + 2 z**-2`` is presented as ``[5, 3, 2]``.
+
+        Returns
+        -------
+        num, den: 1d array_like
+            Sequences representing the coefficients of the numerator and
+            denominator polynomials, in order of descending degree of 'z'.
+            That is, ``5z**2 + 3z + 2`` is presented as ``[5, 3, 2]``.
+        """
+        diff = len(num) - len(den)
+        if diff > 0:
+            den = np.hstack((den, np.zeros(diff)))
+        elif diff < 0:
+            num = np.hstack((num, np.zeros(-diff)))
+        return num, den
+
+
+class TransferFunctionContinuous(TransferFunction, lti):
+    r"""
+    Continuous-time Linear Time Invariant system in transfer function form.
+
+    Represents the system as the transfer function
+    :math:`H(s)=\sum_{i=0}^N b[N-i] s^i / \sum_{j=0}^M a[M-j] s^j`, where
+    :math:`b` are elements of the numerator `num`, :math:`a` are elements of
+    the denominator `den`, and ``N == len(b) - 1``, ``M == len(a) - 1``.
+    Continuous-time `TransferFunction` systems inherit additional
+    functionality from the `lti` class.
+
+    Parameters
+    ----------
+    *system : arguments
+        The `TransferFunction` class can be instantiated with 1 or 2
+        arguments. The following gives the number of input arguments and their
+        interpretation:
+
+        * 1: `lti` system: (`StateSpace`, `TransferFunction` or `ZerosPolesGain`)
+        * 2: array_like: (numerator, denominator)
+
+    See Also
+    --------
+    ZerosPolesGain, StateSpace, lti
+    tf2ss, tf2zpk, tf2sos
+
+    Notes
+    -----
+    Changing the value of properties that are not part of the
+    `TransferFunction` system representation (such as the `A`, `B`, `C`, `D`
+    state-space matrices) is very inefficient and may lead to numerical
+    inaccuracies.  It is better to convert to the specific system
+    representation first. For example, call ``sys = sys.to_ss()`` before
+    accessing/changing the A, B, C, D system matrices.
+
+    If (numerator, denominator) is passed in for ``*system``, coefficients
+    for both the numerator and denominator should be specified in descending
+    exponent order (e.g. ``s^2 + 3s + 5`` would be represented as
+    ``[1, 3, 5]``)
+
+    Examples
+    --------
+    Construct the transfer function
+    :math:`H(s) = \frac{s^2 + 3s + 3}{s^2 + 2s + 1}`:
+
+    >>> from scipy import signal
+
+    >>> num = [1, 3, 3]
+    >>> den = [1, 2, 1]
+
+    >>> signal.TransferFunction(num, den)
+    TransferFunctionContinuous(
+    array([1., 3., 3.]),
+    array([1., 2., 1.]),
+    dt: None
+    )
+
+    """
+
+    def to_discrete(self, dt, method='zoh', alpha=None):
+        """
+        Returns the discretized `TransferFunction` system.
+
+        Parameters
+        ----------
+        dt : float
+            The discretization time step.
+        method : str, optional
+            Which method to use:
+
+            * gbt: generalized bilinear transformation
+            * bilinear: Tustin's approximation ("gbt" with alpha=0.5)
+            * euler: Euler (or forward differencing) method ("gbt" with alpha=0)
+            * backward_diff: Backwards differencing ("gbt" with alpha=1.0)
+            * zoh: zero-order hold (default)
+            * foh: first-order hold
+            * impulse: equivalent impulse response
+
+        alpha : float within [0, 1], optional
+            The generalized bilinear transformation weighting parameter, which
+            should only be specified with method="gbt", and is ignored otherwise
+
+        Returns
+        -------
+        sys: instance of `dlti` and `StateSpace`
+
+        See Also
+        --------
+        cont2discrete
+        """
+        return TransferFunction(*cont2discrete((self.num, self.den),
+                                               dt,
+                                               method=method,
+                                               alpha=alpha)[:-1],
+                                dt=dt)
+
+
+class TransferFunctionDiscrete(TransferFunction, dlti):
+    r"""
+    Discrete-time Linear Time Invariant system in transfer function form.
+
+    Represents the system as the transfer function
+    :math:`H(z)=\sum_{i=0}^N b[N-i] z^i / \sum_{j=0}^M a[M-j] z^j`, where
+    :math:`b` are elements of the numerator `num`, :math:`a` are elements of
+    the denominator `den`, and ``N == len(b) - 1``, ``M == len(a) - 1``.
+    Discrete-time `TransferFunction` systems inherit additional functionality
+    from the `dlti` class.
+
+    Parameters
+    ----------
+    *system : arguments
+        The `TransferFunction` class can be instantiated with 1 or 2
+        arguments. The following gives the number of input arguments and their
+        interpretation:
+
+        * 1: `dlti` system: (`StateSpace`, `TransferFunction` or `ZerosPolesGain`)
+        * 2: array_like: (numerator, denominator)
+    dt : float, optional
+        Sampling time [s] of the discrete-time systems. Defaults to `True`
+        (unspecified sampling time). Must be specified as a keyword argument,
+        for example, ``dt=0.1``.
+
+    See Also
+    --------
+    ZerosPolesGain, StateSpace, dlti
+    tf2ss, tf2zpk, tf2sos
+
+    Notes
+    -----
+    Changing the value of properties that are not part of the
+    `TransferFunction` system representation (such as the `A`, `B`, `C`, `D`
+    state-space matrices) is very inefficient and may lead to numerical
+    inaccuracies.
+
+    If (numerator, denominator) is passed in for ``*system``, coefficients
+    for both the numerator and denominator should be specified in descending
+    exponent order (e.g., ``z^2 + 3z + 5`` would be represented as
+    ``[1, 3, 5]``).
+
+    Examples
+    --------
+    Construct the transfer function
+    :math:`H(z) = \frac{z^2 + 3z + 3}{z^2 + 2z + 1}` with a sampling time of
+    0.5 seconds:
+
+    >>> from scipy import signal
+
+    >>> num = [1, 3, 3]
+    >>> den = [1, 2, 1]
+
+    >>> signal.TransferFunction(num, den, dt=0.5)
+    TransferFunctionDiscrete(
+    array([1., 3., 3.]),
+    array([1., 2., 1.]),
+    dt: 0.5
+    )
+
+    """
+    pass
+
+
+class ZerosPolesGain(LinearTimeInvariant):
+    r"""
+    Linear Time Invariant system class in zeros, poles, gain form.
+
+    Represents the system as the continuous- or discrete-time transfer function
+    :math:`H(s)=k \prod_i (s - z[i]) / \prod_j (s - p[j])`, where :math:`k` is
+    the `gain`, :math:`z` are the `zeros` and :math:`p` are the `poles`.
+    `ZerosPolesGain` systems inherit additional functionality from the `lti`,
+    respectively the `dlti` classes, depending on which system representation
+    is used.
+
+    Parameters
+    ----------
+    *system : arguments
+        The `ZerosPolesGain` class can be instantiated with 1 or 3
+        arguments. The following gives the number of input arguments and their
+        interpretation:
+
+        * 1: `lti` or `dlti` system: (`StateSpace`, `TransferFunction` or
+          `ZerosPolesGain`)
+        * 3: array_like: (zeros, poles, gain)
+    dt : float, optional
+        Sampling time [s] of the discrete-time systems. Defaults to `None`
+        (continuous-time). Must be specified as a keyword argument, for
+        example, ``dt=0.1``.
+
+
+    See Also
+    --------
+    TransferFunction, StateSpace, lti, dlti
+    zpk2ss, zpk2tf, zpk2sos
+
+    Notes
+    -----
+    Changing the value of properties that are not part of the
+    `ZerosPolesGain` system representation (such as the `A`, `B`, `C`, `D`
+    state-space matrices) is very inefficient and may lead to numerical
+    inaccuracies.  It is better to convert to the specific system
+    representation first. For example, call ``sys = sys.to_ss()`` before
+    accessing/changing the A, B, C, D system matrices.
+
+    Examples
+    --------
+    Construct the transfer function
+    :math:`H(s) = \frac{5(s - 1)(s - 2)}{(s - 3)(s - 4)}`:
+
+    >>> from scipy import signal
+
+    >>> signal.ZerosPolesGain([1, 2], [3, 4], 5)
+    ZerosPolesGainContinuous(
+    array([1, 2]),
+    array([3, 4]),
+    5,
+    dt: None
+    )
+
+    Construct the transfer function
+    :math:`H(z) = \frac{5(z - 1)(z - 2)}{(z - 3)(z - 4)}` with a sampling time
+    of 0.1 seconds:
+
+    >>> signal.ZerosPolesGain([1, 2], [3, 4], 5, dt=0.1)
+    ZerosPolesGainDiscrete(
+    array([1, 2]),
+    array([3, 4]),
+    5,
+    dt: 0.1
+    )
+
+    """
+    def __new__(cls, *system, dt=None):
+        """Handle object conversion if input is an instance of `lti`"""
+        if len(system) == 1 and isinstance(system[0], LinearTimeInvariant):
+            return system[0].to_zpk()
+
+        # Choose whether to inherit from `lti` or from `dlti`
+        if cls is ZerosPolesGain:
+            if dt is None:
+                return ZerosPolesGainContinuous.__new__(
+                    ZerosPolesGainContinuous,
+                    *system)
+            else:
+                return ZerosPolesGainDiscrete.__new__(
+                    ZerosPolesGainDiscrete,
+                    *system, dt=dt)
+
+        # No special conversion needed
+        return super().__new__(cls)
+
+    def __init__(self, *system, **kwargs):
+        """Initialize the zeros, poles, gain system."""
+        # Conversion of lti instances is handled in __new__
+        if isinstance(system[0], LinearTimeInvariant):
+            return
+
+        super().__init__(**kwargs)
+
+        self._zeros = None
+        self._poles = None
+        self._gain = None
+
+        self.zeros, self.poles, self.gain = system
+
+    def __repr__(self):
+        """Return representation of the `ZerosPolesGain` system."""
+        return (
+            f'{self.__class__.__name__}(\n'
+            f'{repr(self.zeros)},\n'
+            f'{repr(self.poles)},\n'
+            f'{repr(self.gain)},\n'
+            f'dt: {repr(self.dt)}\n)'
+        )
+
+    @property
+    def zeros(self):
+        """Zeros of the `ZerosPolesGain` system."""
+        return self._zeros
+
+    @zeros.setter
+    def zeros(self, zeros):
+        self._zeros = atleast_1d(zeros)
+
+        # Update dimensions
+        if len(self.zeros.shape) > 1:
+            self.outputs, self.inputs = self.zeros.shape
+        else:
+            self.outputs = 1
+            self.inputs = 1
+
+    @property
+    def poles(self):
+        """Poles of the `ZerosPolesGain` system."""
+        return self._poles
+
+    @poles.setter
+    def poles(self, poles):
+        self._poles = atleast_1d(poles)
+
+    @property
+    def gain(self):
+        """Gain of the `ZerosPolesGain` system."""
+        return self._gain
+
+    @gain.setter
+    def gain(self, gain):
+        self._gain = gain
+
+    def _copy(self, system):
+        """
+        Copy the parameters of another `ZerosPolesGain` system.
+
+        Parameters
+        ----------
+        system : instance of `ZerosPolesGain`
+            The zeros, poles gain system that is to be copied
+
+        """
+        self.poles = system.poles
+        self.zeros = system.zeros
+        self.gain = system.gain
+
+    def to_tf(self):
+        """
+        Convert system representation to `TransferFunction`.
+
+        Returns
+        -------
+        sys : instance of `TransferFunction`
+            Transfer function of the current system
+
+        """
+        return TransferFunction(*zpk2tf(self.zeros, self.poles, self.gain),
+                                **self._dt_dict)
+
+    def to_zpk(self):
+        """
+        Return a copy of the current 'ZerosPolesGain' system.
+
+        Returns
+        -------
+        sys : instance of `ZerosPolesGain`
+            The current system (copy)
+
+        """
+        return copy.deepcopy(self)
+
+    def to_ss(self):
+        """
+        Convert system representation to `StateSpace`.
+
+        Returns
+        -------
+        sys : instance of `StateSpace`
+            State space model of the current system
+
+        """
+        return StateSpace(*zpk2ss(self.zeros, self.poles, self.gain),
+                          **self._dt_dict)
+
+
+class ZerosPolesGainContinuous(ZerosPolesGain, lti):
+    r"""
+    Continuous-time Linear Time Invariant system in zeros, poles, gain form.
+
+    Represents the system as the continuous time transfer function
+    :math:`H(s)=k \prod_i (s - z[i]) / \prod_j (s - p[j])`, where :math:`k` is
+    the `gain`, :math:`z` are the `zeros` and :math:`p` are the `poles`.
+    Continuous-time `ZerosPolesGain` systems inherit additional functionality
+    from the `lti` class.
+
+    Parameters
+    ----------
+    *system : arguments
+        The `ZerosPolesGain` class can be instantiated with 1 or 3
+        arguments. The following gives the number of input arguments and their
+        interpretation:
+
+        * 1: `lti` system: (`StateSpace`, `TransferFunction` or `ZerosPolesGain`)
+        * 3: array_like: (zeros, poles, gain)
+
+    See Also
+    --------
+    TransferFunction, StateSpace, lti
+    zpk2ss, zpk2tf, zpk2sos
+
+    Notes
+    -----
+    Changing the value of properties that are not part of the
+    `ZerosPolesGain` system representation (such as the `A`, `B`, `C`, `D`
+    state-space matrices) is very inefficient and may lead to numerical
+    inaccuracies.  It is better to convert to the specific system
+    representation first. For example, call ``sys = sys.to_ss()`` before
+    accessing/changing the A, B, C, D system matrices.
+
+    Examples
+    --------
+    Construct the transfer function
+    :math:`H(s)=\frac{5(s - 1)(s - 2)}{(s - 3)(s - 4)}`:
+
+    >>> from scipy import signal
+
+    >>> signal.ZerosPolesGain([1, 2], [3, 4], 5)
+    ZerosPolesGainContinuous(
+    array([1, 2]),
+    array([3, 4]),
+    5,
+    dt: None
+    )
+
+    """
+
+    def to_discrete(self, dt, method='zoh', alpha=None):
+        """
+        Returns the discretized `ZerosPolesGain` system.
+
+        Parameters
+        ----------
+        dt : float
+            The discretization time step.
+        method : str, optional
+            Which method to use:
+
+            * gbt: generalized bilinear transformation
+            * bilinear: Tustin's approximation ("gbt" with alpha=0.5)
+            * euler: Euler (or forward differencing) method ("gbt" with alpha=0)
+            * backward_diff: Backwards differencing ("gbt" with alpha=1.0)
+            * zoh: zero-order hold (default)
+            * foh: first-order hold
+            * impulse: equivalent impulse response
+
+        alpha : float within [0, 1], optional
+            The generalized bilinear transformation weighting parameter, which
+            should only be specified with method="gbt", and is ignored otherwise
+
+        Returns
+        -------
+        sys: instance of `dlti` and `ZerosPolesGain`
+
+        See Also
+        --------
+        cont2discrete
+        """
+        return ZerosPolesGain(
+            *cont2discrete((self.zeros, self.poles, self.gain),
+                           dt,
+                           method=method,
+                           alpha=alpha)[:-1],
+            dt=dt)
+
+
+class ZerosPolesGainDiscrete(ZerosPolesGain, dlti):
+    r"""
+    Discrete-time Linear Time Invariant system in zeros, poles, gain form.
+
+    Represents the system as the discrete-time transfer function
+    :math:`H(z)=k \prod_i (z - q[i]) / \prod_j (z - p[j])`, where :math:`k` is
+    the `gain`, :math:`q` are the `zeros` and :math:`p` are the `poles`.
+    Discrete-time `ZerosPolesGain` systems inherit additional functionality
+    from the `dlti` class.
+
+    Parameters
+    ----------
+    *system : arguments
+        The `ZerosPolesGain` class can be instantiated with 1 or 3
+        arguments. The following gives the number of input arguments and their
+        interpretation:
+
+        * 1: `dlti` system: (`StateSpace`, `TransferFunction` or `ZerosPolesGain`)
+        * 3: array_like: (zeros, poles, gain)
+    dt : float, optional
+        Sampling time [s] of the discrete-time systems. Defaults to `True`
+        (unspecified sampling time). Must be specified as a keyword argument,
+        for example, ``dt=0.1``.
+
+    See Also
+    --------
+    TransferFunction, StateSpace, dlti
+    zpk2ss, zpk2tf, zpk2sos
+
+    Notes
+    -----
+    Changing the value of properties that are not part of the
+    `ZerosPolesGain` system representation (such as the `A`, `B`, `C`, `D`
+    state-space matrices) is very inefficient and may lead to numerical
+    inaccuracies.  It is better to convert to the specific system
+    representation first. For example, call ``sys = sys.to_ss()`` before
+    accessing/changing the A, B, C, D system matrices.
+
+    Examples
+    --------
+    Construct the transfer function
+    :math:`H(s) = \frac{5(s - 1)(s - 2)}{(s - 3)(s - 4)}`:
+
+    >>> from scipy import signal
+
+    >>> signal.ZerosPolesGain([1, 2], [3, 4], 5)
+    ZerosPolesGainContinuous(
+    array([1, 2]),
+    array([3, 4]),
+    5,
+    dt: None
+    )
+
+    Construct the transfer function
+    :math:`H(z) = \frac{5(z - 1)(z - 2)}{(z - 3)(z - 4)}` with a sampling time
+    of 0.1 seconds:
+
+    >>> signal.ZerosPolesGain([1, 2], [3, 4], 5, dt=0.1)
+    ZerosPolesGainDiscrete(
+    array([1, 2]),
+    array([3, 4]),
+    5,
+    dt: 0.1
+    )
+
+    """
+    pass
+
+
+class StateSpace(LinearTimeInvariant):
+    r"""
+    Linear Time Invariant system in state-space form.
+
+    Represents the system as the continuous-time, first order differential
+    equation :math:`\dot{x} = A x + B u` or the discrete-time difference
+    equation :math:`x[k+1] = A x[k] + B u[k]`. `StateSpace` systems
+    inherit additional functionality from the `lti`, respectively the `dlti`
+    classes, depending on which system representation is used.
+
+    Parameters
+    ----------
+    *system : arguments
+        The `StateSpace` class can be instantiated with 1 or 4 arguments.
+        The following gives the number of input arguments and their
+        interpretation:
+
+        * 1: `lti` or `dlti` system: (`StateSpace`, `TransferFunction` or
+          `ZerosPolesGain`)
+        * 4: array_like: (A, B, C, D)
+    dt : float, optional
+        Sampling time [s] of the discrete-time systems. Defaults to `None`
+        (continuous-time). Must be specified as a keyword argument, for
+        example, ``dt=0.1``.
+
+    See Also
+    --------
+    TransferFunction, ZerosPolesGain, lti, dlti
+    ss2zpk, ss2tf, zpk2sos
+
+    Notes
+    -----
+    If the parameter `system` is a tuple (A, B, C, D) with four state space matrices,
+    then those matrices are converted into two-dimensional arrays of the same dtype
+    by calling `abcd_normalize`. The resulting dtype will be based on NumPy's dtype
+    promotion rules, except in the case where each of `A`, `B`, `C`, and `D` has
+    integer dtype, in which case the resulting dtype will be the default floating point
+    dtype of ``float64``.
+
+    Changing the value of properties that are not part of the
+    `StateSpace` system representation (such as `zeros` or `poles`) is very
+    inefficient and may lead to numerical inaccuracies.  It is better to
+    convert to the specific system representation first. For example, call
+    ``sys = sys.to_zpk()`` before accessing/changing the zeros, poles or gain.
+
+    The :ref:`tutorial_signal_state_space_representation` section of the
+    :ref:`user_guide` presents the corresponding definitions of continuous-time and
+    disrcete time state space systems.
+
+    Examples
+    --------
+    >>> from scipy import signal
+    >>> import numpy as np
+    >>> a = np.array([[0, 1], [0, 0]])
+    >>> b = np.array([[0], [1]])
+    >>> c = np.array([[1, 0]])
+    >>> d = np.array([[0]])
+
+    >>> sys = signal.StateSpace(a, b, c, d)
+    >>> print(sys)
+    StateSpaceContinuous(
+    array([[0., 1.],
+           [0., 0.]]),
+    array([[0.],
+           [1.]]),
+    array([[1., 0.]]),
+    array([[0.]]),
+    dt: None
+    )
+
+    >>> sys.to_discrete(0.1)
+    StateSpaceDiscrete(
+    array([[1. , 0.1],
+           [0. , 1. ]]),
+    array([[0.005],
+           [0.1  ]]),
+    array([[1., 0.]]),
+    array([[0.]]),
+    dt: 0.1
+    )
+
+    >>> a = np.array([[1, 0.1], [0, 1]])
+    >>> b = np.array([[0.005], [0.1]])
+
+    >>> signal.StateSpace(a, b, c, d, dt=0.1)
+    StateSpaceDiscrete(
+    array([[1. , 0.1],
+           [0. , 1. ]]),
+    array([[0.005],
+           [0.1  ]]),
+    array([[1., 0.]]),
+    array([[0.]]),
+    dt: 0.1
+    )
+
+    """
+
+    # Override NumPy binary operations and ufuncs
+    __array_priority__ = 100.0
+    __array_ufunc__ = None
+
+    def __new__(cls, *system, dt=None):
+        """Create new StateSpace object and settle inheritance."""
+        # Handle object conversion if input is an instance of `lti`
+        if len(system) == 1 and isinstance(system[0], LinearTimeInvariant):
+            return system[0].to_ss()
+
+        # Choose whether to inherit from `lti` or from `dlti`
+        if cls is StateSpace:
+            if dt is None:
+                return StateSpaceContinuous.__new__(StateSpaceContinuous,
+                                                    *system)
+            else:
+                return StateSpaceDiscrete.__new__(StateSpaceDiscrete,
+                                                  *system, dt=dt)
+
+        # No special conversion needed
+        return super().__new__(cls)
+
+    def __init__(self, *system, **kwargs):
+        """Initialize the state space lti/dlti system."""
+        # Conversion of lti instances is handled in __new__
+        if isinstance(system[0], LinearTimeInvariant):
+            return
+
+        # Remove system arguments, not needed by parents anymore
+        super().__init__(**kwargs)
+
+        self._A = None
+        self._B = None
+        self._C = None
+        self._D = None
+
+        # Convert A, B, C, D into 2d arrays of dtype float64 or complex128:
+        self.A, self.B, self.C, self.D = abcd_normalize(*system)
+
+    def __repr__(self):
+        """Return representation of the `StateSpace` system."""
+        return (
+            f'{self.__class__.__name__}(\n'
+            f'{repr(self.A)},\n'
+            f'{repr(self.B)},\n'
+            f'{repr(self.C)},\n'
+            f'{repr(self.D)},\n'
+            f'dt: {repr(self.dt)}\n)'
+        )
+
+    def _check_binop_other(self, other):
+        return isinstance(other, StateSpace | np.ndarray | float | complex |
+                                  np.number | int)
+
+    def __mul__(self, other):
+        """
+        Post-multiply another system or a scalar
+
+        Handles multiplication of systems in the sense of a frequency domain
+        multiplication. That means, given two systems E1(s) and E2(s), their
+        multiplication, H(s) = E1(s) * E2(s), means that applying H(s) to U(s)
+        is equivalent to first applying E2(s), and then E1(s).
+
+        Notes
+        -----
+        For SISO systems the order of system application does not matter.
+        However, for MIMO systems, where the two systems are matrices, the
+        order above ensures standard Matrix multiplication rules apply.
+        """
+        if not self._check_binop_other(other):
+            return NotImplemented
+
+        if isinstance(other, StateSpace):
+            # Disallow mix of discrete and continuous systems.
+            if type(other) is not type(self):
+                return NotImplemented
+
+            if self.dt != other.dt:
+                raise TypeError('Cannot multiply systems with different `dt`.')
+
+            n1 = self.A.shape[0]
+            n2 = other.A.shape[0]
+
+            # Interconnection of systems
+            # x1' = A1 x1 + B1 u1
+            # y1  = C1 x1 + D1 u1
+            # x2' = A2 x2 + B2 y1
+            # y2  = C2 x2 + D2 y1
+            #
+            # Plugging in with u1 = y2 yields
+            # [x1']   [A1 B1*C2 ] [x1]   [B1*D2]
+            # [x2'] = [0  A2    ] [x2] + [B2   ] u2
+            #                    [x1]
+            #  y2   = [C1 D1*C2] [x2] + D1*D2 u2
+            a = np.vstack((np.hstack((self.A, np.dot(self.B, other.C))),
+                           np.hstack((zeros((n2, n1)), other.A))))
+            b = np.vstack((np.dot(self.B, other.D), other.B))
+            c = np.hstack((self.C, np.dot(self.D, other.C)))
+            d = np.dot(self.D, other.D)
+        else:
+            # Assume that other is a scalar / matrix
+            # For post multiplication the input gets scaled
+            a = self.A
+            b = np.dot(self.B, other)
+            c = self.C
+            d = np.dot(self.D, other)
+
+        common_dtype = np.result_type(a.dtype, b.dtype, c.dtype, d.dtype)
+        return StateSpace(np.asarray(a, dtype=common_dtype),
+                          np.asarray(b, dtype=common_dtype),
+                          np.asarray(c, dtype=common_dtype),
+                          np.asarray(d, dtype=common_dtype),
+                          **self._dt_dict)
+
+    def __rmul__(self, other):
+        """Pre-multiply a scalar or matrix (but not StateSpace)"""
+        if not self._check_binop_other(other) or isinstance(other, StateSpace):
+            return NotImplemented
+
+        # For pre-multiplication only the output gets scaled
+        a = self.A
+        b = self.B
+        c = np.dot(other, self.C)
+        d = np.dot(other, self.D)
+
+        common_dtype = np.result_type(a.dtype, b.dtype, c.dtype, d.dtype)
+        return StateSpace(np.asarray(a, dtype=common_dtype),
+                          np.asarray(b, dtype=common_dtype),
+                          np.asarray(c, dtype=common_dtype),
+                          np.asarray(d, dtype=common_dtype),
+                          **self._dt_dict)
+
+    def __neg__(self):
+        """Negate the system (equivalent to pre-multiplying by -1)."""
+        return StateSpace(self.A, self.B, -self.C, -self.D, **self._dt_dict)
+
+    def __add__(self, other):
+        """
+        Adds two systems in the sense of frequency domain addition.
+        """
+        if not self._check_binop_other(other):
+            return NotImplemented
+
+        if isinstance(other, StateSpace):
+            # Disallow mix of discrete and continuous systems.
+            if type(other) is not type(self):
+                raise TypeError(f'Cannot add {type(self)} and {type(other)}')
+
+            if self.dt != other.dt:
+                raise TypeError('Cannot add systems with different `dt`.')
+            # Interconnection of systems
+            # x1' = A1 x1 + B1 u
+            # y1  = C1 x1 + D1 u
+            # x2' = A2 x2 + B2 u
+            # y2  = C2 x2 + D2 u
+            # y   = y1 + y2
+            #
+            # Plugging in yields
+            # [x1']   [A1 0 ] [x1]   [B1]
+            # [x2'] = [0  A2] [x2] + [B2] u
+            #                 [x1]
+            #  y    = [C1 C2] [x2] + [D1 + D2] u
+            a = linalg.block_diag(self.A, other.A)
+            b = np.vstack((self.B, other.B))
+            c = np.hstack((self.C, other.C))
+            d = self.D + other.D
+        else:
+            other = np.atleast_2d(other)
+            if self.D.shape == other.shape:
+                # A scalar/matrix is really just a static system (A=0, B=0, C=0)
+                a = self.A
+                b = self.B
+                c = self.C
+                d = self.D + other
+            else:
+                raise ValueError("Cannot add systems with incompatible "
+                                 f"dimensions ({self.D.shape} and {other.shape})")
+
+        common_dtype = np.result_type(a.dtype, b.dtype, c.dtype, d.dtype)
+        return StateSpace(np.asarray(a, dtype=common_dtype),
+                          np.asarray(b, dtype=common_dtype),
+                          np.asarray(c, dtype=common_dtype),
+                          np.asarray(d, dtype=common_dtype),
+                          **self._dt_dict)
+
+    def __sub__(self, other):
+        if not self._check_binop_other(other):
+            return NotImplemented
+
+        return self.__add__(-other)
+
+    def __radd__(self, other):
+        if not self._check_binop_other(other):
+            return NotImplemented
+
+        return self.__add__(other)
+
+    def __rsub__(self, other):
+        if not self._check_binop_other(other):
+            return NotImplemented
+
+        return (-self).__add__(other)
+
+    def __truediv__(self, other):
+        """
+        Divide by a scalar
+        """
+        # Division by non-StateSpace scalars
+        if not self._check_binop_other(other) or isinstance(other, StateSpace):
+            return NotImplemented
+
+        if isinstance(other, np.ndarray) and other.ndim > 0:
+            # It's ambiguous what this means, so disallow it
+            raise ValueError("Cannot divide StateSpace by non-scalar numpy arrays")
+
+        return self.__mul__(1/other)
+
+    @property
+    def A(self):
+        """State matrix of the `StateSpace` system."""
+        return self._A
+
+    @A.setter
+    def A(self, A):
+        self._A = np.atleast_2d(A) if A is not None else None
+
+    @property
+    def B(self):
+        """Input matrix of the `StateSpace` system."""
+        return self._B
+
+    @B.setter
+    def B(self, B):
+        self._B = np.atleast_2d(B) if B is not None else None
+        self.inputs = self.B.shape[-1]
+
+    @property
+    def C(self):
+        """Output matrix of the `StateSpace` system."""
+        return self._C
+
+    @C.setter
+    def C(self, C):
+        self._C = np.atleast_2d(C) if C is not None else None
+        self.outputs = self.C.shape[0]
+
+    @property
+    def D(self):
+        """Feedthrough matrix of the `StateSpace` system."""
+        return self._D
+
+    @D.setter
+    def D(self, D):
+        self._D = np.atleast_2d(D) if D is not None else None
+
+    def _copy(self, system):
+        """
+        Copy the parameters of another `StateSpace` system.
+
+        Parameters
+        ----------
+        system : instance of `StateSpace`
+            The state-space system that is to be copied
+
+        """
+        self.A = system.A
+        self.B = system.B
+        self.C = system.C
+        self.D = system.D
+
+    def to_tf(self, **kwargs):
+        """
+        Convert system representation to `TransferFunction`.
+
+        Parameters
+        ----------
+        **kwargs
+            Additional keywords passed to `ss2zpk`
+
+        Returns
+        -------
+        sys : instance of `TransferFunction`
+            Transfer function of the current system
+
+        """
+        return TransferFunction(*ss2tf(self._A, self._B, self._C, self._D,
+                                       **kwargs), **self._dt_dict)
+
+    def to_zpk(self, **kwargs):
+        """
+        Convert system representation to `ZerosPolesGain`.
+
+        Parameters
+        ----------
+        **kwargs
+            Additional keywords passed to `ss2zpk`
+
+        Returns
+        -------
+        sys : instance of `ZerosPolesGain`
+            Zeros, poles, gain representation of the current system
+
+        """
+        return ZerosPolesGain(*ss2zpk(self._A, self._B, self._C, self._D,
+                                      **kwargs), **self._dt_dict)
+
+    def to_ss(self):
+        """
+        Return a copy of the current `StateSpace` system.
+
+        Returns
+        -------
+        sys : instance of `StateSpace`
+            The current system (copy)
+
+        """
+        return copy.deepcopy(self)
+
+
+class StateSpaceContinuous(StateSpace, lti):
+    r"""
+    Continuous-time Linear Time Invariant system in state-space form.
+
+    Represents the system as the continuous-time, first order differential
+    equation :math:`\dot{x} = A x + B u`.
+    Continuous-time `StateSpace` systems inherit additional functionality
+    from the `lti` class.
+
+    Parameters
+    ----------
+    *system : arguments
+        The `StateSpace` class can be instantiated with 1 or 3 arguments.
+        The following gives the number of input arguments and their
+        interpretation:
+
+        * 1: `lti` system: (`StateSpace`, `TransferFunction` or `ZerosPolesGain`)
+        * 4: array_like: (A, B, C, D)
+
+    See Also
+    --------
+    TransferFunction, ZerosPolesGain, lti
+    ss2zpk, ss2tf, zpk2sos
+
+    Notes
+    -----
+    Changing the value of properties that are not part of the
+    `StateSpace` system representation (such as `zeros` or `poles`) is very
+    inefficient and may lead to numerical inaccuracies.  It is better to
+    convert to the specific system representation first. For example, call
+    ``sys = sys.to_zpk()`` before accessing/changing the zeros, poles or gain.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import signal
+
+    >>> a = np.array([[0, 1], [0, 0]])
+    >>> b = np.array([[0], [1]])
+    >>> c = np.array([[1, 0]])
+    >>> d = np.array([[0]])
+
+    >>> sys = signal.StateSpace(a, b, c, d)
+    >>> print(sys)
+    StateSpaceContinuous(
+    array([[0., 1.],
+           [0., 0.]]),
+    array([[0.],
+           [1.]]),
+    array([[1., 0.]]),
+    array([[0.]]),
+    dt: None
+    )
+
+    """
+
+    def to_discrete(self, dt, method='zoh', alpha=None):
+        """
+        Returns the discretized `StateSpace` system.
+
+        Parameters
+        ----------
+        dt : float
+            The discretization time step.
+        method : str, optional
+            Which method to use:
+
+            * gbt: generalized bilinear transformation
+            * bilinear: Tustin's approximation ("gbt" with alpha=0.5)
+            * euler: Euler (or forward differencing) method ("gbt" with alpha=0)
+            * backward_diff: Backwards differencing ("gbt" with alpha=1.0)
+            * zoh: zero-order hold (default)
+            * foh: first-order hold
+            * impulse: equivalent impulse response
+
+        alpha : float within [0, 1], optional
+            The generalized bilinear transformation weighting parameter, which
+            should only be specified with method="gbt", and is ignored otherwise
+
+        Returns
+        -------
+        sys: instance of `dlti` and `StateSpace`
+
+        See Also
+        --------
+        cont2discrete
+        """
+        return StateSpace(*cont2discrete((self.A, self.B, self.C, self.D),
+                                         dt,
+                                         method=method,
+                                         alpha=alpha)[:-1],
+                          dt=dt)
+
+
+class StateSpaceDiscrete(StateSpace, dlti):
+    r"""
+    Discrete-time Linear Time Invariant system in state-space form.
+
+    Represents the system as the discrete-time difference equation
+    :math:`x[k+1] = A x[k] + B u[k]`.
+    `StateSpace` systems inherit additional functionality from the `dlti`
+    class.
+
+    Parameters
+    ----------
+    *system : arguments
+        The `StateSpace` class can be instantiated with 1 or 3 arguments.
+        The following gives the number of input arguments and their
+        interpretation:
+
+        * 1: `dlti` system: (`StateSpace`, `TransferFunction` or `ZerosPolesGain`)
+        * 4: array_like: (A, B, C, D)
+    dt : float, optional
+        Sampling time [s] of the discrete-time systems. Defaults to `True`
+        (unspecified sampling time). Must be specified as a keyword argument,
+        for example, ``dt=0.1``.
+
+    See Also
+    --------
+    TransferFunction, ZerosPolesGain, dlti
+    ss2zpk, ss2tf, zpk2sos
+
+    Notes
+    -----
+    Changing the value of properties that are not part of the
+    `StateSpace` system representation (such as `zeros` or `poles`) is very
+    inefficient and may lead to numerical inaccuracies.  It is better to
+    convert to the specific system representation first. For example, call
+    ``sys = sys.to_zpk()`` before accessing/changing the zeros, poles or gain.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import signal
+
+    >>> a = np.array([[1, 0.1], [0, 1]])
+    >>> b = np.array([[0.005], [0.1]])
+    >>> c = np.array([[1, 0]])
+    >>> d = np.array([[0]])
+
+    >>> signal.StateSpace(a, b, c, d, dt=0.1)
+    StateSpaceDiscrete(
+    array([[1. ,  0.1],
+           [0. ,  1. ]]),
+    array([[0.005],
+           [0.1  ]]),
+    array([[1., 0.]]),
+    array([[0.]]),
+    dt: 0.1
+    )
+
+    """
+    pass
+
+
+def lsim(system, U, T, X0=None, interp=True):
+    """
+    Simulate output of a continuous-time linear system.
+
+    Parameters
+    ----------
+    system : an instance of the LTI class or a tuple describing the system
+        The following gives the number of elements in the tuple and
+        the interpretation:
+
+        * 1: (instance of `lti`)
+        * 2: (num, den)
+        * 3: (zeros, poles, gain)
+        * 4: (A, B, C, D)
+
+    U : array_like
+        An input array describing the input at each time `T`
+        (interpolation is assumed between given times).  If there are
+        multiple inputs, then each column of the rank-2 array
+        represents an input.  If U = 0 or None, a zero input is used.
+    T : array_like
+        The time steps at which the input is defined and at which the
+        output is desired.  Must be nonnegative, increasing, and equally spaced.
+    X0 : array_like, optional
+        The initial conditions on the state vector (zero by default).
+    interp : bool, optional
+        Whether to use linear (True, the default) or zero-order-hold (False)
+        interpolation for the input array.
+
+    Returns
+    -------
+    T : 1D ndarray
+        Time values for the output.
+    yout : 1D ndarray
+        System response.
+    xout : ndarray
+        Time evolution of the state vector.
+
+    Notes
+    -----
+    If (num, den) is passed in for ``system``, coefficients for both the
+    numerator and denominator should be specified in descending exponent
+    order (e.g. ``s^2 + 3s + 5`` would be represented as ``[1, 3, 5]``).
+
+    Examples
+    --------
+    We'll use `lsim` to simulate an analog Bessel filter applied to
+    a signal.
+
+    >>> import numpy as np
+    >>> from scipy.signal import bessel, lsim
+    >>> import matplotlib.pyplot as plt
+
+    Create a low-pass Bessel filter with a cutoff of 12 Hz.
+
+    >>> b, a = bessel(N=5, Wn=2*np.pi*12, btype='lowpass', analog=True)
+
+    Generate data to which the filter is applied.
+
+    >>> t = np.linspace(0, 1.25, 500, endpoint=False)
+
+    The input signal is the sum of three sinusoidal curves, with
+    frequencies 4 Hz, 40 Hz, and 80 Hz.  The filter should mostly
+    eliminate the 40 Hz and 80 Hz components, leaving just the 4 Hz signal.
+
+    >>> u = (np.cos(2*np.pi*4*t) + 0.6*np.sin(2*np.pi*40*t) +
+    ...      0.5*np.cos(2*np.pi*80*t))
+
+    Simulate the filter with `lsim`.
+
+    >>> tout, yout, xout = lsim((b, a), U=u, T=t)
+
+    Plot the result.
+
+    >>> plt.plot(t, u, 'r', alpha=0.5, linewidth=1, label='input')
+    >>> plt.plot(tout, yout, 'k', linewidth=1.5, label='output')
+    >>> plt.legend(loc='best', shadow=True, framealpha=1)
+    >>> plt.grid(alpha=0.3)
+    >>> plt.xlabel('t')
+    >>> plt.show()
+
+    In a second example, we simulate a double integrator ``y'' = u``, with
+    a constant input ``u = 1``.  We'll use the state space representation
+    of the integrator.
+
+    >>> from scipy.signal import lti
+    >>> A = np.array([[0.0, 1.0], [0.0, 0.0]])
+    >>> B = np.array([[0.0], [1.0]])
+    >>> C = np.array([[1.0, 0.0]])
+    >>> D = 0.0
+    >>> system = lti(A, B, C, D)
+
+    `t` and `u` define the time and input signal for the system to
+    be simulated.
+
+    >>> t = np.linspace(0, 5, num=50)
+    >>> u = np.ones_like(t)
+
+    Compute the simulation, and then plot `y`.  As expected, the plot shows
+    the curve ``y = 0.5*t**2``.
+
+    >>> tout, y, x = lsim(system, u, t)
+    >>> plt.plot(t, y)
+    >>> plt.grid(alpha=0.3)
+    >>> plt.xlabel('t')
+    >>> plt.show()
+
+    """
+    if isinstance(system, lti):
+        sys = system._as_ss()
+    elif isinstance(system, dlti):
+        raise AttributeError('lsim can only be used with continuous-time '
+                             'systems.')
+    else:
+        sys = lti(*system)._as_ss()
+    T = atleast_1d(T)
+    if len(T.shape) != 1:
+        raise ValueError("T must be a rank-1 array.")
+
+    A, B, C, D = map(np.asarray, (sys.A, sys.B, sys.C, sys.D))
+    n_states = A.shape[0]
+    n_inputs = B.shape[1]
+
+    n_steps = T.size
+    if X0 is None:
+        X0 = zeros(n_states, sys.A.dtype)
+    xout = np.empty((n_steps, n_states), sys.A.dtype)
+
+    if T[0] == 0:
+        xout[0] = X0
+    elif T[0] > 0:
+        # step forward to initial time, with zero input
+        xout[0] = dot(X0, linalg.expm(transpose(A) * T[0]))
+    else:
+        raise ValueError("Initial time must be nonnegative")
+
+    no_input = (U is None or
+                (isinstance(U, int | float) and U == 0.) or
+                not np.any(U))
+
+    if n_steps == 1:
+        yout = squeeze(xout @ C.T)
+        if not no_input:
+            yout += squeeze(U @ D.T)
+        return T, yout, squeeze(xout)
+
+    dt = T[1] - T[0]
+    if not np.allclose(np.diff(T), dt):
+        raise ValueError("Time steps are not equally spaced.")
+
+    if no_input:
+        # Zero input: just use matrix exponential
+        # take transpose because state is a row vector
+        expAT_dt = linalg.expm(A.T * dt)
+        for i in range(1, n_steps):
+            xout[i] = xout[i-1] @ expAT_dt
+        yout = squeeze(xout @ C.T)
+        return T, yout, squeeze(xout)
+
+    # Nonzero input
+    U = atleast_1d(U)
+    if U.ndim == 1:
+        U = U[:, np.newaxis]
+
+    if U.shape[0] != n_steps:
+        raise ValueError("U must have the same number of rows "
+                         "as elements in T.")
+
+    if U.shape[1] != n_inputs:
+        raise ValueError("System does not define that many inputs.")
+
+    if not interp:
+        # Zero-order hold
+        # Algorithm: to integrate from time 0 to time dt, we solve
+        #   xdot = A x + B u,  x(0) = x0
+        #   udot = 0,          u(0) = u0.
+        #
+        # Solution is
+        #   [ x(dt) ]       [ A*dt   B*dt ] [ x0 ]
+        #   [ u(dt) ] = exp [  0     0    ] [ u0 ]
+        M = np.vstack([np.hstack([A * dt, B * dt]),
+                       np.zeros((n_inputs, n_states + n_inputs))])
+        # transpose everything because the state and input are row vectors
+        expMT = linalg.expm(M.T)
+        Ad = expMT[:n_states, :n_states]
+        Bd = expMT[n_states:, :n_states]
+        for i in range(1, n_steps):
+            xout[i] = xout[i-1] @ Ad + U[i-1] @ Bd
+    else:
+        # Linear interpolation between steps
+        # Algorithm: to integrate from time 0 to time dt, with linear
+        # interpolation between inputs u(0) = u0 and u(dt) = u1, we solve
+        #   xdot = A x + B u,        x(0) = x0
+        #   udot = (u1 - u0) / dt,   u(0) = u0.
+        #
+        # Solution is
+        #   [ x(dt) ]       [ A*dt  B*dt  0 ] [  x0   ]
+        #   [ u(dt) ] = exp [  0     0    I ] [  u0   ]
+        #   [u1 - u0]       [  0     0    0 ] [u1 - u0]
+        M = np.vstack([np.hstack([A * dt, B * dt,
+                                  np.zeros((n_states, n_inputs))]),
+                       np.hstack([np.zeros((n_inputs, n_states + n_inputs)),
+                                  np.identity(n_inputs)]),
+                       np.zeros((n_inputs, n_states + 2 * n_inputs))])
+        expMT = linalg.expm(M.T)
+        Ad = expMT[:n_states, :n_states]
+        Bd1 = expMT[n_states+n_inputs:, :n_states]
+        Bd0 = expMT[n_states:n_states + n_inputs, :n_states] - Bd1
+        for i in range(1, n_steps):
+            xout[i] = xout[i-1] @ Ad + U[i-1] @ Bd0 + U[i] @ Bd1
+
+    yout = squeeze(xout @ C.T) + squeeze(U @ D.T)
+    return T, yout, squeeze(xout)
+
+
+def _default_response_times(A, n):
+    """Compute a reasonable set of time samples for the response time.
+
+    This function is used by `impulse` and `step`  to compute the response time
+    when the `T` argument to the function is None.
+
+    Parameters
+    ----------
+    A : array_like
+        The system matrix, which is square.
+    n : int
+        The number of time samples to generate.
+
+    Returns
+    -------
+    t : ndarray
+        The 1-D array of length `n` of time samples at which the response
+        is to be computed.
+    """
+    # Create a reasonable time interval.
+    # TODO: This could use some more work.
+    # For example, what is expected when the system is unstable?
+    vals = linalg.eigvals(A)
+    r = min(abs(real(vals)))
+    if r == 0.0:
+        r = 1.0
+    tc = 1.0 / r
+    t = linspace(0.0, 7 * tc, n)
+    return t
+
+
+def impulse(system, X0=None, T=None, N=None):
+    """Impulse response of continuous-time system.
+
+    Parameters
+    ----------
+    system : an instance of the LTI class or a tuple of array_like
+        describing the system.
+        The following gives the number of elements in the tuple and
+        the interpretation:
+
+        * 1 (instance of `lti`)
+        * 2 (num, den)
+        * 3 (zeros, poles, gain)
+        * 4 (A, B, C, D)
+
+    X0 : array_like, optional
+        Initial state-vector.  Defaults to zero.
+    T : array_like, optional
+        Time points.  Computed if not given.
+    N : int, optional
+        The number of time points to compute (if `T` is not given).
+
+    Returns
+    -------
+    T : ndarray
+        A 1-D array of time points.
+    yout : ndarray
+        A 1-D array containing the impulse response of the system (except for
+        singularities at zero).
+
+    Notes
+    -----
+    If (num, den) is passed in for ``system``, coefficients for both the
+    numerator and denominator should be specified in descending exponent
+    order (e.g. ``s^2 + 3s + 5`` would be represented as ``[1, 3, 5]``).
+
+    Examples
+    --------
+    Compute the impulse response of a second order system with a repeated
+    root: ``x''(t) + 2*x'(t) + x(t) = u(t)``
+
+    >>> from scipy import signal
+    >>> system = ([1.0], [1.0, 2.0, 1.0])
+    >>> t, y = signal.impulse(system)
+    >>> import matplotlib.pyplot as plt
+    >>> plt.plot(t, y)
+
+    """
+    if isinstance(system, lti):
+        sys = system._as_ss()
+    elif isinstance(system, dlti):
+        raise AttributeError('impulse can only be used with continuous-time '
+                             'systems.')
+    else:
+        sys = lti(*system)._as_ss()
+    if X0 is None:
+        X = squeeze(sys.B)
+    else:
+        X = squeeze(sys.B + X0)
+    if N is None:
+        N = 100
+    if T is None:
+        T = _default_response_times(sys.A, N)
+    else:
+        T = asarray(T)
+
+    _, h, _ = lsim(sys, 0., T, X, interp=False)
+    return T, h
+
+
+def step(system, X0=None, T=None, N=None):
+    """Step response of continuous-time system.
+
+    Parameters
+    ----------
+    system : an instance of the LTI class or a tuple of array_like
+        describing the system.
+        The following gives the number of elements in the tuple and
+        the interpretation:
+
+        * 1 (instance of `lti`)
+        * 2 (num, den)
+        * 3 (zeros, poles, gain)
+        * 4 (A, B, C, D)
+
+    X0 : array_like, optional
+        Initial state-vector (default is zero).
+    T : array_like, optional
+        Time points (computed if not given).
+    N : int, optional
+        Number of time points to compute if `T` is not given.
+
+    Returns
+    -------
+    T : 1D ndarray
+        Output time points.
+    yout : 1D ndarray
+        Step response of system.
+
+
+    Notes
+    -----
+    If (num, den) is passed in for ``system``, coefficients for both the
+    numerator and denominator should be specified in descending exponent
+    order (e.g. ``s^2 + 3s + 5`` would be represented as ``[1, 3, 5]``).
+
+    Examples
+    --------
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+    >>> lti = signal.lti([1.0], [1.0, 1.0])
+    >>> t, y = signal.step(lti)
+    >>> plt.plot(t, y)
+    >>> plt.xlabel('Time [s]')
+    >>> plt.ylabel('Amplitude')
+    >>> plt.title('Step response for 1. Order Lowpass')
+    >>> plt.grid()
+
+    """
+    if isinstance(system, lti):
+        sys = system._as_ss()
+    elif isinstance(system, dlti):
+        raise AttributeError('step can only be used with continuous-time '
+                             'systems.')
+    else:
+        sys = lti(*system)._as_ss()
+    if N is None:
+        N = 100
+    if T is None:
+        T = _default_response_times(sys.A, N)
+    else:
+        T = asarray(T)
+    U = ones(T.shape, sys.A.dtype)
+    vals = lsim(sys, U, T, X0=X0, interp=False)
+    return vals[0], vals[1]
+
+
+def bode(system, w=None, n=100):
+    """
+    Calculate Bode magnitude and phase data of a continuous-time system.
+
+    Parameters
+    ----------
+    system : an instance of the LTI class or a tuple describing the system
+        The following gives the number of elements in the tuple and
+        the interpretation:
+
+        * 1 (instance of `lti`)
+        * 2 (num, den)
+        * 3 (zeros, poles, gain)
+        * 4 (A, B, C, D)
+
+    w : array_like, optional
+        Array of frequencies (in rad/s). Magnitude and phase data is calculated
+        for every value in this array. If not given a reasonable set will be
+        calculated.
+    n : int, optional
+        Number of frequency points to compute if `w` is not given. The `n`
+        frequencies are logarithmically spaced in an interval chosen to
+        include the influence of the poles and zeros of the system.
+
+    Returns
+    -------
+    w : 1D ndarray
+        Frequency array [rad/s]
+    mag : 1D ndarray
+        Magnitude array [dB]
+    phase : 1D ndarray
+        Phase array [deg]
+
+    Notes
+    -----
+    If (num, den) is passed in for ``system``, coefficients for both the
+    numerator and denominator should be specified in descending exponent
+    order (e.g. ``s^2 + 3s + 5`` would be represented as ``[1, 3, 5]``).
+
+    .. versionadded:: 0.11.0
+
+    Examples
+    --------
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+
+    >>> sys = signal.TransferFunction([1], [1, 1])
+    >>> w, mag, phase = signal.bode(sys)
+
+    >>> plt.figure()
+    >>> plt.semilogx(w, mag)    # Bode magnitude plot
+    >>> plt.figure()
+    >>> plt.semilogx(w, phase)  # Bode phase plot
+    >>> plt.show()
+
+    """
+    w, y = freqresp(system, w=w, n=n)
+
+    mag = 20.0 * np.log10(abs(y))
+    phase = np.unwrap(np.arctan2(y.imag, y.real)) * 180.0 / np.pi
+
+    return w, mag, phase
+
+
+def freqresp(system, w=None, n=10000):
+    r"""Calculate the frequency response of a continuous-time system.
+
+    Parameters
+    ----------
+    system : an instance of the `lti` class or a tuple describing the system
+        The following gives the number of elements in the tuple and
+        the interpretation:
+
+        * 1 (instance of `lti`)
+        * 2 (num, den)
+        * 3 (zeros, poles, gain)
+        * 4 (A, B, C, D)
+
+    w : array_like, optional
+        Array of frequencies (in rad/s). Magnitude and phase data is
+        calculated for every value in this array. If not given, a reasonable
+        set will be calculated.
+    n : int, optional
+        Number of frequency points to compute if `w` is not given. The `n`
+        frequencies are logarithmically spaced in an interval chosen to
+        include the influence of the poles and zeros of the system.
+
+    Returns
+    -------
+    w : 1D ndarray
+        Frequency array [rad/s]
+    H : 1D ndarray
+        Array of complex magnitude values
+
+    Notes
+    -----
+    If (num, den) is passed in for ``system``, coefficients for both the
+    numerator and denominator should be specified in descending exponent
+    order (e.g. ``s^2 + 3s + 5`` would be represented as ``[1, 3, 5]``).
+
+    Examples
+    --------
+    Generating the Nyquist plot of a transfer function
+
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+
+    Construct the transfer function :math:`H(s) = \frac{5}{(s-1)^3}`:
+
+    >>> s1 = signal.ZerosPolesGain([], [1, 1, 1], [5])
+
+    >>> w, H = signal.freqresp(s1)
+
+    >>> plt.figure()
+    >>> plt.plot(H.real, H.imag, "b")
+    >>> plt.plot(H.real, -H.imag, "r")
+    >>> plt.show()
+    """
+    if isinstance(system, lti):
+        if isinstance(system, TransferFunction | ZerosPolesGain):
+            sys = system
+        else:
+            sys = system._as_zpk()
+    elif isinstance(system, dlti):
+        raise AttributeError('freqresp can only be used with continuous-time '
+                             'systems.')
+    else:
+        sys = lti(*system)._as_zpk()
+
+    if sys.inputs != 1 or sys.outputs != 1:
+        raise ValueError("freqresp() requires a SISO (single input, single "
+                         "output) system.")
+
+    if w is not None:
+        worN = w
+    else:
+        worN = n
+
+    if isinstance(sys, TransferFunction):
+        # In the call to freqs(), sys.num.ravel() is used because there are
+        # cases where sys.num is a 2-D array with a single row.
+        w, h = freqs(sys.num.ravel(), sys.den, worN=worN)
+
+    elif isinstance(sys, ZerosPolesGain):
+        w, h = freqs_zpk(sys.zeros, sys.poles, sys.gain, worN=worN)
+
+    return w, h
+
+
+# This class will be used by place_poles to return its results
+# see https://code.activestate.com/recipes/52308/
+class Bunch:
+    def __init__(self, **kwds):
+        self.__dict__.update(kwds)
+
+
+def _valid_inputs(A, B, poles, method, rtol, maxiter):
+    """
+    Check the poles come in complex conjugate pairs
+    Check shapes of A, B and poles are compatible.
+    Check the method chosen is compatible with provided poles
+    Return update method to use and ordered poles
+
+    """
+    poles = np.asarray(poles)
+    if poles.ndim > 1:
+        raise ValueError("Poles must be a 1D array like.")
+    # Will raise ValueError if poles do not come in complex conjugates pairs
+    poles = _order_complex_poles(poles)
+    if A.ndim > 2:
+        raise ValueError("A must be a 2D array/matrix.")
+    if B.ndim > 2:
+        raise ValueError("B must be a 2D array/matrix")
+    if A.shape[0] != A.shape[1]:
+        raise ValueError("A must be square")
+    if len(poles) > A.shape[0]:
+        raise ValueError(
+            f"maximum number of poles is {A.shape[0]} but you asked for {len(poles)}"
+        )
+    if len(poles) < A.shape[0]:
+        raise ValueError(
+            f"number of poles is {len(poles)} but you should provide {A.shape[0]}"
+        )
+    r = np.linalg.matrix_rank(B)
+    for p in poles:
+        if sum(p == poles) > r:
+            raise ValueError("at least one of the requested pole is repeated "
+                             "more than rank(B) times")
+    # Choose update method
+    update_loop = _YT_loop
+    if method not in ('KNV0','YT'):
+        raise ValueError("The method keyword must be one of 'YT' or 'KNV0'")
+
+    if method == "KNV0":
+        update_loop = _KNV0_loop
+        if not all(np.isreal(poles)):
+            raise ValueError("Complex poles are not supported by KNV0")
+
+    if maxiter < 1:
+        raise ValueError("maxiter must be at least equal to 1")
+
+    # We do not check rtol <= 0 as the user can use a negative rtol to
+    # force maxiter iterations
+    if rtol > 1:
+        raise ValueError("rtol can not be greater than 1")
+
+    return update_loop, poles
+
+
+def _order_complex_poles(poles):
+    """
+    Check we have complex conjugates pairs and reorder P according to YT, ie
+    real_poles, complex_i, conjugate complex_i, ....
+    The lexicographic sort on the complex poles is added to help the user to
+    compare sets of poles.
+    """
+    ordered_poles = np.sort(poles[np.isreal(poles)])
+    im_poles = []
+    for p in np.sort(poles[np.imag(poles) < 0]):
+        if np.conj(p) in poles:
+            im_poles.extend((p, np.conj(p)))
+
+    ordered_poles = np.hstack((ordered_poles, im_poles))
+
+    if poles.shape[0] != len(ordered_poles):
+        raise ValueError("Complex poles must come with their conjugates")
+    return ordered_poles
+
+
+def _KNV0(B, ker_pole, transfer_matrix, j, poles):
+    """
+    Algorithm "KNV0" Kautsky et Al. Robust pole
+    assignment in linear state feedback, Int journal of Control
+    1985, vol 41 p 1129->1155
+    https://la.epfl.ch/files/content/sites/la/files/
+        users/105941/public/KautskyNicholsDooren
+
+    """
+    # Remove xj form the base
+    transfer_matrix_not_j = np.delete(transfer_matrix, j, axis=1)
+    # If we QR this matrix in full mode Q=Q0|Q1
+    # then Q1 will be a single column orthogonal to
+    # Q0, that's what we are looking for !
+
+    # After merge of gh-4249 great speed improvements could be achieved
+    # using QR updates instead of full QR in the line below
+
+    # To debug with numpy qr uncomment the line below
+    # Q, R = np.linalg.qr(transfer_matrix_not_j, mode="complete")
+    Q, R = s_qr(transfer_matrix_not_j, mode="full")
+
+    mat_ker_pj = np.dot(ker_pole[j], ker_pole[j].T)
+    yj = np.dot(mat_ker_pj, Q[:, -1])
+
+    # If Q[:, -1] is "almost" orthogonal to ker_pole[j] its
+    # projection into ker_pole[j] will yield a vector
+    # close to 0.  As we are looking for a vector in ker_pole[j]
+    # simply stick with transfer_matrix[:, j] (unless someone provides me with
+    # a better choice ?)
+
+    if not np.allclose(yj, 0):
+        xj = yj/np.linalg.norm(yj)
+        transfer_matrix[:, j] = xj
+
+        # KNV does not support complex poles, using YT technique the two lines
+        # below seem to work 9 out of 10 times but it is not reliable enough:
+        # transfer_matrix[:, j]=real(xj)
+        # transfer_matrix[:, j+1]=imag(xj)
+
+        # Add this at the beginning of this function if you wish to test
+        # complex support:
+        #    if ~np.isreal(P[j]) and (j>=B.shape[0]-1 or P[j]!=np.conj(P[j+1])):
+        #        return
+        # Problems arise when imag(xj)=>0 I have no idea on how to fix this
+
+
+def _YT_real(ker_pole, Q, transfer_matrix, i, j):
+    """
+    Applies algorithm from YT section 6.1 page 19 related to real pairs
+    """
+    # step 1 page 19
+    u = Q[:, -2, np.newaxis]
+    v = Q[:, -1, np.newaxis]
+
+    # step 2 page 19
+    m = np.dot(np.dot(ker_pole[i].T, np.dot(u, v.T) -
+        np.dot(v, u.T)), ker_pole[j])
+
+    # step 3 page 19
+    um, sm, vm = np.linalg.svd(m)
+    # mu1, mu2 two first columns of U => 2 first lines of U.T
+    mu1, mu2 = um.T[:2, :, np.newaxis]
+    # VM is V.T with numpy we want the first two lines of V.T
+    nu1, nu2 = vm[:2, :, np.newaxis]
+
+    # what follows is a rough python translation of the formulas
+    # in section 6.2 page 20 (step 4)
+    transfer_matrix_j_mo_transfer_matrix_j = np.vstack((
+            transfer_matrix[:, i, np.newaxis],
+            transfer_matrix[:, j, np.newaxis]))
+
+    if not np.allclose(sm[0], sm[1]):
+        ker_pole_imo_mu1 = np.dot(ker_pole[i], mu1)
+        ker_pole_i_nu1 = np.dot(ker_pole[j], nu1)
+        ker_pole_mu_nu = np.vstack((ker_pole_imo_mu1, ker_pole_i_nu1))
+    else:
+        ker_pole_ij = np.vstack((
+                                np.hstack((ker_pole[i],
+                                           np.zeros(ker_pole[i].shape))),
+                                np.hstack((np.zeros(ker_pole[j].shape),
+                                                    ker_pole[j]))
+                                ))
+        mu_nu_matrix = np.vstack(
+            (np.hstack((mu1, mu2)), np.hstack((nu1, nu2)))
+            )
+        ker_pole_mu_nu = np.dot(ker_pole_ij, mu_nu_matrix)
+    transfer_matrix_ij = np.dot(np.dot(ker_pole_mu_nu, ker_pole_mu_nu.T),
+                             transfer_matrix_j_mo_transfer_matrix_j)
+    if not np.allclose(transfer_matrix_ij, 0):
+        transfer_matrix_ij = (np.sqrt(2)*transfer_matrix_ij /
+                              np.linalg.norm(transfer_matrix_ij))
+        transfer_matrix[:, i] = transfer_matrix_ij[
+            :transfer_matrix[:, i].shape[0], 0
+            ]
+        transfer_matrix[:, j] = transfer_matrix_ij[
+            transfer_matrix[:, i].shape[0]:, 0
+            ]
+    else:
+        # As in knv0 if transfer_matrix_j_mo_transfer_matrix_j is orthogonal to
+        # Vect{ker_pole_mu_nu} assign transfer_matrixi/transfer_matrix_j to
+        # ker_pole_mu_nu and iterate. As we are looking for a vector in
+        # Vect{Matker_pole_MU_NU} (see section 6.1 page 19) this might help
+        # (that's a guess, not a claim !)
+        transfer_matrix[:, i] = ker_pole_mu_nu[
+            :transfer_matrix[:, i].shape[0], 0
+            ]
+        transfer_matrix[:, j] = ker_pole_mu_nu[
+            transfer_matrix[:, i].shape[0]:, 0
+            ]
+
+
+def _YT_complex(ker_pole, Q, transfer_matrix, i, j):
+    """
+    Applies algorithm from YT section 6.2 page 20 related to complex pairs
+    """
+    # step 1 page 20
+    ur = np.sqrt(2)*Q[:, -2, np.newaxis]
+    ui = np.sqrt(2)*Q[:, -1, np.newaxis]
+    u = ur + 1j*ui
+
+    # step 2 page 20
+    ker_pole_ij = ker_pole[i]
+    m = np.dot(np.dot(np.conj(ker_pole_ij.T), np.dot(u, np.conj(u).T) -
+               np.dot(np.conj(u), u.T)), ker_pole_ij)
+
+    # step 3 page 20
+    e_val, e_vec = np.linalg.eig(m)
+    # sort eigenvalues according to their module
+    e_val_idx = np.argsort(np.abs(e_val))
+    mu1 = e_vec[:, e_val_idx[-1], np.newaxis]
+    mu2 = e_vec[:, e_val_idx[-2], np.newaxis]
+
+    # what follows is a rough python translation of the formulas
+    # in section 6.2 page 20 (step 4)
+
+    # remember transfer_matrix_i has been split as
+    # transfer_matrix[i]=real(transfer_matrix_i) and
+    # transfer_matrix[j]=imag(transfer_matrix_i)
+    transfer_matrix_j_mo_transfer_matrix_j = (
+        transfer_matrix[:, i, np.newaxis] +
+        1j*transfer_matrix[:, j, np.newaxis]
+        )
+    if not np.allclose(np.abs(e_val[e_val_idx[-1]]),
+                              np.abs(e_val[e_val_idx[-2]])):
+        ker_pole_mu = np.dot(ker_pole_ij, mu1)
+    else:
+        mu1_mu2_matrix = np.hstack((mu1, mu2))
+        ker_pole_mu = np.dot(ker_pole_ij, mu1_mu2_matrix)
+    transfer_matrix_i_j = np.dot(np.dot(ker_pole_mu, np.conj(ker_pole_mu.T)),
+                              transfer_matrix_j_mo_transfer_matrix_j)
+
+    if not np.allclose(transfer_matrix_i_j, 0):
+        transfer_matrix_i_j = (transfer_matrix_i_j /
+            np.linalg.norm(transfer_matrix_i_j))
+        transfer_matrix[:, i] = np.real(transfer_matrix_i_j[:, 0])
+        transfer_matrix[:, j] = np.imag(transfer_matrix_i_j[:, 0])
+    else:
+        # same idea as in YT_real
+        transfer_matrix[:, i] = np.real(ker_pole_mu[:, 0])
+        transfer_matrix[:, j] = np.imag(ker_pole_mu[:, 0])
+
+
+def _YT_loop(ker_pole, transfer_matrix, poles, B, maxiter, rtol):
+    """
+    Algorithm "YT" Tits, Yang. Globally Convergent
+    Algorithms for Robust Pole Assignment by State Feedback
+    https://hdl.handle.net/1903/5598
+    The poles P have to be sorted accordingly to section 6.2 page 20
+
+    """
+    # The IEEE edition of the YT paper gives useful information on the
+    # optimal update order for the real poles in order to minimize the number
+    # of times we have to loop over all poles, see page 1442
+    nb_real = poles[np.isreal(poles)].shape[0]
+    # hnb => Half Nb Real
+    hnb = nb_real // 2
+
+    # Stick to the indices in the paper and then remove one to get numpy array
+    # index it is a bit easier to link the code to the paper this way even if it
+    # is not very clean. The paper is unclear about what should be done when
+    # there is only one real pole => use KNV0 on this real pole seem to work
+    if nb_real > 0:
+        #update the biggest real pole with the smallest one
+        update_order = [[nb_real], [1]]
+    else:
+        update_order = [[],[]]
+
+    r_comp = np.arange(nb_real+1, len(poles)+1, 2)
+    # step 1.a
+    r_p = np.arange(1, hnb+nb_real % 2)
+    update_order[0].extend(2*r_p)
+    update_order[1].extend(2*r_p+1)
+    # step 1.b
+    update_order[0].extend(r_comp)
+    update_order[1].extend(r_comp+1)
+    # step 1.c
+    r_p = np.arange(1, hnb+1)
+    update_order[0].extend(2*r_p-1)
+    update_order[1].extend(2*r_p)
+    # step 1.d
+    if hnb == 0 and np.isreal(poles[0]):
+        update_order[0].append(1)
+        update_order[1].append(1)
+    update_order[0].extend(r_comp)
+    update_order[1].extend(r_comp+1)
+    # step 2.a
+    r_j = np.arange(2, hnb+nb_real % 2)
+    for j in r_j:
+        for i in range(1, hnb+1):
+            update_order[0].append(i)
+            update_order[1].append(i+j)
+    # step 2.b
+    if hnb == 0 and np.isreal(poles[0]):
+        update_order[0].append(1)
+        update_order[1].append(1)
+    update_order[0].extend(r_comp)
+    update_order[1].extend(r_comp+1)
+    # step 2.c
+    r_j = np.arange(2, hnb+nb_real % 2)
+    for j in r_j:
+        for i in range(hnb+1, nb_real+1):
+            idx_1 = i+j
+            if idx_1 > nb_real:
+                idx_1 = i+j-nb_real
+            update_order[0].append(i)
+            update_order[1].append(idx_1)
+    # step 2.d
+    if hnb == 0 and np.isreal(poles[0]):
+        update_order[0].append(1)
+        update_order[1].append(1)
+    update_order[0].extend(r_comp)
+    update_order[1].extend(r_comp+1)
+    # step 3.a
+    for i in range(1, hnb+1):
+        update_order[0].append(i)
+        update_order[1].append(i+hnb)
+    # step 3.b
+    if hnb == 0 and np.isreal(poles[0]):
+        update_order[0].append(1)
+        update_order[1].append(1)
+    update_order[0].extend(r_comp)
+    update_order[1].extend(r_comp+1)
+
+    update_order = np.array(update_order).T-1
+    stop = False
+    nb_try = 0
+    while nb_try < maxiter and not stop:
+        det_transfer_matrixb = np.abs(np.linalg.det(transfer_matrix))
+        for i, j in update_order:
+            if i == j:
+                assert i == 0, "i!=0 for KNV call in YT"
+                assert np.isreal(poles[i]), "calling KNV on a complex pole"
+                _KNV0(B, ker_pole, transfer_matrix, i, poles)
+            else:
+                transfer_matrix_not_i_j = np.delete(transfer_matrix, (i, j),
+                                                    axis=1)
+                # after merge of gh-4249 great speed improvements could be
+                # achieved using QR updates instead of full QR in the line below
+
+                #to debug with numpy qr uncomment the line below
+                #Q, _ = np.linalg.qr(transfer_matrix_not_i_j, mode="complete")
+                Q, _ = s_qr(transfer_matrix_not_i_j, mode="full")
+
+                if np.isreal(poles[i]):
+                    assert np.isreal(poles[j]), "mixing real and complex " + \
+                        "in YT_real" + str(poles)
+                    _YT_real(ker_pole, Q, transfer_matrix, i, j)
+                else:
+                    assert ~np.isreal(poles[i]), "mixing real and complex " + \
+                        "in YT_real" + str(poles)
+                    _YT_complex(ker_pole, Q, transfer_matrix, i, j)
+
+        det_transfer_matrix = np.max((np.sqrt(np.spacing(1)),
+                                  np.abs(np.linalg.det(transfer_matrix))))
+        cur_rtol = np.abs(
+            (det_transfer_matrix -
+             det_transfer_matrixb) /
+            det_transfer_matrix)
+        if cur_rtol < rtol and det_transfer_matrix > np.sqrt(np.spacing(1)):
+            # Convergence test from YT page 21
+            stop = True
+        nb_try += 1
+    return stop, cur_rtol, nb_try
+
+
+def _KNV0_loop(ker_pole, transfer_matrix, poles, B, maxiter, rtol):
+    """
+    Loop over all poles one by one and apply KNV method 0 algorithm
+    """
+    # This method is useful only because we need to be able to call
+    # _KNV0 from YT without looping over all poles, otherwise it would
+    # have been fine to mix _KNV0_loop and _KNV0 in a single function
+    stop = False
+    nb_try = 0
+    while nb_try < maxiter and not stop:
+        det_transfer_matrixb = np.abs(np.linalg.det(transfer_matrix))
+        for j in range(B.shape[0]):
+            _KNV0(B, ker_pole, transfer_matrix, j, poles)
+
+        det_transfer_matrix = np.max((np.sqrt(np.spacing(1)),
+                                  np.abs(np.linalg.det(transfer_matrix))))
+        cur_rtol = np.abs((det_transfer_matrix - det_transfer_matrixb) /
+                       det_transfer_matrix)
+        if cur_rtol < rtol and det_transfer_matrix > np.sqrt(np.spacing(1)):
+            # Convergence test from YT page 21
+            stop = True
+
+        nb_try += 1
+    return stop, cur_rtol, nb_try
+
+
+def place_poles(A, B, poles, method="YT", rtol=1e-3, maxiter=30):
+    """
+    Compute K such that eigenvalues (A - dot(B, K))=poles.
+
+    K is the gain matrix such as the plant described by the linear system
+    ``AX+BU`` will have its closed-loop poles, i.e the eigenvalues ``A - B*K``,
+    as close as possible to those asked for in poles.
+
+    SISO, MISO and MIMO systems are supported.
+
+    Parameters
+    ----------
+    A, B : ndarray
+        State-space representation of linear system ``AX + BU``.
+    poles : array_like
+        Desired real poles and/or complex conjugates poles.
+        Complex poles are only supported with ``method="YT"`` (default).
+    method : {'YT', 'KNV0'}, optional
+        Which method to choose to find the gain matrix K. One of:
+
+        - 'YT': Yang Tits
+        - 'KNV0': Kautsky, Nichols, Van Dooren update method 0
+
+        See References and Notes for details on the algorithms.
+    rtol : float, optional
+        After each iteration the determinant of the eigenvectors of
+        ``A - B*K`` is compared to its previous value, when the relative
+        error between these two values becomes lower than `rtol` the algorithm
+        stops.  Default is 1e-3.
+    maxiter : int, optional
+        Maximum number of iterations to compute the gain matrix.
+        Default is 30.
+
+    Returns
+    -------
+    full_state_feedback : Bunch object
+        full_state_feedback is composed of:
+            gain_matrix : 2-D ndarray
+                The closed loop matrix K such as the eigenvalues of ``A-BK``
+                are as close as possible to the requested poles.
+            computed_poles : 1-D ndarray
+                The poles corresponding to ``A-BK`` sorted as first the real
+                poles in increasing order, then the complex conjugates in
+                lexicographic order.
+            requested_poles : 1-D ndarray
+                The poles the algorithm was asked to place sorted as above,
+                they may differ from what was achieved.
+            X : 2-D ndarray
+                The transfer matrix such as ``X * diag(poles) = (A - B*K)*X``
+                (see Notes)
+            rtol : float
+                The relative tolerance achieved on ``det(X)`` (see Notes).
+                `rtol` will be NaN if it is possible to solve the system
+                ``diag(poles) = (A - B*K)``, or 0 when the optimization
+                algorithms can't do anything i.e when ``B.shape[1] == 1``.
+            nb_iter : int
+                The number of iterations performed before converging.
+                `nb_iter` will be NaN if it is possible to solve the system
+                ``diag(poles) = (A - B*K)``, or 0 when the optimization
+                algorithms can't do anything i.e when ``B.shape[1] == 1``.
+
+    Notes
+    -----
+    The Tits and Yang (YT), [2]_ paper is an update of the original Kautsky et
+    al. (KNV) paper [1]_.  KNV relies on rank-1 updates to find the transfer
+    matrix X such that ``X * diag(poles) = (A - B*K)*X``, whereas YT uses
+    rank-2 updates. This yields on average more robust solutions (see [2]_
+    pp 21-22), furthermore the YT algorithm supports complex poles whereas KNV
+    does not in its original version.  Only update method 0 proposed by KNV has
+    been implemented here, hence the name ``'KNV0'``.
+
+    KNV extended to complex poles is used in Matlab's ``place`` function, YT is
+    distributed under a non-free licence by Slicot under the name ``robpole``.
+    It is unclear and undocumented how KNV0 has been extended to complex poles
+    (Tits and Yang claim on page 14 of their paper that their method can not be
+    used to extend KNV to complex poles), therefore only YT supports them in
+    this implementation.
+
+    As the solution to the problem of pole placement is not unique for MIMO
+    systems, both methods start with a tentative transfer matrix which is
+    altered in various way to increase its determinant.  Both methods have been
+    proven to converge to a stable solution, however depending on the way the
+    initial transfer matrix is chosen they will converge to different
+    solutions and therefore there is absolutely no guarantee that using
+    ``'KNV0'`` will yield results similar to Matlab's or any other
+    implementation of these algorithms.
+
+    Using the default method ``'YT'`` should be fine in most cases; ``'KNV0'``
+    is only provided because it is needed by ``'YT'`` in some specific cases.
+    Furthermore ``'YT'`` gives on average more robust results than ``'KNV0'``
+    when ``abs(det(X))`` is used as a robustness indicator.
+
+    [2]_ is available as a technical report on the following URL:
+    https://hdl.handle.net/1903/5598
+
+    References
+    ----------
+    .. [1] J. Kautsky, N.K. Nichols and P. van Dooren, "Robust pole assignment
+           in linear state feedback", International Journal of Control, Vol. 41
+           pp. 1129-1155, 1985.
+    .. [2] A.L. Tits and Y. Yang, "Globally convergent algorithms for robust
+           pole assignment by state feedback", IEEE Transactions on Automatic
+           Control, Vol. 41, pp. 1432-1452, 1996.
+
+    Examples
+    --------
+    A simple example demonstrating real pole placement using both KNV and YT
+    algorithms.  This is example number 1 from section 4 of the reference KNV
+    publication ([1]_):
+
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+
+    >>> A = np.array([[ 1.380,  -0.2077,  6.715, -5.676  ],
+    ...               [-0.5814, -4.290,   0,      0.6750 ],
+    ...               [ 1.067,   4.273,  -6.654,  5.893  ],
+    ...               [ 0.0480,  4.273,   1.343, -2.104  ]])
+    >>> B = np.array([[ 0,      5.679 ],
+    ...               [ 1.136,  1.136 ],
+    ...               [ 0,      0,    ],
+    ...               [-3.146,  0     ]])
+    >>> P = np.array([-0.2, -0.5, -5.0566, -8.6659])
+
+    Now compute K with KNV method 0, with the default YT method and with the YT
+    method while forcing 100 iterations of the algorithm and print some results
+    after each call.
+
+    >>> fsf1 = signal.place_poles(A, B, P, method='KNV0')
+    >>> fsf1.gain_matrix
+    array([[ 0.20071427, -0.96665799,  0.24066128, -0.10279785],
+           [ 0.50587268,  0.57779091,  0.51795763, -0.41991442]])
+
+    >>> fsf2 = signal.place_poles(A, B, P)  # uses YT method
+    >>> fsf2.computed_poles
+    array([-8.6659, -5.0566, -0.5   , -0.2   ])
+
+    >>> fsf3 = signal.place_poles(A, B, P, rtol=-1, maxiter=100)
+    >>> fsf3.X
+    array([[ 0.52072442+0.j, -0.08409372+0.j, -0.56847937+0.j,  0.74823657+0.j],
+           [-0.04977751+0.j, -0.80872954+0.j,  0.13566234+0.j, -0.29322906+0.j],
+           [-0.82266932+0.j, -0.19168026+0.j, -0.56348322+0.j, -0.43815060+0.j],
+           [ 0.22267347+0.j,  0.54967577+0.j, -0.58387806+0.j, -0.40271926+0.j]])
+
+    The absolute value of the determinant of X is a good indicator to check the
+    robustness of the results, both ``'KNV0'`` and ``'YT'`` aim at maximizing
+    it.  Below a comparison of the robustness of the results above:
+
+    >>> abs(np.linalg.det(fsf1.X)) < abs(np.linalg.det(fsf2.X))
+    True
+    >>> abs(np.linalg.det(fsf2.X)) < abs(np.linalg.det(fsf3.X))
+    True
+
+    Now a simple example for complex poles:
+
+    >>> A = np.array([[ 0,  7/3.,  0,   0   ],
+    ...               [ 0,   0,    0,  7/9. ],
+    ...               [ 0,   0,    0,   0   ],
+    ...               [ 0,   0,    0,   0   ]])
+    >>> B = np.array([[ 0,  0 ],
+    ...               [ 0,  0 ],
+    ...               [ 1,  0 ],
+    ...               [ 0,  1 ]])
+    >>> P = np.array([-3, -1, -2-1j, -2+1j]) / 3.
+    >>> fsf = signal.place_poles(A, B, P, method='YT')
+
+    We can plot the desired and computed poles in the complex plane:
+
+    >>> t = np.linspace(0, 2*np.pi, 401)
+    >>> plt.plot(np.cos(t), np.sin(t), 'k--')  # unit circle
+    >>> plt.plot(fsf.requested_poles.real, fsf.requested_poles.imag,
+    ...          'wo', label='Desired')
+    >>> plt.plot(fsf.computed_poles.real, fsf.computed_poles.imag, 'bx',
+    ...          label='Placed')
+    >>> plt.grid()
+    >>> plt.axis('image')
+    >>> plt.axis([-1.1, 1.1, -1.1, 1.1])
+    >>> plt.legend(bbox_to_anchor=(1.05, 1), loc=2, numpoints=1)
+
+    """
+    # Move away all the inputs checking, it only adds noise to the code
+    update_loop, poles = _valid_inputs(A, B, poles, method, rtol, maxiter)
+
+    # The current value of the relative tolerance we achieved
+    cur_rtol = 0
+    # The number of iterations needed before converging
+    nb_iter = 0
+
+    # Step A: QR decomposition of B page 1132 KN
+    # to debug with numpy qr uncomment the line below
+    # u, z = np.linalg.qr(B, mode="complete")
+    u, z = s_qr(B, mode="full")
+    rankB = np.linalg.matrix_rank(B)
+    u0 = u[:, :rankB]
+    u1 = u[:, rankB:]
+    z = z[:rankB, :]
+
+    # If we can use the identity matrix as X the solution is obvious
+    if B.shape[0] == rankB:
+        # if B is square and full rank there is only one solution
+        # such as (A+BK)=inv(X)*diag(P)*X with X=eye(A.shape[0])
+        # i.e K=inv(B)*(diag(P)-A)
+        # if B has as many lines as its rank (but not square) there are many
+        # solutions and we can choose one using least squares
+        # => use lstsq in both cases.
+        # In both cases the transfer matrix X will be eye(A.shape[0]) and I
+        # can hardly think of a better one so there is nothing to optimize
+        #
+        # for complex poles we use the following trick
+        #
+        # |a -b| has for eigenvalues a+b and a-b
+        # |b a|
+        #
+        # |a+bi 0| has the obvious eigenvalues a+bi and a-bi
+        # |0 a-bi|
+        #
+        # e.g solving the first one in R gives the solution
+        # for the second one in C
+        diag_poles = np.zeros(A.shape)
+        idx = 0
+        while idx < poles.shape[0]:
+            p = poles[idx]
+            diag_poles[idx, idx] = np.real(p)
+            if ~np.isreal(p):
+                diag_poles[idx, idx+1] = -np.imag(p)
+                diag_poles[idx+1, idx+1] = np.real(p)
+                diag_poles[idx+1, idx] = np.imag(p)
+                idx += 1  # skip next one
+            idx += 1
+        gain_matrix = np.linalg.lstsq(B, diag_poles-A, rcond=-1)[0]
+        transfer_matrix = np.eye(A.shape[0])
+        cur_rtol = np.nan
+        nb_iter = np.nan
+    else:
+        # step A (p1144 KNV) and beginning of step F: decompose
+        # dot(U1.T, A-P[i]*I).T and build our set of transfer_matrix vectors
+        # in the same loop
+        ker_pole = []
+
+        # flag to skip the conjugate of a complex pole
+        skip_conjugate = False
+        # select orthonormal base ker_pole for each Pole and vectors for
+        # transfer_matrix
+        for j in range(B.shape[0]):
+            if skip_conjugate:
+                skip_conjugate = False
+                continue
+            pole_space_j = np.dot(u1.T, A-poles[j]*np.eye(B.shape[0])).T
+
+            # after QR Q=Q0|Q1
+            # only Q0 is used to reconstruct  the qr'ed (dot Q, R) matrix.
+            # Q1 is orthogonal to Q0 and will be multiplied by the zeros in
+            # R when using mode "complete". In default mode Q1 and the zeros
+            # in R are not computed
+
+            # To debug with numpy qr uncomment the line below
+            # Q, _ = np.linalg.qr(pole_space_j, mode="complete")
+            Q, _ = s_qr(pole_space_j, mode="full")
+
+            ker_pole_j = Q[:, pole_space_j.shape[1]:]
+
+            # We want to select one vector in ker_pole_j to build the transfer
+            # matrix, however qr returns sometimes vectors with zeros on the
+            # same line for each pole and this yields very long convergence
+            # times.
+            # Or some other times a set of vectors, one with zero imaginary
+            # part and one (or several) with imaginary parts. After trying
+            # many ways to select the best possible one (eg ditch vectors
+            # with zero imaginary part for complex poles) I ended up summing
+            # all vectors in ker_pole_j, this solves 100% of the problems and
+            # is a valid choice for transfer_matrix.
+            # This way for complex poles we are sure to have a non zero
+            # imaginary part that way, and the problem of lines full of zeros
+            # in transfer_matrix is solved too as when a vector from
+            # ker_pole_j has a zero the other one(s) when
+            # ker_pole_j.shape[1]>1) for sure won't have a zero there.
+
+            transfer_matrix_j = np.sum(ker_pole_j, axis=1)[:, np.newaxis]
+            transfer_matrix_j = (transfer_matrix_j /
+                                 np.linalg.norm(transfer_matrix_j))
+            if ~np.isreal(poles[j]):  # complex pole
+                transfer_matrix_j = np.hstack([np.real(transfer_matrix_j),
+                                               np.imag(transfer_matrix_j)])
+                ker_pole.extend([ker_pole_j, ker_pole_j])
+
+                # Skip next pole as it is the conjugate
+                skip_conjugate = True
+            else:  # real pole, nothing to do
+                ker_pole.append(ker_pole_j)
+
+            if j == 0:
+                transfer_matrix = transfer_matrix_j
+            else:
+                transfer_matrix = np.hstack((transfer_matrix, transfer_matrix_j))
+
+        if rankB > 1:  # otherwise there is nothing we can optimize
+            stop, cur_rtol, nb_iter = update_loop(ker_pole, transfer_matrix,
+                                                  poles, B, maxiter, rtol)
+            if not stop and rtol > 0:
+                # if rtol<=0 the user has probably done that on purpose,
+                # don't annoy them
+                err_msg = (
+                    "Convergence was not reached after maxiter iterations.\n"
+                    f"You asked for a tolerance of {rtol}, we got {cur_rtol}."
+                    )
+                warnings.warn(err_msg, stacklevel=2)
+
+        # reconstruct transfer_matrix to match complex conjugate pairs,
+        # ie transfer_matrix_j/transfer_matrix_j+1 are
+        # Re(Complex_pole), Im(Complex_pole) now and will be Re-Im/Re+Im after
+        transfer_matrix = transfer_matrix.astype(complex)
+        idx = 0
+        while idx < poles.shape[0]-1:
+            if ~np.isreal(poles[idx]):
+                rel = transfer_matrix[:, idx].copy()
+                img = transfer_matrix[:, idx+1]
+                # rel will be an array referencing a column of transfer_matrix
+                # if we don't copy() it will changer after the next line and
+                # and the line after will not yield the correct value
+                transfer_matrix[:, idx] = rel-1j*img
+                transfer_matrix[:, idx+1] = rel+1j*img
+                idx += 1  # skip next one
+            idx += 1
+
+        try:
+            m = np.linalg.solve(transfer_matrix.T, np.dot(np.diag(poles),
+                                                          transfer_matrix.T)).T
+            gain_matrix = np.linalg.solve(z, np.dot(u0.T, m-A))
+        except np.linalg.LinAlgError as e:
+            raise ValueError("The poles you've chosen can't be placed. "
+                             "Check the controllability matrix and try "
+                             "another set of poles") from e
+
+    # Beware: Kautsky solves A+BK but the usual form is A-BK
+    gain_matrix = -gain_matrix
+    # K still contains complex with ~=0j imaginary parts, get rid of them
+    gain_matrix = np.real(gain_matrix)
+
+    full_state_feedback = Bunch()
+    full_state_feedback.gain_matrix = gain_matrix
+    full_state_feedback.computed_poles = _order_complex_poles(
+        np.linalg.eig(A - np.dot(B, gain_matrix))[0]
+        )
+    full_state_feedback.requested_poles = poles
+    full_state_feedback.X = transfer_matrix
+    full_state_feedback.rtol = cur_rtol
+    full_state_feedback.nb_iter = nb_iter
+
+    return full_state_feedback
+
+
+def dlsim(system, u, t=None, x0=None):
+    r"""Simulate output of a discrete-time linear system.
+
+    Parameters
+    ----------
+    system : dlti | tuple
+        An instance of the LTI class `dlti` or a tuple describing the system.
+        The number of elements in the tuple determine the interpretation. I.e.:
+
+        * ``system``: Instance of LTI class `dlti`. Note that derived instances, such
+          as instances of `TransferFunction`, `ZerosPolesGain`, or `StateSpace`, are
+          allowed as well.
+        * ``(num, den, dt)``: Rational polynomial as described in `TransferFunction`.
+          The coefficients of the polynomials should be specified in descending
+          exponent order,  e.g., z² + 3z + 5 would be represented as ``[1, 3, 5]``.
+        * ``(zeros, poles, gain, dt)``:  Zeros, poles, gain form as described
+          in `ZerosPolesGain`.
+        * ``(A, B, C, D, dt)``: State-space form as described in `StateSpace`.
+
+
+    u : array_like
+        An input array describing the input at each time `t` (interpolation is
+        assumed between given times).  If there are multiple inputs, then each
+        column of the rank-2 array represents an input.
+    t : array_like, optional
+        The time steps at which the input is defined.  If `t` is given, it
+        must be the same length as `u`, and the final value in `t` determines
+        the number of steps returned in the output.
+    x0 : array_like, optional
+        The initial conditions on the state vector (zero by default).
+
+    Returns
+    -------
+    tout : ndarray
+        Time values for the output, as a 1-D array.
+    yout : ndarray
+        System response, as a 1-D array.
+    xout : ndarray, optional
+        Time-evolution of the state-vector.  Only generated if the input is a
+        `StateSpace` system.
+
+    See Also
+    --------
+    lsim, dstep, dimpulse, cont2discrete
+
+    Examples
+    --------
+    A simple integrator transfer function with a discrete time step of 1.0
+    could be implemented as:
+
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> tf = ([1.0,], [1.0, -1.0], 1.0)
+    >>> t_in = [0.0, 1.0, 2.0, 3.0]
+    >>> u = np.asarray([0.0, 0.0, 1.0, 1.0])
+    >>> t_out, y = signal.dlsim(tf, u, t=t_in)
+    >>> y.T
+    array([[ 0.,  0.,  0.,  1.]])
+
+    """
+    # Convert system to dlti-StateSpace
+    if isinstance(system, lti):
+        raise AttributeError('dlsim can only be used with discrete-time dlti '
+                             'systems.')
+    elif not isinstance(system, dlti):
+        system = dlti(*system[:-1], dt=system[-1])
+
+    # Condition needed to ensure output remains compatible
+    is_ss_input = isinstance(system, StateSpace)
+    system = system._as_ss()
+
+    u = np.atleast_1d(u)
+
+    if u.ndim == 1:
+        u = np.atleast_2d(u).T
+
+    if t is None:
+        out_samples = len(u)
+        stoptime = (out_samples - 1) * system.dt
+    else:
+        stoptime = t[-1]
+        out_samples = int(np.floor(stoptime / system.dt)) + 1
+
+    # Pre-build output arrays
+    xout = np.zeros((out_samples, system.A.shape[0]))
+    yout = np.zeros((out_samples, system.C.shape[0]))
+    tout = np.linspace(0.0, stoptime, num=out_samples)
+
+    # Check initial condition
+    if x0 is None:
+        xout[0, :] = np.zeros((system.A.shape[1],))
+    else:
+        xout[0, :] = np.asarray(x0)
+
+    # Pre-interpolate inputs into the desired time steps
+    if t is None:
+        u_dt = u
+    else:
+        if len(u.shape) == 1:
+            u = u[:, np.newaxis]
+
+        u_dt = make_interp_spline(t, u, k=1)(tout)
+
+    # Simulate the system
+    for i in range(0, out_samples - 1):
+        xout[i+1, :] = (np.dot(system.A, xout[i, :]) +
+                        np.dot(system.B, u_dt[i, :]))
+        yout[i, :] = (np.dot(system.C, xout[i, :]) +
+                      np.dot(system.D, u_dt[i, :]))
+
+    # Last point
+    yout[out_samples-1, :] = (np.dot(system.C, xout[out_samples-1, :]) +
+                              np.dot(system.D, u_dt[out_samples-1, :]))
+
+    if is_ss_input:
+        return tout, yout, xout
+    else:
+        return tout, yout
+
+
+def dimpulse(system, x0=None, t=None, n=None):
+    r"""Impulse response of discrete-time system.
+
+    Parameters
+    ----------
+        system : dlti | tuple
+        An instance of the LTI class `dlti` or a tuple describing the system.
+        The number of elements in the tuple determine the interpretation. I.e.:
+
+        * ``system``: Instance of LTI class `dlti`. Note that derived instances, such
+          as instances of `TransferFunction`, `ZerosPolesGain`, or `StateSpace`, are
+          allowed as well.
+        * ``(num, den, dt)``: Rational polynomial as described in `TransferFunction`.
+          The coefficients of the polynomials should be specified in descending
+          exponent order,  e.g., z² + 3z + 5 would be represented as ``[1, 3, 5]``.
+        * ``(zeros, poles, gain, dt)``:  Zeros, poles, gain form as described
+          in `ZerosPolesGain`.
+        * ``(A, B, C, D, dt)``: State-space form as described in `StateSpace`.
+
+    x0 : array_like, optional
+        Initial state-vector.  Defaults to zero.
+    t : array_like, optional
+        Time points.  Computed if not given.
+    n : int, optional
+        The number of time points to compute (if `t` is not given).
+
+    Returns
+    -------
+    tout : ndarray
+        Time values for the output, as a 1-D array.
+    yout : tuple of ndarray
+        Impulse response of system.  Each element of the tuple represents
+        the output of the system based on an impulse in each input.
+
+    See Also
+    --------
+    impulse, dstep, dlsim, cont2discrete
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+    ...
+    >>> dt = 1  # sampling interval is one => time unit is sample number
+    >>> bb, aa = signal.butter(3, 0.25, fs=1/dt)
+    >>> t, y = signal.dimpulse((bb, aa, dt), n=25)
+    ...
+    >>> fig0, ax0 = plt.subplots()
+    >>> ax0.step(t, np.squeeze(y), '.-', where='post')
+    >>> ax0.set_title(r"Impulse Response of a $3^\text{rd}$ Order Butterworth Filter")
+    >>> ax0.set(xlabel='Sample number', ylabel='Amplitude')
+    >>> ax0.grid()
+    >>> plt.show()
+    """
+    # Convert system to dlti-StateSpace
+    if isinstance(system, dlti):
+        system = system._as_ss()
+    elif isinstance(system, lti):
+        raise AttributeError('dimpulse can only be used with discrete-time '
+                             'dlti systems.')
+    else:
+        system = dlti(*system[:-1], dt=system[-1])._as_ss()
+
+    # Default to 100 samples if unspecified
+    if n is None:
+        n = 100
+
+    # If time is not specified, use the number of samples
+    # and system dt
+    if t is None:
+        t = np.linspace(0, n * system.dt, n, endpoint=False)
+    else:
+        t = np.asarray(t)
+
+    # For each input, implement a step change
+    yout = None
+    for i in range(0, system.inputs):
+        u = np.zeros((t.shape[0], system.inputs))
+        u[0, i] = 1.0
+
+        one_output = dlsim(system, u, t=t, x0=x0)
+
+        if yout is None:
+            yout = (one_output[1],)
+        else:
+            yout = yout + (one_output[1],)
+
+        tout = one_output[0]
+
+    return tout, yout
+
+
+def dstep(system, x0=None, t=None, n=None):
+    r"""Step response of discrete-time system.
+
+    Parameters
+    ----------
+     system : dlti | tuple
+        An instance of the LTI class `dlti` or a tuple describing the system.
+        The number of elements in the tuple determine the interpretation. I.e.:
+
+        * ``system``: Instance of LTI class `dlti`. Note that derived instances, such
+          as instances of `TransferFunction`, `ZerosPolesGain`, or `StateSpace`, are
+          allowed as well.
+        * ``(num, den, dt)``: Rational polynomial as described in `TransferFunction`.
+          The coefficients of the polynomials should be specified in descending
+          exponent order,  e.g., z² + 3z + 5 would be represented as ``[1, 3, 5]``.
+        * ``(zeros, poles, gain, dt)``:  Zeros, poles, gain form as described
+          in `ZerosPolesGain`.
+        * ``(A, B, C, D, dt)``: State-space form as described in `StateSpace`.
+
+    x0 : array_like, optional
+        Initial state-vector.  Defaults to zero.
+    t : array_like, optional
+        Time points.  Computed if not given.
+    n : int, optional
+        The number of time points to compute (if `t` is not given).
+
+    Returns
+    -------
+    tout : ndarray
+        Output time points, as a 1-D array.
+    yout : tuple of ndarray
+        Step response of system.  Each element of the tuple represents
+        the output of the system based on a step response to each input.
+
+    See Also
+    --------
+    step, dimpulse, dlsim, cont2discrete
+
+    Examples
+    --------
+    The following example illustrates how to create a digital Butterworth filer and
+    plot its step response:
+
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+    ...
+    >>> dt = 1  # sampling interval is one => time unit is sample number
+    >>> bb, aa = signal.butter(3, 0.25, fs=1/dt)
+    >>> t, y = signal.dstep((bb, aa, dt), n=25)
+    ...
+    >>> fig0, ax0 = plt.subplots()
+    >>> ax0.step(t, np.squeeze(y), '.-', where='post')
+    >>> ax0.set_title(r"Step Response of a $3^\text{rd}$ Order Butterworth Filter")
+    >>> ax0.set(xlabel='Sample number', ylabel='Amplitude', ylim=(0, 1.1*np.max(y)))
+    >>> ax0.grid()
+    >>> plt.show()
+    """
+    # Convert system to dlti-StateSpace
+    if isinstance(system, dlti):
+        system = system._as_ss()
+    elif isinstance(system, lti):
+        raise AttributeError('dstep can only be used with discrete-time dlti '
+                             'systems.')
+    else:
+        system = dlti(*system[:-1], dt=system[-1])._as_ss()
+
+    # Default to 100 samples if unspecified
+    if n is None:
+        n = 100
+
+    # If time is not specified, use the number of samples
+    # and system dt
+    if t is None:
+        t = np.linspace(0, n * system.dt, n, endpoint=False)
+    else:
+        t = np.asarray(t)
+
+    # For each input, implement a step change
+    yout = None
+    for i in range(0, system.inputs):
+        u = np.zeros((t.shape[0], system.inputs))
+        u[:, i] = np.ones((t.shape[0],))
+
+        one_output = dlsim(system, u, t=t, x0=x0)
+
+        if yout is None:
+            yout = (one_output[1],)
+        else:
+            yout = yout + (one_output[1],)
+
+        tout = one_output[0]
+
+    return tout, yout
+
+
+def dfreqresp(system, w=None, n=10000, whole=False):
+    r"""
+    Calculate the frequency response of a discrete-time system.
+
+    Parameters
+    ----------
+    system : dlti | tuple
+        An instance of the LTI class `dlti` or a tuple describing the system.
+        The number of elements in the tuple determine the interpretation. I.e.:
+
+        * ``system``: Instance of LTI class `dlti`. Note that derived instances, such
+          as instances of `TransferFunction`, `ZerosPolesGain`, or `StateSpace`, are
+          allowed as well.
+        * ``(num, den, dt)``: Rational polynomial as described in `TransferFunction`.
+          The coefficients of the polynomials should be specified in descending
+          exponent order,  e.g., z² + 3z + 5 would be represented as ``[1, 3, 5]``.
+        * ``(zeros, poles, gain, dt)``:  Zeros, poles, gain form as described
+          in `ZerosPolesGain`.
+        * ``(A, B, C, D, dt)``: State-space form as described in `StateSpace`.
+
+    w : array_like, optional
+        Array of frequencies (in radians/sample). Magnitude and phase data is
+        calculated for every value in this array. If not given a reasonable
+        set will be calculated.
+    n : int, optional
+        Number of frequency points to compute if `w` is not given. The `n`
+        frequencies are logarithmically spaced in an interval chosen to
+        include the influence of the poles and zeros of the system.
+    whole : bool, optional
+        Normally, if 'w' is not given, frequencies are computed from 0 to the
+        Nyquist frequency, pi radians/sample (upper-half of unit-circle). If
+        `whole` is True, compute frequencies from 0 to 2*pi radians/sample.
+
+    Returns
+    -------
+    w : 1D ndarray
+        Frequency array [radians/sample]
+    H : 1D ndarray
+        Array of complex magnitude values
+
+    Notes
+    -----
+    If (num, den) is passed in for ``system``, coefficients for both the
+    numerator and denominator should be specified in descending exponent
+    order (e.g. ``z^2 + 3z + 5`` would be represented as ``[1, 3, 5]``).
+
+    .. versionadded:: 0.18.0
+
+    Examples
+    --------
+    The following example generates the Nyquist plot of the transfer function
+    :math:`H(z) = \frac{1}{z^2 + 2z + 3}`  with a sampling time of 0.05 seconds:
+
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+    >>> sys = signal.TransferFunction([1], [1, 2, 3], dt=0.05)  # construct H(z)
+    >>> w, H = signal.dfreqresp(sys)
+    ...
+    >>> fig0, ax0 = plt.subplots()
+    >>> ax0.plot(H.real, H.imag, label=r"$H(z=e^{+j\omega})$")
+    >>> ax0.plot(H.real, -H.imag, label=r"$H(z=e^{-j\omega})$")
+    >>> ax0.set_title(r"Nyquist Plot of $H(z) = 1 / (z^2 + 2z + 3)$")
+    >>> ax0.set(xlabel=r"$\text{Re}\{z\}$", ylabel=r"$\text{Im}\{z\}$",
+    ...         xlim=(-0.2, 0.65), aspect='equal')
+    >>> ax0.plot(H[0].real, H[0].imag, 'k.')  # mark H(exp(1j*w[0]))
+    >>> ax0.text(0.2, 0, r"$H(e^{j0})$")
+    >>> ax0.grid(True)
+    >>> ax0.legend()
+    >>> plt.show()
+    """
+    if not isinstance(system, dlti):
+        if isinstance(system, lti):
+            raise AttributeError('dfreqresp can only be used with '
+                                 'discrete-time systems.')
+
+        system = dlti(*system[:-1], dt=system[-1])
+
+    if isinstance(system, StateSpace):
+        # No SS->ZPK code exists right now, just SS->TF->ZPK
+        system = system._as_tf()
+
+    if not isinstance(system, TransferFunction | ZerosPolesGain):
+        raise ValueError('Unknown system type')
+
+    if system.inputs != 1 or system.outputs != 1:
+        raise ValueError("dfreqresp requires a SISO (single input, single "
+                         "output) system.")
+
+    if w is not None:
+        worN = w
+    else:
+        worN = n
+
+    if isinstance(system, TransferFunction):
+        # Convert numerator and denominator from polynomials in the variable
+        # 'z' to polynomials in the variable 'z^-1', as freqz expects.
+        num, den = TransferFunction._z_to_zinv(system.num.ravel(), system.den)
+        w, h = freqz(num, den, worN=worN, whole=whole)
+
+    elif isinstance(system, ZerosPolesGain):
+        w, h = freqz_zpk(system.zeros, system.poles, system.gain, worN=worN,
+                         whole=whole)
+
+    return w, h
+
+
+def dbode(system, w=None, n=100):
+    r"""Calculate Bode magnitude and phase data of a discrete-time system.
+
+    Parameters
+    ----------
+    system : dlti | tuple
+        An instance of the LTI class `dlti` or a tuple describing the system.
+        The number of elements in the tuple determine the interpretation. I.e.:
+
+        * ``system``: Instance of LTI class `dlti`. Note that derived instances, such
+          as instances of `TransferFunction`, `ZerosPolesGain`, or `StateSpace`, are
+          allowed as well.
+        * ``(num, den, dt)``: Rational polynomial as described in `TransferFunction`.
+          The coefficients of the polynomials should be specified in descending
+          exponent order,  e.g., z² + 3z + 5 would be represented as ``[1, 3, 5]``.
+        * ``(zeros, poles, gain, dt)``:  Zeros, poles, gain form as described
+          in `ZerosPolesGain`.
+        * ``(A, B, C, D, dt)``: State-space form as described in `StateSpace`.
+
+    w : array_like, optional
+        Array of frequencies normalized to the Nyquist frequency being π, i.e.,
+        having unit radiant / sample. Magnitude and phase data is calculated for every
+        value in this array. If not given, a reasonable set will be calculated.
+    n : int, optional
+        Number of frequency points to compute if `w` is not given. The `n`
+        frequencies are logarithmically spaced in an interval chosen to
+        include the influence of the poles and zeros of the system.
+
+    Returns
+    -------
+    w : 1D ndarray
+        Array of frequencies normalized to the Nyquist frequency being ``np.pi/dt``
+        with ``dt`` being the sampling interval of the `system` parameter.
+        The unit is rad/s assuming ``dt`` is in seconds.
+    mag : 1D ndarray
+        Magnitude array in dB
+    phase : 1D ndarray
+        Phase array in degrees
+
+    Notes
+    -----
+    This function is a convenience wrapper around `dfreqresp` for extracting
+    magnitude and phase from the calculated complex-valued amplitude of the
+    frequency response.
+
+    .. versionadded:: 0.18.0
+
+    See Also
+    --------
+    dfreqresp, dlti, TransferFunction, ZerosPolesGain, StateSpace
+
+
+    Examples
+    --------
+    The following example shows how to create a Bode plot of a 5-th order
+    Butterworth lowpass filter with a corner frequency of 100 Hz:
+
+    >>> import matplotlib.pyplot as plt
+    >>> import numpy as np
+    >>> from scipy import signal
+    ...
+    >>> T = 1e-4  # sampling interval in s
+    >>> f_c, o = 1e2, 5  # corner frequency in Hz (i.e., -3 dB value) and filter order
+    >>> bb, aa = signal.butter(o, f_c, 'lowpass', fs=1/T)
+    ...
+    >>> w, mag, phase = signal.dbode((bb, aa, T))
+    >>> w /= 2*np.pi  # convert unit of frequency into Hertz
+    ...
+    >>> fg, (ax0, ax1) = plt.subplots(2, 1, sharex='all', figsize=(5, 4),
+    ...                               tight_layout=True)
+    >>> ax0.set_title("Bode Plot of Butterworth Lowpass Filter " +
+    ...               rf"($f_c={f_c:g}\,$Hz, order={o})")
+    >>> ax0.set_ylabel(r"Magnitude in dB")
+    >>> ax1.set(ylabel=r"Phase in Degrees",
+    ...         xlabel="Frequency $f$ in Hertz", xlim=(w[1], w[-1]))
+    >>> ax0.semilogx(w, mag, 'C0-', label=r"$20\,\log_{10}|G(f)|$")  # Magnitude plot
+    >>> ax1.semilogx(w, phase, 'C1-', label=r"$\angle G(f)$")  # Phase plot
+    ...
+    >>> for ax_ in (ax0, ax1):
+    ...     ax_.axvline(f_c, color='m', alpha=0.25, label=rf"${f_c=:g}\,$Hz")
+    ...     ax_.grid(which='both', axis='x')  # plot major & minor vertical grid lines
+    ...     ax_.grid(which='major', axis='y')
+    ...     ax_.legend()
+    >>> plt.show()
+    """
+    w, y = dfreqresp(system, w=w, n=n)
+
+    if isinstance(system, dlti):
+        dt = system.dt
+    else:
+        dt = system[-1]
+
+    mag = 20.0 * np.log10(abs(y))
+    phase = np.rad2deg(np.unwrap(np.angle(y)))
+
+    return w / dt, mag, phase
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/_max_len_seq.py b/venv/lib/python3.12/site-packages/scipy/signal/_max_len_seq.py
new file mode 100644
index 0000000000000000000000000000000000000000..4d64beaca86d1da50b563668679b6fc52c954ab0
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/_max_len_seq.py
@@ -0,0 +1,139 @@
+# Author: Eric Larson
+# 2014
+
+"""Tools for MLS generation"""
+
+import numpy as np
+
+from ._max_len_seq_inner import _max_len_seq_inner
+
+__all__ = ['max_len_seq']
+
+
+# These are definitions of linear shift register taps for use in max_len_seq()
+_mls_taps = {2: [1], 3: [2], 4: [3], 5: [3], 6: [5], 7: [6], 8: [7, 6, 1],
+             9: [5], 10: [7], 11: [9], 12: [11, 10, 4], 13: [12, 11, 8],
+             14: [13, 12, 2], 15: [14], 16: [15, 13, 4], 17: [14],
+             18: [11], 19: [18, 17, 14], 20: [17], 21: [19], 22: [21],
+             23: [18], 24: [23, 22, 17], 25: [22], 26: [25, 24, 20],
+             27: [26, 25, 22], 28: [25], 29: [27], 30: [29, 28, 7],
+             31: [28], 32: [31, 30, 10]}
+
+def max_len_seq(nbits, state=None, length=None, taps=None):
+    """
+    Maximum length sequence (MLS) generator.
+
+    Parameters
+    ----------
+    nbits : int
+        Number of bits to use. Length of the resulting sequence will
+        be ``(2**nbits) - 1``. Note that generating long sequences
+        (e.g., greater than ``nbits == 16``) can take a long time.
+    state : array_like, optional
+        If array, must be of length ``nbits``, and will be cast to binary
+        (bool) representation. If None, a seed of ones will be used,
+        producing a repeatable representation. If ``state`` is all
+        zeros, an error is raised as this is invalid. Default: None.
+    length : int, optional
+        Number of samples to compute. If None, the entire length
+        ``(2**nbits) - 1`` is computed.
+    taps : array_like, optional
+        Polynomial taps to use (e.g., ``[7, 6, 1]`` for an 8-bit sequence).
+        If None, taps will be automatically selected (for up to
+        ``nbits == 32``).
+
+    Returns
+    -------
+    seq : array
+        Resulting MLS sequence of 0's and 1's.
+    state : array
+        The final state of the shift register.
+
+    Notes
+    -----
+    The algorithm for MLS generation is generically described in:
+
+        https://en.wikipedia.org/wiki/Maximum_length_sequence
+
+    The default values for taps are specifically taken from the first
+    option listed for each value of ``nbits`` in:
+
+        https://web.archive.org/web/20181001062252/http://www.newwaveinstruments.com/resources/articles/m_sequence_linear_feedback_shift_register_lfsr.htm
+
+    .. versionadded:: 0.15.0
+
+    Examples
+    --------
+    MLS uses binary convention:
+
+    >>> from scipy.signal import max_len_seq
+    >>> max_len_seq(4)[0]
+    array([1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0], dtype=int8)
+
+    MLS has a white spectrum (except for DC):
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from numpy.fft import fft, ifft, fftshift, fftfreq
+    >>> seq = max_len_seq(6)[0]*2-1  # +1 and -1
+    >>> spec = fft(seq)
+    >>> N = len(seq)
+    >>> plt.plot(fftshift(fftfreq(N)), fftshift(np.abs(spec)), '.-')
+    >>> plt.margins(0.1, 0.1)
+    >>> plt.grid(True)
+    >>> plt.show()
+
+    Circular autocorrelation of MLS is an impulse:
+
+    >>> acorrcirc = ifft(spec * np.conj(spec)).real
+    >>> plt.figure()
+    >>> plt.plot(np.arange(-N/2+1, N/2+1), fftshift(acorrcirc), '.-')
+    >>> plt.margins(0.1, 0.1)
+    >>> plt.grid(True)
+    >>> plt.show()
+
+    Linear autocorrelation of MLS is approximately an impulse:
+
+    >>> acorr = np.correlate(seq, seq, 'full')
+    >>> plt.figure()
+    >>> plt.plot(np.arange(-N+1, N), acorr, '.-')
+    >>> plt.margins(0.1, 0.1)
+    >>> plt.grid(True)
+    >>> plt.show()
+
+    """
+    taps_dtype = np.int32 if np.intp().itemsize == 4 else np.int64
+    if taps is None:
+        if nbits not in _mls_taps:
+            known_taps = np.array(list(_mls_taps.keys()))
+            raise ValueError(f'nbits must be between {known_taps.min()} and '
+                             f'{known_taps.max()} if taps is None')
+        taps = np.array(_mls_taps[nbits], taps_dtype)
+    else:
+        taps = np.unique(np.array(taps, taps_dtype))[::-1]
+        if np.any(taps < 0) or np.any(taps > nbits) or taps.size < 1:
+            raise ValueError('taps must be non-empty with values between '
+                             'zero and nbits (inclusive)')
+        taps = np.array(taps)  # needed for Cython and Pythran
+    n_max = (2**nbits) - 1
+    if length is None:
+        length = n_max
+    else:
+        length = int(length)
+        if length < 0:
+            raise ValueError('length must be greater than or equal to 0')
+    # We use int8 instead of bool here because NumPy arrays of bools
+    # don't seem to work nicely with Cython
+    if state is None:
+        state = np.ones(nbits, dtype=np.int8, order='c')
+    else:
+        # makes a copy if need be, ensuring it's 0's and 1's
+        state = np.array(state, dtype=bool, order='c').astype(np.int8)
+    if state.ndim != 1 or state.size != nbits:
+        raise ValueError('state must be a 1-D array of size nbits')
+    if np.all(state == 0):
+        raise ValueError('state must not be all zeros')
+
+    seq = np.empty(length, dtype=np.int8, order='c')
+    state = _max_len_seq_inner(taps, state, nbits, length, seq)
+    return seq, state
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/_max_len_seq_inner.cpython-312-x86_64-linux-gnu.so b/venv/lib/python3.12/site-packages/scipy/signal/_max_len_seq_inner.cpython-312-x86_64-linux-gnu.so
new file mode 100644
index 0000000000000000000000000000000000000000..514d8d3726cccaaf8c65ad6fea15f96f89f62bf3
Binary files /dev/null and b/venv/lib/python3.12/site-packages/scipy/signal/_max_len_seq_inner.cpython-312-x86_64-linux-gnu.so differ
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/_peak_finding.py b/venv/lib/python3.12/site-packages/scipy/signal/_peak_finding.py
new file mode 100644
index 0000000000000000000000000000000000000000..a5fe546756dfebddd831de936a110ad05eab2d2b
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/_peak_finding.py
@@ -0,0 +1,1307 @@
+"""
+Functions for identifying peaks in signals.
+"""
+import math
+import numpy as np
+
+from scipy.signal._wavelets import _cwt, _ricker
+from scipy.stats import scoreatpercentile
+
+from ._peak_finding_utils import (
+    _local_maxima_1d,
+    _select_by_peak_distance,
+    _peak_prominences,
+    _peak_widths
+)
+
+
+__all__ = ['argrelmin', 'argrelmax', 'argrelextrema', 'peak_prominences',
+           'peak_widths', 'find_peaks', 'find_peaks_cwt']
+
+
+def _boolrelextrema(data, comparator, axis=0, order=1, mode='clip'):
+    """
+    Calculate the relative extrema of `data`.
+
+    Relative extrema are calculated by finding locations where
+    ``comparator(data[n], data[n+1:n+order+1])`` is True.
+
+    Parameters
+    ----------
+    data : ndarray
+        Array in which to find the relative extrema.
+    comparator : callable
+        Function to use to compare two data points.
+        Should take two arrays as arguments.
+    axis : int, optional
+        Axis over which to select from `data`. Default is 0.
+    order : int, optional
+        How many points on each side to use for the comparison
+        to consider ``comparator(n,n+x)`` to be True.
+    mode : str, optional
+        How the edges of the vector are treated. 'wrap' (wrap around) or
+        'clip' (treat overflow as the same as the last (or first) element).
+        Default 'clip'. See numpy.take.
+
+    Returns
+    -------
+    extrema : ndarray
+        Boolean array of the same shape as `data` that is True at an extrema,
+        False otherwise.
+
+    See Also
+    --------
+    argrelmax, argrelmin
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.signal._peak_finding import _boolrelextrema
+    >>> testdata = np.array([1,2,3,2,1])
+    >>> _boolrelextrema(testdata, np.greater, axis=0)
+    array([False, False,  True, False, False], dtype=bool)
+
+    """
+    if (int(order) != order) or (order < 1):
+        raise ValueError('Order must be an int >= 1')
+
+    datalen = data.shape[axis]
+    locs = np.arange(0, datalen)
+
+    results = np.ones(data.shape, dtype=bool)
+    main = data.take(locs, axis=axis, mode=mode)
+    for shift in range(1, order + 1):
+        plus = data.take(locs + shift, axis=axis, mode=mode)
+        minus = data.take(locs - shift, axis=axis, mode=mode)
+        results &= comparator(main, plus)
+        results &= comparator(main, minus)
+        if ~results.any():
+            return results
+    return results
+
+
+def argrelmin(data, axis=0, order=1, mode='clip'):
+    """
+    Calculate the relative minima of `data`.
+
+    Parameters
+    ----------
+    data : ndarray
+        Array in which to find the relative minima.
+    axis : int, optional
+        Axis over which to select from `data`. Default is 0.
+    order : int, optional
+        How many points on each side to use for the comparison
+        to consider ``comparator(n, n+x)`` to be True.
+    mode : str, optional
+        How the edges of the vector are treated.
+        Available options are 'wrap' (wrap around) or 'clip' (treat overflow
+        as the same as the last (or first) element).
+        Default 'clip'. See numpy.take.
+
+    Returns
+    -------
+    extrema : tuple of ndarrays
+        Indices of the minima in arrays of integers. ``extrema[k]`` is
+        the array of indices of axis `k` of `data`. Note that the
+        return value is a tuple even when `data` is 1-D.
+
+    See Also
+    --------
+    argrelextrema, argrelmax, find_peaks
+
+    Notes
+    -----
+    This function uses `argrelextrema` with np.less as comparator. Therefore, it
+    requires a strict inequality on both sides of a value to consider it a
+    minimum. This means flat minima (more than one sample wide) are not detected.
+    In case of 1-D `data` `find_peaks` can be used to detect all
+    local minima, including flat ones, by calling it with negated `data`.
+
+    .. versionadded:: 0.11.0
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.signal import argrelmin
+    >>> x = np.array([2, 1, 2, 3, 2, 0, 1, 0])
+    >>> argrelmin(x)
+    (array([1, 5]),)
+    >>> y = np.array([[1, 2, 1, 2],
+    ...               [2, 2, 0, 0],
+    ...               [5, 3, 4, 4]])
+    ...
+    >>> argrelmin(y, axis=1)
+    (array([0, 2]), array([2, 1]))
+
+    """
+    return argrelextrema(data, np.less, axis, order, mode)
+
+
+def argrelmax(data, axis=0, order=1, mode='clip'):
+    """
+    Calculate the relative maxima of `data`.
+
+    Parameters
+    ----------
+    data : ndarray
+        Array in which to find the relative maxima.
+    axis : int, optional
+        Axis over which to select from `data`. Default is 0.
+    order : int, optional
+        How many points on each side to use for the comparison
+        to consider ``comparator(n, n+x)`` to be True.
+    mode : str, optional
+        How the edges of the vector are treated.
+        Available options are 'wrap' (wrap around) or 'clip' (treat overflow
+        as the same as the last (or first) element).
+        Default 'clip'. See `numpy.take`.
+
+    Returns
+    -------
+    extrema : tuple of ndarrays
+        Indices of the maxima in arrays of integers. ``extrema[k]`` is
+        the array of indices of axis `k` of `data`. Note that the
+        return value is a tuple even when `data` is 1-D.
+
+    See Also
+    --------
+    argrelextrema, argrelmin, find_peaks
+
+    Notes
+    -----
+    This function uses `argrelextrema` with np.greater as comparator. Therefore,
+    it  requires a strict inequality on both sides of a value to consider it a
+    maximum. This means flat maxima (more than one sample wide) are not detected.
+    In case of 1-D `data` `find_peaks` can be used to detect all
+    local maxima, including flat ones.
+
+    .. versionadded:: 0.11.0
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.signal import argrelmax
+    >>> x = np.array([2, 1, 2, 3, 2, 0, 1, 0])
+    >>> argrelmax(x)
+    (array([3, 6]),)
+    >>> y = np.array([[1, 2, 1, 2],
+    ...               [2, 2, 0, 0],
+    ...               [5, 3, 4, 4]])
+    ...
+    >>> argrelmax(y, axis=1)
+    (array([0]), array([1]))
+    """
+    return argrelextrema(data, np.greater, axis, order, mode)
+
+
+def argrelextrema(data, comparator, axis=0, order=1, mode='clip'):
+    """
+    Calculate the relative extrema of `data`.
+
+    Parameters
+    ----------
+    data : ndarray
+        Array in which to find the relative extrema.
+    comparator : callable
+        Function to use to compare two data points.
+        Should take two arrays as arguments.
+    axis : int, optional
+        Axis over which to select from `data`. Default is 0.
+    order : int, optional
+        How many points on each side to use for the comparison
+        to consider ``comparator(n, n+x)`` to be True.
+    mode : str, optional
+        How the edges of the vector are treated. 'wrap' (wrap around) or
+        'clip' (treat overflow as the same as the last (or first) element).
+        Default is 'clip'. See `numpy.take`.
+
+    Returns
+    -------
+    extrema : tuple of ndarrays
+        Indices of the maxima in arrays of integers. ``extrema[k]`` is
+        the array of indices of axis `k` of `data`. Note that the
+        return value is a tuple even when `data` is 1-D.
+
+    See Also
+    --------
+    argrelmin, argrelmax
+
+    Notes
+    -----
+
+    .. versionadded:: 0.11.0
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.signal import argrelextrema
+    >>> x = np.array([2, 1, 2, 3, 2, 0, 1, 0])
+    >>> argrelextrema(x, np.greater)
+    (array([3, 6]),)
+    >>> y = np.array([[1, 2, 1, 2],
+    ...               [2, 2, 0, 0],
+    ...               [5, 3, 4, 4]])
+    ...
+    >>> argrelextrema(y, np.less, axis=1)
+    (array([0, 2]), array([2, 1]))
+
+    """
+    results = _boolrelextrema(data, comparator,
+                              axis, order, mode)
+    return np.nonzero(results)
+
+
+def _arg_x_as_expected(value):
+    """Ensure argument `x` is a 1-D C-contiguous array of dtype('float64').
+
+    Used in `find_peaks`, `peak_prominences` and `peak_widths` to make `x`
+    compatible with the signature of the wrapped Cython functions.
+
+    Returns
+    -------
+    value : ndarray
+        A 1-D C-contiguous array with dtype('float64').
+    """
+    value = np.asarray(value, order='C', dtype=np.float64)
+    if value.ndim != 1:
+        raise ValueError('`x` must be a 1-D array')
+    return value
+
+
+def _arg_peaks_as_expected(value):
+    """Ensure argument `peaks` is a 1-D C-contiguous array of dtype('intp').
+
+    Used in `peak_prominences` and `peak_widths` to make `peaks` compatible
+    with the signature of the wrapped Cython functions.
+
+    Returns
+    -------
+    value : ndarray
+        A 1-D C-contiguous array with dtype('intp').
+    """
+    value = np.asarray(value)
+    if value.size == 0:
+        # Empty arrays default to np.float64 but are valid input
+        value = np.array([], dtype=np.intp)
+    try:
+        # Safely convert to C-contiguous array of type np.intp
+        value = value.astype(np.intp, order='C', casting='safe',
+                             subok=False, copy=False)
+    except TypeError as e:
+        raise TypeError("cannot safely cast `peaks` to dtype('intp')") from e
+    if value.ndim != 1:
+        raise ValueError('`peaks` must be a 1-D array')
+    return value
+
+
+def _arg_wlen_as_expected(value):
+    """Ensure argument `wlen` is of type `np.intp` and larger than 1.
+
+    Used in `peak_prominences` and `peak_widths`.
+
+    Returns
+    -------
+    value : np.intp
+        The original `value` rounded up to an integer or -1 if `value` was
+        None.
+    """
+    if value is None:
+        # _peak_prominences expects an intp; -1 signals that no value was
+        # supplied by the user
+        value = -1
+    elif 1 < value:
+        # Round up to a positive integer
+        if isinstance(value, float):
+            value = math.ceil(value)
+        value = np.intp(value)
+    else:
+        raise ValueError(f'`wlen` must be larger than 1, was {value}')
+    return value
+
+
+def peak_prominences(x, peaks, wlen=None):
+    """
+    Calculate the prominence of each peak in a signal.
+
+    The prominence of a peak measures how much a peak stands out from the
+    surrounding baseline of the signal and is defined as the vertical distance
+    between the peak and its lowest contour line.
+
+    Parameters
+    ----------
+    x : sequence
+        A signal with peaks.
+    peaks : sequence
+        Indices of peaks in `x`.
+    wlen : int, optional
+        A window length in samples that optionally limits the evaluated area for
+        each peak to a subset of `x`. The peak is always placed in the middle of
+        the window therefore the given length is rounded up to the next odd
+        integer. This parameter can speed up the calculation (see Notes).
+
+    Returns
+    -------
+    prominences : ndarray
+        The calculated prominences for each peak in `peaks`.
+    left_bases, right_bases : ndarray
+        The peaks' bases as indices in `x` to the left and right of each peak.
+        The higher base of each pair is a peak's lowest contour line.
+
+    Raises
+    ------
+    ValueError
+        If a value in `peaks` is an invalid index for `x`.
+
+    Warns
+    -----
+    PeakPropertyWarning
+        For indices in `peaks` that don't point to valid local maxima in `x`,
+        the returned prominence will be 0 and this warning is raised. This
+        also happens if `wlen` is smaller than the plateau size of a peak.
+
+    Warnings
+    --------
+    This function may return unexpected results for data containing NaNs. To
+    avoid this, NaNs should either be removed or replaced.
+
+    See Also
+    --------
+    find_peaks
+        Find peaks inside a signal based on peak properties.
+    peak_widths
+        Calculate the width of peaks.
+
+    Notes
+    -----
+    Strategy to compute a peak's prominence:
+
+    1. Extend a horizontal line from the current peak to the left and right
+       until the line either reaches the window border (see `wlen`) or
+       intersects the signal again at the slope of a higher peak. An
+       intersection with a peak of the same height is ignored.
+    2. On each side find the minimal signal value within the interval defined
+       above. These points are the peak's bases.
+    3. The higher one of the two bases marks the peak's lowest contour line. The
+       prominence can then be calculated as the vertical difference between the
+       peaks height itself and its lowest contour line.
+
+    Searching for the peak's bases can be slow for large `x` with periodic
+    behavior because large chunks or even the full signal need to be evaluated
+    for the first algorithmic step. This evaluation area can be limited with the
+    parameter `wlen` which restricts the algorithm to a window around the
+    current peak and can shorten the calculation time if the window length is
+    short in relation to `x`.
+    However, this may stop the algorithm from finding the true global contour
+    line if the peak's true bases are outside this window. Instead, a higher
+    contour line is found within the restricted window leading to a smaller
+    calculated prominence. In practice, this is only relevant for the highest set
+    of peaks in `x`. This behavior may even be used intentionally to calculate
+    "local" prominences.
+
+    .. versionadded:: 1.1.0
+
+    References
+    ----------
+    .. [1] Wikipedia Article for Topographic Prominence:
+       https://en.wikipedia.org/wiki/Topographic_prominence
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.signal import find_peaks, peak_prominences
+    >>> import matplotlib.pyplot as plt
+
+    Create a test signal with two overlaid harmonics
+
+    >>> x = np.linspace(0, 6 * np.pi, 1000)
+    >>> x = np.sin(x) + 0.6 * np.sin(2.6 * x)
+
+    Find all peaks and calculate prominences
+
+    >>> peaks, _ = find_peaks(x)
+    >>> prominences = peak_prominences(x, peaks)[0]
+    >>> prominences
+    array([1.24159486, 0.47840168, 0.28470524, 3.10716793, 0.284603  ,
+           0.47822491, 2.48340261, 0.47822491])
+
+    Calculate the height of each peak's contour line and plot the results
+
+    >>> contour_heights = x[peaks] - prominences
+    >>> plt.plot(x)
+    >>> plt.plot(peaks, x[peaks], "x")
+    >>> plt.vlines(x=peaks, ymin=contour_heights, ymax=x[peaks])
+    >>> plt.show()
+
+    Let's evaluate a second example that demonstrates several edge cases for
+    one peak at index 5.
+
+    >>> x = np.array([0, 1, 0, 3, 1, 3, 0, 4, 0])
+    >>> peaks = np.array([5])
+    >>> plt.plot(x)
+    >>> plt.plot(peaks, x[peaks], "x")
+    >>> plt.show()
+    >>> peak_prominences(x, peaks)  # -> (prominences, left_bases, right_bases)
+    (array([3.]), array([2]), array([6]))
+
+    Note how the peak at index 3 of the same height is not considered as a
+    border while searching for the left base. Instead, two minima at 0 and 2
+    are found in which case the one closer to the evaluated peak is always
+    chosen. On the right side, however, the base must be placed at 6 because the
+    higher peak represents the right border to the evaluated area.
+
+    >>> peak_prominences(x, peaks, wlen=3.1)
+    (array([2.]), array([4]), array([6]))
+
+    Here, we restricted the algorithm to a window from 3 to 7 (the length is 5
+    samples because `wlen` was rounded up to the next odd integer). Thus, the
+    only two candidates in the evaluated area are the two neighboring samples
+    and a smaller prominence is calculated.
+    """
+    x = _arg_x_as_expected(x)
+    peaks = _arg_peaks_as_expected(peaks)
+    wlen = _arg_wlen_as_expected(wlen)
+    return _peak_prominences(x, peaks, wlen)
+
+
+def peak_widths(x, peaks, rel_height=0.5, prominence_data=None, wlen=None):
+    """
+    Calculate the width of each peak in a signal.
+
+    This function calculates the width of a peak in samples at a relative
+    distance to the peak's height and prominence.
+
+    Parameters
+    ----------
+    x : sequence
+        A signal with peaks.
+    peaks : sequence
+        Indices of peaks in `x`.
+    rel_height : float, optional
+        Chooses the relative height at which the peak width is measured as a
+        percentage of its prominence. 1.0 calculates the width of the peak at
+        its lowest contour line while 0.5 evaluates at half the prominence
+        height. Must be at least 0. See notes for further explanation.
+    prominence_data : tuple, optional
+        A tuple of three arrays matching the output of `peak_prominences` when
+        called with the same arguments `x` and `peaks`. This data are calculated
+        internally if not provided.
+    wlen : int, optional
+        A window length in samples passed to `peak_prominences` as an optional
+        argument for internal calculation of `prominence_data`. This argument
+        is ignored if `prominence_data` is given.
+
+    Returns
+    -------
+    widths : ndarray
+        The widths for each peak in samples.
+    width_heights : ndarray
+        The height of the contour lines at which the `widths` where evaluated.
+    left_ips, right_ips : ndarray
+        Interpolated positions of left and right intersection points of a
+        horizontal line at the respective evaluation height.
+
+    Raises
+    ------
+    ValueError
+        If `prominence_data` is supplied but doesn't satisfy the condition
+        ``0 <= left_base <= peak <= right_base < x.shape[0]`` for each peak,
+        has the wrong dtype, is not C-contiguous or does not have the same
+        shape.
+
+    Warns
+    -----
+    PeakPropertyWarning
+        Raised if any calculated width is 0. This may stem from the supplied
+        `prominence_data` or if `rel_height` is set to 0.
+
+    Warnings
+    --------
+    This function may return unexpected results for data containing NaNs. To
+    avoid this, NaNs should either be removed or replaced.
+
+    See Also
+    --------
+    find_peaks
+        Find peaks inside a signal based on peak properties.
+    peak_prominences
+        Calculate the prominence of peaks.
+
+    Notes
+    -----
+    The basic algorithm to calculate a peak's width is as follows:
+
+    * Calculate the evaluation height :math:`h_{eval}` with the formula
+      :math:`h_{eval} = h_{Peak} - P \\cdot R`, where :math:`h_{Peak}` is the
+      height of the peak itself, :math:`P` is the peak's prominence and
+      :math:`R` a positive ratio specified with the argument `rel_height`.
+    * Draw a horizontal line at the evaluation height to both sides, starting at
+      the peak's current vertical position until the lines either intersect a
+      slope, the signal border or cross the vertical position of the peak's
+      base (see `peak_prominences` for a definition). For the first case,
+      intersection with the signal, the true intersection point is estimated
+      with linear interpolation.
+    * Calculate the width as the horizontal distance between the chosen
+      endpoints on both sides. As a consequence of this the maximal possible
+      width for each peak is the horizontal distance between its bases.
+
+    As shown above to calculate a peak's width its prominence and bases must be
+    known. You can supply these yourself with the argument `prominence_data`.
+    Otherwise, they are internally calculated (see `peak_prominences`).
+
+    .. versionadded:: 1.1.0
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.signal import chirp, find_peaks, peak_widths
+    >>> import matplotlib.pyplot as plt
+
+    Create a test signal with two overlaid harmonics
+
+    >>> x = np.linspace(0, 6 * np.pi, 1000)
+    >>> x = np.sin(x) + 0.6 * np.sin(2.6 * x)
+
+    Find all peaks and calculate their widths at the relative height of 0.5
+    (contour line at half the prominence height) and 1 (at the lowest contour
+    line at full prominence height).
+
+    >>> peaks, _ = find_peaks(x)
+    >>> results_half = peak_widths(x, peaks, rel_height=0.5)
+    >>> results_half[0]  # widths
+    array([ 64.25172825,  41.29465463,  35.46943289, 104.71586081,
+            35.46729324,  41.30429622, 181.93835853,  45.37078546])
+    >>> results_full = peak_widths(x, peaks, rel_height=1)
+    >>> results_full[0]  # widths
+    array([181.9396084 ,  72.99284945,  61.28657872, 373.84622694,
+        61.78404617,  72.48822812, 253.09161876,  79.36860878])
+
+    Plot signal, peaks and contour lines at which the widths where calculated
+
+    >>> plt.plot(x)
+    >>> plt.plot(peaks, x[peaks], "x")
+    >>> plt.hlines(*results_half[1:], color="C2")
+    >>> plt.hlines(*results_full[1:], color="C3")
+    >>> plt.show()
+    """
+    x = _arg_x_as_expected(x)
+    peaks = _arg_peaks_as_expected(peaks)
+    if prominence_data is None:
+        # Calculate prominence if not supplied and use wlen if supplied.
+        wlen = _arg_wlen_as_expected(wlen)
+        prominence_data = _peak_prominences(x, peaks, wlen)
+    return _peak_widths(x, peaks, rel_height, *prominence_data)
+
+
+def _unpack_condition_args(interval, x, peaks):
+    """
+    Parse condition arguments for `find_peaks`.
+
+    Parameters
+    ----------
+    interval : number or ndarray or sequence
+        Either a number or ndarray or a 2-element sequence of the former. The
+        first value is always interpreted as `imin` and the second, if supplied,
+        as `imax`.
+    x : ndarray
+        The signal with `peaks`.
+    peaks : ndarray
+        An array with indices used to reduce `imin` and / or `imax` if those are
+        arrays.
+
+    Returns
+    -------
+    imin, imax : number or ndarray or None
+        Minimal and maximal value in `argument`.
+
+    Raises
+    ------
+    ValueError :
+        If interval border is given as array and its size does not match the size
+        of `x`.
+
+    Notes
+    -----
+
+    .. versionadded:: 1.1.0
+    """
+    try:
+        imin, imax = interval
+    except (TypeError, ValueError):
+        imin, imax = (interval, None)
+
+    # Reduce arrays if arrays
+    if isinstance(imin, np.ndarray):
+        if imin.size != x.size:
+            raise ValueError('array size of lower interval border must match x')
+        imin = imin[peaks]
+    if isinstance(imax, np.ndarray):
+        if imax.size != x.size:
+            raise ValueError('array size of upper interval border must match x')
+        imax = imax[peaks]
+
+    return imin, imax
+
+
+def _select_by_property(peak_properties, pmin, pmax):
+    """
+    Evaluate where the generic property of peaks confirms to an interval.
+
+    Parameters
+    ----------
+    peak_properties : ndarray
+        An array with properties for each peak.
+    pmin : None or number or ndarray
+        Lower interval boundary for `peak_properties`. ``None`` is interpreted as
+        an open border.
+    pmax : None or number or ndarray
+        Upper interval boundary for `peak_properties`. ``None`` is interpreted as
+        an open border.
+
+    Returns
+    -------
+    keep : bool
+        A boolean mask evaluating to true where `peak_properties` confirms to the
+        interval.
+
+    See Also
+    --------
+    find_peaks
+
+    Notes
+    -----
+
+    .. versionadded:: 1.1.0
+    """
+    keep = np.ones(peak_properties.size, dtype=bool)
+    if pmin is not None:
+        keep &= (pmin <= peak_properties)
+    if pmax is not None:
+        keep &= (peak_properties <= pmax)
+    return keep
+
+
+def _select_by_peak_threshold(x, peaks, tmin, tmax):
+    """
+    Evaluate which peaks fulfill the threshold condition.
+
+    Parameters
+    ----------
+    x : ndarray
+        A 1-D array which is indexable by `peaks`.
+    peaks : ndarray
+        Indices of peaks in `x`.
+    tmin, tmax : scalar or ndarray or None
+         Minimal and / or maximal required thresholds. If supplied as ndarrays
+         their size must match `peaks`. ``None`` is interpreted as an open
+         border.
+
+    Returns
+    -------
+    keep : bool
+        A boolean mask evaluating to true where `peaks` fulfill the threshold
+        condition.
+    left_thresholds, right_thresholds : ndarray
+        Array matching `peak` containing the thresholds of each peak on
+        both sides.
+
+    Notes
+    -----
+
+    .. versionadded:: 1.1.0
+    """
+    # Stack thresholds on both sides to make min / max operations easier:
+    # tmin is compared with the smaller, and tmax with the greater threshold to
+    # each peak's side
+    stacked_thresholds = np.vstack([x[peaks] - x[peaks - 1],
+                                    x[peaks] - x[peaks + 1]])
+    keep = np.ones(peaks.size, dtype=bool)
+    if tmin is not None:
+        min_thresholds = np.min(stacked_thresholds, axis=0)
+        keep &= (tmin <= min_thresholds)
+    if tmax is not None:
+        max_thresholds = np.max(stacked_thresholds, axis=0)
+        keep &= (max_thresholds <= tmax)
+
+    return keep, stacked_thresholds[0], stacked_thresholds[1]
+
+
+def find_peaks(x, height=None, threshold=None, distance=None,
+               prominence=None, width=None, wlen=None, rel_height=0.5,
+               plateau_size=None):
+    """
+    Find peaks inside a signal based on peak properties.
+
+    This function takes a 1-D array and finds all local maxima by
+    simple comparison of neighboring values. Optionally, a subset of these
+    peaks can be selected by specifying conditions for a peak's properties.
+
+    Parameters
+    ----------
+    x : sequence
+        A signal with peaks.
+    height : number or ndarray or sequence, optional
+        Required height of peaks. Either a number, ``None``, an array matching
+        `x` or a 2-element sequence of the former. The first element is
+        always interpreted as the  minimal and the second, if supplied, as the
+        maximal required height.
+    threshold : number or ndarray or sequence, optional
+        Required threshold of peaks, the vertical distance to its neighboring
+        samples. Either a number, ``None``, an array matching `x` or a
+        2-element sequence of the former. The first element is always
+        interpreted as the  minimal and the second, if supplied, as the maximal
+        required threshold.
+    distance : number, optional
+        Required minimal horizontal distance (>= 1) in samples between
+        neighbouring peaks. Smaller peaks are removed first until the condition
+        is fulfilled for all remaining peaks.
+    prominence : number or ndarray or sequence, optional
+        Required prominence of peaks. Either a number, ``None``, an array
+        matching `x` or a 2-element sequence of the former. The first
+        element is always interpreted as the  minimal and the second, if
+        supplied, as the maximal required prominence.
+    width : number or ndarray or sequence, optional
+        Required width of peaks in samples. Either a number, ``None``, an array
+        matching `x` or a 2-element sequence of the former. The first
+        element is always interpreted as the  minimal and the second, if
+        supplied, as the maximal required width.
+    wlen : int, optional
+        Used for calculation of the peaks prominences, thus it is only used if
+        one of the arguments `prominence` or `width` is given. See argument
+        `wlen` in `peak_prominences` for a full description of its effects.
+    rel_height : float, optional
+        Used for calculation of the peaks width, thus it is only used if `width`
+        is given. See argument  `rel_height` in `peak_widths` for a full
+        description of its effects.
+    plateau_size : number or ndarray or sequence, optional
+        Required size of the flat top of peaks in samples. Either a number,
+        ``None``, an array matching `x` or a 2-element sequence of the former.
+        The first element is always interpreted as the minimal and the second,
+        if supplied as the maximal required plateau size.
+
+        .. versionadded:: 1.2.0
+
+    Returns
+    -------
+    peaks : ndarray
+        Indices of peaks in `x` that satisfy all given conditions.
+    properties : dict
+        A dictionary containing properties of the returned peaks which were
+        calculated as intermediate results during evaluation of the specified
+        conditions:
+
+        * 'peak_heights'
+              If `height` is given, the height of each peak in `x`.
+        * 'left_thresholds', 'right_thresholds'
+              If `threshold` is given, these keys contain a peaks vertical
+              distance to its neighbouring samples.
+        * 'prominences', 'right_bases', 'left_bases'
+              If `prominence` is given, these keys are accessible. See
+              `peak_prominences` for a description of their content.
+        * 'widths', 'width_heights', 'left_ips', 'right_ips'
+              If `width` is given, these keys are accessible. See `peak_widths`
+              for a description of their content.
+        * 'plateau_sizes', left_edges', 'right_edges'
+              If `plateau_size` is given, these keys are accessible and contain
+              the indices of a peak's edges (edges are still part of the
+              plateau) and the calculated plateau sizes.
+
+              .. versionadded:: 1.2.0
+
+        To calculate and return properties without excluding peaks, provide the
+        open interval ``(None, None)`` as a value to the appropriate argument
+        (excluding `distance`).
+
+    Warns
+    -----
+    PeakPropertyWarning
+        Raised if a peak's properties have unexpected values (see
+        `peak_prominences` and `peak_widths`).
+
+    Warnings
+    --------
+    This function may return unexpected results for data containing NaNs. To
+    avoid this, NaNs should either be removed or replaced.
+
+    See Also
+    --------
+    find_peaks_cwt
+        Find peaks using the wavelet transformation.
+    peak_prominences
+        Directly calculate the prominence of peaks.
+    peak_widths
+        Directly calculate the width of peaks.
+
+    Notes
+    -----
+    In the context of this function, a peak or local maximum is defined as any
+    sample whose two direct neighbours have a smaller amplitude. For flat peaks
+    (more than one sample of equal amplitude wide) the index of the middle
+    sample is returned (rounded down in case the number of samples is even).
+    For noisy signals the peak locations can be off because the noise might
+    change the position of local maxima. In those cases consider smoothing the
+    signal before searching for peaks or use other peak finding and fitting
+    methods (like `find_peaks_cwt`).
+
+    Some additional comments on specifying conditions:
+
+    * Almost all conditions (excluding `distance`) can be given as half-open or
+      closed intervals, e.g., ``1`` or ``(1, None)`` defines the half-open
+      interval :math:`[1, \\infty]` while ``(None, 1)`` defines the interval
+      :math:`[-\\infty, 1]`. The open interval ``(None, None)`` can be specified
+      as well, which returns the matching properties without exclusion of peaks.
+    * The border is always included in the interval used to select valid peaks.
+    * For several conditions the interval borders can be specified with
+      arrays matching `x` in shape which enables dynamic constrains based on
+      the sample position.
+    * The conditions are evaluated in the following order: `plateau_size`,
+      `height`, `threshold`, `distance`, `prominence`, `width`. In most cases
+      this order is the fastest one because faster operations are applied first
+      to reduce the number of peaks that need to be evaluated later.
+    * While indices in `peaks` are guaranteed to be at least `distance` samples
+      apart, edges of flat peaks may be closer than the allowed `distance`.
+    * Use `wlen` to reduce the time it takes to evaluate the conditions for
+      `prominence` or `width` if `x` is large or has many local maxima
+      (see `peak_prominences`).
+
+    .. versionadded:: 1.1.0
+
+    Examples
+    --------
+    To demonstrate this function's usage we use a signal `x` supplied with
+    SciPy (see `scipy.datasets.electrocardiogram`). Let's find all peaks (local
+    maxima) in `x` whose amplitude lies above 0.
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.datasets import electrocardiogram
+    >>> from scipy.signal import find_peaks
+    >>> x = electrocardiogram()[2000:4000]
+    >>> peaks, _ = find_peaks(x, height=0)
+    >>> plt.plot(x)
+    >>> plt.plot(peaks, x[peaks], "x")
+    >>> plt.plot(np.zeros_like(x), "--", color="gray")
+    >>> plt.show()
+
+    We can select peaks below 0 with ``height=(None, 0)`` or use arrays matching
+    `x` in size to reflect a changing condition for different parts of the
+    signal.
+
+    >>> border = np.sin(np.linspace(0, 3 * np.pi, x.size))
+    >>> peaks, _ = find_peaks(x, height=(-border, border))
+    >>> plt.plot(x)
+    >>> plt.plot(-border, "--", color="gray")
+    >>> plt.plot(border, ":", color="gray")
+    >>> plt.plot(peaks, x[peaks], "x")
+    >>> plt.show()
+
+    Another useful condition for periodic signals can be given with the
+    `distance` argument. In this case, we can easily select the positions of
+    QRS complexes within the electrocardiogram (ECG) by demanding a distance of
+    at least 150 samples.
+
+    >>> peaks, _ = find_peaks(x, distance=150)
+    >>> np.diff(peaks)
+    array([186, 180, 177, 171, 177, 169, 167, 164, 158, 162, 172])
+    >>> plt.plot(x)
+    >>> plt.plot(peaks, x[peaks], "x")
+    >>> plt.show()
+
+    Especially for noisy signals peaks can be easily grouped by their
+    prominence (see `peak_prominences`). E.g., we can select all peaks except
+    for the mentioned QRS complexes by limiting the allowed prominence to 0.6.
+
+    >>> peaks, properties = find_peaks(x, prominence=(None, 0.6))
+    >>> properties["prominences"].max()
+    0.5049999999999999
+    >>> plt.plot(x)
+    >>> plt.plot(peaks, x[peaks], "x")
+    >>> plt.show()
+
+    And, finally, let's examine a different section of the ECG which contains
+    beat forms of different shape. To select only the atypical heart beats, we
+    combine two conditions: a minimal prominence of 1 and width of at least 20
+    samples.
+
+    >>> x = electrocardiogram()[17000:18000]
+    >>> peaks, properties = find_peaks(x, prominence=1, width=20)
+    >>> properties["prominences"], properties["widths"]
+    (array([1.495, 2.3  ]), array([36.93773946, 39.32723577]))
+    >>> plt.plot(x)
+    >>> plt.plot(peaks, x[peaks], "x")
+    >>> plt.vlines(x=peaks, ymin=x[peaks] - properties["prominences"],
+    ...            ymax = x[peaks], color = "C1")
+    >>> plt.hlines(y=properties["width_heights"], xmin=properties["left_ips"],
+    ...            xmax=properties["right_ips"], color = "C1")
+    >>> plt.show()
+    """
+    # _argmaxima1d expects array of dtype 'float64'
+    x = _arg_x_as_expected(x)
+    if distance is not None and distance < 1:
+        raise ValueError('`distance` must be greater or equal to 1')
+
+    peaks, left_edges, right_edges = _local_maxima_1d(x)
+    properties = {}
+
+    if plateau_size is not None:
+        # Evaluate plateau size
+        plateau_sizes = right_edges - left_edges + 1
+        pmin, pmax = _unpack_condition_args(plateau_size, x, peaks)
+        keep = _select_by_property(plateau_sizes, pmin, pmax)
+        peaks = peaks[keep]
+        properties["plateau_sizes"] = plateau_sizes
+        properties["left_edges"] = left_edges
+        properties["right_edges"] = right_edges
+        properties = {key: array[keep] for key, array in properties.items()}
+
+    if height is not None:
+        # Evaluate height condition
+        peak_heights = x[peaks]
+        hmin, hmax = _unpack_condition_args(height, x, peaks)
+        keep = _select_by_property(peak_heights, hmin, hmax)
+        peaks = peaks[keep]
+        properties["peak_heights"] = peak_heights
+        properties = {key: array[keep] for key, array in properties.items()}
+
+    if threshold is not None:
+        # Evaluate threshold condition
+        tmin, tmax = _unpack_condition_args(threshold, x, peaks)
+        keep, left_thresholds, right_thresholds = _select_by_peak_threshold(
+            x, peaks, tmin, tmax)
+        peaks = peaks[keep]
+        properties["left_thresholds"] = left_thresholds
+        properties["right_thresholds"] = right_thresholds
+        properties = {key: array[keep] for key, array in properties.items()}
+
+    if distance is not None:
+        # Evaluate distance condition
+        keep = _select_by_peak_distance(peaks, x[peaks], distance)
+        peaks = peaks[keep]
+        properties = {key: array[keep] for key, array in properties.items()}
+
+    if prominence is not None or width is not None:
+        # Calculate prominence (required for both conditions)
+        wlen = _arg_wlen_as_expected(wlen)
+        properties.update(zip(
+            ['prominences', 'left_bases', 'right_bases'],
+            _peak_prominences(x, peaks, wlen=wlen)
+        ))
+
+    if prominence is not None:
+        # Evaluate prominence condition
+        pmin, pmax = _unpack_condition_args(prominence, x, peaks)
+        keep = _select_by_property(properties['prominences'], pmin, pmax)
+        peaks = peaks[keep]
+        properties = {key: array[keep] for key, array in properties.items()}
+
+    if width is not None:
+        # Calculate widths
+        properties.update(zip(
+            ['widths', 'width_heights', 'left_ips', 'right_ips'],
+            _peak_widths(x, peaks, rel_height, properties['prominences'],
+                         properties['left_bases'], properties['right_bases'])
+        ))
+        # Evaluate width condition
+        wmin, wmax = _unpack_condition_args(width, x, peaks)
+        keep = _select_by_property(properties['widths'], wmin, wmax)
+        peaks = peaks[keep]
+        properties = {key: array[keep] for key, array in properties.items()}
+
+    return peaks, properties
+
+
+def _identify_ridge_lines(matr, max_distances, gap_thresh):
+    """
+    Identify ridges in the 2-D matrix.
+
+    Expect that the width of the wavelet feature increases with increasing row
+    number.
+
+    Parameters
+    ----------
+    matr : 2-D ndarray
+        Matrix in which to identify ridge lines.
+    max_distances : 1-D sequence
+        At each row, a ridge line is only connected
+        if the relative max at row[n] is within
+        `max_distances`[n] from the relative max at row[n+1].
+    gap_thresh : int
+        If a relative maximum is not found within `max_distances`,
+        there will be a gap. A ridge line is discontinued if
+        there are more than `gap_thresh` points without connecting
+        a new relative maximum.
+
+    Returns
+    -------
+    ridge_lines : tuple
+        Tuple of 2 1-D sequences. `ridge_lines`[ii][0] are the rows of the
+        ii-th ridge-line, `ridge_lines`[ii][1] are the columns. Empty if none
+        found.  Each ridge-line will be sorted by row (increasing), but the
+        order of the ridge lines is not specified.
+
+    References
+    ----------
+    .. [1] Bioinformatics (2006) 22 (17): 2059-2065.
+       :doi:`10.1093/bioinformatics/btl355`
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.signal._peak_finding import _identify_ridge_lines
+    >>> rng = np.random.default_rng()
+    >>> data = rng.random((5,5))
+    >>> max_dist = 3
+    >>> max_distances = np.full(20, max_dist)
+    >>> ridge_lines = _identify_ridge_lines(data, max_distances, 1)
+
+    Notes
+    -----
+    This function is intended to be used in conjunction with `cwt`
+    as part of `find_peaks_cwt`.
+
+    """
+    if len(max_distances) < matr.shape[0]:
+        raise ValueError('Max_distances must have at least as many rows '
+                         'as matr')
+
+    all_max_cols = _boolrelextrema(matr, np.greater, axis=1, order=1)
+    # Highest row for which there are any relative maxima
+    has_relmax = np.nonzero(all_max_cols.any(axis=1))[0]
+    if len(has_relmax) == 0:
+        return []
+    start_row = has_relmax[-1]
+    # Each ridge line is a 3-tuple:
+    # rows, cols,Gap number
+    ridge_lines = [[[start_row],
+                   [col],
+                   0] for col in np.nonzero(all_max_cols[start_row])[0]]
+    final_lines = []
+    rows = np.arange(start_row - 1, -1, -1)
+    cols = np.arange(0, matr.shape[1])
+    for row in rows:
+        this_max_cols = cols[all_max_cols[row]]
+
+        # Increment gap number of each line,
+        # set it to zero later if appropriate
+        for line in ridge_lines:
+            line[2] += 1
+
+        # XXX These should always be all_max_cols[row]
+        # But the order might be different. Might be an efficiency gain
+        # to make sure the order is the same and avoid this iteration
+        prev_ridge_cols = np.array([line[1][-1] for line in ridge_lines])
+        # Look through every relative maximum found at current row
+        # Attempt to connect them with existing ridge lines.
+        for ind, col in enumerate(this_max_cols):
+            # If there is a previous ridge line within
+            # the max_distance to connect to, do so.
+            # Otherwise start a new one.
+            line = None
+            if len(prev_ridge_cols) > 0:
+                diffs = np.abs(col - prev_ridge_cols)
+                closest = np.argmin(diffs)
+                if diffs[closest] <= max_distances[row]:
+                    line = ridge_lines[closest]
+            if line is not None:
+                # Found a point close enough, extend current ridge line
+                line[1].append(col)
+                line[0].append(row)
+                line[2] = 0
+            else:
+                new_line = [[row],
+                            [col],
+                            0]
+                ridge_lines.append(new_line)
+
+        # Remove the ridge lines with gap_number too high
+        # XXX Modifying a list while iterating over it.
+        # Should be safe, since we iterate backwards, but
+        # still tacky.
+        for ind in range(len(ridge_lines) - 1, -1, -1):
+            line = ridge_lines[ind]
+            if line[2] > gap_thresh:
+                final_lines.append(line)
+                del ridge_lines[ind]
+
+    out_lines = []
+    for line in (final_lines + ridge_lines):
+        sortargs = np.argsort(line[0])
+        rows = np.array(line[0])[sortargs]
+        cols = np.array(line[1])[sortargs]
+        out_lines.append([rows, cols])
+
+    return out_lines
+
+
+def _filter_ridge_lines(cwt, ridge_lines, window_size=None, min_length=None,
+                        min_snr=1, noise_perc=10):
+    """
+    Filter ridge lines according to prescribed criteria. Intended
+    to be used for finding relative maxima.
+
+    Parameters
+    ----------
+    cwt : 2-D ndarray
+        Continuous wavelet transform from which the `ridge_lines` were defined.
+    ridge_lines : 1-D sequence
+        Each element should contain 2 sequences, the rows and columns
+        of the ridge line (respectively).
+    window_size : int, optional
+        Size of window to use to calculate noise floor.
+        Default is ``cwt.shape[1] / 20``.
+    min_length : int, optional
+        Minimum length a ridge line needs to be acceptable.
+        Default is ``cwt.shape[0] / 4``, ie 1/4-th the number of widths.
+    min_snr : float, optional
+        Minimum SNR ratio. Default 1. The signal is the value of
+        the cwt matrix at the shortest length scale (``cwt[0, loc]``), the
+        noise is the `noise_perc`\\ th percentile of datapoints contained within a
+        window of `window_size` around ``cwt[0, loc]``.
+    noise_perc : float, optional
+        When calculating the noise floor, percentile of data points
+        examined below which to consider noise. Calculated using
+        scipy.stats.scoreatpercentile.
+
+    References
+    ----------
+    .. [1] Bioinformatics (2006) 22 (17): 2059-2065.
+       :doi:`10.1093/bioinformatics/btl355`
+
+    """
+    num_points = cwt.shape[1]
+    if min_length is None:
+        min_length = np.ceil(cwt.shape[0] / 4)
+    if window_size is None:
+        window_size = np.ceil(num_points / 20)
+
+    window_size = int(window_size)
+    hf_window, odd = divmod(window_size, 2)
+
+    # Filter based on SNR
+    row_one = cwt[0, :]
+    noises = np.empty_like(row_one)
+    for ind, val in enumerate(row_one):
+        window_start = max(ind - hf_window, 0)
+        window_end = min(ind + hf_window + odd, num_points)
+        noises[ind] = scoreatpercentile(row_one[window_start:window_end],
+                                        per=noise_perc)
+
+    def filt_func(line):
+        if len(line[0]) < min_length:
+            return False
+        snr = abs(cwt[line[0][0], line[1][0]] / noises[line[1][0]])
+        if snr < min_snr:
+            return False
+        return True
+
+    return list(filter(filt_func, ridge_lines))
+
+
+def find_peaks_cwt(vector, widths, wavelet=None, max_distances=None,
+                   gap_thresh=None, min_length=None,
+                   min_snr=1, noise_perc=10, window_size=None):
+    """
+    Find peaks in a 1-D array with wavelet transformation.
+
+    The general approach is to smooth `vector` by convolving it with
+    `wavelet(width)` for each width in `widths`. Relative maxima which
+    appear at enough length scales, and with sufficiently high SNR, are
+    accepted.
+
+    Parameters
+    ----------
+    vector : ndarray
+        1-D array in which to find the peaks.
+    widths : float or sequence
+        Single width or 1-D array-like of widths to use for calculating
+        the CWT matrix. In general,
+        this range should cover the expected width of peaks of interest.
+    wavelet : callable, optional
+        Should take two parameters and return a 1-D array to convolve
+        with `vector`. The first parameter determines the number of points
+        of the returned wavelet array, the second parameter is the scale
+        (`width`) of the wavelet. Should be normalized and symmetric.
+        Default is the ricker wavelet.
+    max_distances : ndarray, optional
+        At each row, a ridge line is only connected if the relative max at
+        ``row[n]`` is within ``max_distances[n]`` from the relative max at
+        ``row[n+1]``.  Default value is ``widths/4``.
+    gap_thresh : float, optional
+        If a relative maximum is not found within `max_distances`,
+        there will be a gap. A ridge line is discontinued if there are more
+        than `gap_thresh` points without connecting a new relative maximum.
+        Default is the first value of the widths array i.e. ``widths[0]``.
+    min_length : int, optional
+        Minimum length a ridge line needs to be acceptable.
+        Default is ``cwt.shape[0] / 4``, ie 1/4-th the number of widths.
+    min_snr : float, optional
+        Minimum SNR ratio. Default 1. The signal is the maximum CWT coefficient
+        on the largest ridge line. The noise is `noise_perc` th percentile of
+        datapoints contained within the same ridge line.
+    noise_perc : float, optional
+        When calculating the noise floor, percentile of data points
+        examined below which to consider noise. Calculated using
+        `stats.scoreatpercentile`.  Default is 10.
+    window_size : int, optional
+        Size of window to use to calculate noise floor.
+        Default is ``cwt.shape[1] / 20``.
+
+    Returns
+    -------
+    peaks_indices : ndarray
+        Indices of the locations in the `vector` where peaks were found.
+        The list is sorted.
+
+    See Also
+    --------
+    find_peaks
+        Find peaks inside a signal based on peak properties.
+
+    Notes
+    -----
+    This approach was designed for finding sharp peaks among noisy data,
+    however with proper parameter selection it should function well for
+    different peak shapes.
+
+    The algorithm is as follows:
+     1. Perform a continuous wavelet transform on `vector`, for the supplied
+        `widths`. This is a convolution of `vector` with `wavelet(width)` for
+        each width in `widths`.
+     2. Identify "ridge lines" in the cwt matrix. These are relative maxima
+        at each row, connected across adjacent rows. See identify_ridge_lines
+     3. Filter the ridge_lines using filter_ridge_lines.
+
+    References
+    ----------
+    .. [1] Bioinformatics (2006) 22 (17): 2059-2065.
+       :doi:`10.1093/bioinformatics/btl355`
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> xs = np.arange(0, np.pi, 0.05)
+    >>> data = np.sin(xs)
+    >>> peakind = signal.find_peaks_cwt(data, np.arange(1,10))
+    >>> peakind, xs[peakind], data[peakind]
+    ([32], array([ 1.6]), array([ 0.9995736]))
+
+    """
+    widths = np.atleast_1d(np.asarray(widths))
+
+    if gap_thresh is None:
+        gap_thresh = np.ceil(widths[0])
+    if max_distances is None:
+        max_distances = widths / 4.0
+    if wavelet is None:
+        wavelet = _ricker
+
+    cwt_dat = _cwt(vector, wavelet, widths)
+    ridge_lines = _identify_ridge_lines(cwt_dat, max_distances, gap_thresh)
+    filtered = _filter_ridge_lines(cwt_dat, ridge_lines, min_length=min_length,
+                                   window_size=window_size, min_snr=min_snr,
+                                   noise_perc=noise_perc)
+    max_locs = np.asarray([x[1][0] for x in filtered])
+    max_locs.sort()
+
+    return max_locs
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/_peak_finding_utils.cpython-312-x86_64-linux-gnu.so b/venv/lib/python3.12/site-packages/scipy/signal/_peak_finding_utils.cpython-312-x86_64-linux-gnu.so
new file mode 100644
index 0000000000000000000000000000000000000000..fe27b99e2fa7b9db0f3e712abe4789c88a7e0461
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/_peak_finding_utils.cpython-312-x86_64-linux-gnu.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:7f547534a9c3f5608284cf93e189e2f4036adcdf0e73989f2d004812e4d25fc3
+size 146296
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/_polyutils.py b/venv/lib/python3.12/site-packages/scipy/signal/_polyutils.py
new file mode 100644
index 0000000000000000000000000000000000000000..28bad89ab4e406d46d736a6f727528e40683fc30
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/_polyutils.py
@@ -0,0 +1,257 @@
+"""Partial replacements for numpy polynomial routines, with Array API compatibility.
+
+This module contains both "old-style", np.poly1d, routines from the main numpy
+namespace, and "new-style", np.polynomial.polynomial, routines.
+
+To distinguish the two sets, the "new-style" routine names start with `npp_`
+"""
+import warnings
+import scipy._external.array_api_extra as xpx
+from scipy._lib._array_api import (
+    xp_promote, xp_default_dtype, xp_size, xp_device, is_numpy
+)
+
+from numpy.exceptions import RankWarning
+
+
+def _sort_cmplx(arr, xp):
+    # xp.sort is undefined for complex dtypes. Here we only need some
+    # consistent way to sort a complex array, including equal magnitude elements.
+    arr = xp.asarray(arr)
+    if xp.isdtype(arr.dtype, 'complex floating'):
+        sorter = abs(arr) + xp.real(arr) + xp.imag(arr)**3
+    else:
+        sorter = arr
+
+    idxs = xp.argsort(sorter)
+    return arr[idxs]
+
+
+def polyroots(coef, *, xp):
+    """numpy.roots, best-effor replacement
+    """
+    if coef.shape[0] < 2:
+        return xp.asarray([], dtype=coef.dtype)
+
+    root_func = getattr(xp, 'roots', None)
+    if root_func:
+        # NB: cupy.roots is broken in CuPy 13.x, but CuPy is handled via delegation
+        # so we never hit this code path with xp being cupy
+        return root_func(coef)
+
+    # companion matrix
+    n = coef.shape[0]
+    a = xp.eye(n - 1, n - 1, k=-1, dtype=coef.dtype)
+    a[:, -1] = -xp.flip(coef[1:]) / coef[0]
+
+    # non-symmetric eigenvalue problem is not in the spec but is available on e.g. torch
+    if hasattr(xp.linalg, 'eigvals'):
+        return xp.linalg.eigvals(a)
+    else:
+        import numpy as np
+        return xp.asarray(np.linalg.eigvals(np.asarray(a)))
+
+
+# https://github.com/numpy/numpy/blob/v2.1.0/numpy/lib/_function_base_impl.py#L1874-L1925
+def _trim_zeros(filt, trim='fb'):
+    first = 0
+    trim = trim.upper()
+    if 'F' in trim:
+        for i in filt:
+            if i != 0.:
+                break
+            else:
+                first = first + 1
+    last = filt.shape[0]
+    if 'B' in trim:
+        for i in filt[::-1]:
+            if i != 0.:
+                break
+            else:
+                last = last - 1
+    return filt[first:last]
+
+
+# For numpy arrays, use scipy.linalg.lstsq;
+# For other backends,
+#   - use xp.linalg.lstsq, if available (cupy, torch, jax.numpy);
+#   - otherwise manually compute pseudoinverse via SVD factorization
+def _lstsq(a, b, xp=None, rcond=None):
+    a, b = xp_promote(a, b, force_floating=True, xp=xp)
+
+    if rcond is None:
+        rcond = xp.finfo(a.dtype).eps
+
+    if is_numpy(xp):
+        from scipy.linalg import lstsq as s_lstsq
+        return s_lstsq(a, b, cond=rcond)
+    elif lstsq_func := getattr(xp.linalg, "lstsq", None):
+        # cupy, torch, jax.numpy all have xp.linalg.lstsq
+        return lstsq_func(a, b, rcond=rcond)
+    else:
+        # unknown array library: LSQ solve via pseudoinverse
+        u, s, vt = xp.linalg.svd(a, full_matrices=False)
+
+        sing_val_mask = s > rcond
+        s = xpx.apply_where(sing_val_mask, (s,), lambda x: 1. / x, fill_value=0.)
+
+        sigma = xp.eye(s.shape[0]) * s    # == np.diag(s)
+        x = vt.T @ sigma @ u.T @ b
+
+        rank = xp.count_nonzero(sing_val_mask)
+
+        # XXX actually compute residuals, when there's a use case
+        residuals = xp.asarray([])
+        return x, residuals, rank, s
+
+
+# ### Old-style routines ###
+
+
+# https://github.com/numpy/numpy/blob/v2.2.0/numpy/lib/_polynomial_impl.py#L1232
+def _poly1d(c_or_r, *, xp):
+    """ Constructor of np.poly1d object from an array of coefficients (r=False)
+    """
+    c_or_r = xpx.atleast_nd(c_or_r, ndim=1, xp=xp)
+    if c_or_r.ndim > 1:
+        raise ValueError("Polynomial must be 1d only.")
+    c_or_r = _trim_zeros(c_or_r, trim='f')
+    if c_or_r.shape[0] == 0:
+        c_or_r = xp.asarray([0], dtype=c_or_r.dtype)
+    return c_or_r
+
+
+# https://github.com/numpy/numpy/blob/v2.2.0/numpy/lib/_polynomial_impl.py#L702-L779
+def polyval(p, x, *, xp):
+    """ Old-style polynomial, `np.polyval`
+    """
+    p = xp.asarray(p)
+    x = xp.asarray(x)
+    y = xp.zeros_like(x)
+
+    # NB: cannot do `for pv in p` since array API iteration
+    # is only defined for 1D arrays.
+    for j in range(p.shape[0]):
+        y = y * x + p[j, ...]
+    return y
+
+
+# https://github.com/numpy/numpy/blob/v2.2.0/numpy/lib/_polynomial_impl.py#L34-L157
+def poly(seq_of_zeros, *, xp):
+    # Only reproduce the 1D variant of np.poly
+    seq_of_zeros = xp.asarray(seq_of_zeros)
+    seq_of_zeros = xpx.atleast_nd(seq_of_zeros, ndim=1, xp=xp)
+
+    if seq_of_zeros.shape[0] == 0:
+        return xp.asarray(1.0, dtype=xp.real(seq_of_zeros).dtype)
+
+    # prefer np.convolve etc, if available
+    convolve_func = getattr(xp, 'convolve', None)
+    if convolve_func is None:
+        from scipy.signal import convolve as convolve_func
+
+    dt = seq_of_zeros.dtype
+    a = xp.ones((1,), dtype=dt)
+    one = xp.ones_like(seq_of_zeros[0])
+    for zero in seq_of_zeros:
+        a = convolve_func(a, xp.stack((one, -zero)), mode='full')
+
+    if xp.isdtype(a.dtype, 'complex floating'):
+        # if complex roots are all complex conjugates, the roots are real.
+        roots = xp.asarray(seq_of_zeros, dtype=xp.complex128)
+        if xp.all(xp.sort(xp.imag(roots)) == xp.sort(xp.imag(xp.conj(roots)))):
+            a = xp.asarray(xp.real(a), copy=True)
+
+    return a
+
+
+# https://github.com/numpy/numpy/blob/v2.2.0/numpy/lib/_polynomial_impl.py#L912
+def polymul(a1, a2, *, xp):
+    a1, a2 = _poly1d(a1, xp=xp), _poly1d(a2, xp=xp)
+
+    # prefer np.convolve etc, if available
+    convolve_func = getattr(xp, 'convolve', None)
+    if convolve_func is None:
+        from scipy.signal import convolve as convolve_func
+
+    val = convolve_func(a1, a2)
+    return val
+
+
+# https://github.com/numpy/numpy/blob/v2.3.3/numpy/lib/_polynomial_impl.py#L459
+def polyfit(x, y, deg, *, xp, rcond=None):
+    # only reproduce the variant with full=False, w=None, cov=False
+    order = int(deg) + 1
+    x = xp.asarray(x)
+    y = xp.asarray(y)
+    x, y = xp_promote(x, y, force_floating=True, xp=xp)
+
+    # check arguments.
+    if deg < 0:
+        raise ValueError("expected deg >= 0")
+    if x.ndim != 1:
+        raise TypeError("expected 1D vector for x")
+    if xp_size(x) == 0:
+        raise TypeError("expected non-empty vector for x")
+    if y.ndim < 1 or y.ndim > 2:
+        raise TypeError("expected 1D or 2D array for y")
+    if x.shape[0] != y.shape[0]:
+        raise TypeError("expected x and y to have same length")
+
+    # set rcond
+    if rcond is None:
+        rcond = x.shape[0] * xp.finfo(x.dtype).eps
+
+    # set up least squares equation for powers of x: lhs = vander(x, order)
+    powers = xp.flip(xp.arange(order, dtype=x.dtype, device=xp_device(x)))
+    lhs = x[:, None] ** powers[None, :]
+
+    # scale lhs to improve condition number and solve
+    scale = xp.sqrt(xp.sum(lhs * lhs, axis=0))
+    lhs /= scale
+
+    c, _, rank, _ = _lstsq(lhs, y, rcond=rcond, xp=xp)
+    c = (c.T / scale).T  # broadcast scale coefficients
+
+    # warn on rank reduction, which indicates an ill conditioned matrix
+    if rank != order:
+        msg = "Polyfit may be poorly conditioned"
+        warnings.warn(msg, RankWarning, stacklevel=2)
+
+    return c
+
+
+# ### New-style routines ###
+
+
+# https://github.com/numpy/numpy/blob/v2.2.0/numpy/polynomial/polynomial.py#L663
+def npp_polyval(x, c, *, xp, tensor=True):
+    if xp.isdtype(c.dtype, 'integral'):
+        c = xp.astype(c, xp_default_dtype(xp))
+
+    c = xpx.atleast_nd(c, ndim=1, xp=xp)
+    if isinstance(x, tuple | list):
+        x = xp.asarray(x)
+    if tensor:
+        c = xp.reshape(c, (c.shape + (1,)*x.ndim))
+
+    c0, _ = xp_promote(c[-1, ...], x, broadcast=True, xp=xp)
+    for i in range(2, c.shape[0] + 1):
+        c0 = c[-i, ...] + c0*x
+    return c0
+
+
+# https://github.com/numpy/numpy/blob/v2.2.0/numpy/polynomial/polynomial.py#L758-L842
+def npp_polyvalfromroots(x, r, *, xp, tensor=True):
+    r = xpx.atleast_nd(r, ndim=1, xp=xp)
+    # if r.dtype.char in '?bBhHiIlLqQpP':
+    #    r = r.astype(np.double)
+
+    if isinstance(x, tuple | list):
+        x = xp.asarray(x)
+
+    if tensor:
+        r = xp.reshape(r, r.shape + (1,) * x.ndim)
+    elif x.ndim >= r.ndim:
+        raise ValueError("x.ndim must be < r.ndim when tensor == False")
+    return xp.prod(x - r, axis=0)
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/_savitzky_golay.py b/venv/lib/python3.12/site-packages/scipy/signal/_savitzky_golay.py
new file mode 100644
index 0000000000000000000000000000000000000000..6c70d9794bbf936526438cd24cabe1d3c7ec5343
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/_savitzky_golay.py
@@ -0,0 +1,391 @@
+from scipy._lib._util import float_factorial
+from scipy._external.array_api_compat import numpy as np_compat
+from scipy._lib._array_api import array_namespace, xp_swapaxes, xp_device
+import scipy._external.array_api_extra as xpx
+
+from scipy.ndimage import convolve1d  # type: ignore[attr-defined]
+from scipy.signal import _polyutils as _pu
+from ._arraytools import axis_slice
+
+
+def savgol_coeffs(window_length, polyorder, deriv=0, delta=1.0, pos=None,
+                  use="conv", *, xp=None, device=None):
+    """Compute the coefficients for a 1-D Savitzky-Golay FIR filter.
+
+    Parameters
+    ----------
+    window_length : int
+        The length of the filter window (i.e., the number of coefficients).
+    polyorder : int
+        The order of the polynomial used to fit the samples.
+        `polyorder` must be less than `window_length`.
+    deriv : int, optional
+        The order of the derivative to compute. This must be a
+        nonnegative integer. The default is 0, which means to filter
+        the data without differentiating.
+    delta : float, optional
+        The spacing of the samples to which the filter will be applied.
+        This is only used if deriv > 0.
+    pos : int or None, optional
+        If pos is not None, it specifies evaluation position within the
+        window. The default is the middle of the window.
+    use : str, optional
+        Either 'conv' or 'dot'. This argument chooses the order of the
+        coefficients. The default is 'conv', which means that the
+        coefficients are ordered to be used in a convolution. With
+        use='dot', the order is reversed, so the filter is applied by
+        dotting the coefficients with the data set.
+    xp : array_namespace, optional
+        Optional array namespace.
+        Should be compatible with the array API standard, or supported by
+        array-api-compat.
+        Default: ``numpy``
+    device : any
+        optional device specification for output. Should match one of the
+        supported device specifications in ``xp``.
+
+    Returns
+    -------
+    coeffs : 1-D ndarray
+        The filter coefficients.
+
+    See Also
+    --------
+    savgol_filter
+
+    Notes
+    -----
+    .. versionadded:: 0.14.0
+
+    References
+    ----------
+    A. Savitzky, M. J. E. Golay, Smoothing and Differentiation of Data by
+    Simplified Least Squares Procedures. Analytical Chemistry, 1964, 36 (8),
+    pp 1627-1639.
+    Jianwen Luo, Kui Ying, and Jing Bai. 2005. Savitzky-Golay smoothing and
+    differentiation filter for even number data. Signal Process.
+    85, 7 (July 2005), 1429-1434.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.signal import savgol_coeffs
+    >>> savgol_coeffs(5, 2)
+    array([-0.08571429,  0.34285714,  0.48571429,  0.34285714, -0.08571429])
+    >>> savgol_coeffs(5, 2, deriv=1)
+    array([ 2.00000000e-01,  1.00000000e-01,  2.07548111e-16, -1.00000000e-01,
+           -2.00000000e-01])
+
+    Note that use='dot' simply reverses the coefficients.
+
+    >>> savgol_coeffs(5, 2, pos=3)
+    array([ 0.25714286,  0.37142857,  0.34285714,  0.17142857, -0.14285714])
+    >>> savgol_coeffs(5, 2, pos=3, use='dot')
+    array([-0.14285714,  0.17142857,  0.34285714,  0.37142857,  0.25714286])
+    >>> savgol_coeffs(4, 2, pos=3, deriv=1, use='dot')
+    array([0.45,  -0.85,  -0.65,  1.05])
+
+    `x` contains data from the parabola x = t**2, sampled at
+    t = -1, 0, 1, 2, 3.  `c` holds the coefficients that will compute the
+    derivative at the last position.  When dotted with `x` the result should
+    be 6.
+
+    >>> x = np.array([1, 0, 1, 4, 9])
+    >>> c = savgol_coeffs(5, 2, pos=4, deriv=1, use='dot')
+    >>> c.dot(x)
+    6.0
+    """
+
+    # An alternative method for finding the coefficients when deriv=0 is
+    #    t = np.arange(window_length)
+    #    unit = (t == pos).astype(int)
+    #    coeffs = np.polyval(np.polyfit(t, unit, polyorder), t)
+    # The method implemented here is faster.
+
+    # To recreate the table of sample coefficients shown in the chapter on
+    # the Savitzy-Golay filter in the Numerical Recipes book, use
+    #    window_length = nL + nR + 1
+    #    pos = nL + 1
+    #    c = savgol_coeffs(window_length, M, pos=pos, use='dot')
+
+    if polyorder >= window_length:
+        raise ValueError("polyorder must be less than window_length.")
+
+    halflen, rem = divmod(window_length, 2)
+
+    if pos is None:
+        if rem == 0:
+            pos = halflen - 0.5
+        else:
+            pos = halflen
+
+    if not (0 <= pos < window_length):
+        raise ValueError("pos must be nonnegative and less than "
+                         "window_length.")
+
+    if use not in ['conv', 'dot']:
+        raise ValueError("`use` must be 'conv' or 'dot'")
+
+    # cf windows/_windows.py
+    xp = np_compat if xp is None else array_namespace(xp.empty(0))
+
+    if deriv > polyorder:
+        coeffs = xp.zeros(window_length, dtype=xp.float64, device=device)
+        return coeffs
+
+    # Form the design matrix A. The columns of A are powers of the integers
+    # from -pos to window_length - pos - 1. The powers (i.e., rows) range
+    # from 0 to polyorder. (That is, A is a vandermonde matrix, but not
+    # necessarily square.)
+    x = xp.arange(-pos, window_length - pos, dtype=xp.float64, device=device)
+
+    if use == "conv":
+        # Reverse so that result can be used in a convolution.
+        x = xp.flip(x)
+
+    order = xp.reshape(
+        xp.arange(polyorder + 1, dtype=xp.float64, device=device), (-1, 1)
+    )
+    A = x ** order
+
+    # y determines which order derivative is returned.
+    y = xp.zeros(polyorder + 1, dtype=xp.float64, device=device)
+    # The coefficient assigned to y[deriv] scales the result to take into
+    # account the order of the derivative and the sample spacing.
+    y = xpx.at(y, deriv).set(float_factorial(deriv) / (delta ** deriv))
+
+    # Find the least-squares solution of A*c = y
+    coeffs, _, _, _ = _pu._lstsq(A, y, xp=xp)
+
+    return coeffs
+
+
+def _polyder(p, m, *, xp):
+    """Differentiate polynomials represented with coefficients.
+
+    p must be a 1-D or 2-D array.  In the 2-D case, each column gives
+    the coefficients of a polynomial; the first row holds the coefficients
+    associated with the highest power. m must be a nonnegative integer.
+    (numpy.polyder doesn't handle the 2-D case.)
+    """
+
+    if m == 0:
+        result = p
+    else:
+        n = p.shape[0]
+        if n <= m:
+            result = xp.zeros_like(p[:1, ...])
+        else:
+            dp = xp.asarray(p[:-m, ...], copy=True)
+            for k in range(m):
+                rng = xp.arange(
+                    n - k - 1, m - k - 1, -1, dtype=p.dtype, device=xp_device(p)
+                )
+                dp *= xp.reshape(rng, (n - m,) + (1,) * (p.ndim - 1))
+            result = dp
+    return result
+
+
+def _fit_edge(x, window_start, window_stop, interp_start, interp_stop,
+              axis, polyorder, deriv, delta, y):
+    """
+    Given an N-d array `x` and the specification of a slice of `x` from
+    `window_start` to `window_stop` along `axis`, create an interpolating
+    polynomial of each 1-D slice, and evaluate that polynomial in the slice
+    from `interp_start` to `interp_stop`. Put the result into the
+    corresponding slice of `y`.
+    """
+    xp = array_namespace(x)
+
+    # Get the edge into a (window_length, -1) array.
+    x_edge = axis_slice(x, start=window_start, stop=window_stop, axis=axis)
+    if axis == 0 or axis == -x.ndim:
+        xx_edge = x_edge
+        swapped = False
+    else:
+        xx_edge = xp_swapaxes(x_edge, axis, 0, xp)
+        swapped = True
+    xx_edge = xp.reshape(xx_edge, (xx_edge.shape[0], -1))
+
+    # Fit the edges.  poly_coeffs has shape (polyorder + 1, -1),
+    # where '-1' is the same as in xx_edge.
+    poly_coeffs = _pu.polyfit(
+        xp.arange(
+            0, window_stop - window_start, dtype=x.dtype, device=xp_device(x)
+        ), xx_edge, polyorder, xp=xp
+    )
+
+    if deriv > 0:
+        poly_coeffs = _polyder(poly_coeffs, deriv, xp=xp)
+
+    # Compute the interpolated values for the edge.
+    i = xp.arange(
+        interp_start - window_start, interp_stop - window_start,
+        dtype=poly_coeffs.dtype, device=xp_device(poly_coeffs)
+    )
+    values = _pu.polyval(poly_coeffs, xp.reshape(i, (-1, 1)), xp=xp) / (delta ** deriv)
+
+    # Now put the values into the appropriate slice of y.
+    # First reshape values to match y.
+    shp = list(y.shape)
+    shp[0], shp[axis] = shp[axis], shp[0]
+    values = xp.reshape(values, (interp_stop - interp_start, *shp[1:]))
+    if swapped:
+        values = xp_swapaxes(values, 0, axis, xp)
+    # Get a view of the data to be replaced by values.
+    y_slice = [slice(None)] * y.ndim
+    y_slice[axis] = slice(interp_start, interp_stop)
+    y = xpx.at(y, tuple(y_slice)).set(values)
+
+    return y
+
+
+
+def _fit_edges_polyfit(x, window_length, polyorder, deriv, delta, axis, y):
+    """
+    Use polynomial interpolation of x at the low and high ends of the axis
+    to fill in the halflen values in y.
+
+    This function just calls _fit_edge twice, once for each end of the axis.
+    """
+    halflen = window_length // 2
+    y = _fit_edge(x, 0, window_length, 0, halflen, axis,
+              polyorder, deriv, delta, y)
+    n = x.shape[axis]
+    y = _fit_edge(x, n - window_length, n, n - halflen, n, axis,
+              polyorder, deriv, delta, y)
+
+    return y
+
+
+def savgol_filter(x, window_length, polyorder, deriv=0, delta=1.0,
+                  axis=-1, mode='interp', cval=0.0):
+    """ Apply a Savitzky-Golay filter to an array.
+
+    This is a 1-D filter. If `x`  has dimension greater than 1, `axis`
+    determines the axis along which the filter is applied.
+
+    Parameters
+    ----------
+    x : array_like
+        The data to be filtered. If `x` is not a single or double precision
+        floating point array, it will be converted to type ``numpy.float64``
+        before filtering.
+    window_length : int
+        The length of the filter window (i.e., the number of coefficients).
+        If `mode` is 'interp', `window_length` must be less than or equal
+        to the size of `x`.
+    polyorder : int
+        The order of the polynomial used to fit the samples.
+        `polyorder` must be less than `window_length`.
+    deriv : int, optional
+        The order of the derivative to compute. This must be a
+        nonnegative integer. The default is 0, which means to filter
+        the data without differentiating.
+    delta : float, optional
+        The spacing of the samples to which the filter will be applied.
+        This is only used if deriv > 0. Default is 1.0.
+    axis : int, optional
+        The axis of the array `x` along which the filter is to be applied.
+        Default is -1.
+    mode : str, optional
+        Must be 'mirror', 'constant', 'nearest', 'wrap' or 'interp'. This
+        determines the type of extension to use for the padded signal to
+        which the filter is applied.  When `mode` is 'constant', the padding
+        value is given by `cval`.  See the Notes for more details on 'mirror',
+        'constant', 'wrap', and 'nearest'.
+        When the 'interp' mode is selected (the default), no extension
+        is used.  Instead, a degree `polyorder` polynomial is fit to the
+        last `window_length` values of the edges, and this polynomial is
+        used to evaluate the last `window_length // 2` output values.
+    cval : scalar, optional
+        Value to fill past the edges of the input if `mode` is 'constant'.
+        Default is 0.0.
+
+    Returns
+    -------
+    y : ndarray, same shape as `x`
+        The filtered data.
+
+    See Also
+    --------
+    savgol_coeffs
+
+    Notes
+    -----
+    Details on the `mode` options:
+
+    - 'mirror':
+      Repeats the values at the edges in reverse order. The value
+      closest to the edge is not included.
+    - 'nearest':
+      The extension contains the nearest input value.
+    - 'constant':
+      The extension contains the value given by the `cval` argument.
+    - 'wrap':
+      The extension contains the values from the other end of the array.
+
+    For example, if the input is [1, 2, 3, 4, 5, 6, 7, 8], and
+    `window_length` is 7, the following shows the extended data for
+    the various `mode` options (assuming `cval` is 0)::
+
+        mode       |   Ext   |         Input          |   Ext
+        -----------+---------+------------------------+---------
+        'mirror'   | 4  3  2 | 1  2  3  4  5  6  7  8 | 7  6  5
+        'nearest'  | 1  1  1 | 1  2  3  4  5  6  7  8 | 8  8  8
+        'constant' | 0  0  0 | 1  2  3  4  5  6  7  8 | 0  0  0
+        'wrap'     | 6  7  8 | 1  2  3  4  5  6  7  8 | 1  2  3
+
+    .. versionadded:: 0.14.0
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.signal import savgol_filter
+    >>> np.set_printoptions(precision=2)  # For compact display.
+    >>> x = np.array([2, 2, 5, 2, 1, 0, 1, 4, 9])
+
+    Filter with a window length of 5 and a degree 2 polynomial.  Use
+    the defaults for all other parameters.
+
+    >>> savgol_filter(x, 5, 2)
+    array([1.66, 3.17, 3.54, 2.86, 0.66, 0.17, 1.  , 4.  , 9.  ])
+
+    Note that the last five values in x are samples of a parabola, so
+    when mode='interp' (the default) is used with polyorder=2, the last
+    three values are unchanged. Compare that to, for example,
+    `mode='nearest'`:
+
+    >>> savgol_filter(x, 5, 2, mode='nearest')
+    array([1.74, 3.03, 3.54, 2.86, 0.66, 0.17, 1.  , 4.6 , 7.97])
+
+    """
+    if mode not in ["mirror", "constant", "nearest", "interp", "wrap"]:
+        raise ValueError("mode must be 'mirror', 'constant', 'nearest' "
+                         "'wrap' or 'interp'.")
+
+    xp = array_namespace(x)
+    x = xp.asarray(x)
+    # Ensure that x is either single or double precision floating point.
+    if x.dtype != xp.float64 and x.dtype != xp.float32:
+        x = xp.astype(x, xp.float64)
+
+    coeffs = savgol_coeffs(
+        window_length, polyorder, deriv=deriv, delta=delta, xp=xp, device=xp_device(x)
+    )
+
+    if mode == "interp":
+        if window_length > x.shape[axis]:
+            raise ValueError("If mode is 'interp', window_length must be less "
+                             "than or equal to the size of x.")
+
+        # Do not pad. Instead, for the elements within `window_length // 2`
+        # of the ends of the sequence, use the polynomial that is fitted to
+        # the last `window_length` elements.
+        y = convolve1d(x, coeffs, axis=axis, mode="constant")
+        y = _fit_edges_polyfit(x, window_length, polyorder, deriv, delta, axis, y)
+    else:
+        # Any mode other than 'interp' is passed on to ndimage.convolve1d.
+        y = convolve1d(x, coeffs, axis=axis, mode=mode, cval=cval)
+
+    return y
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/_short_time_fft.py b/venv/lib/python3.12/site-packages/scipy/signal/_short_time_fft.py
new file mode 100644
index 0000000000000000000000000000000000000000..533b25edd1e1c0985ccd0fd4b7cb7e6c657f5a2b
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/_short_time_fft.py
@@ -0,0 +1,2291 @@
+"""Implementation of an FFT-based Short-time Fourier Transform. """
+
+# Implementation Notes for this file (as of 2025-08)
+# --------------------------------------------------
+# * Since the method `stft` and `istft` have identical names as the legacy
+#   functions in the signal module, referencing them as HTML link in the
+#   docstrings has to be done by an explicit `~ShortTimeFFT.stft` instead of an
+#   ambiguous `stft` (The ``~`` hides the class / module name).
+# * The HTML documentation currently renders each method/property on a separate
+#   page without reference to the parent class. Thus, a link to `ShortTimeFFT`
+#   was added to the "See Also" section of each method/property. These links
+#   can be removed, when SciPy updates ``pydata-sphinx-theme`` to >= 0.13.3
+#   (currently 0.9). Consult Issue 18512 and PR 16660 for further details.
+
+
+# Linter does not allow to import ``Generator`` from ``typing`` module:
+from collections.abc import Generator, Callable
+from functools import partial, cached_property
+from types import GenericAlias
+from typing import get_args, Literal
+
+import numpy as np
+
+import scipy.fft as fft_lib
+from scipy.signal._signaltools import detrend
+from scipy.signal.windows import get_window
+
+__all__ = ['closest_STFT_dual_window', 'ShortTimeFFT']
+
+
+#: Allowed values for parameter `padding` of method `ShortTimeFFT.stft()`:
+PAD_TYPE = Literal['zeros', 'edge', 'even', 'odd']
+
+#: Allowed values for property `ShortTimeFFT.fft_mode`:
+FFT_MODE_TYPE = Literal['twosided', 'centered', 'onesided', 'onesided2X']
+
+
+def _calc_dual_canonical_window(win: np.ndarray, hop: int) -> np.ndarray:
+    """Calculate canonical dual window for 1d window `win` and a time step
+    of `hop` samples.
+
+    A ``ValueError`` is raised if the inversion fails.
+
+    This is a separate function not a method, since it is also used in the
+    class method ``ShortTimeFFT.from_dual()``.
+    """
+    if hop > len(win):
+        raise ValueError(f"{hop=} is larger than window length of {len(win)}" +
+                         " => STFT not invertible!")
+    if issubclass(win.dtype.type, np.integer):
+        raise ValueError("Parameter 'win' cannot be of integer type, but " +
+                         f"{win.dtype=} => STFT not invertible!")
+        # The calculation of `relative_resolution` does not work for ints.
+        # Furthermore, `win / DD` casts the integers away, thus an implicit
+        # cast is avoided, which can always cause confusion when using 32-Bit
+        # floats.
+
+    w2 = win.real**2 + win.imag**2  # win*win.conj() does not ensure w2 is real
+    DD = w2.copy()
+    for k_ in range(hop, len(win), hop):
+        DD[k_:] += w2[:-k_]
+        DD[:-k_] += w2[k_:]
+
+    # check DD > 0:
+    relative_resolution = np.finfo(win.dtype).resolution * max(DD)
+    if not np.all(DD >= relative_resolution):
+        raise ValueError("Short-time Fourier Transform not invertible!")
+
+    return win / DD
+
+
+def closest_STFT_dual_window(win: np.ndarray, hop: int,
+                             desired_dual: np.ndarray | None = None, *,
+                             scaled: bool = True) \
+        -> tuple[np.ndarray, float | complex]:
+    r"""Calculate the STFT dual window of a given window closest to a desired dual
+        window.
+
+        For a given short-time Fourier transform window `win` incremented by `hop`
+        samples, the dual window is calculated, which minimizes
+        ``abs(dual_win - desired_dual)**2`` when `scaled` is ``False``. For `scaled`
+        set to ``True``, ``abs(alpha*dual_win - desired_dual)**2`` is minimized with
+        `alpha` being the optimal scaling factor.
+        A ``ValueError`` is raised if no valid dual window can be determined.
+
+
+        Parameters
+        ----------
+        win : np.ndarray
+            The window must be a real- or complex-valued 1d array.
+        hop : int
+            The increment in samples by which the window is shifted in each step.
+        desired_dual : np.ndarray | None
+            The desired dual window must be a 1d array of the same length as `win`.
+            If set to ``None`` (default), then `desired_dual` is assumed to be the
+            rectangular window, i.e., ``np.ones_like(win)``.
+        scaled : bool
+            If set (default), the closest scaled version instead of closest dual window
+            is calculated.
+
+        Returns
+        -------
+        dual_win : np.ndarray
+            A dual window of ``alpha*win`` (with hop interval `hop`), which is closest
+            to `desired_dual`. Note that the dual window of `win` is `dual_win/alpha`
+            and that the dual window of `dual_win` is `alpha*win`.
+            `dual_win` has the same shape as `win` and `desired_win`.
+        alpha : float | complex
+            Scale factor for `win`. It is always one if `scaled` is set to ``False``.
+
+        Notes
+        -----
+        For a given window and `hop` interval, all possible dual windows are expressed
+        by the `hop` linear conditions of Eq. :math:numref:`eq_STFT_AllDualWinsCond` in
+        the :ref:`tutorial_stft` section of the :ref:`user_guide`. Hence, decreasing
+        `hop`, increases the number of degrees of freedom of the set of all possible
+        dual windows, improving the ability to better approximate a `desired_dual`.
+
+        This function can also be used to determine windows which fulfill the
+        so-called "Constant OverLap Add" (COLA) condition [1]_. It states that summing
+        all touching window values at any given sample position results in the same
+        constant :math:`\alpha`. Eq. :math:numref:`eq_STFT_AllDualWinsCond` shows that
+        this is equal to having a rectangular dual window, i.e., the dual being
+        ``alpha*np.ones(m)``.
+
+        Some examples of windows that satisfy COLA (taken from [2]_):
+
+        - Rectangular window at overlap of 0, 1/2, 2/3, 3/4, ...
+        - Bartlett window at overlap of 1/2, 3/4, 5/6, ...
+        - Hann window at 1/2, 2/3, 3/4, ...
+        - Any Blackman family window at 2/3 overlap
+        - Any window with ``hop=1``
+
+        References
+        ----------
+        .. [1] Julius O. Smith III, "Spectral Audio Signal Processing",
+               online book, 2011, https://www.dsprelated.com/freebooks/sasp/
+        .. [2] G. Heinzel, A. Ruediger and R. Schilling, "Spectrum and spectral density
+               estimation by the Discrete Fourier transform (DFT), including a
+               comprehensive list of window functions and some new at-top windows",
+               2002, http://hdl.handle.net/11858/00-001M-0000-0013-557A-5
+
+        Examples
+        --------
+        Let's show that a Bartlett window with 75% overlap fulfills the COLA condition:
+
+        >>> import matplotlib.pyplot as plt
+        >>> import numpy as np
+        >>> from scipy.signal import closest_STFT_dual_window, windows
+        ...
+        >>> m = 24
+        >>> win, w_rect = windows.bartlett(m, sym=False), np.ones(m)
+        >>> d_win, alpha = closest_STFT_dual_window(win, m//4, w_rect, scaled=True)
+        >>> print(f"COLA: {np.allclose(d_win, w_rect*alpha)}, {alpha = :g}")
+        COLA: True, alpha = 0.5
+
+        We can also determine for which hop intervals the COLA condition is fulfilled:
+
+        >>> hops, deviations, alphas = np.arange(1, 16, dtype=int), [], []
+        >>> for h_ in hops:
+        ...     w_cola, alpha = closest_STFT_dual_window(w_rect, h_, win, scaled=True)
+        ...     deviations.append(np.linalg.norm(w_cola - win*alpha))
+        ...     alphas.append(alpha)
+        ...
+        >>> fg0, (ax0, ax1) = plt.subplots(2, 1, sharex='all', tight_layout=True)
+        >>> ax0.set_title(f"COLA Window closest to a {m}-Sample Bartlett Window")
+        >>> ax0.set(ylabel=r"$||w_\text{cola}-\alpha w||$", xlim=(0, hops[-1]-.5))
+        >>> ax1.set(xlabel="Hop Interval", ylabel=r"Scaling factor $\alpha$",
+        ...         ylim=(0, 1.25))
+        >>> ax0.plot(hops, deviations, 'C0.-')
+        >>> ax1.plot(hops, alphas, 'C1.-')
+        >>> for ax_ in (ax0, ax1):
+        ...     ax_.grid()
+        >>> plt.show()
+
+        The lower plot shows the calculated scaling factor :math:`\alpha` for different
+        `hops` whereas the upper displays the  :math:`L^2`-norm of the difference
+        between the scaled Bartlett window and the calculated window. Since for `hops`
+        1 to 4 as well as for 6 and 12 the :math:`L^2`-norm of the difference is
+        practically zero, the COLA condition is fulfilled for those.
+
+        See Also
+        --------
+        ShortTimeFFT: Short-time Fourier transform which is able to utilize a dual
+                      window for calculating the inverse.
+        ShortTimeFFT.from_win_equals_dual: Create instance where the window and its
+                                           dual are equal.
+
+    """
+    if desired_dual is None:  # default is rectangular window
+        desired_dual = np.ones_like(win)
+    if not (win.ndim == 1 and win.shape == desired_dual.shape):
+        raise ValueError("Parameters `win` and `desired_dual` are not 1d arrays of " +
+                         f"equal length ({win.shape=}, {desired_dual.shape=})!")
+    if not all(np.isfinite(win)):
+        raise ValueError("Parameter win must have finite entries!")
+    if not all(np.isfinite(desired_dual)):
+        raise ValueError("Parameter desired_dual must have finite entries!")
+    if not (1 <= hop <= len(win) and isinstance(hop, int | np.integer)):
+        raise ValueError(f"Parameter {hop=} is not an integer between 1 and " +
+                         f"{len(win)=}!")
+
+    w_d = _calc_dual_canonical_window(win, hop)
+    wdd = win.conjugate() * desired_dual
+    q_d = wdd.copy()
+    for k_ in range(hop, len(win), hop):
+        q_d[k_:] += wdd[:-k_]
+        q_d[:-k_] += wdd[k_:]
+    q_d = w_d * q_d
+
+    if not scaled:
+        return w_d + desired_dual - q_d, 1.
+
+    numerator = q_d.conjugate().T @ w_d
+    denominator = q_d.T.real @ q_d.real + q_d.T.imag @ q_d.imag  # always >= 0
+    if not (abs(numerator) > 0 and denominator > np.finfo(w_d.dtype).resolution):
+        raise ValueError(
+            "Unable to calculate scaled closest dual window due to numerically " +
+            "unstable scaling factor! Try setting parameter `scaled` to False.")
+    alpha = numerator / denominator
+    return w_d + alpha * (desired_dual - q_d), alpha
+
+
+# noinspection PyShadowingNames
+class ShortTimeFFT:
+    r"""Provide a parametrized discrete Short-time Fourier transform (stft)
+    and its inverse (istft).
+
+    .. currentmodule:: scipy.signal.ShortTimeFFT
+
+    The `~ShortTimeFFT.stft` calculates sequential FFTs by sliding a
+    window (`win`) over an input signal by `hop` increments. It can be used to
+    quantify the change of the spectrum over time.
+
+    The `~ShortTimeFFT.stft` is represented by a complex-valued matrix S[q,p]
+    where the p-th column represents an FFT with the window centered at the
+    time t[p] = p * `delta_t` = p * `hop` * `T` where `T` is  the sampling
+    interval of the input signal. The q-th row represents the values at the
+    frequency f[q] = q * `delta_f` with `delta_f` = 1 / (`mfft` * `T`) being
+    the bin width of the FFT.
+
+    The inverse STFT `~ShortTimeFFT.istft` is calculated by reversing the steps
+    of the STFT: Take the IFFT of the p-th slice of S[q,p] and multiply the
+    result with the so-called dual window (see `dual_win`). Shift the result by
+    p * `delta_t` and add the result to previous shifted results to reconstruct
+    the signal. If only the dual window is known and the STFT is invertible,
+    `from_dual` can be used to instantiate this class.
+
+    By default, the so-called canonical dual window is used. It is the window with
+    minimal energy among all possible dual windows. `from_win_equals_dual` and
+    `~scipy.signal.closest_STFT_dual_window` provide means for utilizing alterantive
+    dual windows. Note that `win` is also always a dual window of `dual_win`.
+
+    Due to the convention of time t = 0 being at the first sample of the input
+    signal, the STFT values typically have negative time slots. Hence,
+    negative indexes like `p_min` or `k_min` do not indicate counting
+    backwards from an array's end like in standard Python indexing but being
+    left of t = 0.
+
+    More detailed information can be found in the :ref:`tutorial_stft`
+    section of the :ref:`user_guide`.
+
+    Note that all parameters of the initializer, except `scale_to` (which uses
+    `scaling`) have identical named attributes.
+
+    Parameters
+    ----------
+    win : np.ndarray
+        The window must be a real- or complex-valued 1d array.
+    hop : int
+        The increment in samples, by which the window is shifted in each step.
+    fs : float
+        Sampling frequency of input signal and window. Its relation to the
+        sampling interval `T` is ``T = 1 / fs``.
+    fft_mode : 'twosided', 'centered', 'onesided', 'onesided2X'
+        Mode of FFT to be used (default 'onesided').
+        See property `fft_mode` for details.
+    mfft : int | None
+        Length of the FFT used, if a zero padded FFT is desired.
+        If ``None`` (default), the length of the window `win` is used.
+    dual_win : np.ndarray | None
+        The dual window of `win`. If set to ``None``, it is calculated if
+        needed.
+    scale_to : 'magnitude', 'psd' | None
+        If not ``None`` (default) the window function is scaled, so each STFT
+        column represents either a 'magnitude' or a power spectral density
+        ('psd') spectrum. This parameter sets the property `scaling` to the
+        same value. See method `scale_to` for details.
+    phase_shift : int | None
+        If set, add a linear phase `phase_shift` / `mfft` * `f` to each
+        frequency `f`. The default value of 0 ensures that there is no phase shift
+        on the zeroth slice (in which t=0 is centered). See property
+        `phase_shift` for more details.
+
+    Notes
+    -----
+    A typical STFT application is the creation of various types of time-frequency
+    plots, often subsumed under the term "spectrogram". Note that this term is also
+    used to explecitly refer to the absolute square of a STFT [11]_, as done in
+    :meth:`spectrogram`.
+
+    The STFT can also be used for filtering and filter banks as discussed in [12]_.
+
+
+    References
+    ----------
+    .. [11] Karlheinz Gröchenig: "Foundations of Time-Frequency Analysis",
+           Birkhäuser Boston 2001, `10.1007/978-1-4612-0003-1`
+    .. [12] Julius O. Smith III, "Spectral Audio Signal Processing", online book, 2011,
+           https://www.dsprelated.com/freebooks/sasp/
+
+
+    Examples
+    --------
+    The following example shows the magnitude of the STFT of a sine with
+    varying frequency :math:`f_i(t)` (marked by a red dashed line in the plot):
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.signal import ShortTimeFFT
+    >>> from scipy.signal.windows import gaussian
+    ...
+    >>> T_x, N = 1 / 20, 1000  # 20 Hz sampling rate for 50 s signal
+    >>> t_x = np.arange(N) * T_x  # time indexes for signal
+    >>> f_i = 1 * np.arctan((t_x - t_x[N // 2]) / 2) + 5  # varying frequency
+    >>> x = np.sin(2*np.pi*np.cumsum(f_i)*T_x) # the signal
+
+    The utilized Gaussian window is 50 samples or 2.5 s long. The parameter
+    ``mfft=200`` in `ShortTimeFFT` causes the spectrum to be oversampled
+    by a factor of 4:
+
+    >>> g_std = 8  # standard deviation for Gaussian window in samples
+    >>> w = gaussian(50, std=g_std, sym=True)  # symmetric Gaussian window
+    >>> SFT = ShortTimeFFT(w, hop=10, fs=1/T_x, mfft=200, scale_to='magnitude')
+    >>> Sx = SFT.stft(x)  # perform the STFT
+
+    In the plot, the time extent of the signal `x` is marked by vertical dashed
+    lines. Note that the SFT produces values outside the time range of `x`. The
+    shaded areas on the left and the right indicate border effects caused
+    by the window slices in that area not fully being inside time range of
+    `x`:
+
+    >>> fig1, ax1 = plt.subplots(figsize=(6., 4.))  # enlarge plot a bit
+    >>> t_lo, t_hi = SFT.extent(N)[:2]  # time range of plot
+    >>> ax1.set_title(rf"STFT ({SFT.m_num*SFT.T:g}$\,s$ Gaussian window, " +
+    ...               rf"$\sigma_t={g_std*SFT.T}\,$s)")
+    >>> ax1.set(xlabel=f"Time $t$ in seconds ({SFT.p_num(N)} slices, " +
+    ...                rf"$\Delta t = {SFT.delta_t:g}\,$s)",
+    ...         ylabel=f"Freq. $f$ in Hz ({SFT.f_pts} bins, " +
+    ...                rf"$\Delta f = {SFT.delta_f:g}\,$Hz)",
+    ...         xlim=(t_lo, t_hi))
+    ...
+    >>> im1 = ax1.imshow(abs(Sx), origin='lower', aspect='auto',
+    ...                  extent=SFT.extent(N), cmap='viridis')
+    >>> ax1.plot(t_x, f_i, 'r--', alpha=.5, label='$f_i(t)$')
+    >>> fig1.colorbar(im1, label="Magnitude $|S_x(t, f)|$")
+    ...
+    >>> # Shade areas where window slices stick out to the side:
+    >>> for t0_, t1_ in [(t_lo, SFT.lower_border_end[0] * SFT.T),
+    ...                  (SFT.upper_border_begin(N)[0] * SFT.T, t_hi)]:
+    ...     ax1.axvspan(t0_, t1_, color='w', linewidth=0, alpha=.2)
+    >>> for t_ in [0, N * SFT.T]:  # mark signal borders with vertical line:
+    ...     ax1.axvline(t_, color='y', linestyle='--', alpha=0.5)
+    >>> ax1.legend()
+    >>> fig1.tight_layout()
+    >>> plt.show()
+
+    Reconstructing the signal with the `~ShortTimeFFT.istft` is
+    straightforward, but note that the length of `x1` should be specified,
+    since the STFT length increases in `hop` steps:
+
+    >>> SFT.invertible  # check if invertible
+    True
+    >>> x1 = SFT.istft(Sx, k1=N)
+    >>> np.allclose(x, x1)
+    True
+
+    It is possible to calculate the STFT of signal parts:
+
+    >>> N2 = SFT.nearest_k_p(N // 2)
+    >>> Sx0 = SFT.stft(x[:N2])
+    >>> Sx1 = SFT.stft(x[N2:])
+
+    When assembling sequential STFT parts together, the overlap needs to be
+    considered:
+
+    >>> p0_ub = SFT.upper_border_begin(N2)[1] - SFT.p_min
+    >>> p1_le = SFT.lower_border_end[1] - SFT.p_min
+    >>> Sx01 = np.hstack((Sx0[:, :p0_ub],
+    ...                   Sx0[:, p0_ub:] + Sx1[:, :p1_le],
+    ...                   Sx1[:, p1_le:]))
+    >>> np.allclose(Sx01, Sx)  # Compare with SFT of complete signal
+    True
+
+    It is also possible to calculate the `itsft` for signal parts:
+
+    >>> y_p = SFT.istft(Sx, N//3, N//2)
+    >>> np.allclose(y_p, x[N//3:N//2])
+    True
+
+    """
+    # immutable attributes (only have getters but no setters):
+    _win: np.ndarray  # window
+    _dual_win: np.ndarray | None = None  # canonical dual window
+    _hop: int  # Step of STFT in number of samples
+
+    # mutable attributes:
+    _fs: float  # sampling frequency of input signal and window
+    _fft_mode: FFT_MODE_TYPE = 'onesided'  # Mode of FFT to use
+    _mfft: int  # length of FFT used - defaults to len(win)
+    _scaling: Literal['magnitude', 'psd', 'unitary'] | None = None  # Scaling of _win
+    _phase_shift: int | None  # amount to shift phase of FFT in samples
+
+    # attributes for caching calculated values:
+    _fac_mag: float | None = None
+    _fac_psd: float | None = None
+    _lower_border_end: tuple[int, int] | None = None
+    # The following tuples store parameter(s) and return value(s) of methods for caching
+    # (initialized with invalid parameters; should only be accessed by atomic
+    # read/writes to alleviate potential multithreading issues):
+    _cache_post_padding: tuple[int, tuple[int, int]] = -1, (0, 0)
+    _cache_upper_border_begin: tuple[int, tuple[int, int]] = -1, (0, 0)
+    _cache_t: tuple[tuple[int, int | None, int | None, int, float], np.ndarray] = \
+        (-1, None, None, 0, 0.), np.ndarray([])
+    _cache_f: tuple[tuple[FFT_MODE_TYPE, int, float], np.ndarray] = \
+        ('onesided', -1, 1.), np.ndarray([])
+
+    # generic type compatibility with scipy-stubs
+    __class_getitem__: classmethod = classmethod(GenericAlias)
+
+    def __init__(self, win: np.ndarray, hop: int, fs: float, *,
+                 fft_mode: FFT_MODE_TYPE = 'onesided',
+                 mfft: int | None = None,
+                 dual_win: np.ndarray | None = None,
+                 scale_to: Literal['magnitude', 'psd'] | None = None,
+                 phase_shift: int | None = 0):
+        if not (win.ndim == 1 and win.size > 0):
+            raise ValueError(f"Parameter win must be 1d, but {win.shape=}!")
+        if not all(np.isfinite(win)):
+            raise ValueError("Parameter win must have finite entries!")
+        if not (hop >= 1 and isinstance(hop, int | np.integer)):
+            raise ValueError(f"Parameter {hop=} is not an integer >= 1!")
+
+        self._win, self._hop, self.fs = win, hop, fs
+        self.win.setflags(write=False)
+        self.mfft = len(win) if mfft is None else mfft
+
+        if dual_win is not None:
+            if dual_win.shape != win.shape:
+                raise ValueError(f"{dual_win.shape=} must equal {win.shape=}!")
+            if not all(np.isfinite(dual_win)):
+                raise ValueError("Parameter dual_win must be a finite array!")
+            dual_win.setflags(write=False)
+        self._dual_win = dual_win  # needs to be set before scaling
+
+        if scale_to is not None:  # needs to be set before fft_mode
+            self.scale_to(scale_to)
+
+        self.fft_mode, self.phase_shift = fft_mode, phase_shift
+
+    @classmethod
+    def from_dual(cls, dual_win: np.ndarray, hop: int, fs: float, *,
+                  fft_mode: FFT_MODE_TYPE = 'onesided',
+                  mfft: int | None = None,
+                  scale_to: Literal['magnitude', 'psd'] | None = None,
+                  phase_shift: int | None = 0):
+        r"""Instantiate a `ShortTimeFFT` by only providing a dual window.
+
+        If an STFT is invertible, it is possible to calculate the window `win`
+        from a given dual window `dual_win`. All other parameters have the
+        same meaning as in the initializer of `ShortTimeFFT`.
+
+        As explained in the :ref:`tutorial_stft` section of the
+        :ref:`user_guide`, an invertible STFT can be interpreted as series
+        expansion of time-shifted and frequency modulated dual windows. E.g.,
+        the series coefficient S[q,p] belongs to the term, which shifted
+        `dual_win` by p * `delta_t` and multiplied it by
+        exp( 2 * j * pi * t * q * `delta_f`).
+
+
+        Examples
+        --------
+        The following example discusses decomposing a signal into time- and
+        frequency-shifted Gaussians. A Gaussian with standard deviation of
+        one made up of 51 samples will be used:
+
+        >>> import numpy as np
+        >>> import matplotlib.pyplot as plt
+        >>> from scipy.signal import ShortTimeFFT
+        >>> from scipy.signal.windows import gaussian
+        ...
+        >>> T, N = 0.1, 51
+        >>> d_win = gaussian(N, std=1/T, sym=True)  # symmetric Gaussian window
+        >>> t = T * (np.arange(N) - N//2)
+        ...
+        >>> fg1, ax1 = plt.subplots()
+        >>> ax1.set_title(r"Dual Window: Gaussian with $\sigma_t=1$")
+        >>> ax1.set(xlabel=f"Time $t$ in seconds ({N} samples, $T={T}$ s)",
+        ...        xlim=(t[0], t[-1]), ylim=(0, 1.1*np.max(d_win)))
+        >>> ax1.plot(t, d_win, 'C0-')
+
+        The following plot with the overlap of 41, 11 and 2 samples show how
+        the `hop` interval affects the shape of the window `win`:
+
+        >>> fig2, axx = plt.subplots(3, 1, sharex='all')
+        ...
+        >>> axx[0].set_title(r"Windows for hop$\in\{10, 40, 49\}$")
+        >>> for c_, h_ in enumerate([10, 40, 49]):
+        ...     SFT = ShortTimeFFT.from_dual(d_win, h_, 1/T)
+        ...     axx[c_].plot(t + h_ * T, SFT.win, 'k--', alpha=.3, label=None)
+        ...     axx[c_].plot(t - h_ * T, SFT.win, 'k:', alpha=.3, label=None)
+        ...     axx[c_].plot(t, SFT.win, f'C{c_+1}',
+        ...                     label=r"$\Delta t=%0.1f\,$s" % SFT.delta_t)
+        ...     axx[c_].set_ylim(0, 1.1*max(SFT.win))
+        ...     axx[c_].legend(loc='center')
+        >>> axx[-1].set(xlabel=f"Time $t$ in seconds ({N} samples, $T={T}$ s)",
+        ...             xlim=(t[0], t[-1]))
+        >>> plt.show()
+
+        Beside the window `win` centered at t = 0 the previous (t = -`delta_t`)
+        and following window (t = `delta_t`) are depicted. It can be seen that
+        for small `hop` intervals, the window is compact and smooth, having a
+        good time-frequency concentration in the STFT. For the large `hop`
+        interval of 4.9 s, the window has small values around t = 0, which are
+        not covered by the overlap of the adjacent windows, which could lead to
+        numeric inaccuracies. Furthermore, the peaky shape at the beginning and
+        the end of the window points to a higher bandwidth, resulting in a
+        poorer time-frequency resolution of the STFT.
+        Hence, the choice of the `hop` interval will be a compromise between
+        a time-frequency resolution and memory requirements demanded by small
+        `hop` sizes.
+
+        See Also
+        --------
+        from_window: Create instance by wrapping `get_window`.
+        ShortTimeFFT: Create instance using standard initializer.
+        """
+        win = _calc_dual_canonical_window(dual_win, hop)
+        return cls(win=win, hop=hop, fs=fs, fft_mode=fft_mode, mfft=mfft,
+                   dual_win=dual_win, scale_to=scale_to,
+                   phase_shift=phase_shift)
+
+    @classmethod
+    def from_window(cls, win_param: str | tuple | float,
+                    fs: float, nperseg: int, noverlap: int, *,
+                    symmetric_win: bool = False,
+                    fft_mode: FFT_MODE_TYPE = 'onesided',
+                    mfft: int | None = None,
+                    scale_to: Literal['magnitude', 'psd'] | None = None,
+                    phase_shift: int | None = 0):
+        """Instantiate `ShortTimeFFT` by using `get_window`.
+
+        The method `get_window` is used to create a window of length
+        `nperseg`. The parameter names `noverlap`, and `nperseg` are used here,
+        since they more inline with other classical STFT libraries.
+
+        Parameters
+        ----------
+        win_param: Union[str, tuple, float],
+            Parameters passed to `get_window`. For windows with no parameters,
+            it may be a string (e.g., ``'hann'``), for parametrized windows a
+            tuple, (e.g., ``('gaussian', 2.)``) or a single float specifying
+            the shape parameter of a kaiser window (i.e. ``4.``  and
+            ``('kaiser', 4.)`` are equal. See `get_window` for more details.
+        fs : float
+            Sampling frequency of input signal. Its relation to the
+            sampling interval `T` is ``T = 1 / fs``.
+        nperseg: int
+            Window length in samples, which corresponds to the `m_num`.
+        noverlap: int
+            Window overlap in samples. It relates to the `hop` increment by
+            ``hop = npsereg - noverlap``.
+        symmetric_win: bool
+            If ``True`` then a symmetric window is generated, else a periodic window is
+            generated (default). Though symmetric windows seem for most applications to
+            be more sensible, the default of a periodic windows was chosen to
+            correspond to the default of `get_window`. This parameter is ignored, if
+            the window name in the `window` parameter has a suffix ``'_periodic'`` or
+            ``'_symmetric'`` appended to it (e.g., ``'hann_symmetric'``).
+        fft_mode : 'twosided', 'centered', 'onesided', 'onesided2X'
+            Mode of FFT to be used (default 'onesided').
+            See property `fft_mode` for details.
+        mfft: int | None
+            Length of the FFT used, if a zero padded FFT is desired.
+            If ``None`` (default), the length of the window `win` is used.
+        scale_to : 'magnitude', 'psd' | None
+            If not ``None`` (default) the window function is scaled, so each
+            STFT column represents  either a 'magnitude' or a power spectral
+            density ('psd') spectrum. This parameter sets the property
+            `scaling` to the same value. See method `scale_to` for details.
+        phase_shift : int | None
+            If set, add a linear phase `phase_shift` / `mfft` * `f` to each
+            frequency `f`. The default value 0 ensures that there is no phase
+            shift on the zeroth slice (in which t=0 is centered). See property
+            `phase_shift` for more details.
+
+        Examples
+        --------
+        The following instances ``SFT0`` and ``SFT1`` are equivalent:
+
+        >>> from scipy.signal import ShortTimeFFT, get_window
+        >>> nperseg = 9  # window length
+        >>> w = get_window(('gaussian_periodic', 2.), nperseg)
+        >>> fs = 128  # sampling frequency
+        >>> hop = 3  # increment of STFT time slice
+        >>> SFT0 = ShortTimeFFT(w, hop, fs=fs)
+        >>> SFT1 = ShortTimeFFT.from_window(('gaussian', 2.), fs, nperseg,
+        ...                                 noverlap=nperseg-hop)
+
+        See Also
+        --------
+        scipy.signal.get_window: Return a window of a given length and type.
+        from_dual: Create instance using dual window.
+        ShortTimeFFT: Create instance using standard initializer.
+        """
+        win = get_window(win_param, nperseg, fftbins=not symmetric_win)
+        return cls(win, hop=nperseg-noverlap, fs=fs, fft_mode=fft_mode,
+                   mfft=mfft, scale_to=scale_to, phase_shift=phase_shift)
+
+    @classmethod
+    def from_win_equals_dual(
+            cls, desired_win: np.ndarray, hop: int, fs: float, *,
+            fft_mode: FFT_MODE_TYPE = 'onesided', mfft: int | None = None,
+            scale_to: Literal['magnitude', 'psd', 'unitary'] | None = None,
+            phase_shift: int | None = 0):
+        r"""Create instance where the window and its dual are equal up to a
+        scaling factor.
+
+        An instance is created were window and dual window are equal as well as being
+        closest to the parameter `desired_win` in the least-squares sense, i.e.,
+        minimizing ``abs(win-desired_win)**2``. Hence, `win` has the same length as
+        `desired_win`. Then a scaling factor is applied accoring to the `scale_to`
+        parameter.
+
+        All other parameters have the identical meaning as in the initializer.
+
+        To be able to calculate a valid window, `desired_win` needs to have a valid
+        dual STFT window for the given `hop` interval.
+        If this is not the case, a ``ValueError`` is raised.
+
+        Parameters
+        ----------
+        desired_win : np.ndarray
+            A real-valued or complex-valued 1d array containing the sample of the
+            desired window.
+        hop : int
+            The increment in samples, by which the window is shifted in each step.
+        fs : float
+            Sampling frequency of input signal and window. Its relation to the
+            sampling interval `T` is ``T = 1 / fs``.
+        fft_mode : 'twosided', 'centered', 'onesided', 'onesided2X'
+            Mode of FFT to be used (default 'onesided').
+            See property `fft_mode` for details.
+        mfft : int | None
+            Length of the FFT used, if a zero padded FFT is desired.
+            If ``None`` (default), the length of the window `win` is used.
+        scale_to : 'magnitude' | 'psd' | 'unitary' | None
+            If not ``None`` (default) the window function is scaled, so each STFT
+            column represents either a 'magnitude' or a power spectral density ('psd')
+            spectrum, Alternatively, the STFT can be scaled to a`unitary` mapping,
+            i.e., dividing the window by ``np.sqrt(mfft)`` and multiplying the dual
+            window by the same amount.
+        phase_shift : int | None
+            If set, add a linear phase `phase_shift` / `mfft` * `f` to each
+            frequency `f`. The default value of 0 ensures that there is no phase shift
+            on the zeroth slice (in which t=0 is centered). See property
+            `phase_shift` for more details.
+
+
+        Notes
+        -----
+        The set of all possible windows with identical dual is defined by the set of
+        linear constraints of Eq. :math:numref:`eq_STFT_AllDualWinsCond` in the
+        :ref:`tutorial_stft` section of the :ref:`user_guide`. There it is also
+        derived that ``ShortTimeFFT.dual_win == ShortTimeFFT.m_pts * ShortTimeFFT.win``
+        needs to hold for an STFT to be a unitary mapping.
+
+        A unitary mapping preserves the value of the scalar product, i.e.,
+
+        .. math::
+
+            \langle x, y\rangle = \sum_k x[k]\, \overline{y[k]}
+            \stackrel{\stackrel{\text{unitary}}{\downarrow}}{=}
+            \sum_{q,p} S_x[q,p]\, \overline{S_y[q,p]}
+            = \langle S_x[q,p], S_y[q,p]\rangle\ ,
+
+        with :math:`S_{x,y}` being the STFT of :math:`x,y`. Hence, the energy
+        :math:`E_x=T\sum_k |x[k]|^2` of a signal is also preserved. This is also
+        illustrated in the example below.
+
+        Thie reason of distinguishing between no scaling (i.e., parameter `scale_to` is
+        ``None``) and unitary scaling (i.e., ``scale_to = 'unitary'``) is due to the
+        utilized FFT function not being unitary (i.e., using the default value
+        ``'backward'`` for the `~scipy.fft.fft` parameter `norm`).
+
+
+        See Also
+        --------
+        closest_STFT_dual_window: Calculate the STFT dual window of a given window
+                                  closest to a desired dual window.
+        ShortTimeFFT.spectrogram: Calculate squared STFTs
+        ShortTimeFFT: Class this property belongs to.
+
+        Examples
+        --------
+        The following example shows that an STFT can be indeed unitary:
+
+        >>> import matplotlib.pyplot as plt
+        >>> import numpy as np
+        >>> from scipy.signal import ShortTimeFFT, windows
+        ...
+        >>> m, hop, std = 36, 8, 5
+        >>> desired_win = windows.gaussian(m, std, sym=True)
+        >>> SFT = ShortTimeFFT.from_win_equals_dual(desired_win, hop, fs=1/m,
+        ...                                         fft_mode='twosided',
+        ...                                         scale_to='unitary')
+        >>> np.allclose(SFT.dual_win, SFT.win * SFT.m_num)  # check if STFT is unitary
+        True
+        >>> x1, x2 = np.tile([-1, -1, 1, 1], 5), np.tile([1, -1, -1, 1], 5)
+        >>> np.sum(x1*x2) # scalar product is zero -> orthogonal signals
+        0
+        >>> np.sum(x1**2)  # scalar product of x1 with itself
+        20
+        >>> Sx11, Sx12 = SFT.spectrogram(x1), SFT.spectrogram(x1, x2)
+        >>> np.sum(Sx12)  # STFT scalar product is also zero
+        -4.163336342344337e-16+0j  # may vary
+        >>> np.sum(Sx11)  # == np.sum(x1**2)
+        19.999999999999996  # may vary
+        ...
+        ... # Do the plotting:
+        >>> fg1, (ax11, ax12) = plt.subplots(1, 2, tight_layout=True, figsize=(8, 4))
+        >>> s_fac = np.sqrt(SFT.mfft)
+        >>> _ = fg1.suptitle(f"Scaled Unitary Window of {m} Sample Gaussian with " +
+        ...                  rf"{hop=}, $\sigma={std}$, Scale factor: {s_fac}")
+        >>> ax11.set(ylabel="Amplitude", xlabel="Samples", xlim=(0, m))
+        >>> ax12.set(xlabel="Frequency Bins", ylabel="Magnitude Spectrum",
+        ...          xlim=(0, 15), ylim=(1e-5, 1.5))
+        >>> u_win_str = rf"Unitary $\times{s_fac:g}$"
+        >>> for x_, n_ in zip((desired_win, SFT.win*s_fac), ('Desired', u_win_str)):
+        ...     ax11.plot(x_, '.-', alpha=0.5, label=n_)
+        ...     X_ = np.fft.rfft(x_) / np.sum(abs(x_))
+        ...     ax12.semilogy(abs(X_), '.-', alpha=0.5, label=n_)
+        >>> for ax_ in (ax11, ax12):
+        ...     ax_.grid(True)
+        ...     ax_.legend()
+        >>> plt.show()
+
+        Note that ``fftmode='twosided'`` is used, since we need sum over the complete
+        time frequency plane. Due to passing ``scale_to='unitary'`` the window
+        ``SFT.win`` is scaled by ``1/np.sqrt(SFT.mfft)``. Hence, ``SFT.win`` needs to
+        be scaled by `s_fac` in the plot above.
+        """
+        if not (desired_win.ndim == 1 and desired_win.size > 0):
+            raise ValueError(f"Parameter desired_win is not 1d, but "
+                             f"{desired_win.shape=}!")
+        if issubclass(desired_win.dtype.type, np.integer):
+            raise ValueError("Parameter desired_win cannot be of integer type, " +
+                             f"but {desired_win.dtype=} => cast to float | complex ")
+        if not all(np.isfinite(desired_win)):
+            raise ValueError("Parameter desired_win must have finite entries!")
+        if not (1 <= hop <= len(desired_win) and isinstance(hop, int | np.integer)):
+            raise ValueError(f"Parameter {hop=} is not an integer between 1 and " +
+                             f"{len(desired_win)=}!")
+        if scale_to not in ['magnitude', 'psd', 'unitary', None]:
+            raise ValueError(f"Parameter {scale_to=} not in " +
+                             "['magnitude', 'psd', 'unitary', None]!")
+
+        mfft = len(desired_win) if mfft is None else mfft
+        s_fac = np.sqrt(mfft) if scale_to == 'unitary' else 1
+
+        win = desired_win.copy()  # we do not want to modify input parameters
+        relative_resolution = np.finfo(win.dtype).resolution * max(win)
+        for m in range(hop):
+            a = np.linalg.norm(desired_win[m::hop])
+            if not (a > relative_resolution):
+                raise ValueError("Parameter desired_win does not have valid STFT dual "
+                                 f"window for {hop=}!")
+            win[m::hop] /= a
+
+        SFT = cls(win=win/s_fac, hop=hop, fs=fs, fft_mode=fft_mode, mfft=mfft,
+                  dual_win=win*s_fac, phase_shift=phase_shift,
+                  scale_to=None if scale_to=='unitary' else scale_to)
+
+        if scale_to == 'unitary':
+            SFT._scaling = scale_to
+        return SFT
+
+
+    @property
+    def win(self) -> np.ndarray:
+        """Window function as real- or complex-valued 1d array.
+
+        This attribute is read-only, since `dual_win` depends on it.
+        To make this array immutable, its WRITEABLE flag is set to ``FALSE``.
+
+        See Also
+        --------
+        dual_win: Dual window.
+        m_num: Number of samples in window `win`.
+        m_num_mid: Center index of window `win`.
+        mfft: Length of input for the FFT used - may be larger than `m_num`.
+        hop: ime increment in signal samples for sliding window.
+        win: Window function as real- or complex-valued 1d array.
+        numpy.ndarray.setflags: Modify array flags.
+        ShortTimeFFT: Class this property belongs to.
+        """
+        return self._win
+
+    @property
+    def hop(self) -> int:
+        """Time increment in signal samples for sliding window.
+
+        This attribute is read only, since `dual_win` depends on it.
+
+        See Also
+        --------
+        delta_t: Time increment of STFT (``hop*T``)
+        m_num: Number of samples in window `win`.
+        m_num_mid: Center index of window `win`.
+        mfft: Length of input for the FFT used - may be larger than `m_num`.
+        T: Sampling interval of input signal and of the window.
+        win: Window function as real- or complex-valued 1d array.
+        ShortTimeFFT: Class this property belongs to.
+        """
+        return self._hop
+
+    @property
+    def T(self) -> float:
+        """Sampling interval of input signal and of the window.
+
+        A ``ValueError`` is raised if it is set to a non-positive value.
+
+        See Also
+        --------
+        delta_t: Time increment of STFT (``hop*T``)
+        hop: Time increment in signal samples for sliding window.
+        fs: Sampling frequency (being ``1/T``)
+        t: Times of STFT for an input signal with `n` samples.
+        ShortTimeFFT: Class this property belongs to.
+        """
+        return 1 / self._fs
+
+    @T.setter
+    def T(self, v: float):
+        """Sampling interval of input signal and of the window.
+
+        A ``ValueError`` is raised if it is set to a non-positive value.
+        """
+        if not (v > 0):
+            raise ValueError(f"Sampling interval T={v} must be positive!")
+        self._fs = 1 / v
+
+    @property
+    def fs(self) -> float:
+        """Sampling frequency of input signal and of the window.
+
+        The sampling frequency is the inverse of the sampling interval `T`.
+        A ``ValueError`` is raised if it is set to a non-positive value.
+
+        See Also
+        --------
+        delta_t: Time increment of STFT (``hop*T``)
+        hop: Time increment in signal samples for sliding window.
+        T: Sampling interval of input signal and of the window (``1/fs``).
+        ShortTimeFFT: Class this property belongs to.
+        """
+        return self._fs
+
+    @fs.setter
+    def fs(self, v: float):
+        """Sampling frequency of input signal and of the window.
+
+        The sampling frequency is the inverse of the sampling interval `T`.
+        A ``ValueError`` is raised if it is set to a non-positive value.
+        """
+        if not (v > 0):
+            raise ValueError(f"Sampling frequency fs={v} must be positive!")
+        self._fs = v
+
+    @property
+    def fft_mode(self) -> FFT_MODE_TYPE:
+        """Mode of utilized FFT ('twosided', 'centered', 'onesided' or
+        'onesided2X').
+
+        It can have the following values:
+
+        'twosided':
+            Two-sided FFT, where values for the negative frequencies are in
+            upper half of the array. Corresponds to :func:`~scipy.fft.fft()`.
+        'centered':
+            Two-sided FFT with the values being ordered along monotonically
+            increasing frequencies. Corresponds to applying
+            :func:`~scipy.fft.fftshift()` to :func:`~scipy.fft.fft()`.
+        'onesided':
+            Calculates only values for non-negative frequency values.
+            Corresponds to :func:`~scipy.fft.rfft()`.
+        'onesided2X':
+            Like `onesided`, but the non-zero frequencies are doubled if
+            `scaling` is set to 'magnitude' or multiplied by ``sqrt(2)`` if
+            set to 'psd'. If `scaling` is ``None``, setting `fft_mode` to
+            `onesided2X` is not allowed.
+            If the FFT length `mfft` is even, the last FFT value is not paired,
+            and thus it is not scaled.
+
+        Note that `onesided` and `onesided2X` do not work for complex-valued signals or
+        complex-valued windows. Furthermore, the frequency values can be obtained by
+        reading the `f` property, and the number of samples by accessing the `f_pts`
+        property.
+
+        See Also
+        --------
+        delta_f: Width of the frequency bins of the STFT.
+        f: Frequencies values of the STFT.
+        f_pts: Width of the frequency bins of the STFT.
+        onesided_fft: True if a one-sided FFT is used.
+        scaling: Normalization applied to the window function
+        ShortTimeFFT: Class this property belongs to.
+        """
+        return self._fft_mode
+
+    @fft_mode.setter
+    def fft_mode(self, t: FFT_MODE_TYPE):
+        """Set mode of FFT.
+
+        Allowed values are 'twosided', 'centered', 'onesided', 'onesided2X'.
+        See the property `fft_mode` for more details.
+        """
+        if t not in (fft_mode_types := get_args(FFT_MODE_TYPE)):
+            raise ValueError(f"fft_mode='{t}' not in {fft_mode_types}!")
+
+        if t in {'onesided', 'onesided2X'} and np.iscomplexobj(self.win):
+            raise ValueError(f"One-sided spectra, i.e., fft_mode='{t}', " +
+                             "are not allowed for complex-valued windows!")
+
+        if t == 'onesided2X' and self.scaling is None:
+            raise ValueError(f"For scaling is None, fft_mode='{t}' is invalid!"
+                             "Do scale_to('psd') or scale_to('magnitude')!")
+        self._fft_mode = t
+
+    @property
+    def mfft(self) -> int:
+        """Length of input for the FFT used - may be larger than window
+        length `m_num`.
+
+        If not set, `mfft` defaults to the window length `m_num`.
+
+        See Also
+        --------
+        f_pts: Number of points along the frequency axis.
+        f: Frequencies values of the STFT.
+        m_num: Number of samples in window `win`.
+        ShortTimeFFT: Class this property belongs to.
+        """
+        return self._mfft
+
+    @mfft.setter
+    def mfft(self, n_: int):
+        """Setter for the length of FFT utilized.
+
+        See the property `mfft` for further details.
+        """
+        if not (n_ >= self.m_num):
+            raise ValueError(f"Attribute mfft={n_} needs to be at least the " +
+                             f"window length m_num={self.m_num}!")
+        self._mfft = n_
+
+    @property
+    def scaling(self) -> Literal['magnitude', 'psd', 'unitary'] | None:
+        """Normalization applied to the window function
+        ('magnitude', 'psd', 'unitary', or ``None``).
+
+        If not ``None``, the FFT slices may be either interpreted as a `magnitude` or
+        a power spectral density spectrum (`psd`). If set to `unitary`, the STFT may be
+        interpreted as a unitary mapping, i.e., preserving the value of the scalar
+        product.
+
+        The window function can be scaled by calling the `scale_to` method,
+        or it is set by the initializer parameter ``scale_to``. Note that a
+        window cannot to be scaled to be `unitary`.  Use `from_win_equals_dual`
+        to create a unitary `ShortTimeFFT` instance.
+
+        See Also
+        --------
+        fac_magnitude: Scaling factor for to a magnitude spectrum.
+        fac_psd: Scaling factor for to  a power spectral density spectrum.
+        fft_mode: Mode of utilized FFT
+        scale_to: Scale window to obtain 'magnitude' or 'psd' scaling.
+        from_win_equals_dual: Class-method for creating a unitary instance.
+        ShortTimeFFT: Class this property belongs to.
+        """
+        return self._scaling
+
+    def scale_to(self, scaling: Literal['magnitude', 'psd']):
+        """Scale window to obtain 'magnitude' or 'psd' scaling for the STFT.
+
+        The window of a 'magnitude' spectrum has an integral of one, i.e., unit
+        area for non-negative windows. This ensures that absolute the values of
+        spectrum does not change if the length of the window changes (given
+        the input signal is stationary).
+
+        To represent the power spectral density ('psd') for varying length
+        windows the area of the absolute square of the window needs to be
+        unity.
+
+        The `scaling` property shows the current scaling. The properties
+        `fac_magnitude` and `fac_psd` show the scaling factors required to
+        scale the STFT values to a magnitude or a psd spectrum.
+
+        Note that a window cannot to be scaled to be `unitary`. Use
+        `from_win_equals_dual` to create a unitary `ShortTimeFFT` instance.
+
+        This method is called, if the initializer parameter `scale_to` is set.
+
+        Parameters
+        ----------
+        scaling : {'magnitude', 'psd'}
+            The scaling type to which the window is scaled.
+
+        See Also
+        --------
+        fac_magnitude: Scaling factor for to  a magnitude spectrum.
+        fac_psd: Scaling factor for to  a power spectral density spectrum.
+        fft_mode: Mode of utilized FFT
+        scaling: Normalization applied to the window function.
+        ShortTimeFFT: Class this method belongs to.
+        """
+        if scaling not in (scaling_values := {'magnitude', 'psd'}):
+            raise ValueError(f"{scaling=} not in {scaling_values}!")
+        if self._scaling == scaling:  # do nothing
+            return
+
+        s_fac = self.fac_psd if scaling == 'psd' else self.fac_magnitude
+        self._win = self._win * s_fac
+        self.win.setflags(write=False)
+        if self._dual_win is not None:
+            self._dual_win = self._dual_win / s_fac
+            self.dual_win.setflags(write=False)
+        self._fac_mag, self._fac_psd = None, None  # reset scaling factors
+        self._scaling = scaling
+
+    @property
+    def phase_shift(self) -> int | None:
+        """If set, add linear phase `phase_shift` / `mfft` * `f` to each FFT
+        slice of frequency `f`.
+
+        Shifting (more precisely `rolling`) an `mfft`-point FFT input by
+        `phase_shift` samples results in a multiplication of the output by
+        ``np.exp(2j*np.pi*q*phase_shift/mfft)`` at the frequency q * `delta_f`.
+
+        The default value 0 ensures that there is no phase shift on the
+        zeroth slice (in which t=0 is centered).
+        No phase shift (``phase_shift is None``) is equivalent to
+        ``phase_shift = -mfft//2``. In this case slices are not shifted
+        before calculating the FFT.
+
+        The absolute value of `phase_shift` is limited to be less than `mfft`.
+
+        See Also
+        --------
+        delta_f: Width of the frequency bins of the STFT.
+        f: Frequencies values of the STFT.
+        mfft: Length of input for the FFT used
+        ShortTimeFFT: Class this property belongs to.
+        """
+        return self._phase_shift
+
+    @phase_shift.setter
+    def phase_shift(self, v: int | None):
+        """The absolute value of the phase shift needs to be less than mfft
+        samples.
+
+        See the `phase_shift` getter method for more details.
+        """
+        if v is None:
+            self._phase_shift = v
+            return
+        if not isinstance(v, int | np.integer):
+            raise ValueError(f"phase_shift={v} has the unit samples. Hence " +
+                             "it needs to be an int or it may be None!")
+        if not (-self.mfft < v < self.mfft):
+            raise ValueError("-mfft < phase_shift < mfft does not hold " +
+                             f"for mfft={self.mfft}, phase_shift={v}!")
+        self._phase_shift = v
+
+    def _x_slices(self, x: np.ndarray, k_off: int, p0: int, p1: int,
+                  padding: PAD_TYPE) -> Generator[np.ndarray, None, None]:
+        """Generate signal slices along last axis of `x`.
+
+        This method is only used by `stft_detrend`. The parameters are
+        described in `~ShortTimeFFT.stft`.
+        """
+        if padding not in (padding_types := get_args(PAD_TYPE)):
+            raise ValueError(f"Parameter {padding=} not in {padding_types}!")
+        pad_kws: dict[str, dict] = {  # possible keywords to pass to np.pad:
+            'zeros': dict(mode='constant', constant_values=(0, 0)),
+            'edge': dict(mode='edge'),
+            'even': dict(mode='reflect', reflect_type='even'),
+            'odd': dict(mode='reflect', reflect_type='odd'),
+           }  # typing of pad_kws is needed to make mypy happy
+
+        n, n1 = x.shape[-1], (p1 - p0) * self.hop
+        k0 = p0 * self.hop - self.m_num_mid + k_off  # start sample
+        k1 = k0 + n1 + self.m_num  # end sample
+
+        i0, i1 = max(k0, 0), min(k1, n)  # indexes to shorten x
+        # dimensions for padding x:
+        pad_width = [(0, 0)] * (x.ndim-1) + [(-min(k0, 0), max(k1 - n, 0))]
+
+        x1 = np.pad(x[..., i0:i1], pad_width, **pad_kws[padding])
+        for k_ in range(0, n1, self.hop):
+            yield x1[..., k_:k_ + self.m_num]
+
+    def stft(self, x: np.ndarray, p0: int | None = None,
+             p1: int | None = None, *, k_offset: int = 0,
+             padding: PAD_TYPE = 'zeros', axis: int = -1) \
+            -> np.ndarray:
+        """Perform the short-time Fourier transform.
+
+        A two-dimensional matrix with ``p1-p0`` columns is calculated.
+        The `f_pts` rows represent value at the frequencies `f`. The q-th
+        column of the windowed FFT with the window `win` is centered at t[q].
+        The columns represent the values at the frequencies `f`.
+
+        Parameters
+        ----------
+        x : np.ndarray
+            The input signal as real or complex valued array. For complex values, the
+            property `fft_mode` must be set to 'twosided' or 'centered'.
+        p0 : int | None
+            The first element of the range of slices to calculate. If ``None``
+            then it is set to :attr:`p_min`, which is the smallest possible
+            slice.
+        p1 : int | None
+            The end of the array. If ``None`` then `p_max(n)` is used.
+        k_offset : int
+            Index of first sample (t = 0) in `x`.
+        padding : 'zeros' | 'edge' | 'even' | 'odd'
+            Kind of values which are added, when the sliding window sticks out
+            on either the lower or upper end of the input `x`. Zeros are added
+            if the default 'zeros' is set. For 'edge' either the first or the
+            last value of `x` is used. 'even' pads by reflecting the
+            signal on the first or last sample and 'odd' additionally
+            multiplies it with -1.
+        axis : int
+            The axis of `x` over which to compute the STFT.
+            If not given, the last axis is used.
+
+        Returns
+        -------
+        S : np.ndarray
+            A complex array is returned with the dimension always being larger
+            by one than of `x`. The last axis always represents the time slices
+            of the STFT. `axis` defines the frequency axis (default second to
+            last). E.g., for a one-dimensional `x`, a complex 2d array is
+            returned, with axis 0 representing frequency and axis 1 the time
+            slices.
+
+        See Also
+        --------
+        delta_f: Width of the frequency bins of the STFT.
+        delta_t: Time increment of STFT
+        f: Frequencies values of the STFT.
+        invertible: Check if STFT is invertible.
+        :meth:`~ShortTimeFFT.istft`: Inverse short-time Fourier transform.
+        p_range: Determine and validate slice index range.
+        stft_detrend: STFT with detrended segments.
+        t: Times of STFT for an input signal with `n` samples.
+        :class:`scipy.signal.ShortTimeFFT`: Class this method belongs to.
+        """
+        return self.stft_detrend(x, None, p0, p1, k_offset=k_offset,
+                                 padding=padding, axis=axis)
+
+    def stft_detrend(self, x: np.ndarray,
+                     detr: Callable[[np.ndarray], np.ndarray] | Literal['linear', 'constant'] | None,  # noqa: E501
+                     p0: int | None = None, p1: int | None = None, *,
+                     k_offset: int = 0, padding: PAD_TYPE = 'zeros',
+                     axis: int = -1) \
+            -> np.ndarray:
+        """Calculate short-time Fourier transform with a trend being subtracted from
+        each segment beforehand.
+
+        When the parameter `detr` is ``None``, this method's behavior is identical to
+        the `~ShortTimeFFT.stft` method. Note that due to the detrending, the original
+        signal cannot be reconstructed by the `~ShortTimeFFT.istft`.
+
+        Parameters
+        ----------
+        x : np.ndarray
+            The input signal as real or complex valued array. For complex values, the
+            property `fft_mode` must be set to 'twosided' or 'centered'.
+        detr : 'linear' |  'constant' |  Callable[[np.ndarray], np.ndarray] | None
+            If 'constant', the mean is subtracted, if set to "linear", the linear
+            trend is removed from each segment. This is achieved by calling
+            `~scipy.signal.detrend`. If `detr` is a function with one parameter, `detr`
+            is applied to each segment.
+        p0 : int | None
+            The first element of the range of slices to calculate. If ``None``
+            then it is set to :attr:`p_min`, which is the smallest possible
+            slice.
+        p1 : int | None
+            The end of the array. If ``None`` then `p_max(n)` is used.
+        k_offset : int
+            Index of first sample (t = 0) in `x`.
+        padding : 'zeros' | 'edge' | 'even' | 'odd'
+            Kind of values which are added, when the sliding window sticks out
+            on either the lower or upper end of the input `x`. Zeros are added
+            if the default 'zeros' is set. For 'edge' either the first or the
+            last value of `x` is used. 'even' pads by reflecting the
+            signal on the first or last sample and 'odd' additionally
+            multiplies it with -1.
+        axis : int
+            The axis of `x` over which to compute the STFT.
+            If not given, the last axis is used.
+
+        Returns
+        -------
+        S : np.ndarray
+            A complex array is returned with the dimension always being larger
+            by one than of `x`. The last axis always represents the time slices
+            of the STFT. `axis` defines the frequency axis (default second to
+            last). E.g., for a one-dimensional `x`, a complex 2d array is
+            returned, with axis 0 representing frequency and axis 1 the time
+            slices.
+
+        See Also
+        --------
+        invertible: Check if STFT is invertible.
+        :meth:`~ShortTimeFFT.istft`: Inverse short-time Fourier transform.
+        :meth:`~ShortTimeFFT.stft`: Short-time Fourier transform
+                                   (without detrending).
+        :class:`scipy.signal.ShortTimeFFT`: Class this method belongs to.
+        """
+        if self.onesided_fft and np.iscomplexobj(x):
+            raise ValueError(f"Complex-valued `x` not allowed for {self.fft_mode=}'! "
+                             "Set property `fft_mode` to 'twosided' or 'centered'.")
+        if isinstance(detr, str):
+            detr = partial(detrend, type=detr)
+        elif not (detr is None or callable(detr)):
+            raise ValueError(f"Parameter {detr=} is not a str, function or " +
+                             "None!")
+        n = x.shape[axis]
+        if not (n >= (m2p := self.m_num-self.m_num_mid)):
+            e_str = f'{len(x)=}' if x.ndim == 1 else f'of {axis=} of {x.shape}'
+            raise ValueError(f"{e_str} must be >= ceil(m_num/2) = {m2p}!")
+
+        if x.ndim > 1:  # motivated by the NumPy broadcasting mechanisms:
+            x = np.moveaxis(x, axis, -1)
+        # determine slice index range:
+        p0, p1 = self.p_range(n, p0, p1)
+        S_shape_1d = (self.f_pts, p1 - p0)
+        S_shape = x.shape[:-1] + S_shape_1d if x.ndim > 1 else S_shape_1d
+        S = np.zeros(S_shape, dtype=complex)
+        for p_, x_ in enumerate(self._x_slices(x, k_offset, p0, p1, padding)):
+            if detr is not None:
+                x_ = detr(x_)
+            S[..., :, p_] = self._fft_func(x_ * self.win.conj())
+        if x.ndim > 1:
+            return np.moveaxis(S, -2, axis if axis >= 0 else axis-1)
+        return S
+
+    def spectrogram(self, x: np.ndarray, y: np.ndarray | None = None,
+                    detr: Callable[[np.ndarray], np.ndarray] | Literal['linear', 'constant'] | None = None,  # noqa: E501
+                    *,
+                    p0: int | None = None, p1: int | None = None,
+                    k_offset: int = 0, padding: PAD_TYPE = 'zeros',
+                    axis: int = -1) \
+            -> np.ndarray:
+        r"""Calculate spectrogram or cross-spectrogram.
+
+        The spectrogram is the absolute square of the STFT, i.e., it is
+        ``abs(S[q,p])**2`` for given ``S[q,p]`` and thus is always
+        non-negative.
+        For two STFTs ``Sx[q,p], Sy[q,p]``, the cross-spectrogram is defined
+        as ``Sx[q,p] * np.conj(Sy[q,p])`` and is complex-valued.
+        This is a convenience function for calling `~ShortTimeFFT.stft` /
+        `stft_detrend`, hence all parameters are discussed there.
+
+        Parameters
+        ----------
+        x : np.ndarray
+            The input signal as real or complex valued array. For complex values, the
+            property `fft_mode` must be set to 'twosided' or 'centered'.
+        y : np.ndarray
+            The second input signal of the same shape as `x`. If ``None``, it is
+            assumed to be `x`. For complex values, the property `fft_mode` must be
+            set to 'twosided' or 'centered'.
+        detr : 'linear' |  'constant' |  Callable[[np.ndarray], np.ndarray] | None
+            If 'constant', the mean is subtracted, if set to "linear", the linear
+            trend is removed from each segment. This is achieved by calling
+            `~scipy.signal.detrend`. If `detr` is a function with one parameter, `detr`
+            is applied to each segment. For ``None`` (default), no trends are removed.
+        p0 : int | None
+            The first element of the range of slices to calculate. If ``None``
+            then it is set to :attr:`p_min`, which is the smallest possible
+            slice.
+        p1 : int | None
+            The end of the array. If ``None`` then `p_max(n)` is used.
+        k_offset : int
+            Index of first sample (t = 0) in `x`.
+        padding : 'zeros' | 'edge' | 'even' | 'odd'
+            Kind of values which are added, when the sliding window sticks out
+            on either the lower or upper end of the input `x`. Zeros are added
+            if the default 'zeros' is set. For 'edge' either the first or the
+            last value of `x` is used. 'even' pads by reflecting the
+            signal on the first or last sample and 'odd' additionally
+            multiplies it with -1.
+        axis : int
+            The axis of `x` over which to compute the STFT.
+            If not given, the last axis is used.
+
+        Returns
+        -------
+        S_xy : np.ndarray
+            A real-valued array with non-negative values is returned, if ``x is y`` or
+            `y` is ``None``. The dimension is always by one larger than of `x`. The
+            last axis always represents the time slices of the spectrogram. `axis`
+            defines the frequency axis (default second to last). E.g., for a
+            one-dimensional `x`, a complex 2d array is returned, with axis 0
+            representing frequency and axis 1 the time slices.
+
+        See Also
+        --------
+        :meth:`~ShortTimeFFT.stft`: Perform the short-time Fourier transform.
+        stft_detrend: STFT with a trend subtracted from each segment.
+        :class:`scipy.signal.ShortTimeFFT`: Class this method belongs to.
+
+        Notes
+        -----
+        The cross-spectrogram may be interpreted as the time-frequency analogon of the
+        cross-spectral density (consult `csd`). The absolute square `|Sxy|²` of a
+        cross-spectrogram `Sxy` divided by the spectrograms `Sxx` and `Syy` can be
+        interpreted as a coherence spectrogram ``Cxy := abs(Sxy)**2 / (Sxx*Syy)``,
+        which is the time-frequency analogon to `~coherence`.
+
+        If the STFT is parametrized to be a unitary transform, i.e., utilitzing
+        `~from_win_equals_dual`, then the value of the scalar product, hence also the
+        energy, is preserved.
+
+        Examples
+        --------
+        The following example shows the spectrogram of a square wave with varying
+        frequency :math:`f_i(t)` (marked by a green dashed line in the plot) sampled
+        with 20 Hz. The utilized Gaussian window is 50 samples or 2.5 s long. For the
+        `ShortTimeFFT`, the parameter ``mfft=800`` (oversampling factor 16) and the
+        `hop` interval of 2 in was chosen to produce a sufficient number of points.
+
+        The plot's colormap is logarithmically scaled as the power spectral
+        density is in dB. The time extent of the signal `x` is marked by
+        vertical dashed lines, and the shaded areas mark the presence of border
+        effects.
+
+        >>> import matplotlib.pyplot as plt
+        >>> import numpy as np
+        >>> from scipy.signal import square, ShortTimeFFT
+        >>> from scipy.signal.windows import gaussian
+        ...
+        >>> T_x, N = 1 / 20, 1000  # 20 Hz sampling rate for 50 s signal
+        >>> t_x = np.arange(N) * T_x  # time indexes for signal
+        >>> f_i = 5e-3*(t_x - t_x[N // 3])**2 + 1  # varying frequency
+        >>> x = square(2*np.pi*np.cumsum(f_i)*T_x)  # the signal
+        ...
+        >>> g_std = 12  # standard deviation for Gaussian window in samples
+        >>> win = gaussian(50, std=g_std, sym=True)  # symmetric Gaussian wind.
+        >>> SFT = ShortTimeFFT(win, hop=2, fs=1/T_x, mfft=800, scale_to='psd')
+        >>> Sx2 = SFT.spectrogram(x)  # calculate absolute square of STFT
+        ...
+        >>> fig1, ax1 = plt.subplots(figsize=(6., 4.))  # enlarge plot a bit
+        >>> t_lo, t_hi = SFT.extent(N)[:2]  # time range of plot
+        >>> ax1.set_title(rf"Spectrogram ({SFT.m_num*SFT.T:g}$\,s$ Gaussian " +
+        ...               rf"window, $\sigma_t={g_std*SFT.T:g}\,$s)")
+        >>> ax1.set(xlabel=f"Time $t$ in seconds ({SFT.p_num(N)} slices, " +
+        ...                rf"$\Delta t = {SFT.delta_t:g}\,$s)",
+        ...         ylabel=f"Freq. $f$ in Hz ({SFT.f_pts} bins, " +
+        ...                rf"$\Delta f = {SFT.delta_f:g}\,$Hz)",
+        ...         xlim=(t_lo, t_hi))
+        >>> Sx_dB = 10 * np.log10(np.fmax(Sx2, 1e-4))  # limit range to -40 dB
+        >>> im1 = ax1.imshow(Sx_dB, origin='lower', aspect='auto',
+        ...                  extent=SFT.extent(N), cmap='magma')
+        >>> ax1.plot(t_x, f_i, 'g--', alpha=.5, label='$f_i(t)$')
+        >>> fig1.colorbar(im1, label='Power Spectral Density ' +
+        ...                          r"$20\,\log_{10}|S_x(t, f)|$ in dB")
+        ...
+        >>> # Shade areas where window slices stick out to the side:
+        >>> for t0_, t1_ in [(t_lo, SFT.lower_border_end[0] * SFT.T),
+        ...                  (SFT.upper_border_begin(N)[0] * SFT.T, t_hi)]:
+        ...     ax1.axvspan(t0_, t1_, color='w', linewidth=0, alpha=.3)
+        >>> for t_ in [0, N * SFT.T]:  # mark signal borders with vertical line
+        ...     ax1.axvline(t_, color='c', linestyle='--', alpha=0.5)
+        >>> ax1.legend()
+        >>> fig1.tight_layout()
+        >>> plt.show()
+
+        The logarithmic scaling reveals the odd harmonics of the square wave,
+        which are reflected at the Nyquist frequency of 10 Hz. This aliasing
+        is also the main source of the noise artifacts in the plot.
+        """
+        Sx = self.stft_detrend(x, detr, p0, p1, k_offset=k_offset,
+                               padding=padding, axis=axis)
+        if y is None or y is x:  # do spectrogram:
+            return Sx.real**2 + Sx.imag**2
+        # Cross-spectrogram:
+        Sy = self.stft_detrend(y, detr, p0, p1, k_offset=k_offset,
+                               padding=padding, axis=axis)
+        return Sx * Sy.conj()
+
+    @property
+    def dual_win(self) -> np.ndarray:
+        """Dual window (canonical dual window by default).
+
+        A STFT can be interpreted as the input signal being expressed as a
+        weighted sum of modulated and time-shifted dual windows. If no dual window is
+        given on instantiation, the canonical dual window, i.e., the window with the
+        minimal energy (i.e., minimal L²-norm) is calculated. Alternative means for
+        determining dual windows are provided by `closest_STFT_dual_window` and the
+        `from_win_equals_dual` class-method. Note that `win` is also always a
+        dual window of `dual_win`.
+
+        `dual_win` has same length as `win`, namely `m_num` samples.
+
+        If the dual window cannot be calculated a ``ValueError`` is raised.
+        This attribute is read only and calculated lazily.
+        To make this array immutable, its WRITEABLE flag is set to ``FALSE``.
+
+        See Also
+        --------
+        m_num: Number of samples in window `win` and `dual_win`.
+        win: Window function as real- or complex-valued 1d array.
+        from_win_equals_dual: Create instance where `win` and `dual_win` are equal.
+        closest_STFT_dual_window: Calculate dual window closest to a desired window.
+        numpy.ndarray.setflags: Modify array flags.
+        ShortTimeFFT: Class this property belongs to.
+        """
+        if self._dual_win is None:
+            self._dual_win = _calc_dual_canonical_window(self.win, self.hop)
+            self.dual_win.setflags(write=False)
+        return self._dual_win
+
+    @property
+    def invertible(self) -> bool:
+        """Check if STFT is invertible.
+
+        This is achieved by trying to calculate the canonical dual window.
+
+        See Also
+        --------
+        :meth:`~ShortTimeFFT.istft`: Inverse short-time Fourier transform.
+        m_num: Number of samples in window `win` and `dual_win`.
+        dual_win: Dual window.
+        win: Window for STFT.
+        ShortTimeFFT: Class this property belongs to.
+        """
+        try:
+            return len(self.dual_win) > 0  # call self.dual_win()
+        except ValueError:
+            return False
+
+    def istft(self, S: np.ndarray, k0: int = 0, k1: int | None = None, *,
+              f_axis: int = -2, t_axis: int = -1) \
+            -> np.ndarray:
+        """Inverse short-time Fourier transform.
+
+        Parameters
+        ----------
+        S : ndarray
+            A complex valued array where `f_axis` denotes the frequency
+            values and the `t_axis` dimension the temporal values of the
+            STFT values.
+        k0, k1 : int, optional
+            The start and the end index of the reconstructed signal. The
+            default (``k0 = 0``, ``k1 = None``) assumes that the maximum length
+            signal should be reconstructed.
+        f_axis, t_axis : int, optional
+            The axes in `S` denoting the frequency and the time dimension.
+
+        Returns
+        -------
+        ndarray
+            Array of dimension ``S.ndim - 1``  which is real if `onesided_fft` is set,
+            else complex.
+
+        Raises
+        ------
+        ValueError
+            If the STFT is not invertible, or the parameters are out of bounds.
+
+        See Also
+        --------
+        invertible: Check if STFT is invertible.
+        :meth:`~ShortTimeFFT.stft`: Perform Short-time Fourier transform.
+        :class:`scipy.signal.ShortTimeFFT`: Class this method belongs to.
+
+        Notes
+        -----
+        It is required that `S` has `f_pts` entries along the `f_axis`. For
+        the `t_axis` it is assumed that the first entry corresponds to
+        `p_min` * `delta_t` (being <= 0). The length of `t_axis` needs to be
+        compatible with `k1`. I.e., ``S.shape[t_axis] >= self.p_max(k1)`` must
+        hold, if `k1` is not ``None``. Else `k1` is set to `k_max` with::
+
+            q_max = S.shape[t_range] + self.p_min
+            k_max = (q_max - 1) * self.hop + self.m_num - self.m_num_mid
+
+        The :ref:`tutorial_stft` section of the :ref:`user_guide` discussed the
+        slicing behavior by means of an example.
+        """
+        if f_axis == t_axis:
+            raise ValueError(f"{f_axis=} may not be equal to {t_axis=}!")
+        if S.shape[f_axis] != self.f_pts:
+            raise ValueError(f"{S.shape[f_axis]=} must be equal to " +
+                             f"{self.f_pts=} ({S.shape=})!")
+        n_min = self.m_num-self.m_num_mid  # minimum signal length
+        if not (S.shape[t_axis] >= (q_num := self.p_num(n_min))):
+            raise ValueError(f"{S.shape[t_axis]=} needs to have at least " +
+                             f"{q_num} slices ({S.shape=})!")
+        if t_axis != S.ndim - 1 or f_axis != S.ndim - 2:
+            t_axis = S.ndim + t_axis if t_axis < 0 else t_axis
+            f_axis = S.ndim + f_axis if f_axis < 0 else f_axis
+            S = np.moveaxis(S, (f_axis, t_axis), (-2, -1))
+
+        q_max = S.shape[-1] + self.p_min
+        k_max = (q_max - 1) * self.hop + self.m_num - self.m_num_mid
+
+        k1 = k_max if k1 is None else k1
+        if not (self.k_min <= k0 < k1 <= k_max):
+            raise ValueError(f"({self.k_min=}) <= ({k0=}) < ({k1=}) <= " +
+                             f"({k_max=}) is false!")
+        if not (num_pts := k1 - k0) >= n_min:
+            raise ValueError(f"({k1=}) - ({k0=}) = {num_pts} has to be at " +
+                             f"least the half the window length {n_min}!")
+
+        q0 = (k0 // self.hop + self.p_min if k0 >= 0 else  # p_min always <= 0
+              k0 // self.hop)
+        q1 = min(self.p_max(k1), q_max)
+        k_q0, k_q1 = self.nearest_k_p(k0), self.nearest_k_p(k1, left=False)
+        n_pts = k_q1 - k_q0 + self.m_num - self.m_num_mid
+        x = np.zeros(S.shape[:-2] + (n_pts,),
+                     dtype=float if self.onesided_fft else complex)
+        for q_ in range(q0, q1):
+            xs = self._ifft_func(S[..., :, q_ - self.p_min]) * self.dual_win
+            i0 = q_ * self.hop - self.m_num_mid
+            i1 = min(i0 + self.m_num, n_pts+k0)
+            j0, j1 = 0, i1 - i0
+            if i0 < k0:  # xs sticks out to the left on x:
+                j0 += k0 - i0
+                i0 = k0
+            x[..., i0-k0:i1-k0] += xs[..., j0:j1]
+        x = x[..., :k1-k0]
+        if x.ndim > 1:
+            x = np.moveaxis(x, -1, f_axis if f_axis < x.ndim else t_axis)
+        return x
+
+    @property
+    def fac_magnitude(self) -> float:
+        """Factor to multiply the STFT values by to scale each frequency slice
+        to a magnitude spectrum.
+
+        It is 1 if attribute ``scaling == 'magnitude'``.
+        The window can be scaled to a magnitude spectrum by using the method
+        `scale_to`.
+
+        See Also
+        --------
+        fac_psd: Scaling factor for to a power spectral density spectrum.
+        scale_to: Scale window to obtain 'magnitude' or 'psd' scaling.
+        scaling: Normalization applied to the window function.
+        ShortTimeFFT: Class this property belongs to.
+        """
+        if self.scaling == 'magnitude':
+            return 1
+        if self._fac_mag is None:
+            self._fac_mag = 1 / abs(sum(self.win))
+        return self._fac_mag
+
+    @property
+    def fac_psd(self) -> float:
+        """Factor to multiply the STFT values by to scale each frequency slice
+        to a power spectral density (PSD).
+
+        It is 1 if attribute ``scaling == 'psd'``.
+        The window can be scaled to a psd spectrum by using the method
+        `scale_to`.
+
+        See Also
+        --------
+        fac_magnitude: Scaling factor for to a magnitude spectrum.
+        scale_to: Scale window to obtain 'magnitude' or 'psd' scaling.
+        scaling: Normalization applied to the window function.
+        ShortTimeFFT: Class this property belongs to.
+        """
+        if self.scaling == 'psd':
+            return 1
+        if self._fac_psd is None:
+            self._fac_psd = 1 / np.sqrt(
+                sum(self.win.real**2+self.win.imag**2) / self.T)
+        return self._fac_psd
+
+    @property
+    def m_num(self) -> int:
+        """Number of samples in window `win`.
+
+        Note that the FFT can be oversampled by zero-padding. This is achieved
+        by setting the `mfft` property.
+
+        See Also
+        --------
+        m_num_mid: Center index of window `win`.
+        mfft: Length of input for the FFT used - may be larger than `m_num`.
+        hop: Time increment in signal samples for sliding window.
+        win: Window function as real- or complex-valued 1d array.
+        ShortTimeFFT: Class this property belongs to.
+        """
+        return len(self.win)
+
+    @property
+    def m_num_mid(self) -> int:
+        """Center index of window `win`.
+
+        For odd `m_num`, ``(m_num - 1) / 2`` is returned and
+        for even `m_num` (per definition) ``m_num / 2`` is returned.
+
+        See Also
+        --------
+        m_num: Number of samples in window `win`.
+        mfft: Length of input for the FFT used - may be larger than `m_num`.
+        hop: ime increment in signal samples for sliding window.
+        win: Window function as real- or complex-valued 1d array.
+        ShortTimeFFT: Class this property belongs to.
+        """
+        return self.m_num // 2
+
+    @cached_property
+    def _pre_padding(self) -> tuple[int, int]:
+        """Smallest signal index and slice index due to padding.
+
+         Since, per convention, for time t=0, n,q is zero, the returned values
+         are negative or zero.
+         """
+        w2 = self.win.real**2 + self.win.imag**2
+        # move window to the left until the overlap with t >= 0 vanishes:
+        n0 = -self.m_num_mid
+        for p_, n_ in enumerate(range(n0, n0-self.m_num-1, -self.hop)):
+            n_next = n_ - self.hop
+            if n_next + self.m_num <= 0 or all(w2[n_next:] == 0):
+                return n_, -p_
+        # Make the linter happy:
+        raise RuntimeError("This code line should never run! Please file a bug.")
+
+    @property
+    def k_min(self) -> int:
+        """The smallest possible signal index of the STFT.
+
+        `k_min` is the index of the left-most non-zero value of the lowest
+        slice `p_min`. Since the zeroth slice is centered over the zeroth
+        sample of the input signal, `k_min` is never positive.
+        A detailed example is provided in the :ref:`tutorial_stft_sliding_win`
+        section of the :ref:`user_guide`.
+
+        See Also
+        --------
+        k_max: First sample index after signal end not touched by a time slice.
+        lower_border_end: Where pre-padding effects end.
+        p_min: The smallest possible slice index.
+        p_max: Index of first non-overlapping upper time slice.
+        p_num: Number of time slices, i.e., `p_max` - `p_min`.
+        p_range: Determine and validate slice index range.
+        upper_border_begin: Where post-padding effects start.
+        ShortTimeFFT: Class this property belongs to.
+        """
+        return self._pre_padding[0]
+
+    @property
+    def p_min(self) -> int:
+        """The smallest possible slice index.
+
+        `p_min` is the index of the left-most slice, where the window still
+        sticks into the signal, i.e., has non-zero part for t >= 0.
+        `k_min` is the smallest index where the window function of the slice
+        `p_min` is non-zero.
+
+        Since, per convention the zeroth slice is centered at t=0,
+        `p_min` <= 0 always holds.
+        A detailed example is provided in the :ref:`tutorial_stft_sliding_win`
+        section of the :ref:`user_guide`.
+
+        See Also
+        --------
+        k_min: The smallest possible signal index.
+        k_max: First sample index after signal end not touched by a time slice.
+        p_max: Index of first non-overlapping upper time slice.
+        p_num: Number of time slices, i.e., `p_max` - `p_min`.
+        p_range: Determine and validate slice index range.
+        ShortTimeFFT: Class this property belongs to.
+        """
+        return self._pre_padding[1]
+
+    def _post_padding(self, n: int) -> tuple[int, int]:
+        """Largest signal index and slice index due to padding.
+
+        Parameters
+        ----------
+        n : int
+            Number of samples of input signal (must be ≥ half of the window length).
+
+        Notes
+        -----
+        Note that the return values are cached together with the parameter `n` to avoid
+        unnecessary recalculations.
+        """
+        if not (n >= (m2p := self.m_num - self.m_num_mid)):
+            raise ValueError(f"Parameter n must be >= ceil(m_num/2) = {m2p}!")
+        last_arg, last_return_value = self._cache_post_padding
+        if n == last_arg:  # use cached value:
+            return last_return_value
+        w2 = self.win.real**2 + self.win.imag**2
+        # move window to the right until the overlap for t < t[n] vanishes:
+        q1 = n // self.hop   # last slice index with t[p1] <= t[n]
+        k1 = q1 * self.hop - self.m_num_mid
+        for q_, k_ in enumerate(range(k1, n+self.m_num, self.hop), start=q1):
+            n_next = k_ + self.hop
+            if n_next >= n or all(w2[:n-n_next] == 0):
+                return_value = k_ + self.m_num, q_ + 1
+                self._cache_post_padding = n, return_value
+                return return_value
+        raise RuntimeError("This code line should never run! Please file a bug.")
+        # If this case is reached, it probably means the last slice should be
+        # returned, i.e.: return k1 + self.m_num - self.m_num_mid, q1 + 1
+
+    def k_max(self, n: int) -> int:
+        """First sample index after signal end not touched by a time slice.
+
+        `k_max` - 1 is the largest sample index of the slice `p_max` - 1 for a
+        given input signal of `n` samples.
+        A detailed example is provided in the :ref:`tutorial_stft_sliding_win`
+        section of the :ref:`user_guide`.
+
+        Parameters
+        ----------
+        n : int
+            Number of samples of input signal (must be ≥ half of the window length).
+
+        Returns
+        -------
+        int
+            First sample index after signal end not touched by a time slice.
+
+        See Also
+        --------
+        k_min: The smallest possible signal index.
+        p_min: The smallest possible slice index.
+        p_max: Index of first non-overlapping upper time slice.
+        p_num: Number of time slices, i.e., `p_max` - `p_min`.
+        p_range: Determine and validate slice index range.
+        ShortTimeFFT: Class this method belongs to.
+        """
+        return self._post_padding(n)[0]
+
+    def p_max(self, n: int) -> int:
+        """Index of first non-overlapping upper time slice for `n` sample
+        input.
+
+        Note that center point t[p_max] = (p_max(n)-1) * `delta_t` is typically
+        larger than last time index t[n-1] == (`n`-1) * `T`. The upper border
+        of samples indexes covered by the window slices is given by `k_max`.
+        Furthermore, `p_max` does not denote the number of slices `p_num` since
+        `p_min` is typically less than zero.
+        A detailed example is provided in the :ref:`tutorial_stft_sliding_win`
+        section of the :ref:`user_guide`.
+
+        Parameters
+        ----------
+        n : int
+            Number of samples of input.
+
+        Returns
+        -------
+        int
+            Index of first non-overlapping upper time slice for `n` sample input.
+
+        See Also
+        --------
+        k_min: The smallest possible signal index.
+        k_max: First sample index after signal end not touched by a time slice.
+        p_min: The smallest possible slice index.
+        p_num: Number of time slices, i.e., `p_max` - `p_min`.
+        p_range: Determine and validate slice index range.
+        ShortTimeFFT: Class this method belongs to.
+        """
+        return self._post_padding(n)[1]
+
+    def p_num(self, n: int) -> int:
+        """Number of time slices for an input signal with `n` samples.
+
+        It is given by `p_num` = `p_max` - `p_min` with `p_min` typically
+        being negative.
+        A detailed example is provided in the :ref:`tutorial_stft_sliding_win`
+        section of the :ref:`user_guide`.
+
+        Parameters
+        ----------
+        n : int
+            Number of samples of input signal
+
+        Returns
+        -------
+        p_num : int
+            Number of time slices for input signal with `n` samples.
+
+        See Also
+        --------
+        k_min: The smallest possible signal index.
+        k_max: First sample index after signal end not touched by a time slice.
+        lower_border_end: Where pre-padding effects end.
+        p_min: The smallest possible slice index.
+        p_max: Index of first non-overlapping upper time slice.
+        p_range: Determine and validate slice index range.
+        upper_border_begin: Where post-padding effects start.
+        ShortTimeFFT: Class this method belongs to.
+        """
+        return self.p_max(n) - self.p_min
+
+    @property
+    def lower_border_end(self) -> tuple[int, int]:
+        """First signal index and first slice index unaffected by pre-padding.
+
+        Describes the point where the window does not stick out to the left
+        of the signal domain.
+        A detailed example is provided in the :ref:`tutorial_stft_sliding_win`
+        section of the :ref:`user_guide`.
+
+        See Also
+        --------
+        k_min: The smallest possible signal index.
+        k_max: First sample index after signal end not touched by a time slice.
+        lower_border_end: Where pre-padding effects end.
+        p_min: The smallest possible slice index.
+        p_max: Index of first non-overlapping upper time slice.
+        p_num: Number of time slices, i.e., `p_max` - `p_min`.
+        p_range: Determine and validate slice index range.
+        upper_border_begin: Where post-padding effects start.
+        ShortTimeFFT: Class this property belongs to.
+        """
+        if self._lower_border_end is not None:
+            return self._lower_border_end
+
+        # first non-zero element in self.win:
+        m0 = np.flatnonzero(self.win.real**2 + self.win.imag**2)[0]
+
+        # move window to the right until does not stick out to the left:
+        k0 = -self.m_num_mid + m0
+        for q_, k_ in enumerate(range(k0, self.hop + 1, self.hop)):
+            if k_ + self.hop >= 0:  # next entry does not stick out anymore
+                self._lower_border_end = (k_ + self.m_num, q_ + 1)
+                return self._lower_border_end
+        self._lower_border_end = (0, max(self.p_min, 0))  # ends at first slice
+        return self._lower_border_end
+
+    def upper_border_begin(self, n: int) -> tuple[int, int]:
+        """First signal index and first slice index affected by post-padding.
+
+        Describes the point where the window does begin stick out to the right
+        of the signal domain.
+        A detailed example is given :ref:`tutorial_stft_sliding_win` section
+        of the :ref:`user_guide`.
+
+        Parameters
+        ----------
+        n : int
+            Number of samples of input signal (must be ≥ half of the window length).
+
+        Returns
+        -------
+        k_ub : int
+            Lowest signal index, where a touching time slice sticks out past the
+            signal end.
+        p_ub : int
+            Lowest index of time slice of which the end sticks out past the signal end.
+
+        See Also
+        --------
+        k_min: The smallest possible signal index.
+        k_max: First sample index after signal end not touched by a time slice.
+        lower_border_end: Where pre-padding effects end.
+        p_min: The smallest possible slice index.
+        p_max: Index of first non-overlapping upper time slice.
+        p_num: Number of time slices, i.e., `p_max` - `p_min`.
+        p_range: Determine and validate slice index range.
+        ShortTimeFFT: Class this method belongs to.
+
+        Notes
+        -----
+        Note that the return values are cached together with the parameter `n` to avoid
+        unnecessary recalculations.
+        """
+        if not (n >= (m2p := self.m_num - self.m_num_mid)):
+            raise ValueError(f"Parameter n must be >= ceil(m_num/2) = {m2p}!")
+        last_arg, last_return_value = self._cache_upper_border_begin
+        if n == last_arg:  # use cached value:
+            return last_return_value
+        w2 = self.win.real**2 + self.win.imag**2
+        q2 = n // self.hop + 1  # first t[q] >= t[n]
+        q1 = max((n-self.m_num) // self.hop - 1, -1)
+        # move window left until does not stick out to the right:
+        for q_ in range(q2, q1, -1):
+            k_ = q_ * self.hop + (self.m_num - self.m_num_mid)
+            if k_ <= n or all(w2[n-k_:] == 0):
+                return_value = (q_ + 1) * self.hop - self.m_num_mid, q_ + 1
+                self. _cache_upper_border_begin = n, return_value
+                return return_value
+        # make linter happy:
+        raise RuntimeError("This code line should never run! Please file a bug.")
+
+    @property
+    def delta_t(self) -> float:
+        """Time increment of STFT.
+
+        The time increment `delta_t` = `T` * `hop` represents the sample
+        increment `hop` converted to time based on the sampling interval `T`.
+
+        See Also
+        --------
+        delta_f: Width of the frequency bins of the STFT.
+        hop: Hop size in signal samples for sliding window.
+        t: Times of STFT for an input signal with `n` samples.
+        T: Sampling interval of input signal and window `win`.
+        ShortTimeFFT: Class this property belongs to
+        """
+        return self.T * self.hop
+
+    def p_range(self, n: int, p0: int | None = None,
+                p1: int | None = None) -> tuple[int, int]:
+        """Determine and validate slice index range.
+
+        Parameters
+        ----------
+        n : int
+            Number of samples of input signal, assuming t[0] = 0.
+        p0 : int | None
+            First slice index. If 0 then the first slice is centered at t = 0.
+            If ``None`` then `p_min` is used. Note that p0 may be < 0 if
+            slices are left of t = 0.
+        p1 : int | None
+            End of interval (last value is p1-1).
+            If ``None`` then `p_max(n)` is used.
+
+
+        Returns
+        -------
+        p0_ : int
+            The fist slice index
+        p1_ : int
+            End of interval (last value is p1-1).
+
+        See Also
+        --------
+        k_min: The smallest possible signal index.
+        k_max: First sample index after signal end not touched by a time slice.
+        lower_border_end: Where pre-padding effects end.
+        p_min: The smallest possible slice index.
+        p_max: Index of first non-overlapping upper time slice.
+        p_num: Number of time slices, i.e., `p_max` - `p_min`.
+        upper_border_begin: Where post-padding effects start.
+        ShortTimeFFT: Class this property belongs to.
+
+        Notes
+        -----
+        A ``ValueError`` is raised if ``p_min <= p0 < p1 <= p_max(n)`` does not
+        hold.
+        """
+        p_max = self.p_max(n)  # shorthand
+        p0_ = self.p_min if p0 is None else p0
+        p1_ = p_max if p1 is None else p1
+        if not (self.p_min <= p0_ < p1_ <= p_max):
+            raise ValueError(f"Invalid Parameter {p0=}, {p1=}, i.e., " +
+                             f"{self.p_min=} <= p0 < p1 <= {p_max=} " +
+                             f"does not hold for signal length {n=}!")
+        return p0_, p1_
+
+    def t(self, n: int, p0: int | None = None, p1: int | None = None,
+          k_offset: int = 0) -> np.ndarray:
+        """Times of STFT for an input signal with `n` samples.
+
+        Returns a 1d array with times of the `~ShortTimeFFT.stft` values with
+        the same  parametrization. Note that the slices are
+        ``delta_t = hop * T`` time units apart.
+
+        Parameters
+        ----------
+        n : int
+            Number of sample of the input signal.
+        p0 : int, optional
+            The first element of the range of slices to calculate. If ``None``
+            then it is set to :attr:`p_min`, which is the smallest possible
+            slice.
+        p1 : int, optional
+            The end of the array. If ``None`` then `p_max(n)` is used.
+        k_offset : int
+            Index of first sample (t = 0) in `x`.
+
+        Returns
+        -------
+        t : ndarray
+            1D array of times of the STFT slices from `p0` to `p1` - 1.
+
+        See Also
+        --------
+        delta_t: Time increment of STFT (``hop*T``)
+        hop: Time increment in signal samples for sliding window.
+        nearest_k_p: Nearest sample index k_p for which t[k_p] == t[p] holds.
+        T: Sampling interval of input signal and of the window (``1/fs``).
+        fs: Sampling frequency (being ``1/T``)
+        ShortTimeFFT: Class this method belongs to.
+
+        Notes
+        -----
+        Note that the returned array is cached together with the method's call
+        parameters to avoid unnecessary recalculations.
+        """
+        if not (n > 0 and isinstance(n, int | np.integer)):
+            raise ValueError(f"Parameter {n=} is not a positive integer!")
+        args = n, p0, p1, k_offset, self.T  # since `self.T` is mutable, it's needed too
+        last_args, last_return_value = self._cache_t
+        if args == last_args:  # use cached value:
+            return last_return_value
+
+        p0, p1 = self.p_range(n, p0, p1)
+        return_value = np.arange(p0, p1) * self.delta_t + k_offset * self.T
+
+        self._cache_t = args, return_value
+        return return_value
+
+    def nearest_k_p(self, k: int, left: bool = True) -> int:
+        """Return nearest sample index k_p for which ``t[k_p] == t[p]`` holds.
+
+        The nearest next smaller time sample p (where ``t[p]`` is the center
+        position of the window of the p-th slice) is ``p_k = k // hop``.
+        If `hop` is a divisor of `k` then `k` is returned.
+        If `left` is set then ``p_k * hop`` is returned else ``(p_k+1) * hop``.
+
+        This method can be used to slice an input signal into chunks for
+        calculating the STFT and iSTFT incrementally.
+
+        Parameters
+        ----------
+        k : int
+            Sample index for which the nearest slice center index is sought.
+        left : bool, optional
+            If ``True`` then the nearest smaller index is returned, else the
+            nearest larger index is returned. Defaults to ``True``.
+
+        Returns
+        -------
+        int
+            Nearest sample index k_p for which ``t[k_p] == t[p]`` holds.
+
+        See Also
+        --------
+        delta_t: Time increment of STFT (``hop*T``)
+        hop: Time increment in signal samples for sliding window.
+        T: Sampling interval of input signal and of the window (``1/fs``).
+        fs: Sampling frequency (being ``1/T``)
+        t: Times of STFT for an input signal with `n` samples.
+        ShortTimeFFT: Class this method belongs to.
+        """
+        p_q, remainder = divmod(k, self.hop)
+        if remainder == 0:
+            return k
+        return p_q * self.hop if left else (p_q + 1) * self.hop
+
+    @property
+    def delta_f(self) -> float:
+        """Width of the frequency bins of the STFT.
+
+        Return the frequency interval `delta_f` = 1 / (`mfft` * `T`).
+
+        See Also
+        --------
+        delta_t: Time increment of STFT.
+        f_pts: Number of points along the frequency axis.
+        f: Frequencies values of the STFT.
+        mfft: Length of the input for FFT used.
+        T: Sampling interval.
+        t: Times of STFT for an input signal with `n` samples.
+        ShortTimeFFT: Class this property belongs to.
+        """
+        return 1 / (self.mfft * self.T)
+
+    @property
+    def f_pts(self) -> int:
+        """Number of points along the frequency axis.
+
+        See Also
+        --------
+        delta_f: Width of the frequency bins of the STFT.
+        f: Frequencies values of the STFT.
+        mfft: Length of the input for FFT used.
+        ShortTimeFFT: Class this property belongs to.
+        """
+        return self.mfft // 2 + 1 if self.onesided_fft else self.mfft
+
+    @property
+    def onesided_fft(self) -> bool:
+        """Return True if a one-sided FFT is used.
+
+        Returns ``True`` if `fft_mode` is either 'onesided' or 'onesided2X'.
+
+        See Also
+        --------
+        fft_mode: Utilized FFT ('twosided', 'centered', 'onesided' or
+                 'onesided2X')
+        ShortTimeFFT: Class this property belongs to.
+        """
+        return self.fft_mode in {'onesided', 'onesided2X'}
+
+    @property
+    def f(self) -> np.ndarray:
+        """Frequencies values of the STFT.
+
+        A 1d array of length `f_pts` with `delta_f` spaced entries is returned.
+        This array is calculated lazily.
+
+        See Also
+        --------
+        delta_f: Width of the frequency bins of the STFT.
+        f_pts: Number of points along the frequency axis.
+        mfft: Length of the input for FFT used.
+        ShortTimeFFT: Class this property belongs to.
+        """
+        last_state, last_return_value = self._cache_f
+        current_state = self.fft_mode, self.mfft, self.T
+        if current_state == last_state:  # use cached value:
+            return last_return_value
+
+        if self.fft_mode in {'onesided', 'onesided2X'}:
+            return_value = fft_lib.rfftfreq(self.mfft, self.T)
+        elif self.fft_mode == 'twosided':
+            return_value = fft_lib.fftfreq(self.mfft, self.T)
+        elif self.fft_mode == 'centered':
+            return_value = fft_lib.fftshift(fft_lib.fftfreq(self.mfft, self.T))
+        else:  # This should never happen but makes the Linters happy:
+            fft_modes = get_args(FFT_MODE_TYPE)
+            raise RuntimeError(f"{self.fft_mode=} not in {fft_modes}!")
+        self._cache_f = current_state, return_value
+        return return_value
+
+    def _fft_func(self, x: np.ndarray) -> np.ndarray:
+        """FFT based on the `fft_mode`, `mfft`, `scaling` and `phase_shift`
+        attributes.
+
+        For multidimensional arrays the transformation is carried out on the
+        last axis.
+        """
+        if self.phase_shift is not None:
+            if x.shape[-1] < self.mfft:  # zero pad if needed
+                z_shape = list(x.shape)
+                z_shape[-1] = self.mfft - x.shape[-1]
+                x = np.hstack((x, np.zeros(z_shape, dtype=x.dtype)))
+            p_s = (self.phase_shift + self.m_num_mid) % self.m_num
+            x = np.roll(x, -p_s, axis=-1)
+
+        if self.fft_mode == 'twosided':
+            return fft_lib.fft(x, n=self.mfft, axis=-1)
+        if self.fft_mode == 'centered':
+            return fft_lib.fftshift(fft_lib.fft(x, self.mfft, axis=-1), axes=-1)
+        if self.fft_mode == 'onesided':
+            return fft_lib.rfft(x, n=self.mfft, axis=-1)
+        if self.fft_mode == 'onesided2X':
+            X = fft_lib.rfft(x, n=self.mfft, axis=-1)
+            # Either squared magnitude (psd) or magnitude is doubled:
+            fac = np.sqrt(2) if self.scaling == 'psd' else 2
+            # For even input length, the last entry is unpaired:
+            X[..., 1: -1 if self.mfft % 2 == 0 else None] *= fac
+            return X
+        # This should never happen but makes the Linter happy:
+        fft_modes = get_args(FFT_MODE_TYPE)
+        raise RuntimeError(f"{self.fft_mode=} not in {fft_modes}!")
+
+    def _ifft_func(self, X: np.ndarray) -> np.ndarray:
+        """Inverse to `_fft_func`.
+
+        Returned is an array of length `m_num`. If the FFT is `onesided`
+        then a float array is returned else a complex array is returned.
+        For multidimensional arrays the transformation is carried out on the
+        last axis.
+        """
+        if self.fft_mode == 'twosided':
+            x = fft_lib.ifft(X, n=self.mfft, axis=-1)
+        elif self.fft_mode == 'centered':
+            x = fft_lib.ifft(fft_lib.ifftshift(X, axes=-1), n=self.mfft, axis=-1)
+        elif self.fft_mode == 'onesided':
+            x = fft_lib.irfft(X, n=self.mfft, axis=-1)
+        elif self.fft_mode == 'onesided2X':
+            Xc = X.copy()  # we do not want to modify function parameters
+            fac = np.sqrt(2) if self.scaling == 'psd' else 2
+            # For even length X the last value is not paired with a negative
+            # value on the two-sided FFT:
+            q1 = -1 if self.mfft % 2 == 0 else None
+            Xc[..., 1:q1] /= fac
+            x = fft_lib.irfft(Xc, n=self.mfft, axis=-1)
+        else:  # This should never happen but makes the Linter happy:
+            raise RuntimeError(f"{self.fft_mode=} not in {get_args(FFT_MODE_TYPE)}!")
+
+        if self.phase_shift is None:
+            return x[..., :self.m_num]
+        p_s = (self.phase_shift + self.m_num_mid) % self.m_num
+        return np.roll(x, p_s, axis=-1)[..., :self.m_num]
+
+    def extent(self, n: int, axes_seq: Literal['tf', 'ft'] = 'tf',
+               center_bins: bool = False) -> tuple[float, float, float, float]:
+        """Return minimum and maximum values time-frequency values.
+
+        Parameters
+        ----------
+        n : int
+            Number of samples in input signal.
+        axes_seq : {'tf', 'ft'}
+            Return time extent first and then frequency extent or vice versa.
+        center_bins : bool
+            If set (default ``False``), the values of the time slots and
+            frequency bins are moved from the side the middle. This is useful,
+            when plotting the `~ShortTimeFFT.stft` values as step functions,
+            i.e., with no interpolation.
+
+        Returns
+        -------
+        tuple
+            A tuple with four floats  ``(t0, t1, f0, f1)`` for 'tf' and
+            ``(f0, f1, t0, t1)`` for 'ft' is returned describing the corners
+            of the time-frequency domain of the `~ShortTimeFFT.stft`.
+            That tuple can be passed to `matplotlib.pyplot.imshow` as a parameter
+            with the same name.
+
+        See Also
+        --------
+        :func:`matplotlib.pyplot.imshow`: Display data as an image.
+        :class:`scipy.signal.ShortTimeFFT`: Class this method belongs to.
+
+        Examples
+        --------
+        The following two plots illustrate the effect of the parameter `center_bins`:
+        The grid lines represent the three time and the four frequency values of the
+        STFT.
+        The left plot, where ``(t0, t1, f0, f1) = (0, 3, 0, 4)`` is passed as parameter
+        ``extent`` to `~matplotlib.pyplot.imshow`, shows the standard behavior of the
+        time and frequency values being at the lower edge of the corrsponding bin.
+        The right plot, with ``(t0, t1, f0, f1) = (-0.5, 2.5, -0.5, 3.5)``, shows that
+        the bins are centered over the respective values when passing
+        ``center_bins=True``.
+
+        >>> import matplotlib.pyplot as plt
+        >>> import numpy as np
+        >>> from scipy.signal import ShortTimeFFT
+        ...
+        >>> n, m = 12, 6
+        >>> SFT = ShortTimeFFT.from_window('hann', fs=m, nperseg=m, noverlap=0)
+        >>> Sxx = SFT.stft(np.cos(np.arange(n)))  # produces a colorful plot
+        ...
+        >>> fig, axx = plt.subplots(1, 2, tight_layout=True, figsize=(6., 4.))
+        >>> for ax_, center_bins in zip(axx, (False, True)):
+        ...     ax_.imshow(abs(Sxx), origin='lower', interpolation=None, aspect='equal',
+        ...                cmap='viridis', extent=SFT.extent(n, 'tf', center_bins))
+        ...     ax_.set_title(f"{center_bins=}")
+        ...     ax_.set_xlabel(f"Time ({SFT.p_num(n)} points, Δt={SFT.delta_t})")
+        ...     ax_.set_ylabel(f"Frequency ({SFT.f_pts} points, Δf={SFT.delta_f})")
+        ...     ax_.set_xticks(SFT.t(n))  # vertical grid line are timestamps
+        ...     ax_.set_yticks(SFT.f)  # horizontal grid line are frequency values
+        ...     ax_.grid(True)
+        >>> plt.show()
+
+        Note that the step-like behavior with the constant colors is caused by passing
+        ``interpolation=None`` to `~matplotlib.pyplot.imshow`.
+        """
+        if axes_seq not in ('tf', 'ft'):
+            raise ValueError(f"Parameter {axes_seq=} not in ['tf', 'ft']!")
+
+        if self.onesided_fft:
+            q0, q1 = 0, self.f_pts
+        elif self.fft_mode == 'centered':
+            q0 = -(self.mfft // 2)
+            q1 = self.mfft // 2 if self.mfft % 2 == 0 else self.mfft // 2 + 1
+        else:
+            raise ValueError(f"Attribute fft_mode={self.fft_mode} must be " +
+                             "in ['centered', 'onesided', 'onesided2X']")
+
+        p0, p1 = self.p_min, self.p_max(n)  # shorthand
+        if center_bins:
+            t0, t1 = self.delta_t * (p0 - 0.5), self.delta_t * (p1 - 0.5)
+            f0, f1 = self.delta_f * (q0 - 0.5), self.delta_f * (q1 - 0.5)
+        else:
+            t0, t1 = self.delta_t * p0, self.delta_t * p1
+            f0, f1 = self.delta_f * q0, self.delta_f * q1
+        return (t0, t1, f0, f1) if axes_seq == 'tf' else (f0, f1, t0, t1)
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/_signal_api.py b/venv/lib/python3.12/site-packages/scipy/signal/_signal_api.py
new file mode 100644
index 0000000000000000000000000000000000000000..68d19aaf9be016666f20b78e97bebe8e7fd14d85
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/_signal_api.py
@@ -0,0 +1,31 @@
+"""This is the 'bare' scipy.signal API.
+
+This --- private! --- module only collects implementations of public  API
+for _support_alternative_backends.
+The latter --- also private! --- module adds delegation to CuPy etc and
+re-exports decorated names to __init__.py
+"""
+
+from . import _sigtools, windows         # noqa: F401
+from ._waveforms import *        # noqa: F403
+from ._max_len_seq import max_len_seq       # noqa: F401
+from ._upfirdn import upfirdn         # noqa: F401
+
+from ._spline import sepfir2d          # noqa: F401
+
+from ._spline_filters import *         # noqa: F403
+from ._filter_design import *         # noqa: F403
+from ._fir_filter_design import *         # noqa: F403
+from ._ltisys import *         # noqa: F403
+from ._lti_conversion import *         # noqa: F403
+from ._signaltools import *         # noqa: F403
+from ._savitzky_golay import savgol_coeffs, savgol_filter  # noqa: F401
+from ._spectral_py import *         # noqa: F403
+from ._short_time_fft import *         # noqa: F403
+from ._peak_finding import *         # noqa: F403
+from ._czt import *         # noqa: F403
+from ._whittaker import whittaker_henderson  # noqa: F401
+from .windows import get_window  # keep this one in signal namespace  # noqa: F401
+
+
+__all__ = [s for s in dir() if not s.startswith('_')]
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/_signaltools.py b/venv/lib/python3.12/site-packages/scipy/signal/_signaltools.py
new file mode 100644
index 0000000000000000000000000000000000000000..a230802509a329f5e431d63c8f3766557ab311e9
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/_signaltools.py
@@ -0,0 +1,5369 @@
+# Author: Travis Oliphant
+# 1999 -- 2002
+
+import operator
+import math
+from math import prod as _prod
+import timeit
+import warnings
+from typing import Literal
+
+from numpy._typing import ArrayLike
+
+from scipy.spatial import cKDTree
+from . import _sigtools
+from ._ltisys import dlti
+from ._upfirdn import upfirdn, _output_len, _upfirdn_modes
+from scipy import linalg, fft as sp_fft
+from scipy import ndimage
+from scipy.fft._helper import _init_nd_shape_and_axes
+import numpy as np
+from scipy.special import lambertw
+from .windows import get_window
+from ._arraytools import axis_slice, axis_reverse, odd_ext, even_ext, const_ext
+from ._filter_design import cheby1, _validate_sos, zpk2sos
+from ._fir_filter_design import firwin
+from ._sosfilt import _sosfilt
+
+from scipy._lib._array_api import (
+    array_namespace, is_torch, is_numpy, xp_copy, xp_size, xp_default_dtype,
+    xp_promote, xp_swapaxes,)
+from scipy._external.array_api_compat import is_array_api_obj
+import scipy._external.array_api_extra as xpx
+
+
+__all__ = ['correlate', 'correlation_lags', 'correlate2d',
+           'convolve', 'convolve2d', 'fftconvolve', 'oaconvolve',
+           'order_filter', 'medfilt', 'medfilt2d', 'wiener', 'lfilter',
+           'lfiltic', 'sosfilt', 'deconvolve', 'hilbert', 'hilbert2', 'envelope',
+           'unique_roots', 'invres', 'invresz', 'residue',
+           'residuez', 'resample', 'resample_poly', 'detrend',
+           'lfilter_zi', 'sosfilt_zi', 'sosfiltfilt', 'choose_conv_method',
+           'filtfilt', 'decimate', 'vectorstrength']
+
+
+_modedict = {'valid': 0, 'same': 1, 'full': 2}
+
+_boundarydict = {'fill': 0, 'pad': 0, 'wrap': 2, 'circular': 2, 'symm': 1,
+                 'symmetric': 1, 'reflect': 4}
+
+
+def _valfrommode(mode):
+    try:
+        return _modedict[mode]
+    except KeyError as e:
+        raise ValueError("Acceptable mode flags are 'valid',"
+                         " 'same', or 'full'.") from e
+
+
+def _bvalfromboundary(boundary):
+    try:
+        return _boundarydict[boundary] << 2
+    except KeyError as e:
+        raise ValueError("Acceptable boundary flags are 'fill', 'circular' "
+                         "(or 'wrap'), and 'symmetric' (or 'symm').") from e
+
+
+def _inputs_swap_needed(mode, shape1, shape2, axes=None):
+    """Determine if inputs arrays need to be swapped in `"valid"` mode.
+
+    If in `"valid"` mode, returns whether or not the input arrays need to be
+    swapped depending on whether `shape1` is at least as large as `shape2` in
+    every calculated dimension.
+
+    This is important for some of the correlation and convolution
+    implementations in this module, where the larger array input needs to come
+    before the smaller array input when operating in this mode.
+
+    Note that if the mode provided is not 'valid', False is immediately
+    returned.
+
+    """
+    if mode != 'valid':
+        return False
+
+    if not shape1:
+        return False
+
+    if axes is None:
+        axes = range(len(shape1))
+
+    ok1 = all(shape1[i] >= shape2[i] for i in axes)
+    ok2 = all(shape2[i] >= shape1[i] for i in axes)
+
+    if not (ok1 or ok2):
+        raise ValueError("For 'valid' mode, one must be at least "
+                         "as large as the other in every dimension")
+
+    return not ok1
+
+
+def correlate(in1, in2, mode='full', method='auto'):
+    r"""
+    Cross-correlate two N-dimensional arrays.
+
+    Cross-correlate `in1` and `in2`, with the output size determined by the
+    `mode` argument.
+
+    Parameters
+    ----------
+    in1 : array_like
+        First input.
+    in2 : array_like
+        Second input. Should have the same number of dimensions as `in1`.
+    mode : str {'full', 'valid', 'same'}, optional
+        A string indicating the size of the output:
+
+        ``full``
+           The output is the full discrete linear cross-correlation
+           of the inputs. (Default)
+        ``valid``
+           The output consists only of those elements that do not
+           rely on the zero-padding. In 'valid' mode, either `in1` or `in2`
+           must be at least as large as the other in every dimension.
+        ``same``
+           Output size will be ``N``, the same size as `in1`, centered
+           with respect to the 'full' output.
+           Boundary effects may be visible.
+    method : str {'auto', 'direct', 'fft'}, optional
+        A string indicating which method to use to calculate the correlation.
+
+        ``direct``
+           The correlation is determined directly from sums, the definition of
+           correlation.
+        ``fft``
+           The Fast Fourier Transform is used to perform the correlation more
+           quickly (only available for numerical arrays.)
+        ``auto``
+           Automatically chooses direct or Fourier method based on an estimate
+           of which is faster (default).  See `convolve` Notes for more detail.
+
+           .. versionadded:: 0.19.0
+
+    Returns
+    -------
+    correlate : array
+        An N-dimensional array containing a subset of the discrete linear
+        cross-correlation of `in1` with `in2`.
+
+    See Also
+    --------
+    choose_conv_method : contains more documentation on `method`.
+    correlation_lags : calculates the lag / displacement indices array for 1D
+        cross-correlation.
+
+    Notes
+    -----
+    The correlation z of two d-dimensional arrays x and y is defined as::
+
+        z[...,k,...] = sum[..., i_l, ...] x[..., i_l,...] * conj(y[..., i_l - k,...])
+
+    This way, if ``x`` and ``y`` are 1-D arrays and ``z = correlate(x, y, 'full')``
+    then
+
+    .. math::
+
+          z[k] = \sum_{l=0}^{N-1} x_l \, y_{l-k}^{*}
+
+    for :math:`k = -(M-1), \dots, (N-1)`, where :math:`N` is the length of ``x``,
+    :math:`M` is the length of ``y``, and :math:`y_m = 0` when :math:`m` is outside the
+    valid range :math:`[0, M-1]`. The size of :math:`z` is :math:`N + M - 1` and
+    :math:`y^*` denotes the complex conjugate of :math:`y`.
+
+    ``method='fft'`` only works for numerical arrays as it relies on
+    `fftconvolve`. In certain cases (i.e., arrays of objects or when
+    rounding integers can lose precision), ``method='direct'`` is always used.
+
+    When using ``mode='same'`` with even-length inputs, the outputs of `correlate`
+    and `correlate2d` differ: There is a 1-index offset between them.
+
+    Examples
+    --------
+    Implement a matched filter using cross-correlation, to recover a signal
+    that has passed through a noisy channel.
+
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+    >>> rng = np.random.default_rng()
+
+    >>> sig = np.repeat([0., 1., 1., 0., 1., 0., 0., 1.], 128)
+    >>> sig_noise = sig + rng.standard_normal(len(sig))
+    >>> corr = signal.correlate(sig_noise, np.ones(128), mode='same') / 128
+
+    >>> clock = np.arange(64, len(sig), 128)
+    >>> fig, (ax_orig, ax_noise, ax_corr) = plt.subplots(3, 1, sharex=True)
+    >>> ax_orig.plot(sig)
+    >>> ax_orig.plot(clock, sig[clock], 'ro')
+    >>> ax_orig.set_title('Original signal')
+    >>> ax_noise.plot(sig_noise)
+    >>> ax_noise.set_title('Signal with noise')
+    >>> ax_corr.plot(corr)
+    >>> ax_corr.plot(clock, corr[clock], 'ro')
+    >>> ax_corr.axhline(0.5, ls=':')
+    >>> ax_corr.set_title('Cross-correlated with rectangular pulse')
+    >>> ax_orig.margins(0, 0.1)
+    >>> fig.tight_layout()
+    >>> plt.show()
+
+    Compute the cross-correlation of a noisy signal with the original signal.
+
+    >>> x = np.arange(128) / 128
+    >>> sig = np.sin(2 * np.pi * x)
+    >>> sig_noise = sig + rng.standard_normal(len(sig))
+    >>> corr = signal.correlate(sig_noise, sig)
+    >>> lags = signal.correlation_lags(len(sig), len(sig_noise))
+    >>> corr /= np.max(corr)
+
+    >>> fig, (ax_orig, ax_noise, ax_corr) = plt.subplots(3, 1, figsize=(4.8, 4.8))
+    >>> ax_orig.plot(sig)
+    >>> ax_orig.set_title('Original signal')
+    >>> ax_orig.set_xlabel('Sample Number')
+    >>> ax_noise.plot(sig_noise)
+    >>> ax_noise.set_title('Signal with noise')
+    >>> ax_noise.set_xlabel('Sample Number')
+    >>> ax_corr.plot(lags, corr)
+    >>> ax_corr.set_title('Cross-correlated signal')
+    >>> ax_corr.set_xlabel('Lag')
+    >>> ax_orig.margins(0, 0.1)
+    >>> ax_noise.margins(0, 0.1)
+    >>> ax_corr.margins(0, 0.1)
+    >>> fig.tight_layout()
+    >>> plt.show()
+
+    """
+    xp = array_namespace(in1, in2)
+
+    in1 = xp.asarray(in1)
+    in2 = xp.asarray(in2)
+
+    if in1.ndim == in2.ndim == 0:
+        in2_conj = (xp.conj(in2)
+                    if xp.isdtype(in2.dtype, 'complex floating')
+                    else in2)
+        return in1 * in2_conj
+    elif in1.ndim != in2.ndim:
+        raise ValueError("in1 and in2 should have the same dimensionality")
+
+    # Don't use _valfrommode, since correlate should not accept numeric modes
+    try:
+        val = _modedict[mode]
+    except KeyError as e:
+        raise ValueError("Acceptable mode flags are 'valid',"
+                         " 'same', or 'full'.") from e
+
+    # this either calls fftconvolve or this function with method=='direct'
+    if method in ('fft', 'auto'):
+        return convolve(in1, _reverse_and_conj(in2, xp), mode, method)
+
+    elif method == 'direct':
+        # fastpath to faster numpy.correlate for 1d inputs when possible
+        if _np_conv_ok(in1, in2, mode, xp):
+            a_in1 = np.asarray(in1)
+            a_in2 = np.asarray(in2)
+            out = np.correlate(a_in1, a_in2, mode)
+            return xp.asarray(out)
+
+        # _correlateND is far slower when in2.size > in1.size, so swap them
+        # and then undo the effect afterward if mode == 'full'.  Also, it fails
+        # with 'valid' mode if in2 is larger than in1, so swap those, too.
+        # Don't swap inputs for 'same' mode, since shape of in1 matters.
+        swapped_inputs = ((mode == 'full') and (xp_size(in2) > xp_size(in1)) or
+                          _inputs_swap_needed(mode, in1.shape, in2.shape))
+
+        if swapped_inputs:
+            in1, in2 = in2, in1
+
+        # convert to numpy & back for _sigtools._correlateND
+        a_in1 = np.asarray(in1)
+        a_in2 = np.asarray(in2)
+
+        if mode == 'valid':
+            ps = [i - j + 1 for i, j in zip(in1.shape, in2.shape)]
+            out = np.empty(ps, a_in1.dtype)
+
+            z = _sigtools._correlateND(a_in1, a_in2, out, val)
+
+        else:
+            ps = [i + j - 1 for i, j in zip(in1.shape, in2.shape)]
+
+            # zero pad input
+            in1zpadded = np.zeros(ps, a_in1.dtype)
+            sc = tuple(slice(0, i) for i in in1.shape)
+            in1zpadded[sc] = a_in1.copy()
+
+            if mode == 'full':
+                out = np.empty(ps, a_in1.dtype)
+            elif mode == 'same':
+                out = np.empty(in1.shape, a_in1.dtype)
+
+            z = _sigtools._correlateND(in1zpadded, a_in2, out, val)
+
+        z = xp.asarray(z)
+
+        if swapped_inputs:
+            # Reverse and conjugate to undo the effect of swapping inputs
+            z = _reverse_and_conj(z, xp)
+
+        return z
+
+    else:
+        raise ValueError("Acceptable method flags are 'auto',"
+                         " 'direct', or 'fft'.")
+
+
+def correlation_lags(in1_len, in2_len, mode='full'):
+    r"""
+    Calculates the lag / displacement indices array for 1D cross-correlation.
+
+    Parameters
+    ----------
+    in1_len : int
+        First input size.
+    in2_len : int
+        Second input size.
+    mode : str {'full', 'valid', 'same'}, optional
+        A string indicating the size of the output.
+        See the documentation `correlate` for more information.
+
+    Returns
+    -------
+    lags : array
+        Returns an array containing cross-correlation lag/displacement indices.
+        Indices can be indexed with the np.argmax of the correlation to return
+        the lag/displacement.
+
+    See Also
+    --------
+    correlate : Compute the N-dimensional cross-correlation.
+
+    Notes
+    -----
+    Cross-correlation for continuous functions :math:`f` and :math:`g` is
+    defined as:
+
+    .. math::
+
+        \left ( f\star g \right )\left ( \tau \right )
+        \triangleq \int_{t_0}^{t_0 +T}
+        \overline{f\left ( t \right )}g\left ( t+\tau \right )dt
+
+    Where :math:`\tau` is defined as the displacement, also known as the lag.
+
+    Cross correlation for discrete functions :math:`f` and :math:`g` is
+    defined as:
+
+    .. math::
+        \left ( f\star g \right )\left [ n \right ]
+        \triangleq \sum_{-\infty}^{\infty}
+        \overline{f\left [ m \right ]}g\left [ m+n \right ]
+
+    Where :math:`n` is the lag.
+
+    Examples
+    --------
+    Cross-correlation of a signal with its time-delayed self.
+
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> rng = np.random.default_rng()
+    >>> x = rng.standard_normal(1000)
+    >>> y = np.concatenate([rng.standard_normal(100), x])
+    >>> correlation = signal.correlate(x, y, mode="full")
+    >>> lags = signal.correlation_lags(x.size, y.size, mode="full")
+    >>> lag = lags[np.argmax(correlation)]
+    """
+
+    # calculate lag ranges in different modes of operation
+    if mode == "full":
+        # the output is the full discrete linear convolution
+        # of the inputs. (Default)
+        lags = np.arange(-in2_len + 1, in1_len)
+    elif mode == "same":
+        # the output is the same size as `in1`, centered
+        # with respect to the 'full' output.
+        # calculate the full output
+        lags = np.arange(-in2_len + 1, in1_len)
+        # determine the midpoint in the full output
+        mid = lags.size // 2
+        # determine lag_bound to be used with respect
+        # to the midpoint
+        lag_bound = in1_len // 2
+        # calculate lag ranges for even and odd scenarios
+        if in1_len % 2 == 0:
+            lags = lags[(mid-lag_bound):(mid+lag_bound)]
+        else:
+            lags = lags[(mid-lag_bound):(mid+lag_bound)+1]
+    elif mode == "valid":
+        # the output consists only of those elements that do not
+        # rely on the zero-padding. In 'valid' mode, either `in1` or `in2`
+        # must be at least as large as the other in every dimension.
+
+        # the lag_bound will be either negative or positive
+        # this let's us infer how to present the lag range
+        lag_bound = in1_len - in2_len
+        if lag_bound >= 0:
+            lags = np.arange(lag_bound + 1)
+        else:
+            lags = np.arange(lag_bound, 1)
+    else:
+        raise ValueError(f"Mode {mode} is invalid")
+    return lags
+
+
+def _centered(arr, newshape):
+    # Return the center newshape portion of the array.
+    newshape = np.asarray(newshape)
+    currshape = np.array(arr.shape)
+    startind = (currshape - newshape) // 2
+    endind = startind + newshape
+    myslice = [slice(startind[k], endind[k]) for k in range(len(endind))]
+    return arr[tuple(myslice)]
+
+
+def _init_freq_conv_axes(in1, in2, mode, axes, sorted_axes=False):
+    """Handle the axes argument for frequency-domain convolution.
+
+    Returns the inputs and axes in a standard form, eliminating redundant axes,
+    swapping the inputs if necessary, and checking for various potential
+    errors.
+
+    Parameters
+    ----------
+    in1 : array
+        First input.
+    in2 : array
+        Second input.
+    mode : str {'full', 'valid', 'same'}, optional
+        A string indicating the size of the output.
+        See the documentation `fftconvolve` for more information.
+    axes : list of ints
+        Axes over which to compute the FFTs.
+    sorted_axes : bool, optional
+        If `True`, sort the axes.
+        Default is `False`, do not sort.
+
+    Returns
+    -------
+    in1 : array
+        The first input, possible swapped with the second input.
+    in2 : array
+        The second input, possible swapped with the first input.
+    axes : list of ints
+        Axes over which to compute the FFTs.
+
+    """
+    s1 = in1.shape
+    s2 = in2.shape
+    noaxes = axes is None
+
+    _, axes = _init_nd_shape_and_axes(in1, shape=None, axes=axes)
+
+    if not noaxes and not len(axes):
+        raise ValueError("when provided, axes cannot be empty")
+
+    # Axes of length 1 can rely on broadcasting rules for multiply,
+    # no fft needed.
+    axes = [a for a in axes if s1[a] != 1 and s2[a] != 1]
+
+    if sorted_axes:
+        axes.sort()
+
+    if not all(s1[a] == s2[a] or s1[a] == 1 or s2[a] == 1
+               for a in range(in1.ndim) if a not in axes):
+        raise ValueError("incompatible shapes for in1 and in2:"
+                         f" {s1} and {s2}")
+
+    # Check that input sizes are compatible with 'valid' mode.
+    if _inputs_swap_needed(mode, s1, s2, axes=axes):
+        # Convolution is commutative; order doesn't have any effect on output.
+        in1, in2 = in2, in1
+
+    return in1, in2, axes
+
+
+def _freq_domain_conv(xp, in1, in2, axes, shape, calc_fast_len=False):
+    """Convolve two arrays in the frequency domain.
+
+    This function implements only base the FFT-related operations.
+    Specifically, it converts the signals to the frequency domain, multiplies
+    them, then converts them back to the time domain.  Calculations of axes,
+    shapes, convolution mode, etc. are implemented in higher level-functions,
+    such as `fftconvolve` and `oaconvolve`.  Those functions should be used
+    instead of this one.
+
+    Parameters
+    ----------
+    in1 : array_like
+        First input.
+    in2 : array_like
+        Second input. Should have the same number of dimensions as `in1`.
+    axes : array_like of ints
+        Axes over which to compute the FFTs.
+    shape : array_like of ints
+        The sizes of the FFTs.
+    calc_fast_len : bool, optional
+        If `True`, set each value of `shape` to the next fast FFT length.
+        Default is `False`, use `axes` as-is.
+
+    Returns
+    -------
+    out : array
+        An N-dimensional array containing the discrete linear convolution of
+        `in1` with `in2`.
+
+    """
+    if not len(axes):
+        return in1 * in2
+
+    complex_result = (xp.isdtype(in1.dtype, 'complex floating') or
+                      xp.isdtype(in2.dtype, 'complex floating'))
+
+    if calc_fast_len:
+        # Speed up FFT by padding to optimal size.
+        fshape = [
+            sp_fft.next_fast_len(shape[a], not complex_result) for a in axes]
+    else:
+        fshape = shape
+
+    if not complex_result:
+        fft, ifft = sp_fft.rfftn, sp_fft.irfftn
+    else:
+        fft, ifft = sp_fft.fftn, sp_fft.ifftn
+
+    if xp.isdtype(in1.dtype, 'integral'):
+        in1 = xp.astype(in1, xp_default_dtype(xp))
+    if xp.isdtype(in2.dtype, 'integral'):
+        in2 = xp.astype(in2, xp_default_dtype(xp))
+
+    sp1 = fft(in1, fshape, axes=axes)
+    sp2 = fft(in2, fshape, axes=axes)
+
+    ret = ifft(sp1 * sp2, fshape, axes=axes)
+
+    if calc_fast_len:
+        fslice = tuple([slice(sz) for sz in shape])
+        ret = ret[fslice]
+
+    return ret
+
+
+def _apply_conv_mode(ret, s1, s2, mode, axes, xp):
+    """Calculate the convolution result shape based on the `mode` argument.
+
+    Returns the result sliced to the correct size for the given mode.
+
+    Parameters
+    ----------
+    ret : array
+        The result array, with the appropriate shape for the 'full' mode.
+    s1 : list of int
+        The shape of the first input.
+    s2 : list of int
+        The shape of the second input.
+    mode : str {'full', 'valid', 'same'}
+        A string indicating the size of the output.
+        See the documentation `fftconvolve` for more information.
+    axes : list of ints
+        Axes over which to compute the convolution.
+
+    Returns
+    -------
+    ret : array
+        A copy of `res`, sliced to the correct size for the given `mode`.
+
+    """
+    if mode == "full":
+        return xp_copy(ret, xp=xp)
+    elif mode == "same":
+        return xp_copy(_centered(ret, s1), xp=xp)
+    elif mode == "valid":
+        shape_valid = [ret.shape[a] if a not in axes else s1[a] - s2[a] + 1
+                       for a in range(ret.ndim)]
+        return xp_copy(_centered(ret, shape_valid), xp=xp)
+    else:
+        raise ValueError("acceptable mode flags are 'valid',"
+                         " 'same', or 'full'")
+
+
+def fftconvolve(in1, in2, mode="full", axes=None):
+    """Convolve two N-dimensional arrays using FFT.
+
+    Convolve `in1` and `in2` using the fast Fourier transform method, with
+    the output size determined by the `mode` argument.
+
+    This is generally much faster than `convolve` for large arrays (n > ~500),
+    but can be slower when only a few output values are needed, and can only
+    output float arrays (int or object array inputs will be cast to float).
+
+    As of v0.19, `convolve` automatically chooses this method or the direct
+    method based on an estimation of which is faster.
+
+    Parameters
+    ----------
+    in1 : array_like
+        First input.
+    in2 : array_like
+        Second input. Should have the same number of dimensions as `in1`.
+    mode : str {'full', 'valid', 'same'}, optional
+        A string indicating the size of the output:
+
+        ``full``
+           The output is the full discrete linear convolution
+           of the inputs. (Default)
+        ``valid``
+           The output consists only of those elements that do not
+           rely on the zero-padding. In 'valid' mode, either `in1` or `in2`
+           must be at least as large as the other in every dimension.
+        ``same``
+           Output size will be ``N``, the same size as `in1`, centered
+           with respect to the 'full' output.
+           Boundary effects may be visible.
+    axes : int or array_like of ints or None, optional
+        Axes over which to compute the convolution.
+        The default is over all axes.
+
+    Returns
+    -------
+    out : array
+        An N-dimensional array containing a subset of the discrete linear
+        convolution of `in1` with `in2`.
+
+        The output size along each axis depends on ``mode``. For input
+        sizes ``N`` and ``M`` along a given axis:
+
+        - ``full`` : ``N + M - 1``
+        - ``same`` : ``N`` (same as the size of `in1`)
+        - ``valid`` : ``max(N, M) - min(N, M) + 1``
+
+    See Also
+    --------
+    convolve : Uses the direct convolution or FFT convolution algorithm
+               depending on which is faster.
+    oaconvolve : Uses the overlap-add method to do convolution, which is
+                 generally faster when the input arrays are large and
+                 significantly different in size.
+
+    Examples
+    --------
+    Autocorrelation of white noise is an impulse.
+
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> rng = np.random.default_rng()
+    >>> sig = rng.standard_normal(1000)
+    >>> autocorr = signal.fftconvolve(sig, sig[::-1], mode='full')
+
+    >>> import matplotlib.pyplot as plt
+    >>> fig, (ax_orig, ax_mag) = plt.subplots(2, 1)
+    >>> ax_orig.plot(sig)
+    >>> ax_orig.set_title('White noise')
+    >>> ax_mag.plot(np.arange(-len(sig)+1,len(sig)), autocorr)
+    >>> ax_mag.set_title('Autocorrelation')
+    >>> fig.tight_layout()
+    >>> fig.show()
+
+    Gaussian blur implemented using FFT convolution.  Notice the dark borders
+    around the image, due to the zero-padding beyond its boundaries.
+    The `convolve2d` function allows for other types of image boundaries,
+    but is far slower.
+
+    >>> from scipy import datasets
+    >>> face = datasets.face(gray=True)
+    >>> kernel = np.outer(signal.windows.gaussian(70, 8),
+    ...                   signal.windows.gaussian(70, 8))
+    >>> blurred = signal.fftconvolve(face, kernel, mode='same')
+
+    >>> fig, (ax_orig, ax_kernel, ax_blurred) = plt.subplots(3, 1,
+    ...                                                      figsize=(6, 15))
+    >>> ax_orig.imshow(face, cmap='gray')
+    >>> ax_orig.set_title('Original')
+    >>> ax_orig.set_axis_off()
+    >>> ax_kernel.imshow(kernel, cmap='gray')
+    >>> ax_kernel.set_title('Gaussian kernel')
+    >>> ax_kernel.set_axis_off()
+    >>> ax_blurred.imshow(blurred, cmap='gray')
+    >>> ax_blurred.set_title('Blurred')
+    >>> ax_blurred.set_axis_off()
+    >>> fig.show()
+
+    """
+    xp = array_namespace(in1, in2)
+
+    in1 = xp.asarray(in1)
+    in2 = xp.asarray(in2)
+
+    if in1.ndim == in2.ndim == 0:  # scalar inputs
+        return in1 * in2
+    elif in1.ndim != in2.ndim:
+        raise ValueError("in1 and in2 should have the same dimensionality")
+    elif xp_size(in1) == 0 or xp_size(in2) == 0:  # empty arrays
+        return xp.asarray([])
+
+    in1, in2, axes = _init_freq_conv_axes(in1, in2, mode, axes,
+                                          sorted_axes=False)
+
+    s1 = in1.shape
+    s2 = in2.shape
+
+    shape = [max((s1[i], s2[i])) if i not in axes else s1[i] + s2[i] - 1
+             for i in range(in1.ndim)]
+
+    ret = _freq_domain_conv(xp, in1, in2, axes, shape, calc_fast_len=True)
+
+    return _apply_conv_mode(ret, s1, s2, mode, axes, xp=xp)
+
+
+def _calc_oa_lens(s1, s2):
+    """Calculate the optimal FFT lengths for overlap-add convolution.
+
+    The calculation is done for a single dimension.
+
+    Parameters
+    ----------
+    s1 : int
+        Size of the dimension for the first array.
+    s2 : int
+        Size of the dimension for the second array.
+
+    Returns
+    -------
+    block_size : int
+        The size of the FFT blocks.
+    overlap : int
+        The amount of overlap between two blocks.
+    in1_step : int
+        The size of each step for the first array.
+    in2_step : int
+        The size of each step for the second array.
+
+    """
+    # Set up the arguments for the conventional FFT approach.
+    fallback = (s1+s2-1, None, s1, s2)
+
+    # Use conventional FFT convolve if sizes are same.
+    if s1 == s2 or s1 == 1 or s2 == 1:
+        return fallback
+
+    if s2 > s1:
+        s1, s2 = s2, s1
+        swapped = True
+    else:
+        swapped = False
+
+    # There cannot be a useful block size if s2 is more than half of s1.
+    if s2 >= s1/2:
+        return fallback
+
+    # Derivation of optimal block length
+    # For original formula see:
+    # https://en.wikipedia.org/wiki/Overlap-add_method
+    #
+    # Formula:
+    # K = overlap = s2-1
+    # N = block_size
+    # C = complexity
+    # e = exponential, exp(1)
+    #
+    # C = (N*(log2(N)+1))/(N-K)
+    # C = (N*log2(2N))/(N-K)
+    # C = N/(N-K) * log2(2N)
+    # C1 = N/(N-K)
+    # C2 = log2(2N) = ln(2N)/ln(2)
+    #
+    # dC1/dN = (1*(N-K)-N)/(N-K)^2 = -K/(N-K)^2
+    # dC2/dN = 2/(2*N*ln(2)) = 1/(N*ln(2))
+    #
+    # dC/dN = dC1/dN*C2 + dC2/dN*C1
+    # dC/dN = -K*ln(2N)/(ln(2)*(N-K)^2) + N/(N*ln(2)*(N-K))
+    # dC/dN = -K*ln(2N)/(ln(2)*(N-K)^2) + 1/(ln(2)*(N-K))
+    # dC/dN = -K*ln(2N)/(ln(2)*(N-K)^2) + (N-K)/(ln(2)*(N-K)^2)
+    # dC/dN = (-K*ln(2N) + (N-K)/(ln(2)*(N-K)^2)
+    # dC/dN = (N - K*ln(2N) - K)/(ln(2)*(N-K)^2)
+    #
+    # Solve for minimum, where dC/dN = 0
+    # 0 = (N - K*ln(2N) - K)/(ln(2)*(N-K)^2)
+    # 0 * ln(2)*(N-K)^2 = N - K*ln(2N) - K
+    # 0 = N - K*ln(2N) - K
+    # 0 = N - K*(ln(2N) + 1)
+    # 0 = N - K*ln(2Ne)
+    # N = K*ln(2Ne)
+    # N/K = ln(2Ne)
+    #
+    # e^(N/K) = e^ln(2Ne)
+    # e^(N/K) = 2Ne
+    # 1/e^(N/K) = 1/(2*N*e)
+    # e^(N/-K) = 1/(2*N*e)
+    # e^(N/-K) = K/N*1/(2*K*e)
+    # N/K*e^(N/-K) = 1/(2*e*K)
+    # N/-K*e^(N/-K) = -1/(2*e*K)
+    #
+    # Using Lambert W function
+    # https://en.wikipedia.org/wiki/Lambert_W_function
+    # x = W(y) It is the solution to y = x*e^x
+    # x = N/-K
+    # y = -1/(2*e*K)
+    #
+    # N/-K = W(-1/(2*e*K))
+    #
+    # N = -K*W(-1/(2*e*K))
+    overlap = s2-1
+    opt_size = -overlap*lambertw(-1/(2*math.e*overlap), k=-1).real
+    block_size = sp_fft.next_fast_len(math.ceil(opt_size))
+
+    # Use conventional FFT convolve if there is only going to be one block.
+    if block_size >= s1:
+        return fallback
+
+    if not swapped:
+        in1_step = block_size-s2+1
+        in2_step = s2
+    else:
+        in1_step = s2
+        in2_step = block_size-s2+1
+
+    return block_size, overlap, in1_step, in2_step
+
+
+# may want to look at moving xp_swapaxes and this to array-api-extra,
+# cross-ref https://github.com/data-apis/array-api-extra/issues/97
+def _split(x, indices_or_sections, axis, xp):
+    """A simplified version of np.split, with `indices` being a list.
+    """
+    # https://github.com/numpy/numpy/blob/v2.2.0/numpy/lib/_shape_base_impl.py#L743
+    Ntotal = x.shape[axis]
+
+    # handle array case.
+    Nsections = len(indices_or_sections) + 1
+    div_points = [0] + list(indices_or_sections) + [Ntotal]
+
+    sub_arys = []
+    sary = xp_swapaxes(x, axis, 0, xp=xp)
+    for i in range(Nsections):
+        st = div_points[i]
+        end = div_points[i + 1]
+        sub_arys.append(xp_swapaxes(sary[st:end, ...], axis, 0, xp=xp))
+
+    return sub_arys
+
+
+def oaconvolve(in1, in2, mode="full", axes=None):
+    """Convolve two N-dimensional arrays using the overlap-add method.
+
+    Convolve `in1` and `in2` using the overlap-add method, with
+    the output size determined by the `mode` argument.
+
+    This is generally much faster than `convolve` for large arrays (n > ~500),
+    and generally much faster than `fftconvolve` when one array is much
+    larger than the other, but can be slower when only a few output values are
+    needed or when the arrays are very similar in shape, and can only
+    output float arrays (int or object array inputs will be cast to float).
+
+    Parameters
+    ----------
+    in1 : array_like
+        First input.
+    in2 : array_like
+        Second input. Should have the same number of dimensions as `in1`.
+    mode : str {'full', 'valid', 'same'}, optional
+        A string indicating the size of the output:
+
+        ``full``
+           The output is the full discrete linear convolution
+           of the inputs. (Default)
+        ``valid``
+           The output consists only of those elements that do not
+           rely on the zero-padding. In 'valid' mode, either `in1` or `in2`
+           must be at least as large as the other in every dimension.
+        ``same``
+           Output size will be ``N``, the same size as `in1`, centered
+           with respect to the 'full' output.
+           Boundary effects may be visible.
+    axes : int or array_like of ints or None, optional
+        Axes over which to compute the convolution.
+        The default is over all axes.
+
+    Returns
+    -------
+    out : array
+        An N-dimensional array containing a subset of the discrete linear
+        convolution of `in1` with `in2`.
+
+        The output size along each axis depends on ``mode``. For input
+        sizes ``N`` and ``M`` along a given axis:
+
+        - ``full`` : ``N + M - 1``
+        - ``same`` : ``N`` (same as the size of `in1`)
+        - ``valid`` : ``max(N, M) - min(N, M) + 1``
+
+    See Also
+    --------
+    convolve : Uses the direct convolution or FFT convolution algorithm
+               depending on which is faster.
+    fftconvolve : An implementation of convolution using FFT.
+
+    Notes
+    -----
+    .. versionadded:: 1.4.0
+
+    References
+    ----------
+    .. [1] Wikipedia, "Overlap-add_method".
+           https://en.wikipedia.org/wiki/Overlap-add_method
+    .. [2] Richard G. Lyons. Understanding Digital Signal Processing,
+           Third Edition, 2011. Chapter 13.10.
+           ISBN 13: 978-0137-02741-5
+
+    Examples
+    --------
+    Convolve a 100,000 sample signal with a 512-sample filter.
+
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> rng = np.random.default_rng()
+    >>> sig = rng.standard_normal(100000)
+    >>> filt = signal.firwin(512, 0.01)
+    >>> fsig = signal.oaconvolve(sig, filt)
+
+    >>> import matplotlib.pyplot as plt
+    >>> fig, (ax_orig, ax_mag) = plt.subplots(2, 1)
+    >>> ax_orig.plot(sig)
+    >>> ax_orig.set_title('White noise')
+    >>> ax_mag.plot(fsig)
+    >>> ax_mag.set_title('Filtered noise')
+    >>> fig.tight_layout()
+    >>> fig.show()
+
+    """
+    xp = array_namespace(in1, in2)
+
+    in1 = xp.asarray(in1)
+    in2 = xp.asarray(in2)
+
+    if in1.ndim == in2.ndim == 0:  # scalar inputs
+        return in1 * in2
+    elif in1.ndim != in2.ndim:
+        raise ValueError("in1 and in2 should have the same dimensionality")
+    elif in1.size == 0 or in2.size == 0:  # empty arrays
+        return xp.asarray([])
+    elif in1.shape == in2.shape:  # Equivalent to fftconvolve
+        return fftconvolve(in1, in2, mode=mode, axes=axes)
+
+    in1, in2, axes = _init_freq_conv_axes(in1, in2, mode, axes,
+                                          sorted_axes=True)
+
+    s1 = in1.shape
+    s2 = in2.shape
+
+    if not axes:
+        ret = in1 * in2
+        return _apply_conv_mode(ret, s1, s2, mode, axes, xp)
+
+    # Calculate this now since in1 is changed later
+    shape_final = [None if i not in axes else
+                   s1[i] + s2[i] - 1 for i in range(in1.ndim)]
+
+    # Calculate the block sizes for the output, steps, first and second inputs.
+    # It is simpler to calculate them all together than doing them in separate
+    # loops due to all the special cases that need to be handled.
+    optimal_sizes = ((-1, -1, s1[i], s2[i]) if i not in axes else
+                     _calc_oa_lens(s1[i], s2[i]) for i in range(in1.ndim))
+    block_size, overlaps, \
+        in1_step, in2_step = zip(*optimal_sizes)
+
+    # Fall back to fftconvolve if there is only one block in every dimension.
+    if in1_step == s1 and in2_step == s2:
+        return fftconvolve(in1, in2, mode=mode, axes=axes)
+
+    # Figure out the number of steps and padding.
+    # This would get too complicated in a list comprehension.
+    nsteps1 = []
+    nsteps2 = []
+    pad_size1 = []
+    pad_size2 = []
+    for i in range(in1.ndim):
+        if i not in axes:
+            pad_size1 += [(0, 0)]
+            pad_size2 += [(0, 0)]
+            continue
+
+        if s1[i] > in1_step[i]:
+            curnstep1 = math.ceil((s1[i]+1)/in1_step[i])
+            if (block_size[i] - overlaps[i])*curnstep1 < shape_final[i]:
+                curnstep1 += 1
+
+            curpad1 = curnstep1*in1_step[i] - s1[i]
+        else:
+            curnstep1 = 1
+            curpad1 = 0
+
+        if s2[i] > in2_step[i]:
+            curnstep2 = math.ceil((s2[i]+1)/in2_step[i])
+            if (block_size[i] - overlaps[i])*curnstep2 < shape_final[i]:
+                curnstep2 += 1
+
+            curpad2 = curnstep2*in2_step[i] - s2[i]
+        else:
+            curnstep2 = 1
+            curpad2 = 0
+
+        nsteps1 += [curnstep1]
+        nsteps2 += [curnstep2]
+        pad_size1 += [(0, curpad1)]
+        pad_size2 += [(0, curpad2)]
+
+    # Pad the array to a size that can be reshaped to the desired shape
+    # if necessary.
+    if not all(curpad == (0, 0) for curpad in pad_size1):
+        in1 = xpx.pad(in1, pad_size1, mode='constant', constant_values=0, xp=xp)
+
+    if not all(curpad == (0, 0) for curpad in pad_size2):
+         in2 = xpx.pad(in2, pad_size2, mode='constant', constant_values=0, xp=xp)
+
+    # Reshape the overlap-add parts to input block sizes.
+    split_axes = [iax+i for i, iax in enumerate(axes)]
+    fft_axes = [iax+1 for iax in split_axes]
+
+    # We need to put each new dimension before the corresponding dimension
+    # being reshaped in order to get the data in the right layout at the end.
+    reshape_size1 = list(in1_step)
+    reshape_size2 = list(in2_step)
+    for i, iax in enumerate(split_axes):
+        reshape_size1.insert(iax, nsteps1[i])
+        reshape_size2.insert(iax, nsteps2[i])
+
+    in1 = xp.reshape(in1, tuple(reshape_size1))
+    in2 = xp.reshape(in2, tuple(reshape_size2))
+
+    # Do the convolution.
+    fft_shape = [block_size[i] for i in axes]
+    ret = _freq_domain_conv(xp, in1, in2, fft_axes, fft_shape, calc_fast_len=False)
+
+    # Do the overlap-add.
+    for ax, ax_fft, ax_split in zip(axes, fft_axes, split_axes):
+        overlap = overlaps[ax]
+        if overlap is None:
+            continue
+
+        ret, overpart = _split(ret, [-overlap], ax_fft, xp=xp)
+        overpart = _split(overpart, [-1], ax_split, xp=xp)[0]
+
+        overlap_slice = [slice(None)] * ret.ndim
+        overlap_slice[ax_fft] = slice(0, overlap)
+        overlap_slice[ax_split] = slice(1, None)
+        ret = xpx.at(ret)[tuple(overlap_slice)].add(overpart)
+
+    # Reshape back to the correct dimensionality.
+    shape_ret = [ret.shape[i] if i not in fft_axes else
+                 ret.shape[i]*ret.shape[i-1]
+                 for i in range(ret.ndim) if i not in split_axes]
+    ret = xp.reshape(ret, tuple(shape_ret))
+
+    # Slice to the correct size.
+    slice_final = tuple([slice(islice) for islice in shape_final])
+    ret = ret[slice_final]
+
+    return _apply_conv_mode(ret, s1, s2, mode, axes, xp)
+
+
+def _numeric_arrays(arrays, kinds='buifc', xp=None):
+    """
+    See if a list of arrays are all numeric.
+
+    Parameters
+    ----------
+    arrays : array or list of arrays
+        arrays to check if numeric.
+    kinds : string-like
+        The dtypes of the arrays to be checked. If the dtype.kind of
+        the ndarrays are not in this string the function returns False and
+        otherwise returns True.
+    """
+    if xp is None:
+        xp = array_namespace(*arrays)
+    if not is_numpy(xp):
+        return True
+
+    if type(arrays) is np.ndarray:
+        return arrays.dtype.kind in kinds
+    for array_ in arrays:
+        if array_.dtype.kind not in kinds:
+            return False
+    return True
+
+
+def _conv_ops(x_shape, h_shape, mode):
+    """
+    Find the number of operations required for direct/fft methods of
+    convolution. The direct operations were recorded by making a dummy class to
+    record the number of operations by overriding ``__mul__`` and ``__add__``.
+    The FFT operations rely on the (well-known) computational complexity of the
+    FFT (and the implementation of ``_freq_domain_conv``).
+
+    """
+    if mode == "full":
+        out_shape = [n + k - 1 for n, k in zip(x_shape, h_shape)]
+    elif mode == "valid":
+        out_shape = [abs(n - k) + 1 for n, k in zip(x_shape, h_shape)]
+    elif mode == "same":
+        out_shape = x_shape
+    else:
+        raise ValueError("Acceptable mode flags are 'valid',"
+                         f" 'same', or 'full', not mode={mode}")
+
+    s1, s2 = x_shape, h_shape
+    if len(x_shape) == 1:
+        s1, s2 = s1[0], s2[0]
+        if mode == "full":
+            direct_ops = s1 * s2
+        elif mode == "valid":
+            direct_ops = (s2 - s1 + 1) * s1 if s2 >= s1 else (s1 - s2 + 1) * s2
+        elif mode == "same":
+            direct_ops = (s1 * s2 if s1 < s2 else
+                          s1 * s2 - (s2 // 2) * ((s2 + 1) // 2))
+    else:
+        if mode == "full":
+            direct_ops = min(_prod(s1), _prod(s2)) * _prod(out_shape)
+        elif mode == "valid":
+            direct_ops = min(_prod(s1), _prod(s2)) * _prod(out_shape)
+        elif mode == "same":
+            direct_ops = _prod(s1) * _prod(s2)
+
+    full_out_shape = [n + k - 1 for n, k in zip(x_shape, h_shape)]
+    N = _prod(full_out_shape)
+    fft_ops = 3 * N * np.log(N)  # 3 separate FFTs of size full_out_shape
+    return fft_ops, direct_ops
+
+
+def _fftconv_faster(x, h, mode):
+    """
+    See if using fftconvolve or convolve is faster.
+
+    Parameters
+    ----------
+    x : np.ndarray
+        Signal
+    h : np.ndarray
+        Kernel
+    mode : str
+        Mode passed to convolve
+
+    Returns
+    -------
+    fft_faster : bool
+
+    Notes
+    -----
+    See docstring of `choose_conv_method` for details on tuning hardware.
+
+    See pull request 11031 for more detail:
+    https://github.com/scipy/scipy/pull/11031.
+
+    """
+    fft_ops, direct_ops = _conv_ops(x.shape, h.shape, mode)
+    offset = -1e-3 if x.ndim == 1 else -1e-4
+    constants = {
+            "valid": (1.89095737e-9, 2.1364985e-10, offset),
+            "full": (1.7649070e-9, 2.1414831e-10, offset),
+            "same": (3.2646654e-9, 2.8478277e-10, offset)
+            if h.size <= x.size
+            else (3.21635404e-9, 1.1773253e-8, -1e-5),
+    } if x.ndim == 1 else {
+            "valid": (1.85927e-9, 2.11242e-8, offset),
+            "full": (1.99817e-9, 1.66174e-8, offset),
+            "same": (2.04735e-9, 1.55367e-8, offset),
+    }
+    O_fft, O_direct, O_offset = constants[mode]
+    return O_fft * fft_ops < O_direct * direct_ops + O_offset
+
+
+def _reverse_and_conj(x, xp):
+    """
+    Reverse array `x` in all dimensions and perform the complex conjugate
+    """
+    if not is_torch(xp):
+        reverse = (slice(None, None, -1),) * x.ndim
+        x_rev = x[reverse]
+    else:
+        # NB: is a copy, not a view as torch does not allow negative indices
+        # in slices, x-ref https://github.com/pytorch/pytorch/issues/59786
+        x_rev = xp.flip(x)
+
+    # cf https://github.com/data-apis/array-api/issues/824
+    if xp.isdtype(x.dtype, 'complex floating'):
+        return xp.conj(x_rev)
+    else:
+        return x_rev
+
+
+def _np_conv_ok(volume, kernel, mode, xp):
+    """
+    See if numpy supports convolution of `volume` and `kernel` (i.e. both are
+    1D ndarrays and of the appropriate shape).  NumPy's 'same' mode uses the
+    size of the larger input, while SciPy's uses the size of the first input.
+
+    Invalid mode strings will return False and be caught by the calling func.
+    """
+    if volume.ndim == kernel.ndim == 1:
+        if mode in ('full', 'valid'):
+            return True
+        elif mode == 'same':
+            return xp_size(volume) >= xp_size(kernel)
+    else:
+        return False
+
+
+def _timeit_fast(stmt="pass", setup="pass", repeat=3):
+    """
+    Returns the time the statement/function took, in seconds.
+
+    Faster, less precise version of IPython's timeit. `stmt` can be a statement
+    written as a string or a callable.
+
+    Will do only 1 loop (like IPython's timeit) with no repetitions
+    (unlike IPython) for very slow functions.  For fast functions, only does
+    enough loops to take 5 ms, which seems to produce similar results (on
+    Windows at least), and avoids doing an extraneous cycle that isn't
+    measured.
+
+    """
+    timer = timeit.Timer(stmt, setup)
+
+    # determine number of calls per rep so total time for 1 rep >= 5 ms
+    x = 0
+    for p in range(0, 10):
+        number = 10**p
+        x = timer.timeit(number)  # seconds
+        if x >= 5e-3 / 10:  # 5 ms for final test, 1/10th that for this one
+            break
+    if x > 1:  # second
+        # If it's macroscopic, don't bother with repetitions
+        best = x
+    else:
+        number *= 10
+        r = timer.repeat(repeat, number)
+        best = min(r)
+
+    sec = best / number
+    return sec
+
+
+def choose_conv_method(in1, in2, mode='full', measure=False):
+    """
+    Find the fastest convolution/correlation method.
+
+    This primarily exists to be called during the ``method='auto'`` option in
+    `convolve` and `correlate`. It can also be used to determine the value of
+    ``method`` for many different convolutions of the same dtype/shape.
+    In addition, it supports timing the convolution to adapt the value of
+    ``method`` to a particular set of inputs and/or hardware.
+
+    Parameters
+    ----------
+    in1 : array_like
+        The first argument passed into the convolution function.
+    in2 : array_like
+        The second argument passed into the convolution function.
+    mode : str {'full', 'valid', 'same'}, optional
+        A string indicating the size of the output:
+
+        ``full``
+           The output is the full discrete linear convolution
+           of the inputs. (Default)
+        ``valid``
+           The output consists only of those elements that do not
+           rely on the zero-padding.
+        ``same``
+           Output size will be ``N``, the same size as `in1`, centered
+           with respect to the 'full' output.
+           Boundary effects may be visible.
+    measure : bool, optional
+        If True, run and time the convolution of `in1` and `in2` with both
+        methods and return the fastest. If False (default), predict the fastest
+        method using precomputed values.
+
+    Returns
+    -------
+    method : str
+        A string indicating which convolution method is fastest, either
+        'direct' or 'fft'
+    times : dict, optional
+        A dictionary containing the times (in seconds) needed for each method.
+        This value is only returned if ``measure=True``.
+
+    See Also
+    --------
+    convolve
+    correlate
+
+    Notes
+    -----
+    Generally, this method is 99% accurate for 2D signals and 85% accurate
+    for 1D signals for randomly chosen input sizes. For precision, use
+    ``measure=True`` to find the fastest method by timing the convolution.
+    This can be used to avoid the minimal overhead of finding the fastest
+    ``method`` later, or to adapt the value of ``method`` to a particular set
+    of inputs.
+
+    Experiments were run on an Amazon EC2 r5a.2xlarge machine to test this
+    function. These experiments measured the ratio between the time required
+    when using ``method='auto'`` and the time required for the fastest method
+    (i.e., ``ratio = time_auto / min(time_fft, time_direct)``). In these
+    experiments, we found:
+
+    * There is a 95% chance of this ratio being less than 1.5 for 1D signals
+      and a 99% chance of being less than 2.5 for 2D signals.
+    * The ratio was always less than 2.5/5 for 1D/2D signals respectively.
+    * This function is most inaccurate for 1D convolutions that take between 1
+      and 10 milliseconds with ``method='direct'``. A good proxy for this
+      (at least in our experiments) is ``1e6 <= in1.size * in2.size <= 1e7``.
+
+    The 2D results almost certainly generalize to 3D/4D/etc because the
+    implementation is the same (the 1D implementation is different).
+
+    All the numbers above are specific to the EC2 machine. However, we did find
+    that this function generalizes fairly decently across hardware. The speed
+    tests were of similar quality (and even slightly better) than the same
+    tests performed on the machine to tune this function's numbers (a mid-2014
+    15-inch MacBook Pro with 16GB RAM and a 2.5GHz Intel i7 processor).
+
+    There are cases when `fftconvolve` supports the inputs but this function
+    returns `direct` (e.g., to protect against floating point integer
+    precision).
+
+    .. versionadded:: 0.19
+
+    Examples
+    --------
+    Estimate the fastest method for a given input:
+
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> rng = np.random.default_rng()
+    >>> img = rng.random((32, 32))
+    >>> filter = rng.random((8, 8))
+    >>> method = signal.choose_conv_method(img, filter, mode='same')
+    >>> method
+    'fft'
+
+    This can then be applied to other arrays of the same dtype and shape:
+
+    >>> img2 = rng.random((32, 32))
+    >>> filter2 = rng.random((8, 8))
+    >>> corr2 = signal.correlate(img2, filter2, mode='same', method=method)
+    >>> conv2 = signal.convolve(img2, filter2, mode='same', method=method)
+
+    The output of this function (``method``) works with `correlate` and
+    `convolve`.
+
+    """
+    xp = array_namespace(in1, in2)
+
+    volume = xp.asarray(in1)
+    kernel = xp.asarray(in2)
+
+    if measure:
+        times = {}
+        for method in ['fft', 'direct']:
+            times[method] = _timeit_fast(lambda: convolve(volume, kernel,
+                                         mode=mode, method=method))
+
+        chosen_method = 'fft' if times['fft'] < times['direct'] else 'direct'
+        return chosen_method, times
+
+    # for integer input,
+    # catch when more precision required than float provides (representing an
+    # integer as float can lose precision in fftconvolve if larger than 2**52)
+    if any([_numeric_arrays([x], kinds='ui', xp=xp) for x in [volume, kernel]]):
+        max_value = int(xp.max(xp.abs(volume))) * int(xp.max(xp.abs(kernel)))
+        max_value *= int(min(xp_size(volume), xp_size(kernel)))
+        if max_value > 2**np.finfo('float').nmant - 1:
+            return 'direct'
+
+    if _numeric_arrays([volume, kernel], kinds='b', xp=xp):
+        return 'direct'
+
+    if _numeric_arrays([volume, kernel], xp=xp):
+        if _fftconv_faster(volume, kernel, mode):
+            return 'fft'
+
+    return 'direct'
+
+
+def convolve(in1, in2, mode='full', method='auto'):
+    """
+    Convolve two N-dimensional arrays.
+
+    Convolve `in1` and `in2`, with the output size determined by the
+    `mode` argument.
+
+    Parameters
+    ----------
+    in1 : array_like
+        First input.
+    in2 : array_like
+        Second input. Should have the same number of dimensions as `in1`.
+    mode : str {'full', 'valid', 'same'}, optional
+        A string indicating the size of the output:
+
+        ``full``
+           The output is the full discrete linear convolution
+           of the inputs. (Default)
+        ``valid``
+           The output consists only of those elements that do not
+           rely on the zero-padding. In 'valid' mode, either `in1` or `in2`
+           must be at least as large as the other in every dimension.
+        ``same``
+           Output size will be ``N``, the same size as `in1`, centered
+           with respect to the 'full' output.
+           Boundary effects may be visible.
+    method : str {'auto', 'direct', 'fft'}, optional
+        A string indicating which method to use to calculate the convolution.
+
+        ``direct``
+           The convolution is determined directly from sums, the definition of
+           convolution.
+        ``fft``
+           The Fourier Transform is used to perform the convolution by calling
+           `fftconvolve`.
+        ``auto``
+           Automatically chooses direct or Fourier method based on an estimate
+           of which is faster (default).  See Notes for more detail.
+
+           .. versionadded:: 0.19.0
+
+    Returns
+    -------
+    convolve : array
+        An N-dimensional array containing a subset of the discrete linear
+        convolution of `in1` with `in2`.
+
+        The output size along each axis depends on ``mode``. For input
+        sizes ``N`` and ``M`` along a given axis:
+
+        - ``full`` : ``N + M - 1``
+        - ``same`` : ``N`` (same as the size of `in1`)
+        - ``valid`` : ``max(N, M) - min(N, M) + 1``
+
+    Warns
+    -----
+    RuntimeWarning
+        Use of the FFT convolution on input containing NAN or INF will lead
+        to the entire output being NAN or INF. Use method='direct' when your
+        input contains NAN or INF values.
+
+    See Also
+    --------
+    numpy.polymul : performs polynomial multiplication (same operation, but
+                    also accepts poly1d objects)
+    choose_conv_method : chooses the fastest appropriate convolution method
+    fftconvolve : Always uses the FFT method.
+    oaconvolve : Uses the overlap-add method to do convolution, which is
+                 generally faster when the input arrays are large and
+                 significantly different in size.
+
+    Notes
+    -----
+    By default, `convolve` and `correlate` use ``method='auto'``, which calls
+    `choose_conv_method` to choose the fastest method using pre-computed
+    values (`choose_conv_method` can also measure real-world timing with a
+    keyword argument). Because `fftconvolve` relies on floating point numbers,
+    there are certain constraints that may force ``method='direct'`` (more detail
+    in `choose_conv_method` docstring).
+
+    Examples
+    --------
+    Smooth a square pulse using a Hann window:
+
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> sig = np.repeat([0., 1., 0.], 100)
+    >>> win = signal.windows.hann(50)
+    >>> filtered = signal.convolve(sig, win, mode='same') / sum(win)
+
+    >>> import matplotlib.pyplot as plt
+    >>> fig, (ax_orig, ax_win, ax_filt) = plt.subplots(3, 1, sharex=True)
+    >>> ax_orig.plot(sig)
+    >>> ax_orig.set_title('Original pulse')
+    >>> ax_orig.margins(0, 0.1)
+    >>> ax_win.plot(win)
+    >>> ax_win.set_title('Filter impulse response')
+    >>> ax_win.margins(0, 0.1)
+    >>> ax_filt.plot(filtered)
+    >>> ax_filt.set_title('Filtered signal')
+    >>> ax_filt.margins(0, 0.1)
+    >>> fig.tight_layout()
+    >>> fig.show()
+
+    """
+    xp = array_namespace(in1, in2)
+
+    volume = xp.asarray(in1)
+    kernel = xp.asarray(in2)
+
+    if volume.ndim == kernel.ndim == 0:
+        return volume * kernel
+    elif volume.ndim != kernel.ndim:
+        raise ValueError("volume and kernel should have the same "
+                         "dimensionality")
+
+    if _inputs_swap_needed(mode, volume.shape, kernel.shape):
+        # Convolution is commutative; order doesn't have any effect on output
+        volume, kernel = kernel, volume
+
+    if method == 'auto':
+        method = choose_conv_method(volume, kernel, mode=mode)
+
+    if method == 'fft':
+        out = fftconvolve(volume, kernel, mode=mode)
+        result_type = xp.result_type(volume, kernel)
+        if xp.isdtype(result_type, 'integral'):
+            out = xp.round(out)
+
+        if xp.isnan(xp.reshape(out, (-1,))[0]) or xp.isinf(xp.reshape(out, (-1,))[0]):
+            warnings.warn("Use of fft convolution on input with NAN or inf"
+                          " results in NAN or inf output. Consider using"
+                          " method='direct' instead.",
+                          category=RuntimeWarning, stacklevel=2)
+
+        return xp.astype(out, result_type)
+    elif method == 'direct':
+        # fastpath to faster numpy.convolve for 1d inputs when possible
+        if _np_conv_ok(volume, kernel, mode, xp):
+            # convert to numpy and back
+            a_volume = np.asarray(volume)
+            a_kernel = np.asarray(kernel)
+            out = np.convolve(a_volume, a_kernel, mode)
+            return xp.asarray(out)
+
+        return correlate(volume, _reverse_and_conj(kernel, xp), mode, 'direct')
+    else:
+        raise ValueError("Acceptable method flags are 'auto',"
+                         " 'direct', or 'fft'.")
+
+
+def order_filter(a, domain, rank):
+    """
+    Perform an order filter on an N-D array.
+
+    Perform an order filter on the array in. The domain argument acts as a
+    mask centered over each pixel. The non-zero elements of domain are
+    used to select elements surrounding each input pixel which are placed
+    in a list. The list is sorted, and the output for that pixel is the
+    element corresponding to rank in the sorted list.
+
+    Parameters
+    ----------
+    a : ndarray
+        The N-dimensional input array.
+    domain : array_like
+        A mask array with the same number of dimensions as `a`.
+        Each dimension should have an odd number of elements.
+    rank : int
+        A non-negative integer which selects the element from the
+        sorted list (0 corresponds to the smallest element, 1 is the
+        next smallest element, etc.).
+
+    Returns
+    -------
+    out : ndarray
+        The results of the order filter in an array with the same
+        shape as `a`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> x = np.arange(25).reshape(5, 5)
+    >>> domain = np.identity(3)
+    >>> x
+    array([[ 0,  1,  2,  3,  4],
+           [ 5,  6,  7,  8,  9],
+           [10, 11, 12, 13, 14],
+           [15, 16, 17, 18, 19],
+           [20, 21, 22, 23, 24]])
+    >>> signal.order_filter(x, domain, 0)
+    array([[  0,   0,   0,   0,   0],
+           [  0,   0,   1,   2,   0],
+           [  0,   5,   6,   7,   0],
+           [  0,  10,  11,  12,   0],
+           [  0,   0,   0,   0,   0]])
+    >>> signal.order_filter(x, domain, 2)
+    array([[  6,   7,   8,   9,   4],
+           [ 11,  12,  13,  14,   9],
+           [ 16,  17,  18,  19,  14],
+           [ 21,  22,  23,  24,  19],
+           [ 20,  21,  22,  23,  24]])
+
+    """
+    xp = array_namespace(a, domain)
+
+    domain = xp.asarray(domain)
+    for dimsize in domain.shape:
+        if (dimsize % 2) != 1:
+            raise ValueError("Each dimension of domain argument "
+                             "should have an odd number of elements.")
+
+    a = xp.asarray(a)
+    if not (
+        xp.isdtype(a.dtype, "integral") or a.dtype in (xp.float32, xp.float64)
+    ):
+        raise ValueError(f"dtype={a.dtype} is not supported by order_filter")
+    result = ndimage.rank_filter(a, rank, footprint=domain, mode='constant')
+    return result
+
+
+def medfilt(volume, kernel_size=None):
+    """
+    Perform a median filter on an N-dimensional array.
+
+    Apply a median filter to the input array using a local window-size
+    given by `kernel_size`. The array will automatically be zero-padded.
+
+    Parameters
+    ----------
+    volume : array_like
+        An N-dimensional input array.
+    kernel_size : array_like, optional
+        A scalar or an N-length list giving the size of the median filter
+        window in each dimension.  Elements of `kernel_size` should be odd.
+        If `kernel_size` is a scalar, then this scalar is used as the size in
+        each dimension. Default size is 3 for each dimension.
+
+    Returns
+    -------
+    out : ndarray
+        An array the same size as input containing the median filtered
+        result.
+
+    Warns
+    -----
+    UserWarning
+        If array size is smaller than kernel size along any dimension
+
+    See Also
+    --------
+    scipy.ndimage.median_filter
+    scipy.signal.medfilt2d
+
+    """
+    xp = array_namespace(volume)
+    volume = xp.asarray(volume)
+    if volume.ndim == 0:
+        volume = xpx.atleast_nd(volume, ndim=1, xp=xp)
+
+    if not (xp.isdtype(volume.dtype, "integral") or
+            volume.dtype in [xp.float32, xp.float64]):
+        raise ValueError(f"dtype={volume.dtype} is not supported by medfilt")
+
+    if kernel_size is None:
+        kernel_size = [3] * volume.ndim
+    kernel_size = xp.asarray(kernel_size)
+    if kernel_size.shape == ():
+        kernel_size = xp.repeat(kernel_size, volume.ndim)
+
+    for k in range(volume.ndim):
+        if (kernel_size[k] % 2) != 1:
+            raise ValueError("Each element of kernel_size should be odd.")
+    if any(k > s for k, s in zip(kernel_size, volume.shape)):
+        warnings.warn('kernel_size exceeds volume extent: the volume will be '
+                      'zero-padded.',
+                      stacklevel=2)
+
+    size = math.prod(kernel_size)
+    result = ndimage.rank_filter(volume, size // 2, size=kernel_size,
+                                 mode='constant')
+
+    return result
+
+
+def wiener(im, mysize=None, noise=None):
+    """
+    Perform a Wiener filter on an N-dimensional array.
+
+    Apply a Wiener filter to the N-dimensional array `im`.
+
+    Parameters
+    ----------
+    im : ndarray
+        An N-dimensional array.
+    mysize : int or array_like, optional
+        A scalar or an N-length list giving the size of the Wiener filter
+        window in each dimension.  Elements of mysize should be odd.
+        If mysize is a scalar, then this scalar is used as the size
+        in each dimension.
+    noise : float, optional
+        The noise-power to use. If None, then noise is estimated as the
+        average of the local variance of the input.
+
+    Returns
+    -------
+    out : ndarray
+        Wiener filtered result with the same shape as `im`.
+
+    Notes
+    -----
+    This implementation is similar to wiener2 in Matlab/Octave.
+    For more details see [1]_
+
+    References
+    ----------
+    .. [1] Lim, Jae S., Two-Dimensional Signal and Image Processing,
+           Englewood Cliffs, NJ, Prentice Hall, 1990, p. 548.
+
+    Examples
+    --------
+    >>> from scipy.datasets import face
+    >>> from scipy.signal import wiener
+    >>> import matplotlib.pyplot as plt
+    >>> import numpy as np
+    >>> rng = np.random.default_rng()
+    >>> img = rng.random((40, 40))    #Create a random image
+    >>> filtered_img = wiener(img, (5, 5))  #Filter the image
+    >>> f, (plot1, plot2) = plt.subplots(1, 2)
+    >>> plot1.imshow(img)
+    >>> plot2.imshow(filtered_img)
+    >>> plt.show()
+
+    """
+    xp = array_namespace(im)
+
+    im = xp.asarray(im)
+    if mysize is None:
+        mysize = [3] * im.ndim
+    mysize_arr = xp.asarray(mysize)
+    if mysize_arr.shape == ():
+        mysize = [mysize] * im.ndim
+
+    # Estimate the local mean
+    size = math.prod(mysize)
+    lMean = correlate(im, xp.ones(mysize), 'same')
+    lsize = float(size)
+    lMean = lMean / lsize
+
+    # Estimate the local variance
+    lVar = (correlate(im ** 2, xp.ones(mysize), 'same') / lsize - lMean ** 2)
+
+    # Estimate the noise power if needed.
+    if noise is None:
+        noise = xp.mean(xp.reshape(lVar, (-1,)), axis=0)
+
+    res = (im - lMean)
+    res *= (1 - noise / lVar)
+    res += lMean
+    out = xp.where(lVar < noise, lMean, res)
+
+    return out
+
+
+def convolve2d(in1, in2, mode='full', boundary='fill', fillvalue=0):
+    """
+    Convolve two 2-dimensional arrays.
+
+    Convolve `in1` and `in2` with output size determined by `mode`, and
+    boundary conditions determined by `boundary` and `fillvalue`.
+
+    Parameters
+    ----------
+    in1 : array_like
+        First input.
+    in2 : array_like
+        Second input. Should have the same number of dimensions as `in1`.
+    mode : str {'full', 'valid', 'same'}, optional
+        A string indicating the size of the output:
+
+        ``full``
+           The output is the full discrete linear convolution
+           of the inputs. (Default)
+        ``valid``
+           The output consists only of those elements that do not
+           rely on the zero-padding. In 'valid' mode, either `in1` or `in2`
+           must be at least as large as the other in every dimension.
+        ``same``
+           The output is the same size as `in1`, centered
+           with respect to the 'full' output.
+    boundary : str {'fill', 'wrap', 'symm'}, optional
+        A flag indicating how to handle boundaries:
+
+        ``fill``
+           pad input arrays with fillvalue. (default)
+        ``wrap``
+           circular boundary conditions.
+        ``symm``
+           symmetrical boundary conditions.
+
+    fillvalue : scalar, optional
+        Value to fill pad input arrays with. Default is 0.
+
+    Returns
+    -------
+    out : ndarray
+        A 2-dimensional array containing a subset of the discrete linear
+        convolution of `in1` with `in2`.
+
+    Examples
+    --------
+    Compute the gradient of an image by 2D convolution with a complex Scharr
+    operator.  (Horizontal operator is real, vertical is imaginary.)  Use
+    symmetric boundary condition to avoid creating edges at the image
+    boundaries.
+
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> from scipy import datasets
+    >>> ascent = datasets.ascent()
+    >>> scharr = np.array([[ -3-3j, 0-10j,  +3 -3j],
+    ...                    [-10+0j, 0+ 0j, +10 +0j],
+    ...                    [ -3+3j, 0+10j,  +3 +3j]]) # Gx + j*Gy
+    >>> grad = signal.convolve2d(ascent, scharr, boundary='symm', mode='same')
+
+    >>> import matplotlib.pyplot as plt
+    >>> fig, (ax_orig, ax_mag, ax_ang) = plt.subplots(3, 1, figsize=(6, 15))
+    >>> ax_orig.imshow(ascent, cmap='gray')
+    >>> ax_orig.set_title('Original')
+    >>> ax_orig.set_axis_off()
+    >>> ax_mag.imshow(np.absolute(grad), cmap='gray')
+    >>> ax_mag.set_title('Gradient magnitude')
+    >>> ax_mag.set_axis_off()
+    >>> ax_ang.imshow(np.angle(grad), cmap='hsv') # hsv is cyclic, like angles
+    >>> ax_ang.set_title('Gradient orientation')
+    >>> ax_ang.set_axis_off()
+    >>> fig.show()
+
+    """
+    xp = array_namespace(in1, in2)
+
+    # NB: do work in NumPy, only convert the output
+
+    in1 = np.asarray(in1)
+    in2 = np.asarray(in2)
+
+    if not in1.ndim == in2.ndim == 2:
+        raise ValueError('convolve2d inputs must both be 2-D arrays')
+
+    if _inputs_swap_needed(mode, in1.shape, in2.shape):
+        in1, in2 = in2, in1
+
+    val = _valfrommode(mode)
+    bval = _bvalfromboundary(boundary)
+    out = _sigtools._convolve2d(in1, in2, 1, val, bval, fillvalue)
+    return xp.asarray(out)
+
+
+def correlate2d(in1, in2, mode='full', boundary='fill', fillvalue=0):
+    """
+    Cross-correlate two 2-dimensional arrays.
+
+    Cross correlate `in1` and `in2` with output size determined by `mode`, and
+    boundary conditions determined by `boundary` and `fillvalue`.
+
+    Parameters
+    ----------
+    in1 : array_like
+        First input.
+    in2 : array_like
+        Second input. Should have the same number of dimensions as `in1`.
+    mode : str {'full', 'valid', 'same'}, optional
+        A string indicating the size of the output:
+
+        ``full``
+           The output is the full discrete linear cross-correlation
+           of the inputs. (Default)
+        ``valid``
+           The output consists only of those elements that do not
+           rely on the zero-padding. In 'valid' mode, either `in1` or `in2`
+           must be at least as large as the other in every dimension.
+        ``same``
+           The output is the same size as `in1`, centered
+           with respect to the 'full' output.
+    boundary : str {'fill', 'wrap', 'symm'}, optional
+        A flag indicating how to handle boundaries:
+
+        ``fill``
+           pad input arrays with fillvalue. (default)
+        ``wrap``
+           circular boundary conditions.
+        ``symm``
+           symmetrical boundary conditions.
+
+    fillvalue : scalar, optional
+        Value to fill pad input arrays with. Default is 0.
+
+    Returns
+    -------
+    correlate2d : ndarray
+        A 2-dimensional array containing a subset of the discrete linear
+        cross-correlation of `in1` with `in2`.
+
+    Notes
+    -----
+    When using "same" mode with even-length inputs, the outputs of `correlate`
+    and `correlate2d` differ: There is a 1-index offset between them.
+
+    Examples
+    --------
+    Use 2D cross-correlation to find the location of a template in a noisy
+    image:
+
+    >>> import numpy as np
+    >>> from scipy import signal, datasets, ndimage
+    >>> rng = np.random.default_rng()
+    >>> face = datasets.face(gray=True) - datasets.face(gray=True).mean()
+    >>> face = ndimage.zoom(face[30:500, 400:950], 0.5)  # extract the face
+    >>> template = np.copy(face[135:165, 140:175])  # right eye
+    >>> template -= template.mean()
+    >>> face = face + rng.standard_normal(face.shape) * 50  # add noise
+    >>> corr = signal.correlate2d(face, template, boundary='symm', mode='same')
+    >>> y, x = np.unravel_index(np.argmax(corr), corr.shape)  # find the match
+
+    >>> import matplotlib.pyplot as plt
+    >>> fig, (ax_orig, ax_template, ax_corr) = plt.subplots(3, 1,
+    ...                                                     figsize=(6, 15))
+    >>> ax_orig.imshow(face, cmap='gray')
+    >>> ax_orig.set_title('Original')
+    >>> ax_orig.set_axis_off()
+    >>> ax_template.imshow(template, cmap='gray')
+    >>> ax_template.set_title('Template')
+    >>> ax_template.set_axis_off()
+    >>> ax_corr.imshow(corr, cmap='gray')
+    >>> ax_corr.set_title('Cross-correlation')
+    >>> ax_corr.set_axis_off()
+    >>> ax_orig.plot(x, y, 'ro')
+    >>> fig.show()
+
+    """
+    xp = array_namespace(in1, in2)
+    in1 = np.asarray(in1)
+    in2 = np.asarray(in2)
+
+    if not in1.ndim == in2.ndim == 2:
+        raise ValueError('correlate2d inputs must both be 2-D arrays')
+
+    swapped_inputs = _inputs_swap_needed(mode, in1.shape, in2.shape)
+    if swapped_inputs:
+        in1, in2 = in2, in1
+
+    val = _valfrommode(mode)
+    bval = _bvalfromboundary(boundary)
+    out = _sigtools._convolve2d(in1, in2.conj(), 0, val, bval, fillvalue)
+
+    if swapped_inputs:
+        out = out[::-1, ::-1]
+
+    return xp.asarray(out)
+
+
+def medfilt2d(input, kernel_size=3):
+    """
+    Median filter a 2-dimensional array.
+
+    Apply a median filter to the `input` array using a local window-size
+    given by `kernel_size` (must be odd). The array is zero-padded
+    automatically.
+
+    Parameters
+    ----------
+    input : array_like
+        A 2-dimensional input array.
+    kernel_size : array_like, optional
+        A scalar or a list of length 2, giving the size of the
+        median filter window in each dimension.  Elements of
+        `kernel_size` should be odd.  If `kernel_size` is a scalar,
+        then this scalar is used as the size in each dimension.
+        Default is a kernel of size (3, 3).
+
+    Returns
+    -------
+    out : ndarray
+        An array the same size as input containing the median filtered
+        result.
+
+    See Also
+    --------
+    scipy.ndimage.median_filter
+
+    Notes
+    -----
+    This is faster than `medfilt` when the input dtype is ``uint8``,
+    ``float32``, or ``float64``; for other types, this falls back to
+    `medfilt`. In some situations, `scipy.ndimage.median_filter` may be
+    faster than this function.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> x = np.arange(25).reshape(5, 5)
+    >>> x
+    array([[ 0,  1,  2,  3,  4],
+           [ 5,  6,  7,  8,  9],
+           [10, 11, 12, 13, 14],
+           [15, 16, 17, 18, 19],
+           [20, 21, 22, 23, 24]])
+
+    # Replaces i,j with the median out of 5*5 window
+
+    >>> signal.medfilt2d(x, kernel_size=5)
+    array([[ 0,  0,  2,  0,  0],
+           [ 0,  3,  7,  4,  0],
+           [ 2,  8, 12,  9,  4],
+           [ 0,  8, 12,  9,  0],
+           [ 0,  0, 12,  0,  0]])
+
+    # Replaces i,j with the median out of default 3*3 window
+
+    >>> signal.medfilt2d(x)
+    array([[ 0,  1,  2,  3,  0],
+           [ 1,  6,  7,  8,  4],
+           [ 6, 11, 12, 13,  9],
+           [11, 16, 17, 18, 14],
+           [ 0, 16, 17, 18,  0]])
+
+    # Replaces i,j with the median out of default 5*3 window
+
+    >>> signal.medfilt2d(x, kernel_size=[5,3])
+    array([[ 0,  1,  2,  3,  0],
+           [ 0,  6,  7,  8,  3],
+           [ 5, 11, 12, 13,  8],
+           [ 5, 11, 12, 13,  8],
+           [ 0, 11, 12, 13,  0]])
+
+    # Replaces i,j with the median out of default 3*5 window
+
+    >>> signal.medfilt2d(x, kernel_size=[3,5])
+    array([[ 0,  0,  2,  1,  0],
+           [ 1,  5,  7,  6,  3],
+           [ 6, 10, 12, 11,  8],
+           [11, 15, 17, 16, 13],
+           [ 0, 15, 17, 16,  0]])
+
+    # As seen in the examples,
+    # kernel numbers must be odd and not exceed original array dim
+
+    """
+    xp = array_namespace(input)
+
+    image = np.asarray(input)
+
+    # checking dtype.type, rather than just dtype, is necessary for
+    # excluding np.longdouble with MS Visual C.
+    if image.dtype.type not in (np.ubyte, np.float32, np.float64):
+        return xp.asarray(medfilt(image, kernel_size))
+
+    if kernel_size is None:
+        kernel_size = [3] * 2
+    kernel_size = np.asarray(kernel_size)
+    if kernel_size.shape == ():
+        kernel_size = np.repeat(kernel_size.item(), 2)
+
+    for size in kernel_size:
+        if (size % 2) != 1:
+            raise ValueError("Each element of kernel_size should be odd.")
+
+    result_np = _sigtools._medfilt2d(image, kernel_size)
+    return xp.asarray(result_np)
+
+
+def lfilter(b, a, x, axis=-1, zi=None):
+    """
+    Filter data along one-dimension with an IIR or FIR filter.
+
+    Filter a data sequence, `x`, using a digital filter.  This works for many
+    fundamental data types (including Object type).  The filter is a direct
+    form II transposed implementation of the standard difference equation
+    (see Notes).
+
+    The function `sosfilt` (and filter design using ``output='sos'``) should be
+    preferred over `lfilter` for most filtering tasks, as second-order sections
+    have fewer numerical problems.
+
+    Parameters
+    ----------
+    b : array_like
+        The numerator coefficient vector in a 1-D sequence.
+    a : array_like
+        The denominator coefficient vector in a 1-D sequence.  If ``a[0]``
+        is not 1, then both `a` and `b` are normalized by ``a[0]``.
+    x : array_like
+        An N-dimensional input array.
+    axis : int, optional
+        The axis of the input data array along which to apply the
+        linear filter. The filter is applied to each subarray along
+        this axis.  Default is -1.
+    zi : array_like, optional
+        Initial conditions for the filter delays.  It is a vector
+        (or array of vectors for an N-dimensional input) of length
+        ``max(len(a), len(b)) - 1``.  If `zi` is None or is not given then
+        initial rest is assumed.  See `lfiltic` for more information.
+
+    Returns
+    -------
+    y : array
+        The output of the digital filter.
+    zf : array, optional
+        If `zi` is None, this is not returned, otherwise, `zf` holds the
+        final filter delay values.
+
+    See Also
+    --------
+    lfiltic : Construct initial conditions for `lfilter`.
+    lfilter_zi : Compute initial state (steady state of step response) for
+                 `lfilter`.
+    filtfilt : A forward-backward filter, to obtain a filter with zero phase.
+    savgol_filter : A Savitzky-Golay filter.
+    sosfilt: Filter data using cascaded second-order sections.
+    sosfiltfilt: A forward-backward filter using second-order sections.
+
+    Notes
+    -----
+    The filter function is implemented as a direct II transposed structure.
+    This means that the filter implements::
+
+       a[0]*y[n] = b[0]*x[n] + b[1]*x[n-1] + ... + b[M]*x[n-M]
+                             - a[1]*y[n-1] - ... - a[N]*y[n-N]
+
+    where `M` is the degree of the numerator, `N` is the degree of the
+    denominator, and `n` is the sample number.  It is implemented using
+    the following difference equations (assuming M = N)::
+
+         a[0]*y[n] = b[0] * x[n]               + d[0][n-1]
+           d[0][n] = b[1] * x[n] - a[1] * y[n] + d[1][n-1]
+           d[1][n] = b[2] * x[n] - a[2] * y[n] + d[2][n-1]
+         ...
+         d[N-2][n] = b[N-1]*x[n] - a[N-1]*y[n] + d[N-1][n-1]
+         d[N-1][n] = b[N] * x[n] - a[N] * y[n]
+
+    where `d` are the state variables.
+
+    The rational transfer function describing this filter in the
+    z-transform domain is::
+
+                             -1              -M
+                 b[0] + b[1]z  + ... + b[M] z
+         Y(z) = -------------------------------- X(z)
+                             -1              -N
+                 a[0] + a[1]z  + ... + a[N] z
+
+    Examples
+    --------
+    Generate a noisy signal to be filtered:
+
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+    >>> rng = np.random.default_rng()
+    >>> t = np.linspace(-1, 1, 201)
+    >>> x = (np.sin(2*np.pi*0.75*t*(1-t) + 2.1) +
+    ...      0.1*np.sin(2*np.pi*1.25*t + 1) +
+    ...      0.18*np.cos(2*np.pi*3.85*t))
+    >>> xn = x + rng.standard_normal(len(t)) * 0.08
+
+    Create an order 3 lowpass butterworth filter:
+
+    >>> b, a = signal.butter(3, 0.05)
+
+    Apply the filter to xn.  Use lfilter_zi to choose the initial condition of
+    the filter:
+
+    >>> zi = signal.lfilter_zi(b, a)
+    >>> z, _ = signal.lfilter(b, a, xn, zi=zi*xn[0])
+
+    Apply the filter again, to have a result filtered at an order the same as
+    filtfilt:
+
+    >>> z2, _ = signal.lfilter(b, a, z, zi=zi*z[0])
+
+    Use filtfilt to apply the filter:
+
+    >>> y = signal.filtfilt(b, a, xn)
+
+    Plot the original signal and the various filtered versions:
+
+    >>> plt.figure
+    >>> plt.plot(t, xn, 'b', alpha=0.75)
+    >>> plt.plot(t, z, 'r--', t, z2, 'r', t, y, 'k')
+    >>> plt.legend(('noisy signal', 'lfilter, once', 'lfilter, twice',
+    ...             'filtfilt'), loc='best')
+    >>> plt.grid(True)
+    >>> plt.show()
+
+    """
+    xp = array_namespace(b, a, x, zi)
+
+    b = np.atleast_1d(b)
+    a = np.atleast_1d(a)
+    x = np.asarray(x)
+    if zi is not None:
+       zi = np.asarray(zi)
+
+    if not (b.ndim == 1 and xp_size(b) > 0):
+        raise ValueError(f"Parameter b is not a non-empty 1d array, since {b.shape=}!")
+    if not (a.ndim == 1 and xp_size(a) > 0):
+        raise ValueError(f"Parameter a is not a non-empty 1d array, since {a.shape=}!")
+
+    if len(a) == 1:
+        # This path only supports types fdgFDGO to mirror _linear_filter below.
+        # Any of b, a, x, or zi can set the dtype, but there is no default
+        # casting of other types; instead a NotImplementedError is raised.
+        b = np.asarray(b)
+        a = np.asarray(a)
+        x = _validate_x(x)
+        inputs = [b, a, x]
+        if zi is not None:
+            # _linear_filter does not broadcast zi, but does do expansion of
+            # singleton dims.
+            zi = np.asarray(zi)
+            if zi.ndim != x.ndim:
+                raise ValueError("Dimensions of parameters x and zi must match, but " +
+                                 f"{x.ndim=}, {zi.ndim=}!")
+            expected_shape = list(x.shape)
+            expected_shape[axis] = b.shape[0] - 1
+            expected_shape = tuple(expected_shape)
+            # check the trivial case where zi is the right shape first
+            if zi.shape != expected_shape:
+                strides = zi.ndim * [None]
+                if axis < 0:
+                    axis += zi.ndim
+                for k in range(zi.ndim):
+                    if k == axis and zi.shape[k] == expected_shape[k]:
+                        strides[k] = zi.strides[k]
+                    elif k != axis and zi.shape[k] == expected_shape[k]:
+                        strides[k] = zi.strides[k]
+                    elif k != axis and zi.shape[k] == 1:
+                        strides[k] = 0
+                    else:
+                        raise ValueError('Unexpected shape for parameter zi: expected '
+                                         f'{expected_shape}, found {zi.shape}.')
+                zi = np.lib.stride_tricks.as_strided(zi, expected_shape,
+                                                     strides)
+            inputs.append(zi)
+        dtype = np.result_type(*inputs)
+
+        if dtype.char not in 'fdgFDGO':
+            raise NotImplementedError("Parameter's dtypes produced result type " +
+                                      f"'{dtype}', which is not supported!")
+
+        b = np.array(b, dtype=dtype)
+        a = np.asarray(a, dtype=dtype)
+        b /= a[0]
+        x = np.asarray(x, dtype=dtype)
+
+        out_full = np.apply_along_axis(lambda y: np.convolve(b, y), axis, x)
+        ind = out_full.ndim * [slice(None)]
+        if zi is not None:
+            ind[axis] = slice(zi.shape[axis])
+            out_full[tuple(ind)] += zi
+
+        ind[axis] = slice(out_full.shape[axis] - len(b) + 1)
+        out = out_full[tuple(ind)]
+
+        if zi is None:
+            return xp.asarray(out)
+        else:
+            ind[axis] = slice(out_full.shape[axis] - len(b) + 1, None)
+            zf = out_full[tuple(ind)]
+            return xp.asarray(out), xp.asarray(zf)
+    else:
+        if zi is None:
+            result =_sigtools._linear_filter(b, a, x, axis)
+            return xp.asarray(result)
+        else:
+            out, zf = _sigtools._linear_filter(b, a, x, axis, zi)
+            return xp.asarray(out), xp.asarray(zf)
+
+
+def lfiltic(b, a, y, x=None):
+    """
+    Construct initial conditions for lfilter given input and output vectors.
+
+    Given a linear filter (b, a) and initial conditions on the output `y`
+    and the input `x`, return the initial conditions on the state vector zi
+    which is used by `lfilter` to generate the output given the input.
+
+    Parameters
+    ----------
+    b : array_like
+        Linear filter term.
+    a : array_like
+        Linear filter term.
+    y : array_like
+        Initial conditions.
+
+        If ``N = len(a) - 1``, then ``y = {y[-1], y[-2], ..., y[-N]}``.
+
+        If `y` is too short, it is padded with zeros.
+    x : array_like, optional
+        Initial conditions.
+
+        If ``M = len(b) - 1``, then ``x = {x[-1], x[-2], ..., x[-M]}``.
+
+        If `x` is not given, its initial conditions are assumed zero.
+
+        If `x` is too short, it is padded with zeros.
+
+    Returns
+    -------
+    zi : ndarray
+        The state vector ``zi = {z_0[-1], z_1[-1], ..., z_K-1[-1]}``,
+        where ``K = max(M, N)``.
+
+    See Also
+    --------
+    lfilter, lfilter_zi
+
+    """
+    xp = array_namespace(a, b, y, x)
+
+    a = xpx.atleast_nd(xp.asarray(a), ndim=1, xp=xp)
+    b = xpx.atleast_nd(xp.asarray(b), ndim=1, xp=xp)
+    if a.ndim > 1:
+        raise ValueError('Filter coefficients `a` must be 1-D.')
+    if b.ndim > 1:
+        raise ValueError('Filter coefficients `b` must be 1-D.')
+    N = a.shape[0] - 1
+    M = b.shape[0] - 1
+    K = max(M, N)
+    y = xp.asarray(y)
+
+    if N < 0:
+        raise ValueError("There must be at least one `a` coefficient.")
+
+    if x is None:
+        result_type = xp.result_type(b, a, y)
+        if xp.isdtype(result_type, ('bool', 'integral')):  #'bui':
+            result_type = xp.float64
+        x = xp.zeros(M, dtype=result_type)
+    else:
+        x = xp.asarray(x)
+
+        result_type = xp.result_type(b, a, y, x)
+        if xp.isdtype(result_type, ('bool', 'integral')):  #'bui':
+            result_type = xp.float64
+        x = xp.astype(x, result_type)
+
+        L = xp_size(x)
+        if L < M:
+            x = xp.concat((x, xp.zeros(M - L)))
+
+    y = xp.astype(y, result_type)
+    zi = xp.zeros(K, dtype=result_type)
+
+    L = xp_size(y)
+    if L < N:
+        y = xp.concat((y, xp.zeros(N - L)))
+
+    for m in range(M):
+        zi[m] = xp.sum(b[m + 1:] * x[:M - m], axis=0)
+
+    for m in range(N):
+        zi[m] -= xp.sum(a[m + 1:] * y[:N - m], axis=0)
+
+    if a[0] != 1.:
+        if a[0] == 0.:
+            raise ValueError("First `a` filter coefficient must be non-zero.")
+        zi /= a[0]
+
+    return zi
+
+
+def deconvolve(signal, divisor):
+    """Deconvolves ``divisor`` out of ``signal`` using inverse filtering.
+
+    Returns the quotient and remainder such that
+    ``signal = convolve(divisor, quotient) + remainder``
+
+    Parameters
+    ----------
+    signal : (N,) array_like
+        Signal data, typically a recorded signal
+    divisor : (N,) array_like
+        Divisor data, typically an impulse response or filter that was
+        applied to the original signal
+
+    Returns
+    -------
+    quotient : ndarray
+        Quotient, typically the recovered original signal
+    remainder : ndarray
+        Remainder
+
+    See Also
+    --------
+    numpy.polydiv : performs polynomial division (same operation, but
+                    also accepts poly1d objects)
+
+    Examples
+    --------
+    Deconvolve a signal that's been filtered:
+
+    >>> from scipy import signal
+    >>> original = [0, 1, 0, 0, 1, 1, 0, 0]
+    >>> impulse_response = [2, 1]
+    >>> recorded = signal.convolve(impulse_response, original)
+    >>> recorded
+    array([0, 2, 1, 0, 2, 3, 1, 0, 0])
+    >>> recovered, remainder = signal.deconvolve(recorded, impulse_response)
+    >>> recovered
+    array([ 0.,  1.,  0.,  0.,  1.,  1.,  0.,  0.])
+    >>> remainder
+    array([0., 0., 0., 0., 0., 0., 0., 0., 0.])
+    """
+    xp = array_namespace(signal, divisor)
+
+    num = xpx.atleast_nd(xp.asarray(signal), ndim=1, xp=xp)
+    den = xpx.atleast_nd(xp.asarray(divisor), ndim=1, xp=xp)
+    if not (num.ndim == 1 and xp_size(num) > 0):
+        raise ValueError("Parameter signal must be non-empty 1d array, " +
+                         f"but its shape is {num.shape}!")
+    if not (den.ndim == 1 and xp_size(den) > 0):
+        raise ValueError("Parameter divisor must be non-empty 1d array, " +
+                         f"but its shape is {den.shape}!")
+    N = num.shape[0]
+    D = den.shape[0]
+    if D > N:
+        quot = []
+        rem = num
+    else:
+        input = xp.zeros(N - D + 1, dtype=xp.float64)
+        input = xpx.at(input)[0].set(1)
+        quot = lfilter(num, den, input)
+        rem = num - convolve(den, quot, mode='full')
+    return quot, rem
+
+
+def hilbert(x, N=None, axis=-1):
+    r"""FFT-based computation of the analytic signal.
+
+    The analytic signal is calculated by zeroing out the negative frequencies and
+    doubling the amplitudes of the positive frequencies in the FFT domain.
+    The imaginary part of the result is the hilbert transform of the real-valued input
+    signal.
+
+    The transformation is done along the last axis by default.
+
+    For numpy arrays, `scipy.fft.set_workers` can be used to change the number of
+    workers used for the FFTs.
+
+    Parameters
+    ----------
+    x : array_like
+        Signal data.  Must be real.
+    N : int, optional
+        Number of output samples. `x` is initially cropped or zero-padded to length
+        `N` along `axis`.  Default: ``x.shape[axis]``
+    axis : int, optional
+        Axis along which to do the transformation.  Default: -1.
+
+    Returns
+    -------
+    xa : ndarray
+        Analytic signal of `x`, of each 1-D array along `axis`
+
+    Notes
+    -----
+    The analytic signal ``x_a(t)`` of a real-valued signal ``x(t)``
+    can be expressed as [1]_
+
+    .. math:: x_a = F^{-1}(F(x) 2U) = x + i y\ ,
+
+    where `F` is the Fourier transform, `U` the unit step function,
+    and `y` the Hilbert transform of `x`. [2]_
+
+    In other words, the negative half of the frequency spectrum is zeroed
+    out, turning the real-valued signal into a complex-valued signal.  The Hilbert
+    transformed signal can be obtained from ``np.imag(hilbert(x))``, and the
+    original signal from ``np.real(hilbert(x))``.
+
+    References
+    ----------
+    .. [1] Wikipedia, "Analytic signal".
+           https://en.wikipedia.org/wiki/Analytic_signal
+    .. [2] Wikipedia, "Hilbert Transform".
+           https://en.wikipedia.org/wiki/Hilbert_transform
+    .. [3] Leon Cohen, "Time-Frequency Analysis", 1995. Chapter 2.
+    .. [4] Alan V. Oppenheim, Ronald W. Schafer. Discrete-Time Signal
+           Processing, Third Edition, 2009. Chapter 12.
+           ISBN 13: 978-1292-02572-8
+
+    See Also
+    --------
+    envelope: Compute envelope of a real- or complex-valued signal.
+
+    Examples
+    --------
+    In this example we use the Hilbert transform to determine the amplitude
+    envelope and instantaneous frequency of an amplitude-modulated signal.
+
+    Let's create a chirp of which the frequency increases from 20 Hz to 100 Hz and
+    apply an amplitude modulation:
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.signal import hilbert, chirp
+    ...
+    >>> duration, fs = 1, 400  # 1 s signal with sampling frequency of 400 Hz
+    >>> t = np.arange(int(fs*duration)) / fs  # timestamps of samples
+    >>> signal = chirp(t, 20.0, t[-1], 100.0)
+    >>> signal *= (1.0 + 0.5 * np.sin(2.0*np.pi*3.0*t) )
+
+    The amplitude envelope is given by the magnitude of the analytic signal. The
+    instantaneous frequency can be obtained by differentiating the
+    instantaneous phase in respect to time. The instantaneous phase corresponds
+    to the phase angle of the analytic signal.
+
+    >>> analytic_signal = hilbert(signal)
+    >>> amplitude_envelope = np.abs(analytic_signal)
+    >>> instantaneous_phase = np.unwrap(np.angle(analytic_signal))
+    >>> instantaneous_frequency = np.diff(instantaneous_phase) / (2.0*np.pi) * fs
+    ...
+    >>> fig, (ax0, ax1) = plt.subplots(nrows=2, sharex='all', tight_layout=True)
+    >>> ax0.set_title("Amplitude-modulated Chirp Signal")
+    >>> ax0.set_ylabel("Amplitude")
+    >>> ax0.plot(t, signal, label='Signal')
+    >>> ax0.plot(t, amplitude_envelope, label='Envelope')
+    >>> ax0.legend()
+    >>> ax1.set(xlabel="Time in seconds", ylabel="Frequency in Hz", ylim=(0, 120))
+    >>> ax1.plot(t[1:], instantaneous_frequency, 'C2-',
+    ...          label='Instantaneous Frequency')
+    >>> ax1.legend()
+    >>> plt.show()
+
+    """
+    xp = array_namespace(x)
+
+    x = xp.asarray(x)
+    if xp.isdtype(x.dtype, 'complex floating'):
+        raise ValueError("x must be real.")
+
+    if N is None:
+        N = x.shape[axis]
+    if N <= 0:
+        raise ValueError("N must be positive.")
+
+    Xf = sp_fft.fft(x, N, axis=axis)
+    Xf = xp.moveaxis(Xf, axis, -1)
+    if N % 2 == 0:
+        Xf = xpx.at(Xf)[..., 1: N // 2].multiply(2.0)
+        Xf = xpx.at(Xf)[..., N // 2 + 1:N].set(0.0)
+    else:
+        Xf = xpx.at(Xf)[..., 1: (N + 1) // 2].multiply(2.0)
+        Xf = xpx.at(Xf)[..., (N + 1) // 2:N].set(0.0)
+
+    Xf = xp.moveaxis(Xf, -1, axis)
+    x = sp_fft.ifft(Xf, axis=axis)
+    return x
+
+
+def hilbert2(x, N=None, axes=(-2, -1)):
+    r"""Compute the '2-D' analytic signal of `x`.
+
+    The 2-D analytic signal is calculated as a so-called "single-orthant" transform.
+    This is achieved by applying one-dimensional Hilbert functions (as in
+    `~scipy.signal.hilbert`) to the first and to the second array axis in Fourier space.
+
+    For NumPy arrays, `scipy.fft.set_workers` can be used to change the number of
+    workers used for the FFTs.
+
+    Parameters
+    ----------
+    x : array_like
+        Input signal. Must be at least two-dimensional.
+    N : int or tuple of two ints, optional
+        Number of output samples. `x` is initially cropped or zero-padded to length
+        `N` along `axes`.  Default: ``x.shape[i] for i in axes``
+    axes : tuple of two ints, optional
+        Axes along which to do the transformation.  Default: (-2, -1).
+
+        .. versionchanged:: 1.17
+
+            Added `axes` parameter
+
+    Returns
+    -------
+    xa : ndarray
+        Analytic signal of `x` taken along given axes.
+
+    Notes
+    -----
+    The "single-orthant" transform, as defined in [2]_, is calculated by performing the
+    following steps:
+
+    1. Calculate the two-dimensional FFT of the input, i.e.,
+
+       .. math::
+
+            X[p,q] = \sum_{k,l=0}^{N_0,N_1} x[k,l]\,
+                                                 e^{-2j\pi k p/N_0}\, e^{-2j\pi l q/N_1}
+
+    2. Zero negative frequency bins and double their positive counterparts, i.e.,
+
+       .. math::
+
+           X_a[p,q] = \big(1 + s_{N_0}(p)\big) \big(1 + s_{N_1}(q)\big) X[p,q]
+
+       with :math:`s_N(.)` being a modified sign function defined as
+
+       .. math::
+
+           s_N(p) := \begin{cases}
+                                 -1 & \text{ for } p < 0\ ,\\
+                       \phantom{-}0 & \text{ for } p = 0\ ,\\
+                                 +1 & \text{ for } 1 \leq p < (N+1) // 2\ ,\\
+                       \phantom{-}0 & \text{ elsewhere.}
+                     \end{cases}
+
+       The limitation of the ":math:`+1`" case to the range of ``[1:(N+1)//2]``
+       accounts for the unpaired Nyquist frequency bin at :math:`N/2` for even
+       :math:`N`. Note that :math:`X_a[p] = \big(1 + s_N(p)\big) X[p]` is the
+       one-dimensional Hilbert function (as in `~scipy.signal.hilbert`) in Fourier
+       space.
+
+    3. Produce the analytic signal by performing the inverse FFT, i.e.,
+
+       .. math::
+
+           x_a[k, l] = \frac{1}{N_0 N_1}
+                 \sum_{p,q=0}^{N_0,N_1} X_a[p,q]\, e^{2j\pi k p/N_0}\, e^{2j\pi l q/N_1}
+
+    The "single-orthant" transform is not the only possible definition of an analytic
+    signal in multiple dimensions (as noted in [1]_). Consult [3]_ for a description of
+    properties that this 2-D transform does and does not share with the 1-D transform.
+    The second example below shows one of the downsides of this approach.
+
+    References
+    ----------
+    .. [1] Wikipedia, "Analytic signal",
+        https://en.wikipedia.org/wiki/Analytic_signal
+    .. [2] Hahn, Stefan L. "Multidimensional complex signals with
+        single-orthant spectra." Proceedings of the IEEE 80.8
+        (1992): 1287-1300.
+        `PDF <https://ieeexplore.ieee.org/iel1/5/4083/00158601.pdf>`__
+    .. [3] Bülow, Thomas, and Gerald Sommer. "A novel approach to the 2D analytic
+        signal." In International Conference on Computer Analysis of Images and
+        Patterns, pp. 25-32. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999.
+        `PDF <https://www.informatik.uni-kiel.de/inf/Sommer/doc/Publications/tbl/caip99.pdf>`__
+
+    Examples
+    --------
+    The following example calculates the two-dimensional analytic signal from a single
+    impulse with an added constant offset. The impulse produces an FFT where each bin
+    has a value of one and the constant offset component produces only a non-zero
+    component at the ``(0,0)`` bin.
+
+    >>> import numpy as np
+    >>> from scipy.fft import fft2, fftshift, ifftshift
+    >>> from scipy.signal import hilbert2
+    ...
+    >>> # Input signal is unit impulse with a constant offset:
+    >>> x = np.ones((5, 5)) / 5
+    >>> x[0, 0] += 1
+    ...
+    >>> X = fftshift(fft2(x))  # Zero frequency bin is at center
+    >>> print(X)
+    [[1.-0.j 1.-0.j 1.-0.j 1.+0.j 1.+0.j]
+     [1.-0.j 1.-0.j 1.-0.j 1.+0.j 1.+0.j]
+     [1.-0.j 1.-0.j 6.-0.j 1.+0.j 1.+0.j]
+     [1.-0.j 1.-0.j 1.+0.j 1.+0.j 1.+0.j]
+     [1.-0.j 1.-0.j 1.+0.j 1.+0.j 1.+0.j]]
+    >>> x_a = hilbert2(x)
+    >>> X_a = fftshift(fft2(x_a))
+    >>> print(np.round(X_a, 3))
+    [[ 0.+0.j  0.+0.j -0.+0.j  0.+0.j  0.+0.j]
+     [ 0.+0.j  0.+0.j -0.+0.j  0.+0.j  0.+0.j]
+     [ 0.+0.j  0.+0.j  6.+0.j  2.+0.j  2.+0.j]
+     [ 0.+0.j  0.+0.j  2.+0.j  4.+0.j  4.+0.j]
+     [ 0.+0.j  0.+0.j  2.+0.j  4.+0.j  4.+0.j]]
+
+    The FFT of the result illustrates that the values of the lower right quadrant (or
+    orthant) with purely positive frequency bins have been quadrupled. The values at its
+    borders, where only one frequency component is zero, are doubled. The zero frequency
+    bin ``(0, 0)`` has not been altered. All other quadrants have been set to zero.
+
+    This second example illustrates a problem with the "single-orthant" convention. A
+    purely real signal can produce an analytic signal which is completely zero:
+
+    >>> from scipy.fft import fft2, fftshift, ifft2, ifftshift
+    >>> from scipy.signal import hilbert2
+    ...
+    >>> # Create a real signal by ensuring `Z[-p,-q] == np.conj(Z[p,q])` holds:
+    >>> Z = np.array([[0, 0, 0, 0, 0],
+    ...               [0, 0, 0, 1, 0],
+    ...               [0, 0, 0, 0, 0],
+    ...               [0, 1, 0, 0, 0],
+    ...               [0, 0, 0, 0, 0]]) * 25
+    >>> z = ifft2(ifftshift(Z))
+    >>> np.allclose(z.imag, 0)  # z is a real signal
+    True
+    >>> np.sum(z.real**2)  # z.real is non-zero
+    np.float64(50.0)
+    >>> z_a = hilbert2(z.real)
+    >>> np.allclose(z_a, 0)  # analytic signal is zero
+    True
+
+    """
+    xp = array_namespace(x)
+    x = xpx.atleast_nd(xp.asarray(x), ndim=2, xp=xp)
+    if xp.isdtype(x.dtype, 'complex floating'):
+        raise ValueError("x must be real.")
+    if len(axes) != 2:
+        raise ValueError("axes must be a tuple of length 2")
+    if axes[0] == axes[1]:
+        raise ValueError("axes must contain 2 distinct axes")
+
+    if N is None:
+        N = (x.shape[axes[0]], x.shape[axes[1]])
+    elif isinstance(N, int):
+        if N <= 0:
+            raise ValueError("N must be positive.")
+        N = (N, N)
+    elif len(N) != 2 or np.any(np.asarray(N) <= 0):
+        raise ValueError("When given as a tuple, N must hold exactly "
+                         "two positive integers")
+
+    Xf = sp_fft.fft2(x, N, axes=axes)
+    Xf = xp.moveaxis(Xf, axes, (-2, -1))
+    k0, k1 = (N[0] + 1) // 2, (N[1] + 1) // 2
+
+    if k0 > 1:  # condition k0 > 1 needed for Dask backend
+        Xf = xpx.at(Xf)[..., 1:k0, :].multiply(2.0)
+    if k1 > 1:  # condition k1 > 1 needed for Dask backend
+        Xf = xpx.at(Xf)[..., :, 1:k1].multiply(2.0)
+    Xf = xpx.at(Xf)[..., k0:, :].set(0.0)
+    Xf = xpx.at(Xf)[..., :, k1:].set(0.0)
+
+    Xf = xp.moveaxis(Xf, (-2, -1), axes)
+    x = sp_fft.ifft2(Xf, axes=axes)
+    return x
+
+
+def envelope(z, bp_in: tuple[int | None, int | None] = (1, None), *,
+             n_out: int | None = None, squared: bool = False,
+             residual: Literal['lowpass', 'all', None] = 'lowpass',
+             axis: int = -1):
+    r"""Compute the envelope of a real- or complex-valued signal.
+
+    Parameters
+    ----------
+    z : ndarray
+        Real- or complex-valued input signal, which is assumed to be made up of ``n``
+        samples and having sampling interval ``T``. `z` may also be a multidimensional
+        array with the time axis being defined by `axis`.
+    bp_in : tuple[int | None, int | None], optional
+        2-tuple defining the frequency band ``bp_in[0]:bp_in[1]`` of the input filter.
+        The corner frequencies are specified as integer multiples of ``1/(n*T)`` with
+        ``-n//2 <= bp_in[0] < bp_in[1] <= (n+1)//2`` being the allowed frequency range.
+        ``None`` entries are replaced with ``-n//2`` or ``(n+1)//2`` respectively. The
+        default of ``(1, None)`` removes the mean value as well as the negative
+        frequency components.
+    n_out : int | None, optional
+        If not ``None`` the output will be resampled to `n_out` samples. The default
+        of ``None`` sets the output to the same length as the input `z`.
+    squared : bool, optional
+        If set, the square of the envelope is returned. The bandwidth of the squared
+        envelope is often smaller than the non-squared envelope bandwidth due to the
+        nonlinear nature of the utilized absolute value function. I.e., the embedded
+        square root function typically produces addiational harmonics.
+        The default is ``False``.
+    residual : Literal['lowpass', 'all', None], optional
+        This option determines what kind of residual, i.e., the signal part which the
+        input bandpass filter removes, is returned. ``'all'`` returns everything except
+        the contents of the frequency band ``bp_in[0]:bp_in[1]``, ``'lowpass'``
+        returns the contents of the frequency band ``< bp_in[0]``. If ``None`` then
+        only the envelope is returned. Default: ``'lowpass'``.
+    axis : int, optional
+       Axis of `z` over which to compute the envelope. Default is last the axis.
+
+    Returns
+    -------
+    ndarray
+        If parameter `residual` is ``None`` then an array ``z_env`` with the same shape
+        as the input `z` is returned, containing its envelope. Otherwise, an array with
+        shape ``(2, *z.shape)``, containing the arrays ``z_env`` and ``z_res``, stacked
+        along the first axis, is returned.
+        It allows unpacking, i.e., ``z_env, z_res = envelope(z, residual='all')``.
+        The residual ``z_res`` contains the signal part which the input bandpass filter
+        removed, depending on the parameter `residual`. Note that for real-valued
+        signals, a real-valued residual is returned. Hence, the negative frequency
+        components of `bp_in` are ignored.
+
+    Notes
+    -----
+    Any complex-valued signal :math:`z(t)` can be described by a real-valued
+    instantaneous amplitude :math:`a(t)` and a real-valued instantaneous phase
+    :math:`\phi(t)`, i.e., :math:`z(t) = a(t) \exp\!\big(j \phi(t)\big)`. The
+    envelope is defined as the absolute value of the amplitude :math:`|a(t)| = |z(t)|`,
+    which is at the same time the absolute value of the signal. Hence, :math:`|a(t)|`
+    "envelopes" the class of all signals with amplitude :math:`a(t)` and arbitrary
+    phase :math:`\phi(t)`.
+    For real-valued signals, :math:`x(t) = a(t) \cos\!\big(\phi(t)\big)` is the
+    analogous formulation. Hence, :math:`|a(t)|` can be determined by converting
+    :math:`x(t)` into an analytic signal :math:`z_a(t)` by means of a Hilbert
+    transform, i.e.,
+    :math:`z_a(t) = a(t) \cos\!\big(\phi(t)\big) + j a(t) \sin\!\big(\phi(t) \big)`,
+    which produces a complex-valued signal with the same envelope :math:`|a(t)|`.
+
+    The implementation is based on computing the FFT of the input signal and then
+    performing the necessary operations in Fourier space. Hence, the typical :ref:`FFT
+    caveats <tutorial_FFT_Caveats>` need to be taken into account. The frequency
+    spacing ``1 / (n*T)`` for corner frequencies of the bandpass filter corresponds to
+    the frequencies produced by ``scipy.fft.fftfreq(len(z), T)``.
+
+    If the envelope of a complex-valued signal `z` with no bandpass filtering is
+    desired, i.e., ``bp_in=(None, None)``, then the envelope corresponds to the
+    absolute value. Hence, it is more efficient to use ``np.abs(z)`` instead of this
+    function.
+
+    Although computing the envelope based on the analytic signal [1]_ is the natural
+    method for real-valued signals, other methods are also frequently used. The most
+    popular alternative is probably the so-called "square-law" envelope detector and
+    its relatives [2]_. They do not always compute the correct result for all kinds of
+    signals, but are usually correct and typically computationally more efficient for
+    most kinds of narrowband signals. The definition for an envelope presented here is
+    common where instantaneous amplitude and phase are of interest (e.g., as described
+    in [3]_). There exist also other concepts, which rely on the general mathematical
+    idea of an envelope [4]_: A pragmatic approach is to determine all upper and lower
+    signal peaks and use a spline interpolation to determine the curves [5]_.
+
+
+    References
+    ----------
+    .. [1] "Analytic Signal", Wikipedia,
+       https://en.wikipedia.org/wiki/Analytic_signal
+    .. [2] Lyons, Richard, "Digital envelope detection: The good, the bad, and the
+       ugly", IEEE Signal Processing Magazine 34.4 (2017): 183-187.
+       `PDF <https://community.infineon.com/gfawx74859/attachments/gfawx74859/psoc135/46469/1/R.%20Lyons_envelope_detection_v3.pdf>`__
+    .. [3] T.G. Kincaid, "The complex representation of signals.",
+       TIS R67# MH5, General Electric Co. (1966).
+       `PDF <https://apps.dtic.mil/sti/tr/pdf/ADA953296.pdf>`__
+    .. [4] "Envelope (mathematics)", Wikipedia,
+       https://en.wikipedia.org/wiki/Envelope_(mathematics)
+    .. [5] Yang, Yanli. "A signal theoretic approach for envelope analysis of
+       real-valued signals." IEEE Access 5 (2017): 5623-5630.
+       `PDF <https://ieeexplore.ieee.org/iel7/6287639/6514899/07891054.pdf>`__
+
+
+    See Also
+    --------
+    hilbert: Compute analytic signal by means of Hilbert transform.
+
+
+    Examples
+    --------
+    The following plot illustrates the envelope of a signal with variable frequency and
+    a low-frequency drift. To separate the drift from the envelope, a 4 Hz highpass
+    filter is used. The low-pass residuum of the input bandpass filter is utilized to
+    determine an asymmetric upper and lower bound to enclose the signal. Due to the
+    smoothness of the resulting envelope, it is down-sampled from 500 to 40 samples.
+    Note that the instantaneous amplitude ``a_x`` and the computed envelope ``x_env``
+    are not perfectly identical. This is due to the signal not being perfectly periodic
+    as well as the existence of some spectral overlapping of ``x_carrier`` and
+    ``x_drift``. Hence, they cannot be completely separated by a bandpass filter.
+
+    >>> import matplotlib.pyplot as plt
+    >>> import numpy as np
+    >>> from scipy.signal.windows import gaussian
+    >>> from scipy.signal import envelope
+    ...
+    >>> n, n_out = 500, 40  # number of signal samples and envelope samples
+    >>> T = 2 / n  # sampling interval for 2 s duration
+    >>> t = np.arange(n) * T  # time stamps
+    >>> a_x = gaussian(len(t), 0.4/T)  # instantaneous amplitude
+    >>> phi_x = 30*np.pi*t + 35*np.cos(2*np.pi*0.25*t)  # instantaneous phase
+    >>> x_carrier = a_x * np.cos(phi_x)
+    >>> x_drift = 0.3 * gaussian(len(t), 0.4/T)  # drift
+    >>> x = x_carrier + x_drift
+    ...
+    >>> bp_in = (int(4 * (n*T)), None)  # 4 Hz highpass input filter
+    >>> x_env, x_res = envelope(x, bp_in, n_out=n_out)
+    >>> t_out = np.arange(n_out) * (n / n_out) * T
+    ...
+    >>> fg0, ax0 = plt.subplots(1, 1, tight_layout=True)
+    >>> ax0.set_title(r"$4\,$Hz Highpass Envelope of Drifting Signal")
+    >>> ax0.set(xlabel="Time in seconds", xlim=(0, n*T), ylabel="Amplitude")
+    >>> ax0.plot(t, x, 'C0-', alpha=0.5, label="Signal")
+    >>> ax0.plot(t, x_drift, 'C2--', alpha=0.25, label="Drift")
+    >>> ax0.plot(t_out, x_res+x_env, 'C1.-', alpha=0.5, label="Envelope")
+    >>> ax0.plot(t_out, x_res-x_env, 'C1.-', alpha=0.5, label=None)
+    >>> ax0.grid(True)
+    >>> ax0.legend()
+    >>> plt.show()
+
+    The second example provides a geometric envelope interpretation of complex-valued
+    signals: The following two plots show the complex-valued signal as a blue
+    3d-trajectory and the envelope as an orange round tube with varying diameter, i.e.,
+    as :math:`|a(t)| \exp(j\rho(t))`, with :math:`\rho(t)\in[-\pi,\pi]`. Also, the
+    projection into the 2d real and imaginary coordinate planes of trajectory and tube
+    is depicted. Every point of the complex-valued signal touches the tube's surface.
+
+    The left plot shows an analytic signal, i.e, the phase difference between
+    imaginary and real part is always 90 degrees, resulting in a spiraling trajectory.
+    It can be seen that in this case the real part has also the expected envelope,
+    i.e., representing the absolute value of the instantaneous amplitude.
+
+    The right plot shows the real part of that analytic signal being interpreted
+    as a complex-vauled signal, i.e., having zero imaginary part. There the resulting
+    envelope is not as smooth as in the analytic case and the instantaneous amplitude
+    in the real plane is not recovered. If ``z_re`` had been passed as a real-valued
+    signal, i.e., as ``z_re = z.real`` instead of ``z_re = z.real + 0j``, the result
+    would have been identical to the left plot. The reason for this is that real-valued
+    signals are interpreted as being the real part of a complex-valued analytic signal.
+
+    >>> import matplotlib.pyplot as plt
+    >>> import numpy as np
+    >>> from scipy.signal.windows import gaussian
+    >>> from scipy.signal import envelope
+    ...
+    >>> n, T = 1000, 1/1000  # number of samples and sampling interval
+    >>> t = np.arange(n) * T  # time stamps for 1 s duration
+    >>> f_c = 3  # Carrier frequency for signal
+    >>> z = gaussian(len(t), 0.3/T) * np.exp(2j*np.pi*f_c*t)  # analytic signal
+    >>> z_re = z.real + 0j  # complex signal with zero imaginary part
+    ...
+    >>> e_a, e_r = (envelope(z_, (None, None), residual=None) for z_ in (z, z_re))
+    ...
+    >>> # Generate grids to visualize envelopes as 2d and 3d surfaces:
+    >>> E2d_t, E2_amp = np.meshgrid(t, [-1, 1])
+    >>> E2d_1 = np.ones_like(E2_amp)
+    >>> E3d_t, E3d_phi = np.meshgrid(t, np.linspace(-np.pi, np.pi, 300))
+    >>> ma = 1.8  # maximum axis values in real and imaginary direction
+    ...
+    >>> fg0 = plt.figure(figsize=(6.2, 4.))
+    >>> ax00 = fg0.add_subplot(1, 2, 1, projection='3d')
+    >>> ax01 = fg0.add_subplot(1, 2, 2, projection='3d', sharex=ax00,
+    ...                        sharey=ax00, sharez=ax00)
+    >>> ax00.set_title("Analytic Signal")
+    >>> ax00.set(xlim=(0, 1), ylim=(-ma, ma), zlim=(-ma, ma))
+    >>> ax01.set_title("Real-valued Signal")
+    >>> for z_, e_, ax_ in zip((z, z.real), (e_a, e_r), (ax00, ax01)):
+    ...     ax_.set(xlabel="Time $t$", ylabel="Real Amp. $x(t)$",
+    ...             zlabel="Imag. Amp. $y(t)$")
+    ...     ax_.plot(t, z_.real, 'C0-', zs=-ma, zdir='z', alpha=0.5, label="Real")
+    ...     ax_.plot_surface(E2d_t, e_*E2_amp, -ma*E2d_1, color='C1', alpha=0.25)
+    ...     ax_.plot(t, z_.imag, 'C0-', zs=+ma, zdir='y', alpha=0.5, label="Imag.")
+    ...     ax_.plot_surface(E2d_t, ma*E2d_1, e_*E2_amp, color='C1', alpha=0.25)
+    ...     ax_.plot(t, z_.real, z_.imag, 'C0-', label="Signal")
+    ...     ax_.plot_surface(E3d_t, e_*np.cos(E3d_phi), e_*np.sin(E3d_phi),
+    ...                      color='C1', alpha=0.5, shade=True, label="Envelope")
+    ...     ax_.view_init(elev=22.7, azim=-114.3)
+    >>> fg0.subplots_adjust(left=0.08, right=0.97, wspace=0.15)
+    >>> plt.show()
+    """
+    xp = array_namespace(z)
+    if not (-z.ndim <= axis < z.ndim):
+        raise ValueError(f"Invalid parameter {axis=} for {z.shape=}!")
+    if not (z.shape[axis] > 0):
+        raise ValueError(f"z.shape[axis] not > 0 for {z.shape=}, {axis=}!")
+    if len(bp_in) != 2 or not all((isinstance(b_, int) or b_ is None) for b_ in bp_in):
+        raise ValueError(f"{bp_in=} isn't a 2-tuple of type (int | None, int | None)!")
+    if not ((isinstance(n_out, int) and 0 < n_out) or n_out is None):
+        raise ValueError(f"{n_out=} is not a positive integer or None!")
+    if residual not in ('lowpass', 'all', None):
+        raise ValueError(f"{residual=} not in ['lowpass', 'all', None]!")
+
+    n = z.shape[axis]  # number of time samples of input
+    n_out = n if n_out is None else n_out
+    fak = n_out / n  # scaling factor for resampling
+
+    bp = slice(bp_in[0] if bp_in[0] is not None else -(n//2),
+               bp_in[1] if bp_in[1] is not None else (n+1)//2)
+    if not (-n//2 <= bp.start < bp.stop <= (n+1)//2):
+        raise ValueError("`-n//2 <= bp_in[0] < bp_in[1] <= (n+1)//2` does not hold " +
+                         f"for n={z.shape[axis]=} and {bp_in=}!")
+
+    # moving active axis to end allows to use `...` for indexing:
+    z = xp.moveaxis(z, axis, -1)
+
+    if xp.isdtype(z.dtype, 'complex floating'):
+        Z = sp_fft.fft(z)
+    else:  # avoid calculating negative frequency bins for real signals:
+        dt = sp_fft.rfft(z[..., :1]).dtype
+        Z = xp.zeros_like(z, dtype=dt)
+        Z[..., :n//2 + 1] = sp_fft.rfft(z)
+        if bp.start > 0:  # make signal analytic within bp_in band:
+            Z[..., bp] *= 2
+        elif bp.stop > 0:
+            Z[..., 1:bp.stop] *= 2
+    if not (bp.start <= 0 < bp.stop):  # envelope is invariant to freq. shifts.
+        z_bb = sp_fft.ifft(Z[..., bp], n=n_out) * fak  # baseband signal
+    else:
+        bp_shift = slice(bp.start + n//2, bp.stop + n//2)
+        z_bb = sp_fft.ifft(sp_fft.fftshift(Z, axes=-1)[..., bp_shift], n=n_out) * fak
+
+    z_env = xp.abs(z_bb) if not squared else xp.real(z_bb) ** 2 + xp.imag(z_bb) ** 2
+    z_env = xp.moveaxis(z_env, -1, axis)
+
+    # Calculate the residual from the input bandpass filter:
+    if residual is None:
+        return z_env
+    if not (bp.start <= 0 < bp.stop):
+        Z[..., bp] = 0
+    else:
+        Z[..., :bp.stop], Z[..., bp.start:] = 0, 0
+    if residual == 'lowpass':
+        if bp.stop > 0:
+            Z[..., bp.stop:(n+1) // 2] = 0
+        else:
+            Z[..., bp.start:], Z[..., 0:(n + 1) // 2] = 0, 0
+
+    if xp.isdtype(z.dtype, 'complex floating'):  # resample accounts for unpaired bins:
+        z_res = resample(Z, n_out, axis=-1, domain='freq')  # ifft() with corrections
+    else:  # account for unpaired bin at m//2 before doing irfft():
+        if n_out != n and (m := min(n, n_out)) % 2 == 0:
+            Z[..., m//2] *= 2 if n_out < n else 0.5
+        z_res = fak * sp_fft.irfft(Z, n=n_out)
+    return xp.stack((z_env, xp.moveaxis(z_res, -1, axis)), axis=0)
+
+
+def _cmplx_sort(p):
+    """Sort roots based on magnitude.
+
+    Parameters
+    ----------
+    p : array_like
+        The roots to sort, as a 1-D array.
+
+    Returns
+    -------
+    p_sorted : ndarray
+        Sorted roots.
+    indx : ndarray
+        Array of indices needed to sort the input `p`.
+
+    Examples
+    --------
+    >>> from scipy.signal._signaltools import _cmplx_sort
+    >>> vals = [1, 4, 1+1.j, 3]
+    >>> p_sorted, indx = _cmplx_sort(vals)
+    >>> p_sorted
+    array([1.+0.j, 1.+1.j, 3.+0.j, 4.+0.j])
+    >>> indx
+    array([0, 2, 3, 1])
+    """
+    p = np.asarray(p)
+    indx = np.argsort(abs(p))
+    return np.take(p, indx, 0), indx
+
+
+def unique_roots(p, tol=1e-3, rtype='min'):
+    """Determine unique roots and their multiplicities from a list of roots.
+
+    Parameters
+    ----------
+    p : array_like
+        The list of roots.
+    tol : float, optional
+        The tolerance for two roots to be considered equal in terms of
+        the distance between them. Default is 1e-3. Refer to Notes about
+        the details on roots grouping.
+    rtype : {'max', 'maximum', 'min', 'minimum', 'avg', 'mean'}, optional
+        How to determine the returned root if multiple roots are within
+        `tol` of each other.
+
+        - 'max', 'maximum': pick the maximum of those roots
+        - 'min', 'minimum': pick the minimum of those roots
+        - 'avg', 'mean': take the average of those roots
+
+        When finding minimum or maximum among complex roots they are compared
+        first by the real part and then by the imaginary part.
+
+    Returns
+    -------
+    unique : ndarray
+        The list of unique roots.
+    multiplicity : ndarray
+        The multiplicity of each root.
+
+    Notes
+    -----
+    If we have 3 roots ``a``, ``b`` and ``c``, such that ``a`` is close to
+    ``b`` and ``b`` is close to ``c`` (distance is less than `tol`), then it
+    doesn't necessarily mean that ``a`` is close to ``c``. It means that roots
+    grouping is not unique. In this function we use "greedy" grouping going
+    through the roots in the order they are given in the input `p`.
+
+    This utility function is not specific to roots but can be used for any
+    sequence of values for which uniqueness and multiplicity has to be
+    determined. For a more general routine, see `numpy.unique`.
+
+    Examples
+    --------
+    >>> from scipy import signal
+    >>> vals = [0, 1.3, 1.31, 2.8, 1.25, 2.2, 10.3]
+    >>> uniq, mult = signal.unique_roots(vals, tol=2e-2, rtype='avg')
+
+    Check which roots have multiplicity larger than 1:
+
+    >>> uniq[mult > 1]
+    array([ 1.305])
+    """
+    if rtype in ['max', 'maximum']:
+        reduce = np.max
+    elif rtype in ['min', 'minimum']:
+        reduce = np.min
+    elif rtype in ['avg', 'mean']:
+        reduce = np.mean
+    else:
+        raise ValueError("`rtype` must be one of "
+                         "{'max', 'maximum', 'min', 'minimum', 'avg', 'mean'}")
+
+    p = np.asarray(p)
+
+    points = np.empty((len(p), 2))
+    points[:, 0] = np.real(p)
+    points[:, 1] = np.imag(p)
+    tree = cKDTree(points)
+
+    p_unique = []
+    p_multiplicity = []
+    used = np.zeros(len(p), dtype=bool)
+    for i in range(len(p)):
+        if used[i]:
+            continue
+
+        group = tree.query_ball_point(points[i], tol)
+        group = [x for x in group if not used[x]]
+
+        p_unique.append(reduce(p[group]))
+        p_multiplicity.append(len(group))
+
+        used[group] = True
+
+    return np.asarray(p_unique), np.asarray(p_multiplicity)
+
+
+def invres(r, p, k, tol=1e-3, rtype='avg'):
+    """Compute b(s) and a(s) from partial fraction expansion.
+
+    If `M` is the degree of numerator `b` and `N` the degree of denominator
+    `a`::
+
+              b(s)     b[0] s**(M) + b[1] s**(M-1) + ... + b[M]
+      H(s) = ------ = ------------------------------------------
+              a(s)     a[0] s**(N) + a[1] s**(N-1) + ... + a[N]
+
+    then the partial-fraction expansion H(s) is defined as::
+
+               r[0]       r[1]             r[-1]
+           = -------- + -------- + ... + --------- + k(s)
+             (s-p[0])   (s-p[1])         (s-p[-1])
+
+    If there are any repeated roots (closer together than `tol`), then H(s)
+    has terms like::
+
+          r[i]      r[i+1]              r[i+n-1]
+        -------- + ----------- + ... + -----------
+        (s-p[i])  (s-p[i])**2          (s-p[i])**n
+
+    This function is used for polynomials in positive powers of s or z,
+    such as analog filters or digital filters in controls engineering.  For
+    negative powers of z (typical for digital filters in DSP), use `invresz`.
+
+    Parameters
+    ----------
+    r : array_like
+        Residues corresponding to the poles. For repeated poles, the residues
+        must be ordered to correspond to ascending by power fractions.
+    p : array_like
+        Poles. Equal poles must be adjacent.
+    k : array_like
+        Coefficients of the direct polynomial term.
+    tol : float, optional
+        The tolerance for two roots to be considered equal in terms of
+        the distance between them. Default is 1e-3. See `unique_roots`
+        for further details.
+    rtype : {'avg', 'min', 'max'}, optional
+        Method for computing a root to represent a group of identical roots.
+        Default is 'avg'. See `unique_roots` for further details.
+
+    Returns
+    -------
+    b : ndarray
+        Numerator polynomial coefficients.
+    a : ndarray
+        Denominator polynomial coefficients.
+
+    See Also
+    --------
+    residue, invresz, unique_roots
+
+    """
+    r = np.atleast_1d(r)
+    p = np.atleast_1d(p)
+    k = np.trim_zeros(np.atleast_1d(k), 'f')
+
+    unique_poles, multiplicity = _group_poles(p, tol, rtype)
+    factors, denominator = _compute_factors(unique_poles, multiplicity,
+                                            include_powers=True)
+
+    if len(k) == 0:
+        numerator = 0
+    else:
+        numerator = np.polymul(k, denominator)
+
+    for residue, factor in zip(r, factors):
+        numerator = np.polyadd(numerator, residue * factor)
+
+    return numerator, denominator
+
+
+def _compute_factors(roots, multiplicity, include_powers=False):
+    """Compute the total polynomial divided by factors for each root."""
+    current = np.array([1])
+    suffixes = [current]
+    for pole, mult in zip(roots[-1:0:-1], multiplicity[-1:0:-1]):
+        monomial = np.array([1, -pole])
+        for _ in range(mult):
+            current = np.polymul(current, monomial)
+        suffixes.append(current)
+    suffixes = suffixes[::-1]
+
+    factors = []
+    current = np.array([1])
+    for pole, mult, suffix in zip(roots, multiplicity, suffixes):
+        monomial = np.array([1, -pole])
+        block = []
+        for i in range(mult):
+            if i == 0 or include_powers:
+                block.append(np.polymul(current, suffix))
+            current = np.polymul(current, monomial)
+        factors.extend(reversed(block))
+
+    return factors, current
+
+
+def _compute_residues(poles, multiplicity, numerator):
+    denominator_factors, _ = _compute_factors(poles, multiplicity)
+    numerator = numerator.astype(poles.dtype)
+
+    residues = []
+    for pole, mult, factor in zip(poles, multiplicity,
+                                  denominator_factors):
+        if mult == 1:
+            residues.append(np.polyval(numerator, pole) /
+                            np.polyval(factor, pole))
+        else:
+            numer = numerator.copy()
+            monomial = np.array([1, -pole])
+            factor, d = np.polydiv(factor, monomial)
+
+            block = []
+            for _ in range(mult):
+                numer, n = np.polydiv(numer, monomial)
+                r = n[0] / d[0]
+                numer = np.polysub(numer, r * factor)
+                block.append(r)
+
+            residues.extend(reversed(block))
+
+    return np.asarray(residues)
+
+
+def residue(b, a, tol=1e-3, rtype='avg'):
+    """Compute partial-fraction expansion of b(s) / a(s).
+
+    If `M` is the degree of numerator `b` and `N` the degree of denominator
+    `a`::
+
+              b(s)     b[0] s**(M) + b[1] s**(M-1) + ... + b[M]
+      H(s) = ------ = ------------------------------------------
+              a(s)     a[0] s**(N) + a[1] s**(N-1) + ... + a[N]
+
+    then the partial-fraction expansion H(s) is defined as::
+
+               r[0]       r[1]             r[-1]
+           = -------- + -------- + ... + --------- + k(s)
+             (s-p[0])   (s-p[1])         (s-p[-1])
+
+    If there are any repeated roots (closer together than `tol`), then H(s)
+    has terms like::
+
+          r[i]      r[i+1]              r[i+n-1]
+        -------- + ----------- + ... + -----------
+        (s-p[i])  (s-p[i])**2          (s-p[i])**n
+
+    This function is used for polynomials in positive powers of s or z,
+    such as analog filters or digital filters in controls engineering.  For
+    negative powers of z (typical for digital filters in DSP), use `residuez`.
+
+    See Notes for details about the algorithm.
+
+    Parameters
+    ----------
+    b : array_like
+        Numerator polynomial coefficients.
+    a : array_like
+        Denominator polynomial coefficients.
+    tol : float, optional
+        The tolerance for two roots to be considered equal in terms of
+        the distance between them. Default is 1e-3. See `unique_roots`
+        for further details.
+    rtype : {'avg', 'min', 'max'}, optional
+        Method for computing a root to represent a group of identical roots.
+        Default is 'avg'. See `unique_roots` for further details.
+
+    Returns
+    -------
+    r : ndarray
+        Residues corresponding to the poles. For repeated poles, the residues
+        are ordered to correspond to ascending by power fractions.
+    p : ndarray
+        Poles ordered by magnitude in ascending order.
+    k : ndarray
+        Coefficients of the direct polynomial term.
+
+    See Also
+    --------
+    invres, residuez, numpy.poly, unique_roots
+
+    Notes
+    -----
+    The "deflation through subtraction" algorithm is used for
+    computations --- method 6 in [1]_.
+
+    The form of partial fraction expansion depends on poles multiplicity in
+    the exact mathematical sense. However there is no way to exactly
+    determine multiplicity of roots of a polynomial in numerical computing.
+    Thus you should think of the result of `residue` with given `tol` as
+    partial fraction expansion computed for the denominator composed of the
+    computed poles with empirically determined multiplicity. The choice of
+    `tol` can drastically change the result if there are close poles.
+
+    References
+    ----------
+    .. [1] J. F. Mahoney, B. D. Sivazlian, "Partial fractions expansion: a
+           review of computational methodology and efficiency", Journal of
+           Computational and Applied Mathematics, Vol. 9, 1983.
+    """
+    b = np.asarray(b)
+    a = np.asarray(a)
+    if (np.issubdtype(b.dtype, np.complexfloating)
+            or np.issubdtype(a.dtype, np.complexfloating)):
+        b = b.astype(complex)
+        a = a.astype(complex)
+    else:
+        b = b.astype(float)
+        a = a.astype(float)
+
+    b = np.trim_zeros(np.atleast_1d(b), 'f')
+    a = np.trim_zeros(np.atleast_1d(a), 'f')
+
+    if a.size == 0:
+        raise ValueError("Denominator `a` is zero.")
+
+    poles = np.roots(a)
+    if b.size == 0:
+        return np.zeros(poles.shape), _cmplx_sort(poles)[0], np.array([])
+
+    if len(b) < len(a):
+        k = np.empty(0)
+    else:
+        k, b = np.polydiv(b, a)
+
+    unique_poles, multiplicity = unique_roots(poles, tol=tol, rtype=rtype)
+    unique_poles, order = _cmplx_sort(unique_poles)
+    multiplicity = multiplicity[order]
+
+    residues = _compute_residues(unique_poles, multiplicity, b)
+
+    index = 0
+    for pole, mult in zip(unique_poles, multiplicity):
+        poles[index:index + mult] = pole
+        index += mult
+
+    return residues / a[0], poles, k
+
+
+def residuez(b, a, tol=1e-3, rtype='avg'):
+    """Compute partial-fraction expansion of b(z) / a(z).
+
+    If `M` is the degree of numerator `b` and `N` the degree of denominator
+    `a`::
+
+                b(z)     b[0] + b[1] z**(-1) + ... + b[M] z**(-M)
+        H(z) = ------ = ------------------------------------------
+                a(z)     a[0] + a[1] z**(-1) + ... + a[N] z**(-N)
+
+    then the partial-fraction expansion H(z) is defined as::
+
+                 r[0]                   r[-1]
+         = --------------- + ... + ---------------- + k[0] + k[1]z**(-1) ...
+           (1-p[0]z**(-1))         (1-p[-1]z**(-1))
+
+    If there are any repeated roots (closer than `tol`), then the partial
+    fraction expansion has terms like::
+
+             r[i]              r[i+1]                    r[i+n-1]
+        -------------- + ------------------ + ... + ------------------
+        (1-p[i]z**(-1))  (1-p[i]z**(-1))**2         (1-p[i]z**(-1))**n
+
+    This function is used for polynomials in negative powers of z,
+    such as digital filters in DSP.  For positive powers, use `residue`.
+
+    See Notes of `residue` for details about the algorithm.
+
+    Parameters
+    ----------
+    b : array_like
+        Numerator polynomial coefficients.
+    a : array_like
+        Denominator polynomial coefficients.
+    tol : float, optional
+        The tolerance for two roots to be considered equal in terms of
+        the distance between them. Default is 1e-3. See `unique_roots`
+        for further details.
+    rtype : {'avg', 'min', 'max'}, optional
+        Method for computing a root to represent a group of identical roots.
+        Default is 'avg'. See `unique_roots` for further details.
+
+    Returns
+    -------
+    r : ndarray
+        Residues corresponding to the poles. For repeated poles, the residues
+        are ordered to correspond to ascending by power fractions.
+    p : ndarray
+        Poles ordered by magnitude in ascending order.
+    k : ndarray
+        Coefficients of the direct polynomial term.
+
+    See Also
+    --------
+    invresz, residue, unique_roots
+    """
+    b = np.asarray(b)
+    a = np.asarray(a)
+    if (np.issubdtype(b.dtype, np.complexfloating)
+            or np.issubdtype(a.dtype, np.complexfloating)):
+        b = b.astype(complex)
+        a = a.astype(complex)
+    else:
+        b = b.astype(float)
+        a = a.astype(float)
+
+    b = np.trim_zeros(np.atleast_1d(b), 'b')
+    a = np.trim_zeros(np.atleast_1d(a), 'b')
+
+    if a.size == 0:
+        raise ValueError("Denominator `a` is zero.")
+    elif a[0] == 0:
+        raise ValueError("First coefficient of determinant `a` must be "
+                         "non-zero.")
+
+    poles = np.roots(a)
+    if b.size == 0:
+        return np.zeros(poles.shape), _cmplx_sort(poles)[0], np.array([])
+
+    b_rev = b[::-1]
+    a_rev = a[::-1]
+
+    if len(b_rev) < len(a_rev):
+        k_rev = np.empty(0)
+    else:
+        k_rev, b_rev = np.polydiv(b_rev, a_rev)
+
+    unique_poles, multiplicity = unique_roots(poles, tol=tol, rtype=rtype)
+    unique_poles, order = _cmplx_sort(unique_poles)
+    multiplicity = multiplicity[order]
+
+    residues = _compute_residues(1 / unique_poles, multiplicity, b_rev)
+
+    index = 0
+    powers = np.empty(len(residues), dtype=int)
+    for pole, mult in zip(unique_poles, multiplicity):
+        poles[index:index + mult] = pole
+        powers[index:index + mult] = 1 + np.arange(mult)
+        index += mult
+
+    residues *= (-poles) ** powers / a_rev[0]
+
+    return residues, poles, k_rev[::-1]
+
+
+def _group_poles(poles, tol, rtype):
+    if rtype in ['max', 'maximum']:
+        reduce = np.max
+    elif rtype in ['min', 'minimum']:
+        reduce = np.min
+    elif rtype in ['avg', 'mean']:
+        reduce = np.mean
+    else:
+        raise ValueError("`rtype` must be one of "
+                         "{'max', 'maximum', 'min', 'minimum', 'avg', 'mean'}")
+
+    unique = []
+    multiplicity = []
+
+    pole = poles[0]
+    block = [pole]
+    for i in range(1, len(poles)):
+        if abs(poles[i] - pole) <= tol:
+            block.append(pole)
+        else:
+            unique.append(reduce(block))
+            multiplicity.append(len(block))
+            pole = poles[i]
+            block = [pole]
+
+    unique.append(reduce(block))
+    multiplicity.append(len(block))
+
+    return np.asarray(unique), np.asarray(multiplicity)
+
+
+def invresz(r, p, k, tol=1e-3, rtype='avg'):
+    """Compute b(z) and a(z) from partial fraction expansion.
+
+    If `M` is the degree of numerator `b` and `N` the degree of denominator
+    `a`::
+
+                b(z)     b[0] + b[1] z**(-1) + ... + b[M] z**(-M)
+        H(z) = ------ = ------------------------------------------
+                a(z)     a[0] + a[1] z**(-1) + ... + a[N] z**(-N)
+
+    then the partial-fraction expansion H(z) is defined as::
+
+                 r[0]                   r[-1]
+         = --------------- + ... + ---------------- + k[0] + k[1]z**(-1) ...
+           (1-p[0]z**(-1))         (1-p[-1]z**(-1))
+
+    If there are any repeated roots (closer than `tol`), then the partial
+    fraction expansion has terms like::
+
+             r[i]              r[i+1]                    r[i+n-1]
+        -------------- + ------------------ + ... + ------------------
+        (1-p[i]z**(-1))  (1-p[i]z**(-1))**2         (1-p[i]z**(-1))**n
+
+    This function is used for polynomials in negative powers of z,
+    such as digital filters in DSP.  For positive powers, use `invres`.
+
+    Parameters
+    ----------
+    r : array_like
+        Residues corresponding to the poles. For repeated poles, the residues
+        must be ordered to correspond to ascending by power fractions.
+    p : array_like
+        Poles. Equal poles must be adjacent.
+    k : array_like
+        Coefficients of the direct polynomial term.
+    tol : float, optional
+        The tolerance for two roots to be considered equal in terms of
+        the distance between them. Default is 1e-3. See `unique_roots`
+        for further details.
+    rtype : {'avg', 'min', 'max'}, optional
+        Method for computing a root to represent a group of identical roots.
+        Default is 'avg'. See `unique_roots` for further details.
+
+    Returns
+    -------
+    b : ndarray
+        Numerator polynomial coefficients.
+    a : ndarray
+        Denominator polynomial coefficients.
+
+    See Also
+    --------
+    residuez, unique_roots, invres
+
+    """
+    r = np.atleast_1d(r)
+    p = np.atleast_1d(p)
+    k = np.trim_zeros(np.atleast_1d(k), 'b')
+
+    unique_poles, multiplicity = _group_poles(p, tol, rtype)
+    factors, denominator = _compute_factors(unique_poles, multiplicity,
+                                            include_powers=True)
+
+    if len(k) == 0:
+        numerator = 0
+    else:
+        numerator = np.polymul(k[::-1], denominator[::-1])
+
+    for residue, factor in zip(r, factors):
+        numerator = np.polyadd(numerator, residue * factor[::-1])
+
+    return numerator[::-1], denominator
+
+
+def resample(x, num, t=None, axis=0, window=None, domain='time'):
+    r"""Resample `x` to `num` samples using the Fourier method along the given `axis`.
+
+    The resampling is performed by shortening or zero-padding the FFT of `x`. This has
+    the advantages of providing an ideal antialiasing filter and allowing arbitrary
+    up- or down-sampling ratios. The main drawback is the requirement of assuming `x`
+    to be a periodic signal.
+
+    Parameters
+    ----------
+    x : array_like
+        The input signal made up of equidistant samples. If `x` is a multidimensional
+        array, the parameter `axis` specifies the time/frequency axis. It is assumed
+        here that ``n_x = x.shape[axis]`` specifies the number of samples and ``T`` the
+        sampling interval.
+    num : int
+        The number of samples of the resampled output signal. It may be larger or
+        smaller than ``n_x``.
+    t : array_like, optional
+        If `t` is not ``None``, then the timestamps of the resampled signal are also
+        returned. `t` must contain at least the first two timestamps of the input
+        signal `x` (all others are ignored). The timestamps of the output signal are
+        determined by ``t[0] + T * n_x / num * np.arange(num)`` with
+        ``T = t[1] - t[0]``. Default is ``None``.
+    axis : int, optional
+        The time/frequency axis of `x` along which the resampling take place.
+        The Default is 0.
+    window : array_like, callable, str, float, or tuple, optional
+        If not ``None``, it specifies a filter in the Fourier domain, which is applied
+        before resampling. I.e., the FFT ``X`` of `x` is calculated by
+        ``X = W * fft(x, axis=axis)``. ``W`` may be interpreted as a spectral windowing
+        function ``W(f_X)`` which consumes the frequencies ``f_X = fftfreq(n_x, T)``.
+
+        If `window` is a 1d array of length ``n_x`` then ``W=window``.
+        If `window` is a callable  then ``W = window(f_X)``.
+        Otherwise, `window` is passed to `~scipy.signal.get_window`, i.e.,
+        ``W = fftshift(signal.get_window(window, n_x))``. Default is ``None``.
+
+    domain : 'time' | 'freq', optional
+        If set to ``'time'`` (default) then an FFT is applied to `x`, otherwise
+        (``'freq'``) it is asssmued that an FFT was already applied, i.e.,
+        ``x = fft(x_t, axis=axis)`` with ``x_t`` being the input signal in the time
+        domain.
+
+    Returns
+    -------
+    x_r : ndarray
+        The resampled signal made up of `num` samples and sampling interval
+        ``T * n_x / num``.
+    t_r : ndarray, optional
+        The `num` equidistant timestamps of `x_r`.
+        This is only returned if paramater `t` is not ``None``.
+
+    See Also
+    --------
+    decimate : Downsample a (periodic/non-periodic) signal after applying an FIR
+               or IIR filter.
+    resample_poly : Resample a (periodic/non-periodic) signal using polyphase filtering
+                    and an FIR filter.
+
+    Notes
+    -----
+    This function uses the more efficient one-sided FFT, i.e. `~scipy.fft.rfft` /
+    `~scipy.fft.irfft`, if `x` is real-valued and in the time domain.
+    Else, the two-sided FFT, i.e., `~scipy.fft.fft` / `~scipy.fft.ifft`, is used
+    (all FFT functions are taken from the `scipy.fft` module).
+
+    If a `window` is applied to a real-valued `x`, the one-sided spectral windowing
+    function is determined by taking the average of the negative and the positive
+    frequency component. This ensures that real-valued signals and complex signals with
+    zero imaginary part are treated identically. I.e., passing `x` or passing
+    ``x.astype(np.complex128)`` produce the same numeric result.
+
+    If the number of input  or output samples are prime or have few prime factors, this
+    function may be slow due to utilizing FFTs. Consult `~scipy.fft.prev_fast_len` and
+    `~scipy.fft.next_fast_len` for determining efficient signals lengths.
+    Alternatively, utilizing `resample_poly` to calculate an intermediate signal (as
+    illustrated in the example below) can result in significant speed increases.
+
+    `resample` is intended to be used for periodic signals with equidistant sampling
+    intervals. For non-periodic signals, `resample_poly` may be a better choice.
+    Consult the `scipy.interpolate` module for methods of resampling signals with
+    non-constant sampling intervals.
+
+    Examples
+    --------
+    The following example depicts a signal being up-sampled from 20 samples to 100
+    samples. The ringing at the beginning of the up-sampled signal is due to
+    interpreting the signal being periodic. The red square in the plot illustrates that
+    periodictiy by showing the first sample of the next cycle of the signal.
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.signal import resample
+    ...
+    >>> n0, n1 = 20, 100  # number of samples
+    >>> t0 = np.linspace(0, 10, n0, endpoint=False)  # input time stamps
+    >>> x0 = np.cos(-t0**2/6)  # input signal
+    ...
+    >>> x1 = resample(x0, n1)  # resampled signal
+    >>> t1 = np.linspace(0, 10, n1, endpoint=False)  # timestamps of x1
+    ...
+    >>> fig0, ax0 = plt.subplots(1, 1, tight_layout=True)
+    >>> ax0.set_title(f"Resampling $x(t)$ from {n0} samples to {n1} samples")
+    >>> ax0.set(xlabel="Time $t$", ylabel="Amplitude $x(t)$")
+    >>> ax0.plot(t1, x1, '.-', alpha=.5, label=f"Resampled")
+    >>> ax0.plot(t0, x0, 'o-', alpha=.5, label="Original")
+    >>> ax0.plot(10, x0[0], 'rs', alpha=.5, label="Next Cycle")
+    >>> ax0.legend(loc='best')
+    >>> ax0.grid(True)
+    >>> plt.show()
+
+    The following example compares this function with a naive `~scipy.fft.rfft` /
+    `~scipy.fft.irfft` combination: An input signal with a sampling interval of one
+    second is upsampled by a factor of eight. The first figure depicts an odd number of
+    input samples whereas the second figure an even number. The upper subplots show the
+    signals over time: The input samples are marked by large green dots, the upsampled
+    signals by a continuous and a dashed line. The lower subplots show the magnitude
+    spectrum: The FFT values of the input are depicted by large green dots, which lie
+    in the frequency interval [-0.5, 0.5] Hz, whereas the frequency interval of the
+    upsampled signal is [-4, 4] Hz. The continuous green line depicts the upsampled
+    spectrum without antialiasing filter, which is a periodic continuation of the input
+    spectrum. The blue x's and orange dots depict the FFT values of the signal created
+    by the naive approach as well as this function's result.
+
+    >>> import matplotlib.pyplot as plt
+    >>> import numpy as np
+    >>> from scipy.fft import fftshift, fftfreq, fft, rfft, irfft
+    >>> from scipy.signal import resample, resample_poly
+    ...
+    >>> fac, T0, T1 = 8, 1, 1/8  # upsampling factor and sampling intervals
+    >>> for n0 in (15, 16):  # number of samples of input signal
+    ...     n1 = fac * n0  # number of samples of upsampled signal
+    ...     t0, t1 = T0 * np.arange(n0), T1 * np.arange(n1)  # time stamps
+    ...     x0 = np.zeros(n0)  # input signal has two non-zero sample values
+    ...     x0[n0//2], x0[n0//2+1] = n0 // 2, -(n0 // 2)
+    ...
+    ...     x1n = irfft(rfft(x0), n=n1) * n1 / n0  # naive resampling
+    ...     x1r = resample(x0, n1)  # resample signal
+    ...
+    ...     # Determine magnitude spectrum:
+    ...     x0_up = np.zeros_like(x1r)  # upsampling without antialiasing filter
+    ...     x0_up[::n1 // n0] = x0
+    ...     X0, X0_up = (fftshift(fft(x_)) / n0 for x_ in (x0, x0_up))
+    ...     XX1 = (fftshift(fft(x_)) / n1 for x_ in (x1n, x1r))
+    ...     f0, f1 = fftshift(fftfreq(n0, T0)), fftshift(fftfreq(n1, T1))  # frequencies
+    ...     df = f0[1] - f0[0]  # frequency resolution
+    ...
+    ...     fig, (ax0, ax1) = plt.subplots(2, 1, layout='constrained', figsize=(5, 4))
+    ...     ax0.set_title(rf"Upsampling ${fac}\times$ from {n0} to {n1} samples")
+    ...     ax0.set(xlabel="Time $t$ in seconds", ylabel="Amplitude $x(t)$",
+    ...             xlim=(0, n1*T1))
+    ...     ax0.step(t0, x0, 'C2o-', where='post', alpha=.3, linewidth=2,
+    ...              label="$x_0(t)$ / $X_0(f)$")
+    ...     for x_, l_ in zip((x1n, x1r), ('C0--', 'C1-')):
+    ...         ax0.plot(t1, x_, l_, alpha=.5, label=None)
+    ...     ax0.grid()
+    ...     ax1.set(xlabel=rf"Frequency $f$ in hertz ($\Delta f = {df*1e3:.1f}\,$mHz)",
+    ...             ylabel="Magnitude $|X(f)|$", xlim=(-0.7, 0.7))
+    ...     ax1.axvspan(0.5/T0, f1[-1], color='gray', alpha=.2)
+    ...     ax1.axvspan(f1[0], -0.5/T0, color='gray', alpha=.2)
+    ...     ax1.plot(f1, abs(X0_up), 'C2-', f0, abs(X0),  'C2o', alpha=.3, linewidth=2)
+    ...     for X_, n_, l_ in zip(XX1, ("naive", "resample"), ('C0x--', 'C1.-')):
+    ...         ax1.plot(f1, abs(X_), l_, alpha=.5, label=n_)
+    ...     ax1.grid()
+    ...     fig.legend(loc='outside lower center', ncols=4)
+    >>> plt.show()
+
+    The first figure shows that upsampling an odd number of samples produces identical
+    results. The second figure illustrates that the signal produced with the naive
+    approach (dashed blue line) from an even number of samples does not touch all
+    original samples. This deviation is due to `resample` correctly treating unpaired
+    frequency bins. I.e., the input `x1` has a bin pair ±0.5 Hz, whereas the output has
+    only one unpaired bin at -0.5 Hz, which demands rescaling of that bin pair.
+    Generally, special treatment is required if ``n_x != num`` and ``min(n_x, num)`` is
+    even. If the bin values at `±m` are zero, obviously, no special treatment is
+    needed. Consult the source code of `resample` for details.
+
+    The final example shows how to utilize `resample_poly` to speed up the
+    down-sampling: The input signal a non-zero value at :math:`t=0` and is downsampled
+    from 19937 to 128 samples. Since 19937 is prime, the FFT is expected to be slow. To
+    speed matters up, `resample_poly` is used to downsample first by a factor of ``n0
+    // n1 = 155`` and then pass the result to `resample`. Two parameterization of
+    `resample_poly` are used: Passing ``padtype='wrap'`` treats the input as being
+    periodic wheras the default parametrization performs zero-padding. The upper
+    subplot shows the resulting signals over time whereas the lower subplot depicts the
+    resulting one-sided magnitude spectra.
+
+    >>> import matplotlib.pyplot as plt
+    >>> import numpy as np
+    >>> from scipy.fft import rfftfreq, rfft
+    >>> from scipy.signal import resample, resample_poly
+    ...
+    >>> n0 = 19937 # number of input samples - prime
+    >>> n1 = 128  # number of output samples - fast FFT length
+    >>> T0, T1 = 1/n0, 1/n1  # sampling intervals
+    >>> t0, t1 = np.arange(n0)*T0, np.arange(n1)*T1  # time stamps
+    ...
+    >>> x0 = np.zeros(n0)  # Input has one non-zero sample
+    >>> x0[0] = n0
+    >>>
+    >>> x1r = resample(x0, n1)  # slow due to n0 being prime
+    >>> # This is faster:
+    >>> x1p = resample(resample_poly(x0, 1, n0 // n1, padtype='wrap'), n1)  # periodic
+    >>> x2p = resample(resample_poly(x0, 1, n0 // n1), n1)  # with zero-padding
+    ...
+    >>> X0 = rfft(x0) / n0
+    >>> X1r, X1p, X2p = rfft(x1r) / n1, rfft(x1p) / n1, rfft(x2p) / n1
+    >>> f0, f1 = rfftfreq(n0, T0), rfftfreq(n1, T1)
+    ...
+    >>> fig, (ax0, ax1) = plt.subplots(2, 1, layout='constrained', figsize=(5, 4))
+    >>> ax0.set_title(f"Dowsampled Impulse response (from {n0} to {n1} samples)")
+    >>> ax0.set(xlabel="Time $t$ in seconds", ylabel="Amplitude $x(t)$", xlim=(-T1, 1))
+    >>> for x_ in (x1r, x1p, x2p):
+    ...     ax0.plot(t1, x_, alpha=.5)
+    >>> ax0.grid()
+    >>> ax1.set(xlabel=rf"Frequency $f$ in hertz ($\Delta f = {f1[1]}\,$Hz)",
+    ...         ylabel="Magnitude $|X(f)|$", xlim=(0, 0.55/T1))
+    >>> ax1.axvspan(0.5/T1, f0[-1], color='gray', alpha=.2)
+    >>> ax1.plot(f1, abs(X1r), 'C0.-', alpha=.5, label="resample")
+    >>> ax1.plot(f1, abs(X1p), 'C1.-', alpha=.5, label="resample_poly(padtype='wrap')")
+    >>> ax1.plot(f1, abs(X2p), 'C2x-', alpha=.5, label="resample_poly")
+    >>> ax1.grid()
+    >>> fig.legend(loc='outside lower center', ncols=2)
+    >>> plt.show()
+
+    The plots show that the results of the "pure" `resample` and the usage of the
+    default parameters of `resample_poly` agree well.  The periodic padding of
+    `resample_poly` (``padtype='wrap'``) on the other hand produces significant
+    deviations. This is caused by the disconiuity at the beginning of the signal, for
+    which the default filter of `resample_poly` is not suited well. This example
+    illustrates that for some use cases, adapting the `resample_poly` parameters may
+    be beneficial. `resample` has a big advantage in this regard: It uses the ideal
+    antialiasing filter with the maximum bandwidth by default.
+
+    Note that the doubled spectral magnitude at the Nyqist frequency of 64 Hz is due the
+    even number of ``n1=128`` output samples, which requires a special treatment as
+    discussed in the previous example.
+    """
+    if domain not in ('time', 'freq'):
+        raise ValueError(f"Parameter {domain=} not in ('time', 'freq')!")
+
+    xp = array_namespace(x, t)
+    x = xp.asarray(x)
+    if x.ndim > 1:  # moving active axis to end allows to use `...` in indexing:
+        x = xp.moveaxis(x, axis, -1)
+    n_x = x.shape[-1]  # number of samples along the time/frequency axis
+    s_fac = n_x / num  # scaling factor represents sample interval dilatation
+    m = min(num, n_x)  # number of relevant frequency bins
+    m2 = m // 2 + 1  # number of relevant frequency bins of a one-sided FFT
+
+    if window is None: # Determine spectral windowing function:
+        W = None
+    elif callable(window):
+        W = window(sp_fft.fftfreq(n_x))
+    elif hasattr(window, 'shape'): # must be an array object
+        if window.shape != (n_x,):
+            raise ValueError(f"{window.shape=} != ({n_x},), i.e., window length " +
+                             "is not equal to number of frequency bins!")
+        W = xp.asarray(window, copy=True)  # prevent modifying the function parameters
+    else:
+        W = sp_fft.fftshift(get_window(window, n_x, xp=xp))
+        W = xp.astype(W, xp_default_dtype(xp))   # get_window always returns float64
+
+    if domain == 'time' and not xp.isdtype(x.dtype, 'complex floating'):  # use rfft():
+        X = sp_fft.rfft(x)
+        if W is not None:  # fold window, i.e., W1[l] = (W[l] + W[-l]) / 2 for l > 0
+            n_X = X.shape[-1]
+            W[1:n_X] += xp.flip(W[-n_X+1:])  #W[:-n_X:-1]
+            W[1:n_X] /= 2
+            X *= W[:n_X]  # apply window
+        X = X[..., :m2]  # extract relevant data
+        if m % 2 == 0 and num != n_x:  # Account for unpaired bin at m//2:
+            X[..., m//2] *= 2 if num < n_x else 0.5
+        x_r = sp_fft.irfft(X / s_fac, n=num, overwrite_x=True)
+    else:  # use standard two-sided FFT:
+        X = sp_fft.fft(x) if domain == 'time' else x
+        if W is not None:
+            X = X * W  # writing X *= W could modify parameter x
+        Y = xp.zeros(X.shape[:-1] + (num,), dtype=X.dtype)
+        Y[..., :m2] = X[..., :m2]  # copy part up to Nyquist frequency
+        if m2 < m:  # == m > 2
+            Y[..., m2-m:] = X[..., m2-m:]  # copy negative frequency part
+        if m % 2 == 0:  # Account for unpaired bin at m//2:
+            if num < n_x:  # down-sampling: unite bin pair into one unpaired bin
+                Y[..., -m//2] += X[..., -m//2]
+            elif n_x < num:  # up-sampling: split unpaired bin into bin pair
+                Y[..., m//2] /= 2
+                Y[..., num-m//2] = Y[..., m//2]
+        x_r = sp_fft.ifft(Y / s_fac, n=num, overwrite_x=True)
+
+    if x_r.ndim > 1:  # moving active axis back to original position:
+        x_r = xp.moveaxis(x_r, -1, axis)
+    if t is not None:
+        return x_r, t[0] + (t[1] - t[0]) * s_fac * xp.arange(num)
+    return x_r
+
+
+def resample_poly(x, up, down, axis=0, window=('kaiser', 5.0),
+                  padtype='constant', cval=None):
+    """
+    Resample `x` along the given axis using polyphase filtering.
+
+    The signal `x` is upsampled by the factor `up`, a zero-phase low-pass
+    FIR filter is applied, and then it is downsampled by the factor `down`.
+    The resulting sample rate is ``up / down`` times the original sample
+    rate. By default, values beyond the boundary of the signal are assumed
+    to be zero during the filtering step.
+
+    Parameters
+    ----------
+    x : array_like
+        The data to be resampled.
+    up : int
+        The upsampling factor.
+    down : int
+        The downsampling factor.
+    axis : int, optional
+        The axis of `x` that is resampled. Default is 0.
+    window : str, tuple, or array_like, optional
+        Desired window to use to design the low-pass filter, or the FIR filter
+        coefficients to employ. See below for details.
+    padtype : str, optional
+        `constant`, `line`, `mean`, `median`, `maximum`, `minimum` or any of
+        the other signal extension modes supported by `scipy.signal.upfirdn`.
+        Changes assumptions on values beyond the boundary. If `constant`,
+        assumed to be `cval` (default zero). If `line` assumed to continue a
+        linear trend defined by the first and last points. `mean`, `median`,
+        `maximum` and `minimum` work as in `np.pad` and assume that the values
+        beyond the boundary are the mean, median, maximum or minimum
+        respectively of the array along the axis.
+
+        .. versionadded:: 1.4.0
+    cval : float, optional
+        Value to use if `padtype='constant'`. Default is zero.
+
+        .. versionadded:: 1.4.0
+
+    Returns
+    -------
+    resampled_x : array
+        The resampled array.
+
+    See Also
+    --------
+    decimate : Downsample the signal after applying an FIR or IIR filter.
+    resample : Resample up or down using the FFT method.
+
+    Notes
+    -----
+    This polyphase method will likely be faster than the Fourier method
+    in `scipy.signal.resample` when the number of samples is large and
+    prime, or when the number of samples is large and `up` and `down`
+    share a large greatest common denominator. The length of the FIR
+    filter used will depend on ``max(up, down) // gcd(up, down)``, and
+    the number of operations during polyphase filtering will depend on
+    the filter length and `down` (see `scipy.signal.upfirdn` for details).
+
+    The argument `window` specifies the FIR low-pass filter design.
+
+    If `window` is an array_like it is assumed to be the FIR filter
+    coefficients. Note that the FIR filter is applied after the upsampling
+    step, so it should be designed to operate on a signal at a sampling
+    frequency higher than the original by a factor of `up//gcd(up, down)`.
+    This function's output will be centered with respect to this array, so it
+    is best to pass a symmetric filter with an odd number of samples if, as
+    is usually the case, a zero-phase filter is desired.
+
+    For any other type of `window`, the functions `scipy.signal.get_window`
+    and `scipy.signal.firwin` are called to generate the appropriate filter
+    coefficients.
+
+    The first sample of the returned vector is the same as the first
+    sample of the input vector. The spacing between samples is changed
+    from ``dx`` to ``dx * down / float(up)``.
+
+    Examples
+    --------
+    By default, the end of the resampled data rises to meet the first
+    sample of the next cycle for the FFT method, and gets closer to zero
+    for the polyphase method:
+
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+
+    >>> x = np.linspace(0, 10, 20, endpoint=False)
+    >>> y = np.cos(-x**2/6.0)
+    >>> f_fft = signal.resample(y, 100)
+    >>> f_poly = signal.resample_poly(y, 100, 20)
+    >>> xnew = np.linspace(0, 10, 100, endpoint=False)
+
+    >>> plt.plot(xnew, f_fft, 'b.-', xnew, f_poly, 'r.-')
+    >>> plt.plot(x, y, 'ko-')
+    >>> plt.plot(10, y[0], 'bo', 10, 0., 'ro')  # boundaries
+    >>> plt.legend(['resample', 'resamp_poly', 'data'], loc='best')
+    >>> plt.show()
+
+    This default behaviour can be changed by using the padtype option:
+
+    >>> N = 5
+    >>> x = np.linspace(0, 1, N, endpoint=False)
+    >>> y = 2 + x**2 - 1.7*np.sin(x) + .2*np.cos(11*x)
+    >>> y2 = 1 + x**3 + 0.1*np.sin(x) + .1*np.cos(11*x)
+    >>> Y = np.stack([y, y2], axis=-1)
+    >>> up = 4
+    >>> xr = np.linspace(0, 1, N*up, endpoint=False)
+
+    >>> y2 = signal.resample_poly(Y, up, 1, padtype='constant')
+    >>> y3 = signal.resample_poly(Y, up, 1, padtype='mean')
+    >>> y4 = signal.resample_poly(Y, up, 1, padtype='line')
+
+    >>> for i in [0,1]:
+    ...     plt.figure()
+    ...     plt.plot(xr, y4[:,i], 'g.', label='line')
+    ...     plt.plot(xr, y3[:,i], 'y.', label='mean')
+    ...     plt.plot(xr, y2[:,i], 'r.', label='constant')
+    ...     plt.plot(x, Y[:,i], 'k-')
+    ...     plt.legend()
+    >>> plt.show()
+
+    """
+    xp = array_namespace(x)
+
+    x = xp.asarray(x)
+    if up != int(up):
+        raise ValueError("up must be an integer")
+    if down != int(down):
+        raise ValueError("down must be an integer")
+    up = int(up)
+    down = int(down)
+    if up < 1 or down < 1:
+        raise ValueError('up and down must be >= 1')
+    if cval is not None and padtype != 'constant':
+        raise ValueError('cval has no effect when padtype is ', padtype)
+
+    # Determine our up and down factors
+    # Use a rational approximation to save computation time on really long
+    # signals
+    g_ = math.gcd(up, down)
+    up //= g_
+    down //= g_
+    if up == down == 1:
+        return xp.asarray(x, copy=True)
+    n_in = x.shape[axis]
+    n_out = n_in * up
+    n_out = n_out // down + bool(n_out % down)
+
+    if isinstance(window, list) or is_array_api_obj(window):
+        window = xp.asarray(window, copy=True)  # force a copy (we modify `window`)
+        if window.ndim > 1:
+            raise ValueError('window must be 1-D')
+        half_len = (xp_size(window) - 1) // 2
+        h = window
+    else:
+        # Design a linear-phase low-pass FIR filter
+        max_rate = max(up, down)
+        f_c = 1. / max_rate  # cutoff of FIR filter (rel. to Nyquist)
+        half_len = 10 * max_rate  # reasonable cutoff for sinc-like function
+        if xp.isdtype(x.dtype, ("real floating", "complex floating")):
+            h = firwin(2 * half_len + 1, f_c, window=window)
+            h = xp.asarray(h, dtype=x.dtype)    # match dtype of x
+        else:
+            h = firwin(2 * half_len + 1, f_c, window=window)
+            h = xp.asarray(h)
+
+    h *= up
+
+    # Zero-pad our filter to put the output samples at the center
+    n_pre_pad = (down - half_len % down)
+    n_post_pad = 0
+    n_pre_remove = (half_len + n_pre_pad) // down
+    # We should rarely need to do this given our filter lengths...
+    while _output_len(h.shape[0] + n_pre_pad + n_post_pad, n_in,
+                      up, down) < n_out + n_pre_remove:
+        n_post_pad += 1
+    h = xp.concat((xp.zeros(n_pre_pad, dtype=h.dtype), h,
+                   xp.zeros(n_post_pad, dtype=h.dtype)))
+    n_pre_remove_end = n_pre_remove + n_out
+
+    # XXX consider using stats.quantile, which is natively Array API compatible
+    def _median(x, *args, **kwds):
+        return xp.asarray(np.median(np.asarray(x), *args, **kwds))
+
+    # Remove background depending on the padtype option
+    funcs = {'mean': xp.mean, 'median': _median,
+             'minimum': xp.min, 'maximum': xp.max}
+    upfirdn_kwargs = {'mode': 'constant', 'cval': 0}
+    if padtype in funcs:
+        background_values = funcs[padtype](x, axis=axis, keepdims=True)
+    elif padtype in _upfirdn_modes:
+        upfirdn_kwargs = {'mode': padtype}
+        if padtype == 'constant':
+            if cval is None:
+                cval = 0
+            upfirdn_kwargs['cval'] = cval
+    else:
+        raise ValueError(
+            'padtype must be one of: maximum, mean, median, minimum, ' +
+            ', '.join(_upfirdn_modes))
+
+    if padtype in funcs:
+        x = x - background_values
+
+    # filter then remove excess
+    y = upfirdn(h, x, up, down, axis=axis, **upfirdn_kwargs)
+    keep = [slice(None), ]*x.ndim
+    keep[axis] = slice(n_pre_remove, n_pre_remove_end)
+    y_keep = y[tuple(keep)]
+
+    # Add background back
+    if padtype in funcs:
+        y_keep += background_values
+
+    return y_keep
+
+
+def _angle(z, xp):
+    """np.angle replacement
+    """
+    # XXX: https://github.com/data-apis/array-api/issues/595
+    zimag = xp.imag(z) if xp.isdtype(z.dtype, 'complex floating') else 0.
+    a = xp.atan2(zimag, xp.real(z))
+    return a
+
+
+def vectorstrength(events, period):
+    '''
+    Determine the vector strength of the events corresponding to the given
+    period.
+
+    The vector strength is a measure of phase synchrony, how well the
+    timing of the events is synchronized to a single period of a periodic
+    signal.
+
+    If multiple periods are used, calculate the vector strength of each.
+    This is called the "resonating vector strength".
+
+    Parameters
+    ----------
+    events : 1D array_like
+        An array of time points containing the timing of the events.
+    period : float or array_like
+        The period of the signal that the events should synchronize to.
+        The period is in the same units as `events`.  It can also be an array
+        of periods, in which case the outputs are arrays of the same length.
+
+    Returns
+    -------
+    strength : float or 1D array
+        The strength of the synchronization.  1.0 is perfect synchronization
+        and 0.0 is no synchronization.  If `period` is an array, this is also
+        an array with each element containing the vector strength at the
+        corresponding period.
+    phase : float or array
+        The phase that the events are most strongly synchronized to in radians.
+        If `period` is an array, this is also an array with each element
+        containing the phase for the corresponding period.
+
+    References
+    ----------
+    van Hemmen, JL, Longtin, A, and Vollmayr, AN. Testing resonating vector
+        strength: Auditory system, electric fish, and noise.
+        Chaos 21, 047508 (2011);
+        :doi:`10.1063/1.3670512`.
+    van Hemmen, JL.  Vector strength after Goldberg, Brown, and von Mises:
+        biological and mathematical perspectives.  Biol Cybern.
+        2013 Aug;107(4):385-96. :doi:`10.1007/s00422-013-0561-7`.
+    van Hemmen, JL and Vollmayr, AN.  Resonating vector strength: what happens
+        when we vary the "probing" frequency while keeping the spike times
+        fixed.  Biol Cybern. 2013 Aug;107(4):491-94.
+        :doi:`10.1007/s00422-013-0560-8`.
+    '''
+    xp = array_namespace(events, period)
+
+    events = xp.asarray(events)
+    period = xp.asarray(period)
+    if xp.isdtype(period.dtype, 'integral'):
+        period = xp.astype(period, xp.float64)
+
+    if events.ndim > 1:
+        raise ValueError('events cannot have dimensions more than 1')
+    if period.ndim > 1:
+        raise ValueError('period cannot have dimensions more than 1')
+
+    # we need to know later if period was originally a scalar
+    scalarperiod = not period.ndim
+
+    events = xpx.atleast_nd(events, ndim=2, xp=xp)
+    period = xpx.atleast_nd(period, ndim=2, xp=xp)
+    if xp.any(period <= 0):
+        raise ValueError('periods must be positive')
+
+    # this converts the times to vectors
+    events_ = xp.astype(events, period.dtype)
+    vectors = xp.exp(2j * (xp.pi / period.T @ events_))
+
+    # the vector strength is just the magnitude of the mean of the vectors
+    # the vector phase is the angle of the mean of the vectors
+    vectormean = xp.mean(vectors, axis=1)
+    strength = xp.abs(vectormean)
+    phase = _angle(vectormean, xp)
+
+    # if the original period was a scalar, return scalars
+    if scalarperiod:
+        strength = strength[0]
+        phase = phase[0]
+    return strength, phase
+
+
+def detrend(data: np.ndarray, axis: int = -1,
+            type: Literal['linear', 'constant'] = 'linear',
+            bp: ArrayLike | int = 0, overwrite_data: bool = False) -> np.ndarray:
+    r"""Remove linear or constant trend along axis from data.
+
+    Parameters
+    ----------
+    data : array_like
+        The input data.
+    axis : int, optional
+        The axis along which to detrend the data. By default this is the
+        last axis (-1).
+    type : {'linear', 'constant'}, optional
+        The type of detrending. If ``type == 'linear'`` (default),
+        the result of a linear least-squares fit to `data` is subtracted
+        from `data`.
+        If ``type == 'constant'``, only the mean of `data` is subtracted.
+    bp : array_like of ints, optional
+        A sequence of break points. If given, an individual linear fit is
+        performed for each part of `data` between two break points.
+        Break points are specified as indices into `data`. This parameter
+        only has an effect when ``type == 'linear'``.
+    overwrite_data : bool, optional
+        If True, allow in place detrending and avoid a copy. Default is
+        False. In place modification applies only if ``type == 'linear'``
+        and `data` is of the floating point dtype ``float32``, ``float64``,
+        ``complex64`` or ``complex128``.
+
+    Returns
+    -------
+    ret : ndarray
+        The detrended input data.
+
+    Notes
+    -----
+    Detrending can be interpreted as subtracting a least squares fit polynomial:
+    Setting the parameter `type` to 'constant' corresponds to fitting a zeroth degree
+    polynomial, 'linear' to a first degree polynomial. Consult the example below.
+
+    See Also
+    --------
+    :meth:`numpy.polynomial.polynomial.Polynomial.fit` : Create least squares fit polynomial.
+
+
+    Examples
+    --------
+    The following example detrends the function :math:`x(t) = \sin(\pi t) + 1/4`:
+
+    >>> import matplotlib.pyplot as plt
+    >>> import numpy as np
+    >>> from scipy.signal import detrend
+    ...
+    >>> t = np.linspace(-0.5, 0.5, 21)
+    >>> x = np.sin(np.pi*t) + 1/4
+    ...
+    >>> x_d_const = detrend(x, type='constant')
+    >>> x_d_linear = detrend(x, type='linear')
+    ...
+    >>> fig1, ax1 = plt.subplots()
+    >>> ax1.set_title(r"Detrending $x(t)=\sin(\pi t) + 1/4$")
+    >>> ax1.set(xlabel="t", ylabel="$x(t)$", xlim=(t[0], t[-1]))
+    >>> ax1.axhline(y=0, color='black', linewidth=.5)
+    >>> ax1.axvline(x=0, color='black', linewidth=.5)
+    >>> ax1.plot(t, x, 'C0.-',  label="No detrending")
+    >>> ax1.plot(t, x_d_const, 'C1x-', label="type='constant'")
+    >>> ax1.plot(t, x_d_linear, 'C2+-', label="type='linear'")
+    >>> ax1.legend()
+    >>> plt.show()
+
+    Alternatively, NumPy's `~numpy.polynomial.polynomial.Polynomial` can be used for
+    detrending as well:
+
+    >>> pp0 = np.polynomial.Polynomial.fit(t, x, deg=0)  # fit degree 0 polynomial
+    >>> np.allclose(x_d_const, x - pp0(t))  # compare with constant detrend
+    True
+    >>> pp1 = np.polynomial.Polynomial.fit(t, x, deg=1)  # fit degree 1 polynomial
+    >>> np.allclose(x_d_linear, x - pp1(t))  # compare with linear detrend
+    True
+
+    Note that `~numpy.polynomial.polynomial.Polynomial` also allows fitting higher
+    degree polynomials. Consult its documentation on how to extract the polynomial
+    coefficients.
+    """  # noqa: E501
+    if type not in ['linear', 'l', 'constant', 'c']:
+        raise ValueError("Trend type must be 'linear' or 'constant'.")
+
+    xp = array_namespace(data, bp)
+
+    data = np.asarray(data)
+    dtype = data.dtype.char
+    if dtype not in 'dfDF':
+        dtype = 'd'
+    if type in ['constant', 'c']:
+        ret = data - np.mean(data, axis, keepdims=True)
+        return xp.asarray(ret)
+    else:
+        dshape = data.shape
+        N = dshape[axis]
+        bp = np.asarray(bp)
+        bp = np.sort(np.unique(np.concatenate(np.atleast_1d(0, bp, N))))
+        if np.any(bp > N):
+            raise ValueError("Breakpoints must be less than length "
+                             "of data along given axis.")
+
+        # Restructure data so that axis is along first dimension and
+        #  all other dimensions are collapsed into second dimension
+        rnk = len(dshape)
+        if axis < 0:
+            axis = axis + rnk
+        newdata = np.moveaxis(data, axis, 0)
+        newdata_shape = newdata.shape
+        newdata = newdata.reshape(N, -1)
+
+        if not overwrite_data:
+            newdata = newdata.copy()  # make sure we have a copy
+        if newdata.dtype.char not in 'dfDF':
+            newdata = newdata.astype(dtype)
+
+#        Nreg = len(bp) - 1
+        # Find leastsq fit and remove it for each piece
+        for m in range(len(bp) - 1):
+            Npts = bp[m + 1] - bp[m]
+            A = np.ones((Npts, 2), dtype)
+            A[:, 0] = np.arange(1, Npts + 1, dtype=dtype) / Npts
+            sl = slice(bp[m], bp[m + 1])
+            coef, resids, rank, s = linalg.lstsq(A, newdata[sl])
+            newdata[sl] = newdata[sl] - A @ coef
+
+        # Put data back in original shape.
+        newdata = newdata.reshape(newdata_shape)
+        ret = np.moveaxis(newdata, 0, axis)
+        return xp.asarray(ret)
+
+
+def lfilter_zi(b, a):
+    r"""Construct initial conditions for `lfilter` for step response steady-state.
+
+    Compute an initial state `zi` for the `lfilter` function that corresponds
+    to the steady state of the step response.
+
+    A typical use of this function is to set the initial state so that the
+    output of the filter starts at the same value as the first element of
+    the signal to be filtered.
+
+    Parameters
+    ----------
+    b : array_like
+        The numerator coefficient vector as a 1-D sequence.
+    a : array_like
+        The denominator coefficient vector as a 1-D sequence.  If ``a[0]``
+        is not 1, then both `a` and `b` are normalized by ``a[0]``.
+        Hence, ``a[0] != 0`` must hold.
+
+    Returns
+    -------
+    zi : 1-D ndarray
+        The initial state for the filter.
+
+    Raises
+    ------
+    ValueError
+        If ``a[0] == 0`` (invalid denominator polynomial) or
+        ``sum(a) == 0`` (unstable filter).
+
+    See Also
+    --------
+    lfilter, lfiltic, filtfilt
+
+    Notes
+    -----
+    The parameters `b` and `a` represent a transfer function :math:`H(z) = Y(z)/X(z)`
+    which is defined in the :ref:`tutorial_signal_TransferFunctionRepresentation`
+    section of the :ref:`user_guide`. As discussed in [1]_, the final value of
+    filtering a step response :math:`X(z) = z / (z-1)`, i.e., steady state, is given by
+
+    .. math::
+
+        y_\infty := \lim_{k\to\infty} y[k]
+                  =  \lim_{z\to 1}\ (z-1)\, Y(z)
+                  = \frac{\sum_{i=0}^M b_i}{\sum_{j=0}^N a_j} \,.
+
+    If the denominator is zero, :math:`H(z)` has a pole at :math:`z_\infty=1`, which
+    makes the filter unstable. For the transposed Direct Form II, which is implemented
+    in `lfilter`, the initialization values :math:`z_k` for :math:`H(z)` can be
+    determined by the recurrence equation
+
+    .. math::
+
+        z_k = z_{k+1} + x[0] \big( b_k - y_\infty a_k \big) \,,
+
+    with :math:`x[0]` being the height of the input step function. Note that
+    :math:`a_0=1` is assumed here, which is incorporated into this function by
+    performing a normalization step.
+
+    Examples
+    --------
+    The following code creates a lowpass Butterworth filter to filter a signal made up
+    of ones. As expected of a lowpass filter, the output is also all ones. If the `zi`
+    argument of `lfilter` had not been given, a transient signal would have been
+    produced. The second signal illustrates that using the parameter `zi` supresses
+    transients at the beginning of the output signal:
+
+    >>> import numpy as np
+    >>> from scipy.signal import lfilter, lfilter_zi, butter
+    ...
+    >>> b, a = butter(5, 0.25)
+    >>> zi = lfilter_zi(b, a)
+    >>> y0, zi0 = lfilter(b, a, np.ones(10), zi=zi)
+    >>> y0
+    array([1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.])
+    >>> # Another signal:
+    >>> x = np.array([0.5, 0.5, 0.5, 0.0, 0.0, 0.0, 0.0])
+    >>> y1, zi1 = lfilter(b, a, x, zi=zi*x[0])
+    >>> y1
+    array([ 0.5       ,  0.5       ,  0.5       ,  0.49836039,  0.48610528,
+        0.44399389,  0.35505241])
+
+    Note that the `zi` argument to `lfilter` is computed using `lfilter_zi` and scaled
+    by ``x[0]``. As a result, the output `y1` has no transient until the input drops
+    from 0.5 to 0.
+
+    References
+    ----------
+    .. [1] Boris Likhterov and Norman Kopeika. "Hardware-efficient technique for
+           minimizing startup transients in Direct Form II digital filters". In:
+           International Journal of Electronics -- Volume 90(7), July 2003, pp.
+           471--479. :doi:`10.1080/00207210310001612482`
+    """
+    xp = array_namespace(b, a)
+
+    # Note: As an alternative to this function, using `lfiltic` might work as well.
+    # For example, when b,a = butter(N,Wn), then
+    #    lfiltic(b, a, y=numpy.ones_like(a)*y_inf, x=numpy.ones_like(b)).
+    # should produce the same result. Though, no obvious algorithmic advantages over
+    # this implementation could be identified.
+
+    # We could use scipy.signal.normalize, but it uses warnings in
+    # cases where a ValueError is more appropriate, and it allows
+    # b to be 2D.
+    b, a = xp_promote(b, a, xp=xp, force_floating=True)  # need floats for division
+    b = xpx.atleast_nd(b, ndim=1, xp=xp)
+    a = xpx.atleast_nd(a, ndim=1, xp=xp)
+
+    if not (b.ndim == a.ndim == 1):
+        raise ValueError("Numerator `b` and Denominator `a` must be 1-D arrays, " +
+                         f"but {b.shape = }, {a.shape = }!")
+
+    if a[0] == 0:
+        raise ValueError("First coefficient of parameter `a` must be non-zero!")
+
+    if a[0] != 1:  # Normalize the coefficients so a[0] == 1:
+        b, a = b / a[0], a / a[0]
+
+    if (sum_a := xp.sum(a)) == 0:
+        raise ValueError("Filter not stable due to sum(a) == 0, i.e., " +
+                         "having a pole at z = 1!")
+
+    y_inf = xp.sum(b) / sum_a  # y[k → ∞] for unit-step input
+
+    # Calculate `zi[k] = zi[k+1] + b - y_inf*a` allowing different length for a, b:
+    n_a, n_b = a.shape[0], b.shape[0]
+    n = max(n_a, n_b)
+    b = xpx.pad(b, (0, n-n_b))
+    a = xpx.pad(a, (0, n-n_a))
+    # `xp.cumulative_sum((b - y_inf*a)[::-1])[-2::-1]` does not work in torch due to
+    # unsupported slicing with a negative step index. Hence, `flip` is used:
+    return xp.flip(xp.cumulative_sum(xp.flip(b - y_inf*a)))[1:]
+
+def sosfilt_zi(sos):
+    """
+    Construct initial conditions for sosfilt for step response steady-state.
+
+    Compute an initial state `zi` for the `sosfilt` function that corresponds
+    to the steady state of the step response.
+
+    A typical use of this function is to set the initial state so that the
+    output of the filter starts at the same value as the first element of
+    the signal to be filtered.
+
+    Parameters
+    ----------
+    sos : array_like
+        Array of second-order filter coefficients, must have shape
+        ``(n_sections, 6)``. See `sosfilt` for the SOS filter format
+        specification.
+
+    Returns
+    -------
+    zi : ndarray
+        Initial conditions suitable for use with ``sosfilt``, shape
+        ``(n_sections, 2)``.
+
+    See Also
+    --------
+    sosfilt, zpk2sos
+
+    Notes
+    -----
+    .. versionadded:: 0.16.0
+
+    Examples
+    --------
+    Filter a rectangular pulse that begins at time 0, with and without
+    the use of the `zi` argument of `scipy.signal.sosfilt`.
+
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+
+    >>> sos = signal.butter(9, 0.125, output='sos')
+    >>> zi = signal.sosfilt_zi(sos)
+    >>> x = (np.arange(250) < 100).astype(int)
+    >>> f1 = signal.sosfilt(sos, x)
+    >>> f2, zo = signal.sosfilt(sos, x, zi=zi)
+
+    >>> plt.plot(x, 'k--', label='x')
+    >>> plt.plot(f1, 'b', alpha=0.5, linewidth=2, label='filtered')
+    >>> plt.plot(f2, 'g', alpha=0.25, linewidth=4, label='filtered with zi')
+    >>> plt.legend(loc='best')
+    >>> plt.show()
+
+    """
+    xp = array_namespace(sos)
+
+    sos = xp.asarray(sos)
+    if sos.ndim != 2 or sos.shape[1] != 6:
+        raise ValueError('sos must be shape (n_sections, 6)')
+
+    if xp.isdtype(sos.dtype, ("integral", "bool")):
+        sos = xp.astype(sos, xp.float64)
+
+    n_sections = sos.shape[0]
+    zi = xp.empty((n_sections, 2), dtype=sos.dtype)
+    scale = 1.0
+    for section in range(n_sections):
+        b = sos[section, :3]
+        a = sos[section, 3:]
+        zi[section, ...] = scale * lfilter_zi(b, a)
+        # If H(z) = B(z)/A(z) is this section's transfer function, then
+        # b.sum()/a.sum() is H(1), the gain at omega=0.  That's the steady
+        # state value of this section's step response.
+        scale *= xp.sum(b) / xp.sum(a)
+
+    return zi
+
+
+def _filtfilt_gust(b, a, x, axis=-1, irlen=None):
+    """Forward-backward IIR filter that uses Gustafsson's method.
+
+    Apply the IIR filter defined by ``(b,a)`` to `x` twice, first forward
+    then backward, using Gustafsson's initial conditions [1]_.
+
+    Let ``y_fb`` be the result of filtering first forward and then backward,
+    and let ``y_bf`` be the result of filtering first backward then forward.
+    Gustafsson's method is to compute initial conditions for the forward
+    pass and the backward pass such that ``y_fb == y_bf``.
+
+    Parameters
+    ----------
+    b : scalar or 1-D ndarray
+        Numerator coefficients of the filter.
+    a : scalar or 1-D ndarray
+        Denominator coefficients of the filter.
+    x : ndarray
+        Data to be filtered.
+    axis : int, optional
+        Axis of `x` to be filtered.  Default is -1.
+    irlen : int or None, optional
+        The length of the nonnegligible part of the impulse response.
+        If `irlen` is None, or if the length of the signal is less than
+        ``2 * irlen``, then no part of the impulse response is ignored.
+
+    Returns
+    -------
+    y : ndarray
+        The filtered data.
+    x0 : ndarray
+        Initial condition for the forward filter.
+    x1 : ndarray
+        Initial condition for the backward filter.
+
+    Notes
+    -----
+    Typically the return values `x0` and `x1` are not needed by the
+    caller.  The intended use of these return values is in unit tests.
+
+    References
+    ----------
+    .. [1] F. Gustaffson. Determining the initial states in forward-backward
+           filtering. Transactions on Signal Processing, 46(4):988-992, 1996.
+
+    """
+    # In the comments, "Gustafsson's paper" and [1] refer to the
+    # paper referenced in the docstring.
+
+    b = np.atleast_1d(b)
+    a = np.atleast_1d(a)
+
+    order = max(len(b), len(a)) - 1
+    if order == 0:
+        # The filter is just scalar multiplication, with no state.
+        scale = (b[0] / a[0])**2
+        y = scale * x
+        return y, np.array([]), np.array([])
+
+    if axis != -1 or axis != x.ndim - 1:
+        # Move the axis containing the data to the end.
+        x = np.swapaxes(x, axis, x.ndim - 1)
+
+    # n is the number of samples in the data to be filtered.
+    n = x.shape[-1]
+
+    if irlen is None or n <= 2*irlen:
+        m = n
+    else:
+        m = irlen
+
+    # Create Obs, the observability matrix (called O in the paper).
+    # This matrix can be interpreted as the operator that propagates
+    # an arbitrary initial state to the output, assuming the input is
+    # zero.
+    # In Gustafsson's paper, the forward and backward filters are not
+    # necessarily the same, so he has both O_f and O_b.  We use the same
+    # filter in both directions, so we only need O. The same comment
+    # applies to S below.
+    Obs = np.zeros((m, order))
+    zi = np.zeros(order)
+    zi[0] = 1
+    Obs[:, 0] = lfilter(b, a, np.zeros(m), zi=zi)[0]
+    for k in range(1, order):
+        Obs[k:, k] = Obs[:-k, 0]
+
+    # Obsr is O^R (Gustafsson's notation for row-reversed O)
+    Obsr = Obs[::-1]
+
+    # Create S.  S is the matrix that applies the filter to the reversed
+    # propagated initial conditions.  That is,
+    #     out = S.dot(zi)
+    # is the same as
+    #     tmp, _ = lfilter(b, a, zeros(), zi=zi)  # Propagate ICs.
+    #     out = lfilter(b, a, tmp[::-1])          # Reverse and filter.
+
+    # Equations (5) & (6) of [1]
+    S = lfilter(b, a, Obs[::-1], axis=0)
+
+    # Sr is S^R (row-reversed S)
+    Sr = S[::-1]
+
+    # M is [(S^R - O), (O^R - S)]
+    if m == n:
+        M = np.hstack((Sr - Obs, Obsr - S))
+    else:
+        # Matrix described in section IV of [1].
+        M = np.zeros((2*m, 2*order))
+        M[:m, :order] = Sr - Obs
+        M[m:, order:] = Obsr - S
+
+    # Naive forward-backward and backward-forward filters.
+    # These have large transients because the filters use zero initial
+    # conditions.
+    y_f = lfilter(b, a, x)
+    y_fb = lfilter(b, a, y_f[..., ::-1])[..., ::-1]
+
+    y_b = lfilter(b, a, x[..., ::-1])[..., ::-1]
+    y_bf = lfilter(b, a, y_b)
+
+    delta_y_bf_fb = y_bf - y_fb
+    if m == n:
+        delta = delta_y_bf_fb
+    else:
+        start_m = delta_y_bf_fb[..., :m]
+        end_m = delta_y_bf_fb[..., -m:]
+        delta = np.concatenate((start_m, end_m), axis=-1)
+
+    # ic_opt holds the "optimal" initial conditions.
+    # The following code computes the result shown in the formula
+    # of the paper between equations (6) and (7).
+    if delta.ndim == 1:
+        ic_opt = linalg.lstsq(M, delta)[0]
+    else:
+        # Reshape delta so it can be used as an array of multiple
+        # right-hand-sides in linalg.lstsq.
+        delta2d = delta.reshape(-1, delta.shape[-1]).T
+        ic_opt0 = linalg.lstsq(M, delta2d)[0].T
+        ic_opt = ic_opt0.reshape(delta.shape[:-1] + (M.shape[-1],))
+
+    # Now compute the filtered signal using equation (7) of [1].
+    # First, form [S^R, O^R] and call it W.
+    if m == n:
+        W = np.hstack((Sr, Obsr))
+    else:
+        W = np.zeros((2*m, 2*order))
+        W[:m, :order] = Sr
+        W[m:, order:] = Obsr
+
+    # Equation (7) of [1] says
+    #     Y_fb^opt = Y_fb^0 + W * [x_0^opt; x_{N-1}^opt]
+    # `wic` is (almost) the product on the right.
+    # W has shape (m, 2*order), and ic_opt has shape (..., 2*order),
+    # so we can't use W.dot(ic_opt).  Instead, we dot ic_opt with W.T,
+    # so wic has shape (..., m).
+    wic = ic_opt.dot(W.T)
+
+    # `wic` is "almost" the product of W and the optimal ICs in equation
+    # (7)--if we're using a truncated impulse response (m < n), `wic`
+    # contains only the adjustments required for the ends of the signal.
+    # Here we form y_opt, taking this into account if necessary.
+    y_opt = y_fb
+    if m == n:
+        y_opt += wic
+    else:
+        y_opt[..., :m] += wic[..., :m]
+        y_opt[..., -m:] += wic[..., -m:]
+
+    x0 = ic_opt[..., :order]
+    x1 = ic_opt[..., -order:]
+    if axis != -1 or axis != x.ndim - 1:
+        # Restore the data axis to its original position.
+        x0 = np.swapaxes(x0, axis, x.ndim - 1)
+        x1 = np.swapaxes(x1, axis, x.ndim - 1)
+        y_opt = np.swapaxes(y_opt, axis, x.ndim - 1)
+
+    return y_opt, x0, x1
+
+
+def filtfilt(b, a, x, axis=-1, padtype='odd', padlen=None, method='pad',
+             irlen=None):
+    """
+    Apply a digital filter forward and backward to a signal.
+
+    This function applies a linear digital filter twice, once forward and
+    once backwards.  The combined filter has zero phase and a filter order
+    twice that of the original.
+
+    The function provides options for handling the edges of the signal.
+
+    The function `sosfiltfilt` (and filter design using ``output='sos'``)
+    should be preferred over `filtfilt` for most filtering tasks, as
+    second-order sections have fewer numerical problems.
+
+    Parameters
+    ----------
+    b : (N,) array_like
+        The numerator coefficient vector of the filter.
+    a : (N,) array_like
+        The denominator coefficient vector of the filter.  If ``a[0]``
+        is not 1, then both `a` and `b` are normalized by ``a[0]``.
+    x : array_like
+        The array of data to be filtered.
+    axis : int, optional
+        The axis of `x` to which the filter is applied.
+        Default is -1.
+    padtype : str or None, optional
+        Must be 'odd', 'even', 'constant', or None.  This determines the
+        type of extension to use for the padded signal to which the filter
+        is applied.  If `padtype` is None, no padding is used.  The default
+        is 'odd'.
+    padlen : int or None, optional
+        The number of elements by which to extend `x` at both ends of
+        `axis` before applying the filter.  This value must be less than
+        ``x.shape[axis] - 1``.  ``padlen=0`` implies no padding.
+        The default value is ``3 * max(len(a), len(b))``.
+    method : str, optional
+        Determines the method for handling the edges of the signal, either
+        "pad" or "gust".  When `method` is "pad", the signal is padded; the
+        type of padding is determined by `padtype` and `padlen`, and `irlen`
+        is ignored.  When `method` is "gust", Gustafsson's method is used,
+        and `padtype` and `padlen` are ignored.
+    irlen : int or None, optional
+        When `method` is "gust", `irlen` specifies the length of the
+        impulse response of the filter.  If `irlen` is None, no part
+        of the impulse response is ignored.  For a long signal, specifying
+        `irlen` can significantly improve the performance of the filter.
+
+    Returns
+    -------
+    y : ndarray
+        The filtered output with the same shape as `x`.
+
+    See Also
+    --------
+    sosfiltfilt, lfilter_zi, lfilter, lfiltic, savgol_filter, sosfilt
+
+    Notes
+    -----
+    When `method` is "pad", the function pads the data along the given axis
+    in one of three ways: odd, even or constant.  The odd and even extensions
+    have the corresponding symmetry about the end point of the data.  The
+    constant extension extends the data with the values at the end points. On
+    both the forward and backward passes, the initial condition of the
+    filter is found by using `lfilter_zi` and scaling it by the end point of
+    the extended data.
+
+    When `method` is "gust", Gustafsson's method [1]_ is used.  Initial
+    conditions are chosen for the forward and backward passes so that the
+    forward-backward filter gives the same result as the backward-forward
+    filter.
+
+    The option to use Gustaffson's method was added in scipy version 0.16.0.
+
+    References
+    ----------
+    .. [1] F. Gustaffson, "Determining the initial states in forward-backward
+           filtering", Transactions on Signal Processing, Vol. 46, pp. 988-992,
+           1996.
+
+    Examples
+    --------
+    The examples will use several functions from `scipy.signal`.
+
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+
+    First we create a one second signal that is the sum of two pure sine
+    waves, with frequencies 5 Hz and 250 Hz, sampled at 2000 Hz.
+
+    >>> t = np.linspace(0, 1.0, 2001)
+    >>> xlow = np.sin(2 * np.pi * 5 * t)
+    >>> xhigh = np.sin(2 * np.pi * 250 * t)
+    >>> x = xlow + xhigh
+
+    Now create a lowpass Butterworth filter with a cutoff of 0.125 times
+    the Nyquist frequency, or 125 Hz, and apply it to ``x`` with `filtfilt`.
+    The result should be approximately ``xlow``, with no phase shift.
+
+    >>> b, a = signal.butter(8, 0.125)
+    >>> y = signal.filtfilt(b, a, x, padlen=150)
+    >>> np.abs(y - xlow).max()
+    9.1086182074789912e-06
+
+    We get a fairly clean result for this artificial example because
+    the odd extension is exact, and with the moderately long padding,
+    the filter's transients have dissipated by the time the actual data
+    is reached.  In general, transient effects at the edges are
+    unavoidable.
+
+    The following example demonstrates the option ``method="gust"``.
+
+    First, create a filter.
+
+    >>> b, a = signal.ellip(4, 0.01, 120, 0.125)  # Filter to be applied.
+
+    `sig` is a random input signal to be filtered.
+
+    >>> rng = np.random.default_rng()
+    >>> n = 60
+    >>> sig = rng.standard_normal(n)**3 + 3*rng.standard_normal(n).cumsum()
+
+    Apply `filtfilt` to `sig`, once using the Gustafsson method, and
+    once using padding, and plot the results for comparison.
+
+    >>> fgust = signal.filtfilt(b, a, sig, method="gust")
+    >>> fpad = signal.filtfilt(b, a, sig, padlen=50)
+    >>> plt.plot(sig, 'k-', label='input')
+    >>> plt.plot(fgust, 'b-', linewidth=4, label='gust')
+    >>> plt.plot(fpad, 'c-', linewidth=1.5, label='pad')
+    >>> plt.legend(loc='best')
+    >>> plt.show()
+
+    The `irlen` argument can be used to improve the performance
+    of Gustafsson's method.
+
+    Estimate the impulse response length of the filter.
+
+    >>> z, p, k = signal.tf2zpk(b, a)
+    >>> eps = 1e-9
+    >>> r = np.max(np.abs(p))
+    >>> approx_impulse_len = int(np.ceil(np.log(eps) / np.log(r)))
+    >>> approx_impulse_len
+    137
+
+    Apply the filter to a longer signal, with and without the `irlen`
+    argument.  The difference between `y1` and `y2` is small.  For long
+    signals, using `irlen` gives a significant performance improvement.
+
+    >>> x = rng.standard_normal(4000)
+    >>> y1 = signal.filtfilt(b, a, x, method='gust')
+    >>> y2 = signal.filtfilt(b, a, x, method='gust', irlen=approx_impulse_len)
+    >>> print(np.max(np.abs(y1 - y2)))
+    2.875334415008979e-10
+
+    """
+    xp = array_namespace(b, a, x)
+
+    b = np.atleast_1d(np.asarray(b))
+    a = np.atleast_1d(np.asarray(a))
+    x = np.asarray(x)
+
+    if method not in ["pad", "gust"]:
+        raise ValueError("method must be 'pad' or 'gust'.")
+
+    if method == "gust":
+        y, z1, z2 = _filtfilt_gust(b, a, x, axis=axis, irlen=irlen)
+        return xp.asarray(y)
+
+    # method == "pad"
+    edge, ext = _validate_pad(padtype, padlen, x, axis,
+                              ntaps=max(len(a), len(b)))
+
+    # Get the steady state of the filter's step response.
+    zi = lfilter_zi(b, a)
+
+    # Reshape zi and create x0 so that zi*x0 broadcasts
+    # to the correct value for the 'zi' keyword argument
+    # to lfilter.
+    zi_shape = [1] * x.ndim
+    zi_shape[axis] = zi.size
+    zi = np.reshape(zi, zi_shape)
+    x0 = axis_slice(ext, stop=1, axis=axis)
+
+    # Forward filter.
+    (y, zf) = lfilter(b, a, ext, axis=axis, zi=zi * x0)
+
+    # Backward filter.
+    # Create y0 so zi*y0 broadcasts appropriately.
+    y0 = axis_slice(y, start=-1, axis=axis)
+    (y, zf) = lfilter(b, a, axis_reverse(y, axis=axis), axis=axis, zi=zi * y0)
+
+    # Reverse y.
+    y = axis_reverse(y, axis=axis)
+
+    if edge > 0:
+        # Slice the actual signal from the extended signal.
+        y = axis_slice(y, start=edge, stop=-edge, axis=axis)
+        if is_torch(xp):
+            y = y.copy()    #  pytorch/pytorch#59786 : no negative strides in pytorch
+
+    return xp.asarray(y)
+
+
+def _validate_pad(padtype, padlen, x, axis, ntaps):
+    """Helper to validate padding for filtfilt"""
+    if padtype not in ['even', 'odd', 'constant', None]:
+        raise ValueError(f"Unknown value '{padtype}' given to padtype. "
+                         "padtype must be 'even', 'odd', 'constant', or None.")
+
+    if padtype is None:
+        padlen = 0
+
+    if padlen is None:
+        # Original padding; preserved for backwards compatibility.
+        edge = ntaps * 3
+    else:
+        edge = padlen
+
+    # x's 'axis' dimension must be bigger than edge.
+    if x.shape[axis] <= edge:
+        raise ValueError(
+            f"The length of the input vector x must be greater than padlen, "
+            f"which is {edge}."
+        )
+
+    if padtype is not None and edge > 0:
+        # Make an extension of length `edge` at each
+        # end of the input array.
+        if padtype == 'even':
+            ext = even_ext(x, edge, axis=axis)
+        elif padtype == 'odd':
+            ext = odd_ext(x, edge, axis=axis)
+        else:
+            ext = const_ext(x, edge, axis=axis)
+    else:
+        ext = x
+    return edge, ext
+
+
+def _validate_x(x):
+    x = np.asarray(x)
+    if x.ndim == 0:
+        raise ValueError('x must be at least 1-D')
+    return x
+
+
+def sosfilt(sos, x, axis=-1, zi=None):
+    """
+    Filter data along one dimension using cascaded second-order sections.
+
+    Filter a data sequence, `x`, using a digital IIR filter defined by
+    `sos`.
+
+    Parameters
+    ----------
+    sos : array_like
+        Array of second-order filter coefficients, must have shape
+        ``(n_sections, 6)``. Each row corresponds to a second-order
+        section, with the first three columns providing the numerator
+        coefficients and the last three providing the denominator
+        coefficients.
+    x : array_like
+        An N-dimensional input array.
+    axis : int, optional
+        The axis of the input data array along which to apply the
+        linear filter. The filter is applied to each subarray along
+        this axis.  Default is -1.
+    zi : array_like, optional
+        Initial conditions for the cascaded filter delays.  It is a (at
+        least 2D) vector of shape ``(n_sections, ..., 2, ...)``, where
+        ``..., 2, ...`` denotes the shape of `x`, but with ``x.shape[axis]``
+        replaced by 2.  If `zi` is None or is not given then initial rest
+        (i.e. all zeros) is assumed.
+        Note that these initial conditions are *not* the same as the initial
+        conditions given by `lfiltic` or `lfilter_zi`.
+
+    Returns
+    -------
+    y : ndarray
+        The output of the digital filter.
+    zf : ndarray, optional
+        If `zi` is None, this is not returned, otherwise, `zf` holds the
+        final filter delay values.
+
+    See Also
+    --------
+    zpk2sos, sos2zpk, sosfilt_zi, sosfiltfilt, freqz_sos
+
+    Notes
+    -----
+    The filter function is implemented as a series of second-order filters
+    with direct-form II transposed structure. It is designed to minimize
+    numerical precision errors for high-order filters.
+
+    .. versionadded:: 0.16.0
+
+    Examples
+    --------
+    Plot a 13th-order filter's impulse response using both `lfilter` and
+    `sosfilt`, showing the instability that results from trying to do a
+    13th-order filter in a single stage (the numerical error pushes some poles
+    outside of the unit circle):
+
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy import signal
+    >>> b, a = signal.ellip(13, 0.009, 80, 0.05, output='ba')
+    >>> sos = signal.ellip(13, 0.009, 80, 0.05, output='sos')
+    >>> x = signal.unit_impulse(700)
+    >>> y_tf = signal.lfilter(b, a, x)
+    >>> y_sos = signal.sosfilt(sos, x)
+    >>> plt.plot(y_tf, 'r', label='TF')
+    >>> plt.plot(y_sos, 'k', label='SOS')
+    >>> plt.legend(loc='best')
+    >>> plt.show()
+
+    """
+    xp = array_namespace(sos, x, zi)
+
+    x = _validate_x(x)
+    sos, n_sections = _validate_sos(sos)
+    x_zi_shape = list(x.shape)
+    x_zi_shape[axis] = 2
+    x_zi_shape = tuple([n_sections] + x_zi_shape)
+    inputs = [sos, x]
+    if zi is not None:
+        inputs.append(np.asarray(zi))
+    dtype = np.result_type(*inputs)
+    if dtype.char not in 'fdgFDGO':
+        raise NotImplementedError(f"input type '{dtype}' not supported")
+    if zi is not None:
+        zi = np.asarray(zi, dtype=dtype)
+
+        # make a copy so that we can operate in place
+        # NB: 1. use xp_copy to paper over numpy 1/2 copy= keyword
+        #     2. make sure the copied zi remains a numpy array
+        zi = xp_copy(zi, xp=array_namespace(zi))
+        if zi.shape != x_zi_shape:
+            raise ValueError(
+                f"Invalid zi shape. With axis={axis!r}, "
+                f"an input with shape {x.shape!r}, "
+                f"and an sos array with {n_sections} sections, zi must have "
+                f"shape {x_zi_shape!r}, got {zi.shape!r}."
+            )
+        return_zi = True
+    else:
+        zi = np.zeros(x_zi_shape, dtype=dtype)
+        return_zi = False
+    axis = axis % x.ndim  # make positive
+    x = np.moveaxis(x, axis, -1)
+    zi = np.moveaxis(zi, (0, axis + 1), (-2, -1))
+    x_shape, zi_shape = x.shape, zi.shape
+    x = np.reshape(x, (-1, x.shape[-1]))
+    x = np.array(x, dtype, order='C')  # make a copy, can modify in place
+    zi = np.ascontiguousarray(np.reshape(zi, (-1, n_sections, 2)))
+    sos = sos.astype(dtype, copy=False)
+    _sosfilt(sos, x, zi)
+    x = x.reshape(x_shape)
+    x = np.moveaxis(x, -1, axis)
+    if return_zi:
+        zi = zi.reshape(zi_shape)
+        zi = np.moveaxis(zi, (-2, -1), (0, axis + 1))
+        out = (xp.asarray(x), xp.asarray(zi))
+    else:
+        out = xp.asarray(x)
+    return out
+
+
+def sosfiltfilt(sos, x, axis=-1, padtype='odd', padlen=None):
+    """
+    A forward-backward digital filter using cascaded second-order sections.
+
+    See `filtfilt` for more complete information about this method.
+
+    Parameters
+    ----------
+    sos : array_like
+        Array of second-order filter coefficients, must have shape
+        ``(n_sections, 6)``. Each row corresponds to a second-order
+        section, with the first three columns providing the numerator
+        coefficients and the last three providing the denominator
+        coefficients.
+    x : array_like
+        The array of data to be filtered.
+    axis : int, optional
+        The axis of `x` to which the filter is applied.
+        Default is -1.
+    padtype : str or None, optional
+        Must be 'odd', 'even', 'constant', or None.  This determines the
+        type of extension to use for the padded signal to which the filter
+        is applied.  If `padtype` is None, no padding is used.  The default
+        is 'odd'.
+    padlen : int or None, optional
+        The number of elements by which to extend `x` at both ends of
+        `axis` before applying the filter.  This value must be less than
+        ``x.shape[axis] - 1``.  ``padlen=0`` implies no padding.
+        The default value is::
+
+            3 * (2 * len(sos) + 1 - min((sos[:, 2] == 0).sum(),
+                                        (sos[:, 5] == 0).sum()))
+
+        The extra subtraction at the end attempts to compensate for poles
+        and zeros at the origin (e.g. for odd-order filters) to yield
+        equivalent estimates of `padlen` to those of `filtfilt` for
+        second-order section filters built with `scipy.signal` functions.
+
+    Returns
+    -------
+    y : ndarray
+        The filtered output with the same shape as `x`.
+
+    See Also
+    --------
+    filtfilt, sosfilt, sosfilt_zi, freqz_sos
+
+    Notes
+    -----
+    .. versionadded:: 0.18.0
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.signal import sosfiltfilt, butter
+    >>> import matplotlib.pyplot as plt
+    >>> rng = np.random.default_rng()
+
+    Create an interesting signal to filter.
+
+    >>> n = 201
+    >>> t = np.linspace(0, 1, n)
+    >>> x = 1 + (t < 0.5) - 0.25*t**2 + 0.05*rng.standard_normal(n)
+
+    Create a lowpass Butterworth filter, and use it to filter `x`.
+
+    >>> sos = butter(4, 0.125, output='sos')
+    >>> y = sosfiltfilt(sos, x)
+
+    For comparison, apply an 8th order filter using `sosfilt`.  The filter
+    is initialized using the mean of the first four values of `x`.
+
+    >>> from scipy.signal import sosfilt, sosfilt_zi
+    >>> sos8 = butter(8, 0.125, output='sos')
+    >>> zi = x[:4].mean() * sosfilt_zi(sos8)
+    >>> y2, zo = sosfilt(sos8, x, zi=zi)
+
+    Plot the results.  Note that the phase of `y` matches the input, while
+    `y2` has a significant phase delay.
+
+    >>> plt.plot(t, x, alpha=0.5, label='x(t)')
+    >>> plt.plot(t, y, label='y(t)')
+    >>> plt.plot(t, y2, label='y2(t)')
+    >>> plt.legend(framealpha=1, shadow=True)
+    >>> plt.grid(alpha=0.25)
+    >>> plt.xlabel('t')
+    >>> plt.show()
+
+    """
+    xp = array_namespace(sos, x)
+
+    sos, n_sections = _validate_sos(sos)
+    x = _validate_x(x)
+
+    # `method` is "pad"...
+    ntaps = 2 * n_sections + 1
+    ntaps -= min((sos[:, 2] == 0).sum(), (sos[:, 5] == 0).sum())
+    edge, ext = _validate_pad(padtype, padlen, x, axis,
+                              ntaps=ntaps)
+
+    # These steps follow the same form as filtfilt with modifications
+    zi = sosfilt_zi(sos)  # shape (n_sections, 2) --> (n_sections, ..., 2, ...)
+    zi_shape = [1] * x.ndim
+    zi_shape[axis] = 2
+    zi = zi.reshape([n_sections] + zi_shape)
+    x_0 = axis_slice(ext, stop=1, axis=axis)
+    (y, zf) = sosfilt(sos, ext, axis=axis, zi=zi * x_0)
+    y_0 = axis_slice(y, start=-1, axis=axis)
+    (y, zf) = sosfilt(sos, axis_reverse(y, axis=axis), axis=axis, zi=zi * y_0)
+    y = axis_reverse(y, axis=axis)
+    if edge > 0:
+        y = axis_slice(y, start=edge, stop=-edge, axis=axis)
+    return xp.asarray(y)
+
+
+def decimate(x, q, n=None, ftype='iir', axis=-1, zero_phase=True):
+    """
+    Downsample the signal after applying an anti-aliasing filter.
+
+    By default, an order 8 Chebyshev type I filter is used. A 30 point FIR
+    filter with Hamming window is used if `ftype` is 'fir'.
+
+    Parameters
+    ----------
+    x : array_like
+        The input signal made up of equidistant samples. If `x` is a multidimensional
+        array, the parameter `axis` specifies the time axis.
+    q : int
+        The downsampling factor, which is a postive integer. When using IIR
+        downsampling, it is recommended to call `decimate` multiple times for
+        downsampling factors higher than 13.
+    n : int, optional
+        The order of the filter (1 less than the length for 'fir'). Defaults to
+        8 for 'iir' and 20 times the downsampling factor for 'fir'.
+    ftype : str {'iir', 'fir'} or ``dlti`` instance, optional
+        If 'iir' or 'fir', specifies the type of lowpass filter. If an instance
+        of an `dlti` object, uses that object to filter before downsampling.
+    axis : int, optional
+        The axis along which to decimate.
+    zero_phase : bool, optional
+        Prevent phase shift by filtering with `filtfilt` instead of `lfilter`
+        when using an IIR filter, and shifting the outputs back by the filter's
+        group delay when using an FIR filter. The default value of ``True`` is
+        recommended, since a phase shift is generally not desired.
+
+        .. versionadded:: 0.18.0
+
+    Returns
+    -------
+    y : ndarray
+        The down-sampled signal.
+
+    See Also
+    --------
+    resample : Resample up or down using the FFT method.
+    resample_poly : Resample using polyphase filtering and an FIR filter.
+
+    Notes
+    -----
+    For non-integer downsampling factors, `~scipy.signal.resample` can be used. Consult
+    the `scipy.interpolate` module for methods of resampling signals with non-constant
+    sampling intervals.
+
+    The ``zero_phase`` keyword was added in 0.18.0.
+    The possibility to use instances of ``dlti`` as ``ftype`` was added in
+    0.18.0.
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+
+    Define wave parameters.
+
+    >>> wave_duration = 3
+    >>> sample_rate = 100
+    >>> freq = 2
+    >>> q = 5
+
+    Calculate number of samples.
+
+    >>> samples = wave_duration*sample_rate
+    >>> samples_decimated = int(samples/q)
+
+    Create cosine wave.
+
+    >>> x = np.linspace(0, wave_duration, samples, endpoint=False)
+    >>> y = np.cos(x*np.pi*freq*2)
+
+    Decimate cosine wave.
+
+    >>> ydem = signal.decimate(y, q)
+    >>> xnew = np.linspace(0, wave_duration, samples_decimated, endpoint=False)
+
+    Plot original and decimated waves.
+
+    >>> plt.plot(x, y, '.-', xnew, ydem, 'o-')
+    >>> plt.xlabel('Time, Seconds')
+    >>> plt.legend(['data', 'decimated'], loc='best')
+    >>> plt.show()
+
+    """
+
+    x = np.asarray(x)
+    q = operator.index(q)
+
+    if n is not None:
+        n = operator.index(n)
+
+    result_type = x.dtype
+    if not np.issubdtype(result_type, np.inexact) \
+       or result_type.type == np.float16:
+        # upcast integers and float16 to float64
+        result_type = np.float64
+
+    if ftype == 'fir':
+        if n is None:
+            half_len = 10 * q  # reasonable cutoff for our sinc-like function
+            n = 2 * half_len
+        b, a = firwin(n+1, 1. / q, window='hamming'), 1.
+        b = np.asarray(b, dtype=result_type)
+        a = np.asarray(a, dtype=result_type)
+    elif ftype == 'iir':
+        iir_use_sos = True
+        if n is None:
+            n = 8
+        sos = cheby1(n, 0.05, 0.8 / q, output='sos')
+        sos = np.asarray(sos, dtype=result_type)
+    elif isinstance(ftype, dlti):
+        system = ftype._as_zpk()
+        if system.poles.shape[0] == 0:
+            # FIR
+            system = ftype._as_tf()
+            b, a = system.num, system.den
+            ftype = 'fir'
+        elif (any(np.iscomplex(system.poles))
+              or any(np.iscomplex(system.poles))
+              or np.iscomplex(system.gain)):
+            # sosfilt & sosfiltfilt don't handle complex coeffs
+            iir_use_sos = False
+            system = ftype._as_tf()
+            b, a = system.num, system.den
+        else:
+            iir_use_sos = True
+            sos = zpk2sos(system.zeros, system.poles, system.gain)
+            sos = np.asarray(sos, dtype=result_type)
+    else:
+        raise ValueError('invalid ftype')
+
+    sl = [slice(None)] * x.ndim
+
+    if ftype == 'fir':
+        b = b / a
+        if zero_phase:
+            y = resample_poly(x, 1, q, axis=axis, window=b)
+        else:
+            # upfirdn is generally faster than lfilter by a factor equal to the
+            # downsampling factor, since it only calculates the needed outputs
+            n_out = x.shape[axis] // q + bool(x.shape[axis] % q)
+            y = upfirdn(b, x, up=1, down=q, axis=axis)
+            sl[axis] = slice(None, n_out, None)
+
+    else:  # IIR case
+        if zero_phase:
+            if iir_use_sos:
+                y = sosfiltfilt(sos, x, axis=axis)
+            else:
+                y = filtfilt(b, a, x, axis=axis)
+        else:
+            if iir_use_sos:
+                y = sosfilt(sos, x, axis=axis)
+            else:
+                y = lfilter(b, a, x, axis=axis)
+
+        sl[axis] = slice(None, None, q)
+
+    return y[tuple(sl)]
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/_sigtools.cpython-312-x86_64-linux-gnu.so b/venv/lib/python3.12/site-packages/scipy/signal/_sigtools.cpython-312-x86_64-linux-gnu.so
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--- /dev/null
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@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b95d8dd95b8ceb6cc99e59cf2672a0f98fa516c48cdc4c9a8b6ef30ae9f12c42
+size 108416
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/_sosfilt.cpython-312-x86_64-linux-gnu.so b/venv/lib/python3.12/site-packages/scipy/signal/_sosfilt.cpython-312-x86_64-linux-gnu.so
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+version https://git-lfs.github.com/spec/v1
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+size 110352
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/_spectral_py.py b/venv/lib/python3.12/site-packages/scipy/signal/_spectral_py.py
new file mode 100644
index 0000000000000000000000000000000000000000..7f0dcfe9bad9bedba4b9db33ba479f415a3f3ad5
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/_spectral_py.py
@@ -0,0 +1,2489 @@
+"""Tools for spectral analysis.
+"""
+import numpy as np
+import numpy.typing as npt
+from scipy import fft as sp_fft
+from scipy._lib.deprecation import _deprecate_positional_args, _NoValue
+from . import _signaltools
+from ._short_time_fft import ShortTimeFFT, FFT_MODE_TYPE
+from .windows import get_window
+from ._arraytools import const_ext, even_ext, odd_ext, zero_ext
+import warnings
+from typing import cast, Literal
+
+
+__all__ = ['periodogram', 'welch', 'lombscargle', 'csd', 'coherence',
+           'spectrogram', 'stft', 'istft', 'check_COLA', 'check_NOLA']
+
+
+@_deprecate_positional_args(version="1.19.0")
+def lombscargle(
+    x: npt.ArrayLike,
+    y: npt.ArrayLike,
+    freqs: npt.ArrayLike,
+    *,
+    precenter: bool = _NoValue,  # type:ignore[assignment]
+    normalize: bool | Literal["power", "normalize", "amplitude"] = False,
+    weights: npt.NDArray | None = None,
+    floating_mean: bool = False,
+) -> npt.NDArray:
+    """
+    Compute the generalized Lomb-Scargle periodogram.
+
+    The Lomb-Scargle periodogram was developed by Lomb [1]_ and further
+    extended by Scargle [2]_ to find, and test the significance of weak
+    periodic signals with uneven temporal sampling. The algorithm used
+    here is based on a weighted least-squares fit of the form
+    ``y(ω) = a*cos(ω*x) + b*sin(ω*x) + c``, where the fit is calculated for
+    each frequency independently. This algorithm was developed by Zechmeister
+    and Kürster which improves the Lomb-Scargle periodogram by enabling
+    the weighting of individual samples and calculating an unknown y offset
+    (also called a "floating-mean" model) [3]_. For more details, and practical
+    considerations, see the excellent reference on the Lomb-Scargle periodogram [4]_.
+
+    When *normalize* is False (or "power") (default) the computed periodogram
+    is unnormalized, it takes the value ``(A**2) * N/4`` for a harmonic
+    signal with amplitude A for sufficiently large N. Where N is the length of x or y.
+
+    When *normalize* is True (or "normalize") the computed periodogram is normalized
+    by the residuals of the data around a constant reference model (at zero).
+
+    When *normalize* is "amplitude" the computed periodogram is the complex
+    representation of the amplitude and phase.
+
+    Input arrays should be 1-D of a real floating data type, which are converted into
+    float64 arrays before processing.
+
+    Parameters
+    ----------
+    x : array_like
+        Sample times.
+    y : array_like
+        Measurement values. Values are assumed to have a baseline of ``y = 0``. If
+        there is a possibility of a y offset, it is recommended to set `floating_mean`
+        to True.
+    freqs : array_like
+        Angular frequencies (e.g., having unit rad/s=2π/s for `x` having unit s) for
+        output periodogram. Frequencies are normally >= 0, as any peak at ``-freq`` will
+        also exist at ``+freq``.
+    precenter : bool, optional
+        Pre-center measurement values by subtracting the mean, if True. This is
+        a legacy parameter and unnecessary if `floating_mean` is True.
+
+        .. deprecated:: 1.17.0
+            The `precenter` argument is deprecated and will be removed in SciPy 1.19.0.
+            The functionality can be substituted by passing ``y - y.mean()`` to `y`.
+
+    normalize : bool | str, optional
+        Compute normalized or complex (amplitude + phase) periodogram.
+        Valid options are: ``False``/``"power"``, ``True``/``"normalize"``, or
+        ``"amplitude"``.
+    weights : array_like, optional
+        Weights for each sample. Weights must be nonnegative.
+    floating_mean : bool, optional
+        Determines a y offset for each frequency independently, if True.
+        Else the y offset is assumed to be `0`.
+
+    Returns
+    -------
+    pgram : array_like
+        Lomb-Scargle periodogram.
+
+    Raises
+    ------
+    ValueError
+        If any of the input arrays x, y, freqs, or weights are not 1D, or if any are
+        zero length. Or, if the input arrays x, y, and weights do not have the same
+        shape as each other.
+    ValueError
+        If any weight is < 0, or the sum of the weights is <= 0.
+    ValueError
+        If the normalize parameter is not one of the allowed options.
+
+    See Also
+    --------
+    periodogram: Power spectral density using a periodogram
+    welch: Power spectral density by Welch's method
+    csd: Cross spectral density by Welch's method
+
+    Notes
+    -----
+    The algorithm used will not automatically account for any unknown y offset, unless
+    `floating_mean` is ``True``. Therefore, for most use cases, if there is a
+    possibility of a y offset, it is recommended to set `floating_mean` to ``True``.
+    Furthermore, `floating_mean` accounts for sample weights, and will also correct for
+    any bias due to consistently missing observations at peaks and/or troughs.
+
+    The legacy concept of "pre-centering" entails removing the mean from parameter `y`
+    before processing, i.e., passing ``y - y.mean()`` instead of setting the parameter
+    `floating_mean` to ``True``.
+
+    When the normalize parameter is "amplitude", for any frequency in freqs that is
+    below ``(2*pi)/(x.max() - x.min())``, the predicted amplitude will tend towards
+    infinity. The concept of a "Nyquist frequency" limit (see Nyquist-Shannon sampling
+    theorem) is not generally applicable to unevenly sampled data. Therefore, with
+    unevenly sampled data, valid frequencies in freqs can often be much higher than
+    expected for those familiar with methods like FFT.
+
+    References
+    ----------
+    .. [1] N.R. Lomb "Least-squares frequency analysis of unequally spaced
+           data", Astrophysics and Space Science, vol 39, pp. 447-462, 1976
+           :doi:`10.1007/bf00648343`
+
+    .. [2] J.D. Scargle "Studies in astronomical time series analysis. II -
+           Statistical aspects of spectral analysis of unevenly spaced data",
+           The Astrophysical Journal, vol 263, pp. 835-853, 1982
+           :doi:`10.1086/160554`
+
+    .. [3] M. Zechmeister and M. Kürster, "The generalised Lomb-Scargle periodogram.
+           A new formalism for the floating-mean and Keplerian periodograms,"
+           Astronomy and Astrophysics, vol. 496, pp. 577-584, 2009
+           :doi:`10.1051/0004-6361:200811296`
+
+    .. [4] J.T. VanderPlas, "Understanding the Lomb-Scargle Periodogram,"
+           The Astrophysical Journal Supplement Series, vol. 236, no. 1, p. 16,
+           May 2018
+           :doi:`10.3847/1538-4365/aab766`
+
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> rng = np.random.default_rng()
+
+    First define some input parameters for the signal:
+
+    >>> A = 2.  # amplitude
+    >>> c = 2.  # offset
+    >>> w0 = 1.  # rad/sec
+    >>> nin = 150
+    >>> nout = 1002
+
+    Randomly generate sample times:
+
+    >>> x = rng.uniform(0, 10*np.pi, nin)
+
+    Plot a sine wave for the selected times:
+
+    >>> y = A * np.cos(w0*x) + c
+
+    Define the array of frequencies for which to compute the periodogram:
+
+    >>> w = np.linspace(0.25, 10, nout)
+
+    Calculate Lomb-Scargle periodogram for each of the normalize options:
+
+    >>> from scipy.signal import lombscargle
+    >>> pgram_power = lombscargle(x, y, w, normalize=False)
+    >>> pgram_norm = lombscargle(x, y, w, normalize=True)
+    >>> pgram_amp = lombscargle(x, y, w, normalize='amplitude')
+    ...
+    >>> pgram_power_f = lombscargle(x, y, w, normalize=False, floating_mean=True)
+    >>> pgram_norm_f = lombscargle(x, y, w, normalize=True, floating_mean=True)
+    >>> pgram_amp_f = lombscargle(x, y, w, normalize='amplitude', floating_mean=True)
+
+    Now make a plot of the input data:
+
+    >>> import matplotlib.pyplot as plt
+    >>> fig, (ax_t, ax_p, ax_n, ax_a) = plt.subplots(4, 1, figsize=(5, 6))
+    >>> ax_t.plot(x, y, 'b+')
+    >>> ax_t.set_xlabel('Time [s]')
+    >>> ax_t.set_ylabel('Amplitude')
+
+    Then plot the periodogram for each of the normalize options, as well as with and
+    without floating_mean=True:
+
+    >>> ax_p.plot(w, pgram_power, label='default')
+    >>> ax_p.plot(w, pgram_power_f, label='floating_mean=True')
+    >>> ax_p.set_xlabel('Angular frequency [rad/s]')
+    >>> ax_p.set_ylabel('Power')
+    >>> ax_p.legend(prop={'size': 7})
+    ...
+    >>> ax_n.plot(w, pgram_norm, label='default')
+    >>> ax_n.plot(w, pgram_norm_f, label='floating_mean=True')
+    >>> ax_n.set_xlabel('Angular frequency [rad/s]')
+    >>> ax_n.set_ylabel('Normalized')
+    >>> ax_n.legend(prop={'size': 7})
+    ...
+    >>> ax_a.plot(w, np.abs(pgram_amp), label='default')
+    >>> ax_a.plot(w, np.abs(pgram_amp_f), label='floating_mean=True')
+    >>> ax_a.set_xlabel('Angular frequency [rad/s]')
+    >>> ax_a.set_ylabel('Amplitude')
+    >>> ax_a.legend(prop={'size': 7})
+    ...
+    >>> plt.tight_layout()
+    >>> plt.show()
+
+    """
+
+    # if no weights are provided, assume all data points are equally important
+    if weights is None:
+        weights = np.ones_like(y, dtype=np.float64)
+    else:
+        # if provided, make sure weights is an array and cast to float64
+        weights = np.asarray(weights, dtype=np.float64)
+
+    # make sure other inputs are arrays and cast to float64
+    # done before validation, in case they were not arrays
+    x = np.asarray(x, dtype=np.float64)
+    y = np.asarray(y, dtype=np.float64)
+    freqs = np.asarray(freqs, dtype=np.float64)
+
+    # validate input shapes
+    if not (x.ndim == 1 and x.size > 0 and x.shape == y.shape == weights.shape):
+        raise ValueError("Parameters x, y, weights must be 1-D arrays of "
+                         "equal non-zero length!")
+    if not (freqs.ndim == 1 and freqs.size > 0):
+        raise ValueError("Parameter freqs must be a 1-D array of non-zero length!")
+
+    # validate weights
+    if not (np.all(weights >= 0) and np.sum(weights) > 0):
+        raise ValueError("Parameter weights must have only non-negative entries "
+                         "which sum to a positive value!")
+
+    # validate normalize parameter
+    if isinstance(normalize, bool):
+        # if bool, convert to str literal
+        normalize = "normalize" if normalize else "power"
+
+    if normalize not in ["power", "normalize", "amplitude"]:
+        raise ValueError(
+            "Normalize must be: False (or 'power'), True (or 'normalize'), "
+            "or 'amplitude'."
+        )
+
+    # weight vector must sum to 1
+    weights = weights * (1.0 / weights.sum())
+
+    # if requested, perform precenter
+    if precenter is not _NoValue:
+        msg = ("Use of parameter 'precenter' is deprecated as of SciPy 1.17.0 and "
+               "will be removed in 1.19.0. Please leave 'precenter' unspecified. "
+               "Passing True to 'precenter' "
+               "can be exactly substituted by passing 'y = (y - y.mean())' into "
+               "the input. Consider setting `floating_mean` to True instead.")
+        warnings.warn(msg, DeprecationWarning, stacklevel=2)
+        if precenter:
+            y = y - y.mean()
+
+    # transform arrays
+    # row vector
+    freqs = freqs.reshape(1, -1)
+    # column vectors
+    x = x.reshape(-1, 1)
+    y = y.reshape(-1, 1)  # type:ignore[union-attr]
+    weights = weights.reshape(-1, 1)
+
+    # store frequent intermediates
+    weights_y = weights * y
+    freqst = freqs * x
+    coswt = np.cos(freqst)
+    sinwt = np.sin(freqst)
+
+    Y = np.dot(weights.T, y)  # Eq. 7
+    CC = np.dot(weights.T, coswt * coswt)  # Eq. 13
+    SS = 1.0 - CC  # trig identity: S^2 = 1 - C^2  Eq.14
+    CS = np.dot(weights.T, coswt * sinwt)  # Eq. 15
+
+    if floating_mean:
+        C = np.dot(weights.T, coswt)  # Eq. 8
+        S = np.dot(weights.T, sinwt)  # Eq. 9
+        CC -= C * C  # Eq. 13
+        SS -= S * S  # Eq. 14
+        CS -= C * S  # Eq. 15
+
+    # calculate tau (phase offset to eliminate CS variable)
+    tau = 0.5 * np.arctan2(2.0 * CS, CC - SS)  # Eq. 19
+    freqst_tau = freqst - tau
+
+    # coswt and sinwt are now offset by tau, which eliminates CS
+    coswt_tau = np.cos(freqst_tau)
+    sinwt_tau = np.sin(freqst_tau)
+
+    YC = np.dot(weights_y.T, coswt_tau)  # Eq. 11
+    YS = np.dot(weights_y.T, sinwt_tau)  # Eq. 12
+    CC = np.dot(weights.T, coswt_tau * coswt_tau)  # Eq. 13, CC range is [0.5, 1.0]
+    SS = 1.0 - CC  # trig identity: S^2 = 1 - C^2    Eq. 14, SS range is [0.0, 0.5]
+
+    if floating_mean:
+        C = np.dot(weights.T, coswt_tau)  # Eq. 8
+        S = np.dot(weights.T, sinwt_tau)  # Eq. 9
+        YC -= Y * C  # Eq. 11
+        YS -= Y * S  # Eq. 12
+        CC -= C * C  # Eq. 13, CC range is now [0.0, 1.0]
+        SS -= S * S  # Eq. 14, SS range is now [0.0, 0.5]
+
+    # to prevent division by zero errors with a and b, as well as correcting for
+    # numerical precision errors that lead to CC or SS being approximately -0.0,
+    # make sure CC and SS are both > 0
+    epsneg = np.finfo(dtype=y.dtype).epsneg  # type:ignore[union-attr]
+    CC[CC < epsneg] = epsneg
+    SS[SS < epsneg] = epsneg
+
+    # calculate a and b
+    # where: y(w) = a*cos(w) + b*sin(w) + c
+    a = YC / CC  # Eq. A.4 and 6, eliminating CS
+    b = YS / SS  # Eq. A.4 and 6, eliminating CS
+    # c = Y - a * C - b * S
+
+    # store final value as power in A^2 (i.e., (y units)^2)
+    pgram = 2.0 * (a * YC + b * YS)
+
+    # squeeze back to a vector
+    pgram = np.squeeze(pgram)
+
+    if normalize == "power":  # (default)
+        # return the legacy power units ((A**2) * N/4)
+
+        pgram *= float(x.shape[0]) / 4.0
+
+    elif normalize == "normalize":
+        # return the normalized power (power at current frequency wrt the entire signal)
+        # range will be [0, 1]
+
+        YY = np.dot(weights_y.T, y)  # Eq. 10
+        if floating_mean:
+            YY -= Y * Y  # Eq. 10
+
+        pgram *= 0.5 / np.squeeze(YY)  # Eq. 20
+
+    else:  # normalize == "amplitude":
+        # return the complex representation of the best-fit amplitude and phase
+
+        # squeeze back to vectors
+        a = np.squeeze(a)
+        b = np.squeeze(b)
+        tau = np.squeeze(tau)
+
+        # calculate the complex representation, and correct for tau rotation
+        pgram = (a + 1j * b) * np.exp(1j * tau)
+
+    return pgram
+
+
+def periodogram(x, fs=1.0, window='boxcar', nfft=None, detrend='constant',
+                return_onesided=True, scaling='density', axis=-1):
+    """
+    Estimate power spectral density using a periodogram.
+
+    Parameters
+    ----------
+    x : array_like
+        Time series of measurement values
+    fs : float, optional
+        Sampling frequency of the `x` time series. Defaults to 1.0.
+    window : str or tuple or array_like, optional
+        Desired window to use. If `window` is a string or tuple, it is
+        passed to `get_window` to generate the window values, which are
+        DFT-even by default. See `get_window` for a list of windows and
+        required parameters. If `window` is array_like it will be used
+        directly as the window and its length must be equal to the length
+        of the axis over which the periodogram is computed. Defaults
+        to 'boxcar'.
+    nfft : int, optional
+        Length of the FFT used. If `None` the length of `x` will be
+        used.
+    detrend : str or function or `False`, optional
+        Specifies how to detrend each segment. If `detrend` is a
+        string, it is passed as the `type` argument to the `detrend`
+        function. If it is a function, it takes a segment and returns a
+        detrended segment. If `detrend` is `False`, no detrending is
+        done. Defaults to 'constant'.
+    return_onesided : bool, optional
+        If `True`, return a one-sided spectrum for real data. If
+        `False` return a two-sided spectrum. Defaults to `True`, but for
+        complex data, a two-sided spectrum is always returned.
+    scaling : { 'density', 'spectrum' }, optional
+        Selects between computing the power spectral density ('density')
+        where `Pxx` has units of V²/Hz and computing the squared magnitude
+        spectrum ('spectrum') where `Pxx` has units of V², if `x`
+        is measured in V and `fs` is measured in Hz. Defaults to
+        'density'
+    axis : int, optional
+        Axis along which the periodogram is computed; the default is
+        over the last axis (i.e. ``axis=-1``).
+
+    Returns
+    -------
+    f : ndarray
+        Array of sample frequencies.
+    Pxx : ndarray
+        Power spectral density or power spectrum of `x`.
+
+    See Also
+    --------
+    welch: Estimate power spectral density using Welch's method
+    lombscargle: Lomb-Scargle periodogram for unevenly sampled data
+
+    Notes
+    -----
+    The ratio of the squared magnitude (``scaling='spectrum'``) divided by the spectral
+    power density (``scaling='density'``) is the constant factor of
+    ``sum(abs(window)**2)*fs / abs(sum(window))**2``.
+    If `return_onesided` is ``True``, the values of the negative frequencies are added
+    to values of the corresponding positive ones.
+
+    Consult the :ref:`tutorial_SpectralAnalysis` section of the :ref:`user_guide`
+    for a discussion of the scalings of the power spectral density and
+    the magnitude (squared) spectrum.
+
+    .. versionadded:: 0.12.0
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+    >>> rng = np.random.default_rng()
+
+    Generate a test signal, a 2 Vrms sine wave at 1234 Hz, corrupted by
+    0.001 V**2/Hz of white noise sampled at 10 kHz.
+
+    >>> fs = 10e3
+    >>> N = 1e5
+    >>> amp = 2*np.sqrt(2)
+    >>> freq = 1234.0
+    >>> noise_power = 0.001 * fs / 2
+    >>> time = np.arange(N) / fs
+    >>> x = amp*np.sin(2*np.pi*freq*time)
+    >>> x += rng.normal(scale=np.sqrt(noise_power), size=time.shape)
+
+    Compute and plot the power spectral density.
+
+    >>> f, Pxx_den = signal.periodogram(x, fs)
+    >>> plt.semilogy(f, Pxx_den)
+    >>> plt.ylim([1e-7, 1e2])
+    >>> plt.xlabel('frequency [Hz]')
+    >>> plt.ylabel('PSD [V**2/Hz]')
+    >>> plt.show()
+
+    If we average the last half of the spectral density, to exclude the
+    peak, we can recover the noise power on the signal.
+
+    >>> np.mean(Pxx_den[25000:])
+    0.000985320699252543
+
+    Now compute and plot the power spectrum.
+
+    >>> f, Pxx_spec = signal.periodogram(x, fs, 'flattop', scaling='spectrum')
+    >>> plt.figure()
+    >>> plt.semilogy(f, np.sqrt(Pxx_spec))
+    >>> plt.ylim([1e-4, 1e1])
+    >>> plt.xlabel('frequency [Hz]')
+    >>> plt.ylabel('Linear spectrum [V RMS]')
+    >>> plt.show()
+
+    The peak height in the power spectrum is an estimate of the RMS
+    amplitude.
+
+    >>> np.sqrt(Pxx_spec.max())
+    2.0077340678640727
+
+    """
+    x = np.asarray(x)
+
+    if x.size == 0:
+        return np.empty(x.shape), np.empty(x.shape)
+
+    if window is None:
+        window = 'boxcar'
+
+    if nfft is None:
+        nperseg = x.shape[axis]
+    elif nfft == x.shape[axis]:
+        nperseg = nfft
+    elif nfft > x.shape[axis]:
+        nperseg = x.shape[axis]
+    elif nfft < x.shape[axis]:
+        s = [np.s_[:]]*len(x.shape)
+        s[axis] = np.s_[:nfft]
+        x = x[tuple(s)]
+        nperseg = nfft
+        nfft = None
+
+    if hasattr(window, 'size'):
+        if window.size != nperseg:
+            raise ValueError('the size of the window must be the same size '
+                             'of the input on the specified axis')
+
+    return welch(x, fs=fs, window=window, nperseg=nperseg, noverlap=0,
+                 nfft=nfft, detrend=detrend, return_onesided=return_onesided,
+                 scaling=scaling, axis=axis)
+
+
+def welch(x, fs=1.0, window='hann_periodic', nperseg=None, noverlap=None, nfft=None,
+          detrend='constant', return_onesided=True, scaling='density',
+          axis=-1, average='mean'):
+    r"""
+    Estimate power spectral density using Welch's method.
+
+    Welch's method [1]_ computes an estimate of the power spectral
+    density by dividing the data into overlapping segments, computing a
+    modified periodogram for each segment and averaging the
+    periodograms.
+
+    Parameters
+    ----------
+    x : array_like
+        Time series of measurement values
+    fs : float, optional
+        Sampling frequency of the `x` time series. Defaults to 1.0.
+    window : str or tuple or array_like, optional
+        Desired window to use. If `window` is a string or tuple, it is
+        passed to `get_window` to generate the window values, which are
+        DFT-even by default. See `get_window` for a list of windows and
+        required parameters. If `window` is array_like it will be used
+        directly as the window and its length must be nperseg. Defaults
+        to a periodic Hann window.
+    nperseg : int, optional
+        Length of each segment. Defaults to None, but if window is str or
+        tuple, is set to 256, and if window is array_like, is set to the
+        length of the window.
+    noverlap : int, optional
+        Number of points to overlap between segments. If `None`,
+        ``noverlap = nperseg // 2``. Defaults to `None`.
+    nfft : int, optional
+        Length of the FFT used, if a zero padded FFT is desired. If
+        `None`, the FFT length is `nperseg`. Defaults to `None`.
+    detrend : str or function or `False`, optional
+        Specifies how to detrend each segment. If `detrend` is a
+        string, it is passed as the `type` argument to the `detrend`
+        function. If it is a function, it takes a segment and returns a
+        detrended segment. If `detrend` is `False`, no detrending is
+        done. Defaults to 'constant'.
+    return_onesided : bool, optional
+        If `True`, return a one-sided spectrum for real data. If
+        `False` return a two-sided spectrum. Defaults to `True`, but for
+        complex data, a two-sided spectrum is always returned.
+    scaling : { 'density', 'spectrum' }, optional
+        Selects between computing the power spectral density ('density')
+        where `Pxx` has units of V**2/Hz and computing the squared magnitude
+        spectrum ('spectrum') where `Pxx` has units of V**2, if `x`
+        is measured in V and `fs` is measured in Hz. Defaults to
+        'density'
+    axis : int, optional
+        Axis along which the periodogram is computed; the default is
+        over the last axis (i.e. ``axis=-1``).
+    average : { 'mean', 'median' }, optional
+        Method to use when averaging periodograms. Defaults to 'mean'.
+
+        .. versionadded:: 1.2.0
+
+    Returns
+    -------
+    f : ndarray
+        Array of sample frequencies.
+    Pxx : ndarray
+        Power spectral density or power spectrum of x.
+
+    See Also
+    --------
+    csd: Cross power spectral density using Welch's method
+    periodogram: Simple, optionally modified periodogram
+    lombscargle: Lomb-Scargle periodogram for unevenly sampled data
+
+    Notes
+    -----
+    An appropriate amount of overlap will depend on the choice of window
+    and on your requirements. For the default Hann window an overlap of
+    50% is a reasonable trade-off between accurately estimating the
+    signal power, while not over counting any of the data. Narrower
+    windows may require a larger overlap. If `noverlap` is 0, this
+    method is equivalent to Bartlett's method [2]_.
+
+    The ratio of the squared magnitude (``scaling='spectrum'``) divided by the spectral
+    power density (``scaling='density'``) is the constant factor of
+    ``sum(abs(window)**2)*fs / abs(sum(window))**2``.
+    If `return_onesided` is ``True``, the values of the negative frequencies are added
+    to values of the corresponding positive ones.
+
+    Consult the :ref:`tutorial_SpectralAnalysis` section of the :ref:`user_guide`
+    for a discussion of the scalings of the power spectral density and
+    the (squared) magnitude spectrum.
+
+    .. versionadded:: 0.12.0
+
+    References
+    ----------
+    .. [1] P. Welch, "The use of the fast Fourier transform for the
+           estimation of power spectra: A method based on time averaging
+           over short, modified periodograms", IEEE Trans. Audio
+           Electroacoust. vol. 15, pp. 70-73, 1967.
+    .. [2] M.S. Bartlett, "Periodogram Analysis and Continuous Spectra",
+           Biometrika, vol. 37, pp. 1-16, 1950.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+    >>> rng = np.random.default_rng()
+
+    Generate a test signal, a 2 Vrms sine wave at 1234 Hz, corrupted by
+    0.001 V**2/Hz of white noise sampled at 10 kHz.
+
+    >>> fs = 10e3
+    >>> N = 1e5
+    >>> amp = 2*np.sqrt(2)
+    >>> freq = 1234.0
+    >>> noise_power = 0.001 * fs / 2
+    >>> time = np.arange(N) / fs
+    >>> x = amp*np.sin(2*np.pi*freq*time)
+    >>> x += rng.normal(scale=np.sqrt(noise_power), size=time.shape)
+
+    Compute and plot the power spectral density.
+
+    >>> f, Pxx_den = signal.welch(x, fs, nperseg=1024)
+    >>> plt.semilogy(f, Pxx_den)
+    >>> plt.ylim([0.5e-3, 1])
+    >>> plt.xlabel('frequency [Hz]')
+    >>> plt.ylabel('PSD [V**2/Hz]')
+    >>> plt.show()
+
+    If we average the last half of the spectral density, to exclude the
+    peak, we can recover the noise power on the signal.
+
+    >>> np.mean(Pxx_den[256:])
+    0.0009924865443739191
+
+    Now compute and plot the power spectrum.
+
+    >>> f, Pxx_spec = signal.welch(x, fs, 'flattop', 1024, scaling='spectrum')
+    >>> plt.figure()
+    >>> plt.semilogy(f, np.sqrt(Pxx_spec))
+    >>> plt.xlabel('frequency [Hz]')
+    >>> plt.ylabel('Linear spectrum [V RMS]')
+    >>> plt.show()
+
+    The peak height in the power spectrum is an estimate of the RMS
+    amplitude.
+
+    >>> np.sqrt(Pxx_spec.max())
+    2.0077340678640727
+
+    If we now introduce a discontinuity in the signal, by increasing the
+    amplitude of a small portion of the signal by 50, we can see the
+    corruption of the mean average power spectral density, but using a
+    median average better estimates the normal behaviour.
+
+    >>> x[int(N//2):int(N//2)+10] *= 50.
+    >>> f, Pxx_den = signal.welch(x, fs, nperseg=1024)
+    >>> f_med, Pxx_den_med = signal.welch(x, fs, nperseg=1024, average='median')
+    >>> plt.semilogy(f, Pxx_den, label='mean')
+    >>> plt.semilogy(f_med, Pxx_den_med, label='median')
+    >>> plt.ylim([0.5e-3, 1])
+    >>> plt.xlabel('frequency [Hz]')
+    >>> plt.ylabel('PSD [V**2/Hz]')
+    >>> plt.legend()
+    >>> plt.show()
+
+    """
+    freqs, Pxx = csd(x, x, fs=fs, window=window, nperseg=nperseg,
+                     noverlap=noverlap, nfft=nfft, detrend=detrend,
+                     return_onesided=return_onesided, scaling=scaling,
+                     axis=axis, average=average)
+
+    return freqs, Pxx.real
+
+
+def csd(x, y, fs=1.0, window='hann_periodic', nperseg=None, noverlap=None, nfft=None,
+        detrend='constant', return_onesided=True, scaling='density',
+        axis=-1, average='mean'):
+    r"""
+    Estimate the cross power spectral density, Pxy, using Welch's method.
+
+    Parameters
+    ----------
+    x : array_like
+        Time series of measurement values
+    y : array_like
+        Time series of measurement values
+    fs : float, optional
+        Sampling frequency of the `x` and `y` time series. Defaults
+        to 1.0.
+    window : str or tuple or array_like, optional
+        Desired window to use. If `window` is a string or tuple, it is
+        passed to `get_window` to generate the window values, which are
+        DFT-even by default. See `get_window` for a list of windows and
+        required parameters. If `window` is array_like it will be used
+        directly as the window and its length must be nperseg. Defaults
+        to a periodic Hann window.
+    nperseg : int, optional
+        Length of each segment. Defaults to None, but if window is str or
+        tuple, is set to 256, and if window is array_like, is set to the
+        length of the window.
+    noverlap : int, optional
+        Number of points to overlap between segments. If `None`,
+        ``noverlap = nperseg // 2``. Defaults to `None` and may
+        not be greater than `nperseg`.
+    nfft : int, optional
+        Length of the FFT used, if a zero padded FFT is desired. If
+        `None`, the FFT length is `nperseg`. Defaults to `None`.
+    detrend : str or function or `False`, optional
+        Specifies how to detrend each segment. If `detrend` is a
+        string, it is passed as the `type` argument to the `detrend`
+        function. If it is a function, it takes a segment and returns a
+        detrended segment. If `detrend` is `False`, no detrending is
+        done. Defaults to 'constant'.
+    return_onesided : bool, optional
+        If `True`, return a one-sided spectrum for real data. If
+        `False` return a two-sided spectrum. Defaults to `True`, but for
+        complex data, a two-sided spectrum is always returned.
+    scaling : { 'density', 'spectrum' }, optional
+        Selects between computing the cross spectral density ('density')
+        where `Pxy` has units of V**2/Hz and computing the cross spectrum
+        ('spectrum') where `Pxy` has units of V**2, if `x` and `y` are
+        measured in V and `fs` is measured in Hz. Defaults to 'density'
+    axis : int, optional
+        Axis along which the CSD is computed for both inputs; the
+        default is over the last axis (i.e. ``axis=-1``).
+    average : { 'mean', 'median' }, optional
+        Method to use when averaging periodograms. If the spectrum is
+        complex, the average is computed separately for the real and
+        imaginary parts. Defaults to 'mean'.
+
+        .. versionadded:: 1.2.0
+
+    Returns
+    -------
+    f : ndarray
+        Array of sample frequencies.
+    Pxy : ndarray
+        Cross spectral density or cross power spectrum of x,y.
+
+    See Also
+    --------
+    periodogram: Simple, optionally modified periodogram
+    lombscargle: Lomb-Scargle periodogram for unevenly sampled data
+    welch: Power spectral density by Welch's method. [Equivalent to
+           csd(x,x)]
+    coherence: Magnitude squared coherence by Welch's method.
+
+    Notes
+    -----
+    By convention, Pxy is computed with the conjugate FFT of X
+    multiplied by the FFT of Y.
+
+    If the input series differ in length, the shorter series will be
+    zero-padded to match.
+
+    An appropriate amount of overlap will depend on the choice of window
+    and on your requirements. For the default Hann window an overlap of
+    50% is a reasonable trade-off between accurately estimating the
+    signal power, while not over counting any of the data. Narrower
+    windows may require a larger overlap.
+
+    The ratio of the cross spectrum (``scaling='spectrum'``) divided by the cross
+    spectral density (``scaling='density'``) is the constant factor of
+    ``sum(abs(window)**2)*fs / abs(sum(window))**2``.
+    If `return_onesided` is ``True``, the values of the negative frequencies are added
+    to values of the corresponding positive ones.
+
+    Consult the :ref:`tutorial_SpectralAnalysis` section of the :ref:`user_guide`
+    for a discussion of the scalings of a spectral density and an (amplitude) spectrum.
+
+    Welch's method may be interpreted as taking the average over the time slices of a
+    (cross-) spectrogram. Internally, this function utilizes the  `ShortTimeFFT`  to
+    determine the required (cross-) spectrogram. An example below illustrates that it
+    is straightforward to calculate `Pxy` directly with the `ShortTimeFFT`. However,
+    there are some notable differences in the behavior of the `ShortTimeFFT`:
+
+    * There is no direct `ShortTimeFFT` equivalent for the `csd` parameter
+      combination ``return_onesided=True, scaling='density'``, since
+      ``fft_mode='onesided2X'`` requires ``'psd'`` scaling. The is due to `csd`
+      returning the doubled squared magnitude in this case, which does not have a
+      sensible interpretation.
+    * `ShortTimeFFT` uses `float64` / `complex128` internally, which is due to the
+      behavior of the utilized `~scipy.fft` module. Thus, those are the dtypes being
+      returned. The `csd` function casts the return values to `float32` / `complex64`
+      if the input is `float32` / `complex64` as well.
+    * The `csd` function calculates ``np.conj(Sx[q,p]) * Sy[q,p]``, whereas
+      `~ShortTimeFFT.spectrogram` calculates ``Sx[q,p] * np.conj(Sy[q,p])`` where
+      ``Sx[q,p]``, ``Sy[q,p]`` are the STFTs of `x` and `y`. Also, the window
+      positioning is different.
+
+    .. versionadded:: 0.16.0
+
+    References
+    ----------
+    .. [1] P. Welch, "The use of the fast Fourier transform for the
+           estimation of power spectra: A method based on time averaging
+           over short, modified periodograms", IEEE Trans. Audio
+           Electroacoust. vol. 15, pp. 70-73, 1967.
+    .. [2] Rabiner, Lawrence R., and B. Gold. "Theory and Application of
+           Digital Signal Processing" Prentice-Hall, pp. 414-419, 1975
+
+    Examples
+    --------
+    The following example plots the cross power spectral density of two signals with
+    some common features:
+
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+    >>> rng = np.random.default_rng()
+    ...
+    ... # Generate two test signals with some common features:
+    >>> N, fs = 100_000, 10e3  # number of samples and sampling frequency
+    >>> amp, freq = 20, 1234.0  # amplitude and frequency of utilized sine signal
+    >>> noise_power = 0.001 * fs / 2
+    >>> time = np.arange(N) / fs
+    >>> b, a = signal.butter(2, 0.25, 'low')
+    >>> x = rng.normal(scale=np.sqrt(noise_power), size=time.shape)
+    >>> y = signal.lfilter(b, a, x)
+    >>> x += amp*np.sin(2*np.pi*freq*time)
+    >>> y += rng.normal(scale=0.1*np.sqrt(noise_power), size=time.shape)
+    ...
+    ... # Compute and plot the magnitude of the cross spectral density:
+    >>> nperseg, noverlap, win = 1024, 512, 'hann'
+    >>> f, Pxy = signal.csd(x, y, fs, win, nperseg, noverlap)
+    >>> fig0, ax0 = plt.subplots(tight_layout=True)
+    >>> ax0.set_title(f"CSD ({win.title()}-window, {nperseg=}, {noverlap=})")
+    >>> ax0.set(xlabel="Frequency $f$ in kHz", ylabel="CSD Magnitude in V²/Hz")
+    >>> ax0.semilogy(f/1e3, np.abs(Pxy))
+    >>> ax0.grid()
+    >>> plt.show()
+
+    The cross spectral density is calculated by taking the average over the time slices
+    of a spectrogram:
+
+    >>> SFT = signal.ShortTimeFFT.from_window('hann', fs, nperseg, noverlap,
+    ...                                       scale_to='psd', fft_mode='onesided2X',
+    ...                                       phase_shift=None)
+    >>> Sxy1 = SFT.spectrogram(y, x, detr='constant', k_offset=nperseg//2,
+    ...                        p0=0, p1=(N-noverlap) // SFT.hop)
+    >>> Pxy1 = Sxy1.mean(axis=-1)
+    >>> np.allclose(Pxy, Pxy1)  # same result as with csd()
+    True
+
+    As discussed in the Notes section, the results of using an approach analogous to
+    the code snippet above and the `csd` function may deviate due to implementation
+    details.
+
+    Note that the code snippet above can be easily adapted to determine other
+    statistical properties than the mean value.
+    """
+    # The following lines are resembling the behavior of the originally utilized
+    # `_spectral_helper()` function:
+    same_data, axis = y is x, int(axis)
+    x = np.asarray(x)
+
+    if not same_data:
+        y = np.asarray(y)
+        # Check if we can broadcast the outer axes together
+        x_outer, y_outer  = list(x.shape), list(y.shape)
+        x_outer.pop(axis)
+        y_outer.pop(axis)
+        try:
+            outer_shape = np.broadcast_shapes(x_outer, y_outer)
+        except ValueError as e:
+            raise ValueError('x and y cannot be broadcast together.') from e
+        if x.size == 0 or y.size == 0:
+            out_shape = outer_shape + (min([x.shape[axis], y.shape[axis]]),)
+            empty_out = np.moveaxis(np.empty(out_shape), -1, axis)
+            return empty_out, empty_out
+        out_dtype = np.result_type(x, y, np.complex64)
+    else:  # x is y:
+        if x.size == 0:
+            return np.empty(x.shape), np.empty(x.shape)
+        out_dtype = np.result_type(x, np.complex64)
+
+    n = x.shape[axis] if same_data else max(x.shape[axis], y.shape[axis])
+    if isinstance(window, str) or isinstance(window, tuple):
+        nperseg = int(nperseg) if nperseg is not None else 256
+        if nperseg < 1:
+            raise ValueError(f"Parameter {nperseg=} is not a positive integer!")
+        elif n < nperseg:
+            warnings.warn(f"{nperseg=} is greater than signal length max(len(x), " +
+                          f"len(y)) = {n}, using nperseg = {n}", stacklevel=3)
+            nperseg = n
+        win = get_window(window, nperseg)
+    else:
+        win = np.asarray(window)
+        if nperseg is None:
+            nperseg = len(win)
+    if nperseg != len(win):
+        raise ValueError(f"{nperseg=} does not equal {len(win)=}")
+
+    nfft = int(nfft) if nfft is not None else nperseg
+    if nfft < nperseg:
+        raise ValueError(f"{nfft=} must be greater than or equal to {nperseg=}!")
+    noverlap = int(noverlap) if noverlap is not None else nperseg // 2
+    if noverlap >= nperseg:
+        raise ValueError(f"{noverlap=} must be less than {nperseg=}!")
+    if np.iscomplexobj(x) and return_onesided:
+        return_onesided = False
+
+    if x.shape[axis] < y.shape[axis]:  # zero-pad x to shape of y:
+        z_shape = list(y.shape)
+        z_shape[axis] = y.shape[axis] - x.shape[axis]
+        x = np.concatenate((x, np.zeros(z_shape)), axis=axis)
+    elif y.shape[axis] < x.shape[axis]:  # zero-pad y to shape of x:
+        z_shape = list(x.shape)
+        z_shape[axis] = x.shape[axis] - y.shape[axis]
+        y = np.concatenate((y, np.zeros(z_shape)), axis=axis)
+
+    # using cast() to make mypy happy:
+    fft_mode = cast(FFT_MODE_TYPE, 'onesided' if return_onesided else 'twosided')
+    if scaling not in (scales := {'spectrum': 'magnitude', 'density': 'psd'}):
+        raise ValueError(f"Parameter {scaling=} not in {scales}!")
+
+    SFT = ShortTimeFFT(win, nperseg - noverlap, fs, fft_mode=fft_mode, mfft=nfft,
+                       scale_to=scales[scaling], phase_shift=None)
+    # csd() calculates X.conj()*Y instead of X*Y.conj():
+    Pxy = SFT.spectrogram(y, x, detr=None if detrend is False else detrend,
+                          p0=0, p1=(n - noverlap) // SFT.hop, k_offset=nperseg // 2,
+                          axis=axis)
+
+    # Note:
+    # 'onesided2X' scaling of ShortTimeFFT conflicts with the
+    # scaling='spectrum' parameter, since it doubles the squared magnitude,
+    # which in the view of the ShortTimeFFT implementation does not make sense.
+    # Hence, the doubling of the square is implemented here:
+    if return_onesided:
+        f_axis = Pxy.ndim - 1 + axis if axis < 0 else axis
+        Pxy = np.moveaxis(Pxy, f_axis, -1)
+        Pxy[..., 1:-1 if SFT.mfft % 2 == 0 else None] *= 2
+        Pxy = np.moveaxis(Pxy, -1, f_axis)
+
+    # Average over windows.
+    if Pxy.shape[-1] > 1:
+        if average == 'median':
+            # np.median must be passed real arrays for the desired result
+            bias = _median_bias(Pxy.shape[-1])
+            if np.iscomplexobj(Pxy):
+                Pxy = (np.median(np.real(Pxy), axis=-1) +
+                       np.median(np.imag(Pxy), axis=-1) * 1j)
+            else:
+                Pxy = np.median(Pxy, axis=-1)
+            Pxy /= bias
+        elif average == 'mean':
+            Pxy = Pxy.mean(axis=-1)
+        else:
+            raise ValueError(f"Parameter {average=} must be 'median' or 'mean'!")
+    else:
+        Pxy = np.reshape(Pxy, Pxy.shape[:-1])
+
+    # cast output type;
+    Pxy = Pxy.astype(out_dtype)
+    if same_data:
+        Pxy = Pxy.real
+    return SFT.f, Pxy
+
+
+def spectrogram(x, fs=1.0, window=('tukey_periodic', .25), nperseg=None, noverlap=None,
+                nfft=None, detrend='constant', return_onesided=True,
+                scaling='density', axis=-1, mode='psd'):
+    """Compute a spectrogram with consecutive Fourier transforms (legacy function).
+
+    Spectrograms can be used as a way of visualizing the change of a
+    nonstationary signal's frequency content over time.
+
+    .. legacy:: function
+
+        :class:`ShortTimeFFT` is a newer STFT / ISTFT implementation with more
+        features also including a :meth:`~ShortTimeFFT.spectrogram` method.
+        A :ref:`comparison <tutorial_stft_legacy_stft>` between the
+        implementations can be found in the :ref:`tutorial_stft` section of
+        the :ref:`user_guide`.
+
+    Parameters
+    ----------
+    x : array_like
+        Time series of measurement values
+    fs : float, optional
+        Sampling frequency of the `x` time series. Defaults to 1.0.
+    window : str or tuple or array_like, optional
+        Desired window to use. If `window` is a string or tuple, it is
+        passed to `get_window` to generate the window values, which are
+        DFT-even by default. See `get_window` for a list of windows and
+        required parameters. If `window` is array_like it will be used
+        directly as the window and its length must be nperseg.
+        Defaults to a periodic Tukey window with shape parameter of 0.25.
+    nperseg : int, optional
+        Length of each segment. Defaults to None, but if window is str or
+        tuple, is set to 256, and if window is array_like, is set to the
+        length of the window.
+    noverlap : int, optional
+        Number of points to overlap between segments. If `None`,
+        ``noverlap = nperseg // 8``. Defaults to `None`.
+    nfft : int, optional
+        Length of the FFT used, if a zero padded FFT is desired. If
+        `None`, the FFT length is `nperseg`. Defaults to `None`.
+    detrend : str or function or `False`, optional
+        Specifies how to detrend each segment. If `detrend` is a
+        string, it is passed as the `type` argument to the `detrend`
+        function. If it is a function, it takes a segment and returns a
+        detrended segment. If `detrend` is `False`, no detrending is
+        done. Defaults to 'constant'.
+    return_onesided : bool, optional
+        If `True`, return a one-sided spectrum for real data. If
+        `False` return a two-sided spectrum. Defaults to `True`, but for
+        complex data, a two-sided spectrum is always returned.
+    scaling : { 'density', 'spectrum' }, optional
+        Selects between computing the power spectral density ('density')
+        where `Sxx` has units of V**2/Hz and computing the power
+        spectrum ('spectrum') where `Sxx` has units of V**2, if `x`
+        is measured in V and `fs` is measured in Hz. Defaults to
+        'density'.
+    axis : int, optional
+        Axis along which the spectrogram is computed; the default is over
+        the last axis (i.e. ``axis=-1``).
+    mode : str, optional
+        Defines what kind of return values are expected. Options are
+        ['psd', 'complex', 'magnitude', 'angle', 'phase']. 'complex' is
+        equivalent to the output of `stft` with no padding or boundary
+        extension. 'magnitude' returns the absolute magnitude of the
+        STFT. 'angle' and 'phase' return the complex angle of the STFT,
+        with and without unwrapping, respectively.
+
+    Returns
+    -------
+    f : ndarray
+        Array of sample frequencies.
+    t : ndarray
+        Array of segment times.
+    Sxx : ndarray
+        Spectrogram of x. By default, the last axis of Sxx corresponds
+        to the segment times.
+
+    See Also
+    --------
+    periodogram: Simple, optionally modified periodogram
+    lombscargle: Lomb-Scargle periodogram for unevenly sampled data
+    welch: Power spectral density by Welch's method.
+    csd: Cross spectral density by Welch's method.
+    ShortTimeFFT: Newer STFT/ISTFT implementation providing more features,
+                  which also includes a :meth:`~ShortTimeFFT.spectrogram`
+                  method.
+
+    Notes
+    -----
+    An appropriate amount of overlap will depend on the choice of window
+    and on your requirements. In contrast to welch's method, where the
+    entire data stream is averaged over, one may wish to use a smaller
+    overlap (or perhaps none at all) when computing a spectrogram, to
+    maintain some statistical independence between individual segments.
+    It is for this reason that the default window is a Tukey window with
+    1/8th of a window's length overlap at each end.
+
+
+    .. versionadded:: 0.16.0
+
+    References
+    ----------
+    .. [1] Oppenheim, Alan V., Ronald W. Schafer, John R. Buck
+           "Discrete-Time Signal Processing", Prentice Hall, 1999.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> from scipy.fft import fftshift
+    >>> import matplotlib.pyplot as plt
+    >>> rng = np.random.default_rng()
+
+    Generate a test signal, a 2 Vrms sine wave whose frequency is slowly
+    modulated around 3kHz, corrupted by white noise of exponentially
+    decreasing magnitude sampled at 10 kHz.
+
+    >>> fs = 10e3
+    >>> N = 1e5
+    >>> amp = 2 * np.sqrt(2)
+    >>> noise_power = 0.01 * fs / 2
+    >>> time = np.arange(N) / float(fs)
+    >>> mod = 500*np.cos(2*np.pi*0.25*time)
+    >>> carrier = amp * np.sin(2*np.pi*3e3*time + mod)
+    >>> noise = rng.normal(scale=np.sqrt(noise_power), size=time.shape)
+    >>> noise *= np.exp(-time/5)
+    >>> x = carrier + noise
+
+    Compute and plot the spectrogram.
+
+    >>> f, t, Sxx = signal.spectrogram(x, fs)
+    >>> plt.pcolormesh(t, f, Sxx, shading='gouraud')
+    >>> plt.ylabel('Frequency [Hz]')
+    >>> plt.xlabel('Time [sec]')
+    >>> plt.show()
+
+    Note, if using output that is not one sided, then use the following:
+
+    >>> f, t, Sxx = signal.spectrogram(x, fs, return_onesided=False)
+    >>> plt.pcolormesh(t, fftshift(f), fftshift(Sxx, axes=0), shading='gouraud')
+    >>> plt.ylabel('Frequency [Hz]')
+    >>> plt.xlabel('Time [sec]')
+    >>> plt.show()
+
+    """
+    modelist = ['psd', 'complex', 'magnitude', 'angle', 'phase']
+    if mode not in modelist:
+        raise ValueError(f'unknown value for mode {mode}, must be one of {modelist}')
+
+    # need to set default for nperseg before setting default for noverlap below
+    window, nperseg = _triage_segments(window, nperseg,
+                                       input_length=x.shape[axis])
+
+    # Less overlap than welch, so samples are more statistically independent
+    if noverlap is None:
+        noverlap = nperseg // 8
+
+    if mode == 'psd':
+        freqs, time, Sxx = _spectral_helper(x, x, fs, window, nperseg,
+                                            noverlap, nfft, detrend,
+                                            return_onesided, scaling, axis,
+                                            mode='psd')
+
+    else:
+        freqs, time, Sxx = _spectral_helper(x, x, fs, window, nperseg,
+                                            noverlap, nfft, detrend,
+                                            return_onesided, scaling, axis,
+                                            mode='stft')
+
+        if mode == 'magnitude':
+            Sxx = np.abs(Sxx)
+        elif mode in ['angle', 'phase']:
+            Sxx = np.angle(Sxx)
+            if mode == 'phase':
+                # Sxx has one additional dimension for time strides
+                if axis < 0:
+                    axis -= 1
+                Sxx = np.unwrap(Sxx, axis=axis)
+
+        # mode =='complex' is same as `stft`, doesn't need modification
+
+    return freqs, time, Sxx
+
+
+def check_COLA(window, nperseg, noverlap, tol=1e-10):
+    r"""Check whether the Constant OverLap Add (COLA) constraint is met
+    (legacy function).
+
+    .. legacy:: function
+
+        The COLA constraint is equivalent of having a constant dual window, i.e.,
+        ``all(ShortTimeFFT.dual_win == ShortTimeFFT.dual_win[0])``. Hence,
+        `closest_STFT_dual_window` generalizes this function, as the following
+        example shows:
+
+        >>> import numpy as np
+        >>> from scipy.signal import check_COLA, closest_STFT_dual_window, windows
+        ...
+        >>> w, w_rect, hop = windows.hann(12, sym=False), np.ones(12), 6
+        >>> dual_win, alpha = closest_STFT_dual_window(w, hop, w_rect, scaled=True)
+        >>> np.allclose(dual_win/alpha, w_rect, atol=1e-10, rtol=0)
+        True
+        >>> check_COLA(w, len(w), len(w) - hop)  # equivalent legacy function call
+        True
+
+
+    Parameters
+    ----------
+    window : str or tuple or array_like
+        Desired window to use. If `window` is a string or tuple, it is
+        passed to `get_window` to generate the window values, which are
+        DFT-even by default. See `get_window` for a list of windows and
+        required parameters. If `window` is array_like it will be used
+        directly as the window and its length must be nperseg.
+    nperseg : int
+        Length of each segment.
+    noverlap : int
+        Number of points to overlap between segments.
+    tol : float, optional
+        The allowed variance of a bin's weighted sum from the median bin
+        sum.
+
+    Returns
+    -------
+    verdict : bool
+        `True` if chosen combination satisfies COLA within `tol`,
+        `False` otherwise
+
+    See Also
+    --------
+    closest_STFT_dual_window: Allows determining the closest window meeting the
+                              COLA constraint for a given window
+    check_NOLA: Check whether the Nonzero Overlap Add (NOLA) constraint is met
+    ShortTimeFFT: Provide short-time Fourier transform and its inverse
+    stft: Short-time Fourier transform (legacy)
+    istft: Inverse Short-time Fourier transform (legacy)
+
+    Notes
+    -----
+    In order to invert a short-time Fourier transfrom (STFT) with the so-called
+    "overlap-add method", the signal windowing must obey the constraint of
+    "Constant OverLap Add" (COLA). This ensures that every point in the input
+    data is equally weighted, thereby avoiding aliasing and allowing full
+    reconstruction. Note that the algorithms implemented in `ShortTimeFFT.istft`
+    and in `istft` (legacy) only require that the weaker "nonzero overlap-add"
+    condition (as in `check_NOLA`) is met.
+
+    Some examples of windows that satisfy COLA:
+        - Rectangular window at overlap of 0, 1/2, 2/3, 3/4, ...
+        - Bartlett window at overlap of 1/2, 3/4, 5/6, ...
+        - Hann window at 1/2, 2/3, 3/4, ...
+        - Any Blackman family window at 2/3 overlap
+        - Any window with ``noverlap = nperseg-1``
+
+    A very comprehensive list of other windows may be found in [2]_,
+    wherein the COLA condition is satisfied when the "Amplitude
+    Flatness" is unity.
+
+    .. versionadded:: 0.19.0
+
+    References
+    ----------
+    .. [1] Julius O. Smith III, "Spectral Audio Signal Processing", W3K
+           Publishing, 2011,ISBN 978-0-9745607-3-1.
+    .. [2] G. Heinzel, A. Ruediger and R. Schilling, "Spectrum and
+           spectral density estimation by the Discrete Fourier transform
+           (DFT), including a comprehensive list of window functions and
+           some new at-top windows", 2002,
+           http://hdl.handle.net/11858/00-001M-0000-0013-557A-5
+
+    Examples
+    --------
+    >>> from scipy import signal
+
+    Confirm COLA condition for rectangular window of 75% (3/4) overlap:
+
+    >>> signal.check_COLA(signal.windows.boxcar(100), 100, 75)
+    True
+
+    COLA is not true for 25% (1/4) overlap, though:
+
+    >>> signal.check_COLA(signal.windows.boxcar(100), 100, 25)
+    False
+
+    "Symmetrical" Hann window (for filter design) is not COLA:
+
+    >>> signal.check_COLA(signal.windows.hann(120, sym=True), 120, 60)
+    False
+
+    "Periodic" or "DFT-even" Hann window (for FFT analysis) is COLA for
+    overlap of 1/2, 2/3, 3/4, etc.:
+
+    >>> signal.check_COLA(signal.windows.hann(120, sym=False), 120, 60)
+    True
+
+    >>> signal.check_COLA(signal.windows.hann(120, sym=False), 120, 80)
+    True
+
+    >>> signal.check_COLA(signal.windows.hann(120, sym=False), 120, 90)
+    True
+
+    """
+    nperseg = int(nperseg)
+
+    if nperseg < 1:
+        raise ValueError('nperseg must be a positive integer')
+
+    if noverlap >= nperseg:
+        raise ValueError('noverlap must be less than nperseg.')
+    noverlap = int(noverlap)
+
+    if isinstance(window, str) or type(window) is tuple:
+        win = get_window(window, nperseg)
+    else:
+        win = np.asarray(window)
+        if len(win.shape) != 1:
+            raise ValueError('window must be 1-D')
+        if win.shape[0] != nperseg:
+            raise ValueError('window must have length of nperseg')
+
+    step = nperseg - noverlap
+    binsums = sum(win[ii*step:(ii+1)*step] for ii in range(nperseg//step))
+
+    if nperseg % step != 0:
+        binsums[:nperseg % step] += win[-(nperseg % step):]
+
+    deviation = binsums - np.median(binsums)
+    return np.max(np.abs(deviation)) < tol
+
+
+def check_NOLA(window, nperseg, noverlap, tol=1e-10):
+    r"""Check whether the Nonzero Overlap Add (NOLA) constraint is met.
+
+    Parameters
+    ----------
+    window : str or tuple or array_like
+        Desired window to use. If `window` is a string or tuple, it is
+        passed to `get_window` to generate the window values, which are
+        DFT-even by default. See `get_window` for a list of windows and
+        required parameters. If `window` is array_like it will be used
+        directly as the window and its length must be nperseg.
+    nperseg : int
+        Length of each segment.
+    noverlap : int
+        Number of points to overlap between segments.
+    tol : float, optional
+        The allowed variance of a bin's weighted sum from the median bin
+        sum.
+
+    Returns
+    -------
+    verdict : bool
+        `True` if chosen combination satisfies the NOLA constraint within
+        `tol`, `False` otherwise
+
+    See Also
+    --------
+    check_COLA: Check whether the Constant OverLap Add (COLA) constraint is met
+    stft: Short Time Fourier Transform
+    istft: Inverse Short Time Fourier Transform
+
+    Notes
+    -----
+    In order to enable inversion of an STFT via the inverse STFT in
+    `istft`, the signal windowing must obey the constraint of "nonzero
+    overlap add" (NOLA):
+
+    .. math:: \sum_{t}w^{2}[n-tH] \ne 0
+
+    for all :math:`n`, where :math:`w` is the window function, :math:`t` is the
+    frame index, and :math:`H` is the hop size (:math:`H` = `nperseg` -
+    `noverlap`).
+
+    This ensures that the normalization factors in the denominator of the
+    overlap-add inversion equation are not zero. Only very pathological windows
+    will fail the NOLA constraint.
+
+    .. versionadded:: 1.2.0
+
+    References
+    ----------
+    .. [1] Julius O. Smith III, "Spectral Audio Signal Processing", W3K
+           Publishing, 2011,ISBN 978-0-9745607-3-1.
+    .. [2] G. Heinzel, A. Ruediger and R. Schilling, "Spectrum and
+           spectral density estimation by the Discrete Fourier transform
+           (DFT), including a comprehensive list of window functions and
+           some new at-top windows", 2002,
+           http://hdl.handle.net/11858/00-001M-0000-0013-557A-5
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import signal
+
+    Confirm NOLA condition for rectangular window of 75% (3/4) overlap:
+
+    >>> signal.check_NOLA(signal.windows.boxcar(100), 100, 75)
+    True
+
+    NOLA is also true for 25% (1/4) overlap:
+
+    >>> signal.check_NOLA(signal.windows.boxcar(100), 100, 25)
+    True
+
+    "Symmetrical" Hann window (for filter design) is also NOLA:
+
+    >>> signal.check_NOLA(signal.windows.hann(120, sym=True), 120, 60)
+    True
+
+    As long as there is overlap, it takes quite a pathological window to fail
+    NOLA:
+
+    >>> w = np.ones(64, dtype="float")
+    >>> w[::2] = 0
+    >>> signal.check_NOLA(w, 64, 32)
+    False
+
+    If there is not enough overlap, a window with zeros at the ends will not
+    work:
+
+    >>> signal.check_NOLA(signal.windows.hann(64), 64, 0)
+    False
+    >>> signal.check_NOLA(signal.windows.hann(64), 64, 1)
+    False
+    >>> signal.check_NOLA(signal.windows.hann(64), 64, 2)
+    True
+
+    """
+    nperseg = int(nperseg)
+
+    if nperseg < 1:
+        raise ValueError('nperseg must be a positive integer')
+
+    if noverlap >= nperseg:
+        raise ValueError('noverlap must be less than nperseg')
+    if noverlap < 0:
+        raise ValueError('noverlap must be a nonnegative integer')
+    noverlap = int(noverlap)
+
+    if isinstance(window, str) or type(window) is tuple:
+        win = get_window(window, nperseg)
+    else:
+        win = np.asarray(window)
+        if len(win.shape) != 1:
+            raise ValueError('window must be 1-D')
+        if win.shape[0] != nperseg:
+            raise ValueError('window must have length of nperseg')
+
+    step = nperseg - noverlap
+    binsums = sum(win[ii*step:(ii+1)*step]**2 for ii in range(nperseg//step))
+
+    if nperseg % step != 0:
+        binsums[:nperseg % step] += win[-(nperseg % step):]**2
+
+    return np.min(binsums) > tol
+
+
+def stft(x, fs=1.0, window='hann_periodic', nperseg=256, noverlap=None, nfft=None,
+         detrend=False, return_onesided=True, boundary='zeros', padded=True,
+         axis=-1, scaling='spectrum'):
+    r"""Compute the Short Time Fourier Transform (legacy function).
+
+    STFTs can be used as a way of quantifying the change of a
+    nonstationary signal's frequency and phase content over time.
+
+    .. legacy:: function
+
+        `ShortTimeFFT` is a newer STFT / ISTFT implementation with more
+        features. A :ref:`comparison <tutorial_stft_legacy_stft>` between the
+        implementations can be found in the :ref:`tutorial_stft` section of the
+        :ref:`user_guide`.
+
+    Parameters
+    ----------
+    x : array_like
+        Time series of measurement values
+    fs : float, optional
+        Sampling frequency of the `x` time series. Defaults to 1.0.
+    window : str or tuple or array_like, optional
+        Desired window to use. If `window` is a string or tuple, it is
+        passed to `get_window` to generate the window values, which are
+        DFT-even by default. See `get_window` for a list of windows and
+        required parameters. If `window` is array_like it will be used
+        directly as the window and its length must be nperseg. Defaults
+        to a periodic Hann window.
+    nperseg : int, optional
+        Length of each segment. Defaults to 256.
+    noverlap : int, optional
+        Number of points to overlap between segments. If `None`,
+        ``noverlap = nperseg // 2``. Defaults to `None`. When
+        specified, the COLA constraint must be met (see Notes below).
+    nfft : int, optional
+        Length of the FFT used, if a zero padded FFT is desired. If
+        `None`, the FFT length is `nperseg`. Defaults to `None`.
+    detrend : str or function or `False`, optional
+        Specifies how to detrend each segment. If `detrend` is a
+        string, it is passed as the `type` argument to the `detrend`
+        function. If it is a function, it takes a segment and returns a
+        detrended segment. If `detrend` is `False`, no detrending is
+        done. Defaults to `False`.
+    return_onesided : bool, optional
+        If `True`, return a one-sided spectrum for real data. If
+        `False` return a two-sided spectrum. Defaults to `True`, but for
+        complex data, a two-sided spectrum is always returned.
+    boundary : str or None, optional
+        Specifies whether the input signal is extended at both ends, and
+        how to generate the new values, in order to center the first
+        windowed segment on the first input point. This has the benefit
+        of enabling reconstruction of the first input point when the
+        employed window function starts at zero. Valid options are
+        ``['even', 'odd', 'constant', 'zeros', None]``. Defaults to
+        'zeros', for zero padding extension. I.e. ``[1, 2, 3, 4]`` is
+        extended to ``[0, 1, 2, 3, 4, 0]`` for ``nperseg=3``.
+    padded : bool, optional
+        Specifies whether the input signal is zero-padded at the end to
+        make the signal fit exactly into an integer number of window
+        segments, so that all of the signal is included in the output.
+        Defaults to `True`. Padding occurs after boundary extension, if
+        `boundary` is not `None`, and `padded` is `True`, as is the
+        default.
+    axis : int, optional
+        Axis along which the STFT is computed; the default is over the
+        last axis (i.e. ``axis=-1``).
+    scaling : {'spectrum', 'psd'}
+        The default 'spectrum' scaling allows each frequency line of `Zxx` to
+        be interpreted as a magnitude spectrum. The 'psd' option scales each
+        line to a power spectral density - it allows to calculate the signal's
+        energy by numerically integrating over ``abs(Zxx)**2``.
+
+        .. versionadded:: 1.9.0
+
+    Returns
+    -------
+    f : ndarray
+        Array of sample frequencies.
+    t : ndarray
+        Array of segment times.
+    Zxx : ndarray
+        STFT of `x`. By default, the last axis of `Zxx` corresponds
+        to the segment times.
+
+    See Also
+    --------
+    istft: Inverse Short Time Fourier Transform
+    ShortTimeFFT: Newer STFT/ISTFT implementation providing more features.
+    check_COLA: Check whether the Constant OverLap Add (COLA) constraint
+                is met
+    check_NOLA: Check whether the Nonzero Overlap Add (NOLA) constraint is met
+    welch: Power spectral density by Welch's method.
+    spectrogram: Spectrogram by Welch's method.
+    csd: Cross spectral density by Welch's method.
+    lombscargle: Lomb-Scargle periodogram for unevenly sampled data
+
+    Notes
+    -----
+    In order to enable inversion of an STFT via the inverse STFT in
+    `istft`, the signal windowing must obey the constraint of "Nonzero
+    OverLap Add" (NOLA), and the input signal must have complete
+    windowing coverage (i.e. ``(x.shape[axis] - nperseg) %
+    (nperseg-noverlap) == 0``). The `padded` argument may be used to
+    accomplish this.
+
+    Given a time-domain signal :math:`x[n]`, a window :math:`w[n]`, and a hop
+    size :math:`H` = `nperseg - noverlap`, the windowed frame at time index
+    :math:`t` is given by
+
+    .. math:: x_{t}[n]=x[n]w[n-tH]
+
+    The overlap-add (OLA) reconstruction equation is given by
+
+    .. math:: x[n]=\frac{\sum_{t}x_{t}[n]w[n-tH]}{\sum_{t}w^{2}[n-tH]}
+
+    The NOLA constraint ensures that every normalization term that appears
+    in the denominator of the OLA reconstruction equation is nonzero. Whether a
+    choice of `window`, `nperseg`, and `noverlap` satisfy this constraint can
+    be tested with `check_NOLA`.
+
+
+    .. versionadded:: 0.19.0
+
+    References
+    ----------
+    .. [1] Oppenheim, Alan V., Ronald W. Schafer, John R. Buck
+           "Discrete-Time Signal Processing", Prentice Hall, 1999.
+    .. [2] Daniel W. Griffin, Jae S. Lim "Signal Estimation from
+           Modified Short-Time Fourier Transform", IEEE 1984,
+           10.1109/TASSP.1984.1164317
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+    >>> rng = np.random.default_rng()
+
+    Generate a test signal, a 2 Vrms sine wave whose frequency is slowly
+    modulated around 3kHz, corrupted by white noise of exponentially
+    decreasing magnitude sampled at 10 kHz.
+
+    >>> fs = 10e3
+    >>> N = 1e5
+    >>> amp = 2 * np.sqrt(2)
+    >>> noise_power = 0.01 * fs / 2
+    >>> time = np.arange(N) / float(fs)
+    >>> mod = 500*np.cos(2*np.pi*0.25*time)
+    >>> carrier = amp * np.sin(2*np.pi*3e3*time + mod)
+    >>> noise = rng.normal(scale=np.sqrt(noise_power),
+    ...                    size=time.shape)
+    >>> noise *= np.exp(-time/5)
+    >>> x = carrier + noise
+
+    Compute and plot the STFT's magnitude.
+
+    >>> f, t, Zxx = signal.stft(x, fs, nperseg=1000)
+    >>> plt.pcolormesh(t, f, np.abs(Zxx), vmin=0, vmax=amp, shading='gouraud')
+    >>> plt.title('STFT Magnitude')
+    >>> plt.ylabel('Frequency [Hz]')
+    >>> plt.xlabel('Time [sec]')
+    >>> plt.show()
+
+    Compare the energy of the signal `x` with the energy of its STFT:
+
+    >>> E_x = sum(x**2) / fs  # Energy of x
+    >>> # Calculate a two-sided STFT with PSD scaling:
+    >>> f, t, Zxx = signal.stft(x, fs, nperseg=1000, return_onesided=False,
+    ...                         scaling='psd')
+    >>> # Integrate numerically over abs(Zxx)**2:
+    >>> df, dt = f[1] - f[0], t[1] - t[0]
+    >>> E_Zxx = sum(np.sum(Zxx.real**2 + Zxx.imag**2, axis=0) * df) * dt
+    >>> # The energy is the same, but the numerical errors are quite large:
+    >>> np.isclose(E_x, E_Zxx, rtol=1e-2)
+    True
+
+    """
+    if scaling == 'psd':
+        scaling = 'density'
+    elif scaling != 'spectrum':
+        raise ValueError(f"Parameter {scaling=} not in ['spectrum', 'psd']!")
+
+    freqs, time, Zxx = _spectral_helper(x, x, fs, window, nperseg, noverlap,
+                                        nfft, detrend, return_onesided,
+                                        scaling=scaling, axis=axis,
+                                        mode='stft', boundary=boundary,
+                                        padded=padded)
+
+    return freqs, time, Zxx
+
+
+def istft(Zxx, fs=1.0, window='hann_periodic', nperseg=None, noverlap=None, nfft=None,
+          input_onesided=True, boundary=True, time_axis=-1, freq_axis=-2,
+          scaling='spectrum'):
+    r"""Perform the inverse Short Time Fourier transform (legacy function).
+
+    .. legacy:: function
+
+        `ShortTimeFFT` is a newer STFT / ISTFT implementation with more
+        features. A :ref:`comparison <tutorial_stft_legacy_stft>` between the
+        implementations can be found in the :ref:`tutorial_stft` section of the
+        :ref:`user_guide`.
+
+    Parameters
+    ----------
+    Zxx : array_like
+        STFT of the signal to be reconstructed. If a purely real array
+        is passed, it will be cast to a complex data type.
+    fs : float, optional
+        Sampling frequency of the time series. Defaults to 1.0.
+    window : str or tuple or array_like, optional
+        Desired window to use. If `window` is a string or tuple, it is
+        passed to `get_window` to generate the window values, which are
+        DFT-even by default. See `get_window` for a list of windows and
+        required parameters. If `window` is array_like it will be used
+        directly as the window and its length must be nperseg. Defaults
+        to a periodic Hann window. Must match the window used to generate the
+        STFT for faithful inversion.
+    nperseg : int, optional
+        Number of data points corresponding to each STFT segment. This
+        parameter must be specified if the number of data points per
+        segment is odd, or if the STFT was padded via ``nfft >
+        nperseg``. If `None`, the value depends on the shape of
+        `Zxx` and `input_onesided`. If `input_onesided` is `True`,
+        ``nperseg=2*(Zxx.shape[freq_axis] - 1)``. Otherwise,
+        ``nperseg=Zxx.shape[freq_axis]``. Defaults to `None`.
+    noverlap : int, optional
+        Number of points to overlap between segments. If `None`, half
+        of the segment length. Defaults to `None`. When specified, the
+        COLA constraint must be met (see Notes below), and should match
+        the parameter used to generate the STFT. Defaults to `None`.
+    nfft : int, optional
+        Number of FFT points corresponding to each STFT segment. This
+        parameter must be specified if the STFT was padded via ``nfft >
+        nperseg``. If `None`, the default values are the same as for
+        `nperseg`, detailed above, with one exception: if
+        `input_onesided` is True and
+        ``nperseg==2*Zxx.shape[freq_axis] - 1``, `nfft` also takes on
+        that value. This case allows the proper inversion of an
+        odd-length unpadded STFT using ``nfft=None``. Defaults to
+        `None`.
+    input_onesided : bool, optional
+        If `True`, interpret the input array as one-sided FFTs, such
+        as is returned by `stft` with ``return_onesided=True`` and
+        `numpy.fft.rfft`. If `False`, interpret the input as a a
+        two-sided FFT. Defaults to `True`.
+    boundary : bool, optional
+        Specifies whether the input signal was extended at its
+        boundaries by supplying a non-`None` ``boundary`` argument to
+        `stft`. Defaults to `True`.
+    time_axis : int, optional
+        Where the time segments of the STFT is located; the default is
+        the last axis (i.e. ``axis=-1``).
+    freq_axis : int, optional
+        Where the frequency axis of the STFT is located; the default is
+        the penultimate axis (i.e. ``axis=-2``).
+    scaling : {'spectrum', 'psd'}
+        The default 'spectrum' scaling allows each frequency line of `Zxx` to
+        be interpreted as a magnitude spectrum. The 'psd' option scales each
+        line to a power spectral density - it allows to calculate the signal's
+        energy by numerically integrating over ``abs(Zxx)**2``.
+
+    Returns
+    -------
+    t : ndarray
+        Array of output data times.
+    x : ndarray
+        iSTFT of `Zxx`.
+
+    See Also
+    --------
+    stft: Short Time Fourier Transform
+    ShortTimeFFT: Newer STFT/ISTFT implementation providing more features.
+    check_COLA: Check whether the Constant OverLap Add (COLA) constraint
+                is met
+    check_NOLA: Check whether the Nonzero Overlap Add (NOLA) constraint is met
+
+    Notes
+    -----
+    In order to enable inversion of an STFT via the inverse STFT with
+    `istft`, the signal windowing must obey the constraint of "nonzero
+    overlap add" (NOLA):
+
+    .. math:: \sum_{t}w^{2}[n-tH] \ne 0
+
+    This ensures that the normalization factors that appear in the denominator
+    of the overlap-add reconstruction equation
+
+    .. math:: x[n]=\frac{\sum_{t}x_{t}[n]w[n-tH]}{\sum_{t}w^{2}[n-tH]}
+
+    are not zero. The NOLA constraint can be checked with the `check_NOLA`
+    function.
+
+    An STFT which has been modified (via masking or otherwise) is not
+    guaranteed to correspond to an exactly realizible signal. This
+    function implements the iSTFT via the least-squares estimation
+    algorithm detailed in [2]_, which produces a signal that minimizes
+    the mean squared error between the STFT of the returned signal and
+    the modified STFT.
+
+
+    .. versionadded:: 0.19.0
+
+    References
+    ----------
+    .. [1] Oppenheim, Alan V., Ronald W. Schafer, John R. Buck
+           "Discrete-Time Signal Processing", Prentice Hall, 1999.
+    .. [2] Daniel W. Griffin, Jae S. Lim "Signal Estimation from
+           Modified Short-Time Fourier Transform", IEEE 1984,
+           10.1109/TASSP.1984.1164317
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+    >>> rng = np.random.default_rng()
+
+    Generate a test signal, a 2 Vrms sine wave at 50Hz corrupted by
+    0.001 V**2/Hz of white noise sampled at 1024 Hz.
+
+    >>> fs = 1024
+    >>> N = 10*fs
+    >>> nperseg = 512
+    >>> amp = 2 * np.sqrt(2)
+    >>> noise_power = 0.001 * fs / 2
+    >>> time = np.arange(N) / float(fs)
+    >>> carrier = amp * np.sin(2*np.pi*50*time)
+    >>> noise = rng.normal(scale=np.sqrt(noise_power),
+    ...                    size=time.shape)
+    >>> x = carrier + noise
+
+    Compute the STFT, and plot its magnitude
+
+    >>> f, t, Zxx = signal.stft(x, fs=fs, nperseg=nperseg)
+    >>> plt.figure()
+    >>> plt.pcolormesh(t, f, np.abs(Zxx), vmin=0, vmax=amp, shading='gouraud')
+    >>> plt.ylim([f[1], f[-1]])
+    >>> plt.title('STFT Magnitude')
+    >>> plt.ylabel('Frequency [Hz]')
+    >>> plt.xlabel('Time [sec]')
+    >>> plt.yscale('log')
+    >>> plt.show()
+
+    Zero the components that are 10% or less of the carrier magnitude,
+    then convert back to a time series via inverse STFT
+
+    >>> Zxx = np.where(np.abs(Zxx) >= amp/10, Zxx, 0)
+    >>> _, xrec = signal.istft(Zxx, fs)
+
+    Compare the cleaned signal with the original and true carrier signals.
+
+    >>> plt.figure()
+    >>> plt.plot(time, x, time, xrec, time, carrier)
+    >>> plt.xlim([2, 2.1])
+    >>> plt.xlabel('Time [sec]')
+    >>> plt.ylabel('Signal')
+    >>> plt.legend(['Carrier + Noise', 'Filtered via STFT', 'True Carrier'])
+    >>> plt.show()
+
+    Note that the cleaned signal does not start as abruptly as the original,
+    since some of the coefficients of the transient were also removed:
+
+    >>> plt.figure()
+    >>> plt.plot(time, x, time, xrec, time, carrier)
+    >>> plt.xlim([0, 0.1])
+    >>> plt.xlabel('Time [sec]')
+    >>> plt.ylabel('Signal')
+    >>> plt.legend(['Carrier + Noise', 'Filtered via STFT', 'True Carrier'])
+    >>> plt.show()
+
+    """
+    # Make sure input is an ndarray of appropriate complex dtype
+    Zxx = np.asarray(Zxx) + 0j
+    freq_axis = int(freq_axis)
+    time_axis = int(time_axis)
+
+    if Zxx.ndim < 2:
+        raise ValueError('Input stft must be at least 2d!')
+
+    if freq_axis == time_axis:
+        raise ValueError('Must specify differing time and frequency axes!')
+
+    nseg = Zxx.shape[time_axis]
+
+    if input_onesided:
+        # Assume even segment length
+        n_default = 2*(Zxx.shape[freq_axis] - 1)
+    else:
+        n_default = Zxx.shape[freq_axis]
+
+    # Check windowing parameters
+    if nperseg is None:
+        nperseg = n_default
+    else:
+        nperseg = int(nperseg)
+        if nperseg < 1:
+            raise ValueError('nperseg must be a positive integer')
+
+    if nfft is None:
+        if (input_onesided) and (nperseg == n_default + 1):
+            # Odd nperseg, no FFT padding
+            nfft = nperseg
+        else:
+            nfft = n_default
+    elif nfft < nperseg:
+        raise ValueError('nfft must be greater than or equal to nperseg.')
+    else:
+        nfft = int(nfft)
+
+    if noverlap is None:
+        noverlap = nperseg//2
+    else:
+        noverlap = int(noverlap)
+    if noverlap >= nperseg:
+        raise ValueError('noverlap must be less than nperseg.')
+    nstep = nperseg - noverlap
+
+    # Rearrange axes if necessary
+    if time_axis != Zxx.ndim-1 or freq_axis != Zxx.ndim-2:
+        # Turn negative indices to positive for the call to transpose
+        if freq_axis < 0:
+            freq_axis = Zxx.ndim + freq_axis
+        if time_axis < 0:
+            time_axis = Zxx.ndim + time_axis
+        zouter = list(range(Zxx.ndim))
+        for ax in sorted([time_axis, freq_axis], reverse=True):
+            zouter.pop(ax)
+        Zxx = np.transpose(Zxx, zouter+[freq_axis, time_axis])
+
+    # Get window as array
+    if isinstance(window, str) or type(window) is tuple:
+        win = get_window(window, nperseg)
+    else:
+        win = np.asarray(window)
+        if len(win.shape) != 1:
+            raise ValueError('window must be 1-D')
+        if win.shape[0] != nperseg:
+            raise ValueError(f'window must have length of {nperseg}')
+
+    ifunc = sp_fft.irfft if input_onesided else sp_fft.ifft
+    xsubs = ifunc(Zxx, axis=-2, n=nfft)[..., :nperseg, :]
+
+    # Initialize output and normalization arrays
+    outputlength = nperseg + (nseg-1)*nstep
+    x = np.zeros(list(Zxx.shape[:-2])+[outputlength], dtype=xsubs.dtype)
+    norm = np.zeros(outputlength, dtype=xsubs.dtype)
+
+    if np.result_type(win, xsubs) != xsubs.dtype:
+        win = win.astype(xsubs.dtype)
+
+    if scaling == 'spectrum':
+        xsubs *= win.sum()
+    elif scaling == 'psd':
+        xsubs *= np.sqrt(fs * sum(win**2))
+    else:
+        raise ValueError(f"Parameter {scaling=} not in ['spectrum', 'psd']!")
+
+    # Construct the output from the ifft segments
+    # This loop could perhaps be vectorized/strided somehow...
+    for ii in range(nseg):
+        # Window the ifft
+        x[..., ii*nstep:ii*nstep+nperseg] += xsubs[..., ii] * win
+        norm[..., ii*nstep:ii*nstep+nperseg] += win**2
+
+    # Remove extension points
+    if boundary:
+        x = x[..., nperseg//2:-(nperseg//2)]
+        norm = norm[..., nperseg//2:-(nperseg//2)]
+
+    # Divide out normalization where non-tiny
+    if np.sum(norm > 1e-10) != len(norm):
+        warnings.warn(
+            "NOLA condition failed, STFT may not be invertible."
+            + (" Possibly due to missing boundary" if not boundary else ""),
+            stacklevel=2
+        )
+    x /= np.where(norm > 1e-10, norm, 1.0)
+
+    if input_onesided:
+        x = x.real
+
+    # Put axes back
+    if x.ndim > 1:
+        if time_axis != Zxx.ndim-1:
+            if freq_axis < time_axis:
+                time_axis -= 1
+            x = np.moveaxis(x, -1, time_axis)
+
+    time = np.arange(x.shape[0])/float(fs)
+    return time, x
+
+
+def coherence(x, y, fs=1.0, window='hann_periodic', nperseg=None, noverlap=None,
+              nfft=None, detrend='constant', axis=-1):
+    r"""
+    Estimate the magnitude squared coherence estimate, Cxy, of
+    discrete-time signals X and Y using Welch's method.
+
+    ``Cxy = abs(Pxy)**2/(Pxx*Pyy)``, where `Pxx` and `Pyy` are power
+    spectral density estimates of X and Y, and `Pxy` is the cross
+    spectral density estimate of X and Y.
+
+    Parameters
+    ----------
+    x : array_like
+        Time series of measurement values
+    y : array_like
+        Time series of measurement values
+    fs : float, optional
+        Sampling frequency of the `x` and `y` time series. Defaults
+        to 1.0.
+    window : str or tuple or array_like, optional
+        Desired window to use. If `window` is a string or tuple, it is
+        passed to `get_window` to generate the window values, which are
+        DFT-even by default. See `get_window` for a list of windows and
+        required parameters. If `window` is array_like it will be used
+        directly as the window and its length must be nperseg. Defaults
+        to a periodic Hann window.
+    nperseg : int, optional
+        Length of each segment. Defaults to None, but if window is str or
+        tuple, is set to 256, and if window is array_like, is set to the
+        length of the window.
+    noverlap : int, optional
+        Number of points to overlap between segments. If `None`,
+        ``noverlap = nperseg // 2``. Defaults to `None`.
+    nfft : int, optional
+        Length of the FFT used, if a zero padded FFT is desired. If
+        `None`, the FFT length is `nperseg`. Defaults to `None`.
+    detrend : str or function or `False`, optional
+        Specifies how to detrend each segment. If `detrend` is a
+        string, it is passed as the `type` argument to the `detrend`
+        function. If it is a function, it takes a segment and returns a
+        detrended segment. If `detrend` is `False`, no detrending is
+        done. Defaults to 'constant'.
+    axis : int, optional
+        Axis along which the coherence is computed for both inputs; the
+        default is over the last axis (i.e. ``axis=-1``).
+
+    Returns
+    -------
+    f : ndarray
+        Array of sample frequencies.
+    Cxy : ndarray
+        Magnitude squared coherence of x and y.
+
+    See Also
+    --------
+    periodogram: Simple, optionally modified periodogram
+    lombscargle: Lomb-Scargle periodogram for unevenly sampled data
+    welch: Power spectral density by Welch's method.
+    csd: Cross spectral density by Welch's method.
+
+    Notes
+    -----
+    An appropriate amount of overlap will depend on the choice of window
+    and on your requirements. For the default Hann window an overlap of
+    50% is a reasonable trade-off between accurately estimating the
+    signal power, while not over counting any of the data. Narrower
+    windows may require a larger overlap.
+
+    .. versionadded:: 0.16.0
+
+    References
+    ----------
+    .. [1] P. Welch, "The use of the fast Fourier transform for the
+           estimation of power spectra: A method based on time averaging
+           over short, modified periodograms", IEEE Trans. Audio
+           Electroacoust. vol. 15, pp. 70-73, 1967.
+    .. [2] Stoica, Petre, and Randolph Moses, "Spectral Analysis of
+           Signals" Prentice Hall, 2005
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+    >>> rng = np.random.default_rng()
+
+    Generate two test signals with some common features.
+
+    >>> fs = 10e3
+    >>> N = 1e5
+    >>> amp = 20
+    >>> freq = 1234.0
+    >>> noise_power = 0.001 * fs / 2
+    >>> time = np.arange(N) / fs
+    >>> b, a = signal.butter(2, 0.25, 'low')
+    >>> x = rng.normal(scale=np.sqrt(noise_power), size=time.shape)
+    >>> y = signal.lfilter(b, a, x)
+    >>> x += amp*np.sin(2*np.pi*freq*time)
+    >>> y += rng.normal(scale=0.1*np.sqrt(noise_power), size=time.shape)
+
+    Compute and plot the coherence.
+
+    >>> f, Cxy = signal.coherence(x, y, fs, nperseg=1024)
+    >>> plt.semilogy(f, Cxy)
+    >>> plt.xlabel('frequency [Hz]')
+    >>> plt.ylabel('Coherence')
+    >>> plt.show()
+
+    """
+    freqs, Pxx = welch(x, fs=fs, window=window, nperseg=nperseg,
+                       noverlap=noverlap, nfft=nfft, detrend=detrend,
+                       axis=axis)
+    _, Pyy = welch(y, fs=fs, window=window, nperseg=nperseg, noverlap=noverlap,
+                   nfft=nfft, detrend=detrend, axis=axis)
+    _, Pxy = csd(x, y, fs=fs, window=window, nperseg=nperseg,
+                 noverlap=noverlap, nfft=nfft, detrend=detrend, axis=axis)
+
+    Cxy = np.abs(Pxy)**2 / Pxx / Pyy
+
+    return freqs, Cxy
+
+
+def _spectral_helper(x, y, fs=1.0, window='hann', nperseg=None, noverlap=None,
+                     nfft=None, detrend='constant', return_onesided=True,
+                     scaling='density', axis=-1, mode='psd', boundary=None,
+                     padded=False):
+    """Calculate various forms of windowed FFTs for PSD, CSD, etc.
+
+    .. legacy:: function
+
+        This function is soley used by the legacy functions `spectrogram` and `stft`
+        (which are also in this same source file `scipy/signal/_spectral_py.py`).
+
+    This is a helper function that implements the commonality between
+    the stft, psd, csd, and spectrogram functions. It is not designed to
+    be called externally. The windows are not averaged over; the result
+    from each window is returned.
+
+    Parameters
+    ----------
+    x : array_like
+        Array or sequence containing the data to be analyzed.
+    y : array_like
+        Array or sequence containing the data to be analyzed. If this is
+        the same object in memory as `x` (i.e. ``_spectral_helper(x,
+        x, ...)``), the extra computations are spared.
+    fs : float, optional
+        Sampling frequency of the time series. Defaults to 1.0.
+    window : str or tuple or array_like, optional
+        Desired window to use. If `window` is a string or tuple, it is
+        passed to `get_window` to generate the window values, which are
+        DFT-even by default. See `get_window` for a list of windows and
+        required parameters. If `window` is array_like it will be used
+        directly as the window and its length must be nperseg. Defaults
+        to a Hann window.
+    nperseg : int, optional
+        Length of each segment. Defaults to None, but if window is str or
+        tuple, is set to 256, and if window is array_like, is set to the
+        length of the window.
+    noverlap : int, optional
+        Number of points to overlap between segments. If `None`,
+        ``noverlap = nperseg // 2``. Defaults to `None`.
+    nfft : int, optional
+        Length of the FFT used, if a zero padded FFT is desired. If
+        `None`, the FFT length is `nperseg`. Defaults to `None`.
+    detrend : str or function or `False`, optional
+        Specifies how to detrend each segment. If `detrend` is a
+        string, it is passed as the `type` argument to the `detrend`
+        function. If it is a function, it takes a segment and returns a
+        detrended segment. If `detrend` is `False`, no detrending is
+        done. Defaults to 'constant'.
+    return_onesided : bool, optional
+        If `True`, return a one-sided spectrum for real data. If
+        `False` return a two-sided spectrum. Defaults to `True`, but for
+        complex data, a two-sided spectrum is always returned.
+    scaling : { 'density', 'spectrum' }, optional
+        Selects between computing the cross spectral density ('density')
+        where `Pxy` has units of V²/Hz and computing the cross
+        spectrum ('spectrum') where `Pxy` has units of V², if `x`
+        and `y` are measured in V and `fs` is measured in Hz.
+        Defaults to 'density'
+    axis : int, optional
+        Axis along which the FFTs are computed; the default is over the
+        last axis (i.e. ``axis=-1``).
+    mode: str {'psd', 'stft'}, optional
+        Defines what kind of return values are expected. Defaults to
+        'psd'.
+    boundary : str or None, optional
+        Specifies whether the input signal is extended at both ends, and
+        how to generate the new values, in order to center the first
+        windowed segment on the first input point. This has the benefit
+        of enabling reconstruction of the first input point when the
+        employed window function starts at zero. Valid options are
+        ``['even', 'odd', 'constant', 'zeros', None]``. Defaults to
+        `None`.
+    padded : bool, optional
+        Specifies whether the input signal is zero-padded at the end to
+        make the signal fit exactly into an integer number of window
+        segments, so that all of the signal is included in the output.
+        Defaults to `False`. Padding occurs after boundary extension, if
+        `boundary` is not `None`, and `padded` is `True`.
+
+    Returns
+    -------
+    freqs : ndarray
+        Array of sample frequencies.
+    t : ndarray
+        Array of times corresponding to each data segment
+    result : ndarray
+        Array of output data, contents dependent on *mode* kwarg.
+
+    Notes
+    -----
+    Adapted from matplotlib.mlab
+
+    .. versionadded:: 0.16.0
+    """
+    if mode not in ['psd', 'stft']:
+        raise ValueError(f"Unknown value for mode {mode}, must be one of: "
+                         "{'psd', 'stft'}")
+
+    boundary_funcs = {'even': even_ext,
+                      'odd': odd_ext,
+                      'constant': const_ext,
+                      'zeros': zero_ext,
+                      None: None}
+
+    if boundary not in boundary_funcs:
+        raise ValueError(f"Unknown boundary option '{boundary}', "
+                         f"must be one of: {list(boundary_funcs.keys())}")
+
+    # If x and y are the same object we can save ourselves some computation.
+    same_data = y is x
+
+    if not same_data and mode != 'psd':
+        raise ValueError("x and y must be equal if mode is 'stft'")
+
+    axis = int(axis)
+
+    # Ensure we have np.arrays, get outdtype
+    x = np.asarray(x)
+    if not same_data:
+        y = np.asarray(y)
+        outdtype = np.result_type(x, y, np.complex64)
+    else:
+        outdtype = np.result_type(x, np.complex64)
+
+    if not same_data:
+        # Check if we can broadcast the outer axes together
+        xouter = list(x.shape)
+        youter = list(y.shape)
+        xouter.pop(axis)
+        youter.pop(axis)
+        try:
+            outershape = np.broadcast(np.empty(xouter), np.empty(youter)).shape
+        except ValueError as e:
+            raise ValueError('x and y cannot be broadcast together.') from e
+
+    if same_data:
+        if x.size == 0:
+            return np.empty(x.shape), np.empty(x.shape), np.empty(x.shape)
+    else:
+        if x.size == 0 or y.size == 0:
+            outshape = outershape + (min([x.shape[axis], y.shape[axis]]),)
+            emptyout = np.moveaxis(np.empty(outshape), -1, axis)
+            return emptyout, emptyout, emptyout
+
+    if x.ndim > 1:
+        if axis != -1:
+            x = np.moveaxis(x, axis, -1)
+            if not same_data and y.ndim > 1:
+                y = np.moveaxis(y, axis, -1)
+
+    # Check if x and y are the same length, zero-pad if necessary
+    if not same_data:
+        if x.shape[-1] != y.shape[-1]:
+            if x.shape[-1] < y.shape[-1]:
+                pad_shape = list(x.shape)
+                pad_shape[-1] = y.shape[-1] - x.shape[-1]
+                x = np.concatenate((x, np.zeros(pad_shape)), -1)
+            else:
+                pad_shape = list(y.shape)
+                pad_shape[-1] = x.shape[-1] - y.shape[-1]
+                y = np.concatenate((y, np.zeros(pad_shape)), -1)
+
+    if nperseg is not None:  # if specified by user
+        nperseg = int(nperseg)
+        if nperseg < 1:
+            raise ValueError('nperseg must be a positive integer')
+
+    # parse window; if array like, then set nperseg = win.shape
+    win, nperseg = _triage_segments(window, nperseg, input_length=x.shape[-1])
+
+    if nfft is None:
+        nfft = nperseg
+    elif nfft < nperseg:
+        raise ValueError('nfft must be greater than or equal to nperseg.')
+    else:
+        nfft = int(nfft)
+
+    if noverlap is None:
+        noverlap = nperseg//2
+    else:
+        noverlap = int(noverlap)
+    if noverlap >= nperseg:
+        raise ValueError('noverlap must be less than nperseg.')
+    nstep = nperseg - noverlap
+
+    # Padding occurs after boundary extension, so that the extended signal ends
+    # in zeros, instead of introducing an impulse at the end.
+    # I.e. if x = [..., 3, 2]
+    # extend then pad -> [..., 3, 2, 2, 3, 0, 0, 0]
+    # pad then extend -> [..., 3, 2, 0, 0, 0, 2, 3]
+
+    if boundary is not None:
+        ext_func = boundary_funcs[boundary]
+        x = ext_func(x, nperseg//2, axis=-1)
+        if not same_data:
+            y = ext_func(y, nperseg//2, axis=-1)
+
+    if padded:
+        # Pad to integer number of windowed segments
+        # I.e. make x.shape[-1] = nperseg + (nseg-1)*nstep, with integer nseg
+        nadd = (-(x.shape[-1]-nperseg) % nstep) % nperseg
+        zeros_shape = list(x.shape[:-1]) + [nadd]
+        x = np.concatenate((x, np.zeros(zeros_shape)), axis=-1)
+        if not same_data:
+            zeros_shape = list(y.shape[:-1]) + [nadd]
+            y = np.concatenate((y, np.zeros(zeros_shape)), axis=-1)
+
+    # Handle detrending and window functions
+    if not detrend:
+        def detrend_func(d):
+            return d
+    elif not hasattr(detrend, '__call__'):
+        def detrend_func(d):
+            return _signaltools.detrend(d, type=detrend, axis=-1)
+    elif axis != -1:
+        # Wrap this function so that it receives a shape that it could
+        # reasonably expect to receive.
+        def detrend_func(d):
+            d = np.moveaxis(d, -1, axis)
+            d = detrend(d)
+            return np.moveaxis(d, axis, -1)
+    else:
+        detrend_func = detrend
+
+    if np.result_type(win, np.complex64) != outdtype:
+        win = win.astype(outdtype)
+
+    if scaling == 'density':
+        scale = 1.0 / (fs * (win*win).sum())
+    elif scaling == 'spectrum':
+        scale = 1.0 / win.sum()**2
+    else:
+        raise ValueError(f'Unknown scaling: {scaling!r}')
+
+    if mode == 'stft':
+        scale = np.sqrt(scale)
+
+    if return_onesided:
+        if np.iscomplexobj(x):
+            sides = 'twosided'
+            warnings.warn('Input data is complex, switching to return_onesided=False',
+                          stacklevel=3)
+        else:
+            sides = 'onesided'
+            if not same_data:
+                if np.iscomplexobj(y):
+                    sides = 'twosided'
+                    warnings.warn('Input data is complex, switching to '
+                                  'return_onesided=False',
+                                  stacklevel=3)
+    else:
+        sides = 'twosided'
+
+    if sides == 'twosided':
+        freqs = sp_fft.fftfreq(nfft, 1/fs)
+    elif sides == 'onesided':
+        freqs = sp_fft.rfftfreq(nfft, 1/fs)
+
+    # Perform the windowed FFTs
+    result = _fft_helper(x, win, detrend_func, nperseg, noverlap, nfft, sides)
+
+    if not same_data:
+        # All the same operations on the y data
+        result_y = _fft_helper(y, win, detrend_func, nperseg, noverlap, nfft,
+                               sides)
+        result = np.conjugate(result) * result_y
+    elif mode == 'psd':
+        result = np.conjugate(result) * result
+
+    result *= scale
+    if sides == 'onesided' and mode == 'psd':
+        if nfft % 2:
+            result[..., 1:] *= 2
+        else:
+            # Last point is unpaired Nyquist freq point, don't double
+            result[..., 1:-1] *= 2
+
+    time = np.arange(nperseg/2, x.shape[-1] - nperseg/2 + 1,
+                     nperseg - noverlap)/float(fs)
+    if boundary is not None:
+        time -= (nperseg/2) / fs
+
+    result = result.astype(outdtype)
+
+    # All imaginary parts are zero anyways
+    if same_data and mode != 'stft':
+        result = result.real
+
+    # Output is going to have new last axis for time/window index, so a
+    # negative axis index shifts down one
+    if axis < 0:
+        axis -= 1
+
+    # Roll frequency axis back to axis where the data came from
+    result = np.moveaxis(result, -1, axis)
+
+    return freqs, time, result
+
+
+def _fft_helper(x, win, detrend_func, nperseg, noverlap, nfft, sides):
+    """
+    Calculate windowed FFT, for internal use by
+    `scipy.signal._spectral_helper`.
+
+    .. legacy:: function
+
+        This function is solely used by the legacy `_spectral_helper` function,
+        which is located also in this file.
+
+    This is a helper function that does the main FFT calculation for
+    `_spectral helper`. All input validation is performed there, and the
+    data axis is assumed to be the last axis of x. It is not designed to
+    be called externally. The windows are not averaged over; the result
+    from each window is returned.
+
+    Returns
+    -------
+    result : ndarray
+        Array of FFT data
+
+    Notes
+    -----
+    Adapted from matplotlib.mlab
+
+    .. versionadded:: 0.16.0
+    """
+    # Created sliding window view of array
+    if nperseg == 1 and noverlap == 0:
+        result = x[..., np.newaxis]
+    else:
+        step = nperseg - noverlap
+        result = np.lib.stride_tricks.sliding_window_view(
+            x, window_shape=nperseg, axis=-1, writeable=True
+        )
+        result = result[..., 0::step, :]
+
+    # Detrend each data segment individually
+    result = detrend_func(result)
+
+    # Apply window by multiplication
+    result = win * result
+
+    # Perform the fft. Acts on last axis by default. Zero-pads automatically
+    if sides == 'twosided':
+        func = sp_fft.fft
+    else:
+        result = result.real
+        func = sp_fft.rfft
+    result = func(result, n=nfft)
+
+    return result
+
+
+def _triage_segments(window, nperseg, input_length):
+    """
+    Parses window and nperseg arguments for spectrogram and _spectral_helper.
+    This is a helper function, not meant to be called externally.
+
+    .. legacy:: function
+
+        This function is soley used by the legacy functions `spectrogram` and
+        `_spectral_helper` (which are also in this file).
+
+    Parameters
+    ----------
+    window : str, tuple, or ndarray
+        If window is specified by a string or tuple and nperseg is not
+        specified, nperseg is set to the default of 256 and returns a window of
+        that length.
+        If instead the window is array_like and nperseg is not specified, then
+        nperseg is set to the length of the window. A ValueError is raised if
+        the user supplies both an array_like window and a value for nperseg but
+        nperseg does not equal the length of the window.
+
+    nperseg : int
+        Length of each segment
+
+    input_length: int
+        Length of input signal, i.e. x.shape[-1]. Used to test for errors.
+
+    Returns
+    -------
+    win : ndarray
+        window. If function was called with string or tuple than this will hold
+        the actual array used as a window.
+
+    nperseg : int
+        Length of each segment. If window is str or tuple, nperseg is set to
+        256. If window is array_like, nperseg is set to the length of the
+        window.
+    """
+    # parse window; if array like, then set nperseg = win.shape
+    if isinstance(window, str) or isinstance(window, tuple):
+        # if nperseg not specified
+        if nperseg is None:
+            nperseg = 256  # then change to default
+        if nperseg > input_length:
+            warnings.warn(f'nperseg = {nperseg:d} is greater than input length '
+                          f' = {input_length:d}, using nperseg = {input_length:d}',
+                          stacklevel=3)
+            nperseg = input_length
+        win = get_window(window, nperseg)
+    else:
+        win = np.asarray(window)
+        if len(win.shape) != 1:
+            raise ValueError('window must be 1-D')
+        if input_length < win.shape[-1]:
+            raise ValueError('window is longer than input signal')
+        if nperseg is None:
+            nperseg = win.shape[0]
+        elif nperseg is not None:
+            if nperseg != win.shape[0]:
+                raise ValueError("value specified for nperseg is different"
+                                 " from length of window")
+    return win, nperseg
+
+
+def _median_bias(n):
+    """
+    Returns the bias of the median of a set of periodograms relative to
+    the mean.
+
+    See Appendix B from [1]_ for details.
+
+    Parameters
+    ----------
+    n : int
+        Numbers of periodograms being averaged.
+
+    Returns
+    -------
+    bias : float
+        Calculated bias.
+
+    References
+    ----------
+    .. [1] B. Allen, W.G. Anderson, P.R. Brady, D.A. Brown, J.D.E. Creighton.
+           "FINDCHIRP: an algorithm for detection of gravitational waves from
+           inspiraling compact binaries", Physical Review D 85, 2012,
+           :arxiv:`gr-qc/0509116`
+    """
+    ii_2 = 2 * np.arange(1., (n-1) // 2 + 1)
+    return 1 + np.sum(1. / (ii_2 + 1) - 1. / ii_2)
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/_spline.cpython-312-x86_64-linux-gnu.so b/venv/lib/python3.12/site-packages/scipy/signal/_spline.cpython-312-x86_64-linux-gnu.so
new file mode 100644
index 0000000000000000000000000000000000000000..11ff1cada50622e82b0d8733c599bef355109fa6
Binary files /dev/null and b/venv/lib/python3.12/site-packages/scipy/signal/_spline.cpython-312-x86_64-linux-gnu.so differ
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/_spline.pyi b/venv/lib/python3.12/site-packages/scipy/signal/_spline.pyi
new file mode 100644
index 0000000000000000000000000000000000000000..c4225577db7ea188a2add225ecec1fbec855de06
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/_spline.pyi
@@ -0,0 +1,34 @@
+
+import numpy as np
+from numpy.typing import NDArray
+
+FloatingArray = NDArray[np.float32] | NDArray[np.float64]
+ComplexArray = NDArray[np.complex64] | NDArray[np.complex128]
+FloatingComplexArray = FloatingArray | ComplexArray
+
+
+def symiirorder1_ic(signal: FloatingComplexArray,
+                    c0: float,
+                    z1: float,
+                    precision: float) -> FloatingComplexArray:
+    ...
+
+
+def symiirorder2_ic_fwd(signal: FloatingArray,
+                        r: float,
+                        omega: float,
+                        precision: float) -> FloatingArray:
+    ...
+
+
+def symiirorder2_ic_bwd(signal: FloatingArray,
+                        r: float,
+                        omega: float,
+                        precision: float) -> FloatingArray:
+    ...
+
+
+def sepfir2d(input: FloatingComplexArray,
+             hrow: FloatingComplexArray,
+             hcol: FloatingComplexArray) -> FloatingComplexArray:
+    ...
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/_spline_filters.py b/venv/lib/python3.12/site-packages/scipy/signal/_spline_filters.py
new file mode 100644
index 0000000000000000000000000000000000000000..53100b55bf1e8adab44645db0fe0485e59fb3e69
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/_spline_filters.py
@@ -0,0 +1,847 @@
+import math
+
+from numpy import (zeros_like, array, tan, arange, floor,
+                   r_, atleast_1d, greater, cos, add, sin,
+                   moveaxis, abs, complex64, float32)
+import numpy as np
+
+from scipy._lib._array_api import array_namespace, xp_promote
+
+from scipy._lib._util import normalize_axis_index
+
+# From splinemodule.c
+from ._spline import sepfir2d, symiirorder1_ic, symiirorder2_ic_fwd, symiirorder2_ic_bwd
+from ._signaltools import lfilter, sosfilt, lfiltic
+from ._arraytools import axis_slice, axis_reverse
+
+from scipy.interpolate import BSpline
+
+
+__all__ = ['spline_filter', 'gauss_spline',
+           'cspline1d', 'qspline1d', 'qspline2d', 'cspline2d',
+           'cspline1d_eval', 'qspline1d_eval', 'symiirorder1', 'symiirorder2']
+
+
+def spline_filter(Iin, lmbda=5.0):
+    """Smoothing spline (cubic) filtering of a rank-2 array.
+
+    Filter an input data set, `Iin`, using a (cubic) smoothing spline of
+    fall-off `lmbda`.
+
+    Parameters
+    ----------
+    Iin : array_like
+        input data set
+    lmbda : float, optional
+        spline smoothing fall-off value, default is `5.0`.
+
+    Returns
+    -------
+    res : ndarray
+        filtered input data
+
+    Examples
+    --------
+    We can filter an multi dimensional signal (ex: 2D image) using cubic
+    B-spline filter:
+
+    >>> import numpy as np
+    >>> from scipy.signal import spline_filter
+    >>> import matplotlib.pyplot as plt
+    >>> orig_img = np.eye(20)  # create an image
+    >>> orig_img[10, :] = 1.0
+    >>> sp_filter = spline_filter(orig_img, lmbda=0.1)
+    >>> f, ax = plt.subplots(1, 2, sharex=True)
+    >>> for ind, data in enumerate([[orig_img, "original image"],
+    ...                             [sp_filter, "spline filter"]]):
+    ...     ax[ind].imshow(data[0], cmap='gray_r')
+    ...     ax[ind].set_title(data[1])
+    >>> plt.tight_layout()
+    >>> plt.show()
+
+    """
+    xp = array_namespace(Iin)
+    Iin = np.asarray(Iin)
+
+    if Iin.dtype not in [np.float32, np.float64, np.complex64, np.complex128]:
+        raise TypeError(f"Invalid data type for Iin: {Iin.dtype = }")
+
+    # XXX: note that complex-valued computations are done in single precision
+    # this is historic, and the root reason is unclear,
+    # see https://github.com/scipy/scipy/issues/9209
+    # Attempting to work in complex double precision leads to symiirorder1
+    # failing to converge for the boundary conditions.
+    intype = Iin.dtype
+    hcol = array([1.0, 4.0, 1.0], np.float32) / 6.0
+    if intype == np.complex128:
+        Iin = Iin.astype(np.complex64)
+
+    ck = cspline2d(Iin, lmbda)
+    out = sepfir2d(ck, hcol, hcol)
+    out = out.astype(intype)
+    return xp.asarray(out)
+
+
+_splinefunc_cache = {}
+
+
+def gauss_spline(x, n):
+    r"""Gaussian approximation to B-spline basis function of order n.
+
+    Parameters
+    ----------
+    x : array_like
+        a knot vector
+    n : int
+        The order of the spline. Must be non-negative, i.e., n >= 0
+
+    Returns
+    -------
+    res : ndarray
+        B-spline basis function values approximated by a zero-mean Gaussian
+        function.
+
+    Notes
+    -----
+    The B-spline basis function can be approximated well by a zero-mean
+    Gaussian function with standard-deviation equal to :math:`\sigma=(n+1)/12`
+    for large `n` :
+
+    .. math::  \frac{1}{\sqrt {2\pi\sigma^2}}exp(-\frac{x^2}{2\sigma})
+
+    References
+    ----------
+    .. [1] Bouma H., Vilanova A., Bescos J.O., ter Haar Romeny B.M., Gerritsen
+       F.A. (2007) Fast and Accurate Gaussian Derivatives Based on B-Splines. In:
+       Sgallari F., Murli A., Paragios N. (eds) Scale Space and Variational
+       Methods in Computer Vision. SSVM 2007. Lecture Notes in Computer
+       Science, vol 4485. Springer, Berlin, Heidelberg.
+
+    Examples
+    --------
+    We can calculate B-Spline basis functions approximated by a Gaussian
+    distribution:
+
+    >>> import numpy as np
+    >>> from scipy.signal import gauss_spline
+    >>> knots = np.array([-1.0, 0.0, -1.0])
+    >>> gauss_spline(knots, 3)
+    array([0.15418033, 0.6909883, 0.15418033])  # may vary
+
+    """
+    xp = array_namespace(x)
+    x = xp.asarray(x)
+    signsq = (n + 1) / 12.0
+    return 1 / math.sqrt(2 * math.pi * signsq) * xp.exp(-x ** 2 / 2 / signsq)
+
+
+def _cubic(x):
+    xp = array_namespace(x)
+
+    x = np.asarray(x, dtype=float)
+    b = BSpline.basis_element([-2, -1, 0, 1, 2], extrapolate=False)
+    out = b(x)
+    out[(x < -2) | (x > 2)] = 0
+    return xp.asarray(out)
+
+
+def _quadratic(x):
+    xp = array_namespace(x)
+
+    x = abs(np.asarray(x, dtype=float))
+    b = BSpline.basis_element([-1.5, -0.5, 0.5, 1.5], extrapolate=False)
+    out = b(x)
+    out[(x < -1.5) | (x > 1.5)] = 0
+    return xp.asarray(out)
+
+
+def _coeff_smooth(lam):
+    xi = 1 - 96 * lam + 24 * lam * math.sqrt(3 + 144 * lam)
+    omeg = math.atan2(math.sqrt(144 * lam - 1), math.sqrt(xi))
+    rho = (24 * lam - 1 - math.sqrt(xi)) / (24 * lam)
+    rho = rho * math.sqrt((48 * lam + 24 * lam * math.sqrt(3 + 144 * lam)) / xi)
+    return rho, omeg
+
+
+def _hc(k, cs, rho, omega):
+    return (cs / sin(omega) * (rho ** k) * sin(omega * (k + 1)) *
+            greater(k, -1))
+
+
+def _hs(k, cs, rho, omega):
+    c0 = (cs * cs * (1 + rho * rho) / (1 - rho * rho) /
+          (1 - 2 * rho * rho * cos(2 * omega) + rho ** 4))
+    gamma = (1 - rho * rho) / (1 + rho * rho) / tan(omega)
+    ak = abs(k)
+    return c0 * rho ** ak * (cos(omega * ak) + gamma * sin(omega * ak))
+
+
+def _cubic_smooth_coeff(signal, lamb):
+    signal = np.asarray(signal)
+
+    rho, omega = _coeff_smooth(lamb)
+    cs = 1 - 2 * rho * cos(omega) + rho * rho
+    K = len(signal)
+    k = arange(K)
+
+    zi_2 = (_hc(0, cs, rho, omega) * signal[0] +
+            add.reduce(_hc(k + 1, cs, rho, omega) * signal))
+    zi_1 = (_hc(0, cs, rho, omega) * signal[0] +
+            _hc(1, cs, rho, omega) * signal[1] +
+            add.reduce(_hc(k + 2, cs, rho, omega) * signal))
+
+    # Forward filter:
+    # for n in range(2, K):
+    #     yp[n] = (cs * signal[n] + 2 * rho * cos(omega) * yp[n - 1] -
+    #              rho * rho * yp[n - 2])
+    zi = lfiltic(cs, r_[1, -2 * rho * cos(omega), rho * rho], r_[zi_1, zi_2])
+    zi = zi.reshape(1, -1)
+
+    sos = r_[cs, 0, 0, 1, -2 * rho * cos(omega), rho * rho]
+    sos = sos.reshape(1, -1)
+
+    yp, _ = sosfilt(sos, signal[2:], zi=zi)
+    yp = r_[zi_2, zi_1, yp]
+
+    # Reverse filter:
+    # for n in range(K - 3, -1, -1):
+    #     y[n] = (cs * yp[n] + 2 * rho * cos(omega) * y[n + 1] -
+    #             rho * rho * y[n + 2])
+
+    zi_2 = add.reduce((_hs(k, cs, rho, omega) +
+                       _hs(k + 1, cs, rho, omega)) * signal[::-1])
+    zi_1 = add.reduce((_hs(k - 1, cs, rho, omega) +
+                       _hs(k + 2, cs, rho, omega)) * signal[::-1])
+
+    zi = lfiltic(cs, r_[1, -2 * rho * cos(omega), rho * rho], r_[zi_1, zi_2])
+    zi = zi.reshape(1, -1)
+    y, _ = sosfilt(sos, yp[-3::-1], zi=zi)
+    y = r_[y[::-1], zi_1, zi_2]
+    return y
+
+
+def _cubic_coeff(signal):
+    signal = np.asarray(signal)
+
+    zi = -2 + math.sqrt(3)
+    K = len(signal)
+    powers = zi ** np.arange(K)
+
+    if K == 1:
+        yplus = signal[0] + zi * add.reduce(powers * signal)
+        output = zi / (zi - 1) * yplus
+        return atleast_1d(output)
+
+    # Forward filter:
+    # yplus[0] = signal[0] + zi * add.reduce(powers * signal)
+    # for k in range(1, K):
+    #     yplus[k] = signal[k] + zi * yplus[k - 1]
+
+    state = lfiltic(1, np.r_[1, -zi], np.atleast_1d(add.reduce(powers * signal)))
+
+    b = np.ones(1)
+    a = np.r_[1, -zi]
+    yplus, _ = lfilter(b, a, signal, zi=state)
+
+    # Reverse filter:
+    # output[K - 1] = zi / (zi - 1) * yplus[K - 1]
+    # for k in range(K - 2, -1, -1):
+    #     output[k] = zi * (output[k + 1] - yplus[k])
+    out_last = zi / (zi - 1) * yplus[K - 1]
+    state = lfiltic(-zi, r_[1, -zi], np.atleast_1d(out_last))
+
+    b = np.asarray([-zi])
+    output, _ = lfilter(b, a, yplus[-2::-1], zi=state)
+    output = np.r_[output[::-1], out_last]
+    return output * 6.0
+
+
+def _quadratic_coeff(signal):
+    signal = np.asarray(signal)
+
+    zi = -3 + 2 * math.sqrt(2.0)
+    K = len(signal)
+    powers = zi ** np.arange(K)
+
+    if K == 1:
+        yplus = signal[0] + zi * np.add.reduce(powers * signal)
+        output = zi / (zi - 1) * yplus
+        return atleast_1d(output)
+
+    # Forward filter:
+    # yplus[0] = signal[0] + zi * add.reduce(powers * signal)
+    # for k in range(1, K):
+    #     yplus[k] = signal[k] + zi * yplus[k - 1]
+
+    state = lfiltic(1, np.r_[1, -zi], np.atleast_1d(np.add.reduce(powers * signal)))
+
+    b = np.ones(1)
+    a = np.r_[1, -zi]
+    yplus, _ = lfilter(b, a, signal, zi=state)
+
+    # Reverse filter:
+    # output[K - 1] = zi / (zi - 1) * yplus[K - 1]
+    # for k in range(K - 2, -1, -1):
+    #     output[k] = zi * (output[k + 1] - yplus[k])
+    out_last = zi / (zi - 1) * yplus[K - 1]
+    state = lfiltic(-zi, r_[1, -zi], np.atleast_1d(out_last))
+
+    b = np.asarray([-zi])
+    output, _ = lfilter(b, a, yplus[-2::-1], zi=state)
+    output = np.r_[output[::-1], out_last]
+    return output * 8.0
+
+
+def compute_root_from_lambda(lamb):
+    tmp = math.sqrt(3 + 144 * lamb)
+    xi = 1 - 96 * lamb + 24 * lamb * tmp
+    omega = math.atan(math.sqrt((144 * lamb - 1.0) / xi))
+    tmp2 = math.sqrt(xi)
+    r = ((24 * lamb - 1 - tmp2) / (24 * lamb) *
+         math.sqrt(48*lamb + 24 * lamb * tmp) / tmp2)
+    return r, omega
+
+
+def cspline1d(signal, lamb=0.0):
+    """
+    Compute cubic spline coefficients for rank-1 array.
+
+    Find the cubic spline coefficients for a 1-D signal assuming
+    mirror-symmetric boundary conditions. To obtain the signal back from the
+    spline representation mirror-symmetric-convolve these coefficients with a
+    length 3 FIR window [1.0, 4.0, 1.0]/ 6.0 .
+
+    Parameters
+    ----------
+    signal : ndarray
+        A rank-1 array representing samples of a signal.
+    lamb : float, optional
+        Smoothing coefficient, default is 0.0.
+
+    Returns
+    -------
+    c : ndarray
+        Cubic spline coefficients.
+
+    See Also
+    --------
+    cspline1d_eval : Evaluate a cubic spline at the new set of points.
+
+    Examples
+    --------
+    We can filter a signal to reduce and smooth out high-frequency noise with
+    a cubic spline:
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.signal import cspline1d, cspline1d_eval
+    >>> rng = np.random.default_rng()
+    >>> sig = np.repeat([0., 1., 0.], 100)
+    >>> sig += rng.standard_normal(len(sig))*0.05  # add noise
+    >>> time = np.linspace(0, len(sig))
+    >>> filtered = cspline1d_eval(cspline1d(sig), time)
+    >>> plt.plot(sig, label="signal")
+    >>> plt.plot(time, filtered, label="filtered")
+    >>> plt.legend()
+    >>> plt.show()
+
+    """
+    xp = array_namespace(signal)
+
+    if lamb != 0.0:
+        ret = _cubic_smooth_coeff(signal, lamb)
+    else:
+        ret = _cubic_coeff(signal)
+    return xp.asarray(ret)
+
+
+def qspline1d(signal, lamb=0.0):
+    """Compute quadratic spline coefficients for rank-1 array.
+
+    Parameters
+    ----------
+    signal : ndarray
+        A rank-1 array representing samples of a signal.
+    lamb : float, optional
+        Smoothing coefficient (must be zero for now).
+
+    Returns
+    -------
+    c : ndarray
+        Quadratic spline coefficients.
+
+    See Also
+    --------
+    qspline1d_eval : Evaluate a quadratic spline at the new set of points.
+
+    Notes
+    -----
+    Find the quadratic spline coefficients for a 1-D signal assuming
+    mirror-symmetric boundary conditions. To obtain the signal back from the
+    spline representation mirror-symmetric-convolve these coefficients with a
+    length 3 FIR window [1.0, 6.0, 1.0]/ 8.0 .
+
+    Examples
+    --------
+    We can filter a signal to reduce and smooth out high-frequency noise with
+    a quadratic spline:
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.signal import qspline1d, qspline1d_eval
+    >>> rng = np.random.default_rng()
+    >>> sig = np.repeat([0., 1., 0.], 100)
+    >>> sig += rng.standard_normal(len(sig))*0.05  # add noise
+    >>> time = np.linspace(0, len(sig))
+    >>> filtered = qspline1d_eval(qspline1d(sig), time)
+    >>> plt.plot(sig, label="signal")
+    >>> plt.plot(time, filtered, label="filtered")
+    >>> plt.legend()
+    >>> plt.show()
+
+    """
+    xp = array_namespace(signal)
+
+    if lamb != 0.0:
+        raise ValueError("Smoothing quadratic splines not supported yet.")
+    else:
+        return xp.asarray(_quadratic_coeff(signal))
+
+
+def collapse_2d(x, axis):
+    x = moveaxis(x, axis, -1)
+    x_shape = x.shape
+    x = x.reshape(-1, x.shape[-1])
+    if not x.flags.c_contiguous:
+        x = x.copy()
+    return x, x_shape
+
+
+def symiirorder_nd(func, input, *args, axis=-1, **kwargs):
+    axis = normalize_axis_index(axis, input.ndim)
+    input_shape = input.shape
+    input_ndim = input.ndim
+    if input.ndim > 1:
+        input, input_shape = collapse_2d(input, axis)
+
+    out = func(input, *args, **kwargs)
+
+    if input_ndim > 1:
+        out = out.reshape(input_shape)
+        out = moveaxis(out, -1, axis)
+        if not out.flags.c_contiguous:
+            out = out.copy()
+    return out
+
+
+def qspline2d(signal, lamb=0.0, precision=-1.0):
+    """
+    Coefficients for 2-D quadratic (2nd order) B-spline.
+
+    Return the second-order B-spline coefficients over a regularly spaced
+    input grid for the two-dimensional input image.
+
+    Parameters
+    ----------
+    signal : ndarray
+        The input signal.
+    lamb : float
+        Specifies the amount of smoothing in the transfer function.
+    precision : float
+        Specifies the precision for computing the infinite sum needed to apply
+        mirror-symmetric boundary conditions.
+
+    Returns
+    -------
+    output : ndarray
+        The filtered signal.
+    """
+    if precision < 0.0 or precision >= 1.0:
+        if signal.dtype in [float32, complex64]:
+            precision = 1e-3
+        else:
+            precision = 1e-6
+
+    if lamb > 0:
+        raise ValueError('lambda must be negative or zero')
+
+    # normal quadratic spline
+    r = -3 + 2 * math.sqrt(2.0)
+    c0 = -r * 8.0
+    z1 = r
+
+    out = symiirorder_nd(symiirorder1, signal, c0, z1, precision, axis=-1)
+    out = symiirorder_nd(symiirorder1, out, c0, z1, precision, axis=0)
+    return out
+
+
+def cspline2d(signal, lamb=0.0, precision=-1.0):
+    """
+    Coefficients for 2-D cubic (3rd order) B-spline.
+
+    Return the third-order B-spline coefficients over a regularly spaced
+    input grid for the two-dimensional input image.
+
+    Parameters
+    ----------
+    signal : ndarray
+        The input signal.
+    lamb : float
+        Specifies the amount of smoothing in the transfer function.
+    precision : float
+        Specifies the precision for computing the infinite sum needed to apply
+        mirror-symmetric boundary conditions.
+
+    Returns
+    -------
+    output : ndarray
+        The filtered signal.
+    """
+    xp = array_namespace(signal)
+    signal = np.asarray(signal)
+
+    if precision < 0.0 or precision >= 1.0:
+        if signal.dtype in [np.float32, np.complex64]:
+            precision = 1e-3
+        else:
+            precision = 1e-6
+
+    if lamb <= 1 / 144.0:
+        # Normal cubic spline
+        r = -2 + math.sqrt(3.0)
+        out = symiirorder_nd(
+            symiirorder1, signal, -r * 6.0, r, precision=precision, axis=-1)
+        out = symiirorder_nd(
+            symiirorder1, out, -r * 6.0, r, precision=precision, axis=0)
+        return out
+
+    r, omega = compute_root_from_lambda(lamb)
+    out = symiirorder_nd(symiirorder2, signal, r, omega,
+                         precision=precision, axis=-1)
+    out = symiirorder_nd(symiirorder2, out, r, omega,
+                         precision=precision, axis=0)
+    return xp.asarray(out)
+
+
+def cspline1d_eval(cj, newx, dx=1.0, x0=0):
+    """Evaluate a cubic spline at the new set of points.
+
+    `dx` is the old sample-spacing while `x0` was the old origin. In
+    other-words the old-sample points (knot-points) for which the `cj`
+    represent spline coefficients were at equally-spaced points of::
+
+      oldx = x0 + j*dx  j=0...N-1, with N=len(cj)
+
+    Edges are handled using mirror-symmetric boundary conditions.
+
+    Parameters
+    ----------
+    cj : ndarray
+        cublic spline coefficients
+    newx : ndarray
+        New set of points.
+    dx : float, optional
+        Old sample-spacing, the default value is 1.0.
+    x0 : int, optional
+        Old origin, the default value is 0.
+
+    Returns
+    -------
+    res : ndarray
+        Evaluated a cubic spline points.
+
+    See Also
+    --------
+    cspline1d : Compute cubic spline coefficients for rank-1 array.
+
+    Examples
+    --------
+    We can filter a signal to reduce and smooth out high-frequency noise with
+    a cubic spline:
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.signal import cspline1d, cspline1d_eval
+    >>> rng = np.random.default_rng()
+    >>> sig = np.repeat([0., 1., 0.], 100)
+    >>> sig += rng.standard_normal(len(sig))*0.05  # add noise
+    >>> time = np.linspace(0, len(sig))
+    >>> filtered = cspline1d_eval(cspline1d(sig), time)
+    >>> plt.plot(sig, label="signal")
+    >>> plt.plot(time, filtered, label="filtered")
+    >>> plt.legend()
+    >>> plt.show()
+
+    """
+    xp = array_namespace(cj, newx)
+
+    newx = (np.asarray(newx) - x0) / float(dx)
+    cj = np.asarray(cj)
+
+    if cj.size == 0:
+        raise ValueError("Spline coefficients 'cj' must not be empty.")
+
+    res = zeros_like(newx, dtype=cj.dtype)
+    if res.size == 0:
+        return xp.asarray(res)
+    N = len(cj)
+    cond1 = newx < 0
+    cond2 = newx > (N - 1)
+    cond3 = ~(cond1 | cond2)
+    # handle general mirror-symmetry
+    res[cond1] = cspline1d_eval(cj, -newx[cond1])
+    res[cond2] = cspline1d_eval(cj, 2 * (N - 1) - newx[cond2])
+    newx = newx[cond3]
+    if newx.size == 0:
+        return xp.asarray(res)
+    result = zeros_like(newx, dtype=cj.dtype)
+    jlower = floor(newx - 2).astype(int) + 1
+    for i in range(4):
+        thisj = jlower + i
+        indj = thisj.clip(0, N - 1)  # handle edge cases
+        result += cj[indj] * _cubic(newx - thisj)
+    res[cond3] = result
+    return xp.asarray(res)
+
+
+def qspline1d_eval(cj, newx, dx=1.0, x0=0):
+    """Evaluate a quadratic spline at the new set of points.
+
+    Parameters
+    ----------
+    cj : ndarray
+        Quadratic spline coefficients
+    newx : ndarray
+        New set of points.
+    dx : float, optional
+        Old sample-spacing, the default value is 1.0.
+    x0 : int, optional
+        Old origin, the default value is 0.
+
+    Returns
+    -------
+    res : ndarray
+        Evaluated a quadratic spline points.
+
+    See Also
+    --------
+    qspline1d : Compute quadratic spline coefficients for rank-1 array.
+
+    Notes
+    -----
+    `dx` is the old sample-spacing while `x0` was the old origin. In
+    other-words the old-sample points (knot-points) for which the `cj`
+    represent spline coefficients were at equally-spaced points of::
+
+      oldx = x0 + j*dx  j=0...N-1, with N=len(cj)
+
+    Edges are handled using mirror-symmetric boundary conditions.
+
+    Examples
+    --------
+    We can filter a signal to reduce and smooth out high-frequency noise with
+    a quadratic spline:
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.signal import qspline1d, qspline1d_eval
+    >>> rng = np.random.default_rng()
+    >>> sig = np.repeat([0., 1., 0.], 100)
+    >>> sig += rng.standard_normal(len(sig))*0.05  # add noise
+    >>> time = np.linspace(0, len(sig))
+    >>> filtered = qspline1d_eval(qspline1d(sig), time)
+    >>> plt.plot(sig, label="signal")
+    >>> plt.plot(time, filtered, label="filtered")
+    >>> plt.legend()
+    >>> plt.show()
+
+    """
+    xp = array_namespace(newx, cj)
+
+    newx = (np.asarray(newx) - x0) / dx
+    res = np.zeros_like(newx)
+    if res.size == 0:
+        return xp.asarray(res)
+
+    cj = np.asarray(cj)
+    if cj.size == 0:
+        raise ValueError("Spline coefficients 'cj' must not be empty.")
+    
+    N = len(cj)
+    cond1 = newx < 0
+    cond2 = newx > (N - 1)
+    cond3 = ~(cond1 | cond2)
+    # handle general mirror-symmetry
+    res[cond1] = qspline1d_eval(cj, -newx[cond1])
+    res[cond2] = qspline1d_eval(cj, 2 * (N - 1) - newx[cond2])
+    newx = newx[cond3]
+    if newx.size == 0:
+        return xp.asarray(res)
+    result = zeros_like(newx)
+    jlower = floor(newx - 1.5).astype(int) + 1
+    for i in range(3):
+        thisj = jlower + i
+        indj = thisj.clip(0, N - 1)  # handle edge cases
+        result += cj[indj] * _quadratic(newx - thisj)
+    res[cond3] = result
+    return xp.asarray(res)
+
+
+def symiirorder1(signal, c0, z1, precision=-1.0):
+    """
+    Implement a smoothing IIR filter with mirror-symmetric boundary conditions
+    using a cascade of first-order sections.
+
+    The second section uses a reversed sequence.  This implements a system with
+    the following transfer function and mirror-symmetric boundary conditions::
+
+                           c0
+           H(z) = ---------------------
+                   (1-z1/z) (1 - z1 z)
+
+    The resulting signal will have mirror symmetric boundary conditions
+    as well.
+
+    Parameters
+    ----------
+    signal : ndarray
+        The input signal. If 2D, then the filter will be applied in a batched
+        fashion across the last axis.
+    c0, z1 : scalar
+        Parameters in the transfer function.
+    precision : float, optional
+        Specifies the precision for calculating initial conditions
+        of the recursive filter based on mirror-symmetric input.
+
+    Returns
+    -------
+    output : ndarray
+        The filtered signal.
+    """
+    xp = array_namespace(signal)
+    signal = xp_promote(signal, force_floating=True, xp=xp)
+    # This function uses C internals
+    signal = np.asarray(signal)
+
+    if abs(z1) >= 1:
+        raise ValueError('|z1| must be less than 1.0')
+
+    if signal.ndim > 2:
+        raise ValueError('Input must be 1D or 2D')
+
+    squeeze_dim = False
+    if signal.ndim == 1:
+        signal = signal[None, :]
+        squeeze_dim = True
+
+    y0 = symiirorder1_ic(signal, z1, precision)
+
+    # Apply first the system 1 / (1 - z1 * z^-1)
+    b = np.ones(1, dtype=signal.dtype)
+    a = np.r_[1, -z1]
+    a = a.astype(signal.dtype)
+
+    # Compute the initial state for lfilter.
+    zii = y0 * z1
+
+    y1, _ = lfilter(b, a, axis_slice(signal, 1), zi=zii)
+    y1 = np.c_[y0, y1]
+
+    # Compute backward symmetric condition and apply the system
+    # c0 / (1 - z1 * z)
+    b = np.asarray([c0], dtype=signal.dtype)
+    out_last = -c0 / (z1 - 1.0) * axis_slice(y1, -1)
+
+    # Compute the initial state for lfilter.
+    zii = out_last * z1
+
+    # Apply the system c0 / (1 - z1 * z) by reversing the output of the previous stage
+    out, _ = lfilter(b, a, axis_slice(y1, -2, step=-1), zi=zii)
+    out = np.c_[axis_reverse(out), out_last]
+
+    if squeeze_dim:
+        out = out[0]
+
+    return xp.asarray(out)
+
+
+def symiirorder2(input, r, omega, precision=-1.0):
+    """
+    Implement a smoothing IIR filter with mirror-symmetric boundary conditions
+    using a cascade of second-order sections.
+
+    The second section uses a reversed sequence.  This implements the following
+    transfer function::
+
+                                  cs^2
+         H(z) = ---------------------------------------
+                (1 - a2/z - a3/z^2) (1 - a2 z - a3 z^2 )
+
+    where::
+
+          a2 = 2 * r * cos(omega)
+          a3 = - r ** 2
+          cs = 1 - 2 * r * cos(omega) + r ** 2
+
+    Parameters
+    ----------
+    input : ndarray
+        The input signal.
+    r, omega : float
+        Parameters in the transfer function.
+    precision : float
+        Specifies the precision for calculating initial conditions
+        of the recursive filter based on mirror-symmetric input.
+
+    Returns
+    -------
+    output : ndarray
+        The filtered signal.
+    """
+    xp = array_namespace(input)
+    input = xp_promote(input, force_floating=True, xp=xp)
+    # This function uses C internals
+    input = np.ascontiguousarray(input)
+
+    if r >= 1.0:
+        raise ValueError('r must be less than 1.0')
+
+    if input.ndim > 2:
+        raise ValueError('Input must be 1D or 2D')
+
+    squeeze_dim = False
+    if input.ndim == 1:
+        input = input[None, :]
+        squeeze_dim = True
+
+    rsq = r * r
+    a2 = 2 * r * math.cos(omega)
+    a3 = -rsq
+    cs = 1 - 2 * r * math.cos(omega) + rsq
+    sos = np.asarray([cs, 0, 0, 1, -a2, -a3], dtype=input.dtype)
+
+    # Find the starting (forward) conditions.
+    ic_fwd = symiirorder2_ic_fwd(input, r, omega, precision)
+
+    # Apply first the system cs / (1 - a2 * z^-1 - a3 * z^-2)
+    # Compute the initial conditions in the form expected by sosfilt
+    # coef = np.asarray([[a3, a2], [0, a3]], dtype=input.dtype)
+    coef = np.asarray([[a3, a2], [0, a3]], dtype=input.dtype)
+    zi = np.matmul(coef, ic_fwd[:, :, None])[:, :, 0]
+
+    y_fwd, _ = sosfilt(sos, axis_slice(input, 2), zi=zi[None])
+    y_fwd = np.c_[ic_fwd, y_fwd]
+
+    # Then compute the symmetric backward starting conditions
+    ic_bwd = symiirorder2_ic_bwd(input, r, omega, precision)
+
+    # Apply the system cs / (1 - a2 * z^1 - a3 * z^2)
+    # Compute the initial conditions in the form expected by sosfilt
+    zi = np.matmul(coef, ic_bwd[:, :, None])[:, :, 0]
+    y, _ = sosfilt(sos, axis_slice(y_fwd, -3, step=-1), zi=zi[None])
+    out = np.c_[axis_reverse(y), axis_reverse(ic_bwd)]
+
+    if squeeze_dim:
+        out = out[0]
+
+    return xp.asarray(out)
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/_support_alternative_backends.py b/venv/lib/python3.12/site-packages/scipy/signal/_support_alternative_backends.py
new file mode 100644
index 0000000000000000000000000000000000000000..87540c013c891fc21612a07ffb6cd58f93b7702c
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/_support_alternative_backends.py
@@ -0,0 +1,391 @@
+import functools
+import types
+from scipy._lib._array_api import (
+    is_cupy, is_jax, scipy_namespace_for, SCIPY_ARRAY_API, xp_capabilities
+)
+
+from ._signal_api import *   # noqa: F403
+from . import _signal_api
+from . import _delegators
+__all__ = _signal_api.__all__
+
+
+MODULE_NAME = 'signal'
+
+# jax.scipy.signal has only partial coverage of scipy.signal, so we keep the list
+# of functions we can delegate to JAX
+# https://jax.readthedocs.io/en/latest/jax.scipy.html
+JAX_SIGNAL_FUNCS = [
+    'fftconvolve', 'convolve', 'convolve2d', 'correlate', 'correlate2d',
+    'csd', 'detrend', 'istft', 'welch'
+]
+
+# some cupyx.scipy.signal functions are incompatible with their scipy counterparts
+CUPY_BLACKLIST = [
+    'abcd_normalize', 'bessel', 'besselap', 'envelope', 'get_window', 'lfilter_zi',
+    'sosfilt_zi', 'remez',
+]
+
+# freqz_sos is a sosfreqz rename, and cupy does not have the new name yet (in v13.x)
+CUPY_RENAMES = {'freqz_sos': 'sosfreqz'}
+
+
+def delegate_xp(delegator, module_name):
+    def inner(func):
+        @functools.wraps(func)
+        def wrapper(*args, **kwds):
+            try:
+                xp = delegator(*args, **kwds)
+            except TypeError:
+                # object arrays
+                if func.__name__ == "tf2ss":
+                    import numpy as np
+                    xp = np
+                else:
+                    raise
+
+            # try delegating to a cupyx/jax namesake
+            if is_cupy(xp) and func.__name__ not in CUPY_BLACKLIST:
+                func_name = CUPY_RENAMES.get(func.__name__, func.__name__)
+
+                # https://github.com/cupy/cupy/issues/8336
+                import importlib
+                cupyx_module = importlib.import_module(f"cupyx.scipy.{module_name}")
+                cupyx_func = getattr(cupyx_module, func_name)
+                kwds.pop('xp', None)
+                return cupyx_func(*args, **kwds)
+            elif is_jax(xp) and func.__name__ in JAX_SIGNAL_FUNCS:
+                spx = scipy_namespace_for(xp)
+                jax_module = getattr(spx, module_name)
+                jax_func = getattr(jax_module, func.__name__)
+                kwds.pop('xp', None)
+                return jax_func(*args, **kwds)
+            else:
+                # the original function
+                return func(*args, **kwds)
+        return wrapper
+    return inner
+
+
+# Although most of these functions currently exist in CuPy and some in JAX,
+# there are no alternative backend tests for any of them in the current
+# test suite. Each will be documented as np_only until tests are added.
+untested = {
+    "argrelextrema",
+    "argrelmax",
+    "argrelmin",
+    "band_stop_obj",
+    "bode",
+    "check_NOLA",
+    "chirp",
+    "coherence",
+    "csd",
+    "czt",
+    "czt_points",
+    "dbode",
+    "dfreqresp",
+    "dlsim",
+    "dstep",
+    "find_peaks",
+    "find_peaks_cwt",
+    "freqresp",
+    "gausspulse",
+    "iirdesign", # There's no reason this shouldn't work. It just needs tests.
+    "istft",
+    "lombscargle",
+    "lsim",
+    "max_len_seq",
+    "peak_prominences",
+    "peak_widths",
+    "periodogram",
+    "place_poles",
+    "sawtooth",
+    "sepfir2d",
+    "ss2tf",
+    "ss2zpk",
+    "step",
+    "sweep_poly",
+    "symiirorder1",
+    "symiirorder2",
+    "tf2ss",
+    "unit_impulse",
+    "welch",
+    "zoom_fft",
+    "zpk2ss",
+}
+
+
+def get_default_capabilities(func_name, delegator):
+    if delegator is None or func_name in untested:
+        return xp_capabilities(np_only=True)
+    return xp_capabilities()
+
+bilinear_extra_note = \
+    """CuPy does not accept complex inputs.
+
+    """
+
+uses_choose_conv_extra_note = \
+    """CuPy does not support inputs with ``ndim>1`` when ``method="auto"``
+    but does support higher dimensional arrays for ``method="direct"``
+    and ``method="fft"``.
+
+    """
+
+resample_poly_extra_note = \
+    """CuPy only supports ``padtype="constant"``.
+
+    """
+
+upfirdn_extra_note = \
+    """CuPy only supports ``mode="constant"`` and ``cval=0.0``.
+
+    """
+
+xord_extra_note = \
+    """The ``torch`` backend on GPU does not support the case where
+    `wp` and `ws` specify a Bandstop filter.
+
+    """
+
+convolve2d_extra_note = \
+    """The JAX backend only supports ``boundary="fill"`` and ``fillvalue=0``.
+
+    """
+
+zpk2tf_extra_note = \
+    """The CuPy and JAX backends both support only 1d input.
+
+    """
+
+abcd_normalize_extra_note = \
+    """The result dtype when all array inputs are of integer dtype is the
+    backend's current default floating point dtype.
+
+    """
+
+capabilities_overrides = {
+    "abcd_normalize": xp_capabilities(extra_note=abcd_normalize_extra_note),
+    "bessel": xp_capabilities(cpu_only=True, jax_jit=False, allow_dask_compute=True),
+    "bilinear": xp_capabilities(cpu_only=True, exceptions=["cupy"],
+                                jax_jit=False, allow_dask_compute=True,
+                                reason="Uses np.polynomial.Polynomial",
+                                extra_note=bilinear_extra_note),
+    "bilinear_zpk": xp_capabilities(cpu_only=True, exceptions=["cupy", "torch"],
+                                    jax_jit=False, allow_dask_compute=True),
+    "butter": xp_capabilities(cpu_only=True, exceptions=["cupy"], jax_jit=False,
+                              allow_dask_compute=True),
+    "buttord": xp_capabilities(cpu_only=True, exceptions=["cupy", "torch"],
+                               jax_jit=False, allow_dask_compute=True,
+                               extra_note=xord_extra_note),
+    "cheb1ord": xp_capabilities(cpu_only=True, exceptions=["cupy", "torch"],
+                                jax_jit=False, allow_dask_compute=True,
+                                extra_note=xord_extra_note),
+    "cheb2ord": xp_capabilities(cpu_only=True, exceptions=["cupy", "torch"],
+                                jax_jit=False, allow_dask_compute=True,
+                                extra_note=xord_extra_note),
+    "cheby1": xp_capabilities(cpu_only=True, exceptions=["cupy"], jax_jit=False,
+                              allow_dask_compute=True),
+
+    "cheby2": xp_capabilities(cpu_only=True, exceptions=["cupy"], jax_jit=False,
+                              allow_dask_compute=True),
+    "cont2discrete": xp_capabilities(np_only=True, exceptions=["cupy"]),
+    "convolve": xp_capabilities(cpu_only=True, exceptions=["cupy", "jax.numpy"],
+                                allow_dask_compute=True,
+                                extra_note=uses_choose_conv_extra_note),
+    "convolve2d": xp_capabilities(cpu_only=True, exceptions=["cupy", "jax.numpy"],
+                                  allow_dask_compute=True,
+                                  extra_note=convolve2d_extra_note),
+    "correlate": xp_capabilities(cpu_only=True, exceptions=["cupy", "jax.numpy"],
+                                 allow_dask_compute=True,
+                                 extra_note=uses_choose_conv_extra_note),
+    "correlate2d": xp_capabilities(cpu_only=True, exceptions=["cupy", "jax.numpy"],
+                                   allow_dask_compute=True,
+                                   extra_note=convolve2d_extra_note),
+    "correlation_lags": xp_capabilities(out_of_scope=True),
+    "cspline1d": xp_capabilities(cpu_only=True, exceptions=["cupy"],
+                                 jax_jit=False, allow_dask_compute=True),
+    "cspline1d_eval": xp_capabilities(cpu_only=True, exceptions=["cupy"],
+                                      jax_jit=False, allow_dask_compute=True),
+    "cspline2d": xp_capabilities(cpu_only=True, exceptions=["cupy"],
+                                 jax_jit=False, allow_dask_compute=True),
+    "deconvolve": xp_capabilities(cpu_only=True, exceptions=["cupy"],
+                                  jax_jit=False, allow_dask_compute=True),
+    "decimate": xp_capabilities(np_only=True, exceptions=["cupy"]),
+    "detrend": xp_capabilities(cpu_only=True, exceptions=["cupy", "jax.numpy"],
+                               allow_dask_compute=True),
+    "dimpulse": xp_capabilities(np_only=True, exceptions=["cupy"]),
+    "dlti": xp_capabilities(np_only=True,
+                            reason="works in CuPy but delegation isn't set up yet"),
+    "ellip": xp_capabilities(cpu_only=True, exceptions=["cupy"], jax_jit=False,
+                             allow_dask_compute=True,
+                             reason="scipy.special.ellipk"),
+    "ellipord": xp_capabilities(cpu_only=True, exceptions=["cupy"],
+                                jax_jit=False, allow_dask_compute=True,
+                                reason="scipy.special.ellipk"),
+    "findfreqs": xp_capabilities(cpu_only=True, exceptions=["cupy", "torch"],
+                                 jax_jit=False, allow_dask_compute=True),
+    "firls": xp_capabilities(cpu_only=True, allow_dask_compute=True, jax_jit=False,
+                             reason="lstsq"),
+    "firwin": xp_capabilities(cpu_only=True, exceptions=["cupy", "torch"],
+                              jax_jit=False, allow_dask_compute=True),
+    "firwin2": xp_capabilities(cpu_only=True, exceptions=["cupy"],
+                               jax_jit=False, allow_dask_compute=True,
+                               reason="firwin uses np.interp"),
+    "fftconvolve": xp_capabilities(cpu_only=True,
+                                   exceptions=["cupy", "jax.numpy", "torch"]),
+    "freqs": xp_capabilities(cpu_only=True, exceptions=["cupy", "torch"],
+                             jax_jit=False, allow_dask_compute=True),
+    "freqs_zpk": xp_capabilities(cpu_only=True, exceptions=["cupy", "torch"],
+                                 jax_jit=False, allow_dask_compute=True),
+    "freqz": xp_capabilities(cpu_only=True, exceptions=["cupy", "torch"],
+                             jax_jit=False, allow_dask_compute=True),
+    "freqz_sos": xp_capabilities(cpu_only=True, exceptions=["cupy", "torch"],
+                                 jax_jit=False, allow_dask_compute=True),
+    "group_delay": xp_capabilities(cpu_only=True, exceptions=["cupy"],
+                                   jax_jit=False, allow_dask_compute=True),
+    "invres": xp_capabilities(np_only=True, exceptions=["cupy"]),
+    "invresz": xp_capabilities(np_only=True, exceptions=["cupy"]),
+    "iircomb": xp_capabilities(xfail_backends=[("jax.numpy", "inaccurate")]),
+    "iirfilter": xp_capabilities(cpu_only=True, exceptions=["cupy", "torch"],
+                                 jax_jit=False, allow_dask_compute=True),
+    "kaiser_atten": xp_capabilities(
+        out_of_scope=True, reason="scalars in, scalars out"
+    ),
+    "kaiser_beta": xp_capabilities(out_of_scope=True, reason="scalars in, scalars out"),
+    "kaiserord": xp_capabilities(out_of_scope=True, reason="scalars in, scalars out"),
+    "lfilter": xp_capabilities(cpu_only=True, exceptions=["cupy"],
+                               allow_dask_compute=True, jax_jit=False),
+    "lfilter_zi": xp_capabilities(cpu_only=True, allow_dask_compute=True,
+                                  jax_jit=False),
+    "lfiltic": xp_capabilities(cpu_only=True, exceptions=["cupy"],
+                               allow_dask_compute=True),
+    "lp2bp": xp_capabilities(cpu_only=True, exceptions=["cupy", "torch"],
+                             allow_dask_compute=True, jax_jit=False),
+    "lp2bp_zpk": xp_capabilities(cpu_only=True, exceptions=["cupy", "torch"],
+                                 allow_dask_compute=True, jax_jit=False),
+    "lp2bs": xp_capabilities(cpu_only=True, exceptions=["cupy", "torch"],
+                             allow_dask_compute=True, jax_jit=False),
+    "lp2bs_zpk": xp_capabilities(cpu_only=True, exceptions=["cupy", "torch"],
+                                 allow_dask_compute=True, jax_jit=False),
+    "lp2lp": xp_capabilities(cpu_only=True, exceptions=["cupy", "torch"],
+                             allow_dask_compute=True, jax_jit=False),
+    "lp2lp_zpk": xp_capabilities(cpu_only=True, exceptions=["cupy", "torch"],
+                                 allow_dask_compute=True, jax_jit=False),
+    "lp2hp": xp_capabilities(cpu_only=True, exceptions=["cupy", "torch"],
+                             allow_dask_compute=True, jax_jit=False),
+    "lp2hp_zpk": xp_capabilities(cpu_only=True, exceptions=["cupy", "torch"],
+                                 allow_dask_compute=True, jax_jit=False),
+    "lti": xp_capabilities(np_only=True,
+                            reason="works in CuPy but delegation isn't set up yet"),
+    "medfilt": xp_capabilities(cpu_only=True, exceptions=["cupy"],
+                               allow_dask_compute=True, jax_jit=False,
+                               reason="uses scipy.ndimage.rank_filter"),
+    "medfilt2d": xp_capabilities(cpu_only=True, exceptions=["cupy"],
+                                 allow_dask_compute=True, jax_jit=False,
+                                 reason="c extension module"),
+    "minimum_phase": xp_capabilities(cpu_only=True, exceptions=["cupy", "torch"],
+                                     allow_dask_compute=True, jax_jit=False),
+    "normalize": xp_capabilities(cpu_only=True, exceptions=["cupy", "torch"],
+                                 jax_jit=False, allow_dask_compute=True),
+    "oaconvolve": xp_capabilities(
+        cpu_only=True, exceptions=["cupy", "torch"],
+        xfail_backends=[("dask.array", "wrong answer")],
+    ),
+    "order_filter": xp_capabilities(cpu_only=True, exceptions=["cupy"],
+                                    allow_dask_compute=True, jax_jit=False,
+                                    reason="uses scipy.ndimage.rank_filter"),
+    "qspline1d": xp_capabilities(cpu_only=True, exceptions=["cupy"],
+                                 jax_jit=False, allow_dask_compute=True),
+    "qspline1d_eval": xp_capabilities(cpu_only=True, exceptions=["cupy"],
+                                      jax_jit=False, allow_dask_compute=True),
+    "qspline2d": xp_capabilities(np_only=True, exceptions=["cupy"]),
+    "remez": xp_capabilities(cpu_only=True, allow_dask_compute=True, jax_jit=False),
+    "resample": xp_capabilities(
+        cpu_only=True, exceptions=["cupy"],
+        skip_backends=[
+            ("dask.array", "XXX something in dask"),
+            ("jax.numpy", "XXX: immutable arrays"),
+        ]
+    ),
+    "resample_poly": xp_capabilities(
+        cpu_only=True, exceptions=["cupy"],
+        jax_jit=False, skip_backends=[("dask.array", "XXX something in dask")],
+        extra_note=resample_poly_extra_note,
+    ),
+    "residue": xp_capabilities(np_only=True, exceptions=["cupy"]),
+    "residuez": xp_capabilities(np_only=True, exceptions=["cupy"]),
+    "savgol_filter": xp_capabilities(cpu_only=True, exceptions=["cupy"],
+                                     jax_jit=False,
+                                     reason="convolve1d is cpu-only"),
+    "sawtooth": xp_capabilities(jax_jit=False,
+                                skip_backends=[("dask.array", "dask tests fail")]),
+    "sepfir2d": xp_capabilities(np_only=True),
+    "sos2zpk": xp_capabilities(cpu_only=True, exceptions=["cupy"], jax_jit=False,
+                               allow_dask_compute=True),
+    "sos2tf": xp_capabilities(cpu_only=True, exceptions=["cupy"], jax_jit=False,
+                              allow_dask_compute=True),
+    "sosfilt": xp_capabilities(cpu_only=True, exceptions=["cupy"], jax_jit=False,
+                               allow_dask_compute=True),
+    "sosfilt_zi": xp_capabilities(cpu_only=True, allow_dask_compute=True,
+                                  jax_jit=False),
+    "sosfiltfilt": xp_capabilities(
+        cpu_only=True, exceptions=["cupy"],
+        skip_backends=[
+            (
+                "dask.array",
+                "sosfiltfilt directly sets shape attributes on arrays"
+                " which dask doesn't like"
+            ),
+            ("torch", "negative strides"),
+            ("jax.numpy", "sosfilt works in-place"),
+        ],
+    ),
+    "sosfreqz": xp_capabilities(cpu_only=True, exceptions=["cupy", "torch"],
+                                jax_jit=False, allow_dask_compute=True),
+    "spline_filter": xp_capabilities(cpu_only=True, exceptions=["cupy"],
+                                     jax_jit=False, allow_dask_compute=True),
+    "tf2sos": xp_capabilities(cpu_only=True, exceptions=["cupy"], jax_jit=False,
+                              allow_dask_compute=True),
+    "tf2zpk": xp_capabilities(cpu_only=True, exceptions=["cupy"], jax_jit=False,
+                              allow_dask_compute=True),
+    "unique_roots": xp_capabilities(np_only=True, exceptions=["cupy"]),
+    "upfirdn": xp_capabilities(cpu_only=True, exceptions=["cupy"], jax_jit=False,
+                               allow_dask_compute=True,
+                               reason="Cython implementation",
+                               extra_note=upfirdn_extra_note),
+    "vectorstrength": xp_capabilities(cpu_only=True, exceptions=["cupy", "torch"],
+                                      allow_dask_compute=True, jax_jit=False),
+    "wiener": xp_capabilities(cpu_only=True, exceptions=["cupy", "jax.numpy"],
+                              allow_dask_compute=True, jax_jit=False,
+                              reason="uses scipy.signal.correlate"),
+    "zpk2sos": xp_capabilities(cpu_only=True, exceptions=["cupy"], jax_jit=False,
+                               allow_dask_compute=True),
+    "zpk2tf": xp_capabilities(cpu_only=True, exceptions=["cupy"], jax_jit=False,
+                              allow_dask_compute=True,
+                              extra_note=zpk2tf_extra_note),
+    "spectrogram": xp_capabilities(out_of_scope=True),  # legacy
+    "stft": xp_capabilities(out_of_scope=True),  # legacy
+    "istft": xp_capabilities(out_of_scope=True),  # legacy
+    "check_COLA": xp_capabilities(out_of_scope=True),  # legacy
+}
+
+
+# ### decorate ###
+for obj_name in _signal_api.__all__:
+    bare_obj = getattr(_signal_api, obj_name)
+    delegator = getattr(_delegators, obj_name + "_signature", None)
+
+    if SCIPY_ARRAY_API and delegator is not None:
+        f = delegate_xp(delegator, MODULE_NAME)(bare_obj)
+    else:
+        f = bare_obj
+
+    if not isinstance(f, types.ModuleType):
+        capabilities = capabilities_overrides.get(
+            obj_name, get_default_capabilities(obj_name, delegator)
+        )
+        f = capabilities(f)  # pyrefly:ignore[not-callable]
+
+    # add the decorated function to the namespace, to be imported in __init__.py
+    vars()[obj_name] = f
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/_upfirdn.py b/venv/lib/python3.12/site-packages/scipy/signal/_upfirdn.py
new file mode 100644
index 0000000000000000000000000000000000000000..d01a3a36b15c0172907a49afb16236cf75b565ab
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/_upfirdn.py
@@ -0,0 +1,219 @@
+# Code adapted from "upfirdn" python library with permission:
+#
+# Copyright (c) 2009, Motorola, Inc
+#
+# All Rights Reserved.
+#
+# Redistribution and use in source and binary forms, with or without
+# modification, are permitted provided that the following conditions are
+# met:
+#
+# * Redistributions of source code must retain the above copyright notice,
+# this list of conditions and the following disclaimer.
+#
+# * Redistributions in binary form must reproduce the above copyright
+# notice, this list of conditions and the following disclaimer in the
+# documentation and/or other materials provided with the distribution.
+#
+# * Neither the name of Motorola nor the names of its contributors may be
+# used to endorse or promote products derived from this software without
+# specific prior written permission.
+#
+# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
+# IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO,
+# THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
+# PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+# CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+# EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+# PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+# PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+# LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+# NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+# SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+import numpy as np
+
+from scipy._lib._array_api import array_namespace
+from ._upfirdn_apply import _output_len, _apply, mode_enum
+
+__all__ = ['upfirdn', '_output_len']
+
+_upfirdn_modes = [
+    'constant', 'wrap', 'edge', 'smooth', 'symmetric', 'reflect',
+    'antisymmetric', 'antireflect', 'line',
+]
+
+
+def _pad_h(h, up):
+    """Store coefficients in a transposed, flipped arrangement.
+
+    For example, suppose upRate is 3, and the
+    input number of coefficients is 10, represented as h[0], ..., h[9].
+
+    Then the internal buffer will look like this::
+
+       h[9], h[6], h[3], h[0],   // flipped phase 0 coefs
+       0,    h[7], h[4], h[1],   // flipped phase 1 coefs (zero-padded)
+       0,    h[8], h[5], h[2],   // flipped phase 2 coefs (zero-padded)
+
+    """
+    h_padlen = len(h) + (-len(h) % up)
+    h_full = np.zeros(h_padlen, h.dtype)
+    h_full[:len(h)] = h
+    h_full = h_full.reshape(-1, up).T[:, ::-1].ravel()
+    return h_full
+
+
+def _check_mode(mode):
+    mode = mode.lower()
+    enum = mode_enum(mode)
+    return enum
+
+
+class _UpFIRDn:
+    """Helper for resampling."""
+
+    def __init__(self, h, x_dtype, up, down):
+        h = np.asarray(h)
+        if h.ndim != 1 or h.size == 0:
+            raise ValueError('h must be 1-D with non-zero length')
+        self._output_type = np.result_type(h.dtype, x_dtype, np.float32)
+        h = np.asarray(h, self._output_type)
+        self._up = int(up)
+        self._down = int(down)
+        if self._up < 1 or self._down < 1:
+            raise ValueError('Both up and down must be >= 1')
+        # This both transposes, and "flips" each phase for filtering
+        self._h_trans_flip = _pad_h(h, self._up)
+        self._h_trans_flip = np.ascontiguousarray(self._h_trans_flip)
+        self._h_len_orig = len(h)
+
+    def apply_filter(self, x, axis=-1, mode='constant', cval=0):
+        """Apply the prepared filter to the specified axis of N-D signal x."""
+        output_len = _output_len(self._h_len_orig, x.shape[axis],
+                                 self._up, self._down)
+        # Explicit use of np.int64 for output_shape dtype avoids OverflowError
+        # when allocating large array on platforms where intp is 32 bits.
+        output_shape = np.asarray(x.shape, dtype=np.int64)
+        output_shape[axis] = output_len
+        out = np.zeros(output_shape, dtype=self._output_type, order='C')
+        axis = axis % x.ndim
+        mode = _check_mode(mode)
+        _apply(np.asarray(x, self._output_type),
+               self._h_trans_flip, out,
+               self._up, self._down, axis, mode, cval)
+        return out
+
+
+def upfirdn(h, x, up=1, down=1, axis=-1, mode='constant', cval=0):
+    """Upsample, FIR filter, and downsample.
+
+    Parameters
+    ----------
+    h : array_like
+        1-D FIR (finite-impulse response) filter coefficients.
+    x : array_like
+        Input signal array.
+    up : int, optional
+        Upsampling rate. Default is 1.
+    down : int, optional
+        Downsampling rate. Default is 1.
+    axis : int, optional
+        The axis of the input data array along which to apply the
+        linear filter. The filter is applied to each subarray along
+        this axis. Default is -1.
+    mode : str, optional
+        The signal extension mode to use. The set
+        ``{"constant", "symmetric", "reflect", "edge", "wrap"}`` correspond to
+        modes provided by `numpy.pad`. ``"smooth"`` implements a smooth
+        extension by extending based on the slope of the last 2 points at each
+        end of the array. ``"antireflect"`` and ``"antisymmetric"`` are
+        anti-symmetric versions of ``"reflect"`` and ``"symmetric"``. The mode
+        `"line"` extends the signal based on a linear trend defined by the
+        first and last points along the ``axis``.
+
+        .. versionadded:: 1.4.0
+    cval : float, optional
+        The constant value to use when ``mode == "constant"``.
+
+        .. versionadded:: 1.4.0
+
+    Returns
+    -------
+    y : ndarray
+        The output signal array. Dimensions will be the same as `x` except
+        for along `axis`, which will change size according to the `h`,
+        `up`,  and `down` parameters.
+
+    Notes
+    -----
+    The algorithm is an implementation of the block diagram shown on page 129
+    of the Vaidyanathan text [1]_ (Figure 4.3-8d).
+
+    The direct approach of upsampling by factor of P with zero insertion,
+    FIR filtering of length ``N``, and downsampling by factor of Q is
+    O(N*Q) per output sample. The polyphase implementation used here is
+    O(N/P).
+
+    .. versionadded:: 0.18
+
+    References
+    ----------
+    .. [1] P. P. Vaidyanathan, Multirate Systems and Filter Banks,
+           Prentice Hall, 1993.
+
+    Examples
+    --------
+    Simple operations:
+
+    >>> import numpy as np
+    >>> from scipy.signal import upfirdn
+    >>> upfirdn([1, 1, 1], [1, 1, 1])   # FIR filter
+    array([ 1.,  2.,  3.,  2.,  1.])
+    >>> upfirdn([1], [1, 2, 3], 3)  # upsampling with zeros insertion
+    array([ 1.,  0.,  0.,  2.,  0.,  0.,  3.])
+    >>> upfirdn([1, 1, 1], [1, 2, 3], 3)  # upsampling with sample-and-hold
+    array([ 1.,  1.,  1.,  2.,  2.,  2.,  3.,  3.,  3.])
+    >>> upfirdn([.5, 1, .5], [1, 1, 1], 2)  # linear interpolation
+    array([ 0.5,  1. ,  1. ,  1. ,  1. ,  1. ,  0.5])
+    >>> upfirdn([1], np.arange(10), 1, 3)  # decimation by 3
+    array([ 0.,  3.,  6.,  9.])
+    >>> upfirdn([.5, 1, .5], np.arange(10), 2, 3)  # linear interp, rate 2/3
+    array([ 0. ,  1. ,  2.5,  4. ,  5.5,  7. ,  8.5])
+
+    Apply a single filter to multiple signals:
+
+    >>> x = np.reshape(np.arange(8), (4, 2))
+    >>> x
+    array([[0, 1],
+           [2, 3],
+           [4, 5],
+           [6, 7]])
+
+    Apply along the last dimension of ``x``:
+
+    >>> h = [1, 1]
+    >>> upfirdn(h, x, 2)
+    array([[ 0.,  0.,  1.,  1.],
+           [ 2.,  2.,  3.,  3.],
+           [ 4.,  4.,  5.,  5.],
+           [ 6.,  6.,  7.,  7.]])
+
+    Apply along the 0th dimension of ``x``:
+
+    >>> upfirdn(h, x, 2, axis=0)
+    array([[ 0.,  1.],
+           [ 0.,  1.],
+           [ 2.,  3.],
+           [ 2.,  3.],
+           [ 4.,  5.],
+           [ 4.,  5.],
+           [ 6.,  7.],
+           [ 6.,  7.]])
+    """
+    xp = array_namespace(h, x)
+
+    x = np.asarray(x)
+    ufd = _UpFIRDn(h, x.dtype, up, down)
+    # This is equivalent to (but faster than) using np.apply_along_axis
+    return xp.asarray(ufd.apply_filter(x, axis, mode, cval))
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/_upfirdn_apply.cpython-312-x86_64-linux-gnu.so b/venv/lib/python3.12/site-packages/scipy/signal/_upfirdn_apply.cpython-312-x86_64-linux-gnu.so
new file mode 100644
index 0000000000000000000000000000000000000000..0216b37580109e96b1695c3a99151f0ff364bbeb
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/_upfirdn_apply.cpython-312-x86_64-linux-gnu.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b44aba30d7c5b8efe4d7220439e2f05ece000a1cbd2d66bac7156f90089d64e5
+size 202816
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/_waveforms.py b/venv/lib/python3.12/site-packages/scipy/signal/_waveforms.py
new file mode 100644
index 0000000000000000000000000000000000000000..a41c40b57a330ee9b642970fd9bd6ae802850b42
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/_waveforms.py
@@ -0,0 +1,685 @@
+# Author: Travis Oliphant
+# 2003
+#
+# Feb. 2010: Updated by Warren Weckesser:
+#   Rewrote much of chirp()
+#   Added sweep_poly()
+import numpy as np
+from numpy import asarray, zeros, pi, log, sqrt, \
+    exp, cos, sin, polyval, polyint
+
+from scipy._lib._array_api import array_namespace, xp_promote
+import scipy._external.array_api_extra as xpx
+
+
+__all__ = ['sawtooth', 'square', 'gausspulse', 'chirp', 'sweep_poly',
+           'unit_impulse']
+
+
+def sawtooth(t, width=1.):
+    """
+    Return a periodic sawtooth or triangle waveform.
+
+    The sawtooth waveform has a period ``2*pi``, rises from -1 to 1 on the
+    interval 0 to ``width*2*pi``, then drops from 1 to -1 on the interval
+    ``width*2*pi`` to ``2*pi``. `width` must be in the interval ``[0, 1]``.
+
+    Note that this is not band-limited.  It produces an infinite number
+    of harmonics, which are aliased back and forth across the frequency
+    spectrum.
+
+    Parameters
+    ----------
+    t : array_like
+        Time.
+    width : array_like, optional
+        Width of the rising ramp as a proportion of the total cycle.
+        Default is 1, producing a rising ramp, while 0 produces a falling
+        ramp.  ``width=0.5`` produces a triangle wave.
+        If an array, causes wave shape to change over time, and must be the
+        same length as `t`.
+
+    Returns
+    -------
+    y : ndarray
+        Output array containing the sawtooth waveform.
+
+    Examples
+    --------
+    A 5 Hz waveform sampled at 500 Hz for 1 second:
+
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+    >>> t = np.linspace(0, 1, 500)
+    >>> plt.plot(t, signal.sawtooth(2 * np.pi * 5 * t))
+
+    """
+    xp = array_namespace(t, width)
+    t, w = xp_promote(t, width, broadcast=True, force_floating=True, xp=xp)
+    y = xp.zeros_like(t)
+
+    # width must be between 0 and 1 inclusive
+    mask1 = (w > 1) | (w < 0)
+    y = xpx.at(y, mask1).set(xp.nan)
+
+    # take t modulo 2*pi
+    tmod = t % (2*xp.pi)
+
+    # on the interval 0 to width*2*pi function is tmod / (pi*w) - 1
+    mask2 = ~mask1 & (tmod < w*2*xp.pi)
+    y = xpx.at(y, mask2).set(tmod[mask2]/(xp.pi*w[mask2]) - 1)
+
+    # on the interval width*2*pi to 2*pi function is (pi*(w+1)-tmod) / (pi*(1-w))
+    mask3 = ~(mask1 | mask2)
+    y = xpx.at(y, mask3).set(
+        (xp.pi*(w[mask3] + 1) - tmod[mask3])/(xp.pi*(1 - w[mask3]))
+    )
+    return y
+
+
+def square(t, duty=0.5):
+    """
+    Return a periodic square-wave waveform.
+
+    The square wave has a period ``2*pi``, has value +1 from 0 to
+    ``2*pi*duty`` and -1 from ``2*pi*duty`` to ``2*pi``. `duty` must be in
+    the interval ``[0,1]``.
+
+    Note that this is not band-limited.  It produces an infinite number
+    of harmonics, which are aliased back and forth across the frequency
+    spectrum.
+
+    Parameters
+    ----------
+    t : array_like
+        The input time array.
+    duty : array_like, optional
+        Duty cycle.  Default is 0.5 (50% duty cycle).
+        If an array, causes wave shape to change over time, and must be the
+        same length as t.
+
+    Returns
+    -------
+    y : ndarray
+        Output array containing the square waveform.
+
+    Examples
+    --------
+    A 5 Hz waveform sampled at 500 Hz for 1 second:
+
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+    >>> t = np.linspace(0, 1, 500, endpoint=False)
+    >>> plt.plot(t, signal.square(2 * np.pi * 5 * t))
+    >>> plt.ylim(-2, 2)
+
+    A pulse-width modulated sine wave:
+
+    >>> plt.figure()
+    >>> sig = np.sin(2 * np.pi * t)
+    >>> pwm = signal.square(2 * np.pi * 30 * t, duty=(sig + 1)/2)
+    >>> plt.subplot(2, 1, 1)
+    >>> plt.plot(t, sig)
+    >>> plt.subplot(2, 1, 2)
+    >>> plt.plot(t, pwm)
+    >>> plt.ylim(-1.5, 1.5)
+
+    """
+    xp = array_namespace(t, duty)
+    t, w = xp_promote(t, duty, xp=xp, force_floating=True, broadcast=True)
+
+    y = xp.zeros_like(t)
+
+    # width must be between 0 and 1 inclusive
+    mask1 = (w > 1) | (w < 0)
+    y = xpx.at(y, mask1).set(xp.nan)
+
+    # on the interval 0 to duty*2*pi function is 1
+    tmod = t % (2 * xp.pi)
+    mask2 = ~mask1 & (tmod < w*2*xp.pi)
+    y = xpx.at(y, mask2).set(1)
+
+    # on the interval duty*2*pi to 2*pi function is -1
+    mask3 = ~(mask1 | mask2)
+    y = xpx.at(y, mask3).set(-1)
+    return y
+
+
+def gausspulse(t, fc=1000, bw=0.5, bwr=-6, tpr=-60, retquad=False,
+               retenv=False):
+    """
+    Return a Gaussian modulated sinusoid.
+
+    The formula for the returned signal is given by::
+
+        exp(-a t^2) exp(1j*2*pi*fc*t)
+
+    If `retquad` is True, then return the real and imaginary parts
+    (in-phase and quadrature).
+    If `retenv` is True, then return the envelope (unmodulated signal).
+    Otherwise, return the real part of the modulated sinusoid.
+
+    Parameters
+    ----------
+    t : ndarray or 'cutoff'
+        Input array.
+    fc : float, optional
+        Center frequency (e.g. Hz).  Default is 1000.
+    bw : float, optional
+        Fractional bandwidth in frequency domain of pulse (e.g. Hz).
+        Default is 0.5.
+    bwr : float, optional
+        Reference level at which fractional bandwidth is calculated (dB).
+        Default is -6.
+    tpr : float, optional
+        If `t` is 'cutoff', then the function returns the cutoff
+        time for when the pulse amplitude falls below `tpr` (in dB).
+        Default is -60.
+    retquad : bool, optional
+        If True, return the quadrature (imaginary) as well as the real part
+        of the signal.  Default is False.
+    retenv : bool, optional
+        If True, return the envelope of the signal.  Default is False.
+
+    Returns
+    -------
+    yI : ndarray
+        Real part of signal. Always returned.
+    yQ : ndarray
+        Imaginary part of signal. Only returned if `retquad` is True.
+    yenv : ndarray
+        Envelope of signal. Only returned if `retenv` is True.
+
+    Examples
+    --------
+    Plot real component, imaginary component, and envelope for a 5 Hz pulse,
+    sampled at 100 Hz for 2 seconds:
+
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+    >>> t = np.linspace(-1, 1, 2 * 100, endpoint=False)
+    >>> i, q, e = signal.gausspulse(t, fc=5, retquad=True, retenv=True)
+    >>> plt.plot(t, i, t, q, t, e, '--')
+
+    """ 
+    if fc < 0:
+        raise ValueError(f"Center frequency (fc={fc:.2f}) must be >=0.")
+    if bw <= 0:
+        raise ValueError(f"Fractional bandwidth (bw={bw:.2f}) must be > 0.")
+    if bwr >= 0:
+        raise ValueError(f"Reference level for bandwidth (bwr={bwr:.2f}) "
+                         "must be < 0 dB")
+
+    # exp(-a t^2) <->  sqrt(pi/a) exp(-pi^2/a * f^2)  = g(f)
+
+    ref = pow(10.0, bwr / 20.0)
+    # fdel = fc*bw/2:  g(fdel) = ref --- solve this for a
+    #
+    # pi^2/a * fc^2 * bw^2 /4=-log(ref)
+    a = -(pi * fc * bw) ** 2 / (4.0 * log(ref))
+
+    if isinstance(t, str):
+        if t == 'cutoff':  # compute cut_off point
+            #  Solve exp(-a tc**2) = tref  for tc
+            #   tc = sqrt(-log(tref) / a) where tref = 10^(tpr/20)
+            if tpr >= 0:
+                raise ValueError("Reference level for time cutoff must "
+                                 "be < 0 dB")
+            tref = pow(10.0, tpr / 20.0)
+            return sqrt(-log(tref) / a)
+        else:
+            raise ValueError("If `t` is a string, it must be 'cutoff'")
+
+    yenv = exp(-a * t * t)
+    yI = yenv * cos(2 * pi * fc * t)
+    yQ = yenv * sin(2 * pi * fc * t)
+    if not retquad and not retenv:
+        return yI
+    if not retquad and retenv:
+        return yI, yenv
+    if retquad and not retenv:
+        return yI, yQ
+    if retquad and retenv:
+        return yI, yQ, yenv
+
+
+def chirp(t, f0, t1, f1, method='linear', phi=0, vertex_zero=True, *,
+          complex=False):
+    r"""Frequency-swept cosine generator.
+
+    In the following, 'Hz' should be interpreted as 'cycles per unit';
+    there is no requirement here that the unit is one second.  The
+    important distinction is that the units of rotation are cycles, not
+    radians. Likewise, `t` could be a measurement of space instead of time.
+
+    Parameters
+    ----------
+    t : array_like
+        Times at which to evaluate the waveform.
+    f0 : float
+        Frequency (e.g. Hz) at time t=0.
+    t1 : float
+        Time at which `f1` is specified.
+    f1 : float
+        Frequency (e.g. Hz) of the waveform at time `t1`.
+    method : {'linear', 'quadratic', 'logarithmic', 'hyperbolic'}, optional
+        Kind of frequency sweep.  If not given, `linear` is assumed.  See
+        Notes below for more details.
+    phi : float, optional
+        Phase offset, in degrees. Default is 0.
+    vertex_zero : bool, optional
+        This parameter is only used when `method` is 'quadratic'.
+        It determines whether the vertex of the parabola that is the graph
+        of the frequency is at t=0 or t=t1.
+    complex : bool, optional
+        This parameter creates a complex-valued analytic signal instead of a
+        real-valued signal. It allows the use of complex baseband (in communications
+        domain). Default is False.
+
+        .. versionadded:: 1.15.0
+
+    Returns
+    -------
+    y : ndarray
+        A numpy array containing the signal evaluated at `t` with the requested
+        time-varying frequency.  More precisely, the function returns
+        ``exp(1j*phase + 1j*(pi/180)*phi) if complex else cos(phase + (pi/180)*phi)``
+        where `phase` is the integral (from 0 to `t`) of ``2*pi*f(t)``.
+        The instantaneous frequency ``f(t)`` is defined below.
+
+    See Also
+    --------
+    sweep_poly
+
+    Notes
+    -----
+    There are four possible options for the parameter `method`, which have a (long)
+    standard form and some allowed abbreviations. The formulas for the instantaneous
+    frequency :math:`f(t)` of the generated signal are as follows:
+
+    1. Parameter `method` in ``('linear', 'lin', 'li')``:
+
+       .. math::
+           f(t) = f_0 + \beta\, t           \quad\text{with}\quad
+           \beta = \frac{f_1 - f_0}{t_1}
+
+       Frequency :math:`f(t)` varies linearly over time with a constant rate
+       :math:`\beta`.
+
+    2. Parameter `method` in ``('quadratic', 'quad', 'q')``:
+
+       .. math::
+            f(t) =
+            \begin{cases}
+              f_0 + \beta\, t^2          & \text{if vertex_zero is True,}\\
+              f_1 + \beta\, (t_1 - t)^2  & \text{otherwise,}
+            \end{cases}
+            \quad\text{with}\quad
+            \beta = \frac{f_1 - f_0}{t_1^2}
+
+       The graph of the frequency f(t) is a parabola through :math:`(0, f_0)` and
+       :math:`(t_1, f_1)`.  By default, the vertex of the parabola is at
+       :math:`(0, f_0)`. If `vertex_zero` is ``False``, then the vertex is at
+       :math:`(t_1, f_1)`.
+       To use a more general quadratic function, or an arbitrary
+       polynomial, use the function `scipy.signal.sweep_poly`.
+
+    3. Parameter `method` in ``('logarithmic', 'log', 'lo')``:
+
+       .. math::
+            f(t) = f_0  \left(\frac{f_1}{f_0}\right)^{t/t_1}
+
+       :math:`f_0` and :math:`f_1` must be nonzero and have the same sign.
+       This signal is also known as a geometric or exponential chirp.
+
+    4. Parameter `method` in ``('hyperbolic', 'hyp')``:
+
+       .. math::
+              f(t) = \frac{\alpha}{\beta\, t + \gamma} \quad\text{with}\quad
+              \alpha = f_0 f_1 t_1, \ \beta = f_0 - f_1, \ \gamma = f_1 t_1
+
+       :math:`f_0` and :math:`f_1` must be nonzero.
+
+
+    Examples
+    --------
+    For the first example, a linear chirp ranging from 6 Hz to 1 Hz over 10 seconds is
+    plotted:
+
+    >>> import numpy as np
+    >>> from matplotlib.pyplot import tight_layout
+    >>> from scipy.signal import chirp, square, ShortTimeFFT
+    >>> from scipy.signal.windows import gaussian
+    >>> import matplotlib.pyplot as plt
+    ...
+    >>> N, T = 1000, 0.01  # number of samples and sampling interval for 10 s signal
+    >>> t = np.arange(N) * T  # timestamps
+    ...
+    >>> x_lin = chirp(t, f0=6, f1=1, t1=10, method='linear')
+    ...
+    >>> fg0, ax0 = plt.subplots()
+    >>> ax0.set_title(r"Linear Chirp from $f(0)=6\,$Hz to $f(10)=1\,$Hz")
+    >>> ax0.set(xlabel="Time $t$ in Seconds", ylabel=r"Amplitude $x_\text{lin}(t)$")
+    >>> ax0.plot(t, x_lin)
+    >>> plt.show()
+
+    The following four plots each show the short-time Fourier transform of a chirp
+    ranging from 45 Hz to 5 Hz with different values for the parameter `method`
+    (and `vertex_zero`):
+
+    >>> x_qu0 = chirp(t, f0=45, f1=5, t1=N*T, method='quadratic', vertex_zero=True)
+    >>> x_qu1 = chirp(t, f0=45, f1=5, t1=N*T, method='quadratic', vertex_zero=False)
+    >>> x_log = chirp(t, f0=45, f1=5, t1=N*T, method='logarithmic')
+    >>> x_hyp = chirp(t, f0=45, f1=5, t1=N*T, method='hyperbolic')
+    ...
+    >>> win = gaussian(50, std=12, sym=True)
+    >>> SFT = ShortTimeFFT(win, hop=2, fs=1/T, mfft=800, scale_to='magnitude')
+    >>> ts = ("'quadratic', vertex_zero=True", "'quadratic', vertex_zero=False",
+    ...       "'logarithmic'", "'hyperbolic'")
+    >>> fg1, ax1s = plt.subplots(2, 2, sharex='all', sharey='all',
+    ...                          figsize=(6, 5),  layout="constrained")
+    >>> for x_, ax_, t_ in zip([x_qu0, x_qu1, x_log, x_hyp], ax1s.ravel(), ts):
+    ...     aSx = abs(SFT.stft(x_))
+    ...     im_ = ax_.imshow(aSx, origin='lower', aspect='auto', extent=SFT.extent(N),
+    ...                      cmap='plasma')
+    ...     ax_.set_title(t_)
+    ...     if t_ == "'hyperbolic'":
+    ...         fg1.colorbar(im_, ax=ax1s, label='Magnitude $|S_z(t,f)|$')
+    >>> _ = fg1.supxlabel("Time $t$ in Seconds")  # `_ =` is needed to pass doctests
+    >>> _ = fg1.supylabel("Frequency $f$ in Hertz")
+    >>> plt.show()
+
+    Finally, the short-time Fourier transform of a complex-valued linear chirp
+    ranging from -30 Hz to 30 Hz is depicted:
+
+    >>> z_lin = chirp(t, f0=-30, f1=30, t1=N*T, method="linear", complex=True)
+    >>> SFT.fft_mode = 'centered'  # needed to work with complex signals
+    >>> aSz = abs(SFT.stft(z_lin))
+    ...
+    >>> fg2, ax2 = plt.subplots()
+    >>> ax2.set_title(r"Linear Chirp from $-30\,$Hz to $30\,$Hz")
+    >>> ax2.set(xlabel="Time $t$ in Seconds", ylabel="Frequency $f$ in Hertz")
+    >>> im2 = ax2.imshow(aSz, origin='lower', aspect='auto',
+    ...                  extent=SFT.extent(N), cmap='viridis')
+    >>> fg2.colorbar(im2, label='Magnitude $|S_z(t,f)|$')
+    >>> plt.show()
+
+    Note that using negative frequencies makes only sense with complex-valued signals.
+    Furthermore, the magnitude of the complex exponential function is one whereas the
+    magnitude of the real-valued cosine function is only 1/2.
+    """
+    # 'phase' is computed in _chirp_phase, to make testing easier.
+    phase = _chirp_phase(t, f0, t1, f1, method, vertex_zero) + np.deg2rad(phi)
+    return np.exp(1j*phase) if complex else np.cos(phase)
+
+
+def _chirp_phase(t, f0, t1, f1, method='linear', vertex_zero=True):
+    """
+    Calculate the phase used by `chirp` to generate its output.
+
+    See `chirp` for a description of the arguments.
+
+    """
+    t = asarray(t)
+    f0 = float(f0)
+    t1 = float(t1)
+    f1 = float(f1)
+    if method in ['linear', 'lin', 'li']:
+        beta = (f1 - f0) / t1
+        phase = 2 * pi * (f0 * t + 0.5 * beta * t * t)
+
+    elif method in ['quadratic', 'quad', 'q']:
+        beta = (f1 - f0) / (t1 ** 2)
+        if vertex_zero:
+            phase = 2 * pi * (f0 * t + beta * t ** 3 / 3)
+        else:
+            phase = 2 * pi * (f1 * t + beta * ((t1 - t) ** 3 - t1 ** 3) / 3)
+
+    elif method in ['logarithmic', 'log', 'lo']:
+        if f0 * f1 <= 0.0:
+            raise ValueError("For a logarithmic chirp, f0 and f1 must be "
+                             "nonzero and have the same sign.")
+        if f0 == f1:
+            phase = 2 * pi * f0 * t
+        else:
+            beta = t1 / log(f1 / f0)
+            phase = 2 * pi * beta * f0 * (pow(f1 / f0, t / t1) - 1.0)
+
+    elif method in ['hyperbolic', 'hyp']:
+        if f0 == 0 or f1 == 0:
+            raise ValueError("For a hyperbolic chirp, f0 and f1 must be "
+                             "nonzero.")
+        if f0 == f1:
+            # Degenerate case: constant frequency.
+            phase = 2 * pi * f0 * t
+        else:
+            # Singular point: the instantaneous frequency blows up
+            # when t == sing.
+            sing = -f1 * t1 / (f0 - f1)
+            phase = 2 * pi * (-sing * f0) * log(np.abs(1 - t/sing))
+
+    else:
+        raise ValueError("method must be 'linear', 'quadratic', 'logarithmic', "
+                         f"or 'hyperbolic', but a value of {method!r} was given.")
+
+    return phase
+
+
+def sweep_poly(t, poly, phi=0):
+    """
+    Frequency-swept cosine generator, with a time-dependent frequency.
+
+    This function generates a sinusoidal function whose instantaneous
+    frequency varies with time.  The frequency at time `t` is given by
+    the polynomial `poly`.
+
+    Parameters
+    ----------
+    t : ndarray
+        Times at which to evaluate the waveform.
+    poly : 1-D array_like or instance of numpy.poly1d
+        The desired frequency expressed as a polynomial.  If `poly` is
+        a list or ndarray of length n, then the elements of `poly` are
+        the coefficients of the polynomial, and the instantaneous
+        frequency is::
+
+            f(t) = poly[0]*t**(n-1) + poly[1]*t**(n-2) + ... + poly[n-1]
+
+        If `poly` is an instance of numpy.poly1d, then the
+        instantaneous frequency is::
+
+            f(t) = poly(t)
+
+    phi : float, optional
+        Phase offset, in degrees, Default: 0.
+
+    Returns
+    -------
+    sweep_poly : ndarray
+        A numpy array containing the signal evaluated at `t` with the
+        requested time-varying frequency.  More precisely, the function
+        returns ``cos(phase + (pi/180)*phi)``, where `phase` is the integral
+        (from 0 to t) of ``2 * pi * f(t)``; ``f(t)`` is defined above.
+
+    See Also
+    --------
+    chirp
+
+    Notes
+    -----
+    .. versionadded:: 0.8.0
+
+    If `poly` is a list or ndarray of length `n`, then the elements of
+    `poly` are the coefficients of the polynomial, and the instantaneous
+    frequency is:
+
+        ``f(t) = poly[0]*t**(n-1) + poly[1]*t**(n-2) + ... + poly[n-1]``
+
+    If `poly` is an instance of `numpy.poly1d`, then the instantaneous
+    frequency is:
+
+          ``f(t) = poly(t)``
+
+    Finally, the output `s` is:
+
+        ``cos(phase + (pi/180)*phi)``
+
+    where `phase` is the integral from 0 to `t` of ``2 * pi * f(t)``,
+    ``f(t)`` as defined above.
+
+    Examples
+    --------
+    Compute the waveform with instantaneous frequency::
+
+        f(t) = 0.025*t**3 - 0.36*t**2 + 1.25*t + 2
+
+    over the interval 0 <= t <= 10.
+
+    >>> import numpy as np
+    >>> from scipy.signal import sweep_poly
+    >>> p = np.poly1d([0.025, -0.36, 1.25, 2.0])
+    >>> t = np.linspace(0, 10, 5001)
+    >>> w = sweep_poly(t, p)
+
+    Plot it:
+
+    >>> import matplotlib.pyplot as plt
+    >>> plt.subplot(2, 1, 1)
+    >>> plt.plot(t, w)
+    >>> plt.title("Sweep Poly\\nwith frequency " +
+    ...           "$f(t) = 0.025t^3 - 0.36t^2 + 1.25t + 2$")
+    >>> plt.subplot(2, 1, 2)
+    >>> plt.plot(t, p(t), 'r', label='f(t)')
+    >>> plt.legend()
+    >>> plt.xlabel('t')
+    >>> plt.tight_layout()
+    >>> plt.show()
+
+    """
+    # 'phase' is computed in _sweep_poly_phase, to make testing easier.
+    phase = _sweep_poly_phase(t, poly)
+    # Convert to radians.
+    phi *= pi / 180
+    return cos(phase + phi)
+
+
+def _sweep_poly_phase(t, poly):
+    """
+    Calculate the phase used by sweep_poly to generate its output.
+
+    See `sweep_poly` for a description of the arguments.
+
+    """
+    # polyint handles lists, ndarrays and instances of poly1d automatically.
+    intpoly = polyint(poly)
+    phase = 2 * pi * polyval(intpoly, t)
+    return phase
+
+
+def unit_impulse(shape, idx=None, dtype=float):
+    r"""
+    Unit impulse signal (discrete delta function) or unit basis vector.
+
+    Parameters
+    ----------
+    shape : int or tuple of int
+        Number of samples in the output (1-D), or a tuple that represents the
+        shape of the output (N-D).
+    idx : None or int or tuple of int or 'mid', optional
+        Index at which the value is 1.  If None, defaults to the 0th element.
+        If ``idx='mid'``, the impulse will be centered at ``shape // 2`` in
+        all dimensions.  If an int, the impulse will be at `idx` in all
+        dimensions.
+    dtype : data-type, optional
+        The desired data-type for the array, e.g., ``numpy.int8``.  Default is
+        ``numpy.float64``.
+
+    Returns
+    -------
+    y : ndarray
+        Output array containing an impulse signal.
+
+    Notes
+    -----
+    In digital signal processing literature the unit impulse signal is often
+    represented by the Kronecker delta. [1]_ I.e., a signal :math:`u_k[n]`,
+    which is zero everywhere except being one at the :math:`k`-th sample,
+    can be expressed as
+
+    .. math::
+
+        u_k[n] = \delta[n-k] \equiv \delta_{n,k}\ .
+
+    Furthermore, the unit impulse is frequently interpreted as the discrete-time
+    version of the continuous-time Dirac distribution. [2]_
+
+    References
+    ----------
+    .. [1] "Kronecker delta", *Wikipedia*,
+           https://en.wikipedia.org/wiki/Kronecker_delta#Digital_signal_processing
+    .. [2] "Dirac delta function" *Wikipedia*,
+           https://en.wikipedia.org/wiki/Dirac_delta_function#Relationship_to_the_Kronecker_delta
+
+    .. versionadded:: 0.19.0
+
+    Examples
+    --------
+    An impulse at the 0th element (:math:`\\delta[n]`):
+
+    >>> from scipy import signal
+    >>> signal.unit_impulse(8)
+    array([ 1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.])
+
+    Impulse offset by 2 samples (:math:`\\delta[n-2]`):
+
+    >>> signal.unit_impulse(7, 2)
+    array([ 0.,  0.,  1.,  0.,  0.,  0.,  0.])
+
+    2-dimensional impulse, centered:
+
+    >>> signal.unit_impulse((3, 3), 'mid')
+    array([[ 0.,  0.,  0.],
+           [ 0.,  1.,  0.],
+           [ 0.,  0.,  0.]])
+
+    Impulse at (2, 2), using broadcasting:
+
+    >>> signal.unit_impulse((4, 4), 2)
+    array([[ 0.,  0.,  0.,  0.],
+           [ 0.,  0.,  0.,  0.],
+           [ 0.,  0.,  1.,  0.],
+           [ 0.,  0.,  0.,  0.]])
+
+    Plot the impulse response of a 4th-order Butterworth lowpass filter:
+
+    >>> imp = signal.unit_impulse(100, 'mid')
+    >>> b, a = signal.butter(4, 0.2)
+    >>> response = signal.lfilter(b, a, imp)
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> plt.plot(np.arange(-50, 50), imp)
+    >>> plt.plot(np.arange(-50, 50), response)
+    >>> plt.margins(0.1, 0.1)
+    >>> plt.xlabel('Time [samples]')
+    >>> plt.ylabel('Amplitude')
+    >>> plt.grid(True)
+    >>> plt.show()
+
+    """
+    out = zeros(shape, dtype)
+
+    shape = np.atleast_1d(shape)
+
+    if idx is None:
+        idx = (0,) * len(shape)
+    elif idx == 'mid':
+        idx = tuple(shape // 2)
+    elif not hasattr(idx, "__iter__"):
+        idx = (idx,) * len(shape)
+
+    out[idx] = 1
+    return out
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/_wavelets.py b/venv/lib/python3.12/site-packages/scipy/signal/_wavelets.py
new file mode 100644
index 0000000000000000000000000000000000000000..9da68aed88ed380dfe04f59ce0acad2471c20cfb
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/_wavelets.py
@@ -0,0 +1,29 @@
+import numpy as np
+from scipy.signal._signaltools import convolve
+
+
+def _ricker(points, a):
+    A = 2 / (np.sqrt(3 * a) * (np.pi**0.25))
+    wsq = a**2
+    vec = np.arange(0, points) - (points - 1.0) / 2
+    xsq = vec**2
+    mod = (1 - xsq / wsq)
+    gauss = np.exp(-xsq / (2 * wsq))
+    total = A * mod * gauss
+    return total
+
+
+def _cwt(data, wavelet, widths, dtype=None, **kwargs):
+    # Determine output type
+    if dtype is None:
+        if np.asarray(wavelet(1, widths[0], **kwargs)).dtype.char in 'FDG':
+            dtype = np.complex128
+        else:
+            dtype = np.float64
+
+    output = np.empty((len(widths), len(data)), dtype=dtype)
+    for ind, width in enumerate(widths):
+        N = np.min([10 * width, len(data)])
+        wavelet_data = np.conj(wavelet(N, width, **kwargs)[::-1])
+        output[ind] = convolve(data, wavelet_data, mode='same')
+    return output
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/_whittaker.py b/venv/lib/python3.12/site-packages/scipy/signal/_whittaker.py
new file mode 100644
index 0000000000000000000000000000000000000000..7984f8ba5edbe89b765bc683e87a2a765b40b11b
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/_whittaker.py
@@ -0,0 +1,451 @@
+import warnings
+import numpy as np
+from scipy._lib._util import _RichResult, _validate_int
+from scipy.linalg.lapack import get_lapack_funcs
+from scipy.optimize import minimize_scalar
+from scipy.special import binom
+
+
+def _solveh_banded(ab, b, calc_logdet=False):
+    """
+    Solve the equation ``a @ x = b`` for ``x``,  where ``a`` is the 
+    Hermitian positive-definite banded matrix defined by `ab`.
+
+    Same as scipy.linalg.solveh_banded(lower=True, check_finite=False), but:
+    - also returns the log of the determinant and info
+    - no error is raised if info > 0
+    - no input validation
+    - only real values, no complex
+    - only `lower = True` code path
+    - always overwrite_XX = False
+    - b only a 1-dim array
+
+    Parameters
+    ----------
+    ab : (``u`` + 1, M) array_like
+        Banded matrix
+    b : (M,) array_like
+        Right-hand side
+
+    Returns
+    -------
+    x : (M,) ndarray
+        The solution to the system ``a x = b``. Shape of return matches shape of `b`.
+    logdet : float
+        Logarithm of the determinant of `ab`. Returns 0 if ``calc_logdet=False``.
+    info : int
+    """
+    a1 = ab
+    b1 = b
+    overwrite_b = False
+    overwrite_ab = False
+    logdet = 0.0
+
+    if a1.shape[0] == 2:
+        method = "ptsv"
+        ptsv = get_lapack_funcs(method, (a1, b1), ilp64="preferred")
+        # We assume lower=True and real arrays
+        d = a1[0, :]
+        e = a1[1, :-1]
+        # ptsv uses LDL', returnes d=diag(D), du=diag(L, -1)
+        d, du, x, info = ptsv(d, e, b1, overwrite_ab, overwrite_ab, overwrite_b)
+        if calc_logdet and info == 0:
+            logdet = np.log(d).sum()
+    else:
+        method = "pbsv"
+        pbsv = get_lapack_funcs(method, (a1, b1), ilp64="preferred")
+        # pbsv uses Cholesky LL', returns c=L in ab-storage format
+        c, x, info = pbsv(a1, b1, lower=True, overwrite_ab=overwrite_ab,
+                          overwrite_b=overwrite_b)
+        if calc_logdet and info == 0:
+            logdet = 2 * np.log(c[0, :]).sum()
+    if info < 0:
+        raise ValueError(f"illegal value in {-info}th argument of internal {method}")
+    return x, logdet, info
+
+
+def whittaker_henderson(signal, *, lamb="reml", order=2, weights=None):
+    r"""
+    Whittaker-Henderson (WH) smoothing/graduation of a discrete signal.
+
+    This implements WH smoothing with a difference penalty of the specified ``order``
+    and penalty strength ``lamb``, see [1]_, [2]_ and [3]_. WH can be seen as a
+    penalized B-Spline (P-Spline) of degree zero for equidistant knots at the signal
+    positions.
+
+    In econometrics, the WH graduation of order 2 is referred to as the
+    Hodrick-Prescott filter [4]_.
+    
+    Parameters
+    ----------
+    signal : array_like
+        A one-dimensional array of length ``order + 1`` representing equidistant data
+        points of a signal, e.g. a time series with constant time lag.
+    
+    lamb : str or float, optional
+        Smoothing or penalty parameter, default is ``"reml"`` which minimizes the
+        restricted maximum likelihood (REML) criterion to find the parameter ``lamb``.
+        If a number is passed, it must be non-negative and it is used directly.
+
+    order : int, default: 2
+        The order of the difference penalty, must be at least 1.
+
+    weights : array_like or None, optional
+        A one-dimensional array of case weights with the same length as `signal`.
+        ``None`` is equivalent to an array of all ones, ``np.ones_like(signal)``.
+
+    Returns
+    -------
+     res : _RichResult
+        An object similar to an instance of `scipy.optimize.OptimizeResult` with the
+        following attributes:
+
+        x : ndarray
+            The WH smoothed signal.
+        lamb : float
+            The penalty parameter. If the input ``lamb`` is a number, this value is
+            returned. If the input was ``"reml"``, the penalty parameter that minimized
+            the REML criterion is returned.
+
+    Notes
+    -----
+    For the signal :math:`y = (y_1, y_2, \ldots, y_n)` and weights
+    :math:`w = (w_1, w_2, \ldots, w_n)`, WH of order :math:`p` with smoothing or
+    penalty parameter :math:`\lambda` solves the following optimization problem for
+    :math:`x_i`:
+
+    .. math::
+
+        \operatorname{argmin}_{x_i} \sum_i^n w_i (y_i - x_i)^2
+        + \lambda \sum_i^{n-p} (\Delta^p x_i)^2 \,,
+
+    where :math:`\Delta^p` is the forward difference operator of order :math:`p`,
+    :math:`\Delta x_i = x_{i+1} - x_i` and
+    :math:`\Delta^2 x_i = \Delta(\Delta x_i) = x_{i+2} - 2x_{i+1} + x_i`.
+    For every input value :math:`y_i`, it generates a smoothed value :math:`x_i`.
+
+    One of the nice properties of WH is that it automatically performs inter- and
+    extrapolation of data. Interpolation means filling in values when signal data is
+    only available on the left and on the right. Extrapolation means filling in values
+    after the observed signal ends.
+    Set ``weights = 0`` for regions where you want to extra- or interpolate. The values
+    of `signal` don't matter if ``weights = 0``.
+    WH interpolates a polynomial of ``degree = 2 * order - 1`` and it extrapolates a
+    polynomial of ``degree = order - 1``. For ``order = 2``, this means cubic
+    interpolation and linear extrapolation.
+
+    References
+    ----------
+    .. [1] Whittaker-Henderson smoothing,
+           https://en.wikipedia.org/wiki/Whittaker%E2%80%93Henderson_smoothing
+    .. [2] Eilers, P.H.C. (2003).
+           "A perfect smoother". Analytical Chem. 75, 3631-3636.
+           :doi:`10.1021/AC034173T`
+    .. [3] Weinert, Howard L. (2007).
+           "Efficient computation for Whittaker-Henderson smoothing".
+           Computational Statistics and Data Analysis 52:959-74.
+           :doi:`10.1016/j.csda.2006.11.038`
+    .. [4] Hodrick, R. J., and Prescott, E. C. (1997).
+           "Postwar U.S. Business Cycles: An Empirical Investigation".
+           :doi:`10.2307/2953682`
+
+    Examples
+    --------
+    We use data from https://data.giss.nasa.gov/gistemp/ for global temperature
+    anomalies, i.e., deviations from the corresponding 1951-1980 means (Combined
+    Land-Surface Air and Sea-Surface Water Temperature Anomalies, Land-Ocean Temperature
+    Index, L-OTI).
+    We use weights to indicate where to inter- and extrapolate the missing data.
+
+    >>> from pathlib import Path
+    >>> import numpy as np
+    >>> import scipy
+    >>> from scipy.signal import whittaker_henderson
+    >>> # For the most recent data, use
+    ... # fname="https://data.giss.nasa.gov/gistemp/tabledata_v4/GLB.Ts+dSST.csv"
+    ... # Here, we instead use a copy made in 2026.
+    ... fname = Path(scipy.signal.__file__).parent / "tests/data/GLB.Ts+dSST.csv"
+    >>> data = np.genfromtxt(
+    ...     fname=fname,
+    ...     delimiter=",", skip_header=2, missing_values="***"
+    ... )
+    >>> year = data[:, 0]
+    >>> temperature = data[:, 1:13].ravel()  # monthly temperature anomalies
+    >>> w = np.ones_like(temperature)
+    >>> # We might have some nan values.
+    ... np.sum(np.isnan(temperature))
+    np.int64(10)
+    >>> w[np.isnan(temperature)] = 0
+    >>> res = whittaker_henderson(temperature, weights=w)
+    >>> temperature[:5]
+    array([-0.19, -0.25, -0.09, -0.16, -0.1])
+    >>> res.x[:5]
+    array([-0.18244619, -0.17823282, -0.17409373, -0.17080896, -0.16833158])
+
+    Let us plot measurements and Whittaker-Henderson smoothing.
+
+    >>> import matplotlib.pyplot as plt
+    >>> x = year[0] + np.arange(len(temperature)) / 12
+    >>> plt.plot(x, temperature, label="measurement")
+    >>> plt.plot(x, res.x, label="WH smooth")
+    >>> # Above, we set w = 0 for nan values of temperature. WH automatically
+    ... # inter- or extrapolates for all data points with w = 0.
+    ... plt.plot(x[w==0], res.x[w==0], color="red", label="inter-/extrapolation")
+    >>> plt.xlabel("year")
+    >>> plt.ylabel("temperature deviation [°C]")
+    >>> plt.title("Global Temperature Anomalies (ref. 1951-1980)")
+    >>> plt.legend()
+    >>> plt.show()
+
+    We can see that extrapolation has occurred at the right end of the signal, meaning
+    that NaNs existed in the data for the most recent dates, in particular months of
+    2026 that have not yet happened at the time of the data download in March 2026.
+
+    """
+    order = _validate_int(order, name="order", minimum=1)
+
+    signal = np.asarray(signal)
+    if signal.ndim != 1:
+        msg = f"Input array signal must be of shape (n,); got {signal.shape}"
+        raise ValueError(msg)
+
+    n = signal.shape[0]
+    if n < order + 1:
+        msg = f"Input array signal must be at least of shape ({order + 1},); got {n}."
+        raise ValueError(msg)
+
+    if weights is not None:
+        weights = np.asarray(weights)
+        if weights.shape != signal.shape:
+            msg = "Input array weights must have the same shape as the signal array."
+            raise ValueError(msg)
+        
+    if weights is None:
+        if not np.isfinite(signal).all():
+            raise ValueError("Input array signal must be finite.")
+    else:
+        if not np.isfinite(weights).all():
+            raise ValueError("Input array weights must be finite.")
+        if (mask := ~np.isfinite(signal)).any():
+            # Only weights * y matter in the end and weights must be 0 for all
+            # non-finite elements of signal.
+            if not (weights[mask] == 0).all():
+                raise ValueError("Input array weights must be zero for all non-finite "
+                                 "elements of signal.")
+            signal = np.nan_to_num(signal)
+
+
+    msg = f"Parameter lamb must be string 'reml' or a non-negative float; got {lamb=}."
+    if isinstance(lamb, str):
+        if lamb != "reml":
+            raise ValueError(msg)
+        def criterion(loglamb):
+            return -_reml(lamb=np.exp(loglamb), y=signal, order=order, weights=weights)
+        opt = minimize_scalar(criterion, bracket=[-10, 10])
+        lamb = np.exp(opt.x)
+
+    if lamb < 0:
+        raise ValueError(msg)
+    elif lamb == 0.0:
+        x = np.asarray(signal).copy()
+    else:
+        x, _ = _solve_WH_banded(signal, lamb=lamb, order=order, weights=weights)
+    return _RichResult(x=x, lamb=lamb)
+
+
+def _polynomial_fit(y, lamb, order=2, weights=None, calc_logdet=False):
+    """Polynomial fit equivalent to WH for lamb -> infinity."""
+    n = len(y)
+    x_range = np.arange(n)
+    poly = np.polynomial.Polynomial.fit(x=x_range, y=y, deg=order - 1, w=weights)
+    if calc_logdet:
+        # For large lambda, log|W + lambda D'D| ~ log|lambda D'D|
+        # (with determinant understood as product of non-zero eigenvalues). 
+        logdet_DtD = _logdet_difference_matrix(order=order, n=n)
+        logdet = (n - order) * np.log(lamb) + logdet_DtD
+    else:
+        logdet = 0.0
+    return poly(x_range), logdet
+
+
+def _solve_WH_banded(y, lamb, order=2, weights=None, calc_logdet=False, warn_user=True):
+    """
+    Solve the WH optimization problem via the normal equations.
+    
+    A @ x = y
+    A = I + lamb * P = I + lamb * D' @ D
+    D = difference matrix of order=`order` 
+
+    With weights W = diag(weights):
+    A = W + lamb * P
+    A @ x = W @ y
+
+    Returns
+    -------
+    x : ndarray
+        The solution.
+    logdet : float
+        Logarithm of the determinant of matrix A. Returns 0 if ``calc_logdet=False``.
+    """
+    n = y.shape[0]  # n >= p + 1 was already checked
+    p = order  # order of difference penalty
+    # Construct penalty matrix P = D'D of shape (n-p, n) as if n = 2p+1 (to save
+    # memory).
+    if n < 2*p + 1:
+        D = np.diff(np.eye(n), n=p, axis=0)  # shape (n-p, n)
+    else:
+        D = np.diff(np.eye(2*p + 1), n=p, axis=0)  # shape (p+1, 2p+1)
+    P_raw = D.T @ D  # shape (2p+1, 2p+1) if n >= 2p+1 else (n, n)
+
+    # Because our matrix A = np.eye(n, dtype=np.float64) + lamb * (D.T @ D) is
+    # symmetric and banded with u = l = p, we construct it in the lower "ab"-format
+    # for use in solveh_banded, i.e. each row in ab is a subdiagonal of A:
+    #   ab[0, :]   = np.diagonal(A, 0)
+    #   ab[1, :-1] = np.diagonal(A, 1)
+    #   ab[2, :-2] = np.diagonal(A, 2)
+    #   ..
+    ab = np.zeros((p + 1, min(2*p + 1, n)))
+    for i in range(p + 1):
+        ab[i, :ab.shape[1] - i] = np.diagonal(P_raw, i)
+    ab *= lamb
+    if n > 2*p + 1:
+        ab = np.concat(
+            [
+                ab[:, :p+1],
+                np.repeat(ab[:, p:p+1], n - (2*p+1), axis=1),
+                ab[:, -p:],
+            ],
+            axis=1,
+        )
+
+    if weights is None:
+        # Check if lambda is so large that A = I + lambda D'D = lambda D'D. We even add
+        # a factor of 8, i.e. A should have at least 4 bits from I (not only D'D).
+        # Note that the minimal diagonal element of D'D is always 1.
+        if lamb * np.finfo(np.float64).eps > 8:
+            # If lambda approaches infinity, WH approaches a polynomial fit.
+            x, logdet = _polynomial_fit(
+                y, lamb=lamb, order=order, calc_logdet=calc_logdet
+            )
+            info = 0
+        else:
+            ab[0, :] += 1.0  # This corresponds to np.eye(n).
+            x, logdet, info = _solveh_banded(ab, y, calc_logdet=calc_logdet)
+    else:
+        if (ab[0, :] == ab[0, :] + weights * 8).all():
+            # If lambda approaches infinity, WH approaches a polynomial fit.
+            x, logdet = _polynomial_fit(
+                y, lamb=lamb, order=order, weights=weights, calc_logdet=calc_logdet
+            )
+            info = 0
+        else:
+            ab[0, :] += weights
+            x, logdet, info = _solveh_banded(ab, weights * y, calc_logdet=calc_logdet)
+
+    if info > 0:
+        # LinAlgError(f"{info}th leading minor not positive definite")
+        # For very large values of lamb, we know that
+        #   - the linear solver breaks down
+        #   - the solution approaches a polynomial least squares fit of degree
+        #     order - 1.
+        # Note that for a certain large lamb, WH already reaches the polynomial least
+        # squares fit almost exactly. For larger lamb, WH starts to deviate from the
+        # polynomial (=worse solution due to numerical instability), until the solver
+        # breaks down and reports info > 0.
+        if warn_user:
+            msg_weights = "" if weights is None else " or due to the weights"
+            msg = (
+                "The linear solver in Whittaker-Henderson smoothing detected a "
+                "numerical instability. This is likely due to a very large value of "
+                f"{lamb=}"
+                + msg_weights + ". "
+                "As Whittaker-Henderson approaches a polynomial of degree 'order - 1' "
+                "for large lamb, this polynomial (via least squares) is returned."
+            )
+            warnings.warn(msg, UserWarning, stacklevel=2)
+        x, logdet = _polynomial_fit(
+            y, lamb, order=order, weights=weights, calc_logdet=calc_logdet
+        )
+    return x, logdet
+
+
+def _logdet_difference_matrix(order, n):
+    """Logarithm of the determinant of the difference matrix.
+
+    If D is the difference matrix of order=p, then this computes `log det(D @ D.T)`
+    which equals the sum of the log of non-zero eigenvalues of `D.T @ D`.
+    """
+    # product of eigenvalues =
+    # prod(binom(n+i-1, 2i-1), i=1..p) / prod(binom(2i, i), i=1..p-1)
+    # How to derive this formula? Well, ... some magic.
+    p = order
+    if order == 1:
+        return np.log(n)
+    logdet = 0.0
+    for i in range(1, p+1):
+        logdet += np.log(binom(n + i - 1, 2*i - 1) / binom(2*i, i)) 
+    logdet += np.log(binom(2*p, p))
+    return logdet
+
+
+def _reml(lamb, y, order, weights=None):
+    """Calculate the restricted maximum likelihood (REML).
+    
+    Parameters
+    ----------
+    lamb : penalty
+    y : signal
+    x : smoothed signal
+    order : order of the difference penalty.
+    weights : case weights
+
+    Returns
+    -------
+    reml : REML criterion
+
+    References
+    ----------
+    - Biessy https://arxiv.org/abs/2306.06932 (version 4)
+    - Wood https://doi.org/10.1111/j.1467-9868.2010.00749.x
+    """
+    n = y.shape[0]
+    x, logdet = _solve_WH_banded(
+        y=y, lamb=lamb, order=order, weights=weights, calc_logdet=True, warn_user=False
+    )
+    logdet_DtD = _logdet_difference_matrix(order=order, n=n)
+    residual = y - x
+    # Eq. 12 of Biessy gives the REML criterion:
+    # REML(lambda, sigma) = (log of restriced maximum likelihood)
+    #     = -1/2 ((y - theta) W (y - theta) / sigma^2 + lambda theta D'D theta / sigma^2
+    #             - log|lambda D'D| + log|(W + lambda D'D)| + (n - p) log(sigma^2)
+    #             + const
+    #            )
+    # where the constant term "const" does not depend on lambda or sigma and p is the
+    # order of the difference penalty.
+    # Note that Biessy then does not mention to use the profiled REML criterion, i.e.,
+    # analytically plug in the optimal sigma^2. This gives us
+    #     sigma^2 = r2 / (n - p)
+    #     r^2     = (y - theta) W (y - theta) + lambda theta D'D theta
+    #     profiled REML(lambda) =
+    #         -1/2 (
+    #               (n-p) (1 + log(r^2 / (n-p)))
+    #               -log|lambda D'D| + log|W + lambda D'D| + const
+    #              )
+    # This can be compared to Eq. 41 of Bates et al
+    # https://doi.org/10.18637/jss.v067.i01.
+    # An alternative derivation stems from a mixed model formulation of P-splines, see
+    # Currie and Durban https://doi.org/10.1191/1471082x02st039ob or Boer
+    # https://doi.org/10.1177/1471082X231178591. One then has 2 variance parameters
+    # sigma^2 (from y) and tau^2 (from the random effect) leading to
+    #     -1/2 ((y - theta) W (y - theta) / sigma^2 + theta D'D theta / tau^2 + ...
+    # One then sets tau^2 = sigma^2 / lambda.
+    if weights is None:
+        r2 = residual @ residual
+    else:
+        r2 = residual @ (weights * residual)
+    r2 += lamb * np.sum(np.diff(x, n=order)**2)  # + lambda theta D'D theta
+    reml = (n - order) * (1 + np.log(r2 / (n - order)))
+    reml -= (n - order) * np.log(lamb) + logdet_DtD  # -log|lambda D'D|
+    reml += logdet  # +log|W + lambda D'D|
+    reml *= -0.5
+    return reml
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/bsplines.py b/venv/lib/python3.12/site-packages/scipy/signal/bsplines.py
new file mode 100644
index 0000000000000000000000000000000000000000..0328d45c107bda78cbdbd374148237ca09ac411d
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/bsplines.py
@@ -0,0 +1,21 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.signal` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+__all__ = [  # noqa: F822
+    'spline_filter', 'gauss_spline',
+    'cspline1d', 'qspline1d', 'cspline1d_eval', 'qspline1d_eval',
+    'cspline2d', 'sepfir2d'
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="signal", module="bsplines",
+                                   private_modules=["_spline_filters"], all=__all__,
+                                   attribute=name)
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/filter_design.py b/venv/lib/python3.12/site-packages/scipy/signal/filter_design.py
new file mode 100644
index 0000000000000000000000000000000000000000..41dc230a7f24a7ac3209f821d8d0f9417130afbd
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/filter_design.py
@@ -0,0 +1,28 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.signal` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+__all__ = [  # noqa: F822
+    'findfreqs', 'freqs', 'freqz', 'tf2zpk', 'zpk2tf', 'normalize',
+    'lp2lp', 'lp2hp', 'lp2bp', 'lp2bs', 'bilinear', 'iirdesign',
+    'iirfilter', 'butter', 'cheby1', 'cheby2', 'ellip', 'bessel',
+    'band_stop_obj', 'buttord', 'cheb1ord', 'cheb2ord', 'ellipord',
+    'buttap', 'cheb1ap', 'cheb2ap', 'ellipap', 'besselap',
+    'BadCoefficients', 'freqs_zpk', 'freqz_zpk',
+    'tf2sos', 'sos2tf', 'zpk2sos', 'sos2zpk', 'group_delay',
+    'sosfreqz', 'freqz_sos', 'iirnotch', 'iirpeak', 'bilinear_zpk',
+    'lp2lp_zpk', 'lp2hp_zpk', 'lp2bp_zpk', 'lp2bs_zpk',
+    'gammatone', 'iircomb',
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="signal", module="filter_design",
+                                   private_modules=["_filter_design"], all=__all__,
+                                   attribute=name)
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/fir_filter_design.py b/venv/lib/python3.12/site-packages/scipy/signal/fir_filter_design.py
new file mode 100644
index 0000000000000000000000000000000000000000..4c7be58b151835a55eb494e31047e6b846e2dae8
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/fir_filter_design.py
@@ -0,0 +1,21 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.signal` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+__all__ = [  # noqa: F822
+    'kaiser_beta', 'kaiser_atten', 'kaiserord',
+    'firwin', 'firwin2', 'remez', 'firls', 'minimum_phase',
+    'firwin_2d',
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="signal", module="fir_filter_design",
+                                   private_modules=["_fir_filter_design"], all=__all__,
+                                   attribute=name)
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/lti_conversion.py b/venv/lib/python3.12/site-packages/scipy/signal/lti_conversion.py
new file mode 100644
index 0000000000000000000000000000000000000000..7080990afc9e23e51e8a45aaa146b64c58dda3cf
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/lti_conversion.py
@@ -0,0 +1,20 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.signal` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+__all__ = [  # noqa: F822
+    'tf2ss', 'abcd_normalize', 'ss2tf', 'zpk2ss', 'ss2zpk',
+    'cont2discrete', 'tf2zpk', 'zpk2tf', 'normalize'
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="signal", module="lti_conversion",
+                                   private_modules=["_lti_conversion"], all=__all__,
+                                   attribute=name)
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/ltisys.py b/venv/lib/python3.12/site-packages/scipy/signal/ltisys.py
new file mode 100644
index 0000000000000000000000000000000000000000..5123068de559f124bf444c12ef9824c3d14de64f
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/ltisys.py
@@ -0,0 +1,25 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.signal` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+__all__ = [  # noqa: F822
+    'lti', 'dlti', 'TransferFunction', 'ZerosPolesGain', 'StateSpace',
+    'lsim', 'impulse', 'step', 'bode',
+    'freqresp', 'place_poles', 'dlsim', 'dstep', 'dimpulse',
+    'dfreqresp', 'dbode',
+    'tf2zpk', 'zpk2tf', 'normalize', 'freqs',
+    'freqz', 'freqs_zpk', 'freqz_zpk', 'tf2ss', 'abcd_normalize',
+    'ss2tf', 'zpk2ss', 'ss2zpk', 'cont2discrete',
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="signal", module="ltisys",
+                                   private_modules=["_ltisys"], all=__all__,
+                                   attribute=name)
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/signaltools.py b/venv/lib/python3.12/site-packages/scipy/signal/signaltools.py
new file mode 100644
index 0000000000000000000000000000000000000000..85d426f5fb2605c639fc6dbd1b4d0284a3f11e1b
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/signaltools.py
@@ -0,0 +1,27 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.signal` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+__all__ = [  # noqa: F822
+    'correlate', 'correlation_lags', 'correlate2d',
+    'convolve', 'convolve2d', 'fftconvolve', 'oaconvolve',
+    'order_filter', 'medfilt', 'medfilt2d', 'wiener', 'lfilter',
+    'lfiltic', 'sosfilt', 'deconvolve', 'hilbert', 'hilbert2',
+    'unique_roots', 'invres', 'invresz', 'residue',
+    'residuez', 'resample', 'resample_poly', 'detrend',
+    'lfilter_zi', 'sosfilt_zi', 'sosfiltfilt', 'choose_conv_method',
+    'filtfilt', 'decimate', 'vectorstrength',
+    'dlti', 'upfirdn', 'get_window', 'cheby1', 'firwin'
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="signal", module="signaltools",
+                                   private_modules=["_signaltools"], all=__all__,
+                                   attribute=name)
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/spectral.py b/venv/lib/python3.12/site-packages/scipy/signal/spectral.py
new file mode 100644
index 0000000000000000000000000000000000000000..299ebed781b00a1f1f35e96c54f4c20d9bd9d0fc
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/spectral.py
@@ -0,0 +1,21 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.signal` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+__all__ = [  # noqa: F822
+    'periodogram', 'welch', 'lombscargle', 'csd', 'coherence',
+    'spectrogram', 'stft', 'istft', 'check_COLA', 'check_NOLA',
+    'get_window',
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="signal", module="spectral",
+                                   private_modules=["_spectral_py"], all=__all__,
+                                   attribute=name)
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/spline.py b/venv/lib/python3.12/site-packages/scipy/signal/spline.py
new file mode 100644
index 0000000000000000000000000000000000000000..30fb91ef8bbc17242959947b917dc41d7245cdc2
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/spline.py
@@ -0,0 +1,18 @@
+# This file is not meant for public use and will be removed in the future
+# versions of SciPy. Use the `scipy.signal` namespace for importing the
+# functions included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+
+__all__ = ['sepfir2d']  # noqa: F822
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="signal", module="spline",
+                                   private_modules=["_spline"], all=__all__,
+                                   attribute=name)
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/tests/__init__.py b/venv/lib/python3.12/site-packages/scipy/signal/tests/__init__.py
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diff --git a/venv/lib/python3.12/site-packages/scipy/signal/tests/_scipy_spectral_test_shim.py b/venv/lib/python3.12/site-packages/scipy/signal/tests/_scipy_spectral_test_shim.py
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--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/tests/_scipy_spectral_test_shim.py
@@ -0,0 +1,311 @@
+"""Helpers to utilize existing stft / istft tests for testing `ShortTimeFFT`.
+
+This module provides the functions stft_compare() and istft_compare(), which,
+compares the output between the existing (i)stft() and the shortTimeFFT based
+_(i)stft_wrapper() implementations in this module.
+
+For testing add the following imports to the file ``tests/test_spectral.py``::
+
+    from ._scipy_spectral_test_shim import stft_compare as stft
+    from ._scipy_spectral_test_shim import istft_compare as istft
+
+and remove the existing imports of stft and istft.
+
+The idea of these wrappers is not to provide a backward-compatible interface
+but to demonstrate that the ShortTimeFFT implementation is at least as capable
+as the existing one and delivers comparable results. Furthermore, the
+wrappers highlight the different philosophies of the implementations,
+especially in the border handling.
+"""
+import platform
+from typing import cast, Literal
+
+import numpy as np
+from numpy.testing import assert_allclose
+
+from scipy.signal import ShortTimeFFT
+from scipy.signal import get_window, stft, istft
+from scipy.signal._arraytools import const_ext, even_ext, odd_ext, zero_ext
+from scipy.signal._short_time_fft import FFT_MODE_TYPE
+from scipy.signal._spectral_py import _triage_segments
+
+
+def _stft_wrapper(x, fs=1.0, window='hann', nperseg=256, noverlap=None,
+                  nfft=None, detrend=False, return_onesided=True,
+                  boundary='zeros', padded=True, axis=-1, scaling='spectrum'):
+    """Wrapper for the SciPy `stft()` function based on `ShortTimeFFT` for
+    unit testing.
+
+    Handling the boundary and padding is where `ShortTimeFFT` and `stft()`
+    differ in behavior. Parts of `_spectral_helper()` were copied to mimic
+    the` stft()` behavior.
+
+    This function is meant to be solely used by `stft_compare()`.
+    """
+    if scaling not in ('psd', 'spectrum'):  # same errors as in original stft:
+        raise ValueError(f"Parameter {scaling=} not in ['spectrum', 'psd']!")
+
+    # The following lines are taken from the original _spectral_helper():
+    boundary_funcs = {'even': even_ext,
+                      'odd': odd_ext,
+                      'constant': const_ext,
+                      'zeros': zero_ext,
+                      None: None}
+
+    if boundary not in boundary_funcs:
+        raise ValueError(f"Unknown boundary option '{boundary}', must be one" +
+                         f" of: {list(boundary_funcs.keys())}")
+    if x.size == 0:
+        return np.empty(x.shape), np.empty(x.shape), np.empty(x.shape)
+
+    if nperseg is not None:  # if specified by user
+        nperseg = int(nperseg)
+        if nperseg < 1:
+            raise ValueError('nperseg must be a positive integer')
+
+    # parse window; if array like, then set nperseg = win.shape
+    win, nperseg = _triage_segments(window, nperseg,
+                                    input_length=x.shape[axis])
+
+    if nfft is None:
+        nfft = nperseg
+    elif nfft < nperseg:
+        raise ValueError('nfft must be greater than or equal to nperseg.')
+    else:
+        nfft = int(nfft)
+
+    if noverlap is None:
+        noverlap = nperseg//2
+    else:
+        noverlap = int(noverlap)
+    if noverlap >= nperseg:
+        raise ValueError('noverlap must be less than nperseg.')
+    nstep = nperseg - noverlap
+    n = x.shape[axis]
+
+    # Padding occurs after boundary extension, so that the extended signal ends
+    # in zeros, instead of introducing an impulse at the end.
+    # I.e. if x = [..., 3, 2]
+    # extend then pad -> [..., 3, 2, 2, 3, 0, 0, 0]
+    # pad then extend -> [..., 3, 2, 0, 0, 0, 2, 3]
+
+    if boundary is not None:
+        ext_func = boundary_funcs[boundary]
+        # Extend by nperseg//2 in front and back:
+        x = ext_func(x, nperseg//2, axis=axis)
+
+    if padded:
+        # Pad to integer number of windowed segments
+        # I.e make x.shape[-1] = nperseg + (nseg-1)*nstep, with integer nseg
+        x = np.moveaxis(x, axis, -1)
+
+        # This is an edge case where shortTimeFFT returns one more time slice
+        # than the Scipy stft() shorten to remove last time slice:
+        if n % 2 == 1 and nperseg % 2 == 1 and noverlap % 2 == 1:
+            x = x[..., : -1]
+
+        nadd = (-(x.shape[-1]-nperseg) % nstep) % nperseg
+        zeros_shape = list(x.shape[:-1]) + [nadd]
+        x = np.concatenate((x, np.zeros(zeros_shape)), axis=-1)
+        x = np.moveaxis(x, -1, axis)
+
+    #  ... end original _spectral_helper() code.
+    scale_to = {'spectrum': 'magnitude', 'psd': 'psd'}[scaling]
+
+    if np.iscomplexobj(x) and return_onesided:
+        return_onesided = False
+    # using cast() to make mypy happy:
+    fft_mode = cast(FFT_MODE_TYPE, 'onesided' if return_onesided else 'twosided')
+
+    ST = ShortTimeFFT(win, nstep, fs, fft_mode=fft_mode, mfft=nfft,
+                      scale_to=scale_to, phase_shift=None)
+
+    k_off = nperseg // 2
+    p0 = 0  # ST.lower_border_end[1] + 1
+    nn = x.shape[axis] if padded else n+k_off+1
+    # number of frames akin to legacy stft computation
+    p1 = (x.shape[axis] - nperseg) // nstep + 1 
+
+    detr = None if detrend is False else detrend
+    Sxx = ST.stft_detrend(x, detr, p0, p1, k_offset=k_off, axis=axis)
+    t = ST.t(nn, 0, p1 - p0, k_offset=0 if boundary is not None else k_off)
+    if x.dtype in (np.float32, np.complex64):
+        Sxx = Sxx.astype(np.complex64)
+
+    return ST.f, t, Sxx
+
+
+def _istft_wrapper(Zxx, fs=1.0, window='hann', nperseg=None, noverlap=None,
+                   nfft=None, input_onesided=True, boundary=True, time_axis=-1,
+                   freq_axis=-2, scaling='spectrum') -> \
+        tuple[np.ndarray, np.ndarray, tuple[int, int]]:
+    """Wrapper for the SciPy `istft()` function based on `ShortTimeFFT` for
+        unit testing.
+
+    Note that only option handling is implemented as far as to handle the unit
+    tests. E.g., the case ``nperseg=None`` is not handled.
+
+    This function is meant to be solely used by `istft_compare()`.
+    """
+    # *** Lines are taken from _spectral_py.istft() ***:
+    if Zxx.ndim < 2:
+        raise ValueError('Input stft must be at least 2d!')
+
+    if freq_axis == time_axis:
+        raise ValueError('Must specify differing time and frequency axes!')
+
+    nseg = Zxx.shape[time_axis]
+
+    if input_onesided:
+        # Assume even segment length
+        n_default = 2*(Zxx.shape[freq_axis] - 1)
+    else:
+        n_default = Zxx.shape[freq_axis]
+
+    # Check windowing parameters
+    if nperseg is None:
+        nperseg = n_default
+    else:
+        nperseg = int(nperseg)
+        if nperseg < 1:
+            raise ValueError('nperseg must be a positive integer')
+
+    if nfft is None:
+        if input_onesided and (nperseg == n_default + 1):
+            # Odd nperseg, no FFT padding
+            nfft = nperseg
+        else:
+            nfft = n_default
+    elif nfft < nperseg:
+        raise ValueError('nfft must be greater than or equal to nperseg.')
+    else:
+        nfft = int(nfft)
+
+    if noverlap is None:
+        noverlap = nperseg//2
+    else:
+        noverlap = int(noverlap)
+    if noverlap >= nperseg:
+        raise ValueError('noverlap must be less than nperseg.')
+    nstep = nperseg - noverlap
+
+    # Get window as array
+    if isinstance(window, str) or type(window) is tuple:
+        win = get_window(window, nperseg)
+    else:
+        win = np.asarray(window)
+        if len(win.shape) != 1:
+            raise ValueError('window must be 1-D')
+        if win.shape[0] != nperseg:
+            raise ValueError(f'window must have length of {nperseg}')
+
+    outputlength = nperseg + (nseg-1)*nstep
+    # *** End block of: Taken from _spectral_py.istft() ***
+
+    # Using cast() to make mypy happy:
+    fft_mode = cast(FFT_MODE_TYPE, 'onesided' if input_onesided else 'twosided')
+    scale_to = cast(Literal['magnitude', 'psd'],
+                    {'spectrum': 'magnitude', 'psd': 'psd'}[scaling])
+
+    ST = ShortTimeFFT(win, nstep, fs, fft_mode=fft_mode, mfft=nfft,
+                      scale_to=scale_to, phase_shift=None)
+
+    if boundary:
+        j = nperseg if nperseg % 2 == 0 else nperseg - 1
+        k0 = ST.k_min + nperseg // 2
+        k1 = outputlength - j + k0
+    else:
+        raise NotImplementedError("boundary=False does not make sense with" +
+                                  "ShortTimeFFT.istft()!")
+
+    x = ST.istft(Zxx, k0=k0, k1=k1, f_axis=freq_axis, t_axis=time_axis)
+    t = np.arange(k1 - k0) * ST.T
+    k_hi = ST.upper_border_begin(k1 - k0)[0]
+    # using cast() to make mypy happy:
+    return t, x, (ST.lower_border_end[0], k_hi)
+
+
+def stft_compare(x, fs=1.0, window='hann', nperseg=256, noverlap=None,
+                 nfft=None, detrend=False, return_onesided=True,
+                 boundary='zeros', padded=True, axis=-1, scaling='spectrum'):
+    """Assert that the results from the existing `stft()` and `_stft_wrapper()`
+    are close to each other.
+
+    For comparing the STFT values an absolute tolerance of the floating point
+    resolution was added to circumvent problems with the following tests:
+    * For float32 the tolerances are much higher in
+      TestSTFT.test_roundtrip_float32()).
+    * The TestSTFT.test_roundtrip_scaling() has a high relative deviation.
+      Interestingly this did not appear in Scipy 1.9.1 but only in the current
+      development version.
+    """
+    kw = dict(x=x, fs=fs, window=window, nperseg=nperseg, noverlap=noverlap,
+              nfft=nfft, detrend=detrend, return_onesided=return_onesided,
+              boundary=boundary, padded=padded, axis=axis, scaling=scaling)
+    f, t, Zxx = stft(**kw)
+    f_wrapper, t_wrapper, Zxx_wrapper = _stft_wrapper(**kw)
+
+    e_msg_part = " of `stft_wrapper()` differ from `stft()`."
+    assert_allclose(f_wrapper, f, err_msg=f"Frequencies {e_msg_part}")
+    assert_allclose(t_wrapper, t, err_msg=f"Time slices {e_msg_part}")
+
+    # Adapted tolerances to account for:
+    atol = np.finfo(Zxx.dtype).resolution * 2
+    assert_allclose(Zxx_wrapper, Zxx, atol=atol,
+                    err_msg=f"STFT values {e_msg_part}")
+    return f, t, Zxx
+
+
+def istft_compare(Zxx, fs=1.0, window='hann', nperseg=None, noverlap=None,
+                  nfft=None, input_onesided=True, boundary=True, time_axis=-1,
+                  freq_axis=-2, scaling='spectrum'):
+    """Assert that the results from the existing `istft()` and
+    `_istft_wrapper()` are close to each other.
+
+    Quirks:
+    * If ``boundary=False`` the comparison is skipped, since it does not
+      make sense with ShortTimeFFT.istft(). Only used in test
+      TestSTFT.test_roundtrip_boundary_extension().
+    * If ShortTimeFFT.istft() decides the STFT is not invertible, the
+      comparison is skipped, since istft() only emits a warning and does not
+      return a correct result. Only used in
+      ShortTimeFFT.test_roundtrip_not_nola().
+    * For comparing the signals an absolute tolerance of the floating point
+      resolution was added to account for the low accuracy of float32 (Occurs
+      only in TestSTFT.test_roundtrip_float32()).
+    """
+    kw = dict(Zxx=Zxx, fs=fs, window=window, nperseg=nperseg,
+              noverlap=noverlap, nfft=nfft, input_onesided=input_onesided,
+              boundary=boundary, time_axis=time_axis, freq_axis=freq_axis,
+              scaling=scaling)
+
+    t, x = istft(**kw)
+    if not boundary:  # skip test_roundtrip_boundary_extension():
+        return t, x  # _istft_wrapper does() not implement this case
+    try:  # if inversion fails, istft() only emits a warning:
+        t_wrapper, x_wrapper, (k_lo, k_hi) = _istft_wrapper(**kw)
+    except ValueError as v:  # Do nothing if inversion fails:
+        if v.args[0] == "Short-time Fourier Transform not invertible!":
+            return t, x
+        raise v
+
+    e_msg_part = " of `istft_wrapper()` differ from `istft()`"
+    assert_allclose(t, t_wrapper, err_msg=f"Sample times {e_msg_part}")
+
+    # Adapted tolerances to account for resolution loss:
+    atol = np.finfo(x.dtype).resolution*2  # instead of default atol = 0
+    rtol = 1e-7  # default for np.allclose()
+
+    # Relax atol on 32-Bit platforms a bit to pass CI tests.
+    #  - Not clear why there are discrepancies (in the FFT maybe?)
+    #  - Not sure what changed on 'i686' since earlier on those test passed
+    if x.dtype == np.float32 and platform.machine() == 'i686':
+        # float32 gets only used by TestSTFT.test_roundtrip_float32() so
+        # we are using the tolerances from there to circumvent CI problems
+        atol, rtol = 1e-4, 1e-5
+    else:
+        atol = max(atol, 1e-12)  # 2e-15 seems too tight
+
+    assert_allclose(x_wrapper[k_lo:k_hi], x[k_lo:k_hi], atol=atol, rtol=rtol,
+                    err_msg=f"Signal values {e_msg_part}")
+    return t, x
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/tests/data/GLB.Ts+dSST.csv b/venv/lib/python3.12/site-packages/scipy/signal/tests/data/GLB.Ts+dSST.csv
new file mode 100644
index 0000000000000000000000000000000000000000..7d12a2c67d593bf84b1504d12141af16104d5786
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/tests/data/GLB.Ts+dSST.csv
@@ -0,0 +1,149 @@
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+1998,.58,.88,.63,.63,.68,.77,.66,.65,.42,.42,.43,.54,.61,.61,.68,.65,.69,.42
+1999,.48,.64,.32,.31,.26,.36,.38,.31,.38,.34,.37,.40,.38,.39,.55,.30,.35,.36
+2000,.25,.55,.55,.56,.35,.40,.39,.42,.38,.26,.30,.27,.39,.40,.40,.49,.40,.32
+2001,.45,.43,.55,.50,.57,.52,.59,.48,.51,.49,.72,.55,.53,.51,.38,.54,.53,.57
+2002,.76,.78,.88,.57,.64,.53,.61,.53,.63,.54,.59,.44,.62,.63,.70,.70,.56,.59
+2003,.74,.58,.60,.55,.60,.47,.58,.64,.62,.72,.52,.74,.61,.59,.59,.58,.56,.62
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+2007,1.01,.70,.71,.77,.69,.61,.59,.60,.60,.59,.59,.49,.66,.69,.83,.72,.60,.59
+2008,.30,.38,.74,.53,.49,.49,.60,.45,.60,.66,.69,.53,.54,.54,.39,.59,.51,.65
+2009,.64,.53,.53,.61,.65,.63,.73,.68,.71,.65,.79,.67,.65,.64,.57,.60,.68,.72
+2010,.74,.83,.92,.85,.75,.67,.63,.66,.62,.71,.81,.45,.72,.74,.75,.84,.65,.71
+2011,.52,.47,.65,.64,.53,.62,.70,.74,.55,.65,.59,.60,.61,.59,.48,.61,.69,.60
+2012,.47,.48,.56,.72,.78,.64,.58,.65,.71,.79,.78,.52,.64,.65,.52,.69,.63,.76
+2013,.71,.61,.67,.53,.60,.69,.60,.70,.76,.69,.83,.70,.67,.66,.61,.60,.66,.76
+2014,.76,.55,.78,.80,.86,.67,.58,.83,.87,.80,.67,.78,.75,.74,.67,.81,.69,.78
+2015,.86,.91,.96,.75,.79,.81,.73,.79,.83,1.07,1.05,1.17,.89,.86,.85,.83,.78,.99
+2016,1.17,1.36,1.35,1.08,.95,.80,.84,1.01,.90,.86,.91,.86,1.01,1.03,1.23,1.13,.89,.89
+2017,1.02,1.13,1.16,.93,.91,.71,.82,.87,.74,.88,.87,.93,.91,.91,1.00,1.00,.80,.83
+2018,.82,.84,.88,.88,.81,.76,.83,.78,.80,1.01,.83,.92,.85,.85,.86,.86,.79,.88
+2019,.93,.95,1.17,1.01,.86,.90,.94,.95,.93,1.00,.99,1.11,.98,.96,.94,1.01,.93,.97
+2020,1.18,1.24,1.18,1.12,.99,.91,.89,.86,.96,.87,1.08,.79,1.01,1.03,1.17,1.10,.89,.97
+2021,.81,.64,.89,.76,.79,.85,.92,.81,.92,.98,.92,.87,.85,.84,.75,.81,.86,.94
+2022,.91,.89,1.04,.83,.84,.92,.94,.94,.88,.97,.73,.79,.89,.90,.89,.90,.93,.86
+2023,.87,.96,1.23,.99,.94,1.08,1.19,1.19,1.48,1.34,1.40,1.35,1.17,1.12,.88,1.05,1.15,1.41
+2024,1.25,1.43,1.39,1.31,1.16,1.24,1.20,1.30,1.23,1.34,1.29,1.26,1.28,1.29,1.34,1.29,1.25,1.29
+2025,1.37,1.26,1.37,1.24,1.08,1.06,1.02,1.17,1.25,1.19,1.21,1.07,1.19,1.21,1.30,1.23,1.08,1.21
+2026,1.08,1.24,***,***,***,***,***,***,***,***,***,***,***,***,1.13,***,***,***
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/tests/mpsig.py b/venv/lib/python3.12/site-packages/scipy/signal/tests/mpsig.py
new file mode 100644
index 0000000000000000000000000000000000000000..d129de74e5df00c22bc0b82c7d3f7b52483941f9
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/tests/mpsig.py
@@ -0,0 +1,122 @@
+"""
+Some signal functions implemented using mpmath.
+"""
+
+try:
+    import mpmath
+except ImportError:
+    mpmath = None
+
+
+def _prod(seq):
+    """Returns the product of the elements in the sequence `seq`."""
+    p = 1
+    for elem in seq:
+        p *= elem
+    return p
+
+
+def _relative_degree(z, p):
+    """
+    Return relative degree of transfer function from zeros and poles.
+
+    This is simply len(p) - len(z), which must be nonnegative.
+    A ValueError is raised if len(p) < len(z).
+    """
+    degree = len(p) - len(z)
+    if degree < 0:
+        raise ValueError("Improper transfer function. "
+                         "Must have at least as many poles as zeros.")
+    return degree
+
+
+def _zpkbilinear(z, p, k, fs):
+    """Bilinear transformation to convert a filter from analog to digital."""
+
+    degree = _relative_degree(z, p)
+
+    fs2 = 2*fs
+
+    # Bilinear transform the poles and zeros
+    z_z = [(fs2 + z1) / (fs2 - z1) for z1 in z]
+    p_z = [(fs2 + p1) / (fs2 - p1) for p1 in p]
+
+    # Any zeros that were at infinity get moved to the Nyquist frequency
+    z_z.extend([-1] * degree)
+
+    # Compensate for gain change
+    numer = _prod(fs2 - z1 for z1 in z)
+    denom = _prod(fs2 - p1 for p1 in p)
+    k_z = k * numer / denom
+
+    return z_z, p_z, k_z.real
+
+
+def _zpklp2lp(z, p, k, wo=1):
+    """Transform a lowpass filter to a different cutoff frequency."""
+
+    degree = _relative_degree(z, p)
+
+    # Scale all points radially from origin to shift cutoff frequency
+    z_lp = [wo * z1 for z1 in z]
+    p_lp = [wo * p1 for p1 in p]
+
+    # Each shifted pole decreases gain by wo, each shifted zero increases it.
+    # Cancel out the net change to keep overall gain the same
+    k_lp = k * wo**degree
+
+    return z_lp, p_lp, k_lp
+
+
+def _butter_analog_poles(n):
+    """
+    Poles of an analog Butterworth lowpass filter.
+
+    This is the same calculation as scipy.signal.buttap(n) or
+    scipy.signal.butter(n, 1, analog=True, output='zpk'), but mpmath is used,
+    and only the poles are returned.
+    """
+    poles = [-mpmath.exp(1j*mpmath.pi*k/(2*n)) for k in range(-n+1, n, 2)]
+    return poles
+
+
+def butter_lp(n, Wn):
+    """
+    Lowpass Butterworth digital filter design.
+
+    This computes the same result as scipy.signal.butter(n, Wn, output='zpk'),
+    but it uses mpmath, and the results are returned in lists instead of NumPy
+    arrays.
+    """
+    zeros = []
+    poles = _butter_analog_poles(n)
+    k = 1
+    fs = 2
+    warped = 2 * fs * mpmath.tan(mpmath.pi * Wn / fs)
+    z, p, k = _zpklp2lp(zeros, poles, k, wo=warped)
+    z, p, k = _zpkbilinear(z, p, k, fs=fs)
+    return z, p, k
+
+
+def zpkfreqz(z, p, k, worN=None):
+    """
+    Frequency response of a filter in zpk format, using mpmath.
+
+    This is the same calculation as scipy.signal.freqz, but the input is in
+    zpk format, the calculation is performed using mpath, and the results are
+    returned in lists instead of NumPy arrays.
+    """
+    if worN is None or isinstance(worN, int):
+        N = worN or 512
+        ws = [mpmath.pi * mpmath.mpf(j) / N for j in range(N)]
+    else:
+        ws = worN
+
+    h = []
+    for wk in ws:
+        zm1 = mpmath.exp(1j * wk)
+        numer = _prod([zm1 - t for t in z])
+        denom = _prod([zm1 - t for t in p])
+        hk = k * numer / denom
+        h.append(hk)
+    return ws, h
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/tests/test_array_tools.py b/venv/lib/python3.12/site-packages/scipy/signal/tests/test_array_tools.py
new file mode 100644
index 0000000000000000000000000000000000000000..4bda9716e0bc4b6ad3ed0c3954147043b74c421a
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/tests/test_array_tools.py
@@ -0,0 +1,111 @@
+import numpy as np
+
+from scipy._lib._array_api import xp_assert_equal
+from pytest import raises as assert_raises
+
+from scipy.signal._arraytools import (axis_slice, axis_reverse,
+     odd_ext, even_ext, const_ext, zero_ext)
+
+
+class TestArrayTools:
+
+    def test_axis_slice(self):
+        a = np.arange(12).reshape(3, 4)
+
+        s = axis_slice(a, start=0, stop=1, axis=0)
+        xp_assert_equal(s, a[0:1, :])
+
+        s = axis_slice(a, start=-1, axis=0)
+        xp_assert_equal(s, a[-1:, :])
+
+        s = axis_slice(a, start=0, stop=1, axis=1)
+        xp_assert_equal(s, a[:, 0:1])
+
+        s = axis_slice(a, start=-1, axis=1)
+        xp_assert_equal(s, a[:, -1:])
+
+        s = axis_slice(a, start=0, step=2, axis=0)
+        xp_assert_equal(s, a[::2, :])
+
+        s = axis_slice(a, start=0, step=2, axis=1)
+        xp_assert_equal(s, a[:, ::2])
+
+    def test_axis_reverse(self):
+        a = np.arange(12).reshape(3, 4)
+
+        r = axis_reverse(a, axis=0)
+        xp_assert_equal(r, a[::-1, :])
+
+        r = axis_reverse(a, axis=1)
+        xp_assert_equal(r, a[:, ::-1])
+
+    def test_odd_ext(self):
+        a = np.array([[1, 2, 3, 4, 5],
+                      [9, 8, 7, 6, 5]])
+
+        odd = odd_ext(a, 2, axis=1)
+        expected = np.array([[-1, 0, 1, 2, 3, 4, 5, 6, 7],
+                             [11, 10, 9, 8, 7, 6, 5, 4, 3]])
+        xp_assert_equal(odd, expected)
+
+        odd = odd_ext(a, 1, axis=0)
+        expected = np.array([[-7, -4, -1, 2, 5],
+                             [1, 2, 3, 4, 5],
+                             [9, 8, 7, 6, 5],
+                             [17, 14, 11, 8, 5]])
+        xp_assert_equal(odd, expected)
+
+        assert_raises(ValueError, odd_ext, a, 2, axis=0)
+        assert_raises(ValueError, odd_ext, a, 5, axis=1)
+
+    def test_even_ext(self):
+        a = np.array([[1, 2, 3, 4, 5],
+                      [9, 8, 7, 6, 5]])
+
+        even = even_ext(a, 2, axis=1)
+        expected = np.array([[3, 2, 1, 2, 3, 4, 5, 4, 3],
+                             [7, 8, 9, 8, 7, 6, 5, 6, 7]])
+        xp_assert_equal(even, expected)
+
+        even = even_ext(a, 1, axis=0)
+        expected = np.array([[9, 8, 7, 6, 5],
+                             [1, 2, 3, 4, 5],
+                             [9, 8, 7, 6, 5],
+                             [1, 2, 3, 4, 5]])
+        xp_assert_equal(even, expected)
+
+        assert_raises(ValueError, even_ext, a, 2, axis=0)
+        assert_raises(ValueError, even_ext, a, 5, axis=1)
+
+    def test_const_ext(self):
+        a = np.array([[1, 2, 3, 4, 5],
+                      [9, 8, 7, 6, 5]])
+
+        const = const_ext(a, 2, axis=1)
+        expected = np.array([[1, 1, 1, 2, 3, 4, 5, 5, 5],
+                             [9, 9, 9, 8, 7, 6, 5, 5, 5]])
+        xp_assert_equal(const, expected)
+
+        const = const_ext(a, 1, axis=0)
+        expected = np.array([[1, 2, 3, 4, 5],
+                             [1, 2, 3, 4, 5],
+                             [9, 8, 7, 6, 5],
+                             [9, 8, 7, 6, 5]])
+        xp_assert_equal(const, expected)
+
+    def test_zero_ext(self):
+        a = np.array([[1, 2, 3, 4, 5],
+                      [9, 8, 7, 6, 5]])
+
+        zero = zero_ext(a, 2, axis=1)
+        expected = np.array([[0, 0, 1, 2, 3, 4, 5, 0, 0],
+                             [0, 0, 9, 8, 7, 6, 5, 0, 0]])
+        xp_assert_equal(zero, expected)
+
+        zero = zero_ext(a, 1, axis=0)
+        expected = np.array([[0, 0, 0, 0, 0],
+                             [1, 2, 3, 4, 5],
+                             [9, 8, 7, 6, 5],
+                             [0, 0, 0, 0, 0]])
+        xp_assert_equal(zero, expected)
+
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/tests/test_bsplines.py b/venv/lib/python3.12/site-packages/scipy/signal/tests/test_bsplines.py
new file mode 100644
index 0000000000000000000000000000000000000000..2338132a7f5cf2de4757dcd7656a739b39a32522
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/tests/test_bsplines.py
@@ -0,0 +1,392 @@
+# pylint: disable=missing-docstring
+import math
+import numpy as np
+
+from scipy._lib._array_api import (
+    assert_almost_equal, xp_assert_close, xp_assert_equal, make_xp_test_case,
+    xp_default_dtype, array_namespace, _xp_copy_to_numpy
+)
+import pytest
+from pytest import raises
+
+from scipy import signal
+
+skip_xp_backends = pytest.mark.skip_xp_backends
+xfail_xp_backends = pytest.mark.xfail_xp_backends
+
+lazy_xp_modules = [signal]
+
+
+class TestBSplines:
+    """Test behaviors of B-splines. Some of the values tested against were
+    returned as of SciPy 1.1.0 and are included for regression testing
+    purposes. Others (at integer points) are compared to theoretical
+    expressions (cf. Unser, Aldroubi, Eden, IEEE TSP 1993, Table 1)."""
+
+    @make_xp_test_case(signal.spline_filter)  # type:ignore[attr-defined]
+    def test_spline_filter(self, xp):
+        rng = np.random.RandomState(12457)
+        # Test the type-error branch
+        raises(TypeError, signal.spline_filter, xp.asarray([0]), 0)
+        # Test the real branch
+        data_array_real = rng.rand(12, 12)
+        # make the magnitude exceed 1, and make some negative
+        data_array_real = 10*(1-2*data_array_real)
+        data_array_real = xp.asarray(data_array_real)
+        result_array_real = xp.asarray(
+            [[-.463312621, 8.33391222, .697290949, 5.28390836,
+              5.92066474, 6.59452137, 9.84406950, -8.78324188,
+              7.20675750, -8.17222994, -4.38633345, 9.89917069],
+             [2.67755154, 6.24192170, -3.15730578, 9.87658581,
+              -9.96930425, 3.17194115, -4.50919947, 5.75423446,
+              9.65979824, -8.29066885, .971416087, -2.38331897],
+             [-7.08868346, 4.89887705, -1.37062289, 7.70705838,
+              2.51526461, 3.65885497, 5.16786604, -8.77715342e-03,
+              4.10533325, 9.04761993, -.577960351, 9.86382519],
+             [-4.71444301, -1.68038985, 2.84695116, 1.14315938,
+              -3.17127091, 1.91830461, 7.13779687, -5.35737482,
+              -9.66586425, -9.87717456, 9.93160672, 4.71948144],
+             [9.49551194, -1.92958436, 6.25427993, -9.05582911,
+              3.97562282, 7.68232426, -1.04514824, -5.86021443,
+              -8.43007451, 5.47528997, 2.06330736, -8.65968112],
+             [-8.91720100, 8.87065356, 3.76879937, 2.56222894,
+              -.828387146, 8.72288903, 6.42474741, -6.84576083,
+              9.94724115, 6.90665380, -6.61084494, -9.44907391],
+             [9.25196790, -.774032030, 7.05371046, -2.73505725,
+              2.53953305, -1.82889155, 2.95454824, -1.66362046,
+              5.72478916, -3.10287679, 1.54017123, -7.87759020],
+             [-3.98464539, -2.44316992, -1.12708657, 1.01725672,
+              -8.89294671, -5.42145629, -6.16370321, 2.91775492,
+              9.64132208, .702499998, -2.02622392, 1.56308431],
+             [-2.22050773, 7.89951554, 5.98970713, -7.35861835,
+              5.45459283, -7.76427957, 3.67280490, -4.05521315,
+              4.51967507, -3.22738749, -3.65080177, 3.05630155],
+             [-6.21240584, -.296796126, -8.34800163, 9.21564563,
+              -3.61958784, -4.77120006, -3.99454057, 1.05021988e-03,
+              -6.95982829, 6.04380797, 8.43181250, -2.71653339],
+             [1.19638037, 6.99718842e-02, 6.72020394, -2.13963198,
+              3.75309875, -5.70076744, 5.92143551, -7.22150575,
+              -3.77114594, -1.11903194, -5.39151466, 3.06620093],
+             [9.86326886, 1.05134482, -7.75950607, -3.64429655,
+              7.81848957, -9.02270373, 3.73399754, -4.71962549,
+              -7.71144306, 3.78263161, 6.46034818, -4.43444731]], dtype=xp.float64)
+        xp_assert_close(signal.spline_filter(data_array_real, 0),
+                        result_array_real)
+
+    @xfail_xp_backends("cupy", reason="https://github.com/cupy/cupy/issues/9758")
+    @make_xp_test_case(signal.spline_filter)  # type:ignore[attr-defined]
+    def test_spline_filter_complex(self, xp):
+        rng = np.random.RandomState(12457)
+        data_array_complex = rng.rand(7, 7) + rng.rand(7, 7)*1j
+        # make the magnitude exceed 1, and make some negative
+        data_array_complex = 10*(1+1j-2*data_array_complex)
+        data_array_complex = xp.asarray(data_array_complex)
+
+        result_array_complex = xp.asarray(
+            [[-4.61489230e-01-1.92994022j, 8.33332443+6.25519943j,
+              6.96300745e-01-9.05576038j, 5.28294849+3.97541356j,
+              5.92165565+7.68240595j, 6.59493160-1.04542804j,
+              9.84503460-5.85946894j],
+             [-8.78262329-8.4295969j, 7.20675516+5.47528982j,
+              -8.17223072+2.06330729j, -4.38633347-8.65968037j,
+              9.89916801-8.91720295j, 2.67755103+8.8706522j,
+              6.24192142+3.76879835j],
+             [-3.15627527+2.56303072j, 9.87658501-0.82838702j,
+              -9.96930313+8.72288895j, 3.17193985+6.42474651j,
+              -4.50919819-6.84576082j, 5.75423431+9.94723988j,
+              9.65979767+6.90665293j],
+             [-8.28993416-6.61064005j, 9.71416473e-01-9.44907284j,
+              -2.38331890+9.25196648j, -7.08868170-0.77403212j,
+              4.89887714+7.05371094j, -1.37062311-2.73505688j,
+              7.70705748+2.5395329j],
+             [2.51528406-1.82964492j, 3.65885472+2.95454836j,
+              5.16786575-1.66362023j, -8.77737999e-03+5.72478867j,
+              4.10533333-3.10287571j, 9.04761887+1.54017115j,
+              -5.77960968e-01-7.87758923j],
+             [9.86398506-3.98528528j, -4.71444130-2.44316983j,
+              -1.68038976-1.12708664j, 2.84695053+1.01725709j,
+              1.14315915-8.89294529j, -3.17127085-5.42145538j,
+              1.91830420-6.16370344j],
+             [7.13875294+2.91851187j, -5.35737514+9.64132309j,
+              -9.66586399+0.70250005j, -9.87717438-2.0262239j,
+              9.93160629+1.5630846j, 4.71948051-2.22050714j,
+              9.49550819+7.8995142j]], dtype=xp.complex128)
+        # FIXME: for complex types, the computations are done in
+        # single precision (reason unclear). When this is changed,
+        # this test needs updating.
+        xp_assert_close(signal.spline_filter(data_array_complex, 0),
+                        result_array_complex, rtol=1e-6)
+
+    @make_xp_test_case(signal.gauss_spline)  # type:ignore[attr-defined]
+    def test_gauss_spline(self, xp):
+        assert math.isclose(signal.gauss_spline(0, 0), 1.381976597885342)
+
+        xp_assert_close(signal.gauss_spline(xp.asarray([1.]), 1),
+                        xp.asarray([0.04865217]), atol=1e-9
+        )
+
+    @skip_xp_backends(np_only=True, reason="deliberate: array-likes are accepted")
+    @make_xp_test_case(signal.gauss_spline)  # type:ignore[attr-defined]
+    def test_gauss_spline_list(self, xp):
+        # regression test for gh-12152 (accept array_like)
+        knots = [-1.0, 0.0, -1.0]
+        assert_almost_equal(signal.gauss_spline(knots, 3),
+                            np.asarray([0.15418033, 0.6909883, 0.15418033])
+        )
+
+    @make_xp_test_case(signal.cspline1d)  # type:ignore[attr-defined]
+    def test_cspline1d(self, xp):
+        xp_assert_equal(signal.cspline1d(xp.asarray([0])),
+                        xp.asarray([0.], dtype=xp.float64))
+        c1d = xp.asarray([1.21037185, 1.86293902, 2.98834059, 4.11660378,
+                          4.78893826], dtype=xp.float64)
+        # test lamda != 0
+        xp_assert_close(signal.cspline1d(xp.asarray([1., 2, 3, 4, 5]), 1), c1d)
+        c1d0 = xp.asarray([0.78683946, 2.05333735, 2.99981113, 3.94741812,
+                           5.21051638], dtype=xp.float64)
+        xp_assert_close(signal.cspline1d(xp.asarray([1., 2, 3, 4, 5])), c1d0)
+
+    @make_xp_test_case(signal.qspline1d)  # type:ignore[attr-defined]
+    def test_qspline1d(self, xp):
+        xp_assert_equal(signal.qspline1d(xp.asarray([0])),
+                        xp.asarray([0.], dtype=xp.float64))
+        # test lamda != 0
+        raises(ValueError, signal.qspline1d, xp.asarray([1., 2, 3, 4, 5]), 1.)
+        raises(ValueError, signal.qspline1d, xp.asarray([1., 2, 3, 4, 5]), -1.)
+        q1d0 = xp.asarray([0.85350007, 2.02441743, 2.99999534, 3.97561055,
+                           5.14634135], dtype=xp.float64)
+        xp_assert_close(
+            signal.qspline1d(xp.asarray([1., 2, 3, 4, 5], dtype=xp.float64)), q1d0
+        )
+
+    @xfail_xp_backends("cupy", reason="https://github.com/cupy/cupy/pull/9484")
+    @make_xp_test_case(signal.cspline1d_eval)  # type:ignore[attr-defined]
+    def test_cspline1d_eval(self, xp):
+        r = signal.cspline1d_eval(xp.asarray([0., 0], dtype=xp.float64),
+                               xp.asarray([0.], dtype=xp.float64))
+        xp_assert_close(r, xp.asarray([0.], dtype=xp.float64))
+
+        r = signal.cspline1d_eval(xp.asarray([1., 0, 1], dtype=xp.float64),
+                               xp.asarray([], dtype=xp.float64))
+        xp_assert_equal(r, xp.asarray([], dtype=xp.float64))
+
+        # Test case for newx that gets filtered down to empty
+        r = signal.cspline1d_eval(xp.asarray([1.0, 0, 1], dtype=xp.float64),
+                                  xp.asarray([-1.0], dtype=xp.float64))
+        xp_assert_close(r, xp.asarray([0.33333333], dtype=xp.float64))
+
+        x = [-3, -2, -1, 0, 1, 2, 3, 4, 5, 6]
+        dx = x[1] - x[0]
+        newx = [-6., -5.5, -5., -4.5, -4., -3.5, -3., -2.5, -2., -1.5, -1.,
+                -0.5, 0., 0.5, 1., 1.5, 2., 2.5, 3., 3.5, 4., 4.5, 5., 5.5, 6.,
+                6.5, 7., 7.5, 8., 8.5, 9., 9.5, 10., 10.5, 11., 11.5, 12.,
+                12.5]
+        y = xp.asarray([4.216, 6.864, 3.514, 6.203, 6.759, 7.433, 7.874, 5.879,
+                        1.396, 4.094])
+        cj = xp.asarray(signal.cspline1d(_xp_copy_to_numpy(y)))
+        newy = xp.asarray([6.203, 4.41570658, 3.514, 5.16924703, 6.864, 6.04643068,
+                           4.21600281, 6.04643068, 6.864, 5.16924703, 3.514,
+                           4.41570658, 6.203, 6.80717667, 6.759, 6.98971173, 7.433,
+                           7.79560142, 7.874, 7.41525761, 5.879, 3.18686814, 1.396,
+                           2.24889482, 4.094, 2.24889482, 1.396, 3.18686814, 5.879,
+                           7.41525761, 7.874, 7.79560142, 7.433, 6.98971173, 6.759,
+                           6.80717667, 6.203, 4.41570658], dtype=xp.float64)
+        xp_assert_close(
+            signal.cspline1d_eval(cj, xp.asarray(newx), dx=dx, x0=x[0]), newy
+        )
+
+        with pytest.raises(ValueError,
+                            match="Spline coefficients 'cj' must not be empty."):
+            signal.cspline1d_eval(xp.asarray([], dtype=xp.float64),
+                                  xp.asarray([0.0], dtype=xp.float64))
+
+    @xfail_xp_backends("cupy", reason="https://github.com/cupy/cupy/pull/9484")
+    @make_xp_test_case(signal.qspline1d_eval)  # type:ignore[attr-defined]
+    def test_qspline1d_eval(self, xp):
+        xp_assert_close(signal.qspline1d_eval(xp.asarray([0., 0]), xp.asarray([0.])),
+                        xp.asarray([0.])
+        )
+        xp_assert_equal(signal.qspline1d_eval(xp.asarray([1., 0, 1]), xp.asarray([])),
+                        xp.asarray([])
+        )
+
+        # Test case for newx that gets filtered down to empty
+        r = signal.qspline1d_eval(xp.asarray([1.0, 0, 1], dtype=xp.float64),
+                                  xp.asarray([-1.0], dtype=xp.float64))
+        xp_assert_equal(r, xp.asarray([0.25], dtype=xp.float64))
+
+        x = [-3, -2, -1, 0, 1, 2, 3, 4, 5, 6]
+        dx = x[1] - x[0]
+        newx = [-6., -5.5, -5., -4.5, -4., -3.5, -3., -2.5, -2., -1.5, -1.,
+                -0.5, 0., 0.5, 1., 1.5, 2., 2.5, 3., 3.5, 4., 4.5, 5., 5.5, 6.,
+                6.5, 7., 7.5, 8., 8.5, 9., 9.5, 10., 10.5, 11., 11.5, 12.,
+                12.5]
+        y = xp.asarray([4.216, 6.864, 3.514, 6.203, 6.759, 7.433, 7.874, 5.879,
+                        1.396, 4.094])
+        cj = signal.qspline1d(y)
+        newy = xp.asarray([6.203, 4.49418159, 3.514, 5.18390821, 6.864, 5.91436915,
+                           4.21600002, 5.91436915, 6.864, 5.18390821, 3.514,
+                           4.49418159, 6.203, 6.71900226, 6.759, 7.03980488, 7.433,
+                           7.81016848, 7.874, 7.32718426, 5.879, 3.23872593, 1.396,
+                           2.34046013, 4.094, 2.34046013, 1.396, 3.23872593, 5.879,
+                           7.32718426, 7.874, 7.81016848, 7.433, 7.03980488, 6.759,
+                           6.71900226, 6.203, 4.49418159], dtype=xp.float64)
+        r = signal.qspline1d_eval(
+            cj, xp.asarray(newx, dtype=xp.float64), dx=dx, x0=x[0]
+        )
+        xp_assert_close(r, newy)
+
+        with pytest.raises(ValueError,
+                           match="Spline coefficients 'cj' must not be empty."):
+            signal.qspline1d_eval(xp.asarray([], dtype=xp.float64),
+                                  xp.asarray([0.0], dtype=xp.float64))
+
+
+# i/o dtypes with scipy 1.9.1, likely fixed by backwards compat
+sepfir_dtype_map = {np.uint8: np.float32, int: np.float64,
+                    np.float32: np.float32, float: float,
+                    np.complex64: np.complex64, complex: complex}
+
+
+@make_xp_test_case(signal.sepfir2d)  # type:ignore[attr-defined]
+class TestSepfir2d:
+    def test_sepfir2d_invalid_filter(self, xp):
+        filt = xp.asarray([1.0, 2.0, 4.0, 2.0, 1.0])
+        image = np.random.rand(7, 9)
+        image = xp.asarray(image)
+        # No error for odd lengths
+        signal.sepfir2d(image, filt, filt[2:])
+
+        # Row or column filter must be odd
+        with pytest.raises(ValueError, match="odd length"):
+            signal.sepfir2d(image, filt, filt[1:])
+        with pytest.raises(ValueError, match="odd length"):
+            signal.sepfir2d(image, filt[1:], filt)
+
+        # Filters must be 1-dimensional
+        with pytest.raises(ValueError, match="object too deep"):
+            signal.sepfir2d(image, xp.reshape(filt, (1, -1)), filt)
+        with pytest.raises(ValueError, match="object too deep"):
+            signal.sepfir2d(image, filt, xp.reshape(filt, (1, -1)))
+
+    def test_sepfir2d_invalid_image(self, xp):
+        filt = xp.asarray([1.0, 2.0, 4.0, 2.0, 1.0])
+        image = np.random.rand(8, 8)
+        image = xp.asarray(image)
+
+        # Image must be 2 dimensional
+        with pytest.raises(ValueError, match="object too deep"):
+            signal.sepfir2d(xp.reshape(image, (4, 4, 4)), filt, filt)
+
+        with pytest.raises(ValueError, match="object of too small depth"):
+            signal.sepfir2d(image[0, :], filt, filt)
+
+    @pytest.mark.parametrize('dtyp',
+        [np.uint8, int, np.float32, float, np.complex64, complex]
+    )
+    def test_simple(self, dtyp, xp):
+        # test values on a paper-and-pencil example
+        a = np.array([[1, 2, 3, 3, 2, 1],
+                      [1, 2, 3, 3, 2, 1],
+                      [1, 2, 3, 3, 2, 1],
+                      [1, 2, 3, 3, 2, 1]], dtype=dtyp)
+        h1 = [0.5, 1, 0.5]
+        h2 = [1]
+        result = signal.sepfir2d(a, h1, h2)
+        dt = sepfir_dtype_map[dtyp]
+        expected = np.asarray([[2.5, 4. , 5.5, 5.5, 4. , 2.5],
+                               [2.5, 4. , 5.5, 5.5, 4. , 2.5],
+                               [2.5, 4. , 5.5, 5.5, 4. , 2.5],
+                               [2.5, 4. , 5.5, 5.5, 4. , 2.5]], dtype=dt)
+        xp_assert_close(result, expected, atol=1e-16)
+
+        result = signal.sepfir2d(a, h2, h1)
+        expected = np.asarray([[2., 4., 6., 6., 4., 2.],
+                               [2., 4., 6., 6., 4., 2.],
+                               [2., 4., 6., 6., 4., 2.],
+                               [2., 4., 6., 6., 4., 2.]], dtype=dt)
+        xp_assert_close(result, expected, atol=1e-16)
+
+    @skip_xp_backends(np_only=True, reason="TODO: convert this test")
+    @pytest.mark.parametrize('dtyp',
+        [np.uint8, int, np.float32, float, np.complex64, complex]
+    )
+    def test_strided(self, dtyp, xp):
+        a = np.array([[1, 2, 3, 3, 2, 1, 1, 2, 3],
+                     [1, 2, 3, 3, 2, 1, 1, 2, 3],
+                     [1, 2, 3, 3, 2, 1, 1, 2, 3],
+                     [1, 2, 3, 3, 2, 1, 1, 2, 3]])
+        h1, h2 = [0.5, 1, 0.5], [1]
+        result_strided = signal.sepfir2d(a[:, ::2], h1, h2)
+        result_contig = signal.sepfir2d(a[:, ::2].copy(), h1, h2)
+        xp_assert_close(result_strided, result_contig, atol=1e-15)
+        assert result_strided.dtype == result_contig.dtype
+
+    @skip_xp_backends(np_only=True, reason="TODO: convert this test")
+    @pytest.mark.xfail(reason="XXX: filt.size > image.shape: flaky")
+    def test_sepfir2d_strided_2(self, xp):
+        # XXX: this test is flaky: fails on some reruns, with
+        # result[0, 1] and result[1, 1] being ~1e+224.
+        filt = np.array([1.0, 2.0, 4.0, 2.0, 1.0, 3.0, 2.0])
+        image = np.random.rand(4, 4)
+
+        expected = np.asarray([[36.018162, 30.239061, 38.71187 , 43.878183],
+                                [38.180999, 35.824583, 43.525247, 43.874945],
+                                [43.269533, 40.834018, 46.757772, 44.276423],
+                                [49.120928, 39.681844, 43.596067, 45.085854]])
+        xp_assert_close(signal.sepfir2d(image, filt, filt[::3]), expected)
+
+    @skip_xp_backends(np_only=True, reason="TODO: convert this test")
+    @pytest.mark.xfail(reason="XXX: flaky. pointers OOB on some platforms")
+    @pytest.mark.fail_asan
+    @pytest.mark.parametrize('dtyp',
+        [np.uint8, int, np.float32, float, np.complex64, complex]
+    )
+    def test_sepfir2d_strided_3(self, dtyp, xp):
+        # NB: 'image' and 'filt' dtypes match here. Otherwise we can run into
+        # unsafe casting errors for many combinations. Historically, dtype handling
+        # in `sepfir2d` is a tad baroque; fixing it is an enhancement.
+        filt = np.array([1, 2, 4, 2, 1, 3, 2], dtype=dtyp)
+        image = np.asarray([[0, 3, 0, 1, 2],
+                            [2, 2, 3, 3, 3],
+                            [0, 1, 3, 0, 3],
+                            [2, 3, 0, 1, 3],
+                            [3, 3, 2, 1, 2]], dtype=dtyp)
+
+        expected = [[123., 101.,  91., 136., 127.],
+                    [133., 125., 126., 152., 160.],
+                    [136., 137., 150., 162., 177.],
+                    [133., 124., 132., 148., 147.],
+                    [173., 158., 152., 164., 141.]]
+        expected = np.asarray(expected)
+        result = signal.sepfir2d(image, filt, filt[::3])
+        xp_assert_close(result, expected, atol=1e-15)
+        assert result.dtype == sepfir_dtype_map[dtyp]
+
+        expected = [[22., 35., 41., 31., 47.],
+                    [27., 39., 48., 47., 55.],
+                    [33., 42., 49., 53., 59.],
+                    [39., 44., 41., 36., 48.],
+                    [67., 62., 47., 34., 46.]]
+        expected = np.asarray(expected)
+        result = signal.sepfir2d(image, filt[::3], filt[::3])
+        xp_assert_close(result, expected, atol=1e-15)
+        assert result.dtype == sepfir_dtype_map[dtyp]
+
+
+@make_xp_test_case(signal.cspline2d)  # type:ignore[attr-defined]
+def test_cspline2d(xp):
+    rng = np.random.RandomState(181819142)
+    image = rng.rand(71, 73)
+    image = xp.asarray(image, dtype=xp_default_dtype(xp))
+    result = signal.cspline2d(image, 8.0)
+    assert array_namespace(result) == xp
+
+
+@make_xp_test_case(signal.qspline2d)  # type:ignore[attr-defined]
+def test_qspline2d(xp):
+    rng = np.random.RandomState(181819143)
+    image = rng.rand(71, 73)
+    image = xp.asarray(image, dtype=xp_default_dtype(xp))
+    result = signal.qspline2d(image)
+    assert array_namespace(result) == xp
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/tests/test_cont2discrete.py b/venv/lib/python3.12/site-packages/scipy/signal/tests/test_cont2discrete.py
new file mode 100644
index 0000000000000000000000000000000000000000..11ddb4388ad80394f03b89e20cdac5f5566102c7
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/tests/test_cont2discrete.py
@@ -0,0 +1,439 @@
+import math
+import numpy as np
+from scipy._lib._array_api import (
+    assert_array_almost_equal, xp_assert_close,
+    make_xp_test_case
+)
+
+import pytest
+from scipy.signal import cont2discrete as c2d
+from scipy.signal import dlsim, ss2tf, ss2zpk, lsim, lti
+from scipy.signal import tf2ss, impulse, dimpulse, step, dstep
+
+# Author: Jeffrey Armstrong <jeff@approximatrix.com>
+# March 29, 2011
+
+skip_xp_backends = pytest.mark.skip_xp_backends
+
+
+@make_xp_test_case(c2d)
+class TestC2D:
+    def test_zoh(self, xp):
+        ac = xp.eye(2, dtype=xp.float64)
+        bc = xp.full((2, 1), 0.5, dtype=xp.float64)
+        cc = xp.asarray([[0.75, 1.0], [1.0, 1.0], [1.0, 0.25]])
+        dc = xp.asarray([[0.0], [0.0], [-0.33]])
+
+        ad_truth = 1.648721270700128 * xp.eye(2)
+        bd_truth = xp.full((2, 1), 0.324360635350064)
+        # c and d in discrete should be equal to their continuous counterparts
+        dt_requested = 0.5
+
+        ad, bd, cd, dd, dt = c2d((ac, bc, cc, dc), dt_requested, method='zoh')
+
+        assert_array_almost_equal(ad_truth, ad)
+        assert_array_almost_equal(bd_truth, bd)
+        assert_array_almost_equal(cc, cd)
+        assert_array_almost_equal(dc, dd)
+        assert math.isclose(dt, dt_requested, abs_tol=1e-14)
+
+    def test_foh(self, xp):
+        ac = xp.eye(2)
+        bc = xp.full((2, 1), 0.5)
+        cc = xp.asarray([[0.75, 1.0], [1.0, 1.0], [1.0, 0.25]])
+        dc = xp.asarray([[0.0], [0.0], [-0.33]])
+
+        # True values are verified with Matlab
+        ad_truth = 1.648721270700128 * xp.eye(2)
+        bd_truth = xp.full((2, 1), 0.420839287058789)
+        cd_truth = cc
+        dd_truth = xp.asarray([[0.260262223725224],
+                              [0.297442541400256],
+                              [-0.144098411624840]])
+        dt_requested = 0.5
+
+        ad, bd, cd, dd, dt = c2d((ac, bc, cc, dc), dt_requested, method='foh')
+
+        assert_array_almost_equal(ad_truth, ad)
+        assert_array_almost_equal(bd_truth, bd)
+        assert_array_almost_equal(cd_truth, cd)
+        assert_array_almost_equal(dd_truth, dd)
+        assert math.isclose(dt, dt_requested, abs_tol=1e-14)
+
+    def test_impulse(self, xp):
+        ac = xp.eye(2)
+        bc = xp.full((2, 1), 0.5)
+        cc = xp.asarray([[0.75, 1.0], [1.0, 1.0], [1.0, 0.25]])
+        dc = xp.asarray([[0.0], [0.0], [0.0]])
+
+        # True values are verified with Matlab
+        ad_truth = 1.648721270700128 * xp.eye(2)
+        bd_truth = xp.full((2, 1), 0.412180317675032)
+        cd_truth = cc
+        dd_truth = xp.asarray([[0.4375], [0.5], [0.3125]])
+        dt_requested = 0.5
+
+        ad, bd, cd, dd, dt = c2d((ac, bc, cc, dc), dt_requested,
+                                 method='impulse')
+
+        assert_array_almost_equal(ad_truth, ad)
+        assert_array_almost_equal(bd_truth, bd)
+        assert_array_almost_equal(cd_truth, cd)
+        assert_array_almost_equal(dd_truth, dd)
+        assert math.isclose(dt, dt_requested, abs_tol=1e-14)
+
+    def test_gbt(self, xp):
+        ac = xp.eye(2)
+        bc = xp.full((2, 1), 0.5)
+        cc = xp.asarray([[0.75, 1.0], [1.0, 1.0], [1.0, 0.25]])
+        dc = xp.asarray([[0.0], [0.0], [-0.33]])
+
+        dt_requested = 0.5
+        alpha = 1.0 / 3.0
+
+        ad_truth = 1.6 * xp.eye(2)
+        bd_truth = xp.full((2, 1), 0.3)
+        cd_truth = xp.asarray([[0.9, 1.2],
+                               [1.2, 1.2],
+                               [1.2, 0.3]])
+        dd_truth = xp.asarray([[0.175],
+                               [0.2],
+                               [-0.205]])
+
+        ad, bd, cd, dd, dt = c2d((ac, bc, cc, dc), dt_requested,
+                                 method='gbt', alpha=alpha)
+
+        assert_array_almost_equal(ad_truth, ad)
+        assert_array_almost_equal(bd_truth, bd)
+        assert_array_almost_equal(cd_truth, cd)
+        assert_array_almost_equal(dd_truth, dd)
+
+    def test_euler(self, xp):
+        ac = xp.eye(2)
+        bc = xp.full((2, 1), 0.5)
+        cc = xp.asarray([[0.75, 1.0], [1.0, 1.0], [1.0, 0.25]])
+        dc = xp.asarray([[0.0], [0.0], [-0.33]])
+
+        dt_requested = 0.5
+
+        ad_truth = 1.5 * xp.eye(2)
+        bd_truth = xp.full((2, 1), 0.25)
+        cd_truth = xp.asarray([[0.75, 1.0],
+                               [1.0, 1.0],
+                               [1.0, 0.25]])
+        dd_truth = dc
+
+        ad, bd, cd, dd, dt = c2d((ac, bc, cc, dc), dt_requested,
+                                 method='euler')
+
+        assert_array_almost_equal(ad_truth, ad)
+        assert_array_almost_equal(bd_truth, bd)
+        assert_array_almost_equal(cd_truth, cd)
+        assert_array_almost_equal(dd_truth, dd)
+        assert math.isclose(dt, dt_requested, abs_tol=1e-14)
+
+    def test_backward_diff(self, xp):
+        ac = xp.eye(2)
+        bc = xp.full((2, 1), 0.5)
+        cc = xp.asarray([[0.75, 1.0], [1.0, 1.0], [1.0, 0.25]])
+        dc = xp.asarray([[0.0], [0.0], [-0.33]])
+
+        dt_requested = 0.5
+
+        ad_truth = 2.0 * xp.eye(2)
+        bd_truth = xp.full((2, 1), 0.5)
+        cd_truth = xp.asarray([[1.5, 2.0],
+                               [2.0, 2.0],
+                               [2.0, 0.5]])
+        dd_truth = xp.asarray([[0.875],
+                               [1.0],
+                               [0.295]])
+
+        ad, bd, cd, dd, dt = c2d((ac, bc, cc, dc), dt_requested,
+                                 method='backward_diff')
+
+        assert_array_almost_equal(ad_truth, ad)
+        assert_array_almost_equal(bd_truth, bd)
+        assert_array_almost_equal(cd_truth, cd)
+        assert_array_almost_equal(dd_truth, dd)
+
+    def test_bilinear(self, xp):
+        ac = xp.eye(2)
+        bc = xp.full((2, 1), 0.5)
+        cc = xp.asarray([[0.75, 1.0], [1.0, 1.0], [1.0, 0.25]])
+        dc = xp.asarray([[0.0], [0.0], [-0.33]])
+
+        dt_requested = 0.5
+
+        ad_truth = (5.0 / 3.0) * xp.eye(2)
+        bd_truth = xp.full((2, 1), 1.0 / 3.0)
+        cd_truth = xp.asarray([[1.0, 4.0 / 3.0],
+                               [4.0 / 3.0, 4.0 / 3.0],
+                               [4.0 / 3.0, 1.0 / 3.0]])
+        dd_truth = xp.asarray([[0.291666666666667],
+                               [1.0 / 3.0],
+                               [-0.121666666666667]])
+
+        ad, bd, cd, dd, dt = c2d((ac, bc, cc, dc), dt_requested,
+                                 method='bilinear')
+
+        assert_array_almost_equal(ad_truth, ad)
+        assert_array_almost_equal(bd_truth, bd)
+        assert_array_almost_equal(cd_truth, cd)
+        assert_array_almost_equal(dd_truth, dd)
+        assert math.isclose(dt, dt_requested, abs_tol=1e-14)
+
+        # Same continuous system again, but change sampling rate
+
+        ad_truth = 1.4 * xp.eye(2)
+        bd_truth = xp.full((2, 1), 0.2)
+        cd_truth = xp.asarray([[0.9, 1.2], [1.2, 1.2], [1.2, 0.3]])
+        dd_truth = xp.asarray([[0.175], [0.2], [-0.205]])
+
+        dt_requested = 1.0 / 3.0
+
+        ad, bd, cd, dd, dt = c2d((ac, bc, cc, dc), dt_requested,
+                                 method='bilinear')
+
+        assert_array_almost_equal(ad_truth, ad)
+        assert_array_almost_equal(bd_truth, bd)
+        assert_array_almost_equal(cd_truth, cd)
+        assert_array_almost_equal(dd_truth, dd)
+        assert math.isclose(dt_requested, dt)
+
+    def test_transferfunction(self, xp):
+        numc = xp.asarray([0.25, 0.25, 0.5])
+        denc = xp.asarray([0.75, 0.75, 1.0])
+
+        numd = xp.asarray([[1.0 / 3.0, -0.427419169438754, 0.221654141101125]])
+        dend = xp.asarray([1.0, -1.351394049721225, 0.606530659712634])
+
+        dt_requested = 0.5
+
+        num, den, dt = c2d((numc, denc), dt_requested, method='zoh')
+
+        assert_array_almost_equal(numd, num)
+        assert_array_almost_equal(dend, den)
+        assert math.isclose(dt_requested, dt)
+
+    def test_zerospolesgain(self, xp):
+        zeros_c = xp.array([0.5, -0.5])
+        poles_c = xp.array([1.j / xp.sqrt(2), -1.j / xp.sqrt(2)])
+        k_c = 1.0
+
+        zeros_d = xp.asarray([1.23371727305860, 0.735356894461267])
+        polls_d = xp.asarray([0.938148335039729 + 0.346233593780536j,
+                              0.938148335039729 - 0.346233593780536j])
+        k_d = 1.0
+
+        dt_requested = 0.5
+
+        zeros, poles, k, dt = c2d((zeros_c, poles_c, k_c), dt_requested,
+                                  method='zoh')
+
+        assert_array_almost_equal(zeros_d, zeros)
+        assert_array_almost_equal(polls_d, poles)
+        assert math.isclose(k_d, k)
+        assert math.isclose(dt_requested, dt)
+
+    @skip_xp_backends(np_only=True)
+    def test_gbt_with_sio_tf_and_zpk(self, xp):
+        """Test method='gbt' with alpha=0.25 for tf and zpk cases."""
+        # State space coefficients for the continuous SIO system.
+        A = -1.0
+        B = 1.0
+        C = 1.0
+        D = 0.5
+
+        # The continuous transfer function coefficients.
+        cnum, cden = ss2tf(A, B, C, D)
+
+        # Continuous zpk representation
+        cz, cp, ck = ss2zpk(A, B, C, D)
+
+        h = 1.0
+        alpha = 0.25
+
+        # Explicit formulas, in the scalar case.
+        Ad = (1 + (1 - alpha) * h * A) / (1 - alpha * h * A)
+        Bd = h * B / (1 - alpha * h * A)
+        Cd = C / (1 - alpha * h * A)
+        Dd = D + alpha * C * Bd
+
+        # Convert the explicit solution to tf
+        dnum, dden = ss2tf(Ad, Bd, Cd, Dd)
+
+        # Compute the discrete tf using cont2discrete.
+        c2dnum, c2dden, dt = c2d((cnum, cden), h, method='gbt', alpha=alpha)
+
+        xp_assert_close(dnum, c2dnum)
+        xp_assert_close(dden, c2dden)
+
+        # Convert explicit solution to zpk.
+        dz, dp, dk = ss2zpk(Ad, Bd, Cd, Dd)
+
+        # Compute the discrete zpk using cont2discrete.
+        c2dz, c2dp, c2dk, dt = c2d((cz, cp, ck), h, method='gbt', alpha=alpha)
+
+        xp_assert_close(dz, c2dz)
+        xp_assert_close(dp, c2dp)
+        xp_assert_close(dk, c2dk)
+
+    def test_discrete_approx(self, xp):
+        """
+        Test that the solution to the discrete approximation of a continuous
+        system actually approximates the solution to the continuous system.
+        This is an indirect test of the correctness of the implementation
+        of cont2discrete.
+        """
+
+        def u(t):
+            return xp.sin(2.5 * t)
+
+        a = xp.asarray([[-0.01]])
+        b = xp.asarray([[1.0]])
+        c = xp.asarray([[1.0]])
+        d = xp.asarray([[0.2]])
+        x0 = 1.0
+
+        t = xp.linspace(0, 10.0, 101)
+        dt = t[1] - t[0]
+        u1 = u(t)
+
+        # Use lsim to compute the solution to the continuous system.
+        t, yout, xout = lsim((a, b, c, d), T=t, U=u1, X0=x0)
+
+        # Convert the continuous system to a discrete approximation.
+        dsys = c2d((a, b, c, d), dt, method='bilinear')
+
+        # Use dlsim with the pairwise averaged input to compute the output
+        # of the discrete system.
+        u2 = 0.5 * (u1[:-1] + u1[1:])
+        t2 = t[:-1]
+        td2, yd2, xd2 = dlsim(dsys, u=u2.reshape(-1, 1), t=t2, x0=x0)
+
+        # ymid is the average of consecutive terms of the "exact" output
+        # computed by lsim2.  This is what the discrete approximation
+        # actually approximates.
+        ymid = 0.5 * (yout[:-1] + yout[1:])
+
+        xp_assert_close(yd2.ravel(), ymid, rtol=1e-4)
+
+    @skip_xp_backends(np_only=True)
+    def test_simo_tf(self):
+        # See gh-5753
+        tf = ([[1, 0], [1, 1]], [1, 1])
+        num, den, dt = c2d(tf, 0.01)
+
+        assert dt == 0.01  # sanity check
+        xp_assert_close(den, [1, -0.990404983], rtol=1e-3)
+        xp_assert_close(num, [[1, -1], [1, -0.99004983]], rtol=1e-3)
+
+    @skip_xp_backends(np_only=True)
+    def test_multioutput(self):
+        ts = 0.01  # time step
+
+        tf = ([[1, -3], [1, 5]], [1, 1])
+        num, den, dt = c2d(tf, ts)
+
+        tf1 = (tf[0][0], tf[1])
+        num1, den1, dt1 = c2d(tf1, ts)
+
+        tf2 = (tf[0][1], tf[1])
+        num2, den2, dt2 = c2d(tf2, ts)
+
+        # Sanity checks
+        assert dt == dt1
+        assert dt == dt2
+
+        # Check that we get the same results
+        xp_assert_close(num, np.vstack((num1, num2)), rtol=1e-13)
+
+        # Single input, so the denominator should
+        # not be multidimensional like the numerator
+        xp_assert_close(den, den1, rtol=1e-13)
+        xp_assert_close(den, den2, rtol=1e-13)
+
+
+class TestC2dLti:
+    def test_c2d_ss(self):
+        # StateSpace
+        A = np.array([[-0.3, 0.1], [0.2, -0.7]])
+        B = np.array([[0], [1]])
+        C = np.array([[1, 0]])
+        D = 0
+        dt = 0.05
+
+        A_res = np.array([[0.985136404135682, 0.004876671474795],
+                          [0.009753342949590, 0.965629718236502]])
+        B_res = np.array([[0.000122937599964], [0.049135527547844]])
+        C_res = np.astype(C, np.float64)
+
+        sys_ssc = lti(A, B, C, D)
+        sys_ssd = sys_ssc.to_discrete(dt=dt)
+
+        xp_assert_close(sys_ssd.A, A_res)
+        xp_assert_close(sys_ssd.B, B_res)
+        xp_assert_close(sys_ssd.C, C_res)
+        xp_assert_close(sys_ssd.D, np.zeros_like(sys_ssd.D))
+
+        sys_ssd2 = c2d(sys_ssc, dt=dt)
+
+        xp_assert_close(sys_ssd2.A, A_res)
+        xp_assert_close(sys_ssd2.B, B_res)
+        xp_assert_close(sys_ssd2.C, C_res)
+        xp_assert_close(sys_ssd2.D, np.zeros_like(sys_ssd.D))
+
+    def test_c2d_tf(self):
+
+        sys = lti([0.5, 0.3], [1.0, 0.4])
+        sys = sys.to_discrete(0.005)
+
+        # Matlab results
+        num_res = np.array([0.5, -0.485149004980066])
+        den_res = np.array([1.0, -0.980198673306755])
+
+        # Somehow a lot of numerical errors
+        xp_assert_close(sys.den, den_res, atol=0.02)
+        xp_assert_close(sys.num, num_res, atol=0.02)
+
+
+@make_xp_test_case(c2d)
+class TestC2dInvariants:
+    # Some test cases for checking the invariances.
+    # Array of triplets: (system, sample time, number of samples)
+    cases = [
+        (tf2ss([1, 1], [1, 1.5, 1]), 0.25, 10),
+        (tf2ss([1, 2], [1, 1.5, 3, 1]), 0.5, 10),
+        (tf2ss(0.1, [1, 1, 2, 1]), 0.5, 10),
+    ]
+
+    # Check that systems discretized with the impulse-invariant
+    # method really hold the invariant
+    @make_xp_test_case(impulse, dimpulse)
+    @pytest.mark.parametrize("sys,sample_time,samples_number", cases)
+    def test_impulse_invariant(self, xp, sys, sample_time, samples_number):
+        sys = tuple(map(xp.asarray, sys))
+        time = xp.arange(samples_number) * sample_time
+        _, yout_cont = impulse(sys, T=time)
+        _, yout_disc = dimpulse(c2d(sys, sample_time, method='impulse'),
+                                n=len(time))
+        xp_assert_close(sample_time * yout_cont.ravel(), yout_disc[0].ravel())
+
+    # Step invariant should hold for ZOH discretized systems
+    @pytest.mark.parametrize("sys,sample_time,samples_number", cases)
+    def test_step_invariant(self, xp, sys, sample_time, samples_number):
+        sys = tuple(map(xp.asarray, sys))
+        time = xp.arange(samples_number) * sample_time
+        _, yout_cont = step(sys, T=time)
+        _, yout_disc = dstep(c2d(sys, sample_time, method='zoh'), n=len(time))
+        xp_assert_close(yout_cont.ravel(), yout_disc[0].ravel())
+
+    # Linear invariant should hold for FOH discretized systems
+    @pytest.mark.parametrize("sys,sample_time,samples_number", cases)
+    def test_linear_invariant(self, xp, sys, sample_time, samples_number):
+        sys = tuple(map(xp.asarray, sys))
+        time = xp.arange(samples_number) * sample_time
+        _, yout_cont, _ = lsim(sys, T=time, U=time)
+        _, yout_disc, _ = dlsim(c2d(sys, sample_time, method='foh'), u=time)
+        xp_assert_close(yout_cont.ravel(), yout_disc.ravel())
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/tests/test_czt.py b/venv/lib/python3.12/site-packages/scipy/signal/tests/test_czt.py
new file mode 100644
index 0000000000000000000000000000000000000000..35087d99fec5057131f0735d43e0faa33a74ef82
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/tests/test_czt.py
@@ -0,0 +1,221 @@
+# This program is public domain
+# Authors: Paul Kienzle, Nadav Horesh
+'''
+A unit test module for czt.py
+'''
+import pytest
+from scipy._lib._array_api import xp_assert_close
+from scipy.fft import fft
+from scipy.signal import (czt, zoom_fft, czt_points, CZT, ZoomFFT)
+import numpy as np
+
+
+def check_czt(x):
+    # Check that czt is the equivalent of normal fft
+    y = fft(x)
+    y1 = czt(x)
+    xp_assert_close(y1, y, rtol=1e-13)
+
+    # Check that interpolated czt is the equivalent of normal fft
+    y = fft(x, 100*len(x))
+    y1 = czt(x, 100*len(x))
+    xp_assert_close(y1, y, rtol=1e-12)
+
+
+def check_zoom_fft(x):
+    # Check that zoom_fft is the equivalent of normal fft
+    y = fft(x)
+    y1 = zoom_fft(x, [0, 2-2./len(y)], endpoint=True)
+    xp_assert_close(y1, y, rtol=1e-11, atol=1e-14)
+    y1 = zoom_fft(x, [0, 2])
+    xp_assert_close(y1, y, rtol=1e-11, atol=1e-14)
+
+    # Test fn scalar
+    y1 = zoom_fft(x, 2-2./len(y), endpoint=True)
+    xp_assert_close(y1, y, rtol=1e-11, atol=1e-14)
+    y1 = zoom_fft(x, 2)
+    xp_assert_close(y1, y, rtol=1e-11, atol=1e-14)
+
+    # Check that zoom_fft with oversampling is equivalent to zero padding
+    over = 10
+    yover = fft(x, over*len(x))
+    y2 = zoom_fft(x, [0, 2-2./len(yover)], m=len(yover), endpoint=True)
+    xp_assert_close(y2, yover, rtol=1e-12, atol=1e-10)
+    y2 = zoom_fft(x, [0, 2], m=len(yover))
+    xp_assert_close(y2, yover, rtol=1e-12, atol=1e-10)
+
+    # Check that zoom_fft works on a subrange
+    w = np.linspace(0, 2-2./len(x), len(x))
+    f1, f2 = w[3], w[6]
+    y3 = zoom_fft(x, [f1, f2], m=3*over+1, endpoint=True)
+    idx3 = slice(3*over, 6*over+1)
+    xp_assert_close(y3, yover[idx3], rtol=1e-13)
+
+
+def test_1D():
+    # Test of 1D version of the transforms
+
+    rng = np.random.RandomState(0)  # Deterministic randomness
+
+    # Random signals
+    lengths = rng.randint(8, 200, 20)
+    np.append(lengths, 1)
+    for length in lengths:
+        x = rng.random(length)
+        check_zoom_fft(x)
+        check_czt(x)
+
+    # Gauss
+    t = np.linspace(-2, 2, 128)
+    x = np.exp(-t**2/0.01)
+    check_zoom_fft(x)
+
+    # Linear
+    x = [1, 2, 3, 4, 5, 6, 7]
+    check_zoom_fft(x)
+
+    # Check near powers of two
+    check_zoom_fft(range(126-31))
+    check_zoom_fft(range(127-31))
+    check_zoom_fft(range(128-31))
+    check_zoom_fft(range(129-31))
+    check_zoom_fft(range(130-31))
+
+    # Check transform on n-D array input
+    x = np.reshape(np.arange(3*2*28), (3, 2, 28))
+    y1 = zoom_fft(x, [0, 2-2./28])
+    y2 = zoom_fft(x[2, 0, :], [0, 2-2./28])
+    xp_assert_close(y1[2, 0], y2, rtol=1e-13, atol=1e-12)
+
+    y1 = zoom_fft(x, [0, 2], endpoint=False)
+    y2 = zoom_fft(x[2, 0, :], [0, 2], endpoint=False)
+    xp_assert_close(y1[2, 0], y2, rtol=1e-13, atol=1e-12)
+
+    # Random (not a test condition)
+    x = rng.rand(101)
+    check_zoom_fft(x)
+
+    # Spikes
+    t = np.linspace(0, 1, 128)
+    x = np.sin(2*np.pi*t*5)+np.sin(2*np.pi*t*13)
+    check_zoom_fft(x)
+
+    # Sines
+    x = np.zeros(100, dtype=complex)
+    x[[1, 5, 21]] = 1
+    check_zoom_fft(x)
+
+    # Sines plus complex component
+    x += 1j*np.linspace(0, 0.5, x.shape[0])
+    check_zoom_fft(x)
+
+
+def test_large_prime_lengths():
+    rng = np.random.RandomState(0)  # Deterministic randomness
+    for N in (101, 1009, 10007):
+        x = rng.rand(N)
+        y = fft(x)
+        y1 = czt(x)
+        xp_assert_close(y, y1, rtol=1e-12)
+
+
+@pytest.mark.slow
+def test_czt_vs_fft():
+    rng = np.random.RandomState(123)  # Deterministic randomness
+    random_lengths = rng.exponential(100000, size=10).astype('int')
+    for n in random_lengths:
+        a = rng.randn(n)
+        xp_assert_close(czt(a), fft(a), rtol=1e-11)
+
+
+def test_empty_input():
+    with pytest.raises(ValueError, match='Invalid number of CZT'):
+        czt([])
+    with pytest.raises(ValueError, match='Invalid number of CZT'):
+        zoom_fft([], 0.5)
+
+
+def test_0_rank_input():
+    with pytest.raises(IndexError, match='tuple index out of range'):
+        czt(5)
+    with pytest.raises(IndexError, match='tuple index out of range'):
+        zoom_fft(5, 0.5)
+
+
+@pytest.mark.parametrize('impulse', ([0, 0, 1], [0, 0, 1, 0, 0],
+                                     np.concatenate((np.array([0, 0, 1]),
+                                                     np.zeros(100)))))
+@pytest.mark.parametrize('m', (1, 3, 5, 8, 101, 1021))
+@pytest.mark.parametrize('a', (1, 2, 0.5, 1.1))
+# Step that tests away from the unit circle, but not so far it explodes from
+# numerical error
+@pytest.mark.parametrize('w', (None, 0.98534 + 0.17055j))
+def test_czt_math(impulse, m, w, a):
+    # z-transform of an impulse is 1 everywhere
+    xp_assert_close(czt(impulse[2:], m=m, w=w, a=a),
+                    np.ones(m, dtype=np.complex128), rtol=1e-10)
+
+    # z-transform of a delayed impulse is z**-1
+    xp_assert_close(czt(impulse[1:], m=m, w=w, a=a),
+                    czt_points(m=m, w=w, a=a)**-1, rtol=1e-10)
+
+    # z-transform of a 2-delayed impulse is z**-2
+    xp_assert_close(czt(impulse, m=m, w=w, a=a),
+                    czt_points(m=m, w=w, a=a)**-2, rtol=1e-10)
+
+
+def test_int_args():
+    # Integer argument `a` was producing all 0s
+    xp_assert_close(abs(czt([0, 1], m=10, a=2)), 0.5*np.ones(10), rtol=1e-15)
+    xp_assert_close(czt_points(11, w=2),
+                    1/(2**np.arange(11, dtype=np.complex128)), rtol=1e-30)
+
+
+def test_czt_points():
+    for N in (1, 2, 3, 8, 11, 100, 101, 10007):
+        xp_assert_close(czt_points(N), np.exp(2j*np.pi*np.arange(N)/N),
+                        rtol=1e-30)
+
+    xp_assert_close(czt_points(7, w=1), np.ones(7, dtype=np.complex128), rtol=1e-30)
+    xp_assert_close(czt_points(11, w=2.),
+                    1/(2**np.arange(11, dtype=np.complex128)), rtol=1e-30)
+
+    func = CZT(12, m=11, w=2., a=1)
+    xp_assert_close(func.points(), 1/(2**np.arange(11)), rtol=1e-30)
+
+
+@pytest.mark.parametrize('cls, args', [(CZT, (100,)), (ZoomFFT, (100, 0.2))])
+def test_CZT_size_mismatch(cls, args):
+    # Data size doesn't match function's expected size
+    myfunc = cls(*args)
+    with pytest.raises(ValueError, match='CZT defined for'):
+        myfunc(np.arange(5))
+
+
+def test_invalid_range():
+    with pytest.raises(ValueError, match='2-length sequence'):
+        ZoomFFT(100, [1, 2, 3])
+
+
+@pytest.mark.parametrize('m', [0, -11, 5.5, 4.0])
+def test_czt_points_errors(m):
+    # Invalid number of points
+    with pytest.raises(ValueError, match='Invalid number of CZT'):
+        czt_points(m)
+
+
+@pytest.mark.parametrize('size', [0, -5, 3.5, 4.0])
+def test_nonsense_size(size):
+    # Numpy and Scipy fft() give ValueError for 0 output size, so we do, too
+    with pytest.raises(ValueError, match='Invalid number of CZT'):
+        CZT(size, 3)
+    with pytest.raises(ValueError, match='Invalid number of CZT'):
+        ZoomFFT(size, 0.2, 3)
+    with pytest.raises(ValueError, match='Invalid number of CZT'):
+        CZT(3, size)
+    with pytest.raises(ValueError, match='Invalid number of CZT'):
+        ZoomFFT(3, 0.2, size)
+    with pytest.raises(ValueError, match='Invalid number of CZT'):
+        czt([1, 2, 3], size)
+    with pytest.raises(ValueError, match='Invalid number of CZT'):
+        zoom_fft([1, 2, 3], 0.2, size)
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/tests/test_dltisys.py b/venv/lib/python3.12/site-packages/scipy/signal/tests/test_dltisys.py
new file mode 100644
index 0000000000000000000000000000000000000000..d18313c34b6a261fd688fa913971f94667c7f5cb
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@@ -0,0 +1,601 @@
+# Author: Jeffrey Armstrong <jeff@approximatrix.com>
+# April 4, 2011
+import warnings
+
+import numpy as np
+from pytest import raises as assert_raises
+from scipy._lib._array_api import (
+    assert_array_almost_equal, assert_almost_equal, xp_assert_close, xp_assert_equal,
+)
+
+from scipy.signal import (dlsim, dstep, dimpulse, tf2zpk, lti, dlti,
+                          StateSpace, TransferFunction, ZerosPolesGain,
+                          dfreqresp, dbode, BadCoefficients)
+
+
+class TestDLTI:
+
+    def test_dlsim(self):
+
+        a = np.asarray([[0.9, 0.1], [-0.2, 0.9]])
+        b = np.asarray([[0.4, 0.1, -0.1], [0.0, 0.05, 0.0]])
+        c = np.asarray([[0.1, 0.3]])
+        d = np.asarray([[0.0, -0.1, 0.0]])
+        dt = 0.5
+
+        # Create an input matrix with inputs down the columns (3 cols) and its
+        # respective time input vector
+        u = np.hstack((np.linspace(0, 4.0, num=5)[:, np.newaxis],
+                       np.full((5, 1), 0.01),
+                       np.full((5, 1), -0.002)))
+        t_in = np.linspace(0, 2.0, num=5)
+
+        # Define the known result
+        yout_truth = np.array([[-0.001,
+                                -0.00073,
+                                0.039446,
+                                0.0915387,
+                                0.13195948]]).T
+        xout_truth = np.asarray([[0, 0],
+                                 [0.0012, 0.0005],
+                                 [0.40233, 0.00071],
+                                 [1.163368, -0.079327],
+                                 [2.2402985, -0.3035679]])
+
+        tout, yout, xout = dlsim((a, b, c, d, dt), u, t_in)
+
+        assert_array_almost_equal(yout_truth, yout)
+        assert_array_almost_equal(xout_truth, xout)
+        assert_array_almost_equal(t_in, tout)
+
+        # Make sure input with single-dimension doesn't raise error
+        dlsim((1, 2, 3), 4)
+
+        # Interpolated control - inputs should have different time steps
+        # than the discrete model uses internally
+        u_sparse = u[[0, 4], :]
+        t_sparse = np.asarray([0.0, 2.0])
+
+        tout, yout, xout = dlsim((a, b, c, d, dt), u_sparse, t_sparse)
+
+        assert_array_almost_equal(yout_truth, yout)
+        assert_array_almost_equal(xout_truth, xout)
+        assert len(tout) == len(yout)
+
+        # Transfer functions (assume dt = 0.5)
+        num = np.asarray([1.0, -0.1])
+        den = np.asarray([0.3, 1.0, 0.2])
+        yout_truth = np.array([[0.0,
+                                0.0,
+                                3.33333333333333,
+                                -4.77777777777778,
+                                23.0370370370370]]).T
+
+        # Assume use of the first column of the control input built earlier
+        tout, yout = dlsim((num, den, 0.5), u[:, 0], t_in)
+
+        assert_array_almost_equal(yout, yout_truth)
+        assert_array_almost_equal(t_in, tout)
+
+        # Retest the same with a 1-D input vector
+        uflat = np.asarray(u[:, 0])
+        uflat = uflat.reshape((5,))
+        tout, yout = dlsim((num, den, 0.5), uflat, t_in)
+
+        assert_array_almost_equal(yout, yout_truth)
+        assert_array_almost_equal(t_in, tout)
+
+        # zeros-poles-gain representation
+        zd = np.array([0.5, -0.5])
+        pd = np.array([1.j / np.sqrt(2), -1.j / np.sqrt(2)])
+        k = 1.0
+        yout_truth = np.array([[0.0, 1.0, 2.0, 2.25, 2.5]]).T
+
+        tout, yout = dlsim((zd, pd, k, 0.5), u[:, 0], t_in)
+
+        assert_array_almost_equal(yout, yout_truth)
+        assert_array_almost_equal(t_in, tout)
+
+        # Raise an error for continuous-time systems
+        system = lti([1], [1, 1])
+        assert_raises(AttributeError, dlsim, system, u)
+
+    def test_dstep(self):
+
+        a = np.asarray([[0.9, 0.1], [-0.2, 0.9]])
+        b = np.asarray([[0.4, 0.1, -0.1], [0.0, 0.05, 0.0]])
+        c = np.asarray([[0.1, 0.3]])
+        d = np.asarray([[0.0, -0.1, 0.0]])
+        dt = 0.5
+
+        # Because b.shape[1] == 3, dstep should result in a tuple of three
+        # result vectors
+        yout_step_truth = (np.asarray([0.0, 0.04, 0.052, 0.0404, 0.00956,
+                                       -0.036324, -0.093318, -0.15782348,
+                                       -0.226628324, -0.2969374948]),
+                           np.asarray([-0.1, -0.075, -0.058, -0.04815,
+                                       -0.04453, -0.0461895, -0.0521812,
+                                       -0.061588875, -0.073549579,
+                                       -0.08727047595]),
+                           np.asarray([0.0, -0.01, -0.013, -0.0101, -0.00239,
+                                       0.009081, 0.0233295, 0.03945587,
+                                       0.056657081, 0.0742343737]))
+
+        tout, yout = dstep((a, b, c, d, dt), n=10)
+
+        assert len(yout) == 3
+
+        for i in range(0, len(yout)):
+            assert yout[i].shape[0] == 10
+            assert_array_almost_equal(yout[i].flatten(), yout_step_truth[i])
+
+        # Check that the other two inputs (tf, zpk) will work as well
+        tfin = ([1.0], [1.0, 1.0], 0.5)
+        yout_tfstep = np.asarray([0.0, 1.0, 0.0])
+        tout, yout = dstep(tfin, n=3)
+        assert len(yout) == 1
+        assert_array_almost_equal(yout[0].flatten(), yout_tfstep)
+
+        zpkin = tf2zpk(tfin[0], tfin[1]) + (0.5,)
+        tout, yout = dstep(zpkin, n=3)
+        assert len(yout) == 1
+        assert_array_almost_equal(yout[0].flatten(), yout_tfstep)
+
+        # Raise an error for continuous-time systems
+        system = lti([1], [1, 1])
+        assert_raises(AttributeError, dstep, system)
+
+    def test_dimpulse(self):
+
+        a = np.asarray([[0.9, 0.1], [-0.2, 0.9]])
+        b = np.asarray([[0.4, 0.1, -0.1], [0.0, 0.05, 0.0]])
+        c = np.asarray([[0.1, 0.3]])
+        d = np.asarray([[0.0, -0.1, 0.0]])
+        dt = 0.5
+
+        # Because b.shape[1] == 3, dimpulse should result in a tuple of three
+        # result vectors
+        yout_imp_truth = (np.asarray([0.0, 0.04, 0.012, -0.0116, -0.03084,
+                                      -0.045884, -0.056994, -0.06450548,
+                                      -0.068804844, -0.0703091708]),
+                          np.asarray([-0.1, 0.025, 0.017, 0.00985, 0.00362,
+                                      -0.0016595, -0.0059917, -0.009407675,
+                                      -0.011960704, -0.01372089695]),
+                          np.asarray([0.0, -0.01, -0.003, 0.0029, 0.00771,
+                                      0.011471, 0.0142485, 0.01612637,
+                                      0.017201211, 0.0175772927]))
+
+        tout, yout = dimpulse((a, b, c, d, dt), n=10)
+
+        assert len(yout) == 3
+
+        for i in range(0, len(yout)):
+            assert yout[i].shape[0] == 10
+            assert_array_almost_equal(yout[i].flatten(), yout_imp_truth[i])
+
+        # Check that the other two inputs (tf, zpk) will work as well
+        tfin = ([1.0], [1.0, 1.0], 0.5)
+        yout_tfimpulse = np.asarray([0.0, 1.0, -1.0])
+        tout, yout = dimpulse(tfin, n=3)
+        assert len(yout) == 1
+        assert_array_almost_equal(yout[0].flatten(), yout_tfimpulse)
+
+        zpkin = tf2zpk(tfin[0], tfin[1]) + (0.5,)
+        tout, yout = dimpulse(zpkin, n=3)
+        assert len(yout) == 1
+        assert_array_almost_equal(yout[0].flatten(), yout_tfimpulse)
+
+        # Raise an error for continuous-time systems
+        system = lti([1], [1, 1])
+        assert_raises(AttributeError, dimpulse, system)
+
+    def test_dlsim_trivial(self):
+        a = np.array([[0.0]])
+        b = np.array([[0.0]])
+        c = np.array([[0.0]])
+        d = np.array([[0.0]])
+        n = 5
+        u = np.zeros(n).reshape(-1, 1)
+        tout, yout, xout = dlsim((a, b, c, d, 1), u)
+        xp_assert_equal(tout, np.arange(float(n)))
+        xp_assert_equal(yout, np.zeros((n, 1)))
+        xp_assert_equal(xout, np.zeros((n, 1)))
+
+    def test_dlsim_simple1d(self):
+        a = np.array([[0.5]])
+        b = np.array([[0.0]])
+        c = np.array([[1.0]])
+        d = np.array([[0.0]])
+        n = 5
+        u = np.zeros(n).reshape(-1, 1)
+        tout, yout, xout = dlsim((a, b, c, d, 1), u, x0=1)
+        xp_assert_equal(tout, np.arange(float(n)))
+        expected = (0.5 ** np.arange(float(n))).reshape(-1, 1)
+        xp_assert_equal(yout, expected)
+        xp_assert_equal(xout, expected)
+
+    def test_dlsim_simple2d(self):
+        lambda1 = 0.5
+        lambda2 = 0.25
+        a = np.array([[lambda1, 0.0],
+                      [0.0, lambda2]])
+        b = np.array([[0.0],
+                      [0.0]])
+        c = np.array([[1.0, 0.0],
+                      [0.0, 1.0]])
+        d = np.array([[0.0],
+                      [0.0]])
+        n = 5
+        u = np.zeros(n).reshape(-1, 1)
+        tout, yout, xout = dlsim((a, b, c, d, 1), u, x0=1)
+        xp_assert_equal(tout, np.arange(float(n)))
+        # The analytical solution:
+        expected = (np.array([lambda1, lambda2]) **
+                                np.arange(float(n)).reshape(-1, 1))
+        xp_assert_equal(yout, expected)
+        xp_assert_equal(xout, expected)
+
+    def test_more_step_and_impulse(self):
+        lambda1 = 0.5
+        lambda2 = 0.75
+        a = np.array([[lambda1, 0.0],
+                      [0.0, lambda2]])
+        b = np.array([[1.0, 0.0],
+                      [0.0, 1.0]])
+        c = np.array([[1.0, 1.0]])
+        d = np.array([[0.0, 0.0]])
+
+        n = 10
+
+        # Check a step response.
+        ts, ys = dstep((a, b, c, d, 1), n=n)
+
+        # Create the exact step response.
+        stp0 = (1.0 / (1 - lambda1)) * (1.0 - lambda1 ** np.arange(n))
+        stp1 = (1.0 / (1 - lambda2)) * (1.0 - lambda2 ** np.arange(n))
+
+        xp_assert_close(ys[0][:, 0], stp0)
+        xp_assert_close(ys[1][:, 0], stp1)
+
+        # Check an impulse response with an initial condition.
+        x0 = np.array([1.0, 1.0])
+        ti, yi = dimpulse((a, b, c, d, 1), n=n, x0=x0)
+
+        # Create the exact impulse response.
+        imp = (np.array([lambda1, lambda2]) **
+                            np.arange(-1, n + 1).reshape(-1, 1))
+        imp[0, :] = 0.0
+        # Analytical solution to impulse response
+        y0 = imp[:n, 0] + np.dot(imp[1:n + 1, :], x0)
+        y1 = imp[:n, 1] + np.dot(imp[1:n + 1, :], x0)
+
+        xp_assert_close(yi[0][:, 0], y0)
+        xp_assert_close(yi[1][:, 0], y1)
+
+        # Check that dt=0.1, n=3 gives 3 time values.
+        system = ([1.0], [1.0, -0.5], 0.1)
+        t, (y,) = dstep(system, n=3)
+        xp_assert_close(t, [0, 0.1, 0.2])
+        xp_assert_equal(y.T, [[0, 1.0, 1.5]])
+        t, (y,) = dimpulse(system, n=3)
+        xp_assert_close(t, [0, 0.1, 0.2])
+        xp_assert_equal(y.T, [[0, 1, 0.5]])
+
+
+class TestDlti:
+    def test_dlti_instantiation(self):
+        # Test that lti can be instantiated.
+
+        dt = 0.05
+        # TransferFunction
+        s = dlti([1], [-1], dt=dt)
+        assert isinstance(s, TransferFunction)
+        assert isinstance(s, dlti)
+        assert not isinstance(s, lti)
+        assert s.dt == dt
+
+        # ZerosPolesGain
+        s = dlti(np.array([]), np.array([-1]), 1, dt=dt)
+        assert isinstance(s, ZerosPolesGain)
+        assert isinstance(s, dlti)
+        assert not isinstance(s, lti)
+        assert s.dt == dt
+
+        # StateSpace
+        s = dlti([1], [-1], 1, 3, dt=dt)
+        assert isinstance(s, StateSpace)
+        assert isinstance(s, dlti)
+        assert not isinstance(s, lti)
+        assert s.dt == dt
+
+        # Number of inputs
+        assert_raises(ValueError, dlti, 1)
+        assert_raises(ValueError, dlti, 1, 1, 1, 1, 1)
+
+
+class TestStateSpaceDisc:
+    def test_initialization(self):
+        # Check that all initializations work
+        dt = 0.05
+        StateSpace(1, 1, 1, 1, dt=dt)
+        StateSpace([1], [2], [3], [4], dt=dt)
+        StateSpace(np.array([[1, 2], [3, 4]]), np.array([[1], [2]]),
+                   np.array([[1, 0]]), np.array([[0]]), dt=dt)
+        StateSpace(1, 1, 1, 1, dt=True)
+
+    def test_conversion(self):
+        # Check the conversion functions
+        s = StateSpace(1, 2, 3, 4, dt=0.05)
+        assert isinstance(s.to_ss(), StateSpace)
+        assert isinstance(s.to_tf(), TransferFunction)
+        assert isinstance(s.to_zpk(), ZerosPolesGain)
+
+        # Make sure copies work
+        assert StateSpace(s) is not s
+        assert s.to_ss() is not s
+
+    def test_properties(self):
+        # Test setters/getters for cross class properties.
+        # This implicitly tests to_tf() and to_zpk()
+
+        # Getters
+        s = StateSpace(1, 1, 1, 1, dt=0.05)
+        xp_assert_equal(s.poles, [1.])
+        xp_assert_equal(s.zeros, [0.])
+
+
+class TestTransferFunction:
+    def test_initialization(self):
+        # Check that all initializations work
+        dt = 0.05
+        TransferFunction(1, 1, dt=dt)
+        TransferFunction([1], [2], dt=dt)
+        TransferFunction(np.array([1]), np.array([2]), dt=dt)
+        TransferFunction(1, 1, dt=True)
+
+    def test_conversion(self):
+        # Check the conversion functions
+        s = TransferFunction([1, 0], [1, -1], dt=0.05)
+        assert isinstance(s.to_ss(), StateSpace)
+        assert isinstance(s.to_tf(), TransferFunction)
+        assert isinstance(s.to_zpk(), ZerosPolesGain)
+
+        # Make sure copies work
+        assert TransferFunction(s) is not s
+        assert s.to_tf() is not s
+
+    def test_properties(self):
+        # Test setters/getters for cross class properties.
+        # This implicitly tests to_ss() and to_zpk()
+
+        # Getters
+        s = TransferFunction([1, 0], [1, -1], dt=0.05)
+        xp_assert_equal(s.poles, [1.])
+        xp_assert_equal(s.zeros, [0.])
+
+
+class TestZerosPolesGain:
+    def test_initialization(self):
+        # Check that all initializations work
+        dt = 0.05
+        ZerosPolesGain(1, 1, 1, dt=dt)
+        ZerosPolesGain([1], [2], 1, dt=dt)
+        ZerosPolesGain(np.array([1]), np.array([2]), 1, dt=dt)
+        ZerosPolesGain(1, 1, 1, dt=True)
+
+    def test_conversion(self):
+        # Check the conversion functions
+        s = ZerosPolesGain(1, 2, 3, dt=0.05)
+        assert isinstance(s.to_ss(), StateSpace)
+        assert isinstance(s.to_tf(), TransferFunction)
+        assert isinstance(s.to_zpk(), ZerosPolesGain)
+
+        # Make sure copies work
+        assert ZerosPolesGain(s) is not s
+        assert s.to_zpk() is not s
+
+
+class Test_dfreqresp:
+
+    def test_manual(self):
+        # Test dfreqresp() real part calculation (manual sanity check).
+        # 1st order low-pass filter: H(z) = 1 / (z - 0.2),
+        system = TransferFunction(1, [1, -0.2], dt=0.1)
+        w = [0.1, 1, 10]
+        w, H = dfreqresp(system, w=w)
+
+        # test real
+        expected_re = [1.2383, 0.4130, -0.7553]
+        assert_almost_equal(H.real, expected_re, decimal=4)
+
+        # test imag
+        expected_im = [-0.1555, -1.0214, 0.3955]
+        assert_almost_equal(H.imag, expected_im, decimal=4)
+
+    def test_auto(self):
+        # Test dfreqresp() real part calculation.
+        # 1st order low-pass filter: H(z) = 1 / (z - 0.2),
+        system = TransferFunction(1, [1, -0.2], dt=0.1)
+        w = [0.1, 1, 10, 100]
+        w, H = dfreqresp(system, w=w)
+        jw = np.exp(w * 1j)
+        y = np.polyval(system.num, jw) / np.polyval(system.den, jw)
+
+        # test real
+        expected_re = y.real
+        assert_almost_equal(H.real, expected_re)
+
+        # test imag
+        expected_im = y.imag
+        assert_almost_equal(H.imag, expected_im)
+
+    def test_freq_range(self):
+        # Test that freqresp() finds a reasonable frequency range.
+        # 1st order low-pass filter: H(z) = 1 / (z - 0.2),
+        # Expected range is from 0.01 to 10.
+        system = TransferFunction(1, [1, -0.2], dt=0.1)
+        n = 10
+        expected_w = np.linspace(0, np.pi, 10, endpoint=False)
+        w, H = dfreqresp(system, n=n)
+        assert_almost_equal(w, expected_w)
+
+    def test_pole_one(self):
+        # Test that freqresp() doesn't fail on a system with a pole at 0.
+        # integrator, pole at zero: H(s) = 1 / s
+        system = TransferFunction([1], [1, -1], dt=0.1)
+
+        with warnings.catch_warnings():
+            warnings.filterwarnings("ignore", "divide by zero", RuntimeWarning)
+            warnings.filterwarnings(
+                "ignore", "invalid value encountered", RuntimeWarning)
+            w, H = dfreqresp(system, n=2)
+        assert w[0] == 0.   # a fail would give not-a-number
+
+    def test_error(self):
+        # Raise an error for continuous-time systems
+        system = lti([1], [1, 1])
+        assert_raises(AttributeError, dfreqresp, system)
+
+    def test_from_state_space(self):
+        # H(z) = 2 / z^3 - 0.5 * z^2
+
+        system_TF = dlti([2], [1, -0.5, 0, 0])
+
+        A = np.array([[0.5, 0, 0],
+                      [1, 0, 0],
+                      [0, 1, 0]])
+        B = np.array([[1, 0, 0]]).T
+        C = np.array([[0, 0, 2]])
+        D = 0
+
+        system_SS = dlti(A, B, C, D)
+        w = 10.0**np.arange(-3,0,.5)
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", BadCoefficients)
+            w1, H1 = dfreqresp(system_TF, w=w)
+            w2, H2 = dfreqresp(system_SS, w=w)
+
+        assert_almost_equal(H1, H2)
+
+    def test_from_zpk(self):
+        # 1st order low-pass filter: H(s) = 0.3 / (z - 0.2),
+        system_ZPK = dlti([],[0.2],0.3)
+        system_TF = dlti(0.3, [1, -0.2])
+        w = [0.1, 1, 10, 100]
+        w1, H1 = dfreqresp(system_ZPK, w=w)
+        w2, H2 = dfreqresp(system_TF, w=w)
+        assert_almost_equal(H1, H2)
+
+
+class Test_bode:
+
+    def test_manual(self):
+        # Test bode() magnitude calculation (manual sanity check).
+        # 1st order low-pass filter: H(s) = 0.3 / (z - 0.2),
+        dt = 0.1
+        system = TransferFunction(0.3, [1, -0.2], dt=dt)
+        w = [0.1, 0.5, 1, np.pi]
+        w2, mag, phase = dbode(system, w=w)
+
+        # Test mag
+        expected_mag = [-8.5329, -8.8396, -9.6162, -12.0412]
+        assert_almost_equal(mag, expected_mag, decimal=4)
+
+        # Test phase
+        expected_phase = [-7.1575, -35.2814, -67.9809, -180.0000]
+        assert_almost_equal(phase, expected_phase, decimal=4)
+
+        # Test frequency
+        xp_assert_equal(np.array(w) / dt, w2)
+
+    def test_auto(self):
+        # Test bode() magnitude calculation.
+        # 1st order low-pass filter: H(s) = 0.3 / (z - 0.2),
+        system = TransferFunction(0.3, [1, -0.2], dt=0.1)
+        w = np.array([0.1, 0.5, 1, np.pi])
+        w2, mag, phase = dbode(system, w=w)
+        jw = np.exp(w * 1j)
+        y = np.polyval(system.num, jw) / np.polyval(system.den, jw)
+
+        # Test mag
+        expected_mag = 20.0 * np.log10(abs(y))
+        assert_almost_equal(mag, expected_mag)
+
+        # Test phase
+        expected_phase = np.rad2deg(np.angle(y))
+        assert_almost_equal(phase, expected_phase)
+
+    def test_range(self):
+        # Test that bode() finds a reasonable frequency range.
+        # 1st order low-pass filter: H(s) = 0.3 / (z - 0.2),
+        dt = 0.1
+        system = TransferFunction(0.3, [1, -0.2], dt=0.1)
+        n = 10
+        # Expected range is from 0.01 to 10.
+        expected_w = np.linspace(0, np.pi, n, endpoint=False) / dt
+        w, mag, phase = dbode(system, n=n)
+        assert_almost_equal(w, expected_w)
+
+    def test_pole_one(self):
+        # Test that freqresp() doesn't fail on a system with a pole at 0.
+        # integrator, pole at zero: H(s) = 1 / s
+        system = TransferFunction([1], [1, -1], dt=0.1)
+
+        with warnings.catch_warnings():
+            warnings.filterwarnings("ignore", "divide by zero", RuntimeWarning)
+            warnings.filterwarnings(
+                "ignore", "invalid value encountered", RuntimeWarning)
+            w, mag, phase = dbode(system, n=2)
+        assert w[0] == 0.  # a fail would give not-a-number
+
+    def test_imaginary(self):
+        # bode() should not fail on a system with pure imaginary poles.
+        # The test passes if bode doesn't raise an exception.
+        system = TransferFunction([1], [1, 0, 100], dt=0.1)
+        dbode(system, n=2)
+
+    def test_error(self):
+        # Raise an error for continuous-time systems
+        system = lti([1], [1, 1])
+        assert_raises(AttributeError, dbode, system)
+
+
+class TestTransferFunctionZConversion:
+    """Test private conversions between 'z' and 'z**-1' polynomials."""
+
+    def test_full(self):
+        # Numerator and denominator same order
+        num = np.asarray([2.0, 3, 4])
+        den = np.asarray([5.0, 6, 7])
+        num2, den2 = TransferFunction._z_to_zinv(num, den)
+        xp_assert_equal(num, num2)
+        xp_assert_equal(den, den2)
+
+        num2, den2 = TransferFunction._zinv_to_z(num, den)
+        xp_assert_equal(num, num2)
+        xp_assert_equal(den, den2)
+
+    def test_numerator(self):
+        # Numerator lower order than denominator
+        num = np.asarray([2.0, 3])
+        den = np.asarray([50, 6, 7])
+        num2, den2 = TransferFunction._z_to_zinv(num, den)
+        xp_assert_equal([0.0, 2, 3], num2)
+        xp_assert_equal(den, den2)
+
+        num2, den2 = TransferFunction._zinv_to_z(num, den)
+        xp_assert_equal([2.0, 3, 0], num2)
+        xp_assert_equal(den, den2)
+
+    def test_denominator(self):
+        # Numerator higher order than denominator
+        num = np.asarray([2., 3, 4])
+        den = np.asarray([5.0, 6])
+        num2, den2 = TransferFunction._z_to_zinv(num, den)
+        xp_assert_equal(num, num2)
+        xp_assert_equal([0.0, 5, 6], den2)
+
+        num2, den2 = TransferFunction._zinv_to_z(num, den)
+        xp_assert_equal(num, num2)
+        xp_assert_equal([5.0, 6, 0], den2)
+
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/tests/test_filter_design.py b/venv/lib/python3.12/site-packages/scipy/signal/tests/test_filter_design.py
new file mode 100644
index 0000000000000000000000000000000000000000..265aa19a0017648998535a3515bdfa9a44d29920
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/tests/test_filter_design.py
@@ -0,0 +1,5194 @@
+import math
+import cmath
+import warnings
+import os
+
+from itertools import product
+
+from scipy._external.packaging_version import version
+import numpy as np
+import pytest
+from pytest import raises as assert_raises
+from scipy._lib._array_api import (
+    xp_assert_close, xp_assert_equal, array_namespace,
+    assert_array_almost_equal, xp_size, xp_default_dtype, is_numpy,
+    make_xp_test_case, make_xp_pytest_param, is_cupy, is_torch, scipy_namespace_for,
+    _xp_copy_to_numpy, xp_assert_close_nulp
+)
+import scipy._external.array_api_extra as xpx
+
+from numpy import array, spacing, sin, pi
+from scipy.signal import (argrelextrema, BadCoefficients, bessel, besselap, bilinear,
+                          buttap, butter, buttord, cheb1ap, cheb1ord, cheb2ap,
+                          cheb2ord, cheby1, cheby2, ellip, ellipap, ellipord,
+                          findfreqs, firwin, freqs_zpk, freqs, freqz, freqz_zpk,
+                          gammatone, group_delay, iircomb, iirdesign, iirfilter,
+                          iirnotch, iirpeak, lp2bp, lp2bs, lp2hp, lp2lp, normalize,
+                          sos2tf, sos2zpk, sosfreqz, freqz_sos, tf2sos, tf2zpk, zpk2sos,
+                          zpk2tf, bilinear_zpk, lp2lp_zpk, lp2hp_zpk, lp2bp_zpk,
+                          lp2bs_zpk)
+from scipy.signal._filter_design import (_cplxreal, _cplxpair, _norm_factor,
+                                        _bessel_poly, _bessel_zeros)
+from scipy.signal._filter_design import _logspace
+from scipy.signal import _polyutils as _pu
+from scipy.signal._polyutils import _sort_cmplx
+
+skip_xp_backends = pytest.mark.skip_xp_backends
+xfail_xp_backends = pytest.mark.xfail_xp_backends
+
+
+DEFAULT_F32 = os.getenv('SCIPY_DEFAULT_DTYPE', default='float64') == 'float32'
+
+try:
+    import mpmath
+except ImportError:
+    mpmath = None
+
+
+def mpmath_check(min_ver):
+    return pytest.mark.skipif(
+        mpmath is None
+        or version.parse(mpmath.__version__) < version.Version(min_ver),
+        reason=f"mpmath version >= {min_ver} required",
+    )
+
+
+class TestCplxPair:
+
+    def test_trivial_input(self):
+        assert _cplxpair([]).size == 0
+        assert _cplxpair(1) == 1
+
+    def test_output_order(self):
+        xp_assert_close(_cplxpair([1+1j, 1-1j]), [1-1j, 1+1j])
+
+        a = [1+1j, 1+1j, 1, 1-1j, 1-1j, 2]
+        b = [1-1j, 1+1j, 1-1j, 1+1j, 1, 2]
+        xp_assert_close(_cplxpair(a), b)
+
+        # points spaced around the unit circle
+        z = np.exp(2j*pi*array([4, 3, 5, 2, 6, 1, 0])/7)
+        z1 = np.copy(z)
+        np.random.shuffle(z)
+        xp_assert_close(_cplxpair(z), z1)
+        np.random.shuffle(z)
+        xp_assert_close(_cplxpair(z), z1)
+        np.random.shuffle(z)
+        xp_assert_close(_cplxpair(z), z1)
+
+        # Should be able to pair up all the conjugates
+        x = np.random.rand(10000) + 1j * np.random.rand(10000)
+        y = x.conj()
+        z = np.random.rand(10000)
+        x = np.concatenate((x, y, z))
+        np.random.shuffle(x)
+        c = _cplxpair(x)
+
+        # Every other element of head should be conjugates:
+        xp_assert_close(c[0:20000:2], np.conj(c[1:20000:2]))
+        # Real parts of head should be in sorted order:
+        xp_assert_close(c[0:20000:2].real, np.sort(c[0:20000:2].real))
+        # Tail should be sorted real numbers:
+        xp_assert_close(c[20000:], np.sort(c[20000:]))
+
+    def test_real_integer_input(self):
+        xp_assert_equal(_cplxpair([2, 0, 1]), [0, 1, 2])
+
+    def test_tolerances(self):
+        eps = spacing(1)
+        xp_assert_close(_cplxpair([1j, -1j, 1+1j*eps], tol=2*eps),
+                        [-1j, 1j, 1+1j*eps])
+
+        # sorting close to 0
+        xp_assert_close(_cplxpair([-eps+1j, +eps-1j]), [-1j, +1j])
+        xp_assert_close(_cplxpair([+eps+1j, -eps-1j]), [-1j, +1j])
+        xp_assert_close(_cplxpair([+1j, -1j]), [-1j, +1j])
+
+    def test_unmatched_conjugates(self):
+        # 1+2j is unmatched
+        assert_raises(ValueError, _cplxpair, [1+3j, 1-3j, 1+2j])
+
+        # 1+2j and 1-3j are unmatched
+        assert_raises(ValueError, _cplxpair, [1+3j, 1-3j, 1+2j, 1-3j])
+
+        # 1+3j is unmatched
+        assert_raises(ValueError, _cplxpair, [1+3j, 1-3j, 1+3j])
+
+        # Not conjugates
+        assert_raises(ValueError, _cplxpair, [4+5j, 4+5j])
+        assert_raises(ValueError, _cplxpair, [1-7j, 1-7j])
+
+        # No pairs
+        assert_raises(ValueError, _cplxpair, [1+3j])
+        assert_raises(ValueError, _cplxpair, [1-3j])
+
+
+class TestCplxReal:
+
+    def test_trivial_input(self):
+        assert all(x.size == 0 for x in _cplxreal([]))
+
+        x = _cplxreal(1)
+        assert x[0].size == 0
+        xp_assert_equal(x[1], np.asarray([1]))
+
+
+    def test_output_order(self):
+        zc, zr = _cplxreal(np.roots(array([1, 0, 0, 1])))
+        xp_assert_close(np.append(zc, zr), [1/2 + 1j*sin(pi/3), -1])
+
+        eps = spacing(1)
+
+        a = [0+1j, 0-1j, eps + 1j, eps - 1j, -eps + 1j, -eps - 1j,
+             1, 4, 2, 3, 0, 0,
+             2+3j, 2-3j,
+             1-eps + 1j, 1+2j, 1-2j, 1+eps - 1j,  # sorts out of order
+             3+1j, 3+1j, 3+1j, 3-1j, 3-1j, 3-1j,
+             2-3j, 2+3j]
+        zc, zr = _cplxreal(a)
+        xp_assert_close(zc, [1j, 1j, 1j, 1+1j, 1+2j, 2+3j, 2+3j, 3+1j, 3+1j,
+                             3+1j])
+        xp_assert_close(zr, [0.0, 0, 1, 2, 3, 4])
+
+        z = array([1-eps + 1j, 1+2j, 1-2j, 1+eps - 1j, 1+eps+3j, 1-2*eps-3j,
+                   0+1j, 0-1j, 2+4j, 2-4j, 2+3j, 2-3j, 3+7j, 3-7j, 4-eps+1j,
+                   4+eps-2j, 4-1j, 4-eps+2j])
+
+        zc, zr = _cplxreal(z)
+        xp_assert_close(zc, [1j, 1+1j, 1+2j, 1+3j, 2+3j, 2+4j, 3+7j, 4+1j,
+                             4+2j])
+        xp_assert_equal(zr, np.asarray([]))
+
+    def test_unmatched_conjugates(self):
+        # 1+2j is unmatched
+        assert_raises(ValueError, _cplxreal, [1+3j, 1-3j, 1+2j])
+
+        # 1+2j and 1-3j are unmatched
+        assert_raises(ValueError, _cplxreal, [1+3j, 1-3j, 1+2j, 1-3j])
+
+        # 1+3j is unmatched
+        assert_raises(ValueError, _cplxreal, [1+3j, 1-3j, 1+3j])
+
+        # No pairs
+        assert_raises(ValueError, _cplxreal, [1+3j])
+        assert_raises(ValueError, _cplxreal, [1-3j])
+
+    def test_real_integer_input(self):
+        zc, zr = _cplxreal([2, 0, 1, 4])
+        xp_assert_equal(zc, np.asarray([]))
+        xp_assert_equal(zr, [0, 1, 2, 4])
+
+
+@make_xp_test_case(tf2zpk)
+class TestTf2zpk:
+
+    @skip_xp_backends("dask.array", reason="https://github.com/dask/dask/issues/11883")
+    @pytest.mark.parametrize('dt', ('float64', 'complex128'))
+    def test_simple(self, dt, xp):
+        dtyp = getattr(xp, dt)
+
+        z_r = xp.asarray([0.5, -0.5])
+        p_r = xp.asarray([1.j / math.sqrt(2), -1.j / math.sqrt(2)])
+        # Sort the zeros/poles so that we don't fail the test if the order
+        # changes
+        z_r = _sort_cmplx(z_r, xp=xp)
+        p_r = _sort_cmplx(p_r, xp=xp)
+
+        b = xp.astype(_pu.poly(z_r, xp=xp), dtyp)
+        a = xp.astype(_pu.poly(p_r, xp=xp), dtyp)
+
+        z, p, k = tf2zpk(b, a)
+        z = _sort_cmplx(z, xp=xp)
+        # The real part of `p` is ~0.0, so sort by imaginary part
+        p = p[xp.argsort(xp.imag(p))]
+
+        assert_array_almost_equal(z, z_r)
+        assert_array_almost_equal(p, p_r)
+        assert math.isclose(xp.real(k), 1.)
+        assert k.dtype == dtyp
+
+    def test_bad_filter(self):
+        # Regression test for #651: better handling of badly conditioned
+        # filter coefficients.
+        with warnings.catch_warnings():
+            warnings.simplefilter("error", BadCoefficients)
+            assert_raises(BadCoefficients, tf2zpk, [1e-15], [1.0, 1.0])
+
+
+@make_xp_test_case(zpk2tf)
+class TestZpk2Tf:
+
+    def test_identity(self, xp):
+        """Test the identity transfer function."""
+        z = xp.asarray([])
+        p = xp.asarray([])
+        k = 1.
+        b, a = zpk2tf(z, p, k)
+        b_r = xp.asarray([1.])  # desired result
+        a_r = xp.asarray([1.])  # desired result
+        # The test for the *type* of the return values is a regression
+        # test for ticket #1095. In the case p=[], zpk2tf used to
+        # return the scalar 1.0 instead of array([1.0]).
+        xp_assert_equal(b, b_r)
+        xp_assert_equal(a, a_r)
+        if is_numpy(xp):
+            assert isinstance(b, np.ndarray)
+            assert isinstance(a, np.ndarray)
+
+    @skip_xp_backends("dask.array", reason="https://github.com/dask/dask/issues/11883")
+    def test_conj_pair(self, xp):
+        # conjugate pairs give real-coeff num & den
+        z = xp.asarray([1j, -1j, 2j, -2j])
+        z_np = _xp_copy_to_numpy(z)
+        # shouldn't need elements of pairs to be adjacent
+        p = xp.asarray([1+1j, 3-100j, 3+100j, 1-1j])
+        p_np = _xp_copy_to_numpy(p)
+
+        k = 23
+
+        # np.poly should do the right thing, but be explicit about
+        # taking real part
+        b_np = k * np.poly(z_np).real
+        a_np = np.poly(p_np).real
+        b, a = map(xp.asarray, (b_np, a_np))
+
+        bp, ap = zpk2tf(z, p, k)
+
+        atol = 5e-13 if is_cupy(xp) else 0.0
+        xp_assert_close(b, bp, atol=atol)
+        xp_assert_close(a, ap)
+
+        assert xp.isdtype(bp.dtype, 'real floating')
+        assert xp.isdtype(ap.dtype, 'real floating')
+
+    @skip_xp_backends("dask.array", reason="https://github.com/dask/dask/issues/11883")
+    def test_complexk(self, xp):
+        # regression: z, p real, k complex k gave real b, a
+        b, a = xp.asarray([1j, 1j]), xp.asarray([1.0, 2])
+        b_np, a_np = map(_xp_copy_to_numpy, (b, a))
+        z_np, p_np, k_np = tf2zpk(b_np, a_np)
+        z, p, k = map(xp.asarray, (z_np, p_np, k_np))
+        xp_assert_close(k, xp.asarray(1j), check_0d=False)
+        bp, ap = zpk2tf(z, p, k)
+        xp_assert_close(b, bp)
+        xp_assert_close(a, ap)
+
+    @skip_xp_backends("jax.numpy",
+                      reason="zpk2tf not compatible with jax yet on multi-dim arrays")
+    @skip_xp_backends("cupy",
+                      reason="multi-dim arrays not supported yet on cupy")
+    def test_zpk2tf_with_multi_dimensional_array(self, xp):
+        z = xp.asarray([[1, 2], [3, 4]])  # Multi-dimensional input
+        p = xp.asarray([1, 2])
+        k = 1
+        b, a = zpk2tf(z, p, k)
+        b_ref = xp.asarray([[1, -3, 2], [1, -7, 12]])
+        a_ref = xp.asarray([1, -3, 2])
+        xp_assert_close(b, b_ref, check_dtype=False)
+        xp_assert_close(a, a_ref, check_dtype=False)
+
+    @skip_xp_backends("cupy",
+                      reason="multi-dim arrays not supported yet on cupy")
+    def test_zpk2tf_int_truncation(self, xp):
+        # regression test for gh-24382
+        z =  xp.asarray([[ 1, 2.], [ 0., -1.]], dtype=xp.float64)
+        p = xp.asarray([3., 4.], dtype=xp.float64)
+        k = 2.5
+
+        b, a = zpk2tf(z, p, k)
+
+        # reference values from scipy 1.15.3
+        b_ref = xp.asarray([[ 2.5, -7.5,  5. ], [ 2.5,  2.5,  0. ]], dtype=xp.float64)
+        a_ref = xp.asarray([ 1., -7., 12.], dtype=xp.float64)
+
+        xp_assert_close(b, b_ref, atol=1e-14)
+        xp_assert_close(a, a_ref, atol=1e-14)
+
+    @skip_xp_backends("jax.numpy",
+                      reason="zpk2tf not compatible with jax yet on multi-dim arrays")
+    @skip_xp_backends("cupy",
+                      reason="multi-dim arrays not supported yet on cupy")
+    def test_zpk2tf_complex_k_multi_dim_z(self, xp):
+        # Regression test for gh-24395
+        k = 1j
+        z = xp.asarray([[1., 2.], [0., -1.]])
+        p = xp.asarray([3., 4.])
+
+        b, a = zpk2tf(z, p, k)
+
+        b1, a1 = zpk2tf(z[0, :], p, k)
+        b2, a2 = zpk2tf(z[1, :], p, k)
+
+        xp_assert_close(a, a1)
+        xp_assert_close(a, a2)
+        xp_assert_close(b[0, :], b1)
+        xp_assert_close(b[1, :], b2)
+        assert xp.isdtype(b.dtype, 'complex floating')
+
+
+@make_xp_test_case(sos2zpk)
+class TestSos2Zpk:
+
+    @skip_xp_backends("dask.array", reason="it https://github.com/dask/dask/issues/11883")
+    @xfail_xp_backends("jax.numpy", reason="inaccurate with jax")
+    def test_basic(self, xp):
+        sos = [[1, 0, 1, 1, 0, -0.81],
+               [1, 0, 0, 1, 0, +0.49]]
+        sos = xp.asarray(sos)
+        z, p, k = sos2zpk(sos)
+        z2 = xp.asarray([1j, -1j, 0, 0])
+        p2 = xp.asarray([0.9, -0.9, 0.7j, -0.7j])
+        k2 = 1.
+        assert_array_almost_equal(_sort_cmplx(z, xp), _sort_cmplx(z2, xp), decimal=4)
+        assert_array_almost_equal(_sort_cmplx(p, xp), _sort_cmplx(p2, xp), decimal=4)
+        assert math.isclose(k, k2)
+
+        sos = [[1.00000, +0.61803, 1.0000, 1.00000, +0.60515, 0.95873],
+               [1.00000, -1.61803, 1.0000, 1.00000, -1.58430, 0.95873],
+               [1.00000, +1.00000, 0.0000, 1.00000, +0.97915, 0.00000]]
+        sos = xp.asarray(sos)
+        z, p, k = sos2zpk(sos)
+        z2 = [-0.3090 + 0.9511j, -0.3090 - 0.9511j, 0.8090 + 0.5878j,
+              0.8090 - 0.5878j, -1.0000 + 0.0000j, 0]
+        p2 = [-0.3026 + 0.9312j, -0.3026 - 0.9312j, 0.7922 + 0.5755j,
+              0.7922 - 0.5755j, -0.9791 + 0.0000j, 0]
+        z2 = xp.asarray(z2)
+        p2 = xp.asarray(p2)
+        k2 = 1
+        assert_array_almost_equal(_sort_cmplx(z, xp), _sort_cmplx(z2, xp), decimal=4)
+        assert_array_almost_equal(_sort_cmplx(p, xp), _sort_cmplx(p2, xp), decimal=4)
+
+        sos = array([[1, 2, 3, 1, 0.2, 0.3],
+                     [4, 5, 6, 1, 0.4, 0.5]])
+        z = array([-1 - 1.41421356237310j, -1 + 1.41421356237310j,
+                  -0.625 - 1.05326872164704j, -0.625 + 1.05326872164704j])
+        p = array([-0.2 - 0.678232998312527j, -0.2 + 0.678232998312527j,
+                  -0.1 - 0.538516480713450j, -0.1 + 0.538516480713450j])
+        sos, z, p = map(xp.asarray, (sos, z, p))
+        k = 4
+        z2, p2, k2 = sos2zpk(sos)
+
+        xp_assert_close(_sort_cmplx(z2, xp=xp), _sort_cmplx(z, xp=xp))
+        xp_assert_close(_sort_cmplx(p2, xp=xp), _sort_cmplx(p, xp=xp))
+        assert k2 == k
+
+    def test_fewer_zeros(self, xp):
+        """Test not the expected number of p/z (effectively at origin)."""
+        sos = butter(3, 0.1, output='sos')
+        z, p, k = sos2zpk(xp.asarray(sos))
+        assert z.shape[0] == 4
+        assert p.shape[0] == 4
+
+        sos = butter(12, [5., 30.], 'bandpass', fs=1200., analog=False, output='sos')
+        e = BadCoefficients
+        if is_cupy(xp):
+            e = scipy_namespace_for(xp).signal.BadCoefficients
+        with pytest.warns(e, match='Badly conditioned'):
+            z, p, k = sos2zpk(xp.asarray(sos))
+        assert z.shape[0] == 24
+        assert p.shape[0] == 24
+
+
+@make_xp_test_case(sos2tf)
+class TestSos2Tf:
+
+    def test_basic(self, xp):
+        sos = [[1.0, 1, 1, 1, 0, -1],
+               [-2, 3, 1, 1, 10, 1]]
+        sos = xp.asarray(sos)
+        b, a = sos2tf(sos)
+        assert_array_almost_equal(b, xp.asarray([-2.0, 1, 2, 4, 1]))
+        assert_array_almost_equal(a, xp.asarray([1.0, 10, 0, -10, -1]))
+
+
+@make_xp_test_case(tf2sos)
+class TestTf2Sos:
+
+    def test_basic(self, xp):
+        num = xp.asarray([2., 16, 44, 56, 32])
+        den = xp.asarray([3., 3, -15, 18, -12])
+        sos = tf2sos(num, den)
+        sos2 = [[0.6667, 4.0000, 5.3333, 1.0000, +2.0000, -4.0000],
+                [1.0000, 2.0000, 2.0000, 1.0000, -1.0000, +1.0000]]
+        sos2 = xp.asarray(sos2)
+        assert_array_almost_equal(sos, sos2, decimal=4)
+
+        b = xp.asarray([1.0, -3, 11, -27, 18])
+        a = xp.asarray([16.0, 12, 2, -4, -1])
+        sos = tf2sos(b, a)
+        sos2 = [[0.0625, -0.1875, 0.1250, 1.0000, -0.2500, -0.1250],
+                [1.0000, +0.0000, 9.0000, 1.0000, +1.0000, +0.5000]]
+        sos2 = xp.asarray(sos2)
+        #assert_array_almost_equal(sos, sos2, decimal=4)
+
+    @pytest.mark.parametrize('b, a, analog, sos',
+                             [([1.0], [1.0], False, [[1., 0., 0., 1., 0., 0.]]),
+                              ([1.0], [1.0], True, [[0., 0., 1., 0., 0., 1.]]),
+                              ([1.0], [1., 0., -1.01, 0, 0.01], False,
+                               [[1., 0., 0., 1., 0., -0.01],
+                                [1., 0., 0., 1., 0., -1]]),
+                              ([1.0], [1., 0., -1.01, 0, 0.01], True,
+                               [[0., 0., 1., 1., 0., -1],
+                                [0., 0., 1., 1., 0., -0.01]])])
+    @skip_xp_backends("cupy", reason="https://github.com/cupy/cupy/issues/9376")
+    def test_analog(self, b, a, analog, sos, xp):
+        b, a, sos = map(xp.asarray, (b, a, sos))
+        sos2 = tf2sos(b, a, analog=analog)
+        assert_array_almost_equal(sos, sos2, decimal=4)
+
+
+@make_xp_test_case(zpk2sos)
+class TestZpk2Sos:
+
+#    @pytest.mark.parametrize('dt', 'fdgFDG')
+    # XXX: quietly remove float128 and complex256
+    @pytest.mark.parametrize('dt', ['float32', 'float64', 'complex64', 'complex128'])
+    @pytest.mark.parametrize('pairing, analog',
+                             [('nearest', False),
+                              ('keep_odd', False),
+                              ('minimal', False),
+                              ('minimal', True)])
+    def test_dtypes(self, dt, pairing, analog, xp):
+        dtype = getattr(xp, dt)
+        # the poles have to be complex
+        cdtype = (1j*xp.empty(0, dtype=dtype)).dtype
+
+        z = xp.asarray([-1, -1], dtype=dtype)
+        p = xp.asarray([0.57149 + 0.29360j, 0.57149 - 0.29360j], dtype=cdtype)
+        k = xp.asarray(1, dtype=dtype)
+        sos = zpk2sos(z, p, k, pairing=pairing, analog=analog)
+        # octave & MATLAB
+        sos2 = xp.asarray([[1, 2, 1, 1, -1.14298, 0.41280]], dtype=dtype)
+        assert_array_almost_equal(sos, sos2, decimal=4)
+
+    def test_basic(self, xp):
+        for pairing in ('nearest', 'keep_odd'):
+            #
+            # Cases that match octave
+            #
+
+            z = xp.asarray([-1.0, -1.0])
+            p = xp.asarray([0.57149 + 0.29360j, 0.57149 - 0.29360j])
+            k = 1
+            sos = zpk2sos(z, p, k, pairing=pairing)
+            sos2 = xp.asarray([[1, 2, 1, 1, -1.14298, 0.41280]])  # octave & MATLAB
+            assert_array_almost_equal(sos, sos2, decimal=4)
+
+            z = xp.asarray([1j, -1j])
+            p = xp.asarray([0.9, -0.9, 0.7j, -0.7j])
+            k = 1
+            sos = zpk2sos(z, p, k, pairing=pairing)
+            sos2 = [[1, 0, 1, 1, 0, +0.49],
+                    [1, 0, 0, 1, 0, -0.81]]  # octave
+            sos2 = xp.asarray(sos2)
+            # sos2 = [[0, 0, 1, 1, -0.9, 0],
+            #         [1, 0, 1, 1, 0.9, 0]]  # MATLAB
+            assert_array_almost_equal(sos, sos2, decimal=4)
+
+            z = xp.asarray([])
+            p = xp.asarray([0.8, -0.5+0.25j, -0.5-0.25j])
+            k = 1.
+            sos = zpk2sos(z, p, k, pairing=pairing)
+            sos2 = [[1., 0., 0., 1., 1., 0.3125],
+                    [1., 0., 0., 1., -0.8, 0.]]  # octave, MATLAB fails
+            sos2 = xp.asarray(sos2)
+            assert_array_almost_equal(sos, sos2, decimal=4)
+
+            z = xp.asarray([1., 1., 0.9j, -0.9j])
+            p = xp.asarray([0.99+0.01j, 0.99-0.01j, 0.1+0.9j, 0.1-0.9j])
+            k = 1
+            sos = zpk2sos(z, p, k, pairing=pairing)
+            sos2 = [[1, 0, 0.81, 1, -0.2, 0.82],
+                    [1, -2, 1, 1, -1.98, 0.9802]]  # octave
+            sos2 = xp.asarray(sos2)
+            # sos2 = [[1, -2, 1, 1,  -0.2, 0.82],
+            #         [1, 0, 0.81, 1, -1.98, 0.9802]]  # MATLAB
+            assert_array_almost_equal(sos, sos2, decimal=4)
+
+            z = xp.asarray([0.9+0.1j, 0.9-0.1j, -0.9])
+            p = xp.asarray([0.75+0.25j, 0.75-0.25j, 0.9])
+            k = 1
+            sos = zpk2sos(z, p, k, pairing=pairing)
+            if pairing == 'keep_odd':
+                sos2 = [[1, -1.8, 0.82, 1, -1.5, 0.625],
+                        [1, 0.9, 0, 1, -0.9, 0]]  # octave; MATLAB fails
+                sos2 = xp.asarray(sos2)
+                assert_array_almost_equal(sos, sos2, decimal=4)
+            else:  # pairing == 'nearest'
+                sos2 = [[1, 0.9, 0, 1, -1.5, 0.625],
+                        [1, -1.8, 0.82, 1, -0.9, 0]]  # our algorithm
+                sos2 = xp.asarray(sos2)
+                assert_array_almost_equal(sos, sos2, decimal=4)
+
+            #
+            # Cases that differ from octave:
+            #
+
+            z = [-0.3090 + 0.9511j, -0.3090 - 0.9511j, 0.8090 + 0.5878j,
+                 +0.8090 - 0.5878j, -1.0000 + 0.0000j]
+            p = [-0.3026 + 0.9312j, -0.3026 - 0.9312j, 0.7922 + 0.5755j,
+                 +0.7922 - 0.5755j, -0.9791 + 0.0000j]
+            z = xp.asarray(z)
+            p = xp.asarray(p)
+            k = 1
+            sos = zpk2sos(z, p, k, pairing=pairing)
+            # sos2 = [[1, 0.618, 1, 1, 0.6052, 0.95870],
+            #         [1, -1.618, 1, 1, -1.5844, 0.95878],
+            #         [1, 1, 0, 1, 0.9791, 0]]  # octave, MATLAB fails
+            sos2 = [[1, 1, 0, 1, +0.97915, 0],
+                    [1, 0.61803, 1, 1, +0.60515, 0.95873],
+                    [1, -1.61803, 1, 1, -1.58430, 0.95873]]
+            sos2 = xp.asarray(sos2)
+            assert_array_almost_equal(sos, sos2, decimal=4)
+
+            z = [-1 - 1.4142j, -1 + 1.4142j,
+                 -0.625 - 1.0533j, -0.625 + 1.0533j]
+            p = [-0.2 - 0.6782j, -0.2 + 0.6782j,
+                 -0.1 - 0.5385j, -0.1 + 0.5385j]
+            z = xp.asarray(z)
+            p = xp.asarray(p)
+            k = 4
+            sos = zpk2sos(z, p, k, pairing=pairing)
+            sos2 = [[4, 8, 12, 1, 0.2, 0.3],
+                    [1, 1.25, 1.5, 1, 0.4, 0.5]]  # MATLAB
+            sos2 = xp.asarray(sos2, dtype=xp.float64)
+            # sos2 = [[4, 8, 12, 1, 0.4, 0.5],
+            #         [1, 1.25, 1.5, 1, 0.2, 0.3]]  # octave
+            xp_assert_close(sos, sos2, rtol=1e-4, atol=1e-4)
+
+            z = xp.asarray([])
+            p = xp.asarray([0.2, -0.5+0.25j, -0.5-0.25j])
+            k = 1.
+            sos = zpk2sos(z, p, k, pairing=pairing)
+            sos2 = [[1., 0., 0., 1., -0.2, 0.],
+                    [1., 0., 0., 1., 1., 0.3125]]
+            sos2 = xp.asarray(sos2)
+            # sos2 = [[1., 0., 0., 1., 1., 0.3125],
+            #         [1., 0., 0., 1., -0.2, 0]]  # octave, MATLAB fails
+            assert_array_almost_equal(sos, sos2, decimal=4)
+
+            # The next two examples are adapted from Leland B. Jackson,
+            # "Digital Filters and Signal Processing (1995) p.400:
+            # http://books.google.com/books?id=VZ8uabI1pNMC&lpg=PA400&ots=gRD9pi8Jua&dq=Pole%2Fzero%20pairing%20for%20minimum%20roundoff%20noise%20in%20BSF.&pg=PA400#v=onepage&q=Pole%2Fzero%20pairing%20for%20minimum%20roundoff%20noise%20in%20BSF.&f=false
+
+            deg2rad = xp.pi / 180.
+            k = 1.
+
+            # first example
+            thetas = xp.asarray([22.5, 45, 77.5])
+            mags = xp.asarray([0.8, 0.6, 0.9])
+            z = xp.exp(1j * deg2rad * thetas)
+            z = xp.concat((z, xp.conj(z)))
+            p = xp.exp(1j * deg2rad * thetas) * mags
+            p = xp.concat((p, xp.conj(p)))
+            sos = zpk2sos(z, p, k)
+            # sos2 = [[1, -0.43288, 1, 1, -0.38959, 0.81],  # octave,
+            #         [1, -1.41421, 1, 1, -0.84853, 0.36],  # MATLAB fails
+            #         [1, -1.84776, 1, 1, -1.47821, 0.64]]
+            # Note that pole-zero pairing matches, but ordering is different
+            sos2 = [[1, -1.41421, 1, 1, -0.84853, 0.36],
+                    [1, -1.84776, 1, 1, -1.47821, 0.64],
+                    [1, -0.43288, 1, 1, -0.38959, 0.81]]
+            sos2 = xp.asarray(sos2)
+            assert_array_almost_equal(sos, sos2, decimal=4)
+
+            # second example
+            thetas = xp.asarray([85., 10.])
+            z = xp.exp(1j * deg2rad * thetas)
+            z = xp.concat((z, xp.conj(z), xp.asarray([1.0, -1.0])))
+            sos = zpk2sos(z, p, k)
+
+            # sos2 = [[1, -0.17431, 1, 1, -0.38959, 0.81],  # octave "wrong",
+            #         [1, -1.96962, 1, 1, -0.84853, 0.36],  # MATLAB fails
+            #         [1, 0, -1, 1, -1.47821, 0.64000]]
+            # Our pole-zero pairing matches the text, Octave does not
+            sos2 = [[1, 0, -1, 1, -0.84853, 0.36],
+                    [1, -1.96962, 1, 1, -1.47821, 0.64],
+                    [1, -0.17431, 1, 1, -0.38959, 0.81]]
+            sos2 = xp.asarray(sos2)
+            assert_array_almost_equal(sos, sos2, decimal=4)
+
+    # these examples are taken from the doc string, and show the
+    # effect of the 'pairing' argument
+    @pytest.mark.parametrize('pairing, sos',
+                             [('nearest',
+                               np.array([[1., 1., 0.5, 1., -0.75, 0.],
+                                         [1., 1., 0., 1., -1.6, 0.65]])),
+                              ('keep_odd',
+                               np.array([[1., 1., 0, 1., -0.75, 0.],
+                                         [1., 1., 0.5, 1., -1.6, 0.65]])),
+                              ('minimal',
+                               np.array([[0., 1., 1., 0., 1., -0.75],
+                                         [1., 1., 0.5, 1., -1.6, 0.65]]))])
+    def test_pairing(self, pairing, sos, xp):
+        sos = xp.asarray(sos)
+        z1 = xp.asarray([-1, -0.5-0.5j, -0.5+0.5j])
+        p1 = xp.asarray([0.75, 0.8+0.1j, 0.8-0.1j])
+        sos2 = zpk2sos(z1, p1, 1, pairing=pairing)
+        assert_array_almost_equal(sos, sos2, decimal=4)
+
+    @pytest.mark.parametrize('p, sos_dt',
+                             [([-1, 1, -0.1, 0.1],
+                               [[0., 0., 1., 1., 0., -0.01],
+                                [0., 0., 1., 1., 0., -1]]),
+                              ([-0.7071+0.7071j, -0.7071-0.7071j, -0.1j, 0.1j],
+                               [[0., 0., 1., 1., 0., 0.01],
+                                [0., 0., 1., 1., 1.4142, 1.]])])
+    def test_analog(self, p, sos_dt, xp):
+        # test `analog` argument
+        # for discrete time, poles closest to unit circle should appear last
+        # for cont. time, poles closest to imaginary axis should appear last
+        z, p = xp.asarray([]), xp.asarray(p)
+        sos_dt = xp.asarray(sos_dt)
+        sos2_dt = zpk2sos(z, p, 1, pairing='minimal', analog=False)
+        sos2_ct = zpk2sos(z, p, 1, pairing='minimal', analog=True)
+        assert_array_almost_equal(sos_dt, sos2_dt, decimal=4)
+        assert_array_almost_equal(xp.flip(sos_dt, axis=0), sos2_ct, decimal=4)
+
+    def test_bad_args(self):
+        with pytest.raises(ValueError, match=r'pairing must be one of'):
+            zpk2sos([1], [2], 1, pairing='no_such_pairing')
+
+        with pytest.raises(ValueError, match=r'.*pairing must be "minimal"'):
+            zpk2sos([1], [2], 1, pairing='keep_odd', analog=True)
+
+        with pytest.raises(ValueError,
+                           match=r'.*must have len\(p\)>=len\(z\)'):
+            zpk2sos([1, 1], [2], 1, analog=True)
+
+        with pytest.raises(ValueError, match=r'k must be real'):
+            zpk2sos([1], [2], k=1j)
+
+
+@make_xp_test_case(freqs)
+class TestFreqs:
+
+    def test_basic(self, xp):
+        _, h = freqs(xp.asarray([1.0]), xp.asarray([1.0]), worN=8)
+        assert_array_almost_equal(h, xp.ones(8))
+
+    def test_output(self, xp):
+        # 1st order low-pass filter: H(s) = 1 / (s + 1)
+        w = xp.asarray([0.1, 1, 10, 100])
+        num = xp.asarray([1.])
+        den = xp.asarray([1, 1.])
+        w, H = freqs(num, den, worN=w)
+        s = w * 1j
+        expected = 1 / (s + 1)
+        assert_array_almost_equal(xp.real(H), xp.real(expected))
+        assert_array_almost_equal(xp.imag(H), xp.imag(expected))
+
+    def test_freq_range(self, xp):
+        # Test that freqresp() finds a reasonable frequency range.
+        # 1st order low-pass filter: H(s) = 1 / (s + 1)
+        # Expected range is from 0.01 to 10.
+        num = xp.asarray([1.])
+        den = xp.asarray([1, 1.])
+        n = 10
+        expected_w = _logspace(-2, 1, n, xp=xp)
+        w, H = freqs(num, den, worN=n)
+        assert_array_almost_equal(w, expected_w)
+
+    def test_plot(self, xp):
+
+        def plot(w, h):
+            assert_array_almost_equal(h, xp.ones(8))
+
+        with assert_raises(ZeroDivisionError):
+            freqs([1.0], [1.0], worN=8, plot=lambda w, h: 1 / 0)
+
+        freqs(xp.asarray([1.0]), xp.asarray([1.0]), worN=8, plot=plot)
+
+    def test_backward_compat(self, xp):
+        # For backward compatibility, test if None act as a wrapper for default
+        w1, h1 = freqs(xp.asarray([1.0]), xp.asarray([1.0]))
+        w2, h2 = freqs(xp.asarray([1.0]), xp.asarray([1.0]), None)
+        assert_array_almost_equal(w1, w2)
+        assert_array_almost_equal(h1, h2)
+
+    def test_w_or_N_types(self):
+        # Measure at 8 equally-spaced points
+        for N in (8, np.int8(8), np.int16(8), np.int32(8), np.int64(8),
+                  np.array(8)):
+            w, h = freqs([1.0], [1.0], worN=N)
+            assert len(w) == 8
+            assert_array_almost_equal(h, np.ones(8))
+
+        # Measure at frequency 8 rad/sec
+        for w in (8.0, 8.0+0j):
+            w_out, h = freqs([1.0], [1.0], worN=w)
+            assert_array_almost_equal(w_out, [8])
+            assert_array_almost_equal(h, [1])
+
+
+@make_xp_test_case(freqs_zpk)
+class TestFreqs_zpk:
+
+    def test_basic(self, xp):
+        _, h = freqs_zpk(
+            xp.asarray([1.0]), xp.asarray([1.0]), xp.asarray([1.0]), worN=8
+        )
+        assert_array_almost_equal(h, xp.ones(8))
+
+    def test_output(self, xp):
+        # 1st order low-pass filter: H(s) = 1 / (s + 1)
+        w = xp.asarray([0.1, 1, 10, 100])
+        z = xp.asarray([])
+        p = xp.asarray([-1.0])
+        k = 1
+        w, H = freqs_zpk(z, p, k, worN=w)
+        s = w * 1j
+        expected = 1 / (s + 1)
+        assert_array_almost_equal(xp.real(H), xp.real(expected))
+        assert_array_almost_equal(xp.imag(H), xp.imag(expected))
+
+    def test_freq_range(self, xp):
+        # Test that freqresp() finds a reasonable frequency range.
+        # 1st order low-pass filter: H(s) = 1 / (s + 1)
+        # Expected range is from 0.01 to 10.
+        z = xp.asarray([])
+        p = xp.asarray([-1.])
+        k = 1
+        n = 10
+        expected_w = _logspace(-2, 1, n, xp=xp)
+        w, H = freqs_zpk(z, p, k, worN=n)
+        assert_array_almost_equal(w, expected_w)
+
+    def test_vs_freqs(self, xp):
+        b, a = cheby1(4, 5, 100., analog=True, output='ba')
+        z, p, k = cheby1(4, 5, 100., analog=True, output='zpk')
+
+        w1, h1 = map(xp.asarray, freqs(b, a))
+        z, p, k = map(xp.asarray, (z, p, k))
+        w2, h2 = freqs_zpk(z, p, k)
+        xp_assert_close(w1, w2)
+        xp_assert_close(h1, h2, rtol=1e-6)
+
+    def test_backward_compat(self, xp):
+        # For backward compatibility, test if None act as a wrapper for default
+        # Also, keep testing `k` a length-one list: it is documented as a scalar,
+        # but the implementation was allowing for a one-element array-likes
+        w1, h1 = freqs_zpk(xp.asarray([1.0]), xp.asarray([1.0]), [1.0])
+        w2, h2 = freqs_zpk(xp.asarray([1.0]), xp.asarray([1.0]), [1.0], None)
+        assert_array_almost_equal(w1, w2)
+        assert_array_almost_equal(h1, h2)
+
+    def test_w_or_N_types(self):
+        # Measure at 8 equally-spaced points
+        for N in (8, np.int8(8), np.int16(8), np.int32(8), np.int64(8),
+                  np.array(8)):
+            w, h = freqs_zpk([], [], 1, worN=N)
+            assert len(w) == 8
+            assert_array_almost_equal(h, np.ones(8))
+
+        # Measure at frequency 8 rad/sec
+        for w in (8.0, 8.0+0j):
+            w_out, h = freqs_zpk([], [], 1, worN=w)
+            assert_array_almost_equal(w_out, [8])
+            assert_array_almost_equal(h, [1])
+
+
+@make_xp_test_case(freqz)
+class TestFreqz:
+
+    def test_ticket1441(self, xp):
+        """Regression test for ticket 1441."""
+        # Because freqz previously used arange instead of linspace,
+        # when N was large, it would return one more point than
+        # requested.
+        N = 100000
+        w, h = freqz(xp.asarray([1.0]), worN=N)
+        assert w.shape == (N,)
+
+    def test_gh_22886(self, xp):
+        w, h = freqz(xp.asarray([1.]), worN=xp.asarray([0., 0.1]))
+        xp_assert_equal(w, xp.asarray([0. , 0.1]))
+        xp_assert_equal(h, xp.asarray([1.+0.j, 1.+0.j]))
+
+    def test_basic(self, xp):
+        w, h = freqz(xp.asarray([1.0]), worN=8)
+        assert_array_almost_equal(w, xp.pi * xp.arange(8, dtype=w.dtype) / 8.)
+        assert_array_almost_equal(h, xp.ones(8))
+        w, h = freqz(xp.asarray([1.0]), worN=9)
+        assert_array_almost_equal(w, xp.pi * xp.arange(9, dtype=w.dtype) / 9.)
+        assert_array_almost_equal(h, xp.ones(9))
+
+        for a in [1, xp.ones(2)]:
+            w, h = freqz(xp.ones(2), a, worN=0)
+            assert w.shape == (0,)
+            assert h.shape == (0,)
+            hdt = xp.complex128 if xp_default_dtype(xp) == xp.float64 else xp.complex64
+            assert h.dtype == hdt
+
+    def test_basic2(self, xp):
+        t = xp.linspace(0, 1, 4, endpoint=False)
+        for b, a, h_whole in zip(
+                (xp.asarray([1., 0, 0, 0]), xp.sin(2 * xp.pi * t)),
+                (xp.asarray([1., 0, 0, 0]), xp.asarray([0.5, 0, 0, 0])),
+                (xp.asarray([1., 1., 1., 1.]), xp.asarray([0, -4j, 0, 4j]))
+        ):
+
+            w, h = freqz(b, a, worN=4, whole=True)
+            expected_w = xp.linspace(0, 2 * xp.pi, 4, endpoint=False)
+            assert_array_almost_equal(w, expected_w)
+            assert_array_almost_equal(h, h_whole)
+
+            if is_numpy(xp):
+                # simultaneously check int-like support
+                w, h = freqz(b, a, worN=np.int32(4), whole=True)
+                assert_array_almost_equal(w, expected_w)
+                assert_array_almost_equal(h, h_whole)
+
+            w, h = freqz(b, a, worN=w, whole=True)
+            assert_array_almost_equal(w, expected_w)
+            assert_array_almost_equal(h, h_whole)
+
+    def test_basic3(self):
+        t = np.linspace(0, 1, 4, endpoint=False)
+        expected_w = np.linspace(0, 2 * np.pi, 4, endpoint=False)
+        for b, a, h_whole in zip(
+                (np.asarray([1., 0, 0, 0]), np.sin(2 * np.pi * t)),
+                (np.asarray([1., 0, 0, 0]), np.asarray([0.5, 0, 0, 0])),
+                (np.asarray([1., 1., 1., 1.]), np.asarray([0, -4j, 0, 4j]))
+        ):
+
+            w, h = freqz(b, a, worN=np.int32(4), whole=True)
+            assert_array_almost_equal(w, expected_w)
+            assert_array_almost_equal(h, h_whole)
+
+            w, h = freqz(b, a, worN=w, whole=True)
+            assert_array_almost_equal(w, expected_w)
+            assert_array_almost_equal(h, h_whole)
+
+    def test_basic_whole(self, xp):
+        w, h = freqz(xp.asarray([1.0]), worN=8, whole=True)
+        assert_array_almost_equal(w, 2 * xp.pi * xp.arange(8.0) / 8)
+        assert_array_almost_equal(h, xp.ones(8))
+
+    def test_plot(self, xp):
+
+        def plot(w, h):
+            assert_array_almost_equal(w, xp.pi * xp.arange(8.0) / 8)
+            assert_array_almost_equal(h, xp.ones(8))
+
+        with assert_raises(ZeroDivisionError):
+            freqz(xp.asarray([1.0]), worN=8, plot=lambda w, h: 1 / 0)
+
+        freqz(xp.asarray([1.0]), worN=8, plot=plot)
+
+    def test_fft_wrapping(self, xp):
+        # Some simple real FIR filters
+        bs = list()  # filters
+        as_ = list()
+        hs_whole = list()
+        hs_half = list()
+        # 3 taps
+        t = xp.linspace(0, 1, 3, endpoint=False)
+        bs.append(xp.sin(2 * xp.pi * t))
+        as_.append(3.)
+        hs_whole.append(xp.asarray([0, -0.5j, 0.5j]))
+        hs_half.append(xp.asarray([0, math.sqrt(1./12.), -0.5j]))
+        # 4 taps
+        t = xp.linspace(0, 1, 4, endpoint=False)
+        bs.append(xp.sin(2 * xp.pi * t))
+        as_.append(0.5)
+        hs_whole.append(xp.asarray([0, -4j, 0, 4j]))
+        hs_half.append(xp.asarray([0, math.sqrt(8), -4j, -math.sqrt(8)]))
+        del t
+        for ii, b in enumerate(bs):
+            # whole
+            a = as_[ii]
+            expected_w = xp.linspace(0, 2 * xp.pi, b.shape[0], endpoint=False)
+            w, h = freqz(b, a, worN=expected_w, whole=True)  # polyval
+            err_msg = f'b = {b}, a={a}'
+            assert_array_almost_equal(w, expected_w, err_msg=err_msg)
+            assert_array_almost_equal(h, hs_whole[ii], err_msg=err_msg)
+
+            w, h = freqz(b, a, worN=b.shape[0], whole=True)  # FFT
+            assert_array_almost_equal(w, expected_w, err_msg=err_msg)
+            assert_array_almost_equal(h, hs_whole[ii], err_msg=err_msg)
+
+            # non-whole
+            expected_w = xp.linspace(0, xp.pi, b.shape[0], endpoint=False)
+            w, h = freqz(b, a, worN=expected_w, whole=False)  # polyval
+            assert_array_almost_equal(w, expected_w, err_msg=err_msg)
+            assert_array_almost_equal(h, hs_half[ii], err_msg=err_msg)
+
+            w, h = freqz(b, a, worN=b.shape[0], whole=False)  # FFT
+            assert_array_almost_equal(w, expected_w, err_msg=err_msg)
+            assert_array_almost_equal(h, hs_half[ii], err_msg=err_msg)
+
+        # some random FIR filters (real + complex)
+        # assume polyval is accurate
+        rng = np.random.RandomState(0)
+        for ii in range(2, 10):  # number of taps
+            b = xp.asarray(rng.randn(ii))
+            for kk in range(2):
+                a = xp.asarray(rng.randn(1) if kk == 0 else rng.randn(3))
+                for jj in range(2):
+                    if jj == 1:
+                        b = b + xp.asarray(rng.randn(ii)) * 1j
+
+                    # whole
+                    expected_w = xp.linspace(0, 2 * xp.pi, ii, endpoint=False)
+                    w, expected_h = freqz(b, a, worN=expected_w, whole=True)
+                    assert_array_almost_equal(w, expected_w)
+                    w, h = freqz(b, a, worN=ii, whole=True)
+                    assert_array_almost_equal(w, expected_w)
+                    assert_array_almost_equal(h, expected_h, decimal=4)
+
+                    # half
+                    expected_w = xp.linspace(0, xp.pi, ii, endpoint=False)
+                    w, expected_h = freqz(b, a, worN=expected_w, whole=False)
+                    assert_array_almost_equal(w, expected_w)
+                    w, h = freqz(b, a, worN=ii, whole=False)
+                    assert_array_almost_equal(w, expected_w)
+                    assert_array_almost_equal(h, expected_h, decimal=4)
+
+    def test_broadcasting1(self, xp):
+        # Test broadcasting with worN an integer or a 1-D array,
+        # b and a are n-dimensional arrays.
+        np.random.seed(123)
+        b = np.random.rand(3, 5, 1)
+        a = np.random.rand(2, 1)
+        b, a = map(xp.asarray, (b, a))
+
+        for whole in [False, True]:
+            # Test with worN being integers (one fast for FFT and one not),
+            # a 1-D array, and an empty array.
+            for worN in [16, 17, xp.linspace(0, 1, 10), xp.asarray([])]:
+                w, h = freqz(b, a, worN=worN, whole=whole)
+                for k in range(b.shape[1]):
+                    bk = b[:, k, 0]
+                    ak = a[:, 0]
+                    ww, hh = freqz(bk, ak, worN=worN, whole=whole)
+                    xp_assert_close(ww, w)
+                    xp_assert_close(hh, h[k, ...])
+
+    def test_broadcasting2(self, xp):
+        # Test broadcasting with worN an integer or a 1-D array,
+        # b is an n-dimensional array, and a is left at the default value.
+        np.random.seed(123)
+        b = np.random.rand(3, 5, 1)
+        b = xp.asarray(b)
+        for whole in [False, True]:
+            for worN in [16, 17, xp.linspace(0, 1, 10)]:
+                w, h = freqz(b, worN=worN, whole=whole)
+                for k in range(b.shape[1]):
+                    bk = b[:, k, 0]
+                    ww, hh = freqz(bk, worN=worN, whole=whole)
+                    xp_assert_close(ww, w)
+                    xp_assert_close(hh, h[k, :])
+
+    def test_broadcasting3(self, xp):
+        # Test broadcasting where b.shape[-1] is the same length
+        # as worN, and a is left at the default value.
+        np.random.seed(123)
+        N = 16
+        b = np.random.rand(3, N)
+        b = xp.asarray(b)
+        for whole in [False, True]:
+            for worN in [N, xp.linspace(0, 1, N)]:
+                w, h = freqz(b, worN=worN, whole=whole)
+                assert xp_size(w) == N
+                for k in range(N):
+                    bk = b[:, k]
+                    ww, hh = freqz(bk, worN=w[k], whole=whole)
+                    xp_assert_close(ww, xp.asarray(w[k])[None])
+                    xp_assert_close(hh, xp.asarray(h[k])[None])
+
+    def test_broadcasting4(self, xp):
+        # Test broadcasting with worN a 2-D array.
+        np.random.seed(123)
+        b = np.random.rand(4, 2, 1, 1)
+        a = np.random.rand(5, 2, 1, 1)
+        b, a = map(xp.asarray, (b, a))
+
+        for whole in [False, True]:
+            for worN in [np.random.rand(6, 7), np.empty((6, 0))]:
+                worN = xp.asarray(worN)
+                w, h = freqz(b, a, worN=worN, whole=whole)
+                xp_assert_close(w, worN, rtol=1e-14)
+                assert h.shape == (2,) + worN.shape
+                for k in range(2):
+                    ww, hh = freqz(b[:, k, 0, 0], a[:, k, 0, 0],
+                                   worN=xp.reshape(worN, (-1,)),
+                                   whole=whole)
+                    xp_assert_close(ww, xp.reshape(worN, (-1,)), rtol=1e-14)
+                    xp_assert_close(hh, xp.reshape(h[k, :, :], (-1,)))
+
+    def test_backward_compat(self):
+        # For backward compatibility, test if None act as a wrapper for default
+        w1, h1 = freqz([1.0], 1)
+        w2, h2 = freqz([1.0], 1, None)
+        assert_array_almost_equal(w1, w2)
+        assert_array_almost_equal(h1, h2)
+
+    def test_fs_param(self, xp):
+        fs = 900
+        b = xp.asarray([0.039479155677484369, 0.11843746703245311, 0.11843746703245311,
+                        0.039479155677484369])
+        a = xp.asarray([1.0, -1.3199152021838287, 0.80341991081938424,
+                        -0.16767146321568049])
+
+        # N = None, whole=False
+        w1, h1 = freqz(b, a, fs=fs)
+        w2, h2 = freqz(b, a)
+        xp_assert_close(h1, h2)
+        xp_assert_close(w1, xp.linspace(0, fs/2, 512, endpoint=False))
+
+        # N = None, whole=True
+        w1, h1 = freqz(b, a, whole=True, fs=fs)
+        w2, h2 = freqz(b, a, whole=True)
+        xp_assert_close(h1, h2)
+        xp_assert_close(w1, xp.linspace(0, fs, 512, endpoint=False))
+
+        # N = 5, whole=False
+        w1, h1 = freqz(b, a, 5, fs=fs)
+        w2, h2 = freqz(b, a, 5)
+        xp_assert_close(h1, h2)
+        xp_assert_close(w1, xp.linspace(0, fs/2, 5, endpoint=False))
+
+        # N = 5, whole=True
+        w1, h1 = freqz(b, a, 5, whole=True, fs=fs)
+        w2, h2 = freqz(b, a, 5, whole=True)
+        xp_assert_close(h1, h2)
+        xp_assert_close(w1, xp.linspace(0, fs, 5, endpoint=False))
+
+        if is_numpy(xp):
+            # w is an array_like
+            for w in ([123], (123,), xp.asarray([123]), (50, 123, 230),
+                      xp.asarray([50, 123, 230])):
+                w1, h1 = freqz(b, a, w, fs=fs)
+                w2, h2 = freqz(b, a, 2*pi*xp.asarray(w, dtype=xp.float64)/ fs)
+                xp_assert_close(h1, h2)
+                xp_assert_close(w1, xp.asarray(w), check_dtype=False)
+
+    def test_w_or_N_types(self):
+        # Measure at 7 (polyval) or 8 (fft) equally-spaced points
+        for N in (7, np.int8(7), np.int16(7), np.int32(7), np.int64(7),
+                  np.array(7),
+                  8, np.int8(8), np.int16(8), np.int32(8), np.int64(8),
+                  np.array(8)):
+
+            w, h = freqz([1.0], worN=N)
+            assert_array_almost_equal(w, np.pi * np.arange(N) / N)
+            assert_array_almost_equal(h, np.ones(N))
+
+            w, h = freqz([1.0], worN=N, fs=100)
+            assert_array_almost_equal(w, np.linspace(0, 50, N, endpoint=False))
+            assert_array_almost_equal(h, np.ones(N))
+
+        # Measure at frequency 8 Hz
+        for w in (8.0, 8.0+0j):
+            # Only makes sense when fs is specified
+            w_out, h = freqz(np.asarray([1.0]), worN=w, fs=100)
+            assert_array_almost_equal(w_out, np.asarray([8]))
+            assert_array_almost_equal(h, np.asarray(1.), check_0d=False)
+
+    def test_nyquist(self, xp):
+        w, h = freqz(xp.asarray([1.0]), worN=8, include_nyquist=True)
+        assert_array_almost_equal(w, xp.pi * xp.arange(8, dtype=w.dtype) / 7.)
+        assert_array_almost_equal(h, xp.ones(8))
+        w, h = freqz(xp.asarray([1.0]), worN=9, include_nyquist=True)
+        assert_array_almost_equal(w, xp.pi * xp.arange(9, dtype=w.dtype) / 8.)
+        assert_array_almost_equal(h, xp.ones(9))
+
+        for a in [1, xp.ones(2)]:
+            w, h = freqz(xp.ones(2), a, worN=0, include_nyquist=True)
+            assert w.shape == (0,)
+            assert h.shape == (0,)
+            hdt = xp.complex128 if xp_default_dtype(xp) == xp.float64 else xp.complex64
+            assert h.dtype == hdt
+
+        w1, h1 = freqz(xp.asarray([1.0]), worN=8, whole = True, include_nyquist=True)
+        w2, h2 = freqz(xp.asarray([1.0]), worN=8, whole = True, include_nyquist=False)
+        assert_array_almost_equal(w1, w2)
+        assert_array_almost_equal(h1, h2)
+
+    # https://github.com/scipy/scipy/issues/17289
+    # https://github.com/scipy/scipy/issues/15273
+    @pytest.mark.parametrize('whole,nyquist,worN',
+                             [(False, False, 32),
+                              (False, True, 32),
+                              (True, False, 32),
+                              (True, True, 32),
+                              (False, False, 257),
+                              (False, True, 257),
+                              (True, False, 257),
+                              (True, True, 257)])
+    
+    @xfail_xp_backends("cupy", reason="XXX: CuPy's version suspect")
+    def test_17289(self, whole, nyquist, worN, xp):
+        d = xp.asarray([0.0, 1.0])
+        w, Drfft = freqz(d, worN=32, whole=whole, include_nyquist=nyquist)
+        _, Dpoly = freqz(d, worN=w)
+        xp_assert_close(Drfft, Dpoly)
+
+    def test_fs_validation(self):
+        with pytest.raises(ValueError, match="Sampling.*single scalar"):
+            freqz([1.0], fs=np.array([10, 20]))
+
+        with pytest.raises(ValueError, match="Sampling.*be none."):
+            freqz([1.0], fs=None)
+
+
+
+@make_xp_test_case(freqz_sos)
+class TestFreqz_sos:
+
+    def test_freqz_sos_basic(self, xp):
+        # Compare the results of freqz and freqz_sos for a low order
+        # Butterworth filter.
+
+        N = 500
+
+        b, a = butter(4, 0.2)
+        sos = butter(4, 0.2, output='sos')
+        w, h = freqz(b, a, worN=N)
+
+        w, h, sos = map(xp.asarray, (w, h, sos))
+        w2, h2 = freqz_sos(sos, worN=N)
+        xp_assert_close(w2, w, rtol=1e-15)
+        xp_assert_close(h2, h, rtol=1e-10, atol=1e-14)
+
+        b, a = ellip(3, 1, 30, (0.2, 0.3), btype='bandpass')
+        sos = ellip(3, 1, 30, (0.2, 0.3), btype='bandpass', output='sos')
+        w, h = freqz(b, a, worN=N)
+
+        w, h, sos = map(xp.asarray, (w, h, sos))
+        w2, h2 = freqz_sos(sos, worN=N)
+        xp_assert_close(w2, w, rtol=1e-15)
+        xp_assert_close(h2, h, rtol=1e-10, atol=1e-14)
+
+        # must have at least one section
+        with assert_raises(ValueError):
+            freqz_sos(sos[:0, ...])
+
+    @make_xp_test_case(sosfreqz)
+    def test_backward_compat(self, xp):
+        # For backward compatibility, test if None act as a wrapper for default
+        N = 500
+
+        sos = butter(4, 0.2, output='sos')
+        w2, h2 = sosfreqz(sos, worN=N)
+        sos, w2, h2 = map(xp.asarray, (sos, w2, h2))
+        w1, h1 = freqz_sos(sos, worN=N)
+        assert_array_almost_equal(w1, w2)
+        assert_array_almost_equal(h1, h2)
+
+    @skip_xp_backends("dask.array", reason="float cannot be interpreted as an integer")
+    def test_freqz_sos_design(self, xp):
+        # Compare freqz_sos output against expected values for different
+        # filter types
+        # TODO: split into multiple tests, or parameterize across filter types
+        # in some way.
+
+        # from cheb2ord
+        N, Wn = cheb2ord([0.1, 0.6], [0.2, 0.5], 3, 60)
+        sos = cheby2(N, 60, Wn, 'stop', output='sos')
+        sos = xp.asarray(sos)  # XXX
+        zero = xp.asarray(0., dtype=xp.float64)
+
+        w, h = freqz_sos(sos)
+        h = xp.abs(h)
+        w = w / xp.pi
+        xp_assert_close(20 * xp.log10(h[w <= 0.1]),
+                        zero, atol=3.01,
+                        check_shape=False)
+        xp_assert_close(20 * xp.log10(h[w >= 0.6]),
+                        zero, atol=3.01,
+                        check_shape=False)
+        xp_assert_close(h[(w >= 0.2) & (w <= 0.5)],
+                        zero, atol=1e-3,
+                        check_shape=False)  # <= -60 dB
+
+        N, Wn = cheb2ord([0.1, 0.6], [0.2, 0.5], 3, 150)
+        sos = cheby2(N, 150, Wn, 'stop', output='sos')
+        sos = xp.asarray(sos)
+
+        w, h = freqz_sos(sos)
+        dB = 20*xp.log10(xp.abs(h))
+        w = w / xp.pi
+        xp_assert_close(dB[w <= 0.1], zero, atol=3.01, check_shape=False)
+        xp_assert_close(dB[w >= 0.6], zero, atol=3.01, check_shape=False)
+        assert xp.all(dB[(w >= 0.2) & (w <= 0.5)] < -149.9)
+
+        # from cheb1ord
+        N, Wn = cheb1ord(0.2, 0.3, 3, 40)
+        sos = cheby1(N, 3, Wn, 'low', output='sos')
+        sos = xp.asarray(sos)
+
+        w, h = freqz_sos(sos)
+        h = xp.abs(h)
+        w = w / xp.pi
+        xp_assert_close(20 * xp.log10(h[w <= 0.2]), zero, atol=3.01,
+                        check_shape=False)
+        xp_assert_close(h[w >= 0.3], zero, atol=1e-2,
+                        check_shape=False)  # <= -40 dB
+
+        N, Wn = cheb1ord(0.2, 0.3, 1, 150)
+        sos = cheby1(N, 1, Wn, 'low', output='sos')
+        sos = xp.asarray(sos)
+
+        w, h = freqz_sos(sos)
+        dB = 20*xp.log10(xp.abs(h))
+        w /= np.pi
+        xp_assert_close(dB[w <= 0.2], zero, atol=1.01, check_shape=False)
+        assert xp.all(dB[w >= 0.3] < -149.9)
+
+        # adapted from ellipord
+        N, Wn = ellipord(0.3, 0.2, 3, 60)
+        sos = ellip(N, 0.3, 60, Wn, 'high', output='sos')
+        sos = xp.asarray(sos)
+
+        w, h = freqz_sos(sos)
+        h = xp.abs(h)
+        w = w / xp.pi
+        xp_assert_close(20 * xp.log10(h[w >= 0.3]), zero, atol=3.01,
+                        check_shape=False)
+        xp_assert_close(h[w <= 0.1], zero, atol=1.5e-3,
+                        check_shape=False)  # <= -60 dB (approx)
+
+        # adapted from buttord
+        N, Wn = buttord([0.2, 0.5], [0.14, 0.6], 3, 40)
+        sos = butter(N, Wn, 'band', output='sos')
+        sos = xp.asarray(sos)
+
+        w, h = freqz_sos(sos)
+        h = xp.abs(h)
+        w = w / xp.pi
+
+        h014 = h[w <= 0.14]
+        xp_assert_close(h014, xp.zeros_like(h014), atol=1e-2)  # <= -40 dB
+        h06 = h[w >= 0.6]
+        xp_assert_close(h06, xp.zeros_like(h06), atol=1e-2)  # <= -40 dB
+        h0205 = 20 * xp.log10(h[(w >= 0.2) & (w <= 0.5)])
+        xp_assert_close(h0205, xp.zeros_like(h0205), atol=3.01)
+
+        N, Wn = buttord([0.2, 0.5], [0.14, 0.6], 3, 100)
+        sos = butter(N, Wn, 'band', output='sos')
+        sos = xp.asarray(sos)
+
+        w, h = freqz_sos(sos)
+        dB = 20*xp.log10(xp.maximum(xp.abs(h), xp.asarray(1e-10)))
+        w = w / xp.pi
+
+        assert xp.all(dB[(w > 0) & (w <= 0.14)] < -99.9)
+        assert xp.all(dB[w >= 0.6] < -99.9)
+        db0205 = dB[(w >= 0.2) & (w <= 0.5)]
+        xp_assert_close(db0205, xp.zeros_like(db0205), atol=3.01)
+
+    def test_freqz_sos_design_ellip(self, xp):
+        N, Wn = ellipord(0.3, 0.1, 3, 60)
+        sos = ellip(N, 0.3, 60, Wn, 'high', output='sos')
+        sos = xp.asarray(sos)
+
+        w, h = freqz_sos(sos)
+        h = xp.abs(h)
+        w = w / xp.pi
+
+        h03 = 20 * xp.log10(h[w >= 0.3])
+        xp_assert_close(h03, xp.zeros_like(h03), atol=3.01)
+        h01 = h[w <= 0.1]
+        xp_assert_close(h01, xp.zeros_like(h01), atol=1.5e-3)  # <= -60 dB (approx)
+
+        N, Wn = ellipord(0.3, 0.2, .5, 150)
+        sos = ellip(N, .5, 150, Wn, 'high', output='sos')
+        sos = xp.asarray(sos)
+
+        w, h = freqz_sos(sos)
+        dB = 20*xp.log10(xp.maximum(xp.abs(h), xp.asarray(1e-10)))
+        w = w / xp.pi
+
+        db03 = dB[w >= 0.3]
+        xp_assert_close(db03, xp.zeros_like(db03), atol=.55)
+        # Allow some numerical slop in the upper bound -150, so this is
+        # a check that dB[w <= 0.2] is less than or almost equal to -150.
+        assert xp.max(dB[w <= 0.2]) < -150*(1 - 1e-12)
+
+    @pytest.mark.thread_unsafe(
+        reason=("mpmath gmpy2 backend is not thread-safe, "
+                "see https://github.com/mpmath/mpmath/issues/974"))
+    @mpmath_check("0.10")
+    def test_freqz_sos_against_mp(self, xp):
+        # Compare the result of freqz_sos applied to a high order Butterworth
+        # filter against the result computed using mpmath.  (signal.freqz fails
+        # miserably with such high order filters.)
+        from . import mpsig
+        N = 500
+        order = 25
+        Wn = 0.15
+        with mpmath.workdps(80):
+            z_mp, p_mp, k_mp = mpsig.butter_lp(order, Wn)
+            w_mp, h_mp = mpsig.zpkfreqz(z_mp, p_mp, k_mp, N)
+        w_mp = xp.asarray([float(x) for x in w_mp], dtype=xp.float64)
+        h_mp = xp.asarray([complex(x) for x in h_mp], dtype=xp.complex128)
+
+        sos = butter(order, Wn, output='sos')
+        sos = xp.asarray(sos, dtype=xp.float64)
+        w, h = freqz_sos(sos, worN=N)
+        xp_assert_close(w, w_mp, rtol=1e-12, atol=1e-14)
+        xp_assert_close(h, h_mp, rtol=1e-12, atol=1e-14)
+
+    def test_fs_param(self, xp):
+        fs = 900
+        sos = xp.asarray(
+              [[0.03934683014103762, 0.07869366028207524, 0.03934683014103762,
+                1.0, -0.37256600288916636, 0.0],
+               [1.0, 1.0, 0.0, 1.0, -0.9495739996946778, 0.45125966317124144]]
+        )
+
+        # N = None, whole=False
+        w1, h1 = freqz_sos(sos, fs=fs)
+        w2, h2 = freqz_sos(sos)
+        xp_assert_close(h1, h2)
+        xp_assert_close(w1, xp.linspace(0, fs/2, 512, endpoint=False))
+
+        # N = None, whole=True
+        w1, h1 = freqz_sos(sos, whole=True, fs=fs)
+        w2, h2 = freqz_sos(sos, whole=True)
+        xp_assert_close(h1, h2, atol=1e-27)
+        xp_assert_close(w1, xp.linspace(0, fs, 512, endpoint=False))
+
+        # N = 5, whole=False
+        w1, h1 = freqz_sos(sos, 5, fs=fs)
+        w2, h2 = freqz_sos(sos, 5)
+        xp_assert_close(h1, h2)
+        xp_assert_close(w1, xp.linspace(0, fs/2, 5, endpoint=False))
+
+        # N = 5, whole=True
+        w1, h1 = freqz_sos(sos, 5, whole=True, fs=fs)
+        w2, h2 = freqz_sos(sos, 5, whole=True)
+        xp_assert_close(h1, h2)
+        xp_assert_close(w1, xp.linspace(0, fs, 5, endpoint=False))
+
+    @skip_xp_backends(np_only=True, reason="array-likes")
+    def test_fs_param2(self, xp):
+        fs = 900
+        sos = xp.asarray(
+              [[0.03934683014103762, 0.07869366028207524, 0.03934683014103762,
+                1.0, -0.37256600288916636, 0.0],
+               [1.0, 1.0, 0.0, 1.0, -0.9495739996946778, 0.45125966317124144]]
+        )
+
+        # w is an array_like
+        for w in ([123], (123,), xp.asarray([123]), (50, 123, 230),
+                  xp.asarray([50, 123, 230])):
+            w1, h1 = freqz_sos(sos, w, fs=fs)
+            w1, h1 = map(xp.asarray, (w1, h1))
+
+            w2, h2 = freqz_sos(sos, 2*pi*xp.asarray(w, dtype=sos.dtype)/fs)
+            xp_assert_close(h1, h2)
+            xp_assert_close(w, w1, check_dtype=False)
+
+    def test_w_or_N_types(self):
+        # Measure at 7 (polyval) or 8 (fft) equally-spaced points
+        for N in (7, np.int8(7), np.int16(7), np.int32(7), np.int64(7),
+                  np.array(7),
+                  8, np.int8(8), np.int16(8), np.int32(8), np.int64(8),
+                  np.array(8)):
+
+            w, h = freqz_sos([1, 0, 0, 1, 0, 0], worN=N)
+            assert_array_almost_equal(w, np.pi * np.arange(N) / N)
+            assert_array_almost_equal(h, np.ones(N))
+
+            w, h = freqz_sos([1, 0, 0, 1, 0, 0], worN=N, fs=100)
+            assert_array_almost_equal(w, np.linspace(0, 50, N, endpoint=False))
+            assert_array_almost_equal(h, np.ones(N))
+
+        # Measure at frequency 8 Hz
+        for w in (8.0, 8.0+0j):
+            # Only makes sense when fs is specified
+            w_out, h = freqz_sos([1, 0, 0, 1, 0, 0], worN=w, fs=100)
+            assert_array_almost_equal(w_out, [8])
+            assert_array_almost_equal(h, [1])
+
+    def test_fs_validation(self):
+        sos = butter(4, 0.2, output='sos')
+        with pytest.raises(ValueError, match="Sampling.*single scalar"):
+            freqz_sos(sos, fs=np.array([10, 20]))
+
+
+@make_xp_test_case(freqz_zpk)
+class TestFreqz_zpk:
+
+    def test_ticket1441(self, xp):
+        """Regression test for ticket 1441."""
+        # Because freqz previously used arange instead of linspace,
+        # when N was large, it would return one more point than
+        # requested.
+        N = 100000
+        w, h = freqz_zpk(xp.asarray([0.5]), xp.asarray([0.5]), 1.0, worN=N)
+        assert w.shape == (N,)
+
+    def test_basic(self, xp):
+        w, h = freqz_zpk(xp.asarray([0.5]), xp.asarray([0.5]), 1.0, worN=8)
+        assert_array_almost_equal(w, xp.pi * xp.arange(8.0) / 8)
+        assert_array_almost_equal(h, xp.ones(8))
+
+    def test_basic_whole(self, xp):
+        w, h = freqz_zpk(xp.asarray([0.5]), xp.asarray([0.5]), 1.0, worN=8, whole=True)
+        assert_array_almost_equal(w, 2 * xp.pi * xp.arange(8.0) / 8)
+        assert_array_almost_equal(h, xp.ones(8))
+
+    @pytest.mark.xfail(DEFAULT_F32, reason="wrong answer with torch/float32")
+    def test_vs_freqz(self, xp):
+        b, a = cheby1(4, 5, 0.5, analog=False, output='ba')
+        z, p, k = cheby1(4, 5, 0.5, analog=False, output='zpk')
+
+        w1, h1 = freqz(b, a)
+        z, p, k, w1, h1 = map(xp.asarray, (z, p, k, w1, h1))
+        w2, h2 = freqz_zpk(z, p, k)
+        xp_assert_close(w1, w2)
+        xp_assert_close(h1, h2, rtol=1.3e-6)
+
+    def test_backward_compat(self, xp):
+        # For backward compatibility, test if None act as a wrapper for default
+        w1, h1 = freqz_zpk(xp.asarray([0.5]), xp.asarray([0.5]), 1.0)
+        w2, h2 = freqz_zpk(xp.asarray([0.5]), xp.asarray([0.5]), 1.0, None)
+        assert_array_almost_equal(w1, w2)
+        assert_array_almost_equal(h1, h2)
+
+    def test_fs_param(self, xp):
+        fs = 900
+        z = xp.asarray([-1, -1, -1.0])
+        p = xp.asarray(
+            [0.4747869998473389 + 0.4752230717749344j,
+             0.37256600288916636,
+             0.4747869998473389 - 0.4752230717749344j]
+        )
+        k = 0.03934683014103762
+
+        # N = None, whole=False
+        w1, h1 = freqz_zpk(z, p, k, whole=False, fs=fs)
+        w2, h2 = freqz_zpk(z, p, k, whole=False)
+        xp_assert_close(h1, h2)
+        xp_assert_close(w1, xp.linspace(0, fs/2, 512, endpoint=False))
+
+        # N = None, whole=True
+        w1, h1 = freqz_zpk(z, p, k, whole=True, fs=fs)
+        w2, h2 = freqz_zpk(z, p, k, whole=True)
+        xp_assert_close(h1, h2)
+        xp_assert_close(w1, xp.linspace(0, fs, 512, endpoint=False))
+
+        # N = 5, whole=False
+        w1, h1 = freqz_zpk(z, p, k, 5, fs=fs)
+        w2, h2 = freqz_zpk(z, p, k, 5)
+        xp_assert_close(h1, h2)
+        xp_assert_close(w1, xp.linspace(0, fs/2, 5, endpoint=False))
+
+        # N = 5, whole=True
+        w1, h1 = freqz_zpk(z, p, k, 5, whole=True, fs=fs)
+        w2, h2 = freqz_zpk(z, p, k, 5, whole=True)
+        xp_assert_close(h1, h2)
+        xp_assert_close(w1, xp.linspace(0, fs, 5, endpoint=False))
+
+    @skip_xp_backends(np_only=True, reason="array_likes")
+    def test_fs_param2(self, xp):
+        fs = 900
+        z = xp.asarray([-1, -1, -1.0])
+        p = xp.asarray(
+            [0.4747869998473389 + 0.4752230717749344j,
+             0.37256600288916636,
+             0.4747869998473389 - 0.4752230717749344j]
+        )
+        k = 0.03934683014103762
+
+        # w is an array_like
+        for w in ([123], (123,), xp.asarray([123]), (50, 123, 230),
+                  xp.asarray([50, 123, 230])):
+            w1, h1 = freqz_zpk(z, p, k, w, fs=fs)
+            w2, h2 = freqz_zpk(z, p, k, 2*pi*xp.asarray(w)/fs)
+            xp_assert_close(h1, h2)
+            xp_assert_close(w, w1, check_dtype=False)
+
+    def test_w_or_N_types(self):
+        # Measure at 8 equally-spaced points
+        for N in (8, np.int8(8), np.int16(8), np.int32(8), np.int64(8),
+                  np.array(8)):
+
+            w, h = freqz_zpk([], [], 1, worN=N)
+            assert_array_almost_equal(w, np.pi * np.arange(8) / 8.)
+            assert_array_almost_equal(h, np.ones(8))
+
+            w, h = freqz_zpk([], [], 1, worN=N, fs=100)
+            assert_array_almost_equal(w, np.linspace(0, 50, 8, endpoint=False))
+            assert_array_almost_equal(h, np.ones(8))
+
+        # Measure at frequency 8 Hz
+        for w in (8.0, 8.0+0j):
+            # Only makes sense when fs is specified
+            w_out, h = freqz_zpk([], [], 1, worN=w, fs=100)
+            assert_array_almost_equal(w_out, [8])
+            assert_array_almost_equal(h, [1])
+
+    def test_fs_validation(self):
+        with pytest.raises(ValueError, match="Sampling.*single scalar"):
+            freqz_zpk([1.0], [1.0], [1.0], fs=np.array([10., 20]))
+
+        with pytest.raises(ValueError, match="Sampling.*be none."):
+            freqz_zpk([1.0], [1.0], [1.0], fs=None)
+
+
+@make_xp_test_case(normalize)
+class TestNormalize:
+
+    def test_allclose(self, xp):
+        """Test for false positive on allclose in normalize() in
+        filter_design.py"""
+        # Test to make sure the allclose call within signal.normalize does not
+        # choose false positives. Then check against a known output from MATLAB
+        # to make sure the fix doesn't break anything.
+
+        # These are the coefficients returned from
+        #   `[b,a] = cheby1(8, 0.5, 0.048)'
+        # in MATLAB. There are at least 15 significant figures in each
+        # coefficient, so it makes sense to test for errors on the order of
+        # 1e-13 (this can always be relaxed if different platforms have
+        # different rounding errors)
+        b_matlab = xp.asarray([2.150733144728282e-11, 1.720586515782626e-10,
+                               6.022052805239190e-10, 1.204410561047838e-09,
+                               1.505513201309798e-09, 1.204410561047838e-09,
+                               6.022052805239190e-10, 1.720586515782626e-10,
+                               2.150733144728282e-11])
+        a_matlab = xp.asarray([1.000000000000000e+00, -7.782402035027959e+00,
+                               2.654354569747454e+01, -5.182182531666387e+01,
+                               6.334127355102684e+01, -4.963358186631157e+01,
+                               2.434862182949389e+01, -6.836925348604676e+00,
+                               8.412934944449140e-01])
+
+        # This is the input to signal.normalize after passing through the
+        # equivalent steps in signal.iirfilter as was done for MATLAB
+        b_norm_in = xp.asarray([1.5543135865293012e-06, 1.2434508692234413e-05,
+                                4.3520780422820447e-05, 8.7041560845640893e-05,
+                                1.0880195105705122e-04, 8.7041560845640975e-05,
+                                4.3520780422820447e-05, 1.2434508692234413e-05,
+                                1.5543135865293012e-06])
+        a_norm_in = xp.asarray([7.2269025909127173e+04, -5.6242661430467968e+05,
+                                1.9182761917308895e+06, -3.7451128364682454e+06,
+                                4.5776121393762771e+06, -3.5869706138592605e+06,
+                                1.7596511818472347e+06, -4.9409793515707983e+05,
+                                6.0799461347219651e+04])
+
+        b_output, a_output = normalize(b_norm_in, a_norm_in)
+
+        # The test on b works for decimal=14 but the one for a does not. For
+        # the sake of consistency, both of these are decimal=13. If something
+        # breaks on another platform, it is probably fine to relax this lower.
+        decimal = 13 if xp_default_dtype(xp) == xp.float64 else 5
+        assert_array_almost_equal(b_matlab, b_output, decimal=decimal)
+        assert_array_almost_equal(a_matlab, a_output, decimal=decimal)
+
+    def test_errors(self):
+        """Test the error cases."""
+        # all zero denominator
+        assert_raises(ValueError, normalize, [1, 2], 0)
+
+        # denominator not 1 dimensional
+        assert_raises(ValueError, normalize, [1, 2], [[1]])
+
+        # numerator too many dimensions
+        assert_raises(ValueError, normalize, [[[1, 2]]], 1)
+
+
+@make_xp_test_case(lp2lp)
+class TestLp2lp:
+
+    def test_basic(self, xp):
+        b = xp.asarray([1])
+        a = xp.asarray([1, math.sqrt(2), 1])
+        b_lp, a_lp = lp2lp(b, a, 0.38574256627112119)
+        assert_array_almost_equal(b_lp, xp.asarray([0.1488]), decimal=4)
+        assert_array_almost_equal(a_lp, xp.asarray([1, 0.5455, 0.1488]), decimal=4)
+
+
+@make_xp_test_case(lp2hp)
+class TestLp2hp:
+
+    def test_denominator_order_greater_than_numerator_order(self, xp):
+        b = xp.asarray([0.25059432325190018])
+        a = xp.asarray(
+            [1, 0.59724041654134863, 0.92834805757524175, 0.25059432325190018]
+        )
+        b_hp, a_hp = lp2hp(b, a, 2*math.pi*5000)
+        xp_assert_close(b_hp, xp.asarray([1.0, 0, 0, 0]))
+        xp_assert_close(
+            a_hp, xp.asarray([1, 1.1638e5, 2.3522e9, 1.2373e14]), rtol=1e-4
+        )
+
+    def test_numerator_order_greater_than_denominator_order(self, xp):
+        b = xp.asarray([1.0, 2.0, 3.0])
+        a = xp.asarray([1.0])
+        b_hp, a_hp = lp2hp(b, a, 2.0)
+        xp_assert_close(b_hp, xp.asarray([3.0, 4.0, 4.0]))
+        xp_assert_close(a_hp, xp.asarray([1.0, 0.0, 0.0]))
+
+
+@make_xp_test_case(lp2bp)
+class TestLp2bp:
+
+    def test_denominator_order_greater_than_numerator_order(self, xp):
+        b = xp.asarray([1])
+        a = xp.asarray([1, 2, 2, 1])
+        b_bp, a_bp = lp2bp(b, a, 2*math.pi*4000, 2*math.pi*2000)
+        xp_assert_close(b_bp, xp.asarray([1.9844e12, 0, 0, 0]), rtol=1e-6)
+        xp_assert_close(
+            a_bp,
+            xp.asarray([1, 2.5133e4, 2.2108e9, 3.3735e13,
+                        1.3965e18, 1.0028e22, 2.5202e26]), rtol=1e-4
+        )
+
+    def test_numerator_order_greater_than_denominator_order(self, xp):
+        b = xp.asarray([1.0, 2.0, 3.0])
+        a = xp.asarray([1.0])
+        b_bp, a_bp = lp2bp(b, a, 2.0, 3.0)
+        xp_assert_close(b_bp, xp.asarray([1/9, 2/3, 35/9, 8/3, 16/9]))
+        xp_assert_close(a_bp, xp.asarray([1.0, 0.0, 0.0]))
+
+
+@make_xp_test_case(lp2bs)
+class TestLp2bs:
+
+    def test_denominator_order_greater_than_numerator_order(self, xp):
+        b = xp.asarray([1])
+        a = xp.asarray([1, 1])
+        b_bs, a_bs = lp2bs(b, a, 0.41722257286366754, 0.18460575326152251)
+        assert_array_almost_equal(b_bs, xp.asarray([1, 0, 0.17407]), decimal=5)
+        assert_array_almost_equal(a_bs, xp.asarray([1, 0.18461, 0.17407]), decimal=5)
+
+    def test_numerator_order_greater_than_denominator_order(self, xp):
+        b = xp.asarray([1.0, 2.0, 3.0])
+        a = xp.asarray([1.0])
+        b_bs, a_bs = lp2bs(b, a, 2.0, 3.0)
+        xp_assert_close(b_bs, xp.asarray([3.0, 6.0, 33.0, 24.0, 48.0]))
+        xp_assert_close(a_bs, xp.asarray([1.0, 0.0, 8.0, 0.0, 16.0]))
+
+
+@make_xp_test_case(bilinear)
+class TestBilinear:
+    """Tests for function `signal.bilinear`. """
+
+    def test_exceptions(self):
+        """Raise all exceptions in `bilinear()`. """
+        with pytest.raises(ValueError, match="Parameter a is not .*"):
+            bilinear(1., np.array([[1, 2, 3]]))
+        with pytest.raises(ValueError, match="Parameter b is not .*"):
+            bilinear(np.ones((2,3)), 1. )
+
+    @pytest.mark.xfail(DEFAULT_F32, reason="wrong answer with torch/float32")
+    def test_basic(self, xp):
+        # reference output values computed with sympy
+        b = [0.14879732743343033]
+        a = [1, 0.54552236880522209, 0.14879732743343033]
+        b, a = map(xp.asarray, (b, a))
+
+        b_zref = xp.asarray(
+            [0.08782128175913713, 0.17564256351827426, 0.08782128175913713]
+        )
+        a_zref = xp.asarray(
+            [1.0, -1.0047722097030667, 0.3560573367396151]
+        )
+
+        b_z, a_z = bilinear(b, a, 0.5)
+
+        xp_assert_close_nulp(b_z, b_zref)
+        xp_assert_close_nulp(a_z, a_zref)
+
+        b = xp.asarray([1, 0, 0.17407467530697837])
+        a = xp.asarray([1, 0.18460575326152251, 0.17407467530697837])
+
+        b_zref = xp.asarray(
+            [0.8641286432189045, -1.2157757001964216, 0.8641286432189045]
+        )
+        a_zref = xp.asarray([1.0, -1.2157757001964216, 0.7282572864378091])
+
+        b_z, a_z = bilinear(b, a, 0.5)
+
+        xp_assert_close_nulp(b_z, xp.asarray(b_zref))
+        xp_assert_close_nulp(a_z, xp.asarray(a_zref))
+
+    @pytest.mark.xfail(DEFAULT_F32, reason="wrong answer with torch/float32")
+    @xfail_xp_backends("cupy", reason="https://github.com/cupy/cupy/issues/9404")
+    def test_ignore_leading_zeros(self, xp):
+        # regression for gh-6606
+        # results shouldn't change when leading zeros are added to
+        # input numerator or denominator
+        b = [0.14879732743343033]
+        a = [1, 0.54552236880522209, 0.14879732743343033]
+        b, a = map(xp.asarray, (b, a))
+
+        b_zref = xp.asarray(
+            [0.08782128175913713, 0.17564256351827426, 0.08782128175913713]
+        )
+        a_zref = xp.asarray([1.0, -1.0047722097030667, 0.3560573367396151])
+
+        for lzn, lzd in product(range(4), range(4)):
+            b_z, a_z = bilinear(xpx.pad(b, (lzn, 0), xp=xp),
+                                xpx.pad(a, (lzd, 0), xp=xp),
+                                0.5)
+            xp_assert_close_nulp(b_z, b_zref)
+            xp_assert_close_nulp(a_z, a_zref)
+
+    @pytest.mark.xfail(DEFAULT_F32, reason="wrong answer with torch/float32")
+    @xfail_xp_backends("cupy", reason="complex inputs not supported")
+    def test_complex(self, xp):
+        # reference output values computed with sympy
+        # this is an elliptical filter, 5Hz width, centered at +50Hz:
+        #     z, p, k = signal.ellip(2, 0.5, 20, 2*np.pi*5/2, output='zpk', analog=True)
+        #     z = z.astype(complex) + 2j * np.pi * 50
+        #     p = p.astype(complex) + 2j * np.pi * 50
+        #     b, a = signal.zpk2tf(z, p, k)
+        b = [(0.09999999999999991+0j),
+             -62.831853071795805j,
+             (-9505.857007071314+0j)]
+        a = [(1+0j),
+             (21.09511000343942-628.3185307179587j),
+             (-98310.74322875646-6627.2242613473845j)]
+        b, a = map(xp.asarray, (b, a))
+
+        # sample frequency
+        fs = 1000
+        b_zref = [(0.09905575106715676-0.00013441423112828688j),
+                  (-0.18834281923181084-0.06032810039049478j),
+                  (0.08054306669414343+0.05766172295523972j)]
+        a_zref = [(1+0j),
+                  (-1.8839476369292854-0.606808151331815j),
+                  (0.7954687330018285+0.5717459398142481j)]
+
+        b_zref, a_zref = map(xp.asarray, (b_zref, a_zref))
+
+        b_z, a_z = bilinear(b, a, fs)
+
+        # the 3 ulp difference determined from testing
+        xp_assert_close_nulp(b_z, b_zref, nulp=3)
+        xp_assert_close_nulp(a_z, a_zref, nulp=3)
+
+    def test_fs_validation(self):
+        b = [0.14879732743343033]
+        a = [1, 0.54552236880522209, 0.14879732743343033]
+        with pytest.raises(ValueError, match="Sampling.*single scalar"):
+            bilinear(b, a, fs=np.array([10, 20]))
+
+        with pytest.raises(ValueError, match="Sampling.*be none"):
+            bilinear(b, a, fs=None)
+
+
+@make_xp_test_case(lp2lp_zpk)
+class TestLp2lp_zpk:
+
+    @xfail_xp_backends(
+        'dask.array', reason='https://github.com/dask/dask/issues/11883'
+    )
+    def test_basic(self, xp):
+        z = xp.asarray([])
+        p = xp.asarray([(-1+1j) / math.sqrt(2), (-1-1j) / math.sqrt(2)])
+        k = 1
+        z_lp, p_lp, k_lp = lp2lp_zpk(z, p, k, 5)
+        xp_assert_equal(z_lp, xp.asarray([]))
+        xp_assert_close(_sort_cmplx(p_lp, xp=xp), _sort_cmplx(p, xp=xp) * 5)
+        assert k_lp == 25.
+
+        # Pseudo-Chebyshev with both poles and zeros
+        z = xp.asarray([-2j, +2j])
+        p = xp.asarray([-0.75, -0.5-0.5j, -0.5+0.5j])
+        k = 3
+        z_lp, p_lp, k_lp = lp2lp_zpk(z, p, k, 20)
+        xp_assert_close(
+            _sort_cmplx(z_lp, xp=xp), _sort_cmplx([-40j, +40j], xp=xp)
+        )
+        xp_assert_close(
+            _sort_cmplx(p_lp, xp=xp), _sort_cmplx([-15, -10-10j, -10+10j], xp=xp)
+        )
+        assert k_lp == 60.
+
+    def test_fs_validation(self):
+        z = [-2j, +2j]
+        p = [-0.75, -0.5 - 0.5j, -0.5 + 0.5j]
+        k = 3
+
+        with pytest.raises(ValueError, match="Sampling.*single scalar"):
+            bilinear_zpk(z, p, k, fs=np.array([10, 20]))
+
+        with pytest.raises(ValueError, match="Sampling.*be none"):
+            bilinear_zpk(z, p, k, fs=None)
+
+
+@make_xp_test_case(lp2hp_zpk)
+class TestLp2hp_zpk:
+
+    @xfail_xp_backends(
+        'dask.array', reason='https://github.com/dask/dask/issues/11883'
+    )
+    def test_basic(self, xp):
+        z = xp.asarray([])
+        p = xp.asarray([(-1+1j) / math.sqrt(2), (-1-1j) / math.sqrt(2)])
+        k = 1
+
+        z_hp, p_hp, k_hp = lp2hp_zpk(z, p, k, 5)
+        xp_assert_equal(z_hp, xp.asarray([0.0, 0.0], dtype=z_hp.dtype))
+        xp_assert_close(_sort_cmplx(p_hp, xp=xp), _sort_cmplx(p, xp=xp) * 5)
+        assert math.isclose(k_hp, 1.0, rel_tol=4e-7)
+
+        z = xp.asarray([-2j, +2j])
+        p = xp.asarray([-0.75, -0.5-0.5j, -0.5+0.5j])
+        k = 3
+        z_hp, p_hp, k_hp = lp2hp_zpk(z, p, k, 6)
+        xp_assert_close(
+            _sort_cmplx(z_hp, xp=xp), _sort_cmplx([-3j, 0, +3j], xp=xp)
+        )
+        xp_assert_close(
+            _sort_cmplx(p_hp, xp=xp), _sort_cmplx([-8, -6-6j, -6+6j], xp=xp)
+        )
+        assert k_hp == 32.0
+
+
+@make_xp_test_case(lp2bp_zpk)
+class TestLp2bp_zpk:
+
+    @xfail_xp_backends(
+        'dask.array', reason='https://github.com/dask/dask/issues/11883'
+    )
+    def test_basic(self, xp):
+        z = xp.asarray([-2j, +2j])
+        p = xp.asarray([-0.75, -0.5-0.5j, -0.5+0.5j])
+        k = 3
+        z_bp, p_bp, k_bp = lp2bp_zpk(z, p, k, 15, 8)
+        xp_assert_close(
+            _sort_cmplx(z_bp, xp=xp),
+            _sort_cmplx([-25j, -9j, 0, +9j, +25j], xp=xp), check_dtype=False
+        )
+        xp_assert_close(
+            _sort_cmplx(p_bp, xp=xp),
+            _sort_cmplx(
+                [-3 + 6j*math.sqrt(6), -3 - 6j*math.sqrt(6),
+                 +2j + cmath.sqrt(-8j - 225) - 2, -2j + cmath.sqrt(+8j - 225) - 2,
+                 +2j - cmath.sqrt(-8j - 225) - 2, -2j - cmath.sqrt(+8j - 225) - 2
+                ], xp=xp
+            ), check_dtype=False
+        )
+        assert math.isclose(k_bp, 24.0)
+
+
+@make_xp_test_case(lp2bs_zpk)
+class TestLp2bs_zpk:
+
+    @xfail_xp_backends(
+        'dask.array', reason='https://github.com/dask/dask/issues/11883'
+    )
+    def test_basic(self, xp):
+        z = xp.asarray([-2j, +2j])
+        p = xp.asarray([-0.75, -0.5-0.5j, -0.5+0.5j])
+        k = 3
+
+        z_bs, p_bs, k_bs = lp2bs_zpk(z, p, k, 35, 12)
+
+        xp_assert_close(
+            _sort_cmplx(z_bs, xp=xp),
+            _sort_cmplx([+35j, -35j,
+                         +3j + math.sqrt(1234)*1j,
+                         -3j + math.sqrt(1234)*1j,
+                         +3j - math.sqrt(1234)*1j,
+                         -3j - math.sqrt(1234)*1j], xp=xp), check_dtype=False
+        )
+        xp_assert_close(
+            _sort_cmplx(p_bs, xp=xp),
+            _sort_cmplx([+3j*math.sqrt(129) - 8,
+                         -3j*math.sqrt(129) - 8,
+                         (-6 + 6j) - cmath.sqrt(-1225 - 72j),
+                         (-6 - 6j) - cmath.sqrt(-1225 + 72j),
+                         (-6 + 6j) + cmath.sqrt(-1225 - 72j),
+                         (-6 - 6j) + cmath.sqrt(-1225 + 72j), ], xp=xp),
+            check_dtype=False
+        )
+        assert math.isclose(k_bs, 32.0)
+
+
+@make_xp_test_case(bilinear_zpk)
+class TestBilinear_zpk:
+
+    @xfail_xp_backends(
+        'dask.array', reason='https://github.com/dask/dask/issues/11883'
+    )
+    def test_basic(self, xp):
+        z = xp.asarray([-2j, +2j])
+        p = xp.asarray([-0.75, -0.5-0.5j, -0.5+0.5j])
+        k = 3
+
+        z_d, p_d, k_d = bilinear_zpk(z, p, k, 10)
+
+        xp_assert_close(
+            _sort_cmplx(z_d, xp=xp),
+            _sort_cmplx([(20-2j) / (20+2j), (20+2j) / (20-2j), -1], xp=xp)
+        )
+        xp_assert_close(
+            _sort_cmplx(p_d, xp=xp),
+            _sort_cmplx(
+                [77/83, (1j/2 + 39/2) / (41/2 - 1j/2), (39/2 - 1j/2) / (1j/2 + 41/2)],
+                xp=xp
+            )
+        )
+        assert math.isclose(k_d, 9696/69803, rel_tol=4e-7)
+
+
+class TestPrototypeType:
+
+    def test_output_type(self):
+        # Prototypes should consistently output arrays, not lists
+        # https://github.com/scipy/scipy/pull/441
+        for func in (buttap,
+                     besselap,
+                     lambda N: cheb1ap(N, 1),
+                     lambda N: cheb2ap(N, 20),
+                     lambda N: ellipap(N, 1, 20)):
+            for N in range(7):
+                z, p, k = func(N)
+                assert isinstance(z, np.ndarray)
+                assert isinstance(p, np.ndarray)
+
+    @pytest.mark.parametrize(
+        'base_func,func', [
+            make_xp_pytest_param(buttap, buttap),
+            make_xp_pytest_param(besselap, besselap),
+            make_xp_pytest_param(cheb1ap, lambda N, xp: cheb1ap(N, 1, xp=xp)),
+            make_xp_pytest_param(cheb2ap, lambda N, xp: cheb2ap(N, 20, xp=xp)),
+            make_xp_pytest_param(ellipap, lambda N, xp: ellipap(N, 1, 20, xp=xp)),
+        ],
+        ids=['butter', 'bessel', 'cheb1', 'cheb2', 'ellip']
+    )
+    def test_with_xp(self, base_func, func, xp):
+        func(7, xp=xp)
+
+
+def dB(x):
+    # Return magnitude in decibels, avoiding divide-by-zero warnings
+    # (and deal with some "not less-ordered" errors when -inf shows up)
+    xp = array_namespace(x)
+    tiny = xp.asarray(np.finfo(np.float64).tiny)
+    return 20 * xp.log10(xp.maximum(xp.abs(x), tiny))
+
+
+@make_xp_test_case(buttord)
+@pytest.mark.skipif(DEFAULT_F32, reason="XXX needs figuring out")
+@skip_xp_backends("dask.array", reason="https://github.com/dask/dask/issues/11883")
+class TestButtord:
+
+    def test_lowpass(self, xp):
+        wp = 0.2
+        ws = 0.3
+        rp = 3
+        rs = 60
+        N, Wn = buttord(xp.asarray(wp), ws, rp, rs, False)
+        b, a = butter(N, _xp_copy_to_numpy(Wn), 'lowpass', False)
+        w, h = freqz(b, a)
+        w /= np.pi
+        assert np.all(-rp < dB(h[w <= wp]))
+        assert np.all(dB(h[ws <= w]) < -rs)
+
+        assert N == 16
+        xp_assert_close(Wn,
+                        xp.asarray(2.0002776782743284e-01), rtol=1e-15, check_0d=False)
+
+    def test_highpass(self, xp):
+        wp = 0.3
+        ws = 0.2
+        rp = 3
+        rs = 70
+        N, Wn = buttord(xp.asarray(wp), ws, rp, rs, False)
+        b, a = butter(N, _xp_copy_to_numpy(Wn), 'highpass', False)
+        w, h = freqz(b, a)
+        w /= np.pi
+        assert np.all(-rp < dB(h[wp <= w]))
+        assert np.all(dB(h[w <= ws]) < -rs)
+
+        assert N == 18
+        xp_assert_close(Wn,
+                        xp.asarray(2.9996603079132672e-01), rtol=1e-15, check_0d=False)
+
+    def test_bandpass(self, xp):
+        wp = [0.2, 0.5]
+        ws = [0.1, 0.6]
+        rp = 3
+        rs = 80
+        N, Wn = buttord(xp.asarray(wp), xp.asarray(ws), rp, rs, False)
+        b, a = butter(N, _xp_copy_to_numpy(Wn), 'bandpass', False)
+        w, h = freqz(b, a)
+        w /= np.pi
+
+        assert np.all((-rp - 0.1) < dB(h[np.logical_and(wp[0] <= w, w <= wp[1])]))
+
+        assert np.all(dB(h[np.logical_or(w <= ws[0], ws[1] <= w)]) < (-rs + 0.1))
+
+        assert N == 18
+        xp_assert_close(
+            Wn, xp.asarray([1.9998742411409134e-01, 5.0002139595676276e-01]),
+            rtol=1e-15,
+        )
+
+    @skip_xp_backends(
+        cpu_only=True, exceptions=["cupy"], reason="optimize.fminbound"
+    )
+    def test_bandstop(self, xp):
+        wp = [0.1, 0.6]
+        ws = [0.2, 0.5]
+        rp = 3
+        rs = 90
+        N, Wn = buttord(xp.asarray(wp), xp.asarray(ws), rp, rs, False)
+        b, a = butter(N, _xp_copy_to_numpy(Wn), 'bandstop', False)
+        w, h = freqz(b, a)
+        w /= np.pi
+
+        assert np.all(-rp < dB(h[np.logical_or(w <= wp[0], wp[1] <= w)]))
+        assert np.all(dB(h[np.logical_and(ws[0] <= w, w <= ws[1])]) < -rs)
+
+        assert N == 20
+        xp_assert_close(
+            Wn, xp.asarray([1.4759432329294042e-01, 5.9997365985276407e-01]),
+            rtol=1e-6
+        )
+
+    def test_analog(self, xp):
+        wp = 200.
+        ws = 600.
+        rp = 3
+        rs = 60
+        N, Wn = buttord(xp.asarray(wp), ws, rp, rs, True)
+        b, a = butter(N, _xp_copy_to_numpy(Wn), 'lowpass', True)
+        w, h = freqs(b, a)
+        assert np.all(-rp < dB(h[w <= wp]))
+        assert np.all(dB(h[ws <= w]) < -rs)
+
+        assert N == 7
+        xp_assert_close(
+            Wn, xp.asarray(2.0006785355671877e+02), rtol=1e-15, check_0d=False
+        )
+
+        n, Wn = buttord(1., xp.asarray(550/450), 1, 26, analog=True)
+        assert n == 19
+        xp_assert_close(
+            Wn, xp.asarray(1.0361980524629517), rtol=1e-15, check_0d=False
+        )
+
+        assert buttord(1, xp.asarray(1.2), 1, 80, analog=True)[0] == 55
+
+    def test_fs_param(self, xp):
+        wp = [4410, 11025]
+        ws = [2205, 13230]
+        rp = 3
+        rs = 80
+        fs = 44100
+        N, Wn = buttord(xp.asarray(wp), xp.asarray(ws), rp, rs, False, fs=fs)
+        b, a = butter(N, _xp_copy_to_numpy(Wn), 'bandpass', False, fs=fs)
+        w, h = freqz(b, a, fs=fs)
+
+        assert np.all(-rp - 0.1 < dB(h[np.logical_and(wp[0] <= w, w <= wp[1])]))
+        assert np.all(dB(h[np.logical_or(w <= ws[0], ws[1] <= w)]) < -rs + 0.1)
+
+        assert N == 18
+        xp_assert_close(Wn, xp.asarray([4409.722701715714, 11025.47178084662]),
+                        rtol=1e-15)
+
+    def test_invalid_input(self):
+        with pytest.raises(ValueError) as exc_info:
+            buttord([20, 50], [14, 60], 3, 2)
+        assert "gpass should be smaller than gstop" in str(exc_info.value)
+
+        with pytest.raises(ValueError) as exc_info:
+            buttord([20, 50], [14, 60], -1, 2)
+        assert "gpass should be larger than 0.0" in str(exc_info.value)
+
+        with pytest.raises(ValueError) as exc_info:
+            buttord([20, 50], [14, 60], 1, -2)
+        assert "gstop should be larger than 0.0" in str(exc_info.value)
+
+    def test_runtime_warnings(self):
+        msg = "Order is zero.*|divide by zero encountered"
+        with pytest.warns(RuntimeWarning, match=msg):
+            buttord(0.0, 1.0, 3, 60)
+
+    def test_ellip_butter(self):
+        # The purpose of the test is to compare to some known output from past
+        # scipy versions. The values to compare to are generated with scipy
+        # 1.9.1 (there is nothing special about this particular version though)
+        n, wn = buttord([0.1, 0.6], [0.2, 0.5], 3, 60)
+        assert n == 14
+
+    def test_fs_validation(self):
+        wp = 0.2
+        ws = 0.3
+        rp = 3
+        rs = 60
+
+        with pytest.raises(ValueError, match="Sampling.*single scalar"):
+            buttord(wp, ws, rp, rs, False, fs=np.array([10, 20]))
+
+
+@make_xp_test_case(cheb1ord)
+@skip_xp_backends("dask.array", reason="https://github.com/dask/dask/issues/11883")
+class TestCheb1ord:
+
+    @xfail_xp_backends("torch", reason="accuracy is bad")
+    def test_lowpass(self, xp):
+        wp = 0.2
+        ws = 0.3
+        rp = 3
+        rs = 60
+        N, Wn = cheb1ord(xp.asarray(wp), ws, rp, rs, False)
+        b, a = cheby1(N, rp, _xp_copy_to_numpy(Wn), 'low', False)
+        w, h = freqz(b, a)
+        w /= np.pi
+        assert np.all(-rp - 0.1 < dB(h[w <= wp]))
+        assert np.all(dB(h[ws <= w]) < -rs + 0.1)
+
+        assert N == 8
+        xp_assert_close(Wn, xp.asarray(0.2), rtol=1e-15, check_0d=False)
+
+    @xfail_xp_backends("torch", reason="accuracy is bad")
+    def test_highpass(self, xp):
+        wp = 0.3
+        ws = 0.2
+        rp = 3
+        rs = 70
+        N, Wn = cheb1ord(xp.asarray(wp), ws, rp, rs, False)
+        b, a = cheby1(N, rp, _xp_copy_to_numpy(Wn), 'high', False)
+        w, h = freqz(b, a)
+        w /= np.pi
+        assert np.all(-rp - 0.1 < dB(h[wp <= w]))
+        assert np.all(dB(h[w <= ws]) < -rs + 0.1)
+
+        assert N == 9
+        xp_assert_close(Wn, xp.asarray(0.3), rtol=1e-15, check_0d=False)
+
+    def test_bandpass(self, xp):
+        wp = [0.2, 0.5]
+        ws = [0.1, 0.6]
+        rp = 3
+        rs = 80
+        N, Wn = cheb1ord(xp.asarray(wp), xp.asarray(ws), rp, rs, False)
+        b, a = cheby1(N, rp, _xp_copy_to_numpy(Wn), 'band', False)
+        w, h = freqz(b, a)
+        w /= np.pi
+        assert np.all(-rp - 0.1 < dB(h[np.logical_and(wp[0] <= w, w <= wp[1])]))
+        assert np.all(dB(h[np.logical_or(w <= ws[0], ws[1] <= w)]) < -rs + 0.1)
+
+        assert N == 9
+        xp_assert_close(Wn, xp.asarray([0.2, 0.5]), rtol=1e-15)
+
+    @skip_xp_backends(
+        cpu_only=True, exceptions=["cupy"], reason="optimize.fminbound"
+    )
+    def test_bandstop(self, xp):
+        wp = [0.1, 0.6]
+        ws = [0.2, 0.5]
+        rp = 3
+        rs = 90
+        N, Wn = cheb1ord(xp.asarray(wp), xp.asarray(ws), rp, rs, False)
+        b, a = cheby1(N, rp, _xp_copy_to_numpy(Wn), 'stop', False)
+        w, h = freqz(b, a)
+        w /= np.pi
+        assert np.all(-rp - 0.1 < dB(h[np.logical_or(w <= wp[0], wp[1] <= w)]))
+        assert np.all(dB(h[np.logical_and(ws[0] <= w, w <= ws[1])]) < -rs + 0.1)
+
+        assert N == 10
+        xp_assert_close(Wn, xp.asarray([0.14758232569947785, 0.6]), rtol=1e-5)
+
+    def test_analog(self, xp):
+        wp = 700
+        ws = 100.
+        rp = 3
+        rs = 70
+        N, Wn = cheb1ord(wp, xp.asarray(ws), rp, rs, True)
+        b, a = cheby1(N, rp, _xp_copy_to_numpy(Wn), 'high', True)
+        w, h = freqs(b, a)
+        assert np.all(-rp - 0.1 < dB(h[wp <= w]))
+        assert np.all(dB(h[w <= ws]) < -rs + 0.1)
+
+        assert N == 4
+        assert math.isclose(Wn, 700.0, rel_tol=1e-15)
+        assert array_namespace(Wn) == xp
+        assert cheb1ord(xp.asarray(1), 1.2, 1, 80, analog=True)[0] == 17
+
+    @xfail_xp_backends("torch", reason="accuracy issues")
+    def test_fs_param(self, xp):
+        wp = 4800
+        ws = 7200.
+        rp = 3
+        rs = 60
+        fs = 48000
+        N, Wn = cheb1ord(wp, xp.asarray(ws), rp, rs, False, fs=fs)
+        b, a = cheby1(N, rp, _xp_copy_to_numpy(Wn), 'low', False, fs=fs)
+        w, h = freqz(b, a, fs=fs)
+        assert np.all(-rp - 0.1 < dB(h[w <= wp]))
+        assert np.all(dB(h[ws <= w]) < -rs + 0.1)
+
+        assert N == 8
+        assert math.isclose(Wn, 4800.0, rel_tol=1e-15)
+        assert array_namespace(Wn) == xp
+
+    def test_invalid_input(self):
+        with pytest.raises(ValueError) as exc_info:
+            cheb1ord(0.2, 0.3, 3, 2)
+        assert "gpass should be smaller than gstop" in str(exc_info.value)
+
+        with pytest.raises(ValueError) as exc_info:
+            cheb1ord(0.2, 0.3, -1, 2)
+        assert "gpass should be larger than 0.0" in str(exc_info.value)
+
+        with pytest.raises(ValueError) as exc_info:
+            cheb1ord(0.2, 0.3, 1, -2)
+        assert "gstop should be larger than 0.0" in str(exc_info.value)
+
+    def test_ellip_cheb1(self):
+        # The purpose of the test is to compare to some known output from past
+        # scipy versions. The values to compare to are generated with scipy
+        # 1.9.1 (there is nothing special about this particular version though)
+        n, wn = cheb1ord([0.1, 0.6], [0.2, 0.5], 3, 60)
+        assert n == 7
+
+        n2, w2 = cheb2ord([0.1, 0.6], [0.2, 0.5], 3, 60)
+        assert not (wn == w2).all()
+
+    def test_fs_validation(self):
+        wp = 0.2
+        ws = 0.3
+        rp = 3
+        rs = 60
+
+        with pytest.raises(ValueError, match="Sampling.*single scalar"):
+            cheb1ord(wp, ws, rp, rs, False, fs=np.array([10, 20]))
+
+
+@make_xp_test_case(cheb2ord)
+@pytest.mark.skipif(DEFAULT_F32, reason="XXX needs figuring out")
+@skip_xp_backends("dask.array", reason="https://github.com/dask/dask/issues/11883")
+class TestCheb2ord:
+
+    def test_lowpass(self, xp):
+        wp = 0.2
+        ws = 0.3
+        rp = 3
+        rs = 60
+        N, Wn = cheb2ord(wp, xp.asarray(ws), rp, rs, False)
+        b, a = cheby2(N, rs, _xp_copy_to_numpy(Wn), 'lp', False)
+        w, h = freqz(b, a)
+        w /= np.pi
+        assert np.all(-rp - 0.1 < dB(h[w <= wp]))
+        assert np.all(dB(h[ws <= w]) < -rs + 0.1)
+
+        assert N == 8
+        xp_assert_close(Wn, xp.asarray(0.28647639976553163), rtol=1e-15, check_0d=False)
+
+    def test_highpass(self, xp):
+        wp = 0.3
+        ws = 0.2
+        rp = 3
+        rs = 70
+        N, Wn = cheb2ord(wp, xp.asarray(ws), rp, rs, False)
+        b, a = cheby2(N, rs, _xp_copy_to_numpy(Wn), 'hp', False)
+        w, h = freqz(b, a)
+        w /= np.pi
+        assert np.all(-rp - 0.1 < dB(h[wp <= w]))
+        assert np.all(dB(h[w <= ws]) < -rs + 0.1)
+
+        assert N == 9
+        xp_assert_close(Wn, xp.asarray(0.20697492182903282), rtol=1e-15, check_0d=False)
+
+    def test_bandpass(self, xp):
+        wp = [0.2, 0.5]
+        ws = [0.1, 0.6]
+        rp = 3
+        rs = 80
+        N, Wn = cheb2ord(xp.asarray(wp), xp.asarray(ws), rp, rs, False)
+        b, a = cheby2(N, rs, _xp_copy_to_numpy(Wn), 'bp', False)
+        w, h = freqz(b, a)
+        w /= np.pi
+        assert np.all(-rp - 0.1 < dB(h[np.logical_and(wp[0] <= w, w <= wp[1])]))
+        assert np.all(dB(h[np.logical_or(w <= ws[0], ws[1] <= w)]) < -rs + 0.1)
+
+        assert N == 9
+        xp_assert_close(Wn, xp.asarray([0.14876937565923479, 0.59748447842351482]),
+                        rtol=1e-15)
+
+    @skip_xp_backends(
+        cpu_only=True, exceptions=["cupy"], reason="optimize.fminbound"
+    )
+    def test_bandstop(self, xp):
+        wp = [0.1, 0.6]
+        ws = [0.2, 0.5]
+        rp = 3
+        rs = 90
+        N, Wn = cheb2ord(xp.asarray(wp), xp.asarray(ws), rp, rs, False)
+        b, a = cheby2(N, rs, _xp_copy_to_numpy(Wn), 'bs', False)
+        w, h = freqz(b, a)
+        w /= np.pi
+        assert np.all(-rp - 0.1 < dB(h[np.logical_or(w <= wp[0], wp[1] <= w)]))
+        assert np.all(dB(h[np.logical_and(ws[0] <= w, w <= ws[1])]) < -rs + 0.1)
+
+        assert N == 10
+        xp_assert_close(Wn, xp.asarray([0.19926249974781743, 0.50125246585567362]),
+                        rtol=1e-6)
+
+    def test_analog(self, xp):
+        wp = [20., 50]
+        ws = [10., 60]
+        rp = 3
+        rs = 80
+        N, Wn = cheb2ord(xp.asarray(wp), xp.asarray(ws), rp, rs, True)
+        b, a = cheby2(N, rs, _xp_copy_to_numpy(Wn), 'bp', True)
+        w, h = freqs(b, a)
+        assert np.all(-rp - 0.1 < dB(h[np.logical_and(wp[0] <= w, w <= wp[1])]))
+        assert np.all(dB(h[np.logical_or(w <= ws[0], ws[1] <= w)]) < -rs + 0.1)
+
+        assert N == 11
+        xp_assert_close(Wn, xp.asarray([1.673740595370124e+01, 5.974641487254268e+01]),
+                        rtol=1e-15)
+
+    def test_fs_param(self, xp):
+        wp = 150
+        ws = 100.
+        rp = 3
+        rs = 70
+        fs = 1000
+        N, Wn = cheb2ord(wp, xp.asarray(ws), rp, rs, False, fs=fs)
+        b, a = cheby2(N, rs, _xp_copy_to_numpy(Wn), 'hp', False, fs=fs)
+        w, h = freqz(b, a, fs=fs)
+        assert np.all(-rp - 0.1 < dB(h[wp <= w]))
+        assert np.all(dB(h[w <= ws]) < -rs + 0.1)
+
+        assert N == 9
+        assert math.isclose(Wn, 103.4874609145164, rel_tol=1e-15)
+        assert array_namespace(Wn) == xp
+
+    def test_invalid_input(self):
+        with pytest.raises(ValueError) as exc_info:
+            cheb2ord([0.1, 0.6], [0.2, 0.5], 3, 2)
+        assert "gpass should be smaller than gstop" in str(exc_info.value)
+
+        with pytest.raises(ValueError) as exc_info:
+            cheb2ord([0.1, 0.6], [0.2, 0.5], -1, 2)
+        assert "gpass should be larger than 0.0" in str(exc_info.value)
+
+        with pytest.raises(ValueError) as exc_info:
+            cheb2ord([0.1, 0.6], [0.2, 0.5], 1, -2)
+        assert "gstop should be larger than 0.0" in str(exc_info.value)
+
+    def test_ellip_cheb2(self):
+        # The purpose of the test is to compare to some known output from past
+        # scipy versions. The values to compare to are generated with scipy
+        # 1.9.1 (there is nothing special about this particular version though)
+        n, wn = cheb2ord([0.1, 0.6], [0.2, 0.5], 3, 60)
+        assert n == 7
+
+        n1, w1 = cheb1ord([0.1, 0.6], [0.2, 0.5], 3, 60)
+        assert not (wn == w1).all()
+
+    def test_fs_validation(self):
+        wp = 0.2
+        ws = 0.3
+        rp = 3
+        rs = 60
+
+        with pytest.raises(ValueError, match="Sampling.*single scalar"):
+            cheb2ord(wp, ws, rp, rs, False, fs=np.array([10, 20]))
+
+
+@make_xp_test_case(ellipord)
+@pytest.mark.skipif(DEFAULT_F32, reason="XXX needs figuring out")
+@skip_xp_backends("dask.array", reason="https://github.com/dask/dask/issues/11883")
+class TestEllipord:
+
+    def test_lowpass(self, xp):
+        wp = 0.2
+        ws = 0.3
+        rp = 3
+        rs = 60
+        N, Wn = ellipord(wp, xp.asarray(ws), rp, rs, False)
+        b, a = ellip(N, rp, rs, _xp_copy_to_numpy(Wn), 'lp', False)
+        w, h = freqz(b, a)
+        w /= np.pi
+        assert np.all(-rp - 0.1 < dB(h[w <= wp]))
+        assert np.all(dB(h[ws <= w]) < -rs + 0.1)
+
+        assert N == 5
+        xp_assert_close(Wn, xp.asarray(0.2), rtol=1e-15, check_0d=False)
+
+    def test_lowpass_1000dB(self, xp):
+        # failed when ellipkm1 wasn't used in ellipord and ellipap
+        wp = 0.2
+        ws = 0.3
+        rp = 3
+        rs = 1000
+        N, Wn = ellipord(wp, xp.asarray(ws), rp, rs, False)
+        sos = ellip(N, rp, rs, _xp_copy_to_numpy(Wn), 'lp', False, output='sos')
+        w, h = freqz_sos(sos)
+        w /= np.pi
+        assert np.all(-rp - 0.1 < dB(h[w <= wp]))
+        assert np.all(dB(h[ws <= w]) < -rs + 0.1)
+        assert array_namespace(Wn) == xp
+
+    def test_highpass(self, xp):
+        wp = 0.3
+        ws = 0.2
+        rp = 3
+        rs = 70
+        N, Wn = ellipord(wp, xp.asarray(ws), rp, rs, False)
+        b, a = ellip(N, rp, rs, _xp_copy_to_numpy(Wn), 'hp', False)
+        w, h = freqz(b, a)
+        w /= np.pi
+        assert np.all(-rp - 0.1 < dB(h[wp <= w]))
+        assert np.all(dB(h[w <= ws]) < -rs + 0.1)
+
+        assert N == 6
+        xp_assert_close(Wn, xp.asarray(0.3), rtol=1e-15, check_0d=False)
+        assert array_namespace(Wn) == xp
+
+    def test_bandpass(self, xp):
+        wp = [0.2, 0.5]
+        ws = [0.1, 0.6]
+        rp = 3
+        rs = 80
+        N, Wn = ellipord(xp.asarray(wp), xp.asarray(ws), rp, rs, False)
+        b, a = ellip(N, rp, rs, _xp_copy_to_numpy(Wn), 'bp', False)
+        w, h = freqz(b, a)
+        w /= np.pi
+        assert np.all(-rp - 0.1 < dB(h[np.logical_and(wp[0] <= w, w <= wp[1])]))
+        assert np.all(dB(h[np.logical_or(w <= ws[0], ws[1] <= w)]) < -rs + 0.1)
+
+        assert N == 6
+        xp_assert_close(Wn, xp.asarray([0.2, 0.5]), rtol=1e-15)
+
+    @skip_xp_backends(
+        cpu_only=True, exceptions=["cupy"], reason="optimize.fminbound"
+    )
+    def test_bandstop(self, xp):
+        wp = [0.1, 0.6]
+        ws = [0.2, 0.5]
+        rp = 3
+        rs = 90
+        N, Wn = ellipord(xp.asarray(wp), xp.asarray(ws), rp, rs, False)
+        b, a = ellip(N, rp, rs, _xp_copy_to_numpy(Wn), 'bs', False)
+        w, h = freqz(b, a)
+        w /= np.pi
+        assert np.all(-rp - 0.1 < dB(h[np.logical_or(w <= wp[0], wp[1] <= w)]))
+        assert np.all(dB(h[np.logical_and(ws[0] <= w, w <= ws[1])]) < -rs + 0.1)
+
+        assert N == 7
+        xp_assert_close(Wn, xp.asarray([0.14758232794342988, 0.6]), rtol=1e-5)
+
+    def test_analog(self, xp):
+        wp = [1000.0, 6000]
+        ws = [2000.0, 5000]
+        rp = 3
+        rs = 90
+        N, Wn = ellipord(xp.asarray(wp), xp.asarray(ws), rp, rs, True)
+        b, a = ellip(N, rp, rs, _xp_copy_to_numpy(Wn), 'bs', True)
+        w, h = freqs(b, a)
+        assert np.all(-rp - 0.1 < dB(h[np.logical_or(w <= wp[0], wp[1] <= w)]))
+        assert np.all(dB(h[np.logical_and(ws[0] <= w, w <= ws[1])]) < -rs + 0.1)
+
+        assert N == 8
+        xp_assert_close(Wn, xp.asarray([1666.6666, 6000]))
+
+        assert ellipord(xp.asarray(1), 1.2, 1, 80, analog=True)[0] == 9
+
+    def test_fs_param(self, xp):
+        wp = [400.0, 2400]
+        ws = [800.0, 2000]
+        rp = 3
+        rs = 90
+        fs = 8000
+        N, Wn = ellipord(xp.asarray(wp), xp.asarray(ws), rp, rs, False, fs=fs)
+        b, a = ellip(N, rp, rs, _xp_copy_to_numpy(Wn), 'bs', False, fs=fs)
+        w, h = freqz(b, a, fs=fs)
+        assert np.all(-rp - 0.1 < dB(h[np.logical_or(w <= wp[0], wp[1] <= w)]))
+        assert np.all(dB(h[np.logical_and(ws[0] <= w, w <= ws[1])]) < -rs + 0.1)
+
+        assert N == 7
+        xp_assert_close(Wn, xp.asarray([590.3293117737195, 2400]), rtol=1e-5)
+
+    def test_invalid_input(self):
+        with pytest.raises(ValueError) as exc_info:
+            ellipord(0.2, 0.5, 3, 2)
+        assert "gpass should be smaller than gstop" in str(exc_info.value)
+
+        with pytest.raises(ValueError) as exc_info:
+            ellipord(0.2, 0.5, -1, 2)
+        assert "gpass should be larger than 0.0" in str(exc_info.value)
+
+        with pytest.raises(ValueError) as exc_info:
+            ellipord(0.2, 0.5, 1, -2)
+        assert "gstop should be larger than 0.0" in str(exc_info.value)
+
+    def test_ellip_butter(self, xp):
+        # The purpose of the test is to compare to some known output from past
+        # scipy versions. The values to compare to are generated with scipy
+        # 1.9.1 (there is nothing special about this particular version though)
+        n, Wn = ellipord(xp.asarray([0.1, 0.6]), xp.asarray([0.2, 0.5]), 3, 60)
+        assert array_namespace(Wn) == xp
+        assert n == 5
+
+    def test_fs_validation(self):
+        wp = 0.2
+        ws = 0.3
+        rp = 3
+        rs = 60
+
+        with pytest.raises(ValueError, match="Sampling.*single scalar"):
+            ellipord(wp, ws, rp, rs, False, fs=np.array([10, 20]))
+
+
+# Currently the filter functions tested below (bessel, butter, cheby1, cheby2,
+# and ellip) all return float64 (or complex128) output regardless of input
+# dtype. Therefore reference arrays in these tests are all given an explicit 64
+# bit dtype, because the output will not match the xp_default_dtype when the
+# default dtype is float32. Although the output arrays and all internal
+# calculations are in 64 bit precision, tolerances are still loosened for the
+# float32 case when results are impacted by reduced precision in the inputs.
+
+
+@skip_xp_backends("dask.array", reason="https://github.com/dask/dask/issues/11883")
+@make_xp_test_case(bessel)
+class TestBessel:
+
+    def test_degenerate(self, xp):
+        for norm in ('delay', 'phase', 'mag'):
+            # 0-order filter is just a passthrough
+            b, a = bessel(0, xp.asarray(1), analog=True, norm=norm)
+            xp_assert_equal(b, xp.asarray([1.0], dtype=xp.float64))
+            xp_assert_equal(a, xp.asarray([1.0], dtype=xp.float64))
+
+            # 1-order filter is same for all types
+            b, a = bessel(1, xp.asarray(1.), analog=True, norm=norm)
+
+            xp_assert_close(b, xp.asarray([1.0], dtype=xp.float64), rtol=1e-15)
+            xp_assert_close(a, xp.asarray([1.0, 1], dtype=xp.float64), rtol=1e-15)
+
+            z, p, k = bessel(1, xp.asarray(0.3), analog=True, output='zpk', norm=norm)
+            xp_assert_equal(z, xp.asarray([], dtype=xp.float64))
+            xp_assert_close(
+                p, xp.asarray([-0.3+0j], dtype=xp.complex128),
+                rtol=1e-14 if not DEFAULT_F32 else 1e-7
+            )
+            assert math.isclose(
+                k, 0.3, rel_tol=1e-14 if not DEFAULT_F32 else 1e-6
+            )
+
+    @pytest.mark.xfail(reason="Failing in mypy workflow - see gh-23902")
+    def test_high_order(self, xp):
+        # high even order, 'phase'
+        z, p, k = bessel(24, xp.asarray(100), analog=True, output='zpk')
+        z2 = xp.asarray([], dtype=xp.float64)
+        p2 = [
+             -9.055312334014323e+01 + 4.844005815403969e+00j,
+             -8.983105162681878e+01 + 1.454056170018573e+01j,
+             -8.837357994162065e+01 + 2.426335240122282e+01j,
+             -8.615278316179575e+01 + 3.403202098404543e+01j,
+             -8.312326467067703e+01 + 4.386985940217900e+01j,
+             -7.921695461084202e+01 + 5.380628489700191e+01j,
+             -7.433392285433246e+01 + 6.388084216250878e+01j,
+             -6.832565803501586e+01 + 7.415032695116071e+01j,
+             -6.096221567378025e+01 + 8.470292433074425e+01j,
+             -5.185914574820616e+01 + 9.569048385258847e+01j,
+             -4.027853855197555e+01 + 1.074195196518679e+02j,
+             -2.433481337524861e+01 + 1.207298683731973e+02j,
+             ]
+
+        p2 = np.union1d(p2, np.conj(p2))
+        p2 = xp.asarray(p2, dtype=xp.complex128)
+        k2 = 9.999999999999989e+47
+        xp_assert_equal(z, z2)
+        xp_assert_close(_sort_cmplx(p, xp=xp),
+                        _sort_cmplx(p2, xp=xp))
+        assert math.isclose(k, k2, rel_tol=1e-14)
+
+        # high odd order, 'phase'
+        z, p, k = bessel(23, xp.asarray(1000.), analog=True, output='zpk')
+        z2 = xp.asarray([], dtype=xp.float64)
+        p2 = [
+             -2.497697202208956e+02 + 1.202813187870698e+03j,
+             -4.126986617510172e+02 + 1.065328794475509e+03j,
+             -5.304922463809596e+02 + 9.439760364018479e+02j,
+             -9.027564978975828e+02 + 1.010534334242318e+02j,
+             -8.909283244406079e+02 + 2.023024699647598e+02j,
+             -8.709469394347836e+02 + 3.039581994804637e+02j,
+             -8.423805948131370e+02 + 4.062657947488952e+02j,
+             -8.045561642249877e+02 + 5.095305912401127e+02j,
+             -7.564660146766259e+02 + 6.141594859516342e+02j,
+             -6.965966033906477e+02 + 7.207341374730186e+02j,
+             -6.225903228776276e+02 + 8.301558302815096e+02j,
+             -9.066732476324988e+02]
+        p2 = np.union1d(p2, np.conj(p2))
+        p2 = xp.asarray(p2, dtype=xp.complex128)
+        k2 = 9.999999999999983e+68
+        xp_assert_equal(z, z2)
+        xp_assert_close(_sort_cmplx(p, xp=xp),
+                        _sort_cmplx(p2, xp=xp))
+        assert math.isclose(k, k2, rel_tol=1e-14)
+
+        # high even order, 'delay' (Orchard 1965 "The Roots of the
+        # Maximally Flat-Delay Polynomials" Table 1)
+        z, p, k = bessel(31, xp.asarray(1.), analog=True, output='zpk', norm='delay')
+        p2 = [-20.876706,
+              -20.826543 + 1.735732j,
+              -20.675502 + 3.473320j,
+              -20.421895 + 5.214702j,
+              -20.062802 + 6.961982j,
+              -19.593895 + 8.717546j,
+              -19.009148 + 10.484195j,
+              -18.300400 + 12.265351j,
+              -17.456663 + 14.065350j,
+              -16.463032 + 15.889910j,
+              -15.298849 + 17.746914j,
+              -13.934466 + 19.647827j,
+              -12.324914 + 21.610519j,
+              -10.395893 + 23.665701j,
+              - 8.005600 + 25.875019j,
+              - 4.792045 + 28.406037j,
+              ]
+        p2 = np.union1d(p2, np.conj(p2))
+        p2 = xp.asarray(p2, dtype=xp.complex128)
+        xp_assert_close(_sort_cmplx(p, xp=xp),
+                        _sort_cmplx(p2, xp=xp))
+
+        # high odd order, 'delay'
+        z, p, k = bessel(30, xp.asarray(1.), analog=True, output='zpk', norm='delay')
+        p2 = [-20.201029 + 0.867750j,
+              -20.097257 + 2.604235j,
+              -19.888485 + 4.343721j,
+              -19.572188 + 6.088363j,
+              -19.144380 + 7.840570j,
+              -18.599342 + 9.603147j,
+              -17.929195 + 11.379494j,
+              -17.123228 + 13.173901j,
+              -16.166808 + 14.992008j,
+              -15.039580 + 16.841580j,
+              -13.712245 + 18.733902j,
+              -12.140295 + 20.686563j,
+              -10.250119 + 22.729808j,
+              - 7.901170 + 24.924391j,
+              - 4.734679 + 27.435615j,
+              ]
+        p2 = np.union1d(p2, np.conj(p2))
+        p2 = xp.asarray(p2, dtype=xp.complex128)
+        xp_assert_close(_sort_cmplx(p, xp=xp),
+                        _sort_cmplx(p2, xp=xp))
+
+    def test_refs(self, xp):
+        # Compare to http://www.crbond.com/papers/bsf2.pdf
+        # "Delay Normalized Bessel Polynomial Coefficients"
+        bond_b = xp.asarray([10395.0], dtype=xp.float64)
+        bond_a = xp.asarray([1.0, 21, 210, 1260, 4725, 10395, 10395], dtype=xp.float64)
+        b, a = bessel(6, xp.asarray(1.0), norm='delay', analog=True)
+        xp_assert_close(b, bond_b)
+        xp_assert_close(a, bond_a)
+
+        # "Delay Normalized Bessel Pole Locations"
+        bond_poles = {
+            1: [-1.0000000000],
+            2: [-1.5000000000 + 0.8660254038j],
+            3: [-1.8389073227 + 1.7543809598j, -2.3221853546],
+            4: [-2.1037893972 + 2.6574180419j, -2.8962106028 + 0.8672341289j],
+            5: [-2.3246743032 + 3.5710229203j, -3.3519563992 + 1.7426614162j,
+                -3.6467385953],
+            6: [-2.5159322478 + 4.4926729537j, -3.7357083563 + 2.6262723114j,
+                -4.2483593959 + 0.8675096732j],
+            7: [-2.6856768789 + 5.4206941307j, -4.0701391636 + 3.5171740477j,
+                -4.7582905282 + 1.7392860611j, -4.9717868585],
+            8: [-2.8389839489 + 6.3539112986j, -4.3682892172 + 4.4144425005j,
+                -5.2048407906 + 2.6161751526j, -5.5878860433 + 0.8676144454j],
+            9: [-2.9792607982 + 7.2914636883j, -4.6384398872 + 5.3172716754j,
+                -5.6044218195 + 3.4981569179j, -6.1293679043 + 1.7378483835j,
+                -6.2970191817],
+            10: [-3.1089162336 + 8.2326994591j, -4.8862195669 + 6.2249854825j,
+                 -5.9675283286 + 4.3849471889j, -6.6152909655 + 2.6115679208j,
+                 -6.9220449054 + 0.8676651955j]
+            }
+
+        for N in range(1, 11):
+            p1 = np.sort(bond_poles[N])
+            z, p, k = besselap(N, 'delay', xp=xp)
+            assert array_namespace(z) == array_namespace(p) == xp
+            p2 = np.sort(np.concatenate(_cplxreal(_xp_copy_to_numpy(p))))
+            assert_array_almost_equal(xp.asarray(p2), xp.asarray(p1), decimal=10)
+
+        # "Frequency Normalized Bessel Pole Locations"
+        bond_poles = {
+            1: [-1.0000000000],
+            2: [-1.1016013306 + 0.6360098248j],
+            3: [-1.0474091610 + 0.9992644363j, -1.3226757999],
+            4: [-0.9952087644 + 1.2571057395j, -1.3700678306 + 0.4102497175j],
+            5: [-0.9576765486 + 1.4711243207j, -1.3808773259 + 0.7179095876j,
+                -1.5023162714],
+            6: [-0.9306565229 + 1.6618632689j, -1.3818580976 + 0.9714718907j,
+                -1.5714904036 + 0.3208963742j],
+            7: [-0.9098677806 + 1.8364513530j, -1.3789032168 + 1.1915667778j,
+                -1.6120387662 + 0.5892445069j, -1.6843681793],
+            8: [-0.8928697188 + 1.9983258436j, -1.3738412176 + 1.3883565759j,
+                -1.6369394181 + 0.8227956251j, -1.7574084004 + 0.2728675751j],
+            9: [-0.8783992762 + 2.1498005243j, -1.3675883098 + 1.5677337122j,
+                -1.6523964846 + 1.0313895670j, -1.8071705350 + 0.5123837306j,
+                -1.8566005012],
+            10: [-0.8657569017 + 2.2926048310j, -1.3606922784 + 1.7335057427j,
+                 -1.6618102414 + 1.2211002186j, -1.8421962445 + 0.7272575978j,
+                 -1.9276196914 + 0.2416234710j]
+            }
+
+        for N in range(1, 11):
+            p1 = np.sort(bond_poles[N])
+            z, p, k = besselap(N, 'mag', xp=xp)
+            assert array_namespace(z) == array_namespace(p) == xp
+            p2 = np.sort(np.concatenate(_cplxreal(_xp_copy_to_numpy(p))))
+            assert_array_almost_equal(xp.asarray(p2), xp.asarray(p1), decimal=10)
+
+        # Compare to https://www.ranecommercial.com/legacy/note147.html
+        # "Table 1 - Bessel Crossovers of Second, Third, and Fourth-Order"
+        a = xp.asarray([1, 1, 1/3], dtype=xp.float64)
+        b2, a2 = bessel(2, xp.asarray(1.), norm='delay', analog=True)
+        xp_assert_close(a2/b2, xp.flip(a))
+
+        a = xp.asarray([1, 1, 2/5, 1/15], dtype=xp.float64)
+        b2, a2 = bessel(3, xp.asarray(1.), norm='delay', analog=True)
+        xp_assert_close(a2/b2, xp.flip(a))
+
+        a = xp.asarray([1, 1, 9/21, 2/21, 1/105], dtype=xp.float64)
+        b2, a2 = bessel(4, xp.asarray(1.), norm='delay', analog=True)
+        xp_assert_close(a2/b2, xp.flip(a))
+
+        a = xp.asarray([1, math.sqrt(3), 1], dtype=xp.float64)
+        b2, a2 = bessel(2, xp.asarray(1.), norm='phase', analog=True)
+        xp_assert_close(a2/b2, xp.flip(a))
+
+        # TODO: Why so inaccurate?  Is reference flawed?
+        a = xp.asarray([1, 2.481, 2.463, 1.018], dtype=xp.float64)
+        b2, a2 = bessel(3, xp.asarray(1.), norm='phase', analog=True)
+        assert_array_almost_equal(a2/b2, xp.flip(a), decimal=1)
+
+        # TODO: Why so inaccurate?  Is reference flawed?
+        a = xp.asarray([1, 3.240, 4.5, 3.240, 1.050], dtype=xp.float64)
+        b2, a2 = bessel(4, xp.asarray(1.), norm='phase', analog=True)
+        assert_array_almost_equal(a2/b2, xp.flip(a), decimal=1)
+
+        # Table of -3 dB factors:
+        N, scale = 2, xp.asarray([1.272, 1.272], dtype=xp.complex128)
+        scale2 = besselap(N, 'mag', xp=xp)[1] / besselap(N, 'phase', xp=xp)[1]
+        assert_array_almost_equal(scale2, scale, decimal=3)
+
+        # TODO: Why so inaccurate?  Is reference flawed?
+        N, scale = 3, xp.asarray([1.413, 1.413, 1.413], dtype=xp.complex128)
+        scale2 = besselap(N, 'mag', xp=xp)[1] / besselap(N, 'phase', xp=xp)[1]
+        assert_array_almost_equal(scale2, scale, decimal=2)
+
+        # TODO: Why so inaccurate?  Is reference flawed?
+        N, scale = 4, xp.asarray([1.533]*4, dtype=xp.complex128)
+        scale2 = besselap(N, 'mag', xp=xp)[1] / besselap(N, 'phase', xp=xp)[1]
+        assert_array_almost_equal(scale2, scale, decimal=1)
+
+    @pytest.mark.xfail(reason="Failing in mypy workflow - see gh-23902")
+    def test_hardcoded(self, xp):
+        # Compare to values from original hardcoded implementation
+        originals = {
+            0: [],
+            1: [-1],
+            2: [-.8660254037844386467637229 + .4999999999999999999999996j],
+            3: [-.9416000265332067855971980,
+                -.7456403858480766441810907 + .7113666249728352680992154j],
+            4: [-.6572111716718829545787788 + .8301614350048733772399715j,
+                -.9047587967882449459642624 + .2709187330038746636700926j],
+            5: [-.9264420773877602247196260,
+                -.8515536193688395541722677 + .4427174639443327209850002j,
+                -.5905759446119191779319432 + .9072067564574549539291747j],
+            6: [-.9093906830472271808050953 + .1856964396793046769246397j,
+                -.7996541858328288520243325 + .5621717346937317988594118j,
+                -.5385526816693109683073792 + .9616876881954277199245657j],
+            7: [-.9194871556490290014311619,
+                -.8800029341523374639772340 + .3216652762307739398381830j,
+                -.7527355434093214462291616 + .6504696305522550699212995j,
+                -.4966917256672316755024763 + 1.002508508454420401230220j],
+            8: [-.9096831546652910216327629 + .1412437976671422927888150j,
+                -.8473250802359334320103023 + .4259017538272934994996429j,
+                -.7111381808485399250796172 + .7186517314108401705762571j,
+                -.4621740412532122027072175 + 1.034388681126901058116589j],
+            9: [-.9154957797499037686769223,
+                -.8911217017079759323183848 + .2526580934582164192308115j,
+                -.8148021112269012975514135 + .5085815689631499483745341j,
+                -.6743622686854761980403401 + .7730546212691183706919682j,
+                -.4331415561553618854685942 + 1.060073670135929666774323j],
+            10: [-.9091347320900502436826431 + .1139583137335511169927714j,
+                 -.8688459641284764527921864 + .3430008233766309973110589j,
+                 -.7837694413101441082655890 + .5759147538499947070009852j,
+                 -.6417513866988316136190854 + .8175836167191017226233947j,
+                 -.4083220732868861566219785 + 1.081274842819124562037210j],
+            11: [-.9129067244518981934637318,
+                 -.8963656705721166099815744 + .2080480375071031919692341j,
+                 -.8453044014712962954184557 + .4178696917801248292797448j,
+                 -.7546938934722303128102142 + .6319150050721846494520941j,
+                 -.6126871554915194054182909 + .8547813893314764631518509j,
+                 -.3868149510055090879155425 + 1.099117466763120928733632j],
+            12: [-.9084478234140682638817772 + 95506365213450398415258360e-27j,
+                 -.8802534342016826507901575 + .2871779503524226723615457j,
+                 -.8217296939939077285792834 + .4810212115100676440620548j,
+                 -.7276681615395159454547013 + .6792961178764694160048987j,
+                 -.5866369321861477207528215 + .8863772751320727026622149j,
+                 -.3679640085526312839425808 + 1.114373575641546257595657j],
+            13: [-.9110914665984182781070663,
+                 -.8991314665475196220910718 + .1768342956161043620980863j,
+                 -.8625094198260548711573628 + .3547413731172988997754038j,
+                 -.7987460692470972510394686 + .5350752120696801938272504j,
+                 -.7026234675721275653944062 + .7199611890171304131266374j,
+                 -.5631559842430199266325818 + .9135900338325109684927731j,
+                 -.3512792323389821669401925 + 1.127591548317705678613239j],
+            14: [-.9077932138396487614720659 + 82196399419401501888968130e-27j,
+                 -.8869506674916445312089167 + .2470079178765333183201435j,
+                 -.8441199160909851197897667 + .4131653825102692595237260j,
+                 -.7766591387063623897344648 + .5819170677377608590492434j,
+                 -.6794256425119233117869491 + .7552857305042033418417492j,
+                 -.5418766775112297376541293 + .9373043683516919569183099j,
+                 -.3363868224902037330610040 + 1.139172297839859991370924j],
+            15: [-.9097482363849064167228581,
+                 -.9006981694176978324932918 + .1537681197278439351298882j,
+                 -.8731264620834984978337843 + .3082352470564267657715883j,
+                 -.8256631452587146506294553 + .4642348752734325631275134j,
+                 -.7556027168970728127850416 + .6229396358758267198938604j,
+                 -.6579196593110998676999362 + .7862895503722515897065645j,
+                 -.5224954069658330616875186 + .9581787261092526478889345j,
+                 -.3229963059766444287113517 + 1.149416154583629539665297j],
+            16: [-.9072099595087001356491337 + 72142113041117326028823950e-27j,
+                 -.8911723070323647674780132 + .2167089659900576449410059j,
+                 -.8584264231521330481755780 + .3621697271802065647661080j,
+                 -.8074790293236003885306146 + .5092933751171800179676218j,
+                 -.7356166304713115980927279 + .6591950877860393745845254j,
+                 -.6379502514039066715773828 + .8137453537108761895522580j,
+                 -.5047606444424766743309967 + .9767137477799090692947061j,
+                 -.3108782755645387813283867 + 1.158552841199330479412225j],
+            17: [-.9087141161336397432860029,
+                 -.9016273850787285964692844 + .1360267995173024591237303j,
+                 -.8801100704438627158492165 + .2725347156478803885651973j,
+                 -.8433414495836129204455491 + .4100759282910021624185986j,
+                 -.7897644147799708220288138 + .5493724405281088674296232j,
+                 -.7166893842372349049842743 + .6914936286393609433305754j,
+                 -.6193710717342144521602448 + .8382497252826992979368621j,
+                 -.4884629337672704194973683 + .9932971956316781632345466j,
+                 -.2998489459990082015466971 + 1.166761272925668786676672j],
+            18: [-.9067004324162775554189031 + 64279241063930693839360680e-27j,
+                 -.8939764278132455733032155 + .1930374640894758606940586j,
+                 -.8681095503628830078317207 + .3224204925163257604931634j,
+                 -.8281885016242836608829018 + .4529385697815916950149364j,
+                 -.7726285030739558780127746 + .5852778162086640620016316j,
+                 -.6987821445005273020051878 + .7204696509726630531663123j,
+                 -.6020482668090644386627299 + .8602708961893664447167418j,
+                 -.4734268069916151511140032 + 1.008234300314801077034158j,
+                 -.2897592029880489845789953 + 1.174183010600059128532230j],
+            19: [-.9078934217899404528985092,
+                 -.9021937639390660668922536 + .1219568381872026517578164j,
+                 -.8849290585034385274001112 + .2442590757549818229026280j,
+                 -.8555768765618421591093993 + .3672925896399872304734923j,
+                 -.8131725551578197705476160 + .4915365035562459055630005j,
+                 -.7561260971541629355231897 + .6176483917970178919174173j,
+                 -.6818424412912442033411634 + .7466272357947761283262338j,
+                 -.5858613321217832644813602 + .8801817131014566284786759j,
+                 -.4595043449730988600785456 + 1.021768776912671221830298j,
+                 -.2804866851439370027628724 + 1.180931628453291873626003j],
+            20: [-.9062570115576771146523497 + 57961780277849516990208850e-27j,
+                 -.8959150941925768608568248 + .1740317175918705058595844j,
+                 -.8749560316673332850673214 + .2905559296567908031706902j,
+                 -.8427907479956670633544106 + .4078917326291934082132821j,
+                 -.7984251191290606875799876 + .5264942388817132427317659j,
+                 -.7402780309646768991232610 + .6469975237605228320268752j,
+                 -.6658120544829934193890626 + .7703721701100763015154510j,
+                 -.5707026806915714094398061 + .8982829066468255593407161j,
+                 -.4465700698205149555701841 + 1.034097702560842962315411j,
+                 -.2719299580251652601727704 + 1.187099379810885886139638j],
+            21: [-.9072262653142957028884077,
+                 -.9025428073192696303995083 + .1105252572789856480992275j,
+                 -.8883808106664449854431605 + .2213069215084350419975358j,
+                 -.8643915813643204553970169 + .3326258512522187083009453j,
+                 -.8299435470674444100273463 + .4448177739407956609694059j,
+                 -.7840287980408341576100581 + .5583186348022854707564856j,
+                 -.7250839687106612822281339 + .6737426063024382240549898j,
+                 -.6506315378609463397807996 + .7920349342629491368548074j,
+                 -.5564766488918562465935297 + .9148198405846724121600860j,
+                 -.4345168906815271799687308 + 1.045382255856986531461592j,
+                 -.2640041595834031147954813 + 1.192762031948052470183960j],
+            22: [-.9058702269930872551848625 + 52774908289999045189007100e-27j,
+                 -.8972983138153530955952835 + .1584351912289865608659759j,
+                 -.8799661455640176154025352 + .2644363039201535049656450j,
+                 -.8534754036851687233084587 + .3710389319482319823405321j,
+                 -.8171682088462720394344996 + .4785619492202780899653575j,
+                 -.7700332930556816872932937 + .5874255426351153211965601j,
+                 -.7105305456418785989070935 + .6982266265924524000098548j,
+                 -.6362427683267827226840153 + .8118875040246347267248508j,
+                 -.5430983056306302779658129 + .9299947824439872998916657j,
+                 -.4232528745642628461715044 + 1.055755605227545931204656j,
+                 -.2566376987939318038016012 + 1.197982433555213008346532j],
+            23: [-.9066732476324988168207439,
+                 -.9027564979912504609412993 + .1010534335314045013252480j,
+                 -.8909283242471251458653994 + .2023024699381223418195228j,
+                 -.8709469395587416239596874 + .3039581993950041588888925j,
+                 -.8423805948021127057054288 + .4062657948237602726779246j,
+                 -.8045561642053176205623187 + .5095305912227258268309528j,
+                 -.7564660146829880581478138 + .6141594859476032127216463j,
+                 -.6965966033912705387505040 + .7207341374753046970247055j,
+                 -.6225903228771341778273152 + .8301558302812980678845563j,
+                 -.5304922463810191698502226 + .9439760364018300083750242j,
+                 -.4126986617510148836149955 + 1.065328794475513585531053j,
+                 -.2497697202208956030229911 + 1.202813187870697831365338j],
+            24: [-.9055312363372773709269407 + 48440066540478700874836350e-27j,
+                 -.8983105104397872954053307 + .1454056133873610120105857j,
+                 -.8837358034555706623131950 + .2426335234401383076544239j,
+                 -.8615278304016353651120610 + .3403202112618624773397257j,
+                 -.8312326466813240652679563 + .4386985933597305434577492j,
+                 -.7921695462343492518845446 + .5380628490968016700338001j,
+                 -.7433392285088529449175873 + .6388084216222567930378296j,
+                 -.6832565803536521302816011 + .7415032695091650806797753j,
+                 -.6096221567378335562589532 + .8470292433077202380020454j,
+                 -.5185914574820317343536707 + .9569048385259054576937721j,
+                 -.4027853855197518014786978 + 1.074195196518674765143729j,
+                 -.2433481337524869675825448 + 1.207298683731972524975429j],
+            25: [-.9062073871811708652496104,
+                 -.9028833390228020537142561 + 93077131185102967450643820e-27j,
+                 -.8928551459883548836774529 + .1863068969804300712287138j,
+                 -.8759497989677857803656239 + .2798521321771408719327250j,
+                 -.8518616886554019782346493 + .3738977875907595009446142j,
+                 -.8201226043936880253962552 + .4686668574656966589020580j,
+                 -.7800496278186497225905443 + .5644441210349710332887354j,
+                 -.7306549271849967721596735 + .6616149647357748681460822j,
+                 -.6704827128029559528610523 + .7607348858167839877987008j,
+                 -.5972898661335557242320528 + .8626676330388028512598538j,
+                 -.5073362861078468845461362 + .9689006305344868494672405j,
+                 -.3934529878191079606023847 + 1.082433927173831581956863j,
+                 -.2373280669322028974199184 + 1.211476658382565356579418j],
+            }
+        for N in originals:
+            p1 = xp.asarray(
+                np.union1d(originals[N], np.conj(originals[N])),
+                dtype=xp.complex128
+            )
+            p2 = besselap(N, xp=xp)[1]
+            xp_assert_close(_sort_cmplx(p2, xp=xp),
+                            _sort_cmplx(p1, xp=xp), rtol=1e-14)
+
+    def test_norm_phase(self, xp):
+        # Test some orders and frequencies and see that they have the right
+        # phase at w0
+        if is_torch(xp) and DEFAULT_F32:
+            pytest.xfail(reason="inaccurate on torch with float32")
+        for N in (1, 2, 3, 4, 5, 51, 72):
+            for w0 in (1, 100):
+                b, a = bessel(N, xp.asarray(w0), analog=True, norm='phase')
+                assert array_namespace(b) == array_namespace(a) == xp
+                w = np.linspace(0, w0, 100)
+                w, h = freqs(_xp_copy_to_numpy(b), _xp_copy_to_numpy(a), w)
+                phase = np.unwrap(np.angle(h))
+                xp_assert_close(
+                    xp.asarray(phase[[0, -1]], dtype=xp.float64),
+                    xp.asarray([0, -N*xp.pi/4], dtype=xp.float64), rtol=1e-1
+                )
+
+    def test_norm_mag(self, xp):
+        # Test some orders and frequencies and see that they have the right
+        # mag at w0
+        if DEFAULT_F32 and is_torch(xp):
+            pytest.skip(reason="overflow occurs with float32 on torch")
+        for N in (1, 2, 3, 4, 5, 51, 72):
+            for w0 in (1, 100):
+                b, a = bessel(N, xp.asarray(w0), analog=True, norm='mag')
+                assert array_namespace(b) == array_namespace(a) == xp
+                w = [0.0, w0]
+                w, h = freqs(_xp_copy_to_numpy(b), _xp_copy_to_numpy(a), w)
+                mag = np.abs(h)
+                xp_assert_close(
+                    xp.asarray(mag), xp.asarray([1, 1/math.sqrt(2)], dtype=xp.float64)
+                )
+
+    def test_norm_delay(self, xp):
+        # Test some orders and frequencies and see that they have the right
+        # delay at DC
+        if DEFAULT_F32 and is_torch(xp):
+            pytest.skip(reason="overflow occurs with float32 on torch")
+        for N in (1, 2, 3, 4, 5, 51, 72):
+            for w0 in (1, 100):
+                b, a = bessel(N, xp.asarray(w0), analog=True, norm='delay')
+                w = np.linspace(0, 10*w0, 1000)
+                w, h = freqs(_xp_copy_to_numpy(b), _xp_copy_to_numpy(a), w)
+                unwr_h = np.unwrap(np.angle(h))
+                delay = -np.diff(unwr_h) / np.diff(w)
+                assert math.isclose(delay[0], 1/w0, rel_tol=1e-4)
+
+    def test_norm_factor(self):
+        mpmath_values = {
+            1: 1.0, 2: 1.361654128716130520, 3: 1.755672368681210649,
+            4: 2.113917674904215843, 5: 2.427410702152628137,
+            6: 2.703395061202921876, 7: 2.951722147038722771,
+            8: 3.179617237510651330, 9: 3.391693138911660101,
+            10: 3.590980594569163482, 11: 3.779607416439620092,
+            12: 3.959150821144285315, 13: 4.130825499383535980,
+            14: 4.295593409533637564, 15: 4.454233021624377494,
+            16: 4.607385465472647917, 17: 4.755586548961147727,
+            18: 4.899289677284488007, 19: 5.038882681488207605,
+            20: 5.174700441742707423, 21: 5.307034531360917274,
+            22: 5.436140703250035999, 23: 5.562244783787878196,
+            24: 5.685547371295963521, 25: 5.806227623775418541,
+            50: 8.268963160013226298, 51: 8.352374541546012058,
+            }
+        for N in mpmath_values:
+            z, p, k = besselap(N, 'delay')
+            xp_assert_close(_norm_factor(p, k), mpmath_values[N], rtol=1e-13)
+
+    def test_bessel_poly(self):
+        xp_assert_equal(_bessel_poly(5), [945, 945, 420, 105, 15, 1])
+        xp_assert_equal(_bessel_poly(4, True), [1, 10, 45, 105, 105])
+
+    def test_bessel_zeros(self):
+        xp_assert_equal(_bessel_zeros(0), [])
+
+    def test_invalid(self):
+        assert_raises(ValueError, besselap, 5, 'nonsense')
+        assert_raises(ValueError, besselap, -5)
+        assert_raises(ValueError, besselap, 3.2)
+        assert_raises(ValueError, _bessel_poly, -3)
+        assert_raises(ValueError, _bessel_poly, 3.3)
+
+    @pytest.mark.fail_slow(10)
+    def test_fs_param(self):
+        for norm in ('phase', 'mag', 'delay'):
+            for fs in (900, 900.1, 1234.567):
+                for N in (0, 1, 2, 3, 10):
+                    for fc in (100, 100.1, 432.12345):
+                        for btype in ('lp', 'hp'):
+                            ba1 = bessel(N, fc, btype, norm=norm, fs=fs)
+                            ba2 = bessel(N, fc/(fs/2), btype, norm=norm)
+                            for ba1_, ba2_ in zip(ba1, ba2):
+                                xp_assert_close(ba1_, ba2_)
+                    for fc in ((100, 200), (100.1, 200.2), (321.123, 432.123)):
+                        for btype in ('bp', 'bs'):
+                            ba1 = bessel(N, fc, btype, norm=norm, fs=fs)
+                            for seq in (list, tuple, array):
+                                fcnorm = seq([f/(fs/2) for f in fc])
+                                ba2 = bessel(N, fcnorm, btype, norm=norm)
+                                for ba1_, ba2_ in zip(ba1, ba2):
+                                    xp_assert_close(ba1_, ba2_)
+
+
+@skip_xp_backends("dask.array", reason="https://github.com/dask/dask/issues/11883")
+@make_xp_test_case(butter)
+class TestButter:
+
+    def test_degenerate(self, xp):
+        # 0-order filter is just a passthrough
+        b, a = butter(0, xp.asarray(1), analog=True)
+        xp_assert_equal(b, xp.asarray([1.0], dtype=xp.float64))
+        xp_assert_equal(a, xp.asarray([1.0], dtype=xp.float64))
+
+        # 1-order filter is same for all types
+        b, a = butter(1, xp.asarray(1), analog=True)
+        assert_array_almost_equal(b, xp.asarray([1.0], dtype=xp.float64))
+        assert_array_almost_equal(a, xp.asarray([1.0, 1.0], dtype=xp.float64))
+
+        z, p, k = butter(1, xp.asarray(0.3), output='zpk')
+        xp_assert_equal(z, xp.asarray([-1.0], dtype=xp.float64))
+        xp_assert_close(
+            p,
+            xp.asarray([3.249196962329063e-01 + 0j], dtype=xp.complex128),
+            rtol=1e-14 if not DEFAULT_F32 else 1e-7
+        )
+        assert math.isclose(
+            k, 3.375401518835469e-01, rel_tol=1e-14 if not DEFAULT_F32 else 1e-7
+        )
+
+    def test_basic(self, xp):
+        # analog s-plane
+        for N in range(25):
+            wn = 0.01
+            z, p, k = butter(N, xp.asarray(wn), 'low', analog=True, output='zpk')
+            assert_array_almost_equal(z, xp.asarray([], dtype=xp.float64))
+            assert p.shape[0] == N
+            # All poles should be at distance wn from origin
+            assert_array_almost_equal(xp.abs(p), xp.asarray(wn, dtype=xp.float64))
+            assert all(xp.real(p) <= 0)  # No poles in right half of S-plane
+            assert math.isclose(k, wn**N, rel_tol=1e-9 if not DEFAULT_F32 else 1e-6)
+
+        # digital z-plane
+        for N in range(25):
+            wn = 0.01
+            z, p, k = butter(N, xp.asarray(wn), 'high', analog=False, output='zpk')
+            xp_assert_equal(z, xp.ones(N, dtype=xp.float64))  # All zeros exactly at DC
+            assert xp.all(xp.abs(p) <= 1)  # No poles outside unit circle
+
+        b1, a1 = butter(2, xp.asarray(1), analog=True)
+        assert_array_almost_equal(b1, xp.asarray([1.0], dtype=xp.float64))
+        assert_array_almost_equal(
+            a1, xp.asarray([1, math.sqrt(2), 1], dtype=xp.float64)
+        )
+
+        b2, a2 = butter(5, xp.asarray(1.), analog=True)
+        assert_array_almost_equal(b2, xp.asarray([1], dtype=xp.float64))
+        assert_array_almost_equal(
+            a2, xp.asarray([1, 3.2361, 5.2361,
+                            5.2361, 3.2361, 1], dtype=xp.float64),
+            decimal=4
+        )
+
+        b3, a3 = butter(10, xp.asarray(1.0), analog=True)
+        assert_array_almost_equal(b3, xp.asarray([1.0], dtype=xp.float64))
+        assert_array_almost_equal(
+            a3, xp.asarray([1, 6.3925, 20.4317, 42.8021, 64.8824,
+                            74.2334, 64.8824, 42.8021, 20.4317,
+                            6.3925, 1], dtype=xp.float64),
+            decimal=4
+        )
+
+        b2, a2 = butter(19, xp.asarray(1.0441379169150726), analog=True)
+        assert_array_almost_equal(
+            b2, xp.asarray([2.2720], dtype=xp.float64), decimal=4
+        )
+        assert_array_almost_equal(
+            a2, 1.0e+004 * xp.asarray([
+                0.0001, 0.0013, 0.0080, 0.0335, 0.1045, 0.2570,
+                0.5164, 0.8669, 1.2338, 1.5010, 1.5672, 1.4044,
+                1.0759, 0.6986, 0.3791, 0.1681, 0.0588, 0.0153,
+                0.0026, 0.0002], dtype=xp.float64),
+            decimal=0
+        )
+
+        b, a = butter(5, xp.asarray(0.4))
+        assert_array_almost_equal(
+            b, xp.asarray([0.0219, 0.1097, 0.2194,
+                           0.2194, 0.1097, 0.0219], dtype=xp.float64),
+            decimal=4
+        )
+        assert_array_almost_equal(
+            a, xp.asarray([1.0000, -0.9853, 0.9738,
+                           -0.3864, 0.1112, -0.0113], dtype=xp.float64),
+            decimal=4
+        )
+
+    def test_highpass(self, xp):
+        # highpass, high even order
+        z, p, k = butter(28, xp.asarray(0.43), 'high', output='zpk')
+        z2 = xp.ones(28, dtype=xp.float64)
+        p2 = [
+            2.068257195514592e-01 + 9.238294351481734e-01j,
+            2.068257195514592e-01 - 9.238294351481734e-01j,
+            1.874933103892023e-01 + 8.269455076775277e-01j,
+            1.874933103892023e-01 - 8.269455076775277e-01j,
+            1.717435567330153e-01 + 7.383078571194629e-01j,
+            1.717435567330153e-01 - 7.383078571194629e-01j,
+            1.588266870755982e-01 + 6.564623730651094e-01j,
+            1.588266870755982e-01 - 6.564623730651094e-01j,
+            1.481881532502603e-01 + 5.802343458081779e-01j,
+            1.481881532502603e-01 - 5.802343458081779e-01j,
+            1.394122576319697e-01 + 5.086609000582009e-01j,
+            1.394122576319697e-01 - 5.086609000582009e-01j,
+            1.321840881809715e-01 + 4.409411734716436e-01j,
+            1.321840881809715e-01 - 4.409411734716436e-01j,
+            1.262633413354405e-01 + 3.763990035551881e-01j,
+            1.262633413354405e-01 - 3.763990035551881e-01j,
+            1.214660449478046e-01 + 3.144545234797277e-01j,
+            1.214660449478046e-01 - 3.144545234797277e-01j,
+            1.104868766650320e-01 + 2.771505404367791e-02j,
+            1.104868766650320e-01 - 2.771505404367791e-02j,
+            1.111768629525075e-01 + 8.331369153155753e-02j,
+            1.111768629525075e-01 - 8.331369153155753e-02j,
+            1.125740630842972e-01 + 1.394219509611784e-01j,
+            1.125740630842972e-01 - 1.394219509611784e-01j,
+            1.147138487992747e-01 + 1.963932363793666e-01j,
+            1.147138487992747e-01 - 1.963932363793666e-01j,
+            1.176516491045901e-01 + 2.546021573417188e-01j,
+            1.176516491045901e-01 - 2.546021573417188e-01j,
+            ]
+        p2 = xp.asarray(p2, dtype=xp.complex128)
+        k2 = 1.446671081817286e-06
+        xp_assert_equal(z, z2)
+        xp_assert_close(_sort_cmplx(p, xp), _sort_cmplx(p2, xp), rtol=1e-7)
+        assert math.isclose(k, k2, rel_tol=1e-10 if not DEFAULT_F32 else 1e-6)
+
+        # highpass, high odd order
+        z, p, k = butter(27, xp.asarray(0.56), 'high', output='zpk')
+        z2 = xp.ones(27, dtype=xp.float64)
+        p2 = [
+            -1.772572785680147e-01 + 9.276431102995948e-01j,
+            -1.772572785680147e-01 - 9.276431102995948e-01j,
+            -1.600766565322114e-01 + 8.264026279893268e-01j,
+            -1.600766565322114e-01 - 8.264026279893268e-01j,
+            -1.461948419016121e-01 + 7.341841939120078e-01j,
+            -1.461948419016121e-01 - 7.341841939120078e-01j,
+            -1.348975284762046e-01 + 6.493235066053785e-01j,
+            -1.348975284762046e-01 - 6.493235066053785e-01j,
+            -1.256628210712206e-01 + 5.704921366889227e-01j,
+            -1.256628210712206e-01 - 5.704921366889227e-01j,
+            -1.181038235962314e-01 + 4.966120551231630e-01j,
+            -1.181038235962314e-01 - 4.966120551231630e-01j,
+            -1.119304913239356e-01 + 4.267938916403775e-01j,
+            -1.119304913239356e-01 - 4.267938916403775e-01j,
+            -1.069237739782691e-01 + 3.602914879527338e-01j,
+            -1.069237739782691e-01 - 3.602914879527338e-01j,
+            -1.029178030691416e-01 + 2.964677964142126e-01j,
+            -1.029178030691416e-01 - 2.964677964142126e-01j,
+            -9.978747500816100e-02 + 2.347687643085738e-01j,
+            -9.978747500816100e-02 - 2.347687643085738e-01j,
+            -9.743974496324025e-02 + 1.747028739092479e-01j,
+            -9.743974496324025e-02 - 1.747028739092479e-01j,
+            -9.580754551625957e-02 + 1.158246860771989e-01j,
+            -9.580754551625957e-02 - 1.158246860771989e-01j,
+            -9.484562207782568e-02 + 5.772118357151691e-02j,
+            -9.484562207782568e-02 - 5.772118357151691e-02j,
+            -9.452783117928215e-02
+            ]
+        p2 = xp.asarray(p2, dtype=xp.complex128)
+        k2 = 9.585686688851069e-09
+        xp_assert_equal(z, z2)
+        xp_assert_close(
+            _sort_cmplx(p, xp), _sort_cmplx(p2, xp),
+            rtol=1e-8 if not DEFAULT_F32 else 1e-6
+        )
+        assert math.isclose(k, k2, abs_tol=1e-13)
+
+    def test_bandpass(self, xp):
+        z, p, k = butter(8, xp.asarray([0.25, 0.33]), 'band', output='zpk')
+        z2 = [1 + 0j, 1, 1, 1, 1, 1, 1, 1,
+              -1, -1, -1, -1, -1, -1, -1, -1]
+        p2 = [
+            4.979909925436156e-01 + 8.367609424799387e-01j,
+            4.979909925436156e-01 - 8.367609424799387e-01j,
+            4.913338722555539e-01 + 7.866774509868817e-01j,
+            4.913338722555539e-01 - 7.866774509868817e-01j,
+            5.035229361778706e-01 + 7.401147376726750e-01j,
+            5.035229361778706e-01 - 7.401147376726750e-01j,
+            5.307617160406101e-01 + 7.029184459442954e-01j,
+            5.307617160406101e-01 - 7.029184459442954e-01j,
+            5.680556159453138e-01 + 6.788228792952775e-01j,
+            5.680556159453138e-01 - 6.788228792952775e-01j,
+            6.100962560818854e-01 + 6.693849403338664e-01j,
+            6.100962560818854e-01 - 6.693849403338664e-01j,
+            6.904694312740631e-01 + 6.930501690145245e-01j,
+            6.904694312740631e-01 - 6.930501690145245e-01j,
+            6.521767004237027e-01 + 6.744414640183752e-01j,
+            6.521767004237027e-01 - 6.744414640183752e-01j,
+            ]
+        z2 = xp.asarray(z2, dtype=xp.complex128)
+        p2 = xp.asarray(p2, dtype=xp.complex128)
+        k2 = 3.398854055800844e-08
+        xp_assert_equal(z, z2, check_dtype=False)
+        xp_assert_close(
+            _sort_cmplx(p, xp), _sort_cmplx(p2, xp),
+            rtol=1e-13 if not DEFAULT_F32 else 1e-7
+        )
+        assert math.isclose(k, k2, rel_tol=1e-13 if not DEFAULT_F32 else 1e-5)
+
+        # bandpass analog
+        z, p, k = butter(4, xp.asarray([90.5, 110.5]), 'bp', analog=True, output='zpk')
+        z2 = xp.zeros(4, dtype=xp.complex128)
+        p2 = [
+            -4.179137760733086e+00 + 1.095935899082837e+02j,
+            -4.179137760733086e+00 - 1.095935899082837e+02j,
+            -9.593598668443835e+00 + 1.034745398029734e+02j,
+            -9.593598668443835e+00 - 1.034745398029734e+02j,
+            -8.883991981781929e+00 + 9.582087115567160e+01j,
+            -8.883991981781929e+00 - 9.582087115567160e+01j,
+            -3.474530886568715e+00 + 9.111599925805801e+01j,
+            -3.474530886568715e+00 - 9.111599925805801e+01j,
+            ]
+        p2 = xp.asarray(p2, dtype=xp.complex128)
+        k2 = 1.600000000000001e+05
+        xp_assert_equal(z, z2)
+        xp_assert_close(_sort_cmplx(p, xp), _sort_cmplx(p2, xp))
+        assert math.isclose(k, k2, rel_tol=1e-15)
+
+    def test_bandstop(self, xp):
+        z, p, k = butter(7, xp.asarray([0.45, 0.56]), 'stop', output='zpk')
+        z2 = [-1.594474531383421e-02 + 9.998728744679880e-01j,
+              -1.594474531383421e-02 - 9.998728744679880e-01j,
+              -1.594474531383421e-02 + 9.998728744679880e-01j,
+              -1.594474531383421e-02 - 9.998728744679880e-01j,
+              -1.594474531383421e-02 + 9.998728744679880e-01j,
+              -1.594474531383421e-02 - 9.998728744679880e-01j,
+              -1.594474531383421e-02 + 9.998728744679880e-01j,
+              -1.594474531383421e-02 - 9.998728744679880e-01j,
+              -1.594474531383421e-02 + 9.998728744679880e-01j,
+              -1.594474531383421e-02 - 9.998728744679880e-01j,
+              -1.594474531383421e-02 + 9.998728744679880e-01j,
+              -1.594474531383421e-02 - 9.998728744679880e-01j,
+              -1.594474531383421e-02 + 9.998728744679880e-01j,
+              -1.594474531383421e-02 - 9.998728744679880e-01j]
+        p2 = [-1.766850742887729e-01 + 9.466951258673900e-01j,
+              -1.766850742887729e-01 - 9.466951258673900e-01j,
+               1.467897662432886e-01 + 9.515917126462422e-01j,
+               1.467897662432886e-01 - 9.515917126462422e-01j,
+              -1.370083529426906e-01 + 8.880376681273993e-01j,
+              -1.370083529426906e-01 - 8.880376681273993e-01j,
+               1.086774544701390e-01 + 8.915240810704319e-01j,
+               1.086774544701390e-01 - 8.915240810704319e-01j,
+              -7.982704457700891e-02 + 8.506056315273435e-01j,
+              -7.982704457700891e-02 - 8.506056315273435e-01j,
+               5.238812787110331e-02 + 8.524011102699969e-01j,
+               5.238812787110331e-02 - 8.524011102699969e-01j,
+              -1.357545000491310e-02 + 8.382287744986582e-01j,
+              -1.357545000491310e-02 - 8.382287744986582e-01j]
+        z2 = xp.asarray(z2, dtype=xp.complex128)
+        p2 = xp.asarray(p2, dtype=xp.complex128)
+        k2 = 4.577122512960063e-01
+        xp_assert_close(_sort_cmplx(z, xp), _sort_cmplx(z2, xp))
+        xp_assert_close(_sort_cmplx(p, xp), _sort_cmplx(p2, xp))
+        assert math.isclose(k, k2, rel_tol=1e-14 if not DEFAULT_F32 else 1e-6)
+
+    @xfail_xp_backends("cupy", reason="inaccurate on CuPy")
+    def test_ba_output(self, xp):
+        b, a = butter(4, xp.asarray([100, 300]), 'bandpass', analog=True)
+        b2 = [1.6e+09, 0, 0, 0, 0]
+        a2 = [1.000000000000000e+00, 5.226251859505511e+02,
+              2.565685424949238e+05, 6.794127417357160e+07,
+              1.519411254969542e+10, 2.038238225207147e+12,
+              2.309116882454312e+14, 1.411088002066486e+16,
+              8.099999999999991e+17]
+        b2 = xp.asarray(b2, dtype=xp.float64)
+        a2 = xp.asarray(a2, dtype=xp.float64)
+        xp_assert_close(b, b2, rtol=1e-14)
+        xp_assert_close(a, a2, rtol=1e-14)
+
+    def test_fs_param(self):
+        for fs in (900, 900.1, 1234.567):
+            for N in (0, 1, 2, 3, 10):
+                for fc in (100, 100.1, 432.12345):
+                    for btype in ('lp', 'hp'):
+                        ba1 = butter(N, fc, btype, fs=fs)
+                        ba2 = butter(N, fc/(fs/2), btype)
+                        for ba1_, ba2_ in zip(ba1, ba2):
+                            xp_assert_close(ba1_, ba2_)
+                for fc in ((100, 200), (100.1, 200.2), (321.123, 432.123)):
+                    for btype in ('bp', 'bs'):
+                        ba1 = butter(N, fc, btype, fs=fs)
+                        for seq in (list, tuple, array):
+                            fcnorm = seq([f/(fs/2) for f in fc])
+                            ba2 = butter(N, fcnorm, btype)
+                            for ba1_, ba2_ in zip(ba1, ba2):
+                                xp_assert_close(ba1_, ba2_)
+
+
+@skip_xp_backends("dask.array", reason="https://github.com/dask/dask/issues/11883")
+@make_xp_test_case(cheby1)
+class TestCheby1:
+
+    def test_degenerate(self, xp):
+        # 0-order filter is just a passthrough
+        # Even-order filters have DC gain of -rp dB
+        b, a = cheby1(0, 10*math.log10(2), xp.asarray(1), analog=True)
+        assert_array_almost_equal(
+            b, xp.asarray([1 / math.sqrt(2)], dtype=xp.float64)
+        )
+        xp_assert_equal(a, xp.asarray([1.0], dtype=xp.float64))
+
+        # 1-order filter is same for all types
+        b, a = cheby1(1, 10*math.log10(2), xp.asarray(1), analog=True)
+        assert_array_almost_equal(b, xp.asarray([1.], dtype=xp.float64))
+        assert_array_almost_equal(a, xp.asarray([1., 1], dtype=xp.float64))
+
+        z, p, k = cheby1(1, 0.1, xp.asarray(0.3), output='zpk')
+        xp_assert_equal(z, xp.asarray([-1.0], dtype=xp.float64))
+        xp_assert_close(
+            p, xp.asarray([-5.390126972799615e-01 + 0j], dtype=xp.complex128),
+            rtol=1e-14 if not DEFAULT_F32 else 1e-7
+        )
+        assert math.isclose(
+            k, 7.695063486399808e-01, rel_tol=1e-14 if not DEFAULT_F32 else 1e-7
+        )
+
+    def test_basic(self, xp):
+        for N in range(25):
+            wn = xp.asarray(0.01)
+            z, p, k = cheby1(N, 1, wn, 'low', analog=True, output='zpk')
+            assert_array_almost_equal(z, xp.asarray([], dtype=xp.float64))
+            assert p.shape[0] == N
+            assert xp.all(xp.real(p) <= 0)  # No poles in right half of S-plane
+
+        for N in range(25):
+            wn = xp.asarray(0.01)
+            z, p, k = cheby1(N, 1, wn, 'high', analog=False, output='zpk')
+            xp_assert_equal(z, xp.ones(N, dtype=xp.float64))  # All zeros exactly at DC
+            assert xp.all(xp.abs(p) <= 1)  # No poles outside unit circle
+
+        # Same test as TestNormalize
+        b, a = cheby1(8, 0.5, xp.asarray(0.048))
+        xp_assert_close(
+            b, xp.asarray([2.150733144728282e-11, 1.720586515782626e-10,
+                           6.022052805239190e-10, 1.204410561047838e-09,
+                           1.505513201309798e-09, 1.204410561047838e-09,
+                           6.022052805239190e-10, 1.720586515782626e-10,
+                           2.150733144728282e-11], dtype=xp.float64),
+            rtol=0, atol=1.5e-14
+        )
+        xp_assert_close(
+            a, xp.asarray([1.000000000000000e+00, -7.782402035027959e+00,
+                           2.654354569747454e+01, -5.182182531666387e+01,
+                           6.334127355102684e+01, -4.963358186631157e+01,
+                           2.434862182949389e+01, -6.836925348604676e+00,
+                           8.412934944449140e-01], dtype=xp.float64),
+            rtol=0, atol=5e-14 if not DEFAULT_F32 else 1e-7
+        )
+
+        b, a = cheby1(4, 1, xp.asarray([0.4, 0.7]), btype='band')
+        assert_array_almost_equal(
+            b, xp.asarray([0.0084, 0, -0.0335, 0, 0.0502, 0,
+                           -0.0335, 0, 0.0084], dtype=xp.float64),
+            decimal=4
+        )
+        assert_array_almost_equal(
+            a, xp.asarray([1.0, 1.1191, 2.862, 2.2986, 3.4137,
+                           1.8653, 1.8982, 0.5676, 0.4103], dtype=xp.float64),
+            decimal=4
+        )
+
+        b2, a2 = cheby1(5, 3, xp.asarray(1), analog=True)
+        assert_array_almost_equal(
+            b2, xp.asarray([0.0626], dtype=xp.float64), decimal=4
+        )
+        assert_array_almost_equal(
+            a2, xp.asarray([1, 0.5745, 1.4150, 0.5489, 0.4080,
+                            0.0626], dtype=xp.float64),
+            decimal=4)
+
+        b, a = cheby1(8, 0.5, xp.asarray(0.1))
+        assert_array_almost_equal(
+            b,
+            1.0e-006 * xp.asarray(
+                [0.00703924326028, 0.05631394608227, 0.19709881128793,
+                 0.39419762257586, 0.49274702821983, 0.39419762257586,
+                 0.19709881128793, 0.05631394608227, 0.00703924326028
+                ], dtype=xp.float64
+            ),
+            decimal=13
+        )
+        assert_array_almost_equal(
+            a, xp.asarray(
+                [1.00000000000000, -7.44912258934158, 24.46749067762108,
+                 -46.27560200466141, 55.11160187999928, -42.31640010161038,
+                 20.45543300484147, -5.69110270561444, 0.69770374759022
+                ], dtype=xp.float64
+            ),
+            decimal=13 if not DEFAULT_F32 else 6
+        )
+
+        b, a = cheby1(8, 0.5, xp.asarray(0.25))
+        assert_array_almost_equal(
+            b,
+            1.0e-003 * xp.asarray(
+                [0.00895261138923, 0.07162089111382, 0.25067311889837,
+                 0.50134623779673, 0.62668279724591, 0.50134623779673,
+                 0.25067311889837, 0.07162089111382, 0.00895261138923
+                ], dtype=xp.float64
+            ),
+            decimal=13)
+        assert_array_almost_equal(
+            a,
+            xp.asarray(
+                [1.00000000000000, -5.97529229188545,
+                 16.58122329202101, -27.71423273542923,
+                 30.39509758355313, -22.34729670426879,
+                 10.74509800434910, -3.08924633697497,
+                 0.40707685889802
+                 ], dtype=xp.float64
+            ), decimal=13)
+
+    def test_highpass(self, xp):
+        # high even order
+        z, p, k = cheby1(24, 0.7, xp.asarray(0.2), 'high', output='zpk')
+        z2 = xp.ones(24, dtype=xp.float64)
+        p2 = [-6.136558509657073e-01 + 2.700091504942893e-01j,
+              -6.136558509657073e-01 - 2.700091504942893e-01j,
+              -3.303348340927516e-01 + 6.659400861114254e-01j,
+              -3.303348340927516e-01 - 6.659400861114254e-01j,
+              8.779713780557169e-03 + 8.223108447483040e-01j,
+              8.779713780557169e-03 - 8.223108447483040e-01j,
+              2.742361123006911e-01 + 8.356666951611864e-01j,
+              2.742361123006911e-01 - 8.356666951611864e-01j,
+              4.562984557158206e-01 + 7.954276912303594e-01j,
+              4.562984557158206e-01 - 7.954276912303594e-01j,
+              5.777335494123628e-01 + 7.435821817961783e-01j,
+              5.777335494123628e-01 - 7.435821817961783e-01j,
+              6.593260977749194e-01 + 6.955390907990932e-01j,
+              6.593260977749194e-01 - 6.955390907990932e-01j,
+              7.149590948466562e-01 + 6.559437858502012e-01j,
+              7.149590948466562e-01 - 6.559437858502012e-01j,
+              7.532432388188739e-01 + 6.256158042292060e-01j,
+              7.532432388188739e-01 - 6.256158042292060e-01j,
+              7.794365244268271e-01 + 6.042099234813333e-01j,
+              7.794365244268271e-01 - 6.042099234813333e-01j,
+              7.967253874772997e-01 + 5.911966597313203e-01j,
+              7.967253874772997e-01 - 5.911966597313203e-01j,
+              8.069756417293870e-01 + 5.862214589217275e-01j,
+              8.069756417293870e-01 - 5.862214589217275e-01j]
+        p2 = xp.asarray(p2, dtype=xp.complex128)
+        k2 = 6.190427617192018e-04
+        xp_assert_equal(z, z2)
+        xp_assert_close(
+            _sort_cmplx(p, xp=xp), _sort_cmplx(p2, xp=xp),
+            rtol=1e-10 if not DEFAULT_F32 else 1e-7
+        )
+        assert math.isclose(k, k2, rel_tol=1e-10 if not DEFAULT_F32 else 1e-6)
+
+        # high odd order
+        z, p, k = cheby1(23, 0.8, xp.asarray(0.3), 'high', output='zpk')
+        z2 = xp.ones(23, dtype=xp.float64)
+        p2 = [-7.676400532011010e-01,
+              -6.754621070166477e-01 + 3.970502605619561e-01j,
+              -6.754621070166477e-01 - 3.970502605619561e-01j,
+              -4.528880018446727e-01 + 6.844061483786332e-01j,
+              -4.528880018446727e-01 - 6.844061483786332e-01j,
+              -1.986009130216447e-01 + 8.382285942941594e-01j,
+              -1.986009130216447e-01 - 8.382285942941594e-01j,
+              2.504673931532608e-02 + 8.958137635794080e-01j,
+              2.504673931532608e-02 - 8.958137635794080e-01j,
+              2.001089429976469e-01 + 9.010678290791480e-01j,
+              2.001089429976469e-01 - 9.010678290791480e-01j,
+              3.302410157191755e-01 + 8.835444665962544e-01j,
+              3.302410157191755e-01 - 8.835444665962544e-01j,
+              4.246662537333661e-01 + 8.594054226449009e-01j,
+              4.246662537333661e-01 - 8.594054226449009e-01j,
+              4.919620928120296e-01 + 8.366772762965786e-01j,
+              4.919620928120296e-01 - 8.366772762965786e-01j,
+              5.385746917494749e-01 + 8.191616180796720e-01j,
+              5.385746917494749e-01 - 8.191616180796720e-01j,
+              5.855636993537203e-01 + 8.060680937701062e-01j,
+              5.855636993537203e-01 - 8.060680937701062e-01j,
+              5.688812849391721e-01 + 8.086497795114683e-01j,
+              5.688812849391721e-01 - 8.086497795114683e-01j]
+        p2 = xp.asarray(p2, dtype=xp.complex128)
+        k2 = 1.941697029206324e-05
+        xp_assert_equal(z, z2)
+        xp_assert_close(
+            _sort_cmplx(p, xp=xp), _sort_cmplx(p2, xp=xp),
+            rtol=1e-10 if not DEFAULT_F32 else 1e-7
+        )
+        assert math.isclose(
+            k, k2, rel_tol=1e-10 if not DEFAULT_F32 else 1e-6
+        )
+
+        z, p, k = cheby1(10, 1, xp.asarray(1000), 'high', analog=True, output='zpk')
+        z2 = xp.zeros(10, dtype=xp.float64)
+        p2 = [-3.144743169501551e+03 + 3.511680029092744e+03j,
+              -3.144743169501551e+03 - 3.511680029092744e+03j,
+              -5.633065604514602e+02 + 2.023615191183945e+03j,
+              -5.633065604514602e+02 - 2.023615191183945e+03j,
+              -1.946412183352025e+02 + 1.372309454274755e+03j,
+              -1.946412183352025e+02 - 1.372309454274755e+03j,
+              -7.987162953085479e+01 + 1.105207708045358e+03j,
+              -7.987162953085479e+01 - 1.105207708045358e+03j,
+              -2.250315039031946e+01 + 1.001723931471477e+03j,
+              -2.250315039031946e+01 - 1.001723931471477e+03j]
+        p2 = xp.asarray(p2, dtype=xp.complex128)
+        k2 = 8.912509381337453e-01
+        xp_assert_equal(z, z2)
+        xp_assert_close(_sort_cmplx(p, xp=xp), _sort_cmplx(p2, xp=xp), rtol=1e-13)
+        assert math.isclose(k, k2, rel_tol=1e-15)
+
+    def test_bandpass(self, xp):
+        z, p, k = cheby1(8, 1, xp.asarray([0.3, 0.4]), 'bp', output='zpk')
+        z2 = [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1]
+        p2 = [3.077784854851463e-01 + 9.453307017592942e-01j,
+              3.077784854851463e-01 - 9.453307017592942e-01j,
+              3.280567400654425e-01 + 9.272377218689016e-01j,
+              3.280567400654425e-01 - 9.272377218689016e-01j,
+              3.677912763284301e-01 + 9.038008865279966e-01j,
+              3.677912763284301e-01 - 9.038008865279966e-01j,
+              4.194425632520948e-01 + 8.769407159656157e-01j,
+              4.194425632520948e-01 - 8.769407159656157e-01j,
+              4.740921994669189e-01 + 8.496508528630974e-01j,
+              4.740921994669189e-01 - 8.496508528630974e-01j,
+              5.234866481897429e-01 + 8.259608422808477e-01j,
+              5.234866481897429e-01 - 8.259608422808477e-01j,
+              5.844717632289875e-01 + 8.052901363500210e-01j,
+              5.844717632289875e-01 - 8.052901363500210e-01j,
+              5.615189063336070e-01 + 8.100667803850766e-01j,
+              5.615189063336070e-01 - 8.100667803850766e-01j]
+        z2 = xp.asarray(z2, dtype=xp.float64)
+        p2 = xp.asarray(p2, dtype=xp.complex128)
+        k2 = 5.007028718074307e-09
+        xp_assert_equal(z, z2, check_dtype=False)
+        xp_assert_close(
+            _sort_cmplx(p, xp=xp), _sort_cmplx(p2, xp=xp),
+            rtol=1e-13 if not DEFAULT_F32 else 1e-7
+        )
+        assert math.isclose(k, k2, rel_tol=1e-13 if not DEFAULT_F32 else 1e-6)
+
+    def test_bandstop(self, xp):
+        z, p, k = cheby1(7, 1, xp.asarray([0.5, 0.6]), 'stop', output='zpk')
+        z2 = [-1.583844403245361e-01 + 9.873775210440450e-01j,
+              -1.583844403245361e-01 - 9.873775210440450e-01j,
+              -1.583844403245361e-01 + 9.873775210440450e-01j,
+              -1.583844403245361e-01 - 9.873775210440450e-01j,
+              -1.583844403245361e-01 + 9.873775210440450e-01j,
+              -1.583844403245361e-01 - 9.873775210440450e-01j,
+              -1.583844403245361e-01 + 9.873775210440450e-01j,
+              -1.583844403245361e-01 - 9.873775210440450e-01j,
+              -1.583844403245361e-01 + 9.873775210440450e-01j,
+              -1.583844403245361e-01 - 9.873775210440450e-01j,
+              -1.583844403245361e-01 + 9.873775210440450e-01j,
+              -1.583844403245361e-01 - 9.873775210440450e-01j,
+              -1.583844403245361e-01 + 9.873775210440450e-01j,
+              -1.583844403245361e-01 - 9.873775210440450e-01j]
+        p2 = [-8.942974551472813e-02 + 3.482480481185926e-01j,
+              -8.942974551472813e-02 - 3.482480481185926e-01j,
+               1.293775154041798e-01 + 8.753499858081858e-01j,
+               1.293775154041798e-01 - 8.753499858081858e-01j,
+               3.399741945062013e-02 + 9.690316022705607e-01j,
+               3.399741945062013e-02 - 9.690316022705607e-01j,
+               4.167225522796539e-04 + 9.927338161087488e-01j,
+               4.167225522796539e-04 - 9.927338161087488e-01j,
+              -3.912966549550960e-01 + 8.046122859255742e-01j,
+              -3.912966549550960e-01 - 8.046122859255742e-01j,
+              -3.307805547127368e-01 + 9.133455018206508e-01j,
+              -3.307805547127368e-01 - 9.133455018206508e-01j,
+              -3.072658345097743e-01 + 9.443589759799366e-01j,
+              -3.072658345097743e-01 - 9.443589759799366e-01j]
+        z2 = xp.asarray(z2, dtype=xp.complex128)
+        p2 = xp.asarray(p2, dtype=xp.complex128)
+        k2 = 3.619438310405028e-01
+        xp_assert_close(
+            _sort_cmplx(z, xp=xp), _sort_cmplx(z2, xp=xp),
+            rtol=1e-13 if not DEFAULT_F32 else 1e-6
+        )
+        xp_assert_close(
+            _sort_cmplx(p, xp=xp), _sort_cmplx(p2, xp=xp),
+            rtol=1e-13 if not DEFAULT_F32 else 1e-6
+        )
+        assert math.isclose(
+            k, k2, rel_tol=0, abs_tol=5e-16 if not DEFAULT_F32 else 1e-7
+        )
+
+    @xfail_xp_backends("cupy", reason="inaccurate on CuPy")
+    def test_ba_output(self, xp):
+        # with transfer function conversion,  without digital conversion
+        b, a = cheby1(5, 0.9, xp.asarray([210, 310.0]), 'stop', analog=True)
+        b2 = [1.000000000000006e+00, 0,
+              3.255000000000020e+05, 0,
+              4.238010000000026e+10, 0,
+              2.758944510000017e+15, 0,
+              8.980364380050052e+19, 0,
+              1.169243442282517e+24
+              ]
+        a2 = [1.000000000000000e+00, 4.630555945694342e+02,
+              4.039266454794788e+05, 1.338060988610237e+08,
+              5.844333551294591e+10, 1.357346371637638e+13,
+              3.804661141892782e+15, 5.670715850340080e+17,
+              1.114411200988328e+20, 8.316815934908471e+21,
+              1.169243442282517e+24
+              ]
+        b2, a2 = map(lambda t: xp.asarray(t, dtype=xp.float64), (b2, a2))
+        xp_assert_close(b, b2, rtol=1e-14 if not DEFAULT_F32 else 1e-7)
+        xp_assert_close(a, a2, rtol=1e-14 if not DEFAULT_F32 else 1e-7)
+
+    def test_fs_param(self):
+        for fs in (900, 900.1, 1234.567):
+            for N in (0, 1, 2, 3, 10):
+                for fc in (100, 100.1, 432.12345):
+                    for btype in ('lp', 'hp'):
+                        ba1 = cheby1(N, 1, fc, btype, fs=fs)
+                        ba2 = cheby1(N, 1, fc/(fs/2), btype)
+                        for ba1_, ba2_ in zip(ba1, ba2):
+                            xp_assert_close(ba1_, ba2_)
+                for fc in ((100, 200), (100.1, 200.2), (321.123, 432.123)):
+                    for btype in ('bp', 'bs'):
+                        ba1 = cheby1(N, 1, fc, btype, fs=fs)
+                        for seq in (list, tuple, array):
+                            fcnorm = seq([f/(fs/2) for f in fc])
+                            ba2 = cheby1(N, 1, fcnorm, btype)
+                            for ba1_, ba2_ in zip(ba1, ba2):
+                                xp_assert_close(ba1_, ba2_)
+
+
+@skip_xp_backends("dask.array", reason="https://github.com/dask/dask/issues/11883")
+@make_xp_test_case(cheby2)
+class TestCheby2:
+
+    def test_degenerate(self, xp):
+        # 0-order filter is just a passthrough
+        # Stopband ripple factor doesn't matter
+        b, a = cheby2(0, 123.456, xp.asarray(1), analog=True)
+        xp_assert_equal(b, xp.asarray([1.0], dtype=xp.float64))
+        xp_assert_equal(a, xp.asarray([1.0], dtype=xp.float64))
+
+        # 1-order filter is same for all types
+        b, a = cheby2(1, 10*math.log10(2), xp.asarray(1.), analog=True)
+        assert_array_almost_equal(b, xp.asarray([1], dtype=xp.float64))
+        assert_array_almost_equal(a, xp.asarray([1, 1], dtype=xp.float64))
+
+        z, p, k = cheby2(1, 50, xp.asarray(0.3), output='zpk')
+        xp_assert_equal(z, xp.asarray([-1], dtype=xp.complex128))
+        xp_assert_close(
+            p, xp.asarray([9.967826460175649e-01 + 0j], dtype=xp.complex128),
+            rtol=1e-14 if not DEFAULT_F32 else 1e-7
+        )
+        assert math.isclose(
+            k, 1.608676991217512e-03, rel_tol=1e-14 if not DEFAULT_F32 else 1e-6
+        )
+
+    def test_basic(self, xp):
+        for N in range(25):
+            wn = xp.asarray(0.01)
+            z, p, k = cheby2(N, 40, wn, 'low', analog=True, output='zpk')
+            assert p.shape[0] == N
+            assert all(xp.real(p) <= 0)  # No poles in right half of S-plane
+
+        for N in range(25):
+            wn = xp.asarray(0.01)
+            z, p, k = cheby2(N, 40, wn, 'high', analog=False, output='zpk')
+            assert all(xp.abs(p) <= 1)  # No poles outside unit circle
+
+        B, A = cheby2(18, 100, xp.asarray(0.5))
+        assert_array_almost_equal(
+            B, xp.asarray([
+                0.00167583914216, 0.01249479541868, 0.05282702120282,
+                0.15939804265706, 0.37690207631117, 0.73227013789108,
+                1.20191856962356, 1.69522872823393, 2.07598674519837,
+                2.21972389625291, 2.07598674519838, 1.69522872823395,
+                1.20191856962359, 0.73227013789110, 0.37690207631118,
+                0.15939804265707, 0.05282702120282, 0.01249479541868,
+                0.00167583914216], dtype=xp.float64),
+            decimal=13 if not DEFAULT_F32 else 6
+        )
+        assert_array_almost_equal(
+            A, xp.asarray([
+                1.00000000000000, -0.27631970006174, 3.19751214254060,
+                -0.15685969461355, 4.13926117356269, 0.60689917820044,
+                2.95082770636540, 0.89016501910416, 1.32135245849798,
+                0.51502467236824, 0.38906643866660, 0.15367372690642,
+                0.07255803834919, 0.02422454070134, 0.00756108751837,
+                0.00179848550988, 0.00033713574499, 0.00004258794833,
+                0.00000281030149], dtype=xp.float64),
+            decimal=13 if not DEFAULT_F32 else 6
+        )
+
+    def test_highpass(self, xp):
+        # high even order
+        z, p, k = cheby2(26, 60, xp.asarray(0.3), 'high', output='zpk')
+        z2 = [9.981088955489852e-01 + 6.147058341984388e-02j,
+              9.981088955489852e-01 - 6.147058341984388e-02j,
+              9.832702870387426e-01 + 1.821525257215483e-01j,
+              9.832702870387426e-01 - 1.821525257215483e-01j,
+              9.550760158089112e-01 + 2.963609353922882e-01j,
+              9.550760158089112e-01 - 2.963609353922882e-01j,
+              9.162054748821922e-01 + 4.007087817803773e-01j,
+              9.162054748821922e-01 - 4.007087817803773e-01j,
+              8.700619897368064e-01 + 4.929423232136168e-01j,
+              8.700619897368064e-01 - 4.929423232136168e-01j,
+              5.889791753434985e-01 + 8.081482110427953e-01j,
+              5.889791753434985e-01 - 8.081482110427953e-01j,
+              5.984900456570295e-01 + 8.011302423760501e-01j,
+              5.984900456570295e-01 - 8.011302423760501e-01j,
+              6.172880888914629e-01 + 7.867371958365343e-01j,
+              6.172880888914629e-01 - 7.867371958365343e-01j,
+              6.448899971038180e-01 + 7.642754030030161e-01j,
+              6.448899971038180e-01 - 7.642754030030161e-01j,
+              6.804845629637927e-01 + 7.327624168637228e-01j,
+              6.804845629637927e-01 - 7.327624168637228e-01j,
+              8.202619107108660e-01 + 5.719881098737678e-01j,
+              8.202619107108660e-01 - 5.719881098737678e-01j,
+              7.228410452536148e-01 + 6.910143437705678e-01j,
+              7.228410452536148e-01 - 6.910143437705678e-01j,
+              7.702121399578629e-01 + 6.377877856007792e-01j,
+              7.702121399578629e-01 - 6.377877856007792e-01j]
+        p2 = [7.365546198286450e-01 + 4.842085129329526e-02j,
+              7.365546198286450e-01 - 4.842085129329526e-02j,
+              7.292038510962885e-01 + 1.442201672097581e-01j,
+              7.292038510962885e-01 - 1.442201672097581e-01j,
+              7.151293788040354e-01 + 2.369925800458584e-01j,
+              7.151293788040354e-01 - 2.369925800458584e-01j,
+              6.955051820787286e-01 + 3.250341363856910e-01j,
+              6.955051820787286e-01 - 3.250341363856910e-01j,
+              6.719122956045220e-01 + 4.070475750638047e-01j,
+              6.719122956045220e-01 - 4.070475750638047e-01j,
+              6.461722130611300e-01 + 4.821965916689270e-01j,
+              6.461722130611300e-01 - 4.821965916689270e-01j,
+              5.528045062872224e-01 + 8.162920513838372e-01j,
+              5.528045062872224e-01 - 8.162920513838372e-01j,
+              5.464847782492791e-01 + 7.869899955967304e-01j,
+              5.464847782492791e-01 - 7.869899955967304e-01j,
+              5.488033111260949e-01 + 7.520442354055579e-01j,
+              5.488033111260949e-01 - 7.520442354055579e-01j,
+              6.201874719022955e-01 + 5.500894392527353e-01j,
+              6.201874719022955e-01 - 5.500894392527353e-01j,
+              5.586478152536709e-01 + 7.112676877332921e-01j,
+              5.586478152536709e-01 - 7.112676877332921e-01j,
+              5.958145844148228e-01 + 6.107074340842115e-01j,
+              5.958145844148228e-01 - 6.107074340842115e-01j,
+              5.747812938519067e-01 + 6.643001536914696e-01j,
+              5.747812938519067e-01 - 6.643001536914696e-01j]
+        z2 = xp.asarray(z2, dtype=xp.complex128)
+        p2 = xp.asarray(p2, dtype=xp.complex128)
+        k2 = 6.190427617192018e-04
+        k2 = 9.932997786497189e-02
+        xp_assert_close(
+            _sort_cmplx(z, xp=xp), _sort_cmplx(z2, xp=xp),
+            rtol=1e-13 if not DEFAULT_F32 else 1e-6
+        )
+        xp_assert_close(
+            _sort_cmplx(p, xp=xp), _sort_cmplx(p2, xp=xp),
+            rtol=1e-12 if not DEFAULT_F32 else 1e-6
+        )
+        assert math.isclose(
+            k, k2, rel_tol=1e-11 if not DEFAULT_F32 else 1e-6
+        )
+
+        # high odd order
+        z, p, k = cheby2(25, 80, xp.asarray(0.5), 'high', output='zpk')
+        z2 = [9.690690376586687e-01 + 2.467897896011971e-01j,
+              9.690690376586687e-01 - 2.467897896011971e-01j,
+              9.999999999999492e-01,
+              8.835111277191199e-01 + 4.684101698261429e-01j,
+              8.835111277191199e-01 - 4.684101698261429e-01j,
+              7.613142857900539e-01 + 6.483830335935022e-01j,
+              7.613142857900539e-01 - 6.483830335935022e-01j,
+              6.232625173626231e-01 + 7.820126817709752e-01j,
+              6.232625173626231e-01 - 7.820126817709752e-01j,
+              4.864456563413621e-01 + 8.737108351316745e-01j,
+              4.864456563413621e-01 - 8.737108351316745e-01j,
+              3.618368136816749e-01 + 9.322414495530347e-01j,
+              3.618368136816749e-01 - 9.322414495530347e-01j,
+              2.549486883466794e-01 + 9.669545833752675e-01j,
+              2.549486883466794e-01 - 9.669545833752675e-01j,
+              1.676175432109457e-01 + 9.858520980390212e-01j,
+              1.676175432109457e-01 - 9.858520980390212e-01j,
+              1.975218468277521e-03 + 9.999980492540941e-01j,
+              1.975218468277521e-03 - 9.999980492540941e-01j,
+              1.786959496651858e-02 + 9.998403260399917e-01j,
+              1.786959496651858e-02 - 9.998403260399917e-01j,
+              9.967933660557139e-02 + 9.950196127985684e-01j,
+              9.967933660557139e-02 - 9.950196127985684e-01j,
+              5.013970951219547e-02 + 9.987422137518890e-01j,
+              5.013970951219547e-02 - 9.987422137518890e-01j]
+        p2 = [4.218866331906864e-01,
+              4.120110200127552e-01 + 1.361290593621978e-01j,
+              4.120110200127552e-01 - 1.361290593621978e-01j,
+              3.835890113632530e-01 + 2.664910809911026e-01j,
+              3.835890113632530e-01 - 2.664910809911026e-01j,
+              3.399195570456499e-01 + 3.863983538639875e-01j,
+              3.399195570456499e-01 - 3.863983538639875e-01j,
+              2.855977834508353e-01 + 4.929444399540688e-01j,
+              2.855977834508353e-01 - 4.929444399540688e-01j,
+              2.255765441339322e-01 + 5.851631870205766e-01j,
+              2.255765441339322e-01 - 5.851631870205766e-01j,
+              1.644087535815792e-01 + 6.637356937277153e-01j,
+              1.644087535815792e-01 - 6.637356937277153e-01j,
+              -7.293633845273095e-02 + 9.739218252516307e-01j,
+              -7.293633845273095e-02 - 9.739218252516307e-01j,
+              1.058259206358626e-01 + 7.304739464862978e-01j,
+              1.058259206358626e-01 - 7.304739464862978e-01j,
+              -5.703971947785402e-02 + 9.291057542169088e-01j,
+              -5.703971947785402e-02 - 9.291057542169088e-01j,
+              5.263875132656864e-02 + 7.877974334424453e-01j,
+              5.263875132656864e-02 - 7.877974334424453e-01j,
+              -3.007943405982616e-02 + 8.846331716180016e-01j,
+              -3.007943405982616e-02 - 8.846331716180016e-01j,
+              6.857277464483946e-03 + 8.383275456264492e-01j,
+              6.857277464483946e-03 - 8.383275456264492e-01j]
+        z2 = xp.asarray(z2, dtype=xp.complex128)
+        p2 = xp.asarray(p2, dtype=xp.complex128)
+        k2 = 6.507068761705037e-03
+        xp_assert_close(
+            _sort_cmplx(z, xp=xp), _sort_cmplx(z2, xp=xp),
+            rtol=1e-13 if not DEFAULT_F32 else 1e-6
+        )
+        xp_assert_close(
+            _sort_cmplx(p, xp=xp), _sort_cmplx(p2, xp=xp),
+            rtol=1e-12 if not DEFAULT_F32 else 1e-6
+        )
+        assert math.isclose(k, k2, rel_tol=1e-11 if not DEFAULT_F32 else 1e-6)
+
+    def test_bandpass(self, xp):
+        z, p, k = cheby2(9, 40, xp.asarray([0.07, 0.2]), 'pass', output='zpk')
+        z2 = [-9.999999999999999e-01,
+               3.676588029658514e-01 + 9.299607543341383e-01j,
+               3.676588029658514e-01 - 9.299607543341383e-01j,
+               7.009689684982283e-01 + 7.131917730894889e-01j,
+               7.009689684982283e-01 - 7.131917730894889e-01j,
+               7.815697973765858e-01 + 6.238178033919218e-01j,
+               7.815697973765858e-01 - 6.238178033919218e-01j,
+               8.063793628819866e-01 + 5.913986160941200e-01j,
+               8.063793628819866e-01 - 5.913986160941200e-01j,
+               1.000000000000001e+00,
+               9.944493019920448e-01 + 1.052168511576739e-01j,
+               9.944493019920448e-01 - 1.052168511576739e-01j,
+               9.854674703367308e-01 + 1.698642543566085e-01j,
+               9.854674703367308e-01 - 1.698642543566085e-01j,
+               9.762751735919308e-01 + 2.165335665157851e-01j,
+               9.762751735919308e-01 - 2.165335665157851e-01j,
+               9.792277171575134e-01 + 2.027636011479496e-01j,
+               9.792277171575134e-01 - 2.027636011479496e-01j]
+        p2 = [8.143803410489621e-01 + 5.411056063397541e-01j,
+              8.143803410489621e-01 - 5.411056063397541e-01j,
+              7.650769827887418e-01 + 5.195412242095543e-01j,
+              7.650769827887418e-01 - 5.195412242095543e-01j,
+              6.096241204063443e-01 + 3.568440484659796e-01j,
+              6.096241204063443e-01 - 3.568440484659796e-01j,
+              6.918192770246239e-01 + 4.770463577106911e-01j,
+              6.918192770246239e-01 - 4.770463577106911e-01j,
+              6.986241085779207e-01 + 1.146512226180060e-01j,
+              6.986241085779207e-01 - 1.146512226180060e-01j,
+              8.654645923909734e-01 + 1.604208797063147e-01j,
+              8.654645923909734e-01 - 1.604208797063147e-01j,
+              9.164831670444591e-01 + 1.969181049384918e-01j,
+              9.164831670444591e-01 - 1.969181049384918e-01j,
+              9.630425777594550e-01 + 2.317513360702271e-01j,
+              9.630425777594550e-01 - 2.317513360702271e-01j,
+              9.438104703725529e-01 + 2.193509900269860e-01j,
+              9.438104703725529e-01 - 2.193509900269860e-01j]
+        z2 = xp.asarray(z2, dtype=xp.complex128)
+        p2 = xp.asarray(p2, dtype=xp.complex128)
+        k2 = 9.345352824659604e-03
+        xp_assert_close(
+            _sort_cmplx(z, xp=xp), _sort_cmplx(z2, xp=xp),
+            rtol=1e-13 if not DEFAULT_F32 else 1e-6
+        )
+        xp_assert_close(
+            _sort_cmplx(p, xp=xp), _sort_cmplx(p2, xp=xp),
+            rtol=1e-13 if not DEFAULT_F32 else 1e-6
+        )
+        assert math.isclose(k, k2, rel_tol=1e-11 if not DEFAULT_F32 else 1e-6)
+
+    def test_bandstop(self, xp):
+        z, p, k = cheby2(6, 55, xp.asarray([0.1, 0.9]), 'stop', output='zpk')
+        z2 = [6.230544895101009e-01 + 7.821784343111114e-01j,
+              6.230544895101009e-01 - 7.821784343111114e-01j,
+              9.086608545660115e-01 + 4.175349702471991e-01j,
+              9.086608545660115e-01 - 4.175349702471991e-01j,
+              9.478129721465802e-01 + 3.188268649763867e-01j,
+              9.478129721465802e-01 - 3.188268649763867e-01j,
+              -6.230544895100982e-01 + 7.821784343111109e-01j,
+              -6.230544895100982e-01 - 7.821784343111109e-01j,
+              -9.086608545660116e-01 + 4.175349702472088e-01j,
+              -9.086608545660116e-01 - 4.175349702472088e-01j,
+              -9.478129721465784e-01 + 3.188268649763897e-01j,
+              -9.478129721465784e-01 - 3.188268649763897e-01j]
+        p2 = [-9.464094036167638e-01 + 1.720048695084344e-01j,
+              -9.464094036167638e-01 - 1.720048695084344e-01j,
+              -8.715844103386737e-01 + 1.370665039509297e-01j,
+              -8.715844103386737e-01 - 1.370665039509297e-01j,
+              -8.078751204586425e-01 + 5.729329866682983e-02j,
+              -8.078751204586425e-01 - 5.729329866682983e-02j,
+               9.464094036167665e-01 + 1.720048695084332e-01j,
+               9.464094036167665e-01 - 1.720048695084332e-01j,
+               8.078751204586447e-01 + 5.729329866683007e-02j,
+               8.078751204586447e-01 - 5.729329866683007e-02j,
+               8.715844103386721e-01 + 1.370665039509331e-01j,
+               8.715844103386721e-01 - 1.370665039509331e-01j]
+        z2 = xp.asarray(z2, dtype=xp.complex128)
+        p2 = xp.asarray(p2, dtype=xp.complex128)
+        k2 = 2.917823332763358e-03
+        xp_assert_close(
+            _sort_cmplx(z, xp=xp), _sort_cmplx(z2, xp=xp),
+            rtol=1e-13 if not DEFAULT_F32 else 1e-6
+        )
+        xp_assert_close(
+            _sort_cmplx(p, xp=xp), _sort_cmplx(p2, xp=xp),
+            rtol=1e-13 if not DEFAULT_F32 else 1e-6
+        )
+        assert math.isclose(k, k2, rel_tol=1e-11 if not DEFAULT_F32 else 1e-6)
+
+    @xfail_xp_backends("cupy", reason="inaccurate on CuPy")
+    def test_ba_output(self, xp):
+        # with transfer function conversion, without digital conversion
+        b, a = cheby2(5, 20, xp.asarray([2010, 2100]), 'stop', True)
+        b2 = [1.000000000000000e+00, 0,  # Matlab: 6.683253076978249e-12,
+              2.111512500000000e+07, 0,  # Matlab: 1.134325604589552e-04,
+              1.782966433781250e+14, 0,  # Matlab: 7.216787944356781e+02,
+              7.525901316990656e+20, 0,  # Matlab: 2.039829265789886e+09,
+              1.587960565565748e+27, 0,  # Matlab: 2.161236218626134e+15,
+              1.339913493808585e+33]
+        a2 = [1.000000000000000e+00, 1.849550755473371e+02,
+              2.113222918998538e+07, 3.125114149732283e+09,
+              1.785133457155609e+14, 1.979158697776348e+16,
+              7.535048322653831e+20, 5.567966191263037e+22,
+              1.589246884221346e+27, 5.871210648525566e+28,
+              1.339913493808590e+33]
+        b2 = xp.asarray(b2, dtype=xp.float64)
+        a2 = xp.asarray(a2, dtype=xp.float64)
+        xp_assert_close(b, b2, rtol=5e-14 if not DEFAULT_F32 else 1e-7)
+        xp_assert_close(a, a2, rtol=5e-14 if not DEFAULT_F32 else 1e-7)
+
+    def test_fs_param(self):
+        for fs in (900, 900.1, 1234.567):
+            for N in (0, 1, 2, 3, 10):
+                for fc in (100, 100.1, 432.12345):
+                    for btype in ('lp', 'hp'):
+                        ba1 = cheby2(N, 20, fc, btype, fs=fs)
+                        ba2 = cheby2(N, 20, fc/(fs/2), btype)
+                        for ba1_, ba2_ in zip(ba1, ba2):
+                            xp_assert_close(ba1_, ba2_)
+                for fc in ((100, 200), (100.1, 200.2), (321.123, 432.123)):
+                    for btype in ('bp', 'bs'):
+                        ba1 = cheby2(N, 20, fc, btype, fs=fs)
+                        for seq in (list, tuple, array):
+                            fcnorm = seq([f/(fs/2) for f in fc])
+                            ba2 = cheby2(N, 20, fcnorm, btype)
+                            for ba1_, ba2_ in zip(ba1, ba2):
+                                xp_assert_close(ba1_, ba2_)
+
+
+@skip_xp_backends("dask.array", reason="https://github.com/dask/dask/issues/11883")
+@make_xp_test_case(ellip)
+class TestEllip:
+
+    @xfail_xp_backends("cupy", reason="dtypes do not match")
+    def test_degenerate(self, xp):
+        # 0-order filter is just a passthrough
+        # Even-order filters have DC gain of -rp dB
+        # Stopband ripple factor doesn't matter
+        b, a = ellip(0, 10*math.log10(2), 123.456, xp.asarray(1.), analog=True)
+        assert_array_almost_equal(b, xp.asarray([1/math.sqrt(2)], dtype=xp.float64))
+        xp_assert_equal(a, xp.asarray([1.0], dtype=xp.float64))
+
+        # 1-order filter is same for all types
+        b, a = ellip(1, 10*math.log10(2), 1, xp.asarray(1.), analog=True)
+        assert_array_almost_equal(b, xp.asarray([1.], dtype=xp.float64))
+        assert_array_almost_equal(a, xp.asarray([1., 1], dtype=xp.float64))
+
+        z, p, k = ellip(1, 1, 55, xp.asarray(0.3), output='zpk')
+        xp_assert_close(
+            z, xp.asarray([-9.999999999999998e-01 + 0j], dtype=xp.complex128),
+            rtol=1e-14
+        )
+        xp_assert_close(
+            p, xp.asarray([-6.660721153525525e-04 + 0j], dtype=xp.complex128),
+            rtol=1e-10 if not DEFAULT_F32 else 5e-5
+        )
+        assert math.isclose(
+            k, 5.003330360576763e-01, rel_tol=1e-14 if not DEFAULT_F32 else 1e-7
+        )
+
+    def test_basic(self, xp):
+        for N in range(25):
+            wn = xp.asarray(0.01)
+            z, p, k = ellip(N, 1, 40, wn, 'low', analog=True, output='zpk')
+            assert p.shape[0] == N
+            assert xp.all(xp.real(p) <= 0)  # No poles in right half of S-plane
+
+        for N in range(25):
+            wn = xp.asarray(0.01)
+            z, p, k = ellip(N, 1, 40, wn, 'high', analog=False, output='zpk')
+            assert xp.all(xp.abs(p) <= 1)  # No poles outside unit circle
+
+        b3, a3 = ellip(5, 3, 26, xp.asarray(1.), analog=True)
+        assert_array_almost_equal(
+            b3, xp.asarray([0.1420, 0, 0.3764, 0, 0.2409], dtype=xp.float64),
+            decimal=4
+        )
+        assert_array_almost_equal(
+            a3,
+            xp.asarray([1, 0.5686, 1.8061, 0.8017, 0.8012, 0.2409], dtype=xp.float64),
+            decimal=4
+        )
+
+        b, a = ellip(3, 1, 60, xp.asarray([0.4, 0.7]), 'stop')
+        assert_array_almost_equal(
+            b, xp.asarray([0.3310, 0.3469, 1.1042, 0.7044, 1.1042,
+                           0.3469, 0.3310], dtype=xp.float64),
+            decimal=4
+        )
+        assert_array_almost_equal(
+            a, xp.asarray([1.0000, 0.6973, 1.1441, 0.5878, 0.7323,
+                           0.1131, -0.0060], dtype=xp.float64),
+            decimal=4
+        )
+
+    def test_highpass(self, xp):
+        # high even order
+        z, p, k = ellip(24, 1, 80, xp.asarray(0.3), 'high', output='zpk')
+        z2 = [9.761875332501075e-01 + 2.169283290099910e-01j,
+              9.761875332501075e-01 - 2.169283290099910e-01j,
+              8.413503353963494e-01 + 5.404901600661900e-01j,
+              8.413503353963494e-01 - 5.404901600661900e-01j,
+              7.160082576305009e-01 + 6.980918098681732e-01j,
+              7.160082576305009e-01 - 6.980918098681732e-01j,
+              6.456533638965329e-01 + 7.636306264739803e-01j,
+              6.456533638965329e-01 - 7.636306264739803e-01j,
+              6.127321820971366e-01 + 7.902906256703928e-01j,
+              6.127321820971366e-01 - 7.902906256703928e-01j,
+              5.983607817490196e-01 + 8.012267936512676e-01j,
+              5.983607817490196e-01 - 8.012267936512676e-01j,
+              5.922577552594799e-01 + 8.057485658286990e-01j,
+              5.922577552594799e-01 - 8.057485658286990e-01j,
+              5.896952092563588e-01 + 8.076258788449631e-01j,
+              5.896952092563588e-01 - 8.076258788449631e-01j,
+              5.886248765538837e-01 + 8.084063054565607e-01j,
+              5.886248765538837e-01 - 8.084063054565607e-01j,
+              5.881802711123132e-01 + 8.087298490066037e-01j,
+              5.881802711123132e-01 - 8.087298490066037e-01j,
+              5.879995719101164e-01 + 8.088612386766461e-01j,
+              5.879995719101164e-01 - 8.088612386766461e-01j,
+              5.879354086709576e-01 + 8.089078780868164e-01j,
+              5.879354086709576e-01 - 8.089078780868164e-01j]
+        p2 = [-3.184805259081650e-01 + 4.206951906775851e-01j,
+              -3.184805259081650e-01 - 4.206951906775851e-01j,
+               1.417279173459985e-01 + 7.903955262836452e-01j,
+               1.417279173459985e-01 - 7.903955262836452e-01j,
+               4.042881216964651e-01 + 8.309042239116594e-01j,
+               4.042881216964651e-01 - 8.309042239116594e-01j,
+               5.128964442789670e-01 + 8.229563236799665e-01j,
+               5.128964442789670e-01 - 8.229563236799665e-01j,
+               5.569614712822724e-01 + 8.155957702908510e-01j,
+               5.569614712822724e-01 - 8.155957702908510e-01j,
+               5.750478870161392e-01 + 8.118633973883931e-01j,
+               5.750478870161392e-01 - 8.118633973883931e-01j,
+               5.825314018170804e-01 + 8.101960910679270e-01j,
+               5.825314018170804e-01 - 8.101960910679270e-01j,
+               5.856397379751872e-01 + 8.094825218722543e-01j,
+               5.856397379751872e-01 - 8.094825218722543e-01j,
+               5.869326035251949e-01 + 8.091827531557583e-01j,
+               5.869326035251949e-01 - 8.091827531557583e-01j,
+               5.874697218855733e-01 + 8.090593298213502e-01j,
+               5.874697218855733e-01 - 8.090593298213502e-01j,
+               5.876904783532237e-01 + 8.090127161018823e-01j,
+               5.876904783532237e-01 - 8.090127161018823e-01j,
+               5.877753105317594e-01 + 8.090050577978136e-01j,
+               5.877753105317594e-01 - 8.090050577978136e-01j]
+        z2 = xp.asarray(z2, dtype=xp.complex128)
+        p2 = xp.asarray(p2, dtype=xp.complex128)
+        k2 = 4.918081266957108e-02
+        xp_assert_close(_sort_cmplx(z, xp=xp),
+                        _sort_cmplx(z2, xp=xp), rtol=1e-4)
+        xp_assert_close(_sort_cmplx(p, xp=xp),
+                        _sort_cmplx(p2, xp=xp), rtol=1e-4)
+        assert math.isclose(k, k2, rel_tol=1e-3)
+
+        # high odd order
+        z, p, k = ellip(23, 1, 70, xp.asarray(0.5), 'high', output='zpk')
+        z2 = [9.999999999998661e-01,
+              6.603717261750994e-01 + 7.509388678638675e-01j,
+              6.603717261750994e-01 - 7.509388678638675e-01j,
+              2.788635267510325e-01 + 9.603307416968041e-01j,
+              2.788635267510325e-01 - 9.603307416968041e-01j,
+              1.070215532544218e-01 + 9.942567008268131e-01j,
+              1.070215532544218e-01 - 9.942567008268131e-01j,
+              4.049427369978163e-02 + 9.991797705105507e-01j,
+              4.049427369978163e-02 - 9.991797705105507e-01j,
+              1.531059368627931e-02 + 9.998827859909265e-01j,
+              1.531059368627931e-02 - 9.998827859909265e-01j,
+              5.808061438534933e-03 + 9.999831330689181e-01j,
+              5.808061438534933e-03 - 9.999831330689181e-01j,
+              2.224277847754599e-03 + 9.999975262909676e-01j,
+              2.224277847754599e-03 - 9.999975262909676e-01j,
+              8.731857107534554e-04 + 9.999996187732845e-01j,
+              8.731857107534554e-04 - 9.999996187732845e-01j,
+              3.649057346914968e-04 + 9.999999334218996e-01j,
+              3.649057346914968e-04 - 9.999999334218996e-01j,
+              1.765538109802615e-04 + 9.999999844143768e-01j,
+              1.765538109802615e-04 - 9.999999844143768e-01j,
+              1.143655290967426e-04 + 9.999999934602630e-01j,
+              1.143655290967426e-04 - 9.999999934602630e-01j]
+        p2 = [-6.322017026545028e-01,
+              -4.648423756662754e-01 + 5.852407464440732e-01j,
+              -4.648423756662754e-01 - 5.852407464440732e-01j,
+              -2.249233374627773e-01 + 8.577853017985717e-01j,
+              -2.249233374627773e-01 - 8.577853017985717e-01j,
+              -9.234137570557621e-02 + 9.506548198678851e-01j,
+              -9.234137570557621e-02 - 9.506548198678851e-01j,
+              -3.585663561241373e-02 + 9.821494736043981e-01j,
+              -3.585663561241373e-02 - 9.821494736043981e-01j,
+              -1.363917242312723e-02 + 9.933844128330656e-01j,
+              -1.363917242312723e-02 - 9.933844128330656e-01j,
+              -5.131505238923029e-03 + 9.975221173308673e-01j,
+              -5.131505238923029e-03 - 9.975221173308673e-01j,
+              -1.904937999259502e-03 + 9.990680819857982e-01j,
+              -1.904937999259502e-03 - 9.990680819857982e-01j,
+              -6.859439885466834e-04 + 9.996492201426826e-01j,
+              -6.859439885466834e-04 - 9.996492201426826e-01j,
+              -2.269936267937089e-04 + 9.998686250679161e-01j,
+              -2.269936267937089e-04 - 9.998686250679161e-01j,
+              -5.687071588789117e-05 + 9.999527573294513e-01j,
+              -5.687071588789117e-05 - 9.999527573294513e-01j,
+              -6.948417068525226e-07 + 9.999882737700173e-01j,
+              -6.948417068525226e-07 - 9.999882737700173e-01j]
+        z2 = xp.asarray(z2, dtype=xp.complex128)
+        p2 = xp.asarray(p2, dtype=xp.complex128)
+        k2 = 1.220910020289434e-02
+        xp_assert_close(_sort_cmplx(z, xp=xp),
+                        _sort_cmplx(z2, xp=xp), rtol=1e-4)
+        xp_assert_close(_sort_cmplx(p, xp=xp),
+                        _sort_cmplx(p2, xp=xp), rtol=1e-4)
+        assert math.isclose(k, k2, rel_tol=1e-3)
+
+    def test_bandpass(self, xp):
+        z, p, k = ellip(7, 1, 40, [0.07, 0.2], 'pass', output='zpk')
+        z2 = [-9.999999999999991e-01,
+               6.856610961780020e-01 + 7.279209168501619e-01j,
+               6.856610961780020e-01 - 7.279209168501619e-01j,
+               7.850346167691289e-01 + 6.194518952058737e-01j,
+               7.850346167691289e-01 - 6.194518952058737e-01j,
+               7.999038743173071e-01 + 6.001281461922627e-01j,
+               7.999038743173071e-01 - 6.001281461922627e-01j,
+               9.999999999999999e-01,
+               9.862938983554124e-01 + 1.649980183725925e-01j,
+               9.862938983554124e-01 - 1.649980183725925e-01j,
+               9.788558330548762e-01 + 2.045513580850601e-01j,
+               9.788558330548762e-01 - 2.045513580850601e-01j,
+               9.771155231720003e-01 + 2.127093189691258e-01j,
+               9.771155231720003e-01 - 2.127093189691258e-01j]
+        p2 = [8.063992755498643e-01 + 5.858071374778874e-01j,
+              8.063992755498643e-01 - 5.858071374778874e-01j,
+              8.050395347071724e-01 + 5.639097428109795e-01j,
+              8.050395347071724e-01 - 5.639097428109795e-01j,
+              8.113124936559144e-01 + 4.855241143973142e-01j,
+              8.113124936559144e-01 - 4.855241143973142e-01j,
+              8.665595314082394e-01 + 3.334049560919331e-01j,
+              8.665595314082394e-01 - 3.334049560919331e-01j,
+              9.412369011968871e-01 + 2.457616651325908e-01j,
+              9.412369011968871e-01 - 2.457616651325908e-01j,
+              9.679465190411238e-01 + 2.228772501848216e-01j,
+              9.679465190411238e-01 - 2.228772501848216e-01j,
+              9.747235066273385e-01 + 2.178937926146544e-01j,
+              9.747235066273385e-01 - 2.178937926146544e-01j]
+        z2 = xp.asarray(z2, dtype=xp.complex128)
+        p2 = xp.asarray(p2, dtype=xp.complex128)
+        k2 = 8.354782670263239e-03
+        xp_assert_close(_sort_cmplx(z, xp=xp),
+                        _sort_cmplx(z2, xp=xp), rtol=1e-4)
+        xp_assert_close(_sort_cmplx(p, xp=xp),
+                        _sort_cmplx(p2, xp=xp), rtol=1e-4)
+        assert math.isclose(k, k2, rel_tol=1e-3)
+
+        z, p, k = ellip(5, 1, 75, [90.5, 110.5], 'pass', True, 'zpk')
+        z2 = [-5.583607317695175e-14 + 1.433755965989225e+02j,
+              -5.583607317695175e-14 - 1.433755965989225e+02j,
+               5.740106416459296e-14 + 1.261678754570291e+02j,
+               5.740106416459296e-14 - 1.261678754570291e+02j,
+              -2.199676239638652e-14 + 6.974861996895196e+01j,
+              -2.199676239638652e-14 - 6.974861996895196e+01j,
+              -3.372595657044283e-14 + 7.926145989044531e+01j,
+              -3.372595657044283e-14 - 7.926145989044531e+01j,
+              0]
+        p2 = [-8.814960004852743e-01 + 1.104124501436066e+02j,
+              -8.814960004852743e-01 - 1.104124501436066e+02j,
+              -2.477372459140184e+00 + 1.065638954516534e+02j,
+              -2.477372459140184e+00 - 1.065638954516534e+02j,
+              -3.072156842945799e+00 + 9.995404870405324e+01j,
+              -3.072156842945799e+00 - 9.995404870405324e+01j,
+              -2.180456023925693e+00 + 9.379206865455268e+01j,
+              -2.180456023925693e+00 - 9.379206865455268e+01j,
+              -7.230484977485752e-01 + 9.056598800801140e+01j,
+              -7.230484977485752e-01 - 9.056598800801140e+01j]
+        z2 = xp.asarray(z2, dtype=xp.complex128)
+        p2 = xp.asarray(p2, dtype=xp.complex128)
+        k2 = 3.774571622827070e-02
+        xp_assert_close(_sort_cmplx(z, xp=xp),
+                        _sort_cmplx(z2, xp=xp), rtol=1e-4)
+        xp_assert_close(_sort_cmplx(p, xp=xp),
+                        _sort_cmplx(p2, xp=xp), rtol=1e-6)
+        assert math.isclose(k, k2, rel_tol=1e-3)
+
+    def test_bandstop(self, xp):
+        z, p, k = ellip(8, 1, 65, [0.2, 0.4], 'stop', output='zpk')
+        z2 = [3.528578094286510e-01 + 9.356769561794296e-01j,
+              3.528578094286510e-01 - 9.356769561794296e-01j,
+              3.769716042264783e-01 + 9.262248159096587e-01j,
+              3.769716042264783e-01 - 9.262248159096587e-01j,
+              4.406101783111199e-01 + 8.976985411420985e-01j,
+              4.406101783111199e-01 - 8.976985411420985e-01j,
+              5.539386470258847e-01 + 8.325574907062760e-01j,
+              5.539386470258847e-01 - 8.325574907062760e-01j,
+              6.748464963023645e-01 + 7.379581332490555e-01j,
+              6.748464963023645e-01 - 7.379581332490555e-01j,
+              7.489887970285254e-01 + 6.625826604475596e-01j,
+              7.489887970285254e-01 - 6.625826604475596e-01j,
+              7.913118471618432e-01 + 6.114127579150699e-01j,
+              7.913118471618432e-01 - 6.114127579150699e-01j,
+              7.806804740916381e-01 + 6.249303940216475e-01j,
+              7.806804740916381e-01 - 6.249303940216475e-01j]
+
+        p2 = [-1.025299146693730e-01 + 5.662682444754943e-01j,
+              -1.025299146693730e-01 - 5.662682444754943e-01j,
+               1.698463595163031e-01 + 8.926678667070186e-01j,
+               1.698463595163031e-01 - 8.926678667070186e-01j,
+               2.750532687820631e-01 + 9.351020170094005e-01j,
+               2.750532687820631e-01 - 9.351020170094005e-01j,
+               3.070095178909486e-01 + 9.457373499553291e-01j,
+               3.070095178909486e-01 - 9.457373499553291e-01j,
+               7.695332312152288e-01 + 2.792567212705257e-01j,
+               7.695332312152288e-01 - 2.792567212705257e-01j,
+               8.083818999225620e-01 + 4.990723496863960e-01j,
+               8.083818999225620e-01 - 4.990723496863960e-01j,
+               8.066158014414928e-01 + 5.649811440393374e-01j,
+               8.066158014414928e-01 - 5.649811440393374e-01j,
+               8.062787978834571e-01 + 5.855780880424964e-01j,
+               8.062787978834571e-01 - 5.855780880424964e-01j]
+        z2 = xp.asarray(z2, dtype=xp.complex128)
+        p2 = xp.asarray(p2, dtype=xp.complex128)
+        k2 = 2.068622545291259e-01
+        xp_assert_close(_sort_cmplx(z, xp=xp),
+                        _sort_cmplx(z2, xp=xp), rtol=1e-6)
+        xp_assert_close(_sort_cmplx(p, xp=xp),
+                        _sort_cmplx(p2, xp=xp), rtol=1e-5)
+        assert math.isclose(k, k2, rel_tol=1e-5)
+
+    @xfail_xp_backends("cupy", reason="inaccurate on CuPy")
+    def test_ba_output(self, xp):
+        # with transfer function conversion,  without digital conversion
+        b, a = ellip(5, 1, 40, xp.asarray([201, 240]), 'stop', True)
+        b2 = [
+             1.000000000000000e+00, 0,  # Matlab: 1.743506051190569e-13,
+             2.426561778314366e+05, 0,  # Matlab: 3.459426536825722e-08,
+             2.348218683400168e+10, 0,  # Matlab: 2.559179747299313e-03,
+             1.132780692872241e+15, 0,  # Matlab: 8.363229375535731e+01,
+             2.724038554089566e+19, 0,  # Matlab: 1.018700994113120e+06,
+             2.612380874940186e+23
+             ]
+        a2 = [
+             1.000000000000000e+00, 1.337266601804649e+02,
+             2.486725353510667e+05, 2.628059713728125e+07,
+             2.436169536928770e+10, 1.913554568577315e+12,
+             1.175208184614438e+15, 6.115751452473410e+16,
+             2.791577695211466e+19, 7.241811142725384e+20,
+             2.612380874940182e+23
+             ]
+        b2 = xp.asarray(b2, dtype=xp.float64)
+        a2 = xp.asarray(a2, dtype=xp.float64)
+        xp_assert_close(b, b2, rtol=1e-6)
+        xp_assert_close(a, a2, rtol=1e-4)
+
+    def test_fs_param(self):
+        for fs in (900, 900.1, 1234.567):
+            for N in (0, 1, 2, 3, 10):
+                for fc in (100, 100.1, 432.12345):
+                    for btype in ('lp', 'hp'):
+                        ba1 = ellip(N, 1, 20, fc, btype, fs=fs)
+                        ba2 = ellip(N, 1, 20, fc/(fs/2), btype)
+                        for ba1_, ba2_ in zip(ba1, ba2):
+                            xp_assert_close(ba1_, ba2_)
+                for fc in ((100, 200), (100.1, 200.2), (321.123, 432.123)):
+                    for btype in ('bp', 'bs'):
+                        ba1 = ellip(N, 1, 20, fc, btype, fs=fs)
+                        for seq in (list, tuple, array):
+                            fcnorm = seq([f/(fs/2) for f in fc])
+                            ba2 = ellip(N, 1, 20, fcnorm, btype)
+                            for ba1_, ba2_ in zip(ba1, ba2):
+                                xp_assert_close(ba1_, ba2_)
+
+    def test_fs_validation(self):
+        with pytest.raises(ValueError, match="Sampling.*single scalar"):
+            iirnotch(0.06, 30, fs=np.array([10, 20]))
+
+        with pytest.raises(ValueError, match="Sampling.*be none"):
+            iirnotch(0.06, 30, fs=None)
+
+
+def test_sos_consistency():
+    # Consistency checks of output='sos' for the specialized IIR filter
+    # design functions.
+    design_funcs = [(bessel, (0.1,)),
+                    (butter, (0.1,)),
+                    (cheby1, (45.0, 0.1)),
+                    (cheby2, (0.087, 0.1)),
+                    (ellip, (0.087, 45, 0.1))]
+    for func, args in design_funcs:
+        name = func.__name__
+
+        b, a = func(2, *args, output='ba')
+        sos = func(2, *args, output='sos')
+        xp_assert_close(sos, [np.hstack((b, a))], err_msg=f"{name}(2,...)")
+
+        zpk = func(3, *args, output='zpk')
+        sos = func(3, *args, output='sos')
+        xp_assert_close(sos, zpk2sos(*zpk), err_msg=f"{name}(3,...)")
+
+        zpk = func(4, *args, output='zpk')
+        sos = func(4, *args, output='sos')
+        xp_assert_close(sos, zpk2sos(*zpk), err_msg=f"{name}(4,...)")
+
+
+@make_xp_test_case(iirnotch)
+class TestIIRNotch:
+
+    def test_ba_output(self, xp):
+        # Compare coefficients with Matlab ones
+        # for the equivalent input:
+        b, a = iirnotch(0.06, 30, xp=xp)
+        b2 = xp.asarray([
+             9.9686824e-01, -1.9584219e+00,
+             9.9686824e-01
+             ])
+        a2 = xp.asarray([
+             1.0000000e+00, -1.9584219e+00,
+             9.9373647e-01
+             ])
+
+        xp_assert_close(b, b2, rtol=1e-8)
+        xp_assert_close(a, a2, rtol=1e-8)
+
+    @pytest.mark.xfail(DEFAULT_F32, reason="wrong answer with torch/float32")
+    @skip_xp_backends("dask.array", reason="https://github.com/dask/dask/issues/11883")
+    def test_frequency_response(self, xp):
+        # Get filter coefficients
+        b, a = iirnotch(0.3, 30, xp=xp)
+
+        # Get frequency response
+        w, h = freqz(b, a, 1000)
+
+        # Pick 5 point
+        p = [200,  # w0 = 0.200
+             295,  # w0 = 0.295
+             300,  # w0 = 0.300
+             305,  # w0 = 0.305
+             400]  # w0 = 0.400
+
+        # Get frequency response correspondent to each of those points
+        hp = h[xp.asarray(p)]
+
+        # Check if the frequency response fulfill the specifications:
+        # hp[0] and hp[4]  correspond to frequencies distant from
+        # w0 = 0.3 and should be close to 1
+        assert math.isclose(xp.abs(hp[0]), 1., rel_tol=1e-2)
+        assert math.isclose(xp.abs(hp[4]), 1., rel_tol=1e-2)
+
+        # hp[1] and hp[3] correspond to frequencies approximately
+        # on the edges of the passband and should be close to -3dB
+        assert math.isclose(xp.abs(hp[1]), 1 / math.sqrt(2), rel_tol=1e-2)
+        assert math.isclose(xp.abs(hp[3]), 1 / math.sqrt(2), rel_tol=1e-2)
+
+        # hp[2] correspond to the frequency that should be removed
+        # the frequency response should be very close to 0
+        assert math.isclose(xp.abs(hp[2]), 0.0, abs_tol=1e-10)
+
+    def test_errors(self):
+        # Exception should be raised if w0 > 1 or w0 <0
+        assert_raises(ValueError, iirnotch, w0=2, Q=30)
+        assert_raises(ValueError, iirnotch, w0=-1, Q=30)
+
+        # Exception should be raised if any of the parameters
+        # are not float (or cannot be converted to one)
+        assert_raises(ValueError, iirnotch, w0="blabla", Q=30)
+        assert_raises(TypeError, iirnotch, w0=-1, Q=[1, 2, 3])
+
+    @pytest.mark.xfail(DEFAULT_F32, reason="wrong answer with torch/float32")
+    @skip_xp_backends("dask.array", reason="https://github.com/dask/dask/issues/11883")
+    def test_fs_param(self, xp):
+        # Get filter coefficients
+        b, a = iirnotch(1500, 30, fs=10000, xp=xp)
+
+        # Get frequency response
+        w, h = freqz(b, a, 1000, fs=10000)
+
+        # Pick 5 point
+        p = [200,  # w0 = 1000
+             295,  # w0 = 1475
+             300,  # w0 = 1500
+             305,  # w0 = 1525
+             400]  # w0 = 2000
+
+        # Get frequency response correspondent to each of those points
+        hp = h[xp.asarray(p)]
+
+        # Check if the frequency response fulfill the specifications:
+        # hp[0] and hp[4]  correspond to frequencies distant from
+        # w0 = 1500 and should be close to 1
+        assert math.isclose(xp.abs(hp[0]), 1.0, rel_tol=1e-2)
+        assert math.isclose(xp.abs(hp[4]), 1.0, rel_tol=1e-2)
+
+        # hp[1] and hp[3] correspond to frequencies approximately
+        # on the edges of the passband and should be close to -3dB
+        assert math.isclose(xp.abs(hp[1]), 1 / math.sqrt(2), rel_tol=1e-2)
+        assert math.isclose(xp.abs(hp[3]), 1 / math.sqrt(2), rel_tol=1e-2)
+
+        # hp[2] correspond to the frequency that should be removed
+        # the frequency response should be very close to 0
+        assert math.isclose(xp.abs(hp[2]), 0.0, abs_tol=1e-10)
+
+
+@make_xp_test_case(iirpeak)
+class TestIIRPeak:
+
+    def test_ba_output(self, xp):
+        # Compare coefficients with Matlab ones
+        # for the equivalent input:
+        b, a = iirpeak(0.06, 30, xp=xp)
+        b2 = xp.asarray([
+             3.131764229e-03, 0,
+             -3.131764229e-03
+             ])
+        a2 = xp.asarray([
+             1.0000000e+00, -1.958421917e+00,
+             9.9373647e-01
+             ])
+        xp_assert_close(b, b2, rtol=1e-8)
+        xp_assert_close(a, a2, rtol=1e-8)
+
+    @pytest.mark.xfail(DEFAULT_F32, reason="wrong answer with torch/float32")
+    @skip_xp_backends("dask.array", reason="https://github.com/dask/dask/issues/11883")
+    def test_frequency_response(self, xp):
+        # Get filter coefficients
+        b, a = iirpeak(0.3, 30, xp=xp)
+
+        # Get frequency response
+        w, h = freqz(b, a, 1000)
+
+        # Pick 5 point
+        p = [30,  # w0 = 0.030
+             295,  # w0 = 0.295
+             300,  # w0 = 0.300
+             305,  # w0 = 0.305
+             800]  # w0 = 0.800
+
+        # Get frequency response correspondent to each of those points
+        hp = h[xp.asarray(p)]
+
+        # Check if the frequency response fulfill the specifications:
+        # hp[0] and hp[4]  correspond to frequencies distant from
+        # w0 = 0.3 and should be close to 0
+        assert math.isclose(xp.abs(hp[0]), 0., abs_tol=1e-2)
+        assert math.isclose(xp.abs(hp[4]), 0., abs_tol=1e-2)
+
+        # hp[1] and hp[3] correspond to frequencies approximately
+        # on the edges of the passband and should be close to 10**(-3/20)
+        assert math.isclose(xp.abs(hp[1]), 1 / math.sqrt(2), rel_tol=1e-2)
+        assert math.isclose(xp.abs(hp[3]), 1 / math.sqrt(2), rel_tol=1e-2)
+
+        # hp[2] correspond to the frequency that should be retained and
+        # the frequency response should be very close to 1
+        assert math.isclose(xp.abs(hp[2]), 1.0, rel_tol=1e-10)
+
+    @skip_xp_backends(np_only=True)
+    def test_errors(self):
+        # Exception should be raised if w0 > 1 or w0 <0
+        assert_raises(ValueError, iirpeak, w0=2, Q=30)
+        assert_raises(ValueError, iirpeak, w0=-1, Q=30)
+
+        # Exception should be raised if any of the parameters
+        # are not float (or cannot be converted to one)
+        assert_raises(ValueError, iirpeak, w0="blabla", Q=30)
+        assert_raises(TypeError, iirpeak, w0=-1, Q=[1, 2, 3])
+
+    @pytest.mark.xfail(DEFAULT_F32, reason="wrong answer with torch/float32")
+    @skip_xp_backends("dask.array", reason="https://github.com/dask/dask/issues/11883")
+    def test_fs_param(self, xp):
+        # Get filter coefficients
+        b, a = iirpeak(1200, 30, fs=8000, xp=xp)
+
+        # Get frequency response
+        w, h = freqz(b, a, 1000, fs=8000)
+
+        # Pick 5 point
+        p = [30,  # w0 = 120
+             295,  # w0 = 1180
+             300,  # w0 = 1200
+             305,  # w0 = 1220
+             800]  # w0 = 3200
+
+        # Get frequency response correspondent to each of those points
+        hp = h[xp.asarray(p)]
+
+        # Check if the frequency response fulfill the specifications:
+        # hp[0] and hp[4]  correspond to frequencies distant from
+        # w0 = 1200 and should be close to 0
+        assert math.isclose(abs(hp[0]), 0.0, abs_tol=1e-2)
+        assert math.isclose(abs(hp[4]), 0.0, abs_tol=1e-2)
+
+        # hp[1] and hp[3] correspond to frequencies approximately
+        # on the edges of the passband and should be close to 10**(-3/20)
+        assert math.isclose(abs(hp[1]), 1 / math.sqrt(2), rel_tol=1e-2)
+        assert math.isclose(abs(hp[3]), 1 / math.sqrt(2), rel_tol=1e-2)
+
+        # hp[2] correspond to the frequency that should be retained and
+        # the frequency response should be very close to 1
+        assert math.isclose(abs(hp[2]), 1.0, rel_tol=1e-10)
+
+
+@pytest.mark.xfail(DEFAULT_F32, reason="wrong answers with torch/float32")
+@skip_xp_backends("dask.array", reason="https://github.com/dask/dask/issues/11883")
+@make_xp_test_case(iircomb)
+class TestIIRComb:
+    # Test erroneous input cases
+    @skip_xp_backends(np_only=True)
+    def test_invalid_input(self):
+        # w0 is <= 0 or >= fs / 2
+        fs = 1000
+        for args in [(-fs, 30), (0, 35), (fs / 2, 40), (fs, 35)]:
+            with pytest.raises(ValueError, match='w0 must be between '):
+                iircomb(*args, fs=fs)
+
+        # fs is not divisible by w0
+        for args in [(120, 30), (157, 35)]:
+            with pytest.raises(ValueError, match='fs must be divisible '):
+                iircomb(*args, fs=fs)
+
+        # https://github.com/scipy/scipy/issues/14043#issuecomment-1107349140
+        # Previously, fs=44100, w0=49.999 was rejected, but fs=2,
+        # w0=49.999/int(44100/2) was accepted. Now it is rejected, too.
+        with pytest.raises(ValueError, match='fs must be divisible '):
+            iircomb(w0=49.999/int(44100/2), Q=30)
+
+        with pytest.raises(ValueError, match='fs must be divisible '):
+            iircomb(w0=49.999, Q=30, fs=44100)
+
+        # Filter type is not notch or peak
+        for args in [(0.2, 30, 'natch'), (0.5, 35, 'comb')]:
+            with pytest.raises(ValueError, match='ftype must be '):
+                iircomb(*args)
+
+    # Verify that the filter's frequency response contains a
+    # notch at the cutoff frequency
+    @pytest.mark.parametrize('ftype', ('notch', 'peak'))
+    def test_frequency_response(self, ftype, xp):
+        # Create a notching or peaking comb filter at 1000 Hz
+        b, a = iircomb(1000, 30, ftype=ftype, fs=10000, xp=xp)
+
+        # Compute the frequency response
+        freqs, response = freqz(b, a, 1000, fs=10000)
+
+        # Find the notch using argrelextrema
+        comb_points = argrelextrema(abs(_xp_copy_to_numpy(response)), np.less)[0]
+        comb_points = xp.asarray(comb_points)
+
+        # Verify that the first notch sits at 1000 Hz
+        comb1 = comb_points[0]
+        xp_assert_close(freqs[comb1], xp.asarray(1000.), check_0d=False)
+
+    # Verify pass_zero parameter
+    @pytest.mark.parametrize('ftype,pass_zero,peak,notch',
+                             [('peak', True, 123.45, 61.725),
+                              ('peak', False, 61.725, 123.45),
+                              ('peak', None, 61.725, 123.45),
+                              ('notch', None, 61.725, 123.45),
+                              ('notch', True, 123.45, 61.725),
+                              ('notch', False, 61.725, 123.45)])
+    def test_pass_zero(self, ftype, pass_zero, peak, notch, xp):
+        # Create a notching or peaking comb filter
+        b, a = iircomb(123.45, 30, ftype=ftype, fs=1234.5, pass_zero=pass_zero, xp=xp)
+
+        # Compute the frequency response
+        freqs, response = freqz(b, a, xp.asarray([peak, notch]), fs=1234.5)
+
+        # Verify that expected notches are notches and peaks are peaks
+        assert xp.abs(response[0]) > 0.99
+        assert xp.abs(response[1]) < 1e-10
+
+    # All built-in IIR filters are real, so should have perfectly
+    # symmetrical poles and zeros. Then ba representation (using
+    # numpy.poly) will be purely real instead of having negligible
+    # imaginary parts.
+    def test_iir_symmetry(self, xp):
+        b, a = iircomb(400, 30, fs=24000, xp=xp)
+        z, p, k = tf2zpk(b, a)
+        xp_assert_equal(_sort_cmplx(z, xp=xp), _sort_cmplx(xp.conj(z), xp=xp))
+        xp_assert_equal(_sort_cmplx(p, xp=xp), _sort_cmplx(xp.conj(p), xp=xp))
+        xp_assert_equal(k, xp.real(k))
+
+        isdtype = array_namespace(b).isdtype
+        assert isdtype(b.dtype, ('real floating', 'complex floating'))
+        assert isdtype(a.dtype, ('real floating', 'complex floating'))
+
+    # Verify filter coefficients with MATLAB's iircomb function
+    def test_ba_output(self, xp):
+        b_notch, a_notch = iircomb(60, 35, ftype='notch', fs=600, xp=xp)
+        b_notch2 = [0.957020174408697, 0.0, 0.0, 0.0, 0.0, 0.0,
+                    0.0, 0.0, 0.0, 0.0, -0.957020174408697]
+        a_notch2 = [1.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+                    0.0, 0.0, 0.0, 0.0, -0.914040348817395]
+        b_notch2 = xp.asarray(b_notch2)
+        a_notch2 = xp.asarray(a_notch2)
+        xp_assert_close(b_notch, b_notch2)
+        xp_assert_close(a_notch, a_notch2)
+
+        b_peak, a_peak = iircomb(60, 35, ftype='peak', fs=600, xp=xp)
+        b_peak2 = [0.0429798255913026, 0.0, 0.0, 0.0, 0.0, 0.0,
+                   0.0, 0.0, 0.0, 0.0, -0.0429798255913026]
+        a_peak2 = [1.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+                   0.0, 0.0, 0.0, 0.0, 0.914040348817395]
+        b_peak2 = xp.asarray(b_peak2)
+        a_peak2 = xp.asarray(a_peak2)
+        xp_assert_close(b_peak, b_peak2)
+        xp_assert_close(a_peak, a_peak2)
+
+    # Verify that https://github.com/scipy/scipy/issues/14043 is fixed
+    def test_nearest_divisor(self, xp):
+        # Create a notching comb filter
+        b, a = iircomb(50/int(44100/2), 50.0, ftype='notch', xp=xp)
+
+        # Compute the frequency response at an upper harmonic of 50
+        freqs, response = freqz(b, a, xp.asarray([22000]), fs=44100)
+
+        # Before bug fix, this would produce N = 881, so that 22 kHz was ~0 dB.
+        # Now N = 882 correctly and 22 kHz should be a notch <-220 dB
+        assert xp.abs(response[0]) < 1e-10
+
+    def test_fs_validation(self):
+        with pytest.raises(ValueError, match="Sampling.*single scalar"):
+            iircomb(1000, 30, fs=np.array([10, 20]))
+
+        with pytest.raises(ValueError, match="Sampling.*be none"):
+            iircomb(1000, 30, fs=None)
+
+
+class TestIIRDesign:
+
+    def test_exceptions(self):
+        with pytest.raises(ValueError, match="the same shape"):
+            iirdesign(0.2, [0.1, 0.3], 1, 40)
+        with pytest.raises(ValueError, match="the same shape"):
+            iirdesign(np.array([[0.3, 0.6], [0.3, 0.6]]),
+                      np.array([[0.4, 0.5], [0.4, 0.5]]), 1, 40)
+
+        # discrete filter with non-positive frequency
+        with pytest.raises(ValueError, match="must be greater than 0"):
+            iirdesign(0, 0.5, 1, 40)
+        with pytest.raises(ValueError, match="must be greater than 0"):
+            iirdesign(-0.1, 0.5, 1, 40)
+        with pytest.raises(ValueError, match="must be greater than 0"):
+            iirdesign(0.1, 0, 1, 40)
+        with pytest.raises(ValueError, match="must be greater than 0"):
+            iirdesign(0.1, -0.5, 1, 40)
+        with pytest.raises(ValueError, match="must be greater than 0"):
+            iirdesign([0, 0.3], [0.1, 0.5], 1, 40)
+        with pytest.raises(ValueError, match="must be greater than 0"):
+            iirdesign([-0.1, 0.3], [0.1, 0.5], 1, 40)
+        with pytest.raises(ValueError, match="must be greater than 0"):
+            iirdesign([0.1, 0], [0.1, 0.5], 1, 40)
+        with pytest.raises(ValueError, match="must be greater than 0"):
+            iirdesign([0.1, -0.3], [0.1, 0.5], 1, 40)
+        with pytest.raises(ValueError, match="must be greater than 0"):
+            iirdesign([0.1, 0.3], [0, 0.5], 1, 40)
+        with pytest.raises(ValueError, match="must be greater than 0"):
+            iirdesign([0.1, 0.3], [-0.1, 0.5], 1, 40)
+        with pytest.raises(ValueError, match="must be greater than 0"):
+            iirdesign([0.1, 0.3], [0.1, 0], 1, 40)
+        with pytest.raises(ValueError, match="must be greater than 0"):
+            iirdesign([0.1, 0.3], [0.1, -0.5], 1, 40)
+
+        # analog filter with negative frequency
+        with pytest.raises(ValueError, match="must be greater than 0"):
+            iirdesign(-0.1, 0.5, 1, 40, analog=True)
+        with pytest.raises(ValueError, match="must be greater than 0"):
+            iirdesign(0.1, -0.5, 1, 40, analog=True)
+        with pytest.raises(ValueError, match="must be greater than 0"):
+            iirdesign([-0.1, 0.3], [0.1, 0.5], 1, 40, analog=True)
+        with pytest.raises(ValueError, match="must be greater than 0"):
+            iirdesign([0.1, -0.3], [0.1, 0.5], 1, 40, analog=True)
+        with pytest.raises(ValueError, match="must be greater than 0"):
+            iirdesign([0.1, 0.3], [-0.1, 0.5], 1, 40, analog=True)
+        with pytest.raises(ValueError, match="must be greater than 0"):
+            iirdesign([0.1, 0.3], [0.1, -0.5], 1, 40, analog=True)
+
+        # discrete filter with fs=None, freq > 1
+        with pytest.raises(ValueError, match="must be less than 1"):
+            iirdesign(1, 0.5, 1, 40)
+        with pytest.raises(ValueError, match="must be less than 1"):
+            iirdesign(1.1, 0.5, 1, 40)
+        with pytest.raises(ValueError, match="must be less than 1"):
+            iirdesign(0.1, 1, 1, 40)
+        with pytest.raises(ValueError, match="must be less than 1"):
+            iirdesign(0.1, 1.5, 1, 40)
+        with pytest.raises(ValueError, match="must be less than 1"):
+            iirdesign([1, 0.3], [0.1, 0.5], 1, 40)
+        with pytest.raises(ValueError, match="must be less than 1"):
+            iirdesign([1.1, 0.3], [0.1, 0.5], 1, 40)
+        with pytest.raises(ValueError, match="must be less than 1"):
+            iirdesign([0.1, 1], [0.1, 0.5], 1, 40)
+        with pytest.raises(ValueError, match="must be less than 1"):
+            iirdesign([0.1, 1.1], [0.1, 0.5], 1, 40)
+        with pytest.raises(ValueError, match="must be less than 1"):
+            iirdesign([0.1, 0.3], [1, 0.5], 1, 40)
+        with pytest.raises(ValueError, match="must be less than 1"):
+            iirdesign([0.1, 0.3], [1.1, 0.5], 1, 40)
+        with pytest.raises(ValueError, match="must be less than 1"):
+            iirdesign([0.1, 0.3], [0.1, 1], 1, 40)
+        with pytest.raises(ValueError, match="must be less than 1"):
+            iirdesign([0.1, 0.3], [0.1, 1.5], 1, 40)
+
+        # discrete filter with fs>2, wp, ws < fs/2 must pass
+        iirdesign(100, 500, 1, 40, fs=2000)
+        iirdesign(500, 100, 1, 40, fs=2000)
+        iirdesign([200, 400], [100, 500], 1, 40, fs=2000)
+        iirdesign([100, 500], [200, 400], 1, 40, fs=2000)
+
+        # discrete filter with fs>2, freq > fs/2: this must raise
+        with pytest.raises(ValueError, match="must be less than fs/2"):
+            iirdesign(1000, 400, 1, 40, fs=2000)
+        with pytest.raises(ValueError, match="must be less than fs/2"):
+            iirdesign(1100, 500, 1, 40, fs=2000)
+        with pytest.raises(ValueError, match="must be less than fs/2"):
+            iirdesign(100, 1000, 1, 40, fs=2000)
+        with pytest.raises(ValueError, match="must be less than fs/2"):
+            iirdesign(100, 1100, 1, 40, fs=2000)
+        with pytest.raises(ValueError, match="must be less than fs/2"):
+            iirdesign([1000, 400], [100, 500], 1, 40, fs=2000)
+        with pytest.raises(ValueError, match="must be less than fs/2"):
+            iirdesign([1100, 400], [100, 500], 1, 40, fs=2000)
+        with pytest.raises(ValueError, match="must be less than fs/2"):
+            iirdesign([200, 1000], [100, 500], 1, 40, fs=2000)
+        with pytest.raises(ValueError, match="must be less than fs/2"):
+            iirdesign([200, 1100], [100, 500], 1, 40, fs=2000)
+        with pytest.raises(ValueError, match="must be less than fs/2"):
+            iirdesign([200, 400], [1000, 500], 1, 40, fs=2000)
+        with pytest.raises(ValueError, match="must be less than fs/2"):
+            iirdesign([200, 400], [1100, 500], 1, 40, fs=2000)
+        with pytest.raises(ValueError, match="must be less than fs/2"):
+            iirdesign([200, 400], [100, 1000], 1, 40, fs=2000)
+        with pytest.raises(ValueError, match="must be less than fs/2"):
+            iirdesign([200, 400], [100, 1100], 1, 40, fs=2000)
+
+        with pytest.raises(ValueError, match="strictly inside stopband"):
+            iirdesign([0.1, 0.4], [0.5, 0.6], 1, 40)
+        with pytest.raises(ValueError, match="strictly inside stopband"):
+            iirdesign([0.5, 0.6], [0.1, 0.4], 1, 40)
+        with pytest.raises(ValueError, match="strictly inside stopband"):
+            iirdesign([0.3, 0.6], [0.4, 0.7], 1, 40)
+        with pytest.raises(ValueError, match="strictly inside stopband"):
+            iirdesign([0.4, 0.7], [0.3, 0.6], 1, 40)
+
+    def test_fs_validation(self):
+        with pytest.raises(ValueError, match="Sampling.*single scalar"):
+            iirfilter(1, 1, btype="low", fs=np.array([10, 20]))
+
+
+@skip_xp_backends("dask.array", reason="https://github.com/dask/dask/issues/11883")
+@make_xp_test_case(iirfilter)
+class TestIIRFilter:
+
+    @pytest.mark.parametrize(
+        "func,ftype",
+        [
+            make_xp_pytest_param(butter, "butter"),
+            make_xp_pytest_param(bessel, "bessel"),
+            make_xp_pytest_param(cheby1, "cheby1"),
+            make_xp_pytest_param(cheby2, "cheby2"),
+            make_xp_pytest_param(ellip, "ellip"),
+        ]
+    )
+    def test_symmetry(self, func, ftype, xp):
+        # All built-in IIR filters are real, so should have perfectly
+        # symmetrical poles and zeros. Then ba representation (using
+        # numpy.poly) will be purely real instead of having negligible
+        # imaginary parts.
+        for N in range(1, 26):
+            z, p, k = iirfilter(N, xp.asarray(1.1), 1, 20, 'low', analog=True,
+                                ftype=ftype, output='zpk')
+            xp_assert_close(_sort_cmplx(z, xp=xp), _sort_cmplx(xp.conj(z), xp=xp))
+            xp_assert_close(_sort_cmplx(p, xp=xp), _sort_cmplx(xp.conj(p), xp=xp))
+            assert complex(k).imag == 0
+
+            b, a = iirfilter(N, xp.asarray(1.1), 1, 20, 'low', analog=True,
+                             ftype=ftype, output='ba')
+
+            isdtype = array_namespace(b).isdtype
+            assert isdtype(b.dtype, ('real floating', 'complex floating'))
+            assert isdtype(a.dtype, ('real floating', 'complex floating'))
+
+    @make_xp_test_case(bessel)
+    def test_int_inputs(self, xp):
+        # Using integer frequency arguments and large N should not produce
+        # numpy integers that wraparound to negative numbers
+        k = iirfilter(24, xp.asarray(100), btype='low', analog=True, ftype='bessel',
+                      output='zpk')[2]
+        k2 = 9.999999999999989e+47
+        assert math.isclose(k,  k2)
+        # if fs is specified then the normalization of Wn to have
+        # 0 <= Wn <= 1 should not cause an integer overflow
+        # the following line should not raise an exception
+        iirfilter(20, xp.asarray([1000000000, 1100000000]), btype='bp',
+                      analog=False, fs=6250000000)
+
+    def test_invalid_wn_size(self):
+        # low and high have 1 Wn, band and stop have 2 Wn
+        assert_raises(ValueError, iirfilter, 1, [0.1, 0.9], btype='low')
+        assert_raises(ValueError, iirfilter, 1, [0.2, 0.5], btype='high')
+        assert_raises(ValueError, iirfilter, 1, 0.2, btype='bp')
+        assert_raises(ValueError, iirfilter, 1, 400, btype='bs', analog=True)
+
+    def test_invalid_wn_range(self):
+        # For digital filters, 0 <= Wn <= 1
+        assert_raises(ValueError, iirfilter, 1, 2, btype='low')
+        assert_raises(ValueError, iirfilter, 1, [0.5, 1], btype='band')
+        assert_raises(ValueError, iirfilter, 1, [0., 0.5], btype='band')
+        assert_raises(ValueError, iirfilter, 1, -1, btype='high')
+        assert_raises(ValueError, iirfilter, 1, [1, 2], btype='band')
+        assert_raises(ValueError, iirfilter, 1, [10, 20], btype='stop')
+
+        # analog=True with non-positive critical frequencies
+        with pytest.raises(ValueError, match="must be greater than 0"):
+            iirfilter(2, 0, btype='low', analog=True)
+        with pytest.raises(ValueError, match="must be greater than 0"):
+            iirfilter(2, -1, btype='low', analog=True)
+        with pytest.raises(ValueError, match="must be greater than 0"):
+            iirfilter(2, [0, 100], analog=True)
+        with pytest.raises(ValueError, match="must be greater than 0"):
+            iirfilter(2, [-1, 100], analog=True)
+        with pytest.raises(ValueError, match="must be greater than 0"):
+            iirfilter(2, [10, 0], analog=True)
+        with pytest.raises(ValueError, match="must be greater than 0"):
+            iirfilter(2, [10, -1], analog=True)
+
+    @make_xp_test_case(butter)
+    def test_analog_sos(self, xp):
+        # first order Butterworth filter with Wn = 1 has tf 1/(s+1)
+        sos = xp.asarray([[0., 0., 1., 0., 1., 1.]])
+        sos2 = iirfilter(N=1, Wn=xp.asarray(1), btype='low', analog=True, output='sos')
+        assert_array_almost_equal(sos, sos2)
+
+    def test_wn1_ge_wn0(self):
+        # gh-15773: should raise error if Wn[0] >= Wn[1]
+        with pytest.raises(ValueError,
+                           match=r"Wn\[0\] must be less than Wn\[1\]"):
+            iirfilter(2, [0.5, 0.5])
+        with pytest.raises(ValueError,
+                           match=r"Wn\[0\] must be less than Wn\[1\]"):
+            iirfilter(2, [0.6, 0.5])
+
+
+@skip_xp_backends("dask.array", reason="https://github.com/dask/dask/issues/11883")
+@make_xp_test_case(group_delay)
+class TestGroupDelay:
+    def test_identity_filter(self, xp):
+        w, gd = group_delay((1, xp.asarray(1)))
+        assert_array_almost_equal(w, xp.pi * xp.arange(512, dtype=w.dtype) / 512)
+        assert_array_almost_equal(gd, xp.zeros(512))
+
+        w, gd = group_delay((1, xp.asarray(1)), whole=True)
+        assert_array_almost_equal(w, 2 * xp.pi * xp.arange(512, dtype=w.dtype) / 512)
+        assert_array_almost_equal(gd, xp.zeros(512))
+
+    @xfail_xp_backends("cupy", reason="slightly inaccurate")
+    @pytest.mark.xfail(DEFAULT_F32, reason="wrong answer with torch/float32")
+    def test_fir(self, xp):
+        # Let's design linear phase FIR and check that the group delay
+        # is constant.
+        N = 100
+        b = firwin(N + 1, 0.1)
+        b = xp.asarray(b)
+        w, gd = group_delay((b, 1))
+        xp_assert_close(gd, xp.ones_like(gd)*(0.5 * N), rtol=5e-7)
+
+    @pytest.mark.xfail(DEFAULT_F32, reason="wrong answer with torch/float32")
+    def test_iir(self, xp):
+        # Let's design Butterworth filter and test the group delay at
+        # some points against MATLAB answer.
+        b, a = butter(4, 0.1)
+        b, a = map(xp.asarray, (b, a))
+        w = xp.linspace(0, xp.pi, num=10, endpoint=False)
+        w, gd = group_delay((b, a), w=w)
+        matlab_gd = xp.asarray([8.249313898506037, 11.958947880907104,
+                                2.452325615326005, 1.048918665702008,
+                                0.611382575635897, 0.418293269460578,
+                                0.317932917836572, 0.261371844762525,
+                                0.229038045801298, 0.212185774208521])
+        assert_array_almost_equal(gd, matlab_gd)
+
+    @xfail_xp_backends("cupy", reason="does not warn")
+    @xfail_xp_backends("torch", reason="does not warn")
+    def test_singular(self, xp):
+        # Let's create a filter with zeros and poles on the unit circle and
+        # check if warnings are raised at those frequencies.
+        z1 = np.exp(1j * 0.1 * pi)
+        z2 = np.exp(1j * 0.25 * pi)
+        p1 = np.exp(1j * 0.5 * pi)
+        p2 = np.exp(1j * 0.8 * pi)
+
+        b = np.convolve([1, -z1], [1, -z2])
+        a = np.convolve([1, -p1], [1, -p2])
+        b, a = map(xp.asarray, (b, a))
+
+        w = xp.asarray([0.1 * xp.pi, 0.25 * xp.pi, -0.5 * xp.pi, -0.8 * xp.pi])
+
+        with pytest.warns(UserWarning):
+            w, gd = group_delay((b, a), w=w)
+
+    def test_backward_compat(self, xp):
+        # For backward compatibility, test if None act as a wrapper for default
+        w1, gd1 = group_delay((1, xp.asarray(1)))
+        w2, gd2 = group_delay((1, xp.asarray(1)), None)
+        assert_array_almost_equal(w1, w2)
+        assert_array_almost_equal(gd1, gd2)
+
+    @pytest.mark.xfail(DEFAULT_F32, reason="wrong answer with torch/float32")
+    def test_fs_param(self, xp):
+        # Let's design Butterworth filter and test the group delay at
+        # some points against the normalized frequency answer.
+        b, a = butter(4, 4800, fs=96000)
+        b, a = map(xp.asarray, (b, a))
+        w = xp.linspace(0, 96000/2, num=10, endpoint=False)
+        w, gd = group_delay((b, a), w=w, fs=96000)
+        norm_gd = xp.asarray([8.249313898506037, 11.958947880907104,
+                              2.452325615326005, 1.048918665702008,
+                              0.611382575635897, 0.418293269460578,
+                              0.317932917836572, 0.261371844762525,
+                              0.229038045801298, 0.212185774208521])
+        assert_array_almost_equal(gd, norm_gd)
+
+    @skip_xp_backends(np_only=True, reason='numpy scalars')
+    def test_w_or_N_types(self, xp):
+        # Measure at 8 equally-spaced points
+        for N in (8, np.int8(8), np.int16(8), np.int32(8), np.int64(8),
+                  np.array(8)):
+            w, gd = group_delay((1, 1), N)
+            assert_array_almost_equal(w, pi * np.arange(8) / 8)
+            assert_array_almost_equal(gd, np.zeros(8))
+
+        # Measure at frequency 8 rad/sec
+        for w in (8.0, 8.0+0j):
+            w_out, gd = group_delay((1, 1), w)
+            assert_array_almost_equal(w_out, [8])
+            assert_array_almost_equal(gd, [0])
+
+    @pytest.mark.xfail(DEFAULT_F32, reason="with torch/float32, the rtol is ~1e-7")
+    @xfail_xp_backends("cupy", reason="inaccurate")
+    def test_complex_coef(self, xp):
+        # gh-19586: handle complex coef TFs
+        #
+        # for g(z) = (alpha*z+1)/(1+conjugate(alpha)), group delay is
+        # given by function below.
+        #
+        # def gd_expr(w, alpha):
+        #     num = 1j*(abs(alpha)**2-1)*np.exp(1j*w)
+        #     den = (alpha*np.exp(1j*w)+1)*(np.exp(1j*w)+np.conj(alpha))
+        #     return -np.imag(num/den)
+
+        # arbitrary non-real alpha
+        alpha = -0.6143077933232609 + 0.3355978770229421j
+        # 8 points from from -pi to pi
+        wref = xp.asarray([-3.141592653589793 ,
+                           -2.356194490192345 ,
+                           -1.5707963267948966,
+                           -0.7853981633974483,
+                           0.                ,
+                           0.7853981633974483,
+                           1.5707963267948966,
+                           2.356194490192345 ])
+        gdref =  xp.asarray([0.18759548150354619,
+                             0.17999770352712252,
+                             0.23598047471879877,
+                             0.46539443069907194,
+                             1.9511492420564165 ,
+                             3.478129975138865  ,
+                             0.6228594960517333 ,
+                             0.27067831839471224])
+        b = xp.asarray([alpha, 1])
+        a = xp.asarray([1, alpha.conjugate()])
+        gdtest = group_delay((b, a), wref)[1]
+        # need nulp=14 for macOS arm64 wheel builds; added 2 for some
+        # robustness on other platforms.
+        xp_assert_close_nulp(gdtest, gdref, nulp=16)
+
+    def test_fs_validation(self):
+        with pytest.raises(ValueError, match="Sampling.*single scalar"):
+            group_delay((1, 1), fs=np.array([10, 20]))
+
+        with pytest.raises(ValueError, match="Sampling.*be none"):
+            group_delay((1, 1), fs=None)
+
+
+@skip_xp_backends("dask.array", reason="https://github.com/dask/dask/issues/11883")
+@make_xp_test_case(gammatone)
+class TestGammatone:
+    # Test erroneous input cases.
+    @skip_xp_backends(np_only=True)
+    def test_invalid_input(self, xp):
+        # Cutoff frequency is <= 0 or >= fs / 2.
+        fs = 16000
+        for args in [(-fs, 'iir'), (0, 'fir'), (fs / 2, 'iir'), (fs, 'fir')]:
+            with pytest.raises(ValueError, match='The frequency must be '
+                               'between '):
+                gammatone(*args, fs=fs)
+
+        # Filter type is not fir or iir
+        for args in [(440, 'fie'), (220, 'it')]:
+            with pytest.raises(ValueError, match='ftype must be '):
+                gammatone(*args, fs=fs)
+
+        # Order is <= 0 or > 24 for FIR filter.
+        for args in [(440, 'fir', -50), (220, 'fir', 0), (110, 'fir', 25),
+                     (55, 'fir', 50)]:
+            with pytest.raises(ValueError, match='Invalid order: '):
+                gammatone(*args, numtaps=None, fs=fs)
+
+    # Verify that the filter's frequency response is approximately
+    # 1 at the cutoff frequency.
+    @pytest.mark.xfail(DEFAULT_F32, reason="wrong answer with torch/float32")
+    @xfail_xp_backends("cupy", reason="inaccurate")
+    def test_frequency_response(self, xp):
+        fs = 16000
+        ftypes = ['fir', 'iir']
+        for ftype in ftypes:
+            # Create a gammatone filter centered at 1000 Hz.
+            b, a = gammatone(1000, ftype, fs=fs, xp=xp)
+
+            # Calculate the frequency response.
+            freqs, response = freqz(_xp_copy_to_numpy(b), _xp_copy_to_numpy(a))
+
+            # Determine peak magnitude of the response
+            # and corresponding frequency.
+            response_max = np.max(np.abs(response))
+            freq_hz = freqs[np.argmax(np.abs(response))] / ((2 * np.pi) / fs)
+            response_max, freq_hz = map(xp.asarray, (response_max, freq_hz))
+
+            # Check that the peak magnitude is 1 and the frequency is 1000 Hz.
+            xp_assert_close(response_max,
+                            xp.ones_like(response_max), rtol=1e-2, check_0d=False)
+            xp_assert_close(freq_hz,
+                            1000*xp.ones_like(freq_hz), rtol=1e-2, check_0d=False)
+
+    # All built-in IIR filters are real, so should have perfectly
+    # symmetrical poles and zeros. Then ba representation (using
+    # numpy.poly) will be purely real instead of having negligible
+    # imaginary parts.
+    def test_iir_symmetry(self, xp):
+        b, a = gammatone(440, 'iir', fs=24000, xp=xp)
+        z, p, k = tf2zpk(_xp_copy_to_numpy(b), _xp_copy_to_numpy(a))
+        z, p, k = map(xp.asarray, (z, p, k))
+        xp_assert_equal(_sort_cmplx(z, xp=xp), _sort_cmplx(xp.conj(z), xp=xp))
+        xp_assert_equal(_sort_cmplx(p, xp=xp), _sort_cmplx(xp.conj(p), xp=xp))
+        xp_assert_equal(k, xp.real(k))
+
+        isdtype = array_namespace(b).isdtype
+        assert isdtype(b.dtype, ('real floating', 'complex floating'))
+        assert isdtype(a.dtype, ('real floating', 'complex floating'))
+
+    # Verify FIR filter coefficients with the paper's
+    # Mathematica implementation
+    def test_fir_ba_output(self, xp):
+        b, _ = gammatone(15, 'fir', fs=1000, xp=xp)
+        b2 = [0.0, 2.2608075649884e-04,
+              1.5077903981357e-03, 4.2033687753998e-03,
+              8.1508962726503e-03, 1.2890059089154e-02,
+              1.7833890391666e-02, 2.2392613558564e-02,
+              2.6055195863104e-02, 2.8435872863284e-02,
+              2.9293319149544e-02, 2.852976858014e-02,
+              2.6176557156294e-02, 2.2371510270395e-02,
+              1.7332485267759e-02]
+        b2 = xp.asarray(b2)
+        xp_assert_close(b, b2)
+
+    # Verify IIR filter coefficients with the paper's MATLAB implementation
+    def test_iir_ba_output(self, xp):
+        b, a = gammatone(440, 'iir', fs=16000, xp=xp)
+        b2 = [1.31494461367464e-06, -5.03391196645395e-06,
+              7.00649426000897e-06, -4.18951968419854e-06,
+              9.02614910412011e-07]
+        a2 = [1.0, -7.65646235454218,
+              25.7584699322366, -49.7319214483238,
+              60.2667361289181, -46.9399590980486,
+              22.9474798808461, -6.43799381299034,
+              0.793651554625368]
+        b2, a2 = map(xp.asarray, (b2, a2))
+        xp_assert_close(b, b2, atol=1e-10, rtol=5e-5)
+        xp_assert_close(a, a2, atol=1e-10, rtol=5e-5)
+
+    def test_fs_validation(self):
+        with pytest.raises(ValueError, match="Sampling.*single scalar"):
+            gammatone(440, 'iir', fs=np.asarray([10, 20]))
+
+
+@make_xp_test_case(findfreqs)
+class TestFindFreqs:
+    @pytest.mark.parametrize("kind", ["ba", "zp"])
+    def test_findfreqs_log_spacing(self, xp, kind):
+        N = 30
+        w = findfreqs(xp.asarray([1.2], dtype=xp.float64),
+                      xp.asarray([3.6, 9.8], dtype=xp.float64), N=N, kind=kind)
+        ratio = xp.diff(xp.log10(w))
+        xp_assert_close(ratio, ratio[0]*xp.ones(N - 1, dtype=xp.float64))
+
+    def test_findfreqs_ba_zp_equiv(self, xp):
+        num, den = [1.4, 2], [1, 3.8, 2]
+        zeros = xp.asarray(np.roots(num))
+        poles = xp.asarray(np.roots(den))
+
+        ba = findfreqs(xp.asarray(num, dtype=xp.float64),
+                       xp.asarray(den, dtype=xp.float64), N=30, kind="ba")
+        zp = findfreqs(zeros, poles, N=30, kind="zp")
+
+        xp_assert_close(ba, zp)
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/tests/test_fir_filter_design.py b/venv/lib/python3.12/site-packages/scipy/signal/tests/test_fir_filter_design.py
new file mode 100644
index 0000000000000000000000000000000000000000..11e9b237ee018a29dbcdf6fa53624073c586f191
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/tests/test_fir_filter_design.py
@@ -0,0 +1,884 @@
+import math
+import numpy as np
+
+from pytest import raises as assert_raises, warns as assert_warns
+import pytest
+
+import scipy._external.array_api_extra as xpx
+import scipy.signal as signal
+from scipy._lib._array_api import (
+    xp_assert_close, xp_assert_equal, assert_almost_equal, assert_array_almost_equal,
+    array_namespace, xp_default_dtype, make_xp_test_case, _xp_copy_to_numpy
+)
+from scipy.fft import fft, fft2, rfft
+from scipy.signal import (kaiser_beta, kaiser_atten, kaiserord,
+    firwin, firwin2, freqz, remez, firls, minimum_phase, convolve2d, firwin_2d
+)
+
+skip_xp_backends = pytest.mark.skip_xp_backends
+xfail_xp_backends = pytest.mark.xfail_xp_backends
+
+lazy_xp_modules = [signal]
+
+
+def test_kaiser_beta():
+    b = kaiser_beta(58.7)
+    assert_almost_equal(b, 0.1102 * 50.0)
+    b = kaiser_beta(22.0)
+    assert_almost_equal(b, 0.5842 + 0.07886)
+    b = kaiser_beta(21.0)
+    assert b == 0.0
+    b = kaiser_beta(10.0)
+    assert b == 0.0
+
+
+def test_kaiser_atten():
+    a = kaiser_atten(1, 1.0)
+    assert a == 7.95
+    a = kaiser_atten(2, 1/np.pi)
+    assert a == 2.285 + 7.95
+
+
+def test_kaiserord():
+    assert_raises(ValueError, kaiserord, 1.0, 1.0)
+    numtaps, beta = kaiserord(2.285 + 7.95 - 0.001, 1/np.pi)
+    assert (numtaps, beta) == (2, 0.0)
+
+
+@make_xp_test_case(firwin)
+class TestFirwin:
+
+    def check_response(self, h, expected_response, tol=.05):
+        xp = array_namespace(h)
+        N = h.shape[0]
+        alpha = 0.5 * (N-1)
+        m = xp.arange(0, N, dtype=xp_default_dtype(xp)) - alpha   # time indices of taps
+        for freq, expected in expected_response:
+            actual = abs(xp.sum(h * xp.exp(-1j * xp.pi * m * freq)))
+            mse = abs(actual - expected)**2
+            assert mse < tol, f'response not as expected, mse={mse:g} > {tol:g}'
+
+    def test_response(self, xp):
+        N = 51
+        f = xp.asarray(.5)
+
+        # increase length just to try even/odd
+        h = firwin(N, f)  # low-pass from 0 to f
+        self.check_response(h, [(.25,1), (.75,0)])
+
+        h = firwin(N+1, f, window='nuttall')  # specific window
+        self.check_response(h, [(.25,1), (.75,0)])
+
+        h = firwin(N+2, f, pass_zero=False)  # stop from 0 to f --> high-pass
+        self.check_response(h, [(.25,0), (.75,1)])
+
+        f1, f2, f3, f4 = .2, .4, .6, .8
+        h = firwin(N+3, [f1, f2], pass_zero=False)  # band-pass filter
+        self.check_response(h, [(.1,0), (.3,1), (.5,0)])
+
+        h = firwin(N+4, [f1, f2])  # band-stop filter
+        self.check_response(h, [(.1,1), (.3,0), (.5,1)])
+
+        h = firwin(N+5, [f1, f2, f3, f4], pass_zero=False, scale=False)
+        self.check_response(h, [(.1,0), (.3,1), (.5,0), (.7,1), (.9,0)])
+
+        h = firwin(N+6, [f1, f2, f3, f4])  # multiband filter
+        self.check_response(h, [(.1,1), (.3,0), (.5,1), (.7,0), (.9,1)])
+
+        h = firwin(N+7, 0.1, width=.03)  # low-pass
+        self.check_response(h, [(.05,1), (.75,0)])
+
+        h = firwin(N+8, 0.1, pass_zero=False)  # high-pass
+        self.check_response(h, [(.05,0), (.75,1)])
+
+    def mse(self, h, bands):
+        """Compute mean squared error versus ideal response across frequency
+        band.
+          h -- coefficients
+          bands -- list of (left, right) tuples relative to 1==Nyquist of
+            passbands
+        """
+        xp = array_namespace(h)
+        h_np = _xp_copy_to_numpy(h)
+        w, H = freqz(h_np, worN=1024)
+        w, H = map(xp.asarray, (w, H))
+        f = w/xp.pi
+        passIndicator = xp.zeros(w.shape[0], dtype=xp.bool)
+        for left, right in bands:
+            passIndicator |= (f >= left) & (f < right)
+        Hideal = xp.where(passIndicator, xp.ones_like(passIndicator),
+                          xp.zeros_like(passIndicator))
+        Hideal = xp.astype(Hideal, H.dtype)
+        mse = xp.mean(abs(abs(H)-Hideal)**2)
+        return mse
+
+    @pytest.mark.parametrize(
+        "cutoff,pass_zero,expected_response",
+        [
+            ([0.5], True, (0, 1)),
+            ([0.2, .6], False, (.4, 1)),
+            ([.5], False, (1, 1)),
+        ]
+    )
+    def test_scaling(self, cutoff, pass_zero, expected_response, xp):
+        """
+        For one lowpass, bandpass, and highpass example filter, this test
+        checks two things:
+          - the mean squared error over the frequency domain of the unscaled
+            filter is smaller than the scaled filter (true for rectangular
+            window)
+          - the response of the scaled filter is exactly unity at the center
+            of the first passband
+        """
+        N = 11
+        cutoff = xp.asarray(cutoff)
+        h = firwin(N, cutoff, scale=False, pass_zero=pass_zero, window='ones')
+        hs = firwin(N, cutoff, scale=True, pass_zero=pass_zero, window='ones')
+        if cutoff.shape[0] == 1:
+            if pass_zero:
+                cutoff = xp.concat([xp.asarray([0], dtype=cutoff.dtype), cutoff])
+            else:
+                cutoff = xp.concat([cutoff, xp.asarray([1], dtype=cutoff.dtype)])
+        msg = 'least squares violation'
+        assert self.mse(h, [cutoff]) < self.mse(hs, [cutoff]), msg
+        self.check_response(hs, [expected_response], 1e-12)
+
+    def test_fs_validation(self):
+        with pytest.raises(ValueError, match="Sampling.*single scalar"):
+            firwin(51, .5, fs=np.array([10, 20]))
+
+
+@make_xp_test_case(firwin)
+class TestFirWinMore:
+    """Different author, different style, different tests..."""
+
+    def test_lowpass(self, xp):
+        width = 0.04
+        ntaps, beta = kaiserord(120, width)
+        cutoff = xp.asarray(0.5)
+        kwargs = dict(cutoff=cutoff, window=('kaiser', beta), scale=False)
+        taps = firwin(ntaps, **kwargs)
+
+        # Check the symmetry of taps.
+        assert_array_almost_equal(taps[:ntaps//2], xp.flip(taps)[:ntaps//2])
+
+        # Check the gain at a few samples where
+        # we know it should be approximately 0 or 1.
+        freq_samples = xp.asarray([0.0, 0.25, 0.5-width/2, 0.5+width/2, 0.75, 1.0])
+        freq_samples = _xp_copy_to_numpy(freq_samples)
+        freqs, response = freqz(_xp_copy_to_numpy(taps), worN=np.pi*freq_samples)
+
+        assert_array_almost_equal(
+            xp.abs(xp.asarray(response)),
+            xp.asarray([1.0, 1.0, 1.0, 0.0, 0.0, 0.0]), decimal=5
+        )
+
+        taps_str = firwin(ntaps, pass_zero='lowpass', **kwargs)
+        xp_assert_close(taps, taps_str)
+
+    def test_highpass(self, xp):
+        width = 0.04
+        ntaps, beta = kaiserord(120, width)
+
+        # Ensure that ntaps is odd.
+        ntaps |= 1
+
+        cutoff = xp.asarray(0.5)
+        kwargs = dict(cutoff=cutoff, window=('kaiser', beta), scale=False)
+        taps = firwin(ntaps, pass_zero=False, **kwargs)
+
+        # Check the symmetry of taps.
+        assert_array_almost_equal(taps[:ntaps//2], xp.flip(taps)[:ntaps//2])
+
+        # Check the gain at a few samples where
+        # we know it should be approximately 0 or 1.
+        freq_samples = xp.asarray([0.0, 0.25, 0.5 - width/2, 0.5 + width/2, 0.75, 1.0])
+        freq_samples = _xp_copy_to_numpy(freq_samples)
+        freqs, response = freqz(_xp_copy_to_numpy(taps), worN=np.pi*freq_samples)
+
+        assert_array_almost_equal(xp.abs(xp.asarray(response)),
+                                  xp.asarray([0.0, 0.0, 0.0, 1.0, 1.0, 1.0]), decimal=5)
+
+        taps_str = firwin(ntaps, pass_zero='highpass', **kwargs)
+        xp_assert_close(taps, taps_str)
+
+    def test_bandpass(self, xp):
+        width = 0.04
+        ntaps, beta = kaiserord(120, width)
+        kwargs = dict(
+            cutoff=xp.asarray([0.3, 0.7]), window=('kaiser', beta), scale=False
+        )
+        taps = firwin(ntaps, pass_zero=False, **kwargs)
+
+        # Check the symmetry of taps.
+        assert_array_almost_equal(taps[:ntaps//2], xp.flip(taps)[:ntaps//2])
+
+        # Check the gain at a few samples where
+        # we know it should be approximately 0 or 1.
+        freq_samples = xp.asarray([0.0, 0.2, 0.3 - width/2, 0.3 + width/2, 0.5,
+                                   0.7 - width/2, 0.7 + width/2, 0.8, 1.0])
+        freq_samples = _xp_copy_to_numpy(freq_samples)
+        freqs, response = freqz(_xp_copy_to_numpy(taps), worN=np.pi*freq_samples)
+
+        assert_array_almost_equal(xp.abs(xp.asarray(response)),
+                xp.asarray([0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 0.0, 0.0, 0.0]), decimal=5)
+
+        taps_str = firwin(ntaps, pass_zero='bandpass', **kwargs)
+        xp_assert_close(taps, taps_str)
+
+    def test_bandstop_multi(self, xp):
+        width = 0.04
+        ntaps, beta = kaiserord(120, width)
+        kwargs = dict(cutoff=xp.asarray([0.2, 0.5, 0.8]), window=('kaiser', beta),
+                      scale=False)
+        taps = firwin(ntaps, **kwargs)
+
+        # Check the symmetry of taps.
+        assert_array_almost_equal(taps[:ntaps//2], xp.flip(taps)[:ntaps//2])
+
+        # Check the gain at a few samples where
+        # we know it should be approximately 0 or 1.
+        freq_samples = xp.asarray([0.0, 0.1, 0.2 - width/2, 0.2 + width/2, 0.35,
+                                   0.5 - width/2, 0.5 + width/2, 0.65,
+                                   0.8 - width/2, 0.8 + width/2, 0.9, 1.0])
+        freq_samples = _xp_copy_to_numpy(freq_samples)
+        freqs, response = freqz(_xp_copy_to_numpy(taps), worN=np.pi*freq_samples)
+
+        assert_array_almost_equal(
+            xp.abs(xp.asarray(response)),
+            xp.asarray([1.0, 1.0, 1.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 0.0, 0.0, 0.0]),
+            decimal=5
+        )
+
+        taps_str = firwin(ntaps, pass_zero='bandstop', **kwargs)
+        xp_assert_close(taps, taps_str)
+
+    def test_fs_nyq(self, xp):
+        """Test the fs and nyq keywords."""
+        nyquist = 1000
+        width = 40.0
+        relative_width = width/nyquist
+        ntaps, beta = kaiserord(120, relative_width)
+        taps = firwin(ntaps, cutoff=xp.asarray([300, 700]), window=('kaiser', beta),
+                        pass_zero=False, scale=False, fs=2*nyquist)
+
+        # Check the symmetry of taps.
+        assert_array_almost_equal(taps[:ntaps//2], xp.flip(taps)[:ntaps//2])
+
+        # Check the gain at a few samples where
+        # we know it should be approximately 0 or 1.
+        freq_samples = xp.asarray([0.0, 200, 300 - width/2, 300 + width/2, 500,
+                                   700 - width/2, 700 + width/2, 800, 1000])
+        freq_samples = _xp_copy_to_numpy(freq_samples)
+        freqs, response = freqz(
+            _xp_copy_to_numpy(taps), worN=np.pi*freq_samples/nyquist
+        )
+
+        assert_array_almost_equal(xp.abs(xp.asarray(response)),
+                xp.asarray([0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 0.0, 0.0, 0.0]), decimal=5)
+
+    def test_array_cutoff(self, xp):
+        taps = firwin(3, xp.asarray([.1, .2]))
+        # smoke test against the value computed by scipy==1.5.2
+        xp_assert_close(
+            taps, xp.asarray([-0.00801395, 1.0160279, -0.00801395]), atol=1e-8
+        )
+
+    def test_bad_cutoff(self):
+        """Test that invalid cutoff argument raises ValueError."""
+        # cutoff values must be greater than 0 and less than 1.
+        assert_raises(ValueError, firwin, 99, -0.5)
+        assert_raises(ValueError, firwin, 99, 1.5)
+        # Don't allow 0 or 1 in cutoff.
+        assert_raises(ValueError, firwin, 99, [0, 0.5])
+        assert_raises(ValueError, firwin, 99, [0.5, 1])
+        # cutoff values must be strictly increasing.
+        assert_raises(ValueError, firwin, 99, [0.1, 0.5, 0.2])
+        assert_raises(ValueError, firwin, 99, [0.1, 0.5, 0.5])
+        # Must have at least one cutoff value.
+        assert_raises(ValueError, firwin, 99, [])
+        # 2D array not allowed.
+        assert_raises(ValueError, firwin, 99, [[0.1, 0.2],[0.3, 0.4]])
+        # cutoff values must be less than nyq.
+        assert_raises(ValueError, firwin, 99, 50.0, fs=80)
+        assert_raises(ValueError, firwin, 99, [10, 20, 30], fs=50)
+
+    def test_even_highpass_raises_value_error(self):
+        """Test that attempt to create a highpass filter with an even number
+        of taps raises a ValueError exception."""
+        assert_raises(ValueError, firwin, 40, 0.5, pass_zero=False)
+        assert_raises(ValueError, firwin, 40, [.25, 0.5])
+
+    def test_bad_pass_zero(self):
+        """Test degenerate pass_zero cases."""
+        with assert_raises(ValueError, match="^Parameter pass_zero='foo' not in "):
+            firwin(41, 0.5, pass_zero='foo')
+        with assert_raises(ValueError, match="^Parameter pass_zero=1.0 not in "):
+            firwin(41, 0.5, pass_zero=1.)
+        for pass_zero in ('lowpass', 'highpass'):
+            with assert_raises(ValueError, match='cutoff must have one'):
+                firwin(41, [0.5, 0.6], pass_zero=pass_zero)
+        for pass_zero in ('bandpass', 'bandstop'):
+            with assert_raises(ValueError, match='must have at least two'):
+                firwin(41, [0.5], pass_zero=pass_zero)
+
+    def test_fs_validation(self):
+        with pytest.raises(ValueError, match="Sampling.*single scalar"):
+            firwin2(51, .5, 1, fs=np.array([10, 20]))
+
+
+@make_xp_test_case(firwin2)
+class TestFirwin2:
+
+    def test_invalid_args(self):
+        # `freq` and `gain` have different lengths.
+        with assert_raises(ValueError, match='must be of same length'):
+            firwin2(50, [0, 0.5, 1], [0.0, 1.0])
+        # `nfreqs` is less than `ntaps`.
+        with assert_raises(ValueError, match='ntaps must be less than nfreqs'):
+            firwin2(50, [0, 0.5, 1], [0.0, 1.0, 1.0], nfreqs=33)
+        # Decreasing value in `freq`
+        with assert_raises(ValueError, match='must be nondecreasing'):
+            firwin2(50, [0, 0.5, 0.4, 1.0], [0, .25, .5, 1.0])
+        # Value in `freq` repeated more than once.
+        with assert_raises(ValueError, match='must not occur more than twice'):
+            firwin2(50, [0, .1, .1, .1, 1.0], [0.0, 0.5, 0.75, 1.0, 1.0])
+        # `freq` does not start at 0.0.
+        with assert_raises(ValueError, match='start with 0'):
+            firwin2(50, [0.5, 1.0], [0.0, 1.0])
+        # `freq` does not end at fs/2.
+        with assert_raises(ValueError, match='end with fs/2'):
+            firwin2(50, [0.0, 0.5], [0.0, 1.0])
+        # Value 0 is repeated in `freq`
+        with assert_raises(ValueError, match='0 must not be repeated'):
+            firwin2(50, [0.0, 0.0, 0.5, 1.0], [1.0, 1.0, 0.0, 0.0])
+        # Value fs/2 is repeated in `freq`
+        with assert_raises(ValueError, match='fs/2 must not be repeated'):
+            firwin2(50, [0.0, 0.5, 1.0, 1.0], [1.0, 1.0, 0.0, 0.0])
+        # Value in `freq` that is too close to a repeated number
+        with assert_raises(ValueError, match='cannot contain numbers '
+                                             'that are too close'):
+            firwin2(50, [0.0, 0.5 - np.finfo(float).eps * 0.5, 0.5, 0.5, 1.0],
+                        [1.0, 1.0, 1.0, 0.0, 0.0])
+
+        # Type II filter, but the gain at nyquist frequency is not zero.
+        with assert_raises(ValueError, match='Type II filter'):
+            firwin2(16, [0.0, 0.5, 1.0], [0.0, 1.0, 1.0])
+
+        # Type III filter, but the gains at nyquist and zero rate are not zero.
+        with assert_raises(ValueError, match='Type III filter'):
+            firwin2(17, [0.0, 0.5, 1.0], [0.0, 1.0, 1.0], antisymmetric=True)
+        with assert_raises(ValueError, match='Type III filter'):
+            firwin2(17, [0.0, 0.5, 1.0], [1.0, 1.0, 0.0], antisymmetric=True)
+        with assert_raises(ValueError, match='Type III filter'):
+            firwin2(17, [0.0, 0.5, 1.0], [1.0, 1.0, 1.0], antisymmetric=True)
+
+        # Type IV filter, but the gain at zero rate is not zero.
+        with assert_raises(ValueError, match='Type IV filter'):
+            firwin2(16, [0.0, 0.5, 1.0], [1.0, 1.0, 0.0], antisymmetric=True)
+
+    def test01(self, xp):
+        width = 0.04
+        beta = 12.0
+        ntaps = 400
+        # Filter is 1 from w=0 to w=0.5, then decreases linearly from 1 to 0 as w
+        # increases from w=0.5 to w=1  (w=1 is the Nyquist frequency).
+        freq = xp.asarray([0.0, 0.5, 1.0])
+        gain = xp.asarray([1.0, 1.0, 0.0])
+        taps = firwin2(ntaps, freq, gain, window=('kaiser', beta))
+        freq_samples = xp.asarray([0.0, 0.25, 0.5 - width/2, 0.5 + width/2,
+                                   0.75, 1.0 - width/2])
+        freq_samples = _xp_copy_to_numpy(freq_samples)
+        freqs, response = freqz(_xp_copy_to_numpy(taps), worN=np.pi*freq_samples)
+        assert_array_almost_equal(
+            xp.abs(xp.asarray(response)),
+            xp.asarray([1.0, 1.0, 1.0, 1.0 - width, 0.5, width]), decimal=5
+        )
+
+    @skip_xp_backends("jax.numpy", reason="immutable arrays")
+    def test02(self, xp):
+        width = 0.04
+        beta = 12.0
+        # ntaps must be odd for positive gain at Nyquist.
+        ntaps = 401
+        # An ideal highpass filter.
+        freq = xp.asarray([0.0, 0.5, 0.5, 1.0])
+        gain = xp.asarray([0.0, 0.0, 1.0, 1.0])
+        taps = firwin2(ntaps, freq, gain, window=('kaiser', beta))
+        freq_samples = xp.asarray([0.0, 0.25, 0.5 - width, 0.5 + width, 0.75, 1.0])
+        freq_samples = _xp_copy_to_numpy(freq_samples)
+        freqs, response = freqz(_xp_copy_to_numpy(taps), worN=np.pi*freq_samples)
+        assert_array_almost_equal(
+            xp.abs(xp.asarray(response)),
+            xp.asarray([0.0, 0.0, 0.0, 1.0, 1.0, 1.0]), decimal=5
+        )
+
+    @skip_xp_backends("jax.numpy", reason="immutable arrays")
+    def test03(self, xp):
+        width = 0.02
+        ntaps, beta = kaiserord(120, width)
+        # ntaps must be odd for positive gain at Nyquist.
+        ntaps = int(ntaps) | 1
+        freq = xp.asarray([0.0, 0.4, 0.4, 0.5, 0.5, 1.0])
+        gain = xp.asarray([1.0, 1.0, 0.0, 0.0, 1.0, 1.0])
+        taps = firwin2(ntaps, freq, gain, window=('kaiser', beta))
+        freq_samples = np.array([0.0, 0.4 - width, 0.4 + width, 0.45,
+                                    0.5 - width, 0.5 + width, 0.75, 1.0])
+        freqs, response = freqz(_xp_copy_to_numpy(taps), worN=np.pi*freq_samples)
+        assert_array_almost_equal(
+            xp.abs(xp.asarray(response)),
+            xp.asarray([1.0, 1.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0]), decimal=5
+        )
+
+    @skip_xp_backends("jax.numpy", reason="immutable arrays")
+    def test04(self, xp):
+        """Test firwin2 when window=None."""
+        ntaps = 5
+        # Ideal lowpass: gain is 1 on [0,0.5], and 0 on [0.5, 1.0]
+        freq = xp.asarray([0.0, 0.5, 0.5, 1.0])
+        gain = xp.asarray([1.0, 1.0, 0.0, 0.0])
+
+        taps = firwin2(ntaps, freq, gain, window=None, nfreqs=8193)
+        alpha = 0.5 * (ntaps - 1)
+        m = xp.arange(0, ntaps, dtype=freq.dtype) - alpha
+        h = 0.5 * xpx.sinc(0.5 * m)
+        assert_array_almost_equal(h, taps)
+
+    def test05(self, xp):
+        """Test firwin2 for calculating Type IV filters"""
+        ntaps = 1500
+
+        freq = xp.asarray([0.0, 1.0])
+        gain = xp.asarray([0.0, 1.0])
+        taps = firwin2(ntaps, freq, gain, window=None, antisymmetric=True)
+
+        flip = array_namespace(freq).flip
+        dec = {'decimal': 4.5} if xp_default_dtype(xp) == xp.float32 else {}
+        assert_array_almost_equal(taps[: ntaps // 2], flip(-taps[ntaps // 2:]), **dec)
+
+        freqs, response = freqz(_xp_copy_to_numpy(taps), worN=2048)
+        freqs, response = map(xp.asarray, (freqs, response))
+        assert_array_almost_equal(xp.abs(response), freqs / xp.pi, decimal=4)
+
+    @skip_xp_backends("jax.numpy", reason="immutable arrays")
+    def test06(self, xp):
+        """Test firwin2 for calculating Type III filters"""
+        ntaps = 1501
+
+        freq = xp.asarray([0.0, 0.5, 0.55, 1.0])
+        gain = xp.asarray([0.0, 0.5, 0.0, 0.0])
+        taps = firwin2(ntaps, freq, gain, window=None, antisymmetric=True)
+        assert taps[ntaps // 2] == 0.0
+
+        flip = array_namespace(freq).flip
+        dec = {'decimal': 4.5} if xp_default_dtype(xp) == xp.float32 else {}
+        assert_array_almost_equal(taps[: ntaps // 2],
+                                  flip(-taps[ntaps // 2 + 1:]), **dec
+        )
+
+        freqs, response1 = freqz(_xp_copy_to_numpy(taps), worN=2048)
+        response2 = xp.asarray(
+            np.interp(freqs / np.pi, _xp_copy_to_numpy(freq), _xp_copy_to_numpy(gain))
+        )
+        assert_array_almost_equal(xp.abs(xp.asarray(response1)), response2, decimal=3)
+
+    def test_fs_nyq(self, xp):
+        taps1 = firwin2(80, xp.asarray([0.0, 0.5, 1.0]), xp.asarray([1.0, 1.0, 0.0]))
+        taps2 = firwin2(80, xp.asarray([0.0, 30.0, 60.0]), xp.asarray([1.0, 1.0, 0.0]),
+                        fs=120.0)
+        assert_array_almost_equal(taps1, taps2)
+
+    def test_tuple(self):
+        taps1 = firwin2(150, (0.0, 0.5, 0.5, 1.0), (1.0, 1.0, 0.0, 0.0))
+        taps2 = firwin2(150, [0.0, 0.5, 0.5, 1.0], [1.0, 1.0, 0.0, 0.0])
+        assert_array_almost_equal(taps1, taps2)
+
+    @skip_xp_backends("jax.numpy", reason="immutable arrays")
+    def test_input_modyfication(self, xp):
+        freq1 = xp.asarray([0.0, 0.5, 0.5, 1.0])
+        freq2 = xp.asarray(freq1)
+        firwin2(80, freq1, xp.asarray([1.0, 1.0, 0.0, 0.0]))
+        xp_assert_equal(freq1, freq2)
+
+
+@make_xp_test_case(remez)
+class TestRemez:
+
+    def test_bad_args(self):
+        assert_raises(ValueError, remez, 11, [0.1, 0.4], [1], type='pooka')
+
+    def test_hilbert(self):
+        N = 11  # number of taps in the filter
+        a = 0.1  # width of the transition band
+
+        # design a unity gain hilbert bandpass filter from w to 0.5-w
+        h = remez(11, [a, 0.5-a], [1], type='hilbert')
+
+        # make sure the filter has correct # of taps
+        assert len(h) == N, "Number of Taps"
+
+        # make sure it is type III (anti-symmetric tap coefficients)
+        assert_array_almost_equal(h[:(N-1)//2], -h[:-(N-1)//2-1:-1])
+
+        # Since the requested response is symmetric, all even coefficients
+        # should be zero (or in this case really small)
+        assert (abs(h[1::2]) < 1e-15).all(), "Even Coefficients Equal Zero"
+
+        # now check the frequency response
+        w, H = freqz(h, 1)
+        f = w/2/np.pi
+        Hmag = abs(H)
+
+        # should have a zero at 0 and pi (in this case close to zero)
+        assert (Hmag[[0, -1]] < 0.02).all(), "Zero at zero and pi"
+
+        # check that the pass band is close to unity
+        idx = np.logical_and(f > a, f < 0.5-a)
+        assert (abs(Hmag[idx] - 1) < 0.015).all(), "Pass Band Close To Unity"
+
+    def test_compare(self, xp):
+        # test comparison to MATLAB
+        k = [0.024590270518440, -0.041314581814658, -0.075943803756711,
+             -0.003530911231040, 0.193140296954975, 0.373400753484939,
+             0.373400753484939, 0.193140296954975, -0.003530911231040,
+             -0.075943803756711, -0.041314581814658, 0.024590270518440]
+        h = remez(12, xp.asarray([0, 0.3, 0.5, 1]), xp.asarray([1, 0]), fs=2.)
+        atol_arg = {'atol': 1e-8} if xp_default_dtype(xp) == xp.float32 else {}
+        xp_assert_close(h, xp.asarray(k, dtype=xp.float64), **atol_arg)
+
+        h = [-0.038976016082299, 0.018704846485491, -0.014644062687875,
+             0.002879152556419, 0.016849978528150, -0.043276706138248,
+             0.073641298245579, -0.103908158578635, 0.129770906801075,
+             -0.147163447297124, 0.153302248456347, -0.147163447297124,
+             0.129770906801075, -0.103908158578635, 0.073641298245579,
+             -0.043276706138248, 0.016849978528150, 0.002879152556419,
+             -0.014644062687875, 0.018704846485491, -0.038976016082299]
+        atol_arg = {'atol': 3e-8} if xp_default_dtype(xp) == xp.float32 else {}
+        xp_assert_close(
+            remez(21, xp.asarray([0, 0.8, 0.9, 1]), xp.asarray([0, 1]), fs=2.),
+            xp.asarray(h, dtype=xp.float64), **atol_arg
+        )
+
+    def test_fs_validation(self):
+        with pytest.raises(ValueError, match="Sampling.*single scalar"):
+            remez(11, .1, 1, fs=np.array([10, 20]))
+
+    def test_gh_23266(self, xp):
+        bands = xp.asarray([0.0, 0.2, 0.3, 0.5])
+        desired = xp.asarray([1.0, 0.0])
+        weight = xp.asarray([1.0, 2.0])
+        remez(21, bands, desired, weight=weight)
+
+
+@make_xp_test_case(firls)
+class TestFirls:
+
+    def test_bad_args(self):
+        # even numtaps
+        assert_raises(ValueError, firls, 10, [0.1, 0.2], [0, 0])
+        # odd bands
+        assert_raises(ValueError, firls, 11, [0.1, 0.2, 0.4], [0, 0, 0])
+        # len(bands) != len(desired)
+        assert_raises(ValueError, firls, 11, [0.1, 0.2, 0.3, 0.4], [0, 0, 0])
+        # non-monotonic bands
+        assert_raises(ValueError, firls, 11, [0.2, 0.1], [0, 0])
+        assert_raises(ValueError, firls, 11, [0.1, 0.2, 0.3, 0.3], [0] * 4)
+        assert_raises(ValueError, firls, 11, [0.3, 0.4, 0.1, 0.2], [0] * 4)
+        assert_raises(ValueError, firls, 11, [0.1, 0.3, 0.2, 0.4], [0] * 4)
+        # negative desired
+        assert_raises(ValueError, firls, 11, [0.1, 0.2], [-1, 1])
+        # len(weight) != len(pairs)
+        assert_raises(ValueError, firls, 11, [0.1, 0.2], [0, 0], weight=[1, 2])
+        # negative weight
+        assert_raises(ValueError, firls, 11, [0.1, 0.2], [0, 0], weight=[-1])
+
+    @skip_xp_backends("dask.array", reason="dask fancy indexing shape=(nan,)")
+    def test_firls(self, xp):
+        N = 11  # number of taps in the filter
+        a = 0.1  # width of the transition band
+
+        # design a halfband symmetric low-pass filter
+        h = firls(11, xp.asarray([0, a, 0.5 - a, 0.5]), xp.asarray([1, 1, 0, 0]),
+                  fs=1.0)
+
+        # make sure the filter has correct # of taps
+        assert h.shape[0] == N
+
+        # make sure it is symmetric
+        midx = (N-1) // 2
+        flip = array_namespace(h).flip
+        assert_array_almost_equal(h[:midx],  flip(h[midx+1:])) # h[:-midx-1:-1])
+
+        # make sure the center tap is 0.5
+        assert math.isclose(h[midx], 0.5, abs_tol=1e-8)
+
+        # For halfband symmetric, odd coefficients (except the center)
+        # should be zero (really small)
+        hodd = xp.stack((h[1:midx:2], h[-midx+1::2]))
+        assert_array_almost_equal(hodd, xp.zeros_like(hodd))
+
+        # now check the frequency response
+        w, H = freqz(_xp_copy_to_numpy(h), 1)
+        w, H = xp.asarray(w), xp.asarray(H)
+        f = w/2/xp.pi
+        Hmag = xp.abs(H)
+
+        # check that the pass band is close to unity
+        idx = xp.logical_and(f > 0, f < a)
+        assert_array_almost_equal(Hmag[idx], xp.ones_like(Hmag[idx]), decimal=3)
+
+        # check that the stop band is close to zero
+        idx = xp.logical_and(f > 0.5 - a, f < 0.5)
+        assert_array_almost_equal(Hmag[idx], xp.zeros_like(Hmag[idx]), decimal=3)
+
+    def test_compare(self, xp):
+        # compare to OCTAVE output
+        taps = firls(9, xp.asarray([0, 0.5, 0.55, 1]),
+                    xp.asarray([1, 1, 0, 0]), weight=xp.asarray([1, 2]))
+        # >> taps = firls(8, [0 0.5 0.55 1], [1 1 0 0], [1, 2]);
+        known_taps = [-6.26930101730182e-04, -1.03354450635036e-01,
+                      -9.81576747564301e-03, 3.17271686090449e-01,
+                      5.11409425599933e-01, 3.17271686090449e-01,
+                      -9.81576747564301e-03, -1.03354450635036e-01,
+                      -6.26930101730182e-04]
+        atol_arg = {'atol': 5e-8} if xp_default_dtype(xp) == xp.float32 else {}
+        known_taps = xp.asarray(known_taps, dtype=xp.float64)
+        xp_assert_close(taps, known_taps, **atol_arg)
+
+        # compare to MATLAB output
+        taps = firls(11, xp.asarray([0, 0.5, 0.5, 1]),
+                     xp.asarray([1, 1, 0, 0]), weight=xp.asarray([1, 2]))
+        # >> taps = firls(10, [0 0.5 0.5 1], [1 1 0 0], [1, 2]);
+        known_taps = [
+            0.058545300496815, -0.014233383714318, -0.104688258464392,
+            0.012403323025279, 0.317930861136062, 0.488047220029700,
+            0.317930861136062, 0.012403323025279, -0.104688258464392,
+            -0.014233383714318, 0.058545300496815]
+        known_taps = xp.asarray(known_taps, dtype=xp.float64)
+        atol_arg = {'atol': 3e-8} if xp_default_dtype(xp) == xp.float32 else {}
+        xp_assert_close(taps, known_taps, **atol_arg)
+
+        # With linear changes:
+        taps = firls(7, xp.asarray((0, 1, 2, 3, 4, 5)),
+                     xp.asarray([1, 0, 0, 1, 1, 0]), fs=20)
+        # >> taps = firls(6, [0, 0.1, 0.2, 0.3, 0.4, 0.5], [1, 0, 0, 1, 1, 0])
+        known_taps = [
+            1.156090832768218, -4.1385894727395849, 7.5288619164321826,
+            -8.5530572592947856, 7.5288619164321826, -4.1385894727395849,
+            1.156090832768218]
+        known_taps = xp.asarray(known_taps, dtype=xp.float64)
+        xp_assert_close(taps, known_taps)
+
+    def test_rank_deficient(self, xp):
+        # solve() runs but warns (only sometimes, so here we don't use match)
+        x = firls(21, xp.asarray([0, 0.1, 0.9, 1]), xp.asarray([1, 1, 0, 0]))
+        w, h = freqz(_xp_copy_to_numpy(x), fs=2.)
+        w, h = map(xp.asarray, (w, h))
+        absh2 = xp.abs(h[:2])
+        xp_assert_close(absh2, xp.ones_like(absh2), atol=1e-5)
+        absh2 = xp.abs(h[-2:])
+        xp_assert_close(absh2, xp.zeros_like(absh2), atol=1e-6, rtol=1e-7)
+        # switch to pinvh (tolerances could be higher with longer
+        # filters, but using shorter ones is faster computationally and
+        # the idea is the same)
+        x = firls(101, xp.asarray([0, 0.01, 0.99, 1]), xp.asarray([1, 1, 0, 0]))
+        w, h = freqz(_xp_copy_to_numpy(x), fs=2.)
+        w, h = map(xp.asarray, (w, h))
+        mask = xp.asarray(w < 0.01)
+        h = xp.asarray(h)
+        assert xp.sum(xp.astype(mask, xp.int64)) > 3
+        habs = xp.abs(h[mask])
+        xp_assert_close(habs, xp.ones_like(habs), atol=1e-4)
+        mask = xp.asarray(w > 0.99)
+        assert xp.sum(xp.astype(mask, xp.int64)) > 3
+        habs = xp.abs(h[mask])
+        xp_assert_close(habs, xp.zeros_like(habs), atol=1e-4)
+
+    def test_fs_validation(self):
+        with pytest.raises(ValueError, match="Sampling.*single scalar"):
+            firls(11, .1, 1, fs=np.array([10, 20]))
+
+@make_xp_test_case(minimum_phase)
+class TestMinimumPhase:
+
+    def test_bad_args(self):
+        # not enough taps
+        assert_raises(ValueError, minimum_phase, [1.])
+        assert_raises(ValueError, minimum_phase, [1., 1.])
+        assert_raises(ValueError, minimum_phase, np.full(10, 1j))
+        assert_raises((ValueError, TypeError), minimum_phase, 'foo')
+        assert_raises(ValueError, minimum_phase, np.ones(10), n_fft=8)
+        assert_raises(ValueError, minimum_phase, np.ones(10), method='foo')
+        assert_warns(RuntimeWarning, minimum_phase, np.arange(3))
+        with pytest.raises(ValueError, match="is only supported when"):
+            minimum_phase(np.ones(3), method='hilbert', half=False)
+
+    def test_homomorphic(self):
+        # check that it can recover frequency responses of arbitrary
+        # linear-phase filters
+
+        # for some cases we can get the actual filter back
+        h = [1, -1]
+        h_new = minimum_phase(np.convolve(h, h[::-1]))
+        xp_assert_close(h_new, np.asarray(h, dtype=np.float64), rtol=0.05)
+
+        # but in general we only guarantee we get the magnitude back
+        rng = np.random.RandomState(0)
+        for n in (2, 3, 10, 11, 15, 16, 17, 20, 21, 100, 101):
+            h = rng.randn(n)
+            h_linear = np.convolve(h, h[::-1])
+            h_new = minimum_phase(h_linear)
+            xp_assert_close(np.abs(fft(h_new)), np.abs(fft(h)), rtol=1e-4)
+            h_new = minimum_phase(h_linear, half=False)
+            assert len(h_linear) == len(h_new)
+            xp_assert_close(np.abs(fft(h_new)), np.abs(fft(h_linear)), rtol=1e-4)
+
+    @skip_xp_backends("dask.array", reason="too slow")
+    @make_xp_test_case(signal.hilbert)
+    def test_hilbert(self, xp):
+        # compare to MATLAB output of reference implementation
+
+        # f=[0 0.3 0.5 1];
+        # a=[1 1 0 0];
+        # h=remez(11,f,a);
+        h = remez(12, [0, 0.3, 0.5, 1], [1, 0], fs=2.)
+        k = [0.349585548646686, 0.373552164395447, 0.326082685363438,
+             0.077152207480935, -0.129943946349364, -0.059355880509749]
+        h = xp.asarray(h)
+        k = xp.asarray(k, dtype=xp.float64)
+        m = minimum_phase(h, 'hilbert')
+        xp_assert_close(m, k, rtol=5e-3)
+
+        # f=[0 0.8 0.9 1];
+        # a=[0 0 1 1];
+        # h=remez(20,f,a);
+        h = remez(21, [0, 0.8, 0.9, 1], [0, 1], fs=2.)
+        k = [0.232486803906329, -0.133551833687071, 0.151871456867244,
+             -0.157957283165866, 0.151739294892963, -0.129293146705090,
+             0.100787844523204, -0.065832656741252, 0.035361328741024,
+             -0.014977068692269, -0.158416139047557]
+        h = xp.asarray(h)
+        k = xp.asarray(k, dtype=xp.float64)
+        m = minimum_phase(h, 'hilbert', n_fft=2**19)
+        xp_assert_close(m, k, rtol=2e-3)
+
+    @xfail_xp_backends("cupy", reason="cupy/cupy#9795")
+    @pytest.mark.parametrize("N", (963, 964))
+    @pytest.mark.parametrize("dtype", ("float32", "float64"))
+    def test_nyquist(self, N, dtype, xp):
+        fc = xp.asarray(10)
+        fs = 100
+        h = firwin(N, fc, window="hann", pass_zero="lowpass", scale=False, fs=fs)
+        xp_dtype = getattr(xp, dtype)
+        h = xp.astype(h, xp_dtype)
+        h_min_sig = minimum_phase(h, method="homomorphic", n_fft=N, half=False)
+        H_mag = xp.abs(rfft(h, N))
+        H_min_mag = xp.abs(rfft(h_min_sig, N))
+        error = H_mag - H_min_mag
+        atol = dict(float32=1e-5, float64=1e-13)[dtype]
+        xp_assert_close(error, xp.zeros_like(error), atol=atol)
+
+
+class Testfirwin_2d:
+    def test_invalid_args(self):
+        with pytest.raises(ValueError,
+                           match="hsize must be a 2-element tuple or list"):
+            firwin_2d((50,), window=(("kaiser", 5.0), "boxcar"), fc=0.4)
+
+        with pytest.raises(ValueError,
+                           match="window must be a 2-element tuple or list"):
+            firwin_2d((51, 51), window=("hamming",), fc=0.5)
+
+        with pytest.raises(ValueError,
+                           match="window must be a 2-element tuple or list"):
+            firwin_2d((51, 51), window="invalid_window", fc=0.5)
+
+    def test_filter_design(self):
+        hsize = (51, 51)
+        window = (("kaiser", 8.0), ("kaiser", 8.0))
+        fc = 0.4
+        taps_kaiser = firwin_2d(hsize, window, fc=fc)
+        assert taps_kaiser.shape == (51, 51)
+
+        window = ("hamming", "hamming")
+        taps_hamming = firwin_2d(hsize, window, fc=fc)
+        assert taps_hamming.shape == (51, 51)
+
+    def test_impulse_response(self):
+        hsize = (31, 31)
+        window = ("hamming", "hamming")
+        fc = 0.4
+        taps = firwin_2d(hsize, window, fc=fc)
+
+        impulse = np.zeros((63, 63))
+        impulse[31, 31] = 1
+
+        response = convolve2d(impulse, taps, mode='same')
+
+        expected_response = taps
+        xp_assert_close(response[16:47, 16:47], expected_response, rtol=1e-5)
+
+    def test_frequency_response(self):
+        """Compare 1d and 2d frequency response. """
+        hsize = (31, 31)
+        windows = ("hamming", "hamming")
+        fc = 0.4
+        taps_1d = firwin(numtaps=hsize[0], cutoff=fc, window=windows[0])
+        taps_2d = firwin_2d(hsize, windows, fc=fc)
+
+        f_resp_1d = fft(taps_1d)
+        f_resp_2d = fft2(taps_2d)
+
+        xp_assert_close(f_resp_2d[0, :], f_resp_1d,
+                        err_msg='DC Gain at (0, f1) is not unity!')
+        xp_assert_close(f_resp_2d[:, 0], f_resp_1d,
+                        err_msg='DC Gain at (f0, 0) is not unity!')
+        xp_assert_close(f_resp_2d, np.outer(f_resp_1d, f_resp_1d),
+                        atol=np.finfo(f_resp_2d.dtype).resolution,
+                        err_msg='2d frequency response is not product of 1d responses')
+
+    def test_symmetry(self):
+        hsize = (51, 51)
+        window = ("hamming", "hamming")
+        fc = 0.4
+        taps = firwin_2d(hsize, window, fc=fc)
+        xp_assert_close(taps, np.flip(taps), rtol=1e-5)
+
+    def test_circular_symmetry(self):
+        hsize = (51, 51)
+        window = "hamming"
+        taps = firwin_2d(hsize, window, circular=True, fc=0.5)
+        center = hsize[0] // 2
+        for i in range(hsize[0]):
+            for j in range(hsize[1]):
+                xp_assert_close(taps[i, j],
+                                taps[center - (i - center), center - (j - center)],
+                                rtol=1e-5)
+
+    def test_edge_case_circular(self):
+        hsize = (3, 3)
+        window = "hamming"
+        taps_small = firwin_2d(hsize, window, circular=True, fc=0.5)
+        assert taps_small.shape == (3, 3)
+
+        hsize = (101, 101)
+        taps_large = firwin_2d(hsize, window, circular=True, fc=0.5)
+        assert taps_large.shape == (101, 101)
+
+    def test_known_result(self):
+        hsize = (5, 5)
+        window = ('kaiser', 8.0)
+        fc = 0.1
+        fs = 2
+
+        row_filter = firwin(hsize[0], cutoff=fc, window=window, fs=fs)
+        col_filter = firwin(hsize[1], cutoff=fc, window=window, fs=fs)
+        known_result = np.outer(row_filter, col_filter)
+
+        taps = firwin_2d(hsize, (window, window), fc=fc)
+        assert taps.shape == known_result.shape, (
+            f"Shape mismatch: {taps.shape} vs {known_result.shape}"
+        )
+        assert np.allclose(taps, known_result, rtol=1e-1), (
+            f"Filter shape mismatch: {taps} vs {known_result}"
+        )
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/tests/test_ltisys.py b/venv/lib/python3.12/site-packages/scipy/signal/tests/test_ltisys.py
new file mode 100644
index 0000000000000000000000000000000000000000..1fbf5217f09d03fa42e779be0ec79bdb4ae38459
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/tests/test_ltisys.py
@@ -0,0 +1,1297 @@
+import warnings
+from types import GenericAlias
+
+import numpy as np
+import pytest
+from pytest import raises as assert_raises
+from scipy._lib._array_api import(
+    assert_almost_equal, xp_assert_equal, xp_assert_close, make_xp_test_case,
+    xp_result_type
+)
+
+from scipy.signal import (ss2tf, tf2ss, lti,
+                          dlti, bode, freqresp, lsim, impulse, step,
+                          abcd_normalize, place_poles,
+                          TransferFunction, StateSpace, ZerosPolesGain)
+
+from scipy.signal._filter_design import BadCoefficients
+import scipy.linalg as linalg
+
+
+def _assert_poles_close(P1,P2, rtol=1e-8, atol=1e-8):
+    """
+    Check each pole in P1 is close to a pole in P2 with a 1e-8
+    relative tolerance or 1e-8 absolute tolerance (useful for zero poles).
+    These tolerances are very strict but the systems tested are known to
+    accept these poles so we should not be far from what is requested.
+    """
+    P2 = P2.copy()
+    for p1 in P1:
+        found = False
+        for p2_idx in range(P2.shape[0]):
+            if np.allclose([np.real(p1), np.imag(p1)],
+                           [np.real(P2[p2_idx]), np.imag(P2[p2_idx])],
+                           rtol, atol):
+                found = True
+                np.delete(P2, p2_idx)
+                break
+        if not found:
+            raise ValueError("Can't find pole " + str(p1) + " in " + str(P2))
+
+
+class TestPlacePoles:
+
+    def _check(self, A, B, P, **kwargs):
+        """
+        Perform the most common tests on the poles computed by place_poles
+        and return the Bunch object for further specific tests
+        """
+        fsf = place_poles(A, B, P, **kwargs)
+        expected, _ = np.linalg.eig(A - np.dot(B, fsf.gain_matrix))
+        _assert_poles_close(expected, fsf.requested_poles)
+        _assert_poles_close(expected, fsf.computed_poles)
+        _assert_poles_close(P,fsf.requested_poles)
+        return fsf
+
+    def test_real(self):
+        # Test real pole placement using KNV and YT0 algorithm and example 1 in
+        # section 4 of the reference publication (see place_poles docstring)
+        A = np.array([1.380, -0.2077, 6.715, -5.676, -0.5814, -4.290, 0,
+                      0.6750, 1.067, 4.273, -6.654, 5.893, 0.0480, 4.273,
+                      1.343, -2.104]).reshape(4, 4)
+        B = np.array([0, 5.679, 1.136, 1.136, 0, 0, -3.146,0]).reshape(4, 2)
+        P = np.array([-0.2, -0.5, -5.0566, -8.6659])
+
+        # Check that both KNV and YT compute correct K matrix
+        self._check(A, B, P, method='KNV0')
+        self._check(A, B, P, method='YT')
+
+        # Try to reach the specific case in _YT_real where two singular
+        # values are almost equal. This is to improve code coverage but I
+        # have no way to be sure this code is really reached
+
+        # on some architectures this can lead to a RuntimeWarning invalid
+        # value in divide (see gh-7590), so suppress it for now
+        with np.errstate(invalid='ignore'):
+            self._check(A, B, (2,2,3,3))
+
+    def test_complex(self):
+        # Test complex pole placement on a linearized car model, taken from L.
+        # Jaulin, Automatique pour la robotique, Cours et Exercices, iSTE
+        # editions p 184/185
+        A = np.array([[0, 7, 0, 0],
+                      [0, 0, 0, 7/3.],
+                      [0, 0, 0, 0],
+                      [0, 0, 0, 0]])
+        B = np.array([[0, 0],
+                      [0, 0],
+                      [1, 0],
+                      [0, 1]])
+        # Test complex poles on YT
+        P = np.array([-3, -1, -2-1j, -2+1j])
+        # on macOS arm64 this can lead to a RuntimeWarning invalid
+        # value in divide, so suppress it for now
+        with np.errstate(divide='ignore', invalid='ignore'):
+            self._check(A, B, P)
+
+        # Try to reach the specific case in _YT_complex where two singular
+        # values are almost equal. This is to improve code coverage but I
+        # have no way to be sure this code is really reached
+
+        P = [0-1e-6j,0+1e-6j,-10,10]
+        with np.errstate(divide='ignore', invalid='ignore'):
+            self._check(A, B, P, maxiter=1000)
+
+        # Try to reach the specific case in _YT_complex where the rank two
+        # update yields two null vectors. This test was found via Monte Carlo.
+
+        A = np.array(
+                    [-2148,-2902, -2267, -598, -1722, -1829, -165, -283, -2546,
+                   -167, -754, -2285, -543, -1700, -584, -2978, -925, -1300,
+                   -1583, -984, -386, -2650, -764, -897, -517, -1598, 2, -1709,
+                   -291, -338, -153, -1804, -1106, -1168, -867, -2297]
+                   ).reshape(6,6)
+
+        B = np.array(
+                    [-108, -374, -524, -1285, -1232, -161, -1204, -672, -637,
+                     -15, -483, -23, -931, -780, -1245, -1129, -1290, -1502,
+                     -952, -1374, -62, -964, -930, -939, -792, -756, -1437,
+                     -491, -1543, -686]
+                     ).reshape(6,5)
+        P = [-25.-29.j, -25.+29.j, 31.-42.j, 31.+42.j, 33.-41.j, 33.+41.j]
+        self._check(A, B, P)
+
+        # Use a lot of poles to go through all cases for update_order
+        # in _YT_loop
+
+        big_A = np.ones((11,11))-np.eye(11)
+        big_B = np.ones((11,10))-np.diag([1]*10,1)[:,1:]
+        big_A[:6,:6] = A
+        big_B[:6,:5] = B
+
+        P = [-10,-20,-30,40,50,60,70,-20-5j,-20+5j,5+3j,5-3j]
+        with np.errstate(divide='ignore', invalid='ignore'):
+            self._check(big_A, big_B, P)
+
+        #check with only complex poles and only real poles
+        P = [-10,-20,-30,-40,-50,-60,-70,-80,-90,-100]
+        self._check(big_A[:-1,:-1], big_B[:-1,:-1], P)
+        P = [-10+10j,-20+20j,-30+30j,-40+40j,-50+50j,
+             -10-10j,-20-20j,-30-30j,-40-40j,-50-50j]
+        self._check(big_A[:-1,:-1], big_B[:-1,:-1], P)
+
+        # need a 5x5 array to ensure YT handles properly when there
+        # is only one real pole and several complex
+        A = np.array([0,7,0,0,0,0,0,7/3.,0,0,0,0,0,0,0,0,
+                      0,0,0,5,0,0,0,0,9]).reshape(5,5)
+        B = np.array([0,0,0,0,1,0,0,1,2,3]).reshape(5,2)
+        P = np.array([-2, -3+1j, -3-1j, -1+1j, -1-1j])
+        with np.errstate(divide='ignore', invalid='ignore'):
+            place_poles(A, B, P)
+
+        # same test with an odd number of real poles > 1
+        # this is another specific case of YT
+        P = np.array([-2, -3, -4, -1+1j, -1-1j])
+        with np.errstate(divide='ignore', invalid='ignore'):
+            self._check(A, B, P)
+
+    def test_tricky_B(self):
+        # check we handle as we should the 1 column B matrices and
+        # n column B matrices (with n such as shape(A)=(n, n))
+        A = np.array([1.380, -0.2077, 6.715, -5.676, -0.5814, -4.290, 0,
+                      0.6750, 1.067, 4.273, -6.654, 5.893, 0.0480, 4.273,
+                      1.343, -2.104]).reshape(4, 4)
+        B = np.array([0, 5.679, 1.136, 1.136, 0, 0, -3.146, 0, 1, 2, 3, 4,
+                      5, 6, 7, 8]).reshape(4, 4)
+
+        # KNV or YT are not called here, it's a specific case with only
+        # one unique solution
+        P = np.array([-0.2, -0.5, -5.0566, -8.6659])
+        fsf = self._check(A, B, P)
+        # rtol and nb_iter should be set to np.nan as the identity can be
+        # used as transfer matrix
+        assert np.isnan(fsf.rtol)
+        assert np.isnan(fsf.nb_iter)
+
+        # check with complex poles too as they trigger a specific case in
+        # the specific case :-)
+        P = np.array((-2+1j,-2-1j,-3,-2))
+        fsf = self._check(A, B, P)
+        assert np.isnan(fsf.rtol)
+        assert np.isnan(fsf.nb_iter)
+
+        #now test with a B matrix with only one column (no optimisation)
+        B = B[:,0].reshape(4,1)
+        P = np.array((-2+1j,-2-1j,-3,-2))
+        fsf = self._check(A, B, P)
+
+        #  we can't optimize anything, check they are set to 0 as expected
+        assert fsf.rtol == 0
+        assert fsf.nb_iter == 0
+
+    def test_errors(self):
+        # Test input mistakes from user
+        A = np.array([0,7,0,0,0,0,0,7/3.,0,0,0,0,0,0,0,0]).reshape(4,4)
+        B = np.array([0,0,0,0,1,0,0,1]).reshape(4,2)
+
+        #should fail as the method keyword is invalid
+        assert_raises(ValueError, place_poles, A, B, (-2.1,-2.2,-2.3,-2.4),
+                      method="foo")
+
+        #should fail as poles are not 1D array
+        assert_raises(ValueError, place_poles, A, B,
+                      np.array((-2.1,-2.2,-2.3,-2.4)).reshape(4,1))
+
+        #should fail as A is not a 2D array
+        assert_raises(ValueError, place_poles, A[:,:,np.newaxis], B,
+                      (-2.1,-2.2,-2.3,-2.4))
+
+        #should fail as B is not a 2D array
+        assert_raises(ValueError, place_poles, A, B[:,:,np.newaxis],
+                      (-2.1,-2.2,-2.3,-2.4))
+
+        #should fail as there are too many poles
+        assert_raises(ValueError, place_poles, A, B, (-2.1,-2.2,-2.3,-2.4,-3))
+
+        #should fail as there are not enough poles
+        assert_raises(ValueError, place_poles, A, B, (-2.1,-2.2,-2.3))
+
+        #should fail as the rtol is greater than 1
+        assert_raises(ValueError, place_poles, A, B, (-2.1,-2.2,-2.3,-2.4),
+                      rtol=42)
+
+        #should fail as maxiter is smaller than 1
+        assert_raises(ValueError, place_poles, A, B, (-2.1,-2.2,-2.3,-2.4),
+                      maxiter=-42)
+
+        # should fail as ndim(B) is two
+        assert_raises(ValueError, place_poles, A, B, (-2,-2,-2,-2))
+
+        # uncontrollable system
+        assert_raises(ValueError, place_poles, np.ones((4,4)),
+                      np.ones((4,2)), (1,2,3,4))
+
+        # Should not raise ValueError as the poles can be placed but should
+        # raise a warning as the convergence is not reached
+        with warnings.catch_warnings(record=True) as w:
+            warnings.simplefilter("always")
+            fsf = place_poles(A, B, (-1,-2,-3,-4), rtol=1e-16, maxiter=42)
+            assert len(w) == 1
+            assert issubclass(w[-1].category, UserWarning)
+            assert ("Convergence was not reached after maxiter iterations"
+                    in str(w[-1].message))
+            assert fsf.nb_iter == 42
+
+        # should fail as a complex misses its conjugate
+        assert_raises(ValueError, place_poles, A, B, (-2+1j,-2-1j,-2+3j,-2))
+
+        # should fail as A is not square
+        assert_raises(ValueError, place_poles, A[:,:3], B, (-2,-3,-4,-5))
+
+        # should fail as B has not the same number of lines as A
+        assert_raises(ValueError, place_poles, A, B[:3,:], (-2,-3,-4,-5))
+
+        # should fail as KNV0 does not support complex poles
+        assert_raises(ValueError, place_poles, A, B,
+                      (-2+1j,-2-1j,-2+3j,-2-3j), method="KNV0")
+
+
+class TestSS2TF:
+
+    def check_matrix_shapes(self, p, q, r):
+        ss2tf(np.zeros((p, p)),
+              np.zeros((p, q)),
+              np.zeros((r, p)),
+              np.zeros((r, q)), 0)
+
+    def test_shapes(self):
+        # Each tuple holds:
+        #   number of states, number of inputs, number of outputs
+        for p, q, r in [(3, 3, 3), (1, 3, 3), (1, 1, 1)]:
+            self.check_matrix_shapes(p, q, r)
+
+    def test_basic(self):
+        # Test a round trip through tf2ss and ss2tf.
+        b = np.array([1.0, 3.0, 5.0])
+        a = np.array([1.0, 2.0, 3.0])
+
+        A, B, C, D = tf2ss(b, a)
+        xp_assert_close(A, [[-2., -3], [1, 0]], rtol=1e-13)
+        xp_assert_close(B, [[1.], [0]], rtol=1e-13)
+        xp_assert_close(C, [[1., 2]], rtol=1e-13)
+        xp_assert_close(D, [[1.]], rtol=1e-14)
+
+        bb, aa = ss2tf(A, B, C, D)
+        xp_assert_close(bb[0], b, rtol=1e-13)
+        xp_assert_close(aa, a, rtol=1e-13)
+
+    def test_zero_order_round_trip(self):
+        # See gh-5760
+        tf = (2, 1)
+        A, B, C, D = tf2ss(*tf)
+        xp_assert_close(A, [[0.]], rtol=1e-13)
+        xp_assert_close(B, [[0.]], rtol=1e-13)
+        xp_assert_close(C, [[0.]], rtol=1e-13)
+        xp_assert_close(D, [[2.]], rtol=1e-13)
+
+        num, den = ss2tf(A, B, C, D)
+        xp_assert_close(num, [[2., 0]], rtol=1e-13)
+        xp_assert_close(den, [1., 0], rtol=1e-13)
+
+        tf = ([[5], [2]], 1)
+        A, B, C, D = tf2ss(*tf)
+        xp_assert_close(A, [[0.]], rtol=1e-13)
+        xp_assert_close(B, [[0.]], rtol=1e-13)
+        xp_assert_close(C, [[0.], [0]], rtol=1e-13)
+        xp_assert_close(D, [[5.], [2]], rtol=1e-13)
+
+        num, den = ss2tf(A, B, C, D)
+        xp_assert_close(num, [[5., 0], [2, 0]], rtol=1e-13)
+        xp_assert_close(den, [1., 0], rtol=1e-13)
+
+    def test_simo_round_trip(self):
+        # See gh-5753
+        tf = ([[1, 2], [1, 1]], [1, 2])
+        A, B, C, D = tf2ss(*tf)
+        xp_assert_close(A, [[-2.]], rtol=1e-13)
+        xp_assert_close(B, [[1.]], rtol=1e-13)
+        xp_assert_close(C, [[0.], [-1.]], rtol=1e-13)
+        xp_assert_close(D, [[1.], [1.]], rtol=1e-13)
+
+        num, den = ss2tf(A, B, C, D)
+        xp_assert_close(num, [[1., 2.], [1., 1.]], rtol=1e-13)
+        xp_assert_close(den, [1., 2.], rtol=1e-13)
+
+        tf = ([[1, 0, 1], [1, 1, 1]], [1, 1, 1])
+        A, B, C, D = tf2ss(*tf)
+        xp_assert_close(A, [[-1., -1.], [1., 0.]], rtol=1e-13)
+        xp_assert_close(B, [[1.], [0.]], rtol=1e-13)
+        xp_assert_close(C, [[-1., 0.], [0., 0.]], rtol=1e-13)
+        xp_assert_close(D, [[1.], [1.]], rtol=1e-13)
+
+        num, den = ss2tf(A, B, C, D)
+        xp_assert_close(num, [[1., 0., 1.], [1., 1., 1.]], rtol=1e-13)
+        xp_assert_close(den, [1., 1., 1.], rtol=1e-13)
+
+        tf = ([[1, 2, 3], [1, 2, 3]], [1, 2, 3, 4])
+        A, B, C, D = tf2ss(*tf)
+        xp_assert_close(A, [[-2., -3, -4], [1, 0, 0], [0, 1, 0]], rtol=1e-13)
+        xp_assert_close(B, [[1.], [0], [0]], rtol=1e-13)
+        xp_assert_close(C, [[1., 2, 3], [1, 2, 3]], rtol=1e-13)
+        xp_assert_close(D, [[0.], [0]], rtol=1e-13)
+
+        num, den = ss2tf(A, B, C, D)
+        xp_assert_close(num, [[0., 1, 2, 3], [0, 1, 2, 3]], rtol=1e-13)
+        xp_assert_close(den, [1., 2, 3, 4], rtol=1e-13)
+
+        tf = (np.array([1, [2, 3]], dtype=object), [1, 6])
+        A, B, C, D = tf2ss(*tf)
+        xp_assert_close(A, [[-6.]], rtol=1e-31)
+        xp_assert_close(B, [[1.]], rtol=1e-31)
+        xp_assert_close(C, [[1.], [-9]], rtol=1e-31)
+        xp_assert_close(D, [[0.], [2]], rtol=1e-31)
+
+        num, den = ss2tf(A, B, C, D)
+        xp_assert_close(num, [[0., 1], [2, 3]], rtol=1e-13)
+        xp_assert_close(den, [1., 6], rtol=1e-13)
+
+        tf = (np.array([[1, -3], [1, 2, 3]], dtype=object), [1, 6, 5])
+        A, B, C, D = tf2ss(*tf)
+        xp_assert_close(A, [[-6., -5], [1, 0]], rtol=1e-13)
+        xp_assert_close(B, [[1.], [0]], rtol=1e-13)
+        xp_assert_close(C, [[1., -3], [-4, -2]], rtol=1e-13)
+        xp_assert_close(D, [[0.], [1]], rtol=1e-13)
+
+        num, den = ss2tf(A, B, C, D)
+        xp_assert_close(num, [[0., 1, -3], [1, 2, 3]], rtol=1e-13)
+        xp_assert_close(den, [1., 6, 5], rtol=1e-13)
+
+    def test_all_int_arrays(self):
+        A = [[0, 1, 0], [0, 0, 1], [-3, -4, -2]]
+        B = [[0], [0], [1]]
+        C = [[5, 1, 0]]
+        D = [[0]]
+        num, den = ss2tf(A, B, C, D)
+        xp_assert_close(num, [[0.0, 0.0, 1.0, 5.0]], rtol=1e-13, atol=1e-14)
+        xp_assert_close(den, [1.0, 2.0, 4.0, 3.0], rtol=1e-13)
+
+    def test_multioutput(self):
+        # Regression test for gh-2669.
+
+        # 4 states
+        A = np.array([[-1.0, 0.0, 1.0, 0.0],
+                      [-1.0, 0.0, 2.0, 0.0],
+                      [-4.0, 0.0, 3.0, 0.0],
+                      [-8.0, 8.0, 0.0, 4.0]])
+
+        # 1 input
+        B = np.array([[0.3],
+                      [0.0],
+                      [7.0],
+                      [0.0]])
+
+        # 3 outputs
+        C = np.array([[0.0, 1.0, 0.0, 0.0],
+                      [0.0, 0.0, 0.0, 1.0],
+                      [8.0, 8.0, 0.0, 0.0]])
+
+        D = np.array([[0.0],
+                      [0.0],
+                      [1.0]])
+
+        # Get the transfer functions for all the outputs in one call.
+        b_all, a = ss2tf(A, B, C, D)
+
+        # Get the transfer functions for each output separately.
+        b0, a0 = ss2tf(A, B, C[0], D[0])
+        b1, a1 = ss2tf(A, B, C[1], D[1])
+        b2, a2 = ss2tf(A, B, C[2], D[2])
+
+        # Check that we got the same results.
+        xp_assert_close(a0, a, rtol=1e-13)
+        xp_assert_close(a1, a, rtol=1e-13)
+        xp_assert_close(a2, a, rtol=1e-13)
+        xp_assert_close(b_all, np.vstack((b0, b1, b2)), rtol=1e-13, atol=1e-14)
+
+
+class TestLsim:
+    digits_accuracy = 7
+
+    def lti_nowarn(self, *args):
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", BadCoefficients)
+            system = lti(*args)
+        return system
+
+    def test_first_order(self):
+        # y' = -y
+        # exact solution is y(t) = exp(-t)
+        system = self.lti_nowarn(-1.,1.,1.,0.)
+        t = np.linspace(0,5)
+        u = np.zeros_like(t)
+        tout, y, x = lsim(system, u, t, X0=[1.0])
+        expected_x = np.exp(-tout)
+        assert_almost_equal(x, expected_x)
+        assert_almost_equal(y, expected_x)
+
+    def test_second_order(self):
+        t = np.linspace(0, 10, 1001)
+        u = np.zeros_like(t)
+        # Second order system with a repeated root: x''(t) + 2*x(t) + x(t) = 0.
+        # With initial conditions x(0)=1.0 and x'(t)=0.0, the exact solution
+        # is (1-t)*exp(-t).
+        system = self.lti_nowarn([1.0], [1.0, 2.0, 1.0])
+        tout, y, x = lsim(system, u, t, X0=[1.0, 0.0])
+        expected_x = (1.0 - tout) * np.exp(-tout)
+        assert_almost_equal(x[:, 0], expected_x)
+
+    def test_integrator(self):
+        # integrator: y' = u
+        system = self.lti_nowarn(0., 1., 1., 0.)
+        t = np.linspace(0,5)
+        u = t
+        tout, y, x = lsim(system, u, t)
+        expected_x = 0.5 * tout**2
+        assert_almost_equal(x, expected_x, decimal=self.digits_accuracy)
+        assert_almost_equal(y, expected_x, decimal=self.digits_accuracy)
+
+    def test_two_states(self):
+        # A system with two state variables, two inputs, and one output.
+        A = np.array([[-1.0, 0.0], [0.0, -2.0]])
+        B = np.array([[1.0, 0.0], [0.0, 1.0]])
+        C = np.array([1.0, 0.0])
+        D = np.zeros((1, 2))
+
+        system = self.lti_nowarn(A, B, C, D)
+
+        t = np.linspace(0, 10.0, 21)
+        u = np.zeros((len(t), 2))
+        tout, y, x = lsim(system, U=u, T=t, X0=[1.0, 1.0])
+        expected_y = np.exp(-tout)
+        expected_x0 = np.exp(-tout)
+        expected_x1 = np.exp(-2.0 * tout)
+        assert_almost_equal(y, expected_y)
+        assert_almost_equal(x[:, 0], expected_x0)
+        assert_almost_equal(x[:, 1], expected_x1)
+
+    def test_double_integrator(self):
+        # double integrator: y'' = 2u
+        A = np.array([[0., 1.], [0., 0.]])
+        B = np.array([[0.], [1.]])
+        C = np.array([[2., 0.]])
+        system = self.lti_nowarn(A, B, C, 0.)
+        t = np.linspace(0,5)
+        u = np.ones_like(t)
+        tout, y, x = lsim(system, u, t)
+        expected_x = np.transpose(np.array([0.5 * tout**2, tout]))
+        expected_y = tout**2
+        assert_almost_equal(x, expected_x, decimal=self.digits_accuracy)
+        assert_almost_equal(y, expected_y, decimal=self.digits_accuracy)
+
+    def test_jordan_block(self):
+        # Non-diagonalizable A matrix
+        #   x1' + x1 = x2
+        #   x2' + x2 = u
+        #   y = x1
+        # Exact solution with u = 0 is y(t) = t exp(-t)
+        A = np.array([[-1., 1.], [0., -1.]])
+        B = np.array([[0.], [1.]])
+        C = np.array([[1., 0.]])
+        system = self.lti_nowarn(A, B, C, 0.)
+        t = np.linspace(0,5)
+        u = np.zeros_like(t)
+        tout, y, x = lsim(system, u, t, X0=[0.0, 1.0])
+        expected_y = tout * np.exp(-tout)
+        assert_almost_equal(y, expected_y)
+
+    def test_miso(self):
+        # A system with two state variables, two inputs, and one output.
+        A = np.array([[-1.0, 0.0], [0.0, -2.0]])
+        B = np.array([[1.0, 0.0], [0.0, 1.0]])
+        C = np.array([1.0, 0.0])
+        D = np.zeros((1,2))
+        system = self.lti_nowarn(A, B, C, D)
+
+        t = np.linspace(0, 5.0, 101)
+        u = np.zeros((len(t), 2))
+        tout, y, x = lsim(system, u, t, X0=[1.0, 1.0])
+        expected_y = np.exp(-tout)
+        expected_x0 = np.exp(-tout)
+        expected_x1 = np.exp(-2.0*tout)
+        assert_almost_equal(y, expected_y)
+        assert_almost_equal(x[:,0], expected_x0)
+        assert_almost_equal(x[:,1], expected_x1)
+
+    def test_nonzero_initial_time(self):
+        system = self.lti_nowarn(-1.,1.,1.,0.)
+        t = np.linspace(1,2)
+        u = np.zeros_like(t)
+        tout, y, x = lsim(system, u, t, X0=[1.0])
+        expected_y = np.exp(-tout)
+        assert_almost_equal(y, expected_y)
+
+    def test_nonequal_timesteps(self):
+        t = np.array([0.0, 1.0, 1.0, 3.0])
+        u = np.array([0.0, 0.0, 1.0, 1.0])
+        # Simple integrator: x'(t) = u(t)
+        system = ([1.0], [1.0, 0.0])
+        with assert_raises(ValueError,
+                           match="Time steps are not equally spaced."):
+            tout, y, x = lsim(system, u, t, X0=[1.0])
+
+
+class TestImpulse:
+    def test_first_order(self):
+        # First order system: x'(t) + x(t) = u(t)
+        # Exact impulse response is x(t) = exp(-t).
+        system = ([1.0], [1.0,1.0])
+        tout, y = impulse(system)
+        expected_y = np.exp(-tout)
+        assert_almost_equal(y, expected_y)
+
+    def test_first_order_fixed_time(self):
+        # Specify the desired time values for the output.
+
+        # First order system: x'(t) + x(t) = u(t)
+        # Exact impulse response is x(t) = exp(-t).
+        system = ([1.0], [1.0,1.0])
+        n = 21
+        t = np.linspace(0, 2.0, n)
+        tout, y = impulse(system, T=t)
+        assert tout.shape == (n,)
+        assert_almost_equal(tout, t)
+        expected_y = np.exp(-t)
+        assert_almost_equal(y, expected_y)
+
+    def test_first_order_initial(self):
+        # Specify an initial condition as a scalar.
+
+        # First order system: x'(t) + x(t) = u(t), x(0)=3.0
+        # Exact impulse response is x(t) = 4*exp(-t).
+        system = ([1.0], [1.0,1.0])
+        tout, y = impulse(system, X0=3.0)
+        expected_y = 4.0 * np.exp(-tout)
+        assert_almost_equal(y, expected_y)
+
+    def test_first_order_initial_list(self):
+        # Specify an initial condition as a list.
+
+        # First order system: x'(t) + x(t) = u(t), x(0)=3.0
+        # Exact impulse response is x(t) = 4*exp(-t).
+        system = ([1.0], [1.0,1.0])
+        tout, y = impulse(system, X0=[3.0])
+        expected_y = 4.0 * np.exp(-tout)
+        assert_almost_equal(y, expected_y)
+
+    def test_integrator(self):
+        # Simple integrator: x'(t) = u(t)
+        system = ([1.0], [1.0,0.0])
+        tout, y = impulse(system)
+        expected_y = np.ones_like(tout)
+        assert_almost_equal(y, expected_y)
+
+    def test_second_order(self):
+        # Second order system with a repeated root:
+        #     x''(t) + 2*x(t) + x(t) = u(t)
+        # The exact impulse response is t*exp(-t).
+        system = ([1.0], [1.0, 2.0, 1.0])
+        tout, y = impulse(system)
+        expected_y = tout * np.exp(-tout)
+        assert_almost_equal(y, expected_y)
+
+    def test_array_like(self):
+        # Test that function can accept sequences, scalars.
+        system = ([1.0], [1.0, 2.0, 1.0])
+        # TODO: add meaningful test where X0 is a list
+        tout, y = impulse(system, X0=[3], T=[5, 6])
+        tout, y = impulse(system, X0=[3], T=[5])
+
+    def test_array_like2(self):
+        system = ([1.0], [1.0, 2.0, 1.0])
+        tout, y = impulse(system, X0=3, T=5)
+
+
+class TestStep:
+    def test_first_order(self):
+        # First order system: x'(t) + x(t) = u(t)
+        # Exact step response is x(t) = 1 - exp(-t).
+        system = ([1.0], [1.0,1.0])
+        tout, y = step(system)
+        expected_y = 1.0 - np.exp(-tout)
+        assert_almost_equal(y, expected_y)
+
+    def test_first_order_fixed_time(self):
+        # Specify the desired time values for the output.
+
+        # First order system: x'(t) + x(t) = u(t)
+        # Exact step response is x(t) = 1 - exp(-t).
+        system = ([1.0], [1.0,1.0])
+        n = 21
+        t = np.linspace(0, 2.0, n)
+        tout, y = step(system, T=t)
+        assert tout.shape == (n,)
+        assert_almost_equal(tout, t)
+        expected_y = 1 - np.exp(-t)
+        assert_almost_equal(y, expected_y)
+
+    def test_first_order_initial(self):
+        # Specify an initial condition as a scalar.
+
+        # First order system: x'(t) + x(t) = u(t), x(0)=3.0
+        # Exact step response is x(t) = 1 + 2*exp(-t).
+        system = ([1.0], [1.0,1.0])
+        tout, y = step(system, X0=3.0)
+        expected_y = 1 + 2.0*np.exp(-tout)
+        assert_almost_equal(y, expected_y)
+
+    def test_first_order_initial_list(self):
+        # Specify an initial condition as a list.
+
+        # First order system: x'(t) + x(t) = u(t), x(0)=3.0
+        # Exact step response is x(t) = 1 + 2*exp(-t).
+        system = ([1.0], [1.0,1.0])
+        tout, y = step(system, X0=[3.0])
+        expected_y = 1 + 2.0*np.exp(-tout)
+        assert_almost_equal(y, expected_y)
+
+    def test_integrator(self):
+        # Simple integrator: x'(t) = u(t)
+        # Exact step response is x(t) = t.
+        system = ([1.0],[1.0,0.0])
+        tout, y = step(system)
+        expected_y = tout
+        assert_almost_equal(y, expected_y)
+
+    def test_second_order(self):
+        # Second order system with a repeated root:
+        #     x''(t) + 2*x(t) + x(t) = u(t)
+        # The exact step response is 1 - (1 + t)*exp(-t).
+        system = ([1.0], [1.0, 2.0, 1.0])
+        tout, y = step(system)
+        expected_y = 1 - (1 + tout) * np.exp(-tout)
+        assert_almost_equal(y, expected_y)
+
+    def test_array_like(self):
+        # Test that function can accept sequences, scalars.
+        system = ([1.0], [1.0, 2.0, 1.0])
+        # TODO: add meaningful test where X0 is a list
+        tout, y = step(system, T=[5, 6])
+
+    def test_complex_input(self):
+        # Test that complex input doesn't raise an error.
+        # `step` doesn't seem to have been designed for complex input, but this
+        # works and may be used, so add regression test.  See gh-2654.
+        step(([], [-1], 1+0j))
+
+
+class TestLti:
+    def test_lti_instantiation(self):
+        # Test that lti can be instantiated with sequences, scalars.
+        # See PR-225.
+
+        # TransferFunction
+        s = lti([1], [-1])
+        assert isinstance(s, TransferFunction)
+        assert isinstance(s, lti)
+        assert not isinstance(s, dlti)
+        assert s.dt is None
+
+        # ZerosPolesGain
+        s = lti(np.array([]), np.array([-1]), 1)
+        assert isinstance(s, ZerosPolesGain)
+        assert isinstance(s, lti)
+        assert not isinstance(s, dlti)
+        assert s.dt is None
+
+        # StateSpace
+        s = lti([], [-1], 1)
+        s = lti([1], [-1], 1, 3)
+        assert isinstance(s, StateSpace)
+        assert isinstance(s, lti)
+        assert not isinstance(s, dlti)
+        assert s.dt is None
+
+
+class TestStateSpace:
+    def test_initialization(self):
+        # Check that all initializations work
+        StateSpace(1, 1, 1, 1)
+        StateSpace([1], [2], [3], [4])
+        StateSpace(np.array([[1, 2], [3, 4]]), np.array([[1], [2]]),
+                   np.array([[1, 0]]), np.array([[0]]))
+
+        # Verify that parameter are casted correctly:
+        AA = np.array([1], dtype=np.int64)
+        ss0 = StateSpace(AA, 1, 1, 1)
+        assert ss0.A.dtype == ss0.B.dtype == ss0.C.dtype == ss0.D.dtype == np.float64
+        ss1 = StateSpace(AA, 1, 1, 1+1j)
+        assert ss1.A.dtype == ss1.B.dtype == ss1.C.dtype == ss1.D.dtype == np.complex128
+
+    def test_conversion(self):
+        # Check the conversion functions
+        s = StateSpace(1, 2, 3, 4)
+        assert isinstance(s.to_ss(), StateSpace)
+        assert isinstance(s.to_tf(), TransferFunction)
+        assert isinstance(s.to_zpk(), ZerosPolesGain)
+
+        # Make sure copies work
+        assert StateSpace(s) is not s
+        assert s.to_ss() is not s
+
+    def test_properties(self):
+        # Test setters/getters for cross class properties.
+        # This implicitly tests to_tf() and to_zpk()
+
+        # Getters
+        s = StateSpace(1, 1, 1, 1)
+        xp_assert_equal(s.poles, [1.])
+        xp_assert_equal(s.zeros, [0.])
+        assert s.dt is None
+
+    def test_operators(self):
+        # Test +/-/* operators on systems
+
+        class BadType:
+            pass
+
+        s1 = StateSpace(np.array([[-0.5, 0.7], [0.3, -0.8]]),
+                        np.array([[1], [0]]),
+                        np.array([[1, 0]]),
+                        np.array([[0]]),
+                        )
+
+        s2 = StateSpace(np.array([[-0.2, -0.1], [0.4, -0.1]]),
+                        np.array([[1], [0]]),
+                        np.array([[1, 0]]),
+                        np.array([[0]])
+                        )
+
+        s_discrete = s1.to_discrete(0.1)
+        s2_discrete = s2.to_discrete(0.2)
+        s3_discrete = s2.to_discrete(0.1)
+
+        # Impulse response
+        t = np.linspace(0, 1, 100)
+        u = np.zeros_like(t)
+        u[0] = 1
+
+        # Test multiplication
+        for typ in (int, float, complex, np.float32, np.complex128, np.array):
+            xp_assert_close(lsim(typ(2) * s1, U=u, T=t)[1],
+                            typ(2) * lsim(s1, U=u, T=t)[1])
+
+            xp_assert_close(lsim(s1 * typ(2), U=u, T=t)[1],
+                            lsim(s1, U=u, T=t)[1] * typ(2))
+
+            xp_assert_close(lsim(s1 / typ(2), U=u, T=t)[1],
+                            lsim(s1, U=u, T=t)[1] / typ(2))
+
+            with assert_raises(TypeError):
+                typ(2) / s1
+
+        xp_assert_close(lsim(s1 * 2, U=u, T=t)[1],
+                        lsim(s1, U=2 * u, T=t)[1])
+
+        xp_assert_close(lsim(s1 * s2, U=u, T=t)[1],
+                        lsim(s1, U=lsim(s2, U=u, T=t)[1], T=t)[1],
+                        atol=1e-5)
+
+        with assert_raises(TypeError):
+            s1 / s1
+
+        with assert_raises(TypeError):
+            s1 * s_discrete
+
+        with assert_raises(TypeError):
+            # Check different discretization constants
+            s_discrete * s2_discrete
+
+        with assert_raises(TypeError):
+            s1 * BadType()
+
+        with assert_raises(TypeError):
+            BadType() * s1
+
+        with assert_raises(TypeError):
+            s1 / BadType()
+
+        with assert_raises(TypeError):
+            BadType() / s1
+
+        # Test addition
+        xp_assert_close(lsim(s1 + 2, U=u, T=t)[1],
+                        2 * u + lsim(s1, U=u, T=t)[1])
+
+        # Check for dimension mismatch
+        with assert_raises(ValueError):
+            s1 + np.array([1, 2])
+
+        with assert_raises(ValueError):
+            np.array([1, 2]) + s1
+
+        with assert_raises(TypeError):
+            s1 + s_discrete
+
+        with assert_raises(ValueError):
+            s1 / np.array([[1, 2], [3, 4]])
+
+        with assert_raises(TypeError):
+            # Check different discretization constants
+            s_discrete + s2_discrete
+
+        with assert_raises(TypeError):
+            s1 + BadType()
+
+        with assert_raises(TypeError):
+            BadType() + s1
+
+        xp_assert_close(lsim(s1 + s2, U=u, T=t)[1],
+                        lsim(s1, U=u, T=t)[1] + lsim(s2, U=u, T=t)[1])
+
+        # Test subtraction
+        xp_assert_close(lsim(s1 - 2, U=u, T=t)[1],
+                        -2 * u + lsim(s1, U=u, T=t)[1])
+
+        xp_assert_close(lsim(2 - s1, U=u, T=t)[1],
+                        2 * u + lsim(-s1, U=u, T=t)[1])
+
+        xp_assert_close(lsim(s1 - s2, U=u, T=t)[1],
+                        lsim(s1, U=u, T=t)[1] - lsim(s2, U=u, T=t)[1])
+
+        with assert_raises(TypeError):
+            s1 - BadType()
+
+        with assert_raises(TypeError):
+            BadType() - s1
+
+        s = s_discrete + s3_discrete
+        assert s.dt == 0.1
+
+        s = s_discrete * s3_discrete
+        assert s.dt == 0.1
+
+        s = 3 * s_discrete
+        assert s.dt == 0.1
+
+        s = -s_discrete
+        assert s.dt == 0.1
+
+class TestTransferFunction:
+    def test_initialization(self):
+        # Check that all initializations work
+        TransferFunction(1, 1)
+        TransferFunction([1], [2])
+        TransferFunction(np.array([1]), np.array([2]))
+
+    def test_conversion(self):
+        # Check the conversion functions
+        s = TransferFunction([1, 0], [1, -1])
+        assert isinstance(s.to_ss(), StateSpace)
+        assert isinstance(s.to_tf(), TransferFunction)
+        assert isinstance(s.to_zpk(), ZerosPolesGain)
+
+        # Make sure copies work
+        assert TransferFunction(s) is not s
+        assert s.to_tf() is not s
+
+    def test_properties(self):
+        # Test setters/getters for cross class properties.
+        # This implicitly tests to_ss() and to_zpk()
+
+        # Getters
+        s = TransferFunction([1, 0], [1, -1])
+        xp_assert_equal(s.poles, [1.])
+        xp_assert_equal(s.zeros, [0.])
+
+
+class TestZerosPolesGain:
+    def test_initialization(self):
+        # Check that all initializations work
+        ZerosPolesGain(1, 1, 1)
+        ZerosPolesGain([1], [2], 1)
+        ZerosPolesGain(np.array([1]), np.array([2]), 1)
+
+    def test_conversion(self):
+        #Check the conversion functions
+        s = ZerosPolesGain(1, 2, 3)
+        assert isinstance(s.to_ss(), StateSpace)
+        assert isinstance(s.to_tf(), TransferFunction)
+        assert isinstance(s.to_zpk(), ZerosPolesGain)
+
+        # Make sure copies work
+        assert ZerosPolesGain(s) is not s
+        assert s.to_zpk() is not s
+
+
+@make_xp_test_case(abcd_normalize)
+class Test_abcd_normalize:
+    A = [[1.0, 2.0], [3.0, 4.0]]
+    B = [[-1.0], [5.0]]
+    C = [[4.0, 5.0]]
+    D = [[2.5]]
+
+    def test_no_matrix_fails(self):
+        assert_raises(ValueError, abcd_normalize)
+
+    def test_A_nosquare_fails(self):
+        assert_raises(ValueError, abcd_normalize,
+                      [1, -1], self.B, self.C, self.D)
+
+    def test_AB_mismatch_fails(self):
+        assert_raises(ValueError, abcd_normalize,
+                      self.A, [-1, 5], self.C, self.D)
+
+    def test_AC_mismatch_fails(self):
+        assert_raises(ValueError, abcd_normalize,
+                      self.A, self.B, [[4.0], [5.0]], self.D)
+
+    def test_CD_mismatch_fails(self):
+        assert_raises(ValueError, abcd_normalize,
+                      self.A, self.B, self.C, [2.5, 0])
+
+    def test_BD_mismatch_fails(self, xp):
+        assert_raises(ValueError, abcd_normalize,
+                      self.A, [-1, 5], self.C, self.D)
+
+    def test_normalized_matrices_unchanged(self, xp):
+        A_, B_, C_, D_ = map(
+            lambda t: xp.asarray(t, dtype=xp.float64),
+            (self.A, self.B, self.C, self.D),
+        )
+        A, B, C, D = abcd_normalize(A=A_, B=B_, C=C_, D=D_)
+        xp_assert_equal(A, A_)
+        xp_assert_equal(B, B_)
+        xp_assert_equal(C, C_)
+        xp_assert_equal(D, D_)
+
+    def test_shapes(self):
+        A, B, C, D = abcd_normalize(self.A, self.B, [1, 0], 0)
+        assert A.shape[0] == A.shape[1]
+        assert A.shape[0] == B.shape[0]
+        assert A.shape[0] == C.shape[1]
+        assert C.shape[0] == D.shape[0]
+        assert B.shape[1] == D.shape[1]
+
+    def test_zero_dimension_is_not_none1(self, xp):
+        A_ = xp.asarray(self.A, dtype=xp.float64)
+        B_ = xp.zeros((2, 0), dtype=xp.float64)
+        D_ = xp.zeros((0, 0), dtype=xp.float64)
+        A, B, C, D = abcd_normalize(A=A_, B=B_, D=D_)
+        xp_assert_equal(A, A_)
+        xp_assert_equal(B, B_)
+        xp_assert_equal(D, D_)
+        assert C.shape[0] == D_.shape[0]
+        assert C.shape[1] == A_.shape[0]
+
+    def test_zero_dimension_is_not_none2(self, xp):
+        A_ = xp.asarray(self.A, dtype=xp.float64)
+        B_ = xp.zeros((2, 0), dtype=xp.float64)
+        C_ = xp.zeros((0, 2), dtype=xp.float64)
+        A, B, C, D = abcd_normalize(A=A_, B=B_, C=C_)
+        xp_assert_equal(A, A_)
+        xp_assert_equal(B, B_)
+        xp_assert_equal(C, C_)
+        assert D.shape[0] == C_.shape[0]
+        assert D.shape[1] == B_.shape[1]
+
+    def test_missing_A(self, xp):
+        B_, C_, D_ = map(
+            lambda t: xp.asarray(t, dtype=xp.float64),
+            (self.B, self.C, self.D),
+        )
+        A, B, C, D = abcd_normalize(B=B_, C=C_, D=D_)
+        assert A.shape[0] == A.shape[1]
+        assert A.shape[0] == B.shape[0]
+        assert A.shape == (B_.shape[0], B_.shape[0])
+
+    def test_missing_B(self, xp):
+        A_, C_, D_ = map(xp.asarray, (self.A, self.C, self.D))
+        A, B, C, D = abcd_normalize(A=A_, C=C_, D=D_)
+        assert B.shape[0] == A.shape[0]
+        assert B.shape[1] == D.shape[1]
+        assert B.shape == (A_.shape[0], D_.shape[1])
+
+    def test_missing_C(self, xp):
+        A_, B_, D_ = map(
+            lambda t: xp.asarray(t, dtype=xp.float64),
+            (self.A, self.B, self.D),
+        )
+        A, B, C, D = abcd_normalize(A=A_, B=B_, D=D_)
+        assert C.shape[0] == D.shape[0]
+        assert C.shape[1] == A.shape[0]
+        assert C.shape == (D_.shape[0], A_.shape[0])
+
+    def test_missing_D(self, xp):
+        A_, B_, C_ = map(xp.asarray, (self.A, self.B, self.C))
+        A, B, C, D = abcd_normalize(A=A_, B=B_, C=C_)
+        assert D.shape[0] == C.shape[0]
+        assert D.shape[1] == B.shape[1]
+        assert D.shape == (C_.shape[0], B_.shape[1])
+
+    def test_missing_AB(self, xp):
+        C_, D_ = map(xp.asarray, (self.C, self.D))
+        A, B, C, D = abcd_normalize(C=C_, D=D_)
+        assert A.shape[0] == A.shape[1]
+        assert A.shape[0] == B.shape[0]
+        assert B.shape[1] == D.shape[1]
+        assert A.shape == (C_.shape[1], C_.shape[1])
+        assert B.shape == (C_.shape[1], D_.shape[1])
+
+    def test_missing_AC(self, xp):
+        B_, D_ = map(xp.asarray, (self.B, self.D))
+        A, B, C, D = abcd_normalize(B=B_, D=D_)
+        assert A.shape[0] == A.shape[1]
+        assert A.shape[0] == B.shape[0]
+        assert C.shape[0] == D.shape[0]
+        assert C.shape[1] == A.shape[0]
+        assert A.shape == (B_.shape[0], B_.shape[0])
+        assert C.shape == (D_.shape[0], B_.shape[0])
+
+    def test_missing_AD(self, xp):
+        B_, C_ = map(xp.asarray, (self.B, self.C))
+        A, B, C, D = abcd_normalize(B=B_, C=C_)
+        assert A.shape[0] == A.shape[1]
+        assert A.shape[0] == B.shape[0]
+        assert D.shape[0] == C.shape[0]
+        assert D.shape[1] == B.shape[1]
+        assert A.shape == (B_.shape[0], B_.shape[0])
+        assert D.shape == (C_.shape[0], B_.shape[1])
+
+    def test_missing_BC(self, xp):
+        A_, D_ = map(xp.asarray, (self.A, self.D))
+        A, B, C, D = abcd_normalize(A=A_, D=D_)
+        assert B.shape[0] == A.shape[0]
+        assert B.shape[1] == D.shape[1]
+        assert C.shape[0] == D.shape[0]
+        assert C.shape[1] == A.shape[0]
+        assert B.shape == (A_.shape[0], D_.shape[1])
+        assert C.shape == (D_.shape[0], A_.shape[0])
+
+    def test_missing_ABC_fails(self, xp):
+        assert_raises(ValueError, abcd_normalize, D=xp.asarray(self.D))
+
+    def test_missing_BD_fails(self, xp):
+        A, C = xp.asarray(self.A),xp.asarray(self.C)
+        assert_raises(ValueError, abcd_normalize, A=A, C=C)
+
+    def test_missing_CD_fails(self, xp):
+        A, B = xp.asarray(self.A), xp.asarray(self.B)
+        assert_raises(ValueError, abcd_normalize, A=A, B=B)
+
+
+    @pytest.mark.parametrize(
+        "A_dtype",
+        # A_dtype=None here means to pass None as the value for A
+        [None, "int64", "float32", "float64", "complex64", "complex128"],
+    )
+    @pytest.mark.parametrize(
+        "B_dtype",
+        [None, "int64", "float32", "float64", "complex64", "complex128"],
+    )
+    @pytest.mark.parametrize(
+        "C_dtype",
+        ["int64", "float32", "float64", "complex64", "complex128"],
+    )
+    @pytest.mark.parametrize(
+        "D_dtype",
+        ["int64", "float32", "float64", "complex64", "complex128"],
+    )
+    # Also check case where one input array has size zero.
+    @pytest.mark.parametrize("D", [[[2.5]], [[]]])
+    def test_dtypes(self, D, A_dtype, B_dtype, C_dtype, D_dtype, xp):
+       
+        args = []
+        for X, X_dtype in zip(
+                [self.A, self.B, self.C, D],
+                [A_dtype, B_dtype, C_dtype, D_dtype]
+        ):
+            args.append(
+                xp.asarray(X, dtype=getattr(xp, X_dtype))
+                if X_dtype is not None else None
+            )
+        A, B, C, D = args
+        expected_dtype = xp_result_type(A, B, C, D, xp=xp, force_floating=True)
+        A, B, C, D = abcd_normalize(A=A, B=B, C=C, D=D)
+        assert A.dtype == B.dtype == C.dtype == D.dtype == expected_dtype
+
+
+class Test_bode:
+
+    def test_01(self):
+        # Test bode() magnitude calculation (manual sanity check).
+        # 1st order low-pass filter: H(s) = 1 / (s + 1),
+        # cutoff: 1 rad/s, slope: -20 dB/decade
+        #   H(s=0.1) ~= 0 dB
+        #   H(s=1) ~= -3 dB
+        #   H(s=10) ~= -20 dB
+        #   H(s=100) ~= -40 dB
+        system = lti([1], [1, 1])
+        w = [0.1, 1, 10, 100]
+        w, mag, phase = bode(system, w=w)
+        expected_mag = [0, -3, -20, -40]
+        assert_almost_equal(mag, expected_mag, decimal=1)
+
+    def test_02(self):
+        # Test bode() phase calculation (manual sanity check).
+        # 1st order low-pass filter: H(s) = 1 / (s + 1),
+        #   angle(H(s=0.1)) ~= -5.7 deg
+        #   angle(H(s=1)) ~= -45 deg
+        #   angle(H(s=10)) ~= -84.3 deg
+        system = lti([1], [1, 1])
+        w = [0.1, 1, 10]
+        w, mag, phase = bode(system, w=w)
+        expected_phase = [-5.7, -45, -84.3]
+        assert_almost_equal(phase, expected_phase, decimal=1)
+
+    def test_03(self):
+        # Test bode() magnitude calculation.
+        # 1st order low-pass filter: H(s) = 1 / (s + 1)
+        system = lti([1], [1, 1])
+        w = [0.1, 1, 10, 100]
+        w, mag, phase = bode(system, w=w)
+        jw = w * 1j
+        y = np.polyval(system.num, jw) / np.polyval(system.den, jw)
+        expected_mag = 20.0 * np.log10(abs(y))
+        assert_almost_equal(mag, expected_mag)
+
+    def test_04(self):
+        # Test bode() phase calculation.
+        # 1st order low-pass filter: H(s) = 1 / (s + 1)
+        system = lti([1], [1, 1])
+        w = [0.1, 1, 10, 100]
+        w, mag, phase = bode(system, w=w)
+        jw = w * 1j
+        y = np.polyval(system.num, jw) / np.polyval(system.den, jw)
+        expected_phase = np.arctan2(y.imag, y.real) * 180.0 / np.pi
+        assert_almost_equal(phase, expected_phase)
+
+    def test_05(self):
+        # Test that bode() finds a reasonable frequency range.
+        # 1st order low-pass filter: H(s) = 1 / (s + 1)
+        system = lti([1], [1, 1])
+        n = 10
+        # Expected range is from 0.01 to 10.
+        expected_w = np.logspace(-2, 1, n)
+        w, mag, phase = bode(system, n=n)
+        assert_almost_equal(w, expected_w)
+
+    def test_06(self):
+        # Test that bode() doesn't fail on a system with a pole at 0.
+        # integrator, pole at zero: H(s) = 1 / s
+        system = lti([1], [1, 0])
+        w, mag, phase = bode(system, n=2)
+        assert w[0] == 0.01   # a fail would give not-a-number
+
+    def test_07(self):
+        # bode() should not fail on a system with pure imaginary poles.
+        # The test passes if bode doesn't raise an exception.
+        system = lti([1], [1, 0, 100])
+        w, mag, phase = bode(system, n=2)
+
+    def test_08(self):
+        # Test that bode() return continuous phase, issues/2331.
+        system = lti([], [-10, -30, -40, -60, -70], 1)
+        w, mag, phase = system.bode(w=np.logspace(-3, 40, 100))
+        assert_almost_equal(min(phase), -450, decimal=15)
+
+    def test_from_state_space(self):
+        # Ensure that bode works with a system that was created from the
+        # state space representation matrices A, B, C, D.  In this case,
+        # system.num will be a 2-D array with shape (1, n+1), where (n,n)
+        # is the shape of A.
+        # A Butterworth lowpass filter is used, so we know the exact
+        # frequency response.
+        a = np.array([1.0, 2.0, 2.0, 1.0])
+        A = linalg.companion(a).T
+        B = np.array([[0.0], [0.0], [1.0]])
+        C = np.array([[1.0, 0.0, 0.0]])
+        D = np.array([[0.0]])
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", BadCoefficients)
+            system = lti(A, B, C, D)
+            w, mag, phase = bode(system, n=100)
+
+        expected_magnitude = 20 * np.log10(np.sqrt(1.0 / (1.0 + w**6)))
+        assert_almost_equal(mag, expected_magnitude)
+
+
+class Test_freqresp:
+
+    def test_output_manual(self):
+        # Test freqresp() output calculation (manual sanity check).
+        # 1st order low-pass filter: H(s) = 1 / (s + 1),
+        #   re(H(s=0.1)) ~= 0.99
+        #   re(H(s=1)) ~= 0.5
+        #   re(H(s=10)) ~= 0.0099
+        system = lti([1], [1, 1])
+        w = [0.1, 1, 10]
+        w, H = freqresp(system, w=w)
+        expected_re = [0.99, 0.5, 0.0099]
+        expected_im = [-0.099, -0.5, -0.099]
+        assert_almost_equal(H.real, expected_re, decimal=1)
+        assert_almost_equal(H.imag, expected_im, decimal=1)
+
+    def test_output(self):
+        # Test freqresp() output calculation.
+        # 1st order low-pass filter: H(s) = 1 / (s + 1)
+        system = lti([1], [1, 1])
+        w = [0.1, 1, 10, 100]
+        w, H = freqresp(system, w=w)
+        s = w * 1j
+        expected = np.polyval(system.num, s) / np.polyval(system.den, s)
+        assert_almost_equal(H.real, expected.real)
+        assert_almost_equal(H.imag, expected.imag)
+
+    def test_freq_range(self):
+        # Test that freqresp() finds a reasonable frequency range.
+        # 1st order low-pass filter: H(s) = 1 / (s + 1)
+        # Expected range is from 0.01 to 10.
+        system = lti([1], [1, 1])
+        n = 10
+        expected_w = np.logspace(-2, 1, n)
+        w, H = freqresp(system, n=n)
+        assert_almost_equal(w, expected_w)
+
+    def test_pole_zero(self):
+        # Test that freqresp() doesn't fail on a system with a pole at 0.
+        # integrator, pole at zero: H(s) = 1 / s
+        system = lti([1], [1, 0])
+        w, H = freqresp(system, n=2)
+        assert w[0] == 0.01  # a fail would give not-a-number
+
+    def test_from_state_space(self):
+        # Ensure that freqresp works with a system that was created from the
+        # state space representation matrices A, B, C, D.  In this case,
+        # system.num will be a 2-D array with shape (1, n+1), where (n,n) is
+        # the shape of A.
+        # A Butterworth lowpass filter is used, so we know the exact
+        # frequency response.
+        a = np.array([1.0, 2.0, 2.0, 1.0])
+        A = linalg.companion(a).T
+        B = np.array([[0.0],[0.0],[1.0]])
+        C = np.array([[1.0, 0.0, 0.0]])
+        D = np.array([[0.0]])
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", BadCoefficients)
+            system = lti(A, B, C, D)
+            w, H = freqresp(system, n=100)
+        s = w * 1j
+        expected = (1.0 / (1.0 + 2*s + 2*s**2 + s**3))
+        assert_almost_equal(H.real, expected.real)
+        assert_almost_equal(H.imag, expected.imag)
+
+    def test_from_zpk(self):
+        # 4th order low-pass filter: H(s) = 1 / (s + 1)
+        system = lti([],[-1]*4,[1])
+        w = [0.1, 1, 10, 100]
+        w, H = freqresp(system, w=w)
+        s = w * 1j
+        expected = 1 / (s + 1)**4
+        assert_almost_equal(H.real, expected.real)
+        assert_almost_equal(H.imag, expected.imag)
+
+@pytest.mark.parametrize(
+    "cls", [StateSpace, TransferFunction, ZerosPolesGain, lti, dlti]
+)
+def test_subscriptable_generic_types(cls):
+    assert isinstance(cls[np.float64], GenericAlias)
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/tests/test_max_len_seq.py b/venv/lib/python3.12/site-packages/scipy/signal/tests/test_max_len_seq.py
new file mode 100644
index 0000000000000000000000000000000000000000..7610b3f898571d10d75a64f00d900168c7142fbe
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/tests/test_max_len_seq.py
@@ -0,0 +1,71 @@
+import numpy as np
+from pytest import raises as assert_raises
+from scipy._lib._array_api import xp_assert_close, xp_assert_equal
+
+from numpy.fft import fft, ifft
+
+from scipy.signal import max_len_seq
+
+
+class TestMLS:
+
+    def test_mls_inputs(self):
+        # can't all be zero state
+        assert_raises(ValueError, max_len_seq,
+                      10, state=np.zeros(10))
+        # wrong size state
+        assert_raises(ValueError, max_len_seq, 10,
+                      state=np.ones(3))
+        # wrong length
+        assert_raises(ValueError, max_len_seq, 10, length=-1)
+        xp_assert_equal(max_len_seq(10, length=0)[0],
+                        np.asarray([], dtype=np.int8)
+        )
+        # unknown taps
+        assert_raises(ValueError, max_len_seq, 64)
+        # bad taps
+        assert_raises(ValueError, max_len_seq, 10, taps=[-1, 1])
+
+    def test_mls_output(self):
+        # define some alternate working taps
+        alt_taps = {2: [1], 3: [2], 4: [3], 5: [4, 3, 2], 6: [5, 4, 1], 7: [4],
+                    8: [7, 5, 3]}
+        # assume the other bit levels work, too slow to test higher orders...
+        for nbits in range(2, 8):
+            for state in [None, np.round(np.random.rand(nbits))]:
+                for taps in [None, alt_taps[nbits]]:
+                    if state is not None and np.all(state == 0):
+                        state[0] = 1  # they can't all be zero
+                    orig_m = max_len_seq(nbits, state=state,
+                                         taps=taps)[0]
+                    m = 2. * orig_m - 1.  # convert to +/- 1 representation
+                    # First, make sure we got all 1's or -1
+                    err_msg = "mls had non binary terms"
+                    xp_assert_equal(np.abs(m), np.ones_like(m),
+                                       err_msg=err_msg)
+                    # Test via circular cross-correlation, which is just mult.
+                    # in the frequency domain with one signal conjugated
+                    tester = np.real(ifft(fft(m) * np.conj(fft(m))))
+                    out_len = 2**nbits - 1
+                    # impulse amplitude == test_len
+                    err_msg = "mls impulse has incorrect value"
+                    xp_assert_close(tester[0],
+                                    float(out_len),
+                                    err_msg=err_msg
+                    )
+                    # steady-state is -1
+                    err_msg = "mls steady-state has incorrect value"
+                    xp_assert_close(tester[1:],
+                                    np.full(out_len - 1, -1, dtype=tester.dtype),
+                                    err_msg=err_msg)
+                    # let's do the split thing using a couple options
+                    for n in (1, 2**(nbits - 1)):
+                        m1, s1 = max_len_seq(nbits, state=state, taps=taps,
+                                             length=n)
+                        m2, s2 = max_len_seq(nbits, state=s1, taps=taps,
+                                             length=1)
+                        m3, s3 = max_len_seq(nbits, state=s2, taps=taps,
+                                             length=out_len - n - 1)
+                        new_m = np.concatenate((m1, m2, m3))
+                        xp_assert_equal(orig_m, new_m)
+
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/tests/test_peak_finding.py b/venv/lib/python3.12/site-packages/scipy/signal/tests/test_peak_finding.py
new file mode 100644
index 0000000000000000000000000000000000000000..7aa04f3a8ca47616f1456664fc9ae0f5d0b8e69d
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/tests/test_peak_finding.py
@@ -0,0 +1,970 @@
+import copy
+
+import numpy as np
+import pytest
+from pytest import raises, warns
+from scipy._lib._array_api import xp_assert_close, xp_assert_equal
+
+from scipy.signal._peak_finding import (
+    argrelmax,
+    argrelmin,
+    peak_prominences,
+    peak_widths,
+    _unpack_condition_args,
+    find_peaks,
+    find_peaks_cwt,
+    _identify_ridge_lines
+)
+from scipy.signal.windows import gaussian
+from scipy.signal._peak_finding_utils import _local_maxima_1d, PeakPropertyWarning
+
+
+def _gen_gaussians(center_locs, sigmas, total_length):
+    xdata = np.arange(0, total_length).astype(float)
+    out_data = np.zeros(total_length, dtype=float)
+    for ind, sigma in enumerate(sigmas):
+        tmp = (xdata - center_locs[ind]) / sigma
+        out_data += np.exp(-(tmp**2))
+    return out_data
+
+
+def _gen_gaussians_even(sigmas, total_length):
+    num_peaks = len(sigmas)
+    delta = total_length / (num_peaks + 1)
+    center_locs = np.linspace(delta, total_length - delta, num=num_peaks).astype(int)
+    out_data = _gen_gaussians(center_locs, sigmas, total_length)
+    return out_data, center_locs
+
+
+def _gen_ridge_line(start_locs, max_locs, length, distances, gaps):
+    """
+    Generate coordinates for a ridge line.
+
+    Will be a series of coordinates, starting a start_loc (length 2).
+    The maximum distance between any adjacent columns will be
+    `max_distance`, the max distance between adjacent rows
+    will be `map_gap'.
+
+    `max_locs` should be the size of the intended matrix. The
+    ending coordinates are guaranteed to be less than `max_locs`,
+    although they may not approach `max_locs` at all.
+    """
+
+    def keep_bounds(num, max_val):
+        out = max(num, 0)
+        out = min(out, max_val)
+        return out
+
+    gaps = copy.deepcopy(gaps)
+    distances = copy.deepcopy(distances)
+
+    locs = np.zeros([length, 2], dtype=int)
+    locs[0, :] = start_locs
+    total_length = max_locs[0] - start_locs[0] - sum(gaps)
+    if total_length < length:
+        raise ValueError('Cannot generate ridge line according to constraints')
+    dist_int = length / len(distances) - 1
+    gap_int = length / len(gaps) - 1
+    for ind in range(1, length):
+        nextcol = locs[ind - 1, 1]
+        nextrow = locs[ind - 1, 0] + 1
+        if (ind % dist_int == 0) and (len(distances) > 0):
+            nextcol += ((-1)**ind)*distances.pop()
+        if (ind % gap_int == 0) and (len(gaps) > 0):
+            nextrow += gaps.pop()
+        nextrow = keep_bounds(nextrow, max_locs[0])
+        nextcol = keep_bounds(nextcol, max_locs[1])
+        locs[ind, :] = [nextrow, nextcol]
+
+    return [locs[:, 0], locs[:, 1]]
+
+
+class TestLocalMaxima1d:
+
+    def test_empty(self):
+        """Test with empty signal."""
+        x = np.array([], dtype=np.float64)
+        for array in _local_maxima_1d(x):
+            xp_assert_equal(array, np.array([]), check_dtype=False)
+            assert array.base is None
+
+    def test_linear(self):
+        """Test with linear signal."""
+        x = np.linspace(0, 100)
+        for array in _local_maxima_1d(x):
+            xp_assert_equal(array, np.array([], dtype=np.intp))
+            assert array.base is None
+
+    def test_simple(self):
+        """Test with simple signal."""
+        x = np.linspace(-10, 10, 50)
+        x[2::3] += 1
+        expected = np.arange(2, 50, 3, dtype=np.intp)
+        for array in _local_maxima_1d(x):
+            # For plateaus of size 1, the edges are identical with the
+            # midpoints
+            xp_assert_equal(array, expected, check_dtype=False)
+            assert array.base is None
+
+    def test_flat_maxima(self):
+        """Test if flat maxima are detected correctly."""
+        x = np.array([-1.3, 0, 1, 0, 2, 2, 0, 3, 3, 3, 2.99, 4, 4, 4, 4, -10,
+                      -5, -5, -5, -5, -5, -10])
+        midpoints, left_edges, right_edges = _local_maxima_1d(x)
+        xp_assert_equal(midpoints, np.array([2, 4, 8, 12, 18]), check_dtype=False)
+        xp_assert_equal(left_edges, np.array([2, 4, 7, 11, 16]), check_dtype=False)
+        xp_assert_equal(right_edges, np.array([2, 5, 9, 14, 20]), check_dtype=False)
+
+    @pytest.mark.parametrize('x', [
+        np.array([1., 0, 2]),
+        np.array([3., 3, 0, 4, 4]),
+        np.array([5., 5, 5, 0, 6, 6, 6]),
+    ])
+    def test_signal_edges(self, x):
+        """Test if behavior on signal edges is correct."""
+        for array in _local_maxima_1d(x):
+            xp_assert_equal(array, np.array([], dtype=np.intp))
+            assert array.base is None
+
+    def test_exceptions(self):
+        """Test input validation and raised exceptions."""
+        with raises(ValueError, match="wrong number of dimensions"):
+            _local_maxima_1d(np.ones((1, 1)))
+        with raises(ValueError, match="expected 'const float64_t'"):
+            _local_maxima_1d(np.ones(1, dtype=int))
+        with raises(TypeError, match="list"):
+            _local_maxima_1d([1., 2.])
+        with raises(TypeError, match="'x' must not be None"):
+            _local_maxima_1d(None)
+
+
+class TestRidgeLines:
+
+    def test_empty(self):
+        test_matr = np.zeros([20, 100])
+        lines = _identify_ridge_lines(test_matr, np.full(20, 2), 1)
+        assert len(lines) == 0
+
+    def test_minimal(self):
+        test_matr = np.zeros([20, 100])
+        test_matr[0, 10] = 1
+        lines = _identify_ridge_lines(test_matr, np.full(20, 2), 1)
+        assert len(lines) == 1
+        for line in lines:
+            xp_assert_equal(line[0], np.sort(line[0]))
+
+        test_matr = np.zeros([20, 100])
+        test_matr[0:2, 10] = 1
+        lines = _identify_ridge_lines(test_matr, np.full(20, 2), 1)
+        assert len(lines) == 1
+        for line in lines:
+            xp_assert_equal(line[0], np.sort(line[0]))
+
+    def test_single_pass(self):
+        distances = [0, 1, 2, 5]
+        gaps = [0, 1, 2, 0, 1]
+        test_matr = np.zeros([20, 50]) + 1e-12
+        length = 12
+        line = _gen_ridge_line([0, 25], test_matr.shape, length, distances, gaps)
+        test_matr[line[0], line[1]] = 1
+        max_distances = np.full(20, max(distances))
+        identified_lines = _identify_ridge_lines(test_matr,
+                                                 max_distances,
+                                                 max(gaps) + 1)
+        assert len(identified_lines) == 1
+        for iline in identified_lines:
+            xp_assert_equal(iline[0], np.sort(iline[0]))
+        for iline_, line_ in zip(identified_lines[0], line):
+            xp_assert_equal(iline_, line_, check_dtype=False)
+
+    def test_single_bigdist(self):
+        distances = [0, 1, 2, 5]
+        gaps = [0, 1, 2, 4]
+        test_matr = np.zeros([20, 50])
+        length = 12
+        line = _gen_ridge_line([0, 25], test_matr.shape, length, distances, gaps)
+        test_matr[line[0], line[1]] = 1
+        max_dist = 3
+        max_distances = np.full(20, max_dist)
+        #This should get 2 lines, since the distance is too large
+        identified_lines = _identify_ridge_lines(test_matr,
+                                                 max_distances,
+                                                 max(gaps) + 1)
+        assert len(identified_lines) == 2
+
+        for iline in identified_lines:
+            xp_assert_equal(iline[0], np.sort(iline[0]))
+            adists = np.diff(iline[1])
+            np.testing.assert_array_less(np.abs(adists), max_dist)
+
+            agaps = np.diff(iline[0])
+            np.testing.assert_array_less(np.abs(agaps), max(gaps) + 0.1)
+
+    def test_single_biggap(self):
+        distances = [0, 1, 2, 5]
+        max_gap = 3
+        gaps = [0, 4, 2, 1]
+        test_matr = np.zeros([20, 50])
+        length = 12
+        line = _gen_ridge_line([0, 25], test_matr.shape, length, distances, gaps)
+        test_matr[line[0], line[1]] = 1
+        max_dist = 6
+        max_distances = np.full(20, max_dist)
+        #This should get 2 lines, since the gap is too large
+        identified_lines = _identify_ridge_lines(test_matr, max_distances, max_gap)
+        assert len(identified_lines) == 2
+
+        for iline in identified_lines:
+            xp_assert_equal(iline[0], np.sort(iline[0]))
+            adists = np.diff(iline[1])
+            np.testing.assert_array_less(np.abs(adists), max_dist)
+
+            agaps = np.diff(iline[0])
+            np.testing.assert_array_less(np.abs(agaps), max(gaps) + 0.1)
+
+    def test_single_biggaps(self):
+        distances = [0]
+        max_gap = 1
+        gaps = [3, 6]
+        test_matr = np.zeros([50, 50])
+        length = 30
+        line = _gen_ridge_line([0, 25], test_matr.shape, length, distances, gaps)
+        test_matr[line[0], line[1]] = 1
+        max_dist = 1
+        max_distances = np.full(50, max_dist)
+        #This should get 3 lines, since the gaps are too large
+        identified_lines = _identify_ridge_lines(test_matr, max_distances, max_gap)
+        assert len(identified_lines) == 3
+
+        for iline in identified_lines:
+            xp_assert_equal(iline[0], np.sort(iline[0]))
+            adists = np.diff(iline[1])
+            np.testing.assert_array_less(np.abs(adists), max_dist)
+
+            agaps = np.diff(iline[0])
+            np.testing.assert_array_less(np.abs(agaps), max(gaps) + 0.1)
+
+    def test_sorting(self):
+        test_matr = np.zeros([5, 10])
+        test_matr[4, 5] = 1.0
+        test_matr[3, 4] = 1.0
+        test_matr[3, 6] = 1.0
+        ridge_lines = _identify_ridge_lines(test_matr, np.full(5, 2), 1)
+        for line in ridge_lines:
+            xp_assert_equal(line[0], np.sort(line[0]))
+
+        test_matr = np.zeros([5, 10])
+        test_matr[0, 3] = 1.0
+        test_matr[0, 7] = 1.0
+        test_matr[1, 5] = 1.0
+        ridge_lines = _identify_ridge_lines(test_matr, np.full(5, 3), 1)
+        for line in ridge_lines:
+            xp_assert_equal(line[0], np.sort(line[0]))
+
+        test_matr = np.zeros([5, 15])
+        test_matr[0, 2] = 1.0
+        test_matr[0, 7] = 1.0
+        test_matr[0, 12] = 1.0
+        test_matr[1, 7] = 1.0
+        ridge_lines = _identify_ridge_lines(test_matr, np.full(5, 6), 1)
+        for line in ridge_lines:
+            xp_assert_equal(line[0], np.sort(line[0]))
+
+        test_matr = np.zeros([6, 12])
+        test_matr[5, 5] = 1.0
+        test_matr[4, 3] = 1.0
+        test_matr[4, 7] = 1.0
+        test_matr[3, 5] = 1.0
+        test_matr[2, 5] = 1.0
+        ridge_lines = _identify_ridge_lines(test_matr, np.full(6, 3), 1)
+        for line in ridge_lines:
+            xp_assert_equal(line[0], np.sort(line[0]))
+
+
+class TestArgrel:
+
+    def test_empty(self):
+        # Regression test for gh-2832.
+        # When there are no relative extrema, make sure that
+        # the number of empty arrays returned matches the
+        # dimension of the input.
+
+        empty_array = np.array([], dtype=int)
+
+        z1 = np.zeros(5)
+
+        i = argrelmin(z1)
+        xp_assert_equal(len(i), 1)
+        xp_assert_equal(i[0], empty_array, check_dtype=False)
+
+        z2 = np.zeros((3, 5))
+
+        row, col = argrelmin(z2, axis=0)
+        xp_assert_equal(row, empty_array, check_dtype=False)
+        xp_assert_equal(col, empty_array, check_dtype=False)
+
+        row, col = argrelmin(z2, axis=1)
+        xp_assert_equal(row, empty_array, check_dtype=False)
+        xp_assert_equal(col, empty_array, check_dtype=False)
+
+    def test_basic(self):
+        # Note: the docstrings for the argrel{min,max,extrema} functions
+        # do not give a guarantee of the order of the indices, so we'll
+        # sort them before testing.
+
+        x = np.array([[1, 2, 2, 3, 2],
+                      [2, 1, 2, 2, 3],
+                      [3, 2, 1, 2, 2],
+                      [2, 3, 2, 1, 2],
+                      [1, 2, 3, 2, 1]])
+
+        row, col = argrelmax(x, axis=0)
+        order = np.argsort(row)
+        xp_assert_equal(row[order], [1, 2, 3], check_dtype=False)
+        xp_assert_equal(col[order], [4, 0, 1], check_dtype=False)
+
+        row, col = argrelmax(x, axis=1)
+        order = np.argsort(row)
+        xp_assert_equal(row[order], [0, 3, 4], check_dtype=False)
+        xp_assert_equal(col[order], [3, 1, 2], check_dtype=False)
+
+        row, col = argrelmin(x, axis=0)
+        order = np.argsort(row)
+        xp_assert_equal(row[order], [1, 2, 3], check_dtype=False)
+        xp_assert_equal(col[order], [1, 2, 3], check_dtype=False)
+
+        row, col = argrelmin(x, axis=1)
+        order = np.argsort(row)
+        xp_assert_equal(row[order], [1, 2, 3], check_dtype=False)
+        xp_assert_equal(col[order], [1, 2, 3], check_dtype=False)
+
+    def test_highorder(self):
+        order = 2
+        sigmas = [1.0, 2.0, 10.0, 5.0, 15.0]
+        test_data, act_locs = _gen_gaussians_even(sigmas, 500)
+        test_data[act_locs + order] = test_data[act_locs]*0.99999
+        test_data[act_locs - order] = test_data[act_locs]*0.99999
+        rel_max_locs = argrelmax(test_data, order=order, mode='clip')[0]
+
+        assert len(rel_max_locs) == len(act_locs)
+        assert (rel_max_locs == act_locs).all()
+
+    def test_2d_gaussians(self):
+        sigmas = [1.0, 2.0, 10.0]
+        test_data, act_locs = _gen_gaussians_even(sigmas, 100)
+        rot_factor = 20
+        rot_range = np.arange(0, len(test_data)) - rot_factor
+        test_data_2 = np.vstack([test_data, test_data[rot_range]])
+        rel_max_rows, rel_max_cols = argrelmax(test_data_2, axis=1, order=1)
+
+        for rw in range(0, test_data_2.shape[0]):
+            inds = (rel_max_rows == rw)
+
+            assert len(rel_max_cols[inds]) == len(act_locs)
+            assert (act_locs == (rel_max_cols[inds] - rot_factor*rw)).all()
+
+
+class TestPeakProminences:
+
+    def test_empty(self):
+        """
+        Test if an empty array is returned if no peaks are provided.
+        """
+        out = peak_prominences([1, 2, 3], [])
+        for arr, dtype in zip(out, [np.float64, np.intp, np.intp]):
+            assert arr.size == 0
+            assert arr.dtype == dtype
+
+        out = peak_prominences([], [])
+        for arr, dtype in zip(out, [np.float64, np.intp, np.intp]):
+            assert arr.size == 0
+            assert arr.dtype == dtype
+
+    def test_basic(self):
+        """
+        Test if height of prominences is correctly calculated in signal with
+        rising baseline (peak widths are 1 sample).
+        """
+        # Prepare basic signal
+        x = np.array([-1, 1.2, 1.2, 1, 3.2, 1.3, 2.88, 2.1])
+        peaks = np.array([1, 2, 4, 6])
+        lbases = np.array([0, 0, 0, 5])
+        rbases = np.array([3, 3, 5, 7])
+        proms = x[peaks] - np.max([x[lbases], x[rbases]], axis=0)
+        # Test if calculation matches handcrafted result
+        out = peak_prominences(x, peaks)
+        xp_assert_equal(out[0], proms, check_dtype=False)
+        xp_assert_equal(out[1], lbases, check_dtype=False)
+        xp_assert_equal(out[2], rbases, check_dtype=False)
+
+    def test_edge_cases(self):
+        """
+        Test edge cases.
+        """
+        # Peaks have same height, prominence and bases
+        x = [0, 2, 1, 2, 1, 2, 0]
+        peaks = [1, 3, 5]
+        proms, lbases, rbases = peak_prominences(x, peaks)
+        xp_assert_equal(proms, np.asarray([2.0, 2, 2]), check_dtype=False)
+        xp_assert_equal(lbases, [0, 0, 0], check_dtype=False)
+        xp_assert_equal(rbases, [6, 6, 6], check_dtype=False)
+
+        # Peaks have same height & prominence but different bases
+        x = [0, 1, 0, 1, 0, 1, 0]
+        peaks = np.array([1, 3, 5])
+        proms, lbases, rbases = peak_prominences(x, peaks)
+        xp_assert_equal(proms, np.asarray([1.0, 1, 1]))
+        xp_assert_equal(lbases, peaks - 1, check_dtype=False)
+        xp_assert_equal(rbases, peaks + 1, check_dtype=False)
+
+    def test_non_contiguous(self):
+        """
+        Test with non-C-contiguous input arrays.
+        """
+        x = np.repeat([-9, 9, 9, 0, 3, 1], 2)
+        peaks = np.repeat([1, 2, 4], 2)
+        proms, lbases, rbases = peak_prominences(x[::2], peaks[::2])
+        xp_assert_equal(proms, np.asarray([9.0, 9, 2]))
+        xp_assert_equal(lbases, [0, 0, 3], check_dtype=False)
+        xp_assert_equal(rbases, [3, 3, 5], check_dtype=False)
+
+    def test_wlen(self):
+        """
+        Test if wlen actually shrinks the evaluation range correctly.
+        """
+        x = [0, 1, 2, 3, 1, 0, -1]
+        peak = [3]
+        # Test rounding behavior of wlen
+        proms = peak_prominences(x, peak)
+        for prom, val in zip(proms, [3.0, 0, 6]):
+            assert prom == val
+
+        for wlen, i in [(8, 0), (7, 0), (6, 0), (5, 1), (3.2, 1), (3, 2), (1.1, 2)]:
+            proms = peak_prominences(x, peak, wlen)
+            for prom, val in zip(proms, [3. - i, 0 + i, 6 - i]):
+                assert prom == val
+
+    def test_exceptions(self):
+        """
+        Verify that exceptions and warnings are raised.
+        """
+        # x with dimension > 1
+        with raises(ValueError, match='1-D array'):
+            peak_prominences([[0, 1, 1, 0]], [1, 2])
+        # peaks with dimension > 1
+        with raises(ValueError, match='1-D array'):
+            peak_prominences([0, 1, 1, 0], [[1, 2]])
+        # x with dimension < 1
+        with raises(ValueError, match='1-D array'):
+            peak_prominences(3, [0,])
+
+        # empty x with supplied
+        with raises(ValueError, match='not a valid index'):
+            peak_prominences([], [0])
+        # invalid indices with non-empty x
+        for p in [-100, -1, 3, 1000]:
+            with raises(ValueError, match='not a valid index'):
+                peak_prominences([1, 0, 2], [p])
+
+        # peaks is not cast-able to np.intp
+        with raises(TypeError, match='cannot safely cast'):
+            peak_prominences([0, 1, 1, 0], [1.1, 2.3])
+
+        # wlen < 3
+        with raises(ValueError, match='wlen'):
+            peak_prominences(np.arange(10), [3, 5], wlen=1)
+
+    def test_warnings(self):
+        """
+        Verify that appropriate warnings are raised.
+        """
+        msg = "some peaks have a prominence of 0"
+        for p in [0, 1, 2]:
+            with warns(PeakPropertyWarning, match=msg):
+                peak_prominences([1, 0, 2], [p,])
+        with warns(PeakPropertyWarning, match=msg):
+            peak_prominences([0, 1, 1, 1, 0], [2], wlen=2)
+
+
+class TestPeakWidths:
+
+    def test_empty(self):
+        """
+        Test if an empty array is returned if no peaks are provided.
+        """
+        widths = peak_widths([], [])[0]
+        assert isinstance(widths, np.ndarray)
+        assert widths.size == 0
+        widths = peak_widths([1, 2, 3], [])[0]
+        assert isinstance(widths, np.ndarray)
+        assert widths.size == 0
+        out = peak_widths([], [])
+        for arr in out:
+            assert isinstance(arr, np.ndarray)
+            assert arr.size == 0
+
+    @pytest.mark.filterwarnings("ignore:some peaks have a width of 0")
+    def test_basic(self):
+        """
+        Test a simple use case with easy to verify results at different relative
+        heights.
+        """
+        x = np.array([1, 0, 1, 2, 1, 0, -1])
+        prominence = 2
+        for rel_height, width_true, lip_true, rip_true in [
+            (0., 0., 3., 3.),  # raises warning
+            (0.25, 1., 2.5, 3.5),
+            (0.5, 2., 2., 4.),
+            (0.75, 3., 1.5, 4.5),
+            (1., 4., 1., 5.),
+            (2., 5., 1., 6.),
+            (3., 5., 1., 6.)
+        ]:
+            width_calc, height, lip_calc, rip_calc = peak_widths(
+                x, [3], rel_height)
+            xp_assert_close(width_calc, np.asarray([width_true]))
+            xp_assert_close(height, np.asarray([2 - rel_height * prominence]))
+            xp_assert_close(lip_calc, np.asarray([lip_true]))
+            xp_assert_close(rip_calc, np.asarray([rip_true]))
+
+    def test_non_contiguous(self):
+        """
+        Test with non-C-contiguous input arrays.
+        """
+        x = np.repeat([0, 100, 50], 4)
+        peaks = np.repeat([1], 3)
+        result = peak_widths(x[::4], peaks[::3])
+        xp_assert_equal(result,
+                        np.asarray([[0.75], [75], [0.75], [1.5]])
+        )
+
+    def test_exceptions(self):
+        """
+        Verify that argument validation works as intended.
+        """
+        with raises(ValueError, match='1-D array'):
+            # x with dimension > 1
+            peak_widths(np.zeros((3, 4)), np.ones(3))
+        with raises(ValueError, match='1-D array'):
+            # x with dimension < 1
+            peak_widths(3, [0])
+        with raises(ValueError, match='1-D array'):
+            # peaks with dimension > 1
+            peak_widths(np.arange(10), np.ones((3, 2), dtype=np.intp))
+        with raises(ValueError, match='1-D array'):
+            # peaks with dimension < 1
+            peak_widths(np.arange(10), 3)
+        with raises(ValueError, match='not a valid index'):
+            # peak pos exceeds x.size
+            peak_widths(np.arange(10), [8, 11])
+        with raises(ValueError, match='not a valid index'):
+            # empty x with peaks supplied
+            peak_widths([], [1, 2])
+        with raises(TypeError, match='cannot safely cast'):
+            # peak cannot be safely cast to intp
+            peak_widths(np.arange(10), [1.1, 2.3])
+        with raises(ValueError, match='rel_height'):
+            # rel_height is < 0
+            peak_widths([0, 1, 0, 1, 0], [1, 3], rel_height=-1)
+        with raises(TypeError, match='None'):
+            # prominence data contains None
+            peak_widths([1, 2, 1], [1], prominence_data=(None, None, None))
+
+    def test_warnings(self):
+        """
+        Verify that appropriate warnings are raised.
+        """
+        msg = "some peaks have a width of 0"
+        with warns(PeakPropertyWarning, match=msg):
+            # Case: rel_height is 0
+            peak_widths([0, 1, 0], [1], rel_height=0)
+        with warns(PeakPropertyWarning, match=msg):
+            # Case: prominence is 0 and bases are identical
+            peak_widths(
+                [0, 1, 1, 1, 0], [2],
+                prominence_data=(np.array([0.], np.float64),
+                                 np.array([2], np.intp),
+                                 np.array([2], np.intp))
+            )
+
+    def test_mismatching_prominence_data(self):
+        """Test with mismatching peak and / or prominence data."""
+        x = [0, 1, 0]
+        peak = [1]
+        for i, (prominences, left_bases, right_bases) in enumerate([
+            ((1.,), (-1,), (2,)),  # left base not in x
+            ((1.,), (0,), (3,)),  # right base not in x
+            ((1.,), (2,), (0,)),  # swapped bases same as peak
+            ((1., 1.), (0, 0), (2, 2)),  # array shapes don't match peaks
+            ((1., 1.), (0,), (2,)),  # arrays with different shapes
+            ((1.,), (0, 0), (2,)),  # arrays with different shapes
+            ((1.,), (0,), (2, 2))  # arrays with different shapes
+        ]):
+            # Make sure input is matches output of signal.peak_prominences
+            prominence_data = (np.array(prominences, dtype=np.float64),
+                               np.array(left_bases, dtype=np.intp),
+                               np.array(right_bases, dtype=np.intp))
+            # Test for correct exception
+            if i < 3:
+                match = "prominence data is invalid for peak"
+            else:
+                match = "arrays in `prominence_data` must have the same shape"
+            with raises(ValueError, match=match):
+                peak_widths(x, peak, prominence_data=prominence_data)
+
+    def test_no_zero_division_with_prominence_data(self):
+        # Test with special prominence data that cause zero division error
+        # regression test for gh-20720
+        # note this is probably isn't a realistic input but reproduces
+        # the original issue 
+        x = np.array([0, 1, 1])
+        peak = np.array([1])
+        prominence_data = (np.array([-1.0]), np.array([0]), np.array([2]))
+        result = peak_widths(x, peak, prominence_data=prominence_data)
+        result_expected = np.asarray([[0.5], [1.5], [1.], [1.5]])
+        xp_assert_equal(result, result_expected)
+
+    @pytest.mark.filterwarnings("ignore:some peaks have a width of 0")
+    def test_intersection_rules(self):
+        """Test if x == eval_height counts as an intersection."""
+        # Flatt peak with two possible intersection points if evaluated at 1
+        x = [0, 1, 2, 1, 3, 3, 3, 1, 2, 1, 0]
+        # relative height is 0 -> width is 0 as well, raises warning
+        xp_assert_close(peak_widths(x, peaks=[5], rel_height=0),
+                        [(0.,), (3.,), (5.,), (5.,)])
+        # width_height == x counts as intersection -> nearest 1 is chosen
+        xp_assert_close(peak_widths(x, peaks=[5], rel_height=2/3),
+                        [(4.,), (1.,), (3.,), (7.,)])
+
+
+def test_unpack_condition_args():
+    """
+    Verify parsing of condition arguments for `scipy.signal.find_peaks` function.
+    """
+    x = np.arange(10)
+    amin_true = x
+    amax_true = amin_true + 10
+    peaks = amin_true[1::2]
+
+    # Test unpacking with None or interval
+    assert (None, None) == _unpack_condition_args((None, None), x, peaks)
+    assert (1, None) == _unpack_condition_args(1, x, peaks)
+    assert (1, None) == _unpack_condition_args((1, None), x, peaks)
+    assert (None, 2) == _unpack_condition_args((None, 2), x, peaks)
+    assert (3., 4.5) == _unpack_condition_args((3., 4.5), x, peaks)
+
+    # Test if borders are correctly reduced with `peaks`
+    amin_calc, amax_calc = _unpack_condition_args((amin_true, amax_true), x, peaks)
+    xp_assert_equal(amin_calc, amin_true[peaks])
+    xp_assert_equal(amax_calc, amax_true[peaks])
+
+    # Test raises if array borders don't match x
+    with raises(ValueError, match="array size of lower"):
+        _unpack_condition_args(amin_true, np.arange(11), peaks)
+    with raises(ValueError, match="array size of upper"):
+        _unpack_condition_args((None, amin_true), np.arange(11), peaks)
+
+
+class TestFindPeaks:
+
+    # Keys of optionally returned properties
+    property_keys = {'peak_heights', 'left_thresholds', 'right_thresholds',
+                     'prominences', 'left_bases', 'right_bases', 'widths',
+                     'width_heights', 'left_ips', 'right_ips'}
+
+    def test_constant(self):
+        """
+        Test behavior for signal without local maxima.
+        """
+        open_interval = (None, None)
+        peaks, props = find_peaks(np.ones(10),
+                                  height=open_interval, threshold=open_interval,
+                                  prominence=open_interval, width=open_interval)
+        assert peaks.size == 0
+        for key in self.property_keys:
+            assert props[key].size == 0
+
+    def test_plateau_size(self):
+        """
+        Test plateau size condition for peaks.
+        """
+        # Prepare signal with peaks with peak_height == plateau_size
+        plateau_sizes = np.array([1, 2, 3, 4, 8, 20, 111])
+        x = np.zeros(plateau_sizes.size * 2 + 1)
+        x[1::2] = plateau_sizes
+        repeats = np.ones(x.size, dtype=int)
+        repeats[1::2] = x[1::2]
+        x = np.repeat(x, repeats)
+
+        # Test full output
+        peaks, props = find_peaks(x, plateau_size=(None, None))
+        xp_assert_equal(peaks, [1, 3, 7, 11, 18, 33, 100], check_dtype=False)
+        xp_assert_equal(props["plateau_sizes"], plateau_sizes, check_dtype=False)
+        xp_assert_equal(props["left_edges"], peaks - (plateau_sizes - 1) // 2,
+                        check_dtype=False)
+        xp_assert_equal(props["right_edges"], peaks + plateau_sizes // 2,
+                        check_dtype=False)
+
+        # Test conditions
+        xp_assert_equal(find_peaks(x, plateau_size=4)[0], [11, 18, 33, 100],
+                        check_dtype=False)
+        xp_assert_equal(find_peaks(x, plateau_size=(None, 3.5))[0], [1, 3, 7],
+                        check_dtype=False)
+        xp_assert_equal(find_peaks(x, plateau_size=(5, 50))[0], [18, 33],
+                        check_dtype=False)
+
+    def test_height_condition(self):
+        """
+        Test height condition for peaks.
+        """
+        x = (0., 1/3, 0., 2.5, 0, 4., 0)
+        peaks, props = find_peaks(x, height=(None, None))
+        xp_assert_equal(peaks, np.array([1, 3, 5]), check_dtype=False)
+        xp_assert_equal(props['peak_heights'], np.array([1/3, 2.5, 4.]),
+                        check_dtype=False)
+        xp_assert_equal(find_peaks(x, height=0.5)[0], np.array([3, 5]),
+                        check_dtype=False)
+        xp_assert_equal(find_peaks(x, height=(None, 3))[0], np.array([1, 3]),
+                        check_dtype=False)
+        xp_assert_equal(find_peaks(x, height=(2, 3))[0], np.array([3]),
+                        check_dtype=False)
+
+    def test_threshold_condition(self):
+        """
+        Test threshold condition for peaks.
+        """
+        x = (0, 2, 1, 4, -1)
+        peaks, props = find_peaks(x, threshold=(None, None))
+        xp_assert_equal(peaks, np.array([1, 3]), check_dtype=False)
+        xp_assert_equal(props['left_thresholds'], np.array([2.0, 3.0]))
+        xp_assert_equal(props['right_thresholds'], np.array([1.0, 5.0]))
+        xp_assert_equal(find_peaks(x, threshold=2)[0], np.array([3]),
+                        check_dtype=False)
+        xp_assert_equal(find_peaks(x, threshold=3.5)[0], np.array([], dtype=int),
+                        check_dtype=False)
+        xp_assert_equal(find_peaks(x, threshold=(None, 5))[0], np.array([1, 3]),
+                        check_dtype=False)
+        xp_assert_equal(find_peaks(x, threshold=(None, 4))[0], np.array([1]),
+                        check_dtype=False)
+        xp_assert_equal(find_peaks(x, threshold=(2, 4))[0], np.array([], dtype=int),
+                        check_dtype=False)
+
+    def test_distance_condition(self):
+        """
+        Test distance condition for peaks.
+        """
+        # Peaks of different height with constant distance 3
+        peaks_all = np.arange(1, 21, 3)
+        x = np.zeros(21)
+        x[peaks_all] += np.linspace(1, 2, peaks_all.size)
+
+        # Test if peaks with "minimal" distance are still selected (distance = 3)
+        xp_assert_equal(find_peaks(x, distance=3)[0], peaks_all, check_dtype=False)
+
+        # Select every second peak (distance > 3)
+        peaks_subset = find_peaks(x, distance=3.0001)[0]
+        # Test if peaks_subset is subset of peaks_all
+        assert np.setdiff1d(peaks_subset, peaks_all, assume_unique=True).size == 0
+
+        # Test if every second peak was removed
+        dfs = np.diff(peaks_subset)
+        xp_assert_equal(dfs, 6*np.ones_like(dfs))
+
+        # Test priority of peak removal
+        x = [-2, 1, -1, 0, -3]
+        peaks_subset = find_peaks(x, distance=10)[0]  # use distance > x size
+        assert peaks_subset.size == 1 and peaks_subset[0] == 1
+
+    def test_prominence_condition(self):
+        """
+        Test prominence condition for peaks.
+        """
+        x = np.linspace(0, 10, 100)
+        peaks_true = np.arange(1, 99, 2)
+        offset = np.linspace(1, 10, peaks_true.size)
+        x[peaks_true] += offset
+        prominences = x[peaks_true] - x[peaks_true + 1]
+        interval = (3, 9)
+        keep = np.nonzero(
+            (interval[0] <= prominences) & (prominences <= interval[1]))
+
+        peaks_calc, properties = find_peaks(x, prominence=interval)
+        xp_assert_equal(peaks_calc, peaks_true[keep], check_dtype=False)
+        xp_assert_equal(properties['prominences'], prominences[keep], check_dtype=False)
+        xp_assert_equal(properties['left_bases'],
+                        np.zeros_like(properties['left_bases']))
+        xp_assert_equal(properties['right_bases'], peaks_true[keep] + 1,
+                        check_dtype=False)
+
+    def test_width_condition(self):
+        """
+        Test width condition for peaks.
+        """
+        x = np.array([1, 0, 1, 2, 1, 0, -1, 4, 0])
+        peaks, props = find_peaks(x, width=(None, 2), rel_height=0.75)
+        assert peaks.size == 1
+        xp_assert_equal(peaks, 7*np.ones_like(peaks))
+        xp_assert_close(props['widths'], np.asarray([1.35]))
+        xp_assert_close(props['width_heights'], np.asarray([1.]))
+        xp_assert_close(props['left_ips'], np.asarray([6.4]))
+        xp_assert_close(props['right_ips'], np.asarray([7.75]))
+
+    def test_properties(self):
+        """
+        Test returned properties.
+        """
+        open_interval = (None, None)
+        x = [0, 1, 0, 2, 1.5, 0, 3, 0, 5, 9]
+        peaks, props = find_peaks(x,
+                                  height=open_interval, threshold=open_interval,
+                                  prominence=open_interval, width=open_interval)
+        assert len(props) == len(self.property_keys)
+        for key in self.property_keys:
+            assert peaks.size == props[key].size
+
+    def test_raises(self):
+        """
+        Test exceptions raised by function.
+        """
+        with raises(ValueError, match="1-D array"):
+            find_peaks(np.array(1))
+        with raises(ValueError, match="1-D array"):
+            find_peaks(np.ones((2, 2)))
+        with raises(ValueError, match="distance"):
+            find_peaks(np.arange(10), distance=-1)
+
+    @pytest.mark.filterwarnings("ignore:some peaks have a prominence of 0",
+                                "ignore:some peaks have a width of 0")
+    def test_wlen_smaller_plateau(self):
+        """
+        Test behavior of prominence and width calculation if the given window
+        length is smaller than a peak's plateau size.
+
+        Regression test for gh-9110.
+        """
+        peaks, props = find_peaks([0, 1, 1, 1, 0], prominence=(None, None),
+                                  width=(None, None), wlen=2)
+        xp_assert_equal(peaks, 2 * np.ones_like(peaks))
+        xp_assert_equal(props["prominences"], np.zeros_like(props["prominences"]))
+        xp_assert_equal(props["widths"], np.zeros_like(props["widths"]))
+        xp_assert_equal(props["width_heights"], np.ones_like(props["width_heights"]))
+        for key in ("left_bases", "right_bases", "left_ips", "right_ips"):
+            xp_assert_equal(props[key], peaks, check_dtype=False)
+
+    @pytest.mark.parametrize("kwargs", [
+        {},
+        {"distance": 3.0},
+        {"prominence": (None, None)},
+        {"width": (None, 2)},
+
+    ])
+    def test_readonly_array(self, kwargs):
+        """
+        Test readonly arrays are accepted.
+        """
+        x = np.linspace(0, 10, 15)
+        x_readonly = x.copy()
+        x_readonly.flags.writeable = False
+
+        peaks, _ = find_peaks(x)
+        peaks_readonly, _ = find_peaks(x_readonly, **kwargs)
+
+        xp_assert_close(peaks, peaks_readonly)
+
+
+class TestFindPeaksCwt:
+
+    def test_find_peaks_exact(self):
+        """
+        Generate a series of gaussians and attempt to find the peak locations.
+        """
+        sigmas = [5.0, 3.0, 10.0, 20.0, 10.0, 50.0]
+        num_points = 500
+        test_data, act_locs = _gen_gaussians_even(sigmas, num_points)
+        widths = np.arange(0.1, max(sigmas))
+        found_locs = find_peaks_cwt(test_data, widths, gap_thresh=2, min_snr=0,
+                                         min_length=None)
+        xp_assert_equal(found_locs, act_locs,
+                        check_dtype=False,
+                        err_msg="Found maximum locations did not equal those expected"
+        )
+
+    def test_find_peaks_withnoise(self):
+        """
+        Verify that peak locations are (approximately) found
+        for a series of gaussians with added noise.
+        """
+        sigmas = [5.0, 3.0, 10.0, 20.0, 10.0, 50.0]
+        num_points = 500
+        test_data, act_locs = _gen_gaussians_even(sigmas, num_points)
+        widths = np.arange(0.1, max(sigmas))
+        noise_amp = 0.07
+        rng = np.random.default_rng(18181911)
+        test_data += (rng.random(num_points) - 0.5)*(2*noise_amp)
+        found_locs = find_peaks_cwt(test_data, widths, min_length=15,
+                                         gap_thresh=1, min_snr=noise_amp / 5)
+
+        err_msg ='Different number of peaks found than expected'
+        assert len(found_locs) == len(act_locs), err_msg
+        diffs = np.abs(found_locs - act_locs)
+        max_diffs = np.array(sigmas) / 5
+        np.testing.assert_array_less(diffs, max_diffs, 'Maximum location differed' +
+                                     f'by more than {max_diffs}')
+
+    def test_find_peaks_nopeak(self):
+        """
+        Verify that no peak is found in
+        data that's just noise.
+        """
+        noise_amp = 1.0
+        num_points = 100
+        rng = np.random.RandomState(181819141)
+        test_data = (rng.rand(num_points) - 0.5)*(2*noise_amp)
+        widths = np.arange(10, 50)
+        found_locs = find_peaks_cwt(test_data, widths, min_snr=5, noise_perc=30)
+        assert len(found_locs) == 0
+
+    def test_find_peaks_with_non_default_wavelets(self):
+        x = gaussian(200, 2)
+        widths = np.array([1, 2, 3, 4])
+        a = find_peaks_cwt(x, widths, wavelet=gaussian)
+
+        xp_assert_equal(a, np.asarray([100]), check_dtype=False)
+
+    def test_find_peaks_window_size(self):
+        """
+        Verify that window_size is passed correctly to private function and
+        affects the result.
+        """
+        sigmas = [2.0, 2.0]
+        num_points = 1000
+        test_data, act_locs = _gen_gaussians_even(sigmas, num_points)
+        widths = np.arange(0.1, max(sigmas), 0.2)
+        noise_amp = 0.05
+        rng = np.random.RandomState(18181911)
+        test_data += (rng.rand(num_points) - 0.5)*(2*noise_amp)
+
+        # Possibly contrived negative region to throw off peak finding
+        # when window_size is too large
+        test_data[250:320] -= 1
+
+        found_locs = find_peaks_cwt(test_data, widths, gap_thresh=2, min_snr=3,
+                                    min_length=None, window_size=None)
+        with pytest.raises(AssertionError):
+            assert found_locs.size == act_locs.size
+
+        found_locs = find_peaks_cwt(test_data, widths, gap_thresh=2, min_snr=3,
+                                    min_length=None, window_size=20)
+        assert found_locs.size == act_locs.size
+
+    def test_find_peaks_with_one_width(self):
+        """
+        Verify that the `width` argument
+        in `find_peaks_cwt` can be a float
+        """
+        xs = np.arange(0, np.pi, 0.05)
+        test_data = np.sin(xs)
+        widths = 1
+        found_locs = find_peaks_cwt(test_data, widths)
+
+        np.testing.assert_equal(found_locs, 32)
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/tests/test_result_type.py b/venv/lib/python3.12/site-packages/scipy/signal/tests/test_result_type.py
new file mode 100644
index 0000000000000000000000000000000000000000..a2cadd325a7e36c877df8532ba957712831c2dad
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/tests/test_result_type.py
@@ -0,0 +1,51 @@
+# Regressions tests on result types of some signal functions
+
+import numpy as np
+
+from scipy.signal import (decimate,
+                          lfilter_zi,
+                          lfiltic,
+                          sos2tf,
+                          sosfilt_zi)
+
+
+def test_decimate():
+    ones_f32 = np.ones(32, dtype=np.float32)
+    assert decimate(ones_f32, 2).dtype == np.float32
+
+    ones_i64 = np.ones(32, dtype=np.int64)
+    assert decimate(ones_i64, 2).dtype == np.float64
+    
+
+def test_lfilter_zi():
+    b_f32 = np.array([1, 2, 3], dtype=np.float32)
+    a_f32 = np.array([4, 5, 6], dtype=np.float32)
+    assert lfilter_zi(b_f32, a_f32).dtype == np.float32
+
+
+def test_lfiltic():
+    # this would return f32 when given a mix of f32 / f64 args
+    b_f32 = np.array([1, 2, 3], dtype=np.float32)
+    a_f32 = np.array([4, 5, 6], dtype=np.float32)
+    x_f32 = np.ones(32, dtype=np.float32)
+    
+    b_f64 = b_f32.astype(np.float64)
+    a_f64 = a_f32.astype(np.float64)
+    x_f64 = x_f32.astype(np.float64)
+
+    assert lfiltic(b_f64, a_f32, x_f32).dtype == np.float64
+    assert lfiltic(b_f32, a_f64, x_f32).dtype == np.float64
+    assert lfiltic(b_f32, a_f32, x_f64).dtype == np.float64
+    assert lfiltic(b_f32, a_f32, x_f32, x_f64).dtype == np.float64
+
+
+def test_sos2tf():
+    sos_f32 = np.array([[4, 5, 6, 1, 2, 3]], dtype=np.float32)
+    b, a = sos2tf(sos_f32)
+    assert b.dtype == np.float32
+    assert a.dtype == np.float32
+
+
+def test_sosfilt_zi():
+    sos_f32 = np.array([[4, 5, 6, 1, 2, 3]], dtype=np.float32)
+    assert sosfilt_zi(sos_f32).dtype == np.float32
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/tests/test_savitzky_golay.py b/venv/lib/python3.12/site-packages/scipy/signal/tests/test_savitzky_golay.py
new file mode 100644
index 0000000000000000000000000000000000000000..30096ba9fc771efb378ff755cfd96bb35d9d2070
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/tests/test_savitzky_golay.py
@@ -0,0 +1,397 @@
+import pytest
+import numpy as np
+
+from scipy._lib._array_api import (
+    xp_assert_close, xp_assert_equal, xp_swapaxes, is_torch, make_xp_test_case,
+    _xp_copy_to_numpy
+)
+
+from scipy.ndimage import convolve1d   # type: ignore[attr-defined]
+
+from scipy.signal import savgol_coeffs, savgol_filter
+from scipy.signal._savitzky_golay import _polyder
+
+skip_xp_backends = pytest.mark.skip_xp_backends
+xfail_xp_backends = pytest.mark.xfail_xp_backends
+
+pytestmark = pytest.mark.skip_xp_backends(
+    "dask.array", reason="linalg.lstsq is missing rcond"
+)
+
+
+def check_polyder(p, m, expected, xp):
+    dp = _polyder(p, m, xp=xp)
+    xp_assert_equal(dp, expected)
+
+
+@pytest.mark.uses_xp_capabilities(False, reason="private")
+def test_polyder(xp):
+    cases = [
+        ([5], 0, [5]),
+        ([5], 1, [0]),
+        ([3, 2, 1], 0, [3, 2, 1]),
+        ([3, 2, 1], 1, [6, 2]),
+        ([3, 2, 1], 2, [6]),
+        ([3, 2, 1], 3, [0]),
+        ([[3, 2, 1], [5, 6, 7]], 0, [[3, 2, 1], [5, 6, 7]]),
+        ([[3, 2, 1], [5, 6, 7]], 1, [[6, 2], [10, 6]]),
+        ([[3, 2, 1], [5, 6, 7]], 2, [[6], [10]]),
+        ([[3, 2, 1], [5, 6, 7]], 3, [[0], [0]]),
+    ]
+    for p, m, expected in cases:
+        pp = xp.asarray(p)
+        ee = xp.asarray(expected)
+        check_polyder(
+            pp.T if pp.ndim == 2 else pp,
+            m,
+            ee.T if ee.ndim ==2 else ee,
+            xp
+        )
+
+
+#--------------------------------------------------------------------
+# savgol_coeffs tests
+#--------------------------------------------------------------------
+
+def alt_sg_coeffs(window_length, polyorder, pos, xp):
+    """This is an alternative implementation of the SG coefficients.
+
+    It uses numpy.polyfit and numpy.polyval. The results should be
+    equivalent to those of savgol_coeffs(), but this implementation
+    is slower.
+
+    window_length should be odd.
+
+    """
+    if pos is None:
+        pos = window_length // 2
+    t = np.arange(window_length)
+    unit = (t == pos).astype(int)
+    h = np.polyval(np.polyfit(t, unit, polyorder), t)
+    return xp.asarray(h)
+
+
+@make_xp_test_case(savgol_coeffs)
+def test_sg_coeffs_trivial(xp):
+    # Test a trivial case of savgol_coeffs: polyorder = window_length - 1
+    h = savgol_coeffs(1, 0, xp=xp)
+    xp_assert_close(h, xp.asarray([1.0], dtype=xp.float64))
+
+    h = savgol_coeffs(3, 2, xp=xp)
+    xp_assert_close(h, xp.asarray([0.0, 1, 0], dtype=xp.float64), atol=1e-10)
+
+    h = savgol_coeffs(5, 4, xp=xp)
+    xp_assert_close(h, xp.asarray([0.0, 0, 1, 0, 0], dtype=xp.float64), atol=1e-10)
+
+    h = savgol_coeffs(5, 4, pos=1, xp=xp)
+    xp_assert_close(h, xp.asarray([0.0, 0, 0, 1, 0], dtype=xp.float64), atol=1e-10)
+
+    h = savgol_coeffs(5, 4, pos=1, use='dot', xp=xp)
+    xp_assert_close(h, xp.asarray([0.0, 1, 0, 0, 0], dtype=xp.float64), atol=1e-10)
+
+
+def compare_coeffs_to_alt(window_length, order, xp):
+    # For the given window_length and order, compare the results
+    # of savgol_coeffs and alt_sg_coeffs for pos from 0 to window_length - 1.
+    # Also include pos=None.
+    for pos in [None] + list(range(window_length)):
+        h1 = savgol_coeffs(window_length, order, pos=pos, use='dot', xp=xp)
+        h2 = alt_sg_coeffs(window_length, order, pos=pos, xp=xp)
+        xp_assert_close(
+            h1, h2, atol=2e-10,
+            err_msg=f"window_length = {window_length}, order = {order}, pos = {pos}"
+        )
+
+
+@make_xp_test_case(savgol_coeffs)
+def test_sg_coeffs_compare(xp):
+    # Compare savgol_coeffs() to alt_sg_coeffs().
+    for window_length in range(1, 8, 2):
+        for order in range(window_length):
+            compare_coeffs_to_alt(window_length, order, xp=xp)
+
+
+@make_xp_test_case(savgol_coeffs)
+def test_sg_coeffs_exact(xp):
+    polyorder = 4
+    window_length = 9
+    halflen = window_length // 2
+
+    x = xp.linspace(0, 21, 43)
+    delta = x[1] - x[0]
+
+    # The data is a cubic polynomial.  We'll use an order 4
+    # SG filter, so the filtered values should equal the input data
+    # (except within half window_length of the edges).
+    y = 0.5 * x ** 3 - x
+    h = savgol_coeffs(window_length, polyorder, xp=xp)
+    y0 = xp.asarray(convolve1d(_xp_copy_to_numpy(y), _xp_copy_to_numpy(h)))
+    xp_assert_close(y0[halflen:-halflen], y[halflen:-halflen])
+
+    # Check the same input, but use deriv=1.  dy is the exact result.
+    dy = 1.5 * x ** 2 - 1
+    h = savgol_coeffs(window_length, polyorder, deriv=1, delta=delta, xp=xp)
+    y1 = xp.asarray(convolve1d(_xp_copy_to_numpy(y), _xp_copy_to_numpy(h)))
+    xp_assert_close(y1[halflen:-halflen], dy[halflen:-halflen])
+
+    # Check the same input, but use deriv=2. d2y is the exact result.
+    d2y = 3.0 * x
+    h = savgol_coeffs(window_length, polyorder, deriv=2, delta=delta, xp=xp)
+    y2 = xp.asarray(convolve1d(_xp_copy_to_numpy(y), _xp_copy_to_numpy(h)))
+    xp_assert_close(y2[halflen:-halflen], d2y[halflen:-halflen])
+
+
+@make_xp_test_case(savgol_coeffs)
+def test_sg_coeffs_deriv(xp):
+    # The data in `x` is a sampled parabola, so using savgol_coeffs with an
+    # order 2 or higher polynomial should give exact results.
+    i = xp.asarray([-2.0, 0.0, 2.0, 4.0, 6.0], dtype=xp.float64)
+    x = i ** 2 / 4
+    dx = i / 2
+    d2x = xp.full_like(i, 0.5)
+    for pos in range(x.shape[0]):
+        coeffs0 = savgol_coeffs(5, 3, pos=pos, delta=2.0, use='dot', xp=xp)
+        xp_assert_close(coeffs0 @ x, x[pos], atol=1e-10)
+        coeffs1 = savgol_coeffs(5, 3, pos=pos, delta=2.0, use='dot', deriv=1, xp=xp)
+        xp_assert_close(coeffs1 @ x, dx[pos], atol=1e-10)
+        coeffs2 = savgol_coeffs(5, 3, pos=pos, delta=2.0, use='dot', deriv=2, xp=xp)
+        xp_assert_close(coeffs2 @ x , d2x[pos], atol=1e-10)
+
+
+@make_xp_test_case(savgol_coeffs)
+def test_sg_coeffs_deriv_gt_polyorder(xp):
+    """
+    If deriv > polyorder, the coefficients should be all 0.
+    This is a regression test for a bug where, e.g.,
+        savgol_coeffs(5, polyorder=1, deriv=2)
+    raised an error.
+    """
+    coeffs = savgol_coeffs(5, polyorder=1, deriv=2, xp=xp)
+    xp_assert_equal(coeffs, xp.zeros(5, dtype=xp.float64))
+    coeffs = savgol_coeffs(7, polyorder=4, deriv=6, xp=xp)
+    xp_assert_equal(coeffs, xp.zeros(7, dtype=xp.float64))
+
+
+@xfail_xp_backends(
+    "torch", reason="torch loses precision (worse with f32 default dtype)"
+)
+@make_xp_test_case(savgol_coeffs)
+def test_sg_coeffs_large(xp):
+    # Test that for large values of window_length and polyorder the array of
+    # coefficients returned is symmetric. The aim is to ensure that
+    # no potential numeric overflow occurs.
+    coeffs0 = savgol_coeffs(31, 9, xp=xp)
+    xp_assert_close(
+        coeffs0, xp.flip(coeffs0), atol=5e-4 if is_torch(xp) else 1.5e-6
+    )
+
+    coeffs1 = savgol_coeffs(31, 9, deriv=1, xp=xp)
+    xp_assert_close(
+        coeffs1, -xp.flip(coeffs1), atol=1.2e-2 if is_torch(xp) else 1.5e-6
+    )
+
+# --------------------------------------------------------------------
+# savgol_coeffs tests for even window length
+# --------------------------------------------------------------------
+
+@make_xp_test_case(savgol_coeffs)
+def test_sg_coeffs_even_window_length(xp):
+    # Simple case - deriv=0, polyorder=0, 1
+    window_lengths = [4, 6, 8, 10, 12, 14, 16]
+    for length in window_lengths:
+        h_p_d = savgol_coeffs(length, 0, 0, xp=xp)
+        xp_assert_close(h_p_d, xp.ones_like(h_p_d) / length)
+
+    # Verify with closed forms
+    # deriv=1, polyorder=1, 2
+    def h_p_d_closed_form_1(k, m):
+        return 6*(k - 0.5)/((2*m + 1)*m*(2*m - 1))
+
+    # deriv=2, polyorder=2
+    def h_p_d_closed_form_2(k, m):
+        numer = 15*(-4*m**2 + 1 + 12*(k - 0.5)**2)
+        denom = 4*(2*m + 1)*(m + 1)*m*(m - 1)*(2*m - 1)
+        return numer/denom
+
+    for length in window_lengths:
+        m = length//2
+        expected_output = [h_p_d_closed_form_1(k, m)
+                           for k in range(-m + 1, m + 1)][::-1]
+        expected_output = xp.asarray(expected_output, dtype=xp.float64)
+        actual_output = savgol_coeffs(length, 1, 1, xp=xp)
+        xp_assert_close(actual_output, expected_output)
+        actual_output = savgol_coeffs(length, 2, 1, xp=xp)
+        xp_assert_close(actual_output, expected_output)
+
+        expected_output = [h_p_d_closed_form_2(k, m)
+                           for k in range(-m + 1, m + 1)][::-1]
+        expected_output = xp.asarray(expected_output, dtype=xp.float64)
+        actual_output = savgol_coeffs(length, 2, 2, xp=xp)
+        xp_assert_close(actual_output, expected_output)
+        actual_output = savgol_coeffs(length, 3, 2, xp=xp)
+        xp_assert_close(actual_output, expected_output)
+
+#--------------------------------------------------------------------
+# savgol_filter tests
+#--------------------------------------------------------------------
+
+@make_xp_test_case(savgol_filter)
+def test_sg_filter_trivial(xp):
+    """ Test some trivial edge cases for savgol_filter()."""
+    x = xp.asarray([1.0])
+    y = savgol_filter(x, 1, 0)
+    xp_assert_equal(y, xp.asarray([1.0]))
+
+    # Input is a single value. With a window length of 3 and polyorder 1,
+    # the value in y is from the straight-line fit of (-1,0), (0,3) and
+    # (1, 0) at 0. This is just the average of the three values, hence 1.0.
+    x = xp.asarray([3.0])
+    y = savgol_filter(x, 3, 1, mode='constant')
+    xp_assert_close(y, xp.asarray([1.0]), atol=1.5e-15)
+
+    x = xp.asarray([3.0])
+    y = savgol_filter(x, 3, 1, mode='nearest')
+    xp_assert_close(y, xp.asarray([3.0]), atol=1.5e-15)
+
+    x = xp.asarray([1.0] * 3)
+    y = savgol_filter(x, 3, 1, mode='wrap')
+    xp_assert_close(y, xp.asarray([1.0, 1.0, 1.0]), atol=1.5e-15)
+
+
+@make_xp_test_case(savgol_filter)
+def test_sg_filter_basic(xp):
+    # Some basic test cases for savgol_filter().
+    x = xp.asarray([1.0, 2.0, 1.0])
+    y = savgol_filter(x, 3, 1, mode='constant')
+    xp_assert_close(y, xp.asarray([1.0, 4.0 / 3, 1.0]))
+
+    y = savgol_filter(x, 3, 1, mode='mirror')
+    xp_assert_close(y, xp.asarray([5.0 / 3, 4.0 / 3, 5.0 / 3]))
+
+    y = savgol_filter(x, 3, 1, mode='wrap')
+    xp_assert_close(y, xp.asarray([4.0 / 3, 4.0 / 3, 4.0 / 3]))
+
+
+@make_xp_test_case(savgol_filter)
+def test_sg_filter_2d(xp):
+    x = xp.asarray([[1.0, 2.0, 1.0],
+                    [2.0, 4.0, 2.0]])
+    expected = xp.asarray([[1.0, 4.0 / 3, 1.0],
+                           [2.0, 8.0 / 3, 2.0]])
+    y = savgol_filter(x, 3, 1, mode='constant')
+    xp_assert_close(y, expected)
+
+    y = savgol_filter(x.T, 3, 1, mode='constant', axis=0)
+    xp_assert_close(y, expected.T)
+
+
+@make_xp_test_case(savgol_filter)
+def test_sg_filter_interp_edges(xp):
+    # Another test with low degree polynomial data, for which we can easily
+    # give the exact results. In this test, we use mode='interp', so
+    # savgol_filter should match the exact solution for the entire data set,
+    # including the edges.
+    t = xp.linspace(-5, 5, 21, dtype=xp.float64)
+    delta = t[1] - t[0]
+    # Polynomial test data.
+    x = xp.stack([t,
+                  3 * t ** 2,
+                  t ** 3 - t])
+    dx = xp.stack([xp.ones_like(t),
+                   6 * t,
+                   3 * t ** 2 - 1.0])
+    d2x = xp.stack([xp.zeros_like(t),
+                    xp.full_like(t, 6),
+                    6 * t])
+
+    window_length = 7
+
+    y = savgol_filter(x, window_length, 3, axis=-1, mode='interp')
+    xp_assert_close(y, x, atol=1e-12)
+
+    y1 = savgol_filter(x, window_length, 3, axis=-1, mode='interp',
+                       deriv=1, delta=delta)
+    xp_assert_close(y1, dx, atol=1e-12)
+
+    y2 = savgol_filter(x, window_length, 3, axis=-1, mode='interp',
+                       deriv=2, delta=delta)
+    xp_assert_close(y2, d2x, atol=1e-12)
+
+    # Transpose everything, and test again with axis=0.
+
+    x = x.T
+    dx = dx.T
+    d2x = d2x.T
+
+    y = savgol_filter(x, window_length, 3, axis=0, mode='interp')
+    xp_assert_close(y, x, atol=1e-12)
+
+    y1 = savgol_filter(x, window_length, 3, axis=0, mode='interp',
+                       deriv=1, delta=delta)
+    xp_assert_close(y1, dx, atol=1e-12)
+
+    y2 = savgol_filter(x, window_length, 3, axis=0, mode='interp',
+                       deriv=2, delta=delta)
+    xp_assert_close(y2, d2x, atol=1e-12)
+
+
+@make_xp_test_case(savgol_filter)
+def test_sg_filter_interp_edges_3d(xp):
+    # Test mode='interp' with a 3-D array.
+    t = xp.linspace(-5, 5, 21)
+    delta = t[1] - t[0]
+    x1 = xp.stack([t, -t])
+    x2 = xp.stack([t ** 2, 3 * t ** 2 + 5])
+    x3 = xp.stack([t ** 3, 2 * t ** 3 + t ** 2 - 0.5 * t])
+    dx1 = xp.stack([xp.ones_like(t), -xp.ones_like(t)])
+    dx2 = xp.stack([2 * t, 6 * t])
+    dx3 = xp.stack([3 * t ** 2, 6 * t ** 2 + 2 * t - 0.5])
+
+    # z has shape (3, 2, 21)
+    z = xp.stack([x1, x2, x3])
+    dz = xp.stack([dx1, dx2, dx3])
+
+    y = savgol_filter(z, 7, 3, axis=-1, mode='interp', delta=delta)
+    xp_assert_close(y, z, atol=1e-10)
+
+    dy = savgol_filter(z, 7, 3, axis=-1, mode='interp', deriv=1, delta=delta)
+    xp_assert_close(dy, dz, atol=1e-10)
+
+    # z has shape (3, 21, 2)
+    z = xp.stack([x1.T, x2.T, x3.T])
+    dz = xp.stack([dx1.T, dx2.T, dx3.T])
+
+    y = savgol_filter(z, 7, 3, axis=1, mode='interp', delta=delta)
+    xp_assert_close(y, z, atol=1e-10)
+
+    dy = savgol_filter(z, 7, 3, axis=1, mode='interp', deriv=1, delta=delta)
+    xp_assert_close(dy, dz, atol=1e-10)
+
+    # z has shape (21, 3, 2)
+    z = xp.asarray(xp_swapaxes(z, 0, 1, xp=xp), copy=True)
+    dz = xp.asarray(xp_swapaxes(dz, 0, 1, xp=xp), copy=True)
+
+    y = savgol_filter(z, 7, 3, axis=0, mode='interp', delta=delta)
+    xp_assert_close(y, z, atol=1e-10)
+
+    dy = savgol_filter(z, 7, 3, axis=0, mode='interp', deriv=1, delta=delta)
+    xp_assert_close(dy, dz, atol=1e-10)
+
+
+@make_xp_test_case(savgol_filter)
+def test_sg_filter_valid_window_length_3d(xp):
+    """Tests that the window_length check is using the correct axis."""
+
+    x = xp.ones((10, 20, 30))
+
+    savgol_filter(x, window_length=29, polyorder=3, mode='interp')
+
+    with pytest.raises(ValueError, match='window_length must be less than'):
+        # window_length is more than x.shape[-1].
+        savgol_filter(x, window_length=31, polyorder=3, mode='interp')
+
+    savgol_filter(x, window_length=9, polyorder=3, axis=0, mode='interp')
+
+    with pytest.raises(ValueError, match='window_length must be less than'):
+        # window_length is more than x.shape[0].
+        savgol_filter(x, window_length=11, polyorder=3, axis=0, mode='interp')
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/tests/test_short_time_fft.py b/venv/lib/python3.12/site-packages/scipy/signal/tests/test_short_time_fft.py
new file mode 100644
index 0000000000000000000000000000000000000000..063f44f66d896e7c714d487abcc32654ee11d4b7
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/tests/test_short_time_fft.py
@@ -0,0 +1,1116 @@
+"""Unit tests for module `_short_time_fft`.
+
+This file's structure loosely groups the tests into the following sequential
+categories:
+
+1. Test function `_calc_dual_canonical_window`.
+2. Test for invalid parameters and exceptions in `ShortTimeFFT` (until the
+    `test_from_window` function).
+3. Test algorithmic properties of STFT/ISTFT. Some tests were ported from
+   ``test_spectral.py``.
+
+Notes
+-----
+* Mypy 0.990 does interpret the line::
+
+        from scipy.stats import norm as normal_distribution
+
+  incorrectly (but the code works), hence a ``type: ignore`` was appended.
+"""
+import math
+from itertools import product
+from types import GenericAlias
+from typing import cast, get_args, Literal
+
+import numpy as np
+import pytest
+from scipy._lib._array_api import xp_assert_close, xp_assert_equal
+from scipy.fft import fftshift
+from scipy.stats import norm as normal_distribution  # type: ignore
+from scipy.signal import check_COLA, get_window, welch, stft, istft, spectrogram
+
+from scipy.signal._short_time_fft import FFT_MODE_TYPE, \
+    _calc_dual_canonical_window, closest_STFT_dual_window, ShortTimeFFT, PAD_TYPE
+from scipy.signal.windows import blackman, gaussian, hamming, nuttall, triang
+
+
+def test__calc_dual_canonical_window_roundtrip():
+    """Test dual window calculation with a round trip to verify duality.
+
+    Note that this works only for canonical window pairs (having minimal
+    energy) like a Gaussian.
+
+    The window is the same as in the example of `from ShortTimeFFT.from_dual`.
+    """
+    win = gaussian(51, std=10, sym=True)
+    d_win = _calc_dual_canonical_window(win, 10)
+    win2 = _calc_dual_canonical_window(d_win, 10)
+    xp_assert_close(win2, win)
+
+
+def test__calc_dual_canonical_window_exceptions():
+    """Raise all exceptions in `_calc_dual_canonical_window`."""
+    # Verify that calculation can fail:
+    with pytest.raises(ValueError, match="hop=5 is larger than window len.*"):
+        _calc_dual_canonical_window(np.ones(4), 5)
+    with pytest.raises(ValueError, match=".* Transform not invertible!"):
+        _calc_dual_canonical_window(np.array([.1, .2, .3, 0]), 4)
+
+    # Verify that parameter `win` may not be integers:
+    with pytest.raises(ValueError, match="Parameter 'win' cannot be of int.*"):
+        _calc_dual_canonical_window(np.ones(4, dtype=int), 1)
+
+def test_closest_STFT_dual_window_exceptions():
+    """Raise all exceptions in `closest_STFT_dual_window`."""
+    with pytest.raises(ValueError, match="Parameters `win` and `desired_dual` are.*"):
+        closest_STFT_dual_window(np.ones(4), 2, np.ones(5))
+    with pytest.raises(ValueError, match="Parameters `win` and `desired_dual` are.*"):
+        closest_STFT_dual_window(np.ones((4, 1)), 2, np.ones(4))
+    with pytest.raises(ValueError, match="Parameter win must have finite entries!"):
+        closest_STFT_dual_window(np.ones(4)*np.nan, 2, np.ones(4))
+    with pytest.raises(ValueError, match="Parameter desired_dual must have finite.*"):
+        closest_STFT_dual_window(np.ones(4), 2, np.ones(4)*np.nan)
+    with pytest.raises(ValueError, match="Parameter hop=20 is not an integer.*"):
+        closest_STFT_dual_window(np.ones(4), 20, np.ones(4))
+    with pytest.raises(ValueError, match="Parameter hop=2.0 is not an integer.*"):
+        # noinspection PyTypeChecker
+        closest_STFT_dual_window(np.ones(4), 2., np.ones(4))
+
+    with pytest.raises(ValueError, match="Unable to calculate scaled closest dual.*"):
+        closest_STFT_dual_window(np.ones(4), 2, np.zeros(4), scaled=True)
+
+
+@pytest.mark.parametrize("scaled", (True, False))
+@pytest.mark.parametrize('sym_win', (False, True))
+@pytest.mark.parametrize('hop', (8, 9))
+@pytest.mark.parametrize('m', (16, 17))
+@pytest.mark.parametrize('win_name', ('hann', 'hamming'))
+def test_closest_STFT_dual_window_roundtrip(win_name, m, hop, sym_win, scaled):
+    """Do roundtrip, i.e., compare dual of dual windows.
+
+    The  default for parameter `desired_dual` is also verified.
+    """
+    win = get_window(win_name, m, not sym_win)
+    d1, s1 = closest_STFT_dual_window(win, hop, np.ones_like(win), scaled=scaled)
+    d2, s2 = closest_STFT_dual_window(win, hop, scaled=scaled)  # equals d1, s1
+    d3, s3 = closest_STFT_dual_window(d1, hop, win * s1, scaled=True)  # roundtrip
+
+    # (d1, s1) == (d2, s2) should hold, but the BLAS backend used to calculate the inner
+    # product in `closest_STFT_dual_window` does not guarantee exact reproducibility
+    # due to indeterministic summation order during parallel execution. Hence, only
+    # approximate equality is verified. Consult NumPy 29873 issue for discussion.
+    res = np.finfo(win.dtype).resolution  # 1e-15 for float64
+    err_msg = "Default for parameter `desired_dual` is not ok!"
+    xp_assert_close(d2, d1, atol=res, err_msg=err_msg)
+    xp_assert_close(s2, s1, atol=res, err_msg=err_msg)
+
+    xp_assert_close(s1*s3, 1., atol=res*5, err_msg="Invalid Scale factors")
+    xp_assert_close(d3, win, atol=res*5, err_msg="Roundtrip failed!")
+
+    if scaled:  # check that scaling factor is correct:
+        d3, _ = closest_STFT_dual_window(win, hop, np.ones(m) * s1, scaled=False)
+        xp_assert_close(d3, d1, atol=res, err_msg="Roundtrip failed!")
+
+
+@pytest.mark.parametrize('scaled', (False, True))
+def test_closest_STFT_dual_window_STFT_roundtrip(scaled):
+    """STFT Roundtrip correctness of closest dual window. """
+    np.random.seed(5613830)
+    n, m_num, hop = 15, 7, 3
+    w, desires_dual = hamming(m_num), triang(m_num)
+    d, _ = closest_STFT_dual_window(w, hop, desires_dual, scaled=scaled)
+
+    SFT = ShortTimeFFT(w, hop=hop, dual_win=d, fs=1, scale_to=None, phase_shift=None)
+    x = 10 * np.random.randn(n)
+    Sx = SFT.stft(x)
+    y = SFT.istft(Sx, 0, n)
+
+    atol = np.finfo(w.dtype).resolution * 10
+    xp_assert_close(y, x, atol=atol, err_msg="Invalid closest window")
+
+
+@pytest.mark.parametrize('scaled', (False, True))
+def test_closest_STFT_dual_window_STFT_roundtrip_complex(scaled):
+    """STFT Roundtrip correctness of closest dual window with complex values. """
+    np.random.seed(34905436)
+    n, m_num, hop = 15, 7, 3
+    win = 1j*hamming(m_num) + nuttall(m_num)
+    desires_dual = 1j*triang(m_num) + blackman(m_num)
+    dual, s = closest_STFT_dual_window(win, hop, desires_dual, scaled=scaled)
+
+    SFT = ShortTimeFFT(win, hop=hop, dual_win=dual, fs=1, fft_mode='twosided',
+                       scale_to=None, phase_shift=None)
+    x = 10 * np.random.randn(n) + 10j * np.random.randn(n)
+    Sx = SFT.stft(x)
+    y = SFT.istft(Sx, 0, n)
+
+    atol = np.finfo(win.dtype).resolution * 10
+    xp_assert_close(y, x, atol=atol, err_msg=f"Invalid complex closest window ({s=})")
+
+
+@pytest.mark.parametrize("win_name, nperseg, noverlap, scale_fac", ([
+                         ('boxcar',      16,        8,       1/2),
+                         ('boxcar',      18,       12,       1/3),
+                         ('boxcar',      16,       12,       1/4),
+                         ('bartlett',    16,        8,        1.),
+                         ('bartlett',    16,       12,       1/2),
+                         ('bartlett',    30,       25,       1/3),
+                         ('hann',        16,        8,        1.),
+                         ('hann',        18,       12,       2/3),
+                         ('hann',        16,       12,       1/2),
+                         ('blackman',     9,        6,     50/63),
+                         ('boxcar',       8,        7,       1/8)]))  # hop = 1
+def test_closest_STFT_dual_window_cola(win_name, nperseg, noverlap, scale_fac):
+    """Test if `closest_STFT_dual_window` generalizes `check_COLA`.
+
+    The parameters were taken from the `check_COLA` documentation.
+    Note that `check_COLA` only guarantees the existence of a dual window with constant
+    values but not that those values are unity (which is clear, when investigating the
+    'boxcar' examples). The values for `scale_fac` were determined empirically.
+    """
+    desired_dual = get_window(win_name, nperseg, fftbins=True)
+    assert check_COLA(desired_dual, nperseg, noverlap), "COLA cond. violated!"
+
+    win = np.ones(nperseg)  # check scaled window:
+    d_s, s = closest_STFT_dual_window(win, nperseg-noverlap, desired_dual, scaled=True)
+
+    res = np.finfo(desired_dual.dtype).resolution
+    rel_tol_d = max(abs(d_s))*res*3
+    xp_assert_close(s, scale_fac, atol=res*10,
+                    err_msg=f"Scale factor off by {s/scale_fac}")
+    xp_assert_close(d_s, desired_dual*scale_fac, atol=res*10, rtol=rel_tol_d,
+                    err_msg="Calculated incorrect scaled window!")
+
+    # check unscaled window:
+    d_u, u = closest_STFT_dual_window(win * scale_fac, nperseg - noverlap,
+                                      desired_dual, scaled=False)
+
+    # this should be hard-coded not computed, so no need for allclose
+    assert u == 1., "Scaling factor not 1 for parameter `scaled=True`!"
+    xp_assert_close(d_u, desired_dual, atol=res*10, rtol=rel_tol_d,
+                    err_msg="Calculated incorrect unscaled window!")
+
+
+def test_invalid_initializer_parameters():
+    """Verify that exceptions get raised on invalid parameters when
+    instantiating ShortTimeFFT. """
+    with pytest.raises(ValueError, match=r"Parameter win must be 1d, " +
+                                         r"but win.shape=\(2, 2\)!"):
+        ShortTimeFFT(np.ones((2, 2)), hop=4, fs=1)
+    with pytest.raises(ValueError, match="Parameter win must have " +
+                                         "finite entries"):
+        ShortTimeFFT(np.array([1, np.inf, 2, 3]), hop=4, fs=1)
+    with pytest.raises(ValueError, match="Parameter hop=0 is not " +
+                                         "an integer >= 1!"):
+        ShortTimeFFT(np.ones(4), hop=0, fs=1)
+    with pytest.raises(ValueError, match="Parameter hop=2.0 is not " +
+                                         "an integer >= 1!"):
+        # noinspection PyTypeChecker
+        ShortTimeFFT(np.ones(4), hop=2.0, fs=1)
+    with pytest.raises(ValueError, match=r"dual_win.shape=\(5,\) must equal " +
+                                         r"win.shape=\(4,\)!"):
+        ShortTimeFFT(np.ones(4), hop=2, fs=1, dual_win=np.ones(5))
+    with pytest.raises(ValueError, match="Parameter dual_win must be " +
+                                         "a finite array!"):
+        ShortTimeFFT(np.ones(3), hop=2, fs=1,
+                     dual_win=np.array([np.nan, 2, 3]))
+
+
+def test_exceptions_properties_methods():
+    """Verify that exceptions get raised when setting properties or calling
+    method of ShortTimeFFT to/with invalid values."""
+    SFT = ShortTimeFFT(np.ones(8), hop=4, fs=1)
+    with pytest.raises(ValueError, match="Sampling interval T=-1 must be " +
+                                         "positive!"):
+        SFT.T = -1
+    with pytest.raises(ValueError, match="Sampling frequency fs=-1 must be " +
+                                         "positive!"):
+        SFT.fs = -1
+    with pytest.raises(ValueError, match="fft_mode='invalid_typ' not in " +
+                                         r"\('twosided', 'centered', " +
+                                         r"'onesided', 'onesided2X'\)!"):
+        SFT.fft_mode = 'invalid_typ'
+    with pytest.raises(ValueError, match="For scaling is None, " +
+                                         "fft_mode='onesided2X' is invalid.*"):
+        SFT.fft_mode = 'onesided2X'
+    with pytest.raises(ValueError, match="Attribute mfft=7 needs to be " +
+                                         "at least the window length.*"):
+        SFT.mfft = 7
+    with pytest.raises(ValueError, match="scaling='invalid' not in.*"):
+        # noinspection PyTypeChecker
+        SFT.scale_to('invalid')
+    with pytest.raises(ValueError, match="phase_shift=3.0 has the unit .*"):
+        SFT.phase_shift = 3.0
+    with pytest.raises(ValueError, match="-mfft < phase_shift < mfft " +
+                                         "does not hold.*"):
+        SFT.phase_shift = 2*SFT.mfft
+    with pytest.raises(ValueError, match="Parameter padding='invalid' not.*"):
+        # noinspection PyTypeChecker
+        g = SFT._x_slices(np.zeros(16), k_off=0, p0=0, p1=1, padding='invalid')
+        next(g)  # execute generator
+    with pytest.raises(ValueError, match="Trend type must be 'linear' " +
+                                         "or 'constant'"):
+        # noinspection PyTypeChecker
+        SFT.stft_detrend(np.zeros(16), detr='invalid')
+    with pytest.raises(ValueError, match="Parameter detr=nan is not a str, " +
+                                         "function or None!"):
+        # noinspection PyTypeChecker
+        SFT.stft_detrend(np.zeros(16), detr=np.nan)
+    with pytest.raises(ValueError, match="Invalid Parameter p0=0, p1=200.*"):
+        SFT.p_range(100, 0, 200)
+
+    with pytest.raises(ValueError, match="f_axis=0 may not be equal to " +
+                                         "t_axis=0!"):
+        SFT.istft(np.zeros((SFT.f_pts, 2)), t_axis=0, f_axis=0)
+    with pytest.raises(ValueError, match=r"S.shape\[f_axis\]=2 must be equal" +
+                                         " to self.f_pts=5.*"):
+        SFT.istft(np.zeros((2, 2)))
+    with pytest.raises(ValueError, match=r"S.shape\[t_axis\]=1 needs to have" +
+                                         " at least 2 slices.*"):
+        SFT.istft(np.zeros((SFT.f_pts, 1)))
+    with pytest.raises(ValueError, match=r".*\(k1=100\) <= \(k_max=12\) " +
+                                         "is false!$"):
+        SFT.istft(np.zeros((SFT.f_pts, 3)), k1=100)
+    with pytest.raises(ValueError, match=r"\(k1=1\) - \(k0=0\) = 1 has to " +
+                                         "be at least.* length 4!"):
+        SFT.istft(np.zeros((SFT.f_pts, 3)), k0=0, k1=1)
+
+    with pytest.raises(ValueError, match=r"Parameter axes_seq='invalid' " +
+                                         r"not in \['tf', 'ft'\]!"):
+        # noinspection PyTypeChecker
+        SFT.extent(n=100, axes_seq='invalid')
+    with pytest.raises(ValueError, match="Attribute fft_mode=twosided must.*"):
+        SFT.fft_mode = 'twosided'
+        SFT.extent(n=100)
+
+
+@pytest.mark.parametrize('m', ('onesided', 'onesided2X'))
+def test_exceptions_fft_mode_complex_win(m: FFT_MODE_TYPE):
+    """Verify that one-sided spectra are not allowed with complex-valued
+    windows or with complex-valued signals.
+
+    The reason being, the `rfft` function only accepts real-valued input.
+    """
+    with pytest.raises(ValueError,
+                       match=f"One-sided spectra, i.e., fft_mode='{m}'.*"):
+        ShortTimeFFT(np.ones(8)*1j, hop=4, fs=1, fft_mode=m)
+
+    SFT = ShortTimeFFT(np.ones(8)*1j, hop=4, fs=1, fft_mode='twosided')
+    with pytest.raises(ValueError,
+                       match=f"One-sided spectra, i.e., fft_mode='{m}'.*"):
+        SFT.fft_mode = m
+
+    SFT = ShortTimeFFT(np.ones(8), hop=4, fs=1, scale_to='psd', fft_mode='onesided')
+    with pytest.raises(ValueError, match="Complex-valued `x` not allowed for self.*"):
+        SFT.stft(np.ones(8)*1j)
+    SFT.fft_mode = 'onesided2X'
+    with pytest.raises(ValueError, match="Complex-valued `x` not allowed for self.*"):
+        SFT.stft(np.ones(8)*1j)
+
+
+def test_invalid_fft_mode_RuntimeError():
+    """Ensure exception gets raised when property `fft_mode` is invalid. """
+    SFT = ShortTimeFFT(np.ones(8), hop=4, fs=1)
+    # noinspection PyTypeChecker
+    SFT._fft_mode = 'invalid_typ'
+
+    with pytest.raises(RuntimeError):
+        _ = SFT.f
+    with pytest.raises(RuntimeError):
+        SFT._fft_func(np.ones(8))
+    with pytest.raises(RuntimeError):
+        SFT._ifft_func(np.ones(8))
+
+
+@pytest.mark.parametrize('win_params, Nx', [(('gaussian', 2.), 9),  # in docstr
+                                            ('triang', 7),
+                                            (('kaiser', 4.0), 9),
+                                            (('exponential', None, 1.), 9),
+                                            (4.0, 9)])
+def test_from_window(win_params, Nx: int):
+    """Verify that `from_window()` handles parameters correctly.
+
+    The window parameterizations are documented in the `get_window` docstring.
+    """
+    w_sym, fs = get_window(win_params, Nx, fftbins=False), 16.
+    w_per = get_window(win_params, Nx, fftbins=True)
+    SFT0 = ShortTimeFFT(w_sym, hop=3, fs=fs, fft_mode='twosided',
+                        scale_to='psd', phase_shift=1)
+    nperseg = len(w_sym)
+    noverlap = nperseg - SFT0.hop
+    SFT1 = ShortTimeFFT.from_window(win_params, fs, nperseg, noverlap,
+                                    symmetric_win=True, fft_mode='twosided',
+                                    scale_to='psd', phase_shift=1)
+    # periodic window:
+    SFT2 = ShortTimeFFT.from_window(win_params, fs, nperseg, noverlap,
+                                    symmetric_win=False, fft_mode='twosided',
+                                    scale_to='psd', phase_shift=1)
+    # Be informative when comparing instances:
+    xp_assert_equal(SFT1.win, SFT0.win)
+    xp_assert_close(SFT2.win, w_per / np.sqrt(sum(w_per**2) * fs))
+    for n_ in ('hop', 'T', 'fft_mode', 'mfft', 'scaling', 'phase_shift'):
+        v0, v1, v2 = (getattr(SFT_, n_) for SFT_ in (SFT0, SFT1, SFT2))
+        assert v1 == v0, f"SFT1.{n_}={v1} does not equal SFT0.{n_}={v0}"
+        assert v2 == v0, f"SFT2.{n_}={v2} does not equal SFT0.{n_}={v0}"
+
+
+def test_from_win_equals_dual_exceptions():
+    """Raise all occurring exceptions in `ShortTimeFFT.from_closest_win_equals_dual`.
+    """
+    with pytest.raises(ValueError, match="Parameter desired_win is not 1d, but.*"):
+        ShortTimeFFT.from_win_equals_dual(np.ones((3, 4)), hop=1, fs=1)
+    with pytest.raises(ValueError, match="Parameter desired_win cannot be of int.*"):
+        ShortTimeFFT.from_win_equals_dual(np.ones(4, dtype=int), hop=1, fs=1)
+    with pytest.raises(ValueError, match="Parameter desired_win is not 1d, but.*"):
+        ShortTimeFFT.from_win_equals_dual(np.array([]), hop=1, fs=1)
+    with pytest.raises(ValueError, match="Parameter desired_win must have finite.*"):
+        ShortTimeFFT.from_win_equals_dual(np.ones(3) * np.inf, hop=1, fs=1)
+    with pytest.raises(ValueError, match="Parameter hop=0 is not an integer .*"):
+        ShortTimeFFT.from_win_equals_dual(np.ones(4), hop=0, fs=1)
+    with pytest.raises(ValueError, match="Parameter hop=5 is not an integer .*"):
+        ShortTimeFFT.from_win_equals_dual(np.ones(4), hop=5, fs=1)
+
+    with pytest.raises(ValueError, match="P.+ desired_win does not have valid.*"):
+        w = np.array([1, 0, 1, 0, 1], dtype=float)
+        ShortTimeFFT.from_win_equals_dual(w, hop=2, fs=1)
+    with pytest.raises(ValueError, match="Parameter scale_to='invalid' not in.*"):
+        # noinspection PyTypeChecker
+        ShortTimeFFT.from_win_equals_dual(w, hop=2, fs=1, scale_to='invalid')
+
+@pytest.mark.parametrize('fft_bins', (True, False))
+@pytest.mark.parametrize('m, hop', [(16, 8), (16, 7), (17, 8), (17, 9), (16, 16)])
+def test_from_win_equals_dual_params(m, hop, fft_bins):
+    """Test windows parameterizations for `ShortTimeFFT.from_closest_win_equals_dual`.
+
+    The flattop window is used since it also has negative values.
+    """
+    desired_win = get_window('flattop', m, fftbins=fft_bins)
+    SFT0 = ShortTimeFFT.from_win_equals_dual(desired_win, hop, fs=1)
+    xp_assert_close(SFT0.dual_win, SFT0.win, err_msg="win must equals dual window!")
+
+    SFT1 = ShortTimeFFT(SFT0.win, hop, fs=1)
+    xp_assert_close(SFT1.dual_win, SFT0.win, err_msg="dual win isn't canonical win!")
+
+
+@pytest.mark.parametrize('fft_bins', (True, False))
+@pytest.mark.parametrize('m, hop', [(16, 8), (16, 7), (17, 8), (17, 9), (16, 16)])
+@pytest.mark.parametrize('scale_to', (None, 'unitary'))
+def test_from_win_equals_dual_roundtrip(m, hop, fft_bins, scale_to):
+    """Testing roundtrip verifies that the dual window is correct.
+    """
+    desired_win = get_window('flattop', m, fftbins=fft_bins)
+    SFT0 = ShortTimeFFT.from_win_equals_dual(desired_win, hop, fs=1)
+
+    x = np.cos(np.arange(2*m)**2)
+    x1 = SFT0.istft(SFT0.stft(x), 0, len(x))
+    xp_assert_close(x1, x, err_msg="Roundtrip for win equaling its dual failed!")
+
+
+def test_from_win_equals_dual_unitary():
+    """Check that STFT can be unitary mapping. """
+    m, hop = 8, 4
+    des_win = get_window('hann', m)
+    SFT = ShortTimeFFT.from_win_equals_dual(des_win, hop, 1, fft_mode='twosided',
+                                            scale_to='unitary')
+    # Orthogonal signals:
+    x, y = np.tile([-1, -1, 1, 1], 4), np.tile([1, -1, -1, 1], 4)
+    Sxx, Sxy = SFT.spectrogram(x), SFT.spectrogram(x, y)
+
+    atol = np.finfo(Sxx.dtype).resolution
+    assert sum(x * y) == 0
+    xp_assert_close(np.sum(Sxx), np.sum(x ** 2, dtype=Sxx.dtype), atol=atol,
+                    err_msg="Energies do not match!")
+    xp_assert_close(np.sum(Sxy), 0.0j, atol=atol,
+                    err_msg="STFT scalar product of Sx and Sy not 0!")
+    xp_assert_close(SFT.dual_win, SFT.win*SFT.m_num, atol=atol,
+                    err_msg="Wrong factor for dual_win/win!")
+
+
+def test_dual_win_roundtrip():
+    """Verify the duality of `win` and `dual_win`.
+
+    Note that this test does not work for arbitrary windows, since dual windows
+    are not unique. It always works for invertible STFTs if the windows do not
+    overlap.
+    """
+    # Non-standard values for keyword arguments (except for `scale_to`):
+    kw = dict(hop=4, fs=1, fft_mode='twosided', mfft=8, scale_to=None,
+              phase_shift=2)
+    SFT0 = ShortTimeFFT(np.ones(4), **kw)
+    SFT1 = ShortTimeFFT.from_dual(SFT0.dual_win, **kw)
+    xp_assert_close(SFT1.dual_win, SFT0.win)
+
+
+@pytest.mark.parametrize('scale_to, fac_psd, fac_mag',
+                         [(None, 0.25, 0.125),
+                          ('magnitude', 2.0, 1),
+                          ('psd', 1, 0.5)])
+def test_scaling(scale_to: Literal['magnitude', 'psd'], fac_psd, fac_mag):
+    """Verify scaling calculations.
+
+    * Verify passing `scale_to`parameter  to ``__init__().
+    * Roundtrip while changing scaling factor.
+    """
+    SFT = ShortTimeFFT(np.ones(4) * 2, hop=4, fs=1, scale_to=scale_to)
+    assert SFT.fac_psd == fac_psd
+    assert SFT.fac_magnitude == fac_mag
+    # increase coverage by accessing properties twice:
+    assert SFT.fac_psd == fac_psd
+    assert SFT.fac_magnitude == fac_mag
+
+    x = np.fft.irfft([0, 0, 7, 0, 0, 0, 0])  # periodic signal
+    Sx = SFT.stft(x)
+    Sx_mag, Sx_psd = Sx * SFT.fac_magnitude, Sx * SFT.fac_psd
+
+    SFT.scale_to('magnitude')
+    x_mag = SFT.istft(Sx_mag, k1=len(x))
+    xp_assert_close(x_mag, x)
+
+    SFT.scale_to('psd')
+    x_psd = SFT.istft(Sx_psd, k1=len(x))
+    xp_assert_close(x_psd, x)
+
+
+def test_scale_to():
+    """Verify `scale_to()` method."""
+    SFT = ShortTimeFFT(np.ones(4) * 2, hop=4, fs=1, scale_to=None)
+
+    SFT.scale_to('magnitude')
+    assert SFT.scaling == 'magnitude'
+    assert SFT.fac_psd == 2.0
+    assert SFT.fac_magnitude == 1
+
+    SFT.scale_to('psd')
+    assert SFT.scaling == 'psd'
+    assert SFT.fac_psd == 1
+    assert SFT.fac_magnitude == 0.5
+
+    SFT.scale_to('psd')  # needed for coverage
+
+    for scale, s_fac in zip(('magnitude', 'psd'), (8, 4)):
+        SFT = ShortTimeFFT(np.ones(4) * 2, hop=4, fs=1, scale_to=None)
+        dual_win = SFT.dual_win.copy()
+
+        SFT.scale_to(cast(Literal['magnitude', 'psd'], scale))
+        xp_assert_close(SFT.dual_win, dual_win * s_fac)
+
+
+def test_x_slices_padding():
+    """Verify padding.
+
+    The reference arrays were taken from  the docstrings of `zero_ext`,
+    `const_ext`, `odd_ext()`, and `even_ext()` from the _array_tools module.
+    """
+    SFT = ShortTimeFFT(np.ones(5), hop=4, fs=1)
+    x = np.array([[1, 2, 3, 4, 5], [0, 1, 4, 9, 16]], dtype=float)
+    d = {'zeros': [[[0, 0, 1, 2, 3], [0, 0, 0, 1, 4]],
+                   [[3, 4, 5, 0, 0], [4, 9, 16, 0, 0]]],
+         'edge': [[[1, 1, 1, 2, 3], [0, 0, 0, 1, 4]],
+                  [[3, 4, 5, 5, 5], [4, 9, 16, 16, 16]]],
+         'even': [[[3, 2, 1, 2, 3], [4, 1, 0, 1, 4]],
+                  [[3, 4, 5, 4, 3], [4, 9, 16, 9, 4]]],
+         'odd': [[[-1, 0, 1, 2, 3], [-4, -1, 0, 1, 4]],
+                 [[3, 4, 5, 6, 7], [4, 9, 16, 23, 28]]]}
+    for p_, xx in d.items():
+        gen = SFT._x_slices(np.array(x), 0, 0, 2, padding=cast(PAD_TYPE, p_))
+        yy = np.array([y_.copy() for y_ in gen])  # due to inplace copying
+        xx = np.asarray(xx, dtype=np.float64)
+        xp_assert_equal(yy, xx, err_msg=f"Failed '{p_}' padding.")
+
+
+def test_invertible():
+    """Verify `invertible` property. """
+    SFT = ShortTimeFFT(np.ones(8), hop=4, fs=1)
+    assert SFT.invertible
+    SFT = ShortTimeFFT(np.ones(8), hop=9, fs=1)
+    assert not SFT.invertible
+
+
+def test_border_values():
+    """Ensure that minimum and maximum values of slices are correct."""
+    SFT = ShortTimeFFT(np.ones(8), hop=4, fs=1)
+    assert SFT.p_min == 0
+    assert SFT.k_min == -4
+    assert SFT.lower_border_end == (4, 1)
+    assert SFT.lower_border_end == (4, 1)  # needed to test caching
+    assert SFT.p_max(10) == 4
+    assert SFT.k_max(10) == 16
+    assert SFT.upper_border_begin(10) == (4, 2)
+    assert SFT.upper_border_begin(10) == (4, 2)  # needed to test caching
+    # Raise exceptions:
+    with pytest.raises(ValueError, match="^Parameter n must be"):
+        SFT.upper_border_begin(3)
+    with pytest.raises(ValueError, match="^Parameter n must be"):
+        SFT._post_padding(3)
+    with pytest.raises(RuntimeError):
+        SFT._hop = -1  # illegal hop interval
+        SFT.upper_border_begin(8)
+
+def test_border_values_exotic():
+    """Ensure that the border calculations are correct for windows with
+    zeros. """
+    w = np.array([0, 0, 0, 0, 0, 0, 0, 1.])
+    SFT = ShortTimeFFT(w, hop=1, fs=1)
+    assert SFT.lower_border_end == (0, 0)
+
+    SFT = ShortTimeFFT(np.flip(w), hop=20, fs=1)
+    assert SFT.upper_border_begin(4) == (16, 1)
+    assert SFT.upper_border_begin(5) == (16, 1)
+    assert SFT.upper_border_begin(23) == (36, 2)
+    assert SFT.upper_border_begin(24) == (36, 2)
+    assert SFT.upper_border_begin(25) == (36, 2)
+
+    SFT._hop = -1  # provoke unreachable line
+    with pytest.raises(RuntimeError):
+        _ = SFT.k_max(4)
+    with pytest.raises(RuntimeError):
+        _ = SFT.k_min
+
+
+def test_t():
+    """Verify that the times of the slices are correct. """
+    SFT = ShortTimeFFT(np.ones(8), hop=4, fs=2)
+    assert SFT.T == 1/2
+    assert SFT.fs == 2.
+    assert SFT.delta_t == 4 * 1/2
+    t_stft = np.arange(0, SFT.p_max(10)) * SFT.delta_t
+    xp_assert_equal(SFT.t(10), t_stft)
+    xp_assert_equal(SFT.t(10, 1, 3), t_stft[1:3])
+    SFT.T = 1/4
+    assert SFT.T == 1/4
+    assert SFT.fs == 4
+    SFT.fs = 1/8
+    assert SFT.fs == 1/8
+    assert SFT.T == 8
+    with pytest.raises(ValueError):
+        # noinspection PyTypeChecker
+        SFT.t(1.5)  # only integers allowed
+    with pytest.raises(ValueError):
+        SFT.t(-1)  # only positive `n` allowed
+
+
+@pytest.mark.parametrize('fft_mode, f',
+                         [('onesided', [0., 1., 2.]),
+                          ('onesided2X', [0., 1., 2.]),
+                          ('twosided', [0., 1., 2., -2., -1.]),
+                          ('centered', [-2., -1., 0., 1., 2.])])
+def test_f(fft_mode: FFT_MODE_TYPE, f):
+    """Verify the frequency values property `f`."""
+    SFT = ShortTimeFFT(np.ones(5), hop=4, fs=5, fft_mode=fft_mode,
+                       scale_to='psd')
+    xp_assert_equal(SFT.f, f)
+
+
+@pytest.mark.parametrize('n', [20, 21])
+@pytest.mark.parametrize('m', [5, 6])
+@pytest.mark.parametrize('fft_mode', ['onesided', 'centered'])
+def test_extent(n, m, fft_mode: FFT_MODE_TYPE):
+    """Ensure that the `extent()` method is correct. """
+    SFT = ShortTimeFFT(np.ones(m), hop=m, fs=m, fft_mode=fft_mode)
+
+    t0 = SFT.t(n)[0]  # first timestamp
+    t1 = SFT.t(n)[-1] + SFT.delta_t  # last timestamp + 1
+    t0c, t1c = t0 - SFT.delta_t / 2, t1 - SFT.delta_t / 2  # centered timestamps
+
+    f0 = SFT.f[0]  # first frequency
+    f1 = SFT.f[-1] + SFT.delta_f  # last frequency + 1
+    f0c, f1c = f0 - SFT.delta_f / 2, f1 - SFT.delta_f / 2  # centered frequencies
+
+    assert SFT.extent(n, 'tf', False) == (t0, t1, f0, f1)
+    assert SFT.extent(n, 'ft', False) == (f0, f1, t0, t1)
+    assert SFT.extent(n, 'tf', True) == (t0c, t1c, f0c, f1c)
+    assert SFT.extent(n, 'ft', True) == (f0c, f1c, t0c, t1c)
+
+
+def test_spectrogram():
+    """Verify spectrogram and cross-spectrogram methods. """
+    SFT = ShortTimeFFT(np.ones(8), hop=4, fs=1)
+    x, y = np.ones(10), np.arange(10)
+    X, Y = SFT.stft(x), SFT.stft(y)
+    xp_assert_close(SFT.spectrogram(x), X.real**2+X.imag**2)
+    xp_assert_close(SFT.spectrogram(x, y), X * Y.conj())
+
+
+@pytest.mark.parametrize('n', [8, 9])
+def test_fft_func_roundtrip(n: int):
+    """Test roundtrip `ifft_func(fft_func(x)) == x` for all permutations of
+    relevant parameters. """
+    np.random.seed(2394795)
+    x0 = np.random.rand(n)
+    w, h_n = np.ones(n), 4
+
+    pp = dict(
+        fft_mode=get_args(FFT_MODE_TYPE),
+        mfft=[None, n, n+1, n+2],
+        scaling=[None, 'magnitude', 'psd'],
+        phase_shift=[None, -n+1, 0, n // 2, n-1])
+    for f_typ, mfft, scaling, phase_shift in product(*pp.values()):
+        if f_typ == 'onesided2X' and scaling is None:
+            continue  # this combination is forbidden
+        SFT = ShortTimeFFT(w, h_n, fs=n, fft_mode=f_typ, mfft=mfft,
+                           scale_to=scaling, phase_shift=phase_shift)
+        X0 = SFT._fft_func(x0)
+        x1 = SFT._ifft_func(X0)
+        xp_assert_close(x0.astype(x1.dtype), x1,
+                        err_msg="_fft_func() roundtrip failed for " +
+                        f"{f_typ=}, {mfft=}, {scaling=}, {phase_shift=}")
+
+    SFT = ShortTimeFFT(w, h_n, fs=1)
+    SFT._fft_mode = 'invalid_fft'  # type: ignore
+    with pytest.raises(RuntimeError):
+        SFT._fft_func(x0)
+    with pytest.raises(RuntimeError):
+        SFT._ifft_func(x0)
+
+
+@pytest.mark.parametrize('i', range(19))
+def test_impulse_roundtrip(i):
+    """Roundtrip for an impulse being at different positions `i`."""
+    n = 19
+    w, h_n = np.ones(8), 3
+    x = np.zeros(n)
+    x[i] = 1
+
+    SFT = ShortTimeFFT(w, hop=h_n, fs=1, scale_to=None, phase_shift=None)
+    Sx = SFT.stft(x)
+    # test slicing the input signal into two parts:
+    n_q = SFT.nearest_k_p(n // 2)
+    Sx0 = SFT.stft(x[:n_q], padding='zeros')
+    Sx1 = SFT.stft(x[n_q:], padding='zeros')
+    q0_ub = SFT.upper_border_begin(n_q)[1] - SFT.p_min
+    q1_le = SFT.lower_border_end[1] - SFT.p_min
+    xp_assert_close(Sx0[:, :q0_ub], Sx[:, :q0_ub], err_msg=f"{i=}")
+    xp_assert_close(Sx1[:, q1_le:], Sx[:, q1_le-Sx1.shape[1]:],
+                    err_msg=f"{i=}")
+
+    Sx01 = np.hstack((Sx0[:, :q0_ub],
+                      Sx0[:, q0_ub:] + Sx1[:, :q1_le],
+                      Sx1[:, q1_le:]))
+    xp_assert_close(Sx, Sx01, atol=1e-8, err_msg=f"{i=}")
+
+    y = SFT.istft(Sx, 0, n)
+    xp_assert_close(y, x, atol=1e-8, err_msg=f"{i=}")
+    y0 = SFT.istft(Sx, 0, n//2)
+    xp_assert_close(x[:n//2], y0, atol=1e-8, err_msg=f"{i=}")
+    y1 = SFT.istft(Sx, n // 2, n)
+    xp_assert_close(x[n // 2:], y1, atol=1e-8, err_msg=f"{i=}")
+
+
+@pytest.mark.parametrize('hop', [1, 7, 8])
+def test_asymmetric_window_roundtrip(hop: int):
+    """An asymmetric window could uncover indexing problems. """
+    np.random.seed(23371)
+
+    w = np.arange(16) / 8  # must be of type float
+    w[len(w)//2:] = 1
+    SFT = ShortTimeFFT(w, hop, fs=1)
+
+    x = 10 * np.random.randn(64)
+    Sx = SFT.stft(x)
+    x1 = SFT.istft(Sx, k1=len(x))
+    xp_assert_close(x1, x1, err_msg="Roundtrip for asymmetric window with " +
+                                    f" {hop=} failed!")
+
+
+@pytest.mark.parametrize('m_num', [6, 7])
+def test_minimal_length_signal(m_num):
+    """Verify that the shortest allowed signal works. """
+    SFT = ShortTimeFFT(np.ones(m_num), m_num//2, fs=1)
+    n = math.ceil(m_num/2)
+    x = np.ones(n)
+    Sx = SFT.stft(x)
+    x1 = SFT.istft(Sx, k1=n)
+    xp_assert_close(x1, x, err_msg=f"Roundtrip minimal length signal ({n=})" +
+                                   f" for {m_num} sample window failed!")
+    with pytest.raises(ValueError, match=rf"len\(x\)={n-1} must be >= ceil.*"):
+        SFT.stft(x[:-1])
+    with pytest.raises(ValueError, match=rf"S.shape\[t_axis\]={Sx.shape[1]-1}"
+                       f" needs to have at least {Sx.shape[1]} slices"):
+        SFT.istft(Sx[:, :-1], k1=n)
+
+
+def test_compare_stft_detrend():
+    """Test the detrending in `ShortTimeFFT.stft_detrend()`. """
+    SFT = ShortTimeFFT(np.ones(4), 4, fs=1)
+    x0 = np.zeros(4) # signal without trend
+    x1 = x0 + 3  # signal with constant trend
+    x2 = x0 + np.arange(len(x0))  # signal with linear trend
+
+    kw = dict(k_offset=2, p1=1)  # we want only one slice
+    Sx0 = SFT.stft(x0, **kw)  # no trend
+    Sx1 = SFT.stft_detrend(x1, detr='constant', **kw)
+    Sx2 = SFT.stft_detrend(x2, detr='linear', **kw)
+    Sx3 = SFT.stft_detrend(x1, detr=lambda x: x - np.mean(x), **kw)
+
+    atol = np.finfo(Sx0.dtype).resolution * 5  # needed to compare with array of zeros
+    xp_assert_close(Sx1, Sx0, atol=atol, err_msg="Constant detrending failed!")
+    xp_assert_close(Sx0, Sx2, atol=atol, err_msg="Linear detrending failed!")
+    xp_assert_close(Sx0, Sx3, atol=atol, err_msg="Detrending using a function failed!")
+
+
+def test_tutorial_stft_sliding_win():
+    """Verify example in "Sliding Windows" subsection from the "User Guide".
+
+    In :ref:`tutorial_stft_sliding_win` (file ``signal.rst``) of the
+    :ref:`user_guide` the behavior the border behavior of
+    ``ShortTimeFFT(np.ones(6), 2, fs=1)`` with a 50 sample signal is discussed.
+    This test verifies the presented indexes.
+    """
+    SFT = ShortTimeFFT(np.ones(6), 2, fs=1)
+
+    # Lower border:
+    assert SFT.m_num_mid == 3, f"Slice middle is not 3 but {SFT.m_num_mid=}"
+    assert SFT.p_min == -1, f"Lowest slice {SFT.p_min=} is not -1"
+    assert SFT.k_min == -5, f"Lowest slice sample {SFT.p_min=} is not -5"
+    k_lb, p_lb = SFT.lower_border_end
+    assert p_lb == 2, f"First unaffected slice {p_lb=} is not 2"
+    assert k_lb == 5, f"First unaffected sample {k_lb=} is not 5"
+
+    n = 50  # upper signal border
+    assert (p_max := SFT.p_max(n)) == 27, f"Last slice {p_max=} must be 27"
+    assert (k_max := SFT.k_max(n)) == 55, f"Last sample {k_max=} must be 55"
+    k_ub, p_ub = SFT.upper_border_begin(n)
+    assert p_ub == 24, f"First upper border slice {p_ub=} must be 24"
+    assert k_ub == 45, f"First upper border slice {k_ub=} must be 45"
+
+
+def test_tutorial_stft_legacy_stft():
+    """Verify STFT example in "Comparison with Legacy Implementation" from the
+    "User Guide".
+
+    In :ref:`tutorial_stft_legacy_stft` (file ``signal.rst``) of the
+    :ref:`user_guide` the legacy and the new implementation are compared.
+    """
+    fs, N = 200, 1001  # # 200 Hz sampling rate for 5 s signal
+    t_z = np.arange(N) / fs  # time indexes for signal
+    z = np.exp(2j*np.pi * 70 * (t_z - 0.2 * t_z ** 2))  # complex-valued chirp
+
+    nperseg, noverlap = 50, 40
+    win = ('gaussian', 1e-2 * fs)  # Gaussian with 0.01 s standard deviation
+
+    # Legacy STFT:
+    f0_u, t0, Sz0_u = stft(z, fs, win, nperseg, noverlap,
+                           return_onesided=False, scaling='spectrum')
+    Sz0 = fftshift(Sz0_u, axes=0)
+
+    # New STFT:
+    SFT = ShortTimeFFT.from_window(win, fs, nperseg, noverlap,
+                                   fft_mode='centered',
+                                   scale_to='magnitude', phase_shift=None)
+    Sz1 = SFT.stft(z)
+
+    xp_assert_close(Sz0, Sz1[:, 2:-1])
+
+    xp_assert_close((abs(Sz1[:, 1]).min(), abs(Sz1[:, 1]).max()),
+                    (6.925060911593139e-07, 8.00271269218721e-07))
+
+    t0_r, z0_r = istft(Sz0_u, fs, win, nperseg, noverlap, input_onesided=False,
+                       scaling='spectrum')
+    z1_r = SFT.istft(Sz1, k1=N)
+    assert len(z0_r) == N + 9
+    xp_assert_close(z0_r[:N], z)
+    xp_assert_close(z1_r, z)
+
+    #  Spectrogram is just the absolute square of th STFT:
+    xp_assert_close(SFT.spectrogram(z), abs(Sz1) ** 2)
+
+
+def test_tutorial_stft_legacy_spectrogram():
+    """Verify spectrogram example in "Comparison with Legacy Implementation"
+    from the "User Guide".
+
+    In :ref:`tutorial_stft_legacy_stft` (file ``signal.rst``) of the
+    :ref:`user_guide` the legacy and the new implementation are compared.
+    """
+    fs, N = 200, 1001  # 200 Hz sampling rate for almost 5 s signal
+    t_z = np.arange(N) / fs  # time indexes for signal
+    z = np.exp(2j*np.pi*70 * (t_z - 0.2*t_z**2))  # complex-valued sweep
+
+    nperseg, noverlap = 50, 40
+    win = ('gaussian', 1e-2 * fs)  # Gaussian with 0.01 s standard dev.
+
+    # Legacy spectrogram:
+    f2_u, t2, Sz2_u = spectrogram(z, fs, win, nperseg, noverlap, detrend=None,
+                                  return_onesided=False, scaling='spectrum',
+                                  mode='complex')
+
+    f2, Sz2 = fftshift(f2_u), fftshift(Sz2_u, axes=0)
+
+    # New STFT:
+    SFT = ShortTimeFFT.from_window(win, fs, nperseg, noverlap,
+                                   fft_mode='centered', scale_to='magnitude',
+                                   phase_shift=None)
+    Sz3 = SFT.stft(z, p0=0, p1=(N-noverlap) // SFT.hop, k_offset=nperseg // 2)
+    t3 = SFT.t(N, p0=0, p1=(N-noverlap) // SFT.hop, k_offset=nperseg // 2)
+
+    xp_assert_close(t2, t3)
+    xp_assert_close(f2, SFT.f)
+    xp_assert_close(Sz2, Sz3)
+
+
+def test_permute_axes():
+    """Verify correctness of four-dimensional signal by permuting its
+    shape. """
+    n = 25
+    SFT = ShortTimeFFT(np.ones(8)/8, hop=3, fs=n)
+    x0 = np.arange(n, dtype=np.float64)
+    Sx0 = SFT.stft(x0)
+    Sx0 = Sx0.reshape((Sx0.shape[0], 1, 1, 1, Sx0.shape[-1]))
+    SxT = np.moveaxis(Sx0, (0, -1), (-1, 0))
+
+    atol = 2 * np.finfo(SFT.win.dtype).resolution
+    for i in range(4):
+        y = np.reshape(x0, np.roll((n, 1, 1, 1), i))
+        Sy = SFT.stft(y, axis=i)
+        xp_assert_close(Sy, np.moveaxis(Sx0, 0, i))
+
+        yb0 = SFT.istft(Sy, k1=n, f_axis=i)
+        xp_assert_close(yb0, y, atol=atol)
+        # explicit t-axis parameter (for coverage):
+        yb1 = SFT.istft(Sy, k1=n, f_axis=i, t_axis=Sy.ndim-1)
+        xp_assert_close(yb1, y, atol=atol)
+
+        SyT = np.moveaxis(Sy, (i, -1), (-1, i))
+        xp_assert_close(SyT, np.moveaxis(SxT, 0, i))
+
+        ybT = SFT.istft(SyT, k1=n, t_axis=i, f_axis=-1)
+        xp_assert_close(ybT, y, atol=atol)
+
+
+@pytest.mark.parametrize("fft_mode",
+                         ('twosided', 'centered', 'onesided', 'onesided2X'))
+def test_roundtrip_multidimensional(fft_mode: FFT_MODE_TYPE):
+    """Test roundtrip of a multidimensional input signal versus its components.
+
+    This test can uncover potential problems with `fftshift()`.
+    """
+    n = 9
+    x = np.arange(4*n*2, dtype=np.float64).reshape(4, n, 2)
+    SFT = ShortTimeFFT(get_window('hann', 4), hop=2, fs=1,
+                       scale_to='magnitude', fft_mode=fft_mode)
+    Sx = SFT.stft(x, axis=1)
+    y = SFT.istft(Sx, k1=n, f_axis=1, t_axis=-1)
+    xp_assert_close(y, x.astype(y.dtype), err_msg='Multidim. roundtrip failed!')
+
+    for i, j in product(range(x.shape[0]), range(x.shape[2])):
+        y_ = SFT.istft(Sx[i, :, j, :], k1=n)
+        xp_assert_close(y_, x[i, :, j].astype(y_.dtype),
+                        err_msg="Multidim. roundtrip for component " +
+                        f"x[{i}, :, {j}] and {fft_mode=} failed!")
+
+@pytest.mark.parametrize("phase_shift", (0, 4,  None))
+def test_roundtrip_two_dimensional(phase_shift: int|None):
+    """Test roundtrip of a 2 channel input signal with `mfft` set with different
+    values for `phase_shift`
+
+    Tests for Issue https://github.com/scipy/scipy/issues/21671
+    """
+    n = 21
+    SFT = ShortTimeFFT.from_window('hann', fs=1, nperseg=13, noverlap=7,
+                                   mfft=16, phase_shift=phase_shift)
+    x = np.arange(2*n, dtype=float).reshape(2, n)
+    Sx = SFT.stft(x)
+    y = SFT.istft(Sx, k1=n)
+    xp_assert_close(y, x, atol=2 * np.finfo(SFT.win.dtype).resolution,
+                    err_msg='2-dim. roundtrip failed!')
+
+
+@pytest.mark.parametrize('window, n, nperseg, noverlap',
+                         [('boxcar', 100, 10, 0),     # Test no overlap
+                          ('boxcar', 100, 10, 9),     # Test high overlap
+                          ('bartlett', 101, 51, 26),  # Test odd nperseg
+                          ('hann', 1024, 256, 128),   # Test defaults
+                          (('tukey', 0.5), 1152, 256, 64),  # Test Tukey
+                          ('hann', 1024, 256, 255),   # Test overlapped hann
+                          ('boxcar', 100, 10, 3),     # NOLA True, COLA False
+                          ('bartlett', 101, 51, 37),  # NOLA True, COLA False
+                          ('hann', 1024, 256, 127),   # NOLA True, COLA False
+                          # NOLA True, COLA False:
+                          (('tukey', 0.5), 1152, 256, 14),
+                          ('hann', 1024, 256, 5)])    # NOLA True, COLA False
+def test_roundtrip_windows(window, n: int, nperseg: int, noverlap: int):
+    """Roundtrip test adapted from `test_spectral.TestSTFT`.
+
+    The parameters are taken from the methods test_roundtrip_real(),
+    test_roundtrip_nola_not_cola(), test_roundtrip_float32(),
+    test_roundtrip_complex().
+    """
+    np.random.seed(2394655)
+
+    w = get_window(window, nperseg)
+    SFT = ShortTimeFFT(w, nperseg - noverlap, fs=1, fft_mode='twosided',
+                       phase_shift=None)
+
+    z = 10 * np.random.randn(n) + 10j * np.random.randn(n)
+    Sz = SFT.stft(z)
+    z1 = SFT.istft(Sz, k1=len(z))
+    xp_assert_close(z, z1, err_msg="Roundtrip for complex values failed")
+
+    x = 10 * np.random.randn(n)
+    Sx = SFT.stft(x)
+    x1 = SFT.istft(Sx, k1=len(z))
+    xp_assert_close(x.astype(np.complex128), x1,
+                    err_msg="Roundtrip for float values failed")
+
+    x32 = x.astype(np.float32)
+    Sx32 = SFT.stft(x32)
+    x32_1 = SFT.istft(Sx32, k1=len(x32))
+    x32_1_r = x32_1.real
+    xp_assert_close(x32, x32_1_r.astype(np.float32),
+                    err_msg="Roundtrip for 32 Bit float values failed")
+    xp_assert_close(x32.imag, np.zeros_like(x32.imag),
+                    err_msg="Roundtrip for 32 Bit float values failed")
+
+
+@pytest.mark.parametrize('signal_type', ('real', 'complex'))
+def test_roundtrip_complex_window(signal_type):
+    """Test roundtrip for complex-valued window function
+
+    The purpose of this test is to check if the dual window is calculated
+    correctly for complex-valued windows.
+    """
+    np.random.seed(1354654)
+    win = np.exp(2j*np.linspace(0, np.pi, 8))
+    SFT = ShortTimeFFT(win, 3, fs=1, fft_mode='twosided')
+
+    z = 10 * np.random.randn(11)
+    if signal_type == 'complex':
+        z = z + 2j * z
+    Sz = SFT.stft(z)
+    z1 = SFT.istft(Sz, k1=len(z))
+    xp_assert_close(z.astype(np.complex128), z1,
+                    err_msg="Roundtrip for complex-valued window failed")
+
+
+def test_average_all_segments():
+    """Compare `welch` function with stft mean.
+
+    Ported from `TestSpectrogram.test_average_all_segments` from file
+    ``test__spectral.py``.
+    """
+    x = np.random.randn(1024)
+
+    fs = 1.0
+    window = ('tukey', 0.25)
+    nperseg, noverlap = 16, 2
+    fw, Pw = welch(x, fs, window, nperseg, noverlap)
+    SFT = ShortTimeFFT.from_window(window, fs, nperseg, noverlap,
+                                   fft_mode='onesided2X', scale_to='psd',
+                                   phase_shift=None)
+    # `welch` positions the window differently than the STFT:
+    P = SFT.spectrogram(x, detr='constant', p0=0,
+                        p1=(len(x)-noverlap)//SFT.hop, k_offset=nperseg//2)
+
+    xp_assert_close(SFT.f, fw)
+    xp_assert_close(np.mean(P, axis=-1), Pw)
+
+
+@pytest.mark.parametrize('window, N, nperseg, noverlap, mfft',
+                         # from test_roundtrip_padded_FFT:
+                         [('hann', 1024, 256, 128, 512),
+                          ('hann', 1024, 256, 128, 501),
+                          ('boxcar', 100, 10, 0, 33),
+                          (('tukey', 0.5), 1152, 256, 64, 1024),
+                          # from test_roundtrip_padded_signal:
+                          ('boxcar', 101, 10, 0, None),
+                          ('hann', 1000, 256, 128, None),
+                          # from test_roundtrip_boundary_extension:
+                          ('boxcar', 100, 10, 0, None),
+                          ('boxcar', 100, 10, 9, None)])
+@pytest.mark.parametrize('padding', get_args(PAD_TYPE))
+def test_stft_padding_roundtrip(window, N: int, nperseg: int, noverlap: int,
+                                mfft: int, padding):
+    """Test the parameter 'padding' of `stft` with roundtrips.
+
+    The STFT parametrizations were taken from the methods
+    `test_roundtrip_padded_FFT`, `test_roundtrip_padded_signal` and
+    `test_roundtrip_boundary_extension` from class `TestSTFT` in  file
+    ``test_spectral.py``. Note that the ShortTimeFFT does not need the
+    concept of "boundary extension".
+    """
+    x = normal_distribution.rvs(size=N, random_state=2909)  # real signal
+    z = x * np.exp(1j * np.pi / 4)  # complex signal
+
+    SFT = ShortTimeFFT.from_window(window, 1, nperseg, noverlap,
+                                   fft_mode='twosided', mfft=mfft)
+    Sx = SFT.stft(x, padding=padding)
+    x1 = SFT.istft(Sx, k1=N)
+    xp_assert_close(x1, x.astype(np.complex128),
+                    err_msg=f"Failed real roundtrip with '{padding}' padding")
+
+    Sz = SFT.stft(z, padding=padding)
+    z1 = SFT.istft(Sz, k1=N)
+    xp_assert_close(z1, z, err_msg="Failed complex roundtrip with " +
+                    f" '{padding}' padding")
+
+
+@pytest.mark.parametrize('N_x', (128, 129, 255, 256, 1337))  # signal length
+@pytest.mark.parametrize('w_size', (128, 256))  # window length
+@pytest.mark.parametrize('t_step', (4, 64))  # SFT time hop
+@pytest.mark.parametrize('f_c', (7., 23.))  # frequency of input sine
+def test_energy_conservation(N_x: int, w_size: int, t_step: int, f_c: float):
+    """Test if a `psd`-scaled STFT conserves the L2 norm.
+
+    This test is adapted from MNE-Python [1]_. Besides being battle-tested,
+    this test has the benefit of using non-standard window including
+    non-positive values and a 2d input signal.
+
+    Since `ShortTimeFFT` requires the signal length `N_x` to be at least the
+    window length `w_size`, the parameter `N_x` was changed from
+    ``(127, 128, 255, 256, 1337)`` to ``(128, 129, 255, 256, 1337)`` to be
+    more useful.
+
+    .. [1] File ``test_stft.py`` of MNE-Python
+        https://github.com/mne-tools/mne-python/blob/main/mne/time_frequency/tests/test_stft.py
+    """
+    window = np.sin(np.arange(.5, w_size + .5) / w_size * np.pi)
+    SFT = ShortTimeFFT(window, t_step, fs=1000, fft_mode='onesided2X',
+                       scale_to='psd')
+    atol = 2*np.finfo(window.dtype).resolution
+    N_x = max(N_x, w_size)  # minimal sing
+    # Test with low frequency signal
+    t = np.arange(N_x).astype(np.float64)
+    x = np.sin(2 * np.pi * f_c * t * SFT.T)
+    x = np.array([x, x + 1.])
+    X = SFT.stft(x)
+    xp = SFT.istft(X, k1=N_x)
+
+    max_freq = SFT.f[np.argmax(np.sum(np.abs(X[0]) ** 2, axis=1))]
+
+    assert X.shape[1] == SFT.f_pts
+    assert np.all(SFT.f >= 0.)
+    assert np.abs(max_freq - f_c) < 1.
+    xp_assert_close(x, xp, atol=atol)
+
+    # check L2-norm squared (i.e., energy) conservation:
+    E_x = np.sum(x**2, axis=-1) * SFT.T  # numerical integration
+    aX2 = X.real**2 + X.imag.real**2
+    E_X = np.sum(np.sum(aX2, axis=-1) * SFT.delta_t, axis=-1) * SFT.delta_f
+    xp_assert_close(E_X, E_x, atol=atol)
+
+    # Test with random signal
+    np.random.seed(2392795)
+    x = np.random.randn(2, N_x)
+    X = SFT.stft(x)
+    xp = SFT.istft(X, k1=N_x)
+
+    assert X.shape[1] == SFT.f_pts
+    assert np.all(SFT.f >= 0.)
+    assert np.abs(max_freq - f_c) < 1.
+    xp_assert_close(x, xp, atol=atol)
+
+    # check L2-norm squared (i.e., energy) conservation:
+    E_x = np.sum(x**2, axis=-1) * SFT.T  # numeric integration
+    aX2 = X.real ** 2 + X.imag.real ** 2
+    E_X = np.sum(np.sum(aX2, axis=-1) * SFT.delta_t, axis=-1) * SFT.delta_f
+    xp_assert_close(E_X, E_x, atol=atol)
+
+    # Try with empty array
+    x = np.zeros((0, N_x))
+    X = SFT.stft(x)
+    xp = SFT.istft(X, k1=N_x)
+    assert xp.shape == x.shape
+
+
+def test_subscriptable_generic_type():
+    assert isinstance(ShortTimeFFT[np.float64], GenericAlias)
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/tests/test_signaltools.py b/venv/lib/python3.12/site-packages/scipy/signal/tests/test_signaltools.py
new file mode 100644
index 0000000000000000000000000000000000000000..41651947281f8ffcbd32223f3c5475726f28e28c
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/tests/test_signaltools.py
@@ -0,0 +1,4782 @@
+import sys
+import math
+import warnings
+
+from concurrent.futures import ThreadPoolExecutor, as_completed
+from itertools import product
+from math import gcd
+
+import pytest
+from pytest import raises as assert_raises
+import numpy as np
+from numpy.exceptions import ComplexWarning
+
+from scipy import fft as sp_fft
+from scipy.ndimage import correlate1d
+from scipy.optimize import fmin, linear_sum_assignment
+from scipy import signal
+from scipy.signal import (
+    correlate, correlate2d, correlation_lags, convolve, convolve2d,
+    fftconvolve, oaconvolve, choose_conv_method, envelope,
+    hilbert, hilbert2, lfilter, lfilter_zi, filtfilt, butter, zpk2tf, zpk2sos,
+    invres, invresz, vectorstrength, lfiltic, tf2sos, sosfilt, sosfiltfilt,
+    sosfilt_zi, tf2zpk, BadCoefficients, detrend, unique_roots, residue,
+    residuez)
+from scipy.signal.windows import hann
+from scipy.signal._signaltools import _filtfilt_gust, _compute_factors, _group_poles
+from scipy.signal._upfirdn import _upfirdn_modes
+from scipy._lib import _testutils
+import scipy._external.array_api_extra as xpx
+from scipy._lib._array_api import (
+    xp_assert_close, xp_assert_equal, is_numpy, is_torch, is_jax, is_cupy,
+    assert_array_almost_equal, assert_almost_equal,
+    xp_copy, xp_size, xp_default_dtype, array_namespace, make_xp_test_case,
+    make_xp_pytest_param, SCIPY_DEVICE, _xp_copy_to_numpy
+)
+skip_xp_backends = pytest.mark.skip_xp_backends
+xfail_xp_backends = pytest.mark.xfail_xp_backends
+
+lazy_xp_modules = [signal]
+
+
+@make_xp_test_case(convolve)
+class TestConvolve:
+
+    @skip_xp_backends("jax.numpy",
+        reason="jax returns floats; scipy returns ints; cf gh-6076")
+    def test_basic(self, xp):
+        a = xp.asarray([3, 4, 5, 6, 5, 4])
+        b = xp.asarray([1, 2, 3])
+        c = convolve(a, b)
+        xp_assert_equal(c, xp.asarray([3, 10, 22, 28, 32, 32, 23, 12]))
+
+    @skip_xp_backends("jax.numpy",
+        reason="jax returns floats; scipy returns ints; cf gh-6076")
+    def test_same(self, xp):
+        a = xp.asarray([3, 4, 5])
+        b = xp.asarray([1, 2, 3, 4])
+        c = convolve(a, b, mode="same")
+        xp_assert_equal(c, xp.asarray([10, 22, 34]))
+
+    @skip_xp_backends("jax.numpy",
+        reason="jax returns floats; scipy returns ints; cf gh-6076")
+    def test_same_eq(self, xp):
+        a = xp.asarray([3, 4, 5])
+        b = xp.asarray([1, 2, 3])
+        c = convolve(a, b, mode="same")
+        xp_assert_equal(c, xp.asarray([10, 22, 22]))
+
+    def test_complex(self, xp):
+        x = xp.asarray([1 + 1j, 2 + 1j, 3 + 1j])
+        y = xp.asarray([1 + 1j, 2 + 1j])
+        z = convolve(x, y)
+        xp_assert_equal(z, xp.asarray([2j, 2 + 6j, 5 + 8j, 5 + 5j]))
+
+    @xfail_xp_backends("jax.numpy", reason="wrong output dtype")
+    def test_zero_rank(self, xp):
+        a = xp.asarray(1289)
+        b = xp.asarray(4567)
+        c = convolve(a, b)
+        xp_assert_equal(c, a * b)
+
+    @skip_xp_backends(np_only=True, reason="pure python")
+    def test_zero_rank_python_scalars(self, xp):
+        a = 1289
+        b = 4567
+        c = convolve(a, b)
+        assert c == a * b
+
+    @xfail_xp_backends("jax.numpy", reason="disagreement between methods")
+    def test_broadcastable(self, xp):
+        a = xp.reshape(xp.arange(27), (3, 3, 3))
+        b = xp.arange(3)
+        for i in range(3):
+            b_shape = [1]*3
+            b_shape[i] = 3
+
+            x = convolve(a, xp.reshape(b, tuple(b_shape)), method='direct')
+            y = convolve(a, xp.reshape(b, tuple(b_shape)), method='fft')
+            xp_assert_close(x, y, atol=1e-14)
+
+    @xfail_xp_backends("jax.numpy", reason="wrong output dtype")
+    def test_single_element(self, xp):
+        a = xp.asarray([4967])
+        b = xp.asarray([3920])
+        c = convolve(a, b)
+        xp_assert_equal(c, a * b)
+
+    @skip_xp_backends("jax.numpy",)
+    @skip_xp_backends("cupy")
+    def test_2d_arrays(self, xp):
+        a = xp.asarray([[1, 2, 3], [3, 4, 5]])
+        b = xp.asarray([[2, 3, 4], [4, 5, 6]])
+        c = convolve(a, b)
+        d = xp.asarray([[2, 7, 16, 17, 12],
+                   [10, 30, 62, 58, 38],
+                   [12, 31, 58, 49, 30]])
+        xp_assert_equal(c, d)
+
+    @skip_xp_backends("torch")
+    @skip_xp_backends("cupy")
+    def test_input_swapping(self, xp):
+        small = xp.reshape(xp.arange(8), (2, 2, 2))
+        big = 1j * xp.reshape(xp.arange(27, dtype=xp.complex128), (3, 3, 3))
+        big += xp.reshape(xp.arange(27, dtype=xp.complex128)[::-1], (3, 3, 3))
+
+        out_array = xp.asarray(
+            [[[0 + 0j, 26 + 0j, 25 + 1j, 24 + 2j],
+              [52 + 0j, 151 + 5j, 145 + 11j, 93 + 11j],
+              [46 + 6j, 133 + 23j, 127 + 29j, 81 + 23j],
+              [40 + 12j, 98 + 32j, 93 + 37j, 54 + 24j]],
+
+             [[104 + 0j, 247 + 13j, 237 + 23j, 135 + 21j],
+              [282 + 30j, 632 + 96j, 604 + 124j, 330 + 86j],
+              [246 + 66j, 548 + 180j, 520 + 208j, 282 + 134j],
+              [142 + 66j, 307 + 161j, 289 + 179j, 153 + 107j]],
+
+             [[68 + 36j, 157 + 103j, 147 + 113j, 81 + 75j],
+              [174 + 138j, 380 + 348j, 352 + 376j, 186 + 230j],
+              [138 + 174j, 296 + 432j, 268 + 460j, 138 + 278j],
+              [70 + 138j, 145 + 323j, 127 + 341j, 63 + 197j]],
+
+             [[32 + 72j, 68 + 166j, 59 + 175j, 30 + 100j],
+              [68 + 192j, 139 + 433j, 117 + 455j, 57 + 255j],
+              [38 + 222j, 73 + 499j, 51 + 521j, 21 + 291j],
+              [12 + 144j, 20 + 318j, 7 + 331j, 0 + 182j]]])
+
+        xp_assert_equal(convolve(small, big, 'full'), out_array)
+        xp_assert_equal(convolve(big, small, 'full'), out_array)
+        xp_assert_equal(convolve(small, big, 'same'),
+                           out_array[1:3, 1:3, 1:3])
+        xp_assert_equal(convolve(big, small, 'same'),
+                           out_array[0:3, 0:3, 0:3])
+        xp_assert_equal(convolve(small, big, 'valid'),
+                           out_array[1:3, 1:3, 1:3])
+        xp_assert_equal(convolve(big, small, 'valid'),
+                           out_array[1:3, 1:3, 1:3])
+
+    def test_invalid_params(self, xp):
+        a = xp.asarray([3, 4, 5])
+        b = xp.asarray([1, 2, 3])
+        assert_raises(ValueError, convolve, a, b, mode='spam')
+        assert_raises(ValueError, convolve, a, b, mode='eggs', method='fft')
+        assert_raises(ValueError, convolve, a, b, mode='ham', method='direct')
+        assert_raises(ValueError, convolve, a, b, mode='full', method='bacon')
+        assert_raises(ValueError, convolve, a, b, mode='same', method='bacon')
+
+    @skip_xp_backends("jax.numpy", reason="dtypes do not match")
+    def test_valid_mode2(self, xp):
+        # See gh-5897
+        a = xp.asarray([1, 2, 3, 6, 5, 3])
+        b = xp.asarray([2, 3, 4, 5, 3, 4, 2, 2, 1])
+        expected = xp.asarray([70, 78, 73, 65])
+
+        out = convolve(a, b, 'valid')
+        xp_assert_equal(out, expected)
+
+        out = convolve(b, a, 'valid')
+        xp_assert_equal(out, expected)
+
+        a = xp.asarray([1 + 5j, 2 - 1j, 3 + 0j])
+        b = xp.asarray([2 - 3j, 1 + 0j])
+        expected = xp.asarray([2 - 3j, 8 - 10j])
+
+        out = convolve(a, b, 'valid')
+        xp_assert_equal(out, expected)
+
+        out = convolve(b, a, 'valid')
+        xp_assert_equal(out, expected)
+
+    @skip_xp_backends("jax.numpy", reason="dtypes do not match")
+    def test_same_mode(self, xp):
+        a = xp.asarray([1, 2, 3, 3, 1, 2])
+        b = xp.asarray([1, 4, 3, 4, 5, 6, 7, 4, 3, 2, 1, 1, 3])
+        c = convolve(a, b, 'same')
+        d = xp.asarray([57, 61, 63, 57, 45, 36])
+        xp_assert_equal(c, d)
+
+    @skip_xp_backends("cupy", reason="different exception")
+    def test_invalid_shapes(self, xp):
+        # By "invalid," we mean that no one
+        # array has dimensions that are all at
+        # least as large as the corresponding
+        # dimensions of the other array. This
+        # setup should throw a ValueError.
+        a = xp.reshape(xp.arange(1, 7), (2, 3))
+        b = xp.reshape(xp.arange(-6, 0), (3, 2))
+
+        assert_raises(ValueError, convolve, *(a, b), **{'mode': 'valid'})
+        assert_raises(ValueError, convolve, *(b, a), **{'mode': 'valid'})
+
+    @skip_xp_backends(np_only=True, reason="TODO: convert this test")
+    def test_convolve_method(self, xp, n=100):
+        # this types data structure was manually encoded instead of
+        # using custom filters on the soon-to-be-removed np.sctypes
+        types = {'uint16', 'uint64', 'int64', 'int32',
+                 'complex128', 'float64', 'float16',
+                 'complex64', 'float32', 'int16',
+                 'uint8', 'uint32', 'int8', 'bool'}
+        args = [(t1, t2, mode) for t1 in types for t2 in types
+                               for mode in ['valid', 'full', 'same']]
+
+        # These are random arrays, which means test is much stronger than
+        # convolving testing by convolving two np.ones arrays
+        rng = np.random.RandomState(42)
+        array_types = {'i': rng.choice([0, 1], size=n),
+                       'f': rng.randn(n)}
+        array_types['b'] = array_types['u'] = array_types['i']
+        array_types['c'] = array_types['f'] + 0.5j*array_types['f']
+
+        for t1, t2, mode in args:
+            x1 = array_types[np.dtype(t1).kind].astype(t1)
+            x2 = array_types[np.dtype(t2).kind].astype(t2)
+
+            results = {key: convolve(x1, x2, method=key, mode=mode)
+                       for key in ['fft', 'direct']}
+
+            assert results['fft'].dtype == results['direct'].dtype
+
+            if 'bool' in t1 and 'bool' in t2:
+                assert choose_conv_method(x1, x2) == 'direct'
+                continue
+
+            # Found by experiment. Found approx smallest value for (rtol, atol)
+            # threshold to have tests pass.
+            if any([t in {'complex64', 'float32'} for t in [t1, t2]]):
+                kwargs = {'rtol': 1.0e-4, 'atol': 1e-6}
+            elif 'float16' in [t1, t2]:
+                # atol is default for np.allclose
+                kwargs = {'rtol': 1e-3, 'atol': 1e-3}
+            else:
+                # defaults for np.allclose (different from assert_allclose)
+                kwargs = {'rtol': 1e-5, 'atol': 1e-8}
+
+            xp_assert_close(results['fft'], results['direct'], **kwargs)
+
+    @skip_xp_backends("jax.numpy", reason="dtypes do not match")
+    def test_convolve_method_large_input(self, xp):
+        # This is really a test that convolving two large integers goes to the
+        # direct method even if they're in the fft method.
+        for n in [10, 20, 50, 51, 52, 53, 54, 60, 62]:
+            z = xp.asarray([2**n], dtype=xp.int64)
+            fft = convolve(z, z, method='fft')
+            direct = convolve(z, z, method='direct')
+
+            # this is the case when integer precision gets to us
+            # issue #6076 has more detail, hopefully more tests after resolved
+            # # XXX: revisit check_dtype under np 2.0: 32bit linux & windows
+            if n < 50:
+                val = xp.asarray([2**(2*n)])
+                xp_assert_equal(fft, direct)
+                xp_assert_equal(fft, val, check_dtype=False)
+                xp_assert_equal(direct, val, check_dtype=False)
+
+    @skip_xp_backends(np_only=True)
+    def test_mismatched_dims(self, xp):
+        # Input arrays should have the same number of dimensions
+        assert_raises(ValueError, convolve, [1], 2, method='direct')
+        assert_raises(ValueError, convolve, 1, [2], method='direct')
+        assert_raises(ValueError, convolve, [1], 2, method='fft')
+        assert_raises(ValueError, convolve, 1, [2], method='fft')
+        assert_raises(ValueError, convolve, [1], [[2]])
+        assert_raises(ValueError, convolve, [3], 2)
+
+
+@make_xp_test_case(convolve2d)
+class TestConvolve2d:
+
+    @skip_xp_backends("jax.numpy", reason="dtypes do not match")
+    def test_2d_arrays(self, xp):
+        a = xp.asarray([[1, 2, 3], [3, 4, 5]])
+        b = xp.asarray([[2, 3, 4], [4, 5, 6]])
+        d = xp.asarray([[2, 7, 16, 17, 12],
+                   [10, 30, 62, 58, 38],
+                   [12, 31, 58, 49, 30]])
+        e = convolve2d(a, b)
+        xp_assert_equal(e, d)
+
+    @skip_xp_backends("jax.numpy", reason="dtypes do not match")
+    def test_valid_mode(self, xp):
+        e = xp.asarray([[2, 3, 4, 5, 6, 7, 8], [4, 5, 6, 7, 8, 9, 10]])
+        f = xp.asarray([[1, 2, 3], [3, 4, 5]])
+        h = xp.asarray([[62, 80, 98, 116, 134]])
+
+        g = convolve2d(e, f, 'valid')
+        xp_assert_equal(g, h)
+
+        # See gh-5897
+        g = convolve2d(f, e, 'valid')
+        xp_assert_equal(g, h)
+
+    @skip_xp_backends("torch", reason="dtypes do not match")
+    def test_valid_mode_complx(self, xp):
+        e = xp.asarray([[2, 3, 4, 5, 6, 7, 8], [4, 5, 6, 7, 8, 9, 10]])
+        f = xp.asarray([[1, 2, 3], [3, 4, 5]], dtype=xp.complex128) + 1j
+        h = xp.asarray([[62.+24.j, 80.+30.j, 98.+36.j, 116.+42.j, 134.+48.j]])
+
+        g = convolve2d(e, f, 'valid')
+        xp_assert_close(g, h)
+
+        # See gh-5897
+        g = convolve2d(f, e, 'valid')
+        xp_assert_equal(g, h)
+
+    @skip_xp_backends("jax.numpy", reason="jax only allows fillvalue=0")
+    def test_fillvalue(self, xp):
+        a = xp.asarray([[1, 2, 3], [3, 4, 5]])
+        b = xp.asarray([[2, 3, 4], [4, 5, 6]])
+        fillval = 1
+        c = convolve2d(a, b, 'full', 'fill', fillval)
+        d = xp.asarray([[24, 26, 31, 34, 32],
+                   [28, 40, 62, 64, 52],
+                   [32, 46, 67, 62, 48]])
+        xp_assert_equal(c, d)
+
+    def test_fillvalue_errors(self, xp):
+        msg = "could not cast `fillvalue` directly to the output "
+        with warnings.catch_warnings():
+            warnings.filterwarnings("ignore", "Casting complex values", ComplexWarning)
+            with assert_raises(ValueError, match=msg):
+                convolve2d([[1]], [[1, 2]], fillvalue=1j)
+
+        msg = "`fillvalue` must be scalar or an array with "
+        with assert_raises(ValueError, match=msg):
+            convolve2d([[1]], [[1, 2]], fillvalue=[1, 2])
+
+    def test_fillvalue_empty(self, xp):
+        # Check that fillvalue being empty raises an error:
+        assert_raises(ValueError, convolve2d, [[1]], [[1, 2]],
+                      fillvalue=[])
+
+    @skip_xp_backends("jax.numpy", reason="jax only supports boundary='fill'")
+    def test_wrap_boundary(self, xp):
+        a = xp.asarray([[1, 2, 3], [3, 4, 5]])
+        b = xp.asarray([[2, 3, 4], [4, 5, 6]])
+        c = convolve2d(a, b, 'full', 'wrap')
+        d = xp.asarray([[80, 80, 74, 80, 80],
+                   [68, 68, 62, 68, 68],
+                   [80, 80, 74, 80, 80]])
+        xp_assert_equal(c, d)
+
+    @skip_xp_backends("jax.numpy", reason="jax only supports boundary='fill'")
+    def test_sym_boundary(self, xp):
+        a = xp.asarray([[1, 2, 3], [3, 4, 5]])
+        b = xp.asarray([[2, 3, 4], [4, 5, 6]])
+        c = convolve2d(a, b, 'full', 'symm')
+        d = xp.asarray([[34, 30, 44, 62, 66],
+                   [52, 48, 62, 80, 84],
+                   [82, 78, 92, 110, 114]])
+        xp_assert_equal(c, d)
+
+    @skip_xp_backends("jax.numpy", reason="jax only supports boundary='fill'")
+    @pytest.mark.parametrize('func', [convolve2d, correlate2d])
+    @pytest.mark.parametrize('boundary, expected',
+                             [('symm', [[37.0, 42.0, 44.0, 45.0]]),
+                              ('wrap', [[43.0, 44.0, 42.0, 39.0]])])
+    def test_same_with_boundary(self, func, boundary, expected, xp):
+        # Test boundary='symm' and boundary='wrap' with a "long" kernel.
+        # The size of the kernel requires that the values in the "image"
+        # be extended more than once to handle the requested boundary method.
+        # This is a regression test for gh-8684 and gh-8814.
+        image = xp.asarray([[2.0, -1.0, 3.0, 4.0]])
+        kernel = xp.ones((1, 21))
+        result = func(image, kernel, mode='same', boundary=boundary)
+        # The expected results were calculated "by hand".  Because the
+        # kernel is all ones, the same result is expected for convolve2d
+        # and correlate2d.
+        xp_assert_equal(result, xp.asarray(expected))
+
+    @skip_xp_backends("jax.numpy", reason="jax only supports boundary='fill'")
+    def test_boundary_extension_same(self, xp):
+        # Regression test for gh-12686.
+        # Use ndimage.convolve with appropriate arguments to create the
+        # expected result.
+        import scipy.ndimage as ndi
+        a = xp.reshape(xp.arange(1, 10*3+1, dtype=xp.float64), (10, 3))
+        b = xp.reshape(xp.arange(1, 10*10+1, dtype=xp.float64), (10, 10))
+        c = convolve2d(a, b, mode='same', boundary='wrap')
+        xp_assert_equal(c, ndi.convolve(a, b, mode='wrap', origin=(-1, -1)))
+
+    @skip_xp_backends("jax.numpy", reason="jax only supports boundary='fill'")
+    def test_boundary_extension_full(self, xp):
+        # Regression test for gh-12686.
+        # Use ndimage.convolve with appropriate arguments to create the
+        # expected result.
+        import scipy.ndimage as ndi
+        a = xp.reshape(xp.arange(1, 3*3+1, dtype=xp.float64), (3, 3))
+        b = xp.reshape(xp.arange(1, 6*6+1, dtype=xp.float64), (6, 6))
+        c = convolve2d(a, b, mode='full', boundary='wrap')
+
+        a_np = np.arange(1, 3*3 +1, dtype=float).reshape(3, 3)
+        apad_np = np.pad(a_np, ((3, 3), (3, 3)), 'wrap')
+        apad = xp.asarray(apad_np)
+        xp_assert_equal(c, xp.asarray(ndi.convolve(apad, b, mode='wrap')[:-1, :-1]))
+
+    def test_invalid_shapes(self, xp):
+        # By "invalid," we mean that no one
+        # array has dimensions that are all at
+        # least as large as the corresponding
+        # dimensions of the other array. This
+        # setup should throw a ValueError.
+        a = xp.reshape(xp.arange(1, 7), (2, 3))
+        b = xp.reshape(xp.arange(-6, 0), (3, 2))
+
+        assert_raises(ValueError, convolve2d, *(a, b), **{'mode': 'valid'})
+        assert_raises(ValueError, convolve2d, *(b, a), **{'mode': 'valid'})
+
+    @skip_xp_backends("jax.numpy",
+        reason="jax returns floats; scipy returns ints; cf gh-6076")
+    def test_same_mode(self, xp):
+        e = xp.asarray([[1, 2, 3], [3, 4, 5]])
+        f = xp.asarray([[2, 3, 4, 5, 6, 7, 8], [4, 5, 6, 7, 8, 9, 10]])
+        g = convolve2d(e, f, 'same')
+        h = xp.asarray([[22, 28, 34],
+                   [80, 98, 116]])
+        xp_assert_equal(g, h)
+
+    @skip_xp_backends("jax.numpy",
+        reason="jax returns floats; scipy returns ints; cf gh-6076")
+    def test_valid_mode2(self, xp):
+        # See gh-5897
+        e = xp.asarray([[1, 2, 3], [3, 4, 5]])
+        f = xp.asarray([[2, 3, 4, 5, 6, 7, 8], [4, 5, 6, 7, 8, 9, 10]])
+        expected = xp.asarray([[62, 80, 98, 116, 134]])
+
+        out = convolve2d(e, f, 'valid')
+        xp_assert_equal(out, expected)
+
+        out = convolve2d(f, e, 'valid')
+        xp_assert_equal(out, expected)
+
+        e = xp.asarray([[1 + 1j, 2 - 3j], [3 + 1j, 4 + 0j]])
+        f = xp.asarray([[2 - 1j, 3 + 2j, 4 + 0j], [4 - 0j, 5 + 1j, 6 - 3j]])
+        expected = xp.asarray([[27 - 1j, 46. + 2j]])
+
+        out = convolve2d(e, f, 'valid')
+        xp_assert_equal(out, expected)
+
+        # See gh-5897
+        out = convolve2d(f, e, 'valid')
+        xp_assert_equal(out, expected)
+
+    @skip_xp_backends("torch",
+        reason="only integer tensors of a single element can be converted"
+    )
+    def test_consistency_convolve_funcs(self, xp):
+        # Compare np.convolve, signal.convolve, signal.convolve2d
+        a = xp.arange(5)
+        b = xp.asarray([3.2, 1.4, 3])
+        a_np = _xp_copy_to_numpy(a)
+        b_np = _xp_copy_to_numpy(b)
+
+        for mode in ['full', 'valid', 'same']:
+            xp_assert_close(
+                xp.asarray(np.convolve(a_np, b_np, mode=mode)),
+                signal.convolve(a, b, mode=mode)
+            )
+            xp_assert_close(
+                xp.squeeze(
+                    signal.convolve2d(a[None, :], b[None, :], mode=mode),
+                    axis=0
+                ),
+                signal.convolve(a, b, mode=mode)
+            )
+
+    def test_invalid_dims(self, xp):
+        assert_raises(ValueError, convolve2d, 3, 4)
+        assert_raises(ValueError, convolve2d, [3], [4])
+        assert_raises(ValueError, convolve2d, [[[3]]], [[[4]]])
+
+    @pytest.mark.slow
+    @pytest.mark.xfail_on_32bit("Can't create large array for test")
+    @skip_xp_backends(np_only=True, reason="stride_tricks")
+    def test_large_array(self, xp):
+        # Test indexing doesn't overflow an int (gh-10761)
+        n = 2**31 // (1000 * xp.int64().itemsize)
+        _testutils.check_free_memory(2 * n * 1001 * np.int64().itemsize / 1e6)
+
+        # Create a chequered pattern of 1s and 0s
+        a = xp.zeros(1001 * n, dtype=xp.int64)
+        a[::2] = 1
+        a = np.lib.stride_tricks.as_strided(a, shape=(n, 1000), strides=(8008, 8))
+
+        count = signal.convolve2d(a, [[1, 1]])
+        fails = np.where(count > 1)
+        assert fails[0].size == 0
+
+
+@make_xp_test_case(fftconvolve)
+class TestFFTConvolve:
+
+    @pytest.mark.parametrize('axes', ['', None, 0, [0], -1, [-1]])
+    def test_real(self, axes, xp):
+        a = xp.asarray([1, 2, 3])
+        expected = xp.asarray([1, 4, 10, 12, 9.])
+
+        if axes == '':
+            out = fftconvolve(a, a)
+        else:
+            if isinstance(axes, list):
+                axes = tuple(axes)
+            out = fftconvolve(a, a, axes=axes)
+
+        xp_assert_close(out, expected, atol=1.5e-6)
+
+    @pytest.mark.parametrize('axes', [1, [1], -1, [-1]])
+    def test_real_axes(self, axes, xp):
+        a = xp.asarray([1, 2, 3])
+        expected = xp.asarray([1, 4, 10, 12, 9.])
+
+        a = xp.tile(a, (2, 1))
+        expected = xp.tile(expected, (2, 1))
+
+        if isinstance(axes, list):
+            axes = tuple(axes)
+
+        out = fftconvolve(a, a, axes=axes)
+        xp_assert_close(out, expected, atol=1.5e-6)
+
+    @pytest.mark.parametrize('axes', ['', None, 0, [0], -1, [-1]])
+    def test_complex(self, axes, xp):
+        a = xp.asarray([1 + 1j, 2 + 2j, 3 + 3j])
+        expected = xp.asarray([0 + 2j, 0 + 8j, 0 + 20j, 0 + 24j, 0 + 18j])
+
+        if axes == '':
+            out = fftconvolve(a, a)
+        else:
+            if isinstance(axes, list):
+                axes = tuple(axes)
+            out = fftconvolve(a, a, axes=axes)
+        xp_assert_close(out, expected, atol=1.5e-6)
+
+    @pytest.mark.parametrize('axes', [1, [1], -1, [-1]])
+    def test_complex_axes(self, axes, xp):
+        a = xp.asarray([1 + 1j, 2 + 2j, 3 + 3j])
+        expected = xp.asarray([0 + 2j, 0 + 8j, 0 + 20j, 0 + 24j, 0 + 18j])
+
+        a = xp.tile(a, (2, 1))
+        expected = xp.tile(expected, (2, 1))
+
+        if isinstance(axes, list):
+            axes = tuple(axes)
+
+        out = fftconvolve(a, a, axes=axes)
+        xp_assert_close(out, expected, atol=1.5e-6)
+
+    @pytest.mark.parametrize('axes', ['',
+                                      None,
+                                      [0, 1],
+                                      [1, 0],
+                                      [0, -1],
+                                      [-1, 0],
+                                      [-2, 1],
+                                      [1, -2],
+                                      [-2, -1],
+                                      [-1, -2]])
+    def test_2d_real_same(self, axes, xp):
+        a = xp.asarray([[1.0, 2, 3],
+                        [4, 5, 6]])
+        expected = xp.asarray([[1.0, 4, 10, 12, 9],
+                               [8, 26, 56, 54, 36],
+                               [16, 40, 73, 60, 36]])
+
+        if axes == '':
+            out = fftconvolve(a, a)
+        else:
+            if isinstance(axes, list):
+                axes = tuple(axes)
+            out = fftconvolve(a, a, axes=axes)
+        xp_assert_close(out, expected)
+
+    @pytest.mark.parametrize('axes', [[1, 2],
+                                      [2, 1],
+                                      [1, -1],
+                                      [-1, 1],
+                                      [-2, 2],
+                                      [2, -2],
+                                      [-2, -1],
+                                      [-1, -2]])
+    def test_2d_real_same_axes(self, axes, xp):
+        a = xp.asarray([[1, 2, 3],
+                   [4, 5, 6]])
+        expected = xp.asarray([[1, 4, 10, 12, 9],
+                          [8, 26, 56, 54, 36],
+                          [16, 40, 73, 60, 36]])
+
+        a = xp.tile(a, (2, 1, 1))
+        expected = xp.tile(expected, (2, 1, 1))
+
+        if isinstance(axes, list):
+            axes = tuple(axes)
+
+        out = fftconvolve(a, a, axes=axes)
+        xp_assert_close(out, expected, atol=1.5e-6, check_dtype=False)
+
+    @pytest.mark.parametrize('axes', ['',
+                                      None,
+                                      [0, 1],
+                                      [1, 0],
+                                      [0, -1],
+                                      [-1, 0],
+                                      [-2, 1],
+                                      [1, -2],
+                                      [-2, -1],
+                                      [-1, -2]])
+    def test_2d_complex_same(self, axes, xp):
+        a = xp.asarray([[1 + 2j, 3 + 4j, 5 + 6j],
+                   [2 + 1j, 4 + 3j, 6 + 5j]])
+        expected = xp.asarray([
+            [-3 + 4j, -10 + 20j, -21 + 56j, -18 + 76j, -11 + 60j],
+            [10j, 44j, 118j, 156j, 122j],
+            [3 + 4j, 10 + 20j, 21 + 56j, 18 + 76j, 11 + 60j]
+            ])
+
+        if axes == '':
+            out = fftconvolve(a, a)
+        else:
+            if isinstance(axes, list):
+                axes = tuple(axes)
+            out = fftconvolve(a, a, axes=axes)
+
+        xp_assert_close(out, expected, atol=1.5e-6)
+
+    @pytest.mark.parametrize('axes', [[1, 2],
+                                      [2, 1],
+                                      [1, -1],
+                                      [-1, 1],
+                                      [-2, 2],
+                                      [2, -2],
+                                      [-2, -1],
+                                      [-1, -2]])
+    def test_2d_complex_same_axes(self, axes, xp):
+        a = xp.asarray([[1 + 2j, 3 + 4j, 5 + 6j],
+                   [2 + 1j, 4 + 3j, 6 + 5j]])
+        expected = xp.asarray([
+            [-3 + 4j, -10 + 20j, -21 + 56j, -18 + 76j, -11 + 60j],
+            [10j, 44j, 118j, 156j, 122j],
+            [3 + 4j, 10 + 20j, 21 + 56j, 18 + 76j, 11 + 60j]
+            ])
+
+        a = xp.tile(a, (2, 1, 1))
+        expected = xp.tile(expected, (2, 1, 1))
+
+        if isinstance(axes, list):
+            axes = tuple(axes)
+
+        out = fftconvolve(a, a, axes=axes)
+        xp_assert_close(out, expected, atol=1.5e-6)
+
+    @pytest.mark.parametrize('axes', ['', None, 0, [0], -1, [-1]])
+    def test_real_same_mode(self, axes, xp):
+        a = xp.asarray([1, 2, 3])
+        b = xp.asarray([3, 3, 5, 6, 8, 7, 9, 0, 1])
+        expected_1 = xp.asarray([35., 41., 47.])
+        expected_2 = xp.asarray([9., 20., 25., 35., 41., 47., 39., 28., 2.])
+
+        if axes == '':
+            out = fftconvolve(a, b, 'same')
+        else:
+            if isinstance(axes, list):
+                axes = tuple(axes)
+            out = fftconvolve(a, b, 'same', axes=axes)
+        xp_assert_close(out, expected_1)
+
+        if axes == '':
+            out = fftconvolve(b, a, 'same')
+        else:
+            if isinstance(axes, list):
+                axes = tuple(axes)
+            out = fftconvolve(b, a, 'same', axes=axes)
+        xp_assert_close(out, expected_2, atol=1.5e-6)
+
+    @pytest.mark.parametrize('axes', [1, -1, [1], [-1]])
+    def test_real_same_mode_axes(self, axes, xp):
+        a = xp.asarray([1, 2, 3])
+        b = xp.asarray([3, 3, 5, 6, 8, 7, 9, 0, 1])
+        expected_1 = xp.asarray([35., 41., 47.])
+        expected_2 = xp.asarray([9., 20., 25., 35., 41., 47., 39., 28., 2.])
+
+        a = xp.tile(a, (2, 1))
+        b = xp.tile(b, (2, 1))
+        expected_1 = xp.tile(expected_1, (2, 1))
+        expected_2 = xp.tile(expected_2, (2, 1))
+
+        if isinstance(axes, list):
+            axes = tuple(axes)
+
+        out = fftconvolve(a, b, 'same', axes=axes)
+        xp_assert_close(out, expected_1, atol=1.5e-6)
+
+        out = fftconvolve(b, a, 'same', axes=axes)
+        xp_assert_close(out, expected_2, atol=1.5e-6)
+
+    @pytest.mark.parametrize('axes', ['', None, 0, [0], -1, [-1]])
+    def test_valid_mode_real(self, axes, xp):
+        # See gh-5897
+        a = xp.asarray([3, 2, 1])
+        b = xp.asarray([3, 3, 5, 6, 8, 7, 9, 0, 1])
+        expected = xp.asarray([24., 31., 41., 43., 49., 25., 12.])
+
+        if axes == '':
+            out = fftconvolve(a, b, 'valid')
+        else:
+            if isinstance(axes, list):
+                axes = tuple(axes)
+            out = fftconvolve(a, b, 'valid', axes=axes)
+        xp_assert_close(out, expected, atol=1.5e-6)
+
+        if axes == '':
+            out = fftconvolve(b, a, 'valid')
+        else:
+            if isinstance(axes, list):
+                axes = tuple(axes)
+            out = fftconvolve(b, a, 'valid', axes=axes)
+        xp_assert_close(out, expected, atol=1.5e-6)
+
+    @pytest.mark.parametrize('axes', [1, [1]])
+    def test_valid_mode_real_axes(self, axes, xp):
+        # See gh-5897
+        a = xp.asarray([3, 2, 1])
+        b = xp.asarray([3, 3, 5, 6, 8, 7, 9, 0, 1])
+        expected = xp.asarray([24., 31., 41., 43., 49., 25., 12.])
+
+        a = xp.tile(a, (2, 1))
+        b = xp.tile(b, (2, 1))
+        expected = xp.tile(expected, (2, 1))
+
+        if isinstance(axes, list):
+            axes = tuple(axes)
+
+        out = fftconvolve(a, b, 'valid', axes=axes)
+        xp_assert_close(out, expected, atol=1.5e-6)
+
+    @pytest.mark.parametrize('axes', ['', None, 0, [0], -1, [-1]])
+    def test_valid_mode_complex(self, axes, xp):
+        a = xp.asarray([3 - 1j, 2 + 7j, 1 + 0j])
+        b = xp.asarray([3 + 2j, 3 - 3j, 5 + 0j, 6 - 1j, 8 + 0j])
+        expected = xp.asarray([45. + 12.j, 30. + 23.j, 48 + 32.j])
+
+        if axes == '':
+            out = fftconvolve(a, b, 'valid')
+        else:
+            if isinstance(axes, list):
+                axes = tuple(axes)
+            out = fftconvolve(a, b, 'valid', axes=axes)
+        xp_assert_close(out, expected, atol=1.5e-6)
+
+        if axes == '':
+            out = fftconvolve(b, a, 'valid')
+        else:
+            if isinstance(axes, list):
+                axes = tuple(axes)
+            out = fftconvolve(b, a, 'valid', axes=axes)
+        xp_assert_close(out, expected, atol=1.5e-6)
+
+    @pytest.mark.parametrize('axes', [1, [1], -1, [-1]])
+    def test_valid_mode_complex_axes(self, axes, xp):
+        a = xp.asarray([3 - 1j, 2 + 7j, 1 + 0j])
+        b = xp.asarray([3 + 2j, 3 - 3j, 5 + 0j, 6 - 1j, 8 + 0j])
+        expected = xp.asarray([45. + 12.j, 30. + 23.j, 48 + 32.j])
+
+        a = xp.tile(a, (2, 1))
+        b = xp.tile(b, (2, 1))
+        expected = xp.tile(expected, (2, 1))
+
+        if isinstance(axes, list):
+            axes = tuple(axes)
+
+        out = fftconvolve(a, b, 'valid', axes=axes)
+        xp_assert_close(out, expected, atol=1.5e-6)
+
+        out = fftconvolve(b, a, 'valid', axes=axes)
+        xp_assert_close(out, expected, atol=1.5e-6)
+
+    @skip_xp_backends("jax.numpy", reason="mapped axes must have same shape")
+    def test_valid_mode_ignore_nonaxes(self, xp):
+        # See gh-5897
+        a = xp.asarray([3, 2, 1])
+        b = xp.asarray([3, 3, 5, 6, 8, 7, 9, 0, 1])
+        expected = xp.asarray([24., 31., 41., 43., 49., 25., 12.])
+
+        a = xp.tile(a, (2, 1))
+        b = xp.tile(b, (1, 1))
+        expected = xp.tile(expected, (2, 1))
+
+        out = fftconvolve(a, b, 'valid', axes=1)
+        xp_assert_close(out, expected, atol=1.5e-6)
+
+    @xfail_xp_backends("cupy", reason="dtypes do not match")
+    @xfail_xp_backends("jax.numpy", reason="assorted error messages")
+    @pytest.mark.parametrize("a,b", [([], []), ([5, 6], []), ([], [7])])
+    def test_empty(self, a, b, xp):
+        # Regression test for #1745: crashes with 0-length input.
+        xp_assert_equal(
+            fftconvolve(xp.asarray(a), xp.asarray(b)),
+            xp.asarray([]),
+        )
+
+    @skip_xp_backends("jax.numpy", reason="jnp.pad: pad_width with nd=0")
+    def test_zero_rank(self, xp):
+        a = xp.asarray(4967)
+        b = xp.asarray(3920)
+        out = fftconvolve(a, b)
+        xp_assert_equal(out, a * b)
+
+    def test_single_element(self, xp):
+        a = xp.asarray([4967])
+        b = xp.asarray([3920])
+        out = fftconvolve(a, b)
+        xp_assert_equal(out,
+                        xp.asarray(a * b, dtype=out.dtype))
+
+    @pytest.mark.parametrize('axes', ['', None, 0, [0], -1, [-1]])
+    def test_random_data(self, axes, xp):
+        rng = np.random.default_rng(1234)
+        a_np = np.random.rand(1233) + 1j * rng.random(1233)
+        b_np = np.random.rand(1321) + 1j * rng.random(1321)
+        expected = xp.asarray(np.convolve(a_np, b_np, 'full'))
+        a = xp.asarray(a_np)
+        b = xp.asarray(b_np)
+
+        if axes == '':
+            out = fftconvolve(a, b, 'full')
+        else:
+            if isinstance(axes, list):
+                axes = tuple(axes)
+            out = fftconvolve(a, b, 'full', axes=axes)
+        xp_assert_close(out, expected, rtol=1e-10)
+
+    @pytest.mark.parametrize('axes', [1, [1], -1, [-1]])
+    def test_random_data_axes(self, axes, xp):
+        rng = np.random.default_rng(1234)
+        a_np = np.random.rand(1233) + 1j * rng.random(1233)
+        b_np = np.random.rand(1321) + 1j * rng.random(1321)
+        expected = np.convolve(a_np, b_np, 'full')
+        a_np = np.tile(a_np, [2, 1])
+        b_np = np.tile(b_np, [2, 1])
+        expected = xp.asarray(np.tile(expected, [2, 1]))
+
+        a = xp.asarray(a_np)
+        b = xp.asarray(b_np)
+
+        if isinstance(axes, list):
+            axes = tuple(axes)
+
+        out = fftconvolve(a, b, 'full', axes=axes)
+        xp_assert_close(out, expected, rtol=1e-10)
+
+    @xfail_xp_backends(np_only=True, reason="TODO: swapaxes")
+    @pytest.mark.parametrize('axes', [[1, 4],
+                                      [4, 1],
+                                      [1, -1],
+                                      [-1, 1],
+                                      [-4, 4],
+                                      [4, -4],
+                                      [-4, -1],
+                                      [-1, -4]])
+    def test_random_data_multidim_axes(self, axes, xp):
+        a_shape, b_shape = (123, 22), (132, 11)
+        rng = np.random.default_rng(1234)
+        a = xp.asarray(np.random.rand(*a_shape) + 1j * rng.random(a_shape))
+        b = xp.asarray(np.random.rand(*b_shape) + 1j * rng.random(b_shape))
+        expected = convolve2d(a, b, 'full')
+
+        a = a[:, :, None, None, None]
+        b = b[:, :, None, None, None]
+        expected = expected[:, :, None, None, None]
+
+        a = xp.moveaxis(a.swapaxes(0, 2), 1, 4)
+        b = xp.moveaxis(b.swapaxes(0, 2), 1, 4)
+        expected = xp.moveaxis(expected.swapaxes(0, 2), 1, 4)
+
+        # use 1 for dimension 2 in a and 3 in b to test broadcasting
+        a = xp.tile(a, (2, 1, 3, 1, 1))
+        b = xp.tile(b, (2, 1, 1, 4, 1))
+        expected = xp.tile(expected, (2, 1, 3, 4, 1))
+
+        out = fftconvolve(a, b, 'full', axes=axes)
+        xp_assert_close(out, expected, rtol=1e-10, atol=1e-10)
+
+    @pytest.mark.slow
+    @pytest.mark.parametrize(
+        'n',
+        list(range(1, 100)) +
+        list(range(1000, 1500)) +
+        np.random.RandomState(1234).randint(1001, 10000, 5).tolist())
+    def test_many_sizes(self, n, xp):
+        a_np = np.random.rand(n) + 1j * np.random.rand(n)
+        b_np = np.random.rand(n) + 1j * np.random.rand(n)
+        expected = xp.asarray(np.convolve(a_np, b_np, 'full'))
+        a = xp.asarray(a_np)
+        b = xp.asarray(b_np)
+
+        out = fftconvolve(a, b, 'full')
+        xp_assert_close(out, expected, atol=1e-10)
+
+        out = fftconvolve(a, b, 'full', axes=(0,))
+        xp_assert_close(out, expected, atol=1e-10)
+
+    @skip_xp_backends(np_only=True)
+    def test_fft_nan(self, xp):
+        n = 1000
+        rng = np.random.default_rng(43876432987)
+        sig_nan = xp.asarray(rng.standard_normal(n))
+
+        for val in [np.nan, np.inf]:
+            sig_nan[100] = val
+            coeffs = xp.asarray(signal.firwin(200, 0.2))
+
+            msg = "Use of fft convolution.*|invalid value encountered.*"
+            with pytest.warns(RuntimeWarning, match=msg):
+                signal.convolve(sig_nan, coeffs, mode='same', method='fft')
+
+
+def fftconvolve_err(*args, **kwargs):
+    raise RuntimeError('Fell back to fftconvolve')
+
+
+def gen_oa_shapes(sizes):
+    return [(a, b) for a, b in product(sizes, repeat=2)
+            if abs(a - b) > 3]
+
+
+def gen_oa_shapes_2d(sizes):
+    shapes0 = gen_oa_shapes(sizes)
+    shapes1 = gen_oa_shapes(sizes)
+    shapes = [ishapes0+ishapes1 for ishapes0, ishapes1 in
+              zip(shapes0, shapes1)]
+
+    modes = ['full', 'valid', 'same']
+    return [ishapes+(imode,) for ishapes, imode in product(shapes, modes)
+            if imode != 'valid' or
+            (ishapes[0] > ishapes[1] and ishapes[2] > ishapes[3]) or
+            (ishapes[0] < ishapes[1] and ishapes[2] < ishapes[3])]
+
+
+def gen_oa_shapes_eq(sizes):
+    return [(a, b) for a, b in product(sizes, repeat=2)
+            if a >= b]
+
+
+@make_xp_test_case(oaconvolve)
+class TestOAConvolve:
+    @pytest.mark.slow()
+    @pytest.mark.parametrize('shape_a_0, shape_b_0',
+                             gen_oa_shapes_eq(list(range(1, 100, 1)) +
+                                              list(range(100, 1000, 23)))
+                             )
+    def test_real_manylens(self, shape_a_0, shape_b_0, xp):
+        a = np.random.rand(shape_a_0)
+        b = np.random.rand(shape_b_0)
+        expected = xp.asarray(fftconvolve(a, b))
+        a = xp.asarray(a)
+        b = xp.asarray(b)
+
+        out = oaconvolve(a, b)
+
+        assert_array_almost_equal(out, expected)
+
+    @pytest.mark.parametrize('shape_a_0, shape_b_0',
+                             gen_oa_shapes([50, 47, 6, 4, 1]))
+    @pytest.mark.parametrize('is_complex', [True, False])
+    @pytest.mark.parametrize('mode', ['full', 'valid', 'same'])
+    def test_1d_noaxes(self, shape_a_0, shape_b_0,
+                       is_complex, mode, monkeypatch, xp):
+        a = np.random.rand(shape_a_0)
+        b = np.random.rand(shape_b_0)
+        if is_complex:
+            a = a + 1j*np.random.rand(shape_a_0)
+            b = b + 1j*np.random.rand(shape_b_0)
+        expected = xp.asarray(fftconvolve(a, b, mode=mode))
+        a = xp.asarray(a)
+        b = xp.asarray(b)
+
+        monkeypatch.setattr(signal._signaltools, 'fftconvolve',
+                            fftconvolve_err)
+        out = oaconvolve(a, b, mode=mode)
+
+        assert_array_almost_equal(out, expected)
+
+    @pytest.mark.parametrize('axes', [0, 1])
+    @pytest.mark.parametrize('shape_a_0, shape_b_0',
+                             gen_oa_shapes([50, 47, 6, 4]))
+    @pytest.mark.parametrize('shape_a_extra', [1, 3])
+    @pytest.mark.parametrize('shape_b_extra', [1, 3])
+    @pytest.mark.parametrize('is_complex', [True, False])
+    @pytest.mark.parametrize('mode', ['full', 'valid', 'same'])
+    def test_1d_axes(self, axes, shape_a_0, shape_b_0,
+                     shape_a_extra, shape_b_extra,
+                     is_complex, mode, monkeypatch, xp):
+        ax_a = [shape_a_extra]*2
+        ax_b = [shape_b_extra]*2
+        ax_a[axes] = shape_a_0
+        ax_b[axes] = shape_b_0
+
+        a = np.random.rand(*ax_a)
+        b = np.random.rand(*ax_b)
+        if is_complex:
+            a = a + 1j*np.random.rand(*ax_a)
+            b = b + 1j*np.random.rand(*ax_b)
+
+        expected = xp.asarray(fftconvolve(a, b, mode=mode, axes=axes))
+        a = xp.asarray(a)
+        b = xp.asarray(b)
+
+        monkeypatch.setattr(signal._signaltools, 'fftconvolve',
+                            fftconvolve_err)
+        out = oaconvolve(a, b, mode=mode, axes=axes)
+
+        assert_array_almost_equal(out, expected)
+
+    @pytest.mark.parametrize('shape_a_0, shape_b_0, '
+                             'shape_a_1, shape_b_1, mode',
+                             gen_oa_shapes_2d([50, 47, 6, 4]))
+    @pytest.mark.parametrize('is_complex', [True, False])
+    def test_2d_noaxes(self, shape_a_0, shape_b_0,
+                       shape_a_1, shape_b_1, mode,
+                       is_complex, monkeypatch, xp):
+        a = np.random.rand(shape_a_0, shape_a_1)
+        b = np.random.rand(shape_b_0, shape_b_1)
+        if is_complex:
+            a = a + 1j*np.random.rand(shape_a_0, shape_a_1)
+            b = b + 1j*np.random.rand(shape_b_0, shape_b_1)
+
+        expected = xp.asarray(fftconvolve(a, b, mode=mode))
+        a = xp.asarray(a)
+        b = xp.asarray(b)
+
+        monkeypatch.setattr(signal._signaltools, 'fftconvolve',
+                            fftconvolve_err)
+        out = oaconvolve(a, b, mode=mode)
+
+        assert_array_almost_equal(out, expected)
+
+    @pytest.mark.parametrize('axes', [[0, 1], [0, 2], [1, 2]])
+    @pytest.mark.parametrize('shape_a_0, shape_b_0, '
+                             'shape_a_1, shape_b_1, mode',
+                             gen_oa_shapes_2d([50, 47, 6, 4]))
+    @pytest.mark.parametrize('shape_a_extra', [1, 3])
+    @pytest.mark.parametrize('shape_b_extra', [1, 3])
+    @pytest.mark.parametrize('is_complex', [True, False])
+    def test_2d_axes(self, axes, shape_a_0, shape_b_0,
+                     shape_a_1, shape_b_1, mode,
+                     shape_a_extra, shape_b_extra,
+                     is_complex, monkeypatch, xp):
+        ax_a = [shape_a_extra]*3
+        ax_b = [shape_b_extra]*3
+        ax_a[axes[0]] = shape_a_0
+        ax_b[axes[0]] = shape_b_0
+        ax_a[axes[1]] = shape_a_1
+        ax_b[axes[1]] = shape_b_1
+
+        a = np.random.rand(*ax_a)
+        b = np.random.rand(*ax_b)
+        if is_complex:
+            a = a + 1j*np.random.rand(*ax_a)
+            b = b + 1j*np.random.rand(*ax_b)
+
+        axes = tuple(axes)   # XXX for CuPy
+        expected = xp.asarray(fftconvolve(a, b, mode=mode, axes=axes))
+        a = xp.asarray(a)
+        b = xp.asarray(b)
+
+        monkeypatch.setattr(signal._signaltools, 'fftconvolve',
+                            fftconvolve_err)
+        out = oaconvolve(a, b, mode=mode, axes=axes)
+
+        assert_array_almost_equal(out, expected)
+
+    @xfail_xp_backends("torch", reason="ValueError: Target length must be positive")
+    @pytest.mark.parametrize("a,b", [([], []), ([5, 6], []), ([], [7])])
+    def test_empty(self, a, b, xp):
+        # Regression test for #1745: crashes with 0-length input.
+        xp_assert_equal(
+            oaconvolve(xp.asarray(a), xp.asarray(b)),
+            xp.asarray([]), check_dtype=False
+        )
+
+    def test_zero_rank(self, xp):
+        a = xp.asarray(4967)
+        b = xp.asarray(3920)
+        out = oaconvolve(a, b)
+        xp_assert_equal(out, a * b)
+
+    def test_single_element(self, xp):
+        a = xp.asarray([4967])
+        b = xp.asarray([3920])
+        out = oaconvolve(a, b)
+        xp_assert_equal(out, a * b)
+
+
+@skip_xp_backends(np_only=True, reason="assertions may differ on backends")
+@pytest.mark.parametrize('convapproach',
+                         [make_xp_pytest_param(fftconvolve),
+                          make_xp_pytest_param(oaconvolve)])
+class TestAllFreqConvolves:
+
+    def test_invalid_shapes(self, convapproach, xp):
+        a = np.arange(1, 7).reshape((2, 3))
+        b = np.arange(-6, 0).reshape((3, 2))
+        with assert_raises(ValueError,
+                           match="For 'valid' mode, one must be at least "
+                           "as large as the other in every dimension"):
+            convapproach(a, b, mode='valid')
+
+    def test_invalid_shapes_axes(self, convapproach, xp):
+        a = np.zeros([5, 6, 2, 1])
+        b = np.zeros([5, 6, 3, 1])
+        with assert_raises(ValueError,
+                           match=r"incompatible shapes for in1 and in2:"
+                           r" \(5L?, 6L?, 2L?, 1L?\) and"
+                           r" \(5L?, 6L?, 3L?, 1L?\)"):
+            convapproach(a, b, axes=[0, 1])
+
+    @pytest.mark.parametrize('a,b',
+                             [([1], 2),
+                              (1, [2]),
+                              ([3], [[2]])])
+    def test_mismatched_dims(self, a, b, convapproach, xp):
+        with assert_raises(ValueError,
+                           match="in1 and in2 should have the same"
+                           " dimensionality"):
+            convapproach(a, b)
+
+    def test_invalid_flags(self, convapproach, xp):
+        with assert_raises(ValueError,
+                           match="acceptable mode flags are 'valid',"
+                           " 'same', or 'full'"):
+            convapproach([1], [2], mode='chips')
+
+        with assert_raises(ValueError,
+                           match="when provided, axes cannot be empty"):
+            convapproach([1], [2], axes=[])
+
+        with assert_raises(ValueError, match="axes must be a scalar or "
+                           "iterable of integers"):
+            convapproach([1], [2], axes=[[1, 2], [3, 4]])
+
+        with assert_raises(ValueError, match="axes must be a scalar or "
+                           "iterable of integers"):
+            convapproach([1], [2], axes=[1., 2., 3., 4.])
+
+        with assert_raises(ValueError,
+                           match="axes exceeds dimensionality of input"):
+            convapproach([1], [2], axes=[1])
+
+        with assert_raises(ValueError,
+                           match="axes exceeds dimensionality of input"):
+            convapproach([1], [2], axes=[-2])
+
+        with assert_raises(ValueError,
+                           match="all axes must be unique"):
+            convapproach([1], [2], axes=[0, 0])
+
+
+@skip_xp_backends(np_only=True, reason="assertions may differ on backends")
+@pytest.mark.filterwarnings('ignore::DeprecationWarning')
+@pytest.mark.parametrize('dtype', [np.longdouble, np.clongdouble])
+@make_xp_test_case(convolve, fftconvolve)
+def test_convolve_longdtype_input(dtype, xp):
+    x = np.random.random((27, 27)).astype(dtype)
+    y = np.random.random((4, 4)).astype(dtype)
+    if np.iscomplexobj(dtype()):
+        x += .1j
+        y -= .1j
+
+    res = fftconvolve(x, y)
+    xp_assert_close(res, convolve(x, y, method='direct'))
+    assert res.dtype == dtype
+
+
+class TestMedFilt:
+
+    IN = [[50, 50, 50, 50, 50, 92, 18, 27, 65, 46],
+          [50, 50, 50, 50, 50, 0, 72, 77, 68, 66],
+          [50, 50, 50, 50, 50, 46, 47, 19, 64, 77],
+          [50, 50, 50, 50, 50, 42, 15, 29, 95, 35],
+          [50, 50, 50, 50, 50, 46, 34, 9, 21, 66],
+          [70, 97, 28, 68, 78, 77, 61, 58, 71, 42],
+          [64, 53, 44, 29, 68, 32, 19, 68, 24, 84],
+          [3, 33, 53, 67, 1, 78, 74, 55, 12, 83],
+          [7, 11, 46, 70, 60, 47, 24, 43, 61, 26],
+          [32, 61, 88, 7, 39, 4, 92, 64, 45, 61]]
+
+    OUT = [[0, 50, 50, 50, 42, 15, 15, 18, 27, 0],
+           [0, 50, 50, 50, 50, 42, 19, 21, 29, 0],
+           [50, 50, 50, 50, 50, 47, 34, 34, 46, 35],
+           [50, 50, 50, 50, 50, 50, 42, 47, 64, 42],
+           [50, 50, 50, 50, 50, 50, 46, 55, 64, 35],
+           [33, 50, 50, 50, 50, 47, 46, 43, 55, 26],
+           [32, 50, 50, 50, 50, 47, 46, 45, 55, 26],
+           [7, 46, 50, 50, 47, 46, 46, 43, 45, 21],
+           [0, 32, 33, 39, 32, 32, 43, 43, 43, 0],
+           [0, 7, 11, 7, 4, 4, 19, 19, 24, 0]]
+
+    KERNEL_SIZE = [7,3]
+
+    @make_xp_test_case(signal.medfilt, signal.medfilt2d)
+    def test_basic(self, xp):
+
+        in_ = xp.asarray(self.IN)
+        out_ = xp.asarray(self.OUT)
+        kernel_size = xp.asarray(self.KERNEL_SIZE)
+
+        d = signal.medfilt(in_, kernel_size)
+        e = signal.medfilt2d(xp.asarray(in_, dtype=xp.float64), kernel_size)
+        xp_assert_equal(d, out_)
+        xp_assert_equal(d, e, check_dtype=False)
+
+    @pytest.mark.parametrize('dtype', ["uint8", "int8", "uint16", "int16",
+                                       "uint32", "int32", "uint64", "int64",
+                                       "float32", "float64"])
+    @make_xp_test_case(signal.medfilt, signal.medfilt2d)
+    def test_types(self, dtype, xp):
+        # volume input and output types match
+        if is_torch(xp) and dtype in ["uint16", "uint32", "uint64"]:
+            pytest.skip("torch does not support unisigned ints")
+
+        dtype = getattr(xp, dtype)
+        in_typed = xp.asarray(self.IN, dtype=dtype)
+        assert signal.medfilt(in_typed).dtype == dtype
+        assert signal.medfilt2d(in_typed).dtype == dtype
+
+    @skip_xp_backends(np_only=True, reason="assertions may differ")
+    @pytest.mark.parametrize('dtype', [np.bool_, np.complex64, np.complex128,
+                                       np.clongdouble, np.float16,
+                                       "float96", "float128"])
+    @make_xp_test_case(signal.medfilt, signal.medfilt2d)
+    def test_invalid_dtypes(self, dtype, xp):
+        # We can only test this on platforms that support a native type of float96 or
+        # float128; comparing to np.longdouble allows us to filter out non-native types
+        if (dtype in ["float96", "float128"]
+                and np.finfo(np.longdouble).dtype != dtype):
+            pytest.skip(f"Platform does not support {dtype}")
+
+        in_typed = np.array(self.IN, dtype=dtype)
+        with pytest.raises(ValueError, match="not supported"):
+            signal.medfilt(in_typed)
+
+        with pytest.raises(ValueError, match="not supported"):
+            signal.medfilt2d(in_typed)
+
+    @skip_xp_backends(np_only=True, reason="object arrays")
+    @make_xp_test_case(signal.medfilt)
+    def test_none(self, xp):
+        # gh-1651, trac #1124. Ensure this does not segfault.
+        with assert_raises((ValueError, TypeError)):
+            signal.medfilt(None)
+
+    @skip_xp_backends(np_only=True, reason="strides are only writeable in NumPy")
+    @make_xp_test_case(signal.medfilt)
+    def test_odd_strides(self, xp):
+        # Avoid a regression with possible contiguous
+        # numpy arrays that have odd strides. The stride value below gets
+        # us into wrong memory if used (but it does not need to be used)
+        dummy = xp.arange(10, dtype=xp.float64)
+        a = dummy[5:6]
+        a = np.lib.stride_tricks.as_strided(a, strides=(16,))
+        xp_assert_close(signal.medfilt(a, 1),  xp.asarray([5.]))
+
+    @skip_xp_backends(
+        "jax.numpy",
+        reason="chunk assignment does not work on jax immutable arrays"
+    )
+    @pytest.mark.parametrize("dtype", ["uint8", "float32", "float64"])
+    @make_xp_test_case(signal.medfilt2d)
+    def test_medfilt2d_parallel(self, dtype, xp):
+        dtype = getattr(xp, dtype)
+        in_typed = xp.asarray(self.IN, dtype=dtype)
+        expected = xp.asarray(self.OUT, dtype=dtype)
+
+        # This is used to simplify the indexing calculations.
+        assert in_typed.shape == expected.shape
+
+        # We'll do the calculation in four chunks. M1 and N1 are the dimensions
+        # of the first output chunk. We have to extend the input by half the
+        # kernel size to be able to calculate the full output chunk.
+        M1 = expected.shape[0] // 2
+        N1 = expected.shape[1] // 2
+        offM = self.KERNEL_SIZE[0] // 2 + 1
+        offN = self.KERNEL_SIZE[1] // 2 + 1
+
+        def apply(chunk):
+            # in = slice of in_typed to use.
+            # sel = slice of output to crop it to the correct region.
+            # out = slice of output array to store in.
+            M, N = chunk
+            if M == 0:
+                Min = slice(0, M1 + offM)
+                Msel = slice(0, -offM)
+                Mout = slice(0, M1)
+            else:
+                Min = slice(M1 - offM, None)
+                Msel = slice(offM, None)
+                Mout = slice(M1, None)
+            if N == 0:
+                Nin = slice(0, N1 + offN)
+                Nsel = slice(0, -offN)
+                Nout = slice(0, N1)
+            else:
+                Nin = slice(N1 - offN, None)
+                Nsel = slice(offN, None)
+                Nout = slice(N1, None)
+
+            # Do the calculation, but do not write to the output in the threads.
+            chunk_data = in_typed[Min, Nin]
+            med = signal.medfilt2d(chunk_data, self.KERNEL_SIZE)
+            return med[Msel, Nsel], Mout, Nout
+
+        # Give each chunk to a different thread.
+        output = xp.zeros_like(expected)
+        with ThreadPoolExecutor(max_workers=4) as pool:
+            chunks = {(0, 0), (0, 1), (1, 0), (1, 1)}
+            futures = {pool.submit(apply, chunk) for chunk in chunks}
+
+            # Store each result in the output as it arrives.
+            for future in as_completed(futures):
+                data, Mslice, Nslice = future.result()
+                output[Mslice, Nslice] = data
+
+        xp_assert_equal(output, expected)
+
+
+@make_xp_test_case(signal.wiener)
+class TestWiener:
+
+    @skip_xp_backends("cupy", reason="XXX: can_cast in cupy <= 13.2")
+    def test_basic(self, xp):
+        g = xp.asarray([[5, 6, 4, 3],
+                        [3, 5, 6, 2],
+                        [2, 3, 5, 6],
+                        [1, 6, 9, 7]], dtype=xp.float64)
+        h = xp.asarray([[2.16374269, 3.2222222222, 2.8888888889, 1.6666666667],
+                        [2.666666667, 4.33333333333, 4.44444444444, 2.8888888888],
+                        [2.222222222, 4.4444444444, 5.4444444444, 4.801066874837],
+                        [1.33333333333, 3.92735042735, 6.0712560386, 5.0404040404]])
+        assert_array_almost_equal(signal.wiener(g), h, decimal=6)
+        assert_array_almost_equal(signal.wiener(g, mysize=3), h, decimal=6)
+
+
+padtype_options = ["mean", "median", "minimum", "maximum", "line"]
+padtype_options += _upfirdn_modes
+
+
+class TestResample:
+
+    @make_xp_test_case(signal.resample, signal.resample_poly)
+    @xfail_xp_backends("cupy", reason="does not raise with non-int upsampling factor")
+    def test_basic(self, xp):
+        # Some basic tests
+
+        # Regression test for issue #3603.
+        # window.shape must equal to sig.shape[0]
+        sig = xp.arange(128, dtype=xp.float64)
+        num = 256
+        win = signal.get_window(('kaiser', 8.0), 160, xp=xp)
+        assert_raises(ValueError, signal.resample, sig, num, window=win)
+        assert_raises(ValueError, signal.resample, sig, num, domain='INVALID')
+
+        # Other degenerate conditions
+        assert_raises(ValueError, signal.resample_poly, sig, 'yo', 1)
+        assert_raises(ValueError, signal.resample_poly, sig, 1, 0)
+        assert_raises(ValueError, signal.resample_poly, sig, 1.3, 2)
+        assert_raises(ValueError, signal.resample_poly, sig, 2, 1.3)
+        assert_raises(ValueError, signal.resample_poly, sig, 2, 1, padtype='')
+        assert_raises(ValueError, signal.resample_poly, sig, 2, 1,
+                      padtype='mean', cval=10)
+        assert_raises(ValueError, signal.resample_poly, sig, 2, 1, window=xp.eye(2))
+
+        # test for issue #6505 - should not modify window.shape when axis ≠ 0
+        sig2 = xp.tile(xp.arange(160, dtype=xp.float64), (2, 1))
+        signal.resample(sig2, num, axis=-1, window=win)
+        assert win.shape == (160,)
+
+        # Ensure coverage for parameter cval=None and cval != None:
+        x_ref = signal.resample_poly(sig, 2, 1)
+        x0 = signal.resample_poly(sig, 2, 1, padtype='constant')
+        x1 = signal.resample_poly(sig, 2, 1, padtype='constant', cval=0)
+        xp_assert_equal(x1, x_ref)
+        xp_assert_equal(x0, x_ref)
+
+    @pytest.mark.parametrize('window', (None, 'hamming'))
+    @pytest.mark.parametrize('N', (20, 19))
+    @pytest.mark.parametrize('num', (100, 101, 10, 11))
+    @make_xp_test_case(signal.resample)
+    def test_rfft(self, N, num, window, xp):
+        # Make sure the speed up using rfft gives the same result as the normal
+        # way using fft
+        dt_r = xp_default_dtype(xp)
+        dt_c = xp.complex64 if dt_r == xp.float32 else xp.complex128
+
+        x = xp.linspace(0, 10, N, endpoint=False)
+        y = xp.cos(-x**2/6.0)
+        desired = signal.resample(xp.astype(y, dt_c), num, window=window)
+        xp_assert_close(signal.resample(y, num, window=window),
+                        xp.real(desired))
+
+        y = xp.stack([xp.cos(-x**2/6.0), xp.sin(-x**2/6.0)])
+        y_complex = xp.astype(y, dt_c)
+        resampled = signal.resample(y_complex, num, axis=1, window=window)
+
+        atol = 1e-9 if dt_r == xp.float64 else 3e-7
+
+        xp_assert_close(
+            signal.resample(y, num, axis=1, window=window),
+            xp.real(resampled),
+            atol=atol)
+
+    @make_xp_test_case(signal.resample)
+    def test_input_domain(self, xp):
+        # Test if both input domain modes produce the same results.
+        tsig = xp.astype(xp.arange(256), xp.complex128)
+        fsig = sp_fft.fft(tsig)
+        num = 256
+        xp_assert_close(
+            signal.resample(fsig, num, domain='freq'),
+            signal.resample(tsig, num, domain='time'),
+            atol=1e-9)
+
+    @pytest.mark.parametrize('nx', (1, 2, 3, 5, 8))
+    @pytest.mark.parametrize('ny', (1, 2, 3, 5, 8))
+    @pytest.mark.parametrize('dtype', ('float64', 'complex128'))
+    @make_xp_test_case(signal.resample)
+    def test_dc(self, nx, ny, dtype, xp):
+        dtype = getattr(xp, dtype)
+        x = xp.asarray([1] * nx, dtype=dtype)
+        y = signal.resample(x, ny)
+        xp_assert_close(y, xp.asarray([1] * ny, dtype=y.dtype))
+
+    @skip_xp_backends("cupy", reason="padtype not supported by upfirdn")
+    @pytest.mark.parametrize('padtype', padtype_options)
+    @make_xp_test_case(signal.resample_poly)
+    def test_mutable_window(self, padtype, xp):
+        # Test that a mutable window is not modified
+        impulse = xp.zeros(3)
+        window = xp.asarray(np.random.RandomState(0).randn(2))
+        window_orig = xp.asarray(window, copy=True)
+        signal.resample_poly(impulse, 5, 1, window=window, padtype=padtype)
+        xp_assert_equal(window, window_orig)
+
+    @skip_xp_backends("cupy", reason="padtype not supported by upfirdn")
+    @make_xp_test_case(signal.resample_poly)
+    @pytest.mark.parametrize('padtype', padtype_options)
+    def test_output_float32(self, padtype, xp):
+        # Test that float32 inputs yield a float32 output
+        x = xp.arange(10, dtype=xp.float32)
+        h = xp.asarray([1, 1, 1], dtype=xp.float32)
+        y = signal.resample_poly(x, 1, 2, window=h, padtype=padtype)
+        assert y.dtype == xp.float32
+
+    @pytest.mark.parametrize('padtype', padtype_options)
+    @pytest.mark.parametrize('dtype', ['float32', 'float64'])
+    @skip_xp_backends("cupy", reason="padtype not supported by upfirdn")
+    @make_xp_test_case(signal.resample_poly)
+    def test_output_match_dtype(self, padtype, dtype, xp):
+        # Test that the dtype of x is preserved per issue #14733
+        dtype = getattr(xp, dtype)
+        x = xp.arange(10, dtype=dtype)
+        y = signal.resample_poly(x, 1, 2, padtype=padtype)
+        assert y.dtype == x.dtype
+
+    @skip_xp_backends("cupy", reason="padtype not supported by upfirdn")
+    @pytest.mark.parametrize(
+        "method, ext, padtype",
+        [("fft", False, None)]
+        + list(
+            product(
+                ["polyphase"], [False, True], padtype_options,
+            )
+        ),
+    )
+    @make_xp_test_case(signal.resample, signal.resample_poly)
+    def test_resample_methods(self, method, ext, padtype, xp):
+        # Test resampling of sinusoids and random noise (1-sec)
+        rate = 100
+        rates_to = [49, 50, 51, 99, 100, 101, 199, 200, 201]
+
+        # Sinusoids, windowed to avoid edge artifacts
+        t = xp.arange(rate, dtype=xp.float64) / float(rate)
+        freqs = xp.asarray((1., 10., 40.))[:, xp.newaxis]
+        x = xp.sin(2 * xp.pi * freqs * t) * hann(rate, xp=xp)
+
+        for rate_to in rates_to:
+            t_to = xp.arange(rate_to, dtype=xp.float64) / float(rate_to)
+            y_tos = xp.sin(2 * xp.pi * freqs * t_to) * hann(rate_to, xp=xp)
+            if method == 'fft':
+                y_resamps = signal.resample(x, rate_to, axis=-1)
+            else:
+                if ext and rate_to != rate:
+                    # Match default window design
+                    g = gcd(rate_to, rate)
+                    up = rate_to // g
+                    down = rate // g
+                    max_rate = max(up, down)
+                    f_c = 1. / max_rate
+                    half_len = 10 * max_rate
+                    window = signal.firwin(2 * half_len + 1, f_c,
+                                           window=('kaiser', 5.0))
+                    window = xp.asarray(window)
+                    polyargs = {'window': window, 'padtype': padtype}
+                else:
+                    polyargs = {'padtype': padtype}
+
+                y_resamps = signal.resample_poly(x, rate_to, rate, axis=-1,
+                                                 **polyargs)
+
+            for i in range(y_tos.shape[0]):
+                y_to = y_tos[i, :]
+                y_resamp = y_resamps[i, :]
+                freq = float(freqs[i, 0])
+                if freq >= 0.5 * rate_to:
+                    #y_to.fill(0.)  # mostly low-passed away
+                    y_to = xp.zeros_like(y_to)  # mostly low-passed away
+                    if padtype in ['minimum', 'maximum']:
+                        xp_assert_close(y_resamp, y_to, atol=3e-1)
+                    else:
+                        xp_assert_close(y_resamp, y_to, atol=1e-3)
+                else:
+                    assert y_to.shape == y_resamp.shape
+                    corr = np.corrcoef(y_to, y_resamp)[0, 1]
+                    assert corr > 0.99, (corr, rate, rate_to)
+
+        # Random data
+        rng = np.random.RandomState(0)
+        x = hann(rate) * np.cumsum(rng.randn(rate))  # low-pass, wind
+        x = xp.asarray(x)
+        for rate_to in rates_to:
+            # random data
+            t_to = xp.arange(rate_to, dtype=xp.float64) / float(rate_to)
+            y_to = np.interp(t_to, t, x)
+            if method == 'fft':
+                y_resamp = signal.resample(x, rate_to)
+            else:
+                y_resamp = signal.resample_poly(x, rate_to, rate,
+                                                padtype=padtype)
+            assert y_to.shape == y_resamp.shape
+            corr = xp.asarray(np.corrcoef(y_to, y_resamp)[0, 1])
+            assert corr > 0.99, corr
+
+        # More tests of fft method (Master 0.18.1 fails these)
+        if method == 'fft':
+            x1 = xp.asarray([1.+0.j, 0.+0.j])
+            y1_test = signal.resample(x1, 4)
+            # upsampling a complex array
+            y1_true = xp.asarray([1.+0.j, 0.5+0.j, 0.+0.j, 0.5+0.j])
+            xp_assert_close(y1_test, y1_true, atol=1e-12)
+            x2 = xp.asarray([1., 0.5, 0., 0.5])
+            y2_test = signal.resample(x2, 2)  # downsampling a real array
+            y2_true = xp.asarray([1., 0.])
+            xp_assert_close(y2_test, y2_true, atol=1e-12)
+
+    @pytest.mark.parametrize("n_in", (8, 9))
+    @pytest.mark.parametrize("n_out", (3, 4))
+    @make_xp_test_case(signal.resample)
+    def test_resample_win_func(self, n_in, n_out):
+        """Test callable window function. """
+        x_in = np.ones(n_in)
+
+        def win(freqs):
+            """Scale input by 1/2"""
+            return 0.5 * np.ones_like(freqs)
+
+        y0 = signal.resample(x_in, n_out)
+        y1 = signal.resample(x_in, n_out, window=win)
+
+        xp_assert_close(2*y1, y0, atol=1e-12)
+
+    @pytest.mark.parametrize("n_in", (6, 12))
+    @pytest.mark.parametrize("n_out", (3, 4))
+    @make_xp_test_case(signal.resample)
+    def test__resample_param_t(self, n_in, n_out):
+        """Verify behavior for parameter `t`.
+
+        Note that only `t[0]` and `t[1]` are utilized.
+        """
+        t0, dt = 10, 2
+        x_in = np.ones(n_in)
+
+        y0 = signal.resample(x_in, n_out)
+        y1, t1 = signal.resample(x_in, n_out, t=[t0, t0+dt])
+        t_ref = 10 + np.arange(len(y0)) * dt * n_in / n_out
+
+        xp_assert_equal(y1, y0)  # no influence of `t`
+        xp_assert_close(t1, t_ref, atol=1e-12)
+
+    @pytest.mark.parametrize("n1", (2, 3, 7, 8))
+    @pytest.mark.parametrize("n0", (2, 3, 7, 8))
+    @make_xp_test_case(signal.resample)
+    def test_resample_nyquist(self, n0, n1):
+        """Test behavior at Nyquist frequency to ensure issue #14569 is fixed. """
+        f_ny = min(n0, n1) // 2
+        tt = (np.arange(n_) / n_ for n_ in (n0, n1))
+        x0, x1 = (np.cos(2 * np.pi * f_ny * t_) for t_ in tt)
+
+        y1_r = signal.resample(x0, n1)
+        y1_c = signal.resample(x0 + 0j, n1)
+
+        xp_assert_close(y1_r, x1, atol=1e-12)
+        xp_assert_close(y1_c.real, x1, atol=1e-12)
+
+    @pytest.mark.parametrize('down_factor', [2, 11, 79])
+    @pytest.mark.parametrize("dtype", [int, np.float32, np.complex64, float, complex])
+    @make_xp_test_case(signal.resample_poly)
+    def test_poly_vs_filtfilt(self, down_factor, dtype, xp):
+        # Check that up=1.0 gives same answer as filtfilt + slicing
+        random_state = np.random.RandomState(17)
+        size = 10000
+
+        x = random_state.randn(size).astype(dtype)
+        if dtype in (np.complex64, np.complex128):
+            x += 1j * random_state.randn(size)
+
+        # resample_poly assumes zeros outside of signl, whereas filtfilt
+        # can only constant-pad. Make them equivalent:
+        x[0] = 0
+        x[-1] = 0
+
+        h = signal.firwin(31, 1. / down_factor, window='hamming')
+        yf = filtfilt(h, 1.0, x, padtype='constant')[::down_factor]
+
+        # Need to pass convolved version of filter to resample_poly,
+        # since filtfilt does forward and backward, but resample_poly
+        # only goes forward
+        hc = convolve(h, np.flip(h))
+
+        # Use yf.copy() to avoid negative strides, which are unsupported
+        # in torch.
+        x, hc, yf = map(xp.asarray, (x, hc, yf.copy()))
+        y = signal.resample_poly(x, 1, down_factor, window=hc)
+        xp_assert_close(yf, y, atol=3e-7, rtol=6e-7)
+
+    @make_xp_test_case(signal.resample_poly)
+    def test_correlate1d(self, xp):
+        for down in [2, 4]:
+            for nx in range(1, 40, down):
+                for nweights in (32, 33):
+                    x = np.random.random((nx,))
+                    weights = np.random.random((nweights,))
+                    y_g = correlate1d(x, np.flip(weights), mode='constant')
+                    x, weights, y_g = map(xp.asarray, (x, weights, y_g))
+                    y_s = signal.resample_poly(
+                        x, up=1, down=down, window=weights)
+                    xp_assert_close(y_g[::down], y_s)
+
+    @make_xp_test_case(signal.resample_poly)
+    @pytest.mark.parametrize('dtype', ['int32', 'float32'])
+    @skip_xp_backends("cupy", reason="padtype not supported by upfirdn")
+    def test_gh_15620(self, dtype, xp):
+        dtype = getattr(xp, dtype)
+        data = xp.asarray([0, 1, 2, 3, 2, 1, 0], dtype=dtype)
+        actual = signal.resample_poly(data,
+                                      up=2,
+                                      down=1,
+                                      padtype='smooth')
+        assert np.count_nonzero(actual) > 0
+
+
+@make_xp_test_case(signal.cspline1d_eval)
+class TestCSpline1DEval:
+
+    def test_basic(self, xp):
+        y = np.asarray([1, 2, 3, 4, 3, 2, 1, 2, 3.0])
+        x = np.arange(y.shape[0])
+        dx = x[1] - x[0]
+        cj = xp.asarray(signal.cspline1d(y))
+        x2 = xp.arange(len(y) * 10.0) / 10.0
+        y2 = signal.cspline1d_eval(cj, x2, dx=dx, x0=x[0])
+
+        # make sure interpolated values are on knot points
+        assert_array_almost_equal(y2[::10], xp.asarray(y), decimal=5)
+
+    def test_complex(self, xp):
+        #  create some smoothly varying complex signal to interpolate
+        x = np.arange(2.0)
+        y = np.zeros(x.shape, dtype=np.complex64)
+        T = 10.0
+        f = 1.0 / T
+        y = np.exp(2.0J * np.pi * f * x)
+
+        # get the cspline transform
+        cy = xp.asarray(signal.cspline1d(y))
+
+        # determine new test x value and interpolate
+        xnew = xp.asarray([0.5])
+        ynew = signal.cspline1d_eval(cy, xnew)
+
+        assert ynew.dtype == xp.asarray(y).dtype
+
+
+@make_xp_test_case(signal.order_filter)
+class TestOrderFilt:
+
+    def test_basic(self, xp):
+        actual = signal.order_filter(xp.asarray([1, 2, 3]), xp.asarray([1, 0, 1]), 1)
+        expect = xp.asarray([2, 3, 2])
+        xp_assert_equal(actual, expect)
+
+    def test_doc_example(self, xp):
+        x = xp.reshape(xp.arange(25, dtype=xp_default_dtype(xp)), (5, 5))
+        domain = xp.eye(3, dtype=xp_default_dtype(xp))
+
+        # minimum of elements 1,3,9 (zero-padded) on phone pad
+        # 7,5,3 on numpad
+        expected = xp.asarray(
+            [[0., 0., 0., 0., 0.],
+             [0., 0., 1., 2., 0.],
+             [0., 5., 6., 7., 0.],
+             [0., 10., 11., 12., 0.],
+             [0., 0., 0., 0., 0.]],
+            dtype=xp_default_dtype(xp)
+        )
+        xp_assert_close(signal.order_filter(x, domain, 0), expected)
+
+        # maximum of elements 1,3,9 (zero-padded) on phone pad
+        # 7,5,3 on numpad
+        expected = xp.asarray(
+            [[6., 7., 8., 9., 4.],
+             [11., 12., 13., 14., 9.],
+             [16., 17., 18., 19., 14.],
+             [21., 22., 23., 24., 19.],
+             [20., 21., 22., 23., 24.]],
+        )
+        xp_assert_close(signal.order_filter(x, domain, 2), expected)
+
+        # and, just to complete the set, median of zero-padded elements
+        expected = xp.asarray(
+            [[0, 1, 2, 3, 0],
+             [5, 6, 7, 8, 3],
+             [10, 11, 12, 13, 8],
+             [15, 16, 17, 18, 13],
+             [0, 15, 16, 17, 18]],
+            dtype=xp_default_dtype(xp)
+        )
+        xp_assert_close(signal.order_filter(x, domain, 1), expected)
+
+    @xfail_xp_backends('dask.array', reason='repeat requires an axis')
+    @xfail_xp_backends('torch', reason='array-api-compat#292')
+    @make_xp_test_case(signal.medfilt)
+    def test_medfilt_order_filter(self, xp):
+        x = xp.reshape(xp.arange(25), (5, 5))
+
+        # median of zero-padded elements 1,5,9 on phone pad
+        # 7,5,3 on numpad
+        expected = xp.asarray(
+            [[0, 1, 2, 3, 0],
+             [1, 6, 7, 8, 4],
+             [6, 11, 12, 13, 9],
+             [11, 16, 17, 18, 14],
+             [0, 16, 17, 18, 0]],
+        )
+        xp_assert_close(signal.medfilt(x, 3), expected)
+
+        xp_assert_close(
+            signal.order_filter(x, xp.ones((3, 3)), 4),
+            expected
+        )
+
+    def test_order_filter_asymmetric(self, xp):
+        x = xp.reshape(xp.arange(25), (5, 5))
+        domain = xp.asarray(
+            [[1, 1, 0],
+             [0, 1, 0],
+             [0, 0, 0]],
+        )
+
+        expected = xp.asarray(
+            [[0, 0, 0, 0, 0],
+             [0, 0, 1, 2, 3],
+             [0, 5, 6, 7, 8],
+             [0, 10, 11, 12, 13],
+             [0, 15, 16, 17, 18]]
+        )
+        xp_assert_close(signal.order_filter(x, domain, 0), expected)
+
+        expected = xp.asarray(
+            [[0, 0, 0, 0, 0],
+             [0, 1, 2, 3, 4],
+             [5, 6, 7, 8, 9],
+             [10, 11, 12, 13, 14],
+             [15, 16, 17, 18, 19]]
+        )
+        xp_assert_close(signal.order_filter(x, domain, 1), expected)
+
+
+@make_xp_test_case(lfilter)
+class _TestLinearFilter:
+    def generate(self, shape, xp):
+        prodshape = shape if isinstance(shape, int) else math.prod(shape)
+        x = xp.linspace(0, prodshape - 1, prodshape)
+        if not isinstance(shape, int):
+            x = xp.reshape(x, shape)
+        return self.convert_dtype(x, xp)
+
+    def convert_dtype(self, arr, xp):
+        if self.dtype == np.dtype('O'):
+            arr = np.asarray(arr)
+            out = np.empty(arr.shape, self.dtype)
+            iter = np.nditer([arr, out], ['refs_ok','zerosize_ok'],
+                        [['readonly'],['writeonly']])
+            for x, y in iter:
+                y[...] = self.type(x[()])
+            return out
+        else:
+            dtype = (getattr(xp, self.dtype)
+                     if isinstance(self.dtype, str)
+                     else self.dtype)
+            return xp.asarray(arr, dtype=dtype)
+
+    @skip_xp_backends('cupy', reason='XXX https://github.com/scipy/scipy/issues/23539')
+    def test_invalid_params(self, xp):
+        """Verify all exceptions are raised. """
+        b, a, x = xp.asarray([1]), xp.asarray([2]), xp.asarray([3, 4])
+        with pytest.raises(ValueError, match="^Parameter b is not"):
+            lfilter(xp.eye(2), a, x)  # b not one-dimensional
+        with pytest.raises(ValueError, match="^Parameter b is not"):
+            lfilter(xp.asarray([]), a, x)  # b empty
+        with pytest.raises(ValueError, match="^Parameter a is not"):
+            lfilter(b, xp.eye(2), x)  # a not one-dimensional
+        with pytest.raises(ValueError, match="^Parameter a is not"):
+            lfilter(b, xp.asarray([]), x)  # a empty
+        with pytest.raises(NotImplementedError, match="^Parameter's dtypes produced "):
+            b, a, x = (xp.astype(v_, xp.uint64, copy=False) for v_ in (b, a, x))
+            lfilter(b, a, x)  # fails with uint64 dtype
+
+    def test_rank_1_IIR(self, xp):
+        x = self.generate((6,), xp)
+        b = self.convert_dtype([1, -1], xp)
+        a = self.convert_dtype([0.5, -0.5], xp)
+        y_r = self.convert_dtype([0, 2, 4, 6, 8, 10.], xp)
+        assert_array_almost_equal(lfilter(b, a, x), y_r)
+
+    def test_rank_1_FIR(self, xp):
+        x = self.generate((6,), xp)
+        b = self.convert_dtype([1, 1], xp)
+        a = self.convert_dtype([1], xp)
+        y_r = self.convert_dtype([0, 1, 3, 5, 7, 9.], xp)
+        assert_array_almost_equal(lfilter(b, a, x), y_r)
+
+    @skip_xp_backends('cupy', reason='XXX https://github.com/cupy/cupy/pull/8677')
+    def test_rank_1_IIR_init_cond(self, xp):
+        x = self.generate((6,), xp)
+        b = self.convert_dtype([1, 0, -1], xp)
+        a = self.convert_dtype([0.5, -0.5], xp)
+        zi = self.convert_dtype([1, 2], xp)
+        y_r = self.convert_dtype([1, 5, 9, 13, 17, 21], xp)
+        zf_r = self.convert_dtype([13, -10], xp)
+        y, zf = lfilter(b, a, x, zi=zi)
+        assert_array_almost_equal(y, y_r)
+        assert_array_almost_equal(zf, zf_r)
+
+    @skip_xp_backends('cupy', reason='XXX https://github.com/cupy/cupy/pull/8677')
+    def test_rank_1_FIR_init_cond(self, xp):
+        x = self.generate((6,), xp)
+        b = self.convert_dtype([1, 1, 1], xp)
+        a = self.convert_dtype([1], xp)
+        zi = self.convert_dtype([1, 1], xp)
+        y_r = self.convert_dtype([1, 2, 3, 6, 9, 12.], xp)
+        zf_r = self.convert_dtype([9, 5], xp)
+        y, zf = lfilter(b, a, x, zi=zi)
+        assert_array_almost_equal(y, y_r)
+        assert_array_almost_equal(zf, zf_r)
+
+    def test_rank_2_IIR_axis_0(self, xp):
+        x = self.generate((4, 3), xp)
+        b = self.convert_dtype([1, -1], xp)
+        a = self.convert_dtype([0.5, 0.5], xp)
+        y_r2_a0 = self.convert_dtype([[0, 2, 4], [6, 4, 2], [0, 2, 4],
+                                      [6, 4, 2]], xp)
+        y = lfilter(b, a, x, axis=0)
+        assert_array_almost_equal(y_r2_a0, y)
+
+    def test_rank_2_IIR_axis_1(self, xp):
+        x = self.generate((4, 3), xp)
+        b = self.convert_dtype([1, -1], xp)
+        a = self.convert_dtype([0.5, 0.5], xp)
+        y_r2_a1 = self.convert_dtype([[0, 2, 0], [6, -4, 6], [12, -10, 12],
+                            [18, -16, 18]], xp)
+        y = lfilter(b, a, x, axis=1)
+        assert_array_almost_equal(y_r2_a1, y)
+
+    @skip_xp_backends('cupy', reason='XXX https://github.com/cupy/cupy/pull/8677')
+    def test_rank_2_IIR_axis_0_init_cond(self, xp):
+        x = self.generate((4, 3), xp)
+        b = self.convert_dtype([1, -1], xp)
+        a = self.convert_dtype([0.5, 0.5], xp)
+        zi = self.convert_dtype(np.ones((4,1)), xp)
+
+        y_r2_a0_1 = self.convert_dtype([[1, 1, 1], [7, -5, 7], [13, -11, 13],
+                              [19, -17, 19]], xp)
+        zf_r = self.convert_dtype([-5, -17, -29, -41], xp)[:, np.newaxis]
+        y, zf = lfilter(b, a, x, axis=1, zi=zi)
+        assert_array_almost_equal(y_r2_a0_1, y)
+        assert_array_almost_equal(zf, zf_r)
+
+    @skip_xp_backends('cupy', reason='XXX https://github.com/cupy/cupy/pull/8677')
+    def test_rank_2_IIR_axis_1_init_cond(self, xp):
+        x = self.generate((4, 3), xp)
+        b = self.convert_dtype([1, -1], xp)
+        a = self.convert_dtype([0.5, 0.5], xp)
+        zi = self.convert_dtype(np.ones((1, 3)), xp)
+
+        y_r2_a0_0 = self.convert_dtype([[1, 3, 5], [5, 3, 1],
+                                        [1, 3, 5], [5, 3, 1]], xp)
+        zf_r = self.convert_dtype([[-23, -23, -23]], xp)
+        y, zf = lfilter(b, a, x, axis=0, zi=zi)
+        assert_array_almost_equal(y_r2_a0_0, y)
+        assert_array_almost_equal(zf, zf_r)
+
+    def test_rank_3_IIR(self, xp):
+        x = self.generate((4, 3, 2), xp)
+        b = self.convert_dtype([1, -1], xp)
+        a = self.convert_dtype([0.5, 0.5], xp)
+        a_np, b_np, x_np = map(_xp_copy_to_numpy, (a, b, x))
+        for axis in range(x.ndim):
+            y = lfilter(b, a, x, axis)
+            y_r = np.apply_along_axis(lambda w: lfilter(b_np, a_np, w), axis, x_np)
+            assert_array_almost_equal(y, xp.asarray(y_r))
+
+    @xfail_xp_backends("cupy", reason="inaccurate")
+    def test_rank_3_IIR_init_cond(self, xp):
+        x = self.generate((4, 3, 2), xp)
+        b = self.convert_dtype([1, -1], xp)
+        a = self.convert_dtype([0.5, 0.5], xp)
+
+        for axis in range(x.ndim):
+            zi_shape = list(x.shape)
+            zi_shape[axis] = 1
+            zi = self.convert_dtype(xp.ones(zi_shape), xp)
+            zi1 = self.convert_dtype([1], xp)
+            y, zf = lfilter(b, a, x, axis, zi)
+            b_np, a_np, zi1_np = map(_xp_copy_to_numpy, (b, a, zi1))
+            def lf0(w):
+                return lfilter(b_np, a_np, w, zi=zi1_np)[0]
+            def lf1(w):
+                return lfilter(b_np, a_np, w, zi=zi1_np)[1]
+            y_r = np.apply_along_axis(lf0, axis, _xp_copy_to_numpy(x))
+            zf_r = np.apply_along_axis(lf1, axis, _xp_copy_to_numpy(x))
+            assert_array_almost_equal(y, xp.asarray(y_r))
+            assert_array_almost_equal(zf, xp.asarray(zf_r))
+
+    def test_rank_3_FIR(self, xp):
+        x = self.generate((4, 3, 2), xp)
+        b = self.convert_dtype([1, 0, -1], xp)
+        a = self.convert_dtype([1], xp)
+
+        a_np, b_np, x_np = map(_xp_copy_to_numpy, (a, b, x))
+        for axis in range(x.ndim):
+            y = lfilter(b, a, x, axis)
+            y_r = np.apply_along_axis(lambda w: lfilter(b_np, a_np, w), axis, x_np)
+            assert_array_almost_equal(y, xp.asarray(y_r))
+
+    @xfail_xp_backends("cupy", reason="inaccurate")
+    def test_rank_3_FIR_init_cond(self, xp):
+        x = self.generate((4, 3, 2), xp)
+        b = self.convert_dtype([1, 0, -1], xp)
+        a = self.convert_dtype([1], xp)
+
+        x_np, b_np, a_np = map(_xp_copy_to_numpy, (x, b, a))
+        for axis in range(x.ndim):
+            zi_shape = list(x.shape)
+            zi_shape[axis] = 2
+            zi = self.convert_dtype(xp.ones(zi_shape), xp)
+            zi1 = self.convert_dtype([1, 1], xp)
+            zi1_np = _xp_copy_to_numpy(zi1)
+            y, zf = lfilter(b, a, x, axis, zi)
+            b_np, a_np, zi1_np = map(_xp_copy_to_numpy, (b, a, zi1))
+            def lf0(w):
+                return lfilter(b_np, a_np, w, zi=zi1_np)[0]
+            def lf1(w):
+                return lfilter(b_np, a_np, w, zi=zi1_np)[1]
+            y_r = np.apply_along_axis(lf0, axis, x_np)
+            zf_r = np.apply_along_axis(lf1, axis, x_np)
+            assert_array_almost_equal(y, xp.asarray(y_r))
+            assert_array_almost_equal(zf, xp.asarray(zf_r))
+
+    @skip_xp_backends('cupy', reason='XXX https://github.com/cupy/cupy/pull/8677')
+    def test_zi_pseudobroadcast(self, xp):
+        x = self.generate((4, 5, 20), xp)
+        b, a = signal.butter(8, 0.2, output='ba')
+        b = self.convert_dtype(b, xp)
+        a = self.convert_dtype(a, xp)
+        zi_size = b.shape[0] - 1
+
+        # lfilter requires x.ndim == zi.ndim exactly.  However, zi can have
+        # length 1 dimensions.
+        zi_full = self.convert_dtype(xp.ones((4, 5, zi_size)), xp)
+        zi_sing = self.convert_dtype(xp.ones((1, 1, zi_size)), xp)
+
+        y_full, zf_full = lfilter(b, a, x, zi=zi_full)
+        y_sing, zf_sing = lfilter(b, a, x, zi=zi_sing)
+
+        assert_array_almost_equal(y_sing, y_full)
+        assert_array_almost_equal(zf_full, zf_sing)
+
+        # lfilter does not prepend ones
+        assert_raises(ValueError, lfilter, b, a, x, -1, xp.ones(zi_size))
+
+    @skip_xp_backends('cupy', reason='XXX https://github.com/cupy/cupy/pull/8677')
+    def test_scalar_a(self, xp):
+        # a can be a scalar.
+        x = self.generate(6, xp)
+        b = self.convert_dtype([1, 0, -1], xp)
+        a = self.convert_dtype([1], xp)
+        y_r = self.convert_dtype([0, 1, 2, 2, 2, 2], xp)
+
+        y = lfilter(b, a[0], x)
+        assert_array_almost_equal(y, y_r)
+
+    @skip_xp_backends('cupy', reason='XXX https://github.com/cupy/cupy/pull/8677')
+    def test_zi_some_singleton_dims(self, xp):
+        # lfilter doesn't really broadcast (no prepending of 1's).  But does
+        # do singleton expansion if x and zi have the same ndim.  This was
+        # broken only if a subset of the axes were singletons (gh-4681).
+        x = self.convert_dtype(xp.zeros((3, 2, 5), dtype=xp.int64), xp)
+        b = self.convert_dtype(xp.ones(5, dtype=xp.int64), xp)
+        a = self.convert_dtype(xp.asarray([1, 0, 0]), xp)
+        zi = np.ones((3, 1, 4), dtype=np.int64)
+        zi[1, :, :] *= 2
+        zi[2, :, :] *= 3
+        zi = xp.asarray(zi)
+        zi = self.convert_dtype(zi, xp)
+
+        zf_expected = self.convert_dtype(xp.zeros((3, 2, 4), dtype=xp.int64), xp)
+        y_expected = np.zeros((3, 2, 5), dtype=np.int64)
+        y_expected[:, :, :4] = [[[1]], [[2]], [[3]]]
+        y_expected = xp.asarray(y_expected)
+        y_expected = self.convert_dtype(y_expected, xp)
+
+        # IIR
+        y_iir, zf_iir = lfilter(b, a, x, -1, zi)
+        assert_array_almost_equal(y_iir, y_expected)
+        assert_array_almost_equal(zf_iir, zf_expected)
+
+        # FIR
+        y_fir, zf_fir = lfilter(b, a[0], x, -1, zi)
+        assert_array_almost_equal(y_fir, y_expected)
+        assert_array_almost_equal(zf_fir, zf_expected)
+
+    def base_bad_size_zi(self, b, a, x, axis, zi, xp):
+        b = self.convert_dtype(b, xp)
+        a = self.convert_dtype(a, xp)
+        x = self.convert_dtype(x, xp)
+        zi = self.convert_dtype(zi, xp)
+        assert_raises(ValueError, lfilter, b, a, x, axis, zi)
+
+    @skip_xp_backends('cupy', reason='cupy does not raise')
+    def test_bad_size_zi(self, xp):
+        # rank 1
+        x1 = xp.arange(6)
+        self.base_bad_size_zi([1], [1], x1, -1, [1], xp)
+        self.base_bad_size_zi([1, 1], [1], x1, -1, [0, 1], xp)
+        self.base_bad_size_zi([1, 1], [1], x1, -1, [[0]], xp)
+        self.base_bad_size_zi([1, 1], [1], x1, -1, [0, 1, 2], xp)
+        self.base_bad_size_zi([1, 1, 1], [1], x1, -1, [[0]], xp)
+        self.base_bad_size_zi([1, 1, 1], [1], x1, -1, [0, 1, 2], xp)
+        self.base_bad_size_zi([1], [1, 1], x1, -1, [0, 1], xp)
+        self.base_bad_size_zi([1], [1, 1], x1, -1, [[0]], xp)
+        self.base_bad_size_zi([1], [1, 1], x1, -1, [0, 1, 2], xp)
+        self.base_bad_size_zi([1, 1, 1], [1, 1], x1, -1, [0], xp)
+        self.base_bad_size_zi([1, 1, 1], [1, 1], x1, -1, [[0], [1]], xp)
+        self.base_bad_size_zi([1, 1, 1], [1, 1], x1, -1, [0, 1, 2], xp)
+        self.base_bad_size_zi([1, 1, 1], [1, 1], x1, -1, [0, 1, 2, 3], xp)
+        self.base_bad_size_zi([1, 1], [1, 1, 1], x1, -1, [0], xp)
+        self.base_bad_size_zi([1, 1], [1, 1, 1], x1, -1, [[0], [1]], xp)
+        self.base_bad_size_zi([1, 1], [1, 1, 1], x1, -1, [0, 1, 2], xp)
+        self.base_bad_size_zi([1, 1], [1, 1, 1], x1, -1, [0, 1, 2, 3], xp)
+
+        # rank 2
+        x2 = np.arange(12).reshape((4,3))
+        x2 = xp.asarray(x2)
+        # for axis=0 zi.shape should == (max(len(a),len(b))-1, 3)
+        self.base_bad_size_zi([1], [1], x2, 0, [0], xp)
+
+        # for each of these there are 5 cases tested (in this order):
+        # 1. not deep enough, right # elements
+        # 2. too deep, right # elements
+        # 3. right depth, right # elements, transposed
+        # 4. right depth, too few elements
+        # 5. right depth, too many elements
+
+        self.base_bad_size_zi([1, 1], [1], x2, 0, [0, 1, 2], xp)
+        self.base_bad_size_zi([1, 1], [1], x2, 0, [[[0, 1, 2]]], xp)
+        self.base_bad_size_zi([1, 1], [1], x2, 0, [[0], [1], [2]], xp)
+        self.base_bad_size_zi([1, 1], [1], x2, 0, [[0, 1]], xp)
+        self.base_bad_size_zi([1, 1], [1], x2, 0, [[0, 1, 2, 3]], xp)
+
+        self.base_bad_size_zi([1, 1, 1], [1], x2, 0, [0, 1, 2, 3, 4, 5], xp)
+        self.base_bad_size_zi([1, 1, 1], [1], x2, 0, [[[0, 1, 2], [3, 4, 5]]], xp)
+        self.base_bad_size_zi([1, 1, 1], [1], x2, 0, [[0, 1], [2, 3], [4, 5]], xp)
+        self.base_bad_size_zi([1, 1, 1], [1], x2, 0, [[0, 1], [2, 3]], xp)
+        self.base_bad_size_zi([1, 1, 1], [1], x2, 0, [[0, 1, 2, 3], [4, 5, 6, 7]], xp)
+
+        self.base_bad_size_zi([1], [1, 1], x2, 0, [0, 1, 2], xp)
+        self.base_bad_size_zi([1], [1, 1], x2, 0, [[[0, 1, 2]]], xp)
+        self.base_bad_size_zi([1], [1, 1], x2, 0, [[0], [1], [2]], xp)
+        self.base_bad_size_zi([1], [1, 1], x2, 0, [[0, 1]], xp)
+        self.base_bad_size_zi([1], [1, 1], x2, 0, [[0, 1, 2, 3]], xp)
+
+        self.base_bad_size_zi([1], [1, 1, 1], x2, 0, [0, 1, 2, 3, 4, 5], xp)
+        self.base_bad_size_zi([1], [1, 1, 1], x2, 0, [[[0, 1, 2], [3, 4, 5]]], xp)
+        self.base_bad_size_zi([1], [1, 1, 1], x2, 0, [[0, 1], [2, 3], [4, 5]], xp)
+        self.base_bad_size_zi([1], [1, 1, 1], x2, 0, [[0, 1], [2, 3]], xp)
+        self.base_bad_size_zi([1], [1, 1, 1], x2, 0, [[0, 1, 2, 3], [4, 5, 6, 7]], xp)
+
+        self.base_bad_size_zi([1, 1, 1], [1, 1], x2, 0, [0, 1, 2, 3, 4, 5], xp)
+        self.base_bad_size_zi([1, 1, 1], [1, 1], x2, 0, [[[0, 1, 2], [3, 4, 5]]], xp)
+        self.base_bad_size_zi([1, 1, 1], [1, 1], x2, 0, [[0, 1], [2, 3], [4, 5]], xp)
+        self.base_bad_size_zi([1, 1, 1], [1, 1], x2, 0, [[0, 1], [2, 3]], xp)
+        self.base_bad_size_zi([1, 1, 1], [1, 1], x2, 0,
+                              [[0, 1, 2, 3], [4, 5, 6, 7]], xp)
+
+        # for axis=1 zi.shape should == (4, max(len(a),len(b))-1)
+        self.base_bad_size_zi([1], [1], x2, 1, [0], xp)
+
+        self.base_bad_size_zi([1, 1], [1], x2, 1, [0, 1, 2, 3], xp)
+        self.base_bad_size_zi([1, 1], [1], x2, 1, [[[0], [1], [2], [3]]], xp)
+        self.base_bad_size_zi([1, 1], [1], x2, 1, [[0, 1, 2, 3]], xp)
+        self.base_bad_size_zi([1, 1], [1], x2, 1, [[0], [1], [2]], xp)
+        self.base_bad_size_zi([1, 1], [1], x2, 1, [[0], [1], [2], [3], [4]], xp)
+
+        self.base_bad_size_zi([1, 1, 1], [1], x2, 1, [0, 1, 2, 3, 4, 5, 6, 7], xp)
+        self.base_bad_size_zi([1, 1, 1], [1], x2, 1,
+                              [[[0, 1], [2, 3], [4, 5], [6, 7]]], xp)
+        self.base_bad_size_zi([1, 1, 1], [1], x2, 1, [[0, 1, 2, 3], [4, 5, 6, 7]], xp)
+        self.base_bad_size_zi([1, 1, 1], [1], x2, 1, [[0, 1], [2, 3], [4, 5]], xp)
+        self.base_bad_size_zi([1, 1, 1], [1], x2, 1,
+                              [[0, 1], [2, 3], [4, 5], [6, 7], [8, 9]], xp)
+
+        self.base_bad_size_zi([1], [1, 1], x2, 1, [0, 1, 2, 3], xp)
+        self.base_bad_size_zi([1], [1, 1], x2, 1, [[[0], [1], [2], [3]]], xp)
+        self.base_bad_size_zi([1], [1, 1], x2, 1, [[0, 1, 2, 3]], xp)
+        self.base_bad_size_zi([1], [1, 1], x2, 1, [[0], [1], [2]], xp)
+        self.base_bad_size_zi([1], [1, 1], x2, 1, [[0], [1], [2], [3], [4]], xp)
+
+        self.base_bad_size_zi([1], [1, 1, 1], x2, 1, [0, 1, 2, 3, 4, 5, 6, 7], xp)
+        self.base_bad_size_zi([1], [1, 1, 1], x2, 1,
+                              [[[0, 1], [2, 3], [4, 5], [6, 7]]], xp)
+        self.base_bad_size_zi([1], [1, 1, 1], x2, 1, [[0, 1, 2, 3], [4, 5, 6, 7]], xp)
+        self.base_bad_size_zi([1], [1, 1, 1], x2, 1, [[0, 1], [2, 3], [4, 5]], xp)
+        self.base_bad_size_zi([1], [1, 1, 1], x2, 1, [[0, 1],
+                              [2, 3], [4, 5], [6, 7], [8, 9]], xp)
+
+        self.base_bad_size_zi([1, 1, 1], [1, 1], x2, 1, [0, 1, 2, 3, 4, 5, 6, 7], xp)
+        self.base_bad_size_zi([1, 1, 1], [1, 1], x2, 1,
+                              [[[0, 1], [2, 3], [4, 5], [6, 7]]], xp)
+        self.base_bad_size_zi([1, 1, 1], [1, 1], x2, 1,
+                              [[0, 1, 2, 3], [4, 5, 6, 7]], xp)
+        self.base_bad_size_zi([1, 1, 1], [1, 1], x2, 1, [[0, 1], [2, 3], [4, 5]], xp)
+        self.base_bad_size_zi([1, 1, 1], [1, 1], x2, 1,
+                              [[0, 1], [2, 3], [4, 5], [6, 7], [8, 9]], xp)
+
+    def test_empty_zi(self, xp):
+        # Regression test for #880: empty array for zi crashes.
+        x = self.generate((5,), xp)
+        a = self.convert_dtype([1], xp)
+        b = self.convert_dtype([1], xp)
+        zi = self.convert_dtype([], xp)
+        y, zf = lfilter(b, a, x, zi=zi)
+        assert_array_almost_equal(y, x)
+        assert zf.dtype == (getattr(xp, self.dtype)
+                            if isinstance(self.dtype, str)
+                            else self.dtype)
+        assert xp_size(zf) == 0
+
+    @skip_xp_backends('jax.numpy', reason='jax does not support inplace ops')
+    @pytest.mark.parametrize('a', (1, [1], [1, .5, 1.5], 2, [2], [2, 1, 3]),
+                             ids=str)
+    @make_xp_test_case(lfiltic)
+    def test_lfiltic(self, a, xp):
+        # Test for #22470: lfiltic does not handle `a[0] != 1`
+        # and, more in general, test that lfiltic behaves consistently with lfilter
+        if is_cupy(xp) and isinstance(a, int | float):
+            pytest.skip('cupy does not supoprt scalar filter coefficients')
+        x = self.generate(6, xp)  # arbitrary input
+        b = self.convert_dtype([.5, 1., .2], xp)  # arbitrary b
+        a = self.convert_dtype(a, xp)
+        N = xp_size(a) - 1
+        M = xp_size(b) - 1
+        K = M + N if is_cupy(xp) else max(N, M)
+        # compute reference initial conditions as final conditions of lfilter
+        y1, zi_1 = lfilter(b, a, x, zi=self.generate(K, xp))
+        # copute initial conditions from lfiltic
+        zi_2 = lfiltic(b, a, xp.flip(y1), xp.flip(x))
+        # compare lfiltic's output with reference
+        assert_array_almost_equal(zi_1, zi_2)
+
+    @make_xp_test_case(lfiltic)
+    def test_lfiltic_bad_coeffs(xp):
+        # Test for invalid filter coefficients (wrong shape or zero `a[0]`)
+        assert_raises(ValueError, lfiltic, [1, 2], [], [0, 0], [0, 1])
+        assert_raises(ValueError, lfiltic, [1, 2], [0, 2], [0, 0], [0, 1])
+        assert_raises(ValueError, lfiltic, [1, 2], [[1], [2]], [0, 0], [0, 1])
+        assert_raises(ValueError, lfiltic, [[1], [2]], [1], [0, 0], [0, 1])
+
+    @skip_xp_backends(
+        'array_api_strict', reason='int64 and float64 cannot be promoted together'
+    )
+    @skip_xp_backends('jax.numpy', reason='jax dtype defaults differ')
+    @make_xp_test_case(lfiltic)
+    def test_lfiltic_bad_zi(self, xp):
+        # Regression test for #3699: bad initial conditions
+        a = self.convert_dtype([1], xp)
+        b = self.convert_dtype([1], xp)
+        # "y" sets the datatype of zi, so it truncates if int
+        zi = lfiltic(b, a, xp.asarray([1., 0]))
+        zi_1 = lfiltic(b, a, xp.asarray([1.0, 0]))
+        zi_2 = lfiltic(b, a, xp.asarray([True, False]))
+        xp_assert_equal(zi, zi_1)
+
+        check_dtype_arg = {} if self.dtype == object else {'check_dtype': False}
+        xp_assert_equal(zi, zi_2, **check_dtype_arg)
+
+    @skip_xp_backends('cupy', reason='XXX https://github.com/cupy/cupy/pull/8677')
+    def test_short_x_FIR(self, xp):
+        # regression test for #5116
+        # x shorter than b, with non None zi fails
+        a = self.convert_dtype([1], xp)
+        b = self.convert_dtype([1, 0, -1], xp)
+        zi = self.convert_dtype([2, 7], xp)
+        x = self.convert_dtype([72], xp)
+        ye = self.convert_dtype([74], xp)
+        zfe = self.convert_dtype([7, -72], xp)
+        y, zf = lfilter(b, a, x, zi=zi)
+        assert_array_almost_equal(y, ye)
+        assert_array_almost_equal(zf, zfe)
+
+    @skip_xp_backends('cupy', reason='XXX https://github.com/cupy/cupy/pull/8677')
+    def test_short_x_IIR(self, xp):
+        # regression test for #5116
+        # x shorter than b, with non None zi fails
+        a = self.convert_dtype([1, 1], xp)
+        b = self.convert_dtype([1, 0, -1], xp)
+        zi = self.convert_dtype([2, 7], xp)
+        x = self.convert_dtype([72], xp)
+        ye = self.convert_dtype([74], xp)
+        zfe = self.convert_dtype([-67, -72], xp)
+        y, zf = lfilter(b, a, x, zi=zi)
+        assert_array_almost_equal(y, ye)
+        assert_array_almost_equal(zf, zfe)
+
+    def test_do_not_modify_a_b_IIR(self, xp):
+        x = self.generate((6,), xp)
+        b = self.convert_dtype([1, -1], xp)
+        b0 = xp_copy(b, xp=xp)
+        a = self.convert_dtype([0.5, -0.5], xp)
+        a0 = xp_copy(a, xp=xp)
+        y_r = self.convert_dtype([0, 2, 4, 6, 8, 10.], xp)
+        y_f = lfilter(b, a, x)
+        assert_array_almost_equal(y_f, y_r)
+        xp_assert_equal(b, b0)
+        xp_assert_equal(a, a0)
+
+    def test_do_not_modify_a_b_FIR(self, xp):
+        x = self.generate((6,), xp)
+        b = self.convert_dtype([1, 0, 1], xp)
+        b0 = xp_copy(b, xp=xp)
+        a = self.convert_dtype([2], xp)
+        a0 = xp_copy(a, xp=xp)
+        y_r = self.convert_dtype([0, 0.5, 1, 2, 3, 4.], xp)
+        y_f = lfilter(b, a, x)
+        assert_array_almost_equal(y_f, y_r)
+        xp_assert_equal(b, b0)
+        xp_assert_equal(a, a0)
+
+    @skip_xp_backends(np_only=True)
+    @pytest.mark.parametrize("a", [1.0, [1.0], np.array(1.0)])
+    @pytest.mark.parametrize("b", [1.0, [1.0], np.array(1.0)])
+    def test_scalar_input(self, a, b, xp):
+        data = np.random.randn(10)
+        data = xp.asarray(data)
+        xp_assert_close(
+            lfilter(xp.asarray([1.0]), xp.asarray([1.0]), data),
+            lfilter(b, a, data)
+        )
+
+
+class TestLinearFilterFloat32(_TestLinearFilter):
+    dtype = 'float32'
+
+
+class TestLinearFilterFloat64(_TestLinearFilter):
+    dtype = 'float64'
+
+
+@skip_xp_backends(np_only=True)
+class TestLinearFilterFloatExtended(_TestLinearFilter):
+    dtype = np.dtype('g')
+
+
+class TestLinearFilterComplex64(_TestLinearFilter):
+    dtype = 'complex64'
+
+
+class TestLinearFilterComplex128(_TestLinearFilter):
+    dtype = 'complex128'
+
+
+@skip_xp_backends(np_only=True)
+class TestLinearFilterComplexExtended(_TestLinearFilter):
+    dtype = np.dtype('G')
+
+
+@make_xp_test_case(lfilter)
+def test_lfilter_bad_object(xp):
+    # lfilter: object arrays with non-numeric objects raise TypeError.
+    # Regression test for ticket #1452.
+    if hasattr(sys, 'abiflags') and 'd' in sys.abiflags:
+        pytest.skip('test is flaky when run with python3-dbg')
+    assert_raises(TypeError, lfilter, [1.0], [1.0], [1.0, None, 2.0])
+    assert_raises(TypeError, lfilter, [1.0], [None], [1.0, 2.0, 3.0])
+    assert_raises(TypeError, lfilter, [None], [1.0], [1.0, 2.0, 3.0])
+
+
+@make_xp_test_case(lfilter)
+def test_lfilter_notimplemented_input(xp):
+    # Should not crash, gh-7991
+    assert_raises(NotImplementedError, lfilter, [2,3], [4,5], [1,2,3,4,5])
+
+
+@pytest.mark.parametrize('dt', ["uint8", "int8", "uint16", "int16",
+                                "uint32", "int32",
+                                "uint64", "int64",
+                                "float32", "float64",
+                               ])
+
+@xfail_xp_backends("jax.numpy", reason="fails all around")
+@make_xp_test_case(correlate)
+class TestCorrelateReal:
+    def _setup_rank1(self, dt, xp):
+        a = xp.linspace(0, 3, 4, dtype=dt)
+        b = xp.linspace(1, 2, 2, dtype=dt)
+
+        y_r = xp.asarray([0, 2, 5, 8, 3], dtype=dt)
+        return a, b, y_r
+
+    def equal_tolerance(self, res_dt):
+        # default value of keyword
+        decimal = 6
+        try:
+            dt_info = np.finfo(res_dt)
+            if hasattr(dt_info, 'resolution'):
+                decimal = int(-0.5*np.log10(dt_info.resolution))
+        except Exception:
+            pass
+        return decimal
+
+    def equal_tolerance_fft(self, res_dt):
+        # FFT implementations convert longdouble arguments down to
+        # double so don't expect better precision, see gh-9520
+        if res_dt == np.longdouble:
+            return self.equal_tolerance(np.float64)
+        else:
+            return self.equal_tolerance(res_dt)
+
+    @skip_xp_backends(np_only=True, reason="order='F'")
+    def test_method(self, dt, xp):
+        dt = getattr(xp, dt)
+
+        a, b, y_r = self._setup_rank3(dt, xp)
+        y_fft = correlate(a, b, method='fft')
+        y_direct = correlate(a, b, method='direct')
+
+        assert_array_almost_equal(y_r, y_fft,
+                                  decimal=self.equal_tolerance_fft(y_fft.dtype),)
+        assert_array_almost_equal(y_r, y_direct,
+                                  decimal=self.equal_tolerance(y_direct.dtype),)
+        assert y_fft.dtype == dt
+        assert y_direct.dtype == dt
+
+    def test_rank1_valid(self, dt, xp):
+        if is_torch(xp) and dt in ["uint16", "uint32", "uint64"]:
+           pytest.skip("torch does not support unsigned ints")
+
+        dt = getattr(xp, dt) if isinstance(dt, str) else dt
+        a, b, y_r = self._setup_rank1(dt, xp)
+        y = correlate(a, b, 'valid')
+        assert_array_almost_equal(y, y_r[1:4])
+        assert y.dtype == dt
+
+        # See gh-5897
+        y = correlate(b, a, 'valid')
+        assert_array_almost_equal(y, xp.flip(y_r[1:4]))
+        assert y.dtype == dt
+
+    def test_rank1_same(self, dt, xp):
+        if is_torch(xp) and dt in ["uint16", "uint32", "uint64"]:
+           pytest.skip("torch does not support unsigned ints")
+
+        dt = getattr(xp, dt) if isinstance(dt, str) else dt
+
+        a, b, y_r = self._setup_rank1(dt, xp)
+        y = correlate(a, b, 'same')
+        assert_array_almost_equal(y, y_r[:-1])
+        assert y.dtype == dt
+
+    def test_rank1_full(self, dt, xp):
+        if is_torch(xp) and dt in ["uint16", "uint32", "uint64"]:
+           pytest.skip("torch does not support unsigned ints")
+
+        dt = getattr(xp, dt) if isinstance(dt, str) else dt
+
+        a, b, y_r = self._setup_rank1(dt, xp)
+        y = correlate(a, b, 'full')
+        assert_array_almost_equal(y, y_r)
+        assert y.dtype == dt
+
+    def _setup_rank3(self, dt, xp):
+        a = np.linspace(0, 39, 40).reshape((2, 4, 5), order='F').astype(
+            dt)
+        b = np.linspace(0, 23, 24).reshape((2, 3, 4), order='F').astype(
+            dt)
+
+        y_r = np.array([[[0., 184., 504., 912., 1360., 888., 472., 160.],
+                      [46., 432., 1062., 1840., 2672., 1698., 864., 266.],
+                      [134., 736., 1662., 2768., 3920., 2418., 1168., 314.],
+                      [260., 952., 1932., 3056., 4208., 2580., 1240., 332.],
+                      [202., 664., 1290., 1984., 2688., 1590., 712., 150.],
+                      [114., 344., 642., 960., 1280., 726., 296., 38.]],
+
+                     [[23., 400., 1035., 1832., 2696., 1737., 904., 293.],
+                      [134., 920., 2166., 3680., 5280., 3306., 1640., 474.],
+                      [325., 1544., 3369., 5512., 7720., 4683., 2192., 535.],
+                      [571., 1964., 3891., 6064., 8272., 4989., 2324., 565.],
+                      [434., 1360., 2586., 3920., 5264., 3054., 1312., 230.],
+                      [241., 700., 1281., 1888., 2496., 1383., 532., 39.]],
+
+                     [[22., 214., 528., 916., 1332., 846., 430., 132.],
+                      [86., 484., 1098., 1832., 2600., 1602., 772., 206.],
+                      [188., 802., 1698., 2732., 3788., 2256., 1018., 218.],
+                      [308., 1006., 1950., 2996., 4052., 2400., 1078., 230.],
+                      [230., 692., 1290., 1928., 2568., 1458., 596., 78.],
+                      [126., 354., 636., 924., 1212., 654., 234., 0.]]],
+                    dtype=np.float64).astype(dt)
+
+        return a, b, y_r
+
+    @skip_xp_backends(np_only=True, reason="order='F'")
+    def test_rank3_valid(self, dt, xp):
+        dt = getattr(xp, dt) if isinstance(dt, str) else dt
+        a, b, y_r = self._setup_rank3(dt, xp)
+        y = correlate(a, b, "valid")
+        assert_array_almost_equal(y, y_r[1:2, 2:4, 3:5])
+        assert y.dtype == dt
+
+        # See gh-5897
+        y = correlate(b, a, "valid")
+        assert_array_almost_equal(y, y_r[1:2, 2:4, 3:5][::-1, ::-1, ::-1])
+        assert y.dtype == dt
+
+    @skip_xp_backends(np_only=True, reason="order='F'")
+    def test_rank3_same(self, dt, xp):
+        dt = getattr(xp, dt) if isinstance(dt, str) else dt
+        a, b, y_r = self._setup_rank3(dt, xp)
+        y = correlate(a, b, "same")
+        xp_assert_close(y, y_r[0:-1, 1:-1, 1:-2])
+        assert y.dtype == dt
+
+    @skip_xp_backends(np_only=True, reason="order='F'")
+    def test_rank3_all(self, dt, xp):
+        dt = getattr(xp, dt) if isinstance(dt, str) else dt
+        a, b, y_r = self._setup_rank3(dt, xp)
+        y = correlate(a, b)
+        xp_assert_close(y, y_r)
+        assert y.dtype == dt
+
+
+@make_xp_test_case(correlate)
+class TestCorrelate:
+    # Tests that don't depend on dtype
+
+    @skip_xp_backends(np_only=True)
+    def test_invalid_shapes(self, xp):
+        # By "invalid," we mean that no one
+        # array has dimensions that are all at
+        # least as large as the corresponding
+        # dimensions of the other array. This
+        # setup should throw a ValueError.
+        a = np.arange(1, 7).reshape((2, 3))
+        b = np.arange(-6, 0).reshape((3, 2))
+
+        assert_raises(ValueError, correlate, *(a, b), **{'mode': 'valid'})
+        assert_raises(ValueError, correlate, *(b, a), **{'mode': 'valid'})
+
+    @skip_xp_backends(np_only=True)
+    def test_invalid_params(self, xp):
+        a = [3, 4, 5]
+        b = [1, 2, 3]
+        assert_raises(ValueError, correlate, a, b, mode='spam')
+        assert_raises(ValueError, correlate, a, b, mode='eggs', method='fft')
+        assert_raises(ValueError, correlate, a, b, mode='ham', method='direct')
+        assert_raises(ValueError, correlate, a, b, mode='full', method='bacon')
+        assert_raises(ValueError, correlate, a, b, mode='same', method='bacon')
+
+    @skip_xp_backends(np_only=True)
+    def test_mismatched_dims(self, xp):
+        # Input arrays should have the same number of dimensions
+        assert_raises(ValueError, correlate, [1], 2, method='direct')
+        assert_raises(ValueError, correlate, 1, [2], method='direct')
+        assert_raises(ValueError, correlate, [1], 2, method='fft')
+        assert_raises(ValueError, correlate, 1, [2], method='fft')
+        assert_raises(ValueError, correlate, [1], [[2]])
+        assert_raises(ValueError, correlate, [3], 2)
+
+    @skip_xp_backends(cpu_only=True, exceptions=['cupy'])
+    @skip_xp_backends("jax.numpy", reason="dtype differs")
+    def test_numpy_fastpath(self, xp):
+        a = xp.asarray([1, 2, 3])
+        b = xp.asarray([4, 5])
+        xp_assert_close(correlate(a, b, mode='same'), xp.asarray([5, 14, 23]))
+
+        a = xp.asarray([1, 2, 3])
+        b = xp.asarray([4, 5, 6])
+        xp_assert_close(correlate(a, b, mode='same'), xp.asarray([17, 32, 23]))
+        xp_assert_close(correlate(a, b, mode='full'), xp.asarray([6, 17, 32, 23, 12]))
+        xp_assert_close(correlate(a, b, mode='valid'), xp.asarray([32]))
+
+
+@make_xp_test_case(correlation_lags)
+@pytest.mark.parametrize("mode", ["valid", "same", "full"])
+@pytest.mark.parametrize("behind", [True, False])
+@pytest.mark.parametrize("input_size", [100, 101, 1000, 1001,
+                                        pytest.param(10000, marks=[pytest.mark.slow]),
+                                        pytest.param(10001, marks=[pytest.mark.slow])]
+)
+def test_correlation_lags(mode, behind, input_size, xp):
+    # generate random data
+    rng = np.random.RandomState(0)
+    in1 = rng.standard_normal(input_size)
+    offset = int(input_size/10)
+    # generate offset version of array to correlate with
+    if behind:
+        # y is behind x
+        in2 = np.concatenate([rng.standard_normal(offset), in1])
+        expected = -offset
+    else:
+        # y is ahead of x
+        in2 = in1[offset:]
+        expected = offset
+    # cross correlate, returning lag information
+    correlation = correlate(in1, in2, mode=mode)
+    lags = correlation_lags(in1.size, in2.size, mode=mode)
+    # identify the peak
+    lag_index = np.argmax(correlation)
+    # Check as expected
+    xp_assert_equal(lags[lag_index], expected)
+    # Correlation and lags shape should match
+    assert lags.shape == correlation.shape
+
+
+@make_xp_test_case(correlation_lags)
+def test_correlation_lags_invalid_mode(xp):
+    with pytest.raises(ValueError, match="Mode asdfgh is invalid"):
+        correlation_lags(100, 100, mode="asdfgh")
+
+
+@make_xp_test_case(correlate)
+@pytest.mark.parametrize('dt_name', ['complex64', 'complex128'])
+class TestCorrelateComplex:
+    # The decimal precision to be used for comparing results.
+    # This value will be passed as the 'decimal' keyword argument of
+    # assert_array_almost_equal().
+    # Since correlate may chose to use FFT method which converts
+    # longdoubles to doubles internally don't expect better precision
+    # for longdouble than for double (see gh-9520).
+
+    def decimal(self, dt, xp):
+        if is_numpy(xp) and dt == np.clongdouble:
+            dt = np.cdouble
+
+        # emulate np.finfo(dt).precision for complex64 and complex128
+        prec = {64: 15, 32: 6}[xp.finfo(dt).bits]
+        return int(2 * prec / 3)
+
+    def _setup_rank1(self, dt, mode, xp):
+        rng = np.random.default_rng(9)
+        a = np.random.randn(10).astype(dt)
+        a += 1j * rng.standard_normal(10).astype(dt)
+        b = np.random.randn(8).astype(dt)
+        b += 1j * rng.standard_normal(8).astype(dt)
+
+        y_r = (correlate(a.real, b.real, mode=mode) +
+               correlate(a.imag, b.imag, mode=mode)).astype(dt)
+        y_r += 1j * (-correlate(a.real, b.imag, mode=mode) +
+                     correlate(a.imag, b.real, mode=mode))
+
+        a, b, y_r = xp.asarray(a), xp.asarray(b), xp.asarray(y_r)
+        return a, b, y_r
+
+    def test_rank1_valid(self, dt_name, xp):
+        a, b, y_r = self._setup_rank1(dt_name, 'valid', xp)
+        dt = getattr(xp, dt_name)
+        y = correlate(a, b, 'valid')
+        assert_array_almost_equal(y, y_r, decimal=self.decimal(dt, xp))
+        assert y.dtype == dt
+
+        # See gh-5897
+        y = correlate(b, a, 'valid')
+        assert_array_almost_equal(y, xp.conj(xp.flip(y_r)),
+                                  decimal=self.decimal(dt, xp))
+        assert y.dtype == dt
+
+    def test_rank1_same(self, dt_name, xp):
+        a, b, y_r = self._setup_rank1(dt_name, 'same', xp)
+        dt = getattr(xp, dt_name)
+
+        y = correlate(a, b, 'same')
+        assert_array_almost_equal(y, y_r, decimal=self.decimal(dt, xp))
+        assert y.dtype == dt
+
+    def test_rank1_full(self, dt_name, xp):
+        a, b, y_r = self._setup_rank1(dt_name, 'full', xp)
+        dt = getattr(xp, dt_name)
+        y = correlate(a, b, 'full')
+        assert_array_almost_equal(y, y_r, decimal=self.decimal(dt, xp))
+        assert y.dtype == dt
+
+    def test_swap_full(self, dt_name, xp):
+        dt = getattr(xp, dt_name)
+        d = xp.asarray([0.+0.j, 1.+1.j, 2.+2.j], dtype=dt)
+        k = xp.asarray([1.+3.j, 2.+4.j, 3.+5.j, 4.+6.j], dtype=dt)
+        y = correlate(d, k)
+        xp_assert_close(
+            y, xp.asarray([0.+0.j, 10.-2.j, 28.-6.j, 22.-6.j, 16.-6.j, 8.-4.j]),
+            atol=1e-6, check_dtype=False
+        )
+
+    def test_swap_same(self, dt_name, xp):
+        d = xp.asarray([0.+0.j, 1.+1.j, 2.+2.j])
+        k = xp.asarray([1.+3.j, 2.+4.j, 3.+5.j, 4.+6.j])
+        y = correlate(d, k, mode="same")
+        xp_assert_close(y, xp.asarray([10.-2.j, 28.-6.j, 22.-6.j]))
+
+    @skip_xp_backends("cupy", reason="notimplementederror")
+    def test_rank3(self, dt_name, xp):
+        if is_jax(xp) and SCIPY_DEVICE != "cpu":
+            pytest.xfail(reason="error tolerances exceeded with JAX on gpu")
+        a = np.random.randn(10, 8, 6).astype(dt_name)
+        a += 1j * np.random.randn(10, 8, 6).astype(dt_name)
+        b = np.random.randn(8, 6, 4).astype(dt_name)
+        b += 1j * np.random.randn(8, 6, 4).astype(dt_name)
+
+        y_r = (correlate(a.real, b.real)
+               + correlate(a.imag, b.imag)).astype(dt_name)
+        y_r += 1j * (-correlate(a.real, b.imag) + correlate(a.imag, b.real))
+
+        a, b, y_r = xp.asarray(a), xp.asarray(b), xp.asarray(y_r)
+        dt = getattr(xp, dt_name)
+
+        y = correlate(a, b, 'full')
+        assert_array_almost_equal(y, y_r, decimal=self.decimal(dt, xp) - 1)
+        assert y.dtype == dt
+
+    @skip_xp_backends(np_only=True)  # XXX: check 0D/scalars on backends.
+    def test_rank0(self, dt_name, xp):
+        a = np.array(np.random.randn()).astype(dt_name)
+        a += 1j * np.array(np.random.randn()).astype(dt_name)
+        b = np.array(np.random.randn()).astype(dt_name)
+        b += 1j * np.array(np.random.randn()).astype(dt_name)
+        dt = getattr(xp, dt_name)
+
+        y_r = (correlate(a.real, b.real)
+               + correlate(a.imag, b.imag)).astype(dt)
+        y_r += 1j * np.array(-correlate(a.real, b.imag) +
+                             correlate(a.imag, b.real))
+
+        a, b = xp.asarray(a), xp.asarray(b)
+
+        y = correlate(a, b, 'full')
+        assert_array_almost_equal(y, y_r, decimal=self.decimal(dt, xp) - 1)
+        assert y.dtype == dt
+
+        xp_assert_equal(correlate([1], [2j]), np.asarray(correlate(1, 2j)),
+                        check_shape=False)
+        xp_assert_equal(correlate([2j], [3j]), np.asarray(correlate(2j, 3j)),
+                        check_shape=False)
+        xp_assert_equal(correlate([3j], [4]), np.asarray(correlate(3j, 4)),
+                        check_shape=False)
+
+
+
+class TestCorrelate2d:
+
+    @make_xp_test_case(signal.correlate)
+    def test_consistency_correlate_funcs(self, xp):
+        # Compare np.correlate, signal.correlate, signal.correlate2d
+        a = np.arange(5)
+        b = np.array([3.2, 1.4, 3])
+        for mode in ['full', 'valid', 'same']:
+            a_xp, b_xp = xp.asarray(a), xp.asarray(b)
+            np_corr_result = np.correlate(a, b, mode=mode)
+            assert_almost_equal(signal.correlate(a_xp, b_xp, mode=mode),
+                                xp.asarray(np_corr_result))
+
+            # See gh-5897
+            if mode == 'valid':
+                np_corr_result = np.correlate(b, a, mode=mode)
+                assert_almost_equal(signal.correlate(b_xp, a_xp, mode=mode),
+                                    xp.asarray(np_corr_result))
+
+    @skip_xp_backends(np_only=True)
+    @make_xp_test_case(signal.correlate2d)
+    def test_consistency_correlate_funcs_2(self, xp):
+        # Compare np.correlate, signal.correlate, signal.correlate2d
+        a = np.arange(5)
+        b = np.array([3.2, 1.4, 3])
+        for mode in ['full', 'valid', 'same']:
+            assert_almost_equal(np.squeeze(signal.correlate2d([a], [b],
+                                                              mode=mode)),
+                                signal.correlate(a, b, mode=mode))
+
+            # See gh-5897
+            if mode == 'valid':
+                assert_almost_equal(np.squeeze(signal.correlate2d([b], [a],
+                                                                  mode=mode)),
+                                    signal.correlate(b, a, mode=mode))
+
+
+    @skip_xp_backends(np_only=True)
+    @make_xp_test_case(signal.correlate2d)
+    def test_invalid_shapes(self, xp):
+        # By "invalid," we mean that no one
+        # array has dimensions that are all at
+        # least as large as the corresponding
+        # dimensions of the other array. This
+        # setup should throw a ValueError.
+        a = np.arange(1, 7).reshape((2, 3))
+        b = np.arange(-6, 0).reshape((3, 2))
+
+        assert_raises(ValueError, signal.correlate2d, *(a, b), **{'mode': 'valid'})
+        assert_raises(ValueError, signal.correlate2d, *(b, a), **{'mode': 'valid'})
+
+    @make_xp_test_case(signal.correlate2d)
+    def test_complex_input(self, xp):
+        xp_assert_equal(signal.correlate2d(xp.asarray([[1]]), xp.asarray([[2j]])),
+                        xp.asarray([-2j]), check_shape=False, check_dtype=False)
+        xp_assert_equal(signal.correlate2d(xp.asarray([[2j]]), xp.asarray([[3j]])),
+                        xp.asarray([6+0j]), check_shape=False, check_dtype=False)
+        xp_assert_equal(signal.correlate2d(xp.asarray([[3j]]), xp.asarray([[4]])),
+                        xp.asarray([12j]), check_shape=False, check_dtype=False)
+
+
+@make_xp_test_case(lfilter_zi)
+class TestLFilterZI:
+
+    def test_exceptions(self, xp):
+        """Raise all exceptions in `lfilter_zi`. """
+        with pytest.raises(ValueError, match="^Numerator `b` and Denominator `a` must"):
+             lfilter_zi(b=xp.eye(3), a=1)  # b must be 1-d array
+        with pytest.raises(ValueError, match="^Numerator `b` and Denominator `a` must"):
+             lfilter_zi(b=1, a=xp.eye(3))  # a must be 1-d array
+        with pytest.raises(ValueError, match="^First coefficient of parameter `a` "):
+            lfilter_zi(b=1, a=xp.asarray([0, 0, 0]))
+        with pytest.raises(ValueError, match="^Filter not stable due to sum"):
+            lfilter_zi(b=1, a=xp.asarray([-1, 1, -2, 2]))
+
+    @skip_xp_backends(np_only=True, reason='list inputs are numpy specific')
+    def test_array_like(self, xp):
+        zi_expected = xp.asarray([5.0, -1.0])
+        zi = lfilter_zi([1.0, 0.0, 2.0], [1.0, -1.0, 0.5])
+        assert_array_almost_equal(zi, zi_expected)
+
+    @skip_xp_backends("dask.array", reason="FutureWarning emitted")
+    @pytest.mark.parametrize('b, a, zi_expected,',[
+        ([1., 0., 2.],     [1., -1., 0.5],   [5., -1.]),
+        ([1., 2., 3., 4.], [1.,],            [9.,  7.,  4.]),
+        ([1., 9.],         [1., 2., 3., 4.], [0. ,-7., -4.])])
+    def test_basic(self, b, a, zi_expected, xp):
+        b, a, zi_expected = (xp.asarray(v_) for v_ in (b, a, zi_expected))
+
+        zi = lfilter_zi(b, a)
+        assert_array_almost_equal(zi, zi_expected)
+
+        y = lfilter(b, a, xp.ones(9), zi=zi)[0]  # test for constant filter response
+
+        fill_value = xp.sum(b) / xp.sum(a)
+        y_expected = xp.full_like(y, fill_value=float(fill_value))
+        assert_array_almost_equal(y, y_expected)
+
+    def test_scale_invariance(self, xp):
+        # Regression test.  There was a bug in which b was not correctly
+        # rescaled when a[0] was nonzero.
+        b = xp.asarray([2.0, 8, 5])
+        a = xp.asarray([1.0, 1, 8])
+        zi1 = lfilter_zi(b, a)
+        zi2 = lfilter_zi(2*b, 2*a)
+        xp_assert_close(zi2, zi1, rtol=1e-12)
+
+    @pytest.mark.parametrize('dtype', ['float32', 'float64'])
+    def test_types(self, dtype, xp):
+        dtype = getattr(xp, dtype)
+        b = xp.zeros((8), dtype=dtype)
+        a = xp.asarray([1], dtype=dtype)
+        assert signal.lfilter_zi(b, a).dtype == dtype
+
+
+@make_xp_test_case(filtfilt, sosfiltfilt)
+class TestFiltFilt:
+    filtfilt_kind = 'tf'
+
+    def filtfilt(self, zpk, x, axis=-1, padtype='odd', padlen=None,
+                 method='pad', irlen=None, xp=None):
+        if self.filtfilt_kind == 'tf':
+            b, a = zpk2tf(*zpk)
+            b, a = xp.asarray(b), xp.asarray(a)
+            return filtfilt(b, a, x, axis, padtype, padlen, method, irlen)
+        elif self.filtfilt_kind == 'sos':
+            sos = zpk2sos(*zpk)
+            sos = xp.asarray(sos)
+            return sosfiltfilt(sos, x, axis, padtype, padlen)
+
+    @skip_xp_backends('torch', reason='negative strides')
+    def test_basic(self, xp):
+        if is_jax(xp) and self.filtfilt_kind == 'sos':
+            pytest.skip(reason='sosfilt works in-place')
+
+        zpk = tf2zpk(xp.asarray([1., 2, 3]), xp.asarray([1., 2, 3]))
+        out = self.filtfilt(zpk, xp.arange(12), xp=xp)
+        atol= 4e-9 if is_cupy(xp) else 5.28e-11
+        xp_assert_close(out, xp.arange(12, dtype=xp.float64), atol=atol)
+
+    @skip_xp_backends('torch', reason='negative strides')
+    def test_sine(self, xp):
+        if is_jax(xp) and self.filtfilt_kind == 'sos':
+            pytest.skip(reason='sosfilt works in-place')
+
+        rate = 2000
+        t = xp.linspace(0, 1.0, rate + 1)
+        # A signal with low frequency and a high frequency.
+        xlow = xp.sin(5 * 2 * np.pi * t)
+        xhigh = xp.sin(250 * 2 * np.pi * t)
+        x = xlow + xhigh
+
+        zpk = butter(8, xp.asarray(0.125), output='zpk')
+        # r is the magnitude of the largest pole.
+        r = np.abs(zpk[1]).max()
+        eps = 1e-5
+        # n estimates the number of steps for the
+        # transient to decay by a factor of eps.
+        n = int(np.ceil(np.log(eps) / np.log(r)))
+
+        # High order lowpass filter...
+        y = self.filtfilt(zpk, x, padlen=n, xp=xp)
+        # Result should be just xlow.
+        err = np.abs(y - xlow).max()
+        assert err < 1e-4
+
+        # A 2D case.
+        x2d = xp.asarray(np.vstack([xlow, xlow + xhigh]))
+        y2d = self.filtfilt(zpk, x2d, padlen=n, axis=1, xp=xp)
+        assert y2d.shape == x2d.shape
+        err = np.abs(y2d - xlow).max()
+        assert err < 1e-4
+
+        # Use the previous result to check the use of the axis keyword.
+        # (Regression test for ticket #1620)
+        y2dt = self.filtfilt(zpk, x2d.T, padlen=n, axis=0, xp=xp)
+        xp_assert_equal(y2d, y2dt.T)
+
+    @skip_xp_backends('torch', reason='negative strides')
+    def test_axis(self, xp):
+        if is_jax(xp) and self.filtfilt_kind == 'sos':
+            pytest.skip(reason='sosfilt works in-place')
+
+        # Test the 'axis' keyword on a 3D array.
+        x = np.arange(10.0 * 11.0 * 12.0).reshape(10, 11, 12)
+        x = xp.asarray(x)
+        zpk = butter(3, xp.asarray(0.125), output='zpk')
+        y0 = self.filtfilt(zpk, x, padlen=0, axis=0, xp=xp)
+        y1 = self.filtfilt(
+            zpk, xp.asarray(np.swapaxes(x, 0, 1)), padlen=0, axis=1, xp=xp
+        )
+        xp_assert_equal(y0, xp.asarray(np.swapaxes(y1, 0, 1)))
+        y2 = self.filtfilt(
+            zpk, xp.asarray(np.swapaxes(x, 0, 2)), padlen=0, axis=2, xp=xp
+        )
+        xp_assert_equal(y0, xp.asarray(np.swapaxes(y2, 0, 2)))
+
+    @skip_xp_backends(np_only=True,
+                      reason='python scalars in array_namespace are np-only')
+    def test_acoeff(self, xp):
+        if self.filtfilt_kind != 'tf':
+            return  # only necessary for TF
+        # test for 'a' coefficient as single number
+        out = signal.filtfilt(
+            xp.asarray([.5, .5]), 1, xp.arange(10, dtype=xp.float64)
+        )
+        xp_assert_close(out, xp.arange(10, dtype=xp.float64), rtol=1e-14, atol=1e-14)
+
+    @skip_xp_backends(np_only=True, reason='_filtfilt_gust is np-only')
+    def test_gust_simple(self, xp):
+        if self.filtfilt_kind != 'tf':
+            pytest.skip('gust only implemented for TF systems')
+        # The input array has length 2.  The exact solution for this case
+        # was computed "by hand".
+        x = xp.asarray([1.0, 2.0])
+        b = xp.asarray([0.5])
+        a = xp.asarray([1.0, -0.5])
+        y, z1, z2 = _filtfilt_gust(b, a, x)
+        xp_assert_close(z1[0], 0.3*x[0] + 0.2*x[1])
+        xp_assert_close(z2[0], 0.2*x[0] + 0.3*x[1])
+        xp_assert_close(y,
+                        xp.asarray([z1[0] + 0.25*z2[0] + 0.25*x[0] + 0.125*x[1],
+                                    0.25*z1[0] + z2[0] + 0.125*x[0] + 0.25*x[1]])
+        )
+
+    @skip_xp_backends(np_only=True,
+                      reason='python scalars in array_namespace are np-only')
+    def test_gust_scalars(self, xp):
+        if self.filtfilt_kind != 'tf':
+            pytest.skip('gust only implemented for TF systems')
+        # The filter coefficients are both scalars, so the filter simply
+        # multiplies its input by b/a.  When it is used in filtfilt, the
+        # factor is (b/a)**2.
+        x = xp.arange(12)
+        b = 3.0
+        a = 2.0
+        y = filtfilt(b, a, x, method="gust")
+        expected = (b/a)**2 * x
+        xp_assert_close(y, expected)
+
+
+@make_xp_test_case(sosfiltfilt, filtfilt)
+class TestSOSFiltFilt(TestFiltFilt):
+    filtfilt_kind = 'sos'
+
+    @skip_xp_backends('jax.numpy', reason='sosfilt works in-place')
+    @skip_xp_backends('torch', reason='negative strides')
+    def test_equivalence(self, xp):
+        """Test equivalence between sosfiltfilt and filtfilt"""
+        x = np.random.RandomState(0).randn(1000)
+        x = xp.asarray(x)
+        for order in range(1, 6):
+            zpk = signal.butter(order, 0.35, output='zpk')
+            b, a = zpk2tf(*zpk)
+            sos = zpk2sos(*zpk)
+
+            b, a, sos = map(xp.asarray, (b, a, sos))
+            y = filtfilt(b, a, x)
+            y_sos = sosfiltfilt(sos, x)
+            xp_assert_close(y, y_sos, atol=1e-12, err_msg=f'order={order}')
+
+
+def filtfilt_gust_opt(b, a, x):
+    """
+    An alternative implementation of filtfilt with Gustafsson edges.
+
+    This function computes the same result as
+    `scipy.signal._signaltools._filtfilt_gust`, but only 1-d arrays
+    are accepted.  The problem is solved using `fmin` from `scipy.optimize`.
+    `_filtfilt_gust` is significantly faster than this implementation.
+    """
+    def filtfilt_gust_opt_func(ics, b, a, x):
+        """Objective function used in filtfilt_gust_opt."""
+        m = max(len(a), len(b)) - 1
+        z0f = ics[:m]
+        z0b = ics[m:]
+        y_f = lfilter(b, a, x, zi=z0f)[0]
+        y_fb = lfilter(b, a, y_f[::-1], zi=z0b)[0][::-1]
+
+        y_b = lfilter(b, a, x[::-1], zi=z0b)[0][::-1]
+        y_bf = lfilter(b, a, y_b, zi=z0f)[0]
+        value = np.sum((y_fb - y_bf)**2)
+        return value
+
+    m = max(len(a), len(b)) - 1
+    zi = lfilter_zi(b, a)
+    ics = np.concatenate((x[:m].mean()*zi, x[-m:].mean()*zi))
+    result = fmin(filtfilt_gust_opt_func, ics, args=(b, a, x),
+                  xtol=1e-10, ftol=1e-12,
+                  maxfun=10000, maxiter=10000,
+                  full_output=True, disp=False)
+    opt, fopt, niter, funcalls, warnflag = result
+    if warnflag > 0:
+        raise RuntimeError(
+            f"minimization failed in filtfilt_gust_opt: warnflag={warnflag}"
+        )
+    z0f = opt[:m]
+    z0b = opt[m:]
+
+    # Apply the forward-backward filter using the computed initial
+    # conditions.
+    y_b = lfilter(b, a, x[::-1], zi=z0b)[0][::-1]
+    y = lfilter(b, a, y_b, zi=z0f)[0]
+
+    return y, z0f, z0b
+
+
+def check_filtfilt_gust(b, a, shape, axis, irlen=None):
+    # Generate x, the data to be filtered.
+    rng = np.random.default_rng(123)
+    x = rng.standard_normal(shape)
+
+    # Apply filtfilt to x. This is the main calculation to be checked.
+    y = filtfilt(b, a, x, axis=axis, method="gust", irlen=irlen)
+
+    # Also call the private function so we can test the ICs.
+    yg, zg1, zg2 = _filtfilt_gust(b, a, x, axis=axis, irlen=irlen)
+
+    # filtfilt_gust_opt is an independent implementation that gives the
+    # expected result, but it only handles 1-D arrays, so use some looping
+    # and reshaping shenanigans to create the expected output arrays.
+    xx = np.swapaxes(x, axis, -1)
+    out_shape = xx.shape[:-1]
+    yo = np.empty_like(xx)
+    m = max(len(a), len(b)) - 1
+    zo1 = np.empty(out_shape + (m,))
+    zo2 = np.empty(out_shape + (m,))
+    for indx in product(*[range(d) for d in out_shape]):
+        yo[indx], zo1[indx], zo2[indx] = filtfilt_gust_opt(b, a, xx[indx])
+    yo = np.swapaxes(yo, -1, axis)
+    zo1 = np.swapaxes(zo1, -1, axis)
+    zo2 = np.swapaxes(zo2, -1, axis)
+
+    xp_assert_close(y, yo, rtol=1e-8, atol=1e-9)
+    xp_assert_close(yg, yo, rtol=1e-8, atol=1e-9)
+    xp_assert_close(zg1, zo1, rtol=1e-8, atol=1e-9)
+    xp_assert_close(zg2, zo2, rtol=1e-8, atol=1e-9)
+
+
+@make_xp_test_case(choose_conv_method)
+@pytest.mark.fail_slow(10)
+def test_choose_conv_method(xp):
+    for mode in ['valid', 'same', 'full']:
+        for ndim in [1, 2]:
+            n, k, true_method = 8, 6, 'direct'
+            x = np.random.randn(*((n,) * ndim))
+            h = np.random.randn(*((k,) * ndim))
+
+            method = choose_conv_method(x, h, mode=mode)
+            assert method == true_method
+
+            method_try, times = choose_conv_method(x, h, mode=mode, measure=True)
+            assert method_try in {'fft', 'direct'}
+            assert isinstance(times, dict)
+            assert 'fft' in times.keys() and 'direct' in times.keys()
+
+        n = 10
+        for not_fft_conv_supp in ["complex256", "complex192"]:
+            if hasattr(np, not_fft_conv_supp):
+                x = np.ones(n, dtype=not_fft_conv_supp)
+                h = x.copy()
+                assert choose_conv_method(x, h, mode=mode) == 'direct'
+
+        x = np.array([2**51], dtype=np.int64)
+        h = x.copy()
+        assert choose_conv_method(x, h, mode=mode) == 'direct'
+
+
+@make_xp_test_case(choose_conv_method)
+def test_choose_conv_method_2(xp):
+    for mode in ['valid', 'same', 'full']:
+        n = 10
+        for not_fft_conv_supp in ["complex256", "complex192"]:
+            if hasattr(np, not_fft_conv_supp):
+                x = np.ones(n, dtype=not_fft_conv_supp)
+                h = x.copy()
+                assert choose_conv_method(x, h, mode=mode) == 'direct'
+
+
+@pytest.mark.fail_slow(10)
+def test_filtfilt_gust():
+    # Design a filter.
+    z, p, k = signal.ellip(3, 0.01, 120, 0.0875, output='zpk')
+
+    # Find the approximate impulse response length of the filter.
+    eps = 1e-10
+    r = np.max(np.abs(p))
+    approx_impulse_len = int(np.ceil(np.log(eps) / np.log(r)))
+
+    b, a = zpk2tf(z, p, k)
+    for irlen in [None, approx_impulse_len]:
+        signal_len = 5 * approx_impulse_len
+
+        # 1-d test case
+        check_filtfilt_gust(b, a, (signal_len,), 0, irlen)
+
+        # 3-d test case; test each axis.
+        for axis in range(3):
+            shape = [2, 2, 2]
+            shape[axis] = signal_len
+            check_filtfilt_gust(b, a, shape, axis, irlen)
+
+    # Test case with length less than 2*approx_impulse_len.
+    # In this case, `filtfilt_gust` should behave the same as if
+    # `irlen=None` was given.
+    length = 2*approx_impulse_len - 50
+    check_filtfilt_gust(b, a, (length,), 0, approx_impulse_len)
+
+
+@make_xp_test_case(signal.decimate)
+class TestDecimate:
+    def test_bad_args(self, xp):
+        x = xp.arange(12)
+        assert_raises(TypeError, signal.decimate, x, q=0.5, n=1)
+        assert_raises(TypeError, signal.decimate, x, q=2, n=0.5)
+
+    def test_basic_IIR(self, xp):
+        x = xp.arange(12)
+        y = signal.decimate(x, 2, n=1, ftype='iir', zero_phase=False).round()
+        xp_assert_equal(y, x[::2].astype(float))
+
+    def test_basic_FIR(self, xp):
+        x = xp.arange(12)
+        y = signal.decimate(x, 2, n=1, ftype='fir', zero_phase=False).round()
+        xp_assert_equal(y, x[::2].astype(float))
+
+    def test_shape(self, xp):
+        # Regression test for ticket #1480.
+        z = xp.zeros((30, 30))
+        d0 = signal.decimate(z, 2, axis=0, zero_phase=False)
+        assert d0.shape == (15, 30)
+        d1 = signal.decimate(z, 2, axis=1, zero_phase=False)
+        assert d1.shape == (30, 15)
+
+    @skip_xp_backends(np_only=True, reason="test code is NumPy specific")
+    def test_phaseshift_FIR(self, xp):
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", "Badly conditioned filter", BadCoefficients)
+            self._test_phaseshift(method='fir', zero_phase=False)
+
+    @skip_xp_backends(np_only=True, reason="test code is NumPy specific")
+    def test_zero_phase_FIR(self, xp):
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", "Badly conditioned filter", BadCoefficients)
+            self._test_phaseshift(method='fir', zero_phase=True)
+
+    @skip_xp_backends(np_only=True, reason="test code is NumPy specific")
+    def test_phaseshift_IIR(self, xp):
+        self._test_phaseshift(method='iir', zero_phase=False)
+
+    @skip_xp_backends(np_only=True, reason="test code is NumPy specific")
+    def test_zero_phase_IIR(self, xp):
+        self._test_phaseshift(method='iir', zero_phase=True)
+
+    def _test_phaseshift(self, method, zero_phase):
+        # TODO. Look into making tests using this work for CuPy.
+        rate = 120
+        rates_to = [15, 20, 30, 40]  # q = 8, 6, 4, 3
+
+        t_tot = 100  # Need to let antialiasing filters settle
+        t = np.arange(rate*t_tot+1) / float(rate)
+
+        # Sinusoids at 0.8*nyquist, windowed to avoid edge artifacts
+        freqs = np.array(rates_to) * 0.8 / 2
+        d = (np.exp(1j * 2 * np.pi * freqs[:, np.newaxis] * t)
+             * signal.windows.tukey(t.size, 0.1))
+
+        for rate_to in rates_to:
+            q = rate // rate_to
+            t_to = np.arange(rate_to*t_tot+1) / float(rate_to)
+            d_tos = (np.exp(1j * 2 * np.pi * freqs[:, np.newaxis] * t_to)
+                     * signal.windows.tukey(t_to.size, 0.1))
+
+            # Set up downsampling filters, match v0.17 defaults
+            if method == 'fir':
+                n = 30
+                system = signal.dlti(signal.firwin(n + 1, 1. / q,
+                                                   window='hamming'), 1.)
+            elif method == 'iir':
+                n = 8
+                wc = 0.8*np.pi/q
+                system = signal.dlti(*signal.cheby1(n, 0.05, wc/np.pi))
+
+            # Calculate expected phase response, as unit complex vector
+            if zero_phase is False:
+                _, h_resps = signal.freqz(system.num, system.den,
+                                          freqs/rate*2*np.pi)
+                h_resps /= np.abs(h_resps)
+            else:
+                h_resps = np.ones_like(freqs)
+
+            y_resamps = signal.decimate(d.real, q, n, ftype=system,
+                                        zero_phase=zero_phase)
+
+            # Get phase from complex inner product, like CSD
+            h_resamps = np.sum(d_tos.conj() * y_resamps, axis=-1)
+            h_resamps /= np.abs(h_resamps)
+            subnyq = freqs < 0.5*rate_to
+
+            # Complex vectors should be aligned, only compare below nyquist
+            result = np.angle(h_resps.conj()*h_resamps)[subnyq]
+            xp_assert_close(result, np.zeros_like(result),
+                            atol=1e-3, rtol=1e-3)
+
+    def test_auto_n(self, xp):
+        # Test that our value of n is a reasonable choice (depends on
+        # the downsampling factor)
+        sfreq = 100.
+        n = 1000
+        t = xp.arange(n) / sfreq
+        # will alias for decimations (>= 15)
+        x = xp.asarray(xp.sqrt(2. / n) * xp.sin(2 * xp.pi * (sfreq / 30.) * t))
+        # Use xp.sqrt(x.dot(x)) instead of xp.linalg.vector_norm(x) because
+        # linear algebra extension is not universally available.
+        xp_assert_close(xp.sqrt(x.dot(x)), xp.asarray(1.), rtol=1e-3, check_0d=False)
+        x_out = signal.decimate(x, 30, ftype='fir')
+        assert xp.sqrt(x_out.dot(x_out)) < 0.01
+
+    def test_long_float32(self, xp):
+        # regression: gh-15072.  With 32-bit float and either lfilter
+        # or filtfilt, this is numerically unstable
+        x = signal.decimate(xp.ones(10_000, dtype=xp.float32), 10)
+        assert not any(xp.isnan(x))
+
+    def test_float16_upcast(self):
+        # float16 must be upcast to float64
+        x = signal.decimate(np.ones(100, dtype=np.float16), 10)
+        assert x.dtype.type == np.float64
+
+    @skip_xp_backends(np_only=True, reason="dlti")
+    def test_complex_iir_dlti(self, xp):
+        # regression: gh-17845
+        # centre frequency for filter [Hz]
+        fcentre = 50
+        # filter passband width [Hz]
+        fwidth = 5
+        # sample rate [Hz]
+        fs = 1e3
+
+        z, p, k = signal.butter(2, xp.asarray(2*xp.pi*fwidth/2),
+                                output='zpk', fs=fs)
+        z = z.astype(complex) * xp.exp(xp.asarray(2j * xp.pi * fcentre/fs))
+        p = p.astype(complex) * xp.exp(xp.asarray(2j * xp.pi * fcentre/fs))
+        system = signal.dlti(z, p, k)
+
+        t = xp.arange(200) / fs
+
+        # input
+        u = (xp.exp(2j * xp.pi * fcentre * t)
+             + 0.5 * xp.exp(-2j * xp.pi * fcentre * t))
+
+        ynzp = signal.decimate(u, 2, ftype=system, zero_phase=False)
+        ynzpref = signal.lfilter(*signal.zpk2tf(z, p, k),
+                                 u)[::2]
+
+        xp_assert_equal(ynzp, ynzpref)
+
+        yzp = signal.decimate(u, 2, ftype=system, zero_phase=True)
+        yzpref = signal.filtfilt(*signal.zpk2tf(z, p, k),
+                                 u)[::2]
+
+        xp_assert_close(yzp, yzpref, rtol=1e-10, atol=1e-13)
+
+    @skip_xp_backends(np_only=True, reason="dlti")
+    def test_complex_fir_dlti(self, xp):
+        # centre frequency for filter [Hz]
+        fcentre = 50
+        # filter passband width [Hz]
+        fwidth = 5
+        # sample rate [Hz]
+        fs = 1e3
+        numtaps = 20
+
+        # FIR filter about 0Hz
+        bbase = signal.firwin(numtaps, fwidth/2, fs=fs)
+
+        # rotate these to desired frequency
+        zbase = np.roots(bbase)
+        zrot = zbase * np.exp(2j * np.pi * fcentre/fs)
+        # FIR filter about 50Hz, maintaining passband gain of 0dB
+        bz = bbase[0] * np.poly(zrot)
+
+        system = signal.dlti(bz, 1)
+
+        t = np.arange(200) / fs
+
+        # input
+        u = (np.exp(2j * np.pi * fcentre * t)
+             + 0.5 * np.exp(-2j * np.pi * fcentre * t))
+
+        ynzp = signal.decimate(u, 2, ftype=system, zero_phase=False)
+        ynzpref = signal.upfirdn(bz, u, up=1, down=2)[:100]
+
+        xp_assert_equal(ynzp, ynzpref)
+
+        yzp = signal.decimate(u, 2, ftype=system, zero_phase=True)
+        yzpref = signal.resample_poly(u, 1, 2, window=bz)
+
+        xp_assert_equal(yzp, yzpref)
+
+@make_xp_test_case(hilbert)
+class TestHilbert:
+
+    def test_bad_args(self, xp):
+        x = xp.asarray([1.0 + 0.0j])
+        assert_raises(ValueError, hilbert, x)
+        x = xp.arange(8.0)
+        assert_raises(ValueError, hilbert, x, N=0)
+
+    def test_hilbert_theoretical(self, xp):
+        # test cases by Ariel Rokem
+        decimal = 14
+
+        pi = xp.pi
+        t = xp.arange(0, 2 * pi, pi / 256, dtype=xp.float64)
+        a0 = xp.sin(t)
+        a1 = xp.cos(t)
+        a2 = xp.sin(2 * t)
+        a3 = xp.cos(2 * t)
+        a = xp.stack([a0, a1, a2, a3])
+
+        h = hilbert(a)
+        h_abs = xp.abs(h)
+
+        h_angle = xp.atan2(xp.imag(h), xp.real(h)) #  np.angle(h)
+        h_real = xp.real(h)
+
+        # The real part should be equal to the original signals:
+        assert_almost_equal(h_real, a, decimal)
+        # The absolute value should be one everywhere, for this input:
+        assert_almost_equal(h_abs, xp.ones(a.shape), decimal)
+        # For the 'slow' sine - the phase should go from -pi/2 to pi/2 in
+        # the first 256 bins:
+        assert_almost_equal(h_angle[0, :256],
+                            xp.arange(-pi / 2, pi / 2, pi / 256, dtype=xp.float64),
+                            decimal)
+        # For the 'slow' cosine - the phase should go from 0 to pi in the
+        # same interval:
+        assert_almost_equal(
+            h_angle[1, :256], xp.arange(0, pi, pi / 256, dtype=xp.float64), decimal)
+        # The 'fast' sine should make this phase transition in half the time:
+        assert_almost_equal(h_angle[2, :128],
+                            xp.arange(-pi / 2, pi / 2, pi / 128, dtype=xp.float64),
+                            decimal)
+        # Ditto for the 'fast' cosine:
+        assert_almost_equal(
+            h_angle[3, :128], xp.arange(0, pi, pi / 128, dtype=xp.float64), decimal)
+
+        # The imaginary part of hilbert(cos(t)) = sin(t) Wikipedia
+        assert_almost_equal(xp.imag(h[1, :]), a0, decimal)
+
+    def test_hilbert_axisN(self, xp):
+        # tests for axis and N arguments
+        a = xp.reshape(xp.arange(18, dtype=xp.float64), (3, 6))
+        # test axis
+        aa = hilbert(a, axis=-1)
+        xp_assert_equal(hilbert(a.T, axis=0), aa.T)
+        # test 1d
+        assert_almost_equal(hilbert(a[0, :]), aa[0, :], 14)
+
+        # test N
+        aan = hilbert(a, N=20, axis=-1)
+        assert aan.shape == (3, 20)
+        assert hilbert(a.T, N=20, axis=0).shape == (20, 3)
+        # the next test is just a regression test,
+        # no idea whether numbers make sense
+        a0hilb = np.array([0.000000000000000e+00 - 1.72015830311905j,
+                           1.000000000000000e+00 - 2.047794505137069j,
+                           1.999999999999999e+00 - 2.244055555687583j,
+                           3.000000000000000e+00 - 1.262750302935009j,
+                           4.000000000000000e+00 - 1.066489252384493j,
+                           5.000000000000000e+00 + 2.918022706971047j,
+                           8.881784197001253e-17 + 3.845658908989067j,
+                          -9.444121133484362e-17 + 0.985044202202061j,
+                          -1.776356839400251e-16 + 1.332257797702019j,
+                          -3.996802888650564e-16 + 0.501905089898885j,
+                           1.332267629550188e-16 + 0.668696078880782j,
+                          -1.192678053963799e-16 + 0.235487067862679j,
+                          -1.776356839400251e-16 + 0.286439612812121j,
+                           3.108624468950438e-16 + 0.031676888064907j,
+                           1.332267629550188e-16 - 0.019275656884536j,
+                          -2.360035624836702e-16 - 0.1652588660287j,
+                           0.000000000000000e+00 - 0.332049855010597j,
+                           3.552713678800501e-16 - 0.403810179797771j,
+                           8.881784197001253e-17 - 0.751023775297729j,
+                           9.444121133484362e-17 - 0.79252210110103j])
+        a0hilb = xp.asarray(a0hilb)
+        assert_almost_equal(aan[0, :], a0hilb, 14, err_msg='N regression')
+
+    def test_hilbert_axis_3d(self, xp):
+        a = xp.reshape(xp.arange(3 * 5 * 7, dtype=xp.float64), (3, 5, 7))
+        # test axis
+        aa = hilbert(a, axis=-1)
+        for axis in [0, 1]:
+            aap = hilbert(xp.moveaxis(a, -1, axis), axis=axis)
+            aap = xp.moveaxis(aap, axis, -1)
+            xp_assert_equal(aa, aap)
+
+    @pytest.mark.parametrize('dtype', ['float32', 'float64'])
+    def test_hilbert_types(self, dtype, xp):
+        dtype = getattr(xp, dtype)
+        in_typed = xp.zeros(8, dtype=dtype)
+        assert xp.real(hilbert(in_typed)).dtype == dtype
+
+
+@make_xp_test_case(hilbert2)
+class TestHilbert2:
+    """Test function `signal.hilbert2`. """
+
+    @skip_xp_backends(np_only=True, reason='list inputs are numpy-specific')
+    def test_array_like(self, xp):
+        hilbert2([[1, 2, 3], [4, 5, 6]])
+
+    def test_bad_args(self, xp):
+        """Raise all exceptions in `hilbert2`. """
+        x = xp.reshape(xp.arange(16), (4, 4))
+        with pytest.raises(ValueError, match="^x must be real."):
+            hilbert2(xp.asarray([[1.0 + 0.0j]]))
+        with pytest.raises(ValueError, match="^N must be positive."):
+            hilbert2(x, N=-1)
+        with pytest.raises(ValueError, match="^When given as a tuple, N must hold"):
+            hilbert2(x, N=(1, 1, 1))
+        with pytest.raises(ValueError, match="^When given as a tuple, N must hold"):
+            hilbert2(x, N=(0, 1))
+
+    @skip_xp_backends("cupy", reason="CuPy's hilbert2 does not have axes= argument")
+    def test_bad_args2(self, xp):
+        x = xp.reshape(xp.arange(16), (4, 4))
+        with pytest.raises(ValueError, match="^axes must be a tuple of length 2"):
+            hilbert2(x, axes=(0, 1, 2))
+        with pytest.raises(ValueError, match="^axes must contain 2 distinct axes"):
+            hilbert2(x, axes=(0, 0))
+
+    @pytest.mark.parametrize('dtype', ['float32', 'float64'])
+    def test_hilbert2_types(self, dtype, xp):
+        dtype = getattr(xp, dtype)
+        in_typed = xp.zeros((2, 32), dtype=dtype)
+        out = xp.real(signal.hilbert2(in_typed))
+        assert out.dtype == dtype
+
+    def test_1d_input(self, xp):
+        """Needed for 100% coverage """
+        x = xp.asarray([0., 1., 1., 0., -1., -1.])
+        x0a = signal.hilbert2(xp.reshape(x, (6, 1)))
+        x1a = signal.hilbert2(xp.reshape(x, (1, 6)))
+        xp_assert_close(x0a, x1a.T)
+
+    def test_parameter_N(self, xp):
+        """Compare passing tuple to single int. """
+        x = xp.zeros((5, 5))
+        x0_a = hilbert2(x, N=4)
+        x1_a = hilbert2(x, N=(4, 4))
+        xp_assert_equal(x1_a, x0_a)
+
+    @pytest.mark.parametrize('shape', [(4, 5), (5, 4), (4, 4), (5, 5)])
+    @skip_xp_backends("cupy", reason="Bug in cupy implementation, see cupy#9396")
+    def test_quadrant_values(self, shape, xp):
+        """Compare desired and calculated values in Fourier space. """
+        x_f = xp.ones(shape, dtype=xp.complex128)  # FFT of input signal
+        x_f = xpx.at(x_f)[0, 0].add(7)
+        x = xp.real(sp_fft.ifft2(x_f))  # x.imag is zero
+
+        x_as = hilbert2(x)
+        x_as_f = sp_fft.fft2(x_as)
+
+        # Create slices for bins with purely positive and purely negative frequencies
+        # (can be verified with `sp_fft.fftfreq()`):
+        f0_pos, f0_neg = slice(1, (shape[0] + 1) // 2), slice((shape[0] + 1) // 2, None)
+        f1_pos, f1_neg = slice(1, (shape[1] + 1) // 2), slice((shape[1] + 1) // 2, None)
+        # Verify all values:
+        atol = 1e-12  # for x of dtype complex128
+        xp_assert_close(x_as_f[f0_pos, f1_pos], x_f[f0_pos, f1_pos] * 4, atol=atol)
+        xp_assert_close(x_as_f[0, f1_pos], x_f[0, f1_pos] * 2, atol=atol)
+        xp_assert_close(x_as_f[f0_pos, 0], x_f[f0_pos, 0] * 2, atol=atol)
+        xp_assert_close(x_as_f[0, 0], x_f[0, 0], atol=atol)
+        zz_as_f = x_as_f[f0_neg, f1_neg]  # check for zeroed orthants
+        xp_assert_close(zz_as_f, xp.zeros_like(zz_as_f), atol=atol)
+
+    @pytest.mark.parametrize('shape', [(4, 5), (5, 4), (4, 4), (5, 5)])
+    def test_zero_analytic_signal(self, shape, xp):
+        """Test that a real signal with Z[-p,-q] == np.conj(Z[p,q])
+        produces a zero analytic signal."""
+        c0 = shape[0] // 2
+        c1 = shape[1] // 2
+        x_f = xp.zeros(shape)
+        x_f = xpx.at(x_f)[c0 - 1, c1 + 1].set(1.0)
+        x_f = xpx.at(x_f)[c0 + 1, c1 - 1].set(1.0)
+        x_f = sp_fft.ifftshift(x_f)
+        x = xp.real(sp_fft.ifft2(x_f))
+        assert xp.sum(abs(x)) > 0.0
+        x_as = hilbert2(x)
+        xp_assert_close(x_as, xp.zeros_like(x_as), atol=xp.finfo(x_as.dtype).eps*16)
+
+    @pytest.mark.parametrize('sh0', [4, 5])
+    @pytest.mark.parametrize('sh1', [6, 7])
+    @pytest.mark.parametrize('sh2', [8, 9])
+    @pytest.mark.parametrize('not_axis', [0, 1, 2])
+    @skip_xp_backends("cupy", reason="cupy implementation does not have axes kwarg")
+    def test_3d_vs_slice(self, sh0, sh1, sh2, not_axis, xp):
+        """2d transform on 3d array is equal to 2d transform on 2d slices."""
+        x = xp.reshape(xp.arange(sh0 * sh1 * sh2, dtype=xp.float64), (sh0, sh1, sh2))
+        transform_axes = [0, 1, 2]
+        transform_axes.pop(not_axis)
+        x_as_3d = hilbert2(x, axes=transform_axes)
+        parts = xp.unstack(x, axis=not_axis)
+        x_as_2d = [hilbert2(p) for p in parts]
+        x_as_2d = xp.stack(x_as_2d, axis=not_axis)
+        xp_assert_close(x_as_3d, x_as_2d)
+
+    @skip_xp_backends("cupy", reason="cupy implementation does not have axes kwarg")
+    def test_3d_axis_order(self, xp):
+        """2d transform on equal arrays with moved axis are equal."""
+        x0 = xp.reshape(xp.arange(5 * 7 * 9, dtype=xp.float64), (5, 7, 9))
+        x0_as = hilbert2(x0)
+
+        x1 = xp.moveaxis(x0, 0, 1)
+        x1_as = hilbert2(x1, axes=(0, 2))
+        x1_as = xp.moveaxis(x1_as, 1, 0)
+        xp_assert_close(x0_as, x1_as)
+
+        x2 = xp.moveaxis(x0, 0, 2)
+        x2_as = hilbert2(x2, axes=(0, 1))
+        x2_as = xp.moveaxis(x2_as, 2, 0)
+        xp_assert_close(x0_as, x2_as)
+
+
+@make_xp_test_case(envelope)
+class TestEnvelope:
+    """Unit tests for function `._signaltools.envelope()`. """
+
+    @staticmethod
+    def assert_close(actual, desired, msg, xp):
+        a_r_tol = ({'atol': 1e-12, 'rtol': 1e-12}
+                   if xp_default_dtype(xp) == xp.float64
+                   else {'atol': 1e-5, 'rtol': 1e-5}
+        )
+
+        """Little helper to compare to arrays with proper tolerances"""
+        xp_assert_close(actual, desired, **a_r_tol, err_msg=msg)
+
+    def test_envelope_invalid_parameters(self, xp):
+        """For `envelope()` Raise all exceptions that are used to verify function
+        parameters. """
+        with pytest.raises(ValueError,
+                           match=r"Invalid parameter axis=2 for z.shape=.*"):
+            envelope(np.ones(3), axis=2)
+        with pytest.raises(ValueError,
+                           match=r"z.shape\[axis\] not > 0 for z.shape=.*"):
+            envelope(xp.ones((3, 0)), axis=1)
+        for bp_in in [(0, 1, 2), (0, 2.), (None, 2.)]:
+            ts = ', '.join(map(str, bp_in))
+            with pytest.raises(ValueError,
+                               match=rf"bp_in=\({ts}\) isn't a 2-tuple of.*"):
+                # noinspection PyTypeChecker
+                envelope(xp.ones(4), bp_in=bp_in)
+        with pytest.raises(ValueError,
+                           match="n_out=10.0 is not a positive integer or.*"):
+            # noinspection PyTypeChecker
+            envelope(xp.ones(4), n_out=10.)
+        for bp_in in [(-1, 3), (1, 1), (0, 10)]:
+            with pytest.raises(ValueError,
+                               match=r"`-n//2 <= bp_in\[0\] < bp_in\[1\] <=.*"):
+                envelope(xp.ones(4), bp_in=bp_in)
+        with pytest.raises(ValueError, match="residual='undefined' not in .*"):
+            # noinspection PyTypeChecker
+            envelope(xp.ones(4), residual='undefined')
+
+    @skip_xp_backends("jax.numpy", reason="XXX: immutable arrays")
+    def test_envelope_verify_parameters(self, xp):
+        """Ensure that the various parametrizations produce compatible results. """
+        dt_r = xp_default_dtype(xp)
+        dt_c = xp.complex64 if dt_r == xp.float32 else xp.complex128
+
+        Z = xp.asarray([4.0, 2, 2, 3, 0], dtype=dt_r)
+        Zr_a = xp.asarray([4.0, 0, 0, 6, 0, 0, 0, 0], dtype=dt_r)
+        z = sp_fft.irfft(Z)
+        n = z.shape[0]
+
+        # the reference envelope:
+        ze2_0, zr_0 = xp.unstack(envelope(z, (1, 3), residual='all', squared=True))
+        self.assert_close(sp_fft.rfft(ze2_0),
+                          xp.asarray([4, 2, 0, 0, 0], dtype=dt_c),
+                          msg="Envelope calculation error", xp=xp)
+        self.assert_close(sp_fft.rfft(zr_0),
+                          xp.asarray([4, 0, 0, 3, 0], dtype=dt_c),
+                          msg="Residual calculation error", xp=xp)
+
+        ze_1, zr_1 = xp.unstack(envelope(z, (1, 3), residual='all', squared=False))
+        self.assert_close(ze_1**2, ze2_0,
+                          msg="Unsquared versus Squared envelope calculation error",
+                          xp=xp)
+        self.assert_close(zr_1, zr_0,
+                          msg="Unsquared versus Squared residual calculation error",
+                          xp=xp)
+
+        ze2_2, zr_2 = xp.unstack(
+            envelope(z, (1, 3), residual='all', squared=True, n_out=3*n)
+        )
+        self.assert_close(ze2_2[::3], ze2_0,
+                          msg="3x up-sampled envelope calculation error", xp=xp)
+        self.assert_close(zr_2[::3], zr_0,
+                          msg="3x up-sampled residual calculation error", xp=xp)
+
+        ze2_3, zr_3 = xp.unstack(envelope(z, (1, 3), residual='lowpass', squared=True))
+        self.assert_close(ze2_3, ze2_0,
+                          msg="`residual='lowpass'` envelope calculation error", xp=xp)
+        self.assert_close(sp_fft.rfft(zr_3),
+                          xp.asarray([4, 0, 0, 0, 0], dtype=dt_c),
+                          msg="`residual='lowpass'` residual calculation error", xp=xp)
+
+        ze2_4 = envelope(z, (1, 3), residual=None, squared=True)
+        self.assert_close(ze2_4, ze2_0,
+                          msg="`residual=None` envelope calculation error", xp=xp)
+
+        # compare complex analytic signal to real version
+        Z_a = xp.asarray(Z, copy=True)
+        Z_a[1:] *= 2
+        z_a = sp_fft.ifft(Z_a, n=n)  # analytic signal of Z
+        self.assert_close(xp.real(z_a), z,
+                          msg="Reference analytic signal error", xp=xp)
+        ze2_a, zr_a = xp.unstack(envelope(z_a, (1, 3), residual='all', squared=True))
+        self.assert_close(ze2_a, xp.astype(ze2_0, dt_c),  # dtypes must match
+                          msg="Complex envelope calculation error", xp=xp)
+        self.assert_close(sp_fft.fft(zr_a), xp.asarray(Zr_a, dtype=dt_c),
+                          msg="Complex residual calculation error", xp=xp)
+
+    @skip_xp_backends("jax.numpy", reason="XXX: immutable arrays")
+    @pytest.mark.parametrize(
+        "               Z,        bp_in,     Ze2_desired,      Zr_desired",
+        [([1, 0, 2, 2, 0],    (1, None), [4, 2, 0, 0, 0], [1, 0, 0, 0, 0]),
+         ([4, 0, 2, 0, 0],    (0, None), [4, 0, 2, 0, 0], [0, 0, 0, 0, 0]),
+         ([4, 0, 0, 2, 0], (None, None), [4, 0, 0, 2, 0], [0, 0, 0, 0, 0]),
+         ([0, 0, 2, 2, 0],       (1, 3), [2, 0, 0, 0, 0], [0, 0, 0, 2, 0]),
+         ([4, 0, 2, 2, 0],      (-3, 3), [4, 0, 2, 0, 0], [0, 0, 0, 2, 0]),
+         ([4, 0, 3, 4, 0],    (None, 1), [2, 0, 0, 0, 0], [0, 0, 3, 4, 0]),
+         ([4, 0, 3, 4, 0],    (None, 0), [0, 0, 0, 0, 0], [4, 0, 3, 4, 0])])
+    def test_envelope_real_signals(self, Z, bp_in, Ze2_desired, Zr_desired, xp):
+        """Test envelope calculation with real-valued test signals.
+
+        The comparisons are performed in the Fourier space, since it makes evaluating
+        the bandpass filter behavior straightforward. Note that also the squared
+        envelope can be easily calculated by hand, if one recalls that coefficients of
+        a complex-valued Fourier series representing the signal can be directly
+        determined by an FFT and that the absolute square of a Fourier series is again
+        a Fourier series.
+        """
+        Z = xp.asarray(Z, dtype=xp.float64)
+        Ze2_desired = xp.asarray(Ze2_desired, dtype=xp.float64)
+        Zr_desired = xp.asarray(Zr_desired, dtype=xp.float64)
+
+        z = sp_fft.irfft(Z)
+        ze2, zr = xp.unstack(envelope(z, bp_in, residual='all', squared=True))
+        ze2_lp, zr_lp = xp.unstack(envelope(z, bp_in, residual='lowpass', squared=True))
+        Ze2, Zr, Ze2_lp, Zr_lp = (sp_fft.rfft(z_) for z_ in (ze2, zr, ze2_lp, zr_lp))
+
+        Ze2_desired = xp.asarray(Ze2_desired, dtype=xp.complex128)
+        Zr_desired = xp.asarray(Zr_desired, dtype=xp.complex128)
+        self.assert_close(Ze2, Ze2_desired,
+                          msg="Envelope calculation error (residual='all')", xp=xp)
+        self.assert_close(Zr, Zr_desired,
+                          msg="Residual calculation error (residual='all')", xp=xp)
+
+        if bp_in[1] is not None:
+            Zr_desired[bp_in[1]:] = 0
+        self.assert_close(Ze2_lp, Ze2_desired,
+                          msg="Envelope calculation error (residual='lowpass')", xp=xp)
+        self.assert_close(Zr_lp, Zr_desired,
+                          msg="Residual calculation error (residual='lowpass')", xp=xp)
+
+    @skip_xp_backends("jax.numpy", reason="XXX: immutable arrays")
+    @pytest.mark.parametrize(
+        "               Z,        bp_in,         Ze2_desired,         Zr_desired",
+        [([0, 5, 0, 5, 0], (None, None),    [5, 0, 10, 0, 5],    [0, 0, 0, 0, 0]),
+         ([1, 5, 0, 5, 2],      (-1, 2),    [5, 0, 10, 0, 5],    [1, 0, 0, 0, 2]),
+         ([1, 2, 6, 0, 6, 3],   (-1, 2), [0, 6, 0, 12, 0, 6], [1, 2, 0, 0, 0, 3])
+         ])
+    def test_envelope_complex_signals(self, Z, bp_in, Ze2_desired, Zr_desired, xp):
+        """Test envelope calculation with complex-valued test signals.
+
+        We only need to test for the complex envelope here, since the ``Nones``s in the
+        bandpass filter were already tested in the previous test.
+        """
+        Z = xp.asarray(Z, dtype=xp.float64)
+        Ze2_desired = xp.asarray(Ze2_desired, dtype=xp.complex128)
+        Zr_desired = xp.asarray(Zr_desired, dtype=xp.complex128)
+
+        z = sp_fft.ifft(sp_fft.ifftshift(Z))
+        ze2, zr = xp.unstack(envelope(z, bp_in, residual='all', squared=True))
+        Ze2, Zr = (sp_fft.fftshift(sp_fft.fft(z_)) for z_ in (ze2, zr))
+
+        self.assert_close(Ze2, Ze2_desired,
+                          msg="Envelope calculation error", xp=xp)
+        self.assert_close(Zr, Zr_desired,
+                          msg="Residual calculation error", xp=xp)
+
+    @skip_xp_backends("jax.numpy", reason="XXX: immutable arrays")
+    def test_envelope_verify_axis_parameter(self, xp):
+        """Test for multi-channel envelope calculations. """
+        dt_r = xp_default_dtype(xp)
+        dt_c = xp.complex64 if dt_r == xp.float32 else xp.complex128
+
+        z = sp_fft.irfft(xp.asarray([[1.0, 0, 2, 2, 0], [7, 0, 4, 4, 0]], dtype=dt_r))
+        Ze2_desired = xp.asarray([[4, 2, 0, 0, 0], [16, 8, 0, 0, 0]],
+                                 dtype=dt_c)
+        Zr_desired = xp.asarray([[1, 0, 0, 0, 0], [7, 0, 0, 0, 0]], dtype=dt_c)
+
+        ze2, zr = xp.unstack(envelope(z, squared=True, axis=1))
+        ye2T, yrT = xp.unstack(envelope(z.T, squared=True, axis=0))
+        Ze2, Ye2, Zr, Yr = (sp_fft.rfft(z_) for z_ in (ze2, ye2T.T, zr, yrT.T))
+
+        self.assert_close(Ze2, Ze2_desired, msg="2d envelope calculation error", xp=xp)
+        self.assert_close(Zr, Zr_desired,  msg="2d residual calculation error", xp=xp)
+        self.assert_close(
+            Ye2, Ze2_desired, msg="Transposed 2d envelope calc. error", xp=xp
+        )
+        self.assert_close(
+            Yr, Zr_desired, msg="Transposed 2d residual calc. error", xp=xp
+        )
+
+    @skip_xp_backends("jax.numpy", reason="XXX: immutable arrays")
+    def test_envelope_verify_axis_parameter_complex(self, xp):
+        """Test for multi-channel envelope calculations with complex values. """
+        dt_r = xp_default_dtype(xp)
+        dt_c = xp.complex64 if dt_r == xp.float32 else xp.complex128
+        inp = xp.asarray([[1.0, 5, 0, 5, 2], [1, 10, 0, 10, 2]], dtype=dt_r)
+        z = sp_fft.ifft(sp_fft.ifftshift(inp, axes=1))
+        Ze2_des = xp.asarray([[5, 0, 10, 0, 5], [20, 0, 40, 0, 20],], dtype=dt_c)
+        Zr_des = xp.asarray([[1, 0, 0, 0, 2], [1, 0, 0, 0, 2]], dtype=dt_c)
+
+        kw = dict(bp_in=(-1, 2), residual='all', squared=True)
+        ze2, zr = xp.unstack(envelope(z, axis=1, **kw))
+        ye2T, yrT = xp.unstack(envelope(z.T, axis=0, **kw))
+        Ze2, Ye2, Zr, Yr = (sp_fft.fftshift(sp_fft.fft(z_), axes=1)
+                            for z_ in (ze2, ye2T.T, zr, yrT.T))
+
+        self.assert_close(Ze2, Ze2_des, msg="2d envelope calculation error", xp=xp)
+        self.assert_close(Zr, Zr_des, msg="2d residual calculation error", xp=xp)
+        self.assert_close(
+            Ye2, Ze2_des,  msg="Transposed 2d envelope calc. error", xp=xp
+        )
+        self.assert_close(Yr, Zr_des,  msg="Transposed 2d residual calc. error", xp=xp)
+
+    @skip_xp_backends("jax.numpy", reason="XXX: immutable arrays")
+    @pytest.mark.parametrize('X', [[4, 0, 0, 1, 2], [4, 0, 0, 2, 1, 2]])
+    def test_compare_envelope_hilbert(self, X, xp):
+        """Compare output of `envelope()` and `hilbert()`. """
+        X = xp.asarray(X, dtype=xp.float64)
+        x = sp_fft.irfft(X)
+        e_hil = xp.abs(hilbert(x))
+        e_env = envelope(x, (None, None), residual=None)
+        self.assert_close(e_hil, e_env, msg="Hilbert-Envelope comparison error", xp=xp)
+
+    def test_nyquist(self):
+        """Test behavior when input is a cosine at the Nyquist frequency.
+
+        Resampling even length signals, requires accounting for unpaired bins at the
+        Nyquist frequency (consults the source code of `resample`).
+
+        Since `envelope` excludes the Nyquist frequency from the envelope calculation,
+        only the residues need to be investigated.
+        """
+        x4 = sp_fft.irfft([0, 0, 8])  # = [2, -2, 2, -2]
+        x6 = signal.resample(x4, num=6)  # = [2, -1, -1, 2, -1, -1]
+        y6, y6_res = envelope(x4, n_out=6, residual='all')  # real-valued case
+        z6, z6_res = envelope(x4 + 0j, n_out=6, residual='all')  # complex-valued case
+
+        xp_assert_close(y6, np.zeros(6), atol=1e-12)
+        xp_assert_close(y6_res, x6, atol=1e-12)
+
+        xp_assert_close(z6, np.zeros(6, dtype=z6.dtype), atol=1e-12)
+        xp_assert_close(z6_res, x6.astype(z6.dtype), atol=1e-12)
+
+
+class TestPartialFractionExpansion:
+    @staticmethod
+    def assert_rp_almost_equal(r, p, r_true, p_true, decimal=7):
+        xp = array_namespace(r, p)
+        r_true = xp.asarray(r_true)
+        p_true = xp.asarray(p_true)
+
+        distance = xp.hypot(abs(p[:, None] - p_true),
+                            abs(r[:, None] - r_true))
+
+        rows, cols = linear_sum_assignment(_xp_copy_to_numpy(distance))
+        assert_almost_equal(p[rows], p_true[cols], decimal=decimal)
+        assert_almost_equal(r[rows], r_true[cols], decimal=decimal)
+
+    def test_compute_factors(self):
+        factors, poly = _compute_factors([1, 2, 3], [3, 2, 1])
+        assert len(factors) == 3
+        assert_almost_equal(factors[0], np.poly([2, 2, 3]))
+        assert_almost_equal(factors[1], np.poly([1, 1, 1, 3]))
+        assert_almost_equal(factors[2], np.poly([1, 1, 1, 2, 2]))
+        assert_almost_equal(poly, np.poly([1, 1, 1, 2, 2, 3]))
+
+        factors, poly = _compute_factors([1, 2, 3], [3, 2, 1],
+                                         include_powers=True)
+        assert len(factors) == 6
+        assert_almost_equal(factors[0], np.poly([1, 1, 2, 2, 3]))
+        assert_almost_equal(factors[1], np.poly([1, 2, 2, 3]))
+        assert_almost_equal(factors[2], np.poly([2, 2, 3]))
+        assert_almost_equal(factors[3], np.poly([1, 1, 1, 2, 3]))
+        assert_almost_equal(factors[4], np.poly([1, 1, 1, 3]))
+        assert_almost_equal(factors[5], np.poly([1, 1, 1, 2, 2]))
+        assert_almost_equal(poly, np.poly([1, 1, 1, 2, 2, 3]))
+
+    def test_group_poles(self):
+        unique, multiplicity = _group_poles(
+            [1.0, 1.001, 1.003, 2.0, 2.003, 3.0], 0.1, 'min')
+        xp_assert_close(unique, [1.0, 2.0, 3.0])
+        xp_assert_close(multiplicity, [3, 2, 1])
+
+    @make_xp_test_case(residue)
+    def test_residue_general(self, xp):
+        # Test are taken from issue #4464, note that poles in scipy are
+        # in increasing by absolute value order, opposite to MATLAB.
+        r, p, k = residue(xp.asarray([5, 3, -2, 7]), xp.asarray([-4, 0, 8, 3]))
+        assert_almost_equal(r, xp.asarray([1.3320, -0.6653, -1.4167]), decimal=4)
+        assert_almost_equal(p, xp.asarray([-0.4093, -1.1644, 1.5737]), decimal=4)
+        assert_almost_equal(k, xp.asarray([-1.2500]), decimal=4)
+
+        r, p, k = residue(xp.asarray([-4, 8]), xp.asarray([1, 6, 8]))
+        assert_almost_equal(r, xp.asarray([8, -12]))
+        assert_almost_equal(p, xp.asarray([-2, -4]))
+        assert k.size == 0
+
+        r, p, k = residue(xp.asarray([4, 1]), xp.asarray([1, -1, -2]))
+        assert_almost_equal(r, xp.asarray([1, 3]))
+        assert_almost_equal(p, xp.asarray([-1, 2]))
+        assert k.size == 0
+
+        r, p, k = residue(xp.asarray([4, 3]),
+                          xp.asarray([2, -3.4, 1.98, -0.406]))
+        self.assert_rp_almost_equal(
+            r, p, [-18.125 - 13.125j, -18.125 + 13.125j, 36.25],
+            [0.5 - 0.2j, 0.5 + 0.2j, 0.7])
+        assert k.size == 0
+
+        r, p, k = residue(xp.asarray([2, 1]), xp.asarray([1, 5, 8, 4]))
+        self.assert_rp_almost_equal(r, p, [-1, 1, 3],
+                                    [-1, -2, -2])
+        assert k.size == 0
+
+        r, p, k = residue(xp.asarray([3, -1.1, 0.88, -2.396, 1.348]),
+                          xp.asarray([1, -0.7, -0.14, 0.048]))
+        assert_almost_equal(r, xp.asarray([-3, 4, 1]))
+        assert_almost_equal(p, xp.asarray([0.2, -0.3, 0.8]))
+        assert_almost_equal(k, xp.asarray([3, 1]))
+
+        r, p, k = residue(xp.asarray([1]), xp.asarray([1, 2, -3]))
+        assert_almost_equal(r, xp.asarray([0.25, -0.25]))
+        assert_almost_equal(p, xp.asarray([1, -3]))
+        assert k.size == 0
+
+        r, p, k = residue(xp.asarray([1, 0, -5]), xp.asarray([1, 0, 0, 0, -1]))
+        self.assert_rp_almost_equal(r, p,
+                                    [1, 1.5j, -1.5j, -1],
+                                    [-1, -1j, 1j, 1])
+        assert k.size == 0
+
+        r, p, k = residue(xp.asarray([3, 8, 6]), xp.asarray([1, 3, 3, 1]))
+        self.assert_rp_almost_equal(r, p, [1, 2, 3],
+                                    [-1, -1, -1])
+        assert k.size == 0
+
+        r, p, k = residue(xp.asarray([3, -1]), xp.asarray([1, -3, 2]))
+        assert_almost_equal(r, xp.asarray([-2, 5]))
+        assert_almost_equal(p, xp.asarray([1, 2]))
+        assert k.size == 0
+
+        r, p, k = residue(xp.asarray([2, 3, -1]), xp.asarray([1, -3, 2]))
+        assert_almost_equal(r, xp.asarray([-4, 13]))
+        assert_almost_equal(p, xp.asarray([1, 2]))
+        assert_almost_equal(k, xp.asarray([2]))
+
+        r, p, k = residue(xp.asarray([7, 2, 3, -1]), xp.asarray([1, -3, 2]))
+        assert_almost_equal(r, xp.asarray([-11, 69]))
+        assert_almost_equal(p, xp.asarray([1, 2]))
+        assert_almost_equal(k, xp.asarray([7, 23]))
+
+        r, p, k = residue(xp.asarray([2, 3, -1]), xp.asarray([1, -3, 4, -2]))
+        self.assert_rp_almost_equal(r, p, [4, -1 + 3.5j, -1 - 3.5j],
+                                    [1, 1 - 1j, 1 + 1j])
+        assert k.size == 0
+
+    @make_xp_test_case(residue)
+    def test_residue_leading_zeros(self, xp):
+        # Leading zeros in numerator or denominator must not affect the answer.
+        r0, p0, k0 = residue(xp.asarray([5, 3, -2, 7]), xp.asarray([-4, 0, 8, 3]))
+        r1, p1, k1 = residue(xp.asarray([0, 5, 3, -2, 7]), xp.asarray([-4, 0, 8, 3]))
+        r2, p2, k2 = residue(xp.asarray([5, 3, -2, 7]), xp.asarray([0, -4, 0, 8, 3]))
+        r3, p3, k3 = residue(xp.asarray([0, 0, 5, 3, -2, 7]),
+                             xp.asarray([0, 0, 0, -4, 0, 8, 3]))
+        assert_almost_equal(r0, r1)
+        assert_almost_equal(r0, r2)
+        assert_almost_equal(r0, r3)
+        assert_almost_equal(p0, p1)
+        assert_almost_equal(p0, p2)
+        assert_almost_equal(p0, p3)
+        assert_almost_equal(k0, k1)
+        assert_almost_equal(k0, k2)
+        assert_almost_equal(k0, k3)
+
+    @make_xp_test_case(residue)
+    def test_residue_degenerate(self, xp):
+        # Several tests for zero numerator and denominator.
+        r, p, k = residue(xp.asarray([0, 0]), xp.asarray([1, 6, 8]))
+        assert_almost_equal(r, xp.asarray([0, 0]))
+        assert_almost_equal(p, xp.asarray([-2, -4]))
+        assert k.size == 0
+
+        r, p, k = residue(xp.asarray(0), xp.asarray(1))
+        assert r.size == 0
+        assert p.size == 0
+        assert k.size == 0
+
+        with pytest.raises(ValueError, match="Denominator `a` is zero."):
+            residue(1, 0)
+
+    @make_xp_test_case(residuez)
+    def test_residuez_general(self, xp):
+        r, p, k = residuez(xp.asarray([1, 6, 6, 2]),
+                           xp.asarray([1, -(2 + 1j), (1 + 2j), -1j]))
+        self.assert_rp_almost_equal(r, p, [-2+2.5j, 7.5+7.5j, -4.5-12j],
+                                    [1j, 1, 1])
+        assert_almost_equal(k, xp.asarray([2j]))
+
+        r, p, k = residuez(xp.asarray([1, 2, 1]), xp.asarray([1, -1, 0.3561]))
+        self.assert_rp_almost_equal(r, p,
+                                    [-0.9041 - 5.9928j, -0.9041 + 5.9928j],
+                                    [0.5 + 0.3257j, 0.5 - 0.3257j],
+                                    decimal=4)
+        assert_almost_equal(k, xp.asarray([2.8082]), decimal=4)
+
+        r, p, k = residuez(xp.asarray([1, -1]), xp.asarray([1, -5, 6]))
+        assert_almost_equal(r, xp.asarray([-1, 2]))
+        assert_almost_equal(p, xp.asarray([2, 3]))
+        assert k.size == 0
+
+        r, p, k = residuez(xp.asarray([2, 3, 4]), xp.asarray([1, 3, 3, 1]))
+        self.assert_rp_almost_equal(r, p, [4, -5, 3], [-1, -1, -1])
+        assert k.size == 0
+
+        r, p, k = residuez(xp.asarray([1, -10, -4, 4]), xp.asarray([2, -2, -4]))
+        assert_almost_equal(r, xp.asarray([0.5, -1.5]))
+        assert_almost_equal(p, xp.asarray([-1, 2]))
+        assert_almost_equal(k, xp.asarray([1.5, -1]))
+
+        r, p, k = residuez(xp.asarray([18]), xp.asarray([18, 3, -4, -1]))
+        self.assert_rp_almost_equal(r, p,
+                                    [0.36, 0.24, 0.4], [0.5, -1/3, -1/3])
+        assert k.size == 0
+
+        r, p, k = residuez(xp.asarray([2, 3]),
+                           xp.asarray(np.polymul([1, -1/2], [1, 1/4])))
+        assert_almost_equal(r, xp.asarray([-10/3, 16/3]))
+        assert_almost_equal(p, xp.asarray([-0.25, 0.5]))
+        assert k.size == 0
+
+        r, p, k = residuez(xp.asarray([1, -2, 1]), xp.asarray([1, -1]))
+        assert_almost_equal(r, xp.asarray([0]))
+        assert_almost_equal(p, xp.asarray([1]))
+        assert_almost_equal(k, xp.asarray([1, -1]))
+
+        r, p, k = residuez(xp.asarray(1), xp.asarray([1, -1j]))
+        assert_almost_equal(r, xp.asarray([1]))
+        assert_almost_equal(p, xp.asarray([1j]))
+        assert k.size == 0
+
+        r, p, k = residuez(xp.asarray(1), xp.asarray([1, -1, 0.25]))
+        assert_almost_equal(r, xp.asarray([0, 1]))
+        assert_almost_equal(p, xp.asarray([0.5, 0.5]))
+        assert k.size == 0
+
+        r, p, k = residuez(xp.asarray(1), xp.asarray([1, -0.75, .125]))
+        assert_almost_equal(r, xp.asarray([-1, 2]))
+        assert_almost_equal(p, xp.asarray([0.25, 0.5]))
+        assert k.size == 0
+
+        r, p, k = residuez(xp.asarray([1, 6, 2]), xp.asarray([1, -2, 1]))
+        assert_almost_equal(r, xp.asarray([-10, 9]))
+        assert_almost_equal(p, xp.asarray([1, 1]))
+        assert_almost_equal(k, xp.asarray([2]))
+
+        r, p, k = residuez(xp.asarray([6, 2]), xp.asarray([1, -2, 1]))
+        assert_almost_equal(r, xp.asarray([-2, 8]))
+        assert_almost_equal(p, xp.asarray([1, 1]))
+        assert k.size == 0
+
+        r, p, k = residuez(xp.asarray([1, 6, 6, 2]), xp.asarray([1, -2, 1]))
+        assert_almost_equal(r, xp.asarray([-24, 15]))
+        assert_almost_equal(p, xp.asarray([1, 1]))
+        assert_almost_equal(k, xp.asarray([10, 2]))
+
+        r, p, k = residuez(xp.asarray([1, 0, 1]), xp.asarray([1, 0, 0, 0, 0, -1]))
+        self.assert_rp_almost_equal(r, p,
+                                    [0.2618 + 0.1902j, 0.2618 - 0.1902j,
+                                     0.4, 0.0382 - 0.1176j, 0.0382 + 0.1176j],
+                                    [-0.8090 + 0.5878j, -0.8090 - 0.5878j,
+                                     1.0, 0.3090 + 0.9511j, 0.3090 - 0.9511j],
+                                    decimal=4)
+        assert k.size == 0
+
+    @make_xp_test_case(residuez)
+    def test_residuez_trailing_zeros(self, xp):
+        # Trailing zeros in numerator or denominator must not affect the
+        # answer.
+        r0, p0, k0 = residuez(xp.asarray([5, 3, -2, 7]),
+                              xp.asarray([-4, 0, 8, 3]))
+        r1, p1, k1 = residuez(xp.asarray([5, 3, -2, 7, 0]),
+                              xp.asarray([-4, 0, 8, 3]))
+        r2, p2, k2 = residuez(xp.asarray([5, 3, -2, 7]),
+                              xp.asarray([-4, 0, 8, 3, 0]))
+        r3, p3, k3 = residuez(xp.asarray([5, 3, -2, 7, 0, 0]),
+                              xp.asarray([-4, 0, 8, 3, 0, 0, 0]))
+        assert_almost_equal(r0, r1)
+        assert_almost_equal(r0, r2)
+        assert_almost_equal(r0, r3)
+        assert_almost_equal(p0, p1)
+        assert_almost_equal(p0, p2)
+        assert_almost_equal(p0, p3)
+        assert_almost_equal(k0, k1)
+        assert_almost_equal(k0, k2)
+        assert_almost_equal(k0, k3)
+
+    @make_xp_test_case(residuez)
+    def test_residuez_degenerate(self, xp):
+        r, p, k = residuez(xp.asarray([0, 0]), xp.asarray([1, 6, 8]))
+        assert_almost_equal(r, xp.asarray([0, 0]))
+        assert_almost_equal(p, xp.asarray([-2, -4]))
+        assert k.size == 0
+
+        r, p, k = residuez(xp.asarray(0), xp.asarray(1))
+        assert r.size == 0
+        assert p.size == 0
+        assert k.size == 0
+
+        with pytest.raises(ValueError, match="Denominator `a` is zero."):
+            residuez(xp.asarray(1), xp.asarray(0))
+
+        with pytest.raises(ValueError,
+                           match="First coefficient of determinant `a` must "
+                                 "be non-zero."):
+            residuez(xp.asarray(1), xp.asarray([0, 1, 2, 3]))
+
+    @make_xp_test_case(invres, invresz)
+    def test_inverse_unique_roots_different_rtypes(self, xp):
+        # This test was inspired by github issue 2496.
+        r = xp.asarray([3 / 10, -1 / 6, -2 / 15])
+        p = xp.asarray([0, -2, -5])
+        k = xp.asarray([])
+        b_expected = xp.asarray([0.0, 1, 3])
+        a_expected = xp.asarray([1, 7, 10, 0])
+
+        # With the default tolerance, the rtype does not matter
+        # for this example.
+        for rtype in ('avg', 'mean', 'min', 'minimum', 'max', 'maximum'):
+            b, a = invres(r, p, k, rtype=rtype)
+            xp_assert_close(b, b_expected, atol=5e-16)
+            xp_assert_close(a, a_expected, check_dtype=False, atol=5e-16)
+
+            b, a = invresz(r, p, k, rtype=rtype)
+            xp_assert_close(b, b_expected, atol=5e-16)
+            xp_assert_close(a, a_expected, check_dtype=False, atol=5e-16)
+
+    @make_xp_test_case(invres, invresz)
+    def test_inverse_repeated_roots_different_rtypes(self, xp):
+        r = xp.asarray([3 / 20, -7 / 36, -1 / 6, 2 / 45])
+        p = xp.asarray([0, -2, -2, -5])
+        k = xp.asarray([])
+        b_expected = xp.asarray([0.0, 0, 1, 3])
+        b_expected_z = xp.asarray([-1/6, -2/3, 11/6, 3])
+        a_expected = xp.asarray([1, 9, 24, 20, 0])
+
+        for rtype in ('avg', 'mean', 'min', 'minimum', 'max', 'maximum'):
+            b, a = invres(r, p, k, rtype=rtype)
+            xp_assert_close(b, b_expected, atol=1e-14)
+            xp_assert_close(a, a_expected, check_dtype=False)
+
+            b, a = invresz(r, p, k, rtype=rtype)
+            xp_assert_close(b, b_expected_z, atol=1e-14)
+            xp_assert_close(a, a_expected, check_dtype=False)
+
+    @make_xp_test_case(invres, invresz)
+    def test_inverse_bad_rtype(self, xp):
+        r = xp.asarray([3 / 20, -7 / 36, -1 / 6, 2 / 45])
+        p = xp.asarray([0, -2, -2, -5])
+        k = xp.asarray([])
+        with pytest.raises(ValueError, match="`rtype` must be one of"):
+            invres(r, p, k, rtype='median')
+        with pytest.raises(ValueError, match="`rtype` must be one of"):
+            invresz(r, p, k, rtype='median')
+
+    @make_xp_test_case(invresz)
+    def test_invresz_one_coefficient_bug(self, xp):
+        # Regression test for issue in gh-4646.
+        r = xp.asarray([1])
+        p = xp.asarray([2])
+        k = xp.asarray([0])
+        b, a = invresz(r, p, k)
+        xp_assert_close(b, xp.asarray([1]))
+        xp_assert_close(a, xp.asarray([1.0, -2.0]))
+
+    @make_xp_test_case(invres)
+    def test_invres(self, xp):
+        b, a = invres(xp.asarray([1]), xp.asarray([1]), xp.asarray([]))
+        assert_almost_equal(b, xp.asarray([1]))
+        assert_almost_equal(a, xp.asarray([1, -1]))
+
+        b, a = invres(xp.asarray([1 - 1j, 2, 0.5 - 3j]),
+                      xp.asarray([1, 0.5j, 1 + 1j]), xp.asarray([]))
+        assert_almost_equal(b, xp.asarray([3.5 - 4j, -8.5 + 0.25j, 3.5 + 3.25j]))
+        assert_almost_equal(a, xp.asarray([1, -2 - 1.5j, 0.5 + 2j, 0.5 - 0.5j]))
+
+        b, a = invres(xp.asarray([0.5, 1]), xp.asarray([1 - 1j, 2 + 2j]),
+                      xp.asarray([1, 2, 3]))
+        assert_almost_equal(b, xp.asarray([1, -1 - 1j, 1 - 2j, 0.5 - 3j, 10]))
+        assert_almost_equal(a, xp.asarray([1, -3 - 1j, 4]))
+
+        b, a = invres(xp.asarray([-1, 2, 1j, 3 - 1j, 4, -2]),
+                      xp.asarray([-1, 2 - 1j, 2 - 1j, 3, 3, 3]), xp.asarray([]))
+        assert_almost_equal(b,
+                            xp.asarray([4 - 1j, -28 + 16j, 40 - 62j, 100 + 24j,
+                                        -292 + 219j, 192 - 268j]))
+        assert_almost_equal(a,
+                            xp.asarray([1, -12 + 2j, 53 - 20j, -96 + 68j, 27 - 72j,
+                                        108 - 54j, -81 + 108j]))
+
+        b, a = invres(xp.asarray([-1, 1j]), xp.asarray([1, 1]), xp.asarray([1, 2]))
+        assert_almost_equal(b, xp.asarray([1, 0, -4, 3 + 1j]))
+        assert_almost_equal(a, xp.asarray([1, -2, 1]))
+
+    @make_xp_test_case(invresz)
+    def test_invresz(self, xp):
+        b, a = invresz(xp.asarray([1]), xp.asarray([1]), xp.asarray([]))
+        assert_almost_equal(b, xp.asarray([1]))
+        assert_almost_equal(a, xp.asarray([1, -1]))
+
+        b, a = invresz(xp.asarray([1 - 1j, 2, 0.5 - 3j]),
+                       xp.asarray([1, 0.5j, 1 + 1j]), xp.asarray([]))
+        assert_almost_equal(b, xp.asarray([3.5 - 4j, -8.5 + 0.25j, 3.5 + 3.25j]))
+        assert_almost_equal(a, xp.asarray([1, -2 - 1.5j, 0.5 + 2j, 0.5 - 0.5j]))
+
+        b, a = invresz(xp.asarray([0.5, 1]),
+                       xp.asarray([1 - 1j, 2 + 2j]),
+                       xp.asarray([1, 2, 3]))
+        assert_almost_equal(b, xp.asarray([2.5, -3 - 1j, 1 - 2j, -1 - 3j, 12]))
+        assert_almost_equal(a, xp.asarray([1, -3 - 1j, 4]))
+
+        b, a = invresz(xp.asarray([-1, 2, 1j, 3 - 1j, 4, -2]),
+                       xp.asarray([-1, 2 - 1j, 2 - 1j, 3, 3, 3]),
+                       xp.asarray([]))
+        assert_almost_equal(b,
+                            xp.asarray([6, -50 + 11j, 100 - 72j, 80 + 58j,
+                                        -354 + 228j, 234 - 297j]))
+        assert_almost_equal(a,
+                            xp.asarray([1, -12 + 2j, 53 - 20j, -96 + 68j, 27 - 72j,
+                                        108 - 54j, -81 + 108j]))
+
+        b, a = invresz(xp.asarray([-1, 1j]),
+                       xp.asarray([1, 1]),
+                       xp.asarray([1, 2]))
+        assert_almost_equal(b, xp.asarray([1j, 1, -3, 2]))
+        assert_almost_equal(a, xp.asarray([1, -2, 1]))
+
+    @skip_xp_backends(np_only=True)
+    @make_xp_test_case(invres, invresz)
+    def test_inverse_scalar_arguments(self, xp):
+        b, a = invres(1, 1, 1)
+        assert_almost_equal(b, [1, 0])
+        assert_almost_equal(a, [1, -1])
+
+        b, a = invresz(1, 1, 1)
+        assert_almost_equal(b, [2, -1])
+        assert_almost_equal(a, [1, -1])
+
+
+@make_xp_test_case(vectorstrength)
+class TestVectorstrength:
+
+    def test_single_1dperiod(self, xp):
+        events = xp.asarray([.5])
+        period = 5.
+        targ_strength = 1.
+        targ_phase = .1
+
+        strength, phase = vectorstrength(events, period)
+
+        assert strength.ndim == 0
+        assert phase.ndim == 0
+
+        assert math.isclose(strength, targ_strength, abs_tol=1.5e-7)
+        assert math.isclose(phase, 2 * math.pi * targ_phase, abs_tol=1.5e-7)
+
+    @xfail_xp_backends('torch', reason="phase modulo 2*pi")
+    def test_single_2dperiod(self, xp):
+        events = xp.asarray([.5])
+        period = xp.asarray([1, 2, 5.])
+        targ_strength = xp.asarray([1.] * 3)
+        targ_phase = xp.asarray([.5, .25, .1])
+
+        strength, phase = vectorstrength(events, period)
+
+        assert strength.ndim == 1
+        assert phase.ndim == 1
+        assert_array_almost_equal(strength, targ_strength)
+        assert_almost_equal(phase, 2 * xp.pi * targ_phase)
+
+    def test_equal_1dperiod(self, xp):
+        events = xp.asarray([.25, .25, .25, .25, .25, .25])
+        period = 2
+        targ_strength = 1.
+        targ_phase = .125
+
+        strength, phase = vectorstrength(events, period)
+
+        assert strength.ndim == 0
+        assert phase.ndim == 0
+
+        assert math.isclose(strength, targ_strength, abs_tol=1.5e-7)
+        assert math.isclose(phase, 2 * math.pi * targ_phase, abs_tol=1.5e-7)
+
+    def test_equal_2dperiod(self, xp):
+        events = xp.asarray([.25, .25, .25, .25, .25, .25])
+        period = xp.asarray([1, 2, ])
+        targ_strength = xp.asarray([1.] * 2)
+        targ_phase = xp.asarray([.25, .125])
+
+        strength, phase = vectorstrength(events, period)
+
+        assert strength.ndim == 1
+        assert phase.ndim == 1
+        assert_almost_equal(strength, targ_strength)
+        assert_almost_equal(phase, 2 * xp.pi * targ_phase)
+
+    def test_spaced_1dperiod(self, xp):
+        events = xp.asarray([.1, 1.1, 2.1, 4.1, 10.1])
+        period = 1
+        targ_strength = 1.
+        targ_phase = .1
+
+        strength, phase = vectorstrength(events, period)
+
+        assert strength.ndim == 0
+        assert phase.ndim == 0
+
+        assert math.isclose(strength, targ_strength, abs_tol=1.5e-7)
+        assert math.isclose(phase, 2 * math.pi * targ_phase, abs_tol=1.5e-6)
+
+    def test_spaced_2dperiod(self, xp):
+        events = xp.asarray([.1, 1.1, 2.1, 4.1, 10.1])
+        period = xp.asarray([1, .5])
+        targ_strength = xp.asarray([1.] * 2)
+        targ_phase = xp.asarray([.1, .2])
+
+        strength, phase = vectorstrength(events, period)
+
+        assert strength.ndim == 1
+        assert phase.ndim == 1
+        assert_almost_equal(strength, targ_strength)
+        rtol_kw = {'rtol': 2e-6} if xp_default_dtype(xp) == xp.float32 else {}
+        xp_assert_close(phase, 2 * xp.pi * targ_phase, **rtol_kw)
+
+    def test_partial_1dperiod(self, xp):
+        events = xp.asarray([.25, .5, .75])
+        period = 1
+        targ_strength = 1. / 3.
+        targ_phase = .5
+
+        strength, phase = vectorstrength(events, period)
+
+        assert strength.ndim == 0
+        assert phase.ndim == 0
+
+        assert math.isclose(strength, targ_strength)
+        assert math.isclose(phase, 2 * math.pi * targ_phase)
+
+
+    @xfail_xp_backends("torch", reason="phase modulo 2*pi")
+    def test_partial_2dperiod(self, xp):
+        events = xp.asarray([.25, .5, .75])
+        period = xp.asarray([1., 1., 1., 1.])
+        targ_strength = xp.asarray([1. / 3.] * 4)
+        targ_phase = xp.asarray([.5, .5, .5, .5])
+
+        strength, phase = vectorstrength(events, period)
+
+        assert strength.ndim == 1
+        assert phase.ndim == 1
+        assert_almost_equal(strength, targ_strength)
+        assert_almost_equal(phase, 2 * xp.pi * targ_phase)
+
+    def test_opposite_1dperiod(self, xp):
+        events = xp.asarray([0, .25, .5, .75])
+        period = 1.
+        targ_strength = 0
+
+        strength, phase = vectorstrength(events, period)
+
+        assert strength.ndim == 0
+        assert phase.ndim == 0
+        assert math.isclose(strength, targ_strength, abs_tol=1.5e-7)
+
+    def test_opposite_2dperiod(self, xp):
+        events = xp.asarray([0, .25, .5, .75])
+        period = xp.asarray([1.] * 10)
+        targ_strength = xp.asarray([0.] * 10)
+
+        strength, phase = vectorstrength(events, period)
+
+        assert strength.ndim == 1
+        assert phase.ndim == 1
+        assert_almost_equal(strength, targ_strength)
+
+    def test_2d_events_ValueError(self, xp):
+        events = xp.asarray([[1, 2]])
+        period = 1.
+        assert_raises(ValueError, vectorstrength, events, period)
+
+    def test_2d_period_ValueError(self, xp):
+        events = 1.
+        period = xp.asarray([[1]])
+        assert_raises(ValueError, vectorstrength, events, period)
+
+    def test_zero_period_ValueError(self, xp):
+        events = 1.
+        period = 0
+        assert_raises(ValueError, vectorstrength, events, period)
+
+    def test_negative_period_ValueError(self, xp):
+        events = 1.
+        period = -1
+        assert_raises(ValueError, vectorstrength, events, period)
+
+
+# XXX: restore testing on CuPy, where possible. Multiple issues in this test:
+#  1. _zi functions deliberately incompatible in cupy
+#     (https://github.com/scipy/scipy/pull/21713#issuecomment-2417494443)
+#  2. a CuPy issue to be fixed in 14.0 only
+#      (https://github.com/cupy/cupy/pull/8677)
+#  3. an issue with CuPy's __array__ not numpy-2.0 compatible
+@skip_xp_backends(cpu_only=True)
+@make_xp_test_case(sosfilt)
+@pytest.mark.parametrize('dt', ['float32', 'float64', 'complex64', 'complex128'])
+class TestSOSFilt:
+
+    # The test_rank* tests are pulled from _TestLinearFilter
+    @skip_xp_backends('jax.numpy', reason='buffer array is read-only')
+    def test_rank1(self, dt, xp):
+        dt = getattr(xp, dt)
+        x = xp.linspace(0, 5, 6, dtype=dt)
+        b = xp.asarray([1, -1], dtype=dt)
+        a = xp.asarray([0.5, -0.5], dtype=dt)
+
+        # Test simple IIR
+        y_r = xp.asarray([0, 2, 4, 6, 8, 10.], dtype=dt)
+        bb, aa = map(np.asarray, (b, a))
+        sos = tf2sos(bb, aa)
+        sos = xp.asarray(sos)   # XXX while tf2sos is numpy only
+        assert_array_almost_equal(sosfilt(sos, x), y_r)
+
+        # Test simple FIR
+        b = xp.asarray([1, 1], dtype=dt)
+        # NOTE: This was changed (rel. to TestLinear...) to add a pole @zero:
+        a = xp.asarray([1, 0], dtype=dt)
+        y_r = xp.asarray([0, 1, 3, 5, 7, 9.], dtype=dt)
+        bb, aa = map(np.asarray, (b, a))
+        sos = tf2sos(bb, aa)
+        sos = xp.asarray(sos)   # XXX while tf2sos is numpy only
+        assert_array_almost_equal(sosfilt(sos, x), y_r)
+
+        b = xp.asarray([1.0, 1, 0])
+        a = xp.asarray([1.0, 0, 0])
+        x = xp.ones(8)
+
+        sos = xp.concat((b, a))
+        sos = xp.reshape(sos, (1, 6))
+        y = sosfilt(sos, x)
+        xp_assert_close(y, xp.asarray([1.0, 2, 2, 2, 2, 2, 2, 2]))
+
+    @skip_xp_backends('jax.numpy', reason='buffer array is read-only')
+    def test_rank2(self, dt, xp):
+        dt = getattr(xp, dt)
+        shape = (4, 3)
+        prodshape = math.prod(shape)
+        x = xp.linspace(0, prodshape - 1, prodshape, dtype=dt)
+        x = xp.reshape(x, shape)
+
+        b = xp.asarray([1, -1], dtype=dt)
+        a = xp.asarray([0.5, 0.5], dtype=dt)
+
+        y_r2_a0 = xp.asarray([[0, 2, 4], [6, 4, 2], [0, 2, 4], [6, 4, 2]],
+                           dtype=dt)
+
+        y_r2_a1 = xp.asarray([[0, 2, 0], [6, -4, 6], [12, -10, 12],
+                            [18, -16, 18]], dtype=dt)
+
+        bb, aa = map(np.asarray, (b, a))
+        sos = tf2sos(bb, aa)
+        sos = xp.asarray(sos)   # XXX
+        y = sosfilt(sos, x, axis=0)
+        assert_array_almost_equal(y_r2_a0, y)
+
+        sos = tf2sos(bb, aa)
+        sos = xp.asarray(sos)   # XXX
+        y = sosfilt(sos, x, axis=1)
+        assert_array_almost_equal(y_r2_a1, y)
+
+    @skip_xp_backends('jax.numpy', reason='buffer array is read-only')
+    def test_rank3(self, dt, xp):
+        dt = getattr(xp, dt)
+        shape = (4, 3, 2)
+        prodshape = math.prod(shape)
+        x = xp.linspace(0, prodshape - 1, prodshape)
+        x = xp.reshape(x, shape)
+
+        b = xp.asarray([1, -1], dtype=dt)
+        a = xp.asarray([0.5, 0.5], dtype=dt)
+
+        # Test last axis
+        bb, aa = map(np.asarray, (b, a))  # XXX until tf2sos is array api compatible
+        sos = tf2sos(bb, aa)
+        sos = xp.asarray(sos)   # XXX
+        y = sosfilt(sos, x)
+        for i in range(x.shape[0]):
+            for j in range(x.shape[1]):
+                assert_array_almost_equal(y[i, j, ...], lfilter(b, a, x[i, j, ...]))
+
+    def _get_ab_sos(self, xp):
+        b1, a1 = signal.butter(2, 0.25, 'low')
+        b2, a2 = signal.butter(2, 0.75, 'low')
+        b3, a3 = signal.butter(2, 0.75, 'low')
+        b = np.convolve(np.convolve(b1, b2), b3)
+        a = np.convolve(np.convolve(a1, a2), a3)
+        sos = np.array((np.r_[b1, a1], np.r_[b2, a2], np.r_[b3, a3]))
+
+        a, b, sos = map(xp.asarray, (a, b, sos))
+        return a, b, sos
+
+    @skip_xp_backends('jax.numpy', reason='item assignment')
+    @make_xp_test_case(sosfilt_zi)
+    def test_initial_conditions(self, dt, xp):
+        a, b, sos = self._get_ab_sos(xp)
+
+        x = np.random.rand(50).astype(dt)
+        x = xp.asarray(x)
+
+        dt = getattr(xp, dt)
+
+        # Stopping filtering and continuing
+        y_true, zi = lfilter(b, a, x[:20], zi=xp.zeros(6))
+        y_true = xp.concat((y_true, lfilter(b, a, x[20:], zi=zi)[0]))
+        xp_assert_close(y_true, lfilter(b, a, x))
+
+        y_sos, zi = sosfilt(sos, x[:20], zi=xp.zeros((3, 2)))
+        y_sos = xp.concat((y_sos, sosfilt(sos, x[20:], zi=zi)[0]))
+        xp_assert_close(y_true, y_sos)
+
+        # Use a step function
+        zi = sosfilt_zi(sos)
+        x = xp.ones(8, dtype=dt)
+        y, zf = sosfilt(sos, x, zi=zi)
+
+        xp_assert_close(y, xp.ones(8), check_dtype=False)
+        xp_assert_close(zf, zi, check_dtype=False)
+
+    @skip_xp_backends('jax.numpy', reason='item assignment')
+    @skip_xp_backends('array_api_strict', reason='fancy indexing not supported')
+    @make_xp_test_case(sosfilt_zi)
+    def test_initial_conditions_2(self, dt, xp):
+        dt = getattr(xp, dt)
+        x = xp.ones(8, dtype=dt)
+
+        _, _, sos = self._get_ab_sos(xp)
+        zi = sosfilt_zi(sos)
+
+        # Initial condition shape matching
+        x = xp.reshape(x, (1, 1) + x.shape)  # 3D
+        with pytest.raises(ValueError):
+            sosfilt(sos, x, zi=zi)
+
+        zi_nd = xp_copy(zi, xp=xp)
+        zi_nd = xp.reshape(zi_nd, (zi.shape[0], 1, 1, zi.shape[-1]))
+
+        with pytest.raises(ValueError):
+            sosfilt(sos, x, zi=zi_nd[:, :, :, [0, 1, 1]])
+
+        y, zf = sosfilt(sos, x, zi=zi_nd)
+        xp_assert_close(y[0, 0], xp.ones(8), check_dtype=False)
+        xp_assert_close(zf[:, 0, 0, :], zi, check_dtype=False)
+
+    @skip_xp_backends('jax.numpy', reason='item assignment')
+    @make_xp_test_case(sosfilt_zi)
+    def test_initial_conditions_3d_axis1(self, dt, xp):
+        # Test the use of zi when sosfilt is applied to axis 1 of a 3-d input.
+
+        # Input array is x.
+        x = np.random.RandomState(159).randint(0, 5, size=(2, 15, 3))
+        x = x.astype(dt)
+        x = xp.asarray(x)
+
+        # Design a filter in ZPK format and convert to SOS
+        zpk = signal.butter(6, 0.35, output='zpk')
+        sos = zpk2sos(*zpk)
+        sos = xp.asarray(sos)   # XXX while zpk2sos is numpy-only
+
+        nsections = sos.shape[0]
+
+        # Filter along this axis.
+        axis = 1
+
+        # Initial conditions, all zeros.
+        shp = list(x.shape)
+        shp[axis] = 2
+        shp = tuple([nsections] + shp)
+        z0 = xp.zeros(shp)
+
+        # Apply the filter to x.
+        yf, zf = sosfilt(sos, x, axis=axis, zi=z0)
+
+        # Apply the filter to x in two stages.
+        y1, z1 = sosfilt(sos, x[:, :5, :], axis=axis, zi=z0)
+        y2, z2 = sosfilt(sos, x[:, 5:, :], axis=axis, zi=z1)
+
+        # y should equal yf, and z2 should equal zf.
+        y = xp.concat((y1, y2), axis=axis)
+        xp_assert_close(y, yf, rtol=1e-10, atol=1e-13)
+        xp_assert_close(z2, zf, rtol=1e-10, atol=1e-13)
+
+        # let's try the "step" initial condition
+        zi = sosfilt_zi(sos)
+        zi = xp.reshape(zi, (nsections, 1, 2, 1))
+        zi = zi * x[:, 0:1, :]
+        y = sosfilt(sos, x, axis=axis, zi=zi)[0]
+        # check it against the TF form
+        b, a = zpk2tf(*zpk)
+        b, a = xp.asarray(b), xp.asarray(a)    # XXX while zpk2tf is numpy-only
+
+        zi = lfilter_zi(b, a)
+        zi = xp.reshape(zi, (1, xp_size(zi), 1))
+        zi = zi * x[:, 0:1, :]
+        y_tf = lfilter(b, a, x, axis=axis, zi=zi)[0]
+        xp_assert_close(y, y_tf, rtol=1e-10, atol=1e-13)
+
+    @skip_xp_backends('torch', reason='issues a RuntimeWarning')
+    @skip_xp_backends('jax.numpy', reason='item assignment')
+    def test_bad_zi_shape(self, dt, xp):
+        dt = getattr(xp, dt)
+        # The shape of zi is checked before using any values in the
+        # arguments, so np.empty is fine for creating the arguments.
+        x = xp.empty((3, 15, 3), dtype=dt)
+        sos = xp.zeros((4, 6))
+        zi = xp.empty((4, 3, 3, 2))  # Correct shape is (4, 3, 2, 3)
+        with pytest.raises(ValueError, match='should be all ones'):
+            sosfilt(sos, x, zi=zi, axis=1)
+        sos[:, 3] = 1.
+        with pytest.raises(ValueError, match='Invalid zi shape'):
+            sosfilt(sos, x, zi=zi, axis=1)
+
+    @skip_xp_backends('jax.numpy', reason='item assignment')
+    @make_xp_test_case(sosfilt_zi)
+    def test_sosfilt_zi(self, dt, xp):
+        dt = getattr(xp, dt)
+        sos = signal.butter(6, 0.2, output='sos')
+        sos = xp.asarray(sos)   # XXX while butter is np-only
+        zi = sosfilt_zi(sos)
+
+        y, zf = sosfilt(sos, xp.ones(40, dtype=dt), zi=zi)
+        xp_assert_close(zf, zi, rtol=1e-13, check_dtype=False)
+
+        # Expected steady state value of the step response of this filter:
+        ss = xp.prod(xp.sum(sos[:, :3], axis=-1) / xp.sum(sos[:, 3:], axis=-1))
+        xp_assert_close(y, ss * xp.ones_like(y), rtol=1e-13)
+
+    @skip_xp_backends(np_only=True)
+    @make_xp_test_case(sosfilt_zi)
+    def test_sosfilt_zi_2(self, dt, xp):
+        # zi as array-like
+        dt = getattr(xp, dt)
+        sos = signal.butter(6, 0.2, output='sos')
+        sos = xp.asarray(sos)   # XXX while butter is np-only
+        zi = sosfilt_zi(sos)
+
+        _, zf = sosfilt(sos, xp.ones(40, dtype=dt), zi=zi.tolist())
+        xp_assert_close(zf, zi, rtol=1e-13, check_dtype=False)
+
+
+@make_xp_test_case(signal.deconvolve)
+class TestDeconvolve:
+
+    @skip_xp_backends(np_only=True, reason="list inputs are numpy-specific")
+    def test_array_like(self, xp):
+        # From docstring example: with lists
+        original = [0.0, 1, 0, 0, 1, 1, 0, 0]
+        impulse_response = [2, 1]
+        recorded = xp.asarray([0.0, 2, 1, 0, 2, 3, 1, 0, 0])
+        recovered, remainder = signal.deconvolve(recorded, impulse_response)
+        xp_assert_close(recovered, original)
+
+    def test_basic(self, xp):
+        # From docstring example
+        original = xp.asarray([0.0, 1, 0, 0, 1, 1, 0, 0], dtype=xp.float64)
+        impulse_response = xp.asarray([2, 1])
+        recorded = xp.asarray([0.0, 2, 1, 0, 2, 3, 1, 0, 0])
+        recovered, remainder = signal.deconvolve(recorded, impulse_response)
+        xp_assert_close(recovered, original)
+
+    @xfail_xp_backends("cupy", reason="different error message")
+    def test_n_dimensional_signal(self, xp):
+        recorded = xp.asarray([[0, 0], [0, 0]])
+        impulse_response = xp.asarray([0, 0])
+        with pytest.raises(ValueError, match="^Parameter signal must be non-empty"):
+            quotient, remainder = signal.deconvolve(recorded, impulse_response)
+
+    @xfail_xp_backends("cupy", reason="different error message")
+    def test_n_dimensional_divisor(self, xp):
+        recorded = xp.asarray([0, 0])
+        impulse_response = xp.asarray([[0, 0], [0, 0]])
+        with pytest.raises(ValueError, match="^Parameter divisor must be non-empty"):
+            quotient, remainder = signal.deconvolve(recorded, impulse_response)
+
+    def test_divisor_greater_signal(self, xp):
+        """Return signal as `remainder` when ``len(divisior) > len(signal)``. """
+        sig, div = xp.asarray([0, 1, 2]), xp.asarray([0, 1, 2, 4, 5])
+        quotient, remainder = signal.deconvolve(sig, div)
+        xp_assert_equal(remainder, sig)
+        assert xp_size(xp.asarray(quotient)) == 0
+
+
+@make_xp_test_case(detrend)
+class TestDetrend:
+
+    def test_basic(self, xp):
+        detrended = detrend(xp.asarray([1, 2, 3]))
+        detrended_exact = xp.asarray([0, 0, 0])
+        assert_array_almost_equal(detrended, detrended_exact)
+
+    @skip_xp_backends("jax.numpy", reason="overwrite_data not implemented")
+    def test_copy(self, xp):
+        x = xp.asarray([1, 1.2, 1.5, 1.6, 2.4])
+        copy_array = detrend(x, overwrite_data=False)
+        inplace = detrend(x, overwrite_data=True)
+        assert_array_almost_equal(copy_array, inplace)
+
+    @pytest.mark.parametrize('kind', ['linear', 'constant'])
+    @pytest.mark.parametrize('axis', [0, 1, 2])
+    def test_axis(self, axis, kind, xp):
+        data = xp.reshape(xp.arange(5*6*7), (5, 6, 7))
+        detrended = detrend(data, type=kind, axis=axis)
+        assert detrended.shape == data.shape
+
+    def test_bp(self, xp):
+        data = [0, 1, 2] + [5, 0, -5, -10]
+        data = xp.asarray(data)
+        detrended = detrend(data, type='linear', bp=3)
+        xp_assert_close(detrended, xp.zeros_like(detrended), atol=1e-14)
+
+        # repeat with ndim > 1 and axis
+        data = xp.asarray(data)[None, :, None]
+
+        detrended = detrend(data, type="linear", bp=3, axis=1)
+        xp_assert_close(detrended, xp.zeros_like(detrended), atol=1e-14)
+
+        # breakpoint index > shape[axis]: raises
+        with assert_raises(ValueError):
+            detrend(data, type="linear", bp=3)
+
+    @pytest.mark.parametrize('bp', [np.array([0, 2]), [0, 2]])
+    def test_detrend_array_bp(self, bp, xp):
+        # regression test for https://github.com/scipy/scipy/issues/18675
+        rng = np.random.RandomState(12345)
+        x = rng.rand(10)
+        x = xp.asarray(x, dtype=xp_default_dtype(xp))
+        if isinstance(bp, np.ndarray) and not is_jax(xp):
+            # JAX expects a static array for bp, so don't call xp.asarray
+            # for JAX.
+            bp = xp.asarray(bp)
+        else:
+            if not (is_numpy(xp) or is_jax(xp)):
+                pytest.skip("list bp is currently numpy and jax only")
+
+        res = detrend(x, bp=bp)
+        res_scipy_191 = xp.asarray([-4.44089210e-16, -2.22044605e-16,
+            -1.11128506e-01, -1.69470553e-01,  1.14710683e-01,  6.35468419e-02,
+            3.53533144e-01, -3.67877935e-02, -2.00417675e-02, -1.94362049e-01])
+
+        atol = 3e-7 if xp_default_dtype(xp) == xp.float32 else 1e-14
+        xp_assert_close(res, res_scipy_191, atol=atol)
+
+
+@make_xp_test_case(unique_roots)
+class TestUniqueRoots:
+    def test_real_no_repeat(self, xp):
+        p = xp.asarray([-1.0, -0.5, 0.3, 1.2, 10.0])
+        unique, multiplicity = unique_roots(p)
+        assert_almost_equal(unique, p, decimal=15)
+        xp_assert_equal(multiplicity, xp.ones(len(p), dtype=int))
+
+    def test_real_repeat(self, xp):
+        p = xp.asarray([-1.0, -0.95, -0.89, -0.8, 0.5, 1.0, 1.05])
+
+        unique, multiplicity = unique_roots(p, tol=1e-1, rtype='min')
+        assert_almost_equal(unique, xp.asarray([-1.0, -0.89, 0.5, 1.0]), decimal=15)
+        xp_assert_equal(multiplicity, xp.asarray([2, 2, 1, 2]))
+
+        unique, multiplicity = unique_roots(p, tol=1e-1, rtype='max')
+        assert_almost_equal(unique, xp.asarray([-0.95, -0.8, 0.5, 1.05]), decimal=15)
+        xp_assert_equal(multiplicity, xp.asarray([2, 2, 1, 2]))
+
+        unique, multiplicity = unique_roots(p, tol=1e-1, rtype='avg')
+        assert_almost_equal(unique, xp.asarray([-0.975, -0.845, 0.5, 1.025]),
+                            decimal=15)
+        xp_assert_equal(multiplicity, xp.asarray([2, 2, 1, 2]))
+
+    def test_complex_no_repeat(self, xp):
+        p = xp.asarray([-1.0, 1.0j, 0.5 + 0.5j, -1.0 - 1.0j, 3.0 + 2.0j])
+        unique, multiplicity = unique_roots(p)
+        assert_almost_equal(unique, p, decimal=15)
+        xp_assert_equal(multiplicity, xp.ones(len(p), dtype=int))
+
+    def test_complex_repeat(self, xp):
+        p = xp.asarray([-1.0, -1.0 + 0.05j, -0.95 + 0.15j, -0.90 + 0.15j, 0.0,
+             0.5 + 0.5j, 0.45 + 0.55j])
+
+        unique, multiplicity = unique_roots(p, tol=1e-1, rtype='min')
+        assert_almost_equal(unique,
+                            xp.asarray([-1.0, -0.95 + 0.15j, 0.0, 0.45 + 0.55j]),
+                            decimal=15)
+        xp_assert_equal(multiplicity, xp.asarray([2, 2, 1, 2]))
+
+        unique, multiplicity = unique_roots(p, tol=1e-1, rtype='max')
+        assert_almost_equal(
+            unique,
+            xp.asarray(
+                [-1.0 + 0.05j, -0.90 + 0.15j, 0.0, 0.5 + 0.5j]
+            ),
+            decimal=15,
+        )
+        xp_assert_equal(multiplicity, xp.asarray([2, 2, 1, 2]))
+
+        unique, multiplicity = unique_roots(p, tol=1e-1, rtype='avg')
+        assert_almost_equal(
+            unique,
+            xp.asarray([-1.0 + 0.025j, -0.925 + 0.15j, 0.0, 0.475 + 0.525j]),
+            decimal=15,
+        )
+        xp_assert_equal(multiplicity, xp.asarray([2, 2, 1, 2]))
+
+    def test_gh_4915(self, xp):
+        p = xp.asarray(np.roots(np.convolve(np.ones(5), np.ones(5))))
+        true_roots = xp.asarray(
+            [-(-1)**(1/5), (-1)**(4/5), -(-1)**(3/5), (-1)**(2/5)]
+        )
+
+        unique, multiplicity = unique_roots(p)
+        unique = xp.sort(unique)
+
+        assert_almost_equal(xp.sort(unique), true_roots, decimal=7)
+        xp_assert_equal(multiplicity, xp.asarray([2, 2, 2, 2]))
+
+    def test_complex_roots_extra(self, xp):
+        unique, multiplicity = unique_roots(xp.asarray([1.0, 1.0j, 1.0]))
+        assert_almost_equal(unique, xp.asarray([1.0, 1.0j]), decimal=15)
+        xp_assert_equal(multiplicity, xp.asarray([2, 1]))
+
+        unique, multiplicity = unique_roots(
+            xp.asarray([1, 1 + 2e-9, 1e-9 + 1j]), tol=0.1
+        )
+        assert_almost_equal(unique, xp.asarray([1.0, 1e-9 + 1.0j]), decimal=15)
+        xp_assert_equal(multiplicity, xp.asarray([2, 1]))
+
+    def test_single_unique_root(self, xp):
+        p = xp.asarray(np.random.rand(100) + 1j * np.random.rand(100))
+        unique, multiplicity = unique_roots(p, 2)
+        assert_almost_equal(unique, xp.asarray([np.min(p)]), decimal=15)
+        xp_assert_equal(multiplicity, xp.asarray([100]))
+
+
+def test_gh_22684():
+    actual = signal.resample_poly(np.arange(2000, dtype=np.complex64), 6, 4)
+    assert actual.dtype == np.complex64
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/tests/test_spectral.py b/venv/lib/python3.12/site-packages/scipy/signal/tests/test_spectral.py
new file mode 100644
index 0000000000000000000000000000000000000000..3e1c2284a98ddcf7909a2f8398d7d014cdb7c6b6
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/tests/test_spectral.py
@@ -0,0 +1,2188 @@
+import sys
+import warnings
+
+import numpy as np
+from numpy.testing import (assert_,
+                           assert_allclose, assert_array_equal, assert_equal,
+                           assert_array_almost_equal_nulp)
+import pytest
+from pytest import raises as assert_raises
+
+from scipy import signal
+from scipy._lib._array_api import xp_assert_close
+from scipy.fft import fftfreq, rfftfreq, fft, irfft
+from scipy.integrate import trapezoid
+from scipy.signal import (periodogram, welch, lombscargle, coherence, csd,
+                          spectrogram, check_COLA, check_NOLA)
+from scipy.signal.windows import hann
+from scipy.signal._spectral_py import _spectral_helper
+
+# Compare ShortTimeFFT.stft() / ShortTimeFFT.istft() with stft() / istft():
+from scipy.signal.tests._scipy_spectral_test_shim import stft_compare as stft
+from scipy.signal.tests._scipy_spectral_test_shim import istft_compare as istft
+
+
+class TestPeriodogram:
+    def test_real_onesided_even(self):
+        x = np.zeros(16)
+        x[0] = 1
+        f, p = periodogram(x)
+        assert_allclose(f, np.linspace(0, 0.5, 9))
+        q = np.ones(9)
+        q[0] = 0
+        q[-1] /= 2.0
+        q /= 8
+        assert_allclose(p, q)
+
+    def test_real_onesided_odd(self):
+        x = np.zeros(15)
+        x[0] = 1
+        f, p = periodogram(x)
+        assert_allclose(f, np.arange(8.0)/15.0)
+        q = np.ones(8)
+        q[0] = 0
+        q *= 2.0/15.0
+        assert_allclose(p, q, atol=1e-15)
+
+    def test_real_twosided(self):
+        x = np.zeros(16)
+        x[0] = 1
+        f, p = periodogram(x, return_onesided=False)
+        assert_allclose(f, fftfreq(16, 1.0))
+        q = np.full(16, 1/16.0)
+        q[0] = 0
+        assert_allclose(p, q)
+
+    def test_real_spectrum(self):
+        x = np.zeros(16)
+        x[0] = 1
+        f, p = periodogram(x, scaling='spectrum')
+        g, q = periodogram(x, scaling='density')
+        assert_allclose(f, np.linspace(0, 0.5, 9))
+        assert_allclose(p, q/16.0)
+
+    def test_integer_even(self):
+        x = np.zeros(16, dtype=int)
+        x[0] = 1
+        f, p = periodogram(x)
+        assert_allclose(f, np.linspace(0, 0.5, 9))
+        q = np.ones(9)
+        q[0] = 0
+        q[-1] /= 2.0
+        q /= 8
+        assert_allclose(p, q)
+
+    def test_integer_odd(self):
+        x = np.zeros(15, dtype=int)
+        x[0] = 1
+        f, p = periodogram(x)
+        assert_allclose(f, np.arange(8.0)/15.0)
+        q = np.ones(8)
+        q[0] = 0
+        q *= 2.0/15.0
+        assert_allclose(p, q, atol=1e-15)
+
+    def test_integer_twosided(self):
+        x = np.zeros(16, dtype=int)
+        x[0] = 1
+        f, p = periodogram(x, return_onesided=False)
+        assert_allclose(f, fftfreq(16, 1.0))
+        q = np.full(16, 1/16.0)
+        q[0] = 0
+        assert_allclose(p, q)
+
+    def test_complex(self):
+        x = np.zeros(16, np.complex128)
+        x[0] = 1.0 + 2.0j
+        f, p = periodogram(x, return_onesided=False)
+        assert_allclose(f, fftfreq(16, 1.0))
+        q = np.full(16, 5.0/16.0)
+        q[0] = 0
+        assert_allclose(p, q)
+
+    def test_unk_scaling(self):
+        assert_raises(ValueError, periodogram, np.zeros(4, np.complex128),
+                scaling='foo')
+
+    @pytest.mark.skipif(
+        sys.maxsize <= 2**32,
+        reason="On some 32-bit tolerance issue"
+    )
+    def test_nd_axis_m1(self):
+        x = np.zeros(20, dtype=np.float64)
+        x = x.reshape((2,1,10))
+        x[:,:,0] = 1.0
+        f, p = periodogram(x)
+        assert_array_equal(p.shape, (2, 1, 6))
+        assert_array_almost_equal_nulp(p[0,0,:], p[1,0,:], 60)
+        f0, p0 = periodogram(x[0,0,:])
+        assert_array_almost_equal_nulp(p0[np.newaxis,:], p[1,:], 60)
+
+    @pytest.mark.skipif(
+        sys.maxsize <= 2**32,
+        reason="On some 32-bit tolerance issue"
+    )
+    def test_nd_axis_0(self):
+        x = np.zeros(20, dtype=np.float64)
+        x = x.reshape((10,2,1))
+        x[0,:,:] = 1.0
+        f, p = periodogram(x, axis=0)
+        assert_array_equal(p.shape, (6,2,1))
+        assert_array_almost_equal_nulp(p[:,0,0], p[:,1,0], 60)
+        f0, p0 = periodogram(x[:,0,0])
+        assert_array_almost_equal_nulp(p0, p[:,1,0])
+
+    def test_window_external(self):
+        x = np.zeros(16)
+        x[0] = 1
+        f, p = periodogram(x, 10, 'hann')
+        win = signal.get_window('hann', 16)
+        fe, pe = periodogram(x, 10, win)
+        assert_array_almost_equal_nulp(p, pe)
+        assert_array_almost_equal_nulp(f, fe)
+        win_err = signal.get_window('hann', 32)
+        assert_raises(ValueError, periodogram, x,
+                      10, win_err)  # win longer than signal
+
+    def test_padded_fft(self):
+        x = np.zeros(16)
+        x[0] = 1
+        f, p = periodogram(x)
+        fp, pp = periodogram(x, nfft=32)
+        assert_allclose(f, fp[::2])
+        assert_allclose(p, pp[::2])
+        assert_array_equal(pp.shape, (17,))
+
+    def test_empty_input(self):
+        f, p = periodogram([])
+        assert_array_equal(f.shape, (0,))
+        assert_array_equal(p.shape, (0,))
+        for shape in [(0,), (3,0), (0,5,2)]:
+            f, p = periodogram(np.empty(shape))
+            assert_array_equal(f.shape, shape)
+            assert_array_equal(p.shape, shape)
+
+    def test_empty_input_other_axis(self):
+        for shape in [(3,0), (0,5,2)]:
+            f, p = periodogram(np.empty(shape), axis=1)
+            assert_array_equal(f.shape, shape)
+            assert_array_equal(p.shape, shape)
+
+    def test_short_nfft(self):
+        x = np.zeros(18)
+        x[0] = 1
+        f, p = periodogram(x, nfft=16)
+        assert_allclose(f, np.linspace(0, 0.5, 9))
+        q = np.ones(9)
+        q[0] = 0
+        q[-1] /= 2.0
+        q /= 8
+        assert_allclose(p, q)
+
+    def test_nfft_is_xshape(self):
+        x = np.zeros(16)
+        x[0] = 1
+        f, p = periodogram(x, nfft=16)
+        assert_allclose(f, np.linspace(0, 0.5, 9))
+        q = np.ones(9)
+        q[0] = 0
+        q[-1] /= 2.0
+        q /= 8
+        assert_allclose(p, q)
+
+    def test_real_onesided_even_32(self):
+        x = np.zeros(16, 'f')
+        x[0] = 1
+        f, p = periodogram(x)
+        assert_allclose(f, np.linspace(0, 0.5, 9))
+        q = np.ones(9, 'f')
+        q[0] = 0
+        q[-1] /= 2.0
+        q /= 8
+        assert_allclose(p, q)
+        assert_(p.dtype == q.dtype)
+
+    def test_real_onesided_odd_32(self):
+        x = np.zeros(15, 'f')
+        x[0] = 1
+        f, p = periodogram(x)
+        assert_allclose(f, np.arange(8.0)/15.0)
+        q = np.ones(8, 'f')
+        q[0] = 0
+        q *= 2.0/15.0
+        assert_allclose(p, q, atol=1e-7)
+        assert_(p.dtype == q.dtype)
+
+    def test_real_twosided_32(self):
+        x = np.zeros(16, 'f')
+        x[0] = 1
+        f, p = periodogram(x, return_onesided=False)
+        assert_allclose(f, fftfreq(16, 1.0))
+        q = np.full(16, 1/16.0, 'f')
+        q[0] = 0
+        assert_allclose(p, q)
+        assert_(p.dtype == q.dtype)
+
+    def test_complex_32(self):
+        x = np.zeros(16, 'F')
+        x[0] = 1.0 + 2.0j
+        f, p = periodogram(x, return_onesided=False)
+        assert_allclose(f, fftfreq(16, 1.0))
+        q = np.full(16, 5.0/16.0, 'f')
+        q[0] = 0
+        assert_allclose(p, q)
+        assert_(p.dtype == q.dtype)
+
+    def test_shorter_window_error(self):
+        x = np.zeros(16)
+        x[0] = 1
+        win = signal.get_window('hann', 10)
+        expected_msg = ('the size of the window must be the same size '
+                        'of the input on the specified axis')
+        with assert_raises(ValueError, match=expected_msg):
+            periodogram(x, window=win)
+
+
+class TestWelch:
+    def test_real_onesided_even(self):
+        x = np.zeros(16)
+        x[0] = 1
+        x[8] = 1
+        f, p = welch(x, nperseg=8)
+        assert_allclose(f, np.linspace(0, 0.5, 5))
+        q = np.array([0.08333333, 0.15277778, 0.22222222, 0.22222222,
+                      0.11111111])
+        assert_allclose(p, q, atol=1e-7, rtol=1e-7)
+
+    def test_real_onesided_odd(self):
+        x = np.zeros(16)
+        x[0] = 1
+        x[8] = 1
+        f, p = welch(x, nperseg=9)
+        assert_allclose(f, np.arange(5.0)/9.0)
+        q = np.array([0.12477455, 0.23430933, 0.17072113, 0.17072113,
+                      0.17072113])
+        assert_allclose(p, q, atol=1e-7, rtol=1e-7)
+
+    def test_real_twosided(self):
+        x = np.zeros(16)
+        x[0] = 1
+        x[8] = 1
+        f, p = welch(x, nperseg=8, return_onesided=False)
+        assert_allclose(f, fftfreq(8, 1.0))
+        q = np.array([0.08333333, 0.07638889, 0.11111111, 0.11111111,
+                      0.11111111, 0.11111111, 0.11111111, 0.07638889])
+        assert_allclose(p, q, atol=1e-7, rtol=1e-7)
+
+    def test_real_spectrum(self):
+        x = np.zeros(16)
+        x[0] = 1
+        x[8] = 1
+        f, p = welch(x, nperseg=8, scaling='spectrum')
+        assert_allclose(f, np.linspace(0, 0.5, 5))
+        q = np.array([0.015625, 0.02864583, 0.04166667, 0.04166667,
+                      0.02083333])
+        assert_allclose(p, q, atol=1e-7, rtol=1e-7)
+
+    def test_integer_onesided_even(self):
+        x = np.zeros(16, dtype=int)
+        x[0] = 1
+        x[8] = 1
+        f, p = welch(x, nperseg=8)
+        assert_allclose(f, np.linspace(0, 0.5, 5))
+        q = np.array([0.08333333, 0.15277778, 0.22222222, 0.22222222,
+                      0.11111111])
+        assert_allclose(p, q, atol=1e-7, rtol=1e-7)
+
+    def test_integer_onesided_odd(self):
+        x = np.zeros(16, dtype=int)
+        x[0] = 1
+        x[8] = 1
+        f, p = welch(x, nperseg=9)
+        assert_allclose(f, np.arange(5.0)/9.0)
+        q = np.array([0.12477455, 0.23430933, 0.17072113, 0.17072113,
+                      0.17072113])
+        assert_allclose(p, q, atol=1e-7, rtol=1e-7)
+
+    def test_integer_twosided(self):
+        x = np.zeros(16, dtype=int)
+        x[0] = 1
+        x[8] = 1
+        f, p = welch(x, nperseg=8, return_onesided=False)
+        assert_allclose(f, fftfreq(8, 1.0))
+        q = np.array([0.08333333, 0.07638889, 0.11111111, 0.11111111,
+                      0.11111111, 0.11111111, 0.11111111, 0.07638889])
+        assert_allclose(p, q, atol=1e-7, rtol=1e-7)
+
+    def test_complex(self):
+        x = np.zeros(16, np.complex128)
+        x[0] = 1.0 + 2.0j
+        x[8] = 1.0 + 2.0j
+        f, p = welch(x, nperseg=8, return_onesided=False)
+        assert_allclose(f, fftfreq(8, 1.0))
+        q = np.array([0.41666667, 0.38194444, 0.55555556, 0.55555556,
+                      0.55555556, 0.55555556, 0.55555556, 0.38194444])
+        assert_allclose(p, q, atol=1e-7, rtol=1e-7)
+
+    def test_unk_scaling(self):
+        assert_raises(ValueError, welch, np.zeros(4, np.complex128),
+                      scaling='foo', nperseg=4)
+
+    def test_detrend_linear(self):
+        x = np.arange(10, dtype=np.float64) + 0.04
+        f, p = welch(x, nperseg=10, detrend='linear')
+        assert_allclose(p, np.zeros_like(p), atol=1e-15)
+
+    def test_no_detrending(self):
+        x = np.arange(10, dtype=np.float64) + 0.04
+        f1, p1 = welch(x, nperseg=10, detrend=False)
+        f2, p2 = welch(x, nperseg=10, detrend=lambda x: x)
+        assert_allclose(f1, f2, atol=1e-15)
+        assert_allclose(p1, p2, atol=1e-15)
+
+    def test_detrend_external(self):
+        x = np.arange(10, dtype=np.float64) + 0.04
+        f, p = welch(x, nperseg=10,
+                     detrend=lambda seg: signal.detrend(seg, type='l'))
+        assert_allclose(p, np.zeros_like(p), atol=1e-15)
+
+    def test_detrend_external_nd_m1(self):
+        x = np.arange(40, dtype=np.float64) + 0.04
+        x = x.reshape((2,2,10))
+        f, p = welch(x, nperseg=10,
+                     detrend=lambda seg: signal.detrend(seg, type='l'))
+        assert_allclose(p, np.zeros_like(p), atol=1e-15)
+
+    def test_detrend_external_nd_0(self):
+        x = np.arange(20, dtype=np.float64) + 0.04
+        x = x.reshape((2,1,10))
+        x = np.moveaxis(x, 2, 0)
+        f, p = welch(x, nperseg=10, axis=0,
+                     detrend=lambda seg: signal.detrend(seg, axis=0, type='l'))
+        assert_allclose(p, np.zeros_like(p), atol=1e-15)
+
+    def test_nd_axis_m1(self):
+        x = np.arange(20, dtype=np.float64) + 0.04
+        x = x.reshape((2,1,10))
+        f, p = welch(x, nperseg=10)
+        assert_array_equal(p.shape, (2, 1, 6))
+        assert_allclose(p[0,0,:], p[1,0,:], atol=1e-13, rtol=1e-13)
+        f0, p0 = welch(x[0,0,:], nperseg=10)
+        assert_allclose(p0[np.newaxis,:], p[1,:], atol=1e-13, rtol=1e-13)
+
+    def test_nd_axis_0(self):
+        x = np.arange(20, dtype=np.float64) + 0.04
+        x = x.reshape((10,2,1))
+        f, p = welch(x, nperseg=10, axis=0)
+        assert_array_equal(p.shape, (6,2,1))
+        assert_allclose(p[:,0,0], p[:,1,0], atol=1e-13, rtol=1e-13)
+        f0, p0 = welch(x[:,0,0], nperseg=10)
+        assert_allclose(p0, p[:,1,0], atol=1e-13, rtol=1e-13)
+
+    def test_window_external(self):
+        x = np.zeros(16)
+        x[0] = 1
+        x[8] = 1
+        f, p = welch(x, 10, 'hann', nperseg=8)
+        win = signal.get_window('hann', 8)
+        fe, pe = welch(x, 10, win, nperseg=None)
+        assert_array_almost_equal_nulp(p, pe)
+        assert_array_almost_equal_nulp(f, fe)
+        assert_array_equal(fe.shape, (5,))  # because win length used as nperseg
+        assert_array_equal(pe.shape, (5,))
+        assert_raises(ValueError, welch, x,
+                      10, win, nperseg=4)  # because nperseg != win.shape[-1]
+        win_err = signal.get_window('hann', 32)
+        assert_raises(ValueError, welch, x,
+                      10, win_err, nperseg=None)  # win longer than signal
+
+    def test_empty_input(self):
+        f, p = welch([])
+        assert_array_equal(f.shape, (0,))
+        assert_array_equal(p.shape, (0,))
+        for shape in [(0,), (3,0), (0,5,2)]:
+            f, p = welch(np.empty(shape))
+            assert_array_equal(f.shape, shape)
+            assert_array_equal(p.shape, shape)
+
+    def test_empty_input_other_axis(self):
+        for shape in [(3,0), (0,5,2)]:
+            f, p = welch(np.empty(shape), axis=1)
+            assert_array_equal(f.shape, shape)
+            assert_array_equal(p.shape, shape)
+
+    def test_short_data(self):
+        x = np.zeros(8)
+        x[0] = 1
+        #for string-like window, input signal length < nperseg value gives
+        #UserWarning, sets nperseg to x.shape[-1]
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", "nperseg=256 is greater than signal.*", UserWarning)
+            f, p = welch(x,window='hann')  # default nperseg
+            f1, p1 = welch(x,window='hann', nperseg=256)  # user-specified nperseg
+        f2, p2 = welch(x, nperseg=8)  # valid nperseg, doesn't give warning
+        assert_allclose(f, f2)
+        assert_allclose(p, p2)
+        assert_allclose(f1, f2)
+        assert_allclose(p1, p2)
+
+    def test_window_long_or_nd(self):
+        assert_raises(ValueError, welch, np.zeros(4), 1, np.array([1,1,1,1,1]))
+        assert_raises(ValueError, welch, np.zeros(4), 1,
+                      np.arange(6).reshape((2,3)))
+
+    def test_nondefault_noverlap(self):
+        x = np.zeros(64)
+        x[::8] = 1
+        f, p = welch(x, nperseg=16, noverlap=4)
+        q = np.array([0, 1./12., 1./3., 1./5., 1./3., 1./5., 1./3., 1./5.,
+                      1./6.])
+        assert_allclose(p, q, atol=1e-12)
+
+    def test_bad_noverlap(self):
+        assert_raises(ValueError, welch, np.zeros(4), 1, 'hann', 2, 7)
+
+    def test_nfft_too_short(self):
+        assert_raises(ValueError, welch, np.ones(12), nfft=3, nperseg=4)
+
+    def test_real_onesided_even_32(self):
+        x = np.zeros(16, 'f')
+        x[0] = 1
+        x[8] = 1
+        f, p = welch(x, nperseg=8)
+        assert_allclose(f, np.linspace(0, 0.5, 5))
+        q = np.array([0.08333333, 0.15277778, 0.22222222, 0.22222222,
+                      0.11111111], 'f')
+        assert_allclose(p, q, atol=1e-7, rtol=1e-7)
+        assert_(p.dtype == q.dtype)
+
+    def test_real_onesided_odd_32(self):
+        x = np.zeros(16, 'f')
+        x[0] = 1
+        x[8] = 1
+        f, p = welch(x, nperseg=9)
+        assert_allclose(f, np.arange(5.0)/9.0)
+        q = np.array([0.12477458, 0.23430935, 0.17072113, 0.17072116,
+                      0.17072113], 'f')
+        assert_allclose(p, q, atol=1e-7, rtol=1e-7)
+        assert_(p.dtype == q.dtype)
+
+    def test_real_twosided_32(self):
+        x = np.zeros(16, 'f')
+        x[0] = 1
+        x[8] = 1
+        f, p = welch(x, nperseg=8, return_onesided=False)
+        assert_allclose(f, fftfreq(8, 1.0))
+        q = np.array([0.08333333, 0.07638889, 0.11111111,
+                      0.11111111, 0.11111111, 0.11111111, 0.11111111,
+                      0.07638889], 'f')
+        assert_allclose(p, q, atol=1e-7, rtol=1e-7)
+        assert_(p.dtype == q.dtype)
+
+    def test_complex_32(self):
+        x = np.zeros(16, 'F')
+        x[0] = 1.0 + 2.0j
+        x[8] = 1.0 + 2.0j
+        f, p = welch(x, nperseg=8, return_onesided=False)
+        assert_allclose(f, fftfreq(8, 1.0))
+        q = np.array([0.41666666, 0.38194442, 0.55555552, 0.55555552,
+                      0.55555558, 0.55555552, 0.55555552, 0.38194442], 'f')
+        assert_allclose(p, q, atol=1e-7, rtol=1e-7)
+        assert_(p.dtype == q.dtype,
+                f'dtype mismatch, {p.dtype}, {q.dtype}')
+
+    def test_padded_freqs(self):
+        x = np.zeros(12)
+
+        nfft = 24
+        f = fftfreq(nfft, 1.0)[:nfft//2+1]
+        f[-1] *= -1
+        fodd, _ = welch(x, nperseg=5, nfft=nfft)
+        feven, _ = welch(x, nperseg=6, nfft=nfft)
+        assert_allclose(f, fodd)
+        assert_allclose(f, feven)
+
+        nfft = 25
+        f = fftfreq(nfft, 1.0)[:(nfft + 1)//2]
+        fodd, _ = welch(x, nperseg=5, nfft=nfft)
+        feven, _ = welch(x, nperseg=6, nfft=nfft)
+        assert_allclose(f, fodd)
+        assert_allclose(f, feven)
+
+    def test_window_correction(self):
+        A = 20
+        fs = 1e4
+        nperseg = int(fs//10)
+        fsig = 300
+        ii = int(fsig*nperseg//fs)  # Freq index of fsig
+
+        tt = np.arange(fs)/fs
+        x = A*np.sin(2*np.pi*fsig*tt)
+
+        for window in ['hann', 'bartlett', ('tukey', 0.1), 'flattop']:
+            _, p_spec = welch(x, fs=fs, nperseg=nperseg, window=window,
+                              scaling='spectrum')
+            freq, p_dens = welch(x, fs=fs, nperseg=nperseg, window=window,
+                                 scaling='density')
+
+            # Check peak height at signal frequency for 'spectrum'
+            assert_allclose(p_spec[ii], A**2/2.0)
+            # Check integrated spectrum RMS for 'density'
+            assert_allclose(np.sqrt(trapezoid(p_dens, freq)), A*np.sqrt(2)/2,
+                            rtol=1e-3)
+
+    def test_axis_rolling(self):
+        np.random.seed(1234)
+
+        x_flat = np.random.randn(1024)
+        _, p_flat = welch(x_flat)
+
+        for a in range(3):
+            newshape = [1,]*3
+            newshape[a] = -1
+            x = x_flat.reshape(newshape)
+
+            _, p_plus = welch(x, axis=a)  # Positive axis index
+            _, p_minus = welch(x, axis=a-x.ndim)  # Negative axis index
+
+            assert_equal(p_flat, p_plus.squeeze(), err_msg=a)
+            assert_equal(p_flat, p_minus.squeeze(), err_msg=a-x.ndim)
+
+    def test_average(self):
+        x = np.zeros(16)
+        x[0] = 1
+        x[8] = 1
+        f, p = welch(x, nperseg=8, average='median')
+        assert_allclose(f, np.linspace(0, 0.5, 5))
+        q = np.array([.1, .05, 0., 1.54074396e-33, 0.])
+        assert_allclose(p, q, atol=1e-7, rtol=1e-7)
+
+        assert_raises(ValueError, welch, x, nperseg=8,
+                      average='unrecognised-average')
+
+    def test_ratio_scale_to(self):
+        """Verify the factor of ``sum(abs(window)**2)*fs / abs(sum(window))**2``
+        used in the `welch`  and `csd` docstrs. """
+        x, win, fs = np.array([1., 0, 0, 0]), np.ones(4), 12
+        params = dict(fs=fs, window=win, return_onesided=False, detrend=None)
+        p_dens = welch(x, scaling='density', **params)[1]
+        p_spec = welch(x, scaling='spectrum', **params)[1]
+        p_fac = sum(win**2)*fs / abs(sum(win))**2
+        assert_allclose(p_spec / p_dens, p_fac)
+
+class TestCSD:
+    def test_pad_shorter_x(self):
+        x = np.zeros(8)
+        y = np.zeros(12)
+
+        f = np.linspace(0, 0.5, 7)
+        c = np.zeros(7,dtype=np.complex128)
+        f1, c1 = csd(x, y, nperseg=12)
+
+        assert_allclose(f, f1)
+        assert_allclose(c, c1)
+
+    def test_pad_shorter_y(self):
+        x = np.zeros(12)
+        y = np.zeros(8)
+
+        f = np.linspace(0, 0.5, 7)
+        c = np.zeros(7,dtype=np.complex128)
+        f1, c1 = csd(x, y, nperseg=12)
+
+        assert_allclose(f, f1)
+        assert_allclose(c, c1)
+
+    def test_unequal_length_input_1D(self):
+        """Test zero-padding for input `x.shape[axis] != y.shape[axis]` for 1d arrays.
+
+        This test ensures that issue 23036 is fixed.
+        """
+        x = np.tile([4, 0, -4, 0], 4)
+
+        kw = dict(fs=len(x), window='boxcar', nperseg=4)
+        X0 = signal.csd(x, np.copy(x), **kw)[1]  # `x is x` must be False
+        X1 = signal.csd(x, x[:8], **kw)[1]
+        X2 = signal.csd(x[:8], x, **kw)[1]
+        xp_assert_close(X1, X0 / 2)
+        xp_assert_close(X2, X0 / 2)
+
+    def test_unequal_length_input_3D(self):
+        """Test zero-padding for input `x.shape[axis] != y.shape[axis]` for 3d arrays.
+
+        This test ensures that issue 23036 is fixed.
+        """
+        n = 8
+        x = np.zeros(2 * 3 * n).reshape(2, n, 3)
+        x[:, 0, :] = n
+
+        kw = dict(fs=n, window='boxcar', nperseg=n, detrend=None, axis=1)
+        X0 = signal.csd(x, x.copy(), **kw)[1]  # `x is x` must be False
+        X1 = signal.csd(x, x[:, :2, :], **kw)[1]
+        X2 = signal.csd(x[:, :2, :], x, **kw)[1]
+        xp_assert_close(X1, X0)
+        xp_assert_close(X2, X0)
+
+    def test_real_onesided_even(self):
+        x = np.zeros(16)
+        x[0] = 1
+        x[8] = 1
+        f, p = csd(x, x, nperseg=8)
+        assert_allclose(f, np.linspace(0, 0.5, 5))
+        q = np.array([0.08333333, 0.15277778, 0.22222222, 0.22222222,
+                      0.11111111])
+        assert_allclose(p, q, atol=1e-7, rtol=1e-7)
+
+    def test_real_onesided_odd(self):
+        x = np.zeros(16)
+        x[0] = 1
+        x[8] = 1
+        f, p = csd(x, x, nperseg=9)
+        assert_allclose(f, np.arange(5.0)/9.0)
+        q = np.array([0.12477455, 0.23430933, 0.17072113, 0.17072113,
+                      0.17072113])
+        assert_allclose(p, q, atol=1e-7, rtol=1e-7)
+
+    def test_real_twosided(self):
+        x = np.zeros(16)
+        x[0] = 1
+        x[8] = 1
+        f, p = csd(x, x, nperseg=8, return_onesided=False)
+        assert_allclose(f, fftfreq(8, 1.0))
+        q = np.array([0.08333333, 0.07638889, 0.11111111, 0.11111111,
+                      0.11111111, 0.11111111, 0.11111111, 0.07638889])
+        assert_allclose(p, q, atol=1e-7, rtol=1e-7)
+
+    def test_real_spectrum(self):
+        x = np.zeros(16)
+        x[0] = 1
+        x[8] = 1
+        f, p = csd(x, x, nperseg=8, scaling='spectrum')
+        assert_allclose(f, np.linspace(0, 0.5, 5))
+        q = np.array([0.015625, 0.02864583, 0.04166667, 0.04166667,
+                      0.02083333])
+        assert_allclose(p, q, atol=1e-7, rtol=1e-7)
+
+    def test_integer_onesided_even(self):
+        x = np.zeros(16, dtype=int)
+        x[0] = 1
+        x[8] = 1
+        f, p = csd(x, x, nperseg=8)
+        assert_allclose(f, np.linspace(0, 0.5, 5))
+        q = np.array([0.08333333, 0.15277778, 0.22222222, 0.22222222,
+                      0.11111111])
+        assert_allclose(p, q, atol=1e-7, rtol=1e-7)
+
+    def test_integer_onesided_odd(self):
+        x = np.zeros(16, dtype=int)
+        x[0] = 1
+        x[8] = 1
+        f, p = csd(x, x, nperseg=9)
+        assert_allclose(f, np.arange(5.0)/9.0)
+        q = np.array([0.12477455, 0.23430933, 0.17072113, 0.17072113,
+                      0.17072113])
+        assert_allclose(p, q, atol=1e-7, rtol=1e-7)
+
+    def test_integer_twosided(self):
+        x = np.zeros(16, dtype=int)
+        x[0] = 1
+        x[8] = 1
+        f, p = csd(x, x, nperseg=8, return_onesided=False)
+        assert_allclose(f, fftfreq(8, 1.0))
+        q = np.array([0.08333333, 0.07638889, 0.11111111, 0.11111111,
+                      0.11111111, 0.11111111, 0.11111111, 0.07638889])
+        assert_allclose(p, q, atol=1e-7, rtol=1e-7)
+
+    def test_complex(self):
+        x = np.zeros(16, np.complex128)
+        x[0] = 1.0 + 2.0j
+        x[8] = 1.0 + 2.0j
+        f, p = csd(x, x, nperseg=8, return_onesided=False)
+        assert_allclose(f, fftfreq(8, 1.0))
+        q = np.array([0.41666667, 0.38194444, 0.55555556, 0.55555556,
+                      0.55555556, 0.55555556, 0.55555556, 0.38194444])
+        assert_allclose(p, q, atol=1e-7, rtol=1e-7)
+
+    def test_unk_scaling(self):
+        assert_raises(ValueError, csd, np.zeros(4, np.complex128),
+                      np.ones(4, np.complex128), scaling='foo', nperseg=4)
+
+    def test_detrend_linear(self):
+        x = np.arange(10, dtype=np.float64) + 0.04
+        f, p = csd(x, x, nperseg=10, detrend='linear')
+        assert_allclose(p, np.zeros_like(p), atol=1e-15)
+
+    def test_no_detrending(self):
+        x = np.arange(10, dtype=np.float64) + 0.04
+        f1, p1 = csd(x, x, nperseg=10, detrend=False)
+        f2, p2 = csd(x, x, nperseg=10, detrend=lambda x: x)
+        assert_allclose(f1, f2, atol=1e-15)
+        assert_allclose(p1, p2, atol=1e-15)
+
+    def test_detrend_external(self):
+        x = np.arange(10, dtype=np.float64) + 0.04
+        f, p = csd(x, x, nperseg=10,
+                   detrend=lambda seg: signal.detrend(seg, type='l'))
+        assert_allclose(p, np.zeros_like(p), atol=1e-15)
+
+    def test_detrend_external_nd_m1(self):
+        x = np.arange(40, dtype=np.float64) + 0.04
+        x = x.reshape((2,2,10))
+        f, p = csd(x, x, nperseg=10,
+                   detrend=lambda seg: signal.detrend(seg, type='l'))
+        assert_allclose(p, np.zeros_like(p), atol=1e-15)
+
+    def test_detrend_external_nd_0(self):
+        x = np.arange(20, dtype=np.float64) + 0.04
+        x = x.reshape((2,1,10))
+        x = np.moveaxis(x, 2, 0)
+        f, p = csd(x, x, nperseg=10, axis=0,
+                   detrend=lambda seg: signal.detrend(seg, axis=0, type='l'))
+        assert_allclose(p, np.zeros_like(p), atol=1e-15)
+
+    def test_nd_axis_m1(self):
+        x = np.arange(20, dtype=np.float64) + 0.04
+        x = x.reshape((2,1,10))
+        f, p = csd(x, x, nperseg=10)
+        assert_array_equal(p.shape, (2, 1, 6))
+        assert_allclose(p[0,0,:], p[1,0,:], atol=1e-13, rtol=1e-13)
+        f0, p0 = csd(x[0,0,:], x[0,0,:], nperseg=10)
+        assert_allclose(p0[np.newaxis,:], p[1,:], atol=1e-13, rtol=1e-13)
+
+    def test_nd_axis_0(self):
+        x = np.arange(20, dtype=np.float64) + 0.04
+        x = x.reshape((10,2,1))
+        f, p = csd(x, x, nperseg=10, axis=0)
+        assert_array_equal(p.shape, (6,2,1))
+        assert_allclose(p[:,0,0], p[:,1,0], atol=1e-13, rtol=1e-13)
+        f0, p0 = csd(x[:,0,0], x[:,0,0], nperseg=10)
+        assert_allclose(p0, p[:,1,0], atol=1e-13, rtol=1e-13)
+
+    def test_window_external(self):
+        x = np.zeros(16)
+        x[0] = 1
+        x[8] = 1
+        f, p = csd(x, x, 10, 'hann', 8)
+        win = signal.get_window('hann', 8)
+        fe, pe = csd(x, x, 10, win, nperseg=None)
+        assert_array_almost_equal_nulp(p, pe)
+        assert_array_almost_equal_nulp(f, fe)
+        assert_array_equal(fe.shape, (5,))  # because win length used as nperseg
+        assert_array_equal(pe.shape, (5,))
+        assert_raises(ValueError, csd, x, x,
+                      10, win, nperseg=256)  # because nperseg != win.shape[-1]
+        win_err = signal.get_window('hann', 32)
+        assert_raises(ValueError, csd, x, x,
+              10, win_err, nperseg=None)  # because win longer than signal
+        with pytest.raises(ValueError, match="Parameter nperseg=0.*"):
+            csd(x, x, 0, nperseg=0)
+
+    def test_empty_input(self):
+        f, p = csd([],np.zeros(10))
+        assert_array_equal(f.shape, (0,))
+        assert_array_equal(p.shape, (0,))
+
+        f, p = csd(np.zeros(10),[])
+        assert_array_equal(f.shape, (0,))
+        assert_array_equal(p.shape, (0,))
+
+        for shape in [(0,), (3,0), (0,5,2)]:
+            f, p = csd(np.empty(shape), np.empty(shape))
+            assert_array_equal(f.shape, shape)
+            assert_array_equal(p.shape, shape)
+
+        f, p = csd(np.ones(10), np.empty((5,0)))
+        assert_array_equal(f.shape, (5,0))
+        assert_array_equal(p.shape, (5,0))
+
+        f, p = csd(np.empty((5,0)), np.ones(10))
+        assert_array_equal(f.shape, (5,0))
+        assert_array_equal(p.shape, (5,0))
+
+    def test_empty_input_other_axis(self):
+        for shape in [(3,0), (0,5,2)]:
+            f, p = csd(np.empty(shape), np.empty(shape), axis=1)
+            assert_array_equal(f.shape, shape)
+            assert_array_equal(p.shape, shape)
+
+        f, p = csd(np.empty((10,10,3)), np.zeros((10,0,1)), axis=1)
+        assert_array_equal(f.shape, (10,0,3))
+        assert_array_equal(p.shape, (10,0,3))
+
+        f, p = csd(np.empty((10,0,1)), np.zeros((10,10,3)), axis=1)
+        assert_array_equal(f.shape, (10,0,3))
+        assert_array_equal(p.shape, (10,0,3))
+
+    def test_short_data(self):
+        x = np.zeros(8)
+        x[0] = 1
+
+        #for string-like window, input signal length < nperseg value gives
+        #UserWarning, sets nperseg to x.shape[-1]
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", "nperseg=256 is greater than signal length.*", UserWarning)
+            f, p = csd(x, x, window='hann')  # default nperseg
+            f1, p1 = csd(x, x, window='hann', nperseg=256)  # user-specified nperseg
+        f2, p2 = csd(x, x, nperseg=8)  # valid nperseg, doesn't give warning
+        assert_allclose(f, f2)
+        assert_allclose(p, p2)
+        assert_allclose(f1, f2)
+        assert_allclose(p1, p2)
+
+    def test_window_long_or_nd(self):
+        assert_raises(ValueError, csd, np.zeros(4), np.ones(4), 1,
+                      np.array([1,1,1,1,1]))
+        assert_raises(ValueError, csd, np.zeros(4), np.ones(4), 1,
+                      np.arange(6).reshape((2,3)))
+
+    def test_nondefault_noverlap(self):
+        x = np.zeros(64)
+        x[::8] = 1
+        f, p = csd(x, x, nperseg=16, noverlap=4)
+        q = np.array([0, 1./12., 1./3., 1./5., 1./3., 1./5., 1./3., 1./5.,
+                      1./6.])
+        assert_allclose(p, q, atol=1e-12)
+
+    def test_bad_noverlap(self):
+        assert_raises(ValueError, csd, np.zeros(4), np.ones(4), 1, 'hann',
+                      2, 7)
+
+    def test_nfft_too_short(self):
+        assert_raises(ValueError, csd, np.ones(12), np.zeros(12), nfft=3,
+                      nperseg=4)
+
+    def test_incompatible_inputs(self):
+        with pytest.raises(ValueError, match='x and y cannot be broadcast.*'):
+            csd(np.ones((1, 8, 1)), np.ones((2, 8)), nperseg=4)
+
+
+    def test_real_onesided_even_32(self):
+        x = np.zeros(16, 'f')
+        x[0] = 1
+        x[8] = 1
+        f, p = csd(x, x, nperseg=8)
+        assert_allclose(f, np.linspace(0, 0.5, 5))
+        q = np.array([0.08333333, 0.15277778, 0.22222222, 0.22222222,
+                      0.11111111], 'f')
+        assert_allclose(p, q, atol=1e-7, rtol=1e-7)
+        assert_(p.dtype == q.dtype)
+
+    def test_real_onesided_odd_32(self):
+        x = np.zeros(16, 'f')
+        x[0] = 1
+        x[8] = 1
+        f, p = csd(x, x, nperseg=9)
+        assert_allclose(f, np.arange(5.0)/9.0)
+        q = np.array([0.12477458, 0.23430935, 0.17072113, 0.17072116,
+                      0.17072113], 'f')
+        assert_allclose(p, q, atol=1e-7, rtol=1e-7)
+        assert_(p.dtype == q.dtype)
+
+    def test_real_twosided_32(self):
+        x = np.zeros(16, 'f')
+        x[0] = 1
+        x[8] = 1
+        f, p = csd(x, x, nperseg=8, return_onesided=False)
+        assert_allclose(f, fftfreq(8, 1.0))
+        q = np.array([0.08333333, 0.07638889, 0.11111111,
+                      0.11111111, 0.11111111, 0.11111111, 0.11111111,
+                      0.07638889], 'f')
+        assert_allclose(p, q, atol=1e-7, rtol=1e-7)
+        assert_(p.dtype == q.dtype)
+
+    def test_complex_32(self):
+        x = np.zeros(16, 'F')
+        x[0] = 1.0 + 2.0j
+        x[8] = 1.0 + 2.0j
+        f, p = csd(x, x, nperseg=8, return_onesided=False)
+        assert_allclose(f, fftfreq(8, 1.0))
+        q = np.array([0.41666666, 0.38194442, 0.55555552, 0.55555552,
+                      0.55555558, 0.55555552, 0.55555552, 0.38194442], 'f')
+        assert_allclose(p, q, atol=1e-7, rtol=1e-7)
+        assert_(p.dtype == q.dtype,
+                f'dtype mismatch, {p.dtype}, {q.dtype}')
+
+    def test_padded_freqs(self):
+        x = np.zeros(12)
+        y = np.ones(12)
+
+        nfft = 24
+        f = fftfreq(nfft, 1.0)[:nfft//2+1]
+        f[-1] *= -1
+        fodd, _ = csd(x, y, nperseg=5, nfft=nfft)
+        feven, _ = csd(x, y, nperseg=6, nfft=nfft)
+        assert_allclose(f, fodd)
+        assert_allclose(f, feven)
+
+        nfft = 25
+        f = fftfreq(nfft, 1.0)[:(nfft + 1)//2]
+        fodd, _ = csd(x, y, nperseg=5, nfft=nfft)
+        feven, _ = csd(x, y, nperseg=6, nfft=nfft)
+        assert_allclose(f, fodd)
+        assert_allclose(f, feven)
+
+    def test_copied_data(self):
+        x = np.random.randn(64)
+        y = x.copy()
+
+        _, p_same = csd(x, x, nperseg=8, average='mean',
+                        return_onesided=False)
+        _, p_copied = csd(x, y, nperseg=8, average='mean',
+                          return_onesided=False)
+        assert_allclose(p_same, p_copied)
+
+        _, p_same = csd(x, x, nperseg=8, average='median',
+                        return_onesided=False)
+        _, p_copied = csd(x, y, nperseg=8, average='median',
+                          return_onesided=False)
+        assert_allclose(p_same, p_copied)
+
+
+class TestCoherence:
+    def test_identical_input(self):
+        x = np.random.randn(20)
+        y = np.copy(x)  # So `y is x` -> False
+
+        f = np.linspace(0, 0.5, 6)
+        C = np.ones(6)
+        f1, C1 = coherence(x, y, nperseg=10)
+
+        assert_allclose(f, f1)
+        assert_allclose(C, C1)
+
+    def test_phase_shifted_input(self):
+        x = np.random.randn(20)
+        y = -x
+
+        f = np.linspace(0, 0.5, 6)
+        C = np.ones(6)
+        f1, C1 = coherence(x, y, nperseg=10)
+
+        assert_allclose(f, f1)
+        assert_allclose(C, C1)
+
+
+class TestSpectrogram:
+    def test_average_all_segments(self):
+        x = np.random.randn(1024)
+
+        fs = 1.0
+        window = ('tukey', 0.25)
+        nperseg = 16
+        noverlap = 2
+
+        f, _, P = spectrogram(x, fs, window, nperseg, noverlap)
+        fw, Pw = welch(x, fs, window, nperseg, noverlap)
+        assert_allclose(f, fw)
+        assert_allclose(np.mean(P, axis=-1), Pw)
+
+    def test_window_external(self):
+        x = np.random.randn(1024)
+
+        fs = 1.0
+        window = ('tukey', 0.25)
+        nperseg = 16
+        noverlap = 2
+        f, _, P = spectrogram(x, fs, window, nperseg, noverlap)
+
+        win = signal.get_window(('tukey', 0.25), 16)
+        fe, _, Pe = spectrogram(x, fs, win, nperseg=None, noverlap=2)
+        assert_array_equal(fe.shape, (9,))  # because win length used as nperseg
+        assert_array_equal(Pe.shape, (9,73))
+        assert_raises(ValueError, spectrogram, x,
+                      fs, win, nperseg=8)  # because nperseg != win.shape[-1]
+        win_err = signal.get_window(('tukey', 0.25), 2048)
+        assert_raises(ValueError, spectrogram, x,
+                      fs, win_err, nperseg=None)  # win longer than signal
+
+    def test_short_data(self):
+        x = np.random.randn(1024)
+        fs = 1.0
+
+        #for string-like window, input signal length < nperseg value gives
+        #UserWarning, sets nperseg to x.shape[-1]
+        f, _, p = spectrogram(x, fs, window=('tukey',0.25))  # default nperseg
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore",
+                "nperseg = 1025 is greater than input length  = 1024, "
+                "using nperseg = 1024",
+                UserWarning,
+            )
+            f1, _, p1 = spectrogram(x, fs, window=('tukey',0.25),
+                                    nperseg=1025)  # user-specified nperseg
+        f2, _, p2 = spectrogram(x, fs, nperseg=256)  # to compare w/default
+        f3, _, p3 = spectrogram(x, fs, nperseg=1024)  # compare w/user-spec'd
+        assert_allclose(f, f2)
+        assert_allclose(p, p2)
+        assert_allclose(f1, f3)
+        assert_allclose(p1, p3)
+
+class TestLombscargle:
+    def test_frequency(self):
+        """Test if frequency location of peak corresponds to frequency of
+        generated input signal.
+        """
+
+        # Input parameters
+        ampl = 2.
+        w = 1.
+        phi = 0.5 * np.pi
+        nin = 100
+        nout = 1000
+        p = 0.7  # Fraction of points to select
+
+        # Randomly select a fraction of an array with timesteps
+        rng = np.random.RandomState(2353425)
+        r = rng.rand(nin)
+        t = np.linspace(0.01*np.pi, 10.*np.pi, nin)[r >= p]
+
+        # Plot a sine wave for the selected times
+        y = ampl * np.sin(w*t + phi)
+
+        # Define the array of frequencies for which to compute the periodogram
+        f = np.linspace(0.01, 10., nout)
+
+        # Calculate Lomb-Scargle periodogram
+        P = lombscargle(t, y, f)
+
+        # Check if difference between found frequency maximum and input
+        # frequency is less than accuracy
+        delta = f[1] - f[0]
+        assert(w - f[np.argmax(P)] < (delta/2.))
+
+        # also, check that it works with weights
+        P = lombscargle(t, y, f, weights=np.ones_like(t, dtype=f.dtype))
+
+        # Check if difference between found frequency maximum and input
+        # frequency is less than accuracy
+        delta = f[1] - f[0]
+        assert(w - f[np.argmax(P)] < (delta/2.))
+
+    def test_amplitude(self):
+        # Test if height of peak in unnormalized Lomb-Scargle periodogram
+        # corresponds to amplitude of the generated input signal.
+
+        # Input parameters
+        ampl = 2.
+        w = 1.
+        phi = 0.5 * np.pi
+        nin = 1000
+        nout = 1000
+        p = 0.7  # Fraction of points to select
+
+        # Randomly select a fraction of an array with timesteps
+        rng = np.random.RandomState(2353425)
+        r = rng.rand(nin)
+        t = np.linspace(0.01*np.pi, 10.*np.pi, nin)[r >= p]
+
+        # Plot a sine wave for the selected times
+        y = ampl * np.sin(w*t + phi)
+
+        # Define the array of frequencies for which to compute the periodogram
+        f = np.linspace(0.01, 10., nout)
+
+        # Calculate Lomb-Scargle periodogram
+        pgram = lombscargle(t, y, f)
+
+        # convert to the amplitude
+        pgram = np.sqrt(4.0 * pgram / t.shape[0])
+
+        # Check if amplitude is correct (this will not exactly match, due to
+        # numerical differences when data is removed)
+        assert_allclose(pgram[f==w], ampl, rtol=5e-2)
+
+    @pytest.mark.filterwarnings("ignore::DeprecationWarning")
+    def test_precenter(self):
+        # Test if precenter gives the same result as manually precentering
+        # (for a very simple offset)
+
+        # Input parameters
+        ampl = 2.
+        w = 1.
+        phi = 0.5 * np.pi
+        nin = 100
+        nout = 1000
+        p = 0.7  # Fraction of points to select
+        offset = 0.15  # Offset to be subtracted in pre-centering
+
+        # Randomly select a fraction of an array with timesteps
+        rng = np.random.RandomState(2353425)
+        r = rng.rand(nin)
+        t = np.linspace(0.01*np.pi, 10.*np.pi, nin)[r >= p]
+
+        # Plot a sine wave for the selected times
+        y = ampl * np.sin(w*t + phi) + offset
+
+        # Define the array of frequencies for which to compute the periodogram
+        f = np.linspace(0.01, 10., nout)
+
+        # Calculate Lomb-Scargle periodogram
+        pgram = lombscargle(t, y, f, precenter=True)
+        pgram2 = lombscargle(t, y - y.mean(), f, precenter=False)
+
+        # check if centering worked
+        assert_allclose(pgram, pgram2)
+
+        # do this again, but with floating_mean=True
+
+        # Calculate Lomb-Scargle periodogram
+        pgram = lombscargle(t, y, f, precenter=True, floating_mean=True)
+        pgram2 = lombscargle(t, y - y.mean(), f, precenter=False, floating_mean=True)
+
+        # check if centering worked
+        assert_allclose(pgram, pgram2)
+
+    def test_normalize(self):
+        # Test normalize option of Lomb-Scarge.
+
+        # Input parameters
+        ampl = 2.
+        w = 1.
+        phi = 0.5 * np.pi
+        nin = 100
+        nout = 1000
+        p = 0.7  # Fraction of points to select
+
+        # Randomly select a fraction of an array with timesteps
+        rng = np.random.RandomState(2353425)
+        r = rng.rand(nin)
+        t = np.linspace(0.01*np.pi, 10.*np.pi, nin)[r >= p]
+
+        # Plot a sine wave for the selected times
+        y = ampl * np.sin(w*t + phi)
+
+        # Define the array of frequencies for which to compute the periodogram
+        f = np.linspace(0.01, 10., nout)
+
+        # Calculate Lomb-Scargle periodogram
+        pgram = lombscargle(t, y, f)
+        pgram2 = lombscargle(t, y, f, normalize=True)
+
+        # Calculate the scale to convert from unnormalized to normalized
+        weights = np.ones_like(t)/float(t.shape[0])
+        YY_hat = (weights * y * y).sum()
+        YY = YY_hat  # correct formula for floating_mean=False
+        scale_to_use = 2/(YY*t.shape[0])
+
+        # check if normalization works as expected
+        assert_allclose(pgram * scale_to_use, pgram2)
+        assert_allclose(np.max(pgram2), 1.0)
+
+    def test_wrong_shape(self):
+
+        # different length t and y
+        t = np.linspace(0, 1, 1)
+        y = np.linspace(0, 1, 2)
+        f = np.linspace(0, 1, 3) + 0.1
+        assert_raises(ValueError, lombscargle, t, y, f)
+
+        # t is 2D, with both axes length > 1
+        t = np.repeat(np.expand_dims(np.linspace(0, 1, 2), 1), 2, axis=1)
+        y = np.linspace(0, 1, 2)
+        f = np.linspace(0, 1, 3) + 0.1
+        assert_raises(ValueError, lombscargle, t, y, f)
+
+        # y is 2D, with both axes length > 1
+        t = np.linspace(0, 1, 2)
+        y = np.repeat(np.expand_dims(np.linspace(0, 1, 2), 1), 2, axis=1)
+        f = np.linspace(0, 1, 3) + 0.1
+        assert_raises(ValueError, lombscargle, t, y, f)
+
+        # f is 2D, with both axes length > 1
+        t = np.linspace(0, 1, 2)
+        y = np.linspace(0, 1, 2)
+        f = np.repeat(np.expand_dims(np.linspace(0, 1, 3), 1) + 0.1, 2, axis=1)
+        assert_raises(ValueError, lombscargle, t, y, f)
+
+        # weights is 2D, with both axes length > 1
+        t = np.linspace(0, 1, 2)
+        y = np.linspace(0, 1, 2)
+        f = np.linspace(0, 1, 3) + 0.1
+        weights = np.repeat(np.expand_dims(np.linspace(0, 1, 2), 1), 2, axis=1)
+        assert_raises(ValueError, lombscargle, t, y, f, weights=weights)
+
+    def test_lombscargle_atan_vs_atan2(self):
+        # https://github.com/scipy/scipy/issues/3787
+        # This raised a ZeroDivisionError.
+        t = np.linspace(0, 10, 1000, endpoint=False)
+        y = np.sin(4*t)
+        f = np.linspace(0, 50, 500, endpoint=False) + 0.1
+        lombscargle(t, y, f*2*np.pi)
+
+    def test_wrong_shape_weights(self):
+        # Weights must be the same shape as t
+
+        t = np.linspace(0, 1, 1)
+        y = np.linspace(0, 1, 1)
+        f = np.linspace(0, 1, 3) + 0.1
+        weights = np.linspace(1, 2, 2)
+        assert_raises(ValueError, lombscargle, t, y, f, weights=weights)
+
+    def test_zero_division_weights(self):
+        # Weights cannot sum to 0
+
+        t = np.zeros(1)
+        y = np.zeros(1)
+        f = np.ones(1)
+        weights = np.zeros(1)
+        assert_raises(ValueError, lombscargle, t, y, f, weights=weights)
+
+    def test_normalize_parameter(self):
+        # Test the validity of the normalize parameter input
+
+        # Input parameters
+        ampl = 2.
+        w = 1.
+        phi = 0
+        nin = 100
+        nout = 1000
+        p = 0.7  # Fraction of points to select
+
+        # Randomly select a fraction of an array with timesteps
+        rng = np.random.RandomState(2353425)
+        r = rng.rand(nin)
+        t = np.linspace(0.01*np.pi, 10.*np.pi, nin)[r >= p]
+
+        # Plot a sine wave for the selected times
+        y = ampl * np.sin(w*t + phi)
+
+        # Define the array of frequencies for which to compute the periodogram
+        f = np.linspace(0.01, 10., nout)
+
+        # check each of the valid inputs
+        pgram_false = lombscargle(t, y, f, normalize=False)
+        pgram_true = lombscargle(t, y, f, normalize=True)
+        pgram_power = lombscargle(t, y, f, normalize='power')
+        pgram_norm = lombscargle(t, y, f, normalize='normalize')
+        pgram_amp = lombscargle(t, y, f, normalize='amplitude')
+
+        # validate the results that should be the same
+        assert_allclose(pgram_false, pgram_power)
+        assert_allclose(pgram_true, pgram_norm)
+
+        # validate that the power and norm outputs are proper wrt each other
+        weights = np.ones_like(y)/float(y.shape[0])
+        YY_hat = (weights * y * y).sum()
+        YY = YY_hat  # correct formula for floating_mean=False
+        assert_allclose(pgram_power * 2.0 / (float(t.shape[0]) * YY), pgram_norm)
+
+        # validate that the amp output is correct for the given input
+        f_i = np.where(f==w)[0][0]
+        assert_allclose(np.abs(pgram_amp[f_i]), ampl)
+
+        # check invalid inputs
+        #  1) a string that is not allowed
+        assert_raises(ValueError, lombscargle, t, y, f, normalize='lomb')
+        #  2) something besides a bool or str
+        assert_raises(ValueError, lombscargle, t, y, f, normalize=2)
+
+    def test_offset_removal(self):
+        # Verify that the amplitude is the same, even with an offset
+        # must use floating_mean=True, otherwise it will not remove an offset
+
+        # Input parameters
+        ampl = 2.
+        w = 1.
+        phi = 0.5 * np.pi
+        nin = 100
+        nout = 1000
+        p = 0.7  # Fraction of points to select
+        offset = 2.15  # Large offset
+
+        # Randomly select a fraction of an array with timesteps
+        rng = np.random.RandomState(2353425)
+        r = rng.rand(nin)
+        t = np.linspace(0.01*np.pi, 10.*np.pi, nin)[r >= p]
+
+        # Plot a sine wave for the selected times
+        y = ampl * np.sin(w*t + phi)
+
+        # Define the array of frequencies for which to compute the periodogram
+        f = np.linspace(0.01, 10., nout)
+
+        # Calculate Lomb-Scargle periodogram
+        pgram = lombscargle(t, y, f, floating_mean=True)
+        pgram_offset = lombscargle(t, y + offset, f, floating_mean=True)
+
+        # check if offset removal works as expected
+        assert_allclose(pgram, pgram_offset)
+
+    def test_floating_mean_false(self):
+        # Verify that when disabling the floating_mean, the calculations are correct
+
+        # Input parameters
+        ampl = 2.
+        w = 1.
+        phi = 0
+        nin = 1000
+        nout = 1000
+        p = 0.7  # Fraction of points to select
+        offset = 2  # Large offset
+
+        # Randomly select a fraction of an array with timesteps
+        rng = np.random.RandomState(2353425)
+        r = rng.rand(nin)
+        t = np.linspace(0.01*np.pi, 10.*np.pi, nin)[r >= p]
+
+        # Plot a cos wave for the selected times
+        y = ampl * np.cos(w*t + phi)
+
+        # Define the array of frequencies for which to compute the periodogram
+        f = np.linspace(0.01, 10., nout)
+
+        # Calculate Lomb-Scargle periodogram
+        pgram = lombscargle(t, y, f, normalize=True, floating_mean=False)
+        pgram_offset = lombscargle(t, y + offset, f, normalize=True,
+                                   floating_mean=False)
+
+        # check if disabling floating_mean works as expected
+        # nearly-zero for no offset, exact value will change based on seed
+        assert(pgram[0] < 0.01)
+        # significant value with offset, exact value will change based on seed
+        assert(pgram_offset[0] > 0.5)
+
+    def test_amplitude_is_correct(self):
+        # Verify that the amplitude is correct (when normalize='amplitude')
+
+        # Input parameters
+        ampl = 2.
+        w = 1.
+        phi = 0.12
+        nin = 100
+        nout = 1000
+        p = 0.7  # Fraction of points to select
+        offset = 2.15  # Large offset
+
+        # Randomly select a fraction of an array with timesteps
+        rng = np.random.RandomState(2353425)
+        r = rng.rand(nin)
+        t = np.linspace(0.01*np.pi, 10.*np.pi, nin)[r >= p]
+
+        # Plot a sine wave for the selected times
+        y = ampl * np.cos(w*t + phi) + offset
+
+        # Define the array of frequencies for which to compute the periodogram
+        f = np.linspace(0.01, 10., nout)
+
+        # Get the index of where the exact result should be
+        f_indx = np.where(f==w)[0][0]
+
+        # Calculate Lomb-Scargle periodogram (amplitude + phase)
+        pgram = lombscargle(t, y, f, normalize='amplitude', floating_mean=True)
+
+        # Check if amplitude is correct
+        assert_allclose(np.abs(pgram[f_indx]), ampl)
+
+        # Check if phase is correct
+        # (phase angle is the negative of the phase offset)
+        assert_allclose(-np.angle(pgram[f_indx]), phi)
+
+    def test_negative_weight(self):
+        # Test that a negative weight produces an error
+
+        t = np.zeros(1)
+        y = np.zeros(1)
+        f = np.ones(1)
+        weights = -np.ones(1)
+        assert_raises(ValueError, lombscargle, t, y, f, weights=weights)
+
+    @pytest.mark.filterwarnings("ignore::DeprecationWarning")
+    def test_list_input(self):
+        # Test that input can be passsed in as lists and with a numerical issue
+        # https://github.com/scipy/scipy/issues/8787
+
+        t = [1.98201652e+09, 1.98201752e+09, 1.98201852e+09, 1.98201952e+09,
+            1.98202052e+09, 1.98202152e+09, 1.98202252e+09, 1.98202352e+09,
+            1.98202452e+09, 1.98202552e+09, 1.98202652e+09, 1.98202752e+09,
+            1.98202852e+09, 1.98202952e+09, 1.98203052e+09, 1.98203152e+09,
+            1.98203252e+09, 1.98203352e+09, 1.98203452e+09, 1.98203552e+09,
+            1.98205452e+09, 1.98205552e+09, 1.98205652e+09, 1.98205752e+09,
+            1.98205852e+09, 1.98205952e+09, 1.98206052e+09, 1.98206152e+09,
+            1.98206252e+09, 1.98206352e+09, 1.98206452e+09, 1.98206552e+09,
+            1.98206652e+09, 1.98206752e+09, 1.98206852e+09, 1.98206952e+09,
+            1.98207052e+09, 1.98207152e+09, 1.98207252e+09, 1.98207352e+09,
+            1.98209652e+09, 1.98209752e+09, 1.98209852e+09, 1.98209952e+09,
+            1.98210052e+09, 1.98210152e+09, 1.98210252e+09, 1.98210352e+09,
+            1.98210452e+09, 1.98210552e+09, 1.98210652e+09, 1.98210752e+09,
+            1.98210852e+09, 1.98210952e+09, 1.98211052e+09, 1.98211152e+09,
+            1.98211252e+09, 1.98211352e+09, 1.98211452e+09, 1.98211552e+09,
+            1.98217252e+09, 1.98217352e+09, 1.98217452e+09, 1.98217552e+09,
+            1.98217652e+09, 1.98217752e+09, 1.98217852e+09, 1.98217952e+09,
+            1.98218052e+09, 1.98218152e+09, 1.98218252e+09, 1.98218352e+09,
+            1.98218452e+09, 1.98218552e+09, 1.98218652e+09, 1.98218752e+09,
+            1.98218852e+09, 1.98218952e+09, 1.98219052e+09, 1.98219152e+09,
+            1.98219352e+09, 1.98219452e+09, 1.98219552e+09, 1.98219652e+09,
+            1.98219752e+09, 1.98219852e+09, 1.98219952e+09, 1.98220052e+09,
+            1.98220152e+09, 1.98220252e+09, 1.98220352e+09, 1.98220452e+09,
+            1.98220552e+09, 1.98220652e+09, 1.98220752e+09, 1.98220852e+09,
+            1.98220952e+09, 1.98221052e+09, 1.98221152e+09, 1.98221252e+09,
+            1.98222752e+09, 1.98222852e+09, 1.98222952e+09, 1.98223052e+09,
+            1.98223152e+09, 1.98223252e+09, 1.98223352e+09, 1.98223452e+09,
+            1.98223552e+09, 1.98223652e+09, 1.98223752e+09, 1.98223852e+09,
+            1.98223952e+09, 1.98224052e+09, 1.98224152e+09, 1.98224252e+09,
+            1.98224352e+09, 1.98224452e+09, 1.98224552e+09, 1.98224652e+09,
+            1.98224752e+09]
+        y = [2.97600000e+03, 3.18200000e+03, 3.74900000e+03, 4.53500000e+03,
+            5.43300000e+03, 6.38000000e+03, 7.34000000e+03, 8.29200000e+03,
+            9.21900000e+03, 1.01120000e+04, 1.09620000e+04, 1.17600000e+04,
+            1.25010000e+04, 1.31790000e+04, 1.37900000e+04, 1.43290000e+04,
+            1.47940000e+04, 1.51800000e+04, 1.54870000e+04, 1.57110000e+04,
+            5.74200000e+03, 4.82300000e+03, 3.99100000e+03, 3.33600000e+03,
+            2.99600000e+03, 3.08400000e+03, 3.56700000e+03, 4.30700000e+03,
+            5.18200000e+03, 6.11900000e+03, 7.07900000e+03, 8.03400000e+03,
+            8.97000000e+03, 9.87300000e+03, 1.07350000e+04, 1.15480000e+04,
+            1.23050000e+04, 1.30010000e+04, 1.36300000e+04, 1.41890000e+04,
+            6.00000000e+03, 5.06800000e+03, 4.20500000e+03, 3.49000000e+03,
+            3.04900000e+03, 3.01600000e+03, 3.40400000e+03, 4.08800000e+03,
+            4.93500000e+03, 5.86000000e+03, 6.81700000e+03, 7.77500000e+03,
+            8.71800000e+03, 9.63100000e+03, 1.05050000e+04, 1.13320000e+04,
+            1.21050000e+04, 1.28170000e+04, 1.34660000e+04, 1.40440000e+04,
+            1.32730000e+04, 1.26040000e+04, 1.18720000e+04, 1.10820000e+04,
+            1.02400000e+04, 9.35300000e+03, 8.43000000e+03, 7.48100000e+03,
+            6.52100000e+03, 5.57000000e+03, 4.66200000e+03, 3.85400000e+03,
+            3.24600000e+03, 2.97900000e+03, 3.14700000e+03, 3.68800000e+03,
+            4.45900000e+03, 5.35000000e+03, 6.29400000e+03, 7.25400000e+03,
+            9.13800000e+03, 1.00340000e+04, 1.08880000e+04, 1.16910000e+04,
+            1.24370000e+04, 1.31210000e+04, 1.37380000e+04, 1.42840000e+04,
+            1.47550000e+04, 1.51490000e+04, 1.54630000e+04, 1.56950000e+04,
+            1.58430000e+04, 1.59070000e+04, 1.58860000e+04, 1.57800000e+04,
+            1.55910000e+04, 1.53190000e+04, 1.49650000e+04, 1.45330000e+04,
+            3.01000000e+03, 3.05900000e+03, 3.51200000e+03, 4.23400000e+03,
+            5.10000000e+03, 6.03400000e+03, 6.99300000e+03, 7.95000000e+03,
+            8.88800000e+03, 9.79400000e+03, 1.06600000e+04, 1.14770000e+04,
+            1.22400000e+04, 1.29410000e+04, 1.35770000e+04, 1.41430000e+04,
+            1.46350000e+04, 1.50500000e+04, 1.53850000e+04, 1.56400000e+04,
+            1.58110000e+04]
+
+        periods = np.linspace(400, 120, 1000)
+        angular_freq = 2 * np.pi / periods
+
+        lombscargle(t, y, angular_freq, precenter=True, normalize=True)
+
+    def test_zero_freq(self):
+        # Verify that function works when freqs includes 0
+        # The value at f=0 will depend on the seed
+
+        # Input parameters
+        ampl = 2.
+        w = 1.
+        phi = 0.12
+        nin = 100
+        nout = 1001
+        p = 0.7  # Fraction of points to select
+        offset = 0
+
+        # Randomly select a fraction of an array with timesteps
+        rng = np.random.RandomState(2353425)
+        r = rng.rand(nin)
+        t = np.linspace(0.01*np.pi, 10.*np.pi, nin)[r >= p]
+
+        # Plot a sine wave for the selected times
+        y = ampl * np.cos(w*t + phi) + offset
+
+        # Define the array of frequencies for which to compute the periodogram
+        f = np.linspace(0, 10., nout)
+
+        # Calculate Lomb-Scargle periodogram
+        pgram = lombscargle(t, y, f, normalize=True, floating_mean=True)
+
+        # exact value will change based on seed
+        # testing to make sure it is very small
+        assert(pgram[0] < 1e-4)
+
+    def test_simple_div_zero(self):
+        # these are bare-minimum examples that would, without the eps adjustments,
+        # cause division-by-zero errors
+
+        # first, test with example that will cause first SS sum to be 0.0
+        t = [t + 1 for t in range(0, 32)]
+        y = np.ones(len(t))
+        freqs = [2.0*np.pi] * 2  # must have 2+ elements
+        lombscargle(t, y, freqs)
+
+        # second, test with example that will cause first CC sum to be 0.0
+        t = [t*4 + 1 for t in range(0, 32)]
+        y = np.ones(len(t))
+        freqs = [np.pi/2.0] * 2  # must have 2+ elements
+
+        lombscargle(t, y, freqs)
+
+    @pytest.mark.filterwarnings("ignore::DeprecationWarning")
+    def test_input_mutation(self):
+        # this tests for mutation of the input arrays
+        # https://github.com/scipy/scipy/issues/23474
+
+        # Input parameters
+        ampl = 2.
+        w = 1.
+        phi = 0.5 * np.pi
+        nin = 100
+        nout = 1000
+        p = 0.7  # Fraction of points to select
+
+        # Randomly select a fraction of an array with timesteps
+        rng = np.random.default_rng()
+        r = rng.random(nin)
+        t = np.linspace(0.01*np.pi, 10.*np.pi, nin)[r >= p]
+
+        # Plot a sine wave for the selected times
+        y = ampl * np.sin(w*t + phi)
+
+        # Define the array of frequencies for which to compute the periodogram
+        f = np.linspace(0.01, 10., nout)
+
+        weights = np.ones_like(y)
+
+        # create original copies before passing
+        t_org = t.copy()
+        y_org = y.copy()
+        f_org = f.copy()
+        weights_org = weights.copy()
+
+        lombscargle(t, y, f, precenter=True, weights=weights)
+
+        # check all 4 array inputs
+        assert_array_equal(t, t_org)
+        assert_array_equal(y, y_org)
+        assert_array_equal(f, f_org)
+        assert_array_equal(weights, weights_org)
+
+    def test_precenter_deprecation(self):
+        # test that precenter deprecation warning is raised
+
+        # Input parameters
+        ampl = 2.
+        w = 1.
+        phi = 0.5 * np.pi
+        nin = 100
+        nout = 1000
+        p = 0.7  # Fraction of points to select
+        offset = 0.15  # Offset to be subtracted in pre-centering
+
+        # Randomly select a fraction of an array with timesteps
+        rng = np.random.default_rng()
+        r = rng.random(nin)
+        t = np.linspace(0.01*np.pi, 10.*np.pi, nin)[r >= p]
+
+        # Plot a sine wave for the selected times
+        y = ampl * np.sin(w*t + phi) + offset
+
+        # Define the array of frequencies for which to compute the periodogram
+        f = np.linspace(0.01, 10., nout)
+
+        # Calculate Lomb-Scargle periodogram
+        with pytest.deprecated_call(match="leave 'precenter' unspecified"):
+            lombscargle(t, y, f, precenter=True)
+        # Should warn for explicit `False` too
+        with pytest.deprecated_call(match="leave 'precenter' unspecified"):
+            lombscargle(t, y, f, precenter=False)
+            
+    @pytest.mark.filterwarnings(
+        "ignore:.*leave 'precenter' unspecified.*:DeprecationWarning"
+    )
+    def test_positional_args_deprecation(self):
+        with pytest.deprecated_call(match="use keyword arguments"):
+            one = np.asarray([1.0])
+            lombscargle(one, one, one, False)
+
+
+class TestSTFT:
+    def test_input_validation(self):
+
+        def chk_VE(match):
+            """Assert for a ValueError matching regexp `match`.
+
+            This little wrapper allows a more concise code layout.
+            """
+            return pytest.raises(ValueError, match=match)
+
+        # Checks for check_COLA():
+        with chk_VE('nperseg must be a positive integer'):
+            check_COLA('hann', -10, 0)
+        with chk_VE('noverlap must be less than nperseg.'):
+            check_COLA('hann', 10, 20)
+        with chk_VE('window must be 1-D'):
+            check_COLA(np.ones((2, 2)), 10, 0)
+        with chk_VE('window must have length of nperseg'):
+            check_COLA(np.ones(20), 10, 0)
+
+        # Checks for check_NOLA():
+        with chk_VE('nperseg must be a positive integer'):
+            check_NOLA('hann', -10, 0)
+        with chk_VE('noverlap must be less than nperseg'):
+            check_NOLA('hann', 10, 20)
+        with chk_VE('window must be 1-D'):
+            check_NOLA(np.ones((2, 2)), 10, 0)
+        with chk_VE('window must have length of nperseg'):
+            check_NOLA(np.ones(20), 10, 0)
+        with chk_VE('noverlap must be a nonnegative integer'):
+            check_NOLA('hann', 64, -32)
+
+        x = np.zeros(1024)
+        z = stft(x)[2]
+
+        # Checks for stft():
+        with chk_VE('window must be 1-D'):
+            stft(x, window=np.ones((2, 2)))
+        with chk_VE('value specified for nperseg is different ' +
+                    'from length of window'):
+            stft(x, window=np.ones(10), nperseg=256)
+        with chk_VE('nperseg must be a positive integer'):
+            stft(x, nperseg=-256)
+        with chk_VE('noverlap must be less than nperseg.'):
+            stft(x, nperseg=256, noverlap=1024)
+        with chk_VE('nfft must be greater than or equal to nperseg.'):
+            stft(x, nperseg=256, nfft=8)
+
+        # Checks for istft():
+        with chk_VE('Input stft must be at least 2d!'):
+            istft(x)
+        with chk_VE('window must be 1-D'):
+            istft(z, window=np.ones((2, 2)))
+        with chk_VE('window must have length of 256'):
+            istft(z, window=np.ones(10), nperseg=256)
+        with chk_VE('nperseg must be a positive integer'):
+            istft(z, nperseg=-256)
+        with chk_VE('noverlap must be less than nperseg.'):
+            istft(z, nperseg=256, noverlap=1024)
+        with chk_VE('nfft must be greater than or equal to nperseg.'):
+            istft(z, nperseg=256, nfft=8)
+        with pytest.warns(UserWarning, match="NOLA condition failed, " +
+                          "STFT may not be invertible"):
+            istft(z, nperseg=256, noverlap=0, window='hann')
+        with chk_VE('Must specify differing time and frequency axes!'):
+            istft(z, time_axis=0, freq_axis=0)
+
+        # Checks for _spectral_helper():
+        with chk_VE("Unknown value for mode foo, must be one of: " +
+                    r"\{'psd', 'stft'\}"):
+            _spectral_helper(x, x, mode='foo')
+        with chk_VE("x and y must be equal if mode is 'stft'"):
+            _spectral_helper(x[:512], x[512:], mode='stft')
+        with chk_VE("Unknown boundary option 'foo', must be one of: " +
+                    r"\['even', 'odd', 'constant', 'zeros', None\]"):
+            _spectral_helper(x, x, boundary='foo')
+
+        scaling = "not_valid"
+        with chk_VE(fr"Parameter {scaling=} not in \['spectrum', 'psd'\]!"):
+            stft(x, scaling=scaling)
+        with chk_VE(fr"Parameter {scaling=} not in \['spectrum', 'psd'\]!"):
+            istft(z, scaling=scaling)
+
+    def test_check_COLA(self):
+        settings = [
+                    ('boxcar', 10, 0),
+                    ('boxcar', 10, 9),
+                    ('bartlett', 51, 26),
+                    ('hann', 256, 128),
+                    ('hann', 256, 192),
+                    ('blackman', 300, 200),
+                    (('tukey', 0.5), 256, 64),
+                    ('hann', 256, 255),
+                    ]
+
+        for setting in settings:
+            msg = '{}, {}, {}'.format(*setting)
+            assert_equal(True, check_COLA(*setting), err_msg=msg)
+
+    def test_check_NOLA(self):
+        settings_pass = [
+                    ('boxcar', 10, 0),
+                    ('boxcar', 10, 9),
+                    ('boxcar', 10, 7),
+                    ('bartlett', 51, 26),
+                    ('bartlett', 51, 10),
+                    ('hann', 256, 128),
+                    ('hann', 256, 192),
+                    ('hann', 256, 37),
+                    ('blackman', 300, 200),
+                    ('blackman', 300, 123),
+                    (('tukey', 0.5), 256, 64),
+                    (('tukey', 0.5), 256, 38),
+                    ('hann', 256, 255),
+                    ('hann', 256, 39),
+                    ]
+        for setting in settings_pass:
+            msg = '{}, {}, {}'.format(*setting)
+            assert_equal(True, check_NOLA(*setting), err_msg=msg)
+
+        w_fail = np.ones(16)
+        w_fail[::2] = 0
+        settings_fail = [
+                    (w_fail, len(w_fail), len(w_fail) // 2),
+                    ('hann', 64, 0),
+        ]
+        for setting in settings_fail:
+            msg = '{}, {}, {}'.format(*setting)
+            assert_equal(False, check_NOLA(*setting), err_msg=msg)
+
+    def test_average_all_segments(self):
+        rng = np.random.RandomState(1234)
+        x = rng.randn(1024)
+
+        fs = 1.0
+        window = 'hann'
+        nperseg = 16
+        noverlap = 8
+
+        # Compare twosided, because onesided welch doubles non-DC terms to
+        # account for power at negative frequencies. stft doesn't do this,
+        # because it breaks invertibility.
+        f, _, Z = stft(x, fs, window, nperseg, noverlap, padded=False,
+                       return_onesided=False, boundary=None)
+        fw, Pw = welch(x, fs, window, nperseg, noverlap, return_onesided=False,
+                       scaling='spectrum', detrend=False)
+
+        assert_allclose(f, fw)
+        assert_allclose(np.mean(np.abs(Z)**2, axis=-1), Pw)
+
+    def test_permute_axes(self):
+        rng = np.random.RandomState(1234)
+        x = rng.randn(1024)
+
+        fs = 1.0
+        window = 'hann'
+        nperseg = 16
+        noverlap = 8
+
+        f1, t1, Z1 = stft(x, fs, window, nperseg, noverlap)
+        f2, t2, Z2 = stft(x.reshape((-1, 1, 1)), fs, window, nperseg, noverlap,
+                          axis=0)
+
+        t3, x1 = istft(Z1, fs, window, nperseg, noverlap)
+        t4, x2 = istft(Z2.T, fs, window, nperseg, noverlap, time_axis=0,
+                       freq_axis=-1)
+
+        assert_allclose(f1, f2)
+        assert_allclose(t1, t2)
+        assert_allclose(t3, t4)
+        assert_allclose(Z1, Z2[:, 0, 0, :])
+        assert_allclose(x1, x2[:, 0, 0])
+
+    @pytest.mark.parametrize('scaling', ['spectrum', 'psd'])
+    def test_roundtrip_real(self, scaling):
+        rng = np.random.RandomState(1234)
+
+        settings = [
+                    ('boxcar', 100, 10, 0),           # Test no overlap
+                    ('boxcar', 100, 10, 9),           # Test high overlap
+                    ('bartlett', 101, 51, 26),        # Test odd nperseg
+                    ('hann', 1024, 256, 128),         # Test defaults
+                    (('tukey', 0.5), 1152, 256, 64),  # Test Tukey
+                    ('hann', 1024, 256, 255),         # Test overlapped hann
+                    ]
+
+        for window, N, nperseg, noverlap in settings:
+            t = np.arange(N)
+            x = 10*rng.randn(t.size)
+
+            _, _, zz = stft(x, nperseg=nperseg, noverlap=noverlap,
+                            window=window, detrend=None, padded=False,
+                            scaling=scaling)
+
+            tr, xr = istft(zz, nperseg=nperseg, noverlap=noverlap,
+                           window=window, scaling=scaling)
+
+            msg = f'{window}, {noverlap}'
+            assert_allclose(t, tr, err_msg=msg)
+            assert_allclose(x, xr, err_msg=msg)
+
+    def test_roundtrip_not_nola(self):
+        rng = np.random.RandomState(1234)
+
+        w_fail = np.ones(16)
+        w_fail[::2] = 0
+        settings = [
+                    (w_fail, 256, len(w_fail), len(w_fail) // 2),
+                    ('hann', 256, 64, 0),
+        ]
+
+        for window, N, nperseg, noverlap in settings:
+            msg = f'{window}, {N}, {nperseg}, {noverlap}'
+            assert not check_NOLA(window, nperseg, noverlap), msg
+
+            t = np.arange(N)
+            x = 10 * rng.randn(t.size)
+
+            _, _, zz = stft(x, nperseg=nperseg, noverlap=noverlap,
+                            window=window, detrend=None, padded=True,
+                            boundary='zeros')
+            with pytest.warns(UserWarning, match='NOLA'):
+                tr, xr = istft(zz, nperseg=nperseg, noverlap=noverlap,
+                               window=window, boundary=True)
+
+            assert np.allclose(t, tr[:len(t)]), msg
+            assert not np.allclose(x, xr[:len(x)]), msg
+
+    def test_roundtrip_nola_not_cola(self):
+        rng = np.random.RandomState(1234)
+
+        settings = [
+                    ('boxcar', 100, 10, 3),           # NOLA True, COLA False
+                    ('bartlett', 101, 51, 37),        # NOLA True, COLA False
+                    ('hann', 1024, 256, 127),         # NOLA True, COLA False
+                    (('tukey', 0.5), 1152, 256, 14),  # NOLA True, COLA False
+                    ('hann', 1024, 256, 5),           # NOLA True, COLA False
+                    ]
+
+        for window, N, nperseg, noverlap in settings:
+            msg = f'{window}, {nperseg}, {noverlap}'
+            assert check_NOLA(window, nperseg, noverlap), msg
+            assert not check_COLA(window, nperseg, noverlap), msg
+
+            t = np.arange(N)
+            x = 10 * rng.randn(t.size)
+
+            _, _, zz = stft(x, nperseg=nperseg, noverlap=noverlap,
+                            window=window, detrend=None, padded=True,
+                            boundary='zeros')
+
+            tr, xr = istft(zz, nperseg=nperseg, noverlap=noverlap,
+                           window=window, boundary=True)
+
+            msg = f'{window}, {noverlap}'
+            assert_allclose(t, tr[:len(t)], err_msg=msg)
+            assert_allclose(x, xr[:len(x)], err_msg=msg)
+
+    def test_roundtrip_float32(self):
+        rng = np.random.RandomState(1234)
+
+        settings = [('hann', 1024, 256, 128)]
+
+        for window, N, nperseg, noverlap in settings:
+            t = np.arange(N)
+            x = 10*rng.randn(t.size)
+            x = x.astype(np.float32)
+
+            _, _, zz = stft(x, nperseg=nperseg, noverlap=noverlap,
+                            window=window, detrend=None, padded=False)
+
+            tr, xr = istft(zz, nperseg=nperseg, noverlap=noverlap,
+                           window=window)
+
+            msg = f'{window}, {noverlap}'
+            assert_allclose(t, t, err_msg=msg)
+            assert_allclose(x, xr, err_msg=msg, rtol=1e-4, atol=1e-5)
+            assert_(x.dtype == xr.dtype)
+
+    @pytest.mark.parametrize('scaling', ['spectrum', 'psd'])
+    def test_roundtrip_complex(self, scaling):
+        rng = np.random.RandomState(1234)
+
+        settings = [
+                    ('boxcar', 100, 10, 0),           # Test no overlap
+                    ('boxcar', 100, 10, 9),           # Test high overlap
+                    ('bartlett', 101, 51, 26),        # Test odd nperseg
+                    ('hann', 1024, 256, 128),         # Test defaults
+                    (('tukey', 0.5), 1152, 256, 64),  # Test Tukey
+                    ('hann', 1024, 256, 255),         # Test overlapped hann
+                    ]
+
+        for window, N, nperseg, noverlap in settings:
+            t = np.arange(N)
+            x = 10*rng.randn(t.size) + 10j*rng.randn(t.size)
+
+            _, _, zz = stft(x, nperseg=nperseg, noverlap=noverlap,
+                            window=window, detrend=None, padded=False,
+                            return_onesided=False, scaling=scaling)
+
+            tr, xr = istft(zz, nperseg=nperseg, noverlap=noverlap,
+                           window=window, input_onesided=False,
+                           scaling=scaling)
+
+            msg = f'{window}, {nperseg}, {noverlap}'
+            assert_allclose(t, tr, err_msg=msg)
+            assert_allclose(x, xr, err_msg=msg)
+
+        # Check that asking for onesided switches to twosided
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore",
+                "Input data is complex, switching to return_onesided=False",
+                UserWarning,
+            )
+            _, _, zz = stft(x, nperseg=nperseg, noverlap=noverlap,
+                            window=window, detrend=None, padded=False,
+                            return_onesided=True, scaling=scaling)
+
+        tr, xr = istft(zz, nperseg=nperseg, noverlap=noverlap,
+                       window=window, input_onesided=False, scaling=scaling)
+
+        msg = f'{window}, {nperseg}, {noverlap}'
+        assert_allclose(t, tr, err_msg=msg)
+        assert_allclose(x, xr, err_msg=msg)
+
+    def test_roundtrip_boundary_extension(self):
+        rng = np.random.RandomState(1234)
+
+        # Test against boxcar, since window is all ones, and thus can be fully
+        # recovered with no boundary extension
+
+        settings = [
+                    ('boxcar', 100, 10, 0),           # Test no overlap
+                    ('boxcar', 100, 10, 9),           # Test high overlap
+                    ]
+
+        for window, N, nperseg, noverlap in settings:
+            t = np.arange(N)
+            x = 10*rng.randn(t.size)
+
+            _, _, zz = stft(x, nperseg=nperseg, noverlap=noverlap,
+                           window=window, detrend=None, padded=True,
+                           boundary=None)
+
+            _, xr = istft(zz, noverlap=noverlap, window=window, boundary=False)
+
+            for boundary in ['even', 'odd', 'constant', 'zeros']:
+                _, _, zz_ext = stft(x, nperseg=nperseg, noverlap=noverlap,
+                                window=window, detrend=None, padded=True,
+                                boundary=boundary)
+
+                _, xr_ext = istft(zz_ext, noverlap=noverlap, window=window,
+                                boundary=True)
+
+                msg = f'{window}, {noverlap}, {boundary}'
+                assert_allclose(x, xr, err_msg=msg)
+                assert_allclose(x, xr_ext, err_msg=msg)
+
+    def test_roundtrip_padded_signal(self):
+        rng = np.random.RandomState(1234)
+
+        settings = [
+                    ('boxcar', 101, 10, 0),
+                    ('hann', 1000, 256, 128),
+                    ]
+
+        for window, N, nperseg, noverlap in settings:
+            t = np.arange(N)
+            x = 10*rng.randn(t.size)
+
+            _, _, zz = stft(x, nperseg=nperseg, noverlap=noverlap,
+                            window=window, detrend=None, padded=True)
+
+            tr, xr = istft(zz, noverlap=noverlap, window=window)
+
+            msg = f'{window}, {noverlap}'
+            # Account for possible zero-padding at the end
+            assert_allclose(t, tr[:t.size], err_msg=msg)
+            assert_allclose(x, xr[:x.size], err_msg=msg)
+
+    def test_roundtrip_padded_FFT(self):
+        rng = np.random.RandomState(1234)
+
+        settings = [
+                    ('hann', 1024, 256, 128, 512),
+                    ('hann', 1024, 256, 128, 501),
+                    ('boxcar', 100, 10, 0, 33),
+                    (('tukey', 0.5), 1152, 256, 64, 1024),
+                    ]
+
+        for window, N, nperseg, noverlap, nfft in settings:
+            t = np.arange(N)
+            x = 10*rng.randn(t.size)
+            xc = x*np.exp(1j*np.pi/4)
+
+            # real signal
+            _, _, z = stft(x, nperseg=nperseg, noverlap=noverlap, nfft=nfft,
+                            window=window, detrend=None, padded=True)
+
+            # complex signal
+            _, _, zc = stft(xc, nperseg=nperseg, noverlap=noverlap, nfft=nfft,
+                            window=window, detrend=None, padded=True,
+                            return_onesided=False)
+
+            tr, xr = istft(z, nperseg=nperseg, noverlap=noverlap, nfft=nfft,
+                           window=window)
+
+            tr, xcr = istft(zc, nperseg=nperseg, noverlap=noverlap, nfft=nfft,
+                            window=window, input_onesided=False)
+
+            msg = f'{window}, {noverlap}'
+            assert_allclose(t, tr, err_msg=msg)
+            assert_allclose(x, xr, err_msg=msg)
+            assert_allclose(xc, xcr, err_msg=msg)
+
+    def test_axis_rolling(self):
+        rng = np.random.RandomState(1234)
+
+        x_flat = rng.randn(1024)
+        _, _, z_flat = stft(x_flat)
+
+        for a in range(3):
+            newshape = [1,]*3
+            newshape[a] = -1
+            x = x_flat.reshape(newshape)
+
+            _, _, z_plus = stft(x, axis=a)  # Positive axis index
+            _, _, z_minus = stft(x, axis=a-x.ndim)  # Negative axis index
+
+            assert_equal(z_flat, z_plus.squeeze(), err_msg=a)
+            assert_equal(z_flat, z_minus.squeeze(), err_msg=a-x.ndim)
+
+        # z_flat has shape [n_freq, n_time]
+
+        # Test vs. transpose
+        _, x_transpose_m = istft(z_flat.T, time_axis=-2, freq_axis=-1)
+        _, x_transpose_p = istft(z_flat.T, time_axis=0, freq_axis=1)
+
+        assert_allclose(x_flat, x_transpose_m, err_msg='istft transpose minus')
+        assert_allclose(x_flat, x_transpose_p, err_msg='istft transpose plus')
+
+    def test_roundtrip_scaling(self):
+        """Verify behavior of scaling parameter. """
+        # Create 1024 sample cosine signal with amplitude 2:
+        X = np.zeros(513, dtype=complex)
+        X[256] = 1024
+        x = np.fft.irfft(X)
+        power_x = sum(x**2) / len(x)  # power of signal x is 2
+
+        # Calculate magnitude-scaled STFT:
+        Zs = stft(x, boundary='even', scaling='spectrum')[2]
+
+        # Test round trip:
+        x1 = istft(Zs, boundary=True, scaling='spectrum')[1]
+        assert_allclose(x1, x)
+
+        # For a Hann-windowed 256 sample length FFT, we expect a peak at
+        # frequency 64 (since it is 1/4 the length of X) with a height of 1
+        # (half the amplitude). A Hann window of a perfectly centered sine has
+        # the magnitude [..., 0, 0, 0.5, 1, 0.5, 0, 0, ...].
+        # Note that in this case the 'even' padding works for the beginning
+        # but not for the end of the STFT.
+        assert_allclose(abs(Zs[63, :-1]), 0.5)
+        assert_allclose(abs(Zs[64, :-1]), 1)
+        assert_allclose(abs(Zs[65, :-1]), 0.5)
+        # All other values should be zero:
+        Zs[63:66, :-1] = 0
+        # Note since 'rtol' does not have influence here, atol needs to be set:
+        assert_allclose(Zs[:, :-1], 0, atol=np.finfo(Zs.dtype).resolution)
+
+        # Calculate two-sided psd-scaled STFT:
+        #  - using 'even' padding since signal is axis symmetric - this ensures
+        #    stationary behavior on the boundaries
+        #  - using the two-sided transform allows determining the spectral
+        #    power by `sum(abs(Zp[:, k])**2) / len(f)` for the k-th time slot.
+        Zp = stft(x, return_onesided=False, boundary='even', scaling='psd')[2]
+
+        # Calculate spectral power of Zd by summing over the frequency axis:
+        psd_Zp = np.sum(Zp.real**2 + Zp.imag**2, axis=0) / Zp.shape[0]
+        # Spectral power of Zp should be equal to the signal's power:
+        assert_allclose(psd_Zp, power_x)
+
+        # Test round trip:
+        x1 = istft(Zp, input_onesided=False, boundary=True, scaling='psd')[1]
+        assert_allclose(x1, x)
+
+        # The power of the one-sided psd-scaled STFT can be determined
+        # analogously (note that the two sides are not of equal shape):
+        Zp0 = stft(x, return_onesided=True, boundary='even', scaling='psd')[2]
+
+        # Since x is real, its Fourier transform is conjugate symmetric, i.e.,
+        # the missing 'second side' can be expressed through the 'first side':
+        Zp1 = np.conj(Zp0[-2:0:-1, :])  # 'second side' is conjugate reversed
+        assert_allclose(Zp[:129, :], Zp0)
+        assert_allclose(Zp[129:, :], Zp1)
+
+        # Calculate the spectral power:
+        s2 = (np.sum(Zp0.real ** 2 + Zp0.imag ** 2, axis=0) +
+              np.sum(Zp1.real ** 2 + Zp1.imag ** 2, axis=0))
+        psd_Zp01 = s2 / (Zp0.shape[0] + Zp1.shape[0])
+        assert_allclose(psd_Zp01, power_x)
+
+        # Test round trip:
+        x1 = istft(Zp0, input_onesided=True, boundary=True, scaling='psd')[1]
+        assert_allclose(x1, x)
+
+
+class TestSampledSpectralRepresentations:
+    """Check energy/power relations from `Spectral Analysis` section in the user guide.
+
+    A 32 sample cosine signal is used to compare the numerical to the expected results
+    stated in :ref:`tutorial_SpectralAnalysis` in
+    file ``doc/source/tutorial/signal.rst``
+    """
+    n: int = 32  #: number of samples
+    T: float = 1/16  #: sampling interval
+    a_ref: float = 3  #: amplitude of reference
+    l_a: int = 3  #: index in fft for defining frequency of test signal
+
+    x_ref: np.ndarray  #: reference signal
+    X_ref: np.ndarray  #: two-sided FFT of x_ref
+    E_ref: float  #: energy of signal
+    P_ref: float  #: power of signal
+
+    def setup_method(self):
+        """Create Cosine signal with amplitude a from spectrum. """
+        f = rfftfreq(self.n, self.T)
+        X_ref = np.zeros_like(f)
+        self.l_a = 3
+        X_ref[self.l_a] = self.a_ref/2 * self.n  # set amplitude
+        self.x_ref = irfft(X_ref)
+        self.X_ref = fft(self.x_ref)
+
+        # Closed form expression for continuous-time signal:
+        self.E_ref = self.tau * self.a_ref**2 / 2  # energy of signal
+        self.P_ref = self.a_ref**2 / 2  # power of signal
+
+    @property
+    def tau(self) -> float:
+        """Duration of signal. """
+        return self.n * self.T
+
+    @property
+    def delta_f(self) -> float:
+        """Bin width """
+        return 1 / (self.n * self.T)
+
+    def test_reference_signal(self):
+        """Test energy and power formulas. """
+        # Verify that amplitude is a:
+        assert_allclose(2*self.a_ref, np.ptp(self.x_ref), rtol=0.1)
+        # Verify that energy expression for sampled signal:
+        assert_allclose(self.T * sum(self.x_ref ** 2), self.E_ref)
+
+        # Verify that spectral energy and power formulas are correct:
+        sum_X_ref_squared = sum(self.X_ref.real**2 + self.X_ref.imag**2)
+        assert_allclose(self.T/self.n * sum_X_ref_squared, self.E_ref)
+        assert_allclose(1/self.n**2 * sum_X_ref_squared, self.P_ref)
+
+    def test_windowed_DFT(self):
+        """Verify spectral representations of windowed DFT.
+
+        Furthermore, the scalings of `periodogram` and `welch` are verified.
+        """
+        w = hann(self.n, sym=False)
+        c_amp, c_rms = abs(sum(w)), np.sqrt(sum(w.real**2 + w.imag**2))
+        Xw = fft(self.x_ref*w)  # unnormalized windowed DFT
+
+        # Verify that the *spectrum* peak is consistent:
+        assert_allclose(self.tau * Xw[self.l_a] / c_amp, self.a_ref * self.tau / 2)
+        # Verify that the *amplitude spectrum* peak is consistent:
+        assert_allclose(Xw[self.l_a] / c_amp, self.a_ref/2)
+
+        # Verify spectral power/energy equals signal's power/energy:
+        X_ESD = self.tau * self.T * abs(Xw / c_rms)**2  # Energy Spectral Density
+        X_PSD = self.T * abs(Xw / c_rms)**2  # Power Spectral Density
+        assert_allclose(self.delta_f * sum(X_ESD), self.E_ref)
+        assert_allclose(self.delta_f * sum(X_PSD), self.P_ref)
+
+        # Verify scalings of periodogram:
+        kw = dict(fs=1/self.T, window=w, detrend=False, return_onesided=False)
+        _, P_mag = periodogram(self.x_ref, scaling='spectrum', **kw)
+        _, P_psd = periodogram(self.x_ref, scaling='density', **kw)
+
+        # Verify that periodogram calculates a squared magnitude spectrum:
+        float_res = np.finfo(P_mag.dtype).resolution
+        assert_allclose(P_mag, abs(Xw/c_amp)**2, atol=float_res*max(P_mag))
+        # Verify that periodogram calculates a PSD:
+        assert_allclose(P_psd, X_PSD, atol=float_res*max(P_psd))
+
+        # Ensure that scaling of welch is the same as of periodogram:
+        kw = dict(nperseg=len(self.x_ref), noverlap=0, **kw)
+        assert_allclose(welch(self.x_ref, scaling='spectrum', **kw)[1], P_mag,
+                        atol=float_res*max(P_mag))
+        assert_allclose(welch(self.x_ref, scaling='density', **kw)[1], P_psd,
+                        atol=float_res*max(P_psd))
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/tests/test_splines.py b/venv/lib/python3.12/site-packages/scipy/signal/tests/test_splines.py
new file mode 100644
index 0000000000000000000000000000000000000000..22f703bf2787896b43f81173bb79abcecae46742
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/tests/test_splines.py
@@ -0,0 +1,423 @@
+# pylint: disable=missing-docstring
+import math
+import numpy as np
+import pytest
+from scipy._lib._array_api import is_cupy, xp_assert_close, xp_default_dtype, concat_1d
+
+from scipy.signal._spline import (
+    symiirorder1_ic, symiirorder2_ic_fwd, symiirorder2_ic_bwd)
+from scipy.signal import symiirorder1, symiirorder2
+
+skip_xp_backends = pytest.mark.skip_xp_backends
+xfail_xp_backends = pytest.mark.xfail_xp_backends
+
+
+def _compute_symiirorder2_bwd_hs(k, cs, rsq, omega):
+    cssq = cs * cs
+    k = np.abs(k)
+    rsupk = np.power(rsq, k / 2.0)
+
+    c0 = (cssq * (1.0 + rsq) / (1.0 - rsq) /
+          (1 - 2 * rsq * np.cos(2 * omega) + rsq * rsq))
+    gamma = (1.0 - rsq) / (1.0 + rsq) / np.tan(omega)
+    return c0 * rsupk * (np.cos(omega * k) + gamma * np.sin(omega * k))
+
+
+@pytest.mark.uses_xp_capabilities(False, reason="private")
+class TestSymIIR:
+
+    @skip_xp_backends(np_only=True, reason="_ic functions are private and numpy-only")
+    @pytest.mark.parametrize(
+        'dtype', ['float32', 'float64', 'complex64', 'complex128'])
+    @pytest.mark.parametrize('precision', [-1.0, 0.7, 0.5, 0.25, 0.0075])
+    def test_symiir1_ic(self, dtype, precision, xp):
+
+        dtype = getattr(xp, dtype)
+
+        c_precision = precision
+        if precision <= 0.0 or precision > 1.0:
+            if dtype in {xp.float32, xp.complex64}:
+                c_precision = 1e-6
+            else:
+                c_precision = 1e-11
+
+        # Symmetrical initial conditions for a IIR filter of order 1 are:
+        # x[0] + z1 * \sum{k = 0}^{n - 1} x[k] * z1^k
+
+        # Check the initial condition for a low-pass filter
+        # with coefficient b = 0.85 on a step signal. The initial condition is
+        # a geometric series: 1 + b * \sum_{k = 0}^{n - 1} u[k] b^k.
+
+        # Finding the initial condition corresponds to
+        # 1. Computing the index n such that b**n < precision, which
+        # corresponds to ceil(log(precision) / log(b))
+        # 2. Computing the geometric series until n, this can be computed
+        # using the partial sum formula: (1 - b**n) / (1 - b)
+        # This holds due to the input being a step signal.
+        b = 0.85
+        n_exp = int(math.ceil(math.log(c_precision) / math.log(b)))
+        expected = xp.asarray([[(1 - b ** n_exp) / (1 - b)]], dtype=dtype)
+        expected = 1 + b * expected
+
+        # Create a step signal of size n + 1
+        x = xp.ones(n_exp + 1, dtype=dtype)
+        xp_assert_close(symiirorder1_ic(x, b, precision), expected,
+                        atol=2e-6, rtol=2e-7)
+
+        # Check the conditions for an exponential decreasing signal with base 2.
+        # Same conditions hold, as the product of 0.5^n * 0.85^n is
+        # still a geometric series
+        b_d = xp.asarray(b, dtype=dtype)
+        expected = np.asarray(
+            [[(1 - (0.5 * b_d) ** n_exp) / (1 - (0.5 * b_d))]], dtype=dtype)
+        expected = 1 + b_d * expected
+
+        # Create an exponential decreasing signal of size n + 1
+        x = 2 ** -xp.arange(n_exp + 1, dtype=dtype)
+        xp_assert_close(symiirorder1_ic(x, b, precision), expected,
+                        atol=2e-6, rtol=2e-7)
+
+    @skip_xp_backends(np_only=True, reason="_ic functions are private and numpy-only")
+    def test_symiir1_ic_fails(self, xp):
+        # Test that symiirorder1_ic fails whenever \sum_{n = 1}^{n} b^n > eps
+        b = 0.85
+        # Create a step signal of size 100
+        x = xp.ones(100, dtype=xp.float64)
+
+        # Compute the closed form for the geometrical series
+        precision = 1 / (1 - b)
+        pytest.raises(ValueError, symiirorder1_ic, x, b, precision)
+
+        # Test that symiirorder1_ic fails when |z1| >= 1
+        pytest.raises(ValueError, symiirorder1_ic, x, 1.0, -1)
+        pytest.raises(ValueError, symiirorder1_ic, x, 2.0, -1)
+
+    @skip_xp_backends(
+        cpu_only=True, exceptions=["cupy"], reason="internals are numpy-only"
+    )
+    @xfail_xp_backends("cupy", reason="sum did not converge")
+    @skip_xp_backends("jax.numpy", reason="item assignment in tests")
+    @pytest.mark.parametrize(
+        'dtype', ['float32', 'float64', 'complex64', 'complex128'])
+    @pytest.mark.parametrize('precision', [-1.0, 0.7, 0.5, 0.25, 0.0075])
+    def test_symiir1(self, dtype, precision, xp):
+        dtype = getattr(xp, dtype)
+
+        c_precision = precision
+        if precision <= 0.0 or precision > 1.0:
+            if dtype in {xp.float32, xp.complex64}:
+                c_precision = 1e-6
+            else:
+                c_precision = 1e-11
+
+        # Test for a low-pass filter with c0 = 0.15 and z1 = 0.85
+        # using a unit step over 200 samples.
+        c0 = 0.15
+        z1 = 0.85
+        n = 200
+        signal = xp.ones(n, dtype=dtype)
+
+        # Find the initial condition. See test_symiir1_ic for a detailed
+        # explanation
+        n_exp = int(math.ceil(math.log(c_precision) / math.log(z1)))
+        initial = xp.asarray((1 - z1 ** n_exp) / (1 - z1), dtype=dtype)
+        initial = 1 + z1 * initial
+
+        # Forward pass
+        # The transfer function for the system 1 / (1 - z1 * z^-1) when
+        # applied to a unit step with initial conditions y0 is
+        # 1 / (1 - z1 * z^-1) * (z^-1 / (1 - z^-1) + y0)
+
+        # Solving the inverse Z-transform for the given expression yields:
+        # y[n] = y0 * z1**n * u[n] +
+        #        -z1 / (1 - z1) * z1**(k - 1) * u[k - 1] +
+        #        1 / (1 - z1) * u[k - 1]
+        # d is the Kronecker delta function, and u is the unit step
+
+        # y0 * z1**n * u[n]
+        pos = xp.astype(xp.arange(n), dtype)
+        comp1 = initial * z1**pos
+
+        # -z1 / (1 - z1) * z1**(k - 1) * u[k - 1]
+        comp2 = xp.zeros(n, dtype=dtype)
+        comp2[1:] = -z1 / (1 - z1) * z1**pos[:-1]
+
+        # 1 / (1 - z1) * u[k - 1]
+        comp3 = xp.zeros(n, dtype=dtype)
+        comp3[1:] = 1 / (1 - z1)
+
+        expected_fwd = comp1 + comp2 + comp3
+
+        # Reverse condition
+        sym_cond = -c0 / (z1 - 1.0) * expected_fwd[-1]
+
+        # Backward pass
+        # The transfer function for the forward result is equivalent to
+        # the forward system times c0 / (1 - z1 * z).
+
+        # Computing a closed form for the complete expression is difficult
+        # The result will be computed iteratively from the difference equation
+        exp_out = xp.zeros(n, dtype=dtype)
+        exp_out[0] = sym_cond
+
+        for i in range(1, n):
+            exp_out[i] = c0 * expected_fwd[n - 1 - i] + z1 * exp_out[i - 1]
+
+        exp_out = xp.flip(exp_out)
+
+        out = symiirorder1(signal, c0, z1, precision)
+        xp_assert_close(out, exp_out, atol=4e-6, rtol=6e-7)
+
+    @xfail_xp_backends("cupy", reason="sum did not converge")
+    @skip_xp_backends(
+        cpu_only=True, exceptions=["cupy"], reason="internals are numpy-only"
+    )
+    @pytest.mark.parametrize('dtype', ['float32', 'float64'])
+    def test_symiir1_values(self, dtype, xp):
+        rng = np.random.RandomState(1234)
+        s = rng.uniform(size=16).astype(dtype)
+        dtype = getattr(xp, dtype)
+        s = xp.asarray(s)
+        res = symiirorder1(s, 0.5, 0.1)
+
+        # values from scipy 1.9.1
+        exp_res = xp.asarray([
+            0.14387447, 0.35166047, 0.29735238, 0.46295986, 0.45174927,
+            0.19982875, 0.20355805, 0.47378628, 0.57232247, 0.51597393,
+            0.25935107, 0.31438554, 0.41096728, 0.4190693 , 0.25812255,
+            0.33671467], dtype=res.dtype)
+        atol = {xp.float64: 1e-15, xp.float32: 1e-7}[dtype]
+        xp_assert_close(res, exp_res, atol=atol)
+
+        I1 = xp.asarray(
+            1 + 1j, dtype=xp.result_type(s, xp.complex64)
+        )
+        s = s * I1
+        res = symiirorder1(s, 0.5, 0.1)
+        assert res.dtype == xp.complex64 if dtype == xp.float32 else xp.complex128
+        xp_assert_close(res, I1 * exp_res, atol=atol)
+
+    @skip_xp_backends(np_only=True,
+                      reason="_initial_fwd functions are private and numpy-only")
+    @pytest.mark.parametrize(
+        'dtype', ['float32', 'float64'])
+    @pytest.mark.parametrize('precision', [-1.0, 0.7, 0.5, 0.25, 0.0075])
+    def test_symiir2_initial_fwd(self, dtype, precision, xp):
+        dtype = getattr(xp, dtype)
+        c_precision = precision
+        if precision <= 0.0 or precision > 1.0:
+            if dtype in {xp.float32, xp.complex64}:
+                c_precision = 1e-6
+            else:
+                c_precision = 1e-11
+
+        # Compute the initial conditions for a order-two symmetrical low-pass
+        # filter with r = 0.5 and omega = pi / 3 for an unit step input.
+        r = xp.asarray(0.5, dtype=dtype)
+        omega = xp.asarray(np.pi / 3.0, dtype=dtype)
+        cs = 1 - 2 * r * xp.cos(omega) + r**2
+
+        # The index n for the initial condition is bound from 0 to the
+        # first position where sin(omega * (n + 2)) = 0 => omega * (n + 2) = pi
+        # For omega = pi / 3, the maximum initial condition occurs when
+        # sqrt(3) / 2 * r**n < precision.
+        # => n = log(2 * sqrt(3) / 3 * precision) / log(r)
+        ub = xp.ceil(xp.log(c_precision / xp.sin(omega)) / math.log(c_precision))
+        lb = xp.ceil(math.pi / omega) - 2
+        n_exp = min(ub, lb)
+
+        # The forward initial condition for a filter of order two is:
+        # \frac{cs}{\sin(\omega)} \sum_{n = 0}^{N - 1} {
+        #    r^(n + 1) \sin{\omega(n + 2)}} + cs
+        # The closed expression for this sum is:
+        # s[n] = 2 * r * np.cos(omega) -
+        #        r**2 - r**(n + 2) * np.sin(omega * (n + 3)) / np.sin(omega) +
+        #        r**(n + 3) * np.sin(omega * (n + 2)) / np.sin(omega) + cs
+        fwd_initial_1 = (
+            cs +
+            2 * r * xp.cos(omega) -
+            r**2 -
+            r**(n_exp + 2) * xp.sin(omega * (n_exp + 3)) / xp.sin(omega) +
+            r**(n_exp + 3) * xp.sin(omega * (n_exp + 2)) / xp.sin(omega))
+
+        # The second initial condition is given by
+        # s[n] = 1 / np.sin(omega) * (
+        #        r**2 * np.sin(3 * omega) -
+        #        r**3 * np.sin(2 * omega) -
+        #        r**(n + 3) * np.sin(omega * (n + 4)) +
+        #        r**(n + 4) * np.sin(omega * (n + 3)))
+        ub = xp.ceil(xp.log(c_precision / xp.sin(omega)) / math.log(c_precision))
+        lb = xp.ceil(xp.pi / omega) - 3
+        n_exp = min(ub, lb)
+
+        fwd_initial_2 = (
+            cs + cs * 2 * r * xp.cos(omega) +
+            (r**2 * xp.sin(3 * omega) -
+             r**3 * xp.sin(2 * omega) -
+             r**(n_exp + 3) * xp.sin(omega * (n_exp + 4)) +
+             r**(n_exp + 4) * xp.sin(omega * (n_exp + 3))) / xp.sin(omega))
+
+        expected = concat_1d(xp, fwd_initial_1, fwd_initial_2)[None, :]
+        expected = xp.astype(expected, dtype)
+
+        n = 100
+        signal = np.ones(n, dtype=dtype)
+
+        out = symiirorder2_ic_fwd(signal, r, omega, precision)
+        xp_assert_close(out, expected, atol=4e-6, rtol=6e-7)
+
+    @skip_xp_backends(np_only=True,
+                      reason="_initial_bwd functions are private and numpy-only")
+    @pytest.mark.parametrize(
+        'dtype', ['float32', 'float64'])
+    @pytest.mark.parametrize('precision', [-1.0, 0.7, 0.5, 0.25, 0.0075])
+    def test_symiir2_initial_bwd(self, dtype, precision, xp):
+        dtype = getattr(xp, dtype)
+
+        c_precision = precision
+        if precision <= 0.0 or precision > 1.0:
+            if dtype in {xp.float32, xp.complex64}:
+                c_precision = 1e-6
+            else:
+                c_precision = 1e-11
+
+        r = xp.asarray(0.5, dtype=dtype)
+        omega = xp.asarray(xp.pi / 3.0, dtype=dtype)
+        cs = 1 - 2 * r * xp.cos(omega) + r * r
+        a2 = 2 * r * xp.cos(omega)
+        a3 = -r * r
+
+        n = 100
+        signal = xp.ones(n, dtype=dtype)
+
+        # Compute initial forward conditions
+        ic = symiirorder2_ic_fwd(signal, r, omega, precision)
+        out = xp.zeros(n + 2, dtype=dtype)
+        out[:2] = ic[0]
+
+        # Apply the forward system cs / (1 - a2 * z^-1 - a3 * z^-2))
+        for i in range(2, n + 2):
+            out[i] = cs * signal[i - 2] + a2 * out[i - 1] + a3 * out[i - 2]
+
+        # Find the backward initial conditions
+        ic2 = xp.zeros(2, dtype=dtype)
+        idx = xp.arange(n)
+
+        diff = (_compute_symiirorder2_bwd_hs(idx, cs, r * r, omega) +
+                _compute_symiirorder2_bwd_hs(idx + 1, cs, r * r, omega))
+        ic2_0_all = np.cumsum(diff * out[:1:-1])
+        pos = xp.nonzero(diff ** 2 < c_precision)[0]
+        ic2[0] = ic2_0_all[pos[0]]
+
+        diff = (_compute_symiirorder2_bwd_hs(idx - 1, cs, r * r, omega) +
+                _compute_symiirorder2_bwd_hs(idx + 2, cs, r * r, omega))
+
+        ic2_1_all = xp.cumulative_sum(diff * out[:1:-1])
+        pos = xp.nonzero(diff ** 2 < c_precision)[0]
+        ic2[1] = ic2_1_all[pos[0]]
+
+        out_ic = symiirorder2_ic_bwd(out, r, omega, precision)[0]
+        xp_assert_close(out_ic, ic2, atol=4e-6, rtol=6e-7)
+
+    @skip_xp_backends(cpu_only=True, reason="internals are numpy-only")
+    @skip_xp_backends("jax.numpy", reason="item assignment in tests")
+    @pytest.mark.parametrize(
+        'dtype', ['float32', 'float64'])
+    @pytest.mark.parametrize('precision', [-1.0, 0.7, 0.5, 0.25, 0.0075])
+    def test_symiir2(self, dtype, precision, xp):
+        dtype = getattr(xp, dtype)
+
+        r = 0.5
+        omega = math.pi / 3.0
+        cs = 1 - 2 * r * math.cos(omega) + r * r
+        a2 = 2 * r * math.cos(omega)
+        a3 = -r * r
+
+        n = 100
+        signal = xp.ones(n, dtype=dtype)
+
+        # Compute initial forward conditions
+        signal_np = np.asarray(signal)
+        ic = symiirorder2_ic_fwd(signal_np, r, omega, precision)
+        ic = xp.asarray(ic)
+        out1 = xp.zeros(n + 2, dtype=dtype)
+        out1[:2] = ic[0, :]
+
+        # Apply the forward system cs / (1 - a2 * z^-1 - a3 * z^-2))
+        for i in range(2, n + 2):
+            out1[i] = cs * signal[i - 2] + a2 * out1[i - 1] + a3 * out1[i - 2]
+
+        # Find the backward initial conditions
+        ic2 = symiirorder2_ic_bwd(np.asarray(out1), r, omega, precision)[0]
+        ic2 = xp.asarray(ic2)
+
+        # Apply the system cs / (1 - a2 * z - a3 * z^2)) in backwards
+        exp = xp.empty(n, dtype=dtype)
+
+        exp[-2:] = xp.flip(ic2)
+
+        for i in range(n - 3, -1, -1):
+            exp[i] = cs * out1[i] + a2 * exp[i + 1] + a3 * exp[i + 2]
+
+        out = symiirorder2(signal, r, omega, precision)
+        xp_assert_close(out, exp, atol=4e-6, rtol=6e-7)
+
+    @skip_xp_backends(cpu_only=True, exceptions=["cupy"], reason="C internals")
+    @pytest.mark.parametrize('dtyp', ['float32', 'float64'])
+    def test_symiir2_values(self, dtyp, xp):
+        rng = np.random.RandomState(1234)
+        s = rng.uniform(size=16).astype(dtyp)
+        s = xp.asarray(s)
+
+        # cupy returns f64 for f32 inputs
+        dtype = xp.float64 if is_cupy(xp) else getattr(xp, dtyp)
+
+        res = symiirorder2(s, 0.1, 0.1, precision=1e-10)
+
+        # values from scipy 1.9.1
+        exp_res = xp.asarray(
+            [0.26572609, 0.53408018, 0.51032696, 0.72115829, 0.69486885,
+             0.3649055 , 0.37349478, 0.74165032, 0.89718521, 0.80582483,
+             0.46758053, 0.51898709, 0.65025605, 0.65394321, 0.45273595,
+             0.53539183], dtype=dtype
+        )
+
+        # The values in SciPy 1.14 agree with those in SciPy 1.9.1 to this
+        # accuracy only. Implementation differences are twofold:
+        # 1. boundary conditions are computed differently
+        # 2. the filter itself uses sosfilt instead of a hardcoded iteration
+        # The boundary conditions seem are tested separately (see
+        # test_symiir2_initial_{fwd,bwd} above, so the difference is likely
+        # due to a different way roundoff errors accumulate in the filter.
+        # In that respect, sosfilt is likely doing a better job.
+        xp_assert_close(res, exp_res, atol=2e-6)
+
+        I1 = xp.asarray(1 + 1j, dtype=xp.result_type(s, xp.complex64))
+        s = s * I1
+
+        with pytest.raises((TypeError, ValueError)):
+            res = symiirorder2(s, 0.5, 0.1)
+
+    @skip_xp_backends(cpu_only=True, exceptions=["cupy"], reason="C internals")
+    @xfail_xp_backends("cupy", reason="cupy does not accept integer arrays")
+    def test_symiir1_integer_input(self, xp):
+        s = xp.where(
+            xp.astype(xp.arange(100) % 2, xp.bool),
+            xp.asarray(-1),
+            xp.asarray(1),
+        )
+        expected = symiirorder1(xp.astype(s, xp_default_dtype(xp)), 0.5, 0.5)
+        out = symiirorder1(s, 0.5, 0.5)
+        xp_assert_close(out, expected)
+
+    @skip_xp_backends(cpu_only=True, exceptions=["cupy"], reason="C internals")
+    @xfail_xp_backends("cupy", reason="cupy does not accept integer arrays")
+    def test_symiir2_integer_input(self, xp):
+        s = xp.where(
+            xp.astype(xp.arange(100) % 2, xp.bool),
+            xp.asarray(-1),
+            xp.asarray(1),
+        )
+        expected = symiirorder2(xp.astype(s, xp_default_dtype(xp)), 0.5, xp.pi / 3.0)
+        out = symiirorder2(s, 0.5, xp.pi / 3.0)
+        xp_assert_close(out, expected)
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/tests/test_upfirdn.py b/venv/lib/python3.12/site-packages/scipy/signal/tests/test_upfirdn.py
new file mode 100644
index 0000000000000000000000000000000000000000..57d8f0accc86c7bc1e93f2f330be0db2d02d0c7f
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/tests/test_upfirdn.py
@@ -0,0 +1,335 @@
+# Code adapted from "upfirdn" python library with permission:
+#
+# Copyright (c) 2009, Motorola, Inc
+#
+# All Rights Reserved.
+#
+# Redistribution and use in source and binary forms, with or without
+# modification, are permitted provided that the following conditions are
+# met:
+#
+# * Redistributions of source code must retain the above copyright notice,
+# this list of conditions and the following disclaimer.
+#
+# * Redistributions in binary form must reproduce the above copyright
+# notice, this list of conditions and the following disclaimer in the
+# documentation and/or other materials provided with the distribution.
+#
+# * Neither the name of Motorola nor the names of its contributors may be
+# used to endorse or promote products derived from this software without
+# specific prior written permission.
+#
+# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
+# IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO,
+# THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
+# PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+# CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+# EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+# PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+# PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+# LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+# NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+# SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+
+import numpy as np
+from itertools import product
+
+from pytest import raises as assert_raises
+import pytest
+
+from scipy._external import array_api_extra as xpx
+from scipy._lib._array_api import (
+    xp_assert_close, array_namespace, _xp_copy_to_numpy, is_cupy,
+    make_xp_test_case
+)
+from scipy._external.array_api_compat import numpy as np_compat
+from scipy.signal import upfirdn, firwin
+from scipy.signal._upfirdn import _output_len, _upfirdn_modes
+from scipy.signal._upfirdn_apply import _pad_test
+
+skip_xp_backends = pytest.mark.skip_xp_backends
+
+
+
+def upfirdn_naive(x, h, up=1, down=1):
+    """Naive upfirdn processing in Python.
+
+    Note: arg order (x, h) differs to facilitate apply_along_axis use.
+    """
+    x = np.asarray(x)
+    h = np.asarray(h)
+    out = np.zeros(len(x) * up, x.dtype)
+    out[::up] = x
+    out = np.convolve(h, out)[::down][:_output_len(len(h), len(x), up, down)]
+    return out
+
+
+class UpFIRDnCase:
+    """Test _UpFIRDn object"""
+    def __init__(self, up, down, h, x_dtype, *, xp=None):
+        if xp is None:
+            xp = np_compat
+        self.up = up
+        self.down = down
+        self.h = np.atleast_1d(h)
+        self.x_dtype = x_dtype
+        self.rng = np.random.RandomState(17)
+        self.xp = xp
+
+    def __call__(self):
+        # tiny signal
+        self.scrub(np.ones(1, self.x_dtype))
+        # ones
+        self.scrub(np.ones(10, self.x_dtype))  # ones
+        # randn
+        x = self.rng.randn(10).astype(self.x_dtype)
+        if self.x_dtype in (np.complex64, np.complex128):
+            x += 1j * self.rng.randn(10)
+        self.scrub(x)
+        # ramp
+        self.scrub(np.arange(10).astype(self.x_dtype))
+        # 3D, random
+        if is_cupy(self.xp):
+            # ndim > 2 is unsupported in CuPy.
+            return
+        size = (2, 3, 5)
+        x = self.rng.randn(*size).astype(self.x_dtype)
+        if self.x_dtype in (np.complex64, np.complex128):
+            x += 1j * self.rng.randn(*size)
+        for axis in range(len(size)):
+            self.scrub(x, axis=axis)
+        x = x[:, ::2, 1::3].T
+        for axis in range(len(size)):
+            self.scrub(x, axis=axis)
+
+    def scrub(self, x, axis=-1):
+        xp = self.xp
+        yr = np.apply_along_axis(upfirdn_naive, axis, x,
+                                 self.h, self.up, self.down)
+        want_len = _output_len(len(self.h), x.shape[axis], self.up, self.down)
+        assert yr.shape[axis] == want_len
+        y = upfirdn(xp.asarray(self.h), xp.asarray(x), self.up, self.down,
+                    axis=axis)
+        assert y.shape[axis] == want_len
+        assert y.shape == yr.shape
+        dtypes = (self.h.dtype, x.dtype)
+        if all(d == np.complex64 for d in dtypes):
+            assert y.dtype == xp.complex64
+        elif np.complex64 in dtypes and np.float32 in dtypes:
+            assert y.dtype == xp.complex64
+        elif all(d == np.float32 for d in dtypes):
+            assert y.dtype == xp.float32
+        elif np.complex128 in dtypes or np.complex64 in dtypes:
+            assert y.dtype == xp.complex128
+        else:
+            assert y.dtype == xp.float64
+        yr = xp.asarray(yr, dtype=y.dtype)
+        xp_assert_close(yr, y)
+
+
+_UPFIRDN_TYPES = ("int64", "float32", "complex64", "float64", "complex128")
+
+
+@make_xp_test_case(upfirdn)
+class TestUpfirdn:
+
+    @skip_xp_backends(np_only=True, reason="enough to only test on numpy")
+    def test_valid_input(self, xp):
+        assert_raises(ValueError, upfirdn, [1], [1], 1, 0)  # up or down < 1
+        assert_raises(ValueError, upfirdn, [], [1], 1, 1)  # h.ndim != 1
+        assert_raises(ValueError, upfirdn, [[1]], [1], 1, 1)
+
+    @pytest.mark.parametrize('len_h', [1, 2, 3, 4, 5])
+    @pytest.mark.parametrize('len_x', [1, 2, 3, 4, 5])
+    def test_singleton(self, len_h, len_x, xp):
+        # gh-9844: lengths producing expected outputs
+        h = xp.zeros(len_h)
+        h = xpx.at(h)[len_h // 2].set(1.)  # make h a delta
+        x = xp.ones(len_x)
+        y = upfirdn(h, x, 1, 1)
+        want = xpx.pad(x, (len_h // 2, (len_h - 1) // 2), 'constant', xp=xp)
+        xp_assert_close(y, want)
+
+    def test_shift_x(self, xp):
+        # gh-9844: shifted x can change values?
+        y = upfirdn(xp.asarray([1, 1]), xp.asarray([1.]), 1, 1)
+        xp_assert_close(
+            y, xp.asarray([1.0, 1.0], dtype=xp.float64)  # was [0, 1] in the issue
+        )
+        y = upfirdn(xp.asarray([1, 1]), xp.asarray([0., 1.]), 1, 1)
+        xp_assert_close(y, xp.asarray([0.0, 1.0, 1.0], dtype=xp.float64))
+
+    # A bunch of lengths/factors chosen because they exposed differences
+    # between the "old way" and new way of computing length, and then
+    # got `expected` from MATLAB
+    @pytest.mark.parametrize('len_h, len_x, up, down, expected', [
+        (2, 2, 5, 2, [1, 0, 0, 0]),
+        (2, 3, 6, 3, [1, 0, 1, 0, 1]),
+        (2, 4, 4, 3, [1, 0, 0, 0, 1]),
+        (3, 2, 6, 2, [1, 0, 0, 1, 0]),
+        (4, 11, 3, 5, [1, 0, 0, 1, 0, 0, 1]),
+    ])
+    def test_length_factors(self, len_h, len_x, up, down, expected, xp):
+        # gh-9844: weird factors
+        h = xp.zeros(len_h)
+        h = xpx.at(h)[0].set(1.)
+        x = xp.ones(len_x, dtype=xp.float64)
+        y = upfirdn(h, x, up, down)
+        expected = xp.asarray(expected, dtype=xp.float64)
+        xp_assert_close(y, expected)
+
+    @pytest.mark.parametrize(
+        'dtype', ["int64", "float32", "complex64", "float64", "complex128"]
+    )
+    @pytest.mark.parametrize('down, want_len', [  # lengths from MATLAB
+        (2, 5015),
+        (11, 912),
+        (79, 127),
+    ])
+    def test_vs_convolve(self, down, want_len, dtype, xp):
+        # Check that up=1.0 gives same answer as convolve + slicing
+        random_state = np.random.RandomState(17)
+        size = 10000
+
+        np_dtype = getattr(np, dtype)
+        x = random_state.randn(size).astype(np_dtype)
+        if np_dtype in (np.complex64, np.complex128):
+            x += 1j * random_state.randn(size)
+
+        dtype = getattr(xp, dtype)
+        x = xp.asarray(x, dtype=dtype)
+
+        h = xp.asarray(firwin(31, 1. / down, window='hamming'))
+        yl = xp.asarray(
+            upfirdn_naive(_xp_copy_to_numpy(x), _xp_copy_to_numpy(h), 1, down)
+        )
+        y = upfirdn(h, x, up=1, down=down)
+        assert y.shape == (want_len,)
+        assert yl.shape[0] == y.shape[0]
+        xp_assert_close(yl, y, atol=1e-7, rtol=1e-7)
+
+    @pytest.mark.parametrize('x_dtype', _UPFIRDN_TYPES)
+    @pytest.mark.parametrize('h', (1., 1j))
+    @pytest.mark.parametrize('up, down', [(1, 1), (2, 2), (3, 2), (2, 3)])
+    def test_vs_naive_delta(self, x_dtype, h, up, down, xp):
+        UpFIRDnCase(up, down, h, x_dtype, xp=xp)()
+
+    @pytest.mark.parametrize('x_dtype', _UPFIRDN_TYPES)
+    @pytest.mark.parametrize('h_dtype', _UPFIRDN_TYPES)
+    @pytest.mark.parametrize('p_max, q_max',
+                             list(product((10, 100), (10, 100))))
+    def test_vs_naive(self, x_dtype, h_dtype, p_max, q_max, xp):
+        tests = self._random_factors(p_max, q_max, h_dtype, x_dtype, xp=xp)
+        for test in tests:
+            test()
+
+    def _random_factors(self, p_max, q_max, h_dtype, x_dtype, *, xp):
+        n_rep = 3
+        longest_h = 25
+        random_state = np.random.RandomState(17)
+        tests = []
+
+        for _ in range(n_rep):
+            # Randomize the up/down factors somewhat
+            p_add = q_max if p_max > q_max else 1
+            q_add = p_max if q_max > p_max else 1
+            p = random_state.randint(p_max) + p_add
+            q = random_state.randint(q_max) + q_add
+
+            # Generate random FIR coefficients
+            len_h = random_state.randint(longest_h) + 1
+            h = np.atleast_1d(random_state.randint(len_h))
+            h = h.astype(h_dtype)
+            if h_dtype is complex:
+                h += 1j * random_state.randint(len_h)
+
+            tests.append(UpFIRDnCase(p, q, h, x_dtype, xp=xp))
+
+        return tests
+
+    @pytest.mark.parametrize('mode', _upfirdn_modes)
+    def test_extensions(self, mode, xp):
+        """Test vs. manually computed results for modes not in numpy's pad."""
+        x = np.asarray([1, 2, 3, 1], dtype=np.float64)
+        npre, npost = 6, 6
+        y = _pad_test(x, npre=npre, npost=npost, mode=mode)
+
+        x = xp.asarray(x)
+        y = xp.asarray(y)
+        if mode == 'antisymmetric':
+            y_expected = xp.asarray(
+                [3.0, 1, -1, -3, -2, -1, 1, 2, 3, 1, -1, -3, -2, -1, 1, 2])
+        elif mode == 'antireflect':
+            y_expected = xp.asarray(
+                [1.0, 2, 3, 1, -1, 0, 1, 2, 3, 1, -1, 0, 1, 2, 3, 1])
+        elif mode == 'smooth':
+            y_expected = xp.asarray(
+                [-5.0, -4, -3, -2, -1, 0, 1, 2, 3, 1, -1, -3, -5, -7, -9, -11])
+        elif mode == "line":
+            lin_slope = (x[-1] - x[0]) / (x.shape[0] - 1)
+            left = x[0] + xp.arange(-npre, 0, 1, dtype=xp.float64) * lin_slope
+            right = x[-1] + xp.arange(1, npost + 1, dtype=xp.float64) * lin_slope
+            concat = array_namespace(left).concat
+            y_expected = concat((left, x, right))
+        else:
+            y_expected = np.pad(_xp_copy_to_numpy(x), (npre, npost), mode=mode)
+            y_expected = xp.asarray(y_expected)
+
+        y_expected = xp.asarray(y_expected, dtype=xp.float64)
+        xp_assert_close(y, y_expected)
+
+    @pytest.mark.parametrize(
+        'size, h_len, mode, dtype',
+        list(product(
+            [8],
+            [4, 5, 26],  # include cases with h_len > 2*size
+            _upfirdn_modes,
+            ["float32", "float64", "complex64", "complex128"],
+        ))
+    )
+    def test_modes(self, size, h_len, mode, dtype, xp):
+        if is_cupy(xp) and mode != "constant":
+            pytest.skip(reason="only mode='constant' supported by CuPy")
+        dtype_np = getattr(np, dtype)
+        dtype_xp = getattr(xp, dtype)
+
+        random_state = np.random.RandomState(5)
+        x = random_state.randn(size).astype(dtype_np)
+        if dtype in ("complex64", "complex128"):
+            x += 1j * random_state.randn(size)
+        h = np.arange(1, 1 + h_len, dtype=x.real.dtype)
+
+        x = xp.asarray(x, dtype=dtype_xp)
+        h = xp.asarray(h)
+
+        y = upfirdn(h, x, up=1, down=1, mode=mode)
+        # expected result: pad the input, filter with zero padding, then crop
+        npad = h_len - 1
+        if mode in ['antisymmetric', 'antireflect', 'smooth', 'line']:
+            # use _pad_test test function for modes not supported by np.pad.
+            xpad = _pad_test(_xp_copy_to_numpy(x), npre=npad, npost=npad, mode=mode)
+        else:
+            xpad = np.pad(_xp_copy_to_numpy(x), npad, mode=mode)
+
+        xpad = xp.asarray(xpad)
+        ypad = upfirdn(h, xpad, up=1, down=1, mode='constant')
+        y_expected = ypad[npad:-npad]
+
+        atol = rtol = xp.finfo(dtype_xp).eps * 1e2
+        xp_assert_close(y, y_expected, atol=atol, rtol=rtol)
+
+
+@make_xp_test_case(upfirdn)
+def test_output_len_long_input(xp):
+    # Regression test for gh-17375.  On Windows, a large enough input
+    # that should have been well within the capabilities of 64 bit integers
+    # would result in a 32 bit overflow because of a bug in Cython 0.29.32.
+    len_h = 1001
+    in_len = 10**8
+    up = 320
+    down = 441
+    out_len = _output_len(len_h, in_len, up, down)
+    # The expected value was computed "by hand" from the formula
+    #   (((in_len - 1) * up + len_h) - 1) // down + 1
+    assert out_len == 72562360
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/tests/test_waveforms.py b/venv/lib/python3.12/site-packages/scipy/signal/tests/test_waveforms.py
new file mode 100644
index 0000000000000000000000000000000000000000..ba57f52dcd6253c69ab67b8f2ba717b93372e82d
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/tests/test_waveforms.py
@@ -0,0 +1,476 @@
+import numpy as np
+import pytest
+from pytest import raises as assert_raises
+from scipy._lib._array_api import (
+    assert_almost_equal, xp_assert_equal, xp_assert_close, _xp_copy_to_numpy,
+    make_xp_test_case, xp_default_dtype
+)
+
+import scipy.signal._waveforms as waveforms
+from scipy.signal import square, sawtooth  # type:ignore[attr-defined]
+
+
+# These chirp_* functions are the instantaneous frequencies of the signals
+# returned by chirp().
+
+def chirp_linear(t, f0, f1, t1):
+    f = f0 + (f1 - f0) * t / t1
+    return f
+
+
+def chirp_quadratic(t, f0, f1, t1, vertex_zero=True):
+    if vertex_zero:
+        f = f0 + (f1 - f0) * t**2 / t1**2
+    else:
+        f = f1 - (f1 - f0) * (t1 - t)**2 / t1**2
+    return f
+
+
+def chirp_geometric(t, f0, f1, t1):
+    f = f0 * (f1/f0)**(t/t1)
+    return f
+
+
+def chirp_hyperbolic(t, f0, f1, t1):
+    f = f0*f1*t1 / ((f0 - f1)*t + f1*t1)
+    return f
+
+
+def compute_frequency(t, theta):
+    """
+    Compute theta'(t)/(2*pi), where theta'(t) is the derivative of theta(t).
+    """
+    # Assume theta and t are 1-D NumPy arrays.
+    # Assume that t is uniformly spaced.
+    dt = t[1] - t[0]
+    f = np.diff(theta)/(2*np.pi) / dt
+    tf = 0.5*(t[1:] + t[:-1])
+    return tf, f
+
+
+class TestChirp:
+
+    def test_linear_at_zero(self):
+        w = waveforms.chirp(t=0, f0=1.0, f1=2.0, t1=1.0, method='linear')
+        assert_almost_equal(w, 1.0)
+
+    def test_linear_freq_01(self):
+        method = 'linear'
+        f0 = 1.0
+        f1 = 2.0
+        t1 = 1.0
+        t = np.linspace(0, t1, 100)
+        phase = waveforms._chirp_phase(t, f0, t1, f1, method)
+        tf, f = compute_frequency(t, phase)
+        abserr = np.max(np.abs(f - chirp_linear(tf, f0, f1, t1)))
+        assert abserr < 1e-6
+
+    def test_linear_freq_02(self):
+        method = 'linear'
+        f0 = 200.0
+        f1 = 100.0
+        t1 = 10.0
+        t = np.linspace(0, t1, 100)
+        phase = waveforms._chirp_phase(t, f0, t1, f1, method)
+        tf, f = compute_frequency(t, phase)
+        abserr = np.max(np.abs(f - chirp_linear(tf, f0, f1, t1)))
+        assert abserr < 1e-6
+
+    def test_linear_complex_power(self):
+        method = 'linear'
+        f0 = 1.0
+        f1 = 2.0
+        t1 = 1.0
+        t = np.linspace(0, t1, 100)
+        w_real = waveforms.chirp(t, f0, t1, f1, method, complex=False)
+        w_complex = waveforms.chirp(t, f0, t1, f1, method, complex=True)
+        w_pwr_r = np.var(w_real)
+        w_pwr_c = np.var(w_complex)
+
+        # Making sure that power of the real part is not affected with
+        # complex conversion operation
+        err = w_pwr_r - np.real(w_pwr_c)
+
+        assert(err < 1e-6)
+
+    def test_linear_complex_at_zero(self):
+        w = waveforms.chirp(t=0, f0=-10.0, f1=1.0, t1=1.0, method='linear',
+                            complex=True)
+        xp_assert_close(w, 1.0+0.0j)  # dtype must match
+
+    def test_quadratic_at_zero(self):
+        w = waveforms.chirp(t=0, f0=1.0, f1=2.0, t1=1.0, method='quadratic')
+        assert_almost_equal(w, 1.0)
+
+    def test_quadratic_at_zero2(self):
+        w = waveforms.chirp(t=0, f0=1.0, f1=2.0, t1=1.0, method='quadratic',
+                            vertex_zero=False)
+        assert_almost_equal(w, 1.0)
+
+    def test_quadratic_complex_at_zero(self):
+        w = waveforms.chirp(t=0, f0=-1.0, f1=2.0, t1=1.0, method='quadratic',
+                            complex=True)
+        xp_assert_close(w, 1.0+0j)
+
+    def test_quadratic_freq_01(self):
+        method = 'quadratic'
+        f0 = 1.0
+        f1 = 2.0
+        t1 = 1.0
+        t = np.linspace(0, t1, 2000)
+        phase = waveforms._chirp_phase(t, f0, t1, f1, method)
+        tf, f = compute_frequency(t, phase)
+        abserr = np.max(np.abs(f - chirp_quadratic(tf, f0, f1, t1)))
+        assert abserr < 1e-6
+
+    def test_quadratic_freq_02(self):
+        method = 'quadratic'
+        f0 = 20.0
+        f1 = 10.0
+        t1 = 10.0
+        t = np.linspace(0, t1, 2000)
+        phase = waveforms._chirp_phase(t, f0, t1, f1, method)
+        tf, f = compute_frequency(t, phase)
+        abserr = np.max(np.abs(f - chirp_quadratic(tf, f0, f1, t1)))
+        assert abserr < 1e-6
+
+    def test_logarithmic_at_zero(self):
+        w = waveforms.chirp(t=0, f0=1.0, f1=2.0, t1=1.0, method='logarithmic')
+        assert_almost_equal(w, 1.0)
+
+    def test_logarithmic_freq_01(self):
+        method = 'logarithmic'
+        f0 = 1.0
+        f1 = 2.0
+        t1 = 1.0
+        t = np.linspace(0, t1, 10000)
+        phase = waveforms._chirp_phase(t, f0, t1, f1, method)
+        tf, f = compute_frequency(t, phase)
+        abserr = np.max(np.abs(f - chirp_geometric(tf, f0, f1, t1)))
+        assert abserr < 1e-6
+
+    def test_logarithmic_freq_02(self):
+        method = 'logarithmic'
+        f0 = 200.0
+        f1 = 100.0
+        t1 = 10.0
+        t = np.linspace(0, t1, 10000)
+        phase = waveforms._chirp_phase(t, f0, t1, f1, method)
+        tf, f = compute_frequency(t, phase)
+        abserr = np.max(np.abs(f - chirp_geometric(tf, f0, f1, t1)))
+        assert abserr < 1e-6
+
+    def test_logarithmic_freq_03(self):
+        method = 'logarithmic'
+        f0 = 100.0
+        f1 = 100.0
+        t1 = 10.0
+        t = np.linspace(0, t1, 10000)
+        phase = waveforms._chirp_phase(t, f0, t1, f1, method)
+        tf, f = compute_frequency(t, phase)
+        abserr = np.max(np.abs(f - chirp_geometric(tf, f0, f1, t1)))
+        assert abserr < 1e-6
+
+    def test_hyperbolic_at_zero(self):
+        w = waveforms.chirp(t=0, f0=10.0, f1=1.0, t1=1.0, method='hyperbolic')
+        assert_almost_equal(w, 1.0)
+
+    def test_hyperbolic_freq_01(self):
+        method = 'hyperbolic'
+        t1 = 1.0
+        t = np.linspace(0, t1, 10000)
+        #           f0     f1
+        cases = [[10.0, 1.0],
+                 [1.0, 10.0],
+                 [-10.0, -1.0],
+                 [-1.0, -10.0]]
+        for f0, f1 in cases:
+            phase = waveforms._chirp_phase(t, f0, t1, f1, method)
+            tf, f = compute_frequency(t, phase)
+            expected = chirp_hyperbolic(tf, f0, f1, t1)
+            xp_assert_close(f, expected, atol=1e-7)
+
+    def test_hyperbolic_zero_freq(self):
+        # f0=0 or f1=0 must raise a ValueError.
+        method = 'hyperbolic'
+        t1 = 1.0
+        t = np.linspace(0, t1, 5)
+        assert_raises(ValueError, waveforms.chirp, t, 0, t1, 1, method)
+        assert_raises(ValueError, waveforms.chirp, t, 1, t1, 0, method)
+
+    def test_unknown_method(self):
+        method = "foo"
+        f0 = 10.0
+        f1 = 20.0
+        t1 = 1.0
+        t = np.linspace(0, t1, 10)
+        assert_raises(ValueError, waveforms.chirp, t, f0, t1, f1, method)
+
+    def test_integer_t1(self):
+        f0 = 10.0
+        f1 = 20.0
+        t = np.linspace(-1, 1, 11)
+        t1 = 3.0
+        float_result = waveforms.chirp(t, f0, t1, f1)
+        t1 = 3
+        int_result = waveforms.chirp(t, f0, t1, f1)
+        err_msg = "Integer input 't1=3' gives wrong result"
+        xp_assert_equal(int_result, float_result, err_msg=err_msg)
+
+    def test_integer_f0(self):
+        f1 = 20.0
+        t1 = 3.0
+        t = np.linspace(-1, 1, 11)
+        f0 = 10.0
+        float_result = waveforms.chirp(t, f0, t1, f1)
+        f0 = 10
+        int_result = waveforms.chirp(t, f0, t1, f1)
+        err_msg = "Integer input 'f0=10' gives wrong result"
+        xp_assert_equal(int_result, float_result, err_msg=err_msg)
+
+    def test_integer_f1(self):
+        f0 = 10.0
+        t1 = 3.0
+        t = np.linspace(-1, 1, 11)
+        f1 = 20.0
+        float_result = waveforms.chirp(t, f0, t1, f1)
+        f1 = 20
+        int_result = waveforms.chirp(t, f0, t1, f1)
+        err_msg = "Integer input 'f1=20' gives wrong result"
+        xp_assert_equal(int_result, float_result, err_msg=err_msg)
+
+    def test_integer_all(self):
+        f0 = 10
+        t1 = 3
+        f1 = 20
+        t = np.linspace(-1, 1, 11)
+        float_result = waveforms.chirp(t, float(f0), float(t1), float(f1))
+        int_result = waveforms.chirp(t, f0, t1, f1)
+        err_msg = "Integer input 'f0=10, t1=3, f1=20' gives wrong result"
+        xp_assert_equal(int_result, float_result, err_msg=err_msg)
+
+
+class TestSweepPoly:
+
+    def test_sweep_poly_quad1(self):
+        p = np.poly1d([1.0, 0.0, 1.0])
+        t = np.linspace(0, 3.0, 10000)
+        phase = waveforms._sweep_poly_phase(t, p)
+        tf, f = compute_frequency(t, phase)
+        expected = p(tf)
+        abserr = np.max(np.abs(f - expected))
+        assert abserr < 1e-6
+
+    def test_sweep_poly_const(self):
+        p = np.poly1d(2.0)
+        t = np.linspace(0, 3.0, 10000)
+        phase = waveforms._sweep_poly_phase(t, p)
+        tf, f = compute_frequency(t, phase)
+        expected = p(tf)
+        abserr = np.max(np.abs(f - expected))
+        assert abserr < 1e-6
+
+    def test_sweep_poly_linear(self):
+        p = np.poly1d([-1.0, 10.0])
+        t = np.linspace(0, 3.0, 10000)
+        phase = waveforms._sweep_poly_phase(t, p)
+        tf, f = compute_frequency(t, phase)
+        expected = p(tf)
+        abserr = np.max(np.abs(f - expected))
+        assert abserr < 1e-6
+
+    def test_sweep_poly_quad2(self):
+        p = np.poly1d([1.0, 0.0, -2.0])
+        t = np.linspace(0, 3.0, 10000)
+        phase = waveforms._sweep_poly_phase(t, p)
+        tf, f = compute_frequency(t, phase)
+        expected = p(tf)
+        abserr = np.max(np.abs(f - expected))
+        assert abserr < 1e-6
+
+    def test_sweep_poly_cubic(self):
+        p = np.poly1d([2.0, 1.0, 0.0, -2.0])
+        t = np.linspace(0, 2.0, 10000)
+        phase = waveforms._sweep_poly_phase(t, p)
+        tf, f = compute_frequency(t, phase)
+        expected = p(tf)
+        abserr = np.max(np.abs(f - expected))
+        assert abserr < 1e-6
+
+    def test_sweep_poly_cubic2(self):
+        """Use an array of coefficients instead of a poly1d."""
+        p = np.array([2.0, 1.0, 0.0, -2.0])
+        t = np.linspace(0, 2.0, 10000)
+        phase = waveforms._sweep_poly_phase(t, p)
+        tf, f = compute_frequency(t, phase)
+        expected = np.poly1d(p)(tf)
+        abserr = np.max(np.abs(f - expected))
+        assert abserr < 1e-6
+
+    def test_sweep_poly_cubic3(self):
+        """Use a list of coefficients instead of a poly1d."""
+        p = [2.0, 1.0, 0.0, -2.0]
+        t = np.linspace(0, 2.0, 10000)
+        phase = waveforms._sweep_poly_phase(t, p)
+        tf, f = compute_frequency(t, phase)
+        expected = np.poly1d(p)(tf)
+        abserr = np.max(np.abs(f - expected))
+        assert abserr < 1e-6
+
+
+class TestGaussPulse:
+
+    def test_integer_fc(self):
+        float_result = waveforms.gausspulse('cutoff', fc=1000.0)
+        int_result = waveforms.gausspulse('cutoff', fc=1000)
+        err_msg = "Integer input 'fc=1000' gives wrong result"
+        xp_assert_equal(int_result, float_result, err_msg=err_msg)
+
+    def test_integer_bw(self):
+        float_result = waveforms.gausspulse('cutoff', bw=1.0)
+        int_result = waveforms.gausspulse('cutoff', bw=1)
+        err_msg = "Integer input 'bw=1' gives wrong result"
+        xp_assert_equal(int_result, float_result, err_msg=err_msg)
+
+    def test_integer_bwr(self):
+        float_result = waveforms.gausspulse('cutoff', bwr=-6.0)
+        int_result = waveforms.gausspulse('cutoff', bwr=-6)
+        err_msg = "Integer input 'bwr=-6' gives wrong result"
+        xp_assert_equal(int_result, float_result, err_msg=err_msg)
+
+    def test_integer_tpr(self):
+        float_result = waveforms.gausspulse('cutoff', tpr=-60.0)
+        int_result = waveforms.gausspulse('cutoff', tpr=-60)
+        err_msg = "Integer input 'tpr=-60' gives wrong result"
+        xp_assert_equal(int_result, float_result, err_msg=err_msg)
+
+
+class TestUnitImpulse:
+
+    def test_no_index(self):
+        xp_assert_equal(waveforms.unit_impulse(7),
+                        np.asarray([1.0, 0, 0, 0, 0, 0, 0]))
+        xp_assert_equal(waveforms.unit_impulse((3, 3)),
+                        np.asarray([[1.0, 0, 0], [0, 0, 0], [0, 0, 0]]))
+
+    def test_index(self):
+        xp_assert_equal(waveforms.unit_impulse(10, 3),
+                        np.asarray([0.0, 0, 0, 1, 0, 0, 0, 0, 0, 0]))
+        xp_assert_equal(waveforms.unit_impulse((3, 3), (1, 1)),
+                        np.asarray([[0.0, 0, 0], [0, 1, 0], [0, 0, 0]]))
+
+        # Broadcasting
+        imp = waveforms.unit_impulse((4, 4), 2)
+        xp_assert_equal(imp, np.asarray([[0.0, 0, 0, 0],
+                                         [0.0, 0, 0, 0],
+                                         [0.0, 0, 1, 0],
+                                         [0.0, 0, 0, 0]]))
+
+    def test_mid(self):
+        xp_assert_equal(waveforms.unit_impulse((3, 3), 'mid'),
+                        np.asarray([[0.0, 0, 0], [0, 1, 0], [0, 0, 0]]))
+        xp_assert_equal(waveforms.unit_impulse(9, 'mid'),
+                        np.asarray([0.0, 0, 0, 0, 1, 0, 0, 0, 0]))
+
+    def test_dtype(self):
+        imp = waveforms.unit_impulse(7)
+        assert np.issubdtype(imp.dtype, np.floating)
+
+        imp = waveforms.unit_impulse(5, 3, dtype=int)
+        assert np.issubdtype(imp.dtype, np.integer)
+
+        imp = waveforms.unit_impulse((5, 2), (3, 1), dtype=complex)
+        assert np.issubdtype(imp.dtype, np.complexfloating)
+
+
+@make_xp_test_case(sawtooth)
+class TestSawtoothWaveform:
+    @pytest.mark.xfail_xp_backends("cupy", reason="cupy/cupy/issues/9541")
+    @pytest.mark.parametrize("t_dtype", ["float32", "float64"])
+    @pytest.mark.parametrize("width_dtype", ["float32", "float64"])
+    def test_dtype(self, t_dtype, width_dtype, xp):
+        t_dtype = getattr(xp, t_dtype)
+        width_dtype = getattr(xp, width_dtype)
+        waveform = sawtooth(
+            xp.asarray(1, dtype=t_dtype), width=xp.asarray(1, dtype=width_dtype)
+        )
+        assert waveform.dtype == xp.result_type(t_dtype, width_dtype)
+
+    def test_periodic(self, xp):
+        t = xp.linspace(0, 2*xp.pi, 100, dtype=xp.float64)
+        y1 = sawtooth(t, width=0.4)
+        y2 = sawtooth(t + 2*xp.pi, width=0.4)
+        xp_assert_close(y1, y2)
+
+    def test_known_values(self, xp):
+        eps = xp.finfo(xp_default_dtype(xp)).eps
+        t = xp.asarray([0, xp.pi, 2*xp.pi - 10*eps, 2*xp.pi])
+        y = sawtooth(t)
+        xp_assert_close(y, xp.asarray([-1., 0., 1., -1.]))
+
+    def test_invalid_width_nan(self, xp):
+        t = xp.linspace(0, 2*xp.pi, 10)
+        y = sawtooth(t, width=1.5)
+        assert xp.all(xp.isnan(y))
+
+    @pytest.mark.xfail_xp_backends("cupy", reason="cupy/cupy/issues/9568")
+    def test_triangle_symmetry(self, xp):
+        t = xp.linspace(0, 2*xp.pi, 1000)
+        y = sawtooth(t, width=0.5)
+        xp_assert_close(y, xp.flip(y))
+        xp_assert_close(sawtooth(-t, 0.)[1:-1], sawtooth(t)[1:-1])
+
+
+@make_xp_test_case(square)
+class TestSquareWaveform:
+    def test_unique(self, xp):
+        t = xp.linspace(0, 2*np.pi, 1000)
+        y = square(t)
+        assert y.shape == t.shape
+        unique = np.unique(_xp_copy_to_numpy(y))
+        assert set(unique).issubset({-1.0, 1.0})
+
+    @pytest.mark.xfail_xp_backends("cupy", reason="cupy/cupy/issues/9541")
+    @pytest.mark.parametrize("t_dtype", ["float32", "float64"])
+    @pytest.mark.parametrize("duty_dtype", ["float32", "float64"])
+    def test_dtype(self, t_dtype, duty_dtype, xp):
+        t_dtype = getattr(xp, t_dtype)
+        duty_dtype = getattr(xp, duty_dtype)
+        waveform = square(xp.asarray(1, dtype=t_dtype),
+                          duty=xp.asarray(0.5, dtype=duty_dtype))
+        assert waveform.dtype == xp.result_type(t_dtype, duty_dtype)
+
+    @pytest.mark.xfail_xp_backends("cupy", reason="cupy/cupy/issues/9541")
+    @pytest.mark.parametrize("dtype", [None, "float32", "float64"])
+    @pytest.mark.parametrize("duty", [0.1, 0.25, 0.5, 0.75])
+    def test_duty_cycle_fraction(self, dtype, duty, xp):
+        dtype = dtype if dtype is None else getattr(xp, dtype)  # duty is Python float
+        # imperfect arithmetic w/ JAX `float32` causes trouble with duty=0.5
+        # t = xp.linspace(0, 2*xp.pi, 10000, endpoint=False, dtype=dtype)
+        t = xp.arange(10000., dtype=dtype) / 10000 * 2*xp.pi
+        y = square(t, duty=duty)
+
+        dtype = xp_default_dtype(xp) if dtype is None else dtype
+        fraction_high = xp.mean(xp.asarray(y == 1.0, dtype=dtype))
+        xp_assert_close(fraction_high, xp.asarray(duty, dtype=dtype)[()])
+        xp_assert_close(xp.mean(y), xp.asarray(2*duty - 1, dtype=dtype)[()])
+
+    @pytest.mark.parametrize("duty, expected", [(1., 1.), (0., -1.)])
+    def test_duty_edge_cases(self, duty, expected, xp):
+        t = xp.linspace(0, 2*xp.pi, 100)
+        y = square(t, duty=duty)
+        xp_assert_equal(y, xp.full(t.shape, expected))
+
+    def test_periodic(self, xp):
+        t = xp.linspace(0, 2*xp.pi, 10, endpoint=False, dtype=xp.float64)
+        y1 = square(t, duty=0.4)
+        y2 = square(t + 2*xp.pi, duty=0.4)
+
+        xp_assert_equal(y1, y2)
+
+    @pytest.mark.parametrize("duty", [-0.1, 1.1, 2.0])
+    def test_invalid_duty(self, duty, xp):
+        t = xp.linspace(0, 2*np.pi, 10)
+        y = square(t, duty=duty)
+
+        assert xp.all(xp.isnan(y))
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/tests/test_wavelets.py b/venv/lib/python3.12/site-packages/scipy/signal/tests/test_wavelets.py
new file mode 100644
index 0000000000000000000000000000000000000000..7a357d2eaf4a530930d612358b8ca69a18b5248e
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/tests/test_wavelets.py
@@ -0,0 +1,59 @@
+import numpy as np
+from numpy.testing import assert_array_equal, assert_array_almost_equal
+
+import scipy.signal._wavelets as wavelets
+
+
+class TestWavelets:
+    def test_ricker(self):
+        w = wavelets._ricker(1.0, 1)
+        expected = 2 / (np.sqrt(3 * 1.0) * (np.pi ** 0.25))
+        assert_array_equal(w, expected)
+
+        lengths = [5, 11, 15, 51, 101]
+        for length in lengths:
+            w = wavelets._ricker(length, 1.0)
+            assert len(w) == length
+            max_loc = np.argmax(w)
+            assert max_loc == (length // 2)
+
+        points = 100
+        w = wavelets._ricker(points, 2.0)
+        half_vec = np.arange(0, points // 2)
+        # Wavelet should be symmetric
+        assert_array_almost_equal(w[half_vec], w[-(half_vec + 1)])
+
+        # Check zeros
+        aas = [5, 10, 15, 20, 30]
+        points = 99
+        for a in aas:
+            w = wavelets._ricker(points, a)
+            vec = np.arange(0, points) - (points - 1.0) / 2
+            exp_zero1 = np.argmin(np.abs(vec - a))
+            exp_zero2 = np.argmin(np.abs(vec + a))
+            assert_array_almost_equal(w[exp_zero1], 0)
+            assert_array_almost_equal(w[exp_zero2], 0)
+
+    def test_cwt(self):
+        widths = [1.0]
+        def delta_wavelet(s, t):
+            return np.array([1])
+        len_data = 100
+        test_data = np.sin(np.pi * np.arange(0, len_data) / 10.0)
+
+        # Test delta function input gives same data as output
+        cwt_dat = wavelets._cwt(test_data, delta_wavelet, widths)
+        assert cwt_dat.shape == (len(widths), len_data)
+        assert_array_almost_equal(test_data, cwt_dat.flatten())
+
+        # Check proper shape on output
+        widths = [1, 3, 4, 5, 10]
+        cwt_dat = wavelets._cwt(test_data, wavelets._ricker, widths)
+        assert cwt_dat.shape == (len(widths), len_data)
+
+        widths = [len_data * 10]
+        # Note: this wavelet isn't defined quite right, but is fine for this test
+        def flat_wavelet(l, w):
+            return np.full(w, 1 / w)
+        cwt_dat = wavelets._cwt(test_data, flat_wavelet, widths)
+        assert_array_almost_equal(cwt_dat, np.mean(test_data))
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/tests/test_whittaker.py b/venv/lib/python3.12/site-packages/scipy/signal/tests/test_whittaker.py
new file mode 100644
index 0000000000000000000000000000000000000000..a6573d54106071dac1410934661a7720cf39cd3e
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/tests/test_whittaker.py
@@ -0,0 +1,425 @@
+import numpy as np
+import pytest
+from numpy.testing import assert_allclose
+from scipy.signal import whittaker_henderson  # type: ignore[attr-defined]
+from scipy.signal._whittaker import (
+    _logdet_difference_matrix, _polynomial_fit, _reml, _solveh_banded, _solve_WH_banded,
+)
+from scipy.stats import special_ortho_group
+
+
+def _solve_WH_order2_fast(y, lamb):
+    """Efficiently solve WH of order 2 according to Weinert.
+
+    Needs order = 2 and n >= 3 (data points).
+
+    Weinert (2007)
+    "Efficient computation for Whittaker-Henderson smoothing".
+    Computational Statistics and Data Analysis 52:959-74.
+    https://doi.org/10.1016/j.csda.2006.11.038
+    """
+    n = y.shape[0]
+    # Convert penalty to convention of Weinert (2007), i.e. A = lambda I + D'D.
+    # Note that Weinert denotes the difference matrix M instead of D.
+    lamb = 1 / lamb
+    # A = LDL' decompositon, i.e. L is unit lower triangular and banded
+    # (bandwith=2) and D diagonal.
+    # First subdiagonal of L is (-e_1, .., -e_{n-1}) and 2nd subdiagonal
+    # (f_1, .., f_{n-2}). Diagonal of D is (d_1, .., d_n).
+    # The equation A @ x = lamb * y becomes
+    # LD @ b = lamb * y  (I)
+    # L.T @ x = b        (II)
+    # We shift Weinert's 1-based indices to 0-based indices, Eq. 2.2-2.6
+    # Solve problem (I)
+    b = np.empty(n)
+    e = np.empty(n)
+    f = np.empty(n)
+    # i=0
+    d = 1 + lamb
+    f[0] = 1 / d
+    mu = 2
+    e[0] = mu * f[0]
+    b[0] = f[0] * lamb * y[0]
+    mu_old = mu
+    # i=1
+    if n == 3:
+        d = 4 + lamb - mu_old * e[0]
+        mu = 2 - e[0]
+    else:
+        d = 5 + lamb - mu_old * e[0]
+        mu = 4 - e[0]
+    f[1] = 1 / d
+    e[1] = mu * f[1]
+    b[1] = f[1] * (lamb * y[1] + mu_old * b[0])
+    mu_old = mu
+    for i in range(2, n-2):
+        d = 6 + lamb - mu_old * e[i-1] - f[i-2]
+        f[i] = 1 / d
+        mu = 4 - e[i-1]
+        e[i] = mu * f[i]
+        b[i] = f[i] * (lamb * y[i] + mu_old * b[i-1] - b[i-2])
+        mu_old = mu
+    # i=n-2
+    if n >= 4:
+        i = n - 2
+        d = 5 + lamb - mu_old * e[i-1] - f[i-2]
+        f[i] = 1 / d
+        mu = 2 - e[i-1]
+        e[i] = mu * f[i]
+        b[i] = f[i] * (lamb * y[i] + mu_old * b[i-1] - b[i-2])
+        mu_old = mu
+    # i=n-1
+    i = n - 1
+    d = 1 + lamb - mu_old * e[i-1] - f[i-2]
+    f[i] = 1 / d
+    b[i] = f[i] * (lamb * y[i] + mu_old * b[i-1] - b[i-2])
+
+    # Solve problem (II)
+    x = np.empty(n)
+    x[n-1] = b[n-1]
+    x[n-2] = b[n-2] + e[n-2] * x[n-1]
+    for i in range(n-3, -1, -1):
+        x[i] = b[i] + e[i] * x[i+1] - f[i] * x[i+2]
+    return x
+
+
+def test_solveh_banded():
+    n = 10
+    # construct positive definite matrix A
+    Q = special_ortho_group(n, seed=1234).rvs()
+    A = Q @ np.diag(1 + np.arange(n)) @ Q.T
+    b = np.arange(n)
+    ab = np.zeros((n, n))
+    ab[0, :] = np.diagonal(A, 0)
+    for i in range(1, n):
+        ab[i, :-i] = np.diagonal(A, i)
+    x, logdet, _ = _solveh_banded(ab, b, calc_logdet=True)
+    assert_allclose(x, np.linalg.solve(A, b), rtol=1e-11)
+    assert_allclose(logdet, np.log(np.linalg.det(A)), rtol=1e-11)
+
+    # tridiagonal case
+    x, logdet, _ = _solveh_banded(ab[:2], b, calc_logdet=True)
+    A_tri = (
+        np.diag(np.diag(A)) + np.diag(np.diag(A, -1), -1) + np.diag(np.diag(A, 1), 1)
+    )
+    assert_allclose(logdet, np.log(np.linalg.det(A_tri)), rtol=1e-11)
+
+
+@pytest.mark.parametrize(
+        ["order", "n"],
+        [
+            (1, 2), (1, 10),
+            (2, 3), (2, 4), (2, 5), (2, 20),
+            (5, 6), (5, 7), (5, 10), (5, 20),
+            (6, 7), (6, 10), (6, 20),
+        ])
+def test_logdet_difference_matrix(order, n):
+    p = order
+    logdet = _logdet_difference_matrix(order=p, n=n)
+    D = np.diff(np.eye(n), n=p, axis=0)  # shape (n-p, n)
+    assert_allclose(logdet, np.log(np.linalg.det(D @ D.T)), rtol=1e-11)
+    eigvals = np.linalg.eigvals(D.T @ D)
+    assert_allclose(logdet, np.sum(np.log(eigvals[eigvals > 1e-8])), rtol=1e-11)
+
+
+@pytest.mark.parametrize("calc_logdet", [False, True])
+@pytest.mark.parametrize("lamb", [0.1, 1e20])
+def test_polynomial_fit(calc_logdet, lamb):
+    """Test that _polynomial_fit works as expected."""
+    n = 20
+    y = np.sin(2 * np.pi * np.linspace(0, 1, n))
+    poly, logdet = _polynomial_fit(y, lamb, calc_logdet=calc_logdet)
+
+    if not calc_logdet:
+        assert logdet == 0
+    
+    poly2, logdet2 = _polynomial_fit(
+        y, lamb, weights=1.23 * np.ones(n), calc_logdet=calc_logdet
+    )
+    assert logdet2 == pytest.approx(logdet, rel=1e-12)
+    assert_allclose(poly2, poly)
+
+
+@pytest.mark.parametrize(
+        ["signal", "lamb", "order", "weights", "err", "msg"],
+        [
+            ([[1, 2, 3] * 3], 1, 2, None, ValueError,
+             "Input array signal must be of shape \\(n,\\)"),
+            (np.zeros(2), 1, 2, None, ValueError,
+             "Input array signal must be at least of shape"),
+            (np.arange(10), -0.9, 2, None, ValueError,
+             "Parameter lamb must be string"),
+            ([1, 2, 3], "XXX", 1, None, ValueError,
+             "Parameter lamb must be string 'reml'"),
+            ([1, 2, 3], 1, 1.5, None, TypeError,
+             "order must be an integer."),
+            ([1, 2, 3], 1, 0, None, ValueError,
+             "order must be an integer not less than 1"),
+            ([1, 2, 3], 1, 2, [0, 1], ValueError,
+             "Input array weights must have the same shape as the signal array."),
+            ([1, 2, 3], 1, 2, [[0]], ValueError,
+             "Input array weights must have the same shape as the signal array."),
+            ([1, 2, np.nan], 1, 2, None, ValueError,
+             "Input array signal must be finite."),
+            ([1, 2, 3], 1, 2, [1, 2, np.nan], ValueError,
+             "Input array weights must be finite."),
+            ([1, 2, np.nan], 1, 2, [1, 2, 3], ValueError,
+             "Input array weights must be zero for all non-finite"),
+        ])
+def test_whittaker_raises(signal, lamb, order, weights, err, msg):
+    """Test that whittaker raises errors."""
+    with pytest.raises(err, match=msg):
+        whittaker_henderson(signal, lamb=lamb, order=order, weights=weights)
+
+
+def test_whittaker_small_data():
+    """Test that whittaker works on a few data points."""
+    # Should work on order + 1 data points. The first 2*order+1 are special.
+    la = 1
+    y = np.arange(2)
+    wh = whittaker_henderson(y, order=1, lamb=la)
+    # Analytical solution for order=1 and n=2
+    res = (np.array([[1 + la, la], [la, 1 + la]]) / (1 + 2 * la)) @ y
+    assert_allclose(wh.x, res, atol=1e-15)
+    whittaker_henderson(np.arange(3), order=1, lamb=la)
+
+    y = np.arange(3)
+    wh = whittaker_henderson(y, order=2, lamb=la)
+    # Analytical solution for order=2 and n=3:
+    # import numpy as np
+    # from sympy import eye, Symbol
+    # n, order = 3, 2
+    # la = Symbol("la")
+    # D = np.diff(eye(n), n=order, axis=0)
+    # A = eye(n) + la * D.T @ D
+    # A.inv()
+    res = (
+        np.array([
+            [1 + 5 * la,     2 * la,        -la],
+            [    2 * la, 1 + 2 * la,     2 * la],
+            [       -la,     2 * la, 1 + 5 * la],
+        ]) / (1 + 6 * la)) @ y
+    assert_allclose(wh.x, res, atol=1e-15)
+    assert wh.lamb == la
+    
+    y = np.arange(4)
+    wh = whittaker_henderson(y, order=2, lamb=la)
+    la2 = la ** 2
+    res =(np.array([
+        [14*la2 + 11*la + 1, 8*la2 + 2*la    , 2*la2 -   la,     -4*la2            ],
+        [ 8*la2 +  2*la    , 6*la2 + 7*la + 1, 4*la2 + 4*la,      2*la2 -  la      ],
+        [ 2*la2 -    la    , 4*la2 + 4*la    , 6*la2 + 7*la + 1,  8*la2 + 2*la     ],
+        [-4*la2            , 2*la2 -   la    , 8*la2 + 2*la    , 14*la2 + 11*la + 1],
+    ]) /(20*la2 + 12*la + 1)) @ y
+    assert_allclose(wh.x, res, atol=1e-15)
+    whittaker_henderson(np.arange(5), order=2, lamb=la)
+
+    whittaker_henderson(np.arange(4), order=3, lamb=la)
+    whittaker_henderson(np.arange(5), order=3, lamb=la)
+    whittaker_henderson(np.arange(6), order=3, lamb=la)
+    whittaker_henderson(np.arange(7), order=3, lamb=la)
+
+
+@pytest.mark.parametrize("n", [3, 4, 5, 100])
+def test_whittaker_direct_vs_fast_order2(n):
+    """Test equivalent results"""
+    rng = np.random.default_rng(42)
+    signal = np.sin(2 * np.pi * np.linspace(0, 1, n)) + rng.standard_normal(n)
+    x1, _ = _solve_WH_banded(signal, lamb=1.23, order=2)
+    x2 = _solve_WH_order2_fast(signal, lamb=1.23)
+    assert_allclose(x1, x2, rtol=1e-11)
+
+    wh = whittaker_henderson(signal, lamb=1.23, order=2)
+    assert_allclose(wh.x, x1, rtol=1e-11)
+
+
+@pytest.mark.parametrize("order", [1, 2, 3, 4])
+def test_whittaker_limit_zero_penalty(order):
+    """Test whittaker for penalty lamb close to zero."""
+    rng = np.random.default_rng(42)
+    n = 100
+    y = np.sin(2*np.pi * np.linspace(0, 1, n))
+    noise = rng.standard_normal(n)
+    signal = y + noise
+
+    # In the limit of a zero penalty, the smoothing results in reproducing the signal.
+    wh = whittaker_henderson(signal, lamb=1e-7, order=order)
+    assert_allclose(wh.x, signal, rtol=1e-4, atol=1e-5)
+    assert wh.lamb == 1e-7
+
+
+@pytest.mark.parametrize("weights", [None, "ones"])
+@pytest.mark.parametrize("order", [1, 2, 3, 4])
+def test_whittaker_limit_infinity_penalty(weights, order):
+    """Test whittaker for penalty lamb close to infinity."""
+    n = 100
+    y = np.sin(2*np.pi * np.linspace(0, 1, n))
+    w = None if weights is None else np.ones_like(y)
+
+    # In the limit of an infinite penalty, the smoothing results in an interpolation
+    # polynom of degree = penalty order - 1 (order=2 => linear)
+    wh = whittaker_henderson(y, lamb=1e11, order=order, weights=w)
+    x_poly = np.arange(len(y))
+    poly = np.polynomial.Polynomial.fit(x=x_poly, y=y, deg=order - 1)
+    assert_allclose(wh.x, poly(x_poly), rtol=10**(-6 + order), atol=1e-5)
+    if order == 2:
+        # Linear interpolation:
+        # As the sine is positive fom 0 to pi and negative from pi to 2*pi, we expect
+        # a negative slope.
+        assert np.diff(wh.x)[0] < 0
+
+    if order > 2:
+        # Very large lambda should trigger a user warning and produce the exact
+        # polynomial fit (separate code path where linear solver breaks down).
+        with pytest.warns(
+            UserWarning,
+            match="The linear solver in Whittaker-Henderson smoothing detected",
+        ):
+            wh = whittaker_henderson(y, lamb=1e15, order=order, weights=w)
+    else:
+        wh = whittaker_henderson(y, lamb=1e20, order=order, weights=w)
+    assert_allclose(wh.x, poly(x_poly), rtol=1e-10)
+
+
+def test_whittaker_unpenalized():
+    """Test whittaker for lamb=0."""
+    n = 10
+    y = np.sin(2*np.pi * np.linspace(0, 1, n))
+    wh = whittaker_henderson(y, lamb=0)
+    assert_allclose(wh.x, y, rtol=1e-11)
+    assert not np.may_share_memory(wh.x, y)
+
+
+def test_whittaker_weights():
+    """Test that whittaker with weights of 1 is same as without weights."""
+    rng = np.random.default_rng(42)
+    n = 100
+    y = np.sin(2*np.pi * np.linspace(0, 1, n))
+    noise = rng.standard_normal(n)
+    signal = y + noise
+    wh1 = whittaker_henderson(signal, lamb=1)
+    w = np.ones_like(signal)
+    wh2 = whittaker_henderson(signal, lamb=1, weights=w)
+    assert_allclose(wh1.x, wh2.x, rtol=1e-11)
+
+    # Multiplying penalty and weights by the same number does not change the result.
+    wh3 = whittaker_henderson(signal, lamb=3, weights=3*w)
+    assert_allclose(wh3.x, wh1.x, rtol=1e-11)
+
+
+@pytest.mark.parametrize("missing_value", [np.nan, np.inf, 1e-20])
+def test_whittaker_zero_weight_interpolation(missing_value):
+    """Test that whittaker interpolates where weights are zero."""
+    n = 100
+    signal = np.sin(2*np.pi * np.linspace(0, 1, n))
+    signal[50:] += 2
+    w = np.ones_like(signal)
+    signal[40:60] = missing_value  # value does not matter
+    w[40:60] = 0
+    # Note: interpolation is a polynomial of degree = 2 * order - 1.
+
+    # order = 1 => linear interpolation
+    wh = whittaker_henderson(signal, lamb=1, order=1, weights=w)
+    interp = np.interp(np.arange(40, 60), [39, 60], [wh.x[39], wh.x[60]])
+    assert_allclose(wh.x[40:60], interp, rtol=1e-11)
+
+    # order = 2 => cubic interpolation
+    wh = whittaker_henderson(signal, lamb=1, order=2, weights=w)
+    poly = np.polynomial.Polynomial.fit(
+        x=[38, 39, 60, 61], y=[wh.x[38], wh.x[39], wh.x[60], wh.x[61]], deg=3
+    )
+    assert_allclose(wh.x[40:60], poly(np.arange(40, 60)), rtol=1e-11)
+
+
+def test_whittaker_zero_weight_extrapolation():
+    """Test that whittaker extrapolates where weights are zero."""
+    n = 100
+    signal = np.sin(2*np.pi * np.linspace(0, 1, n))
+    signal[50:] += 2
+    w = np.ones_like(signal)
+    signal[80:] = np.nan  # value does not matter, np.nan to check arg validation
+    w[80:] = 0
+    # Note: extrapolation is a polynomial of degree = order - 1.
+
+    # order = 1 => constant extrapolation
+    wh = whittaker_henderson(signal, lamb=1, order=1, weights=w)
+    assert_allclose(wh.x[80:], wh.x[79], rtol=1e-11)
+
+    # order 2 => linear extrapolation
+    wh = whittaker_henderson(signal, lamb=1, order=2, weights=w)
+    poly = np.polynomial.Polynomial.fit(x=[78, 79], y=wh.x[78:80], deg=1)
+    assert_allclose(wh.x[80:], poly(np.arange(80, 100)), rtol=1e-11)
+
+    # order = 3 => quadratic extrapolation
+    wh = whittaker_henderson(signal, lamb=1, order=3, weights=w)
+    poly = np.polynomial.Polynomial.fit(x=[77, 78, 79], y=wh.x[77:80], deg=2)
+    assert_allclose(wh.x[80:], poly(np.arange(80, 100)), rtol=1e-9)
+
+
+@pytest.mark.parametrize("order", [1, 2, 3])
+def test_reml_criterion(order):
+    la = 1.2345
+    n = 10
+    y = np.sin(2*np.pi * np.linspace(0, 1, n))
+    D = np.diff(np.eye(n), n=order, axis=0)
+    M = D.T @ D
+
+    def test_reml(la, y):
+        # See docstring and comment of _reml.
+        A = np.eye(n) + la * M
+        x = np.linalg.solve(A, y)
+        resid = y - x
+        r2 = resid @ resid + la * x @ M @ x
+        return -0.5 * ((n-order) * (1 + np.log(r2 / (n - order)))
+                       - np.log(np.linalg.det(la * D @ D.T))
+                       + np.log(np.linalg.det(A)))
+
+    r1 = _reml(lamb=la, y=y, order=order)
+    r2 = test_reml(la=la, y=y)
+    assert_allclose(r1, r2, rtol=1e-11)
+
+
+@pytest.mark.parametrize("weights", [None, "ones"])
+def test_whittaker_reml(weights):
+    """Test that whittaker with REML criterion works."""
+    n = 10
+    order = 2
+    signal = np.sin(2*np.pi * np.linspace(0, 1, n))
+    y = signal.copy()
+    # add some (deterministic) noise
+    y[::2] += 0.2
+    y[1::2] -= 0.2
+    w = None if weights is None else np.ones_like(y)
+
+    wh = whittaker_henderson(y, lamb="reml", order=order, weights=w)
+    assert wh.lamb > 0
+
+    # Validate against R mgcv
+    # library(mgcv)
+    # n = 10
+    # order = 2
+    # signal = sin(2*pi * 0:(n-1) / (n-1))
+    # y = signal
+    # # add some (deterministic) noise
+    # y[seq(1, n, 2)] = y[seq(1, n, 2)] + 0.2
+    # y[seq(2, n, 2)] = y[seq(2, n, 2)] - 0.2
+    # x <- 1:n
+    # b <- gam(y ~ s(x, bs="ps", k=n, m=c(0, 2)), family = gaussian(),
+    #          knots = list(x=0:11), method="REML",
+    #          control = list(epsilon = 1e-12, mgcv.tol = 1e-12, efs.tol = 1e-12))
+    # options(digits=12)
+    # b$fitted.values
+    expected = [
+        0.209959334732, 0.589996568382, 0.938965773497, 0.766582291904, 0.349462653088,
+        -0.349462653088, -0.766582291904, -0.938965773497, -0.589996568382,
+        -0.209959334732,
+    ]
+    assert_allclose(wh.x, expected, rtol=1e-7)
+    # b$sp
+    expected_sp = 5.12904626508
+    expected_sp /= 16  # not 100% sure how to justify this 16.
+    assert wh.lamb == pytest.approx(expected_sp, rel=1e-7)
+
+    # Double weights should result in double lamb.
+    wh2 = whittaker_henderson(y, lamb="reml", order=order, weights=2 * np.ones_like(y))
+    assert wh2.lamb == pytest.approx(2 * wh.lamb, rel=1e-7)
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/tests/test_windows.py b/venv/lib/python3.12/site-packages/scipy/signal/tests/test_windows.py
new file mode 100644
index 0000000000000000000000000000000000000000..d5434173978fa5dca88a52bfb44bdf3cfcfa13c4
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/tests/test_windows.py
@@ -0,0 +1,1186 @@
+import math
+import warnings
+
+import numpy as np
+from numpy import array
+import pytest
+from pytest import raises as assert_raises
+
+from scipy.fft import fft
+from scipy.signal import windows, get_window, resample
+from scipy.signal.windows._windows import _WIN_FUNC_DATA, _WIN_FUNCS
+from scipy._lib._array_api import (
+    xp_assert_close, xp_assert_equal, array_namespace, is_torch, is_jax, is_cupy,
+    assert_array_almost_equal, SCIPY_DEVICE, is_numpy, make_xp_test_case,
+    make_xp_pytest_param, _xp_copy_to_numpy
+)
+
+skip_xp_backends = pytest.mark.skip_xp_backends
+xfail_xp_backends = pytest.mark.xfail_xp_backends
+
+lazy_xp_modules = [windows]
+
+
+window_funcs = [
+    ('boxcar', ()),
+    ('triang', ()),
+    ('parzen', ()),
+    ('bohman', ()),
+    ('blackman', ()),
+    ('nuttall', ()),
+    ('blackmanharris', ()),
+    ('flattop', ()),
+    ('bartlett', ()),
+    ('barthann', ()),
+    ('hamming', ()),
+    ('kaiser', (1,)),
+    ('dpss', (2,)),
+    ('gaussian', (0.5,)),
+    ('general_gaussian', (1.5, 2)),
+    ('chebwin', (1,)),
+    ('cosine', ()),
+    ('hann', ()),
+    ('exponential', ()),
+    ('taylor', ()),
+    ('tukey', (0.5,)),
+    ('lanczos', ()),
+    ]
+
+
+@make_xp_test_case(windows.barthann)
+class TestBartHann:
+
+    def test_basic(self, xp):
+        xp_assert_close(windows.barthann(6, sym=True, xp=xp),
+                        xp.asarray([0, 0.35857354213752, 0.8794264578624801,
+                         0.8794264578624801, 0.3585735421375199, 0], dtype=xp.float64),
+                        rtol=1e-15, atol=1e-15)
+        xp_assert_close(windows.barthann(7, xp=xp),
+                        xp.asarray([0, 0.27, 0.73, 1.0, 0.73, 0.27, 0],
+                                   dtype=xp.float64),
+                        rtol=1e-15, atol=1e-15)
+        xp_assert_close(windows.barthann(6, False, xp=xp),
+                        xp.asarray([0, 0.27, 0.73, 1.0, 0.73, 0.27], dtype=xp.float64),
+                        rtol=1e-15, atol=1e-15)
+
+
+@make_xp_test_case(windows.bartlett)
+class TestBartlett:
+
+    def test_basic(self, xp):
+        xp_assert_close(windows.bartlett(6, xp=xp),
+                        xp.asarray([0, 0.4, 0.8, 0.8, 0.4, 0], dtype=xp.float64))
+        xp_assert_close(windows.bartlett(7, xp=xp),
+                        xp.asarray([0, 1/3, 2/3, 1.0, 2/3, 1/3, 0], dtype=xp.float64))
+        xp_assert_close(windows.bartlett(6, False, xp=xp),
+                        xp.asarray([0, 1/3, 2/3, 1.0, 2/3, 1/3], dtype=xp.float64))
+
+
+@make_xp_test_case(windows.blackman)
+class TestBlackman:
+
+    def test_basic(self, xp):
+        xp_assert_close(windows.blackman(6, sym=False, xp=xp),
+                        xp.asarray([0, 0.13, 0.63, 1.0, 0.63, 0.13], dtype=xp.float64),
+                        atol=1e-14)
+        xp_assert_close(windows.blackman(7, sym=False, xp=xp),
+                        xp.asarray([0, 0.09045342435412804, 0.4591829575459636,
+                                    0.9203636180999081, 0.9203636180999081,
+                                    0.4591829575459636, 0.09045342435412804],
+                                    dtype=xp.float64),
+                        atol=1e-8)
+        xp_assert_close(windows.blackman(6, xp=xp),
+                        xp.asarray([0, 0.2007701432625305, 0.8492298567374694,
+                                    0.8492298567374694, 0.2007701432625305, 0],
+                                    dtype=xp.float64),
+                        atol=1e-14)
+        xp_assert_close(windows.blackman(7, True, xp=xp),
+                        xp.asarray([0, 0.13, 0.63, 1.0, 0.63, 0.13, 0],
+                        dtype=xp.float64), atol=1e-14)
+
+
+@make_xp_test_case(windows.blackmanharris)
+class TestBlackmanHarris:
+
+    def test_basic(self, xp):
+        xp_assert_close(windows.blackmanharris(6, False, xp=xp),
+                        xp.asarray([6.0e-05, 0.055645, 0.520575,
+                                    1.0, 0.520575, 0.055645], dtype=xp.float64))
+        xp_assert_close(windows.blackmanharris(7, sym=False, xp=xp),
+                        xp.asarray([6.0e-05, 0.03339172347815117, 0.332833504298565,
+                                    0.8893697722232837, 0.8893697722232838,
+                                    0.3328335042985652, 0.03339172347815122],
+                                    dtype=xp.float64))
+        xp_assert_close(windows.blackmanharris(6, xp=xp),
+                        xp.asarray([6.0e-05, 0.1030114893456638, 0.7938335106543362,
+                                    0.7938335106543364, 0.1030114893456638, 6.0e-05],
+                                    dtype=xp.float64))
+        xp_assert_close(windows.blackmanharris(7, sym=True, xp=xp),
+                        xp.asarray([6.0e-05, 0.055645, 0.520575, 1.0, 0.520575,
+                                    0.055645, 6.0e-05], dtype=xp.float64))
+
+
+@make_xp_test_case(windows.taylor)
+class TestTaylor:
+
+    def test_normalized(self, xp):
+        """Tests windows of small length that are normalized to 1. See the
+        documentation for the Taylor window for more information on
+        normalization.
+        """
+        xp_assert_close(windows.taylor(1, 2, 15, xp=xp),
+                        xp.asarray([1.0], dtype=xp.float64))
+        xp_assert_close(
+            windows.taylor(5, 2, 15, xp=xp),
+            xp.asarray([0.75803341, 0.90757699, 1.0, 0.90757699, 0.75803341],
+                       dtype=xp.float64)
+        )
+        xp_assert_close(
+            windows.taylor(6, 2, 15, xp=xp),
+            xp.asarray([
+                0.7504082, 0.86624416, 0.98208011, 0.98208011, 0.86624416,
+                0.7504082
+            ], dtype=xp.float64)
+        )
+
+    def test_non_normalized(self, xp):
+        """Test windows of small length that are not normalized to 1. See
+        the documentation for the Taylor window for more information on
+        normalization.
+        """
+        xp_assert_close(
+            windows.taylor(5, 2, 15, norm=False, xp=xp),
+            xp.asarray([
+                0.87508054, 1.04771499, 1.15440894, 1.04771499, 0.87508054
+            ], dtype=xp.float64)
+        )
+        xp_assert_close(
+            windows.taylor(6, 2, 15, norm=False, xp=xp),
+            xp.asarray([
+                0.86627793, 1.0, 1.13372207, 1.13372207, 1.0, 0.86627793
+            ], dtype=xp.float64)
+        )
+
+    def test_correctness(self, xp):
+        """This test ensures the correctness of the implemented Taylor
+        Windowing function. A Taylor Window of 1024 points is created, its FFT
+        is taken, and the Peak Sidelobe Level (PSLL) and 3dB and 18dB bandwidth
+        are found and checked.
+
+        A publication from Sandia National Laboratories was used as reference
+        for the correctness values [1]_.
+
+        References
+        -----
+        .. [1] Armin Doerry, "Catalog of Window Taper Functions for
+               Sidelobe Control", 2017.
+               https://www.researchgate.net/profile/Armin_Doerry/publication/316281181_Catalog_of_Window_Taper_Functions_for_Sidelobe_Control/links/58f92cb2a6fdccb121c9d54d/Catalog-of-Window-Taper-Functions-for-Sidelobe-Control.pdf
+        """
+        M_win = 1024
+        N_fft = 131072
+        # Set norm=False for correctness as the values obtained from the
+        # scientific publication do not normalize the values. Normalizing
+        # changes the sidelobe level from the desired value.
+        w = windows.taylor(M_win, nbar=4, sll=35, norm=False, sym=False, xp=xp)
+        f_np = fft(_xp_copy_to_numpy(w), N_fft)
+
+        spec = 20 * np.log10(np.abs(f_np / np.max(f_np)))
+
+        first_zero = np.argmax(np.diff(spec) > 0)
+
+        PSLL = np.max(spec[first_zero:-first_zero])
+
+        BW_3dB = 2*np.argmax(spec <= -3.0102999566398121) / N_fft * M_win
+        BW_18dB = 2*np.argmax(spec <= -18.061799739838872) / N_fft * M_win
+
+        assert math.isclose(PSLL, -35.1672, abs_tol=1)
+        assert math.isclose(BW_3dB, 1.1822, abs_tol=0.1)
+        assert math.isclose(BW_18dB, 2.6112, abs_tol=0.1)
+
+
+@make_xp_test_case(windows.bohman)
+class TestBohman:
+
+    def test_basic(self, xp):
+        xp_assert_close(windows.bohman(6, xp=xp),
+                        xp.asarray([0, 0.1791238937062839, 0.8343114522576858,
+                                    0.8343114522576858, 0.1791238937062838, 0],
+                                    dtype=xp.float64))
+        xp_assert_close(windows.bohman(7, sym=True, xp=xp),
+                        xp.asarray([0, 0.1089977810442293, 0.6089977810442293, 1.0,
+                                    0.6089977810442295, 0.1089977810442293, 0],
+                                    dtype=xp.float64))
+        xp_assert_close(windows.bohman(6, False, xp=xp),
+                        xp.asarray([0, 0.1089977810442293, 0.6089977810442293, 1.0,
+                                    0.6089977810442295, 0.1089977810442293],
+                                    dtype=xp.float64))
+
+
+@make_xp_test_case(windows.boxcar)
+class TestBoxcar:
+
+    def test_basic(self, xp):
+        xp_assert_close(windows.boxcar(6, xp=xp),
+                        xp.asarray([1.0, 1, 1, 1, 1, 1], dtype=xp.float64))
+        xp_assert_close(windows.boxcar(7, xp=xp),
+                        xp.asarray([1.0, 1, 1, 1, 1, 1, 1], dtype=xp.float64))
+        xp_assert_close(windows.boxcar(6, False, xp=xp),
+                        xp.asarray([1.0, 1, 1, 1, 1, 1], dtype=xp.float64))
+
+
+cheb_odd_true = [0.200938, 0.107729, 0.134941, 0.165348,
+                 0.198891, 0.235450, 0.274846, 0.316836,
+                 0.361119, 0.407338, 0.455079, 0.503883,
+                 0.553248, 0.602637, 0.651489, 0.699227,
+                 0.745266, 0.789028, 0.829947, 0.867485,
+                 0.901138, 0.930448, 0.955010, 0.974482,
+                 0.988591, 0.997138, 1.000000, 0.997138,
+                 0.988591, 0.974482, 0.955010, 0.930448,
+                 0.901138, 0.867485, 0.829947, 0.789028,
+                 0.745266, 0.699227, 0.651489, 0.602637,
+                 0.553248, 0.503883, 0.455079, 0.407338,
+                 0.361119, 0.316836, 0.274846, 0.235450,
+                 0.198891, 0.165348, 0.134941, 0.107729,
+                 0.200938]
+
+cheb_even_true = [0.203894, 0.107279, 0.133904,
+                  0.163608, 0.196338, 0.231986,
+                  0.270385, 0.311313, 0.354493,
+                  0.399594, 0.446233, 0.493983,
+                  0.542378, 0.590916, 0.639071,
+                  0.686302, 0.732055, 0.775783,
+                  0.816944, 0.855021, 0.889525,
+                  0.920006, 0.946060, 0.967339,
+                  0.983557, 0.994494, 1.000000,
+                  1.000000, 0.994494, 0.983557,
+                  0.967339, 0.946060, 0.920006,
+                  0.889525, 0.855021, 0.816944,
+                  0.775783, 0.732055, 0.686302,
+                  0.639071, 0.590916, 0.542378,
+                  0.493983, 0.446233, 0.399594,
+                  0.354493, 0.311313, 0.270385,
+                  0.231986, 0.196338, 0.163608,
+                  0.133904, 0.107279, 0.203894]
+
+
+@make_xp_test_case(windows.chebwin)
+class TestChebWin:
+
+    def test_basic(self, xp):
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", "This window is not suitable", UserWarning)
+            xp_assert_close(windows.chebwin(6, 100, xp=xp),
+                            xp.asarray([0.1046401879356917, 0.5075781475823447,
+                                        1.0, 1.0,
+                                        0.5075781475823447, 0.1046401879356917],
+                                        dtype=xp.float64),
+                            atol=1e-8
+            )
+            xp_assert_close(windows.chebwin(7, 100, xp=xp),
+                            xp.asarray([0.05650405062850233, 0.316608530648474,
+                                        0.7601208123539079, 1.0, 0.7601208123539079,
+                                        0.316608530648474, 0.05650405062850233],
+                                        dtype=xp.float64))
+            xp_assert_close(windows.chebwin(6, 10, xp=xp),
+                            xp.asarray([1.0, 0.6071201674458373, 0.6808391469897297,
+                                        0.6808391469897297, 0.6071201674458373, 1.0],
+                                        dtype=xp.float64))
+            xp_assert_close(windows.chebwin(7, 10, xp=xp),
+                            xp.asarray([1.0, 0.5190521247588651, 0.5864059018130382,
+                                        0.6101519801307441, 0.5864059018130382,
+                                        0.5190521247588651, 1.0], dtype=xp.float64))
+            xp_assert_close(windows.chebwin(6, 10, False, xp=xp),
+                            xp.asarray([1.0, 0.5190521247588651, 0.5864059018130382,
+                                        0.6101519801307441, 0.5864059018130382,
+                                        0.5190521247588651], dtype=xp.float64))
+
+    def test_cheb_odd_high_attenuation(self, xp):
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", "This window is not suitable", UserWarning)
+            cheb_odd = windows.chebwin(53, at=-40, xp=xp)
+        assert_array_almost_equal(cheb_odd, xp.asarray(cheb_odd_true), decimal=4)
+
+    def test_cheb_even_high_attenuation(self, xp):
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", "This window is not suitable", UserWarning)
+            cheb_even = windows.chebwin(54, at=40, xp=xp)
+        assert_array_almost_equal(cheb_even, xp.asarray(cheb_even_true), decimal=4)
+
+    def test_cheb_odd_low_attenuation(self, xp):
+        cheb_odd_low_at_true = xp.asarray([1.000000, 0.519052, 0.586405,
+                                           0.610151, 0.586405, 0.519052,
+                                           1.000000], dtype=xp.float64)
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", "This window is not suitable", UserWarning)
+            cheb_odd = windows.chebwin(7, at=10, xp=xp)
+        assert_array_almost_equal(cheb_odd, cheb_odd_low_at_true, decimal=4)
+
+    def test_cheb_even_low_attenuation(self, xp):
+        cheb_even_low_at_true = xp.asarray([1.000000, 0.451924, 0.51027,
+                                            0.541338, 0.541338, 0.51027,
+                                            0.451924, 1.000000], dtype=xp.float64)
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", "This window is not suitable", UserWarning)
+            cheb_even = windows.chebwin(8, at=-10, xp=xp)
+        assert_array_almost_equal(cheb_even, cheb_even_low_at_true, decimal=4)
+
+
+exponential_data = {
+    (4, None, 0.2, False):
+        array([4.53999297624848542e-05,
+               6.73794699908546700e-03, 1.00000000000000000e+00,
+               6.73794699908546700e-03]),
+    (4, None, 0.2, True): array([0.00055308437014783, 0.0820849986238988,
+                                 0.0820849986238988, 0.00055308437014783]),
+    (4, None, 1.0, False): array([0.1353352832366127, 0.36787944117144233, 1.,
+                                  0.36787944117144233]),
+    (4, None, 1.0, True): array([0.22313016014842982, 0.60653065971263342,
+                                 0.60653065971263342, 0.22313016014842982]),
+    (4, 2, 0.2, False):
+        array([4.53999297624848542e-05, 6.73794699908546700e-03,
+               1.00000000000000000e+00, 6.73794699908546700e-03]),
+    (4, 2, 0.2, True): None,
+    (4, 2, 1.0, False): array([0.1353352832366127, 0.36787944117144233, 1.,
+                               0.36787944117144233]),
+    (4, 2, 1.0, True): None,
+    (5, None, 0.2, True):
+        array([4.53999297624848542e-05,
+               6.73794699908546700e-03, 1.00000000000000000e+00,
+               6.73794699908546700e-03, 4.53999297624848542e-05]),
+    (5, None, 1.0, True): array([0.1353352832366127, 0.36787944117144233, 1.,
+                                 0.36787944117144233, 0.1353352832366127]),
+    (5, 2, 0.2, True): None,
+    (5, 2, 1.0, True): None
+}
+
+
+@make_xp_test_case(windows.exponential)
+def test_exponential(xp):
+    for k, v in exponential_data.items():
+        if v is None:
+            assert_raises(ValueError, windows.exponential, *k, xp=xp)
+        else:
+            win = windows.exponential(*k, xp=xp)
+            xp_assert_close(win, xp.asarray(v), rtol=1e-14)
+
+
+@make_xp_test_case(windows.flattop)
+class TestFlatTop:
+
+    def test_basic(self, xp):
+        xp_assert_close(windows.flattop(6, sym=False, xp=xp),
+                        xp.asarray([-0.000421051, -0.051263156, 0.19821053, 1.0,
+                                     0.19821053, -0.051263156], dtype=xp.float64))
+        xp_assert_close(windows.flattop(7, sym=False, xp=xp),
+                        xp.asarray([-0.000421051, -0.03684078115492348,
+                                     0.01070371671615342, 0.7808739149387698,
+                                     0.7808739149387698, 0.01070371671615342,
+                                    -0.03684078115492348], dtype=xp.float64))
+        xp_assert_close(windows.flattop(6, xp=xp),
+                        xp.asarray([-0.000421051, -0.0677142520762119,
+                                     0.6068721525762117, 0.6068721525762117,
+                                    -0.0677142520762119, -0.000421051],
+                                    dtype=xp.float64))
+        xp_assert_close(windows.flattop(7, True, xp=xp),
+                        xp.asarray([-0.000421051, -0.051263156, 0.19821053, 1.0,
+                                     0.19821053, -0.051263156, -0.000421051],
+                                     dtype=xp.float64))
+
+
+@make_xp_test_case(windows.gaussian)
+class TestGaussian:
+
+    def test_basic(self, xp):
+        xp_assert_close(windows.gaussian(6, 1.0, xp=xp),
+                        xp.asarray([0.04393693362340742, 0.3246524673583497,
+                                    0.8824969025845955, 0.8824969025845955,
+                                    0.3246524673583497, 0.04393693362340742],
+                                    dtype=xp.float64))
+        xp_assert_close(windows.gaussian(7, 1.2, xp=xp),
+                        xp.asarray([0.04393693362340742, 0.2493522087772962,
+                                    0.7066482778577162, 1.0, 0.7066482778577162,
+                                    0.2493522087772962, 0.04393693362340742],
+                                    dtype=xp.float64))
+        xp_assert_close(windows.gaussian(7, 3, xp=xp),
+                        xp.asarray([0.6065306597126334, 0.8007374029168081,
+                                    0.9459594689067654, 1.0, 0.9459594689067654,
+                                    0.8007374029168081, 0.6065306597126334],
+                                    dtype=xp.float64))
+        xp_assert_close(windows.gaussian(6, 3, False, xp=xp),
+                        xp.asarray([0.6065306597126334, 0.8007374029168081,
+                                    0.9459594689067654, 1.0, 0.9459594689067654,
+                                    0.8007374029168081], dtype=xp.float64))
+
+
+@make_xp_test_case(windows.general_cosine)
+class TestGeneralCosine:
+
+    def test_basic(self, xp):
+        a = xp.asarray([0.5, 0.3, 0.2])
+        xp_assert_close(windows.general_cosine(5, a),
+                        xp.asarray([0.4, 0.3, 1, 0.3, 0.4], dtype=xp.float64))
+
+        a = xp.asarray([0.5, 0.3, 0.2])
+        xp_assert_close(windows.general_cosine(4, a, sym=False),
+                        xp.asarray([0.4, 0.3, 1, 0.3], dtype=xp.float64))
+
+
+@make_xp_test_case(windows.general_hamming)
+class TestGeneralHamming:
+
+    def test_basic(self, xp):
+        xp_assert_close(windows.general_hamming(5, 0.7, xp=xp),
+                        xp.asarray([0.4, 0.7, 1.0, 0.7, 0.4], dtype=xp.float64))
+        xp_assert_close(windows.general_hamming(5, 0.75, sym=False, xp=xp),
+                        xp.asarray([0.5, 0.6727457514, 0.9522542486,
+                                    0.9522542486, 0.6727457514], dtype=xp.float64))
+        xp_assert_close(windows.general_hamming(6, 0.75, sym=True, xp=xp),
+                        xp.asarray([0.5, 0.6727457514, 0.9522542486,
+                                    0.9522542486, 0.6727457514, 0.5], dtype=xp.float64))
+
+
+@make_xp_test_case(windows.hamming)
+class TestHamming:
+
+    def test_basic(self, xp):
+        xp_assert_close(windows.hamming(6, False, xp=xp),
+                        xp.asarray([0.08, 0.31, 0.77, 1.0, 0.77, 0.31],
+                                   dtype=xp.float64))
+        xp_assert_close(windows.hamming(7, sym=False, xp=xp),
+                        xp.asarray([0.08, 0.2531946911449826, 0.6423596296199047,
+                                    0.9544456792351128, 0.9544456792351128,
+                                    0.6423596296199047, 0.2531946911449826],
+                                    dtype=xp.float64))
+        xp_assert_close(windows.hamming(6, xp=xp),
+                        xp.asarray([0.08, 0.3978521825875242, 0.9121478174124757,
+                                    0.9121478174124757, 0.3978521825875242, 0.08],
+                                    dtype=xp.float64))
+        xp_assert_close(windows.hamming(7, sym=True, xp=xp),
+                        xp.asarray([0.08, 0.31, 0.77, 1.0, 0.77, 0.31, 0.08],
+                                   dtype=xp.float64))
+
+
+@make_xp_test_case(windows.hann)
+class TestHann:
+
+    def test_basic(self, xp):
+        xp_assert_close(windows.hann(6, sym=False, xp=xp),
+                        xp.asarray([0, 0.25, 0.75, 1.0, 0.75, 0.25], dtype=xp.float64),
+                        rtol=1e-15, atol=1e-15)
+        xp_assert_close(windows.hann(7, sym=False, xp=xp),
+                        xp.asarray([0, 0.1882550990706332, 0.6112604669781572,
+                                    0.9504844339512095, 0.9504844339512095,
+                                    0.6112604669781572, 0.1882550990706332],
+                                    dtype=xp.float64),
+                        rtol=1e-15, atol=1e-15)
+        xp_assert_close(windows.hann(6, True, xp=xp),
+                        xp.asarray([0, 0.3454915028125263, 0.9045084971874737,
+                                    0.9045084971874737, 0.3454915028125263, 0],
+                                    dtype=xp.float64),
+                        rtol=1e-15, atol=1e-15)
+        xp_assert_close(windows.hann(7, xp=xp),
+                        xp.asarray([0, 0.25, 0.75, 1.0, 0.75, 0.25, 0],
+                        dtype=xp.float64),
+                        rtol=1e-15, atol=1e-15)
+
+
+@make_xp_test_case(windows.kaiser)
+class TestKaiser:
+
+    def test_basic(self, xp):
+        xp_assert_close(windows.kaiser(6, 0.5, xp=xp),
+                        xp.asarray([0.9403061933191572, 0.9782962393705389,
+                                    0.9975765035372042, 0.9975765035372042,
+                                    0.9782962393705389, 0.9403061933191572],
+                                    dtype=xp.float64))
+        xp_assert_close(windows.kaiser(7, 0.5, xp=xp),
+                        xp.asarray([0.9403061933191572, 0.9732402256999829,
+                                    0.9932754654413773, 1.0, 0.9932754654413773,
+                                    0.9732402256999829, 0.9403061933191572],
+                                    dtype=xp.float64))
+        xp_assert_close(windows.kaiser(6, 2.7, xp=xp),
+                        xp.asarray([0.2603047507678832, 0.6648106293528054,
+                                    0.9582099802511439, 0.9582099802511439,
+                                    0.6648106293528054, 0.2603047507678832],
+                                    dtype=xp.float64))
+        xp_assert_close(windows.kaiser(7, 2.7, xp=xp),
+                        xp.asarray([0.2603047507678832, 0.5985765418119844,
+                                    0.8868495172060835, 1.0, 0.8868495172060835,
+                                    0.5985765418119844, 0.2603047507678832],
+                                    dtype=xp.float64))
+        xp_assert_close(windows.kaiser(6, 2.7, False, xp=xp),
+                        xp.asarray([0.2603047507678832, 0.5985765418119844,
+                                    0.8868495172060835, 1.0, 0.8868495172060835,
+                                    0.5985765418119844], dtype=xp.float64))
+
+
+@make_xp_test_case(windows.kaiser_bessel_derived)
+class TestKaiserBesselDerived:
+
+    def test_basic(self, xp):
+        # cover case `M < 1`
+        w = windows.kaiser_bessel_derived(0.5, beta=4.0, xp=xp)
+        xp_assert_equal(w, xp.asarray([]))
+
+        M = 100
+        w = windows.kaiser_bessel_derived(M, beta=4.0, xp=xp)
+        w2 = windows.get_window(('kaiser bessel derived', 4.0),
+                                M, fftbins=False, xp=xp)
+        xp_assert_close(w, w2)
+
+        # Test for Princen-Bradley condition
+        actual = w[:M // 2] ** 2 + w[-M // 2:] ** 2
+        xp_assert_close(actual, xp.ones(actual.shape, dtype=actual.dtype))
+
+        # Test actual values from other implementations
+        # M = 2:  sqrt(2) / 2
+        # M = 4:  0.518562710536, 0.855039598640
+        # M = 6:  0.436168993154, 0.707106781187, 0.899864772847
+        # Ref:https://github.com/scipy/scipy/pull/4747#issuecomment-172849418
+        actual = windows.kaiser_bessel_derived(2, beta=np.pi / 2, xp=xp)[:1]
+        desired = xp.ones_like(actual) * math.sqrt(2) / 2.0
+        xp_assert_close(actual, desired)
+
+        xp_assert_close(windows.kaiser_bessel_derived(4, beta=np.pi / 2, xp=xp)[:2],
+                        xp.asarray([0.518562710536, 0.855039598640], dtype=xp.float64))
+
+        xp_assert_close(windows.kaiser_bessel_derived(6, beta=np.pi / 2, xp=xp)[:3],
+                        xp.asarray([0.436168993154, 0.707106781187, 0.899864772847],
+                                   dtype=xp.float64))
+
+    def test_exceptions(self, xp):
+        M = 100
+        # Assert ValueError for odd window length
+        msg = ("Kaiser-Bessel Derived windows are only defined for even "
+               "number of points")
+        with assert_raises(ValueError, match=msg):
+            windows.kaiser_bessel_derived(M + 1, beta=4., xp=xp)
+
+        # Assert ValueError for non-symmetric setting
+        msg = ("Kaiser-Bessel Derived windows are only defined for "
+               "symmetric shapes")
+        with assert_raises(ValueError, match=msg):
+            windows.kaiser_bessel_derived(M + 1, beta=4., sym=False, xp=xp)
+
+
+@make_xp_test_case(windows.nuttall)
+class TestNuttall:
+
+    def test_basic(self, xp):
+        xp_assert_close(windows.nuttall(6, sym=False, xp=xp),
+                        xp.asarray([0.0003628, 0.0613345, 0.5292298, 1.0, 0.5292298,
+                                    0.0613345], dtype=xp.float64))
+        xp_assert_close(windows.nuttall(7, sym=False, xp=xp),
+                        xp.asarray([0.0003628, 0.03777576895352025,
+                                    0.3427276199688195,
+                                    0.8918518610776603, 0.8918518610776603,
+                                    0.3427276199688196, 0.0377757689535203],
+                                    dtype=xp.float64))
+        xp_assert_close(windows.nuttall(6, xp=xp),
+                        xp.asarray([0.0003628, 0.1105152530498718,
+                                    0.7982580969501282, 0.7982580969501283,
+                                    0.1105152530498719, 0.0003628], dtype=xp.float64))
+        xp_assert_close(windows.nuttall(7, True, xp=xp),
+                        xp.asarray([0.0003628, 0.0613345, 0.5292298, 1.0,
+                                    0.5292298, 0.0613345, 0.0003628], dtype=xp.float64))
+
+
+@make_xp_test_case(windows.parzen)
+class TestParzen:
+
+    def test_basic(self, xp):
+        xp_assert_close(windows.parzen(6, xp=xp),
+                        xp.asarray([0.009259259259259254, 0.25, 0.8611111111111112,
+                                    0.8611111111111112, 0.25, 0.009259259259259254],
+                                    dtype=xp.float64))
+        xp_assert_close(windows.parzen(7, sym=True, xp=xp),
+                        xp.asarray([0.00583090379008747, 0.1574344023323616,
+                                    0.6501457725947521, 1.0, 0.6501457725947521,
+                                    0.1574344023323616, 0.00583090379008747],
+                                    dtype=xp.float64))
+        xp_assert_close(windows.parzen(6, False, xp=xp),
+                        xp.asarray([0.00583090379008747, 0.1574344023323616,
+                                    0.6501457725947521, 1.0, 0.6501457725947521,
+                                    0.1574344023323616], dtype=xp.float64))
+
+
+@make_xp_test_case(windows.triang)
+class TestTriang:
+
+    def test_basic(self, xp):
+
+        xp_assert_close(windows.triang(6, True, xp=xp),
+                        xp.asarray([1/6, 1/2, 5/6, 5/6, 1/2, 1/6], dtype=xp.float64))
+        xp_assert_close(windows.triang(7, xp=xp),
+                        xp.asarray([1/4, 1/2, 3/4, 1, 3/4, 1/2, 1/4], dtype=xp.float64))
+        xp_assert_close(windows.triang(6, sym=False, xp=xp),
+                        xp.asarray([1/4, 1/2, 3/4, 1, 3/4, 1/2], dtype=xp.float64))
+
+
+tukey_data = {
+    (4, 0.5, True): array([0.0, 1.0, 1.0, 0.0]),
+    (4, 0.9, True): array([0.0, 0.84312081893436686,
+                           0.84312081893436686, 0.0]),
+    (4, 1.0, True): array([0.0, 0.75, 0.75, 0.0]),
+    (4, 0.5, False): array([0.0, 1.0, 1.0, 1.0]),
+    (4, 0.9, False): array([0.0, 0.58682408883346526,
+                            1.0, 0.58682408883346526]),
+    (4, 1.0, False): array([0.0, 0.5, 1.0, 0.5]),
+    (5, 0.0, True): array([1.0, 1.0, 1.0, 1.0, 1.0]),
+    (5, 0.8, True): array([0.0, 0.69134171618254492,
+                           1.0, 0.69134171618254492, 0.0]),
+    (5, 1.0, True): array([0.0, 0.5, 1.0, 0.5, 0.0]),
+
+    (6, 0): [1.0, 1, 1, 1, 1, 1],
+    (7, 0): [1.0, 1, 1, 1, 1, 1, 1],
+    (6, .25): [0.0, 1, 1, 1, 1, 0],
+    (7, .25): [0.0, 1, 1, 1, 1, 1, 0],
+    (6,): [0, 0.9045084971874737, 1.0, 1.0, 0.9045084971874735, 0],
+    (7,): [0, 0.75, 1.0, 1.0, 1.0, 0.75, 0],
+    (6, .75): [0, 0.5522642316338269, 1.0, 1.0, 0.5522642316338267, 0],
+    (7, .75): [0, 0.4131759111665348, 0.9698463103929542, 1.0,
+               0.9698463103929542, 0.4131759111665347, 0],
+    (6, 1): [0, 0.3454915028125263, 0.9045084971874737, 0.9045084971874737,
+             0.3454915028125263, 0],
+    (7, 1): [0, 0.25, 0.75, 1.0, 0.75, 0.25, 0],
+}
+
+
+@make_xp_test_case(windows.tukey)
+class TestTukey:
+
+    def test_basic(self, xp):
+        # Test against hardcoded data
+        for k, v in tukey_data.items():
+            if v is None:
+                assert_raises(ValueError, windows.tukey, *k, xp=xp)
+            else:
+                if is_torch(xp) and k in [(6,), (6, .75), (7, .75), (6,1)]:
+                     atol_rtol = {'rtol': 3e-8, 'atol': 1e-8}
+                else:
+                     atol_rtol = {'rtol': 1e-15, 'atol': 1e-15 }
+
+                win = windows.tukey(*k, xp=xp)
+                xp_assert_close(win, xp.asarray(v),
+                                check_dtype=False, **atol_rtol)
+
+    def test_extremes(self, xp):
+        # Test extremes of alpha correspond to boxcar and hann
+        tuk0 = windows.tukey(100, 0, xp=xp)
+        box0 = windows.boxcar(100, xp=xp)
+        xp_assert_close(tuk0, box0)
+
+        tuk1 = windows.tukey(100, 1, xp=xp)
+        han1 = windows.hann(100, xp=xp)
+        xp_assert_close(tuk1, han1)
+
+
+dpss_data = {
+    # All values from MATLAB:
+    # * taper[1] of (3, 1.4, 3) sign-flipped
+    # * taper[3] of (5, 1.5, 5) sign-flipped
+    (4, 0.1, 2): ([[0.497943898, 0.502047681, 0.502047681, 0.497943898], [0.670487993, 0.224601537, -0.224601537, -0.670487993]], [0.197961815, 0.002035474]),  # noqa: E501
+    (3, 1.4, 3): ([[0.410233151, 0.814504464, 0.410233151], [0.707106781, 0.0, -0.707106781], [0.575941629, -0.580157287, 0.575941629]], [0.999998093, 0.998067480, 0.801934426]),  # noqa: E501
+    (5, 1.5, 5): ([[0.1745071052, 0.4956749177, 0.669109327, 0.495674917, 0.174507105], [0.4399493348, 0.553574369, 0.0, -0.553574369, -0.439949334], [0.631452756, 0.073280238, -0.437943884, 0.073280238, 0.631452756], [0.553574369, -0.439949334, 0.0, 0.439949334, -0.553574369], [0.266110290, -0.498935248, 0.600414741, -0.498935248, 0.266110290147157]], [0.999728571, 0.983706916, 0.768457889, 0.234159338, 0.013947282907567]),  # noqa: E501
+    (100, 2, 4): ([[0.0030914414, 0.0041266922, 0.005315076, 0.006665149, 0.008184854, 0.0098814158, 0.011761239, 0.013829809, 0.016091597, 0.018549973, 0.02120712, 0.02406396, 0.027120092, 0.030373728, 0.033821651, 0.037459181, 0.041280145, 0.045276872, 0.049440192, 0.053759447, 0.058222524, 0.062815894, 0.067524661, 0.072332638, 0.077222418, 0.082175473, 0.087172252, 0.092192299, 0.097214376, 0.1022166, 0.10717657, 0.11207154, 0.11687856, 0.12157463, 0.12613686, 0.13054266, 0.13476986, 0.13879691, 0.14260302, 0.14616832, 0.14947401, 0.1525025, 0.15523755, 0.15766438, 0.15976981, 0.16154233, 0.16297223, 0.16405162, 0.16477455, 0.16513702, 0.16513702, 0.16477455, 0.16405162, 0.16297223, 0.16154233, 0.15976981, 0.15766438, 0.15523755, 0.1525025, 0.14947401, 0.14616832, 0.14260302, 0.13879691, 0.13476986, 0.13054266, 0.12613686, 0.12157463, 0.11687856, 0.11207154, 0.10717657, 0.1022166, 0.097214376, 0.092192299, 0.087172252, 0.082175473, 0.077222418, 0.072332638, 0.067524661, 0.062815894, 0.058222524, 0.053759447, 0.049440192, 0.045276872, 0.041280145, 0.037459181, 0.033821651, 0.030373728, 0.027120092, 0.02406396, 0.02120712, 0.018549973, 0.016091597, 0.013829809, 0.011761239, 0.0098814158, 0.008184854, 0.006665149, 0.005315076, 0.0041266922, 0.0030914414], [0.018064449, 0.022040342, 0.026325013, 0.030905288, 0.035764398, 0.040881982, 0.046234148, 0.051793558, 0.057529559, 0.063408356, 0.069393216, 0.075444716, 0.081521022, 0.087578202, 0.093570567, 0.099451049, 0.10517159, 0.11068356, 0.11593818, 0.12088699, 0.12548227, 0.12967752, 0.1334279, 0.13669069, 0.13942569, 0.1415957, 0.14316686, 0.14410905, 0.14439626, 0.14400686, 0.14292389, 0.1411353, 0.13863416, 0.13541876, 0.13149274, 0.12686516, 0.12155045, 0.1155684, 0.10894403, 0.10170748, 0.093893752, 0.08554251, 0.076697768, 0.067407559, 0.057723559, 0.04770068, 0.037396627, 0.026871428, 0.016186944, 0.0054063557, -0.0054063557, -0.016186944, -0.026871428, -0.037396627, -0.04770068, -0.057723559, -0.067407559, -0.076697768, -0.08554251, -0.093893752, -0.10170748, -0.10894403, -0.1155684, -0.12155045, -0.12686516, -0.13149274, -0.13541876, -0.13863416, -0.1411353, -0.14292389, -0.14400686, -0.14439626, -0.14410905, -0.14316686, -0.1415957, -0.13942569, -0.13669069, -0.1334279, -0.12967752, -0.12548227, -0.12088699, -0.11593818, -0.11068356, -0.10517159, -0.099451049, -0.093570567, -0.087578202, -0.081521022, -0.075444716, -0.069393216, -0.063408356, -0.057529559, -0.051793558, -0.046234148, -0.040881982, -0.035764398, -0.030905288, -0.026325013, -0.022040342, -0.018064449], [0.064817553, 0.072567801, 0.080292992, 0.087918235, 0.095367076, 0.10256232, 0.10942687, 0.1158846, 0.12186124, 0.12728523, 0.13208858, 0.13620771, 0.13958427, 0.14216587, 0.14390678, 0.14476863, 0.1447209, 0.14374148, 0.14181704, 0.13894336, 0.13512554, 0.13037812, 0.1247251, 0.11819984, 0.11084487, 0.10271159, 0.093859853, 0.084357497, 0.074279719, 0.063708406, 0.052731374, 0.041441525, 0.029935953, 0.018314987, 0.0066811877, -0.0048616765, -0.016209689, -0.027259848, -0.037911124, -0.048065512, -0.05762905, -0.066512804, -0.0746338, -0.081915903, -0.088290621, -0.09369783, -0.098086416, -0.10141482, -0.10365146, -0.10477512, -0.10477512, -0.10365146, -0.10141482, -0.098086416, -0.09369783, -0.088290621, -0.081915903, -0.0746338, -0.066512804, -0.05762905, -0.048065512, -0.037911124, -0.027259848, -0.016209689, -0.0048616765, 0.0066811877, 0.018314987, 0.029935953, 0.041441525, 0.052731374, 0.063708406, 0.074279719, 0.084357497, 0.093859853, 0.10271159, 0.11084487, 0.11819984, 0.1247251, 0.13037812, 0.13512554, 0.13894336, 0.14181704, 0.14374148, 0.1447209, 0.14476863, 0.14390678, 0.14216587, 0.13958427, 0.13620771, 0.13208858, 0.12728523, 0.12186124, 0.1158846, 0.10942687, 0.10256232, 0.095367076, 0.087918235, 0.080292992, 0.072567801, 0.064817553], [0.14985551, 0.15512305, 0.15931467, 0.16236806, 0.16423291, 0.16487165, 0.16426009, 0.1623879, 0.1592589, 0.15489114, 0.14931693, 0.14258255, 0.13474785, 0.1258857, 0.11608124, 0.10543095, 0.094041635, 0.082029213, 0.069517411, 0.056636348, 0.043521028, 0.030309756, 0.017142511, 0.0041592774, -0.0085016282, -0.020705223, -0.032321494, -0.043226982, -0.053306291, -0.062453515, -0.070573544, -0.077583253, -0.083412547, -0.088005244, -0.091319802, -0.093329861, -0.094024602, -0.093408915, -0.091503383, -0.08834406, -0.08398207, -0.078483012, -0.071926192, -0.064403681, -0.056019215, -0.046886954, -0.037130106, -0.026879442, -0.016271713, -0.005448, 0.005448, 0.016271713, 0.026879442, 0.037130106, 0.046886954, 0.056019215, 0.064403681, 0.071926192, 0.078483012, 0.08398207, 0.08834406, 0.091503383, 0.093408915, 0.094024602, 0.093329861, 0.091319802, 0.088005244, 0.083412547, 0.077583253, 0.070573544, 0.062453515, 0.053306291, 0.043226982, 0.032321494, 0.020705223, 0.0085016282, -0.0041592774, -0.017142511, -0.030309756, -0.043521028, -0.056636348, -0.069517411, -0.082029213, -0.094041635, -0.10543095, -0.11608124, -0.1258857, -0.13474785, -0.14258255, -0.14931693, -0.15489114, -0.1592589, -0.1623879, -0.16426009, -0.16487165, -0.16423291, -0.16236806, -0.15931467, -0.15512305, -0.14985551]], [0.999943140, 0.997571533, 0.959465463, 0.721862496]),  # noqa: E501
+}
+
+
+@make_xp_test_case(windows.dpss)
+class TestDPSS:
+
+    def test_basic(self, xp):
+        # Test against hardcoded data
+        for k, v in dpss_data.items():
+            win, ratios = windows.dpss(*k, return_ratios=True, xp=xp)
+            xp_assert_close(win, v[0], atol=1e-7, err_msg=k)
+            xp_assert_close(ratios, v[1], rtol=1e-5, atol=1e-7, err_msg=k)
+
+    def test_unity(self, xp):
+        # Test unity value handling (gh-2221)
+        for M in range(1, 21):
+            # corrected w/approximation (default)
+            win = windows.dpss(M, M / 2.1, xp=xp)
+            expected = M % 2  # one for odd, none for even
+            xp_assert_equal(np.isclose(win, 1.).sum(), expected,
+                         err_msg=f'{win}')
+            # corrected w/subsample delay (slower)
+            win_sub = windows.dpss(M, M / 2.1, norm='subsample', xp=xp)
+            if M > 2:
+                # @M=2 the subsample doesn't do anything
+                xp_assert_equal(np.isclose(win_sub, 1.).sum(), expected,
+                             err_msg=f'{win_sub}')
+                xp_assert_close(win, win_sub, rtol=0.03)  # within 3%
+            # not the same, l2-norm
+            win_2 = windows.dpss(M, M / 2.1, norm=2, xp=xp)
+            expected = 1 if M == 1 else 0
+            xp_assert_equal(np.isclose(win_2, 1.).sum(), expected,
+                         err_msg=f'{win_2}')
+
+    def test_extremes(self, xp):
+        # Test extremes of alpha
+        lam = windows.dpss(31, 6, 4, return_ratios=True, xp=xp)[1]
+        xp_assert_close(lam, xp.ones_like(lam))
+        lam = windows.dpss(31, 7, 4, return_ratios=True, xp=xp)[1]
+        xp_assert_close(lam, xp.ones_like(lam))
+        lam = windows.dpss(31, 8, 4, return_ratios=True, xp=xp)[1]
+        xp_assert_close(lam, xp.ones_like(lam))
+
+    def test_degenerate(self, xp):
+        # Test failures
+        assert_raises(ValueError, windows.dpss, 4, 1.5, -1)  # Bad Kmax
+        assert_raises(ValueError, windows.dpss, 4, 1.5, -5)
+        assert_raises(TypeError, windows.dpss, 4, 1.5, 1.1)
+        assert_raises(ValueError, windows.dpss, 3, 1.5, 3)  # NW must be < N/2.
+        assert_raises(ValueError, windows.dpss, 3, -1, 3)  # NW must be pos
+        assert_raises(ValueError, windows.dpss, 3, 0, 3)
+        assert_raises(ValueError, windows.dpss, -1, 1, 3)  # negative M
+
+    @skip_xp_backends(np_only=True)
+    def test_degenerate_signle_samples(self, xp):
+        # Single samples
+        w = windows.dpss(1, 1.)
+        xp_assert_equal(w, [1.])
+        w, ratio = windows.dpss(1, 1., return_ratios=True)
+        xp_assert_equal(w, [1.])
+        assert ratio == 1.
+        w, ratio = windows.dpss(1, 1., Kmax=4, return_ratios=True)
+        xp_assert_equal(w, [1.])
+        assert isinstance(ratio, np.ndarray)
+        xp_assert_equal(ratio, [1.])
+
+        assert_raises(ValueError, windows.dpss, 4, 1.5, -1, xp=xp)  # Bad Kmax
+        assert_raises(ValueError, windows.dpss, 4, 1.5, -5, xp=xp)
+        assert_raises(TypeError, windows.dpss, 4, 1.5, 1.1, xp=xp)
+        assert_raises(ValueError, windows.dpss, 3, 1.5, 3, xp=xp)  # NW must be < N/2.
+        assert_raises(ValueError, windows.dpss, 3, -1, 3, xp=xp)  # NW must be pos
+        assert_raises(ValueError, windows.dpss, 3, 0, 3, xp=xp)
+        assert_raises(ValueError, windows.dpss, -1, 1, 3, xp=xp)  # negative M
+
+
+@make_xp_test_case(windows.lanczos)
+class TestLanczos:
+
+    def test_basic(self, xp):
+        # Analytical results:
+        # sinc(x) = sinc(-x)
+        # sinc(pi) = 0, sinc(0) = 1
+        # Hand computation on WolframAlpha:
+        # sinc(2 pi / 3) = 0.413496672
+        # sinc(pi / 3) = 0.826993343
+        # sinc(3 pi / 5) = 0.504551152
+        # sinc(pi / 5) = 0.935489284
+        xp_assert_close(windows.lanczos(6, sym=False, xp=xp),
+                        xp.asarray([0., 0.413496672,
+                                    0.826993343, 1., 0.826993343,
+                                    0.413496672], dtype=xp.float64),
+                        atol=1e-9)
+        xp_assert_close(windows.lanczos(6, xp=xp),
+                        xp.asarray([0., 0.504551152,
+                                    0.935489284, 0.935489284,
+                                    0.504551152, 0.], dtype=xp.float64),
+                        atol=1e-9)
+        xp_assert_close(windows.lanczos(7, sym=True, xp=xp),
+                        xp.asarray([0., 0.413496672,
+                                    0.826993343, 1., 0.826993343,
+                                    0.413496672, 0.], dtype=xp.float64),
+                        atol=1e-9)
+
+    def test_array_size(self, xp):
+        for n in [0, 10, 11]:
+            assert windows.lanczos(n, sym=False, xp=xp).shape[0] == n
+            assert windows.lanczos(n, sym=True, xp=xp).shape[0] == n
+
+
+@make_xp_test_case(windows.get_window)
+class TestGetWindow:
+    """Unit test for `scipy.signal.get_windows`. """
+
+    def test_WIN_FUNC_DATA_integrity(self):
+        """Verify that the `_windows._WIN_FUNC_DATA` dict is consistent.
+
+          The keys of _WIN_FUNC_DATA are made of tuples of strings of allowed window
+          names. Its values are 2-tuples made up of the window function and a
+          entry characterizing the existence of window parameters as ``True``,
+          ``False`` or ``'OPTIONAL'``.
+
+
+          It is verified that the correct window name (i.e., corresponding to the
+          function in the value tuple) is included in the key tuple. It is also checked
+          that the second entry in the value tuple is either ``True``, ``False`` or
+          ``'OPTIONAL'``.
+          """
+        for nn_, v_ in _WIN_FUNC_DATA.items():
+            func_name = v_[0].__name__
+            msg = f"Function name in {nn_} does not contain name of actual function!"
+            assert func_name in nn_, msg
+            assert v_[1] in (True, False, 'OPTIONAL')
+
+    @make_xp_test_case(windows.boxcar)
+    def test_boxcar(self, xp):
+        w = windows.get_window('boxcar', 12, xp=xp)
+        xp_assert_equal(w, xp.ones_like(w))
+
+        # window is a tuple of len 1
+        w = windows.get_window(('boxcar',), 16, xp=xp)
+        xp_assert_equal(w, xp.ones_like(w))
+
+    @make_xp_test_case(windows.chebwin)
+    def test_cheb_odd(self, xp):
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", "This window is not suitable", UserWarning)
+            w = windows.get_window(('chebwin', -40), 53, fftbins=False, xp=xp)
+        assert_array_almost_equal(
+            w, xp.asarray(cheb_odd_true, dtype=xp.float64), decimal=4
+        )
+
+    @make_xp_test_case(windows.chebwin)
+    def test_cheb_even(self, xp):
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", "This window is not suitable", UserWarning)
+            w = windows.get_window(('chebwin', 40), 54, fftbins=False, xp=xp)
+        assert_array_almost_equal(w, xp.asarray(cheb_even_true), decimal=4)
+
+    @make_xp_test_case(windows.dpss)
+    def test_dpss(self, xp):
+        win1 = windows.get_window(('dpss', 3), 64, fftbins=False, xp=xp)
+        win2 = windows.dpss(64, 3, xp=xp)
+        xp_assert_equal(win1, win2)
+
+    @make_xp_test_case(windows.kaiser)
+    def test_kaiser_float(self, xp):
+        win1 = windows.get_window(7.2, 64, xp=xp)
+        win2 = windows.kaiser(64, 7.2, False, xp=xp)
+        if is_jax(xp):
+            # On JAX with jit enabled, there is a very small discrepancy
+            # in the results.
+            xp_assert_close(win1, win2, rtol=xp.finfo(win1.dtype).eps)
+        else:
+            xp_assert_equal(win1, win2)
+
+    @pytest.mark.parametrize('Nx', [-1, 3.0, np.float64(3)])
+    @make_xp_test_case(windows.hann)
+    def test_invalid_parameter_NX(self, Nx, xp):
+        with pytest.raises(ValueError, match="^Parameter Nx=.*"):
+            windows.get_window('hann', Nx, xp=xp)
+
+    # noinspection PyTypeChecker
+    def test_invalid_inputs(self, xp):
+        """Raise all exceptions (except those concerning parameter `Nx`). """
+        with pytest.raises(ValueError, match="^Parameter fftbins=.*"):
+            windows.get_window('hann', 5, fftbins=1, xp=xp)
+        with pytest.raises(ValueError, match="^Parameter window=.*"):
+            windows.get_window(['hann',], 5, xp=xp)
+        with pytest.raises(ValueError, match="^First tuple entry of parameter win.*"):
+            windows.get_window((42,), 5, xp=xp)
+        with pytest.raises(ValueError, match="^Invalid window name 'INVALID'.*"):
+            windows.get_window('INVALID', 5, xp=xp)
+        with pytest.raises(ValueError, match="^'hann' does not allow parameters.*"):
+            windows.get_window(('hann', 1), 5, xp=xp)
+        with pytest.raises(ValueError, match="^'kaiser' must have parameters.*"):
+            windows.get_window('kaiser', 5, xp=xp)
+        with pytest.raises(ValueError, match="^Window dpss must have one.*"):
+            windows.get_window(('dpss', 1, 2), 5, xp=xp)
+        with pytest.raises(ValueError, match="^'general_cosine' does not accept.*"):
+            xp_ = xp or np  # ensure parameter xp_ is not None
+            windows.get_window(('general cosine', [1, 2]), 5, xp=xp_)
+
+    @make_xp_test_case(windows.bartlett)
+    def test_symmetric_periodic(self, xp):
+        """Ensure that suffixes `_periodic` and `_symmetric` work for window names. """
+        w_sym = windows.bartlett(5, sym=True, xp=xp)
+        xp_assert_close(get_window('bartlett', 5, fftbins=False, xp=xp), w_sym)
+        xp_assert_close(get_window('bartlett_symmetric', 5, xp=xp), w_sym)
+        # overwrite parameter `fftbins`:
+        xp_assert_close(get_window('bartlett_symmetric', 5, fftbins=True, xp=xp), w_sym)
+
+        w_per = windows.bartlett(5, sym=False, xp=xp)
+        xp_assert_close(get_window('bartlett', 5, xp=xp), w_per)
+        xp_assert_close(get_window('bartlett', 5, fftbins=True, xp=xp), w_per)
+        xp_assert_close(get_window('bartlett_periodic', 5, xp=xp), w_per)
+        # overwrite parameter `fftbins`:
+        xp_assert_close(get_window('bartlett_periodic', 5, fftbins=False, xp=xp),
+                        w_per)
+
+    @make_xp_test_case(windows.kaiser)
+    def test_array_as_window(self, xp):
+        # github issue 3603
+        osfactor = 128
+        sig = xp.arange(128)
+
+        win = windows.get_window(('kaiser', 8.0), osfactor // 2, xp=xp)
+        mesg = "^window must|^window.shape="
+        with assert_raises(ValueError, match=mesg):
+            resample(sig, sig.shape[0] * osfactor, window=win)
+
+    @make_xp_test_case(windows.general_cosine)
+    def test_general_cosine(self, xp):
+        xp_assert_close(get_window(('general_cosine', xp.asarray([0.5, 0.3, 0.2])), 4),
+                        xp.asarray([0.4, 0.3, 1, 0.3], dtype=xp.float64))
+        xp_assert_close(get_window(('general_cosine', xp.asarray([0.5, 0.3, 0.2])), 4,
+                                   fftbins=False),
+                        xp.asarray([0.4, 0.55, 0.55, 0.4], dtype=xp.float64))
+
+        with pytest.raises(ValueError):
+            get_window(('general_cosine', [0.5, 0.3, 0.2]), 4, xp=xp)
+
+    @make_xp_test_case(windows.general_hamming)
+    def test_general_hamming(self, xp):
+        xp_assert_close(get_window(('general_hamming', 0.7), 5, xp=xp),
+                        xp.asarray([0.4, 0.6072949, 0.9427051, 0.9427051, 0.6072949],
+                                   dtype=xp.float64))
+        xp_assert_close(get_window(('general_hamming', 0.7), 5, fftbins=False, xp=xp),
+                        xp.asarray([0.4, 0.7, 1.0, 0.7, 0.4], dtype=xp.float64))
+
+    @make_xp_test_case(windows.lanczos)
+    def test_lanczos(self, xp):
+        xp_assert_close(get_window('lanczos', 6, xp=xp),
+                        xp.asarray([0., 0.413496672, 0.826993343, 1., 0.826993343,
+                                    0.413496672], dtype=xp.float64), atol=1e-9)
+        xp_assert_close(get_window('lanczos', 6, fftbins=False, xp=xp),
+                        xp.asarray([0., 0.504551152, 0.935489284, 0.935489284,
+                                    0.504551152, 0.], dtype=xp.float64), atol=1e-9)
+        xp_assert_close(get_window('lanczos', 6, xp=xp),
+                        get_window('sinc', 6, xp=xp))
+
+    def test_xp_default(self, xp):
+        # no explicit xp= argument, default to numpy
+        win = get_window('lanczos', 6)
+        assert isinstance(win, np.ndarray)
+
+        win = get_window('lanczos', 6, xp=xp)
+        if not is_numpy(xp):
+            assert not isinstance(win, np.ndarray)
+
+
+@make_xp_test_case(windows.general_gaussian)
+class TestGeneralGaussian:
+
+    @pytest.mark.parametrize('M', (6, 7))
+    @pytest.mark.parametrize('p', (1, 1.5))
+    @pytest.mark.parametrize('sig', (1., 2.))
+    @pytest.mark.parametrize('sym', (True, False))
+    def test_basic(self, M, p, sig, sym, xp):
+        """Verify basic parametrizations. """
+        if sym:
+            t = xp.arange(M, dtype=xp.float64) - (M-1) / 2
+        else:
+            t = xp.arange(M+1, dtype=xp.float64) - M / 2
+            t = t[:-1]
+        x_ref = xp.exp(-0.5 * abs(t / sig) ** (2*p))
+        x = windows.general_gaussian(M, p, sig, sym, xp=xp)
+        xp_assert_close(x, x_ref, atol=1e-12)
+
+    def test_default_func_parameter(self, xp):
+        """Verify the correctness of the default value of function parameter `sym`. """
+        x = windows.general_gaussian(6, 1, 1, xp=xp)
+        x_ref = windows.general_gaussian(6, 1, 1, sym=True, xp=xp)
+        xp_assert_equal(x, x_ref)
+
+    def test_p1_equals_gaussian(self,xp):
+        """Testing that `general_gaussian` with p = 1 is equivalent to the normal
+        `gaussian` window. """
+        w1 = windows.general_gaussian(7, p=1.0, sig=2.0, xp=xp)
+        w2 = windows.gaussian(7, std=2.0, xp=xp)
+        xp_assert_close(w1, w2)
+
+    def test_peak_value(self, xp):
+        """ Testing that if M is odd, the peak is at 1. """
+        w = windows.general_gaussian(7, p=3, sig=2.0, xp=xp)
+        assert float(xp.max(w)) == 1.0
+
+        # Testing that if M is even, the peak is less than 1.0
+        w = windows.general_gaussian(6, p=1.5, sig=2.0, xp=xp)
+        assert float(xp.max(w)) < 1.0
+
+    def test_len_edge_cases(self, xp):
+        """Test the length edge cases are handled correctly. """
+        # length = 0 should return an empty array:
+        assert windows.general_gaussian(0, 1, 1, xp=xp).shape[0] == 0
+
+        # length = 1 should return an array of length 1 containing 1.0:
+        xp_assert_close(windows.general_gaussian(1, 1, 1, xp=xp),
+                        xp.asarray([1.0], dtype=xp.float64))
+
+        with pytest.raises(ValueError):  # Negative values should raise an error:
+            windows.general_gaussian(-1, 1, 1, xp=xp)
+
+
+@make_xp_test_case(windows.cosine)
+class TestCosine:
+    @pytest.mark.parametrize('M', (3, 4))
+    @pytest.mark.parametrize('sym', (True, False))
+    def test_basic(self, M, sym, xp):
+        """Verify basic parametrizations. """
+        if sym:
+            t = (xp.arange(M, dtype=xp.float64) + 0.5) / M
+        else:
+            t = (xp.arange(M+1, dtype=xp.float64) + 0.5) / (M+1)
+            t = t[:-1]
+        x_ref = xp.sin(xp.pi * t)
+        x = windows.cosine(M, sym=sym, xp=xp)
+        xp_assert_close(x, x_ref, atol=1e-12)
+
+    def test_default_func_parameter(self, xp):
+        """Verify the correctness of the default value of function parameter `sym`. """
+        x = windows.cosine(6, xp=xp)
+        x_ref = windows.cosine(6, sym=True, xp=xp)
+        xp_assert_equal(x, x_ref)
+
+    def test_len_edge_cases(self, xp):
+        """Testing that the length edge cases are handled correctly."""
+        # length = 0 should return an empty array:
+        assert windows.cosine(0, xp=xp).shape[0] == 0
+
+        # length = 1 should return an array of length 1 containing 1.0:
+        xp_assert_close(windows.cosine(1, xp=xp),
+                        xp.asarray([1.0], dtype=xp.float64))
+
+        with pytest.raises(ValueError):
+            windows.cosine(-1, xp=xp) # negative values should return an error
+
+
+@skip_xp_backends("dask.array", reason="https://github.com/dask/dask/issues/2620")
+@pytest.mark.parametrize(
+    "window,window_name,params",
+    [
+        make_xp_pytest_param(getattr(windows, window_name), window_name, params)
+        for window_name, params in window_funcs
+    ]
+)
+def test_windowfunc_basics(window, window_name, params, xp):
+    window = getattr(windows, window_name)
+    if is_jax(xp) and window_name in ['taylor', 'chebwin']:
+        pytest.skip(reason=f'{window_name = }: item assignment')
+    if window_name in ['dpss']:
+        if is_cupy(xp):
+            pytest.skip(reason='dpss window is not implemented for cupy')
+        if is_torch(xp) and SCIPY_DEVICE != 'cpu':
+            pytest.skip(reason='needs eight_tridiagonal which is CPU only')
+
+    with warnings.catch_warnings():
+        warnings.filterwarnings(
+            "ignore", "This window is not suitable", UserWarning)
+        # Check symmetry for odd and even lengths
+        w1 = window(8, *params, sym=True, xp=xp)
+        w2 = window(7, *params, sym=False, xp=xp)
+        xp_assert_close(w1[:-1], w2)
+
+        w1 = window(9, *params, sym=True, xp=xp)
+        w2 = window(8, *params, sym=False, xp=xp)
+        xp_assert_close(w1[:-1], w2)
+
+        # Check that functions run and output lengths are correct
+        assert window(6, *params, sym=True, xp=xp).shape[0] == 6
+        assert window(6, *params, sym=False, xp=xp).shape[0] == 6
+        assert window(7, *params, sym=True, xp=xp).shape[0] == 7
+        assert window(7, *params, sym=False, xp=xp).shape[0] == 7
+
+        # Check invalid lengths
+        assert_raises(ValueError, window, 5.5, *params, xp=xp)
+        assert_raises(ValueError, window, -7, *params, xp=xp)
+
+        # Check degenerate cases
+        xp_assert_equal(window(0, *params, sym=True, xp=xp),
+                        xp.asarray([], dtype=xp.float64))
+        xp_assert_equal(window(0, *params, sym=False, xp=xp),
+                        xp.asarray([], dtype=xp.float64))
+        xp_assert_equal(window(1, *params, sym=True, xp=xp),
+                        xp.asarray([1.], dtype=xp.float64))
+        xp_assert_equal(window(1, *params, sym=False, xp=xp),
+                        xp.asarray([1.], dtype=xp.float64))
+
+        # Check dtype
+        assert window(0, *params, sym=True, xp=xp).dtype == xp.float64
+        assert window(0, *params, sym=False, xp=xp).dtype == xp.float64
+        assert window(1, *params, sym=True, xp=xp).dtype == xp.float64
+        assert window(1, *params, sym=False, xp=xp).dtype == xp.float64
+        assert window(6, *params, sym=True, xp=xp).dtype == xp.float64
+        assert window(6, *params, sym=False, xp=xp).dtype == xp.float64
+
+        # Check normalization
+        assert xp.all(window(10, *params, sym=True, xp=xp) < 1.01)
+        assert xp.all(window(10, *params, sym=False, xp=xp) < 1.01)
+        assert xp.all(window(9, *params, sym=True, xp=xp) < 1.01)
+        assert xp.all(window(9, *params, sym=False, xp=xp) < 1.01)
+
+        # Check that DFT-even spectrum is purely real for odd and even
+        res = fft(window(10, *params, sym=False, xp=xp))
+        res = xp.imag(res)
+        xp_assert_close(res, xp.zeros_like(res), atol=1e-14)
+
+        res = fft(window(11, *params, sym=False, xp=xp))
+        res = xp.imag(res)
+        xp_assert_close(res, xp.zeros_like(res), atol=1e-14)
+
+
+@make_xp_test_case(get_window)
+def test_needs_params(xp):
+    for winstr in ['kaiser', 'ksr', 'kaiser_bessel_derived', 'kbd',
+                   'gaussian', 'gauss', 'gss',
+                   'general gaussian', 'general_gaussian',
+                   'general gauss', 'general_gauss', 'ggs',
+                   'dss', 'dpss', 'general cosine', 'general_cosine',
+                   'chebwin', 'cheb', 'general hamming', 'general_hamming',
+                   ]:
+        assert_raises(ValueError, get_window, winstr, 7, xp=xp)
+
+
+_winstr = ['barthann',
+           'bartlett',
+           'blackman',
+           'blackmanharris',
+           'bohman',
+           'boxcar',
+           'cosine',
+           'flattop',
+           'hamming',
+           'nuttall',
+           'parzen',
+           'taylor',
+           'exponential',
+           'poisson',
+           'tukey',
+           'tuk',
+           'triangle',
+           'lanczos',
+           'sinc',
+]
+
+
+@pytest.mark.parametrize(
+    'window,winstr',
+    [
+        make_xp_pytest_param(_WIN_FUNCS[winstr][0], winstr)
+        for winstr in _winstr
+    ]
+)
+@make_xp_test_case(get_window)
+def test_not_needs_params(xp, window, winstr):
+    if is_jax(xp) and winstr in ['taylor']:
+        pytest.skip(reason=f'{winstr}: item assignment')
+    win = get_window(winstr, 7, xp=xp)
+    assert win.shape[0] == 7
+
+
+@make_xp_test_case(windows.lanczos)
+def test_symmetric(xp):
+
+    for win in [windows.lanczos]:
+        # Even sampling points
+        w = win(4096, xp=xp)
+        flip = array_namespace(w).flip
+        error = xp.max(xp.abs(w - flip(w)))
+        xp_assert_equal(error, xp.asarray(0.0), check_dtype=False, check_0d=False)
+
+        # Odd sampling points
+        w = win(4097, xp=xp)
+        error = xp.max(xp.abs(w - flip(w)))
+        xp_assert_equal(error, xp.asarray(0.0), check_dtype=False, check_0d=False)
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/waveforms.py b/venv/lib/python3.12/site-packages/scipy/signal/waveforms.py
new file mode 100644
index 0000000000000000000000000000000000000000..30e71348d04276a66470a4053d97cefc60f7136e
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/waveforms.py
@@ -0,0 +1,20 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.signal` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+__all__ = [  # noqa: F822
+    'sawtooth', 'square', 'gausspulse', 'chirp', 'sweep_poly',
+    'unit_impulse',
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="signal", module="waveforms",
+                                   private_modules=["_waveforms"], all=__all__,
+                                   attribute=name)
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/wavelets.py b/venv/lib/python3.12/site-packages/scipy/signal/wavelets.py
new file mode 100644
index 0000000000000000000000000000000000000000..fc897a2483536df7e995faaa29af621e25fe38c7
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/wavelets.py
@@ -0,0 +1,17 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.signal` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+__all__: list[str] = []
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="signal", module="wavelets",
+                                   private_modules=["_wavelets"], all=__all__,
+                                   attribute=name)
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/windows/__init__.py b/venv/lib/python3.12/site-packages/scipy/signal/windows/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..f260df1367a5f9457b1f6e916def853c6c461924
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/windows/__init__.py
@@ -0,0 +1,52 @@
+"""
+Window functions (:mod:`scipy.signal.windows`)
+==============================================
+
+The suite of window functions for filtering and spectral estimation.
+
+.. currentmodule:: scipy.signal.windows
+
+.. autosummary::
+   :toctree: generated/
+
+   get_window              -- Convenience function for creating various windows.
+
+   barthann                -- Bartlett-Hann window
+   bartlett                -- Bartlett window
+   blackman                -- Blackman window
+   blackmanharris          -- Minimum 4-term Blackman-Harris window
+   bohman                  -- Bohman window
+   boxcar                  -- Boxcar window
+   chebwin                 -- Dolph-Chebyshev window
+   cosine                  -- Cosine window
+   dpss                    -- Discrete prolate spheroidal sequences
+   exponential             -- Exponential window
+   flattop                 -- Flat top window
+   gaussian                -- Gaussian window
+   general_cosine          -- Generalized Cosine window
+   general_gaussian        -- Generalized Gaussian window
+   general_hamming         -- Generalized Hamming window
+   hamming                 -- Hamming window
+   hann                    -- Hann window
+   kaiser                  -- Kaiser window
+   kaiser_bessel_derived   -- Kaiser-Bessel derived window
+   lanczos                 -- Lanczos window also known as a sinc window
+   nuttall                 -- Nuttall's minimum 4-term Blackman-Harris window
+   parzen                  -- Parzen window
+   taylor                  -- Taylor window
+   triang                  -- Triangular window
+   tukey                   -- Tukey window
+
+"""
+
+from ._windows import *
+
+# Deprecated namespaces, to be removed in v2.0.0
+from . import windows
+
+__all__ = ['boxcar', 'triang', 'parzen', 'bohman', 'blackman', 'nuttall',
+           'blackmanharris', 'flattop', 'bartlett', 'barthann',
+           'hamming', 'kaiser', 'kaiser_bessel_derived', 'gaussian',
+           'general_gaussian', 'general_cosine', 'general_hamming',
+           'chebwin', 'cosine', 'hann', 'exponential', 'tukey', 'taylor',
+           'get_window', 'dpss', 'lanczos']
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/windows/__pycache__/__init__.cpython-312.pyc b/venv/lib/python3.12/site-packages/scipy/signal/windows/__pycache__/__init__.cpython-312.pyc
new file mode 100644
index 0000000000000000000000000000000000000000..b02fd1c4ea8f3f1462ee8b1294afcc8ef19c6d27
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diff --git a/venv/lib/python3.12/site-packages/scipy/signal/windows/__pycache__/_windows.cpython-312.pyc b/venv/lib/python3.12/site-packages/scipy/signal/windows/__pycache__/_windows.cpython-312.pyc
new file mode 100644
index 0000000000000000000000000000000000000000..668a0e28058f24d02756db1e4bfd79f57174549a
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/windows/__pycache__/_windows.cpython-312.pyc
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:dbb2a464ebf8261df0573828b4b4c8a48d3be20250ebc892a9594b5121501a0a
+size 103532
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/windows/__pycache__/windows.cpython-312.pyc b/venv/lib/python3.12/site-packages/scipy/signal/windows/__pycache__/windows.cpython-312.pyc
new file mode 100644
index 0000000000000000000000000000000000000000..d35897741f253e12dc513a96044b525e3bc9a145
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diff --git a/venv/lib/python3.12/site-packages/scipy/signal/windows/_windows.py b/venv/lib/python3.12/site-packages/scipy/signal/windows/_windows.py
new file mode 100644
index 0000000000000000000000000000000000000000..be9acf3ac5f0cfc5dd4a3728203e87a1be1babb8
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/windows/_windows.py
@@ -0,0 +1,2608 @@
+"""The suite of window functions."""
+
+import math
+import numbers
+import operator
+import warnings
+from scipy._lib import doccer
+
+from scipy import linalg, special, fft as sp_fft
+from scipy._external.array_api_compat import numpy as np_compat
+from scipy._lib._array_api import array_namespace, xp_device
+from scipy._lib._array_api import xp_capabilities
+from scipy._external import array_api_extra as xpx
+
+__all__ = ['boxcar', 'triang', 'parzen', 'bohman', 'blackman', 'nuttall',
+           'blackmanharris', 'flattop', 'bartlett', 'barthann',
+           'hamming', 'kaiser', 'kaiser_bessel_derived', 'gaussian',
+           'general_cosine', 'general_gaussian', 'general_hamming',
+           'chebwin', 'cosine', 'hann', 'exponential', 'tukey', 'taylor',
+           'dpss', 'get_window', 'lanczos']
+
+
+def _len_guards(M):
+    """Handle small or incorrect window lengths"""
+    if int(M) != M or M < 0:
+        raise ValueError('Window length M must be a non-negative integer')
+    return M <= 1
+
+
+def _extend(M, sym):
+    """Extend window by 1 sample if needed for DFT-even symmetry"""
+    if not sym:
+        return M + 1, True
+    else:
+        return M, False
+
+
+def _truncate(w, needed):
+    """Truncate window by 1 sample if needed for DFT-even symmetry"""
+    if needed:
+        return w[:-1]
+    else:
+        return w
+
+
+def _namespace(xp):
+    """A shim for the `device` arg of `np.asarray(x, device=device)` and acos/arccos.
+
+    Will be able to replace with `np_compat if xp is None else xp` when we drop
+    support for numpy 1.x and cupy 13.x
+    """
+    return np_compat if xp is None else array_namespace(xp.empty(0))
+
+
+def _general_cosine_impl(M, a, xp, device, sym=True):
+    if _len_guards(M):
+        return xp.ones(M, dtype=xp.float64, device=device)
+    M, needs_trunc = _extend(M, sym)
+
+    fac = xp.linspace(-xp.pi, xp.pi, M, dtype=xp.float64, device=device)
+    w = xp.zeros(M, dtype=xp.float64, device=device)
+    for k in range(a.shape[0]):
+        w += a[k] * xp.cos(k * fac)
+
+    return _truncate(w, needs_trunc)
+
+
+@xp_capabilities()
+def general_cosine(M, a, sym=True):
+    r"""
+    Generic weighted sum of cosine terms window.
+
+    Parameters
+    ----------
+    M : int
+        Number of points in the output window
+    a : array_like
+        Sequence of weighting coefficients. This uses the convention of being
+        centered on the origin, so these will typically all be positive
+        numbers, not alternating sign.
+    sym : bool, optional
+        When True (default), generates a symmetric window, for use in filter
+        design.
+        When False, generates a periodic window, for use in spectral analysis.
+
+    Returns
+    -------
+    w : ndarray
+        The array of window values.
+
+    References
+    ----------
+    .. [1] A. Nuttall, "Some windows with very good sidelobe behavior," IEEE
+           Transactions on Acoustics, Speech, and Signal Processing, vol. 29,
+           no. 1, pp. 84-91, Feb 1981. :doi:`10.1109/TASSP.1981.1163506`.
+    .. [2] Heinzel G. et al., "Spectrum and spectral density estimation by the
+           Discrete Fourier transform (DFT), including a comprehensive list of
+           window functions and some new flat-top windows", February 15, 2002
+           https://holometer.fnal.gov/GH_FFT.pdf
+
+    Examples
+    --------
+    Heinzel describes a flat-top window named "HFT90D" with formula: [2]_
+
+    .. math::  w_j = 1 - 1.942604 \cos(z) + 1.340318 \cos(2z)
+               - 0.440811 \cos(3z) + 0.043097 \cos(4z)
+
+    where
+
+    .. math::  z = \frac{2 \pi j}{N}, j = 0...N - 1
+
+    Since this uses the convention of starting at the origin, to reproduce the
+    window, we need to convert every other coefficient to a positive number:
+
+    >>> HFT90D = [1, 1.942604, 1.340318, 0.440811, 0.043097]
+
+    The paper states that the highest sidelobe is at -90.2 dB.  Reproduce
+    Figure 42 by plotting the window and its frequency response, and confirm
+    the sidelobe level in red:
+
+    >>> import numpy as np
+    >>> from scipy.signal.windows import general_cosine
+    >>> from scipy.fft import fft, fftshift
+    >>> import matplotlib.pyplot as plt
+
+    >>> window = general_cosine(1000, HFT90D, sym=False)
+    >>> plt.plot(window)
+    >>> plt.title("HFT90D window")
+    >>> plt.ylabel("Amplitude")
+    >>> plt.xlabel("Sample")
+
+    >>> plt.figure()
+    >>> A = fft(window, 10000) / (len(window)/2.0)
+    >>> freq = np.linspace(-0.5, 0.5, len(A))
+    >>> response = np.abs(fftshift(A / abs(A).max()))
+    >>> response = 20 * np.log10(np.maximum(response, 1e-10))
+    >>> plt.plot(freq, response)
+    >>> plt.axis([-50/1000, 50/1000, -140, 0])
+    >>> plt.title("Frequency response of the HFT90D window")
+    >>> plt.ylabel("Normalized magnitude [dB]")
+    >>> plt.xlabel("Normalized frequency [cycles per sample]")
+    >>> plt.axhline(-90.2, color='red')
+    >>> plt.show()
+    """
+    xp = array_namespace(a)
+    a = xp.asarray(a)
+    device = xp_device(a)
+    return _general_cosine_impl(M, a, xp, device, sym=sym)
+
+
+@xp_capabilities()
+def boxcar(M, sym=True, *, xp=None, device=None):
+    """Return a boxcar or rectangular window.
+
+    Also known as a rectangular window or Dirichlet window, this is equivalent
+    to no window at all.
+
+    Parameters
+    ----------
+    M : int
+        Number of points in the output window. If zero, an empty array
+        is returned. An exception is thrown when it is negative.
+    sym : bool, optional
+        Whether the window is symmetric. (Has no effect for boxcar.)
+    %(xp_device_snippet)s
+
+    Returns
+    -------
+    w : ndarray
+        The window, with the maximum value normalized to 1.
+
+    Examples
+    --------
+    Plot the window and its frequency response:
+
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> from scipy.fft import fft, fftshift
+    >>> import matplotlib.pyplot as plt
+
+    >>> window = signal.windows.boxcar(51)
+    >>> plt.plot(window)
+    >>> plt.title("Boxcar window")
+    >>> plt.ylabel("Amplitude")
+    >>> plt.xlabel("Sample")
+
+    >>> plt.figure()
+    >>> A = fft(window, 2048) / (len(window)/2.0)
+    >>> freq = np.linspace(-0.5, 0.5, len(A))
+    >>> response = 20 * np.log10(np.abs(fftshift(A / abs(A).max())))
+    >>> plt.plot(freq, response)
+    >>> plt.axis([-0.5, 0.5, -120, 0])
+    >>> plt.title("Frequency response of the boxcar window")
+    >>> plt.ylabel("Normalized magnitude [dB]")
+    >>> plt.xlabel("Normalized frequency [cycles per sample]")
+
+    """
+    xp = _namespace(xp)
+
+    if _len_guards(M):
+        return xp.ones(M, dtype=xp.float64, device=device)
+    M, needs_trunc = _extend(M, sym)
+
+    w = xp.ones(M, dtype=xp.float64, device=device)
+
+    return _truncate(w, needs_trunc)
+
+
+@xp_capabilities()
+def triang(M, sym=True, *, xp=None, device=None):
+    """Return a triangular window.
+
+    Parameters
+    ----------
+    M : int
+        Number of points in the output window. If zero, an empty array
+        is returned. An exception is thrown when it is negative.
+    sym : bool, optional
+        When True (default), generates a symmetric window, for use in filter
+        design.
+        When False, generates a periodic window, for use in spectral analysis.
+    %(xp_device_snippet)s
+
+    Returns
+    -------
+    w : ndarray
+        The window, with the maximum value normalized to 1 (though the value 1
+        does not appear if `M` is even and `sym` is True).
+
+    See Also
+    --------
+    bartlett : A triangular window that touches zero
+
+    Examples
+    --------
+    Plot the window and its frequency response:
+
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> from scipy.fft import fft, fftshift
+    >>> import matplotlib.pyplot as plt
+
+    >>> window = signal.windows.triang(51)
+    >>> plt.plot(window)
+    >>> plt.title("Triangular window")
+    >>> plt.ylabel("Amplitude")
+    >>> plt.xlabel("Sample")
+
+    >>> plt.figure()
+    >>> A = fft(window, 2048) / (len(window)/2.0)
+    >>> freq = np.linspace(-0.5, 0.5, len(A))
+    >>> response = np.abs(fftshift(A / abs(A).max()))
+    >>> response = 20 * np.log10(np.maximum(response, 1e-10))
+    >>> plt.plot(freq, response)
+    >>> plt.axis([-0.5, 0.5, -120, 0])
+    >>> plt.title("Frequency response of the triangular window")
+    >>> plt.ylabel("Normalized magnitude [dB]")
+    >>> plt.xlabel("Normalized frequency [cycles per sample]")
+
+    """
+    xp = _namespace(xp)
+
+    if _len_guards(M):
+        return xp.ones(M, dtype=xp.float64, device=device)
+    M, needs_trunc = _extend(M, sym)
+
+    n = xp.arange(1, (M + 1) // 2 + 1, dtype=xp.float64, device=device)
+    if M % 2 == 0:
+        w = (2 * n - 1.0) / M
+        w = xp.concat([w, xp.flip(w)])
+    else:
+        w = 2 * n / (M + 1.0)
+        w = xp.concat([w, xp.flip(w[:-1])])
+
+    return _truncate(w, needs_trunc)
+
+
+@xp_capabilities()
+def parzen(M, sym=True, *, xp=None, device=None):
+    """Return a Parzen window.
+
+    Parameters
+    ----------
+    M : int
+        Number of points in the output window. If zero, an empty array
+        is returned. An exception is thrown when it is negative.
+    sym : bool, optional
+        When True (default), generates a symmetric window, for use in filter
+        design.
+        When False, generates a periodic window, for use in spectral analysis.
+    %(xp_device_snippet)s
+
+    Returns
+    -------
+    w : ndarray
+        The window, with the maximum value normalized to 1 (though the value 1
+        does not appear if `M` is even and `sym` is True).
+
+    References
+    ----------
+    .. [1] E. Parzen, "Mathematical Considerations in the Estimation of
+           Spectra", Technometrics,  Vol. 3, No. 2 (May, 1961), pp. 167-190
+
+    Examples
+    --------
+    Plot the window and its frequency response:
+
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> from scipy.fft import fft, fftshift
+    >>> import matplotlib.pyplot as plt
+
+    >>> window = signal.windows.parzen(51)
+    >>> plt.plot(window)
+    >>> plt.title("Parzen window")
+    >>> plt.ylabel("Amplitude")
+    >>> plt.xlabel("Sample")
+
+    >>> plt.figure()
+    >>> A = fft(window, 2048) / (len(window)/2.0)
+    >>> freq = np.linspace(-0.5, 0.5, len(A))
+    >>> response = 20 * np.log10(np.abs(fftshift(A / abs(A).max())))
+    >>> plt.plot(freq, response)
+    >>> plt.axis([-0.5, 0.5, -120, 0])
+    >>> plt.title("Frequency response of the Parzen window")
+    >>> plt.ylabel("Normalized magnitude [dB]")
+    >>> plt.xlabel("Normalized frequency [cycles per sample]")
+
+    """
+    xp = _namespace(xp)
+
+    if _len_guards(M):
+        return xp.ones(M, dtype=xp.float64, device=device)
+    M, needs_trunc = _extend(M, sym)
+
+    n = xp.arange(-(M - 1) / 2.0, (M - 1) / 2.0 + 0.5, 1.0,
+                  dtype=xp.float64, device=device)
+    w = xp.where(abs(n) <= (M - 1) / 4.0,
+                 (1 - 6 * (abs(n) / (M / 2.0)) ** 2.0 +
+                  6 * (abs(n) / (M / 2.0)) ** 3.0),
+                 2 * (1 - abs(n) / (M / 2.0)) ** 3.0)
+    return _truncate(w, needs_trunc)
+
+
+@xp_capabilities()
+def bohman(M, sym=True, *, xp=None, device=None):
+    """Return a Bohman window.
+
+    Parameters
+    ----------
+    M : int
+        Number of points in the output window. If zero, an empty array
+        is returned. An exception is thrown when it is negative.
+    sym : bool, optional
+        When True (default), generates a symmetric window, for use in filter
+        design.
+        When False, generates a periodic window, for use in spectral analysis.
+    %(xp_device_snippet)s
+
+    Returns
+    -------
+    w : ndarray
+        The window, with the maximum value normalized to 1 (though the value 1
+        does not appear if `M` is even and `sym` is True).
+
+    Examples
+    --------
+    Plot the window and its frequency response:
+
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> from scipy.fft import fft, fftshift
+    >>> import matplotlib.pyplot as plt
+
+    >>> window = signal.windows.bohman(51)
+    >>> plt.plot(window)
+    >>> plt.title("Bohman window")
+    >>> plt.ylabel("Amplitude")
+    >>> plt.xlabel("Sample")
+
+    >>> plt.figure()
+    >>> A = fft(window, 2047) / (len(window)/2.0)
+    >>> freq = np.linspace(-0.5, 0.5, len(A))
+    >>> response = 20 * np.log10(np.abs(fftshift(A / abs(A).max())))
+    >>> plt.plot(freq, response)
+    >>> plt.axis([-0.5, 0.5, -120, 0])
+    >>> plt.title("Frequency response of the Bohman window")
+    >>> plt.ylabel("Normalized magnitude [dB]")
+    >>> plt.xlabel("Normalized frequency [cycles per sample]")
+
+    """
+    xp = _namespace(xp)
+
+    if _len_guards(M):
+        return xp.ones(M, dtype=xp.float64, device=device)
+    M, needs_trunc = _extend(M, sym)
+
+    fac = abs(xp.linspace(-1, 1, M, dtype=xp.float64, device=device)[1:-1])
+    w = (1 - fac) * xp.cos(xp.pi * fac) + 1.0 / xp.pi * xp.sin(xp.pi * fac)
+    one = xp.zeros(1, dtype=xp.float64, device=device)
+    w = xp.concat([one, w, one])
+
+    return _truncate(w, needs_trunc)
+
+
+@xp_capabilities()
+def blackman(M, sym=True, *, xp=None, device=None):
+    r"""
+    Return a Blackman window.
+
+    The Blackman window is a taper formed by using the first three terms of
+    a summation of cosines. It was designed to have close to the minimal
+    leakage possible.  It is close to optimal, only slightly worse than a
+    Kaiser window.
+
+    Parameters
+    ----------
+    M : int
+        Number of points in the output window. If zero, an empty array
+        is returned. An exception is thrown when it is negative.
+    sym : bool, optional
+        When True (default), generates a symmetric window, for use in filter
+        design.
+        When False, generates a periodic window, for use in spectral analysis.
+    %(xp_device_snippet)s
+
+    Returns
+    -------
+    w : ndarray
+        The window, with the maximum value normalized to 1 (though the value 1
+        does not appear if `M` is even and `sym` is True).
+
+    Notes
+    -----
+    The Blackman window is defined as
+
+    .. math::  w(n) = 0.42 - 0.5 \cos(2\pi n/M) + 0.08 \cos(4\pi n/M)
+
+    The "exact Blackman" window was designed to null out the third and fourth
+    sidelobes, but has discontinuities at the boundaries, resulting in a
+    6 dB/oct fall-off.  This window is an approximation of the "exact" window,
+    which does not null the sidelobes as well, but is smooth at the edges,
+    improving the fall-off rate to 18 dB/oct. [3]_
+
+    Most references to the Blackman window come from the signal processing
+    literature, where it is used as one of many windowing functions for
+    smoothing values.  It is also known as an apodization (which means
+    "removing the foot", i.e. smoothing discontinuities at the beginning
+    and end of the sampled signal) or tapering function. It is known as a
+    "near optimal" tapering function, almost as good (by some measures)
+    as the Kaiser window.
+
+    References
+    ----------
+    .. [1] Blackman, R.B. and Tukey, J.W., (1958) The measurement of power
+           spectra, Dover Publications, New York.
+    .. [2] Oppenheim, A.V., and R.W. Schafer. Discrete-Time Signal Processing.
+           Upper Saddle River, NJ: Prentice-Hall, 1999, pp. 468-471.
+    .. [3] Harris, Fredric J. (Jan 1978). "On the use of Windows for Harmonic
+           Analysis with the Discrete Fourier Transform". Proceedings of the
+           IEEE 66 (1): 51-83. :doi:`10.1109/PROC.1978.10837`.
+
+    Examples
+    --------
+    Plot the window and its frequency response:
+
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> from scipy.fft import fft, fftshift
+    >>> import matplotlib.pyplot as plt
+
+    >>> window = signal.windows.blackman(51)
+    >>> plt.plot(window)
+    >>> plt.title("Blackman window")
+    >>> plt.ylabel("Amplitude")
+    >>> plt.xlabel("Sample")
+
+    >>> plt.figure()
+    >>> A = fft(window, 2048) / (len(window)/2.0)
+    >>> freq = np.linspace(-0.5, 0.5, len(A))
+    >>> response = np.abs(fftshift(A / abs(A).max()))
+    >>> response = 20 * np.log10(np.maximum(response, 1e-10))
+    >>> plt.plot(freq, response)
+    >>> plt.axis([-0.5, 0.5, -120, 0])
+    >>> plt.title("Frequency response of the Blackman window")
+    >>> plt.ylabel("Normalized magnitude [dB]")
+    >>> plt.xlabel("Normalized frequency [cycles per sample]")
+
+    """
+    # Docstring adapted from NumPy's blackman function
+    xp = _namespace(xp)
+    a = xp.asarray([0.42, 0.50, 0.08], dtype=xp.float64, device=device)
+    device = xp_device(a)
+    return _general_cosine_impl(M, a, xp, device, sym=sym)
+
+
+@xp_capabilities()
+def nuttall(M, sym=True, *, xp=None, device=None):
+    """Return a minimum 4-term Blackman-Harris window according to Nuttall.
+
+    This variation is called "Nuttall4c" by Heinzel. [2]_
+
+    Parameters
+    ----------
+    M : int
+        Number of points in the output window. If zero, an empty array
+        is returned. An exception is thrown when it is negative.
+    sym : bool, optional
+        When True (default), generates a symmetric window, for use in filter
+        design.
+        When False, generates a periodic window, for use in spectral analysis.
+    %(xp_device_snippet)s
+
+    Returns
+    -------
+    w : ndarray
+        The window, with the maximum value normalized to 1 (though the value 1
+        does not appear if `M` is even and `sym` is True).
+
+    References
+    ----------
+    .. [1] A. Nuttall, "Some windows with very good sidelobe behavior," IEEE
+           Transactions on Acoustics, Speech, and Signal Processing, vol. 29,
+           no. 1, pp. 84-91, Feb 1981. :doi:`10.1109/TASSP.1981.1163506`.
+    .. [2] Heinzel G. et al., "Spectrum and spectral density estimation by the
+           Discrete Fourier transform (DFT), including a comprehensive list of
+           window functions and some new flat-top windows", February 15, 2002
+           https://holometer.fnal.gov/GH_FFT.pdf
+
+    Examples
+    --------
+    Plot the window and its frequency response:
+
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> from scipy.fft import fft, fftshift
+    >>> import matplotlib.pyplot as plt
+
+    >>> window = signal.windows.nuttall(51)
+    >>> plt.plot(window)
+    >>> plt.title("Nuttall window")
+    >>> plt.ylabel("Amplitude")
+    >>> plt.xlabel("Sample")
+
+    >>> plt.figure()
+    >>> A = fft(window, 2048) / (len(window)/2.0)
+    >>> freq = np.linspace(-0.5, 0.5, len(A))
+    >>> response = 20 * np.log10(np.abs(fftshift(A / abs(A).max())))
+    >>> plt.plot(freq, response)
+    >>> plt.axis([-0.5, 0.5, -120, 0])
+    >>> plt.title("Frequency response of the Nuttall window")
+    >>> plt.ylabel("Normalized magnitude [dB]")
+    >>> plt.xlabel("Normalized frequency [cycles per sample]")
+
+    """
+    xp = _namespace(xp)
+    a = xp.asarray(
+        [0.3635819, 0.4891775, 0.1365995, 0.0106411], dtype=xp.float64, device=device
+    )
+    device = xp_device(a)
+    return _general_cosine_impl(M, a, xp, device, sym=sym)
+
+
+@xp_capabilities()
+def blackmanharris(M, sym=True, *, xp=None, device=None):
+    """Return a minimum 4-term Blackman-Harris window.
+
+    Parameters
+    ----------
+    M : int
+        Number of points in the output window. If zero, an empty array
+        is returned. An exception is thrown when it is negative.
+    sym : bool, optional
+        When True (default), generates a symmetric window, for use in filter
+        design.
+        When False, generates a periodic window, for use in spectral analysis.
+    %(xp_device_snippet)s
+
+    Returns
+    -------
+    w : ndarray
+        The window, with the maximum value normalized to 1 (though the value 1
+        does not appear if `M` is even and `sym` is True).
+
+    Examples
+    --------
+    Plot the window and its frequency response:
+
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> from scipy.fft import fft, fftshift
+    >>> import matplotlib.pyplot as plt
+
+    >>> window = signal.windows.blackmanharris(51)
+    >>> plt.plot(window)
+    >>> plt.title("Blackman-Harris window")
+    >>> plt.ylabel("Amplitude")
+    >>> plt.xlabel("Sample")
+
+    >>> plt.figure()
+    >>> A = fft(window, 2048) / (len(window)/2.0)
+    >>> freq = np.linspace(-0.5, 0.5, len(A))
+    >>> response = 20 * np.log10(np.abs(fftshift(A / abs(A).max())))
+    >>> plt.plot(freq, response)
+    >>> plt.axis([-0.5, 0.5, -120, 0])
+    >>> plt.title("Frequency response of the Blackman-Harris window")
+    >>> plt.ylabel("Normalized magnitude [dB]")
+    >>> plt.xlabel("Normalized frequency [cycles per sample]")
+
+    """
+    xp = _namespace(xp)
+    a = xp.asarray(
+        [0.35875, 0.48829, 0.14128, 0.01168], dtype=xp.float64, device=device
+    )
+    device = xp_device(a)
+    return _general_cosine_impl(M, a, xp, device, sym=sym)
+
+
+@xp_capabilities()
+def flattop(M, sym=True, *, xp=None, device=None):
+    """Return a flat top window.
+
+    Parameters
+    ----------
+    M : int
+        Number of points in the output window. If zero, an empty array
+        is returned. An exception is thrown when it is negative.
+    sym : bool, optional
+        When True (default), generates a symmetric window, for use in filter
+        design.
+        When False, generates a periodic window, for use in spectral analysis.
+    %(xp_device_snippet)s
+
+    Returns
+    -------
+    w : ndarray
+        The window, with the maximum value normalized to 1 (though the value 1
+        does not appear if `M` is even and `sym` is True).
+
+    Notes
+    -----
+    Flat top windows are used for taking accurate measurements of signal
+    amplitude in the frequency domain, with minimal scalloping error from the
+    center of a frequency bin to its edges, compared to others.  This is a
+    5th-order cosine window, with the 5 terms optimized to make the main lobe
+    maximally flat. [1]_
+
+    References
+    ----------
+    .. [1] D'Antona, Gabriele, and A. Ferrero, "Digital Signal Processing for
+           Measurement Systems", Springer Media, 2006, p. 70
+           :doi:`10.1007/0-387-28666-7`.
+
+    Examples
+    --------
+    Plot the window and its frequency response:
+
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> from scipy.fft import fft, fftshift
+    >>> import matplotlib.pyplot as plt
+
+    >>> window = signal.windows.flattop(51)
+    >>> plt.plot(window)
+    >>> plt.title("Flat top window")
+    >>> plt.ylabel("Amplitude")
+    >>> plt.xlabel("Sample")
+
+    >>> plt.figure()
+    >>> A = fft(window, 2048) / (len(window)/2.0)
+    >>> freq = np.linspace(-0.5, 0.5, len(A))
+    >>> response = 20 * np.log10(np.abs(fftshift(A / abs(A).max())))
+    >>> plt.plot(freq, response)
+    >>> plt.axis([-0.5, 0.5, -120, 0])
+    >>> plt.title("Frequency response of the flat top window")
+    >>> plt.ylabel("Normalized magnitude [dB]")
+    >>> plt.xlabel("Normalized frequency [cycles per sample]")
+
+    """
+    xp = _namespace(xp)
+    a = xp.asarray(
+        [0.21557895, 0.41663158, 0.277263158, 0.083578947, 0.006947368],
+        dtype=xp.float64, device=device
+    )
+    device = xp_device(a)
+    return _general_cosine_impl(M, a, xp, device, sym=sym)
+
+
+@xp_capabilities()
+def bartlett(M, sym=True, *, xp=None, device=None):
+    r"""
+    Return a Bartlett window.
+
+    The Bartlett window is very similar to a triangular window, except
+    that the end points are at zero.  It is often used in signal
+    processing for tapering a signal, without generating too much
+    ripple in the frequency domain.
+
+    Parameters
+    ----------
+    M : int
+        Number of points in the output window. If zero, an empty array
+        is returned. An exception is thrown when it is negative.
+    sym : bool, optional
+        When True (default), generates a symmetric window, for use in filter
+        design.
+        When False, generates a periodic window, for use in spectral analysis.
+    %(xp_device_snippet)s
+
+    Returns
+    -------
+    w : ndarray
+        The triangular window, with the first and last samples equal to zero
+        and the maximum value normalized to 1 (though the value 1 does not
+        appear if `M` is even and `sym` is True).
+
+    See Also
+    --------
+    triang : A triangular window that does not touch zero at the ends
+
+    Notes
+    -----
+    The Bartlett window is defined as
+
+    .. math:: w(n) = \frac{2}{M-1} \left(
+              \frac{M-1}{2} - \left|n - \frac{M-1}{2}\right|
+              \right)
+
+    Most references to the Bartlett window come from the signal
+    processing literature, where it is used as one of many windowing
+    functions for smoothing values.  Note that convolution with this
+    window produces linear interpolation.  It is also known as an
+    apodization (which means"removing the foot", i.e. smoothing
+    discontinuities at the beginning and end of the sampled signal) or
+    tapering function. The Fourier transform of the Bartlett is the product
+    of two sinc functions.
+    Note the excellent discussion in Kanasewich. [2]_
+
+    References
+    ----------
+    .. [1] M.S. Bartlett, "Periodogram Analysis and Continuous Spectra",
+           Biometrika 37, 1-16, 1950.
+    .. [2] E.R. Kanasewich, "Time Sequence Analysis in Geophysics",
+           The University of Alberta Press, 1975, pp. 109-110.
+    .. [3] A.V. Oppenheim and R.W. Schafer, "Discrete-Time Signal
+           Processing", Prentice-Hall, 1999, pp. 468-471.
+    .. [4] Wikipedia, "Window function",
+           https://en.wikipedia.org/wiki/Window_function
+    .. [5] W.H. Press,  B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling,
+           "Numerical Recipes", Cambridge University Press, 1986, page 429.
+
+    Examples
+    --------
+    Plot the window and its frequency response:
+
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> from scipy.fft import fft, fftshift
+    >>> import matplotlib.pyplot as plt
+
+    >>> window = signal.windows.bartlett(51)
+    >>> plt.plot(window)
+    >>> plt.title("Bartlett window")
+    >>> plt.ylabel("Amplitude")
+    >>> plt.xlabel("Sample")
+
+    >>> plt.figure()
+    >>> A = fft(window, 2048) / (len(window)/2.0)
+    >>> freq = np.linspace(-0.5, 0.5, len(A))
+    >>> response = 20 * np.log10(np.abs(fftshift(A / abs(A).max())))
+    >>> plt.plot(freq, response)
+    >>> plt.axis([-0.5, 0.5, -120, 0])
+    >>> plt.title("Frequency response of the Bartlett window")
+    >>> plt.ylabel("Normalized magnitude [dB]")
+    >>> plt.xlabel("Normalized frequency [cycles per sample]")
+
+    """
+    # Docstring adapted from NumPy's bartlett function
+    xp = _namespace(xp)
+
+    if _len_guards(M):
+        return xp.ones(M, dtype=xp.float64, device=device)
+    M, needs_trunc = _extend(M, sym)
+
+    n = xp.arange(0, M, dtype=xp.float64, device=device)
+
+    # cf https://github.com/data-apis/array-api-strict/issues/77
+    w = xp.where(n <= (M - 1) / 2.0,
+                 2.0 * n / (M - 1), 2.0 - 2.0 * n / (M - 1))
+
+    return _truncate(w, needs_trunc)
+
+
+@xp_capabilities()
+def hann(M, sym=True, *, xp=None, device=None):
+    r"""
+    Return a Hann window.
+
+    The Hann window is a taper formed by using a raised cosine or sine-squared
+    with ends that touch zero.
+
+    Parameters
+    ----------
+    M : int
+        Number of points in the output window. If zero, an empty array
+        is returned. An exception is thrown when it is negative.
+    sym : bool, optional
+        When True (default), generates a symmetric window, for use in filter
+        design.
+        When False, generates a periodic window, for use in spectral analysis.
+    %(xp_device_snippet)s
+
+    Returns
+    -------
+    w : ndarray
+        The window, with the maximum value normalized to 1 (though the value 1
+        does not appear if `M` is even and `sym` is True).
+
+    Notes
+    -----
+    The Hann window is defined as
+
+    .. math::  w(n) = 0.5 - 0.5 \cos\left(\frac{2\pi{n}}{M-1}\right)
+               \qquad 0 \leq n \leq M-1
+
+    The window was named for Julius von Hann, an Austrian meteorologist. It is
+    also known as the Cosine Bell. It is sometimes erroneously referred to as
+    the "Hanning" window, from the use of "hann" as a verb in the original
+    paper and confusion with the very similar Hamming window.
+
+    Most references to the Hann window come from the signal processing
+    literature, where it is used as one of many windowing functions for
+    smoothing values.  It is also known as an apodization (which means
+    "removing the foot", i.e. smoothing discontinuities at the beginning
+    and end of the sampled signal) or tapering function.
+
+    References
+    ----------
+    .. [1] Blackman, R.B. and Tukey, J.W., (1958) The measurement of power
+           spectra, Dover Publications, New York.
+    .. [2] E.R. Kanasewich, "Time Sequence Analysis in Geophysics",
+           The University of Alberta Press, 1975, pp. 106-108.
+    .. [3] Wikipedia, "Window function",
+           https://en.wikipedia.org/wiki/Window_function
+    .. [4] W.H. Press,  B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling,
+           "Numerical Recipes", Cambridge University Press, 1986, page 425.
+
+    Examples
+    --------
+    Plot the window and its frequency response:
+
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> from scipy.fft import fft, fftshift
+    >>> import matplotlib.pyplot as plt
+
+    >>> window = signal.windows.hann(51)
+    >>> plt.plot(window)
+    >>> plt.title("Hann window")
+    >>> plt.ylabel("Amplitude")
+    >>> plt.xlabel("Sample")
+
+    >>> plt.figure()
+    >>> A = fft(window, 2048) / (len(window)/2.0)
+    >>> freq = np.linspace(-0.5, 0.5, len(A))
+    >>> response = np.abs(fftshift(A / abs(A).max()))
+    >>> response = 20 * np.log10(np.maximum(response, 1e-10))
+    >>> plt.plot(freq, response)
+    >>> plt.axis([-0.5, 0.5, -120, 0])
+    >>> plt.title("Frequency response of the Hann window")
+    >>> plt.ylabel("Normalized magnitude [dB]")
+    >>> plt.xlabel("Normalized frequency [cycles per sample]")
+
+    """
+    # Docstring adapted from NumPy's hanning function
+    return general_hamming(M, 0.5, sym, xp=xp, device=device)
+
+
+@xp_capabilities()
+def tukey(M, alpha=0.5, sym=True, *, xp=None, device=None):
+    r"""Return a Tukey window, also known as a tapered cosine window.
+
+    Parameters
+    ----------
+    M : int
+        Number of points in the output window. If zero, an empty array
+        is returned. An exception is thrown when it is negative.
+    alpha : float, optional
+        Shape parameter of the Tukey window, representing the fraction of the
+        window inside the cosine tapered region.
+        If zero, the Tukey window is equivalent to a rectangular window.
+        If one, the Tukey window is equivalent to a Hann window.
+    sym : bool, optional
+        When True (default), generates a symmetric window, for use in filter
+        design.
+        When False, generates a periodic window, for use in spectral analysis.
+    %(xp_device_snippet)s
+
+    Returns
+    -------
+    w : ndarray
+        The window, with the maximum value normalized to 1 (though the value 1
+        does not appear if `M` is even and `sym` is True).
+
+    References
+    ----------
+    .. [1] Harris, Fredric J. (Jan 1978). "On the use of Windows for Harmonic
+           Analysis with the Discrete Fourier Transform". Proceedings of the
+           IEEE 66 (1): 51-83. :doi:`10.1109/PROC.1978.10837`
+    .. [2] Wikipedia, "Window function",
+           https://en.wikipedia.org/wiki/Window_function#Tukey_window
+
+    Examples
+    --------
+    Plot the window and its frequency response:
+
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> from scipy.fft import fft, fftshift
+    >>> import matplotlib.pyplot as plt
+
+    >>> window = signal.windows.tukey(51)
+    >>> plt.plot(window)
+    >>> plt.title("Tukey window")
+    >>> plt.ylabel("Amplitude")
+    >>> plt.xlabel("Sample")
+    >>> plt.ylim([0, 1.1])
+
+    >>> plt.figure()
+    >>> A = fft(window, 2048) / (len(window)/2.0)
+    >>> freq = np.linspace(-0.5, 0.5, len(A))
+    >>> response = 20 * np.log10(np.abs(fftshift(A / abs(A).max())))
+    >>> plt.plot(freq, response)
+    >>> plt.axis([-0.5, 0.5, -120, 0])
+    >>> plt.title("Frequency response of the Tukey window")
+    >>> plt.ylabel("Normalized magnitude [dB]")
+    >>> plt.xlabel("Normalized frequency [cycles per sample]")
+
+    """
+    xp = _namespace(xp)
+
+    if _len_guards(M):
+        return xp.ones(M, dtype=xp.float64, device=device)
+
+    if alpha <= 0:
+        return xp.ones(M, dtype=xp.float64, device=device)
+    elif alpha >= 1.0:
+        return hann(M, sym=sym, xp=xp, device=device)
+
+    M, needs_trunc = _extend(M, sym)
+
+    n = xp.arange(0, M, dtype=xp.float64, device=device)
+    width = int(math.floor(alpha*(M-1)/2.0))
+    n1 = n[0:width+1]
+    n2 = n[width+1:M-width-1]
+    n3 = n[M-width-1:]
+
+    w1 = 0.5 * (1 + xp.cos(xp.pi * (-1 + 2.0*n1/alpha/(M-1))))
+    w2 = xp.ones(n2.shape, device=device)
+    w3 = 0.5 * (1 + xp.cos(xp.pi * (-2.0/alpha + 1 + 2.0*n3/alpha/(M-1))))
+
+    w = xp.concat((w1, w2, w3))
+
+    return _truncate(w, needs_trunc)
+
+
+@xp_capabilities()
+def barthann(M, sym=True, *, xp=None, device=None):
+    """Return a modified Bartlett-Hann window.
+
+    Parameters
+    ----------
+    M : int
+        Number of points in the output window. If zero, an empty array
+        is returned. An exception is thrown when it is negative.
+    sym : bool, optional
+        When True (default), generates a symmetric window, for use in filter
+        design.
+        When False, generates a periodic window, for use in spectral analysis.
+    %(xp_device_snippet)s
+
+    Returns
+    -------
+    w : ndarray
+        The window, with the maximum value normalized to 1 (though the value 1
+        does not appear if `M` is even and `sym` is True).
+
+    Examples
+    --------
+    Plot the window and its frequency response:
+
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> from scipy.fft import fft, fftshift
+    >>> import matplotlib.pyplot as plt
+
+    >>> window = signal.windows.barthann(51)
+    >>> plt.plot(window)
+    >>> plt.title("Bartlett-Hann window")
+    >>> plt.ylabel("Amplitude")
+    >>> plt.xlabel("Sample")
+
+    >>> plt.figure()
+    >>> A = fft(window, 2048) / (len(window)/2.0)
+    >>> freq = np.linspace(-0.5, 0.5, len(A))
+    >>> response = 20 * np.log10(np.abs(fftshift(A / abs(A).max())))
+    >>> plt.plot(freq, response)
+    >>> plt.axis([-0.5, 0.5, -120, 0])
+    >>> plt.title("Frequency response of the Bartlett-Hann window")
+    >>> plt.ylabel("Normalized magnitude [dB]")
+    >>> plt.xlabel("Normalized frequency [cycles per sample]")
+
+    """
+    xp = _namespace(xp)
+
+    if _len_guards(M):
+        return xp.ones(M, dtype=xp.float64, device=device)
+    M, needs_trunc = _extend(M, sym)
+
+    n = xp.arange(0, M, dtype=xp.float64, device=device)
+    fac = abs(n / (M - 1.0) - 0.5)
+    w = 0.62 - 0.48 * fac + 0.38 * xp.cos(2 * xp.pi * fac)
+
+    return _truncate(w, needs_trunc)
+
+
+@xp_capabilities()
+def general_hamming(M, alpha, sym=True, *, xp=None, device=None):
+    r"""Return a generalized Hamming window.
+
+    The generalized Hamming window is constructed by multiplying a rectangular
+    window by one period of a cosine function [1]_.
+
+    Parameters
+    ----------
+    M : int
+        Number of points in the output window. If zero, an empty array
+        is returned. An exception is thrown when it is negative.
+    alpha : float
+        The window coefficient, :math:`\alpha`
+    sym : bool, optional
+        When True (default), generates a symmetric window, for use in filter
+        design.
+        When False, generates a periodic window, for use in spectral analysis.
+    %(xp_device_snippet)s
+
+    Returns
+    -------
+    w : ndarray
+        The window, with the maximum value normalized to 1 (though the value 1
+        does not appear if `M` is even and `sym` is True).
+
+    See Also
+    --------
+    hamming, hann
+
+    Notes
+    -----
+    The generalized Hamming window is defined as
+
+    .. math:: w(n) = \alpha - \left(1 - \alpha\right)
+              \cos\left(\frac{2\pi{n}}{M-1}\right) \qquad 0 \leq n \leq M-1
+
+    Both the common Hamming window and Hann window are special cases of the
+    generalized Hamming window with :math:`\alpha` = 0.54 and :math:`\alpha` =
+    0.5, respectively [2]_.
+
+    References
+    ----------
+    .. [1] DSPRelated, "Generalized Hamming Window Family",
+           https://www.dsprelated.com/freebooks/sasp/Generalized_Hamming_Window_Family.html
+    .. [2] Wikipedia, "Window function",
+           https://en.wikipedia.org/wiki/Window_function
+    .. [3] Riccardo Piantanida ESA, "Sentinel-1 Level 1 Detailed Algorithm
+           Definition",
+           https://sentinel.esa.int/documents/247904/1877131/Sentinel-1-Level-1-Detailed-Algorithm-Definition
+    .. [4] Matthieu Bourbigot ESA, "Sentinel-1 Product Definition",
+           https://sentinel.esa.int/documents/247904/1877131/Sentinel-1-Product-Definition
+
+    Examples
+    --------
+    The Sentinel-1A/B Instrument Processing Facility uses generalized Hamming
+    windows in the processing of spaceborne Synthetic Aperture Radar (SAR)
+    data [3]_. The facility uses various values for the :math:`\alpha`
+    parameter based on operating mode of the SAR instrument. Some common
+    :math:`\alpha` values include 0.75, 0.7 and 0.52 [4]_. As an example, we
+    plot these different windows.
+
+    >>> import numpy as np
+    >>> from scipy.signal.windows import general_hamming
+    >>> from scipy.fft import fft, fftshift
+    >>> import matplotlib.pyplot as plt
+
+    >>> fig1, spatial_plot = plt.subplots()
+    >>> spatial_plot.set_title("Generalized Hamming Windows")
+    >>> spatial_plot.set_ylabel("Amplitude")
+    >>> spatial_plot.set_xlabel("Sample")
+
+    >>> fig2, freq_plot = plt.subplots()
+    >>> freq_plot.set_title("Frequency Responses")
+    >>> freq_plot.set_ylabel("Normalized magnitude [dB]")
+    >>> freq_plot.set_xlabel("Normalized frequency [cycles per sample]")
+
+    >>> for alpha in [0.75, 0.7, 0.52]:
+    ...     window = general_hamming(41, alpha)
+    ...     spatial_plot.plot(window, label="{:.2f}".format(alpha))
+    ...     A = fft(window, 2048) / (len(window)/2.0)
+    ...     freq = np.linspace(-0.5, 0.5, len(A))
+    ...     response = 20 * np.log10(np.abs(fftshift(A / abs(A).max())))
+    ...     freq_plot.plot(freq, response, label="{:.2f}".format(alpha))
+    >>> freq_plot.legend(loc="upper right")
+    >>> spatial_plot.legend(loc="upper right")
+
+    """
+    xp = _namespace(xp)
+    a = xp.asarray([alpha, 1. - alpha], dtype=xp.float64, device=device)
+    device = xp_device(a)
+    return _general_cosine_impl(M, a, xp, device, sym=sym)
+
+
+@xp_capabilities()
+def hamming(M, sym=True, *, xp=None, device=None):
+    r"""Return a Hamming window.
+
+    The Hamming window is a taper formed by using a raised cosine with
+    non-zero endpoints, optimized to minimize the nearest side lobe.
+
+    Parameters
+    ----------
+    M : int
+        Number of points in the output window. If zero, an empty array
+        is returned. An exception is thrown when it is negative.
+    sym : bool, optional
+        When True (default), generates a symmetric window, for use in filter
+        design.
+        When False, generates a periodic window, for use in spectral analysis.
+    %(xp_device_snippet)s
+
+    Returns
+    -------
+    w : ndarray
+        The window, with the maximum value normalized to 1 (though the value 1
+        does not appear if `M` is even and `sym` is True).
+
+    Notes
+    -----
+    The Hamming window is defined as
+
+    .. math::  w(n) = 0.54 - 0.46 \cos\left(\frac{2\pi{n}}{M-1}\right)
+               \qquad 0 \leq n \leq M-1
+
+    The Hamming was named for R. W. Hamming, an associate of J. W. Tukey and
+    is described in Blackman and Tukey. It was recommended for smoothing the
+    truncated autocovariance function in the time domain.
+    Most references to the Hamming window come from the signal processing
+    literature, where it is used as one of many windowing functions for
+    smoothing values.  It is also known as an apodization (which means
+    "removing the foot", i.e. smoothing discontinuities at the beginning
+    and end of the sampled signal) or tapering function.
+
+    References
+    ----------
+    .. [1] Blackman, R.B. and Tukey, J.W., (1958) The measurement of power
+           spectra, Dover Publications, New York.
+    .. [2] E.R. Kanasewich, "Time Sequence Analysis in Geophysics", The
+           University of Alberta Press, 1975, pp. 109-110.
+    .. [3] Wikipedia, "Window function",
+           https://en.wikipedia.org/wiki/Window_function
+    .. [4] W.H. Press,  B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling,
+           "Numerical Recipes", Cambridge University Press, 1986, page 425.
+
+    Examples
+    --------
+    Plot the window and its frequency response:
+
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> from scipy.fft import fft, fftshift
+    >>> import matplotlib.pyplot as plt
+
+    >>> window = signal.windows.hamming(51)
+    >>> plt.plot(window)
+    >>> plt.title("Hamming window")
+    >>> plt.ylabel("Amplitude")
+    >>> plt.xlabel("Sample")
+
+    >>> plt.figure()
+    >>> A = fft(window, 2048) / (len(window)/2.0)
+    >>> freq = np.linspace(-0.5, 0.5, len(A))
+    >>> response = 20 * np.log10(np.abs(fftshift(A / abs(A).max())))
+    >>> plt.plot(freq, response)
+    >>> plt.axis([-0.5, 0.5, -120, 0])
+    >>> plt.title("Frequency response of the Hamming window")
+    >>> plt.ylabel("Normalized magnitude [dB]")
+    >>> plt.xlabel("Normalized frequency [cycles per sample]")
+
+    """
+    # Docstring adapted from NumPy's hamming function
+    return general_hamming(M, 0.54, sym, xp=xp, device=device)
+
+
+@xp_capabilities()
+def kaiser(M, beta, sym=True, *, xp=None, device=None):
+    r"""Return a Kaiser window.
+
+    The Kaiser window is a taper formed by using a Bessel function.
+
+    Parameters
+    ----------
+    M : int
+        Number of points in the output window. If zero, an empty array
+        is returned. An exception is thrown when it is negative.
+    beta : float
+        Shape parameter, determines trade-off between main-lobe width and
+        side lobe level. As beta gets large, the window narrows.
+    sym : bool, optional
+        When True (default), generates a symmetric window, for use in filter
+        design.
+        When False, generates a periodic window, for use in spectral analysis.
+    %(xp_device_snippet)s
+
+    Returns
+    -------
+    w : ndarray
+        The window, with the maximum value normalized to 1 (though the value 1
+        does not appear if `M` is even and `sym` is True).
+
+    Notes
+    -----
+    The Kaiser window is defined as
+
+    .. math::  w(n) = I_0\left( \beta \sqrt{1-\frac{4n^2}{(M-1)^2}}
+               \right)/I_0(\beta)
+
+    with
+
+    .. math:: \quad -\frac{M-1}{2} \leq n \leq \frac{M-1}{2},
+
+    where :math:`I_0` is the modified zeroth-order Bessel function.
+
+    The Kaiser was named for Jim Kaiser, who discovered a simple approximation
+    to the DPSS window based on Bessel functions.
+    The Kaiser window is a very good approximation to the discrete prolate
+    spheroidal sequence, or Slepian window, which is the transform which
+    maximizes the energy in the main lobe of the window relative to total
+    energy.
+
+    The Kaiser can approximate other windows by varying the beta parameter.
+    (Some literature uses alpha = beta/pi.) [4]_
+
+    ====  =======================
+    beta  Window shape
+    ====  =======================
+    0     Rectangular
+    5     Similar to a Hamming
+    6     Similar to a Hann
+    8.6   Similar to a Blackman
+    ====  =======================
+
+    A beta value of 14 is probably a good starting point. Note that as beta
+    gets large, the window narrows, and so the number of samples needs to be
+    large enough to sample the increasingly narrow spike, otherwise NaNs will
+    be returned.
+
+    Most references to the Kaiser window come from the signal processing
+    literature, where it is used as one of many windowing functions for
+    smoothing values.  It is also known as an apodization (which means
+    "removing the foot", i.e. smoothing discontinuities at the beginning
+    and end of the sampled signal) or tapering function.
+
+    References
+    ----------
+    .. [1] J. F. Kaiser, "Digital Filters" - Ch 7 in "Systems analysis by
+           digital computer", Editors: F.F. Kuo and J.F. Kaiser, p 218-285.
+           John Wiley and Sons, New York, (1966).
+    .. [2] E.R. Kanasewich, "Time Sequence Analysis in Geophysics", The
+           University of Alberta Press, 1975, pp. 177-178.
+    .. [3] Wikipedia, "Window function",
+           https://en.wikipedia.org/wiki/Window_function
+    .. [4] F. J. Harris, "On the use of windows for harmonic analysis with the
+           discrete Fourier transform," Proceedings of the IEEE, vol. 66,
+           no. 1, pp. 51-83, Jan. 1978. :doi:`10.1109/PROC.1978.10837`.
+
+    Examples
+    --------
+    Plot the window and its frequency response:
+
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> from scipy.fft import fft, fftshift
+    >>> import matplotlib.pyplot as plt
+
+    >>> window = signal.windows.kaiser(51, beta=14)
+    >>> plt.plot(window)
+    >>> plt.title(r"Kaiser window ($\beta$=14)")
+    >>> plt.ylabel("Amplitude")
+    >>> plt.xlabel("Sample")
+
+    >>> plt.figure()
+    >>> A = fft(window, 2048) / (len(window)/2.0)
+    >>> freq = np.linspace(-0.5, 0.5, len(A))
+    >>> response = 20 * np.log10(np.abs(fftshift(A / abs(A).max())))
+    >>> plt.plot(freq, response)
+    >>> plt.axis([-0.5, 0.5, -120, 0])
+    >>> plt.title(r"Frequency response of the Kaiser window ($\beta$=14)")
+    >>> plt.ylabel("Normalized magnitude [dB]")
+    >>> plt.xlabel("Normalized frequency [cycles per sample]")
+
+    """
+    xp = _namespace(xp)
+
+    # Docstring adapted from NumPy's kaiser function
+    if _len_guards(M):
+        return xp.ones(M, dtype=xp.float64, device=device)
+    M, needs_trunc = _extend(M, sym)
+
+    n = xp.arange(0, M, dtype=xp.float64, device=device)
+    alpha = (M - 1) / 2.0
+    w = (special.i0(beta * xp.sqrt(1 - ((n - alpha) / alpha) ** 2.0)) /
+         special.i0(xp.asarray(beta, dtype=xp.float64)))
+
+    return _truncate(w, needs_trunc)
+
+
+@xp_capabilities()
+def kaiser_bessel_derived(M, beta, *, sym=True, xp=None, device=None):
+    """Return a Kaiser-Bessel derived window.
+
+    Parameters
+    ----------
+    M : int
+        Number of points in the output window. If zero, an empty array
+        is returned. An exception is thrown when it is negative.
+        Note that this window is only defined for an even
+        number of points.
+    beta : float
+        Kaiser window shape parameter.
+    sym : bool, optional
+        This parameter only exists to comply with the interface offered by
+        the other window functions and to be callable by `get_window`.
+        When True (default), generates a symmetric window, for use in filter
+        design.
+    %(xp_device_snippet)s
+
+    Returns
+    -------
+    w : ndarray
+        The window, normalized to fulfil the Princen-Bradley condition.
+
+    See Also
+    --------
+    kaiser
+
+    Notes
+    -----
+    It is designed to be suitable for use with the modified discrete cosine
+    transform (MDCT) and is mainly used in audio signal processing and
+    audio coding.
+
+    .. versionadded:: 1.9.0
+
+    References
+    ----------
+    .. [1] Bosi, Marina, and Richard E. Goldberg. Introduction to Digital
+           Audio Coding and Standards. Dordrecht: Kluwer, 2003.
+    .. [2] Wikipedia, "Kaiser window",
+           https://en.wikipedia.org/wiki/Kaiser_window
+
+    Examples
+    --------
+    Plot the Kaiser-Bessel derived window based on the wikipedia
+    reference [2]_:
+
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+    >>> fig, ax = plt.subplots()
+    >>> N = 50
+    >>> for alpha in [0.64, 2.55, 7.64, 31.83]:
+    ...     ax.plot(signal.windows.kaiser_bessel_derived(2*N, np.pi*alpha),
+    ...             label=f"{alpha=}")
+    >>> ax.grid(True)
+    >>> ax.set_title("Kaiser-Bessel derived window")
+    >>> ax.set_ylabel("Amplitude")
+    >>> ax.set_xlabel("Sample")
+    >>> ax.set_xticks([0, N, 2*N-1])
+    >>> ax.set_xticklabels(["0", "N", "2N+1"])  # doctest: +SKIP
+    >>> ax.set_yticks([0.0, 0.2, 0.4, 0.6, 0.707, 0.8, 1.0])
+    >>> fig.legend(loc="center")
+    >>> fig.tight_layout()
+    >>> fig.show()
+    """
+    xp = _namespace(xp)
+
+    if not sym:
+        raise ValueError(
+            "Kaiser-Bessel Derived windows are only defined for symmetric "
+            "shapes"
+        )
+    elif M < 1:
+        return xp.asarray([])
+    elif M % 2:
+        raise ValueError(
+            "Kaiser-Bessel Derived windows are only defined for even number "
+            "of points"
+        )
+
+    kaiser_window = kaiser(M // 2 + 1, beta, xp=xp, device=device)
+    csum = xp.cumulative_sum(kaiser_window)
+    half_window = xp.sqrt(csum[:-1] / csum[-1])
+    w = xp.concat((half_window, xp.flip(half_window)), axis=0)
+    return xp.asarray(w, device=device)
+
+
+@xp_capabilities()
+def gaussian(M, std, sym=True, *, xp=None, device=None):
+    r"""Return a Gaussian window.
+
+    Parameters
+    ----------
+    M : int
+        Number of points in the output window. If zero, an empty array
+        is returned. An exception is thrown when it is negative.
+    std : float
+        The standard deviation, sigma.
+    sym : bool, optional
+        When True (default), generates a symmetric window, for use in filter
+        design.
+        When False, generates a periodic window, for use in spectral analysis.
+    %(xp_device_snippet)s
+
+    Returns
+    -------
+    w : ndarray
+        The window, with the maximum value normalized to 1 (though the value 1
+        does not appear if `M` is even and `sym` is True).
+
+    Notes
+    -----
+    The Gaussian window is defined as
+
+    .. math::  w(n) = e^{ -\frac{1}{2}\left(\frac{n}{\sigma}\right)^2 }
+
+    Examples
+    --------
+    Plot the window and its frequency response:
+
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> from scipy.fft import fft, fftshift
+    >>> import matplotlib.pyplot as plt
+
+    >>> window = signal.windows.gaussian(51, std=7)
+    >>> plt.plot(window)
+    >>> plt.title(r"Gaussian window ($\sigma$=7)")
+    >>> plt.ylabel("Amplitude")
+    >>> plt.xlabel("Sample")
+
+    >>> plt.figure()
+    >>> A = fft(window, 2048) / (len(window)/2.0)
+    >>> freq = np.linspace(-0.5, 0.5, len(A))
+    >>> response = 20 * np.log10(np.abs(fftshift(A / abs(A).max())))
+    >>> plt.plot(freq, response)
+    >>> plt.axis([-0.5, 0.5, -120, 0])
+    >>> plt.title(r"Frequency response of the Gaussian window ($\sigma$=7)")
+    >>> plt.ylabel("Normalized magnitude [dB]")
+    >>> plt.xlabel("Normalized frequency [cycles per sample]")
+
+    """
+    xp = _namespace(xp)
+
+    if _len_guards(M):
+        return xp.ones(M, dtype=xp.float64, device=device)
+    M, needs_trunc = _extend(M, sym)
+
+    n = xp.arange(0, M, dtype=xp.float64, device=device) - (M - 1.0) / 2.0
+    sig2 = 2 * std * std
+    w = xp.exp(-n ** 2 / sig2)
+
+    return _truncate(w, needs_trunc)
+
+
+@xp_capabilities()
+def general_gaussian(M, p, sig, sym=True, *, xp=None, device=None):
+    r"""Return a window with a generalized Gaussian shape.
+
+    Parameters
+    ----------
+    M : int
+        Number of points in the output window. If zero, an empty array
+        is returned. An exception is thrown when it is negative.
+    p : float
+        Shape parameter.  p = 1 is identical to `gaussian`, p = 0.5 is
+        the same shape as the Laplace distribution.
+    sig : float
+        The standard deviation, sigma.
+    sym : bool, optional
+        When True (default), generates a symmetric window, for use in filter
+        design.
+        When False, generates a periodic window, for use in spectral analysis.
+    %(xp_device_snippet)s
+
+    Returns
+    -------
+    w : ndarray
+        The window, with the maximum value normalized to 1 (though the value 1
+        does not appear if `M` is even and `sym` is True).
+
+    Notes
+    -----
+    The generalized Gaussian window is defined as
+
+    .. math::  w(n) = e^{ -\frac{1}{2}\left|\frac{n}{\sigma}\right|^{2p} }
+
+    the half-power point is at
+
+    .. math::  (2 \log(2))^{1/(2 p)} \sigma
+
+    Examples
+    --------
+    Plot the window and its frequency response:
+
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> from scipy.fft import fft, fftshift
+    >>> import matplotlib.pyplot as plt
+
+    >>> window = signal.windows.general_gaussian(51, p=1.5, sig=7)
+    >>> plt.plot(window)
+    >>> plt.title(r"Generalized Gaussian window (p=1.5, $\sigma$=7)")
+    >>> plt.ylabel("Amplitude")
+    >>> plt.xlabel("Sample")
+
+    >>> plt.figure()
+    >>> A = fft(window, 2048) / (len(window)/2.0)
+    >>> freq = np.linspace(-0.5, 0.5, len(A))
+    >>> response = 20 * np.log10(np.abs(fftshift(A / abs(A).max())))
+    >>> plt.plot(freq, response)
+    >>> plt.axis([-0.5, 0.5, -120, 0])
+    >>> plt.title(r"Freq. resp. of the gen. Gaussian "
+    ...           r"window (p=1.5, $\sigma$=7)")
+    >>> plt.ylabel("Normalized magnitude [dB]")
+    >>> plt.xlabel("Normalized frequency [cycles per sample]")
+
+    """
+    xp = _namespace(xp)
+
+    if _len_guards(M):
+        return xp.ones(M, dtype=xp.float64, device=device)
+    M, needs_trunc = _extend(M, sym)
+
+    n = xp.arange(0, M, dtype=xp.float64, device=device) - (M - 1.0) / 2.0
+    w = xp.exp(-0.5 * abs(n / sig) ** (2 * p))
+
+    return _truncate(w, needs_trunc)
+
+
+# `chebwin` contributed by Kumar Appaiah.
+@xp_capabilities(skip_backends=(("jax.numpy", "item assignment"),
+                                ("dask.array", "data-dependent output shapes")))
+def chebwin(M, at, sym=True, *, xp=None, device=None):
+    r"""Return a Dolph-Chebyshev window.
+
+    Parameters
+    ----------
+    M : int
+        Number of points in the output window. If zero, an empty array
+        is returned. An exception is thrown when it is negative.
+    at : float
+        Attenuation (in dB).
+    sym : bool, optional
+        When True (default), generates a symmetric window, for use in filter
+        design.
+        When False, generates a periodic window, for use in spectral analysis.
+    %(xp_device_snippet)s
+
+    Returns
+    -------
+    w : ndarray
+        The window, with the maximum value always normalized to 1
+
+    Notes
+    -----
+    This window optimizes for the narrowest main lobe width for a given order
+    `M` and sidelobe equiripple attenuation `at`, using Chebyshev
+    polynomials.  It was originally developed by Dolph to optimize the
+    directionality of radio antenna arrays.
+
+    Unlike most windows, the Dolph-Chebyshev is defined in terms of its
+    frequency response:
+
+    .. math:: W(k) = \frac
+              {\cos\{M \cos^{-1}[\beta \cos(\frac{\pi k}{M})]\}}
+              {\cosh[M \cosh^{-1}(\beta)]}
+
+    where
+
+    .. math:: \beta = \cosh \left [\frac{1}{M}
+              \cosh^{-1}(10^\frac{A}{20}) \right ]
+
+    and 0 <= abs(k) <= M-1. A is the attenuation in decibels (`at`).
+
+    The time domain window is then generated using the IFFT, so
+    power-of-two `M` are the fastest to generate, and prime number `M` are
+    the slowest.
+
+    The equiripple condition in the frequency domain creates impulses in the
+    time domain, which appear at the ends of the window.
+
+    References
+    ----------
+    .. [1] C. Dolph, "A current distribution for broadside arrays which
+           optimizes the relationship between beam width and side-lobe level",
+           Proceedings of the IEEE, Vol. 34, Issue 6
+    .. [2] Peter Lynch, "The Dolph-Chebyshev Window: A Simple Optimal Filter",
+           American Meteorological Society (April 1997)
+           http://mathsci.ucd.ie/~plynch/Publications/Dolph.pdf
+    .. [3] F. J. Harris, "On the use of windows for harmonic analysis with the
+           discrete Fourier transforms", Proceedings of the IEEE, Vol. 66,
+           No. 1, January 1978
+
+    Examples
+    --------
+    Plot the window and its frequency response:
+
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> from scipy.fft import fft, fftshift
+    >>> import matplotlib.pyplot as plt
+
+    >>> window = signal.windows.chebwin(51, at=100)
+    >>> plt.plot(window)
+    >>> plt.title("Dolph-Chebyshev window (100 dB)")
+    >>> plt.ylabel("Amplitude")
+    >>> plt.xlabel("Sample")
+
+    >>> plt.figure()
+    >>> A = fft(window, 2048) / (len(window)/2.0)
+    >>> freq = np.linspace(-0.5, 0.5, len(A))
+    >>> response = 20 * np.log10(np.abs(fftshift(A / abs(A).max())))
+    >>> plt.plot(freq, response)
+    >>> plt.axis([-0.5, 0.5, -120, 0])
+    >>> plt.title("Frequency response of the Dolph-Chebyshev window (100 dB)")
+    >>> plt.ylabel("Normalized magnitude [dB]")
+    >>> plt.xlabel("Normalized frequency [cycles per sample]")
+
+    """
+    xp = _namespace(xp)
+
+    if abs(at) < 45:
+        warnings.warn("This window is not suitable for spectral analysis "
+                      "for attenuation values lower than about 45dB because "
+                      "the equivalent noise bandwidth of a Chebyshev window "
+                      "does not grow monotonically with increasing sidelobe "
+                      "attenuation when the attenuation is smaller than "
+                      "about 45 dB.",
+                      stacklevel=2)
+    if _len_guards(M):
+        return xp.ones(M, dtype=xp.float64, device=device)
+    M, needs_trunc = _extend(M, sym)
+
+    # compute the parameter beta
+    order = M - 1.0
+    _val = xp.asarray(10 ** (abs(at) / 20.), dtype=xp.float64, device=device)
+    beta = xp.cosh(1.0 / order * xp.acosh(_val))
+    k = xp.arange(M, dtype=xp.float64, device=device)
+    x = beta * xp.cos(xp.pi * k / M)
+    # Find the window's DFT coefficients
+    # Use analytic definition of Chebyshev polynomial instead of expansion
+    # from scipy.special. Using the expansion in scipy.special leads to errors.
+    p = xp.zeros_like(x)
+    p[x > 1] = xp.cosh(order * xp.acosh(x[x > 1]))
+    p[x < -1] = (2 * (M % 2) - 1) * xp.cosh(order * xp.acosh(-x[x < -1]))
+    p[abs(x) <= 1] = xp.cos(order * xp.acos(x[abs(x) <= 1]))
+
+    # Appropriate IDFT and filling up
+    # depending on even/odd M
+    if M % 2:
+        w = xp.real(sp_fft.fft(p))
+        n = (M + 1) // 2
+        w = w[:n]
+        w = xp.concat((xp.flip(w[1:n]), w))
+    else:
+        p = p * xp.exp(1j * xp.pi / M * xp.arange(M, dtype=xp.float64, device=device))
+        w = xp.real(sp_fft.fft(p))
+        n = M // 2 + 1
+        w = xp.concat((xp.flip(w[1:n]), w[1:n]))
+    w = w / xp.max(w)
+
+    return _truncate(w, needs_trunc)
+
+
+@xp_capabilities()
+def cosine(M, sym=True, *, xp=None, device=None):
+    """Return a window with a simple cosine shape.
+
+    Parameters
+    ----------
+    M : int
+        Number of points in the output window. If zero, an empty array
+        is returned. An exception is thrown when it is negative.
+    sym : bool, optional
+        When True (default), generates a symmetric window, for use in filter
+        design.
+        When False, generates a periodic window, for use in spectral analysis.
+    %(xp_device_snippet)s
+
+    Returns
+    -------
+    w : ndarray
+        The window, with the maximum value normalized to 1 (though the value 1
+        does not appear if `M` is even and `sym` is True).
+
+    Notes
+    -----
+
+    .. versionadded:: 0.13.0
+
+    Examples
+    --------
+    Plot the window and its frequency response:
+
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> from scipy.fft import fft, fftshift
+    >>> import matplotlib.pyplot as plt
+
+    >>> window = signal.windows.cosine(51)
+    >>> plt.plot(window)
+    >>> plt.title("Cosine window")
+    >>> plt.ylabel("Amplitude")
+    >>> plt.xlabel("Sample")
+
+    >>> plt.figure()
+    >>> A = fft(window, 2047) / (len(window)/2.0)
+    >>> freq = np.linspace(-0.5, 0.5, len(A))
+    >>> response = 20 * np.log10(np.abs(fftshift(A / abs(A).max())))
+    >>> plt.plot(freq, response)
+    >>> plt.axis([-0.5, 0.5, -120, 0])
+    >>> plt.title("Frequency response of the cosine window")
+    >>> plt.ylabel("Normalized magnitude [dB]")
+    >>> plt.xlabel("Normalized frequency [cycles per sample]")
+    >>> plt.show()
+
+    """
+    xp = _namespace(xp)
+
+    if _len_guards(M):
+        return xp.ones(M, dtype=xp.float64, device=device)
+    M, needs_trunc = _extend(M, sym)
+
+    w = xp.sin(xp.pi / M * (xp.arange(M, dtype=xp.float64, device=device) + .5))
+
+    return _truncate(w, needs_trunc)
+
+
+@xp_capabilities()
+def exponential(M, center=None, tau=1., sym=True, *, xp=None, device=None):
+    r"""Return an exponential (or Poisson) window.
+
+    Parameters
+    ----------
+    M : int
+        Number of points in the output window. If zero, an empty array
+        is returned. An exception is thrown when it is negative.
+    center : float, optional
+        Parameter defining the center location of the window function.
+        The default value if not given is ``center = (M-1) / 2``.  This
+        parameter must take its default value for symmetric windows.
+    tau : float, optional
+        Parameter defining the decay.  For ``center = 0`` use
+        ``tau = -(M-1) / ln(x)`` if ``x`` is the fraction of the window
+        remaining at the end.
+    sym : bool, optional
+        When True (default), generates a symmetric window, for use in filter
+        design.
+        When False, generates a periodic window, for use in spectral analysis.
+    %(xp_device_snippet)s
+
+    Returns
+    -------
+    w : ndarray
+        The window, with the maximum value normalized to 1 (though the value 1
+        does not appear if `M` is even and `sym` is True).
+
+    Notes
+    -----
+    The Exponential window is defined as
+
+    .. math::  w(n) = e^{-|n-center| / \tau}
+
+    References
+    ----------
+    .. [1] S. Gade and H. Herlufsen, "Windows to FFT analysis (Part I)",
+           Technical Review 3, Bruel & Kjaer, 1987.
+
+    Examples
+    --------
+    Plot the symmetric window and its frequency response:
+
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> from scipy.fft import fft, fftshift
+    >>> import matplotlib.pyplot as plt
+
+    >>> M = 51
+    >>> tau = 3.0
+    >>> window = signal.windows.exponential(M, tau=tau)
+    >>> plt.plot(window)
+    >>> plt.title("Exponential Window (tau=3.0)")
+    >>> plt.ylabel("Amplitude")
+    >>> plt.xlabel("Sample")
+
+    >>> plt.figure()
+    >>> A = fft(window, 2048) / (len(window)/2.0)
+    >>> freq = np.linspace(-0.5, 0.5, len(A))
+    >>> response = 20 * np.log10(np.abs(fftshift(A / abs(A).max())))
+    >>> plt.plot(freq, response)
+    >>> plt.axis([-0.5, 0.5, -35, 0])
+    >>> plt.title("Frequency response of the Exponential window (tau=3.0)")
+    >>> plt.ylabel("Normalized magnitude [dB]")
+    >>> plt.xlabel("Normalized frequency [cycles per sample]")
+
+    This function can also generate non-symmetric windows:
+
+    >>> tau2 = -(M-1) / np.log(0.01)
+    >>> window2 = signal.windows.exponential(M, 0, tau2, False)
+    >>> plt.figure()
+    >>> plt.plot(window2)
+    >>> plt.ylabel("Amplitude")
+    >>> plt.xlabel("Sample")
+    """
+    xp = _namespace(xp)
+
+    if sym and center is not None:
+        raise ValueError("If sym==True, center must be None.")
+    if _len_guards(M):
+        return xp.ones(M, dtype=xp.float64, device=device)
+    M, needs_trunc = _extend(M, sym)
+
+    if center is None:
+        center = (M-1) / 2
+
+    n = xp.arange(0, M, dtype=xp.float64, device=device)
+    w = xp.exp(-abs(n-center) / tau)
+
+    return _truncate(w, needs_trunc)
+
+
+@xp_capabilities(skip_backends=[("jax.numpy", "item assignment")])
+def taylor(M, nbar=4, sll=30, norm=True, sym=True, *, xp=None, device=None):
+    """
+    Return a Taylor window.
+
+    The Taylor window taper function approximates the Dolph-Chebyshev window's
+    constant sidelobe level for a parameterized number of near-in sidelobes,
+    but then allows a taper beyond [2]_.
+
+    The SAR (synthetic aperture radar) community commonly uses Taylor
+    weighting for image formation processing because it provides strong,
+    selectable sidelobe suppression with minimum broadening of the
+    mainlobe [1]_.
+
+    Parameters
+    ----------
+    M : int
+        Number of points in the output window. If zero, an empty array
+        is returned. An exception is thrown when it is negative.
+    nbar : int, optional
+        Number of nearly constant level sidelobes adjacent to the mainlobe.
+    sll : float, optional
+        Desired suppression of sidelobe level in decibels (dB) relative to the
+        DC gain of the mainlobe. This should be a positive number.
+    norm : bool, optional
+        When True (default), divides the window by the largest (middle) value
+        for odd-length windows or the value that would occur between the two
+        repeated middle values for even-length windows such that all values
+        are less than or equal to 1. When False the DC gain will remain at 1
+        (0 dB) and the sidelobes will be `sll` dB down.
+    sym : bool, optional
+        When True (default), generates a symmetric window, for use in filter
+        design.
+        When False, generates a periodic window, for use in spectral analysis.
+    %(xp_device_snippet)s
+
+    Returns
+    -------
+    out : array
+        The window. When `norm` is True (default), the maximum value is
+        normalized to 1 (though the value 1 does not appear if `M` is
+        even and `sym` is True).
+
+    See Also
+    --------
+    chebwin, kaiser, bartlett, blackman, hamming, hann
+
+    References
+    ----------
+    .. [1] W. Carrara, R. Goodman, and R. Majewski, "Spotlight Synthetic
+           Aperture Radar: Signal Processing Algorithms" Pages 512-513,
+           July 1995.
+    .. [2] Armin Doerry, "Catalog of Window Taper Functions for
+           Sidelobe Control", 2017.
+           https://www.researchgate.net/profile/Armin_Doerry/publication/316281181_Catalog_of_Window_Taper_Functions_for_Sidelobe_Control/links/58f92cb2a6fdccb121c9d54d/Catalog-of-Window-Taper-Functions-for-Sidelobe-Control.pdf
+
+    Examples
+    --------
+    Plot the window and its frequency response:
+
+    >>> import numpy as np
+    >>> from scipy import signal
+    >>> from scipy.fft import fft, fftshift
+    >>> import matplotlib.pyplot as plt
+
+    >>> window = signal.windows.taylor(51, nbar=20, sll=100, norm=False)
+    >>> plt.plot(window)
+    >>> plt.title("Taylor window (100 dB)")
+    >>> plt.ylabel("Amplitude")
+    >>> plt.xlabel("Sample")
+
+    >>> plt.figure()
+    >>> A = fft(window, 2048) / (len(window)/2.0)
+    >>> freq = np.linspace(-0.5, 0.5, len(A))
+    >>> response = 20 * np.log10(np.abs(fftshift(A / abs(A).max())))
+    >>> plt.plot(freq, response)
+    >>> plt.axis([-0.5, 0.5, -120, 0])
+    >>> plt.title("Frequency response of the Taylor window (100 dB)")
+    >>> plt.ylabel("Normalized magnitude [dB]")
+    >>> plt.xlabel("Normalized frequency [cycles per sample]")
+
+    """  # noqa: E501
+    xp = _namespace(xp)
+
+    if _len_guards(M):
+        return xp.ones(M, dtype=xp.float64, device=device)
+    M, needs_trunc = _extend(M, sym)
+
+    # Original text uses a negative sidelobe level parameter and then negates
+    # it in the calculation of B. To keep consistent with other methods we
+    # assume the sidelobe level parameter to be positive.
+    B = xp.asarray(10**(sll / 20), device=device)
+    A = xp.acosh(B) / xp.pi
+    s2 = nbar**2 / (A**2 + (nbar - 0.5)**2)
+    ma = xp.arange(1, nbar, dtype=xp.float64, device=device)
+
+    Fm = xp.empty(nbar - 1, dtype=xp.float64, device=device)
+    signs = xp.empty_like(ma)
+    signs[::2] = 1
+    signs[1::2] = -1
+    m2 = ma*ma
+    for mi, m in enumerate(ma):
+        numer = signs[mi] * xp.prod(1 - m2[mi]/s2/(A**2 + (ma - 0.5)**2))
+        denom = 2 * xp.prod(1 - m2[mi]/m2[:mi]) * xp.prod(1 - m2[mi]/m2[mi+1:])
+        Fm[mi] = numer / denom
+
+    def W(n):
+        return 1 + 2*xp.matmul(Fm, xp.cos(
+            2*xp.pi*ma[:, xp.newaxis]*(n-M/2.+0.5)/M))
+
+    w = W(xp.arange(M, dtype=xp.float64, device=device))
+
+    # normalize (Note that this is not described in the original text [1])
+    if norm:
+        scale = 1.0 / W((M - 1) / 2)
+        w *= scale
+
+    return _truncate(w, needs_trunc)
+
+
+@xp_capabilities(np_only=True, reason='banded linear algebra is numpy-only')
+def dpss(M, NW, Kmax=None, sym=True, norm=None, return_ratios=False,
+         *, xp=None, device=None):
+    """
+    Compute the Discrete Prolate Spheroidal Sequences (DPSS).
+
+    DPSS (or Slepian sequences) are often used in multitaper power spectral
+    density estimation (see [1]_). The first window in the sequence can be
+    used to maximize the energy concentration in the main lobe, and is also
+    called the Slepian window.
+
+    Parameters
+    ----------
+    M : int
+        Window length.
+    NW : float
+        Standardized half bandwidth corresponding to ``2*NW = BW/f0 = BW*M*dt``
+        where ``dt`` is taken as 1.
+    Kmax : int | None, optional
+        Number of DPSS windows to return (orders ``0`` through ``Kmax-1``).
+        If None (default), return only a single window of shape ``(M,)``
+        instead of an array of windows of shape ``(Kmax, M)``.
+    sym : bool, optional
+        When True (default), generates a symmetric window, for use in filter
+        design.
+        When False, generates a periodic window, for use in spectral analysis.
+    norm : {2, 'approximate', 'subsample'} | None, optional
+        If 'approximate' or 'subsample', then the windows are normalized by the
+        maximum, and a correction scale-factor for even-length windows
+        is applied either using ``M**2/(M**2+NW)`` ("approximate") or
+        a FFT-based subsample shift ("subsample"), see Notes for details.
+        If None, then "approximate" is used when ``Kmax=None`` and 2 otherwise
+        (which uses the l2 norm).
+    return_ratios : bool, optional
+        If True, also return the concentration ratios in addition to the
+        windows.
+    %(xp_device_snippet)s
+
+    Returns
+    -------
+    v : ndarray, shape (Kmax, M) or (M,)
+        The DPSS windows. Will be 1D if `Kmax` is None.
+    r : ndarray, shape (Kmax,) or float, optional
+        The concentration ratios for the windows. Only returned if
+        `return_ratios` evaluates to True. Will be 0D if `Kmax` is None.
+
+    Notes
+    -----
+    This computation uses the tridiagonal eigenvector formulation given
+    in [2]_.
+
+    The default normalization for ``Kmax=None``, i.e. window-generation mode,
+    simply using the l-infinity norm would create a window with two unity
+    values, which creates slight normalization differences between even and odd
+    orders. The approximate correction of ``M**2/float(M**2+NW)`` for even
+    sample numbers is used to counteract this effect (see Examples below).
+
+    For very long signals (e.g., 1e6 elements), it can be useful to compute
+    windows orders of magnitude shorter and use interpolation (e.g.,
+    `scipy.interpolate.interp1d`) to obtain tapers of length `M`,
+    but this in general will not preserve orthogonality between the tapers.
+
+    .. versionadded:: 1.1
+
+    References
+    ----------
+    .. [1] Percival DB, Walden WT. Spectral Analysis for Physical Applications:
+       Multitaper and Conventional Univariate Techniques.
+       Cambridge University Press; 1993.
+    .. [2] Slepian, D. Prolate spheroidal wave functions, Fourier analysis, and
+       uncertainty V: The discrete case. Bell System Technical Journal,
+       Volume 57 (1978), 1371430.
+    .. [3] Kaiser, JF, Schafer RW. On the Use of the I0-Sinh Window for
+       Spectrum Analysis. IEEE Transactions on Acoustics, Speech and
+       Signal Processing. ASSP-28 (1): 105-107; 1980.
+
+    Examples
+    --------
+    We can compare the window to `kaiser`, which was invented as an alternative
+    that was easier to calculate [3]_ (example adapted from
+    `here <https://ccrma.stanford.edu/~jos/sasp/Kaiser_DPSS_Windows_Compared.html>`_):
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.signal import windows, freqz
+    >>> M = 51
+    >>> fig, axes = plt.subplots(3, 2, figsize=(5, 7))
+    >>> for ai, alpha in enumerate((1, 3, 5)):
+    ...     win_dpss = windows.dpss(M, alpha)
+    ...     beta = alpha*np.pi
+    ...     win_kaiser = windows.kaiser(M, beta)
+    ...     for win, c in ((win_dpss, 'k'), (win_kaiser, 'r')):
+    ...         win /= win.sum()
+    ...         axes[ai, 0].plot(win, color=c, lw=1.)
+    ...         axes[ai, 0].set(xlim=[0, M-1], title=rf'$\\alpha$ = {alpha}',
+    ...                         ylabel='Amplitude')
+    ...         w, h = freqz(win)
+    ...         axes[ai, 1].plot(w, 20 * np.log10(np.abs(h)), color=c, lw=1.)
+    ...         axes[ai, 1].set(xlim=[0, np.pi],
+    ...                         title=rf'$\\beta$ = {beta:0.2f}',
+    ...                         ylabel='Magnitude (dB)')
+    >>> for ax in axes.ravel():
+    ...     ax.grid(True)
+    >>> axes[2, 1].legend(['DPSS', 'Kaiser'])
+    >>> fig.tight_layout()
+    >>> plt.show()
+
+    And here are examples of the first four windows, along with their
+    concentration ratios:
+
+    >>> M = 512
+    >>> NW = 2.5
+    >>> win, eigvals = windows.dpss(M, NW, 4, return_ratios=True)
+    >>> fig, ax = plt.subplots(1)
+    >>> ax.plot(win.T, linewidth=1.)
+    >>> ax.set(xlim=[0, M-1], ylim=[-0.1, 0.1], xlabel='Samples',
+    ...        title=f'DPSS, {M:d}, {NW:0.1f}')
+    >>> ax.legend([f'win[{ii}] ({ratio:0.4f})'
+    ...            for ii, ratio in enumerate(eigvals)])
+    >>> fig.tight_layout()
+    >>> plt.show()
+
+    Using a standard :math:`l_{\\infty}` norm would produce two unity values
+    for even `M`, but only one unity value for odd `M`. This produces uneven
+    window power that can be counteracted by the approximate correction
+    ``M**2/float(M**2+NW)``, which can be selected by using
+    ``norm='approximate'`` (which is the same as ``norm=None`` when
+    ``Kmax=None``, as is the case here). Alternatively, the slower
+    ``norm='subsample'`` can be used, which uses subsample shifting in the
+    frequency domain (FFT) to compute the correction:
+
+    >>> Ms = np.arange(1, 41)
+    >>> factors = (50, 20, 10, 5, 2.0001)
+    >>> energy = np.empty((3, len(Ms), len(factors)))
+    >>> for mi, M in enumerate(Ms):
+    ...     for fi, factor in enumerate(factors):
+    ...         NW = M / float(factor)
+    ...         # Corrected using empirical approximation (default)
+    ...         win = windows.dpss(M, NW)
+    ...         energy[0, mi, fi] = np.sum(win ** 2) / np.sqrt(M)
+    ...         # Corrected using subsample shifting
+    ...         win = windows.dpss(M, NW, norm='subsample')
+    ...         energy[1, mi, fi] = np.sum(win ** 2) / np.sqrt(M)
+    ...         # Uncorrected (using l-infinity norm)
+    ...         win /= win.max()
+    ...         energy[2, mi, fi] = np.sum(win ** 2) / np.sqrt(M)
+    >>> fig, ax = plt.subplots(1)
+    >>> hs = ax.plot(Ms, energy[2], '-o', markersize=4,
+    ...              markeredgecolor='none')
+    >>> leg = [hs[-1]]
+    >>> for hi, hh in enumerate(hs):
+    ...     h1 = ax.plot(Ms, energy[0, :, hi], '-o', markersize=4,
+    ...                  color=hh.get_color(), markeredgecolor='none',
+    ...                  alpha=0.66)
+    ...     h2 = ax.plot(Ms, energy[1, :, hi], '-o', markersize=4,
+    ...                  color=hh.get_color(), markeredgecolor='none',
+    ...                  alpha=0.33)
+    ...     if hi == len(hs) - 1:
+    ...         leg.insert(0, h1[0])
+    ...         leg.insert(0, h2[0])
+    >>> ax.set(xlabel='M (samples)', ylabel=r'Power / $\\sqrt{M}$')
+    >>> ax.legend(leg, ['Uncorrected', r'Corrected: $\\frac{M^2}{M^2+NW}$',
+    ...                 'Corrected (subsample)'])
+    >>> fig.tight_layout()
+
+    """
+    xp = _namespace(xp)
+
+    if norm is None:
+        norm = 'approximate' if Kmax is None else 2
+    known_norms = (2, 'approximate', 'subsample')
+    if norm not in known_norms:
+        raise ValueError(f'norm must be one of {known_norms}, got {norm}')
+    if Kmax is None:
+        singleton = True
+        Kmax = 1
+    else:
+        singleton = False
+    if _len_guards(M):
+        if not return_ratios:
+            return xp.ones(M, dtype=xp.float64)
+        elif singleton:
+            return xp.ones(M, dtype=xp.float64), 1.
+        else:
+            return xp.ones(M, dtype=xp.float64), xp.ones(1, dtype=xp.float64)
+    Kmax = operator.index(Kmax)
+    if not 0 < Kmax <= M:
+        raise ValueError('Kmax must be greater than 0 and less than M')
+    if NW >= M/2.:
+        raise ValueError('NW must be less than M/2.')
+    if NW <= 0:
+        raise ValueError('NW must be positive')
+    M, needs_trunc = _extend(M, sym)
+    W = float(NW) / M
+    nidx = xp.arange(M, dtype=xp.float64, device=device)
+
+    # Here we want to set up an optimization problem to find a sequence
+    # whose energy is maximally concentrated within band [-W,W].
+    # Thus, the measure lambda(T,W) is the ratio between the energy within
+    # that band, and the total energy. This leads to the eigen-system
+    # (A - (l1)I)v = 0, where the eigenvector corresponding to the largest
+    # eigenvalue is the sequence with maximally concentrated energy. The
+    # collection of eigenvectors of this system are called Slepian
+    # sequences, or discrete prolate spheroidal sequences (DPSS). Only the
+    # first K, K = 2NW/dt orders of DPSS will exhibit good spectral
+    # concentration
+    # [see https://en.wikipedia.org/wiki/Spectral_concentration_problem]
+
+    # Here we set up an alternative symmetric tri-diagonal eigenvalue
+    # problem such that
+    # (B - (l2)I)v = 0, and v are our DPSS (but eigenvalues l2 != l1)
+    # the main diagonal = ([M-1-2*t]/2)**2 cos(2PIW), t=[0,1,2,...,M-1]
+    # and the first off-diagonal = t(M-t)/2, t=[1,2,...,M-1]
+    # [see Percival and Walden, 1993]
+    d = ((M - 1 - 2 * nidx) / 2.) ** 2 * xp.cos(xp.asarray(2 * xp.pi * W))
+    e = nidx[1:] * (M - nidx[1:]) / 2.
+
+    # only calculate the highest Kmax eigenvalues
+    w, windows = linalg.eigh_tridiagonal(
+        d, e, select='i', select_range=(M - Kmax, M - 1))
+    w = w[::-1]
+    windows = windows[:, ::-1].T
+
+    # By convention (Percival and Walden, 1993 pg 379)
+    # * symmetric tapers (k=0,2,4,...) should have a positive average.
+    fix_even = (windows[::2, ...].sum(axis=1) < 0)
+    for i, f in enumerate(fix_even):
+        if f:
+            windows[2 * i] *= -1
+    # * antisymmetric tapers should begin with a positive lobe
+    #   (this depends on the definition of "lobe", here we'll take the first
+    #   point above the numerical noise, which should be good enough for
+    #   sufficiently smooth functions, and more robust than relying on an
+    #   algorithm that uses max(abs(w)), which is susceptible to numerical
+    #   noise problems)
+    thresh = max(1e-7, 1. / M)
+    for i, w in enumerate(windows[1::2, ...]):
+        if w[w * w > thresh][0] < 0:
+            windows[2 * i + 1] *= -1
+
+    # Now find the eigenvalues of the original spectral concentration problem
+    # Use the autocorr sequence technique from Percival and Walden, 1993 pg 390
+    if return_ratios:
+        dpss_rxx = _fftautocorr(xp.asarray(windows))
+        r = 4 * W * xpx.sinc(xp.asarray(2 * W * nidx), xp=xp)
+        r[0] = 2 * W
+        ratios = xp.matmul(dpss_rxx, r)
+        if singleton:
+            ratios = ratios[0]
+        ratios = xp.asarray(ratios, device=device)
+    # Deal with sym and Kmax=None
+    if norm != 2:
+        windows /= windows.max()
+        if M % 2 == 0:
+            if norm == 'approximate':
+                correction = M**2 / float(M**2 + NW)
+            else:
+                s = sp_fft.rfft(windows[0])
+                shift = -(1 - 1./M) * xp.arange(1, M//2 + 1, dtype=xp.float64)
+                s[1:] *= 2 * xp.exp(-1j * xp.pi * shift)
+                correction = M / s.real.sum()
+            windows *= correction
+    # else we're already l2 normed, so do nothing
+    if needs_trunc:
+        windows = windows[:, :-1]
+    if singleton:
+        windows = windows[0]
+    windows = xp.asarray(windows, device=device)
+    return (windows, ratios) if return_ratios else windows
+
+
+@xp_capabilities()
+def lanczos(M, *, sym=True, xp=None, device=None):
+    r"""Return a Lanczos window also known as a sinc window.
+
+    Parameters
+    ----------
+    M : int
+        Number of points in the output window. If zero, an empty array
+        is returned. An exception is thrown when it is negative.
+    sym : bool, optional
+        When True (default), generates a symmetric window, for use in filter
+        design.
+        When False, generates a periodic window, for use in spectral analysis.
+    %(xp_device_snippet)s
+
+    Returns
+    -------
+    w : ndarray
+        The window, with the maximum value normalized to 1 (though the value 1
+        does not appear if `M` is even and `sym` is True).
+
+    Notes
+    -----
+    The Lanczos window is defined as
+
+    .. math::  w(n) = sinc \left( \frac{2n}{M - 1} - 1 \right)
+
+    where
+
+    .. math::  sinc(x) = \frac{\sin(\pi x)}{\pi x}
+
+    The Lanczos window has reduced Gibbs oscillations and is widely used for
+    filtering climate timeseries with good properties in the physical and
+    spectral domains.
+
+    .. versionadded:: 1.10
+
+    References
+    ----------
+    .. [1] Lanczos, C., and Teichmann, T. (1957). Applied analysis.
+           Physics Today, 10, 44.
+    .. [2] Duchon C. E. (1979) Lanczos Filtering in One and Two Dimensions.
+           Journal of Applied Meteorology, Vol 18, pp 1016-1022.
+    .. [3] Thomson, R. E. and Emery, W. J. (2014) Data Analysis Methods in
+           Physical Oceanography (Third Edition), Elsevier, pp 593-637.
+    .. [4] Wikipedia, "Window function",
+           http://en.wikipedia.org/wiki/Window_function
+
+    Examples
+    --------
+    Plot the window
+
+    >>> import numpy as np
+    >>> from scipy.signal.windows import lanczos
+    >>> from scipy.fft import fft, fftshift
+    >>> import matplotlib.pyplot as plt
+    >>> fig, ax = plt.subplots(1)
+    >>> window = lanczos(51)
+    >>> ax.plot(window)
+    >>> ax.set_title("Lanczos window")
+    >>> ax.set_ylabel("Amplitude")
+    >>> ax.set_xlabel("Sample")
+    >>> fig.tight_layout()
+    >>> plt.show()
+
+    and its frequency response:
+
+    >>> fig, ax = plt.subplots(1)
+    >>> A = fft(window, 2048) / (len(window)/2.0)
+    >>> freq = np.linspace(-0.5, 0.5, len(A))
+    >>> response = 20 * np.log10(np.abs(fftshift(A / abs(A).max())))
+    >>> ax.plot(freq, response)
+    >>> ax.set_xlim(-0.5, 0.5)
+    >>> ax.set_ylim(-120, 0)
+    >>> ax.set_title("Frequency response of the lanczos window")
+    >>> ax.set_ylabel("Normalized magnitude [dB]")
+    >>> ax.set_xlabel("Normalized frequency [cycles per sample]")
+    >>> fig.tight_layout()
+    >>> plt.show()
+    """
+    xp = _namespace(xp)
+
+    if _len_guards(M):
+        return xp.ones(M, dtype=xp.float64, device=device)
+    M, needs_trunc = _extend(M, sym)
+
+    # To make sure that the window is symmetric, we concatenate the right hand
+    # half of the window and the flipped one which is the left hand half of
+    # the window.
+    def _calc_right_side_lanczos(n, m):
+        return xpx.sinc(2. * xp.arange(n, m, dtype=xp.float64) / (m - 1) - 1.0, xp=xp)
+
+    if M % 2 == 0:
+        wh = _calc_right_side_lanczos(M/2, M)
+        w = xp.concat([xp.flip(wh), wh])
+    else:
+        wh = _calc_right_side_lanczos((M+1)/2, M)
+        w = xp.concat([xp.flip(wh), xp.ones(1), wh])
+
+    return _truncate(w, needs_trunc)
+
+
+def _fftautocorr(x):
+    """Compute the autocorrelation of a real array and crop the result."""
+    N = x.shape[-1]
+    use_N = sp_fft.next_fast_len(2*N-1)
+    x_fft = sp_fft.rfft(x, use_N, axis=-1)
+    cxy = sp_fft.irfft(x_fft * x_fft.conj(), n=use_N)[:, :N]
+    # Or equivalently (but in most cases slower):
+    # cxy = xp.asarray([xp.convolve(xx, yy[::-1], mode='full')
+    #                   for xx, yy in zip(x, x)])[:, N-1:2*N-1]
+    return cxy
+
+_WIN_FUNC_DATA = { # Format: {(name0, name1, ...): (function, needs parameters)
+    ('barthann', 'brthan', 'bth'): (barthann, False),
+    ('bartlett', 'bart', 'brt'): (bartlett, False),
+    ('blackman', 'black', 'blk'): (blackman, False),
+    ('blackmanharris', 'blackharr', 'bkh'): (blackmanharris, False),
+    ('bohman', 'bman', 'bmn'): (bohman, False),
+    ('boxcar', 'box', 'ones', 'rect', 'rectangular'): (boxcar, False),
+    ('chebwin', 'cheb'): (chebwin, True),
+    ('cosine', 'halfcosine'): (cosine, False),
+    ('dpss',): (dpss, True),
+    ('exponential', 'poisson'): (exponential, 'OPTIONAL'),
+    ('flattop', 'flat', 'flt'): (flattop, False),
+    ('gaussian', 'gauss', 'gss'): (gaussian, True),
+    ('general cosine', 'general_cosine'): (general_cosine, True),
+    ('general gaussian', 'general_gaussian', 'general gauss',
+     'general_gauss', 'ggs'): (general_gaussian, True),
+    ('general hamming', 'general_hamming'): (general_hamming, True),
+    ('hamming', 'hamm', 'ham'): (hamming, False),
+    ('hann', 'han'): (hann, False),
+    ('kaiser', 'ksr'): (kaiser, True),
+    ('kaiser bessel derived', 'kaiser_bessel_derived',
+     'kbd'): (kaiser_bessel_derived, True),
+    ('lanczos', 'sinc'): (lanczos, False),
+    ('nuttall', 'nutl', 'nut'): (nuttall, False),
+    ('parzen', 'parz', 'par'): (parzen, False),
+    ('taylor', 'taylorwin'): (taylor, 'OPTIONAL'),
+    ('triangle', 'triang', 'tri'): (triang, False),
+    ('tukey', 'tuk'): (tukey, 'OPTIONAL'), }
+_WIN_FUNCS = dict()
+for nn_, v_ in _WIN_FUNC_DATA.items():
+    _WIN_FUNCS.update({n_: v_ for n_ in nn_})
+
+
+@xp_capabilities()
+def get_window(window, Nx, fftbins=True, *, xp=None, device=None):
+    r"""Convenience function for creating various windows.
+
+    This function is a wrapper for the window functions provided in the
+    `scipy.signal.windows` namespace.
+
+    Parameters
+    ----------
+    window : str | tuple | float
+        Either a string with the window name or a tuple consisting of window name and
+        window parameters. If it is a float, a `~scipy.singal.kaiser` window is
+        created with `window` being the shape parameter. Consult the Notes below for
+        more details.
+    Nx : int
+        The number of samples in the window.
+    fftbins : bool, optional
+        If ``True`` (default), create a periodic window, ready to use with `ifftshift`
+        and be multiplied by the result of an FFT (see also
+        :func:`~scipy.fft.fftfreq`). If ``False``, create a symmetric window, for use
+        in filter design. This parameter is ignored, if the window name in the
+        `window` parameter has a suffix ``'_periodic'`` or ``'_symmetric'`` appended to
+        it (e.g., ``'hann_symmetric'``).
+    %(xp_device_snippet)s
+
+    Returns
+    -------
+    get_window : ndarray
+        Returns the created window as a one-dimensional array made of `Nx` samples.
+
+    Raises
+    ------
+    ValueError
+        If the provided parameters do not allow to choose a valid window function
+        with valid parameters.
+
+    Notes
+    -----
+    Note that by default this function returns a periodic window, whereas the wrapped
+    window functions return a symmetric window by default. This is caused by the
+    `fftbins` parameter having the inverse meaning of the `sym` parameter of the
+    wrapped function, which are both ``True`` by default.
+
+    .. currentmodule:: scipy.signal.windows
+
+    The following list shows the wrapped window functions with the respective settings
+    of the `window` parameter followed by a short description. Aliases for alternative
+    window names are given in parenthesis.
+
+    `barthann` / ``'barthann'``:
+        Modified Bartlett-Hann window (aliases: ``'brthan', 'bth'``)
+    `bartlett` / ``'bartlett'``:
+        Bartlett window (aliases: ``'bart', 'brt'``)
+    `blackman`/ ``'blackman'``:
+        Blackman window (aliases: ``'black', 'blk'``)
+    `blackmanharris` / ``'blackmanharris'``:
+        4-term Blackman-Harris window (aliases: ``'blackharr', 'bkh'``)
+    `bohman` / ``'bohman'``:
+        Bohman window (aliases: ``'bman', 'bmn'``)
+    `boxcar` / ``'boxcar'``:
+        Rectangular window (aliases: ``'box', 'ones', 'rect', 'rectangular'``)
+    `chebwin` / ``('chebwin', at)``:
+        Dolph-Chebyshev window with `at` dB attenuation (aliases: ``'cheb'``)
+    `cosine` / ``'cosine'``:
+        Cosine window (aliases: ``'halfcosine'``)
+    `dpss` / ``('dpss', NW)``:
+        First window of discrete prolate spheroidal sequence with standardized half
+        bandwidth ``NW`` and "approximate" norm.
+    `exponential` / ``'exponential'`` / ``('exponential', center, tau)``:
+        Exponential / Poisson window centered at ``center`` (default: ``None``) with
+        deacy ``tau`` (default: ``1``) (aliases: ``'poisson'``)
+    `flattop`/ ``'flattop'``:
+        Flat top window (aliases: ``'flat', 'flt'``)
+    `gaussian` / ``('gaussian', std)``:
+        Gaussian with standard deviation `std` (aliases: ``'gauss', 'gss'``)
+    `general_cosine` / ``('general cosine', a)``:
+        Generic weighted sum of cosine terms with weighting coefficients ``a``
+        (aliases: ``'general_cosine'``)
+    `general_gaussian` / ``('general gaussian', p, sig)``:
+        Generalized Gaussian with shape parameter ``p`` and standard deviation ``sig``
+        (aliases: ``'general_gaussian', 'general gauss', 'general_gauss', 'ggs'``)
+    `general_hamming` / ``('general hamming', alpha)``:
+        Generalized Hamming window with coefficent ``alpha``
+        (aliases: ``'general_hamming'``)
+    `hamming` / ``'hamming'``:
+        Hamming window (aliases: ``'hamm', 'ham'``)
+    `hann` / ``'hann'``:
+        Hann window (aliases: ``'han'``)
+    `kaiser` / ``('kaiser', beta)``:
+        Kaiser window with shape parameter ``beta`` (aliases: ``'ksr'``)
+    `kaiser_bessel_derived` / ``('kaiser bessel derived', beta)``:
+        Kaiser-Bessel derived window with shape parameter ``beta``
+        (aliases: ``'kaiser_bessel_derived', 'kbd'``)
+    `lanczos` / ``'lanczos'``:
+        Lanczos / sinc window (aliases: ``'sinc'``)
+    `nuttall`/ ``'nuttall'``:
+        Minimum 4-term Blackman-Harris window according to Nuttall
+        (aliases: ``'nutl', 'nut'``)
+    `parzen` / ``'parzen'``:
+        Parzen window (aliases: ``'parz', 'par'``)
+    `taylor` / ``'taylor'`` / (``'taylor', nbar, sll, norm)``:
+        Taylor window with ``nbar`` adjascent sidelobes (default: ``4``)), ``sll`` dB
+        suppression level (default: ``30``) and boolean value ``norm``
+        (default: ``True``) (aliases: ``taylorwin``)
+    `triang`/ ``'triangle'``:
+        Triangle window (aliases: ``'triang', 'tri'``)
+    `tukey` / ``'tukey'`` / ``('tukey', alpha)``:
+        Tukey window with shape parameter ``alpha`` (default: ``0.5``)
+        (aliases: ``'tuk'``)
+
+
+    Examples
+    --------
+    This example shows different usages of the `window` parameter:
+
+    >>> from scipy.signal import get_window
+    >>> get_window('triang', 7)
+    array([ 0.125,  0.375,  0.625,  0.875,  0.875,  0.625,  0.375])
+    >>> get_window(('exponential', None, 1.), 9)
+    array([ 0.011109  ,  0.03019738,  0.082085  ,  0.22313016,  0.60653066,
+            0.60653066,  0.22313016,  0.082085  ,  0.03019738])
+    >>> get_window(('kaiser', 4.0), 9)
+    array([ 0.08848053,  0.29425961,  0.56437221,  0.82160913,  0.97885093,
+            0.97885093,  0.82160913,  0.56437221,  0.29425961])
+    >>> get_window(4.0, 9)  # same as previous call
+    array([ 0.08848053,  0.29425961,  0.56437221,  0.82160913,  0.97885093,
+            0.97885093,  0.82160913,  0.56437221,  0.29425961])
+
+    The following snippet shows different ways to create identical symmetric and
+    periodic Bartlett windows:
+
+    >>> from scipy.signal import get_window, windows
+    >>> # Symmetric window:
+    >>> windows.bartlett(5)  # Parameter `sym` defaults to True
+    array([0. , 0.5, 1. , 0.5, 0. ])
+    >>> get_window('bartlett', 5, fftbins=False)
+    array([0. , 0.5, 1. , 0.5, 0. ])
+    >>> get_window('bartlett_symmetric', 5)
+    array([0. , 0.5, 1. , 0.5, 0. ])
+    >>> # Periodic window:
+    >>> windows.bartlett(4, sym=False)
+    array([0. , 0.5, 1. , 0.5])
+    >>> get_window('bartlett', 4)  # Parameter `fftbins` defaults to True
+    array([0. , 0.5, 1. , 0.5])
+    >>> get_window('bartlett_periodic', 4)
+    array([0. , 0.5, 1. , 0.5])
+    >>> # `_periodic' suffix overrides `fftbins` parameter:
+    >>> get_window('bartlett_periodic', 4, fftbins=False)
+    array([0. , 0.5, 1. , 0.5])
+
+    Note that a periodic window can be created out of a symmetric window by discarding
+    the last sample.
+    """
+    if not (Nx > 0 and isinstance(Nx, numbers.Integral)):
+        raise ValueError(f"Parameter {Nx=} is not a positive integer")
+    if not isinstance(fftbins, bool):
+        raise ValueError(f"Parameter {fftbins=} is not of type bool!")
+
+    if not isinstance(window, str | tuple):
+        try: # if parameter window can be converted to a float, return kaiser window:
+            beta = float(window)
+        except Exception as float_exception:
+            err_msg = f"Parameter {window=} must be a tuple, a string or a float!"
+            raise ValueError(err_msg) from float_exception
+        return kaiser(Nx, beta, not fftbins, xp=xp, device=device)
+
+    if isinstance(window, tuple) and not isinstance(window[0], str):
+        raise ValueError(f"First tuple entry of parameter {window=} is not a str!")
+
+    sym = not fftbins
+    win_name = window if isinstance(window, str) else window[0]
+    if win_name.endswith('_symmetric'):  # overwrite `fftbins` / `sym` if needed
+        sym, win_name = True, win_name[:-10]  # remove '_symmetric' from `win_name`
+    elif win_name.endswith('_periodic'):
+        sym, win_name = False, win_name[:-9]  # remove '_periodic' from `win_name`
+
+    if win_name not in _WIN_FUNCS:
+        raise ValueError(f"Invalid window name '{win_name}' in parameter {window=}!")
+
+    func, has_args = _WIN_FUNCS[win_name]
+    args = window[1:] if isinstance(window, tuple) else tuple()
+    if len(args) > 0 and has_args is False:
+        raise ValueError(f"'{win_name}' does not allow parameters, but {window=}!")
+    if len(args) == 0 and has_args is True:
+        raise ValueError(f"'{win_name}' must have parameters, but {window=}!")
+    # has_args == 'OPTIONAL' allows len(args) == 0 as well as len(args) > 0
+
+    if not has_args:
+        return func(Nx, sym=sym, xp=xp, device=device)
+
+    # special cases taken from original implementation:
+    if func is dpss:
+        if len(args) != 1:
+            raise ValueError(f"Window {win_name} must have one parameter but {window=}")
+        return dpss(Nx, args[0], Kmax=None, sym=sym, xp=xp, device=device)
+    if func is general_cosine:
+        if not (xp is None and device is None):
+            raise ValueError("'general_cosine' does not accept the parameters xp " +
+                             "and device not being None!")
+        return general_cosine(Nx, *args, sym=sym)
+
+    return func(Nx, *args, sym=sym, xp=xp, device=device)
+
+
+########## complete the docstrings, on import
+_xp_device_snippet = {'xp_device_snippet':
+"""\
+xp : array_namespace, optional
+    Optional array namespace.
+    Should be compatible with the array API standard, or supported by array-api-compat.
+    Default: ``numpy``
+device : any
+    optional device specification for output. Should match one of the
+    supported device specification in ``xp``.
+"""
+}
+
+
+_names = [x for x in __all__ if x != 'general_cosine']
+for name in _names:
+    window = vars()[name]
+    window.__doc__ = doccer.docformat(window.__doc__, _xp_device_snippet)
diff --git a/venv/lib/python3.12/site-packages/scipy/signal/windows/windows.py b/venv/lib/python3.12/site-packages/scipy/signal/windows/windows.py
new file mode 100644
index 0000000000000000000000000000000000000000..6858f71aceeb29ca6110864d01fb250e8c8ce403
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/signal/windows/windows.py
@@ -0,0 +1,23 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.signal.windows` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+__all__ = [  # noqa: F822
+    'boxcar', 'triang', 'parzen', 'bohman', 'blackman', 'nuttall',
+    'blackmanharris', 'flattop', 'bartlett', 'barthann',
+    'hamming', 'kaiser', 'gaussian', 'general_cosine',
+    'general_gaussian', 'general_hamming', 'chebwin', 'cosine',
+    'hann', 'exponential', 'tukey', 'taylor', 'dpss', 'get_window',
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="signal.windows", module="windows",
+                                   private_modules=["_windows"], all=__all__,
+                                   attribute=name)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/__init__.py b/venv/lib/python3.12/site-packages/scipy/sparse/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..d7438fa56b398877592e6485fd99974f70660f78
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/__init__.py
@@ -0,0 +1,296 @@
+"""
+===================================
+Sparse arrays (:mod:`scipy.sparse`)
+===================================
+
+.. currentmodule:: scipy.sparse
+
+.. toctree::
+   :hidden:
+
+   sparse.csgraph
+   sparse.linalg
+   sparse.migration_to_sparray
+   sparse.spmatrix_api
+
+SciPy 2-D sparse array package for numeric data.
+
+.. warning::
+
+   SciPy sparse is shifting from a sparse matrix interface to a sparse
+   array interface. In the next few releases we expect to deprecate the
+   sparse matrix interface. For documentation of the matrix
+   interface, see the :ref:`spmatrix interface docs <spmatrix_api>`.
+   For guidance on converting existing code to sparse arrays, see
+   :ref:`Migration from spmatrix to sparray <migration_to_sparray>`.
+
+
+Submodules
+==========
+
+.. autosummary::
+
+   csgraph - Compressed sparse graph routines
+   linalg - Sparse linear algebra routines
+
+
+Sparse array classes
+====================
+
+.. autosummary::
+   :toctree: generated/
+
+   bsr_array - Block Sparse Row array
+   coo_array - A sparse array in COOrdinate format
+   csc_array - Compressed Sparse Column array
+   csr_array - Compressed Sparse Row array
+   dia_array - Sparse array with DIAgonal storage
+   dok_array - Dictionary Of Keys based sparse array
+   lil_array - Row-based list of lists sparse array
+   sparray - Sparse array base class
+
+.. _sparse-construction-functions:
+
+Building sparse arrays
+----------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   diags_array - Return a sparse array from diagonals
+   eye_array - Sparse MxN array whose k-th diagonal is all ones
+   random_array - Random values in a given shape array
+   block_array - Build a sparse array from sub-blocks
+
+.. _combining-arrays:
+
+Combining arrays
+----------------
+
+.. autosummary::
+   :toctree: generated/
+
+   kron - Kronecker product of two sparse arrays
+   kronsum - Kronecker sum of sparse arrays
+   block_diag - Build a block diagonal sparse array
+   tril - Lower triangular portion of a sparse array
+   triu - Upper triangular portion of a sparse array
+   hstack - Stack sparse arrays horizontally (column wise)
+   vstack - Stack sparse arrays vertically (row wise)
+
+Manipulating arrays
+-------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   matrix_transpose - Transpose a matrix (or a batch of matrices)
+   swapaxes - swap two axes of a sparse array
+   expand_dims - add a new (trivial) axis to a sparse array
+   permute_dims - reorder the axes of a sparse array
+
+Sparse tools
+------------
+
+.. autosummary::
+   :toctree: generated/
+
+   save_npz - Save a sparse array to a file using ``.npz`` format.
+   load_npz - Load a sparse array from a file using ``.npz`` format.
+   find - Return the indices and values of the nonzero elements
+   get_index_dtype - determine a good dtype for index arrays.
+   safely_cast_index_arrays - cast index array dtype or raise if shape too big
+
+Identifying sparse arrays
+-------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   issparse - Check if the argument is a sparse object (array or matrix).
+   isspmatrix - Check if the argument is an old style sparse matrix.
+
+
+Warnings
+========
+
+.. autosummary::
+   :toctree: generated/
+
+   SparseEfficiencyWarning
+   SparseWarning
+
+
+Usage information
+=================
+
+There are seven available sparse array types:
+
+1. csc_array: Compressed Sparse Column format
+2. csr_array: Compressed Sparse Row format
+3. bsr_array: Block Sparse Row format
+4. lil_array: List of Lists format
+5. dok_array: Dictionary of Keys format
+6. coo_array: COOrdinate format (aka IJV, triplet format)
+7. dia_array: DIAgonal format
+
+To construct an array efficiently, use any of `coo_array`,
+`dok_array` or `lil_array`. They each support basic slicing
+and fancy indexing with a similar syntax to NumPy arrays.
+The COO format is recommended and other formats use it under the hood to
+allow efficient construction using data values and coordinate arrays.
+
+Despite their similarity to NumPy arrays, it is **strongly discouraged**
+to use NumPy functions directly on these arrays because NumPy typically
+treats them as generic Python objects rather than arrays, leading to
+unexpected (and incorrect) results. If you are tempted to apply a NumPy
+function to these arrays, check if SciPy has its own implementation
+for the given sparse array class and, if not, **convert the sparse array
+to a NumPy array** (e.g., using the `toarray` method of the class)
+before applying the method.
+
+All conversions among the CSR, CSC, and COO formats are efficient,
+linear-time operations.
+
+To perform manipulations such as multiplication or inversion, first
+convert the array to either CSC or CSR format. The `lil_array`
+format is row-based, so conversion to CSR is efficient, but
+conversion to CSC is less so.
+
+Matrix vector product
+---------------------
+
+To do a vector product between a 2D sparse array and a vector use
+the matmul operator (i.e., ``@``) which performs a dot product (like the
+``dot`` method):
+
+>>> import numpy as np
+>>> from scipy.sparse import csr_array
+>>> A = csr_array([[1, 2, 0], [0, 0, 3], [4, 0, 5]])
+>>> v = np.array([1, 0, -1])
+>>> A @ v
+array([ 1, -3, -1], dtype=int64)
+
+The CSR format is especially suitable for fast matrix vector products.
+
+Example 1
+---------
+
+Construct a 1000x1000 `lil_array` and add some values to it:
+
+>>> from scipy.sparse import lil_array
+>>> from scipy.sparse.linalg import spsolve
+>>> from numpy.linalg import solve, norm
+>>> from numpy.random import rand
+
+>>> A = lil_array((1000, 1000))
+>>> A[0, :100] = rand(100)
+>>> A.setdiag(rand(1000))
+
+Now convert it to CSR format and solve A x = b for x:
+
+>>> A = A.tocsr()
+>>> b = rand(1000)
+>>> x = spsolve(A, b)
+
+Convert it to a dense array and solve, and check that the result
+is the same:
+
+>>> x_ = solve(A.toarray(), b)
+
+Now we can compute norm of the error with:
+
+>>> err = norm(x-x_)
+>>> err < 1e-9
+True
+
+It should be small :)
+
+
+Example 2
+---------
+
+Construct an array in COO format:
+
+>>> from scipy import sparse
+>>> from numpy import array
+>>> I = array([0,3,1,0])
+>>> J = array([0,3,1,2])
+>>> V = array([4,5,7,9])
+>>> A = sparse.coo_array((V,(I,J)),shape=(4,4))
+
+Notice that the indices do not need to be sorted.
+
+Duplicate (i,j) entries are summed when converting to CSR or CSC.
+
+>>> I = array([0,0,1,3,1,0,0])
+>>> J = array([0,2,1,3,1,0,0])
+>>> V = array([1,1,1,1,1,1,1])
+>>> B = sparse.coo_array((V,(I,J)),shape=(4,4)).tocsr()
+
+This is useful for constructing finite-element stiffness and mass matrices.
+
+Further details
+---------------
+
+CSR column indices are not necessarily sorted. Likewise for CSC row
+indices. And similarly for COO coordinates. Use the ``.sorted_indices()``
+and ``.sort_indices()`` methods when sorted indices are required (e.g.,
+when passing data to other libraries).
+
+"""
+
+# Original code by Travis Oliphant.
+# Modified and extended by Ed Schofield, Robert Cimrman,
+# Nathan Bell, and Jake Vanderplas.
+
+import warnings as _warnings
+import importlib as _importlib
+
+from ._base import *
+from ._csr import *
+from ._csc import *
+from ._lil import *
+from ._dok import *
+from ._coo import *
+from ._dia import *
+from ._bsr import *
+from ._construct import *
+from ._extract import *
+from ._matrix import spmatrix
+from ._matrix_io import *
+from ._sputils import get_index_dtype, safely_cast_index_arrays
+
+
+# Deprecated namespaces, to be removed in v2.0.0
+from . import (
+    base, bsr, compressed, construct, coo, csc, csr, data, dia, dok, extract,
+    lil, sparsetools, sputils
+)
+
+_submodules = ["csgraph", "linalg"]
+
+__all__ = [s for s in dir() if not s.startswith('_')] + _submodules
+
+# Filter PendingDeprecationWarning for np.matrix introduced with numpy 1.15
+msg = 'the matrix subclass is not the recommended way'
+_warnings.filterwarnings('ignore', message=msg)
+
+def __dir__():
+   return __all__
+
+
+def __getattr__(name):
+    if name in _submodules:
+        return _importlib.import_module(f'scipy.sparse.{name}')
+    else:
+        try:
+            return globals()[name]
+        except KeyError:
+            raise AttributeError(
+                f"Module 'scipy.sparse' has no attribute '{name}'"
+            )
+
+from scipy._lib._testutils import PytestTester
+test = PytestTester(__name__)
+del PytestTester
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--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/_base.py
@@ -0,0 +1,1792 @@
+"""Base class for sparse matrices"""
+
+from warnings import warn
+import math
+import numpy as np
+import operator
+
+from ._sputils import (asmatrix, check_shape,
+                       get_sum_dtype, isdense, isscalarlike, _todata,
+                       matrix, validateaxis, getdtype, is_pydata_spmatrix)
+from scipy._lib._sparse import SparseABC, issparse
+
+from ._matrix import spmatrix
+
+__all__ = ['isspmatrix', 'issparse', 'sparray',
+           'SparseWarning', 'SparseEfficiencyWarning']
+
+
+class SparseWarning(Warning):
+    """General warning for :mod:`scipy.sparse`."""
+    pass
+
+
+class SparseFormatWarning(SparseWarning):
+    pass
+
+
+class SparseEfficiencyWarning(SparseWarning):
+    """The warning emitted when the operation is
+    inefficient for sparse matrices.
+    """
+    pass
+
+
+# The formats that we might potentially understand.
+_formats = {'csc': [0, "Compressed Sparse Column"],
+            'csr': [1, "Compressed Sparse Row"],
+            'dok': [2, "Dictionary Of Keys"],
+            'lil': [3, "List of Lists"],
+            'dod': [4, "Dictionary of Dictionaries"],
+            'sss': [5, "Symmetric Sparse Skyline"],
+            'coo': [6, "COOrdinate"],
+            'lba': [7, "Linpack BAnded"],
+            'egd': [8, "Ellpack-itpack Generalized Diagonal"],
+            'dia': [9, "DIAgonal"],
+            'bsr': [10, "Block Sparse Row"],
+            'msr': [11, "Modified compressed Sparse Row"],
+            'bsc': [12, "Block Sparse Column"],
+            'msc': [13, "Modified compressed Sparse Column"],
+            'ssk': [14, "Symmetric SKyline"],
+            'nsk': [15, "Nonsymmetric SKyline"],
+            'jad': [16, "JAgged Diagonal"],
+            'uss': [17, "Unsymmetric Sparse Skyline"],
+            'vbr': [18, "Variable Block Row"],
+            'und': [19, "Undefined"]
+            }
+
+
+# These univariate ufuncs preserve zeros.
+_ufuncs_with_fixed_point_at_zero = frozenset([
+        np.sin, np.tan, np.arcsin, np.arctan, np.sinh, np.tanh, np.arcsinh,
+        np.arctanh, np.rint, np.sign, np.expm1, np.log1p, np.deg2rad,
+        np.rad2deg, np.floor, np.ceil, np.trunc, np.sqrt])
+
+
+MAXPRINT = 50
+
+
+# helper dicts to manipulate comparison operators
+# We negate operators (with warning) when all implicit values would be True
+op_neg = {operator.eq: operator.ne, operator.ne: operator.eq,
+          operator.lt: operator.ge, operator.ge: operator.lt,
+          operator.gt: operator.le, operator.le: operator.gt}
+
+
+# We use symbolic version of operators in warning messages.
+op_sym = {operator.eq: '==', operator.ge: '>=', operator.le: '<=',
+          operator.ne: '!=', operator.gt: '>', operator.lt: '<'}
+
+
+# `_spbase` is a subclass of `SparseABC`.
+# This allows other submodules to check for instances of sparse subclasses
+# via `scipy._lib._sparse.issparse`, without introducing
+# an import dependency on `scipy.sparse`.
+class _spbase(SparseABC):
+    """ This class provides a base class for all sparse array and matrix classes.
+    It cannot be instantiated.  Most of the work is provided by subclasses.
+    """
+
+    __array_priority__ = 10.1
+    _format = 'und'  # undefined
+    _allow_nd: tuple[int, ...] = (2,)
+
+    @property
+    def ndim(self) -> int:
+        return len(self._shape)
+
+    @property
+    def _shape_as_2d(self):
+        s = self._shape
+        return (1, s[-1]) if len(s) == 1 else s
+
+    @property
+    def _bsr_container(self):
+        from ._bsr import bsr_array
+        return bsr_array
+
+    @property
+    def _coo_container(self):
+        from ._coo import coo_array
+        return coo_array
+
+    @property
+    def _csc_container(self):
+        from ._csc import csc_array
+        return csc_array
+
+    @property
+    def _csr_container(self):
+        from ._csr import csr_array
+        return csr_array
+
+    @property
+    def _dia_container(self):
+        from ._dia import dia_array
+        return dia_array
+
+    @property
+    def _dok_container(self):
+        from ._dok import dok_array
+        return dok_array
+
+    @property
+    def _lil_container(self):
+        from ._lil import lil_array
+        return lil_array
+
+    def __init__(self, arg1, *, maxprint=None):
+        self._shape = None
+        if self.__class__.__name__ == '_spbase':
+            raise ValueError("This class is not intended"
+                             " to be instantiated directly.")
+        if isinstance(self, sparray) and np.isscalar(arg1):
+            raise ValueError(
+                "scipy sparse array classes do not support instantiation from a scalar"
+            )
+        self.maxprint = MAXPRINT if maxprint is None else maxprint
+
+    @property
+    def shape(self):
+        return self._shape
+
+    def reshape(self, *shape, order="C", copy=False):
+        """reshape(self, shape, order='C', copy=False)
+
+        Gives a new shape to a sparse array/matrix without changing its data.
+
+        Parameters
+        ----------
+        *shape : int
+            Integers specifying the new shape.
+            The new shape should be compatible with the original shape.
+        order : {'C', 'F'}, optional
+            Read the elements using this index order. 'C' means to read and
+            write the elements using C-like index order; e.g., read entire first
+            row, then second row, etc. 'F' means to read and write the elements
+            using Fortran-like index order; e.g., read entire first column, then
+            second column, etc.
+        copy : bool, optional
+            Indicates whether or not attributes of self should be copied
+            whenever possible. The degree to which attributes are copied varies
+            depending on the type of sparse array being used.
+
+        Returns
+        -------
+        reshaped : sparse array/matrix
+            A sparse array/matrix with the given `shape`, not necessarily of the same
+            format as the current object.
+
+        See Also
+        --------
+        numpy.reshape : NumPy's implementation of 'reshape' for ndarrays
+        """
+        # If the shape already matches, don't bother doing an actual reshape
+        # Otherwise, the default is to convert to COO and use its reshape
+        # Don't restrict ndim on this first call. That happens in constructor
+        shape = check_shape(shape, self.shape, allow_nd=range(1, 65))
+        if shape == self.shape:
+            if copy:
+                return self.copy()
+            else:
+                return self
+
+        return self.tocoo(copy=copy).reshape(shape, order=order, copy=False)
+
+    def resize(self, *shape):
+        """Resize the array/matrix in-place to dimensions given by ``shape``.
+
+        Any elements that lie within the new shape will remain at the same
+        indices, while non-zero elements lying outside the new shape are
+        removed.
+
+        Parameters
+        ----------
+        *shape : int
+            number of rows and columns in the new array/matrix
+
+        Notes
+        -----
+        The semantics are not identical to `numpy.ndarray.resize` or
+        `numpy.resize`. Here, the same data will be maintained at each index
+        before and after reshape, if that index is within the new bounds. In
+        numpy, resizing maintains contiguity of the array, moving elements
+        around in the logical array but not within a flattened representation.
+
+        We give no guarantees about whether the underlying data attributes
+        (arrays, etc.) will be modified in place or replaced with new objects.
+        """
+        # As an inplace operation, this requires implementation in each format.
+        raise NotImplementedError(
+            f'{type(self).__name__}.resize is not implemented')
+
+    def astype(self, dtype, casting='unsafe', copy=True):
+        """Cast the array/matrix elements to a specified type.
+
+        Parameters
+        ----------
+        dtype : str or numpy dtype
+            Typecode or data-type to which to cast the data.
+        casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional
+            Controls what kind of data casting may occur.
+            Defaults to 'unsafe' for backwards compatibility.
+            'no' means the data types should not be cast at all.
+            'equiv' means only byte-order changes are allowed.
+            'safe' means only casts which can preserve values are allowed.
+            'same_kind' means only safe casts or casts within a kind,
+            like float64 to float32, are allowed.
+            'unsafe' means any data conversions may be done.
+        copy : bool, optional
+            If `copy` is `False`, the result might share some memory with this
+            array/matrix. If `copy` is `True`, it is guaranteed that the result and
+            this array/matrix do not share any memory.
+
+        Returns
+        -------
+        array/matrix
+            This array/matrix with data type `dtype`.
+        """
+
+        dtype = getdtype(dtype)
+        if self.dtype != dtype:
+            return self.tocsr().astype(
+                dtype, casting=casting, copy=copy).asformat(self.format)
+        elif copy:
+            return self.copy()
+        else:
+            return self
+
+    @classmethod
+    def _ascontainer(cls, X, **kwargs):
+        if issubclass(cls, sparray):
+            return np.asarray(X, **kwargs)
+        else:
+            return asmatrix(X, **kwargs)
+
+    @classmethod
+    def _container(cls, X, **kwargs):
+        if issubclass(cls, sparray):
+            return np.array(X, **kwargs)
+        else:
+            return matrix(X, **kwargs)
+
+    def _asfptype(self):
+        """Upcast array to a floating point format (if necessary)"""
+
+        fp_types = ['f', 'd', 'F', 'D']
+
+        if self.dtype.char in fp_types:
+            return self
+        else:
+            for fp_type in fp_types:
+                if self.dtype <= np.dtype(fp_type):
+                    return self.astype(fp_type, copy=False)
+
+            raise TypeError(
+                f'cannot upcast [{self.dtype.name}] to a floating point format'
+            )
+
+    def __iter__(self):
+        for r in range(self.shape[0]):
+            yield self[r]
+
+    def _getmaxprint(self):
+        """Maximum number of elements to display when printed."""
+        return self.maxprint
+
+    def count_nonzero(self, axis=None):
+        """Number of non-zero entries.
+
+        This is equivalent to::
+
+            np.count_nonzero(a.toarray(), axis=axis)
+
+        Unlike the nnz property, which return the number of stored
+        entries (the length of the data attribute), this method counts the
+        actual number of non-zero entries in data.
+
+        Duplicate entries are summed before counting.
+
+        Parameters
+        ----------
+        axis : {-2, -1, 0, 1, None} optional
+            Count nonzeros for the whole array, or along a specified axis.
+
+            .. versionadded:: 1.15.0
+
+        Returns
+        -------
+        numpy array
+            A reduced array (no axis `axis`) holding the number of nonzero values
+            for each of the indices of the nonaxis dimensions.
+
+        Notes
+        -----
+        If you want to count nonzero and explicit zero stored values (e.g. nnz)
+        along an axis, two fast idioms are provided by `numpy` functions for the
+        common CSR, CSC, COO formats.
+
+        For the major axis in CSR (rows) and CSC (cols) use `np.diff`:
+
+            >>> import numpy as np
+            >>> import scipy as sp
+            >>> A = sp.sparse.csr_array([[4, 5, 0], [7, 0, 0]])
+            >>> major_axis_stored_values = np.diff(A.indptr)  # -> np.array([2, 1])
+
+        For the minor axis in CSR (cols) and CSC (rows) use `numpy.bincount` with
+        minlength ``A.shape[1]`` for CSR and ``A.shape[0]`` for CSC:
+
+            >>> csr_minor_stored_values = np.bincount(A.indices, minlength=A.shape[1])
+
+        For COO, use the minor axis approach for either `axis`:
+
+            >>> A = A.tocoo()
+            >>> coo_axis0_stored_values = np.bincount(A.coords[0], minlength=A.shape[1])
+            >>> coo_axis1_stored_values = np.bincount(A.coords[1], minlength=A.shape[0])
+
+        Examples
+        --------
+
+            >>> A = sp.sparse.csr_array([[4, 5, 0], [7, 0, 0]])
+            >>> A.count_nonzero(axis=0)
+            array([2, 1, 0])
+        """
+        clsname = self.__class__.__name__
+        raise NotImplementedError(f"count_nonzero not implemented for {clsname}.")
+
+    def _getnnz(self, axis=None):
+        """Number of stored values, including explicit zeros.
+
+        Parameters
+        ----------
+        axis : {-2, -1, 0, 1, None} optional
+            Report stored values for the whole array, or along a specified axis.
+
+        See Also
+        --------
+        count_nonzero : Number of non-zero entries
+        """
+        clsname = self.__class__.__name__
+        raise NotImplementedError(f"getnnz not implemented for {clsname}.")
+
+    @property
+    def nnz(self) -> int:
+        """Number of stored values, including explicit zeros.
+
+        See Also
+        --------
+        count_nonzero : Number of non-zero entries
+        """
+        return self._getnnz()
+
+    @property
+    def size(self) -> int:
+        """Number of stored values.
+
+        See Also
+        --------
+        count_nonzero : Number of non-zero values.
+        """
+        return self._getnnz()
+
+    @property
+    def format(self) -> str:
+        """Format string for matrix."""
+        return self._format
+
+    @property
+    def T(self):
+        """Transpose."""
+        return self.transpose()
+    
+    @property
+    def mT(self):
+        """Matrix transpose.
+        
+        See Also
+        --------
+        scipy.sparse.matrix_transpose : equivalent function
+        """
+        if (n := self.ndim) < 2:
+            raise ValueError(f"Array must be at least 2-dimensional, but it is {n}-D")
+        assert n == 2
+        return self.transpose()
+
+    @property
+    def real(self):
+        return self._real()
+
+    @property
+    def imag(self):
+        return self._imag()
+
+    def __repr__(self):
+        _, format_name = _formats[self.format]
+        sparse_cls = 'array' if isinstance(self, sparray) else 'matrix'
+        return (
+            f"<{format_name} sparse {sparse_cls} of dtype '{self.dtype}'\n"
+            f"\twith {self.nnz} stored elements and shape {self.shape}>"
+        )
+
+    def __str__(self):
+        maxprint = self._getmaxprint()
+
+        A = self.tocoo()
+
+        # helper function, outputs "(i,j)  v"
+        def tostr(coords, data):
+            pairs = zip(zip(*(c.tolist() for c in coords)), data)
+            return '\n'.join(f'  {idx}\t{val}' for idx, val in pairs)
+
+        out = repr(self)
+        if self.nnz == 0:
+            return out
+
+        out += '\n  Coords\tValues\n'
+        if self.nnz > maxprint:
+            half = maxprint // 2
+            out += tostr(tuple(c[:half] for c in A.coords), A.data[:half])
+            out += "\n  :\t:\n"
+            half = maxprint - half
+            out += tostr(tuple(c[-half:] for c in A.coords), A.data[-half:])
+        else:
+            out += tostr(A.coords, A.data)
+
+        return out
+
+    def __bool__(self):  # Simple -- other ideas?
+        if self.shape == (1, 1):
+            return self.nnz != 0
+        else:
+            raise ValueError("The truth value of an array with more than one "
+                             "element is ambiguous. Use a.any() or a.all().")
+
+    # What should len(sparse) return? For consistency with dense matrices,
+    # perhaps it should be the number of rows?  But for some uses the number of
+    # non-zeros is more important.  For now, raise an exception!
+    def __len__(self):
+        raise TypeError("sparse array length is ambiguous; use getnnz()"
+                        " or shape[0]")
+
+    def asformat(self, format, copy=False):
+        """Return this array/matrix in the passed format.
+
+        Parameters
+        ----------
+        format : {str, None}
+            The desired sparse format ("csr", "csc", "lil", "dok", "array", ...)
+            or None for no conversion.
+        copy : bool, optional
+            If True, the result is guaranteed to not share data with self.
+
+        Returns
+        -------
+        A : array/matrix
+            This array/matrix in the passed format.
+        """
+        if format is None or format == self.format:
+            if copy:
+                return self.copy()
+            else:
+                return self
+        else:
+            try:
+                convert_method = getattr(self, 'to' + format)
+            except AttributeError as e:
+                raise ValueError(f'Format {format} is unknown.') from e
+
+            # Forward the copy kwarg, if it's accepted.
+            try:
+                return convert_method(copy=copy)
+            except TypeError:
+                return convert_method()
+
+    ###################################################################
+    #  NOTE: All arithmetic operations use csr_matrix by default.
+    # Therefore a new sparse array format just needs to define a
+    # .tocsr() method to provide arithmetic support. Any of these
+    # methods can be overridden for efficiency.
+    ####################################################################
+
+    def multiply(self, other):
+        """Element-wise multiplication by another array/matrix.
+
+        Parameters
+        ----------
+        other : sparse array or array_like
+            Array to multiply by.
+
+        Returns
+        -------
+        sparse array/matrix
+            Result of element-wise multiplication.
+        """
+        if isscalarlike(other):
+            return self._mul_scalar(other)
+
+        if self.ndim < 3:
+            try:
+                return self._multiply_2d_with_broadcasting(other)
+            except AttributeError:
+                return self.tocsr()._multiply_2d_with_broadcasting(other)
+
+        if not (issparse(other) or isdense(other)):
+            # If it's a list or whatever, treat it like an array
+            other_a = np.asanyarray(other)
+            if other_a.ndim == 0 and other_a.dtype == np.object_:
+                # numpy creates a 0d object array if all else fails.
+                # Not interpretable as an array; return NotImplemented so
+                # other's __rmul__ can kick in if that's implemented.
+                return NotImplemented
+            # Allow custom sparse class indicated by attr sparse gh-6520
+            try:
+                other.shape
+            except AttributeError:
+                other = other_a
+
+        if self.shape != other.shape:
+            raise ValueError("inconsistent shapes: >2D multiply() does not yet "
+                             "support broadcasting")
+
+        # self is >2D so must be COO
+        if isdense(other):
+            data = np.multiply(self.data, other[self.coords])
+            result = self.copy()
+            result.data = data.view(np.ndarray).ravel()
+            return result
+
+        elif issparse(other):
+            csr_self = self.reshape(1, -1).tocsr()
+            csr_other = other.reshape(1, -1).tocsr()
+            return csr_self._binopt(csr_other, '_elmul_').reshape(self.shape)
+
+        else:
+            # Not scalar, dense or sparse. Return NotImplemented so that
+            # other's __rmul__ can kick in if that's implemented.
+            return NotImplemented
+
+    def _maximum_minimum(self, other, np_op):
+        if not (issparse(other) or isdense(other) or isscalarlike(other)):
+            # If it's a list or whatever, treat it like an array
+            other_a = np.asanyarray(other)
+            if other_a.ndim == 0 and other_a.dtype == np.object_:
+                # numpy creates a 0d object array if all else fails.
+                # We don't know how to handle it either.
+                raise NotImplementedError('maximum or minimum with an unrecognized '
+                                          'array type is not supported')
+            # Allow custom sparse class indicated by attr sparse gh-6520
+            try:
+                other.shape
+            except AttributeError:
+                other = other_a
+
+        if isscalarlike(other):
+            if np_op(0, other):
+                pos_neg = 'positive' if np_op == np.maximum else 'negative'
+                warn(f"Taking {np_op.__name__} with a {pos_neg} number results in a"
+                     " dense matrix.", SparseEfficiencyWarning, stacklevel=3)
+                return self.__class__(np_op(self.toarray(), other))
+            else:
+                if self.ndim < 3:
+                    cs_self = self if self.format in ('csr', 'csc') else self.tocsr()
+                    return cs_self._scalar_binopt(other, np_op)
+                csr_self = self.reshape(1, -1).tocsr()
+                result = csr_self._scalar_binopt(other, np_op)
+                return result.tocoo().reshape(self.shape)
+        elif isdense(other):
+            return np_op(self.todense(), other)
+        elif issparse(other):
+            if self.shape != other.shape:
+                raise ValueError(f"inconsistent shapes {self.shape=} {other.shape=}")
+            if self.ndim < 3:  # shape is same so other.ndim < 3
+                cs_self = self if self.format in ('csr', 'csc') else self.tocsr()
+                return cs_self._binopt(other, f'_{np_op.__name__}_')
+            csr_self = self.reshape(1, -1).tocsr()
+            csr_other = other.reshape(1, -1).tocsr()
+            result = csr_self._binopt(csr_other, f'_{np_op.__name__}_')
+            return result.tocoo().reshape(self.shape)
+        else:
+            raise ValueError("Operands not compatible.")
+
+    def maximum(self, other):
+        """Element-wise maximum between this and another array/matrix.
+
+        Parameters
+        ----------
+        other : array_like or sparse array
+            Array to compare against.
+
+        Returns
+        -------
+        sparse array/matrix or ndarray
+            Result of element-wise minimum. The type depends on `other`:
+
+            - If `other` is a scalar, the result is a sparse array/matrix.
+            - If `other` is an ndarray, the result is an ndarray.
+        """
+        return self._maximum_minimum(other, np.maximum)
+
+    def minimum(self, other):
+        """Element-wise minimum between this and another array/matrix.
+
+        Parameters
+        ----------
+        other : array_like or sparse array
+            Array to compare against.
+
+        Returns
+        -------
+        sparse array/matrix or ndarray
+            Result of element-wise minimum. The type depends on `other`:
+
+            - If `other` is a scalar, the result is a sparse array/matrix.
+            - If `other` is an ndarray, the result is an ndarray.
+        """
+        return self._maximum_minimum(other, np.minimum)
+
+    def dot(self, other):
+        """Ordinary dot product.
+
+        Parameters
+        ----------
+        other : array_like or sparse array
+            Array to take dot product with.
+
+        Returns
+        -------
+        sparse array/matrix or ndarray
+            Result of dot product. The type depends on `other`:
+
+            - If `other` is a scalar, the result is a sparse array/matrix.
+            - If `other` is an ndarray, the result is an ndarray.
+
+        Examples
+        --------
+        >>> import numpy as np
+        >>> from scipy.sparse import csr_array
+        >>> A = csr_array([[1, 2, 0], [0, 0, 3], [4, 0, 5]])
+        >>> v = np.array([1, 0, -1])
+        >>> A.dot(v)
+        array([ 1, -3, -1], dtype=int64)
+
+        """
+        if np.isscalar(other):
+            return self * other
+        else:
+            return self @ other
+
+    def power(self, n, dtype=None):
+        """Element-wise power.
+
+        Parameters
+        ----------
+        n : scalar
+            `n` is a non-zero scalar (nonzero avoids dense ones creation)
+            If zero power is desired, special case it to use `numpy.ones`
+        dtype : dtype, optional
+            If `dtype` is not specified, the current dtype will be preserved.
+
+        Returns
+        -------
+        csr array/matrix
+            Result of raising all elements to the power `n`.
+        """
+        return self.tocsr().power(n, dtype=dtype)
+
+    def _broadcast_to(self, shape, /, copy=False):
+        if self.shape == shape:
+            return self.copy() if copy else self
+        else:
+            return self.tocsr()._broadcast_to(shape, copy)
+
+    def _comparison(self, other, op):
+        # We convert to CSR format and use methods _binopt or _scalar_binopt
+        # If ndim>2 we reshape to 2D, compare and then reshape back to nD
+        if not (issparse(other) or isdense(other) or isscalarlike(other)):
+            if is_pydata_spmatrix(other):
+                # cannot compare with pydata other, but it might compare with us.
+                return NotImplemented
+            # If it's a list or whatever, treat it like an array
+            other_a = np.asanyarray(other)
+            if other_a.ndim == 0 and other_a.dtype == np.object_:
+                # numpy creates a 0d object array if all else fails.
+                # Not interpretable as an array; return NotImplemented so
+                # other's dunder methods can kick in if implemented.
+                return NotImplemented
+            # Allow custom sparse class indicated by attr sparse gh-6520
+            try:
+                other.shape
+            except AttributeError:
+                other = other_a
+
+        if isscalarlike(other):
+            if not op(0, other):
+                if np.isnan(other):  # op is not `ne`, so results are all False.
+                    return self.__class__(self.shape, dtype=np.bool_)
+                if self.ndim < 3:
+                    cs_self = self if self.format in ('csc', 'csr') else self.tocsr()
+                    return cs_self._scalar_binopt(other, op)
+                csr_self = self.reshape(1, -1).tocsr()
+                result = csr_self._scalar_binopt(other, op)
+                return result.tocoo().reshape(self.shape)
+            else:
+                warn(f"Comparing a sparse matrix with {other} using {op_sym[op]} "
+                     f"is inefficient. Try using {op_sym[op_neg[op]]} instead.",
+                     SparseEfficiencyWarning, stacklevel=3)
+                if np.isnan(other):
+                    # op is `ne` cuz op(0, other) and isnan(other). Return all True.
+                    return self.__class__(np.ones(self.shape, dtype=np.bool_))
+
+                # op is eq, le, or ge. Use negated op and then negate.
+                if self.ndim < 3:
+                    cs_self = self if self.format in ('csc', 'csr') else self.tocsr()
+                    inv = cs_self._scalar_binopt(other, op_neg[op])
+                    all_true = cs_self.__class__(np.ones(cs_self.shape, dtype=np.bool_))
+                    return all_true - inv
+
+                csr_self = self.reshape(1, -1).tocsr()
+                inv = csr_self._scalar_binopt(other, op_neg[op])
+                all_true = csr_self.__class__(np.ones(csr_self.shape, dtype=np.bool_))
+                result = all_true - inv
+                return result.tocoo().reshape(self.shape)
+
+        elif isdense(other):
+            return op(self.todense(), other)
+
+        elif issparse(other):
+            # TODO sparse broadcasting
+            if self.shape != other.shape:
+                # eq and ne return True or False instead of an array when the shapes
+                # don't match. Numpy doesn't do this. Is this what we want?
+                if op in (operator.eq, operator.ne):
+                    return op is operator.ne
+                raise ValueError("inconsistent shape")
+
+            if self.ndim < 3:
+                cs_self = self if self.format in ('csc', 'csr') else self.tocsr()
+                cs_other = other
+            else:
+                cs_self = self.reshape(1, -1).tocsr()
+                cs_other = other.reshape(1, -1).tocsr()
+            if not op(0, 0):
+                result = cs_self._binopt(cs_other, f'_{op.__name__}_')
+                return result if self.ndim < 3 else result.tocoo().reshape(self.shape)
+            else:
+                # result will not be sparse. Use negated op and then negate.
+                warn(f"Comparing two sparse matrices using {op_sym[op]} "
+                     f"is inefficient. Try using {op_sym[op_neg[op]]} instead.",
+                     SparseEfficiencyWarning, stacklevel=3)
+                inv = cs_self._binopt(cs_other, f'_{op_neg[op].__name__}_')
+                all_true = cs_self.__class__(np.ones(cs_self.shape, dtype=np.bool_))
+                result = all_true - inv
+                return result if self.ndim < 3 else result.tocoo().reshape(self.shape)
+        else:
+            # cannot compare with other, but it might compare with us.
+            return NotImplemented
+
+    def __eq__(self, other):
+        return self._comparison(other, operator.eq)
+
+    def __ne__(self, other):
+        return self._comparison(other, operator.ne)
+
+    def __lt__(self, other):
+        return self._comparison(other, operator.lt)
+
+    def __gt__(self, other):
+        return self._comparison(other, operator.gt)
+
+    def __le__(self, other):
+        return self._comparison(other, operator.le)
+
+    def __ge__(self, other):
+        return self._comparison(other, operator.ge)
+
+    def __abs__(self):
+        return abs(self.tocsr())
+
+    def __round__(self, ndigits=0):
+        return round(self.tocsr(), ndigits=ndigits)
+
+    def _add_sparse(self, other):
+        return self.tocsr()._add_sparse(other)
+
+    def _add_dense(self, other):
+        return self.tocoo()._add_dense(other)
+
+    def _sub_sparse(self, other):
+        return self.tocsr()._sub_sparse(other)
+
+    def _sub_dense(self, other):
+        return self.todense() - other
+
+    def _rsub_dense(self, other):
+        # note: this can't be replaced by other + (-self) for unsigned types
+        return other - self.todense()
+
+    def __add__(self, other):  # self + other
+        if isscalarlike(other):
+            if other == 0:
+                return self.copy()
+            # Now we would add this scalar to every element.
+            raise NotImplementedError('adding a nonzero scalar to a '
+                                      'sparse array is not supported')
+        elif issparse(other):
+            if other.shape != self.shape:
+                raise ValueError("inconsistent shapes")
+            return self._add_sparse(other)
+        elif isdense(other):
+            other = np.broadcast_to(other, self.shape)
+            return self._add_dense(other)
+        else:
+            return NotImplemented
+
+    def __radd__(self,other):  # other + self
+        return self.__add__(other)
+
+    def __sub__(self, other):  # self - other
+        if isscalarlike(other):
+            if other == 0:
+                return self.copy()
+            raise NotImplementedError('subtracting a nonzero scalar from a '
+                                      'sparse array is not supported')
+        elif issparse(other):
+            if other.shape != self.shape:
+                raise ValueError("inconsistent shapes")
+            return self._sub_sparse(other)
+        elif isdense(other):
+            other = np.broadcast_to(other, self.shape)
+            return self._sub_dense(other)
+        else:
+            return NotImplemented
+
+    def __rsub__(self,other):  # other - self
+        if isscalarlike(other):
+            if other == 0:
+                return -self.copy()
+            raise NotImplementedError('subtracting a sparse array from a '
+                                      'nonzero scalar is not supported')
+        elif isdense(other):
+            other = np.broadcast_to(other, self.shape)
+            return self._rsub_dense(other)
+        else:
+            return NotImplemented
+
+    def _matmul_dispatch(self, other):
+        """np.array-like matmul & `np.matrix`-like mul, i.e. `dot` or `NotImplemented`
+
+        interpret other and call one of the following
+        self._mul_scalar()
+        self._matmul_vector()
+        self._matmul_multivector()
+        self._matmul_sparse()
+        """
+        # This method has to be different from `__matmul__` because it is also
+        # called by sparse matrix classes.
+
+        # Currently matrix multiplication is only supported
+        # for 2D arrays. Hence we unpacked and use only the
+        # two last axes' lengths.
+        M, N = self._shape_as_2d
+
+        if other.__class__ is np.ndarray:
+            # Fast path for the most common case
+            if other.shape == (N,):
+                return self._matmul_vector(other)
+            elif other.shape == (N, 1):
+                result = self._matmul_vector(other.ravel())
+                if self.ndim == 1:
+                    return result.reshape(1)
+                return result.reshape(M, 1)
+            elif other.ndim == 2 and other.shape[0] == N:
+                return self._matmul_multivector(other)
+
+        if isscalarlike(other):
+            # scalar value
+            return self._mul_scalar(other)
+
+        err_prefix = "matmul: dimension mismatch with signature"
+        if issparse(other):
+            if N != other.shape[0]:
+                raise ValueError(
+                    f"{err_prefix} (n,k={N}),(k={other.shape[0]},m)->(n,m)"
+                )
+            return self._matmul_sparse(other)
+
+        # If it's a list or whatever, treat it like an array
+        other_a = np.asanyarray(other)
+        if other_a.ndim == 0 and other_a.dtype == np.object_:
+            # numpy creates a 0d object array if all else fails.
+            # Not interpretable as an array; return NotImplemented so that
+            # other's __rmatmul__ can kick in if that's implemented.
+            return NotImplemented
+        # Allow custom sparse class indicated by attr sparse gh-6520
+        try:
+            other.shape
+        except AttributeError:
+            other = other_a
+
+        if other.ndim == 1 or other.ndim == 2 and other.shape[1] == 1:
+            # dense row or column vector
+            if other.shape[0] != N:
+                raise ValueError(
+                    f"{err_prefix} (n,k={N}),(k={other.shape[0]},1?)->(n,1?)"
+                )
+
+            result = self._matmul_vector(np.ravel(other))
+
+            if isinstance(other, np.matrix):
+                result = self._ascontainer(result)
+
+            if other.ndim == 2 and other.shape[1] == 1:
+                # If 'other' was an (nx1) column vector, reshape the result
+                if self.ndim == 1:
+                    result = result.reshape(1)
+                else:
+                    result = result.reshape(-1, 1)
+
+            return result
+
+        elif other.ndim == 2:
+            ##
+            # dense 2D array or matrix ("multivector")
+
+            if other.shape[0] != N:
+                raise ValueError(
+                    f"{err_prefix} (n,k={N}),(k={other.shape[0]},m)->(n,m)"
+                )
+
+            result = self._matmul_multivector(np.asarray(other))
+
+            if isinstance(other, np.matrix):
+                result = self._ascontainer(result)
+
+            return result
+
+        else:
+            raise ValueError('could not interpret dimensions')
+
+    def __mul__(self, other):
+        return self.multiply(other)
+
+    def __rmul__(self, other):  # other * self
+        return self.multiply(other)
+
+    # by default, use CSR for __mul__ handlers
+    def _mul_scalar(self, other):
+        return self.tocsr()._mul_scalar(other)
+
+    def _matmul_vector(self, other):
+        return self.tocsr()._matmul_vector(other)
+
+    def _matmul_multivector(self, other):
+        return self.tocsr()._matmul_multivector(other)
+
+    def _matmul_sparse(self, other):
+        return self.tocsr()._matmul_sparse(other)
+
+    def _rmatmul_dispatch(self, other):
+        if isscalarlike(other):
+            return self._mul_scalar(other)
+        else:
+            # Don't use asarray unless we have to
+            try:
+                tr = other.transpose()
+            except AttributeError:
+                tr = np.asarray(other).transpose()
+            ret = self.transpose()._matmul_dispatch(tr)
+            if ret is NotImplemented:
+                return NotImplemented
+            return ret.transpose()
+
+    #######################
+    # matmul (@) operator #
+    #######################
+
+    def __matmul__(self, other):
+        if isscalarlike(other):
+            raise ValueError("Scalar operands are not allowed, "
+                             "use '*' instead")
+        return self._matmul_dispatch(other)
+
+    def __rmatmul__(self, other):
+        if isscalarlike(other):
+            raise ValueError("Scalar operands are not allowed, "
+                             "use '*' instead")
+        return self._rmatmul_dispatch(other)
+
+    ####################
+    # Other Arithmetic #
+    ####################
+
+    def _divide(self, other, *, rdivide=False):
+        if not (issparse(other) or isdense(other) or isscalarlike(other)):
+            # If it's a list or whatever, treat it like an array
+            other_a = np.asanyarray(other)
+            if other_a.ndim == 0 and other_a.dtype == np.object_:
+                # numpy creates a 0d object array if all else fails.
+                # Not interpretable as an array; return NotImplemented so that
+                # other's __rtruediv__ can kick in if that's implemented.
+                return NotImplemented
+            # Allow custom sparse class indicated by attr sparse gh-6520
+            try:
+                other.shape
+            except AttributeError:
+                other = other_a
+
+        if isscalarlike(other):
+            if rdivide:
+                return np.divide(other, self.todense())
+
+            if np.can_cast(self.dtype, np.float64):
+                return self.astype(np.float64, copy=False)._mul_scalar(1 / other)
+            else:
+                r = self._mul_scalar(1 / other)
+
+                scalar_dtype = np.asarray(other).dtype
+                if (np.issubdtype(self.dtype, np.integer) and
+                        np.issubdtype(scalar_dtype, np.integer)):
+                    return r.astype(self.dtype, copy=False)
+                else:
+                    return r
+
+        elif isdense(other):
+            if rdivide:
+                return np.divide(other, self.todense())
+
+            return self.multiply(np.divide(1, other))
+
+        elif issparse(other):
+            if rdivide:
+                return other._divide(self, rdivide=False)
+
+            csr_self = (self if self.ndim < 3 else self.reshape(1, -1)).tocsr()
+            csr_other = (other if self.ndim < 3 else other.reshape(1, -1)).tocsr()
+            if np.can_cast(self.dtype, np.float64):
+                csr_self = csr_self.astype(np.float64, copy=False)
+            result = csr_self._divide_sparse(csr_other)
+            return result if self.ndim < 3 else result.reshape(self.shape)
+        else:
+            # not scalar, dense or sparse. Return NotImplemented so
+            # other's __rtruediv__ can kick in if that's implemented.
+            return NotImplemented
+
+    def __truediv__(self, other):
+        return self._divide(other)
+
+    def __rtruediv__(self, other):
+        # Implementing this as the inverse would be too magical -- bail out
+        return NotImplemented
+
+    def __neg__(self):
+        return -self.tocsr()
+
+    def __iadd__(self, other):
+        return NotImplemented
+
+    def __isub__(self, other):
+        return NotImplemented
+
+    def __imul__(self, other):
+        return NotImplemented
+
+    def __itruediv__(self, other):
+        return NotImplemented
+
+    def __pow__(self, *args, **kwargs):
+        return self.power(*args, **kwargs)
+
+    def transpose(self, axes=None, copy=False):
+        """
+        Reverses the dimensions of the sparse array/matrix.
+
+        Parameters
+        ----------
+        axes : None, optional
+            This argument is in the signature *solely* for NumPy
+            compatibility reasons. Do not pass in anything except
+            for the default value.
+        copy : bool, optional
+            Indicates whether or not attributes of `self` should be
+            copied whenever possible. The degree to which attributes
+            are copied varies depending on the type of sparse array/matrix
+            being used.
+
+        Returns
+        -------
+        p : sparse array/matrix
+            The transpose of the array/matrix.
+
+        See Also
+        --------
+        numpy.transpose : NumPy's implementation of 'transpose' for ndarrays
+
+        Notes
+        -----
+        If `self` is a `csr_array` or a `csc_array`, then this will return a
+        `csc_array` or a `csr_array`, respectively.
+        """
+        return self.tocsr(copy=copy).transpose(axes=axes, copy=False)
+
+    def conjugate(self, copy=True):
+        """Element-wise complex conjugation.
+
+        If the array/matrix is of non-complex data type and `copy` is False,
+        this method does nothing and the data is not copied.
+
+        Parameters
+        ----------
+        copy : bool, optional
+            If True, the result is guaranteed to not share data with self.
+
+        Returns
+        -------
+        A : sparse array/matrix
+            The element-wise complex conjugate.
+        """
+        if np.issubdtype(self.dtype, np.complexfloating):
+            return self.tocsr(copy=copy).conjugate(copy=False)
+        elif copy:
+            return self.copy()
+        else:
+            return self
+
+    def conj(self, copy=True):
+        return self.conjugate(copy=copy)
+
+    conj.__doc__ = conjugate.__doc__
+
+    def _real(self):
+        return self.tocsr()._real()
+
+    def _imag(self):
+        return self.tocsr()._imag()
+
+    def nonzero(self):
+        """Nonzero indices of the array/matrix.
+
+        Returns
+        -------
+        row : ndarray
+            Row indices of non-zero elements.
+        col : ndarray
+            Column indices of non-zero elements.
+
+        Examples
+        --------
+        >>> from scipy.sparse import csr_array
+        >>> A = csr_array([[1, 2, 0], [0, 0, 3], [4, 0, 5]])
+        >>> A.nonzero()
+        (array([0, 0, 1, 2, 2], dtype=int32), array([0, 1, 2, 0, 2], dtype=int32))
+
+        """
+
+        # convert to COOrdinate format
+        A = self.tocoo()
+        nz_mask = A.data != 0
+        return tuple(idx[nz_mask] for idx in A.coords)
+
+    def _getcol(self, j, /):
+        """Returns a copy of column j of the array, as an (m x 1) sparse
+        array (column vector).
+        """
+        if self.ndim == 1:
+            raise ValueError("getcol not provided for 1d arrays. Use indexing A[j]")
+        # Subclasses should override this method for efficiency.
+        # Post-multiply by a (n x 1) column vector 'a' containing all zeros
+        # except for a_j = 1
+        N = self.shape[-1]
+        if j < 0:
+            j += N
+        if j < 0 or j >= N:
+            raise IndexError("index out of bounds")
+        col_selector = self._csc_container(([1], [[j], [0]]),
+                                           shape=(N, 1), dtype=self.dtype)
+        result = self @ col_selector
+        return result
+
+    def _getrow(self, i):
+        """Returns a copy of row i of the array, as a (1 x n) sparse
+        array (row vector).
+        """
+        if self.ndim == 1:
+            raise ValueError("getrow not meaningful for a 1d array")
+        # Subclasses should override this method for efficiency.
+        # Pre-multiply by a (1 x m) row vector 'a' containing all zeros
+        # except for a_i = 1
+        M = self.shape[0]
+        if i < 0:
+            i += M
+        if i < 0 or i >= M:
+            raise IndexError("index out of bounds")
+        row_selector = self._csr_container(([1], [[0], [i]]),
+                                           shape=(1, M), dtype=self.dtype)
+        return row_selector @ self
+
+    # The following dunder methods cannot be implemented.
+    #
+    # def __array__(self):
+    #     # Sparse matrices rely on NumPy wrapping them in object arrays under
+    #     # the hood to make unary ufuncs work on them. So we cannot raise
+    #     # TypeError here - which would be handy to not give users object
+    #     # arrays they probably don't want (they're looking for `.toarray()`).
+    #     #
+    #     # Conversion with `toarray()` would also break things because of the
+    #     # behavior discussed above, plus we want to avoid densification by
+    #     # accident because that can too easily blow up memory.
+    #
+    # def __array_ufunc__(self):
+    #     # We cannot implement __array_ufunc__ due to mismatching semantics.
+    #     # See gh-7707 and gh-7349 for details.
+    #
+    # def __array_function__(self):
+    #     # We cannot implement __array_function__ due to mismatching semantics.
+    #     # See gh-10362 for details.
+
+    def todense(self, order=None, out=None):
+        """
+        Return a dense representation of this sparse array.
+
+        Parameters
+        ----------
+        order : {'C', 'F'}, optional
+            Whether to store multi-dimensional data in C (row-major)
+            or Fortran (column-major) order in memory. The default
+            is 'None', which provides no ordering guarantees.
+            Cannot be specified in conjunction with the `out`
+            argument.
+
+        out : ndarray, 2-D, optional
+            If specified, uses this array as the output buffer
+            instead of allocating a new array to return. The
+            provided array must have the same shape and dtype as
+            the sparse array on which you are calling the method.
+
+        Returns
+        -------
+        arr : ndarray, 2-D
+            An array with the same shape and containing the same
+            data represented by the sparse array, with the requested
+            memory order. If `out` was passed, the same object is
+            returned after being modified in-place to contain the
+            appropriate values.
+        """
+        return self._ascontainer(self.toarray(order=order, out=out))
+
+    def toarray(self, order=None, out=None):
+        """
+        Return a dense ndarray representation of this sparse array/matrix.
+
+        Parameters
+        ----------
+        order : {'C', 'F'}, optional
+            Whether to store multidimensional data in C (row-major)
+            or Fortran (column-major) order in memory. The default
+            is 'None', which provides no ordering guarantees.
+            Cannot be specified in conjunction with the `out`
+            argument.
+
+        out : ndarray, 2-D, optional
+            If specified, uses this array as the output buffer
+            instead of allocating a new array to return. The provided
+            array must have the same shape and dtype as the sparse
+            array/matrix on which you are calling the method. For most
+            sparse types, `out` is required to be memory contiguous
+            (either C or Fortran ordered).
+
+        Returns
+        -------
+        arr : ndarray, 2-D
+            An array with the same shape and containing the same
+            data represented by the sparse array/matrix, with the requested
+            memory order. If `out` was passed, the same object is
+            returned after being modified in-place to contain the
+            appropriate values.
+        """
+        return self.tocoo(copy=False).toarray(order=order, out=out)
+
+    # Any sparse array format deriving from _spbase must define one of
+    # tocsr or tocoo. The other conversion methods may be implemented for
+    # efficiency, but are not required.
+    def tocsr(self, copy=False):
+        """Convert this array/matrix to Compressed Sparse Row format.
+
+        Parameters
+        ----------
+        copy : bool, optional
+            With ``copy=False``, the data/indices may be shared between this
+            array/matrix and the resultant csr_array/matrix.
+
+        Returns
+        -------
+        csr array/matrix
+            The converted array/matrix in CSR format.
+        """
+        return self.tocoo(copy=copy).tocsr(copy=False)
+
+    def todok(self, copy=False):
+        """Convert this array/matrix to Dictionary Of Keys format.
+
+        Parameters
+        ----------
+        copy : bool, optional
+            With ``copy=False``, the data/indices may be shared between this
+            array/matrix and the resultant dok_array/matrix.
+
+        Returns
+        -------
+        dok array/matrix
+            The converted array/matrix in DOK format.
+        """
+        return self.tocoo(copy=copy).todok(copy=False)
+
+    def tocoo(self, copy=False):
+        """Convert this array/matrix to COOrdinate format.
+
+        Parameters
+        ----------
+        copy : bool, optional
+            With ``copy=False``, the data/indices may be shared between this
+            array/matrix and the resultant coo_array/matrix.
+
+        Returns
+        -------
+        coo array/matrix
+            The converted array/matrix in COO format.
+        """
+        return self.tocsr(copy=False).tocoo(copy=copy)
+
+    def tolil(self, copy=False):
+        """Convert this array/matrix to List of Lists format.
+
+        Parameters
+        ----------
+        copy : bool, optional
+            With ``copy=False``, the data/indices may be shared between this
+            array/matrix and the resultant lil_array/matrix.
+
+        Returns
+        -------
+        lil array/matrix
+            The converted array/matrix in LIL format.
+        """
+        return self.tocsr(copy=False).tolil(copy=copy)
+
+    def todia(self, copy=False):
+        """Convert this array/matrix to sparse DIAgonal format.
+
+        Parameters
+        ----------
+        copy : bool, optional
+            With ``copy=False``, the data/indices may be shared between this
+            array/matrix and the resultant dia_array/matrix.
+
+        Returns
+        -------
+        dia array/matrix
+            The converted array/matrix in DIA format.
+        """
+        return self.tocoo(copy=copy).todia(copy=False)
+
+    def tobsr(self, blocksize=None, copy=False):
+        """Convert this array/matrix to Block Sparse Row format.
+
+        Parameters
+        ----------
+        blocksize : tuple of ints, optional
+            When ``blocksize=(R, C)`` is provided, it will be used for construction of
+            the bsr_array/matrix.
+        copy : bool, option
+            With ``copy=False``, the data/indices may be shared between this
+            array/matrix and the resultant bsr_array/matrix.
+
+        Returns
+        -------
+        bsr array/matrix
+            The converted array/matrix in BSR format.
+        """
+        return self.tocsr(copy=False).tobsr(blocksize=blocksize, copy=copy)
+
+    def tocsc(self, copy=False):
+        """Convert this array/matrix to Compressed Sparse Column format.
+
+        Parameters
+        ----------
+        copy : bool, optional
+            With ``copy=False``, the data/indices may be shared between this
+            array/matrix and the resultant csc_array/matrix.
+
+        Returns
+        -------
+        csc array/matrix
+            The converted array/matrix in CSC format.
+        """
+        return self.tocsr(copy=copy).tocsc(copy=False)
+
+    def copy(self):
+        """Returns a copy of this array/matrix.
+
+        No data/indices will be shared between the returned value and current
+        array/matrix.
+
+        Returns
+        -------
+        sparse array/matrix
+            A copy of this array/matrix.
+        """
+        return self.__class__(self, copy=True)
+
+    def sum(self, axis=None, dtype=None, out=None):
+        """
+        Sum the array/matrix elements over a given axis.
+
+        Parameters
+        ----------
+        axis : {-2, -1, 0, 1, None} optional
+            Axis along which the sum is computed. The default is to
+            compute the sum of all the array/matrix elements, returning a scalar
+            (i.e., `axis` = `None`).
+        dtype : dtype, optional
+            The type of the returned array/matrix and of the accumulator in which
+            the elements are summed.  The dtype of `a` is used by default
+            unless `a` has an integer dtype of less precision than the default
+            platform integer.  In that case, if `a` is signed then the platform
+            integer is used while if `a` is unsigned then an unsigned integer
+            of the same precision as the platform integer is used.
+
+            .. versionadded:: 0.18.0
+
+        out : np.matrix, optional
+            Alternative output matrix in which to place the result. It must
+            have the same shape as the expected output, but the type of the
+            output values will be cast if necessary.
+
+            .. versionadded:: 0.18.0
+
+        Returns
+        -------
+        sum_along_axis : np.matrix
+            A matrix with the same shape as `self`, with the specified
+            axis removed.
+
+        See Also
+        --------
+        numpy.matrix.sum : NumPy's implementation of 'sum' for matrices
+
+        """
+        axis = validateaxis(axis, ndim=self.ndim)
+
+        # Mimic numpy's casting.
+        res_dtype = get_sum_dtype(self.dtype)
+
+        if dtype is not None:
+            # Before casting to the requested dtype, canonicalize duplicates and zeros.
+            if hasattr(self, 'sum_duplicates'):
+                self.sum_duplicates()
+            temp = self.astype(dtype, copy=False).sum(axis=axis, dtype=None, out=out)
+            return temp.astype(dtype, copy=False)
+
+        # Note: all valid 1D axis values are canonically `None`.
+        if axis is None:
+            if self.nnz == 0:
+                return np.sum(self._ascontainer([0]), dtype=dtype or res_dtype, out=out)
+            return np.sum(self._ascontainer(_todata(self)), dtype=dtype, out=out)
+        elif isinstance(self, sparray):
+            new_shape = tuple(self.shape[i] for i in range(self.ndim) if i not in axis)
+        else:
+            # Ensure spmatrix sums stay 2D
+            new_shape = (1, self.shape[1]) if axis == (0,) else (self.shape[0], 1)
+
+        if out is None:
+            # create out array with desired dtype
+            out = self._ascontainer(np.zeros(new_shape, dtype=dtype or res_dtype))
+        else:
+            if out.shape != new_shape:
+                raise ValueError("out dimensions do not match shape")
+
+        if self.ndim > 2:
+            return self._sum_nd(axis, res_dtype, out)
+
+        # We use multiplication by a matrix of ones to sum.
+        # For some sparse array formats more efficient methods are
+        # possible -- these should override this function.
+        if axis == (0,):
+            ones = self._ascontainer(np.ones((1, self.shape[0]), dtype=res_dtype))
+            # sets dtype while loading into out
+            out[...] = (ones @ self).reshape(new_shape)
+        else:  # axis == (1,)
+            ones = self._ascontainer(np.ones((self.shape[1], 1), dtype=res_dtype))
+            # sets dtype while loading into out
+            out[...] = (self @ ones).reshape(new_shape)
+        return out
+
+    def mean(self, axis=None, dtype=None, out=None):
+        """
+        Compute the arithmetic mean along the specified axis.
+
+        Returns the average of the array/matrix elements. The average is taken
+        over all elements in the array/matrix by default, otherwise over the
+        specified axis. `float64` intermediate and return values are used
+        for integer inputs.
+
+        Parameters
+        ----------
+        axis : {-2, -1, 0, 1, None} optional
+            Axis along which the mean is computed. The default is to compute
+            the mean of all elements in the array/matrix (i.e., `axis` = `None`).
+        dtype : data-type, optional
+            Type to use in computing the mean. For integer inputs, the default
+            is `float64`; for floating point inputs, it is the same as the
+            input dtype.
+
+            .. versionadded:: 0.18.0
+
+        out : np.matrix, optional
+            Alternative output matrix in which to place the result. It must
+            have the same shape as the expected output, but the type of the
+            output values will be cast if necessary.
+
+            .. versionadded:: 0.18.0
+
+        Returns
+        -------
+        m : np.matrix
+            Mean along the specified axis.
+
+        See Also
+        --------
+        numpy.matrix.mean : NumPy's implementation of 'mean' for matrices
+
+        """
+        axis = validateaxis(axis, ndim=self.ndim)
+
+        integral = (np.issubdtype(self.dtype, np.integer) or
+                    np.issubdtype(self.dtype, np.bool_))
+
+        # intermediate dtype for summation
+        inter_dtype = np.float64 if integral else self.dtype
+        inter_self = self.astype(inter_dtype, copy=False)
+
+        if axis is None:
+            denom = math.prod(self.shape)
+        else:
+            denom = math.prod(self.shape[ax] for ax in axis)
+        res = (inter_self * (1.0 / denom)).sum(axis=axis, dtype=inter_dtype, out=out)
+        if dtype is not None and out is None:
+            return res.astype(dtype, copy=False)
+        return res
+
+
+    def diagonal(self, k=0):
+        """Returns the kth diagonal of the array/matrix.
+
+        Parameters
+        ----------
+        k : int, optional
+            Which diagonal to get, corresponding to elements a[i, i+k].
+            Default: 0 (the main diagonal).
+
+            .. versionadded:: 1.0
+
+        Returns
+        -------
+        d : ndarray
+            The specified diagonal of the array/matrix.
+
+        See Also
+        --------
+        numpy.diagonal : Equivalent numpy function.
+
+        Examples
+        --------
+        >>> from scipy.sparse import csr_array
+        >>> A = csr_array([[1, 2, 0], [0, 0, 3], [4, 0, 5]])
+        >>> A.diagonal()
+        array([1, 0, 5])
+        >>> A.diagonal(k=1)
+        array([2, 3])
+        """
+        return self.tocsr().diagonal(k=k)
+
+    def trace(self, offset=0):
+        """Returns the sum along diagonals of the sparse array/matrix.
+
+        Parameters
+        ----------
+        offset : int, optional
+            Which diagonal to get, corresponding to elements a[i, i+offset].
+            Default: 0 (the main diagonal).
+
+        Returns
+        -------
+        scalar
+            The sum of the specified diagonal of the array/matrix.
+        """
+        return self.diagonal(k=offset).sum()
+
+    def setdiag(self, values, k=0):
+        """
+        Set diagonal or off-diagonal elements of the array/matrix.
+
+        Parameters
+        ----------
+        values : array_like
+            New values of the diagonal elements.
+
+            Values may have any length. If the diagonal is longer than values,
+            then the remaining diagonal entries will not be set. If values are
+            longer than the diagonal, then the remaining values are ignored.
+
+            If a scalar value is given, all of the diagonal is set to it.
+
+        k : int, optional
+            Which off-diagonal to set, corresponding to elements a[i,i+k].
+            Default: 0 (the main diagonal).
+
+        """
+        M, N = self.shape
+        if (k > 0 and k >= N) or (k < 0 and -k >= M):
+            raise ValueError("k exceeds array dimensions")
+        self._setdiag(np.asarray(values), k)
+
+    def _setdiag(self, values, k):
+        """This part of the implementation gets overridden by the
+        different formats.
+        """
+        M, N = self.shape
+        if k < 0:
+            if values.ndim == 0:
+                # broadcast
+                max_index = min(M+k, N)
+                for i in range(max_index):
+                    self[i - k, i] = values
+            else:
+                max_index = min(M+k, N, len(values))
+                if max_index <= 0:
+                    return
+                for i, v in enumerate(values[:max_index]):
+                    self[i - k, i] = v
+        else:
+            if values.ndim == 0:
+                # broadcast
+                max_index = min(M, N-k)
+                for i in range(max_index):
+                    self[i, i + k] = values
+            else:
+                max_index = min(M, N-k, len(values))
+                if max_index <= 0:
+                    return
+                for i, v in enumerate(values[:max_index]):
+                    self[i, i + k] = v
+
+    def _process_toarray_args(self, order, out):
+        if out is not None:
+            if order is not None:
+                raise ValueError('order cannot be specified if out '
+                                 'is not None')
+            if out.shape != self.shape or out.dtype != self.dtype:
+                raise ValueError('out array must be same dtype and shape as '
+                                 'sparse array')
+            out[...] = 0.
+            return out
+        else:
+            return np.zeros(self.shape, dtype=self.dtype, order=order)
+
+    def _get_index_dtype(self, arrays=(), maxval=None, check_contents=False):
+        """
+        Determine index dtype for array.
+
+        This wraps _sputils.get_index_dtype, providing compatibility for both
+        array and matrix API sparse matrices. Matrix API sparse matrices would
+        attempt to downcast the indices - which can be computationally
+        expensive and undesirable for users. The array API changes this
+        behaviour.
+
+        See discussion: https://github.com/scipy/scipy/issues/16774
+
+        The get_index_dtype import is due to implementation details of the test
+        suite. It allows the decorator ``with_64bit_maxval_limit`` to mock a
+        lower int32 max value for checks on the matrix API's downcasting
+        behaviour.
+        """
+        from ._sputils import get_index_dtype
+
+        # Don't check contents for array API
+        return get_index_dtype(arrays,
+                               maxval,
+                               (check_contents and not isinstance(self, sparray)))
+
+
+class sparray:
+    """A namespace class to separate sparray from spmatrix.
+
+    This class serves as the namespace for SciPy sparse array types.
+    It cannot be instantiated and is designed as a mixin class.
+    """
+
+    @classmethod
+    def __class_getitem__(cls, arg, /):
+        """
+        Return a parametrized wrapper around the `~scipy.sparse.sparray` type.
+
+        .. versionadded:: 1.16.0
+
+        Returns
+        -------
+        alias : types.GenericAlias
+            A parametrized `~scipy.sparse.sparray` type.
+
+        Examples
+        --------
+        >>> import numpy as np
+        >>> from scipy.sparse import coo_array
+
+        >>> coo_array[np.int8, tuple[int]]
+        scipy.sparse._coo.coo_array[numpy.int8, tuple[int]]
+        """
+        from types import GenericAlias
+        return GenericAlias(cls, arg)
+
+
+sparray.__doc__ = _spbase.__doc__
+
+
+def isspmatrix(x):
+    """Is `x` of a sparse matrix type?
+
+    .. warning::
+
+        scipy.sparse is switching to the sparse array interface.
+
+        The ``isspmatrix`` function returns ``False`` for sparse arrays.
+        It will remain after the switch to sparse arrays (sparray).
+        So this is a future proof way to check for sparray vs spmatrix.
+        If you just want to check for sparse, use ``issparse(A)``.
+        For more general information about sparrays, see
+        :ref:`Migration from spmatrix to sparray <migration_to_sparray>`.
+        The switch to sparse arrays will occur no earlier than v1.21.
+
+    Parameters
+    ----------
+    x
+        object to check for being a sparse matrix
+
+    Returns
+    -------
+    bool
+        True if `x` is a sparse matrix, False otherwise
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.sparse import csr_array, csr_matrix, isspmatrix
+    >>> isspmatrix(csr_matrix([[5]]))
+    True
+    >>> isspmatrix(csr_array([[5]]))
+    False
+    >>> isspmatrix(np.array([[5]]))
+    False
+    >>> isspmatrix(5)
+    False
+    """
+    return isinstance(x, spmatrix)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/_bsr.py b/venv/lib/python3.12/site-packages/scipy/sparse/_bsr.py
new file mode 100644
index 0000000000000000000000000000000000000000..2375ccc4e2c98d70924bb1a072c39be316a453c9
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/_bsr.py
@@ -0,0 +1,904 @@
+"""Compressed Block Sparse Row format"""
+
+__docformat__ = "restructuredtext en"
+
+__all__ = ['bsr_array', 'bsr_matrix', 'isspmatrix_bsr']
+
+from warnings import warn
+
+import numpy as np
+
+from scipy._lib._util import copy_if_needed
+from ._matrix import spmatrix
+from ._data import _data_matrix, _minmax_mixin
+from ._compressed import _cs_matrix
+from ._base import issparse, _formats, _spbase, sparray
+from ._sputils import (isshape, getdtype, getdata, to_native, upcast,
+                       check_shape)
+from . import _sparsetools
+from ._sparsetools import (bsr_matvec, bsr_matvecs, csr_matmat_maxnnz,
+                           bsr_matmat, bsr_transpose, bsr_sort_indices,
+                           bsr_tocsr)
+
+
+class _bsr_base(_cs_matrix, _minmax_mixin):
+    _format = 'bsr'
+
+    def __init__(self, arg1, shape=None, dtype=None, copy=False,
+                 blocksize=None, *, maxprint=None):
+        _data_matrix.__init__(self, arg1, maxprint=maxprint)
+
+        if issparse(arg1):
+            if arg1.format == self.format and copy:
+                arg1 = arg1.copy()
+            else:
+                arg1 = arg1.tobsr(blocksize=blocksize)
+            self.indptr, self.indices, self.data, self._shape = (
+                arg1.indptr, arg1.indices, arg1.data, arg1._shape
+            )
+
+        elif isinstance(arg1,tuple):
+            if isshape(arg1):
+                # it's a tuple of matrix dimensions (M,N)
+                self._shape = check_shape(arg1)
+                M,N = self.shape
+                # process blocksize
+                if blocksize is None:
+                    blocksize = (1,1)
+                else:
+                    if not isshape(blocksize):
+                        raise ValueError(f'invalid blocksize={blocksize}')
+                    blocksize = tuple(blocksize)
+                self.data = np.zeros((0,) + blocksize, getdtype(dtype, default=float))
+
+                R,C = blocksize
+                if (M % R) != 0 or (N % C) != 0:
+                    raise ValueError('shape must be multiple of blocksize')
+
+                # Select index dtype large enough to pass array and
+                # scalar parameters to sparsetools
+                idx_dtype = self._get_index_dtype(maxval=max(M//R, N//C, R, C))
+                self.indices = np.zeros(0, dtype=idx_dtype)
+                self.indptr = np.zeros(M//R + 1, dtype=idx_dtype)
+
+            elif len(arg1) == 2:
+                # (data,(row,col)) format
+                coo = self._coo_container(arg1, dtype=dtype, shape=shape)
+                bsr = coo.tobsr(blocksize=blocksize)
+                self.indptr, self.indices, self.data, self._shape = (
+                    bsr.indptr, bsr.indices, bsr.data, bsr._shape
+                )
+
+            elif len(arg1) == 3:
+                # (data,indices,indptr) format
+                (data, indices, indptr) = arg1
+
+                # Select index dtype large enough to pass array and
+                # scalar parameters to sparsetools
+                maxval = 1
+                if shape is not None:
+                    maxval = max(shape)
+                if blocksize is not None:
+                    maxval = max(maxval, max(blocksize))
+                idx_dtype = self._get_index_dtype((indices, indptr), maxval=maxval,
+                                                  check_contents=True)
+                if not copy:
+                    copy = copy_if_needed
+                self.indices = np.array(indices, copy=copy, dtype=idx_dtype)
+                self.indptr = np.array(indptr, copy=copy, dtype=idx_dtype)
+                self.data = getdata(data, copy=copy, dtype=dtype)
+                if self.data.ndim != 3:
+                    raise ValueError(
+                        f'BSR data must be 3-dimensional, got shape={self.data.shape}'
+                    )
+                if blocksize is not None:
+                    if not isshape(blocksize):
+                        raise ValueError(f'invalid blocksize={blocksize}')
+                    if tuple(blocksize) != self.data.shape[1:]:
+                        raise ValueError(
+                            f'mismatching blocksize={blocksize}'
+                            f' vs {self.data.shape[1:]}'
+                        )
+            else:
+                raise ValueError('unrecognized bsr_array constructor usage')
+        else:
+            # must be dense
+            try:
+                arg1 = np.asarray(arg1)
+            except Exception as e:
+                raise ValueError("unrecognized form for "
+                                 f"{self.format}_matrix constructor") from e
+            if isinstance(self, sparray) and arg1.ndim != 2:
+                raise ValueError(f"BSR arrays don't support {arg1.ndim}D input. Use 2D")
+            arg1 = self._coo_container(arg1, dtype=dtype).tobsr(blocksize=blocksize)
+            self.indptr, self.indices, self.data, self._shape = (
+                arg1.indptr, arg1.indices, arg1.data, arg1._shape
+            )
+
+        if shape is not None:
+            self._shape = check_shape(shape)
+        else:
+            if self.shape is None:
+                # shape not already set, try to infer dimensions
+                try:
+                    M = len(self.indptr) - 1
+                    N = self.indices.max() + 1
+                except Exception as e:
+                    raise ValueError('unable to infer matrix dimensions') from e
+                else:
+                    R,C = self.blocksize
+                    self._shape = check_shape((M*R,N*C))
+
+        if self.shape is None:
+            if shape is None:
+                # TODO infer shape here
+                raise ValueError('need to infer shape')
+            else:
+                self._shape = check_shape(shape)
+
+        if dtype is not None:
+            self.data = self.data.astype(getdtype(dtype, self.data), copy=False)
+
+        self.check_format(full_check=False)
+
+    def check_format(self, full_check=True):
+        """Check whether the array/matrix respects the BSR format.
+
+        Parameters
+        ----------
+        full_check : bool, optional
+            If `True`, run rigorous check, scanning arrays for valid values.
+            Note that activating those check might copy arrays for casting,
+            modifying indices and index pointers' inplace.
+            If `False`, run basic checks on attributes. O(1) operations.
+            Default is `True`.
+        """
+        M,N = self.shape
+        R,C = self.blocksize
+
+        # index arrays should have integer data types
+        if self.indptr.dtype.kind != 'i':
+            warn(f"indptr array has non-integer dtype ({self.indptr.dtype.name})",
+                 stacklevel=2)
+        if self.indices.dtype.kind != 'i':
+            warn(f"indices array has non-integer dtype ({self.indices.dtype.name})",
+                 stacklevel=2)
+
+        # check array shapes
+        if self.indices.ndim != 1 or self.indptr.ndim != 1:
+            raise ValueError("indices, and indptr should be 1-D")
+        if self.data.ndim != 3:
+            raise ValueError("data should be 3-D")
+
+        # check index pointer
+        if (len(self.indptr) != M//R + 1):
+            raise ValueError(
+                f"index pointer size ({len(self.indptr)}) should be ({M//R + 1})"
+            )
+        if (self.indptr[0] != 0):
+            raise ValueError("index pointer should start with 0")
+
+        # check index and data arrays
+        if (len(self.indices) != len(self.data)):
+            raise ValueError("indices and data should have the same size")
+        if (self.indptr[-1] > len(self.indices)):
+            raise ValueError("Last value of index pointer should be less than "
+                                "the size of index and data arrays")
+
+        self.prune()
+
+        if full_check:
+            # check format validity (more expensive)
+            if self.nnz > 0:
+                if self.indices.max() >= N//C:
+                    raise ValueError(
+                        f"column index values must be < {N//C}"
+                        f" (now max {self.indices.max()})"
+                    )
+                if self.indices.min() < 0:
+                    raise ValueError("column index values must be >= 0")
+                if np.diff(self.indptr).min() < 0:
+                    raise ValueError("index pointer values must form a "
+                                        "non-decreasing sequence")
+
+            idx_dtype = self._get_index_dtype((self.indices, self.indptr))
+            self.indptr = np.asarray(self.indptr, dtype=idx_dtype)
+            self.indices = np.asarray(self.indices, dtype=idx_dtype)
+            self.data = to_native(self.data)
+        # if not self.has_sorted_indices():
+        #    warn('Indices were not in sorted order. Sorting indices.')
+        #    self.sort_indices(check_first=False)
+
+    @property
+    def blocksize(self) -> tuple:
+        """Block size of the matrix."""
+        return self.data.shape[1:]
+
+    def _getnnz(self, axis=None):
+        if axis is not None:
+            raise NotImplementedError("_getnnz over an axis is not implemented "
+                                      "for BSR format")
+        R, C = self.blocksize
+        return int(self.indptr[-1]) * R * C
+
+    _getnnz.__doc__ = _spbase._getnnz.__doc__
+
+    def count_nonzero(self, axis=None):
+        if axis is not None:
+            return self.tocsr().count_nonzero(axis=axis)
+        return np.count_nonzero(self._deduped_data())
+
+    count_nonzero.__doc__ = _spbase.count_nonzero.__doc__
+
+    def __repr__(self):
+        _, fmt = _formats[self.format]
+        sparse_cls = 'array' if isinstance(self, sparray) else 'matrix'
+        b = 'x'.join(str(x) for x in self.blocksize)
+        return (
+            f"<{fmt} sparse {sparse_cls} of dtype '{self.dtype}'\n"
+            f"\twith {self.nnz} stored elements (blocksize={b}) and shape {self.shape}>"
+        )
+
+    def diagonal(self, k=0):
+        rows, cols = self.shape
+        if k <= -rows or k >= cols:
+            return np.empty(0, dtype=self.data.dtype)
+        R, C = self.blocksize
+        y = np.zeros(min(rows + min(k, 0), cols - max(k, 0)),
+                     dtype=upcast(self.dtype))
+        _sparsetools.bsr_diagonal(k, rows // R, cols // C, R, C,
+                                  self.indptr, self.indices,
+                                  np.ravel(self.data), y)
+        return y
+
+    diagonal.__doc__ = _spbase.diagonal.__doc__
+
+    ##########################
+    # NotImplemented methods #
+    ##########################
+
+    def __getitem__(self,key):
+        raise NotImplementedError
+
+    def __setitem__(self,key,val):
+        raise NotImplementedError
+
+    ######################
+    # Arithmetic methods #
+    ######################
+
+    def _add_dense(self, other):
+        return self.tocoo(copy=False)._add_dense(other)
+
+    def _matmul_vector(self, other):
+        M,N = self.shape
+        R,C = self.blocksize
+
+        result = np.zeros(self.shape[0], dtype=upcast(self.dtype, other.dtype))
+
+        bsr_matvec(M//R, N//C, R, C,
+            self.indptr, self.indices, self.data.ravel(),
+            other, result)
+
+        return result
+
+    def _matmul_multivector(self,other):
+        R,C = self.blocksize
+        M,N = self.shape
+        n_vecs = other.shape[1]  # number of column vectors
+
+        result = np.zeros((M,n_vecs), dtype=upcast(self.dtype,other.dtype))
+
+        bsr_matvecs(M//R, N//C, n_vecs, R, C,
+                self.indptr, self.indices, self.data.ravel(),
+                other.ravel(), result.ravel())
+
+        return result
+
+    def _matmul_sparse(self, other):
+        M, K1 = self.shape
+        K2, N = other.shape
+
+        R,n = self.blocksize
+
+        # convert to this format
+        if other.format == "bsr":
+            C = other.blocksize[1]
+        else:
+            C = 1
+
+        if other.format == "csr" and n == 1:
+            other = other.tobsr(blocksize=(n,C), copy=False)  # lightweight conversion
+        else:
+            other = other.tobsr(blocksize=(n,C))
+
+        idx_dtype = self._get_index_dtype((self.indptr, self.indices,
+                                           other.indptr, other.indices))
+
+        n_brow = M // R
+        n_bcol = N // C
+        bnnz = csr_matmat_maxnnz(n_brow, n_bcol,
+                                 self.indptr.astype(idx_dtype, copy=False),
+                                 self.indices.astype(idx_dtype, copy=False),
+                                 other.indptr.astype(idx_dtype, copy=False),
+                                 other.indices.astype(idx_dtype, copy=False))
+
+        idx_dtype = self._get_index_dtype((self.indptr, self.indices,
+                                           other.indptr, other.indices),
+                                          maxval=bnnz)
+        indptr = np.empty(self.indptr.shape, dtype=idx_dtype)
+        indices = np.empty(bnnz, dtype=idx_dtype)
+        data = np.empty(R*C*bnnz, dtype=upcast(self.dtype,other.dtype))
+
+        bsr_matmat(bnnz, n_brow, n_bcol, R, C, n,
+                   self.indptr.astype(idx_dtype, copy=False),
+                   self.indices.astype(idx_dtype, copy=False),
+                   np.ravel(self.data),
+                   other.indptr.astype(idx_dtype, copy=False),
+                   other.indices.astype(idx_dtype, copy=False),
+                   np.ravel(other.data),
+                   indptr,
+                   indices,
+                   data)
+
+        data = data.reshape(-1,R,C)
+
+        # TODO eliminate zeros
+
+        return self._bsr_container(
+            (data, indices, indptr), shape=(M, N), blocksize=(R, C)
+        )
+
+    ######################
+    # Conversion methods #
+    ######################
+
+    def tobsr(self, blocksize=None, copy=False):
+        if blocksize not in [None, self.blocksize]:
+            return self.tocsr().tobsr(blocksize=blocksize)
+        if copy:
+            return self.copy()
+        else:
+            return self
+
+    tobsr.__doc__ = _spbase.tobsr.__doc__
+
+    def tocsr(self, copy=False):
+        M, N = self.shape
+        R, C = self.blocksize
+        nnz = self.nnz
+        idx_dtype = self._get_index_dtype((self.indptr, self.indices),
+                                          maxval=max(nnz, N))
+        indptr = np.empty(M + 1, dtype=idx_dtype)
+        indices = np.empty(nnz, dtype=idx_dtype)
+        data = np.empty(nnz, dtype=upcast(self.dtype))
+
+        bsr_tocsr(M // R,  # n_brow
+                  N // C,  # n_bcol
+                  R, C,
+                  self.indptr.astype(idx_dtype, copy=False),
+                  self.indices.astype(idx_dtype, copy=False),
+                  self.data,
+                  indptr,
+                  indices,
+                  data)
+        return self._csr_container((data, indices, indptr), shape=self.shape)
+
+    tocsr.__doc__ = _spbase.tocsr.__doc__
+
+    def tocsc(self, copy=False):
+        return self.tocsr(copy=False).tocsc(copy=copy)
+
+    tocsc.__doc__ = _spbase.tocsc.__doc__
+
+    def tocoo(self, copy=True):
+        M,N = self.shape
+        R,C = self.blocksize
+
+        indptr_diff = np.diff(self.indptr)
+        if indptr_diff.dtype.itemsize > np.dtype(np.intp).itemsize:
+            # Check for potential overflow
+            indptr_diff_limited = indptr_diff.astype(np.intp)
+            if np.any(indptr_diff_limited != indptr_diff):
+                raise ValueError("Matrix too big to convert")
+            indptr_diff = indptr_diff_limited
+
+        idx_dtype = self._get_index_dtype(maxval=max(M, N))
+        row = (R * np.arange(M//R, dtype=idx_dtype)).repeat(indptr_diff)
+        row = row.repeat(R*C).reshape(-1,R,C)
+        row += np.tile(np.arange(R, dtype=idx_dtype).reshape(-1,1), (1,C))
+        row = row.reshape(-1)
+
+        col = ((C * self.indices).astype(idx_dtype, copy=False)
+               .repeat(R*C).reshape(-1,R,C))
+        col += np.tile(np.arange(C, dtype=idx_dtype), (R,1))
+        col = col.reshape(-1)
+
+        data = self.data.reshape(-1)
+
+        if copy:
+            data = data.copy()
+
+        return self._coo_container(
+            (data, (row, col)), shape=self.shape
+        )
+
+    tocoo.__doc__ = _spbase.tocoo.__doc__
+
+    def toarray(self, order=None, out=None):
+        return self.tocoo(copy=False).toarray(order=order, out=out)
+
+    toarray.__doc__ = _spbase.toarray.__doc__
+
+    def transpose(self, axes=None, copy=False):
+        if axes is not None and axes != (1, 0):
+            raise ValueError("Sparse matrices do not support "
+                              "an 'axes' parameter because swapping "
+                              "dimensions is the only logical permutation.")
+
+        R, C = self.blocksize
+        M, N = self.shape
+        NBLK = self.nnz//(R*C)
+
+        if self.nnz == 0:
+            return self._bsr_container((N, M), blocksize=(C, R),
+                                       dtype=self.dtype, copy=copy)
+
+        indptr = np.empty(N//C + 1, dtype=self.indptr.dtype)
+        indices = np.empty(NBLK, dtype=self.indices.dtype)
+        data = np.empty((NBLK, C, R), dtype=self.data.dtype)
+
+        bsr_transpose(M//R, N//C, R, C,
+                      self.indptr, self.indices, self.data.ravel(),
+                      indptr, indices, data.ravel())
+
+        return self._bsr_container((data, indices, indptr),
+                                   shape=(N, M), copy=copy)
+
+    transpose.__doc__ = _spbase.transpose.__doc__
+
+    ##############################################################
+    # methods that examine or modify the internal data structure #
+    ##############################################################
+
+    def eliminate_zeros(self):
+        """Remove zero elements in-place."""
+
+        if not self.nnz:
+            return  # nothing to do
+
+        R,C = self.blocksize
+        M,N = self.shape
+
+        mask = (self.data != 0).reshape(-1,R*C).sum(axis=1)  # nonzero blocks
+
+        nonzero_blocks = mask.nonzero()[0]
+
+        self.data[:len(nonzero_blocks)] = self.data[nonzero_blocks]
+
+        # modifies self.indptr and self.indices *in place*
+        _sparsetools.csr_eliminate_zeros(M//R, N//C, self.indptr,
+                                         self.indices, mask)
+        self.prune()
+
+    def sum_duplicates(self):
+        """Eliminate duplicate array/matrix entries by adding them together.
+
+        The is an *in place* operation
+        """
+        if self.has_canonical_format:
+            return
+        self.sort_indices()
+        R, C = self.blocksize
+        M, N = self.shape
+
+        # port of _sparsetools.csr_sum_duplicates
+        n_row = M // R
+        nnz = 0
+        row_end = 0
+        for i in range(n_row):
+            jj = row_end
+            row_end = self.indptr[i+1]
+            while jj < row_end:
+                j = self.indices[jj]
+                x = self.data[jj]
+                jj += 1
+                while jj < row_end and self.indices[jj] == j:
+                    x += self.data[jj]
+                    jj += 1
+                self.indices[nnz] = j
+                self.data[nnz] = x
+                nnz += 1
+            self.indptr[i+1] = nnz
+
+        self.prune()  # nnz may have changed
+        self.has_canonical_format = True
+
+    def sort_indices(self):
+        """Sort the indices of this array/matrix *in place*.
+        """
+        if self.has_sorted_indices:
+            return
+
+        R,C = self.blocksize
+        M,N = self.shape
+
+        bsr_sort_indices(M//R, N//C, R, C, self.indptr, self.indices, self.data.ravel())
+
+        self.has_sorted_indices = True
+
+    def prune(self):
+        """Remove empty space after all non-zero elements.
+        """
+
+        R,C = self.blocksize
+        M,N = self.shape
+
+        if len(self.indptr) != M//R + 1:
+            raise ValueError("index pointer has invalid length")
+
+        bnnz = self.indptr[-1]
+
+        if len(self.indices) < bnnz:
+            raise ValueError("indices array has too few elements")
+        if len(self.data) < bnnz:
+            raise ValueError("data array has too few elements")
+
+        self.data = self.data[:bnnz]
+        self.indices = self.indices[:bnnz]
+
+    # utility functions
+    def _binopt(self, other, op, in_shape=None, out_shape=None):
+        """Apply the binary operation fn to two sparse matrices."""
+
+        # Ideally we'd take the GCDs of the blocksize dimensions
+        # and explode self and other to match.
+        other = self.__class__(other, blocksize=self.blocksize)
+
+        # e.g. bsr_plus_bsr, etc.
+        fn = getattr(_sparsetools, self.format + op + self.format)
+
+        R,C = self.blocksize
+
+        max_bnnz = len(self.data) + len(other.data)
+        idx_dtype = self._get_index_dtype((self.indptr, self.indices,
+                                           other.indptr, other.indices),
+                                          maxval=max_bnnz)
+        indptr = np.empty(self.indptr.shape, dtype=idx_dtype)
+        indices = np.empty(max_bnnz, dtype=idx_dtype)
+
+        bool_ops = ['_ne_', '_lt_', '_gt_', '_le_', '_ge_']
+        if op in bool_ops:
+            data = np.empty(R*C*max_bnnz, dtype=np.bool_)
+        else:
+            data = np.empty(R*C*max_bnnz, dtype=upcast(self.dtype,other.dtype))
+
+        fn(self.shape[0]//R, self.shape[1]//C, R, C,
+           self.indptr.astype(idx_dtype, copy=False),
+           self.indices.astype(idx_dtype, copy=False),
+           self.data,
+           other.indptr.astype(idx_dtype, copy=False),
+           other.indices.astype(idx_dtype, copy=False),
+           np.ravel(other.data),
+           indptr,
+           indices,
+           data)
+
+        actual_bnnz = indptr[-1]
+        indices = indices[:actual_bnnz]
+        data = data[:R*C*actual_bnnz]
+
+        if actual_bnnz < max_bnnz/2:
+            indices = indices.copy()
+            data = data.copy()
+
+        data = data.reshape(-1,R,C)
+
+        return self.__class__((data, indices, indptr), shape=self.shape)
+
+    # needed by _data_matrix
+    def _with_data(self,data,copy=True):
+        """Returns a matrix with the same sparsity structure as self,
+        but with different data.  By default the structure arrays
+        (i.e. .indptr and .indices) are copied.
+        """
+        if copy:
+            return self.__class__((data,self.indices.copy(),self.indptr.copy()),
+                                   shape=self.shape,dtype=data.dtype)
+        else:
+            return self.__class__((data,self.indices,self.indptr),
+                                   shape=self.shape,dtype=data.dtype)
+
+#    # these functions are used by the parent class
+#    # to remove redundancy between bsc_matrix and bsr_matrix
+#    def _swap(self,x):
+#        """swap the members of x if this is a column-oriented matrix
+#        """
+#        return (x[0],x[1])
+
+    def _broadcast_to(self, shape, copy=False):
+        return _spbase._broadcast_to(self, shape, copy)
+
+
+def isspmatrix_bsr(x):
+    """Is `x` of a bsr_matrix type?
+
+    .. warning::
+
+       SciPy sparse is shifting from a sparse matrix interface to a sparse
+       array interface. In the next few releases we expect to deprecate the
+       sparse matrix interface. For documentation of the matrix
+       interface, see the :ref:`spmatrix interface docs <spmatrix_api>`.
+       For guidance on converting existing code to sparse arrays, see
+       :ref:`Migration from spmatrix to sparray <migration_to_sparray>`.
+
+    Parameters
+    ----------
+    x
+        object to check for being a bsr matrix
+
+    Returns
+    -------
+    bool
+        True if `x` is a bsr matrix, False otherwise
+
+    Examples
+    --------
+    >>> from scipy.sparse import bsr_array, bsr_matrix, csr_matrix, isspmatrix_bsr
+    >>> isspmatrix_bsr(bsr_matrix([[5]]))
+    True
+    >>> isspmatrix_bsr(bsr_array([[5]]))
+    False
+    >>> isspmatrix_bsr(csr_matrix([[5]]))
+    False
+    """
+    return isinstance(x, bsr_matrix)
+
+
+# This namespace class separates array from matrix with isinstance
+class bsr_array(_bsr_base, sparray):
+    """
+    Block Sparse Row format sparse array.
+
+    This can be instantiated in several ways:
+        bsr_array(D, [blocksize=(R,C)])
+            where D is a 2-D ndarray.
+
+        bsr_array(S, [blocksize=(R,C)])
+            with another sparse array or matrix S (equivalent to S.tobsr())
+
+        bsr_array((M, N), [blocksize=(R,C), dtype])
+            to construct an empty sparse array with shape (M, N)
+            dtype is optional, defaulting to dtype='d'.
+
+        bsr_array((data, ij), [blocksize=(R,C), shape=(M, N)])
+            where ``data`` and ``ij`` satisfy ``a[ij[0, k], ij[1, k]] = data[k]``
+
+        bsr_array((data, indices, indptr), [shape=(M, N)])
+            is the standard BSR representation where the block column
+            indices for row i are stored in ``indices[indptr[i]:indptr[i+1]]``
+            and their corresponding block values are stored in
+            ``data[ indptr[i]: indptr[i+1] ]``. If the shape parameter is not
+            supplied, the array dimensions are inferred from the index arrays.
+
+    Attributes
+    ----------
+    data : ndarray
+        BSR format data array of the array
+    indices : ndarray
+        BSR format index array of the array
+    indptr : ndarray
+        BSR format index pointer array of the array
+    blocksize : 2-tuple of integers
+        Block size (R, C)
+    has_sorted_indices : bool
+        Whether indices are sorted
+    has_canonical_format : bool
+        Whether indices are sorted and no duplicate entries exist
+    dtype : dtype
+        Data type of the array
+    shape : 2-tuple
+        Shape of the array
+    ndim : int
+        Number of dimensions (this is always 2)
+    format : str
+        Three letter code for the format of the array storage, e.g. 'bsr'
+    nnz : int
+        Number of values stored in the array
+    size : int
+        Number of values stored in the array
+    T : bsr_array
+        The transpose of the array
+    mT : bsr_array
+        The matrix transpose of the array
+
+    Notes
+    -----
+    Sparse arrays can be used in arithmetic operations: they support
+    addition, subtraction, multiplication, division, and matrix power.
+
+    **Summary of BSR format**
+
+    The Block Sparse Row (BSR) format is very similar to the Compressed
+    Sparse Row (CSR) format. BSR is appropriate for sparse matrices with dense
+    sub matrices like the last example below. Such sparse block matrices often
+    arise in vector-valued finite element discretizations. In such cases, BSR is
+    considerably more efficient than CSR and CSC for many sparse arithmetic
+    operations.
+
+    **Blocksize**
+
+    The blocksize (R,C) must evenly divide the shape of the sparse array (M,N).
+    That is, R and C must satisfy the relationship ``M % R = 0`` and
+    ``N % C = 0``.
+
+    If no blocksize is specified, a simple heuristic is applied to determine
+    an appropriate blocksize.
+
+    **Canonical Format**
+
+    In canonical format, there are no duplicate blocks and indices are sorted
+    per row.
+
+    **Limitations**
+
+    Block Sparse Row format sparse arrays do not support slicing.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.sparse import bsr_array
+    >>> bsr_array((3, 4), dtype=np.int8).toarray()
+    array([[0, 0, 0, 0],
+           [0, 0, 0, 0],
+           [0, 0, 0, 0]], dtype=int8)
+
+    >>> row = np.array([0, 0, 1, 2, 2, 2])
+    >>> col = np.array([0, 2, 2, 0, 1, 2])
+    >>> data = np.array([1, 2, 3 ,4, 5, 6])
+    >>> bsr_array((data, (row, col)), shape=(3, 3)).toarray()
+    array([[1, 0, 2],
+           [0, 0, 3],
+           [4, 5, 6]])
+
+    >>> indptr = np.array([0, 2, 3, 6])
+    >>> indices = np.array([0, 2, 2, 0, 1, 2])
+    >>> data = np.array([1, 2, 3, 4, 5, 6]).repeat(4).reshape(6, 2, 2)
+    >>> bsr_array((data,indices,indptr), shape=(6, 6)).toarray()
+    array([[1, 1, 0, 0, 2, 2],
+           [1, 1, 0, 0, 2, 2],
+           [0, 0, 0, 0, 3, 3],
+           [0, 0, 0, 0, 3, 3],
+           [4, 4, 5, 5, 6, 6],
+           [4, 4, 5, 5, 6, 6]])
+
+    """  # numpydoc ignore=PR01
+
+
+class bsr_matrix(spmatrix, _bsr_base):
+    """
+    Block Sparse Row format sparse matrix.
+
+    .. warning::
+
+       SciPy sparse is shifting from a sparse matrix interface to a sparse
+       array interface. In the next few releases we expect to deprecate the
+       sparse matrix interface. For documentation of the matrix
+       interface, see the :ref:`spmatrix interface docs <spmatrix_api>`.
+       For guidance on converting existing code to sparse arrays, see
+       :ref:`Migration from spmatrix to sparray <migration_to_sparray>`.
+
+    This can be instantiated in several ways:
+        bsr_matrix(D, [blocksize=(R,C)])
+            where D is a 2-D ndarray.
+
+        bsr_matrix(S, [blocksize=(R,C)])
+            with another sparse array or matrix S (equivalent to S.tobsr())
+
+        bsr_matrix((M, N), [blocksize=(R,C), dtype])
+            to construct an empty sparse matrix with shape (M, N)
+            dtype is optional, defaulting to dtype='d'.
+
+        bsr_matrix((data, ij), [blocksize=(R,C), shape=(M, N)])
+            where ``data`` and ``ij`` satisfy ``a[ij[0, k], ij[1, k]] = data[k]``
+
+        bsr_matrix((data, indices, indptr), [shape=(M, N)])
+            is the standard BSR representation where the block column
+            indices for row i are stored in ``indices[indptr[i]:indptr[i+1]]``
+            and their corresponding block values are stored in
+            ``data[ indptr[i]: indptr[i+1] ]``. If the shape parameter is not
+            supplied, the matrix dimensions are inferred from the index arrays.
+
+    Attributes
+    ----------
+    data : ndarray
+        BSR format data array of the matrix
+    indices : ndarray
+        BSR format index array of the matrix
+    indptr : ndarray
+        BSR format index pointer array of the matrix
+    blocksize : 2-tuple of integers
+        Block size (R, C)
+    has_sorted_indices : bool
+        Whether indices are sorted
+    has_canonical_format : bool
+        Whether indices are sorted and no duplicate entries exist
+    dtype : dtype
+        Data type of the matrix
+    shape : 2-tuple
+        Shape of the matrix
+    ndim : int
+        Number of dimensions (this is always 2)
+    format : str
+        Three letter code for the format of the matrix storage, e.g. 'bsr'
+    nnz : int
+        Number of values stored in the matrix
+    size : int
+        Number of values stored in the matrix
+    T : bsr_matrix
+        The transpose of the matrix
+    mT : bsr_matrix
+        The matrix transpose
+
+    Notes
+    -----
+    Sparse matrices can be used in arithmetic operations: they support
+    addition, subtraction, multiplication, division, and matrix power.
+
+    **Summary of BSR format**
+
+    The Block Sparse Row (BSR) format is very similar to the Compressed
+    Sparse Row (CSR) format. BSR is appropriate for sparse matrices with dense
+    sub matrices like the last example below. Such sparse block matrices often
+    arise in vector-valued finite element discretizations. In such cases, BSR is
+    considerably more efficient than CSR and CSC for many sparse arithmetic
+    operations.
+
+    **Blocksize**
+
+    The blocksize (R,C) must evenly divide the shape of the sparse matrix (M,N).
+    That is, R and C must satisfy the relationship ``M % R = 0`` and
+    ``N % C = 0``.
+
+    If no blocksize is specified, a simple heuristic is applied to determine
+    an appropriate blocksize.
+
+    **Canonical Format**
+
+    In canonical format, there are no duplicate blocks and indices are sorted
+    per row.
+
+    **Limitations**
+
+    Block Sparse Row format sparse matrices do not support slicing.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.sparse import bsr_matrix
+    >>> bsr_matrix((3, 4), dtype=np.int8).toarray()
+    array([[0, 0, 0, 0],
+           [0, 0, 0, 0],
+           [0, 0, 0, 0]], dtype=int8)
+
+    >>> row = np.array([0, 0, 1, 2, 2, 2])
+    >>> col = np.array([0, 2, 2, 0, 1, 2])
+    >>> data = np.array([1, 2, 3 ,4, 5, 6])
+    >>> bsr_matrix((data, (row, col)), shape=(3, 3)).toarray()
+    array([[1, 0, 2],
+           [0, 0, 3],
+           [4, 5, 6]])
+
+    >>> indptr = np.array([0, 2, 3, 6])
+    >>> indices = np.array([0, 2, 2, 0, 1, 2])
+    >>> data = np.array([1, 2, 3, 4, 5, 6]).repeat(4).reshape(6, 2, 2)
+    >>> bsr_matrix((data,indices,indptr), shape=(6, 6)).toarray()
+    array([[1, 1, 0, 0, 2, 2],
+           [1, 1, 0, 0, 2, 2],
+           [0, 0, 0, 0, 3, 3],
+           [0, 0, 0, 0, 3, 3],
+           [4, 4, 5, 5, 6, 6],
+           [4, 4, 5, 5, 6, 6]])
+
+    """
+
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/_compressed.py b/venv/lib/python3.12/site-packages/scipy/sparse/_compressed.py
new file mode 100644
index 0000000000000000000000000000000000000000..99c1d459f8b08efe840912073d1c919eccb6130f
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/_compressed.py
@@ -0,0 +1,1351 @@
+"""Base class for sparse matrix formats using compressed storage."""
+__all__ = []
+
+from warnings import warn
+import itertools
+
+import numpy as np
+from scipy._lib._util import _prune_array, copy_if_needed
+
+from ._base import _spbase, issparse, sparray, SparseEfficiencyWarning
+from ._data import _data_matrix, _minmax_mixin
+from . import _sparsetools
+from ._sparsetools import (get_csr_submatrix, csr_sample_offsets, csr_todense,
+                           csr_sample_values, csr_row_index, csr_row_slice,
+                           csr_column_index1, csr_column_index2, csr_diagonal,
+                           expandptr, csr_has_canonical_format, csr_eliminate_zeros,
+                           csr_sum_duplicates, csr_has_sorted_indices, csr_sort_indices,
+                           csr_matmat_maxnnz, csr_matmat)
+from ._index import IndexMixin
+from ._sputils import (upcast, upcast_char, to_native, isshape,
+                       getdtype, isintlike, downcast_intp_index,
+                       get_sum_dtype, check_shape, get_index_dtype, broadcast_shapes)
+
+
+class _cs_matrix(_data_matrix, _minmax_mixin, IndexMixin):
+    """
+    base array/matrix class for compressed row- and column-oriented arrays/matrices
+    """
+
+    def __init__(self, arg1, shape=None, dtype=None, copy=False, *, maxprint=None):
+        _data_matrix.__init__(self, arg1, maxprint=maxprint)
+
+        if issparse(arg1):
+            if arg1.format == self.format and copy:
+                arg1 = arg1.copy()
+            else:
+                arg1 = arg1.asformat(self.format)
+            self.indptr, self.indices, self.data, self._shape = (
+                arg1.indptr, arg1.indices, arg1.data, arg1._shape
+            )
+
+        elif isinstance(arg1, tuple):
+            if isshape(arg1, allow_nd=self._allow_nd):
+                # It's a tuple of matrix dimensions (M, N)
+                # create empty matrix
+                self._shape = check_shape(arg1, allow_nd=self._allow_nd)
+                M, N = self._swap(self._shape_as_2d)
+                # Select index dtype large enough to pass array and
+                # scalar parameters to sparsetools
+                idx_dtype = self._get_index_dtype(maxval=max(self.shape))
+                self.data = np.zeros(0, getdtype(dtype, default=float))
+                self.indices = np.zeros(0, idx_dtype)
+                self.indptr = np.zeros(M + 1, dtype=idx_dtype)
+            else:
+                if len(arg1) == 2:
+                    # (data, ij) format
+                    coo = self._coo_container(arg1, shape=shape, dtype=dtype)
+                    arrays = coo._coo_to_compressed(self._swap)
+                    self.indptr, self.indices, self.data, self._shape = arrays
+                    self.sum_duplicates()
+                elif len(arg1) == 3:
+                    # (data, indices, indptr) format
+                    (data, indices, indptr) = arg1
+
+                    # Select index dtype large enough to pass array and
+                    # scalar parameters to sparsetools
+                    maxval = None
+                    if shape is not None and 0 not in shape:
+                        maxval = max(shape)
+                    idx_dtype = self._get_index_dtype((indices, indptr),
+                                                maxval=maxval,
+                                                check_contents=True)
+
+                    if not copy:
+                        copy = copy_if_needed
+                    self.indices = np.array(indices, copy=copy, dtype=idx_dtype)
+                    self.indptr = np.array(indptr, copy=copy, dtype=idx_dtype)
+                    self.data = np.array(data, copy=copy, dtype=dtype)
+                else:
+                    raise ValueError(f"unrecognized {self.__class__.__name__} "
+                                     f"constructor input: {arg1}")
+
+        else:
+            # must be dense
+            try:
+                arg1 = np.asarray(arg1)
+            except Exception as e:
+                raise ValueError(f"unrecognized {self.__class__.__name__} "
+                                 f"constructor input: {arg1}") from e
+            if isinstance(self, sparray) and arg1.ndim != 2 and self.format == "csc":
+                raise ValueError(f"CSC arrays don't support {arg1.ndim}D input. Use 2D")
+            if arg1.ndim > 2:
+                raise ValueError(f"CSR arrays don't yet support {arg1.ndim}D.")
+
+            coo = self._coo_container(arg1, dtype=dtype)
+            arrays = coo._coo_to_compressed(self._swap)
+            self.indptr, self.indices, self.data, self._shape = arrays
+
+        # Read matrix dimensions given, if any
+        if shape is not None:
+            self._shape = check_shape(shape, allow_nd=self._allow_nd)
+        elif self.shape is None:
+            # shape not already set, try to infer dimensions
+            try:
+                M = len(self.indptr) - 1
+                N = self.indices.max() + 1
+            except Exception as e:
+                raise ValueError('unable to infer matrix dimensions') from e
+
+            self._shape = check_shape(self._swap((M, N)), allow_nd=self._allow_nd)
+
+        if dtype is not None:
+            newdtype = getdtype(dtype)
+            self.data = self.data.astype(newdtype, copy=False)
+
+        self.check_format(full_check=False)
+
+    def _getnnz(self, axis=None):
+        if axis is None:
+            return int(self.indptr[-1])
+        elif self.ndim == 1:
+            if axis in (0, -1):
+                return int(self.indptr[-1])
+            raise ValueError('axis out of bounds')
+        else:
+            if axis < 0:
+                axis += 2
+            axis, _ = self._swap((axis, 1 - axis))
+            _, N = self._swap(self.shape)
+            if axis == 0:
+                return np.bincount(downcast_intp_index(self.indices), minlength=N)
+            elif axis == 1:
+                return np.diff(self.indptr)
+            raise ValueError('axis out of bounds')
+
+    _getnnz.__doc__ = _spbase._getnnz.__doc__
+
+    def count_nonzero(self, axis=None):
+        self.sum_duplicates()
+        if axis is None:
+            return np.count_nonzero(self.data)
+
+        if self.ndim == 1:
+            if axis not in (0, -1):
+                raise ValueError('axis out of bounds')
+            return np.count_nonzero(self.data)
+
+        if axis < 0:
+            axis += 2
+        axis, _ = self._swap((axis, 1 - axis))
+        if axis == 0:
+            _, N = self._swap(self.shape)
+            mask = self.data != 0
+            idx = self.indices if mask.all() else self.indices[mask]
+            return np.bincount(downcast_intp_index(idx), minlength=N)
+        elif axis == 1:
+            if self.data.all():
+                return np.diff(self.indptr)
+            pairs = itertools.pairwise(self.indptr)
+            return np.array([np.count_nonzero(self.data[i:j]) for i, j in pairs])
+        else:
+            raise ValueError('axis out of bounds')
+
+    count_nonzero.__doc__ = _spbase.count_nonzero.__doc__
+
+    def check_format(self, full_check=True):
+        """Check whether the array/matrix respects the CSR or CSC format.
+
+        Parameters
+        ----------
+        full_check : bool, optional
+            If `True`, run rigorous check, scanning arrays for valid values.
+            Note that activating those check might copy arrays for casting,
+            modifying indices and index pointers' inplace.
+            If `False`, run basic checks on attributes. O(1) operations.
+            Default is `True`.
+        """
+        # index arrays should have integer data types
+        if self.indptr.dtype.kind != 'i':
+            warn(f"indptr array has non-integer dtype ({self.indptr.dtype.name})",
+                 stacklevel=3)
+        if self.indices.dtype.kind != 'i':
+            warn(f"indices array has non-integer dtype ({self.indices.dtype.name})",
+                 stacklevel=3)
+
+        # check array shapes
+        for x in [self.data.ndim, self.indices.ndim, self.indptr.ndim]:
+            if x != 1:
+                raise ValueError('data, indices, and indptr should be 1-D')
+
+        # check index pointer. Use _swap to determine proper bounds
+        M, N = self._swap(self._shape_as_2d)
+
+        if (len(self.indptr) != M + 1):
+            raise ValueError(f"index pointer size {len(self.indptr)} should be {M + 1}")
+        if (self.indptr[0] != 0):
+            raise ValueError("index pointer should start with 0")
+
+        # check index and data arrays
+        if (len(self.indices) != len(self.data)):
+            raise ValueError("indices and data should have the same size")
+        if (self.indptr[-1] > len(self.indices)):
+            raise ValueError("Last value of index pointer should be less than "
+                             "the size of index and data arrays")
+
+        self.prune()
+
+        if full_check:
+            # check format validity (more expensive)
+            if self.nnz > 0:
+                if self.indices.max() >= N:
+                    raise ValueError(f"indices must be < {N}")
+                if self.indices.min() < 0:
+                    raise ValueError("indices must be >= 0")
+                if np.diff(self.indptr).min() < 0:
+                    raise ValueError("indptr must be a non-decreasing sequence")
+
+            idx_dtype = self._get_index_dtype((self.indptr, self.indices))
+            self.indptr = np.asarray(self.indptr, dtype=idx_dtype)
+            self.indices = np.asarray(self.indices, dtype=idx_dtype)
+            self.data = to_native(self.data)
+
+        # if not self.has_sorted_indices():
+        #    warn('Indices were not in sorted order.  Sorting indices.')
+        #    self.sort_indices()
+        #    assert(self.has_sorted_indices())
+        # TODO check for duplicates?
+
+    #######################
+    # Boolean comparisons #
+    #######################
+
+    def _scalar_binopt(self, other, op):
+        """Scalar version of self._binopt, for cases in which no new nonzeros
+        are added. Produces a new sparse array in canonical form.
+        """
+        self.sum_duplicates()
+        res = self._with_data(op(self.data, other), copy=True)
+        res.eliminate_zeros()
+        return res
+
+    #################################
+    # Arithmetic operator overrides #
+    #################################
+
+    def _add_dense(self, other):
+        if other.shape != self.shape:
+            raise ValueError(f'Incompatible shapes ({self.shape} and {other.shape})')
+        dtype = upcast_char(self.dtype.char, other.dtype.char)
+        order = self._swap('CF')[0]
+        result = np.array(other, dtype=dtype, order=order, copy=True)
+        y = result if result.flags.c_contiguous else result.T
+        M, N = self._swap(self._shape_as_2d)
+        csr_todense(M, N, self.indptr, self.indices, self.data, y)
+        return self._container(result, copy=False)
+
+    def _add_sparse(self, other):
+        return self._binopt(other, '_plus_')
+
+    def _sub_sparse(self, other):
+        return self._binopt(other, '_minus_')
+
+    def _multiply_2d_with_broadcasting(self, other):
+        """Element-wise multiplication by array/matrix, vector, or scalar."""
+        # Called after checking that other is not scalarlike and self.ndim <=2
+        if issparse(other):
+            if self.shape == other.shape:
+                other = self.__class__(other)
+                return self._binopt(other, '_elmul_')
+            # Single element.
+            if other.shape == (1, 1):
+                result = self._mul_scalar(other.toarray()[0, 0])
+                if self.ndim == 1:
+                    return result.reshape((1, self.shape[0]))
+                return result
+            if other.shape == (1,):
+                return self._mul_scalar(other.toarray()[0])
+            if self.shape in ((1,), (1, 1)):
+                return other._mul_scalar(self.data.sum())
+
+            # broadcast. treat 1d like a row
+            sM, sN = self._shape_as_2d
+            oM, oN = other._shape_as_2d
+            # A row times a column.
+            if sM == 1 and oN == 1:
+                return other._matmul_sparse(self.reshape(sM, sN).tocsc())
+            if sN == 1 and oM == 1:
+                return self._matmul_sparse(other.reshape(oM, oN).tocsc())
+
+            is_array = isinstance(self, sparray)
+            # Other is a row.
+            if oM == 1 and sN == oN:
+                new_other = _make_diagonal_csr(other.toarray().ravel(), is_array)
+                result = self._matmul_sparse(new_other)
+                return result if self.ndim == 2 else result.reshape((1, oN))
+            # self is a row.
+            if sM == 1 and sN == oN:
+                copy = _make_diagonal_csr(self.toarray().ravel(), is_array)
+                return other._matmul_sparse(copy)
+
+            # Other is a column.
+            if oN == 1 and sM == oM:
+                new_other = _make_diagonal_csr(other.toarray().ravel(), is_array)
+                return new_other._matmul_sparse(self)
+            # self is a column.
+            if sN == 1 and sM == oM:
+                new_self = _make_diagonal_csr(self.toarray().ravel(), is_array)
+                return new_self._matmul_sparse(other)
+            raise ValueError(f"inconsistent shapes {self.shape} and {other.shape}")
+
+        # Assume other is a dense matrix/array, which produces a single-item
+        # object array if other isn't convertible to ndarray.
+        other = np.asanyarray(other)
+
+        if other.ndim > 2:
+            return np.multiply(self.toarray(), other)
+        # Single element / wrapped object.
+        if other.size == 1:
+            if other.dtype == np.object_:
+                # 'other' not convertible to ndarray.
+                return NotImplemented
+            bshape = broadcast_shapes(self.shape, other.shape)
+            return self._mul_scalar(other.flat[0]).reshape(bshape)
+        # Fast case for trivial sparse matrix.
+        if self.shape in ((1,), (1, 1)):
+            bshape = broadcast_shapes(self.shape, other.shape)
+            return np.multiply(self.data.sum(), other).reshape(bshape)
+
+        ret = self.tocoo()
+        # Matching shapes.
+        if self.shape == other.shape:
+            data = np.multiply(ret.data, other[ret.coords])
+            ret.data = data.view(np.ndarray).ravel()
+            return ret
+
+        # convert other to 2d
+        other2d = np.atleast_2d(other)
+        # Sparse row vector times...
+        if self.shape[0] == 1 or self.ndim == 1:
+            if other2d.shape[1] == 1:  # Dense column vector.
+                data = np.multiply(ret.data, other2d)
+            elif other2d.shape[1] == self.shape[-1]:  # Dense 2d matrix.
+                data = np.multiply(ret.data, other2d[:, ret.col])
+            else:
+                raise ValueError(f"inconsistent shapes {self.shape} and {other.shape}")
+            idx_dtype = self._get_index_dtype(ret.col,
+                                              maxval=ret.nnz * other2d.shape[0])
+            row = np.repeat(np.arange(other2d.shape[0], dtype=idx_dtype), ret.nnz)
+            col = np.tile(ret.col.astype(idx_dtype, copy=False), other2d.shape[0])
+            return self._coo_container(
+                (data.view(np.ndarray).ravel(), (row, col)),
+                shape=(other2d.shape[0], self.shape[-1]),
+                copy=False
+            )
+        # Sparse column vector times...
+        if self.shape[1] == 1:
+            if other2d.shape[0] == 1:  # Dense row vector.
+                data = np.multiply(ret.data[:, None], other2d)
+            elif other2d.shape[0] == self.shape[0]:  # Dense 2d array.
+                data = np.multiply(ret.data[:, None], other2d[ret.row])
+            else:
+                raise ValueError(f"inconsistent shapes {self.shape} and {other.shape}")
+            idx_dtype = self._get_index_dtype(ret.row,
+                                              maxval=ret.nnz * other2d.shape[1])
+            row = np.repeat(ret.row.astype(idx_dtype, copy=False), other2d.shape[1])
+            col = np.tile(np.arange(other2d.shape[1], dtype=idx_dtype), ret.nnz)
+            return self._coo_container(
+                (data.view(np.ndarray).ravel(), (row, col)),
+                shape=(self.shape[0], other2d.shape[1]),
+                copy=False
+            )
+        # Sparse matrix times dense row vector.
+        if other2d.shape[0] == 1 and self.shape[1] == other2d.shape[1]:
+            data = np.multiply(ret.data, other2d[:, ret.col].ravel())
+        # Sparse matrix times dense column vector.
+        elif other2d.shape[1] == 1 and self.shape[0] == other2d.shape[0]:
+            data = np.multiply(ret.data, other2d[ret.row].ravel())
+        else:
+            raise ValueError(f"inconsistent shapes {self.shape} and {other.shape}")
+        ret.data = data.view(np.ndarray).ravel()
+        return ret
+
+    ###########################
+    # Multiplication handlers #
+    ###########################
+
+    def _matmul_vector(self, other):
+        M, N = self._shape_as_2d
+
+        # output array
+        result = np.zeros(M, dtype=upcast_char(self.dtype.char, other.dtype.char))
+
+        # csr_matvec or csc_matvec
+        fn = getattr(_sparsetools, self.format + '_matvec')
+        fn(M, N, self.indptr, self.indices, self.data, other, result)
+
+        return result[0] if self.ndim == 1 else result
+
+    def _matmul_multivector(self, other):
+        M, N = self._shape_as_2d
+        n_vecs = other.shape[-1]  # number of column vectors
+
+        result = np.zeros((M, n_vecs),
+                          dtype=upcast_char(self.dtype.char, other.dtype.char))
+
+        # csr_matvecs or csc_matvecs
+        fn = getattr(_sparsetools, self.format + '_matvecs')
+        fn(M, N, n_vecs, self.indptr, self.indices, self.data,
+           other.ravel(), result.ravel())
+
+        if self.ndim == 1:
+            return result.reshape((n_vecs,))
+        return result
+
+    def _matmul_sparse(self, other):
+        M, K1 = self._shape_as_2d
+        # if other is 1d, treat as a **column**
+        o_ndim = other.ndim
+        if o_ndim == 1:
+            # convert 1d array to a 2d column when on the right of @
+            other = other.reshape((1, other.shape[0])).T  # Note: converts to CSC
+        K2, N = other._shape if other.ndim == 2 else (other.shape[0], 1)
+
+        # find new_shape: (M, N), (M,), (N,) or ()
+        new_shape = ()
+        if self.ndim == 2:
+            new_shape += (M,)
+        if o_ndim == 2:
+            new_shape += (N,)
+        faux_shape = (M if self.ndim == 2 else 1, N if o_ndim == 2 else 1)
+
+        other = self.__class__(other)  # convert to this format
+        index_arrays = (self.indptr, self.indices, other.indptr, other.indices)
+
+        M, N = self._swap((M, N))
+        s, o = self._swap((self, other))
+
+        idx_dtype = self._get_index_dtype(index_arrays)
+        s_indptr = np.asarray(s.indptr, dtype=idx_dtype)
+        s_indices = np.asarray(s.indices, dtype=idx_dtype)
+        o_indptr = np.asarray(o.indptr, dtype=idx_dtype)
+        o_indices = np.asarray(o.indices, dtype=idx_dtype)
+
+        nnz = csr_matmat_maxnnz(M, N, s_indptr, s_indices, o_indptr, o_indices)
+        if nnz == 0:
+            if new_shape == ():
+                return np.array(0, dtype=upcast(self.dtype, other.dtype))
+            return self.__class__(new_shape, dtype=upcast(self.dtype, other.dtype))
+
+        new_idx_dtype = self._get_index_dtype(index_arrays, maxval=nnz)
+        if new_idx_dtype != idx_dtype:
+            idx_dtype = new_idx_dtype
+            s_indptr = np.asarray(s.indptr, dtype=idx_dtype)
+            s_indices = np.asarray(s.indices, dtype=idx_dtype)
+            o_indptr = np.asarray(o.indptr, dtype=idx_dtype)
+            o_indices = np.asarray(o.indices, dtype=idx_dtype)
+
+        indptr = np.empty(M + 1, dtype=idx_dtype)
+        indices = np.empty(nnz, dtype=idx_dtype)
+        data = np.empty(nnz, dtype=upcast(self.dtype, other.dtype))
+
+        csr_matmat(M, N,
+                   s_indptr, s_indices, s.data,
+                   o_indptr, o_indices, o.data,
+                   indptr, indices, data)
+
+        if new_shape == ():
+            return np.array(data[0])
+        res = self.__class__((data, indices, indptr), shape=faux_shape)
+        if faux_shape != new_shape:
+            if res.format != 'csr':
+                res = res.tocsr()
+            res = res.reshape(new_shape)
+        return res
+
+    def diagonal(self, k=0):
+        M, N = self._swap(self.shape)
+        k, _ = self._swap((k, -k))
+
+        if k <= -M or k >= N:
+            return np.empty(0, dtype=self.data.dtype)
+        y = np.empty(min(M + min(k, 0), N - max(k, 0)), dtype=upcast(self.dtype))
+        csr_diagonal(k, M, N, self.indptr, self.indices, self.data, y)
+        return y
+
+    diagonal.__doc__ = _spbase.diagonal.__doc__
+
+    #####################
+    # Reduce operations #
+    #####################
+
+    def sum(self, axis=None, dtype=None, out=None):
+        """Sum the array/matrix over the given axis.  If the axis is None, sum
+        over both rows and columns, returning a scalar.
+        """
+        # The _spbase base class already does axis=None and major axis efficiently
+        # so we only do the case axis= minor axis
+        if (self.ndim == 2 and not hasattr(self, 'blocksize') and
+                axis in self._swap(((1, -1), (0, -2)))[0]):
+            # faster than multiplication for large minor axis in CSC/CSR
+            
+            res_dtype = get_sum_dtype(self.dtype) if dtype is None else dtype
+            self_to_reduce = self.astype(res_dtype, copy=False)
+            
+            # Fast path: reduce along minor axis
+            ret = np.zeros(len(self_to_reduce.indptr) - 1, dtype=res_dtype)
+            major_index, value = self_to_reduce._minor_reduce(np.add)
+            ret[major_index] = value
+            ret = self_to_reduce._ascontainer(ret)
+            if axis % 2 == 1:
+                ret = ret.T
+
+            return ret.sum(axis=(), dtype=res_dtype, out=out)
+        else:
+            return _spbase.sum(self, axis=axis, dtype=dtype, out=out)
+
+    sum.__doc__ = _spbase.sum.__doc__
+
+    def _minor_reduce(self, ufunc, data=None):
+        """Reduce nonzeros with a ufunc over the minor axis when non-empty
+
+        Can be applied to a function of self.data by supplying data parameter.
+
+        Warning: this does not call sum_duplicates()
+
+        Returns
+        -------
+        major_index : array of ints
+            Major indices where nonzero
+
+        value : array of self.dtype
+            Reduce result for nonzeros in each major_index
+        """
+        if data is None:
+            data = self.data
+        major_index = np.flatnonzero(np.diff(self.indptr))
+        value = ufunc.reduceat(data,
+                               downcast_intp_index(self.indptr[major_index]))
+        return major_index, value
+
+    #######################
+    # Getting and Setting #
+    #######################
+
+    def _get_intXint(self, row, col):
+        M, N = self._swap(self.shape)
+        major, minor = self._swap((row, col))
+        indptr, indices, data = get_csr_submatrix(
+            M, N, self.indptr, self.indices, self.data,
+            major, major + 1, minor, minor + 1)
+        return data.sum(dtype=self.dtype)
+
+    def _get_sliceXslice(self, row, col):
+        major, minor = self._swap((row, col))
+        if major.step in (1, None) and minor.step in (1, None):
+            return self._get_submatrix(major, minor, copy=True)
+        return self._major_slice(major)._minor_slice(minor)
+
+    def _get_arrayXarray(self, row, col):
+        # inner indexing
+        idx_dtype = self.indices.dtype
+        M, N = self._swap(self.shape)
+        major, minor = self._swap((row, col))
+        major = np.asarray(major, dtype=idx_dtype)
+        minor = np.asarray(minor, dtype=idx_dtype)
+
+        val = np.empty(major.size, dtype=self.dtype)
+        csr_sample_values(M, N, self.indptr, self.indices, self.data,
+                          major.size, major.ravel(), minor.ravel(), val)
+        if major.ndim == 1:
+            return self._ascontainer(val)
+        return self.__class__(val.reshape(major.shape))
+
+    def _get_columnXarray(self, row, col):
+        # outer indexing
+        major, minor = self._swap((row, col))
+        return self._major_index_fancy(major)._minor_index_fancy(minor)
+
+    def _major_index_fancy(self, idx):
+        """Index along the major axis where idx is an array of ints.
+        """
+        idx_dtype = self._get_index_dtype((self.indptr, self.indices))
+        indices = np.asarray(idx, dtype=idx_dtype).ravel()
+
+        N = self._swap(self._shape_as_2d)[1]
+        M = len(indices)
+        new_shape = self._swap((M, N)) if self.ndim == 2 else (M,)
+        if M == 0:
+            return self.__class__(new_shape, dtype=self.dtype)
+
+        self_indptr = self.indptr.astype(idx_dtype, copy=False)
+        self_indices = self.indices.astype(idx_dtype, copy=False)
+
+        row_nnz = self_indptr[indices + 1] - self_indptr[indices]
+        res_indptr = np.zeros(M + 1, dtype=idx_dtype)
+        np.cumsum(row_nnz, out=res_indptr[1:])
+
+        nnz = res_indptr[-1]
+        res_indices = np.empty(nnz, dtype=idx_dtype)
+        res_data = np.empty(nnz, dtype=self.dtype)
+        csr_row_index(
+            M,
+            indices,
+            self_indptr,
+            self_indices,
+            self.data,
+            res_indices,
+            res_data
+        )
+
+        return self.__class__((res_data, res_indices, res_indptr),
+                              shape=new_shape, copy=False)
+
+    def _major_slice(self, idx, copy=False):
+        """Index along the major axis where idx is a slice object.
+        """
+        if idx == slice(None):
+            return self.copy() if copy else self
+
+        M, N = self._swap(self._shape_as_2d)
+        start, stop, step = idx.indices(M)
+        M = len(range(start, stop, step))
+        new_shape = self._swap((M, N)) if self.ndim == 2 else (M,)
+        if M == 0:
+            return self.__class__(new_shape, dtype=self.dtype)
+
+        # Work out what slices are needed for `row_nnz`
+        # start,stop can be -1, only if step is negative
+        start0, stop0 = start, stop
+        if stop == -1 and start >= 0:
+            stop0 = None
+        start1, stop1 = start + 1, stop + 1
+
+        row_nnz = self.indptr[start1:stop1:step] - \
+            self.indptr[start0:stop0:step]
+        idx_dtype = self.indices.dtype
+        res_indptr = np.zeros(M+1, dtype=idx_dtype)
+        np.cumsum(row_nnz, out=res_indptr[1:])
+
+        if step == 1:
+            all_idx = slice(self.indptr[start], self.indptr[stop])
+            res_indices = np.array(self.indices[all_idx], copy=copy)
+            res_data = np.array(self.data[all_idx], copy=copy)
+        else:
+            nnz = res_indptr[-1]
+            res_indices = np.empty(nnz, dtype=idx_dtype)
+            res_data = np.empty(nnz, dtype=self.dtype)
+            csr_row_slice(start, stop, step, self.indptr, self.indices,
+                          self.data, res_indices, res_data)
+
+        return self.__class__((res_data, res_indices, res_indptr),
+                              shape=new_shape, copy=False)
+
+    def _minor_index_fancy(self, idx):
+        """Index along the minor axis where idx is an array of ints.
+        """
+        idx_dtype = self._get_index_dtype((self.indices, self.indptr))
+        indices = self.indices.astype(idx_dtype, copy=False)
+        indptr = self.indptr.astype(idx_dtype, copy=False)
+
+        idx = np.asarray(idx, dtype=idx_dtype).ravel()
+
+        M, N = self._swap(self._shape_as_2d)
+        k = len(idx)
+        new_shape = self._swap((M, k)) if self.ndim == 2 else (k,)
+        if k == 0:
+            return self.__class__(new_shape, dtype=self.dtype)
+
+        # pass 1: count idx entries and compute new indptr
+        col_offsets = np.zeros(N, dtype=idx_dtype)
+        res_indptr = np.empty_like(self.indptr, dtype=idx_dtype)
+        csr_column_index1(
+            k,
+            idx,
+            M,
+            N,
+            indptr,
+            indices,
+            col_offsets,
+            res_indptr,
+        )
+
+        # pass 2: copy indices/data for selected idxs
+        col_order = np.argsort(idx).astype(idx_dtype, copy=False)
+        nnz = res_indptr[-1]
+        res_indices = np.empty(nnz, dtype=idx_dtype)
+        res_data = np.empty(nnz, dtype=self.dtype)
+        csr_column_index2(col_order, col_offsets, len(self.indices),
+                          indices, self.data, res_indices, res_data)
+        return self.__class__((res_data, res_indices, res_indptr),
+                              shape=new_shape, copy=False)
+
+    def _minor_slice(self, idx, copy=False):
+        """Index along the minor axis where idx is a slice object.
+        """
+        if idx == slice(None):
+            return self.copy() if copy else self
+
+        M, N = self._swap(self._shape_as_2d)
+        start, stop, step = idx.indices(N)
+        N = len(range(start, stop, step))
+        if N == 0:
+            return self.__class__(self._swap((M, N)), dtype=self.dtype)
+        if step == 1:
+            return self._get_submatrix(minor=idx, copy=copy)
+        # TODO: don't fall back to fancy indexing here
+        return self._minor_index_fancy(np.arange(start, stop, step))
+
+    def _get_submatrix(self, major=None, minor=None, copy=False):
+        """Return a submatrix of this matrix.
+
+        major, minor: None, int, or slice with step 1
+        """
+        M, N = self._swap(self._shape_as_2d)
+        i0, i1 = _process_slice(major, M)
+        j0, j1 = _process_slice(minor, N)
+
+        if i0 == 0 and j0 == 0 and i1 == M and j1 == N:
+            return self.copy() if copy else self
+
+        indptr, indices, data = get_csr_submatrix(
+            M, N, self.indptr, self.indices, self.data, i0, i1, j0, j1)
+
+        shape = self._swap((i1 - i0, j1 - j0))
+        if self.ndim == 1:
+            shape = (shape[1],)
+        return self.__class__((data, indices, indptr), shape=shape,
+                              dtype=self.dtype, copy=False)
+
+    def _set_intXint(self, row, col, x):
+        i, j = self._swap((row, col))
+        self._set_many(i, j, x)
+
+    def _set_arrayXarray(self, row, col, x):
+        i, j = self._swap((row, col))
+        self._set_many(i, j, x)
+
+    def _set_arrayXarray_sparse(self, row, col, x):
+        # clear entries that will be overwritten
+        self._zero_many(*self._swap((row, col)))
+
+        M, N = row.shape  # matches col.shape
+        broadcast_row = M != 1 and x.shape[0] == 1
+        broadcast_col = N != 1 and x.shape[1] == 1
+        r, c = x.row, x.col
+
+        x = np.asarray(x.data, dtype=self.dtype)
+        if x.size == 0:
+            return
+
+        if broadcast_row:
+            r = np.repeat(np.arange(M), len(r))
+            c = np.tile(c, M)
+            x = np.tile(x, M)
+        if broadcast_col:
+            r = np.repeat(r, N)
+            c = np.tile(np.arange(N), len(c))
+            x = np.repeat(x, N)
+        # only assign entries in the new sparsity structure
+        i, j = self._swap((row[r, c], col[r, c]))
+        self._set_many(i, j, x)
+
+    def _setdiag(self, values, k):
+        if 0 in self.shape:
+            return
+        if self.ndim == 1:
+            raise NotImplementedError('diagonals cant be set in 1d arrays')
+
+        M, N = self.shape
+        broadcast = (values.ndim == 0)
+
+        if k < 0:
+            if broadcast:
+                max_index = min(M + k, N)
+            else:
+                max_index = min(M + k, N, len(values))
+            i = np.arange(-k, max_index - k, dtype=self.indices.dtype)
+            j = np.arange(max_index, dtype=self.indices.dtype)
+
+        else:
+            if broadcast:
+                max_index = min(M, N - k)
+            else:
+                max_index = min(M, N - k, len(values))
+            i = np.arange(max_index, dtype=self.indices.dtype)
+            j = np.arange(k, k + max_index, dtype=self.indices.dtype)
+
+        if not broadcast:
+            values = values[:len(i)]
+
+        x = np.atleast_1d(np.asarray(values, dtype=self.dtype)).ravel()
+        if x.squeeze().shape != i.squeeze().shape:
+            x = np.broadcast_to(x, i.shape)
+        if x.size == 0:
+            return
+
+        M, N = self._swap((M, N))
+        i, j = self._swap((i, j))
+        n_samples = x.size
+        offsets = np.empty(n_samples, dtype=self.indices.dtype)
+        ret = csr_sample_offsets(M, N, self.indptr, self.indices, n_samples,
+                                 i, j, offsets)
+        if ret == 1:
+            # rinse and repeat
+            self.sum_duplicates()
+            csr_sample_offsets(M, N, self.indptr, self.indices, n_samples,
+                               i, j, offsets)
+        if -1 not in offsets:
+            # only affects existing non-zero cells
+            self.data[offsets] = x
+            return
+
+        is_existing = (offsets >= 0)
+        N_new = len(is_existing) - np.count_nonzero(is_existing)
+
+        # Boundary between csc and convert to coo
+        # The value 0.001 is justified in gh-19962#issuecomment-1920499678
+        if N_new < self.nnz * 0.001:
+            # replace existing entries
+            self.data[offsets[is_existing]] = x[is_existing]
+            # create new entries
+            is_new = np.logical_not(is_existing, out=is_existing)
+            del is_existing
+            self._insert_many(i[is_new], j[is_new], x[is_new])
+        else:
+            # convert to coo for _set_diag
+            do_sort = self.has_sorted_indices
+            coo = self.tocoo()
+            coo._setdiag(values, k)
+            arrays = coo._coo_to_compressed(self._swap)
+            self.indptr, self.indices, self.data, _ = arrays
+            # Sort the indices (like in _insert_many)
+            if do_sort:
+                self.has_sorted_indices = False  # force a sort
+                self.sort_indices()
+
+    def _prepare_indices(self, i, j):
+        M, N = self._swap(self._shape_as_2d)
+
+        def check_bounds(indices, bound):
+            idx = indices.max()
+            if idx >= bound:
+                raise IndexError(f'index ({idx}) out of range (>= {bound})')
+            idx = indices.min()
+            if idx < -bound:
+                raise IndexError(f'index ({idx}) out of range (< -{bound})')
+
+        i = np.atleast_1d(np.asarray(i, dtype=self.indices.dtype)).ravel()
+        j = np.atleast_1d(np.asarray(j, dtype=self.indices.dtype)).ravel()
+        check_bounds(i, M)
+        check_bounds(j, N)
+        return i, j, M, N
+
+    def _set_many(self, i, j, x):
+        """Sets value at each (i, j) to x
+
+        Here (i,j) index major and minor respectively, and must not contain
+        duplicate entries.
+        """
+        i, j, M, N = self._prepare_indices(i, j)
+        x = np.atleast_1d(np.asarray(x, dtype=self.dtype)).ravel()
+
+        n_samples = x.size
+        offsets = np.empty(n_samples, dtype=self.indices.dtype)
+        ret = csr_sample_offsets(M, N, self.indptr, self.indices, n_samples,
+                                 i, j, offsets)
+        if ret == 1:
+            # rinse and repeat
+            self.sum_duplicates()
+            csr_sample_offsets(M, N, self.indptr, self.indices, n_samples,
+                               i, j, offsets)
+
+        if -1 not in offsets:
+            # only affects existing non-zero cells
+            self.data[offsets] = x
+            return
+
+        else:
+            warn(f"Changing the sparsity structure of a {self.__class__.__name__} is"
+                 " expensive. lil and dok are more efficient.",
+                 SparseEfficiencyWarning, stacklevel=3)
+            # replace where possible
+            mask = offsets > -1
+            self.data[offsets[mask]] = x[mask]
+            # only insertions remain
+            mask = ~mask
+            i = i[mask]
+            i[i < 0] += M
+            j = j[mask]
+            j[j < 0] += N
+            self._insert_many(i, j, x[mask])
+
+    def _zero_many(self, i, j):
+        """Sets value at each (i, j) to zero, preserving sparsity structure.
+
+        Here (i,j) index major and minor respectively.
+        """
+        i, j, M, N = self._prepare_indices(i, j)
+
+        n_samples = len(i)
+        offsets = np.empty(n_samples, dtype=self.indices.dtype)
+        ret = csr_sample_offsets(M, N, self.indptr, self.indices, n_samples,
+                                 i, j, offsets)
+        if ret == 1:
+            # rinse and repeat
+            self.sum_duplicates()
+            csr_sample_offsets(M, N, self.indptr, self.indices, n_samples,
+                               i, j, offsets)
+
+        # only assign zeros to the existing sparsity structure
+        self.data[offsets[offsets > -1]] = 0
+
+    def _insert_many(self, i, j, x):
+        """Inserts new nonzero at each (i, j) with value x
+
+        Here (i,j) index major and minor respectively.
+        i, j and x must be non-empty, 1d arrays.
+        Inserts each major group (e.g. all entries per row) at a time.
+        Maintains has_sorted_indices property.
+        Modifies i, j, x in place.
+        """
+        order = np.argsort(i, kind='mergesort')  # stable for duplicates
+        i = i.take(order, mode='clip')
+        j = j.take(order, mode='clip')
+        x = x.take(order, mode='clip')
+
+        do_sort = self.has_sorted_indices
+
+        # Update index data type
+        idx_dtype = self._get_index_dtype((self.indices, self.indptr),
+                                    maxval=(self.indptr[-1].item() + x.size))
+        self.indptr = np.asarray(self.indptr, dtype=idx_dtype)
+        self.indices = np.asarray(self.indices, dtype=idx_dtype)
+        i = np.asarray(i, dtype=idx_dtype)
+        j = np.asarray(j, dtype=idx_dtype)
+
+        # Collate old and new in chunks by major index
+        indices_parts = []
+        data_parts = []
+
+        # TODO: explore creating a native sparsetools version of:
+        # ui, ui_indptr = np.unique(i, return_index=True)
+        # These 2 lines are equiv to np.unique but avoid big memory use. See gh-24951
+        ui_indptr = np.diff(np.concatenate(([-1], i))).nonzero()[0]
+        ui = i[ui_indptr]
+
+        ui_indptr = np.concatenate((ui_indptr, [len(j)]))
+        new_nnzs = np.diff(ui_indptr)
+        prev = 0
+        for c, (ii, js, je) in enumerate(zip(ui, ui_indptr, ui_indptr[1:])):
+            # old entries
+            start = self.indptr[prev]
+            stop = self.indptr[ii]
+            indices_parts.append(self.indices[start:stop])
+            data_parts.append(self.data[start:stop])
+
+            # handle duplicate j: keep last setting
+            uj, uj_indptr = np.unique(j[js:je][::-1], return_index=True)
+            if len(uj) == je - js:
+                indices_parts.append(j[js:je])
+                data_parts.append(x[js:je])
+            else:
+                indices_parts.append(j[js:je][::-1][uj_indptr])
+                data_parts.append(x[js:je][::-1][uj_indptr])
+                new_nnzs[c] = len(uj)
+
+            prev = ii
+
+        # remaining old entries
+        start = self.indptr[ii]
+        indices_parts.append(self.indices[start:])
+        data_parts.append(self.data[start:])
+
+        # update attributes
+        self.indices = np.concatenate(indices_parts)
+        self.data = np.concatenate(data_parts)
+        nnzs = np.empty(self.indptr.shape, dtype=idx_dtype)
+        nnzs[0] = idx_dtype(0)
+        indptr_diff = np.diff(self.indptr)
+        indptr_diff[ui] += new_nnzs
+        nnzs[1:] = indptr_diff
+        self.indptr = np.cumsum(nnzs, out=nnzs)
+
+        if do_sort:
+            # TODO: only sort where necessary
+            self.has_sorted_indices = False
+            self.sort_indices()
+
+        self.check_format(full_check=False)
+
+    ######################
+    # Conversion methods #
+    ######################
+
+    def tocoo(self, copy=True):
+        if self.ndim == 1:
+            csr = self.tocsr()
+            return self._coo_container((csr.data, (csr.indices,)), csr.shape, copy=copy)
+        major_dim, minor_dim = self._swap(self.shape)
+        minor_indices = self.indices
+        major_indices = np.empty(len(minor_indices), dtype=self.indices.dtype)
+        expandptr(major_dim, self.indptr, major_indices)
+        coords = self._swap((major_indices, minor_indices))
+
+        return self._coo_container(
+            (self.data, coords), self.shape, copy=copy, dtype=self.dtype
+        )
+
+    tocoo.__doc__ = _spbase.tocoo.__doc__
+
+    def toarray(self, order=None, out=None):
+        if out is None and order is None:
+            order = self._swap('cf')[0]
+        out = self._process_toarray_args(order, out)
+        if not (out.flags.c_contiguous or out.flags.f_contiguous):
+            raise ValueError('Output array must be C or F contiguous')
+        # align ideal order with output array order
+        if out.flags.c_contiguous:
+            x = self.tocsr()
+            y = out
+        else:
+            x = self.tocsc()
+            y = out.T
+        M, N = x._swap(x._shape_as_2d)
+        csr_todense(M, N, x.indptr, x.indices, x.data, y)
+        return out
+
+    toarray.__doc__ = _spbase.toarray.__doc__
+
+    ##############################################################
+    # methods that examine or modify the internal data structure #
+    ##############################################################
+
+    def eliminate_zeros(self):
+        """Remove zero entries from the array/matrix.
+
+        This is an *in place* operation.
+        """
+        M, N = self._swap(self._shape_as_2d)
+        csr_eliminate_zeros(M, N, self.indptr, self.indices, self.data)
+        self.prune()  # nnz may have changed
+
+    @property
+    def has_canonical_format(self) -> bool:
+        """Whether the array/matrix has sorted indices and no duplicates
+
+        Returns
+            - True: if the above applies
+            - False: otherwise
+
+        has_canonical_format implies has_sorted_indices, so if the latter flag
+        is False, so will the former be; if the former is found True, the
+        latter flag is also set.
+        """
+        # first check to see if result was cached
+        if not getattr(self, '_has_sorted_indices', True):
+            # not sorted => not canonical
+            self._has_canonical_format = False
+        elif not hasattr(self, '_has_canonical_format'):
+            M = len(self.indptr) - 1
+            self.has_canonical_format = bool(
+                csr_has_canonical_format(M, self.indptr, self.indices)
+            )
+        return self._has_canonical_format
+
+    @has_canonical_format.setter
+    def has_canonical_format(self, val: bool):
+        self._has_canonical_format = bool(val)
+        if val:
+            self.has_sorted_indices = True
+
+    def sum_duplicates(self):
+        """Eliminate duplicate entries by adding them together.
+
+        This is an *in place* operation.
+        """
+        if self.has_canonical_format:
+            return
+        self.sort_indices()
+
+        M, N = self._swap(self._shape_as_2d)
+        csr_sum_duplicates(M, N, self.indptr, self.indices, self.data)
+
+        self.prune()  # nnz may have changed
+        self.has_canonical_format = True
+
+    @property
+    def has_sorted_indices(self) -> bool:
+        """Whether the indices are sorted
+
+        Returns
+            - True: if the indices of the array/matrix are in sorted order
+            - False: otherwise
+        """
+        # first check to see if result was cached
+        if not hasattr(self, '_has_sorted_indices'):
+            M = len(self.indptr) - 1
+            self._has_sorted_indices = bool(
+                csr_has_sorted_indices(M, self.indptr, self.indices)
+            )
+        return self._has_sorted_indices
+
+    @has_sorted_indices.setter
+    def has_sorted_indices(self, val: bool):
+        self._has_sorted_indices = bool(val)
+
+
+    def sorted_indices(self):
+        """Return a copy of this array/matrix with sorted indices.
+
+        Returns
+        -------
+        sparse array/matrix
+            A copy of this array/matrix with sorted indices.
+        """
+        A = self.copy()
+        A.sort_indices()
+        return A
+
+        # an alternative that has linear complexity is the following
+        # although the previous option is typically faster
+        # return self.toother().toother()
+
+    def sort_indices(self):
+        """Sort the indices of this array/matrix *in place*.
+        """
+        if not self.has_sorted_indices:
+            M = len(self.indptr) - 1
+            csr_sort_indices(M, self.indptr, self.indices, self.data)
+            self.has_sorted_indices = True
+
+    def prune(self):
+        """Remove empty space after all non-zero elements.
+        """
+        major_dim = self._swap(self._shape_as_2d)[0]
+
+        if len(self.indptr) != major_dim + 1:
+            raise ValueError('index pointer has invalid length')
+        if len(self.indices) < self.nnz:
+            raise ValueError('indices array has fewer than nnz elements')
+        if len(self.data) < self.nnz:
+            raise ValueError('data array has fewer than nnz elements')
+
+        self.indices = _prune_array(self.indices[:self.nnz])
+        self.data = _prune_array(self.data[:self.nnz])
+
+    def resize(self, *shape):
+        shape = check_shape(shape, allow_nd=self._allow_nd)
+
+        if hasattr(self, 'blocksize'):
+            bm, bn = self.blocksize
+            new_M, rm = divmod(shape[0], bm)
+            new_N, rn = divmod(shape[1], bn)
+            if rm or rn:
+                raise ValueError(f"shape must be divisible into {self.blocksize}"
+                                 f" blocks. Got {shape}")
+            M, N = self.shape[0] // bm, self.shape[1] // bn
+        else:
+            new_M, new_N = self._swap(shape if len(shape)>1 else (1, shape[0]))
+            M, N = self._swap(self._shape_as_2d)
+
+        if new_M < M:
+            self.indices = self.indices[:self.indptr[new_M]]
+            self.data = self.data[:self.indptr[new_M]]
+            self.indptr = self.indptr[:new_M + 1]
+        elif new_M > M:
+            self.indptr = np.resize(self.indptr, new_M + 1)
+            self.indptr[M + 1:].fill(self.indptr[M])
+
+        if new_N < N:
+            mask = self.indices < new_N
+            if not np.all(mask):
+                self.indices = self.indices[mask]
+                self.data = self.data[mask]
+                major_index, val = self._minor_reduce(np.add, mask)
+                self.indptr.fill(0)
+                self.indptr[1:][major_index] = val
+                np.cumsum(self.indptr, out=self.indptr)
+
+        self._shape = shape
+
+    resize.__doc__ = _spbase.resize.__doc__
+
+    ###################
+    # utility methods #
+    ###################
+
+    # needed by _data_matrix
+    def _with_data(self, data, copy=True):
+        """Returns a matrix with the same sparsity structure as self,
+        but with different data.  By default the structure arrays
+        (i.e. .indptr and .indices) are copied.
+        """
+        if copy:
+            return self.__class__((data, self.indices.copy(),
+                                   self.indptr.copy()),
+                                  shape=self.shape,
+                                  dtype=data.dtype)
+        else:
+            return self.__class__((data, self.indices, self.indptr),
+                                  shape=self.shape, dtype=data.dtype)
+
+    def _binopt(self, other, op):
+        """apply the binary operation fn to two sparse matrices."""
+        other = self.__class__(other)
+
+        # e.g. csr_plus_csr, csr_minus_csr, etc.
+        fn = getattr(_sparsetools, "csr" + op + "csr")
+
+        maxnnz = self.nnz + other.nnz
+        idx_dtype = self._get_index_dtype((self.indptr, self.indices,
+                                     other.indptr, other.indices),
+                                    maxval=maxnnz)
+        indptr = np.empty(self.indptr.shape, dtype=idx_dtype)
+        indices = np.empty(maxnnz, dtype=idx_dtype)
+
+        bool_ops = ['_ne_', '_lt_', '_gt_', '_le_', '_ge_']
+        if op in bool_ops:
+            data = np.empty(maxnnz, dtype=np.bool_)
+        else:
+            data = np.empty(maxnnz, dtype=upcast(self.dtype, other.dtype))
+
+        M, N = self._swap(self._shape_as_2d)
+        fn(M, N,
+           np.asarray(self.indptr, dtype=idx_dtype),
+           np.asarray(self.indices, dtype=idx_dtype),
+           self.data,
+           np.asarray(other.indptr, dtype=idx_dtype),
+           np.asarray(other.indices, dtype=idx_dtype),
+           other.data,
+           indptr, indices, data)
+
+        A = self.__class__((data, indices, indptr), shape=self.shape)
+        A.prune()
+
+        return A
+
+    def _divide_sparse(self, other):
+        """
+        Divide this matrix by a second sparse matrix.
+        """
+        if other.shape != self.shape:
+            raise ValueError(f"inconsistent shapes {self.shape} and {other.shape}")
+
+        r = self._binopt(other, '_eldiv_')
+
+        if np.issubdtype(r.dtype, np.inexact):
+            # Eldiv leaves entries outside the combined sparsity
+            # pattern empty, so they must be filled manually.
+            # Everything outside of other's sparsity is NaN, and everything
+            # inside it is either zero or defined by eldiv.
+            out = np.empty(self.shape, dtype=self.dtype)
+            out.fill(np.nan)
+            coords = other.nonzero()
+            if self.ndim == 1:
+                coords = (coords[-1],)
+            out[coords] = 0
+            r = r.tocoo()
+            out[r.coords] = r.data
+            return self._container(out)
+        else:
+            # integers types go with nan <-> 0
+            out = r
+            return out
+
+    def _broadcast_to(self, shape, copy=False):
+        if self.shape == shape:
+            return self.copy() if copy else self
+
+        shape = check_shape(shape, allow_nd=(self._allow_nd))
+
+        if broadcast_shapes(self.shape, shape) != shape:
+            raise ValueError("cannot be broadcast")
+
+        if len(self.shape) == 1 and len(shape) == 1:
+            self.sum_duplicates()
+            if self.nnz == 0: # array has no non zero elements
+                return self.__class__(shape, dtype=self.dtype, copy=False)
+
+            N = shape[0]
+            data = np.full(N, self.data[0])
+            indices = np.arange(0,N)
+            indptr = np.array([0, N])
+            return self._csr_container((data, indices, indptr), shape=shape, copy=False)
+
+        # treat 1D as a 2D row
+        old_shape = self._shape_as_2d
+
+        if len(shape) != 2:
+            ndim = len(shape)
+            raise ValueError(f'CSR/CSC broadcast_to cannot have shape >2D. Got {ndim}D')
+
+        if self.nnz == 0: # array has no non zero elements
+            return self.__class__(shape, dtype=self.dtype, copy=False)
+
+        self.sum_duplicates()
+        M, N = self._swap(shape)
+        oM, oN = self._swap(old_shape)
+        if all(s == 1 for s in old_shape):
+            # Broadcast a single element to the entire shape
+            data = np.full(M * N, self.data[0])
+            indices = np.tile(np.arange(N), M)
+            indptr = np.arange(0, len(data) + 1, N)
+        elif oM == 1 and oN == N:
+            # Broadcast row-wise (columns for CSC)
+            data = np.tile(self.data, M)
+            indices = np.tile(self.indices, M)
+            indptr = np.arange(0, len(data) + 1, len(self.data))
+        elif oN == 1 and oM == M:
+            # Broadcast column-wise (rows for CSC)
+            data = np.repeat(self.data, N)
+            indices = np.tile(np.arange(N), len(self.data))
+            indptr = self.indptr * N
+        return self.__class__((data, indices, indptr), shape=shape, copy=False)
+
+
+def _make_diagonal_csr(data, is_array=False):
+    """build diagonal csc_array/csr_array => self._csr_container
+
+    Parameter `data` should be a raveled numpy array holding the
+    values on the diagonal of the resulting sparse matrix.
+    """
+    from ._csr import csr_array, csr_matrix
+    csr_array = csr_array if is_array else csr_matrix
+
+    N = len(data)
+    idx_dtype = get_index_dtype(maxval=N)
+    indptr = np.arange(N + 1, dtype=idx_dtype)
+    indices = indptr[:-1]
+
+    return csr_array((data, indices, indptr), shape=(N, N))
+
+
+def _process_slice(sl, num):
+    if sl is None:
+        i0, i1 = 0, num
+    elif isinstance(sl, slice):
+        i0, i1, stride = sl.indices(num)
+        if stride != 1:
+            raise ValueError('slicing with step != 1 not supported')
+        i0 = min(i0, i1)  # give an empty slice when i0 > i1
+    elif isintlike(sl):
+        if sl < 0:
+            sl += num
+        i0, i1 = sl, sl + 1
+        if i0 < 0 or i1 > num:
+            raise IndexError(f'index out of bounds: 0 <= {i0} < {i1} <= {num}')
+    else:
+        raise TypeError('expected slice or scalar')
+
+    return i0, i1
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/_construct.py b/venv/lib/python3.12/site-packages/scipy/sparse/_construct.py
new file mode 100644
index 0000000000000000000000000000000000000000..78c07cfd1e76613535871ae965c82e777498d54e
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/_construct.py
@@ -0,0 +1,1839 @@
+"""Functions to construct sparse matrices and arrays
+"""
+
+__docformat__ = "restructuredtext en"
+
+__all__ = ['kron', 'kronsum', 'hstack', 'vstack', 'block_diag',
+           'diags_array', 'block_array', 'eye_array', 'random_array',
+           'expand_dims', 'permute_dims', 'swapaxes', 'matrix_transpose',
+           'spdiags', 'eye', 'identity', 'bmat', 'rand', 'random', 'diags']
+
+import numbers
+import math
+import os
+from warnings import warn
+import numpy as np
+
+from scipy._lib._util import check_random_state, rng_integers, _transition_to_rng
+from scipy._lib.deprecation import _NoValue
+from ._sputils import upcast, get_index_dtype, isscalarlike, isintlike
+
+from ._sparsetools import csr_hstack
+from ._bsr import bsr_matrix, bsr_array
+from ._coo import coo_matrix, coo_array
+from ._csc import csc_matrix, csc_array
+from ._csr import csr_matrix, csr_array
+from ._dia import dia_matrix, dia_array
+
+from ._base import issparse, sparray, spmatrix
+
+
+def expand_dims(A, /, *, axis=0):
+    """
+    Add trivial axes to an array. Shape gets a ``1`` inserted at position `axis`.
+
+    Parameters
+    ----------
+    A : sparse array
+        Input array.
+    axis : int
+        Position in the expanded axes where the new axis (or axes) is placed.
+        For a dimension ``N`` array, a valid axis is an integer on the
+        closed-interval ``[-N-1, N]``. Negative values work from the end of
+        the shape. ``0`` prepends an axis, as does ``-N-1``. ``-1`` appends
+        an axis, as does ``N``. The new axis has shape ``1`` and indices are
+        created with the value ``0``.
+
+    Returns
+    -------
+    out : sparse array
+        An expanded copy output in COO format with the same dtype as `A`.
+
+    Raises
+    ------
+    ValueError
+        If provided a non-integer or out of range ``[-N-1, N]`` axis,
+        where ``N`` is ``A.ndim``.
+
+    Examples
+    --------
+    >>> from scipy.sparse import csr_array, expand_dims
+    >>> A = csr_array([[1, 2], [2, 0]])
+    >>> A.shape
+    (2, 2)
+    >>> expand_dims(A, axis=1).shape
+    (2, 1, 2)
+
+    """
+    if not isintlike(axis):
+        raise ValueError(f"Invalid axis {axis}. Must be an integer.")
+    idx = axis if axis >= 0 else axis + A.ndim + 1
+    if idx < 0 or idx > A.ndim:
+        raise ValueError(f"Invalid axis {axis} for N={A.ndim}. Must be in [-N-1, N].")
+
+    newA = A.tocoo(copy=True)
+    new_coord = np.zeros_like(newA.coords[0])
+
+    newA.coords = newA.coords[:idx] + (new_coord,) + newA.coords[idx:]
+    newA._shape = newA.shape[:idx] + (1,) + newA.shape[idx:]
+    if A.format == "coo":
+        newA.has_canonical_format = A.has_canonical_format
+    return newA
+
+
+def swapaxes(A, axis1, axis2):
+    """Interchange two axes of an array.
+
+    Parameters
+    ----------
+    A : sparse array
+        Input array.
+    axis1 : int
+        First axis.
+    axis2 : int
+        Second axis.
+
+    Returns
+    -------
+    a_swapped : sparse array in COO format
+        A copy of the input array with the two identified axes swapped.
+
+    Raises
+    ------
+    ValueError
+        If provided a non-integer or out of range ``[-N, N-1]`` axis,
+        where ``N`` is ``A.ndim``.
+
+    Examples
+    --------
+    >>> from scipy.sparse import coo_array, swapaxes
+    >>> A = coo_array([[[1, 2, 3], [2, 0, 0]]])
+    >>> A.shape
+    (1, 2, 3)
+    >>> swapaxes(A, 1, 2).shape
+    (1, 3, 2)
+
+    """
+    axes = np.arange(A.ndim)
+    try:
+        axes[[axis1, axis2]] = axes[[axis2, axis1]]
+    except IndexError as err:
+        # original msg looks like: "index -4 is out of bounds for axis 0 with size 2"
+        msg = str(err)
+        msg = msg.removeprefix('index ').split(' axis ', 1)[0]
+        # Final error is: "Invalid axis: -4 is out of bounds for ndim=2"
+        raise ValueError(f"Invalid axis: {msg} ndim={A.ndim}")
+
+    axes = tuple(axes)
+    return permute_dims(A, axes=axes, copy=True)
+
+
+def permute_dims(A, axes=None, copy=False):
+    """Permute the axes of the sparse array `A` to the order `axes`.
+
+    Parameters
+    ----------
+    A : sparse array
+        Input array.
+    axes : tuple or list of ints, optional
+        If specified, it must be a tuple or list which contains a permutation
+        of ``[0, 1, ..., N-1]`` where ``N`` is ``A.ndim``. The ith
+        axis of the returned array will correspond to the axis numbered ``axes[i]``
+        of the input. If not specified, defaults to ``range(A.ndim)[::-1]``,
+        which reverses the order of the axes.
+    copy : bool, optional (default: False)
+        Whether to return the permutation as a copy. If False, an in-place
+        permutation is provided if possible depending on format.
+
+    Returns
+    -------
+    out : sparse array in COO format
+        A copy of `A` with permuted axes.
+
+    Raises
+    ------
+    ValueError
+        If provided a non-integer or out of range ``[-N, N-1]`` axis,
+        where ``N`` is ``A.ndim``.
+
+    Examples
+    --------
+    >>> from scipy.sparse import coo_array, permute_dims
+    >>> A = coo_array([[[1, 2, 3], [2, 0, 0]]])
+    >>> A.shape
+    (1, 2, 3)
+    >>> permute_dims(A, axes=(1, 2, 0)).shape
+    (2, 3, 1)
+
+    """
+    ndim = A.ndim
+    if axes is None:
+        axes = tuple(range(ndim)[::-1])
+    elif len(axes) != ndim:
+        raise ValueError(f"Incorrect number of axes: {ndim} instead of {A.ndim}")
+
+    # -------------This is from _sputils.validateaxis which almost does what we want
+    # TODO stop _sputils.validateaxis from returning `None` when len(axes)==ndim
+    if not isinstance(axes, tuple | list):
+        # If not a tuple, check that the provided axes is actually
+        # an integer and raise a TypeError similar to NumPy's
+        if not np.issubdtype(np.dtype(type(axes)), np.integer):
+            raise TypeError(f'axis must be an integer/tuple of ints, not {type(axes)}')
+        axes = (axes,)
+
+    canon_axes = []
+    for ax in axes:
+        if not isintlike(ax):
+            raise TypeError(f"axis must be an integer. (given {ax})")
+        if ax < 0:
+            ax += ndim
+        if ax < 0 or ax >= ndim:
+            raise ValueError("axis out of range for ndim")
+        canon_axes.append(ax)
+
+    if len(canon_axes) != len(set(canon_axes)):
+        raise ValueError("duplicate value in axis")
+    # -------------End of code from  _sputils.validateaxis
+    axes = canon_axes
+    if axes == list(range(ndim)):
+        return A if not copy else A.copy()
+
+    A = A.tocoo(copy=copy)
+    A._shape = tuple(A.shape[idx] for idx in axes)
+    A.coords = tuple(A.coords[idx] for idx in axes)
+    A.has_canonical_format = False  # data usually no longer sorted
+    return A
+
+
+def matrix_transpose(A):
+    """Return the matrix transpose of `A`.
+
+    Parameters
+    ----------
+    A : sparse array
+        Input array.
+
+    Returns
+    -------
+    sparse array
+        The matrix transpose of `A`.
+
+    See Also
+    --------
+    coo_array.mT : equivalent attribute
+    coo_array.T : full transposition reversing all dimensions
+    numpy.matrix_transpose : equivalent function in NumPy
+
+    Notes
+    -----
+    This is equivalent to ``A.T`` for 2-D arrays, and interprets
+    greater dimensional `A` as a stack of 2-D arrays on which
+    to perform the transpose.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.sparse import coo_array, matrix_transpose
+    >>> data = np.array([[[1, 2], [3, 4]], [[5, 6], [7, 8]]])
+    >>> array = coo_array(data)
+    >>> array.T.toarray()
+    array([[[1, 5],
+            [3, 7]],
+    <BLANKLINE>
+           [[2, 6],
+            [4, 8]]])
+    >>> matrix_transpose(array).toarray()
+    array([[[1, 3],
+            [2, 4]],
+    <BLANKLINE>
+           [[5, 7],
+            [6, 8]]])
+    """
+    return A.mT
+
+
+def spdiags(data, diags, m=None, n=None, format=None):
+    """
+    Return a sparse matrix from diagonals.
+
+    .. warning::
+
+        This function returns a sparse matrix -- not a sparse array.
+        You are encouraged to use `dia_array` to take advantage
+        of the sparse array functionality. (See Notes below.)
+
+    Parameters
+    ----------
+    data : array_like
+        Matrix diagonals stored row-wise
+    diags : sequence of int or an int
+        Diagonals to set:
+
+        * k = 0  the main diagonal
+        * k > 0  the kth upper diagonal
+        * k < 0  the kth lower diagonal
+    m, n : int, tuple, optional
+        Shape of the result. If `n` is None and `m` is a given tuple,
+        the shape is this tuple. If omitted, the matrix is square and
+        its shape is ``len(data[0])``.
+    format : str, optional
+        Format of the result. By default (format=None) an appropriate sparse
+        matrix format is returned. This choice is subject to change.
+
+    Returns
+    -------
+    new_matrix : sparse matrix
+        `dia_matrix` format with values in ``data`` on diagonals from ``diags``.
+
+    See Also
+    --------
+    diags_array : more convenient form of this function.
+    diags : matrix version of diags_array.
+    dia_matrix : the sparse DIAgonal format.
+
+    Notes
+    -----
+    This function can be replaced by an equivalent call to `dia_matrix` as::
+
+        dia_matrix((data, diags), shape=(m, n)).asformat(format)
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.sparse import spdiags
+    >>> data = np.array([[1, 2, 3, 4], [1, 2, 3, 4], [1, 2, 3, 4]])
+    >>> diags = np.array([0, -1, 2])
+    >>> spdiags(data, diags, 4, 4).toarray()
+    array([[1, 0, 3, 0],
+           [1, 2, 0, 4],
+           [0, 2, 3, 0],
+           [0, 0, 3, 4]])
+    """
+    if m is None and n is None:
+        m = n = len(data[0])
+    elif n is None:
+        m, n = m
+    return dia_matrix((data, diags), shape=(m, n)).asformat(format)
+
+
+def diags_array(diagonals, /, *, offsets=0, shape=None, format=None, dtype=_NoValue):
+    """
+    Construct a sparse array from diagonals.
+
+    Parameters
+    ----------
+    diagonals : sequence of array_like
+        Sequence of arrays containing the array diagonals,
+        corresponding to `offsets`.
+    offsets : sequence of int or an int, optional
+        Diagonals to set (repeated offsets are not allowed):
+          - k = 0  the main diagonal (default)
+          - k > 0  the kth upper diagonal
+          - k < 0  the kth lower diagonal
+    shape : tuple of int, optional
+        Shape of the result. If omitted, a square array large enough
+        to contain the diagonals is returned.
+    format : {"dia", "csr", "csc", "lil", ...}, optional
+        Matrix format of the result. By default (format=None) an
+        appropriate sparse array format is returned. This choice is
+        subject to change.
+    dtype : dtype, optional
+        Data type of the array.  If `dtype` is None, the output
+        data type is determined by the data type of the input diagonals.
+
+        Up until SciPy 1.19, the default behavior will be to return an array
+        with an inexact (floating point) data type.  In particular, integer
+        input will be converted to double precision floating point.  This
+        behavior is deprecated, and in SciPy 1.19, the default behavior
+        will be changed to return an array with the same data type as the
+        input diagonals.  To adopt this behavior before version 1.19, use
+        ``dtype=None``.
+
+    Returns
+    -------
+    new_array : dia_array
+        `dia_array` holding the values in `diagonals` offset from the main diagonal
+        as indicated in `offsets`.
+
+    See Also
+    --------
+    dia_array : constructor for the sparse DIAgonal format.
+
+    Notes
+    -----
+    Repeated diagonal offsets are disallowed.
+
+    The result from ``diags_array`` is the sparse equivalent of::
+
+        np.diag(diagonals[0], offsets[0])
+        + ...
+        + np.diag(diagonals[k], offsets[k])
+
+    ``diags_array`` differs from `dia_array` in the way it handles off-diagonals.
+    Specifically, `dia_array` assumes the data input includes padding
+    (ignored values) at the start/end of the rows for positive/negative
+    offset, while ``diags_array`` assumes the input data has no padding.
+    Each value in the input `diagonals` is used.
+
+    .. versionadded:: 1.11
+
+    Examples
+    --------
+    >>> from scipy.sparse import diags_array
+    >>> diagonals = [[1.0, 2.0, 3.0, 4.0], [1.0, 2.0, 3.0], [1.0, 2.0]]
+    >>> diags_array(diagonals, offsets=[0, -1, 2]).toarray()
+    array([[1., 0., 1., 0.],
+           [1., 2., 0., 2.],
+           [0., 2., 3., 0.],
+           [0., 0., 3., 4.]])
+
+    Broadcasting of scalars is supported (but shape needs to be
+    specified):
+
+    >>> diags_array([1.0, -2.0, 1.0], offsets=[-1, 0, 1], shape=(4, 4)).toarray()
+    array([[-2.,  1.,  0.,  0.],
+           [ 1., -2.,  1.,  0.],
+           [ 0.,  1., -2.,  1.],
+           [ 0.,  0.,  1., -2.]])
+
+
+    If only one diagonal is wanted (as in `numpy.diag`), the following
+    works as well:
+
+    >>> diags_array([1.0, 2.0, 3.0], offsets=1).toarray()
+    array([[ 0.,  1.,  0.,  0.],
+           [ 0.,  0.,  2.,  0.],
+           [ 0.,  0.,  0.,  3.],
+           [ 0.,  0.,  0.,  0.]])
+    """
+    # if offsets is not a sequence, assume that there's only one diagonal
+    if isscalarlike(offsets):
+        # now check that there's actually only one diagonal
+        if len(diagonals) == 0 or isscalarlike(diagonals[0]):
+            diagonals = [np.atleast_1d(diagonals)]
+        else:
+            raise ValueError("Different number of diagonals and offsets.")
+    else:
+        diagonals = list(map(np.atleast_1d, diagonals))
+
+    offsets = np.atleast_1d(offsets)
+
+    # Basic check
+    if len(diagonals) != len(offsets):
+        raise ValueError("Different number of diagonals and offsets.")
+
+    # Determine shape, if omitted
+    if shape is None:
+        m = len(diagonals[0]) + abs(int(offsets[0]))
+        shape = (m, m)
+
+    # Determine data type, if omitted
+    if dtype is None:
+        dtype = np.result_type(*diagonals)
+    elif dtype is _NoValue:
+        # This is the old deprecated behavior that uses np.common_type().
+        # After the deprecation period, this elif branch can be removed,
+        # and the default for the `dtype` parameter changed back to `None`.
+        dtype = np.dtype(np.common_type(*diagonals))
+        future_dtype = np.result_type(*diagonals)
+        if (dtype != future_dtype):
+            warn(
+                f"Input has data type {future_dtype}, but the output has been cast "
+                f"to {dtype}.  In the future, the output data type will match the "
+                "input. To avoid this warning, set the `dtype` parameter to `None` "
+                "to have the output dtype match the input, or set it to the "
+                "desired output data type.",
+                FutureWarning,
+                skip_file_prefixes=(os.path.dirname(__file__),)
+            )
+
+    # Construct data array
+    m, n = shape
+
+    M = max([min(m + offset, n - offset) + max(0, offset)
+             for offset in offsets])
+    M = max(0, M)
+    data_arr = np.zeros((len(offsets), M), dtype=dtype)
+
+    K = min(m, n)
+
+    for j, diagonal in enumerate(diagonals):
+        offset = offsets[j]
+        k = max(0, offset)
+        length = min(m + offset, n - offset, K)
+        if length < 0:
+            raise ValueError(f"Offset {offset} (index {j}) out of bounds")
+        try:
+            data_arr[j, k:k+length] = diagonal[...,:length]
+        except ValueError as e:
+            if len(diagonal) != length and len(diagonal) != 1:
+                raise ValueError(
+                    f"Diagonal length (index {j}: {len(diagonal)} at"
+                    f" offset {offset}) does not agree with array size ({m}, {n})."
+                ) from e
+            raise
+
+    return dia_array((data_arr, offsets), shape=(m, n)).asformat(format)
+
+
+def diags(diagonals, offsets=0, shape=None, format=None, dtype=_NoValue):
+    """
+    Construct a sparse matrix from diagonals.
+
+    .. warning::
+
+        This function returns a sparse matrix -- not a sparse array.
+        You are encouraged to use `diags_array` to take advantage
+        of the sparse array functionality.
+
+    Parameters
+    ----------
+    diagonals : sequence of array_like
+        Sequence of arrays containing the matrix diagonals,
+        corresponding to `offsets`.
+    offsets : sequence of int or an int, optional
+        Diagonals to set (repeated offsets are not allowed):
+          - k = 0  the main diagonal (default)
+          - k > 0  the kth upper diagonal
+          - k < 0  the kth lower diagonal
+    shape : tuple of int, optional
+        Shape of the result. If omitted, a square matrix large enough
+        to contain the diagonals is returned.
+    format : {"dia", "csr", "csc", "lil", ...}, optional
+        Matrix format of the result. By default (format=None) an
+        appropriate sparse matrix format is returned. This choice is
+        subject to change.
+    dtype : dtype, optional
+        Data type of the matrix.  If `dtype` is None, the output
+        data type is determined by the data type of the input diagonals.
+
+        Up until SciPy 1.19, the default behavior will be to return a matrix
+        with an inexact (floating point) data type.  In particular, integer
+        input will be converted to double precision floating point.  This
+        behavior is deprecated, and in SciPy 1.19, the default behavior
+        will be changed to return a matrix with the same data type as the
+        input diagonals.  To adopt this behavior before version 1.19, use
+        `dtype=None`.
+
+    Returns
+    -------
+    new_matrix : dia_matrix
+        `dia_matrix` holding the values in `diagonals` offset from the main diagonal
+        as indicated in `offsets`.
+
+    See Also
+    --------
+    spdiags : construct matrix from diagonals
+    diags_array : construct sparse array instead of sparse matrix
+
+    Notes
+    -----
+    Repeated diagonal offsets are disallowed.
+
+    The result from ``diags`` is the sparse equivalent of::
+
+        np.diag(diagonals[0], offsets[0])
+        + ...
+        + np.diag(diagonals[k], offsets[k])
+
+    ``diags`` differs from `dia_matrix` in the way it handles off-diagonals.
+    Specifically, `dia_matrix` assumes the data input includes padding
+    (ignored values) at the start/end of the rows for positive/negative
+    offset, while ``diags`` assumes the input data has no padding.
+    Each value in the input `diagonals` is used.
+
+    .. versionadded:: 0.11
+
+    Examples
+    --------
+    >>> from scipy.sparse import diags
+    >>> diagonals = [[1.0, 2.0, 3.0, 4.0], [1.0, 2.0, 3.0], [1.0, 2.0]]
+    >>> diags(diagonals, [0, -1, 2]).toarray()
+    array([[1., 0., 1., 0.],
+           [1., 2., 0., 2.],
+           [0., 2., 3., 0.],
+           [0., 0., 3., 4.]])
+
+    Broadcasting of scalars is supported (but shape needs to be
+    specified):
+
+    >>> diags([1.0, -2.0, 1.0], [-1, 0, 1], shape=(4, 4)).toarray()
+    array([[-2.,  1.,  0.,  0.],
+           [ 1., -2.,  1.,  0.],
+           [ 0.,  1., -2.,  1.],
+           [ 0.,  0.,  1., -2.]])
+
+
+    If only one diagonal is wanted (as in `numpy.diag`), the following
+    works as well:
+
+    >>> diags([1.0, 2.0, 3.0], 1).toarray()
+    array([[ 0.,  1.,  0.,  0.],
+           [ 0.,  0.,  2.,  0.],
+           [ 0.,  0.,  0.,  3.],
+           [ 0.,  0.,  0.,  0.]])
+    """
+    A = diags_array(diagonals, offsets=offsets, shape=shape, dtype=dtype)
+    return dia_matrix(A).asformat(format)
+
+
+def identity(n, dtype='d', format=None):
+    """Identity matrix in sparse format.
+
+    Returns an identity matrix with shape ``(n, n)`` using a given
+    sparse format and dtype. This differs from `eye_array` in
+    that it has a square shape with ones only on the main diagonal.
+    It is thus the multiplicative identity. `eye_array` allows
+    rectangular shapes and the diagonal can be offset from the main one.
+
+    .. warning::
+
+        This function returns a sparse matrix -- not a sparse array.
+        You are encouraged to use `eye_array` to take advantage
+        of the sparse array functionality.
+
+    Parameters
+    ----------
+    n : int
+        Shape of the identity matrix.
+    dtype : dtype, optional
+        Data type of the matrix
+    format : str, optional
+        Sparse format of the result, e.g., format="csr", etc.
+
+    Returns
+    -------
+    new_matrix : sparse matrix
+        A square sparse matrix with ones on the main diagonal and zeros elsewhere.
+
+    See Also
+    --------
+    eye_array : Sparse array of chosen shape with ones on a specified diagonal.
+    eye : Sparse matrix of chosen shape with ones on a specified diagonal.
+
+    Examples
+    --------
+    >>> import scipy as sp
+    >>> sp.sparse.identity(3).toarray()
+    array([[ 1.,  0.,  0.],
+           [ 0.,  1.,  0.],
+           [ 0.,  0.,  1.]])
+    >>> sp.sparse.identity(3, dtype='int8', format='dia')
+    <DIAgonal sparse matrix of dtype 'int8'
+        with 3 stored elements (1 diagonals) and shape (3, 3)>
+    >>> sp.sparse.eye_array(3, dtype='int8', format='dia')
+    <DIAgonal sparse array of dtype 'int8'
+        with 3 stored elements (1 diagonals) and shape (3, 3)>
+
+    """
+    return eye(n, n, dtype=dtype, format=format)
+
+
+def eye_array(m, n=None, *, k=0, dtype=float, format=None):
+    """Sparse array of chosen shape with ones on the kth diagonal and zeros elsewhere.
+
+    Return a sparse array with ones on diagonal.
+    Specifically a sparse array (m x n) where the kth diagonal
+    is all ones and everything else is zeros.
+
+    Parameters
+    ----------
+    m : int
+        Number of rows requested.
+    n : int, optional
+        Number of columns. Default: `m`.
+    k : int, optional
+        Diagonal to place ones on. Default: 0 (main diagonal).
+    dtype : dtype, optional
+        Data type of the array
+    format : str, optional (default: "dia")
+        Sparse format of the result, e.g., format="csr", etc.
+
+    Returns
+    -------
+    new_array : sparse array
+        Sparse array of chosen shape with ones on the kth diagonal and zeros elsewhere.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import scipy as sp
+    >>> sp.sparse.eye_array(3).toarray()
+    array([[ 1.,  0.,  0.],
+           [ 0.,  1.,  0.],
+           [ 0.,  0.,  1.]])
+    >>> sp.sparse.eye_array(3, dtype=np.int8)
+    <DIAgonal sparse array of dtype 'int8'
+        with 3 stored elements (1 diagonals) and shape (3, 3)>
+
+    """
+    # TODO: delete next 15 lines [combine with _eye()] once spmatrix removed
+    return _eye(m, n, k, dtype, format)
+
+
+def _eye(m, n, k, dtype, format, as_sparray=True):
+    if as_sparray:
+        csr_sparse = csr_array
+        csc_sparse = csc_array
+        coo_sparse = coo_array
+        diags_sparse = diags_array
+    else:
+        csr_sparse = csr_matrix
+        csc_sparse = csc_matrix
+        coo_sparse = coo_matrix
+        diags_sparse = diags
+
+    if n is None:
+        n = m
+    m, n = int(m), int(n)
+
+    if m == n and k == 0:
+        # fast branch for special formats
+        if format in ['csr', 'csc']:
+            idx_dtype = get_index_dtype(maxval=n)
+            indptr = np.arange(n+1, dtype=idx_dtype)
+            indices = np.arange(n, dtype=idx_dtype)
+            data = np.ones(n, dtype=dtype)
+            cls = {'csr': csr_sparse, 'csc': csc_sparse}[format]
+            return cls((data, indices, indptr), (n, n))
+
+        elif format == 'coo':
+            idx_dtype = get_index_dtype(maxval=n)
+            row = np.arange(n, dtype=idx_dtype)
+            col = np.arange(n, dtype=idx_dtype)
+            data = np.ones(n, dtype=dtype)
+            return coo_sparse((data, (row, col)), (n, n))
+
+    data = np.ones((1, max(0, min(m + k, n))), dtype=dtype)
+    return diags_sparse(data, offsets=[k], shape=(m, n), dtype=dtype).asformat(format)
+
+
+def eye(m, n=None, k=0, dtype=float, format=None):
+    """Sparse matrix of chosen shape with ones on the kth diagonal and zeros elsewhere.
+
+    Returns a sparse matrix (m x n) where the kth diagonal
+    is all ones and everything else is zeros.
+
+    .. warning::
+
+        This function returns a sparse matrix -- not a sparse array.
+        You are encouraged to use `eye_array` to take advantage
+        of the sparse array functionality.
+
+    Parameters
+    ----------
+    m : int
+        Number of rows in the matrix.
+    n : int, optional
+        Number of columns. Default: `m`.
+    k : int, optional
+        Diagonal to place ones on. Default: 0 (main diagonal).
+    dtype : dtype, optional
+        Data type of the matrix.
+    format : str, optional
+        Sparse format of the result, e.g., format="csr", etc.
+
+    Returns
+    -------
+    new_matrix : sparse matrix
+        Sparse matrix of chosen shape with ones on the kth diagonaland zeros elsewhere.
+
+    See Also
+    --------
+    eye_array : Sparse array of chosen shape with ones on a specified diagonal.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import scipy as sp
+    >>> sp.sparse.eye(3).toarray()
+    array([[ 1.,  0.,  0.],
+           [ 0.,  1.,  0.],
+           [ 0.,  0.,  1.]])
+    >>> sp.sparse.eye(3, dtype=np.int8)
+    <DIAgonal sparse matrix of dtype 'int8'
+        with 3 stored elements (1 diagonals) and shape (3, 3)>
+
+    """
+    return _eye(m, n, k, dtype, format, False)
+
+
+def kron(A, B, format=None):
+    """Sparse representation of the Kronecker product of `A` and `B`.
+
+    Computes the Kronecker product, a composite sparse array
+    made of blocks consisting of the second input array multiplied
+    by each element of the first input array.
+
+    .. warning::
+
+        `kron` is switching to the sparse array interface.
+
+        For the case where no input arrays are sparse, this function is
+        switching to returning a sparse array instead of sparse matrix.
+        Control the sparse return class by making at least one input sparse,
+        e.g., ``kron(coo_matrix(A), B)``, or ``kron(coo_array(A), B)``.
+        That removes any deprecation warnings as well.
+        For more general information about sparrays, see
+        :ref:`Migration from spmatrix to sparray <migration_to_sparray>`.
+        Handling of this no sparse input case will change no earlier than v1.20.
+
+    Parameters
+    ----------
+    A : sparse or dense array
+        first array of the product
+    B : sparse or dense array
+        second array of the product
+    format : str, optional (default: 'bsr' or 'coo')
+        format of the result (e.g. "csr")
+        If None, choose 'bsr' for relatively dense 2D arrays and 'coo' for others
+
+    Returns
+    -------
+    sparse matrix or array
+        kronecker product in a sparse format. Returns a sparse matrix unless either
+        `A` or `B` is a sparse array in which case returns a sparse array.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import scipy as sp
+    >>> A = sp.sparse.csr_array(np.array([[0, 2], [5, 0]]))
+    >>> B = sp.sparse.csr_array(np.array([[1, 2], [3, 4]]))
+    >>> sp.sparse.kron(A, B).toarray()
+    array([[ 0,  0,  2,  4],
+           [ 0,  0,  6,  8],
+           [ 5, 10,  0,  0],
+           [15, 20,  0,  0]])
+
+    >>> sp.sparse.kron(A, [[1, 2], [3, 4]]).toarray()
+    array([[ 0,  0,  2,  4],
+           [ 0,  0,  6,  8],
+           [ 5, 10,  0,  0],
+           [15, 20,  0,  0]])
+
+    """
+    # TODO: delete this if-clause and replace _sparse with _array when spmatrix removed
+    if isinstance(A, sparray) or isinstance(B, sparray):
+        # convert to local variables
+        bsr_sparse = bsr_array
+        csr_sparse = csr_array
+        coo_sparse = coo_array
+    elif isinstance(A, spmatrix) or isinstance(B, spmatrix):
+        bsr_sparse = bsr_matrix
+        csr_sparse = csr_matrix
+        coo_sparse = coo_matrix
+    else:  # all dense
+        msg = """`kron` is switching to the sparse array interface.
+
+        For the case where input arrays are numpy arrays, this function is
+        switching to returning a sparse array instead of sparse matrix.
+        Recover the sparse matrix return value by making one input a sparse matrix.
+        For example, kron(coo_matrix(A), B).
+        Avoid this message for sparse array output by using kron(coo_array(A), B).
+        For more information, see the spmatrix to sparray migration guide
+        https://docs.scipy.org/doc/scipy/reference/sparse.migration_to_sparray.html
+
+        This function will be changed no earlier than v1.20.
+        """
+        prefixes = (os.path.dirname(__file__),)
+        warn(msg, category=DeprecationWarning, skip_file_prefixes=prefixes)
+        # default when all input are ndarray
+        bsr_sparse = bsr_matrix
+        csr_sparse = csr_matrix
+        coo_sparse = coo_matrix
+
+    B = coo_sparse(B)
+
+    # B is 2D and fairly dense, and format aligns with bsr, compute using BSR
+    if (
+        (format is None or format == "bsr") and
+        B.ndim == 2 and 2*B.nnz >= math.prod(B.shape)
+    ):
+        if not hasattr(A, 'ndim') or A.ndim != 2:
+            # CSR routes thru COO in constructor so can make COO to check ndim
+            A = coo_sparse(A)
+        if A.ndim == 2:
+            A = csr_sparse(A, copy=True)
+            output_shape = (A.shape[0]*B.shape[0], A.shape[1]*B.shape[1])
+
+            if A.nnz == 0 or B.nnz == 0:
+                # kronecker product is the zero matrix
+                return coo_sparse(output_shape).asformat(format)
+
+            B = B.toarray()
+            data = A.data.repeat(B.size).reshape(-1, B.shape[0], B.shape[1])
+            data = data * B
+
+            return bsr_sparse((data, A.indices, A.indptr), shape=output_shape)
+    else:
+        A = coo_sparse(A)  # no copy needed as we use np.repeat below
+
+    # compute using COO (convert to desired format just before return)
+    if coo_sparse is coo_matrix:
+        output_shape = (A.shape[0] * B.shape[0], A.shape[1] * B.shape[1])
+        ndim_diff = 0
+    else:
+        ndim_diff = A.ndim - B.ndim
+        A_shape = A.shape if ndim_diff >= 0 else (1,) * (-ndim_diff) + A.shape
+        B_shape = B.shape if ndim_diff <= 0 else (1,) * ndim_diff + B.shape
+        output_shape = tuple(a * b for a, b in zip(A_shape, B_shape))
+
+    if A.nnz == 0 or B.nnz == 0:
+        # kronecker product is the zero matrix
+        return coo_sparse(output_shape).asformat(format)
+
+    # expand entries of a into blocks
+    data = A.data.repeat(B.nnz)
+    idx_dtype = get_index_dtype(A.coords, maxval=max(output_shape))
+    coords = [np.asarray(co, dtype=idx_dtype).repeat(B.nnz) for co in A.coords]
+    if ndim_diff < 0:
+        new_co = np.zeros_like(coords[0])
+        coords = [new_co] + [new_co.copy() for _ in range(-ndim_diff - 1)] + coords
+
+    # The last B.ndim coords need to be updated. Any previous columns in B are from
+    # prepending (1,)s, so coord from A is what we need (B coord axis is all 0)
+    for co, B_shape_i in zip(coords[-B.ndim:], B.shape):
+        co *= B_shape_i
+
+    # increment block indices
+    coords[-B.ndim:] = [(co.reshape(-1, B.nnz) + Bco).ravel()
+                        for co, Bco in zip(coords[-B.ndim:], B.coords)]
+    # compute block entries
+    data = (data.reshape(-1, B.nnz) * B.data).ravel()
+
+    return coo_sparse((data, tuple(coords)), shape=output_shape).asformat(format)
+
+
+def kronsum(A, B, format=None):
+    """Kronecker sum of square sparse matrices `A` and `B`.
+
+    Kronecker sum of two sparse matrices is a sum of two Kronecker
+    products ``kron(I_n,A) + kron(B,I_m)`` where `A` has shape ``(m, m)``
+    and `B` has shape ``(n, n)`` and ``I_m`` and ``I_n`` are identity matrices
+    of shape ``(m, m)`` and ``(n, n)``, respectively.
+
+    .. warning::
+
+        `kronsum` is switching to the sparse array interface.
+
+        For the case where no input arrays are sparse, this function is
+        switching to returning a sparse array instead of sparse matrix.
+        Control the sparse return class by making at least one input sparse,
+        e.g., ``kronsum(coo_matrix(A), B)``, or ``kronsum(coo_array(A), B)``.
+        That removes any deprecation warnings as well.
+        For more general information about sparrays, see
+        :ref:`Migration from spmatrix to sparray <migration_to_sparray>`.
+        Handling of this no sparse input case will change no earlier than v1.20.
+
+    Parameters
+    ----------
+    A : sparse matrix or array
+        Square matrix
+    B : sparse array or array
+        Square matrix
+    format : str
+        format of the result (e.g. "csr")
+
+    Returns
+    -------
+    sparse matrix or array
+        kronecker sum in a sparse format. Returns a sparse matrix unless either
+        `A` or `B` is a sparse array in which case returns a sparse array.
+
+    Examples
+    --------
+    `kronsum` can be used to construct a finite difference discretization of the 2D
+    Laplacian from a 1D discretization.
+
+    >>> from scipy.sparse import diags_array, kronsum
+    >>> from matplotlib import pyplot as plt
+    >>> import numpy as np
+    >>> ex = np.ones(10)
+    >>> D_x = diags_array([ex, -ex[1:]], offsets=[0, -1])  # 1D first derivative
+    >>> D_xx = D_x.T @ D_x  # 1D second derivative
+    >>> L = kronsum(D_xx, D_xx)  # 2D Laplacian
+    >>> plt.spy(L.toarray())
+    >>> plt.show()
+
+    """
+    # TODO: delete this if-clause and replace _sparse with _array when spmatrix removed
+    if isinstance(A, sparray) or isinstance(B, sparray):
+        # convert to local variables
+        coo_sparse = coo_array
+        identity_sparse = eye_array
+    elif isinstance(A, spmatrix) or isinstance(B, spmatrix):
+        coo_sparse = coo_matrix
+        identity_sparse = identity
+    else:  # all dense
+        msg = """`kronsum` is switching to the sparse array interface.
+
+        For the case where input arrays are numpy arrays, this function is
+        switching to returning a sparse array instead of sparse matrix.
+        Recover the sparse matrix return value by making one input a sparse matrix.
+        For example, kronsum(coo_matrix(A), B).
+        Avoid this message for sparse array output by using kronsum(coo_array(A), B).
+        For more information, see the spmatrix to sparray migration guide
+        https://docs.scipy.org/doc/scipy/reference/sparse.migration_to_sparray.html
+
+        This function will be changed no earlier than v1.20.
+        """
+        prefixes = (os.path.dirname(__file__),)
+        warn(msg, category=DeprecationWarning, skip_file_prefixes=prefixes)
+        # default when all input are ndarray
+        coo_sparse = coo_matrix
+        identity_sparse = identity
+
+    A = coo_sparse(A)
+    B = coo_sparse(B)
+
+    if A.ndim != 2:
+        raise ValueError(f"kronsum requires 2D inputs. `A` is {A.ndim}D.")
+    if B.ndim != 2:
+        raise ValueError(f"kronsum requires 2D inputs. `B` is {B.ndim}D.")
+    if A.shape[0] != A.shape[1]:
+        raise ValueError('A is not square')
+    if B.shape[0] != B.shape[1]:
+        raise ValueError('B is not square')
+
+    dtype = upcast(A.dtype, B.dtype)
+
+    I_n = identity_sparse(A.shape[0], dtype=dtype)
+    I_m = identity_sparse(B.shape[0], dtype=dtype)
+    L = kron(I_m, A, format='coo')
+    R = kron(B, I_n, format='coo')
+
+    return (L + R).asformat(format)
+
+
+def _compressed_sparse_stack(blocks, axis, return_spmatrix):
+    """
+    Stacking fast path for CSR/CSC matrices or arrays
+    (i) vstack for CSR, (ii) hstack for CSC.
+    """
+    other_axis = 1 if axis == 0 else 0
+    data = np.concatenate([b.data for b in blocks])
+    constant_dim = blocks[0]._shape_as_2d[other_axis]
+    idx_dtype = get_index_dtype(arrays=[b.indptr for b in blocks],
+                                maxval=max(data.size, constant_dim))
+    indices = np.empty(data.size, dtype=idx_dtype)
+    indptr = np.empty(sum(b._shape_as_2d[axis] for b in blocks) + 1, dtype=idx_dtype)
+    last_indptr = idx_dtype(0)
+    sum_dim = 0
+    sum_indices = 0
+    for b in blocks:
+        if b._shape_as_2d[other_axis] != constant_dim:
+            raise ValueError(f'incompatible dimensions for axis {other_axis}')
+        indices[sum_indices:sum_indices+b.indices.size] = b.indices
+        sum_indices += b.indices.size
+        idxs = slice(sum_dim, sum_dim + b._shape_as_2d[axis])
+        indptr[idxs] = b.indptr[:-1]
+        indptr[idxs] += last_indptr
+        sum_dim += b._shape_as_2d[axis]
+        last_indptr += b.indptr[-1]
+    indptr[-1] = last_indptr
+    # TODO remove this if-structure when sparse matrices removed
+    if return_spmatrix:
+        if axis == 0:
+            return csr_matrix((data, indices, indptr),
+                              shape=(sum_dim, constant_dim))
+        else:
+            return csc_matrix((data, indices, indptr),
+                              shape=(constant_dim, sum_dim))
+
+    if axis == 0:
+        return csr_array((data, indices, indptr),
+                          shape=(sum_dim, constant_dim))
+    else:
+        return csc_array((data, indices, indptr),
+                          shape=(constant_dim, sum_dim))
+
+
+def _stack_along_minor_axis(blocks, axis):
+    """
+    Stacking fast path for CSR/CSC matrices along the minor axis
+    (i) hstack for CSR, (ii) vstack for CSC.
+    """
+    n_blocks = len(blocks)
+    if n_blocks == 0:
+        raise ValueError('Missing block matrices')
+
+    if n_blocks == 1:
+        return blocks[0]
+
+    # check for incompatible dimensions
+    other_axis = 1 if axis == 0 else 0
+    other_axis_dims = {b._shape_as_2d[other_axis] for b in blocks}
+    if len(other_axis_dims) > 1:
+        raise ValueError(f'Mismatching dimensions along axis {other_axis}: '
+                         f'{other_axis_dims}')
+    constant_dim, = other_axis_dims
+
+    # Do the stacking
+    indptr_list = [b.indptr for b in blocks]
+    data_cat = np.concatenate([b.data for b in blocks])
+
+    # Need to check if any indices/indptr, would be too large post-
+    # concatenation for np.int32:
+    # - The max value of indices is the output array's stacking-axis length - 1
+    # - The max value in indptr is the number of non-zero entries. This is
+    #   exceedingly unlikely to require int64, but is checked out of an
+    #   abundance of caution.
+    sum_dim = sum(b._shape_as_2d[axis] for b in blocks)
+    nnz = sum(len(b.indices) for b in blocks)
+    idx_dtype = get_index_dtype(indptr_list, maxval=max(sum_dim - 1, nnz))
+    stack_dim_cat = np.array([b._shape_as_2d[axis] for b in blocks], dtype=idx_dtype)
+    if data_cat.size > 0:
+        indptr_cat = np.concatenate(indptr_list, dtype=idx_dtype)
+        indices_cat = np.concatenate([b.indices for b in blocks], dtype=idx_dtype)
+        indptr = np.empty(constant_dim + 1, dtype=idx_dtype)
+        indices = np.empty_like(indices_cat)
+        data = np.empty_like(data_cat)
+        csr_hstack(n_blocks, constant_dim, stack_dim_cat,
+                   indptr_cat, indices_cat, data_cat,
+                   indptr, indices, data)
+    else:
+        indptr = np.zeros(constant_dim + 1, dtype=idx_dtype)
+        indices = np.empty(0, dtype=idx_dtype)
+        data = np.empty(0, dtype=data_cat.dtype)
+
+    if axis == 0:
+        return blocks[0]._csc_container((data, indices, indptr),
+                          shape=(sum_dim, constant_dim))
+    else:
+        return blocks[0]._csr_container((data, indices, indptr),
+                          shape=(constant_dim, sum_dim))
+
+
+def hstack(blocks, format=None, dtype=None):
+    """
+    Stack sparse matrices horizontally (column wise).
+
+    Parameters
+    ----------
+    blocks : sequence of sparse matrices or arrays
+        sequence of sparse matrices with compatible shapes
+    format : str
+        sparse format of the result (e.g., "csr")
+        by default an appropriate sparse matrix format is returned.
+        This choice is subject to change.
+    dtype : dtype, optional
+        The data-type of the output matrix. If not given, the dtype is
+        determined from that of `blocks`.
+
+    Returns
+    -------
+    new_array : sparse matrix or array
+        If any block in blocks is a sparse array, return a sparse array.
+        Otherwise return a sparse matrix.
+
+        If you want a sparse array built from blocks that are not sparse
+        arrays, use ``block(hstack(blocks))`` or convert one block
+        e.g. ``blocks[0] = csr_array(blocks[0])``.
+
+    See Also
+    --------
+    vstack : stack sparse matrices vertically (row wise)
+
+    Examples
+    --------
+    >>> from scipy.sparse import coo_matrix, hstack
+    >>> A = coo_matrix([[1, 2], [3, 4]])
+    >>> B = coo_matrix([[5], [6]])
+    >>> hstack([A,B]).toarray()
+    array([[1, 2, 5],
+           [3, 4, 6]])
+
+    """
+    blocks = np.asarray(blocks, dtype='object')
+    if any(isinstance(b, sparray) for b in blocks.flat):
+        return _block([blocks], format, dtype)
+    else:
+        return _block([blocks], format, dtype, return_spmatrix=True)
+
+
+def vstack(blocks, format=None, dtype=None):
+    """
+    Stack sparse arrays vertically (row wise).
+
+    Parameters
+    ----------
+    blocks : sequence of sparse matrices or arrays
+        sequence of sparse arrays with compatible shapes
+    format : str, optional
+        sparse format of the result (e.g., "csr")
+        by default an appropriate sparse array format is returned.
+        This choice is subject to change.
+    dtype : dtype, optional
+        The data-type of the output array. If not given, the dtype is
+        determined from that of `blocks`.
+
+    Returns
+    -------
+    new_array : sparse matrix or array
+        If any block in blocks is a sparse array, return a sparse array.
+        Otherwise return a sparse matrix.
+
+        If you want a sparse array built from blocks that are not sparse
+        arrays, use ``block(vstack(blocks))`` or convert one block
+        e.g. ``blocks[0] = csr_array(blocks[0])``.
+
+    See Also
+    --------
+    hstack : stack sparse matrices horizontally (column wise)
+
+    Examples
+    --------
+    >>> from scipy.sparse import coo_array, vstack
+    >>> A = coo_array([[1, 2], [3, 4]])
+    >>> B = coo_array([[5, 6]])
+    >>> vstack([A, B]).toarray()
+    array([[1, 2],
+           [3, 4],
+           [5, 6]])
+
+    """
+    blocks = np.asarray(blocks, dtype='object')
+    if any(isinstance(b, sparray) for b in blocks.flat):
+        return _block([[b] for b in blocks], format, dtype)
+    else:
+        return _block([[b] for b in blocks], format, dtype, return_spmatrix=True)
+
+
+def bmat(blocks, format=None, dtype=None):
+    """
+    Build a sparse array or matrix from sparse sub-blocks.
+
+    Note: `block_array` is preferred over ``bmat``. They are the same function
+    except that ``bmat`` returns a deprecated sparse matrix when none of the
+    inputs are sparse arrays.
+
+    .. warning::
+
+        This function returns a sparse matrix when no inputs are sparse arrays.
+        You are encouraged to use `block_array` to take advantage
+        of the sparse array functionality.
+
+    Parameters
+    ----------
+    blocks : array_like
+        Grid of sparse matrices with compatible shapes.
+        An entry of None implies an all-zero matrix.
+    format : {'bsr', 'coo', 'csc', 'csr', 'dia', 'dok', 'lil'}, optional
+        The sparse format of the result (e.g. "csr"). By default an
+        appropriate sparse matrix format is returned.
+        This choice is subject to change.
+    dtype : dtype, optional
+        The data-type of the output matrix. If not given, the dtype is
+        determined from that of `blocks`.
+
+    Returns
+    -------
+    bmat : sparse matrix or array
+        If any block in blocks is a sparse array, return a sparse array.
+        Otherwise return a sparse matrix.
+
+        If you want a sparse array built from blocks that are not sparse
+        arrays, use ``block_array()``.
+
+    See Also
+    --------
+    block_array
+
+    Examples
+    --------
+    >>> from scipy.sparse import coo_array, bmat
+    >>> A = coo_array([[1, 2], [3, 4]])
+    >>> B = coo_array([[5], [6]])
+    >>> C = coo_array([[7]])
+    >>> bmat([[A, B], [None, C]]).toarray()
+    array([[1, 2, 5],
+           [3, 4, 6],
+           [0, 0, 7]])
+
+    >>> bmat([[A, None], [None, C]]).toarray()
+    array([[1, 2, 0],
+           [3, 4, 0],
+           [0, 0, 7]])
+
+    """
+    blocks = np.asarray(blocks, dtype='object')
+    if any(isinstance(b, sparray) for b in blocks.flat):
+        return _block(blocks, format, dtype)
+    else:
+        return _block(blocks, format, dtype, return_spmatrix=True)
+
+
+def block_array(blocks, *, format=None, dtype=None):
+    """
+    Build a sparse array from sparse sub-blocks.
+
+    Parameters
+    ----------
+    blocks : array_like
+        Grid of sparse arrays with compatible shapes.
+        An entry of None implies an all-zero array.
+    format : {'bsr', 'coo', 'csc', 'csr', 'dia', 'dok', 'lil'}, optional
+        The sparse format of the result (e.g. "csr"). By default an
+        appropriate sparse array format is returned.
+        This choice is subject to change.
+    dtype : dtype, optional
+        The data-type of the output array. If not given, the dtype is
+        determined from that of `blocks`.
+
+    Returns
+    -------
+    block : sparse array
+        Sparse array formed from specified blocks.
+
+    See Also
+    --------
+    block_diag : specify blocks along the main diagonals
+    diags : specify (possibly offset) diagonals
+
+    Examples
+    --------
+    >>> from scipy.sparse import coo_array, block_array
+    >>> A = coo_array([[1, 2], [3, 4]])
+    >>> B = coo_array([[5], [6]])
+    >>> C = coo_array([[7]])
+    >>> block_array([[A, B], [None, C]]).toarray()
+    array([[1, 2, 5],
+           [3, 4, 6],
+           [0, 0, 7]])
+
+    >>> block_array([[A, None], [None, C]]).toarray()
+    array([[1, 2, 0],
+           [3, 4, 0],
+           [0, 0, 7]])
+
+    """
+    return _block(blocks, format, dtype)
+
+
+def _block(blocks, format, dtype, return_spmatrix=False):
+    blocks = np.asarray(blocks, dtype='object')
+
+    if blocks.ndim != 2:
+        raise ValueError('blocks must be 2-D, and some must be sparse')
+
+    M,N = blocks.shape
+
+    # check for fast path cases
+    if (format in (None, 'csr') and
+        all(issparse(b) and b.format == 'csr' for b in blocks.flat)
+    ):
+        if N > 1:
+            # stack along columns (axis 1): must have shape (M, 1)
+            blocks = [[_stack_along_minor_axis(blocks[b, :], 1)] for b in range(M)]
+            blocks = np.asarray(blocks, dtype='object')
+
+        # stack along rows (axis 0):
+        A = _compressed_sparse_stack(blocks[:, 0], 0, return_spmatrix)
+        if dtype is not None:
+            A = A.astype(dtype, copy=False)
+        return A
+    elif (format in (None, 'csc') and
+          all(issparse(b) and b.format == 'csc' for b in blocks.flat)
+    ):
+        if M > 1:
+            # stack along rows (axis 0): must have shape (1, N)
+            blocks = [[_stack_along_minor_axis(blocks[:, b], 0) for b in range(N)]]
+            blocks = np.asarray(blocks, dtype='object')
+
+        # stack along columns (axis 1):
+        A = _compressed_sparse_stack(blocks[0, :], 1, return_spmatrix)
+        if dtype is not None:
+            A = A.astype(dtype, copy=False)
+        return A
+
+    block_mask = np.zeros(blocks.shape, dtype=bool)
+    brow_lengths = np.zeros(M, dtype=np.int64)
+    bcol_lengths = np.zeros(N, dtype=np.int64)
+
+    # convert everything to COO format
+    for i in range(M):
+        for j in range(N):
+            if blocks[i,j] is not None:
+                A = coo_array(blocks[i,j])
+                blocks[i,j] = A
+                block_mask[i,j] = True
+
+                if brow_lengths[i] == 0:
+                    brow_lengths[i] = A._shape_as_2d[0]
+                elif brow_lengths[i] != A._shape_as_2d[0]:
+                    msg = (f'blocks[{i},:] has incompatible row dimensions. '
+                           f'Got blocks[{i},{j}].shape[0] == {A._shape_as_2d[0]}, '
+                           f'expected {brow_lengths[i]}.')
+                    raise ValueError(msg)
+
+                if bcol_lengths[j] == 0:
+                    bcol_lengths[j] = A._shape_as_2d[1]
+                elif bcol_lengths[j] != A._shape_as_2d[1]:
+                    msg = (f'blocks[:,{j}] has incompatible column '
+                           f'dimensions. '
+                           f'Got blocks[{i},{j}].shape[1] == {A._shape_as_2d[1]}, '
+                           f'expected {bcol_lengths[j]}.')
+                    raise ValueError(msg)
+
+    nnz = sum(block.nnz for block in blocks[block_mask])
+    if dtype is None:
+        all_dtypes = [blk.dtype for blk in blocks[block_mask]]
+        dtype = upcast(*all_dtypes) if all_dtypes else None
+
+    row_offsets = np.append(0, np.cumsum(brow_lengths))
+    col_offsets = np.append(0, np.cumsum(bcol_lengths))
+
+    shape = (row_offsets[-1], col_offsets[-1])
+
+    data = np.empty(nnz, dtype=dtype)
+    idx_dtype = get_index_dtype([b.coords[0] for b in blocks[block_mask]],
+                                maxval=max(shape))
+    row = np.empty(nnz, dtype=idx_dtype)
+    col = np.empty(nnz, dtype=idx_dtype)
+
+    nnz = 0
+    ii, jj = np.nonzero(block_mask)
+    for i, j in zip(ii, jj):
+        B = blocks[i, j]
+        idx = slice(nnz, nnz + B.nnz)
+        data[idx] = B.data
+        np.add(B.row, row_offsets[i], out=row[idx], dtype=idx_dtype)
+        np.add(B.col, col_offsets[j], out=col[idx], dtype=idx_dtype)
+        nnz += B.nnz
+
+    if return_spmatrix:
+        return coo_matrix((data, (row, col)), shape=shape).asformat(format)
+    return coo_array((data, (row, col)), shape=shape).asformat(format)
+
+
+def block_diag(mats, format=None, dtype=None):
+    """
+    Build a block diagonal sparse matrix or array from provided matrices.
+
+    .. warning::
+
+        `block_diag` is switching to the sparse array interface.
+
+        For the case where no input arrays are sparse, this function is
+        switching to returning a sparse array instead of sparse matrix.
+        Control the sparse return class by making at least one input sparse,
+        e.g., ``block_diag([coo_matrix(A), B])``, or ``block_diag([coo_array(A), B])``.
+        That removes any deprecation warnings as well.
+        For more general information about sparrays, see
+        :ref:`Migration from spmatrix to sparray <migration_to_sparray>`.
+        Handling of this no sparse input case will change no earlier than v1.20.
+
+    Parameters
+    ----------
+    mats : sequence of matrices or arrays
+        Input matrices or arrays.
+    format : str, optional
+        The sparse format of the result (e.g., "csr"). If not given, the result
+        is returned in "coo" format.
+    dtype : dtype specifier, optional
+        The data-type of the output. If not given, the dtype is
+        determined from that of `blocks`.
+
+    Returns
+    -------
+    res : sparse matrix or array
+        If at least one input is a sparse array, the output is a sparse array.
+        Otherwise the output is a sparse matrix.
+
+    See Also
+    --------
+    block_array
+    diags_array
+
+    Notes
+    -----
+
+    .. versionadded:: 0.11.0
+
+    Examples
+    --------
+    >>> from scipy.sparse import coo_array, block_diag
+    >>> A = coo_array([[1, 2], [3, 4]])
+    >>> B = coo_array([[5], [6]])
+    >>> C = coo_array([[7]])
+    >>> block_diag((A, B, C)).toarray()
+    array([[1, 2, 0, 0],
+           [3, 4, 0, 0],
+           [0, 0, 5, 0],
+           [0, 0, 6, 0],
+           [0, 0, 0, 7]])
+    """
+    if any(isinstance(a, sparray) for a in mats):
+        container = coo_array
+    elif any(isinstance(a, spmatrix) for a in mats):
+        container = coo_matrix
+    else:  # all dense
+        msg = """`block_diag` is switching to the sparse array interface.
+
+        For the case where input arrays are numpy arrays, this function is
+        switching to returning a sparse array instead of sparse matrix.
+        Recover the sparse matrix return value by making one input a sparse matrix.
+        For example, block_diag([coo_matrix(A), B]).
+        Avoid this message for sparse array output using block_diag([coo_array(A), B]).
+        For more information, see the spmatrix to sparray migration guide
+        https://docs.scipy.org/doc/scipy/reference/sparse.migration_to_sparray.html
+
+        This function will be changed no earlier than v1.20.
+        """
+        prefixes = (os.path.dirname(__file__),)
+        warn(msg, category=DeprecationWarning, skip_file_prefixes=prefixes)
+
+        # default when all input are ndarray
+        container = coo_matrix
+
+    row = []
+    col = []
+    data = []
+    idx_arrays = []  # track idx_dtype of incoming sparse arrays
+    r_idx = 0
+    c_idx = 0
+    for a in mats:
+        if isinstance(a, (list | numbers.Number)):
+            a = coo_array(np.atleast_2d(a))
+        if issparse(a):
+            a = a.tocoo()
+            if not idx_arrays and a.coords[0].dtype == np.int64:
+                idx_arrays.append(a.coords[0])
+            nrows, ncols = a._shape_as_2d
+            row.append(a.row + r_idx)
+            col.append(a.col + c_idx)
+            data.append(a.data)
+        else:
+            nrows, ncols = a.shape
+            a_row, a_col = np.divmod(np.arange(nrows*ncols), ncols)
+            row.append(a_row + r_idx)
+            col.append(a_col + c_idx)
+            data.append(a.ravel())
+        r_idx += nrows
+        c_idx += ncols
+    idx_dtype = get_index_dtype(idx_arrays, maxval=max(r_idx, c_idx))
+    row = np.concatenate(row, dtype=idx_dtype)
+    col = np.concatenate(col, dtype=idx_dtype)
+    data = np.concatenate(data)
+    new_shape = (r_idx, c_idx)
+
+    return container((data, (row, col)), shape=new_shape, dtype=dtype).asformat(format)
+
+
+@_transition_to_rng("random_state")
+def random_array(shape, *, density=0.01, format='coo', dtype=None,
+                 rng=None, data_sampler=None):
+    """Return a sparse array of uniformly random numbers in [0, 1).
+
+    Returns a sparse array with the given shape and density
+    where values are generated uniformly randomly in the range [0, 1).
+
+    Parameters
+    ----------
+    shape : tuple of int
+        shape of the array.
+    density : real, optional (default: 0.01)
+        density of the generated matrix: density equal to one means a full
+        matrix, density of 0 means a matrix with no non-zero items.
+    format : str, optional (default: 'coo')
+        sparse matrix format.
+    dtype : dtype, optional (default: np.float64)
+        type of the returned matrix values.
+    rng : `numpy.random.Generator`, optional
+        Pseudorandom number generator state. When `rng` is None, a new
+        `numpy.random.Generator` is created using entropy from the
+        operating system. Types other than `numpy.random.Generator` are
+        passed to `numpy.random.default_rng` to instantiate a ``Generator``.
+
+        This random state will be used for sampling ``indices`` (the sparsity
+        structure), and by default for the data values too (see `data_sampler`).
+    data_sampler : callable, optional (default depends on dtype)
+        Sampler of random data values with keyword arg ``size``.
+        This function should take a single keyword argument ``size`` specifying
+        the length of its returned ndarray. It is used to generate the nonzero
+        values in the matrix after the locations of those values are chosen.
+        By default, uniform [0, 1) random values are used unless `dtype` is
+        an integer (default uniform integers from that dtype) or
+        complex (default uniform over the unit square in the complex plane).
+        For these, the `rng` is used e.g. ``rng.uniform(size=size)``.
+
+    Returns
+    -------
+    res : sparse array
+        Random sparse array.
+
+    Examples
+    --------
+
+    Passing a ``np.random.Generator`` instance for better performance:
+
+    >>> import numpy as np
+    >>> import scipy as sp
+    >>> rng = np.random.default_rng()
+
+    Default sampling uniformly from [0, 1):
+
+    >>> S = sp.sparse.random_array((3, 4), density=0.25, rng=rng)
+
+    Providing a sampler for the values:
+
+    >>> rvs = sp.stats.poisson(25, loc=10).rvs
+    >>> S = sp.sparse.random_array((3, 4), density=0.25,
+    ...                            rng=rng, data_sampler=rvs)
+    >>> S.toarray()
+    array([[ 36.,   0.,  33.,   0.],   # random
+           [  0.,   0.,   0.,   0.],
+           [  0.,   0.,  36.,   0.]])
+
+    Providing a sampler for uint values:
+
+    >>> def random_uint32_to_100(size=None):
+    ...     return rng.integers(100, size=size, dtype=np.uint32)
+    >>> S = sp.sparse.random_array((3, 4), density=0.25, rng=rng,
+    ...                            data_sampler=random_uint32_to_100)
+
+    Building a custom distribution.
+    This example builds a squared normal from np.random:
+
+    >>> def np_normal_squared(size=None, rng=rng):
+    ...     return rng.standard_normal(size) ** 2
+    >>> S = sp.sparse.random_array((3, 4), density=0.25, rng=rng,
+    ...                            data_sampler=np_normal_squared)
+
+    Or we can build it from sp.stats style rvs functions:
+
+    >>> def sp_stats_normal_squared(size=None, rng=rng):
+    ...     std_normal = sp.stats.distributions.norm_gen().rvs
+    ...     return std_normal(size=size, random_state=rng) ** 2
+    >>> S = sp.sparse.random_array((3, 4), density=0.25, rng=rng,
+    ...                            data_sampler=sp_stats_normal_squared)
+
+    Or we can subclass sp.stats rv_continuous or rv_discrete:
+
+    >>> class NormalSquared(sp.stats.rv_continuous):
+    ...     def _rvs(self,  size=None, random_state=rng):
+    ...         return rng.standard_normal(size) ** 2
+    >>> X = NormalSquared()
+    >>> Y = X().rvs
+    >>> S = sp.sparse.random_array((3, 4), density=0.25,
+    ...                            rng=rng, data_sampler=Y)
+    """
+    data, ind = _random(shape, density, format, dtype, rng, data_sampler)
+
+    # downcast, if safe, before calling coo_constructor
+    idx_dtype = get_index_dtype(maxval=max(shape))
+    ind = tuple(np.asarray(co, dtype=idx_dtype) for co in ind)
+    return coo_array((data, ind), shape=shape).asformat(format)
+
+
+def _random(shape, density=0.01, format=None, dtype=None,
+            rng=None, data_sampler=None):
+    if density < 0 or density > 1:
+        raise ValueError("density expected to be 0 <= density <= 1")
+
+    tot_prod = math.prod(shape)  # use `math` for when prod is >= 2**64
+
+    # Number of non zero values
+    size = int(round(density * tot_prod))
+
+    rng = check_random_state(rng)
+
+    if data_sampler is None:
+        if np.issubdtype(dtype, np.integer):
+            def data_sampler(size):
+                return rng_integers(rng,
+                                    np.iinfo(dtype).min,
+                                    np.iinfo(dtype).max,
+                                    size,
+                                    dtype=dtype)
+        elif np.issubdtype(dtype, np.complexfloating):
+            def data_sampler(size):
+                return (rng.uniform(size=size) +
+                        rng.uniform(size=size) * 1j)
+        else:
+            data_sampler = rng.uniform
+
+    idx_dtype = get_index_dtype(maxval=max(shape))
+    # rng.choice uses int64 if first arg is an int
+    if tot_prod <= np.iinfo(np.int64).max:
+        raveled_ind = rng.choice(tot_prod, size=size, replace=False)
+        ind = np.unravel_index(raveled_ind, shape=shape, order='F')
+        ind = tuple(np.asarray(co, idx_dtype) for co in ind)
+    else:
+        # for ravel indices bigger than dtype max, use sets to remove duplicates
+        ndim = len(shape)
+        seen = set()
+        while len(seen) < size:
+            dsize = size - len(seen)
+            seen.update(map(tuple, rng_integers(rng, shape, size=(dsize, ndim))))
+        ind = tuple(np.array(list(seen), dtype=idx_dtype).T)
+
+    # size kwarg allows eg data_sampler=partial(np.random.poisson, lam=5)
+    vals = data_sampler(size=size).astype(dtype, copy=False)
+    return vals, ind
+
+
+@_transition_to_rng("random_state", position_num=5)
+def random(m, n, density=0.01, format='coo', dtype=None,
+           rng=None, data_rvs=None):
+    """Generate a sparse matrix of the given shape and density with randomly
+    distributed values.
+
+    .. warning::
+
+        This function returns a sparse matrix -- not a sparse array.
+        You are encouraged to use `random_array` to take advantage of the
+        sparse array functionality.
+
+    Parameters
+    ----------
+    m, n : int
+        shape of the matrix
+    density : real, optional
+        density of the generated matrix: density equal to one means a full
+        matrix, density of 0 means a matrix with no non-zero items.
+    format : str, optional
+        sparse matrix format.
+    dtype : dtype, optional
+        type of the returned matrix values.
+    rng : `numpy.random.Generator`, optional
+        Pseudorandom number generator state. When `rng` is None, a new
+        `numpy.random.Generator` is created using entropy from the
+        operating system. Types other than `numpy.random.Generator` are
+        passed to `numpy.random.default_rng` to instantiate a ``Generator``.
+
+        This random state will be used for sampling the sparsity structure, but
+        not necessarily for sampling the values of the structurally nonzero
+        entries of the matrix.
+    data_rvs : callable, optional
+        Samples a requested number of random values.
+        This function should take a single argument specifying the length
+        of the ndarray that it will return. The structurally nonzero entries
+        of the sparse random matrix will be taken from the array sampled
+        by this function. By default, uniform [0, 1) random values will be
+        sampled using the same random state as is used for sampling
+        the sparsity structure.
+
+    Returns
+    -------
+    res : sparse matrix
+        Random sparse matrix.
+
+    See Also
+    --------
+    random_array : constructs sparse arrays instead of sparse matrices
+
+    Examples
+    --------
+
+    Passing a ``np.random.Generator`` instance for better performance:
+
+    >>> import scipy as sp
+    >>> import numpy as np
+    >>> rng = np.random.default_rng()
+    >>> S = sp.sparse.random(3, 4, density=0.25, rng=rng)
+
+    Providing a sampler for the values:
+
+    >>> rvs = sp.stats.poisson(25, loc=10).rvs
+    >>> S = sp.sparse.random(3, 4, density=0.25, rng=rng, data_rvs=rvs)
+    >>> S.toarray()
+    array([[ 36.,   0.,  33.,   0.],   # random
+           [  0.,   0.,   0.,   0.],
+           [  0.,   0.,  36.,   0.]])
+
+    Building a custom distribution.
+    This example builds a squared normal from np.random:
+
+    >>> def np_normal_squared(size=None, rng=rng):
+    ...     return rng.standard_normal(size) ** 2
+    >>> S = sp.sparse.random(3, 4, density=0.25, rng=rng,
+    ...                      data_rvs=np_normal_squared)
+
+    Or we can build it from sp.stats style rvs functions:
+
+    >>> def sp_stats_normal_squared(size=None, rng=rng):
+    ...     std_normal = sp.stats.distributions.norm_gen().rvs
+    ...     return std_normal(size=size, random_state=rng) ** 2
+    >>> S = sp.sparse.random(3, 4, density=0.25, rng=rng,
+    ...                      data_rvs=sp_stats_normal_squared)
+
+    Or we can subclass sp.stats rv_continuous or rv_discrete:
+
+    >>> class NormalSquared(sp.stats.rv_continuous):
+    ...     def _rvs(self,  size=None, random_state=rng):
+    ...         return rng.standard_normal(size) ** 2
+    >>> X = NormalSquared()
+    >>> Y = X()  # get a frozen version of the distribution
+    >>> S = sp.sparse.random(3, 4, density=0.25, rng=rng, data_rvs=Y.rvs)
+    """
+    if n is None:
+        n = m
+    m, n = int(m), int(n)
+    # make keyword syntax work for data_rvs e.g. data_rvs(size=7)
+    if data_rvs is not None:
+        def data_rvs_kw(size):
+            return data_rvs(size)
+    else:
+        data_rvs_kw = None
+    vals, ind = _random((m, n), density, format, dtype, rng, data_rvs_kw)
+    return coo_matrix((vals, ind), shape=(m, n)).asformat(format)
+
+
+@_transition_to_rng("random_state", position_num=5)
+def rand(m, n, density=0.01, format="coo", dtype=None, rng=None):
+    """Generate a sparse matrix of the given shape and density with uniformly
+    distributed values.
+
+    .. warning::
+
+        This function returns a sparse matrix -- not a sparse array.
+        You are encouraged to use `random_array` to take advantage
+        of the sparse array functionality.
+
+    Parameters
+    ----------
+    m, n : int
+        shape of the matrix
+    density : real, optional
+        density of the generated matrix: density equal to one means a full
+        matrix, density of 0 means a matrix with no non-zero items.
+    format : str, optional
+        sparse matrix format.
+    dtype : dtype, optional
+        type of the returned matrix values.
+    rng : `numpy.random.Generator`, optional
+        Pseudorandom number generator state. When `rng` is None, a new
+        `numpy.random.Generator` is created using entropy from the
+        operating system. Types other than `numpy.random.Generator` are
+        passed to `numpy.random.default_rng` to instantiate a ``Generator``.
+
+    Returns
+    -------
+    res : sparse matrix
+        Random sparse matrix.
+
+    Notes
+    -----
+    Only float types are supported for now.
+
+    See Also
+    --------
+    random : Similar function allowing a custom random data sampler
+    random_array : Similar to random() but returns a sparse array
+
+    Examples
+    --------
+    >>> from scipy.sparse import rand
+    >>> matrix = rand(3, 4, density=0.25, format="csr", rng=42)
+    >>> matrix
+    <Compressed Sparse Row sparse matrix of dtype 'float64'
+        with 3 stored elements and shape (3, 4)>
+    >>> matrix.toarray()
+    array([[0.05641158, 0.        , 0.        , 0.65088847],  # random
+           [0.        , 0.        , 0.        , 0.14286682],
+           [0.        , 0.        , 0.        , 0.        ]])
+
+    """
+    return random(m, n, density, format, dtype, rng)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/_coo.py b/venv/lib/python3.12/site-packages/scipy/sparse/_coo.py
new file mode 100644
index 0000000000000000000000000000000000000000..a27f5e0ed104ccf9a9360eb0d60508349421278a
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/_coo.py
@@ -0,0 +1,1948 @@
+""" A sparse matrix in COOrdinate or 'triplet' format"""
+
+__docformat__ = "restructuredtext en"
+
+__all__ = ['coo_array', 'coo_matrix', 'isspmatrix_coo']
+
+import math
+from warnings import warn
+
+import numpy as np
+
+from .._lib._util import copy_if_needed
+from ._matrix import spmatrix
+from ._sparsetools import (coo_tocsr, coo_todense, coo_todense_nd,
+                           coo_matvec, coo_matvec_nd, coo_matmat_dense,
+                           coo_matmat_dense_nd)
+from ._base import issparse, SparseEfficiencyWarning, _spbase, sparray
+from ._data import _data_matrix, _minmax_mixin
+from ._sputils import (upcast_char, to_native, isshape, getdtype,
+                       getdata, downcast_intp_index, get_index_dtype,
+                       check_shape, isscalarlike,
+                       isintlike, isdense)
+from ._index import _validate_indices, _broadcast_arrays
+
+import operator
+
+
+class _coo_base(_data_matrix, _minmax_mixin):
+    _format = 'coo'
+    _allow_nd = tuple(range(1, 65))
+
+    def __init__(self, arg1, shape=None, dtype=None, copy=False, *, maxprint=None):
+        _data_matrix.__init__(self, arg1, maxprint=maxprint)
+        if not copy:
+            copy = copy_if_needed
+
+        if isinstance(arg1, tuple):
+            if isshape(arg1, allow_nd=self._allow_nd):
+                self._shape = check_shape(arg1, allow_nd=self._allow_nd)
+                idx_dtype = self._get_index_dtype(maxval=max(self._shape))
+                data_dtype = getdtype(dtype, default=float)
+                self.coords = tuple(np.array([], dtype=idx_dtype)
+                                     for _ in range(len(self._shape)))
+                self.data = np.array([], dtype=data_dtype)
+                self.has_canonical_format = True
+            else:
+                try:
+                    obj, coords = arg1
+                except (TypeError, ValueError) as e:
+                    raise TypeError('invalid input format') from e
+
+                if shape is None:
+                    if any(len(idx) == 0 for idx in coords):
+                        raise ValueError('cannot infer dimensions from zero '
+                                         'sized index arrays')
+                    shape = tuple(operator.index(np.max(idx)) + 1
+                                  for idx in coords)
+                self._shape = check_shape(shape, allow_nd=self._allow_nd)
+                idx_dtype = self._get_index_dtype(coords,
+                                                  maxval=max(self.shape),
+                                                  check_contents=True)
+                self.coords = tuple(np.array(idx, copy=copy, dtype=idx_dtype)
+                                     for idx in coords)
+                self.data = getdata(obj, copy=copy, dtype=dtype)
+                self.has_canonical_format = False
+        else:
+            if issparse(arg1):
+                if arg1.format == self.format and copy:
+                    self.coords = tuple(idx.copy() for idx in arg1.coords)
+                    self.data = arg1.data.astype(getdtype(dtype, arg1))  # copy=True
+                    self._shape = check_shape(arg1.shape, allow_nd=self._allow_nd)
+                    self.has_canonical_format = arg1.has_canonical_format
+                else:
+                    coo = arg1.tocoo(copy=copy)
+                    self.coords = tuple(coo.coords)
+                    self.data = coo.data.astype(getdtype(dtype, coo), copy=False)
+                    self._shape = check_shape(coo.shape, allow_nd=self._allow_nd)
+                    self.has_canonical_format = False
+            else:
+                # dense argument
+                M = np.asarray(arg1)
+                if not isinstance(self, sparray):
+                    M = np.atleast_2d(M)
+                    if M.ndim != 2:
+                        raise TypeError(f'expected 2D array or matrix, not {M.ndim}D')
+
+                self._shape = check_shape(M.shape, allow_nd=self._allow_nd)
+                if shape is not None:
+                    if check_shape(shape, allow_nd=self._allow_nd) != self._shape:
+                        message = f'inconsistent shapes: {shape} != {self._shape}'
+                        raise ValueError(message)
+
+                index_dtype = self._get_index_dtype(maxval=max(self._shape))
+                coords = M.nonzero()
+                self.coords = tuple(idx.astype(index_dtype, copy=False)
+                                     for idx in coords)
+                self.data = getdata(M[coords], copy=copy, dtype=dtype)
+                self.has_canonical_format = True
+
+        if len(self._shape) > 2:
+            self.coords = tuple(idx.astype(np.int64, copy=False) for idx in self.coords)
+
+        self._check()
+
+    @property
+    def row(self):
+        if self.ndim > 1:
+            return self.coords[-2]
+        result = np.zeros_like(self.col)
+        result.setflags(write=False)
+        return result
+
+
+    @row.setter
+    def row(self, new_row):
+        if self.ndim < 2:
+            raise ValueError('cannot set row attribute of a 1-dimensional sparse array')
+        new_row = np.asarray(new_row, dtype=self.coords[-2].dtype)
+        self.coords = self.coords[:-2] + (new_row,) + self.coords[-1:]
+
+    @property
+    def col(self):
+        return self.coords[-1]
+
+    @col.setter
+    def col(self, new_col):
+        new_col = np.asarray(new_col, dtype=self.coords[-1].dtype)
+        self.coords = self.coords[:-1] + (new_col,)
+
+    def reshape(self, *shape, order="C", copy=False):
+        shape = check_shape(shape, self.shape, allow_nd=self._allow_nd)
+
+        # Return early if reshape is not required
+        if shape == self.shape:
+            if copy:
+                return self.copy()
+            else:
+                return self
+
+        # When reducing the number of dimensions, we need to be careful about
+        # index overflow. This is why we can't simply call
+        # `np.ravel_multi_index()` followed by `np.unravel_index()` here.
+        flat_coords = _ravel_coords(self.coords, self.shape, order=order)
+        if len(shape) == 2:
+            if order == 'C':
+                new_coords = divmod(flat_coords, shape[1])
+            else:
+                new_coords = divmod(flat_coords, shape[0])[::-1]
+        else:
+            new_coords = np.unravel_index(flat_coords, shape, order=order)
+
+        idx_dtype = self._get_index_dtype(self.coords, maxval=max(shape))
+        new_coords = tuple(np.asarray(co, dtype=idx_dtype) for co in new_coords)
+
+        # Handle copy here rather than passing on to the constructor so that no
+        # copy will be made of `new_coords` regardless.
+        if copy:
+            new_data = self.data.copy()
+        else:
+            new_data = self.data
+
+        return self.__class__((new_data, new_coords), shape=shape, copy=False)
+
+    reshape.__doc__ = _spbase.reshape.__doc__
+
+    def _getnnz(self, axis=None):
+        if axis is None or (axis == 0 and self.ndim == 1):
+            nnz = len(self.data)
+            if any(len(idx) != nnz for idx in self.coords):
+                raise ValueError('all index and data arrays must have the '
+                                 'same length')
+
+            if self.data.ndim != 1 or any(idx.ndim != 1 for idx in self.coords):
+                raise ValueError('coordinates and data arrays must be 1-D')
+
+            return int(nnz)
+
+        if axis < 0:
+            axis += self.ndim
+        if axis >= self.ndim:
+            raise ValueError('axis out of bounds')
+
+        return np.bincount(downcast_intp_index(self.coords[1 - axis]),
+                           minlength=self.shape[1 - axis])
+
+    _getnnz.__doc__ = _spbase._getnnz.__doc__
+
+    def count_nonzero(self, axis=None):
+        self.sum_duplicates()
+        if axis is None:
+            return np.count_nonzero(self.data)
+
+        if axis < 0:
+            axis += self.ndim
+        if axis < 0 or axis >= self.ndim:
+            raise ValueError('axis out of bounds')
+        mask = self.data != 0
+        coord = self.coords[1 - axis][mask]
+        return np.bincount(downcast_intp_index(coord), minlength=self.shape[1 - axis])
+
+    count_nonzero.__doc__ = _spbase.count_nonzero.__doc__
+
+    def _check(self):
+        """ Checks data structure for consistency """
+        if self.ndim != len(self.coords):
+            raise ValueError('mismatching number of index arrays for shape; '
+                             f'got {len(self.coords)}, expected {self.ndim}')
+
+        # index arrays should have integer data types
+        for i, idx in enumerate(self.coords):
+            if idx.dtype.kind != 'i':
+                warn(f'index array {i} has non-integer dtype ({idx.dtype.name})',
+                     stacklevel=3)
+
+        idx_dtype = self._get_index_dtype(self.coords, maxval=max(self.shape))
+        self.coords = tuple(np.asarray(idx, dtype=idx_dtype)
+                             for idx in self.coords)
+        self.data = to_native(self.data)
+
+        if self.nnz > 0:
+            for i, idx in enumerate(self.coords):
+                if idx.max() >= self.shape[i]:
+                    raise ValueError(f'axis {i} index {idx.max()} exceeds '
+                                     f'matrix dimension {self.shape[i]}')
+                if idx.min() < 0:
+                    raise ValueError(f'negative axis {i} index: {idx.min()}')
+
+    def transpose(self, axes=None, copy=False):
+        if axes is None:
+            axes = range(self.ndim)[::-1]
+        elif isinstance(self, sparray):
+            if not hasattr(axes, "__len__") or len(axes) != self.ndim:
+                raise ValueError("axes don't match matrix dimensions")
+            if len(set(axes)) != self.ndim:
+                raise ValueError("repeated axis in transpose")
+        elif axes != (1, 0):
+            raise ValueError("Sparse matrices do not support an 'axes' "
+                             "parameter because swapping dimensions is the "
+                             "only logical permutation.")
+
+        permuted_shape = tuple(self._shape[i] for i in axes)
+        permuted_coords = tuple(self.coords[i] for i in axes)
+        return self.__class__((self.data, permuted_coords),
+                              shape=permuted_shape, copy=copy)
+
+    transpose.__doc__ = _spbase.transpose.__doc__
+    
+    @property
+    def mT(self):
+        if (n := self.ndim) < 2:
+            raise ValueError(f"Array must be at least 2-dimensional, but it is {n}-D")
+        axes = None if n == 2 else tuple(range(n - 2)) + (-1, -2)
+        return self.transpose(axes=axes)
+    
+    mT.__doc__ = _spbase.mT.__doc__
+
+    def resize(self, *shape) -> None:
+        shape = check_shape(shape, allow_nd=self._allow_nd)
+        if self.ndim > 2:
+            raise ValueError("only 1-D or 2-D input accepted")
+        if len(shape) > 2:
+            raise ValueError("shape argument must be 1-D or 2-D")
+        # Check for added dimensions.
+        if len(shape) > self.ndim:
+            flat_coords = _ravel_coords(self.coords, self.shape)
+            max_size = math.prod(shape)
+            self.coords = np.unravel_index(flat_coords[:max_size], shape)
+            self.data = self.data[:max_size]
+            self._shape = shape
+            return
+
+        # Check for removed dimensions.
+        if len(shape) < self.ndim:
+            tmp_shape = (
+                self._shape[:len(shape) - 1]  # Original shape without last axis
+                + (-1,)  # Last axis is used to flatten the array
+                + (1,) * (self.ndim - len(shape))  # Pad with ones
+            )
+            tmp = self.reshape(tmp_shape)
+            self.coords = tmp.coords[:len(shape)]
+            self._shape = tmp.shape[:len(shape)]
+
+        # Handle truncation of existing dimensions.
+        is_truncating = any(old > new for old, new in zip(self.shape, shape))
+        if is_truncating:
+            mask = np.logical_and.reduce([
+                idx < size for idx, size in zip(self.coords, shape)
+            ])
+            if not mask.all():
+                self.coords = tuple(idx[mask] for idx in self.coords)
+                self.data = self.data[mask]
+
+        self._shape = shape
+
+    resize.__doc__ = _spbase.resize.__doc__
+
+    def toarray(self, order=None, out=None):
+        B = self._process_toarray_args(order, out)
+        fortran = int(B.flags.f_contiguous)
+        if not fortran and not B.flags.c_contiguous:
+            raise ValueError("Output array must be C or F contiguous")
+        # This handles both 0D and 1D cases correctly regardless of the
+        # original shape.
+        if self.ndim == 1:
+            coo_todense_nd(np.array([1]), self.nnz, self.ndim,
+                           self.coords[0], self.data, B.ravel('A'), fortran)
+        elif self.ndim == 2:
+            M, N = self.shape
+            coo_todense(M, N, self.nnz, self.row, self.col, self.data,
+                        B.ravel('A'), fortran)
+        else:  # dim>2
+            if fortran:
+                strides = np.append(1, np.cumprod(self.shape[:-1]))
+            else:
+                strides = np.append(np.cumprod(self.shape[1:][::-1])[::-1], 1)
+            coords = np.concatenate(self.coords)
+            coo_todense_nd(strides, self.nnz, self.ndim,
+                           coords, self.data, B.ravel('A'), fortran)
+        # Note: reshape() doesn't copy here, but does return a new array (view).
+        return B.reshape(self.shape)
+
+    toarray.__doc__ = _spbase.toarray.__doc__
+
+    def tocsc(self, copy=False):
+        """Convert this array/matrix to Compressed Sparse Column format.
+
+        Duplicate entries will be summed together.
+
+        Parameters
+        ----------
+        copy : bool, optional
+            Unused. A copy is always made in the 2D case. And CSC is 2D.
+
+        Returns
+        -------
+        csc array/matrix
+            The converted array/matrix in CSC format.
+
+        Examples
+        --------
+        >>> from numpy import array
+        >>> from scipy.sparse import coo_array
+        >>> row  = array([0, 0, 1, 3, 1, 0, 0])
+        >>> col  = array([0, 2, 1, 3, 1, 0, 0])
+        >>> data = array([1, 1, 1, 1, 1, 1, 1])
+        >>> A = coo_array((data, (row, col)), shape=(4, 4)).tocsc()
+        >>> A.toarray()
+        array([[3, 0, 1, 0],
+               [0, 2, 0, 0],
+               [0, 0, 0, 0],
+               [0, 0, 0, 1]])
+
+        """
+        if self.ndim != 2:
+            raise ValueError(f'Cannot convert. CSC format must be 2D. Got {self.ndim}D')
+        if self.nnz == 0:
+            return self._csc_container(self.shape, dtype=self.dtype)
+        else:
+            # _coo_to_compressed copy kwarg only for 1D. CSC cant be 1D. See gh-24676
+            from ._csc import csc_array
+            indptr, indices, data, shape = self._coo_to_compressed(csc_array._swap)
+
+            x = self._csc_container((data, indices, indptr), shape=shape)
+            if not self.has_canonical_format:
+                x.sum_duplicates()
+            return x
+
+    def tocsr(self, copy=False):
+        """Convert this array/matrix to Compressed Sparse Row format.
+
+        Duplicate entries will be summed together.
+
+        Parameters
+        ----------
+        copy : bool, optional
+            With ``copy=False``, the data/indices may be shared between this
+            array/matrix and the resultant csr_array/matrix. But only for 1D.
+            For 2D, a copy will always be made.
+
+        Returns
+        -------
+        csr array/matrix
+            The converted array/matrix in CSR format.
+
+        Examples
+        --------
+        >>> from numpy import array
+        >>> from scipy.sparse import coo_array
+        >>> row  = array([0, 0, 1, 3, 1, 0, 0])
+        >>> col  = array([0, 2, 1, 3, 1, 0, 0])
+        >>> data = array([1, 1, 1, 1, 1, 1, 1])
+        >>> A = coo_array((data, (row, col)), shape=(4, 4)).tocsr()
+        >>> A.toarray()
+        array([[3, 0, 1, 0],
+               [0, 2, 0, 0],
+               [0, 0, 0, 0],
+               [0, 0, 0, 1]])
+
+        """
+        if self.ndim > 2:
+            raise ValueError(f'Cannot convert. CSR must be 1D or 2D. Got {self.ndim}D')
+        if self.nnz == 0:
+            return self._csr_container(self.shape, dtype=self.dtype)
+        else:
+            from ._csr import csr_array
+            arrays = self._coo_to_compressed(csr_array._swap, copy=copy)
+            indptr, indices, data, shape = arrays
+
+            x = self._csr_container((data, indices, indptr), shape=self.shape)
+            if not self.has_canonical_format:
+                x.sum_duplicates()
+            return x
+
+    def _coo_to_compressed(self, swap, copy=False):
+        """convert (shape, coords, data) to (indptr, indices, data, shape)"""
+        M, N = swap(self._shape_as_2d)
+        # convert idx_dtype intc to int32 for pythran.
+        # tested in scipy/optimize/tests/test__numdiff.py::test_group_columns
+        idx_dtype = self._get_index_dtype(self.coords, maxval=max(self.nnz, N))
+
+        if self.ndim == 1:
+            indices = self.coords[0].copy() if copy else self.coords[0]
+            nnz = len(indices)
+            indptr = np.array([0, nnz], dtype=idx_dtype)
+            data = self.data.copy() if copy else self.data
+            return indptr, indices, data, self.shape
+
+        # ndim == 2
+        major, minor = swap(self.coords)
+        nnz = len(major)
+        major = major.astype(idx_dtype, copy=False)
+        minor = minor.astype(idx_dtype, copy=False)
+
+        indptr = np.empty(M + 1, dtype=idx_dtype)
+        indices = np.empty_like(minor, dtype=idx_dtype)
+        data = np.empty_like(self.data, dtype=self.dtype)
+
+        coo_tocsr(M, N, nnz, major, minor, self.data, indptr, indices, data)
+        return indptr, indices, data, self.shape
+
+    def tocoo(self, copy=False):
+        if copy:
+            return self.copy()
+        else:
+            return self
+
+    tocoo.__doc__ = _spbase.tocoo.__doc__
+
+    def todia(self, copy=False):
+        if self.ndim != 2:
+            raise ValueError(f'Cannot convert. DIA format must be 2D. Got {self.ndim}D')
+        self.sum_duplicates()
+        ks = self.col - self.row  # the diagonal for each nonzero
+        diags, diag_idx = np.unique(ks, return_inverse=True)
+
+        if len(diags) > 100:
+            # probably undesired, should todia() have a maxdiags parameter?
+            warn(f"Constructing a DIA matrix with {len(diags)} diagonals "
+                 "is inefficient",
+                 SparseEfficiencyWarning, stacklevel=2)
+
+        #initialize and fill in data array
+        if self.data.size == 0:
+            data = np.zeros((0, 0), dtype=self.dtype)
+        else:
+            data = np.zeros((len(diags), self.col.max()+1), dtype=self.dtype)
+            data[diag_idx, self.col] = self.data
+
+        return self._dia_container((data, diags), shape=self.shape)
+
+    todia.__doc__ = _spbase.todia.__doc__
+
+    def todok(self, copy=False):
+        if self.ndim > 2:
+            raise ValueError(f'Cannot convert. DOK must be 1D or 2D. Got {self.ndim}D')
+        self.sum_duplicates()
+        dok = self._dok_container(self.shape, dtype=self.dtype)
+        # ensure that 1d coordinates are not tuples
+        if self.ndim == 1:
+            coords = self.coords[0]
+        else:
+            coords = zip(*self.coords)
+
+        dok._dict = dict(zip(coords, self.data))
+        return dok
+
+    todok.__doc__ = _spbase.todok.__doc__
+
+    def diagonal(self, k=0):
+        if self.ndim != 2:
+            raise ValueError("diagonal requires two dimensions")
+        rows, cols = self.shape
+        if k <= -rows or k >= cols:
+            return np.empty(0, dtype=self.data.dtype)
+        diag = np.zeros(min(rows + min(k, 0), cols - max(k, 0)),
+                        dtype=self.dtype)
+        diag_mask = (self.row + k) == self.col
+
+        if self.has_canonical_format:
+            row = self.row[diag_mask]
+            data = self.data[diag_mask]
+        else:
+            inds = tuple(idx[diag_mask] for idx in self.coords)
+            (row, _), data = self._sum_duplicates(inds, self.data[diag_mask])
+        diag[row + min(k, 0)] = data
+
+        return diag
+
+    diagonal.__doc__ = _data_matrix.diagonal.__doc__
+
+    def _setdiag(self, values, k):
+        if self.ndim != 2:
+            raise ValueError("setting a diagonal requires two dimensions")
+        M, N = self.shape
+        if values.ndim and not len(values):
+            return
+        idx_dtype = self.row.dtype
+
+        # Determine which triples to keep and where to put the new ones.
+        full_keep = self.col - self.row != k
+        if k < 0:
+            max_index = min(M+k, N)
+            if values.ndim:
+                max_index = min(max_index, len(values))
+            keep = np.logical_or(full_keep, self.col >= max_index)
+            new_row = np.arange(-k, -k + max_index, dtype=idx_dtype)
+            new_col = np.arange(max_index, dtype=idx_dtype)
+        else:
+            max_index = min(M, N-k)
+            if values.ndim:
+                max_index = min(max_index, len(values))
+            keep = np.logical_or(full_keep, self.row >= max_index)
+            new_row = np.arange(max_index, dtype=idx_dtype)
+            new_col = np.arange(k, k + max_index, dtype=idx_dtype)
+
+        # Define the array of data consisting of the entries to be added.
+        if values.ndim:
+            new_data = values[:max_index]
+        else:
+            new_data = np.empty(max_index, dtype=self.dtype)
+            new_data[:] = values
+
+        # Update the internal structure.
+        self.coords = (np.concatenate((self.row[keep], new_row)),
+                       np.concatenate((self.col[keep], new_col)))
+        self.data = np.concatenate((self.data[keep], new_data))
+        self.has_canonical_format = False
+
+    # needed by _data_matrix
+    def _with_data(self, data, copy=True):
+        """Returns a matrix with the same sparsity structure as self,
+        but with different data. By default the index arrays are copied.
+        """
+        if copy:
+            coords = tuple(idx.copy() for idx in self.coords)
+        else:
+            coords = self.coords
+        return self.__class__((data, coords), shape=self.shape, dtype=data.dtype)
+
+    def __getitem__(self, key):
+        index, new_shape, arr_int_pos, none_pos = _validate_indices(
+            key, self.shape, self.format
+        )
+        # handle int, slice and int-array indices
+        index_mask = np.ones(len(self.data), dtype=np.bool_)
+        slice_coords = []
+        arr_coords = []
+        arr_indices = []
+        for i, (idx, co) in enumerate(zip(index, self.coords)):
+            if isinstance(idx, int):
+                index_mask &= (co == idx)
+            elif isinstance(idx, slice):
+                if idx == slice(None):
+                    slice_coords.append(co)
+                else:
+                    start, stop, step = idx.indices(self.shape[i])
+                    if step != 1:
+                        if step < 0:
+                            in_range = (co <= start) & (co > stop)
+                        else:
+                            in_range = (co >= start) & (co < stop)
+                        new_ix, m = np.divmod(co - start, step)
+                        index_mask &= (m == 0) & in_range
+                    else:
+                        in_range = (co >= start) & (co < stop)
+                        new_ix = co - start
+                        index_mask &= in_range
+                    slice_coords.append(new_ix)
+            else:  # array
+                arr_coords.append(co)
+                arr_indices.append(idx)
+        # shortcut for scalar output
+        if new_shape == ():
+            return self.data[index_mask].sum().astype(self.dtype, copy=False)
+
+        new_coords = [co[index_mask] for co in slice_coords]
+        new_data = self.data[index_mask]
+
+        # handle array indices
+        if arr_indices:
+            arr_indices = _broadcast_arrays(*arr_indices)
+            arr_shape = arr_indices[0].shape  # already broadcast in validate_indices
+            # There are three dimensions required to check array indices against coords
+            # Their lengths are described as:
+            # a) number of indices that are arrays - arr_dim
+            # b) number of coords to check - masked_nnz (already masked by slices)
+            # c) size of the index arrays - arr_size
+            # Note for this, integer indices are treated like slices, not like arrays.
+            #
+            # Goal:
+            # Find new_coords and index positions that match across all arr_dim axes.
+            # Approach: Track matches using bool array. Size: masked_nnz by arr_size.
+            # True means all arr_indices match at that coord and index position.
+            # Equate with broadcasting and check for all equal across (arr_dim) axis 0.
+            # 1st array is "keyarr" (arr_dim by 1 by arr_size) from arr_indices.
+            # 2nd array is "arr_coords" (arr_dim by masked_nnz by 1) from arr_coords.
+            keyarr = np.array(arr_indices).reshape(len(arr_indices), 1, -1)
+            arr_coords = np.array([co[index_mask] for co in arr_coords])[:, :, None]
+            found = (keyarr == arr_coords).all(axis=0)
+            arr_co, arr_ix = found.nonzero()
+            new_data = new_data[arr_co]
+            new_coords = [co[arr_co] for co in new_coords]
+            new_arr_coords = list(np.unravel_index(arr_ix, shape=arr_shape))
+
+            # check for contiguous positions of array and int indices
+            if len(arr_int_pos) == arr_int_pos[-1] - arr_int_pos[0] + 1:
+                # Contiguous. Put all array index shape at pos of array indices
+                pos = arr_int_pos[0]
+                new_coords = new_coords[:pos] + new_arr_coords + new_coords[pos:]
+            else:
+                # Not contiguous. Put all array coords at front
+                new_coords = new_arr_coords + new_coords
+
+        if none_pos:
+            if new_coords:
+                coord_like = np.zeros_like(new_coords[0])
+            else:
+                coord_like = np.zeros(len(new_data), dtype=self.coords[0].dtype)
+            new_coords.insert(none_pos[0], coord_like)
+            for i in none_pos[1:]:
+                new_coords.insert(i, coord_like.copy())
+        return coo_array((new_data, new_coords), shape=new_shape, dtype=self.dtype)
+
+    def __setitem__(self, key, x):
+        # enact self[key] = x
+        index, new_shape, arr_int_pos, none_pos = _validate_indices(
+            key, self.shape, self.format
+        )
+
+        # remove None's at beginning of index. Should not impact indexing coords
+        # and will mistakenly align with x_coord columns if not removed.
+        if none_pos:
+            new_shape = list(new_shape)
+            for j in none_pos[::-1]:
+                new_shape.pop(j)
+            new_shape = tuple(new_shape)
+
+        # broadcast arrays
+        if arr_int_pos:
+            index = list(index)
+            arr_pos = {i: arr for i in arr_int_pos if not isintlike(arr := index[i])}
+            arr_indices = _broadcast_arrays(*arr_pos.values())
+            for i, arr in zip(arr_pos, arr_indices):
+                index[i] = arr
+
+        # get coords and data from x
+        if issparse(x):
+            if 0 in x.shape:
+                return  # Nothing to set.
+            x_data, x_coords = _get_sparse_data_and_coords(x, new_shape, self.dtype)
+        else:
+            x = np.asarray(x, dtype=self.dtype)
+            if x.size == 0:
+                return  # Nothing to set.
+            x_data, x_coords = _get_dense_data_and_coords(x, new_shape)
+
+        # Approach:
+        # Set indexed values to zero (drop from `self.coords` and `self.data`)
+        # create new coords and data arrays for setting nonzeros
+        # concatenate old (undropped) values with new coords and data
+
+        old_data, old_coords = self._zero_many(index)
+
+        if len(x_coords) == 1 and len(x_coords[0]) == 0:
+            self.data, self.coords = old_data, old_coords
+            # leave self.has_canonical_format unchanged
+            return
+
+        # To process array indices, need the x_coords for those axes
+        # and need to ravel the array part of x_coords to build new_coords
+        # Along the way, Find pos and shape of array-index portion of key.
+        # arr_shape is None and pos = -1 when no arrays are used as indices.
+        arr_shape = None
+        pos = -1
+        if arr_int_pos:
+            # Get arr_shape if any arrays are in the index.
+            # Also ravel the corresponding x_coords.
+            for idx in index:
+                if not isinstance(idx, slice) and not isintlike(idx):
+                    arr_shape = idx.shape
+
+                    # Find x_coord pos of integer and array portion of index.
+                    # If contiguous put int and array axes at pos of those indices.
+                    # If not contiguous, put all int and array axes at pos=0.
+                    if len(arr_int_pos) == (arr_int_pos[-1] - arr_int_pos[0] + 1):
+                        pos = arr_int_pos[0]
+                    else:
+                        pos = 0
+
+                    # compute the raveled coords of the array part of x_coords.
+                    # Used to build the new coords from the index arrays.
+                    x_arr_coo = x_coords[pos:pos + len(arr_shape)]
+                    # could use np.ravel_multi_index but _ravel_coords avoids overflow
+                    x_arr_coo_ravel = _ravel_coords(x_arr_coo, arr_shape)
+                    break
+
+        # find map from x_coord slice axes to index axes
+        x_ax = 0
+        x_axes = {}
+        for i, idx in enumerate(index):
+            if i == pos:
+                x_ax += len(arr_shape)
+            if isinstance(idx, slice):
+                x_axes[i] = x_ax
+                x_ax += 1
+
+        # Build new_coords and new_data
+        new_coords = [None] * self.ndim
+        new_nnz = len(x_data)
+        for i, idx in enumerate(index):
+            if isintlike(idx):
+                new_coords[i] = (np.broadcast_to(idx, (new_nnz,)))
+                continue
+            elif isinstance(idx, slice):
+                start, stop, step = idx.indices(self.shape[i])
+                new_coords[i] = (start + x_coords[x_axes[i]] * step)
+            else:  # array idx
+                new_coords[i] = idx.ravel()[x_arr_coo_ravel]
+        # seems like a copy is prudent when setting data in this array
+        new_data = x_data.copy()
+
+        # deduplicate entries created by multiple coords matching in the array index
+        # NumPy does not specify which value is put into the spot (last one assigned)
+        # so only one value should appear if we want to match NumPy.
+        # If matching NumPy is not crucial, we could make dups a feature where
+        # integer array indices  with repeated indices creates duplicate values.
+        # Not doing that here. We are just removing duplicates (keep 1st data found)
+        new_coords = np.array(new_coords)
+        _, ind = np.unique(new_coords, axis=1, return_index=True)
+
+        # update values with stack of old and new data and coords.
+        self.data = np.hstack([old_data, new_data[ind]])
+        self.coords = tuple(np.hstack(c) for c in zip(old_coords, new_coords[:, ind]))
+        self.has_canonical_format = False
+
+    def _zero_many(self, index):
+        # handle int, slice and integer-array indices
+        # index_mask accumulates a bool array of nonzeros that match index
+        index_mask=np.ones(len(self.data), dtype=np.bool_)
+        arr_coords = []
+        arr_indices = []
+        for i, (idx, co) in enumerate(zip(index, self.coords)):
+            if isinstance(idx, int):
+                index_mask &= (co == idx)
+            elif isinstance(idx, slice) and idx != slice(None):
+                start, stop, step = idx.indices(self.shape[i])
+                if step != 1:
+                    if step < 0:
+                        in_range = (co <= start) & (co > stop)
+                    else:
+                        in_range = (co >= start) & (co < stop)
+                    m = np.mod(co - start, step)
+                    index_mask &= (m == 0) & in_range
+                else:
+                    in_range = (co >= start) & (co < stop)
+                    index_mask &= in_range
+            elif isinstance(idx, slice) and idx == slice(None):
+                # slice is full axis so no changes to index_mask
+                pass
+            else:  # array
+                arr_coords.append(co)
+                arr_indices.append(idx)
+
+        # match array indices with masked coords. See comments in __getitem__
+        if arr_indices:
+            keyarr = np.array(arr_indices).reshape(len(arr_indices), 1, -1)
+            arr_coords = np.array([co[index_mask] for co in arr_coords])[:, :, None]
+            found = (keyarr == arr_coords).all(axis=0)
+            arr_coo, _ = found.nonzero()
+            arr_index_mask = np.zeros_like(index_mask)
+            arr_index_mask[index_mask.nonzero()[0][arr_coo]] = True
+            index_mask &= arr_index_mask
+
+        # remove matching coords and data to set them to zero
+        pruned_coords = [co[~index_mask] for co in self.coords]
+        pruned_data = self.data[~index_mask]
+        return pruned_data, pruned_coords
+
+    def sum_duplicates(self) -> None:
+        """Eliminate duplicate entries by adding them together.
+
+        This is an *in place* operation
+        """
+        if self.has_canonical_format:
+            return
+        summed = self._sum_duplicates(self.coords, self.data)
+        self.coords, self.data = summed
+        self.has_canonical_format = True
+
+    def _sum_duplicates(self, coords, data):
+        # Assumes coords not in canonical format.
+        if len(data) == 0:
+            return coords, data
+        # Sort coords w.r.t. rows, then cols. This corresponds to C-order,
+        # which we rely on for argmin/argmax to return the first index in the
+        # same way that numpy does (in the case of ties).
+        order = np.lexsort(coords[::-1])
+        coords = tuple(idx[order] for idx in coords)
+        data = data[order]
+        unique_mask = np.logical_or.reduce([
+            idx[1:] != idx[:-1] for idx in coords
+        ])
+        unique_mask = np.append(True, unique_mask)
+        coords = tuple(idx[unique_mask] for idx in coords)
+        unique_inds, = np.nonzero(unique_mask)
+        data = np.add.reduceat(data, downcast_intp_index(unique_inds), dtype=self.dtype)
+        return coords, data
+
+    def eliminate_zeros(self):
+        """Remove zero entries from the array/matrix.
+
+        This is an *in place* operation.
+        """
+        mask = self.data != 0
+        self.data = self.data[mask]
+        self.coords = tuple(idx[mask] for idx in self.coords)
+
+    #######################
+    # Arithmetic handlers #
+    #######################
+
+    def _add_dense(self, other):
+        if other.shape != self.shape:
+            raise ValueError(f'Incompatible shapes ({self.shape} and {other.shape})')
+        dtype = upcast_char(self.dtype.char, other.dtype.char)
+        result = np.array(other, dtype=dtype, copy=True)
+        fortran = int(result.flags.f_contiguous)
+        if self.ndim == 1:
+            coo_todense_nd(np.array([1]), self.nnz, self.ndim,
+                           self.coords[0], self.data, result.ravel('A'), fortran)
+        elif self.ndim == 2:
+            M, N = self._shape_as_2d
+            coo_todense(M, N, self.nnz, self.row, self.col, self.data,
+                        result.ravel('A'), fortran)
+        else:
+            if fortran:
+                strides = np.append(1, np.cumprod(self.shape[:-1]))
+            else:
+                strides = np.append(np.cumprod(self.shape[1:][::-1])[::-1], 1)
+            coords = np.concatenate(self.coords)
+            coo_todense_nd(strides, self.nnz, self.ndim,
+                           coords, self.data, result.ravel('A'), fortran)
+        return self._container(result, copy=False)
+
+
+    def _add_sparse(self, other):
+        if self.ndim < 3:
+            return self.tocsr()._add_sparse(other)
+
+        if other.shape != self.shape:
+            raise ValueError(f'Incompatible shapes ({self.shape} and {other.shape})')
+        other = self.__class__(other)
+        new_data = np.concatenate((self.data, other.data))
+        new_coords = tuple(np.concatenate((self.coords, other.coords), axis=1))
+        A = self.__class__((new_data, new_coords), shape=self.shape)
+        return A
+
+    def _sub_sparse(self, other):
+        if self.ndim < 3:
+            return self.tocsr()._sub_sparse(other)
+
+        if other.shape != self.shape:
+            raise ValueError(f'Incompatible shapes ({self.shape} and {other.shape})')
+        other = self.__class__(other)
+        new_data = np.concatenate((self.data, -other.data))
+        new_coords = tuple(np.concatenate((self.coords, other.coords), axis=1))
+        A = coo_array((new_data, new_coords), shape=self.shape)
+        return A
+
+    def _matmul_vector(self, other):
+        if self.ndim > 2:
+            result = np.zeros(math.prod(self.shape[:-1]),
+                              dtype=upcast_char(self.dtype.char, other.dtype.char))
+            shape = np.array(self.shape)
+            strides = np.append(np.cumprod(shape[:-1][::-1])[::-1][1:], 1)
+            coords = np.concatenate(self.coords)
+            coo_matvec_nd(self.nnz, len(self.shape), strides, coords, self.data,
+                          other, result)
+
+            result = result.reshape(self.shape[:-1])
+            return result
+
+        # self.ndim <= 2
+        result_shape = self.shape[0] if self.ndim > 1 else 1
+        result = np.zeros(result_shape,
+                          dtype=upcast_char(self.dtype.char, other.dtype.char))
+        if self.ndim == 2:
+            col = self.col
+            row = self.row
+        elif self.ndim == 1:
+            col = self.coords[0]
+            row = np.zeros_like(col)
+        else:
+            raise NotImplementedError(
+                f"coo_matvec not implemented for ndim={self.ndim}")
+
+        coo_matvec(self.nnz, row, col, self.data, other, result)
+        # Array semantics return a scalar here, not a single-element array.
+        if isinstance(self, sparray) and result_shape == 1:
+            return result[0]
+        return result
+
+    def _rmatmul_dispatch(self, other):
+        if isscalarlike(other):
+            return self._mul_scalar(other)
+        else:
+            # Don't use asarray unless we have to
+            try:
+                o_ndim = other.ndim
+            except AttributeError:
+                other = np.asarray(other)
+                o_ndim = other.ndim
+            perm = tuple(range(o_ndim)[:-2]) + tuple(range(o_ndim)[-2:][::-1])
+            tr = other.transpose(perm)
+
+            s_ndim = self.ndim
+            perm = tuple(range(s_ndim)[:-2]) + tuple(range(s_ndim)[-2:][::-1])
+            ret = self.transpose(perm)._matmul_dispatch(tr)
+            if ret is NotImplemented:
+                return NotImplemented
+
+            if s_ndim == 1 or o_ndim == 1:
+                perm = range(ret.ndim)
+            else:
+                perm = tuple(range(ret.ndim)[:-2]) + tuple(range(ret.ndim)[-2:][::-1])
+            return ret.transpose(perm)
+
+    def _matmul_dispatch(self, other):
+        if isscalarlike(other):
+            return self.multiply(other)
+
+        if not (issparse(other) or isdense(other)):
+            # If it's a list or whatever, treat it like an array
+            other_a = np.asanyarray(other)
+
+            if other_a.ndim == 0 and other_a.dtype == np.object_:
+                # Not interpretable as an array; return NotImplemented so that
+                # other's __rmatmul__ can kick in if that's implemented.
+                return NotImplemented
+            # Allow custom sparse class indicated by attr sparse gh-6520
+            try:
+                other.shape
+            except AttributeError:
+                other = other_a
+
+        if self.ndim < 3 and other.ndim < 3:
+            return _spbase._matmul_dispatch(self, other)
+
+        N = self.shape[-1]
+        err_prefix = "matmul: dimension mismatch with signature"
+        if other.__class__ is np.ndarray:
+            if other.shape == (N,):
+                return self._matmul_vector(other)
+            if other.shape == (N, 1):
+                result = self._matmul_vector(other.ravel())
+                return result.reshape(*self.shape[:-1], 1)
+            if other.ndim == 1:
+                msg = f"{err_prefix} (n,k={N}),(k={other.shape[0]},)->(n,)"
+                raise ValueError(msg)
+            if other.shape[-2] == N:
+                # check for batch dimensions compatibility
+                batch_shape_A = self.shape[:-2]
+                batch_shape_B = other.shape[:-2]
+                if batch_shape_A != batch_shape_B:
+                    try:
+                        # This will raise an error if the shapes are not broadcastable
+                        np.broadcast_shapes(batch_shape_A, batch_shape_B)
+                    except ValueError:
+                        raise ValueError("Batch dimensions are not broadcastable")
+
+                return self._matmul_multivector(other)
+            else:
+                raise ValueError(
+                    f"{err_prefix} (n,..,k={N}),(k={other.shape[-2]},..,m)->(n,..,m)"
+                )
+
+        if isscalarlike(other):
+            # scalar value
+            return self._mul_scalar(other)
+
+        if issparse(other):
+            self_is_1d = self.ndim == 1
+            other_is_1d = other.ndim == 1
+
+            # reshape to 2-D if self or other is 1-D
+            if self_is_1d:
+                self = self.reshape(self._shape_as_2d) # prepend 1 to shape
+
+            if other_is_1d:
+                other = other.reshape((other.shape[0], 1)) # append 1 to shape
+
+            # Check if the inner dimensions match for matrix multiplication
+            if N != other.shape[-2]:
+                raise ValueError(
+                    f"{err_prefix} (n,..,k={N}),(k={other.shape[-2]},..,m)->(n,..,m)"
+                )
+
+            # If A or B has more than 2 dimensions, check for
+            # batch dimensions compatibility
+            if self.ndim > 2 or other.ndim > 2:
+                batch_shape_A = self.shape[:-2]
+                batch_shape_B = other.shape[:-2]
+                if batch_shape_A != batch_shape_B:
+                    try:
+                        # This will raise an error if the shapes are not broadcastable
+                        np.broadcast_shapes(batch_shape_A, batch_shape_B)
+                    except ValueError:
+                        raise ValueError("Batch dimensions are not broadcastable")
+
+            result = self._matmul_sparse(other)
+
+            # reshape back if a or b were originally 1-D
+            if self_is_1d:
+                # if self was originally 1-D, reshape result accordingly
+                result = result.reshape(tuple(result.shape[:-2]) +
+                                        tuple(result.shape[-1:]))
+            if other_is_1d:
+                result = result.reshape(result.shape[:-1])
+            return result
+
+    def _matmul_multivector(self, other):
+        result_dtype = upcast_char(self.dtype.char, other.dtype.char)
+        if self.ndim >= 3 or other.ndim >= 3:
+            # if self has shape (N,), reshape to (1,N)
+            if self.ndim == 1:
+                result = self.reshape(1, self.shape[0])._matmul_multivector(other)
+                return result.reshape(tuple(other.shape[:-2]) + tuple(other.shape[-1:]))
+
+            broadcast_shape = np.broadcast_shapes(self.shape[:-2], other.shape[:-2])
+            self_shape = broadcast_shape + self.shape[-2:]
+            other_shape = broadcast_shape + other.shape[-2:]
+
+            self = self._broadcast_to(self_shape)
+            other = np.broadcast_to(other, other_shape)
+            result_shape = broadcast_shape + self.shape[-2:-1] + other.shape[-1:]
+            result = np.zeros(result_shape, dtype=result_dtype)
+            coo_matmat_dense_nd(self.nnz, len(self.shape), other.shape[-1],
+                                np.array(other_shape), np.array(result_shape),
+                                np.concatenate(self.coords),
+                                self.data, other.ravel('C'), result)
+            return result
+
+        if self.ndim == 2:
+            result_shape = (self.shape[0], other.shape[1])
+            col = self.col
+            row = self.row
+        elif self.ndim == 1:
+            result_shape = (other.shape[1],)
+            col = self.coords[0]
+            row = np.zeros_like(col)
+        result = np.zeros(result_shape, dtype=result_dtype)
+        coo_matmat_dense(self.nnz, other.shape[-1], row, col,
+                         self.data, other.ravel('C'), result)
+        return result.view(type=type(other))
+
+    def dot(self, other):
+        """Return the dot product of two arrays.
+
+        Strictly speaking a dot product involves two vectors.
+        But in the sense that an array with ndim >= 1 is a collection
+        of vectors, the function computes the collection of dot products
+        between each vector in the first array with each vector in the
+        second array. The axis upon which the sum of products is performed
+        is the last axis of the first array and the second to last axis of
+        the second array. If the second array is 1-D, the last axis is used.
+
+        Thus, if both arrays are 1-D, the inner product is returned.
+        If both are 2-D, we have matrix multiplication. If `other` is 1-D,
+        the sum product is taken along the last axis of each array. If
+        `other` is N-D for N>=2, the sum product is over the last axis of
+        the first array and the second-to-last axis of the second array.
+
+        Parameters
+        ----------
+        other : array_like or sparse array
+            Second array
+
+        Returns
+        -------
+        output : array (sparse or dense)
+            The dot product of this array with `other`.
+            It will be dense/sparse if `other` is dense/sparse.
+
+        Examples
+        --------
+
+        >>> import numpy as np
+        >>> from scipy.sparse import coo_array
+        >>> A = coo_array([[1, 2, 0], [0, 0, 3], [4, 0, 5]])
+        >>> v = np.array([1, 0, -1])
+        >>> A.dot(v)
+        array([ 1, -3, -1], dtype=int64)
+
+        For 2-D arrays it is the matrix product:
+
+        >>> A = coo_array([[1, 0], [0, 1]])
+        >>> B = coo_array([[4, 1], [2, 2]])
+        >>> A.dot(B).toarray()
+        array([[4, 1],
+               [2, 2]])
+
+        For 3-D arrays the shape extends unused axes by other unused axes.
+
+        >>> A = coo_array(np.arange(3*4*5*6)).reshape((3,4,5,6))
+        >>> B = coo_array(np.arange(3*4*5*6)).reshape((5,4,6,3))
+        >>> A.dot(B).shape
+        (3, 4, 5, 5, 4, 3)
+        """
+        # handle non-array input:  lists, ints, etc
+        if not (issparse(other) or isdense(other) or isscalarlike(other)):
+            # If it's a list or whatever, treat it like an array
+            o_array = np.asanyarray(other)
+
+            if o_array.ndim == 0 and o_array.dtype == np.object_:
+                raise TypeError(f"dot argument not supported type: '{type(other)}'")
+            try:
+                other.shape
+            except AttributeError:
+                other = o_array
+
+        # Handle scalar multiplication
+        if isscalarlike(other):
+            return self * other
+
+        # other.shape[-2:][0] gets last index of 1d, next to last index of >1d
+        if self.shape[-1] != other.shape[-2:][0]:
+            raise ValueError(f"shapes {self.shape} and {other.shape}"
+                             " are not aligned for n-D dot")
+
+        if self.ndim < 3 and other.ndim < 3:
+            return self @ other
+        if isdense(other):
+            return self._dense_dot(other)
+        return self._sparse_dot(other.tocoo())
+
+    def _sparse_dot(self, other):
+        # already checked: at least one is >2d, neither scalar, both are coo
+        # Ravel non-reduced axes coordinates
+        self_2d, s_new_shape = _convert_to_2d(self, [self.ndim - 1])
+        other_2d, o_new_shape = _convert_to_2d(other, [max(0, other.ndim - 2)])
+
+        prod = self_2d @ other_2d.T  # routes via 2-D CSR
+        prod = prod.tocoo()
+
+        # Combine the shapes of the non-contracted axes
+        combined_shape = s_new_shape + o_new_shape
+
+        # Unravel the 2D coordinates to get multi-dimensional coordinates
+        coords = []
+        new_shapes = (s_new_shape, o_new_shape) if s_new_shape else (o_new_shape,)
+        for c, s in zip(prod.coords, new_shapes):
+            coords.extend(np.unravel_index(c, s))
+
+        # Construct the resulting COO array with coords and shape
+        return coo_array((prod.data, coords), shape=combined_shape)
+
+    def _dense_dot(self, other):
+        # already checked: self is >0d, other is dense and >0d
+        # Ravel non-reduced axes coordinates
+        s_ndim = self.ndim
+        if s_ndim <= 2:
+            s_new_shape = () if s_ndim == 1 else (self.shape[0],)
+            self_2d = self
+        else:
+            self_2d, s_new_shape = _convert_to_2d(self, [self.ndim - 1])
+
+        o_ndim = other.ndim
+        if o_ndim <= 2:
+            o_new_shape = () if o_ndim == 1 else (other.shape[-1],)
+            other_2d = other
+        else:
+            o_new_shape = other.shape[:-2] + other.shape[-1:]
+            reorder_dims = (o_ndim - 2, *range(o_ndim - 2), o_ndim - 1)
+            o_reorg = np.transpose(other, reorder_dims)
+            other_2d = o_reorg.reshape((other.shape[-2], math.prod(o_new_shape)))
+
+        prod = self_2d @ other_2d  # routes via 2-D CSR
+
+        # Combine the shapes of the non-contracted axes
+        combined_shape = s_new_shape + o_new_shape
+        return prod.reshape(combined_shape)
+
+
+    def tensordot(self, other, axes=2):
+        """Return the tensordot product with another array along the given axes.
+
+        The tensordot differs from dot and matmul in that any axis can be
+        chosen for each of the first and second array and the sum of the
+        products is computed just like for matrix multiplication, only not
+        just for the rows of the first times the columns of the second. It
+        takes the dot product of the collection of vectors along the specified
+        axes.  Here we can even take the sum of the products along two or even
+        more axes if desired. So, tensordot is a dot product computation
+        applied to arrays of any dimension >= 1. It is like matmul but over
+        arbitrary axes for each matrix.
+
+        Given two tensors, `a` and `b`, and the desired axes specified as a
+        2-tuple/list/array containing two sequences of axis numbers,
+        ``(a_axes, b_axes)``, sum the products of `a`'s and `b`'s elements
+        (components) over the axes specified by ``a_axes`` and ``b_axes``.
+        The `axes` input can be a single non-negative integer, ``N``;
+        if it is, then the last ``N`` dimensions of `a` and the first
+        ``N`` dimensions of `b` are summed over.
+
+        Parameters
+        ----------
+        other : array_like
+            Tensor to "dot".
+        axes : int or (2,) array_like
+            * integer_like
+              If an int N, sum over the last N axes of `a` and the first N axes
+              of `b` in order. The sizes of the corresponding axes must match.
+            * (2,) array_like
+              A 2-tuple of sequences of axes to be summed over, the first applying
+              to `a`, the second to `b`. The sequences must be the same length.
+              The shape of the corresponding axes must match between `a` and `b`.
+
+        Returns
+        -------
+        output : coo_array
+            The tensor dot product of this array with `other`.
+            It will be dense/sparse if `other` is dense/sparse.
+
+        See Also
+        --------
+        dot
+
+        Examples
+        --------
+        >>> import numpy as np
+        >>> import scipy.sparse
+        >>> A = scipy.sparse.coo_array([[[2, 3], [0, 0]], [[0, 1], [0, 5]]])
+        >>> A.shape
+        (2, 2, 2)
+
+        Integer axes N are shorthand for (range(-N, 0), range(0, N)):
+
+        >>> A.tensordot(A, axes=1).toarray()
+        array([[[[ 4,  9],
+                 [ 0, 15]],
+        <BLANKLINE>
+                [[ 0,  0],
+                 [ 0,  0]]],
+        <BLANKLINE>
+        <BLANKLINE>
+               [[[ 0,  1],
+                 [ 0,  5]],
+        <BLANKLINE>
+                [[ 0,  5],
+                 [ 0, 25]]]])
+        >>> A.tensordot(A, axes=2).toarray()
+        array([[ 4,  6],
+               [ 0, 25]])
+        >>> A.tensordot(A, axes=3)
+        array(39)
+
+        Using tuple for axes:
+
+        >>> a = scipy.sparse.coo_array(np.arange(60).reshape(3,4,5))
+        >>> b = np.arange(24).reshape(4,3,2)
+        >>> c = a.tensordot(b, axes=([1,0],[0,1]))
+        >>> c.shape
+        (5, 2)
+        >>> c
+        array([[4400, 4730],
+               [4532, 4874],
+               [4664, 5018],
+               [4796, 5162],
+               [4928, 5306]])
+
+        """
+        if not isdense(other) and not issparse(other):
+            # If it's a list or whatever, treat it like an array
+            other_array = np.asanyarray(other)
+
+            if other_array.ndim == 0 and other_array.dtype == np.object_:
+                raise TypeError(f"tensordot arg not supported type: '{type(other)}'")
+            try:
+                other.shape
+            except AttributeError:
+                other = other_array
+
+        axes_self, axes_other = _process_axes(self.ndim, other.ndim, axes)
+
+        # Check for shape compatibility along specified axes
+        if any(self.shape[ax] != other.shape[bx]
+               for ax, bx in zip(axes_self, axes_other)):
+            raise ValueError("sizes of the corresponding axes must match")
+
+        if isdense(other):
+            return self._dense_tensordot(other, axes_self, axes_other)
+        else:
+            return self._sparse_tensordot(other, axes_self, axes_other)
+
+    def _sparse_tensordot(self, other, s_axes, o_axes):
+        # Prepare the tensors for tensordot operation
+        # Ravel non-reduced axes coordinates
+        self_2d, s_new_shape = _convert_to_2d(self, s_axes)
+        other_2d, o_new_shape = _convert_to_2d(other, o_axes)
+
+        # Perform matrix multiplication (routed via 2-D CSR)
+        prod = self_2d @ other_2d.T
+        # handle case of scalar result (axis includes all axes for both)
+        if not issparse(prod):
+            return prod
+        prod = prod.tocoo()
+
+        # Combine the shapes of the non-contracted axes
+        combined_shape = s_new_shape + o_new_shape
+
+        # Unravel the 2D coordinates to get multi-dimensional coordinates
+        coords = []
+        new_shapes = (s_new_shape, o_new_shape) if s_new_shape else (o_new_shape,)
+        for c, s in zip(prod.coords, new_shapes):
+            if s:
+                coords.extend(np.unravel_index(c, s))
+
+        # Construct the resulting COO array with coords and shape
+        return coo_array((prod.data, coords), shape=combined_shape)
+
+    def _dense_tensordot(self, other, s_axes, o_axes):
+        s_ndim = len(self.shape)
+        o_ndim = len(other.shape)
+
+        s_non_axes = [i for i in range(s_ndim) if i not in s_axes]
+        s_axes_shape = [self.shape[i] for i in s_axes]
+        s_non_axes_shape = [self.shape[i] for i in s_non_axes]
+
+        o_non_axes = [i for i in range(o_ndim) if i not in o_axes]
+        o_axes_shape = [other.shape[i] for i in o_axes]
+        o_non_axes_shape = [other.shape[i] for i in o_non_axes]
+
+        left = self.transpose(s_non_axes + s_axes)
+        right = np.transpose(other, o_non_axes[:-1] + o_axes + o_non_axes[-1:])
+
+        reshape_left = (*s_non_axes_shape, math.prod(s_axes_shape))
+        reshape_right = (*o_non_axes_shape[:-1], math.prod(o_axes_shape),
+                         *o_non_axes_shape[-1:])
+
+        return left.reshape(reshape_left).dot(right.reshape(reshape_right))
+
+    def _matmul_sparse(self, other):
+        """
+        Perform sparse-sparse matrix multiplication for two n-D COO arrays.
+        The method converts input n-D arrays to 2-D block array format,
+        uses csr_matmat to multiply them, and then converts the
+        result back to n-D COO array.
+
+        Parameters:
+        self (COO): The first n-D sparse array in COO format.
+        other (COO): The second n-D sparse array in COO format.
+
+        Returns:
+        prod (COO): The resulting n-D sparse array after multiplication.
+        """
+        if self.ndim < 3 and other.ndim < 3:
+            return _spbase._matmul_sparse(self, other)
+
+        # Get the shapes of self and other
+        self_shape = self.shape
+        other_shape = other.shape
+
+        # Determine the new shape to broadcast self and other
+        broadcast_shape = np.broadcast_shapes(self_shape[:-2], other_shape[:-2])
+        self_new_shape = tuple(broadcast_shape) + self_shape[-2:]
+        other_new_shape = tuple(broadcast_shape) + other_shape[-2:]
+
+        self_broadcasted = self._broadcast_to(self_new_shape)
+        other_broadcasted = other._broadcast_to(other_new_shape)
+
+        # Convert n-D COO arrays to 2-D block diagonal arrays
+        self_block_diag = _block_diag(self_broadcasted)
+        other_block_diag = _block_diag(other_broadcasted)
+
+        # Use csr_matmat to perform sparse matrix multiplication
+        prod_block_diag = (self_block_diag @ other_block_diag).tocoo()
+
+        # Convert the 2-D block diagonal array back to n-D
+        return _extract_block_diag(
+            prod_block_diag,
+            shape=(*broadcast_shape, self.shape[-2], other.shape[-1]),
+        )
+
+    def _broadcast_to(self, new_shape, copy=False):
+        if self.shape == new_shape:
+            return self.copy() if copy else self
+
+        old_shape = self.shape
+
+        # Check if the new shape is compatible for broadcasting
+        if len(new_shape) < len(old_shape):
+            raise ValueError("New shape must have at least as many dimensions"
+                             " as the current shape")
+
+        # Add leading ones to shape to ensure same length as `new_shape`
+        shape = (1,) * (len(new_shape) - len(old_shape)) + tuple(old_shape)
+
+        # Ensure the old shape can be broadcast to the new shape
+        if any((o != 1 and o != n) for o, n in zip(shape, new_shape)):
+            raise ValueError(f"current shape {old_shape} cannot be "
+                             "broadcast to new shape {new_shape}")
+
+        # Reshape the COO array to match the new dimensions
+        self = self.reshape(shape)
+
+        idx_dtype = get_index_dtype(self.coords, maxval=max(new_shape))
+        coords = self.coords
+        new_data = self.data
+        new_coords = coords[-1:]  # Copy last coordinate to start
+        cum_repeat = 1 # Cumulative repeat factor for broadcasting
+
+        if shape[-1] != new_shape[-1]: # broadcasting the n-th (col) dimension
+            repeat_count = new_shape[-1]
+            cum_repeat *= repeat_count
+            new_data = np.tile(new_data, repeat_count)
+            new_dim = np.repeat(np.arange(0, repeat_count, dtype=idx_dtype), self.nnz)
+            new_coords = (new_dim,)
+
+        for i in range(-2, -(len(shape)+1), -1):
+            if shape[i] != new_shape[i]:
+                repeat_count = new_shape[i] # number of times to repeat data, coords
+                cum_repeat *= repeat_count # update cumulative repeat factor
+                nnz = len(new_data) # Number of non-zero elements so far
+
+                # Tile data and coordinates to match the new repeat count
+                new_data = np.tile(new_data, repeat_count)
+                new_coords = tuple(np.tile(new_coords[i+1:], repeat_count))
+
+                # Create new dimensions and stack them
+                new_dim = np.repeat(np.arange(0, repeat_count, dtype=idx_dtype), nnz)
+                new_coords = (new_dim,) + new_coords
+            else:
+                # If no broadcasting needed, tile the coordinates
+                new_dim = np.tile(coords[i], cum_repeat)
+                new_coords = (new_dim,) + new_coords
+
+        return coo_array((new_data, new_coords), new_shape)
+
+    def _sum_nd(self, axis, res_dtype, out):
+        # axis and out are preprocessed. out.shape is new_shape
+        A2d, new_shape = _convert_to_2d(self, axis)
+        ones = np.ones((A2d.shape[1], 1), dtype=res_dtype)
+        # sets dtype while loading into out
+        out[...] = (A2d @ ones).reshape(new_shape)
+        return out
+
+    def _min_or_max_axis_nd(self, axis, min_or_max, explicit):
+        A2d, new_shape = _convert_to_2d(self, axis)
+        res = A2d._min_or_max_axis(1, min_or_max, explicit)
+        unraveled_coords = np.unravel_index(res.coords[0], new_shape)
+
+        return coo_array((res.data, unraveled_coords), new_shape)
+
+    def _argminmax_axis_nd(self, axis, argminmax, compare, explicit):
+        A2d, new_shape = _convert_to_2d(self, axis)
+        res_flat = A2d._argminmax_axis(1, argminmax, compare, explicit)
+        return res_flat.reshape(new_shape)
+
+
+def _block_diag(self):
+    """
+    Converts an N-D COO array into a 2-D COO array in block diagonal form.
+
+    Parameters:
+    self (coo_array): An N-Dimensional COO sparse array.
+
+    Returns:
+    coo_array: A 2-Dimensional COO sparse array in block diagonal form.
+    """
+    if self.ndim<2:
+        raise ValueError("array must have atleast dim=2")
+    num_blocks = math.prod(self.shape[:-2])
+    n_col = self.shape[-1]
+    n_row = self.shape[-2]
+    res_arr = self.reshape((num_blocks, n_row, n_col))
+    new_coords = (
+        res_arr.coords[1] + res_arr.coords[0] * res_arr.shape[1],
+        res_arr.coords[2] + res_arr.coords[0] * res_arr.shape[2],
+    )
+
+    new_shape = (num_blocks * n_row, num_blocks * n_col)
+    return coo_array((self.data, tuple(new_coords)), shape=new_shape)
+
+
+def _extract_block_diag(self, shape):
+    n_row, n_col = shape[-2], shape[-1]
+
+    # Extract data and coordinates from the block diagonal COO array
+    data = self.data
+    row, col = self.row, self.col
+
+    # Initialize new coordinates array
+    new_coords = np.empty((len(shape), self.nnz), dtype=int)
+
+    # Calculate within-block indices
+    new_coords[-2] = row % n_row
+    new_coords[-1] = col % n_col
+
+    # Calculate coordinates for higher dimensions
+    temp_block_idx = row // n_row
+    for i in range(len(shape) - 3, -1, -1):
+        size = shape[i]
+        new_coords[i] = temp_block_idx % size
+        temp_block_idx = temp_block_idx // size
+
+    # Create the new COO array with the original n-D shape
+    return coo_array((data, tuple(new_coords)), shape=shape)
+
+
+def _get_sparse_data_and_coords(x, new_shape, dtype):
+    x = x.tocoo()
+    x.sum_duplicates()
+
+    x_coords = list(x.coords)
+    x_data = x.data.astype(dtype, copy=False)
+    x_shape = x.shape
+
+    if new_shape == x_shape:
+        return x_data, x_coords
+
+    # broadcasting needed
+    len_diff = len(new_shape) - len(x_shape)
+    if len_diff > 0:
+        # prepend ones to shape of x to match ndim
+        x_shape = [1] * len_diff + list(x_shape)
+        coord_zeros = np.zeroslike(x_coords[0])
+        x_coords = tuple([coord_zeros] * len_diff + x_coords)
+    # taking away axes (squeezing) is not part of broadcasting, but long
+    # spmatrix history of using 2d vectors in 1d space, so we manually
+    # squeeze the front and back axes here to be compatible
+    if len_diff < 0:
+        for _ in range(-len_diff):
+            if x_shape[0] == 1:
+                x_shape = x_shape[1:]
+                x_coords = x_coords[1:]
+            elif x_shape[-1] == 1:
+                x_shape = x_shape[:-1]
+                x_coords = x_coords[:-1]
+            else:
+                raise ValueError("shape mismatch in assignment")
+    # broadcast with copy (will need to copy eventually anyway)
+    tot_expand = 1
+    for i, (nn, nx) in enumerate(zip(new_shape, x_shape)):
+        if nn == nx:
+            continue
+        if nx != 1:
+            raise ValueError("shape mismatch in assignment")
+        x_nnz = len(x_coords[0])
+        x_coords[i] = np.repeat(np.arange(nn), x_nnz)
+        for j, co in enumerate(x_coords):
+            if j == i:
+                continue
+            x_coords[j] = np.tile(co, nn)
+        tot_expand *= nn
+    x_data = np.tile(x_data.ravel(), tot_expand)
+    return x_data, x_coords
+
+
+def _get_dense_data_and_coords(x, new_shape):
+    if x.shape != new_shape:
+        x = np.broadcast_to(x.squeeze(), new_shape)
+    # shift scalar input to 1d so has coords
+    if new_shape == ():
+        x_coords = tuple([np.array([0])] * len(new_shape))
+        x_data = x.ravel()
+    else:
+        x_coords = x.nonzero()
+        x_data = x[x_coords]
+    return x_data, x_coords
+
+
+def _process_axes(ndim_a, ndim_b, axes):
+    if isinstance(axes, int):
+        if axes < 1 or axes > min(ndim_a, ndim_b):
+            raise ValueError("axes integer is out of bounds for input arrays")
+        axes_a = list(range(ndim_a - axes, ndim_a))
+        axes_b = list(range(axes))
+    elif isinstance(axes, tuple | list):
+        if len(axes) != 2:
+            raise ValueError("axes must be a tuple/list of length 2")
+        axes_a, axes_b = axes
+        if len(axes_a) != len(axes_b):
+            raise ValueError("axes lists/tuples must be of the same length")
+        if any(ax >= ndim_a or ax < -ndim_a for ax in axes_a) or \
+           any(bx >= ndim_b or bx < -ndim_b for bx in axes_b):
+            raise ValueError("axes indices are out of bounds for input arrays")
+    else:
+        raise TypeError("axes must be an integer or a tuple/list of integers")
+
+    axes_a = [axis + ndim_a if axis < 0 else axis for axis in axes_a]
+    axes_b = [axis + ndim_b if axis < 0 else axis for axis in axes_b]
+    return axes_a, axes_b
+
+
+def _convert_to_2d(coo, axis):
+    axis_coords = tuple(coo.coords[i] for i in axis)
+    axis_shape = tuple(coo.shape[i] for i in axis)
+    axis_ravel = _ravel_coords(axis_coords, axis_shape)
+
+    ndim = len(coo.coords)
+    non_axis = tuple(i for i in range(ndim) if i not in axis)
+    if non_axis:
+        non_axis_coords = tuple(coo.coords[i] for i in non_axis)
+        non_axis_shape = tuple(coo.shape[i] for i in non_axis)
+        non_axis_ravel = _ravel_coords(non_axis_coords, non_axis_shape)
+        coords_2d = (non_axis_ravel, axis_ravel)
+        shape_2d = (math.prod(non_axis_shape), math.prod(axis_shape))
+    else:  # all axes included in axis so result will have 1 element
+        coords_2d = (axis_ravel,)
+        shape_2d = (math.prod(axis_shape),)
+        non_axis_shape = ()
+
+    new_coo = coo_array((coo.data, coords_2d), shape=shape_2d)
+    return new_coo, non_axis_shape
+
+
+def _ravel_coords(coords, shape, order='C'):
+    """Like np.ravel_multi_index, but avoids some overflow issues."""
+    if len(coords) == 1:
+        return coords[0]
+    # Handle overflow as in https://github.com/scipy/scipy/pull/9132
+    if len(coords) == 2:
+        nrows, ncols = shape
+        row, col = coords
+        if order == 'C':
+            maxval = (ncols * max(0, nrows - 1) + max(0, ncols - 1))
+            idx_dtype = get_index_dtype(maxval=maxval)
+            return np.multiply(ncols, row, dtype=idx_dtype) + col
+        elif order == 'F':
+            maxval = (nrows * max(0, ncols - 1) + max(0, nrows - 1))
+            idx_dtype = get_index_dtype(maxval=maxval)
+            return np.multiply(nrows, col, dtype=idx_dtype) + row
+        else:
+            raise ValueError("'order' must be 'C' or 'F'")
+    return np.ravel_multi_index(coords, shape, order=order)
+
+
+def isspmatrix_coo(x):
+    """Is `x` of coo_matrix type?
+
+    .. warning::
+
+       SciPy sparse is shifting from a sparse matrix interface to a sparse
+       array interface. In the next few releases we expect to deprecate the
+       sparse matrix interface. For documentation of the matrix
+       interface, see the :ref:`spmatrix interface docs <spmatrix_api>`.
+       For guidance on converting existing code to sparse arrays, see
+       :ref:`Migration from spmatrix to sparray <migration_to_sparray>`.
+
+    Parameters
+    ----------
+    x
+        object to check for being a coo matrix
+
+    Returns
+    -------
+    bool
+        True if `x` is a coo matrix, False otherwise
+
+    Examples
+    --------
+    >>> from scipy.sparse import coo_array, coo_matrix, csr_matrix, isspmatrix_coo
+    >>> isspmatrix_coo(coo_matrix([[5]]))
+    True
+    >>> isspmatrix_coo(coo_array([[5]]))
+    False
+    >>> isspmatrix_coo(csr_matrix([[5]]))
+    False
+    """
+    return isinstance(x, coo_matrix)
+
+
+# This namespace class separates array from matrix with isinstance
+class coo_array(_coo_base, sparray):
+    """
+    A sparse array in COOrdinate format.
+
+    Also known as the 'ijv' or 'triplet' format.
+
+    This can be instantiated in several ways:
+        coo_array(D)
+            where D is an ndarray
+
+        coo_array(S)
+            with another sparse array or matrix S (equivalent to S.tocoo())
+
+        coo_array(shape, [dtype])
+            to construct an empty sparse array with shape `shape`
+            dtype is optional, defaulting to dtype='d'.
+
+        coo_array((data, coords), [shape])
+            to construct from existing data and index arrays:
+                1. data[:]       the entries of the sparse array, in any order
+                2. coords[i][:]  the axis-i coordinates of the data entries
+
+            Where ``A[coords] = data``, and coords is a tuple of index arrays.
+            When shape is not specified, it is inferred from the index arrays.
+
+    Attributes
+    ----------
+    data : ndarray
+        COO format data array of the sparse array
+    coords : tuple of ndarray
+        COO format tuple of index arrays
+    has_canonical_format : bool
+        Whether the matrix has sorted coordinates and no duplicates
+    dtype : dtype
+        Data type of the array
+    shape : tuple of integers
+        Shape of the array
+    ndim : int
+        Number of dimensions of the array
+    format : str
+        Three letter code for the format of the array storage, e.g. 'coo'
+    nnz : int
+        Number of values stored in the array
+    size : int
+        Number of values stored in the array
+    T : coo_array
+        The transpose of the array
+    mT : coo_array
+        The matrix transpose of the array
+
+    Notes
+    -----
+
+    Sparse arrays can be used in arithmetic operations: they support
+    addition, subtraction, multiplication, division, and matrix power.
+
+    Advantages of the COO format
+        - facilitates fast conversion among sparse formats
+        - permits duplicate entries (see example)
+        - very fast conversion to and from CSR/CSC formats
+
+    Disadvantages of the COO format
+        - does not directly support:
+            + arithmetic operations
+            + slicing
+
+    Intended Usage
+        - COO is a fast format for constructing sparse arrays
+        - Once a COO array has been constructed, convert to CSR or
+          CSC format for fast arithmetic and matrix vector operations
+        - By default when converting to CSR or CSC format, duplicate (i,j)
+          entries will be summed together.  This facilitates efficient
+          construction of finite element matrices and the like. (see example)
+
+    Canonical format
+        - Entries and coordinates sorted by row, then column.
+        - There are no duplicate entries (i.e. duplicate (i,j) locations)
+        - Data arrays MAY have explicit zeros.
+
+    Examples
+    --------
+
+    >>> # Constructing an empty sparse array
+    >>> import numpy as np
+    >>> from scipy.sparse import coo_array
+    >>> coo_array((3, 4), dtype=np.int8).toarray()
+    array([[0, 0, 0, 0],
+           [0, 0, 0, 0],
+           [0, 0, 0, 0]], dtype=int8)
+
+    >>> # Constructing a sparse array using ijv format
+    >>> row  = np.array([0, 3, 1, 0])
+    >>> col  = np.array([0, 3, 1, 2])
+    >>> data = np.array([4, 5, 7, 9])
+    >>> coo_array((data, (row, col)), shape=(4, 4)).toarray()
+    array([[4, 0, 9, 0],
+           [0, 7, 0, 0],
+           [0, 0, 0, 0],
+           [0, 0, 0, 5]])
+
+    >>> # Constructing a sparse array with duplicate coordinates
+    >>> row  = np.array([0, 0, 1, 3, 1, 0, 0])
+    >>> col  = np.array([0, 2, 1, 3, 1, 0, 0])
+    >>> data = np.array([1, 1, 1, 1, 1, 1, 1])
+    >>> coo = coo_array((data, (row, col)), shape=(4, 4))
+    >>> # Duplicate coordinates are maintained until implicitly or explicitly summed
+    >>> np.max(coo.data)
+    1
+    >>> coo.toarray()
+    array([[3, 0, 1, 0],
+           [0, 2, 0, 0],
+           [0, 0, 0, 0],
+           [0, 0, 0, 1]])
+
+    """  # numpydoc ignore=PR01
+
+
+class coo_matrix(spmatrix, _coo_base):
+    """
+    A sparse matrix in COOrdinate format.
+
+    Also known as the 'ijv' or 'triplet' format.
+
+    .. warning::
+
+       SciPy sparse is shifting from a sparse matrix interface to a sparse
+       array interface. In the next few releases we expect to deprecate the
+       sparse matrix interface. For documentation of the matrix
+       interface, see the :ref:`spmatrix interface docs <spmatrix_api>`.
+       For guidance on converting existing code to sparse arrays, see
+       :ref:`Migration from spmatrix to sparray <migration_to_sparray>`.
+
+    This can be instantiated in several ways:
+        coo_matrix(D)
+            where D is a 2-D ndarray
+
+        coo_matrix(S)
+            with another sparse array or matrix S (equivalent to S.tocoo())
+
+        coo_matrix((M, N), [dtype])
+            to construct an empty matrix with shape (M, N)
+            dtype is optional, defaulting to dtype='d'.
+
+        coo_matrix((data, (i, j)), [shape=(M, N)])
+            to construct from three arrays:
+                1. data[:]   the entries of the matrix, in any order
+                2. i[:]      the row indices of the matrix entries
+                3. j[:]      the column indices of the matrix entries
+
+            Where ``A[i[k], j[k]] = data[k]``.  When shape is not
+            specified, it is inferred from the index arrays
+
+    Attributes
+    ----------
+    data : ndarray
+        COO format data array of the sparse matrix
+    coords : tuple of ndarray
+        COO format tuple of index matrix
+    has_canonical_format : bool
+        Whether the matrix has sorted coordinates and no duplicates
+    dtype : dtype
+        Data type of the matrix
+    shape : tuple of integers
+        Shape of the matrix
+    ndim : int
+        Number of dimensions of the matrix
+    format : str
+        Three letter code for the format of the matrix storage, e.g. 'coo'
+    nnz : int
+        Number of values stored in the matrix
+    size : int
+        Number of values stored in the matrix
+    T : coo_matrix
+        The transpose of the matrix
+    mT : coo_matrix
+        The matrix transpose
+
+    Notes
+    -----
+
+    Sparse matrices can be used in arithmetic operations: they support
+    addition, subtraction, multiplication, division, and matrix power.
+
+    Advantages of the COO format
+        - facilitates fast conversion among sparse formats
+        - permits duplicate entries (see example)
+        - very fast conversion to and from CSR/CSC formats
+
+    Disadvantages of the COO format
+        - does not directly support:
+            + arithmetic operations
+            + slicing
+
+    Intended Usage
+        - COO is a fast format for constructing sparse matrices
+        - Once a COO matrix has been constructed, convert to CSR or
+          CSC format for fast arithmetic and matrix vector operations
+        - By default when converting to CSR or CSC format, duplicate (i,j)
+          entries will be summed together.  This facilitates efficient
+          construction of finite element matrices and the like. (see example)
+
+    Canonical format
+        - Entries and coordinates sorted by row, then column.
+        - There are no duplicate entries (i.e. duplicate (i,j) locations)
+        - Data arrays MAY have explicit zeros.
+
+    Examples
+    --------
+
+    >>> # Constructing an empty matrix
+    >>> import numpy as np
+    >>> from scipy.sparse import coo_matrix
+    >>> coo_matrix((3, 4), dtype=np.int8).toarray()
+    array([[0, 0, 0, 0],
+           [0, 0, 0, 0],
+           [0, 0, 0, 0]], dtype=int8)
+
+    >>> # Constructing a matrix using ijv format
+    >>> row  = np.array([0, 3, 1, 0])
+    >>> col  = np.array([0, 3, 1, 2])
+    >>> data = np.array([4, 5, 7, 9])
+    >>> coo_matrix((data, (row, col)), shape=(4, 4)).toarray()
+    array([[4, 0, 9, 0],
+           [0, 7, 0, 0],
+           [0, 0, 0, 0],
+           [0, 0, 0, 5]])
+
+    >>> # Constructing a matrix with duplicate coordinates
+    >>> row  = np.array([0, 0, 1, 3, 1, 0, 0])
+    >>> col  = np.array([0, 2, 1, 3, 1, 0, 0])
+    >>> data = np.array([1, 1, 1, 1, 1, 1, 1])
+    >>> coo = coo_matrix((data, (row, col)), shape=(4, 4))
+    >>> # Duplicate coordinates are maintained until implicitly or explicitly summed
+    >>> np.max(coo.data)
+    1
+    >>> coo.toarray()
+    array([[3, 0, 1, 0],
+           [0, 2, 0, 0],
+           [0, 0, 0, 0],
+           [0, 0, 0, 1]])
+
+    """
+
+    def __setstate__(self, state):
+        if 'coords' not in state:
+            # For retro-compatibility with the previous attributes
+            # storing nnz coordinates for 2D COO matrix.
+            state['coords'] = (state.pop('row'), state.pop('col'))
+        self.__dict__.update(state)
+
+    def __getitem__(self, key):
+        raise TypeError("'coo_matrix' object is not subscriptable")
+
+    def __setitem__(self, key, x):
+        raise TypeError("'coo_matrix' object does not support item assignment")
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/_csc.py b/venv/lib/python3.12/site-packages/scipy/sparse/_csc.py
new file mode 100644
index 0000000000000000000000000000000000000000..a9917071a9e2cebfc0da6dfb75ddfae14c86c92a
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/_csc.py
@@ -0,0 +1,403 @@
+"""Compressed Sparse Column matrix format"""
+__docformat__ = "restructuredtext en"
+
+__all__ = ['csc_array', 'csc_matrix', 'isspmatrix_csc']
+
+
+import numpy as np
+
+from ._matrix import spmatrix
+from ._base import _spbase, sparray
+from ._sparsetools import csr_tocsc, expandptr
+from ._sputils import upcast
+
+from ._compressed import _cs_matrix
+
+
+class _csc_base(_cs_matrix):
+    _format = 'csc'
+
+    def transpose(self, axes=None, copy=False):
+        if axes is not None and axes != (1, 0):
+            raise ValueError("Sparse arrays/matrices do not support "
+                              "an 'axes' parameter because swapping "
+                              "dimensions is the only logical permutation.")
+
+        M, N = self.shape
+
+        return self._csr_container((self.data, self.indices,
+                                    self.indptr), (N, M), copy=copy)
+
+    transpose.__doc__ = _spbase.transpose.__doc__
+
+    def __iter__(self):
+        yield from self.tocsr()
+
+    def tocsc(self, copy=False):
+        if copy:
+            return self.copy()
+        else:
+            return self
+
+    tocsc.__doc__ = _spbase.tocsc.__doc__
+
+    def tocsr(self, copy=False):
+        M,N = self.shape
+        idx_dtype = self._get_index_dtype((self.indptr, self.indices),
+                                    maxval=max(self.nnz, N))
+        indptr = np.empty(M + 1, dtype=idx_dtype)
+        indices = np.empty(self.nnz, dtype=idx_dtype)
+        data = np.empty(self.nnz, dtype=upcast(self.dtype))
+
+        csr_tocsc(N, M,
+                  self.indptr.astype(idx_dtype, copy=False),
+                  self.indices.astype(idx_dtype, copy=False),
+                  self.data,
+                  indptr,
+                  indices,
+                  data)
+
+        A = self._csr_container(
+            (data, indices, indptr),
+            shape=self.shape, copy=False
+        )
+        A.has_sorted_indices = True
+        return A
+
+    tocsr.__doc__ = _spbase.tocsr.__doc__
+
+    def nonzero(self):
+        # CSC can't use _cs_matrix's .nonzero method because it
+        # returns the indices sorted for self transposed.
+
+        # Get row and col indices, from _cs_matrix.tocoo
+        major_dim, minor_dim = self._swap(self.shape)
+        minor_indices = self.indices
+        major_indices = np.empty(len(minor_indices), dtype=self.indices.dtype)
+        expandptr(major_dim, self.indptr, major_indices)
+        row, col = self._swap((major_indices, minor_indices))
+
+        # Remove explicit zeros
+        nz_mask = self.data != 0
+        row = row[nz_mask]
+        col = col[nz_mask]
+
+        # Sort them to be in C-style order
+        ind = np.argsort(row, kind='mergesort')
+        row = row[ind]
+        col = col[ind]
+
+        return row, col
+
+    nonzero.__doc__ = _cs_matrix.nonzero.__doc__
+
+    def _getrow(self, i):
+        """Returns a copy of row i of the matrix, as a (1 x n)
+        CSR matrix (row vector).
+        """
+        M, N = self.shape
+        i = int(i)
+        if i < 0:
+            i += M
+        if i < 0 or i >= M:
+            raise IndexError(f'index ({i}) out of range')
+        return self._get_submatrix(minor=i).tocsr()
+
+    def _getcol(self, i):
+        """Returns a copy of column i of the matrix, as a (m x 1)
+        CSC matrix (column vector).
+        """
+        M, N = self.shape
+        i = int(i)
+        if i < 0:
+            i += N
+        if i < 0 or i >= N:
+            raise IndexError(f'index ({i}) out of range')
+        return self._get_submatrix(major=i, copy=True)
+
+    def _get_intXarray(self, row, col):
+        return self._major_index_fancy(col)._get_submatrix(minor=row)
+
+    def _get_intXslice(self, row, col):
+        if col.step in (1, None):
+            return self._get_submatrix(major=col, minor=row, copy=True)
+        return self._major_slice(col)._get_submatrix(minor=row)
+
+    def _get_sliceXint(self, row, col):
+        if row.step in (1, None):
+            return self._get_submatrix(major=col, minor=row, copy=True)
+        return self._get_submatrix(major=col)._minor_slice(row)
+
+    def _get_sliceXarray(self, row, col):
+        return self._major_index_fancy(col)._minor_slice(row)
+
+    def _get_arrayXint(self, row, col):
+        res = self._get_submatrix(major=col)._minor_index_fancy(row)
+        if row.ndim > 1:
+            return res.reshape(row.shape)
+        return res
+
+    def _get_arrayXslice(self, row, col):
+        return self._major_slice(col)._minor_index_fancy(row)
+
+    # these functions are used by the parent class (_cs_matrix)
+    # to remove redundancy between csc_array and csr_matrix
+    @staticmethod
+    def _swap(x):
+        """swap the members of x if this is a column-oriented matrix
+        """
+        return x[1], x[0]
+
+
+def isspmatrix_csc(x):
+    """Is `x` of csc_matrix type?
+
+    .. warning::
+
+       SciPy sparse is shifting from a sparse matrix interface to a sparse
+       array interface. In the next few releases we expect to deprecate the
+       sparse matrix interface. For documentation of the matrix
+       interface, see the :ref:`spmatrix interface docs <spmatrix_api>`.
+       For guidance on converting existing code to sparse arrays, see
+       :ref:`Migration from spmatrix to sparray <migration_to_sparray>`.
+
+    Parameters
+    ----------
+    x
+        object to check for being a csc matrix
+
+    Returns
+    -------
+    bool
+        True if `x` is a csc matrix, False otherwise
+
+    Examples
+    --------
+    >>> from scipy.sparse import csc_array, csc_matrix, coo_matrix, isspmatrix_csc
+    >>> isspmatrix_csc(csc_matrix([[5]]))
+    True
+    >>> isspmatrix_csc(csc_array([[5]]))
+    False
+    >>> isspmatrix_csc(coo_matrix([[5]]))
+    False
+    """
+    return isinstance(x, csc_matrix)
+
+
+# This namespace class separates array from matrix with isinstance
+class csc_array(_csc_base, sparray):
+    """
+    Compressed Sparse Column array.
+
+    This can be instantiated in several ways:
+        csc_array(D)
+            where D is a 2-D ndarray
+
+        csc_array(S)
+            with another sparse array or matrix S (equivalent to S.tocsc())
+
+        csc_array((M, N), [dtype])
+            to construct an empty array with shape (M, N)
+            dtype is optional, defaulting to dtype='d'.
+
+        csc_array((data, (row_ind, col_ind)), [shape=(M, N)])
+            where ``data``, ``row_ind`` and ``col_ind`` satisfy the
+            relationship ``a[row_ind[k], col_ind[k]] = data[k]``.
+
+        csc_array((data, indices, indptr), [shape=(M, N)])
+            is the standard CSC representation where the row indices for
+            column i are stored in ``indices[indptr[i]:indptr[i+1]]``
+            and their corresponding values are stored in
+            ``data[indptr[i]:indptr[i+1]]``.  If the shape parameter is
+            not supplied, the array dimensions are inferred from
+            the index arrays.
+
+    Attributes
+    ----------
+    data : ndarray
+        CSC format data array of the array
+    indices : ndarray
+        CSC format index array of the array
+    indptr : ndarray
+        CSC format index pointer array of the array
+    has_sorted_indices : bool
+        Whether indices are sorted
+    has_canonical_format : bool
+        Whether indices are sorted and no duplicate entries exist
+    dtype : dtype
+        Data type of the array
+    shape : 2-tuple
+        Shape of the array
+    ndim : int
+        Number of dimensions (this is always 2)
+    format : str
+        Three letter code for the format of the array storage, e.g. 'csc'
+    nnz : int
+        Number of values stored in the array
+    size : int
+        Number of values stored in the array
+    T : csc_array
+        The transpose of the array
+    mT : csc_array
+        The matrix transpose of the array
+
+    Notes
+    -----
+
+    Sparse arrays can be used in arithmetic operations: they support
+    addition, subtraction, multiplication, division, and matrix power.
+
+    Advantages of the CSC format
+        - efficient arithmetic operations CSC + CSC, CSC * CSC, etc.
+        - efficient column slicing
+        - fast matrix vector products (CSR, BSR may be faster)
+
+    Disadvantages of the CSC format
+      - slow row slicing operations (consider CSR)
+      - changes to the sparsity structure are expensive (consider LIL or DOK)
+
+    Canonical format
+      - Within each column, indices are sorted by row.
+      - There are no duplicate entries.
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> from scipy.sparse import csc_array
+    >>> csc_array((3, 4), dtype=np.int8).toarray()
+    array([[0, 0, 0, 0],
+           [0, 0, 0, 0],
+           [0, 0, 0, 0]], dtype=int8)
+
+    >>> row = np.array([0, 2, 2, 0, 1, 2])
+    >>> col = np.array([0, 0, 1, 2, 2, 2])
+    >>> data = np.array([1, 2, 3, 4, 5, 6])
+    >>> csc_array((data, (row, col)), shape=(3, 3)).toarray()
+    array([[1, 0, 4],
+           [0, 0, 5],
+           [2, 3, 6]])
+
+    >>> indptr = np.array([0, 2, 3, 6])
+    >>> indices = np.array([0, 2, 2, 0, 1, 2])
+    >>> data = np.array([1, 2, 3, 4, 5, 6])
+    >>> csc_array((data, indices, indptr), shape=(3, 3)).toarray()
+    array([[1, 0, 4],
+           [0, 0, 5],
+           [2, 3, 6]])
+
+    """  # numpydoc ignore=PR01
+
+
+class csc_matrix(spmatrix, _csc_base):
+    """
+    Compressed Sparse Column matrix.
+
+    .. warning::
+
+       SciPy sparse is shifting from a sparse matrix interface to a sparse
+       array interface. In the next few releases we expect to deprecate the
+       sparse matrix interface. For documentation of the matrix
+       interface, see the :ref:`spmatrix interface docs <spmatrix_api>`.
+       For guidance on converting existing code to sparse arrays, see
+       :ref:`Migration from spmatrix to sparray <migration_to_sparray>`.
+
+    This can be instantiated in several ways:
+        csc_matrix(D)
+            where D is a 2-D ndarray
+
+        csc_matrix(S)
+            with another sparse array or matrix S (equivalent to S.tocsc())
+
+        csc_matrix((M, N), [dtype])
+            to construct an empty matrix with shape (M, N)
+            dtype is optional, defaulting to dtype='d'.
+
+        csc_matrix((data, (row_ind, col_ind)), [shape=(M, N)])
+            where ``data``, ``row_ind`` and ``col_ind`` satisfy the
+            relationship ``a[row_ind[k], col_ind[k]] = data[k]``.
+
+        csc_matrix((data, indices, indptr), [shape=(M, N)])
+            is the standard CSC representation where the row indices for
+            column i are stored in ``indices[indptr[i]:indptr[i+1]]``
+            and their corresponding values are stored in
+            ``data[indptr[i]:indptr[i+1]]``.  If the shape parameter is
+            not supplied, the matrix dimensions are inferred from
+            the index arrays.
+
+    Attributes
+    ----------
+    data : ndarray
+        CSC format data array of the matrix
+    indices : ndarray
+        CSC format index array of the matrix
+    indptr : ndarray
+        CSC format index pointer array of the matrix
+    has_sorted_indices : bool
+        Whether indices are sorted
+    has_canonical_format : bool
+        Whether indices are sorted and no duplicate entries exist
+    dtype : dtype
+        Data type of the matrix
+    shape : 2-tuple
+        Shape of the matrix
+    ndim : int
+        Number of dimensions (this is always 2)
+    format : str
+        Three letter code for the format of the matrix storage, e.g. 'csc'
+    nnz : int
+        Number of values stored in the matrix
+    size : int
+        Number of values stored in the matrix
+    T : csc_matrix
+        The transpose of the matrix
+    mT : csc_matrix
+        The matrix transpose
+
+    Notes
+    -----
+
+    Sparse matrices can be used in arithmetic operations: they support
+    addition, subtraction, multiplication, division, and matrix power.
+
+    Advantages of the CSC format
+        - efficient arithmetic operations CSC + CSC, CSC * CSC, etc.
+        - efficient column slicing
+        - fast matrix vector products (CSR, BSR may be faster)
+
+    Disadvantages of the CSC format
+      - slow row slicing operations (consider CSR)
+      - changes to the sparsity structure are expensive (consider LIL or DOK)
+
+    Canonical format
+      - Within each column, indices are sorted by row.
+      - There are no duplicate entries.
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> from scipy.sparse import csc_matrix
+    >>> csc_matrix((3, 4), dtype=np.int8).toarray()
+    array([[0, 0, 0, 0],
+           [0, 0, 0, 0],
+           [0, 0, 0, 0]], dtype=int8)
+
+    >>> row = np.array([0, 2, 2, 0, 1, 2])
+    >>> col = np.array([0, 0, 1, 2, 2, 2])
+    >>> data = np.array([1, 2, 3, 4, 5, 6])
+    >>> csc_matrix((data, (row, col)), shape=(3, 3)).toarray()
+    array([[1, 0, 4],
+           [0, 0, 5],
+           [2, 3, 6]])
+
+    >>> indptr = np.array([0, 2, 3, 6])
+    >>> indices = np.array([0, 2, 2, 0, 1, 2])
+    >>> data = np.array([1, 2, 3, 4, 5, 6])
+    >>> csc_matrix((data, indices, indptr), shape=(3, 3)).toarray()
+    array([[1, 0, 4],
+           [0, 0, 5],
+           [2, 3, 6]])
+
+    """
+
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/_csparsetools.cpython-312-x86_64-linux-gnu.so b/venv/lib/python3.12/site-packages/scipy/sparse/_csparsetools.cpython-312-x86_64-linux-gnu.so
new file mode 100644
index 0000000000000000000000000000000000000000..910b4ba1d676077c68b7cc68f9cf46b657cd0bfb
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/_csparsetools.cpython-312-x86_64-linux-gnu.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b7ca396a0686f87c2767e5bbeddf2eb5d6d40894d0283774584aed7cde87b19d
+size 441808
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/_csr.py b/venv/lib/python3.12/site-packages/scipy/sparse/_csr.py
new file mode 100644
index 0000000000000000000000000000000000000000..fd1e6ac6d2c8ecab7ed000e1f527dc317bb0a3a8
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/_csr.py
@@ -0,0 +1,604 @@
+"""Compressed Sparse Row matrix format"""
+
+__docformat__ = "restructuredtext en"
+
+__all__ = ['csr_array', 'csr_matrix', 'isspmatrix_csr']
+
+import numpy as np
+
+from ._matrix import spmatrix
+from ._base import _spbase, sparray
+from ._sparsetools import (csr_tocsc, csr_tobsr, csr_count_blocks,
+                           get_csr_submatrix, csr_sample_values)
+from ._sputils import upcast
+
+from ._compressed import _cs_matrix
+
+
+class _csr_base(_cs_matrix):
+    _format = 'csr'
+    _allow_nd = (1, 2)
+
+    def transpose(self, axes=None, copy=False):
+        if axes is not None and axes != (1, 0):
+            raise ValueError("Sparse arrays/matrices do not support "
+                              "an 'axes' parameter because swapping "
+                              "dimensions is the only logical permutation.")
+
+        if self.ndim == 1:
+            return self.copy() if copy else self
+        M, N = self.shape
+        return self._csc_container((self.data, self.indices,
+                                    self.indptr), shape=(N, M), copy=copy)
+
+    transpose.__doc__ = _spbase.transpose.__doc__
+
+    def tolil(self, copy=False):
+        if self.ndim != 2:
+            raise ValueError("Cannot convert a 1d sparse array to lil format")
+        lil = self._lil_container(self.shape, dtype=self.dtype)
+
+        self.sum_duplicates()
+        ptr,ind,dat = self.indptr,self.indices,self.data
+        rows, data = lil.rows, lil.data
+
+        for n in range(self.shape[0]):
+            start = ptr[n]
+            end = ptr[n+1]
+            rows[n] = ind[start:end].tolist()
+            data[n] = dat[start:end].tolist()
+
+        return lil
+
+    tolil.__doc__ = _spbase.tolil.__doc__
+
+    def tocsr(self, copy=False):
+        if copy:
+            return self.copy()
+        else:
+            return self
+
+    tocsr.__doc__ = _spbase.tocsr.__doc__
+
+    def tocoo(self, copy=False):
+        A = super().tocoo(copy=copy)
+        # CSR-to-COO conversion always preserves [non-]canonicity
+        # (indices sorting, presense of duplicate elements).
+        # Handled here instead of _cs_matrix because CSC-to-COO generally does not.
+        A.has_canonical_format = self.has_canonical_format
+        return A
+
+    tocoo.__doc__ = _spbase.tocoo.__doc__
+
+    def tocsc(self, copy=False):
+        if self.ndim != 2:
+            raise ValueError("Cannot convert a 1d sparse array to csc format")
+        M, N = self.shape
+        idx_dtype = self._get_index_dtype((self.indptr, self.indices),
+                                    maxval=max(self.nnz, M))
+        indptr = np.empty(N + 1, dtype=idx_dtype)
+        indices = np.empty(self.nnz, dtype=idx_dtype)
+        data = np.empty(self.nnz, dtype=upcast(self.dtype))
+
+        csr_tocsc(M, N,
+                  self.indptr.astype(idx_dtype, copy=False),
+                  self.indices.astype(idx_dtype, copy=False),
+                  self.data,
+                  indptr,
+                  indices,
+                  data)
+
+        A = self._csc_container((data, indices, indptr), shape=self.shape)
+        A.has_sorted_indices = True
+        return A
+
+    tocsc.__doc__ = _spbase.tocsc.__doc__
+
+    def tobsr(self, blocksize=None, copy=True):
+        if self.ndim != 2:
+            raise ValueError("Cannot convert a 1d sparse array to bsr format")
+        if blocksize is None:
+            from ._spfuncs import estimate_blocksize
+            return self.tobsr(blocksize=estimate_blocksize(self))
+
+        elif blocksize == (1,1):
+            arg1 = (self.data.reshape(-1,1,1),self.indices,self.indptr)
+            return self._bsr_container(arg1, shape=self.shape, copy=copy)
+
+        else:
+            R,C = blocksize
+            M,N = self.shape
+
+            if R < 1 or C < 1 or M % R != 0 or N % C != 0:
+                raise ValueError(f'invalid blocksize {blocksize}')
+
+            blks = csr_count_blocks(M,N,R,C,self.indptr,self.indices)
+
+            idx_dtype = self._get_index_dtype((self.indptr, self.indices),
+                                        maxval=max(N//C, blks))
+            indptr = np.empty(M//R+1, dtype=idx_dtype)
+            indices = np.empty(blks, dtype=idx_dtype)
+            data = np.zeros((blks,R,C), dtype=self.dtype)
+
+            csr_tobsr(M, N, R, C,
+                      self.indptr.astype(idx_dtype, copy=False),
+                      self.indices.astype(idx_dtype, copy=False),
+                      self.data,
+                      indptr, indices, data.ravel())
+
+            return self._bsr_container(
+                (data, indices, indptr), shape=self.shape
+            )
+
+    tobsr.__doc__ = _spbase.tobsr.__doc__
+
+    # these functions are used by the parent class (_cs_matrix)
+    # to remove redundancy between csc_matrix and csr_array
+    @staticmethod
+    def _swap(x):
+        """swap the members of x if this is a column-oriented matrix
+        """
+        return x
+
+    def __iter__(self):
+        if self.ndim == 1:
+            zero = self.dtype.type(0)
+            u = 0
+            for v, d in zip(self.indices, self.data):
+                for _ in range(v - u):
+                    yield zero
+                yield d
+                u = v + 1
+            for _ in range(self.shape[0] - u):
+                yield zero
+            return
+
+        indptr = np.zeros(2, dtype=self.indptr.dtype)
+        # return 1d (sparray) or 2drow (spmatrix)
+        shape = self.shape[1:] if isinstance(self, sparray) else (1, self.shape[1])
+        i0 = 0
+        for i1 in self.indptr[1:]:
+            indptr[1] = i1 - i0
+            indices = self.indices[i0:i1]
+            data = self.data[i0:i1]
+            yield self.__class__((data, indices, indptr), shape=shape, copy=True)
+            i0 = i1
+
+    def _getrow(self, i):
+        """Returns a copy of row i of the matrix, as a (1 x n)
+        CSR matrix (row vector).
+        """
+        if self.ndim == 1:
+            if i not in (0, -1):
+                raise IndexError(f'index ({i}) out of range')
+            return self.reshape((1, self.shape[0]), copy=True)
+
+        M, N = self.shape
+        i = int(i)
+        if i < 0:
+            i += M
+        if i < 0 or i >= M:
+            raise IndexError(f'index ({i}) out of range')
+        indptr, indices, data = get_csr_submatrix(
+            M, N, self.indptr, self.indices, self.data, i, i + 1, 0, N)
+        return self.__class__((data, indices, indptr), shape=(1, N),
+                              dtype=self.dtype, copy=False)
+
+    def _getcol(self, i):
+        """Returns a copy of column i. A (m x 1) sparse array (column vector).
+        """
+        if self.ndim == 1:
+            raise ValueError("getcol not provided for 1d arrays. Use indexing A[j]")
+        M, N = self.shape
+        i = int(i)
+        if i < 0:
+            i += N
+        if i < 0 or i >= N:
+            raise IndexError(f'index ({i}) out of range')
+        indptr, indices, data = get_csr_submatrix(
+            M, N, self.indptr, self.indices, self.data, 0, M, i, i + 1)
+        return self.__class__((data, indices, indptr), shape=(M, 1),
+                              dtype=self.dtype, copy=False)
+
+    def _get_int(self, idx):
+        spot = np.flatnonzero(self.indices == idx)
+        if spot.size:
+            return self.data[spot[0]]
+        return self.data.dtype.type(0)
+
+    def _get_slice(self, idx):
+        if idx == slice(None):
+            return self.copy()
+        if idx.step in (1, None):
+            ret = self._get_submatrix(0, idx, copy=True)
+            return ret.reshape(ret.shape[-1])
+        return self._minor_slice(idx)
+
+    def _get_array(self, idx):
+        idx_dtype = self._get_index_dtype(self.indices)
+        idx = np.asarray(idx, dtype=idx_dtype)
+        if idx.size == 0:
+            return self.__class__([], dtype=self.dtype)
+
+        M, N = 1, self.shape[0]
+        row = np.zeros_like(idx, dtype=idx_dtype)
+        col = np.asarray(idx, dtype=idx_dtype)
+        val = np.empty(row.size, dtype=self.dtype)
+        csr_sample_values(M, N, self.indptr, self.indices, self.data,
+                          row.size, row, col, val)
+
+        new_shape = col.shape if col.shape[0] > 1 else (col.shape[0],)
+        return self.__class__(val.reshape(new_shape))
+
+    def _get_intXarray(self, row, col):
+        return self._getrow(row)._minor_index_fancy(col)
+
+    def _get_intXslice(self, row, col):
+        if col.step in (1, None):
+            return self._get_submatrix(row, col, copy=True)
+        # TODO: uncomment this once it's faster:
+        # return self._getrow(row)._minor_slice(col)
+
+        M, N = self.shape
+        start, stop, stride = col.indices(N)
+
+        ii, jj = self.indptr[row:row+2]
+        row_indices = self.indices[ii:jj]
+        row_data = self.data[ii:jj]
+
+        if stride > 0:
+            ind = (row_indices >= start) & (row_indices < stop)
+        else:
+            ind = (row_indices <= start) & (row_indices > stop)
+
+        if abs(stride) > 1:
+            ind &= (row_indices - start) % stride == 0
+
+        row_indices = (row_indices[ind] - start) // stride
+        row_data = row_data[ind]
+        row_indptr = np.array([0, len(row_indices)])
+
+        if stride < 0:
+            row_data = row_data[::-1]
+            row_indices = abs(row_indices[::-1])
+
+        shape = (1, max(0, int(np.ceil(float(stop - start) / stride))))
+        return self.__class__((row_data, row_indices, row_indptr), shape=shape,
+                              dtype=self.dtype, copy=False)
+
+    def _get_sliceXint(self, row, col):
+        if row.step in (1, None):
+            return self._get_submatrix(row, col, copy=True)
+        return self._major_slice(row)._get_submatrix(minor=col)
+
+    def _get_sliceXarray(self, row, col):
+        return self._major_slice(row)._minor_index_fancy(col)
+
+    def _get_arrayXint(self, row, col):
+        res = self._major_index_fancy(row)._get_submatrix(minor=col)
+        if row.ndim > 1:
+            return res.reshape(row.shape)
+        return res
+
+    def _get_arrayXslice(self, row, col):
+        if col.step not in (1, None):
+            col = np.arange(*col.indices(self.shape[1]))
+            return self._get_arrayXarray(row, col)
+        return self._major_index_fancy(row)._get_submatrix(minor=col)
+
+    def _set_int(self, idx, x):
+        self._set_many(0, idx, x)
+
+    def _set_array(self, idx, x):
+        x = np.broadcast_to(x, idx.shape)
+        self._set_many(np.zeros_like(idx), idx, x)
+
+
+def isspmatrix_csr(x):
+    """Is `x` of csr_matrix type?
+
+    .. warning::
+
+       SciPy sparse is shifting from a sparse matrix interface to a sparse
+       array interface. In the next few releases we expect to deprecate the
+       sparse matrix interface. For documentation of the matrix
+       interface, see the :ref:`spmatrix interface docs <spmatrix_api>`.
+       For guidance on converting existing code to sparse arrays, see
+       :ref:`Migration from spmatrix to sparray <migration_to_sparray>`.
+
+    Parameters
+    ----------
+    x
+        object to check for being a csr matrix
+
+    Returns
+    -------
+    bool
+        True if `x` is a csr matrix, False otherwise
+
+    Examples
+    --------
+    >>> from scipy.sparse import csr_array, csr_matrix, coo_matrix, isspmatrix_csr
+    >>> isspmatrix_csr(csr_matrix([[5]]))
+    True
+    >>> isspmatrix_csr(csr_array([[5]]))
+    False
+    >>> isspmatrix_csr(coo_matrix([[5]]))
+    False
+    """
+    return isinstance(x, csr_matrix)
+
+
+# This namespace class separates array from matrix with isinstance
+class csr_array(_csr_base, sparray):
+    """
+    Compressed Sparse Row array.
+
+    This can be instantiated in several ways:
+        csr_array(D)
+            where D is a 2-D ndarray
+
+        csr_array(S)
+            with another sparse array or matrix S (equivalent to S.tocsr())
+
+        csr_array((M, N), [dtype])
+            to construct an empty array with shape (M, N)
+            dtype is optional, defaulting to dtype='d'.
+
+        csr_array((data, (row_ind, col_ind)), [shape=(M, N)])
+            where ``data``, ``row_ind`` and ``col_ind`` satisfy the
+            relationship ``a[row_ind[k], col_ind[k]] = data[k]``.
+
+        csr_array((data, indices, indptr), [shape=(M, N)])
+            is the standard CSR representation where the column indices for
+            row i are stored in ``indices[indptr[i]:indptr[i+1]]`` and their
+            corresponding values are stored in ``data[indptr[i]:indptr[i+1]]``.
+            If the shape parameter is not supplied, the array dimensions
+            are inferred from the index arrays.
+
+    Attributes
+    ----------
+    data : ndarray
+        CSR format data array of the array
+    indices : ndarray
+        CSR format index array of the array
+    indptr : ndarray
+        CSR format index pointer array of the array
+    has_sorted_indices : bool
+        Whether indices are sorted
+    has_canonical_format : bool
+        Whether indices are sorted and no duplicate entries exist
+    dtype : dtype
+        Data type of the array
+    shape : 2-tuple
+        Shape of the array
+    ndim : int
+        Number of dimensions (this is always 2)
+    format : str
+        Three letter code for the format of the array storage, e.g. 'csr'
+    nnz : int
+        Number of values stored in the array
+    size : int
+        Number of values stored in the array
+    T : csr_array
+        The transpose of the array
+    mT : csr_array
+        The matrix transpose of the array
+
+    Notes
+    -----
+
+    Sparse arrays can be used in arithmetic operations: they support
+    addition, subtraction, multiplication, division, and matrix power.
+
+    Advantages of the CSR format
+      - efficient arithmetic operations CSR + CSR, CSR * CSR, etc.
+      - efficient row slicing
+      - fast matrix vector products
+
+    Disadvantages of the CSR format
+      - slow column slicing operations (consider CSC)
+      - changes to the sparsity structure are expensive (consider LIL or DOK)
+
+    Canonical Format
+        - Within each row, indices are sorted by column.
+        - There are no duplicate entries.
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> from scipy.sparse import csr_array
+    >>> csr_array((3, 4), dtype=np.int8).toarray()
+    array([[0, 0, 0, 0],
+           [0, 0, 0, 0],
+           [0, 0, 0, 0]], dtype=int8)
+
+    >>> row = np.array([0, 0, 1, 2, 2, 2])
+    >>> col = np.array([0, 2, 2, 0, 1, 2])
+    >>> data = np.array([1, 2, 3, 4, 5, 6])
+    >>> csr_array((data, (row, col)), shape=(3, 3)).toarray()
+    array([[1, 0, 2],
+           [0, 0, 3],
+           [4, 5, 6]])
+
+    >>> indptr = np.array([0, 2, 3, 6])
+    >>> indices = np.array([0, 2, 2, 0, 1, 2])
+    >>> data = np.array([1, 2, 3, 4, 5, 6])
+    >>> csr_array((data, indices, indptr), shape=(3, 3)).toarray()
+    array([[1, 0, 2],
+           [0, 0, 3],
+           [4, 5, 6]])
+
+    Duplicate entries are summed together:
+
+    >>> row = np.array([0, 1, 2, 0])
+    >>> col = np.array([0, 1, 1, 0])
+    >>> data = np.array([1, 2, 4, 8])
+    >>> csr_array((data, (row, col)), shape=(3, 3)).toarray()
+    array([[9, 0, 0],
+           [0, 2, 0],
+           [0, 4, 0]])
+
+    As an example of how to construct a CSR array incrementally,
+    the following snippet builds a term-document array from texts:
+
+    >>> docs = [["hello", "world", "hello"], ["goodbye", "cruel", "world"]]
+    >>> indptr = [0]
+    >>> indices = []
+    >>> data = []
+    >>> vocabulary = {}
+    >>> for d in docs:
+    ...     for term in d:
+    ...         index = vocabulary.setdefault(term, len(vocabulary))
+    ...         indices.append(index)
+    ...         data.append(1)
+    ...     indptr.append(len(indices))
+    ...
+    >>> csr_array((data, indices, indptr), dtype=int).toarray()
+    array([[2, 1, 0, 0],
+           [0, 1, 1, 1]])
+
+    """  # numpydoc ignore=PR01
+
+
+class csr_matrix(spmatrix, _csr_base):
+    """
+    Compressed Sparse Row matrix.
+
+    .. warning::
+
+       SciPy sparse is shifting from a sparse matrix interface to a sparse
+       array interface. In the next few releases we expect to deprecate the
+       sparse matrix interface. For documentation of the matrix
+       interface, see the :ref:`spmatrix interface docs <spmatrix_api>`.
+       For guidance on converting existing code to sparse arrays, see
+       :ref:`Migration from spmatrix to sparray <migration_to_sparray>`.
+
+    This can be instantiated in several ways:
+        csr_matrix(D)
+            where D is a 2-D ndarray
+
+        csr_matrix(S)
+            with another sparse array or matrix S (equivalent to S.tocsr())
+
+        csr_matrix((M, N), [dtype])
+            to construct an empty matrix with shape (M, N)
+            dtype is optional, defaulting to dtype='d'.
+
+        csr_matrix((data, (row_ind, col_ind)), [shape=(M, N)])
+            where ``data``, ``row_ind`` and ``col_ind`` satisfy the
+            relationship ``a[row_ind[k], col_ind[k]] = data[k]``.
+
+        csr_matrix((data, indices, indptr), [shape=(M, N)])
+            is the standard CSR representation where the column indices for
+            row i are stored in ``indices[indptr[i]:indptr[i+1]]`` and their
+            corresponding values are stored in ``data[indptr[i]:indptr[i+1]]``.
+            If the shape parameter is not supplied, the matrix dimensions
+            are inferred from the index arrays.
+
+    Attributes
+    ----------
+    data : ndarray
+        CSR format data array of the matrix
+    indices : ndarray
+        CSR format index array of the matrix
+    indptr : ndarray
+        CSR format index pointer array of the matrix
+    has_sorted_indices : bool
+        Whether indices are sorted
+    has_canonical_format : bool
+        Whether indices are sorted and no duplicate entries exist
+    dtype : dtype
+        Data type of the matrix
+    shape : 2-tuple
+        Shape of the matrix
+    ndim : int
+        Number of dimensions (this is always 2)
+    format : str
+        Three letter code for the format of the matrix storage, e.g. 'csr'
+    nnz : int
+        Number of values stored in the matrix
+    size : int
+        Number of values stored in the matrix
+    T : csr_matrix
+        The transpose of the matrix
+    mT : csr_matrix
+        The matrix transpose
+
+    Notes
+    -----
+
+    Sparse matrices can be used in arithmetic operations: they support
+    addition, subtraction, multiplication, division, and matrix power.
+
+    Advantages of the CSR format
+      - efficient arithmetic operations CSR + CSR, CSR * CSR, etc.
+      - efficient row slicing
+      - fast matrix vector products
+
+    Disadvantages of the CSR format
+      - slow column slicing operations (consider CSC)
+      - changes to the sparsity structure are expensive (consider LIL or DOK)
+
+    Canonical Format
+        - Within each row, indices are sorted by column.
+        - There are no duplicate entries.
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> from scipy.sparse import csr_matrix
+    >>> csr_matrix((3, 4), dtype=np.int8).toarray()
+    array([[0, 0, 0, 0],
+           [0, 0, 0, 0],
+           [0, 0, 0, 0]], dtype=int8)
+
+    >>> row = np.array([0, 0, 1, 2, 2, 2])
+    >>> col = np.array([0, 2, 2, 0, 1, 2])
+    >>> data = np.array([1, 2, 3, 4, 5, 6])
+    >>> csr_matrix((data, (row, col)), shape=(3, 3)).toarray()
+    array([[1, 0, 2],
+           [0, 0, 3],
+           [4, 5, 6]])
+
+    >>> indptr = np.array([0, 2, 3, 6])
+    >>> indices = np.array([0, 2, 2, 0, 1, 2])
+    >>> data = np.array([1, 2, 3, 4, 5, 6])
+    >>> csr_matrix((data, indices, indptr), shape=(3, 3)).toarray()
+    array([[1, 0, 2],
+           [0, 0, 3],
+           [4, 5, 6]])
+
+    Duplicate entries are summed together:
+
+    >>> row = np.array([0, 1, 2, 0])
+    >>> col = np.array([0, 1, 1, 0])
+    >>> data = np.array([1, 2, 4, 8])
+    >>> csr_matrix((data, (row, col)), shape=(3, 3)).toarray()
+    array([[9, 0, 0],
+           [0, 2, 0],
+           [0, 4, 0]])
+
+    As an example of how to construct a CSR matrix incrementally,
+    the following snippet builds a term-document matrix from texts:
+
+    >>> docs = [["hello", "world", "hello"], ["goodbye", "cruel", "world"]]
+    >>> indptr = [0]
+    >>> indices = []
+    >>> data = []
+    >>> vocabulary = {}
+    >>> for d in docs:
+    ...     for term in d:
+    ...         index = vocabulary.setdefault(term, len(vocabulary))
+    ...         indices.append(index)
+    ...         data.append(1)
+    ...     indptr.append(len(indices))
+    ...
+    >>> csr_matrix((data, indices, indptr), dtype=int).toarray()
+    array([[2, 1, 0, 0],
+           [0, 1, 1, 1]])
+
+    """
+
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/_data.py b/venv/lib/python3.12/site-packages/scipy/sparse/_data.py
new file mode 100644
index 0000000000000000000000000000000000000000..0edea989fee4ab800303550e3772d239dfec616a
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/_data.py
@@ -0,0 +1,583 @@
+"""Base class for sparse matrice with a .data attribute
+
+    subclasses must provide a _with_data() method that
+    creates a new matrix with the same sparsity pattern
+    as self but with a different data array
+
+"""
+
+import math
+import numpy as np
+
+from ._base import _spbase, sparray, _ufuncs_with_fixed_point_at_zero
+from ._sputils import isscalarlike, validateaxis
+
+__all__ = []
+
+
+# TODO implement all relevant operations
+# use .data.__methods__() instead of /=, *=, etc.
+class _data_matrix(_spbase):
+    def __init__(self, arg1, *, maxprint=None):
+        _spbase.__init__(self, arg1, maxprint=maxprint)
+
+    @property
+    def dtype(self):
+        return self.data.dtype
+
+    @dtype.setter
+    def dtype(self, newtype):
+        self.data = self.data.view(newtype)
+
+    def _deduped_data(self):
+        if hasattr(self, 'sum_duplicates'):
+            self.sum_duplicates()
+        return self.data
+
+    def __abs__(self):
+        return self._with_data(abs(self._deduped_data()))
+
+    def __round__(self, ndigits=0):
+        return self._with_data(np.around(self._deduped_data(), decimals=ndigits))
+
+    def _real(self):
+        return self._with_data(self.data.real)
+
+    def _imag(self):
+        return self._with_data(self.data.imag)
+
+    def __neg__(self):
+        if self.dtype.kind == 'b':
+            raise NotImplementedError('negating a boolean sparse array is not '
+                                      'supported')
+        return self._with_data(-self.data)
+
+    def __imul__(self, other):  # self *= other
+        if isscalarlike(other):
+            self.data *= other
+            return self
+        return NotImplemented
+
+    def __itruediv__(self, other):  # self /= other
+        if isscalarlike(other):
+            recip = 1.0 / other
+            self.data *= recip
+            return self
+        else:
+            return NotImplemented
+
+    def astype(self, dtype, casting='unsafe', copy=True):
+        dtype = np.dtype(dtype)
+        if self.dtype != dtype:
+            matrix = self._with_data(
+                self.data.astype(dtype, casting=casting, copy=True),
+                copy=True
+            )
+            return matrix._with_data(matrix._deduped_data(), copy=False)
+        elif copy:
+            return self.copy()
+        else:
+            return self
+
+    astype.__doc__ = _spbase.astype.__doc__
+
+    def conjugate(self, copy=True):
+        if np.issubdtype(self.dtype, np.complexfloating):
+            return self._with_data(self.data.conjugate(), copy=copy)
+        elif copy:
+            return self.copy()
+        else:
+            return self
+
+    conjugate.__doc__ = _spbase.conjugate.__doc__
+
+    def copy(self):
+        return self._with_data(self.data.copy(), copy=True)
+
+    copy.__doc__ = _spbase.copy.__doc__
+
+    def power(self, n, dtype=None):
+        """
+        This function performs element-wise power.
+
+        Parameters
+        ----------
+        n : scalar
+            n is a non-zero scalar (nonzero avoids dense ones creation)
+            If zero power is desired, special case it to use `numpy.ones`
+
+        dtype : dtype, optional
+            If dtype is not specified, the current dtype will be preserved.
+
+        Returns
+        -------
+        sparse array/matrix
+            Result of raising all elements to the power `n`.
+
+        Raises
+        ------
+        NotImplementedError : if n is a zero scalar
+            If zero power is desired, special case it to use
+            ``np.ones(A.shape, dtype=A.dtype)``
+        """
+        if not isscalarlike(n):
+            raise NotImplementedError("input is not scalar")
+        if not n:
+            raise NotImplementedError(
+                "zero power is not supported as it would densify the matrix.\n"
+                "Use `np.ones(A.shape, dtype=A.dtype)` for this case."
+            )
+
+        data = self._deduped_data()
+        if dtype is not None:
+            data = data.astype(dtype, copy=False)
+        return self._with_data(data ** n)
+
+    ###########################
+    # Multiplication handlers #
+    ###########################
+
+    def _mul_scalar(self, other):
+        return self._with_data(self.data * other)
+
+
+# Add the numpy unary ufuncs for which func(0) = 0 to _data_matrix.
+for npfunc in _ufuncs_with_fixed_point_at_zero:
+    name = npfunc.__name__
+
+    def _create_method(op):
+        def method(self):
+            result = op(self._deduped_data())
+            return self._with_data(result, copy=True)
+
+        method.__doc__ = (
+            f"""Element-wise {name}.
+                See `numpy.{name}` for more information.
+
+                Returns
+                -------
+                {name} : sparse array / matrix
+                    Result of applying `numpy.{name}` to the data of this sparse matrix.
+            """
+        )
+        method.__name__ = name
+
+        return method
+
+    setattr(_data_matrix, name, _create_method(npfunc))
+
+
+def _find_missing_index(ind, n):
+    for k, a in enumerate(ind):
+        if k != a:
+            return k
+
+    k += 1
+    if k < n:
+        return k
+    else:
+        return -1
+
+
+class _minmax_mixin:
+    """Mixin for min and max methods.
+
+    These are not implemented for dia_matrix, hence the separate class.
+    """
+
+    def _min_or_max_axis(self, axis, min_or_max, explicit):
+        # already checked that self.shape[axis] is not zero
+        N = self.shape[axis]
+        M = self.shape[1 - axis]
+        idx_dtype = self._get_index_dtype(maxval=M)
+
+        mat = self.tocsc() if axis == 0 else self.tocsr()
+        mat.sum_duplicates()
+
+        major_index, value = mat._minor_reduce(min_or_max)
+        if not explicit:
+            not_full = np.diff(mat.indptr)[major_index] < N
+            value[not_full] = min_or_max(value[not_full], 0)
+
+        mask = value != 0
+        major_index = np.compress(mask, major_index).astype(idx_dtype, copy=False)
+        value = np.compress(mask, value)
+
+        if isinstance(self, sparray):
+            coords = (major_index,)
+            shape = (M,)
+            return self._coo_container((value, coords), shape=shape, dtype=self.dtype)
+
+        if axis == 0:
+            return self._coo_container(
+                (value, (np.zeros(len(value), dtype=idx_dtype), major_index)),
+                dtype=self.dtype, shape=(1, M)
+            )
+        else:
+            return self._coo_container(
+                (value, (major_index, np.zeros(len(value), dtype=idx_dtype))),
+                dtype=self.dtype, shape=(M, 1)
+            )
+
+    def _min_or_max(self, axis, out, min_or_max, explicit):
+        if out is not None:
+            raise ValueError("Sparse min/max does not support an 'out' parameter.")
+
+        axis = validateaxis(axis, ndim=self.ndim)
+
+        if axis is None:
+            if 0 in self.shape:
+                raise ValueError("zero-size array to reduction operation")
+
+            zero = self.dtype.type(0)
+            if self.nnz == 0:
+                return zero
+            m = min_or_max.reduce(self._deduped_data().ravel())
+            if self.nnz != math.prod(self.shape) and not explicit:
+                m = min_or_max(zero, m)
+            return m
+
+        if any(self.shape[d] == 0 for d in axis):
+            raise ValueError("zero-size array to reduction operation")
+
+        if self.ndim == 2:
+            # note: 2D ensures that len(axis)==1 so we pass in the int axis[0]
+            return self._min_or_max_axis(axis[0], min_or_max, explicit)
+        return self._min_or_max_axis_nd(axis, min_or_max, explicit)
+
+    def _argminmax_axis(self, axis, argminmax, compare, explicit):
+        zero = self.dtype.type(0)
+
+        mat = self.tocsc() if axis == 0 else self.tocsr()
+        mat.sum_duplicates()
+
+        ret_size, line_size = mat._swap(mat.shape)
+        ret = np.zeros(ret_size, dtype=int)
+
+        nz_lines, = np.nonzero(np.diff(mat.indptr))
+        for i in nz_lines:
+            p, q = mat.indptr[i:i + 2]
+            data = mat.data[p:q]
+            indices = mat.indices[p:q]
+            extreme_index = argminmax(data)
+            extreme_value = data[extreme_index]
+            if explicit:
+                if q - p > 0:
+                    ret[i] = indices[extreme_index]
+            else:
+                if compare(extreme_value, zero) or q - p == line_size:
+                    ret[i] = indices[extreme_index]
+                else:
+                    zero_ind = _find_missing_index(indices, line_size)
+                    if extreme_value == zero:
+                        ret[i] = min(extreme_index, zero_ind)
+                    else:
+                        ret[i] = zero_ind
+
+        if isinstance(self, sparray):
+            return ret
+
+        if axis == 1:
+            ret = ret.reshape(-1, 1)
+
+        return self._ascontainer(ret)
+
+    def _argminmax(self, axis, out, argminmax, compare, explicit):
+        if out is not None:
+            minmax = "argmin" if argminmax == np.argmin else "argmax"
+            raise ValueError(f"Sparse {minmax} does not support an 'out' parameter.")
+
+        axis = validateaxis(axis, ndim=self.ndim)
+
+        if axis is not None:
+            if any(self.shape[i] == 0 for i in axis):
+                minmax = "argmin" if argminmax == np.argmin else "argmax"
+                raise ValueError(f"Cannot apply {minmax} along a zero-sized dimension.")
+
+            if self.ndim == 2:
+                # note: 2D ensures that len(axis)==1 so we pass in the int axis[0]
+                return self._argminmax_axis(axis[0], argminmax, compare, explicit)
+            return self._argminmax_axis_nd(axis, argminmax, compare, explicit)
+
+        if 0 in self.shape:
+            minmax = "argmin" if argminmax == np.argmin else "argmax"
+            raise ValueError(f"Cannot apply {minmax} to an empty matrix.")
+
+        if self.nnz == 0:
+            if explicit:
+                minmax = "argmin" if argminmax == np.argmin else "argmax"
+                raise ValueError(f"Cannot apply {minmax} to zero matrix "
+                                 "when explicit=True.")
+            return 0
+
+        zero = self.dtype.type(0)
+        mat = self.tocoo()
+        # Convert to canonical form: no duplicates, sorted indices.
+        mat.sum_duplicates()
+        extreme_index = argminmax(mat.data)
+        if explicit:
+            return extreme_index
+        extreme_value = mat.data[extreme_index]
+
+        if mat.ndim > 2:
+            mat = mat.reshape(-1)
+        # If the min value is less than zero, or max is greater than zero,
+        # then we do not need to worry about implicit zeros.
+        # And we use a "cheap test" for the rare case of no implicit zeros.
+        maxnnz = math.prod(self.shape)
+        if compare(extreme_value, zero) or mat.nnz == maxnnz:
+            # cast to Python int to avoid overflow and RuntimeError
+            if mat.ndim == 1:  # includes nD case that was reshaped above
+                return int(mat.col[extreme_index])
+            # ndim == 2
+            num_col = mat.shape[-1]
+            return int(mat.row[extreme_index]) * num_col + int(mat.col[extreme_index])
+
+        # At this stage, any implicit zero could be the min or max value.
+        # After sum_duplicates(), the `row` and `col` arrays are guaranteed to
+        # be sorted in C-order, which means the linearized indices are sorted.
+        if mat.ndim == 1:  # includes nD case that was reshaped above
+            linear_indices = mat.coords[-1]
+        else:  # ndim == 2
+            num_col = mat.shape[-1]
+            linear_indices = mat.row * num_col + mat.col
+        first_implicit_zero_index = _find_missing_index(linear_indices, maxnnz)
+        if extreme_value == zero:
+            return min(first_implicit_zero_index, extreme_index)
+        return first_implicit_zero_index
+
+    def max(self, axis=None, out=None, *, explicit=False):
+        """Return the maximum of the array/matrix or maximum along an axis.
+
+        By default, all elements are taken into account, not just the non-zero ones.
+        But with `explicit` set, only the stored elements are considered.
+
+        Parameters
+        ----------
+        axis : {-2, -1, 0, 1, None} optional
+            Axis along which the sum is computed. The default is to
+            compute the maximum over all elements, returning
+            a scalar (i.e., `axis` = `None`).
+
+        out : None, optional
+            This argument is in the signature *solely* for NumPy
+            compatibility reasons. Do not pass in anything except
+            for the default value, as this argument is not used.
+
+        explicit : {False, True} optional (default: False)
+            When set to True, only the stored elements will be considered.
+            If a row/column is empty, the sparse.coo_array returned
+            has no stored element (i.e. an implicit zero) for that row/column.
+
+            .. versionadded:: 1.15.0
+
+        Returns
+        -------
+        amax : coo_array or scalar
+            Maximum of `a`. If `axis` is None, the result is a scalar value.
+            If `axis` is given, the result is a sparse.coo_array of dimension
+            ``a.ndim - 1``.
+
+        See Also
+        --------
+        min : The minimum value of a sparse array/matrix along a given axis.
+        numpy.max : NumPy's implementation of 'max'
+
+        """
+        return self._min_or_max(axis, out, np.maximum, explicit)
+
+    def min(self, axis=None, out=None, *, explicit=False):
+        """Return the minimum of the array/matrix or maximum along an axis.
+
+        By default, all elements are taken into account, not just the non-zero ones.
+        But with `explicit` set, only the stored elements are considered.
+
+        Parameters
+        ----------
+        axis : {-2, -1, 0, 1, None} optional
+            Axis along which the sum is computed. The default is to
+            compute the minimum over all elements, returning
+            a scalar (i.e., `axis` = `None`).
+
+        out : None, optional
+            This argument is in the signature *solely* for NumPy
+            compatibility reasons. Do not pass in anything except for
+            the default value, as this argument is not used.
+
+        explicit : {False, True} optional (default: False)
+            When set to True, only the stored elements will be considered.
+            If a row/column is empty, the sparse.coo_array returned
+            has no stored element (i.e. an implicit zero) for that row/column.
+
+            .. versionadded:: 1.15.0
+
+        Returns
+        -------
+        amin : coo_matrix or scalar
+            Minimum of `a`. If `axis` is None, the result is a scalar value.
+            If `axis` is given, the result is a sparse.coo_array of dimension
+            ``a.ndim - 1``.
+
+        See Also
+        --------
+        max : The maximum value of a sparse array/matrix along a given axis.
+        numpy.min : NumPy's implementation of 'min'
+
+        """
+        return self._min_or_max(axis, out, np.minimum, explicit)
+
+    def nanmax(self, axis=None, out=None, *, explicit=False):
+        """Return the maximum, ignoring any Nans, along an axis.
+
+        Return the maximum, ignoring any Nans, of the array/matrix along an axis.
+        By default this takes all elements into account, but with `explicit` set,
+        only stored elements are considered.
+
+        .. versionadded:: 1.11.0
+
+        Parameters
+        ----------
+        axis : {-2, -1, 0, 1, None} optional
+            Axis along which the maximum is computed. The default is to
+            compute the maximum over all elements, returning
+            a scalar (i.e., `axis` = `None`).
+
+        out : None, optional
+            This argument is in the signature *solely* for NumPy
+            compatibility reasons. Do not pass in anything except
+            for the default value, as this argument is not used.
+
+        explicit : {False, True} optional (default: False)
+            When set to True, only the stored elements will be considered.
+            If a row/column is empty, the sparse.coo_array returned
+            has no stored element (i.e. an implicit zero) for that row/column.
+
+            .. versionadded:: 1.15.0
+
+        Returns
+        -------
+        amax : coo_array or scalar
+            Maximum of `a`. If `axis` is None, the result is a scalar value.
+            If `axis` is given, the result is a sparse.coo_array of dimension
+            ``a.ndim - 1``.
+
+        See Also
+        --------
+        nanmin : The minimum value of a sparse array/matrix along a given axis,
+                 ignoring NaNs.
+        max : The maximum value of a sparse array/matrix along a given axis,
+              propagating NaNs.
+        numpy.nanmax : NumPy's implementation of 'nanmax'.
+
+        """
+        return self._min_or_max(axis, out, np.fmax, explicit)
+
+    def nanmin(self, axis=None, out=None, *, explicit=False):
+        """Return the minimum, ignoring any Nans, along an axis.
+
+        Return the minimum, ignoring any Nans, of the array/matrix along an axis.
+        By default this takes all elements into account, but with `explicit` set,
+        only stored elements are considered.
+
+        .. versionadded:: 1.11.0
+
+        Parameters
+        ----------
+        axis : {-2, -1, 0, 1, None} optional
+            Axis along which the minimum is computed. The default is to
+            compute the minimum over all elements, returning
+            a scalar (i.e., `axis` = `None`).
+
+        out : None, optional
+            This argument is in the signature *solely* for NumPy
+            compatibility reasons. Do not pass in anything except for
+            the default value, as this argument is not used.
+
+        explicit : {False, True} optional (default: False)
+            When set to True, only the stored elements will be considered.
+            If a row/column is empty, the sparse.coo_array returned
+            has no stored element (i.e. an implicit zero) for that row/column.
+
+            .. versionadded:: 1.15.0
+
+        Returns
+        -------
+        amin : coo_array or scalar
+            Minimum of `a`. If `axis` is None, the result is a scalar value.
+            If `axis` is given, the result is a sparse.coo_array of dimension
+            ``a.ndim - 1``.
+
+        See Also
+        --------
+        nanmax : The maximum value of a sparse array/matrix along a given axis,
+                 ignoring NaNs.
+        min : The minimum value of a sparse array/matrix along a given axis,
+              propagating NaNs.
+        numpy.nanmin : NumPy's implementation of 'nanmin'.
+
+        """
+        return self._min_or_max(axis, out, np.fmin, explicit)
+
+    def argmax(self, axis=None, out=None, *, explicit=False):
+        """Return indices of maximum elements along an axis.
+
+        By default, implicit zero elements are taken into account. If there are
+        several minimum values, the index of the first occurrence is returned.
+        If `explicit` is set, only explicitly stored elements will be considered.
+
+        Parameters
+        ----------
+        axis : {-2, -1, 0, 1, None}, optional
+            Axis along which the argmax is computed. If None (default), index
+            of the maximum element in the flatten data is returned.
+
+        out : None, optional
+            This argument is in the signature *solely* for NumPy
+            compatibility reasons. Do not pass in anything except for
+            the default value, as this argument is not used.
+
+        explicit : {False, True} optional (default: False)
+            When set to True, only explicitly stored elements will be considered.
+            If axis is not None and an axis has no stored elements, argmax
+            is undefined, so the index ``0`` is returned for that row/column.
+
+            .. versionadded:: 1.15.0
+
+        Returns
+        -------
+        ind : numpy.matrix or int
+            Indices of maximum elements. If matrix, its size along `axis` is 1.
+        """
+        return self._argminmax(axis, out, np.argmax, np.greater, explicit)
+
+    def argmin(self, axis=None, out=None, *, explicit=False):
+        """Return indices of minimum elements along an axis.
+
+        By default, implicit zero elements are taken into account. If there are
+        several minimum values, the index of the first occurrence is returned.
+        If `explicit` is set, only explicitly stored elements will be considered.
+
+        Parameters
+        ----------
+        axis : {-2, -1, 0, 1, None}, optional
+            Axis along which the argmin is computed. If None (default), index
+            of the minimum element in the flatten data is returned.
+
+        out : None, optional
+            This argument is in the signature *solely* for NumPy
+            compatibility reasons. Do not pass in anything except for
+            the default value, as this argument is not used.
+
+        explicit : {False, True} optional (default: False)
+            When set to True, only explicitly stored elements will be considered.
+            If axis is not None and an axis has no stored elements, argmin
+            is undefined, so the index ``0`` is returned for that row/column.
+
+            .. versionadded:: 1.15.0
+
+        Returns
+        -------
+         ind : numpy.matrix or int
+            Indices of minimum elements. If matrix, its size along `axis` is 1.
+        """
+        return self._argminmax(axis, out, np.argmin, np.less, explicit)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/_dia.py b/venv/lib/python3.12/site-packages/scipy/sparse/_dia.py
new file mode 100644
index 0000000000000000000000000000000000000000..42fa23cddad8c18a6400d0b53e0784d35bb0ab47
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/_dia.py
@@ -0,0 +1,731 @@
+"""Sparse DIAgonal format"""
+
+__docformat__ = "restructuredtext en"
+
+__all__ = ['dia_array', 'dia_matrix', 'isspmatrix_dia']
+
+import numpy as np
+
+from .._lib._util import _prune_array, copy_if_needed
+from ._matrix import spmatrix
+from ._base import issparse, _formats, _spbase, sparray
+from ._data import _data_matrix
+from ._sputils import (
+    isdense, isscalarlike, isshape, upcast_char, getdtype, get_sum_dtype,
+    validateaxis, check_shape
+)
+from ._sparsetools import dia_matmat, dia_matvec, dia_matvecs, dia_tocsr
+
+
+class _dia_base(_data_matrix):
+    _format = 'dia'
+
+    def __init__(self, arg1, shape=None, dtype=None, copy=False, *, maxprint=None):
+        _data_matrix.__init__(self, arg1, maxprint=maxprint)
+
+        if issparse(arg1):
+            if arg1.format == "dia":
+                if copy:
+                    arg1 = arg1.copy()
+                self.data = arg1.data
+                self.offsets = arg1.offsets
+                self._shape = check_shape(arg1.shape)
+            else:
+                if arg1.format == self.format and copy:
+                    A = arg1.copy()
+                else:
+                    A = arg1.todia()
+                self.data = A.data
+                self.offsets = A.offsets
+                self._shape = check_shape(A.shape)
+        elif isinstance(arg1, tuple):
+            if isshape(arg1):
+                # It's a tuple of matrix dimensions (M, N)
+                # create empty matrix
+                self._shape = check_shape(arg1)
+                self.data = np.zeros((0,0), getdtype(dtype, default=float))
+                idx_dtype = self._get_index_dtype(maxval=max(self.shape))
+                self.offsets = np.zeros((0), dtype=idx_dtype)
+            else:
+                try:
+                    # Try interpreting it as (data, offsets)
+                    data, offsets = arg1
+                except Exception as e:
+                    message = 'unrecognized form for dia_array constructor'
+                    raise ValueError(message) from e
+                else:
+                    if shape is None:
+                        raise ValueError('expected a shape argument')
+                    if not copy:
+                        copy = copy_if_needed
+                    self.data = np.atleast_2d(np.array(arg1[0], dtype=dtype, copy=copy))
+                    offsets = np.array(arg1[1],
+                                       dtype=self._get_index_dtype(maxval=max(shape)),
+                                       copy=copy)
+                    self.offsets = np.atleast_1d(offsets)
+                    self._shape = check_shape(shape)
+        else:
+            # must be dense, convert to COO first, then to DIA
+            try:
+                arg1 = np.asarray(arg1)
+            except Exception as e:
+                raise ValueError("unrecognized form for "
+                                 f"{self.format}_matrix constructor") from e
+            if isinstance(self, sparray) and arg1.ndim != 2:
+                raise ValueError(f"DIA arrays don't support {arg1.ndim}D input. Use 2D")
+            A = self._coo_container(arg1, dtype=dtype, shape=shape).todia()
+            self.data = A.data
+            self.offsets = A.offsets
+            self._shape = check_shape(A.shape)
+
+        if dtype is not None:
+            newdtype = getdtype(dtype)
+            self.data = self.data.astype(newdtype, copy=False)
+
+        # check format
+        if self.offsets.ndim != 1:
+            raise ValueError('offsets array must have rank 1')
+
+        if self.data.ndim != 2:
+            raise ValueError('data array must have rank 2')
+
+        if self.data.shape[0] != len(self.offsets):
+            raise ValueError(
+                f'number of diagonals ({self.data.shape[0]}) does not match the number '
+                f'of offsets ({len(self.offsets)})'
+            )
+        if len(np.unique(self.offsets)) != len(self.offsets):
+            raise ValueError('offset array contains duplicate values')
+
+    def __repr__(self):
+        _, fmt = _formats[self.format]
+        sparse_cls = 'array' if isinstance(self, sparray) else 'matrix'
+        d = self.data.shape[0]
+        return (
+            f"<{fmt} sparse {sparse_cls} of dtype '{self.dtype}'\n"
+            f"\twith {self.nnz} stored elements ({d} diagonals) and shape {self.shape}>"
+        )
+
+    def _data_mask(self):
+        """Returns a mask of the same shape as self.data, where
+        mask[i,j] is True when data[i,j] corresponds to a stored element."""
+        num_rows, num_cols = self.shape
+        offset_inds = np.arange(self.data.shape[1])
+        row = offset_inds - self.offsets[:,None]
+        mask = (row >= 0)
+        mask &= (row < num_rows)
+        mask &= (offset_inds < num_cols)
+        return mask
+
+    def count_nonzero(self, axis=None):
+        if axis is not None:
+            raise NotImplementedError(
+                "count_nonzero over an axis is not implemented for DIA format"
+            )
+        mask = self._data_mask()
+        return np.count_nonzero(self.data[mask])
+
+    count_nonzero.__doc__ = _spbase.count_nonzero.__doc__
+
+    def _getnnz(self, axis=None):
+        if axis is not None:
+            raise NotImplementedError("_getnnz over an axis is not implemented "
+                                      "for DIA format")
+        M, N = self.shape
+        L = min(self.data.shape[1], N)
+        return int(np.maximum(np.minimum(M + self.offsets, L) -
+                              np.maximum(self.offsets, 0),
+                              0).sum())
+
+    _getnnz.__doc__ = _spbase._getnnz.__doc__
+
+    def sum(self, axis=None, dtype=None, out=None):
+        axis = validateaxis(axis)
+
+        res_dtype = dtype if dtype is not None else get_sum_dtype(self.dtype)
+        num_rows, num_cols = self.shape
+        ret = None
+
+        if axis == (0,):
+            mask = self._data_mask()
+            x = (self.data * mask).sum(dtype=res_dtype, axis=0)
+            if x.shape[0] == num_cols:
+                res = x
+            else:
+                res = np.zeros(num_cols, dtype=x.dtype)
+                res[:x.shape[0]] = x
+            ret = self._ascontainer(res, dtype=res_dtype)
+
+        else:  # axis is None or (1,)
+            row_sums = np.zeros((num_rows, 1), dtype=res_dtype)
+            one = np.ones(num_cols, dtype=res_dtype)
+            dia_matvec(num_rows, num_cols, len(self.offsets),
+                       self.data.shape[1], self.offsets, 
+                       self.data.astype(res_dtype), one, row_sums)
+
+            row_sums = self._ascontainer(row_sums)
+
+            if axis is None:
+                return row_sums.sum(dtype=dtype, out=out)
+
+            ret = self._ascontainer(row_sums.sum(axis=axis))
+
+        return ret.sum(axis=(), dtype=dtype, out=out)
+
+    sum.__doc__ = _spbase.sum.__doc__
+
+    def _add_sparse(self, other, sub=False):
+        # If other is not DIA format, let them handle us instead.
+        if not isinstance(other, _dia_base):
+            return other._add_sparse(self)
+
+        # Fast path for exact equality of the sparsity structure.
+        if np.array_equal(self.offsets, other.offsets):
+            return self._with_data(self.data - other.data if sub else
+                                   self.data + other.data)
+
+        # Find the union of the offsets (which will be sorted and unique).
+        new_offsets = np.union1d(self.offsets, other.offsets)
+        self_idx = np.searchsorted(new_offsets, self.offsets)
+        other_idx = np.searchsorted(new_offsets, other.offsets)
+
+        self_d = self.data.shape[1]
+        other_d = other.data.shape[1]
+        # Fast path for a sparsity structure where the final offsets are a
+        # permutation of the existing offsets and the diagonal lengths match.
+        if self_d == other_d and len(new_offsets) == len(self.offsets):
+            new_data = self.data[_invert_index(self_idx)]
+            if sub:
+                new_data[other_idx, :] -= other.data
+            else:
+                new_data[other_idx, :] += other.data
+        elif self_d == other_d and len(new_offsets) == len(other.offsets):
+            if sub:
+                new_data = -other.data[_invert_index(other_idx)]
+            else:
+                new_data = other.data[_invert_index(other_idx)]
+            new_data[self_idx, :] += self.data
+        else:
+            # Maximum diagonal length of the result.
+            d = min(self.shape[0] + new_offsets[-1], self.shape[1])
+
+            # Add all diagonals to a freshly allocated data array.
+            new_data = np.zeros(
+                (len(new_offsets), d),
+                dtype=np.result_type(self.data, other.data),
+            )
+            new_data[self_idx, :self_d] += self.data[:, :d]
+            if sub:
+                new_data[other_idx, :other_d] -= other.data[:, :d]
+            else:
+                new_data[other_idx, :other_d] += other.data[:, :d]
+        return self._dia_container((new_data, new_offsets), shape=self.shape)
+
+    def _sub_sparse(self, other):
+        # If other is not DIA format, use default handler.
+        if not isinstance(other, _dia_base):
+            return super()._sub_sparse(other)
+
+        return self._add_sparse(other, sub=True)
+
+    def _mul_scalar(self, other):
+        return self._with_data(self.data * other)
+
+    def multiply(self, other):
+        if isscalarlike(other):
+            return self._mul_scalar(other)
+
+        if isdense(other):
+            if other.ndim > 2:
+                return self.toarray() * other
+
+            # Use default handler for pathological cases.
+            if 0 in self.shape or 1 in self.shape or 0 in other.shape:
+                return super().multiply(other)
+
+            other = np.atleast_2d(other)
+            other_rows, other_cols = other.shape
+            rows, cols = self.shape
+            L = min(self.data.shape[1], cols)
+            data = self.data[:, :L].astype(np.result_type(self.data, other))  # copy
+            if other_rows == 1:
+                data *= other[0, :L]
+            elif other_rows != rows:
+                raise ValueError('inconsistent shapes')
+            else:
+                j = np.arange(L)
+                if L > rows:
+                    i = (j - self.offsets[:, None]) % rows
+                else:  # can use faster method
+                    i = j - self.offsets[:, None] % rows
+                if other_cols == 1:
+                    j = 0
+                elif other_cols != cols:
+                    raise ValueError('inconsistent shapes')
+                data *= other[i, j]
+            return self._with_data(data)
+
+        # If other is not DIA format or needs broadcasting (unreasonable
+        # use case for DIA anyway), use default handler.
+        if not isinstance(other, _dia_base) or other.shape != self.shape:
+            return super().multiply(other)
+
+        # Find common offsets (unique diagonals don't contribute)
+        # and indices corresponding to them in multiplicand and multiplier.
+        offsets, self_idx, other_idx = \
+            np.intersect1d(self.offsets, other.offsets,
+                           assume_unique=True, return_indices=True)
+        # Only overlapping length of diagonals can have non-zero products.
+        L = min(self.data.shape[1], other.data.shape[1])
+        data = self.data[self_idx, :L] * other.data[other_idx, :L]
+        return self._dia_container((data, offsets), shape=self.shape)
+
+    multiply.__doc__ = _data_matrix.multiply.__doc__
+
+    def _matmul_vector(self, other):
+        x = other
+
+        y = np.zeros(self.shape[0], dtype=upcast_char(self.dtype.char,
+                                                       x.dtype.char))
+
+        L = self.data.shape[1]
+
+        M,N = self.shape
+
+        dia_matvec(M,N, len(self.offsets), L, self.offsets, self.data,
+                   x.ravel(), y.ravel())
+
+        return y
+
+    def _matmul_multivector(self, other):
+        res = np.zeros((self.shape[0], other.shape[1]),
+                       dtype=np.result_type(self.data, other))
+        dia_matvecs(*self.shape, *self.data.shape, self.offsets, self.data,
+                    other.shape[1], other, res)
+        return res
+
+    def _matmul_sparse(self, other):
+        # If other is not DIA format, use default handler.
+        if not isinstance(other, _dia_base):
+            return super()._matmul_sparse(other)
+
+        # If any dimension is zero, return empty array immediately.
+        if 0 in self.shape or 0 in other.shape:
+            return self._dia_container((self.shape[0], other.shape[1]))
+
+        offsets, data = dia_matmat(*self.shape, *self.data.shape,
+                                   self.offsets, self.data,
+                                   other.shape[1], *other.data.shape,
+                                   other.offsets, other.data)
+        return self._dia_container((data.reshape(len(offsets), -1), offsets),
+                                   (self.shape[0], other.shape[1]))
+
+    def _setdiag(self, values, k=0):
+        M, N = self.shape
+
+        if values.ndim == 0:
+            # broadcast
+            values_n = np.inf
+        else:
+            values_n = len(values)
+
+        if k < 0:
+            n = min(M + k, N, values_n)
+            min_index = 0
+            max_index = n
+        else:
+            n = min(M, N - k, values_n)
+            min_index = k
+            max_index = k + n
+
+        if values.ndim != 0:
+            # allow also longer sequences
+            values = values[:n]
+
+        data_rows, data_cols = self.data.shape
+        if k in self.offsets:
+            if max_index > data_cols:
+                data = np.zeros((data_rows, max_index), dtype=self.data.dtype)
+                data[:, :data_cols] = self.data
+                self.data = data
+            self.data[self.offsets == k, min_index:max_index] = values
+        else:
+            self.offsets = np.append(self.offsets, self.offsets.dtype.type(k))
+            m = max(max_index, data_cols)
+            data = np.zeros((data_rows + 1, m), dtype=self.data.dtype)
+            data[:-1, :data_cols] = self.data
+            data[-1, min_index:max_index] = values
+            self.data = data
+
+    def todia(self, copy=False):
+        if copy:
+            return self.copy()
+        else:
+            return self
+
+    todia.__doc__ = _spbase.todia.__doc__
+
+    def transpose(self, axes=None, copy=False):
+        if axes is not None and axes != (1, 0):
+            raise ValueError("Sparse arrays/matrices do not support "
+                              "an 'axes' parameter because swapping "
+                              "dimensions is the only logical permutation.")
+
+        num_rows, num_cols = self.shape
+        max_dim = max(self.shape)
+
+        # flip diagonal offsets
+        offsets = -self.offsets
+
+        # re-align the data matrix
+        r = np.arange(len(offsets), dtype=np.intc)[:, None]
+        c = np.arange(num_rows, dtype=np.intc) - (offsets % max_dim)[:, None]
+        pad_amount = max(0, max_dim-self.data.shape[1])
+        data = np.hstack((self.data, np.zeros((self.data.shape[0], pad_amount),
+                                              dtype=self.data.dtype)))
+        data = data[r, c]
+        return self._dia_container((data, offsets), shape=(
+            num_cols, num_rows), copy=copy)
+
+    transpose.__doc__ = _spbase.transpose.__doc__
+
+    def diagonal(self, k=0):
+        rows, cols = self.shape
+        if k <= -rows or k >= cols:
+            return np.empty(0, dtype=self.data.dtype)
+        idx, = np.nonzero(self.offsets == k)
+        first_col = max(0, k)
+        last_col = min(rows + k, cols)
+        result_size = last_col - first_col
+        if idx.size == 0:
+            return np.zeros(result_size, dtype=self.data.dtype)
+        result = self.data[idx[0], first_col:last_col]
+        padding = result_size - len(result)
+        if padding > 0:
+            result = np.pad(result, (0, padding), mode='constant')
+        return result
+
+    diagonal.__doc__ = _spbase.diagonal.__doc__
+
+    def tocsr(self, copy=False):
+        if 0 in self.shape or len(self.offsets) == 0:
+            return self._csr_container(self.shape, dtype=self.dtype)
+
+        n_rows, n_cols = self.shape
+        max_nnz = self.nnz
+        # np.argsort always returns dtype=int, which can cause automatic dtype
+        # expansion for everything else even if not needed (see gh19245), but
+        # CSR wants common dtype for indices, indptr and shape, so care should
+        # be taken to use appropriate indexing dtype throughout.
+        idx_dtype = self._get_index_dtype(maxval=max(max_nnz, n_rows, n_cols))
+        order = np.argsort(self.offsets).astype(idx_dtype, copy=False)
+        csr_data = np.empty(max_nnz, dtype=self.dtype)
+        indices = np.empty(max_nnz, dtype=idx_dtype)
+        indptr = np.empty(1 + n_rows, dtype=idx_dtype)
+        # Conversion eliminates explicit zeros and returns actual nnz.
+        nnz = dia_tocsr(n_rows, n_cols, *self.data.shape,
+                        self.offsets.astype(idx_dtype, copy=False), self.data,
+                        order, csr_data, indices, indptr)
+        # Shrink indexing dtype, if needed, and prune arrays.
+        idx_dtype = self._get_index_dtype(maxval=max(nnz, n_rows, n_cols))
+        csr_data = _prune_array(csr_data[:nnz])
+        indices = _prune_array(indices[:nnz].astype(idx_dtype, copy=False))
+        indptr = indptr.astype(idx_dtype, copy=False)
+        out = self._csr_container((csr_data, indices, indptr),
+                                  shape=self.shape, dtype=self.dtype)
+        out.has_canonical_format = True
+        return out
+
+    tocsr.__doc__ = _spbase.tocsr.__doc__
+
+    # needed by _data_matrix
+    def _with_data(self, data, copy=True):
+        """Returns a matrix with the same sparsity structure as self,
+        but with different data.  By default the structure arrays are copied.
+        """
+        if copy:
+            return self._dia_container(
+                (data, self.offsets.copy()), shape=self.shape
+            )
+        else:
+            return self._dia_container(
+                (data, self.offsets), shape=self.shape
+            )
+
+    def resize(self, *shape):
+        shape = check_shape(shape)
+        M, N = shape
+        # we do not need to handle the case of expanding N
+        self.data = self.data[:, :N]
+
+        if (M > self.shape[0] and
+                np.any(self.offsets + self.shape[0] < self.data.shape[1])):
+            # explicitly clear values that were previously hidden
+            mask = (self.offsets[:, None] + self.shape[0] <=
+                    np.arange(self.data.shape[1]))
+            self.data[mask] = 0
+
+        self._shape = shape
+
+    resize.__doc__ = _spbase.resize.__doc__
+
+
+def _invert_index(idx):
+    """Helper function to invert an index array."""
+    inv = np.zeros_like(idx)
+    inv[idx] = np.arange(len(idx))
+    return inv
+
+
+def isspmatrix_dia(x):
+    """Is `x` of dia_matrix type?
+
+    .. warning::
+
+       SciPy sparse is shifting from a sparse matrix interface to a sparse
+       array interface. In the next few releases we expect to deprecate the
+       sparse matrix interface. For documentation of the matrix
+       interface, see the :ref:`spmatrix interface docs <spmatrix_api>`.
+       For guidance on converting existing code to sparse arrays, see
+       :ref:`Migration from spmatrix to sparray <migration_to_sparray>`.
+
+    Parameters
+    ----------
+    x
+        object to check for being a dia matrix
+
+    Returns
+    -------
+    bool
+        True if `x` is a dia matrix, False otherwise
+
+    Examples
+    --------
+    >>> from scipy.sparse import dia_array, dia_matrix, coo_matrix, isspmatrix_dia
+    >>> isspmatrix_dia(dia_matrix([[5]]))
+    True
+    >>> isspmatrix_dia(dia_array([[5]]))
+    False
+    >>> isspmatrix_dia(coo_matrix([[5]]))
+    False
+    """
+    return isinstance(x, dia_matrix)
+
+
+# This namespace class separates array from matrix with isinstance
+class dia_array(_dia_base, sparray):
+    """
+    Sparse array with DIAgonal storage.
+
+    This can be instantiated in several ways:
+        dia_array(D)
+            where D is a 2-D ndarray
+
+        dia_array(S)
+            with another sparse array or matrix S (equivalent to S.todia())
+
+        dia_array((M, N), [dtype])
+            to construct an empty array with shape (M, N),
+            dtype is optional, defaulting to dtype='d'.
+
+        dia_array((data, offsets), shape=(M, N))
+            where the ``data[k,:]`` stores the diagonal entries for
+            diagonal ``offsets[k]`` (See example below)
+
+    Attributes
+    ----------
+    data
+        DIA format data array of the array
+    offsets
+        DIA format offset array of the array
+    dtype : dtype
+        Data type of the array
+    shape : 2-tuple
+        Shape of the array
+    ndim : int
+        Number of dimensions (this is always 2)
+    format : str
+        Three letter code for the format of the array storage, e.g. 'dia'
+    nnz : int
+        Number of values stored in the array
+    size : int
+        Number of values stored in the array
+    T : dia_array
+        The transpose of the array
+    mT : dia_array
+        The matrix transpose of the array
+
+    Notes
+    -----
+
+    Sparse arrays can be used in arithmetic operations: they support
+    addition, subtraction, multiplication, division, and matrix power.
+    Sparse arrays with DIAgonal storage do not support slicing.
+
+    **Format details**
+
+    The ``data`` array stores the diagonal elements. The alignment of these
+    elements within the rows of ``data`` depends on their position relative
+    to the main diagonal:
+
+    * **Main diagonal** (``offsets[i] == 0``): Elements start at column 0.
+    * **Super-diagonals** (``offsets[i] > 0``): Elements are right-aligned
+      (padded with zeros on the left).
+    * **Sub-diagonals** (``offsets[i] < 0``): Elements are left-aligned
+      (padded with zeros on the right).
+
+    Each column of ``data`` corresponds to a diagonal in the resulting matrix.
+
+    Mathematically, the element at row ``r`` and column ``c`` of the matrix is
+    stored in the ``data`` array at row ``i`` and column
+    ``c - max(0, -offsets[i])``, where ``i`` is the index of the diagonal
+    in ``offsets``.
+
+    Note that if ``offsets`` is provided in decreasing order, this format
+    matches the BLAS/LAPACK general band format (e.g., as used in ``dgbmv``).
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> from scipy.sparse import dia_array
+    >>> dia_array((3, 4), dtype=np.int8).toarray()
+    array([[0, 0, 0, 0],
+           [0, 0, 0, 0],
+           [0, 0, 0, 0]], dtype=int8)
+
+    >>> data = np.array([[1, 2, 3, 4]]).repeat(3, axis=0)
+    >>> offsets = np.array([0, -1, 2])
+    >>> dia_array((data, offsets), shape=(4, 4)).toarray()
+    array([[1, 0, 3, 0],
+           [1, 2, 0, 4],
+           [0, 2, 3, 0],
+           [0, 0, 3, 4]])
+
+    >>> from scipy.sparse import dia_array
+    >>> n = 10
+    >>> ex = np.ones(n)
+    >>> data = np.array([ex, 2 * ex, ex])
+    >>> offsets = np.array([-1, 0, 1])
+    >>> dia_array((data, offsets), shape=(n, n)).toarray()
+    array([[2., 1., 0., ..., 0., 0., 0.],
+           [1., 2., 1., ..., 0., 0., 0.],
+           [0., 1., 2., ..., 0., 0., 0.],
+           ...,
+           [0., 0., 0., ..., 2., 1., 0.],
+           [0., 0., 0., ..., 1., 2., 1.],
+           [0., 0., 0., ..., 0., 1., 2.]])
+    """  # numpydoc ignore=PR01
+
+
+class dia_matrix(spmatrix, _dia_base):
+    """
+    Sparse matrix with DIAgonal storage.
+
+    .. warning::
+
+       SciPy sparse is shifting from a sparse matrix interface to a sparse
+       array interface. In the next few releases we expect to deprecate the
+       sparse matrix interface. For documentation of the matrix
+       interface, see the :ref:`spmatrix interface docs <spmatrix_api>`.
+       For guidance on converting existing code to sparse arrays, see
+       :ref:`Migration from spmatrix to sparray <migration_to_sparray>`.
+
+    This can be instantiated in several ways:
+        dia_matrix(D)
+            where D is a 2-D ndarray
+
+        dia_matrix(S)
+            with another sparse array or matrix S (equivalent to S.todia())
+
+        dia_matrix((M, N), [dtype])
+            to construct an empty matrix with shape (M, N),
+            dtype is optional, defaulting to dtype='d'.
+
+        dia_matrix((data, offsets), shape=(M, N))
+            where the ``data[k,:]`` stores the diagonal entries for
+            diagonal ``offsets[k]`` (See example below)
+
+    Attributes
+    ----------
+    data
+        DIA format data array of the matrix
+    offsets
+        DIA format offset array of the matrix
+    dtype : dtype
+        Data type of the matrix
+    shape : 2-tuple
+        Shape of the matrix
+    ndim : int
+        Number of dimensions (this is always 2)
+    format : str
+        Three letter code for the format of the matrix storage, e.g. 'dia'
+    nnz : int
+        Number of values stored in the matrix
+    size : int
+        Number of values stored in the matrix
+    T : dia_matrix
+        The transpose of the matrix
+    mT : dia_matrix
+        The matrix transpose
+
+    Notes
+    -----
+    Sparse matrices can be used in arithmetic operations: they support
+    addition, subtraction, multiplication, division, and matrix power.
+    Sparse arrays with DIAgonal storage do not support slicing.
+
+    **Format details**
+
+    The ``data`` array stores the diagonal elements. The alignment of these
+    elements within the rows of ``data`` depends on their position relative
+    to the main diagonal:
+
+    * **Main diagonal** (``offsets[i] == 0``): Elements start at column 0.
+    * **Super-diagonals** (``offsets[i] > 0``): Elements are right-aligned
+      (padded with zeros on the left).
+    * **Sub-diagonals** (``offsets[i] < 0``): Elements are left-aligned
+      (padded with zeros on the right).
+
+    Each column of ``data`` corresponds to a diagonal in the resulting matrix.
+
+    Mathematically, the element at row ``r`` and column ``c`` of the matrix is
+    stored in the ``data`` array at row ``i`` and column
+    ``c - max(0, -offsets[i])``, where ``i`` is the index of the diagonal
+    in ``offsets``.
+
+    Note that if ``offsets`` is provided in decreasing order, this format
+    matches the BLAS/LAPACK general band format (e.g., as used in ``dgbmv``).
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> from scipy.sparse import dia_matrix
+    >>> dia_matrix((3, 4), dtype=np.int8).toarray()
+    array([[0, 0, 0, 0],
+           [0, 0, 0, 0],
+           [0, 0, 0, 0]], dtype=int8)
+
+    >>> data = np.array([[1, 2, 3, 4]]).repeat(3, axis=0)
+    >>> offsets = np.array([0, -1, 2])
+    >>> dia_matrix((data, offsets), shape=(4, 4)).toarray()
+    array([[1, 0, 3, 0],
+           [1, 2, 0, 4],
+           [0, 2, 3, 0],
+           [0, 0, 3, 4]])
+
+    >>> from scipy.sparse import dia_matrix
+    >>> n = 10
+    >>> ex = np.ones(n)
+    >>> data = np.array([ex, 2 * ex, ex])
+    >>> offsets = np.array([-1, 0, 1])
+    >>> dia_matrix((data, offsets), shape=(n, n)).toarray()
+    array([[2., 1., 0., ..., 0., 0., 0.],
+           [1., 2., 1., ..., 0., 0., 0.],
+           [0., 1., 2., ..., 0., 0., 0.],
+           ...,
+           [0., 0., 0., ..., 2., 1., 0.],
+           [0., 0., 0., ..., 1., 2., 1.],
+           [0., 0., 0., ..., 0., 1., 2.]])
+    """
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/_dok.py b/venv/lib/python3.12/site-packages/scipy/sparse/_dok.py
new file mode 100644
index 0000000000000000000000000000000000000000..405ffaa57d93ee3e36b17d6be546feb214c6a992
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/_dok.py
@@ -0,0 +1,828 @@
+"""Dictionary Of Keys based matrix"""
+
+__docformat__ = "restructuredtext en"
+
+__all__ = ['dok_array', 'dok_matrix', 'isspmatrix_dok']
+
+import itertools
+import numpy as np
+
+from ._matrix import spmatrix
+from ._base import _spbase, sparray, issparse
+from ._index import IndexMixin
+from ._sputils import (isdense, getdtype, isshape, isintlike, isscalarlike,
+                       upcast, upcast_scalar, check_shape)
+
+
+_NoValue = object()
+
+
+class _dok_base(_spbase, IndexMixin, dict):
+    _format = 'dok'
+    _allow_nd = (1, 2)
+
+    def __init__(self, arg1, shape=None, dtype=None, copy=False, *, maxprint=None):
+        _spbase.__init__(self, arg1, maxprint=maxprint)
+
+        if isinstance(arg1, tuple) and isshape(arg1, allow_nd=self._allow_nd):
+            self._shape = check_shape(arg1, allow_nd=self._allow_nd)
+            self._dict = {}
+            self.dtype = getdtype(dtype, default=float)
+        elif issparse(arg1):  # Sparse ctor
+            if arg1.format == self.format:
+                arg1 = arg1.copy() if copy else arg1
+            else:
+                arg1 = arg1.todok()
+
+            if dtype is not None:
+                arg1 = arg1.astype(dtype, copy=False)
+
+            self._dict = arg1._dict
+            self._shape = check_shape(arg1.shape, allow_nd=self._allow_nd)
+            self.dtype = getdtype(arg1.dtype)
+        else:  # Dense ctor
+            try:
+                arg1 = np.asarray(arg1)
+            except Exception as e:
+                raise TypeError('Invalid input format.') from e
+
+            if arg1.ndim > 2:
+                raise ValueError(f"DOK arrays don't yet support {arg1.ndim}D input.")
+
+            if arg1.ndim == 1:
+                if dtype is not None:
+                    arg1 = arg1.astype(dtype, copy=False)
+                self._dict = {i: v for i, v in enumerate(arg1) if v != 0}
+                self.dtype = getdtype(arg1.dtype)
+            else:
+                d = self._coo_container(arg1, shape=shape, dtype=dtype).todok()
+                self._dict = d._dict
+                self.dtype = getdtype(d.dtype)
+            self._shape = check_shape(arg1.shape, allow_nd=self._allow_nd)
+
+    def update(self, val):  # pyrefly:ignore[bad-override]
+        """Update values from a dict, sparse dok or iterable of 2-tuples like
+        ``.items()``.
+
+        Parameters
+        ----------
+        val : dict, dok_array, iterable of 2-tuples
+            The values to update in the dok_array. If a dict or dok_array is
+            provided, the keys and values will be taken from it. If an iterable
+            of 2-tuples is provided, each tuple should contain a key and a value.
+            Keys of the input must be sequences of nonnegative integers less than
+            the shape for each axis.
+        """
+        if isinstance(val, dict):
+            inputs = val.items()
+        else:
+            inputs = val
+
+        for key, value in inputs:
+            index = (key,) if isintlike(key) else tuple(key)
+            if len(index) != self.ndim:
+                raise IndexError(f'Index {key} length needs to match self.shape')
+            if not all(
+                isintlike(idx) and 0 <= idx < max_idx
+                for idx, max_idx in zip(index, self.shape)
+            ):
+                # Error handling. Re-search to find which error occurred
+                for idx, max_idx in zip(index, self.shape):
+                    if not isintlike(idx):
+                        raise IndexError(f'integer keys required for update. Got {key}')
+                    if idx < 0:
+                        raise IndexError(f'negative index {key} not allowed in update')
+                    if idx >= max_idx:
+                        raise IndexError(f'index {key} is too large for self.shape')
+        # do the update
+        self._dict.update(inputs)
+
+    def _getnnz(self, axis=None):
+        if axis is not None:
+            raise NotImplementedError(
+                "_getnnz over an axis is not implemented for DOK format."
+            )
+        return len(self._dict)
+
+    def count_nonzero(self, axis=None):
+        if axis is not None:
+            return self.tocoo().count_nonzero(axis=axis)
+        return sum(x != 0 for x in self.values())
+
+    _getnnz.__doc__ = _spbase._getnnz.__doc__
+    count_nonzero.__doc__ = _spbase.count_nonzero.__doc__
+
+    def __len__(self):
+        return len(self._dict)
+
+    def __contains__(self, key):
+        return key in self._dict
+
+    def setdefault(self, key, default=None, /):
+        """Insert key with a value of default if key is not in the dictionary.
+
+        Parameters
+        ----------
+        key : int or tuple of int
+            The key to look for in the dok_array.
+        default : optional
+            The value to insert if `key` is not found. Default is None.
+
+        Returns
+        -------
+        scalar
+            The value for `key` if `key` is in the dictionary, else `default`.
+        """
+        return self._dict.setdefault(key, default)
+
+    def __delitem__(self, key, /):
+        del self._dict[key]
+
+    def clear(self):
+        """Remove all items from the dok_array."""
+        self._dict.clear()
+
+    def pop(self, key, default=_NoValue, /):
+        """Remove specified key and return the corresponding value.
+
+        Parameters
+        ----------
+        key : tuple
+            The key to remove from the dok_array.
+        default : optional
+            The value to return if `key` is not found. If not provided and
+            `key` is not found, a KeyError is raised.
+
+        Returns
+        -------
+        scalar
+            The value associated with the removed key.
+
+        Raises
+        ------
+        KeyError
+            If the key is not found and default is not provided.
+        """
+        if default is _NoValue:
+            return self._dict.pop(key)
+        else:
+            return self._dict.pop(key, default)
+
+    def __reversed__(self):
+        raise TypeError("reversed is not defined for dok_array type")
+
+    def __or__(self, other):
+        type_names = f"{type(self).__name__} and {type(other).__name__}"
+        raise TypeError(f"unsupported operand type for |: {type_names}")
+
+    def __ror__(self, other):
+        type_names = f"{type(self).__name__} and {type(other).__name__}"
+        raise TypeError(f"unsupported operand type for |: {type_names}")
+
+    def __ior__(self, other):
+        type_names = f"{type(self).__name__} and {type(other).__name__}"
+        raise TypeError(f"unsupported operand type for |: {type_names}")
+
+    def popitem(self):
+        """
+        Remove and return a (key, value) pair as a 2-tuple, returned in LIFO (last-in,
+        first-out) order.
+
+        Returns
+        -------
+        key : tuple
+            The key of the removed item.
+        value : scalar
+            The value of the removed item.
+
+        Raises
+        ------
+        KeyError
+            If the dict is empty.
+        """
+        return self._dict.popitem()
+
+    def items(self):
+        """
+        Return a set-like object providing a view on the array's items.
+
+        Returns
+        -------
+        dict_items
+            A view object displaying a list of a array's key-value tuple pairs.
+        """
+        return self._dict.items()
+
+    def keys(self):
+        """
+        Return a set-like object providing a view on the dict's keys.
+
+        Returns
+        -------
+        dict_keys
+            A view object displaying a list of all the keys in the dictionary.
+        """
+        return self._dict.keys()
+
+    def values(self):
+        """
+        Return an object providing a view on the dict's values.
+
+        Returns
+        -------
+        dict_values
+            A view object displaying a list of all the values in the dictionary.
+        """
+        return self._dict.values()
+
+    def get(self, key, default=0.0):
+        """This provides dict.get method functionality with type checking.
+
+        Parameters
+        ----------
+        key : int or tuple of int
+            The key to look for in the dok_array.
+        default : optional
+            The value to return if `key` is not found. Default is 0.0.
+
+        Returns
+        -------
+        value
+            The value associated with `key` if it exists, otherwise `default`.
+        """
+        if key in self._dict:
+            return self._dict[key]
+        if isintlike(key) and self.ndim == 1:
+            key = (key,)
+        if self.ndim != len(key):
+            raise IndexError(f'Index {key} length needs to match self.shape')
+        try:
+            for i in key:
+                assert isintlike(i)
+        except (AssertionError, TypeError, ValueError) as e:
+            raise IndexError('Index must be or consist of integers.') from e
+        key = tuple(i + M if i < 0 else i for i, M in zip(key, self.shape))
+        if any(i < 0 or i >= M for i, M in zip(key, self.shape)):
+            raise IndexError('Index out of bounds.')
+        if self.ndim == 1:
+            key = key[0]
+        return self._dict.get(key, default)
+
+    # 1D get methods
+    def _get_int(self, idx):
+        return self._dict.get(idx, self.dtype.type(0))
+
+    def _get_slice(self, idx):
+        i_range = range(*idx.indices(self.shape[0]))
+        return self._get_array(list(i_range))
+
+    def _get_array(self, idx):
+        idx = np.asarray(idx)
+        if idx.ndim == 0:
+            val = self._dict.get(int(idx), self.dtype.type(0))
+            return np.array(val, stype=self.dtype)
+        new_dok = self._dok_container(idx.shape, dtype=self.dtype)
+        dok_vals = [self._dict.get(i, 0) for i in idx.ravel()]
+        if dok_vals:
+            if len(idx.shape) == 1:
+                for i, v in enumerate(dok_vals):
+                    if v:
+                        new_dok._dict[i] = v
+            else:
+                new_idx = np.unravel_index(np.arange(len(dok_vals)), idx.shape)
+                new_idx = new_idx[0] if len(new_idx) == 1 else zip(*new_idx)
+                for i, v in zip(new_idx, dok_vals, strict=True):
+                    if v:
+                        new_dok._dict[i] = v
+        return new_dok
+
+    # 2D get methods
+    def _get_intXint(self, row, col):
+        return self._dict.get((row, col), self.dtype.type(0))
+
+    def _get_intXslice(self, row, col):
+        return self._get_sliceXslice(slice(row, row + 1), col)
+
+    def _get_sliceXint(self, row, col):
+        return self._get_sliceXslice(row, slice(col, col + 1))
+
+    def _get_sliceXslice(self, row, col):
+        row_start, row_stop, row_step = row.indices(self.shape[0])
+        col_start, col_stop, col_step = col.indices(self.shape[1])
+        row_range = range(row_start, row_stop, row_step)
+        col_range = range(col_start, col_stop, col_step)
+        shape = (len(row_range), len(col_range))
+        # Switch paths only when advantageous
+        # (count the iterations in the loops, adjust for complexity)
+        if len(self) >= 2 * shape[0] * shape[1]:
+            # O(nr*nc) path: loop over <row x col>
+            return self._get_columnXarray(row_range, col_range)
+        # O(nnz) path: loop over entries of self
+        newdok = self._dok_container(shape, dtype=self.dtype)
+        for key in self.keys():
+            i, ri = divmod(int(key[0]) - row_start, row_step)
+            if ri != 0 or i < 0 or i >= shape[0]:
+                continue
+            j, rj = divmod(int(key[1]) - col_start, col_step)
+            if rj != 0 or j < 0 or j >= shape[1]:
+                continue
+            newdok._dict[i, j] = self._dict[key]
+        return newdok
+
+    def _get_intXarray(self, row, col):
+        return self._get_columnXarray([row], col.ravel())
+
+    def _get_arrayXint(self, row, col):
+        res = self._get_columnXarray(row.ravel(), [col])
+        if row.ndim > 1:
+            return res.reshape(row.shape)
+        return res
+
+    def _get_sliceXarray(self, row, col):
+        row = list(range(*row.indices(self.shape[0])))
+        return self._get_columnXarray(row, col)
+
+    def _get_arrayXslice(self, row, col):
+        col = list(range(*col.indices(self.shape[1])))
+        return self._get_columnXarray(row, col)
+
+    def _get_columnXarray(self, row, col):
+        # outer indexing
+        newdok = self._dok_container((len(row), len(col)), dtype=self.dtype)
+
+        for i, r in enumerate(row):
+            for j, c in enumerate(col):
+                v = self._dict.get((r, c), 0)
+                if v:
+                    newdok._dict[i, j] = v
+        return newdok
+
+    def _get_arrayXarray(self, row, col):
+        # inner indexing
+        i, j = map(np.atleast_2d, np.broadcast_arrays(row, col))
+        newdok = self._dok_container(i.shape, dtype=self.dtype)
+
+        for key in itertools.product(range(i.shape[0]), range(i.shape[1])):
+            v = self._dict.get((i[key], j[key]), 0)
+            if v:
+                newdok._dict[key] = v
+        return newdok
+
+    # 1D set methods
+    def _set_int(self, idx, x):
+        if x:
+            self._dict[idx] = x
+        elif idx in self._dict:
+            del self._dict[idx]
+
+    def _set_array(self, idx, x):
+        idx_set = idx.ravel()
+        x_set = x.ravel()
+        if len(idx_set) != len(x_set):
+            if len(x_set) == 1:
+                x_set = np.full(len(idx_set), x_set[0], dtype=self.dtype)
+            else:
+              raise ValueError("Need len(index)==len(data) or len(data)==1")
+        for i, v in zip(idx_set, x_set):
+            if v:
+                self._dict[i] = v
+            elif i in self._dict:
+                del self._dict[i]
+
+    # 2D set methods
+    def _set_intXint(self, row, col, x):
+        key = (row, col)
+        if x:
+            self._dict[key] = x
+        elif key in self._dict:
+            del self._dict[key]
+
+    def _set_arrayXarray(self, row, col, x):
+        row = list(map(int, row.ravel()))
+        col = list(map(int, col.ravel()))
+        x = x.ravel()
+        self._dict.update(zip(zip(row, col), x))
+
+        for i in np.nonzero(x == 0)[0]:
+            key = (row[i], col[i])
+            if self._dict[key] == 0:
+                # may have been superseded by later update
+                del self._dict[key]
+
+    def __add__(self, other):
+        if isscalarlike(other):
+            res_dtype = upcast_scalar(self.dtype, other)
+            new = self._dok_container(self.shape, dtype=res_dtype)
+            # Add this scalar to each element.
+            for key in itertools.product(*[range(d) for d in self.shape]):
+                aij = self._dict.get(key, 0) + other
+                if aij:
+                    new[key] = aij
+        elif issparse(other):
+            if other.shape != self.shape:
+                raise ValueError("Matrix dimensions are not equal.")
+            res_dtype = upcast(self.dtype, other.dtype)
+            new = self._dok_container(self.shape, dtype=res_dtype)
+            new._dict = self._dict.copy()
+            if other.format == "dok":
+                o_items = other.items()
+            else:
+                other = other.tocoo()
+                if self.ndim == 1:
+                    o_items = zip(other.coords[0], other.data)
+                else:
+                    o_items = zip(zip(*other.coords), other.data)
+            with np.errstate(over='ignore'):
+                new._dict.update((k, new[k] + v) for k, v in o_items)
+        elif isdense(other):
+            new = self.todense() + other
+        else:
+            return NotImplemented
+        return new
+
+    def __radd__(self, other):
+        return self + other  # addition is commutative
+
+    def __neg__(self):
+        if self.dtype.kind == 'b':
+            raise NotImplementedError(
+                'Negating a sparse boolean matrix is not supported.'
+            )
+        new = self._dok_container(self.shape, dtype=self.dtype)
+        new._dict.update((k, -v) for k, v in self.items())
+        return new
+
+    def _mul_scalar(self, other):
+        res_dtype = upcast_scalar(self.dtype, other)
+        # Multiply this scalar by every element.
+        new = self._dok_container(self.shape, dtype=res_dtype)
+        new._dict.update(((k, v * other) for k, v in self.items()))
+        return new
+
+    def _matmul_vector(self, other):
+        res_dtype = upcast(self.dtype, other.dtype)
+
+        # vector @ vector
+        if self.ndim == 1:
+            if issparse(other):
+                if other.format == "dok":
+                    keys = self.keys() & other.keys()
+                else:
+                    keys = self.keys() & other.tocoo().coords[0]
+                return res_dtype(sum(self._dict[k] * other._dict[k] for k in keys))
+            elif isdense(other):
+                return res_dtype(sum(other[k] * v for k, v in self.items()))
+            else:
+                return NotImplemented
+
+        # matrix @ vector
+        result = np.zeros(self.shape[0], dtype=res_dtype)
+        for (i, j), v in self.items():
+            result[i] += v * other[j]
+        return result
+
+    def _matmul_multivector(self, other):
+        result_dtype = upcast(self.dtype, other.dtype)
+        # vector @ multivector
+        if self.ndim == 1:
+            # works for other 1d or 2d
+            return sum(v * other[j] for j, v in self._dict.items())
+
+        # matrix @ multivector
+        M = self.shape[0]
+        new_shape = (M,) if other.ndim == 1 else (M, other.shape[1])
+        result = np.zeros(new_shape, dtype=result_dtype)
+        for (i, j), v in self.items():
+            result[i] += v * other[j]
+        return result
+
+    def __imul__(self, other):
+        if isscalarlike(other):
+            self._dict.update((k, v * other) for k, v in self.items())
+            return self
+        return NotImplemented
+
+    def __truediv__(self, other):
+        if isscalarlike(other):
+            res_dtype = upcast_scalar(self.dtype, other)
+            new = self._dok_container(self.shape, dtype=res_dtype)
+            new._dict.update(((k, v / other) for k, v in self.items()))
+            return new
+        return self.tocsr() / other
+
+    def __itruediv__(self, other):
+        if isscalarlike(other):
+            self._dict.update((k, v / other) for k, v in self.items())
+            return self
+        return NotImplemented
+
+    def __reduce__(self):
+        # this approach is necessary because __setstate__ is called after
+        # __setitem__ upon unpickling and since __init__ is not called there
+        # is no shape attribute hence it is not possible to unpickle it.
+        return dict.__reduce__(self)
+
+    def diagonal(self, k=0):
+        if self.ndim == 2:
+            return super().diagonal(k)
+        raise ValueError("diagonal requires two dimensions")
+
+    diagonal.__doc__ = _spbase.diagonal.__doc__
+
+    def transpose(self, axes=None, copy=False):
+        if self.ndim == 1:
+            return self.copy()
+
+        if axes is not None and axes != (1, 0):
+            raise ValueError(
+                "Sparse arrays/matrices do not support "
+                "an 'axes' parameter because swapping "
+                "dimensions is the only logical permutation."
+            )
+
+        M, N = self.shape
+        new = self._dok_container((N, M), dtype=self.dtype, copy=copy)
+        new._dict.update((((right, left), val) for (left, right), val in self.items()))
+        return new
+
+    transpose.__doc__ = _spbase.transpose.__doc__
+
+    def copy(self):
+        new = self._dok_container(self.shape, dtype=self.dtype)
+        new._dict.update(self._dict)
+        return new
+
+    copy.__doc__ = _spbase.copy.__doc__
+
+    @classmethod
+    def fromkeys(cls, iterable, value=1, /):
+        tmp = dict.fromkeys(iterable, value)
+        if isinstance(next(iter(tmp)), tuple):
+            shape = tuple(max(idx) + 1 for idx in zip(*tmp))
+        else:
+            shape = (max(tmp) + 1,)
+        result = cls(shape, dtype=type(value))
+        result._dict = tmp
+        return result
+
+    def tocoo(self, copy=False):
+        nnz = self.nnz
+        if nnz == 0:
+            return self._coo_container(self.shape, dtype=self.dtype)
+
+        idx_dtype = self._get_index_dtype(maxval=max(self.shape))
+        data = np.fromiter(self.values(), dtype=self.dtype, count=nnz)
+        # handle 1d keys specially b/c not a tuple
+        inds = zip(*self.keys()) if self.ndim > 1 else (self.keys(),)
+        coords = tuple(np.fromiter(ix, dtype=idx_dtype, count=nnz) for ix in inds)
+        A = self._coo_container((data, coords), shape=self.shape, dtype=self.dtype)
+        A.has_canonical_format = True
+        return A
+
+    tocoo.__doc__ = _spbase.tocoo.__doc__
+
+    def todok(self, copy=False):
+        if copy:
+            return self.copy()
+        return self
+
+    todok.__doc__ = _spbase.todok.__doc__
+
+    def tocsc(self, copy=False):
+        if self.ndim == 1:
+            raise NotImplementedError("tocsr() not valid for 1d sparse array")
+        return self.tocoo(copy=False).tocsc(copy=copy)
+
+    tocsc.__doc__ = _spbase.tocsc.__doc__
+
+    def resize(self, *shape):
+        shape = check_shape(shape, allow_nd=self._allow_nd)
+        if len(shape) != len(self.shape):
+            # TODO implement resize across dimensions
+            raise NotImplementedError
+
+        if self.ndim == 1:
+            newN = shape[-1]
+            for i in list(self._dict):
+                if i >= newN:
+                    del self._dict[i]
+            self._shape = shape
+            return
+
+        newM, newN = shape
+        M, N = self.shape
+        if newM < M or newN < N:
+            # Remove all elements outside new dimensions
+            for i, j in list(self.keys()):
+                if i >= newM or j >= newN:
+                    del self._dict[i, j]
+        self._shape = shape
+
+    resize.__doc__ = _spbase.resize.__doc__
+
+    # Added for 1d to avoid `tocsr` from _base.py
+    def astype(self, dtype, casting='unsafe', copy=True):
+        dtype = np.dtype(dtype)
+        if self.dtype != dtype:
+            result = self._dok_container(self.shape, dtype=dtype)
+            data = np.array(list(self._dict.values()), dtype=dtype)
+            result._dict = dict(zip(self._dict, data))
+            return result
+        elif copy:
+            return self.copy()
+        return self
+
+    astype.__doc__ = _spbase.astype.__doc__
+
+
+def isspmatrix_dok(x):
+    """Is `x` of dok_array type?
+
+    .. warning::
+
+       SciPy sparse is shifting from a sparse matrix interface to a sparse
+       array interface. In the next few releases we expect to deprecate the
+       sparse matrix interface. For documentation of the matrix
+       interface, see the :ref:`spmatrix interface docs <spmatrix_api>`.
+       For guidance on converting existing code to sparse arrays, see
+       :ref:`Migration from spmatrix to sparray <migration_to_sparray>`.
+
+    Parameters
+    ----------
+    x
+        object to check for being a dok matrix
+
+    Returns
+    -------
+    bool
+        True if `x` is a dok matrix, False otherwise
+
+    Examples
+    --------
+    >>> from scipy.sparse import dok_array, dok_matrix, coo_matrix, isspmatrix_dok
+    >>> isspmatrix_dok(dok_matrix([[5]]))
+    True
+    >>> isspmatrix_dok(dok_array([[5]]))
+    False
+    >>> isspmatrix_dok(coo_matrix([[5]]))
+    False
+    """
+    return isinstance(x, dok_matrix)
+
+
+# This namespace class separates array from matrix with isinstance
+class dok_array(_dok_base, sparray):
+    """
+    Dictionary Of Keys based sparse array.
+
+    This is an efficient structure for constructing sparse
+    arrays incrementally.
+
+    This can be instantiated in several ways:
+        dok_array(D)
+            where D is a 2-D ndarray
+
+        dok_array(S)
+            with another sparse array or matrix S (equivalent to S.todok())
+
+        dok_array((M,N), [dtype])
+            create the array with initial shape (M,N)
+            dtype is optional, defaulting to dtype='d'
+
+    Attributes
+    ----------
+    dtype : dtype
+        Data type of the array
+    shape : 2-tuple
+        Shape of the array
+    ndim : int
+        Number of dimensions (this is always 2)
+    format : str
+        Three letter code for the format of the array storage, e.g. 'dok'
+    nnz : int
+        Number of values stored in the array
+    size : int
+        Number of values stored in the array
+    T : dok_array
+        The transpose of the array
+    mT : dok_array
+        The matrix transpose of the array
+
+    Notes
+    -----
+
+    Sparse arrays can be used in arithmetic operations: they support
+    addition, subtraction, multiplication, division, and matrix power.
+
+    - Allows for efficient O(1) access of individual elements.
+    - Duplicates are not allowed.
+    - Can be efficiently converted to a coo_array once constructed.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.sparse import dok_array
+    >>> S = dok_array((5, 5), dtype=np.float32)
+    >>> for i in range(5):
+    ...     for j in range(5):
+    ...         S[i, j] = i + j    # Update element
+
+    """  # numpydoc ignore=PR01
+
+
+class dok_matrix(spmatrix, _dok_base):
+    """
+    Dictionary Of Keys based sparse matrix.
+
+    This is an efficient structure for constructing sparse
+    matrices incrementally.
+
+    .. warning::
+
+       SciPy sparse is shifting from a sparse matrix interface to a sparse
+       array interface. In the next few releases we expect to deprecate the
+       sparse matrix interface. For documentation of the matrix
+       interface, see the :ref:`spmatrix interface docs <spmatrix_api>`.
+       For guidance on converting existing code to sparse arrays, see
+       :ref:`Migration from spmatrix to sparray <migration_to_sparray>`.
+
+    This can be instantiated in several ways:
+        dok_matrix(D)
+            where D is a 2-D ndarray
+
+        dok_matrix(S)
+            with another sparse array or matrix S (equivalent to S.todok())
+
+        dok_matrix((M,N), [dtype])
+            create the matrix with initial shape (M,N)
+            dtype is optional, defaulting to dtype='d'
+
+    Attributes
+    ----------
+    dtype : dtype
+        Data type of the matrix
+    shape : 2-tuple
+        Shape of the matrix
+    ndim : int
+        Number of dimensions (this is always 2)
+    format : str
+        Three letter code for the format of the matrix storage, e.g. 'dok'
+    nnz : int
+        Number of values stored in the matrix
+    size : int
+        Number of values stored in the matrix
+    T : dok_matrix
+        The transpose of the matrix
+    mT : dok_matrix
+        The matrix transpose
+
+    Notes
+    -----
+
+    Sparse matrices can be used in arithmetic operations: they support
+    addition, subtraction, multiplication, division, and matrix power.
+
+    - Allows for efficient O(1) access of individual elements.
+    - Duplicates are not allowed.
+    - Can be efficiently converted to a coo_matrix once constructed.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.sparse import dok_matrix
+    >>> S = dok_matrix((5, 5), dtype=np.float32)
+    >>> for i in range(5):
+    ...     for j in range(5):
+    ...         S[i, j] = i + j    # Update element
+
+    """
+
+    def set_shape(self, shape):
+        new_matrix = self.reshape(shape, copy=False).asformat(self.format)
+        self.__dict__ = new_matrix.__dict__
+
+    def get_shape(self):
+        """Get shape of a sparse matrix."""
+        return self._shape
+
+    shape = property(fget=get_shape, fset=set_shape)
+
+    def __reversed__(self):
+        return self._dict.__reversed__()
+
+    def __or__(self, other):
+        if isinstance(other, _dok_base):
+            return self._dict | other._dict
+        return self._dict | other
+
+    def __ror__(self, other):
+        if isinstance(other, _dok_base):
+            return self._dict | other._dict
+        return self._dict | other
+
+    def __ior__(self, other):
+        if isinstance(other, _dok_base):
+            self._dict |= other._dict
+        else:
+            self._dict |= other
+        return self
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/_extract.py b/venv/lib/python3.12/site-packages/scipy/sparse/_extract.py
new file mode 100644
index 0000000000000000000000000000000000000000..656e98adc59f8d4bd471f6d3286017c0fffe1237
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/_extract.py
@@ -0,0 +1,246 @@
+"""Functions to extract parts of sparse matrices
+"""
+
+__docformat__ = "restructuredtext en"
+
+__all__ = ['find', 'tril', 'triu']
+
+import os
+from warnings import warn
+
+from ._coo import coo_array, coo_matrix
+from ._base import sparray, spmatrix
+
+
+def find(A):
+    """Return the indices and values of the nonzero elements of a matrix.
+
+    Parameters
+    ----------
+    A : dense or sparse array or matrix
+        Matrix whose nonzero elements are desired.
+
+    Returns
+    -------
+    (I,J,V) : tuple of arrays
+        I,J, and V contain the row indices, column indices, and values
+        of the nonzero entries.
+
+
+    Examples
+    --------
+    >>> from scipy.sparse import csr_array, find
+    >>> A = csr_array([[7.0, 8.0, 0],[0, 0, 9.0]])
+    >>> find(A)
+    (array([0, 0, 1], dtype=int32),
+     array([0, 1, 2], dtype=int32),
+     array([ 7.,  8.,  9.]))
+
+    """
+
+    A = coo_array(A, copy=True)
+    A.sum_duplicates()
+    # remove explicit zeros
+    nz_mask = A.data != 0
+    return A.row[nz_mask], A.col[nz_mask], A.data[nz_mask]
+
+
+def tril(A, k=0, format=None):
+    """Return the lower triangular portion of a sparse array or matrix.
+
+    Returns the elements on or below the k-th diagonal of A.
+        - k = 0 corresponds to the main diagonal
+        - k > 0 is above the main diagonal
+        - k < 0 is below the main diagonal
+
+    .. warning::
+
+        `tril` is switching to the sparse array interface.
+
+        For the case where no input arrays are sparse, this function is
+        switching to returning a sparse array instead of sparse matrix.
+        Control the sparse return class by making at least one input sparse,
+        e.g., ``tril(coo_matrix(A))``, or ``tril(coo_array(A))``.
+        That removes any deprecation warnings as well.
+        For more general information about sparrays, see
+        :ref:`Migration from spmatrix to sparray <migration_to_sparray>`.
+        Handling of this no sparse input case will change no earlier than v1.20.
+
+    Parameters
+    ----------
+    A : dense or sparse array or matrix
+        Matrix whose lower trianglar portion is desired.
+    k : int : optional
+        The top-most diagonal of the lower triangle.
+    format : str
+        Sparse format of the result, e.g. format="csr", etc.
+
+    Returns
+    -------
+    L : sparse matrix
+        Lower triangular portion of A in sparse format.
+
+    See Also
+    --------
+    triu : upper triangle in sparse format
+
+    Examples
+    --------
+    >>> from scipy.sparse import csr_array, tril
+    >>> A = csr_array([[1, 2, 0, 0, 3], [4, 5, 0, 6, 7], [0, 0, 8, 9, 0]],
+    ...               dtype='int32')
+    >>> A.toarray()
+    array([[1, 2, 0, 0, 3],
+           [4, 5, 0, 6, 7],
+           [0, 0, 8, 9, 0]], dtype=int32)
+    >>> tril(A).toarray()
+    array([[1, 0, 0, 0, 0],
+           [4, 5, 0, 0, 0],
+           [0, 0, 8, 0, 0]], dtype=int32)
+    >>> tril(A).nnz
+    4
+    >>> tril(A, k=1).toarray()
+    array([[1, 2, 0, 0, 0],
+           [4, 5, 0, 0, 0],
+           [0, 0, 8, 9, 0]], dtype=int32)
+    >>> tril(A, k=-1).toarray()
+    array([[0, 0, 0, 0, 0],
+           [4, 0, 0, 0, 0],
+           [0, 0, 0, 0, 0]], dtype=int32)
+    >>> tril(A, format='csc')
+    <Compressed Sparse Column sparse array of dtype 'int32'
+        with 4 stored elements and shape (3, 5)>
+
+    """
+    if isinstance(A, sparray):
+        coo_sparse = coo_array
+    elif isinstance(A, spmatrix):
+        coo_sparse = coo_matrix
+    else:  # dense
+        msg = """`tril` is switching to the sparse array interface.
+
+        For the case where input arrays are numpy arrays, this function is
+        switching to returning a sparse array instead of sparse matrix.
+        Recover the sparse matrix return value by making one input a sparse matrix.
+        For example, tril(coo_matrix(A)).
+        Avoid this message for sparse array output by using tril(coo_array(A)).
+        For more information, see the spmatrix to sparray migration guide
+        https://docs.scipy.org/doc/scipy/reference/sparse.migration_to_sparray.html
+
+        This function will be changed no earlier than v1.20.
+        """
+        prefixes = (os.path.dirname(__file__),)
+        warn(msg, category=DeprecationWarning, skip_file_prefixes=prefixes)
+        # default when input is ndarray
+        coo_sparse = coo_matrix
+
+    # convert to COOrdinate format where things are easy
+    A = coo_sparse(A, copy=False)
+    mask = A.row + k >= A.col
+
+    row = A.row[mask]
+    col = A.col[mask]
+    data = A.data[mask]
+    new_coo = coo_sparse((data, (row, col)), shape=A.shape, dtype=A.dtype)
+    return new_coo.asformat(format)
+
+
+def triu(A, k=0, format=None):
+    """Return the upper triangular portion of a sparse array or matrix.
+
+    Returns the elements on or above the k-th diagonal of A.
+        - k = 0 corresponds to the main diagonal
+        - k > 0 is above the main diagonal
+        - k < 0 is below the main diagonal
+
+    .. warning::
+
+        `triu` is switching to the sparse array interface.
+
+        For the case where no input arrays are sparse, this function is
+        switching to returning a sparse array instead of sparse matrix.
+        Control the sparse return class by making at least one input sparse,
+        e.g., ``triu(coo_matrix(A))``, or ``triu(coo_array(A))``.
+        That removes any deprecation warnings as well.
+        For more general information about sparrays, see
+        :ref:`Migration from spmatrix to sparray <migration_to_sparray>`.
+        Handling of this no sparse input case will change no earlier than v1.20.
+
+    Parameters
+    ----------
+    A : dense or sparse array or matrix
+        Matrix whose upper trianglar portion is desired.
+    k : int : optional
+        The bottom-most diagonal of the upper triangle.
+    format : str
+        Sparse format of the result, e.g. format="csr", etc.
+
+    Returns
+    -------
+    L : sparse array or matrix
+        Upper triangular portion of A in sparse format.
+        Sparse array if A is a sparse array, otherwise matrix.
+
+    See Also
+    --------
+    tril : lower triangle in sparse format
+
+    Examples
+    --------
+    >>> from scipy.sparse import csr_array, triu
+    >>> A = csr_array([[1, 2, 0, 0, 3], [4, 5, 0, 6, 7], [0, 0, 8, 9, 0]],
+    ...                dtype='int32')
+    >>> A.toarray()
+    array([[1, 2, 0, 0, 3],
+           [4, 5, 0, 6, 7],
+           [0, 0, 8, 9, 0]], dtype=int32)
+    >>> triu(A).toarray()
+    array([[1, 2, 0, 0, 3],
+           [0, 5, 0, 6, 7],
+           [0, 0, 8, 9, 0]], dtype=int32)
+    >>> triu(A).nnz
+    8
+    >>> triu(A, k=1).toarray()
+    array([[0, 2, 0, 0, 3],
+           [0, 0, 0, 6, 7],
+           [0, 0, 0, 9, 0]], dtype=int32)
+    >>> triu(A, k=-1).toarray()
+    array([[1, 2, 0, 0, 3],
+           [4, 5, 0, 6, 7],
+           [0, 0, 8, 9, 0]], dtype=int32)
+    >>> triu(A, format='csc')
+    <Compressed Sparse Column sparse array of dtype 'int32'
+        with 8 stored elements and shape (3, 5)>
+
+    """
+    if isinstance(A, sparray):
+        coo_sparse = coo_array
+    elif isinstance(A, spmatrix):
+        coo_sparse = coo_matrix
+    else:  # dense
+        msg = """`triu` is switching to the sparse array interface.
+
+        For the case where input arrays are numpy arrays, this function is
+        switching to returning a sparse array instead of sparse matrix.
+        Recover the sparse matrix return value by making one input a sparse matrix.
+        For example, triu(coo_matrix(A)).
+        Avoid this message for sparse array output by using triu(coo_array(A)).
+        For more information, see the spmatrix to sparray migration guide
+        https://docs.scipy.org/doc/scipy/reference/sparse.migration_to_sparray.html
+
+        This function will be changed no earlier than v1.20.
+        """
+        prefixes = (os.path.dirname(__file__),)
+        warn(msg, category=DeprecationWarning, skip_file_prefixes=prefixes)
+        # default when input is ndarray
+        coo_sparse = coo_matrix
+
+    # convert to COOrdinate format where things are easy
+    A = coo_sparse(A, copy=False)
+    mask = A.row + k <= A.col
+
+    row = A.row[mask]
+    col = A.col[mask]
+    data = A.data[mask]
+    new_coo = coo_sparse((data, (row, col)), shape=A.shape, dtype=A.dtype)
+    return new_coo.asformat(format)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/_index.py b/venv/lib/python3.12/site-packages/scipy/sparse/_index.py
new file mode 100644
index 0000000000000000000000000000000000000000..0121bc3420816807c15e8c8c9fa0a35c9e3b7bdf
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/_index.py
@@ -0,0 +1,491 @@
+"""Indexing mixin for sparse array/matrix classes.
+"""
+import numpy as np
+from ._sputils import isintlike
+from ._base import sparray, issparse
+
+INT_TYPES = (int, np.integer)
+
+
+def _broadcast_arrays(*arrays):
+    """
+    Same as np.broadcast_arrays(a, b) but old writeability rules.
+
+    NumPy >= 1.17.0 transitions broadcast_arrays to return
+    read-only arrays. Set writeability explicitly to avoid warnings.
+    Retain the old writeability rules, as our Cython code assumes
+    the old behavior.
+    """
+    broadcast_arrays = np.broadcast_arrays(*arrays)
+    for x, a in zip(broadcast_arrays, arrays):
+        x.flags.writeable = a.flags.writeable
+    return broadcast_arrays
+
+
+class IndexMixin:
+    """
+    This class provides common dispatching and validation logic for indexing.
+    """
+    def __getitem__(self, key, /):
+        index, new_shape, _, _ = _validate_indices(key, self.shape, self.format)
+        if len(new_shape) > 2:
+            raise IndexError("Indexing that leads to >2D is not supported by "
+                             f"{self.format} format. Try converting to COO format")
+
+        # 1D array
+        if len(index) == 1:
+            idx = index[0]
+            if isinstance(idx, np.ndarray):
+                if idx.shape == ():
+                    idx = idx.item()
+            if isinstance(idx, INT_TYPES):
+                res = self._get_int(idx)
+            elif isinstance(idx, slice):
+                res = self._get_slice(idx)
+            else:  # assume array idx
+                res = self._get_array(idx)
+
+            # package the result and return
+            if not isinstance(self, sparray):
+                return res
+            # handle np.newaxis in idx when result would otherwise be a scalar
+            if res.shape == () and new_shape != ():
+                if len(new_shape) == 1:
+                    return self.__class__([res], shape=new_shape, dtype=self.dtype)
+                if len(new_shape) == 2:
+                    return self.__class__([[res]], shape=new_shape, dtype=self.dtype)
+            return res.reshape(new_shape)
+
+        # 2D array
+        row, col = index
+
+        # Dispatch to specialized methods.
+        if isinstance(row, INT_TYPES):
+            if isinstance(col, INT_TYPES):
+                res = self._get_intXint(row, col)
+            elif isinstance(col, slice):
+                res = self._get_intXslice(row, col)
+            elif col.ndim == 1:
+                res = self._get_intXarray(row, col)
+            elif col.ndim == 2:
+                res = self._get_intXarray(row, col)
+            else:
+                raise IndexError('index results in >2 dimensions')
+        elif isinstance(row, slice):
+            if isinstance(col, INT_TYPES):
+                res = self._get_sliceXint(row, col)
+            elif isinstance(col, slice):
+                if row == slice(None) and row == col:
+                    res = self.copy()
+                else:
+                    res = self._get_sliceXslice(row, col)
+            elif col.ndim == 1:
+                res = self._get_sliceXarray(row, col)
+            else:
+                raise IndexError('index results in >2 dimensions')
+        else:
+            if isinstance(col, INT_TYPES):
+                res = self._get_arrayXint(row, col)
+            elif isinstance(col, slice):
+                res = self._get_arrayXslice(row, col)
+            # arrayXarray preprocess
+            elif (row.ndim == 2 and row.shape[1] == 1
+                  and (col.ndim == 1 or col.shape[0] == 1)):
+                # outer indexing
+                res = self._get_columnXarray(row[:, 0], col.reshape(-1))
+            else:
+                # inner indexing
+                row, col = _broadcast_arrays(row, col)
+                if row.shape != col.shape:
+                    raise IndexError('number of row and column indices differ')
+                if row.size == 0:
+                    res = self.__class__(np.atleast_2d(row).shape, dtype=self.dtype)
+                else:
+                    res = self._get_arrayXarray(row, col)
+
+        # handle spmatrix (must be 2d, dont let 1d new_shape start reshape)
+        if not isinstance(self, sparray):
+            if new_shape == () or (len(new_shape) == 1 and res.ndim != 0):
+                # res handles cases not inflated by None
+                return res
+            if len(new_shape) == 1:
+                # shape inflated to 1D by None in index. Make 2D
+                new_shape = (1,) + new_shape
+            # reshape if needed (when None changes shape, e.g. A[1,:,None])
+            return res if new_shape == res.shape else res.reshape(new_shape)
+
+        # package the result and return
+        if res.shape != new_shape:
+            # handle formats that support indexing but not 1D (lil for now)
+            if self.format == "lil" and len(new_shape) != 2:
+                if res.shape == ():
+                    return self._coo_container([res], shape = new_shape)
+                return res.tocoo().reshape(new_shape)
+            return res.reshape(new_shape)
+        return res
+
+    def __setitem__(self, key, x, /):
+        index, new_shape, _, _ = _validate_indices(key, self.shape, self.format)
+
+        # 1D array
+        if len(index) == 1:
+            idx = index[0]
+
+            if issparse(x):
+                x = x.toarray()
+            else:
+                x = np.asarray(x, dtype=self.dtype)
+
+            if isinstance(idx, INT_TYPES):
+                if x.size != 1:
+                    raise ValueError('Trying to assign a sequence to an item')
+                self._set_int(idx, x.flat[0])
+                return
+
+            if isinstance(idx, slice):
+                # check for simple case of slice that gives 1 item
+                # Note: Python `range` does not use lots of memory
+                idx_range = range(*idx.indices(self.shape[0]))
+                N = len(idx_range)
+                if N == 1 and x.size == 1:
+                    self._set_int(idx_range[0], x.flat[0])
+                    return
+                idx = np.arange(*idx.indices(self.shape[0]))
+                idx_shape = idx.shape
+            else:
+                idx_shape = idx.squeeze().shape
+            # broadcast scalar to full 1d
+            if x.squeeze().shape != idx_shape:
+                x = np.broadcast_to(x, idx.shape)
+            if x.size != 0:
+                self._set_array(idx, x)
+            return
+
+        # 2D array
+        row, col = index
+
+        if isinstance(row, INT_TYPES) and isinstance(col, INT_TYPES):
+            if issparse(x):
+                x = x.toarray()
+            else:
+                x = np.asarray(x, dtype=self.dtype)
+            if x.size != 1:
+                raise ValueError('Trying to assign a sequence to an item')
+            self._set_intXint(row, col, x.flat[0])
+            return
+
+        if isinstance(row, slice):
+            row = np.arange(*row.indices(self.shape[0]))[:, None]
+        else:
+            row = np.atleast_1d(row)
+
+        if isinstance(col, slice):
+            col = np.arange(*col.indices(self.shape[1]))[None, :]
+            if row.ndim == 1:
+                row = row[:, None]
+        else:
+            col = np.atleast_1d(col)
+
+        i, j = _broadcast_arrays(row, col)
+        if i.shape != j.shape:
+            raise IndexError('number of row and column indices differ')
+
+        if issparse(x):
+            if 0 in x.shape:
+                return
+            if i.ndim == 1:
+                # Inner indexing, so treat them like row vectors.
+                i = i[None]
+                j = j[None]
+            x = x.tocoo(copy=False).reshape(x._shape_as_2d, copy=True)
+            broadcast_row = x.shape[0] == 1 and i.shape[0] != 1
+            broadcast_col = x.shape[1] == 1 and i.shape[1] != 1
+            if not ((broadcast_row or x.shape[0] == i.shape[0]) and
+                    (broadcast_col or x.shape[1] == i.shape[1])):
+                raise ValueError('shape mismatch in assignment')
+            x.sum_duplicates()
+            self._set_arrayXarray_sparse(i, j, x)
+        else:
+            # Make x and i into the same shape
+            x = np.asarray(x, dtype=self.dtype)
+            if x.squeeze().shape != i.squeeze().shape:
+                x = np.broadcast_to(x, i.shape)
+            if x.size == 0:
+                return
+            x = x.reshape(i.shape)
+            self._set_arrayXarray(i, j, x)
+
+    def _getrow(self, i):
+        """Return a copy of row i of the matrix, as a (1 x n) row vector.
+        """
+        M, N = self.shape
+        i = int(i)
+        if i < -M or i >= M:
+            raise IndexError(f'index ({i}) out of range')
+        if i < 0:
+            i += M
+        return self._get_intXslice(i, slice(None))
+
+    def _getcol(self, i):
+        """Return a copy of column i of the matrix, as a (m x 1) column vector.
+        """
+        M, N = self.shape
+        i = int(i)
+        if i < -N or i >= N:
+            raise IndexError(f'index ({i}) out of range')
+        if i < 0:
+            i += N
+        return self._get_sliceXint(slice(None), i)
+
+    def _get_int(self, idx):
+        raise NotImplementedError()
+
+    def _get_slice(self, idx):
+        raise NotImplementedError()
+
+    def _get_array(self, idx):
+        raise NotImplementedError()
+
+    def _get_intXint(self, row, col):
+        raise NotImplementedError()
+
+    def _get_intXarray(self, row, col):
+        raise NotImplementedError()
+
+    def _get_intXslice(self, row, col):
+        raise NotImplementedError()
+
+    def _get_sliceXint(self, row, col):
+        raise NotImplementedError()
+
+    def _get_sliceXslice(self, row, col):
+        raise NotImplementedError()
+
+    def _get_sliceXarray(self, row, col):
+        raise NotImplementedError()
+
+    def _get_arrayXint(self, row, col):
+        raise NotImplementedError()
+
+    def _get_arrayXslice(self, row, col):
+        raise NotImplementedError()
+
+    def _get_columnXarray(self, row, col):
+        raise NotImplementedError()
+
+    def _get_arrayXarray(self, row, col):
+        raise NotImplementedError()
+
+    def _set_int(self, idx, x):
+        raise NotImplementedError()
+
+    def _set_array(self, idx, x):
+        raise NotImplementedError()
+
+    def _set_intXint(self, row, col, x):
+        raise NotImplementedError()
+
+    def _set_arrayXarray(self, row, col, x):
+        raise NotImplementedError()
+
+    def _set_arrayXarray_sparse(self, row, col, x):
+        # Fall back to densifying x
+        x = np.asarray(x.toarray(), dtype=self.dtype)
+        x, _ = _broadcast_arrays(x, row)
+        self._set_arrayXarray(row, col, x)
+
+
+def _validate_indices(key, self_shape, self_format):
+    """Returns four sequences: (index, requested shape, arrays, nones)
+
+    index : tuple of validated idx objects. bool arrays->nonzero(),
+            arrays broadcast, ints and slices as they are, Nones removed
+    requested shape : the shape of the indexed space, including Nones
+    arr_pos : position within index of all arrays or ints (for array fancy indexing)
+    none_pos : insert positions to put newaxis coords in indexed space.
+    """
+    self_ndim = len(self_shape)
+    # single ellipsis
+    if key is Ellipsis:
+        return (slice(None),) * self_ndim, self_shape, [], []
+
+    if not isinstance(key, tuple):
+        key = [key]
+
+    # pass 1:
+    # - expand ellipsis to allow matching to self_shape
+    # - preprocess boolean array index
+    # - error on sparse array as an index
+    # - count the ndim of the index and check if too long
+    ellps_pos = None
+    index_1st = []
+    prelim_ndim = 0
+    for i, idx in enumerate(key):
+        if idx is Ellipsis:
+            if ellps_pos is not None:
+                raise IndexError('an index can only have a single ellipsis')
+            ellps_pos = i
+        elif idx is None:
+            index_1st.append(idx)
+        elif isinstance(idx, slice) or isintlike(idx):
+            index_1st.append(idx)
+            prelim_ndim += 1
+        elif (ix := _compatible_boolean_index(idx, self_ndim)) is not None:
+            # can't check the shape of ix until we resolve ellipsis (pass 2)
+            index_1st.append(ix)
+            prelim_ndim += ix.ndim
+        elif issparse(idx):
+            # TODO: make sparse indexing work for sparray
+            raise IndexError(
+                'Indexing with sparse matrices is not supported '
+                'except boolean indexing where matrix and index '
+                'are equal shapes.')
+        else:  # dense array
+            index_1st.append(np.asarray(idx))
+            prelim_ndim += 1
+    if prelim_ndim > self_ndim:
+        raise IndexError(
+            'Too many indices for array or tuple index out of range. '
+            f'Key {key} needs {prelim_ndim}D. Array is {self_ndim}D'
+        )
+    ellip_slices = (self_ndim - prelim_ndim) * [slice(None)]
+    if ellip_slices:
+        if ellps_pos is None:
+            index_1st.extend(ellip_slices)
+        else:
+            index_1st = index_1st[:ellps_pos] + ellip_slices + index_1st[ellps_pos:]
+
+    # second pass (have processed ellipsis and preprocessed arrays)
+    # pass 2:
+    # note: integer arrays provide info for one axis even if >1D array.
+    #       The shape of array affects outgoing(get)/incoming(set) shape only
+    # - form `new_shape` (shape of outgo/incom-ing result of key
+    # - form `index` (validated form of each slice/int/array index)
+    # - validate and make canonical: slice and int
+    # - turn bool arrays to int arrays via `.nonzero()`
+    # - collect positions of Newaxis/None in `none_positions`
+    # - collect positions of "array or int" in `arr_int_pos`
+    idx_shape = []
+    index_ndim = 0
+    index = []
+    array_indices = []
+    none_positions = []
+    arr_int_pos = []  # track positions of arrays and integers
+
+    for i, idx in enumerate(index_1st):
+        if idx is None:
+            none_positions.append(len(idx_shape))
+            idx_shape.append(1)
+        elif isinstance(idx, slice):
+            index.append(idx)
+            Ms = self_shape[index_ndim]
+            len_slice = len(range(*idx.indices(Ms)))
+            idx_shape.append(len_slice)
+            index_ndim += 1
+        elif isintlike(idx):
+            N = self_shape[index_ndim]
+            if not (-N <= idx < N):
+                raise IndexError(f'index ({idx}) out of range')
+            idx = int(idx + N if idx < 0 else idx)
+            index.append(idx)
+            arr_int_pos.append(index_ndim)
+            index_ndim += 1
+        # bool array (checked in first pass)
+        elif idx.dtype.kind == 'b':
+            tmp_ndim = index_ndim + idx.ndim
+            mid_shape = self_shape[index_ndim:tmp_ndim]
+            if idx.shape != mid_shape:
+                raise IndexError(
+                    f"bool index {i} has shape {mid_shape} instead of {idx.shape}"
+                )
+            index.extend(idx.nonzero())
+            array_indices.extend(range(index_ndim, tmp_ndim))
+            arr_int_pos.extend(range(index_ndim, tmp_ndim))
+            index_ndim = tmp_ndim
+        else:  # dense array
+            N = self_shape[index_ndim]
+            idx = _asindices(idx, N, self_format)
+            index.append(idx)
+            arr_int_pos.append(index_ndim)
+            array_indices.append(index_ndim)
+            index_ndim += 1
+    if len(array_indices) > 1:
+        arr_shapes = [index[i].shape for i in array_indices]
+        try:
+            arr_shape = np.broadcast_shapes(*arr_shapes)
+        except ValueError:
+            shapes = " ".join(str(shp) for shp in arr_shapes)
+            msg = (f'shape mismatch: indexing arrays could not be broadcast '
+                   f'together with shapes {shapes}')
+            raise IndexError(msg)
+        # len(array_indices) implies arr_int_pos has at least one element
+        # if arrays and ints not adjacent, move to front of shape
+        if len(arr_int_pos) != (arr_int_pos[-1] - arr_int_pos[0] + 1):
+            idx_shape = list(arr_shape) + idx_shape
+        else:
+            arr_pos = arr_int_pos[0]
+            idx_shape = idx_shape[:arr_pos] + list(arr_shape) + idx_shape[arr_pos:]
+    elif len(array_indices) == 1:
+        arr_shape = index[array_indices[0]].shape
+        arr_pos = arr_int_pos[0]
+        idx_shape = idx_shape[:arr_pos] + list(arr_shape) + idx_shape[arr_pos:]
+    return tuple(index), tuple(idx_shape), arr_int_pos, none_positions
+
+
+def _asindices(idx, length, format):
+    """Convert `idx` to a valid index for an axis with a given length.
+
+    Subclasses that need special validation can override this method.
+    """
+    try:
+        ix = np.asarray(idx)
+    except (ValueError, TypeError, MemoryError) as e:
+        raise IndexError('invalid index') from e
+
+    if format != "coo" and ix.ndim not in (1, 2) or format == "coo" and ix.ndim == 0:
+        raise IndexError(f'Index dimension must be 1 or 2. Got {ix.ndim}')
+
+    # LIL routines handle bounds-checking for us, so don't do it here.
+    if format == "lil":
+        return ix
+
+    if ix.size == 0:
+        return ix
+
+    # Check bounds
+    max_indx = ix.max()
+    if max_indx >= length:
+        raise IndexError(f'index ({max_indx}) out of range')
+
+    min_indx = ix.min()
+    if min_indx < 0:
+        if min_indx < -length:
+            raise IndexError(f'index ({min_indx}) out of range')
+        if ix is idx or not ix.flags.owndata:
+            ix = ix.copy()
+        ix[ix < 0] += length
+    return ix
+
+
+def _compatible_boolean_index(idx, desired_ndim):
+    """Check for boolean array or array-like. peek before asarray for array-like"""
+    # use attribute ndim to indicate a compatible array and check dtype
+    # if not, look at 1st element as quick rejection of bool, else slower asanyarray
+    if not hasattr(idx, 'ndim'):
+        # is first element boolean?
+        try:
+            ix = next(iter(idx), None)
+            for _ in range(desired_ndim):
+                if isinstance(ix, bool):
+                    break
+                ix = next(iter(ix), None)
+            else:
+                return None
+        except TypeError:
+            return None
+        # since first is boolean, construct array and check all elements
+        idx = np.asanyarray(idx)
+
+    if idx.dtype.kind == 'b':
+        return idx
+    return None
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/_lil.py b/venv/lib/python3.12/site-packages/scipy/sparse/_lil.py
new file mode 100644
index 0000000000000000000000000000000000000000..1fb85280af3242b52b2a4123a0bb161c13d93dec
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/_lil.py
@@ -0,0 +1,676 @@
+"""List of Lists sparse matrix class
+"""
+
+__docformat__ = "restructuredtext en"
+
+__all__ = ['lil_array', 'lil_matrix', 'isspmatrix_lil']
+
+from bisect import bisect_left
+
+import numpy as np
+
+from ._matrix import spmatrix
+from ._base import _spbase, sparray, issparse
+from ._index import IndexMixin, INT_TYPES, _broadcast_arrays
+from ._sputils import (getdtype, isshape, isscalarlike, upcast_scalar,
+                       check_shape)
+from . import _csparsetools
+
+
+class _lil_base(_spbase, IndexMixin):
+    _format = 'lil'
+
+    def __init__(self, arg1, shape=None, dtype=None, copy=False, *, maxprint=None):
+        _spbase.__init__(self, arg1, maxprint=maxprint)
+        self.dtype = getdtype(dtype, arg1, default=float)
+
+        # First get the shape
+        if issparse(arg1):
+            if arg1.format == "lil" and copy:
+                A = arg1.copy()
+            else:
+                A = arg1.tolil()
+
+            if dtype is not None:
+                newdtype = getdtype(dtype)
+                A = A.astype(newdtype, copy=False)
+
+            self._shape = check_shape(A.shape)
+            self.dtype = A.dtype
+            self.rows = A.rows
+            self.data = A.data
+        elif isinstance(arg1,tuple):
+            if isshape(arg1):
+                if shape is not None:
+                    raise ValueError('invalid use of shape parameter')
+                M, N = arg1
+                self._shape = check_shape((M, N))
+                self.rows = np.empty((M,), dtype=object)
+                self.data = np.empty((M,), dtype=object)
+                for i in range(M):
+                    self.rows[i] = []
+                    self.data[i] = []
+            else:
+                raise TypeError('unrecognized lil_array constructor usage')
+        else:
+            # assume A is dense
+            try:
+                A = self._ascontainer(arg1)
+            except TypeError as e:
+                raise TypeError('unsupported matrix type') from e
+            if isinstance(self, sparray) and A.ndim != 2:
+                raise ValueError(f"LIL arrays don't support {A.ndim}D input. Use 2D")
+            A = self._csr_container(A, dtype=dtype).tolil()
+
+            self._shape = check_shape(A.shape)
+            self.dtype = getdtype(A.dtype)
+            self.rows = A.rows
+            self.data = A.data
+
+    def __iadd__(self,other):
+        self[:,:] = self + other
+        return self
+
+    def __isub__(self,other):
+        self[:,:] = self - other
+        return self
+
+    def __imul__(self,other):
+        if isscalarlike(other):
+            self[:,:] = self * other
+            return self
+        else:
+            return NotImplemented
+
+    def __itruediv__(self,other):
+        if isscalarlike(other):
+            self[:,:] = self / other
+            return self
+        else:
+            return NotImplemented
+
+    # Whenever the dimensions change, empty lists should be created for each
+    # row
+
+    def _getnnz(self, axis=None):
+        if axis is None:
+            return sum([len(rowvals) for rowvals in self.data])
+        if axis < 0:
+            axis += 2
+        if axis == 0:
+            out = np.zeros(self.shape[1], dtype=np.intp)
+            for row in self.rows:
+                out[row] += 1
+            return out
+        elif axis == 1:
+            return np.array([len(rowvals) for rowvals in self.data], dtype=np.intp)
+        else:
+            raise ValueError('axis out of bounds')
+
+    _getnnz.__doc__ = _spbase._getnnz.__doc__
+
+    def count_nonzero(self, axis=None):
+        if axis is None:
+            return sum(np.count_nonzero(rowvals) for rowvals in self.data)
+
+        if axis < 0:
+            axis += 2
+        if axis == 0:
+            out = np.zeros(self.shape[1], dtype=np.intp)
+            for row, data in zip(self.rows, self.data):
+                mask = [c for c, d in zip(row, data) if d != 0]
+                out[mask] += 1
+            return out
+        elif axis == 1:
+            return np.array(
+                [np.count_nonzero(rowvals) for rowvals in self.data], dtype=np.intp,
+            )
+        else:
+            raise ValueError('axis out of bounds')
+
+    count_nonzero.__doc__ = _spbase.count_nonzero.__doc__
+
+    def getrowview(self, i):
+        """Returns a view of the 'i'th row (without copying).
+
+        Parameters
+        ----------
+        i : int
+            Row to return view of.
+
+        Returns
+        -------
+        lil_array or lil_matrix
+            A view of the 'i'th row.
+        """
+        new = self._lil_container((1, self.shape[1]), dtype=self.dtype)
+        new.rows[0] = self.rows[i]
+        new.data[0] = self.data[i]
+        return new
+
+    def getrow(self, i):
+        """Returns a copy of the 'i'th row.
+
+        Parameters
+        ----------
+        i : int
+            Row to return a copy of.
+
+        Returns
+        -------
+        lil_array or lil_matrix
+            A copy of the 'i'th row.
+        """
+        M, N = self.shape
+        if i < 0:
+            i += M
+        if i < 0 or i >= M:
+            raise IndexError('row index out of bounds')
+        new = self._lil_container((1, N), dtype=self.dtype)
+        new.rows[0] = self.rows[i][:]
+        new.data[0] = self.data[i][:]
+        return new
+
+    def __getitem__(self, key):
+        # Fast path for simple (int, int) indexing.
+        if (isinstance(key, tuple) and len(key) == 2 and
+                isinstance(key[0], INT_TYPES) and
+                isinstance(key[1], INT_TYPES)):
+            # lil_get1 handles validation for us.
+            return self._get_intXint(*key)
+        # Everything else takes the normal path.
+        return IndexMixin.__getitem__(self, key)
+
+    def _get_intXint(self, row, col):
+        v = _csparsetools.lil_get1(self.shape[0], self.shape[1], self.rows,
+                                   self.data, row, col)
+        return self.dtype.type(v)
+
+    def _get_sliceXint(self, row, col):
+        row = range(*row.indices(self.shape[0]))
+        return self._get_row_ranges(row, slice(col, col+1))
+
+    def _get_arrayXint(self, row, col):
+        res = self._get_row_ranges(row.ravel(), slice(col, col+1))
+        if row.ndim > 1:
+            return res.reshape(row.shape)
+        return res
+
+    def _get_intXslice(self, row, col):
+        return self._get_row_ranges((row,), col)
+
+    def _get_sliceXslice(self, row, col):
+        row = range(*row.indices(self.shape[0]))
+        return self._get_row_ranges(row, col)
+
+    def _get_arrayXslice(self, row, col):
+        return self._get_row_ranges(row, col)
+
+    def _get_intXarray(self, row, col):
+        row = np.array(row, dtype=col.dtype, ndmin=1)
+        return self._get_columnXarray(row, col)
+
+    def _get_sliceXarray(self, row, col):
+        row = np.arange(*row.indices(self.shape[0]))
+        return self._get_columnXarray(row, col)
+
+    def _get_columnXarray(self, row, col):
+        # outer indexing
+        row, col = _broadcast_arrays(row[:,None], col)
+        return self._get_arrayXarray(row, col)
+
+    def _get_arrayXarray(self, row, col):
+        # inner indexing
+        i, j = map(np.atleast_2d, _prepare_index_for_memoryview(row, col))
+        new = self._lil_container(i.shape, dtype=self.dtype)
+        _csparsetools.lil_fancy_get(self.shape[0], self.shape[1],
+                                    self.rows, self.data,
+                                    new.rows, new.data,
+                                    i, j)
+        return new
+
+    def _get_row_ranges(self, rows, col_slice):
+        """
+        Fast path for indexing in the case where column index is slice.
+
+        This gains performance improvement over brute force by more
+        efficient skipping of zeros, by accessing the elements
+        column-wise in order.
+
+        Parameters
+        ----------
+        rows : sequence or range
+            Rows indexed. If range, must be within valid bounds.
+        col_slice : slice
+            Columns indexed
+
+        """
+        j_start, j_stop, j_stride = col_slice.indices(self.shape[1])
+        col_range = range(j_start, j_stop, j_stride)
+        nj = len(col_range)
+        new = self._lil_container((len(rows), nj), dtype=self.dtype)
+
+        _csparsetools.lil_get_row_ranges(self.shape[0], self.shape[1],
+                                         self.rows, self.data,
+                                         new.rows, new.data,
+                                         rows,
+                                         j_start, j_stop, j_stride, nj)
+
+        return new
+
+    def _set_intXint(self, row, col, x):
+        _csparsetools.lil_insert(self.shape[0], self.shape[1], self.rows,
+                                 self.data, row, col, x)
+
+    def _set_arrayXarray(self, row, col, x):
+        i, j, x = map(np.atleast_2d, _prepare_index_for_memoryview(row, col, x))
+        _csparsetools.lil_fancy_set(self.shape[0], self.shape[1],
+                                    self.rows, self.data,
+                                    i, j, x)
+
+    def _set_arrayXarray_sparse(self, row, col, x):
+        # Fall back to densifying x
+        x = np.asarray(x.toarray(), dtype=self.dtype)
+        x, _ = _broadcast_arrays(x, row)
+        self._set_arrayXarray(row, col, x)
+
+    def __setitem__(self, key, x):
+        if isinstance(key, tuple) and len(key) == 2:
+            row, col = key
+            # Fast path for simple (int, int) indexing.
+            if isinstance(row, INT_TYPES) and isinstance(col, INT_TYPES):
+                if issparse(x):
+                    x = x.toarray()
+                if isinstance(x, np.ndarray):
+                    x = x.item()
+                x = self.dtype.type(x)
+                if x.size > 1:
+                    raise ValueError("Trying to assign a sequence to an item")
+                return self._set_intXint(row, col, x)
+            # Fast path for full-matrix sparse assignment.
+            if (isinstance(row, slice) and isinstance(col, slice) and
+                    row == slice(None) and col == slice(None) and
+                    issparse(x) and x.shape == self.shape):
+                x = self._lil_container(x, dtype=self.dtype)
+                self.rows = x.rows
+                self.data = x.data
+                return
+        # Everything else takes the normal path.
+        IndexMixin.__setitem__(self, key, x)
+
+    def _mul_scalar(self, other):
+        if other == 0:
+            # Multiply by zero: return the zero matrix
+            new = self._lil_container(self.shape, dtype=self.dtype)
+        else:
+            res_dtype = upcast_scalar(self.dtype, other)
+
+            new = self.astype(res_dtype)  # sure to make a copy
+            # Multiply this scalar by every element.
+            for j, rowvals in enumerate(new.data):
+                new.data[j] = [val*other for val in rowvals]
+        return new
+
+    def __truediv__(self, other):           # self / other
+        if isscalarlike(other):
+            new = self.copy()
+            new.dtype = np.result_type(self, other)
+            # Divide every element by this scalar
+            for j, rowvals in enumerate(new.data):
+                new.data[j] = [val/other for val in rowvals]
+            return new
+        else:
+            return self.tocsr() / other
+
+    def copy(self):
+        M, N = self.shape
+        new = self._lil_container(self.shape, dtype=self.dtype)
+        # This is ~14x faster than calling deepcopy() on rows and data.
+        _csparsetools.lil_get_row_ranges(M, N, self.rows, self.data,
+                                         new.rows, new.data, range(M),
+                                         0, N, 1, N)
+        return new
+
+    copy.__doc__ = _spbase.copy.__doc__
+
+    def reshape(self, *shape, order="C", copy=False):
+        shape = check_shape(shape, self.shape)
+
+        # Return early if reshape is not required
+        if shape == self.shape:
+            if copy:
+                return self.copy()
+            else:
+                return self
+
+        new = self._lil_container(shape, dtype=self.dtype)
+
+        if order == 'C':
+            ncols = self.shape[1]
+            for i, row in enumerate(self.rows):
+                for col, j in enumerate(row):
+                    new_r, new_c = np.unravel_index(i * ncols + j, shape)
+                    new[new_r, new_c] = self[i, j]
+        elif order == 'F':
+            nrows = self.shape[0]
+            for i, row in enumerate(self.rows):
+                for col, j in enumerate(row):
+                    new_r, new_c = np.unravel_index(i + j * nrows, shape, order)
+                    new[new_r, new_c] = self[i, j]
+        else:
+            raise ValueError("'order' must be 'C' or 'F'")
+
+        return new
+
+    reshape.__doc__ = _spbase.reshape.__doc__
+
+    def resize(self, *shape):
+        shape = check_shape(shape)
+        new_M, new_N = shape
+        M, N = self.shape
+
+        if new_M < M:
+            self.rows = self.rows[:new_M]
+            self.data = self.data[:new_M]
+        elif new_M > M:
+            self.rows = np.resize(self.rows, new_M)
+            self.data = np.resize(self.data, new_M)
+            for i in range(M, new_M):
+                self.rows[i] = []
+                self.data[i] = []
+
+        if new_N < N:
+            for row, data in zip(self.rows, self.data):
+                trunc = bisect_left(row, new_N)
+                del row[trunc:]
+                del data[trunc:]
+
+        self._shape = shape
+
+    resize.__doc__ = _spbase.resize.__doc__
+
+    def toarray(self, order=None, out=None):
+        d = self._process_toarray_args(order, out)
+        for i, row in enumerate(self.rows):
+            for pos, j in enumerate(row):
+                d[i, j] = self.data[i][pos]
+        return d
+
+    toarray.__doc__ = _spbase.toarray.__doc__
+
+    def transpose(self, axes=None, copy=False):
+        return self.tocsr(copy=copy).transpose(axes=axes, copy=False).tolil(copy=False)
+
+    transpose.__doc__ = _spbase.transpose.__doc__
+
+    def tolil(self, copy=False):
+        if copy:
+            return self.copy()
+        else:
+            return self
+
+    tolil.__doc__ = _spbase.tolil.__doc__
+
+    def tocsr(self, copy=False):
+        M, N = self.shape
+        if M == 0 or N == 0:
+            return self._csr_container((M, N), dtype=self.dtype)
+
+        # construct indptr array
+        if M*N <= np.iinfo(np.int32).max:
+            # fast path: it is known that 64-bit indexing will not be needed.
+            idx_dtype = np.int32
+            indptr = np.empty(M + 1, dtype=idx_dtype)
+            indptr[0] = 0
+            _csparsetools.lil_get_lengths(self.rows, indptr[1:])
+            np.cumsum(indptr, out=indptr)
+            nnz = indptr[-1]
+        else:
+            idx_dtype = self._get_index_dtype(maxval=N)
+            lengths = np.empty(M, dtype=idx_dtype)
+            _csparsetools.lil_get_lengths(self.rows, lengths)
+            nnz = lengths.sum(dtype=np.int64)
+            idx_dtype = self._get_index_dtype(maxval=max(N, nnz))
+            indptr = np.empty(M + 1, dtype=idx_dtype)
+            indptr[0] = 0
+            np.cumsum(lengths, dtype=idx_dtype, out=indptr[1:])
+
+        indices = np.empty(nnz, dtype=idx_dtype)
+        data = np.empty(nnz, dtype=self.dtype)
+        _csparsetools.lil_flatten_to_array(self.rows, indices)
+        _csparsetools.lil_flatten_to_array(self.data, data)
+
+        # init csr matrix
+        return self._csr_container((data, indices, indptr), shape=self.shape)
+
+    tocsr.__doc__ = _spbase.tocsr.__doc__
+
+
+def _prepare_index_for_memoryview(i, j, x=None):
+    """
+    Convert index and data arrays to form suitable for passing to the
+    Cython fancy getset routines.
+
+    The conversions are necessary since to (i) ensure the integer
+    index arrays are in one of the accepted types, and (ii) to ensure
+    the arrays are writable so that Cython memoryview support doesn't
+    choke on them.
+
+    Parameters
+    ----------
+    i, j
+        Index arrays
+    x : optional
+        Data arrays
+
+    Returns
+    -------
+    i, j, x
+        Re-formatted arrays (x is omitted, if input was None)
+
+    """
+    if i.dtype > j.dtype:
+        j = j.astype(i.dtype)
+    elif i.dtype < j.dtype:
+        i = i.astype(j.dtype)
+
+    if not i.flags.writeable or i.dtype not in (np.int32, np.int64):
+        i = i.astype(np.intp)
+    if not j.flags.writeable or j.dtype not in (np.int32, np.int64):
+        j = j.astype(np.intp)
+
+    if x is not None:
+        if not x.flags.writeable:
+            x = x.copy()
+        return i, j, x
+    else:
+        return i, j
+
+
+def isspmatrix_lil(x):
+    """Is `x` of lil_matrix type?
+
+    .. warning::
+
+       SciPy sparse is shifting from a sparse matrix interface to a sparse
+       array interface. In the next few releases we expect to deprecate the
+       sparse matrix interface. For documentation of the matrix
+       interface, see the :ref:`spmatrix interface docs <spmatrix_api>`.
+       For guidance on converting existing code to sparse arrays, see
+       :ref:`Migration from spmatrix to sparray <migration_to_sparray>`.
+
+    Parameters
+    ----------
+    x
+        object to check for being a lil matrix
+
+    Returns
+    -------
+    bool
+        True if `x` is a lil matrix, False otherwise
+
+    Examples
+    --------
+    >>> from scipy.sparse import lil_array, lil_matrix, coo_matrix, isspmatrix_lil
+    >>> isspmatrix_lil(lil_matrix([[5]]))
+    True
+    >>> isspmatrix_lil(lil_array([[5]]))
+    False
+    >>> isspmatrix_lil(coo_matrix([[5]]))
+    False
+    """
+    return isinstance(x, lil_matrix)
+
+
+# This namespace class separates array from matrix with isinstance
+class lil_array(_lil_base, sparray):
+    """
+    Row-based LIst of Lists sparse array.
+
+    This is a structure for constructing sparse arrays incrementally.
+    Note that inserting a single item can take linear time in the worst case;
+    to construct the array efficiently, make sure the items are pre-sorted by
+    index, per row.
+
+    This can be instantiated in several ways:
+        lil_array(D)
+            where D is a 2-D ndarray
+
+        lil_array(S)
+            with another sparse array or matrix S (equivalent to S.tolil())
+
+        lil_array((M, N), [dtype])
+            to construct an empty array with shape (M, N)
+            dtype is optional, defaulting to dtype='d'.
+
+    Attributes
+    ----------
+    data : ndarray
+        LIL format data array of the array
+    rows : ndarray
+        LIL format row index array of the array
+    dtype : dtype
+        Data type of the array
+    shape : 2-tuple
+        Shape of the array
+    ndim : int
+        Number of dimensions (this is always 2)
+    format : str
+        Three letter code for the format of the array storage, e.g. 'lil'
+    nnz : int
+        Number of values stored in the array
+    size : int
+        Number of values stored in the array
+    T : lil_array
+        The transpose of the array
+    mT : lil_array
+        The matrix transpose of the array
+
+    Notes
+    -----
+    Sparse arrays can be used in arithmetic operations: they support
+    addition, subtraction, multiplication, division, and matrix power.
+
+    Advantages of the LIL format
+        - supports flexible slicing
+        - changes to the array sparsity structure are efficient
+
+    Disadvantages of the LIL format
+        - arithmetic operations LIL + LIL are slow (consider CSR or CSC)
+        - slow column slicing (consider CSC)
+        - slow matrix vector products (consider CSR or CSC)
+
+    Intended Usage
+        - LIL is a convenient format for constructing sparse arrays
+        - once an array has been constructed, convert to CSR or
+          CSC format for fast arithmetic and matrix vector operations
+        - consider using the COO format when constructing large arrays
+
+    Data Structure
+        - An array (``self.rows``) of rows, each of which is a sorted
+          list of column indices of non-zero elements.
+        - The corresponding nonzero values are stored in similar
+          fashion in ``self.data``.
+
+    """  # numpydoc ignore=PR01
+
+
+class lil_matrix(spmatrix, _lil_base):
+    """
+    Row-based LIst of Lists sparse matrix.
+
+    This is a structure for constructing sparse matrices incrementally.
+    Note that inserting a single item can take linear time in the worst case;
+    to construct the matrix efficiently, make sure the items are pre-sorted by
+    index, per row.
+
+    .. warning::
+
+       SciPy sparse is shifting from a sparse matrix interface to a sparse
+       array interface. In the next few releases we expect to deprecate the
+       sparse matrix interface. For documentation of the matrix
+       interface, see the :ref:`spmatrix interface docs <spmatrix_api>`.
+       For guidance on converting existing code to sparse arrays, see
+       :ref:`Migration from spmatrix to sparray <migration_to_sparray>`.
+
+    This can be instantiated in several ways:
+        lil_matrix(D)
+            where D is a 2-D ndarray
+
+        lil_matrix(S)
+            with another sparse array or matrix S (equivalent to S.tolil())
+
+        lil_matrix((M, N), [dtype])
+            to construct an empty matrix with shape (M, N)
+            dtype is optional, defaulting to dtype='d'.
+
+    Attributes
+    ----------
+    data : ndarray
+        LIL format data array of the matrix
+    rows : ndarray
+        LIL format row index array of the matrix
+    dtype : dtype
+        Data type of the matrix
+    shape : 2-tuple
+        Shape of the matrix
+    ndim : int
+        Number of dimensions (this is always 2)
+    format : str
+        Three letter code for the format of the matrix storage, e.g. 'lil'
+    nnz : int
+        Number of values stored in the matrix
+    size : int
+        Number of values stored in the matrix
+    T : lil_matrix
+        The transpose of the matrix
+    mT : lil_array
+        The transpose of the matrix
+
+    Notes
+    -----
+    Sparse matrices can be used in arithmetic operations: they support
+    addition, subtraction, multiplication, division, and matrix power.
+
+    Advantages of the LIL format
+        - supports flexible slicing
+        - changes to the matrix sparsity structure are efficient
+
+    Disadvantages of the LIL format
+        - arithmetic operations LIL + LIL are slow (consider CSR or CSC)
+        - slow column slicing (consider CSC)
+        - slow matrix vector products (consider CSR or CSC)
+
+    Intended Usage
+        - LIL is a convenient format for constructing sparse matrices
+        - once a matrix has been constructed, convert to CSR or
+          CSC format for fast arithmetic and matrix vector operations
+        - consider using the COO format when constructing large matrices
+
+    Data Structure
+        - An array (``self.rows``) of rows, each of which is a sorted
+          list of column indices of non-zero elements.
+        - The corresponding nonzero values are stored in similar
+          fashion in ``self.data``.
+
+    """
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/_matrix.py b/venv/lib/python3.12/site-packages/scipy/sparse/_matrix.py
new file mode 100644
index 0000000000000000000000000000000000000000..4840d33d91a652fa69f567411a88cce1d5da842b
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/_matrix.py
@@ -0,0 +1,179 @@
+class spmatrix:
+    """This class provides a base class for all sparse matrix classes.
+
+    .. warning::
+
+       SciPy sparse is shifting from a sparse matrix interface to a sparse
+       array interface. In the next few releases we expect to deprecate the
+       sparse matrix interface. For documentation of the matrix
+       interface, see the :ref:`spmatrix interface docs <spmatrix_api>`.
+       For guidance on converting existing code to sparse arrays, see
+       :ref:`Migration from spmatrix to sparray <migration_to_sparray>`.
+
+    This class also serves as the namespace for SciPy sparse matrix types.
+    It cannot be instantiated.  Most of the work is provided by subclasses.
+    """
+    _allow_nd: tuple[int, ...] = (2,)
+
+    @property
+    def _bsr_container(self):
+        from ._bsr import bsr_matrix
+        return bsr_matrix
+
+    @property
+    def _coo_container(self):
+        from ._coo import coo_matrix
+        return coo_matrix
+
+    @property
+    def _csc_container(self):
+        from ._csc import csc_matrix
+        return csc_matrix
+
+    @property
+    def _csr_container(self):
+        from ._csr import csr_matrix
+        return csr_matrix
+
+    @property
+    def _dia_container(self):
+        from ._dia import dia_matrix
+        return dia_matrix
+
+    @property
+    def _dok_container(self):
+        from ._dok import dok_matrix
+        return dok_matrix
+
+    @property
+    def _lil_container(self):
+        from ._lil import lil_matrix
+        return lil_matrix
+
+    # Restore matrix multiplication
+    def __mul__(self, other):
+        return self._matmul_dispatch(other)
+
+    def __rmul__(self, other):
+        return self._rmatmul_dispatch(other)
+
+    # Restore matrix power
+    def __pow__(self, power):
+        from .linalg import matrix_power
+
+        return matrix_power(self, power)
+
+    ## Backward compatibility
+
+    def set_shape(self, shape):
+        """Set the shape of the matrix in-place"""
+        # Make sure copy is False since this is in place
+        # Make sure format is unchanged because we are doing a __dict__ swap
+        new_self = self.reshape(shape, copy=False).asformat(self.format)
+        self.__dict__ = new_self.__dict__
+
+    def get_shape(self):
+        """Get the shape of the matrix"""
+        return self._shape
+
+    shape = property(fget=get_shape, fset=set_shape,
+                     doc="Shape of the matrix")
+
+    def asfptype(self):
+        """Upcast matrix to a floating point format (if necessary)"""
+        return self._asfptype()
+
+    def getmaxprint(self):
+        """Maximum number of elements to display when printed."""
+        return self._getmaxprint()
+
+    def getformat(self):
+        """Matrix storage format"""
+        return self.format
+
+    def getnnz(self, axis=None):
+        """Number of stored values, including explicit zeros.
+
+        Parameters
+        ----------
+        axis : None, 0, or 1
+            Select between the number of values across the whole array, in
+            each column, or in each row.
+        """
+        return self._getnnz(axis=axis)
+
+    def getH(self):
+        """Return the Hermitian transpose of this matrix.
+
+        See Also
+        --------
+        numpy.matrix.getH : NumPy's implementation of `getH` for matrices
+        """
+        return self.conjugate().transpose()
+
+    def getcol(self, j):
+        """Returns a copy of column j of the matrix, as an (m x 1) sparse
+        matrix (column vector).
+        """
+        return self._getcol(j)
+
+    def getrow(self, i):
+        """Returns a copy of row i of the matrix, as a (1 x n) sparse
+        matrix (row vector).
+        """
+        return self._getrow(i)
+
+    def todense(self, order=None, out=None):
+        """
+        Return a dense representation of this sparse matrix.
+
+        Parameters
+        ----------
+        order : {'C', 'F'}, optional
+            Whether to store multi-dimensional data in C (row-major)
+            or Fortran (column-major) order in memory. The default
+            is 'None', which provides no ordering guarantees.
+            Cannot be specified in conjunction with the `out`
+            argument.
+
+        out : ndarray, 2-D, optional
+            If specified, uses this array (or `numpy.matrix`) as the
+            output buffer instead of allocating a new array to
+            return. The provided array must have the same shape and
+            dtype as the sparse matrix on which you are calling the
+            method.
+
+        Returns
+        -------
+        arr : numpy.matrix, 2-D
+            A NumPy matrix object with the same shape and containing
+            the same data represented by the sparse matrix, with the
+            requested memory order. If `out` was passed and was an
+            array (rather than a `numpy.matrix`), it will be filled
+            with the appropriate values and returned wrapped in a
+            `numpy.matrix` object that shares the same memory.
+        """
+        return super().todense(order, out)
+
+    @classmethod
+    def __class_getitem__(cls, arg, /):
+        """
+        Return a parametrized wrapper around the `~scipy.sparse.spmatrix` type.
+
+        .. versionadded:: 1.16.0
+
+        Returns
+        -------
+        alias : types.GenericAlias
+            A parametrized `~scipy.sparse.spmatrix` type.
+
+        Examples
+        --------
+        >>> import numpy as np
+        >>> from scipy.sparse import coo_matrix
+
+        >>> coo_matrix[np.int8]
+        scipy.sparse._coo.coo_matrix[numpy.int8]
+        """
+        from types import GenericAlias
+        return GenericAlias(cls, arg)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/_matrix_io.py b/venv/lib/python3.12/site-packages/scipy/sparse/_matrix_io.py
new file mode 100644
index 0000000000000000000000000000000000000000..424af914a4336bc9102c16059d4ed827fe4ac614
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/_matrix_io.py
@@ -0,0 +1,172 @@
+import numpy as np
+import scipy as sp
+
+__all__ = ['save_npz', 'load_npz']
+
+
+# Make loading safe vs. malicious input
+PICKLE_KWARGS = dict(allow_pickle=False)
+
+
+def save_npz(file, matrix, compressed=True):
+    """ Save a sparse matrix or array to a file using ``.npz`` format.
+
+    Parameters
+    ----------
+    file : str or file-like object
+        Either the file name (string) or an open file (file-like object)
+        where the data will be saved. If file is a string, the ``.npz``
+        extension will be appended to the file name if it is not already
+        there.
+    matrix : spmatrix or sparray
+        The sparse matrix or array to save.
+        Supported formats: ``csc``, ``csr``, ``bsr``, ``dia`` or ``coo``.
+    compressed : bool, optional
+        Allow compressing the file. Default: True
+
+    See Also
+    --------
+    scipy.sparse.load_npz: Load a sparse matrix from a file using ``.npz`` format.
+    numpy.savez: Save several arrays into a ``.npz`` archive.
+    numpy.savez_compressed : Save several arrays into a compressed ``.npz`` archive.
+
+    Examples
+    --------
+    Store sparse matrix to disk, and load it again:
+
+    >>> import numpy as np
+    >>> import scipy as sp
+    >>> sparse_array = sp.sparse.csc_array([[0, 0, 3], [4, 0, 0]])
+    >>> sparse_array
+    <Compressed Sparse Column sparse array of dtype 'int64'
+        with 2 stored elements and shape (2, 3)>
+    >>> sparse_array.toarray()
+    array([[0, 0, 3],
+           [4, 0, 0]], dtype=int64)
+
+    >>> sp.sparse.save_npz('/tmp/sparse_array.npz', sparse_array)
+    >>> sparse_array = sp.sparse.load_npz('/tmp/sparse_array.npz')
+
+    >>> sparse_array
+    <Compressed Sparse Column sparse array of dtype 'int64'
+        with 2 stored elements and shape (2, 3)>
+    >>> sparse_array.toarray()
+    array([[0, 0, 3],
+           [4, 0, 0]], dtype=int64)
+    """
+    arrays_dict = {}
+    if matrix.format in ('csc', 'csr', 'bsr'):
+        arrays_dict.update(indices=matrix.indices, indptr=matrix.indptr)
+    elif matrix.format == 'dia':
+        arrays_dict.update(offsets=matrix.offsets)
+    elif matrix.format == 'coo':
+        if matrix.ndim == 2:
+            # TODO: After a few releases, switch 2D case to save with coords only.
+            arrays_dict.update(row=matrix.row, col=matrix.col)
+        else:
+            arrays_dict.update(coords=matrix.coords)
+    else:
+        msg = f'Save is not implemented for sparse matrix of format {matrix.format}.'
+        raise NotImplementedError(msg)
+    arrays_dict.update(
+        format=matrix.format.encode('ascii'),
+        shape=matrix.shape,
+        data=matrix.data
+    )
+    if isinstance(matrix, sp.sparse.sparray):
+        arrays_dict.update(_is_array=True)
+    if compressed:
+        np.savez_compressed(file, **arrays_dict)
+    else:
+        np.savez(file, **arrays_dict)
+
+
+def load_npz(file):
+    """ Load a sparse array/matrix from a file using ``.npz`` format.
+
+    Parameters
+    ----------
+    file : str or file-like object
+        Either the file name (string) or an open file (file-like object)
+        where the data will be loaded.
+
+    Returns
+    -------
+    result : csc_array, csr_array, bsr_array, dia_array or coo_array
+        A sparse array/matrix containing the loaded data.
+
+    Raises
+    ------
+    OSError
+        If the input file does not exist or cannot be read.
+
+    See Also
+    --------
+    scipy.sparse.save_npz: Save a sparse array/matrix to a file using ``.npz`` format.
+    numpy.load: Load several arrays from a ``.npz`` archive.
+
+    Examples
+    --------
+    Store sparse array/matrix to disk, and load it again:
+
+    >>> import numpy as np
+    >>> import scipy as sp
+    >>> sparse_array = sp.sparse.csc_array([[0, 0, 3], [4, 0, 0]])
+    >>> sparse_array
+    <Compressed Sparse Column sparse array of dtype 'int64'
+        with 2 stored elements and shape (2, 3)>
+    >>> sparse_array.toarray()
+    array([[0, 0, 3],
+           [4, 0, 0]], dtype=int64)
+
+    >>> sp.sparse.save_npz('/tmp/sparse_array.npz', sparse_array)
+    >>> sparse_array = sp.sparse.load_npz('/tmp/sparse_array.npz')
+
+    >>> sparse_array
+    <Compressed Sparse Column sparse array of dtype 'int64'
+        with 2 stored elements and shape (2, 3)>
+    >>> sparse_array.toarray()
+    array([[0, 0, 3],
+           [4, 0, 0]], dtype=int64)
+
+    In this example we force the result to be csr_array from csr_matrix
+    >>> sparse_matrix = sp.sparse.csc_matrix([[0, 0, 3], [4, 0, 0]])
+    >>> sp.sparse.save_npz('/tmp/sparse_matrix.npz', sparse_matrix)
+    >>> tmp = sp.sparse.load_npz('/tmp/sparse_matrix.npz')
+    >>> sparse_array = sp.sparse.csr_array(tmp)
+    """
+    with np.load(file, **PICKLE_KWARGS) as loaded:
+        sparse_format = loaded.get('format')
+        if sparse_format is None:
+            raise ValueError(f'The file {file} does not contain '
+                             f'a sparse array or matrix.')
+        sparse_format = sparse_format.item()
+
+        if not isinstance(sparse_format, str):
+            # Play safe with Python 2 vs 3 backward compatibility;
+            # files saved with SciPy < 1.0.0 may contain unicode or bytes.
+            sparse_format = sparse_format.decode('ascii')
+
+        if loaded.get('_is_array'):
+            sparse_type = sparse_format + '_array'
+        else:
+            sparse_type = sparse_format + '_matrix'
+
+        try:
+            cls = getattr(sp.sparse, f'{sparse_type}')
+        except AttributeError as e:
+            raise ValueError(f'Unknown format "{sparse_type}"') from e
+
+        if sparse_format in ('csc', 'csr', 'bsr'):
+            return cls((loaded['data'], loaded['indices'], loaded['indptr']),
+                       shape=loaded['shape'])
+        elif sparse_format == 'dia':
+            return cls((loaded['data'], loaded['offsets']), shape=loaded['shape'])
+        elif sparse_format == 'coo':
+            if 'coords' in loaded:
+                return cls((loaded['data'], loaded['coords']), shape=loaded['shape'])
+            return cls((loaded['data'], (loaded['row'], loaded['col'])),
+                       shape=loaded['shape'])
+        else:
+            raise NotImplementedError(f'Load is not implemented for '
+                                      f'sparse matrix of format {sparse_format}.')
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/_sparsetools.cpython-312-x86_64-linux-gnu.so b/venv/lib/python3.12/site-packages/scipy/sparse/_sparsetools.cpython-312-x86_64-linux-gnu.so
new file mode 100644
index 0000000000000000000000000000000000000000..131eeb6bfb98f738727235c1eb8a774dc5bcc100
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/_sparsetools.cpython-312-x86_64-linux-gnu.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:cc0a6897bae0bc9e0b8be15e38a3d9d15dcb34e3acf1b22656171117af71fcc5
+size 4554512
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/_spfuncs.py b/venv/lib/python3.12/site-packages/scipy/sparse/_spfuncs.py
new file mode 100644
index 0000000000000000000000000000000000000000..8e9b0abcede6387e74538baf839a303c6cc1b6be
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/_spfuncs.py
@@ -0,0 +1,76 @@
+""" Functions that operate on sparse matrices
+"""
+
+__all__ = ['count_blocks','estimate_blocksize']
+
+from ._base import issparse
+from ._csr import csr_array
+from ._sparsetools import csr_count_blocks
+
+
+def estimate_blocksize(A,efficiency=0.7):
+    """Attempt to determine the blocksize of a sparse matrix
+
+    Returns a blocksize=(r,c) such that
+        - A.nnz / A.tobsr( (r,c) ).nnz > efficiency
+    """
+    if not (issparse(A) and A.format in ("csc", "csr")):
+        A = csr_array(A)
+
+    if A.nnz == 0:
+        return (1,1)
+
+    if not 0 < efficiency < 1.0:
+        raise ValueError('efficiency must satisfy 0.0 < efficiency < 1.0')
+
+    high_efficiency = (1.0 + efficiency) / 2.0
+    nnz = float(A.nnz)
+    M,N = A.shape
+
+    if M % 2 == 0 and N % 2 == 0:
+        e22 = nnz / (4 * count_blocks(A,(2,2)))
+    else:
+        e22 = 0.0
+
+    if M % 3 == 0 and N % 3 == 0:
+        e33 = nnz / (9 * count_blocks(A,(3,3)))
+    else:
+        e33 = 0.0
+
+    if e22 > high_efficiency and e33 > high_efficiency:
+        e66 = nnz / (36 * count_blocks(A,(6,6)))
+        if e66 > efficiency:
+            return (6,6)
+        else:
+            return (3,3)
+    else:
+        if M % 4 == 0 and N % 4 == 0:
+            e44 = nnz / (16 * count_blocks(A,(4,4)))
+        else:
+            e44 = 0.0
+
+        if e44 > efficiency:
+            return (4,4)
+        elif e33 > efficiency:
+            return (3,3)
+        elif e22 > efficiency:
+            return (2,2)
+        else:
+            return (1,1)
+
+
+def count_blocks(A,blocksize):
+    """For a given blocksize=(r,c) count the number of occupied
+    blocks in a sparse matrix A
+    """
+    r,c = blocksize
+    if r < 1 or c < 1:
+        raise ValueError('r and c must be positive')
+
+    if issparse(A):
+        if A.format == "csr":
+            M,N = A.shape
+            return csr_count_blocks(M,N,r,c,A.indptr,A.indices)
+        elif A.format == "csc":
+            return count_blocks(A.T,(c,r))
+    return count_blocks(csr_array(A),blocksize)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/_sputils.py b/venv/lib/python3.12/site-packages/scipy/sparse/_sputils.py
new file mode 100644
index 0000000000000000000000000000000000000000..6930aee29c201e1b3636bec3629c0a9e00f1ab94
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/_sputils.py
@@ -0,0 +1,614 @@
+""" Utility functions for sparse matrix module
+"""
+
+import sys
+from typing import Any, Literal
+import operator
+import numpy as np
+from math import prod
+import scipy.sparse as sp
+
+
+__all__ = ['upcast', 'getdtype', 'getdata', 'isscalarlike', 'isintlike',
+           'isshape', 'issequence', 'isdense', 'ismatrix', 'get_sum_dtype',
+           'broadcast_shapes']
+
+supported_dtypes = [np.bool_, np.byte, np.ubyte, np.short, np.ushort, np.intc,
+                    np.uintc, np.long, np.ulong, np.longlong, np.ulonglong,
+                    np.float32, np.float64, np.longdouble,
+                    np.complex64, np.complex128, np.clongdouble]
+
+_upcast_memo = {}
+
+
+def upcast(*args):
+    """Returns the nearest supported sparse dtype for the
+    combination of one or more types.
+
+    upcast(t0, t1, ..., tn) -> T  where T is a supported dtype
+
+    Examples
+    --------
+    >>> from scipy.sparse._sputils import upcast
+    >>> upcast('int32')
+    <class 'numpy.int32'>
+    >>> upcast('bool')
+    <class 'numpy.bool'>
+    >>> upcast('int32','float32')
+    <class 'numpy.float64'>
+    >>> upcast('bool',complex,float)
+    <class 'numpy.complex128'>
+
+    """
+
+    t = _upcast_memo.get(hash(args))
+    if t is not None:
+        return t
+
+    upcast = np.result_type(*args)
+
+    for t in supported_dtypes:
+        if np.can_cast(upcast, t):
+            _upcast_memo[hash(args)] = t
+            return t
+
+    raise TypeError(f'no supported conversion for types: {args!r}')
+
+
+def upcast_char(*args):
+    """Same as `upcast` but taking dtype.char as input (faster)."""
+    t = _upcast_memo.get(args)
+    if t is not None:
+        return t
+    t = upcast(*map(np.dtype, args))
+    _upcast_memo[args] = t
+    return t
+
+
+def upcast_scalar(dtype, scalar):
+    """Determine data type for binary operation between an array of
+    type `dtype` and a scalar.
+    """
+    return (np.array([0], dtype=dtype) * scalar).dtype
+
+
+def downcast_intp_index(arr):
+    """
+    Down-cast index array to np.intp dtype if it is of a larger dtype.
+
+    Raise an error if the array contains a value that is too large for
+    intp.
+    """
+    if arr.dtype.itemsize > np.dtype(np.intp).itemsize:
+        if arr.size == 0:
+            return arr.astype(np.intp)
+        maxval = arr.max()
+        minval = arr.min()
+        if maxval > np.iinfo(np.intp).max or minval < np.iinfo(np.intp).min:
+            raise ValueError("Cannot deal with arrays with indices larger "
+                             "than the machine maximum address size "
+                             "(e.g. 64-bit indices on 32-bit machine).")
+        return arr.astype(np.intp)
+    return arr
+
+
+def to_native(A):
+    """
+    Ensure that the data type of the NumPy array `A` has native byte order.
+
+    `A` must be a NumPy array.  If the data type of `A` does not have native
+    byte order, a copy of `A` with a native byte order is returned. Otherwise
+    `A` is returned.
+    """
+    dt = A.dtype
+    if dt.isnative:
+        # Don't call `asarray()` if A is already native, to avoid unnecessarily
+        # creating a view of the input array.
+        return A
+    return np.asarray(A, dtype=dt.newbyteorder('native'))
+
+
+def getdtype(dtype, a=None, default=None):
+    """Form a supported numpy dtype based on input arguments.
+
+    Returns a valid ``numpy.dtype`` from `dtype` if not None,
+    or else ``a.dtype`` if possible, or else the given `default`
+    if not None, or else raise a ``TypeError``.
+
+    The resulting ``dtype`` must be in ``supported_dtypes``:
+        bool_, int8, uint8, int16, uint16, int32, uint32,
+        int64, uint64, longlong, ulonglong, float32, float64,
+        longdouble, complex64, complex128, clongdouble
+    """
+    if dtype is None:
+        try:
+            newdtype = a.dtype
+        except AttributeError as e:
+            if default is not None:
+                newdtype = np.dtype(default)
+            else:
+                raise TypeError("could not interpret data type") from e
+    else:
+        newdtype = np.dtype(dtype)
+
+    if newdtype not in supported_dtypes:
+        supported_dtypes_fmt = ", ".join(t.__name__ for t in supported_dtypes)
+        raise ValueError(f"scipy.sparse does not support dtype {newdtype}. "
+                         f"The only supported types are: {supported_dtypes_fmt}.")
+    return newdtype
+
+
+def getdata(obj, dtype=None, copy=False) -> np.ndarray:
+    """
+    This is a wrapper of `np.array(obj, dtype=dtype, copy=copy)`
+    that will generate a warning if the result is an object array.
+    """
+    data = np.array(obj, dtype=dtype, copy=copy)
+    # Defer to getdtype for checking that the dtype is OK.
+    # This is called for the validation only; we don't need the return value.
+    getdtype(data.dtype)
+    return data
+
+
+def safely_cast_index_arrays(A, idx_dtype=np.int32, msg=""):
+    """Safely cast sparse array indices to `idx_dtype`.
+
+    Check the shape of `A` to determine if it is safe to cast its index
+    arrays to dtype `idx_dtype`. If any dimension in shape is larger than
+    fits in the dtype, casting is unsafe so raise ``ValueError``.
+    If safe, cast the index arrays to `idx_dtype` and return the result
+    without changing the input `A`. The caller can assign results to `A`
+    attributes if desired or use the recast index arrays directly.
+
+    Unless downcasting is needed, the original index arrays are returned.
+    You can test e.g. ``A.indptr is new_indptr`` to see if downcasting occurred.
+
+    .. versionadded:: 1.15.0
+
+    Parameters
+    ----------
+    A : sparse array or matrix
+        The array for which index arrays should be downcast.
+    idx_dtype : dtype
+        Desired dtype. Should be an integer dtype (default: ``np.int32``).
+        Most of scipy.sparse uses either int64 or int32.
+    msg : str, optional
+        A string to be added to the end of the ValueError message
+        if the array shape is too big to fit in `idx_dtype`.
+        The error message is ``f"<index> values too large for {msg}"``
+        It should indicate why the downcasting is needed, e.g. "SuperLU",
+        and defaults to f"dtype {idx_dtype}".
+
+    Returns
+    -------
+    idx_arrays : ndarray or tuple of ndarrays
+        Based on ``A.format``, index arrays are returned after casting to `idx_dtype`.
+        For CSC/CSR, returns ``(indices, indptr)``.
+        For COO, returns ``coords``.
+        For DIA, returns ``offsets``.
+        For BSR, returns ``(indices, indptr)``.
+
+    Raises
+    ------
+    ValueError
+        If the array has shape that would not fit in the new dtype, or if
+        the sparse format does not use index arrays.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import sparse
+    >>> data = [3]
+    >>> coords = (np.array([3]), np.array([1]))  # Note: int64 arrays
+    >>> A = sparse.coo_array((data, coords))
+    >>> A.coords[0].dtype
+    dtype('int64')
+
+    >>> # rescast after construction, raising exception if shape too big
+    >>> coords = sparse.safely_cast_index_arrays(A, np.int32)
+    >>> A.coords[0] is coords[0]  # False if casting is needed
+    False
+    >>> A.coords = coords  # set the index dtype of A
+    >>> A.coords[0].dtype
+    dtype('int32')
+    """
+    if not msg:
+        msg = f"dtype {idx_dtype}"
+    # check for safe downcasting
+    max_value = np.iinfo(idx_dtype).max
+
+    if A.format in ("csc", "csr"):
+        # indptr[-1] is max b/c indptr always sorted
+        if A.indptr[-1] > max_value:
+            raise ValueError(f"indptr values too large for {msg}")
+
+        # check shape vs dtype
+        if max(*A.shape) > max_value:
+            if (A.indices > max_value).any():
+                raise ValueError(f"indices values too large for {msg}")
+
+        indices = A.indices.astype(idx_dtype, copy=False)
+        indptr = A.indptr.astype(idx_dtype, copy=False)
+        return indices, indptr
+
+    elif A.format == "coo":
+        if max(*A.shape) > max_value:
+            if any((co > max_value).any() for co in A.coords):
+                raise ValueError(f"coords values too large for {msg}")
+        return tuple(co.astype(idx_dtype, copy=False) for co in A.coords)
+
+    elif A.format == "dia":
+        if max(*A.shape) > max_value:
+            if (A.offsets > max_value).any():
+                raise ValueError(f"offsets values too large for {msg}")
+        offsets = A.offsets.astype(idx_dtype, copy=False)
+        return offsets
+
+    elif A.format == 'bsr':
+        R, C = A.blocksize
+        if A.indptr[-1] * R > max_value:
+            raise ValueError("indptr values too large for {msg}")
+        if max(*A.shape) > max_value:
+            if (A.indices * C > max_value).any():
+                raise ValueError(f"indices values too large for {msg}")
+        indices = A.indices.astype(idx_dtype, copy=False)
+        indptr = A.indptr.astype(idx_dtype, copy=False)
+        return indices, indptr
+
+    else:
+        raise TypeError(f'Format {A.format} is not associated with index arrays. '
+                        'DOK and LIL have dict and list, not array.')
+
+
+def get_index_dtype(arrays=(), maxval=None, check_contents=False):
+    """
+    Based on input (integer) arrays `a`, determine a suitable index data
+    type that can hold the data in the arrays.
+
+    Parameters
+    ----------
+    arrays : tuple of array_like
+        Input arrays whose types/contents to check
+    maxval : float, optional
+        Maximum value needed
+    check_contents : bool, optional
+        Whether to check the values in the arrays and not just their types.
+        Default: False (check only the types)
+
+    Returns
+    -------
+    dtype : dtype
+        Suitable index data type (int32 or int64)
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import sparse
+    >>> # select index dtype based on shape
+    >>> shape = (3, 3)
+    >>> idx_dtype = sparse.get_index_dtype(maxval=max(shape))
+    >>> data = [1.1, 3.0, 1.5]
+    >>> indices = np.array([0, 1, 0], dtype=idx_dtype)
+    >>> indptr = np.array([0, 2, 3, 3], dtype=idx_dtype)
+    >>> A = sparse.csr_array((data, indices, indptr), shape=shape)
+    >>> A.indptr.dtype
+    dtype('int32')
+
+    >>> # select based on larger of existing arrays and shape
+    >>> shape = (3, 3)
+    >>> idx_dtype = sparse.get_index_dtype(A.indptr, maxval=max(shape))
+    >>> idx_dtype
+    <class 'numpy.int32'>
+    """
+    # not using intc directly due to misinteractions with pythran
+    if np.intc().itemsize != 4:
+        return np.int64
+
+    int32min = np.int32(np.iinfo(np.int32).min)
+    int32max = np.int32(np.iinfo(np.int32).max)
+
+    if maxval is not None:
+        maxval = np.int64(maxval)
+        if maxval > int32max:
+            return np.int64
+
+    if isinstance(arrays, np.ndarray):
+        arrays = (arrays,)
+
+    for arr in arrays:
+        arr = np.asarray(arr)
+        if not np.can_cast(arr.dtype, np.int32):
+            if check_contents:
+                if arr.size == 0:
+                    # a bigger type not needed
+                    continue
+                elif np.issubdtype(arr.dtype, np.integer):
+                    maxval = arr.max()
+                    minval = arr.min()
+                    if minval >= int32min and maxval <= int32max:
+                        # a bigger type not needed
+                        continue
+            return np.int64
+    return np.int32
+
+
+def get_sum_dtype(dtype: np.dtype) -> np.dtype | type[np.generic]:
+    """Mimic numpy's casting for np.sum"""
+    if dtype.kind == 'u' and np.can_cast(dtype, np.uint):
+        return np.uint
+    if np.can_cast(dtype, np.int_):
+        return np.int_
+    return dtype
+
+
+def isscalarlike(x) -> bool:
+    """Is x either a scalar, an array scalar, or a 0-dim array?"""
+    return np.isscalar(x) or (isdense(x) and x.ndim == 0)
+
+
+def isintlike(x) -> bool:
+    """Is x appropriate as an index into a sparse matrix? Returns True
+    if it can be cast safely to a machine int.
+    """
+    # Fast-path check to eliminate non-scalar values. operator.index would
+    # catch this case too, but the exception catching is slow.
+    if np.ndim(x) != 0:
+        return False
+    try:
+        operator.index(x)
+    except (TypeError, ValueError):
+        try:
+            loose_int = bool(int(x) == x)
+        except (TypeError, ValueError):
+            return False
+        if loose_int:
+            msg = "Inexact indices into sparse matrices are not allowed"
+            raise ValueError(msg)
+        return loose_int
+    return True
+
+
+def isshape(x, nonneg=False, *, allow_nd=(2,), check_nd=True) -> bool:
+    """Is x a valid tuple of dimensions?
+
+    If nonneg, also checks that the dimensions are non-negative.
+    Shapes of length in the tuple allow_nd are allowed.
+    """
+    ndim = len(x)
+    if check_nd and ndim not in allow_nd:
+        return False
+
+    for d in x:
+        if not isintlike(d):
+            return False
+        if nonneg and d < 0:
+            return False
+    return True
+
+
+def issequence(t) -> bool:
+    return ((isinstance(t, list | tuple) and
+            (len(t) == 0 or np.isscalar(t[0]))) or
+            (isinstance(t, np.ndarray) and (t.ndim == 1)))
+
+
+def ismatrix(t) -> bool:
+    return ((isinstance(t, list | tuple) and
+             len(t) > 0 and issequence(t[0])) or
+            (isinstance(t, np.ndarray) and t.ndim == 2))
+
+
+def isdense(x) -> bool:
+    return isinstance(x, np.ndarray)
+
+
+def validateaxis(axis, *, ndim=2) -> tuple[int, ...] | None:
+    if axis is None:
+        return None
+
+    if axis == ():
+        raise ValueError(
+            "sparse does not accept 0D axis (). Either use toarray (for dense) "
+            "or copy (for sparse)."
+        )
+
+    if not isinstance(axis, tuple):
+        # If not a tuple, check that the provided axis is actually
+        # an integer and raise a TypeError similar to NumPy's
+        if not np.issubdtype(np.dtype(type(axis)), np.integer):
+            raise TypeError(f'axis must be an integer/tuple of ints, not {type(axis)}')
+        axis = (axis,)
+
+    canon_axis = []
+    for ax in axis:
+        if not isintlike(ax):
+            raise TypeError(f"axis must be an integer. (given {ax})")
+        if ax < 0:
+            ax += ndim
+        if ax < 0 or ax >= ndim:
+            raise ValueError("axis out of range for ndim")
+        canon_axis.append(ax)
+
+    len_axis = len(canon_axis)
+    if len_axis != len(set(canon_axis)):
+        raise ValueError("duplicate value in axis")
+    elif len_axis > ndim:
+        raise ValueError("axis tuple has too many elements")
+    elif len_axis == ndim:
+        return None
+    else:
+        return tuple(canon_axis)
+
+
+def check_shape(args, current_shape=None, *, allow_nd=(2,)) -> tuple[int, ...]:
+    """Imitate numpy.matrix handling of shape arguments
+
+    Parameters
+    ----------
+    args : array_like
+        Data structures providing information about the shape of the sparse array.
+    current_shape : tuple, optional
+        The current shape of the sparse array or matrix.
+        If None (default), the current shape will be inferred from args.
+    allow_nd : tuple of ints, optional default: (2,)
+        If shape does not have a length in the tuple allow_nd an error is raised.
+
+    Returns
+    -------
+    new_shape: tuple
+        The new shape after validation.
+    """
+    if len(args) == 0:
+        raise TypeError("function missing 1 required positional argument: 'shape'")
+    if len(args) == 1:
+        try:
+            shape_iter = iter(args[0])
+        except TypeError:
+            new_shape = (operator.index(args[0]), )
+        else:
+            new_shape = tuple(operator.index(arg) for arg in shape_iter)
+    else:
+        new_shape = tuple(operator.index(arg) for arg in args)
+
+    if current_shape is None:
+        if len(new_shape) not in allow_nd:
+            raise ValueError(f'shape must have length in {allow_nd}. Got {new_shape=}')
+        if any(d < 0 for d in new_shape):
+            raise ValueError("'shape' elements cannot be negative")
+    else:
+        # Check the current size only if needed
+        current_size = prod(current_shape)
+
+        # Check for negatives
+        negative_indexes = [i for i, x in enumerate(new_shape) if x < 0]
+        if not negative_indexes:
+            new_size = prod(new_shape)
+            if new_size != current_size:
+                raise ValueError(f'cannot reshape array of size {current_size}'
+                                 f' into shape {new_shape}')
+        elif len(negative_indexes) == 1:
+            skip = negative_indexes[0]
+            specified = prod(new_shape[:skip] + new_shape[skip+1:])
+            unspecified, remainder = divmod(current_size, specified)
+            if remainder != 0:
+                err_shape = tuple('newshape' if x < 0 else x for x in new_shape)
+                raise ValueError(f'cannot reshape array of size {current_size}'
+                                 f' into shape {err_shape}')
+            new_shape = new_shape[:skip] + (unspecified,) + new_shape[skip+1:]
+        else:
+            raise ValueError('can only specify one unknown dimension')
+
+    if len(new_shape) not in allow_nd:
+        raise ValueError(f'shape must have length in {allow_nd}. Got {new_shape=}')
+
+    return new_shape
+
+
+def broadcast_shapes(*shapes):
+    """Check if shapes can be broadcast and return resulting shape
+
+    This is similar to the NumPy ``broadcast_shapes`` function but
+    does not check memory consequences of the resulting dense matrix.
+
+    Parameters
+    ----------
+    *shapes : tuple of shape tuples
+        The tuple of shapes to be considered for broadcasting.
+        Shapes should be tuples of non-negative integers.
+
+    Returns
+    -------
+    new_shape : tuple of integers
+        The shape that results from broadcasting th input shapes.
+    """
+    if not shapes:
+        return ()
+    shapes = [shp if isinstance(shp, tuple | list) else (shp,) for shp in shapes]
+    big_shp = max(shapes, key=len)
+    out = list(big_shp)
+    for shp in shapes:
+        if shp is big_shp:
+            continue
+        for i, x in enumerate(shp, start=-len(shp)):
+            if x != 1 and x != out[i]:
+                if out[i] != 1:
+                    raise ValueError("shapes cannot be broadcast to a single shape.")
+                out[i] = x
+    return (*out,)
+
+
+def is_pydata_spmatrix(m) -> bool:
+    """
+    Check whether object is pydata/sparse matrix, avoiding importing the module.
+    """
+    base_cls = getattr(sys.modules.get('sparse'), 'SparseArray', None)
+    return base_cls is not None and isinstance(m, base_cls)
+
+
+def convert_pydata_sparse_to_scipy(
+    arg: Any,
+    target_format: None | Literal["csc", "csr"] = None,
+    accept_fv: Any = None,
+) -> "sp.spmatrix | Any":
+    """
+    Convert a pydata/sparse array to scipy sparse matrix,
+    pass through anything else.
+    """
+    if is_pydata_spmatrix(arg):
+        # The `accept_fv` keyword is new in PyData Sparse 0.15.4 (May 2024),
+        # remove the `except` once the minimum supported version is >=0.15.4
+        try:
+            arg = arg.to_scipy_sparse(accept_fv=accept_fv)
+        except TypeError:
+            arg = arg.to_scipy_sparse()
+        if target_format is not None:
+            arg = arg.asformat(target_format)
+        elif arg.format not in ("csc", "csr"):
+            arg = arg.tocsc()
+    return arg
+
+
+###############################################################################
+# Wrappers for NumPy types that are deprecated
+
+# Numpy versions of these functions raise deprecation warnings, the
+# ones below do not.
+
+def matrix(*args, **kwargs):
+    return np.array(*args, **kwargs).view(np.matrix)
+
+
+def asmatrix(data, dtype=None):
+    if isinstance(data, np.matrix) and (dtype is None or data.dtype == dtype):
+        return data
+    return np.asarray(data, dtype=dtype).view(np.matrix)
+
+###############################################################################
+
+
+def _todata(s) -> np.ndarray:
+    """Access nonzero values, possibly after summing duplicates.
+
+    Parameters
+    ----------
+    s : sparse array
+        Input sparse array.
+
+    Returns
+    -------
+    data: ndarray
+      Nonzero values of the array, with shape (s.nnz,)
+
+    """
+    if isinstance(s, sp._data._data_matrix):
+        return s._deduped_data()
+
+    if isinstance(s, sp.dok_array):
+        return np.fromiter(s.values(), dtype=s.dtype, count=s.nnz)
+
+    if isinstance(s, sp.lil_array):
+        data = np.empty(s.nnz, dtype=s.dtype)
+        sp._csparsetools.lil_flatten_to_array(s.data, data)
+        return data
+
+    return s.tocoo()._deduped_data()
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/base.py b/venv/lib/python3.12/site-packages/scipy/sparse/base.py
new file mode 100644
index 0000000000000000000000000000000000000000..0550455cd291073208f4e55bb684b1db655faec0
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/base.py
@@ -0,0 +1,24 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.sparse` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+
+__all__ = [  # noqa: F822
+    'SparseEfficiencyWarning',
+    'SparseWarning',
+    'issparse',
+    'isspmatrix',
+    'spmatrix',
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="sparse", module="base",
+                                   private_modules=["_base"], all=__all__,
+                                   attribute=name)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/bsr.py b/venv/lib/python3.12/site-packages/scipy/sparse/bsr.py
new file mode 100644
index 0000000000000000000000000000000000000000..4cac6f7a3b94e3b0ef7d1fb3c8f1b48caa2dd28e
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/bsr.py
@@ -0,0 +1,22 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.sparse` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+
+__all__ = [  # noqa: F822
+    'bsr_matrix',
+    'isspmatrix_bsr',
+    'spmatrix',
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="sparse", module="bsr",
+                                   private_modules=["_bsr"], all=__all__,
+                                   attribute=name)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/compressed.py b/venv/lib/python3.12/site-packages/scipy/sparse/compressed.py
new file mode 100644
index 0000000000000000000000000000000000000000..dd240c40188acfbc8505c6d21c18eb689498061a
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/compressed.py
@@ -0,0 +1,20 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.sparse` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+
+__all__ = [  # noqa: F822
+    'SparseEfficiencyWarning',
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="sparse", module="compressed",
+                                   private_modules=["_compressed"], all=__all__,
+                                   attribute=name)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/construct.py b/venv/lib/python3.12/site-packages/scipy/sparse/construct.py
new file mode 100644
index 0000000000000000000000000000000000000000..3f70e57b2677cc8107854222034184f57aa64c5a
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/construct.py
@@ -0,0 +1,38 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.sparse` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+
+__all__ = [  # noqa: F822
+    'block_diag',
+    'bmat',
+    'bsr_matrix',
+    'coo_matrix',
+    'csc_matrix',
+    'csr_matrix',
+    'dia_matrix',
+    'diags',
+    'eye',
+    'get_index_dtype',
+    'hstack',
+    'identity',
+    'issparse',
+    'kron',
+    'kronsum',
+    'rand',
+    'random',
+    'spdiags',
+    'vstack',
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="sparse", module="construct",
+                                   private_modules=["_construct"], all=__all__,
+                                   attribute=name)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/coo.py b/venv/lib/python3.12/site-packages/scipy/sparse/coo.py
new file mode 100644
index 0000000000000000000000000000000000000000..ccdcf78879fe8957ea339228131ed95e8fb88d8f
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/coo.py
@@ -0,0 +1,23 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.sparse` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+
+__all__ = [  # noqa: F822
+    'SparseEfficiencyWarning',
+    'coo_matrix',
+    'isspmatrix_coo',
+    'spmatrix',
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="sparse", module="coo",
+                                   private_modules=["_coo"], all=__all__,
+                                   attribute=name)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/csc.py b/venv/lib/python3.12/site-packages/scipy/sparse/csc.py
new file mode 100644
index 0000000000000000000000000000000000000000..b3815acdc1b66f18ce45261175bf61896cbdd996
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/csc.py
@@ -0,0 +1,22 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.sparse` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+
+__all__ = [  # noqa: F822
+    'csc_matrix',
+    'isspmatrix_csc',
+    'spmatrix',
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="sparse", module="csc",
+                                   private_modules=["_csc"], all=__all__,
+                                   attribute=name)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/__init__.py b/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..00ab19af4748147d748fccb51a3710d5c711f4b4
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/__init__.py
@@ -0,0 +1,210 @@
+r"""
+Compressed sparse graph routines (:mod:`scipy.sparse.csgraph`)
+==============================================================
+
+.. currentmodule:: scipy.sparse.csgraph
+
+Fast graph algorithms based on sparse matrix representations.
+
+Contents
+--------
+
+.. autosummary::
+   :toctree: generated/
+
+   connected_components -- determine connected components of a graph
+   laplacian -- compute the laplacian of a graph
+   shortest_path -- compute the shortest path between points on a positive graph
+   dijkstra -- use Dijkstra's algorithm for shortest path
+   floyd_warshall -- use the Floyd-Warshall algorithm for shortest path
+   bellman_ford -- use the Bellman-Ford algorithm for shortest path
+   johnson -- use Johnson's algorithm for shortest path
+   yen -- use Yen's algorithm for K-shortest paths between to nodes.
+   breadth_first_order -- compute a breadth-first order of nodes
+   depth_first_order -- compute a depth-first order of nodes
+   breadth_first_tree -- construct the breadth-first tree from a given node
+   depth_first_tree -- construct a depth-first tree from a given node
+   minimum_spanning_tree -- construct the minimum spanning tree of a graph
+   reverse_cuthill_mckee -- compute permutation for reverse Cuthill-McKee ordering
+   maximum_flow -- solve the maximum flow problem for a graph
+   maximum_bipartite_matching -- compute a maximum matching of a bipartite graph
+   min_weight_full_bipartite_matching - compute a minimum weight full matching of a bipartite graph
+   structural_rank -- compute the structural rank of a graph
+   NegativeCycleError
+
+.. autosummary::
+   :toctree: generated/
+
+   construct_dist_matrix
+   csgraph_from_dense
+   csgraph_from_masked
+   csgraph_masked_from_dense
+   csgraph_to_dense
+   csgraph_to_masked
+   reconstruct_path
+
+Graph Representations
+---------------------
+This module uses graphs which are stored in a matrix format. A
+graph with N nodes can be represented by an (N x N) adjacency matrix G.
+If there is a connection from node i to node j, then G[i, j] = w, where
+w is the weight of the connection. For nodes i and j which are
+not connected, the value depends on the representation:
+
+- for dense array representations, non-edges are represented by
+  G[i, j] = 0, infinity, or NaN.
+
+- for dense masked representations (of type np.ma.MaskedArray), non-edges
+  are represented by masked values. This can be useful when graphs with
+  zero-weight edges are desired.
+
+- for sparse array representations, non-edges are represented by
+  non-entries in the matrix. This sort of sparse representation also
+  allows for edges with zero weights.
+
+As a concrete example, imagine that you would like to represent the following
+undirected graph::
+
+              G
+
+             (0)
+            /   \
+           1     2
+          /       \
+        (2)       (1)
+
+This graph has three nodes, where node 0 and 1 are connected by an edge of
+weight 2, and nodes 0 and 2 are connected by an edge of weight 1.
+We can construct the dense, masked, and sparse representations as follows,
+keeping in mind that an undirected graph is represented by a symmetric matrix::
+
+    >>> import numpy as np
+    >>> G_dense = np.array([[0, 2, 1],
+    ...                     [2, 0, 0],
+    ...                     [1, 0, 0]])
+    >>> G_masked = np.ma.masked_values(G_dense, 0)
+    >>> from scipy.sparse import csr_array
+    >>> G_sparse = csr_array(G_dense)
+
+This becomes more difficult when zero edges are significant. For example,
+consider the situation when we slightly modify the above graph::
+
+             G2
+
+             (0)
+            /   \
+           0     2
+          /       \
+        (2)       (1)
+
+This is identical to the previous graph, except nodes 0 and 2 are connected
+by an edge of zero weight. In this case, the dense representation above
+leads to ambiguities: how can non-edges be represented if zero is a meaningful
+value? In this case, either a masked or sparse representation must be used
+to eliminate the ambiguity::
+
+    >>> import numpy as np
+    >>> G2_data = np.array([[np.inf, 2,      0     ],
+    ...                     [2,      np.inf, np.inf],
+    ...                     [0,      np.inf, np.inf]])
+    >>> G2_masked = np.ma.masked_invalid(G2_data)
+    >>> from scipy.sparse.csgraph import csgraph_from_dense
+    >>> # G2_sparse = csr_array(G2_data) would give the wrong result
+    >>> G2_sparse = csgraph_from_dense(G2_data, null_value=np.inf)
+    >>> G2_sparse.data
+    array([ 2.,  0.,  2.,  0.])
+
+Here we have used a utility routine from the csgraph submodule in order to
+convert the dense representation to a sparse representation which can be
+understood by the algorithms in submodule. By viewing the data array, we
+can see that the zero values are explicitly encoded in the graph.
+
+Directed vs. undirected
+^^^^^^^^^^^^^^^^^^^^^^^
+Matrices may represent either directed or undirected graphs. This is
+specified throughout the csgraph module by a boolean keyword. Graphs are
+assumed to be directed by default. In a directed graph, traversal from node
+i to node j can be accomplished over the edge G[i, j], but not the edge
+G[j, i].  Consider the following dense graph::
+
+    >>> import numpy as np
+    >>> G_dense = np.array([[0, 1, 0],
+    ...                     [2, 0, 3],
+    ...                     [0, 4, 0]])
+
+When ``directed=True`` we get the graph::
+
+      ---1--> ---3-->
+    (0)     (1)     (2)
+      <--2--- <--4---
+
+In a non-directed graph, traversal from node i to node j can be
+accomplished over either G[i, j] or G[j, i].  If both edges are not null,
+and the two have unequal weights, then the smaller of the two is used.
+
+So for the same graph, when ``directed=False`` we get the graph::
+
+    (0)--1--(1)--3--(2)
+
+Note that a symmetric matrix will represent an undirected graph, regardless
+of whether the 'directed' keyword is set to True or False. In this case,
+using ``directed=True`` generally leads to more efficient computation.
+
+The routines in this module accept as input either scipy.sparse representations
+(csr, csc, or lil format), masked representations, or dense representations
+with non-edges indicated by zeros, infinities, and NaN entries.
+"""  # noqa: E501
+
+__docformat__ = "restructuredtext en"
+
+__all__ = ['connected_components',
+           'laplacian',
+           'shortest_path',
+           'floyd_warshall',
+           'dijkstra',
+           'bellman_ford',
+           'johnson',
+           'yen',
+           'breadth_first_order',
+           'depth_first_order',
+           'breadth_first_tree',
+           'depth_first_tree',
+           'minimum_spanning_tree',
+           'reverse_cuthill_mckee',
+           'maximum_flow',
+           'maximum_bipartite_matching',
+           'min_weight_full_bipartite_matching',
+           'structural_rank',
+           'construct_dist_matrix',
+           'reconstruct_path',
+           'csgraph_masked_from_dense',
+           'csgraph_from_dense',
+           'csgraph_from_masked',
+           'csgraph_to_dense',
+           'csgraph_to_masked',
+           'NegativeCycleError']
+
+from ._laplacian import laplacian
+from ._shortest_path import (
+    shortest_path, floyd_warshall, dijkstra, bellman_ford, johnson, yen,
+    NegativeCycleError
+)
+from ._traversal import (
+    breadth_first_order, depth_first_order, breadth_first_tree,
+    depth_first_tree, connected_components
+)
+from ._min_spanning_tree import minimum_spanning_tree
+from ._flow import maximum_flow
+from ._matching import (
+    maximum_bipartite_matching, min_weight_full_bipartite_matching
+)
+from ._reordering import reverse_cuthill_mckee, structural_rank
+from ._tools import (
+    construct_dist_matrix, reconstruct_path, csgraph_from_dense,
+    csgraph_to_dense, csgraph_masked_from_dense, csgraph_from_masked,
+    csgraph_to_masked
+)
+
+from scipy._lib._testutils import PytestTester
+test = PytestTester(__name__)
+del PytestTester
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diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/_flow.cpython-312-x86_64-linux-gnu.so b/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/_flow.cpython-312-x86_64-linux-gnu.so
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index 0000000000000000000000000000000000000000..e8a28472de5b6f2e41bdb4609ed0fc6206452eae
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+++ b/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/_flow.cpython-312-x86_64-linux-gnu.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e916fb4555f097547989807d6e4e23978d195ba9f3ff8a60b6117bc5d9032e02
+size 184304
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/_laplacian.py b/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/_laplacian.py
new file mode 100644
index 0000000000000000000000000000000000000000..762158e0d86ff92293a9f181b1ad444bd02706c9
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/_laplacian.py
@@ -0,0 +1,563 @@
+"""
+Laplacian of a compressed-sparse graph
+"""
+
+import numpy as np
+from scipy.sparse import issparse
+from scipy.sparse.linalg import LinearOperator
+from scipy.sparse._sputils import convert_pydata_sparse_to_scipy, is_pydata_spmatrix
+
+
+###############################################################################
+# Graph laplacian
+def laplacian(
+    csgraph,
+    normed=False,
+    return_diag=False,
+    use_out_degree=False,
+    *,
+    copy=True,
+    form="array",
+    dtype=None,
+    symmetrized=False,
+):
+    """
+    Return the Laplacian of a directed graph.
+
+    Parameters
+    ----------
+    csgraph : array_like or sparse array or matrix, 2 dimensions
+        compressed-sparse graph, with shape (N, N).
+    normed : bool, optional
+        If True, then compute symmetrically normalized Laplacian.
+        Default: False.
+    return_diag : bool, optional
+        If True, then also return an array related to vertex degrees.
+        Default: False.
+    use_out_degree : bool, optional
+        If True, then use out-degree instead of in-degree.
+        This distinction matters only if the graph is asymmetric.
+        Default: False.
+    copy : bool, optional
+        If False, then change `csgraph` in place if possible,
+        avoiding doubling the memory use.
+        Default: True, for backward compatibility.
+    form : 'array', or 'function', or 'lo'
+        Determines the format of the output Laplacian:
+
+        * 'array' is a numpy array;
+        * 'function' is a pointer to evaluating the Laplacian-vector
+          or Laplacian-matrix product;
+        * 'lo' results in the format of the `LinearOperator`.
+
+        Choosing 'function' or 'lo' always avoids doubling
+        the memory use, ignoring `copy` value.
+        Default: 'array', for backward compatibility.
+    dtype : None or one of numeric numpy dtypes, optional
+        The dtype of the output. If ``dtype=None``, the dtype of the
+        output matches the dtype of the input csgraph, except for
+        the case ``normed=True`` and integer-like csgraph, where
+        the output dtype is 'float' allowing accurate normalization,
+        but dramatically increasing the memory use.
+        Default: None, for backward compatibility.
+    symmetrized : bool, optional
+        If True, then the output Laplacian is symmetric/Hermitian.
+        The symmetrization is done by ``csgraph + csgraph.T.conj``
+        without dividing by 2 to preserve integer dtypes if possible
+        prior to the construction of the Laplacian.
+        The symmetrization will increase the memory footprint of
+        sparse matrices unless the sparsity pattern is symmetric or
+        `form` is 'function' or 'lo'.
+        Default: False, for backward compatibility.
+
+    Returns
+    -------
+    lap : ndarray, or sparse array or matrix, or `LinearOperator`
+        The N x N Laplacian of csgraph. It will be a NumPy array (dense)
+        if the input was dense, or a sparse array otherwise, or
+        the format of a function or `LinearOperator` if
+        `form` equals 'function' or 'lo', respectively.
+    diag : ndarray, optional
+        The length-N main diagonal of the Laplacian matrix.
+        For the normalized Laplacian, this is the array of square roots
+        of vertex degrees or 1 if the degree is zero.
+
+    Notes
+    -----
+    The Laplacian matrix of a graph is sometimes referred to as the
+    "Kirchhoff matrix" or just the "Laplacian", and is useful in many
+    parts of spectral graph theory.
+    In particular, the eigen-decomposition of the Laplacian can give
+    insight into many properties of the graph, e.g.,
+    is commonly used for spectral data embedding and clustering.
+
+    The constructed Laplacian doubles the memory use if ``copy=True`` and
+    ``form="array"`` which is the default.
+    Choosing ``copy=False`` has no effect unless ``form="array"``
+    or the matrix is sparse in the ``coo`` format, or dense array, except
+    for the integer input with ``normed=True`` that forces the float output.
+
+    Sparse input is reformatted into ``coo`` if ``form="array"``,
+    which is the default.
+
+    If the input adjacency matrix is not symmetric, the Laplacian is
+    also non-symmetric unless ``symmetrized=True`` is used.
+
+    Diagonal entries of the input adjacency matrix are ignored and
+    replaced with zeros for the purpose of normalization where ``normed=True``.
+    The normalization uses the inverse square roots of row-sums of the input
+    adjacency matrix, and thus may fail if the row-sums contain
+    negative or complex with a non-zero imaginary part values.
+
+    The normalization is symmetric, making the normalized Laplacian also
+    symmetric if the input csgraph was symmetric.
+
+    References
+    ----------
+    .. [1] Laplacian matrix. https://en.wikipedia.org/wiki/Laplacian_matrix
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.sparse import csgraph
+
+    Our first illustration is the symmetric graph
+
+    >>> G = np.arange(4) * np.arange(4)[:, np.newaxis]
+    >>> G
+    array([[0, 0, 0, 0],
+           [0, 1, 2, 3],
+           [0, 2, 4, 6],
+           [0, 3, 6, 9]])
+
+    and its symmetric Laplacian matrix
+
+    >>> csgraph.laplacian(G)
+    array([[ 0,  0,  0,  0],
+           [ 0,  5, -2, -3],
+           [ 0, -2,  8, -6],
+           [ 0, -3, -6,  9]])
+
+    The non-symmetric graph
+
+    >>> G = np.arange(9).reshape(3, 3)
+    >>> G
+    array([[0, 1, 2],
+           [3, 4, 5],
+           [6, 7, 8]])
+
+    has different row- and column sums, resulting in two varieties
+    of the Laplacian matrix, using an in-degree, which is the default
+
+    >>> L_in_degree = csgraph.laplacian(G)
+    >>> L_in_degree
+    array([[ 9, -1, -2],
+           [-3,  8, -5],
+           [-6, -7,  7]])
+
+    or alternatively an out-degree
+
+    >>> L_out_degree = csgraph.laplacian(G, use_out_degree=True)
+    >>> L_out_degree
+    array([[ 3, -1, -2],
+           [-3,  8, -5],
+           [-6, -7, 13]])
+
+    Constructing a symmetric Laplacian matrix, one can add the two as
+
+    >>> L_in_degree + L_out_degree.T
+    array([[ 12,  -4,  -8],
+            [ -4,  16, -12],
+            [ -8, -12,  20]])
+
+    or use the ``symmetrized=True`` option
+
+    >>> csgraph.laplacian(G, symmetrized=True)
+    array([[ 12,  -4,  -8],
+           [ -4,  16, -12],
+           [ -8, -12,  20]])
+
+    that is equivalent to symmetrizing the original graph
+
+    >>> csgraph.laplacian(G + G.T)
+    array([[ 12,  -4,  -8],
+           [ -4,  16, -12],
+           [ -8, -12,  20]])
+
+    The goal of normalization is to make the non-zero diagonal entries
+    of the Laplacian matrix to be all unit, also scaling off-diagonal
+    entries correspondingly. The normalization can be done manually, e.g.,
+
+    >>> G = np.array([[0, 1, 1], [1, 0, 1], [1, 1, 0]])
+    >>> L, d = csgraph.laplacian(G, return_diag=True)
+    >>> L
+    array([[ 2, -1, -1],
+           [-1,  2, -1],
+           [-1, -1,  2]])
+    >>> d
+    array([2, 2, 2])
+    >>> scaling = np.sqrt(d)
+    >>> scaling
+    array([1.41421356, 1.41421356, 1.41421356])
+    >>> (1/scaling)*L*(1/scaling)
+    array([[ 1. , -0.5, -0.5],
+           [-0.5,  1. , -0.5],
+           [-0.5, -0.5,  1. ]])
+
+    Or using ``normed=True`` option
+
+    >>> L, d = csgraph.laplacian(G, return_diag=True, normed=True)
+    >>> L
+    array([[ 1. , -0.5, -0.5],
+           [-0.5,  1. , -0.5],
+           [-0.5, -0.5,  1. ]])
+
+    which now instead of the diagonal returns the scaling coefficients
+
+    >>> d
+    array([1.41421356, 1.41421356, 1.41421356])
+
+    Zero scaling coefficients are substituted with 1s, where scaling
+    has thus no effect, e.g.,
+
+    >>> G = np.array([[0, 0, 0], [0, 0, 1], [0, 1, 0]])
+    >>> G
+    array([[0, 0, 0],
+           [0, 0, 1],
+           [0, 1, 0]])
+    >>> L, d = csgraph.laplacian(G, return_diag=True, normed=True)
+    >>> L
+    array([[ 0., -0., -0.],
+           [-0.,  1., -1.],
+           [-0., -1.,  1.]])
+    >>> d
+    array([1., 1., 1.])
+
+    Only the symmetric normalization is implemented, resulting
+    in a symmetric Laplacian matrix if and only if its graph is symmetric
+    and has all non-negative degrees, like in the examples above.
+
+    The output Laplacian matrix is by default a dense array or a sparse
+    array or matrix inferring its class, shape, format, and dtype from
+    the input graph matrix:
+
+    >>> G = np.array([[0, 1, 1], [1, 0, 1], [1, 1, 0]]).astype(np.float32)
+    >>> G
+    array([[0., 1., 1.],
+           [1., 0., 1.],
+           [1., 1., 0.]], dtype=float32)
+    >>> csgraph.laplacian(G)
+    array([[ 2., -1., -1.],
+           [-1.,  2., -1.],
+           [-1., -1.,  2.]], dtype=float32)
+
+    but can alternatively be generated matrix-free as a LinearOperator:
+
+    >>> L = csgraph.laplacian(G, form="lo")
+    >>> L
+    <3x3 _CustomLinearOperator with dtype=float32>
+    >>> L(np.eye(3))
+    array([[ 2., -1., -1.],
+           [-1.,  2., -1.],
+           [-1., -1.,  2.]])
+
+    or as a lambda-function:
+
+    >>> L = csgraph.laplacian(G, form="function")
+    >>> L
+    <function _laplace.<locals>.<lambda> at 0x0000012AE6F5A598>
+    >>> L(np.eye(3))
+    array([[ 2., -1., -1.],
+           [-1.,  2., -1.],
+           [-1., -1.,  2.]])
+
+    The Laplacian matrix is used for
+    spectral data clustering and embedding
+    as well as for spectral graph partitioning.
+    Our final example illustrates the latter
+    for a noisy directed linear graph.
+
+    >>> from scipy.sparse import diags_array, random_array
+    >>> from scipy.sparse.linalg import lobpcg
+
+    Create a directed linear graph with ``N=35`` vertices
+    using a sparse adjacency matrix ``G``:
+
+    >>> N = 35
+    >>> G = diags_array(np.ones(N - 1), offsets=1, format="csr")
+
+    Fix a random seed ``rng`` and add a random sparse noise to the graph ``G``:
+
+    >>> rng = np.random.default_rng()
+    >>> G += 1e-2 * random_array((N, N), density=0.1, rng=rng)
+
+    Set initial approximations for eigenvectors:
+
+    >>> X = rng.random((N, 2))
+
+    The constant vector of ones is always a trivial eigenvector
+    of the non-normalized Laplacian to be filtered out:
+
+    >>> Y = np.ones((N, 1))
+
+    Alternating (1) the sign of the graph weights allows determining
+    labels for spectral max- and min- cuts in a single loop.
+    Since the graph is undirected, the option ``symmetrized=True``
+    must be used in the construction of the Laplacian.
+    The option ``normed=True`` cannot be used in (2) for the negative weights
+    here as the symmetric normalization evaluates square roots.
+    The option ``form="lo"`` in (2) is matrix-free, i.e., guarantees
+    a fixed memory footprint and read-only access to the graph.
+    Calling the eigenvalue solver ``lobpcg`` (3) computes the Fiedler vector
+    that determines the labels as the signs of its components in (5).
+    Since the sign in an eigenvector is not deterministic and can flip,
+    we fix the sign of the first component to be always +1 in (4).
+
+    >>> for cut in ["max", "min"]:
+    ...     G = -G  # 1.
+    ...     L = csgraph.laplacian(G, symmetrized=True, form="lo")  # 2.
+    ...     _, eves = lobpcg(L, X, Y=Y, largest=False, tol=1e-2)  # 3.
+    ...     eves *= np.sign(eves[0, 0])  # 4.
+    ...     print(cut + "-cut labels:\\n", 1 * (eves[:, 0]>0))  # 5.
+    max-cut labels:
+    [1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1]
+    min-cut labels:
+    [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
+
+    As anticipated for a (slightly noisy) linear graph,
+    the max-cut strips all the edges of the graph coloring all
+    odd vertices into one color and all even vertices into another one,
+    while the balanced min-cut partitions the graph
+    in the middle by deleting a single edge.
+    Both determined partitions are optimal.
+    """
+    is_pydata_sparse = is_pydata_spmatrix(csgraph)
+    if is_pydata_sparse:
+        pydata_sparse_cls = csgraph.__class__
+        csgraph = convert_pydata_sparse_to_scipy(csgraph)
+    if csgraph.ndim != 2 or csgraph.shape[0] != csgraph.shape[1]:
+        raise ValueError('csgraph must be a square matrix or array')
+
+    if normed and (
+        np.issubdtype(csgraph.dtype, np.signedinteger)
+        or np.issubdtype(csgraph.dtype, np.uint)
+    ):
+        csgraph = csgraph.astype(np.float64)
+
+    if form == "array":
+        create_lap = (
+            _laplacian_sparse if issparse(csgraph) else _laplacian_dense
+        )
+    else:
+        create_lap = (
+            _laplacian_sparse_flo
+            if issparse(csgraph)
+            else _laplacian_dense_flo
+        )
+
+    degree_axis = 1 if use_out_degree else 0
+
+    lap, d = create_lap(
+        csgraph,
+        normed=normed,
+        axis=degree_axis,
+        copy=copy,
+        form=form,
+        dtype=dtype,
+        symmetrized=symmetrized,
+    )
+    if is_pydata_sparse:
+        lap = pydata_sparse_cls.from_scipy_sparse(lap)
+    if return_diag:
+        return lap, d
+    return lap
+
+
+def _setdiag_dense(m, d):
+    step = len(d) + 1
+    m.flat[::step] = d
+
+
+def _laplace(m, d):
+    return lambda v: v * d[:, np.newaxis] - m @ v
+
+
+def _laplace_normed(m, d, nd):
+    laplace = _laplace(m, d)
+    return lambda v: nd[:, np.newaxis] * laplace(v * nd[:, np.newaxis])
+
+
+def _laplace_sym(m, d):
+    return (
+        lambda v: v * d[:, np.newaxis]
+        - m @ v
+        - np.transpose(np.conjugate(np.transpose(np.conjugate(v)) @ m))
+    )
+
+
+def _laplace_normed_sym(m, d, nd):
+    laplace_sym = _laplace_sym(m, d)
+    return lambda v: nd[:, np.newaxis] * laplace_sym(v * nd[:, np.newaxis])
+
+
+def _linearoperator(mv, shape, dtype):
+    return LinearOperator(matvec=mv, matmat=mv, shape=shape, dtype=dtype)
+
+
+def _laplacian_sparse_flo(graph, normed, axis, copy, form, dtype, symmetrized):
+    # The keyword argument `copy` is unused and has no effect here.
+    del copy
+
+    if dtype is None:
+        dtype = graph.dtype
+
+    graph_sum = np.asarray(graph.sum(axis=axis)).ravel()
+    graph_diagonal = graph.diagonal()
+    diag = graph_sum - graph_diagonal
+    if symmetrized:
+        graph_sum += np.asarray(graph.sum(axis=1 - axis)).ravel()
+        diag = graph_sum - graph_diagonal - graph_diagonal
+
+    if normed:
+        isolated_node_mask = diag == 0
+        w = np.where(isolated_node_mask, 1, np.sqrt(diag))
+        if symmetrized:
+            md = _laplace_normed_sym(graph, graph_sum, 1.0 / w)
+        else:
+            md = _laplace_normed(graph, graph_sum, 1.0 / w)
+        if form == "function":
+            return md, w.astype(dtype, copy=False)
+        elif form == "lo":
+            m = _linearoperator(md, shape=graph.shape, dtype=dtype)
+            return m, w.astype(dtype, copy=False)
+        else:
+            raise ValueError(f"Invalid form: {form!r}")
+    else:
+        if symmetrized:
+            md = _laplace_sym(graph, graph_sum)
+        else:
+            md = _laplace(graph, graph_sum)
+        if form == "function":
+            return md, diag.astype(dtype, copy=False)
+        elif form == "lo":
+            m = _linearoperator(md, shape=graph.shape, dtype=dtype)
+            return m, diag.astype(dtype, copy=False)
+        else:
+            raise ValueError(f"Invalid form: {form!r}")
+
+
+def _laplacian_sparse(graph, normed, axis, copy, form, dtype, symmetrized):
+    # The keyword argument `form` is unused and has no effect here.
+    del form
+
+    if dtype is None:
+        dtype = graph.dtype
+
+    needs_copy = False
+    if graph.format in ('lil', 'dok'):
+        m = graph.tocoo()
+    else:
+        m = graph
+        if copy:
+            needs_copy = True
+
+    if symmetrized:
+        m += m.T.conj()
+
+    w = np.asarray(m.sum(axis=axis)).ravel() - m.diagonal()
+    if normed:
+        m = m.tocoo(copy=needs_copy)
+        isolated_node_mask = (w == 0)
+        w = np.where(isolated_node_mask, 1, np.sqrt(w))
+        m.data /= w[m.row]
+        m.data /= w[m.col]
+        m.data *= -1
+        m.setdiag(1 - isolated_node_mask)
+    else:
+        if m.format == 'dia':
+            m = m.copy()
+        else:
+            m = m.tocoo(copy=needs_copy)
+        m.data *= -1
+        m.setdiag(w)
+
+    return m.astype(dtype, copy=False), w.astype(dtype)
+
+
+def _laplacian_dense_flo(graph, normed, axis, copy, form, dtype, symmetrized):
+
+    if copy:
+        m = np.array(graph)
+    else:
+        m = np.asarray(graph)
+
+    if dtype is None:
+        dtype = m.dtype
+
+    graph_sum = m.sum(axis=axis)
+    graph_diagonal = m.diagonal()
+    diag = graph_sum - graph_diagonal
+    if symmetrized:
+        graph_sum += m.sum(axis=1 - axis)
+        diag = graph_sum - graph_diagonal - graph_diagonal
+
+    if normed:
+        isolated_node_mask = diag == 0
+        w = np.where(isolated_node_mask, 1, np.sqrt(diag))
+        if symmetrized:
+            md = _laplace_normed_sym(m, graph_sum, 1.0 / w)
+        else:
+            md = _laplace_normed(m, graph_sum, 1.0 / w)
+        if form == "function":
+            return md, w.astype(dtype, copy=False)
+        elif form == "lo":
+            m = _linearoperator(md, shape=graph.shape, dtype=dtype)
+            return m, w.astype(dtype, copy=False)
+        else:
+            raise ValueError(f"Invalid form: {form!r}")
+    else:
+        if symmetrized:
+            md = _laplace_sym(m, graph_sum)
+        else:
+            md = _laplace(m, graph_sum)
+        if form == "function":
+            return md, diag.astype(dtype, copy=False)
+        elif form == "lo":
+            m = _linearoperator(md, shape=graph.shape, dtype=dtype)
+            return m, diag.astype(dtype, copy=False)
+        else:
+            raise ValueError(f"Invalid form: {form!r}")
+
+
+def _laplacian_dense(graph, normed, axis, copy, form, dtype, symmetrized):
+
+    if form != "array":
+        raise ValueError(f'{form!r} must be "array"')
+
+    if dtype is None:
+        dtype = graph.dtype
+
+    if copy:
+        m = np.array(graph)
+    else:
+        m = np.asarray(graph)
+
+    if dtype is None:
+        dtype = m.dtype
+
+    if symmetrized:
+        m += m.T.conj()
+    np.fill_diagonal(m, 0)
+    w = m.sum(axis=axis)
+    if normed:
+        isolated_node_mask = (w == 0)
+        w = np.where(isolated_node_mask, 1, np.sqrt(w))
+        m /= w
+        m /= w[:, np.newaxis]
+        m *= -1
+        _setdiag_dense(m, 1 - isolated_node_mask)
+    else:
+        m *= -1
+        _setdiag_dense(m, w)
+
+    return m.astype(dtype, copy=False), w.astype(dtype, copy=False)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/_matching.cpython-312-x86_64-linux-gnu.so b/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/_matching.cpython-312-x86_64-linux-gnu.so
new file mode 100644
index 0000000000000000000000000000000000000000..29ea54615131f05f69b308f2235bfbabcb61b3b9
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/_matching.cpython-312-x86_64-linux-gnu.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:57636d89fcb29cdf654ffa5b6d0120ff25d1fb8d0d608b68e7aaaf5b2cf6c919
+size 183048
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diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/_reordering.cpython-312-x86_64-linux-gnu.so b/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/_reordering.cpython-312-x86_64-linux-gnu.so
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+++ b/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/_reordering.cpython-312-x86_64-linux-gnu.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:1354563644ee9209f297761697bc215cdb22c79b718cd57c916926037ac1c9e9
+size 153224
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/_shortest_path.cpython-312-x86_64-linux-gnu.so b/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/_shortest_path.cpython-312-x86_64-linux-gnu.so
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+++ b/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/_shortest_path.cpython-312-x86_64-linux-gnu.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:432679757ec4e8c34a4c0903d1e1aaceec6d0232043e2014f1de436a0094a088
+size 499264
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/_tools.cpython-312-x86_64-linux-gnu.so b/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/_tools.cpython-312-x86_64-linux-gnu.so
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+++ b/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/_tools.cpython-312-x86_64-linux-gnu.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e1ec508d60f12cc7d38621513c0fa994593a0ff3dda89ab806fa9e9bb2de4b16
+size 179264
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/_traversal.cpython-312-x86_64-linux-gnu.so b/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/_traversal.cpython-312-x86_64-linux-gnu.so
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+++ b/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/_traversal.cpython-312-x86_64-linux-gnu.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:8a110bc9b246c65b4290a529e4f5f87667da30781dcbd690e0833b7f25bf1abb
+size 359392
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/_validation.py b/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/_validation.py
new file mode 100644
index 0000000000000000000000000000000000000000..57ce3951ed4fae5f600f683bd3a98b43ac7f653b
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/_validation.py
@@ -0,0 +1,71 @@
+import numpy as np
+from scipy.sparse import issparse
+from scipy.sparse._sputils import convert_pydata_sparse_to_scipy
+from scipy.sparse.csgraph._tools import (
+    csgraph_to_dense, csgraph_from_dense,
+    csgraph_masked_from_dense, csgraph_from_masked
+)
+
+DTYPE = np.float64
+
+
+def validate_graph(csgraph, directed, dtype=DTYPE,
+                   csr_output=True, dense_output=True,
+                   copy_if_dense=False, copy_if_sparse=False,
+                   null_value_in=0, null_value_out=np.inf,
+                   infinity_null=True, nan_null=True):
+    """Routine for validation and conversion of csgraph inputs"""
+    if not (csr_output or dense_output):
+        raise ValueError("Internal: dense or csr output must be true")
+
+    accept_fv = [null_value_in]
+    if infinity_null:
+        accept_fv.append(np.inf)
+    if nan_null:
+        accept_fv.append(np.nan)
+    csgraph = convert_pydata_sparse_to_scipy(csgraph, accept_fv=accept_fv)
+
+    # if undirected and csc storage, then transposing in-place
+    # is quicker than later converting to csr.
+    if (not directed) and issparse(csgraph) and csgraph.format == "csc":
+        csgraph = csgraph.T
+
+    if issparse(csgraph):
+        if csr_output:
+            if csgraph.format == "bsr":
+                csgraph = csgraph.tocsr(copy=copy_if_sparse)
+                csgraph.eliminate_zeros()
+                csgraph = csgraph.astype(dtype, copy=False)
+            else:
+                csgraph = csgraph.tocsr(copy=copy_if_sparse).astype(dtype, copy=False)
+        else:
+            csgraph = csgraph_to_dense(csgraph, null_value=null_value_out)
+    elif np.ma.isMaskedArray(csgraph):
+        if dense_output:
+            mask = csgraph.mask
+            csgraph = np.array(csgraph.data, dtype=dtype, copy=copy_if_dense)
+            csgraph[mask] = null_value_out
+        else:
+            csgraph = csgraph_from_masked(csgraph)
+    else:
+        if dense_output:
+            csgraph = csgraph_masked_from_dense(csgraph,
+                                                copy=copy_if_dense,
+                                                null_value=null_value_in,
+                                                nan_null=nan_null,
+                                                infinity_null=infinity_null)
+            mask = csgraph.mask
+            csgraph = np.asarray(csgraph.data, dtype=dtype)
+            csgraph[mask] = null_value_out
+        else:
+            csgraph = csgraph_from_dense(csgraph, null_value=null_value_in,
+                                         infinity_null=infinity_null,
+                                         nan_null=nan_null)
+
+    if csgraph.ndim != 2:
+        raise ValueError("compressed-sparse graph must be 2-D")
+
+    if csgraph.shape[0] != csgraph.shape[1]:
+        raise ValueError("compressed-sparse graph must be shape (N, N)")
+
+    return csgraph
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diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/tests/test_connected_components.py b/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/tests/test_connected_components.py
new file mode 100644
index 0000000000000000000000000000000000000000..9dce1c56d7411e4069f562ff7aa89629c73fd413
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/tests/test_connected_components.py
@@ -0,0 +1,162 @@
+import numpy as np
+from numpy.testing import assert_allclose, assert_equal, assert_array_almost_equal
+import pytest
+from scipy.sparse import bsr_array, csgraph, csr_array
+
+
+def test_weak_connections():
+    Xde = np.array([[0, 1, 0],
+                    [0, 0, 0],
+                    [0, 0, 0]])
+
+    Xsp = csgraph.csgraph_from_dense(Xde, null_value=0)
+
+    for X in Xsp, Xde:
+        n_components, labels =\
+            csgraph.connected_components(X, directed=True,
+                                         connection='weak')
+
+        assert_equal(n_components, 2)
+        assert_array_almost_equal(labels, [0, 0, 1])
+
+
+def test_strong_connections():
+    X1de = np.array([[0, 1, 0],
+                     [0, 0, 0],
+                     [0, 0, 0]])
+    X2de = X1de + X1de.T
+
+    X1sp = csgraph.csgraph_from_dense(X1de, null_value=0)
+    X2sp = csgraph.csgraph_from_dense(X2de, null_value=0)
+
+    for X in X1sp, X1de:
+        n_components, labels =\
+            csgraph.connected_components(X, directed=True,
+                                         connection='strong')
+
+        assert_equal(n_components, 3)
+        labels.sort()
+        assert_array_almost_equal(labels, [0, 1, 2])
+
+    for X in X2sp, X2de:
+        n_components, labels =\
+            csgraph.connected_components(X, directed=True,
+                                         connection='strong')
+
+        assert_equal(n_components, 2)
+        labels.sort()
+        assert_array_almost_equal(labels, [0, 0, 1])
+
+
+def test_strong_connections2():
+    X = np.array([[0, 0, 0, 0, 0, 0],
+                  [1, 0, 1, 0, 0, 0],
+                  [0, 0, 0, 1, 0, 0],
+                  [0, 0, 1, 0, 1, 0],
+                  [0, 0, 0, 0, 0, 0],
+                  [0, 0, 0, 0, 1, 0]])
+    n_components, labels =\
+        csgraph.connected_components(X, directed=True,
+                                     connection='strong')
+    assert_equal(n_components, 5)
+    labels.sort()
+    assert_array_almost_equal(labels, [0, 1, 2, 2, 3, 4])
+
+
+def test_weak_connections2():
+    X = np.array([[0, 0, 0, 0, 0, 0],
+                  [1, 0, 0, 0, 0, 0],
+                  [0, 0, 0, 1, 0, 0],
+                  [0, 0, 1, 0, 1, 0],
+                  [0, 0, 0, 0, 0, 0],
+                  [0, 0, 0, 0, 1, 0]])
+    n_components, labels =\
+        csgraph.connected_components(X, directed=True,
+                                     connection='weak')
+    assert_equal(n_components, 2)
+    labels.sort()
+    assert_array_almost_equal(labels, [0, 0, 1, 1, 1, 1])
+
+
+def test_ticket1876():
+    # Regression test: this failed in the original implementation
+    # There should be two strongly-connected components; previously gave one
+    g = np.array([[0, 1, 1, 0],
+                  [1, 0, 0, 1],
+                  [0, 0, 0, 1],
+                  [0, 0, 1, 0]])
+    n_components, labels = csgraph.connected_components(g, connection='strong')
+
+    assert_equal(n_components, 2)
+    assert_equal(labels[0], labels[1])
+    assert_equal(labels[2], labels[3])
+
+
+def test_fully_connected_graph():
+    # Fully connected dense matrices raised an exception.
+    # https://github.com/scipy/scipy/issues/3818
+    g = np.ones((4, 4))
+    n_components, labels = csgraph.connected_components(g)
+    assert_equal(n_components, 1)
+
+
+def test_int64_indices_undirected():
+    # See https://github.com/scipy/scipy/issues/18716
+    g = csr_array(([1], np.array([[0], [1]], dtype=np.int64)), shape=(2, 2))
+    assert g.indices.dtype == np.int64
+    n, labels = csgraph.connected_components(g, directed=False)
+    assert n == 1
+    assert_array_almost_equal(labels, [0, 0])
+
+
+def test_int64_indices_directed():
+    # See https://github.com/scipy/scipy/issues/18716
+    g = csr_array(([1], np.array([[0], [1]], dtype=np.int64)), shape=(2, 2))
+    assert g.indices.dtype == np.int64
+    n, labels = csgraph.connected_components(g, directed=True,
+                                             connection='strong')
+    assert n == 2
+    assert_array_almost_equal(labels, [1, 0])
+
+
+def test_single_scc_early_exit():
+    # Exercises the early-exit check
+    rows = [0, 1, 1, 2, 3, 3, 4, 5]
+    cols = [1, 2, 5, 3, 1, 4, 0, 2]
+    data = np.ones(len(rows), dtype=np.int32)
+    g = csr_array((data, (rows, cols)), shape=(6, 6))
+    n_components, labels = csgraph.connected_components(
+        g, directed=True, connection='strong')
+    assert_equal(n_components, 1)
+    assert_equal(len(np.unique(labels)), 1)
+
+
+# regression test for gh-23142
+@pytest.mark.parametrize("graph", [
+    np.array([[1, 0, 1, 0],
+              [0, 1, 0, 0],
+              [0, 0, 1, 0],
+              [0, 0, 0, 1]]),
+    np.array([[1, 0, 0, 0],
+              [0, 1, 0, 0],
+              [0, 0, 1, 0],
+              [0, 0, 0, 1]]),
+    np.array([[1, 0, 0, 0],
+              [0, 1, 0, 0],
+              [0, 0, 0, 0],
+              [0, 0, 0, 0]]),
+])
+def test_bsr_blocksize_connected_components(graph):
+    reference_graph = bsr_array(graph, blocksize=(1, 1)).astype(bool)
+    sparse_graph = bsr_array(graph, blocksize=(2, 2)).astype(bool)
+
+    n_expected, lbl_expected = csgraph.connected_components(
+        reference_graph, directed=False, return_labels=True, connection="weak"
+    )
+    n_actual, lbl_actual = csgraph.connected_components(
+        sparse_graph, directed=False, return_labels=True, connection="weak"
+    )
+
+    assert_equal(n_actual, n_expected)
+    assert_allclose(lbl_actual, lbl_expected)
+
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/tests/test_conversions.py b/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/tests/test_conversions.py
new file mode 100644
index 0000000000000000000000000000000000000000..705f036c66b9b66115fd3d7c07a9506b1aad1bba
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/tests/test_conversions.py
@@ -0,0 +1,75 @@
+import numpy as np
+import pytest
+from numpy.testing import assert_array_almost_equal
+from scipy.sparse import csr_array
+from scipy.sparse.csgraph import csgraph_from_dense, csgraph_to_dense, reconstruct_path
+
+
+def test_csgraph_from_dense():
+    np.random.seed(1234)
+    G = np.random.random((10, 10))
+    some_nulls = (G < 0.4)
+    all_nulls = (G < 0.8)
+
+    for null_value in [0, np.nan, np.inf]:
+        G[all_nulls] = null_value
+        with np.errstate(invalid="ignore"):
+            G_csr = csgraph_from_dense(G, null_value=0)
+
+        G[all_nulls] = 0
+        assert_array_almost_equal(G, G_csr.toarray())
+
+    for null_value in [np.nan, np.inf]:
+        G[all_nulls] = 0
+        G[some_nulls] = null_value
+        with np.errstate(invalid="ignore"):
+            G_csr = csgraph_from_dense(G, null_value=0)
+
+        G[all_nulls] = 0
+        assert_array_almost_equal(G, G_csr.toarray())
+
+
+def test_csgraph_to_dense():
+    np.random.seed(1234)
+    G = np.random.random((10, 10))
+    nulls = (G < 0.8)
+    G[nulls] = np.inf
+
+    G_csr = csgraph_from_dense(G)
+
+    for null_value in [0, 10, -np.inf, np.inf]:
+        G[nulls] = null_value
+        assert_array_almost_equal(G, csgraph_to_dense(G_csr, null_value))
+
+
+def test_multiple_edges():
+    # create a random square matrix with an even number of elements
+    np.random.seed(1234)
+    X = np.random.random((10, 10))
+    Xcsr = csr_array(X)
+
+    # now double-up every other column
+    Xcsr.indices[::2] = Xcsr.indices[1::2]
+
+    # normal sparse toarray() will sum the duplicated edges
+    Xdense = Xcsr.toarray()
+    assert_array_almost_equal(Xdense[:, 1::2],
+                              X[:, ::2] + X[:, 1::2])
+
+    # csgraph_to_dense chooses the minimum of each duplicated edge
+    Xdense = csgraph_to_dense(Xcsr)
+    assert_array_almost_equal(Xdense[:, 1::2],
+                              np.minimum(X[:, ::2], X[:, 1::2]))
+
+
+class TestReconstructPath:
+    def test_gh23577(self):
+        row_indices = [0, 1, 1, 3, 3]
+        col_indices = [0, 2, 3, 1, 4]
+        data = [9, -6, -8, 6, 8]
+        matrix = csr_array((data, (row_indices, col_indices)), shape=(5, 5),
+                           dtype=np.int64)
+        predecessors = np.array([np.nan, np.nan, np.nan])
+        with pytest.raises(ValueError, match="integral"):
+            reconstruct_path(matrix, predecessors)
+
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/tests/test_flow.py b/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/tests/test_flow.py
new file mode 100644
index 0000000000000000000000000000000000000000..c92eb985a1145c4b7c1777f0449bb423402f6d66
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/tests/test_flow.py
@@ -0,0 +1,209 @@
+import numpy as np
+from numpy.testing import assert_array_equal
+import pytest
+
+from scipy.sparse import csr_array, csc_array, csr_matrix
+from scipy.sparse.csgraph import maximum_flow
+from scipy.sparse.csgraph._flow import (
+    _add_reverse_edges, _make_edge_pointers, _make_tails
+)
+
+methods = ['edmonds_karp', 'dinic']
+
+def test_raises_on_dense_input():
+    with pytest.raises(TypeError):
+        graph = np.array([[0, 1], [0, 0]])
+        maximum_flow(graph, 0, 1)
+        maximum_flow(graph, 0, 1, method='edmonds_karp')
+
+
+def test_raises_on_csc_input():
+    with pytest.raises(TypeError):
+        graph = csc_array([[0, 1], [0, 0]])
+        maximum_flow(graph, 0, 1)
+        maximum_flow(graph, 0, 1, method='edmonds_karp')
+
+
+def test_raises_on_floating_point_input():
+    with pytest.raises(ValueError):
+        graph = csr_array([[0, 1.5], [0, 0]], dtype=np.float64)
+        maximum_flow(graph, 0, 1)
+        maximum_flow(graph, 0, 1, method='edmonds_karp')
+
+
+def test_raises_on_non_square_input():
+    with pytest.raises(ValueError):
+        graph = csr_array([[0, 1, 2], [2, 1, 0]])
+        maximum_flow(graph, 0, 1)
+
+
+def test_raises_when_source_is_sink():
+    with pytest.raises(ValueError):
+        graph = csr_array([[0, 1], [0, 0]])
+        maximum_flow(graph, 0, 0)
+        maximum_flow(graph, 0, 0, method='edmonds_karp')
+
+
+@pytest.mark.parametrize('method', methods)
+@pytest.mark.parametrize('source', [-1, 2, 3])
+def test_raises_when_source_is_out_of_bounds(source, method):
+    with pytest.raises(ValueError):
+        graph = csr_array([[0, 1], [0, 0]])
+        maximum_flow(graph, source, 1, method=method)
+
+
+@pytest.mark.parametrize('method', methods)
+@pytest.mark.parametrize('sink', [-1, 2, 3])
+def test_raises_when_sink_is_out_of_bounds(sink, method):
+    with pytest.raises(ValueError):
+        graph = csr_array([[0, 1], [0, 0]])
+        maximum_flow(graph, 0, sink, method=method)
+
+
+@pytest.mark.parametrize('method', methods)
+def test_simple_graph(method):
+    # This graph looks as follows:
+    #     (0) --5--> (1)
+    graph = csr_array([[0, 5], [0, 0]])
+    res = maximum_flow(graph, 0, 1, method=method)
+    assert res.flow_value == 5
+    expected_flow = np.array([[0, 5], [-5, 0]])
+    assert_array_equal(res.flow.toarray(), expected_flow)
+
+
+@pytest.mark.parametrize('method', methods)
+def test_return_type(method):
+    graph = csr_array([[0, 5], [0, 0]])
+    assert isinstance(maximum_flow(graph, 0, 1, method=method).flow, csr_array)
+    graph = csr_matrix([[0, 5], [0, 0]])
+    assert isinstance(maximum_flow(graph, 0, 1, method=method).flow, csr_matrix)
+
+
+@pytest.mark.parametrize('method', methods)
+def test_bottle_neck_graph(method):
+    # This graph cannot use the full capacity between 0 and 1:
+    #     (0) --5--> (1) --3--> (2)
+    graph = csr_array([[0, 5, 0], [0, 0, 3], [0, 0, 0]])
+    res = maximum_flow(graph, 0, 2, method=method)
+    assert res.flow_value == 3
+    expected_flow = np.array([[0, 3, 0], [-3, 0, 3], [0, -3, 0]])
+    assert_array_equal(res.flow.toarray(), expected_flow)
+
+
+@pytest.mark.parametrize('method', methods)
+def test_backwards_flow(method):
+    # This example causes backwards flow between vertices 3 and 4,
+    # and so this test ensures that we handle that accordingly. See
+    #     https://stackoverflow.com/q/38843963/5085211
+    # for more information.
+    graph = csr_array([[0, 10, 0, 0, 10, 0, 0, 0],
+                       [0, 0, 10, 0, 0, 0, 0, 0],
+                       [0, 0, 0, 10, 0, 0, 0, 0],
+                       [0, 0, 0, 0, 0, 0, 0, 10],
+                       [0, 0, 0, 10, 0, 10, 0, 0],
+                       [0, 0, 0, 0, 0, 0, 10, 0],
+                       [0, 0, 0, 0, 0, 0, 0, 10],
+                       [0, 0, 0, 0, 0, 0, 0, 0]])
+    res = maximum_flow(graph, 0, 7, method=method)
+    assert res.flow_value == 20
+    expected_flow = np.array([[0, 10, 0, 0, 10, 0, 0, 0],
+                              [-10, 0, 10, 0, 0, 0, 0, 0],
+                              [0, -10, 0, 10, 0, 0, 0, 0],
+                              [0, 0, -10, 0, 0, 0, 0, 10],
+                              [-10, 0, 0, 0, 0, 10, 0, 0],
+                              [0, 0, 0, 0, -10, 0, 10, 0],
+                              [0, 0, 0, 0, 0, -10, 0, 10],
+                              [0, 0, 0, -10, 0, 0, -10, 0]])
+    assert_array_equal(res.flow.toarray(), expected_flow)
+
+
+@pytest.mark.parametrize('method', methods)
+def test_example_from_clrs_chapter_26_1(method):
+    # See page 659 in CLRS second edition, but note that the maximum flow
+    # we find is slightly different than the one in CLRS; we push a flow of
+    # 12 to v_1 instead of v_2.
+    graph = csr_array([[0, 16, 13, 0, 0, 0],
+                       [0, 0, 10, 12, 0, 0],
+                       [0, 4, 0, 0, 14, 0],
+                       [0, 0, 9, 0, 0, 20],
+                       [0, 0, 0, 7, 0, 4],
+                       [0, 0, 0, 0, 0, 0]])
+    res = maximum_flow(graph, 0, 5, method=method)
+    assert res.flow_value == 23
+    expected_flow = np.array([[0, 12, 11, 0, 0, 0],
+                              [-12, 0, 0, 12, 0, 0],
+                              [-11, 0, 0, 0, 11, 0],
+                              [0, -12, 0, 0, -7, 19],
+                              [0, 0, -11, 7, 0, 4],
+                              [0, 0, 0, -19, -4, 0]])
+    assert_array_equal(res.flow.toarray(), expected_flow)
+
+
+@pytest.mark.parametrize('method', methods)
+def test_disconnected_graph(method):
+    # This tests the following disconnected graph:
+    #     (0) --5--> (1)    (2) --3--> (3)
+    graph = csr_array([[0, 5, 0, 0],
+                       [0, 0, 0, 0],
+                       [0, 0, 9, 3],
+                       [0, 0, 0, 0]])
+    res = maximum_flow(graph, 0, 3, method=method)
+    assert res.flow_value == 0
+    expected_flow = np.zeros((4, 4), dtype=np.int32)
+    assert_array_equal(res.flow.toarray(), expected_flow)
+
+
+@pytest.mark.parametrize('method', methods)
+def test_add_reverse_edges_large_graph(method):
+    # Regression test for https://github.com/scipy/scipy/issues/14385
+    n = 100_000
+    indices = np.arange(1, n)
+    indptr = np.array(list(range(n)) + [n - 1])
+    data = np.ones(n - 1, dtype=np.int32)
+    graph = csr_array((data, indices, indptr), shape=(n, n))
+    res = maximum_flow(graph, 0, n - 1, method=method)
+    assert res.flow_value == 1
+    expected_flow = graph - graph.transpose()
+    assert_array_equal(res.flow.data, expected_flow.data)
+    assert_array_equal(res.flow.indices, expected_flow.indices)
+    assert_array_equal(res.flow.indptr, expected_flow.indptr)
+
+
+@pytest.mark.parametrize("a,b_data_expected", [
+    ([[]], []),
+    ([[0], [0]], []),
+    ([[1, 0, 2], [0, 0, 0], [0, 3, 0]], [1, 2, 0, 0, 3]),
+    ([[9, 8, 7], [4, 5, 6], [0, 0, 0]], [9, 8, 7, 4, 5, 6, 0, 0])])
+def test_add_reverse_edges(a, b_data_expected):
+    """Test that the reversal of the edges of the input graph works
+    as expected.
+    """
+    a = csr_array(a, dtype=np.int32, shape=(len(a), len(a)))
+    b = _add_reverse_edges(a)
+    assert_array_equal(b.data, b_data_expected)
+
+
+@pytest.mark.parametrize("a,expected", [
+    ([[]], []),
+    ([[0]], []),
+    ([[1]], [0]),
+    ([[0, 1], [10, 0]], [1, 0]),
+    ([[1, 0, 2], [0, 0, 3], [4, 5, 0]], [0, 3, 4, 1, 2])
+])
+def test_make_edge_pointers(a, expected):
+    a = csr_array(a, dtype=np.int32)
+    rev_edge_ptr = _make_edge_pointers(a)
+    assert_array_equal(rev_edge_ptr, expected)
+
+
+@pytest.mark.parametrize("a,expected", [
+    ([[]], []),
+    ([[0]], []),
+    ([[1]], [0]),
+    ([[0, 1], [10, 0]], [0, 1]),
+    ([[1, 0, 2], [0, 0, 3], [4, 5, 0]], [0, 0, 1, 2, 2])
+])
+def test_make_tails(a, expected):
+    a = csr_array(a, dtype=np.int32)
+    tails = _make_tails(a)
+    assert_array_equal(tails, expected)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/tests/test_graph_laplacian.py b/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/tests/test_graph_laplacian.py
new file mode 100644
index 0000000000000000000000000000000000000000..46536ff7dac6b8775c29b6918128420a02f53dab
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/tests/test_graph_laplacian.py
@@ -0,0 +1,367 @@
+import pytest
+import numpy as np
+from numpy.testing import assert_allclose
+from pytest import raises as assert_raises
+from scipy import sparse
+
+from scipy.sparse import csgraph
+
+
+def check_int_type(mat):
+    return np.issubdtype(mat.dtype, np.signedinteger) or np.issubdtype(
+        mat.dtype, np.ulong
+    )
+
+
+def test_laplacian_value_error():
+    for t in int, float, complex:
+        for m in ([1, 1],
+                  [[[1]]],
+                  [[1, 2, 3], [4, 5, 6]],
+                  [[1, 2], [3, 4], [5, 5]]):
+            A = np.array(m, dtype=t)
+            assert_raises(ValueError, csgraph.laplacian, A)
+
+
+def _explicit_laplacian(x, normed=False):
+    if sparse.issparse(x):
+        x = x.toarray()
+    x = np.asarray(x)
+    y = -1.0 * x
+    for j in range(y.shape[0]):
+        y[j,j] = x[j,j+1:].sum() + x[j,:j].sum()
+    if normed:
+        d = np.diag(y).copy()
+        d[d == 0] = 1.0
+        y /= d[:,None]**.5
+        y /= d[None,:]**.5
+    return y
+
+
+def _check_symmetric_graph_laplacian(mat, normed, copy=True):
+    if not hasattr(mat, 'shape'):
+        mat = eval(mat, dict(np=np, sparse=sparse))
+
+    if sparse.issparse(mat):
+        sp_mat = mat
+        mat = sp_mat.toarray()
+    else:
+        sp_mat = sparse.csr_array(mat)
+
+    mat_copy = np.copy(mat)
+    sp_mat_copy = sparse.csr_array(sp_mat, copy=True)
+
+    n_nodes = mat.shape[0]
+    explicit_laplacian = _explicit_laplacian(mat, normed=normed)
+    laplacian = csgraph.laplacian(mat, normed=normed, copy=copy)
+    sp_laplacian = csgraph.laplacian(sp_mat, normed=normed,
+                                     copy=copy)
+
+    if copy:
+        assert_allclose(mat, mat_copy)
+        _assert_allclose_sparse(sp_mat, sp_mat_copy)
+    else:
+        if not (normed and check_int_type(mat)):
+            assert_allclose(laplacian, mat)
+            if sp_mat.format == 'coo':
+                _assert_allclose_sparse(sp_laplacian, sp_mat)
+
+    assert_allclose(laplacian, sp_laplacian.toarray())
+
+    for tested in [laplacian, sp_laplacian.toarray()]:
+        if not normed:
+            assert_allclose(tested.sum(axis=0), np.zeros(n_nodes))
+        assert_allclose(tested.T, tested)
+        assert_allclose(tested, explicit_laplacian)
+
+
+def test_symmetric_graph_laplacian():
+    symmetric_mats = (
+        'np.arange(10) * np.arange(10)[:, np.newaxis]',
+        'np.ones((7, 7))',
+        'np.eye(19)',
+        'sparse.diags_array([1.0, 1.0], offsets=[-1, 1], shape=(4, 4))',
+        'sparse.diags_array([1.0, 1.0], offsets=[-1, 1], shape=(4, 4)).toarray()',
+        'sparse.diags_array([1.0, 1.0], offsets=[-1, 1], shape=(4, 4)).todense()',
+        'np.vander(np.arange(4)) + np.vander(np.arange(4)).T'
+    )
+    for mat in symmetric_mats:
+        for normed in True, False:
+            for copy in True, False:
+                _check_symmetric_graph_laplacian(mat, normed, copy)
+
+
+def _assert_allclose_sparse(a, b, **kwargs):
+    # helper function that can deal with sparse matrices
+    if sparse.issparse(a):
+        a = a.toarray()
+    if sparse.issparse(b):
+        b = b.toarray()
+    assert_allclose(a, b, **kwargs)
+
+
+def _check_laplacian_dtype_none(
+    A, desired_L, desired_d, normed, use_out_degree, copy, dtype, arr_type
+):
+    mat = arr_type(A, dtype=dtype)
+    L, d = csgraph.laplacian(
+        mat,
+        normed=normed,
+        return_diag=True,
+        use_out_degree=use_out_degree,
+        copy=copy,
+        dtype=None,
+    )
+    if normed and check_int_type(mat):
+        assert L.dtype == np.float64
+        assert d.dtype == np.float64
+        _assert_allclose_sparse(L, desired_L, atol=1e-12)
+        _assert_allclose_sparse(d, desired_d, atol=1e-12)
+    else:
+        assert L.dtype == dtype
+        assert d.dtype == dtype
+        desired_L = np.asarray(desired_L).astype(dtype)
+        desired_d = np.asarray(desired_d).astype(dtype)
+        _assert_allclose_sparse(L, desired_L, atol=1e-12)
+        _assert_allclose_sparse(d, desired_d, atol=1e-12)
+
+    if not copy:
+        if not (normed and check_int_type(mat)):
+            if type(mat) is np.ndarray:
+                assert_allclose(L, mat)
+            elif mat.format == "coo":
+                _assert_allclose_sparse(L, mat)
+
+
+def _check_laplacian_dtype(
+    A, desired_L, desired_d, normed, use_out_degree, copy, dtype, arr_type
+):
+    mat = arr_type(A, dtype=dtype)
+    L, d = csgraph.laplacian(
+        mat,
+        normed=normed,
+        return_diag=True,
+        use_out_degree=use_out_degree,
+        copy=copy,
+        dtype=dtype,
+    )
+    assert L.dtype == dtype
+    assert d.dtype == dtype
+    desired_L = np.asarray(desired_L).astype(dtype)
+    desired_d = np.asarray(desired_d).astype(dtype)
+    _assert_allclose_sparse(L, desired_L, atol=1e-12)
+    _assert_allclose_sparse(d, desired_d, atol=1e-12)
+
+    if not copy:
+        if not (normed and check_int_type(mat)):
+            if type(mat) is np.ndarray:
+                assert_allclose(L, mat)
+            elif mat.format == 'coo':
+                _assert_allclose_sparse(L, mat)
+
+
+INT_DTYPES = (np.intc, np.long, np.longlong)
+REAL_DTYPES = (np.float32, np.float64, np.longdouble)
+COMPLEX_DTYPES = (np.complex64, np.complex128, np.clongdouble)
+DTYPES = INT_DTYPES + REAL_DTYPES + COMPLEX_DTYPES
+
+
+@pytest.mark.parametrize("dtype", DTYPES)
+@pytest.mark.parametrize("arr_type", [np.array,
+                                      sparse.csr_matrix,
+                                      sparse.coo_matrix,
+                                      sparse.csr_array,
+                                      sparse.coo_array])
+@pytest.mark.parametrize("copy", [True, False])
+@pytest.mark.parametrize("normed", [True, False])
+@pytest.mark.parametrize("use_out_degree", [True, False])
+def test_asymmetric_laplacian(use_out_degree, normed,
+                              copy, dtype, arr_type):
+    # adjacency matrix
+    A = [[0, 1, 0],
+         [4, 2, 0],
+         [0, 0, 0]]
+    A = arr_type(np.array(A), dtype=dtype)
+    A_copy = A.copy()
+
+    if not normed and use_out_degree:
+        # Laplacian matrix using out-degree
+        L = [[1, -1, 0],
+             [-4, 4, 0],
+             [0, 0, 0]]
+        d = [1, 4, 0]
+
+    if normed and use_out_degree:
+        # normalized Laplacian matrix using out-degree
+        L = [[1, -0.5, 0],
+             [-2, 1, 0],
+             [0, 0, 0]]
+        d = [1, 2, 1]
+
+    if not normed and not use_out_degree:
+        # Laplacian matrix using in-degree
+        L = [[4, -1, 0],
+             [-4, 1, 0],
+             [0, 0, 0]]
+        d = [4, 1, 0]
+
+    if normed and not use_out_degree:
+        # normalized Laplacian matrix using in-degree
+        L = [[1, -0.5, 0],
+             [-2, 1, 0],
+             [0, 0, 0]]
+        d = [2, 1, 1]
+
+    _check_laplacian_dtype_none(
+        A,
+        L,
+        d,
+        normed=normed,
+        use_out_degree=use_out_degree,
+        copy=copy,
+        dtype=dtype,
+        arr_type=arr_type,
+    )
+
+    _check_laplacian_dtype(
+        A_copy,
+        L,
+        d,
+        normed=normed,
+        use_out_degree=use_out_degree,
+        copy=copy,
+        dtype=dtype,
+        arr_type=arr_type,
+    )
+
+
+@pytest.mark.parametrize("fmt", ['csr', 'csc', 'coo', 'lil',
+                                 'dok', 'dia', 'bsr'])
+@pytest.mark.parametrize("normed", [True, False])
+@pytest.mark.parametrize("copy", [True, False])
+def test_sparse_formats(fmt, normed, copy):
+    mat = sparse.diags_array([1.0, 1.0], offsets=[-1, 1], shape=(4, 4), format=fmt)
+    _check_symmetric_graph_laplacian(mat, normed, copy)
+
+
+@pytest.mark.parametrize(
+    "arr_type", [np.asarray,
+                 sparse.csr_matrix,
+                 sparse.coo_matrix,
+                 sparse.csr_array,
+                 sparse.coo_array]
+)
+@pytest.mark.parametrize("form", ["array", "function", "lo"])
+def test_laplacian_symmetrized(arr_type, form):
+    # adjacency matrix
+    n = 3
+    mat = arr_type(np.arange(n * n).reshape(n, n))
+    L_in, d_in = csgraph.laplacian(
+        mat,
+        return_diag=True,
+        form=form,
+    )
+    L_out, d_out = csgraph.laplacian(
+        mat,
+        return_diag=True,
+        use_out_degree=True,
+        form=form,
+    )
+    Ls, ds = csgraph.laplacian(
+        mat,
+        return_diag=True,
+        symmetrized=True,
+        form=form,
+    )
+    Ls_normed, ds_normed = csgraph.laplacian(
+        mat,
+        return_diag=True,
+        symmetrized=True,
+        normed=True,
+        form=form,
+    )
+    mat += mat.T
+    Lss, dss = csgraph.laplacian(mat, return_diag=True, form=form)
+    Lss_normed, dss_normed = csgraph.laplacian(
+        mat,
+        return_diag=True,
+        normed=True,
+        form=form,
+    )
+
+    assert_allclose(ds, d_in + d_out)
+    assert_allclose(ds, dss)
+    assert_allclose(ds_normed, dss_normed)
+
+    d = {}
+    for L in ["L_in", "L_out", "Ls", "Ls_normed", "Lss", "Lss_normed"]:
+        if form == "array":
+            d[L] = eval(L)
+        else:
+            d[L] = eval(L)(np.eye(n, dtype=mat.dtype))
+
+    _assert_allclose_sparse(d["Ls"], d["L_in"] + d["L_out"].T)
+    _assert_allclose_sparse(d["Ls"], d["Lss"])
+    _assert_allclose_sparse(d["Ls_normed"], d["Lss_normed"])
+
+
+@pytest.mark.parametrize(
+    "arr_type", [np.asarray,
+                 sparse.csr_matrix,
+                 sparse.coo_matrix,
+                 sparse.csr_array,
+                 sparse.coo_array]
+)
+@pytest.mark.parametrize("dtype", DTYPES)
+@pytest.mark.parametrize("normed", [True, False])
+@pytest.mark.parametrize("symmetrized", [True, False])
+@pytest.mark.parametrize("use_out_degree", [True, False])
+@pytest.mark.parametrize("form", ["function", "lo"])
+def test_format(dtype, arr_type, normed, symmetrized, use_out_degree, form):
+    n = 3
+    mat = [[0, 1, 0], [4, 2, 0], [0, 0, 0]]
+    mat = arr_type(np.array(mat), dtype=dtype)
+    Lo, do = csgraph.laplacian(
+        mat,
+        return_diag=True,
+        normed=normed,
+        symmetrized=symmetrized,
+        use_out_degree=use_out_degree,
+        dtype=dtype,
+    )
+    La, da = csgraph.laplacian(
+        mat,
+        return_diag=True,
+        normed=normed,
+        symmetrized=symmetrized,
+        use_out_degree=use_out_degree,
+        dtype=dtype,
+        form="array",
+    )
+    assert_allclose(do, da)
+    _assert_allclose_sparse(Lo, La)
+
+    L, d = csgraph.laplacian(
+        mat,
+        return_diag=True,
+        normed=normed,
+        symmetrized=symmetrized,
+        use_out_degree=use_out_degree,
+        dtype=dtype,
+        form=form,
+    )
+    assert_allclose(d, do)
+    assert d.dtype == dtype
+    Lm = L(np.eye(n, dtype=mat.dtype)).astype(dtype)
+    _assert_allclose_sparse(Lm, Lo, rtol=2e-7, atol=2e-7)
+    x = np.arange(6).reshape(3, 2)
+    if not (normed and dtype in INT_DTYPES):
+        assert_allclose(L(x), Lo @ x)
+    else:
+        # Normalized Lo is casted to integer, but L() is not
+        pass
+
+
+def test_format_error_message():
+    with pytest.raises(ValueError, match="Invalid form: 'toto'"):
+        _ = csgraph.laplacian(np.eye(1), form='toto')
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/tests/test_index_arrays_dtype.py b/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/tests/test_index_arrays_dtype.py
new file mode 100644
index 0000000000000000000000000000000000000000..5148f1e11390ceb50a19a3ad9dc30e15e3c96e64
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/tests/test_index_arrays_dtype.py
@@ -0,0 +1,107 @@
+"""Test of csgraph public API with int64 index arrays in csr format.
+
+See gh-24629
+"""
+import numpy as np
+import pytest
+
+from scipy.sparse import csr_array
+import scipy.sparse.csgraph as csgraph_subpackage
+from scipy.sparse.csgraph import (
+    connected_components,
+    laplacian,
+    shortest_path,
+    floyd_warshall,
+    dijkstra,
+    bellman_ford,
+    johnson,
+    yen,
+    breadth_first_order,
+    depth_first_order,
+    breadth_first_tree,
+    depth_first_tree,
+    minimum_spanning_tree,
+    reverse_cuthill_mckee,
+    maximum_flow,
+    maximum_bipartite_matching,
+    min_weight_full_bipartite_matching,
+    structural_rank,
+    construct_dist_matrix,
+    reconstruct_path,
+    csgraph_to_dense,
+    csgraph_to_masked,
+)
+
+
+@pytest.fixture()
+def A():
+    A = csr_array([[0, 1, 2], [2, 1, 0], [0, 1, 0]])
+    A.indptr = A.indptr.astype(np.int64)
+    A.indices = A.indices.astype(np.int64)
+    return A
+
+
+check_these_functions = [
+    # (csgraph_function, args),
+    (connected_components, ()),
+    (laplacian, ()),
+    (floyd_warshall, ()),
+    (dijkstra, ()),
+    (bellman_ford, ()),
+    (johnson, ()),
+    (yen, (0, 1, 1)),
+    (breadth_first_order, (0,)),
+    (depth_first_order, (0,)),
+    (breadth_first_tree, (0,)),
+    (depth_first_tree, (0,)),
+    (minimum_spanning_tree, ()),
+    (reverse_cuthill_mckee, ()),
+    (maximum_flow, (0, 1)),
+    (maximum_bipartite_matching, ()),
+    (min_weight_full_bipartite_matching, ()),
+    (structural_rank, ()),
+    (csgraph_to_dense, ()),
+    (csgraph_to_masked, ()),
+]
+
+
+def test_new_functions_untested_here():
+    #This tests whether any new code has arrived that isn't in the list above.
+
+    # funcs tested individually outside of check_these_functions
+    handled = ["shortest_path", "construct_dist_matrix", "reconstruct_path",
+               "csgraph_from_dense", "csgraph_from_masked", "csgraph_masked_from_dense"]
+
+    # look for functions that should be tested
+    functions = [fname for fname in dir(csgraph_subpackage)
+                 if fname[0] != "_"
+                 if not fname.endswith("Error")
+                 if not fname.startswith("test")
+                 if fname not in handled]
+
+    checked_funcs = [x[0].__name__ for x in check_these_functions]
+    for func in functions:
+        if func not in checked_funcs:
+            msg = (f'function "{func}" in csgraph is not tested. '
+                   'It should be added to the `check_these_functions` list above or '
+                   'handled separately if its signature has many required parameters')
+            raise ValueError(msg)
+
+
+@pytest.mark.parametrize("csgraph_function, args", check_these_functions)
+def test_smoke_from_int64_index_arrays(csgraph_function, args, A):
+    csgraph_function(A, *args)
+
+
+def test_smoke_from_int64_construct_dist_matrix(A):
+    _, preds = shortest_path(A, return_predecessors=True)
+    construct_dist_matrix(A, preds)
+
+
+def test_smoke_from_int64_shortest_path(A):
+    shortest_path(A, method='auto')
+
+
+def test_smoke_from_int64_reconstruct_path(A):
+    pred = np.array([-9999, 0, 1])
+    reconstruct_path(A, pred)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/tests/test_matching.py b/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/tests/test_matching.py
new file mode 100644
index 0000000000000000000000000000000000000000..502927788540cc58138da8c948fcd0a570515af5
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/tests/test_matching.py
@@ -0,0 +1,306 @@
+from itertools import product
+
+import numpy as np
+from numpy.testing import assert_array_equal, assert_equal
+import pytest
+
+from scipy.sparse import csr_array, coo_array, diags_array
+from scipy.sparse.csgraph import (
+    maximum_bipartite_matching, min_weight_full_bipartite_matching
+)
+
+
+def test_maximum_bipartite_matching_raises_on_dense_input():
+    with pytest.raises(TypeError):
+        graph = np.array([[0, 1], [0, 0]])
+        maximum_bipartite_matching(graph)
+
+
+def test_maximum_bipartite_matching_empty_graph():
+    graph = csr_array((0, 0))
+    x = maximum_bipartite_matching(graph, perm_type='row')
+    y = maximum_bipartite_matching(graph, perm_type='column')
+    expected_matching = np.array([])
+    assert_array_equal(expected_matching, x)
+    assert_array_equal(expected_matching, y)
+
+
+def test_maximum_bipartite_matching_empty_left_partition():
+    graph = csr_array((2, 0))
+    x = maximum_bipartite_matching(graph, perm_type='row')
+    y = maximum_bipartite_matching(graph, perm_type='column')
+    assert_array_equal(np.array([]), x)
+    assert_array_equal(np.array([-1, -1]), y)
+
+
+def test_maximum_bipartite_matching_empty_right_partition():
+    graph = csr_array((0, 3))
+    x = maximum_bipartite_matching(graph, perm_type='row')
+    y = maximum_bipartite_matching(graph, perm_type='column')
+    assert_array_equal(np.array([-1, -1, -1]), x)
+    assert_array_equal(np.array([]), y)
+
+
+def test_maximum_bipartite_matching_graph_with_no_edges():
+    graph = csr_array((2, 2))
+    x = maximum_bipartite_matching(graph, perm_type='row')
+    y = maximum_bipartite_matching(graph, perm_type='column')
+    assert_array_equal(np.array([-1, -1]), x)
+    assert_array_equal(np.array([-1, -1]), y)
+
+
+def test_maximum_bipartite_matching_graph_that_causes_augmentation():
+    # In this graph, column 1 is initially assigned to row 1, but it should be
+    # reassigned to make room for row 2.
+    graph = csr_array([[1, 1], [1, 0]])
+    x = maximum_bipartite_matching(graph, perm_type='column')
+    y = maximum_bipartite_matching(graph, perm_type='row')
+    expected_matching = np.array([1, 0])
+    assert_array_equal(expected_matching, x)
+    assert_array_equal(expected_matching, y)
+
+
+def test_maximum_bipartite_matching_graph_with_more_rows_than_columns():
+    graph = csr_array([[1, 1], [1, 0], [0, 1]])
+    x = maximum_bipartite_matching(graph, perm_type='column')
+    y = maximum_bipartite_matching(graph, perm_type='row')
+    assert_array_equal(np.array([0, -1, 1]), x)
+    assert_array_equal(np.array([0, 2]), y)
+
+
+def test_maximum_bipartite_matching_graph_with_more_columns_than_rows():
+    graph = csr_array([[1, 1, 0], [0, 0, 1]])
+    x = maximum_bipartite_matching(graph, perm_type='column')
+    y = maximum_bipartite_matching(graph, perm_type='row')
+    assert_array_equal(np.array([0, 2]), x)
+    assert_array_equal(np.array([0, -1, 1]), y)
+
+
+def test_maximum_bipartite_matching_explicit_zeros_count_as_edges():
+    data = [0, 0]
+    indices = [1, 0]
+    indptr = [0, 1, 2]
+    graph = csr_array((data, indices, indptr), shape=(2, 2))
+    x = maximum_bipartite_matching(graph, perm_type='row')
+    y = maximum_bipartite_matching(graph, perm_type='column')
+    expected_matching = np.array([1, 0])
+    assert_array_equal(expected_matching, x)
+    assert_array_equal(expected_matching, y)
+
+
+def test_maximum_bipartite_matching_feasibility_of_result():
+    # This is a regression test for GitHub issue #11458
+    data = np.ones(50, dtype=int)
+    indices = [11, 12, 19, 22, 23, 5, 22, 3, 8, 10, 5, 6, 11, 12, 13, 5, 13,
+               14, 20, 22, 3, 15, 3, 13, 14, 11, 12, 19, 22, 23, 5, 22, 3, 8,
+               10, 5, 6, 11, 12, 13, 5, 13, 14, 20, 22, 3, 15, 3, 13, 14]
+    indptr = [0, 5, 7, 10, 10, 15, 20, 22, 22, 23, 25, 30, 32, 35, 35, 40, 45,
+              47, 47, 48, 50]
+    graph = csr_array((data, indices, indptr), shape=(20, 25))
+    x = maximum_bipartite_matching(graph, perm_type='row')
+    y = maximum_bipartite_matching(graph, perm_type='column')
+    assert (x != -1).sum() == 13
+    assert (y != -1).sum() == 13
+    # Ensure that each element of the matching is in fact an edge in the graph.
+    for u, v in zip(range(graph.shape[0]), y):
+        if v != -1:
+            assert graph[u, v]
+    for u, v in zip(x, range(graph.shape[1])):
+        if u != -1:
+            assert graph[u, v]
+
+
+def test_matching_large_random_graph_with_one_edge_incident_to_each_vertex():
+    np.random.seed(42)
+    A = diags_array(np.ones(25), offsets=0, format='csr')
+    rand_perm = np.random.permutation(25)
+    rand_perm2 = np.random.permutation(25)
+
+    Rrow = np.arange(25)
+    Rcol = rand_perm
+    Rdata = np.ones(25, dtype=int)
+    Rmat = csr_array((Rdata, (Rrow, Rcol)))
+
+    Crow = rand_perm2
+    Ccol = np.arange(25)
+    Cdata = np.ones(25, dtype=int)
+    Cmat = csr_array((Cdata, (Crow, Ccol)))
+    # Randomly permute identity matrix
+    B = Rmat @ A @ Cmat
+
+    # Row permute
+    perm = maximum_bipartite_matching(B, perm_type='row')
+    Rrow = np.arange(25)
+    Rcol = perm
+    Rdata = np.ones(25, dtype=int)
+    Rmat = csr_array((Rdata, (Rrow, Rcol)))
+    C1 = Rmat @ B
+
+    # Column permute
+    perm2 = maximum_bipartite_matching(B, perm_type='column')
+    Crow = perm2
+    Ccol = np.arange(25)
+    Cdata = np.ones(25, dtype=int)
+    Cmat = csr_array((Cdata, (Crow, Ccol)))
+    C2 = B @ Cmat
+
+    # Should get identity matrix back
+    assert_equal(any(C1.diagonal() == 0), False)
+    assert_equal(any(C2.diagonal() == 0), False)
+
+
+@pytest.mark.parametrize('num_rows,num_cols', [(0, 0), (2, 0), (0, 3)])
+def test_min_weight_full_matching_trivial_graph(num_rows, num_cols):
+    biadjacency = csr_array((num_cols, num_rows))
+    biadjacency1 = coo_array((num_cols, num_rows))
+
+    row_ind, col_ind = min_weight_full_bipartite_matching(biadjacency)
+    assert len(row_ind) == 0
+    assert len(col_ind) == 0
+
+    row_ind1, col_ind1 = min_weight_full_bipartite_matching(biadjacency1)
+    assert len(row_ind1) == 0
+    assert len(col_ind1) == 0
+
+
+@pytest.mark.parametrize('biadjacency',
+                         [
+                            [[1, 1, 1], [1, 0, 0], [1, 0, 0]],
+                            [[1, 1, 1], [0, 0, 1], [0, 0, 1]],
+                            [[1, 0, 0, 1], [1, 1, 0, 1], [0, 0, 0, 0]],
+                            [[1, 0, 0], [2, 0, 0]],
+                            [[0, 1, 0], [0, 2, 0]],
+                            [[1, 0], [2, 0], [5, 0]]
+                         ])
+def test_min_weight_full_matching_infeasible_problems(biadjacency):
+    with pytest.raises(ValueError):
+        min_weight_full_bipartite_matching(csr_array(biadjacency))
+    with pytest.raises(ValueError):
+        min_weight_full_bipartite_matching(coo_array(biadjacency))
+
+
+def test_min_weight_full_matching_large_infeasible():
+    # Regression test for GitHub issue #17269
+    a = np.asarray([
+        [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+         0.0, 0.0, 0.001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
+        [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+         0.0, 0.0, 0.0, 0.001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
+        [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+         0.0, 0.0, 0.0, 0.0, 0.001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
+        [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+         0.0, 0.0, 0.0, 0.0, 0.0, 0.001, 0.0, 0.0, 0.0, 0.0, 0.0],
+        [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+         0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001, 0.0, 0.0, 0.0, 0.0],
+        [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+         0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001, 0.0, 0.0, 0.0],
+        [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+         0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001, 0.0, 0.0],
+        [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+         0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001, 0.0],
+        [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+         0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001],
+        [0.0, 0.11687445, 0.0, 0.0, 0.01319788, 0.07509257, 0.0,
+         0.0, 0.0, 0.74228317, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+         0.0, 0.0, 0.0, 0.0, 0.0],
+        [0.0, 0.0, 0.0, 0.81087935, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+         0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
+        [0.0, 0.0, 0.0, 0.0, 0.8408466, 0.0, 0.0, 0.0, 0.0, 0.01194389,
+         0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
+        [0.0, 0.82994211, 0.0, 0.0, 0.0, 0.11468516, 0.0, 0.0, 0.0,
+         0.11173505, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+         0.0, 0.0],
+        [0.18796507, 0.0, 0.04002318, 0.0, 0.0, 0.0, 0.0, 0.0, 0.75883335,
+         0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
+        [0.0, 0.0, 0.71545464, 0.0, 0.0, 0.0, 0.0, 0.0, 0.02748488,
+         0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
+        [0.78470564, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.14829198,
+         0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
+        [0.0, 0.10870609, 0.0, 0.0, 0.0, 0.8918677, 0.0, 0.0, 0.0, 0.06306644,
+         0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
+        [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+         0.63844085, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
+        [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.7442354, 0.0, 0.0, 0.0,
+         0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
+        [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.09850549, 0.0, 0.0, 0.18638258,
+         0.2769244, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
+        [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.73182464, 0.0, 0.0, 0.46443561,
+         0.38589284, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
+        [0.29510278, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.09666032, 0.0,
+         0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
+        ])
+    with pytest.raises(ValueError, match='no full matching exists'):
+        min_weight_full_bipartite_matching(csr_array(a))
+    with pytest.raises(ValueError, match='no full matching exists'):
+        min_weight_full_bipartite_matching(coo_array(a))
+
+
+def test_explicit_zero_causes_warning():
+    biadjacency = csr_array(((2, 0, 3), (0, 1, 1), (0, 2, 3)))
+    with pytest.warns(UserWarning):
+        min_weight_full_bipartite_matching(biadjacency)
+    with pytest.warns(UserWarning):
+        min_weight_full_bipartite_matching(biadjacency.tocoo())
+
+
+# General test for linear sum assignment solvers to make it possible to rely
+# on the same tests for scipy.optimize.linear_sum_assignment.
+def linear_sum_assignment_assertions(
+    solver, array_type, sign, test_case
+):
+    cost_matrix, expected_cost = test_case
+    maximize = sign == -1
+    cost_matrix = sign * array_type(cost_matrix)
+    expected_cost = sign * np.array(expected_cost)
+
+    row_ind, col_ind = solver(cost_matrix, maximize=maximize)
+    assert_array_equal(row_ind, np.sort(row_ind))
+    assert_array_equal(expected_cost,
+                       np.array(cost_matrix[row_ind, col_ind]).flatten())
+
+    cost_matrix = cost_matrix.T
+    row_ind, col_ind = solver(cost_matrix, maximize=maximize)
+    assert_array_equal(row_ind, np.sort(row_ind))
+    assert_array_equal(np.sort(expected_cost),
+                       np.sort(np.array(
+                           cost_matrix[row_ind, col_ind])).flatten())
+
+
+linear_sum_assignment_test_cases = list(product(
+    [-1, 1],
+    [
+        # Square
+        ([[400, 150, 400],
+          [400, 450, 600],
+          [300, 225, 300]],
+         [150, 400, 300]),
+
+        # Rectangular variant
+        ([[400, 150, 400, 1],
+          [400, 450, 600, 2],
+          [300, 225, 300, 3]],
+         [150, 2, 300]),
+
+        ([[10, 10, 8],
+          [9, 8, 1],
+          [9, 7, 4]],
+         [10, 1, 7]),
+
+        # Square
+        ([[10, 10, 8, 11],
+          [9, 8, 1, 1],
+          [9, 7, 4, 10]],
+         [10, 1, 4]),
+
+        # Rectangular variant
+        ([[10, float("inf"), float("inf")],
+          [float("inf"), float("inf"), 1],
+          [float("inf"), 7, float("inf")]],
+         [10, 1, 7])
+    ]))
+
+
+@pytest.mark.parametrize('sign,test_case', linear_sum_assignment_test_cases)
+def test_min_weight_full_matching_small_inputs(sign, test_case):
+    linear_sum_assignment_assertions(
+        min_weight_full_bipartite_matching, csr_array, sign, test_case)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/tests/test_pydata_sparse.py b/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/tests/test_pydata_sparse.py
new file mode 100644
index 0000000000000000000000000000000000000000..bc751ecfdee8ca325cc7422cd24526470c6f062a
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/tests/test_pydata_sparse.py
@@ -0,0 +1,197 @@
+import pytest
+
+import numpy as np
+import scipy.sparse as sp
+import scipy.sparse.csgraph as spgraph
+from scipy._external.packaging_version import version
+
+from numpy.testing import assert_equal
+
+try:
+    import sparse
+except Exception:
+    sparse = None
+
+pytestmark = pytest.mark.skipif(sparse is None,
+                                reason="pydata/sparse not installed")
+
+
+msg = "pydata/sparse (0.15.1) does not implement necessary operations"
+
+
+sparse_params = (pytest.param("COO"),
+                 pytest.param("DOK", marks=[pytest.mark.xfail(reason=msg)]))
+
+
+def check_sparse_version(min_ver):
+    if sparse is None:
+        return pytest.mark.skip(reason="sparse is not installed")
+    return pytest.mark.skipif(
+        version.parse(sparse.__version__) < version.Version(min_ver),
+        reason=f"sparse version >= {min_ver} required"
+    )
+
+
+@pytest.fixture(params=sparse_params)
+def sparse_cls(request):
+    return getattr(sparse, request.param)
+
+
+@pytest.fixture
+def graphs(sparse_cls):
+    graph = [
+        [0, 1, 1, 0, 0],
+        [0, 0, 1, 0, 0],
+        [0, 0, 0, 0, 0],
+        [0, 0, 0, 0, 1],
+        [0, 0, 0, 0, 0],
+    ]
+    A_dense = np.array(graph)
+    A_sparse = sparse_cls(A_dense)
+    return A_dense, A_sparse
+
+
+@pytest.mark.parametrize(
+    "func",
+    [
+        spgraph.shortest_path,
+        spgraph.dijkstra,
+        spgraph.floyd_warshall,
+        spgraph.bellman_ford,
+        spgraph.johnson,
+        spgraph.reverse_cuthill_mckee,
+        spgraph.maximum_bipartite_matching,
+        spgraph.structural_rank,
+    ]
+)
+def test_csgraph_equiv(func, graphs):
+    A_dense, A_sparse = graphs
+    actual = func(A_sparse)
+    desired = func(sp.csc_array(A_dense))
+    assert_equal(actual, desired)
+
+
+def test_connected_components(graphs):
+    A_dense, A_sparse = graphs
+    func = spgraph.connected_components
+
+    actual_comp, actual_labels = func(A_sparse)
+    desired_comp, desired_labels, = func(sp.csc_array(A_dense))
+
+    assert actual_comp == desired_comp
+    assert_equal(actual_labels, desired_labels)
+
+
+def test_laplacian(graphs):
+    A_dense, A_sparse = graphs
+    sparse_cls = type(A_sparse)
+    func = spgraph.laplacian
+
+    actual = func(A_sparse)
+    desired = func(sp.csc_array(A_dense))
+
+    assert isinstance(actual, sparse_cls)
+
+    assert_equal(actual.todense(), desired.todense())
+
+
+@pytest.mark.parametrize(
+    "func", [spgraph.breadth_first_order, spgraph.depth_first_order]
+)
+def test_order_search(graphs, func):
+    A_dense, A_sparse = graphs
+
+    actual = func(A_sparse, 0)
+    desired = func(sp.csc_array(A_dense), 0)
+
+    assert_equal(actual, desired)
+
+
+@pytest.mark.parametrize(
+    "func", [spgraph.breadth_first_tree, spgraph.depth_first_tree]
+)
+def test_tree_search(graphs, func):
+    A_dense, A_sparse = graphs
+    sparse_cls = type(A_sparse)
+
+    actual = func(A_sparse, 0)
+    desired = func(sp.csc_array(A_dense), 0)
+
+    assert isinstance(actual, sparse_cls)
+
+    assert_equal(actual.todense(), desired.todense())
+
+
+def test_minimum_spanning_tree(graphs):
+    A_dense, A_sparse = graphs
+    sparse_cls = type(A_sparse)
+    func = spgraph.minimum_spanning_tree
+
+    actual = func(A_sparse)
+    desired = func(sp.csc_array(A_dense))
+
+    assert isinstance(actual, sparse_cls)
+
+    assert_equal(actual.todense(), desired.todense())
+
+
+def test_maximum_flow(graphs):
+    A_dense, A_sparse = graphs
+    sparse_cls = type(A_sparse)
+    func = spgraph.maximum_flow
+
+    actual = func(A_sparse, 0, 2)
+    desired = func(sp.csr_array(A_dense), 0, 2)
+
+    assert actual.flow_value == desired.flow_value
+    assert isinstance(actual.flow, sparse_cls)
+
+    assert_equal(actual.flow.todense(), desired.flow.todense())
+
+
+def test_min_weight_full_bipartite_matching(graphs):
+    A_dense, A_sparse = graphs
+    func = spgraph.min_weight_full_bipartite_matching
+
+    actual = func(A_sparse[0:2, 1:3])
+    A_csc = sp.csc_array(A_dense)
+    desired = func(A_csc[0:2, 1:3])
+    desired1 = func(A_csc[0:2, 1:3].tocoo())
+
+    assert_equal(actual, desired)
+    assert_equal(actual, desired1)
+
+
+@check_sparse_version("0.15.4")
+@pytest.mark.parametrize(
+    "func",
+    [
+        spgraph.shortest_path,
+        spgraph.dijkstra,
+        spgraph.floyd_warshall,
+        spgraph.bellman_ford,
+        spgraph.johnson,
+        spgraph.minimum_spanning_tree,
+    ]
+)
+@pytest.mark.parametrize(
+    "fill_value, comp_func",
+    [(np.inf, np.isposinf), (np.nan, np.isnan)],
+)
+def test_nonzero_fill_value(graphs, func, fill_value, comp_func):
+    A_dense, A_sparse = graphs
+    A_sparse = A_sparse.astype(float)
+    A_sparse.fill_value = fill_value
+    sparse_cls = type(A_sparse)
+
+    actual = func(A_sparse)
+    desired = func(sp.csc_array(A_dense))
+
+    if func == spgraph.minimum_spanning_tree:
+        assert isinstance(actual, sparse_cls)
+        assert comp_func(actual.fill_value)
+        actual = actual.todense()
+        actual[comp_func(actual)] = 0.0
+        assert_equal(actual, desired.todense())
+    else:
+        assert_equal(actual, desired)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/tests/test_reordering.py b/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/tests/test_reordering.py
new file mode 100644
index 0000000000000000000000000000000000000000..add76cdc29c39c079f386a6ca73075bb90b0a6e8
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/tests/test_reordering.py
@@ -0,0 +1,70 @@
+import numpy as np
+from numpy.testing import assert_equal
+from scipy.sparse.csgraph import reverse_cuthill_mckee, structural_rank
+from scipy.sparse import csc_array, csr_array, coo_array
+
+
+def test_graph_reverse_cuthill_mckee():
+    A = np.array([[1, 0, 0, 0, 1, 0, 0, 0],
+                [0, 1, 1, 0, 0, 1, 0, 1],
+                [0, 1, 1, 0, 1, 0, 0, 0],
+                [0, 0, 0, 1, 0, 0, 1, 0],
+                [1, 0, 1, 0, 1, 0, 0, 0],
+                [0, 1, 0, 0, 0, 1, 0, 1],
+                [0, 0, 0, 1, 0, 0, 1, 0],
+                [0, 1, 0, 0, 0, 1, 0, 1]], dtype=int)
+
+    graph = csr_array(A)
+    perm = reverse_cuthill_mckee(graph)
+    correct_perm = np.array([6, 3, 7, 5, 1, 2, 4, 0])
+    assert_equal(perm, correct_perm)
+
+    # Test int64 indices input
+    graph.indices = graph.indices.astype('int64')
+    graph.indptr = graph.indptr.astype('int64')
+    perm = reverse_cuthill_mckee(graph, True)
+    assert_equal(perm, correct_perm)
+
+
+def test_graph_reverse_cuthill_mckee_ordering():
+    data = np.ones(63,dtype=int)
+    rows = np.array([0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2,
+                2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5,
+                6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9,
+                9, 10, 10, 10, 10, 10, 11, 11, 11, 11,
+                12, 12, 12, 13, 13, 13, 13, 14, 14, 14,
+                14, 15, 15, 15, 15, 15])
+    cols = np.array([0, 2, 5, 8, 10, 1, 3, 9, 11, 0, 2,
+                7, 10, 1, 3, 11, 4, 6, 12, 14, 0, 7, 13,
+                15, 4, 6, 14, 2, 5, 7, 15, 0, 8, 10, 13,
+                1, 9, 11, 0, 2, 8, 10, 15, 1, 3, 9, 11,
+                4, 12, 14, 5, 8, 13, 15, 4, 6, 12, 14,
+                5, 7, 10, 13, 15])
+    graph = csr_array((data, (rows,cols)))
+    perm = reverse_cuthill_mckee(graph)
+    correct_perm = np.array([12, 14, 4, 6, 10, 8, 2, 15,
+                0, 13, 7, 5, 9, 11, 1, 3])
+    assert_equal(perm, correct_perm)
+
+
+def test_graph_structural_rank():
+    # Test square matrix #1
+    A = csc_array([[1, 1, 0],
+                   [1, 0, 1],
+                   [0, 1, 0]])
+    assert_equal(structural_rank(A), 3)
+
+    # Test square matrix #2
+    rows = np.array([0,0,0,0,0,1,1,2,2,3,3,3,3,3,3,4,4,5,5,6,6,7,7])
+    cols = np.array([0,1,2,3,4,2,5,2,6,0,1,3,5,6,7,4,5,5,6,2,6,2,4])
+    data = np.ones_like(rows)
+    B = coo_array((data,(rows,cols)), shape=(8,8))
+    assert_equal(structural_rank(B), 6)
+
+    #Test non-square matrix
+    C = csc_array([[1, 0, 2, 0],
+                   [2, 0, 4, 0]])
+    assert_equal(structural_rank(C), 2)
+
+    #Test tall matrix
+    assert_equal(structural_rank(C.T), 2)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/tests/test_shortest_path.py b/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/tests/test_shortest_path.py
new file mode 100644
index 0000000000000000000000000000000000000000..761a35e1a4ed5e12de3950b399a88b63c8fe6359
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/tests/test_shortest_path.py
@@ -0,0 +1,547 @@
+from io import StringIO
+import warnings
+import numpy as np
+from numpy.testing import assert_array_almost_equal, assert_array_equal, assert_allclose
+from pytest import raises as assert_raises
+from scipy.sparse.csgraph import (shortest_path, dijkstra, johnson,
+                                  bellman_ford, construct_dist_matrix, yen,
+                                  NegativeCycleError)
+import scipy.sparse
+from scipy.io import mmread
+import pytest
+
+directed_G = np.array([[0, 3, 3, 0, 0],
+                       [0, 0, 0, 2, 4],
+                       [0, 0, 0, 0, 0],
+                       [1, 0, 0, 0, 0],
+                       [2, 0, 0, 2, 0]], dtype=float)
+
+# Undirected version of directed_G
+undirected_G = np.array([[0, 3, 3, 1, 2],
+                         [3, 0, 0, 2, 4],
+                         [3, 0, 0, 0, 0],
+                         [1, 2, 0, 0, 2],
+                         [2, 4, 0, 2, 0]], dtype=float)
+
+unweighted_G = (directed_G > 0).astype(float)
+
+# Correct shortest path lengths for directed_G and undirected_G
+directed_SP = [[0, 3, 3, 5, 7],
+               [3, 0, 6, 2, 4],
+               [np.inf, np.inf, 0, np.inf, np.inf],
+               [1, 4, 4, 0, 8],
+               [2, 5, 5, 2, 0]]
+
+directed_2SP_0_to_3 = [[-9999, 0, -9999, 1, -9999],
+                       [-9999, 0, -9999, 4, 1]]
+
+undirected_SP = np.array([[0, 3, 3, 1, 2],
+                          [3, 0, 6, 2, 4],
+                          [3, 6, 0, 4, 5],
+                          [1, 2, 4, 0, 2],
+                          [2, 4, 5, 2, 0]], dtype=float)
+
+undirected_SP_limit_2 = np.array([[0, np.inf, np.inf, 1, 2],
+                                  [np.inf, 0, np.inf, 2, np.inf],
+                                  [np.inf, np.inf, 0, np.inf, np.inf],
+                                  [1, 2, np.inf, 0, 2],
+                                  [2, np.inf, np.inf, 2, 0]], dtype=float)
+
+undirected_SP_limit_0 = np.ones((5, 5), dtype=float) - np.eye(5)
+undirected_SP_limit_0[undirected_SP_limit_0 > 0] = np.inf
+
+# Correct predecessors for directed_G and undirected_G
+directed_pred = np.array([[-9999, 0, 0, 1, 1],
+                          [3, -9999, 0, 1, 1],
+                          [-9999, -9999, -9999, -9999, -9999],
+                          [3, 0, 0, -9999, 1],
+                          [4, 0, 0, 4, -9999]], dtype=float)
+
+undirected_pred = np.array([[-9999, 0, 0, 0, 0],
+                            [1, -9999, 0, 1, 1],
+                            [2, 0, -9999, 0, 0],
+                            [3, 3, 0, -9999, 3],
+                            [4, 4, 0, 4, -9999]], dtype=float)
+
+# Other graphs
+directed_sparse_zero_G = scipy.sparse.csr_array(
+    (
+        [0, 1, 2, 3, 1],
+        ([0, 1, 2, 3, 4], [1, 2, 0, 4, 3]),
+    ),
+    shape=(5, 5),
+)
+
+directed_sparse_zero_SP = [[0, 0, 1, np.inf, np.inf],
+                      [3, 0, 1, np.inf, np.inf],
+                      [2, 2, 0, np.inf, np.inf],
+                      [np.inf, np.inf, np.inf, 0, 3],
+                      [np.inf, np.inf, np.inf, 1, 0]]
+
+undirected_sparse_zero_G = scipy.sparse.csr_array(
+    (
+        [0, 0, 1, 1, 2, 2, 1, 1],
+        ([0, 1, 1, 2, 2, 0, 3, 4], [1, 0, 2, 1, 0, 2, 4, 3])
+    ),
+    shape=(5, 5),
+)
+
+undirected_sparse_zero_SP = [[0, 0, 1, np.inf, np.inf],
+                        [0, 0, 1, np.inf, np.inf],
+                        [1, 1, 0, np.inf, np.inf],
+                        [np.inf, np.inf, np.inf, 0, 1],
+                        [np.inf, np.inf, np.inf, 1, 0]]
+
+directed_negative_weighted_G = np.array([[0, 0, 0],
+                                         [-1, 0, 0],
+                                         [0, -1, 0]], dtype=float)
+
+directed_negative_weighted_SP = np.array([[0, np.inf, np.inf],
+                                          [-1, 0, np.inf],
+                                          [-2, -1, 0]], dtype=float)
+
+methods = ['auto', 'FW', 'D', 'BF', 'J']
+
+
+def test_dijkstra_limit():
+    limits = [0, 2, np.inf]
+    results = [undirected_SP_limit_0,
+               undirected_SP_limit_2,
+               undirected_SP]
+
+    def check(limit, result):
+        SP = dijkstra(undirected_G, directed=False, limit=limit)
+        assert_array_almost_equal(SP, result)
+
+    for limit, result in zip(limits, results):
+        check(limit, result)
+
+
+def test_directed():
+    def check(method):
+        SP = shortest_path(directed_G, method=method, directed=True,
+                           overwrite=False)
+        assert_array_almost_equal(SP, directed_SP)
+
+    for method in methods:
+        check(method)
+
+
+def test_undirected():
+    def check(method, directed_in):
+        if directed_in:
+            SP1 = shortest_path(directed_G, method=method, directed=False,
+                                overwrite=False)
+            assert_array_almost_equal(SP1, undirected_SP)
+        else:
+            SP2 = shortest_path(undirected_G, method=method, directed=True,
+                                overwrite=False)
+            assert_array_almost_equal(SP2, undirected_SP)
+
+    for method in methods:
+        for directed_in in (True, False):
+            check(method, directed_in)
+
+
+def test_directed_sparse_zero():
+    # test directed sparse graph with zero-weight edge and two connected components
+    def check(method):
+        SP = shortest_path(directed_sparse_zero_G, method=method, directed=True,
+                           overwrite=False)
+        assert_array_almost_equal(SP, directed_sparse_zero_SP)
+
+    for method in methods:
+        check(method)
+
+
+def test_undirected_sparse_zero():
+    def check(method, directed_in):
+        if directed_in:
+            SP1 = shortest_path(directed_sparse_zero_G, method=method, directed=False,
+                                overwrite=False)
+            assert_array_almost_equal(SP1, undirected_sparse_zero_SP)
+        else:
+            SP2 = shortest_path(undirected_sparse_zero_G, method=method, directed=True,
+                                overwrite=False)
+            assert_array_almost_equal(SP2, undirected_sparse_zero_SP)
+
+    for method in methods:
+        for directed_in in (True, False):
+            check(method, directed_in)
+
+
+@pytest.mark.parametrize('directed, SP_ans',
+                         ((True, directed_SP),
+                          (False, undirected_SP)))
+@pytest.mark.parametrize('indices', ([0, 2, 4], [0, 4], [3, 4], [0, 0]))
+def test_dijkstra_indices_min_only(directed, SP_ans, indices):
+    SP_ans = np.array(SP_ans)
+    indices = np.array(indices, dtype=np.int64)
+    min_ind_ans = indices[np.argmin(SP_ans[indices, :], axis=0)]
+    min_d_ans = np.zeros(SP_ans.shape[0], SP_ans.dtype)
+    for k in range(SP_ans.shape[0]):
+        min_d_ans[k] = SP_ans[min_ind_ans[k], k]
+    min_ind_ans[np.isinf(min_d_ans)] = -9999
+
+    SP, pred, sources = dijkstra(directed_G,
+                                 directed=directed,
+                                 indices=indices,
+                                 min_only=True,
+                                 return_predecessors=True)
+    assert_array_almost_equal(SP, min_d_ans)
+    assert_array_equal(min_ind_ans, sources)
+    SP = dijkstra(directed_G,
+                  directed=directed,
+                  indices=indices,
+                  min_only=True,
+                  return_predecessors=False)
+    assert_array_almost_equal(SP, min_d_ans)
+
+
+@pytest.mark.parametrize('n', (10, 100, 1000))
+def test_dijkstra_min_only_random(n):
+    rng = np.random.default_rng(7345782358920239234)
+    data = scipy.sparse.random_array((n, n), density=0.5, format='lil',
+                                     rng=rng, dtype=np.float64)
+    data.setdiag(np.zeros(n, dtype=np.bool_))
+    # choose some random vertices
+    v = np.arange(n)
+    rng.shuffle(v)
+    indices = v[:int(n*.1)]
+    ds, pred, sources = dijkstra(data,
+                                 directed=True,
+                                 indices=indices,
+                                 min_only=True,
+                                 return_predecessors=True)
+    for k in range(n):
+        p = pred[k]
+        s = sources[k]
+        while p != -9999:
+            assert sources[p] == s
+            p = pred[p]
+
+
+@pytest.mark.parametrize('n', (10, 100))
+@pytest.mark.parametrize("method", ['FW', 'J', 'BF'])
+@pytest.mark.parametrize('directed', (True, False))
+def test_star_graph(n, method, directed):
+    # Build the star graph
+    star_arr = np.zeros((n, n), dtype=float)
+    star_center_idx = 0
+    star_arr[star_center_idx, :] = star_arr[:, star_center_idx] = range(n)
+    G = scipy.sparse.csr_array(star_arr, shape=(n, n))
+    # Build the distances matrix
+    SP_solution = np.zeros((n, n), dtype=float)
+    SP_solution[:] = star_arr[star_center_idx]
+    for idx in range(1, n):
+        SP_solution[idx] += star_arr[idx, star_center_idx]
+    np.fill_diagonal(SP_solution, 0)
+
+    SP = shortest_path(G, method=method, directed=directed)
+    assert_allclose(
+        SP_solution, SP
+    )
+
+
+def test_dijkstra_random():
+    # reproduces the hang observed in gh-17782
+    n = 10
+    indices = [0, 4, 4, 5, 7, 9, 0, 6, 2, 3, 7, 9, 1, 2, 9, 2, 5, 6]
+    indptr = [0, 0, 2, 5, 6, 7, 8, 12, 15, 18, 18]
+    data = [0.33629, 0.40458, 0.47493, 0.42757, 0.11497, 0.91653, 0.69084,
+            0.64979, 0.62555, 0.743, 0.01724, 0.99945, 0.31095, 0.15557,
+            0.02439, 0.65814, 0.23478, 0.24072]
+    graph = scipy.sparse.csr_array((data, indices, indptr), shape=(n, n))
+    dijkstra(graph, directed=True, return_predecessors=True)
+
+
+def test_gh_17782_segfault():
+    text = """%%MatrixMarket matrix coordinate real general
+                84 84 22
+                2 1 4.699999809265137e+00
+                6 14 1.199999973177910e-01
+                9 6 1.199999973177910e-01
+                10 16 2.012000083923340e+01
+                11 10 1.422000026702881e+01
+                12 1 9.645999908447266e+01
+                13 18 2.012000083923340e+01
+                14 13 4.679999828338623e+00
+                15 11 1.199999973177910e-01
+                16 12 1.199999973177910e-01
+                18 15 1.199999973177910e-01
+                32 2 2.299999952316284e+00
+                33 20 6.000000000000000e+00
+                33 32 5.000000000000000e+00
+                36 9 3.720000028610229e+00
+                36 37 3.720000028610229e+00
+                36 38 3.720000028610229e+00
+                37 44 8.159999847412109e+00
+                38 32 7.903999328613281e+01
+                43 20 2.400000000000000e+01
+                43 33 4.000000000000000e+00
+                44 43 6.028000259399414e+01
+    """
+    data = mmread(StringIO(text), spmatrix=False)
+    dijkstra(data, directed=True, return_predecessors=True)
+
+
+def test_shortest_path_indices():
+    indices = np.arange(4)
+
+    def check(func, indshape):
+        outshape = indshape + (5,)
+        SP = func(directed_G, directed=False,
+                  indices=indices.reshape(indshape))
+        assert_array_almost_equal(SP, undirected_SP[indices].reshape(outshape))
+
+    for indshape in [(4,), (4, 1), (2, 2)]:
+        for func in (dijkstra, bellman_ford, johnson, shortest_path):
+            check(func, indshape)
+
+    assert_raises(ValueError, shortest_path, directed_G, method='FW',
+                  indices=indices)
+
+
+def test_predecessors():
+    SP_res = {True: directed_SP,
+              False: undirected_SP}
+    pred_res = {True: directed_pred,
+                False: undirected_pred}
+
+    def check(method, directed):
+        SP, pred = shortest_path(directed_G, method, directed=directed,
+                                 overwrite=False,
+                                 return_predecessors=True)
+        assert_array_almost_equal(SP, SP_res[directed])
+        assert_array_almost_equal(pred, pred_res[directed])
+
+    for method in methods:
+        for directed in (True, False):
+            check(method, directed)
+
+
+def test_construct_shortest_path():
+    def check(method, directed):
+        SP1, pred = shortest_path(directed_G,
+                                  directed=directed,
+                                  overwrite=False,
+                                  return_predecessors=True)
+        SP2 = construct_dist_matrix(directed_G, pred, directed=directed)
+        assert_array_almost_equal(SP1, SP2)
+
+    for method in methods:
+        for directed in (True, False):
+            check(method, directed)
+
+@pytest.mark.parametrize("directed", [True, False])
+def test_construct_dist_matrix_predecessors_error(directed):
+    SP1, pred = shortest_path(directed_G,
+                                directed=directed,
+                                overwrite=False,
+                                return_predecessors=True)
+    assert_raises(TypeError, construct_dist_matrix,
+                  directed_G, pred.astype(np.int64), directed)
+
+
+def test_unweighted_path():
+    def check(method, directed):
+        SP1 = shortest_path(directed_G,
+                            directed=directed,
+                            overwrite=False,
+                            unweighted=True)
+        SP2 = shortest_path(unweighted_G,
+                            directed=directed,
+                            overwrite=False,
+                            unweighted=False)
+        assert_array_almost_equal(SP1, SP2)
+
+    for method in methods:
+        for directed in (True, False):
+            check(method, directed)
+
+
+def test_negative_cycles():
+    # create a small graph with a negative cycle
+    graph = np.ones([5, 5])
+    graph.flat[::6] = 0
+    graph[1, 2] = -2
+
+    def check(method, directed):
+        assert_raises(NegativeCycleError, shortest_path, graph, method,
+                      directed)
+
+    for directed in (True, False):
+        for method in ['FW', 'J', 'BF']:
+            check(method, directed)
+
+        assert_raises(NegativeCycleError, yen, graph, 0, 1, 1,
+                      directed=directed)
+
+
+@pytest.mark.parametrize("method", ['FW', 'J', 'BF'])
+def test_negative_weights(method):
+    SP = shortest_path(directed_negative_weighted_G, method, directed=True)
+    assert_allclose(SP, directed_negative_weighted_SP, atol=1e-10)
+
+
+def test_masked_input():
+    np.ma.masked_equal(directed_G, 0)
+
+    def check(method):
+        SP = shortest_path(directed_G, method=method, directed=True,
+                           overwrite=False)
+        assert_array_almost_equal(SP, directed_SP)
+
+    for method in methods:
+        check(method)
+
+
+def test_overwrite():
+    G = np.array([[0, 3, 3, 1, 2],
+                  [3, 0, 0, 2, 4],
+                  [3, 0, 0, 0, 0],
+                  [1, 2, 0, 0, 2],
+                  [2, 4, 0, 2, 0]], dtype=float)
+    foo = G.copy()
+    shortest_path(foo, overwrite=False)
+    assert_array_equal(foo, G)
+
+
+@pytest.mark.parametrize('method', methods)
+def test_buffer(method):
+    # Smoke test that sparse matrices with read-only buffers (e.g., those from
+    # joblib workers) do not cause::
+    #
+    #     ValueError: buffer source array is read-only
+    #
+    G = scipy.sparse.csr_array([[1.]])
+    G.data.flags['WRITEABLE'] = False
+    shortest_path(G, method=method)
+
+
+def test_NaN_warnings():
+    with warnings.catch_warnings(record=True) as record:
+        shortest_path(np.array([[0, 1], [np.nan, 0]]))
+    for r in record:
+        assert r.category is not RuntimeWarning
+
+
+def test_sparse_matrices():
+    # Test that using lil,csr and csc sparse matrix do not cause error
+    G_dense = np.array([[0, 3, 0, 0, 0],
+                        [0, 0, -1, 0, 0],
+                        [0, 0, 0, 2, 0],
+                        [0, 0, 0, 0, 4],
+                        [0, 0, 0, 0, 0]], dtype=float)
+    SP = shortest_path(G_dense)
+    G_csr = scipy.sparse.csr_array(G_dense)
+    G_csc = scipy.sparse.csc_array(G_dense)
+    G_lil = scipy.sparse.lil_array(G_dense)
+    assert_array_almost_equal(SP, shortest_path(G_csr))
+    assert_array_almost_equal(SP, shortest_path(G_csc))
+    assert_array_almost_equal(SP, shortest_path(G_lil))
+
+
+def test_yen_directed():
+    distances, predecessors = yen(
+                            directed_G,
+                            source=0,
+                            sink=3,
+                            K=2,
+                            return_predecessors=True
+                        )
+    assert_allclose(distances, [5., 9.])
+    assert_allclose(predecessors, directed_2SP_0_to_3)
+
+
+def test_yen_dense():
+    dense_undirected_G = np.array([
+                       [0, 3, 3, 1, 2],
+                       [3, 0, 7, 6, 5],
+                       [3, 7, 0, 4, 0],
+                       [1, 6, 4, 0, 2],
+                       [2, 5, 0, 2, 0]], dtype=float)
+    distances = yen(
+                dense_undirected_G,
+                source=0,
+                sink=4,
+                K=5,
+                directed=False,
+            )
+    assert_allclose(distances, [2., 3., 8., 9., 11.])
+
+
+def test_yen_undirected():
+    distances = yen(
+        undirected_G,
+        source=0,
+        sink=3,
+        K=4,
+        directed=False,
+    )
+    assert_allclose(distances, [1., 4., 5., 8.])
+
+
+def test_yen_unweighted():
+    # Ask for more paths than there are, verify only the available paths are returned
+    distances, predecessors = yen(
+        directed_G,
+        source=0,
+        sink=3,
+        K=4,
+        unweighted=True,
+        return_predecessors=True,
+    )
+    assert_allclose(distances, [2., 3.])
+    assert_allclose(predecessors, directed_2SP_0_to_3)
+
+
+def test_yen_no_paths():
+    distances = yen(
+        directed_G,
+        source=2,
+        sink=3,
+        K=1,
+    )
+    assert distances.size == 0
+
+
+def test_yen_negative_weights():
+    distances = yen(
+        directed_negative_weighted_G,
+        source=2,
+        sink=0,
+        K=1,
+    )
+    assert_allclose(distances, [-2.])
+
+
+@pytest.mark.parametrize('source, sink', [(0, -1), (10000, 1), (2, 6)])
+def test_yen_source_sink_validation(source, sink):
+    # directed_G has shape (6, 6)
+    with pytest.raises(ValueError, match="must have 0 <="):
+        yen(directed_G, source, sink, 2)
+
+
+@pytest.mark.parametrize("min_only", (True, False))
+@pytest.mark.parametrize("directed", (True, False))
+@pytest.mark.parametrize("return_predecessors", (True, False))
+@pytest.mark.parametrize("index_dtype", (np.int32, np.int64))
+@pytest.mark.parametrize("indices", (None, [1]))
+def test_20904(min_only, directed, return_predecessors, index_dtype, indices):
+    """Test two failures from gh-20904: int32 and indices-as-None."""
+    adj_mat = scipy.sparse.eye_array(4, format="csr")
+    adj_mat = scipy.sparse.csr_array(
+        (
+            adj_mat.data,
+            adj_mat.indices.astype(index_dtype),
+            adj_mat.indptr.astype(index_dtype),
+        ),
+    )
+    dijkstra(
+        adj_mat,
+        directed,
+        indices=indices,
+        min_only=min_only,
+        return_predecessors=return_predecessors,
+    )
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/tests/test_spanning_tree.py b/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/tests/test_spanning_tree.py
new file mode 100644
index 0000000000000000000000000000000000000000..3237a14584d42022184a54f174b809a2b06d16ed
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/tests/test_spanning_tree.py
@@ -0,0 +1,66 @@
+"""Test the minimum spanning tree function"""
+import numpy as np
+from numpy.testing import assert_
+import numpy.testing as npt
+from scipy.sparse import csr_array
+from scipy.sparse.csgraph import minimum_spanning_tree
+
+
+def test_minimum_spanning_tree():
+
+    # Create a graph with two connected components.
+    graph = [[0,1,0,0,0],
+             [1,0,0,0,0],
+             [0,0,0,8,5],
+             [0,0,8,0,1],
+             [0,0,5,1,0]]
+    graph = np.asarray(graph)
+
+    # Create the expected spanning tree.
+    expected = [[0,1,0,0,0],
+                [0,0,0,0,0],
+                [0,0,0,0,5],
+                [0,0,0,0,1],
+                [0,0,0,0,0]]
+    expected = np.asarray(expected)
+
+    # Ensure minimum spanning tree code gives this expected output.
+    csgraph = csr_array(graph)
+    mintree = minimum_spanning_tree(csgraph)
+    mintree_array = mintree.toarray()
+    npt.assert_array_equal(mintree_array, expected,
+                           'Incorrect spanning tree found.')
+
+    # Ensure that the original graph was not modified.
+    npt.assert_array_equal(csgraph.toarray(), graph,
+        'Original graph was modified.')
+
+    # Now let the algorithm modify the csgraph in place.
+    mintree = minimum_spanning_tree(csgraph, overwrite=True)
+    npt.assert_array_equal(mintree.toarray(), expected,
+        'Graph was not properly modified to contain MST.')
+
+    np.random.seed(1234)
+    for N in (5, 10, 15, 20):
+
+        # Create a random graph.
+        graph = 3 + np.random.random((N, N))
+        csgraph = csr_array(graph)
+
+        # The spanning tree has at most N - 1 edges.
+        mintree = minimum_spanning_tree(csgraph)
+        assert_(mintree.nnz < N)
+
+        # Set the sub diagonal to 1 to create a known spanning tree.
+        idx = np.arange(N-1)
+        graph[idx,idx+1] = 1
+        csgraph = csr_array(graph)
+        mintree = minimum_spanning_tree(csgraph)
+
+        # We expect to see this pattern in the spanning tree and otherwise
+        # have this zero.
+        expected = np.zeros((N, N))
+        expected[idx, idx+1] = 1
+
+        npt.assert_array_equal(mintree.toarray(), expected,
+            'Incorrect spanning tree found.')
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/tests/test_traversal.py b/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/tests/test_traversal.py
new file mode 100644
index 0000000000000000000000000000000000000000..1716cf044d5fa27b833225c9a8675f02944f132e
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/csgraph/tests/test_traversal.py
@@ -0,0 +1,150 @@
+import warnings
+import numpy as np
+import pytest
+from numpy.testing import assert_array_almost_equal
+from scipy.sparse import csr_array, csr_matrix, coo_array, coo_matrix
+from scipy.sparse.csgraph import (breadth_first_tree, depth_first_tree,
+    csgraph_to_dense, csgraph_from_dense, csgraph_masked_from_dense)
+
+
+def test_graph_breadth_first():
+    csgraph = np.array([[0, 1, 2, 0, 0],
+                        [1, 0, 0, 0, 3],
+                        [2, 0, 0, 7, 0],
+                        [0, 0, 7, 0, 1],
+                        [0, 3, 0, 1, 0]])
+    csgraph = csgraph_from_dense(csgraph, null_value=0)
+
+    bfirst = np.array([[0, 1, 2, 0, 0],
+                       [0, 0, 0, 0, 3],
+                       [0, 0, 0, 7, 0],
+                       [0, 0, 0, 0, 0],
+                       [0, 0, 0, 0, 0]])
+
+    for directed in [True, False]:
+        bfirst_test = breadth_first_tree(csgraph, 0, directed)
+        assert_array_almost_equal(csgraph_to_dense(bfirst_test),
+                                  bfirst)
+
+
+def test_graph_depth_first():
+    csgraph = np.array([[0, 1, 2, 0, 0],
+                        [1, 0, 0, 0, 3],
+                        [2, 0, 0, 7, 0],
+                        [0, 0, 7, 0, 1],
+                        [0, 3, 0, 1, 0]])
+    csgraph = csgraph_from_dense(csgraph, null_value=0)
+
+    dfirst = np.array([[0, 1, 0, 0, 0],
+                       [0, 0, 0, 0, 3],
+                       [0, 0, 0, 0, 0],
+                       [0, 0, 7, 0, 0],
+                       [0, 0, 0, 1, 0]])
+
+    for directed in [True, False]:
+        dfirst_test = depth_first_tree(csgraph, 0, directed)
+        assert_array_almost_equal(csgraph_to_dense(dfirst_test), dfirst)
+
+
+def test_return_type():
+    from .._laplacian import laplacian
+    from .._min_spanning_tree import minimum_spanning_tree
+
+    np_csgraph = np.array([[0, 1, 2, 0, 0],
+                           [1, 0, 0, 0, 3],
+                           [2, 0, 0, 7, 0],
+                           [0, 0, 7, 0, 1],
+                           [0, 3, 0, 1, 0]])
+    csgraph = csr_array(np_csgraph)
+    assert isinstance(laplacian(csgraph), coo_array)
+    assert isinstance(minimum_spanning_tree(csgraph), csr_array)
+    for directed in [True, False]:
+        assert isinstance(depth_first_tree(csgraph, 0, directed), csr_array)
+        assert isinstance(breadth_first_tree(csgraph, 0, directed), csr_array)
+
+    csgraph = csgraph_from_dense(np_csgraph, null_value=0)
+    assert isinstance(csgraph, csr_array)
+    assert isinstance(laplacian(csgraph), coo_array)
+    assert isinstance(minimum_spanning_tree(csgraph), csr_array)
+    for directed in [True, False]:
+        assert isinstance(depth_first_tree(csgraph, 0, directed), csr_array)
+        assert isinstance(breadth_first_tree(csgraph, 0, directed), csr_array)
+
+    csgraph = csgraph_masked_from_dense(np_csgraph, null_value=0)
+    assert isinstance(csgraph, np.ma.MaskedArray)
+    assert csgraph._baseclass is np.ndarray
+    # laplacian doesnt work with masked arrays so not here
+    assert isinstance(minimum_spanning_tree(csgraph), csr_array)
+    for directed in [True, False]:
+        assert isinstance(depth_first_tree(csgraph, 0, directed), csr_array)
+        assert isinstance(breadth_first_tree(csgraph, 0, directed), csr_array)
+
+    # start of testing with matrix/spmatrix types
+    with warnings.catch_warnings():
+        warnings.filterwarnings("ignore", "the matrix subclass.*", DeprecationWarning)
+        warnings.filterwarnings(
+            "ignore", "the matrix subclass.*", PendingDeprecationWarning)
+
+        nm_csgraph = np.matrix([[0, 1, 2, 0, 0],
+                                [1, 0, 0, 0, 3],
+                                [2, 0, 0, 7, 0],
+                                [0, 0, 7, 0, 1],
+                                [0, 3, 0, 1, 0]])
+
+    csgraph = csr_matrix(nm_csgraph)
+    assert isinstance(laplacian(csgraph), coo_matrix)
+    assert isinstance(minimum_spanning_tree(csgraph), csr_matrix)
+    for directed in [True, False]:
+        assert isinstance(depth_first_tree(csgraph, 0, directed), csr_matrix)
+        assert isinstance(breadth_first_tree(csgraph, 0, directed), csr_matrix)
+
+    csgraph = csgraph_from_dense(nm_csgraph, null_value=0)
+    assert isinstance(csgraph, csr_matrix)
+    assert isinstance(laplacian(csgraph), coo_matrix)
+    assert isinstance(minimum_spanning_tree(csgraph), csr_matrix)
+    for directed in [True, False]:
+        assert isinstance(depth_first_tree(csgraph, 0, directed), csr_matrix)
+        assert isinstance(breadth_first_tree(csgraph, 0, directed), csr_matrix)
+
+    mm_csgraph = csgraph_masked_from_dense(nm_csgraph, null_value=0)
+    assert isinstance(mm_csgraph, np.ma.MaskedArray)
+    # laplacian doesnt work with masked arrays so not here
+    assert isinstance(minimum_spanning_tree(csgraph), csr_matrix)
+    for directed in [True, False]:
+        assert isinstance(depth_first_tree(csgraph, 0, directed), csr_matrix)
+        assert isinstance(breadth_first_tree(csgraph, 0, directed), csr_matrix)
+    # end of testing with matrix/spmatrix types
+
+
+def test_graph_breadth_first_trivial_graph():
+    csgraph = np.array([[0]])
+    csgraph = csgraph_from_dense(csgraph, null_value=0)
+
+    bfirst = np.array([[0]])
+
+    for directed in [True, False]:
+        bfirst_test = breadth_first_tree(csgraph, 0, directed)
+        assert_array_almost_equal(csgraph_to_dense(bfirst_test), bfirst)
+
+
+def test_graph_depth_first_trivial_graph():
+    csgraph = np.array([[0]])
+    csgraph = csgraph_from_dense(csgraph, null_value=0)
+
+    bfirst = np.array([[0]])
+
+    for directed in [True, False]:
+        bfirst_test = depth_first_tree(csgraph, 0, directed)
+        assert_array_almost_equal(csgraph_to_dense(bfirst_test),
+                                  bfirst)
+
+
+@pytest.mark.parametrize('directed', [True, False])
+@pytest.mark.parametrize('tree_func', [breadth_first_tree, depth_first_tree])
+def test_int64_indices(tree_func, directed):
+    # See https://github.com/scipy/scipy/issues/18716
+    g = csr_array(([1], np.array([[0], [1]], dtype=np.int64)), shape=(2, 2))
+    assert g.indices.dtype == np.int64
+    tree = tree_func(g, 0, directed=directed)
+    assert_array_almost_equal(csgraph_to_dense(tree), [[0, 1], [0, 0]])
+
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/csr.py b/venv/lib/python3.12/site-packages/scipy/sparse/csr.py
new file mode 100644
index 0000000000000000000000000000000000000000..62cb27795f8e70b21b1864d8066aea12f45d0693
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/csr.py
@@ -0,0 +1,22 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.sparse` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+
+__all__ = [  # noqa: F822
+    'csr_matrix',
+    'isspmatrix_csr',
+    'spmatrix',
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="sparse", module="csr",
+                                   private_modules=["_csr"], all=__all__,
+                                   attribute=name)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/data.py b/venv/lib/python3.12/site-packages/scipy/sparse/data.py
new file mode 100644
index 0000000000000000000000000000000000000000..b020b3e1b657b8b904ac437d347a062bb355ecf2
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/data.py
@@ -0,0 +1,18 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.sparse` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+
+__all__ : list[str] = []
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="sparse", module="data",
+                                   private_modules=["_data"], all=__all__,
+                                   attribute=name)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/dia.py b/venv/lib/python3.12/site-packages/scipy/sparse/dia.py
new file mode 100644
index 0000000000000000000000000000000000000000..55f4443ad7f7bd0007b25f1223459a3ee5a89748
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/dia.py
@@ -0,0 +1,22 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.sparse` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+
+__all__ = [  # noqa: F822
+    'dia_matrix',
+    'isspmatrix_dia',
+    'spmatrix',
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="sparse", module="dia",
+                                   private_modules=["_dia"], all=__all__,
+                                   attribute=name)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/dok.py b/venv/lib/python3.12/site-packages/scipy/sparse/dok.py
new file mode 100644
index 0000000000000000000000000000000000000000..6672823ef28e6a0f9e9c8a481fc851b13aaf4158
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/dok.py
@@ -0,0 +1,22 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.sparse` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+
+__all__ = [  # noqa: F822
+    'dok_matrix',
+    'isspmatrix_dok',
+    'spmatrix',
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="sparse", module="dok",
+                                   private_modules=["_dok"], all=__all__,
+                                   attribute=name)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/extract.py b/venv/lib/python3.12/site-packages/scipy/sparse/extract.py
new file mode 100644
index 0000000000000000000000000000000000000000..be5e161b6f99e57e2b2a6b3d4f1ef6427c07658d
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/extract.py
@@ -0,0 +1,23 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.sparse` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+
+__all__ = [  # noqa: F822
+    'coo_matrix',
+    'find',
+    'tril',
+    'triu',
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="sparse", module="extract",
+                                   private_modules=["_extract"], all=__all__,
+                                   attribute=name)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/lil.py b/venv/lib/python3.12/site-packages/scipy/sparse/lil.py
new file mode 100644
index 0000000000000000000000000000000000000000..5f7bf8eb03bb36a1b2fa77c5fc0840e532ab64fd
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/lil.py
@@ -0,0 +1,22 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.sparse` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+
+__all__ = [  # noqa: F822
+    'isspmatrix_lil',
+    'lil_array',
+    'lil_matrix',
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="sparse", module="lil",
+                                   private_modules=["_lil"], all=__all__,
+                                   attribute=name)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/__init__.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e32dd362f8d45f747642719cb60eab8def9af43b
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/__init__.py
@@ -0,0 +1,150 @@
+"""
+Sparse linear algebra (:mod:`scipy.sparse.linalg`)
+==================================================
+
+.. currentmodule:: scipy.sparse.linalg
+
+Abstract linear operators
+-------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   LinearOperator -- abstract representation of a linear operator
+   aslinearoperator -- convert an object to an abstract linear operator
+
+Matrix Operations
+-----------------
+
+.. autosummary::
+   :toctree: generated/
+
+   inv -- compute the sparse matrix inverse
+   expm -- compute the sparse matrix exponential
+   expm_multiply -- compute the product of a matrix exponential and a matrix
+   funm_multiply_krylov -- use a Krylov method to compute f(A)b for a general f
+   matrix_power -- compute the matrix power by raising a matrix to an exponent
+
+Matrix norms
+------------
+
+.. autosummary::
+   :toctree: generated/
+
+   norm -- Norm of a sparse matrix
+   onenormest -- Estimate the 1-norm of a sparse matrix
+
+Solving linear problems
+-----------------------
+
+Direct methods for linear equation systems:
+
+.. autosummary::
+   :toctree: generated/
+
+   spsolve -- Solve the sparse linear system Ax=b
+   spsolve_triangular -- Solve sparse linear system Ax=b for a triangular A.
+   is_sptriangular -- Check if sparse A is triangular.
+   spbandwidth -- Find the bandwidth of a sparse matrix.
+   factorized -- Pre-factorize matrix to a function solving a linear system
+   MatrixRankWarning -- Warning on exactly singular matrices
+   use_solver -- Select direct solver to use
+
+Iterative methods for linear equation systems:
+
+.. autosummary::
+   :toctree: generated/
+
+   bicg -- Use BIConjugate Gradient iteration to solve Ax = b
+   bicgstab -- Use BIConjugate Gradient STABilized iteration to solve Ax = b
+   cg -- Use Conjugate Gradient iteration to solve Ax = b
+   cgs -- Use Conjugate Gradient Squared iteration to solve Ax = b
+   gmres -- Use Generalized Minimal RESidual iteration to solve Ax = b
+   lgmres -- Solve a matrix equation using the LGMRES algorithm
+   minres -- Use MINimum RESidual iteration to solve Ax = b
+   qmr -- Use Quasi-Minimal Residual iteration to solve Ax = b
+   gcrotmk -- Solve a matrix equation using the GCROT(m,k) algorithm
+   tfqmr -- Use Transpose-Free Quasi-Minimal Residual iteration to solve Ax = b
+
+Iterative methods for least-squares problems:
+
+.. autosummary::
+   :toctree: generated/
+
+   lsqr -- Find the least-squares solution to a sparse linear equation system
+   lsmr -- Find the least-squares solution to a sparse linear equation system
+
+Matrix factorizations
+---------------------
+
+Eigenvalue problems:
+
+.. autosummary::
+   :toctree: generated/
+
+   eigs -- Find k eigenvalues and eigenvectors of the square matrix A
+   eigsh -- Find k eigenvalues and eigenvectors of a symmetric matrix
+   lobpcg -- Solve symmetric partial eigenproblems with optional preconditioning
+
+Singular values problems:
+
+.. autosummary::
+   :toctree: generated/
+
+   svds -- Compute k singular values/vectors for a sparse matrix
+
+The `svds` function supports the following solvers:
+
+.. toctree::
+
+    sparse.linalg.svds-arpack
+    sparse.linalg.svds-lobpcg
+    sparse.linalg.svds-propack
+
+Complete or incomplete LU factorizations
+
+.. autosummary::
+   :toctree: generated/
+
+   splu -- Compute a LU decomposition for a sparse matrix
+   spilu -- Compute an incomplete LU decomposition for a sparse matrix
+   SuperLU -- Object representing an LU factorization
+
+Sparse arrays with structure
+----------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   LaplacianNd -- Laplacian on a uniform rectangular grid in ``N`` dimensions
+
+Exceptions
+----------
+
+.. autosummary::
+   :toctree: generated/
+
+   ArpackNoConvergence
+   ArpackError
+
+"""
+
+from ._isolve import *
+from ._dsolve import *
+from ._interface import *
+from ._eigen import *
+from ._matfuncs import *
+from ._onenormest import *
+from ._norm import *
+from ._expm_multiply import *
+from ._funm_multiply_krylov import *
+from ._special_sparse_arrays import *
+
+# Deprecated namespaces, to be removed in v2.0.0
+from . import isolve, dsolve, interface, eigen, matfuncs
+
+__all__ = [s for s in dir() if not s.startswith('_')]
+
+from scipy._lib._testutils import PytestTester
+test = PytestTester(__name__)
+del PytestTester
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diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_dsolve/__init__.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_dsolve/__init__.py
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index 0000000000000000000000000000000000000000..90005e3af863d2f7913e6fc4ea8de85962a3efdf
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_dsolve/__init__.py
@@ -0,0 +1,71 @@
+"""
+Linear Solvers
+==============
+
+The default solver is SuperLU (included in the scipy distribution),
+which can solve real or complex linear systems in both single and
+double precisions.  It is automatically replaced by UMFPACK, if
+available.  Note that UMFPACK works in double precision only, so
+switch it off by::
+
+    >>> from scipy.sparse.linalg import spsolve, use_solver
+    >>> use_solver(useUmfpack=False)
+
+to solve in the single precision. See also use_solver documentation.
+
+Example session::
+
+    >>> from scipy.sparse import csc_array, dia_array
+    >>> from numpy import array
+    >>>
+    >>> print("Inverting a sparse linear system:")
+    >>> print("The sparse matrix (constructed from diagonals):")
+    >>> a = dia_array(([[1, 2, 3, 4, 5], [6, 5, 8, 9, 10]], [0, 1]), shape=(5, 5))
+    >>> b = array([1, 2, 3, 4, 5])
+    >>> print("Solve: single precision complex:")
+    >>> use_solver( useUmfpack = False )
+    >>> a = a.astype('F')
+    >>> x = spsolve(a, b)
+    >>> print(x)
+    >>> print("Error: ", a@x-b)
+    >>>
+    >>> print("Solve: double precision complex:")
+    >>> use_solver( useUmfpack = True )
+    >>> a = a.astype('D')
+    >>> x = spsolve(a, b)
+    >>> print(x)
+    >>> print("Error: ", a@x-b)
+    >>>
+    >>> print("Solve: double precision:")
+    >>> a = a.astype('d')
+    >>> x = spsolve(a, b)
+    >>> print(x)
+    >>> print("Error: ", a@x-b)
+    >>>
+    >>> print("Solve: single precision:")
+    >>> use_solver( useUmfpack = False )
+    >>> a = a.astype('f')
+    >>> x = spsolve(a, b.astype('f'))
+    >>> print(x)
+    >>> print("Error: ", a@x-b)
+
+"""
+
+#import umfpack
+#__doc__ = '\n\n'.join( (__doc__,  umfpack.__doc__) )
+#del umfpack
+
+from .linsolve import *
+from ._superlu import SuperLU
+from . import _add_newdocs
+from . import linsolve
+
+__all__ = [
+    'MatrixRankWarning', 'SuperLU', 'factorized',
+    'spilu', 'splu', 'spsolve', 'is_sptriangular',
+    'spsolve_triangular', 'use_solver', 'spbandwidth',
+]
+
+from scipy._lib._testutils import PytestTester
+test = PytestTester(__name__)
+del PytestTester
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diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_dsolve/_add_newdocs.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_dsolve/_add_newdocs.py
new file mode 100644
index 0000000000000000000000000000000000000000..cec34dca456b36a1f77e64f853fc1d821f5215eb
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_dsolve/_add_newdocs.py
@@ -0,0 +1,147 @@
+from numpy.lib import add_newdoc
+
+add_newdoc('scipy.sparse.linalg._dsolve._superlu', 'SuperLU',
+    """
+    LU factorization of a sparse matrix.
+
+    Factorization is represented as::
+
+        Pr @ A @ Pc = L @ U
+
+    To construct these `SuperLU` objects, call the `splu` and `spilu`
+    functions.
+
+    Attributes
+    ----------
+    shape
+    nnz
+    perm_c
+    perm_r
+    L
+    U
+
+    Methods
+    -------
+    solve
+
+    Notes
+    -----
+
+    .. versionadded:: 0.14.0
+
+    Examples
+    --------
+    The LU decomposition can be used to solve matrix equations. Consider:
+
+    >>> import numpy as np
+    >>> from scipy.sparse import csc_array
+    >>> from scipy.sparse.linalg import splu
+    >>> A = csc_array([[1,2,0,4], [1,0,0,1], [1,0,2,1], [2,2,1,0.]])
+
+    This can be solved for a given right-hand side:
+
+    >>> lu = splu(A)
+    >>> b = np.array([1, 2, 3, 4])
+    >>> x = lu.solve(b)
+    >>> A.dot(x)
+    array([ 1.,  2.,  3.,  4.])
+
+    The ``lu`` object also contains an explicit representation of the
+    decomposition. The permutations are represented as mappings of
+    indices:
+
+    >>> lu.perm_r
+    array([2, 1, 3, 0], dtype=int32)  # may vary
+    >>> lu.perm_c
+    array([0, 1, 3, 2], dtype=int32)  # may vary
+
+    The L and U factors are sparse matrices in CSC format:
+
+    >>> lu.L.toarray()
+    array([[ 1. ,  0. ,  0. ,  0. ],  # may vary
+           [ 0.5,  1. ,  0. ,  0. ],
+           [ 0.5, -1. ,  1. ,  0. ],
+           [ 0.5,  1. ,  0. ,  1. ]])
+    >>> lu.U.toarray()
+    array([[ 2. ,  2. ,  0. ,  1. ],  # may vary
+           [ 0. , -1. ,  1. , -0.5],
+           [ 0. ,  0. ,  5. , -1. ],
+           [ 0. ,  0. ,  0. ,  2. ]])
+
+    The permutation matrices can be constructed:
+
+    >>> Pr = csc_array((np.ones(4), (lu.perm_r, np.arange(4))))
+    >>> Pc = csc_array((np.ones(4), (np.arange(4), lu.perm_c)))
+
+    We can reassemble the original matrix:
+
+    >>> (Pr.T @ (lu.L @ lu.U) @ Pc.T).toarray()
+    array([[ 1.,  2.,  0.,  4.],
+           [ 1.,  0.,  0.,  1.],
+           [ 1.,  0.,  2.,  1.],
+           [ 2.,  2.,  1.,  0.]])
+    """)
+
+add_newdoc('scipy.sparse.linalg._dsolve._superlu', 'SuperLU', ('solve',
+    """
+    solve(rhs[, trans])
+
+    Solves linear system of equations with one or several right-hand sides.
+
+    Parameters
+    ----------
+    rhs : ndarray, shape (n,) or (n, k)
+        Right hand side(s) of equation
+    trans : {'N', 'T', 'H'}, optional
+        Type of system to solve::
+
+            'N':   A   @ x == rhs  (default)
+            'T':   A^T @ x == rhs
+            'H':   A^H @ x == rhs
+
+        i.e., normal, transposed, and hermitian conjugate.
+
+    Returns
+    -------
+    x : ndarray, shape ``rhs.shape``
+        Solution vector(s)
+    """))
+
+add_newdoc('scipy.sparse.linalg._dsolve._superlu', 'SuperLU', ('L',
+    """
+    Lower triangular factor with unit diagonal as a
+    `scipy.sparse.csc_array`.
+
+    .. versionadded:: 0.14.0
+    """))
+
+add_newdoc('scipy.sparse.linalg._dsolve._superlu', 'SuperLU', ('U',
+    """
+    Upper triangular factor as a `scipy.sparse.csc_array`.
+
+    .. versionadded:: 0.14.0
+    """))
+
+add_newdoc('scipy.sparse.linalg._dsolve._superlu', 'SuperLU', ('shape',
+    """
+    Shape of the original matrix as a tuple of ints.
+    """))
+
+add_newdoc('scipy.sparse.linalg._dsolve._superlu', 'SuperLU', ('nnz',
+    """
+    Number of nonzero elements in the matrix.
+    """))
+
+add_newdoc('scipy.sparse.linalg._dsolve._superlu', 'SuperLU', ('perm_c',
+    """
+    Permutation Pc represented as an array of indices.
+
+    See the `SuperLU` docstring for details.
+    """))
+
+add_newdoc('scipy.sparse.linalg._dsolve._superlu', 'SuperLU', ('perm_r',
+    """
+    Permutation Pr represented as an array of indices.
+
+    See the `SuperLU` docstring for details.
+    """))
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_dsolve/_superlu.cpython-312-x86_64-linux-gnu.so b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_dsolve/_superlu.cpython-312-x86_64-linux-gnu.so
new file mode 100644
index 0000000000000000000000000000000000000000..110fe94ce6720de405b20cd8d3ea254a4be09600
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_dsolve/_superlu.cpython-312-x86_64-linux-gnu.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b7cc362fe1b3a25a1f1c0fa36b5350869901273c79b8692392cc2f8ef273dc54
+size 436625
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_dsolve/linsolve.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_dsolve/linsolve.py
new file mode 100644
index 0000000000000000000000000000000000000000..f7012ed0f961c3ff520382a9cca211d7610575d9
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_dsolve/linsolve.py
@@ -0,0 +1,933 @@
+from warnings import warn, catch_warnings, simplefilter
+
+import numpy as np
+from numpy import asarray
+from scipy.sparse import (issparse, SparseEfficiencyWarning,
+                          csr_array, csc_array, eye_array, diags_array)
+from scipy.sparse._sputils import (is_pydata_spmatrix, convert_pydata_sparse_to_scipy,
+                                   get_index_dtype, safely_cast_index_arrays)
+from scipy.linalg import LinAlgError
+import copy
+import threading
+
+from . import _superlu
+
+noScikit = False
+try:
+    import scikits.umfpack as umfpack
+except ImportError:
+    noScikit = True
+
+useUmfpack = threading.local()
+
+
+__all__ = ['use_solver', 'spsolve', 'splu', 'spilu', 'factorized',
+           'MatrixRankWarning', 'spsolve_triangular', 'is_sptriangular', 'spbandwidth']
+
+
+class MatrixRankWarning(UserWarning):
+    """Warning for exactly singular matrices."""
+    pass
+
+
+def use_solver(**kwargs):
+    """
+    Select default sparse direct solver to be used.
+
+    Parameters
+    ----------
+    **kwargs
+        The following options may be passed as keyword arguments.
+
+        useUmfpack : bool, optional
+            Use UMFPACK [1]_, [2]_, [3]_, [4]_. over SuperLU. Has effect only
+            if ``scikits.umfpack`` is installed. Default: True
+        assumeSortedIndices : bool, optional
+            Allow UMFPACK to skip the step of sorting indices for a CSR/CSC matrix.
+            Has effect only if useUmfpack is True and ``scikits.umfpack`` is
+            installed. Default: False
+
+    Notes
+    -----
+    The default sparse solver is UMFPACK when available
+    (``scikits.umfpack`` is installed). This can be changed by passing
+    useUmfpack = False, which then causes the always present SuperLU
+    based solver to be used.
+
+    UMFPACK requires a CSR/CSC matrix to have sorted column/row indices. If
+    sure that the matrix fulfills this, pass ``assumeSortedIndices=True``
+    to gain some speed.
+
+    References
+    ----------
+    .. [1] T. A. Davis, Algorithm 832:  UMFPACK - an unsymmetric-pattern
+           multifrontal method with a column pre-ordering strategy, ACM
+           Trans. on Mathematical Software, 30(2), 2004, pp. 196--199.
+           :doi:`10.1145/992200.992206`.
+
+    .. [2] T. A. Davis, A column pre-ordering strategy for the
+           unsymmetric-pattern multifrontal method, ACM Trans.
+           on Mathematical Software, 30(2), 2004, pp. 165--195.
+           :doi:`10.1145/992200.992205`.
+
+    .. [3] T. A. Davis and I. S. Duff, A combined unifrontal/multifrontal
+           method for unsymmetric sparse matrices, ACM Trans. on
+           Mathematical Software, 25(1), 1999, pp. 1--19.
+           :doi:`10.1145/305658.287640`.
+
+    .. [4] T. A. Davis and I. S. Duff, An unsymmetric-pattern multifrontal
+           method for sparse LU factorization, SIAM J. Matrix Analysis and
+           Computations, 18(1), 1997, pp. 140--158.
+           :doi:`10.1137/S0895479894246905T`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.sparse.linalg import use_solver, spsolve
+    >>> from scipy.sparse import csc_array
+    >>> R = np.random.randn(5, 5)
+    >>> A = csc_array(R)
+    >>> b = np.random.randn(5)
+    >>> use_solver(useUmfpack=False) # enforce superLU over UMFPACK
+    >>> x = spsolve(A, b)
+    >>> np.allclose(A.dot(x), b)
+    True
+    >>> use_solver(useUmfpack=True) # reset umfPack usage to default
+    """
+    global useUmfpack
+    if 'useUmfpack' in kwargs:
+        useUmfpack.u = kwargs['useUmfpack']
+    if useUmfpack.u and 'assumeSortedIndices' in kwargs:
+        umfpack.configure(assumeSortedIndices=kwargs['assumeSortedIndices'])
+
+def _get_umf_family(A):
+    """Get umfpack family string given the sparse matrix dtype."""
+    _families = {
+        (np.float64, np.int32): 'di',
+        (np.complex128, np.int32): 'zi',
+        (np.float64, np.int64): 'dl',
+        (np.complex128, np.int64): 'zl'
+    }
+
+    # A.dtype.name can only be "float64" or
+    # "complex128" in control flow
+    f_type = getattr(np, A.dtype.name)
+    # control flow may allow for more index
+    # types to get through here
+    i_type = getattr(np, A.indices.dtype.name)
+
+    try:
+        family = _families[(f_type, i_type)]
+
+    except KeyError as e:
+        msg = ('only float64 or complex128 matrices with int32 or int64 '
+               f'indices are supported! (got: matrix: {f_type}, indices: {i_type})')
+        raise ValueError(msg) from e
+
+    # See gh-8278. Considered converting only if
+    # A.shape[0]*A.shape[1] > np.iinfo(np.int32).max,
+    # but that didn't always fix the issue.
+    family = family[0] + "l"
+    A_new = copy.copy(A)
+    A_new.indptr = np.asarray(A.indptr, dtype=np.int64)
+    A_new.indices = np.asarray(A.indices, dtype=np.int64)
+
+    return family, A_new
+
+def spsolve(A, b, permc_spec=None, use_umfpack=True):
+    """Solve the sparse linear system Ax=b, where b may be a vector or a matrix.
+
+    Parameters
+    ----------
+    A : ndarray or sparse array or matrix
+        The square matrix A will be converted into CSC or CSR form
+    b : ndarray or sparse array or matrix
+        The matrix or vector representing the right hand side of the equation.
+        If a vector, b.shape must be (n,) or (n, 1).
+    permc_spec : str, optional
+        How to permute the columns of the matrix for sparsity preservation.
+        (default: 'COLAMD')
+
+        - ``NATURAL``: natural ordering.
+        - ``MMD_ATA``: minimum degree ordering on the structure of A^T A.
+        - ``MMD_AT_PLUS_A``: minimum degree ordering on the structure of A^T+A.
+        - ``COLAMD``: approximate minimum degree column ordering [1]_, [2]_.
+
+    use_umfpack : bool, optional
+        if True (default) then use UMFPACK for the solution [3]_, [4]_, [5]_,
+        [6]_ . This is only referenced if b is a vector and
+        ``scikits.umfpack`` is installed.
+
+    Returns
+    -------
+    x : ndarray or sparse array or matrix
+        the solution of the sparse linear equation.
+        If b is a vector, then x is a vector of size A.shape[1]
+        If b is a matrix, then x is a matrix of size (A.shape[1], b.shape[1])
+
+    Notes
+    -----
+    For solving the matrix expression AX = B, this solver assumes the resulting
+    matrix X is sparse, as is often the case for very sparse inputs.  If the
+    resulting X is dense, the construction of this sparse result will be
+    relatively expensive.  In that case, consider converting A to a dense
+    matrix and using scipy.linalg.solve or its variants.
+
+    References
+    ----------
+    .. [1] T. A. Davis, J. R. Gilbert, S. Larimore, E. Ng, Algorithm 836:
+           COLAMD, an approximate column minimum degree ordering algorithm,
+           ACM Trans. on Mathematical Software, 30(3), 2004, pp. 377--380.
+           :doi:`10.1145/1024074.1024080`
+
+    .. [2] T. A. Davis, J. R. Gilbert, S. Larimore, E. Ng, A column approximate
+           minimum degree ordering algorithm, ACM Trans. on Mathematical
+           Software, 30(3), 2004, pp. 353--376. :doi:`10.1145/1024074.1024079`
+
+    .. [3] T. A. Davis, Algorithm 832:  UMFPACK - an unsymmetric-pattern
+           multifrontal method with a column pre-ordering strategy, ACM
+           Trans. on Mathematical Software, 30(2), 2004, pp. 196--199.
+           :doi:`10.1145/992200.992206`.
+
+    .. [4] T. A. Davis, A column pre-ordering strategy for the
+           unsymmetric-pattern multifrontal method, ACM Trans.
+           on Mathematical Software, 30(2), 2004, pp. 165--195.
+           :doi:`10.1145/992200.992205`.
+
+    .. [5] T. A. Davis and I. S. Duff, A combined unifrontal/multifrontal
+           method for unsymmetric sparse matrices, ACM Trans. on
+           Mathematical Software, 25(1), 1999, pp. 1--19.
+           :doi:`10.1145/305658.287640`.
+
+    .. [6] T. A. Davis and I. S. Duff, An unsymmetric-pattern multifrontal
+           method for sparse LU factorization, SIAM J. Matrix Analysis and
+           Computations, 18(1), 1997, pp. 140--158.
+           :doi:`10.1137/S0895479894246905T`.
+
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.sparse import csc_array
+    >>> from scipy.sparse.linalg import spsolve
+    >>> A = csc_array([[3, 2, 0], [1, -1, 0], [0, 5, 1]], dtype=float)
+    >>> B = csc_array([[2, 0], [-1, 0], [2, 0]], dtype=float)
+    >>> x = spsolve(A, B)
+    >>> np.allclose(A.dot(x).toarray(), B.toarray())
+    True
+    """
+    is_pydata_sparse = is_pydata_spmatrix(b)
+    pydata_sparse_cls = b.__class__ if is_pydata_sparse else None
+    A = convert_pydata_sparse_to_scipy(A)
+    b = convert_pydata_sparse_to_scipy(b)
+
+    if not (issparse(A) and A.format in ("csc", "csr")):
+        A = csc_array(A)
+        warn('spsolve requires A be CSC or CSR matrix format',
+             SparseEfficiencyWarning, stacklevel=2)
+
+    # b is a vector only if b have shape (n,) or (n, 1)
+    b_is_sparse = issparse(b)
+    if not b_is_sparse:
+        b = asarray(b)
+    b_is_vector = ((b.ndim == 1) or (b.ndim == 2 and b.shape[1] == 1))
+
+    # sum duplicates for non-canonical format
+    A.sum_duplicates()
+    A = A._asfptype()  # upcast to a floating point format
+    result_dtype = np.promote_types(A.dtype, b.dtype)
+    if A.dtype != result_dtype:
+        A = A.astype(result_dtype)
+    if b.dtype != result_dtype:
+        b = b.astype(result_dtype)
+
+    # validate input shapes
+    M, N = A.shape
+    if (M != N):
+        raise ValueError(f"matrix must be square (has shape {(M, N)})")
+
+    if M != b.shape[0]:
+        raise ValueError(f"matrix - rhs dimension mismatch ({A.shape} - {b.shape[0]})")
+
+    if not hasattr(useUmfpack, 'u'):
+        useUmfpack.u = not noScikit
+
+    use_umfpack = use_umfpack and useUmfpack.u
+
+    if b_is_vector and use_umfpack:
+        if b_is_sparse:
+            b_vec = b.toarray()
+        else:
+            b_vec = b
+        b_vec = asarray(b_vec, dtype=A.dtype).ravel()
+
+        if noScikit:
+            raise RuntimeError('Scikits.umfpack not installed.')
+
+        if A.dtype.char not in 'dD':
+            raise ValueError("convert matrix data to double, please, using"
+                  " .astype(), or set linsolve.useUmfpack.u = False")
+
+        umf_family, A = _get_umf_family(A)
+        umf = umfpack.UmfpackContext(umf_family)
+        x = umf.linsolve(umfpack.UMFPACK_A, A, b_vec,
+                         autoTranspose=True)
+    else:
+        if b_is_vector and b_is_sparse:
+            b = b.toarray()
+            b_is_sparse = False
+
+        if not b_is_sparse:
+            if A.format == "csc":
+                flag = 1  # CSC format
+            else:
+                flag = 0  # CSR format
+
+            indices = A.indices.astype(np.intc, copy=False)
+            indptr = A.indptr.astype(np.intc, copy=False)
+            options = dict(ColPerm=permc_spec)
+            x, info = _superlu.gssv(N, A.nnz, A.data, indices, indptr,
+                                    b, flag, options=options)
+            if info == 0:
+                pass  # Success
+            elif 0 < info <= N:
+                warn("Matrix is exactly singular", MatrixRankWarning, stacklevel=2)
+                x.fill(np.nan)
+            elif info > N:
+                raise MemoryError("Out of memory during gssv")
+            else:
+                # gssv is not supposed to return any info < 0
+                # However, it calls gstrf, which can set info < 0
+                raise Exception(f"gssv exited with unknown exit code {info}")
+            if b_is_vector:
+                x = x.ravel()
+        else:
+            # b is sparse
+            Afactsolve = factorized(A)
+
+            if not (b.format == "csc" or is_pydata_spmatrix(b)):
+                warn('spsolve is more efficient when sparse b '
+                     'is in the CSC matrix format',
+                     SparseEfficiencyWarning, stacklevel=2)
+                b = csc_array(b)
+
+            # Create a sparse output matrix by repeatedly applying
+            # the sparse factorization to solve columns of b.
+            data_segs = []
+            row_segs = []
+            col_segs = []
+            for j in range(b.shape[1]):
+                bj = b[:, j].toarray().ravel()
+                xj = Afactsolve(bj)
+                w = np.flatnonzero(xj)
+                segment_length = w.shape[0]
+                row_segs.append(w)
+                col_segs.append(np.full(segment_length, j, dtype=int))
+                data_segs.append(np.asarray(xj[w], dtype=A.dtype))
+            sparse_data = np.concatenate(data_segs)
+            idx_dtype = get_index_dtype(maxval=max(b.shape))
+            sparse_row = np.concatenate(row_segs, dtype=idx_dtype)
+            sparse_col = np.concatenate(col_segs, dtype=idx_dtype)
+            x = A.__class__((sparse_data, (sparse_row, sparse_col)),
+                           shape=b.shape, dtype=A.dtype)
+
+            if is_pydata_sparse:
+                x = pydata_sparse_cls.from_scipy_sparse(x)
+
+    return x
+
+
+def splu(A, permc_spec=None, diag_pivot_thresh=None,
+         relax=None, panel_size=None, options=None):
+    """
+    Compute the LU decomposition of a sparse, square matrix.
+
+    Parameters
+    ----------
+    A : sparse array or matrix
+        Sparse array to factorize. Most efficient when provided in CSC
+        format. Other formats will be converted to CSC before factorization.
+    permc_spec : str, optional
+        How to permute the columns of the matrix for sparsity preservation.
+        (default: 'COLAMD')
+
+        - ``NATURAL``: natural ordering.
+        - ``MMD_ATA``: minimum degree ordering on the structure of A^T A.
+        - ``MMD_AT_PLUS_A``: minimum degree ordering on the structure of A^T+A.
+        - ``COLAMD``: approximate minimum degree column ordering
+
+    diag_pivot_thresh : float, optional
+        Threshold used for a diagonal entry to be an acceptable pivot.
+        See SuperLU user's guide for details [1]_
+    relax : int, optional
+        Expert option for customizing the degree of relaxing supernodes.
+        See SuperLU user's guide for details [1]_
+    panel_size : int, optional
+        Expert option for customizing the panel size.
+        See SuperLU user's guide for details [1]_
+    options : dict, optional
+        Dictionary containing additional expert options to SuperLU.
+        See SuperLU user guide [1]_ (section 2.4 on the 'Options' argument)
+        for more details. For example, you can specify
+        ``options=dict(Equil=False, IterRefine='SINGLE'))``
+        to turn equilibration off and perform a single iterative refinement.
+
+    Returns
+    -------
+    invA : scipy.sparse.linalg.SuperLU
+        Object, which has a ``solve`` method.
+
+    See Also
+    --------
+    spilu : incomplete LU decomposition
+
+    Notes
+    -----
+    When a real array is factorized and the returned SuperLU object's ``solve()``
+    method is used with complex arguments an error is generated. Instead, cast the
+    initial array to complex and then factorize.
+
+    This function uses the SuperLU library.
+
+    References
+    ----------
+    .. [1] SuperLU https://portal.nersc.gov/project/sparse/superlu/
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.sparse import csc_array
+    >>> from scipy.sparse.linalg import splu
+    >>> A = csc_array([[1., 0., 0.], [5., 0., 2.], [0., -1., 0.]], dtype=float)
+    >>> B = splu(A)
+    >>> x = np.array([1., 2., 3.], dtype=float)
+    >>> B.solve(x)
+    array([ 1. , -3. , -1.5])
+    >>> A.dot(B.solve(x))
+    array([ 1.,  2.,  3.])
+    >>> B.solve(A.dot(x))
+    array([ 1.,  2.,  3.])
+    """
+
+    if is_pydata_spmatrix(A):
+        A_cls = type(A)
+        def csc_construct_func(*a, cls=A_cls):
+            return cls.from_scipy_sparse(csc_array(*a))
+        A = A.to_scipy_sparse().tocsc()
+    else:
+        csc_construct_func = csc_array
+
+    if not (issparse(A) and A.format == "csc"):
+        A = csc_array(A)
+        warn('splu converted its input to CSC format',
+             SparseEfficiencyWarning, stacklevel=2)
+
+    # sum duplicates for non-canonical format
+    A.sum_duplicates()
+    A = A._asfptype()  # upcast to a floating point format
+
+    M, N = A.shape
+    if (M != N):
+        raise ValueError("can only factor square matrices")  # is this true?
+
+    indices, indptr = safely_cast_index_arrays(A, np.intc, "SuperLU")
+
+    _options = dict(DiagPivotThresh=diag_pivot_thresh, ColPerm=permc_spec,
+                    PanelSize=panel_size, Relax=relax)
+    if options is not None:
+        _options.update(options)
+
+    # Ensure that no column permutations are applied
+    if (_options["ColPerm"] == "NATURAL"):
+        _options["SymmetricMode"] = True
+
+    return _superlu.gstrf(N, A.nnz, A.data, indices, indptr,
+                          csc_construct_func=csc_construct_func,
+                          ilu=False, options=_options)
+
+
+def spilu(A, drop_tol=None, fill_factor=None, drop_rule=None, permc_spec=None,
+          diag_pivot_thresh=None, relax=None, panel_size=None, options=None):
+    """
+    Compute an incomplete LU decomposition for a sparse, square matrix.
+
+    The resulting object is an approximation to the inverse of `A`.
+
+    Parameters
+    ----------
+    A : (N, N) array_like
+        Sparse array to factorize. Most efficient when provided in CSC format.
+        Other formats will be converted to CSC before factorization.
+    drop_tol : float, optional
+        Drop tolerance (``0 <= tol <= 1``) for an incomplete LU decomposition.
+        (default: 1e-4)
+
+        Note that `drop_tol` primarily affects entries generated as fill-in
+        during the ILU factorization; for matrices that produce little or no
+        fill-in, changing this parameter may have no visible effect on the
+        sparsity pattern of the factors.
+    fill_factor : float, optional
+        Specifies the fill ratio upper bound (``>= 1.0``) for ILU. (default: 10)
+    drop_rule : str, optional
+        Comma-separated string of drop rules to use.
+        Available rules: ``basic``, ``prows``, ``column``, ``area``,
+        ``secondary``, ``dynamic``, ``interp``. (Default: ``basic,area``)
+
+        See SuperLU documentation for details.
+    permc_spec : str, optional
+        How to permute the columns of the matrix for sparsity preservation.
+        (default: 'COLAMD')
+
+        - ``NATURAL``: natural ordering.
+        - ``MMD_ATA``: minimum degree ordering on the structure of A^T A.
+        - ``MMD_AT_PLUS_A``: minimum degree ordering on the structure of A^T+A.
+        - ``COLAMD``: approximate minimum degree column ordering
+
+    diag_pivot_thresh : float, optional
+        Threshold used for a diagonal entry to be an acceptable pivot.
+        See SuperLU user's guide for details [1]_
+    relax : int, optional
+        Expert option for customizing the degree of relaxing supernodes.
+        See SuperLU user's guide for details [1]_
+    panel_size : int, optional
+        Expert option for customizing the panel size.
+        See SuperLU user's guide for details [1]_
+    options : dict, optional
+        Dictionary containing additional expert options to SuperLU.
+        See SuperLU user guide [1]_ (section 2.4 on the 'Options' argument)
+        for more details. For example, you can specify
+        ``options=dict(Equil=False, IterRefine='SINGLE'))``
+        to turn equilibration off and perform a single iterative refinement.
+
+    Returns
+    -------
+    invA_approx : scipy.sparse.linalg.SuperLU
+        Object, which has a ``solve`` method.
+
+    See Also
+    --------
+    splu : complete LU decomposition
+
+    Notes
+    -----
+    When a real array is factorized and the returned SuperLU object's ``solve()`` method
+    is used with complex arguments an error is generated. Instead, cast the initial
+    array to complex and then factorize.
+
+    To improve the better approximation to the inverse, you may need to
+    increase `fill_factor` AND decrease `drop_tol`.
+
+    The effect of `drop_tol` is matrix-dependent. In particular, `drop_tol`
+    does not guarantee that existing off-diagonal entries will be removed;
+    it controls dropping of candidate entries during factorization (often
+    fill-in). For some sparsity patterns, the ILU factors can be identical
+    to the full LU factors even for large `drop_tol`.
+
+    This function uses the SuperLU library.
+
+    References
+    ----------
+    .. [1] SuperLU https://portal.nersc.gov/project/sparse/superlu/
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.sparse import csc_array
+    >>> from scipy.sparse.linalg import spilu
+    >>> A = csc_array([[1., 0., 0.], [5., 0., 2.], [0., -1., 0.]], dtype=float)
+    >>> B = spilu(A)
+    >>> x = np.array([1., 2., 3.], dtype=float)
+    >>> B.solve(x)
+    array([ 1. , -3. , -1.5])
+    >>> A.dot(B.solve(x))
+    array([ 1.,  2.,  3.])
+    >>> B.solve(A.dot(x))
+    array([ 1.,  2.,  3.])
+    """
+
+    if is_pydata_spmatrix(A):
+        A_cls = type(A)
+        def csc_construct_func(*a, cls=A_cls):
+            return cls.from_scipy_sparse(csc_array(*a))
+        A = A.to_scipy_sparse().tocsc()
+    else:
+        csc_construct_func = csc_array
+
+    if not (issparse(A) and A.format == "csc"):
+        A = csc_array(A)
+        warn('spilu converted its input to CSC format',
+             SparseEfficiencyWarning, stacklevel=2)
+
+    # sum duplicates for non-canonical format
+    A.sum_duplicates()
+    A = A._asfptype()  # upcast to a floating point format
+
+    M, N = A.shape
+    if (M != N):
+        raise ValueError("can only factor square matrices")  # is this true?
+
+    indices, indptr = safely_cast_index_arrays(A, np.intc, "SuperLU")
+
+    _options = dict(ILU_DropRule=drop_rule, ILU_DropTol=drop_tol,
+                    ILU_FillFactor=fill_factor,
+                    DiagPivotThresh=diag_pivot_thresh, ColPerm=permc_spec,
+                    PanelSize=panel_size, Relax=relax)
+    if options is not None:
+        _options.update(options)
+
+    # Ensure that no column permutations are applied
+    if (_options["ColPerm"] == "NATURAL"):
+        _options["SymmetricMode"] = True
+
+    return _superlu.gstrf(N, A.nnz, A.data, indices, indptr,
+                          csc_construct_func=csc_construct_func,
+                          ilu=True, options=_options)
+
+
+def factorized(A):
+    """
+    Return a function for solving a sparse linear system, with A pre-factorized.
+
+    Parameters
+    ----------
+    A : (N, N) array_like
+        Input. A in CSC format is most efficient. A CSR format matrix will
+        be converted to CSC before factorization.
+
+    Returns
+    -------
+    solve : callable
+        To solve the linear system of equations given in `A`, the `solve`
+        callable should be passed an ndarray of shape (N,).
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.sparse.linalg import factorized
+    >>> from scipy.sparse import csc_array
+    >>> A = np.array([[ 3. ,  2. , -1. ],
+    ...               [ 2. , -2. ,  4. ],
+    ...               [-1. ,  0.5, -1. ]])
+    >>> solve = factorized(csc_array(A)) # Makes LU decomposition.
+    >>> rhs1 = np.array([1, -2, 0])
+    >>> solve(rhs1) # Uses the LU factors.
+    array([ 1., -2., -2.])
+
+    """
+    if is_pydata_spmatrix(A):
+        A = A.to_scipy_sparse().tocsc()
+
+    if not hasattr(useUmfpack, 'u'):
+        useUmfpack.u = not noScikit
+
+    if useUmfpack.u:
+        if noScikit:
+            raise RuntimeError('Scikits.umfpack not installed.')
+
+        if not (issparse(A) and A.format == "csc"):
+            A = csc_array(A)
+            warn('splu converted its input to CSC format',
+                 SparseEfficiencyWarning, stacklevel=2)
+
+        A = A._asfptype()  # upcast to a floating point format
+
+        if A.dtype.char not in 'dD':
+            raise ValueError("convert matrix data to double, please, using"
+                  " .astype(), or set linsolve.useUmfpack.u = False")
+
+        umf_family, A = _get_umf_family(A)
+        umf = umfpack.UmfpackContext(umf_family)
+
+        # Make LU decomposition.
+        umf.numeric(A)
+
+        def solve(b):
+            with np.errstate(divide="ignore", invalid="ignore"):
+                # Ignoring warnings with numpy >= 1.23.0, see gh-16523
+                result = umf.solve(umfpack.UMFPACK_A, A, b, autoTranspose=True)
+
+            return result
+
+        return solve
+    else:
+        return splu(A).solve
+
+
+def spsolve_triangular(A, b, lower=True, overwrite_A=False, overwrite_b=False,
+                       unit_diagonal=False):
+    """
+    Solve the equation ``A x = b`` for `x`, assuming A is a triangular matrix.
+
+    Parameters
+    ----------
+    A : (M, M) sparse array or matrix
+        A sparse square triangular matrix. Should be in CSR or CSC format.
+    b : (M,) or (M, N) array_like
+        Right-hand side matrix in ``A x = b``
+    lower : bool, optional
+        Whether `A` is a lower or upper triangular matrix.
+        Default is lower triangular matrix.
+    overwrite_A : bool, optional
+        Allow changing `A`.
+        Enabling gives a performance gain. Default is False.
+    overwrite_b : bool, optional
+        Allow overwriting data in `b`.
+        Enabling gives a performance gain. Default is False.
+        If `overwrite_b` is True, it should be ensured that
+        `b` has an appropriate dtype to be able to store the result.
+    unit_diagonal : bool, optional
+        If True, diagonal elements of `a` are assumed to be 1.
+
+        .. versionadded:: 1.4.0
+
+    Returns
+    -------
+    x : (M,) or (M, N) ndarray
+        Solution to the system ``A x = b``. Shape of return matches shape
+        of `b`.
+
+    Raises
+    ------
+    LinAlgError
+        If `A` is singular or not triangular.
+    ValueError
+        If shape of `A` or shape of `b` do not match the requirements.
+
+    Notes
+    -----
+    .. versionadded:: 0.19.0
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.sparse import csc_array
+    >>> from scipy.sparse.linalg import spsolve_triangular
+    >>> A = csc_array([[3, 0, 0], [1, -1, 0], [2, 0, 1]], dtype=float)
+    >>> B = np.array([[2, 0], [-1, 0], [2, 0]], dtype=float)
+    >>> x = spsolve_triangular(A, B)
+    >>> np.allclose(A.dot(x), B)
+    True
+    """
+
+    if is_pydata_spmatrix(A):
+        A = A.to_scipy_sparse().tocsc()
+
+    trans = "N"
+    if issparse(A) and A.format == "csr":
+        A = A.T
+        trans = "T"
+        lower = not lower
+
+    if not (issparse(A) and A.format == "csc"):
+        warn('CSC or CSR matrix format is required. Converting to CSC matrix.',
+             SparseEfficiencyWarning, stacklevel=2)
+        A = csc_array(A)
+    elif not overwrite_A:
+        A = A.copy()
+
+
+    M, N = A.shape
+    if M != N:
+        raise ValueError(
+            f'A must be a square matrix but its shape is {A.shape}.')
+
+    if unit_diagonal:
+        with catch_warnings():
+            simplefilter('ignore', SparseEfficiencyWarning)
+            A.setdiag(1)
+    else:
+        diag = A.diagonal()
+        if np.any(diag == 0):
+            raise LinAlgError(
+                'A is singular: zero entry on diagonal.')
+        invdiag = 1/diag
+        if trans == "N":
+            A = A @ diags_array(invdiag)
+        else:
+            A = (A.T @ diags_array(invdiag)).T
+
+    # sum duplicates for non-canonical format
+    A.sum_duplicates()
+
+    b = np.asanyarray(b)
+
+    if b.ndim not in [1, 2]:
+        raise ValueError(
+            f'b must have 1 or 2 dims but its shape is {b.shape}.')
+    if M != b.shape[0]:
+        raise ValueError(
+            'The size of the dimensions of A must be equal to '
+            'the size of the first dimension of b but the shape of A is '
+            f'{A.shape} and the shape of b is {b.shape}.'
+        )
+
+    result_dtype = np.promote_types(np.promote_types(A.dtype, np.float32), b.dtype)
+    if A.dtype != result_dtype:
+        A = A.astype(result_dtype)
+    if b.dtype != result_dtype:
+        b = b.astype(result_dtype)
+    elif not overwrite_b:
+        b = b.copy()
+
+    if lower:
+        L = A
+        U = csc_array((N, N), dtype=result_dtype)
+    else:
+        L = eye_array(N, dtype=result_dtype, format='csc')
+        U = A
+        U.setdiag(0)
+
+    L_indices, L_indptr = safely_cast_index_arrays(L, np.intc, "SuperLU")
+    U_indices, U_indptr = safely_cast_index_arrays(U, np.intc, "SuperLU")
+
+    x, info = _superlu.gstrs(trans,
+                             N, L.nnz, L.data, L_indices, L_indptr,
+                             N, U.nnz, U.data, U_indices, U_indptr,
+                             b)
+    if info:
+        raise LinAlgError('A is singular.')
+
+    if not unit_diagonal:
+        invdiag = invdiag.reshape(-1, *([1] * (len(x.shape) - 1)))
+        x = x * invdiag
+
+    return x
+
+
+def is_sptriangular(A):
+    """Returns 2-tuple indicating lower/upper triangular structure for sparse ``A``.
+
+    Checks for triangular structure in ``A``. The result is summarized in
+    two boolean values ``lower`` and ``upper`` to designate whether ``A`` is
+    lower triangular or upper triangular respectively. Diagonal ``A`` will
+    result in both being True. Non-triangular structure results in False for both.
+
+    Only the sparse structure is used here. Values are not checked for zeros.
+
+    This function will convert a copy of ``A`` to CSC format if it is not already
+    CSR or CSC format. So it may be more efficient to convert it yourself if you
+    have other uses for the CSR/CSC version.
+
+    If ``A`` is not square, the portions outside the upper left square of the
+    matrix do not affect its triangular structure. You probably want to work
+    with the square portion of the matrix, though it is not requred here.
+
+    Parameters
+    ----------
+    A : SciPy sparse array or matrix
+        A sparse matrix preferrably in CSR or CSC format.
+
+    Returns
+    -------
+    lower, upper : 2-tuple of bool
+        Whether `A` is lower / upper triangular.
+
+        .. versionadded:: 1.15.0
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.sparse import csc_array, eye_array
+    >>> from scipy.sparse.linalg import is_sptriangular
+    >>> A = csc_array([[3, 0, 0], [1, -1, 0], [2, 0, 1]], dtype=float)
+    >>> is_sptriangular(A)
+    (True, False)
+    >>> D = eye_array(3, format='csr')
+    >>> is_sptriangular(D)
+    (True, True)
+    """
+    if not (issparse(A) and A.format in ("csc", "csr", "coo", "dia", "dok", "lil")):
+        warn('is_sptriangular needs sparse and not BSR format. Converting to CSR.',
+             SparseEfficiencyWarning, stacklevel=2)
+        A = csr_array(A)
+
+    # bsr is better off converting to csr
+    if A.format == "dia":
+        return A.offsets.max() <= 0, A.offsets.min() >= 0
+    elif A.format == "coo":
+        rows, cols = A.coords
+        return (cols <= rows).all(), (cols >= rows).all()
+    elif A.format == "dok":
+        return all(c <= r for r, c in A.keys()), all(c >= r for r, c in A.keys())
+    elif A.format == "lil":
+        lower = all(col <= row for row, cols in enumerate(A.rows) for col in cols)
+        upper = all(col >= row for row, cols in enumerate(A.rows) for col in cols)
+        return lower, upper
+    # format in ("csc", "csr")
+    indptr, indices = A.indptr, A.indices
+    N = len(indptr) - 1
+
+    lower, upper = True, True
+    # check middle, 1st, last col (treat as CSC and switch at end if CSR)
+    for col in [N // 2, 0, -1]:
+        rows = indices[indptr[col]:indptr[col + 1]]
+        upper = upper and (col >= rows).all()
+        lower = lower and (col <= rows).all()
+        if not upper and not lower:
+            return False, False
+    # check all cols
+    cols = np.repeat(np.arange(N), np.diff(indptr))
+    rows = indices
+    upper = upper and (cols >= rows).all()
+    lower = lower and (cols <= rows).all()
+    if A.format == 'csr':
+        return upper, lower
+    return lower, upper
+
+
+def spbandwidth(A):
+    """Return the lower and upper bandwidth of a 2D numeric array.
+
+    Computes the lower and upper limits on the bandwidth of the
+    sparse 2D array ``A``. The result is summarized as a 2-tuple
+    of positive integers ``(lo, hi)``. A zero denotes no sub/super
+    diagonal entries on that side (triangular). The maximum value
+    for ``lo`` (``hi``) is one less than the number of rows(cols).
+
+    Only the sparse structure is used here. Values are not checked for zeros.
+
+    Parameters
+    ----------
+    A : SciPy sparse array or matrix
+        A sparse matrix preferrably in CSR or CSC format.
+
+    Returns
+    -------
+    below, above : 2-tuple of int
+        The distance to the farthest non-zero diagonal below/above the
+        main diagonal.
+
+        .. versionadded:: 1.15.0
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.sparse.linalg import spbandwidth
+    >>> from scipy.sparse import csc_array, eye_array
+    >>> A = csc_array([[3, 0, 0], [1, -1, 0], [2, 0, 1]], dtype=float)
+    >>> spbandwidth(A)
+    (2, 0)
+    >>> D = eye_array(3, format='csr')
+    >>> spbandwidth(D)
+    (0, 0)
+    """
+    if not (issparse(A) and A.format in ("csc", "csr", "coo", "dia", "dok")):
+        warn('spbandwidth needs sparse format not LIL and BSR. Converting to CSR.',
+             SparseEfficiencyWarning, stacklevel=2)
+        A = csr_array(A)
+
+    # bsr and lil are better off converting to csr
+    if A.format == "dia":
+        return max(0, -A.offsets.min().item()), max(0, A.offsets.max().item())
+    if A.format in ("csc", "csr"):
+        indptr, indices = A.indptr, A.indices
+        N = len(indptr) - 1
+        gap = np.repeat(np.arange(N), np.diff(indptr)) - indices
+        if A.format == 'csr':
+            gap = -gap
+    elif A.format == "coo":
+        gap = A.coords[1] - A.coords[0]
+    elif A.format == "dok":
+        gap = [(c - r) for r, c in A.keys()] + [0]
+        return -min(gap), max(gap)
+    return max(-np.min(gap).item(), 0), max(np.max(gap).item(), 0)
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+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_dsolve/tests/test_linsolve.py
@@ -0,0 +1,930 @@
+import sys
+import threading
+import warnings
+
+import numpy as np
+from numpy import array, finfo, arange, eye, all, unique, ones, dot
+from numpy.exceptions import ComplexWarning
+from numpy.testing import (
+        assert_array_almost_equal, assert_almost_equal,
+        assert_equal, assert_array_equal, assert_, assert_allclose)
+import pytest
+from pytest import raises as assert_raises, warns as assert_warns
+
+import scipy.linalg
+from scipy.linalg import norm, inv
+from scipy.sparse import (issparse, SparseEfficiencyWarning,
+                          csc_array, csr_array, coo_array, dia_array,
+                          dok_array, lil_array, bsr_array,
+                          eye_array, random_array, tril, triu, kron)
+from scipy.sparse.linalg import SuperLU
+from scipy.sparse.linalg._dsolve import (spsolve, use_solver, splu, spilu,
+        MatrixRankWarning, _superlu, spsolve_triangular, factorized,
+        is_sptriangular, spbandwidth)
+import scipy.sparse
+
+from scipy._lib._testutils import check_free_memory
+
+
+# scikits.umfpack is not a SciPy dependency but it is optionally used in
+# dsolve, so check whether it's available
+try:
+    import scikits.umfpack as umfpack
+    has_umfpack = True
+except ImportError:
+    has_umfpack = False
+
+def toarray(a):
+    if issparse(a):
+        return a.toarray()
+    else:
+        return a
+
+
+def setup_bug_8278():
+    N = 2 ** 6
+    h = 1/N
+    Ah1D = dia_array(([-1, 2, -1], [-1, 0, 1]), shape=(N-1, N-1))/(h**2)
+    eyeN = eye_array(N - 1)
+    A = (kron(eyeN, kron(eyeN, Ah1D))
+         + kron(eyeN, kron(Ah1D, eyeN))
+         + kron(Ah1D, kron(eyeN, eyeN)))
+    b = np.random.rand((N-1)**3)
+    return A, b
+
+
+class TestFactorized:
+    def setup_method(self):
+        n = 5
+        d = arange(n) + 1
+        self.n = n
+        self.A = dia_array(((d, 2*d, d[::-1]), (-3, 0, 5)), shape=(n,n)).tocsc()
+
+    def _check_singular(self):
+        A = csc_array((5,5), dtype='d')
+        b = ones(5)
+        assert_array_almost_equal(0. * b, factorized(A)(b))
+
+    def _check_non_singular(self):
+        # Make a diagonal dominant, to make sure it is not singular
+        n = 5
+        rng = np.random.default_rng(14332)
+        a = csc_array(rng.random((n, n)))
+        b = ones(n)
+
+        expected = splu(a).solve(b)
+        assert_array_almost_equal(factorized(a)(b), expected)
+
+    def test_singular_without_umfpack(self):
+        use_solver(useUmfpack=False)
+        with assert_raises(RuntimeError, match="Factor is exactly singular"):
+            self._check_singular()
+
+    @pytest.mark.skipif(not has_umfpack, reason="umfpack not available")
+    def test_singular_with_umfpack(self):
+        use_solver(useUmfpack=True)
+        with warnings.catch_warnings():
+            msg = "divide by zero encountered in double_scalars"
+            warnings.filterwarnings("ignore", msg, RuntimeWarning)
+            assert_warns(umfpack.UmfpackWarning, self._check_singular)
+
+    def test_non_singular_without_umfpack(self):
+        use_solver(useUmfpack=False)
+        self._check_non_singular()
+
+    @pytest.mark.skipif(not has_umfpack, reason="umfpack not available")
+    def test_non_singular_with_umfpack(self):
+        use_solver(useUmfpack=True)
+        self._check_non_singular()
+
+    def test_cannot_factorize_nonsquare_matrix_without_umfpack(self):
+        use_solver(useUmfpack=False)
+        msg = "can only factor square matrices"
+        with assert_raises(ValueError, match=msg):
+            factorized(self.A[:, :4])
+
+    @pytest.mark.skipif(not has_umfpack, reason="umfpack not available")
+    def test_factorizes_nonsquare_matrix_with_umfpack(self):
+        use_solver(useUmfpack=True)
+        # does not raise
+        factorized(self.A[:,:4])
+
+    def test_call_with_incorrectly_sized_matrix_without_umfpack(self):
+        use_solver(useUmfpack=False)
+        solve = factorized(self.A)
+
+        rng = np.random.default_rng(230498)
+        b = rng.random(4)
+        B = rng.random((4, 3))
+        BB = rng.random((self.n, 3, 9))
+
+        with assert_raises(ValueError, match="is of incompatible size"):
+            solve(b)
+        with assert_raises(ValueError, match="is of incompatible size"):
+            solve(B)
+        with assert_raises(ValueError,
+                           match="object too deep for desired array"):
+            solve(BB)
+
+    @pytest.mark.skipif(not has_umfpack, reason="umfpack not available")
+    def test_call_with_incorrectly_sized_matrix_with_umfpack(self):
+        use_solver(useUmfpack=True)
+        solve = factorized(self.A)
+
+        rng = np.random.default_rng(643095823)
+        b = rng.random(4)
+        B = rng.random((4, 3))
+        BB = rng.random((self.n, 3, 9))
+
+        # does not raise
+        solve(b)
+        msg = "object too deep for desired array"
+        with assert_raises(ValueError, match=msg):
+            solve(B)
+        with assert_raises(ValueError, match=msg):
+            solve(BB)
+
+    def test_call_with_cast_to_complex_without_umfpack(self):
+        use_solver(useUmfpack=False)
+        solve = factorized(self.A)
+        rng = np.random.default_rng(23454)
+        b = rng.random(4)
+        for t in [np.complex64, np.complex128]:
+            with assert_raises(TypeError, match="Cannot cast array data"):
+                solve(b.astype(t))
+
+    @pytest.mark.skipif(not has_umfpack, reason="umfpack not available")
+    def test_call_with_cast_to_complex_with_umfpack(self):
+        use_solver(useUmfpack=True)
+        solve = factorized(self.A)
+        rng = np.random.default_rng(23454)
+        b = rng.random(4)
+        for t in [np.complex64, np.complex128]:
+            assert_warns(ComplexWarning, solve, b.astype(t))
+
+    @pytest.mark.skipif(not has_umfpack, reason="umfpack not available")
+    def test_assume_sorted_indices_flag(self):
+        # a sparse matrix with unsorted indices
+        unsorted_inds = np.array([2, 0, 1, 0])
+        data = np.array([10, 16, 5, 0.4])
+        indptr = np.array([0, 1, 2, 4])
+        A = csc_array((data, unsorted_inds, indptr), (3, 3))
+        b = ones(3)
+
+        # should raise when incorrectly assuming indices are sorted
+        use_solver(useUmfpack=True, assumeSortedIndices=True)
+        with assert_raises(RuntimeError,
+                           match="UMFPACK_ERROR_invalid_matrix"):
+            factorized(A)
+
+        # should sort indices and succeed when not assuming indices are sorted
+        use_solver(useUmfpack=True, assumeSortedIndices=False)
+        expected = splu(A.copy()).solve(b)
+
+        assert_equal(A.has_sorted_indices, 0)
+        assert_array_almost_equal(factorized(A)(b), expected)
+
+    @pytest.mark.slow
+    @pytest.mark.skipif(not has_umfpack, reason="umfpack not available")
+    def test_bug_8278(self):
+        check_free_memory(8000)
+        use_solver(useUmfpack=True)
+        A, b = setup_bug_8278()
+        A = A.tocsc()
+        f = factorized(A)
+        x = f(b)
+        assert_array_almost_equal(A @ x, b)
+
+
+class TestLinsolve:
+    def setup_method(self):
+        use_solver(useUmfpack=False)
+
+    def test_singular(self):
+        A = csc_array((5,5), dtype='d')
+        b = array([1, 2, 3, 4, 5],dtype='d')
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", "Matrix is exactly singular", MatrixRankWarning)
+            x = spsolve(A, b)
+        assert_(not np.isfinite(x).any())
+
+    def test_singular_gh_3312(self):
+        # "Bad" test case that leads SuperLU to call LAPACK with invalid
+        # arguments. Check that it fails moderately gracefully.
+        ij = np.array([(17, 0), (17, 6), (17, 12), (10, 13)], dtype=np.int32)
+        v = np.array([0.284213, 0.94933781, 0.15767017, 0.38797296])
+        A = csc_array((v, ij.T), shape=(20, 20))
+        b = np.arange(20)
+
+        try:
+            # should either raise a runtime error or return value
+            # appropriate for singular input (which yields the warning)
+            with warnings.catch_warnings():
+                warnings.filterwarnings(
+                    "ignore", "Matrix is exactly singular", MatrixRankWarning)
+                x = spsolve(A, b)
+            assert not np.isfinite(x).any()
+        except RuntimeError:
+            pass
+
+    @pytest.mark.parametrize('format', ['csc', 'csr'])
+    @pytest.mark.parametrize('idx_dtype', [np.int32, np.int64])
+    def test_twodiags(self, format: str, idx_dtype: np.dtype):
+        A = dia_array(([[1, 2, 3, 4, 5], [6, 5, 8, 9, 10]], [0, 1]),
+                        shape=(5, 5)).asformat(format)
+        b = array([1, 2, 3, 4, 5])
+
+        # condition number of A
+        cond_A = norm(A.toarray(), 2) * norm(inv(A.toarray()), 2)
+
+        for t in ['f','d','F','D']:
+            eps = finfo(t).eps  # floating point epsilon
+            b = b.astype(t)
+            Asp = A.astype(t)
+            Asp.indices = Asp.indices.astype(idx_dtype, copy=False)
+            Asp.indptr = Asp.indptr.astype(idx_dtype, copy=False)
+
+            x = spsolve(Asp, b)
+            assert_(norm(b - Asp@x) < 10 * cond_A * eps)
+
+    def test_bvector_smoketest(self):
+        Adense = array([[0., 1., 1.],
+                        [1., 0., 1.],
+                        [0., 0., 1.]])
+        As = csc_array(Adense)
+        rng = np.random.default_rng(1234)
+        x = rng.standard_normal(3)
+        b = As@x
+        x2 = spsolve(As, b)
+
+        assert_array_almost_equal(x, x2)
+
+    def test_bmatrix_smoketest(self):
+        Adense = array([[0., 1., 1.],
+                        [1., 0., 1.],
+                        [0., 0., 1.]])
+        As = csc_array(Adense)
+        rng = np.random.default_rng(1234)
+        x = rng.standard_normal((3, 4))
+        Bdense = As.dot(x)
+        Bs = csc_array(Bdense)
+        x2 = spsolve(As, Bs)
+        assert_array_almost_equal(x, x2.toarray())
+
+    def test_non_square(self):
+        with warnings.catch_warnings():
+            warnings.simplefilter('ignore', SparseEfficiencyWarning)
+            # A is not square.
+            A = ones((3, 4))
+            b = ones((4, 1))
+            assert_raises(ValueError, spsolve, A, b)
+            # A2 and b2 have incompatible shapes.
+            A2 = csc_array(eye(3))
+            b2 = array([1.0, 2.0])
+            assert_raises(ValueError, spsolve, A2, b2)
+
+    def test_example_comparison(self):
+        with warnings.catch_warnings():
+            warnings.simplefilter('ignore', SparseEfficiencyWarning)
+            row = array([0,0,1,2,2,2])
+            col = array([0,2,2,0,1,2])
+            data = array([1,2,3,-4,5,6])
+            sM = csr_array((data,(row,col)), shape=(3,3), dtype=float)
+            M = sM.toarray()
+
+            row = array([0,0,1,1,0,0])
+            col = array([0,2,1,1,0,0])
+            data = array([1,1,1,1,1,1])
+            sN = csr_array((data, (row,col)), shape=(3,3), dtype=float)
+            N = sN.toarray()
+
+            sX = spsolve(sM, sN)
+            X = scipy.linalg.solve(M, N)
+
+            assert_array_almost_equal(X, sX.toarray())
+
+    @pytest.mark.skipif(not has_umfpack, reason="umfpack not available")
+    def test_shape_compatibility(self):
+        with warnings.catch_warnings():
+            warnings.simplefilter('ignore', SparseEfficiencyWarning)
+            use_solver(useUmfpack=True)
+            A = csc_array([[1., 0], [0, 2]])
+            bs = [
+                [1, 6],
+                array([1, 6]),
+                [[1], [6]],
+                array([[1], [6]]),
+                csc_array([[1], [6]]),
+                csr_array([[1], [6]]),
+                dok_array([[1], [6]]),
+                bsr_array([[1], [6]]),
+                array([[1., 2., 3.], [6., 8., 10.]]),
+                csc_array([[1., 2., 3.], [6., 8., 10.]]),
+                csr_array([[1., 2., 3.], [6., 8., 10.]]),
+                dok_array([[1., 2., 3.], [6., 8., 10.]]),
+                bsr_array([[1., 2., 3.], [6., 8., 10.]]),
+            ]
+
+        for b in bs:
+            x = np.linalg.solve(A.toarray(), toarray(b))
+            for spmattype in [csc_array, csr_array, dok_array, lil_array]:
+                x1 = spsolve(spmattype(A), b, use_umfpack=True)
+                x2 = spsolve(spmattype(A), b, use_umfpack=False)
+
+                # check solution
+                if x.ndim == 2 and x.shape[1] == 1:
+                    # interprets also these as "vectors"
+                    x = x.ravel()
+
+                assert_array_almost_equal(toarray(x1), x,
+                                          err_msg=repr((b, spmattype, 1)))
+                assert_array_almost_equal(toarray(x2), x,
+                                          err_msg=repr((b, spmattype, 2)))
+
+                # dense vs. sparse output  ("vectors" are always dense)
+                if issparse(b) and x.ndim > 1:
+                    assert_(issparse(x1), repr((b, spmattype, 1)))
+                    assert_(issparse(x2), repr((b, spmattype, 2)))
+                else:
+                    assert_(isinstance(x1, np.ndarray), repr((b, spmattype, 1)))
+                    assert_(isinstance(x2, np.ndarray), repr((b, spmattype, 2)))
+
+                # check output shape
+                if x.ndim == 1:
+                    # "vector"
+                    assert_equal(x1.shape, (A.shape[1],))
+                    assert_equal(x2.shape, (A.shape[1],))
+                else:
+                    # "matrix"
+                    assert_equal(x1.shape, x.shape)
+                    assert_equal(x2.shape, x.shape)
+
+        A = csc_array((3, 3))
+        b = csc_array((1, 3))
+        assert_raises(ValueError, spsolve, A, b)
+
+    def test_ndarray_support(self):
+        with warnings.catch_warnings():
+            warnings.simplefilter('ignore', SparseEfficiencyWarning)
+            A = array([[1., 2.], [2., 0.]])
+            x = array([[1., 1.], [0.5, -0.5]])
+            b = array([[2., 0.], [2., 2.]])
+
+            assert_array_almost_equal(x, spsolve(A, b))
+
+    def test_gssv_badinput(self):
+        N = 10
+        d = arange(N) + 1.0
+        A = dia_array(((d, 2*d, d[::-1]), (-3, 0, 5)), shape=(N, N))
+
+        for container in (csc_array, csr_array):
+            A = container(A)
+            b = np.arange(N)
+
+            def not_c_contig(x):
+                return x.repeat(2)[::2]
+
+            def not_1dim(x):
+                return x[:,None]
+
+            def bad_type(x):
+                return x.astype(bool)
+
+            def too_short(x):
+                return x[:-1]
+
+            badops = [not_c_contig, not_1dim, bad_type, too_short]
+
+            for badop in badops:
+                msg = f"{container!r} {badop!r}"
+                # Not C-contiguous
+                assert_raises((ValueError, TypeError), _superlu.gssv,
+                              N, A.nnz, badop(A.data), A.indices, A.indptr,
+                              b, int(A.format == 'csc'), err_msg=msg)
+                assert_raises((ValueError, TypeError), _superlu.gssv,
+                              N, A.nnz, A.data, badop(A.indices), A.indptr,
+                              b, int(A.format == 'csc'), err_msg=msg)
+                assert_raises((ValueError, TypeError), _superlu.gssv,
+                              N, A.nnz, A.data, A.indices, badop(A.indptr),
+                              b, int(A.format == 'csc'), err_msg=msg)
+
+    def test_sparsity_preservation(self):
+        ident = csc_array([
+            [1, 0, 0],
+            [0, 1, 0],
+            [0, 0, 1]])
+        b = csc_array([
+            [0, 1],
+            [1, 0],
+            [0, 0]])
+        x = spsolve(ident, b)
+        assert_equal(ident.nnz, 3)
+        assert_equal(b.nnz, 2)
+        assert_equal(x.nnz, 2)
+        assert_allclose(x.toarray(), b.toarray(), atol=1e-12, rtol=1e-12)
+
+    def test_dtype_cast(self):
+        A_real = csr_array([[1, 2, 0],
+                            [0, 0, 3],
+                            [4, 0, 5]])
+        A_complex = csr_array([[1, 2, 0],
+                               [0, 0, 3],
+                               [4, 0, 5 + 1j]])
+        b_real = np.array([1,1,1])
+        b_complex = np.array([1,1,1]) + 1j*np.array([1,1,1])
+        x = spsolve(A_real, b_real)
+        assert_(np.issubdtype(x.dtype, np.floating))
+        x = spsolve(A_real, b_complex)
+        assert_(np.issubdtype(x.dtype, np.complexfloating))
+        x = spsolve(A_complex, b_real)
+        assert_(np.issubdtype(x.dtype, np.complexfloating))
+        x = spsolve(A_complex, b_complex)
+        assert_(np.issubdtype(x.dtype, np.complexfloating))
+
+    @pytest.mark.slow
+    @pytest.mark.skipif(not has_umfpack, reason="umfpack not available")
+    def test_bug_8278(self):
+        check_free_memory(8000)
+        use_solver(useUmfpack=True)
+        A, b = setup_bug_8278()
+        x = spsolve(A, b)
+        assert_array_almost_equal(A @ x, b)
+
+
+class TestSplu:
+    def setup_method(self):
+        use_solver(useUmfpack=False)
+        n = 40
+        d = arange(n) + 1
+        self.n = n
+        self.A = dia_array(((d, 2*d, d[::-1]), (-3, 0, 5)), shape=(n, n)).tocsc()
+
+    def _smoketest(self, spxlu, check, dtype, idx_dtype):
+        if np.issubdtype(dtype, np.complexfloating):
+            A = self.A + 1j*self.A.T
+        else:
+            A = self.A
+
+        A = A.astype(dtype)
+        A.indices = A.indices.astype(idx_dtype, copy=False)
+        A.indptr = A.indptr.astype(idx_dtype, copy=False)
+        lu = spxlu(A)
+
+        rng = np.random.RandomState(1234)
+
+        # Input shapes
+        for k in [None, 1, 2, self.n, self.n+2]:
+            msg = f"k={k!r}"
+
+            if k is None:
+                b = rng.rand(self.n)
+            else:
+                b = rng.rand(self.n, k)
+
+            if np.issubdtype(dtype, np.complexfloating):
+                b = b + 1j*rng.rand(*b.shape)
+            b = b.astype(dtype)
+
+            x = lu.solve(b)
+            check(A, b, x, msg)
+
+            x = lu.solve(b, 'T')
+            check(A.T, b, x, msg)
+
+            x = lu.solve(b, 'H')
+            check(A.T.conj(), b, x, msg)
+
+    def test_splu_smoketest(self):
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", SparseEfficiencyWarning)
+            self._internal_test_splu_smoketest()
+
+    def _internal_test_splu_smoketest(self):
+        # Check that splu works at all
+        def check(A, b, x, msg=""):
+            eps = np.finfo(A.dtype).eps
+            r = A @ x
+            assert_(abs(r - b).max() < 1e3*eps, msg)
+
+        for dtype in [np.float32, np.float64, np.complex64, np.complex128]:
+            for idx_dtype in [np.int32, np.int64]:
+                self._smoketest(splu, check, dtype, idx_dtype)
+
+    def test_spilu_smoketest(self):
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", SparseEfficiencyWarning)
+            self._internal_test_spilu_smoketest()
+
+    def _internal_test_spilu_smoketest(self):
+        errors = []
+
+        def check(A, b, x, msg=""):
+            r = A @ x
+            err = abs(r - b).max()
+            assert_(err < 1e-2, msg)
+            if b.dtype in (np.float64, np.complex128):
+                errors.append(err)
+
+        for dtype in [np.float32, np.float64, np.complex64, np.complex128]:
+            for idx_dtype in [np.int32, np.int64]:
+                self._smoketest(spilu, check, dtype, idx_dtype)
+
+        assert_(max(errors) > 1e-5)
+
+    def test_spilu_drop_rule(self):
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", SparseEfficiencyWarning)
+            # Test passing in the drop_rule argument to spilu.
+            A = eye_array(2)
+
+            rules = [
+                b'basic,area'.decode('ascii'),  # unicode
+                b'basic,area',  # ascii
+                [b'basic', b'area'.decode('ascii')]
+            ]
+            for rule in rules:
+                # Argument should be accepted
+                assert_(isinstance(spilu(A, drop_rule=rule), SuperLU))
+
+    def test_splu_nnz0(self):
+        A = csc_array((5,5), dtype='d')
+        assert_raises(RuntimeError, splu, A)
+
+    def test_spilu_nnz0(self):
+        A = csc_array((5,5), dtype='d')
+        assert_raises(RuntimeError, spilu, A)
+
+    def test_splu_basic(self):
+        # Test basic splu functionality.
+        n = 30
+        rng = np.random.RandomState(12)
+        a = rng.rand(n, n)
+        a[a < 0.95] = 0
+        # First test with a singular matrix
+        a[:, 0] = 0
+        a_ = csc_array(a)
+        # Matrix is exactly singular
+        assert_raises(RuntimeError, splu, a_)
+
+        # Make a diagonal dominant, to make sure it is not singular
+        a += 4*eye(n)
+        a_ = csc_array(a)
+        lu = splu(a_)
+        b = ones(n)
+        x = lu.solve(b)
+        assert_almost_equal(dot(a, x), b)
+
+    def test_splu_perm(self):
+        # Test the permutation vectors exposed by splu.
+        n = 30
+        rng = np.random.default_rng(1342354)
+        a = rng.random((n, n))
+        a[a < 0.95] = 0
+        # Make a diagonal dominant, to make sure it is not singular
+        a += 4*eye(n)
+        a_ = csc_array(a)
+        lu = splu(a_)
+        # Check that the permutation indices do belong to [0, n-1].
+        for perm in (lu.perm_r, lu.perm_c):
+            assert_(all(perm > -1))
+            assert_(all(perm < n))
+            assert_equal(len(unique(perm)), len(perm))
+
+        # Now make a symmetric, and test that the two permutation vectors are
+        # the same
+        # Note: a += a.T relies on undefined behavior.
+        a = a + a.T
+        a_ = csc_array(a)
+        lu = splu(a_)
+        assert_array_equal(lu.perm_r, lu.perm_c)
+
+    @pytest.mark.parametrize("splu_fun, rtol", [(splu, 1e-7), (spilu, 1e-1)])
+    def test_natural_permc(self, splu_fun, rtol):
+        # Test that the "NATURAL" permc_spec does not permute the matrix
+        rng = np.random.RandomState(42)
+        n = 500
+        p = 0.01
+        A = random_array((n, n), density=p, random_state=rng)
+        x = rng.rand(n)
+        # Make A diagonal dominant to make sure it is not singular
+        A += (n + 1) * eye_array(n)
+        A_ = csc_array(A)
+        b = A_ @ x
+
+        # without permc_spec, permutation is not identity
+        lu = splu_fun(A_)
+        assert_(np.any(lu.perm_c != np.arange(n)))
+
+        # with permc_spec="NATURAL", permutation is identity
+        lu = splu_fun(A_, permc_spec="NATURAL")
+        assert_array_equal(lu.perm_c, np.arange(n))
+
+        # Also, lu decomposition is valid
+        x2 = lu.solve(b)
+        assert_allclose(x, x2, rtol=rtol)
+
+    @pytest.mark.skipif(not hasattr(sys, 'getrefcount'), reason="no sys.getrefcount")
+    def test_lu_refcount(self):
+        # Test that we are keeping track of the reference count with splu.
+        n = 30
+        rng = np.random.default_rng(1342354)
+        a = rng.random((n, n))
+        a[a < 0.95] = 0
+        # Make a diagonal dominant, to make sure it is not singular
+        a += 4*eye(n)
+        a_ = csc_array(a)
+        lu = splu(a_)
+
+        # And now test that we don't have a refcount bug
+        rc = sys.getrefcount(lu)
+        for attr in ('perm_r', 'perm_c'):
+            perm = getattr(lu, attr)
+            assert_equal(sys.getrefcount(lu), rc + 1)
+            del perm
+            assert_equal(sys.getrefcount(lu), rc)
+
+    def test_bad_inputs(self):
+        A = self.A.tocsc()
+        rng = np.random.default_rng(235634)
+
+        assert_raises(ValueError, splu, A[:,:4])
+        assert_raises(ValueError, spilu, A[:,:4])
+
+        for lu in [splu(A), spilu(A)]:
+            b = rng.random(42)
+            B = rng.random((42, 3))
+            BB = rng.random((self.n, 3, 9))
+            assert_raises(ValueError, lu.solve, b)
+            assert_raises(ValueError, lu.solve, B)
+            assert_raises(ValueError, lu.solve, BB)
+            assert_raises(TypeError, lu.solve,
+                          b.astype(np.complex64))
+            assert_raises(TypeError, lu.solve,
+                          b.astype(np.complex128))
+
+    def test_superlu_dlamch_i386_nan(self):
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", SparseEfficiencyWarning)
+            # SuperLU 4.3 calls some functions returning floats without
+            # declaring them. On i386@linux call convention, this fails to
+            # clear floating point registers after call. As a result, NaN
+            # can appear in the next floating point operation made.
+            #
+            # Here's a test case that triggered the issue.
+            n = 8
+            d = np.arange(n) + 1
+            A = dia_array(((d, 2*d, d[::-1]), (-3, 0, 5)), shape=(n, n))
+            A = A.astype(np.float32)
+            spilu(A)
+            A = A + 1j*A
+            B = A.toarray()
+            assert_(not np.isnan(B).any())
+
+    def test_lu_attr(self):
+        def check(dtype, complex_2=False):
+            with warnings.catch_warnings():
+                warnings.simplefilter("ignore", SparseEfficiencyWarning)
+
+                A = self.A.astype(dtype)
+
+                if complex_2:
+                    A = A + 1j*A.T
+
+                n = A.shape[0]
+                lu = splu(A)
+
+                # Check that the decomposition is as advertised
+
+                Pc = np.zeros((n, n))
+                Pc[np.arange(n), lu.perm_c] = 1
+
+                Pr = np.zeros((n, n))
+                Pr[lu.perm_r, np.arange(n)] = 1
+
+                Ad = A.toarray()
+                lhs = Pr.dot(Ad).dot(Pc)
+                rhs = (lu.L @ lu.U).toarray()
+
+                eps = np.finfo(dtype).eps
+
+                assert_allclose(lhs, rhs, atol=100*eps)
+
+        check(np.float32)
+        check(np.float64)
+        check(np.complex64)
+        check(np.complex128)
+        check(np.complex64, True)
+        check(np.complex128, True)
+
+    @pytest.mark.slow
+    def test_threads_parallel(self):
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", SparseEfficiencyWarning)
+            oks = []
+
+            def worker():
+                try:
+                    self.test_splu_basic()
+                    self._internal_test_splu_smoketest()
+                    self._internal_test_spilu_smoketest()
+                    oks.append(True)
+                except Exception:
+                    pass
+
+            threads = [threading.Thread(target=worker)
+                       for k in range(20)]
+            for t in threads:
+                t.start()
+            for t in threads:
+                t.join()
+
+            assert_equal(len(oks), 20)
+
+    def test_singular_matrix(self):
+        # Test that SuperLU does not print to stdout when a singular matrix is
+        # passed. See gh-20993.
+        A = eye_array(10, format='csr')
+        A[-1, -1] = 0
+        b = np.zeros(10)
+        with pytest.warns(MatrixRankWarning):
+            res = spsolve(A, b)
+            assert np.isnan(res).all()
+
+
+class TestGstrsErrors:
+    def setup_method(self):
+      self.A = csc_array([[1.0,2.0,3.0],[4.0,5.0,6.0],[7.0,8.0,9.0]], dtype=np.float64)
+      self.b = np.array([[1.0],[2.0],[3.0]], dtype=np.float64)
+
+    def test_trans(self):
+        L = tril(self.A, format='csc')
+        U = triu(self.A, k=1, format='csc')
+        with assert_raises(ValueError, match="trans must be N, T, or H"):
+            _superlu.gstrs('X', L.shape[0], L.nnz, L.data, L.indices, L.indptr,
+                                U.shape[0], U.nnz, U.data, U.indices, U.indptr, self.b)
+
+    def test_shape_LU(self):
+        L = tril(self.A[0:2,0:2], format='csc')
+        U = triu(self.A, k=1, format='csc')
+        with assert_raises(ValueError, match="L and U must have the same dimension"):
+            _superlu.gstrs('N', L.shape[0], L.nnz, L.data, L.indices, L.indptr,
+                                U.shape[0], U.nnz, U.data, U.indices, U.indptr, self.b)
+
+    def test_shape_b(self):
+        L = tril(self.A, format='csc')
+        U = triu(self.A, k=1, format='csc')
+        with assert_raises(ValueError, match="right hand side array has invalid shape"):
+            _superlu.gstrs('N', L.shape[0], L.nnz, L.data, L.indices, L.indptr,
+                                U.shape[0], U.nnz, U.data, U.indices, U.indptr,
+                                self.b[0:2])
+
+    def test_types_differ(self):
+        L = tril(self.A.astype(np.float32), format='csc')
+        U = triu(self.A, k=1, format='csc')
+        with assert_raises(TypeError, match="nzvals types of L and U differ"):
+            _superlu.gstrs('N', L.shape[0], L.nnz, L.data, L.indices, L.indptr,
+                                U.shape[0], U.nnz, U.data, U.indices, U.indptr, self.b)
+
+    def test_types_unsupported(self):
+        L = tril(self.A.astype(np.uint8), format='csc')
+        U = triu(self.A.astype(np.uint8), k=1, format='csc')
+        with assert_raises(TypeError, match="nzvals is not of a type supported"):
+            _superlu.gstrs('N', L.shape[0], L.nnz, L.data, L.indices, L.indptr,
+                                U.shape[0], U.nnz, U.data, U.indices, U.indptr,
+                                self.b.astype(np.uint8))
+
+class TestSpsolveTriangular:
+    def setup_method(self):
+        use_solver(useUmfpack=False)
+
+    @pytest.mark.parametrize("fmt",["csr","csc"])
+    def test_zero_diagonal(self,fmt):
+        n = 5
+        rng = np.random.default_rng(43876432987)
+        A = coo_array(rng.standard_normal((n, n)))
+        b = np.arange(n)
+        A = tril(A, k=0, format=fmt)
+
+        x = spsolve_triangular(A, b, unit_diagonal=True, lower=True)
+
+        A.setdiag(1)
+        assert_allclose(A.dot(x), b)
+
+        # Regression test from gh-15199
+        A = np.array([[0, 0, 0], [1, 0, 0], [1, 1, 0]], dtype=np.float64)
+        b = np.array([1., 2., 3.])
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", "CSC or CSR matrix format is", SparseEfficiencyWarning)
+            spsolve_triangular(A, b, unit_diagonal=True)
+
+    @pytest.mark.parametrize("fmt",["csr","csc"])
+    def test_singular(self,fmt):
+        n = 5
+        if fmt == "csr":
+            A = csr_array((n, n))
+        else:
+            A = csc_array((n, n))
+        b = np.arange(n)
+        for lower in (True, False):
+            assert_raises(scipy.linalg.LinAlgError,
+                          spsolve_triangular, A, b, lower=lower)
+
+    def test_bad_shape(self):
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", SparseEfficiencyWarning)
+            # A is not square.
+            A = np.zeros((3, 4))
+            b = ones((4, 1))
+            assert_raises(ValueError, spsolve_triangular, A, b)
+            # A2 and b2 have incompatible shapes.
+            A2 = csr_array(eye(3))
+            b2 = array([1.0, 2.0])
+            assert_raises(ValueError, spsolve_triangular, A2, b2)
+
+    def test_input_types(self):
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", SparseEfficiencyWarning)
+            A = array([[1., 0.], [1., 2.]])
+            b = array([[2., 0.], [2., 2.]])
+            for matrix_type in (array, csc_array, csr_array):
+                x = spsolve_triangular(matrix_type(A), b, lower=True)
+                assert_array_almost_equal(A.dot(x), b)
+
+    @pytest.mark.slow
+    @pytest.mark.parametrize("n", [10, 10**2, 10**3])
+    @pytest.mark.parametrize("m", [1, 10])
+    @pytest.mark.parametrize("lower", [True, False])
+    @pytest.mark.parametrize("format", ["csr", "csc"])
+    @pytest.mark.parametrize("unit_diagonal", [False, True])
+    @pytest.mark.parametrize("choice_of_A", ["real", "complex"])
+    @pytest.mark.parametrize("choice_of_b", ["floats", "ints", "complexints"])
+    def test_random(self, n, m, lower, format, unit_diagonal, choice_of_A, choice_of_b):
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", SparseEfficiencyWarning)
+            def random_triangle_matrix(n, lower=True, format="csr", choice_of_A="real"):
+                if choice_of_A == "real":
+                    dtype = np.float64
+                elif choice_of_A == "complex":
+                    dtype = np.complex128
+                else:
+                    raise ValueError("choice_of_A must be 'real' or 'complex'.")
+                rng = np.random.default_rng(789002319)
+                rvs = rng.random
+                A = random_array((n, n), density=0.1, format='lil', dtype=dtype,
+                                 random_state=rng, data_sampler=rvs)
+                if lower:
+                    A = tril(A, format="lil")
+                else:
+                    A = triu(A, format="lil")
+                for i in range(n):
+                    A[i, i] = np.random.rand() + 1
+                if format == "csc":
+                    A = A.tocsc(copy=False)
+                else:
+                    A = A.tocsr(copy=False)
+                return A
+
+            rng = np.random.default_rng(1234)
+            A = random_triangle_matrix(n, lower=lower)
+            if choice_of_b == "floats":
+                b = rng.random((n, m))
+            elif choice_of_b == "ints":
+                b = rng.integers(-9, 9, (n, m))
+            elif choice_of_b == "complexints":
+                b = rng.integers(-9, 9, (n, m)) + rng.integers(-9, 9, (n, m)) * 1j
+            else:
+                raise ValueError(
+                    "choice_of_b must be 'floats', 'ints', or 'complexints'.")
+            x = spsolve_triangular(A, b, lower=lower, unit_diagonal=unit_diagonal)
+            if unit_diagonal:
+                A.setdiag(1)
+            assert_allclose(A.dot(x), b, atol=1.5e-6)
+
+
+@pytest.mark.parametrize("nnz", [10, 10**2, 10**3])
+@pytest.mark.parametrize("fmt", ["csr", "csc", "coo", "dia", "dok", "lil"])
+def test_is_sptriangular_and_spbandwidth(nnz, fmt):
+    with warnings.catch_warnings():
+        warnings.simplefilter('ignore', SparseEfficiencyWarning)
+        rng = np.random.default_rng(42)
+
+        N = nnz // 2
+        dens = 0.1
+        A = random_array((N, N), density=dens, format="csr", rng=rng)
+        A[1, 3] = A[3, 1] = 22  # ensure not upper or lower
+        A = A.asformat(fmt)
+        AU = triu(A, format=fmt)
+        AL = tril(A, format=fmt)
+        D = 0.1 * eye_array(N, format=fmt)
+
+        assert is_sptriangular(A) == (False, False)
+        assert is_sptriangular(AL) == (True, False)
+        assert is_sptriangular(AU) == (False, True)
+        assert is_sptriangular(D) == (True, True)
+
+        assert spbandwidth(A) == scipy.linalg.bandwidth(A.toarray())
+        assert spbandwidth(AU) == scipy.linalg.bandwidth(AU.toarray())
+        assert spbandwidth(AL) == scipy.linalg.bandwidth(AL.toarray())
+        assert spbandwidth(D) == scipy.linalg.bandwidth(D.toarray())
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_eigen/__init__.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_eigen/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..25278d34ecd3353d409a25f7a94797902fe6ef93
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_eigen/__init__.py
@@ -0,0 +1,22 @@
+"""
+Sparse Eigenvalue Solvers
+-------------------------
+
+The submodules of sparse.linalg._eigen:
+    1. lobpcg: Locally Optimal Block Preconditioned Conjugate Gradient Method
+
+"""
+from .arpack import *
+from .lobpcg import *
+from ._svds import svds
+
+from . import arpack
+
+__all__ = [
+    'ArpackError', 'ArpackNoConvergence',
+    'eigs', 'eigsh', 'lobpcg', 'svds'
+]
+
+from scipy._lib._testutils import PytestTester
+test = PytestTester(__name__)
+del PytestTester
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diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_eigen/__pycache__/_svds_doc.cpython-312.pyc b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_eigen/__pycache__/_svds_doc.cpython-312.pyc
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diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_eigen/_svds.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_eigen/_svds.py
new file mode 100644
index 0000000000000000000000000000000000000000..2400cbbcdf0dcd437df83d66e2367a4e673370e7
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_eigen/_svds.py
@@ -0,0 +1,535 @@
+import math
+import numpy as np
+from . import eigsh
+
+from scipy._lib._util import _transition_to_rng, check_random_state
+from scipy.sparse.linalg._interface import LinearOperator, aslinearoperator
+from scipy.sparse.linalg._eigen.lobpcg import lobpcg  # type: ignore[no-redef]
+from scipy.sparse.linalg._svdp import _svdp
+from scipy.linalg import svd
+
+__all__ = ['svds']
+
+
+def _herm(x):
+    return x.T.conj()
+
+
+def _iv(A, k, ncv, tol, which, v0, maxiter,
+        return_singular, solver, rng):
+
+    # input validation/standardization for `solver`
+    # out of order because it's needed for other parameters
+    solver = str(solver).lower()
+    solvers = {"arpack", "lobpcg", "propack"}
+    if solver not in solvers:
+        raise ValueError(f"solver must be one of {solvers}.")
+
+    # input validation/standardization for `A`
+    A = aslinearoperator(A)  # this takes care of some input validation
+    if not np.issubdtype(A.dtype, np.number):
+        message = "`A` must be of numeric data type."
+        raise ValueError(message)
+    if math.prod(A.shape) == 0:
+        message = "`A` must not be empty."
+        raise ValueError(message)
+    if A.ndim != 2:
+        raise ValueError("Only 2-D input is supported for `A` (a single matrix)")
+
+    # input validation/standardization for `k`
+    kmax = min(A.shape) if solver == 'propack' else min(A.shape) - 1
+    if int(k) != k or not (0 < k <= kmax):
+        message = "`k` must be an integer satisfying `0 < k < min(A.shape)`."
+        raise ValueError(message)
+    k = int(k)
+
+    # input validation/standardization for `ncv`
+    if solver == "arpack" and ncv is not None:
+        if int(ncv) != ncv or not (k < ncv < min(A.shape)):
+            message = ("`ncv` must be an integer satisfying "
+                       "`k < ncv < min(A.shape)`.")
+            raise ValueError(message)
+        ncv = int(ncv)
+
+    # input validation/standardization for `tol`
+    if tol < 0 or not np.isfinite(tol):
+        message = "`tol` must be a non-negative floating point value."
+        raise ValueError(message)
+    tol = float(tol)
+
+    # input validation/standardization for `which`
+    which = str(which).upper()
+    whichs = {'LM', 'SM'}
+    if which not in whichs:
+        raise ValueError(f"`which` must be in {whichs}.")
+
+    # input validation/standardization for `v0`
+    if v0 is not None:
+        v0 = np.atleast_1d(v0)
+        if not (np.issubdtype(v0.dtype, np.complexfloating)
+                or np.issubdtype(v0.dtype, np.floating)):
+            message = ("`v0` must be of floating or complex floating "
+                       "data type.")
+            raise ValueError(message)
+
+        shape = (A.shape[0],) if solver == 'propack' else (min(A.shape),)
+        if v0.shape != shape:
+            message = f"`v0` must have shape {shape}."
+            raise ValueError(message)
+
+    # input validation/standardization for `maxiter`
+    if maxiter is not None and (int(maxiter) != maxiter or maxiter <= 0):
+        message = "`maxiter` must be a positive integer."
+        raise ValueError(message)
+    maxiter = int(maxiter) if maxiter is not None else maxiter
+
+    # input validation/standardization for `return_singular_vectors`
+    # not going to be flexible with this; too complicated for little gain
+    rs_options = {True, False, "vh", "u"}
+    if return_singular not in rs_options:
+        raise ValueError(f"`return_singular_vectors` must be in {rs_options}.")
+
+    rng = check_random_state(rng)
+
+    return (A, k, ncv, tol, which, v0, maxiter,
+            return_singular, solver, rng)
+
+
+@_transition_to_rng("random_state", position_num=9)
+def svds(A, k=6, ncv=None, tol=0, which='LM', v0=None,
+         maxiter=None, return_singular_vectors=True,
+         solver='arpack', rng=None, options=None):
+    """
+    Partial singular value decomposition of a sparse matrix.
+
+    Compute the largest or smallest `k` singular values and corresponding
+    singular vectors of a sparse matrix `A`. The order in which the singular
+    values are returned is not guaranteed.
+
+    In the descriptions below, let ``M, N = A.shape``.
+
+    Parameters
+    ----------
+    A : ndarray, sparse matrix, or LinearOperator
+        Matrix to decompose of a floating point numeric dtype.
+    k : int, default: 6
+        Number of singular values and singular vectors to compute.
+        Must satisfy ``1 <= k <= kmax``, where ``kmax=min(M, N)`` for
+        ``solver='propack'`` and ``kmax=min(M, N) - 1`` otherwise.
+    ncv : int, optional
+        When ``solver='arpack'``, this is the number of Lanczos vectors
+        generated. See :ref:`'arpack' <sparse.linalg.svds-arpack>` for details.
+        When ``solver='lobpcg'`` or ``solver='propack'``, this parameter is
+        ignored.
+    tol : float, optional
+        Tolerance for singular values. Zero (default) means machine precision.
+    which : {'LM', 'SM'}
+        Which `k` singular values to find: either the largest magnitude ('LM')
+        or smallest magnitude ('SM') singular values.
+    v0 : ndarray, optional
+        The starting vector for iteration; see method-specific
+        documentation (:ref:`'arpack' <sparse.linalg.svds-arpack>`,
+        :ref:`'lobpcg' <sparse.linalg.svds-lobpcg>`), or
+        :ref:`'propack' <sparse.linalg.svds-propack>` for details.
+    maxiter : int, optional
+        Maximum number of iterations; see method-specific
+        documentation (:ref:`'arpack' <sparse.linalg.svds-arpack>`,
+        :ref:`'lobpcg' <sparse.linalg.svds-lobpcg>`), or
+        :ref:`'propack' <sparse.linalg.svds-propack>` for details.
+    return_singular_vectors : {True, False, "u", "vh"}
+        Singular values are always computed and returned; this parameter
+        controls the computation and return of singular vectors.
+
+        - ``True``: return singular vectors.
+        - ``False``: do not return singular vectors.
+        - ``"u"``: if ``M <= N``, compute only the left singular vectors and
+          return ``None`` for the right singular vectors. Otherwise, compute
+          all singular vectors.
+        - ``"vh"``: if ``M > N``, compute only the right singular vectors and
+          return ``None`` for the left singular vectors. Otherwise, compute
+          all singular vectors.
+
+        If ``solver='propack'``, the option is respected regardless of the
+        matrix shape.
+
+    solver :  {'arpack', 'propack', 'lobpcg'}, optional
+            The solver used.
+            :ref:`'arpack' <sparse.linalg.svds-arpack>`,
+            :ref:`'lobpcg' <sparse.linalg.svds-lobpcg>`, and
+            :ref:`'propack' <sparse.linalg.svds-propack>` are supported.
+            Default: `'arpack'`.
+    rng : `numpy.random.Generator`, optional
+        Pseudorandom number generator state. When `rng` is None, a new
+        `numpy.random.Generator` is created using entropy from the
+        operating system. Types other than `numpy.random.Generator` are
+        passed to `numpy.random.default_rng` to instantiate a ``Generator``.
+    options : dict, optional
+        A dictionary of solver-specific options. No solver-specific options
+        are currently supported; this parameter is reserved for future use.
+
+    Returns
+    -------
+    u : ndarray, shape=(M, k)
+        Unitary matrix having left singular vectors as columns.
+    s : ndarray, shape=(k,)
+        The singular values.
+    vh : ndarray, shape=(k, N)
+        Unitary matrix having right singular vectors as rows.
+
+    Notes
+    -----
+    When ARPACK or LOBPCG is selected as the method, the singular values and
+    singular vectors are computed as the eigenvalues and eigenvectors of the
+    corresponding Gram matrix, either ``A.conj().T @ A`` or ``A @ A.conj().T``,
+    depending on which one is computationally cheaper. It is then followed by
+    the Rayleigh-Ritz method as postprocessing; see Using the normal matrix,
+    in Rayleigh-Ritz method, (2022, Nov. 19), Wikipedia, https://w.wiki/4zms.
+
+    Alternatively, the PROPACK solver can be called.
+
+    Dtype of `A` is mapped, if possible, to float(32,64) and complex(64,128)
+    for internal computations.
+
+    Examples
+    --------
+    Construct a matrix `A` from singular values and vectors.
+
+    >>> import numpy as np
+    >>> from scipy import sparse, linalg, stats
+    >>> from scipy.sparse.linalg import svds, aslinearoperator, LinearOperator
+
+    Construct a dense matrix `A` from singular values and vectors.
+
+    >>> rng = np.random.default_rng(258265244568965474821194062361901728911)
+    >>> orthogonal = stats.ortho_group.rvs(10, random_state=rng)
+    >>> s = [1e-3, 1, 2, 3, 4]  # non-zero singular values
+    >>> u = orthogonal[:, :5]         # left singular vectors
+    >>> vT = orthogonal[:, 5:].T      # right singular vectors
+    >>> A = u @ np.diag(s) @ vT
+
+    With only four singular values/vectors, the SVD approximates the original
+    matrix.
+
+    >>> u4, s4, vT4 = svds(A, k=4)
+    >>> A4 = u4 @ np.diag(s4) @ vT4
+    >>> np.allclose(A4, A, atol=1e-3)
+    True
+
+    With all five non-zero singular values/vectors, we can reproduce
+    the original matrix more accurately.
+
+    >>> u5, s5, vT5 = svds(A, k=5)
+    >>> A5 = u5 @ np.diag(s5) @ vT5
+    >>> np.allclose(A5, A)
+    True
+
+    The singular values match the expected singular values.
+
+    >>> np.allclose(s5, s)
+    True
+
+    Since the singular values are not close to each other in this example,
+    every singular vector matches as expected up to a difference in sign.
+
+    >>> (np.allclose(np.abs(u5), np.abs(u)) and
+    ...  np.allclose(np.abs(vT5), np.abs(vT)))
+    True
+
+    The singular vectors are also orthogonal.
+
+    >>> (np.allclose(u5.T @ u5, np.eye(5)) and
+    ...  np.allclose(vT5 @ vT5.T, np.eye(5)))
+    True
+
+    If there are (nearly) multiple singular values, the corresponding
+    individual singular vectors may be unstable, but the whole invariant
+    subspace containing all such singular vectors is computed accurately
+    as can be measured by angles between subspaces via 'subspace_angles'.
+
+    >>> rng = np.random.default_rng(178686584221410808734965903901790843963)
+    >>> s = [1, 1 + 1e-6]  # non-zero singular values
+    >>> u, _ = np.linalg.qr(rng.standard_normal((99, 2)))
+    >>> v, _ = np.linalg.qr(rng.standard_normal((99, 2)))
+    >>> vT = v.T
+    >>> A = u @ np.diag(s) @ vT
+    >>> A = A.astype(np.float32)
+    >>> u2, s2, vT2 = svds(A, k=2, rng=rng)
+    >>> np.allclose(s2, s)
+    True
+
+    The angles between the individual exact and computed singular vectors
+    may not be so small. To check use:
+
+    >>> (linalg.subspace_angles(u2[:, :1], u[:, :1]) +
+    ...  linalg.subspace_angles(u2[:, 1:], u[:, 1:]))
+    array([0.06562513])  # may vary
+    >>> (linalg.subspace_angles(vT2[:1, :].T, vT[:1, :].T) +
+    ...  linalg.subspace_angles(vT2[1:, :].T, vT[1:, :].T))
+    array([0.06562507])  # may vary
+
+    As opposed to the angles between the 2-dimensional invariant subspaces
+    that these vectors span, which are small for rights singular vectors
+
+    >>> linalg.subspace_angles(u2, u).sum() < 1e-6
+    True
+
+    as well as for left singular vectors.
+
+    >>> linalg.subspace_angles(vT2.T, vT.T).sum() < 1e-6
+    True
+
+    The next example follows that of 'sklearn.decomposition.TruncatedSVD'.
+
+    >>> rng = np.random.default_rng(0)
+    >>> X_dense = rng.random(size=(100, 100))
+    >>> X_dense[:, 2 * np.arange(50)] = 0
+    >>> X = sparse.csr_array(X_dense)
+    >>> _, singular_values, _ = svds(X, k=5, rng=rng)
+    >>> print(singular_values)
+    [ 4.3221...  4.4043...  4.4907...  4.5858... 35.4549...]
+
+    The function can be called without the transpose of the input matrix
+    ever explicitly constructed.
+
+    >>> rng = np.random.default_rng(102524723947864966825913730119128190974)
+    >>> G = sparse.random_array((8, 9), density=0.5, rng=rng)
+    >>> Glo = aslinearoperator(G)
+    >>> _, singular_values_svds, _ = svds(Glo, k=5, rng=rng)
+    >>> _, singular_values_svd, _ = linalg.svd(G.toarray())
+    >>> np.allclose(singular_values_svds, singular_values_svd[-4::-1])
+    True
+
+    The most memory efficient scenario is where neither
+    the original matrix, nor its transpose, is explicitly constructed.
+    Our example computes the smallest singular values and vectors
+    of 'LinearOperator' constructed from the numpy function 'np.diff' used
+    column-wise to be consistent with 'LinearOperator' operating on columns.
+
+    >>> diff0 = lambda a: np.diff(a, axis=0)
+
+    Let us create the matrix from 'diff0' to be used for validation only.
+
+    >>> n = 5  # The dimension of the space.
+    >>> M_from_diff0 = diff0(np.eye(n))
+    >>> print(M_from_diff0.astype(int))
+    [[-1  1  0  0  0]
+     [ 0 -1  1  0  0]
+     [ 0  0 -1  1  0]
+     [ 0  0  0 -1  1]]
+
+    The matrix 'M_from_diff0' is bi-diagonal and could be alternatively
+    created directly by
+
+    >>> M = - np.eye(n - 1, n, dtype=int)
+    >>> np.fill_diagonal(M[:,1:], 1)
+    >>> np.allclose(M, M_from_diff0)
+    True
+
+    Its transpose
+
+    >>> print(M.T)
+    [[-1  0  0  0]
+     [ 1 -1  0  0]
+     [ 0  1 -1  0]
+     [ 0  0  1 -1]
+     [ 0  0  0  1]]
+
+    can be viewed as the incidence matrix; see
+    Incidence matrix, (2022, Nov. 19), Wikipedia, https://w.wiki/5YXU,
+    of a linear graph with 5 vertices and 4 edges. The 5x5 normal matrix
+    ``M.T @ M`` thus is
+
+    >>> print(M.T @ M)
+    [[ 1 -1  0  0  0]
+     [-1  2 -1  0  0]
+     [ 0 -1  2 -1  0]
+     [ 0  0 -1  2 -1]
+     [ 0  0  0 -1  1]]
+
+    the graph Laplacian, while the actually used in 'svds' smaller size
+    4x4 normal matrix ``M @ M.T``
+
+    >>> print(M @ M.T)
+    [[ 2 -1  0  0]
+     [-1  2 -1  0]
+     [ 0 -1  2 -1]
+     [ 0  0 -1  2]]
+
+    is the so-called edge-based Laplacian; see
+    Symmetric Laplacian via the incidence matrix, in Laplacian matrix,
+    (2022, Nov. 19), Wikipedia, https://w.wiki/5YXW.
+
+    The 'LinearOperator' setup needs the options 'rmatvec' and 'rmatmat'
+    of multiplication by the matrix transpose ``M.T``, but we want to be
+    matrix-free to save memory, so knowing how ``M.T`` looks like, we
+    manually construct the following function to be
+    used in ``rmatmat=diff0t``.
+
+    >>> def diff0t(a):
+    ...     if a.ndim == 1:
+    ...         a = a[:,np.newaxis]  # Turn 1D into 2D array
+    ...     d = np.zeros((a.shape[0] + 1, a.shape[1]), dtype=a.dtype)
+    ...     d[0, :] = - a[0, :]
+    ...     d[1:-1, :] = a[0:-1, :] - a[1:, :]
+    ...     d[-1, :] = a[-1, :]
+    ...     return d
+
+    We check that our function 'diff0t' for the matrix transpose is valid.
+
+    >>> np.allclose(M.T, diff0t(np.eye(n-1)))
+    True
+
+    Now we setup our matrix-free 'LinearOperator' called 'diff0_func_aslo'
+    and for validation the matrix-based 'diff0_matrix_aslo'.
+
+    >>> def diff0_func_aslo_def(n):
+    ...     return LinearOperator(matvec=diff0,
+    ...                           matmat=diff0,
+    ...                           rmatvec=diff0t,
+    ...                           rmatmat=diff0t,
+    ...                           shape=(n - 1, n))
+    >>> diff0_func_aslo = diff0_func_aslo_def(n)
+    >>> diff0_matrix_aslo = aslinearoperator(M_from_diff0)
+
+    And validate both the matrix and its transpose in 'LinearOperator'.
+
+    >>> np.allclose(diff0_func_aslo(np.eye(n)),
+    ...             diff0_matrix_aslo(np.eye(n)))
+    True
+    >>> np.allclose(diff0_func_aslo.T(np.eye(n-1)),
+    ...             diff0_matrix_aslo.T(np.eye(n-1)))
+    True
+
+    Having the 'LinearOperator' setup validated, we run the solver.
+
+    >>> n = 100
+    >>> diff0_func_aslo = diff0_func_aslo_def(n)
+    >>> u, s, vT = svds(diff0_func_aslo, k=3, which='SM')
+
+    The singular values squared and the singular vectors are known
+    explicitly; see
+    Pure Dirichlet boundary conditions, in
+    Eigenvalues and eigenvectors of the second derivative,
+    (2022, Nov. 19), Wikipedia, https://w.wiki/5YX6,
+    since 'diff' corresponds to first
+    derivative, and its smaller size n-1 x n-1 normal matrix
+    ``M @ M.T`` represent the discrete second derivative with the Dirichlet
+    boundary conditions. We use these analytic expressions for validation.
+
+    >>> se = 2. * np.sin(np.pi * np.arange(1, 4) / (2. * n))
+    >>> ue = np.sqrt(2 / n) * np.sin(np.pi * np.outer(np.arange(1, n),
+    ...                              np.arange(1, 4)) / n)
+    >>> np.allclose(s, se, atol=1e-3)
+    True
+    >>> np.allclose(np.abs(u), np.abs(ue), atol=1e-6)
+    True
+
+    """
+    args = _iv(A, k, ncv, tol, which, v0, maxiter, return_singular_vectors,
+               solver, rng)
+    (A, k, ncv, tol, which, v0, maxiter,
+     return_singular_vectors, solver, rng) = args
+
+    largest = (which == 'LM')
+    n, m = A.shape
+
+    if n >= m:
+        X_dot = A.matvec
+        X_matmat = A.matmat
+        XH_dot = A.rmatvec
+        XH_mat = A.rmatmat
+        transpose = False
+    else:
+        X_dot = A.rmatvec
+        X_matmat = A.rmatmat
+        XH_dot = A.matvec
+        XH_mat = A.matmat
+        transpose = True
+
+        dtype = getattr(A, 'dtype', None)
+        if dtype is None:
+            dtype = A.dot(np.zeros([m, 1])).dtype
+
+    def matvec_XH_X(x):
+        return XH_dot(X_dot(x))
+
+    def matmat_XH_X(x):
+        return XH_mat(X_matmat(x))
+
+    XH_X = LinearOperator(matvec=matvec_XH_X, dtype=A.dtype,
+                          matmat=matmat_XH_X,
+                          shape=(min(A.shape), min(A.shape)))
+
+    # Get a low rank approximation of the implicitly defined gramian matrix.
+    # This is not a stable way to approach the problem.
+    if solver == 'lobpcg':
+
+        if k == 1 and v0 is not None:
+            X = np.reshape(v0, (-1, 1))
+        else:
+            X = rng.standard_normal(size=(min(A.shape), k))
+
+        _, eigvec = lobpcg(XH_X, X, tol=tol ** 2, maxiter=maxiter,
+                           largest=largest)
+
+    elif solver == 'propack':
+        jobu = return_singular_vectors in {True, 'u'}
+        jobv = return_singular_vectors in {True, 'vh'}
+        irl_mode = (which == 'SM')
+        res = _svdp(A, k=k, tol=tol**2, which=which, maxiter=None,
+                    compute_u=jobu, compute_v=jobv, irl_mode=irl_mode,
+                    kmax=maxiter, v0=v0, rng=rng)
+
+        u, s, vh, _ = res  # but we'll ignore bnd, the last output
+
+        # PROPACK order appears to be largest first. `svds` output order is not
+        # guaranteed, according to documentation, but for ARPACK and LOBPCG
+        # they actually are ordered smallest to largest, so reverse for
+        # consistency.
+        s = s[::-1]
+        u = u[:, ::-1]
+        vh = vh[::-1]
+
+        u = u if jobu else None
+        vh = vh if jobv else None
+
+        if return_singular_vectors:
+            return u, s, vh
+        else:
+            return s
+
+    elif solver == 'arpack' or solver is None:
+        if v0 is None:
+            v0 = rng.standard_normal(size=(min(A.shape),))
+        _, eigvec = eigsh(XH_X, k=k, tol=tol ** 2, maxiter=maxiter,
+                          ncv=ncv, which=which, v0=v0)
+        # arpack do not guarantee exactly orthonormal eigenvectors
+        # for clustered eigenvalues, especially in complex arithmetic
+        eigvec, _ = np.linalg.qr(eigvec)
+
+    # the eigenvectors eigvec must be orthonomal here; see gh-16712
+    Av = X_matmat(eigvec)
+    if not return_singular_vectors:
+        s = svd(Av, compute_uv=False, overwrite_a=True)
+        return s[::-1]
+
+    # compute the left singular vectors of X and update the right ones
+    # accordingly
+    u, s, vh = svd(Av, full_matrices=False, overwrite_a=True)
+    u = u[:, ::-1]
+    s = s[::-1]
+    vh = vh[::-1]
+
+    jobu = return_singular_vectors in {True, 'u'}
+    jobv = return_singular_vectors in {True, 'vh'}
+
+    if transpose:
+        u_tmp = eigvec @ _herm(vh) if jobu else None
+        vh = _herm(u) if jobv else None
+        u = u_tmp
+    else:
+        if not jobu:
+            u = None
+        vh = vh @ _herm(eigvec) if jobv else None
+
+    return u, s, vh
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_eigen/_svds_doc.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_eigen/_svds_doc.py
new file mode 100644
index 0000000000000000000000000000000000000000..90b85876d2a69dd3c2efa56445e46c93bf0eaa9e
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_eigen/_svds_doc.py
@@ -0,0 +1,382 @@
+def _svds_arpack_doc(A, k=6, ncv=None, tol=0, which='LM', v0=None,
+                     maxiter=None, return_singular_vectors=True,
+                     solver='arpack', rng=None):
+    """
+    Partial singular value decomposition of a sparse matrix using ARPACK.
+
+    Compute the largest or smallest `k` singular values and corresponding
+    singular vectors of a sparse matrix `A`. The order in which the singular
+    values are returned is not guaranteed.
+
+    In the descriptions below, let ``M, N = A.shape``.
+
+    Parameters
+    ----------
+    A : sparse matrix or LinearOperator
+        Matrix to decompose.
+    k : int, optional
+        Number of singular values and singular vectors to compute.
+        Must satisfy ``1 <= k <= min(M, N) - 1``.
+        Default is 6.
+    ncv : int, optional
+        The number of Lanczos vectors generated.
+        The default is ``min(n, max(2*k + 1, 20))``.
+        If specified, must satisfy ``k + 1 < ncv < min(M, N)``; ``ncv > 2*k``
+        is recommended.
+    tol : float, optional
+        Tolerance for singular values. Zero (default) means machine precision.
+    which : {'LM', 'SM'}
+        Which `k` singular values to find: either the largest magnitude ('LM')
+        or smallest magnitude ('SM') singular values.
+    v0 : ndarray, optional
+        The starting vector for iteration:
+        an (approximate) left singular vector if ``N > M`` and a right singular
+        vector otherwise. Must be of length ``min(M, N)``.
+        Default: random
+    maxiter : int, optional
+        Maximum number of Arnoldi update iterations allowed;
+        default is ``min(M, N) * 10``.
+    return_singular_vectors : {True, False, "u", "vh"}
+        Singular values are always computed and returned; this parameter
+        controls the computation and return of singular vectors.
+
+        - ``True``: return singular vectors.
+        - ``False``: do not return singular vectors.
+        - ``"u"``: if ``M <= N``, compute only the left singular vectors and
+          return ``None`` for the right singular vectors. Otherwise, compute
+          all singular vectors.
+        - ``"vh"``: if ``M > N``, compute only the right singular vectors and
+          return ``None`` for the left singular vectors. Otherwise, compute
+          all singular vectors.
+
+    solver :  {'arpack', 'propack', 'lobpcg'}, optional
+            This is the solver-specific documentation for ``solver='arpack'``.
+            :ref:`'lobpcg' <sparse.linalg.svds-lobpcg>` and
+            :ref:`'propack' <sparse.linalg.svds-propack>`
+            are also supported.
+    rng : `numpy.random.Generator`, optional
+        Pseudorandom number generator state. When `rng` is None, a new
+        `numpy.random.Generator` is created using entropy from the
+        operating system. Types other than `numpy.random.Generator` are
+        passed to `numpy.random.default_rng` to instantiate a ``Generator``.
+    options : dict, optional
+        A dictionary of solver-specific options. No solver-specific options
+        are currently supported; this parameter is reserved for future use.
+
+    Returns
+    -------
+    u : ndarray, shape=(M, k)
+        Unitary matrix having left singular vectors as columns.
+    s : ndarray, shape=(k,)
+        The singular values.
+    vh : ndarray, shape=(k, N)
+        Unitary matrix having right singular vectors as rows.
+
+    Notes
+    -----
+    This is a naive implementation using ARPACK as an eigensolver
+    on ``A.conj().T @ A`` or ``A @ A.conj().T``, depending on which one is more
+    efficient.
+
+    Examples
+    --------
+    Construct a matrix ``A`` from singular values and vectors.
+
+    >>> import numpy as np
+    >>> from scipy.stats import ortho_group
+    >>> from scipy.sparse import csc_array, diags_array
+    >>> from scipy.sparse.linalg import svds
+    >>> rng = np.random.default_rng()
+    >>> orthogonal = csc_array(ortho_group.rvs(10, random_state=rng))
+    >>> s = [0.0001, 0.001, 3, 4, 5]  # singular values
+    >>> u = orthogonal[:, :5]         # left singular vectors
+    >>> vT = orthogonal[:, 5:].T      # right singular vectors
+    >>> A = u @ diags_array(s) @ vT
+
+    With only three singular values/vectors, the SVD approximates the original
+    matrix.
+
+    >>> u2, s2, vT2 = svds(A, k=3, solver='arpack')
+    >>> A2 = u2 @ np.diag(s2) @ vT2
+    >>> np.allclose(A2, A.toarray(), atol=1e-3)
+    True
+
+    With all five singular values/vectors, we can reproduce the original
+    matrix.
+
+    >>> u3, s3, vT3 = svds(A, k=5, solver='arpack')
+    >>> A3 = u3 @ np.diag(s3) @ vT3
+    >>> np.allclose(A3, A.toarray())
+    True
+
+    The singular values match the expected singular values, and the singular
+    vectors are as expected up to a difference in sign.
+
+    >>> (np.allclose(s3, s) and
+    ...  np.allclose(np.abs(u3), np.abs(u.toarray())) and
+    ...  np.allclose(np.abs(vT3), np.abs(vT.toarray())))
+    True
+
+    The singular vectors are also orthogonal.
+
+    >>> (np.allclose(u3.T @ u3, np.eye(5)) and
+    ...  np.allclose(vT3 @ vT3.T, np.eye(5)))
+    True
+    """
+    pass
+
+
+def _svds_lobpcg_doc(A, k=6, ncv=None, tol=0, which='LM', v0=None,
+                     maxiter=None, return_singular_vectors=True,
+                     solver='lobpcg', rng=None):
+    """
+    Partial singular value decomposition of a sparse matrix using LOBPCG.
+
+    Compute the largest or smallest `k` singular values and corresponding
+    singular vectors of a sparse matrix `A`. The order in which the singular
+    values are returned is not guaranteed.
+
+    In the descriptions below, let ``M, N = A.shape``.
+
+    Parameters
+    ----------
+    A : sparse matrix or LinearOperator
+        Matrix to decompose.
+    k : int, default: 6
+        Number of singular values and singular vectors to compute.
+        Must satisfy ``1 <= k <= min(M, N) - 1``.
+    ncv : int, optional
+        Ignored.
+    tol : float, optional
+        Tolerance for singular values. Zero (default) means machine precision.
+    which : {'LM', 'SM'}
+        Which `k` singular values to find: either the largest magnitude ('LM')
+        or smallest magnitude ('SM') singular values.
+    v0 : ndarray, optional
+        If `k` is 1, the starting vector for iteration:
+        an (approximate) left singular vector if ``N > M`` and a right singular
+        vector otherwise. Must be of length ``min(M, N)``.
+        Ignored otherwise.
+        Default: random
+    maxiter : int, default: 20
+        Maximum number of iterations.
+    return_singular_vectors : {True, False, "u", "vh"}
+        Singular values are always computed and returned; this parameter
+        controls the computation and return of singular vectors.
+
+        - ``True``: return singular vectors.
+        - ``False``: do not return singular vectors.
+        - ``"u"``: if ``M <= N``, compute only the left singular vectors and
+          return ``None`` for the right singular vectors. Otherwise, compute
+          all singular vectors.
+        - ``"vh"``: if ``M > N``, compute only the right singular vectors and
+          return ``None`` for the left singular vectors. Otherwise, compute
+          all singular vectors.
+
+    solver :  {'arpack', 'propack', 'lobpcg'}, optional
+            This is the solver-specific documentation for ``solver='lobpcg'``.
+            :ref:`'arpack' <sparse.linalg.svds-arpack>` and
+            :ref:`'propack' <sparse.linalg.svds-propack>`
+            are also supported.
+    rng : `numpy.random.Generator`, optional
+        Pseudorandom number generator state. When `rng` is None, a new
+        `numpy.random.Generator` is created using entropy from the
+        operating system. Types other than `numpy.random.Generator` are
+        passed to `numpy.random.default_rng` to instantiate a ``Generator``.
+    options : dict, optional
+        A dictionary of solver-specific options. No solver-specific options
+        are currently supported; this parameter is reserved for future use.
+
+    Returns
+    -------
+    u : ndarray, shape=(M, k)
+        Unitary matrix having left singular vectors as columns.
+    s : ndarray, shape=(k,)
+        The singular values.
+    vh : ndarray, shape=(k, N)
+        Unitary matrix having right singular vectors as rows.
+
+    Notes
+    -----
+    This is a naive implementation using LOBPCG as an eigensolver
+    on ``A.conj().T @ A`` or ``A @ A.conj().T``, depending on which one is more
+    efficient.
+
+    Examples
+    --------
+    Construct a matrix ``A`` from singular values and vectors.
+
+    >>> import numpy as np
+    >>> from scipy.stats import ortho_group
+    >>> from scipy.sparse import csc_array, diags_array
+    >>> from scipy.sparse.linalg import svds
+    >>> rng = np.random.default_rng()
+    >>> orthogonal = csc_array(ortho_group.rvs(10, random_state=rng))
+    >>> s = [0.0001, 0.001, 3, 4, 5]  # singular values
+    >>> u = orthogonal[:, :5]         # left singular vectors
+    >>> vT = orthogonal[:, 5:].T      # right singular vectors
+    >>> A = u @ diags_array(s) @ vT
+
+    With only three singular values/vectors, the SVD approximates the original
+    matrix.
+
+    >>> u2, s2, vT2 = svds(A, k=3, solver='lobpcg')
+    >>> A2 = u2 @ np.diag(s2) @ vT2
+    >>> np.allclose(A2, A.toarray(), atol=1e-3)
+    True
+
+    With all five singular values/vectors, we can reproduce the original
+    matrix.
+
+    >>> u3, s3, vT3 = svds(A, k=5, solver='lobpcg')
+    >>> A3 = u3 @ np.diag(s3) @ vT3
+    >>> np.allclose(A3, A.toarray())
+    True
+
+    The singular values match the expected singular values, and the singular
+    vectors are as expected up to a difference in sign.
+
+    >>> (np.allclose(s3, s) and
+    ...  np.allclose(np.abs(u3), np.abs(u.todense())) and
+    ...  np.allclose(np.abs(vT3), np.abs(vT.todense())))
+    True
+
+    The singular vectors are also orthogonal.
+
+    >>> (np.allclose(u3.T @ u3, np.eye(5)) and
+    ...  np.allclose(vT3 @ vT3.T, np.eye(5)))
+    True
+
+    """
+    pass
+
+
+def _svds_propack_doc(A, k=6, ncv=None, tol=0, which='LM', v0=None,
+                      maxiter=None, return_singular_vectors=True,
+                      solver='propack', rng=None):
+    """
+    Partial singular value decomposition of a sparse matrix using PROPACK.
+
+    Compute the largest or smallest `k` singular values and corresponding
+    singular vectors of a sparse matrix `A`. The order in which the singular
+    values are returned is not guaranteed.
+
+    In the descriptions below, let ``M, N = A.shape``.
+
+    Parameters
+    ----------
+    A : sparse matrix or LinearOperator
+        Matrix to decompose. If `A` is a ``LinearOperator``
+        object, it must define both ``matvec`` and ``rmatvec`` methods.
+    k : int, default: 6
+        Number of singular values and singular vectors to compute.
+        Must satisfy ``1 <= k <= min(M, N)``.
+    ncv : int, optional
+        Ignored.
+    tol : float, optional
+        The desired relative accuracy for computed singular values.
+        Zero (default) means machine precision.
+    which : {'LM', 'SM'}
+        Which `k` singular values to find: either the largest magnitude ('LM')
+        or smallest magnitude ('SM') singular values. Note that choosing
+        ``which='SM'`` will force the ``irl`` option to be set ``True``.
+    v0 : ndarray, optional
+        Starting vector for iterations: must be of length ``A.shape[0]``.
+        If not specified, PROPACK will generate a starting vector.
+    maxiter : int, optional
+        Maximum number of iterations / maximal dimension of the Krylov
+        subspace. Default is ``10 * k``.
+    return_singular_vectors : {True, False, "u", "vh"}
+        Singular values are always computed and returned; this parameter
+        controls the computation and return of singular vectors.
+
+        - ``True``: return singular vectors.
+        - ``False``: do not return singular vectors.
+        - ``"u"``: compute only the left singular vectors; return ``None`` for
+          the right singular vectors.
+        - ``"vh"``: compute only the right singular vectors; return ``None``
+          for the left singular vectors.
+
+    solver :  {'arpack', 'propack', 'lobpcg'}, optional
+            This is the solver-specific documentation for ``solver='propack'``.
+            :ref:`'arpack' <sparse.linalg.svds-arpack>` and
+            :ref:`'lobpcg' <sparse.linalg.svds-lobpcg>`
+            are also supported.
+    rng : `numpy.random.Generator`, optional
+        Pseudorandom number generator state. When `rng` is None, a new
+        `numpy.random.Generator` is created using entropy from the
+        operating system. Types other than `numpy.random.Generator` are
+        passed to `numpy.random.default_rng` to instantiate a ``Generator``.
+    options : dict, optional
+        A dictionary of solver-specific options. No solver-specific options
+        are currently supported; this parameter is reserved for future use.
+
+    Returns
+    -------
+    u : ndarray, shape=(M, k)
+        Unitary matrix having left singular vectors as columns.
+    s : ndarray, shape=(k,)
+        The singular values.
+    vh : ndarray, shape=(k, N)
+        Unitary matrix having right singular vectors as rows.
+
+    Notes
+    -----
+    This is an interface to the Fortran library PROPACK [1]_.
+    The current default is to run with IRL mode disabled unless seeking the
+    smallest singular values/vectors (``which='SM'``).
+
+    References
+    ----------
+
+    .. [1] Larsen, Rasmus Munk. "PROPACK-Software for large and sparse SVD
+       calculations." Available online. URL
+       http://sun.stanford.edu/~rmunk/PROPACK (2004): 2008-2009.
+
+    Examples
+    --------
+    Construct a matrix ``A`` from singular values and vectors.
+
+    >>> import numpy as np
+    >>> from scipy.stats import ortho_group
+    >>> from scipy.sparse import csc_array, diags_array
+    >>> from scipy.sparse.linalg import svds
+    >>> rng = np.random.default_rng()
+    >>> orthogonal = csc_array(ortho_group.rvs(10, random_state=rng))
+    >>> s = [0.0001, 0.001, 3, 4, 5]  # singular values
+    >>> u = orthogonal[:, :5]         # left singular vectors
+    >>> vT = orthogonal[:, 5:].T      # right singular vectors
+    >>> A = u @ diags_array(s) @ vT
+
+    With only three singular values/vectors, the SVD approximates the original
+    matrix.
+
+    >>> u2, s2, vT2 = svds(A, k=3, solver='propack')
+    >>> A2 = u2 @ np.diag(s2) @ vT2
+    >>> np.allclose(A2, A.todense(), atol=1e-3)
+    True
+
+    With all five singular values/vectors, we can reproduce the original
+    matrix.
+
+    >>> u3, s3, vT3 = svds(A, k=5, solver='propack')
+    >>> A3 = u3 @ np.diag(s3) @ vT3
+    >>> np.allclose(A3, A.todense())
+    True
+
+    The singular values match the expected singular values, and the singular
+    vectors are as expected up to a difference in sign.
+
+    >>> (np.allclose(s3, s) and
+    ...  np.allclose(np.abs(u3), np.abs(u.toarray())) and
+    ...  np.allclose(np.abs(vT3), np.abs(vT.toarray())))
+    True
+
+    The singular vectors are also orthogonal.
+
+    >>> (np.allclose(u3.T @ u3, np.eye(5)) and
+    ...  np.allclose(vT3 @ vT3.T, np.eye(5)))
+    True
+
+    """
+    pass
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_eigen/arpack/__init__.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_eigen/arpack/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..679b94480d7ff5a11e037ffb758f2214c6e5097f
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_eigen/arpack/__init__.py
@@ -0,0 +1,20 @@
+"""
+Eigenvalue solver using iterative methods.
+
+Find k eigenvectors and eigenvalues of a matrix A using the
+Arnoldi/Lanczos iterative methods from ARPACK [1]_,[2]_.
+
+These methods are most useful for large sparse matrices.
+
+  - eigs(A,k)
+  - eigsh(A,k)
+
+References
+----------
+.. [1] ARPACK Software, http://www.caam.rice.edu/software/ARPACK/
+.. [2] R. B. Lehoucq, D. C. Sorensen, and C. Yang,  ARPACK USERS GUIDE:
+   Solution of Large Scale Eigenvalue Problems by Implicitly Restarted
+   Arnoldi Methods. SIAM, Philadelphia, PA, 1998.
+
+"""
+from .arpack import *
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_eigen/arpack/__pycache__/__init__.cpython-312.pyc b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_eigen/arpack/__pycache__/__init__.cpython-312.pyc
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diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_eigen/arpack/_arpacklib.cpython-312-x86_64-linux-gnu.so b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_eigen/arpack/_arpacklib.cpython-312-x86_64-linux-gnu.so
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--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_eigen/arpack/_arpacklib.cpython-312-x86_64-linux-gnu.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:be1f166a30bc7ab506a81922430d82b16ad2013cb0dfb7917ea15510106b46c3
+size 223721
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_eigen/arpack/arpack.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_eigen/arpack/arpack.py
new file mode 100644
index 0000000000000000000000000000000000000000..fb706eb66e2a69f55230970becdcdeaab3b45d03
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_eigen/arpack/arpack.py
@@ -0,0 +1,1789 @@
+"""
+Find a few eigenvectors and eigenvalues of a matrix.
+
+
+Uses ARPACK: https://github.com/opencollab/arpack-ng
+
+"""
+# Wrapper implementation notes
+#
+# ARPACK Entry Points
+# -------------------
+# The entry points to ARPACK are
+# - (s,d)seupd : single and double precision symmetric matrix
+# - (s,d,c,z)neupd: single,double,complex,double complex general matrix
+# This wrapper puts the *neupd (general matrix) interfaces in eigs()
+# and the *seupd (symmetric matrix) in eigsh().
+# There is no specialized interface for complex Hermitian matrices.
+# To find eigenvalues of a complex Hermitian matrix you
+# may use eigsh(), but eigsh() will simply call eigs()
+# and return the real part of the eigenvalues thus obtained.
+
+# Number of eigenvalues returned and complex eigenvalues
+# ------------------------------------------------------
+# The ARPACK nonsymmetric real and double interface (s,d)naupd return
+# eigenvalues and eigenvectors in real (float,double) arrays.
+# Since the eigenvalues and eigenvectors are, in general, complex
+# ARPACK puts the real and imaginary parts in consecutive entries
+# in real-valued arrays.   This wrapper puts the real entries
+# into complex data types and attempts to return the requested eigenvalues
+# and eigenvectors.
+
+
+# Solver modes
+# ------------
+# ARPACK and handle shifted and shift-inverse computations
+# for eigenvalues by providing a shift (sigma) and a solver.
+
+import numpy as np
+import warnings
+from scipy.sparse.linalg._interface import aslinearoperator, LinearOperator
+from scipy.sparse import eye_array, issparse
+from scipy.linalg import eig, eigh, lu_factor, lu_solve
+from scipy.linalg.lapack import HAS_ILP64
+from scipy.sparse._sputils import (
+    convert_pydata_sparse_to_scipy, isdense, is_pydata_spmatrix,
+)
+from scipy.sparse.linalg import gmres, splu
+
+from . import _arpacklib
+
+_int_dtype = np.int64 if HAS_ILP64 else np.int32
+
+__docformat__ = "restructuredtext en"
+
+__all__ = ['eigs', 'eigsh', 'ArpackError', 'ArpackNoConvergence']
+
+
+_type_conv = {'f': 's', 'd': 'd', 'F': 'c', 'D': 'z'}
+_ndigits = {'f': 5, 'd': 12, 'F': 5, 'D': 12}
+
+DNAUPD_ERRORS = {
+    0: "Normal exit.",
+    1: "Maximum number of iterations taken. "
+       "All possible eigenvalues of OP has been found. IPARAM(5) "
+       "returns the number of wanted converged Ritz values.",
+    2: "No longer an informational error. Deprecated starting "
+       "with release 2 of ARPACK.",
+    3: "No shifts could be applied during a cycle of the "
+       "Implicitly restarted Arnoldi iteration. One possibility "
+       "is to increase the size of NCV relative to NEV. ",
+    -1: "N must be positive.",
+    -2: "NEV must be positive.",
+    -3: "NCV-NEV >= 2 and less than or equal to N.",
+    -4: "The maximum number of Arnoldi update iterations allowed "
+        "must be greater than zero.",
+    -5: " WHICH must be one of 'LM', 'SM', 'LR', 'SR', 'LI', 'SI'",
+    -6: "BMAT must be one of 'I' or 'G'.",
+    -7: "Length of private work array WORKL is not sufficient.",
+    -8: "Error return from LAPACK eigenvalue calculation;",
+    -9: "Starting vector is zero.",
+    -10: "IPARAM(7) must be 1,2,3,4.",
+    -11: "IPARAM(7) = 1 and BMAT = 'G' are incompatible.",
+    -12: "IPARAM(1) must be equal to 0 or 1.",
+    -13: "NEV and WHICH = 'BE' are incompatible.",
+    -9999: "Could not build an Arnoldi factorization. "
+           "IPARAM(5) returns the size of the current Arnoldi "
+           "factorization. The user is advised to check that "
+           "enough workspace and array storage has been allocated."
+}
+
+SNAUPD_ERRORS = DNAUPD_ERRORS
+
+ZNAUPD_ERRORS = DNAUPD_ERRORS.copy()
+ZNAUPD_ERRORS[-10] = "IPARAM(7) must be 1,2,3."
+
+CNAUPD_ERRORS = ZNAUPD_ERRORS
+
+DSAUPD_ERRORS = {
+    0: "Normal exit.",
+    1: "Maximum number of iterations taken. "
+       "All possible eigenvalues of OP has been found.",
+    2: "No longer an informational error. Deprecated starting with "
+       "release 2 of ARPACK.",
+    3: "No shifts could be applied during a cycle of the Implicitly "
+       "restarted Arnoldi iteration. One possibility is to increase "
+       "the size of NCV relative to NEV. ",
+    -1: "N must be positive.",
+    -2: "NEV must be positive.",
+    -3: "NCV must be greater than NEV and less than or equal to N.",
+    -4: "The maximum number of Arnoldi update iterations allowed "
+        "must be greater than zero.",
+    -5: "WHICH must be one of 'LM', 'SM', 'LA', 'SA' or 'BE'.",
+    -6: "BMAT must be one of 'I' or 'G'.",
+    -7: "Length of private work array WORKL is not sufficient.",
+    -8: "Error return from trid. eigenvalue calculation; "
+        "Informational error from LAPACK routine dsteqr .",
+    -9: "Starting vector is zero.",
+    -10: "IPARAM(7) must be 1,2,3,4,5.",
+    -11: "IPARAM(7) = 1 and BMAT = 'G' are incompatible.",
+    -12: "IPARAM(1) must be equal to 0 or 1.",
+    -13: "NEV and WHICH = 'BE' are incompatible. ",
+    -9999: "Could not build an Arnoldi factorization. "
+           "IPARAM(5) returns the size of the current Arnoldi "
+           "factorization. The user is advised to check that "
+           "enough workspace and array storage has been allocated.",
+}
+
+SSAUPD_ERRORS = DSAUPD_ERRORS
+
+DNEUPD_ERRORS = {
+    0: "Normal exit.",
+    1: "The Schur form computed by LAPACK routine dlahqr "
+       "could not be reordered by LAPACK routine dtrsen. "
+       "Re-enter subroutine dneupd  with IPARAM(5)NCV and "
+       "increase the size of the arrays DR and DI to have "
+       "dimension at least dimension NCV and allocate at least NCV "
+       "columns for Z. NOTE: Not necessary if Z and V share "
+       "the same space. Please notify the authors if this error"
+       "occurs.",
+    -1: "N must be positive.",
+    -2: "NEV must be positive.",
+    -3: "NCV-NEV >= 2 and less than or equal to N.",
+    -5: "WHICH must be one of 'LM', 'SM', 'LR', 'SR', 'LI', 'SI'",
+    -6: "BMAT must be one of 'I' or 'G'.",
+    -7: "Length of private work WORKL array is not sufficient.",
+    -8: "Error return from calculation of a real Schur form. "
+        "Informational error from LAPACK routine dlahqr .",
+    -9: "Error return from calculation of eigenvectors. "
+        "Informational error from LAPACK routine dtrevc.",
+    -10: "IPARAM(7) must be 1,2,3,4.",
+    -11: "IPARAM(7) = 1 and BMAT = 'G' are incompatible.",
+    -12: "HOWMNY = 'S' not yet implemented",
+    -13: "HOWMNY must be one of 'A' or 'P' if RVEC = .true.",
+    -14: "DNAUPD  did not find any eigenvalues to sufficient "
+         "accuracy.",
+    -15: "DNEUPD got a different count of the number of converged "
+         "Ritz values than DNAUPD got.  This indicates the user "
+         "probably made an error in passing data from DNAUPD to "
+         "DNEUPD or that the data was modified before entering "
+         "DNEUPD",
+}
+
+SNEUPD_ERRORS = DNEUPD_ERRORS.copy()
+SNEUPD_ERRORS[1] = ("The Schur form computed by LAPACK routine slahqr "
+                    "could not be reordered by LAPACK routine strsen . "
+                    "Re-enter subroutine dneupd  with IPARAM(5)=NCV and "
+                    "increase the size of the arrays DR and DI to have "
+                    "dimension at least dimension NCV and allocate at least "
+                    "NCV columns for Z. NOTE: Not necessary if Z and V share "
+                    "the same space. Please notify the authors if this error "
+                    "occurs.")
+SNEUPD_ERRORS[-14] = ("SNAUPD did not find any eigenvalues to sufficient "
+                      "accuracy.")
+SNEUPD_ERRORS[-15] = ("SNEUPD got a different count of the number of "
+                      "converged Ritz values than SNAUPD got.  This indicates "
+                      "the user probably made an error in passing data from "
+                      "SNAUPD to SNEUPD or that the data was modified before "
+                      "entering SNEUPD")
+
+ZNEUPD_ERRORS = {0: "Normal exit.",
+                 1: "The Schur form computed by LAPACK routine csheqr "
+                    "could not be reordered by LAPACK routine ztrsen. "
+                    "Re-enter subroutine zneupd with IPARAM(5)=NCV and "
+                    "increase the size of the array D to have "
+                    "dimension at least dimension NCV and allocate at least "
+                    "NCV columns for Z. NOTE: Not necessary if Z and V share "
+                    "the same space. Please notify the authors if this error "
+                    "occurs.",
+                 -1: "N must be positive.",
+                 -2: "NEV must be positive.",
+                 -3: "NCV-NEV >= 1 and less than or equal to N.",
+                 -5: "WHICH must be one of 'LM', 'SM', 'LR', 'SR', 'LI', 'SI'",
+                 -6: "BMAT must be one of 'I' or 'G'.",
+                 -7: "Length of private work WORKL array is not sufficient.",
+                 -8: "Error return from LAPACK eigenvalue calculation. "
+                     "This should never happened.",
+                 -9: "Error return from calculation of eigenvectors. "
+                     "Informational error from LAPACK routine ztrevc.",
+                 -10: "IPARAM(7) must be 1,2,3",
+                 -11: "IPARAM(7) = 1 and BMAT = 'G' are incompatible.",
+                 -12: "HOWMNY = 'S' not yet implemented",
+                 -13: "HOWMNY must be one of 'A' or 'P' if RVEC = .true.",
+                 -14: "ZNAUPD did not find any eigenvalues to sufficient "
+                      "accuracy.",
+                 -15: "ZNEUPD got a different count of the number of "
+                      "converged Ritz values than ZNAUPD got.  This "
+                      "indicates the user probably made an error in passing "
+                      "data from ZNAUPD to ZNEUPD or that the data was "
+                      "modified before entering ZNEUPD"
+                 }
+
+CNEUPD_ERRORS = ZNEUPD_ERRORS.copy()
+CNEUPD_ERRORS[-14] = ("CNAUPD did not find any eigenvalues to sufficient "
+                      "accuracy.")
+CNEUPD_ERRORS[-15] = ("CNEUPD got a different count of the number of "
+                      "converged Ritz values than CNAUPD got.  This indicates "
+                      "the user probably made an error in passing data from "
+                      "CNAUPD to CNEUPD or that the data was modified before "
+                      "entering CNEUPD")
+
+DSEUPD_ERRORS = {
+    0: "Normal exit.",
+    -1: "N must be positive.",
+    -2: "NEV must be positive.",
+    -3: "NCV must be greater than NEV and less than or equal to N.",
+    -5: "WHICH must be one of 'LM', 'SM', 'LA', 'SA' or 'BE'.",
+    -6: "BMAT must be one of 'I' or 'G'.",
+    -7: "Length of private work WORKL array is not sufficient.",
+    -8: ("Error return from trid. eigenvalue calculation; "
+         "Information error from LAPACK routine dsteqr."),
+    -9: "Starting vector is zero.",
+    -10: "IPARAM(7) must be 1,2,3,4,5.",
+    -11: "IPARAM(7) = 1 and BMAT = 'G' are incompatible.",
+    -12: "NEV and WHICH = 'BE' are incompatible.",
+    -14: "DSAUPD  did not find any eigenvalues to sufficient accuracy.",
+    -15: "HOWMNY must be one of 'A' or 'S' if RVEC = .true.",
+    -16: "HOWMNY = 'S' not yet implemented",
+    -17: ("DSEUPD  got a different count of the number of converged "
+          "Ritz values than DSAUPD  got.  This indicates the user "
+          "probably made an error in passing data from DSAUPD  to "
+          "DSEUPD  or that the data was modified before entering  "
+          "DSEUPD.")
+}
+
+SSEUPD_ERRORS = DSEUPD_ERRORS.copy()
+SSEUPD_ERRORS[-14] = ("SSAUPD  did not find any eigenvalues "
+                      "to sufficient accuracy.")
+SSEUPD_ERRORS[-17] = ("SSEUPD  got a different count of the number of "
+                      "converged "
+                      "Ritz values than SSAUPD  got.  This indicates the user "
+                      "probably made an error in passing data from SSAUPD  to "
+                      "SSEUPD  or that the data was modified before entering  "
+                      "SSEUPD.")
+
+_SAUPD_ERRORS = {'d': DSAUPD_ERRORS,
+                 's': SSAUPD_ERRORS}
+_NAUPD_ERRORS = {'d': DNAUPD_ERRORS,
+                 's': SNAUPD_ERRORS,
+                 'z': ZNAUPD_ERRORS,
+                 'c': CNAUPD_ERRORS}
+_SEUPD_ERRORS = {'d': DSEUPD_ERRORS,
+                 's': SSEUPD_ERRORS}
+_NEUPD_ERRORS = {'d': DNEUPD_ERRORS,
+                 's': SNEUPD_ERRORS,
+                 'z': ZNEUPD_ERRORS,
+                 'c': CNEUPD_ERRORS}
+
+# accepted values of parameter WHICH in _SEUPD
+_SEUPD_WHICH = ['LM', 'SM', 'LA', 'SA', 'BE']
+
+# accepted values of parameter WHICH in _NAUPD
+_NEUPD_WHICH = ['LM', 'SM', 'LR', 'SR', 'LI', 'SI']
+
+# The enum values for the parameter WHICH in _NAUPD and _SEUPD
+WHICH_DICT = {
+    'LM': 0, 'SM': 1, 'LR': 2, 'SR': 3, 'LI': 4, 'SI': 5, 'LA': 6, 'SA': 7, 'BE': 8
+}
+
+# The enum values for the parameter HOWMNY in _NEUPD and _SEUPD
+HOWMNY_DICT = {'A': 0, 'P': 1, 'S': 2}
+
+class ArpackError(RuntimeError):
+    """
+    ARPACK error.
+
+    Parameters
+    ----------
+    info : int or str
+        Key for `infodict` to get error message.
+    infodict : dict, optional
+        Dictionary mapping `info` keys to error messages.
+    """
+
+    def __init__(self, info, infodict=None):
+        if infodict is None:
+            infodict = _NAUPD_ERRORS
+
+        msg = infodict.get(info, "Unknown error")
+        super().__init__(f"ARPACK error {info}: {msg}")
+
+
+
+class ArpackNoConvergence(ArpackError):
+    """
+    ARPACK iteration did not converge.
+
+    Parameters
+    ----------
+    msg : str
+        Error message.
+    eigenvalues : ndarray
+        Conveged eigenvalues.
+    eigenvectors : ndarray
+        Converged eigenvectors.
+
+    Attributes
+    ----------
+    eigenvalues : ndarray
+        Partial result. Converged eigenvalues.
+    eigenvectors : ndarray
+        Partial result. Converged eigenvectors.
+
+    """
+
+    def __init__(self, msg, eigenvalues, eigenvectors):
+        ArpackError.__init__(self, -1, {-1: msg})
+        self.eigenvalues = eigenvalues
+        self.eigenvectors = eigenvectors
+
+
+def choose_ncv(k):
+    """
+    Choose number of lanczos vectors based on target number
+    of singular/eigen values and vectors to compute, k.
+    """
+    return max(2 * k + 1, 20)
+
+
+class _ArpackParams:
+    def __init__(self, n, k, tp, rng, mode=1, sigma=None, ncv=None, v0=None,
+                 maxiter=None, which="LM", tol=0):
+        if k <= 0:
+            raise ValueError(f"k must be positive, k={k}")
+
+        if maxiter is None:
+            maxiter = n * 10
+        if maxiter <= 0:
+            raise ValueError(f"maxiter must be positive, maxiter={maxiter}")
+
+        if tp not in 'fdFD':
+            # Use `float64` libraries from integer dtypes.
+            if np.can_cast(tp, 'd'):
+                tp = 'd'
+            else:
+                raise ValueError("matrix type must be 'f', 'd', 'F', or 'D'")
+
+        if v0 is not None:
+            # ARPACK overwrites its initial resid,  make a copy
+            self.resid = np.array(v0, copy=True, dtype=tp)
+            info = 1
+        else:
+            # ARPACK will use a random initial vector.
+            self.resid = rng.uniform(low=-1.0, high=1.0, size=[n]).astype(tp)
+            info = 0
+
+        if sigma is None:
+            #sigma not used
+            self.sigma = 0
+        else:
+            self.sigma = sigma
+
+        if ncv is None:
+            ncv = choose_ncv(k)
+        self.ncv = min(ncv, n)
+        self.n = n
+        self.v = np.zeros((n, ncv), tp)  # holds Ritz vectors
+        self.which = which
+
+        # set solver mode and parameters
+        self.mode = mode
+        self.arpack_dict = {
+            'tol': tol,
+            'getv0_rnorm0': 0.0,
+            'aitr_betaj': 0.0,
+            'aitr_rnorm1': 0.0,
+            'aitr_wnorm': 0.0,
+            'aup2_rnorm': 0.0,
+            'ido': 0,
+            'which': WHICH_DICT[which],
+            'bmat': 0,
+            'info': info,
+            'iter': 0,
+            'maxiter': int(maxiter),
+            'mode': mode,
+            'n': n,
+            'nconv': 0,
+            'ncv': self.ncv,
+            'nev': k,
+            'np': 0,
+            'shift': 1,
+            'getv0_first': 0,
+            'getv0_iter': 0,
+            'getv0_itry': 0,
+            'getv0_orth': 0,
+            'aitr_iter': 0,
+            'aitr_j': 0,
+            'aitr_orth1': 0,
+            'aitr_orth2': 0,
+            'aitr_restart': 0,
+            'aitr_step3': 0,
+            'aitr_step4': 0,
+            'aitr_ierr': 0,
+            'aup2_initv': 0,
+            'aup2_iter': 0,
+            'aup2_getv0': 0,
+            'aup2_cnorm': 0,
+            'aup2_kplusp': 0,
+            'aup2_nev': 0,
+            'aup2_nev0': 0,
+            'aup2_np0': 0,
+            'aup2_numcnv': 0,
+            'aup2_update': 0,
+            'aup2_ushift': 0,
+        }
+
+        self.k = k
+        self.tp = tp
+        self.converged = False
+
+    def _raise_no_convergence(self):
+        msg = "No convergence (%d iterations, %d/%d eigenvectors converged)"
+        k_ok = self.arpack_dict['nconv']
+        num_iter = self.arpack_dict['iter']
+        try:
+            ev, vec = self.extract(True)
+        except ArpackError as err:
+            msg = f"{msg} [{err}]"
+            ev = np.zeros((0,))
+            vec = np.zeros((self.n, 0))
+            k_ok = 0
+        raise ArpackNoConvergence(f"No convergence ({num_iter} iterations, "
+                                  f"{k_ok}/{self.k} eigenvectors converged)",
+                                  ev, vec)
+
+
+class _SymmetricArpackParams(_ArpackParams):
+    def __init__(self, n, k, tp, matvec, mode=1, M_matvec=None, Minv_matvec=None,
+                 sigma=None, ncv=None, v0=None, maxiter=None, which="LM", tol=0,
+                 rng=None):
+        # The following modes are supported:
+        #  mode = 1:
+        #    Solve the standard eigenvalue problem:
+        #      A*x = lambda*x :
+        #       A - symmetric
+        #    Arguments should be
+        #       matvec      = left multiplication by A
+        #       M_matvec    = None [not used]
+        #       Minv_matvec = None [not used]
+        #
+        #  mode = 2:
+        #    Solve the general eigenvalue problem:
+        #      A*x = lambda*M*x
+        #       A - symmetric
+        #       M - symmetric positive definite
+        #    Arguments should be
+        #       matvec      = left multiplication by A
+        #       M_matvec    = left multiplication by M
+        #       Minv_matvec = left multiplication by M^-1
+        #
+        #  mode = 3:
+        #    Solve the general eigenvalue problem in shift-invert mode:
+        #      A*x = lambda*M*x
+        #       A - symmetric
+        #       M - symmetric positive semi-definite
+        #    Arguments should be
+        #       matvec      = None [not used]
+        #       M_matvec    = left multiplication by M
+        #                     or None, if M is the identity
+        #       Minv_matvec = left multiplication by [A-sigma*M]^-1
+        #
+        #  mode = 4:
+        #    Solve the general eigenvalue problem in Buckling mode:
+        #      A*x = lambda*AG*x
+        #       A  - symmetric positive semi-definite
+        #       AG - symmetric indefinite
+        #    Arguments should be
+        #       matvec      = left multiplication by A
+        #       M_matvec    = None [not used]
+        #       Minv_matvec = left multiplication by [A-sigma*AG]^-1
+        #
+        #  mode = 5:
+        #    Solve the general eigenvalue problem in Cayley-transformed mode:
+        #      A*x = lambda*M*x
+        #       A - symmetric
+        #       M - symmetric positive semi-definite
+        #    Arguments should be
+        #       matvec      = left multiplication by A
+        #       M_matvec    = left multiplication by M
+        #                     or None, if M is the identity
+        #       Minv_matvec = left multiplication by [A-sigma*M]^-1
+        if mode == 1:
+            if matvec is None:
+                raise ValueError("matvec must be specified for mode=1")
+            if M_matvec is not None:
+                raise ValueError("M_matvec cannot be specified for mode=1")
+            if Minv_matvec is not None:
+                raise ValueError("Minv_matvec cannot be specified for mode=1")
+
+            self.OP = matvec
+            self.B = lambda x: x
+            self.bmat = 'I'
+        elif mode == 2:
+            if matvec is None:
+                raise ValueError("matvec must be specified for mode=2")
+            if M_matvec is None:
+                raise ValueError("M_matvec must be specified for mode=2")
+            if Minv_matvec is None:
+                raise ValueError("Minv_matvec must be specified for mode=2")
+
+            self.OP = lambda x: Minv_matvec(matvec(x))
+            self.OPa = Minv_matvec
+            self.OPb = matvec
+            self.B = M_matvec
+            self.bmat = 'G'
+        elif mode == 3:
+            if matvec is not None:
+                raise ValueError("matvec must not be specified for mode=3")
+            if Minv_matvec is None:
+                raise ValueError("Minv_matvec must be specified for mode=3")
+
+            if M_matvec is None:
+                self.OP = Minv_matvec
+                self.OPa = Minv_matvec
+                self.B = lambda x: x
+                self.bmat = 'I'
+            else:
+                self.OP = lambda x: Minv_matvec(M_matvec(x))
+                self.OPa = Minv_matvec
+                self.B = M_matvec
+                self.bmat = 'G'
+        elif mode == 4:
+            if matvec is None:
+                raise ValueError("matvec must be specified for mode=4")
+            if M_matvec is not None:
+                raise ValueError("M_matvec must not be specified for mode=4")
+            if Minv_matvec is None:
+                raise ValueError("Minv_matvec must be specified for mode=4")
+            self.OPa = Minv_matvec
+            self.OP = lambda x: self.OPa(matvec(x))
+            self.B = matvec
+            self.bmat = 'G'
+        elif mode == 5:
+            if matvec is None:
+                raise ValueError("matvec must be specified for mode=5")
+            if Minv_matvec is None:
+                raise ValueError("Minv_matvec must be specified for mode=5")
+
+            self.OPa = Minv_matvec
+            self.A_matvec = matvec
+
+            if M_matvec is None:
+                self.OP = lambda x: Minv_matvec(matvec(x) + sigma * x)
+                self.B = lambda x: x
+                self.bmat = 'I'
+            else:
+                self.OP = lambda x: Minv_matvec(matvec(x)
+                                                + sigma * M_matvec(x))
+                self.B = M_matvec
+                self.bmat = 'G'
+        else:
+            raise ValueError(f"mode={mode} not implemented")
+
+        if which not in _SEUPD_WHICH:
+            raise ValueError(f"which must be one of {' '.join(_SEUPD_WHICH)}")
+        if k >= n:
+            raise ValueError(f"k must be less than ndim(A), k={k}")
+
+        self.rng = np.random.default_rng(rng)
+        _ArpackParams.__init__(self, n, k, tp, self.rng, mode, sigma, ncv, v0,
+                               maxiter, which, tol)
+
+        self.arpack_dict['bmat'] = 0 if self.bmat == 'I' else 1
+
+        if self.ncv > n or self.ncv <= k:
+            raise ValueError(f"ncv must be k<ncv<=n, ncv={self.ncv}")
+
+        self.workd = np.zeros(3 * n, dtype=self.tp)
+        self.workl = np.zeros(self.ncv * (self.ncv + 8), dtype=self.tp)
+
+        ltr = _type_conv[self.tp]
+        if ltr not in ["s", "d"]:
+            raise ValueError("Input matrix is not real-valued.")
+
+        self._arpack_solver = _arpacklib.__dict__[ltr + 'saupd_wrap']
+        self._arpack_extract = _arpacklib.__dict__[ltr + 'seupd_wrap']
+
+        self.iterate_infodict = _SAUPD_ERRORS[ltr]
+        self.extract_infodict = _SEUPD_ERRORS[ltr]
+
+        self.ipntr = np.zeros(11, dtype=_int_dtype)
+
+    def iterate(self):
+        self._arpack_solver(self.arpack_dict, self.resid, self.v, self.ipntr,
+                            self.workd, self.workl)
+
+        xslice = slice(self.ipntr[0], self.ipntr[0] + self.n)
+        yslice = slice(self.ipntr[1], self.ipntr[1] + self.n)
+        if self.arpack_dict['ido'] == 1:
+            # compute y = Op*x
+            if self.mode == 1:
+                self.workd[yslice] = self.OP(self.workd[xslice])
+            elif self.mode == 2:
+                self.workd[xslice] = self.OPb(self.workd[xslice])
+                self.workd[yslice] = self.OPa(self.workd[xslice])
+            elif self.mode == 5:
+                Bxslice = slice(self.ipntr[2], self.ipntr[2] + self.n)
+                Ax = self.A_matvec(self.workd[xslice])
+                self.workd[yslice] = self.OPa(Ax + (self.sigma *
+                                                    self.workd[Bxslice]))
+            else:
+                Bxslice = slice(self.ipntr[2], self.ipntr[2] + self.n)
+                self.workd[yslice] = self.OPa(self.workd[Bxslice])
+
+        elif self.arpack_dict['ido'] == 2:
+            self.workd[yslice] = self.B(self.workd[xslice])
+
+        elif self.arpack_dict['ido'] == 3:
+            raise ValueError("ARPACK requested user shifts. Assure ISHIFT==0")
+
+        elif self.arpack_dict['ido'] == 4:
+            # Generate random vector into resid
+            self.resid[:] = self.rng.uniform(low=-1.0, high=1.0,
+                                             size=[self.n]).astype(self.tp)
+
+        elif self.arpack_dict['ido'] == 5:
+            self.workd[yslice] = self.OP(self.workd[xslice])
+
+        else:
+            self.converged = True
+
+            if self.arpack_dict['info'] == 0:
+                pass
+            elif self.arpack_dict['info'] == 1:
+                self._raise_no_convergence()
+            else:
+                raise ArpackError(self.arpack_dict['info'],
+                                  infodict=self.iterate_infodict)
+
+    def extract(self, return_eigenvectors):
+        rvec = return_eigenvectors
+        ierr = 0
+        self.arpack_dict['info'] = 0  # Clear, if any, previous error from naupd
+        howmny = HOWMNY_DICT["A"]  # return all eigenvectors
+        sselect = np.zeros(self.ncv, dtype=_int_dtype)
+        d = np.zeros(self.k, dtype=self.tp)
+        z = np.zeros((self.n, self.ncv), dtype=self.tp, order='F')
+
+        self._arpack_extract(
+            self.arpack_dict, rvec, howmny, sselect, d, z, self.sigma,
+            self.resid, self.v, self.ipntr, self.workd, #[0:2 * self.n],
+            self.workl
+        )
+
+        ierr = self.arpack_dict['info']
+        if ierr != 0:
+            raise ArpackError(ierr, infodict=self.extract_infodict)
+        k_ok = self.arpack_dict['nconv']
+        d = d[:k_ok]
+
+        if return_eigenvectors:
+            z = z[:, :k_ok].copy(order='C')
+            return d, z
+        else:
+            return d
+
+
+class _UnsymmetricArpackParams(_ArpackParams):
+    def __init__(self, n, k, tp, matvec, mode=1, M_matvec=None,
+                 Minv_matvec=None, sigma=None,
+                 ncv=None, v0=None, maxiter=None, which="LM", tol=0, rng=None):
+        # The following modes are supported:
+        #  mode = 1:
+        #    Solve the standard eigenvalue problem:
+        #      A*x = lambda*x
+        #       A - square matrix
+        #    Arguments should be
+        #       matvec      = left multiplication by A
+        #       M_matvec    = None [not used]
+        #       Minv_matvec = None [not used]
+        #
+        #  mode = 2:
+        #    Solve the generalized eigenvalue problem:
+        #      A*x = lambda*M*x
+        #       A - square matrix
+        #       M - symmetric, positive semi-definite
+        #    Arguments should be
+        #       matvec      = left multiplication by A
+        #       M_matvec    = left multiplication by M
+        #       Minv_matvec = left multiplication by M^-1
+        #
+        #  mode = 3,4:
+        #    Solve the general eigenvalue problem in shift-invert mode:
+        #      A*x = lambda*M*x
+        #       A - square matrix
+        #       M - symmetric, positive semi-definite
+        #    Arguments should be
+        #       matvec      = None [not used]
+        #       M_matvec    = left multiplication by M
+        #                     or None, if M is the identity
+        #       Minv_matvec = left multiplication by [A-sigma*M]^-1
+        #    if A is real and mode==3, use the real part of Minv_matvec
+        #    if A is real and mode==4, use the imag part of Minv_matvec
+        #    if A is complex and mode==3,
+        #       use real and imag parts of Minv_matvec
+        if mode == 1:
+            if matvec is None:
+                raise ValueError("matvec must be specified for mode=1")
+            if M_matvec is not None:
+                raise ValueError("M_matvec cannot be specified for mode=1")
+            if Minv_matvec is not None:
+                raise ValueError("Minv_matvec cannot be specified for mode=1")
+
+            self.OP = matvec
+            self.B = lambda x: x
+            self.bmat = 'I'
+        elif mode == 2:
+            if matvec is None:
+                raise ValueError("matvec must be specified for mode=2")
+            if M_matvec is None:
+                raise ValueError("M_matvec must be specified for mode=2")
+            if Minv_matvec is None:
+                raise ValueError("Minv_matvec must be specified for mode=2")
+
+            self.OP = lambda x: Minv_matvec(matvec(x))
+            self.OPa = Minv_matvec
+            self.OPb = matvec
+            self.B = M_matvec
+            self.bmat = 'G'
+        elif mode in (3, 4):
+            if matvec is None:
+                raise ValueError("matvec must be specified "
+                                 "for mode in (3,4)")
+            if Minv_matvec is None:
+                raise ValueError("Minv_matvec must be specified "
+                                 "for mode in (3,4)")
+
+            self.matvec = matvec
+            if tp in 'DF':  # complex type
+                if mode == 3:
+                    self.OPa = Minv_matvec
+                else:
+                    raise ValueError("mode=4 invalid for complex A")
+            else:  # real type
+                if mode == 3:
+                    self.OPa = lambda x: np.real(Minv_matvec(x))
+                else:
+                    self.OPa = lambda x: np.imag(Minv_matvec(x))
+            if M_matvec is None:
+                self.B = lambda x: x
+                self.bmat = 'I'
+                self.OP = self.OPa
+            else:
+                self.B = M_matvec
+                self.bmat = 'G'
+                self.OP = lambda x: self.OPa(M_matvec(x))
+        else:
+            raise ValueError(f"mode={mode} not implemented")
+
+        if which not in _NEUPD_WHICH:
+            raise ValueError("Parameter which must be one of"
+                             f" {' '.join(_NEUPD_WHICH)}")
+        if k >= n - 1:
+            raise ValueError(f"k must be less than ndim(A)-1, k={k}")
+
+        self.rng = np.random.default_rng(rng)
+        _ArpackParams.__init__(self, n, k, tp, rng, mode, sigma, ncv, v0, maxiter,
+                               which, tol)
+
+        self.arpack_dict['bmat'] = 0 if self.bmat == 'I' else 1
+
+        if self.ncv > n or self.ncv <= k + 1:
+            raise ValueError(f"ncv must be k+1<ncv<=n, ncv={self.ncv}")
+
+        self.workd = np.zeros(3 * n, dtype=self.tp)
+        self.workl = np.zeros(3 * self.ncv * (self.ncv + 2), dtype=self.tp)
+
+        ltr = _type_conv[self.tp]
+        self._arpack_solver = _arpacklib.__dict__[ltr + 'naupd_wrap']
+        self._arpack_extract = _arpacklib.__dict__[ltr + 'neupd_wrap']
+
+        self.iterate_infodict = _NAUPD_ERRORS[ltr]
+        self.extract_infodict = _NEUPD_ERRORS[ltr]
+
+        self.ipntr = np.zeros(14, dtype=_int_dtype)
+
+        if self.tp in 'FD':
+            self.rwork = np.zeros(self.ncv, dtype=self.tp.lower())
+        else:
+            self.rwork = None
+
+    def iterate(self):
+        if self.tp in 'fd':
+            self._arpack_solver(
+                self.arpack_dict, self.resid, self.v, self.ipntr, self.workd,
+                self.workl
+            )
+
+        else:
+            self._arpack_solver(
+                self.arpack_dict, self.resid, self.v, self.ipntr, self.workd,
+                self.workl, self.rwork
+            )
+
+        xslice = slice(self.ipntr[0], self.ipntr[0] + self.n)
+        yslice = slice(self.ipntr[1], self.ipntr[1] + self.n)
+
+        if self.arpack_dict['ido'] == 1:
+            # compute y = Op*x
+            if self.mode in (1, 2):
+                self.workd[yslice] = self.OP(self.workd[xslice])
+            else:
+                Bxslice = slice(self.ipntr[2], self.ipntr[2] + self.n)
+                self.workd[yslice] = self.OPa(self.workd[Bxslice])
+
+        elif self.arpack_dict['ido'] == 2:
+            self.workd[yslice] = self.B(self.workd[xslice])
+
+        elif self.arpack_dict['ido'] == 3:
+            raise ValueError("ARPACK requested user shifts. Assure ISHIFT==0")
+
+        elif self.arpack_dict['ido'] == 4:
+            if self.tp in 'fd':
+                # Generate random vector into resid
+                self.resid[:] = self.rng.uniform(low=-1.0, high=1.0,
+                                                 size=[self.n]).astype(self.tp)
+            else:
+                # Generate complex random vector into resid
+                self.resid[:] = self.rng.uniform(low=-1.0, high=1.0, size=[self.n, 2]
+                ).view(np.complex128).astype(self.tp).ravel()
+
+        elif self.arpack_dict['ido'] == 5:
+            self.workd[yslice] = self.OP(self.workd[xslice])
+
+        else:
+            self.converged = True
+
+            if self.arpack_dict['info'] == 0:
+                pass
+            elif self.arpack_dict['info'] == 1:
+                self._raise_no_convergence()
+            else:
+                raise ArpackError(info=self.arpack_dict['info'],
+                                  infodict=self.iterate_infodict)
+
+    def extract(self, return_eigenvectors):
+        k, n = self.k, self.n
+
+        ierr = 0
+        self.arpack_dict['info'] = 0  # Clear, if any, previous error from naupd
+        howmny = HOWMNY_DICT['A']  # return all eigenvectors
+        sselect = np.zeros(self.ncv, dtype=_int_dtype)
+        sigmar = float(np.real(self.sigma))
+        sigmai = float(np.imag(self.sigma))
+        workev = np.zeros(3 * self.ncv, self.tp)
+
+        if self.tp in 'fd':
+            dr = np.zeros([k + 1], dtype=self.tp)
+            di = np.zeros([k + 1], dtype=self.tp)
+            # Using a Fortran ordered array for NumPy parse the result correctly
+            zr = np.zeros([n, k + 1], dtype=self.tp, order='F')
+
+            # ARPACK _neupd call
+            self._arpack_extract(
+                self.arpack_dict, return_eigenvectors, howmny, sselect, dr, di,
+                zr, sigmar, sigmai, workev, self.resid, self.v, self.ipntr,
+                self.workd, self.workl
+            )
+
+            ierr = self.arpack_dict['info']
+
+            if ierr != 0:
+                raise ArpackError(ierr, infodict=self.extract_infodict)
+            nreturned = self.arpack_dict['nconv']  # number of good eigs returned
+
+            # Build complex eigenvalues from real and imaginary parts
+            d = dr + 1.0j * di
+
+            # Arrange the eigenvectors: complex eigenvectors are stored as
+            # real,imaginary in consecutive columns
+            z = zr.astype(self.tp.upper())
+
+            # The ARPACK nonsymmetric real and double interface (s,d)naupd
+            # return eigenvalues and eigenvectors in real (float,double)
+            # arrays.
+
+            # Efficiency: this should check that return_eigenvectors == True
+            #  before going through this construction.
+            if sigmai == 0:
+                i = 0
+                while i <= k:
+                    # check if complex
+                    if abs(d[i].imag) != 0:
+                        # this is a complex conjugate pair with eigenvalues
+                        # in consecutive columns
+                        if i < k:
+                            z[:, i] = zr[:, i] + 1.0j * zr[:, i + 1]
+                            z[:, i + 1] = z[:, i].conjugate()
+                            i += 1
+                        else:
+                            #last eigenvalue is complex: the imaginary part of
+                            # the eigenvector has not been returned
+                            #this can only happen if nreturned > k, so we'll
+                            # throw out this case.
+                            nreturned -= 1
+                    i += 1
+
+            else:
+                # real matrix, mode 3 or 4, imag(sigma) is nonzero:
+                # see remark 3 in <s,d>neupd.f
+                # Build complex eigenvalues from real and imaginary parts
+                i = 0
+                while i <= k:
+                    if abs(d[i].imag) == 0:
+                        d[i] = np.dot(zr[:, i], self.matvec(zr[:, i]))
+                    else:
+                        if i < k:
+                            z[:, i] = zr[:, i] + 1.0j * zr[:, i + 1]
+                            z[:, i + 1] = z[:, i].conjugate()
+                            d[i] = ((np.dot(zr[:, i],
+                                            self.matvec(zr[:, i]))
+                                     + np.dot(zr[:, i + 1],
+                                              self.matvec(zr[:, i + 1])))
+                                    + 1j * (np.dot(zr[:, i],
+                                                   self.matvec(zr[:, i + 1]))
+                                            - np.dot(zr[:, i + 1],
+                                                     self.matvec(zr[:, i]))))
+                            d[i + 1] = d[i].conj()
+                            i += 1
+                        else:
+                            #last eigenvalue is complex: the imaginary part of
+                            # the eigenvector has not been returned
+                            #this can only happen if nreturned > k, so we'll
+                            # throw out this case.
+                            nreturned -= 1
+                    i += 1
+
+            # Now we have k+1 possible eigenvalues and eigenvectors
+            # Return the ones specified by the keyword "which"
+
+            if nreturned <= k:
+                # we got less or equal as many eigenvalues we wanted
+                d = d[:nreturned]
+                z = z[:, :nreturned]
+            else:
+                # we got one extra eigenvalue (likely a cc pair, but which?)
+                if self.mode in (1, 2):
+                    rd = d
+                elif self.mode in (3, 4):
+                    rd = 1 / (d - self.sigma)
+
+                if self.which in ['LR', 'SR']:
+                    ind = np.argsort(rd.real)
+                elif self.which in ['LI', 'SI']:
+                    # for LI,SI ARPACK returns largest,smallest
+                    # abs(imaginary) (complex pairs come together)
+                    ind = np.argsort(abs(rd.imag))
+                else:
+                    ind = np.argsort(abs(rd))
+
+                if self.which in ['LR', 'LM', 'LI']:
+                    ind = ind[-k:][::-1]
+                elif self.which in ['SR', 'SM', 'SI']:
+                    ind = ind[:k]
+
+                d = d[ind]
+                z = z[:, ind]
+        else:
+            d = np.zeros([k], dtype=self.tp)
+            z = np.zeros([n, k], dtype=self.tp, order='F')
+            self._arpack_extract(
+                self.arpack_dict, return_eigenvectors, howmny, sselect, d, z,
+                self.sigma, workev, self.resid, self.v, self.ipntr, self.workd,
+                self.workl, self.rwork)
+
+            ierr = self.arpack_dict['info']
+
+            if ierr != 0:
+                raise ArpackError(ierr, infodict=self.extract_infodict)
+
+            k_ok = self.arpack_dict['nconv']
+            d = d[:k_ok]
+            z = z[:, :k_ok]
+
+        if return_eigenvectors:
+            return d, z
+        else:
+            return d
+
+class SpLuInv(LinearOperator):
+    """
+    SpLuInv:
+       helper class to repeatedly solve M*x=b
+       using a sparse LU-decomposition of M
+    """
+
+    def __init__(self, M):
+        self.M_lu = splu(M)
+        super().__init__(dtype=M.dtype, shape=M.shape)
+        self.isreal = not np.issubdtype(self.dtype, np.complexfloating)
+
+    def _matvec(self, x):
+        # careful here: splu.solve will throw away imaginary
+        # part of x if M is real
+        x = np.asarray(x)
+        if self.isreal and np.issubdtype(x.dtype, np.complexfloating):
+            return (self.M_lu.solve(np.real(x).astype(self.dtype))
+                    + 1j * self.M_lu.solve(np.imag(x).astype(self.dtype)))
+        else:
+            return self.M_lu.solve(x.astype(self.dtype))
+
+
+class LuInv(LinearOperator):
+    """
+    LuInv:
+       helper class to repeatedly solve M*x=b
+       using an LU-decomposition of M
+    """
+
+    def __init__(self, M):
+        self.M_lu = lu_factor(M)
+        super().__init__(dtype=M.dtype, shape=M.shape)
+
+    def _matvec(self, x):
+        return lu_solve(self.M_lu, x)
+
+
+def gmres_loose(A, b, tol):
+    """
+    gmres with looser termination condition.
+    """
+    b = np.asarray(b)
+    min_tol = 1000 * np.sqrt(b.size) * np.finfo(b.dtype).eps
+    return gmres(A, b, rtol=max(tol, min_tol), atol=0)
+
+
+class IterInv(LinearOperator):
+    """
+    IterInv:
+       helper class to repeatedly solve M*x=b
+       using an iterative method.
+    """
+
+    def __init__(self, M, ifunc=gmres_loose, tol=0):
+        self.M = M
+        if hasattr(M, 'dtype'):
+            dtype = M.dtype
+        else:
+            x = np.zeros(M.shape[1])
+            dtype = (M * x).dtype
+        super().__init__(dtype=dtype, shape=M.shape)
+
+        if tol <= 0:
+            # when tol=0, ARPACK uses machine tolerance as calculated
+            # by LAPACK's _LAMCH function.  We should match this
+            tol = 2 * np.finfo(self.dtype).eps
+        self.ifunc = ifunc
+        self.tol = tol
+
+    def _matvec(self, x):
+        b, info = self.ifunc(self.M, x, tol=self.tol)
+        if info != 0:
+            raise ValueError(
+                f"Error in inverting M: function {self.ifunc.__name__} "
+                f"did not converge (info = {info})."
+            )
+        return b
+
+
+class IterOpInv(LinearOperator):
+    """
+    IterOpInv:
+       helper class to repeatedly solve [A-sigma*M]*x = b
+       using an iterative method
+    """
+
+    def __init__(self, A, M, sigma, ifunc=gmres_loose, tol=0):
+        self.A = A
+        self.M = M
+        self.sigma = sigma
+
+        def mult_func(x):
+            return A.matvec(x) - sigma * M.matvec(x)
+
+        def mult_func_M_None(x):
+            return A.matvec(x) - sigma * x
+
+        x = np.zeros(A.shape[1])
+        if M is None:
+            dtype = mult_func_M_None(x).dtype
+            self.OP = LinearOperator(self.A.shape,
+                                     mult_func_M_None,
+                                     dtype=dtype)
+        else:
+            dtype = mult_func(x).dtype
+            self.OP = LinearOperator(self.A.shape,
+                                     mult_func,
+                                     dtype=dtype)
+        super().__init__(dtype=dtype, shape=A.shape)
+
+        if tol <= 0:
+            # when tol=0, ARPACK uses machine tolerance as calculated
+            # by LAPACK's _LAMCH function.  We should match this
+            tol = 2 * np.finfo(self.OP.dtype).eps
+        self.ifunc = ifunc
+        self.tol = tol
+
+    def _matvec(self, x):
+        b, info = self.ifunc(self.OP, x, tol=self.tol)
+        if info != 0:
+            raise ValueError(
+                f"Error in inverting [A-sigma*M]: function {self.ifunc.__name__} "
+                f"did not converge (info = {info})."
+            )
+        return b
+
+
+def _fast_spmatrix_to_csc(A, hermitian=False):
+    """Convert sparse matrix to CSC (by transposing, if possible)"""
+    if (A.format == "csr" and hermitian
+            and not np.issubdtype(A.dtype, np.complexfloating)):
+        return A.T
+    elif is_pydata_spmatrix(A):
+        # No need to convert
+        return A
+    else:
+        return A.tocsc()
+
+
+def get_inv_matvec(M, hermitian=False, tol=0):
+    if isdense(M):
+        return LuInv(M).matvec
+    elif issparse(M) or is_pydata_spmatrix(M):
+        M = _fast_spmatrix_to_csc(M, hermitian=hermitian)
+        return SpLuInv(M).matvec
+    else:
+        return IterInv(M, tol=tol).matvec
+
+
+def get_OPinv_matvec(A, M, sigma, hermitian=False, tol=0):
+    if sigma == 0:
+        return get_inv_matvec(A, hermitian=hermitian, tol=tol)
+
+    if M is None:
+        #M is the identity matrix
+        if isdense(A):
+            if (np.issubdtype(A.dtype, np.complexfloating)
+                    or np.imag(sigma) == 0):
+                A = np.copy(A)
+            else:
+                A = A + 0j
+            A.flat[::A.shape[1] + 1] -= sigma
+            return LuInv(A).matvec
+        elif issparse(A) or is_pydata_spmatrix(A):
+            A = A - sigma * eye_array(A.shape[0])
+            A = _fast_spmatrix_to_csc(A, hermitian=hermitian)
+            return SpLuInv(A).matvec
+        else:
+            return IterOpInv(aslinearoperator(A),
+                             M, sigma, tol=tol).matvec
+    else:
+        if ((not isdense(A) and not issparse(A) and not is_pydata_spmatrix(A)) or
+                (not isdense(M) and not issparse(M) and not is_pydata_spmatrix(M))):
+            return IterOpInv(aslinearoperator(A),
+                             aslinearoperator(M),
+                             sigma, tol=tol).matvec
+        elif isdense(A) or isdense(M):
+            return LuInv(A - sigma * M).matvec
+        else:
+            OP = A - sigma * M
+            OP = _fast_spmatrix_to_csc(OP, hermitian=hermitian)
+            return SpLuInv(OP).matvec
+
+
+def eigs(A, k=6, M=None, sigma=None, which='LM', v0=None,
+         ncv=None, maxiter=None, tol=0, return_eigenvectors=True,
+         Minv=None, OPinv=None, OPpart=None, rng=None):
+    """
+    Find k eigenvalues and eigenvectors of the square matrix A.
+
+    Solves ``A @ x[i] = w[i] * x[i]``, the standard eigenvalue problem
+    for w[i] eigenvalues with corresponding eigenvectors x[i].
+
+    If M is specified, solves ``A @ x[i] = w[i] * M @ x[i]``, the
+    generalized eigenvalue problem for w[i] eigenvalues
+    with corresponding eigenvectors x[i]
+
+    Parameters
+    ----------
+    A : ndarray, sparse matrix or LinearOperator
+        An array, sparse matrix, or LinearOperator representing
+        the operation ``A @ x``, where A is a real or complex square matrix.
+    k : int, optional
+        The number of eigenvalues and eigenvectors desired.
+        `k` must be smaller than N-1. It is not possible to compute all
+        eigenvectors of a matrix.
+    M : ndarray, sparse matrix or LinearOperator, optional
+        An array, sparse matrix, or LinearOperator representing
+        the operation M@x for the generalized eigenvalue problem::
+
+            A @ x = w * M @ x.
+
+        M must represent a real symmetric matrix if A is real, and must
+        represent a complex Hermitian matrix if A is complex. For best
+        results, the data type of M should be the same as that of A.
+        Additionally:
+
+        - If `sigma` is None, M is positive definite
+        - If `sigma` is specified, M is positive semi-definite
+
+        If sigma is None, eigs requires an operator to compute the solution
+        of the linear equation ``M @ x = b``.  This is done internally via a
+        (sparse) LU decomposition for an explicit matrix M, or via an
+        iterative solver for a general linear operator.  Alternatively,
+        the user can supply the matrix or operator Minv, which gives
+        ``x = Minv @ b = M^-1 @ b``.
+    sigma : real or complex, optional
+        Find eigenvalues near sigma using shift-invert mode.  This requires
+        an operator to compute the solution of the linear system
+        ``[A - sigma * M] @ x = b``, where M is the identity matrix if
+        unspecified. This is computed internally via a (sparse) LU
+        decomposition for explicit matrices A & M, or via an iterative
+        solver if either A or M is a general linear operator.
+        Alternatively, the user can supply the matrix or operator OPinv,
+        which gives ``x = OPinv @ b = [A - sigma * M]^-1 @ b``.
+        For a real matrix A, shift-invert can either be done in imaginary
+        mode or real mode, specified by the parameter OPpart ('r' or 'i').
+        Note that when sigma is specified, the keyword 'which' (below)
+        refers to the shifted eigenvalues ``w'[i]`` where:
+
+        - If A is real and OPpart == 'r' (default),
+          ``w'[i] = 1/2 * [1/(w[i]-sigma) + 1/(w[i]-conj(sigma))]``.
+        - If A is real and OPpart == 'i',
+          ``w'[i] = 1/2i * [1/(w[i]-sigma) - 1/(w[i]-conj(sigma))]``.
+        - If A is complex, ``w'[i] = 1/(w[i]-sigma)``.
+
+    which : str, ['LM' | 'SM' | 'LR' | 'SR' | 'LI' | 'SI'], optional
+        Which `k` eigenvectors and eigenvalues to find:
+
+        - 'LM' : largest magnitude
+        - 'SM' : smallest magnitude
+        - 'LR' : largest real part
+        - 'SR' : smallest real part
+        - 'LI' : largest imaginary part
+        - 'SI' : smallest imaginary part
+
+        When sigma != None, 'which' refers to the shifted eigenvalues w'[i]
+        (see discussion in 'sigma', above).  ARPACK is generally better
+        at finding large values than small values.  If small eigenvalues are
+        desired, consider using shift-invert mode for better performance.
+    v0 : ndarray, optional
+        Starting vector for iteration.
+        Default: random
+    ncv : int, optional
+        The number of Lanczos vectors generated
+        `ncv` must be greater than `k`; it is recommended that ``ncv > 2*k``.
+        Default: ``min(n, max(2*k + 1, 20))``
+    maxiter : int, optional
+        Maximum number of Arnoldi update iterations allowed
+        Default: ``n*10``
+    tol : float, optional
+        Relative accuracy for eigenvalues (stopping criterion)
+        The default value of 0 implies machine precision.
+    return_eigenvectors : bool, optional
+        Return eigenvectors (True) in addition to eigenvalues
+    Minv : ndarray, sparse matrix or LinearOperator, optional
+        See notes in M, above.
+    OPinv : ndarray, sparse matrix or LinearOperator, optional
+        See notes in sigma, above.
+    OPpart : {'r' or 'i'}, optional
+        See notes in sigma, above
+    rng : `numpy.random.Generator`, optional
+        Pseudorandom number generator state. When `rng` is None, a new
+        `numpy.random.Generator` is created using entropy from the
+        operating system. Types other than `numpy.random.Generator` are
+        passed to `numpy.random.default_rng` to instantiate a ``Generator``.
+
+        .. versionadded:: 1.17.0
+
+    Returns
+    -------
+    w : ndarray
+        Array of k eigenvalues.
+    v : ndarray
+        An array of `k` eigenvectors.
+        ``v[:, i]`` is the eigenvector corresponding to the eigenvalue w[i].
+
+    Raises
+    ------
+    ArpackNoConvergence
+        When the requested convergence is not obtained.
+        The currently converged eigenvalues and eigenvectors can be found
+        as ``eigenvalues`` and ``eigenvectors`` attributes of the exception
+        object.
+
+    See Also
+    --------
+    eigsh : eigenvalues and eigenvectors for symmetric matrix A
+    svds : singular value decomposition for a matrix A
+
+    Notes
+    -----
+    This function is a wrapper to the ARPACK [1]_ SNEUPD, DNEUPD, CNEUPD,
+    ZNEUPD, functions which use the Implicitly Restarted Arnoldi Method to
+    find the eigenvalues and eigenvectors [2]_.
+
+    References
+    ----------
+    .. [1] ARPACK Software, https://github.com/opencollab/arpack-ng
+    .. [2] R. B. Lehoucq, D. C. Sorensen, and C. Yang,  ARPACK USERS GUIDE:
+       Solution of Large Scale Eigenvalue Problems by Implicitly Restarted
+       Arnoldi Methods. SIAM, Philadelphia, PA, 1998.
+
+    Examples
+    --------
+    Find 6 eigenvectors of the identity matrix:
+
+    >>> import numpy as np
+    >>> from scipy.sparse.linalg import eigs
+    >>> id = np.eye(13)
+    >>> vals, vecs = eigs(id, k=6)
+    >>> vals
+    array([ 1.+0.j,  1.+0.j,  1.+0.j,  1.+0.j,  1.+0.j,  1.+0.j])
+    >>> vecs.shape
+    (13, 6)
+
+    """
+    A = convert_pydata_sparse_to_scipy(A)
+    if (A_ndim := len(A.shape)) > 2:
+        raise ValueError(f"{A_ndim}-dimensional `A` is unsupported, expected 2-D.")
+    M = convert_pydata_sparse_to_scipy(M)
+    if A.shape[0] != A.shape[1]:
+        raise ValueError(f'expected square matrix (shape={A.shape})')
+    if M is not None:
+        if M.shape != A.shape:
+            raise ValueError(f'wrong M dimensions {M.shape}, should be {A.shape}')
+        if np.dtype(M.dtype).char.lower() != np.dtype(A.dtype).char.lower():
+            warnings.warn('M does not have the same type precision as A. '
+                          'This may adversely affect ARPACK convergence',
+                          stacklevel=2)
+
+    n = A.shape[0]
+
+    if k <= 0:
+        raise ValueError(f"k={k} must be greater than 0.")
+
+    if k >= n - 1:
+        warnings.warn("k >= N - 1 for N * N square matrix. "
+                      "Attempting to use scipy.linalg.eig instead.",
+                      RuntimeWarning, stacklevel=2)
+
+        if issparse(A):
+            raise TypeError("Cannot use scipy.linalg.eig for sparse A with "
+                            "k >= N - 1. Use scipy.linalg.eig(A.toarray()) or"
+                            " reduce k.")
+        if isinstance(A, LinearOperator):
+            raise TypeError("Cannot use scipy.linalg.eig for LinearOperator "
+                            "A with k >= N - 1.")
+        if isinstance(M, LinearOperator):
+            raise TypeError("Cannot use scipy.linalg.eig for LinearOperator "
+                            "M with k >= N - 1.")
+
+        return eig(A, b=M, right=return_eigenvectors)
+
+    if sigma is None:
+        matvec = aslinearoperator(A).matvec
+
+        if OPinv is not None:
+            raise ValueError("OPinv should not be specified "
+                             "with sigma = None.")
+        if OPpart is not None:
+            raise ValueError("OPpart should not be specified with "
+                             "sigma = None or complex A")
+
+        if M is None:
+            #standard eigenvalue problem
+            mode = 1
+            M_matvec = None
+            Minv_matvec = None
+            if Minv is not None:
+                raise ValueError("Minv should not be "
+                                 "specified with M = None.")
+        else:
+            #general eigenvalue problem
+            mode = 2
+            if Minv is None:
+                Minv_matvec = get_inv_matvec(M, hermitian=True, tol=tol)
+            else:
+                Minv = aslinearoperator(Minv)
+                Minv_matvec = Minv.matvec
+            M_matvec = aslinearoperator(M).matvec
+    else:
+        #sigma is not None: shift-invert mode
+        if np.issubdtype(A.dtype, np.complexfloating):
+            if OPpart is not None:
+                raise ValueError("OPpart should not be specified "
+                                 "with sigma=None or complex A")
+            mode = 3
+        elif OPpart is None or OPpart.lower() == 'r':
+            mode = 3
+        elif OPpart.lower() == 'i':
+            if np.imag(sigma) == 0:
+                raise ValueError("OPpart cannot be 'i' if sigma is real")
+            mode = 4
+        else:
+            raise ValueError("OPpart must be one of ('r','i')")
+
+        matvec = aslinearoperator(A).matvec
+        if Minv is not None:
+            raise ValueError("Minv should not be specified when sigma is"
+                             "specified.")
+        if OPinv is None:
+            Minv_matvec = get_OPinv_matvec(A, M, sigma,
+                                           hermitian=False, tol=tol)
+        else:
+            OPinv = aslinearoperator(OPinv)
+            Minv_matvec = OPinv.matvec
+        if M is None:
+            M_matvec = None
+        else:
+            M_matvec = aslinearoperator(M).matvec
+
+    rng = np.random.default_rng(rng)
+    params = _UnsymmetricArpackParams(n, k, A.dtype.char, matvec, mode,
+                                      M_matvec, Minv_matvec, sigma,
+                                      ncv, v0, maxiter, which, tol, rng)
+
+    while not params.converged:
+        params.iterate()
+
+    return params.extract(return_eigenvectors)
+
+
+def eigsh(A, k=6, M=None, sigma=None, which='LM', v0=None,
+          ncv=None, maxiter=None, tol=0, return_eigenvectors=True,
+          Minv=None, OPinv=None, mode='normal', rng=None):
+    """
+    Find k eigenvalues and eigenvectors of the real symmetric square matrix
+    or complex Hermitian matrix A.
+
+    Solves ``A @ x[i] = w[i] * x[i]``, the standard eigenvalue problem for
+    w[i] eigenvalues with corresponding eigenvectors x[i].
+
+    If M is specified, solves ``A @ x[i] = w[i] * M @ x[i]``, the
+    generalized eigenvalue problem for w[i] eigenvalues
+    with corresponding eigenvectors x[i].
+
+    Note that there is no specialized routine for the case when A is a complex
+    Hermitian matrix. In this case, ``eigsh()`` will call ``eigs()`` and return
+    the real parts of the eigenvalues thus obtained.
+
+    Parameters
+    ----------
+    A : ndarray, sparse matrix or LinearOperator
+        A square operator representing the operation ``A @ x``, where ``A`` is
+        real symmetric or complex Hermitian. For buckling mode (see below)
+        ``A`` must additionally be positive-definite.
+    k : int, optional
+        The number of eigenvalues and eigenvectors desired.
+        `k` must be smaller than N. It is not possible to compute all
+        eigenvectors of a matrix.
+
+    Returns
+    -------
+    w : array
+        Array of k eigenvalues.
+    v : array
+        An array representing the `k` eigenvectors.  The column ``v[:, i]`` is
+        the eigenvector corresponding to the eigenvalue ``w[i]``.
+
+    Other Parameters
+    ----------------
+    M : An N x N matrix, array, sparse matrix, or linear operator representing
+        the operation ``M @ x`` for the generalized eigenvalue problem::
+
+            A @ x = w * M @ x.
+
+        M must represent a real symmetric matrix if A is real, and must
+        represent a complex Hermitian matrix if A is complex. For best
+        results, the data type of M should be the same as that of A.
+        Additionally:
+
+        - If sigma is None, M is symmetric positive definite.
+        - If sigma is specified, M is symmetric positive semi-definite.
+        - In buckling mode, M is symmetric indefinite.
+
+        If sigma is None, eigsh requires an operator to compute the solution
+        of the linear equation ``M @ x = b``. This is done internally via a
+        (sparse) LU decomposition for an explicit matrix M, or via an
+        iterative solver for a general linear operator.  Alternatively,
+        the user can supply the matrix or operator Minv, which gives
+        ``x = Minv @ b = M^-1 @ b``.
+    sigma : real
+        Find eigenvalues near sigma using shift-invert mode.  This requires
+        an operator to compute the solution of the linear system
+        ``[A - sigma * M] x = b``, where M is the identity matrix if
+        unspecified.  This is computed internally via a (sparse) LU
+        decomposition for explicit matrices A & M, or via an iterative
+        solver if either A or M is a general linear operator.
+        Alternatively, the user can supply the matrix or operator `OPinv`,
+        which gives ``x = OPinv @ b = [A - sigma * M]^-1 @ b``.
+        Regardless of the selected mode (normal, cayley, or buckling),
+        `OPinv` should always be supplied as ``OPinv = [A - sigma * M]^-1``.
+
+        Note that when sigma is specified, the keyword 'which' refers to
+        the shifted eigenvalues ``w'[i]`` where:
+
+        - if ``mode == 'normal'``: ``w'[i] = 1 / (w[i] - sigma)``.
+        - if ``mode == 'cayley'``:  ``w'[i] = (w[i] + sigma) / (w[i] - sigma)``.
+        - if ``mode == 'buckling'``: ``w'[i] = w[i] / (w[i] - sigma)``.
+
+        (see further discussion in 'mode' below)
+    which : str ['LM' | 'SM' | 'LA' | 'SA' | 'BE']
+        If A is a complex Hermitian matrix, 'BE' is invalid.
+        Which `k` eigenvectors and eigenvalues to find:
+
+        - 'LM' : Largest (in magnitude) eigenvalues.
+        - 'SM' : Smallest (in magnitude) eigenvalues.
+        - 'LA' : Largest (algebraic) eigenvalues.
+        - 'SA' : Smallest (algebraic) eigenvalues.
+        - 'BE' : Half (k/2) from each end of the spectrum.
+
+        When k is odd, return one more (k/2+1) from the high end.
+        When sigma != None, 'which' refers to the shifted eigenvalues ``w'[i]``
+        (see discussion in 'sigma', above).  ARPACK is generally better
+        at finding large values than small values.  If small eigenvalues are
+        desired, consider using shift-invert mode for better performance.
+    v0 : ndarray, optional
+        Starting vector for iteration. Default: random
+    ncv : int, optional
+        The number of Lanczos vectors generated ncv must be greater than k and
+        smaller than n; it is recommended that ``ncv > 2*k``.
+        Default: ``min(n, max(2*k + 1, 20))``
+    maxiter : int, optional
+        Maximum number of Arnoldi update iterations allowed.
+        Default: ``n*10``
+    tol : float
+        Relative accuracy for eigenvalues (stopping criterion).
+        The default value of 0 implies machine precision.
+    return_eigenvectors : bool
+        Return eigenvectors (True) in addition to eigenvalues.
+        This value determines the order in which eigenvalues are sorted.
+        The sort order is also dependent on the `which` variable.
+
+        - For which = 'LM' or 'SA':
+
+          - If `return_eigenvectors` is True, eigenvalues are sorted by
+            algebraic value.
+          - If `return_eigenvectors` is False, eigenvalues are sorted by
+            absolute value.
+
+        - For which = 'BE' or 'LA':
+
+          - eigenvalues are always sorted by algebraic value.
+
+        - For which = 'SM':
+
+          - If `return_eigenvectors` is True, eigenvalues are sorted by
+            algebraic value.
+          - If `return_eigenvectors` is False, eigenvalues are sorted by
+            decreasing absolute value.
+
+    Minv : N x N matrix, array, sparse matrix, or LinearOperator
+        See notes in M, above.
+    OPinv : N x N matrix, array, sparse matrix, or LinearOperator
+        See notes in sigma, above.
+    mode : str ['normal' | 'buckling' | 'cayley']
+        Specify strategy to use for shift-invert mode.  This argument applies
+        only for real-valued A and sigma != None.  For shift-invert mode,
+        ARPACK internally solves the eigenvalue problem
+        ``OP @ x'[i] = w'[i] * B @ x'[i]``
+        and transforms the resulting Ritz vectors x'[i] and Ritz values w'[i]
+        into the desired eigenvectors and eigenvalues of the problem
+        ``A @ x[i] = w[i] * M @ x[i]``.
+        The modes are as follows:
+
+        - 'normal'::
+
+            OP = [A - sigma * M]^-1 @ M,
+            B = M,
+            w'[i] = 1 / (w[i] - sigma)
+
+        - 'buckling'::
+
+            OP = [A - sigma * M]^-1 @ A,
+            B = A,
+            w'[i] = w[i] / (w[i] - sigma)
+
+        - 'cayley'::
+
+            OP = [A - sigma * M]^-1 @ [A + sigma * M],
+            B = M,
+            w'[i] = (w[i] + sigma) / (w[i] - sigma)
+
+        The choice of mode will affect which eigenvalues are selected by
+        the keyword 'which', and can also impact the stability of
+        convergence (see [2]_ for a discussion).
+    rng : `numpy.random.Generator`, optional
+        Pseudorandom number generator state. When `rng` is None, a new
+        `numpy.random.Generator` is created using entropy from the
+        operating system. Types other than `numpy.random.Generator` are
+        passed to `numpy.random.default_rng` to instantiate a ``Generator``.
+
+        .. versionadded:: 1.17.0
+
+    Raises
+    ------
+    ArpackNoConvergence
+        When the requested convergence is not obtained.
+
+        The currently converged eigenvalues and eigenvectors can be found
+        as ``eigenvalues`` and ``eigenvectors`` attributes of the exception
+        object.
+
+    See Also
+    --------
+    eigs : eigenvalues and eigenvectors for a general (nonsymmetric) matrix A
+    svds : singular value decomposition for a matrix A
+
+    Notes
+    -----
+    This function is a wrapper to the ARPACK [1]_ SSEUPD and DSEUPD
+    functions which use the Implicitly Restarted Lanczos Method to
+    find the eigenvalues and eigenvectors [2]_.
+
+    References
+    ----------
+    .. [1] ARPACK Software, https://github.com/opencollab/arpack-ng
+    .. [2] R. B. Lehoucq, D. C. Sorensen, and C. Yang,  ARPACK USERS GUIDE:
+       Solution of Large Scale Eigenvalue Problems by Implicitly Restarted
+       Arnoldi Methods. SIAM, Philadelphia, PA, 1998.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.sparse.linalg import eigsh
+    >>> identity = np.eye(13)
+    >>> eigenvalues, eigenvectors = eigsh(identity, k=6)
+    >>> eigenvalues
+    array([1., 1., 1., 1., 1., 1.])
+    >>> eigenvectors.shape
+    (13, 6)
+
+    """
+    # complex Hermitian matrices should be solved with eigs
+    if np.issubdtype(A.dtype, np.complexfloating):
+        if mode != 'normal':
+            raise ValueError(f"mode={mode} cannot be used with complex matrix A")
+        if which == 'BE':
+            raise ValueError("which='BE' cannot be used with complex matrix A")
+        elif which == 'LA':
+            which = 'LR'
+        elif which == 'SA':
+            which = 'SR'
+        ret = eigs(A, k, M=M, sigma=sigma, which=which, v0=v0,
+                   ncv=ncv, maxiter=maxiter, tol=tol,
+                   return_eigenvectors=return_eigenvectors, Minv=Minv,
+                   OPinv=OPinv)
+
+        if return_eigenvectors:
+            return ret[0].real, ret[1]
+        else:
+            return ret.real
+
+    if (A_ndim := len(A.shape)) > 2:
+        raise ValueError(f"{A_ndim}-dimensional `A` is unsupported, expected 2-D.")
+    if A.shape[0] != A.shape[1]:
+        raise ValueError(f'expected square matrix (shape={A.shape})')
+    if M is not None:
+        if M.shape != A.shape:
+            raise ValueError(f'wrong M dimensions {M.shape}, should be {A.shape}')
+        if np.dtype(M.dtype).char.lower() != np.dtype(A.dtype).char.lower():
+            warnings.warn('M does not have the same type precision as A. '
+                          'This may adversely affect ARPACK convergence',
+                          stacklevel=2)
+
+    n = A.shape[0]
+
+    if k <= 0:
+        raise ValueError("k must be greater than 0.")
+
+    if k >= n:
+        warnings.warn("k >= N for N * N square matrix. "
+                      "Attempting to use scipy.linalg.eigh instead.",
+                      RuntimeWarning, stacklevel=2)
+
+        if issparse(A):
+            raise TypeError("Cannot use scipy.linalg.eigh for sparse A with "
+                            "k >= N. Use scipy.linalg.eigh(A.toarray()) or"
+                            " reduce k.")
+        if isinstance(A, LinearOperator):
+            raise TypeError("Cannot use scipy.linalg.eigh for LinearOperator "
+                            "A with k >= N.")
+        if isinstance(M, LinearOperator):
+            raise TypeError("Cannot use scipy.linalg.eigh for LinearOperator "
+                            "M with k >= N.")
+
+        return eigh(A, b=M, eigvals_only=not return_eigenvectors)
+
+    if sigma is None:
+        A = aslinearoperator(A)
+        matvec = A.matvec
+
+        if OPinv is not None:
+            raise ValueError("OPinv should not be specified with sigma = None.")
+        if M is None:
+            #standard eigenvalue problem
+            mode = 1
+            M_matvec = None
+            Minv_matvec = None
+            if Minv is not None:
+                raise ValueError("Minv should not be specified with M = None.")
+        else:
+            #general eigenvalue problem
+            mode = 2
+            if Minv is None:
+                Minv_matvec = get_inv_matvec(M, hermitian=True, tol=tol)
+            else:
+                Minv = aslinearoperator(Minv)
+                Minv_matvec = Minv.matvec
+            M_matvec = aslinearoperator(M).matvec
+    else:
+        # sigma is not None: shift-invert mode
+        if Minv is not None:
+            raise ValueError("Minv should not be specified when sigma is "
+                             "specified.")
+
+        # normal mode
+        if mode == 'normal':
+            mode = 3
+            matvec = None
+            if OPinv is None:
+                Minv_matvec = get_OPinv_matvec(A, M, sigma,
+                                               hermitian=True, tol=tol)
+            else:
+                OPinv = aslinearoperator(OPinv)
+                Minv_matvec = OPinv.matvec
+            if M is None:
+                M_matvec = None
+            else:
+                M = aslinearoperator(M)
+                M_matvec = M.matvec
+
+        # buckling mode
+        elif mode == 'buckling':
+            mode = 4
+            if OPinv is None:
+                Minv_matvec = get_OPinv_matvec(A, M, sigma,
+                                               hermitian=True, tol=tol)
+            else:
+                Minv_matvec = aslinearoperator(OPinv).matvec
+            matvec = aslinearoperator(A).matvec
+            M_matvec = None
+
+        # cayley-transform mode
+        elif mode == 'cayley':
+            mode = 5
+            matvec = aslinearoperator(A).matvec
+            if OPinv is None:
+                Minv_matvec = get_OPinv_matvec(A, M, sigma,
+                                               hermitian=True, tol=tol)
+            else:
+                Minv_matvec = aslinearoperator(OPinv).matvec
+            if M is None:
+                M_matvec = None
+            else:
+                M_matvec = aslinearoperator(M).matvec
+
+        # unrecognized mode
+        else:
+            raise ValueError(f"unrecognized mode '{mode}'")
+    rng = np.random.default_rng(rng)
+    params = _SymmetricArpackParams(n, k, A.dtype.char, matvec, mode,
+                                    M_matvec, Minv_matvec, sigma,
+                                    ncv, v0, maxiter, which, tol, rng)
+
+    while not params.converged:
+        params.iterate()
+
+    return params.extract(return_eigenvectors)
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+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_eigen/arpack/tests/test_arpack.py
@@ -0,0 +1,717 @@
+import threading
+import itertools
+import warnings
+
+import numpy as np
+
+from numpy.testing import assert_allclose, assert_equal
+from pytest import raises as assert_raises
+import pytest
+
+from numpy import dot, conj
+from scipy.linalg import eig, eigh
+from scipy.sparse import csc_array, csr_array, diags_array, random_array
+from scipy.sparse.linalg import LinearOperator, aslinearoperator
+from scipy.sparse.linalg._eigen.arpack import (eigs, eigsh, arpack,
+                                              ArpackNoConvergence)
+
+
+from scipy._lib._gcutils import assert_deallocated
+
+
+# precision for tests
+_ndigits = {'f': 3, 'd': 11, 'F': 3, 'D': 11}
+
+
+def _get_test_tolerance(type_char, mattype=None, D_type=None, which=None):
+    """
+    Return tolerance values suitable for a given test:
+
+    Parameters
+    ----------
+    type_char : {'f', 'd', 'F', 'D'}
+        Data type in ARPACK eigenvalue problem
+    mattype : {csr_array, aslinearoperator, asarray}, optional
+        Linear operator type
+
+    Returns
+    -------
+    tol
+        Tolerance to pass to the ARPACK routine
+    rtol
+        Relative tolerance for outputs
+    atol
+        Absolute tolerance for outputs
+
+    """
+
+    rtol = {'f': 3000 * np.finfo(np.float32).eps,
+            'F': 3000 * np.finfo(np.float32).eps,
+            'd': 2000 * np.finfo(np.float64).eps,
+            'D': 2000 * np.finfo(np.float64).eps}[type_char]
+    atol = rtol
+    tol = 0
+
+    if mattype is aslinearoperator and type_char in ('f', 'F'):
+        # iterative methods in single precision: worse errors
+        # also: bump ARPACK tolerance so that the iterative method converges
+        tol = 30 * np.finfo(np.float32).eps
+        rtol *= 5
+
+    if (
+        isinstance(mattype, type) and issubclass(mattype, csr_array)
+        and type_char in ('f', 'F')
+    ):
+        # sparse in single precision: worse errors
+        rtol *= 5
+
+    if (
+        which in ('LM', 'SM', 'LA')
+        and D_type.name == "gen-hermitian-Mc"
+    ):
+        if type_char == 'F':
+            # missing case 1, 2, and more, from PR 14798
+            rtol *= 5
+
+        if type_char == 'D':
+            # missing more cases, from PR 14798
+            rtol *= 10
+            atol *= 10
+
+    return tol, rtol, atol
+
+
+def generate_matrix(N, complex_=False, hermitian=False,
+                    pos_definite=False, sparse=False, rng=None):
+    M = rng.random((N, N))
+    if complex_:
+        M = M + 1j * rng.random((N, N))
+
+    if hermitian:
+        if pos_definite:
+            if sparse:
+                i = np.arange(N)
+                j = rng.randint(N, size=N-2)
+                i, j = np.meshgrid(i, j)
+                M[i, j] = 0
+            M = np.dot(M.conj(), M.T)
+        else:
+            M = np.dot(M.conj(), M.T)
+            if sparse:
+                i = rng.randint(N, size=N * N // 4)
+                j = rng.randint(N, size=N * N // 4)
+                ind = np.nonzero(i == j)
+                j[ind] = (j[ind] + 1) % N
+                M[i, j] = 0
+                M[j, i] = 0
+    else:
+        if sparse:
+            i = rng.randint(N, size=N * N // 2)
+            j = rng.randint(N, size=N * N // 2)
+            M[i, j] = 0
+    return M
+
+
+def generate_matrix_symmetric(N, pos_definite=False, sparse=False, rng=None):
+    M = rng.random((N, N))
+
+    M = 0.5 * (M + M.T)  # Make M symmetric
+
+    if pos_definite:
+        Id = N * np.eye(N)
+        if sparse:
+            M = csr_array(M)
+        M += Id
+    else:
+        if sparse:
+            M = csr_array(M)
+
+    return M
+
+
+def assert_allclose_cc(actual, desired, **kw):
+    """Almost equal or complex conjugates almost equal"""
+    try:
+        assert_allclose(actual, desired, **kw)
+    except AssertionError:
+        assert_allclose(actual, conj(desired), **kw)
+
+
+def argsort_which(eigenvalues, typ, k, which,
+                  sigma=None, OPpart=None, mode=None):
+    """Return sorted indices of eigenvalues using the "which" keyword
+    from eigs and eigsh"""
+    if sigma is None:
+        reval = np.round(eigenvalues, decimals=_ndigits[typ])
+    else:
+        if mode is None or mode == 'normal':
+            if OPpart is None:
+                reval = 1. / (eigenvalues - sigma)
+            elif OPpart == 'r':
+                reval = 0.5 * (1. / (eigenvalues - sigma)
+                               + 1. / (eigenvalues - np.conj(sigma)))
+            elif OPpart == 'i':
+                reval = -0.5j * (1. / (eigenvalues - sigma)
+                                 - 1. / (eigenvalues - np.conj(sigma)))
+        elif mode == 'cayley':
+            reval = (eigenvalues + sigma) / (eigenvalues - sigma)
+        elif mode == 'buckling':
+            reval = eigenvalues / (eigenvalues - sigma)
+        else:
+            raise ValueError(f"mode='{mode}' not recognized")
+
+        reval = np.round(reval, decimals=_ndigits[typ])
+
+    if which in ['LM', 'SM']:
+        ind = np.argsort(abs(reval))
+    elif which in ['LR', 'SR', 'LA', 'SA', 'BE']:
+        ind = np.argsort(np.real(reval))
+    elif which in ['LI', 'SI']:
+        # for LI,SI ARPACK returns largest,smallest abs(imaginary) why?
+        if typ.islower():
+            ind = np.argsort(abs(np.imag(reval)))
+        else:
+            ind = np.argsort(np.imag(reval))
+    else:
+        raise ValueError(f"which='{which}' is unrecognized")
+
+    if which in ['LM', 'LA', 'LR', 'LI']:
+        return ind[-k:]
+    elif which in ['SM', 'SA', 'SR', 'SI']:
+        return ind[:k]
+    elif which == 'BE':
+        return np.concatenate((ind[:k//2], ind[k//2-k:]))
+
+
+def eval_evec(symmetric, d, typ, k, which, v0=None, sigma=None,
+              mattype=np.asarray, OPpart=None, mode='normal', rng=None):
+    general = ('bmat' in d)
+
+    if symmetric:
+        eigs_func = eigsh
+    else:
+        eigs_func = eigs
+
+    if general:
+        err = (f"error for {eigs_func.__name__}:general, typ={typ}, which={which}, "
+               f"sigma={sigma}, mattype={mattype.__name__},"
+               f" OPpart={OPpart}, mode={mode}")
+    else:
+        err = (f"error for {eigs_func.__name__}:standard, typ={typ}, which={which}, "
+               f"sigma={sigma}, mattype={mattype.__name__}, "
+               f"OPpart={OPpart}, mode={mode}")
+
+    a = d['mat'].astype(typ)
+    ac = mattype(a)
+
+    if general:
+        b = d['bmat'].astype(typ)
+        bc = mattype(b)
+
+    # get exact eigenvalues
+    exact_eval = d['eval'].astype(typ.upper())
+    ind = argsort_which(exact_eval, typ, k, which,
+                        sigma, OPpart, mode)
+    exact_eval = exact_eval[ind]
+
+    # compute arpack eigenvalues
+    kwargs = dict(which=which, v0=v0, sigma=sigma, rng=rng)
+    if eigs_func is eigsh:
+        kwargs['mode'] = mode
+    else:
+        kwargs['OPpart'] = OPpart
+
+    # compute suitable tolerances
+    kwargs['tol'], rtol, atol = _get_test_tolerance(typ, mattype, d, which)
+    # on rare occasions, ARPACK routines return results that are proper
+    # eigenvalues and -vectors, but not necessarily the ones requested in
+    # the parameter which. This is inherent to the Krylov methods, and
+    # should not be treated as a failure. If such a rare situation
+    # occurs, the calculation is tried again (but at most a few times).
+    ntries = 0
+    while ntries < 5:
+        # solve
+        if general:
+            try:
+                eigenvalues, evec = eigs_func(ac, k, bc, **kwargs)
+            except ArpackNoConvergence:
+                kwargs['maxiter'] = 20*a.shape[0]
+                eigenvalues, evec = eigs_func(ac, k, bc, **kwargs)
+        else:
+            try:
+                eigenvalues, evec = eigs_func(ac, k, **kwargs)
+            except ArpackNoConvergence:
+                kwargs['maxiter'] = 20*a.shape[0]
+                eigenvalues, evec = eigs_func(ac, k, **kwargs)
+
+        ind = argsort_which(eigenvalues, typ, k, which,
+                            sigma, OPpart, mode)
+        eigenvalues = eigenvalues[ind]
+        evec = evec[:, ind]
+
+        try:
+            # check eigenvalues
+            assert_allclose_cc(eigenvalues, exact_eval, rtol=rtol, atol=atol,
+                               err_msg=err)
+            check_evecs = True
+        except AssertionError:
+            check_evecs = False
+            ntries += 1
+
+        if check_evecs:
+            # check eigenvectors
+            LHS = np.dot(a, evec)
+            if general:
+                RHS = eigenvalues * np.dot(b, evec)
+            else:
+                RHS = eigenvalues * evec
+
+            assert_allclose(LHS, RHS, rtol=rtol, atol=atol, err_msg=err)
+            break
+
+    # check eigenvalues
+    assert_allclose_cc(eigenvalues, exact_eval, rtol=rtol, atol=atol, err_msg=err)
+
+
+class DictWithRepr(dict):
+    def __init__(self, name):
+        self.name = name
+
+    def __repr__(self):
+        return f"<{self.name}>"
+
+
+class SymmetricParams:
+    def __init__(self):
+        self.eigs = eigsh
+        self.which = ['LM', 'SM', 'LA', 'SA', 'BE']
+        self.mattypes = [csr_array, aslinearoperator, np.asarray]
+        self.sigmas_modes = {None: ['normal'],
+                             0.5: ['normal', 'buckling', 'cayley']}
+
+        # generate matrices
+        # these should all be float32 so that the eigenvalues
+        # are the same in float32 and float64
+        N = 6
+        rng = np.random.RandomState(2300)
+        Ar = generate_matrix(N, hermitian=True,
+                             pos_definite=True,
+                             rng=rng).astype('f').astype('d')
+        M = generate_matrix(N, hermitian=True,
+                            pos_definite=True,
+                            rng=rng).astype('f').astype('d')
+        Ac = generate_matrix(N, hermitian=True, pos_definite=True,
+                             complex_=True, rng=rng).astype('F').astype('D')
+        Mc = generate_matrix(N, hermitian=True, pos_definite=True,
+                             complex_=True, rng=rng).astype('F').astype('D')
+        v0 = rng.random(N)
+
+        # standard symmetric problem
+        SS = DictWithRepr("std-symmetric")
+        SS['mat'] = Ar
+        SS['v0'] = v0
+        SS['eval'] = eigh(SS['mat'], eigvals_only=True)
+
+        # general symmetric problem
+        GS = DictWithRepr("gen-symmetric")
+        GS['mat'] = Ar
+        GS['bmat'] = M
+        GS['v0'] = v0
+        GS['eval'] = eigh(GS['mat'], GS['bmat'], eigvals_only=True)
+
+        # standard hermitian problem
+        SH = DictWithRepr("std-hermitian")
+        SH['mat'] = Ac
+        SH['v0'] = v0
+        SH['eval'] = eigh(SH['mat'], eigvals_only=True)
+
+        # general hermitian problem
+        GH = DictWithRepr("gen-hermitian")
+        GH['mat'] = Ac
+        GH['bmat'] = M
+        GH['v0'] = v0
+        GH['eval'] = eigh(GH['mat'], GH['bmat'], eigvals_only=True)
+
+        # general hermitian problem with hermitian M
+        GHc = DictWithRepr("gen-hermitian-Mc")
+        GHc['mat'] = Ac
+        GHc['bmat'] = Mc
+        GHc['v0'] = v0
+        GHc['eval'] = eigh(GHc['mat'], GHc['bmat'], eigvals_only=True)
+
+        self.real_test_cases = [SS, GS]
+        self.complex_test_cases = [SH, GH, GHc]
+
+
+class NonSymmetricParams:
+    def __init__(self):
+        self.eigs = eigs
+        self.which = ['LM', 'LR', 'LI']  # , 'SM', 'LR', 'SR', 'LI', 'SI']
+        self.mattypes = [csr_array, aslinearoperator, np.asarray]
+        self.sigmas_OPparts = {None: [None],
+                               0.1: ['r'],
+                               0.1 + 0.1j: ['r', 'i']}
+
+        # generate matrices
+        # these should all be float32 so that the eigenvalues
+        # are the same in float32 and float64
+        N = 6
+        rng = np.random.RandomState(2300)
+        Ar = generate_matrix(N, rng=rng).astype('f').astype('d')
+        M = generate_matrix(N, hermitian=True,
+                            pos_definite=True, rng=rng).astype('f').astype('d')
+        Ac = generate_matrix(N, complex_=True, rng=rng).astype('F').astype('D')
+        v0 = rng.random(N)
+
+        # standard real nonsymmetric problem
+        SNR = DictWithRepr("std-real-nonsym")
+        SNR['mat'] = Ar
+        SNR['v0'] = v0
+        SNR['eval'] = eig(SNR['mat'], left=False, right=False)
+
+        # general real nonsymmetric problem
+        GNR = DictWithRepr("gen-real-nonsym")
+        GNR['mat'] = Ar
+        GNR['bmat'] = M
+        GNR['v0'] = v0
+        GNR['eval'] = eig(GNR['mat'], GNR['bmat'], left=False, right=False)
+
+        # standard complex nonsymmetric problem
+        SNC = DictWithRepr("std-cmplx-nonsym")
+        SNC['mat'] = Ac
+        SNC['v0'] = v0
+        SNC['eval'] = eig(SNC['mat'], left=False, right=False)
+
+        # general complex nonsymmetric problem
+        GNC = DictWithRepr("gen-cmplx-nonsym")
+        GNC['mat'] = Ac
+        GNC['bmat'] = M
+        GNC['v0'] = v0
+        GNC['eval'] = eig(GNC['mat'], GNC['bmat'], left=False, right=False)
+
+        self.real_test_cases = [SNR, GNR]
+        self.complex_test_cases = [SNC, GNC]
+
+
+@pytest.mark.parametrize("sigma, mode", [(None, 'normal'), (0.5, 'normal'),
+                                         (0.5, 'buckling'), (0.5, 'cayley')])
+@pytest.mark.parametrize("mattype", [csr_array, aslinearoperator, np.asarray])
+@pytest.mark.parametrize("which", ['LM', 'SM', 'LA', 'SA', 'BE'])
+@pytest.mark.parametrize("typ", ['f', 'd'])
+@pytest.mark.parametrize("D", SymmetricParams().real_test_cases)
+def test_symmetric_modes(D, typ, which, mattype, sigma, mode):
+    rng = np.random.default_rng(1749531508689996)
+    k = 2
+    eval_evec(True, D, typ, k, which, None, sigma, mattype, None, mode, rng=rng)
+
+
+@pytest.mark.parametrize("sigma", [None, 0.5])
+@pytest.mark.parametrize("mattype", [csr_array, aslinearoperator, np.asarray])
+@pytest.mark.parametrize("which", ['LM', 'SM', 'LA', 'SA'])
+@pytest.mark.parametrize("typ", ['F', 'D'])
+@pytest.mark.parametrize("D", SymmetricParams().complex_test_cases)
+def test_hermitian_modes(D, typ, which, mattype, sigma):
+    rng = np.random.default_rng(1749531706842957)
+    k = 2
+    eval_evec(True, D, typ, k, which, None, sigma, mattype, rng=rng)
+
+
+@pytest.mark.parametrize("typ", ['f', 'd'])
+@pytest.mark.parametrize("D", SymmetricParams().real_test_cases)
+@pytest.mark.parametrize("k", [1, 2, 3, 4, 5])
+def test_symmetric_starting_vector(k, D, typ):
+    rng = np.random.default_rng(1749532110418901)
+    v0 = rng.uniform(size=len(D['v0'])).astype(typ)
+    eval_evec(True, D, typ, k, 'LM', v0, rng=rng)
+
+
+def test_symmetric_no_convergence():
+    rng = np.random.RandomState(1234)
+    m = generate_matrix(30, hermitian=True, pos_definite=True, rng=rng)
+    tol, rtol, atol = _get_test_tolerance('d')
+    try:
+        w, v = eigsh(m, 4, which='LM', v0=m[:, 0], maxiter=5, tol=tol, ncv=9)
+        raise AssertionError("Spurious no-error exit")
+    except ArpackNoConvergence as err:
+        k = len(err.eigenvalues)
+        if k <= 0:
+            raise AssertionError("Spurious no-eigenvalues-found case") from err
+        w, v = err.eigenvalues, err.eigenvectors
+        assert_allclose(dot(m, v), w * v, rtol=rtol, atol=atol)
+
+
+@pytest.mark.parametrize("sigma, OPpart", [(None, None), (0.1, 'r'),
+                                            (0.1 + 0.1j, 'r'), (0.1 + 0.1j, 'i')])
+@pytest.mark.parametrize("mattype", [csr_array, aslinearoperator, np.asarray])
+@pytest.mark.parametrize("which", ['LM', 'LR', 'LI'])
+@pytest.mark.parametrize("typ", ['f', 'd'])
+@pytest.mark.parametrize("D", NonSymmetricParams().real_test_cases)
+def test_real_nonsymmetric_modes(D, typ, which, mattype,
+                                 sigma, OPpart):
+    rng = np.random.default_rng(174953334412726)
+    k = 2
+    eval_evec(False, D, typ, k, which, None, sigma, mattype, OPpart, rng=rng)
+
+
+@pytest.mark.parametrize("sigma", [None, 0.1, 0.1 + 0.1j])
+@pytest.mark.parametrize("mattype", [csr_array, aslinearoperator, np.asarray])
+@pytest.mark.parametrize("which", ['LM', 'LR', 'LI'])
+@pytest.mark.parametrize("typ", ['F', 'D'])
+@pytest.mark.parametrize("D", NonSymmetricParams().complex_test_cases)
+def test_complex_nonsymmetric_modes(D, typ, which, mattype, sigma):
+    rng = np.random.default_rng(1749533536274527)
+    k = 2
+    eval_evec(False, D, typ, k, which, None, sigma, mattype, rng=rng)
+
+
+@pytest.mark.parametrize("typ", ['F', 'D'])
+@pytest.mark.parametrize("D", NonSymmetricParams().complex_test_cases)
+@pytest.mark.parametrize("k", [1, 2, 3, 4])
+def test_nonsymmetric_starting_vector(k, D, typ):
+    rng = np.random.default_rng(174953366983161)
+    A = D['mat']
+    n = A.shape[0]
+    v0 = rng.uniform(size=n).astype(typ)
+    eval_evec(False, D, typ, k, "LM", v0, sigma=None, rng=rng)
+
+
+def test_standard_nonsymmetric_no_convergence():
+    rng = np.random.RandomState(1234)
+    m = generate_matrix(30, complex_=True, rng=rng)
+    tol, rtol, atol = _get_test_tolerance('d')
+    try:
+        w, v = eigs(m, 4, which='LM', v0=m[:, 0], maxiter=5, tol=tol)
+        raise AssertionError("Spurious no-error exit")
+    except ArpackNoConvergence as err:
+        k = len(err.eigenvalues)
+        if k <= 0:
+            raise AssertionError("Spurious no-eigenvalues-found case") from err
+        w, v = err.eigenvalues, err.eigenvectors
+        for ww, vv in zip(w, v.T):
+            assert_allclose(dot(m, vv), ww * vv, rtol=rtol, atol=atol)
+
+
+def test_eigen_bad_shapes():
+    # A is not square.
+    A = csc_array(np.zeros((2, 3)))
+    assert_raises(ValueError, eigs, A)
+
+
+def test_eigen_bad_kwargs():
+    # Test eigen on wrong keyword argument
+    A = csc_array(np.zeros((8, 8)))
+    assert_raises(ValueError, eigs, A, which='XX')
+
+
+def test_ticket_1459_arpack_crash():
+    for dtype in [np.float32, np.float64]:
+        # This test does not seem to catch the issue for float32,
+        # but we made the same fix there, just to be sure
+
+        N = 6
+        k = 2
+
+        np.random.seed(2301)
+        A = np.random.random((N, N)).astype(dtype)
+        v0 = np.array([-0.71063568258907849895, -0.83185111795729227424,
+                       -0.34365925382227402451, 0.46122533684552280420,
+                       -0.58001341115969040629, -0.78844877570084292984e-01],
+                      dtype=dtype)
+
+        # Should not crash:
+        evals, evecs = eigs(A, k, v0=v0)
+
+
+def test_linearoperator_deallocation():
+    # Check that the linear operators used by the Arpack wrappers are
+    # deallocatable by reference counting -- they are big objects, so
+    # Python's cyclic GC may not collect them fast enough before
+    # running out of memory if eigs/eigsh are called in a tight loop.
+
+    M_d = np.eye(10)
+    M_s = csc_array(M_d)
+    M_o = aslinearoperator(M_d)
+
+    with assert_deallocated(lambda: arpack.SpLuInv(M_s)):
+        pass
+    with assert_deallocated(lambda: arpack.LuInv(M_d)):
+        pass
+    with assert_deallocated(lambda: arpack.IterInv(M_s)):
+        pass
+    with assert_deallocated(lambda: arpack.IterOpInv(M_o, None, 0.3)):
+        pass
+    with assert_deallocated(lambda: arpack.IterOpInv(M_o, M_o, 0.3)):
+        pass
+
+
+def test_parallel_threads(num_parallel_threads):
+    results = []
+    rng = np.random.default_rng(1234)
+    v0 = rng.random(50)
+
+    def worker():
+        x = diags_array([1.0, -2.0, 1.0], offsets=[-1, 0, 1], shape=(50, 50))
+        w, v = eigs(x, k=3, v0=v0)
+        results.append(w)
+
+        w, v = eigsh(x, k=3, v0=v0)
+        results.append(w)
+
+    nthreads = 9 // num_parallel_threads + 1
+    threads = [threading.Thread(target=worker) for _ in range(nthreads)]
+    for t in threads:
+        t.start()
+    for t in threads:
+        t.join()
+
+    worker()
+
+    for r in results:
+        assert_allclose(r, results[-1])
+
+
+def test_reentering():
+    # Just some linear operator that calls eigs recursively
+    def A_matvec(x):
+        x = diags_array([1.0, -2.0, 1.0], offsets=[-1, 0, 1], shape=(50, 50))
+        w, v = eigs(x, k=1)
+        return v.real / w[0].real
+    A = LinearOperator(matvec=A_matvec, dtype=float, shape=(50, 50))
+
+    # ================= Old Fortran tests ==================
+    # The Fortran code is not reentrant, so this fails (gracefully, not crashing)
+    # assert_raises(RuntimeError, eigs, A, k=1)
+    # assert_raises(RuntimeError, eigsh, A, k=1)
+    #
+    # These should not crash upon reentrance
+    eigs(A, k=1)
+    eigsh(A, k=1)
+
+
+def test_regression_arpackng_1315():
+    # Check that issue arpack-ng/#1315 is not present.
+    # Adapted from arpack-ng/TESTS/bug_1315_single.c
+    # If this fails, then the installed ARPACK library is faulty.
+
+    for dtype in [np.float32, np.float64]:
+        np.random.seed(1234)
+
+        w0 = np.arange(1, 1000+1).astype(dtype)
+        A = diags_array([w0], offsets=[0], shape=(1000, 1000))
+
+        v0 = np.random.rand(1000).astype(dtype)
+        w, v = eigs(A, k=9, ncv=2*9+1, which="LM", v0=v0)
+
+        assert_allclose(np.sort(w), np.sort(w0[-9:]),
+                        rtol=1e-4)
+
+
+def test_eigs_for_k_greater():
+    # Test eigs() for k beyond limits.
+    rng = np.random.RandomState(1234)
+    A_sparse = diags_array([1.0, -2.0, 1.0], offsets=[-1, 0, 1], shape=(4, 4))
+    A = generate_matrix(4, sparse=False, rng=rng)
+    M_dense = rng.random((4, 4))
+    M_sparse = generate_matrix(4, sparse=True, rng=rng)
+    M_linop = aslinearoperator(M_dense)
+    eig_tuple1 = eig(A, b=M_dense)
+    eig_tuple2 = eig(A, b=M_sparse)
+
+    with warnings.catch_warnings():
+        warnings.simplefilter("ignore", RuntimeWarning)
+
+        assert_equal(eigs(A, M=M_dense, k=3), eig_tuple1)
+        assert_equal(eigs(A, M=M_dense, k=4), eig_tuple1)
+        assert_equal(eigs(A, M=M_dense, k=5), eig_tuple1)
+        assert_equal(eigs(A, M=M_sparse, k=5), eig_tuple2)
+
+        # M as LinearOperator
+        assert_raises(TypeError, eigs, A, M=M_linop, k=3)
+
+        # Test 'A' for different types
+        assert_raises(TypeError, eigs, aslinearoperator(A), k=3)
+        assert_raises(TypeError, eigs, A_sparse, k=3)
+
+
+def test_eigsh_for_k_greater():
+    # Test eigsh() for k beyond limits.
+    rng = np.random.RandomState(1234)
+    A_sparse = diags_array([1.0, -2.0, 1.0], offsets=[-1, 0, 1], shape=(4, 4))
+    A = generate_matrix(4, sparse=False, rng=rng)
+    M_dense = generate_matrix_symmetric(4, pos_definite=True, rng=rng)
+    M_sparse = generate_matrix_symmetric(
+        4, pos_definite=True, sparse=True, rng=rng)
+    M_linop = aslinearoperator(M_dense)
+    eig_tuple1 = eigh(A, b=M_dense)
+    eig_tuple2 = eigh(A, b=M_sparse)
+
+    with warnings.catch_warnings():
+        warnings.simplefilter("ignore", RuntimeWarning)
+
+        assert_equal(eigsh(A, M=M_dense, k=4), eig_tuple1)
+        assert_equal(eigsh(A, M=M_dense, k=5), eig_tuple1)
+        assert_equal(eigsh(A, M=M_sparse, k=5), eig_tuple2)
+
+        # M as LinearOperator
+        assert_raises(TypeError, eigsh, A, M=M_linop, k=4)
+
+        # Test 'A' for different types
+        assert_raises(TypeError, eigsh, aslinearoperator(A), k=4)
+        assert_raises(TypeError, eigsh, A_sparse, M=M_dense, k=4)
+
+
+def test_real_eigs_real_k_subset():
+    rng = np.random.default_rng(2)
+
+    n = 10
+    A = random_array(shape=(n, n), density=0.5, rng=rng)
+    A.data *= 2
+    A.data -= 1
+    A += A.T  # make symmetric to test real eigenvalues
+
+    v0 = np.ones(n)
+
+    whichs = ['LM', 'SM', 'LR', 'SR', 'LI', 'SI']
+    dtypes = [np.float32, np.float64]
+
+    for which, sigma, dtype in itertools.product(whichs, [None, 0, 5], dtypes):
+        prev_w = np.array([], dtype=dtype)
+        eps = np.finfo(dtype).eps
+        for k in range(1, 9):
+            w, z = eigs(A.astype(dtype), k=k, which=which, sigma=sigma,
+                        v0=v0.astype(dtype), tol=0)
+            assert_allclose(np.linalg.norm(A.dot(z) - z * w), 0, atol=np.sqrt(eps))
+
+            # Check that the set of eigenvalues for `k` is a subset of that for `k+1`
+            dist = abs(prev_w[:,None] - w).min(axis=1)
+            assert_allclose(dist, 0, atol=np.sqrt(eps))
+
+            prev_w = w
+
+
+@pytest.mark.parametrize("dtype", [np.float32, np.float64, np.complex64, np.complex128])
+def test_gh24358(dtype):
+    # gh-24358: eigs with which="SR" returned zeros due to nev variable was modifed
+    #  after naupd calls in the C ARPACK implementation. This was due to hitting a
+    # complex valued eig but requesting only one of them.
+
+    # Test the specific issue in gh-24358
+    A = csr_array(np.array([[-1.3, 2.7, 0.2],
+                            [0.8, 4.1, 2.2],
+                            [2.1, 4.4, -1.9]], dtype=dtype))
+    w, z = eigs(A, 1, which="SR")
+    atol = 1e-4 if dtype in [np.float32, np.complex64] else 1e-6
+    assert_allclose(w.real, -2.495689365014214, atol=atol, rtol=0.0)
+    # ARPACK can sometimes pick up the conjugate
+    assert_allclose(np.abs(w.imag), 0.5173365219668336, atol=atol, rtol=0.0)
+    assert_allclose(A @ z, w * z, atol=atol, rtol=0.0)
+
+
+@pytest.mark.parametrize("func", [eigs, eigsh])
+def test_nD(func):
+    """Check that >2-D operators are rejected cleanly."""
+    def id(x):
+        return x
+    A = LinearOperator(shape=(2, 2, 2), matvec=id, dtype=np.float64)
+    with pytest.raises(ValueError, match="expected 2-D"):
+        func(A)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_eigen/lobpcg/__init__.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_eigen/lobpcg/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..6ab5330361a6bcc2a8403f9b3788aedae750d57f
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_eigen/lobpcg/__init__.py
@@ -0,0 +1,16 @@
+"""
+Locally Optimal Block Preconditioned Conjugate Gradient Method (LOBPCG)
+
+LOBPCG is a preconditioned eigensolver for large symmetric positive definite
+(SPD) generalized eigenproblems.
+
+Call the function lobpcg - see help for lobpcg.lobpcg.
+
+"""
+from .lobpcg import *
+
+__all__ = [s for s in dir() if not s.startswith('_')]
+
+from scipy._lib._testutils import PytestTester
+test = PytestTester(__name__)
+del PytestTester
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diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_eigen/lobpcg/lobpcg.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_eigen/lobpcg/lobpcg.py
new file mode 100644
index 0000000000000000000000000000000000000000..84b4a5e0ef83bc97b1ce09edd05af573a558f429
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_eigen/lobpcg/lobpcg.py
@@ -0,0 +1,1109 @@
+"""
+Locally Optimal Block Preconditioned Conjugate Gradient Method (LOBPCG).
+
+References
+----------
+.. [1] A. V. Knyazev (2001),
+       Toward the Optimal Preconditioned Eigensolver: Locally Optimal
+       Block Preconditioned Conjugate Gradient Method.
+       SIAM Journal on Scientific Computing 23, no. 2,
+       pp. 517-541. :doi:`10.1137/S1064827500366124`
+
+.. [2] A. V. Knyazev, I. Lashuk, M. E. Argentati, and E. Ovchinnikov (2007),
+       Block Locally Optimal Preconditioned Eigenvalue Xolvers (BLOPEX)
+       in hypre and PETSc.  :arxiv:`0705.2626`
+
+.. [3] A. V. Knyazev's C and MATLAB implementations:
+       https://github.com/lobpcg/blopex
+"""
+
+import warnings
+import numpy as np
+from scipy.linalg import (inv, eigh, cho_factor, cho_solve,
+                          cholesky, LinAlgError)
+from scipy.sparse.linalg import LinearOperator
+from scipy.sparse import issparse
+
+__all__ = ["lobpcg"]
+
+
+def _report_nonhermitian(M, name):
+    """
+    Report if `M` is not a Hermitian matrix given its type.
+    """
+    from scipy.linalg import norm
+
+    md = M - M.T.conj()
+    nmd = norm(md, 1)
+    tol = 10 * np.finfo(M.dtype).eps
+    tol = max(tol, tol * norm(M, 1))
+    if nmd > tol:
+        warnings.warn(
+              f"Matrix {name} of the type {M.dtype} is not Hermitian: "
+              f"condition: {nmd} < {tol} fails.",
+              UserWarning, stacklevel=4
+         )
+
+def _as2d(ar):
+    """
+    If the input array is 2D return it, if it is 1D, append a dimension,
+    making it a column vector.
+    """
+    if ar.ndim == 2:
+        return ar
+    else:  # Assume 1!
+        aux = np.asarray(ar).reshape((ar.shape[0], 1))
+        return aux
+
+
+def _makeMatMat(m):
+    if m is None:
+        return None
+    elif callable(m):
+        return lambda v: m(v)
+    else:
+        return lambda v: m @ v
+
+
+def _matmul_inplace(x, y, verbosityLevel=0):
+    """Perform 'np.matmul' in-place if possible.
+
+    If some sufficient conditions for inplace matmul are met, do so.
+    Otherwise try inplace update and fall back to overwrite if that fails.
+    """
+    if x.flags["CARRAY"] and x.shape[1] == y.shape[1] and x.dtype == y.dtype:
+        # conditions where we can guarantee that inplace updates will work;
+        # i.e. x is not a view/slice, x & y have compatible dtypes, and the
+        # shape of the result of x @ y matches the shape of x.
+        np.matmul(x, y, out=x)
+    else:
+        # ideally, we'd have an exhaustive list of conditions above when
+        # inplace updates are possible; since we don't, we opportunistically
+        # try if it works, and fall back to overwriting if necessary
+        try:
+            np.matmul(x, y, out=x)
+        except Exception:
+            if verbosityLevel:
+                warnings.warn(
+                    "Inplace update of x = x @ y failed, "
+                    "x needs to be overwritten.",
+                    UserWarning, stacklevel=3
+                )
+            x = x @ y
+    return x
+
+
+def _applyConstraints(blockVectorV, factYBY, blockVectorBY, blockVectorY):
+    """Changes blockVectorV in-place."""
+    YBV = blockVectorBY.T.conj() @ blockVectorV
+    tmp = cho_solve(factYBY, YBV)
+    blockVectorV -= blockVectorY @ tmp
+
+
+def _b_orthonormalize(B, blockVectorV, blockVectorBV=None,
+                      verbosityLevel=0):
+    """in-place B-orthonormalize the given block vector using Cholesky."""
+    if blockVectorBV is None:
+        if B is None:
+            blockVectorBV = blockVectorV
+        else:
+            try:
+                blockVectorBV = B(blockVectorV)
+            except Exception as e:
+                if verbosityLevel:
+                    warnings.warn(
+                        f"Secondary MatMul call failed with error\n"
+                        f"{e}\n",
+                        UserWarning, stacklevel=3
+                    )
+                    return None, None, None
+            if blockVectorBV.shape != blockVectorV.shape:
+                raise ValueError(
+                    f"The shape {blockVectorV.shape} "
+                    f"of the orthogonalized matrix not preserved\n"
+                    f"and changed to {blockVectorBV.shape} "
+                    f"after multiplying by the secondary matrix.\n"
+                )
+
+    VBV = blockVectorV.T.conj() @ blockVectorBV
+    try:
+        # VBV is a Cholesky factor from now on...
+        VBV = cholesky(VBV, overwrite_a=True)
+        VBV = inv(VBV, overwrite_a=True)
+        blockVectorV = _matmul_inplace(
+            blockVectorV, VBV,
+            verbosityLevel=verbosityLevel
+        )
+        if B is not None:
+            blockVectorBV = _matmul_inplace(
+                blockVectorBV, VBV,
+                verbosityLevel=verbosityLevel
+            )
+        return blockVectorV, blockVectorBV, VBV
+    except LinAlgError:
+        if verbosityLevel:
+            warnings.warn(
+                "Cholesky has failed.",
+                UserWarning, stacklevel=3
+            )
+        return None, None, None
+
+
+def _get_indx(_lambda, num, largest):
+    """Get `num` indices into `_lambda` depending on `largest` option."""
+    ii = np.argsort(_lambda)
+    if largest:
+        ii = ii[:-num - 1:-1]
+    else:
+        ii = ii[:num]
+
+    return ii
+
+
+def _handle_gramA_gramB_verbosity(gramA, gramB, verbosityLevel):
+    if verbosityLevel:
+        _report_nonhermitian(gramA, "gramA")
+        _report_nonhermitian(gramB, "gramB")
+
+
+def lobpcg(
+    A,
+    X,
+    B=None,
+    M=None,
+    Y=None,
+    tol=None,
+    maxiter=None,
+    largest=True,
+    verbosityLevel=0,
+    retLambdaHistory=False,
+    retResidualNormsHistory=False,
+    restartControl=20,
+):
+    """Locally Optimal Block Preconditioned Conjugate Gradient Method (LOBPCG).
+
+    LOBPCG is a preconditioned eigensolver for large real symmetric and complex
+    Hermitian definite generalized eigenproblems.
+
+    Parameters
+    ----------
+    A : {sparse matrix, ndarray, LinearOperator, callable object}
+        The Hermitian linear operator of the problem, usually given by a
+        sparse matrix.  Often called the "stiffness matrix".
+    X : ndarray, float32 or float64
+        Initial approximation to the ``k`` eigenvectors (non-sparse).
+        If `A` has ``shape=(n,n)`` then `X` must have ``shape=(n,k)``.
+    B : {sparse matrix, ndarray, LinearOperator, callable object}
+        Optional. By default ``B = None``, which is equivalent to identity.
+        The right hand side operator in a generalized eigenproblem if present.
+        Often called the "mass matrix". Must be Hermitian positive definite.
+    M : {sparse matrix, ndarray, LinearOperator, callable object}
+        Optional. By default ``M = None``, which is equivalent to identity.
+        Preconditioner aiming to accelerate convergence.
+    Y : ndarray, float32 or float64, default: None
+        An ``n-by-sizeY`` ndarray of constraints with ``sizeY < n``.
+        The iterations will be performed in the ``B``-orthogonal complement
+        of the column-space of `Y`. `Y` must be full rank if present.
+    tol : scalar, optional
+        The default is ``tol=n*sqrt(eps)``.
+        Solver tolerance for the stopping criterion.
+    maxiter : int, default: 20
+        Maximum number of iterations.
+    largest : bool, default: True
+        When True, solve for the largest eigenvalues, otherwise the smallest.
+    verbosityLevel : int, optional
+        By default ``verbosityLevel=0`` no output.
+        Controls the solver standard/screen output.
+    retLambdaHistory : bool, default: False
+        Whether to return iterative eigenvalue history.
+    retResidualNormsHistory : bool, default: False
+        Whether to return iterative history of residual norms.
+    restartControl : int, optional
+        Iterations restart if the residuals jump ``2**restartControl`` times
+        compared to the smallest recorded in ``retResidualNormsHistory``.
+        The default is ``restartControl=20``, making the restarts rare for
+        backward compatibility.
+
+    Returns
+    -------
+    lambda : ndarray of the shape ``(k, )``.
+        Array of ``k`` approximate eigenvalues.
+    v : ndarray of the same shape as ``X.shape``.
+        An array of ``k`` approximate eigenvectors.
+    lambdaHistory : ndarray, optional.
+        The eigenvalue history, if `retLambdaHistory` is ``True``.
+    ResidualNormsHistory : ndarray, optional.
+        The history of residual norms, if `retResidualNormsHistory`
+        is ``True``.
+
+    Notes
+    -----
+    The iterative loop runs ``maxit=maxiter`` (20 if ``maxit=None``)
+    iterations at most and finishes earlier if the tolerance is met.
+    Breaking backward compatibility with the previous version, LOBPCG
+    now returns the block of iterative vectors with the best accuracy rather
+    than the last one iterated, as a cure for possible divergence.
+
+    If ``X.dtype == np.float32`` and user-provided operations/multiplications
+    by `A`, `B`, and `M` all preserve the ``np.float32`` data type,
+    all the calculations and the output are in ``np.float32``.
+
+    The size of the iteration history output equals to the number of the best
+    (limited by `maxit`) iterations plus 3: initial, final, and postprocessing.
+
+    If both `retLambdaHistory` and `retResidualNormsHistory` are ``True``,
+    the return tuple has the following format
+    ``(lambda, V, lambda history, residual norms history)``.
+
+    In the following ``n`` denotes the matrix size and ``k`` the number
+    of required eigenvalues (smallest or largest).
+
+    The LOBPCG code internally solves eigenproblems of the size ``3k`` on every
+    iteration by calling the dense eigensolver `eigh`, so if ``k`` is not
+    small enough compared to ``n``, it makes no sense to call the LOBPCG code.
+    Moreover, if one calls the LOBPCG algorithm for ``5k > n``, it would likely
+    break internally, so the code calls the standard function `eigh` instead.
+    It is not that ``n`` should be large for the LOBPCG to work, but rather the
+    ratio ``n / k`` should be large. It you call LOBPCG with ``k=1``
+    and ``n=10``, it works though ``n`` is small. The method is intended
+    for extremely large ``n / k``.
+
+    The convergence speed depends basically on three factors:
+
+    1. Quality of the initial approximations `X` to the seeking eigenvectors.
+       Randomly distributed around the origin vectors work well if no better
+       choice is known.
+
+    2. Relative separation of the desired eigenvalues from the rest
+       of the eigenvalues. One can vary ``k`` to improve the separation.
+
+    3. Proper preconditioning to shrink the spectral spread.
+       For example, a rod vibration test problem (under tests
+       directory) is ill-conditioned for large ``n``, so convergence will be
+       slow, unless efficient preconditioning is used. For this specific
+       problem, a good simple preconditioner function would be a linear solve
+       for `A`, which is easy to code since `A` is tridiagonal.
+
+    References
+    ----------
+    .. [1] A. V. Knyazev (2001),
+           Toward the Optimal Preconditioned Eigensolver: Locally Optimal
+           Block Preconditioned Conjugate Gradient Method.
+           SIAM Journal on Scientific Computing 23, no. 2,
+           pp. 517-541. :doi:`10.1137/S1064827500366124`
+
+    .. [2] A. V. Knyazev, I. Lashuk, M. E. Argentati, and E. Ovchinnikov
+           (2007), Block Locally Optimal Preconditioned Eigenvalue Xolvers
+           (BLOPEX) in hypre and PETSc. :arxiv:`0705.2626`
+
+    .. [3] A. V. Knyazev's C and MATLAB implementations:
+           https://github.com/lobpcg/blopex
+
+    Examples
+    --------
+    Our first example is minimalistic - find the largest eigenvalue of
+    a diagonal matrix by solving the non-generalized eigenvalue problem
+    ``A x = lambda x`` without constraints or preconditioning.
+
+    >>> import numpy as np
+    >>> from scipy.sparse import diags_array
+    >>> from scipy.sparse.linalg import LinearOperator, aslinearoperator
+    >>> from scipy.sparse.linalg import lobpcg
+
+    The square matrix size is
+
+    >>> n = 100
+
+    and its diagonal entries are 1, ..., 100 defined by
+
+    >>> vals = np.arange(1, n + 1).astype(np.int16)
+
+    The first mandatory input parameter in this test is
+    the sparse diagonal matrix `A`
+    of the eigenvalue problem ``A x = lambda x`` to solve.
+
+    >>> A = diags_array(vals, offsets=0, shape=(n, n), dtype=None)
+    >>> A.toarray()
+    array([[  1,   0,   0, ...,   0,   0,   0],
+           [  0,   2,   0, ...,   0,   0,   0],
+           [  0,   0,   3, ...,   0,   0,   0],
+           ...,
+           [  0,   0,   0, ...,  98,   0,   0],
+           [  0,   0,   0, ...,   0,  99,   0],
+           [  0,   0,   0, ...,   0,   0, 100]], shape=(100, 100), dtype=int16)
+
+    The second mandatory input parameter `X` is a 2D array with the
+    row dimension determining the number of requested eigenvalues.
+    `X` is an initial guess for targeted eigenvectors.
+    `X` must have linearly independent columns.
+    If no initial approximations available, randomly oriented vectors
+    commonly work best, e.g., with components normally distributed
+    around zero or uniformly distributed on the interval [-1 1].
+    Setting the initial approximations to dtype ``np.float32``
+    forces all iterative values to dtype ``np.float32`` speeding up
+    the run while still allowing accurate eigenvalue computations.
+
+    >>> k = 1
+    >>> rng = np.random.default_rng()
+    >>> X = rng.normal(size=(n, k))
+    >>> X = X.astype(np.float32)
+
+    >>> eigenvalues, _ = lobpcg(A, X, maxiter=60)
+    >>> eigenvalues
+    array([100.], dtype=float32)
+
+    `lobpcg` needs only access the matrix product with `A` rather
+    then the matrix itself. Since the matrix `A` is diagonal in
+    this example, one can write a function of the matrix product
+    ``A @ X`` using the diagonal values ``vals`` only, e.g., by
+    element-wise multiplication with broadcasting in the lambda-function
+
+    >>> A_lambda = lambda X: vals[:, np.newaxis] * X
+
+    or the regular function
+
+    >>> def A_matmat(X):
+    ...     return vals[:, np.newaxis] * X
+
+    and use the handle to one of these callables as an input
+
+    >>> eigenvalues, _ = lobpcg(A_lambda, X, maxiter=60)
+    >>> eigenvalues
+    array([100.], dtype=float32)
+    >>> eigenvalues, _ = lobpcg(A_matmat, X, maxiter=60)
+    >>> eigenvalues
+    array([100.], dtype=float32)
+
+    The traditional callable `LinearOperator` is no longer
+    necessary but still supported as the input to `lobpcg`.
+    Specifying ``matmat=A_matmat`` explicitly improves performance. 
+
+    >>> A_lo = LinearOperator((n, n), matvec=A_matmat, matmat=A_matmat, dtype=np.int16)
+    >>> eigenvalues, _ = lobpcg(A_lo, X, maxiter=80)
+    >>> eigenvalues
+    array([100.], dtype=float32)
+
+    The least efficient callable option is `aslinearoperator`:
+
+    >>> eigenvalues, _ = lobpcg(aslinearoperator(A), X, maxiter=80)
+    >>> eigenvalues
+    array([100.], dtype=float32)
+
+    We now switch to computing the three smallest eigenvalues specifying
+
+    >>> k = 3
+    >>> X = np.random.default_rng().normal(size=(n, k))
+
+    and ``largest=False`` parameter
+
+    >>> eigenvalues, _ = lobpcg(A, X, largest=False, maxiter=90)
+    >>> print(eigenvalues)  
+    [1. 2. 3.]
+
+    The next example illustrates computing 3 smallest eigenvalues of
+    the same matrix `A` given by the function handle ``A_matmat`` but
+    with constraints and preconditioning.
+
+    Constraints - an optional input parameter is a 2D array comprising
+    of column vectors that the eigenvectors must be orthogonal to
+
+    >>> Y = np.eye(n, 3)
+
+    The preconditioner acts as the inverse of `A` in this example, but
+    in the reduced precision ``np.float32`` even though the initial `X`
+    and thus all iterates and the output are in full ``np.float64``.
+
+    >>> inv_vals = 1./vals
+    >>> inv_vals = inv_vals.astype(np.float32)
+    >>> M = lambda X: inv_vals[:, np.newaxis] * X
+
+    Let us now solve the eigenvalue problem for the matrix `A` first
+    without preconditioning requesting 80 iterations
+
+    >>> eigenvalues, _ = lobpcg(A_matmat, X, Y=Y, largest=False, maxiter=80)
+    >>> eigenvalues
+    array([4., 5., 6.])
+    >>> eigenvalues.dtype
+    dtype('float64')
+
+    With preconditioning we need only 20 iterations from the same `X`
+
+    >>> eigenvalues, _ = lobpcg(A_matmat, X, Y=Y, M=M, largest=False, maxiter=20)
+    >>> eigenvalues
+    array([4., 5., 6.])
+
+    Note that the vectors passed in `Y` are the eigenvectors of the 3
+    smallest eigenvalues. The results returned above are orthogonal to those.
+
+    The primary matrix `A` may be indefinite, e.g., after shifting
+    ``vals`` by 50 from 1, ..., 100 to -49, ..., 50, we still can compute
+    the 3 smallest or largest eigenvalues.
+
+    >>> vals = vals - 50
+    >>> X = rng.normal(size=(n, k))
+    >>> eigenvalues, _ = lobpcg(A_matmat, X, largest=False, maxiter=99)
+    >>> eigenvalues
+    array([-49., -48., -47.])
+    >>> eigenvalues, _ = lobpcg(A_matmat, X, largest=True, maxiter=99)
+    >>> eigenvalues
+    array([50., 49., 48.])
+
+    """
+    blockVectorX = X
+    bestblockVectorX = blockVectorX
+    blockVectorY = Y
+    residualTolerance = tol
+    if maxiter is None:
+        maxiter = 20
+
+    bestIterationNumber = maxiter
+
+    sizeY = 0
+    if blockVectorY is not None:
+        if len(blockVectorY.shape) != 2:
+            warnings.warn(
+                f"Expected rank-2 array for argument Y, instead got "
+                f"{len(blockVectorY.shape)}, "
+                f"so ignore it and use no constraints.",
+                UserWarning, stacklevel=2
+            )
+            blockVectorY = None
+        else:
+            sizeY = blockVectorY.shape[1]
+
+    # Block size.
+    if blockVectorX is None:
+        raise ValueError("The mandatory initial matrix X cannot be None")
+    if len(blockVectorX.shape) != 2:
+        raise ValueError("expected rank-2 array for argument X")
+
+    n, sizeX = blockVectorX.shape
+
+    # Data type of iterates, determined by X, must be inexact
+    if not np.issubdtype(blockVectorX.dtype, np.inexact):
+        warnings.warn(
+            f"Data type for argument X is {blockVectorX.dtype}, "
+            f"which is not inexact, so casted to np.float32.",
+            UserWarning, stacklevel=2
+        )
+        blockVectorX = np.asarray(blockVectorX, dtype=np.float32)
+
+    if retLambdaHistory:
+        lambdaHistory = np.zeros((maxiter + 3, sizeX),
+                                 dtype=blockVectorX.dtype)
+    if retResidualNormsHistory:
+        residualNormsHistory = np.zeros((maxiter + 3, sizeX),
+                                        dtype=blockVectorX.dtype)
+
+    if verbosityLevel:
+        aux = "Solving "
+        if B is None:
+            aux += "standard"
+        else:
+            aux += "generalized"
+        aux += " eigenvalue problem with"
+        if M is None:
+            aux += "out"
+        aux += " preconditioning\n\n"
+        aux += f"matrix size {n}\n"
+        aux += f"block size {sizeX}\n\n"
+        if blockVectorY is None:
+            aux += "No constraints\n\n"
+        else:
+            if sizeY > 1:
+                aux += f"{sizeY} constraints\n\n"
+            else:
+                aux += f"{sizeY} constraint\n\n"
+        print(aux)
+
+    if (n - sizeY) < (5 * sizeX):
+        warnings.warn(
+            f"The problem size {n} minus the constraints size {sizeY} "
+            f"is too small relative to the block size {sizeX}. "
+            f"Using a dense eigensolver instead of LOBPCG iterations."
+            f"No output of the history of the iterations.",
+            UserWarning, stacklevel=2
+        )
+
+        sizeX = min(sizeX, n)
+
+        if blockVectorY is not None:
+            raise NotImplementedError(
+                "The dense eigensolver does not support constraints."
+            )
+
+        # Define the closed range of indices of eigenvalues to return.
+        if largest:
+            eigvals = (n - sizeX, n - 1)
+        else:
+            eigvals = (0, sizeX - 1)
+
+        try:
+            if isinstance(A, LinearOperator):
+                A = A(np.eye(n, dtype=int))
+            elif callable(A):
+                A = A(np.eye(n, dtype=int))
+                if A.shape != (n, n):
+                    raise ValueError(
+                        f"The shape {A.shape} of the primary matrix\n"
+                        f"defined by a callable object is wrong.\n"
+                        f"Expected {(n, n)}."
+                    )
+            elif issparse(A):
+                A = A.toarray()
+            else:
+                A = np.asarray(A)
+        except Exception as e:
+            raise Exception(
+                f"Primary MatMul call failed with error\n"
+                f"{e}\n")
+
+        if B is not None:
+            try:
+                if isinstance(B, LinearOperator):
+                    B = B(np.eye(n, dtype=int))
+                elif callable(B):
+                    B = B(np.eye(n, dtype=int))
+                    if B.shape != (n, n):
+                        raise ValueError(
+                            f"The shape {B.shape} of the secondary matrix\n"
+                            f"defined by a callable object is wrong.\n"
+                        )
+                elif issparse(B):
+                    B = B.toarray()
+                else:
+                    B = np.asarray(B)
+            except Exception as e:
+                raise Exception(
+                    f"Secondary MatMul call failed with error\n"
+                    f"{e}\n")
+
+        try:
+            vals, vecs = eigh(A,
+                              B,
+                              subset_by_index=eigvals,
+                              check_finite=False)
+            if largest:
+                # Reverse order to be compatible with eigs() in 'LM' mode.
+                vals = vals[::-1]
+                vecs = vecs[:, ::-1]
+
+            return vals, vecs
+        except Exception as e:
+            raise Exception(
+                f"Dense eigensolver failed with error\n"
+                f"{e}\n"
+            )
+
+    if (residualTolerance is None) or (residualTolerance <= 0.0):
+        residualTolerance = np.sqrt(np.finfo(blockVectorX.dtype).eps) * n
+
+    A = _makeMatMat(A)
+    B = _makeMatMat(B)
+    M = _makeMatMat(M)
+
+    # Apply constraints to X.
+    if blockVectorY is not None:
+
+        if B is not None:
+            blockVectorBY = B(blockVectorY)
+            if blockVectorBY.shape != blockVectorY.shape:
+                raise ValueError(
+                    f"The shape {blockVectorY.shape} "
+                    f"of the constraint not preserved\n"
+                    f"and changed to {blockVectorBY.shape} "
+                    f"after multiplying by the secondary matrix.\n"
+                )
+        else:
+            blockVectorBY = blockVectorY
+
+        # gramYBY is a dense array.
+        gramYBY = blockVectorY.T.conj() @ blockVectorBY
+        try:
+            # gramYBY is a Cholesky factor from now on...
+            gramYBY = cho_factor(gramYBY, overwrite_a=True)
+        except LinAlgError as e:
+            raise ValueError("Linearly dependent constraints") from e
+
+        _applyConstraints(blockVectorX, gramYBY, blockVectorBY, blockVectorY)
+
+    ##
+    # B-orthonormalize X.
+    blockVectorX, blockVectorBX, _ = _b_orthonormalize(
+        B, blockVectorX, verbosityLevel=verbosityLevel)
+    if blockVectorX is None:
+        raise ValueError("Linearly dependent initial approximations")
+
+    ##
+    # Compute the initial Ritz vectors: solve the eigenproblem.
+    blockVectorAX = A(blockVectorX)
+    if blockVectorAX.shape != blockVectorX.shape:
+        raise ValueError(
+            f"The shape {blockVectorX.shape} "
+            f"of the initial approximations not preserved\n"
+            f"and changed to {blockVectorAX.shape} "
+            f"after multiplying by the primary matrix.\n"
+        )
+
+    gramXAX = blockVectorX.T.conj() @ blockVectorAX
+
+    _lambda, eigBlockVector = eigh(gramXAX, check_finite=False)
+    ii = _get_indx(_lambda, sizeX, largest)
+    _lambda = _lambda[ii]
+    if retLambdaHistory:
+        lambdaHistory[0, :] = _lambda
+
+    eigBlockVector = np.asarray(eigBlockVector[:, ii])
+    blockVectorX = _matmul_inplace(
+        blockVectorX, eigBlockVector,
+        verbosityLevel=verbosityLevel
+    )
+    blockVectorAX = _matmul_inplace(
+        blockVectorAX, eigBlockVector,
+        verbosityLevel=verbosityLevel
+    )
+    if B is not None:
+        blockVectorBX = _matmul_inplace(
+            blockVectorBX, eigBlockVector,
+            verbosityLevel=verbosityLevel
+        )
+
+    ##
+    # Active index set.
+    activeMask = np.ones((sizeX,), dtype=bool)
+
+    ##
+    # Main iteration loop.
+
+    blockVectorP = None  # set during iteration
+    blockVectorAP = None
+    blockVectorBP = None
+
+    smallestResidualNorm = np.abs(np.finfo(blockVectorX.dtype).max)
+
+    iterationNumber = -1
+    restart = True
+    forcedRestart = False
+    explicitGramFlag = False
+    while iterationNumber < maxiter:
+        iterationNumber += 1
+
+        if B is not None:
+            aux = blockVectorBX * _lambda[np.newaxis, :]
+        else:
+            aux = blockVectorX * _lambda[np.newaxis, :]
+
+        blockVectorR = blockVectorAX - aux
+
+        aux = np.sum(blockVectorR.conj() * blockVectorR, 0)
+        residualNorms = np.sqrt(np.abs(aux))
+        if retResidualNormsHistory:
+            residualNormsHistory[iterationNumber, :] = residualNorms
+        residualNorm = np.sum(np.abs(residualNorms)) / sizeX
+
+        if residualNorm < smallestResidualNorm:
+            smallestResidualNorm = residualNorm
+            bestIterationNumber = iterationNumber
+            bestblockVectorX = blockVectorX
+        elif residualNorm > 2**restartControl * smallestResidualNorm:
+            forcedRestart = True
+            blockVectorAX = A(blockVectorX)
+            if blockVectorAX.shape != blockVectorX.shape:
+                raise ValueError(
+                    f"The shape {blockVectorX.shape} "
+                    f"of the restarted iterate not preserved\n"
+                    f"and changed to {blockVectorAX.shape} "
+                    f"after multiplying by the primary matrix.\n"
+                )
+            if B is not None:
+                blockVectorBX = B(blockVectorX)
+                if blockVectorBX.shape != blockVectorX.shape:
+                    raise ValueError(
+                        f"The shape {blockVectorX.shape} "
+                        f"of the restarted iterate not preserved\n"
+                        f"and changed to {blockVectorBX.shape} "
+                        f"after multiplying by the secondary matrix.\n"
+                    )
+
+        ii = np.where(residualNorms > residualTolerance, True, False)
+        activeMask = activeMask & ii
+        currentBlockSize = activeMask.sum()
+
+        if verbosityLevel:
+            print(f"iteration {iterationNumber}")
+            print(f"current block size: {currentBlockSize}")
+            print(f"eigenvalue(s):\n{_lambda}")
+            print(f"residual norm(s):\n{residualNorms}")
+
+        if currentBlockSize == 0:
+            break
+
+        activeBlockVectorR = _as2d(blockVectorR[:, activeMask])
+
+        if iterationNumber > 0:
+            activeBlockVectorP = _as2d(blockVectorP[:, activeMask])
+            activeBlockVectorAP = _as2d(blockVectorAP[:, activeMask])
+            if B is not None:
+                activeBlockVectorBP = _as2d(blockVectorBP[:, activeMask])
+
+        if M is not None:
+            # Apply preconditioner T to the active residuals.
+            activeBlockVectorR = M(activeBlockVectorR)
+
+        ##
+        # Apply constraints to the preconditioned residuals.
+        if blockVectorY is not None:
+            _applyConstraints(activeBlockVectorR,
+                              gramYBY,
+                              blockVectorBY,
+                              blockVectorY)
+
+        ##
+        # B-orthogonalize the preconditioned residuals to X.
+        if B is not None:
+            activeBlockVectorR = activeBlockVectorR - (
+                blockVectorX @
+                (blockVectorBX.T.conj() @ activeBlockVectorR)
+            )
+        else:
+            activeBlockVectorR = activeBlockVectorR - (
+                blockVectorX @
+                (blockVectorX.T.conj() @ activeBlockVectorR)
+            )
+
+        ##
+        # B-orthonormalize the preconditioned residuals.
+        aux = _b_orthonormalize(
+            B, activeBlockVectorR, verbosityLevel=verbosityLevel)
+        activeBlockVectorR, activeBlockVectorBR, _ = aux
+
+        if activeBlockVectorR is None:
+            warnings.warn(
+                f"Failed at iteration {iterationNumber} with accuracies "
+                f"{residualNorms}\n not reaching the requested "
+                f"tolerance {residualTolerance}.",
+                UserWarning, stacklevel=2
+            )
+            break
+        activeBlockVectorAR = A(activeBlockVectorR)
+
+        if iterationNumber > 0:
+            if B is not None:
+                aux = _b_orthonormalize(
+                    B, activeBlockVectorP, activeBlockVectorBP,
+                    verbosityLevel=verbosityLevel
+                )
+                activeBlockVectorP, activeBlockVectorBP, invR = aux
+            else:
+                aux = _b_orthonormalize(B, activeBlockVectorP,
+                                        verbosityLevel=verbosityLevel)
+                activeBlockVectorP, _, invR = aux
+            # Function _b_orthonormalize returns None if Cholesky fails
+            if activeBlockVectorP is not None:
+                activeBlockVectorAP = _matmul_inplace(
+                    activeBlockVectorAP, invR,
+                    verbosityLevel=verbosityLevel
+                )
+                restart = forcedRestart
+            else:
+                restart = True
+
+        ##
+        # Perform the Rayleigh Ritz Procedure:
+        # Compute symmetric Gram matrices:
+
+        if activeBlockVectorAR.dtype == "float32":
+            myeps = 1
+        else:
+            myeps = np.sqrt(np.finfo(activeBlockVectorR.dtype).eps)
+
+        if residualNorms.max() > myeps and not explicitGramFlag:
+            explicitGramFlag = False
+        else:
+            # Once explicitGramFlag, forever explicitGramFlag.
+            explicitGramFlag = True
+
+        # Shared memory assignments to simplify the code
+        if B is None:
+            blockVectorBX = blockVectorX
+            activeBlockVectorBR = activeBlockVectorR
+            if not restart:
+                activeBlockVectorBP = activeBlockVectorP
+
+        # Common submatrices:
+        gramXAR = np.dot(blockVectorX.T.conj(), activeBlockVectorAR)
+        gramRAR = np.dot(activeBlockVectorR.T.conj(), activeBlockVectorAR)
+
+        gramDtype = activeBlockVectorAR.dtype
+        if explicitGramFlag:
+            gramRAR = (gramRAR + gramRAR.T.conj()) / 2
+            gramXAX = np.dot(blockVectorX.T.conj(), blockVectorAX)
+            gramXAX = (gramXAX + gramXAX.T.conj()) / 2
+            gramXBX = np.dot(blockVectorX.T.conj(), blockVectorBX)
+            gramRBR = np.dot(activeBlockVectorR.T.conj(), activeBlockVectorBR)
+            gramXBR = np.dot(blockVectorX.T.conj(), activeBlockVectorBR)
+        else:
+            gramXAX = np.diag(_lambda).astype(gramDtype)
+            gramXBX = np.eye(sizeX, dtype=gramDtype)
+            gramRBR = np.eye(currentBlockSize, dtype=gramDtype)
+            gramXBR = np.zeros((sizeX, currentBlockSize), dtype=gramDtype)
+
+        if not restart:
+            gramXAP = np.dot(blockVectorX.T.conj(), activeBlockVectorAP)
+            gramRAP = np.dot(activeBlockVectorR.T.conj(), activeBlockVectorAP)
+            gramPAP = np.dot(activeBlockVectorP.T.conj(), activeBlockVectorAP)
+            gramXBP = np.dot(blockVectorX.T.conj(), activeBlockVectorBP)
+            gramRBP = np.dot(activeBlockVectorR.T.conj(), activeBlockVectorBP)
+            if explicitGramFlag:
+                gramPAP = (gramPAP + gramPAP.T.conj()) / 2
+                gramPBP = np.dot(activeBlockVectorP.T.conj(),
+                                 activeBlockVectorBP)
+            else:
+                gramPBP = np.eye(currentBlockSize, dtype=gramDtype)
+
+            gramA = np.block(
+                [
+                    [gramXAX, gramXAR, gramXAP],
+                    [gramXAR.T.conj(), gramRAR, gramRAP],
+                    [gramXAP.T.conj(), gramRAP.T.conj(), gramPAP],
+                ]
+            )
+            gramB = np.block(
+                [
+                    [gramXBX, gramXBR, gramXBP],
+                    [gramXBR.T.conj(), gramRBR, gramRBP],
+                    [gramXBP.T.conj(), gramRBP.T.conj(), gramPBP],
+                ]
+            )
+
+            _handle_gramA_gramB_verbosity(gramA, gramB, verbosityLevel)
+
+            try:
+                _lambda, eigBlockVector = eigh(gramA,
+                                               gramB,
+                                               check_finite=False)
+            except LinAlgError as e:
+                # raise ValueError("eigh failed in lobpcg iterations") from e
+                if verbosityLevel:
+                    warnings.warn(
+                        f"eigh failed at iteration {iterationNumber} \n"
+                        f"with error {e} causing a restart.\n",
+                        UserWarning, stacklevel=2
+                    )
+                # try again after dropping the direction vectors P from RR
+                restart = True
+
+        if restart:
+            gramA = np.block([[gramXAX, gramXAR], [gramXAR.T.conj(), gramRAR]])
+            gramB = np.block([[gramXBX, gramXBR], [gramXBR.T.conj(), gramRBR]])
+
+            _handle_gramA_gramB_verbosity(gramA, gramB, verbosityLevel)
+
+            try:
+                _lambda, eigBlockVector = eigh(gramA,
+                                               gramB,
+                                               check_finite=False)
+            except LinAlgError as e:
+                # raise ValueError("eigh failed in lobpcg iterations") from e
+                warnings.warn(
+                    f"eigh failed at iteration {iterationNumber} with error\n"
+                    f"{e}\n",
+                    UserWarning, stacklevel=2
+                )
+                break
+
+        ii = _get_indx(_lambda, sizeX, largest)
+        _lambda = _lambda[ii]
+        eigBlockVector = eigBlockVector[:, ii]
+        if retLambdaHistory:
+            lambdaHistory[iterationNumber + 1, :] = _lambda
+
+        # Compute Ritz vectors.
+        if B is not None:
+            if not restart:
+                eigBlockVectorX = eigBlockVector[:sizeX]
+                eigBlockVectorR = eigBlockVector[sizeX:
+                                                 sizeX + currentBlockSize]
+                eigBlockVectorP = eigBlockVector[sizeX + currentBlockSize:]
+
+                pp = np.dot(activeBlockVectorR, eigBlockVectorR)
+                pp += np.dot(activeBlockVectorP, eigBlockVectorP)
+
+                app = np.dot(activeBlockVectorAR, eigBlockVectorR)
+                app += np.dot(activeBlockVectorAP, eigBlockVectorP)
+
+                bpp = np.dot(activeBlockVectorBR, eigBlockVectorR)
+                bpp += np.dot(activeBlockVectorBP, eigBlockVectorP)
+            else:
+                eigBlockVectorX = eigBlockVector[:sizeX]
+                eigBlockVectorR = eigBlockVector[sizeX:]
+
+                pp = np.dot(activeBlockVectorR, eigBlockVectorR)
+                app = np.dot(activeBlockVectorAR, eigBlockVectorR)
+                bpp = np.dot(activeBlockVectorBR, eigBlockVectorR)
+
+            blockVectorX = np.dot(blockVectorX, eigBlockVectorX) + pp
+            blockVectorAX = np.dot(blockVectorAX, eigBlockVectorX) + app
+            blockVectorBX = np.dot(blockVectorBX, eigBlockVectorX) + bpp
+
+            blockVectorP, blockVectorAP, blockVectorBP = pp, app, bpp
+
+        else:
+            if not restart:
+                eigBlockVectorX = eigBlockVector[:sizeX]
+                eigBlockVectorR = eigBlockVector[sizeX:
+                                                 sizeX + currentBlockSize]
+                eigBlockVectorP = eigBlockVector[sizeX + currentBlockSize:]
+
+                pp = np.dot(activeBlockVectorR, eigBlockVectorR)
+                pp += np.dot(activeBlockVectorP, eigBlockVectorP)
+
+                app = np.dot(activeBlockVectorAR, eigBlockVectorR)
+                app += np.dot(activeBlockVectorAP, eigBlockVectorP)
+            else:
+                eigBlockVectorX = eigBlockVector[:sizeX]
+                eigBlockVectorR = eigBlockVector[sizeX:]
+
+                pp = np.dot(activeBlockVectorR, eigBlockVectorR)
+                app = np.dot(activeBlockVectorAR, eigBlockVectorR)
+
+            blockVectorX = np.dot(blockVectorX, eigBlockVectorX) + pp
+            blockVectorAX = np.dot(blockVectorAX, eigBlockVectorX) + app
+
+            blockVectorP, blockVectorAP = pp, app
+
+    if B is not None:
+        aux = blockVectorBX * _lambda[np.newaxis, :]
+    else:
+        aux = blockVectorX * _lambda[np.newaxis, :]
+
+    blockVectorR = blockVectorAX - aux
+
+    aux = np.sum(blockVectorR.conj() * blockVectorR, 0)
+    residualNorms = np.sqrt(np.abs(aux))
+    # Use old lambda in case of early loop exit.
+    if retLambdaHistory:
+        lambdaHistory[iterationNumber + 1, :] = _lambda
+    if retResidualNormsHistory:
+        residualNormsHistory[iterationNumber + 1, :] = residualNorms
+    residualNorm = np.sum(np.abs(residualNorms)) / sizeX
+    if residualNorm < smallestResidualNorm:
+        smallestResidualNorm = residualNorm
+        bestIterationNumber = iterationNumber + 1
+        bestblockVectorX = blockVectorX
+
+    if np.max(np.abs(residualNorms)) > residualTolerance:
+        warnings.warn(
+            f"Exited at iteration {iterationNumber} with accuracies \n"
+            f"{residualNorms}\n"
+            f"not reaching the requested tolerance {residualTolerance}.\n"
+            f"Use iteration {bestIterationNumber} instead with accuracy \n"
+            f"{smallestResidualNorm}.\n",
+            UserWarning, stacklevel=2
+        )
+
+    if verbosityLevel:
+        print(f"Final iterative eigenvalue(s):\n{_lambda}")
+        print(f"Final iterative residual norm(s):\n{residualNorms}")
+
+    blockVectorX = bestblockVectorX
+    # Making eigenvectors "exactly" satisfy the blockVectorY constrains
+    if blockVectorY is not None:
+        _applyConstraints(blockVectorX,
+                          gramYBY,
+                          blockVectorBY,
+                          blockVectorY)
+
+    # Making eigenvectors "exactly" othonormalized by final "exact" RR
+    blockVectorAX = A(blockVectorX)
+    if blockVectorAX.shape != blockVectorX.shape:
+        raise ValueError(
+            f"The shape {blockVectorX.shape} "
+            f"of the postprocessing iterate not preserved\n"
+            f"and changed to {blockVectorAX.shape} "
+            f"after multiplying by the primary matrix.\n"
+        )
+    gramXAX = np.dot(blockVectorX.T.conj(), blockVectorAX)
+
+    blockVectorBX = blockVectorX
+    if B is not None:
+        blockVectorBX = B(blockVectorX)
+        if blockVectorBX.shape != blockVectorX.shape:
+            raise ValueError(
+                f"The shape {blockVectorX.shape} "
+                f"of the postprocessing iterate not preserved\n"
+                f"and changed to {blockVectorBX.shape} "
+                f"after multiplying by the secondary matrix.\n"
+            )
+
+    gramXBX = np.dot(blockVectorX.T.conj(), blockVectorBX)
+    _handle_gramA_gramB_verbosity(gramXAX, gramXBX, verbosityLevel)
+    gramXAX = (gramXAX + gramXAX.T.conj()) / 2
+    gramXBX = (gramXBX + gramXBX.T.conj()) / 2
+    try:
+        _lambda, eigBlockVector = eigh(gramXAX,
+                                       gramXBX,
+                                       check_finite=False)
+    except LinAlgError as e:
+        raise ValueError("eigh has failed in lobpcg postprocessing") from e
+
+    ii = _get_indx(_lambda, sizeX, largest)
+    _lambda = _lambda[ii]
+    eigBlockVector = np.asarray(eigBlockVector[:, ii])
+
+    blockVectorX = np.dot(blockVectorX, eigBlockVector)
+    blockVectorAX = np.dot(blockVectorAX, eigBlockVector)
+
+    if B is not None:
+        blockVectorBX = np.dot(blockVectorBX, eigBlockVector)
+        aux = blockVectorBX * _lambda[np.newaxis, :]
+    else:
+        aux = blockVectorX * _lambda[np.newaxis, :]
+
+    blockVectorR = blockVectorAX - aux
+
+    aux = np.sum(blockVectorR.conj() * blockVectorR, 0)
+    residualNorms = np.sqrt(np.abs(aux))
+
+    if retLambdaHistory:
+        lambdaHistory[bestIterationNumber + 1, :] = _lambda
+    if retResidualNormsHistory:
+        residualNormsHistory[bestIterationNumber + 1, :] = residualNorms
+
+    if retLambdaHistory:
+        lambdaHistory = lambdaHistory[
+            : bestIterationNumber + 2, :]
+    if retResidualNormsHistory:
+        residualNormsHistory = residualNormsHistory[
+            : bestIterationNumber + 2, :]
+
+    if np.max(np.abs(residualNorms)) > residualTolerance:
+        warnings.warn(
+            f"Exited postprocessing with accuracies \n"
+            f"{residualNorms}\n"
+            f"not reaching the requested tolerance {residualTolerance}.",
+            UserWarning, stacklevel=2
+        )
+
+    if verbosityLevel:
+        print(f"Final postprocessing eigenvalue(s):\n{_lambda}")
+        print(f"Final residual norm(s):\n{residualNorms}")
+
+    if retLambdaHistory:
+        lambdaHistory = np.vsplit(lambdaHistory, np.shape(lambdaHistory)[0])
+        lambdaHistory = [np.squeeze(i) for i in lambdaHistory]
+    if retResidualNormsHistory:
+        residualNormsHistory = np.vsplit(residualNormsHistory,
+                                         np.shape(residualNormsHistory)[0])
+        residualNormsHistory = [np.squeeze(i) for i in residualNormsHistory]
+
+    if retLambdaHistory:
+        if retResidualNormsHistory:
+            return _lambda, blockVectorX, lambdaHistory, residualNormsHistory
+        else:
+            return _lambda, blockVectorX, lambdaHistory
+    else:
+        if retResidualNormsHistory:
+            return _lambda, blockVectorX, residualNormsHistory
+        else:
+            return _lambda, blockVectorX
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+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_eigen/lobpcg/tests/test_lobpcg.py
@@ -0,0 +1,722 @@
+""" Test functions for the sparse.linalg._eigen.lobpcg module
+"""
+
+import itertools
+import platform
+import sys
+import pytest
+import numpy as np
+from numpy import ones, r_, diag
+from numpy.testing import (assert_almost_equal, assert_equal,
+                           assert_allclose, assert_array_less)
+
+from scipy import sparse
+from scipy.linalg import (eigh, toeplitz,
+                          cholesky_banded, cho_solve_banded)
+from scipy.sparse import dia_array, eye_array, csr_array
+from scipy.sparse.linalg import eigsh, LinearOperator
+from scipy.sparse.linalg._eigen.lobpcg import lobpcg
+from scipy.sparse.linalg._eigen.lobpcg.lobpcg import _b_orthonormalize
+from scipy.sparse.linalg._special_sparse_arrays import (Sakurai,
+                                                        MikotaPair)
+
+_IS_32BIT = (sys.maxsize < 2**32)
+
+INT_DTYPES = (np.intc, np.long, np.longlong, np.uintc, np.ulong, np.ulonglong)
+# np.half is unsupported on many test systems so excluded
+REAL_DTYPES = (np.float32, np.float64, np.longdouble)
+COMPLEX_DTYPES = (np.complex64, np.complex128, np.clongdouble)
+INEXACTDTYPES = REAL_DTYPES + COMPLEX_DTYPES
+ALLDTYPES = INT_DTYPES + INEXACTDTYPES
+
+
+def sign_align(A, B):
+    """Align signs of columns of A match those of B: column-wise remove
+    sign of A by multiplying with its sign then multiply in sign of B.
+    """
+    return np.array([col_A * np.sign(col_A[0]) * np.sign(col_B[0])
+                     for col_A, col_B in zip(A.T, B.T)]).T
+
+def ElasticRod(n):
+    """Build the matrices for the generalized eigenvalue problem of the
+    fixed-free elastic rod vibration model.
+    """
+    L = 1.0
+    le = L/n
+    rho = 7.85e3
+    S = 1.e-4
+    E = 2.1e11
+    mass = rho*S*le/6.
+    k = E*S/le
+    A = k*(diag(r_[2.*ones(n-1), 1])-diag(ones(n-1), 1)-diag(ones(n-1), -1))
+    B = mass*(diag(r_[4.*ones(n-1), 2])+diag(ones(n-1), 1)+diag(ones(n-1), -1))
+    return A, B
+
+
+@pytest.mark.filterwarnings("ignore:The problem size")
+@pytest.mark.parametrize("n", [10, 20])
+@pytest.mark.filterwarnings("ignore:Exited at iteration")
+@pytest.mark.filterwarnings("ignore:Exited postprocessing")
+def test_ElasticRod(n):
+    """Check eigh vs. lobpcg consistency for elastic rod model.
+    """
+    A, B = ElasticRod(n)
+    m = 2
+    rnd = np.random.RandomState(0)
+    X = rnd.standard_normal((n, m))
+    eigvals, _ = lobpcg(A, X, B=B, tol=1e-2, maxiter=50, largest=False)
+    eigvals.sort()
+    w, _ = eigh(A, b=B)
+    w.sort()
+    assert_almost_equal(w[:int(m/2)], eigvals[:int(m/2)], decimal=2)
+
+
+@pytest.mark.parametrize("n", [50])
+@pytest.mark.parametrize("m", [1, 2, 10])
+@pytest.mark.filterwarnings("ignore:Casting complex values to real")
+@pytest.mark.filterwarnings("ignore::DeprecationWarning")
+@pytest.mark.filterwarnings("ignore:An ill-conditioned matrix")
+@pytest.mark.parametrize("Vdtype", INEXACTDTYPES)
+@pytest.mark.parametrize("Bdtype", ALLDTYPES)
+@pytest.mark.parametrize("BVdtype", INEXACTDTYPES)
+def test_b_orthonormalize(n, m, Vdtype, Bdtype, BVdtype):
+    """Test B-orthonormalization by Cholesky with callable 'B'.
+    The function '_b_orthonormalize' is key in LOBPCG but may
+    lead to numerical instabilities. The input vectors are often
+    badly scaled, so the function needs scale-invariant Cholesky;
+    see https://netlib.org/lapack/lawnspdf/lawn14.pdf.
+    """
+    rnd = np.random.RandomState(0)
+    X = rnd.standard_normal((n, m)).astype(Vdtype)
+    Xcopy = np.copy(X)
+    vals = np.arange(1, n+1, dtype=float)
+    B = dia_array(([vals], [0]), shape=(n, n)).astype(Bdtype)
+    BX = B @ X
+    BX = BX.astype(BVdtype)
+    is_all_complex = (np.issubdtype(Vdtype, np.complexfloating) and
+                     np.issubdtype(BVdtype, np.complexfloating))
+    is_all_notcomplex = (not np.issubdtype(Vdtype, np.complexfloating) and
+                        not np.issubdtype(Bdtype, np.complexfloating) and
+                        not np.issubdtype(BVdtype, np.complexfloating))
+
+    # All complex or all not complex can calculate in-place
+    check_inplace = is_all_complex or is_all_notcomplex
+    # np.longdouble tol cannot be achieved on most systems
+    atol = m * n * max(np.finfo(Vdtype).eps,
+                       np.finfo(BVdtype).eps,
+                       np.finfo(np.float64).eps)
+
+    Xo, BXo, _ = _b_orthonormalize(lambda v: B @ v, X, BX)
+    if check_inplace:
+        # Check in-place
+        assert_equal(X, Xo)
+        assert_equal(id(X), id(Xo))
+        assert_equal(BX, BXo)
+        assert_equal(id(BX), id(BXo))
+    # Check BXo
+    assert_allclose(B @ Xo, BXo, atol=atol, rtol=atol)
+    # Check B-orthonormality
+    assert_allclose(Xo.T.conj() @ B @ Xo, np.identity(m),
+                    atol=atol, rtol=atol)
+    # Repeat without BX in outputs
+    X = np.copy(Xcopy)
+    Xo1, BXo1, _ = _b_orthonormalize(lambda v: B @ v, X)
+    assert_allclose(Xo, Xo1, atol=atol, rtol=atol)
+    assert_allclose(BXo, BXo1, atol=atol, rtol=atol)
+    if check_inplace:
+        # Check in-place.
+        assert_equal(X, Xo1)
+        assert_equal(id(X), id(Xo1))
+    # Check BXo1
+    assert_allclose(B @ Xo1, BXo1, atol=atol, rtol=atol)
+
+    # Introduce column-scaling in X
+    scaling = 1.0 / np.geomspace(10, 1e10, num=m)
+    X = Xcopy * scaling
+    X = X.astype(Vdtype)
+    BX = B @ X
+    BX = BX.astype(BVdtype)
+    # Check scaling-invariance of Cholesky-based orthonormalization
+    # XXX: internally, _b_orthonormalize tries to invert an ill-conditioned matrix
+    Xo1, BXo1, _ = _b_orthonormalize(lambda v: B @ v, X, BX)
+    # The output should be the same, up the signs of the columns
+    Xo1 =  sign_align(Xo1, Xo)
+    assert_allclose(Xo, Xo1, atol=atol, rtol=atol)
+    BXo1 =  sign_align(BXo1, BXo)
+    assert_allclose(BXo, BXo1, atol=atol, rtol=atol)
+
+
+@pytest.mark.filterwarnings("ignore:Exited at iteration 0")
+@pytest.mark.filterwarnings("ignore:Exited postprocessing")
+def test_nonhermitian_warning(capsys):
+    """Check the warning of a Ritz matrix being not Hermitian
+    by feeding a non-Hermitian input matrix.
+    Also check stdout since verbosityLevel=1 and lack of stderr.
+    """
+    n = 10
+    X = np.arange(n * 2).reshape(n, 2).astype(np.float32)
+    A = np.arange(n * n).reshape(n, n).astype(np.float32)
+    with pytest.warns(UserWarning, match="Matrix gramA"):
+        _, _ = lobpcg(A, X, verbosityLevel=1, maxiter=0)
+    out, err = capsys.readouterr()  # Capture output
+    assert out.startswith("Solving standard eigenvalue")  # Test stdout
+    assert err == ''  # Test empty stderr
+    # Make the matrix symmetric and the UserWarning disappears.
+    A += A.T
+    _, _ = lobpcg(A, X, verbosityLevel=1, maxiter=0)
+    out, err = capsys.readouterr()  # Capture output
+    assert out.startswith("Solving standard eigenvalue")  # Test stdout
+    assert err == ''  # Test empty stderr
+
+
+def test_regression():
+    """Check the eigenvalue of the identity matrix is one.
+    """
+    # https://mail.python.org/pipermail/scipy-user/2010-October/026944.html
+    n = 10
+    X = np.ones((n, 1))
+    A = np.identity(n)
+    w, _ = lobpcg(A, X)
+    assert_allclose(w, [1])
+
+
+@pytest.mark.filterwarnings("ignore:The problem size")
+@pytest.mark.parametrize('n, m, m_excluded', [(30, 4, 3), (4, 2, 0)])
+def test_diagonal(n, m, m_excluded):
+    """Test ``m - m_excluded`` eigenvalues and eigenvectors of
+    diagonal matrices of the size ``n`` varying matrix formats:
+    dense array, spare matrix, and ``LinearOperator`` for both
+    matrixes in the generalized eigenvalue problem ``Av = cBv``
+    and for the preconditioner.
+    """
+    rnd = np.random.RandomState(0)
+
+    # Define the generalized eigenvalue problem Av = cBv
+    # where (c, v) is a generalized eigenpair,
+    # A is the diagonal matrix whose entries are 1,...n,
+    # B is the identity matrix.
+    vals = np.arange(1, n+1, dtype=float)
+    A_s = dia_array(([vals], [0]), shape=(n, n))
+    A_a = A_s.toarray()
+
+    def A_f(x):
+        return A_s @ x
+
+    A_lo = LinearOperator(matvec=A_f,
+                          matmat=A_f,
+                          shape=(n, n), dtype=float)
+
+    B_a = eye_array(n)
+    B_s = csr_array(B_a)
+
+    def B_f(x):
+        return B_a @ x
+
+    B_lo = LinearOperator(matvec=B_f,
+                          matmat=B_f,
+                          shape=(n, n), dtype=float)
+
+    # Let the preconditioner M be the inverse of A.
+    M_s = dia_array(([1./vals], [0]), shape=(n, n))
+    M_a = M_s.toarray()
+
+    def M_f(x):
+        return M_s @ x
+
+    M_lo = LinearOperator(matvec=M_f,
+                          matmat=M_f,
+                          shape=(n, n), dtype=float)
+
+    # Pick random initial vectors.
+    X = rnd.normal(size=(n, m))
+
+    # Require that the returned eigenvectors be in the orthogonal complement
+    # of the first few standard basis vectors.
+    if m_excluded > 0:
+        Y = np.eye(n, m_excluded)
+    else:
+        Y = None
+
+    for A in [A_a, A_s, A_lo]:
+        for B in [B_a, B_s, B_lo]:
+            for M in [M_a, M_s, M_lo]:
+                eigvals, vecs = lobpcg(A, X, B, M=M, Y=Y,
+                                       maxiter=40, largest=False)
+
+                assert_allclose(eigvals, np.arange(1+m_excluded,
+                                                   1+m_excluded+m))
+                _check_eigen(A, eigvals, vecs, rtol=1e-3, atol=1e-3)
+
+
+def _check_eigen(M, w, V, rtol=1e-8, atol=1e-14):
+    """Check if the eigenvalue residual is small.
+    """
+    mult_wV = np.multiply(w, V)
+    dot_MV = M.dot(V)
+    assert_allclose(mult_wV, dot_MV, rtol=rtol, atol=atol)
+
+
+def _check_fiedler(n, p):
+    """Check the Fiedler vector computation.
+    """
+    # This is not necessarily the recommended way to find the Fiedler vector.
+    col = np.zeros(n)
+    col[1] = 1
+    A = toeplitz(col)
+    D = np.diag(A.sum(axis=1))
+    L = D - A
+    # Compute the full eigendecomposition using tricks, e.g.
+    # http://www.cs.yale.edu/homes/spielman/561/2009/lect02-09.pdf
+    tmp = np.pi * np.arange(n) / n
+    analytic_w = 2 * (1 - np.cos(tmp))
+    analytic_V = np.cos(np.outer(np.arange(n) + 1/2, tmp))
+    _check_eigen(L, analytic_w, analytic_V)
+    # Compute the full eigendecomposition using eigh.
+    eigh_w, eigh_V = eigh(L)
+    _check_eigen(L, eigh_w, eigh_V)
+    # Check that the first eigenvalue is near zero and that the rest agree.
+    assert_array_less(np.abs([eigh_w[0], analytic_w[0]]), 1e-14)
+    assert_allclose(eigh_w[1:], analytic_w[1:])
+
+    # Check small lobpcg eigenvalues.
+    X = analytic_V[:, :p]
+    lobpcg_w, lobpcg_V = lobpcg(L, X, largest=False)
+    assert_equal(lobpcg_w.shape, (p,))
+    assert_equal(lobpcg_V.shape, (n, p))
+    _check_eigen(L, lobpcg_w, lobpcg_V)
+    assert_array_less(np.abs(np.min(lobpcg_w)), 1e-14)
+    assert_allclose(np.sort(lobpcg_w)[1:], analytic_w[1:p])
+
+    # Check large lobpcg eigenvalues.
+    X = analytic_V[:, -p:]
+    lobpcg_w, lobpcg_V = lobpcg(L, X, largest=True)
+    assert_equal(lobpcg_w.shape, (p,))
+    assert_equal(lobpcg_V.shape, (n, p))
+    _check_eigen(L, lobpcg_w, lobpcg_V)
+    assert_allclose(np.sort(lobpcg_w), analytic_w[-p:])
+
+    # Look for the Fiedler vector using good but not exactly correct guesses.
+    fiedler_guess = np.concatenate((np.ones(n//2), -np.ones(n-n//2)))
+    X = np.vstack((np.ones(n), fiedler_guess)).T
+    lobpcg_w, _ = lobpcg(L, X, largest=False)
+    # Mathematically, the smaller eigenvalue should be zero
+    # and the larger should be the algebraic connectivity.
+    lobpcg_w = np.sort(lobpcg_w)
+    assert_allclose(lobpcg_w, analytic_w[:2], atol=1e-14)
+
+
+def test_fiedler_small_8():
+    """Check the dense workaround path for small matrices.
+    """
+    # This triggers the dense path because 8 < 2*5.
+    with pytest.warns(UserWarning, match="The problem size"):
+        _check_fiedler(8, 2)
+
+
+def test_fiedler_large_12():
+    """Check the dense workaround path avoided for non-small matrices.
+    """
+    # This does not trigger the dense path, because 2*5 <= 12.
+    _check_fiedler(12, 2)
+
+
+@pytest.mark.filterwarnings("ignore:Failed at iteration")
+@pytest.mark.filterwarnings("ignore:Exited at iteration")
+@pytest.mark.filterwarnings("ignore:Exited postprocessing")
+def test_failure_to_run_iterations():
+    """Check that the code exits gracefully without breaking. Issue #10974.
+    The code may or not issue a warning, filtered out. Issue #15935, #17954.
+    """
+    rnd = np.random.RandomState(0)
+    X = rnd.standard_normal((100, 10))
+    A = X @ X.T
+    Q = rnd.standard_normal((X.shape[0], 4))
+    eigenvalues, _ = lobpcg(A, Q, maxiter=40, tol=1e-12)
+    assert np.max(eigenvalues) > 0
+
+
+def test_failure_to_run_iterations_nonsymmetric():
+    """Check that the code exists gracefully without breaking
+    if the matrix in not symmetric.
+    """
+    A = np.zeros((10, 10))
+    A[0, 1] = 1
+    Q = np.ones((10, 1))
+    msg = "Exited at iteration 2|Exited postprocessing with accuracies.*"
+    with pytest.warns(UserWarning, match=msg):
+        eigenvalues, _ = lobpcg(A, Q, maxiter=20)
+    assert np.max(eigenvalues) > 0
+
+
+@pytest.mark.filterwarnings("ignore:The problem size")
+def test_hermitian():
+    """Check complex-value Hermitian cases.
+    """
+    rnd = np.random.RandomState(0)
+
+    sizes = [3, 12]
+    ks = [1, 2]
+    gens = [True, False]
+
+    for s, k, gen, dh, dx, db in (
+        itertools.product(sizes, ks, gens, gens, gens, gens)
+    ):
+        H = rnd.random((s, s)) + 1.j * rnd.random((s, s))
+        H = 10 * np.eye(s) + H + H.T.conj()
+        H = H.astype(np.complex128) if dh else H.astype(np.complex64)
+
+        X = rnd.standard_normal((s, k))
+        X = X + 1.j * rnd.standard_normal((s, k))
+        X = X.astype(np.complex128) if dx else X.astype(np.complex64)
+
+        if not gen:
+            B = np.eye(s)
+            w, v = lobpcg(H, X, maxiter=99, verbosityLevel=0)
+            # Also test mixing complex H with real B.
+            wb, _ = lobpcg(H, X, B, maxiter=99, verbosityLevel=0)
+            assert_allclose(w, wb, rtol=1e-6)
+            w0, _ = eigh(H)
+        else:
+            B = rnd.random((s, s)) + 1.j * rnd.random((s, s))
+            B = 10 * np.eye(s) + B.dot(B.T.conj())
+            B = B.astype(np.complex128) if db else B.astype(np.complex64)
+            w, v = lobpcg(H, X, B, maxiter=99, verbosityLevel=0)
+            w0, _ = eigh(H, B)
+
+        for wx, vx in zip(w, v.T):
+            # Check eigenvector
+            assert_allclose(np.linalg.norm(H.dot(vx) - B.dot(vx) * wx)
+                            / np.linalg.norm(H.dot(vx)),
+                            0, atol=5e-2, rtol=0)
+
+            # Compare eigenvalues
+            j = np.argmin(abs(w0 - wx))
+            assert_allclose(wx, w0[j], rtol=1e-4)
+
+
+# The n=5 case tests the alternative small matrix code path that uses eigh().
+@pytest.mark.filterwarnings("ignore:The problem size")
+@pytest.mark.parametrize('n, atol', [(20, 1e-3), (5, 1e-8)])
+def test_eigsh_consistency(n, atol):
+    """Check eigsh vs. lobpcg consistency.
+    """
+    vals = np.arange(1, n+1, dtype=np.float64)
+    A = dia_array((vals, 0), shape=(n, n))
+    rnd = np.random.RandomState(0)
+    X = rnd.standard_normal((n, 2))
+    lvals, lvecs = lobpcg(A, X, largest=True, maxiter=100)
+    vals, _ = eigsh(A, k=2)
+
+    _check_eigen(A, lvals, lvecs, atol=atol, rtol=0)
+    assert_allclose(np.sort(vals), np.sort(lvals), atol=1e-14)
+
+
+def test_verbosity():
+    """Check that nonzero verbosity level code runs.
+    """
+    rnd = np.random.RandomState(0)
+    X = rnd.standard_normal((10, 10))
+    A = X @ X.T
+    Q = rnd.standard_normal((X.shape[0], 1))
+    msg = "Exited at iteration.*|Exited postprocessing with accuracies.*"
+    with pytest.warns(UserWarning, match=msg):
+        _, _ = lobpcg(A, Q, maxiter=3, verbosityLevel=9)
+
+
+@pytest.mark.xfail(_IS_32BIT and sys.platform == 'win32',
+                   reason="tolerance violation on windows")
+@pytest.mark.xfail(platform.machine() == 'ppc64le',
+                   reason="fails on ppc64le")
+@pytest.mark.filterwarnings("ignore:Exited postprocessing")
+def test_tolerance_float32():
+    """Check lobpcg for attainable tolerance in float32.
+    """
+    rnd = np.random.RandomState(0)
+    n = 50
+    m = 3
+    vals = -np.arange(1, n + 1)
+    A = dia_array(([vals], [0]), shape=(n, n))
+    A = A.astype(np.float32)
+    X = rnd.standard_normal((n, m))
+    X = X.astype(np.float32)
+    eigvals, _ = lobpcg(A, X, tol=1.25e-5, maxiter=50, verbosityLevel=0)
+    assert_allclose(eigvals, -np.arange(1, 1 + m), atol=2e-5, rtol=1e-5)
+
+
+@pytest.mark.filterwarnings("ignore::DeprecationWarning")
+@pytest.mark.parametrize("vdtype", INEXACTDTYPES)
+@pytest.mark.parametrize("mdtype", ALLDTYPES)
+@pytest.mark.parametrize("arr_type", [np.array,
+                                      sparse.csr_array,
+                                      sparse.coo_array])
+def test_dtypes(vdtype, mdtype, arr_type):
+    """Test lobpcg in various dtypes.
+    """
+    rnd = np.random.RandomState(0)
+    n = 12
+    m = 2
+    A = arr_type(np.diag(np.arange(1, n + 1)).astype(mdtype))
+    X = rnd.random((n, m))
+    X = X.astype(vdtype)
+    eigvals, eigvecs = lobpcg(A, X, tol=1e-2, largest=False)
+    assert_allclose(eigvals, np.arange(1, 1 + m), atol=1e-1)
+    # eigenvectors must be nearly real in any case
+    assert_allclose(np.sum(np.abs(eigvecs - eigvecs.conj())), 0, atol=1e-2)
+
+
+@pytest.mark.filterwarnings("ignore:Exited at iteration")
+@pytest.mark.filterwarnings("ignore:Exited postprocessing")
+def test_inplace_warning():
+    """Check lobpcg gives a warning in '_b_orthonormalize'
+    that in-place orthogonalization is impossible due to dtype mismatch.
+    """
+    rnd = np.random.RandomState(0)
+    n = 6
+    m = 1
+    vals = -np.arange(1, n + 1)
+    A = dia_array(([vals], [0]), shape=(n, n))
+    A = A.astype(np.cdouble)
+    X = rnd.standard_normal((n, m))
+    with pytest.warns(UserWarning, match="Inplace update"):
+        eigvals, _ = lobpcg(A, X, maxiter=2, verbosityLevel=1)
+
+
+def test_maxit():
+    """Check lobpcg if maxit=maxiter runs maxiter iterations and
+    if maxit=None runs 20 iterations (the default)
+    by checking the size of the iteration history output, which should
+    be the number of iterations plus 3 (initial, final, and postprocessing)
+    typically when maxiter is small and the choice of the best is passive.
+    """
+    rnd = np.random.RandomState(0)
+    n = 50
+    m = 4
+    vals = -np.arange(1, n + 1)
+    A = dia_array(([vals], [0]), shape=(n, n))
+    A = A.astype(np.float32)
+    X = rnd.standard_normal((n, m))
+    X = X.astype(np.float64)
+    msg = "Exited at iteration.*|Exited postprocessing with accuracies.*"
+    for maxiter in range(1, 4):
+        with pytest.warns(UserWarning, match=msg):
+            _, _, l_h, r_h = lobpcg(A, X, tol=1e-8, maxiter=maxiter,
+                                    retLambdaHistory=True,
+                                    retResidualNormsHistory=True)
+        assert_allclose(np.shape(l_h)[0], maxiter+3)
+        assert_allclose(np.shape(r_h)[0], maxiter+3)
+    with pytest.warns(UserWarning, match=msg):
+        l, _, l_h, r_h = lobpcg(A, X, tol=1e-8,
+                                retLambdaHistory=True,
+                                retResidualNormsHistory=True)
+    assert_allclose(np.shape(l_h)[0], 20+3)
+    assert_allclose(np.shape(r_h)[0], 20+3)
+    # Check that eigenvalue output is the last one in history
+    assert_allclose(l, l_h[-1])
+    # Make sure that both history outputs are lists
+    assert isinstance(l_h, list)
+    assert isinstance(r_h, list)
+    # Make sure that both history lists are arrays-like
+    assert_allclose(np.shape(l_h), np.shape(np.asarray(l_h)))
+    assert_allclose(np.shape(r_h), np.shape(np.asarray(r_h)))
+
+
+@pytest.mark.xslow
+@pytest.mark.filterwarnings("ignore:Exited at iteration")
+@pytest.mark.filterwarnings("ignore:Exited postprocessing")
+def test_sakurai():
+    """Check lobpcg and eighs accuracy for the Sakurai example
+    already used in `benchmarks/benchmarks/sparse_linalg_lobpcg.py`.
+    """
+    n = 50
+    tol = 100 * n * n * n* np.finfo(float).eps
+    sakurai_obj = Sakurai(n, dtype='int')
+    A = sakurai_obj
+    m = 3
+    ee = sakurai_obj.eigenvalues(3)
+    rng = np.random.default_rng(0)
+    X = rng.normal(size=(n, m))
+    el, _ = lobpcg(A, X, tol=1e-9, maxiter=5000, largest=False)
+    accuracy = max(abs(ee - el) / ee)
+    assert_allclose(accuracy, 0., atol=tol)
+    a_l = LinearOperator((n, n), matvec=A, matmat=A, dtype='float64')
+    ea, _ = eigsh(a_l, k=m, which='SA', tol=1e-9, maxiter=15000,
+                  v0 = rng.normal(size=(n, 1)))
+    accuracy = max(abs(ee - ea) / ee)
+    assert_allclose(accuracy, 0., atol=tol)
+
+
+@pytest.mark.parametrize("n", [500, 1000])
+@pytest.mark.filterwarnings("ignore:Exited at iteration")
+@pytest.mark.filterwarnings("ignore:Exited postprocessing")
+def test_sakurai_inverse(n):
+    """Check lobpcg and eighs accuracy for the sakurai_inverse example
+    already used in `benchmarks/benchmarks/sparse_linalg_lobpcg.py`.
+    """
+    def a(x):
+        return cho_solve_banded((c, False), x)
+    tol = 100 * n * n * n* np.finfo(float).eps
+    sakurai_obj = Sakurai(n)
+    A = sakurai_obj.tobanded().astype(np.float64)
+    m = 3
+    ee = sakurai_obj.eigenvalues(3)
+    rng = np.random.default_rng(0)
+    X = rng.normal(size=(n, m))
+    c = cholesky_banded(A)
+    el, _ = lobpcg(a, X, tol=1e-9, maxiter=8)
+    accuracy = max(abs(ee - 1. / el) / ee)
+    assert_allclose(accuracy, 0., atol=tol)
+    a_l = LinearOperator((n, n), matvec=a, matmat=a, dtype='float64')
+    ea, _ = eigsh(a_l, k=m, which='LA', tol=1e-9, maxiter=8,
+                  v0 = rng.normal(size=(n, 1)))
+    accuracy = max(abs(ee - np.sort(1. / ea)) / ee)
+    assert_allclose(accuracy, 0., atol=tol)
+
+
+@pytest.mark.filterwarnings("ignore:The problem size")
+@pytest.mark.parametrize("n", [10, 20, 128, 256, 512, 1024, 2048])
+@pytest.mark.filterwarnings("ignore:Exited at iteration")
+@pytest.mark.filterwarnings("ignore:Exited postprocessing")
+def test_MikotaPair(n):
+    """Check lobpcg and eighs accuracy for the Mikota example
+    already used in `benchmarks/benchmarks/sparse_linalg_lobpcg.py`.
+    """
+    def a(x):
+        return cho_solve_banded((c, False), x)
+    mik = MikotaPair(n)
+    mik_k = mik.k
+    mik_m = mik.m
+    Ac = mik_k
+    Bc = mik_m
+    Ab = mik_k.tobanded()
+    eigenvalues = mik.eigenvalues
+    if n == 10:
+        m = 3 # lobpcg calls eigh
+    elif n == 20:
+        m = 2
+    else:
+        m = 10
+    ee = eigenvalues(m)
+    tol = 100 * m * n * n * np.finfo(float).eps
+    rng = np.random.default_rng(0)
+    X = rng.normal(size=(n, m))
+    c = cholesky_banded(Ab.astype(np.float32))
+    el, _ = lobpcg(Ac, X, Bc, M=a, tol=1e-4,
+                   maxiter=40, largest=False)
+    accuracy = max(abs(ee - el) / ee)
+    assert_allclose(accuracy, 0., atol=tol)
+    B = LinearOperator((n, n), matvec=Bc, matmat=Bc, dtype='float64')
+    A = LinearOperator((n, n), matvec=Ac, matmat=Ac, dtype='float64')
+    c = cholesky_banded(Ab)
+    a_l = LinearOperator((n, n), matvec=a, matmat=a, dtype='float64')
+    ea, _ = eigsh(B, k=m, M=A, Minv=a_l, which='LA', tol=1e-4, maxiter=50,
+                  v0 = rng.normal(size=(n, 1)))
+    accuracy = max(abs(ee - np.sort(1./ea)) / ee)
+    assert_allclose(accuracy, 0., atol=tol)
+
+
+@pytest.mark.slow
+@pytest.mark.parametrize("n", [15])
+@pytest.mark.parametrize("m", [1, 2])
+@pytest.mark.filterwarnings("ignore:Exited at iteration")
+@pytest.mark.filterwarnings("ignore:Exited postprocessing")
+def test_diagonal_data_types(n, m):
+    """Check lobpcg for diagonal matrices for all matrix types.
+    Constraints are imposed, so a dense eigensolver eig cannot run.
+    """
+    rnd = np.random.RandomState(0)
+    # Define the generalized eigenvalue problem Av = cBv
+    # where (c, v) is a generalized eigenpair,
+    # and where we choose A  and B to be diagonal.
+    vals = np.arange(1, n + 1)
+
+    list_sparse_format = ['bsr', 'coo', 'csc', 'csr', 'dia', 'dok', 'lil']
+    for s_f_i, s_f in enumerate(list_sparse_format):
+
+        As64 = dia_array(([vals * vals], [0]), shape=(n, n)).asformat(s_f)
+        As32 = As64.astype(np.float32)
+        Af64 = As64.toarray()
+        Af32 = Af64.astype(np.float32)
+
+        def As32f(x):
+            return As32 @ x
+        As32LO = LinearOperator(matvec=As32f,
+                                matmat=As32f,
+                                shape=(n, n),
+                                dtype=As32.dtype)
+
+        listA = [Af64, As64, Af32, As32, As32f, As32LO, lambda v: As32 @ v]
+
+        Bs64 = dia_array(([vals], [0]), shape=(n, n)).asformat(s_f)
+        Bf64 = Bs64.toarray()
+        Bs32 = Bs64.astype(np.float32)
+
+        def Bs32f(x):
+            return Bs32 @ x
+        Bs32LO = LinearOperator(matvec=Bs32f,
+                                matmat=Bs32f,
+                                shape=(n, n),
+                                dtype=Bs32.dtype)
+        listB = [Bf64, Bs64, Bs32, Bs32f, Bs32LO, lambda v: Bs32 @ v]
+
+        # Define the preconditioner function as LinearOperator.
+        Ms64 = dia_array(([1./vals], [0]), shape=(n, n)).asformat(s_f)
+
+        def Ms64precond(x):
+            return Ms64 @ x
+        Ms64precondLO = LinearOperator(matvec=Ms64precond,
+                                       matmat=Ms64precond,
+                                       shape=(n, n),
+                                       dtype=Ms64.dtype)
+        Mf64 = Ms64.toarray()
+
+        def Mf64precond(x):
+            return Mf64 @ x
+        Mf64precondLO = LinearOperator(matvec=Mf64precond,
+                                       matmat=Mf64precond,
+                                       shape=(n, n),
+                                       dtype=Mf64.dtype)
+        Ms32 = Ms64.astype(np.float32)
+
+        def Ms32precond(x):
+            return Ms32 @ x
+        Ms32precondLO = LinearOperator(matvec=Ms32precond,
+                                       matmat=Ms32precond,
+                                       shape=(n, n),
+                                       dtype=Ms32.dtype)
+        Mf32 = Ms32.toarray()
+
+        def Mf32precond(x):
+            return Mf32 @ x
+        Mf32precondLO = LinearOperator(matvec=Mf32precond,
+                                       matmat=Mf32precond,
+                                       shape=(n, n),
+                                       dtype=Mf32.dtype)
+        listM = [None, Ms64, Ms64precondLO, Mf64precondLO, Ms64precond,
+                 Ms32, Ms32precondLO, Mf32precondLO, Ms32precond]
+
+        # Setup matrix of the initial approximation to the eigenvectors
+        # (cannot be sparse array).
+        Xf64 = rnd.random((n, m))
+        Xf32 = Xf64.astype(np.float32)
+        listX = [Xf64, Xf32]
+
+        # Require that the returned eigenvectors be in the orthogonal complement
+        # of the first few standard basis vectors (cannot be sparse array).
+        m_excluded = 3
+        Yf64 = np.eye(n, m_excluded, dtype=float)
+        Yf32 = np.eye(n, m_excluded, dtype=np.float32)
+        listY = [Yf64, Yf32]
+
+        tests = list(itertools.product(listA, listB, listM, listX, listY))
+
+        for A, B, M, X, Y in tests:
+            # This is one of the slower tests because there are >1,000 configs
+            # to test here. Flip a biased coin to decide whether to run  each
+            # test to get decent coverage in less time.
+            if rnd.random() < 0.98:
+                continue  # too many tests
+            eigvals, _ = lobpcg(A, X, B=B, M=M, Y=Y, tol=1e-4,
+                                maxiter=100, largest=False)
+            assert_allclose(eigvals,
+                            np.arange(1 + m_excluded, 1 + m_excluded + m),
+                            atol=1e-5)
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+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_eigen/tests/test_svds.py
@@ -0,0 +1,893 @@
+import re
+import copy
+import numpy as np
+
+from numpy.testing import assert_allclose, assert_equal, assert_array_equal
+import pytest
+
+from scipy._lib._array_api import SCIPY_ARRAY_API
+from scipy.linalg import svd, null_space
+from scipy.sparse import csc_array, issparse, dia_array, random_array
+from scipy.sparse.linalg import LinearOperator, aslinearoperator
+from scipy.sparse.linalg import svds
+from scipy.sparse.linalg._eigen.arpack import ArpackNoConvergence
+
+
+# --- Helper Functions / Classes ---
+
+
+def sorted_svd(m, k, which='LM'):
+    # Compute svd of a dense matrix m, and return singular vectors/values
+    # sorted.
+    if issparse(m):
+        m = m.toarray()
+    u, s, vh = svd(m)
+    if which == 'LM':
+        ii = np.argsort(s)[-k:]
+    elif which == 'SM':
+        ii = np.argsort(s)[:k]
+    else:
+        raise ValueError(f"unknown which={which!r}")
+
+    return u[:, ii], s[ii], vh[ii]
+
+
+def _check_svds(A, k, u, s, vh, which="LM", check_usvh_A=False,
+                check_svd=True, atol=1e-10, rtol=1e-7):
+    n, m = A.shape
+
+    # Check shapes.
+    assert_equal(u.shape, (n, k))
+    assert_equal(s.shape, (k,))
+    assert_equal(vh.shape, (k, m))
+
+    # Check that the original matrix can be reconstituted.
+    A_rebuilt = (u*s).dot(vh)
+    assert_equal(A_rebuilt.shape, A.shape)
+    if check_usvh_A:
+        assert_allclose(A_rebuilt, A, atol=atol, rtol=rtol)
+
+    # Check that u is a semi-orthogonal matrix.
+    uh_u = np.dot(u.T.conj(), u)
+    assert_equal(uh_u.shape, (k, k))
+    assert_allclose(uh_u, np.identity(k), atol=atol, rtol=rtol)
+
+    # Check that vh is a semi-orthogonal matrix.
+    vh_v = np.dot(vh, vh.T.conj())
+    assert_equal(vh_v.shape, (k, k))
+    assert_allclose(vh_v, np.identity(k), atol=atol, rtol=rtol)
+
+    # Check that scipy.sparse.linalg.svds ~ scipy.linalg.svd
+    if check_svd:
+        u2, s2, vh2 = sorted_svd(A, k, which)
+        assert_allclose(np.abs(u), np.abs(u2), atol=atol, rtol=rtol)
+        assert_allclose(s, s2, atol=atol, rtol=rtol)
+        assert_allclose(np.abs(vh), np.abs(vh2), atol=atol, rtol=rtol)
+
+
+def _check_svds_n(A, k, u, s, vh, which="LM", check_res=True,
+                  check_svd=True, atol=1e-10, rtol=1e-7):
+    n, m = A.shape
+
+    # Check shapes.
+    assert_equal(u.shape, (n, k))
+    assert_equal(s.shape, (k,))
+    assert_equal(vh.shape, (k, m))
+
+    # Check that u is a semi-orthogonal matrix.
+    uh_u = np.dot(u.T.conj(), u)
+    assert_equal(uh_u.shape, (k, k))
+    error = np.sum(np.abs(uh_u - np.identity(k))) / (k * k)
+    assert_allclose(error, 0.0, atol=atol, rtol=rtol)
+
+    # Check that vh is a semi-orthogonal matrix.
+    vh_v = np.dot(vh, vh.T.conj())
+    assert_equal(vh_v.shape, (k, k))
+    error = np.sum(np.abs(vh_v - np.identity(k))) / (k * k)
+    assert_allclose(error, 0.0, atol=atol, rtol=rtol)
+
+    # Check residuals
+    if check_res:
+        ru = A.T.conj() @ u - vh.T.conj() * s
+        rus = np.sum(np.abs(ru)) / (n * k)
+        rvh = A @ vh.T.conj() - u * s
+        rvhs = np.sum(np.abs(rvh)) / (m * k)
+        assert_allclose(rus, 0.0, atol=atol, rtol=rtol)
+        assert_allclose(rvhs, 0.0, atol=atol, rtol=rtol)
+
+    # Check that scipy.sparse.linalg.svds ~ scipy.linalg.svd
+    if check_svd:
+        u2, s2, vh2 = sorted_svd(A, k, which)
+        assert_allclose(s, s2, atol=atol, rtol=rtol)
+        A_rebuilt_svd = (u2*s2).dot(vh2)
+        A_rebuilt = (u*s).dot(vh)
+        assert_equal(A_rebuilt.shape, A.shape)
+        error = np.sum(np.abs(A_rebuilt_svd - A_rebuilt)) / (k * k)
+        assert_allclose(error, 0.0, atol=atol, rtol=rtol)
+
+
+class CheckingLinearOperator(LinearOperator):
+    def __init__(self, A):
+        self.A = A
+        super().__init__(dtype=A.dtype, shape=A.shape)
+
+    def _matvec(self, x):
+        assert_equal(max(x.shape), np.size(x))
+        return self.A.dot(x)
+
+    def _rmatvec(self, x):
+        assert_equal(max(x.shape), np.size(x))
+        return self.A.T.conjugate().dot(x)
+
+
+# --- Test Input Validation ---
+# Tests input validation on parameters `k` and `which`.
+# Needs better input validation checks for all other parameters.
+
+class SVDSCommonTests:
+
+    solver = None
+
+    # some of these IV tests could run only once, say with solver=None
+
+    _A_empty_msg = "`A` must not be empty."
+    _A_dtype_msg = "`A` must be of numeric data type"
+    _A_type_msg = "type not understood"
+    _A_ndim_msg = "Only 2-D input"
+    _A_validation_inputs = [
+        (np.asarray([[]]), ValueError, _A_empty_msg),
+        (
+            np.array([['a', 'b'], ['c', 'd']], dtype='object'),
+            TypeError if SCIPY_ARRAY_API else ValueError,
+            "only boolean and numerical dtypes" if SCIPY_ARRAY_API else _A_dtype_msg
+        ),
+        ("hi", TypeError, _A_type_msg),
+        (np.asarray([[[1., 2.], [3., 4.]]]), ValueError, _A_ndim_msg)]
+
+    @pytest.mark.parametrize("args", _A_validation_inputs)
+    def test_svds_input_validation_A(self, args):
+        A, error_type, message = args
+        with pytest.raises(error_type, match=message):
+            svds(A, k=1, solver=self.solver, rng=0)
+
+    @pytest.mark.parametrize("which", ["LM", "SM"])
+    def test_svds_int_A(self, which):
+        A = np.asarray([[1, 2], [3, 4]])
+        if self.solver == 'lobpcg':
+            with pytest.warns(UserWarning, match="The problem size"):
+                res = svds(A, k=1, which=which, solver=self.solver, rng=0)
+        else:
+            res = svds(A, k=1, which=which, solver=self.solver, rng=0)
+        _check_svds(A, 1, *res, which=which, atol=8e-10)
+
+    def test_svds_diff0_docstring_example(self):
+        def diff0(a):
+            return np.diff(a, axis=0)
+        def diff0t(a):
+            if a.ndim == 1:
+                a = a[:,np.newaxis]  # Turn 1D into 2D array
+            d = np.zeros((a.shape[0] + 1, a.shape[1]), dtype=a.dtype)
+            d[0, :] = - a[0, :]
+            d[1:-1, :] = a[0:-1, :] - a[1:, :]
+            d[-1, :] = a[-1, :]
+            return d
+        def diff0_func_aslo_def(n):
+            return LinearOperator(matvec=diff0,
+                                  matmat=diff0,
+                                  rmatvec=diff0t,
+                                  rmatmat=diff0t,
+                                  shape=(n - 1, n))
+        n = 100
+        diff0_func_aslo = diff0_func_aslo_def(n)
+        rng = np.random.default_rng(1758043640965324)
+        u, s, _ = svds(diff0_func_aslo, k=3, which='SM', rng=rng)
+        se = 2. * np.sin(np.pi * np.arange(1, 4) / (2. * n))
+        ue = np.sqrt(2 / n) * np.sin(np.pi * np.outer(np.arange(1, n),
+                                     np.arange(1, 4)) / n)
+        assert_allclose(s, se, atol=1e-3)
+        assert_allclose(np.abs(u), np.abs(ue), atol=1e-6)
+
+    @pytest.mark.parametrize("k", [-1, 0, 3, 4, 5, 1.5, "1"])
+    def test_svds_input_validation_k_1(self, k):
+        rng = np.random.default_rng(0)
+        A = rng.random((4, 3))
+
+        # propack can do complete SVD
+        if self.solver == 'propack' and k == 3:
+            res = svds(A, k=k, solver=self.solver, rng=0)
+            _check_svds(A, k, *res, check_usvh_A=True, check_svd=True)
+            return
+
+        message = ("`k` must be an integer satisfying")
+        with pytest.raises(ValueError, match=message):
+            svds(A, k=k, solver=self.solver, rng=0)
+
+    def test_svds_input_validation_k_2(self):
+        # I think the stack trace is reasonable when `k` can't be converted
+        # to an int.
+        message = "int() argument must be a"
+        with pytest.raises(TypeError, match=re.escape(message)):
+            svds(np.eye(10), k=[], solver=self.solver, rng=0)
+
+        message = "invalid literal for int()"
+        with pytest.raises(ValueError, match=message):
+            svds(np.eye(10), k="hi", solver=self.solver, rng=0)
+
+    @pytest.mark.parametrize("tol", (-1, np.inf, np.nan))
+    def test_svds_input_validation_tol_1(self, tol):
+        message = "`tol` must be a non-negative floating point value."
+        with pytest.raises(ValueError, match=message):
+            svds(np.eye(10), tol=tol, solver=self.solver, rng=0)
+
+    @pytest.mark.parametrize("tol", ([], 'hi'))
+    def test_svds_input_validation_tol_2(self, tol):
+        # I think the stack trace is reasonable here
+        message = "'<' not supported between instances"
+        with pytest.raises(TypeError, match=message):
+            svds(np.eye(10), tol=tol, solver=self.solver, rng=0)
+
+    @pytest.mark.parametrize("which", ('LA', 'SA', 'ekki', 0))
+    def test_svds_input_validation_which(self, which):
+        # Regression test for a github issue.
+        # https://github.com/scipy/scipy/issues/4590
+        # Function was not checking for eigenvalue type and unintended
+        # values could be returned.
+        with pytest.raises(ValueError, match="`which` must be in"):
+            svds(np.eye(10), which=which, solver=self.solver, rng=0)
+
+    @pytest.mark.parametrize("transpose", (True, False))
+    @pytest.mark.parametrize("n", range(4, 9))
+    def test_svds_input_validation_v0_1(self, transpose, n):
+        rng = np.random.default_rng(0)
+        A = rng.random((5, 7))
+        v0 = rng.random(n)
+        if transpose:
+            A = A.T
+        k = 2
+        message = "`v0` must have shape"
+
+        required_length = (A.shape[0] if self.solver == 'propack'
+                           else min(A.shape))
+        if n != required_length:
+            with pytest.raises(ValueError, match=message):
+                svds(A, k=k, v0=v0, solver=self.solver, rng=0)
+
+    def test_svds_input_validation_v0_2(self):
+        A = np.ones((10, 10))
+        v0 = np.ones((1, 10))
+        message = "`v0` must have shape"
+        with pytest.raises(ValueError, match=message):
+            svds(A, k=1, v0=v0, solver=self.solver, rng=0)
+
+    @pytest.mark.parametrize("v0", ("hi", 1, np.ones(10, dtype=int)))
+    def test_svds_input_validation_v0_3(self, v0):
+        A = np.ones((10, 10))
+        message = "`v0` must be of floating or complex floating data type."
+        with pytest.raises(ValueError, match=message):
+            svds(A, k=1, v0=v0, solver=self.solver, rng=0)
+
+    @pytest.mark.parametrize("maxiter", (-1, 0, 5.5))
+    def test_svds_input_validation_maxiter_1(self, maxiter):
+        message = ("`maxiter` must be a positive integer.")
+        with pytest.raises(ValueError, match=message):
+            svds(np.eye(10), maxiter=maxiter, solver=self.solver, rng=0)
+
+    def test_svds_input_validation_maxiter_2(self):
+        # I think the stack trace is reasonable when `k` can't be converted
+        # to an int.
+        message = "int() argument must be a"
+        with pytest.raises(TypeError, match=re.escape(message)):
+            svds(np.eye(10), maxiter=[], solver=self.solver, rng=0)
+
+        message = "invalid literal for int()"
+        with pytest.raises(ValueError, match=message):
+            svds(np.eye(10), maxiter="hi", solver=self.solver, rng=0)
+
+    @pytest.mark.parametrize("rsv", ('ekki', 10))
+    def test_svds_input_validation_return_singular_vectors(self, rsv):
+        message = "`return_singular_vectors` must be in"
+        with pytest.raises(ValueError, match=message):
+            svds(np.eye(10), return_singular_vectors=rsv, solver=self.solver, rng=0)
+
+    # --- Test Parameters ---
+    @pytest.mark.parametrize("k", [3, 5])
+    @pytest.mark.parametrize("which", ["LM", "SM"])
+    def test_svds_parameter_k_which(self, k, which):
+        # check that the `k` parameter sets the number of eigenvalues/
+        # eigenvectors returned.
+        # Also check that the `which` parameter sets whether the largest or
+        # smallest eigenvalues are returned
+        rng = np.random.default_rng(0)
+        A = rng.random((10, 10))
+        if self.solver == 'lobpcg':
+            with pytest.warns(UserWarning, match="The problem size"):
+                res = svds(A, k=k, which=which, solver=self.solver, rng=0)
+        else:
+            res = svds(A, k=k, which=which, solver=self.solver, rng=0)
+        _check_svds(A, k, *res, which=which, atol=1e-9, rtol=2e-13)
+
+    @pytest.mark.filterwarnings("ignore:Exited",
+                                reason="Ignore LOBPCG early exit.")
+    # loop instead of parametrize for simplicity
+    def test_svds_parameter_tol(self):
+        # check the effect of the `tol` parameter on solver accuracy by solving
+        # the same problem with varying `tol` and comparing the eigenvalues
+        # against ground truth computed
+        n = 100  # matrix size
+        k = 3    # number of eigenvalues to check
+
+        # generate a random, sparse-ish matrix
+        # effect isn't apparent for matrices that are too small
+        rng = np.random.default_rng(0)
+        A = rng.random((n, n))
+        A[A > .1] = 0
+        A = A @ A.T
+
+        _, s, _ = svd(A)  # calculate ground truth
+
+        # calculate the error as a function of `tol`
+        A = csc_array(A)
+
+        def err(tol):
+            _, s2, _ = svds(A, k=k, v0=np.ones(n), maxiter=1000,
+                            solver=self.solver, tol=tol, rng=0)
+            return np.linalg.norm((s2 - s[k-1::-1])/s[k-1::-1])
+
+        tols = [1e-4, 1e-2, 1e0]  # tolerance levels to check
+        # for 'arpack' and 'propack', accuracies make discrete steps
+        accuracies = {'propack': [1e-12, 1e-6, 1e-4],
+                      'arpack': [2.5e-15, 1e-10, 1e-10],
+                      'lobpcg': [2e-12, 4e-2, 2]}
+
+        for tol, accuracy in zip(tols, accuracies[self.solver]):
+            error = err(tol)
+            assert error < accuracy
+
+    def test_svd_v0(self):
+        # check that the `v0` parameter affects the solution
+        n = 100
+        k = 1
+        # If k != 1, LOBPCG needs more initial vectors, which are generated
+        # with rng, so it does not pass w/ k >= 2.
+        # For some other values of `n`, the AssertionErrors are not raised
+        # with different v0s, which is reasonable.
+
+        rng = np.random.default_rng(0)
+        A = rng.random((n, n))
+
+        # with the same v0, solutions are the same, and they are accurate
+        # v0 takes precedence over rng
+        v0a = rng.random(n)
+        res1a = svds(A, k, v0=v0a, solver=self.solver, rng=0)
+        res2a = svds(A, k, v0=v0a, solver=self.solver, rng=1)
+        for idx in range(3):
+            assert_allclose(res1a[idx], res2a[idx], rtol=1e-15, atol=2e-16)
+        _check_svds(A, k, *res1a)
+
+        # with the same v0, solutions are the same, and they are accurate
+        v0b = rng.random(n)
+        res1b = svds(A, k, v0=v0b, solver=self.solver, rng=2)
+        res2b = svds(A, k, v0=v0b, solver=self.solver, rng=3)
+        for idx in range(3):
+            assert_allclose(res1b[idx], res2b[idx], rtol=1e-15, atol=2e-16)
+        _check_svds(A, k, *res1b)
+
+        # with different v0, solutions can be numerically different
+        message = "Arrays are not equal"
+        with pytest.raises(AssertionError, match=message):
+            assert_equal(res1a, res1b)
+
+    def test_svd_rng(self):
+        # check that the `rng` parameter affects the solution
+        # Admittedly, `n` and `k` are chosen so that all solver pass all
+        # these checks. That's a tall order, since LOBPCG doesn't want to
+        # achieve the desired accuracy and ARPACK often returns the same
+        # singular values/vectors for different v0.
+        n = 100
+        k = 1
+
+        rng = np.random.default_rng(0)
+        A = rng.random((n, n))
+
+        # with the same rng, solutions are the same and accurate
+        res1a = svds(A, k, solver=self.solver, rng=0)
+        res2a = svds(A, k, solver=self.solver, rng=0)
+        for idx in range(3):
+            assert_allclose(res1a[idx], res2a[idx], rtol=1e-15, atol=2e-16)
+        _check_svds(A, k, *res1a)
+
+        # with the same rng, solutions are the same and accurate
+        res1b = svds(A, k, solver=self.solver, rng=1)
+        res2b = svds(A, k, solver=self.solver, rng=1)
+        for idx in range(3):
+            assert_allclose(res1b[idx], res2b[idx], rtol=1e-15, atol=2e-16)
+        _check_svds(A, k, *res1b)
+
+        # with different rng, solutions can be numerically different
+        message = "Arrays are not equal"
+        with pytest.raises(AssertionError, match=message):
+            assert_equal(res1a, res1b)
+
+    def test_svd_rng_2(self):
+        n = 100
+        k = 1
+
+        rng = np.random.default_rng(234981)
+        A = rng.random((n, n))
+        rng_2 = copy.deepcopy(rng)
+
+        # with the same rng, solutions are the same and accurate
+        res1a = svds(A, k, solver=self.solver, rng=rng)
+        res2a = svds(A, k, solver=self.solver, rng=rng_2)
+        for idx in range(3):
+            assert_allclose(res1a[idx], res2a[idx], rtol=1e-15, atol=2e-16)
+        _check_svds(A, k, *res1a)
+
+    def test_svd_random_state(self):
+        # the legacy `random_state` argument should work for now,
+        # even with NumPy <2.2.
+        # Regression test for gh-25069
+        rng = np.random.default_rng(0)
+        A = rng.random((5, 5))
+        res = svds(A, 1, solver=self.solver, random_state=np.random.RandomState(0))
+        _check_svds(A, 1, *res)
+
+    @pytest.mark.filterwarnings("ignore:Exited",
+                                reason="Ignore LOBPCG early exit.")
+    def test_svd_rng_3(self):
+        n = 100
+        k = 5
+
+        rng1 = np.random.default_rng(0)
+        rng2 = np.random.default_rng(234832)
+        A = rng1.random((n, n))
+
+        # rng in different state produces accurate - but not
+        # not necessarily identical - results
+        res1a = svds(A, k, solver=self.solver, rng=rng1, maxiter=1000)
+        res2a = svds(A, k, solver=self.solver, rng=rng2, maxiter=1000)
+        _check_svds(A, k, *res1a, atol=2e-7)
+        _check_svds(A, k, *res2a, atol=2e-7)
+
+        message = "Arrays are not equal"
+        with pytest.raises(AssertionError, match=message):
+            assert_equal(res1a, res2a)
+
+    @pytest.mark.filterwarnings("ignore:Exited postprocessing")
+    def test_svd_maxiter(self):
+        # check that maxiter works as expected: should not return accurate
+        # solution after 1 iteration, but should with default `maxiter`
+        A = np.diag(np.arange(9)).astype(np.float64)
+        k = 1
+        u, s, vh = sorted_svd(A, k)
+        # Use default maxiter by default
+        maxiter = None
+
+        if self.solver == 'arpack':
+            message = "ARPACK error -1: No convergence"
+            with pytest.raises(ArpackNoConvergence, match=message):
+                svds(A, k, ncv=3, maxiter=1, solver=self.solver, rng=0)
+        elif self.solver == 'lobpcg':
+            # Set maxiter higher so test passes without changing
+            # default and breaking backward compatibility (gh-20221)
+            maxiter = 30
+            with pytest.warns(UserWarning, match="Exited at iteration"):
+                svds(A, k, maxiter=1, solver=self.solver, rng=0)
+        elif self.solver == 'propack':
+            message = "k=1 singular triplets did not converge within"
+            with pytest.raises(np.linalg.LinAlgError, match=message):
+                svds(A, k, maxiter=1, solver=self.solver, rng=0)
+
+        ud, sd, vhd = svds(A, k, solver=self.solver, maxiter=maxiter, rng=0)
+        _check_svds(A, k, ud, sd, vhd, atol=1e-8)
+        assert_allclose(np.abs(ud), np.abs(u), atol=1e-8)
+        assert_allclose(np.abs(vhd), np.abs(vh), atol=1e-8)
+        assert_allclose(np.abs(sd), np.abs(s), atol=1e-9)
+
+    @pytest.mark.parametrize("rsv", (True, False, 'u', 'vh'))
+    @pytest.mark.parametrize("shape", ((5, 7), (6, 6), (7, 5)))
+    def test_svd_return_singular_vectors(self, rsv, shape):
+        # check that the return_singular_vectors parameter works as expected
+        rng = np.random.default_rng(0)
+        A = rng.random(shape)
+        k = 2
+        M, N = shape
+        u, s, vh = sorted_svd(A, k)
+
+        respect_u = True if self.solver == 'propack' else M <= N
+        respect_vh = True if self.solver == 'propack' else M > N
+
+        if self.solver == 'lobpcg':
+            with pytest.warns(UserWarning, match="The problem size"):
+                if rsv is False:
+                    s2 = svds(A, k, return_singular_vectors=rsv,
+                              solver=self.solver, rng=rng)
+                    assert_allclose(s2, s)
+                elif rsv == 'u' and respect_u:
+                    u2, s2, vh2 = svds(A, k, return_singular_vectors=rsv,
+                                       solver=self.solver, rng=rng)
+                    assert_allclose(np.abs(u2), np.abs(u))
+                    assert_allclose(s2, s)
+                    assert vh2 is None
+                elif rsv == 'vh' and respect_vh:
+                    u2, s2, vh2 = svds(A, k, return_singular_vectors=rsv,
+                                       solver=self.solver, rng=rng)
+                    assert u2 is None
+                    assert_allclose(s2, s)
+                    assert_allclose(np.abs(vh2), np.abs(vh))
+                else:
+                    u2, s2, vh2 = svds(A, k, return_singular_vectors=rsv,
+                                       solver=self.solver, rng=rng)
+                    if u2 is not None:
+                        assert_allclose(np.abs(u2), np.abs(u))
+                    assert_allclose(s2, s)
+                    if vh2 is not None:
+                        assert_allclose(np.abs(vh2), np.abs(vh))
+        else:
+            if rsv is False:
+                s2 = svds(A, k, return_singular_vectors=rsv,
+                          solver=self.solver, rng=rng)
+                assert_allclose(s2, s)
+            elif rsv == 'u' and respect_u:
+                u2, s2, vh2 = svds(A, k, return_singular_vectors=rsv,
+                                   solver=self.solver, rng=rng)
+                assert_allclose(np.abs(u2), np.abs(u))
+                assert_allclose(s2, s)
+                assert vh2 is None
+            elif rsv == 'vh' and respect_vh:
+                u2, s2, vh2 = svds(A, k, return_singular_vectors=rsv,
+                                   solver=self.solver, rng=rng)
+                assert u2 is None
+                assert_allclose(s2, s)
+                assert_allclose(np.abs(vh2), np.abs(vh))
+            else:
+                u2, s2, vh2 = svds(A, k, return_singular_vectors=rsv,
+                                   solver=self.solver, rng=rng)
+                if u2 is not None:
+                    assert_allclose(np.abs(u2), np.abs(u))
+                assert_allclose(s2, s)
+                if vh2 is not None:
+                    assert_allclose(np.abs(vh2), np.abs(vh))
+
+    # --- Test Basic Functionality ---
+    # Tests the accuracy of each solver for real and complex matrices provided
+    # as list, dense array, sparse matrix, and LinearOperator.
+
+    A1 = [[1, 2, 3], [3, 4, 3], [1 + 1j, 0, 2], [0, 0, 1]]
+    A2 = [[1, 2, 3, 8 + 5j], [3 - 2j, 4, 3, 5], [1, 0, 2, 3], [0, 0, 1, 0]]
+
+    @pytest.mark.filterwarnings("ignore:k >= N - 1",
+                                reason="needed to demonstrate #16725")
+    @pytest.mark.parametrize('A', (A1, A2))
+    @pytest.mark.parametrize('k', range(1, 5))
+    # PROPACK fails a lot if @pytest.mark.parametrize('which', ("SM", "LM"))
+    @pytest.mark.parametrize('real', (True, False))
+    @pytest.mark.parametrize('transpose', (False, True))
+    # In gh-14299, it was suggested the `svds` should _not_ work with lists
+    @pytest.mark.parametrize('lo_type', (np.asarray, csc_array,
+                                         aslinearoperator))
+    def test_svd_simple(self, A, k, real, transpose, lo_type):
+
+        A = np.asarray(A)
+        A = np.real(A) if real else A
+        A = A.T if transpose else A
+        A2 = lo_type(A)
+
+        # could check for the appropriate errors, but that is tested above
+        if k > min(A.shape):
+            pytest.skip("`k` cannot be greater than `min(A.shape)`")
+        if self.solver != 'propack' and k >= min(A.shape):
+            pytest.skip("Only PROPACK supports complete SVD")
+        if self.solver == 'arpack' and not real and k == min(A.shape) - 1:
+            pytest.skip("#16725")
+
+        atol = 3e-10
+        if self.solver == 'propack':
+            atol = 3e-9  # otherwise test fails on Linux aarch64 (see gh-19855)
+
+        if self.solver == 'lobpcg':
+            with pytest.warns(UserWarning, match="The problem size"):
+                u, s, vh = svds(A2, k, solver=self.solver, rng=0)
+        else:
+            u, s, vh = svds(A2, k, solver=self.solver, rng=0)
+        _check_svds(A, k, u, s, vh, atol=atol)
+
+    def test_svd_linop(self):
+        solver = self.solver
+
+        nmks = [(6, 7, 3),
+                (9, 5, 4),
+                (10, 8, 5)]
+
+        def reorder(args):
+            U, s, VH = args
+            j = np.argsort(s)
+            return U[:, j], s[j], VH[j, :]
+
+        for n, m, k in nmks:
+            # Test svds on a LinearOperator.
+            A = np.random.RandomState(52).randn(n, m)
+            L = CheckingLinearOperator(A)
+
+            if solver == 'propack':
+                v0 = np.ones(n)
+            else:
+                v0 = np.ones(min(A.shape))
+            if solver == 'lobpcg':
+                with pytest.warns(UserWarning, match="The problem size"):
+                    U1, s1, VH1 = reorder(svds(A, k, v0=v0, solver=solver, rng=0))
+                    U2, s2, VH2 = reorder(svds(L, k, v0=v0, solver=solver, rng=0))
+            else:
+                U1, s1, VH1 = reorder(svds(A, k, v0=v0, solver=solver, rng=0))
+                U2, s2, VH2 = reorder(svds(L, k, v0=v0, solver=solver, rng=0))
+
+            assert_allclose(np.abs(U1), np.abs(U2))
+            assert_allclose(s1, s2)
+            assert_allclose(np.abs(VH1), np.abs(VH2))
+            assert_allclose(np.dot(U1, np.dot(np.diag(s1), VH1)),
+                            np.dot(U2, np.dot(np.diag(s2), VH2)))
+
+            # Try again with which="SM".
+            A = np.random.RandomState(1909).randn(n, m)
+            L = CheckingLinearOperator(A)
+
+            # TODO: arpack crashes when v0=v0, which="SM"
+            kwargs = {'v0': v0} if solver not in {None, 'arpack'} else {}
+            if self.solver == 'lobpcg':
+                with pytest.warns(UserWarning, match="The problem size"):
+                    U1, s1, VH1 = reorder(svds(A, k, which="SM", solver=solver,
+                                               rng=0, **kwargs))
+                    U2, s2, VH2 = reorder(svds(L, k, which="SM", solver=solver,
+                                               rng=0, **kwargs))
+            else:
+                U1, s1, VH1 = reorder(svds(A, k, which="SM", solver=solver,
+                                           rng=0, **kwargs))
+                U2, s2, VH2 = reorder(svds(L, k, which="SM", solver=solver,
+                                           rng=0, **kwargs))
+
+            assert_allclose(np.abs(U1), np.abs(U2))
+            assert_allclose(s1 + 1, s2 + 1)
+            assert_allclose(np.abs(VH1), np.abs(VH2))
+            assert_allclose(np.dot(U1, np.dot(np.diag(s1), VH1)),
+                            np.dot(U2, np.dot(np.diag(s2), VH2)))
+
+            if k < min(n, m) - 1:
+                # Complex input and explicit which="LM".
+                for (dt, eps) in [(complex, 1e-7), (np.complex64, 3e-3)]:
+                    rng = np.random.RandomState(1648)
+                    A = (rng.randn(n, m) + 1j * rng.randn(n, m)).astype(dt)
+                    L = CheckingLinearOperator(A)
+
+                    if self.solver == 'lobpcg':
+                        with pytest.warns(UserWarning,
+                                          match="The problem size"):
+                            U1, s1, VH1 = reorder(svds(A, k, which="LM",
+                                                       solver=solver, rng=0))
+                            U2, s2, VH2 = reorder(svds(L, k, which="LM",
+                                                       solver=solver, rng=0))
+                    else:
+                        U1, s1, VH1 = reorder(svds(A, k, which="LM",
+                                                   solver=solver, rng=0))
+                        U2, s2, VH2 = reorder(svds(L, k, which="LM",
+                                                   solver=solver, rng=0))
+
+                    assert_allclose(np.abs(U1), np.abs(U2), rtol=eps)
+                    assert_allclose(s1, s2, rtol=eps)
+                    assert_allclose(np.abs(VH1), np.abs(VH2), rtol=eps)
+                    assert_allclose(np.dot(U1, np.dot(np.diag(s1), VH1)),
+                                    np.dot(U2, np.dot(np.diag(s2), VH2)),
+                                    rtol=eps)
+
+    SHAPES = ((100, 100), (100, 101), (101, 100))
+
+    @pytest.mark.filterwarnings("ignore:Exited at iteration")
+    @pytest.mark.filterwarnings("ignore:Exited postprocessing")
+    @pytest.mark.parallel_threads_limit(4)  # Very slow
+    @pytest.mark.parametrize("shape", SHAPES)
+    @pytest.mark.parametrize("dtype", (np.float32, np.float64,
+                                       np.complex64, np.complex128))
+    def test_small_sigma_sparse(self, shape, dtype):
+        # https://github.com/scipy/scipy/pull/11829
+        solver = self.solver
+        # 2do: PROPACK fails orthogonality of singular vectors
+        # if dtype == complex and self.solver == 'propack':
+        #    pytest.skip("PROPACK unsupported for complex dtype")
+        rng = np.random.default_rng(0)
+        k = 5
+        (m, n) = shape
+        S = random_array(shape=(m, n), density=0.1, rng=rng)
+        if dtype is complex:
+            S = + 1j * random_array(shape=(m, n), density=0.1, rng=rng)
+        e = np.ones(m)
+        e[0:5] *= 1e1 ** np.arange(-5, 0, 1)
+        S = dia_array((e, 0), shape=(m, m)) @ S
+        S = S.astype(dtype)
+        u, s, vh = svds(S, k, which='SM', solver=solver, maxiter=1000, rng=0)
+        c_svd = False  # partial SVD can be different from full SVD
+        _check_svds_n(S, k, u, s, vh, which="SM", check_svd=c_svd, atol=2e-1)
+
+    # --- Test Edge Cases ---
+    # Checks a few edge cases.
+    @pytest.mark.parametrize("shape", ((6, 5), (5, 5), (5, 6)))
+    @pytest.mark.parametrize("dtype", (float, complex))
+    def test_svd_LM_ones_matrix(self, shape, dtype):
+        # Check that svds can deal with matrix_rank less than k in LM mode.
+        k = 3
+        n, m = shape
+        A = np.ones((n, m), dtype=dtype)
+
+        if self.solver == 'lobpcg':
+            with pytest.warns(UserWarning, match="The problem size"):
+                U, s, VH = svds(A, k, solver=self.solver, rng=0)
+        else:
+            U, s, VH = svds(A, k, solver=self.solver, rng=0)
+
+        _check_svds(A, k, U, s, VH, check_usvh_A=True, check_svd=False)
+
+        # Check that the largest singular value is near sqrt(n*m)
+        # and the other singular values have been forced to zero.
+        assert_allclose(np.max(s), np.sqrt(n*m))
+        s = np.array(sorted(s)[:-1]) + 1
+        z = np.ones_like(s)
+        assert_allclose(s, z)
+
+    @pytest.mark.filterwarnings("ignore:k >= N - 1",
+                                reason="needed to demonstrate #16725")
+    @pytest.mark.parametrize("shape", ((3, 4), (4, 4), (4, 3), (4, 2)))
+    @pytest.mark.parametrize("dtype", (float, complex))
+    def test_zero_matrix(self, shape, dtype):
+        # Check that svds can deal with matrices containing only zeros;
+        # see https://github.com/scipy/scipy/issues/3452/
+        # shape = (4, 2) is included because it is the particular case
+        # reported in the issue
+        k = 1
+        n, m = shape
+        A = np.zeros((n, m), dtype=dtype)
+
+        if (self.solver == 'arpack'):
+            pytest.skip('See gh-21110.')
+
+        if (self.solver == 'arpack' and dtype is complex
+                and k == min(A.shape) - 1):
+            pytest.skip("#16725")
+
+        if self.solver == 'propack':
+            pytest.skip("PROPACK failures unrelated to PR #16712")
+
+        if self.solver == 'lobpcg':
+            with pytest.warns(UserWarning, match="The problem size"):
+                U, s, VH = svds(A, k, solver=self.solver, rng=0)
+        else:
+            U, s, VH = svds(A, k, solver=self.solver, rng=0)
+
+        # Check some generic properties of svd.
+        _check_svds(A, k, U, s, VH, check_usvh_A=True, check_svd=False)
+
+        # Check that the singular values are zero.
+        assert_array_equal(s, 0)
+
+    @pytest.mark.parametrize("shape", ((20, 20), (20, 21), (21, 20)))
+    @pytest.mark.parametrize("dtype", (np.float32, np.float64,
+                                       np.complex64, np.complex128))
+    @pytest.mark.filterwarnings("ignore:Exited",
+                                reason="Ignore LOBPCG early exit.")
+    def test_small_sigma(self, shape, dtype):
+        rng = np.random.default_rng(179847540)
+        A = rng.random(shape).astype(dtype)
+        u, _, vh = svd(A, full_matrices=False)
+        if dtype in [np.float32, np.complex64]:
+            e = 10.0
+        else:
+            e = 100.0
+        t = e**(-np.arange(len(vh))).astype(dtype)
+        A = (u*t).dot(vh)
+        k = 4
+        u, s, vh = svds(A, k, solver=self.solver, maxiter=100, rng=0)
+        t = np.sum(s > 0)
+        assert_equal(t, k)
+        # LOBPCG needs larger atol and rtol to pass
+        _check_svds_n(A, k, u, s, vh, atol=1e-3, rtol=1e0, check_svd=False)
+
+    @pytest.mark.filterwarnings("ignore:The problem size")
+    @pytest.mark.parametrize("dtype", (np.float32, np.float64,
+                                       np.complex64, np.complex128))
+    def test_small_sigma2(self, dtype):
+        rng = np.random.default_rng(179847540)
+        # create a 10x10 singular matrix with a 4-dim null space
+        dim = 4
+        size = 10
+        x = rng.random((size, size-dim))
+        y = x[:, :dim] * rng.random(dim)
+        mat = np.hstack((x, y))
+        mat = mat.astype(dtype)
+
+        nz = null_space(mat)
+        assert_equal(nz.shape[1], dim)
+
+        # Tolerances atol and rtol adjusted to pass np.float32
+        # Use non-sparse svd
+        u, s, vh = svd(mat)
+        # Singular values are 0:
+        assert_allclose(s[-dim:], 0, atol=1e-6, rtol=1e0)
+        # Smallest right singular vectors in null space:
+        assert_allclose(mat @ vh[-dim:, :].T, 0, atol=1e-6, rtol=1e0)
+
+        # Smallest singular values should be 0
+        sp_mat = csc_array(mat)
+        su, ss, svh = svds(sp_mat, k=dim, which='SM', solver=self.solver, rng=0)
+        # Smallest dim singular values are 0:
+        assert_allclose(ss, 0, atol=1e-5, rtol=1e0)
+        # Smallest singular vectors via svds in null space:
+        n, m = mat.shape
+        if n < m:  # else the assert fails with some libraries unclear why
+            assert_allclose(sp_mat.transpose() @ su, 0, atol=1e-5, rtol=1e0)
+        assert_allclose(sp_mat @ svh.T, 0, atol=1e-5, rtol=1e0)
+
+# --- Perform tests with each solver ---
+
+
+class Test_SVDS_once:
+    @pytest.mark.parametrize("solver", ['ekki', object])
+    def test_svds_input_validation_solver(self, solver):
+        message = "solver must be one of"
+        with pytest.raises(ValueError, match=message):
+            svds(np.ones((3, 4)), k=2, solver=solver, rng=0)
+
+
+class Test_SVDS_ARPACK(SVDSCommonTests):
+
+    def setup_method(self):
+        self.solver = 'arpack'
+
+    @pytest.mark.parametrize("ncv", list(range(-1, 8)) + [4.5, "5"])
+    def test_svds_input_validation_ncv_1(self, ncv):
+        rng = np.random.default_rng(0)
+        A = rng.random((6, 7))
+        k = 3
+        if ncv in {4, 5}:
+            u, s, vh = svds(A, k=k, ncv=ncv, solver=self.solver, rng=0)
+        # partial decomposition, so don't check that u@diag(s)@vh=A;
+        # do check that scipy.sparse.linalg.svds ~ scipy.linalg.svd
+            _check_svds(A, k, u, s, vh)
+        else:
+            message = ("`ncv` must be an integer satisfying")
+            with pytest.raises(ValueError, match=message):
+                svds(A, k=k, ncv=ncv, solver=self.solver, rng=0)
+
+    def test_svds_input_validation_ncv_2(self):
+        # I think the stack trace is reasonable when `ncv` can't be converted
+        # to an int.
+        message = "int() argument must be a"
+        with pytest.raises(TypeError, match=re.escape(message)):
+            svds(np.eye(10), ncv=[], solver=self.solver, rng=0)
+
+        message = "invalid literal for int()"
+        with pytest.raises(ValueError, match=message):
+            svds(np.eye(10), ncv="hi", solver=self.solver, rng=0)
+
+    # I can't see a robust relationship between `ncv` and relevant outputs
+    # (e.g. accuracy, time), so no test of the parameter.
+
+
+class Test_SVDS_LOBPCG(SVDSCommonTests):
+
+    def setup_method(self):
+        self.solver = 'lobpcg'
+
+
+class Test_SVDS_PROPACK(SVDSCommonTests):
+
+    def setup_method(self):
+        self.solver = 'propack'
+
+    def test_svd_LM_ones_matrix(self):
+        message = ("PROPACK does not return orthonormal singular vectors "
+                   "associated with zero singular values.")
+        # There are some other issues with this matrix of all ones, e.g.
+        # `which='sm'` and `k=1` returns the largest singular value
+        pytest.xfail(message)
+
+    def test_svd_LM_zeros_matrix(self):
+        message = ("PROPACK does not return orthonormal singular vectors "
+                   "associated with zero singular values.")
+        pytest.xfail(message)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_expm_multiply.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_expm_multiply.py
new file mode 100644
index 0000000000000000000000000000000000000000..04f88285620624a1f87ac65d5fe6e9c6b1e1b732
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_expm_multiply.py
@@ -0,0 +1,816 @@
+"""Compute the action of the matrix exponential."""
+from warnings import warn
+
+import numpy as np
+
+import scipy.linalg
+import scipy.sparse.linalg
+from scipy.linalg._decomp_qr import qr
+from scipy.sparse._sputils import is_pydata_spmatrix
+from scipy.sparse.linalg import aslinearoperator
+from scipy.sparse.linalg._interface import IdentityOperator
+from scipy.sparse.linalg._onenormest import onenormest
+
+__all__ = ['expm_multiply']
+
+
+def _exact_inf_norm(A):
+    # A compatibility function which should eventually disappear.
+    if scipy.sparse.issparse(A):
+        return max(abs(A).sum(axis=1).flat)
+    elif is_pydata_spmatrix(A):
+        return max(abs(A).sum(axis=1))
+    else:
+        return np.linalg.norm(A, np.inf)
+
+
+def _exact_1_norm(A):
+    # A compatibility function which should eventually disappear.
+    if scipy.sparse.issparse(A):
+        return max(abs(A).sum(axis=0).flat)
+    elif is_pydata_spmatrix(A):
+        return max(abs(A).sum(axis=0))
+    else:
+        return np.linalg.norm(A, 1)
+
+
+def _trace(A):
+    # A compatibility function which should eventually disappear.
+    if is_pydata_spmatrix(A):
+        return A.to_scipy_sparse().trace()
+    else:
+        return A.trace()
+
+
+def traceest(A, m3, seed=None):
+    """Estimate `np.trace(A)` using `3*m3` matrix-vector products.
+
+    The result is not deterministic.
+
+    Parameters
+    ----------
+    A : LinearOperator
+        Linear operator whose trace will be estimated. Has to be square.
+    m3 : int
+        Number of matrix-vector products divided by 3 used to estimate the
+        trace.
+    seed : optional
+        Seed for `numpy.random.default_rng`.
+        Can be provided to obtain deterministic results.
+
+    Returns
+    -------
+    trace : LinearOperator.dtype
+        Estimate of the trace
+
+    Notes
+    -----
+    This is the Hutch++ algorithm given in [1]_.
+
+    References
+    ----------
+    .. [1] Meyer, Raphael A., Cameron Musco, Christopher Musco, and David P.
+       Woodruff. "Hutch++: Optimal Stochastic Trace Estimation." In Symposium
+       on Simplicity in Algorithms (SOSA), pp. 142-155. Society for Industrial
+       and Applied Mathematics, 2021.
+       :doi:`10.1137/1.9781611976496.16`.
+
+    """
+    rng = np.random.default_rng(seed)
+    if len(A.shape) != 2 or A.shape[-1] != A.shape[-2]:
+        raise ValueError("Expected A to be like a square matrix.")
+    n = A.shape[-1]
+    S = rng.choice([-1.0, +1.0], [n, m3])
+    Q, _ = qr(A.matmat(S), overwrite_a=True, mode='economic')
+    trQAQ = np.trace(Q.conj().T @ A.matmat(Q))
+    G = rng.choice([-1, +1], [n, m3])
+    right = G - Q@(Q.conj().T @ G)
+    trGAG = np.trace(right.conj().T @ A.matmat(right))
+    return trQAQ + trGAG/m3
+
+
+def _ident_like(A):
+    # A compatibility function which should eventually disappear.
+    if scipy.sparse.issparse(A):
+        # Creates a sparse matrix in dia format
+        out = scipy.sparse.eye(A.shape[0], A.shape[1], dtype=A.dtype)
+        if scipy.sparse.issparse(A):
+            return out.asformat(A.format)
+        return scipy.sparse.dia_array(out).asformat(A.format)
+    elif is_pydata_spmatrix(A):
+        import sparse
+        return sparse.eye(A.shape[0], A.shape[1], dtype=A.dtype)
+    elif isinstance(A, scipy.sparse.linalg.LinearOperator):
+        return IdentityOperator(A.shape, dtype=A.dtype)
+    else:
+        return np.eye(A.shape[0], A.shape[1], dtype=A.dtype)
+
+
+def expm_multiply(A, B, start=None, stop=None, num=None,
+                  endpoint=None, traceA=None):
+    """
+    Compute the action of the matrix exponential of A on B.
+
+    Parameters
+    ----------
+    A : transposable linear operator
+        The operator whose exponential is of interest.
+    B : ndarray, sparse array
+        The matrix or vector to be multiplied by the matrix exponential of A.
+    start : scalar, optional
+        The starting time point of the sequence.
+    stop : scalar, optional
+        The end time point of the sequence, unless `endpoint` is set to False.
+        In that case, the sequence consists of all but the last of ``num + 1``
+        evenly spaced time points, so that `stop` is excluded.
+        Note that the step size changes when `endpoint` is False.
+    num : int, optional
+        Number of time points to use.
+    endpoint : bool, optional
+        If True, `stop` is the last time point.  Otherwise, it is not included.
+    traceA : scalar, optional
+        Trace of `A`. If not given the trace is estimated for linear operators,
+        or calculated exactly for sparse matrices. It is used to precondition
+        `A`, thus an approximate trace is acceptable.
+        For linear operators, `traceA` should be provided to ensure performance
+        as the estimation is not guaranteed to be reliable for all cases.
+
+        .. versionadded:: 1.9.0
+
+    Returns
+    -------
+    expm_A_B : ndarray
+         The result of the action :math:`e^{t_k A} B`.
+
+    Warns
+    -----
+    UserWarning
+        If `A` is a linear operator and ``traceA=None`` (default).
+
+    Notes
+    -----
+    The optional arguments defining the sequence of evenly spaced time points
+    are compatible with the arguments of `numpy.linspace`.
+
+    The output ndarray shape is somewhat complicated so I explain it here.
+    The ndim of the output could be either 1, 2, or 3.
+    It would be 1 if you are computing the expm action on a single vector
+    at a single time point.
+    It would be 2 if you are computing the expm action on a vector
+    at multiple time points, or if you are computing the expm action
+    on a matrix at a single time point.
+    It would be 3 if you want the action on a matrix with multiple
+    columns at multiple time points.
+    If multiple time points are requested, expm_A_B[0] will always
+    be the action of the expm at the first time point,
+    regardless of whether the action is on a vector or a matrix.
+
+    References
+    ----------
+    .. [1] Awad H. Al-Mohy and Nicholas J. Higham (2011)
+           "Computing the Action of the Matrix Exponential,
+           with an Application to Exponential Integrators."
+           SIAM Journal on Scientific Computing,
+           33 (2). pp. 488-511. ISSN 1064-8275
+           http://eprints.ma.man.ac.uk/1591/
+
+    .. [2] Nicholas J. Higham and Awad H. Al-Mohy (2010)
+           "Computing Matrix Functions."
+           Acta Numerica,
+           19. 159-208. ISSN 0962-4929
+           http://eprints.ma.man.ac.uk/1451/
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.sparse import csc_array
+    >>> from scipy.sparse.linalg import expm, expm_multiply
+    >>> A = csc_array([[1, 0], [0, 1]])
+    >>> A.toarray()
+    array([[1, 0],
+           [0, 1]], dtype=int64)
+    >>> B = np.array([np.exp(-1.), np.exp(-2.)])
+    >>> B
+    array([ 0.36787944,  0.13533528])
+    >>> expm_multiply(A, B, start=1, stop=2, num=3, endpoint=True)
+    array([[ 1.        ,  0.36787944],
+           [ 1.64872127,  0.60653066],
+           [ 2.71828183,  1.        ]])
+    >>> expm(A).dot(B)                  # Verify 1st timestep
+    array([ 1.        ,  0.36787944])
+    >>> expm(1.5*A).dot(B)              # Verify 2nd timestep
+    array([ 1.64872127,  0.60653066])
+    >>> expm(2*A).dot(B)                # Verify 3rd timestep
+    array([ 2.71828183,  1.        ])
+    """
+    if all(arg is None for arg in (start, stop, num, endpoint)):
+        X = _expm_multiply_simple(A, B, traceA=traceA)
+    else:
+        X, status = _expm_multiply_interval(A, B, start, stop, num,
+                                            endpoint, traceA=traceA)
+    return X
+
+
+def _expm_multiply_simple(A, B, t=1.0, traceA=None, balance=False):
+    """
+    Compute the action of the matrix exponential at a single time point.
+
+    Parameters
+    ----------
+    A : transposable linear operator
+        The operator whose exponential is of interest.
+    B : ndarray
+        The matrix to be multiplied by the matrix exponential of A.
+    t : float
+        A time point.
+    traceA : scalar, optional
+        Trace of `A`. If not given the trace is estimated for linear operators,
+        or calculated exactly for sparse matrices. It is used to precondition
+        `A`, thus an approximate trace is acceptable
+    balance : bool
+        Indicates whether or not to apply balancing.
+
+    Returns
+    -------
+    F : ndarray
+        :math:`e^{t A} B`
+
+    Notes
+    -----
+    This is algorithm (3.2) in Al-Mohy and Higham (2011).
+
+    """
+    if balance:
+        raise NotImplementedError
+    if len(A.shape) != 2 or A.shape[0] != A.shape[1]:
+        raise ValueError('expected A to be like a square matrix')
+    if A.shape[1] != B.shape[0]:
+        raise ValueError(f'shapes of matrices A {A.shape} and B {B.shape}'
+                         ' are incompatible')
+    ident = _ident_like(A)
+    is_linear_operator = isinstance(A, scipy.sparse.linalg.LinearOperator)
+    n = A.shape[0]
+    if len(B.shape) == 1:
+        n0 = 1
+    elif len(B.shape) == 2:
+        n0 = B.shape[1]
+    else:
+        raise ValueError('expected B to be like a matrix or a vector')
+    u_d = 2**-53
+    tol = u_d
+    if traceA is None:
+        if is_linear_operator:
+            warn("Trace of LinearOperator not available, it will be estimated."
+                 " Provide `traceA` to ensure performance.", stacklevel=3)
+        # m3=1 is bit arbitrary choice, a more accurate trace (larger m3) might
+        # speed up exponential calculation, but trace estimation is more costly
+        traceA = traceest(A, m3=1) if is_linear_operator else _trace(A)
+    mu = traceA / float(n)
+    A = A - mu * ident
+    A_1_norm = onenormest(A) if is_linear_operator else _exact_1_norm(A)
+    if t*A_1_norm == 0:
+        m_star, s = 0, 1
+    else:
+        ell = 2
+        norm_info = LazyOperatorNormInfo(t*A, A_1_norm=t*A_1_norm, ell=ell)
+        m_star, s = _fragment_3_1(norm_info, n0, tol, ell=ell)
+    return _expm_multiply_simple_core(A, B, t, mu, m_star, s, tol, balance)
+
+
+def _expm_multiply_simple_core(A, B, t, mu, m_star, s, tol=None, balance=False):
+    """
+    A helper function.
+    """
+    if balance:
+        raise NotImplementedError
+    if tol is None:
+        u_d = 2 ** -53
+        tol = u_d
+    F = B
+    eta = np.exp(t*mu / float(s))
+    for i in range(s):
+        c1 = _exact_inf_norm(B)
+        for j in range(m_star):
+            coeff = t / float(s*(j+1))
+            B = coeff * A.dot(B)
+            c2 = _exact_inf_norm(B)
+            F = F + B
+            if c1 + c2 <= tol * _exact_inf_norm(F):
+                break
+            c1 = c2
+        F = eta * F
+        B = F
+    return F
+
+
+# This table helps to compute bounds.
+# They seem to have been difficult to calculate, involving symbolic
+# manipulation of equations, followed by numerical root finding.
+_theta = {
+        # The first 30 values are from table A.3 of Computing Matrix Functions.
+        1: 2.29e-16,
+        2: 2.58e-8,
+        3: 1.39e-5,
+        4: 3.40e-4,
+        5: 2.40e-3,
+        6: 9.07e-3,
+        7: 2.38e-2,
+        8: 5.00e-2,
+        9: 8.96e-2,
+        10: 1.44e-1,
+        # 11
+        11: 2.14e-1,
+        12: 3.00e-1,
+        13: 4.00e-1,
+        14: 5.14e-1,
+        15: 6.41e-1,
+        16: 7.81e-1,
+        17: 9.31e-1,
+        18: 1.09,
+        19: 1.26,
+        20: 1.44,
+        # 21
+        21: 1.62,
+        22: 1.82,
+        23: 2.01,
+        24: 2.22,
+        25: 2.43,
+        26: 2.64,
+        27: 2.86,
+        28: 3.08,
+        29: 3.31,
+        30: 3.54,
+        # The rest are from table 3.1 of
+        # Computing the Action of the Matrix Exponential.
+        35: 4.7,
+        40: 6.0,
+        45: 7.2,
+        50: 8.5,
+        55: 9.9,
+        }
+
+
+def _onenormest_matrix_power(A, p,
+        t=2, itmax=5, compute_v=False, compute_w=False):
+    """
+    Efficiently estimate the 1-norm of A^p.
+
+    Parameters
+    ----------
+    A : ndarray
+        Matrix whose 1-norm of a power is to be computed.
+    p : int
+        Non-negative integer power.
+    t : int, optional
+        A positive parameter controlling the tradeoff between
+        accuracy versus time and memory usage.
+        Larger values take longer and use more memory
+        but give more accurate output.
+    itmax : int, optional
+        Use at most this many iterations.
+    compute_v : bool, optional
+        Request a norm-maximizing linear operator input vector if True.
+    compute_w : bool, optional
+        Request a norm-maximizing linear operator output vector if True.
+
+    Returns
+    -------
+    est : float
+        An underestimate of the 1-norm of the sparse matrix.
+    v : ndarray, optional
+        The vector such that ||Av||_1 == est*||v||_1.
+        It can be thought of as an input to the linear operator
+        that gives an output with particularly large norm.
+    w : ndarray, optional
+        The vector Av which has relatively large 1-norm.
+        It can be thought of as an output of the linear operator
+        that is relatively large in norm compared to the input.
+
+    """
+    #XXX Eventually turn this into an API function in the  _onenormest module,
+    #XXX and remove its underscore,
+    #XXX but wait until expm_multiply goes into scipy.
+    from scipy.sparse.linalg._onenormest import onenormest
+    return onenormest(aslinearoperator(A) ** p)
+
+class LazyOperatorNormInfo:
+    """
+    Information about an operator is lazily computed.
+
+    The information includes the exact 1-norm of the operator,
+    in addition to estimates of 1-norms of powers of the operator.
+    This uses the notation of Computing the Action (2011).
+    This class is specialized enough to probably not be of general interest
+    outside of this module.
+
+    """
+
+    def __init__(self, A, A_1_norm=None, ell=2, scale=1):
+        """
+        Provide the operator and some norm-related information.
+
+        Parameters
+        ----------
+        A : linear operator
+            The operator of interest.
+        A_1_norm : float, optional
+            The exact 1-norm of A.
+        ell : int, optional
+            A technical parameter controlling norm estimation quality.
+        scale : int, optional
+            If specified, return the norms of scale*A instead of A.
+
+        """
+        self._A = A
+        self._A_1_norm = A_1_norm
+        self._ell = ell
+        self._d = {}
+        self._scale = scale
+
+    def set_scale(self,scale):
+        """
+        Set the scale parameter.
+        """
+        self._scale = scale
+
+    def onenorm(self):
+        """
+        Compute the exact 1-norm.
+        """
+        if self._A_1_norm is None:
+            self._A_1_norm = _exact_1_norm(self._A)
+        return self._scale*self._A_1_norm
+
+    def d(self, p):
+        """
+        Lazily estimate :math:`d_p(A) ~= || A^p ||^(1/p)`
+        where :math:`||.||` is the 1-norm.
+        """
+        if p not in self._d:
+            est = _onenormest_matrix_power(self._A, p, self._ell)
+            self._d[p] = est ** (1.0 / p)
+        return self._scale*self._d[p]
+
+    def alpha(self, p):
+        """
+        Lazily compute max(d(p), d(p+1)).
+        """
+        return max(self.d(p), self.d(p+1))
+
+def _compute_cost_div_m(m, p, norm_info):
+    """
+    A helper function for computing bounds.
+
+    This is equation (3.10).
+    It measures cost in terms of the number of required matrix products.
+
+    Parameters
+    ----------
+    m : int
+        A valid key of _theta.
+    p : int
+        A matrix power.
+    norm_info : LazyOperatorNormInfo
+        Information about 1-norms of related operators.
+
+    Returns
+    -------
+    cost_div_m : int
+        Required number of matrix products divided by m.
+
+    """
+    return int(np.ceil(norm_info.alpha(p) / _theta[m]))
+
+
+def _compute_p_max(m_max):
+    """
+    Compute the largest positive integer p such that p*(p-1) <= m_max + 1.
+
+    Do this in a slightly dumb way, but safe and not too slow.
+
+    Parameters
+    ----------
+    m_max : int
+        A count related to bounds.
+
+    """
+    sqrt_m_max = np.sqrt(m_max)
+    p_low = int(np.floor(sqrt_m_max))
+    p_high = int(np.ceil(sqrt_m_max + 1))
+    return max(p for p in range(p_low, p_high+1) if p*(p-1) <= m_max + 1)
+
+
+def _fragment_3_1(norm_info, n0, tol, m_max=55, ell=2):
+    """
+    A helper function for the _expm_multiply_* functions.
+
+    Parameters
+    ----------
+    norm_info : LazyOperatorNormInfo
+        Information about norms of certain linear operators of interest.
+    n0 : int
+        Number of columns in the _expm_multiply_* B matrix.
+    tol : float
+        Expected to be
+        :math:`2^{-24}` for single precision or
+        :math:`2^{-53}` for double precision.
+    m_max : int
+        A value related to a bound.
+    ell : int
+        The number of columns used in the 1-norm approximation.
+        This is usually taken to be small, maybe between 1 and 5.
+
+    Returns
+    -------
+    best_m : int
+        Related to bounds for error control.
+    best_s : int
+        Amount of scaling.
+
+    Notes
+    -----
+    This is code fragment (3.1) in Al-Mohy and Higham (2011).
+    The discussion of default values for m_max and ell
+    is given between the definitions of equation (3.11)
+    and the definition of equation (3.12).
+
+    """
+    if ell < 1:
+        raise ValueError('expected ell to be a positive integer')
+    best_m = None
+    best_s = None
+    if _condition_3_13(norm_info.onenorm(), n0, m_max, ell):
+        for m, theta in _theta.items():
+            s = int(np.ceil(norm_info.onenorm() / theta))
+            if best_m is None or m * s < best_m * best_s:
+                best_m = m
+                best_s = s
+    else:
+        # Equation (3.11).
+        for p in range(2, _compute_p_max(m_max) + 1):
+            for m in range(p*(p-1)-1, m_max+1):
+                if m in _theta:
+                    s = _compute_cost_div_m(m, p, norm_info)
+                    if best_m is None or m * s < best_m * best_s:
+                        best_m = m
+                        best_s = s
+        best_s = max(best_s, 1)
+    return best_m, best_s
+
+
+def _condition_3_13(A_1_norm, n0, m_max, ell):
+    """
+    A helper function for the _expm_multiply_* functions.
+
+    Parameters
+    ----------
+    A_1_norm : float
+        The precomputed 1-norm of A.
+    n0 : int
+        Number of columns in the _expm_multiply_* B matrix.
+    m_max : int
+        A value related to a bound.
+    ell : int
+        The number of columns used in the 1-norm approximation.
+        This is usually taken to be small, maybe between 1 and 5.
+
+    Returns
+    -------
+    value : bool
+        Indicates whether or not the condition has been met.
+
+    Notes
+    -----
+    This is condition (3.13) in Al-Mohy and Higham (2011).
+
+    """
+
+    # This is the rhs of equation (3.12).
+    p_max = _compute_p_max(m_max)
+    a = 2 * ell * p_max * (p_max + 3)
+
+    # Evaluate the condition (3.13).
+    b = _theta[m_max] / float(n0 * m_max)
+    return A_1_norm <= a * b
+
+
+def _expm_multiply_interval(A, B, start=None, stop=None, num=None,
+                            endpoint=None, traceA=None, balance=False,
+                            status_only=False):
+    """
+    Compute the action of the matrix exponential at multiple time points.
+
+    Parameters
+    ----------
+    A : transposable linear operator
+        The operator whose exponential is of interest.
+    B : ndarray
+        The matrix to be multiplied by the matrix exponential of A.
+    start : scalar, optional
+        The starting time point of the sequence.
+    stop : scalar, optional
+        The end time point of the sequence, unless `endpoint` is set to False.
+        In that case, the sequence consists of all but the last of ``num + 1``
+        evenly spaced time points, so that `stop` is excluded.
+        Note that the step size changes when `endpoint` is False.
+    num : int, optional
+        Number of time points to use.
+    traceA : scalar, optional
+        Trace of `A`. If not given the trace is estimated for linear operators,
+        or calculated exactly for sparse matrices. It is used to precondition
+        `A`, thus an approximate trace is acceptable
+    endpoint : bool, optional
+        If True, `stop` is the last time point. Otherwise, it is not included.
+    balance : bool
+        Indicates whether or not to apply balancing.
+    status_only : bool
+        A flag that is set to True for some debugging and testing operations.
+
+    Returns
+    -------
+    F : ndarray
+        :math:`e^{t_k A} B`
+    status : int
+        An integer status for testing and debugging.
+
+    Notes
+    -----
+    This is algorithm (5.2) in Al-Mohy and Higham (2011).
+
+    There seems to be a typo, where line 15 of the algorithm should be
+    moved to line 6.5 (between lines 6 and 7).
+
+    """
+    if balance:
+        raise NotImplementedError
+    if len(A.shape) != 2 or A.shape[0] != A.shape[1]:
+        raise ValueError('expected A to be like a square matrix')
+    if A.shape[1] != B.shape[0]:
+        raise ValueError(f'shapes of matrices A {A.shape} and B {B.shape}'
+                         ' are incompatible')
+    ident = _ident_like(A)
+    is_linear_operator = isinstance(A, scipy.sparse.linalg.LinearOperator)
+    n = A.shape[0]
+    if len(B.shape) == 1:
+        n0 = 1
+    elif len(B.shape) == 2:
+        n0 = B.shape[1]
+    else:
+        raise ValueError('expected B to be like a matrix or a vector')
+    u_d = 2**-53
+    tol = u_d
+    if traceA is None:
+        if is_linear_operator:
+            warn("Trace of LinearOperator not available, it will be estimated."
+                 " Provide `traceA` to ensure performance.", stacklevel=3)
+        # m3=5 is bit arbitrary choice, a more accurate trace (larger m3) might
+        # speed up exponential calculation, but trace estimation is also costly
+        # an educated guess would need to consider the number of time points
+        traceA = traceest(A, m3=5) if is_linear_operator else _trace(A)
+    mu = traceA / float(n)
+
+    # Get the linspace samples, attempting to preserve the linspace defaults.
+    linspace_kwargs = {'retstep': True}
+    if num is not None:
+        linspace_kwargs['num'] = num
+    if endpoint is not None:
+        linspace_kwargs['endpoint'] = endpoint
+    samples, step = np.linspace(start, stop, **linspace_kwargs)
+
+    # Convert the linspace output to the notation used by the publication.
+    nsamples = len(samples)
+    if nsamples < 2:
+        raise ValueError('at least two time points are required')
+    q = nsamples - 1
+    h = step
+    t_0 = samples[0]
+    t_q = samples[q]
+
+    # Define the output ndarray.
+    # Use an ndim=3 shape, such that the last two indices
+    # are the ones that may be involved in level 3 BLAS operations.
+    X_shape = (nsamples,) + B.shape
+    X = np.empty(X_shape, dtype=np.result_type(A.dtype, B.dtype, float))
+    t = t_q - t_0
+    A = A - mu * ident
+    A_1_norm = onenormest(A) if is_linear_operator else _exact_1_norm(A)
+    ell = 2
+    norm_info = LazyOperatorNormInfo(t*A, A_1_norm=t*A_1_norm, ell=ell)
+    if t*A_1_norm == 0:
+        m_star, s = 0, 1
+    else:
+        m_star, s = _fragment_3_1(norm_info, n0, tol, ell=ell)
+
+    # Compute the expm action up to the initial time point.
+    action_t0 = _expm_multiply_simple_core(A, B, t_0, mu, m_star, s)
+    if scipy.sparse.issparse(action_t0):
+        action_t0 = action_t0.toarray()
+    elif is_pydata_spmatrix(action_t0):
+        action_t0 = action_t0.todense()
+    X[0] = action_t0
+
+    # Compute the expm action at the rest of the time points.
+    if q <= s:
+        if status_only:
+            return 0
+        else:
+            return _expm_multiply_interval_core_0(A, X,
+                    h, mu, q, norm_info, tol, ell,n0)
+    elif not (q % s):
+        if status_only:
+            return 1
+        else:
+            return _expm_multiply_interval_core_1(A, X,
+                    h, mu, m_star, s, q, tol)
+    elif (q % s):
+        if status_only:
+            return 2
+        else:
+            return _expm_multiply_interval_core_2(A, X,
+                    h, mu, m_star, s, q, tol)
+    else:
+        raise Exception('internal error')
+
+
+def _expm_multiply_interval_core_0(A, X, h, mu, q, norm_info, tol, ell, n0):
+    """
+    A helper function, for the case q <= s.
+    """
+
+    # Compute the new values of m_star and s which should be applied
+    # over intervals of size t/q
+    if norm_info.onenorm() == 0:
+        m_star, s = 0, 1
+    else:
+        norm_info.set_scale(1./q)
+        m_star, s = _fragment_3_1(norm_info, n0, tol, ell=ell)
+        norm_info.set_scale(1)
+
+    for k in range(q):
+        X[k+1] = _expm_multiply_simple_core(A, X[k], h, mu, m_star, s)
+    return X, 0
+
+
+def _expm_multiply_interval_core_1(A, X, h, mu, m_star, s, q, tol):
+    """
+    A helper function, for the case q > s and q % s == 0.
+    """
+    d = q // s
+    input_shape = X.shape[1:]
+    K_shape = (m_star + 1, ) + input_shape
+    K = np.empty(K_shape, dtype=X.dtype)
+    for i in range(s):
+        Z = X[i*d]
+        K[0] = Z
+        high_p = 0
+        for k in range(1, d+1):
+            F = K[0]
+            c1 = _exact_inf_norm(F)
+            for p in range(1, m_star+1):
+                if p > high_p:
+                    K[p] = h * A.dot(K[p-1]) / float(p)
+                coeff = float(pow(k, p))
+                F = F + coeff * K[p]
+                inf_norm_K_p_1 = _exact_inf_norm(K[p])
+                c2 = coeff * inf_norm_K_p_1
+                if c1 + c2 <= tol * _exact_inf_norm(F):
+                    break
+                c1 = c2
+            X[k + i*d] = np.exp(k*h*mu) * F
+    return X, 1
+
+
+def _expm_multiply_interval_core_2(A, X, h, mu, m_star, s, q, tol):
+    """
+    A helper function, for the case q > s and q % s > 0.
+    """
+    d = q // s
+    j = q // d
+    r = q - d * j
+    input_shape = X.shape[1:]
+    K_shape = (m_star + 1, ) + input_shape
+    K = np.empty(K_shape, dtype=X.dtype)
+    for i in range(j + 1):
+        Z = X[i*d]
+        K[0] = Z
+        high_p = 0
+        if i < j:
+            effective_d = d
+        else:
+            effective_d = r
+        for k in range(1, effective_d+1):
+            F = K[0]
+            c1 = _exact_inf_norm(F)
+            for p in range(1, m_star+1):
+                if p == high_p + 1:
+                    K[p] = h * A.dot(K[p-1]) / float(p)
+                    high_p = p
+                coeff = float(pow(k, p))
+                F = F + coeff * K[p]
+                inf_norm_K_p_1 = _exact_inf_norm(K[p])
+                c2 = coeff * inf_norm_K_p_1
+                if c1 + c2 <= tol * _exact_inf_norm(F):
+                    break
+                c1 = c2
+            X[k + i*d] = np.exp(k*h*mu) * F
+    return X, 2
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_funm_multiply_krylov.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_funm_multiply_krylov.py
new file mode 100644
index 0000000000000000000000000000000000000000..eea90f384b08adcb09e5e6d0412b42cb360a7a0b
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_funm_multiply_krylov.py
@@ -0,0 +1,340 @@
+"""
+  Restared Krylov method for evaluating f(A)b
+
+  The original code was written in MATLAB by Stefan Guttel.
+  It was later adapted to C++ and Python by Nicolas Guidotti.
+  Both authors agrees to relicense the code under the BSD license.
+
+  Copyright (C) 2025 Nicolas Guidotti and Stefan Guttel.
+  All rights reserved.
+
+  Redistribution and use in source and binary forms, with or without
+  modification, are permitted provided that the following conditions are met:
+
+  1. Redistributions of source code must retain the above copyright notice, this
+  list of conditions and the following disclaimer.
+
+  2. Redistributions in binary form must reproduce the above copyright notice,
+  this list of conditions and the following disclaimer in the documentation
+  and/or other materials provided with the distribution.
+
+  3. Neither the name of the copyright holder nor the names of its contributors
+  may be used to endorse or promote products derived from this software without
+  specific prior written permission.
+
+  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+  AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+  IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+  DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
+  FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+  DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+  SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+  CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
+  OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+  OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+"""
+
+import numpy as np
+from scipy.linalg import norm
+from ._isolve.iterative import _get_atol_rtol
+
+__all__ = ['funm_multiply_krylov']
+
+def _funm_multiply_krylov_arnoldi(A, b, bnorm, V, H, m):
+    """
+    The Arnoldi iteration for constructing the basis V and the projection H = V * A V
+    for the Krylov subspace Km(A, b) of order m.
+
+    Parameters
+    ----------
+    A : transposable linear operator
+        The operator whose matrix function is of interest.
+    b : ndarray
+        The vector b to multiply the f(A) with.
+    V : ndarray
+        The n x (m + 1) matrix whose columns determines the basis for
+        Krylov subspace Km(A, b).
+    H : ndarray
+        A (m + 1) x m upper Hessenberg matrix representing the projection of A
+        onto Km(A, b).
+    m : int
+        The order of the Krylov subspace.
+
+    Returns
+    -------
+    breakdown : bool
+        Indicate if the Arnoldi broke down or not
+
+    iter : int
+        Returns the last valid iteration.
+
+    """
+
+    dotprod = np.vdot if np.iscomplexobj(b) else np.dot
+    norm_tol = np.finfo(b.dtype.char).eps ** 2
+    V[:, 0] = b / bnorm
+
+    for k in range(0, m):
+        V[:, k + 1] = A.dot(V[:, k])
+
+        # Uses the modified Gram-Schmift process to orthogonalize V[:, k + 1]
+        # against the previous basis vectors
+        for i in range(0, k + 1):
+            H[i, k] = dotprod(V[:, i], V[:, k + 1])
+            V[:, k + 1] = V[:, k + 1] - H[i, k] * V[:, i]
+
+        H[k + 1, k] = norm(V[:, k + 1])
+        if H[k + 1, k] < norm_tol:
+            return True, k
+
+        V[:, k + 1] = V[:, k + 1] / H[k + 1, k]
+
+    return False, m
+
+def _funm_multiply_krylov_lanczos(A, b, bnorm, V, H, m):
+    """
+    The Lanczos iteration for constructing the basis V and the projection H = V * A V
+    for the Krylov subspace Km(A, b) of order m. A must be Hermitian.
+
+    Parameters
+    ----------
+    A : transposable linear operator
+        The operator whose matrix function is of interest.
+    b : ndarray
+        The vector b to multiply the f(A) with.
+    V : ndarray
+        The n x (m + 1) matrix whose columns determines the basis for
+        Krylov subspace Km(A, b).
+    H : ndarray
+        A (m + 1) x m upper Hessenberg matrix representing the projection of A
+        onto Km(A, b).
+    m : int
+        The order of the Krylov subspace.
+
+    Returns
+    -------
+    breakdown : bool
+        Indicate if the Arnoldi broke down or not
+
+    iter : int
+        Returns the last valid iteration.
+
+    """
+    dotprod = np.vdot if np.iscomplexobj(b) else np.dot
+    norm_tol = np.finfo(b.dtype.char).eps ** 2
+    V[:, 0] = b / bnorm
+
+    for k in range(0, m):
+        if k > 0:
+            V[:, k + 1] = A.dot(V[:, k]) - H[k, k - 1] * V[:, k - 1]
+        else:
+            V[:, k + 1] = A.dot(V[:, k])
+
+        H[k, k] = dotprod(V[:, k + 1], V[:, k])
+        V[:, k + 1] = V[:, k + 1] - H[k, k] * V[:, k]
+
+        H[k + 1, k] = norm(V[:, k + 1])
+
+        if H[k + 1, k] < norm_tol:
+            return True, k
+
+        V[:, k + 1] = V[:, k + 1] / H[k + 1, k]
+        if k < m - 1:
+            H[k, k + 1] = H[k + 1, k]
+
+    return False, m
+
+
+def funm_multiply_krylov(f, A, b, *, assume_a = "general", t = 1.0, atol = 0.0,
+                         rtol = 1e-6, restart_every_m = None, max_restarts = 20):
+    """
+    A restarted Krylov method for evaluating ``y = f(tA) b`` from [1]_ [2]_.
+
+    Parameters
+    ----------
+    f : callable
+        Callable object that computes the matrix function ``F = f(X)``.
+    A : {sparse array, ndarray, LinearOperator}
+        A real or complex N-by-N matrix.
+        Alternatively, `A` can be a linear operator which can
+        produce ``Ax`` using, e.g., ``scipy.sparse.linalg.LinearOperator``.
+    b : ndarray
+        A vector to multiply the ``f(tA)`` with.
+    assume_a : str, optional
+        Indicate the structure of ``A``. The algorithm will use this information
+        to select the appropriated code path. The available options are
+        'hermitian'/'her' and 'general'/'gen'. If ommited, then it is assumed
+        that ``A`` has a 'general' structure.
+    t : float, optional
+        The value to scale the matrix ``A`` with. The default is ``t = 1.0``
+    atol, rtol : float, optional
+        Parameters for the convergence test. For convergence,
+        ``norm(||y_k - y_k-1||) <= max(rtol*norm(b), atol)`` should be satisfied.
+        The default is ``atol=0.`` and ``rtol=1e-6``.
+    restart_every_m : int
+        If the iteration number reaches this value a restart is triggered.
+        Larger values increase iteration cost but may be necessary for convergence.
+        If omitted, ``min(20, n)`` is used.
+    max_restarts : int, optional
+        Maximum number of restart cycles. The algorithm will stop
+        after max_restarts cycles even if the specified tolerance has not been
+        achieved. The default is ``max_restarts=20``
+
+    Returns
+    -------
+    y : ndarray
+        The result of ``f(tA) b``.
+
+    Notes
+    -----
+    The convergence of the Krylov method heavily depends on the spectrum
+    of ``A`` and the function ``f``. With restarting, there are only formal
+    proofs for functions of order 1 (e.g., ``exp``, ``sin``, ``cos``) and
+    Stieltjes functions [2]_ [3]_, while the general case remains an open problem.
+
+    References
+    ----------
+    .. [1] M. Afanasjew, M. Eiermann, O. G. Ernst, and S. Güttel,
+           "Implementation of a restarted Krylov subspace method for the
+           evaluation of matrix functions," Linear Algebra and its Applications,
+           vol. 429, no. 10, pp. 2293-2314, Nov. 2008, :doi:`10.1016/j.laa.2008.06.029`.
+
+    .. [2] M. Eiermann and O. G. Ernst, "A Restarted Krylov Subspace Method
+           for the Evaluation of Matrix Functions," SIAM J. Numer. Anal., vol. 44,
+           no. 6, pp. 2481-2504, Jan. 2006, :doi:`10.1137/050633846`.
+
+    .. [3] A. Frommer, S. Güttel, and M. Schweitzer, "Convergence of Restarted
+           Krylov Subspace Methods for Stieltjes Functions of Matrices," SIAM J.
+           Matrix Anal. Appl., vol. 35, no. 4, pp. 1602-1624,
+           Jan. 2014, :doi:`10.1137/140973463`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.sparse import csr_array
+    >>> from scipy.sparse.linalg import funm_multiply_krylov
+    >>> from scipy.linalg import expm, solve
+    >>> A = csr_array([[3, 2, 0], [1, -1, 0], [0, 5, 1]], dtype=float)
+    >>> b = np.array([2, 4, -1], dtype=float)
+    >>> t = 0.1
+
+    Compute ``y = exp(tA) b``.
+
+    >>> y = funm_multiply_krylov(expm, A, b, t = t)
+    >>> y
+    array([3.6164913 , 3.88421511 , 0.96073457])
+
+    >>> ref = expm(t * A.todense()) @ b
+    >>> err = y - ref
+    >>> err
+    array([4.44089210e-16 , 0.00000000e+00 , 2.22044605e-16])
+
+    Compute :math:`y = (A^3 - A) b`.
+
+    >>> poly = lambda X : X @ X @ X - X
+    >>> y = funm_multiply_krylov(poly, A, b)
+    >>> y
+    array([132. , 24. , 70.])
+
+    >>> ref = poly(A.todense()) @ b
+    >>> err = y - ref
+    >>> err
+    array([ 0.00000000e+00 , 7.10542736e-15 , -2.84217094e-14])
+
+    Compute :math:`y = f(tA) b`, where  :math:`f(X) = X^{-1}(e^{X} - I)`. This is
+    known as the "phi function" from the exponential integrator literature.
+
+    >>> phim_1 = lambda X : solve(X, expm(X) - np.eye(X.shape[0]))
+    >>> y = funm_multiply_krylov(phim_1, A, b, t = t)
+    >>> y
+    array([ 2.76984306 , 3.92769192 , -0.03111392])
+
+    >>> ref = phim_1(t * A.todense()) @ b
+    >>> err = y - ref
+    >>> err
+    array([ 0.00000000e+00 , 8.88178420e-16 , -4.60742555e-15])
+    """
+
+    if assume_a not in {'hermitian', 'general', 'her', 'gen'}:
+        raise ValueError(f'scipy.sparse.linalg.funm_multiply_krylov: {assume_a} '
+                         'is not a recognized matrix structure')
+    is_hermitian = (assume_a == 'her') or (assume_a == 'hermitian')
+
+    if len(b.shape) != 1:
+        raise ValueError("scipy.sparse.linalg.funm_multiply_krylov: "
+                         "argument 'b' must be a 1D array.")
+    n = b.shape[0]
+
+    if restart_every_m is None:
+        restart_every_m = min(20, n)
+
+    restart_every_m = int(restart_every_m)
+    max_restarts = int(max_restarts)
+
+    if restart_every_m <= 0:
+        raise ValueError("scipy.sparse.linalg.funm_multiply_krylov: "
+                         "argument 'restart_every_m' must be positive.")
+
+    if max_restarts <= 0:
+            raise ValueError("scipy.sparse.linalg.funm_multiply_krylov: "
+                             "argument 'max_restarts' must be positive.")
+
+    m = restart_every_m
+    max_restarts = min(max_restarts, int(n / m) + 1)
+    mmax = m * max_restarts
+
+    bnorm = norm(b)
+    atol, _ = _get_atol_rtol("funm_multiply_krylov", bnorm, atol, rtol)
+
+    if bnorm == 0:
+        y = np.array(b)
+        return y
+
+    # Preallocate the maximum memory space.
+    # Using the column major order here since we work with
+    # each individual column separately.
+    internal_type = np.common_type(A, b)
+    V = np.zeros((n, m + 1), dtype = internal_type, order = 'F')
+    H = np.zeros((mmax + 1, mmax), dtype = internal_type, order = 'F')
+
+    restart = 1
+
+    if is_hermitian:
+        breakdown, j = _funm_multiply_krylov_lanczos(A, b, bnorm, V,
+                                                        H[:m + 1, :m], m)
+    else:
+        breakdown, j = _funm_multiply_krylov_arnoldi(A, b, bnorm, V,
+                                                        H[:m + 1, :m], m)
+
+    fH = f(t * H[:j, :j])
+    y = bnorm * V[:, :j].dot(fH[:, 0])
+
+    if breakdown:
+        return y
+
+    update_norm = norm(bnorm * fH[:, 0])
+
+    while restart < max_restarts and update_norm > atol:
+        begin = restart * m
+        end = (restart + 1) * m
+
+        if is_hermitian:
+            breakdown, j = _funm_multiply_krylov_lanczos(A, V[:, m], 1, V,
+                                                         H[begin:end + 1, begin:end], m)
+        else:
+            breakdown, j = _funm_multiply_krylov_arnoldi(A, V[:, m], 1, V,
+                                                         H[begin:end + 1, begin:end], m)
+
+        if breakdown:
+            end = begin + j
+            fH = f(t * H[:end, :end])
+            y[:end] = y[:end] + bnorm * V[:, :m].dot(fH[begin:end, 0])
+            return y
+
+        fH = f(t * H[:end, :end])
+        y = y + bnorm * V[:, :m].dot(fH[begin:end, 0])
+        update_norm = norm(bnorm * fH[begin:end, 0])
+        restart += 1
+
+    return y
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_interface.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_interface.py
new file mode 100644
index 0000000000000000000000000000000000000000..f822e7316a3ac54a053a8ee9c68aa7304245d706
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_interface.py
@@ -0,0 +1,1236 @@
+"""Abstract linear algebra library.
+
+This module defines a class hierarchy that implements a kind of "lazy"
+matrix representation, called the ``LinearOperator``. It can be used to do
+linear algebra with extremely large sparse or structured matrices, without
+representing those explicitly in memory. Such matrices can be added,
+multiplied, transposed, etc.
+
+As a motivating example, suppose you want have a matrix where almost all of
+the elements have the value one. The standard sparse matrix representation
+skips the storage of zeros, but not ones. By contrast, a LinearOperator is
+able to represent such matrices efficiently. First, we need a compact way to
+represent an all-ones matrix::
+
+    >>> import numpy as np
+    >>> from scipy.sparse.linalg._interface import LinearOperator
+    >>> class Ones(LinearOperator):
+    ...     def __init__(self, shape):
+    ...         super().__init__(dtype=None, shape=shape)
+    ...     def _matvec(self, x):
+    ...         return np.repeat(x.sum(), self.shape[0])
+
+Instances of this class emulate ``np.ones(shape)``, but using a constant
+amount of storage, independent of ``shape``. The ``_matvec`` method specifies
+how this linear operator multiplies with (operates on) a vector. We can now
+add this operator to a sparse matrix that stores only offsets from one::
+
+    >>> from scipy.sparse.linalg._interface import aslinearoperator
+    >>> from scipy.sparse import csr_array
+    >>> offsets = csr_array([[1, 0, 2], [0, -1, 0], [0, 0, 3]])
+    >>> A = aslinearoperator(offsets) + Ones(offsets.shape)
+    >>> A.dot([1, 2, 3])
+    array([13,  4, 15])
+
+The result is the same as that given by its dense, explicitly-stored
+counterpart::
+
+    >>> (np.ones(A.shape, A.dtype) + offsets.toarray()).dot([1, 2, 3])
+    array([13,  4, 15])
+
+Several algorithms in the ``scipy.sparse`` library are able to operate on
+``LinearOperator`` instances.
+"""
+
+import os
+import types
+import warnings
+
+import numpy as np
+
+from scipy import sparse
+from scipy._external import array_api_extra as xpx
+from scipy._lib._array_api import (
+    SCIPY_ARRAY_API,
+    _asarray,
+    array_namespace,
+    is_array_api_obj,
+    is_pydata_sparse_array,
+    np_compat,
+    xp_capabilities,
+    xp_copy,
+    xp_isscalar,
+    xp_result_type,
+)
+from scipy.sparse import issparse
+from scipy.sparse._sputils import asmatrix, is_pydata_spmatrix, isintlike, isshape
+
+__all__ = ["LinearOperator", "aslinearoperator"]
+
+
+@xp_capabilities()
+class LinearOperator:
+    """Common interface for performing matrix vector products.
+
+    Many iterative methods (e.g. `cg`, `gmres`) do not need to know the
+    individual entries of a matrix to solve a linear system ``A@x = b``.
+    Such solvers only require the computation of matrix vector
+    products, ``A@v``, where ``v`` is a dense vector.  This class serves as
+    an abstract interface between iterative solvers and matrix-like
+    objects.
+
+    To construct a concrete `LinearOperator`, either pass appropriate
+    callables to the constructor of this class, or subclass it.
+
+    A subclass must implement either one of the methods ``_matvec``
+    and ``_matmat``, and the attributes/properties ``shape`` (pair of
+    integers, optionally with additional batch dimensions at the front)
+    and ``dtype`` (may be None). It may call the ``__init__``
+    on this class to have these attributes validated. Implementing
+    ``_matvec`` automatically implements ``_matmat`` (using a naive
+    algorithm) and vice-versa.
+
+    Optionally, a subclass may implement ``_rmatvec`` or ``_adjoint``
+    to implement the Hermitian adjoint (conjugate transpose). As with
+    ``_matvec`` and ``_matmat``, implementing either ``_rmatvec`` or
+    ``_adjoint`` implements the other automatically. Implementing
+    ``_adjoint`` is preferable; ``_rmatvec`` is mostly there for
+    backwards compatibility.
+
+    The defined operator may have additional "batch" dimensions
+    prepended to the core shape, to represent a batch of 2-D operators;
+    see :ref:`linalg_batch` for details.
+
+    Parameters
+    ----------
+    shape : tuple
+        Matrix dimensions ``(..., M, N)``,
+        where ``...`` represents any additional batch dimensions.
+    matvec : callable f(v)
+        Applies ``A`` to ``v``, where ``v`` is a dense vector
+        with shape ``(..., N)``.
+    rmatvec : callable f(v)
+        Applies ``A^H`` to ``v``, where ``A^H`` is the conjugate transpose of ``A``,
+        and ``v`` is a dense vector of shape ``(..., M)``.
+    matmat : callable f(V)
+        Returns ``A @ V``, where ``V`` is a dense matrix
+        with dimensions ``(..., N, K)``.
+    rmatmat : callable f(V)
+        Returns ``A^H @ V``, where ``A^H`` is the conjugate transpose of ``A``,
+        and where ``V`` is a dense matrix with dimensions ``(..., M, K)``.
+    dtype : dtype
+        Data type of the matrix or matrices.
+    xp : array_namespace, optional
+        A namespace compatible with the array API standard for use in array operations.
+        Default: ``numpy``.
+
+    Attributes
+    ----------
+    args : tuple
+        For linear operators describing products etc. of other linear
+        operators, the operands of the binary operation.
+    ndim : int
+        Number of dimensions (greater than 2 in the case of batch dimensions).
+    T : LinearOperator
+        Transpose.
+    H : LinearOperator
+        Hermitian adjoint.
+
+    Methods
+    -------
+    matvec
+    matmat
+    adjoint
+    transpose
+    rmatvec
+    rmatmat
+    dot
+    rdot
+    __mul__
+    __matmul__
+    __call__
+    __add__
+    __truediv__
+    __rmul__
+    __rmatmul__
+
+    See Also
+    --------
+    aslinearoperator : Construct a `LinearOperator`.
+
+    Notes
+    -----
+    The user-defined `matvec` function must properly handle the case
+    where ``v`` has shape ``(..., N)``.
+
+    It is highly recommended to explicitly specify the `dtype`, otherwise
+    it is determined automatically at the cost of a single matvec application
+    on ``int8`` zero vector using the promoted `dtype` of the output.
+    It is assumed that `matmat`, `rmatvec`, and `rmatmat` would result in
+    the same dtype of the output given an ``int8`` input as `matvec`.
+
+    `LinearOperator` instances can also be multiplied, added with each
+    other, and raised to integral powers, all lazily: the result of these
+    operations
+    is always a new, composite `LinearOperator`, that defers linear
+    operations to the original operators and combines the results.
+
+    More details regarding how to subclass a `LinearOperator` and several
+    examples of concrete `LinearOperator` instances can be found in the
+    external project `PyLops <https://pylops.readthedocs.io>`_.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.sparse.linalg import LinearOperator
+    >>> def mv(v):
+    ...     return np.array([2*v[0], 3*v[1]])
+    ...
+    >>> A = LinearOperator((2,2), matvec=mv)
+    >>> A
+    <2x2 _CustomLinearOperator with dtype=int8>
+    >>> A.matvec(np.ones(2))
+    array([ 2.,  3.])
+    >>> A @ np.ones(2)
+    array([ 2.,  3.])
+
+    """  # numpydoc ignore=PR01,PR02
+
+    # Necessary for right matmul with numpy arrays.
+    __array_ufunc__ = None
+
+    # generic type compatibility with scipy-stubs
+    __class_getitem__: classmethod = classmethod(types.GenericAlias)
+
+    ndim: int
+
+    def __new__(cls, *args, **kwargs):
+        if cls is LinearOperator:
+            # Operate as _CustomLinearOperator factory.
+            return super().__new__(_CustomLinearOperator)
+        else:
+            obj = super().__new__(cls)
+
+            if (
+                type(obj)._matvec == LinearOperator._matvec
+                and type(obj)._matmat == LinearOperator._matmat
+            ):
+                warnings.warn(
+                    "LinearOperator subclass should implement"
+                    " at least one of _matvec and _matmat.",
+                    category=RuntimeWarning,
+                    stacklevel=2,
+                )
+
+            return obj
+
+    def __init__(self, dtype, shape, xp=None):
+        """Initialize this LinearOperator.
+
+        To be called by subclasses. ``dtype`` may be None; ``shape`` should
+        be convertible to a length >=2 tuple.
+        """
+        xp = np_compat if xp is None else xp
+        if dtype is not None:
+            dtype = xp.empty(0, dtype=dtype).dtype
+
+        shape = tuple(shape)
+        if len(shape) < 2:
+            raise ValueError(f"invalid shape {shape!r} (must be at least 2-d)")
+        if not isshape(shape, check_nd=False):
+            raise ValueError(f"invalid shape {shape!r}")
+
+        self.dtype = dtype
+        self.shape = shape
+        self.ndim = len(shape)
+        self._xp = xp
+
+    def __getstate__(self):
+        state = self.__dict__.copy()
+        state["_xp"] = state["_xp"].empty(0)
+        return state
+
+    def __setstate__(self, state):
+        self._xp = array_namespace(state.pop("_xp"))
+        self.__dict__.update(state)
+
+    def _init_dtype(self):
+        """Determine the dtype by executing `matvec` on an `int8` test vector.
+
+        In `np.promote_types` hierarchy, the type `int8` is the smallest,
+        so we call `matvec` on `int8` and use the promoted dtype of the output
+        to set the default `dtype` of the `LinearOperator`.
+        We assume that `matmat`, `rmatvec`, and `rmatmat` would result in
+        the same dtype of the output given an `int8` input as `matvec`.
+
+        Called from subclasses at the end of the __init__ routine.
+        """
+        if self.dtype is None:
+            xp = self._xp
+            v = xp.zeros(self.shape[-1], dtype=xp.int8)
+            try:
+                matvec_v = xp.asarray(self.matvec(v))
+            except (OverflowError, TypeError, RuntimeError):
+                self.dtype = xpx.default_dtype(xp=xp, kind="integral")
+            else:
+                self.dtype = matvec_v.dtype
+
+    def _matmat(self, X, /):
+        """Default matrix-matrix multiplication handler.
+
+        If ``self`` is a linear operator of shape ``(..., M, N)``,
+        then this method will be called on a shape ``(..., N, K)`` array,
+        and should return a shape ``(..., M, K)`` array.
+
+        Falls back to `_matvec`, so defining that will
+        define matrix multiplication too (though in a very suboptimal way).
+        """
+        xp = self._xp
+
+        # NOTE: we can't use `_matvec` directly (for the unbatched case)
+        # as we can't assume that user-defined `matvec` functions support batching.
+        # TODO: determine whether user-defined `_matvec` supports batching,
+        # and use it directly.
+        return xp.stack(
+            [self._matvec(X[..., :, i]) for i in range(X.shape[-1])], axis=-1
+        )
+
+    def _matvec(self, x):
+        """Default matrix-vector multiplication handler.
+
+        If ``self`` is a linear operator of shape ``(..., M, N)``,
+        then this method will be called on a shape
+        ``(..., N)`` array,
+        and should return a shape ``(..., M)`` array.
+
+        Falls back to `_matmat`, so defining that
+        will define matrix-vector multiplication as well.
+        """
+        xp = self._xp
+        return self._matmat(x[..., xp.newaxis])[..., 0]
+
+    def _shared_matvec(self, x, adjoint: bool = False):
+        xp = self._xp
+
+        x = _asarray(x, subok=True, xp=xp)
+
+        *self_broadcast_dims, M, N = self.shape
+        inner_dim, outer_dim = (M, N) if adjoint else (N, M)
+
+        # TODO: deprecate `np.matrix` support
+        if isinstance(x, np.matrix):
+            y = self._rmatvec(x) if adjoint else self._matvec(x)
+            if x.shape == (inner_dim, 1):
+                y = y.reshape(outer_dim, 1)
+            return asmatrix(y)
+
+        x_broadcast_dims: tuple[int, ...] = ()
+        row_vector: bool = False
+        if column_vector := x.shape == (inner_dim, 1):
+            func_name = "`rmatvec`" if adjoint else "`matvec`"
+            matmat_func_name = "`rmatmat`" if adjoint else "`matmat`"
+            msg = (
+                f"Calling {func_name} on 'column vectors' of shape "
+                f"`({inner_dim}, 1)` was deprecated in SciPy 1.18.0 and will no "
+                f"longer be possible in SciPy 1.20.0. "
+                f"Please call {matmat_func_name} instead for identical behaviour."
+            )
+            warnings.warn(
+                msg, FutureWarning, skip_file_prefixes=(os.path.dirname(__file__),)
+            )
+            x = xp.reshape(x, (inner_dim,))
+        elif x.ndim >= 1 and (row_vector := x.shape[-1] == inner_dim):
+            x_broadcast_dims = x.shape[:-1]
+
+        if not (row_vector or column_vector):
+            msg = (
+                f"Dimension mismatch: `x` must have a shape ending in "
+                f"`({inner_dim},)`, or shape `({inner_dim}, 1)`. "
+                f"Given shape: {x.shape}"
+            )
+            raise ValueError(msg)
+
+        y = self._rmatvec(x) if adjoint else self._matvec(x)
+
+        broadcasted_dims = xpx.broadcast_shapes(self_broadcast_dims, x_broadcast_dims)
+        if row_vector:
+            y = xp.reshape(y, (*broadcasted_dims, outer_dim))
+        elif column_vector:
+            y = xp.reshape(y, (*broadcasted_dims, outer_dim, 1))
+
+        return y
+
+    def matvec(self, x):
+        """Matrix-vector multiplication.
+
+        Applies ``A`` to `x`, where ``A`` is an ``M`` x ``N``
+        linear operator (or batch of linear operators)
+        and `x` is a row vector (or batch of such vectors).
+
+        Parameters
+        ----------
+        x : {matrix, ndarray}
+            An array with shape ``(..., N)`` representing a row vector
+            (or batch of row vectors).
+
+            .. versionadded:: 1.18.0
+                A ``FutureWarning`` is emitted for column vector input of shape
+                ``(N, 1)``, for which an array with shape ``(M, 1)`` is returned.
+                `matmat` can be called instead for identical behaviour on such input.
+
+        Returns
+        -------
+        y : {matrix, ndarray}
+            An array with shape ``(..., M)``.
+
+        Notes
+        -----
+        This method wraps the user-specified ``matvec`` routine or overridden
+        ``_matvec`` method to ensure that `y` has the correct shape and type.
+        """
+        return self._shared_matvec(x)
+
+    def rmatvec(self, x):
+        """Adjoint matrix-vector multiplication.
+
+        Applies ``A^H`` to `x`, where ``A`` is an
+        ``M`` x ``N`` linear operator (or batch of linear operators)
+        and `x` is a row vector (or batch of such vectors).
+
+        Parameters
+        ----------
+        x : {matrix, ndarray}
+            An array with shape ``(..., M)`` representing a row vector
+            (or batch of row vectors),
+            or an array with shape ``(M, 1)`` representing a column vector.
+
+            .. versionadded:: 1.18.0
+                A ``FutureWarning`` is now emitted for column vector input of shape
+                ``(M, 1)``, for which an array with shape ``(N, 1)`` is returned.
+                `rmatmat` can be called instead for identical behaviour on such input.
+
+        Returns
+        -------
+        y : {matrix, ndarray}
+            An array with shape ``(..., N)``.
+
+        Notes
+        -----
+        This method wraps the user-specified ``rmatvec`` routine or overridden
+        ``_rmatvec`` method to ensure that `y` has the correct shape and type.
+        """
+        return self._shared_matvec(x, adjoint=True)
+
+    def _rmatvec(self, x):
+        """Default implementation of `_rmatvec`.
+        Defers to `_rmatmat` or `adjoint`."""
+        if type(self)._adjoint == LinearOperator._adjoint:
+            # _adjoint not overridden, prevent infinite recursion
+            if (
+                hasattr(self, "_rmatmat")
+                and type(self)._rmatmat != LinearOperator._rmatmat
+            ):
+                xp = self._xp
+                # Try to use _rmatmat as a fallback
+                return self._rmatmat(x[..., xp.newaxis])[..., 0]
+            raise NotImplementedError
+        else:
+            return self.H._matvec(x)
+
+    def _shared_matmat(self, X, adjoint: bool = False):
+        if not (issparse(X) or is_pydata_spmatrix(X)):
+            X = _asarray(X, subok=True, xp=self._xp)
+
+        if X.ndim < 2:
+            raise ValueError(f"Expected at least 2-d ndarray or matrix, not {X.ndim}-d")
+
+        if X.shape[-2] != (self.shape[-2] if adjoint else self.shape[-1]):
+            raise ValueError(f"Dimension mismatch: {self.shape}, {X.shape}")
+
+        try:
+            Y = self._rmatmat(X) if adjoint else self._matmat(X)
+        except Exception as e:
+            if issparse(X) or is_pydata_spmatrix(X):
+                raise TypeError(
+                    "Multipliying LinearOperator with a sparse matrix failed."
+                    " Try wrapping the matrix with `aslinearoperator` first,"
+                    " or ensuring the operator's `matmat` function"
+                    " supports sparse input."
+                ) from e
+            raise
+
+        if isinstance(Y, np.matrix):
+            Y = asmatrix(Y)
+
+        return Y
+
+    def matmat(self, X):
+        """Matrix-matrix multiplication.
+
+        Performs the operation ``A @ X`` where ``A`` is an ``M`` x ``N``
+        linear operator (or batch of linear operators)
+        and `X` is a dense ``N`` x ``K`` matrix
+        (or batch of dense matrices).
+
+        Parameters
+        ----------
+        X : {matrix, ndarray}
+            An array with shape ``(..., N, K)`` representing the dense matrix
+            (or batch of dense matrices).
+
+        Returns
+        -------
+        Y : {matrix, ndarray}
+            An array with shape ``(..., M, K)``.
+
+        Notes
+        -----
+        This method wraps any user-specified ``matmat`` routine or overridden
+        ``_matmat`` method to ensure that `Y` has the correct type.
+        """
+        return self._shared_matmat(X)
+
+    def rmatmat(self, X):
+        """Adjoint matrix-matrix multiplication.
+
+        Performs the operation ``A^H @ X`` where ``A`` is an ``M`` x ``N``
+        linear operator (or batch of linear operators)
+        and `X` is a dense ``M`` x ``K`` matrix
+        (or batch of dense matrices).
+        The default implementation defers to the adjoint.
+
+        Parameters
+        ----------
+        X : {matrix, ndarray}
+            An array with shape ``(..., M, K)`` representing the dense matrix
+            (or batch of dense matrices).
+
+        Returns
+        -------
+        Y : {matrix, ndarray}
+            An array with shape ``(..., N, K)``.
+
+        Notes
+        -----
+        This method wraps any user-specified ``rmatmat`` routine or overridden
+        ``_rmatmat`` method to ensure that `Y` has the correct type.
+
+        """
+        return self._shared_matmat(X, adjoint=True)
+
+    def _rmatmat(self, X, /):
+        """Default implementation of `_rmatmat`; defers to `rmatvec` or `adjoint`."""
+        if type(self)._adjoint == LinearOperator._adjoint:
+            xp = self._xp
+
+            # NOTE: we can't use `_rmatvec` directly as we can't assume that
+            # user-defined `rmatvec` functions support batching.
+            return xp.stack(
+                [self._rmatvec(X[..., :, i]) for i in range(X.shape[-1])], axis=-1
+            )
+        else:
+            return self.H._matmat(X)
+
+    def __call__(self, x):
+        """Apply this linear operator.
+
+        Equivalent to `__matmul__`.
+        """
+        return self @ x
+
+    def __mul__(self, x):
+        """Multiplication.
+
+        Used by the ``*`` operator. Equivalent to `dot`.
+        """
+        return self.dot(x)
+
+    def __truediv__(self, other):
+        """Scalar Division.
+
+        Returns a lazily scaled linear operator.
+        """
+        if not xp_isscalar(other):
+            raise ValueError("Can only divide a linear operator by a scalar.")
+
+        return _ScaledLinearOperator(self, 1.0 / other, xp=self._xp)
+
+    def _check_matching_namespace(self, x):
+        xp_x = getattr(x, "_xp", None)
+        if xp_x is None:
+            xp_x = array_namespace(x, self._xp.empty(0), sparse_ok=True)
+        if xp_x != self._xp:
+            msg = (
+                f"Mismatched array namespaces."
+                f"Namespace for self is {self._xp}, namespace for x is {xp_x}"
+            )
+            raise TypeError(msg)
+
+    def dot(self, x):
+        """Multi-purpose multiplication method.
+
+        Parameters
+        ----------
+        x : array_like or `LinearOperator` or scalar
+            Array-like input will be interpreted as a 1-D row vector or
+            2-D matrix (or batch of matrices)
+            depending on its shape. See the Returns section for details.
+
+        Returns
+        -------
+        Ax : array or `LinearOperator`
+            - For `LinearOperator` input, operator composition is performed.
+
+            - For scalar input, a lazily scaled operator is returned.
+
+            - Otherwise, the input is expected to take the form of a dense
+              1-D vector or 2-D matrix (or batch of matrices),
+              interpreted as follows
+              (where ``self`` is an ``M`` by ``N`` linear operator):
+
+              - If `x` has shape ``(N,)``
+                it is interpreted as a row vector
+                and `matvec` is called.
+              - If `x` has shape ``(..., N, K)`` for some
+                integer ``K``, it is interpreted as a matrix
+                (or batch of matrices if there are batch dimensions)
+                and `matmat` is called.
+
+        See Also
+        --------
+        __mul__ : Equivalent method used by the ``*`` operator.
+        __matmul__ :
+            Method used by the ``@`` operator which rejects scalar
+            input before calling this method.
+
+        Notes
+        -----
+        To perform matrix-vector multiplication on batches of vectors,
+        use `matvec`.
+
+        For clarity, it is recommended to use the `matvec` or
+        `matmat` methods directly instead of this method
+        when interacting with dense vectors and matrices.
+
+        """
+        self._check_matching_namespace(x)
+        if isinstance(x, LinearOperator):
+            return _ProductLinearOperator(self, x, xp=self._xp)
+        elif xp_isscalar(x):
+            return _ScaledLinearOperator(self, x, xp=self._xp)
+        else:
+            if not issparse(x) and not is_pydata_spmatrix(x):
+                # scipy.sparse arrays shouldn't be converted to numpy arrays
+                # pydata_sparse arrays do not require conversion
+                # (and should avoid hitting https://github.com/pydata/sparse/pull/918)
+                x = self._xp.asarray(x)
+
+            N = self.shape[-1]
+
+            # treat 1-D input as a vector and >1-D input as a matrix, if the shape fits
+            vector = x.shape == (N,)
+            matrix = x.ndim >= 2 and x.shape[-2] == N
+
+            if not (vector or matrix):
+                msg = (
+                    f"Dimension mismatch: array input `x` must have shape `({N},)` "
+                    f"or a shape ending in `({N}, K)` for some integer `K`. "
+                    f"Given shape: {x.shape}"
+                )
+                raise ValueError(msg)
+
+            if vector:
+                return self.matvec(x)
+            elif matrix:
+                return self.matmat(x)
+
+    def __matmul__(self, other):
+        """Matrix Multiplication.
+
+        Used by the ``@`` operator.
+        Rejects scalar input.
+        Otherwise, equivalent to `dot`.
+        """
+        if xp_isscalar(other):
+            raise ValueError("Scalar operands are not allowed, use '*' instead")
+        return self.__mul__(other)
+
+    def __rmatmul__(self, other):
+        """Matrix Multiplication from the right.
+
+        Used by the ``@`` operator from the right.
+        Rejects scalar input.
+        Otherwise, equivalent to `rdot`.
+        """
+        if xp_isscalar(other):
+            raise ValueError("Scalar operands are not allowed, use '*' instead")
+        return self.__rmul__(other)
+
+    def __rmul__(self, x):
+        """Multiplication from the right.
+
+        Used by the ``*`` operator from the right. Equivalent to `rdot`.
+        """
+        return self.rdot(x)
+
+    def rdot(self, x):
+        """Multi-purpose multiplication method from the right.
+
+        .. note ::
+
+            This method returns ``x A``.
+            To perform adjoint multiplication instead, use one of
+            `rmatvec` or `rmatmat`, or take the adjoint first,
+            like ``self.H.rdot(x)`` or ``x * self.H``.
+
+        Parameters
+        ----------
+        x : array_like or `LinearOperator` or scalar
+            Array-like input will be interpreted as a 1-D row vector or
+            2-D matrix (or batch of matrices)
+            depending on its shape. See the Returns section for details.
+
+        Returns
+        -------
+        xA : array or `LinearOperator`
+            - For `LinearOperator` input, operator composition is performed.
+
+            - For scalar input, a lazily scaled operator is returned.
+
+            - Otherwise, the input is expected to take the form of a dense
+              1-D vector or 2-D matrix (or batch of matrices),
+              interpreted as follows
+              (where ``self`` is an ``M`` by ``N`` linear operator):
+
+              - If `x` has shape ``(M,)``
+                it is interpreted as a row vector.
+              - If `x` has shape ``(..., K, M)`` for some
+                integer ``K``, it is interpreted as a matrix
+                (or batch of matrices if there are batch dimensions).
+
+        See Also
+        --------
+        dot : Multi-purpose multiplication method from the left.
+        __rmul__ :
+            Equivalent method, used by the ``*`` operator from the right.
+        __rmatmul__ :
+            Method used by the ``@`` operator from the right
+            which rejects scalar input before calling this method.
+        """
+        self._check_matching_namespace(x)
+        if isinstance(x, LinearOperator):
+            return _ProductLinearOperator(x, self, xp=self._xp)
+        elif xp_isscalar(x):
+            return _ScaledLinearOperator(self, x, xp=self._xp)
+        else:
+            if not issparse(x) and not is_pydata_spmatrix(x):
+                # scipy.sparse arrays shouldn't be converted to numpy arrays
+                # pydata_sparse arrays do not require conversion
+                # (and should avoid hitting https://github.com/pydata/sparse/pull/918)
+                x = self._xp.asarray(x)
+
+            M = self.shape[-2]
+
+            # treat 1-D input as a vector and >1-D input as a matrix, if the shape fits
+            vector = x.shape == (M,)
+            matrix = x.ndim >= 2 and x.shape[-1] == M
+
+            if not (vector or matrix):
+                msg = (
+                    f"Dimension mismatch: `x` must have shape `({M},)` "
+                    f"or a shape ending in `(K, {M})` for some integer `K`. "
+                    f"Given shape: {x.shape}."
+                )
+                raise ValueError(msg)
+
+            # We use transpose instead of rmatvec/rmatmat to avoid
+            # unnecessary complex conjugation if possible.
+            # scipy/scipy#24157
+            def mT(x):
+                match x.ndim:
+                    case 0 | 1:
+                        return x
+                    case 2:
+                        return x.T
+                    case _:
+                        return self._xp.moveaxis(x, -2, -1)
+            if vector:
+                return self.T.matvec(mT(x))
+            elif matrix:
+                return mT(self.T.matmat(mT(x)))
+
+    def __pow__(self, p):
+        self._check_matching_namespace(p)
+        if xp_isscalar(p):
+            return _PowerLinearOperator(self, p, xp=self._xp)
+        else:
+            return NotImplemented
+
+    def __add__(self, x):
+        """Linear operator addition.
+
+        The input must be a `LinearOperator`.
+        A lazily summed linear operator is returned.
+        """
+        self._check_matching_namespace(x)
+        if isinstance(x, LinearOperator):
+            return _SumLinearOperator(self, x, xp=self._xp)
+        else:
+            return NotImplemented
+
+    def __neg__(self):
+        return _ScaledLinearOperator(self, -1, xp=self._xp)
+
+    def __sub__(self, x):
+        return self.__add__(-x)
+
+    def __repr__(self):
+        if self.dtype is None:
+            dt = "unspecified dtype"
+        else:
+            dt = "dtype=" + str(self.dtype)
+
+        shape = "x".join(str(dim) for dim in self.shape)
+        return f"<{shape} {self.__class__.__name__} with {dt}>"
+
+    def adjoint(self):
+        """Hermitian adjoint.
+
+        Returns the Hermitian adjoint of this linear operator,
+        also known as the Hermitian
+        conjugate or Hermitian transpose. For a complex matrix, the
+        Hermitian adjoint is equal to the conjugate transpose.
+
+        Returns
+        -------
+        `LinearOperator`
+            Hermitian adjoint of self.
+
+        See Also
+        --------
+        :attr:`~scipy.sparse.linalg.LinearOperator.H` : Equivalent attribute.
+        """
+        return self._adjoint()
+
+    @property
+    def H(self):
+        """Hermitian adjoint.
+
+        See Also
+        --------
+        scipy.sparse.linalg.LinearOperator.adjoint : Equivalent method.
+        """
+        return self.adjoint()
+
+    def transpose(self):
+        """Transpose.
+
+        Returns
+        -------
+        `LinearOperator`
+            Transpose of the linear operator.
+
+        See Also
+        --------
+        :attr:`~scipy.sparse.linalg.LinearOperator.T` : Equivalent attribute.
+        """
+        return self._transpose()
+
+    @property
+    def T(self):
+        """Transpose.
+
+        See Also
+        --------
+        scipy.sparse.linalg.LinearOperator.transpose : Equivalent method.
+        """
+        return self.transpose()
+
+    def _adjoint(self):
+        """Default implementation of `_adjoint`.
+        Defers to adjoint functions, e.g. `_rmatvec` for `_matvec`."""
+        return _AdjointLinearOperator(self, xp=self._xp)
+
+    def _transpose(self):
+        """Default implementation of `_transpose`.
+        For `_matvec`, defers to `_rmatvec` + `np.conj`."""
+        return _TransposedLinearOperator(self, xp=self._xp)
+
+
+class _CustomLinearOperator(LinearOperator):
+    """Linear operator defined in terms of user-specified operations."""
+
+    def __init__(
+        self,
+        shape,
+        matvec,
+        rmatvec=None,
+        matmat=None,
+        dtype=None,
+        rmatmat=None,
+        xp=None,
+    ):
+        super().__init__(dtype, shape, xp)
+
+        self.args = ()
+
+        self.__matvec_impl = matvec
+        self.__rmatvec_impl = rmatvec
+        self.__rmatmat_impl = rmatmat
+        self.__matmat_impl = matmat
+
+        self._init_dtype()
+
+    def _matmat(self, X):
+        if self.__matmat_impl is not None:
+            return self.__matmat_impl(X)
+        else:
+            return super()._matmat(X)
+
+    def _matvec(self, x):
+        return self.__matvec_impl(x)
+
+    def _rmatvec(self, x):
+        func = self.__rmatvec_impl
+        if func is None:
+            raise NotImplementedError("rmatvec is not defined")
+        return self.__rmatvec_impl(x)
+
+    def _rmatmat(self, X):
+        if self.__rmatmat_impl is not None:
+            return self.__rmatmat_impl(X)
+        else:
+            return super()._rmatmat(X)
+
+    def _adjoint(self):
+        return _CustomLinearOperator(
+            shape=(*self.shape[:-2], self.shape[-1], self.shape[-2]),
+            matvec=self.__rmatvec_impl,
+            rmatvec=self.__matvec_impl,
+            matmat=self.__rmatmat_impl,
+            rmatmat=self.__matmat_impl,
+            dtype=self.dtype,
+            xp=self._xp,
+        )
+
+
+class _AdjointLinearOperator(LinearOperator):
+    """Adjoint of arbitrary Linear Operator"""
+
+    def __init__(self, A, xp=None):
+        shape = (*A.shape[:-2], A.shape[-1], A.shape[-2])
+        super().__init__(A.dtype, shape, xp)
+        self.A = A
+        self.args = (A,)
+
+    def _matvec(self, x):
+        return self.A._rmatvec(x)
+
+    def _rmatvec(self, x):
+        return self.A._matvec(x)
+
+    def _matmat(self, x):
+        return self.A._rmatmat(x)
+
+    def _rmatmat(self, x):
+        return self.A._matmat(x)
+
+
+class _TransposedLinearOperator(LinearOperator):
+    """Transposition of arbitrary Linear Operator"""
+
+    def __init__(self, A, xp=None):
+        shape = (*A.shape[:-2], A.shape[-1], A.shape[-2])
+        super().__init__(A.dtype, shape, xp)
+        self.A = A
+        self.args = (A,)
+
+    def _matvec(self, x):
+        return self._xp.conj(self.A._rmatvec(self._xp.conj(x)))
+
+    def _rmatvec(self, x):
+        return self._xp.conj(self.A._matvec(self._xp.conj(x)))
+
+    def _matmat(self, x):
+        return self._xp.conj(self.A._rmatmat(self._xp.conj(x)))
+
+    def _rmatmat(self, x):
+        return self._xp.conj(self.A._matmat(self._xp.conj(x)))
+
+
+def _get_dtype(operators, dtypes=None, xp=None):
+    """Returns the promoted dtype from input dtypes and operators."""
+    xp = np_compat if xp is None else xp
+    if dtypes is None:
+        dtypes = []
+    for obj in operators:
+        if obj is not None and hasattr(obj, "dtype"):
+            dtypes.append(obj.dtype)
+    return xp_result_type(*dtypes, xp=xp)
+
+
+class _SumLinearOperator(LinearOperator):
+    """Representing ``A + B``"""
+
+    def __init__(self, A, B, xp=None):
+        if not isinstance(A, LinearOperator) or not isinstance(B, LinearOperator):
+            raise ValueError("both operands have to be a LinearOperator")
+        *A_broadcast_dims, A_M, A_N = A.shape
+        *B_broadcast_dims, B_M, B_N = B.shape
+        if (A_M, A_N) != (B_M, B_N):
+            raise ValueError(f"cannot add {A} and {B}: shape mismatch")
+        broadcasted_dims = xpx.broadcast_shapes(A_broadcast_dims, B_broadcast_dims)
+        self.args = (A, B)
+        super().__init__(_get_dtype([A, B], xp=xp), (*broadcasted_dims, A_M, A_N), xp)
+
+    def _matvec(self, x):
+        return self.args[0].matvec(x) + self.args[1].matvec(x)
+
+    def _rmatvec(self, x):
+        return self.args[0].rmatvec(x) + self.args[1].rmatvec(x)
+
+    def _rmatmat(self, x):
+        return self.args[0].rmatmat(x) + self.args[1].rmatmat(x)
+
+    def _matmat(self, x):
+        return self.args[0].matmat(x) + self.args[1].matmat(x)
+
+    def _adjoint(self):
+        A, B = self.args
+        return A.H + B.H
+
+
+class _ProductLinearOperator(LinearOperator):
+    """Representing ``A @ B``"""
+
+    def __init__(self, A, B, xp=None):
+        if not isinstance(A, LinearOperator) or not isinstance(B, LinearOperator):
+            raise ValueError("both operands have to be a LinearOperator")
+        *A_broadcast_dims, A_M, A_N = A.shape
+        *B_broadcast_dims, B_M, B_N = B.shape
+        if A_N != B_M:
+            raise ValueError(f"cannot multiply {A} and {B}: shape mismatch")
+        broadcasted_dims = np.broadcast_shapes(A_broadcast_dims, B_broadcast_dims)
+        super().__init__(_get_dtype([A, B], xp=xp), (*broadcasted_dims, A_M, B_N), xp)
+        self.args = (A, B)
+
+    def _matvec(self, x):
+        return self.args[0].matvec(self.args[1].matvec(x))
+
+    def _rmatvec(self, x):
+        return self.args[1].rmatvec(self.args[0].rmatvec(x))
+
+    def _rmatmat(self, x):
+        return self.args[1].rmatmat(self.args[0].rmatmat(x))
+
+    def _matmat(self, x):
+        return self.args[0].matmat(self.args[1].matmat(x))
+
+    def _adjoint(self):
+        A, B = self.args
+        return B.H @ A.H
+
+
+class _ScaledLinearOperator(LinearOperator):
+    """Representing ``alpha * A``"""
+
+    def __init__(self, A, alpha, xp=None):
+        if not isinstance(A, LinearOperator):
+            raise ValueError("LinearOperator expected as A")
+        if not np.isscalar(alpha):
+            raise ValueError("scalar expected as alpha")
+        if isinstance(A, _ScaledLinearOperator):
+            A, alpha_original = A.args
+            # Avoid in-place multiplication so that we don't accidentally mutate
+            # the original prefactor.
+            alpha = alpha * alpha_original
+
+        dtype = _get_dtype([A], [alpha], xp=xp)
+        super().__init__(dtype, A.shape, xp)
+        self.args = (A, alpha)
+        # Note: args[1] is alpha (a scalar), so use `*` below, not `@`
+
+    def _matvec(self, x):
+        return self.args[1] * self.args[0].matvec(x)
+
+    def _rmatvec(self, x):
+        return self.args[1].conjugate() * self.args[0].rmatvec(x)
+
+    def _rmatmat(self, x):
+        return self.args[1].conjugate() * self.args[0].rmatmat(x)
+
+    def _matmat(self, x):
+        return self.args[1] * self.args[0].matmat(x)
+
+    def _adjoint(self):
+        A, alpha = self.args
+        return A.H * alpha.conjugate()
+
+
+class _PowerLinearOperator(LinearOperator):
+    """Representing ``A ** p``"""
+
+    def __init__(self, A, p, xp=None):
+        if not isinstance(A, LinearOperator):
+            raise ValueError("LinearOperator expected as A")
+        if A.shape[-2] != A.shape[-1]:
+            msg = f"square core-dimensions of LinearOperator expected, got {A!r}"
+            raise ValueError(msg)
+        if not isintlike(p) or p < 0:
+            raise ValueError("non-negative integer expected as p")
+
+        super().__init__(_get_dtype([A], xp=xp), A.shape, xp)
+        self.args = (A, p)
+
+    def _power(self, fun, x):
+        res = xp_copy(x)
+        for i in range(self.args[1]):
+            res = fun(res)
+        return res
+
+    def _matvec(self, x):
+        return self._power(self.args[0].matvec, x)
+
+    def _rmatvec(self, x):
+        return self._power(self.args[0].rmatvec, x)
+
+    def _rmatmat(self, x):
+        return self._power(self.args[0].rmatmat, x)
+
+    def _matmat(self, x):
+        return self._power(self.args[0].matmat, x)
+
+    def _adjoint(self):
+        A, p = self.args
+        return A.H**p
+
+
+class MatrixLinearOperator(LinearOperator):
+    """Operator defined by a matrix `A` which implements ``@``."""
+
+    def __init__(self, A, xp=None):
+        super().__init__(A.dtype, A.shape, xp)
+        self.A = A
+        self.__adj = None
+        self.args = (A,)
+
+    def _matmat(self, X):
+        return self.A @ X
+
+    def _adjoint(self):
+        if self.__adj is None:
+            self.__adj = _AdjointMatrixOperator(self.A, xp=self._xp)
+        return self.__adj
+
+
+class _AdjointMatrixOperator(MatrixLinearOperator):
+    """Representing ``A.H``, for `MatrixLinearOperator` `A`."""
+
+    def __init__(self, A, xp=None):
+        xp = np_compat if xp is None else xp
+        if A.ndim > 2:
+            if issparse(A):
+                A_T = sparse.swapaxes(A, -1, -2)
+            else:
+                A_T = A.mT
+        else:
+            A_T = A.T
+        super().__init__(xp.conj(A_T), xp=xp)
+        self.args = (A,)  # override to ensure `self.args[0]` is accurate
+
+    def _adjoint(self):
+        return MatrixLinearOperator(self.args[0], xp=self._xp)
+
+
+class IdentityOperator(LinearOperator):
+    def __init__(self, shape, dtype=None, xp=None):
+        super().__init__(dtype, shape, xp)
+
+    def _matvec(self, x):
+        return x
+
+    def _rmatvec(self, x):
+        return x
+
+    def _rmatmat(self, x):
+        return x
+
+    def _matmat(self, x):
+        return x
+
+    def _adjoint(self):
+        return self
+
+
+@xp_capabilities()
+def aslinearoperator(A):
+    """Return `A` as a `LinearOperator`.
+
+    See the `LinearOperator` documentation for additional information.
+
+    Parameters
+    ----------
+    A : object
+        Object to convert to a `LinearOperator`. May be any one of the following types:
+
+        - `numpy.ndarray`
+        - `numpy.matrix`
+        - `scipy.sparse` array
+          (e.g. `~scipy.sparse.csr_array`, `~scipy.sparse.lil_array`, etc.)
+        - `LinearOperator`
+        - An object with ``.shape`` and ``.matvec`` attributes
+
+    Returns
+    -------
+    B : LinearOperator
+        A `LinearOperator` corresponding with `A`
+
+    Notes
+    -----
+    If `A` has no ``.dtype`` attribute, the data type is determined by calling
+    :func:`LinearOperator.matvec()` - set the ``.dtype`` attribute to prevent this
+    call upon the linear operator creation.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.sparse.linalg import aslinearoperator
+    >>> M = np.array([[1,2,3],[4,5,6]], dtype=np.int32)
+    >>> aslinearoperator(M)
+    <2x3 MatrixLinearOperator with dtype=int32>
+    """
+    if isinstance(A, LinearOperator):
+        return A
+
+    # https://github.com/data-apis/array-api-compat/issues/388
+    if is_array_api_obj(A) and not isinstance(A, np.matrix):
+        xp = array_namespace(A)
+        if is_pydata_sparse_array(A) and not SCIPY_ARRAY_API:
+            pass  # skip `atleast_nd`, since `xp=np` does not work with `sparse`
+        else:
+            A = xpx.atleast_nd(A, ndim=2, xp=xp)
+        return MatrixLinearOperator(A, xp=xp)
+
+    if issparse(A):
+        return MatrixLinearOperator(A)
+
+    if isinstance(A, np.matrix):
+        A = np.atleast_2d(np.asarray(A))
+        return MatrixLinearOperator(A)
+
+    if hasattr(A, "shape") and hasattr(A, "matvec"):
+        rmatvec = None
+        rmatmat = None
+        dtype = None
+
+        if hasattr(A, "rmatvec"):
+            rmatvec = A.rmatvec
+        if hasattr(A, "rmatmat"):
+            rmatmat = A.rmatmat
+        if hasattr(A, "dtype"):
+            dtype = A.dtype
+        return LinearOperator(
+            A.shape, A.matvec, rmatvec=rmatvec, rmatmat=rmatmat, dtype=dtype
+        )
+
+    raise TypeError("type not understood")
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_isolve/__init__.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_isolve/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..3b57274542928e79c234bb6955849a90be21990e
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_isolve/__init__.py
@@ -0,0 +1,20 @@
+"Iterative Solvers for Sparse Linear Systems"
+
+#from info import __doc__
+from .iterative import *
+from .minres import minres
+from .lgmres import lgmres
+from .lsqr import lsqr
+from .lsmr import lsmr
+from ._gcrotmk import gcrotmk
+from .tfqmr import tfqmr
+
+__all__ = [
+    'bicg', 'bicgstab', 'cg', 'cgs', 'gcrotmk', 'gmres',
+    'lgmres', 'lsmr', 'lsqr',
+    'minres', 'qmr', 'tfqmr'
+]
+
+from scipy._lib._testutils import PytestTester
+test = PytestTester(__name__)
+del PytestTester
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diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_isolve/_gcrotmk.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_isolve/_gcrotmk.py
new file mode 100644
index 0000000000000000000000000000000000000000..2d70b4225750c91ec9ce862b682a4f4edfb77e24
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_isolve/_gcrotmk.py
@@ -0,0 +1,506 @@
+# Copyright (C) 2015, Pauli Virtanen <pav@iki.fi>
+# Distributed under the same license as SciPy.
+
+import numpy as np
+from numpy.linalg import LinAlgError
+# pyrefly:ignore[missing-module-attribute]
+from scipy.linalg import get_blas_funcs, qr, solve, svd, qr_insert, lstsq
+from .iterative import _get_atol_rtol
+from scipy.sparse.linalg._isolve.utils import make_system
+from scipy._lib._array_api import xp_capabilities
+
+
+__all__ = ['gcrotmk']
+
+
+def _fgmres(matvec, v0, m, atol, lpsolve=None, rpsolve=None, cs=(), outer_v=(),
+            prepend_outer_v=False):
+    """
+    FGMRES Arnoldi process, with optional projection or augmentation
+
+    Parameters
+    ----------
+    matvec : callable
+        Operation A*x
+    v0 : ndarray
+        Initial vector, normalized to nrm2(v0) == 1
+    m : int
+        Number of GMRES rounds
+    atol : float
+        Absolute tolerance for early exit
+    lpsolve : callable
+        Left preconditioner L
+    rpsolve : callable
+        Right preconditioner R
+    cs : list of (ndarray, ndarray)
+        Columns of matrices C and U in GCROT
+    outer_v : list of ndarrays
+        Augmentation vectors in LGMRES
+    prepend_outer_v : bool, optional
+        Whether augmentation vectors come before or after
+        Krylov iterates
+
+    Raises
+    ------
+    LinAlgError
+        If nans encountered
+
+    Returns
+    -------
+    Q, R : ndarray
+        QR decomposition of the upper Hessenberg H=QR
+    B : ndarray
+        Projections corresponding to matrix C
+    vs : list of ndarray
+        Columns of matrix V
+    zs : list of ndarray
+        Columns of matrix Z
+    y : ndarray
+        Solution to ||H y - e_1||_2 = min!
+    res : float
+        The final (preconditioned) residual norm
+
+    """
+
+    if lpsolve is None:
+        def lpsolve(x):
+            return x
+    if rpsolve is None:
+        def rpsolve(x):
+            return x
+
+    axpy, dot, scal, nrm2 = get_blas_funcs(['axpy', 'dot', 'scal', 'nrm2'], (v0,))
+
+    vs = [v0]
+    zs = []
+    y = None
+    res = np.nan
+
+    m = m + len(outer_v)
+
+    # Orthogonal projection coefficients
+    B = np.zeros((len(cs), m), dtype=v0.dtype)
+
+    # H is stored in QR factorized form
+    Q = np.ones((1, 1), dtype=v0.dtype)
+    R = np.zeros((1, 0), dtype=v0.dtype)
+
+    eps = np.finfo(v0.dtype).eps
+
+    breakdown = False
+
+    # FGMRES Arnoldi process
+    for j in range(m):
+        # L A Z = C B + V H
+
+        if prepend_outer_v and j < len(outer_v):
+            z, w = outer_v[j]
+        elif prepend_outer_v and j == len(outer_v):
+            z = rpsolve(v0)
+            w = None
+        elif not prepend_outer_v and j >= m - len(outer_v):
+            z, w = outer_v[j - (m - len(outer_v))]
+        else:
+            z = rpsolve(vs[-1])
+            w = None
+
+        if w is None:
+            w = lpsolve(matvec(z))
+        else:
+            # w is clobbered below
+            w = w.copy()
+
+        w_norm = nrm2(w)
+
+        # GCROT projection: L A -> (1 - C C^H) L A
+        # i.e. orthogonalize against C
+        for i, c in enumerate(cs):
+            alpha = dot(c, w)
+            B[i,j] = alpha
+            w = axpy(c, w, c.shape[0], -alpha)  # w -= alpha*c
+
+        # Orthogonalize against V
+        hcur = np.zeros(j+2, dtype=Q.dtype)
+        for i, v in enumerate(vs):
+            alpha = dot(v, w)
+            hcur[i] = alpha
+            w = axpy(v, w, v.shape[0], -alpha)  # w -= alpha*v
+        hcur[i+1] = nrm2(w)
+
+        with np.errstate(over='ignore', divide='ignore'):
+            # Careful with denormals
+            alpha = 1/hcur[-1]
+
+        if np.isfinite(alpha):
+            w = scal(alpha, w)
+
+        if not (hcur[-1] > eps * w_norm):
+            # w essentially in the span of previous vectors,
+            # or we have nans. Bail out after updating the QR
+            # solution.
+            breakdown = True
+
+        vs.append(w)
+        zs.append(z)
+
+        # Arnoldi LSQ problem
+
+        # Add new column to H=Q@R, padding other columns with zeros
+        Q2 = np.zeros((j+2, j+2), dtype=Q.dtype, order='F')
+        Q2[:j+1,:j+1] = Q
+        Q2[j+1,j+1] = 1
+
+        R2 = np.zeros((j+2, j), dtype=R.dtype, order='F')
+        R2[:j+1,:] = R
+
+        Q, R = qr_insert(Q2, R2, hcur, j, which='col',
+                         overwrite_qru=True, check_finite=False)
+
+        # Transformed least squares problem
+        # || Q R y - inner_res_0 * e_1 ||_2 = min!
+        # Since R = [R'; 0], solution is y = inner_res_0 (R')^{-1} (Q^H)[:j,0]
+
+        # Residual is immediately known
+        res = abs(Q[0,-1])
+
+        # Check for termination
+        if res < atol or breakdown:
+            break
+
+    if not np.isfinite(R[j,j]):
+        # nans encountered, bail out
+        raise LinAlgError()
+
+    # -- Get the LSQ problem solution
+
+    # The problem is triangular, but the condition number may be
+    # bad (or in case of breakdown the last diagonal entry may be
+    # zero), so use lstsq instead of trtrs.
+    y, _, _, _, = lstsq(R[:j+1,:j+1], Q[0,:j+1].conj())
+
+    B = B[:,:j+1]
+
+    return Q, R, B, vs, zs, y, res
+
+
+@xp_capabilities(np_only=True)
+def gcrotmk(A, b, x0=None, *, rtol=1e-5, atol=0., maxiter=1000, M=None, callback=None,
+            m=20, k=None, CU=None, discard_C=False, truncate='oldest'):
+    """
+    Solve ``Ax = b`` with the flexible GCROT(m,k) algorithm.
+
+    Parameters
+    ----------
+    A : {sparse array, ndarray, LinearOperator}
+        The real or complex N-by-N matrix of the linear system.
+        Alternatively, `A` can be a linear operator which can
+        produce ``Ax`` using, e.g.,
+        `LinearOperator`.
+    b : ndarray
+        Right hand side of the linear system. Has shape (N,) or (N,1).
+    x0 : ndarray
+        Starting guess for the solution.
+    rtol, atol : float, optional
+        Parameters for the convergence test. For convergence,
+        ``norm(b - A @ x) <= max(rtol*norm(b), atol)`` should be satisfied.
+        The default is ``rtol=1e-5`` and ``atol=0.0``.
+    maxiter : int, optional
+        Maximum number of iterations.  Iteration will stop after maxiter
+        steps even if the specified tolerance has not been achieved. The
+        default is ``1000``.
+    M : {sparse array, ndarray, LinearOperator}, optional
+        Preconditioner for `A`.  The preconditioner should approximate the
+        inverse of `A`. gcrotmk is a 'flexible' algorithm and the preconditioner
+        can vary from iteration to iteration. Effective preconditioning
+        dramatically improves the rate of convergence, which implies that
+        fewer iterations are needed to reach a given error tolerance.
+    callback : function, optional
+        User-supplied function to call after each iteration.  It is called
+        as ``callback(xk)``, where ``xk`` is the current solution vector.
+    m : int, optional
+        Number of inner FGMRES iterations per each outer iteration.
+        Default: 20
+    k : int, optional
+        Number of vectors to carry between inner FGMRES iterations.
+        According to [2]_, good values are around `m`.
+        Default: `m`
+    CU : list of tuples, optional
+        List of tuples ``(c, u)`` which contain the columns of the matrices
+        C and U in the GCROT(m,k) algorithm. For details, see [2]_.
+        The list given and vectors contained in it are modified in-place.
+        If not given, start from empty matrices. The ``c`` elements in the
+        tuples can be ``None``, in which case the vectors are recomputed
+        via ``c = A u`` on start and orthogonalized as described in [3]_.
+    discard_C : bool, optional
+        Discard the C-vectors at the end. Useful if recycling Krylov subspaces
+        for different linear systems.
+    truncate : {'oldest', 'smallest'}, optional
+        Truncation scheme to use. Drop: oldest vectors, or vectors with
+        smallest singular values using the scheme discussed in [1,2].
+        See [2]_ for detailed comparison.
+        Default: 'oldest'
+
+    Returns
+    -------
+    x : ndarray
+        The solution found.
+    info : int
+        Provides convergence information:
+
+        * 0  : successful exit
+        * >0 : convergence to tolerance not achieved, number of iterations
+
+    References
+    ----------
+    .. [1] E. de Sturler, ''Truncation strategies for optimal Krylov subspace
+           methods'', SIAM J. Numer. Anal. 36, 864 (1999).
+    .. [2] J.E. Hicken and D.W. Zingg, ''A simplified and flexible variant
+           of GCROT for solving nonsymmetric linear systems'',
+           SIAM J. Sci. Comput. 32, 172 (2010).
+    .. [3] M.L. Parks, E. de Sturler, G. Mackey, D.D. Johnson, S. Maiti,
+           ''Recycling Krylov subspaces for sequences of linear systems'',
+           SIAM J. Sci. Comput. 28, 1651 (2006).
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.sparse import csc_array
+    >>> from scipy.sparse.linalg import gcrotmk
+    >>> R = np.random.randn(5, 5)
+    >>> A = csc_array(R)
+    >>> b = np.random.randn(5)
+    >>> x, exit_code = gcrotmk(A, b, atol=1e-5)
+    >>> print(exit_code)
+    0
+    >>> np.allclose(A.dot(x), b)
+    True
+
+    """
+    A,M,x,b = make_system(A,M,x0,b)
+
+    if not np.isfinite(b).all():
+        raise ValueError("RHS must contain only finite numbers")
+
+    if truncate not in ('oldest', 'smallest'):
+        raise ValueError(f"Invalid value for 'truncate': {truncate!r}")
+
+    matvec = A.matvec
+    psolve = M.matvec
+
+    if CU is None:
+        CU = []
+
+    if k is None:
+        k = m
+
+    axpy, dot, scal = None, None, None
+
+    if x0 is None:
+        r = b.copy()
+    else:
+        r = b - matvec(x)
+
+    axpy, dot, scal, nrm2 = get_blas_funcs(['axpy', 'dot', 'scal', 'nrm2'], (x, r))
+
+    b_norm = nrm2(b)
+
+    # we call this to get the right atol/rtol and raise errors as necessary
+    atol, rtol = _get_atol_rtol('gcrotmk', b_norm, atol, rtol)
+
+    if b_norm == 0:
+        x = b
+        return (x, 0)
+
+    if discard_C:
+        CU[:] = [(None, u) for c, u in CU]
+
+    # Reorthogonalize old vectors
+    if CU:
+        # Sort already existing vectors to the front
+        CU.sort(key=lambda cu: cu[0] is not None)
+
+        # Fill-in missing ones
+        C = np.empty((A.shape[0], len(CU)), dtype=r.dtype, order='F')
+        us = []
+        j = 0
+        while CU:
+            # More memory-efficient: throw away old vectors as we go
+            c, u = CU.pop(0)
+            if c is None:
+                c = matvec(u)
+            C[:,j] = c
+            j += 1
+            us.append(u)
+
+        # Orthogonalize
+        Q, R, P = qr(C, overwrite_a=True, mode='economic', pivoting=True)
+        del C
+
+        # C := Q
+        cs = list(Q.T)
+
+        # U := U P R^-1,  back-substitution
+        new_us = []
+        for j in range(len(cs)):
+            u = us[P[j]]
+            for i in range(j):
+                u = axpy(us[P[i]], u, u.shape[0], -R[i,j])
+            if abs(R[j,j]) < 1e-12 * abs(R[0,0]):
+                # discard rest of the vectors
+                break
+            u = scal(1.0/R[j,j], u)
+            new_us.append(u)
+
+        # Form the new CU lists
+        CU[:] = list(zip(cs, new_us))[::-1]
+
+    if CU:
+        axpy, dot = get_blas_funcs(['axpy', 'dot'], (r,))
+
+        # Solve first the projection operation with respect to the CU
+        # vectors. This corresponds to modifying the initial guess to
+        # be
+        #
+        #     x' = x + U y
+        #     y = argmin_y || b - A (x + U y) ||^2
+        #
+        # The solution is y = C^H (b - A x)
+        for c, u in CU:
+            yc = dot(c, r)
+            x = axpy(u, x, x.shape[0], yc)
+            r = axpy(c, r, r.shape[0], -yc)
+
+    # GCROT main iteration
+    for j_outer in range(maxiter):
+        # -- callback
+        if callback is not None:
+            callback(x)
+
+        beta = nrm2(r)
+
+        # -- check stopping condition
+        beta_tol = max(atol, rtol * b_norm)
+
+        if beta <= beta_tol and (j_outer > 0 or CU):
+            # recompute residual to avoid rounding error
+            r = b - matvec(x)
+            beta = nrm2(r)
+
+        if beta <= beta_tol:
+            j_outer = -1
+            break
+
+        ml = m + max(k - len(CU), 0)
+
+        cs = [c for c, u in CU]
+
+        try:
+            Q, R, B, vs, zs, y, pres = _fgmres(matvec,
+                                               r/beta,
+                                               ml,
+                                               rpsolve=psolve,
+                                               atol=max(atol, rtol*b_norm)/beta,
+                                               cs=cs)
+            y *= beta
+        except LinAlgError:
+            # Floating point over/underflow, non-finite result from
+            # matmul etc. -- report failure.
+            break
+
+        #
+        # At this point,
+        #
+        #     [A U, A Z] = [C, V] G;   G =  [ I  B ]
+        #                                   [ 0  H ]
+        #
+        # where [C, V] has orthonormal columns, and r = beta v_0. Moreover,
+        #
+        #     || b - A (x + Z y + U q) ||_2 = || r - C B y - V H y - C q ||_2 = min!
+        #
+        # from which y = argmin_y || beta e_1 - H y ||_2, and q = -B y
+        #
+
+        #
+        # GCROT(m,k) update
+        #
+
+        # Define new outer vectors
+
+        # ux := (Z - U B) y
+        ux = zs[0]*y[0]
+        for z, yc in zip(zs[1:], y[1:]):
+            ux = axpy(z, ux, ux.shape[0], yc)  # ux += z*yc
+        by = B.dot(y)
+        for cu, byc in zip(CU, by):
+            c, u = cu
+            ux = axpy(u, ux, ux.shape[0], -byc)  # ux -= u*byc
+
+        # cx := V H y
+        with np.errstate(invalid="ignore"):
+            hy = Q.dot(R.dot(y))
+        cx = vs[0] * hy[0]
+        for v, hyc in zip(vs[1:], hy[1:]):
+            cx = axpy(v, cx, cx.shape[0], hyc)  # cx += v*hyc
+
+        # Normalize cx, maintaining cx = A ux
+        # This new cx is orthogonal to the previous C, by construction
+        try:
+            alpha = 1/nrm2(cx)
+            if not np.isfinite(alpha):
+                raise FloatingPointError()
+        except (FloatingPointError, ZeroDivisionError):
+            # Cannot update, so skip it
+            continue
+
+        cx = scal(alpha, cx)
+        ux = scal(alpha, ux)
+
+        # Update residual and solution
+        gamma = dot(cx, r)
+        r = axpy(cx, r, r.shape[0], -gamma)  # r -= gamma*cx
+        x = axpy(ux, x, x.shape[0], gamma)  # x += gamma*ux
+
+        # Truncate CU
+        if truncate == 'oldest':
+            while len(CU) >= k and CU:
+                del CU[0]
+        elif truncate == 'smallest':
+            if len(CU) >= k and CU:
+                # cf. [1,2]
+                D = solve(R[:-1,:].T, B.T).T
+                W, sigma, V = svd(D)
+
+                # C := C W[:,:k-1],  U := U W[:,:k-1]
+                new_CU = []
+                for j, w in enumerate(W[:,:k-1].T):
+                    c, u = CU[0]
+                    c = c * w[0]
+                    u = u * w[0]
+                    for cup, wp in zip(CU[1:], w[1:]):
+                        cp, up = cup
+                        c = axpy(cp, c, c.shape[0], wp)
+                        u = axpy(up, u, u.shape[0], wp)
+
+                    # Reorthogonalize at the same time; not necessary
+                    # in exact arithmetic, but floating point error
+                    # tends to accumulate here
+                    for cp, up in new_CU:
+                        alpha = dot(cp, c)
+                        c = axpy(cp, c, c.shape[0], -alpha)
+                        u = axpy(up, u, u.shape[0], -alpha)
+                    alpha = nrm2(c)
+                    c = scal(1.0/alpha, c)
+                    u = scal(1.0/alpha, u)
+
+                    new_CU.append((c, u))
+                CU[:] = new_CU
+
+        # Add new vector to CU
+        CU.append((cx, ux))
+
+    # Include the solution vector to the span
+    CU.append((None, x.copy()))
+    if discard_C:
+        CU[:] = [(None, uz) for cz, uz in CU]
+
+    return x, j_outer + 1
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_isolve/iterative.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_isolve/iterative.py
new file mode 100644
index 0000000000000000000000000000000000000000..df3fbf52ade58b530d048edb0d854d51d4dca95c
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_isolve/iterative.py
@@ -0,0 +1,1058 @@
+import warnings
+import numpy as np
+from scipy.sparse.linalg._interface import LinearOperator
+from .utils import make_system
+from scipy.linalg import get_lapack_funcs
+from scipy._lib._array_api import xp_capabilities
+
+__all__ = ['bicg', 'bicgstab', 'cg', 'cgs', 'gmres', 'qmr']
+
+
+def _get_atol_rtol(name, b_norm, atol=0., rtol=1e-5):
+    """
+    A helper function to handle tolerance normalization
+    """
+    if atol == 'legacy' or atol is None or atol < 0:
+        msg = (f"'scipy.sparse.linalg.{name}' called with invalid `atol`={atol}; "
+               "if set, `atol` must be a real, non-negative number.")
+        raise ValueError(msg)
+
+    atol = max(float(atol), float(rtol) * float(b_norm))
+
+    return atol, rtol
+
+
+@xp_capabilities(np_only=True)
+def bicg(A, b, x0=None, *, rtol=1e-5, atol=0., maxiter=None, M=None, callback=None):
+    """
+    Solve ``Ax = b`` with the BIConjugate Gradient method.
+
+    Parameters
+    ----------
+    A : {sparse array, ndarray, LinearOperator}
+        The real or complex N-by-N matrix of the linear system.
+        Alternatively, `A` can be a linear operator which can
+        produce ``Ax`` and ``A^T x`` using, e.g.,
+        ``scipy.sparse.linalg.LinearOperator``.
+    b : ndarray
+        Right hand side of the linear system. Has shape (N,) or (N,1).
+    x0 : ndarray
+        Starting guess for the solution.
+    rtol, atol : float, optional
+        Parameters for the convergence test. For convergence,
+        ``norm(b - A @ x) <= max(rtol*norm(b), atol)`` should be satisfied.
+        The default is ``atol=0.`` and ``rtol=1e-5``.
+    maxiter : int
+        Maximum number of iterations.  Iteration will stop after maxiter
+        steps even if the specified tolerance has not been achieved.
+    M : {sparse array, ndarray, LinearOperator}
+        Preconditioner for `A`. It should approximate the
+        inverse of `A` (see Notes). Effective preconditioning dramatically improves the
+        rate of convergence, which implies that fewer iterations are needed
+        to reach a given error tolerance.
+    callback : function
+        User-supplied function to call after each iteration.  It is called
+        as ``callback(xk)``, where ``xk`` is the current solution vector.
+
+    Returns
+    -------
+    x : ndarray
+        The converged solution.
+    info : int
+        Provides convergence information:
+            0  : successful exit
+            >0 : convergence to tolerance not achieved, number of iterations
+            <0 : parameter breakdown
+
+    Notes
+    -----
+    The preconditioner `M` should be a matrix such that ``M @ A`` has a smaller
+    condition number than `A`, see [1]_ .
+
+    References
+    ----------
+    .. [1] "Preconditioner", Wikipedia, 
+           https://en.wikipedia.org/wiki/Preconditioner
+    .. [2] "Biconjugate gradient method", Wikipedia, 
+           https://en.wikipedia.org/wiki/Biconjugate_gradient_method
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.sparse import csc_array
+    >>> from scipy.sparse.linalg import bicg
+    >>> A = csc_array([[3, 2, 0], [1, -1, 0], [0, 5, 1.]])
+    >>> b = np.array([2., 4., -1.])
+    >>> x, exitCode = bicg(A, b, atol=1e-5)
+    >>> print(exitCode)  # 0 indicates successful convergence
+    0
+    >>> np.allclose(A.dot(x), b)
+    True
+    """
+    A, M, x, b = make_system(A, M, x0, b)
+    bnrm2 = np.linalg.norm(b)
+
+    atol, _ = _get_atol_rtol('bicg', bnrm2, atol, rtol)
+
+    if bnrm2 == 0:
+        return b, 0
+
+    n = len(b)
+    dotprod = np.vdot if np.iscomplexobj(x) else np.dot
+
+    if maxiter is None:
+        maxiter = n*10
+
+    matvec, rmatvec = A.matvec, A.rmatvec
+    psolve, rpsolve = M.matvec, M.rmatvec
+
+    rhotol = np.finfo(x.dtype.char).eps**2
+
+    # Dummy values to initialize vars, silence linter warnings
+    rho_prev, p, ptilde = None, None, None
+
+    r = b - matvec(x) if x.any() else b.copy()
+    rtilde = r.copy()
+
+    for iteration in range(maxiter):
+        if np.linalg.norm(r) < atol:  # Are we done?
+            return x, 0
+
+        z = psolve(r)
+        ztilde = rpsolve(rtilde)
+        # order matters in this dot product
+        rho_cur = dotprod(rtilde, z)
+
+        if np.abs(rho_cur) < rhotol:  # Breakdown case
+            return x, -10
+
+        if iteration > 0:
+            beta = rho_cur / rho_prev
+            p *= beta
+            p += z
+            ptilde *= beta.conj()
+            ptilde += ztilde
+        else:  # First spin
+            p = z.copy()
+            ptilde = ztilde.copy()
+
+        q = matvec(p)
+        qtilde = rmatvec(ptilde)
+        rv = dotprod(ptilde, q)
+
+        if rv == 0:
+            return x, -11
+
+        alpha = rho_cur / rv
+        x += alpha*p
+        r -= alpha*q
+        rtilde -= alpha.conj()*qtilde
+        rho_prev = rho_cur
+
+        if callback:
+            callback(x)
+
+    else:  # for loop exhausted
+        # Return incomplete progress
+        return x, maxiter
+
+
+@xp_capabilities(np_only=True)
+def bicgstab(A, b, x0=None, *, rtol=1e-5, atol=0., maxiter=None, M=None,
+             callback=None):
+    """
+    Solve ``Ax = b`` with the BIConjugate Gradient STABilized method.
+
+    Parameters
+    ----------
+    A : {sparse array, ndarray, LinearOperator}
+        The real or complex N-by-N matrix of the linear system.
+        Alternatively, `A` can be a linear operator which can
+        produce ``Ax`` and ``A^T x`` using, e.g.,
+        ``scipy.sparse.linalg.LinearOperator``.
+    b : ndarray
+        Right hand side of the linear system. Has shape (N,) or (N,1).
+    x0 : ndarray
+        Starting guess for the solution.
+    rtol, atol : float, optional
+        Parameters for the convergence test. For convergence,
+        ``norm(b - A @ x) <= max(rtol*norm(b), atol)`` should be satisfied.
+        The default is ``atol=0.`` and ``rtol=1e-5``.
+    maxiter : int
+        Maximum number of iterations.  Iteration will stop after maxiter
+        steps even if the specified tolerance has not been achieved.
+    M : {sparse array, ndarray, LinearOperator}
+        Preconditioner for `A`. It should approximate the
+        inverse of `A` (see Notes). Effective preconditioning dramatically improves the
+        rate of convergence, which implies that fewer iterations are needed
+        to reach a given error tolerance.
+    callback : function
+        User-supplied function to call after each iteration.  It is called
+        as ``callback(xk)``, where ``xk`` is the current solution vector.
+
+    Returns
+    -------
+    x : ndarray
+        The converged solution.
+    info : int
+        Provides convergence information:
+            0  : successful exit
+            >0 : convergence to tolerance not achieved, number of iterations
+            <0 : parameter breakdown
+
+    Notes
+    -----
+    The preconditioner `M` should be a matrix such that ``M @ A`` has a smaller
+    condition number than `A`, see [1]_ .
+
+    References
+    ----------
+    .. [1] "Preconditioner", Wikipedia, 
+           https://en.wikipedia.org/wiki/Preconditioner
+    .. [2] "Biconjugate gradient stabilized method", 
+           Wikipedia, https://en.wikipedia.org/wiki/Biconjugate_gradient_stabilized_method
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.sparse import csc_array
+    >>> from scipy.sparse.linalg import bicgstab
+    >>> R = np.array([[4, 2, 0, 1],
+    ...               [3, 0, 0, 2],
+    ...               [0, 1, 1, 1],
+    ...               [0, 2, 1, 0]])
+    >>> A = csc_array(R)
+    >>> b = np.array([-1, -0.5, -1, 2])
+    >>> x, exit_code = bicgstab(A, b, atol=1e-5)
+    >>> print(exit_code)  # 0 indicates successful convergence
+    0
+    >>> np.allclose(A.dot(x), b)
+    True
+    """
+    A, M, x, b = make_system(A, M, x0, b)
+    bnrm2 = np.linalg.norm(b)
+
+    atol, _ = _get_atol_rtol('bicgstab', bnrm2, atol, rtol)
+
+    if bnrm2 == 0:
+        return b, 0
+
+    n = len(b)
+
+    dotprod = np.vdot if np.iscomplexobj(x) else np.dot
+
+    if maxiter is None:
+        maxiter = n*10
+
+    matvec = A.matvec
+    psolve = M.matvec
+
+    # These values make no sense but coming from original Fortran code
+    # sqrt might have been meant instead.
+    rhotol = np.finfo(x.dtype.char).eps**2
+    omegatol = rhotol
+
+    # Dummy values to initialize vars, silence linter warnings
+    rho_prev, omega, alpha, p, v = None, None, None, None, None
+
+    r = b - matvec(x) if x.any() else b.copy()
+    rtilde = r.copy()
+
+    for iteration in range(maxiter):
+        if np.linalg.norm(r) < atol:  # Are we done?
+            return x, 0
+
+        rho = dotprod(rtilde, r)
+        if np.abs(rho) < rhotol:  # rho breakdown
+            return x, -10
+
+        if iteration > 0:
+            if np.abs(omega) < omegatol:  # omega breakdown
+                return x, -11
+
+            beta = (rho / rho_prev) * (alpha / omega)
+            p -= omega*v
+            p *= beta
+            p += r
+        else:  # First spin
+            s = np.empty_like(r)
+            p = r.copy()
+
+        phat = psolve(p)
+        v = matvec(phat)
+        rv = dotprod(rtilde, v)
+        if rv == 0:
+            return x, -11
+        alpha = rho / rv
+        r -= alpha*v
+        s[:] = r[:]
+
+        if np.linalg.norm(s) < atol:
+            x += alpha*phat
+            return x, 0
+
+        shat = psolve(s)
+        t = matvec(shat)
+        omega = dotprod(t, s) / dotprod(t, t)
+        x += alpha*phat
+        x += omega*shat
+        r -= omega*t
+        rho_prev = rho
+
+        if callback:
+            callback(x)
+
+    else:  # for loop exhausted
+        # Return incomplete progress
+        return x, maxiter
+
+
+@xp_capabilities(np_only=True)
+def cg(A, b, x0=None, *, rtol=1e-5, atol=0., maxiter=None, M=None, callback=None):
+    """
+    Solve ``Ax = b`` with the Conjugate Gradient method, for a symmetric,
+    positive-definite `A`.
+
+    Parameters
+    ----------
+    A : {sparse array, ndarray, LinearOperator}
+        The real or complex N-by-N matrix of the linear system.
+        `A` must represent a hermitian, positive definite matrix.
+        Alternatively, `A` can be a linear operator which can
+        produce ``Ax`` using, e.g.,
+        ``scipy.sparse.linalg.LinearOperator``.
+    b : ndarray
+        Right hand side of the linear system. Has shape (N,) or (N,1).
+    x0 : ndarray
+        Starting guess for the solution.
+    rtol, atol : float, optional
+        Parameters for the convergence test. For convergence,
+        ``norm(b - A @ x) <= max(rtol*norm(b), atol)`` should be satisfied.
+        The default is ``atol=0.`` and ``rtol=1e-5``.
+    maxiter : int
+        Maximum number of iterations.  Iteration will stop after maxiter
+        steps even if the specified tolerance has not been achieved.
+    M : {sparse array, ndarray, LinearOperator}
+        Preconditioner for `A`. `M` must represent a hermitian, positive definite
+        matrix. It should approximate the inverse of `A` (see Notes).
+        Effective preconditioning dramatically improves the
+        rate of convergence, which implies that fewer iterations are needed
+        to reach a given error tolerance.
+    callback : function
+        User-supplied function to call after each iteration.  It is called
+        as ``callback(xk)``, where ``xk`` is the current solution vector.
+
+    Returns
+    -------
+    x : ndarray
+        The converged solution.
+    info : int
+        Provides convergence information:
+            0  : successful exit
+            >0 : convergence to tolerance not achieved, number of iterations
+
+    Notes
+    -----
+    The preconditioner `M` should be a matrix such that ``M @ A`` has a smaller
+    condition number than `A`, see [2]_.
+
+    References
+    ----------
+    .. [1] "Conjugate Gradient Method, Wikipedia, 
+           https://en.wikipedia.org/wiki/Conjugate_gradient_method
+    .. [2] "Preconditioner", 
+           Wikipedia, https://en.wikipedia.org/wiki/Preconditioner
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.sparse import csc_array
+    >>> from scipy.sparse.linalg import cg
+    >>> P = np.array([[4, 0, 1, 0],
+    ...               [0, 5, 0, 0],
+    ...               [1, 0, 3, 2],
+    ...               [0, 0, 2, 4]])
+    >>> A = csc_array(P)
+    >>> b = np.array([-1, -0.5, -1, 2])
+    >>> x, exit_code = cg(A, b, atol=1e-5)
+    >>> print(exit_code)    # 0 indicates successful convergence
+    0
+    >>> np.allclose(A.dot(x), b)
+    True
+    """
+    A, M, x, b = make_system(A, M, x0, b)
+    bnrm2 = np.linalg.norm(b)
+
+    atol, _ = _get_atol_rtol('cg', bnrm2, atol, rtol)
+
+    if bnrm2 == 0:
+        return b, 0
+
+    n = len(b)
+
+    if maxiter is None:
+        maxiter = n*10
+
+    dotprod = np.vdot if np.iscomplexobj(x) else np.dot
+
+    matvec = A.matvec
+    psolve = M.matvec
+    r = b - matvec(x) if x.any() else b.copy()
+
+    # Dummy value to initialize var, silences warnings
+    rho_prev, p = None, None
+
+    for iteration in range(maxiter):
+        if np.linalg.norm(r) < atol:  # Are we done?
+            return x, 0
+
+        z = psolve(r)
+        rho_cur = dotprod(r, z)
+        if iteration > 0:
+            beta = rho_cur / rho_prev
+            p *= beta
+            p += z
+        else:  # First spin
+            p = np.empty_like(r)
+            p[:] = z[:]
+
+        q = matvec(p)
+        alpha = rho_cur / dotprod(p, q)
+        x += alpha*p
+        r -= alpha*q
+        rho_prev = rho_cur
+
+        if callback:
+            callback(x)
+
+    else:  # for loop exhausted
+        # Return incomplete progress
+        return x, maxiter
+
+
+@xp_capabilities(np_only=True)
+def cgs(A, b, x0=None, *, rtol=1e-5, atol=0., maxiter=None, M=None, callback=None):
+    """
+    Solve ``Ax = b`` with the Conjugate Gradient Squared method.
+
+    Parameters
+    ----------
+    A : {sparse array, ndarray, LinearOperator}
+        The real-valued N-by-N matrix of the linear system.
+        Alternatively, `A` can be a linear operator which can
+        produce ``Ax`` using, e.g.,
+        ``scipy.sparse.linalg.LinearOperator``.
+    b : ndarray
+        Right hand side of the linear system. Has shape (N,) or (N,1).
+    x0 : ndarray
+        Starting guess for the solution.
+    rtol, atol : float, optional
+        Parameters for the convergence test. For convergence,
+        ``norm(b - A @ x) <= max(rtol*norm(b), atol)`` should be satisfied.
+        The default is ``atol=0.`` and ``rtol=1e-5``.
+    maxiter : int
+        Maximum number of iterations.  Iteration will stop after maxiter
+        steps even if the specified tolerance has not been achieved.
+    M : {sparse array, ndarray, LinearOperator}
+        Preconditioner for ``A``. It should approximate the
+        inverse of `A` (see Notes). Effective preconditioning dramatically improves the
+        rate of convergence, which implies that fewer iterations are needed
+        to reach a given error tolerance.
+    callback : function
+        User-supplied function to call after each iteration.  It is called
+        as ``callback(xk)``, where ``xk`` is the current solution vector.
+
+    Returns
+    -------
+    x : ndarray
+        The converged solution.
+    info : int
+        Provides convergence information:
+            0  : successful exit
+            >0 : convergence to tolerance not achieved, number of iterations
+            <0 : parameter breakdown
+
+    Notes
+    -----
+    The preconditioner `M` should be a matrix such that ``M @ A`` has a smaller
+    condition number than `A`, see [1]_.
+
+    References
+    ----------
+    .. [1] "Preconditioner", Wikipedia, 
+           https://en.wikipedia.org/wiki/Preconditioner
+    .. [2] "Conjugate gradient squared", Wikipedia,
+           https://en.wikipedia.org/wiki/Conjugate_gradient_squared_method
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.sparse import csc_array
+    >>> from scipy.sparse.linalg import cgs
+    >>> R = np.array([[4, 2, 0, 1],
+    ...               [3, 0, 0, 2],
+    ...               [0, 1, 1, 1],
+    ...               [0, 2, 1, 0]])
+    >>> A = csc_array(R)
+    >>> b = np.array([-1, -0.5, -1, 2])
+    >>> x, exit_code = cgs(A, b)
+    >>> print(exit_code)  # 0 indicates successful convergence
+    0
+    >>> np.allclose(A.dot(x), b)
+    True
+    """
+    A, M, x, b = make_system(A, M, x0, b)
+    bnrm2 = np.linalg.norm(b)
+
+    atol, _ = _get_atol_rtol('cgs', bnrm2, atol, rtol)
+
+    if bnrm2 == 0:
+        return b, 0
+
+    n = len(b)
+
+    dotprod = np.vdot if np.iscomplexobj(x) else np.dot
+
+    if maxiter is None:
+        maxiter = n*10
+
+    matvec = A.matvec
+    psolve = M.matvec
+
+    rhotol = np.finfo(x.dtype.char).eps**2
+
+    r = b - matvec(x) if x.any() else b.copy()
+
+    rtilde = r.copy()
+    bnorm = np.linalg.norm(b)
+    if bnorm == 0:
+        bnorm = 1
+
+    # Dummy values to initialize vars, silence linter warnings
+    rho_prev, p, u, q = None, None, None, None
+
+    for iteration in range(maxiter):
+        rnorm = np.linalg.norm(r)
+        if rnorm < atol:  # Are we done?
+            return x, 0
+
+        rho_cur = dotprod(rtilde, r)
+        if np.abs(rho_cur) < rhotol:  # Breakdown case
+            return x, -10
+
+        if iteration > 0:
+            beta = rho_cur / rho_prev
+
+            # u = r + beta * q
+            # p = u + beta * (q + beta * p);
+            u[:] = r[:]
+            u += beta*q
+
+            p *= beta
+            p += q
+            p *= beta
+            p += u
+
+        else:  # First spin
+            p = r.copy()
+            u = r.copy()
+            q = np.empty_like(r)
+
+        phat = psolve(p)
+        vhat = matvec(phat)
+        rv = dotprod(rtilde, vhat)
+
+        if rv == 0:  # Dot product breakdown
+            return x, -11
+
+        alpha = rho_cur / rv
+        q[:] = u[:]
+        q -= alpha*vhat
+        uhat = psolve(u + q)
+        x += alpha*uhat
+
+        # Due to numerical error build-up the actual residual is computed
+        # instead of the following two lines that were in the original
+        # FORTRAN templates, still using a single matvec.
+
+        # qhat = matvec(uhat)
+        # r -= alpha*qhat
+        r = b - matvec(x)
+
+        rho_prev = rho_cur
+
+        if callback:
+            callback(x)
+
+    else:  # for loop exhausted
+        # Return incomplete progress
+        return x, maxiter
+
+
+@xp_capabilities(np_only=True)
+def gmres(A, b, x0=None, *, rtol=1e-5, atol=0., restart=None, maxiter=None, M=None,
+          callback=None, callback_type=None):
+    """
+    Solve ``Ax = b`` with the Generalized Minimal RESidual method.
+
+    Parameters
+    ----------
+    A : {sparse array, ndarray, LinearOperator}
+        The real or complex N-by-N matrix of the linear system.
+        Alternatively, `A` can be a linear operator which can
+        produce ``Ax`` using, e.g.,
+        ``scipy.sparse.linalg.LinearOperator``.
+    b : ndarray
+        Right hand side of the linear system. Has shape (N,) or (N,1).
+    x0 : ndarray
+        Starting guess for the solution (a vector of zeros by default).
+    rtol, atol : float
+        Parameters for the convergence test. For convergence,
+        ``norm(b - A @ x) <= max(rtol*norm(b), atol)`` should be satisfied.
+        The default is ``atol=0.`` and ``rtol=1e-5``.
+    restart : int, optional
+        Number of iterations between restarts. Larger values increase
+        iteration cost, but may be necessary for convergence.
+        If omitted, ``min(20, n)`` is used.
+    maxiter : int, optional
+        Maximum number of iterations (restart cycles).  Iteration will stop
+        after maxiter steps even if the specified tolerance has not been
+        achieved. See `callback_type`.
+    M : {sparse array, ndarray, LinearOperator}
+        Inverse of the preconditioner of `A`.  `M` should approximate the
+        inverse of `A` and be easy to solve for (see Notes).  Effective
+        preconditioning dramatically improves the rate of convergence,
+        which implies that fewer iterations are needed to reach a given
+        error tolerance.  By default, no preconditioner is used.
+        In this implementation, left preconditioning is used,
+        and the preconditioned residual is minimized. However, the final
+        convergence is tested with respect to the ``b - A @ x`` residual.
+    callback : function
+        User-supplied function to call after each iteration.  It is called
+        as ``callback(args)``, where ``args`` are selected by `callback_type`.
+    callback_type : {'x', 'pr_norm', 'legacy'}, optional
+        Callback function argument requested:
+          - ``x``: current iterate (ndarray), called on every restart
+          - ``pr_norm``: relative (preconditioned) residual norm (float),
+            called on every inner iteration
+          - ``legacy`` (default): same as ``pr_norm``, but also changes the
+            meaning of `maxiter` to count inner iterations instead of restart
+            cycles.
+
+        This keyword has no effect if `callback` is not set.
+
+    Returns
+    -------
+    x : ndarray
+        The converged solution.
+    info : int
+        Provides convergence information:
+            0  : successful exit
+            >0 : convergence to tolerance not achieved, number of iterations
+
+    See Also
+    --------
+    LinearOperator
+
+    Notes
+    -----
+    A preconditioner, P, is chosen such that P is close to A but easy to solve
+    for. The preconditioner parameter required by this routine is
+    ``M = P^-1``. The inverse should preferably not be calculated
+    explicitly.  Rather, use the following template to produce M::
+
+      # Construct a linear operator that computes P^-1 @ x.
+      import scipy.sparse.linalg as spla
+      M_x = lambda x: spla.spsolve(P, x)
+      M = spla.LinearOperator((n, n), M_x)
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.sparse import csc_array
+    >>> from scipy.sparse.linalg import gmres
+    >>> A = csc_array([[3, 2, 0], [1, -1, 0], [0, 5, 1]], dtype=float)
+    >>> b = np.array([2, 4, -1], dtype=float)
+    >>> x, exitCode = gmres(A, b, atol=1e-5)
+    >>> print(exitCode)            # 0 indicates successful convergence
+    0
+    >>> np.allclose(A.dot(x), b)
+    True
+    """
+    if callback is not None and callback_type is None:
+        # Warn about 'callback_type' semantic changes.
+        # Probably should be removed only in far future, Scipy 2.0 or so.
+        msg = ("scipy.sparse.linalg.gmres called without specifying "
+               "`callback_type`. The default value will be changed in"
+               " a future release. For compatibility, specify a value "
+               "for `callback_type` explicitly, e.g., "
+               "``gmres(..., callback_type='pr_norm')``, or to retain the "
+               "old behavior ``gmres(..., callback_type='legacy')``"
+               )
+        warnings.warn(msg, category=DeprecationWarning, stacklevel=3)
+
+    if callback_type is None:
+        callback_type = 'legacy'
+
+    if callback_type not in ('x', 'pr_norm', 'legacy'):
+        raise ValueError(f"Unknown callback_type: {callback_type!r}")
+
+    if callback is None:
+        callback_type = None
+
+    A, M, x, b = make_system(A, M, x0, b)
+    matvec = A.matvec
+    psolve = M.matvec
+    n = len(b)
+    bnrm2 = np.linalg.norm(b)
+
+    atol, _ = _get_atol_rtol('gmres', bnrm2, atol, rtol)
+
+    if bnrm2 == 0:
+        return b, 0
+
+    eps = np.finfo(x.dtype.char).eps
+
+    dotprod = np.vdot if np.iscomplexobj(x) else np.dot
+
+    if maxiter is None:
+        maxiter = n*10
+
+    if restart is None:
+        restart = 20
+    restart = min(restart, n)
+
+    Mb_nrm2 = np.linalg.norm(psolve(b))
+
+    # ====================================================
+    # =========== Tolerance control from gh-8400 =========
+    # ====================================================
+    # Tolerance passed to GMRESREVCOM applies to the inner
+    # iteration and deals with the left-preconditioned
+    # residual.
+    ptol_max_factor = 1.
+    ptol = Mb_nrm2 * min(ptol_max_factor, atol / bnrm2)
+    presid = 0.
+    # ====================================================
+    lartg = get_lapack_funcs('lartg', dtype=x.dtype)
+
+    # allocate internal variables
+    v = np.empty([restart+1, n], dtype=x.dtype)
+    h = np.zeros([restart, restart+1], dtype=x.dtype)
+    givens = np.zeros([restart, 2], dtype=x.dtype)
+
+    # legacy iteration count
+    inner_iter = 0
+
+    for iteration in range(maxiter):
+        if iteration == 0:
+            r = b - matvec(x) if x.any() else b.copy()
+            if np.linalg.norm(r) < atol:  # Are we done?
+                return x, 0
+
+        v[0, :] = psolve(r)
+        tmp = np.linalg.norm(v[0, :])
+        v[0, :] *= (1 / tmp)
+        # RHS of the Hessenberg problem
+        S = np.zeros(restart+1, dtype=x.dtype)
+        S[0] = tmp
+
+        breakdown = False
+        for col in range(restart):
+            av = matvec(v[col, :])
+            w = psolve(av)
+
+            # Modified Gram-Schmidt
+            h0 = np.linalg.norm(w)
+            for k in range(col+1):
+                tmp = dotprod(v[k, :], w)
+                h[col, k] = tmp
+                w -= tmp*v[k, :]
+
+            h1 = np.linalg.norm(w)
+            h[col, col + 1] = h1
+            v[col + 1, :] = w[:]
+
+            # Exact solution indicator
+            if h1 <= eps*h0:
+                h[col, col + 1] = 0
+                breakdown = True
+            else:
+                v[col + 1, :] *= (1 / h1)
+
+            # apply past Givens rotations to current h column
+            for k in range(col):
+                c, s = givens[k, 0], givens[k, 1]
+                n0, n1 = h[col, [k, k+1]]
+                h[col, [k, k + 1]] = [c*n0 + s*n1, -s.conj()*n0 + c*n1]
+
+            # get and apply current rotation to h and S
+            c, s, mag = lartg(h[col, col], h[col, col+1])
+            givens[col, :] = [c, s]
+            h[col, [col, col+1]] = mag, 0
+
+            # S[col+1] component is always 0
+            tmp = -np.conjugate(s)*S[col]
+            S[[col, col + 1]] = [c*S[col], tmp]
+            presid = np.abs(tmp)
+            inner_iter += 1
+
+            if callback_type in ('legacy', 'pr_norm'):
+                callback(presid / bnrm2)
+            # Legacy behavior
+            if callback_type == 'legacy' and inner_iter == maxiter:
+                break
+            if presid <= ptol or breakdown:
+                break
+
+        # Solve h(col, col) upper triangular system and allow pseudo-solve
+        # singular cases as in (but without the f2py copies):
+        # y = trsv(h[:col+1, :col+1].T, S[:col+1])
+
+        if h[col, col] == 0:
+            S[col] = 0
+
+        y = np.zeros([col+1], dtype=x.dtype)
+        y[:] = S[:col+1]
+        for k in range(col, 0, -1):
+            if y[k] != 0:
+                y[k] /= h[k, k]
+                tmp = y[k]
+                y[:k] -= tmp*h[k, :k]
+        if y[0] != 0:
+            y[0] /= h[0, 0]
+
+        x += y @ v[:col+1, :]
+
+        r = b - matvec(x)
+        rnorm = np.linalg.norm(r)
+
+        # Legacy exit
+        if callback_type == 'legacy' and inner_iter == maxiter:
+            return x, 0 if rnorm <= atol else maxiter
+
+        if callback_type == 'x':
+            callback(x)
+
+        if rnorm <= atol:
+            break
+        elif breakdown:
+            # Reached breakdown (= exact solution), but the external
+            # tolerance check failed. Bail out with failure.
+            break
+        elif presid <= ptol:
+            # Inner loop passed but outer didn't
+            ptol_max_factor = max(eps, 0.25 * ptol_max_factor)
+        else:
+            ptol_max_factor = min(1.0, 1.5 * ptol_max_factor)
+
+        ptol = presid * min(ptol_max_factor, atol / rnorm)
+
+    info = 0 if (rnorm <= atol) else maxiter
+    return x, info
+
+
+@xp_capabilities(np_only=True)
+def qmr(A, b, x0=None, *, rtol=1e-5, atol=0., maxiter=None, M1=None, M2=None,
+        callback=None):
+    """
+    Solve ``Ax = b`` with the Quasi-Minimal Residual method.
+
+    Parameters
+    ----------
+    A : {sparse array, ndarray, LinearOperator}
+        The real-valued N-by-N matrix of the linear system.
+        Alternatively, ``A`` can be a linear operator which can
+        produce ``Ax`` and ``A^T x`` using, e.g.,
+        ``scipy.sparse.linalg.LinearOperator``.
+    b : ndarray
+        Right hand side of the linear system. Has shape (N,) or (N,1).
+    x0 : ndarray
+        Starting guess for the solution.
+    rtol, atol : float, optional
+        Parameters for the convergence test. For convergence,
+        ``norm(b - A @ x) <= max(rtol*norm(b), atol)`` should be satisfied.
+        The default is ``atol=0.`` and ``rtol=1e-5``.
+    maxiter : int
+        Maximum number of iterations.  Iteration will stop after maxiter
+        steps even if the specified tolerance has not been achieved.
+    M1 : {sparse array, ndarray, LinearOperator}
+        Left preconditioner for A.
+    M2 : {sparse array, ndarray, LinearOperator}
+        Right preconditioner for A. Used together with the left
+        preconditioner M1.  The matrix M1@A@M2 should have better
+        conditioned than A alone.
+    callback : function
+        User-supplied function to call after each iteration.  It is called
+        as callback(xk), where xk is the current solution vector.
+
+    Returns
+    -------
+    x : ndarray
+        The converged solution.
+    info : int
+        Provides convergence information:
+            0  : successful exit
+            >0 : convergence to tolerance not achieved, number of iterations
+            <0 : parameter breakdown
+
+    See Also
+    --------
+    LinearOperator
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.sparse import csc_array
+    >>> from scipy.sparse.linalg import qmr
+    >>> A = csc_array([[3., 2., 0.], [1., -1., 0.], [0., 5., 1.]])
+    >>> b = np.array([2., 4., -1.])
+    >>> x, exitCode = qmr(A, b, atol=1e-5)
+    >>> print(exitCode)            # 0 indicates successful convergence
+    0
+    >>> np.allclose(A.dot(x), b)
+    True
+    """
+    A_ = A
+    A, M, x, b = make_system(A, None, x0, b)
+    bnrm2 = np.linalg.norm(b)
+
+    atol, _ = _get_atol_rtol('qmr', bnrm2, atol, rtol)
+
+    if bnrm2 == 0:
+        return b, 0
+
+    if M1 is None and M2 is None:
+        if hasattr(A_, 'psolve'):
+            def left_psolve(b):
+                return A_.psolve(b, 'left')
+
+            def right_psolve(b):
+                return A_.psolve(b, 'right')
+
+            def left_rpsolve(b):
+                return A_.rpsolve(b, 'left')
+
+            def right_rpsolve(b):
+                return A_.rpsolve(b, 'right')
+            M1 = LinearOperator(A.shape,
+                                matvec=left_psolve,
+                                rmatvec=left_rpsolve)
+            M2 = LinearOperator(A.shape,
+                                matvec=right_psolve,
+                                rmatvec=right_rpsolve)
+        else:
+            def id(b):
+                return b
+            M1 = LinearOperator(A.shape, matvec=id, rmatvec=id)
+            M2 = LinearOperator(A.shape, matvec=id, rmatvec=id)
+
+    n = len(b)
+    if maxiter is None:
+        maxiter = n*10
+
+    dotprod = np.vdot if np.iscomplexobj(x) else np.dot
+
+    rhotol = np.finfo(x.dtype.char).eps
+    betatol = rhotol
+    gammatol = rhotol
+    deltatol = rhotol
+    epsilontol = rhotol
+    xitol = rhotol
+
+    r = b - A.matvec(x) if x.any() else b.copy()
+
+    vtilde = r.copy()
+    y = M1.matvec(vtilde)
+    rho = np.linalg.norm(y)
+    wtilde = r.copy()
+    z = M2.rmatvec(wtilde)
+    xi = np.linalg.norm(z)
+    gamma, eta, theta = 1, -1, 0
+    v = np.empty_like(vtilde)
+    w = np.empty_like(wtilde)
+
+    # Dummy values to initialize vars, silence linter warnings
+    epsilon, q, d, p, s = None, None, None, None, None
+
+    for iteration in range(maxiter):
+        if np.linalg.norm(r) < atol:  # Are we done?
+            return x, 0
+        if np.abs(rho) < rhotol:  # rho breakdown
+            return x, -10
+        if np.abs(xi) < xitol:  # xi breakdown
+            return x, -15
+
+        v[:] = vtilde[:]
+        v *= (1 / rho)
+        y *= (1 / rho)
+        w[:] = wtilde[:]
+        w *= (1 / xi)
+        z *= (1 / xi)
+        delta = dotprod(z, y)
+
+        if np.abs(delta) < deltatol:  # delta breakdown
+            return x, -13
+
+        ytilde = M2.matvec(y)
+        ztilde = M1.rmatvec(z)
+
+        if iteration > 0:
+            ytilde -= (xi * delta / epsilon) * p
+            p[:] = ytilde[:]
+            ztilde -= (rho * (delta / epsilon).conj()) * q
+            q[:] = ztilde[:]
+        else:  # First spin
+            p = ytilde.copy()
+            q = ztilde.copy()
+
+        ptilde = A.matvec(p)
+        epsilon = dotprod(q, ptilde)
+        if np.abs(epsilon) < epsilontol:  # epsilon breakdown
+            return x, -14
+
+        beta = epsilon / delta
+        if np.abs(beta) < betatol:  # beta breakdown
+            return x, -11
+
+        vtilde[:] = ptilde[:]
+        vtilde -= beta*v
+        y = M1.matvec(vtilde)
+
+        rho_prev = rho
+        rho = np.linalg.norm(y)
+        wtilde[:] = w[:]
+        wtilde *= - beta.conj()
+        wtilde += A.rmatvec(q)
+        z = M2.rmatvec(wtilde)
+        xi = np.linalg.norm(z)
+        gamma_prev = gamma
+        theta_prev = theta
+        theta = rho / (gamma_prev * np.abs(beta))
+        gamma = 1 / np.sqrt(1 + theta**2)
+
+        if np.abs(gamma) < gammatol:  # gamma breakdown
+            return x, -12
+
+        eta *= -(rho_prev / beta) * (gamma / gamma_prev)**2
+
+        if iteration > 0:
+            d *= (theta_prev * gamma) ** 2
+            d += eta*p
+            s *= (theta_prev * gamma) ** 2
+            s += eta*ptilde
+        else:
+            d = p.copy()
+            d *= eta
+            s = ptilde.copy()
+            s *= eta
+
+        x += d
+        r -= s
+
+        if callback:
+            callback(x)
+
+    else:  # for loop exhausted
+        # Return incomplete progress
+        return x, maxiter
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_isolve/lgmres.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_isolve/lgmres.py
new file mode 100644
index 0000000000000000000000000000000000000000..a23ba71ba52d27c0e4b4bea544b1f7541092213e
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_isolve/lgmres.py
@@ -0,0 +1,232 @@
+# Copyright (C) 2009, Pauli Virtanen <pav@iki.fi>
+# Distributed under the same license as SciPy.
+
+import numpy as np
+from numpy.linalg import LinAlgError
+from scipy._lib._array_api import xp_capabilities
+from scipy.linalg import get_blas_funcs
+from .iterative import _get_atol_rtol
+from .utils import make_system
+
+from ._gcrotmk import _fgmres
+
+__all__ = ['lgmres']
+
+
+@xp_capabilities(np_only=True)
+def lgmres(A, b, x0=None, *, rtol=1e-5, atol=0., maxiter=1000, M=None, callback=None,
+           inner_m=30, outer_k=3, outer_v=None, store_outer_Av=True,
+           prepend_outer_v=False):
+    """
+    Solve ``Ax = b`` with the LGMRES algorithm.
+
+    The LGMRES algorithm [1]_ [2]_ is designed to avoid some problems
+    in the convergence in restarted GMRES, and often converges in fewer
+    iterations.
+
+    Parameters
+    ----------
+    A : {sparse array, ndarray, LinearOperator}
+        The real or complex N-by-N matrix of the linear system.
+        Alternatively, ``A`` can be a linear operator which can
+        produce ``Ax`` using, e.g.,
+        ``scipy.sparse.linalg.LinearOperator``.
+    b : ndarray
+        Right hand side of the linear system. Has shape (N,) or (N,1).
+    x0 : ndarray
+        Starting guess for the solution.
+    rtol, atol : float, optional
+        Parameters for the convergence test. For convergence,
+        ``norm(b - A @ x) <= max(rtol*norm(b), atol)`` should be satisfied.
+        The default is ``rtol=1e-5``, the default for ``atol`` is ``0.0``.
+    maxiter : int, optional
+        Maximum number of iterations.  Iteration will stop after maxiter
+        steps even if the specified tolerance has not been achieved.
+    M : {sparse array, ndarray, LinearOperator}, optional
+        Preconditioner for A.  The preconditioner should approximate the
+        inverse of A.  Effective preconditioning dramatically improves the
+        rate of convergence, which implies that fewer iterations are needed
+        to reach a given error tolerance.
+    callback : function, optional
+        User-supplied function to call after each iteration.  It is called
+        as callback(xk), where xk is the current solution vector.
+    inner_m : int, optional
+        Number of inner GMRES iterations per each outer iteration.
+    outer_k : int, optional
+        Number of vectors to carry between inner GMRES iterations.
+        According to [1]_, good values are in the range of 1...3.
+        However, note that if you want to use the additional vectors to
+        accelerate solving multiple similar problems, larger values may
+        be beneficial.
+    outer_v : list of tuples, optional
+        List containing tuples ``(v, Av)`` of vectors and corresponding
+        matrix-vector products, used to augment the Krylov subspace, and
+        carried between inner GMRES iterations. The element ``Av`` can
+        be `None` if the matrix-vector product should be re-evaluated.
+        This parameter is modified in-place by `lgmres`, and can be used
+        to pass "guess" vectors in and out of the algorithm when solving
+        similar problems.
+    store_outer_Av : bool, optional
+        Whether LGMRES should store also A@v in addition to vectors `v`
+        in the `outer_v` list. Default is True.
+    prepend_outer_v : bool, optional
+        Whether to put outer_v augmentation vectors before Krylov iterates.
+        In standard LGMRES, prepend_outer_v=False.
+
+    Returns
+    -------
+    x : ndarray
+        The converged solution.
+    info : int
+        Provides convergence information:
+
+            - 0  : successful exit
+            - >0 : convergence to tolerance not achieved, number of iterations
+            - <0 : illegal input or breakdown
+
+    Notes
+    -----
+    The LGMRES algorithm [1]_ [2]_ is designed to avoid the
+    slowing of convergence in restarted GMRES, due to alternating
+    residual vectors. Typically, it often outperforms GMRES(m) of
+    comparable memory requirements by some measure, or at least is not
+    much worse.
+
+    Another advantage in this algorithm is that you can supply it with
+    'guess' vectors in the `outer_v` argument that augment the Krylov
+    subspace. If the solution lies close to the span of these vectors,
+    the algorithm converges faster. This can be useful if several very
+    similar matrices need to be inverted one after another, such as in
+    Newton-Krylov iteration where the Jacobian matrix often changes
+    little in the nonlinear steps.
+
+    References
+    ----------
+    .. [1] A.H. Baker and E.R. Jessup and T. Manteuffel, "A Technique for
+             Accelerating the Convergence of Restarted GMRES", SIAM J. Matrix
+             Anal. Appl. 26, 962 (2005).
+    .. [2] A.H. Baker, "On Improving the Performance of the Linear Solver
+             restarted GMRES", PhD thesis, University of Colorado (2003).
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.sparse import csc_array
+    >>> from scipy.sparse.linalg import lgmres
+    >>> A = csc_array([[3, 2, 0], [1, -1, 0], [0, 5, 1]], dtype=float)
+    >>> b = np.array([2, 4, -1], dtype=float)
+    >>> x, exitCode = lgmres(A, b, atol=1e-5)
+    >>> print(exitCode)            # 0 indicates successful convergence
+    0
+    >>> np.allclose(A.dot(x), b)
+    True
+    """
+    A,M,x,b = make_system(A,M,x0,b)
+
+    if not np.isfinite(b).all():
+        raise ValueError("RHS must contain only finite numbers")
+
+    matvec = A.matvec
+    psolve = M.matvec
+
+    if outer_v is None:
+        outer_v = []
+
+    axpy, dot, scal = None, None, None
+    nrm2 = get_blas_funcs('nrm2', [b])
+
+    b_norm = nrm2(b)
+
+    # we call this to get the right atol/rtol and raise errors as necessary
+    atol, rtol = _get_atol_rtol('lgmres', b_norm, atol, rtol)
+
+    if b_norm == 0:
+        x = b
+        return (x, 0)
+
+    ptol_max_factor = 1.0
+
+    for k_outer in range(maxiter):
+        r_outer = matvec(x) - b
+
+        # -- callback
+        if callback is not None:
+            callback(x)
+
+        # -- determine input type routines
+        if axpy is None:
+            if np.iscomplexobj(r_outer) and not np.iscomplexobj(x):
+                x = x.astype(r_outer.dtype)
+            axpy, dot, scal, nrm2 = get_blas_funcs(['axpy', 'dot', 'scal', 'nrm2'],
+                                                   (x, r_outer))
+
+        # -- check stopping condition
+        r_norm = nrm2(r_outer)
+        if r_norm <= max(atol, rtol * b_norm):
+            break
+
+        # -- inner LGMRES iteration
+        v0 = -psolve(r_outer)
+        inner_res_0 = nrm2(v0)
+
+        if inner_res_0 == 0:
+            rnorm = nrm2(r_outer)
+            raise RuntimeError("Preconditioner returned a zero vector; "
+                               f"|v| ~ {rnorm:.1g}, |M v| = 0")
+
+        v0 = scal(1.0/inner_res_0, v0)
+
+        ptol = min(ptol_max_factor, max(atol, rtol*b_norm)/r_norm)
+
+        try:
+            Q, R, B, vs, zs, y, pres = _fgmres(matvec,
+                                               v0,
+                                               inner_m,
+                                               lpsolve=psolve,
+                                               atol=ptol,
+                                               outer_v=outer_v,
+                                               prepend_outer_v=prepend_outer_v)
+            y *= inner_res_0
+            if not np.isfinite(y).all():
+                # Overflow etc. in computation. There's no way to
+                # recover from this, so we have to bail out.
+                raise LinAlgError()
+        except LinAlgError:
+            # Floating point over/underflow, non-finite result from
+            # matmul etc. -- report failure.
+            return x, k_outer + 1
+
+        # Inner loop tolerance control
+        if pres > ptol:
+            ptol_max_factor = min(1.0, 1.5 * ptol_max_factor)
+        else:
+            ptol_max_factor = max(1e-16, 0.25 * ptol_max_factor)
+
+        # -- GMRES terminated: eval solution
+        dx = zs[0]*y[0]
+        for w, yc in zip(zs[1:], y[1:]):
+            dx = axpy(w, dx, dx.shape[0], yc)  # dx += w*yc
+
+        # -- Store LGMRES augmentation vectors
+        nx = nrm2(dx)
+        if nx > 0:
+            if store_outer_Av:
+                q = Q.dot(R.dot(y))
+                ax = vs[0]*q[0]
+                for v, qc in zip(vs[1:], q[1:]):
+                    ax = axpy(v, ax, ax.shape[0], qc)
+                outer_v.append((dx/nx, ax/nx))
+            else:
+                outer_v.append((dx/nx, None))
+
+        # -- Retain only a finite number of augmentation vectors
+        while len(outer_v) > outer_k:
+            del outer_v[0]
+
+        # -- Apply step
+        x += dx
+    else:
+        # didn't converge ...
+        return x, maxiter
+
+    return x, 0
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_isolve/lsmr.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_isolve/lsmr.py
new file mode 100644
index 0000000000000000000000000000000000000000..5081ebee1315024be20bd14da2922555ce846759
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_isolve/lsmr.py
@@ -0,0 +1,494 @@
+"""
+Copyright (C) 2010 David Fong and Michael Saunders
+
+LSMR uses an iterative method.
+
+07 Jun 2010: Documentation updated
+03 Jun 2010: First release version in Python
+
+David Chin-lung Fong            clfong@stanford.edu
+Institute for Computational and Mathematical Engineering
+Stanford University
+
+Michael Saunders                saunders@stanford.edu
+Systems Optimization Laboratory
+Dept of MS&E, Stanford University.
+
+"""
+
+__all__ = ['lsmr']
+
+from numpy import zeros, inf, atleast_1d, result_type
+from numpy.linalg import norm
+from math import sqrt
+from scipy.sparse.linalg._interface import aslinearoperator
+
+from scipy.sparse.linalg._isolve.lsqr import _sym_ortho
+
+
+def lsmr(A, b, damp=0.0, atol=1e-6, btol=1e-6, conlim=1e8,
+         maxiter=None, show=False, x0=None):
+    """Iterative solver for least-squares problems.
+
+    lsmr solves the system of linear equations ``Ax = b``. If the system
+    is inconsistent, it solves the least-squares problem ``min ||b - Ax||_2``.
+    ``A`` is a rectangular matrix of dimension m-by-n, where all cases are
+    allowed: m = n, m > n, or m < n. ``b`` is a vector of length m.
+    The matrix A may be dense or sparse (usually sparse).
+
+    Parameters
+    ----------
+    A : {sparse array, ndarray, LinearOperator}
+        Matrix A in the linear system.
+        Alternatively, ``A`` can be a linear operator which can
+        produce ``Ax`` and ``A^H x`` using, e.g.,
+        ``scipy.sparse.linalg.LinearOperator``.
+    b : array_like, shape (m,)
+        Vector ``b`` in the linear system.
+    damp : float
+        Damping factor for regularized least-squares. `lsmr` solves
+        the regularized least-squares problem::
+
+         min ||(b) - (  A   )x||
+             ||(0)   (damp*I) ||_2
+
+        where damp is a scalar.  If damp is None or 0, the system
+        is solved without regularization. Default is 0.
+    atol, btol : float, optional
+        Stopping tolerances. `lsmr` continues iterations until a
+        certain backward error estimate is smaller than some quantity
+        depending on atol and btol.  Let ``r = b - Ax`` be the
+        residual vector for the current approximate solution ``x``.
+        If ``Ax = b`` seems to be consistent, `lsmr` terminates
+        when ``norm(r) <= atol * norm(A) * norm(x) + btol * norm(b)``.
+        Otherwise, `lsmr` terminates when ``norm(A^H r) <=
+        atol * norm(A) * norm(r)``.  If both tolerances are 1.0e-6 (default),
+        the final ``norm(r)`` should be accurate to about 6
+        digits. (The final ``x`` will usually have fewer correct digits,
+        depending on ``cond(A)`` and the size of LAMBDA.)  If `atol`
+        or `btol` is None, a default value of 1.0e-6 will be used.
+        Ideally, they should be estimates of the relative error in the
+        entries of ``A`` and ``b`` respectively.  For example, if the entries
+        of ``A`` have 7 correct digits, set ``atol = 1e-7``. This prevents
+        the algorithm from doing unnecessary work beyond the
+        uncertainty of the input data.
+    conlim : float, optional
+        `lsmr` terminates if an estimate of ``cond(A)`` exceeds
+        `conlim`.  For compatible systems ``Ax = b``, conlim could be
+        as large as 1.0e+12 (say).  For least-squares problems,
+        `conlim` should be less than 1.0e+8. If `conlim` is None, the
+        default value is 1e+8.  Maximum precision can be obtained by
+        setting ``atol = btol = conlim = 0``, but the number of
+        iterations may then be excessive. Default is 1e8.
+    maxiter : int, optional
+        `lsmr` terminates if the number of iterations reaches
+        `maxiter`.  The default is ``maxiter = min(m, n)``.  For
+        ill-conditioned systems, a larger value of `maxiter` may be
+        needed. Default is False.
+    show : bool, optional
+        Print iterations logs if ``show=True``. Default is False.
+    x0 : array_like, shape (n,), optional
+        Initial guess of ``x``, if None zeros are used. Default is None.
+
+        .. versionadded:: 1.0.0
+
+    Returns
+    -------
+    x : ndarray of float
+        Least-square solution returned.
+    istop : int
+        istop gives the reason for stopping::
+
+          istop   = 0 means x=0 is a solution.  If x0 was given, then x=x0 is a
+                      solution.
+                  = 1 means x is an approximate solution to A@x = B,
+                      according to atol and btol.
+                  = 2 means x approximately solves the least-squares problem
+                      according to atol.
+                  = 3 means COND(A) seems to be greater than CONLIM.
+                  = 4 is the same as 1 with atol = btol = eps (machine
+                      precision)
+                  = 5 is the same as 2 with atol = eps.
+                  = 6 is the same as 3 with CONLIM = 1/eps.
+                  = 7 means ITN reached maxiter before the other stopping
+                      conditions were satisfied.
+
+    itn : int
+        Number of iterations used.
+    normr : float
+        ``norm(b-Ax)``
+    normar : float
+        ``norm(A^H (b - Ax))``
+    norma : float
+        ``norm(A)``
+    conda : float
+        Condition number of A.
+    normx : float
+        ``norm(x)``
+
+    Notes
+    -----
+
+    .. versionadded:: 0.11.0
+
+    References
+    ----------
+    .. [1] D. C.-L. Fong and M. A. Saunders,
+           "LSMR: An iterative algorithm for sparse least-squares problems",
+           SIAM J. Sci. Comput., vol. 33, pp. 2950-2971, 2011.
+           :arxiv:`1006.0758`
+    .. [2] LSMR Software, https://web.stanford.edu/group/SOL/software/lsmr/
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.sparse import csc_array
+    >>> from scipy.sparse.linalg import lsmr
+    >>> A = csc_array([[1., 0.], [1., 1.], [0., 1.]], dtype=float)
+
+    The first example has the trivial solution ``[0, 0]``
+
+    >>> b = np.array([0., 0., 0.], dtype=float)
+    >>> x, istop, itn, normr = lsmr(A, b)[:4]
+    >>> istop
+    0
+    >>> x
+    array([0., 0.])
+
+    The stopping code ``istop=0`` returned indicates that a vector of zeros was
+    found as a solution. The returned solution `x` indeed contains
+    ``[0., 0.]``. The next example has a non-trivial solution:
+
+    >>> b = np.array([1., 0., -1.], dtype=float)
+    >>> x, istop, itn, normr = lsmr(A, b)[:4]
+    >>> istop
+    1
+    >>> x
+    array([ 1., -1.])
+    >>> itn
+    1
+    >>> normr
+    4.440892098500627e-16
+
+    As indicated by ``istop=1``, `lsmr` found a solution obeying the tolerance
+    limits. The given solution ``[1., -1.]`` obviously solves the equation. The
+    remaining return values include information about the number of iterations
+    (`itn=1`) and the remaining difference of left and right side of the solved
+    equation.
+    The final example demonstrates the behavior in the case where there is no
+    solution for the equation:
+
+    >>> b = np.array([1., 0.01, -1.], dtype=float)
+    >>> x, istop, itn, normr = lsmr(A, b)[:4]
+    >>> istop
+    2
+    >>> x
+    array([ 1.00333333, -0.99666667])
+    >>> A.dot(x)-b
+    array([ 0.00333333, -0.00333333,  0.00333333])
+    >>> normr
+    0.005773502691896255
+
+    `istop` indicates that the system is inconsistent and thus `x` is rather an
+    approximate solution to the corresponding least-squares problem. `normr`
+    contains the minimal distance that was found.
+    """
+
+    A = aslinearoperator(A)
+    if A.ndim > 2:
+        raise ValueError(f"{A.ndim}-dimensional `A` is unsupported, expected 2-D.")
+    b = atleast_1d(b)
+    if b.ndim > 1:
+        b = b.squeeze()
+
+    msg = ('The exact solution is x = 0, or x = x0, if x0 was given  ',
+           'Ax - b is small enough, given atol, btol                  ',
+           'The least-squares solution is good enough, given atol     ',
+           'The estimate of cond(Abar) has exceeded conlim            ',
+           'Ax - b is small enough for this machine                   ',
+           'The least-squares solution is good enough for this machine',
+           'Cond(Abar) seems to be too large for this machine         ',
+           'The iteration limit has been reached                      ')
+
+    hdg1 = '   itn      x(1)       norm r    norm Ar'
+    hdg2 = ' compatible   LS      norm A   cond A'
+    pfreq = 20   # print frequency (for repeating the heading)
+    pcount = 0   # print counter
+
+    m, n = A.shape
+
+    # stores the num of singular values
+    minDim = min([m, n])
+
+    if maxiter is None:
+        maxiter = minDim
+
+    if x0 is None:
+        dtype = result_type(A, b, float)
+    else:
+        dtype = result_type(A, b, x0, float)
+
+    if show:
+        print(' ')
+        print('LSMR            Least-squares solution of  Ax = b\n')
+        print(f'The matrix A has {m} rows and {n} columns')
+        print(f'damp = {damp:20.14e}\n')
+        print(f'atol = {atol:8.2e}                 conlim = {conlim:8.2e}\n')
+        print(f'btol = {btol:8.2e}             maxiter = {maxiter:8g}\n')
+
+    u = b
+    normb = norm(b)
+    if x0 is None:
+        x = zeros(n, dtype)
+        beta = normb.copy()
+    else:
+        x = atleast_1d(x0.copy())
+        u = u - A.matvec(x)
+        beta = norm(u)
+
+    if beta > 0:
+        u = (1 / beta) * u
+        v = A.rmatvec(u)
+        alpha = norm(v)
+    else:
+        v = zeros(n, dtype)
+        alpha = 0
+
+    if alpha > 0:
+        v = (1 / alpha) * v
+
+    # Initialize variables for 1st iteration.
+
+    itn = 0
+    zetabar = alpha * beta
+    alphabar = alpha
+    rho = 1
+    rhobar = 1
+    cbar = 1
+    sbar = 0
+
+    h = v.copy()
+    hbar = zeros(n, dtype)
+
+    # Initialize variables for estimation of ||r||.
+
+    betadd = beta
+    betad = 0
+    rhodold = 1
+    tautildeold = 0
+    thetatilde = 0
+    zeta = 0
+    d = 0
+
+    # Initialize variables for estimation of ||A|| and cond(A)
+
+    normA2 = alpha * alpha
+    maxrbar = 0
+    minrbar = 1e+100
+    normA = sqrt(normA2)
+    condA = 1
+    normx = 0
+
+    # Initialize print strings
+    str1 = ''
+    str2 = ''
+    str3 = ''
+    str4 = ''
+
+    # Items for use in stopping rules, normb set earlier
+    istop = 0
+    ctol = 0
+    if conlim > 0:
+        ctol = 1 / conlim
+    normr = beta
+
+    # Reverse the order here from the original matlab code because
+    # there was an error on return when arnorm==0
+    normar = alpha * beta
+    if normar == 0:
+        if show:
+            print(msg[0])
+        return x, istop, itn, normr, normar, normA, condA, normx
+
+    if normb == 0:
+        x[()] = 0
+        return x, istop, itn, normr, normar, normA, condA, normx
+
+    if show:
+        print(' ')
+        print(hdg1, hdg2)
+        test1 = 1
+        test2 = alpha / beta
+        str1 = f'{itn:6g} {x[0]:12.5e}'
+        str2 = f' {normr:10.3e} {normar:10.3e}'
+        str3 = f'  {test1:8.1e} {test2:8.1e}'
+        print(''.join([str1, str2, str3]))
+
+    # Main iteration loop.
+    while itn < maxiter:
+        itn = itn + 1
+
+        # Perform the next step of the bidiagonalization to obtain the
+        # next  beta, u, alpha, v.  These satisfy the relations
+        #         beta*u  =  A@v   -  alpha*u,
+        #        alpha*v  =  A'@u  -  beta*v.
+
+        u *= -alpha
+        u += A.matvec(v)
+        beta = norm(u)
+
+        if beta > 0:
+            u *= (1 / beta)
+            v *= -beta
+            v += A.rmatvec(u)
+            alpha = norm(v)
+            if alpha > 0:
+                v *= (1 / alpha)
+
+        # At this point, beta = beta_{k+1}, alpha = alpha_{k+1}.
+
+        # Construct rotation Qhat_{k,2k+1}.
+
+        chat, shat, alphahat = _sym_ortho(alphabar, damp)
+
+        # Use a plane rotation (Q_i) to turn B_i to R_i
+
+        rhoold = rho
+        c, s, rho = _sym_ortho(alphahat, beta)
+        thetanew = s*alpha
+        alphabar = c*alpha
+
+        # Use a plane rotation (Qbar_i) to turn R_i^T to R_i^bar
+
+        rhobarold = rhobar
+        zetaold = zeta
+        thetabar = sbar * rho
+        rhotemp = cbar * rho
+        cbar, sbar, rhobar = _sym_ortho(cbar * rho, thetanew)
+        zeta = cbar * zetabar
+        zetabar = - sbar * zetabar
+
+        # Update h, h_hat, x.
+
+        hbar *= - (thetabar * rho / (rhoold * rhobarold))
+        hbar += h
+        x += (zeta / (rho * rhobar)) * hbar
+        h *= - (thetanew / rho)
+        h += v
+
+        # Estimate of ||r||.
+
+        # Apply rotation Qhat_{k,2k+1}.
+        betaacute = chat * betadd
+        betacheck = -shat * betadd
+
+        # Apply rotation Q_{k,k+1}.
+        betahat = c * betaacute
+        betadd = -s * betaacute
+
+        # Apply rotation Qtilde_{k-1}.
+        # betad = betad_{k-1} here.
+
+        thetatildeold = thetatilde
+        ctildeold, stildeold, rhotildeold = _sym_ortho(rhodold, thetabar)
+        thetatilde = stildeold * rhobar
+        rhodold = ctildeold * rhobar
+        betad = - stildeold * betad + ctildeold * betahat
+
+        # betad   = betad_k here.
+        # rhodold = rhod_k  here.
+
+        tautildeold = (zetaold - thetatildeold * tautildeold) / rhotildeold
+        taud = (zeta - thetatilde * tautildeold) / rhodold
+        d = d + betacheck * betacheck
+        normr = sqrt(d + (betad - taud)**2 + betadd * betadd)
+
+        # Estimate ||A||.
+        normA2 = normA2 + beta * beta
+        normA = sqrt(normA2)
+        normA2 = normA2 + alpha * alpha
+
+        # Estimate cond(A).
+        maxrbar = max(maxrbar, rhobarold)
+        if itn > 1:
+            minrbar = min(minrbar, rhobarold)
+        condA = max(maxrbar, rhotemp) / min(minrbar, rhotemp)
+
+        # Test for convergence.
+
+        # Compute norms for convergence testing.
+        normar = abs(zetabar)
+        normx = norm(x)
+
+        # Now use these norms to estimate certain other quantities,
+        # some of which will be small near a solution.
+
+        test1 = normr / normb
+        if (normA * normr) != 0:
+            test2 = normar / (normA * normr)
+        else:
+            test2 = inf
+        test3 = 1 / condA
+        t1 = test1 / (1 + normA * normx / normb)
+        rtol = btol + atol * normA * normx / normb
+
+        # The following tests guard against extremely small values of
+        # atol, btol or ctol.  (The user may have set any or all of
+        # the parameters atol, btol, conlim  to 0.)
+        # The effect is equivalent to the normAl tests using
+        # atol = eps,  btol = eps,  conlim = 1/eps.
+
+        if itn >= maxiter:
+            istop = 7
+        if 1 + test3 <= 1:
+            istop = 6
+        if 1 + test2 <= 1:
+            istop = 5
+        if 1 + t1 <= 1:
+            istop = 4
+
+        # Allow for tolerances set by the user.
+
+        if test3 <= ctol:
+            istop = 3
+        if test2 <= atol:
+            istop = 2
+        if test1 <= rtol:
+            istop = 1
+
+        # See if it is time to print something.
+
+        if show:
+            if (n <= 40) or (itn <= 10) or (itn >= maxiter - 10) or \
+               (itn % 10 == 0) or (test3 <= 1.1 * ctol) or \
+               (test2 <= 1.1 * atol) or (test1 <= 1.1 * rtol) or \
+               (istop != 0):
+
+                if pcount >= pfreq:
+                    pcount = 0
+                    print(' ')
+                    print(hdg1, hdg2)
+                pcount = pcount + 1
+                str1 = f'{itn:6g} {x[0]:12.5e}'
+                str2 = f' {normr:10.3e} {normar:10.3e}'
+                str3 = f'  {test1:8.1e} {test2:8.1e}'
+                str4 = f' {normA:8.1e} {condA:8.1e}'
+                print(''.join([str1, str2, str3, str4]))
+
+        if istop > 0:
+            break
+
+    # Print the stopping condition.
+
+    if show:
+        print(' ')
+        print('LSMR finished')
+        print(msg[istop])
+        print(f'istop ={istop:8g}    normr ={normr:8.1e}')
+        print(f'    normA ={normA:8.1e}    normAr ={normar:8.1e}')
+        print(f'itn   ={itn:8g}    condA ={condA:8.1e}')
+        print(f'    normx ={normx:8.1e}')
+        print(str1, str2)
+        print(str3, str4)
+
+    return x, istop, itn, normr, normar, normA, condA, normx
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_isolve/lsqr.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_isolve/lsqr.py
new file mode 100644
index 0000000000000000000000000000000000000000..abedfb855ffea6e38ff0027c15e54334e7352e73
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_isolve/lsqr.py
@@ -0,0 +1,591 @@
+"""Sparse Equations and Least Squares.
+
+The original Fortran code was written by C. C. Paige and M. A. Saunders as
+described in
+
+C. C. Paige and M. A. Saunders, LSQR: An algorithm for sparse linear
+equations and sparse least squares, TOMS 8(1), 43--71 (1982).
+
+C. C. Paige and M. A. Saunders, Algorithm 583; LSQR: Sparse linear
+equations and least-squares problems, TOMS 8(2), 195--209 (1982).
+
+It is licensed under the following BSD license:
+
+Copyright (c) 2006, Systems Optimization Laboratory
+All rights reserved.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are
+met:
+
+    * Redistributions of source code must retain the above copyright
+      notice, this list of conditions and the following disclaimer.
+
+    * Redistributions in binary form must reproduce the above
+      copyright notice, this list of conditions and the following
+      disclaimer in the documentation and/or other materials provided
+      with the distribution.
+
+    * Neither the name of Stanford University nor the names of its
+      contributors may be used to endorse or promote products derived
+      from this software without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+The Fortran code was translated to Python for use in CVXOPT by Jeffery
+Kline with contributions by Mridul Aanjaneya and Bob Myhill.
+
+Adapted for SciPy by Stefan van der Walt.
+
+"""
+
+__all__ = ['lsqr']
+
+import numpy as np
+from math import sqrt
+from scipy.sparse.linalg._interface import aslinearoperator
+from scipy.sparse._sputils import convert_pydata_sparse_to_scipy
+
+eps = np.finfo(np.float64).eps
+
+
+def _sym_ortho(a, b):
+    """
+    Stable implementation of Givens rotation.
+
+    Notes
+    -----
+    The routine 'SymOrtho' was added for numerical stability. This is
+    recommended by S.-C. Choi in [1]_.  It removes the unpleasant potential of
+    ``1/eps`` in some important places (see, for example text following
+    "Compute the next plane rotation Qk" in minres.py).
+
+    References
+    ----------
+    .. [1] S.-C. Choi, "Iterative Methods for Singular Linear Equations
+           and Least-Squares Problems", Dissertation,
+           http://www.stanford.edu/group/SOL/dissertations/sou-cheng-choi-thesis.pdf
+
+    """
+    if b == 0:
+        return np.sign(a), 0, abs(a)
+    elif a == 0:
+        return 0, np.sign(b), abs(b)
+    elif abs(b) > abs(a):
+        tau = a / b
+        s = np.sign(b) / sqrt(1 + tau * tau)
+        c = s * tau
+        r = b / s
+    else:
+        tau = b / a
+        c = np.sign(a) / sqrt(1+tau*tau)
+        s = c * tau
+        r = a / c
+    return c, s, r
+
+
+def lsqr(A, b, damp=0.0, atol=1e-6, btol=1e-6, conlim=1e8,
+         iter_lim=None, show=False, calc_var=False, x0=None):
+    """Find the least-squares solution to a large, sparse, linear system
+    of equations.
+
+    The function solves ``Ax = b``  or  ``min ||Ax - b||^2`` or
+    ``min ||Ax - b||^2 + d^2 ||x - x0||^2``.
+
+    The matrix A may be square or rectangular (over-determined or
+    under-determined), and may have any rank.
+
+    ::
+
+      1. Unsymmetric equations --    solve  Ax = b
+
+      2. Linear least squares  --    solve  Ax = b
+                                     in the least-squares sense
+
+      3. Damped least squares  --    solve  (   A    )*x = (    b    )
+                                            ( damp*I )     ( damp*x0 )
+                                     in the least-squares sense
+
+    Parameters
+    ----------
+    A : {sparse array, ndarray, LinearOperator}
+        Representation of an m-by-n matrix.
+        Alternatively, ``A`` can be a linear operator which can
+        produce ``Ax`` and ``A^T x`` using, e.g.,
+        ``scipy.sparse.linalg.LinearOperator``.
+    b : array_like, shape (m,)
+        Right-hand side vector ``b``.
+    damp : float
+        Damping coefficient. Default is 0.
+    atol, btol : float, optional
+        Stopping tolerances. `lsqr` continues iterations until a
+        certain backward error estimate is smaller than some quantity
+        depending on atol and btol.  Let ``r = b - Ax`` be the
+        residual vector for the current approximate solution ``x``.
+        If ``Ax = b`` seems to be consistent, `lsqr` terminates
+        when ``norm(r) <= atol * norm(A) * norm(x) + btol * norm(b)``.
+        Otherwise, `lsqr` terminates when ``norm(A^H r) <=
+        atol * norm(A) * norm(r)``.  If both tolerances are 1.0e-6 (default),
+        the final ``norm(r)`` should be accurate to about 6
+        digits. (The final ``x`` will usually have fewer correct digits,
+        depending on ``cond(A)`` and the size of LAMBDA.)  If `atol`
+        or `btol` is None, a default value of 1.0e-6 will be used.
+        Ideally, they should be estimates of the relative error in the
+        entries of ``A`` and ``b`` respectively.  For example, if the entries
+        of ``A`` have 7 correct digits, set ``atol = 1e-7``. This prevents
+        the algorithm from doing unnecessary work beyond the
+        uncertainty of the input data.
+    conlim : float, optional
+        Another stopping tolerance.  lsqr terminates if an estimate of
+        ``cond(A)`` exceeds `conlim`.  For compatible systems ``Ax =
+        b``, `conlim` could be as large as 1.0e+12 (say).  For
+        least-squares problems, conlim should be less than 1.0e+8.
+        Maximum precision can be obtained by setting ``atol = btol =
+        conlim = zero``, but the number of iterations may then be
+        excessive. Default is 1e8.
+    iter_lim : int, optional
+        Explicit limitation on number of iterations (for safety).
+    show : bool, optional
+        Display an iteration log. Default is False.
+    calc_var : bool, optional
+        Whether to estimate diagonals of ``(A'A + damp^2*I)^{-1}``.
+    x0 : array_like, shape (n,), optional
+        Initial guess of x, if None zeros are used. Default is None.
+
+        .. versionadded:: 1.0.0
+
+    Returns
+    -------
+    x : ndarray of float
+        The final solution.
+    istop : int
+        Gives the reason for termination.
+        1 means x is an approximate solution to Ax = b.
+        2 means x approximately solves the least-squares problem.
+    itn : int
+        Iteration number upon termination.
+    r1norm : float
+        ``norm(r)``, where ``r = b - Ax``.
+    r2norm : float
+        ``sqrt( norm(r)^2  +  damp^2 * norm(x - x0)^2 )``.  Equal to `r1norm`
+        if ``damp == 0``.
+    anorm : float
+        Estimate of Frobenius norm of ``Abar = [[A]; [damp*I]]``.
+    acond : float
+        Estimate of ``cond(Abar)``.
+    arnorm : float
+        Estimate of ``norm(A'@r - damp^2*(x - x0))``.
+    xnorm : float
+        ``norm(x)``
+    var : ndarray of float
+        If ``calc_var`` is True, estimates all diagonals of
+        ``(A'A)^{-1}`` (if ``damp == 0``) or more generally ``(A'A +
+        damp^2*I)^{-1}``.  This is well defined if A has full column
+        rank or ``damp > 0``.  (Not sure what var means if ``rank(A)
+        < n`` and ``damp = 0.``)
+
+    Notes
+    -----
+    LSQR uses an iterative method to approximate the solution.  The
+    number of iterations required to reach a certain accuracy depends
+    strongly on the scaling of the problem.  Poor scaling of the rows
+    or columns of A should therefore be avoided where possible.
+
+    For example, in problem 1 the solution is unaltered by
+    row-scaling.  If a row of A is very small or large compared to
+    the other rows of A, the corresponding row of ( A  b ) should be
+    scaled up or down.
+
+    In problems 1 and 2, the solution x is easily recovered
+    following column-scaling.  Unless better information is known,
+    the nonzero columns of A should be scaled so that they all have
+    the same Euclidean norm (e.g., 1.0).
+
+    In problem 3, there is no freedom to re-scale if damp is
+    nonzero.  However, the value of damp should be assigned only
+    after attention has been paid to the scaling of A.
+
+    The parameter damp is intended to help regularize
+    ill-conditioned systems, by preventing the true solution from
+    being very large.  Another aid to regularization is provided by
+    the parameter acond, which may be used to terminate iterations
+    before the computed solution becomes very large.
+
+    If some initial estimate ``x0`` is known and if ``damp == 0``,
+    one could proceed as follows:
+
+      1. Compute a residual vector ``r0 = b - A@x0``.
+      2. Use LSQR to solve the system  ``A@dx = r0``.
+      3. Add the correction dx to obtain a final solution ``x = x0 + dx``.
+
+    This requires that ``x0`` be available before and after the call
+    to LSQR.  To judge the benefits, suppose LSQR takes k1 iterations
+    to solve A@x = b and k2 iterations to solve A@dx = r0.
+    If x0 is "good", norm(r0) will be smaller than norm(b).
+    If the same stopping tolerances atol and btol are used for each
+    system, k1 and k2 will be similar, but the final solution x0 + dx
+    should be more accurate.  The only way to reduce the total work
+    is to use a larger stopping tolerance for the second system.
+    If some value btol is suitable for A@x = b, the larger value
+    btol*norm(b)/norm(r0)  should be suitable for A@dx = r0.
+
+    Preconditioning is another way to reduce the number of iterations.
+    If it is possible to solve a related system ``M@x = b``
+    efficiently, where M approximates A in some helpful way (e.g. M -
+    A has low rank or its elements are small relative to those of A),
+    LSQR may converge more rapidly on the system ``A@M(inverse)@z =
+    b``, after which x can be recovered by solving M@x = z.
+
+    If A is symmetric, LSQR should not be used!
+
+    Alternatives are the symmetric conjugate-gradient method (cg)
+    and/or SYMMLQ.  SYMMLQ is an implementation of symmetric cg that
+    applies to any symmetric A and will converge more rapidly than
+    LSQR.  If A is positive definite, there are other implementations
+    of symmetric cg that require slightly less work per iteration than
+    SYMMLQ (but will take the same number of iterations).
+
+    References
+    ----------
+    .. [1] C. C. Paige and M. A. Saunders (1982a).
+           "LSQR: An algorithm for sparse linear equations and
+           sparse least squares", ACM TOMS 8(1), 43-71.
+    .. [2] C. C. Paige and M. A. Saunders (1982b).
+           "Algorithm 583.  LSQR: Sparse linear equations and least
+           squares problems", ACM TOMS 8(2), 195-209.
+    .. [3] M. A. Saunders (1995).  "Solution of sparse rectangular
+           systems using LSQR and CRAIG", BIT 35, 588-604.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.sparse import csc_array
+    >>> from scipy.sparse.linalg import lsqr
+    >>> A = csc_array([[1., 0.], [1., 1.], [0., 1.]], dtype=float)
+
+    The first example has the trivial solution ``[0, 0]``
+
+    >>> b = np.array([0., 0., 0.], dtype=float)
+    >>> x, istop, itn, normr = lsqr(A, b)[:4]
+    >>> istop
+    0
+    >>> x
+    array([ 0.,  0.])
+
+    The stopping code ``istop=0`` returned indicates that a vector of zeros was
+    found as a solution. The returned solution `x` indeed contains
+    ``[0., 0.]``. The next example has a non-trivial solution:
+
+    >>> b = np.array([1., 0., -1.], dtype=float)
+    >>> x, istop, itn, r1norm = lsqr(A, b)[:4]
+    >>> istop
+    1
+    >>> x
+    array([ 1., -1.])
+    >>> itn
+    1
+    >>> r1norm
+    4.440892098500627e-16
+
+    As indicated by ``istop=1``, `lsqr` found a solution obeying the tolerance
+    limits. The given solution ``[1., -1.]`` obviously solves the equation. The
+    remaining return values include information about the number of iterations
+    (`itn=1`) and the remaining difference of left and right side of the solved
+    equation.
+    The final example demonstrates the behavior in the case where there is no
+    solution for the equation:
+
+    >>> b = np.array([1., 0.01, -1.], dtype=float)
+    >>> x, istop, itn, r1norm = lsqr(A, b)[:4]
+    >>> istop
+    2
+    >>> x
+    array([ 1.00333333, -0.99666667])
+    >>> A.dot(x)-b
+    array([ 0.00333333, -0.00333333,  0.00333333])
+    >>> r1norm
+    0.005773502691896255
+
+    `istop` indicates that the system is inconsistent and thus `x` is rather an
+    approximate solution to the corresponding least-squares problem. `r1norm`
+    contains the norm of the minimal residual that was found.
+    """
+    A = convert_pydata_sparse_to_scipy(A)
+    A = aslinearoperator(A)
+    if A.ndim > 2:
+        raise ValueError(f"{A.ndim}-dimensional `A` is unsupported, expected 2-D.")
+    b = np.atleast_1d(b)
+    if b.ndim > 1:
+        b = b.squeeze()
+
+    m, n = A.shape
+    if iter_lim is None:
+        iter_lim = 2 * n
+    var = np.zeros(n)
+
+    msg = ('The exact solution is  x = 0                              ',
+           'Ax - b is small enough, given atol, btol                  ',
+           'The least-squares solution is good enough, given atol     ',
+           'The estimate of cond(Abar) has exceeded conlim            ',
+           'Ax - b is small enough for this machine                   ',
+           'The least-squares solution is good enough for this machine',
+           'Cond(Abar) seems to be too large for this machine         ',
+           'The iteration limit has been reached                      ')
+
+    if show:
+        print(' ')
+        print('LSQR            Least-squares solution of  Ax = b')
+        str1 = f'The matrix A has {m} rows and {n} columns'
+        str2 = f'damp = {damp:20.14e}   calc_var = {calc_var:8g}'
+        str3 = f'atol = {atol:8.2e}                 conlim = {conlim:8.2e}'
+        str4 = f'btol = {btol:8.2e}               iter_lim = {iter_lim:8g}'
+        print(str1)
+        print(str2)
+        print(str3)
+        print(str4)
+
+    itn = 0
+    istop = 0
+    ctol = 0
+    if conlim > 0:
+        ctol = 1/conlim
+    anorm = 0
+    acond = 0
+    dampsq = damp**2
+    ddnorm = 0
+    res2 = 0
+    xnorm = 0
+    xxnorm = 0
+    z = 0
+    cs2 = -1
+    sn2 = 0
+
+    # Set up the first vectors u and v for the bidiagonalization.
+    # These satisfy  beta*u = b - A@x,  alfa*v = A'@u.
+    u = b
+    bnorm = np.linalg.norm(b)
+
+    if x0 is None:
+        x = np.zeros(n)
+        beta = bnorm.copy()
+    else:
+        x = np.asarray(x0)
+        u = u - A.matvec(x)
+        beta = np.linalg.norm(u)
+
+    if beta > 0:
+        u = (1/beta) * u
+        v = A.rmatvec(u)
+        alfa = np.linalg.norm(v)
+    else:
+        v = x.copy()
+        alfa = 0
+
+    if alfa > 0:
+        v = (1/alfa) * v
+    w = v.copy()
+
+    rhobar = alfa
+    phibar = beta
+    rnorm = beta
+    r1norm = rnorm
+    r2norm = rnorm
+
+    # Reverse the order here from the original matlab code because
+    # there was an error on return when arnorm==0
+    arnorm = alfa * beta
+    if arnorm == 0:
+        if show:
+            print(msg[0])
+        return x, istop, itn, r1norm, r2norm, anorm, acond, arnorm, xnorm, var
+
+    head1 = '   Itn      x[0]       r1norm     r2norm '
+    head2 = ' Compatible    LS      Norm A   Cond A'
+
+    if show:
+        print(' ')
+        print(head1, head2)
+        test1 = 1
+        test2 = alfa / beta
+        str1 = f'{itn:6g} {x[0]:12.5e}'
+        str2 = f' {r1norm:10.3e} {r2norm:10.3e}'
+        str3 = f'  {test1:8.1e} {test2:8.1e}'
+        print(str1, str2, str3)
+
+    # Main iteration loop.
+    while itn < iter_lim:
+        itn = itn + 1
+        # Perform the next step of the bidiagonalization to obtain the
+        # next  beta, u, alfa, v. These satisfy the relations
+        #     beta*u  =  a@v   -  alfa*u,
+        #     alfa*v  =  A'@u  -  beta*v.
+        u = A.matvec(v) - alfa * u
+        beta = np.linalg.norm(u)
+
+        if beta > 0:
+            u = (1/beta) * u
+            anorm = sqrt(anorm**2 + alfa**2 + beta**2 + dampsq)
+            v = A.rmatvec(u) - beta * v
+            alfa = np.linalg.norm(v)
+            if alfa > 0:
+                v = (1 / alfa) * v
+
+        # Use a plane rotation to eliminate the damping parameter.
+        # This alters the diagonal (rhobar) of the lower-bidiagonal matrix.
+        if damp > 0:
+            rhobar1 = sqrt(rhobar**2 + dampsq)
+            cs1 = rhobar / rhobar1
+            sn1 = damp / rhobar1
+            psi = sn1 * phibar
+            phibar = cs1 * phibar
+        else:
+            # cs1 = 1 and sn1 = 0
+            rhobar1 = rhobar
+            psi = 0.
+
+        # Use a plane rotation to eliminate the subdiagonal element (beta)
+        # of the lower-bidiagonal matrix, giving an upper-bidiagonal matrix.
+        cs, sn, rho = _sym_ortho(rhobar1, beta)
+
+        theta = sn * alfa
+        rhobar = -cs * alfa
+        phi = cs * phibar
+        phibar = sn * phibar
+        tau = sn * phi
+
+        # Update x and w.
+        t1 = phi / rho
+        t2 = -theta / rho
+        dk = (1 / rho) * w
+
+        x = x + t1 * w
+        w = v + t2 * w
+        ddnorm = ddnorm + np.linalg.norm(dk)**2
+
+        if calc_var:
+            var = var + dk**2
+
+        # Use a plane rotation on the right to eliminate the
+        # super-diagonal element (theta) of the upper-bidiagonal matrix.
+        # Then use the result to estimate norm(x).
+        delta = sn2 * rho
+        gambar = -cs2 * rho
+        rhs = phi - delta * z
+        zbar = rhs / gambar
+        xnorm = sqrt(xxnorm + zbar**2)
+        gamma = sqrt(gambar**2 + theta**2)
+        cs2 = gambar / gamma
+        sn2 = theta / gamma
+        z = rhs / gamma
+        xxnorm = xxnorm + z**2
+
+        # Test for convergence.
+        # First, estimate the condition of the matrix  Abar,
+        # and the norms of  rbar  and  Abar'rbar.
+        acond = anorm * sqrt(ddnorm)
+        res1 = phibar**2
+        res2 = res2 + psi**2
+        rnorm = sqrt(res1 + res2)
+        arnorm = alfa * abs(tau)
+
+        # Distinguish between
+        #    r1norm = ||b - Ax|| and
+        #    r2norm = rnorm in current code
+        #           = sqrt(r1norm^2 + damp^2*||x - x0||^2).
+        #    Estimate r1norm from
+        #    r1norm = sqrt(r2norm^2 - damp^2*||x - x0||^2).
+        # Although there is cancellation, it might be accurate enough.
+        if damp > 0:
+            r1sq = rnorm**2 - dampsq * xxnorm
+            r1norm = sqrt(abs(r1sq))
+            if r1sq < 0:
+                r1norm = -r1norm
+        else:
+            r1norm = rnorm
+        r2norm = rnorm
+
+        # Now use these norms to estimate certain other quantities,
+        # some of which will be small near a solution.
+        test1 = rnorm / bnorm
+        test2 = arnorm / (anorm * rnorm + eps)
+        test3 = 1 / (acond + eps)
+        t1 = test1 / (1 + anorm * xnorm / bnorm)
+        rtol = btol + atol * anorm * xnorm / bnorm
+
+        # The following tests guard against extremely small values of
+        # atol, btol  or  ctol.  (The user may have set any or all of
+        # the parameters  atol, btol, conlim  to 0.)
+        # The effect is equivalent to the normal tests using
+        # atol = eps,  btol = eps,  conlim = 1/eps.
+        if itn >= iter_lim:
+            istop = 7
+        if 1 + test3 <= 1:
+            istop = 6
+        if 1 + test2 <= 1:
+            istop = 5
+        if 1 + t1 <= 1:
+            istop = 4
+
+        # Allow for tolerances set by the user.
+        if test3 <= ctol:
+            istop = 3
+        if test2 <= atol:
+            istop = 2
+        if test1 <= rtol:
+            istop = 1
+
+        if show:
+            # See if it is time to print something.
+            prnt = False
+            if n <= 40:
+                prnt = True
+            if itn <= 10:
+                prnt = True
+            if itn >= iter_lim-10:
+                prnt = True
+            # if itn%10 == 0: prnt = True
+            if test3 <= 2*ctol:
+                prnt = True
+            if test2 <= 10*atol:
+                prnt = True
+            if test1 <= 10*rtol:
+                prnt = True
+            if istop != 0:
+                prnt = True
+
+            if prnt:
+                str1 = f'{itn:6g} {x[0]:12.5e}'
+                str2 = f' {r1norm:10.3e} {r2norm:10.3e}'
+                str3 = f'  {test1:8.1e} {test2:8.1e}'
+                str4 = f' {anorm:8.1e} {acond:8.1e}'
+                print(str1, str2, str3, str4)
+
+        if istop != 0:
+            break
+
+    # End of iteration loop.
+    # Print the stopping condition.
+    if show:
+        print(' ')
+        print('LSQR finished')
+        print(msg[istop])
+        print(' ')
+        str1 = f'istop ={istop:8g}   r1norm ={r1norm:8.1e}'
+        str2 = f'anorm ={anorm:8.1e}   arnorm ={arnorm:8.1e}'
+        str3 = f'itn   ={itn:8g}   r2norm ={r2norm:8.1e}'
+        str4 = f'acond ={acond:8.1e}   xnorm  ={xnorm:8.1e}'
+        print(str1 + '   ' + str2)
+        print(str3 + '   ' + str4)
+        print(' ')
+
+    return x, istop, itn, r1norm, r2norm, anorm, acond, arnorm, xnorm, var
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_isolve/minres.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_isolve/minres.py
new file mode 100644
index 0000000000000000000000000000000000000000..bf6fdd2b333c4bbf38d636243495c1f7559bae5d
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_isolve/minres.py
@@ -0,0 +1,379 @@
+from numpy import inner, vdot, iscomplexobj, zeros, inf, finfo
+from numpy.linalg import norm
+from math import sqrt
+
+from scipy._lib._array_api import xp_capabilities
+
+from .utils import make_system
+
+__all__ = ['minres']
+
+
+@xp_capabilities(np_only=True)
+def minres(A, b, x0=None, *, rtol=1e-5, shift=0.0, maxiter=None,
+           M=None, callback=None, show=False, check=False):
+    """
+    Solve ``Ax = b`` with the MINimum RESidual method,
+    for a real symmetric or complex hermitian matrix `A`.
+
+    MINRES minimizes ``norm(Ax - b)`` for a real symmetric or complex hermitian
+    matrix `A`. Unlike the Conjugate Gradient method, `A` can be indefinite
+    or singular.
+
+    If ``shift != 0`` then the method solves ``(A - shift*I)x = b``.
+
+    Parameters
+    ----------
+    A : {sparse array, ndarray, LinearOperator}
+        The real symmetric or complex hermitian N-by-N matrix of the
+        linear system. Alternatively, `A` can be a linear operator which can
+        produce ``Ax`` using, e.g.,
+        ``scipy.sparse.linalg.LinearOperator``.
+    b : ndarray
+        Right hand side of the linear system. Has shape (N,) or (N,1).
+
+    Returns
+    -------
+    x : ndarray
+        The converged solution.
+    info : int
+        Provides convergence information:
+            0  : successful exit
+            >0 : convergence to tolerance not achieved, number of iterations
+            <0 : illegal input or breakdown
+
+    Other Parameters
+    ----------------
+    x0 : ndarray
+        Starting guess for the solution.
+    rtol : float
+        Tolerance to achieve. The algorithm terminates when the relative
+        residual is below ``rtol``.
+    shift : float
+        Value to apply to the system ``(A - shift * I)x = b``. Default is 0.
+    maxiter : int
+        Maximum number of iterations.  Iteration will stop after maxiter
+        steps even if the specified tolerance has not been achieved.
+    M : {sparse array, ndarray, LinearOperator}
+        Preconditioner for `A`.  The preconditioner should approximate the
+        inverse of `A`.  Effective preconditioning dramatically improves the
+        rate of convergence, which implies that fewer iterations are needed
+        to reach a given error tolerance.
+    callback : function
+        User-supplied function to call after each iteration.  It is called
+        as ``callback(xk)``, where ``xk`` is the current solution vector.
+    show : bool
+        If ``True``, print out a summary and metrics related to the solution
+        during iterations. Default is ``False``.
+    check : bool
+        If ``True``, run additional input validation to check that `A` and
+        `M` (if specified) are symmetric. Default is ``False``.
+
+    Notes
+    -----
+    This file is a translation of the MATLAB implementation [2]_.
+
+    References
+    ----------
+    .. [1] Solution of sparse indefinite systems of linear equations,
+          C. C. Paige and M. A. Saunders (1975),
+          SIAM J. Numer. Anal. 12(4), pp. 617-629.
+          https://web.stanford.edu/group/SOL/software/minres/
+    .. [2] https://web.stanford.edu/group/SOL/software/minres/minres-matlab.zip
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.sparse import csc_array
+    >>> from scipy.sparse.linalg import minres
+    >>> A = csc_array([[3, 2, 0], [1, -1, 0], [0, 5, 1]], dtype=float)
+    >>> A = A + A.T
+    >>> b = np.array([2, 4, -1], dtype=float)
+    >>> x, exitCode = minres(A, b)
+    >>> print(exitCode)            # 0 indicates successful convergence
+    0
+    >>> np.allclose(A.dot(x), b)
+    True
+    """
+    A, M, x, b = make_system(A, M, x0, b)
+
+    dotprod = vdot if iscomplexobj(A) else inner
+    matvec = A.matvec
+    psolve = M.matvec
+
+    first = 'Enter minres.   '
+    last = 'Exit  minres.   '
+
+    n = A.shape[0]
+
+    if maxiter is None:
+        maxiter = 5 * n
+
+    msg = [' beta2 = 0.  If M = I, b and x are eigenvectors    ',   # -1
+            ' beta1 = 0.  The exact solution is x0          ',   # 0
+            ' A solution to Ax = b was found, given rtol        ',   # 1
+            ' A least-squares solution was found, given rtol    ',   # 2
+            ' Reasonable accuracy achieved, given eps           ',   # 3
+            ' x has converged to an eigenvector                 ',   # 4
+            ' acond has exceeded 0.1/eps                        ',   # 5
+            ' The iteration limit was reached                   ',   # 6
+            ' A  does not define a symmetric matrix             ',   # 7
+            ' M  does not define a symmetric matrix             ',   # 8
+            ' M  does not define a pos-def preconditioner       ']   # 9
+
+    if show:
+        print(first + 'Solution of symmetric Ax = b')
+        print(first + f'n      =  {n:3g}     shift  =  {shift:23.14e}')
+        print(first + f'itnlim =  {maxiter:3g}     rtol   =  {rtol:11.2e}')
+        print()
+
+    istop = 0
+    itn = 0
+    Anorm = 0
+    Acond = 0
+    rnorm = 0
+    ynorm = 0
+
+    xtype = x.dtype
+
+    eps = finfo(xtype).eps
+
+    # Set up y and v for the first Lanczos vector v1.
+    # y  =  beta1 P' v1,  where  P = C**(-1).
+    # v is really P' v1.
+
+    if x0 is None:
+        r1 = b.copy()
+    else:
+        r1 = b - A@x
+    y = psolve(r1)
+
+    beta1 = dotprod(r1, y)
+
+    if beta1 < 0:
+        raise ValueError('indefinite preconditioner')
+    elif beta1 == 0:
+        return (x, 0)
+
+    bnorm = norm(b)
+    if bnorm == 0:
+        x = b
+        return (x, 0)
+
+    beta1 = sqrt(beta1.real)
+
+    if check:
+        # are these too strict?
+
+        # see if A is symmetric
+        w = matvec(y)
+        r2 = matvec(w)
+        s = dotprod(w,w)
+        t = dotprod(y,r2)
+        z = abs(s - t)
+        epsa = (s + eps) * eps**(1.0/3.0)
+        if z > epsa:
+            raise ValueError('non-symmetric matrix')
+
+        # see if M is symmetric
+        r2 = psolve(y)
+        s = dotprod(y,y)
+        t = dotprod(r1,r2)
+        z = abs(s - t)
+        epsa = (s + eps) * eps**(1.0/3.0)
+        if z > epsa:
+            raise ValueError('non-symmetric preconditioner')
+
+    # Initialize other quantities
+    oldb = 0
+    beta = beta1
+    dbar = 0
+    epsln = 0
+    qrnorm = beta1
+    phibar = beta1
+    rhs1 = beta1
+    rhs2 = 0
+    tnorm2 = 0
+    gmax = 0
+    gmin = finfo(xtype).max
+    cs = -1
+    sn = 0
+    w = zeros(n, dtype=xtype)
+    w2 = zeros(n, dtype=xtype)
+    r2 = r1
+
+    if show:
+        print()
+        print()
+        print('   Itn     x(1)     Compatible    LS       norm(A)  cond(A) gbar/|A|')
+
+    while itn < maxiter:
+        itn += 1
+
+        s = 1.0/beta
+        v = s*y
+
+        y = matvec(v)
+        y = y - shift * v
+
+        if itn >= 2:
+            y = y - (beta/oldb)*r1
+
+        alfa = dotprod(v,y)
+        y = y - (alfa/beta)*r2
+        r1 = r2
+        r2 = y
+        y = psolve(r2)
+        oldb = beta
+        beta = dotprod(r2,y)
+        if beta < 0:
+            raise ValueError('non-symmetric matrix')
+        beta = sqrt(beta.real)
+        tnorm2 += alfa**2 + oldb**2 + beta**2
+
+        if itn == 1:
+            if beta/beta1 <= 10*eps:
+                istop = -1  # Terminate later
+
+        # Apply previous rotation Qk-1 to get
+        #   [deltak epslnk+1] = [cs  sn][dbark    0   ]
+        #   [gbar k dbar k+1]   [sn -cs][alfak betak+1].
+
+        oldeps = epsln
+        delta = cs * dbar + sn * alfa   # delta1 = 0         deltak
+        gbar = sn * dbar - cs * alfa   # gbar 1 = alfa1     gbar k
+        epsln = sn * beta     # epsln2 = 0         epslnk+1
+        dbar = - cs * beta   # dbar 2 = beta2     dbar k+1
+        root = norm([gbar, dbar])
+        Arnorm = phibar * root
+
+        # Compute the next plane rotation Qk
+
+        gamma = norm([gbar, beta]).astype(xtype)  # gammak
+        gamma = max(gamma, eps)
+        cs = gbar / gamma             # ck
+        sn = beta / gamma             # sk
+        phi = cs * phibar              # phik
+        phibar = sn * phibar              # phibark+1
+
+        # Update  x.
+
+        denom = 1.0/gamma
+        w1 = w2
+        w2 = w
+        w = (v - oldeps*w1 - delta*w2) * denom
+        x = x + phi*w
+
+        # Go round again.
+
+        gmax = max(gmax, gamma)
+        gmin = min(gmin, gamma)
+        z = rhs1 / gamma
+        rhs1 = rhs2 - delta*z
+        rhs2 = - epsln*z
+
+        # Estimate various norms and test for convergence.
+
+        Anorm = sqrt(tnorm2.real)
+        ynorm = norm(x)
+        epsa = Anorm * eps
+        epsx = Anorm * ynorm * eps
+        epsr = Anorm * ynorm * rtol
+        diag = gbar
+
+        if diag == 0:
+            diag = epsa
+
+        qrnorm = phibar
+        rnorm = qrnorm
+        if ynorm == 0 or Anorm == 0:
+            test1 = inf
+        else:
+            test1 = rnorm / (Anorm*ynorm)    # ||r||  / (||A|| ||x||)
+        if Anorm == 0:
+            test2 = inf
+        else:
+            test2 = root / Anorm            # ||Ar|| / (||A|| ||r||)
+
+        # Estimate  cond(A).
+        # In this version we look at the diagonals of  R  in the
+        # factorization of the lower Hessenberg matrix,  Q @ H = R,
+        # where H is the tridiagonal matrix from Lanczos with one
+        # extra row, beta(k+1) e_k^T.
+
+        Acond = gmax/gmin
+
+        # See if any of the stopping criteria are satisfied.
+        # In rare cases, istop is already -1 from above (Abar = const*I).
+
+        if istop == 0:
+            t1 = 1 + test1      # These tests work if rtol < eps
+            t2 = 1 + test2
+            if t2 <= 1:
+                istop = 2
+            if t1 <= 1:
+                istop = 1
+
+            if itn >= maxiter:
+                istop = 6
+            if Acond >= 0.1/eps:
+                istop = 4
+            if epsx >= beta1:
+                istop = 3
+            # if rnorm <= epsx   : istop = 2
+            # if rnorm <= epsr   : istop = 1
+            if test2 <= rtol:
+                istop = 2
+            if test1 <= rtol:
+                istop = 1
+
+        # See if it is time to print something.
+
+        prnt = False
+        if n <= 40:
+            prnt = True
+        if itn <= 10:
+            prnt = True
+        if itn >= maxiter-10:
+            prnt = True
+        if itn % 10 == 0:
+            prnt = True
+        if qrnorm <= 10*epsx:
+            prnt = True
+        if qrnorm <= 10*epsr:
+            prnt = True
+        if Acond <= 1e-2/eps:
+            prnt = True
+        if istop != 0:
+            prnt = True
+
+        if show and prnt:
+            str1 = f'{itn:6g} {x[0]:12.5e} {test1:10.3e}'
+            str2 = f' {test2:10.3e}'
+            str3 = f' {Anorm:8.1e} {Acond:8.1e} {gbar/Anorm:8.1e}'
+
+            print(str1 + str2 + str3)
+
+            if itn % 10 == 0:
+                print()
+
+        if callback is not None:
+            callback(x)
+
+        if istop != 0:
+            break  # TODO check this
+
+    if show:
+        print()
+        print(last + f' istop   =  {istop:3g}               itn   ={itn:5g}')
+        print(last + f' Anorm   =  {Anorm:12.4e}      Acond =  {Acond:12.4e}')
+        print(last + f' rnorm   =  {rnorm:12.4e}      ynorm =  {ynorm:12.4e}')
+        print(last + f' Arnorm  =  {Arnorm:12.4e}')
+        print(last + msg[istop+1])
+
+    if istop == 6:
+        info = maxiter
+    else:
+        info = 0
+
+    return (x,info)
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diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_isolve/tests/test_gcrotmk.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_isolve/tests/test_gcrotmk.py
new file mode 100644
index 0000000000000000000000000000000000000000..25fb61d1c06adc06d93b115d6cbcdb6a986d4459
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_isolve/tests/test_gcrotmk.py
@@ -0,0 +1,189 @@
+#!/usr/bin/env python
+"""Tests for the linalg._isolve.gcrotmk module
+"""
+import threading
+import warnings
+
+from numpy.testing import (assert_, assert_allclose, assert_equal)
+
+import numpy as np
+from numpy import zeros, array, allclose
+from scipy.linalg import norm
+from scipy.sparse import csr_array, eye_array, random_array
+
+from scipy.sparse.linalg._interface import LinearOperator
+from scipy.sparse.linalg import splu
+from scipy.sparse.linalg._isolve import gcrotmk, gmres
+
+
+Am = csr_array(array([[-2,1,0,0,0,9],
+                       [1,-2,1,0,5,0],
+                       [0,1,-2,1,0,0],
+                       [0,0,1,-2,1,0],
+                       [0,3,0,1,-2,1],
+                       [1,0,0,0,1,-2]]))
+b = array([1,2,3,4,5,6])
+count = threading.local()  # [0]
+niter = threading.local()  # [0]
+
+
+def matvec(v):
+    if not hasattr(count, 'c'):
+        count.c = [0]
+    count.c[0] += 1
+    return Am@v
+
+
+def cb(v):
+    if not hasattr(niter, 'n'):
+        niter.n = [0]
+    niter.n[0] += 1
+
+
+A = LinearOperator(matvec=matvec, shape=Am.shape, dtype=Am.dtype)
+
+
+def do_solve(**kw):
+    if not hasattr(niter, 'n'):
+        niter.n = [0]
+
+    if not hasattr(count, 'c'):
+        count.c = [0]
+
+    count.c[0] = 0
+    with warnings.catch_warnings():
+        warnings.filterwarnings(
+            "ignore", ".*called without specifying.*", DeprecationWarning)
+        x0, flag = gcrotmk(A, b, x0=zeros(A.shape[0]), rtol=1e-14, **kw)
+    count_0 = count.c[0]
+    assert_(allclose(A@x0, b, rtol=1e-12, atol=1e-12), norm(A@x0-b))
+    return x0, count_0
+
+
+class TestGCROTMK:
+    def test_preconditioner(self):
+        # Check that preconditioning works
+        pc = splu(Am.tocsc())
+        M = LinearOperator(matvec=pc.solve, shape=A.shape, dtype=A.dtype)
+
+        x0, count_0 = do_solve()
+        niter.n[0] = 0
+        x1, count_1 = do_solve(M=M, callback=cb)
+
+        assert_equal(count_1, 3)
+        assert count_1 < count_0/2
+        assert allclose(x1, x0, rtol=1e-14)
+        assert niter.n[0] < 3
+
+    def test_arnoldi(self):
+        rng = np.random.default_rng(1)
+
+        A = eye_array(2000) + random_array((2000, 2000), density=5e-4, rng=rng)
+        b = rng.random(2000)
+
+        # The inner arnoldi should be equivalent to gmres
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", ".*called without specifying.*", DeprecationWarning)
+            x0, flag0 = gcrotmk(A, b, x0=zeros(A.shape[0]), m=10, k=0, maxiter=1)
+            x1, flag1 = gmres(A, b, x0=zeros(A.shape[0]), restart=10, maxiter=1)
+
+        assert_equal(flag0, 1)
+        assert_equal(flag1, 1)
+        assert np.linalg.norm(A.dot(x0) - b) > 1e-4
+
+        assert_allclose(x0, x1)
+
+    def test_cornercase(self):
+        np.random.seed(1234)
+
+        # Rounding error may prevent convergence with tol=0 --- ensure
+        # that the return values in this case are correct, and no
+        # exceptions are raised
+
+        for n in [3, 5, 10, 100]:
+            A = 2*eye_array(n)
+
+            with warnings.catch_warnings():
+                warnings.filterwarnings(
+                    "ignore", ".*called without specifying.*", DeprecationWarning)
+                b = np.ones(n)
+                x, info = gcrotmk(A, b, maxiter=10)
+                assert_equal(info, 0)
+                assert_allclose(A.dot(x) - b, 0, atol=1e-14)
+
+                x, info = gcrotmk(A, b, rtol=0, maxiter=10)
+                if info == 0:
+                    assert_allclose(A.dot(x) - b, 0, atol=1e-14)
+
+                b = np.random.rand(n)
+                x, info = gcrotmk(A, b, maxiter=10)
+                assert_equal(info, 0)
+                assert_allclose(A.dot(x) - b, 0, atol=1e-14)
+
+                x, info = gcrotmk(A, b, rtol=0, maxiter=10)
+                if info == 0:
+                    assert_allclose(A.dot(x) - b, 0, atol=1e-14)
+
+    def test_nans(self):
+        A = eye_array(3, format='lil')
+        A[1,1] = np.nan
+        b = np.ones(3)
+
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", ".*called without specifying.*", DeprecationWarning)
+            x, info = gcrotmk(A, b, rtol=0, maxiter=10)
+            assert_equal(info, 1)
+
+    def test_truncate(self):
+        np.random.seed(1234)
+        A = np.random.rand(30, 30) + np.eye(30)
+        b = np.random.rand(30)
+
+        for truncate in ['oldest', 'smallest']:
+            with warnings.catch_warnings():
+                warnings.filterwarnings(
+                    "ignore", ".*called without specifying.*", DeprecationWarning)
+                x, info = gcrotmk(A, b, m=10, k=10, truncate=truncate,
+                                  rtol=1e-4, maxiter=200)
+            assert_equal(info, 0)
+            assert_allclose(A.dot(x) - b, 0, atol=1e-3)
+
+    def test_CU(self):
+        for discard_C in (True, False):
+            # Check that C,U behave as expected
+            CU = []
+            x0, count_0 = do_solve(CU=CU, discard_C=discard_C)
+            assert_(len(CU) > 0)
+            assert_(len(CU) <= 6)
+
+            if discard_C:
+                for c, u in CU:
+                    assert_(c is None)
+
+            # should converge immediately
+            x1, count_1 = do_solve(CU=CU, discard_C=discard_C)
+            if discard_C:
+                assert_equal(count_1, 2 + len(CU))
+            else:
+                assert_equal(count_1, 3)
+            assert_(count_1 <= count_0/2)
+            assert_allclose(x1, x0, atol=1e-14)
+
+    def test_denormals(self):
+        # Check that no warnings are emitted if the matrix contains
+        # numbers for which 1/x has no float representation, and that
+        # the solver behaves properly.
+        A = np.array([[1, 2], [3, 4]], dtype=float)
+        A *= 100 * np.nextafter(0, 1)
+
+        b = np.array([1, 1])
+
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", ".*called without specifying.*", DeprecationWarning)
+            xp, info = gcrotmk(A, b)
+
+        if info == 0:
+            assert_allclose(A.dot(xp), b)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_isolve/tests/test_iterative.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_isolve/tests/test_iterative.py
new file mode 100644
index 0000000000000000000000000000000000000000..496aa9d3ff2256766955bb1ca2dcaaca0a5ddc25
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_isolve/tests/test_iterative.py
@@ -0,0 +1,930 @@
+""" Test functions for the sparse.linalg._isolve module
+"""
+
+from contextlib import nullcontext
+import itertools
+import platform
+import pytest
+import types
+
+import numpy as np
+from numpy.testing import assert_allclose
+from numpy import zeros, arange, array, ones, eye, iscomplexobj
+
+from scipy._lib._array_api import (
+    is_numpy, make_xp_pytest_param, make_xp_pytest_marks,
+    xp_assert_close, xp_assert_less, xp_vector_norm, xp_assert_equal,
+    xp_assert_less_equal,
+)
+from scipy._external import array_api_extra as xpx
+from scipy._lib._sparse import issparse
+from scipy.sparse import dia_array, csr_array, kronsum
+
+from scipy.sparse.linalg import LinearOperator, aslinearoperator
+from scipy.sparse.linalg._isolve import (bicg, bicgstab, cg, cgs,
+                                         gcrotmk, gmres, lgmres,
+                                         minres, qmr, tfqmr)
+from scipy.sparse.linalg._interface import IdentityOperator
+
+# TODO check that method preserve shape and type
+# TODO test both preconditioner methods
+
+
+# list of all solvers under test
+_SOLVERS = [bicg, bicgstab, cg, cgs, gcrotmk, gmres, lgmres,
+            minres, qmr, tfqmr]
+
+CB_TYPE_FILTER = ".*called without specifying `callback_type`.*"
+
+
+def _assert_success(*, A, x, b, xp, rtol=1.0, atol=0.0, less_equal=False):
+    Ax = xp.squeeze(A @ x[..., xp.newaxis], axis=-1)
+    residual = Ax - b
+    err = xp_vector_norm(residual, axis=-1)
+    assertion = xp_assert_less_equal if less_equal else xp_assert_less
+    limit = atol + rtol * xp_vector_norm(b, axis=-1)
+    assertion(err, limit)
+
+
+# create parametrized fixture for easy reuse in tests
+@pytest.fixture(
+    scope="session",
+    params=[make_xp_pytest_param(func) for func in _SOLVERS],
+)
+def solver(request):
+    """
+    Fixture for all solvers in scipy.sparse.linalg._isolve
+    """
+    return request.param
+
+
+class Case:
+    def __init__(self, name, A, b=None, skip=None, nonconvergence=None):
+        self.name = name
+        self.A = A
+        if b is None:
+            self.b = arange(A.shape[0], dtype=A.dtype)
+        else:
+            self.b = b
+        if skip is None:
+            self.skip = []
+        else:
+            self.skip = skip
+        if nonconvergence is None:
+            self.nonconvergence = []
+        else:
+            self.nonconvergence = nonconvergence
+
+
+class SingleTest:
+    # case with a specific solver
+    def __init__(self, A, b, solver, casename, convergence=True):
+        self.A = A
+        self.b = b
+        self.solver = solver
+        self.casename = casename
+        self.name = casename + '-' + solver.__name__
+        self.convergence = convergence
+
+    def __repr__(self):
+        return f"<{self.name}>"
+
+
+def xp_case(case, xp, batch_A, batch_b, rng=None):
+    sparse = issparse(case.A)
+
+    if (not_np := not is_numpy(xp)) and sparse: # TODO: pydata/sparse for sparse tests?
+        pytest.skip("sparse tests run only with `np` backend")
+
+    A = xp.asarray(case.A) if not_np else case.A
+    b = xp.asarray(case.b) if not_np else case.b
+
+    rng = np.random.default_rng(rng)
+    if sparse and (batch_A or batch_b):
+        A = A.tocoo()
+    if batch_A:
+        # apply some random scaling to each system in batch,
+        # preserving symmetry, (non-)positive definiteness, Hermiticity
+        scaling = np.abs(rng.standard_normal(batch_A + (1, 1)))
+        batch_array = xp.asarray(scaling, dtype=A.dtype)
+        A = batch_array * A
+    if batch_b:
+        # apply some random scaling to each RHS in batch
+        b = b * xp.asarray(rng.random(batch_b + (1,)), dtype=b.dtype)
+
+    return types.SimpleNamespace(
+        name=case.name,
+        A=A,
+        b=b,
+        convergence=case.convergence,
+        solver=case.solver,
+        casename=case.casename,
+    )
+
+
+class IterativeParams:
+    def __init__(self):
+        sym_solvers = [minres, cg]
+        posdef_solvers = [cg]
+        real_solvers = [minres]
+
+        # list of Cases
+        self.cases = []
+
+        # Symmetric and Positive Definite
+        N = 40
+        data = ones((3, N))
+        data[0, :] = 2
+        data[1, :] = -1
+        data[2, :] = -1
+        Poisson1D = dia_array((data, [0, -1, 1]), shape=(N, N)).tocsr()
+        self.cases.append(Case("poisson1d", Poisson1D))
+        # note: minres fails for single precision
+        self.cases.append(Case("poisson1d-F", Poisson1D.astype(np.float32),
+                               skip=[minres]))
+
+        # Symmetric and Negative Definite
+        self.cases.append(Case("neg-poisson1d", -Poisson1D,
+                               skip=posdef_solvers))
+        # note: minres fails for single precision
+        self.cases.append(Case("neg-poisson1d-F", (-Poisson1D).astype('f'),
+                               skip=posdef_solvers + [minres]))
+
+        # 2-dimensional Poisson equations
+        Poisson2D = kronsum(Poisson1D, Poisson1D)
+        # note: minres fails for 2-d poisson problem,
+        # it will be fixed in the future PR
+        self.cases.append(Case("poisson2d", Poisson2D, skip=[minres]))
+        # note: minres fails for single precision
+        self.cases.append(Case("poisson2d-F", Poisson2D.astype('f'),
+                               skip=[minres]))
+
+        # Symmetric and Indefinite
+        data = array([[6, -5, 2, 7, -1, 10, 4, -3, -8, 9]], dtype='d')
+        RandDiag = dia_array((data, [0]), shape=(10, 10)).tocsr()
+        self.cases.append(Case("rand-diag", RandDiag, skip=posdef_solvers))
+        self.cases.append(Case("rand-diag-F", RandDiag.astype('f'),
+                               skip=posdef_solvers))
+
+        # Random real-valued
+        rng = np.random.RandomState(1234)
+        data = rng.rand(4, 4)
+        self.cases.append(Case("rand", data,
+                               skip=posdef_solvers + sym_solvers))
+        self.cases.append(Case("rand-F", data.astype('f'),
+                               skip=posdef_solvers + sym_solvers))
+
+        # Random symmetric real-valued
+        rng = np.random.RandomState(1234)
+        data = rng.rand(4, 4)
+        data = data + data.T
+        self.cases.append(Case("rand-sym", data, skip=posdef_solvers))
+        self.cases.append(Case("rand-sym-F", data.astype('f'),
+                               skip=posdef_solvers))
+
+        # Random pos-def symmetric real
+        np.random.seed(1234)
+        data = np.random.rand(9, 9)
+        data = np.dot(data.conj(), data.T)
+        self.cases.append(Case("rand-sym-pd", data))
+        # note: minres fails for single precision
+        self.cases.append(Case("rand-sym-pd-F", data.astype('f'),
+                               skip=[minres]))
+
+        # Random complex-valued
+        rng = np.random.RandomState(1234)
+        data = rng.rand(4, 4) + 1j * rng.rand(4, 4)
+        skip_cmplx = posdef_solvers + sym_solvers + real_solvers
+        self.cases.append(Case("rand-cmplx", data, skip=skip_cmplx))
+        self.cases.append(Case("rand-cmplx-F", data.astype('F'),
+                               skip=skip_cmplx))
+
+        # Random hermitian complex-valued
+        rng = np.random.RandomState(1234)
+        data = rng.rand(4, 4) + 1j * rng.rand(4, 4)
+        data = data + data.T.conj()
+        self.cases.append(Case("rand-cmplx-herm", data,
+                               skip=posdef_solvers + real_solvers))
+        self.cases.append(Case("rand-cmplx-herm-F", data.astype('F'),
+                               skip=posdef_solvers + real_solvers))
+
+        # Random pos-def hermitian complex-valued
+        rng = np.random.RandomState(1234)
+        data = rng.rand(9, 9) + 1j * rng.rand(9, 9)
+        data = np.dot(data.conj(), data.T)
+        self.cases.append(Case(
+            "rand-cmplx-sym-pd", data, skip=real_solvers)
+        )
+        self.cases.append(Case("rand-cmplx-sym-pd-F", data.astype('F'),
+                               skip=real_solvers))
+
+        # Non-symmetric and Positive Definite
+        #
+        # cgs, qmr, bicg and tfqmr fail to converge on this one
+        #   -- algorithmic limitation apparently
+        data = ones((2, 10))
+        data[0, :] = 2
+        data[1, :] = -1
+        A = dia_array((data, [0, -1]), shape=(10, 10)).tocsr()
+        self.cases.append(Case("nonsymposdef", A,
+                               skip=sym_solvers + [cgs, qmr, bicg, tfqmr]))
+        self.cases.append(Case("nonsymposdef-F", A.astype('F'),
+                               skip=sym_solvers + [cgs, qmr, bicg, tfqmr]))
+
+        # Symmetric, non-pd, hitting cgs/bicg/bicgstab/qmr/tfqmr breakdown
+        A = np.array([[0, 0, 0, 0, 0, 1, -1, -0, -0, -0, -0],
+                      [0, 0, 0, 0, 0, 2, -0, -1, -0, -0, -0],
+                      [0, 0, 0, 0, 0, 2, -0, -0, -1, -0, -0],
+                      [0, 0, 0, 0, 0, 2, -0, -0, -0, -1, -0],
+                      [0, 0, 0, 0, 0, 1, -0, -0, -0, -0, -1],
+                      [1, 2, 2, 2, 1, 0, -0, -0, -0, -0, -0],
+                      [-1, 0, 0, 0, 0, 0, -1, -0, -0, -0, -0],
+                      [0, -1, 0, 0, 0, 0, -0, -1, -0, -0, -0],
+                      [0, 0, -1, 0, 0, 0, -0, -0, -1, -0, -0],
+                      [0, 0, 0, -1, 0, 0, -0, -0, -0, -1, -0],
+                      [0, 0, 0, 0, -1, 0, -0, -0, -0, -0, -1]], dtype=float)
+        b = np.array([0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], dtype=float)
+        assert (A == A.T).all()
+        self.cases.append(Case("sym-nonpd", A, b,
+                               skip=posdef_solvers,
+                               nonconvergence=[cgs, bicg, bicgstab, qmr, tfqmr]
+                               )
+                          )
+
+    def generate_tests(self):
+        # generate test cases with skips applied
+        tests = []
+        for case in self.cases:
+            for solver in _SOLVERS:
+                if (solver in case.skip):
+                    continue
+                if solver in case.nonconvergence:
+                    tests += [SingleTest(case.A, case.b, solver, case.name,
+                                         convergence=False)]
+                else:
+                    tests += [
+                        SingleTest(case.A, case.b, solver, case.name)
+                    ]
+        return tests
+
+
+cases = IterativeParams().generate_tests()
+
+
+@pytest.fixture(
+    params=[pytest.param(c, marks=make_xp_pytest_marks(c.solver)) for c in cases],
+    ids=[x.name for x in cases],
+    scope="module"
+)
+def case(request):
+    """
+    Fixture for all cases in IterativeParams
+    """
+    return request.param
+
+
+@pytest.mark.parametrize("batch_A", [()])
+@pytest.mark.parametrize("batch_b", [()])
+def test_maxiter(case, xp, batch_A, batch_b):
+    case = xp_case(case, xp, batch_A, batch_b, rng=38)
+    if not case.convergence:
+        pytest.skip("Solver - Breakdown case, see gh-8829")
+    A = case.A
+    rtol = 1e-12
+
+    b = case.b
+    x0 = 0 * b
+
+    residuals = []
+
+    def callback(x):
+        if x.ndim == 0:
+            residuals.append(xp_vector_norm(b - case.A * x))
+        else:
+            Ax = xp.squeeze(case.A @ x[..., xp.newaxis], axis=-1)
+            residuals.append(xp_vector_norm(b - Ax, axis=-1))
+
+    if case.solver == gmres:
+        with pytest.warns(DeprecationWarning, match=CB_TYPE_FILTER):
+            x, info = case.solver(A, b, x0=x0, rtol=rtol, maxiter=1, callback=callback)
+    else:
+        x, info = case.solver(A, b, x0=x0, rtol=rtol, maxiter=1, callback=callback)
+
+    assert len(residuals) == 1
+    assert info == 1
+
+
+@pytest.mark.parametrize("batch_A", [()])
+@pytest.mark.parametrize("batch_b", [()])
+def test_convergence(case, xp, batch_A, batch_b):
+    if (case.solver is tfqmr) and ("poisson2d-F" in case.name):
+        pytest.skip("Struggles to converge with single precision on some platforms")
+    case = xp_case(case, xp, batch_A, batch_b, rng=38)
+    A = case.A
+
+    if A.dtype in (xp.float64, xp.complex128):
+        rtol = 1e-8
+    else:
+        rtol = 1e-2
+
+    b = case.b
+    x0 = 0 * b
+
+    x, info = case.solver(A, b, x0=x0, rtol=rtol)
+    xp_assert_equal(x0, 0 * b)  # ensure that x0 is not overwritten
+
+    if case.convergence:
+        assert info == 0
+        _assert_success(A=A, x=x, b=b, xp=xp, rtol=rtol)
+    else:
+        assert info != 0
+        _assert_success(A=A, x=x, b=b, xp=xp, rtol=1, less_equal=True)
+
+
+@pytest.mark.parametrize("batch_A", [()])
+@pytest.mark.parametrize("batch_b", [()])
+def test_precond_dummy(case, xp, batch_A, batch_b):
+    dtype = case.A.dtype
+    case = xp_case(case, xp, batch_A, batch_b)
+    if (case.solver is cgs) and ("pd-F" in case.name):
+        pytest.skip("Struggles to converge with single precision")
+    if (case.solver is tfqmr) and ("poisson2d-F" in case.name):
+        pytest.skip("Hits divide-by-zero with single precision")
+    if not case.convergence:
+        pytest.skip("Solver - Breakdown case, see gh-8829")
+
+    rtol = 1e-8 if np.finfo(dtype).eps < 1e-8 else 1.2e-3
+
+    A = case.A
+    
+    # NOTE: the following was previously uncommented as dead code --
+    # was the intention to set `A = dia_array(...)`?
+
+    # _, M, N = A.shape
+    # # Ensure the diagonal elements of A are non-zero before calculating
+    # # 1.0 / xp.linalg.diagonal(A)
+    # diagOfA = xp.linalg.diagonal(A) if not is_numpy(xp) else A.diagonal()
+    # if xp.count_nonzero(diagOfA) == diagOfA.shape[0]:
+    #     dia_array(([1.0 / diagOfA], [0]), shape=(M, N))
+
+    b = case.b
+    x0 = 0 * b
+
+    precond = IdentityOperator(shape=A.shape)
+
+    if case.solver is qmr:
+        x, info = case.solver(A, b, M1=precond, M2=precond, x0=x0, rtol=rtol)
+    else:
+        x, info = case.solver(A, b, M=precond, x0=x0, rtol=rtol)
+
+    assert info == 0
+    _assert_success(A=A, x=x, b=b, xp=np, rtol=rtol)
+
+    A = aslinearoperator(A)
+
+    x, info = case.solver(A, b, x0=x0, rtol=rtol)
+    assert info == 0
+    _assert_success(A=A, x=x, b=b, xp=np, rtol=rtol)
+
+
+@pytest.mark.parametrize("batch_A", [()])
+@pytest.mark.parametrize("batch_b", [()])
+@pytest.mark.fail_slow(10)
+def test_precond_inverse(case, xp, batch_A, batch_b):
+    if case.casename not in ('poisson1d', 'poisson2d'):
+        pytest.skip("specific to poisson1d and poisson2d cases")
+    if case.solver is qmr:
+        pytest.skip("skipped for qmr")
+    
+    case = xp_case(case, xp, batch_A, batch_b, rng=38)
+    rtol = 1e-8
+
+    def inverse(b, which=None):
+        """inverse preconditioner"""
+        A = case.A
+        if is_numpy(xp) and not isinstance(A, np.ndarray):
+            A = A.toarray()
+        return xp.linalg.solve(A, b[..., np.newaxis])
+
+    def rinverse(b, which=None):
+        """inverse preconditioner"""
+        A = case.A
+        if is_numpy(xp) and not isinstance(A, np.ndarray):
+            A = A.toarray()
+        return xp.linalg.solve(A.T, b[..., np.newaxis])
+
+    matvec_count = [0]
+
+    def matvec(b):
+        matvec_count[0] += 1
+        return case.A @ b[..., np.newaxis]
+
+    def rmatvec(b):
+        matvec_count[0] += 1
+        return case.A.T @ b[..., np.newaxis]
+
+    b = case.b
+    x0 = 0 * b
+
+    A = LinearOperator(case.A.shape, matvec, rmatvec=rmatvec)
+    precond = LinearOperator(case.A.shape, inverse, rmatvec=rinverse)
+
+    # Solve with preconditioner
+    matvec_count = [0]
+    x, info = case.solver(A, b, M=precond, x0=x0, rtol=rtol)
+
+    assert info == 0
+    _assert_success(A=case.A, x=x, b=b, xp=xp, rtol=rtol)
+
+    # Solution should be nearly instant
+    assert matvec_count[0] <= 3
+
+
+@pytest.mark.skip_xp_backends("dask.array", reason="https://github.com/dask/dask/issues/11711")
+@pytest.mark.parametrize("batch_A", [()])
+@pytest.mark.parametrize("batch_b", [()])
+def test_atol(solver, xp, batch_A, batch_b):
+    # TODO: minres / tfqmr. It didn't historically use absolute tolerances, so
+    # fixing it is less urgent.
+    if solver in (minres, tfqmr):
+        pytest.skip("TODO: Add atol to minres/tfqmr")
+
+    # Historically this is tested as below, all pass but for some reason
+    # gcrotmk is over-sensitive to difference between random.seed/rng.random
+    # Hence tol lower bound is changed from -10 to -9
+    # np.random.seed(1234)
+    # A = np.random.rand(10, 10)
+    # A = A @ A.T + 10 * np.eye(10)
+    # b = 1e3*np.random.rand(10)
+
+    rng = np.random.default_rng(168441431005389)
+    A = rng.uniform(size=(*batch_A, 10, 10))
+    A = A @ A.mT + 10*np.eye(10)
+    b = 1e3 * rng.uniform(size=(*batch_b, 10))
+
+    dtype = xpx.default_dtype(xp)
+    A = xp.asarray(A, dtype=dtype) 
+    b = xp.asarray(b, dtype=dtype)
+
+    tols = np.r_[0, np.logspace(-9, 2, 7), np.inf]
+
+    # Check effect of badly scaled preconditioners
+    M0 = rng.standard_normal(size=(*batch_A, 10, 10))
+    M0 = xp.asarray(M0)
+    M0 = M0 @ M0.mT
+    Ms = [None, 1e-6 * M0, 1e6 * M0]
+
+    for M, rtol, atol in itertools.product(Ms, tols, tols):
+        if rtol == 0 and atol == 0:
+            continue
+
+        if solver is qmr:
+            if M is not None:
+                M = aslinearoperator(M)
+                M2 = IdentityOperator(shape=(*batch_A, 10, 10))
+            else:
+                M2 = None
+            x, info = solver(A, b, M1=M, M2=M2, rtol=rtol, atol=atol)
+        else:
+            x, info = solver(A, b, M=M, rtol=rtol, atol=atol)
+
+        assert info == 0
+        _assert_success(A=A, x=x, b=b, xp=xp, rtol=rtol, atol=atol)
+
+
+@pytest.mark.skip_xp_backends("dask.array", reason="https://github.com/dask/dask/issues/11711")
+@pytest.mark.parametrize("batch_A", [()])
+@pytest.mark.parametrize("batch_b", [()])
+def test_zero_rhs(solver, xp, batch_A, batch_b):
+    rng = np.random.default_rng(1684414984100503)
+    dtype = xpx.default_dtype(xp) 
+    A = xp.asarray(rng.random(size=(*batch_A, 10, 10)), dtype=dtype)
+    A = A @ A.mT + 10 * xp.eye(10)
+
+    b = xp.zeros((*batch_b, 10), dtype=dtype)
+    tols = np.r_[np.logspace(-10, 2, 7)]
+
+    expected = xp.broadcast_to(b, (*np.broadcast_shapes(batch_A, batch_b), 10))
+    for tol in tols:
+        tol = float(tol)
+        x, info = solver(A, b, rtol=tol)
+        assert info == 0
+        xp_assert_close(x, expected, atol=1e-15)
+
+        x, info = solver(A, b, rtol=tol, x0=xp.ones((*batch_b, 10)))
+        assert info == 0
+        xp_assert_close(x, expected, atol=tol)
+
+        if solver is not minres:
+            x, info = solver(A, b, rtol=tol, atol=0.0, x0=xp.ones((*batch_b, 10)))
+            if info == 0:
+                xp_assert_close(x, expected)
+
+            x, info = solver(A, b, rtol=tol, atol=tol)
+            assert info == 0
+            xp_assert_close(x, expected, atol=1e-300)
+
+            x, info = solver(A, b, rtol=tol, atol=0.0)
+            assert info == 0
+            xp_assert_close(x, expected, atol=1e-300)
+
+
+# unbatched test
+@pytest.mark.xfail(reason="see gh-18697")
+def test_maxiter_worsening(solver, xp):
+    if solver not in (gmres, lgmres, qmr):
+        # these were skipped from the very beginning, see gh-9201; gh-14160
+        pytest.skip("Solver breakdown case")
+    # Check error does not grow (boundlessly) with increasing maxiter.
+    # This can occur due to the solvers hitting close to breakdown,
+    # which they should detect and halt as necessary.
+    # cf. gh-9100
+    if (solver is lgmres and
+            platform.machine() not in ['x86_64' 'x86', 'aarch64', 'arm64']):
+        # see gh-17839
+        pytest.xfail(reason="fails on at least ppc64le, ppc64 and riscv64")
+
+    # Singular matrix, rhs numerically not in range
+    A = np.array([[-0.1112795288033378, 0, 0, 0.16127952880333685],
+                  [0, -0.13627952880333782 + 6.283185307179586j, 0, 0],
+                  [0, 0, -0.13627952880333782 - 6.283185307179586j, 0],
+                  [0.1112795288033368, 0j, 0j, -0.16127952880333785]])
+    v = np.ones(4)
+    dtype = xpx.default_dtype(xp)
+    A, v = (xp.asarray(arr, dtype=dtype) for arr in [A, v])
+    best_error = np.inf
+
+    # Unable to match the Fortran code tolerance levels with this example
+    # Original tolerance values
+
+    # slack_tol = 7 if platform.machine() == 'aarch64' else 5
+    slack_tol = 9
+
+    rtol = 1e-8
+    for maxiter in range(1, 20):
+        x, info = solver(A, v, maxiter=maxiter, rtol=rtol, atol=0.0)
+        if info == 0:
+            _assert_success(A=A, x=x, b=v, xp=xp, rtol=rtol)
+
+        # Check with slack
+        error = xp_vector_norm(A @ x - v)
+        best_error = xp.min(best_error, error)
+        assert error <= slack_tol * best_error
+
+
+def _setup_random_system(xp, batch_A, batch_b):
+    rng = np.random.default_rng(1685363802304750)
+    n = 10
+    A = rng.random(size=(*batch_A, n, n))
+    A = A @ A.mT
+    b = rng.random((*batch_b, n))
+    x0 = rng.random((*batch_b, n))
+    dtype = xpx.default_dtype(xp)
+    A, b, x0 = (xp.asarray(arr, dtype=dtype) for arr in [A, b, x0])
+    return A, b, x0
+
+
+@pytest.mark.parametrize("batch_A", [()])
+@pytest.mark.parametrize("batch_b", [()])
+def test_x0_working(solver, xp, batch_A, batch_b):
+    # Easy problem
+    A, b, x0 = _setup_random_system(xp, batch_A, batch_b)
+
+    if solver is minres:
+        kw = dict(rtol=1e-6)
+    else:
+        kw = dict(atol=0.0, rtol=1e-6)
+
+    x, info = solver(A, b, **kw)
+    assert info == 0
+
+    _assert_success(A=A, x=x, b=b, xp=xp, rtol=1e-6)
+
+    x, info = solver(A, b, x0=x0, **kw)
+    assert info == 0
+    _assert_success(A=A, x=x, b=b, xp=xp, rtol=1e-5)
+
+
+@pytest.mark.parametrize("batch_A", [()])
+@pytest.mark.parametrize("batch_b", [()])
+def test_x0_equals_Mb(case, xp, batch_A, batch_b):
+    dtype = case.A.dtype
+    case = xp_case(case, xp, batch_A, batch_b, rng=38)
+    if (case.solver is cgs) and ("pd-F" in case.name):
+        pytest.skip("Struggles to converge with single precision")
+    if (case.solver is bicgstab) and (case.name == 'nonsymposdef-bicgstab'):
+        pytest.skip("Solver fails due to numerical noise "
+                    "on some architectures (see gh-15533).")
+    if case.solver is tfqmr:
+        pytest.skip("Solver does not support x0='Mb'")
+
+    A = case.A
+    b = case.b
+    x0 = 'Mb'
+    rtol = 1e-8 if np.finfo(dtype).eps < 1e-8 else 1.5e-3
+    x, info = case.solver(A, b, x0=x0, rtol=rtol)
+
+    assert x0 == 'Mb'  # ensure that x0 is not overwritten
+    assert info == 0
+    _assert_success(A=A, x=x, b=b, xp=xp, rtol=rtol)
+
+
+@pytest.mark.parametrize("batch_A", [()])
+@pytest.mark.parametrize("batch_b", [()])
+def test_x0_solves_problem_exactly(solver, xp, batch_A, batch_b):
+    # See gh-19948
+    dtype = xpx.default_dtype(xp)
+    mat = xp.tile(xp.eye(2, dtype=dtype), (*batch_A, 1, 1))
+    rhs = xp.tile(xp.asarray([-1., -1.], dtype=dtype), (*batch_b, 1))
+
+    sol, info = solver(mat, rhs, x0=rhs)
+    expected = xp.broadcast_to(rhs, (*np.broadcast_shapes(batch_A, batch_b), 2))
+    xp_assert_close(sol, expected)
+    assert info == 0
+
+
+@pytest.mark.parametrize("batch_A", [()])
+@pytest.mark.parametrize("batch_b", [()])
+def test_show(case, capsys, xp, batch_A, batch_b):
+    if case.solver != tfqmr:
+        pytest.skip("tfqmr specific test")
+    if "poisson2d-F" in case.name:
+        pytest.skip("Hits divide-by-zero with single precision")
+    if "pd-F" in case.name:
+        pytest.skip("Struggles to converge with single precision on some platforms")
+    case = xp_case(case, xp, batch_A, batch_b)
+    def cb(x):
+        pass
+
+    ctx = (
+        np.errstate(all='ignore')
+        if case.casename == "nonsymposdef"
+        else nullcontext()
+    )
+    with ctx:
+        x, info = tfqmr(case.A, case.b, callback=cb, show=True)
+
+    out, err = capsys.readouterr()
+
+    if case.casename == "sym-nonpd":
+        # no logs for some reason
+        exp = ""
+    elif case.casename in ("nonsymposdef", "nonsymposdef-F"):
+        # Asymmetric and Positive Definite
+        exp = "TFQMR: Linear solve not converged due to reach MAXIT iterations"
+    else:  # all other cases
+        exp = "TFQMR: Linear solve converged due to reach TOL iterations"
+
+    assert out.startswith(exp)
+    assert err == ""
+
+
+@pytest.mark.parametrize("batch_A", [()])
+@pytest.mark.parametrize("batch_b", [()])
+def test_positional_error(solver, xp, batch_A, batch_b):
+    A, b, x0 = _setup_random_system(xp, batch_A, batch_b)
+    with pytest.raises(TypeError):
+        solver(A, b, x0, 1e-5)
+
+
+@pytest.mark.parametrize("batch_A", [()])
+@pytest.mark.parametrize("batch_b", [()])
+@pytest.mark.parametrize("atol", ["legacy", None, -1])
+def test_invalid_atol(solver, atol, xp, batch_A, batch_b):
+    if solver == minres:
+        pytest.skip("minres has no `atol` argument")
+    A, b, x0 = _setup_random_system(xp, batch_A, batch_b)
+    with pytest.raises(ValueError):
+        solver(A, b, x0, atol=atol)
+
+
+class TestQMR:
+    @pytest.mark.filterwarnings('ignore::scipy.sparse.SparseEfficiencyWarning')
+    def test_leftright_precond(self):
+        """Check that QMR works with left and right preconditioners"""
+
+        from scipy.sparse.linalg._dsolve import splu
+        from scipy.sparse.linalg._interface import LinearOperator
+
+        n = 100
+
+        dat = ones(n)
+        A = dia_array(([-2 * dat, 4 * dat, -dat], [-1, 0, 1]), shape=(n, n))
+        b = arange(n, dtype='d')
+
+        L = dia_array(([-dat / 2, dat], [-1, 0]), shape=(n, n))
+        U = dia_array(([4 * dat, -dat], [0, 1]), shape=(n, n))
+        L_solver = splu(L)
+        U_solver = splu(U)
+
+        def L_solve(b):
+            return L_solver.solve(b)
+
+        def U_solve(b):
+            return U_solver.solve(b)
+
+        def LT_solve(b):
+            return L_solver.solve(b, 'T')
+
+        def UT_solve(b):
+            return U_solver.solve(b, 'T')
+
+        M1 = LinearOperator((n, n), matvec=L_solve, rmatvec=LT_solve)
+        M2 = LinearOperator((n, n), matvec=U_solve, rmatvec=UT_solve)
+
+        rtol = 1e-8
+        x, info = qmr(A, b, rtol=rtol, maxiter=15, M1=M1, M2=M2)
+
+        assert info == 0
+        assert xp_vector_norm(A @ x - b) <= rtol * xp_vector_norm(b)
+
+
+class TestGMRES:
+    def test_basic(self):
+        A = np.vander(np.arange(10) + 1)[:, ::-1]
+        b = np.zeros(10)
+        b[0] = 1
+
+        x_gm, err = gmres(A, b, restart=5, maxiter=1)
+
+        assert_allclose(x_gm[0], 0.359, rtol=1e-2)
+
+    @pytest.mark.filterwarnings(f"ignore:{CB_TYPE_FILTER}:DeprecationWarning")
+    def test_callback(self):
+
+        def store_residual(r, rvec):
+            rvec[rvec.nonzero()[0].max() + 1] = r
+
+        # Define, A,b
+        A = csr_array(array([[-2, 1, 0, 0, 0, 0],
+                             [1, -2, 1, 0, 0, 0],
+                             [0, 1, -2, 1, 0, 0],
+                             [0, 0, 1, -2, 1, 0],
+                             [0, 0, 0, 1, -2, 1],
+                             [0, 0, 0, 0, 1, -2]]))
+        b = ones((A.shape[0],))
+        maxiter = 1
+        rvec = zeros(maxiter + 1)
+        rvec[0] = 1.0
+
+        def callback(r):
+            return store_residual(r, rvec)
+
+        x, flag = gmres(A, b, x0=zeros(A.shape[0]), rtol=1e-16,
+                        maxiter=maxiter, callback=callback)
+
+        # Expected output from SciPy 1.0.0
+        assert_allclose(rvec, array([1.0, 0.81649658092772603]), rtol=1e-10)
+
+        # Test preconditioned callback
+        M = 1e-3 * np.eye(A.shape[0])
+        rvec = zeros(maxiter + 1)
+        rvec[0] = 1.0
+        x, flag = gmres(A, b, M=M, rtol=1e-16, maxiter=maxiter,
+                        callback=callback)
+
+        # Expected output from SciPy 1.0.0
+        # (callback has preconditioned residual!)
+        assert_allclose(rvec, array([1.0, 1e-3 * 0.81649658092772603]),
+                        rtol=1e-10)
+
+    def test_abi(self):
+        # Check we don't segfault on gmres with complex argument
+        A = eye(2)
+        b = ones(2)
+        r_x, r_info = gmres(A, b)
+        r_x = r_x.astype(complex)
+        x, info = gmres(A.astype(complex), b.astype(complex))
+
+        assert iscomplexobj(x)
+        assert_allclose(r_x, x)
+        assert r_info == info
+
+    @pytest.mark.fail_slow(10)
+    def test_atol_legacy(self):
+
+        A = eye(2)
+        b = ones(2)
+        x, info = gmres(A, b, rtol=1e-5)
+        assert xp_vector_norm(A @ x - b) <= 1e-5 * xp_vector_norm(b)
+        assert_allclose(x, b, atol=0.0, rtol=1e-8)
+
+        rndm = np.random.RandomState(12345)
+        A = rndm.rand(30, 30)
+        b = 1e-6 * ones(30)
+        x, info = gmres(A, b, rtol=1e-7, restart=20)
+        assert xp_vector_norm(A @ x - b) > 1e-7
+
+        A = eye(2)
+        b = 1e-10 * ones(2)
+        x, info = gmres(A, b, rtol=1e-8, atol=0.0)
+        assert xp_vector_norm(A @ x - b) <= 1e-8 * xp_vector_norm(b)
+
+    def test_defective_precond_breakdown(self):
+        # Breakdown due to defective preconditioner
+        M = np.eye(3)
+        M[2, 2] = 0
+
+        b = np.array([0, 1, 1])
+        x = np.array([1, 0, 0])
+        A = np.diag([2, 3, 4])
+
+        x, info = gmres(A, b, x0=x, M=M, rtol=1e-15, atol=0.0)
+
+        # Should not return nans, nor terminate with false success
+        assert not np.isnan(x).any()
+        if info == 0:
+            assert xp_vector_norm(A @ x - b) <= 1e-15 * xp_vector_norm(b)
+
+        # The solution should be OK outside null space of M
+        assert_allclose(M @ (A @ x), M @ b)
+
+    def test_defective_matrix_breakdown(self):
+        # Breakdown due to defective matrix
+        A = np.array([[0, 1, 0], [1, 0, 0], [0, 0, 0]])
+        b = np.array([1, 0, 1])
+        rtol = 1e-8
+        x, info = gmres(A, b, rtol=rtol, atol=0)
+
+        # Should not return nans, nor terminate with false success
+        assert not np.isnan(x).any()
+        if info == 0:
+            assert xp_vector_norm(A @ x - b) <= rtol * xp_vector_norm(b)
+
+        # The solution should be OK outside null space of A
+        assert_allclose(A @ (A @ x), A @ b)
+
+    @pytest.mark.filterwarnings(f"ignore:{CB_TYPE_FILTER}:DeprecationWarning")
+    def test_callback_type(self):
+        # The legacy callback type changes meaning of 'maxiter'
+        np.random.seed(1)
+        A = np.random.rand(20, 20)
+        b = np.random.rand(20)
+
+        cb_count = [0]
+
+        def pr_norm_cb(r):
+            cb_count[0] += 1
+            assert isinstance(r, float)
+
+        def x_cb(x):
+            cb_count[0] += 1
+            assert isinstance(x, np.ndarray)
+
+        # 2 iterations is not enough to solve the problem
+        cb_count = [0]
+        x, info = gmres(A, b, rtol=1e-6, atol=0.0, callback=pr_norm_cb,
+                        maxiter=2, restart=50)
+        assert info == 2
+        assert cb_count[0] == 2
+
+        # With `callback_type` specified, no warning should be raised
+        cb_count = [0]
+        x, info = gmres(A, b, rtol=1e-6, atol=0.0, callback=pr_norm_cb,
+                        maxiter=2, restart=50, callback_type='legacy')
+        assert info == 2
+        assert cb_count[0] == 2
+
+        # 2 restart cycles is enough to solve the problem
+        cb_count = [0]
+        x, info = gmres(A, b, rtol=1e-6, atol=0.0, callback=pr_norm_cb,
+                        maxiter=2, restart=50, callback_type='pr_norm')
+        assert info == 0
+        assert cb_count[0] > 2
+
+        # 2 restart cycles is enough to solve the problem
+        cb_count = [0]
+        x, info = gmres(A, b, rtol=1e-6, atol=0.0, callback=x_cb, maxiter=2,
+                        restart=50, callback_type='x')
+        assert info == 0
+        assert cb_count[0] == 1
+
+    def test_callback_x_monotonic(self):
+        # Check that callback_type='x' gives monotonic norm decrease
+        rng = np.random.RandomState(1)
+        A = rng.rand(20, 20) + np.eye(20)
+        b = rng.rand(20)
+
+        prev_r = [np.inf]
+        count = [0]
+
+        def x_cb(x):
+            r = xp_vector_norm(A @ x - b)
+            assert r <= prev_r[0]
+            prev_r[0] = r
+            count[0] += 1
+
+        x, info = gmres(A, b, rtol=1e-6, atol=0.0, callback=x_cb, maxiter=20,
+                        restart=10, callback_type='x')
+        assert info == 20
+        assert count[0] == 20
+
+
+def test_nD(solver, xp):
+    """Check that >2-D operators are rejected cleanly."""
+    def id(x):
+        return x
+    A = LinearOperator(shape=(2, 2, 2), matvec=id, dtype=xp.float64, xp=xp)
+    b = xp.ones((2, 2))
+    with pytest.raises(ValueError, match="expected 2-D"):
+        solver(A, b)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_isolve/tests/test_lgmres.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_isolve/tests/test_lgmres.py
new file mode 100644
index 0000000000000000000000000000000000000000..d66f0b950f3d70d5e36223c767d65cf2718e8287
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_isolve/tests/test_lgmres.py
@@ -0,0 +1,228 @@
+"""Tests for the linalg._isolve.lgmres module
+"""
+import threading
+import warnings
+
+from numpy.testing import (assert_, assert_allclose, assert_equal)
+
+
+import numpy as np
+from numpy import zeros, array, allclose
+from scipy.linalg import norm
+from scipy.sparse import csr_array, eye_array, random_array
+
+from scipy.sparse.linalg._interface import LinearOperator
+from scipy.sparse.linalg import splu
+from scipy.sparse.linalg._isolve import lgmres, gmres
+
+
+Am = csr_array(array([[-2, 1, 0, 0, 0, 9],
+                      [1, -2, 1, 0, 5, 0],
+                      [0, 1, -2, 1, 0, 0],
+                      [0, 0, 1, -2, 1, 0],
+                      [0, 3, 0, 1, -2, 1],
+                      [1, 0, 0, 0, 1, -2]]))
+b = array([1, 2, 3, 4, 5, 6])
+count = threading.local()  # [0]
+niter = threading.local()  # [0]
+
+
+def matvec(v):
+    if not hasattr(count, 'c'):
+        count.c = [0]
+    count.c[0] += 1
+    return Am@v
+
+
+def cb(v):
+    if not hasattr(niter, 'n'):
+        niter.n = [0]
+    niter.n[0] += 1
+
+
+A = LinearOperator(matvec=matvec, shape=Am.shape, dtype=Am.dtype)
+
+
+def do_solve(**kw):
+    if not hasattr(niter, 'n'):
+        niter.n = [0]
+    if not hasattr(count, 'c'):
+        count.c = [0]
+    count.c[0] = 0
+    with warnings.catch_warnings():
+        warnings.filterwarnings(
+            "ignore", ".*called without specifying.*", DeprecationWarning)
+        x0, flag = lgmres(A, b, x0=zeros(A.shape[0]),
+                          inner_m=6, rtol=1e-14, **kw)
+    count_0 = count.c[0]
+    assert_(allclose(A@x0, b, rtol=1e-12, atol=1e-12), norm(A@x0-b))
+    return x0, count_0
+
+
+class TestLGMRES:
+    def test_preconditioner(self):
+        # Check that preconditioning works
+        pc = splu(Am.tocsc())
+        M = LinearOperator(matvec=pc.solve, shape=A.shape, dtype=A.dtype)
+
+        x0, count_0 = do_solve()
+        niter.n[0] = 0
+        x1, count_1 = do_solve(M=M, callback=cb)
+
+        assert count_1 == 3
+        assert count_1 < count_0/2
+        assert allclose(x1, x0, rtol=1e-14)
+        assert niter.n[0] < 3
+
+    def test_outer_v(self):
+        # Check that the augmentation vectors behave as expected
+
+        outer_v = []
+        x0, count_0 = do_solve(outer_k=6, outer_v=outer_v)
+        assert_(len(outer_v) > 0)
+        assert_(len(outer_v) <= 6)
+
+        x1, count_1 = do_solve(outer_k=6, outer_v=outer_v,
+                               prepend_outer_v=True)
+        assert_(count_1 == 2, count_1)
+        assert_(count_1 < count_0/2)
+        assert_(allclose(x1, x0, rtol=1e-14))
+
+        # ---
+
+        outer_v = []
+        x0, count_0 = do_solve(outer_k=6, outer_v=outer_v,
+                               store_outer_Av=False)
+        assert_(array([v[1] is None for v in outer_v]).all())
+        assert_(len(outer_v) > 0)
+        assert_(len(outer_v) <= 6)
+
+        x1, count_1 = do_solve(outer_k=6, outer_v=outer_v,
+                               prepend_outer_v=True)
+        assert_(count_1 == 3, count_1)
+        assert_(count_1 < count_0/2)
+        assert_(allclose(x1, x0, rtol=1e-14))
+
+    def test_arnoldi(self):
+        rng = np.random.default_rng(123)
+
+        A = eye_array(2000) + random_array((2000, 2000), density=5e-4, rng=rng)
+        b = rng.random(2000)
+
+        # The inner arnoldi should be equivalent to gmres
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", ".*called without specifying.*", DeprecationWarning)
+            x0, flag0 = lgmres(A, b, x0=zeros(A.shape[0]), inner_m=10, maxiter=1)
+            x1, flag1 = gmres(A, b, x0=zeros(A.shape[0]), restart=10, maxiter=1)
+
+        assert_equal(flag0, 1)
+        assert_equal(flag1, 1)
+        norm = np.linalg.norm(A.dot(x0) - b)
+        assert_(norm > 1e-4)
+        assert_allclose(x0, x1)
+
+    def test_cornercase(self):
+        rng = np.random.RandomState(1234)
+
+        # Rounding error may prevent convergence with tol=0 --- ensure
+        # that the return values in this case are correct, and no
+        # exceptions are raised
+
+        for n in [3, 5, 10, 100]:
+            A = 2*eye_array(n)
+
+            with warnings.catch_warnings():
+                warnings.filterwarnings(
+                    "ignore", ".*called without specifying.*", DeprecationWarning)
+
+                b = np.ones(n)
+                x, info = lgmres(A, b, maxiter=10)
+                assert_equal(info, 0)
+                assert_allclose(A.dot(x) - b, 0, atol=1e-14)
+
+                x, info = lgmres(A, b, rtol=0, maxiter=10)
+                if info == 0:
+                    assert_allclose(A.dot(x) - b, 0, atol=1e-14)
+
+                b = rng.rand(n)
+                x, info = lgmres(A, b, maxiter=10)
+                assert_equal(info, 0)
+                assert_allclose(A.dot(x) - b, 0, atol=1e-14)
+
+                x, info = lgmres(A, b, rtol=0, maxiter=10)
+                if info == 0:
+                    assert_allclose(A.dot(x) - b, 0, atol=1e-14)
+
+    def test_nans(self):
+        A = eye_array(3, format='lil')
+        A[1, 1] = np.nan
+        b = np.ones(3)
+
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", ".*called without specifying.*", DeprecationWarning)
+            x, info = lgmres(A, b, rtol=0, maxiter=10)
+            assert_equal(info, 1)
+
+    def test_breakdown_with_outer_v(self):
+        A = np.array([[1, 2], [3, 4]], dtype=float)
+        b = np.array([1, 2])
+
+        x = np.linalg.solve(A, b)
+        v0 = np.array([1, 0])
+
+        # The inner iteration should converge to the correct solution,
+        # since it's in the outer vector list
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", ".*called without specifying.*", DeprecationWarning)
+            xp, info = lgmres(A, b, outer_v=[(v0, None), (x, None)], maxiter=1)
+
+        assert_allclose(xp, x, atol=1e-12)
+
+    def test_breakdown_underdetermined(self):
+        # Should find LSQ solution in the Krylov span in one inner
+        # iteration, despite solver breakdown from nilpotent A.
+        A = np.array([[0, 1, 1, 1],
+                      [0, 0, 1, 1],
+                      [0, 0, 0, 1],
+                      [0, 0, 0, 0]], dtype=float)
+
+        bs = [
+            np.array([1, 1, 1, 1]),
+            np.array([1, 1, 1, 0]),
+            np.array([1, 1, 0, 0]),
+            np.array([1, 0, 0, 0]),
+        ]
+
+        for b in bs:
+            with warnings.catch_warnings():
+                warnings.filterwarnings(
+                    "ignore", ".*called without specifying.*", DeprecationWarning)
+                xp, info = lgmres(A, b, maxiter=1)
+            resp = np.linalg.norm(A.dot(xp) - b)
+
+            K = np.c_[b, A.dot(b), A.dot(A.dot(b)), A.dot(A.dot(A.dot(b)))]
+            y, _, _, _ = np.linalg.lstsq(A.dot(K), b, rcond=-1)
+            x = K.dot(y)
+            res = np.linalg.norm(A.dot(x) - b)
+
+            assert_allclose(resp, res, err_msg=repr(b))
+
+    def test_denormals(self):
+        # Check that no warnings are emitted if the matrix contains
+        # numbers for which 1/x has no float representation, and that
+        # the solver behaves properly.
+        A = np.array([[1, 2], [3, 4]], dtype=float)
+        A *= 100 * np.nextafter(0, 1)
+
+        b = np.array([1, 1])
+
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", ".*called without specifying.*", DeprecationWarning)
+            xp, info = lgmres(A, b)
+
+        if info == 0:
+            assert_allclose(A.dot(xp), b)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_isolve/tests/test_lsmr.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_isolve/tests/test_lsmr.py
new file mode 100644
index 0000000000000000000000000000000000000000..71a7c9ecb1387f54e3c5857adbe701a738e80f1c
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_isolve/tests/test_lsmr.py
@@ -0,0 +1,205 @@
+"""
+Copyright (C) 2010 David Fong and Michael Saunders
+Distributed under the same license as SciPy
+
+Testing Code for LSMR.
+
+03 Jun 2010: First version release with lsmr.py
+
+David Chin-lung Fong            clfong@stanford.edu
+Institute for Computational and Mathematical Engineering
+Stanford University
+
+Michael Saunders                saunders@stanford.edu
+Systems Optimization Laboratory
+Dept of MS&E, Stanford University.
+
+"""
+
+import numpy as np
+from numpy import array, arange, eye, zeros, ones, transpose, hstack
+from numpy.linalg import norm
+from numpy.testing import assert_allclose
+import pytest
+from scipy.sparse import coo_array
+from scipy.sparse.linalg import lsmr, LinearOperator, aslinearoperator
+from .test_lsqr import G, b
+
+
+class TestLSMR:
+    def setup_method(self):
+        self.n = 10
+        self.m = 10
+
+    def assertCompatibleSystem(self, A, xtrue):
+        Afun = aslinearoperator(A)
+        b = Afun.matvec(xtrue)
+        x = lsmr(A, b)[0]
+        assert norm(x - xtrue) == pytest.approx(0, abs=1e-5)
+
+    def testIdentityACase1(self):
+        A = eye(self.n)
+        xtrue = zeros((self.n,))
+        self.assertCompatibleSystem(A, xtrue)
+
+    def testIdentityACase2(self):
+        A = eye(self.n)
+        xtrue = ones((self.n,))
+        self.assertCompatibleSystem(A, xtrue)
+
+    def testIdentityACase3(self):
+        A = eye(self.n)
+        xtrue = transpose(arange(self.n,0,-1))
+        self.assertCompatibleSystem(A, xtrue)
+
+    def testBidiagonalA(self):
+        A = lowerBidiagonalMatrix(20,self.n)
+        xtrue = transpose(arange(self.n,0,-1))
+        self.assertCompatibleSystem(A,xtrue)
+
+    def testScalarB(self):
+        A = array([[1.0, 2.0]])
+        b = 3.0
+        x = lsmr(A, b)[0]
+        assert norm(A.dot(x) - b) == pytest.approx(0)
+
+    def testComplexX(self):
+        A = eye(self.n)
+        xtrue = transpose(arange(self.n, 0, -1) * (1 + 1j))
+        self.assertCompatibleSystem(A, xtrue)
+
+    def testComplexX0(self):
+        A = 4 * eye(self.n) + ones((self.n, self.n))
+        xtrue = transpose(arange(self.n, 0, -1))
+        b = aslinearoperator(A).matvec(xtrue)
+        x0 = zeros(self.n, dtype=complex)
+        x = lsmr(A, b, x0=x0)[0]
+        assert norm(x - xtrue) == pytest.approx(0, abs=1e-5)
+
+    def testComplexA(self):
+        A = 4 * eye(self.n) + 1j * ones((self.n, self.n))
+        xtrue = transpose(arange(self.n, 0, -1).astype(complex))
+        self.assertCompatibleSystem(A, xtrue)
+
+    def testComplexB(self):
+        A = 4 * eye(self.n) + ones((self.n, self.n))
+        xtrue = transpose(arange(self.n, 0, -1) * (1 + 1j))
+        b = aslinearoperator(A).matvec(xtrue)
+        x = lsmr(A, b)[0]
+        assert norm(x - xtrue) == pytest.approx(0, abs=1e-5)
+
+    def testColumnB(self):
+        A = eye(self.n)
+        b = ones((self.n, 1))
+        x = lsmr(A, b)[0]
+        assert norm(A.dot(x) - b.ravel()) == pytest.approx(0)
+
+    def testInitialization(self):
+        # Test that the default setting is not modified
+        x_ref, _, itn_ref, normr_ref, *_ = lsmr(G, b)
+        assert_allclose(norm(b - G@x_ref), normr_ref, atol=1e-6)
+
+        # Test passing zeros yields similar result
+        x0 = zeros(b.shape)
+        x = lsmr(G, b, x0=x0)[0]
+        assert_allclose(x, x_ref)
+
+        # Test warm-start with single iteration
+        x0 = lsmr(G, b, maxiter=1)[0]
+
+        x, _, itn, normr, *_ = lsmr(G, b, x0=x0)
+        assert_allclose(norm(b - G@x), normr, atol=1e-6)
+
+        # NOTE(gh-12139): This doesn't always converge to the same value as
+        # ref because error estimates will be slightly different when calculated
+        # from zeros vs x0 as a result only compare norm and itn (not x).
+
+        # x generally converges 1 iteration faster because it started at x0.
+        # itn == itn_ref means that lsmr(x0) took an extra iteration see above.
+        # -1 is technically possible but is rare (1 in 100000) so it's more
+        # likely to be an error elsewhere.
+        assert itn - itn_ref in (0, 1)
+
+        # If an extra iteration is performed normr may be 0, while normr_ref
+        # may be much larger.
+        assert normr < normr_ref * (1 + 1e-6)
+
+
+class TestLSMRReturns:
+    def setup_method(self):
+        self.n = 10
+        self.A = lowerBidiagonalMatrix(20, self.n)
+        self.xtrue = transpose(arange(self.n, 0, -1))
+        self.Afun = aslinearoperator(self.A)
+        self.b = self.Afun.matvec(self.xtrue)
+        self.x0 = ones(self.n)
+        self.x00 = self.x0.copy()
+        self.returnValues = lsmr(self.A, self.b)
+        self.returnValuesX0 = lsmr(self.A, self.b, x0=self.x0)
+
+    def test_unchanged_x0(self):
+        x, istop, itn, normr, normar, normA, condA, normx = self.returnValuesX0
+        assert_allclose(self.x00, self.x0)
+
+    def testNormr(self):
+        x, istop, itn, normr, normar, normA, condA, normx = self.returnValues
+        assert norm(self.b - self.Afun.matvec(x)) == pytest.approx(normr)
+
+    def testNormar(self):
+        x, istop, itn, normr, normar, normA, condA, normx = self.returnValues
+        assert (norm(self.Afun.rmatvec(self.b - self.Afun.matvec(x)))
+                == pytest.approx(normar))
+
+    def testNormx(self):
+        x, istop, itn, normr, normar, normA, condA, normx = self.returnValues
+        assert norm(x) == pytest.approx(normx)
+
+
+def lowerBidiagonalMatrix(m, n):
+    # This is a simple example for testing LSMR.
+    # It uses the leading m*n submatrix from
+    # A = [ 1
+    #       1 2
+    #         2 3
+    #           3 4
+    #             ...
+    #               n ]
+    # suitably padded by zeros.
+    #
+    # 04 Jun 2010: First version for distribution with lsmr.py
+    if m <= n:
+        row = hstack((arange(m, dtype=int),
+                      arange(1, m, dtype=int)))
+        col = hstack((arange(m, dtype=int),
+                      arange(m-1, dtype=int)))
+        data = hstack((arange(1, m+1, dtype=float),
+                       arange(1,m, dtype=float)))
+        return coo_array((data, (row, col)), shape=(m,n))
+    else:
+        row = hstack((arange(n, dtype=int),
+                      arange(1, n+1, dtype=int)))
+        col = hstack((arange(n, dtype=int),
+                      arange(n, dtype=int)))
+        data = hstack((arange(1, n+1, dtype=float),
+                       arange(1,n+1, dtype=float)))
+        return coo_array((data,(row, col)), shape=(m,n))
+
+def test_lsmr_maxiter_zero_with_show():
+    # Test that lsmr does not crash when maxiter=0 and show=True
+    # Regression test for gh-23748 (str4 undefined variable bug)
+    A = eye(3)
+    b = ones(3)
+    result = lsmr(A, b, maxiter=0, show=True)
+    # Check that we get a valid result with zero iterations
+    assert result[0] is not None  # x should exist
+    assert result[1] == 0  # istop should be 0
+    assert result[2] == 0  # itn should be 0
+
+def test_nD():
+    """Check that >2-D operators are rejected cleanly."""
+    def id(x):
+        return x
+    A = LinearOperator(shape=(2, 2, 2), matvec=id, dtype=np.float64)
+    b = np.ones((2, 2))
+    with pytest.raises(ValueError, match="expected 2-D"):
+        lsmr(A, b)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_isolve/tests/test_lsqr.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_isolve/tests/test_lsqr.py
new file mode 100644
index 0000000000000000000000000000000000000000..339704b0a339a52cc970354bddfe62f9ad372b61
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_isolve/tests/test_lsqr.py
@@ -0,0 +1,128 @@
+import numpy as np
+from numpy.testing import assert_allclose, assert_array_equal, assert_equal
+import pytest
+import scipy.sparse
+from scipy.sparse.linalg import lsqr, LinearOperator
+
+# Set up a test problem
+n = 35
+G = np.eye(n)
+normal = np.random.normal
+norm = np.linalg.norm
+
+for jj in range(5):
+    gg = normal(size=n)
+    hh = gg * gg.T
+    G += (hh + hh.T) * 0.5
+    G += normal(size=n) * normal(size=n)
+
+b = normal(size=n)
+
+# tolerance for atol/btol keywords of lsqr()
+tol = 2e-10
+# tolerances for testing the results of the lsqr() call with assert_allclose
+# These tolerances are a bit fragile - see discussion in gh-15301.
+atol_test = 4e-10
+rtol_test = 2e-8
+show = False
+maxit = None
+
+
+def test_lsqr_basic():
+    b_copy = b.copy()
+    xo, *_ = lsqr(G, b, show=show, atol=tol, btol=tol, iter_lim=maxit)
+    assert_array_equal(b_copy, b)
+
+    svx = np.linalg.solve(G, b)
+    assert_allclose(xo, svx, atol=atol_test, rtol=rtol_test)
+
+    # Now the same but with damp > 0.
+    # This is equivalent to solving the extended system:
+    # ( G      ) @ x = ( b )
+    # ( damp*I )       ( 0 )
+    damp = 1.5
+    xo, *_ = lsqr(
+        G, b, damp=damp, show=show, atol=tol, btol=tol, iter_lim=maxit)
+
+    Gext = np.r_[G, damp * np.eye(G.shape[1])]
+    bext = np.r_[b, np.zeros(G.shape[1])]
+    svx, *_ = np.linalg.lstsq(Gext, bext, rcond=None)
+    assert_allclose(xo, svx, atol=atol_test, rtol=rtol_test)
+
+
+def test_gh_2466():
+    row = np.array([0, 0])
+    col = np.array([0, 1])
+    val = np.array([1, -1])
+    A = scipy.sparse.coo_array((val, (row, col)), shape=(1, 2))
+    b = np.asarray([4])
+    lsqr(A, b)
+
+
+def test_well_conditioned_problems():
+    # Test that sparse the lsqr solver returns the right solution
+    # on various problems with different random seeds.
+    # This is a non-regression test for a potential ZeroDivisionError
+    # raised when computing the `test2` & `test3` convergence conditions.
+    n = 10
+    A_sparse = scipy.sparse.eye_array(n, n)
+    A_dense = A_sparse.toarray()
+
+    with np.errstate(invalid='raise'):
+        for seed in range(30):
+            rng = np.random.RandomState(seed + 10)
+            beta = rng.rand(n)
+            beta[beta == 0] = 0.00001  # ensure that all the betas are not null
+            b = A_sparse @ beta[:, np.newaxis]
+            output = lsqr(A_sparse, b, show=show)
+
+            # Check that the termination condition corresponds to an approximate
+            # solution to Ax = b
+            assert_equal(output[1], 1)
+            solution = output[0]
+
+            # Check that we recover the ground truth solution
+            assert_allclose(solution, beta)
+
+            # Sanity check: compare to the dense array solver
+            reference_solution = np.linalg.solve(A_dense, b).ravel()
+            assert_allclose(solution, reference_solution)
+
+
+def test_b_shapes():
+    # Test b being a scalar.
+    A = np.array([[1.0, 2.0]])
+    b = 3.0
+    x = lsqr(A, b)[0]
+    assert norm(A.dot(x) - b) == pytest.approx(0)
+
+    # Test b being a column vector.
+    A = np.eye(10)
+    b = np.ones((10, 1))
+    x = lsqr(A, b)[0]
+    assert norm(A.dot(x) - b.ravel()) == pytest.approx(0)
+
+
+def test_initialization():
+    # Test the default setting is the same as zeros
+    b_copy = b.copy()
+    x_ref = lsqr(G, b, show=show, atol=tol, btol=tol, iter_lim=maxit)
+    x0 = np.zeros(x_ref[0].shape)
+    x = lsqr(G, b, show=show, atol=tol, btol=tol, iter_lim=maxit, x0=x0)
+    assert_array_equal(b_copy, b)
+    assert_allclose(x_ref[0], x[0])
+
+    # Test warm-start with single iteration
+    x0 = lsqr(G, b, show=show, atol=tol, btol=tol, iter_lim=1)[0]
+    x = lsqr(G, b, show=show, atol=tol, btol=tol, iter_lim=maxit, x0=x0)
+    assert_allclose(x_ref[0], x[0])
+    assert_array_equal(b_copy, b)
+
+def test_nD():
+    """Check that >2-D operators are rejected cleanly."""
+    def id(x):
+        return x
+    A = LinearOperator(shape=(2, 2, 2), matvec=id, dtype=np.float64)
+    b = np.ones((2, 2))
+    with pytest.raises(ValueError, match="expected 2-D"):
+        lsqr(A, b)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_isolve/tests/test_minres.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_isolve/tests/test_minres.py
new file mode 100644
index 0000000000000000000000000000000000000000..847eb75771b976d7f42dff0975dece49be092a26
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_isolve/tests/test_minres.py
@@ -0,0 +1,134 @@
+import numpy as np
+from numpy.linalg import norm
+from numpy.testing import assert_equal, assert_allclose, assert_
+from scipy.sparse.linalg._isolve import minres
+import pytest
+from functools import lru_cache
+
+from pytest import raises as assert_raises
+
+@lru_cache
+def _cached_sample_problem(make_complex: bool):
+    # A random 10 x 10 symmetric matrix
+    rng = np.random.RandomState(1234)
+    if make_complex:
+        matrix = rng.rand(10, 10) + 1j * rng.rand(10, 10)
+        matrix = matrix + matrix.T.conj()
+    else:
+        matrix = rng.rand(10, 10)
+        matrix = matrix + matrix.T
+    # A random vector of length 10
+    vector = rng.rand(10)
+    return matrix, vector
+
+def get_sample_problem():
+    A, b = _cached_sample_problem(False)
+    return A.copy(), b.copy()
+
+def get_sample_problem_complex():
+    A, b = _cached_sample_problem(True)
+    return A.copy(), b.copy()
+
+@pytest.mark.parametrize("problem_func",
+                         [get_sample_problem, get_sample_problem_complex])
+def test_singular(problem_func):
+    A, b = problem_func()
+    A[0, ] = 0
+    b[0] = 0
+    xp, info = minres(A, b)
+    assert_equal(info, 0)
+    assert norm(A @ xp - b) <= 1e-5 * norm(b)
+
+@pytest.mark.parametrize("problem_func",
+                         [get_sample_problem, get_sample_problem_complex])
+def test_x0_is_used_by(problem_func):
+    A, b = problem_func()
+    # Random x0 to feed minres
+    rng = np.random.RandomState(12345)
+    x0 = rng.rand(10)
+    trace = []
+
+    def trace_iterates(xk):
+        trace.append(xk)
+    minres(A, b, x0=x0, callback=trace_iterates)
+    trace_with_x0 = trace
+
+    trace = []
+    minres(A, b, callback=trace_iterates)
+    assert_(not np.array_equal(trace_with_x0[0], trace[0]))
+
+@pytest.mark.parametrize("problem_func",
+                         [get_sample_problem, get_sample_problem_complex])
+def test_shift(problem_func):
+    A, b = problem_func()
+    shift = 0.5
+    shifted_A = A - shift * np.eye(10)
+    x1, info1 = minres(A, b, shift=shift)
+    x2, info2 = minres(shifted_A, b)
+    assert_equal(info1, 0)
+    assert_allclose(x1, x2, rtol=1e-5)
+
+@pytest.mark.parametrize("problem_func",
+                         [get_sample_problem, get_sample_problem_complex])
+def test_asymmetric_fail(problem_func):
+    """Asymmetric matrix should raise `ValueError` when check=True"""
+    A, b = problem_func()
+    A[1, 2] = 1
+    A[2, 1] = 2
+    with assert_raises(ValueError):
+        xp, info = minres(A, b, check=True)
+
+@pytest.mark.parametrize("problem_func",
+                         [get_sample_problem, get_sample_problem_complex])
+def test_asymmetric_preconditioner_fail(problem_func):
+    """Non-symmetric (non-Hermitian) preconditioner M
+       should raise ValueError when check=True."""
+    A, b = problem_func()
+    rng = np.random.RandomState(4321)
+    if np.iscomplexobj(A):
+        M = rng.rand(10, 10) + 1j * rng.rand(10, 10)
+        M = M + M.T.conj()
+        M[1, 2] = 1 + 2j
+        M[2, 1] = 3 + 0j  # break Hermitian symmetry
+    else:
+        M = rng.rand(10, 10)
+        M = M + M.T
+        M[1, 2] = 1.0
+        M[2, 1] = 2.0  # break symmetry
+    with assert_raises(ValueError):
+        xp, info = minres(A, b, M=M, check=True)
+
+@pytest.mark.parametrize("make_complex", [False, True])
+def test_minres_non_default_x0(make_complex):
+    rng = np.random.RandomState(1234)
+    rtol = 1e-6
+    a = rng.randn(5, 5) if not make_complex else rng.randn(5, 5) + 1j * rng.randn(5, 5)
+    a = np.dot(a, a.T) if not make_complex else np.dot(a, a.T.conj())
+    b = rng.randn(5)
+    c = rng.randn(5)
+    x = minres(a, b, x0=c, rtol=rtol)[0]
+    assert norm(a @ x - b) <= rtol * norm(b)
+
+@pytest.mark.parametrize("make_complex", [False, True])
+def test_minres_precond_non_default_x0(make_complex):
+    rng = np.random.RandomState(12345)
+    rtol = 1e-6
+    a = rng.randn(5, 5) if not make_complex else rng.randn(5, 5) + 1j * rng.randn(5, 5)
+    a = np.dot(a, a.T) if not make_complex else np.dot(a, a.T.conj())
+    b = rng.randn(5)
+    c = rng.randn(5)
+    m = rng.randn(5, 5)
+    m = np.dot(m, m.T)
+    x = minres(a, b, M=m, x0=c, rtol=rtol)[0]
+    assert norm(a @ x - b) <= rtol * norm(b)
+
+def test_minres_precond_exact_x0():
+    rng = np.random.RandomState(1234)
+    rtol = 1e-6
+    a = np.eye(10)
+    b = np.ones(10)
+    c = np.ones(10)
+    m = rng.randn(10, 10)
+    m = np.dot(m, m.T)
+    x = minres(a, b, M=m, x0=c, rtol=rtol)[0]
+    assert norm(a @ x - b) <= rtol * norm(b)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_isolve/tests/test_utils.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_isolve/tests/test_utils.py
new file mode 100644
index 0000000000000000000000000000000000000000..bb62e2223d515288bd5aa6c5a70028279c4f6d30
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_isolve/tests/test_utils.py
@@ -0,0 +1,9 @@
+import numpy as np
+from pytest import raises as assert_raises
+
+import scipy.sparse.linalg._isolve.utils as utils
+
+
+def test_make_system_bad_shape():
+    assert_raises(ValueError,
+                  utils.make_system, np.zeros((5,3)), None, np.zeros(4), np.zeros(4))
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_isolve/tfqmr.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_isolve/tfqmr.py
new file mode 100644
index 0000000000000000000000000000000000000000..5ed70d39f5660c659855e0a4febf378987ed5625
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_isolve/tfqmr.py
@@ -0,0 +1,182 @@
+import numpy as np
+
+from scipy._lib._array_api import xp_capabilities
+from .iterative import _get_atol_rtol
+from .utils import make_system
+
+
+__all__ = ['tfqmr']
+
+
+@xp_capabilities(np_only=True)
+def tfqmr(A, b, x0=None, *, rtol=1e-5, atol=0., maxiter=None, M=None,
+          callback=None, show=False):
+    """
+    Solve ``Ax = b`` with the Transpose-Free Quasi-Minimal Residual method.
+
+    Parameters
+    ----------
+    A : {sparse array, ndarray, LinearOperator}
+        The real or complex N-by-N matrix of the linear system.
+        Alternatively, `A` can be a linear operator which can
+        produce ``Ax`` using, e.g.,
+        `scipy.sparse.linalg.LinearOperator`.
+    b : {ndarray}
+        Right hand side of the linear system. Has shape (N,) or (N,1).
+    x0 : {ndarray}
+        Starting guess for the solution.
+    rtol, atol : float, optional
+        Parameters for the convergence test. For convergence,
+        ``norm(b - A @ x) <= max(rtol*norm(b), atol)`` should be satisfied.
+        The default is ``rtol=1e-5``, the default for ``atol`` is ``0.0``.
+    maxiter : int, optional
+        Maximum number of iterations.  Iteration will stop after maxiter
+        steps even if the specified tolerance has not been achieved.
+        Default is ``min(10000, ndofs * 10)``, where ``ndofs = A.shape[0]``.
+    M : {sparse array, ndarray, LinearOperator}
+        Inverse of the preconditioner of A.  M should approximate the
+        inverse of A and be easy to solve for (see Notes).  Effective
+        preconditioning dramatically improves the rate of convergence,
+        which implies that fewer iterations are needed to reach a given
+        error tolerance.  By default, no preconditioner is used.
+    callback : function, optional
+        User-supplied function to call after each iteration.  It is called
+        as ``callback(xk)``, where ``xk`` is the current solution vector.
+    show : bool, optional
+        Specify ``show = True`` to show the convergence, ``show = False`` is
+        to close the output of the convergence.
+        Default is `False`.
+
+    Returns
+    -------
+    x : ndarray
+        The converged solution.
+    info : int
+        Provides convergence information:
+
+        - 0  : successful exit
+        - >0 : convergence to tolerance not achieved, number of iterations
+        - <0 : illegal input or breakdown
+
+    Notes
+    -----
+    The Transpose-Free QMR algorithm is derived from the CGS algorithm.
+    However, unlike CGS, the convergence curves for the TFQMR method is
+    smoothed by computing a quasi minimization of the residual norm. The
+    implementation supports left preconditioner, and the "residual norm"
+    to compute in convergence criterion is actually an upper bound on the
+    actual residual norm ``||b - Axk||``.
+
+    References
+    ----------
+    .. [1] R. W. Freund, A Transpose-Free Quasi-Minimal Residual Algorithm for
+           Non-Hermitian Linear Systems, SIAM J. Sci. Comput., 14(2), 470-482,
+           1993.
+    .. [2] Y. Saad, Iterative Methods for Sparse Linear Systems, 2nd edition,
+           SIAM, Philadelphia, 2003.
+    .. [3] C. T. Kelley, Iterative Methods for Linear and Nonlinear Equations,
+           number 16 in Frontiers in Applied Mathematics, SIAM, Philadelphia,
+           1995.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.sparse import csc_array
+    >>> from scipy.sparse.linalg import tfqmr
+    >>> A = csc_array([[3, 2, 0], [1, -1, 0], [0, 5, 1]], dtype=float)
+    >>> b = np.array([2, 4, -1], dtype=float)
+    >>> x, exitCode = tfqmr(A, b, atol=0.0)
+    >>> print(exitCode)            # 0 indicates successful convergence
+    0
+    >>> np.allclose(A.dot(x), b)
+    True
+    """
+
+    # Check data type
+    dtype = A.dtype
+    if np.issubdtype(dtype, np.int64):
+        dtype = float
+        A = A.astype(dtype)
+    if np.issubdtype(b.dtype, np.int64):
+        b = b.astype(dtype)
+
+    A, M, x, b = make_system(A, M, x0, b)
+
+    # Check if the R.H.S is a zero vector
+    if np.linalg.norm(b) == 0.:
+        x = b.copy()
+        return (x, 0)
+
+    ndofs = A.shape[0]
+    if maxiter is None:
+        maxiter = min(10000, ndofs * 10)
+
+    if x0 is None:
+        r = b.copy()
+    else:
+        r = b - A.matvec(x)
+    u = r
+    w = r.copy()
+    # Take rstar as b - Ax0, that is rstar := r = b - Ax0 mathematically
+    rstar = r
+    v = M.matvec(A.matvec(r))
+    uhat = v
+    d = theta = eta = 0.
+    # at this point we know rstar == r, so rho is always real
+    rho = np.inner(rstar.conjugate(), r).real
+    rhoLast = rho
+    r0norm = np.sqrt(rho)
+    tau = r0norm
+    if r0norm == 0:
+        return (x, 0)
+
+    # we call this to get the right atol and raise errors as necessary
+    atol, _ = _get_atol_rtol('tfqmr', r0norm, atol, rtol)
+
+    for iter in range(maxiter):
+        even = iter % 2 == 0
+        if (even):
+            vtrstar = np.inner(rstar.conjugate(), v)
+            # Check breakdown
+            if vtrstar == 0.:
+                return (x, -1)
+            alpha = rho / vtrstar
+            uNext = u - alpha * v  # [1]-(5.6)
+        w -= alpha * uhat  # [1]-(5.8)
+        d = u + (theta**2 / alpha) * eta * d  # [1]-(5.5)
+        # [1]-(5.2)
+        theta = np.linalg.norm(w) / tau
+        c = np.sqrt(1. / (1 + theta**2))
+        tau *= theta * c
+        # Calculate step and direction [1]-(5.4)
+        eta = (c**2) * alpha
+        z = M.matvec(d)
+        x += eta * z
+
+        if callback is not None:
+            callback(x)
+
+        # Convergence criterion
+        if tau * np.sqrt(iter+1) < atol:
+            if (show):
+                print("TFQMR: Linear solve converged due to reach TOL "
+                      f"iterations {iter+1}")
+            return (x, 0)
+
+        if (not even):
+            # [1]-(5.7)
+            rho = np.inner(rstar.conjugate(), w)
+            beta = rho / rhoLast
+            u = w + beta * u
+            v = beta * uhat + (beta**2) * v
+            uhat = M.matvec(A.matvec(u))
+            v += uhat
+        else:
+            uhat = M.matvec(A.matvec(uNext))
+            u = uNext
+            rhoLast = rho
+
+    if (show):
+        print("TFQMR: Linear solve not converged due to reach MAXIT "
+              f"iterations {iter+1}")
+    return (x, maxiter)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_isolve/utils.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_isolve/utils.py
new file mode 100644
index 0000000000000000000000000000000000000000..334d9692187d8e775e5c2dc6b8446857a1e25b0b
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_isolve/utils.py
@@ -0,0 +1,123 @@
+__docformat__ = "restructuredtext en"
+
+__all__ = []
+
+
+from numpy import asanyarray, asarray, array, zeros
+
+from scipy.sparse.linalg._interface import aslinearoperator, LinearOperator, \
+     IdentityOperator
+
+_coerce_rules = {('f','f'):'f', ('f','d'):'d', ('f','F'):'F',
+                 ('f','D'):'D', ('d','f'):'d', ('d','d'):'d',
+                 ('d','F'):'D', ('d','D'):'D', ('F','f'):'F',
+                 ('F','d'):'D', ('F','F'):'F', ('F','D'):'D',
+                 ('D','f'):'D', ('D','d'):'D', ('D','F'):'D',
+                 ('D','D'):'D'}
+
+
+def coerce(x,y):
+    if x not in 'fdFD':
+        x = 'd'
+    if y not in 'fdFD':
+        y = 'd'
+    return _coerce_rules[x,y]
+
+
+def id(x):
+    return x
+
+
+def make_system(A, M, x0, b):
+    """Make a linear system Ax=b
+
+    Parameters
+    ----------
+    A : LinearOperator
+        sparse or dense matrix (or any valid input to aslinearoperator)
+    M : {LinearOperator, Nones}
+        preconditioner
+        sparse or dense matrix (or any valid input to aslinearoperator)
+    x0 : {array_like, str, None}
+        initial guess to iterative method.
+        ``x0 = 'Mb'`` means using the nonzero initial guess ``M @ b``.
+        Default is `None`, which means using the zero initial guess.
+    b : array_like
+        right hand side
+
+    Returns
+    -------
+    (A, M, x, b)
+        A : LinearOperator
+            matrix of the linear system
+        M : LinearOperator
+            preconditioner
+        x : rank 1 ndarray
+            initial guess
+        b : rank 1 ndarray
+            right hand side
+
+    """
+    A_ = A
+    A = aslinearoperator(A)
+    if A.ndim > 2:
+        raise ValueError(f"{A.ndim}-dimensional `A` is unsupported, expected 2-D.")
+
+    if A.shape[0] != A.shape[1]:
+        raise ValueError(f'expected square matrix, but got shape={(A.shape,)}')
+
+    N = A.shape[0]
+
+    b = asanyarray(b)
+
+    if not (b.shape == (N,1) or b.shape == (N,)):
+        raise ValueError(f'shapes of A {A.shape} and b {b.shape} are '
+                         'incompatible')
+
+    if b.dtype.char not in 'fdFD':
+        b = b.astype('d')  # upcast non-FP types to double
+
+    if hasattr(A,'dtype'):
+        xtype = A.dtype.char
+    else:
+        xtype = A.matvec(b).dtype.char
+    xtype = coerce(xtype, b.dtype.char)
+
+    b = asarray(b,dtype=xtype)  # make b the same type as x
+    b = b.ravel()
+
+    # process preconditioner
+    if M is None:
+        if hasattr(A_,'psolve'):
+            psolve = A_.psolve
+        else:
+            psolve = id
+        if hasattr(A_,'rpsolve'):
+            rpsolve = A_.rpsolve
+        else:
+            rpsolve = id
+        if psolve is id and rpsolve is id:
+            M = IdentityOperator(shape=A.shape, dtype=A.dtype)
+        else:
+            M = LinearOperator(A.shape, matvec=psolve, rmatvec=rpsolve,
+                               dtype=A.dtype)
+    else:
+        M = aslinearoperator(M)
+        if A.shape != M.shape:
+            raise ValueError('matrix and preconditioner have different shapes')
+
+    # set initial guess
+    if x0 is None:
+        x = zeros(N, dtype=xtype)
+    elif isinstance(x0, str):
+        if x0 == 'Mb':  # use nonzero initial guess ``M @ b``
+            bCopy = b.copy()
+            x = M.matvec(bCopy)
+    else:
+        x = array(x0, dtype=xtype)
+        if not (x.shape == (N, 1) or x.shape == (N,)):
+            raise ValueError(f'shapes of A {A.shape} and '
+                             f'x0 {x.shape} are incompatible')
+        x = x.ravel()
+
+    return A, M, x, b
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_matfuncs.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_matfuncs.py
new file mode 100644
index 0000000000000000000000000000000000000000..794738572ac1246380bb850a3e170e00dea4a73d
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_matfuncs.py
@@ -0,0 +1,939 @@
+"""
+Sparse matrix functions
+"""
+
+#
+# Authors: Travis Oliphant, March 2002
+#          Anthony Scopatz, August 2012 (Sparse Updates)
+#          Jake Vanderplas, August 2012 (Sparse Updates)
+#
+
+__all__ = ['expm', 'inv', 'matrix_power']
+
+import numpy as np
+from scipy.linalg._basic import solve, solve_triangular
+
+from scipy.sparse._base import issparse
+from scipy.sparse.linalg import spsolve
+from scipy.sparse._sputils import is_pydata_spmatrix, isintlike
+
+import scipy.sparse
+import scipy.sparse.linalg
+from scipy.sparse.linalg._interface import LinearOperator
+from scipy.sparse._construct import eye_array
+
+from ._expm_multiply import _ident_like, _exact_1_norm as _onenorm
+
+
+UPPER_TRIANGULAR = 'upper_triangular'
+
+
+def inv(A):
+    """
+    Compute the inverse of a sparse arrays.
+
+    Parameters
+    ----------
+    A : (M, M) sparse arrays
+        square matrix to be inverted
+
+    Returns
+    -------
+    Ainv : (M, M) sparse arrays
+        inverse of `A`
+
+    Notes
+    -----
+    This computes the sparse inverse of `A`. If the inverse of `A` is expected
+    to be non-sparse, it will likely be faster to convert `A` to dense and use
+    `scipy.linalg.inv`.
+
+    Examples
+    --------
+    >>> from scipy.sparse import csc_array
+    >>> from scipy.sparse.linalg import inv
+    >>> A = csc_array([[1., 0.], [1., 2.]])
+    >>> Ainv = inv(A)
+    >>> Ainv
+    <Compressed Sparse Column sparse array of dtype 'float64'
+        with 3 stored elements and shape (2, 2)>
+    >>> A.dot(Ainv)
+    <Compressed Sparse Column sparse array of dtype 'float64'
+        with 2 stored elements and shape (2, 2)>
+    >>> A.dot(Ainv).toarray()
+    array([[ 1.,  0.],
+           [ 0.,  1.]])
+
+    .. versionadded:: 0.12.0
+
+    """
+    # Check input
+    if not (issparse(A) or is_pydata_spmatrix(A)):
+        raise TypeError('Input must be a sparse arrays')
+
+    # Use sparse direct solver to solve "AX = I" accurately
+    I = _ident_like(A)
+    Ainv = spsolve(A, I)
+    return Ainv
+
+
+def _onenorm_matrix_power_nnm(A, p):
+    """
+    Compute the 1-norm of a non-negative integer power of a non-negative matrix.
+
+    Parameters
+    ----------
+    A : a square ndarray or matrix or sparse arrays
+        Input matrix with non-negative entries.
+    p : non-negative integer
+        The power to which the matrix is to be raised.
+
+    Returns
+    -------
+    out : float
+        The 1-norm of the matrix power p of A.
+
+    """
+    # Check input
+    if int(p) != p or p < 0:
+        raise ValueError('expected non-negative integer p')
+    p = int(p)
+    if len(A.shape) != 2 or A.shape[0] != A.shape[1]:
+        raise ValueError('expected A to be like a square matrix')
+
+    # Explicitly make a column vector so that this works when A is a
+    # numpy matrix (in addition to ndarray and sparse arrays).
+    v = np.ones((A.shape[0], 1), dtype=float)
+    M = A.T
+    for i in range(p):
+        v = M.dot(v)
+    return np.max(v)
+
+
+def _is_upper_triangular(A):
+    # This function could possibly be of wider interest.
+    if issparse(A):
+        lower_part = scipy.sparse.tril(A, -1)
+        # Check structural upper triangularity,
+        # then coincidental upper triangularity if needed.
+        return lower_part.nnz == 0 or lower_part.count_nonzero() == 0
+    elif is_pydata_spmatrix(A):
+        import sparse
+        lower_part = sparse.tril(A, -1)
+        return lower_part.nnz == 0
+    else:
+        return not np.tril(A, -1).any()
+
+
+def _smart_matrix_product(A, B, alpha=None, structure=None):
+    """
+    A matrix product that knows about sparse and structured matrices.
+
+    Parameters
+    ----------
+    A : 2d ndarray
+        First matrix.
+    B : 2d ndarray
+        Second matrix.
+    alpha : float
+        The matrix product will be scaled by this constant.
+    structure : str, optional
+        A string describing the structure of both matrices `A` and `B`.
+        Only `upper_triangular` is currently supported.
+
+    Returns
+    -------
+    M : 2d ndarray
+        Matrix product of A and B.
+
+    """
+    if len(A.shape) != 2:
+        raise ValueError('expected A to be a rectangular matrix')
+    if len(B.shape) != 2:
+        raise ValueError('expected B to be a rectangular matrix')
+    f = None
+    if structure == UPPER_TRIANGULAR:
+        if (not issparse(A) and not issparse(B)
+                and not is_pydata_spmatrix(A) and not is_pydata_spmatrix(B)):
+            f, = scipy.linalg.get_blas_funcs(('trmm',), (A, B))
+    if f is not None:
+        if alpha is None:
+            alpha = 1.
+        out = f(alpha, A, B)
+    else:
+        if alpha is None:
+            out = A.dot(B)
+        else:
+            out = alpha * A.dot(B)
+    return out
+
+
+class MatrixPowerOperator(LinearOperator):
+
+    def __init__(self, A, p, structure=None):
+        if A.ndim != 2 or A.shape[0] != A.shape[1]:
+            raise ValueError('expected A to be like a square matrix')
+        if p < 0:
+            raise ValueError('expected p to be a non-negative integer')
+        self._A = A
+        self._p = p
+        self._structure = structure
+        super().__init__(dtype = A.dtype, shape=A.shape)
+
+    def _matvec(self, x):
+        for i in range(self._p):
+            x = self._A.dot(x)
+        return x
+
+    def _rmatvec(self, x):
+        A_T = self._A.T
+        x = x.ravel()
+        for i in range(self._p):
+            x = A_T.dot(x)
+        return x
+
+    def _matmat(self, X):
+        for i in range(self._p):
+            X = _smart_matrix_product(self._A, X, structure=self._structure)
+        return X
+
+    @property
+    def T(self):
+        return MatrixPowerOperator(self._A.T, self._p)
+
+
+class ProductOperator(LinearOperator):
+    """
+    For now, this is limited to products of multiple square matrices.
+    """
+
+    def __init__(self, *args, **kwargs):
+        self._structure = kwargs.get('structure', None)
+        for A in args:
+            if len(A.shape) != 2 or A.shape[0] != A.shape[1]:
+                raise ValueError(
+                        'For now, the ProductOperator implementation is '
+                        'limited to the product of multiple square matrices.')
+        shape = None
+        if args:
+            n = args[0].shape[0]
+            for A in args:
+                for d in A.shape:
+                    if d != n:
+                        raise ValueError(
+                                'The square matrices of the ProductOperator '
+                                'must all have the same shape.')
+            shape = (n, n)
+        dtype = np.result_type(*[x.dtype for x in args])
+        super().__init__(dtype=dtype, shape=shape)
+        self._operator_sequence = args
+
+    def _matvec(self, x):
+        for A in reversed(self._operator_sequence):
+            x = A.dot(x)
+        return x
+
+    def _rmatvec(self, x):
+        x = x.ravel()
+        for A in self._operator_sequence:
+            x = A.T.dot(x)
+        return x
+
+    def _matmat(self, X):
+        for A in reversed(self._operator_sequence):
+            X = _smart_matrix_product(A, X, structure=self._structure)
+        return X
+
+    @property
+    def T(self):
+        T_args = [A.T for A in reversed(self._operator_sequence)]
+        return ProductOperator(*T_args)
+
+
+def _onenormest_matrix_power(A, p,
+        t=2, itmax=5, compute_v=False, compute_w=False, structure=None):
+    """
+    Efficiently estimate the 1-norm of A^p.
+
+    Parameters
+    ----------
+    A : ndarray
+        Matrix whose 1-norm of a power is to be computed.
+    p : int
+        Non-negative integer power.
+    t : int, optional
+        A positive parameter controlling the tradeoff between
+        accuracy versus time and memory usage.
+        Larger values take longer and use more memory
+        but give more accurate output.
+    itmax : int, optional
+        Use at most this many iterations.
+    compute_v : bool, optional
+        Request a norm-maximizing linear operator input vector if True.
+    compute_w : bool, optional
+        Request a norm-maximizing linear operator output vector if True.
+
+    Returns
+    -------
+    est : float
+        An underestimate of the 1-norm of the sparse arrays.
+    v : ndarray, optional
+        The vector such that ||Av||_1 == est*||v||_1.
+        It can be thought of as an input to the linear operator
+        that gives an output with particularly large norm.
+    w : ndarray, optional
+        The vector Av which has relatively large 1-norm.
+        It can be thought of as an output of the linear operator
+        that is relatively large in norm compared to the input.
+
+    """
+    return scipy.sparse.linalg.onenormest(
+            MatrixPowerOperator(A, p, structure=structure))
+
+
+def _onenormest_product(operator_seq,
+        t=2, itmax=5, compute_v=False, compute_w=False, structure=None):
+    """
+    Efficiently estimate the 1-norm of the matrix product of the args.
+
+    Parameters
+    ----------
+    operator_seq : linear operator sequence
+        Matrices whose 1-norm of product is to be computed.
+    t : int, optional
+        A positive parameter controlling the tradeoff between
+        accuracy versus time and memory usage.
+        Larger values take longer and use more memory
+        but give more accurate output.
+    itmax : int, optional
+        Use at most this many iterations.
+    compute_v : bool, optional
+        Request a norm-maximizing linear operator input vector if True.
+    compute_w : bool, optional
+        Request a norm-maximizing linear operator output vector if True.
+    structure : str, optional
+        A string describing the structure of all operators.
+        Only `upper_triangular` is currently supported.
+
+    Returns
+    -------
+    est : float
+        An underestimate of the 1-norm of the sparse arrays.
+    v : ndarray, optional
+        The vector such that ||Av||_1 == est*||v||_1.
+        It can be thought of as an input to the linear operator
+        that gives an output with particularly large norm.
+    w : ndarray, optional
+        The vector Av which has relatively large 1-norm.
+        It can be thought of as an output of the linear operator
+        that is relatively large in norm compared to the input.
+
+    """
+    return scipy.sparse.linalg.onenormest(
+            ProductOperator(*operator_seq, structure=structure))
+
+
+class _ExpmPadeHelper:
+    """
+    Help lazily evaluate a matrix exponential.
+
+    The idea is to not do more work than we need for high expm precision,
+    so we lazily compute matrix powers and store or precompute
+    other properties of the matrix.
+
+    """
+
+    def __init__(self, A, structure=None, use_exact_onenorm=False):
+        """
+        Initialize the object.
+
+        Parameters
+        ----------
+        A : a dense or sparse square numpy matrix or ndarray
+            The matrix to be exponentiated.
+        structure : str, optional
+            A string describing the structure of matrix `A`.
+            Only `upper_triangular` is currently supported.
+        use_exact_onenorm : bool, optional
+            If True then only the exact one-norm of matrix powers and products
+            will be used. Otherwise, the one-norm of powers and products
+            may initially be estimated.
+        """
+        self.A = A
+        self._A2 = None
+        self._A4 = None
+        self._A6 = None
+        self._A8 = None
+        self._A10 = None
+        self._d4_exact = None
+        self._d6_exact = None
+        self._d8_exact = None
+        self._d10_exact = None
+        self._d4_approx = None
+        self._d6_approx = None
+        self._d8_approx = None
+        self._d10_approx = None
+        self.ident = _ident_like(A)
+        self.structure = structure
+        self.use_exact_onenorm = use_exact_onenorm
+
+    @property
+    def A2(self):
+        if self._A2 is None:
+            self._A2 = _smart_matrix_product(
+                    self.A, self.A, structure=self.structure)
+        return self._A2
+
+    @property
+    def A4(self):
+        if self._A4 is None:
+            self._A4 = _smart_matrix_product(
+                    self.A2, self.A2, structure=self.structure)
+        return self._A4
+
+    @property
+    def A6(self):
+        if self._A6 is None:
+            self._A6 = _smart_matrix_product(
+                    self.A4, self.A2, structure=self.structure)
+        return self._A6
+
+    @property
+    def A8(self):
+        if self._A8 is None:
+            self._A8 = _smart_matrix_product(
+                    self.A6, self.A2, structure=self.structure)
+        return self._A8
+
+    @property
+    def A10(self):
+        if self._A10 is None:
+            self._A10 = _smart_matrix_product(
+                    self.A4, self.A6, structure=self.structure)
+        return self._A10
+
+    @property
+    def d4_tight(self):
+        if self._d4_exact is None:
+            self._d4_exact = _onenorm(self.A4)**(1/4.)
+        return self._d4_exact
+
+    @property
+    def d6_tight(self):
+        if self._d6_exact is None:
+            self._d6_exact = _onenorm(self.A6)**(1/6.)
+        return self._d6_exact
+
+    @property
+    def d8_tight(self):
+        if self._d8_exact is None:
+            self._d8_exact = _onenorm(self.A8)**(1/8.)
+        return self._d8_exact
+
+    @property
+    def d10_tight(self):
+        if self._d10_exact is None:
+            self._d10_exact = _onenorm(self.A10)**(1/10.)
+        return self._d10_exact
+
+    @property
+    def d4_loose(self):
+        if self.use_exact_onenorm:
+            return self.d4_tight
+        if self._d4_exact is not None:
+            return self._d4_exact
+        else:
+            if self._d4_approx is None:
+                self._d4_approx = _onenormest_matrix_power(self.A2, 2,
+                        structure=self.structure)**(1/4.)
+            return self._d4_approx
+
+    @property
+    def d6_loose(self):
+        if self.use_exact_onenorm:
+            return self.d6_tight
+        if self._d6_exact is not None:
+            return self._d6_exact
+        else:
+            if self._d6_approx is None:
+                self._d6_approx = _onenormest_matrix_power(self.A2, 3,
+                        structure=self.structure)**(1/6.)
+            return self._d6_approx
+
+    @property
+    def d8_loose(self):
+        if self.use_exact_onenorm:
+            return self.d8_tight
+        if self._d8_exact is not None:
+            return self._d8_exact
+        else:
+            if self._d8_approx is None:
+                self._d8_approx = _onenormest_matrix_power(self.A4, 2,
+                        structure=self.structure)**(1/8.)
+            return self._d8_approx
+
+    @property
+    def d10_loose(self):
+        if self.use_exact_onenorm:
+            return self.d10_tight
+        if self._d10_exact is not None:
+            return self._d10_exact
+        else:
+            if self._d10_approx is None:
+                self._d10_approx = _onenormest_product((self.A4, self.A6),
+                        structure=self.structure)**(1/10.)
+            return self._d10_approx
+
+    def pade3(self):
+        b = (120., 60., 12., 1.)
+        U = _smart_matrix_product(self.A,
+                b[3]*self.A2 + b[1]*self.ident,
+                structure=self.structure)
+        V = b[2]*self.A2 + b[0]*self.ident
+        return U, V
+
+    def pade5(self):
+        b = (30240., 15120., 3360., 420., 30., 1.)
+        U = _smart_matrix_product(self.A,
+                b[5]*self.A4 + b[3]*self.A2 + b[1]*self.ident,
+                structure=self.structure)
+        V = b[4]*self.A4 + b[2]*self.A2 + b[0]*self.ident
+        return U, V
+
+    def pade7(self):
+        b = (17297280., 8648640., 1995840., 277200., 25200., 1512., 56., 1.)
+        U = _smart_matrix_product(self.A,
+                b[7]*self.A6 + b[5]*self.A4 + b[3]*self.A2 + b[1]*self.ident,
+                structure=self.structure)
+        V = b[6]*self.A6 + b[4]*self.A4 + b[2]*self.A2 + b[0]*self.ident
+        return U, V
+
+    def pade9(self):
+        b = (17643225600., 8821612800., 2075673600., 302702400., 30270240.,
+                2162160., 110880., 3960., 90., 1.)
+        U = _smart_matrix_product(self.A,
+                (b[9]*self.A8 + b[7]*self.A6 + b[5]*self.A4 +
+                    b[3]*self.A2 + b[1]*self.ident),
+                structure=self.structure)
+        V = (b[8]*self.A8 + b[6]*self.A6 + b[4]*self.A4 +
+                b[2]*self.A2 + b[0]*self.ident)
+        return U, V
+
+    def pade13_scaled(self, s):
+        b = (64764752532480000., 32382376266240000., 7771770303897600.,
+                1187353796428800., 129060195264000., 10559470521600.,
+                670442572800., 33522128640., 1323241920., 40840800., 960960.,
+                16380., 182., 1.)
+        B = self.A * 2**-s
+        B2 = self.A2 * 2**(-2*s)
+        B4 = self.A4 * 2**(-4*s)
+        B6 = self.A6 * 2**(-6*s)
+        U2 = _smart_matrix_product(B6,
+                b[13]*B6 + b[11]*B4 + b[9]*B2,
+                structure=self.structure)
+        U = _smart_matrix_product(B,
+                (U2 + b[7]*B6 + b[5]*B4 +
+                    b[3]*B2 + b[1]*self.ident),
+                structure=self.structure)
+        V2 = _smart_matrix_product(B6,
+                b[12]*B6 + b[10]*B4 + b[8]*B2,
+                structure=self.structure)
+        V = V2 + b[6]*B6 + b[4]*B4 + b[2]*B2 + b[0]*self.ident
+        return U, V
+
+
+def expm(A):
+    """
+    Compute the matrix exponential using Pade approximation.
+
+    Parameters
+    ----------
+    A : (M,M) array_like or sparse array
+        2D Array or Matrix (sparse or dense) to be exponentiated
+
+    Returns
+    -------
+    expA : (M,M) ndarray
+        Matrix exponential of `A`
+
+    Notes
+    -----
+    This is algorithm (6.1) which is a simplification of algorithm (5.1).
+
+    .. versionadded:: 0.12.0
+
+    References
+    ----------
+    .. [1] Awad H. Al-Mohy and Nicholas J. Higham (2009)
+           "A New Scaling and Squaring Algorithm for the Matrix Exponential."
+           SIAM Journal on Matrix Analysis and Applications.
+           31 (3). pp. 970-989. ISSN 1095-7162
+
+    Examples
+    --------
+    >>> from scipy.sparse import csc_array
+    >>> from scipy.sparse.linalg import expm
+    >>> A = csc_array([[1, 0, 0], [0, 2, 0], [0, 0, 3]])
+    >>> A.toarray()
+    array([[1, 0, 0],
+           [0, 2, 0],
+           [0, 0, 3]], dtype=int64)
+    >>> Aexp = expm(A)
+    >>> Aexp
+    <Compressed Sparse Column sparse array of dtype 'float64'
+        with 3 stored elements and shape (3, 3)>
+    >>> Aexp.toarray()
+    array([[  2.71828183,   0.        ,   0.        ],
+           [  0.        ,   7.3890561 ,   0.        ],
+           [  0.        ,   0.        ,  20.08553692]])
+    """
+    return _expm(A, use_exact_onenorm='auto')
+
+
+def _expm(A, use_exact_onenorm):
+    # Core of expm, separated to allow testing exact and approximate
+    # algorithms.
+
+    # Avoid indiscriminate asarray() to allow sparse or other strange arrays.
+    if isinstance(A, list | tuple | np.matrix):
+        A = np.asarray(A)
+    if len(A.shape) != 2 or A.shape[0] != A.shape[1]:
+        raise ValueError('expected a square matrix')
+
+    # gracefully handle size-0 input,
+    # carefully handling sparse scenario
+    if A.shape == (0, 0):
+        out = np.zeros([0, 0], dtype=A.dtype)
+        if issparse(A) or is_pydata_spmatrix(A):
+            return A.__class__(out)
+        return out
+
+    # Trivial case
+    if A.shape == (1, 1):
+        out = [[np.exp(A[0, 0])]]
+
+        # Avoid indiscriminate casting to ndarray to
+        # allow for sparse or other strange arrays
+        if issparse(A) or is_pydata_spmatrix(A):
+            return A.__class__(out)
+
+        return np.array(out)
+
+    # Ensure input is of float type, to avoid integer overflows etc.
+    if ((isinstance(A, np.ndarray) or issparse(A) or is_pydata_spmatrix(A))
+            and not np.issubdtype(A.dtype, np.inexact)):
+        A = A.astype(float)
+
+    # Detect upper triangularity.
+    structure = UPPER_TRIANGULAR if _is_upper_triangular(A) else None
+
+    if use_exact_onenorm == "auto":
+        # Hardcode a matrix order threshold for exact vs. estimated one-norms.
+        use_exact_onenorm = A.shape[0] < 200
+
+    # Track functions of A to help compute the matrix exponential.
+    h = _ExpmPadeHelper(
+            A, structure=structure, use_exact_onenorm=use_exact_onenorm)
+
+    # Try Pade order 3.
+    eta_1 = max(h.d4_loose, h.d6_loose)
+    if eta_1 < 1.495585217958292e-002 and _ell(h.A, 3) == 0:
+        U, V = h.pade3()
+        return _solve_P_Q(U, V, structure=structure)
+
+    # Try Pade order 5.
+    eta_2 = max(h.d4_tight, h.d6_loose)
+    if eta_2 < 2.539398330063230e-001 and _ell(h.A, 5) == 0:
+        U, V = h.pade5()
+        return _solve_P_Q(U, V, structure=structure)
+
+    # Try Pade orders 7 and 9.
+    eta_3 = max(h.d6_tight, h.d8_loose)
+    if eta_3 < 9.504178996162932e-001 and _ell(h.A, 7) == 0:
+        U, V = h.pade7()
+        return _solve_P_Q(U, V, structure=structure)
+    if eta_3 < 2.097847961257068e+000 and _ell(h.A, 9) == 0:
+        U, V = h.pade9()
+        return _solve_P_Q(U, V, structure=structure)
+
+    # Use Pade order 13.
+    eta_4 = max(h.d8_loose, h.d10_loose)
+    eta_5 = min(eta_3, eta_4)
+    theta_13 = 4.25
+
+    # Choose smallest s>=0 such that 2**(-s) eta_5 <= theta_13
+    if eta_5 == 0:
+        # Nilpotent special case
+        s = 0
+    else:
+        s = max(int(np.ceil(np.log2(eta_5 / theta_13))), 0)
+    s = s + _ell(2**-s * h.A, 13)
+    U, V = h.pade13_scaled(s)
+    X = _solve_P_Q(U, V, structure=structure)
+    if structure == UPPER_TRIANGULAR:
+        # Invoke Code Fragment 2.1.
+        X = _fragment_2_1(X, h.A, s)
+    else:
+        # X = r_13(A)^(2^s) by repeated squaring.
+        for i in range(s):
+            X = X.dot(X)
+    return X
+
+
+def _solve_P_Q(U, V, structure=None):
+    """
+    A helper function for expm_2009.
+
+    Parameters
+    ----------
+    U : ndarray
+        Pade numerator.
+    V : ndarray
+        Pade denominator.
+    structure : str, optional
+        A string describing the structure of both matrices `U` and `V`.
+        Only `upper_triangular` is currently supported.
+
+    Notes
+    -----
+    The `structure` argument is inspired by similar args
+    for theano and cvxopt functions.
+
+    """
+    P = U + V
+    Q = -U + V
+    if issparse(U) or is_pydata_spmatrix(U):
+        return spsolve(Q, P)
+    elif structure is None:
+        return solve(Q, P)
+    elif structure == UPPER_TRIANGULAR:
+        return solve_triangular(Q, P)
+    else:
+        raise ValueError('unsupported matrix structure: ' + str(structure))
+
+
+def _exp_sinch(a, x):
+    """
+    Stably evaluate exp(a)*sinh(x)/x
+
+    Notes
+    -----
+    The strategy of falling back to a sixth order Taylor expansion
+    was suggested by the Spallation Neutron Source docs
+    which was found on the internet by google search.
+    http://www.ornl.gov/~t6p/resources/xal/javadoc/gov/sns/tools/math/ElementaryFunction.html
+    The details of the cutoff point and the Horner-like evaluation
+    was picked without reference to anything in particular.
+
+    Note that sinch is not currently implemented in scipy.special,
+    whereas the "engineer's" definition of sinc is implemented.
+    The implementation of sinc involves a scaling factor of pi
+    that distinguishes it from the "mathematician's" version of sinc.
+
+    """
+
+    # If x is small then use sixth order Taylor expansion.
+    # How small is small? I am using the point where the relative error
+    # of the approximation is less than 1e-14.
+    # If x is large then directly evaluate sinh(x) / x.
+    if abs(x) < 0.0135:
+        x2 = x*x
+        return np.exp(a) * (1 + (x2/6.)*(1 + (x2/20.)*(1 + (x2/42.))))
+    else:
+        return (np.exp(a + x) - np.exp(a - x)) / (2*x)
+
+
+def _eq_10_42(lam_1, lam_2, t_12):
+    """
+    Equation (10.42) of Functions of Matrices: Theory and Computation.
+
+    Notes
+    -----
+    This is a helper function for _fragment_2_1 of expm_2009.
+    Equation (10.42) is on page 251 in the section on Schur algorithms.
+    In particular, section 10.4.3 explains the Schur-Parlett algorithm.
+    expm([[lam_1, t_12], [0, lam_1])
+    =
+    [[exp(lam_1), t_12*exp((lam_1 + lam_2)/2)*sinch((lam_1 - lam_2)/2)],
+    [0, exp(lam_2)]
+    """
+
+    # The plain formula t_12 * (exp(lam_2) - exp(lam_2)) / (lam_2 - lam_1)
+    # apparently suffers from cancellation, according to Higham's textbook.
+    # A nice implementation of sinch, defined as sinh(x)/x,
+    # will apparently work around the cancellation.
+    a = 0.5 * (lam_1 + lam_2)
+    b = 0.5 * (lam_1 - lam_2)
+    return t_12 * _exp_sinch(a, b)
+
+
+def _fragment_2_1(X, T, s):
+    """
+    A helper function for expm_2009.
+
+    Notes
+    -----
+    The argument X is modified in-place, but this modification is not the same
+    as the returned value of the function.
+    This function also takes pains to do things in ways that are compatible
+    with sparse arrays, for example by avoiding fancy indexing
+    and by using methods of the matrices whenever possible instead of
+    using functions of the numpy or scipy libraries themselves.
+
+    """
+    # Form X = r_m(2^-s T)
+    # Replace diag(X) by exp(2^-s diag(T)).
+    n = X.shape[0]
+    diag_T = np.ravel(T.diagonal().copy())
+
+    # Replace diag(X) by exp(2^-s diag(T)).
+    scale = 2 ** -s
+    exp_diag = np.exp(scale * diag_T)
+    for k in range(n):
+        X[k, k] = exp_diag[k]
+
+    for i in range(s-1, -1, -1):
+        X = X.dot(X)
+
+        # Replace diag(X) by exp(2^-i diag(T)).
+        scale = 2 ** -i
+        exp_diag = np.exp(scale * diag_T)
+        for k in range(n):
+            X[k, k] = exp_diag[k]
+
+        # Replace (first) superdiagonal of X by explicit formula
+        # for superdiagonal of exp(2^-i T) from Eq (10.42) of
+        # the author's 2008 textbook
+        # Functions of Matrices: Theory and Computation.
+        for k in range(n-1):
+            lam_1 = scale * diag_T[k]
+            lam_2 = scale * diag_T[k+1]
+            t_12 = scale * T[k, k+1]
+            value = _eq_10_42(lam_1, lam_2, t_12)
+            X[k, k+1] = value
+
+    # Return the updated X matrix.
+    return X
+
+
+def _ell(A, m):
+    """
+    A helper function for expm_2009.
+
+    Parameters
+    ----------
+    A : linear operator
+        A linear operator whose norm of power we care about.
+    m : int
+        The power of the linear operator
+
+    Returns
+    -------
+    value : int
+        A value related to a bound.
+
+    """
+    if len(A.shape) != 2 or A.shape[0] != A.shape[1]:
+        raise ValueError('expected A to be like a square matrix')
+
+    # The c_i are explained in (2.2) and (2.6) of the 2005 expm paper.
+    # They are coefficients of terms of a generating function series expansion.
+    c_i = {3: 100800.,
+           5: 10059033600.,
+           7: 4487938430976000.,
+           9: 5914384781877411840000.,
+           13: 113250775606021113483283660800000000.
+           }
+    abs_c_recip = c_i[m]
+
+    # This is explained after Eq. (1.2) of the 2009 expm paper.
+    # It is the "unit roundoff" of IEEE double precision arithmetic.
+    u = 2**-53
+
+    # Compute the one-norm of matrix power p of abs(A).
+    A_abs_onenorm = _onenorm_matrix_power_nnm(abs(A), 2*m + 1)
+
+    # Treat zero norm as a special case.
+    if not A_abs_onenorm:
+        return 0
+
+    alpha = A_abs_onenorm / (_onenorm(A) * abs_c_recip)
+    log2_alpha_div_u = np.log2(alpha/u)
+    value = int(np.ceil(log2_alpha_div_u / (2 * m)))
+    return max(value, 0)
+
+def matrix_power(A, power):
+    """
+    Raise a square matrix to the integer power, `power`.
+
+    For non-negative integers, ``A**power`` is computed using repeated
+    matrix multiplications. Negative integers are not supported. 
+
+    Parameters
+    ----------
+    A : (M, M) square sparse array or matrix
+        sparse array that will be raised to power `power`
+    power : int
+        Exponent used to raise sparse array `A`
+
+    Returns
+    -------
+    A**power : (M, M) sparse array or matrix
+        The output matrix will be the same shape as A, and will preserve
+        the class of A, but the format of the output may be changed.
+    
+    Notes
+    -----
+    This uses a recursive implementation of the matrix power. For computing
+    the matrix power using a reasonably large `power`, this may be less efficient
+    than computing the product directly, using A @ A @ ... @ A.
+    This is contingent upon the number of nonzero entries in the matrix. 
+
+    .. versionadded:: 1.12.0
+
+    Examples
+    --------
+    >>> from scipy import sparse
+    >>> A = sparse.csc_array([[0,1,0],[1,0,1],[0,1,0]])
+    >>> A.todense()
+    array([[0, 1, 0],
+           [1, 0, 1],
+           [0, 1, 0]])
+    >>> (A @ A).todense()
+    array([[1, 0, 1],
+           [0, 2, 0],
+           [1, 0, 1]])
+    >>> A2 = sparse.linalg.matrix_power(A, 2)
+    >>> A2.todense()
+    array([[1, 0, 1],
+           [0, 2, 0],
+           [1, 0, 1]])
+    >>> A4 = sparse.linalg.matrix_power(A, 4)
+    >>> A4.todense()
+    array([[2, 0, 2],
+           [0, 4, 0],
+           [2, 0, 2]])
+
+    """
+    M, N = A.shape
+    if M != N:
+        raise TypeError('sparse matrix is not square')
+
+    if isintlike(power):
+        power = int(power)
+        if power < 0:
+            raise ValueError('exponent must be >= 0')
+
+        if power == 0:
+            return eye_array(M, dtype=A.dtype)
+
+        if power == 1:
+            return A.copy()
+
+        tmp = matrix_power(A, power // 2)
+        if power % 2:
+            return A @ tmp @ tmp
+        else:
+            return tmp @ tmp
+    else:
+        raise ValueError("exponent must be an integer")
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_norm.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_norm.py
new file mode 100644
index 0000000000000000000000000000000000000000..7ecc009015b32a2a6717ef934ffb4a58f0eca996
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_norm.py
@@ -0,0 +1,201 @@
+"""Sparse matrix norms.
+
+"""
+import numpy as np
+from scipy.sparse import issparse
+from scipy.sparse.linalg import svds
+from scipy.sparse._sputils import convert_pydata_sparse_to_scipy
+import scipy.sparse as sp
+
+from numpy import sqrt, abs
+
+__all__ = ['norm']
+
+
+def _sparse_frobenius_norm(x):
+    data = sp._sputils._todata(x)
+    return np.linalg.norm(data)
+
+
+def norm(x, ord=None, axis=None):
+    """
+    Norm of a sparse matrix.
+
+    This function is able to return one of seven different matrix norms,
+    depending on the value of the ``ord`` parameter.
+
+    Parameters
+    ----------
+    x : a sparse array
+        Input sparse array.
+    ord : {non-zero int, inf, -inf, 'fro'}, optional
+        Order of the norm (see table under ``Notes``). inf means numpy's
+        `inf` object.
+    axis : {int, 2-tuple of ints, None}, optional
+        If `axis` is an integer, it specifies the axis of `x` along which to
+        compute the vector norms.  If `axis` is a 2-tuple, it specifies the
+        axes that hold 2-D matrices, and the matrix norms of these matrices
+        are computed.  If `axis` is None then either a vector norm (when `x`
+        is 1-D) or a matrix norm (when `x` is 2-D) is returned.
+
+    Returns
+    -------
+    n : float or ndarray
+        The selected norm of `x`.
+
+    Notes
+    -----
+    Some of the ord are not implemented because some associated functions like,
+    _multi_svd_norm, are not yet available for sparse array.
+
+    This docstring is modified based on numpy.linalg.norm.
+    https://github.com/numpy/numpy/blob/main/numpy/linalg/linalg.py
+
+    The following norms can be calculated:
+
+    =====  ============================
+    ord    norm for sparse arrays
+    =====  ============================
+    None   Frobenius norm
+    'fro'  Frobenius norm
+    inf    max(sum(abs(x), axis=1))
+    -inf   min(sum(abs(x), axis=1))
+    0      abs(x).sum(axis=axis)
+    1      max(sum(abs(x), axis=0))
+    -1     min(sum(abs(x), axis=0))
+    2      Spectral norm (the largest singular value)
+    -2     Not implemented
+    other  Not implemented
+    =====  ============================
+
+    The Frobenius norm is given by [1]_:
+
+    :math:`||A||_F = [\\sum_{i,j} abs(a_{i,j})^2]^{1/2}`
+
+    References
+    ----------
+    .. [1] G. H. Golub and C. F. Van Loan, *Matrix Computations*,
+        Baltimore, MD, Johns Hopkins University Press, 1985, pg. 15
+
+    Examples
+    --------
+    >>> from scipy.sparse import csr_array, diags_array
+    >>> import numpy as np
+    >>> from scipy.sparse.linalg import norm
+    >>> a = np.arange(9) - 4
+    >>> a
+    array([-4, -3, -2, -1, 0, 1, 2, 3, 4])
+    >>> b = a.reshape((3, 3))
+    >>> b
+    array([[-4, -3, -2],
+           [-1, 0, 1],
+           [ 2, 3, 4]])
+
+    >>> b = csr_array(b)
+    >>> norm(b)
+    7.745966692414834
+    >>> norm(b, 'fro')
+    7.745966692414834
+    >>> norm(b, np.inf)
+    9
+    >>> norm(b, -np.inf)
+    2
+    >>> norm(b, 1)
+    7
+    >>> norm(b, -1)
+    6
+
+    The matrix 2-norm or the spectral norm is the largest singular
+    value, computed approximately and with limitations.
+
+    >>> b = diags_array([-1, 1], offsets=[0, 1], shape=(9, 10))
+    >>> norm(b, 2)
+    1.9753...
+    """
+    x = convert_pydata_sparse_to_scipy(x, target_format="csr")
+    if not issparse(x):
+        raise TypeError("input is not sparse. use numpy.linalg.norm")
+
+    # Check the default case first and handle it immediately.
+    if axis is None and ord in (None, 'fro', 'f'):
+        return _sparse_frobenius_norm(x)
+
+    # DIA format doesn't support .max() or .min() methods.
+    if x.format == 'dia':
+        x = x.tocsr()
+
+    if axis is None:
+        axis = tuple(range(x.ndim))
+    elif not isinstance(axis, tuple):
+        msg = "'axis' must be None, an integer or a tuple of integers"
+        try:
+            int_axis = int(axis)
+        except TypeError as e:
+            raise TypeError(msg) from e
+        if axis != int_axis:
+            raise TypeError(msg)
+        axis = (int_axis,)
+
+    nd = x.ndim
+    if len(axis) == 2:
+        row_axis, col_axis = axis
+        if not (-nd <= row_axis < nd and -nd <= col_axis < nd):
+            message = f'Invalid axis {axis!r} for an array with shape {x.shape!r}'
+            raise ValueError(message)
+        if row_axis % nd == col_axis % nd:
+            raise ValueError('Duplicate axes given.')
+        if ord == 2:
+            _, s, _ = svds(x, k=1, solver="arpack", rng=None)
+            return s[0]
+        if ord == -2:
+            raise NotImplementedError
+            #return _multi_svd_norm(x, row_axis, col_axis, amin)
+        if ord in (None, 'f', 'fro'):
+            # The axis order does not matter for this norm.
+            return _sparse_frobenius_norm(x)
+        if np.can_cast(x.dtype, float):
+            x = x.astype(float, copy=False)
+        if ord == 1:
+            return abs(x).sum(axis=row_axis).max()
+        elif ord == np.inf:
+            return abs(x).sum(axis=col_axis).max()
+        elif ord == -1:
+            return abs(x).sum(axis=row_axis).min()
+        elif ord == -np.inf:
+            return abs(x).sum(axis=col_axis).min()
+        else:
+            raise ValueError("Invalid norm order for matrices.")
+    elif len(axis) == 1:
+        a, = axis
+        if not (-nd <= a < nd):
+            message = f'Invalid axis {axis!r} for an array with shape {x.shape!r}'
+            raise ValueError(message)
+        if ord == 0:
+            return x.count_nonzero(axis=a)
+        if np.can_cast(x.dtype, float):
+            x = x.astype(float, copy=False)
+        if ord == np.inf:
+            return _ravel(abs(x).max(axis=a))
+        if ord == -np.inf:
+            return _ravel(abs(x).min(axis=a))
+        if ord == 1:
+            # special case for speedup
+            return _ravel(abs(x).sum(axis=a))
+        if ord in (2, None):
+            return _ravel(sqrt(abs(x).power(2).sum(axis=a)))
+        try:
+            ord + 1
+        except TypeError as e:
+            raise ValueError('Invalid norm order for vectors.') from e
+        return np.power(abs(x).power(ord).sum(axis=a), 1 / ord)
+    else:
+        raise ValueError("Improper number of dimensions to norm.")
+
+
+def _ravel(M):
+    if hasattr(M, 'toarray'):
+        return M.toarray().ravel()
+    elif hasattr(M, 'A'):
+        return M.A.ravel()
+    else:
+        return M.ravel()
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_onenormest.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_onenormest.py
new file mode 100644
index 0000000000000000000000000000000000000000..6da6a9faa86294583955fc29549ac8d29819d4b9
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_onenormest.py
@@ -0,0 +1,364 @@
+"""Sparse block 1-norm estimator.
+"""
+
+import numpy as np
+from scipy.sparse.linalg import aslinearoperator
+
+
+__all__ = ['onenormest']
+
+
+def onenormest(A, t=2, itmax=5, compute_v=False, compute_w=False):
+    """
+    Compute a lower bound of the 1-norm of a sparse array.
+
+    Parameters
+    ----------
+    A : ndarray or other linear operator
+        A linear operator that can be transposed and that can
+        produce matrix products.
+    t : int, optional
+        A positive parameter controlling the tradeoff between
+        accuracy versus time and memory usage.
+        Larger values take longer and use more memory
+        but give more accurate output.
+    itmax : int, optional
+        Use at most this many iterations.
+    compute_v : bool, optional
+        Request a norm-maximizing linear operator input vector if True.
+    compute_w : bool, optional
+        Request a norm-maximizing linear operator output vector if True.
+
+    Returns
+    -------
+    est : float
+        An underestimate of the 1-norm of the sparse array.
+    v : ndarray, optional
+        The vector such that ||Av||_1 == est*||v||_1.
+        It can be thought of as an input to the linear operator
+        that gives an output with particularly large norm.
+    w : ndarray, optional
+        The vector Av which has relatively large 1-norm.
+        It can be thought of as an output of the linear operator
+        that is relatively large in norm compared to the input.
+
+    Notes
+    -----
+    This is algorithm 2.4 of [1]_.
+
+    In [2]_ it is described as follows.
+    "This algorithm typically requires the evaluation of
+    about 4t matrix-vector products and almost invariably
+    produces a norm estimate (which is, in fact, a lower
+    bound on the norm) correct to within a factor 3."
+
+    .. versionadded:: 0.13.0
+
+    References
+    ----------
+    .. [1] Nicholas J. Higham and Francoise Tisseur (2000),
+           "A Block Algorithm for Matrix 1-Norm Estimation,
+           with an Application to 1-Norm Pseudospectra."
+           SIAM J. Matrix Anal. Appl. Vol. 21, No. 4, pp. 1185-1201.
+
+    .. [2] Awad H. Al-Mohy and Nicholas J. Higham (2009),
+           "A new scaling and squaring algorithm for the matrix exponential."
+           SIAM J. Matrix Anal. Appl. Vol. 31, No. 3, pp. 970-989.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.sparse import csc_array
+    >>> from scipy.sparse.linalg import onenormest
+    >>> A = csc_array([[1., 0., 0.], [5., 8., 2.], [0., -1., 0.]], dtype=float)
+    >>> A.toarray()
+    array([[ 1.,  0.,  0.],
+           [ 5.,  8.,  2.],
+           [ 0., -1.,  0.]])
+    >>> onenormest(A)
+    9.0
+    >>> np.linalg.norm(A.toarray(), ord=1)
+    9.0
+    """
+
+    # Check the input.
+    A = aslinearoperator(A)
+    if A.shape[0] != A.shape[1]:
+        raise ValueError('expected the operator to act like a square matrix')
+
+    # If the operator size is small compared to t,
+    # then it is easier to compute the exact norm.
+    # Otherwise estimate the norm.
+    n = A.shape[1]
+    if t >= n:
+        A_explicit = np.asarray(aslinearoperator(A).matmat(np.identity(n)))
+        if A_explicit.shape != (n, n):
+            raise Exception('internal error: ',
+                    'unexpected shape ' + str(A_explicit.shape))
+        col_abs_sums = abs(A_explicit).sum(axis=0)
+        if col_abs_sums.shape != (n, ):
+            raise Exception('internal error: ',
+                    'unexpected shape ' + str(col_abs_sums.shape))
+        argmax_j = np.argmax(col_abs_sums)
+        v = elementary_vector(n, argmax_j)
+        w = A_explicit[:, argmax_j]
+        est = col_abs_sums[argmax_j]
+    else:
+        est, v, w, nmults, nresamples = _onenormest_core(A, A.H, t, itmax)
+
+    # Report the norm estimate along with some certificates of the estimate.
+    if compute_v or compute_w:
+        result = (est,)
+        if compute_v:
+            result += (v,)
+        if compute_w:
+            result += (w,)
+        return result
+    else:
+        return est
+
+
+def _blocked_elementwise(func):
+    """
+    Decorator for an elementwise function, to apply it blockwise along
+    first dimension, to avoid excessive memory usage in temporaries.
+    """
+    block_size = 2**20
+
+    def wrapper(x):
+        if x.shape[0] < block_size:
+            return func(x)
+        else:
+            y0 = func(x[:block_size])
+            y = np.zeros((x.shape[0],) + y0.shape[1:], dtype=y0.dtype)
+            y[:block_size] = y0
+            del y0
+            for j in range(block_size, x.shape[0], block_size):
+                y[j:j+block_size] = func(x[j:j+block_size])
+            return y
+    return wrapper
+
+
+@_blocked_elementwise
+def sign_round_up(X):
+    """
+    This should do the right thing for both real and complex matrices.
+
+    From Higham and Tisseur:
+    "Everything in this section remains valid for complex matrices
+    provided that sign(A) is redefined as the matrix (aij / |aij|)
+    (and sign(0) = 1) transposes are replaced by conjugate transposes."
+
+    """
+    Y = X.copy()
+    Y[Y == 0] = 1
+    Y /= np.abs(Y)
+    return Y
+
+
+@_blocked_elementwise
+def _max_abs_axis1(X):
+    return np.max(np.abs(X), axis=1)
+
+
+def _sum_abs_axis0(X):
+    block_size = 2**20
+    r = None
+    for j in range(0, X.shape[0], block_size):
+        y = np.sum(np.abs(X[j:j+block_size]), axis=0)
+        if r is None:
+            r = y
+        else:
+            r += y
+    return r
+
+
+def elementary_vector(n, i):
+    v = np.zeros(n, dtype=float)
+    v[i] = 1
+    return v
+
+
+def vectors_are_parallel(v, w):
+    # Columns are considered parallel when they are equal or negative.
+    # Entries are required to be in {-1, 1},
+    # which guarantees that the magnitudes of the vectors are identical.
+    if v.ndim != 1 or v.shape != w.shape:
+        raise ValueError('expected conformant vectors with entries in {-1,1}')
+    n = v.shape[0]
+    return np.dot(v, w) == n
+
+
+def every_col_of_X_is_parallel_to_a_col_of_Y(X, Y):
+    for v in X.T:
+        if not any(vectors_are_parallel(v, w) for w in Y.T):
+            return False
+    return True
+
+
+def column_needs_resampling(i, X, Y=None):
+    # column i of X needs resampling if either
+    # it is parallel to a previous column of X or
+    # it is parallel to a column of Y
+    n, t = X.shape
+    v = X[:, i]
+    if any(vectors_are_parallel(v, X[:, j]) for j in range(i)):
+        return True
+    if Y is not None:
+        if any(vectors_are_parallel(v, w) for w in Y.T):
+            return True
+    return False
+
+
+def resample_column(i, X):
+    X[:, i] = np.random.randint(0, 2, size=X.shape[0])*2 - 1
+
+
+def less_than_or_close(a, b):
+    return np.allclose(a, b) or (a < b)
+
+
+def _onenormest_core(A, AT, t, itmax):
+    """
+    Compute a lower bound of the 1-norm of a sparse array.
+
+    Parameters
+    ----------
+    A : ndarray or other linear operator
+        A linear operator that can produce matrix products.
+    AT : ndarray or other linear operator
+        The transpose of A.
+    t : int, optional
+        A positive parameter controlling the tradeoff between
+        accuracy versus time and memory usage.
+    itmax : int, optional
+        Use at most this many iterations.
+
+    Returns
+    -------
+    est : float
+        An underestimate of the 1-norm of the sparse array.
+    v : ndarray, optional
+        The vector such that ||Av||_1 == est*||v||_1.
+        It can be thought of as an input to the linear operator
+        that gives an output with particularly large norm.
+    w : ndarray, optional
+        The vector Av which has relatively large 1-norm.
+        It can be thought of as an output of the linear operator
+        that is relatively large in norm compared to the input.
+    nmults : int, optional
+        The number of matrix products that were computed.
+    nresamples : int, optional
+        The number of times a parallel column was observed,
+        necessitating a re-randomization of the column.
+
+    Notes
+    -----
+    This is algorithm 2.4.
+
+    """
+    # This function is a more or less direct translation
+    # of Algorithm 2.4 from the Higham and Tisseur (2000) paper.
+    A_linear_operator = aslinearoperator(A)
+    AT_linear_operator = aslinearoperator(AT)
+    if itmax < 2:
+        raise ValueError('at least two iterations are required')
+    if t < 1:
+        raise ValueError('at least one column is required')
+    n = A.shape[0]
+    if t >= n:
+        raise ValueError('t should be smaller than the order of A')
+    # Track the number of big*small matrix multiplications
+    # and the number of resamplings.
+    nmults = 0
+    nresamples = 0
+    # "We now explain our choice of starting matrix.  We take the first
+    # column of X to be the vector of 1s [...] This has the advantage that
+    # for a matrix with nonnegative elements the algorithm converges
+    # with an exact estimate on the second iteration, and such matrices
+    # arise in applications [...]"
+    X = np.ones((n, t), dtype=float)
+    # "The remaining columns are chosen as rand{-1,1},
+    # with a check for and correction of parallel columns,
+    # exactly as for S in the body of the algorithm."
+    if t > 1:
+        for i in range(1, t):
+            # These are technically initial samples, not resamples,
+            # so the resampling count is not incremented.
+            resample_column(i, X)
+        for i in range(t):
+            while column_needs_resampling(i, X):
+                resample_column(i, X)
+                nresamples += 1
+    # "Choose starting matrix X with columns of unit 1-norm."
+    X /= float(n)
+    # "indices of used unit vectors e_j"
+    ind_hist = np.zeros(0, dtype=np.intp)
+    est_old = 0
+    S = np.zeros((n, t), dtype=float)
+    k = 1
+    ind = None
+    while True:
+        Y = np.asarray(A_linear_operator.matmat(X))
+        nmults += 1
+        mags = _sum_abs_axis0(Y)
+        est = np.max(mags)
+        best_j = np.argmax(mags)
+        if est > est_old or k == 2:
+            if k >= 2:
+                ind_best = ind[best_j]
+            w = Y[:, best_j]
+        # (1)
+        if k >= 2 and est <= est_old:
+            est = est_old
+            break
+        est_old = est
+        S_old = S
+        if k > itmax:
+            break
+        S = sign_round_up(Y)
+        del Y
+        # (2)
+        if every_col_of_X_is_parallel_to_a_col_of_Y(S, S_old):
+            break
+        if t > 1:
+            # "Ensure that no column of S is parallel to another column of S
+            # or to a column of S_old by replacing columns of S by rand{-1,1}."
+            for i in range(t):
+                while column_needs_resampling(i, S, S_old):
+                    resample_column(i, S)
+                    nresamples += 1
+        del S_old
+        # (3)
+        Z = np.asarray(AT_linear_operator.matmat(S))
+        nmults += 1
+        h = _max_abs_axis1(Z)
+        del Z
+        # (4)
+        if k >= 2 and max(h) == h[ind_best]:
+            break
+        # "Sort h so that h_first >= ... >= h_last
+        # and re-order ind correspondingly."
+        #
+        # Later on, we will need at most t+len(ind_hist) largest
+        # entries, so drop the rest
+        ind = np.argsort(h)[::-1][:t+len(ind_hist)].copy()
+        del h
+        if t > 1:
+            # (5)
+            # Break if the most promising t vectors have been visited already.
+            if np.isin(ind[:t], ind_hist).all():
+                break
+            # Put the most promising unvisited vectors at the front of the list
+            # and put the visited vectors at the end of the list.
+            # Preserve the order of the indices induced by the ordering of h.
+            seen = np.isin(ind, ind_hist)
+            ind = np.concatenate((ind[~seen], ind[seen]))
+        for j in range(t):
+            X[:, j] = elementary_vector(n, ind[j])
+
+        new_ind = ind[:t][~np.isin(ind[:t], ind_hist)]
+        ind_hist = np.concatenate((ind_hist, new_ind))
+        k += 1
+    v = elementary_vector(n, ind_best)
+    return est, v, w, nmults, nresamples
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_propack.cpython-312-x86_64-linux-gnu.so b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_propack.cpython-312-x86_64-linux-gnu.so
new file mode 100644
index 0000000000000000000000000000000000000000..08d275924a1835c735f28b19abc7b728e92f02e2
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_propack.cpython-312-x86_64-linux-gnu.so
@@ -0,0 +1,3 @@
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+oid sha256:b0fc98a02b3367027b9f22f2afacca2e5ae57b656077e216946398bfc5eb028e
+size 149313
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_special_sparse_arrays.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_special_sparse_arrays.py
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+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_special_sparse_arrays.py
@@ -0,0 +1,952 @@
+import numpy as np
+from scipy.sparse.linalg import LinearOperator
+from scipy.sparse import kron, eye_array, dia_array
+
+__all__ = ['LaplacianNd']
+# Sakurai and Mikota classes are intended for tests and benchmarks
+# and explicitly not included in the public API of this module.
+
+
+class LaplacianNd(LinearOperator):
+    """
+    The grid Laplacian in ``N`` dimensions and its eigenvalues/eigenvectors.
+
+    Construct Laplacian on a uniform rectangular grid in `N` dimensions
+    and output its eigenvalues and eigenvectors.
+    The Laplacian ``L`` is square, negative definite, real symmetric array
+    with signed integer entries and zeros otherwise.
+
+    Parameters
+    ----------
+    grid_shape : tuple
+        A tuple of integers of length ``N`` (corresponding to the dimension of
+        the Lapacian), where each entry gives the size of that dimension. The
+        Laplacian matrix is square of the size ``np.prod(grid_shape)``.
+    boundary_conditions : {'neumann', 'dirichlet', 'periodic'}, optional
+        The type of the boundary conditions on the boundaries of the grid.
+        Valid values are ``'dirichlet'`` or ``'neumann'``(default) or
+        ``'periodic'``.
+    dtype : dtype
+        Numerical type of the array. Default is ``np.int8``.
+
+    Methods
+    -------
+    toarray()
+        Construct a dense array from Laplacian data
+    tosparse()
+        Construct a sparse array from Laplacian data
+    eigenvalues(m=None)
+        Construct a 1D array of `m` largest (smallest in absolute value)
+        eigenvalues of the Laplacian matrix in ascending order.
+    eigenvectors(m=None):
+        Construct the array with columns made of `m` eigenvectors (``float``)
+        of the ``Nd`` Laplacian corresponding to the `m` ordered eigenvalues.
+
+    .. versionadded:: 1.12.0
+
+    Notes
+    -----
+    Compared to the MATLAB/Octave implementation [1] of 1-, 2-, and 3-D
+    Laplacian, this code allows the arbitrary N-D case and the matrix-free
+    callable option, but is currently limited to pure Dirichlet, Neumann or
+    Periodic boundary conditions only.
+
+    The Laplacian matrix of a graph (`scipy.sparse.csgraph.laplacian`) of a
+    rectangular grid corresponds to the negative Laplacian with the Neumann
+    conditions, i.e., ``boundary_conditions = 'neumann'``.
+
+    All eigenvalues and eigenvectors of the discrete Laplacian operator for
+    an ``N``-dimensional  regular grid of shape `grid_shape` with the grid
+    step size ``h=1`` are analytically known [2].
+
+    References
+    ----------
+    .. [1] https://github.com/lobpcg/blopex/blob/master/blopex_\
+tools/matlab/laplacian/laplacian.m
+    .. [2] "Eigenvalues and eigenvectors of the second derivative", Wikipedia
+           https://en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors_\
+of_the_second_derivative
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.sparse.linalg import LaplacianNd
+    >>> from scipy.sparse import diags_array, csgraph
+    >>> from scipy.linalg import eigvalsh
+
+    The one-dimensional Laplacian demonstrated below for pure Neumann boundary
+    conditions on a regular grid with ``n=6`` grid points is exactly the
+    negative graph Laplacian for the undirected linear graph with ``n``
+    vertices using the sparse adjacency matrix ``G`` represented by the
+    famous tri-diagonal matrix:
+
+    >>> n = 6
+    >>> G = diags_array(np.ones(n - 1), offsets=1, format='csr')
+    >>> Lf = csgraph.laplacian(G, symmetrized=True, form='function')
+    >>> grid_shape = (n, )
+    >>> lap = LaplacianNd(grid_shape, boundary_conditions='neumann')
+    >>> np.array_equal(lap.matmat(np.eye(n)), -Lf(np.eye(n)))
+    True
+
+    Since all matrix entries of the Laplacian are integers, ``'int8'`` is
+    the default dtype for storing matrix representations.
+
+    >>> lap.tosparse()
+    <DIAgonal sparse array of dtype 'int8'
+        with 16 stored elements (3 diagonals) and shape (6, 6)>
+    >>> lap.toarray()
+    array([[-1,  1,  0,  0,  0,  0],
+           [ 1, -2,  1,  0,  0,  0],
+           [ 0,  1, -2,  1,  0,  0],
+           [ 0,  0,  1, -2,  1,  0],
+           [ 0,  0,  0,  1, -2,  1],
+           [ 0,  0,  0,  0,  1, -1]], dtype=int8)
+    >>> np.array_equal(lap.matmat(np.eye(n)), lap.toarray())
+    True
+    >>> np.array_equal(lap.tosparse().toarray(), lap.toarray())
+    True
+
+    Any number of extreme eigenvalues and/or eigenvectors can be computed.
+
+    >>> lap = LaplacianNd(grid_shape, boundary_conditions='periodic')
+    >>> lap.eigenvalues()
+    array([-4., -3., -3., -1., -1.,  0.])
+    >>> lap.eigenvalues()[-2:]
+    array([-1.,  0.])
+    >>> lap.eigenvalues(2)
+    array([-1.,  0.])
+    >>> lap.eigenvectors(1)
+    array([[0.40824829],
+           [0.40824829],
+           [0.40824829],
+           [0.40824829],
+           [0.40824829],
+           [0.40824829]])
+    >>> lap.eigenvectors(2)
+    array([[ 0.28867513,  0.40824829],
+           [ 0.57735027,  0.40824829],
+           [ 0.28867513,  0.40824829],
+           [-0.28867513,  0.40824829],
+           [-0.57735027,  0.40824829],
+           [-0.28867513,  0.40824829]])
+    >>> lap.eigenvectors()
+    array([[ 0.40824829,  0.5       ,  0.28867513,  0.28867513,  0.5       ,
+             0.40824829],
+           [-0.40824829,  0.        , -0.57735027,  0.57735027,  0.        ,
+             0.40824829],
+           [ 0.40824829, -0.5       ,  0.28867513,  0.28867513, -0.5       ,
+             0.40824829],
+           [-0.40824829,  0.5       ,  0.28867513, -0.28867513, -0.5       ,
+             0.40824829],
+           [ 0.40824829,  0.        , -0.57735027, -0.57735027,  0.        ,
+             0.40824829],
+           [-0.40824829, -0.5       ,  0.28867513, -0.28867513,  0.5       ,
+             0.40824829]])
+
+    The two-dimensional Laplacian is illustrated on a regular grid with
+    ``grid_shape = (2, 3)`` points in each dimension.
+
+    >>> grid_shape = (2, 3)
+    >>> n = np.prod(grid_shape)
+
+    Numeration of grid points is as follows:
+
+    >>> np.arange(n).reshape(grid_shape + (-1,))
+    array([[[0],
+            [1],
+            [2]],
+    <BLANKLINE>
+           [[3],
+            [4],
+            [5]]])
+
+    Each of the boundary conditions ``'dirichlet'``, ``'periodic'``, and
+    ``'neumann'`` is illustrated separately; with ``'dirichlet'``
+
+    >>> lap = LaplacianNd(grid_shape, boundary_conditions='dirichlet')
+    >>> lap.tosparse()
+    <Compressed Sparse Row sparse array of dtype 'int8'
+        with 20 stored elements and shape (6, 6)>
+    >>> lap.toarray()
+    array([[-4,  1,  0,  1,  0,  0],
+           [ 1, -4,  1,  0,  1,  0],
+           [ 0,  1, -4,  0,  0,  1],
+           [ 1,  0,  0, -4,  1,  0],
+           [ 0,  1,  0,  1, -4,  1],
+           [ 0,  0,  1,  0,  1, -4]], dtype=int8)
+    >>> np.array_equal(lap.matmat(np.eye(n)), lap.toarray())
+    True
+    >>> np.array_equal(lap.tosparse().toarray(), lap.toarray())
+    True
+    >>> lap.eigenvalues()
+    array([-6.41421356, -5.        , -4.41421356, -3.58578644, -3.        ,
+           -1.58578644])
+    >>> eigvals = eigvalsh(lap.toarray().astype(np.float64))
+    >>> np.allclose(lap.eigenvalues(), eigvals)
+    True
+    >>> np.allclose(lap.toarray() @ lap.eigenvectors(),
+    ...             lap.eigenvectors() @ np.diag(lap.eigenvalues()))
+    True
+
+    with ``'periodic'``
+
+    >>> lap = LaplacianNd(grid_shape, boundary_conditions='periodic')
+    >>> lap.tosparse()
+    <Compressed Sparse Row sparse array of dtype 'int8'
+        with 24 stored elements and shape (6, 6)>
+    >>> lap.toarray()
+        array([[-4,  1,  1,  2,  0,  0],
+               [ 1, -4,  1,  0,  2,  0],
+               [ 1,  1, -4,  0,  0,  2],
+               [ 2,  0,  0, -4,  1,  1],
+               [ 0,  2,  0,  1, -4,  1],
+               [ 0,  0,  2,  1,  1, -4]], dtype=int8)
+    >>> np.array_equal(lap.matmat(np.eye(n)), lap.toarray())
+    True
+    >>> np.array_equal(lap.tosparse().toarray(), lap.toarray())
+    True
+    >>> lap.eigenvalues()
+    array([-7., -7., -4., -3., -3.,  0.])
+    >>> eigvals = eigvalsh(lap.toarray().astype(np.float64))
+    >>> np.allclose(lap.eigenvalues(), eigvals)
+    True
+    >>> np.allclose(lap.toarray() @ lap.eigenvectors(),
+    ...             lap.eigenvectors() @ np.diag(lap.eigenvalues()))
+    True
+
+    and with ``'neumann'``
+
+    >>> lap = LaplacianNd(grid_shape, boundary_conditions='neumann')
+    >>> lap.tosparse()
+    <Compressed Sparse Row sparse array of dtype 'int8'
+        with 20 stored elements and shape (6, 6)>
+    >>> lap.toarray()
+    array([[-2,  1,  0,  1,  0,  0],
+           [ 1, -3,  1,  0,  1,  0],
+           [ 0,  1, -2,  0,  0,  1],
+           [ 1,  0,  0, -2,  1,  0],
+           [ 0,  1,  0,  1, -3,  1],
+           [ 0,  0,  1,  0,  1, -2]], dtype=int8)
+    >>> np.array_equal(lap.matmat(np.eye(n)), lap.toarray())
+    True
+    >>> np.array_equal(lap.tosparse().toarray(), lap.toarray())
+    True
+    >>> lap.eigenvalues()
+    array([-5., -3., -3., -2., -1.,  0.])
+    >>> eigvals = eigvalsh(lap.toarray().astype(np.float64))
+    >>> np.allclose(lap.eigenvalues(), eigvals)
+    True
+    >>> np.allclose(lap.toarray() @ lap.eigenvectors(),
+    ...             lap.eigenvectors() @ np.diag(lap.eigenvalues()))
+    True
+
+    """
+
+    def __init__(self, grid_shape, *,
+                 boundary_conditions='neumann',
+                 dtype=np.int8):
+
+        if boundary_conditions not in ('dirichlet', 'neumann', 'periodic'):
+            raise ValueError(
+                f"Unknown value {boundary_conditions!r} is given for "
+                "'boundary_conditions' parameter. The valid options are "
+                "'dirichlet', 'periodic', and 'neumann' (default)."
+            )
+
+        self.grid_shape = grid_shape
+        self.boundary_conditions = boundary_conditions
+        # LaplacianNd folds all dimensions in `grid_shape` into a single one
+        N = np.prod(grid_shape)
+        super().__init__(dtype=dtype, shape=(N, N))
+
+    def _eigenvalue_ordering(self, m):
+        """Compute `m` largest eigenvalues in each of the ``N`` directions,
+        i.e., up to ``m * N`` total, order them and return `m` largest.
+        """
+        grid_shape = self.grid_shape
+        if m is None:
+            indices = np.indices(grid_shape)
+            Leig = np.zeros(grid_shape)
+        else:
+            grid_shape_min = min(grid_shape,
+                                 tuple(np.ones_like(grid_shape) * m))
+            indices = np.indices(grid_shape_min)
+            Leig = np.zeros(grid_shape_min)
+
+        for j, n in zip(indices, grid_shape):
+            if self.boundary_conditions == 'dirichlet':
+                Leig += -4 * np.sin(np.pi * (j + 1) / (2 * (n + 1))) ** 2
+            elif self.boundary_conditions == 'neumann':
+                Leig += -4 * np.sin(np.pi * j / (2 * n)) ** 2
+            else:  # boundary_conditions == 'periodic'
+                Leig += -4 * np.sin(np.pi * np.floor((j + 1) / 2) / n) ** 2
+
+        Leig_ravel = Leig.ravel()
+        ind = np.argsort(Leig_ravel)
+        eigenvalues = Leig_ravel[ind]
+        if m is not None:
+            eigenvalues = eigenvalues[-m:]
+            ind = ind[-m:]
+
+        return eigenvalues, ind
+
+    def eigenvalues(self, m=None):
+        """Return the requested number of eigenvalues.
+
+        Parameters
+        ----------
+        m : int, optional
+            The positive number of smallest eigenvalues to return.
+            If not provided, then all eigenvalues will be returned.
+
+        Returns
+        -------
+        eigenvalues : float array
+            The requested `m` smallest or all eigenvalues, in ascending order.
+        """
+        eigenvalues, _ = self._eigenvalue_ordering(m)
+        return eigenvalues
+
+    def _ev1d(self, j, n):
+        """Return 1 eigenvector in 1d with index `j`
+        and number of grid points `n` where ``j < n``.
+        """
+        if self.boundary_conditions == 'dirichlet':
+            i = np.pi * (np.arange(n) + 1) / (n + 1)
+            ev = np.sqrt(2. / (n + 1.)) * np.sin(i * (j + 1))
+        elif self.boundary_conditions == 'neumann':
+            i = np.pi * (np.arange(n) + 0.5) / n
+            ev = np.sqrt((1. if j == 0 else 2.) / n) * np.cos(i * j)
+        else:  # boundary_conditions == 'periodic'
+            if j == 0:
+                ev = np.sqrt(1. / n) * np.ones(n)
+            elif j + 1 == n and n % 2 == 0:
+                ev = np.sqrt(1. / n) * np.tile([1, -1], n//2)
+            elif (j + 1) % 2 == 0:
+                i = np.pi * (np.arange(n) + 0.5) / n
+                ev = np.sqrt(2. / n) * np.sin(i * (j + 1))
+            else:
+                i = np.pi * (np.arange(n) + 0.5) / n
+                ev = np.sqrt(2. / n) * np.cos(i * j)
+        # make small values exact zeros correcting round-off errors
+        # due to symmetry of eigenvectors the exact 0. is correct
+        ev[np.abs(ev) < np.finfo(np.float64).eps] = 0.
+        return ev
+
+    def _one_eve(self, k):
+        """Return 1 eigenvector in Nd with multi-index `j`
+        as a tensor product of the corresponding 1d eigenvectors.
+        """
+        phi = [self._ev1d(j, n) for j, n in zip(k, self.grid_shape)]
+        result = phi[0]
+        for phi in phi[1:]:
+            result = np.tensordot(result, phi, axes=0)
+        return np.asarray(result).ravel()
+
+    def eigenvectors(self, m=None):
+        """Return the requested number of eigenvectors for ordered eigenvalues.
+
+        Parameters
+        ----------
+        m : int, optional
+            The positive number of eigenvectors to return. If not provided,
+            then all eigenvectors will be returned.
+
+        Returns
+        -------
+        eigenvectors : float array
+            An array with columns made of the requested `m` or all eigenvectors.
+            The columns are ordered according to the `m` ordered eigenvalues.
+        """
+        _, ind = self._eigenvalue_ordering(m)
+        if m is None:
+            grid_shape_min = self.grid_shape
+        else:
+            grid_shape_min = min(self.grid_shape,
+                                tuple(np.ones_like(self.grid_shape) * m))
+
+        N_indices = np.unravel_index(ind, grid_shape_min)
+        N_indices = [tuple(x) for x in zip(*N_indices)]
+        eigenvectors_list = [self._one_eve(k) for k in N_indices]
+        return np.column_stack(eigenvectors_list)
+
+    def toarray(self):
+        """
+        Converts the Laplacian data to a dense array.
+
+        Returns
+        -------
+        L : ndarray
+            The shape is ``(N, N)`` where ``N = np.prod(grid_shape)``.
+
+        """
+        grid_shape = self.grid_shape
+        n = np.prod(grid_shape)
+        L = np.zeros([n, n], dtype=np.int8)
+        # Scratch arrays
+        L_i = np.empty_like(L)
+        Ltemp = np.empty_like(L)
+
+        for ind, dim in enumerate(grid_shape):
+            # Start zeroing out L_i
+            L_i[:] = 0
+            # Allocate the top left corner with the kernel of L_i
+            # Einsum returns writable view of arrays
+            np.einsum("ii->i", L_i[:dim, :dim])[:] = -2
+            np.einsum("ii->i", L_i[: dim - 1, 1:dim])[:] = 1
+            np.einsum("ii->i", L_i[1:dim, : dim - 1])[:] = 1
+
+            if self.boundary_conditions == 'neumann':
+                L_i[0, 0] = -1
+                L_i[dim - 1, dim - 1] = -1
+            elif self.boundary_conditions == 'periodic':
+                if dim > 1:
+                    L_i[0, dim - 1] += 1
+                    L_i[dim - 1, 0] += 1
+                else:
+                    L_i[0, 0] += 1
+
+            # kron is too slow for large matrices hence the next two tricks
+            # 1- kron(eye, mat) is block_diag(mat, mat, ...)
+            # 2- kron(mat, eye) can be performed by 4d stride trick
+
+            # 1-
+            new_dim = dim
+            # for block_diag we tile the top left portion on the diagonal
+            if ind > 0:
+                tiles = np.prod(grid_shape[:ind])
+                for j in range(1, tiles):
+                    L_i[j*dim:(j+1)*dim, j*dim:(j+1)*dim] = L_i[:dim, :dim]
+                    new_dim += dim
+            # 2-
+            # we need the keep L_i, but reset the array
+            Ltemp[:new_dim, :new_dim] = L_i[:new_dim, :new_dim]
+            tiles = int(np.prod(grid_shape[ind+1:]))
+            # Zero out the top left, the rest is already 0
+            L_i[:new_dim, :new_dim] = 0
+            idx = [x for x in range(tiles)]
+            L_i.reshape(
+                (new_dim, tiles,
+                 new_dim, tiles)
+                )[:, idx, :, idx] = Ltemp[:new_dim, :new_dim]
+
+            L += L_i
+
+        return L.astype(self.dtype)
+
+    def tosparse(self):
+        """
+        Constructs a sparse array from the Laplacian data. The returned sparse
+        array format is dependent on the selected boundary conditions.
+
+        Returns
+        -------
+        L : scipy.sparse.sparray
+            The shape is ``(N, N)`` where ``N = np.prod(grid_shape)``.
+
+        """
+        N = len(self.grid_shape)
+        p = np.prod(self.grid_shape)
+        L = dia_array((p, p), dtype=np.int8)
+
+        for i in range(N):
+            dim = self.grid_shape[i]
+            data = np.ones([3, dim], dtype=np.int8)
+            data[1, :] *= -2
+
+            if self.boundary_conditions == 'neumann':
+                data[1, 0] = -1
+                data[1, -1] = -1
+
+            L_i = dia_array((data, [-1, 0, 1]), shape=(dim, dim),
+                            dtype=np.int8
+                            )
+
+            if self.boundary_conditions == 'periodic':
+                t = dia_array((dim, dim), dtype=np.int8)
+                t.setdiag([1], k=-dim+1)
+                t.setdiag([1], k=dim-1)
+                L_i += t
+
+            for j in range(i):
+                L_i = kron(eye_array(self.grid_shape[j], dtype=np.int8), L_i)
+            for j in range(i + 1, N):
+                L_i = kron(L_i, eye_array(self.grid_shape[j], dtype=np.int8))
+            L += L_i
+        return L.astype(self.dtype)
+
+    def _matvec(self, x):
+        grid_shape = self.grid_shape
+        N = len(grid_shape)
+        X = x.reshape(grid_shape + (-1,))
+        Y = -2 * N * X
+        for i in range(N):
+            Y += np.roll(X, 1, axis=i)
+            Y += np.roll(X, -1, axis=i)
+            if self.boundary_conditions in ('neumann', 'dirichlet'):
+                Y[(slice(None),)*i + (0,) + (slice(None),)*(N-i-1)
+                  ] -= np.roll(X, 1, axis=i)[
+                    (slice(None),) * i + (0,) + (slice(None),) * (N-i-1)
+                ]
+                Y[
+                    (slice(None),) * i + (-1,) + (slice(None),) * (N-i-1)
+                ] -= np.roll(X, -1, axis=i)[
+                    (slice(None),) * i + (-1,) + (slice(None),) * (N-i-1)
+                ]
+
+                if self.boundary_conditions == 'neumann':
+                    Y[
+                        (slice(None),) * i + (0,) + (slice(None),) * (N-i-1)
+                    ] += np.roll(X, 0, axis=i)[
+                        (slice(None),) * i + (0,) + (slice(None),) * (N-i-1)
+                    ]
+                    Y[
+                        (slice(None),) * i + (-1,) + (slice(None),) * (N-i-1)
+                    ] += np.roll(X, 0, axis=i)[
+                        (slice(None),) * i + (-1,) + (slice(None),) * (N-i-1)
+                    ]
+
+        return Y.reshape(-1, X.shape[-1])
+
+    def _matmat(self, x):
+        return self._matvec(x)
+
+    def _adjoint(self):
+        return self
+
+    def _transpose(self):
+        return self
+
+
+class Sakurai(LinearOperator):
+    """
+    Construct a Sakurai matrix in various formats and its eigenvalues.
+
+    Constructs the "Sakurai" matrix motivated by reference [1]_:
+    square real symmetric positive definite and 5-diagonal
+    with the main diagonal ``[5, 6, 6, ..., 6, 6, 5], the ``+1`` and ``-1``
+    diagonals filled with ``-4``, and the ``+2`` and ``-2`` diagonals
+    made of ``1``. Its eigenvalues are analytically known to be
+    ``16. * np.power(np.cos(0.5 * k * np.pi / (n + 1)), 4)``.
+    The matrix gets ill-conditioned with its size growing.
+    It is useful for testing and benchmarking sparse eigenvalue solvers
+    especially those taking advantage of its banded 5-diagonal structure.
+    See the notes below for details.
+
+    Parameters
+    ----------
+    n : int
+        The size of the matrix.
+    dtype : dtype
+        Numerical type of the array. Default is ``np.int8``.
+
+    Methods
+    -------
+    toarray()
+        Construct a dense array from Laplacian data
+    tosparse()
+        Construct a sparse array from Laplacian data
+    tobanded()
+        The Sakurai matrix in the format for banded symmetric matrices,
+        i.e., (3, n) ndarray with 3 upper diagonals
+        placing the main diagonal at the bottom.
+    eigenvalues
+        All eigenvalues of the Sakurai matrix ordered ascending.
+
+    Notes
+    -----
+    Reference [1]_ introduces a generalized eigenproblem for the matrix pair
+    `A` and `B` where `A` is the identity so we turn it into an eigenproblem
+    just for the matrix `B` that this function outputs in various formats
+    together with its eigenvalues.
+
+    .. versionadded:: 1.12.0
+
+    References
+    ----------
+    .. [1] T. Sakurai, H. Tadano, Y. Inadomi, and U. Nagashima,
+       "A moment-based method for large-scale generalized
+       eigenvalue problems",
+       Appl. Num. Anal. Comp. Math. Vol. 1 No. 2 (2004).
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.sparse.linalg._special_sparse_arrays import Sakurai
+    >>> from scipy.linalg import eig_banded
+    >>> n = 6
+    >>> sak = Sakurai(n)
+
+    Since all matrix entries are small integers, ``'int8'`` is
+    the default dtype for storing matrix representations.
+
+    >>> sak.toarray()
+    array([[ 5, -4,  1,  0,  0,  0],
+           [-4,  6, -4,  1,  0,  0],
+           [ 1, -4,  6, -4,  1,  0],
+           [ 0,  1, -4,  6, -4,  1],
+           [ 0,  0,  1, -4,  6, -4],
+           [ 0,  0,  0,  1, -4,  5]], dtype=int8)
+    >>> sak.tobanded()
+    array([[ 1,  1,  1,  1,  1,  1],
+           [-4, -4, -4, -4, -4, -4],
+           [ 5,  6,  6,  6,  6,  5]], dtype=int8)
+    >>> sak.tosparse()
+    <DIAgonal sparse array of dtype 'int8'
+        with 24 stored elements (5 diagonals) and shape (6, 6)>
+    >>> np.array_equal(sak.dot(np.eye(n)), sak.tosparse().toarray())
+    True
+    >>> sak.eigenvalues()
+    array([0.03922866, 0.56703972, 2.41789479, 5.97822974,
+           10.54287655, 14.45473055])
+    >>> sak.eigenvalues(2)
+    array([0.03922866, 0.56703972])
+
+    The banded form can be used in scipy functions for banded matrices, e.g.,
+
+    >>> e = eig_banded(sak.tobanded(), eigvals_only=True)
+    >>> np.allclose(sak.eigenvalues(), e, atol= n * n * n * np.finfo(float).eps)
+    True
+
+    """
+    def __init__(self, n, dtype=np.int8):
+        self.n = n
+        self.dtype = dtype
+        shape = (n, n)
+        super().__init__(dtype, shape)
+
+    def eigenvalues(self, m=None):
+        """Return the requested number of eigenvalues.
+
+        Parameters
+        ----------
+        m : int, optional
+            The positive number of smallest eigenvalues to return.
+            If not provided, then all eigenvalues will be returned.
+
+        Returns
+        -------
+        eigenvalues : `np.float64` array
+            The requested `m` smallest or all eigenvalues, in ascending order.
+        """
+        if m is None:
+            m = self.n
+        k = np.arange(self.n + 1 -m, self.n + 1)
+        return np.flip(16. * np.power(np.cos(0.5 * k * np.pi / (self.n + 1)), 4))
+
+    def tobanded(self):
+        """
+        Construct the Sakurai matrix as a banded array.
+        """
+        d0 = np.r_[5, 6 * np.ones(self.n - 2, dtype=self.dtype), 5]
+        d1 = -4 * np.ones(self.n, dtype=self.dtype)
+        d2 = np.ones(self.n, dtype=self.dtype)
+        return np.array([d2, d1, d0]).astype(self.dtype)
+
+    def tosparse(self):
+        """
+        Construct the Sakurai matrix in a sparse format.
+        """
+        from scipy.sparse import diags_array
+        d = self.tobanded()
+        # the banded format has the main diagonal at the bottom
+        # `diags_array` inherits dtype from banded
+        return diags_array([d[0], d[1], d[2], d[1], d[0]], offsets=[-2, -1, 0, 1, 2],
+                           shape=(self.n, self.n), dtype=d.dtype)
+
+    def toarray(self):
+        return self.tosparse().toarray()
+
+    def _matvec(self, x):
+        """
+        Construct matrix-free callable banded-matrix-vector multiplication by
+        the Sakurai matrix without constructing or storing the matrix itself
+        using the knowledge of its entries and the 5-diagonal format.
+        """
+        x = x.reshape(self.n, -1)
+        result_dtype = np.promote_types(x.dtype, self.dtype)
+        sx = np.zeros_like(x, dtype=result_dtype)
+        sx[0, :] = 5 * x[0, :] - 4 * x[1, :] + x[2, :]
+        sx[-1, :] = 5 * x[-1, :] - 4 * x[-2, :] + x[-3, :]
+        sx[1: -1, :] = (6 * x[1: -1, :] - 4 * (x[:-2, :] + x[2:, :])
+                      + np.pad(x[:-3, :], ((1, 0), (0, 0)))
+                      + np.pad(x[3:, :], ((0, 1), (0, 0))))
+        return sx
+
+    def _matmat(self, x):
+        """
+        Construct matrix-free callable matrix-matrix multiplication by
+        the Sakurai matrix without constructing or storing the matrix itself
+        by reusing the ``_matvec(x)`` that supports both 1D and 2D arrays ``x``.
+        """
+        return self._matvec(x)
+
+    def _adjoint(self):
+        return self
+
+    def _transpose(self):
+        return self
+
+
+class MikotaM(LinearOperator):
+    """
+    Construct a mass matrix in various formats of Mikota pair.
+
+    The mass matrix `M` is square real diagonal
+    positive definite with entries that are reciprocal to integers.
+
+    Parameters
+    ----------
+    shape : tuple of int
+        The shape of the matrix.
+    dtype : dtype
+        Numerical type of the array. Default is ``np.float64``.
+
+    Methods
+    -------
+    toarray()
+        Construct a dense array from Mikota data
+    tosparse()
+        Construct a sparse array from Mikota data
+    tobanded()
+        The format for banded symmetric matrices,
+        i.e., (1, n) ndarray with the main diagonal.
+    """
+    def __init__(self, shape, dtype=np.float64):
+        self.shape = shape
+        self.dtype = dtype
+        super().__init__(dtype, shape)
+
+    def _diag(self):
+        # The matrix is constructed from its diagonal 1 / [1, ..., N+1];
+        # compute in a function to avoid duplicated code & storage footprint
+        return (1. / np.arange(1, self.shape[0] + 1)).astype(self.dtype)
+
+    def tobanded(self):
+        return self._diag()
+
+    def tosparse(self):
+        from scipy.sparse import diags_array
+        return diags_array([self._diag()], offsets=[0],
+                           shape=self.shape, dtype=self.dtype)
+
+    def toarray(self):
+        return np.diag(self._diag()).astype(self.dtype)
+
+    def _matvec(self, x):
+        """
+        Construct matrix-free callable banded-matrix-vector multiplication by
+        the Mikota mass matrix without constructing or storing the matrix itself
+        using the knowledge of its entries and the diagonal format.
+        """
+        x = x.reshape(self.shape[0], -1)
+        return self._diag()[:, np.newaxis] * x
+
+    def _matmat(self, x):
+        """
+        Construct matrix-free callable matrix-matrix multiplication by
+        the Mikota mass matrix without constructing or storing the matrix itself
+        by reusing the ``_matvec(x)`` that supports both 1D and 2D arrays ``x``.
+        """
+        return self._matvec(x)
+
+    def _adjoint(self):
+        return self
+
+    def _transpose(self):
+        return self
+
+
+class MikotaK(LinearOperator):
+    """
+    Construct a stiffness matrix in various formats of Mikota pair.
+
+    The stiffness matrix `K` is square real tri-diagonal symmetric
+    positive definite with integer entries.
+
+    Parameters
+    ----------
+    shape : tuple of int
+        The shape of the matrix.
+    dtype : dtype
+        Numerical type of the array. Default is ``np.int32``.
+
+    Methods
+    -------
+    toarray()
+        Construct a dense array from Mikota data
+    tosparse()
+        Construct a sparse array from Mikota data
+    tobanded()
+        The format for banded symmetric matrices,
+        i.e., (2, n) ndarray with 2 upper diagonals
+        placing the main diagonal at the bottom.
+    """
+    def __init__(self, shape, dtype=np.int32):
+        self.shape = shape
+        self.dtype = dtype
+        super().__init__(dtype, shape)
+        # The matrix is constructed from its diagonals;
+        # we precompute these to avoid duplicating the computation
+        n = shape[0]
+        self._diag0 = np.arange(2 * n - 1, 0, -2, dtype=self.dtype)
+        self._diag1 = - np.arange(n - 1, 0, -1, dtype=self.dtype)
+
+    def tobanded(self):
+        return np.array([np.pad(self._diag1, (1, 0), 'constant'), self._diag0])
+
+    def tosparse(self):
+        from scipy.sparse import diags_array
+        return diags_array([self._diag1, self._diag0, self._diag1], offsets=[-1, 0, 1],
+                           shape=self.shape, dtype=self.dtype)
+
+    def toarray(self):
+        return self.tosparse().toarray()
+
+    def _matvec(self, x):
+        """
+        Construct matrix-free callable banded-matrix-vector multiplication by
+        the Mikota stiffness matrix without constructing or storing the matrix
+        itself using the knowledge of its entries and the 3-diagonal format.
+        """
+        x = x.reshape(self.shape[0], -1)
+        result_dtype = np.promote_types(x.dtype, self.dtype)
+        kx = np.zeros_like(x, dtype=result_dtype)
+        d1 = self._diag1
+        d0 = self._diag0
+        kx[0, :] = d0[0] * x[0, :] + d1[0] * x[1, :]
+        kx[-1, :] = d1[-1] * x[-2, :] + d0[-1] * x[-1, :]
+        kx[1: -1, :] = (d1[:-1, None] * x[: -2, :]
+                        + d0[1: -1, None] * x[1: -1, :]
+                        + d1[1:, None] * x[2:, :])
+        return kx
+
+    def _matmat(self, x):
+        """
+        Construct matrix-free callable matrix-matrix multiplication by
+        the Stiffness mass matrix without constructing or storing the matrix itself
+        by reusing the ``_matvec(x)`` that supports both 1D and 2D arrays ``x``.
+        """
+        return self._matvec(x)
+
+    def _adjoint(self):
+        return self
+
+    def _transpose(self):
+        return self
+
+
+class MikotaPair:
+    """
+    Construct the Mikota pair of matrices in various formats and
+    eigenvalues of the generalized eigenproblem with them.
+
+    The Mikota pair of matrices [1, 2]_ models a vibration problem
+    of a linear mass-spring system with the ends attached where
+    the stiffness of the springs and the masses increase along
+    the system length such that vibration frequencies are subsequent
+    integers 1, 2, ..., `n` where `n` is the number of the masses. Thus,
+    eigenvalues of the generalized eigenvalue problem for
+    the matrix pair `K` and `M` where `K` is the system stiffness matrix
+    and `M` is the system mass matrix are the squares of the integers,
+    i.e., 1, 4, 9, ..., ``n * n``.
+
+    The stiffness matrix `K` is square real tri-diagonal symmetric
+    positive definite. The mass matrix `M` is diagonal with diagonal
+    entries 1, 1/2, 1/3, ...., ``1/n``. Both matrices get
+    ill-conditioned with `n` growing.
+
+    Parameters
+    ----------
+    n : int
+        The size of the matrices of the Mikota pair.
+    dtype : dtype
+        Numerical type of the array. Default is ``np.float64``.
+
+    Attributes
+    ----------
+    eigenvalues : 1D ndarray, ``np.uint64``
+        All eigenvalues of the Mikota pair ordered ascending.
+
+    Methods
+    -------
+    MikotaK()
+        A `LinearOperator` custom object for the stiffness matrix.
+    MikotaM()
+        A `LinearOperator` custom object for the mass matrix.
+
+    .. versionadded:: 1.12.0
+
+    References
+    ----------
+    .. [1] J. Mikota, "Frequency tuning of chain structure multibody oscillators
+       to place the natural frequencies at omega1 and N-1 integer multiples
+       omega2,..., omegaN", Z. Angew. Math. Mech. 81 (2001), S2, S201-S202.
+       Appl. Num. Anal. Comp. Math. Vol. 1 No. 2 (2004).
+    .. [2] Peter C. Muller and Metin Gurgoze,
+       "Natural frequencies of a multi-degree-of-freedom vibration system",
+       Proc. Appl. Math. Mech. 6, 319-320 (2006).
+       :doi:`10.1002/pamm.200610141`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.sparse.linalg._special_sparse_arrays import MikotaPair
+    >>> n = 6
+    >>> mik = MikotaPair(n)
+    >>> mik_k = mik.k
+    >>> mik_m = mik.m
+    >>> mik_k.toarray()
+    array([[11., -5.,  0.,  0.,  0.,  0.],
+           [-5.,  9., -4.,  0.,  0.,  0.],
+           [ 0., -4.,  7., -3.,  0.,  0.],
+           [ 0.,  0., -3.,  5., -2.,  0.],
+           [ 0.,  0.,  0., -2.,  3., -1.],
+           [ 0.,  0.,  0.,  0., -1.,  1.]])
+    >>> mik_k.tobanded()
+    array([[ 0., -5., -4., -3., -2., -1.],
+           [11.,  9.,  7.,  5.,  3.,  1.]])
+    >>> mik_m.tobanded()
+    array([1.        , 0.5       , 0.33333333, 0.25      , 0.2       ,
+        0.16666667])
+    >>> mik_k.tosparse()
+    <DIAgonal sparse array of dtype 'float64'
+        with 16 stored elements (3 diagonals) and shape (6, 6)>
+    >>> mik_m.tosparse()
+    <DIAgonal sparse array of dtype 'float64'
+        with 6 stored elements (1 diagonals) and shape (6, 6)>
+    >>> np.array_equal(mik_k(np.eye(n)), mik_k.toarray())
+    True
+    >>> np.array_equal(mik_m(np.eye(n)), mik_m.toarray())
+    True
+    >>> mik.eigenvalues()
+    array([ 1,  4,  9, 16, 25, 36])
+    >>> mik.eigenvalues(2)
+    array([ 1,  4])
+
+    """
+    def __init__(self, n, dtype=np.float64):
+        self.n = n
+        self.dtype = dtype
+        self.shape = (n, n)
+        self.m = MikotaM(self.shape, self.dtype)
+        self.k = MikotaK(self.shape, self.dtype)
+
+    def eigenvalues(self, m=None):
+        """Return the requested number of eigenvalues.
+
+        Parameters
+        ----------
+        m : int, optional
+            The positive number of smallest eigenvalues to return.
+            If not provided, then all eigenvalues will be returned.
+
+        Returns
+        -------
+        eigenvalues : `np.uint64` array
+            The requested `m` smallest or all eigenvalues, in ascending order.
+        """
+        if m is None:
+            m = self.n
+        arange_plus1 = np.arange(1, m + 1, dtype=np.uint64)
+        return arange_plus1 * arange_plus1
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_svdp.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_svdp.py
new file mode 100644
index 0000000000000000000000000000000000000000..17ee447cd58ac96d28180000c645c09889ef8447
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/_svdp.py
@@ -0,0 +1,304 @@
+__all__ = ['_svdp']
+
+import numpy as np
+from scipy.linalg.lapack import HAS_ILP64
+
+from scipy.sparse.linalg import aslinearoperator
+from scipy.linalg import LinAlgError
+
+from . import _propack  # type: ignore[attr-defined]
+
+
+_lansvd_dict = {
+    'f': _propack.slansvd,
+    'd': _propack.dlansvd,
+    'F': _propack.clansvd,
+    'D': _propack.zlansvd,
+}
+
+
+_lansvd_irl_dict = {
+    'f': _propack.slansvd_irl,
+    'd': _propack.dlansvd_irl,
+    'F': _propack.clansvd_irl,
+    'D': _propack.zlansvd_irl,
+}
+
+
+_which_converter = {
+    'LM': 1,
+    'SM': 0,
+}
+
+
+class _AProd:
+    """
+    Wrapper class for linear operator
+
+    The call signature of the __call__ method matches the callback of
+    the PROPACK routines.
+    """
+    def __init__(self, A):
+        try:
+            self.A = aslinearoperator(A)
+        except TypeError:
+            self.A = aslinearoperator(np.asarray(A))
+
+    def __call__(self, transa, m, n, x, y):
+        if transa == 0:
+            y[:] = self.A.matvec(x)
+        else:
+            y[:] = self.A.rmatvec(x)
+
+    @property
+    def shape(self):
+        return self.A.shape
+
+    @property
+    def dtype(self):
+        try:
+            return self.A.dtype
+        except AttributeError:
+            return self.A.matvec(np.zeros(self.A.shape[1])).dtype
+
+
+def _svdp(A, k, which='LM', irl_mode=True, kmax=None,
+          compute_u=True, compute_v=True, v0=None, full_output=False, tol=0,
+          delta=None, eta=None, anorm=0, cgs=False, elr=True,
+          min_relgap=0.002, shifts=None, maxiter=None, rng=None):
+    """
+    Compute the singular value decomposition of a linear operator using PROPACK
+
+    Parameters
+    ----------
+    A : array_like, sparse matrix, or LinearOperator
+        Operator for which SVD will be computed.  If `A` is a LinearOperator
+        object, it must define both ``matvec`` and ``rmatvec`` methods.
+    k : int
+        Number of singular values/vectors to compute
+    which : {"LM", "SM"}
+        Which singular triplets to compute:
+        - 'LM': compute triplets corresponding to the `k` largest singular
+                values
+        - 'SM': compute triplets corresponding to the `k` smallest singular
+                values
+        `which='SM'` requires `irl_mode=True`.  Computes largest singular
+        values by default.
+    irl_mode : bool, optional
+        If `True`, then compute SVD using IRL (implicitly restarted Lanczos)
+        mode.  Default is `True`.
+    kmax : int, optional
+        Maximal number of iterations / maximal dimension of the Krylov
+        subspace. Default is ``10 * k``.
+    compute_u : bool, optional
+        If `True` (default) then compute left singular vectors, `u`.
+    compute_v : bool, optional
+        If `True` (default) then compute right singular vectors, `v`.
+    tol : float, optional
+        The desired relative accuracy for computed singular values.
+        If not specified, it will be set based on machine precision.
+    v0 : array_like, optional
+        Starting vector for iterations: must be of length ``A.shape[0]``.
+        If not specified, PROPACK will generate a starting vector.
+    full_output : bool, optional
+        If `True`, then return sigma_bound.  Default is `False`.
+    delta : float, optional
+        Level of orthogonality to maintain between Lanczos vectors.
+        Default is set based on machine precision.
+    eta : float, optional
+        Orthogonality cutoff.  During reorthogonalization, vectors with
+        component larger than `eta` along the Lanczos vector will be purged.
+        Default is set based on machine precision.
+    anorm : float, optional
+        Estimate of ``||A||``.  Default is ``0``.
+    cgs : bool, optional
+        If `True`, reorthogonalization is done using classical Gram-Schmidt.
+        If `False` (default), it is done using modified Gram-Schmidt.
+    elr : bool, optional
+        If `True` (default), then extended local orthogonality is enforced
+        when obtaining singular vectors.
+    min_relgap : float, optional
+        The smallest relative gap allowed between any shift in IRL mode.
+        Default is ``0.001``.  Accessed only if ``irl_mode=True``.
+    shifts : int, optional
+        Number of shifts per restart in IRL mode.  Default is determined
+        to satisfy ``k <= min(kmax-shifts, m, n)``.  Must be
+        >= 0, but choosing 0 might lead to performance degradation.
+        Accessed only if ``irl_mode=True``.
+    maxiter : int, optional
+        Maximum number of restarts in IRL mode.  Default is ``1000``.
+        Accessed only if ``irl_mode=True``.
+    rng : `numpy.random.Generator`, optional
+        Pseudorandom number generator state. When `rng` is None, a new
+        `numpy.random.Generator` is created using entropy from the
+        operating system. Types other than `numpy.random.Generator` are
+        passed to `numpy.random.default_rng` to instantiate a ``Generator``.
+
+    Returns
+    -------
+    u : ndarray
+        The `k` largest (``which="LM"``) or smallest (``which="SM"``) left
+        singular vectors, ``shape == (A.shape[0], 3)``, returned only if
+        ``compute_u=True``.
+    sigma : ndarray
+        The top `k` singular values, ``shape == (k,)``
+    vt : ndarray
+        The `k` largest (``which="LM"``) or smallest (``which="SM"``) right
+        singular vectors, ``shape == (3, A.shape[1])``, returned only if
+        ``compute_v=True``.
+    sigma_bound : ndarray
+        the error bounds on the singular values sigma, returned only if
+        ``full_output=True``.
+
+    """
+    if rng is None:
+        raise ValueError("`rng` must be a normalized numpy.random.Generator instance")
+
+    which = which.upper()
+    if which not in {'LM', 'SM'}:
+        raise ValueError("`which` must be either 'LM' or 'SM'")
+    if not irl_mode and which == 'SM':
+        raise ValueError("`which`='SM' requires irl_mode=True")
+
+    aprod = _AProd(A)
+    typ = aprod.dtype.char
+
+    try:
+        lansvd_irl = _lansvd_irl_dict[typ]
+        lansvd = _lansvd_dict[typ]
+    except KeyError:
+        # work with non-supported types using native system precision
+        if np.iscomplexobj(np.empty(0, dtype=typ)):
+            typ = 'D'
+        else:
+            typ = 'd'
+        lansvd_irl = _lansvd_irl_dict[typ]
+        lansvd = _lansvd_dict[typ]
+
+    m, n = aprod.shape
+    if (k < 1) or (k > min(m, n)):
+        raise ValueError("k must be positive and not greater than m or n")
+
+    if kmax is None:
+        kmax = 10*k
+    if maxiter is None:
+        maxiter = 1000
+
+    # guard against unnecessarily large kmax
+    kmax = min(m + 1, n + 1, kmax)
+    if kmax < k:
+        raise ValueError(
+            "kmax must be greater than or equal to k, "
+            f"but kmax ({kmax}) < k ({k})")
+
+    # convert python args to fortran args
+    jobu = 1 if compute_u else 0
+    jobv = 1 if compute_v else 0
+
+    # these will be the output arrays
+    u = np.zeros((m, kmax + 1), order='F', dtype=typ)
+    v = np.zeros((n, kmax), order='F', dtype=typ)
+    sigma = np.zeros(k, order='F', dtype=typ.lower())
+    bnd = np.zeros(k, order='F', dtype=typ.lower())
+
+    # Specify the starting vector.  if v0 is all zero, PROPACK will generate
+    # a random starting vector: the random seed cannot be controlled in that
+    # case, so we'll instead use numpy to generate a random vector
+    if v0 is None:
+        u[:, 0] = rng.uniform(size=m)
+        if np.iscomplexobj(np.empty(0, dtype=typ)):  # complex type
+            u[:, 0] += 1j * rng.uniform(size=m)
+    else:
+        try:
+            u[:, 0] = v0
+        except ValueError:
+            raise ValueError(f"v0 must be of length {m}")
+
+    # process options for the fit
+    if delta is None:
+        delta = np.sqrt(np.finfo(typ).eps)
+    if eta is None:
+        eta = np.finfo(typ).eps ** 0.75
+
+    if irl_mode:
+        doption = np.array((delta, eta, anorm, min_relgap), dtype=typ.lower())
+
+        # validate or find default shifts
+        if shifts is None:
+            shifts = kmax - k
+        if k > min(kmax - shifts, m, n):
+            raise ValueError('shifts must satisfy '
+                             'k <= min(kmax-shifts, m, n)!')
+        elif shifts < 0:
+            raise ValueError('shifts must be >= 0!')
+
+    else:
+        doption = np.array((delta, eta, anorm), dtype=typ.lower())
+
+    int_dtype = np.int64 if HAS_ILP64 else np.int32
+    ioption = np.array((int(bool(cgs)), int(bool(elr))), dtype=int_dtype)
+
+    # PROPACK uses a few LAPACK functions that require sufficiently large
+    # work arrays to utilize BLAS level 3 operations. In almost all relevant
+    # architectures, the blocksize is 32 or 64. We use 32 here to be on
+    # the conservative side.
+    NB = 32
+
+    # Determine lwork & liwork:
+    # the required lengths are specified in the PROPACK documentation
+    if compute_u or compute_v:
+        lwork = m + n + 5*kmax**2 + 9*kmax + 4
+        lwork += max(3*kmax**2 + 4*kmax + 4, NB*max(m, n))
+        liwork = 8*kmax
+    else:
+        lwork = m + n + 9*kmax + 2*kmax**2 + 4 + max(m + n, 4*kmax + 4)
+        liwork = 2*kmax + 2
+    work = np.empty(lwork, dtype=typ.lower())
+    iwork = np.empty(liwork, dtype=int_dtype)
+
+    # dummy arguments: these are passed to aprod, and not used in this wrapper
+    dparm = np.empty(1, dtype=typ.lower())
+    iparm = np.empty(1, dtype=int_dtype)
+
+    if typ.isupper():
+        zwork = np.empty(m + n + kmax, dtype=typ)
+        works = work, zwork, iwork
+    else:
+        works = work, iwork
+
+    # Generate the seed for the PROPACK random float generator.
+    # TODO: once `svds` drops legacy positional `random_state` support,
+    # or once `_lib._util.check_random_state` is adjusted to always
+    # coerce `RandomState` input to a `Generator` instance
+    # (possible from NumPy >=2.2),
+    # the legacy branch can be removed here.
+    if hasattr(rng, "integers"):
+        rng_state = rng.integers(
+            low=0, high=np.iinfo(np.int64).max, size=4, dtype=np.uint64
+        )
+    else:  # legacy np.random.RandomState
+        rng_state = rng.randint(
+            low=0, high=np.iinfo(np.int64).max, size=4, dtype=np.uint64
+        )
+
+    if irl_mode:
+        info = lansvd_irl(_which_converter[which], jobu,
+                          jobv, m, n, shifts, k, maxiter, tol,
+                          aprod, u, sigma, bnd, v, *works, doption,
+                          ioption, dparm, iparm, rng_state)
+    else:
+        info = lansvd(jobu, jobv, m, n, k, kmax, tol, aprod, u, sigma, bnd, v,
+                      *works, doption, ioption, dparm, iparm, rng_state)
+
+    if info > 0:
+        raise LinAlgError(
+            f"An invariant subspace of dimension {info} was found.")
+    elif info < 0:
+        raise LinAlgError(
+            f"k={k} singular triplets did not converge within "
+            f"kmax={kmax} iterations")
+
+    # info == 0: The K largest (or smallest) singular triplets were computed
+    # successfully!
+
+    return u[:, :k], sigma, v[:, :k].conj().T, bnd
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/dsolve.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/dsolve.py
new file mode 100644
index 0000000000000000000000000000000000000000..45139f6b280d047386652577d9e1c8d2aaeb7033
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/dsolve.py
@@ -0,0 +1,22 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.sparse.linalg` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+
+__all__ = [  # noqa: F822
+    'MatrixRankWarning', 'SuperLU', 'factorized',
+    'spilu', 'splu', 'spsolve',
+    'spsolve_triangular', 'use_solver', 'test'
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="sparse.linalg", module="dsolve",
+                                   private_modules=["_dsolve"], all=__all__,
+                                   attribute=name)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/eigen.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/eigen.py
new file mode 100644
index 0000000000000000000000000000000000000000..588986d6650aad334e6a9a682ed76cef94295298
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/eigen.py
@@ -0,0 +1,21 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.sparse.linalg` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+
+__all__ = [  # noqa: F822
+    'ArpackError', 'ArpackNoConvergence', 'ArpackError',
+    'eigs', 'eigsh', 'lobpcg', 'svds', 'test'
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="sparse.linalg", module="eigen",
+                                   private_modules=["_eigen"], all=__all__,
+                                   attribute=name)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/interface.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/interface.py
new file mode 100644
index 0000000000000000000000000000000000000000..24f40f185b1328b16e7e239e5a165cc6b1ed4317
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/interface.py
@@ -0,0 +1,20 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.sparse.linalg` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+
+__all__ = [  # noqa: F822
+    'LinearOperator', 'aslinearoperator',
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="sparse.linalg", module="interface",
+                                   private_modules=["_interface"], all=__all__,
+                                   attribute=name)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/isolve.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/isolve.py
new file mode 100644
index 0000000000000000000000000000000000000000..e032ddd9c673be3bc8790adad3bdae1839127050
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/isolve.py
@@ -0,0 +1,22 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.sparse.linalg` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+
+__all__ = [  # noqa: F822
+    'bicg', 'bicgstab', 'cg', 'cgs', 'gcrotmk', 'gmres',
+    'lgmres', 'lsmr', 'lsqr',
+    'minres', 'qmr', 'tfqmr', 'test'
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="sparse.linalg", module="isolve",
+                                   private_modules=["_isolve"], all=__all__,
+                                   attribute=name)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/matfuncs.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/matfuncs.py
new file mode 100644
index 0000000000000000000000000000000000000000..8ed877ff1aa6f5a5466ce94729b9225dcce37b36
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/matfuncs.py
@@ -0,0 +1,18 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.sparse.linalg` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+
+__all__ = ["expm", "inv", "spsolve", "LinearOperator"]  # noqa: F822
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="sparse.linalg", module="matfuncs",
+                                   private_modules=["_matfuncs"], all=__all__,
+                                   attribute=name)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/tests/__init__.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/tests/__init__.py
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diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/tests/propack_test_data.npz b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/tests/propack_test_data.npz
new file mode 100644
index 0000000000000000000000000000000000000000..9d45bf727f957b84e5f0ad2f2892d66aa4d377da
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/tests/propack_test_data.npz
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:25d42e05bb6cb5672db22ebf8df7f113e4cb21b1817491fadc996341a542346d
+size 600259
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/tests/test_expm_multiply.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/tests/test_expm_multiply.py
new file mode 100644
index 0000000000000000000000000000000000000000..fa21cd2672727bc49dc7ea270fc00c40d3b0ebc2
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/tests/test_expm_multiply.py
@@ -0,0 +1,370 @@
+"""Test functions for the sparse.linalg._expm_multiply module."""
+import warnings
+
+from functools import partial
+from itertools import product
+
+import numpy as np
+import pytest
+from numpy.testing import (assert_allclose, assert_, assert_equal)
+from scipy.sparse import SparseEfficiencyWarning
+import scipy.sparse
+from scipy.sparse.linalg import aslinearoperator
+import scipy.linalg
+from scipy.sparse.linalg import expm as sp_expm
+from scipy.sparse.linalg._expm_multiply import (_theta, _compute_p_max,
+        _onenormest_matrix_power, expm_multiply, _expm_multiply_simple,
+        _expm_multiply_interval)
+
+
+IMPRECISE = {np.single, np.csingle}
+REAL_DTYPES = (np.intc, np.long, np.longlong,
+               np.float32, np.float64, np.longdouble)
+COMPLEX_DTYPES = (np.complex64, np.complex128, np.clongdouble)
+DTYPES = REAL_DTYPES + COMPLEX_DTYPES
+
+
+def estimated_warns():
+    """If trace is estimated, it should warn.
+
+    We warn that estimation of trace might impact performance.
+    All result have to be correct nevertheless!
+    """
+    return pytest.warns(UserWarning, match="Trace of LinearOperator not available")
+
+
+def less_than_or_close(a, b):
+    return np.allclose(a, b) or (a < b)
+
+
+class TestExpmActionSimple:
+    """
+    These tests do not consider the case of multiple time steps in one call.
+    """
+
+    def test_theta_monotonicity(self):
+        pairs = sorted(_theta.items())
+        for (m_a, theta_a), (m_b, theta_b) in zip(pairs[:-1], pairs[1:]):
+            assert_(theta_a < theta_b)
+
+    def test_p_max_default(self):
+        m_max = 55
+        expected_p_max = 8
+        observed_p_max = _compute_p_max(m_max)
+        assert_equal(observed_p_max, expected_p_max)
+
+    def test_p_max_range(self):
+        for m_max in range(1, 55+1):
+            p_max = _compute_p_max(m_max)
+            assert_(p_max*(p_max - 1) <= m_max + 1)
+            p_too_big = p_max + 1
+            assert_(p_too_big*(p_too_big - 1) > m_max + 1)
+
+    def test_onenormest_matrix_power(self):
+        rng = np.random.RandomState(1234)
+        n = 40
+        nsamples = 10
+        for i in range(nsamples):
+            A = scipy.linalg.inv(rng.randn(n, n))
+            for p in range(4):
+                if not p:
+                    M = np.identity(n)
+                else:
+                    M = np.dot(M, A)
+                estimated = _onenormest_matrix_power(A, p)
+                exact = np.linalg.norm(M, 1)
+                assert_(less_than_or_close(estimated, exact))
+                assert_(less_than_or_close(exact, 3*estimated))
+
+    def test_expm_multiply(self):
+        rng = np.random.default_rng(1234)
+        n = 40
+        k = 3
+        nsamples = 10
+        for i in range(nsamples):
+            A = scipy.linalg.inv(rng.standard_normal((n, n)))
+            B = rng.standard_normal((n, k))
+            observed = expm_multiply(A, B)
+            expected = np.dot(sp_expm(A), B)
+            assert_allclose(observed, expected)
+            with estimated_warns():
+                observed = expm_multiply(aslinearoperator(A), B)
+            assert_allclose(observed, expected)
+            traceA = np.trace(A)
+            observed = expm_multiply(aslinearoperator(A), B, traceA=traceA)
+            assert_allclose(observed, expected)
+
+    def test_matrix_vector_multiply(self):
+        rng = np.random.default_rng(1234)
+        n = 40
+        nsamples = 10
+        for i in range(nsamples):
+            A = scipy.linalg.inv(rng.standard_normal((n, n)))
+            v = rng.standard_normal(n)
+            observed = expm_multiply(A, v)
+            expected = np.dot(sp_expm(A), v)
+            assert_allclose(observed, expected)
+            with estimated_warns():
+                observed = expm_multiply(aslinearoperator(A), v)
+            assert_allclose(observed, expected)
+
+    def test_scaled_expm_multiply(self):
+        rng = np.random.default_rng(1234)
+        n = 40
+        k = 3
+        nsamples = 10
+        for i, t in product(range(nsamples), [0.2, 1.0, 1.5]):
+            with np.errstate(invalid='ignore'):
+                A = scipy.linalg.inv(rng.standard_normal((n, n)))
+                B = rng.standard_normal((n, k))
+                observed = _expm_multiply_simple(A, B, t=t)
+                expected = np.dot(sp_expm(t*A), B)
+                assert_allclose(observed, expected)
+                with estimated_warns():
+                    observed = _expm_multiply_simple(aslinearoperator(A), B, t=t)
+                assert_allclose(observed, expected)
+
+    def test_scaled_expm_multiply_single_timepoint(self):
+        rng = np.random.default_rng(1234)
+        t = 0.1
+        n = 5
+        k = 2
+        A = rng.standard_normal((n, n))
+        B = rng.standard_normal((n, k))
+        observed = _expm_multiply_simple(A, B, t=t)
+        expected = sp_expm(t*A).dot(B)
+        assert_allclose(observed, expected)
+        with estimated_warns():
+            observed = _expm_multiply_simple(aslinearoperator(A), B, t=t)
+        assert_allclose(observed, expected)
+
+    def test_sparse_expm_multiply(self):
+        rng = np.random.default_rng(1234)
+        n = 40
+        k = 3
+        nsamples = 10
+        for i in range(nsamples):
+            A = scipy.sparse.random_array((n, n), density=0.05, rng=rng)
+            B = rng.standard_normal((n, k))
+            observed = expm_multiply(A, B)
+            with warnings.catch_warnings():
+                warnings.filterwarnings(
+                    "ignore",
+                    "splu converted its input to CSC format",
+                    SparseEfficiencyWarning,
+                )
+                warnings.filterwarnings(
+                    "ignore",
+                    "spsolve is more efficient when sparse b is in the "
+                    "CSC matrix format",
+                    SparseEfficiencyWarning,
+                )
+                expected = sp_expm(A).dot(B)
+            assert_allclose(observed, expected)
+            with estimated_warns():
+                observed = expm_multiply(aslinearoperator(A), B)
+            assert_allclose(observed, expected)
+
+    def test_complex(self):
+        A = np.array([
+            [1j, 1j],
+            [0, 1j]], dtype=complex)
+        B = np.array([1j, 1j])
+        observed = expm_multiply(A, B)
+        expected = np.array([
+            1j * np.exp(1j) + 1j * (1j*np.cos(1) - np.sin(1)),
+            1j * np.exp(1j)], dtype=complex)
+        assert_allclose(observed, expected)
+        with estimated_warns():
+            observed = expm_multiply(aslinearoperator(A), B)
+        assert_allclose(observed, expected)
+
+
+class TestExpmActionInterval:
+
+    @pytest.mark.fail_slow(20)
+    def test_sparse_expm_multiply_interval(self):
+        rng = np.random.default_rng(1234)
+        start = 0.1
+        stop = 3.2
+        n = 40
+        k = 3
+        endpoint = True
+        for num in (14, 13, 2):
+            A = scipy.sparse.random_array((n, n), density=0.05, rng=rng)
+            B = rng.standard_normal((n, k))
+            v = rng.standard_normal((n,))
+            for target in (B, v):
+                X = expm_multiply(A, target, start=start, stop=stop,
+                                  num=num, endpoint=endpoint)
+                samples = np.linspace(start=start, stop=stop,
+                                      num=num, endpoint=endpoint)
+                with warnings.catch_warnings():
+                    warnings.filterwarnings(
+                        "ignore",
+                        "splu converted its input to CSC format",
+                        SparseEfficiencyWarning,
+                    )
+                    warnings.filterwarnings(
+                        "ignore",
+                        "spsolve is more efficient when sparse b is in"
+                        " the CSC matrix format",
+                        SparseEfficiencyWarning,
+                    )
+                    for solution, t in zip(X, samples):
+                        assert_allclose(solution, sp_expm(t*A).dot(target))
+
+    @pytest.mark.fail_slow(20)
+    def test_expm_multiply_interval_vector(self):
+        rng = np.random.default_rng(1234)
+        interval = {'start': 0.1, 'stop': 3.2, 'endpoint': True}
+        for num, n in product([14, 13, 2], [1, 2, 5, 20, 40]):
+            A = scipy.linalg.inv(rng.standard_normal((n, n)))
+            v = rng.standard_normal(n)
+            samples = np.linspace(num=num, **interval)
+            X = expm_multiply(A, v, num=num, **interval)
+            for solution, t in zip(X, samples):
+                assert_allclose(solution, sp_expm(t*A).dot(v))
+            # test for linear operator with unknown trace -> estimate trace
+            with estimated_warns():
+                Xguess = expm_multiply(aslinearoperator(A), v, num=num, **interval)
+            # test for linear operator with given trace
+            Xgiven = expm_multiply(aslinearoperator(A), v, num=num, **interval,
+                                   traceA=np.trace(A))
+            # test robustness for linear operator with wrong trace
+            Xwrong = expm_multiply(aslinearoperator(A), v, num=num, **interval,
+                                   traceA=np.trace(A)*5)
+            for sol_guess, sol_given, sol_wrong, t in zip(Xguess, Xgiven,
+                                                          Xwrong, samples):
+                correct = sp_expm(t*A).dot(v)
+                assert_allclose(sol_guess, correct)
+                assert_allclose(sol_given, correct)
+                assert_allclose(sol_wrong, correct)
+
+    @pytest.mark.fail_slow(20)
+    def test_expm_multiply_interval_matrix(self):
+        rng = np.random.default_rng(1234)
+        interval = {'start': 0.1, 'stop': 3.2, 'endpoint': True}
+        for num, n, k in product([14, 13, 2], [1, 2, 5, 20, 40], [1, 2]):
+            A = scipy.linalg.inv(rng.standard_normal((n, n)))
+            B = rng.standard_normal((n, k))
+            samples = np.linspace(num=num, **interval)
+            X = expm_multiply(A, B, num=num, **interval)
+            for solution, t in zip(X, samples):
+                assert_allclose(solution, sp_expm(t*A).dot(B))
+            with estimated_warns():
+                X = expm_multiply(aslinearoperator(A), B, num=num, **interval)
+            for solution, t in zip(X, samples):
+                assert_allclose(solution, sp_expm(t*A).dot(B))
+
+    def test_sparse_expm_multiply_interval_dtypes(self):
+        # Test A & B int
+        A = scipy.sparse.diags_array(np.arange(5),format='csr', dtype=int)
+        B = np.ones(5, dtype=int)
+        Aexpm = scipy.sparse.diags_array(np.exp(np.arange(5)),format='csr')
+        BI = np.identity(5, dtype=int)
+        BI_sparse = scipy.sparse.csr_array(BI)
+        assert_allclose(expm_multiply(A,B,0,1)[-1], Aexpm.dot(B))
+        assert_allclose(np.diag(expm_multiply(A, BI_sparse, 0, 1)[-1]), Aexpm.dot(B))
+
+        # Test A complex, B int
+        A = scipy.sparse.diags_array(-1j*np.arange(5),format='csr', dtype=complex)
+        B = np.ones(5, dtype=int)
+        Aexpm = scipy.sparse.diags_array(np.exp(-1j*np.arange(5)),format='csr')
+        assert_allclose(expm_multiply(A,B,0,1)[-1], Aexpm.dot(B))
+        assert_allclose(np.diag(expm_multiply(A, BI_sparse, 0, 1)[-1]), Aexpm.dot(B))
+
+        # Test A int, B complex
+        A = scipy.sparse.diags_array(np.arange(5),format='csr', dtype=int)
+        B = np.full(5, 1j, dtype=complex)
+        Aexpm = scipy.sparse.diags_array(np.exp(np.arange(5)),format='csr')
+        assert_allclose(expm_multiply(A,B,0,1)[-1], Aexpm.dot(B))
+        BI = np.identity(5, dtype=complex)*1j
+        assert_allclose(
+            np.diag(expm_multiply(A, scipy.sparse.csr_array(BI), 0, 1)[-1]),
+            Aexpm.dot(B)
+        )
+
+    def test_expm_multiply_interval_status_0(self):
+        self._help_test_specific_expm_interval_status(0)
+
+    def test_expm_multiply_interval_status_1(self):
+        self._help_test_specific_expm_interval_status(1)
+
+    def test_expm_multiply_interval_status_2(self):
+        self._help_test_specific_expm_interval_status(2)
+
+    def _help_test_specific_expm_interval_status(self, target_status):
+        rng = np.random.RandomState(1234)
+        start = 0.1
+        stop = 3.2
+        num = 13
+        endpoint = True
+        n = 5
+        k = 2
+        nrepeats = 10
+        nsuccesses = 0
+        for num in [14, 13, 2] * nrepeats:
+            A = rng.randn(n, n)
+            B = rng.randn(n, k)
+            status = _expm_multiply_interval(A, B,
+                    start=start, stop=stop, num=num, endpoint=endpoint,
+                    status_only=True)
+            if status == target_status:
+                X, status = _expm_multiply_interval(A, B,
+                        start=start, stop=stop, num=num, endpoint=endpoint,
+                        status_only=False)
+                assert_equal(X.shape, (num, n, k))
+                samples = np.linspace(start=start, stop=stop,
+                        num=num, endpoint=endpoint)
+                for solution, t in zip(X, samples):
+                    assert_allclose(solution, sp_expm(t*A).dot(B))
+                nsuccesses += 1
+        if not nsuccesses:
+            msg = 'failed to find a status-' + str(target_status) + ' interval'
+            raise Exception(msg)
+
+
+@pytest.mark.filterwarnings("ignore::DeprecationWarning")
+@pytest.mark.parametrize("dtype_a", DTYPES)
+@pytest.mark.parametrize("dtype_b", DTYPES)
+@pytest.mark.parametrize("b_is_matrix", [False, True])
+def test_expm_multiply_dtype(dtype_a, dtype_b, b_is_matrix):
+    """Make sure `expm_multiply` handles all numerical dtypes correctly."""
+    assert_allclose_ = (partial(assert_allclose, rtol=1.8e-3, atol=1e-5)
+                        if {dtype_a, dtype_b} & IMPRECISE else assert_allclose)
+    rng = np.random.default_rng(1234)
+    # test data
+    n = 7
+    b_shape = (n, 3) if b_is_matrix else (n, )
+    if dtype_a in REAL_DTYPES:
+        A = scipy.linalg.inv(rng.random([n, n])).astype(dtype_a)
+    else:
+        A = scipy.linalg.inv(
+            rng.random([n, n]) + 1j*rng.random([n, n])
+        ).astype(dtype_a)
+    if dtype_b in REAL_DTYPES:
+        B = (2*rng.random(b_shape)).astype(dtype_b)
+    else:
+        B = (rng.random(b_shape) + 1j*rng.random(b_shape)).astype(dtype_b)
+
+    # single application
+    sol_mat = expm_multiply(A, B)
+    with estimated_warns():
+        sol_op = expm_multiply(aslinearoperator(A), B)
+    direct_sol = np.dot(sp_expm(A), B)
+    assert_allclose_(sol_mat, direct_sol)
+    assert_allclose_(sol_op, direct_sol)
+    sol_op = expm_multiply(aslinearoperator(A), B, traceA=np.trace(A))
+    assert_allclose_(sol_op, direct_sol)
+
+    # for time points
+    interval = {'start': 0.1, 'stop': 3.2, 'num': 13, 'endpoint': True}
+    samples = np.linspace(**interval)
+    X_mat = expm_multiply(A, B, **interval)
+    with estimated_warns():
+        X_op = expm_multiply(aslinearoperator(A), B, **interval)
+    for sol_mat, sol_op, t in zip(X_mat, X_op, samples):
+        direct_sol = sp_expm(t*A).dot(B)
+        assert_allclose_(sol_mat, direct_sol)
+        assert_allclose_(sol_op, direct_sol)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/tests/test_funm_multiply_krylov.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/tests/test_funm_multiply_krylov.py
new file mode 100644
index 0000000000000000000000000000000000000000..3fab8a535c402b8b32742f3e28b0d3bff3b3ad2c
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/tests/test_funm_multiply_krylov.py
@@ -0,0 +1,185 @@
+"""Test functions for the sparse.linalg._krylov_funm module."""
+from functools import partial
+
+import numpy as np
+import pytest
+from numpy.testing import (assert_allclose)
+import scipy.sparse
+import scipy.linalg
+from scipy.sparse.linalg import aslinearoperator
+from scipy.linalg import (expm, cosm, coshm, sinm, sinhm)
+
+from scipy.sparse.linalg._funm_multiply_krylov import funm_multiply_krylov
+
+REAL_DTYPES = (np.float32, np.float64)
+COMPLEX_DTYPES = (np.complex64, np.complex128)
+DTYPES = REAL_DTYPES + COMPLEX_DTYPES
+
+# This the phi_1 function from exponential integrators: phi_1 (z) = (e^z - 1) / z
+def custom(X):
+    return scipy.linalg.solve(X, expm(X) - np.eye(X.shape[0]))
+
+FUNCS = (expm, cosm, coshm, sinm, sinhm, custom)
+
+class TestKrylovFunmv:
+
+    def test_krylov_funm_zero_vector(self):
+        n = 20
+        A = np.zeros((n, n))
+        b = np.zeros(n)
+        observed = funm_multiply_krylov(expm, A, b)
+        expected = np.zeros(n)
+        assert_allclose(observed, expected)
+
+    @pytest.mark.parametrize("f", FUNCS)
+    def test_funm_multiply_krylov_nonhermitian_dense(self, f):
+        rng = np.random.default_rng(1738151906092735)
+        n = 60
+        nsamples = 10
+
+        for i in range(nsamples):
+            A = rng.standard_normal((n, n))
+            b = rng.standard_normal(n)
+
+            fA = f(A)
+            expected = fA @ b
+            observed = funm_multiply_krylov(f, A, b)
+            assert_allclose(observed, expected, rtol = 1E-6, atol = 1E-8)
+            observed = funm_multiply_krylov(f, aslinearoperator(A), b)
+            assert_allclose(observed, expected, rtol = 1E-6, atol = 1E-8)
+
+    @pytest.mark.parametrize("f", FUNCS)
+    def test_funm_multiply_krylov_nonhermitian_sparse(self, f, num_parallel_threads):
+
+        rng = np.random.default_rng(1738151906092735)
+        n = 100
+        nsamples = 1 + 9 // num_parallel_threads  # Very slow otherwise
+
+        for i in range(nsamples):
+            D = scipy.sparse.diags_array(rng.standard_normal(n))
+            A = scipy.sparse.random_array((n, n), density = 0.01, rng = rng) + D
+            denseA = A.todense()
+            b = rng.standard_normal(n)
+
+            fA = f(denseA)
+            expected = fA @ b
+            observed = funm_multiply_krylov(f, A, b)
+            assert_allclose(observed, expected, rtol = 1E-6, atol = 1E-8)
+            observed = funm_multiply_krylov(f, aslinearoperator(A), b)
+            assert_allclose(observed, expected, rtol = 1E-6, atol = 1E-8)
+
+    @pytest.mark.parametrize("f", FUNCS)
+    def test_funm_multiply_krylov_hermitian_dense(self, f):
+
+        rng = np.random.default_rng(1738151906092735)
+        n = 60
+        nsamples = 10
+
+        for i in range(nsamples):
+            R = np.triu(rng.standard_normal((n, n)))
+            A = R.T + R
+            b = rng.standard_normal(n)
+
+            fA = f(A)
+            expected = fA @ b
+            observed = funm_multiply_krylov(f, A, b, assume_a = 'her')
+            assert_allclose(observed, expected, rtol = 1E-6, atol = 1E-8)
+            observed = funm_multiply_krylov(f, aslinearoperator(A), b, assume_a = 'her')
+            assert_allclose(observed, expected, rtol = 1E-6, atol = 1E-8)
+
+    @pytest.mark.parametrize("f", FUNCS)
+    def test_funm_multiply_krylov_hermitian_sparse(self, f, num_parallel_threads):
+
+        rng = np.random.default_rng(1738151906092735)
+        n = 100
+        nsamples = 1 + 9 // num_parallel_threads  # Very slow otherwise
+
+        for i in range(nsamples):
+            D = scipy.sparse.diags_array(rng.standard_normal(n))
+            A = scipy.sparse.random_array((n, n), density = 0.01, rng = rng)
+            R = scipy.sparse.triu(A)
+            A = R + R.T + D
+            denseA = A.todense()
+            b = rng.standard_normal(n)
+
+            fA = f(denseA)
+            expected = fA @ b
+            observed = funm_multiply_krylov(f, A, b, assume_a = 'her')
+            assert_allclose(observed, expected, rtol = 1E-6, atol = 1E-8)
+
+            observed = funm_multiply_krylov(f, aslinearoperator(A), b, assume_a = 'her')
+            assert_allclose(observed, expected, rtol = 1E-6, atol = 1E-8)
+
+    def test_funm_multiply_krylov_breakdown(self):
+        rng = np.random.default_rng(1738151906092735)
+
+        # From test_iterative
+        A = np.array([[0, 0, 0, 0, 0, 1, -1, -0, -0, -0, -0],
+                      [0, 0, 0, 0, 0, 2, -0, -1, -0, -0, -0],
+                      [0, 0, 0, 0, 0, 2, -0, -0, -1, -0, -0],
+                      [0, 0, 0, 0, 0, 2, -0, -0, -0, -1, -0],
+                      [0, 0, 0, 0, 0, 1, -0, -0, -0, -0, -1],
+                      [1, 2, 2, 2, 1, 0, -0, -0, -0, -0, -0],
+                      [-1, 0, 0, 0, 0, 0, -1, -0, -0, -0, -0],
+                      [0, -1, 0, 0, 0, 0, -0, -1, -0, -0, -0],
+                      [0, 0, -1, 0, 0, 0, -0, -0, -1, -0, -0],
+                      [0, 0, 0, -1, 0, 0, -0, -0, -0, -1, -0],
+                      [0, 0, 0, 0, -1, 0, -0, -0, -0, -0, -1]], dtype = float)
+        b = rng.standard_normal(A.shape[0])
+
+        fA = expm(A)
+        expected = fA @ b
+        observed = funm_multiply_krylov(expm, A, b, restart_every_m = 40)
+        assert_allclose(observed, expected)
+
+    def test_funm_multiply_krylov_invalid_input(self):
+            A = np.array([[1, 2], [3, 4]])  # Non-hermitian matrix
+            b = np.array([1.0, 2.0])  # Ensure 'b' is a 1D array of floats
+
+            # Test for invalid 'b' (not 1D)
+            b_invalid = np.array([[1.0], [2.0]])  # 2D array
+            with pytest.raises(ValueError, 
+                    match="argument 'b' must be a 1D array."): 
+                funm_multiply_krylov(np.exp, A, b_invalid)
+
+            # Test for invalid restart parameter
+            with pytest.raises(ValueError, 
+                    match="argument 'restart_every_m' must be positive."): 
+                funm_multiply_krylov(np.exp, A, b, restart_every_m=0)
+
+            # Test for invalid max_restarts
+            with pytest.raises(ValueError, 
+                    match="argument 'max_restarts' must be positive."): 
+                funm_multiply_krylov(np.exp, A, b, max_restarts=0)
+
+            # Test for invalid 'assume_a' string
+            with pytest.raises(ValueError, 
+                    match="is not a recognized matrix structure"): 
+                funm_multiply_krylov(np.exp, A, b, assume_a='invalid')
+
+
+@pytest.mark.parametrize("dtype_a", DTYPES)
+@pytest.mark.parametrize("dtype_b", DTYPES)
+def test_funm_multiply_krylov_types(dtype_a, dtype_b):
+    assert_allclose_ = (partial(assert_allclose, rtol = 1.8e-3, atol = 1e-5)
+                        if {dtype_a, dtype_b} else assert_allclose)
+
+    rng = np.random.default_rng(1738151906092735)
+    n = 50
+
+    if dtype_a in REAL_DTYPES:
+        A = rng.random([n, n]).astype(dtype_a)
+    else:
+        A = (rng.random([n, n]) + 1j * rng.random([n, n])).astype(dtype_a)
+
+    if dtype_b in REAL_DTYPES:
+        b = (2 * rng.random(n)).astype(dtype_b)
+    else:
+        b = (rng.random(n) + 1j * rng.random(n)).astype(dtype_b)
+
+        expA = expm(A)
+        expected = expA @ b
+        observed = funm_multiply_krylov(expm, A, b)
+        assert_allclose_(observed, expected)
+        observed = funm_multiply_krylov(expm, aslinearoperator(A), b)
+        assert_allclose_(observed, expected)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/tests/test_interface.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/tests/test_interface.py
new file mode 100644
index 0000000000000000000000000000000000000000..2d8ebeb6db20bb63d6f7bb88fe256b2e186d3847
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/tests/test_interface.py
@@ -0,0 +1,1297 @@
+"""Test functions for the sparse.linalg._interface module
+"""
+
+import contextlib
+from functools import partial
+from itertools import product
+import operator
+from types import ModuleType
+from typing import NamedTuple
+
+import pytest
+from pytest import raises as assert_raises, warns
+from numpy.testing import assert_, assert_equal
+
+import numpy as np
+from scipy._lib._array_api import (
+    SCIPY_ARRAY_API, SCIPY_DEVICE, is_torch, xp_assert_close, is_lazy_array,
+    xp_assert_equal, xp_ravel, is_numpy, make_xp_pytest_marks, is_jax_array,
+)
+from scipy._external import array_api_extra as xpx
+import scipy.sparse as sparse
+
+import scipy.sparse.linalg._interface as interface
+from scipy.sparse.linalg import LinearOperator, aslinearoperator
+from scipy.sparse._sputils import matrix
+from scipy._lib._gcutils import assert_deallocated
+
+pytestmark = make_xp_pytest_marks(
+    (LinearOperator, "__init__"),
+    (LinearOperator, "matvec"),
+    (LinearOperator, "matmat"),
+    (LinearOperator, "dot"),
+    (LinearOperator, "rdot"),
+    (LinearOperator, "rmatvec"),
+    (LinearOperator, "rmatmat"),
+    aslinearoperator
+)
+
+def generate_broadcastable_shapes(nshapes, *, ndim=2, min=0, max=10, rng=None):
+    rng = np.random.default_rng(rng)
+    min = np.broadcast_to(min, ndim)  # so min and max can be scalars or array-like 
+    max = np.broadcast_to(max, ndim)
+    batch_shape = tuple(rng.integers(min_, max_+1) for min_, max_ in zip(min, max))
+    shapes = np.repeat([batch_shape], nshapes, axis=0)
+
+    # make some elements of some shapes 1 (while preserving overall batch shape)
+    for column in shapes.T:
+        column[rng.integers(1, nshapes):] = 1
+    # permute elements between shapes (while preserving overall batch shape)
+    shapes = list(rng.permuted(shapes, axis=0))
+    # potentially trim preceeding 1s from a shape
+    for i in range(len(shapes)):
+        shape = shapes[i]
+        j = np.where(shape != 1)[0][0] if np.any(shape != 1) else ndim
+        if rng.random() < 0.25:
+            shapes[i] = shape[rng.integers(j+1):]
+            break
+
+    assert np.broadcast_shapes(*shapes) == batch_shape
+    return [tuple(int(el) for el in shape) for shape in shapes]
+
+
+class TestLinearOperator:
+    def setup_method(self):
+        self.A = np.array([[1,2,3],
+                           [4,5,6]])
+        self.B = np.array([[1,2],
+                           [3,4],
+                           [5,6]])
+        self.C = np.array([[1,2],
+                           [3,4]])
+
+    def test_matvec(self, xp):
+        def get_matvecs(A):
+            return [{
+                'shape': A.shape,
+                'dtype': xp.float64,
+                'matvec': lambda x: A @ x,
+                'rmatvec': lambda x: xp.conj(A.T) @ x,
+                'rmatmat': lambda x: xp.conj(A.T) @ x,
+                'matmat': lambda x: A @ x
+            }]
+        
+        _asarray = partial(xp.asarray, dtype=xp.complex128)
+
+        for matvecs in get_matvecs(_asarray(self.A)):
+            A = interface.LinearOperator(**matvecs, xp=xp)
+
+            assert A.args == ()
+
+            xp_assert_equal(A.matvec(_asarray([1,2,3])), _asarray([14,32]))
+            with pytest.warns(FutureWarning, match="column vectors"):
+                xp_assert_equal(
+                    A.matvec(_asarray([[1],[2],[3]])),
+                    _asarray([[14],[32]]),
+                )
+            xp_assert_equal(A @ _asarray([1,2,3]), _asarray([14,32]))
+            xp_assert_equal(A @ _asarray([[1],[2],[3]]), _asarray([[14],[32]]))
+            xp_assert_equal(A.dot(_asarray([1,2,3])), _asarray([14,32]))
+            xp_assert_equal(A.dot(_asarray([[1],[2],[3]])), _asarray([[14],[32]]))
+
+            if not SCIPY_ARRAY_API:
+                xp_assert_equal(
+                    A.matvec(matrix([[1],[2],[3]])),
+                    _asarray([[14],[32]]),
+                )
+                xp_assert_equal(A @ matrix([[1],[2],[3]]), _asarray([[14],[32]]))
+                xp_assert_equal(A.dot(matrix([[1],[2],[3]])), _asarray([[14],[32]]))
+
+            xp_assert_equal((2*A) @ _asarray([1,1,1]), _asarray([12,30]))
+            xp_assert_equal((2 * A).rmatvec(_asarray([1, 1])), _asarray([10, 14, 18]))
+            xp_assert_equal((2*A).H.matvec(_asarray([1,1])), _asarray([10, 14, 18]))
+            xp_assert_equal(
+                (2*A).adjoint().matvec(_asarray([1,1])),
+                _asarray([10, 14, 18]),
+            )
+            xp_assert_equal((2*A) @ _asarray([[1],[1],[1]]), _asarray([[12],[30]]))
+            xp_assert_equal(
+                (2 * A).matmat(_asarray([[1], [1], [1]])),
+                _asarray([[12], [30]]),
+            )
+            xp_assert_equal((A*2) @ _asarray([1,1,1]), _asarray([12,30]))
+            xp_assert_equal((A*2) @ _asarray([[1],[1],[1]]), _asarray([[12],[30]]))
+            xp_assert_equal((2j*A) @ _asarray([1,1,1]), _asarray([12j,30j]))
+            xp_assert_equal((A+A) @ _asarray([1,1,1]), _asarray([12, 30]))
+            xp_assert_equal((A + A).rmatvec(_asarray([1, 1])), _asarray([10, 14, 18]))
+            xp_assert_equal((A+A).H.matvec(_asarray([1,1])), _asarray([10, 14, 18]))
+            xp_assert_equal(
+                (A + A).adjoint().matvec(_asarray([1,1])),
+                _asarray([10, 14, 18]),
+            )
+            xp_assert_equal((A+A) @ _asarray([[1],[1],[1]]), _asarray([[12], [30]]))
+            xp_assert_equal(
+                (A+A).matmat(_asarray([[1],[1],[1]])),
+                _asarray([[12], [30]])
+            )
+            xp_assert_equal((-A) @ _asarray([1,1,1]), _asarray([-6,-15]))
+            xp_assert_equal((-A) @ _asarray([[1],[1],[1]]), _asarray([[-6],[-15]]))
+            xp_assert_equal((A-A) @ _asarray([1,1,1]), _asarray([0,0]))
+            xp_assert_equal((A - A) @ _asarray([[1], [1], [1]]), _asarray([[0], [0]]))
+
+            A_ = xp.asarray(self.A, dtype=xp.complex128)
+            X = xp.asarray([[1, 2], [3, 4]], dtype=xp.complex128)
+            xp_assert_equal((2 * A).rmatmat(X), (2 * A_).T @ X)
+            xp_assert_equal((A * 2).rmatmat(X), (A_ * 2).T @ X)
+            xp_assert_equal((2j * A).rmatmat(X), xp.conj((2j * A_).T) @ X)
+            xp_assert_equal((A * 2j).rmatmat(X), xp.conj((A_ * 2j).T) @ X)
+            xp_assert_equal((A + A).rmatmat(X), (A_ + A_).T @ X)
+            xp_assert_equal((A + 2j * A).rmatmat(X), xp.conj((A_ + 2j * A_).T) @ X)
+            xp_assert_equal((-A).rmatmat(X), (-A_).T @ X)
+            xp_assert_equal((A - A).rmatmat(X), (A_ - A_).T @ X)
+            xp_assert_equal((2j * A).rmatmat(2j * X), xp.conj((2j * A_).T) @ (2j * X))
+
+            z = A+A
+            assert len(z.args) == 2 and z.args[0] is A and z.args[1] is A
+            z = 2*A
+            assert len(z.args) == 2
+            if not is_lazy_array(xp.empty(0)):
+                # lazy_xp_function breaks object identity
+                assert z.args[0] is A and z.args[1] == 2
+
+            array_object = type(xp.empty(0))
+            assert isinstance(A.matvec(_asarray([1, 2, 3])), array_object)
+            ctx = (
+                pytest.warns(FutureWarning, match="column vectors")
+                if not is_jax_array(xp.empty(0))
+                else contextlib.nullcontext()
+            )
+            with ctx:
+                assert isinstance(A.matvec(_asarray([[1],[2],[3]])), array_object)
+            assert isinstance(A @ _asarray([1,2,3]), array_object)
+            assert isinstance(A @ _asarray([[1],[2],[3]]), array_object)
+            assert isinstance(A.dot(_asarray([1,2,3])), array_object)
+            assert isinstance(A.dot(_asarray([[1],[2],[3]])), array_object)
+
+            if not SCIPY_ARRAY_API:
+                assert isinstance(A.matvec(matrix([[1],[2],[3]])), array_object)
+                assert isinstance(A @ matrix([[1],[2],[3]]), array_object)
+                assert isinstance(A.dot(matrix([[1],[2],[3]])), array_object)
+
+            assert isinstance(2*A, interface._ScaledLinearOperator)
+            assert isinstance(2j*A, interface._ScaledLinearOperator)
+            assert isinstance(A+A, interface._SumLinearOperator)
+            assert isinstance(-A, interface._ScaledLinearOperator)
+            assert isinstance(A-A, interface._SumLinearOperator)
+            assert isinstance(A/2, interface._ScaledLinearOperator)
+            assert isinstance(A/2j, interface._ScaledLinearOperator)
+
+            if not is_lazy_array(xp.empty(0)):
+                # lazy_xp_function breaks object identity
+                assert ((A * 3) / 3).args[0] is A  # check for simplification
+
+            # Test that prefactor is of _ScaledLinearOperator is not mutated
+            # when the operator is multiplied by a number
+            result = A @ _asarray([1, 2, 3])
+            B = A * 3
+            C = A / 5
+            xp_assert_equal(A @ _asarray([1, 2, 3]), result)
+
+            assert (2j * A).dtype == xp.complex128
+
+            # Test division by non-scalar
+            msg = "Can only divide a linear operator by a scalar."
+            with assert_raises(ValueError, match=msg):
+                _ = A / xp.asarray([1, 2])
+
+            assert_raises(ValueError, A.matvec, xp.asarray([1,2]))
+            assert_raises(ValueError, A.matvec, xp.asarray([1,2,3,4]))
+            assert_raises(ValueError, A.matvec, xp.asarray([[1],[2]]))
+            assert_raises(ValueError, A.matvec, xp.asarray([[1],[2],[3],[4]]))
+
+            assert_raises(ValueError, lambda: A@A)
+            assert_raises(ValueError, lambda: A**2)
+
+        for matvecsA, matvecsB in product(get_matvecs(_asarray(self.A)),
+                                          get_matvecs(_asarray(self.B))):
+            A = interface.LinearOperator(**matvecsA, xp=xp)
+            B = interface.LinearOperator(**matvecsB, xp=xp)
+            AtimesB = _asarray(self.A @ self.B)
+            X = _asarray([[1, 2], [3, 4]])
+
+            xp_assert_equal((A @ B).rmatmat(X), AtimesB.T @ X)
+            xp_assert_equal((2j * A @ B).rmatmat(X), xp.conj((2j * AtimesB).T) @ X)
+
+            xp_assert_equal((A @ B) @ _asarray([1,1]), _asarray([50,113]))
+            xp_assert_equal((A @ B) @ _asarray([[1],[1]]), _asarray([[50],[113]]))
+            xp_assert_equal((A @ B).matmat(_asarray([[1],[1]])), _asarray([[50],[113]]))
+
+            xp_assert_equal((A @ B).rmatvec(_asarray([1, 1])), _asarray([71, 92]))
+            xp_assert_equal((A @ B).H.matvec(_asarray([1, 1])), _asarray([71, 92]))
+            xp_assert_equal(
+                (A @ B).adjoint().matvec(_asarray([1, 1])),
+                _asarray([71, 92]),
+            )
+
+            assert isinstance(A@B, interface._ProductLinearOperator)
+
+            assert_raises(ValueError, lambda: A+B)
+            assert_raises(ValueError, lambda: A**2)
+
+            z = A@B
+            assert len(z.args) == 2
+            if not is_lazy_array(xp.empty(0)):
+                # lazy_xp_function breaks object identity
+                assert z.args[0] is A and z.args[1] is B
+
+        for matvecsC in get_matvecs(_asarray(self.C)):
+            C = interface.LinearOperator(**matvecsC, xp=xp)
+            X = _asarray([[1, 2], [3, 4]])
+            C_ = _asarray(self.C)
+
+            xp_assert_equal(C.rmatmat(X), (C_).T @ X)
+            xp_assert_equal((C**2).rmatmat(X), (C_ @ C_).T @ X)
+
+            xp_assert_equal((C**2)@_asarray([1,1]), _asarray([17,37]))
+            xp_assert_equal((C**2).rmatvec(_asarray([1, 1])), _asarray([22, 32]))
+            xp_assert_equal((C**2).H.matvec(_asarray([1, 1])), _asarray([22, 32]))
+            xp_assert_equal(
+                (C**2).adjoint().matvec(_asarray([1, 1])),
+                _asarray([22, 32]),
+            )
+            xp_assert_equal((C**2).matmat(_asarray([[1],[1]])), _asarray([[17],[37]]))
+
+            assert isinstance(C**2, interface._PowerLinearOperator)
+
+    @pytest.mark.skip_xp_backends(
+        "array_api_strict",
+        reason="https://github.com/data-apis/array-api-strict/issues/188",
+    )
+    def test_matmul(self, xp):
+        _asarray = partial(xp.asarray, dtype=xp.complex128)
+        A_ = _asarray(self.A)
+        D = {'shape': A_.shape,
+             'dtype': xp.complex128,
+             'matvec': lambda x: xp.reshape(A_ @ x, (A_.shape[0],)),
+             'rmatvec': lambda x: xp.reshape(xp.conj(A_.T) @ x, (A_.shape[1],)),
+             'rmatmat': lambda x: xp.conj(A_.T) @ x,
+             'matmat': lambda x: A_ @ x}
+        A = interface.LinearOperator(**D, xp=xp)
+        B = _asarray([[1 + 1j, 2, 3],
+                      [4, 5, 6],
+                      [7, 8, 9]])
+        b = B[0, ...]
+
+        xp_assert_equal(operator.matmul(A, b), A * b)
+        xp_assert_equal(
+            operator.matmul(A, xp.reshape(b, (-1, 1))),
+            A * xp.reshape(b, (-1, 1)),
+        )
+        xp_assert_equal(operator.matmul(A, B), A @ B)
+        xp_assert_equal(operator.matmul(b, A.H), b * A.H)
+        xp_assert_equal(operator.matmul(b, A.adjoint()), b * A.adjoint())
+        xp_assert_equal(
+            operator.matmul(xp.reshape(b, (1, -1)), A.H),
+            xp.reshape(b, (1, -1)) * A.H,
+        )
+        xp_assert_equal(
+            operator.matmul(b.reshape(1, -1), A.adjoint()),
+            b.reshape(1, -1) * A.adjoint(),
+        )
+        xp_assert_equal(operator.matmul(B, A.H), B @ A.H)
+        xp_assert_equal(operator.matmul(B, A.adjoint()), B @ A.adjoint())
+        assert_raises(ValueError, operator.matmul, A, 2)
+        assert_raises(ValueError, operator.matmul, 2, A)
+
+    def test_dimension_mismatch(self, xp):
+        msg = "(D|d)imension mismatch"
+        A = interface.aslinearoperator(xp.ones((3, 4)))
+        # matvec
+        A.matvec(xp.ones(4))
+        with pytest.raises(ValueError, match=msg):
+            A.matvec(xp.ones(3))
+        # rmatvec
+        A.rmatvec(xp.ones(3))
+        with pytest.raises(ValueError, match=msg):
+            A.rmatvec(xp.ones(4))
+        # matmat
+        A.matmat(xp.ones((4, 3)))
+        with pytest.raises(ValueError, match=msg):
+            A.matmat(xp.ones((3, 3)))
+        # rmatmat
+        A.rmatmat(xp.ones((3, 3)))
+        with pytest.raises(ValueError, match=msg):
+            A.rmatmat(xp.ones((4, 4)))
+        # dot
+        A.dot(xp.ones((4, 3)))
+        with pytest.raises(ValueError, match=msg):
+            A.dot(xp.ones((3, 3)))
+        # rdot
+        A.rdot(xp.ones((3, 3)))
+        with pytest.raises(ValueError, match=msg):
+            A.rdot(xp.ones((4, 4)))
+        
+
+@pytest.mark.skip_xp_backends("dask.array", reason="https://github.com/dask/dask/issues/11711")
+class TestDotTests:
+    """
+    This class aims to help ensure correctness of the LinearOperator
+    interface, by verifying correctness properties based on equivalent
+    computations using 'forward' and 'adjoint' modes.
+    """
+    class OperatorArgs(NamedTuple):
+        """
+        shape: (core) shape of the operator
+        op_dtype: dtype of the operator
+        data_dtype: real dtype corresponding to op_dtype for data generation
+        complex: the operator has a complex dtype
+        """
+        shape: tuple[int, ...]
+        op_dtype: str
+        data_dtype: str
+        complex: bool
+
+    real_square_args: OperatorArgs = OperatorArgs(
+        (12, 12), "float64", "float64", False
+    )
+    integer_square_args: OperatorArgs = OperatorArgs(
+        (9, 9), "int32", "float32", False
+    )
+    complex_square_args: OperatorArgs = OperatorArgs(
+        (13, 13), "complex64", "float32", True
+    )
+    real_overdetermined_args: OperatorArgs = OperatorArgs(
+        (17, 11), "float64", "float64", False
+    )
+    complex_overdetermined_args: OperatorArgs = OperatorArgs(
+        (17, 11), "complex128", "float64", True
+    )
+    real_underdetermined_args: OperatorArgs = OperatorArgs(
+        (5, 9), "float64", "float64", False
+    )
+
+    square_args_list: list[OperatorArgs] = [
+        real_square_args, integer_square_args, complex_square_args
+    ]
+    all_args_list: list[OperatorArgs]  = square_args_list + [
+        real_overdetermined_args, complex_overdetermined_args, real_underdetermined_args
+    ]
+
+    def check_matvec(
+        self, xp: ModuleType, op: interface.LinearOperator, data_dtype: str,
+        complex_data: bool = False,
+    ):
+        """
+        This check verifies the equivalence of the forward and adjoint computation,
+        using `matvec` and `rmatvec` respectively, on randomised data.
+
+        Data is generated with the real dtype `data_dtype` and operated on by the
+        linear operator `op`.
+
+        If `complex_data` is set to `True`, complex data is instead generated
+        by combining randomised real and imaginary components, each generated
+        with `data_dtype`.
+
+        If `check_operators` is set to `True`, equivalence is checked between
+        `matvec` and `*` and `@`,
+        and between `rmatvec` and the composition of `.H` and `*`.
+
+        If `check_dot` is set to `True`, equivalence is checked between
+        `matvec` and `.dot`,
+        and between `rmatvec` and the composition of `.H` and `.dot`.
+        """
+        rng = np.random.default_rng(42)
+
+        dtype = np.dtype(data_dtype)
+        *batch_shape, M, N = op.shape
+
+        u_broadcast, v_broadcast = generate_broadcastable_shapes(
+            2, ndim=3, min=0, max=5, rng=63
+        )
+
+        for u_shape, v_shape in (
+            # test broadcasting for unbatched RHS
+            ((N,), (M,)),
+            # as well as with the batch shape of `op` + 3-D broadcast dims
+            ((*u_broadcast, *batch_shape, N), (*v_broadcast, *batch_shape, M))
+        ):
+            u = rng.standard_normal(u_shape, dtype=dtype)
+            v = rng.standard_normal(v_shape, dtype=dtype)
+            if complex_data:
+                u = u + (1j * rng.standard_normal(u_shape, dtype=dtype))
+                v = v + (1j * rng.standard_normal(v_shape, dtype=dtype))
+            u = xp.asarray(u)
+            v = xp.asarray(v)
+    
+            op_u = op.matvec(u)
+            opH_v = op.rmatvec(v)
+    
+            op_u_H_v = xp.vecdot(op_u, v, axis=-1)
+            uH_opH_v = xp.vecdot(u, opH_v, axis=-1)
+    
+            rtol = 1e-12 if np.finfo(data_dtype).eps < 1e-8 else 1e-5
+            atol = 2e-15 if np.finfo(data_dtype).eps < 1e-8 else 1e-5
+            xp_assert_close(op_u_H_v, uH_opH_v, rtol=rtol, atol=atol)
+
+    def check_matmat(
+        self, xp, op: interface.LinearOperator, data_dtype: str,
+        complex_data: bool = False, check_operators: bool = False,
+        check_dot: bool = False,
+    ):
+        """
+        This check verifies the equivalence of the forward and adjoint computation,
+        using `matmat` and `rmatmat` respectively, on randomised data.
+
+        Data is generated with the real dtype `data_dtype` and operated on by the
+        linear operator `op`.
+
+        If `complex_data` is set to `True`, complex data is instead generated
+        by combining randomised real and imaginary components, each generated
+        with `data_dtype`.
+
+        If `check_operators` is set to `True`, equivalence is checked between
+        `matmat` and `*` and `@`,
+        and between `rmatvec` and the composition of `.H` and `@`.
+
+        If `check_dot` is set to `True`, equivalence is checked between
+        `matmat` and `.dot`,
+        and between `rmatmat` and the composition of `.H` and `.dot`.
+        """
+        rng = np.random.default_rng(42)
+        k = rng.integers(2, 100)
+
+        dtype = np.dtype(data_dtype)
+        *batch_shape, M, N = op.shape
+
+        # Test `U` and `V` with the same batch shape as `op`
+        U = rng.standard_normal(size=(*batch_shape, N, k), dtype=dtype)
+        V = rng.standard_normal(size=(*batch_shape, M, k), dtype=dtype)
+        if complex_data:
+            U = U + (1j * rng.standard_normal(size=(*batch_shape, N, k), dtype=dtype))
+            V = V + (1j * rng.standard_normal(size=(*batch_shape, M, k), dtype=dtype))
+        U = xp.asarray(U)
+        V = xp.asarray(V)
+
+        op_U = op.matmat(U)
+        opH_V = op.rmatmat(V)
+
+        if check_operators:
+            xp_assert_close(op_U, op * U)
+            xp_assert_close(op_U, op @ U)
+            xp_assert_close(opH_V, op.H * V)
+            xp_assert_close(opH_V, op.H @ V)
+
+        if check_dot:
+            xp_assert_close(op_U, op.dot(U))
+            xp_assert_close(opH_V, op.H.dot(V))
+
+        op_U_H = xp.conj(op_U).mT
+        UH = xp.conj(U).mT
+
+        op_U_H_V = xp.matmul(op_U_H, V)
+        UH_opH_V = xp.matmul(UH, opH_V)
+
+        rtol = 1e-12 if np.finfo(data_dtype).eps < 1e-8 else 1e-5
+        atol = 2e-15 if np.finfo(data_dtype).eps < 1e-8 else 1e-5
+        xp_assert_close(op_U_H_V, UH_opH_V, rtol=rtol, atol=atol)
+
+    @pytest.mark.parametrize("batch_shape", [(), (3,), (3, 4, 5,), (0,)])
+    @pytest.mark.parametrize("args", square_args_list)
+    def test_identity_square(
+        self, args: OperatorArgs, batch_shape: tuple[int, ...], xp
+    ):
+        """
+        Simple identity operator on square matrices.
+        Tests batches of RHS via `args.batch_shape`.
+        """
+        def identity(x):
+            shape = (*xpx.broadcast_shapes(batch_shape, x.shape[:-1]), x.shape[-1])
+            return xp.broadcast_to(x, shape)
+
+        shape = batch_shape + args.shape
+        dtype = getattr(xp, args.op_dtype)
+        op = interface.LinearOperator(  # type:ignore[call-arg]
+            shape=shape, dtype=dtype,
+            matvec=identity, rmatvec=identity, xp=xp,
+        )
+
+        self.check_matvec(xp, op, data_dtype=args.data_dtype, complex_data=args.complex)
+        self.check_matmat(xp, op, data_dtype=args.data_dtype, complex_data=args.complex)
+
+    @pytest.mark.parametrize("batch_shape", [(), (3,), (3, 4, 5,), (0,)])
+    @pytest.mark.parametrize("args", all_args_list)
+    def test_identity_nonsquare(
+        self, args: OperatorArgs, batch_shape: tuple[int, ...], xp
+    ):
+        """
+        Identity operator with zero-padding on non-square matrices.
+        Tests batches of RHS via `args.batch_shape`.
+        """
+        M, N = args.shape
+
+        def pad_core_dim(x, target_size):
+            pad_widths = [(0, 0)] * x.ndim # no padding for batch dims
+            pad_widths[-1] = (0, target_size - x.shape[-1]) # padding for core dim
+            return xpx.pad(x, pad_widths, mode="constant")
+
+        def mv(x):
+            match np.sign(x.shape[-1] - M):
+                case 0:  # square
+                    pass
+                case 1:  # crop x to size
+                    x = x[..., :M]
+                case -1:  # pad with zeros
+                    x = pad_core_dim(x, target_size=M)
+
+            shape = (*xpx.broadcast_shapes(batch_shape, x.shape[:-1]), x.shape[-1])
+            return xp.broadcast_to(x, shape)
+
+        def rmv(x):            
+            match np.sign(N - x.shape[-1]):
+                case 0:  # square
+                    pass
+                case 1:  # pad with zeros
+                    x = pad_core_dim(x, target_size=N)
+                case -1:  # crop x to size
+                    x = x[..., :N]
+
+            shape = (*xpx.broadcast_shapes(batch_shape, x.shape[:-1]), x.shape[-1])
+            return xp.broadcast_to(x, shape)
+
+        shape = batch_shape + args.shape
+        dtype = getattr(xp, args.op_dtype)
+        op = interface.LinearOperator(  # type:ignore[call-arg]
+            shape=shape, dtype=dtype, matvec=mv, rmatvec=rmv, xp=xp
+        )
+        
+        self.check_matvec(xp, op, data_dtype=args.data_dtype, complex_data=args.complex)
+        self.check_matmat(xp, op, data_dtype=args.data_dtype, complex_data=args.complex)
+
+    @pytest.mark.parametrize("batch_shape", [(), (3,), (3, 4, 5,), (0,)])
+    @pytest.mark.parametrize("args", square_args_list)
+    def test_scaling_square(self, args: OperatorArgs, batch_shape: tuple[int, ...], xp):
+        """
+        Simple (complex) scaling operator on square matrices.
+        Tests batches of RHS via `args.batch_shape`.
+        """
+        def scale(x):
+            scale = (3 + 2j) / abs(3 + 2j)
+            shape = (*xpx.broadcast_shapes(batch_shape, x.shape[:-1]), x.shape[-1])
+            return xp.broadcast_to(scale * x, shape)
+
+        def r_scale(x):
+            scale = (3 - 2j) / abs(3 - 2j)
+            shape = (*xpx.broadcast_shapes(batch_shape, x.shape[:-1]), x.shape[-1])
+            return xp.broadcast_to(scale * x, shape)
+
+        shape = batch_shape + args.shape
+        dtype = getattr(xp, args.op_dtype)
+        op = interface.LinearOperator(  # type:ignore[call-arg]
+            shape=shape, dtype=dtype, matvec=scale, rmatvec=r_scale, xp=xp
+        )
+        self.check_matvec(xp, op, data_dtype=args.data_dtype, complex_data=args.complex)
+        self.check_matmat(xp, op, data_dtype=args.data_dtype, complex_data=args.complex)
+
+    @pytest.mark.parametrize("batch_shape", [(), (3,), (3, 4, 5,), (0,)])
+    def test_subclass_matmat(self, batch_shape: tuple[int, ...], xp):
+        """
+        Simple rotation operator defined by `matmat` and `adjoint`,
+        subclassing `LinearOperator`.
+        Tests batches of RHS via `batch_shape`.
+        """
+        class RotOp(interface.LinearOperator):
+
+            def __init__(self, dtype, shape, theta):
+                self._theta = theta
+                super().__init__(dtype, shape, xp=xp)
+
+            def _matmat(self, X):
+                theta = self._theta
+                R = xp.asarray([
+                    [np.cos(theta), -np.sin(theta)],
+                    [np.sin(theta),  np.cos(theta)]
+                ])
+                B = R @ X
+                shape = xpx.broadcast_shapes(batch_shape, X.shape[:-2]) + X.shape[-2:]
+                return xp.broadcast_to(B, shape)
+
+            def _adjoint(self):
+                negative_theta = -self._theta
+                return RotOp(self.dtype, self.shape, negative_theta)
+
+        theta = xp.pi / 2
+        data_dtype = "float64"
+        op = RotOp(shape=(*batch_shape, 2, 2), dtype=xp.float64, theta=theta)
+
+        self.check_matvec(xp, op, data_dtype=data_dtype, complex_data=False)
+        self.check_matmat(xp, op, data_dtype=data_dtype, complex_data=False)
+
+    @pytest.mark.parametrize("batch_shape", [(), (3,), (3, 4, 5,), (0,)])
+    @pytest.mark.skip_xp_backends("dask.array", reason="https://github.com/dask/dask/issues/11711")
+    def test_aslinearop_dense(
+        self, batch_shape: tuple[int, ...], xp
+    ):
+        """
+        Test operators coming from `aslinearoperator`,
+        *including batched LHS*.
+        """
+        rng = np.random.default_rng(42)
+        matrix = xp.asarray(
+            rng.standard_normal((*batch_shape, 4, 4)),
+            dtype=xp.complex128,
+        )
+        op = interface.aslinearoperator(matrix)
+        data_dtype = "float64"
+        self.check_matvec(xp, op, data_dtype=data_dtype, complex_data=True)
+        self.check_matmat(xp, op, data_dtype=data_dtype, complex_data=True)
+
+    @pytest.mark.parametrize("batch_shape", [(), (3,), (3, 4, 5,), (0,)])
+    @pytest.mark.skip_xp_backends(np_only=True)
+    def test_aslinearop_sparse(self, batch_shape: tuple[int, ...], xp):
+        """
+        Test operators coming from `aslinearoperator` with sparse arrays,
+        *including batched LHS*
+        """
+        matrix = sparse.random_array((*batch_shape, 4, 4), dtype=xp.complex128)
+        op = interface.aslinearoperator(matrix)
+        data_dtype = "float64"
+        self.check_matvec(xp, op, data_dtype=data_dtype, complex_data=True)
+        self.check_matmat(xp, op, data_dtype=data_dtype, complex_data=True)
+
+
+class TestAsLinearOperator:
+    def make_cases(self, original, dtype, xp=None):
+        cases = []
+
+        # Test default implementations of _adjoint and _rmatvec, which
+        # refer to each other.
+        _xp = xp if xp is not None else np
+        def mv(x):
+            y = original @ x
+            if len(x.shape) == 2:
+                y = _xp.reshape(y, (-1, 1))
+            return y
+
+        def rmv(x):
+            return _xp.conj(original.T) @ x
+
+        class BaseMatlike(interface.LinearOperator):
+            args = ()
+
+            def __init__(self, dtype):
+                super().__init__(
+                    dtype=dtype,
+                    shape=original.shape,
+                    xp=xp,
+                )
+
+            def _matvec(self, x):
+                return mv(x)
+
+        class HasRmatvec(BaseMatlike):
+            args = ()
+
+            def _rmatvec(self,x):
+                return rmv(x)
+
+        class HasAdjoint(BaseMatlike):
+            args = ()
+
+            def _adjoint(self):
+                shape = self.shape[1], self.shape[0]
+                matvec = partial(rmv)
+                rmatvec = partial(mv)
+                return interface.LinearOperator(matvec=matvec,
+                                                rmatvec=rmatvec,
+                                                dtype=dtype,
+                                                shape=shape,
+                                                xp=xp,)
+
+        class HasRmatmat(HasRmatvec):
+            def _matmat(self, x):
+                return original @ x
+
+            def _rmatmat(self, x):
+                return _xp.conj(original.T) @ x
+
+        if xp:
+            cases.append((original, original))
+
+            cases.append((HasRmatvec(dtype), original))
+            cases.append((HasAdjoint(dtype), original))
+            cases.append((HasRmatmat(dtype), original))
+            
+            cases.append((interface.aslinearoperator(original.T).T, original))
+            cases.append((
+                interface.aslinearoperator(original.T).H,
+                xp.conj(original),
+            ))
+            cases.append((
+                interface.aslinearoperator(original.T).adjoint(),
+                xp.conj(original)),
+            )
+
+            return cases
+        
+        cases.append((matrix(original, dtype=dtype), original))
+        cases.append((np.array(original, dtype=dtype), original))
+        cases.append((sparse.csr_array(original, dtype=dtype), original))
+
+        cases.append((HasRmatvec(dtype), original))
+        cases.append((HasAdjoint(dtype), original))
+        cases.append((HasRmatmat(dtype), original))
+        return cases
+    
+    def setup_method(self):
+        self.cases = []
+        make_cases = self.make_cases
+        original = np.array([[1,2,3], [4,5,6]])
+        self.cases += make_cases(original, np.int32)
+        self.cases += make_cases(original, np.float32)
+        self.cases += make_cases(original, np.float64)
+        self.cases += [(interface.aslinearoperator(M).T, A.T)
+                       for M, A in make_cases(original.T, np.float64)]
+        self.cases += [(interface.aslinearoperator(M).H, A.T.conj())
+                       for M, A in make_cases(original.T, np.float64)]
+        self.cases += [(interface.aslinearoperator(M).adjoint(), A.T.conj())
+                       for M, A in make_cases(original.T, np.float64)]
+
+        original = np.array([[1, 2j, 3j], [4j, 5j, 6]])
+        self.cases += make_cases(original, np.complex128)
+        self.cases += [(interface.aslinearoperator(M).T, A.T)
+                       for M, A in make_cases(original.T, np.complex128)]
+        self.cases += [(interface.aslinearoperator(M).H, A.T.conj())
+                       for M, A in make_cases(original.T, np.complex128)]
+        self.cases += [(interface.aslinearoperator(M).adjoint(), A.T.conj())
+                       for M, A in make_cases(original.T, np.complex128)]
+
+    @pytest.mark.skip_xp_backends(np_only=True)
+    def test_basic(self, xp):
+
+        for M, A_array in self.cases:
+            A = interface.aslinearoperator(M)
+
+            xs = [np.array([1, 2, 3]),
+                  np.array([[1], [2], [3]])]
+            ys = [np.array([1, 2]), np.array([[1], [2]])]
+
+            if A.dtype == np.complex128:
+                xs += [np.array([1, 2j, 3j]),
+                       np.array([[1], [2j], [3j]])]
+                ys += [np.array([1, 2j]), np.array([[1], [2j]])]
+
+            x2 = np.array([[1, 4], [2, 5], [3, 6]])
+
+            for x in xs:
+                ctx = (
+                    pytest.warns(FutureWarning, match="column vectors")
+                    if x.shape[-1] == 1
+                    else contextlib.nullcontext()
+                )
+                with ctx:
+                    assert_equal(A.matvec(x), A_array.dot(x))
+
+                assert_equal(A @ x, A_array.dot(x))
+
+            assert_equal(A.matmat(x2), A_array.dot(x2))
+            assert_equal(A @ x2, A_array.dot(x2))
+
+            for y in ys:
+                ctx = (
+                    pytest.warns(FutureWarning, match="column vectors")
+                    if y.shape[-1] == 1
+                    else contextlib.nullcontext()
+                )
+                with ctx:
+                    assert_equal(A.rmatvec(y), A_array.T.conj().dot(y))
+                    assert_equal(A.T.matvec(y), A_array.T.dot(y))
+                    assert_equal(A.H.matvec(y), A_array.T.conj().dot(y))
+                    assert_equal(A.adjoint().matvec(y), A_array.T.conj().dot(y))
+
+            for y in ys:
+                if y.ndim < 2:
+                    continue
+                assert_equal(A.rmatmat(y), A_array.T.conj().dot(y))
+                assert_equal(A.T.matmat(y), A_array.T.dot(y))
+                assert_equal(A.H.matmat(y), A_array.T.conj().dot(y))
+                assert_equal(A.adjoint().matmat(y), A_array.T.conj().dot(y))
+
+            if hasattr(M,'dtype'):
+                assert_equal(A.dtype, M.dtype)
+
+            assert_(hasattr(A, 'args'))
+
+    @pytest.mark.skip_xp_backends(np_only=True)
+    def test_dot(self, xp):
+
+        for M, A_array in self.cases:
+            A = interface.aslinearoperator(M)
+
+            x0 = np.array([1, 2, 3])
+            x1 = np.array([[1], [2], [3]])
+            x2 = np.array([[1, 4], [2, 5], [3, 6]])
+
+            assert_equal(A.dot(x0), A_array.dot(x0))
+            assert_equal(A.dot(x1), A_array.dot(x1))
+            assert_equal(A.dot(x2), A_array.dot(x2))
+
+    @pytest.mark.parametrize("dtype", ["int64", "float64", "complex128"])
+    def test_xp(self, dtype, xp):
+        if dtype == "int64" and is_torch(xp) and SCIPY_DEVICE != "cpu":
+            pytest.skip("\"addmm_cuda\" not implemented for 'Long'")
+        dtype = getattr(xp, dtype)
+        original = xp.asarray([[1, 2, 3], [4, 5, 6]], dtype=dtype)
+        for M, A_array in self.make_cases(original, dtype, xp=xp):
+            A = interface.aslinearoperator(M)
+
+            xs = [xp.asarray([1, 2, 3]),
+                  xp.asarray([[1], [2], [3]])]
+            ys = [xp.asarray([1, 2]), xp.asarray([[1], [2]])]
+
+            if A.dtype == xp.complex128:
+                xs += [xp.asarray([1, 2j, 3j]),
+                       xp.asarray([[1], [2j], [3j]])]
+                ys += [xp.asarray([1, 2j]), xp.asarray([[1], [2j]])]
+
+            x2 = xp.asarray([[1, 4], [2, 5], [3, 6]], dtype=dtype)
+
+            for x in xs:
+                x = xp.astype(x, dtype)
+                xp_assert_equal(A @ x, A_array @ x)
+
+            xp_assert_equal(A.matmat(x2), A_array @ x2)
+            xp_assert_equal(A @ x2, A_array @ x2)
+
+            for y in ys:
+                if y.ndim < 2:
+                    continue
+                y = xp.astype(y, dtype)
+                xp_assert_equal(A.rmatmat(y), xp.conj(A_array.T) @ y)
+                xp_assert_equal(A.T.matmat(y), xp.conj(A_array.T) @ y)
+                xp_assert_equal(A.H.matmat(y), xp.conj(A_array.T) @ y)
+                xp_assert_equal(A.adjoint().matmat(y), xp.conj(A_array.T) @ y)
+
+            if hasattr(M, 'dtype'):
+                assert_equal(A.dtype, M.dtype)
+
+            assert hasattr(A, 'args')
+            
+
+def test_repr(xp):
+    A = interface.LinearOperator(shape=(1, 1), matvec=lambda x: xp.asarray([1]), xp=xp)
+    repr_A = repr(A)
+    assert 'unspecified dtype' not in repr_A, repr_A
+
+
+def test_identity(xp):
+    ident = interface.IdentityOperator((3, 3), xp=xp)
+    xp_assert_equal(ident @ xp.asarray([1, 2, 3]), xp.asarray([1, 2, 3]))
+    xp_assert_equal(xp_ravel(ident.dot(xp.reshape(xp.arange(9), (3, 3)))), xp.arange(9))
+
+    assert_raises(ValueError, ident.matvec, xp.asarray([1, 2, 3, 4]))
+
+
+def test_attributes(xp):
+    A = interface.aslinearoperator(xp.reshape(xp.arange(16, dtype=xp.float64), (4, 4)))
+
+    def always_four_ones(x):
+        x = xp.asarray(x)
+        assert x.shape == (3,) or x.shape == (3, 1)
+        return xp.ones(4)
+
+    B = interface.LinearOperator(shape=(4, 3), matvec=always_four_ones, xp=xp)
+
+    ops = [A, B, A * B, A @ B, A.H, A.adjoint(), A + A, B + B, A**4]
+    for op in ops:
+        assert hasattr(op, "dtype")
+        assert hasattr(op, "shape")
+        assert hasattr(op, "_matvec")
+
+
+def matvec_for_pickle(x):
+    """ Needed for test_pickle as local functions are not pickleable """
+    return x
+
+
+@pytest.mark.skip_xp_backends(
+    "array_api_strict",
+    reason="pickle-ability is not guaranteed by the standard"
+)
+def test_pickle(xp):
+    import pickle
+
+    protocol_min = 0 if is_numpy(xp) else 2
+    for protocol in range(protocol_min, pickle.HIGHEST_PROTOCOL + 1):
+        A = interface.LinearOperator((3, 3), matvec_for_pickle, xp=xp)
+        s = pickle.dumps(A, protocol=protocol)
+        B = pickle.loads(s)
+
+        for k in A.__dict__:
+            assert getattr(A, k) == getattr(B, k)
+
+
+def test_inheritance(xp):
+    class Empty(interface.LinearOperator):
+        pass
+
+    with warns(RuntimeWarning, match="should implement at least"):
+        assert_raises(TypeError, Empty)
+
+    class Identity(interface.LinearOperator):
+        def __init__(self, n):
+            super().__init__(dtype=None, shape=(n, n), xp=xp)
+
+        def _matvec(self, x):
+            return x
+
+    id3 = Identity(3)
+    xp_assert_equal(id3.matvec(xp.asarray([1, 2, 3])), xp.asarray([1, 2, 3]))
+    assert_raises(NotImplementedError, id3.rmatvec, xp.asarray([4, 5, 6]))
+
+    class MatmatOnly(interface.LinearOperator):
+        def __init__(self, A):
+            super().__init__(A.dtype, A.shape, xp=xp)
+            self.A = A
+
+        def _matmat(self, x):
+            return self.A @ x
+
+    mm = MatmatOnly(xp.asarray(np.random.randn(5, 3)))
+    assert mm.matvec(xp.asarray(np.random.randn(3))).shape == (5,)
+
+
+def test_dtypes_of_operator_sum(xp):
+    # gh-6078
+
+    mat_complex = xp.asarray(np.random.rand(2,2) + 1j * np.random.rand(2,2))
+    mat_real = xp.asarray(np.random.rand(2,2))
+
+    complex_operator = interface.aslinearoperator(mat_complex)
+    real_operator = interface.aslinearoperator(mat_real)
+
+    sum_complex = complex_operator + complex_operator
+    sum_real = real_operator + real_operator
+
+    assert sum_real.dtype == xp.float64
+    assert sum_complex.dtype == xp.complex128
+
+
+def test_no_double_init(xp):
+    call_count = [0]
+
+    def matvec(v):
+        call_count[0] += 1
+        return v
+
+    # It should call matvec exactly once (in order to determine the
+    # operator dtype)
+    interface.LinearOperator((2, 2), matvec=matvec, xp=xp)
+    assert_equal(call_count[0], 1)
+
+
+INT_DTYPES = (np.int8, np.int16, np.int32, np.int64)
+REAL_DTYPES = (np.float32, np.float64, np.longdouble)
+COMPLEX_DTYPES = (np.complex64, np.complex128, np.clongdouble)
+INEXACTDTYPES = REAL_DTYPES + COMPLEX_DTYPES
+ALLDTYPES = INT_DTYPES + INEXACTDTYPES
+
+
+@pytest.mark.parametrize("test_dtype", ALLDTYPES)
+def test_determine_lo_dtype_from_matvec(test_dtype, xp):
+    if "longdouble" in test_dtype.__name__ and not is_numpy(xp):
+        pytest.skip("longdoubles are only tested for `np`")
+    # gh-19209
+    scalar = xp.asarray(np.array(1, dtype=test_dtype))
+    def mv(v):
+        return xp.stack([scalar * v[0], v[1]])
+
+    lo = interface.LinearOperator((2, 2), matvec=mv, xp=xp)
+    # expected dtype depends on if mixed exact-inexact promotion is defined
+    # since dtype determination follows the following procedure:
+    # - take the dtype from calling `matvec` on an `int8`
+    # - unless that fails (e.g. via overflow or no mixed exact-inexact promotion),
+    #   in which case use the default integral dtype
+    expected = scalar.dtype
+    if xp.isdtype(expected, ("real floating", "complex floating")):
+        try:
+            xp.asarray(2) + xp.asarray(2.0)
+        except TypeError:
+            expected = xpx.default_dtype(xp, kind="integral")
+    assert lo.dtype == expected
+
+
+def test_determine_lo_dtype_for_int(xp):
+    # gh-19209
+    # test Python int larger than int8 max cast to some int
+    def mv(v):
+        return xp.asarray([128 * v[0], v[1]])
+
+    lo = interface.LinearOperator((2, 2), matvec=mv, xp=xp)
+    assert xp.isdtype(lo.dtype, "integral")
+
+
+def test_adjoint_conjugate(xp):
+    X = xp.asarray([[1j]], dtype=xp.complex128)
+    A = interface.aslinearoperator(X)
+
+    B = 1j * A
+    Y = 1j * X
+
+    v = xp.asarray([1], dtype=xp.complex128)
+
+    xp_assert_equal(B.dot(v), xp.vecdot(Y, v))
+    xp_assert_equal(B.H.dot(v), xp.vecdot(xp.conj(Y.T), v))
+    xp_assert_equal(B.adjoint().dot(v), xp.vecdot(xp.conj(Y.T), v))
+
+
+def test_ndim(xp):
+    X = xp.asarray([[1]])
+    A = interface.aslinearoperator(X)
+    assert A.ndim == 2
+
+
+def test_transpose_noconjugate(xp):
+    X = xp.asarray([[1j]], dtype=xp.complex128)
+    A = interface.aslinearoperator(X)
+
+    B = 1j * A
+    Y = 1j * X
+
+    v = xp.asarray([1], dtype=xp.complex128)
+
+    xp_assert_equal(B.dot(v), xp.vecdot(Y, v))
+    xp_assert_equal(B.T.dot(v), xp.vecdot(Y.T, v))
+
+
+@pytest.mark.skip_xp_backends("dask.array", reason="https://github.com/dask/dask/issues/11711")
+@pytest.mark.skip_xp_backends(
+    "array_api_strict",
+    reason="https://github.com/data-apis/array-api-strict/issues/188"
+)
+def test_transpose_multiplication(xp):
+    _asarray = partial(xp.asarray, dtype=xp.complex128)
+    class MyMatrix(interface.LinearOperator):
+        def __init__(self, A):
+            super().__init__(A.dtype, A.shape, xp=xp)
+            self.A = A
+        def _matmat(self, other): return self.A @ other
+        def _rmatmat(self, other): return self.A.mT @ other
+
+    A = MyMatrix(_asarray([[1, 2], [3, 4]]))
+    X = _asarray([1, 2])
+    X_T = X
+    B = _asarray([[10, 20], [30, 40]])
+    X2 = xp.reshape(X, (-1, 1))
+    Y = _asarray([[1, 2], [3, 4]])
+
+    xp_assert_equal(A @ B, Y @ B)
+    xp_assert_equal(B.T @ A, B.T @ Y)
+    xp_assert_equal(A.T @ B, Y.mT @ B)
+    xp_assert_equal(A @ X, Y @ X)
+    xp_assert_equal(X_T @ A, X_T @ Y)
+    xp_assert_equal(A.T @ X, Y.mT @ X)
+    xp_assert_equal(A @ X2, Y @ X2)
+    xp_assert_equal(X2.mT @ A, X2.mT @ Y)
+    xp_assert_equal(A.T @ X2, Y.mT @ X2)
+
+
+@pytest.mark.skip_xp_backends(np_only=True)
+def test_sparse_matmat_exception():
+    B = sparse.eye_array(2)
+    # well defined matmat via `aslinearoperator`
+    A = interface.aslinearoperator(sparse.eye_array(2))
+    assert isinstance(A @ B, sparse.sparray)
+    assert isinstance(B @ A, sparse.sparray)
+    xp_assert_equal((A @ B).toarray(), np.eye(2))
+    xp_assert_equal((B @ A).toarray(), np.eye(2))
+    # ill-defined matmat via default fallback to matvec
+    A = interface.LinearOperator((2, 2), matvec=lambda x: x)
+    msg = "Try wrapping the matrix with `aslinearoperator` first."
+    with assert_raises(TypeError, match=msg):
+        A @ B
+    with assert_raises(TypeError, match=msg):
+        B @ A
+    # after using `aslinearoperator`
+    B = interface.aslinearoperator(B)
+    assert isinstance(A @ B, interface.LinearOperator)
+    assert isinstance(B @ A, interface.LinearOperator)
+    xp_assert_equal((A @ B).matvec(np.ones(2)), np.ones(2))
+
+
+@pytest.mark.skip_xp_backends(
+    "jax.numpy", reason="remaining reference (due to lazy_xp_function?)"
+)
+def test_MatrixLinearOperator_refcycle(xp):
+    # gh-10634
+    # Test that MatrixLinearOperator can be automatically garbage collected
+    A = xp.eye(2)
+    with assert_deallocated(interface.MatrixLinearOperator, A, xp) as op:
+        op.adjoint()
+        del op
+
+
+@pytest.mark.parametrize("left", [False, True])
+@pytest.mark.parametrize("operator_definition", ["subclass_matvec", "subclass_matmat",
+                                                 "__init__matvec", "__init__matmat",
+                                                 "aslinearoperator"])
+@pytest.mark.parametrize("batch_A", [(), (5,), (0,)])
+@pytest.mark.parametrize("batch_x", [(), (6, 1), (0, 1)])
+@pytest.mark.parametrize("dtype", [np.float64, np.complex128])
+@pytest.mark.skip_xp_backends("dask.array", reason="https://github.com/dask/dask/issues/11711")
+@pytest.mark.skip_xp_backends(
+    "array_api_strict",
+    reason="https://github.com/data-apis/array-api-strict/issues/188"
+)
+def test_batch(left, operator_definition, batch_A, batch_x, dtype, xp):
+    # TODO ideas:
+    # - test lower-precision types
+    # - test `transpose`, `adjoint`, `__mul__`, etc.
+    # - test composite LinearOperators
+    rng = np.random.default_rng(41981392342349823)
+
+    m, n, k = 4, 3, 2
+    A_ = rng.random((*batch_A, m, n))
+    x_row = rng.random((*batch_x, n if left else m))
+    x_col = rng.random((*batch_x, n if left else m, 1))
+    x_mat = rng.random((*batch_x, n if left else m, k))
+
+    if dtype == np.complex128:
+        A_ = A_ + 1j * rng.random(A_.shape)
+        x_row = x_row + 1j * rng.random(x_row.shape)
+        x_col = x_col + 1j * rng.random(x_col.shape)
+        x_mat = x_mat + 1j * rng.random(x_mat.shape)
+    
+    A_, x_row, x_col, x_mat = (xp.asarray(x) for x in (A_, x_row, x_col, x_mat))
+
+    def matvec(A, x):
+        if not batch_x:
+            assert x.ndim == 1
+            return A @ x
+        else:
+            # It might make it easier on the author of LinearOperators to
+            # "ravel" all batch dimensions into one before calling their `matvec`
+            # implementation. That way, they only have to think about vectorizing
+            # w.r.t. one batch dimension rather than an arbitrary number of batch
+            # dimensions. In this case, `x.ndim` would be exactly 2.
+            assert x.ndim >= 2
+            return (A @ (x[..., xp.newaxis]))[..., 0]
+
+    def matmat(A, X):
+        if not batch_x:
+            assert X.ndim == 2
+        else:
+            # Similar to above, we could ravel all batch dimensions before calling
+            # the user's `matmat`. Then `x.ndim` would be exactly 3.
+            assert X.ndim >= 3
+        return A @ X
+
+    if operator_definition == "aslinearoperator":
+        A = interface.aslinearoperator(A_)
+    elif operator_definition == "__init__matvec":
+        A = interface.LinearOperator(
+            shape=A_.shape, dtype=A_.dtype,
+            matvec=lambda x: matvec(A_, x),
+            rmatvec=lambda x: matvec(xp.conj(A_.mT), x),
+            xp=xp,
+        )
+    elif operator_definition == "__init__matmat":
+        # A = interface.LinearOperator(shape=A_.shape, dtype=A_.dtype,
+        #                              matmat=lambda X: matmat(A_, X))
+        pytest.skip("should work but doesn't - see gh-24510")
+    elif operator_definition == "subclass_matvec":
+        class MyLinearOperator(interface.LinearOperator):
+            def _matvec(self, x):
+                return matvec(A_, x)
+            def _rmatvec(self, x):
+                return matvec(xp.conj(A_.mT), x)
+        A = MyLinearOperator(shape=A_.shape, dtype=A_.dtype, xp=xp)
+    elif operator_definition == "subclass_matmat":
+        class MyLinearOperator(interface.LinearOperator):
+            def _matmat(self, X):
+                return matmat(A_, X)
+            def _rmatmat(self, X):
+                return matmat(xp.conj(A_.mT), X)
+        A = MyLinearOperator(shape=A_.shape, dtype=A_.dtype, xp=xp)
+
+    # Test matvec
+    # a. with row vector (or batch of row vectors)
+    xp_assert_close(
+        A.matvec(x_row) if left else A.rmatvec(x_row),
+        matvec(A_, x_row) if left else matvec(xp.conj(A_.mT), x_row)
+    )
+    # b. with column vector (or batch of column vectors)
+    if batch_x:
+        message = "Dimension mismatch:..."
+        with pytest.raises(ValueError, match=message):
+            A.matvec(x_col) if left else A.rmatvec(x_col)
+    else:
+        message = ("Calling `matvec` on 'column vectors'..." if left
+                   else "Calling `rmatvec` on 'column vectors'...")
+        with pytest.warns(FutureWarning, match=message):
+            xp_assert_close(
+                A.matvec(x_col) if left else A.rmatvec(x_col),
+                A_ @ x_col if left else xp.conj(A_.mT) @ x_col,
+            )
+    # c. with matrix (or batch of matrices)
+    with pytest.raises(ValueError, match="Dimension mismatch:..."):
+        A.matvec(x_mat) if left else A.rmatvec(x_mat)
+
+    # Test matmat
+    # a. with row vector (or batch of row vectors)
+    message = "Dimension mismatch:..." if batch_x else "Expected at least 2-d..."
+    with pytest.raises(ValueError, match=message):
+        A.matmat(x_row) if left else A.rmatmat(x_row)
+    # b. with column vector (or batch of column vectors)
+    xp_assert_close(
+        A.matmat(x_col) if left else A.rmatmat(x_col),
+        A_ @ x_col if left else xp.conj(A_.mT) @ x_col,
+    )
+    # c. with matrix (or batch of matrices)
+    xp_assert_close(
+        A.matmat(x_mat) if left else A.rmatmat(x_mat),
+        A_ @ x_mat if left else xp.conj(A_.mT) @ x_mat,
+    )
+
+    # test __matmul__ (via `@`), `__call__`, and `dot`
+    if left:
+        # a. with row vector (or batch of row vectors)
+        if batch_x:
+            with pytest.raises(ValueError, match="Dimension mismatch:..."):
+                A @ x_row
+        else:
+            xp_assert_close(A @ x_row, A_ @ x_row)
+            xp_assert_close(A(x_row), A_ @ x_row)
+            xp_assert_close(A.dot(x_row), A_ @ x_row)
+        # b. with column vector (or batch of column vectors)
+        xp_assert_close(A @ x_col, A_ @ x_col)
+        xp_assert_close(A(x_col), A_ @ x_col)
+        xp_assert_close(A.dot(x_col), A_ @ x_col)
+        # c. with matrix (or batch of matrices)
+        xp_assert_close(A @ x_mat, A_ @ x_mat)
+        xp_assert_close(A(x_mat), A_ @ x_mat)
+        xp_assert_close(A.dot(x_mat), A_ @ x_mat)
+    else:
+        # a. with row vector (or batch of row vectors)
+        broadcastable = True
+        try:
+            # `batch_x[-1]` becomes part of the core shape for matrix
+            # multiplication with 1-D row vector
+            # success thus depends on whether `batch_A` can broadcast
+            # with `batch_x[:-1]`
+            np.broadcast_shapes(batch_A, batch_x[:-1])
+        except ValueError:
+            broadcastable = False
+        if not broadcastable:
+            # Maybe should be "Dimension mismatch..."?
+            msg = "Incompatible shapes|size of tensor|could not be broadcast..."
+            with pytest.raises((ValueError, RuntimeError), match=msg):
+                x_row @ A
+        else:
+            xp_assert_close(x_row @ A, x_row @ A_)
+            xp_assert_close(A.rdot(x_row), x_row @ A_)
+        # b. with column vector (or batch of column vectors)
+        with pytest.raises(ValueError, match="Dimension mismatch:..."):
+            x_col @ A
+        # c. with matrix (or batch of matrices)
+        xp_assert_close(xp.conj(x_mat.mT) @ A, xp.conj(x_mat.mT) @ A_)
+        xp_assert_close(A.rdot(xp.conj(x_mat.mT)), xp.conj(x_mat.mT) @ A_)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/tests/test_matfuncs.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/tests/test_matfuncs.py
new file mode 100644
index 0000000000000000000000000000000000000000..14bfff88769db7a4d08b4f10e0fb13778c52dd02
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/tests/test_matfuncs.py
@@ -0,0 +1,599 @@
+#
+# Created by: Pearu Peterson, March 2002
+#
+""" Test functions for scipy.linalg._matfuncs module
+
+"""
+import math
+import warnings
+
+import numpy as np
+from numpy import array, eye, exp, random
+from numpy.testing import (
+        assert_allclose, assert_, assert_array_almost_equal, assert_equal,
+        assert_array_almost_equal_nulp)
+
+from scipy.sparse import csc_array, SparseEfficiencyWarning
+from scipy.sparse._construct import eye_array
+from scipy.sparse.linalg._matfuncs import (expm, _expm,
+        ProductOperator, MatrixPowerOperator,
+        _onenorm_matrix_power_nnm, matrix_power)
+from scipy.sparse._sputils import matrix
+from scipy.linalg import logm
+from scipy.special import factorial, binom
+import scipy.sparse
+import scipy.sparse.linalg
+
+
+def _burkardt_13_power(n, p):
+    """
+    A helper function for testing matrix functions.
+
+    Parameters
+    ----------
+    n : int greater than 1
+        Order of the square matrix to be returned.
+    p : non-negative integer
+        Power of the matrix.
+
+    Returns
+    -------
+    out : ndarray representing a square matrix
+        A Forsythe matrix of order n, raised to the power p.
+
+    """
+    # Input validation.
+    if n != int(n) or n < 2:
+        raise ValueError('n must be an integer greater than 1')
+    n = int(n)
+    if p != int(p) or p < 0:
+        raise ValueError('p must be a non-negative integer')
+    p = int(p)
+
+    # Construct the matrix explicitly.
+    a, b = divmod(p, n)
+    large = np.power(10.0, -n*a)
+    small = large * np.power(10.0, -n)
+    return np.diag([large]*(n-b), b) + np.diag([small]*b, b-n)
+
+
+def test_onenorm_matrix_power_nnm():
+    np.random.seed(1234)
+    for n in range(1, 5):
+        for p in range(5):
+            M = np.random.random((n, n))
+            Mp = np.linalg.matrix_power(M, p)
+            observed = _onenorm_matrix_power_nnm(M, p)
+            expected = np.linalg.norm(Mp, 1)
+            assert_allclose(observed, expected)
+
+def test_matrix_power():
+    np.random.seed(1234)
+    row, col = np.random.randint(0, 4, size=(2, 6))
+    data = np.random.random(size=(6,))
+    Amat = csc_array((data, (row, col)), shape=(4, 4))
+    A = csc_array((data, (row, col)), shape=(4, 4))
+    Adense = A.toarray()
+    for power in (2, 5, 6):
+        Apow = matrix_power(A, power).toarray()
+        Amat_pow = matrix_power(Amat, power).toarray()
+        Adense_pow = np.linalg.matrix_power(Adense, power)
+        assert_allclose(Apow, Adense_pow)
+        assert_allclose(Apow, Amat_pow)
+
+
+class TestExpM:
+    def test_zero_ndarray(self):
+        a = array([[0.,0],[0,0]])
+        assert_array_almost_equal(expm(a),[[1,0],[0,1]])
+
+    def test_zero_sparse(self):
+        a = csc_array([[0.,0],[0,0]])
+        assert_array_almost_equal(expm(a).toarray(),[[1,0],[0,1]])
+
+    def test_zero_matrix(self):
+        a = matrix([[0.,0],[0,0]])
+        assert_array_almost_equal(expm(a),[[1,0],[0,1]])
+
+    def test_misc_types(self):
+        A = expm(np.array([[1]]))
+        assert_allclose(expm(((1,),)), A)
+        assert_allclose(expm([[1]]), A)
+        assert_allclose(expm(matrix([[1]])), A)
+        assert_allclose(expm(np.array([[1]])), A)
+        assert_allclose(expm(csc_array([[1]])).toarray(), A)
+        B = expm(np.array([[1j]]))
+        assert_allclose(expm(((1j,),)), B)
+        assert_allclose(expm([[1j]]), B)
+        assert_allclose(expm(matrix([[1j]])), B)
+        assert_allclose(expm(csc_array([[1j]])).toarray(), B)
+
+    def test_bidiagonal_sparse(self):
+        A = csc_array([
+            [1, 3, 0],
+            [0, 1, 5],
+            [0, 0, 2]], dtype=float)
+        e1 = math.exp(1)
+        e2 = math.exp(2)
+        expected = np.array([
+            [e1, 3*e1, 15*(e2 - 2*e1)],
+            [0, e1, 5*(e2 - e1)],
+            [0, 0, e2]], dtype=float)
+        observed = expm(A).toarray()
+        assert_array_almost_equal(observed, expected)
+
+    def test_padecases_dtype_float(self):
+        for dtype in [np.float32, np.float64]:
+            for scale in [1e-2, 1e-1, 5e-1, 1, 10]:
+                A = scale * eye(3, dtype=dtype)
+                observed = expm(A)
+                expected = exp(scale, dtype=dtype) * eye(3, dtype=dtype)
+                assert_array_almost_equal_nulp(observed, expected, nulp=100)
+
+    def test_padecases_dtype_complex(self):
+        for dtype in [np.complex64, np.complex128]:
+            for scale in [1e-2, 1e-1, 5e-1, 1, 10]:
+                A = scale * eye(3, dtype=dtype)
+                observed = expm(A)
+                expected = exp(scale, dtype=dtype) * eye(3, dtype=dtype)
+                assert_array_almost_equal_nulp(observed, expected, nulp=100)
+
+    def test_padecases_dtype_sparse_float(self):
+        # float32 and complex64 lead to errors in spsolve/UMFpack
+        dtype = np.float64
+        for scale in [1e-2, 1e-1, 5e-1, 1, 10]:
+            a = scale * eye_array(3, 3, dtype=dtype, format='csc')
+            e = exp(scale, dtype=dtype) * eye(3, dtype=dtype)
+            with warnings.catch_warnings():
+                msg = "Changing the sparsity structure"
+                warnings.filterwarnings("ignore", msg, SparseEfficiencyWarning)
+                exact_onenorm = _expm(a, use_exact_onenorm=True).toarray()
+                inexact_onenorm = _expm(a, use_exact_onenorm=False).toarray()
+            assert_array_almost_equal_nulp(exact_onenorm, e, nulp=100)
+            assert_array_almost_equal_nulp(inexact_onenorm, e, nulp=100)
+
+    def test_padecases_dtype_sparse_complex(self):
+        # float32 and complex64 lead to errors in spsolve/UMFpack
+        dtype = np.complex128
+        for scale in [1e-2, 1e-1, 5e-1, 1, 10]:
+            a = scale * eye_array(3, 3, dtype=dtype, format='csc')
+            e = exp(scale) * eye(3, dtype=dtype)
+            with warnings.catch_warnings():
+                msg = "Changing the sparsity structure"
+                warnings.filterwarnings("ignore", msg, SparseEfficiencyWarning)
+                assert_array_almost_equal_nulp(expm(a).toarray(), e, nulp=100)
+
+    def test_logm_consistency(self):
+        random.seed(1234)
+        for dtype in [np.float64, np.complex128]:
+            for n in range(1, 10):
+                for scale in [1e-4, 1e-3, 1e-2, 1e-1, 1, 1e1, 1e2]:
+                    # make logm(A) be of a given scale
+                    A = (eye(n) + random.rand(n, n) * scale).astype(dtype)
+                    if np.iscomplexobj(A):
+                        A = A + 1j * random.rand(n, n) * scale
+                    assert_array_almost_equal(expm(logm(A)), A)
+
+    def test_integer_matrix(self):
+        Q = np.array([
+            [-3, 1, 1, 1],
+            [1, -3, 1, 1],
+            [1, 1, -3, 1],
+            [1, 1, 1, -3]])
+        assert_allclose(expm(Q), expm(1.0 * Q))
+
+    def test_integer_matrix_2(self):
+        # Check for integer overflows
+        Q = np.array([[-500, 500, 0, 0],
+                      [0, -550, 360, 190],
+                      [0, 630, -630, 0],
+                      [0, 0, 0, 0]], dtype=np.int16)
+        assert_allclose(expm(Q), expm(1.0 * Q))
+
+        Q = csc_array(Q)
+        assert_allclose(expm(Q).toarray(), expm(1.0 * Q).toarray())
+
+    def test_triangularity_perturbation(self):
+        # Experiment (1) of
+        # Awad H. Al-Mohy and Nicholas J. Higham (2012)
+        # Improved Inverse Scaling and Squaring Algorithms
+        # for the Matrix Logarithm.
+        A = np.array([
+            [3.2346e-1, 3e4, 3e4, 3e4],
+            [0, 3.0089e-1, 3e4, 3e4],
+            [0, 0, 3.221e-1, 3e4],
+            [0, 0, 0, 3.0744e-1]],
+            dtype=float)
+        A_logm = np.array([
+            [-1.12867982029050462e+00, 9.61418377142025565e+04,
+             -4.52485573953179264e+09, 2.92496941103871812e+14],
+            [0.00000000000000000e+00, -1.20101052953082288e+00,
+             9.63469687211303099e+04, -4.68104828911105442e+09],
+            [0.00000000000000000e+00, 0.00000000000000000e+00,
+             -1.13289322264498393e+00, 9.53249183094775653e+04],
+            [0.00000000000000000e+00, 0.00000000000000000e+00,
+             0.00000000000000000e+00, -1.17947533272554850e+00]],
+            dtype=float)
+        assert_allclose(expm(A_logm), A, rtol=1e-4)
+
+        # Perturb the upper triangular matrix by tiny amounts,
+        # so that it becomes technically not upper triangular.
+        random.seed(1234)
+        tiny = 1e-17
+        A_logm_perturbed = A_logm.copy()
+        A_logm_perturbed[1, 0] = tiny
+        with warnings.catch_warnings():
+            warnings.filterwarnings("ignore", "Ill-conditioned.*", RuntimeWarning)
+            warnings.filterwarnings("ignore", "An ill-conditioned.*", RuntimeWarning)
+
+            A_expm_logm_perturbed = expm(A_logm_perturbed)
+        rtol = 1e-4
+        atol = 100 * tiny
+        assert_(not np.allclose(A_expm_logm_perturbed, A, rtol=rtol, atol=atol))
+
+    def test_burkardt_1(self):
+        # This matrix is diagonal.
+        # The calculation of the matrix exponential is simple.
+        #
+        # This is the first of a series of matrix exponential tests
+        # collected by John Burkardt from the following sources.
+        #
+        # Alan Laub,
+        # Review of "Linear System Theory" by Joao Hespanha,
+        # SIAM Review,
+        # Volume 52, Number 4, December 2010, pages 779--781.
+        #
+        # Cleve Moler and Charles Van Loan,
+        # Nineteen Dubious Ways to Compute the Exponential of a Matrix,
+        # Twenty-Five Years Later,
+        # SIAM Review,
+        # Volume 45, Number 1, March 2003, pages 3--49.
+        #
+        # Cleve Moler,
+        # Cleve's Corner: A Balancing Act for the Matrix Exponential,
+        # 23 July 2012.
+        #
+        # Robert Ward,
+        # Numerical computation of the matrix exponential
+        # with accuracy estimate,
+        # SIAM Journal on Numerical Analysis,
+        # Volume 14, Number 4, September 1977, pages 600--610.
+        exp1 = np.exp(1)
+        exp2 = np.exp(2)
+        A = np.array([
+            [1, 0],
+            [0, 2],
+            ], dtype=float)
+        desired = np.array([
+            [exp1, 0],
+            [0, exp2],
+            ], dtype=float)
+        actual = expm(A)
+        assert_allclose(actual, desired)
+
+    def test_burkardt_2(self):
+        # This matrix is symmetric.
+        # The calculation of the matrix exponential is straightforward.
+        A = np.array([
+            [1, 3],
+            [3, 2],
+            ], dtype=float)
+        desired = np.array([
+            [39.322809708033859, 46.166301438885753],
+            [46.166301438885768, 54.711576854329110],
+            ], dtype=float)
+        actual = expm(A)
+        assert_allclose(actual, desired)
+
+    def test_burkardt_3(self):
+        # This example is due to Laub.
+        # This matrix is ill-suited for the Taylor series approach.
+        # As powers of A are computed, the entries blow up too quickly.
+        exp1 = np.exp(1)
+        exp39 = np.exp(39)
+        A = np.array([
+            [0, 1],
+            [-39, -40],
+            ], dtype=float)
+        desired = np.array([
+            [
+                39/(38*exp1) - 1/(38*exp39),
+                -np.expm1(-38) / (38*exp1)],
+            [
+                39*np.expm1(-38) / (38*exp1),
+                -1/(38*exp1) + 39/(38*exp39)],
+            ], dtype=float)
+        actual = expm(A)
+        assert_allclose(actual, desired)
+
+    def test_burkardt_4(self):
+        # This example is due to Moler and Van Loan.
+        # The example will cause problems for the series summation approach,
+        # as well as for diagonal Pade approximations.
+        A = np.array([
+            [-49, 24],
+            [-64, 31],
+            ], dtype=float)
+        U = np.array([[3, 1], [4, 2]], dtype=float)
+        V = np.array([[1, -1/2], [-2, 3/2]], dtype=float)
+        w = np.array([-17, -1], dtype=float)
+        desired = np.dot(U * np.exp(w), V)
+        actual = expm(A)
+        assert_allclose(actual, desired)
+
+    def test_burkardt_5(self):
+        # This example is due to Moler and Van Loan.
+        # This matrix is strictly upper triangular
+        # All powers of A are zero beyond some (low) limit.
+        # This example will cause problems for Pade approximations.
+        A = np.array([
+            [0, 6, 0, 0],
+            [0, 0, 6, 0],
+            [0, 0, 0, 6],
+            [0, 0, 0, 0],
+            ], dtype=float)
+        desired = np.array([
+            [1, 6, 18, 36],
+            [0, 1, 6, 18],
+            [0, 0, 1, 6],
+            [0, 0, 0, 1],
+            ], dtype=float)
+        actual = expm(A)
+        assert_allclose(actual, desired)
+
+    def test_burkardt_6(self):
+        # This example is due to Moler and Van Loan.
+        # This matrix does not have a complete set of eigenvectors.
+        # That means the eigenvector approach will fail.
+        exp1 = np.exp(1)
+        A = np.array([
+            [1, 1],
+            [0, 1],
+            ], dtype=float)
+        desired = np.array([
+            [exp1, exp1],
+            [0, exp1],
+            ], dtype=float)
+        actual = expm(A)
+        assert_allclose(actual, desired)
+
+    def test_burkardt_7(self):
+        # This example is due to Moler and Van Loan.
+        # This matrix is very close to example 5.
+        # Mathematically, it has a complete set of eigenvectors.
+        # Numerically, however, the calculation will be suspect.
+        exp1 = np.exp(1)
+        eps = np.spacing(1)
+        A = np.array([
+            [1 + eps, 1],
+            [0, 1 - eps],
+            ], dtype=float)
+        desired = np.array([
+            [exp1, exp1],
+            [0, exp1],
+            ], dtype=float)
+        actual = expm(A)
+        assert_allclose(actual, desired)
+
+    def test_burkardt_8(self):
+        # This matrix was an example in Wikipedia.
+        exp4 = np.exp(4)
+        exp16 = np.exp(16)
+        A = np.array([
+            [21, 17, 6],
+            [-5, -1, -6],
+            [4, 4, 16],
+            ], dtype=float)
+        desired = np.array([
+            [13*exp16 - exp4, 13*exp16 - 5*exp4, 2*exp16 - 2*exp4],
+            [-9*exp16 + exp4, -9*exp16 + 5*exp4, -2*exp16 + 2*exp4],
+            [16*exp16, 16*exp16, 4*exp16],
+            ], dtype=float) * 0.25
+        actual = expm(A)
+        assert_allclose(actual, desired)
+
+    def test_burkardt_9(self):
+        # This matrix is due to the NAG Library.
+        # It is an example for function F01ECF.
+        A = np.array([
+            [1, 2, 2, 2],
+            [3, 1, 1, 2],
+            [3, 2, 1, 2],
+            [3, 3, 3, 1],
+            ], dtype=float)
+        desired = np.array([
+            [740.7038, 610.8500, 542.2743, 549.1753],
+            [731.2510, 603.5524, 535.0884, 542.2743],
+            [823.7630, 679.4257, 603.5524, 610.8500],
+            [998.4355, 823.7630, 731.2510, 740.7038],
+            ], dtype=float)
+        actual = expm(A)
+        assert_allclose(actual, desired)
+
+    def test_burkardt_10(self):
+        # This is Ward's example #1.
+        # It is defective and nonderogatory.
+        A = np.array([
+            [4, 2, 0],
+            [1, 4, 1],
+            [1, 1, 4],
+            ], dtype=float)
+        assert_allclose(sorted(scipy.linalg.eigvals(A)), (3, 3, 6))
+        desired = np.array([
+            [147.8666224463699, 183.7651386463682, 71.79703239999647],
+            [127.7810855231823, 183.7651386463682, 91.88256932318415],
+            [127.7810855231824, 163.6796017231806, 111.9681062463718],
+            ], dtype=float)
+        actual = expm(A)
+        assert_allclose(actual, desired)
+
+    def test_burkardt_11(self):
+        # This is Ward's example #2.
+        # It is a symmetric matrix.
+        A = np.array([
+            [29.87942128909879, 0.7815750847907159, -2.289519314033932],
+            [0.7815750847907159, 25.72656945571064, 8.680737820540137],
+            [-2.289519314033932, 8.680737820540137, 34.39400925519054],
+            ], dtype=float)
+        assert_allclose(scipy.linalg.eigvalsh(A), (20, 30, 40))
+        desired = np.array([
+             [
+                 5.496313853692378E+15,
+                 -1.823188097200898E+16,
+                 -3.047577080858001E+16],
+             [
+                -1.823188097200899E+16,
+                6.060522870222108E+16,
+                1.012918429302482E+17],
+             [
+                -3.047577080858001E+16,
+                1.012918429302482E+17,
+                1.692944112408493E+17],
+            ], dtype=float)
+        actual = expm(A)
+        assert_allclose(actual, desired)
+
+    def test_burkardt_12(self):
+        # This is Ward's example #3.
+        # Ward's algorithm has difficulty estimating the accuracy
+        # of its results.
+        A = np.array([
+            [-131, 19, 18],
+            [-390, 56, 54],
+            [-387, 57, 52],
+            ], dtype=float)
+        assert_allclose(sorted(scipy.linalg.eigvals(A)), (-20, -2, -1))
+        desired = np.array([
+            [-1.509644158793135, 0.3678794391096522, 0.1353352811751005],
+            [-5.632570799891469, 1.471517758499875, 0.4060058435250609],
+            [-4.934938326088363, 1.103638317328798, 0.5413411267617766],
+            ], dtype=float)
+        actual = expm(A)
+        assert_allclose(actual, desired)
+
+    def test_burkardt_13(self):
+        # This is Ward's example #4.
+        # This is a version of the Forsythe matrix.
+        # The eigenvector problem is badly conditioned.
+        # Ward's algorithm has difficulty estimating the accuracy
+        # of its results for this problem.
+        #
+        # Check the construction of one instance of this family of matrices.
+        A4_actual = _burkardt_13_power(4, 1)
+        A4_desired = [[0, 1, 0, 0],
+                      [0, 0, 1, 0],
+                      [0, 0, 0, 1],
+                      [1e-4, 0, 0, 0]]
+        assert_allclose(A4_actual, A4_desired)
+        # Check the expm for a few instances.
+        for n in (2, 3, 4, 10):
+            # Approximate expm using Taylor series.
+            # This works well for this matrix family
+            # because each matrix in the summation,
+            # even before dividing by the factorial,
+            # is entrywise positive with max entry 10**(-floor(p/n)*n).
+            k = max(1, int(np.ceil(16/n)))
+            desired = np.zeros((n, n), dtype=float)
+            for p in range(n*k):
+                Ap = _burkardt_13_power(n, p)
+                assert_equal(np.min(Ap), 0)
+                assert_allclose(np.max(Ap), np.power(10, -np.floor(p/n)*n))
+                desired += Ap / factorial(p)
+            actual = expm(_burkardt_13_power(n, 1))
+            assert_allclose(actual, desired)
+
+    def test_burkardt_14(self):
+        # This is Moler's example.
+        # This badly scaled matrix caused problems for MATLAB's expm().
+        A = np.array([
+            [0, 1e-8, 0],
+            [-(2e10 + 4e8/6.), -3, 2e10],
+            [200./3., 0, -200./3.],
+            ], dtype=float)
+        desired = np.array([
+            [0.446849468283175, 1.54044157383952e-09, 0.462811453558774],
+            [-5743067.77947947, -0.0152830038686819, -4526542.71278401],
+            [0.447722977849494, 1.54270484519591e-09, 0.463480648837651],
+            ], dtype=float)
+        actual = expm(A)
+        assert_allclose(actual, desired)
+
+    def test_pascal(self):
+        # Test pascal triangle.
+        # Nilpotent exponential, used to trigger a failure (gh-8029)
+
+        for scale in [1.0, 1e-3, 1e-6]:
+            for n in range(0, 80, 3):
+                sc = scale ** np.arange(n, -1, -1)
+                if np.any(sc < 1e-300):
+                    break
+
+                A = np.diag(np.arange(1, n + 1), -1) * scale
+                B = expm(A)
+
+                got = B
+                expected = binom(np.arange(n + 1)[:,None],
+                                 np.arange(n + 1)[None,:]) * sc[None,:] / sc[:,None]
+                atol = 1e-13 * abs(expected).max()
+                assert_allclose(got, expected, atol=atol)
+
+    def test_matrix_input(self):
+        # Large np.matrix inputs should work, gh-5546
+        A = np.zeros((200, 200))
+        A[-1,0] = 1
+        B0 = expm(A)
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", "the matrix subclass.*", DeprecationWarning)
+            warnings.filterwarnings(
+                "ignore", "the matrix subclass.*", PendingDeprecationWarning)
+            B = expm(np.matrix(A))
+        assert_allclose(B, B0)
+
+    def test_exp_sinch_overflow(self):
+        # Check overflow in intermediate steps is fixed (gh-11839)
+        L = np.array([[1.0, -0.5, -0.5, 0.0, 0.0, 0.0, 0.0],
+                      [0.0, 1.0, 0.0, -0.5, -0.5, 0.0, 0.0],
+                      [0.0, 0.0, 1.0, 0.0, 0.0, -0.5, -0.5],
+                      [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
+                      [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
+                      [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
+                      [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]])
+
+        E0 = expm(-L)
+        E1 = expm(-2**11 * L)
+        E2 = E0
+        for j in range(11):
+            E2 = E2 @ E2
+
+        assert_allclose(E1, E2)
+
+
+class TestOperators:
+
+    def test_product_operator(self):
+        random.seed(1234)
+        n = 5
+        k = 2
+        nsamples = 10
+        for i in range(nsamples):
+            A = np.random.randn(n, n)
+            B = np.random.randn(n, n)
+            C = np.random.randn(n, n)
+            D = np.random.randn(n, k)
+            op = ProductOperator(A, B, C)
+            assert_allclose(op.matmat(D), A.dot(B).dot(C).dot(D))
+            assert_allclose(op.T.matmat(D), (A.dot(B).dot(C)).T.dot(D))
+
+    def test_matrix_power_operator(self):
+        random.seed(1234)
+        n = 5
+        k = 2
+        p = 3
+        nsamples = 10
+        for i in range(nsamples):
+            A = np.random.randn(n, n)
+            B = np.random.randn(n, k)
+            op = MatrixPowerOperator(A, p)
+            assert_allclose(op.matmat(B), np.linalg.matrix_power(A, p).dot(B))
+            assert_allclose(op.T.matmat(B), np.linalg.matrix_power(A, p).T.dot(B))
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/tests/test_norm.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/tests/test_norm.py
new file mode 100644
index 0000000000000000000000000000000000000000..1704e42afc5b8311e688243fb38626d746fa881b
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/tests/test_norm.py
@@ -0,0 +1,150 @@
+"""Test functions for the sparse.linalg.norm module
+"""
+
+import numpy as np
+from numpy.linalg import norm as npnorm
+from numpy.testing import assert_allclose, assert_equal
+from pytest import raises as assert_raises
+
+import scipy.sparse
+from scipy.sparse.linalg import norm as spnorm
+
+
+# https://github.com/scipy/scipy/issues/16031
+# https://github.com/scipy/scipy/issues/21690
+def test_sparray_norm():
+    row = np.array([0, 0, 1, 1])
+    col = np.array([0, 1, 2, 3])
+    data = np.array([4, 5, 7, 9])
+    test_arr = scipy.sparse.coo_array((data, (row, col)), shape=(2, 4))
+    test_mat = scipy.sparse.coo_matrix((data, (row, col)), shape=(2, 4))
+    for ord in (1, np.inf, None):
+        for ax in [0, 1, None, (0, 1), (1, 0)]:
+            for A in (test_arr, test_mat):
+                expected = npnorm(A.toarray(), ord=ord, axis=ax)
+                actual = spnorm(A, ord=ord, axis=ax)
+                assert hasattr(actual, "dtype")
+                assert_equal(actual, expected)
+    # test 1d array and 1d-like (column) matrix
+    test_arr_1d = scipy.sparse.coo_array((data, (col,)), shape=(4,))
+    test_mat_col = scipy.sparse.coo_matrix((data, (col, [0, 0, 0, 0])), shape=(4, 1))
+    for ord in (1, np.inf, None):
+        for ax in [0, None]:
+            for A in (test_arr_1d, test_mat_col):
+                expected = npnorm(A.toarray(), ord=ord, axis=ax)
+                assert_equal(spnorm(A, ord=ord, axis=ax), expected)
+
+
+class TestNorm:
+    def setup_method(self):
+        a = np.arange(9) - 4
+        b = a.reshape((3, 3))
+        self.b = scipy.sparse.csr_array(b)
+
+    def test_matrix_norm(self):
+
+        # Frobenius norm is the default
+        assert_allclose(spnorm(self.b), 7.745966692414834)
+        assert_allclose(spnorm(self.b, 'fro'), 7.745966692414834)
+
+        assert_allclose(spnorm(self.b, np.inf), 9)
+        assert_allclose(spnorm(self.b, -np.inf), 2)
+        assert_allclose(spnorm(self.b, 1), 7)
+        assert_allclose(spnorm(self.b, -1), 6)
+        assert_allclose(spnorm(self.b.astype(np.float64), 2), 7.348469228349534)
+
+        # _multi_svd_norm is not implemented for sparse array
+        assert_raises(NotImplementedError, spnorm, self.b, -2)
+
+    def test_matrix_norm_axis(self):
+        for m, axis in ((self.b, None), (self.b, (0, 1)), (self.b.T, (1, 0))):
+            assert_allclose(spnorm(m, axis=axis), 7.745966692414834)
+            assert_allclose(spnorm(m, 'fro', axis=axis), 7.745966692414834)
+            assert_allclose(spnorm(m, np.inf, axis=axis), 9)
+            assert_allclose(spnorm(m, -np.inf, axis=axis), 2)
+            assert_allclose(spnorm(m, 1, axis=axis), 7)
+            assert_allclose(spnorm(m, -1, axis=axis), 6)
+
+    def test_vector_norm(self):
+        v = [4.5825756949558398, 4.2426406871192848, 4.5825756949558398]
+        for m, a in (self.b, 0), (self.b.T, 1):
+            for axis in a, (a, ), a-2, (a-2, ):
+                assert_allclose(spnorm(m, 1, axis=axis), [7, 6, 7])
+                assert_allclose(spnorm(m, np.inf, axis=axis), [4, 3, 4])
+                assert_allclose(spnorm(m, axis=axis), v)
+                assert_allclose(spnorm(m, ord=2, axis=axis), v)
+                assert_allclose(spnorm(m, ord=None, axis=axis), v)
+
+    def test_norm_exceptions(self):
+        m = self.b
+        assert_raises(TypeError, spnorm, m, None, 1.5)
+        assert_raises(TypeError, spnorm, m, None, [2])
+        assert_raises(ValueError, spnorm, m, None, ())
+        assert_raises(ValueError, spnorm, m, None, (0, 1, 2))
+        assert_raises(ValueError, spnorm, m, None, (0, 0))
+        assert_raises(ValueError, spnorm, m, None, (0, 2))
+        assert_raises(ValueError, spnorm, m, None, (-3, 0))
+        assert_raises(ValueError, spnorm, m, None, 2)
+        assert_raises(ValueError, spnorm, m, None, -3)
+        assert_raises(ValueError, spnorm, m, 'plate_of_shrimp', 0)
+        assert_raises(ValueError, spnorm, m, 'plate_of_shrimp', (0, 1))
+
+
+class TestVsNumpyNorm:
+    _sparse_types = (
+            scipy.sparse.bsr_array,
+            scipy.sparse.coo_array,
+            scipy.sparse.csc_array,
+            scipy.sparse.csr_array,
+            scipy.sparse.dia_array,
+            scipy.sparse.dok_array,
+            scipy.sparse.lil_array,
+            )
+    _test_matrices = (
+            (np.arange(9) - 4).reshape((3, 3)),
+            [
+                [1, 2, 3],
+                [-1, 1, 4]],
+            [
+                [1, 0, 3],
+                [-1, 1, 4j]],
+            np.array([[-128, 127], [127, -128]], dtype=np.int8),
+            )
+
+    def test_sparse_matrix_norms(self):
+        for sparse_type in self._sparse_types:
+            for M in self._test_matrices:
+                S = sparse_type(M)
+                assert_allclose(spnorm(S), npnorm(M))
+                assert_allclose(spnorm(S, 'fro'), npnorm(M, 'fro'))
+                assert_allclose(spnorm(S, np.inf), npnorm(M, np.inf))
+                assert_allclose(spnorm(S, -np.inf), npnorm(M, -np.inf))
+                assert_allclose(spnorm(S, 1), npnorm(M, 1))
+                assert_allclose(spnorm(S, -1), npnorm(M, -1))
+
+    def test_sparse_matrix_norms_with_axis(self):
+        for sparse_type in self._sparse_types:
+            for M in self._test_matrices:
+                S = sparse_type(M)
+                for axis in None, (0, 1), (1, 0):
+                    assert_allclose(spnorm(S, axis=axis), npnorm(M, axis=axis))
+                    for ord in 'fro', np.inf, -np.inf, 1, -1:
+                        assert_allclose(spnorm(S, ord, axis=axis),
+                                        npnorm(M, ord, axis=axis))
+                # Some numpy matrix norms are allergic to negative axes.
+                for axis in (-2, -1), (-1, -2), (1, -2):
+                    assert_allclose(spnorm(S, axis=axis), npnorm(M, axis=axis))
+                    assert_allclose(spnorm(S, 'f', axis=axis),
+                                    npnorm(M, 'f', axis=axis))
+                    assert_allclose(spnorm(S, 'fro', axis=axis),
+                                    npnorm(M, 'fro', axis=axis))
+
+    def test_sparse_vector_norms(self):
+        for sparse_type in self._sparse_types:
+            for M in self._test_matrices:
+                S = sparse_type(M)
+                for axis in (0, 1, -1, -2, (0, ), (1, ), (-1, ), (-2, )):
+                    assert_allclose(spnorm(S, axis=axis), npnorm(M, axis=axis))
+                    for ord in None, 2, np.inf, -np.inf, 1, 0.5, 0.42, 0:
+                        assert_allclose(spnorm(S, ord, axis=axis),
+                                        npnorm(M, ord, axis=axis))
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/tests/test_onenormest.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/tests/test_onenormest.py
new file mode 100644
index 0000000000000000000000000000000000000000..dc55c73884d3fbc6ea07f2fb8d18894752c7402f
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/tests/test_onenormest.py
@@ -0,0 +1,229 @@
+"""Test functions for the sparse.linalg._onenormest module
+"""
+
+import numpy as np
+from numpy.testing import assert_allclose, assert_equal, assert_
+import pytest
+import scipy.linalg
+import scipy.sparse.linalg
+from scipy.sparse.linalg._onenormest import _onenormest_core
+
+
+class MatrixProductOperator(scipy.sparse.linalg.LinearOperator):
+    """
+    This is purely for onenormest testing.
+    """
+
+    def __init__(self, A, B):
+        if A.ndim != 2 or B.ndim != 2:
+            raise ValueError('expected ndarrays representing matrices')
+        if A.shape[1] != B.shape[0]:
+            raise ValueError('incompatible shapes')
+        super().__init__(dtype=None, shape=(A.shape[0], B.shape[1]))
+        self.A = A
+        self.B = B
+
+    def _matvec(self, x):
+        return np.dot(self.A, np.dot(self.B, x))
+
+    def _rmatvec(self, x):
+        return np.dot(np.dot(x, self.A), self.B)
+
+    def _matmat(self, X):
+        return np.dot(self.A, np.dot(self.B, X))
+
+    @property
+    def T(self):
+        return MatrixProductOperator(self.B.T, self.A.T)
+
+
+class TestOnenormest:
+
+    @pytest.mark.xslow
+    def test_onenormest_table_3_t_2(self):
+        # This will take multiple seconds if your computer is slow like mine.
+        # It is stochastic, so the tolerance could be too strict.
+        np.random.seed(1234)
+        t = 2
+        n = 100
+        itmax = 5
+        nsamples = 5000
+        observed = []
+        expected = []
+        nmult_list = []
+        nresample_list = []
+        for i in range(nsamples):
+            A = scipy.linalg.inv(np.random.randn(n, n))
+            est, v, w, nmults, nresamples = _onenormest_core(A, A.T, t, itmax)
+            observed.append(est)
+            expected.append(scipy.linalg.norm(A, 1))
+            nmult_list.append(nmults)
+            nresample_list.append(nresamples)
+        observed = np.array(observed, dtype=float)
+        expected = np.array(expected, dtype=float)
+        relative_errors = np.abs(observed - expected) / expected
+
+        # check the mean underestimation ratio
+        underestimation_ratio = observed / expected
+        assert_(0.99 < np.mean(underestimation_ratio) < 1.0)
+
+        # check the max and mean required column resamples
+        assert_equal(np.max(nresample_list), 2)
+        assert_(0.05 < np.mean(nresample_list) < 0.2)
+
+        # check the proportion of norms computed exactly correctly
+        nexact = np.count_nonzero(relative_errors < 1e-14)
+        proportion_exact = nexact / float(nsamples)
+        assert_(0.9 < proportion_exact < 0.95)
+
+        # check the average number of matrix*vector multiplications
+        assert_(3.5 < np.mean(nmult_list) < 4.5)
+
+    @pytest.mark.xslow
+    def test_onenormest_table_4_t_7(self):
+        # This will take multiple seconds if your computer is slow like mine.
+        # It is stochastic, so the tolerance could be too strict.
+        np.random.seed(1234)
+        t = 7
+        n = 100
+        itmax = 5
+        nsamples = 5000
+        observed = []
+        expected = []
+        nmult_list = []
+        nresample_list = []
+        for i in range(nsamples):
+            A = np.random.randint(-1, 2, size=(n, n))
+            est, v, w, nmults, nresamples = _onenormest_core(A, A.T, t, itmax)
+            observed.append(est)
+            expected.append(scipy.linalg.norm(A, 1))
+            nmult_list.append(nmults)
+            nresample_list.append(nresamples)
+        observed = np.array(observed, dtype=float)
+        expected = np.array(expected, dtype=float)
+        relative_errors = np.abs(observed - expected) / expected
+
+        # check the mean underestimation ratio
+        underestimation_ratio = observed / expected
+        assert_(0.90 < np.mean(underestimation_ratio) < 0.99)
+
+        # check the required column resamples
+        assert_equal(np.max(nresample_list), 0)
+
+        # check the proportion of norms computed exactly correctly
+        nexact = np.count_nonzero(relative_errors < 1e-14)
+        proportion_exact = nexact / float(nsamples)
+        assert_(0.15 < proportion_exact < 0.25)
+
+        # check the average number of matrix*vector multiplications
+        assert_(3.5 < np.mean(nmult_list) < 4.5)
+
+    def test_onenormest_table_5_t_1(self):
+        # "note that there is no randomness and hence only one estimate for t=1"
+        t = 1
+        n = 100
+        itmax = 5
+        alpha = 1 - 1e-6
+        A = -scipy.linalg.inv(np.identity(n) + alpha*np.eye(n, k=1))
+        first_col = np.array([1] + [0]*(n-1))
+        first_row = np.array([(-alpha)**i for i in range(n)])
+        B = -scipy.linalg.toeplitz(first_col, first_row)
+        assert_allclose(A, B)
+        est, v, w, nmults, nresamples = _onenormest_core(B, B.T, t, itmax)
+        exact_value = scipy.linalg.norm(B, 1)
+        underest_ratio = est / exact_value
+        assert_allclose(underest_ratio, 0.05, rtol=1e-4)
+        assert_equal(nmults, 11)
+        assert_equal(nresamples, 0)
+        # check the non-underscored version of onenormest
+        est_plain = scipy.sparse.linalg.onenormest(B, t=t, itmax=itmax)
+        assert_allclose(est, est_plain)
+
+    @pytest.mark.xslow
+    def test_onenormest_table_6_t_2(self):
+        #TODO this test seems to give estimates that match the table,
+        #TODO even though no attempt has been made to deal with
+        #TODO complex numbers in the one-norm estimation.
+        # This will take multiple seconds if your computer is slow like mine.
+        # It is stochastic, so the tolerance could be too strict.
+        np.random.seed(1234)
+        t = 2
+        n = 100
+        itmax = 5
+        nsamples = 5000
+        observed = []
+        expected = []
+        nmult_list = []
+        nresample_list = []
+        for i in range(nsamples):
+            A_inv = np.random.rand(n, n) + 1j * np.random.rand(n, n)
+            A = scipy.linalg.inv(A_inv)
+            est, v, w, nmults, nresamples = _onenormest_core(A, A.T, t, itmax)
+            observed.append(est)
+            expected.append(scipy.linalg.norm(A, 1))
+            nmult_list.append(nmults)
+            nresample_list.append(nresamples)
+        observed = np.array(observed, dtype=float)
+        expected = np.array(expected, dtype=float)
+        relative_errors = np.abs(observed - expected) / expected
+
+        # check the mean underestimation ratio
+        underestimation_ratio = observed / expected
+        underestimation_ratio_mean = np.mean(underestimation_ratio)
+        assert_(0.90 < underestimation_ratio_mean < 0.99)
+
+        # check the required column resamples
+        max_nresamples = np.max(nresample_list)
+        assert_equal(max_nresamples, 0)
+
+        # check the proportion of norms computed exactly correctly
+        nexact = np.count_nonzero(relative_errors < 1e-14)
+        proportion_exact = nexact / float(nsamples)
+        assert_(0.7 < proportion_exact < 0.8)
+
+        # check the average number of matrix*vector multiplications
+        mean_nmult = np.mean(nmult_list)
+        assert_(4 < mean_nmult < 5)
+
+    def _help_product_norm_slow(self, A, B):
+        # for profiling
+        C = np.dot(A, B)
+        return scipy.linalg.norm(C, 1)
+
+    def _help_product_norm_fast(self, A, B):
+        # for profiling
+        t = 2
+        itmax = 5
+        D = MatrixProductOperator(A, B)
+        est, v, w, nmults, nresamples = _onenormest_core(D, D.T, t, itmax)
+        return est
+
+    @pytest.mark.slow
+    def test_onenormest_linear_operator(self):
+        # Define a matrix through its product A B.
+        # Depending on the shapes of A and B,
+        # it could be easy to multiply this product by a small matrix,
+        # but it could be annoying to look at all of
+        # the entries of the product explicitly.
+        np.random.seed(1234)
+        n = 6000
+        k = 3
+        A = np.random.randn(n, k)
+        B = np.random.randn(k, n)
+        fast_estimate = self._help_product_norm_fast(A, B)
+        exact_value = self._help_product_norm_slow(A, B)
+        assert_(fast_estimate <= exact_value <= 3*fast_estimate,
+                f'fast: {fast_estimate:g}\nexact:{exact_value:g}')
+
+    def test_returns(self):
+        np.random.seed(1234)
+        A = scipy.sparse.random_array((50, 50), density=0.1)
+
+        s0 = scipy.linalg.norm(A.toarray(), 1)
+        s1, v = scipy.sparse.linalg.onenormest(A, compute_v=True)
+        s2, w = scipy.sparse.linalg.onenormest(A, compute_w=True)
+        s3, v2, w2 = scipy.sparse.linalg.onenormest(A, compute_w=True, compute_v=True)
+
+        assert_allclose(s1, s0, rtol=1e-9)
+        assert_allclose(np.linalg.norm(A.dot(v), 1), s0*np.linalg.norm(v, 1), rtol=1e-9)
+        assert_allclose(A.dot(v), w, rtol=1e-9)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/tests/test_propack.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/tests/test_propack.py
new file mode 100644
index 0000000000000000000000000000000000000000..4cdb235aef1407b9b5ec2c1c39acddb1f7090278
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/tests/test_propack.py
@@ -0,0 +1,203 @@
+import os
+import pytest
+
+import numpy as np
+from numpy.testing import assert_allclose
+from pytest import raises as assert_raises
+from scipy.sparse.linalg._svdp import _svdp
+from scipy.sparse import csr_array, csc_array
+
+
+# dtype_flavour to tolerance
+TOLS = {
+    np.float32: 1e-4,
+    np.float64: 1e-8,
+    np.complex64: 1e-4,
+    np.complex128: 1e-8,
+}
+
+
+def is_complex_type(dtype):
+    return np.dtype(dtype).kind == "c"
+
+
+_dtypes = []
+for dtype_flavour in TOLS.keys():
+    marks = []
+    if is_complex_type(dtype_flavour):
+        marks = [pytest.mark.slow]
+    _dtypes.append(pytest.param(dtype_flavour, marks=marks,
+                                id=dtype_flavour.__name__))
+_dtypes = tuple(_dtypes)  # type: ignore[assignment]
+
+
+# The test function here is adapted from the original Fortran PROPACK tests.
+# It is not very robust to arbitrary seeding since partial reorthogonalization
+# does not have a predictable upperbound on the number of iterations.
+def check_svdp(n, m, constructor, dtype, k, irl_mode, which, f=0.8, rng=None):
+    tol = TOLS[dtype]
+
+    if rng is None:
+        rng = np.random.default_rng(0)
+
+    # Legacy clamp for the generator
+    rng2 = np.random.default_rng(0)
+    if is_complex_type(dtype):
+        M = (- 5 + 10 * rng2.uniform(size=[n, m])
+             - 5j + 10j * rng2.uniform(size=[n, m])).astype(dtype)
+    else:
+        M = (-5 + 10 * rng2.uniform(size=[n, m])).astype(dtype)
+    M[M.real > 10 * f - 5] = 0
+    Msp = constructor(M)
+
+    u1, sigma1, vt1 = np.linalg.svd(M, full_matrices=False)
+    u2, sigma2, vt2, _ = _svdp(Msp, k=k,which=which, irl_mode=irl_mode,
+                               tol=tol, rng=rng)
+
+    # check the which
+    if which.upper() == 'SM':
+        u1 = np.roll(u1, k, 1)
+        vt1 = np.roll(vt1, k, 0)
+        sigma1 = np.roll(sigma1, k)
+
+    # check that singular values agree
+    assert_allclose(sigma1[:k], sigma2, rtol=tol, atol=tol)
+
+    # check that singular vectors are orthogonal
+    assert_allclose(np.abs(u1.conj().T @ u2), np.eye(n, k), rtol=tol, atol=tol)
+    assert_allclose(np.abs(vt1.conj() @ vt2.T), np.eye(n, k), rtol=tol, atol=tol)
+
+
+@pytest.mark.parametrize('ctor', (np.array, csr_array, csc_array))
+@pytest.mark.parametrize('dtype', [np.float32, np.float64,
+                                   np.complex64, np.complex128])
+@pytest.mark.parametrize('irl', (True, False))
+@pytest.mark.parametrize('which', ('LM', 'SM'))
+def test_svdp(ctor, dtype, irl, which):
+    rng = np.random.default_rng(1757937293955503)
+    n, m, k = 10, 20, 3
+    if which == 'SM' and not irl:
+        message = "`which`='SM' requires irl_mode=True"
+        with assert_raises(ValueError, match=message):
+            check_svdp(n, m, ctor, dtype, k, irl, which, rng=rng)
+    else:
+        check_svdp(n, m, ctor, dtype, k, irl, which, rng=rng)
+
+
+@pytest.mark.xslow
+@pytest.mark.parametrize('dtype', _dtypes)
+@pytest.mark.parametrize('irl', (False, True))
+def test_examples(dtype, irl):
+    # Note: atol for complex64 bumped from 1e-4 to 1e-3 due to test failures
+    # with BLIS, Netlib, and MKL+AVX512 - see
+    # https://github.com/conda-forge/scipy-feedstock/pull/198#issuecomment-999180432
+    atol = {
+        np.float32: 1.3e-4,
+        np.float64: 1e-9,
+        np.complex64: 1e-3,
+        np.complex128: 1e-9,
+    }[dtype]
+
+    path_prefix = os.path.dirname(__file__)
+    # Test matrices from `illc1850.coord` and `mhd1280b.cua` distributed with
+    # PROPACK 2.1: http://sun.stanford.edu/~rmunk/PROPACK/
+    relative_path = "propack_test_data.npz"
+    filename = os.path.join(path_prefix, relative_path)
+    with np.load(filename, allow_pickle=True) as data:
+        if is_complex_type(dtype):
+            A = data['A_complex'].item().astype(dtype)
+        else:
+            A = data['A_real'].item().astype(dtype)
+
+    k = 200
+    u, s, vh, _ = _svdp(A, k, irl_mode=irl, rng=np.random.default_rng(0))
+
+    # complex example matrix has many repeated singular values, so check only
+    # beginning non-repeated singular vectors to avoid permutations
+    sv_check = 27 if is_complex_type(dtype) else k
+    u = u[:, :sv_check]
+    vh = vh[:sv_check, :]
+    s = s[:sv_check]
+
+    # Check orthogonality of singular vectors
+    assert_allclose(np.eye(u.shape[1]), u.conj().T @ u, atol=atol)
+    assert_allclose(np.eye(vh.shape[0]), vh @ vh.conj().T, atol=atol)
+
+    # Ensure the norm of the difference between the np.linalg.svd and
+    # PROPACK reconstructed matrices is small
+    u3, s3, vh3 = np.linalg.svd(A.todense())
+    u3 = u3[:, :sv_check]
+    s3 = s3[:sv_check]
+    vh3 = vh3[:sv_check, :]
+    A3 = u3 @ np.diag(s3) @ vh3
+    recon = u @ np.diag(s) @ vh
+    assert_allclose(np.linalg.norm(A3 - recon), 0, atol=atol)
+
+
+@pytest.mark.parametrize('shifts', (None, -10, 0, 1, 10, 70))
+@pytest.mark.parametrize('dtype', _dtypes[:2])
+def test_shifts(shifts, dtype):
+    rng = np.random.default_rng(0)
+    n, k = 70, 10
+    A = rng.random((n, n))
+    if shifts is not None and ((shifts < 0) or (k > min(n-1-shifts, n))):
+        with pytest.raises(ValueError):
+            _svdp(A, k, shifts=shifts, kmax=5*k, irl_mode=True, rng=rng)
+    else:
+        _svdp(A, k, shifts=shifts, kmax=5*k, irl_mode=True, rng=rng)
+
+
+@pytest.mark.slow
+@pytest.mark.xfail()
+def test_shifts_accuracy():
+    rng = np.random.default_rng(0)
+    n, k = 70, 10
+    A = rng.random((n, n)).astype(np.float64)
+    u1, s1, vt1, _ = _svdp(A, k, shifts=None, which='SM', irl_mode=True, rng=rng)
+    u2, s2, vt2, _ = _svdp(A, k, shifts=32, which='SM', irl_mode=True, rng=rng)
+    # shifts <= 32 doesn't agree with shifts > 32
+    # Does agree when which='LM' instead of 'SM'
+    assert_allclose(s1, s2)
+
+
+@pytest.mark.parametrize('irl_mode', [False, True])
+@pytest.mark.parametrize('dtype', (np.float32, np.float64))
+def test_thin_hilbert(irl_mode, dtype):
+    rng = np.random.default_rng(1757951587606893)
+    m, n = 200, 4
+
+    # Generate a Hilbert matrix of size m x n
+    A = np.array([[1 / (i + j + 1) for j in range(n)] for i in range(m)], dtype=dtype)
+    uu, ss, vv = np.linalg.svd(A, full_matrices=False)
+    u, s, vt, _ = _svdp(A, k=4, which='LM', irl_mode=irl_mode, rng=rng)
+    assert_allclose(s, ss, atol=TOLS[dtype])
+
+    # Check orthogonality of singular vectors
+    assert_allclose(np.eye(u.shape[1]), u.T @ u, atol=TOLS[dtype])
+    assert_allclose(np.eye(vt.shape[0]), vt @ vt.T, atol=TOLS[dtype])
+
+    # Check orthogonality against numpy svd results
+    assert_allclose(np.abs(uu.T @ u), np.eye(n), atol=TOLS[dtype])
+    assert_allclose(np.abs(vv @ vt.T), np.eye(n), atol=TOLS[dtype])
+
+
+@pytest.mark.parametrize('dtype', (np.float32, np.float64, np.complex64, np.complex128))
+def test_fat_random(dtype):
+    rng = np.random.default_rng(1758046113948869)
+    m, n = 3, 100
+
+    A = rng.uniform(size=(m, n)).astype(dtype)
+    if dtype in (np.complex64, np.complex128):
+        A += dtype(1j) * rng.uniform(size=(m, n)).astype(dtype)
+
+    uu, ss, vv = np.linalg.svd(A, full_matrices=False)
+    u, s, vt, _ = _svdp(A, k=3, which='LM', irl_mode=True, rng=rng)
+    assert_allclose(s, ss, atol=TOLS[dtype])
+
+    # Check orthogonality of singular vectors
+    assert_allclose(np.eye(u.shape[1]), u.conj().T @ u, atol=TOLS[dtype])
+    assert_allclose(np.eye(vt.shape[0]), vt @ vt.conj().T, atol=TOLS[dtype])
+
+    # Check orthogonality against numpy svd results
+    assert_allclose(np.abs(uu.conj().T @ u), np.eye(m), atol=TOLS[dtype])
+    assert_allclose(np.abs(vv @ vt.conj().T), np.eye(m), atol=TOLS[dtype])
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/tests/test_pydata_sparse.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/tests/test_pydata_sparse.py
new file mode 100644
index 0000000000000000000000000000000000000000..0b6a304f4b7fce9761f9225ab538db53e72741be
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/tests/test_pydata_sparse.py
@@ -0,0 +1,272 @@
+import pytest
+
+import numpy as np
+import scipy.sparse as sp
+import scipy.sparse.linalg as splin
+
+from numpy.testing import assert_allclose, assert_equal
+
+try:
+    import sparse
+except Exception:
+    sparse = None
+
+pytestmark = pytest.mark.skipif(sparse is None,
+                                reason="pydata/sparse not installed")
+
+
+msg = "pydata/sparse (0.15.1) does not implement necessary operations"
+
+
+sparse_params = (pytest.param("COO"),
+                 pytest.param("DOK", marks=[pytest.mark.xfail(reason=msg)]))
+
+scipy_sparse_classes = [
+    sp.bsr_array,
+    sp.csr_array,
+    sp.coo_array,
+    sp.csc_array,
+    sp.dia_array,
+    sp.dok_array
+]
+
+
+@pytest.fixture(params=sparse_params)
+def sparse_cls(request):
+    return getattr(sparse, request.param)
+
+
+@pytest.fixture(params=scipy_sparse_classes)
+def sp_sparse_cls(request):
+    return request.param
+
+
+@pytest.fixture
+def same_matrix(sparse_cls, sp_sparse_cls):
+    np.random.seed(1234)
+    A_dense = np.random.rand(9, 9)
+    return sp_sparse_cls(A_dense), sparse_cls(A_dense)
+
+
+@pytest.fixture
+def matrices(sparse_cls):
+    np.random.seed(1234)
+    A_dense = np.random.rand(9, 9)
+    A_dense = A_dense @ A_dense.T
+    A_sparse = sparse_cls(A_dense)
+    b = np.random.rand(9)
+    return A_dense, A_sparse, b
+
+
+def test_isolve_gmres(matrices):
+    # Several of the iterative solvers use the same
+    # isolve.utils.make_system wrapper code, so test just one of them.
+    A_dense, A_sparse, b = matrices
+    x, info = splin.gmres(A_sparse, b, atol=1e-15)
+    assert info == 0
+    assert isinstance(x, np.ndarray)
+    assert_allclose(A_sparse @ x, b)
+
+
+def test_lsmr(matrices):
+    A_dense, A_sparse, b = matrices
+    res0 = splin.lsmr(A_dense, b)
+    res = splin.lsmr(A_sparse, b)
+    assert_allclose(res[0], res0[0], atol=1e-3)
+
+
+# test issue 17012
+def test_lsmr_output_shape():
+    x = splin.lsmr(A=np.ones((10, 1)), b=np.zeros(10), x0=np.ones(1))[0]
+    assert_equal(x.shape, (1,))
+
+
+def test_lsqr(matrices):
+    A_dense, A_sparse, b = matrices
+    res0 = splin.lsqr(A_dense, b)
+    res = splin.lsqr(A_sparse, b)
+    assert_allclose(res[0], res0[0], atol=1e-5)
+
+
+def test_eigs(matrices):
+    A_dense, A_sparse, v0 = matrices
+
+    M_dense = np.diag(v0**2)
+    M_sparse = A_sparse.__class__(M_dense)
+
+    w_dense, v_dense = splin.eigs(A_dense, k=3, v0=v0)
+    w, v = splin.eigs(A_sparse, k=3, v0=v0)
+
+    assert_allclose(w, w_dense)
+    assert_allclose(v, v_dense)
+
+    for M in [M_sparse, M_dense]:
+        w_dense, v_dense = splin.eigs(A_dense, M=M_dense, k=3, v0=v0)
+        w, v = splin.eigs(A_sparse, M=M, k=3, v0=v0)
+
+        assert_allclose(w, w_dense)
+        assert_allclose(v, v_dense)
+
+        w_dense, v_dense = splin.eigsh(A_dense, M=M_dense, k=3, v0=v0)
+        w, v = splin.eigsh(A_sparse, M=M, k=3, v0=v0)
+
+        assert_allclose(w, w_dense)
+        assert_allclose(v, v_dense)
+
+
+def test_svds(matrices):
+    A_dense, A_sparse, v0 = matrices
+
+    u0, s0, vt0 = splin.svds(A_dense, k=2, v0=v0)
+    u, s, vt = splin.svds(A_sparse, k=2, v0=v0)
+
+    assert_allclose(s, s0)
+    assert_allclose(np.abs(u), np.abs(u0))
+    assert_allclose(np.abs(vt), np.abs(vt0))
+
+
+def test_lobpcg(matrices):
+    A_dense, A_sparse, x = matrices
+    X = x[:,None]
+
+    w_dense, v_dense = splin.lobpcg(A_dense, X)
+    w, v = splin.lobpcg(A_sparse, X)
+
+    assert_allclose(w, w_dense)
+    assert_allclose(v, v_dense)
+
+
+def test_spsolve(matrices):
+    A_dense, A_sparse, b = matrices
+    b2 = np.random.rand(len(b), 3)
+
+    x0 = splin.spsolve(sp.csc_array(A_dense), b)
+    x = splin.spsolve(A_sparse, b)
+    assert isinstance(x, np.ndarray)
+    assert_allclose(x, x0)
+
+    x0 = splin.spsolve(sp.csc_array(A_dense), b)
+    x = splin.spsolve(A_sparse, b, use_umfpack=True)
+    assert isinstance(x, np.ndarray)
+    assert_allclose(x, x0)
+
+    x0 = splin.spsolve(sp.csc_array(A_dense), b2)
+    x = splin.spsolve(A_sparse, b2)
+    assert isinstance(x, np.ndarray)
+    assert_allclose(x, x0)
+
+    x0 = splin.spsolve(sp.csc_array(A_dense),
+                       sp.csc_array(A_dense))
+    x = splin.spsolve(A_sparse, A_sparse)
+    assert isinstance(x, type(A_sparse))
+    assert_allclose(x.todense(), x0.todense())
+
+
+def test_splu(matrices):
+    A_dense, A_sparse, b = matrices
+    n = len(b)
+    sparse_cls = type(A_sparse)
+
+    lu = splin.splu(A_sparse)
+
+    assert isinstance(lu.L, sparse_cls)
+    assert isinstance(lu.U, sparse_cls)
+
+    _Pr_scipy = sp.csc_array((np.ones(n), (lu.perm_r, np.arange(n))))
+    _Pc_scipy = sp.csc_array((np.ones(n), (np.arange(n), lu.perm_c)))
+    Pr = sparse_cls.from_scipy_sparse(_Pr_scipy)
+    Pc = sparse_cls.from_scipy_sparse(_Pc_scipy)
+    A2 = Pr.T @ lu.L @ lu.U @ Pc.T
+
+    assert_allclose(A2.todense(), A_sparse.todense())
+
+    z = lu.solve(A_sparse.todense())
+    assert_allclose(z, np.eye(n), atol=1e-10)
+
+
+def test_spilu(matrices):
+    A_dense, A_sparse, b = matrices
+    sparse_cls = type(A_sparse)
+
+    lu = splin.spilu(A_sparse)
+
+    assert isinstance(lu.L, sparse_cls)
+    assert isinstance(lu.U, sparse_cls)
+
+    z = lu.solve(A_sparse.todense())
+    assert_allclose(z, np.eye(len(b)), atol=1e-3)
+
+
+def test_spsolve_triangular(matrices):
+    A_dense, A_sparse, b = matrices
+    A_sparse = sparse.tril(A_sparse)
+
+    x = splin.spsolve_triangular(A_sparse, b)
+    assert_allclose(A_sparse @ x, b)
+
+
+def test_onenormest(matrices):
+    A_dense, A_sparse, b = matrices
+    est0 = splin.onenormest(A_dense)
+    est = splin.onenormest(A_sparse)
+    assert_allclose(est, est0)
+
+
+def test_norm(matrices):
+    A_dense, A_sparse, b = matrices
+    norm0 = splin.norm(sp.csr_array(A_dense))
+    norm = splin.norm(A_sparse)
+    assert_allclose(norm, norm0)
+
+
+def test_inv(matrices):
+    A_dense, A_sparse, b = matrices
+    x0 = splin.inv(sp.csc_array(A_dense))
+    x = splin.inv(A_sparse)
+    assert_allclose(x.todense(), x0.todense())
+
+
+def test_expm(matrices):
+    A_dense, A_sparse, b = matrices
+    x0 = splin.expm(sp.csc_array(A_dense))
+    x = splin.expm(A_sparse)
+    assert_allclose(x.todense(), x0.todense())
+
+
+def test_expm_multiply(matrices):
+    A_dense, A_sparse, b = matrices
+    x0 = splin.expm_multiply(A_dense, b)
+    x = splin.expm_multiply(A_sparse, b)
+    assert_allclose(x, x0)
+
+    x0 = splin.expm_multiply(A_dense, A_dense)
+    x = splin.expm_multiply(A_sparse, A_sparse)
+    assert_allclose(x.todense(), x0)
+
+
+def test_eq(same_matrix):
+    sp_sparse, pd_sparse = same_matrix
+    # temporary splint until pydata sparse support sparray equality
+    sp_sparse = sp.coo_matrix(sp_sparse).asformat(sp_sparse.format)
+    assert (sp_sparse == pd_sparse).all()
+
+
+def test_ne(same_matrix):
+    sp_sparse, pd_sparse = same_matrix
+    # temporary splint until pydata sparse support sparray equality
+    sp_sparse = sp.coo_matrix(sp_sparse).asformat(sp_sparse.format)
+    assert not (sp_sparse != pd_sparse).any()
+
+
+def test_ge(same_matrix):
+    sp_sparse, pd_sparse = same_matrix
+    # temporary splint until pydata sparse support sparray equality
+    sp_sparse = sp.coo_matrix(sp_sparse).asformat(sp_sparse.format)
+    assert (sp_sparse >= pd_sparse).all()
+
+
+def test_gt(same_matrix):
+    sp_sparse, pd_sparse = same_matrix
+    # temporary splint until pydata sparse support sparray equality
+    sp_sparse = sp.coo_matrix(sp_sparse).asformat(sp_sparse.format)
+    assert not (sp_sparse > pd_sparse).any()
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/linalg/tests/test_special_sparse_arrays.py b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/tests/test_special_sparse_arrays.py
new file mode 100644
index 0000000000000000000000000000000000000000..0af5aa2481b15c042e3649925aaed1b10eaa621c
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/linalg/tests/test_special_sparse_arrays.py
@@ -0,0 +1,342 @@
+import pytest
+import numpy as np
+from numpy.testing import assert_array_equal, assert_allclose
+
+from scipy.sparse import diags_array, csgraph
+from scipy.linalg import eigh
+
+from scipy.sparse.linalg import LaplacianNd
+from scipy.sparse.linalg._special_sparse_arrays import Sakurai
+from scipy.sparse.linalg._special_sparse_arrays import MikotaPair
+
+INT_DTYPES = [np.int8, np.int16, np.int32, np.int64]
+REAL_DTYPES = [np.float32, np.float64]
+COMPLEX_DTYPES = [np.complex64, np.complex128]
+ALLDTYPES = INT_DTYPES + REAL_DTYPES + COMPLEX_DTYPES
+
+
+class TestLaplacianNd:
+    """
+    LaplacianNd tests
+    """
+
+    @pytest.mark.parametrize('bc', ['neumann', 'dirichlet', 'periodic'])
+    def test_1d_specific_shape(self, bc):
+        lap = LaplacianNd(grid_shape=(6, ), boundary_conditions=bc)
+        lapa = lap.toarray()
+        if bc == 'neumann':
+            a = np.array(
+                [
+                    [-1, 1, 0, 0, 0, 0],
+                    [1, -2, 1, 0, 0, 0],
+                    [0, 1, -2, 1, 0, 0],
+                    [0, 0, 1, -2, 1, 0],
+                    [0, 0, 0, 1, -2, 1],
+                    [0, 0, 0, 0, 1, -1],
+                ]
+            )
+        elif bc == 'dirichlet':
+            a = np.array(
+                [
+                    [-2, 1, 0, 0, 0, 0],
+                    [1, -2, 1, 0, 0, 0],
+                    [0, 1, -2, 1, 0, 0],
+                    [0, 0, 1, -2, 1, 0],
+                    [0, 0, 0, 1, -2, 1],
+                    [0, 0, 0, 0, 1, -2],
+                ]
+            )
+        else:
+            a = np.array(
+                [
+                    [-2, 1, 0, 0, 0, 1],
+                    [1, -2, 1, 0, 0, 0],
+                    [0, 1, -2, 1, 0, 0],
+                    [0, 0, 1, -2, 1, 0],
+                    [0, 0, 0, 1, -2, 1],
+                    [1, 0, 0, 0, 1, -2],
+                ]
+            )
+        assert_array_equal(a, lapa)
+
+    def test_1d_with_graph_laplacian(self):
+        n = 6
+        G = diags_array(np.ones(n - 1), offsets=1, format='dia')
+        Lf = csgraph.laplacian(G, symmetrized=True, form='function')
+        La = csgraph.laplacian(G, symmetrized=True, form='array')
+        grid_shape = (n,)
+        bc = 'neumann'
+        lap = LaplacianNd(grid_shape, boundary_conditions=bc)
+        assert_array_equal(lap(np.eye(n)), -Lf(np.eye(n)))
+        assert_array_equal(lap.toarray(), -La.toarray())
+        # https://github.com/numpy/numpy/issues/24351
+        assert_array_equal(lap.tosparse().toarray(), -La.toarray())
+
+    @pytest.mark.parametrize('grid_shape', [(6, ), (2, 3), (2, 3, 4)])
+    @pytest.mark.parametrize('bc', ['neumann', 'dirichlet', 'periodic'])
+    def test_eigenvalues(self, grid_shape, bc):
+        lap = LaplacianNd(grid_shape, boundary_conditions=bc, dtype=np.float64)
+        L = lap.toarray()
+        eigvals = eigh(L, eigvals_only=True)
+        n = np.prod(grid_shape)
+        eigenvalues = lap.eigenvalues()
+        dtype = eigenvalues.dtype
+        atol = n * n * np.finfo(dtype).eps
+        # test the default ``m = None``
+        assert_allclose(eigenvalues, eigvals, atol=atol)
+        # test every ``m > 0``
+        for m in np.arange(1, n + 1):
+            assert_array_equal(lap.eigenvalues(m), eigenvalues[-m:])
+
+    @pytest.mark.parametrize('grid_shape', [(6, ), (2, 3), (2, 3, 4)])
+    @pytest.mark.parametrize('bc', ['neumann', 'dirichlet', 'periodic'])
+    def test_eigenvectors(self, grid_shape, bc):
+        lap = LaplacianNd(grid_shape, boundary_conditions=bc, dtype=np.float64)
+        n = np.prod(grid_shape)
+        eigenvalues = lap.eigenvalues()
+        eigenvectors = lap.eigenvectors()
+        dtype = eigenvectors.dtype
+        atol = n * n * max(np.finfo(dtype).eps, np.finfo(np.double).eps)
+        # test the default ``m = None`` every individual eigenvector
+        for i in np.arange(n):
+            r = lap.toarray() @ eigenvectors[:, i] - eigenvectors[:, i] * eigenvalues[i]
+            assert_allclose(r, np.zeros_like(r), atol=atol)
+        # test every ``m > 0``
+        for m in np.arange(1, n + 1):
+            e = lap.eigenvalues(m)
+            ev = lap.eigenvectors(m)
+            r = lap.toarray() @ ev - ev @ np.diag(e)
+            assert_allclose(r, np.zeros_like(r), atol=atol)
+        # test orthogonality
+        assert_allclose(eigenvectors @ eigenvectors.T, np.eye(n), atol=atol)
+        # test full eigendecomposition
+        L = eigenvectors @ np.diag(eigenvalues) @ eigenvectors.T
+        assert_allclose(L, lap.toarray(), atol=atol)
+
+    @pytest.mark.parametrize('grid_shape', [(6, ), (2, 3), (2, 3, 4)])
+    @pytest.mark.parametrize('bc', ['neumann', 'dirichlet', 'periodic'])
+    def test_toarray_tosparse_consistency(self, grid_shape, bc):
+        lap = LaplacianNd(grid_shape, boundary_conditions=bc)
+        n = np.prod(grid_shape)
+        assert_array_equal(lap.toarray(), lap(np.eye(n)))
+        assert_array_equal(lap.tosparse().toarray(), lap.toarray())
+
+    @pytest.mark.parametrize('dtype', ALLDTYPES)
+    @pytest.mark.parametrize('grid_shape', [(6, ), (2, 3), (2, 3, 4)])
+    @pytest.mark.parametrize('bc', ['neumann', 'dirichlet', 'periodic'])
+    def test_linearoperator_shape_dtype(self, grid_shape, bc, dtype):
+        lap = LaplacianNd(grid_shape, boundary_conditions=bc, dtype=dtype)
+        n = np.prod(grid_shape)
+        assert lap.shape == (n, n)
+        assert lap.dtype == dtype
+        assert_array_equal(
+            LaplacianNd(
+                grid_shape, boundary_conditions=bc, dtype=dtype
+            ).toarray(),
+            LaplacianNd(grid_shape, boundary_conditions=bc)
+            .toarray()
+            .astype(dtype),
+        )
+        assert_array_equal(
+            LaplacianNd(grid_shape, boundary_conditions=bc, dtype=dtype)
+            .tosparse()
+            .toarray(),
+            LaplacianNd(grid_shape, boundary_conditions=bc)
+            .tosparse()
+            .toarray()
+            .astype(dtype),
+        )
+
+    @pytest.mark.parametrize('dtype', ALLDTYPES)
+    @pytest.mark.parametrize('grid_shape', [(6, ), (2, 3), (2, 3, 4)])
+    @pytest.mark.parametrize('bc', ['neumann', 'dirichlet', 'periodic'])
+    def test_dot(self, grid_shape, bc, dtype):
+        """ Test the dot-product for type preservation and consistency.
+        """
+        lap = LaplacianNd(grid_shape, boundary_conditions=bc)
+        n = np.prod(grid_shape)
+        x0 = np.arange(n)
+        x1 = x0.reshape((-1, 1))
+        x2 = np.arange(2 * n).reshape((n, 2))
+        input_set = [x0, x1, x2]
+        for x in input_set:
+            y = lap.dot(x.astype(dtype))
+            assert x.shape == y.shape
+            assert y.dtype == dtype
+            if x.ndim == 2:
+                yy = lap.toarray() @ x.astype(dtype)
+                assert yy.dtype == dtype
+                np.array_equal(y, yy)
+
+    def test_boundary_conditions_value_error(self):
+        with pytest.raises(ValueError, match="Unknown value 'robin'"):
+            LaplacianNd(grid_shape=(6, ), boundary_conditions='robin')
+
+
+class TestSakurai:
+    """
+    Sakurai tests
+    """
+
+    def test_specific_shape(self):
+        sak = Sakurai(6)
+        assert_array_equal(sak.toarray(), sak(np.eye(6)))
+        a = np.array(
+            [
+                [ 5, -4,  1,  0,  0,  0],
+                [-4,  6, -4,  1,  0,  0],
+                [ 1, -4,  6, -4,  1,  0],
+                [ 0,  1, -4,  6, -4,  1],
+                [ 0,  0,  1, -4,  6, -4],
+                [ 0,  0,  0,  1, -4,  5]
+            ]
+        )
+
+        np.array_equal(a, sak.toarray())
+        np.array_equal(sak.tosparse().toarray(), sak.toarray())
+        ab = np.array(
+            [
+                [ 1,  1,  1,  1,  1,  1],
+                [-4, -4, -4, -4, -4, -4],
+                [ 5,  6,  6,  6,  6,  5]
+            ]
+        )
+        np.array_equal(ab, sak.tobanded())
+        e = np.array(
+                [0.03922866, 0.56703972, 2.41789479, 5.97822974,
+                 10.54287655, 14.45473055]
+            )
+        np.array_equal(e, sak.eigenvalues())
+        np.array_equal(e[:2], sak.eigenvalues(2))
+
+    # `Sakurai` default `dtype` is `np.int8` as its entries are small integers
+    @pytest.mark.parametrize('dtype', ALLDTYPES)
+    def test_linearoperator_shape_dtype(self, dtype):
+        n = 7
+        sak = Sakurai(n, dtype=dtype)
+        assert sak.shape == (n, n)
+        assert sak.dtype == dtype
+        assert_array_equal(sak.toarray(), Sakurai(n).toarray().astype(dtype))
+        assert_array_equal(sak.tosparse().toarray(),
+                           Sakurai(n).tosparse().toarray().astype(dtype))
+
+    @pytest.mark.parametrize('dtype', ALLDTYPES)
+    @pytest.mark.parametrize('argument_dtype', ALLDTYPES)
+    def test_dot(self, dtype, argument_dtype):
+        """ Test the dot-product for type preservation and consistency.
+        """
+        result_dtype = np.promote_types(argument_dtype, dtype)
+        n = 5
+        sak = Sakurai(n)
+        x0 = np.arange(n)
+        x1 = x0.reshape((-1, 1))
+        x2 = np.arange(2 * n).reshape((n, 2))
+        input_set = [x0, x1, x2]
+        for x in input_set:
+            y = sak.dot(x.astype(argument_dtype))
+            assert x.shape == y.shape
+            assert np.can_cast(y.dtype, result_dtype)
+            if x.ndim == 2:
+                ya = sak.toarray() @ x.astype(argument_dtype)
+                np.array_equal(y, ya)
+                assert np.can_cast(ya.dtype, result_dtype)
+                ys = sak.tosparse() @ x.astype(argument_dtype)
+                np.array_equal(y, ys)
+                assert np.can_cast(ys.dtype, result_dtype)
+
+class TestMikotaPair:
+    """
+    MikotaPair tests
+    """
+    # both MikotaPair `LinearOperator`s share the same dtype
+    # while `MikotaK` `dtype` can be as small as its default `np.int32`
+    # since its entries are integers, the `MikotaM` involves inverses
+    # so its smallest still accurate `dtype` is `np.float32`
+    tested_types = REAL_DTYPES + COMPLEX_DTYPES
+
+    def test_specific_shape(self):
+        n = 6
+        mik = MikotaPair(n)
+        mik_k = mik.k
+        mik_m = mik.m
+        assert_array_equal(mik_k.toarray(), mik_k(np.eye(n)))
+        assert_array_equal(mik_m.toarray(), mik_m(np.eye(n)))
+
+        k = np.array(
+            [
+                [11, -5,  0,  0,  0,  0],
+                [-5,  9, -4,  0,  0,  0],
+                [ 0, -4,  7, -3,  0,  0],
+                [ 0,  0, -3,  5, -2,  0],
+                [ 0,  0,  0, -2,  3, -1],
+                [ 0,  0,  0,  0, -1,  1]
+            ]
+        )
+        np.array_equal(k, mik_k.toarray())
+        np.array_equal(mik_k.tosparse().toarray(), k)
+        kb = np.array(
+            [
+                [ 0, -5, -4, -3, -2, -1],
+                [11,  9,  7,  5,  3,  1]
+            ]
+        )
+        np.array_equal(kb, mik_k.tobanded())
+
+        minv = np.arange(1, n + 1)
+        np.array_equal(np.diag(1. / minv), mik_m.toarray())
+        np.array_equal(mik_m.tosparse().toarray(), mik_m.toarray())
+        np.array_equal(1. / minv, mik_m.tobanded())
+
+        e = np.array([ 1,  4,  9, 16, 25, 36])
+        np.array_equal(e, mik.eigenvalues())
+        np.array_equal(e[:2], mik.eigenvalues(2))
+
+    @pytest.mark.parametrize('dtype', tested_types)
+    def test_linearoperator_shape_dtype(self, dtype):
+        n = 7
+        mik = MikotaPair(n, dtype=dtype)
+        mik_k = mik.k
+        mik_m = mik.m
+        assert mik_k.shape == (n, n)
+        assert mik_k.dtype == dtype
+        assert mik_m.shape == (n, n)
+        assert mik_m.dtype == dtype
+        mik_default_dtype = MikotaPair(n)
+        mikd_k = mik_default_dtype.k
+        mikd_m = mik_default_dtype.m
+        assert mikd_k.shape == (n, n)
+        assert mikd_k.dtype == np.float64
+        assert mikd_m.shape == (n, n)
+        assert mikd_m.dtype == np.float64
+        assert_array_equal(mik_k.toarray(),
+                           mikd_k.toarray().astype(dtype))
+        assert_array_equal(mik_k.tosparse().toarray(),
+                           mikd_k.tosparse().toarray().astype(dtype))
+
+    @pytest.mark.parametrize('dtype', tested_types)
+    @pytest.mark.parametrize('argument_dtype', ALLDTYPES)
+    def test_dot(self, dtype, argument_dtype):
+        """ Test the dot-product for type preservation and consistency.
+        """
+        result_dtype = np.promote_types(argument_dtype, dtype)
+        n = 5
+        mik = MikotaPair(n, dtype=dtype)
+        mik_k = mik.k
+        mik_m = mik.m
+        x0 = np.arange(n)
+        x1 = x0.reshape((-1, 1))
+        x2 = np.arange(2 * n).reshape((n, 2))
+        lo_set = [mik_k, mik_m]
+        input_set = [x0, x1, x2]
+        for lo in lo_set:
+            for x in input_set:
+                y = lo.dot(x.astype(argument_dtype))
+                assert x.shape == y.shape
+                assert np.can_cast(y.dtype, result_dtype)
+                if x.ndim == 2:
+                    ya = lo.toarray() @ x.astype(argument_dtype)
+                    np.array_equal(y, ya)
+                    assert np.can_cast(ya.dtype, result_dtype)
+                    ys = lo.tosparse() @ x.astype(argument_dtype)
+                    np.array_equal(y, ys)
+                    assert np.can_cast(ys.dtype, result_dtype)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/sparsetools.py b/venv/lib/python3.12/site-packages/scipy/sparse/sparsetools.py
new file mode 100644
index 0000000000000000000000000000000000000000..404e431d89d479520d2198ae73b9eab7b23a80f7
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/sparsetools.py
@@ -0,0 +1,17 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.sparse` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+__all__: list[str] = []
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="sparse", module="sparsetools",
+                                   private_modules=["_sparsetools"], all=__all__,
+                                   attribute=name)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/spfuncs.py b/venv/lib/python3.12/site-packages/scipy/sparse/spfuncs.py
new file mode 100644
index 0000000000000000000000000000000000000000..911969e414d4a1d3888900ad8392b5fc2177c850
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/spfuncs.py
@@ -0,0 +1,17 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.sparse` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+__all__: list[str] = []
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="sparse", module="spfuncs",
+                                   private_modules=["_spfuncs"], all=__all__,
+                                   attribute=name)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/sputils.py b/venv/lib/python3.12/site-packages/scipy/sparse/sputils.py
new file mode 100644
index 0000000000000000000000000000000000000000..4ddd27a43889609b0642bd7579e13c8e3c460a8b
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/sputils.py
@@ -0,0 +1,17 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.sparse` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+__all__: list[str] = []
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="sparse", module="sputils",
+                                   private_modules=["_sputils"], all=__all__,
+                                   attribute=name)
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diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_64bit.py b/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_64bit.py
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--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_64bit.py
@@ -0,0 +1,304 @@
+""" Test functions involving 64bit or 32bit indexing """
+import pytest
+import numpy as np
+from scipy.sparse import (
+    bsr_array, coo_array, csc_array, csr_array, dia_array,
+    bsr_matrix, coo_matrix, csc_matrix, csr_matrix, dia_matrix,
+)
+
+# rename to avoid pytest collecting them in this module
+from .test_base import (
+    TestBSR as _TestBSR,
+    TestCOO as _TestCOO,
+    TestCSC as _TestCSC,
+    TestCSR as _TestCSR,
+    TestDIA as _TestDIA,
+    TestDOK as _TestDOK,
+    TestLIL as _TestLIL,
+    TestBSRMatrix as _TestBSRMatrix,
+    TestCOOMatrix as _TestCOOMatrix,
+    TestCSCMatrix as _TestCSCMatrix,
+    TestCSRMatrix as _TestCSRMatrix,
+    TestDIAMatrix as _TestDIAMatrix,
+    TestDOKMatrix as _TestDOKMatrix,
+    TestLILMatrix as _TestLILMatrix,
+    with_64bit_maxval_limit,
+)
+
+
+# name : reason not tested here
+SKIP_TESTS = {
+    'test_expm': 'expm for 64-bit indices not available',
+    'test_inv': 'linsolve for 64-bit indices not available',
+    'test_solve': 'linsolve for 64-bit indices not available',
+    'test_scalar_idx_dtype': 'test implemented in base class',
+    'test_large_dimensions_reshape': 'test actually requires 64-bit to work',
+    'test_constructor_smallcol': 'test verifies int32 indexes',
+    'test_constructor_largecol': 'test verifies int64 indexes',
+    'test_sparse_format_conversions': 'test produces deprecation warning',
+    'test_tocoo_tocsr_tocsc_gh19245': 'test verifies int32 indexes',
+}
+
+
+def cases_64bit(sp_api):
+    """Yield all tests for all formats
+
+    This is more than testing get_index_dtype. It allows checking whether upcasting
+    or downcasting the index dtypes affects test results. The approach used here
+    does not try to figure out which tests might fail due to 32/64-bit issues.
+    We just run them all.
+    So, each test method in that uses cases_64bit reruns most of the test suite!
+    """
+    if sp_api == "sparray":
+        TEST_CLASSES = [_TestBSR, _TestCOO, _TestCSC, _TestCSR, _TestDIA]
+    elif sp_api == "sparray-extra":
+        # lil/dok->other conversion operations use get_index_dtype
+        # so we include lil & dok test suite even though they do not
+        # use get_index_dtype within the class. That means many of
+        # these tests are superfluous, but it's hard to pick which
+        TEST_CLASSES = [_TestDOK, _TestLIL]
+    elif sp_api == "spmatrix":
+        TEST_CLASSES = [_TestBSRMatrix, _TestCOOMatrix, _TestCSCMatrix,
+                        _TestCSRMatrix, _TestDIAMatrix]
+    elif sp_api == "spmatrix-extra":
+        # lil/dok->other conversion operations use get_index_dtype
+        TEST_CLASSES = [_TestDOKMatrix, _TestLILMatrix]
+    else:
+        raise ValueError(f"parameter {sp_api=} is not valid")
+
+    for cls in TEST_CLASSES:
+        for method_name in sorted(dir(cls)):
+            method = getattr(cls, method_name)
+            if (method_name.startswith('test_') and
+                    not getattr(method, 'slow', False)):
+                marks = []
+
+                msg = SKIP_TESTS.get(method_name)
+                if msg:
+                    marks.append(pytest.mark.skip(reason=msg))
+
+                markers = getattr(method, 'pytestmark', [])
+                for mark in markers:
+                    if mark.name in ('skipif', 'skip', 'xfail', 'xslow'):
+                        marks.append(mark)
+
+                yield pytest.param(cls, method_name, marks=marks)
+
+
+@pytest.mark.thread_unsafe(reason="fails in parallel")
+class RunAll64Bit:
+    def _check_resiliency(self, cls, method_name, **kw):
+        # Resiliency test, to check that sparse matrices deal reasonably
+        # with varying index data types.
+
+        @with_64bit_maxval_limit(**kw)
+        def check(cls, method_name):
+            instance = cls()
+            if hasattr(instance, 'setup_method'):
+                instance.setup_method()
+            try:
+                getattr(instance, method_name)()
+            finally:
+                if hasattr(instance, 'teardown_method'):
+                    instance.teardown_method()
+
+        check(cls, method_name)
+
+
+class Test64BitArray(RunAll64Bit):
+    # inheritance of pytest test classes does not separate marks for subclasses.
+    # So we define these functions in both Array and Matrix versions.
+    @pytest.mark.parametrize('cls,method_name', list(cases_64bit("sparray")))
+    def test_resiliency_limit_10(self, cls, method_name):
+        self._check_resiliency(cls, method_name, maxval_limit=10)
+
+    @pytest.mark.parametrize('cls,method_name', list(cases_64bit("sparray")))
+    def test_resiliency_all_32(self, cls, method_name):
+        self._check_resiliency(cls, method_name, fixed_dtype=np.int32)
+
+    @pytest.mark.parametrize('cls,method_name', list(cases_64bit("sparray")))
+    def test_resiliency_all_64(self, cls, method_name):
+        self._check_resiliency(cls, method_name, fixed_dtype=np.int64)
+
+    @pytest.mark.fail_slow(2)
+    @pytest.mark.parametrize('cls,method_name', list(cases_64bit("sparray")))
+    def test_resiliency_random(self, cls, method_name):
+        self._check_resiliency(cls, method_name)
+
+
+class Test64BitMatrix(RunAll64Bit):
+    # assert_32bit=True only for spmatrix cuz sparray does not check index content
+    @pytest.mark.fail_slow(5)
+    @pytest.mark.parametrize('cls,method_name', list(cases_64bit("spmatrix")))
+    def test_no_64(self, cls, method_name):
+        self._check_resiliency(cls, method_name, assert_32bit=True)
+
+
+class Test64BitMatrixSameAsArray(RunAll64Bit):
+    # inheritance of pytest test classes does not separate marks for subclasses.
+    # So we define these functions in both Array and Matrix versions.
+    @pytest.mark.parametrize('cls,method_name', list(cases_64bit("spmatrix")))
+    def test_resiliency_limit_10(self, cls, method_name):
+        self._check_resiliency(cls, method_name, maxval_limit=10)
+
+    @pytest.mark.parametrize('cls,method_name', list(cases_64bit("spmatrix")))
+    def test_resiliency_all_32(self, cls, method_name):
+        self._check_resiliency(cls, method_name, fixed_dtype=np.int32)
+
+    @pytest.mark.parametrize('cls,method_name', list(cases_64bit("spmatrix")))
+    def test_resiliency_all_64(self, cls, method_name):
+        self._check_resiliency(cls, method_name, fixed_dtype=np.int64)
+
+    @pytest.mark.fail_slow(2)
+    @pytest.mark.parametrize('cls,method_name', list(cases_64bit("spmatrix")))
+    def test_resiliency_random(self, cls, method_name):
+        # Resiliency check that sparse deals with varying index data types.
+        self._check_resiliency(cls, method_name)
+
+# Extra: LIL and DOK classes. no direct get_index_dtype, but convert to classes that do
+@pytest.mark.xslow
+class Test64BitArrayExtra(RunAll64Bit):
+    # inheritance of pytest test classes does not separate marks for subclasses.
+    # So we define these functions in both Array and Matrix versions.
+    @pytest.mark.parametrize('cls,method_name', list(cases_64bit("sparray-extra")))
+    def test_resiliency_limit_10(self, cls, method_name):
+        self._check_resiliency(cls, method_name, maxval_limit=10)
+
+    @pytest.mark.parametrize('cls,method_name', list(cases_64bit("sparray-extra")))
+    def test_resiliency_all_32(self, cls, method_name):
+        self._check_resiliency(cls, method_name, fixed_dtype=np.int32)
+
+    @pytest.mark.parametrize('cls,method_name', list(cases_64bit("sparray-extra")))
+    def test_resiliency_all_64(self, cls, method_name):
+        self._check_resiliency(cls, method_name, fixed_dtype=np.int64)
+
+    @pytest.mark.fail_slow(2)
+    @pytest.mark.parametrize('cls,method_name', list(cases_64bit("sparray-extra")))
+    def test_resiliency_random(self, cls, method_name):
+        # Resiliency check that sparse deals with varying index data types.
+        self._check_resiliency(cls, method_name)
+
+
+# Extra: LIL and DOK classes. no direct get_index_dtype, but convert to classes that do
+@pytest.mark.xslow
+class Test64BitMatrixExtra(RunAll64Bit):
+    # assert_32bit=True only for spmatrix cuz sparray does not check index content
+    @pytest.mark.fail_slow(5)
+    @pytest.mark.parametrize('cls,method_name', list(cases_64bit("spmatrix-extra")))
+    def test_no_64(self, cls, method_name):
+        self._check_resiliency(cls, method_name, assert_32bit=True)
+
+    # inheritance of pytest test classes does not separate marks for subclasses.
+    # So we define these functions in both Array and Matrix versions.
+    @pytest.mark.parametrize('cls,method_name', list(cases_64bit("spmatrix-extra")))
+    def test_resiliency_limit_10(self, cls, method_name):
+        self._check_resiliency(cls, method_name, maxval_limit=10)
+
+    @pytest.mark.parametrize('cls,method_name', list(cases_64bit("spmatrix-extra")))
+    def test_resiliency_all_32(self, cls, method_name):
+        self._check_resiliency(cls, method_name, fixed_dtype=np.int32)
+
+    @pytest.mark.parametrize('cls,method_name', list(cases_64bit("spmatrix-extra")))
+    def test_resiliency_all_64(self, cls, method_name):
+        self._check_resiliency(cls, method_name, fixed_dtype=np.int64)
+
+    @pytest.mark.fail_slow(2)
+    @pytest.mark.parametrize('cls,method_name', list(cases_64bit("spmatrix-extra")))
+    def test_resiliency_random(self, cls, method_name):
+        # Resiliency check that sparse deals with varying index data types.
+        self._check_resiliency(cls, method_name)
+
+
+@pytest.mark.thread_unsafe(reason="Fails in parallel for unknown reasons")
+class Test64BitTools:
+    # classes that use get_index_dtype
+    MAT_CLASSES = [
+        bsr_matrix, coo_matrix, csc_matrix, csr_matrix, dia_matrix,
+        bsr_array, coo_array, csc_array, csr_array, dia_array,
+    ]
+
+    def _compare_index_dtype(self, m, dtype):
+        dtype = np.dtype(dtype)
+        if m.format in ['csc', 'csr', 'bsr']:
+            return (m.indices.dtype == dtype) and (m.indptr.dtype == dtype)
+        elif m.format == 'coo':
+            return (m.row.dtype == dtype) and (m.col.dtype == dtype)
+        elif m.format == 'dia':
+            return (m.offsets.dtype == dtype)
+        else:
+            raise ValueError(f"matrix {m!r} has no integer indices")
+
+    def test_decorator_maxval_limit(self):
+        # Test that the with_64bit_maxval_limit decorator works
+
+        @with_64bit_maxval_limit(maxval_limit=10)
+        def check(mat_cls):
+            m = mat_cls(np.random.rand(10, 1))
+            assert self._compare_index_dtype(m, np.int32)
+            m = mat_cls(np.random.rand(11, 1))
+            assert self._compare_index_dtype(m, np.int64)
+
+        for mat_cls in self.MAT_CLASSES:
+            check(mat_cls)
+
+    def test_decorator_maxval_random(self):
+        # Test that the with_64bit_maxval_limit decorator works (2)
+
+        @with_64bit_maxval_limit(random=True)
+        def check(mat_cls):
+            seen_32 = False
+            seen_64 = False
+            for k in range(100):
+                m = mat_cls(np.random.rand(9, 9))
+                seen_32 = seen_32 or self._compare_index_dtype(m, np.int32)
+                seen_64 = seen_64 or self._compare_index_dtype(m, np.int64)
+                if seen_32 and seen_64:
+                    break
+            else:
+                raise AssertionError("both 32 and 64 bit indices not seen")
+
+        for mat_cls in self.MAT_CLASSES:
+            check(mat_cls)
+
+    def test_downcast_intp(self):
+        # Check that bincount and ufunc.reduceat intp downcasts are
+        # dealt with. The point here is to trigger points in the code
+        # that can fail on 32-bit systems when using 64-bit indices,
+        # due to use of functions that only work with intp-size indices.
+
+        @with_64bit_maxval_limit(fixed_dtype=np.int64, downcast_maxval=1)
+        def check_limited(csc_container, csr_container, coo_container):
+            # These involve indices larger than `downcast_maxval`
+            a = csc_container([[1, 2], [3, 4], [5, 6]])
+            pytest.raises(AssertionError, a.count_nonzero, axis=1)
+            pytest.raises(AssertionError, a.sum, axis=0)
+
+            a = csr_container([[1, 2, 3], [3, 4, 6]])
+            pytest.raises(AssertionError, a.count_nonzero, axis=0)
+            pytest.raises(AssertionError, a.sum, axis=1)
+
+            a = coo_container([[1, 2, 3], [3, 4, 5]])
+            pytest.raises(AssertionError, a.count_nonzero, axis=0)
+            a.has_canonical_format = False
+            pytest.raises(AssertionError, a.sum_duplicates)
+
+        @with_64bit_maxval_limit(fixed_dtype=np.int64)
+        def check_unlimited(csc_container, csr_container, coo_container):
+            # These involve indices smaller than `downcast_maxval`
+            a = csc_container([[1, 2], [3, 4], [5, 6]])
+            a.count_nonzero(axis=1)
+            a.sum(axis=0)
+
+            a = csr_container([[1, 2, 3], [3, 4, 6]])
+            a.count_nonzero(axis=0)
+            a.sum(axis=1)
+
+            a = coo_container([[1, 2, 3], [3, 4, 5]])
+            a.count_nonzero(axis=0)
+            a.has_canonical_format = False
+            a.sum_duplicates()
+
+        check_limited(csc_array, csr_array, coo_array)
+        check_unlimited(csc_array, csr_array, coo_array)
+        check_limited(csc_matrix, csr_matrix, coo_matrix)
+        check_unlimited(csc_matrix, csr_matrix, coo_matrix)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_arithmetic1d.py b/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_arithmetic1d.py
new file mode 100644
index 0000000000000000000000000000000000000000..62b56f5fe2f69d9188d1c01cf02521f7dd2f1e9d
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_arithmetic1d.py
@@ -0,0 +1,341 @@
+"""Test of 1D arithmetic operations"""
+
+import pytest
+
+import numpy as np
+from numpy.testing import assert_equal, assert_allclose
+
+from scipy.sparse import coo_array, csr_array
+from scipy.sparse._sputils import isscalarlike
+
+
+spcreators = [coo_array, csr_array]
+math_dtypes = [np.int64, np.float64, np.complex128]
+
+
+def toarray(a):
+    if isinstance(a, np.ndarray) or isscalarlike(a):
+        return a
+    return a.toarray()
+
+@pytest.fixture
+def dat1d():
+    return np.array([3, 0, 1, 0], 'd')
+
+
+@pytest.fixture
+def datsp_math_dtypes(dat1d):
+    dat_dtypes = {dtype: dat1d.astype(dtype) for dtype in math_dtypes}
+    return {
+        sp: [(dtype, dat, sp(dat)) for dtype, dat in dat_dtypes.items()]
+        for sp in spcreators
+    }
+
+
+@pytest.mark.parametrize("spcreator", spcreators)
+class TestArithmetic1D:
+    def test_empty_arithmetic(self, spcreator):
+        shape = (5,)
+        for mytype in [
+            np.dtype('int32'),
+            np.dtype('float32'),
+            np.dtype('float64'),
+            np.dtype('complex64'),
+            np.dtype('complex128'),
+        ]:
+            a = spcreator(shape, dtype=mytype)
+            b = a + a
+            c = 2 * a
+            assert isinstance(a @ a.tocsr(), np.ndarray)
+            assert isinstance(a @ a.tocoo(), np.ndarray)
+            for m in [a, b, c]:
+                assert m @ m == a.toarray() @ a.toarray()
+                assert m.dtype == mytype
+                assert toarray(m).dtype == mytype
+
+    def test_abs(self, spcreator):
+        A = np.array([-1, 0, 17, 0, -5, 0, 1, -4, 0, 0, 0, 0], 'd')
+        assert_equal(abs(A), abs(spcreator(A)).toarray())
+
+    def test_round(self, spcreator):
+        A = np.array([-1.35, 0.56, 17.25, -5.98], 'd')
+        Asp = spcreator(A)
+        assert_equal(np.around(A, decimals=1), round(Asp, ndigits=1).toarray())
+
+    def test_elementwise_power(self, spcreator):
+        A = np.array([-4, -3, -2, -1, 0, 1, 2, 3, 4], 'd')
+        Asp = spcreator(A)
+        assert_equal(np.power(A, 2), Asp.power(2).toarray())
+
+        # element-wise power function needs a scalar power
+        with pytest.raises(NotImplementedError, match='input is not scalar'):
+            spcreator(A).power(A)
+
+    def test_real(self, spcreator):
+        D = np.array([1 + 3j, 2 - 4j])
+        A = spcreator(D)
+        assert_equal(A.real.toarray(), D.real)
+
+    def test_imag(self, spcreator):
+        D = np.array([1 + 3j, 2 - 4j])
+        A = spcreator(D)
+        assert_equal(A.imag.toarray(), D.imag)
+
+    def test_mul_scalar(self, spcreator, datsp_math_dtypes):
+        for dtype, dat, datsp in datsp_math_dtypes[spcreator]:
+            assert_equal(dat * 2, (datsp * 2).toarray())
+            assert_equal(dat * 17.3, (datsp * 17.3).toarray())
+
+    def test_rmul_scalar(self, spcreator, datsp_math_dtypes):
+        for dtype, dat, datsp in datsp_math_dtypes[spcreator]:
+            assert_equal(2 * dat, (2 * datsp).toarray())
+            assert_equal(17.3 * dat, (17.3 * datsp).toarray())
+
+    def test_sub(self, spcreator, datsp_math_dtypes):
+        for dtype, dat, datsp in datsp_math_dtypes[spcreator]:
+            if dtype == np.dtype('bool'):
+                # boolean array subtraction deprecated in 1.9.0
+                continue
+
+            assert_equal((datsp - datsp).toarray(), np.zeros(4))
+            assert_equal((datsp - 0).toarray(), dat)
+
+            A = spcreator([1, -4, 0, 2], dtype='d')
+            assert_equal((datsp - A).toarray(), dat - A.toarray())
+            assert_equal((A - datsp).toarray(), A.toarray() - dat)
+
+            # test broadcasting
+            assert_equal(datsp.toarray() - dat[0], dat - dat[0])
+
+    def test_add0(self, spcreator, datsp_math_dtypes):
+        for dtype, dat, datsp in datsp_math_dtypes[spcreator]:
+            # Adding 0 to a sparse matrix
+            assert_equal((datsp + 0).toarray(), dat)
+            # use sum (which takes 0 as a starting value)
+            sumS = sum([k * datsp for k in range(1, 3)])
+            sumD = sum([k * dat for k in range(1, 3)])
+            assert_allclose(sumS.toarray(), sumD)
+
+    def test_elementwise_multiply(self, spcreator):
+        # real/real
+        A = np.array([4, 0, 9])
+        B = np.array([0, 7, -1])
+        Asp = spcreator(A)
+        Bsp = spcreator(B)
+        assert_allclose(Asp.multiply(Bsp).toarray(), A * B)  # sparse/sparse
+        assert_allclose(Asp.multiply(B).toarray(), A * B)  # sparse/dense
+
+        # complex/complex
+        C = np.array([1 - 2j, 0 + 5j, -1 + 0j])
+        D = np.array([5 + 2j, 7 - 3j, -2 + 1j])
+        Csp = spcreator(C)
+        Dsp = spcreator(D)
+        assert_allclose(Csp.multiply(Dsp).toarray(), C * D)  # sparse/sparse
+        assert_allclose(Csp.multiply(D).toarray(), C * D)  # sparse/dense
+
+        # real/complex
+        assert_allclose(Asp.multiply(Dsp).toarray(), A * D)  # sparse/sparse
+        assert_allclose(Asp.multiply(D).toarray(), A * D)  # sparse/dense
+
+    def test_elementwise_multiply_broadcast(self, spcreator):
+        A = np.array([4])
+        B = np.array([[-9]])
+        C = np.array([1, -1, 0])
+        D = np.array([[7, 9, -9]])
+        E = np.array([[3], [2], [1]])
+        F = np.array([[8, 6, 3], [-4, 3, 2], [6, 6, 6]])
+        G = [1, 2, 3]
+        H = np.ones((3, 4))
+        J = H.T
+        K = np.array([[0]])
+        L = np.array([[[1, 2], [0, 1]]])
+
+        # Some arrays can't be cast as spmatrices (A, C, L) so leave
+        # them out.
+        Asp = spcreator(A)
+        Csp = spcreator(C)
+        Gsp = spcreator(G)
+        # 2d arrays
+        Bsp = spcreator(B)
+        Dsp = spcreator(D)
+        Esp = spcreator(E)
+        Fsp = spcreator(F)
+        Hsp = spcreator(H)
+        Hspp = spcreator(H[0, None])
+        Jsp = spcreator(J)
+        Jspp = spcreator(J[:, 0, None])
+        Ksp = spcreator(K)
+
+        matrices = [A, B, C, D, E, F, G, H, J, K, L]
+        spmatrices = [Asp, Bsp, Csp, Dsp, Esp, Fsp, Gsp, Hsp, Hspp, Jsp, Jspp, Ksp]
+        sp1dmatrices = [Asp, Csp, Gsp]
+
+        # sparse/sparse
+        for i in sp1dmatrices:
+            for j in spmatrices:
+                try:
+                    dense_mult = i.toarray() * j.toarray()
+                except ValueError:
+                    with pytest.raises(ValueError, match='inconsistent shapes'):
+                        i.multiply(j)
+                    continue
+                sp_mult = i.multiply(j)
+                assert_allclose(sp_mult.toarray(), dense_mult)
+
+        # sparse/dense
+        for i in sp1dmatrices:
+            for j in matrices:
+                try:
+                    dense_mult = i.toarray() * j
+                except TypeError:
+                    continue
+                except ValueError:
+                    matchme = 'broadcast together|inconsistent shapes'
+                    with pytest.raises(ValueError, match=matchme):
+                        i.multiply(j)
+                    continue
+                try:
+                    sp_mult = i.multiply(j)
+                except ValueError:
+                    continue
+                assert_allclose(toarray(sp_mult), dense_mult)
+
+    def test_elementwise_divide(self, spcreator, dat1d):
+        datsp = spcreator(dat1d)
+        expected = np.array([1, np.nan, 1, np.nan])
+        actual = datsp / datsp
+        # need assert_array_equal to handle nan values
+        np.testing.assert_array_equal(actual, expected)
+
+        denom = spcreator([1, 0, 0, 4], dtype='d')
+        expected = [3, np.nan, np.inf, 0]
+        np.testing.assert_array_equal(datsp / denom, expected)
+
+        # complex
+        A = np.array([1 - 2j, 0 + 5j, -1 + 0j])
+        B = np.array([5 + 2j, 7 - 3j, -2 + 1j])
+        Asp = spcreator(A)
+        Bsp = spcreator(B)
+        assert_allclose(Asp / Bsp, A / B)
+
+        # integer
+        A = np.array([1, 2, 3])
+        B = np.array([0, 1, 2])
+        Asp = spcreator(A)
+        Bsp = spcreator(B)
+        with np.errstate(divide='ignore'):
+            assert_equal(Asp / Bsp, A / B)
+
+        # mismatching sparsity patterns
+        A = np.array([0, 1])
+        B = np.array([1, 0])
+        Asp = spcreator(A)
+        Bsp = spcreator(B)
+        with np.errstate(divide='ignore', invalid='ignore'):
+            assert_equal(Asp / Bsp, A / B)
+
+    def test_pow(self, spcreator):
+        A = np.array([1, 0, 2, 0])
+        B = spcreator(A)
+
+        # unusual exponents
+        with pytest.raises(ValueError, match='negative integer powers'):
+            B**-1
+        with pytest.raises(NotImplementedError, match='zero power'):
+            B**0
+
+        for exponent in [1, 2, 3, 2.2]:
+            ret_sp = B**exponent
+            ret_np = A**exponent
+            assert_equal(ret_sp.toarray(), ret_np)
+            assert_equal(ret_sp.dtype, ret_np.dtype)
+
+    def test_dot_scalar(self, spcreator, dat1d):
+        A = spcreator(dat1d)
+        scalar = 10
+        actual = A.dot(scalar)
+        expected = A * scalar
+
+        assert_allclose(actual.toarray(), expected.toarray())
+
+    def test_matmul(self, spcreator):
+        Msp = spcreator([2, 0, 3.0])
+        B = spcreator(np.array([[0, 1], [1, 0], [0, 2]], 'd'))
+        col = np.array([[1, 2, 3]]).T
+
+        # check sparse @ dense 2d column
+        assert_allclose(Msp @ col, Msp.toarray() @ col)
+
+        # check sparse1d @ sparse2d, sparse1d @ dense2d, dense1d @ sparse2d
+        assert_allclose((Msp @ B).toarray(), (Msp @ B).toarray())
+        assert_allclose(Msp.toarray() @ B, (Msp @ B).toarray())
+        assert_allclose(Msp @ B.toarray(), (Msp @ B).toarray())
+
+        # check sparse1d @ dense1d, sparse1d @ sparse1d
+        V = np.array([0, 0, 1])
+        assert_allclose(Msp @ V, Msp.toarray() @ V)
+
+        Vsp = spcreator(V)
+        Msp_Vsp = Msp @ Vsp
+        assert isinstance(Msp_Vsp, np.ndarray)
+        assert Msp_Vsp.shape == ()
+
+        # output is 0-dim ndarray
+        assert_allclose(np.array(3), Msp_Vsp)
+        assert_allclose(np.array(3), Msp.toarray() @ Vsp)
+        assert_allclose(np.array(3), Msp @ Vsp.toarray())
+        assert_allclose(np.array(3), Msp.toarray() @ Vsp.toarray())
+
+        # check error on matrix-scalar
+        with pytest.raises(ValueError, match='Scalar operands are not allowed'):
+            Msp @ 1
+        with pytest.raises(ValueError, match='Scalar operands are not allowed'):
+            1 @ Msp
+
+    def test_sub_dense(self, spcreator, datsp_math_dtypes):
+        # subtracting a dense matrix to/from a sparse matrix
+        for dtype, dat, datsp in datsp_math_dtypes[spcreator]:
+            if dtype == np.dtype('bool'):
+                # boolean array subtraction deprecated in 1.9.0
+                continue
+
+            # Manually add to avoid upcasting from scalar
+            # multiplication.
+            sum1 = (dat + dat + dat) - datsp
+            assert_equal(sum1, dat + dat)
+            sum2 = (datsp + datsp + datsp) - dat
+            assert_equal(sum2, dat + dat)
+
+    def test_size_zero_matrix_arithmetic(self, spcreator):
+        # Test basic matrix arithmetic with shapes like 0, (1, 0), (0, 3), etc.
+        mat = np.array([])
+        a = mat.reshape(0)
+        d = mat.reshape((1, 0))
+        f = np.ones([5, 5])
+
+        asp = spcreator(a)
+        dsp = spcreator(d)
+        # bad shape for addition
+        with pytest.raises(ValueError, match='inconsistent shapes'):
+            asp.__add__(dsp)
+
+        # matrix product.
+        assert_equal(asp.dot(asp), np.dot(a, a))
+
+        # bad matrix products
+        with pytest.raises(ValueError, match='dimension mismatch|shapes.*not aligned'):
+            asp.dot(f)
+
+        # elemente-wise multiplication
+        assert_equal(asp.multiply(asp).toarray(), np.multiply(a, a))
+
+        assert_equal(asp.multiply(a).toarray(), np.multiply(a, a))
+
+        assert_equal(asp.multiply(6).toarray(), np.multiply(a, 6))
+
+        # bad element-wise multiplication
+        with pytest.raises(ValueError, match='inconsistent shapes'):
+            asp.multiply(f)
+
+        # Addition
+        assert_equal(asp.__add__(asp).toarray(), a.__add__(a))
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_array_api.py b/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_array_api.py
new file mode 100644
index 0000000000000000000000000000000000000000..ee84fb1952d57c3896107e10ab4f31a50cc33a97
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_array_api.py
@@ -0,0 +1,576 @@
+import pytest
+import numpy as np
+import numpy.testing as npt
+import scipy.sparse
+import scipy.sparse.linalg as spla
+
+
+sparray_types = ('bsr', 'coo', 'csc', 'csr', 'dia', 'dok', 'lil')
+
+sparray_classes = [
+    getattr(scipy.sparse, f'{T}_array') for T in sparray_types
+]
+
+A = np.array([
+    [0, 1, 2, 0],
+    [2, 0, 0, 3],
+    [1, 4, 0, 0]
+])
+
+B = np.array([
+    [0, 1],
+    [2, 0]
+])
+
+X = np.array([
+    [1, 0, 0, 1],
+    [2, 1, 2, 0],
+    [0, 2, 1, 0],
+    [0, 0, 1, 2]
+], dtype=float)
+
+
+sparrays = [sparray(A) for sparray in sparray_classes]
+square_sparrays = [sparray(B) for sparray in sparray_classes]
+eig_sparrays = [sparray(X) for sparray in sparray_classes]
+
+parametrize_sparrays = pytest.mark.parametrize(
+    "A", sparrays, ids=sparray_types
+)
+parametrize_square_sparrays = pytest.mark.parametrize(
+    "B", square_sparrays, ids=sparray_types
+)
+parametrize_eig_sparrays = pytest.mark.parametrize(
+    "X", eig_sparrays, ids=sparray_types
+)
+
+
+@parametrize_sparrays
+def test_sum(A):
+    assert not isinstance(A.sum(axis=0), np.matrix), \
+        "Expected array, got matrix"
+    assert A.sum(axis=0).shape == (4,)
+    assert A.sum(axis=1).shape == (3,)
+
+
+@parametrize_sparrays
+def test_mean(A):
+    assert not isinstance(A.mean(axis=1), np.matrix), \
+        "Expected array, got matrix"
+
+
+@parametrize_sparrays
+def test_min_max(A):
+    # Some formats don't support min/max operations, so we skip those here.
+    if hasattr(A, 'min'):
+        assert not isinstance(A.min(axis=1), np.matrix), \
+            "Expected array, got matrix"
+    if hasattr(A, 'max'):
+        assert not isinstance(A.max(axis=1), np.matrix), \
+            "Expected array, got matrix"
+    if hasattr(A, 'argmin'):
+        assert not isinstance(A.argmin(axis=1), np.matrix), \
+            "Expected array, got matrix"
+    if hasattr(A, 'argmax'):
+        assert not isinstance(A.argmax(axis=1), np.matrix), \
+            "Expected array, got matrix"
+
+
+@parametrize_sparrays
+def test_todense(A):
+    assert not isinstance(A.todense(), np.matrix), \
+        "Expected array, got matrix"
+
+
+@parametrize_sparrays
+def test_indexing(A):
+    if A.__class__.__name__[:3] in ('dia', 'coo', 'bsr'):
+        return
+
+    all_res = (
+        A[1, :],
+        A[:, 1],
+        A[1, [1, 2]],
+        A[[1, 2], 1],
+        A[[0]],
+        A[:, [1, 2]],
+        A[[1, 2], :],
+        A[1, [[1, 2]]],
+        A[[[1, 2]], 1],
+    )
+
+    for res in all_res:
+        assert isinstance(res, scipy.sparse.sparray), \
+            f"Expected sparse array, got {res._class__.__name__}"
+
+
+@parametrize_sparrays
+def test_dense_addition(A):
+    X = np.random.random(A.shape)
+    assert not isinstance(A + X, np.matrix), "Expected array, got matrix"
+
+
+@parametrize_sparrays
+def test_sparse_addition(A):
+    assert isinstance((A + A), scipy.sparse.sparray), "Expected array, got matrix"
+
+
+@parametrize_sparrays
+def test_elementwise_mul(A):
+    assert np.all((A * A).todense() == A.power(2).todense())
+
+
+@parametrize_sparrays
+def test_elementwise_rmul(A):
+    with pytest.raises(TypeError):
+        None * A
+
+    with pytest.raises(ValueError):
+        np.eye(3) * scipy.sparse.csr_array(np.arange(6).reshape(2, 3))
+
+    assert np.all((2 * A) == (A.todense() * 2))
+
+    assert np.all((A.todense() * A) == (A.todense() ** 2))
+
+
+@parametrize_sparrays
+def test_matmul(A):
+    assert np.all((A @ A.T).todense() == A.dot(A.T).todense())
+
+
+@parametrize_sparrays
+def test_power_operator(A):
+    assert isinstance((A**2), scipy.sparse.sparray), "Expected array, got matrix"
+
+    # https://github.com/scipy/scipy/issues/15948
+    npt.assert_equal((A**2).todense(), (A.todense())**2)
+
+    # power of zero is all ones (dense) so helpful msg exception
+    with pytest.raises(NotImplementedError, match="zero power"):
+        A**0
+
+
+@parametrize_sparrays
+def test_sparse_divide(A):
+    assert isinstance(A / A, np.ndarray)
+
+@parametrize_sparrays
+def test_sparse_dense_divide(A):
+    with pytest.warns(RuntimeWarning):
+        assert isinstance((A / A.todense()), scipy.sparse.sparray)
+
+@parametrize_sparrays
+def test_dense_divide(A):
+    assert isinstance((A / 2), scipy.sparse.sparray), "Expected array, got matrix"
+
+
+@parametrize_sparrays
+def test_no_A_attr(A):
+    with pytest.raises(AttributeError):
+        A.A
+
+
+@parametrize_sparrays
+def test_no_H_attr(A):
+    with pytest.raises(AttributeError):
+        A.H
+
+
+@parametrize_sparrays
+def test_getrow_getcol(A):
+    assert isinstance(A._getcol(0), scipy.sparse.sparray)
+    assert isinstance(A._getrow(0), scipy.sparse.sparray)
+
+
+# -- linalg --
+
+@parametrize_sparrays
+def test_as_linearoperator(A):
+    L = spla.aslinearoperator(A)
+    npt.assert_allclose(L * [1, 2, 3, 4], A @ [1, 2, 3, 4])
+
+
+@parametrize_square_sparrays
+def test_inv(B):
+    if B.__class__.__name__[:3] != 'csc':
+        return
+
+    C = spla.inv(B)
+
+    assert isinstance(C, scipy.sparse.sparray)
+    npt.assert_allclose(C.todense(), np.linalg.inv(B.todense()))
+
+
+@parametrize_square_sparrays
+def test_expm(B):
+    if B.__class__.__name__[:3] != 'csc':
+        return
+
+    Bmat = scipy.sparse.csc_matrix(B)
+
+    C = spla.expm(B)
+
+    assert isinstance(C, scipy.sparse.sparray)
+    npt.assert_allclose(
+        C.todense(),
+        spla.expm(Bmat).todense()
+    )
+
+
+@parametrize_square_sparrays
+def test_expm_multiply(B):
+    if B.__class__.__name__[:3] != 'csc':
+        return
+
+    npt.assert_allclose(
+        spla.expm_multiply(B, np.array([1, 2])),
+        spla.expm(B) @ [1, 2]
+    )
+
+
+@parametrize_sparrays
+def test_norm(A):
+    C = spla.norm(A)
+    npt.assert_allclose(C, np.linalg.norm(A.todense()))
+
+
+@parametrize_square_sparrays
+def test_onenormest(B):
+    C = spla.onenormest(B)
+    npt.assert_allclose(C, np.linalg.norm(B.todense(), 1))
+
+
+@parametrize_square_sparrays
+def test_spsolve(B):
+    if B.__class__.__name__[:3] not in ('csc', 'csr'):
+        return
+
+    npt.assert_allclose(
+        spla.spsolve(B, [1, 2]),
+        np.linalg.solve(B.todense(), [1, 2])
+    )
+
+
+@pytest.mark.parametrize("fmt",["csr","csc"])
+def test_spsolve_triangular(fmt):
+    arr = [
+        [1, 0, 0, 0],
+        [2, 1, 0, 0],
+        [3, 2, 1, 0],
+        [4, 3, 2, 1],
+    ]
+    if fmt == "csr":
+      X = scipy.sparse.csr_array(arr)
+    else:
+      X = scipy.sparse.csc_array(arr)
+    spla.spsolve_triangular(X, [1, 2, 3, 4])
+
+
+@parametrize_square_sparrays
+def test_factorized(B):
+    if B.__class__.__name__[:3] != 'csc':
+        return
+
+    LU = spla.factorized(B)
+    npt.assert_allclose(
+        LU(np.array([1, 2])),
+        np.linalg.solve(B.todense(), [1, 2])
+    )
+
+
+@parametrize_square_sparrays
+@pytest.mark.parametrize(
+    "solver",
+    ["bicg", "bicgstab", "cg", "cgs", "gmres", "lgmres", "minres", "qmr",
+     "gcrotmk", "tfqmr"]
+)
+def test_solvers(B, solver):
+    if solver == "minres":
+        kwargs = {}
+    else:
+        kwargs = {'atol': 1e-5}
+
+    x, info = getattr(spla, solver)(B, np.array([1, 2]), **kwargs)
+    assert info >= 0  # no errors, even if perhaps did not converge fully
+    npt.assert_allclose(x, [1, 1], atol=1e-1)
+
+
+@parametrize_sparrays
+@pytest.mark.parametrize(
+    "solver",
+    ["lsqr", "lsmr"]
+)
+def test_lstsqr(A, solver):
+    x, *_ = getattr(spla, solver)(A, [1, 2, 3])
+    npt.assert_allclose(A @ x, [1, 2, 3])
+
+
+@parametrize_eig_sparrays
+def test_eigs(X):
+    e, v = spla.eigs(X, k=1)
+    npt.assert_allclose(
+        X @ v,
+        e[0] * v
+    )
+
+
+@parametrize_eig_sparrays
+def test_eigsh(X):
+    X = X + X.T
+    e, v = spla.eigsh(X, k=1)
+    npt.assert_allclose(
+        X @ v,
+        e[0] * v
+    )
+
+
+@parametrize_eig_sparrays
+def test_svds(X):
+    u, s, vh = spla.svds(X, k=3)
+    u2, s2, vh2 = np.linalg.svd(X.todense())
+    s = np.sort(s)
+    s2 = np.sort(s2[:3])
+    npt.assert_allclose(s, s2, atol=1e-3)
+
+
+def test_splu():
+    X = scipy.sparse.csc_array([
+        [1, 0, 0, 0],
+        [2, 1, 0, 0],
+        [3, 2, 1, 0],
+        [4, 3, 2, 1],
+    ])
+    LU = spla.splu(X)
+    npt.assert_allclose(
+        LU.solve(np.array([1, 2, 3, 4])),
+        np.asarray([1, 0, 0, 0], dtype=np.float64),
+        rtol=1e-14, atol=3e-16
+    )
+
+
+def test_spilu():
+    X = scipy.sparse.csc_array([
+        [1, 0, 0, 0],
+        [2, 1, 0, 0],
+        [3, 2, 1, 0],
+        [4, 3, 2, 1],
+    ])
+    LU = spla.spilu(X)
+    npt.assert_allclose(
+        LU.solve(np.array([1, 2, 3, 4])),
+        np.asarray([1, 0, 0, 0], dtype=np.float64),
+        rtol=1e-14, atol=3e-16
+    )
+
+
+@pytest.mark.parametrize(
+    "cls,indices_attrs",
+    [
+        (
+            scipy.sparse.csr_array,
+            ["indices", "indptr"],
+        ),
+        (
+            scipy.sparse.csc_array,
+            ["indices", "indptr"],
+        ),
+        (
+            scipy.sparse.coo_array,
+            ["row", "col"],
+        ),
+    ]
+)
+@pytest.mark.parametrize("expected_dtype", [np.int64, np.int32])
+def test_index_dtype_compressed(cls, indices_attrs, expected_dtype):
+    input_array = scipy.sparse.coo_array(np.arange(9).reshape(3, 3))
+    coo_tuple = (
+        input_array.data,
+        (
+            input_array.row.astype(expected_dtype),
+            input_array.col.astype(expected_dtype),
+        )
+    )
+
+    result = cls(coo_tuple)
+    for attr in indices_attrs:
+        assert getattr(result, attr).dtype == expected_dtype
+
+    result = cls(coo_tuple, shape=(3, 3))
+    for attr in indices_attrs:
+        assert getattr(result, attr).dtype == expected_dtype
+
+    if issubclass(cls, scipy.sparse._compressed._cs_matrix):
+        input_array_csr = input_array.tocsr()
+        csr_tuple = (
+            input_array_csr.data,
+            input_array_csr.indices.astype(expected_dtype),
+            input_array_csr.indptr.astype(expected_dtype),
+        )
+
+        result = cls(csr_tuple)
+        for attr in indices_attrs:
+            assert getattr(result, attr).dtype == expected_dtype
+
+        result = cls(csr_tuple, shape=(3, 3))
+        for attr in indices_attrs:
+            assert getattr(result, attr).dtype == expected_dtype
+
+
+def test_default_is_matrix_diags():
+    m = scipy.sparse.diags([0.0, 1.0, 2.0])
+    assert not isinstance(m, scipy.sparse.sparray)
+
+
+def test_default_is_matrix_eye():
+    m = scipy.sparse.eye(3)
+    assert not isinstance(m, scipy.sparse.sparray)
+
+
+def test_default_is_matrix_spdiags():
+    m = scipy.sparse.spdiags([1.0, 2.0, 3.0], 0, 3, 3)
+    assert not isinstance(m, scipy.sparse.sparray)
+
+
+def test_default_is_matrix_identity():
+    m = scipy.sparse.identity(3)
+    assert not isinstance(m, scipy.sparse.sparray)
+
+
+@pytest.mark.filterwarnings("ignore:.*switching.*sparse array int:DeprecationWarning")
+def test_default_is_matrix_kron_dense():
+    m = scipy.sparse.kron(
+        np.array([[1, 2], [3, 4]]), np.array([[4, 3], [2, 1]])
+    )
+    assert not isinstance(m, scipy.sparse.sparray)
+
+
+@pytest.mark.filterwarnings("ignore:.*switching.*sparse array int:DeprecationWarning")
+def test_default_is_matrix_kron_sparse():
+    m = scipy.sparse.kron(
+        np.array([[1, 2], [3, 4]]), np.array([[1, 0], [0, 0]])
+    )
+    assert not isinstance(m, scipy.sparse.sparray)
+
+
+@pytest.mark.filterwarnings("ignore:.*switching.*sparse array int:DeprecationWarning")
+def test_default_is_matrix_kronsum():
+    m = scipy.sparse.kronsum(
+        np.array([[1, 0], [0, 1]]), np.array([[0, 1], [1, 0]])
+    )
+    assert not isinstance(m, scipy.sparse.sparray)
+
+
+def test_default_is_matrix_random():
+    m = scipy.sparse.random(3, 3)
+    assert not isinstance(m, scipy.sparse.sparray)
+
+
+def test_default_is_matrix_rand():
+    m = scipy.sparse.rand(3, 3)
+    assert not isinstance(m, scipy.sparse.sparray)
+
+
+@pytest.mark.parametrize("fn", (scipy.sparse.hstack, scipy.sparse.vstack))
+def test_default_is_matrix_stacks(fn):
+    """Same idea as `test_default_construction_fn_matrices`, but for the
+    stacking creation functions."""
+    A = scipy.sparse.coo_matrix(np.eye(2))
+    B = scipy.sparse.coo_matrix([[0, 1], [1, 0]])
+    m = fn([A, B])
+    assert not isinstance(m, scipy.sparse.sparray)
+
+
+@pytest.mark.filterwarnings("ignore:.*switching.*sparse array int:DeprecationWarning")
+def test_blocks_default_construction_fn_matrices():
+    """Same idea as `test_default_construction_fn_matrices`, but block functions"""
+    A = scipy.sparse.coo_matrix(np.eye(2))
+    B = scipy.sparse.coo_matrix([[2], [0]])
+    C = scipy.sparse.coo_matrix([[3]])
+
+    # block diag
+    m = scipy.sparse.block_diag((A, B, C))
+    assert not isinstance(m, scipy.sparse.sparray)
+
+    # bmat
+    m = scipy.sparse.bmat([[A, None], [None, C]])
+    assert not isinstance(m, scipy.sparse.sparray)
+
+    # ndarray input
+    A = np.eye(2)
+    B = [[2], [0]]
+    C = [[3]]
+
+    # block diag
+    m = scipy.sparse.block_diag((A, B, C))
+    assert not isinstance(m, scipy.sparse.sparray)
+
+    # bmat
+    m = scipy.sparse.bmat([[A, None], [None, C]])
+    assert not isinstance(m, scipy.sparse.sparray)
+
+
+def test_format_property():
+    for fmt in sparray_types:
+        arr_cls = getattr(scipy.sparse, f"{fmt}_array")
+        M = arr_cls([[1, 2]])
+        assert M.format == fmt
+        assert M._format == fmt
+        with pytest.raises(AttributeError):
+            M.format = "qqq"
+
+
+def test_issparse():
+    m = scipy.sparse.eye(3)
+    a = scipy.sparse.csr_array(m)
+    assert not isinstance(m, scipy.sparse.sparray)
+    assert isinstance(a, scipy.sparse.sparray)
+
+    # Both sparse arrays and sparse matrices should be sparse
+    assert scipy.sparse.issparse(a)
+    assert scipy.sparse.issparse(m)
+
+    # ndarray and array_likes are not sparse
+    assert not scipy.sparse.issparse(a.todense())
+    assert not scipy.sparse.issparse(m.todense())
+
+
+def test_isspmatrix():
+    m = scipy.sparse.eye(3)
+    a = scipy.sparse.csr_array(m)
+    assert not isinstance(m, scipy.sparse.sparray)
+    assert isinstance(a, scipy.sparse.sparray)
+
+    # Should only be true for sparse matrices, not sparse arrays
+    assert not scipy.sparse.isspmatrix(a)
+    assert scipy.sparse.isspmatrix(m)
+
+    # ndarray and array_likes are not sparse
+    assert not scipy.sparse.isspmatrix(a.todense())
+    assert not scipy.sparse.isspmatrix(m.todense())
+
+
+@pytest.mark.parametrize(
+    ("fmt", "fn"),
+    (
+        ("bsr", scipy.sparse.isspmatrix_bsr),
+        ("coo", scipy.sparse.isspmatrix_coo),
+        ("csc", scipy.sparse.isspmatrix_csc),
+        ("csr", scipy.sparse.isspmatrix_csr),
+        ("dia", scipy.sparse.isspmatrix_dia),
+        ("dok", scipy.sparse.isspmatrix_dok),
+        ("lil", scipy.sparse.isspmatrix_lil),
+    ),
+)
+def test_isspmatrix_format(fmt, fn):
+    m = scipy.sparse.eye(3, format=fmt)
+    a = scipy.sparse.csr_array(m).asformat(fmt)
+    assert not isinstance(m, scipy.sparse.sparray)
+    assert isinstance(a, scipy.sparse.sparray)
+
+    # Should only be true for sparse matrices, not sparse arrays
+    assert not fn(a)
+    assert fn(m)
+
+    # ndarray and array_likes are not sparse
+    assert not fn(a.todense())
+    assert not fn(m.todense())
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_base.py b/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_base.py
new file mode 100644
index 0000000000000000000000000000000000000000..ebcf4e9af80a12b49efefe23942e45d0f3038f62
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_base.py
@@ -0,0 +1,5971 @@
+#
+# Authors: Travis Oliphant, Ed Schofield, Robert Cimrman, Nathan Bell, and others
+
+""" Test functions for sparse matrices. Each class in the "Matrix class
+based tests" section become subclasses of the classes in the "Generic
+tests" section. This is done by the functions in the "Tailored base
+class for generic tests" section.
+
+"""
+
+
+import contextlib
+import functools
+import operator
+import platform
+import itertools
+import sys
+import warnings
+
+import pytest
+from pytest import raises as assert_raises
+
+import numpy as np
+from numpy import (arange, zeros, array, dot, asarray,
+                   vstack, ndarray, transpose, diag, kron, inf, conjugate,
+                   int8)
+
+import random
+from numpy.testing import (assert_equal, assert_array_equal,
+        assert_array_almost_equal, assert_almost_equal, assert_,
+        assert_allclose)
+from numpy.exceptions import ComplexWarning
+
+from types import GenericAlias
+
+import scipy.linalg
+
+import scipy.sparse as sparse
+from scipy.sparse import (csc_matrix, csr_matrix, dok_matrix,
+        coo_matrix, lil_matrix, dia_matrix, bsr_matrix,
+        csc_array, csr_array, dok_array,
+        coo_array, lil_array, dia_array, bsr_array,
+        eye, issparse, SparseEfficiencyWarning, sparray, spmatrix,
+        matrix_transpose,)
+from scipy.sparse._base import _formats
+from scipy.sparse._sputils import (supported_dtypes, isscalarlike,
+                                   get_index_dtype, asmatrix, matrix)
+from scipy.sparse.linalg import splu, expm, inv
+
+IS_COLAB = ('google.colab' in sys.modules)
+
+
+def assert_in(member, collection, msg=None):
+    message = msg if msg is not None else f"{member!r} not found in {collection!r}"
+    assert_(member in collection, msg=message)
+
+
+def assert_array_equal_dtype(x, y, **kwargs):
+    assert_(x.dtype == y.dtype)
+    assert_array_equal(x, y, **kwargs)
+
+
+NON_ARRAY_BACKED_FORMATS = frozenset(['dok'])
+
+WMSG = "Changing the sparsity structure"
+
+def sparse_may_share_memory(A, B):
+    # Checks if A and B have any numpy array sharing memory.
+
+    def _underlying_arrays(x):
+        # Given any object (e.g. a sparse array), returns all numpy arrays
+        # stored in any attribute.
+
+        arrays = []
+        for a in x.__dict__.values():
+            if isinstance(a, np.ndarray | np.generic):
+                arrays.append(a)
+        return arrays
+
+    for a in _underlying_arrays(A):
+        for b in _underlying_arrays(B):
+            if np.may_share_memory(a, b):
+                return True
+    return False
+
+
+def with_64bit_maxval_limit(maxval_limit=None, random=False, fixed_dtype=None,
+                            downcast_maxval=None, assert_32bit=False):
+    """
+    Monkeypatch the maxval threshold at which scipy.sparse switches to
+    64-bit index arrays, or make it (pseudo-)random.
+
+    """
+    if maxval_limit is None:
+        maxval_limit = np.int64(10)
+    else:
+        # Ensure we use numpy scalars rather than Python scalars (matters for
+        # NEP 50 casting rule changes)
+        maxval_limit = np.int64(maxval_limit)
+
+    if assert_32bit:
+        def new_get_index_dtype(arrays=(), maxval=None, check_contents=False):
+            tp = get_index_dtype(arrays, maxval, check_contents)
+            assert_equal(np.iinfo(tp).max, np.iinfo(np.int32).max)
+            assert_(tp == np.int32 or tp == np.intc)
+            return tp
+    elif fixed_dtype is not None:
+        def new_get_index_dtype(arrays=(), maxval=None, check_contents=False):
+            return fixed_dtype
+    elif random:
+        rng = np.random.default_rng(1234)
+        def new_get_index_dtype(arrays=(), maxval=None, check_contents=False):
+            return (np.int32, np.int64)[rng.integers(2)]
+    else:
+        def new_get_index_dtype(arrays=(), maxval=None, check_contents=False):
+            dtype = np.int32
+            if maxval is not None:
+                if maxval > maxval_limit:
+                    dtype = np.int64
+            for arr in arrays:
+                arr = np.asarray(arr)
+                if arr.dtype > np.int32:
+                    if check_contents:
+                        if arr.size == 0:
+                            # a bigger type not needed
+                            continue
+                        elif np.issubdtype(arr.dtype, np.integer):
+                            maxval = arr.max()
+                            minval = arr.min()
+                            if minval >= -maxval_limit and maxval <= maxval_limit:
+                                # a bigger type not needed
+                                continue
+                    dtype = np.int64
+            return dtype
+
+    if downcast_maxval is not None:
+        def new_downcast_intp_index(arr):
+            if arr.max() > downcast_maxval:
+                raise AssertionError("downcast limited")
+            return arr.astype(np.intp)
+
+    def decorator(func):
+        backup = []
+        modules = [scipy.sparse._bsr, scipy.sparse._coo, scipy.sparse._csc,
+                   scipy.sparse._csr, scipy.sparse._dia, scipy.sparse._dok,
+                   scipy.sparse._lil, scipy.sparse._sputils,
+                   scipy.sparse._compressed, scipy.sparse._construct]
+
+        @functools.wraps(func)
+        def wrapper(*a, **kw):
+            try:
+                for mod in modules:
+                    backup.append((
+                        mod,
+                        'get_index_dtype',
+                        getattr(mod, 'get_index_dtype', None)
+                    ))
+                    setattr(mod, 'get_index_dtype', new_get_index_dtype)
+
+                    if downcast_maxval is not None:
+                        backup.append((
+                            mod,
+                            'downcast_intp_index',
+                            getattr(mod, 'downcast_intp_index', None)
+                        ))
+                        setattr(mod, 'downcast_intp_index', new_downcast_intp_index)
+
+                return func(*a, **kw)
+            finally:
+                for mod, name, oldfunc in backup:
+                    if oldfunc is not None:
+                        setattr(mod, name, oldfunc)
+        return wrapper
+    return decorator
+
+
+def toarray(a):
+    if isinstance(a, np.ndarray) or isscalarlike(a):
+        return a
+    return a.toarray()
+
+
+class BinopTester:
+    # Custom type to test binary operations on sparse matrices.
+
+    def __add__(self, mat):
+        return "matrix on the right"
+
+    def __mul__(self, mat):
+        return "matrix on the right"
+
+    def __sub__(self, mat):
+        return "matrix on the right"
+
+    def __radd__(self, mat):
+        return "matrix on the left"
+
+    def __rmul__(self, mat):
+        return "matrix on the left"
+
+    def __rsub__(self, mat):
+        return "matrix on the left"
+
+    def __matmul__(self, mat):
+        return "matrix on the right"
+
+    def __rmatmul__(self, mat):
+        return "matrix on the left"
+
+class BinopTester_with_shape:
+    # Custom type to test binary operations on sparse matrices
+    # with object which has shape attribute.
+    def __init__(self,shape):
+        self._shape = shape
+
+    def shape(self):
+        return self._shape
+
+    def ndim(self):
+        return len(self._shape)
+
+    def __add__(self, mat):
+        return "matrix on the right"
+
+    def __mul__(self, mat):
+        return "matrix on the right"
+
+    def __sub__(self, mat):
+        return "matrix on the right"
+
+    def __radd__(self, mat):
+        return "matrix on the left"
+
+    def __rmul__(self, mat):
+        return "matrix on the left"
+
+    def __rsub__(self, mat):
+        return "matrix on the left"
+
+    def __matmul__(self, mat):
+        return "matrix on the right"
+
+    def __rmatmul__(self, mat):
+        return "matrix on the left"
+
+class ComparisonTester:
+    # Custom type to test comparison operations on sparse matrices.
+    def __eq__(self, other):
+        return "eq"
+
+    def __ne__(self, other):
+        return "ne"
+
+    def __lt__(self, other):
+        return "lt"
+
+    def __le__(self, other):
+        return "le"
+
+    def __gt__(self, other):
+        return "gt"
+
+    def __ge__(self, other):
+        return "ge"
+
+
+#------------------------------------------------------------------------------
+# Generic tests
+#------------------------------------------------------------------------------
+
+
+class _MatrixMixin:
+    """mixin to easily allow tests of both sparray and spmatrix"""
+    bsr_container = bsr_matrix
+    coo_container = coo_matrix
+    csc_container = csc_matrix
+    csr_container = csr_matrix
+    dia_container = dia_matrix
+    dok_container = dok_matrix
+    lil_container = lil_matrix
+    asdense = staticmethod(asmatrix)
+
+    def test_getrow(self):
+        assert_array_equal(self.datsp.getrow(1).toarray(), self.dat[[1], :])
+        assert_array_equal(self.datsp.getrow(-1).toarray(), self.dat[[-1], :])
+
+    def test_getcol(self):
+        assert_array_equal(self.datsp.getcol(1).toarray(), self.dat[:, [1]])
+        assert_array_equal(self.datsp.getcol(-1).toarray(), self.dat[:, [-1]])
+
+    def test_asfptype(self):
+        A = self.spcreator(arange(6,dtype='int32').reshape(2,3))
+
+        assert_equal(A.asfptype().dtype, np.dtype('float64'))
+        assert_equal(A.asfptype().format, A.format)
+        assert_equal(A.astype('int16').asfptype().dtype, np.dtype('float32'))
+        assert_equal(A.astype('complex128').asfptype().dtype, np.dtype('complex128'))
+
+        B = A.asfptype()
+        C = B.asfptype()
+        assert_(B is C)
+
+
+# TODO test prune
+# TODO test has_sorted_indices
+class _TestCommon:
+    """test common functionality shared by all sparse formats"""
+    math_dtypes = supported_dtypes
+
+    bsr_container = bsr_array
+    coo_container = coo_array
+    csc_container = csc_array
+    csr_container = csr_array
+    dia_container = dia_array
+    dok_container = dok_array
+    lil_container = lil_array
+    asdense = array
+
+    @classmethod
+    def init_class(cls):
+        # Canonical data.
+        cls.dat = array([[1, 0, 0, 2], [3, 0, 1, 0], [0, 2, 0, 0]], 'd')
+        cls.datsp = cls.spcreator(cls.dat)
+
+        # Some sparse and dense matrices with data for every supported dtype.
+        # This set union is a workaround for numpy#6295, which means that
+        # two np.int64 dtypes don't hash to the same value.
+        cls.checked_dtypes = set(supported_dtypes).union(cls.math_dtypes)
+        cls.dat_dtypes = {}
+        cls.datsp_dtypes = {}
+        for dtype in cls.checked_dtypes:
+            cls.dat_dtypes[dtype] = cls.dat.astype(dtype)
+            cls.datsp_dtypes[dtype] = cls.spcreator(cls.dat.astype(dtype))
+
+        # Check that the original data is equivalent to the
+        # corresponding dat_dtypes & datsp_dtypes.
+        assert_equal(cls.dat, cls.dat_dtypes[np.float64])
+        assert_equal(cls.datsp.toarray(),
+                     cls.datsp_dtypes[np.float64].toarray())
+
+        cls.is_array_test = isinstance(cls.datsp, sparray)
+
+    def test_bool(self):
+        def check(dtype):
+            datsp = self.datsp_dtypes[dtype]
+
+            assert_raises(ValueError, bool, datsp)
+            assert_(self.spcreator([[1]]))
+            assert_(not self.spcreator([[0]]))
+
+        if isinstance(self, TestDOK):
+            pytest.skip("Cannot create a rank <= 2 DOK matrix.")
+        for dtype in self.checked_dtypes:
+            check(dtype)
+
+    def test_bool_rollover(self):
+        # bool's underlying dtype is 1 byte, check that it does not
+        # rollover True -> False at 256.
+        dat = array([[True, False]])
+        datsp = self.spcreator(dat)
+
+        for _ in range(10):
+            datsp = datsp + datsp
+            dat = dat + dat
+        assert_array_equal(dat, datsp.toarray())
+
+    def test_eq(self):
+
+        def check(dtype):
+            with warnings.catch_warnings():
+                warnings.simplefilter("ignore", SparseEfficiencyWarning)
+                warnings.simplefilter("ignore", ComplexWarning)
+                dat = self.dat_dtypes[dtype]
+                datsp = self.datsp_dtypes[dtype]
+                dat2 = dat.copy()
+                dat2[:,0] = 0
+                datsp2 = self.spcreator(dat2)
+                datbsr = self.bsr_container(dat)
+                datcsr = self.csr_container(dat)
+                datcsc = self.csc_container(dat)
+                datlil = self.lil_container(dat)
+
+                # sparse/sparse
+                assert_array_equal_dtype(dat == dat2, (datsp == datsp2).toarray())
+                # mix sparse types
+                assert_array_equal_dtype(dat == dat2, (datbsr == datsp2).toarray())
+                assert_array_equal_dtype(dat == dat2, (datcsr == datsp2).toarray())
+                assert_array_equal_dtype(dat == dat2, (datcsc == datsp2).toarray())
+                assert_array_equal_dtype(dat == dat2, (datlil == datsp2).toarray())
+                # sparse/dense
+                assert_array_equal_dtype(dat == datsp2, datsp2 == dat)
+                # sparse/scalar
+                assert_array_equal_dtype(dat == 0, (datsp == 0).toarray())
+                assert_array_equal_dtype(dat == 1, (datsp == 1).toarray())
+                assert_array_equal_dtype(dat == np.nan,
+                                         (datsp == np.nan).toarray())
+
+        if self.datsp.format not in ['bsr', 'csc', 'csr']:
+            pytest.skip("Bool comparisons only implemented for BSR, CSC, and CSR.")
+        for dtype in self.checked_dtypes:
+            check(dtype)
+
+    def test_ne(self):
+        def check(dtype):
+            with warnings.catch_warnings():
+                warnings.simplefilter("ignore", SparseEfficiencyWarning)
+                warnings.simplefilter("ignore", ComplexWarning)
+                dat = self.dat_dtypes[dtype]
+                datsp = self.datsp_dtypes[dtype]
+                dat2 = dat.copy()
+                dat2[:,0] = 0
+                datsp2 = self.spcreator(dat2)
+                datbsr = self.bsr_container(dat)
+                datcsc = self.csc_container(dat)
+                datcsr = self.csr_container(dat)
+                datlil = self.lil_container(dat)
+
+                # sparse/sparse
+                assert_array_equal_dtype(dat != dat2, (datsp != datsp2).toarray())
+                # mix sparse types
+                assert_array_equal_dtype(dat != dat2, (datbsr != datsp2).toarray())
+                assert_array_equal_dtype(dat != dat2, (datcsc != datsp2).toarray())
+                assert_array_equal_dtype(dat != dat2, (datcsr != datsp2).toarray())
+                assert_array_equal_dtype(dat != dat2, (datlil != datsp2).toarray())
+                # sparse/dense
+                assert_array_equal_dtype(dat != datsp2, datsp2 != dat)
+                # sparse/scalar
+                assert_array_equal_dtype(dat != 0, (datsp != 0).toarray())
+                assert_array_equal_dtype(dat != 1, (datsp != 1).toarray())
+                assert_array_equal_dtype(0 != dat, (0 != datsp).toarray())
+                assert_array_equal_dtype(1 != dat, (1 != datsp).toarray())
+                assert_array_equal_dtype(dat != np.nan,
+                                         (datsp != np.nan).toarray())
+
+        if self.datsp.format not in ['bsr', 'csc', 'csr']:
+            pytest.skip("Bool comparisons only implemented for BSR, CSC, and CSR.")
+        for dtype in self.checked_dtypes:
+            check(dtype)
+
+    def test_eq_ne_different_shapes(self):
+        if self.datsp.format not in ['bsr', 'csc', 'csr']:
+            pytest.skip("Bool comparisons only implemented for BSR, CSC, and CSR.")
+        # Is this what we want? numpy raises when shape differs. we return False.
+        assert (self.datsp == self.datsp.T) is False
+        assert (self.datsp != self.datsp.T) is True
+
+    def test_lt(self):
+        def check(dtype):
+            with warnings.catch_warnings():
+                warnings.simplefilter("ignore", SparseEfficiencyWarning)
+                warnings.simplefilter("ignore", ComplexWarning)
+                # data
+                dat = self.dat_dtypes[dtype]
+                datsp = self.datsp_dtypes[dtype]
+                dat2 = dat.copy()
+                dat2[:,0] = 0
+                datsp2 = self.spcreator(dat2)
+                datcomplex = dat.astype(complex)
+                datcomplex[:,0] = 1 + 1j
+                datspcomplex = self.spcreator(datcomplex)
+                datbsr = self.bsr_container(dat)
+                datcsc = self.csc_container(dat)
+                datcsr = self.csr_container(dat)
+                datlil = self.lil_container(dat)
+
+                # sparse/sparse
+                assert_array_equal_dtype(dat < dat2, (datsp < datsp2).toarray())
+                assert_array_equal_dtype(datcomplex < dat2,
+                                         (datspcomplex < datsp2).toarray())
+                # mix sparse types
+                assert_array_equal_dtype(dat < dat2, (datbsr < datsp2).toarray())
+                assert_array_equal_dtype(dat < dat2, (datcsc < datsp2).toarray())
+                assert_array_equal_dtype(dat < dat2, (datcsr < datsp2).toarray())
+                assert_array_equal_dtype(dat < dat2, (datlil < datsp2).toarray())
+
+                assert_array_equal_dtype(dat2 < dat, (datsp2 < datbsr).toarray())
+                assert_array_equal_dtype(dat2 < dat, (datsp2 < datcsc).toarray())
+                assert_array_equal_dtype(dat2 < dat, (datsp2 < datcsr).toarray())
+                assert_array_equal_dtype(dat2 < dat, (datsp2 < datlil).toarray())
+                # sparse/dense
+                assert_array_equal_dtype(dat < dat2, datsp < dat2)
+                assert_array_equal_dtype(datcomplex < dat2, datspcomplex < dat2)
+                # sparse/scalar
+                for val in [2, 1, 0, -1, -2]:
+                    val = np.int64(val)  # avoid Python scalar (due to NEP 50 changes)
+                    assert_array_equal_dtype((datsp < val).toarray(), dat < val)
+                    assert_array_equal_dtype((val < datsp).toarray(), val < dat)
+
+                with np.errstate(invalid='ignore'):
+                    assert_array_equal_dtype((datsp < np.nan).toarray(),
+                                             dat < np.nan)
+
+                # data
+                dat = self.dat_dtypes[dtype]
+                datsp = self.datsp_dtypes[dtype]
+                dat2 = dat.copy()
+                dat2[:,0] = 0
+                datsp2 = self.spcreator(dat2)
+
+                # dense rhs
+                assert_array_equal_dtype(dat < datsp2, datsp < dat2)
+
+        if self.datsp.format not in ['bsr', 'csc', 'csr']:
+            pytest.skip("Bool comparisons only implemented for BSR, CSC, and CSR.")
+        for dtype in self.checked_dtypes:
+            check(dtype)
+
+    def test_gt(self):
+        def check(dtype):
+            with warnings.catch_warnings():
+                warnings.simplefilter("ignore", SparseEfficiencyWarning)
+                warnings.simplefilter("ignore", ComplexWarning)
+                dat = self.dat_dtypes[dtype]
+                datsp = self.datsp_dtypes[dtype]
+                dat2 = dat.copy()
+                dat2[:,0] = 0
+                datsp2 = self.spcreator(dat2)
+                datcomplex = dat.astype(complex)
+                datcomplex[:,0] = 1 + 1j
+                datspcomplex = self.spcreator(datcomplex)
+                datbsr = self.bsr_container(dat)
+                datcsc = self.csc_container(dat)
+                datcsr = self.csr_container(dat)
+                datlil = self.lil_container(dat)
+
+                # sparse/sparse
+                assert_array_equal_dtype(dat > dat2, (datsp > datsp2).toarray())
+                assert_array_equal_dtype(datcomplex > dat2,
+                                         (datspcomplex > datsp2).toarray())
+                # mix sparse types
+                assert_array_equal_dtype(dat > dat2, (datbsr > datsp2).toarray())
+                assert_array_equal_dtype(dat > dat2, (datcsc > datsp2).toarray())
+                assert_array_equal_dtype(dat > dat2, (datcsr > datsp2).toarray())
+                assert_array_equal_dtype(dat > dat2, (datlil > datsp2).toarray())
+
+                assert_array_equal_dtype(dat2 > dat, (datsp2 > datbsr).toarray())
+                assert_array_equal_dtype(dat2 > dat, (datsp2 > datcsc).toarray())
+                assert_array_equal_dtype(dat2 > dat, (datsp2 > datcsr).toarray())
+                assert_array_equal_dtype(dat2 > dat, (datsp2 > datlil).toarray())
+                # sparse/dense
+                assert_array_equal_dtype(dat > dat2, datsp > dat2)
+                assert_array_equal_dtype(datcomplex > dat2, datspcomplex > dat2)
+                # sparse/scalar
+                for val in [2, 1, 0, -1, -2]:
+                    val = np.int64(val)  # avoid Python scalar (due to NEP 50 changes)
+                    assert_array_equal_dtype((datsp > val).toarray(), dat > val)
+                    assert_array_equal_dtype((val > datsp).toarray(), val > dat)
+
+                with np.errstate(invalid='ignore'):
+                    assert_array_equal_dtype((datsp > np.nan).toarray(),
+                                             dat > np.nan)
+
+                # data
+                dat = self.dat_dtypes[dtype]
+                datsp = self.datsp_dtypes[dtype]
+                dat2 = dat.copy()
+                dat2[:,0] = 0
+                datsp2 = self.spcreator(dat2)
+
+                # dense rhs
+                assert_array_equal_dtype(dat > datsp2, datsp > dat2)
+
+        if self.datsp.format not in ['bsr', 'csc', 'csr']:
+            pytest.skip("Bool comparisons only implemented for BSR, CSC, and CSR.")
+        for dtype in self.checked_dtypes:
+            check(dtype)
+
+    def test_le(self):
+        def check(dtype):
+            with warnings.catch_warnings():
+                warnings.simplefilter("ignore", SparseEfficiencyWarning)
+                warnings.simplefilter("ignore", ComplexWarning)
+                dat = self.dat_dtypes[dtype]
+                datsp = self.datsp_dtypes[dtype]
+                dat2 = dat.copy()
+                dat2[:,0] = 0
+                datsp2 = self.spcreator(dat2)
+                datcomplex = dat.astype(complex)
+                datcomplex[:,0] = 1 + 1j
+                datspcomplex = self.spcreator(datcomplex)
+                datbsr = self.bsr_container(dat)
+                datcsc = self.csc_container(dat)
+                datcsr = self.csr_container(dat)
+                datlil = self.lil_container(dat)
+
+                # sparse/sparse
+                assert_array_equal_dtype(dat <= dat2, (datsp <= datsp2).toarray())
+                assert_array_equal_dtype(datcomplex <= dat2,
+                                         (datspcomplex <= datsp2).toarray())
+                # mix sparse types
+                assert_array_equal_dtype((datbsr <= datsp2).toarray(), dat <= dat2)
+                assert_array_equal_dtype((datcsc <= datsp2).toarray(), dat <= dat2)
+                assert_array_equal_dtype((datcsr <= datsp2).toarray(), dat <= dat2)
+                assert_array_equal_dtype((datlil <= datsp2).toarray(), dat <= dat2)
+
+                assert_array_equal_dtype((datsp2 <= datbsr).toarray(), dat2 <= dat)
+                assert_array_equal_dtype((datsp2 <= datcsc).toarray(), dat2 <= dat)
+                assert_array_equal_dtype((datsp2 <= datcsr).toarray(), dat2 <= dat)
+                assert_array_equal_dtype((datsp2 <= datlil).toarray(), dat2 <= dat)
+                # sparse/dense
+                assert_array_equal_dtype(datsp <= dat2, dat <= dat2)
+                assert_array_equal_dtype(datspcomplex <= dat2, datcomplex <= dat2)
+                # sparse/scalar
+                for val in [2, 1, -1, -2]:
+                    val = np.int64(val)  # avoid Python scalar (due to NEP 50 changes)
+                    assert_array_equal_dtype((datsp <= val).toarray(), dat <= val)
+                    assert_array_equal_dtype((val <= datsp).toarray(), val <= dat)
+
+                # data
+                dat = self.dat_dtypes[dtype]
+                datsp = self.datsp_dtypes[dtype]
+                dat2 = dat.copy()
+                dat2[:,0] = 0
+                datsp2 = self.spcreator(dat2)
+
+                # dense rhs
+                assert_array_equal_dtype(dat <= datsp2, datsp <= dat2)
+
+        if self.datsp.format not in ['bsr', 'csc', 'csr']:
+            pytest.skip("Bool comparisons only implemented for BSR, CSC, and CSR.")
+        for dtype in self.checked_dtypes:
+            check(dtype)
+
+    def test_ge(self):
+        def check(dtype):
+            with warnings.catch_warnings():
+                warnings.simplefilter("ignore", SparseEfficiencyWarning)
+                warnings.simplefilter("ignore", ComplexWarning)
+                dat = self.dat_dtypes[dtype]
+                datsp = self.datsp_dtypes[dtype]
+                dat2 = dat.copy()
+                dat2[:,0] = 0
+                datsp2 = self.spcreator(dat2)
+                datcomplex = dat.astype(complex)
+                datcomplex[:,0] = 1 + 1j
+                datspcomplex = self.spcreator(datcomplex)
+                datbsr = self.bsr_container(dat)
+                datcsc = self.csc_container(dat)
+                datcsr = self.csr_container(dat)
+                datlil = self.lil_container(dat)
+
+                # sparse/sparse
+                assert_array_equal_dtype(dat >= dat2, (datsp >= datsp2).toarray())
+                assert_array_equal_dtype(datcomplex >= dat2,
+                                         (datspcomplex >= datsp2).toarray())
+                # mix sparse types
+                assert_array_equal_dtype((datbsr >= datsp2).toarray(), dat >= dat2)
+                assert_array_equal_dtype((datcsc >= datsp2).toarray(), dat >= dat2)
+                assert_array_equal_dtype((datcsr >= datsp2).toarray(), dat >= dat2)
+                assert_array_equal_dtype((datlil >= datsp2).toarray(), dat >= dat2)
+
+                assert_array_equal_dtype((datsp2 >= datbsr).toarray(), dat2 >= dat)
+                assert_array_equal_dtype((datsp2 >= datcsc).toarray(), dat2 >= dat)
+                assert_array_equal_dtype((datsp2 >= datcsr).toarray(), dat2 >= dat)
+                assert_array_equal_dtype((datsp2 >= datlil).toarray(), dat2 >= dat)
+                # sparse/dense
+                assert_array_equal_dtype(datsp >= dat2, dat >= dat2)
+                assert_array_equal_dtype(datspcomplex >= dat2, datcomplex >= dat2)
+                # sparse/scalar
+                for val in [2, 1, -1, -2]:
+                    val = np.int64(val)  # avoid Python scalar (due to NEP 50 changes)
+                    assert_array_equal_dtype((datsp >= val).toarray(), dat >= val)
+                    assert_array_equal_dtype((val >= datsp).toarray(), val >= dat)
+
+                # dense data
+                dat = self.dat_dtypes[dtype]
+                datsp = self.datsp_dtypes[dtype]
+                dat2 = dat.copy()
+                dat2[:,0] = 0
+                datsp2 = self.spcreator(dat2)
+
+                # dense rhs
+                assert_array_equal_dtype(dat >= datsp2, datsp >= dat2)
+
+        if self.datsp.format not in ['bsr', 'csc', 'csr']:
+            pytest.skip("Bool comparisons only implemented for BSR, CSC, and CSR.")
+        for dtype in self.checked_dtypes:
+            check(dtype)
+
+    def test_empty(self):
+        # create empty matrices
+        assert_equal(self.spcreator((3, 3)).toarray(), zeros((3, 3)))
+        assert_equal(self.spcreator((3, 3)).nnz, 0)
+        assert_equal(self.spcreator((3, 3)).count_nonzero(), 0)
+        if self.datsp.format != "dia":
+            assert_equal(self.spcreator((3, 3)).count_nonzero(axis=0), array([0, 0, 0]))
+
+    def test_count_nonzero(self):
+        axis_support = self.datsp.format != "dia"
+        axes = [None, 0, 1, -1, -2] if axis_support else [None]
+
+        for A in (self.datsp, self.datsp.T):
+            for ax in axes:
+                expected = np.count_nonzero(A.toarray(), axis=ax)
+                assert_equal(A.count_nonzero(axis=ax), expected)
+
+        if not axis_support:
+            with assert_raises(NotImplementedError, match="not implemented .* format"):
+                self.datsp.count_nonzero(axis=0)
+
+    def test_invalid_shapes(self):
+        assert_raises(ValueError, self.spcreator, (-1,3))
+        assert_raises(ValueError, self.spcreator, (3,-1))
+        assert_raises(ValueError, self.spcreator, (-1,-1))
+
+    def test_repr(self):
+        datsp = self.spcreator([[1, 0, 0], [0, 0, 0], [0, 0, -2]])
+        extra = (
+            "(1 diagonals) " if datsp.format == "dia"
+            else "(blocksize=1x1) " if datsp.format == "bsr"
+            else ""
+        )
+        _, fmt = _formats[datsp.format]
+        sparse_cls = "array" if self.is_array_test else "matrix"
+        expected = (
+            f"<{fmt} sparse {sparse_cls} of dtype '{datsp.dtype}'\n"
+            f"\twith {datsp.nnz} stored elements {extra}and shape {datsp.shape}>"
+        )
+        assert repr(datsp) == expected
+
+    def test_str_maxprint(self):
+        datsp = self.spcreator(np.arange(75).reshape(5, 15))
+        assert datsp.maxprint == 50
+        assert len(str(datsp).split('\n')) == 51 + 3
+
+        dat = np.arange(15).reshape(5,3)
+        datsp = self.spcreator(dat)
+        # format dia reports nnz=15, but we want 14
+        nnz_small = 14 if datsp.format == 'dia' else datsp.nnz
+        datsp_mp6 = self.spcreator(dat, maxprint=6)
+
+        assert len(str(datsp).split('\n')) == nnz_small + 3
+        assert len(str(datsp_mp6).split('\n')) == 6 + 4
+
+        # Check parameter `maxprint` is keyword only
+        datsp = self.spcreator(dat, shape=(5, 3), dtype='i', copy=False, maxprint=4)
+        datsp = self.spcreator(dat, (5, 3), 'i', False, maxprint=4)
+        with pytest.raises(TypeError, match="positional argument|unpack non-iterable"):
+            self.spcreator(dat, (5, 3), 'i', False, 4)
+
+    def test_str(self):
+        datsp = self.spcreator([[1, 0, 0], [0, 0, 0], [0, 0, -2]])
+        if datsp.nnz != 2:
+            return
+        extra = (
+            "(1 diagonals) " if datsp.format == "dia"
+            else "(blocksize=1x1) " if datsp.format == "bsr"
+            else ""
+        )
+        _, fmt = _formats[datsp.format]
+        sparse_cls = "array" if self.is_array_test else "matrix"
+        expected = (
+            f"<{fmt} sparse {sparse_cls} of dtype '{datsp.dtype}'\n"
+            f"\twith {datsp.nnz} stored elements {extra}and shape {datsp.shape}>"
+            "\n  Coords\tValues"
+            "\n  (0, 0)\t1"
+            "\n  (2, 2)\t-2"
+        )
+        assert str(datsp) == expected
+
+    def test_empty_arithmetic(self):
+        # Test manipulating empty matrices. Fails in SciPy SVN <= r1768
+        shape = (5, 5)
+        for mytype in [np.dtype('int32'), np.dtype('float32'),
+                np.dtype('float64'), np.dtype('complex64'),
+                np.dtype('complex128')]:
+            a = self.spcreator(shape, dtype=mytype)
+            b = a + a
+            c = 2 * a
+            d = a @ a.tocsc()
+            e = a @ a.tocsr()
+            f = a @ a.tocoo()
+            for m in [a,b,c,d,e,f]:
+                assert_equal(m.toarray(), a.toarray()@a.toarray())
+                # These fail in all revisions <= r1768:
+                assert_equal(m.dtype,mytype)
+                assert_equal(m.toarray().dtype,mytype)
+
+    def test_abs(self):
+        A = array([[-1, 0, 17], [0, -5, 0], [1, -4, 0], [0, 0, 0]], 'd')
+        assert_equal(abs(A), abs(self.spcreator(A)).toarray())
+
+    def test_round(self):
+        decimal = 1
+        A = array([[-1.35, 0.56], [17.25, -5.98]], 'd')
+        assert_equal(np.around(A, decimals=decimal),
+                     round(self.spcreator(A), ndigits=decimal).toarray())
+
+    def test_elementwise_power(self):
+        A = array([[-4, -3, -2], [-1, 0, 1], [2, 3, 4]], 'd')
+        assert_equal(np.power(A, 2), self.spcreator(A).power(2).toarray())
+
+        #it's element-wise power function, input has to be a scalar
+        assert_raises(NotImplementedError, self.spcreator(A).power, A)
+
+    def test_neg(self):
+        A = array([[-1, 0, 17], [0, -5, 0], [1, -4, 0], [0, 0, 0]], 'd')
+        assert_equal(-A, (-self.spcreator(A)).toarray())
+
+        # see gh-5843
+        A = array([[True, False, False], [False, False, True]])
+        assert_raises(NotImplementedError, self.spcreator(A).__neg__)
+
+    def test_real(self):
+        D = array([[1 + 3j, 2 - 4j]])
+        A = self.spcreator(D)
+        assert_equal(A.real.toarray(), D.real)
+
+    def test_imag(self):
+        D = array([[1 + 3j, 2 - 4j]])
+        A = self.spcreator(D)
+        assert_equal(A.imag.toarray(), D.imag)
+
+    def test_diagonal(self):
+        # Does the matrix's .diagonal() method work?
+        mats = []
+        mats.append([[1,0,2]])
+        mats.append([[1],[0],[2]])
+        mats.append([[0,1],[0,2],[0,3]])
+        mats.append([[0,0,1],[0,0,2],[0,3,0]])
+        mats.append([[1,0],[0,0]])
+
+        mats.append(kron(mats[0],[[1,2]]))
+        mats.append(kron(mats[0],[[1],[2]]))
+        mats.append(kron(mats[1],[[1,2],[3,4]]))
+        mats.append(kron(mats[2],[[1,2],[3,4]]))
+        mats.append(kron(mats[3],[[1,2],[3,4]]))
+        mats.append(kron(mats[3],[[1,2,3,4]]))
+
+        for m in mats:
+            rows, cols = array(m).shape
+            sparse_mat = self.spcreator(m)
+            for k in range(-rows-1, cols+2):
+                assert_equal(sparse_mat.diagonal(k=k), diag(m, k=k))
+            # Test for k beyond boundaries(issue #11949)
+            assert_equal(sparse_mat.diagonal(k=10), diag(m, k=10))
+            assert_equal(sparse_mat.diagonal(k=-99), diag(m, k=-99))
+
+        # Test all-zero matrix.
+        assert_equal(self.spcreator((40, 16130)).diagonal(), np.zeros(40))
+        # Test empty matrix
+        # https://github.com/scipy/scipy/issues/11949
+        assert_equal(self.spcreator((0, 0)).diagonal(), np.empty(0))
+        assert_equal(self.spcreator((15, 0)).diagonal(), np.empty(0))
+        assert_equal(self.spcreator((0, 5)).diagonal(10), np.empty(0))
+
+    def test_trace(self):
+        # For square matrix
+        A = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
+        B = self.spcreator(A)
+        for k in range(-2, 3):
+            assert_equal(A.trace(offset=k), B.trace(offset=k))
+
+        # For rectangular matrix
+        A = np.array([[1, 2, 3], [4, 5, 6]])
+        B = self.spcreator(A)
+        for k in range(-1, 3):
+            assert_equal(A.trace(offset=k), B.trace(offset=k))
+
+    def test_reshape(self):
+        x = self.spcreator([[1, 0, 7], [0, 0, 0], [0, 3, 0], [0, 0, 5]])
+        for order in ['C', 'F']:
+            for s in [(12, 1), (1, 12)]:
+                assert_array_equal(x.reshape(s, order=order).toarray(),
+                                   x.toarray().reshape(s, order=order))
+
+        # This example is taken from the stackoverflow answer at
+        # https://stackoverflow.com/q/16511879
+        x = self.spcreator([[0, 10, 0, 0], [0, 0, 0, 0], [0, 20, 30, 40]])
+        y = x.reshape((2, 6))  # Default order is 'C'
+        desired = [[0, 10, 0, 0, 0, 0], [0, 0, 0, 20, 30, 40]]
+        assert_array_equal(y.toarray(), desired)
+
+        # Reshape with negative indexes
+        y = x.reshape((2, -1))
+        assert_array_equal(y.toarray(), desired)
+        y = x.reshape((-1, 6))
+        assert_array_equal(y.toarray(), desired)
+        assert_raises(ValueError, x.reshape, (-1, -1))
+
+        # Reshape with star args
+        y = x.reshape(2, 6)
+        assert_array_equal(y.toarray(), desired)
+        assert_raises(TypeError, x.reshape, 2, 6, not_an_arg=1)
+
+        # Reshape with same size is noop unless copy=True
+        y = x.reshape((3, 4))
+        assert_(y is x)
+        y = x.reshape((3, 4), copy=True)
+        assert_(y is not x)
+
+        # Ensure reshape did not alter original size
+        assert_array_equal(x.shape, (3, 4))
+
+        if self.is_array_test:
+            with assert_raises(AttributeError, match="has no setter|n't set attribute"):
+                x.shape = (2, 6)
+        else:  # spmatrix test
+            # Reshape in place
+            x.shape = (2, 6)
+            assert_array_equal(x.toarray(), desired)
+
+        # Reshape to bad ndim
+        assert_raises(ValueError, x.reshape, (x.size,))
+        assert_raises(ValueError, x.reshape, (1, x.size, 1))
+
+    @pytest.mark.slow
+    def test_setdiag_comprehensive(self):
+        def dense_setdiag(a, v, k):
+            v = np.asarray(v)
+            if k >= 0:
+                n = min(a.shape[0], a.shape[1] - k)
+                if v.ndim != 0:
+                    n = min(n, len(v))
+                    v = v[:n]
+                i = np.arange(0, n)
+                j = np.arange(k, k + n)
+                a[i,j] = v
+            elif k < 0:
+                dense_setdiag(a.T, v, -k)
+
+        def check_setdiag(a, b, k):
+            # Check setting diagonal using a scalar, a vector of
+            # correct length, and too short or too long vectors
+            for r in [-1, len(np.diag(a, k)), 2, 30]:
+                if r < 0:
+                    v = np.random.choice(range(1, 20))
+                else:
+                    v = np.random.randint(1, 20, size=r)
+
+                dense_setdiag(a, v, k)
+                with warnings.catch_warnings():
+                    warnings.filterwarnings("ignore", WMSG, SparseEfficiencyWarning)
+                    b.setdiag(v, k)
+
+                # check that dense_setdiag worked
+                d = np.diag(a, k)
+                if np.asarray(v).ndim == 0:
+                    assert_array_equal(d, v, err_msg="{msg} {r}")
+                else:
+                    n = min(len(d), len(v))
+                    assert_array_equal(d[:n], v[:n], err_msg="{msg} {r}")
+                # check that sparse setdiag worked
+                assert_array_equal(b.toarray(), a, err_msg="{msg} {r}")
+
+        # comprehensive test
+        np.random.seed(1234)
+        shapes = [(0,5), (5,0), (1,5), (5,1), (5,5)]
+        for dtype in [np.int8, np.float64]:
+            for m,n in shapes:
+                ks = np.arange(-m+1, n-1)
+                for k in ks:
+                    a = np.zeros((m, n), dtype=dtype)
+                    b = self.spcreator((m, n), dtype=dtype)
+
+                    check_setdiag(a, b, k)
+
+                    # check overwriting etc
+                    for k2 in np.random.choice(ks, size=min(len(ks), 5)):
+                        check_setdiag(a, b, k2)
+
+    def test_setdiag(self):
+        # simple test cases
+        m = self.spcreator(np.eye(3))
+        m2 = self.spcreator((4, 4))
+        values = [3, 2, 1]
+        with warnings.catch_warnings():
+            warnings.filterwarnings("ignore", WMSG, SparseEfficiencyWarning)
+            assert_raises(ValueError, m.setdiag, values, k=4)
+            m.setdiag(values)
+            assert_array_equal(m.diagonal(), values)
+            m.setdiag(values, k=1)
+            assert_array_equal(m.toarray(), np.array([[3, 3, 0],
+                                                      [0, 2, 2],
+                                                      [0, 0, 1]]))
+            m.setdiag(values, k=-2)
+            assert_array_equal(m.toarray(), np.array([[3, 3, 0],
+                                                      [0, 2, 2],
+                                                      [3, 0, 1]]))
+            m.setdiag((9,), k=2)
+            assert_array_equal(m.toarray()[0,2], 9)
+            m.setdiag((9,), k=-2)
+            assert_array_equal(m.toarray()[2,0], 9)
+            # test short values on an empty matrix
+            m2.setdiag([1], k=2)
+            assert_array_equal(m2.toarray()[0], [0, 0, 1, 0])
+            # test overwriting that same diagonal
+            m2.setdiag([1, 1], k=2)
+            assert_array_equal(m2.toarray()[:2], [[0, 0, 1, 0],
+                                                  [0, 0, 0, 1]])
+
+    def test_nonzero(self):
+        A = array([[1, 0, 1],[0, 1, 1],[0, 0, 1]])
+        Asp = self.spcreator(A)
+
+        A_nz = {tuple(ij) for ij in transpose(A.nonzero())}
+        Asp_nz = {tuple(ij) for ij in transpose(Asp.nonzero())}
+
+        assert_equal(A_nz, Asp_nz)
+
+    def test_numpy_nonzero(self):
+        # See gh-5987
+        A = array([[1, 0, 1], [0, 1, 1], [0, 0, 1]])
+        Asp = self.spcreator(A)
+
+        A_nz = {tuple(ij) for ij in transpose(np.nonzero(A))}
+        Asp_nz = {tuple(ij) for ij in transpose(np.nonzero(Asp))}
+
+        assert_equal(A_nz, Asp_nz)
+
+    def test_sum(self):
+        np.random.seed(1234)
+        dat_1 = np.array([[0, 1, 2],
+                        [3, -4, 5],
+                        [-6, 7, 9]])
+        dat_2 = np.random.rand(5, 5)
+        dat_3 = np.array([[]])
+        dat_4 = np.zeros((40, 40))
+        dat_5 = sparse.rand(5, 5, density=1e-2).toarray()
+        matrices = [dat_1, dat_2, dat_3, dat_4, dat_5]
+
+        def check(dtype, j):
+            dat = self.asdense(matrices[j], dtype=dtype)
+            datsp = self.spcreator(dat, dtype=dtype)
+            with np.errstate(over='ignore'):
+                assert_array_almost_equal(dat.sum(), datsp.sum())
+                assert_equal(dat.sum().dtype, datsp.sum().dtype)
+                assert_(np.isscalar(datsp.sum(axis=None)))
+                assert_array_almost_equal(dat.sum(axis=None), datsp.sum(axis=None))
+                assert_equal(dat.sum(axis=None).dtype, datsp.sum(axis=None).dtype)
+                assert_array_almost_equal(dat.sum(axis=0), datsp.sum(axis=0))
+                assert_equal(dat.sum(axis=0).dtype, datsp.sum(axis=0).dtype)
+                assert_array_almost_equal(dat.sum(axis=1), datsp.sum(axis=1))
+                assert_equal(dat.sum(axis=1).dtype, datsp.sum(axis=1).dtype)
+                assert_array_almost_equal(dat.sum(axis=-2), datsp.sum(axis=-2))
+                assert_equal(dat.sum(axis=-2).dtype, datsp.sum(axis=-2).dtype)
+                assert_array_almost_equal(dat.sum(axis=-1), datsp.sum(axis=-1))
+                assert_equal(dat.sum(axis=-1).dtype, datsp.sum(axis=-1).dtype)
+                assert_array_almost_equal(dat.sum(axis=(0, 1)), datsp.sum(axis=(0, 1)))
+                assert_equal(dat.sum(axis=(0, 1)).dtype, datsp.sum(axis=(0, 1)).dtype)
+
+        for dtype in self.checked_dtypes:
+            for j in range(len(matrices)):
+                check(dtype, j)
+
+    def test_sum_invalid_params(self):
+        out = np.zeros((1, 3))
+        dat = array([[0, 1, 2],
+                     [3, -4, 5],
+                     [-6, 7, 9]])
+        datsp = self.spcreator(dat)
+
+        with assert_raises(ValueError, match="axis out of range"):
+            datsp.sum(axis=3)
+        with assert_raises(ValueError, match="axis out of range"):
+            datsp.sum(axis=(0, 3))
+        with assert_raises(TypeError, match="axis must be an integer"):
+            datsp.sum(axis=1.5)
+        # error msg varies by sparray (1d result) or spmatrix (2d result)
+        with assert_raises(ValueError, match="do.*n.t match.*shape|wrong.*dimensions"):
+            datsp.mean(axis=1, out=out)
+
+    def test_sum_dtype(self):
+        dat = array([[0, 1, 2],
+                     [3, -4, 5],
+                     [-6, 7, 9]])
+        datsp = self.spcreator(dat)
+
+        def check(dtype):
+            dat_sum = dat.sum(dtype=dtype)
+            datsp_sum = datsp.sum(dtype=dtype)
+
+            assert_array_almost_equal(dat_sum, datsp_sum)
+            assert_equal(dat_sum.dtype, datsp_sum.dtype)
+
+        for dtype in self.checked_dtypes:
+            check(dtype)
+
+    def test_sum_dtype_pair_of_dtypes(self):
+        # Test sum with dtype on data of various input dtypes 
+        # to ensure elements are cast before summing
+        base_dat = array([[0.6, 0.7],
+                          [0.8, 0.9]])
+
+        for input_dtype in self.checked_dtypes:
+            dat = base_dat.astype(input_dtype)
+            datsp = self.spcreator(dat)
+
+            with warnings.catch_warnings():
+                warnings.filterwarnings("ignore", category=PendingDeprecationWarning)
+                if not self.is_array_test:
+                    dat = np.matrix(dat)
+
+            for output_dtype in self.checked_dtypes:
+                # Skip problematic dtype combinations (complex to real, etc.)
+                # by catching exceptions when numpy itself fails
+                try:
+                    with np.errstate(all='raise'):
+                        _ = dat.sum(dtype=output_dtype)
+                except Exception:
+                    # Skip this combination if NumPy can't handle it
+                    continue
+                
+                # Check axis=None
+                with np.errstate(over='ignore'):
+                    dat_sum = dat.sum(dtype=output_dtype)
+                    datsp_sum = datsp.sum(dtype=output_dtype)
+                    assert_allclose(datsp_sum, dat_sum)
+                    assert_equal(datsp_sum.dtype, dat_sum.dtype)
+
+                    # Check axis=0
+                    dat_sum = dat.sum(axis=0, dtype=output_dtype)
+                    datsp_sum = datsp.sum(axis=0, dtype=output_dtype)
+                    assert_allclose(datsp_sum, dat_sum)
+                    assert_equal(datsp_sum.dtype, dat_sum.dtype)
+
+                    # Check axis=1
+                    dat_sum = dat.sum(axis=1, dtype=output_dtype)
+                    datsp_sum = datsp.sum(axis=1, dtype=output_dtype)
+                    assert_allclose(datsp_sum, dat_sum)
+                    assert_equal(datsp_sum.dtype, dat_sum.dtype)
+
+    def test_sum_dtype_fractional_to_int(self):
+        # Test sum with dtype=int on data of float input dtype
+        # to ensure elements are cast before summing
+        datsp = self.spcreator([[0.6, 0.7],
+                          [0.8, 0.9]])
+        
+        correct_res = array([0, 0] if self.is_array_test else [[0, 0]])
+        t_correct_res = array([0, 0] if self.is_array_test else [[0], [0]])
+            
+        assert_equal(datsp.sum(dtype=int), 0) # Check axis=None
+        assert_equal(datsp.sum(axis=0, dtype=int), correct_res) # Check axis=0
+        assert_equal(datsp.sum(axis=1, dtype=int), t_correct_res) # Check axis=1
+
+    def test_sum_out(self):
+        keep = not self.is_array_test
+        dat = array([[0, 1, 2],
+                     [3, -4, 5],
+                     [-6, 7, 9]])
+        datsp = self.spcreator(dat)
+
+        dat_out = array(0) if self.is_array_test else array([[0]])
+        datsp_out = array(0) if self.is_array_test else matrix([[0]])
+
+        dat.sum(out=dat_out, keepdims=keep)
+        datsp.sum(out=datsp_out)
+        assert_array_almost_equal(dat_out, datsp_out)
+
+        dat_out = np.zeros((3,)) if self.is_array_test else np.zeros((3, 1))
+        datsp_out = np.zeros((3,)) if self.is_array_test else matrix(np.zeros((3, 1)))
+
+        dat.sum(axis=1, out=dat_out, keepdims=keep)
+        datsp.sum(axis=1, out=datsp_out)
+        assert_array_almost_equal(dat_out, datsp_out)
+
+        # check that wrong shape out parameter raises
+        with assert_raises(ValueError, match="output parameter"):
+            datsp.sum(out=array([0]))
+        with assert_raises(ValueError, match="output parameter"):
+            datsp.sum(out=array([[0]] if self.is_array_test else 0))
+
+    def test_numpy_sum(self):
+        # See gh-5987
+        dat = array([[0, 1, 2],
+                     [3, -4, 5],
+                     [-6, 7, 9]])
+        datsp = self.spcreator(dat)
+
+        dat_sum = np.sum(dat)
+        datsp_sum = np.sum(datsp)
+
+        assert_array_almost_equal(dat_sum, datsp_sum)
+        assert_equal(dat_sum.dtype, datsp_sum.dtype)
+
+    def test_sum_mean_container_type(self):
+        dat = array([[0, 1, 2],
+                     [3, -4, 5],
+                     [-6, 7, 9]])
+        datsp = self.spcreator(dat)
+
+        assert isscalarlike(datsp.sum())
+        matrix_or_array = ndarray if self.is_array_test else np.matrix
+        assert isinstance(datsp.sum(axis=0), matrix_or_array)
+        assert isinstance(datsp.sum(axis=1), matrix_or_array)
+
+        assert isscalarlike(datsp.mean())
+        assert isinstance(datsp.mean(axis=0), matrix_or_array)
+        assert isinstance(datsp.mean(axis=1), matrix_or_array)
+
+    def test_mean(self):
+        keep = not self.is_array_test
+        def check(dtype):
+            dat = array([[0, 1, 2],
+                         [3, 4, 5],
+                         [6, 7, 9]], dtype=dtype)
+            datsp = self.spcreator(dat, dtype=dtype)
+
+            assert_array_almost_equal(dat.mean(), datsp.mean())
+            assert_equal(dat.mean().dtype, datsp.mean().dtype)
+            assert_(np.isscalar(datsp.mean(axis=None)))
+            assert_array_almost_equal(
+                dat.mean(axis=None, keepdims=keep), datsp.mean(axis=None)
+            )
+            assert_equal(dat.mean(axis=None).dtype, datsp.mean(axis=None).dtype)
+            assert_array_almost_equal(
+                dat.mean(axis=0, keepdims=keep), datsp.mean(axis=0)
+            )
+            assert_equal(dat.mean(axis=0).dtype, datsp.mean(axis=0).dtype)
+            assert_array_almost_equal(
+                dat.mean(axis=1, keepdims=keep), datsp.mean(axis=1)
+            )
+            assert_equal(dat.mean(axis=1).dtype, datsp.mean(axis=1).dtype)
+            assert_array_almost_equal(
+                dat.mean(axis=-2, keepdims=keep), datsp.mean(axis=-2)
+            )
+            assert_equal(dat.mean(axis=-2).dtype, datsp.mean(axis=-2).dtype)
+            assert_array_almost_equal(
+                dat.mean(axis=-1, keepdims=keep), datsp.mean(axis=-1)
+            )
+            assert_equal(dat.mean(axis=-1).dtype, datsp.mean(axis=-1).dtype)
+            assert_array_almost_equal(
+                dat.mean(axis=(0, 1), keepdims=keep), datsp.mean(axis=(0, 1))
+            )
+            assert_equal(dat.mean(axis=(0, 1)).dtype, datsp.mean(axis=(0, 1)).dtype)
+
+
+        for dtype in self.checked_dtypes:
+            check(dtype)
+
+    def test_mean_invalid_param(self):
+        out = self.asdense(np.zeros((1, 3)))
+        dat = array([[0, 1, 2],
+                     [3, -4, 5],
+                     [-6, 7, 9]])
+        datsp = self.spcreator(dat)
+
+        with assert_raises(ValueError, match="axis out of range"):
+            datsp.mean(axis=3)
+        with assert_raises(ValueError, match="axis out of range"):
+            datsp.mean(axis=(0, 3))
+        with assert_raises(TypeError, match="axis must be an integer"):
+            datsp.mean(axis=1.5)
+        # error msg varies by sparray (1d result) or spmatrix (2d result)
+        with assert_raises(ValueError, match="do.*n.t match.*shape|wrong.*dimensions"):
+            datsp.mean(axis=1, out=out)
+
+    def test_mean_dtype(self):
+        dat = array([[0, 1, 2],
+                     [3, -4, 5],
+                     [-6, 7, 9]])
+        datsp = self.spcreator(dat)
+
+        def check(dtype):
+            dat_mean = dat.mean(dtype=dtype)
+            datsp_mean = datsp.mean(dtype=dtype)
+
+            assert_array_almost_equal(dat_mean, datsp_mean)
+            assert_equal(dat_mean.dtype, datsp_mean.dtype)
+
+        for dtype in self.checked_dtypes:
+            check(dtype)
+
+    def test_mean_out(self):
+        keep = not self.is_array_test
+        dat = array([[0, 1, 2],
+                     [3, -4, 5],
+                     [-6, 7, 9]])
+        datsp = self.spcreator(dat)
+
+        dat_out = array(0) if self.is_array_test else array([[0]])
+        datsp_out = array(0) if self.is_array_test else matrix([[0]])
+
+        dat.mean(out=dat_out, keepdims=keep)
+        datsp.mean(out=datsp_out)
+        assert_array_almost_equal(dat_out, datsp_out)
+
+        dat_out = np.zeros((3,)) if self.is_array_test else np.zeros((3, 1))
+        datsp_out = np.zeros((3,)) if self.is_array_test else matrix(np.zeros((3, 1)))
+
+        dat.mean(axis=1, out=dat_out, keepdims=keep)
+        datsp.mean(axis=1, out=datsp_out)
+        assert_array_almost_equal(dat_out, datsp_out)
+
+        # check that wrong shape out parameter raises
+        with assert_raises(ValueError, match="output parameter.*wrong.*dimension"):
+            datsp.mean(out=array([0]))
+        with assert_raises(ValueError, match="output parameter.*wrong.*dimension"):
+            datsp.mean(out=array([[0]] if self.is_array_test else 0))
+
+    def test_numpy_mean(self):
+        # See gh-5987
+        dat = array([[0, 1, 2],
+                     [3, -4, 5],
+                     [-6, 7, 9]])
+        datsp = self.spcreator(dat)
+
+        dat_mean = np.mean(dat)
+        datsp_mean = np.mean(datsp)
+
+        assert_array_almost_equal(dat_mean, datsp_mean)
+        assert_equal(dat_mean.dtype, datsp_mean.dtype)
+
+    def test_expm(self):
+        M = array([[1, 0, 2], [0, 0, 3], [-4, 5, 6]], float)
+        sM = self.spcreator(M, shape=(3,3), dtype=float)
+        Mexp = scipy.linalg.expm(M)
+
+        N = array([[3., 0., 1.], [0., 2., 0.], [0., 0., 0.]])
+        sN = self.spcreator(N, shape=(3,3), dtype=float)
+        Nexp = scipy.linalg.expm(N)
+
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore",
+                "splu converted its input to CSC format",
+                SparseEfficiencyWarning,
+            )
+            warnings.filterwarnings(
+                "ignore",
+                "spsolve is more efficient when sparse b is in the CSC matrix format",
+                SparseEfficiencyWarning,
+            )
+            warnings.filterwarnings(
+                "ignore",
+                "spsolve requires A be CSC or CSR matrix format",
+                SparseEfficiencyWarning,
+            )
+            sMexp = expm(sM).toarray()
+            sNexp = expm(sN).toarray()
+
+        assert_array_almost_equal((sMexp - Mexp), zeros((3, 3)))
+        assert_array_almost_equal((sNexp - Nexp), zeros((3, 3)))
+
+    def test_inv(self):
+        def check(dtype):
+            M = array([[1, 0, 2], [0, 0, 3], [-4, 5, 6]], dtype)
+            with warnings.catch_warnings():
+                warnings.filterwarnings(
+                    "ignore",
+                    "spsolve requires A be CSC or CSR matrix format",
+                    SparseEfficiencyWarning,
+                )
+                warnings.filterwarnings(
+                    "ignore",
+                    "spsolve is more efficient when sparse b "
+                    "is in the CSC matrix format",
+                    SparseEfficiencyWarning,
+                )
+                warnings.filterwarnings(
+                    "ignore",
+                    "splu converted its input to CSC format",
+                    SparseEfficiencyWarning,
+                )
+                sM = self.spcreator(M, shape=(3,3), dtype=dtype)
+                sMinv = inv(sM)
+            assert_array_almost_equal(sMinv.dot(sM).toarray(), np.eye(3))
+            assert_raises(TypeError, inv, M)
+        for dtype in [float]:
+            check(dtype)
+
+    def test_from_array(self):
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", ComplexWarning)
+            A = array([[1,0,0],[2,3,4],[0,5,0],[0,0,0]])
+            assert_array_equal(self.spcreator(A).toarray(), A)
+
+            A = array([[1.0 + 3j, 0, 0],
+                       [0, 2.0 + 5, 0],
+                       [0, 0, 0]])
+            assert_array_equal(self.spcreator(A).toarray(), A)
+            assert_array_equal(
+                self.spcreator(A, dtype='int16').toarray(),A.astype('int16'))
+
+
+    def test_from_matrix(self):
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", ComplexWarning)
+            A = self.asdense([[1, 0, 0], [2, 3, 4], [0, 5, 0], [0, 0, 0]])
+            assert_array_equal(self.spcreator(A).todense(), A)
+
+            A = self.asdense([[1.0 + 3j, 0, 0],
+                              [0, 2.0 + 5, 0],
+                              [0, 0, 0]])
+            assert_array_equal(self.spcreator(A).todense(), A)
+            assert_array_equal(
+                self.spcreator(A, dtype='int16').todense(), A.astype('int16')
+            )
+
+    def test_from_list(self):
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", ComplexWarning)
+            A = [[1,0,0],[2,3,4],[0,5,0],[0,0,0]]
+            assert_array_equal(self.spcreator(A).toarray(), A)
+
+            A = [[1.0 + 3j, 0, 0],
+                 [0, 2.0 + 5, 0],
+                 [0, 0, 0]]
+            assert_array_equal(self.spcreator(A).toarray(), array(A))
+            assert_array_equal(
+                self.spcreator(A, dtype='int16').toarray(), array(A).astype('int16')
+            )
+
+    def test_from_sparse(self):
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", ComplexWarning)
+            D = array([[1,0,0],[2,3,4],[0,5,0],[0,0,0]])
+            S = self.csr_container(D)
+            assert_array_equal(self.spcreator(S).toarray(), D)
+            S = self.spcreator(D)
+            assert_array_equal(self.spcreator(S).toarray(), D)
+
+            D = array([[1.0 + 3j, 0, 0],
+                       [0, 2.0 + 5, 0],
+                       [0, 0, 0]])
+            S = self.csr_container(D)
+            assert_array_equal(self.spcreator(S).toarray(), D)
+            assert_array_equal(self.spcreator(S, dtype='int16').toarray(),
+                               D.astype('int16'))
+            S = self.spcreator(D)
+            assert_array_equal(self.spcreator(S).toarray(), D)
+            assert_array_equal(self.spcreator(S, dtype='int16').toarray(),
+                               D.astype('int16'))
+
+    # def test_array(self):
+    #    """test array(A) where A is in sparse format"""
+    #    assert_equal( array(self.datsp), self.dat )
+
+    def test_todense(self):
+        # Check C- or F-contiguous (default).
+        chk = self.datsp.todense()
+        assert isinstance(chk, np.ndarray if self.is_array_test else np.matrix)
+        assert_array_equal(chk, self.dat)
+        assert_(chk.flags.c_contiguous != chk.flags.f_contiguous)
+        # Check C-contiguous (with arg).
+        chk = self.datsp.todense(order='C')
+        assert_array_equal(chk, self.dat)
+        assert_(chk.flags.c_contiguous)
+        assert_(not chk.flags.f_contiguous)
+        # Check F-contiguous (with arg).
+        chk = self.datsp.todense(order='F')
+        assert_array_equal(chk, self.dat)
+        assert_(not chk.flags.c_contiguous)
+        assert_(chk.flags.f_contiguous)
+        # Check with out argument (array).
+        out = np.zeros(self.datsp.shape, dtype=self.datsp.dtype)
+        chk = self.datsp.todense(out=out)
+        assert_array_equal(self.dat, out)
+        assert_array_equal(self.dat, chk)
+        assert np.may_share_memory(chk, out)
+        # Check with out array (matrix).
+        out = self.asdense(np.zeros(self.datsp.shape, dtype=self.datsp.dtype))
+        chk = self.datsp.todense(out=out)
+        assert_array_equal(self.dat, out)
+        assert_array_equal(self.dat, chk)
+        assert np.may_share_memory(chk, out)
+        a = array([[1.,2.,3.]])
+        dense_dot_dense = a @ self.dat
+        check = a @ self.datsp.todense()
+        assert_array_equal(dense_dot_dense, check)
+        b = array([[1.,2.,3.,4.]]).T
+        dense_dot_dense = self.dat @ b
+        check2 = self.datsp.todense() @ b
+        assert_array_equal(dense_dot_dense, check2)
+        # Check bool data works.
+        spbool = self.spcreator(self.dat, dtype=bool)
+        matbool = self.dat.astype(bool)
+        assert_array_equal(spbool.todense(), matbool)
+
+    def test_toarray(self):
+        # Check C- or F-contiguous (default).
+        dat = asarray(self.dat)
+        chk = self.datsp.toarray()
+        assert_array_equal(chk, dat)
+        assert_(chk.flags.c_contiguous != chk.flags.f_contiguous)
+        # Check C-contiguous (with arg).
+        chk = self.datsp.toarray(order='C')
+        assert_array_equal(chk, dat)
+        assert_(chk.flags.c_contiguous)
+        assert_(not chk.flags.f_contiguous)
+        # Check F-contiguous (with arg).
+        chk = self.datsp.toarray(order='F')
+        assert_array_equal(chk, dat)
+        assert_(not chk.flags.c_contiguous)
+        assert_(chk.flags.f_contiguous)
+        # Check with output arg.
+        out = np.zeros(self.datsp.shape, dtype=self.datsp.dtype)
+        self.datsp.toarray(out=out)
+        assert_array_equal(chk, dat)
+        # Check that things are fine when we don't initialize with zeros.
+        out[...] = 1.
+        self.datsp.toarray(out=out)
+        assert_array_equal(chk, dat)
+        a = array([1.,2.,3.])
+        dense_dot_dense = dot(a, dat)
+        check = dot(a, self.datsp.toarray())
+        assert_array_equal(dense_dot_dense, check)
+        b = array([1.,2.,3.,4.])
+        dense_dot_dense = dot(dat, b)
+        check2 = dot(self.datsp.toarray(), b)
+        assert_array_equal(dense_dot_dense, check2)
+        # Check bool data works.
+        spbool = self.spcreator(self.dat, dtype=bool)
+        arrbool = dat.astype(bool)
+        assert_array_equal(spbool.toarray(), arrbool)
+
+    def test_astype(self):
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", ComplexWarning)
+            D = array([[2.0 + 3j, 0, 0],
+                       [0, 4.0 + 5j, 0],
+                       [0, 0, 0]])
+            S = self.spcreator(D)
+
+            for x in supported_dtypes:
+                # Check correctly casted
+                D_casted = D.astype(x)
+                for copy in (True, False):
+                    S_casted = S.astype(x, copy=copy)
+                    assert_equal(S_casted.dtype, D_casted.dtype)  # correct type
+                    assert_equal(S_casted.toarray(), D_casted)    # correct values
+                    assert_equal(S_casted.format, S.format)       # format preserved
+                # Check correctly copied
+                assert_(S_casted.astype(x, copy=False) is S_casted)
+                S_copied = S_casted.astype(x, copy=True)
+                assert_(S_copied is not S_casted)
+
+                def check_equal_but_not_same_array_attribute(attribute):
+                    a = getattr(S_casted, attribute)
+                    b = getattr(S_copied, attribute)
+                    assert_array_equal(a, b)
+                    assert_(a is not b)
+                    i = (0,) * b.ndim
+                    b_i = b[i]
+                    b[i] = not b[i]
+                    assert_(a[i] != b[i])
+                    b[i] = b_i
+
+                if S_casted.format in ('csr', 'csc', 'bsr'):
+                    for attribute in ('indices', 'indptr', 'data'):
+                        check_equal_but_not_same_array_attribute(attribute)
+                elif S_casted.format == 'coo':
+                    for attribute in ('row', 'col', 'data'):
+                        check_equal_but_not_same_array_attribute(attribute)
+                elif S_casted.format == 'dia':
+                    for attribute in ('offsets', 'data'):
+                        check_equal_but_not_same_array_attribute(attribute)
+
+    def test_astype_immutable(self):
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", ComplexWarning)
+            D = array([[2.0 + 3j, 0, 0],
+                       [0, 4.0 + 5j, 0],
+                       [0, 0, 0]])
+            S = self.spcreator(D)
+            if hasattr(S, 'data'):
+                S.data.flags.writeable = False
+            if S.format in ('csr', 'csc', 'bsr'):
+                S.indptr.flags.writeable = False
+                S.indices.flags.writeable = False
+            for x in supported_dtypes:
+                D_casted = D.astype(x)
+                S_casted = S.astype(x)
+                assert_equal(S_casted.dtype, D_casted.dtype)
+
+    def test_mul_scalar(self):
+        def check(dtype):
+            dat = self.dat_dtypes[dtype]
+            datsp = self.datsp_dtypes[dtype]
+
+            assert_array_equal(dat*2, (datsp*2).toarray())
+            assert_array_equal(dat*17.3, (datsp*17.3).toarray())
+
+        for dtype in self.math_dtypes:
+            check(dtype)
+
+    def test_rmul_scalar(self):
+        def check(dtype):
+            dat = self.dat_dtypes[dtype]
+            datsp = self.datsp_dtypes[dtype]
+
+            assert_array_equal(2*dat, (2*datsp).toarray())
+            assert_array_equal(17.3*dat, (17.3*datsp).toarray())
+
+        for dtype in self.math_dtypes:
+            check(dtype)
+
+    # GitHub issue #15210
+    def test_rmul_scalar_type_error(self):
+        datsp = self.datsp_dtypes[np.float64]
+        with assert_raises(TypeError):
+            None * datsp
+
+    def test_add(self):
+        def check(dtype):
+            dat = self.dat_dtypes[dtype]
+            datsp = self.datsp_dtypes[dtype]
+
+            a = dat.copy()
+            a[0,2] = 2.0
+            b = datsp
+            c = b + a
+            assert_array_equal(c, b.toarray() + a)
+
+            c = b + b.tocsr()
+            assert_array_equal(c.toarray(),
+                               b.toarray() + b.toarray())
+
+            # test broadcasting
+            c = b + a[0]
+            assert_array_equal(c, b.toarray() + a[0])
+
+        for dtype in self.math_dtypes:
+            check(dtype)
+
+    def test_radd(self):
+        def check(dtype):
+            dat = self.dat_dtypes[dtype]
+            datsp = self.datsp_dtypes[dtype]
+
+            a = dat.copy()
+            a[0,2] = 2.0
+            b = datsp
+            c = a + b
+            assert_array_equal(c, a + b.toarray())
+
+        for dtype in self.math_dtypes:
+            check(dtype)
+
+    def test_sub(self):
+        def check(dtype):
+            dat = self.dat_dtypes[dtype]
+            datsp = self.datsp_dtypes[dtype]
+
+            assert_array_equal((datsp - datsp).toarray(), np.zeros((3, 4)))
+            assert_array_equal((datsp - 0).toarray(), dat)
+
+            A = self.spcreator(
+                np.array([[1, 0, 0, 4], [-1, 0, 0, 0], [0, 8, 0, -5]], 'd')
+            )
+            assert_array_equal((datsp - A).toarray(), dat - A.toarray())
+            assert_array_equal((A - datsp).toarray(), A.toarray() - dat)
+
+            # test broadcasting
+            assert_array_equal(datsp - dat[0], dat - dat[0])
+
+        for dtype in self.math_dtypes:
+            if dtype == np.dtype('bool'):
+                # boolean array subtraction deprecated in 1.9.0
+                continue
+
+            check(dtype)
+
+    def test_rsub(self):
+        def check(dtype):
+            dat = self.dat_dtypes[dtype]
+            datsp = self.datsp_dtypes[dtype]
+
+            assert_array_equal((dat - datsp),[[0,0,0,0],[0,0,0,0],[0,0,0,0]])
+            assert_array_equal((datsp - dat),[[0,0,0,0],[0,0,0,0],[0,0,0,0]])
+            assert_array_equal((0 - datsp).toarray(), -dat)
+
+            A = self.spcreator([[1,0,0,4],[-1,0,0,0],[0,8,0,-5]],dtype='d')
+            assert_array_equal((dat - A), dat - A.toarray())
+            assert_array_equal((A - dat), A.toarray() - dat)
+            assert_array_equal(A.toarray() - datsp, A.toarray() - dat)
+            assert_array_equal(datsp - A.toarray(), dat - A.toarray())
+
+            # test broadcasting
+            assert_array_equal(dat[0] - datsp, dat[0] - dat)
+
+        for dtype in self.math_dtypes:
+            if dtype == np.dtype('bool'):
+                # boolean array subtraction deprecated in 1.9.0
+                continue
+
+            check(dtype)
+
+    def test_add0(self):
+        def check(dtype):
+            dat = self.dat_dtypes[dtype]
+            datsp = self.datsp_dtypes[dtype]
+
+            # Adding 0 to a sparse matrix
+            assert_array_equal((datsp + 0).toarray(), dat)
+            # use sum (which takes 0 as a starting value)
+            sumS = sum([k * datsp for k in range(1, 3)])
+            sumD = sum([k * dat for k in range(1, 3)])
+            assert_almost_equal(sumS.toarray(), sumD)
+
+        for dtype in self.math_dtypes:
+            check(dtype)
+
+    def test_elementwise_multiply(self):
+        # real/real
+        A = array([[4,0,9],[2,-3,5]])
+        B = array([[0,7,0],[0,-4,0]])
+        Asp = self.spcreator(A)
+        Bsp = self.spcreator(B)
+        # check output format
+        out_fmt = Asp.format if Asp.format in ('csc', 'dia', 'bsr') else 'csr'
+        assert (Asp.multiply(Bsp)).format == out_fmt
+        assert_almost_equal(Asp.multiply(Bsp).toarray(), A*B)  # sparse/sparse
+        assert_almost_equal(Asp.multiply(B).toarray(), A*B)  # sparse/dense
+
+        # complex/complex
+        C = array([[1-2j,0+5j,-1+0j],[4-3j,-3+6j,5]])
+        D = array([[5+2j,7-3j,-2+1j],[0-1j,-4+2j,9]])
+        Csp = self.spcreator(C)
+        Dsp = self.spcreator(D)
+        assert_almost_equal(Csp.multiply(Dsp).toarray(), C*D)  # sparse/sparse
+        assert_almost_equal(Csp.multiply(D).toarray(), C*D)  # sparse/dense
+
+        # real/complex
+        assert_almost_equal(Asp.multiply(Dsp).toarray(), A*D)  # sparse/sparse
+        assert_almost_equal(Asp.multiply(D).toarray(), A*D)  # sparse/dense
+
+    def test_elementwise_multiply_broadcast(self):
+        A = array([4])
+        B = array([[-9]])
+        C = array([1,-1,0])
+        D = array([[7,9,-9]])
+        E = array([[3],[2],[1]])
+        F = array([[8,6,3],[-4,3,2],[6,6,6]])
+        G = [1, 2, 3]
+        H = np.ones((3, 4))
+        J = H.T
+        K = array([[0]])
+        L = array([[[1,2],[0,1]]])
+
+        # Some arrays can't be cast as spmatrices (A,C,L) so leave
+        # them out.
+        Bsp = self.spcreator(B)
+        Dsp = self.spcreator(D)
+        Esp = self.spcreator(E)
+        Fsp = self.spcreator(F)
+        Hsp = self.spcreator(H)
+        Hspp = self.spcreator(H[0,None])
+        Jsp = self.spcreator(J)
+        Jspp = self.spcreator(J[:,0,None])
+        Ksp = self.spcreator(K)
+
+        matrices = [A, B, C, D, E, F, G, H, J, K, L]
+        spmatrices = [Bsp, Dsp, Esp, Fsp, Hsp, Hspp, Jsp, Jspp, Ksp]
+
+        # sparse/sparse
+        for i in spmatrices:
+            for j in spmatrices:
+                try:
+                    dense_mult = i.toarray() * j.toarray()
+                except ValueError:
+                    assert_raises(ValueError, i.multiply, j)
+                    continue
+                sp_mult = i.multiply(j)
+                assert_almost_equal(sp_mult.toarray(), dense_mult)
+
+        # sparse/dense
+        for i in spmatrices:
+            for j in matrices:
+                try:
+                    dense_mult = i.toarray() * j
+                except TypeError:
+                    continue
+                except ValueError:
+                    assert_raises(ValueError, i.multiply, j)
+                    continue
+                try:
+                    sp_mult = i.multiply(j)
+                except ValueError:
+                    continue
+                if issparse(sp_mult):
+                    assert_almost_equal(sp_mult.toarray(), dense_mult)
+                else:
+                    assert_almost_equal(sp_mult, dense_mult)
+
+    def test_elementwise_divide(self):
+        expected = [[1,np.nan,np.nan,1],
+                    [1,np.nan,1,np.nan],
+                    [np.nan,1,np.nan,np.nan]]
+        assert_array_equal(toarray(self.datsp / self.datsp), expected)
+
+        denom = self.spcreator([[1,0,0,4],[-1,0,0,0],[0,8,0,-5]],dtype='d')
+        expected = [[1,np.nan,np.nan,0.5],
+                    [-3,np.nan,inf,np.nan],
+                    [np.nan,0.25,np.nan,0]]
+        assert_array_equal(toarray(self.datsp / denom), expected)
+
+        # complex
+        A = array([[1-2j,0+5j,-1+0j],[4-3j,-3+6j,5]])
+        B = array([[5+2j,7-3j,-2+1j],[0-1j,-4+2j,9]])
+        Asp = self.spcreator(A)
+        Bsp = self.spcreator(B)
+        assert_almost_equal(toarray(Asp / Bsp), A/B)
+
+        # integer
+        A = array([[1,2,3],[-3,2,1]])
+        B = array([[0,1,2],[0,-2,3]])
+        Asp = self.spcreator(A)
+        Bsp = self.spcreator(B)
+        with np.errstate(divide='ignore'):
+            assert_array_equal(toarray(Asp / Bsp), A / B)
+
+        # mismatching sparsity patterns
+        A = array([[0,1],[1,0]])
+        B = array([[1,0],[1,0]])
+        Asp = self.spcreator(A)
+        Bsp = self.spcreator(B)
+        with np.errstate(divide='ignore', invalid='ignore'):
+            assert_array_equal(np.array(toarray(Asp / Bsp)), A / B)
+
+    def test_pow(self):
+        A = array([[1, 0, 2, 0], [0, 3, 4, 0], [0, 5, 0, 0], [0, 6, 7, 8]])
+        B = self.spcreator(A)
+
+        if self.is_array_test:  # sparrays use element-wise power
+            for exponent in [1, 2, 2.2, 3, 1+3j]:
+                ret_sp = B**exponent
+                ret_np = A**exponent
+                assert_array_equal(ret_sp.toarray(), ret_np)
+                assert_equal(ret_sp.dtype, ret_np.dtype)
+
+            # invalid exponents
+            assert_raises(NotImplementedError, B.__pow__, 0)
+            assert_raises(ValueError, B.__pow__, -1)
+
+            # nonsquare matrix
+            B = self.spcreator(A[:3,:])
+            assert_equal((B**1).toarray(), B.toarray())
+        else:  # test sparse matrix. spmatrices use matrix multiplicative power
+            for exponent in [0,1,2,3]:
+                ret_sp = B**exponent
+                ret_np = np.linalg.matrix_power(A, exponent)
+                assert_array_equal(ret_sp.toarray(), ret_np)
+                assert_equal(ret_sp.dtype, ret_np.dtype)
+
+            # invalid exponents
+            for exponent in [-1, 2.2, 1 + 3j]:
+                assert_raises(ValueError, B.__pow__, exponent)
+
+            # nonsquare matrix
+            B = self.spcreator(A[:3,:])
+            assert_raises(TypeError, B.__pow__, 1)
+
+    def test_rmatvec(self):
+        M = self.spcreator([[3,0,0],[0,1,0],[2,0,3.0],[2,3,0]])
+        assert_array_almost_equal([1,2,3,4] @ M, dot([1,2,3,4], M.toarray()))
+        row = array([[1,2,3,4]])
+        assert_array_almost_equal(row @ M, row @ M.toarray())
+
+    def test_small_multiplication(self):
+        # test that A*x works for x with shape () (1,) (1,1) and (1,0)
+        A = self.spcreator([[1],[2],[3]])
+
+        assert_(issparse(A * array(1)))
+        assert_equal((A * array(1)).toarray(), [[1], [2], [3]])
+
+        assert_equal(A @ array([1]), array([1, 2, 3]))
+        assert_equal(A @ array([[1]]), array([[1], [2], [3]]))
+        assert_equal(A @ np.ones((1, 1)), array([[1], [2], [3]]))
+        assert_equal(A @ np.ones((1, 0)), np.ones((3, 0)))
+
+    def test_star_vs_at_sign_for_sparray_and_spmatrix(self):
+        # test that * is matmul for spmatrix and mul for sparray
+        A = np.array([[1], [2], [3]])
+        Asp = self.spcreator(A)
+
+        if self.is_array_test:
+            assert_array_almost_equal((Asp * np.ones((3, 1))).toarray(), A)
+            assert_array_almost_equal((Asp * array([[1]])).toarray(), A)
+        else:
+            assert_equal(Asp * array([1]), array([1, 2, 3]))
+            assert_equal(Asp * array([[1]]), array([[1], [2], [3]]))
+            assert_equal(Asp * np.ones((1, 0)), np.ones((3, 0)))
+
+    def test_binop_custom_type(self):
+        # Non-regression test: previously, binary operations would raise
+        # NotImplementedError instead of returning NotImplemented
+        # (https://docs.python.org/library/constants.html#NotImplemented)
+        # so overloading Custom + matrix etc. didn't work.
+        A = self.spcreator([[1], [2], [3]])
+        B = BinopTester()
+        assert_equal(A + B, "matrix on the left")
+        assert_equal(A - B, "matrix on the left")
+        assert_equal(A * B, "matrix on the left")
+        assert_equal(B + A, "matrix on the right")
+        assert_equal(B - A, "matrix on the right")
+        assert_equal(B * A, "matrix on the right")
+
+        assert_equal(A @ B, "matrix on the left")
+        assert_equal(B @ A, "matrix on the right")
+
+    def test_binop_custom_type_with_shape(self):
+        A = self.spcreator([[1], [2], [3]])
+        B = BinopTester_with_shape((3,1))
+        assert_equal(A + B, "matrix on the left")
+        assert_equal(A - B, "matrix on the left")
+        assert_equal(A * B, "matrix on the left")
+        assert_equal(B + A, "matrix on the right")
+        assert_equal(B - A, "matrix on the right")
+        assert_equal(B * A, "matrix on the right")
+
+        assert_equal(A @ B, "matrix on the left")
+        assert_equal(B @ A, "matrix on the right")
+
+    def test_mul_custom_type(self):
+        class Custom:
+            def __init__(self, scalar):
+                self.scalar = scalar
+
+            def __rmul__(self, other):
+                return other * self.scalar
+
+        scalar = 2
+        A = self.spcreator([[1],[2],[3]])
+        c = Custom(scalar)
+        A_scalar = A * scalar
+        A_c = A * c
+        assert_array_equal_dtype(A_scalar.toarray(), A_c.toarray())
+        assert_equal(A_scalar.format, A_c.format)
+
+    def test_comparisons_custom_type(self):
+        A = self.spcreator([[1], [2], [3]])
+        B = ComparisonTester()
+        assert_equal(A == B, "eq")
+        assert_equal(A != B, "ne")
+        assert_equal(A > B, "lt")
+        assert_equal(A >= B, "le")
+        assert_equal(A < B, "gt")
+        assert_equal(A <= B, "ge")
+
+    def test_dot_scalar(self):
+        M = self.spcreator(array([[3,0,0],[0,1,0],[2,0,3.0],[2,3,0]]))
+        scalar = 10
+        actual = M.dot(scalar)
+        expected = M * scalar
+
+        assert_allclose(actual.toarray(), expected.toarray())
+
+    def test_matmul(self):
+        M = self.spcreator(array([[3,0,0],[0,1,0],[2,0,3.0],[2,3,0]]))
+        B = self.spcreator(array([[0,1],[1,0],[0,2]],'d'))
+        col = array([[1,2,3]]).T
+
+        matmul = operator.matmul
+        # check matrix-vector
+        assert_array_almost_equal(matmul(M, col), M.toarray() @ col)
+
+        # check matrix-matrix
+        assert_array_almost_equal(matmul(M, B).toarray(), (M @ B).toarray())
+        assert_array_almost_equal(matmul(M.toarray(), B), (M @ B).toarray())
+        assert_array_almost_equal(matmul(M, B.toarray()), (M @ B).toarray())
+
+        # check error on matrix-scalar
+        assert_raises(ValueError, matmul, M, 1)
+        assert_raises(ValueError, matmul, 1, M)
+
+    def test_matvec(self):
+        M = self.spcreator([[3,0,0],[0,1,0],[2,0,3.0],[2,3,0]])
+        col = array([[1,2,3]]).T
+
+        assert_array_almost_equal(M @ col, M.toarray() @ col)
+
+        # check result dimensions (ticket #514)
+        assert_equal((M @ array([1,2,3])).shape,(4,))
+        assert_equal((M @ array([[1],[2],[3]])).shape,(4,1))
+        assert_equal((M @ matrix([[1],[2],[3]])).shape,(4,1))
+
+        # check result type
+        assert_(isinstance(M @ array([1,2,3]), ndarray))
+        matrix_or_array = ndarray if self.is_array_test else np.matrix
+        assert_(isinstance(M @ matrix([1,2,3]).T, matrix_or_array))
+
+        # ensure exception is raised for improper dimensions
+        bad_vecs = [array([1,2]), array([1,2,3,4]), array([[1],[2]]),
+                    matrix([1,2,3]), matrix([[1],[2]])]
+        for x in bad_vecs:
+            assert_raises(ValueError, M.__matmul__, x)
+
+        # The current relationship between sparse matrix products and array
+        # products is as follows:
+        assert_almost_equal(M@array([1,2,3]), dot(M.toarray(),[1,2,3]))
+        assert_almost_equal(M@[[1],[2],[3]], np.atleast_2d(dot(M.toarray(),[1,2,3])).T)
+        # Note that the result of M * x is dense if x has a singleton dimension.
+
+        # Currently M.matvec(asarray(col)) is rank-1, whereas M.matvec(col)
+        # is rank-2.  Is this desirable?
+
+    def test_matmat_sparse(self):
+        a = matrix([[3,0,0],[0,1,0],[2,0,3.0],[2,3,0]])
+        a2 = array([[3,0,0],[0,1,0],[2,0,3.0],[2,3,0]])
+        b = matrix([[0,1],[1,0],[0,2]],'d')
+        asp = self.spcreator(a)
+        bsp = self.spcreator(b)
+        assert_array_almost_equal((asp @ bsp).toarray(), a @ b)
+        assert_array_almost_equal(asp @ b, a @ b)
+        assert_array_almost_equal(a @ bsp, a @ b)
+        assert_array_almost_equal(a2 @ bsp, a @ b)
+
+        # Now try performing cross-type multiplication:
+        csp = bsp.tocsc()
+        c = b
+        want = a @ c
+        assert_array_almost_equal((asp @ csp).toarray(), want)
+        assert_array_almost_equal(asp @ c, want)
+
+        assert_array_almost_equal(a @ csp, want)
+        assert_array_almost_equal(a2 @ csp, want)
+        csp = bsp.tocsr()
+        assert_array_almost_equal((asp @ csp).toarray(), want)
+        assert_array_almost_equal(asp @ c, want)
+
+        assert_array_almost_equal(a @ csp, want)
+        assert_array_almost_equal(a2 @ csp, want)
+        csp = bsp.tocoo()
+        assert_array_almost_equal((asp @ csp).toarray(), want)
+        assert_array_almost_equal(asp @ c, want)
+
+        assert_array_almost_equal(a @ csp, want)
+        assert_array_almost_equal(a2 @ csp, want)
+
+        # Test provided by Andy Fraser, 2006-03-26
+        L = 30
+        frac = .3
+        random.seed(0)  # make runs repeatable
+        A = zeros((L,2))
+        for i in range(L):
+            for j in range(2):
+                r = random.random()
+                if r < frac:
+                    A[i,j] = r/frac
+
+        A = self.spcreator(A)
+        B = A @ A.T
+        assert_array_almost_equal(B.toarray(), A.toarray() @ A.T.toarray())
+        assert_array_almost_equal(B.toarray(), A.toarray() @ A.toarray().T)
+
+        # check dimension mismatch 2x2 times 3x2
+        A = self.spcreator([[1,2],[3,4]])
+        B = self.spcreator([[1,2],[3,4],[5,6]])
+        assert_raises(ValueError, A.__matmul__, B)
+        if self.is_array_test:
+            assert_raises(ValueError, A.__mul__, B)
+
+    def test_matmat_dense(self):
+        a = [[3,0,0],[0,1,0],[2,0,3.0],[2,3,0]]
+        asp = self.spcreator(a)
+
+        # check both array and matrix types
+        bs = [array([[1,2],[3,4],[5,6]]), matrix([[1,2],[3,4],[5,6]])]
+
+        for b in bs:
+            result = asp @ b
+            assert_(isinstance(result, ndarray if self.is_array_test else type(b)))
+            assert_equal(result.shape, (4,2))
+            assert_equal(result, dot(a,b))
+
+    @pytest.mark.filterwarnings("ignore:.*switching.*sparse array:DeprecationWarning")
+    def test_sparse_format_conversions(self):
+        A = sparse.kron([[1,0,2],[0,3,4],[5,0,0]], [[1,2],[0,3]])
+        D = A.toarray()
+        A = self.spcreator(A)
+
+        for format in ['bsr','coo','csc','csr','dia','dok','lil']:
+            a = A.asformat(format)
+            assert_equal(a.format,format)
+            assert_array_equal(a.toarray(), D)
+
+            b = self.spcreator(D+3j).asformat(format)
+            assert_equal(b.format,format)
+            assert_array_equal(b.toarray(), D+3j)
+
+            c = self.spcreator(D).asformat(format)
+            assert_equal(c.format,format)
+            assert_array_equal(c.toarray(), D)
+
+        for format in ['array', 'dense']:
+            a = A.asformat(format)
+            assert_array_equal(a, D)
+
+            b = self.spcreator(D+3j).asformat(format)
+            assert_array_equal(b, D+3j)
+
+    def test_tobsr(self):
+        x = array([[1,0,2,0],[0,0,0,0],[0,0,4,5]])
+        y = array([[0,1,2],[3,0,5]])
+        A = kron(x,y)
+        Asp = self.spcreator(A)
+        for format in ['bsr']:
+            fn = getattr(Asp, 'to' + format)
+
+            for X in [1, 2, 3, 6]:
+                for Y in [1, 2, 3, 4, 6, 12]:
+                    assert_equal(fn(blocksize=(X, Y)).toarray(), A)
+
+    def test_transpose(self):
+        dat_1 = self.dat
+        dat_2 = np.array([[]])
+        matrices = [dat_1, dat_2]
+
+        def check(dtype, j):
+            dat = array(matrices[j], dtype=dtype)
+            datsp = self.spcreator(dat)
+
+            a = datsp.transpose()
+            b = dat.transpose()
+
+            assert_array_equal(a.toarray(), b)
+            assert_array_equal(a.transpose().toarray(), dat)
+            assert_array_equal(datsp.transpose(axes=(1, 0)).toarray(), b)
+            assert_array_equal(datsp.mT.toarray(), b)
+            assert_array_equal(matrix_transpose(datsp).toarray(), b)
+            assert_equal(a.dtype, b.dtype)
+
+        # See gh-5987
+        empty = self.spcreator((3, 4))
+        assert_array_equal(np.transpose(empty).toarray(),
+                           np.transpose(zeros((3, 4))))
+        assert_array_equal(empty.T.toarray(), zeros((4, 3)))
+        assert_array_equal(empty.mT.toarray(), empty.T.toarray())
+        assert_array_equal(matrix_transpose(empty).toarray(), empty.T.toarray())
+        assert_raises(ValueError, empty.transpose, axes=0)
+
+        for dtype in self.checked_dtypes:
+            for j in range(len(matrices)):
+                check(dtype, j)
+
+    def test_add_dense(self):
+        def check(dtype):
+            dat = self.dat_dtypes[dtype]
+            datsp = self.datsp_dtypes[dtype]
+
+            # adding a dense matrix to a sparse matrix
+            sum1 = dat + datsp
+            assert_array_equal(sum1, dat + dat)
+            sum2 = datsp + dat
+            assert_array_equal(sum2, dat + dat)
+
+        for dtype in self.math_dtypes:
+            check(dtype)
+
+    def test_sub_dense(self):
+        # subtracting a dense matrix to/from a sparse matrix
+        def check(dtype):
+            dat = self.dat_dtypes[dtype]
+            datsp = self.datsp_dtypes[dtype]
+
+            # Behavior is different for bool.
+            if dat.dtype == bool:
+                sum1 = dat - datsp
+                assert_array_equal(sum1, dat - dat)
+                sum2 = datsp - dat
+                assert_array_equal(sum2, dat - dat)
+            else:
+                # Manually add to avoid upcasting from scalar
+                # multiplication.
+                sum1 = (dat + dat + dat) - datsp
+                assert_array_equal(sum1, dat + dat)
+                sum2 = (datsp + datsp + datsp) - dat
+                assert_array_equal(sum2, dat + dat)
+
+        for dtype in self.math_dtypes:
+            if dtype == np.dtype('bool'):
+                # boolean array subtraction deprecated in 1.9.0
+                continue
+
+            check(dtype)
+
+    def test_maximum_minimum(self):
+        A_dense = np.array([[1, 0, 3], [0, 4, 5], [0, 0, 0]])
+        B_dense = np.array([[1, 1, 2], [0, 3, 6], [1, -1, 0]])
+
+        A_dense_cpx = np.array([[1, 0, 3], [0, 4+2j, 5], [0, 1j, -1j]])
+
+        def check(dtype, dtype2, btype):
+            if np.issubdtype(dtype, np.complexfloating):
+                A = self.spcreator(A_dense_cpx.astype(dtype))
+            else:
+                A = self.spcreator(A_dense.astype(dtype))
+            if btype == 'scalar':
+                B = dtype2.type(1)
+            elif btype == 'scalar2':
+                B = dtype2.type(-1)
+            elif btype == 'dense':
+                B = B_dense.astype(dtype2)
+            elif btype == 'sparse':
+                B = self.spcreator(B_dense.astype(dtype2))
+            else:
+                raise ValueError()
+
+            with warnings.catch_warnings():
+                warnings.filterwarnings(
+                    "ignore",
+                    "Taking (maximum|minimum) with a (positive|negative) number "
+                    "results in a dense matrix",
+                    SparseEfficiencyWarning,
+                )
+
+                max_s = A.maximum(B)
+                min_s = A.minimum(B)
+
+            max_d = np.maximum(toarray(A), toarray(B))
+            assert_array_equal(toarray(max_s), max_d)
+            assert_equal(max_s.dtype, max_d.dtype)
+
+            min_d = np.minimum(toarray(A), toarray(B))
+            assert_array_equal(toarray(min_s), min_d)
+            assert_equal(min_s.dtype, min_d.dtype)
+
+        for dtype in self.math_dtypes:
+            for dtype2 in [np.int8, np.float64, np.complex128]:
+                for btype in ['scalar', 'scalar2', 'dense', 'sparse']:
+                    check(np.dtype(dtype), np.dtype(dtype2), btype)
+
+    def test_copy(self):
+        # Check whether the copy=True and copy=False keywords work
+        A = self.datsp
+
+        # check that copy preserves format
+        assert_equal(A.copy().format, A.format)
+        assert_equal(A.__class__(A,copy=True).format, A.format)
+        assert_equal(A.__class__(A,copy=False).format, A.format)
+
+        assert_equal(A.copy().toarray(), A.toarray())
+        assert_equal(A.__class__(A, copy=True).toarray(), A.toarray())
+        assert_equal(A.__class__(A, copy=False).toarray(), A.toarray())
+
+        # check that XXX_array.toXXX() works
+        toself = getattr(A,'to' + A.format)
+        assert_(toself() is A)
+        assert_(toself(copy=False) is A)
+        assert_equal(toself(copy=True).format, A.format)
+        assert_equal(toself(copy=True).toarray(), A.toarray())
+
+        # check whether the data is copied?
+        assert_(not sparse_may_share_memory(A.copy(), A))
+
+    # test that __iter__ is compatible with NumPy matrix
+    def test_iterator(self):
+        B = self.asdense(np.arange(50).reshape(5, 10))
+        A = self.spcreator(B)
+
+        for x, y in zip(A, B):
+            assert_equal(x.toarray(), y)
+
+    def test_size_zero_matrix_arithmetic(self):
+        # Test basic matrix arithmetic with shapes like (0,0), (10,0),
+        # (0, 3), etc.
+        mat = array([])
+        a = mat.reshape((0, 0))
+        b = mat.reshape((0, 1))
+        c = mat.reshape((0, 5))
+        d = mat.reshape((1, 0))
+        e = mat.reshape((5, 0))
+        f = np.ones([5, 5])
+
+        asp = self.spcreator(a)
+        bsp = self.spcreator(b)
+        csp = self.spcreator(c)
+        dsp = self.spcreator(d)
+        esp = self.spcreator(e)
+        fsp = self.spcreator(f)
+
+        # matrix product.
+        assert_array_equal(asp.dot(asp).toarray(), np.dot(a, a))
+        assert_array_equal(bsp.dot(dsp).toarray(), np.dot(b, d))
+        assert_array_equal(dsp.dot(bsp).toarray(), np.dot(d, b))
+        assert_array_equal(csp.dot(esp).toarray(), np.dot(c, e))
+        assert_array_equal(csp.dot(fsp).toarray(), np.dot(c, f))
+        assert_array_equal(esp.dot(csp).toarray(), np.dot(e, c))
+        assert_array_equal(dsp.dot(csp).toarray(), np.dot(d, c))
+        assert_array_equal(fsp.dot(esp).toarray(), np.dot(f, e))
+
+        # bad matrix products
+        assert_raises(ValueError, dsp.dot, e)
+        assert_raises(ValueError, asp.dot, d)
+
+        # elemente-wise multiplication
+        assert_array_equal(asp.multiply(asp).toarray(), np.multiply(a, a))
+        assert_array_equal(bsp.multiply(bsp).toarray(), np.multiply(b, b))
+        assert_array_equal(dsp.multiply(dsp).toarray(), np.multiply(d, d))
+
+        assert_array_equal(asp.multiply(a).toarray(), np.multiply(a, a))
+        assert_array_equal(bsp.multiply(b).toarray(), np.multiply(b, b))
+        assert_array_equal(dsp.multiply(d).toarray(), np.multiply(d, d))
+
+        assert_array_equal(asp.multiply(6).toarray(), np.multiply(a, 6))
+        assert_array_equal(bsp.multiply(6).toarray(), np.multiply(b, 6))
+        assert_array_equal(dsp.multiply(6).toarray(), np.multiply(d, 6))
+
+        # bad element-wise multiplication
+        assert_raises(ValueError, asp.multiply, c)
+        assert_raises(ValueError, esp.multiply, c)
+
+        # Addition
+        assert_array_equal(asp.__add__(asp).toarray(), a.__add__(a))
+        assert_array_equal(bsp.__add__(bsp).toarray(), b.__add__(b))
+        assert_array_equal(dsp.__add__(dsp).toarray(), d.__add__(d))
+
+        # bad addition
+        assert_raises(ValueError, asp.__add__, dsp)
+        assert_raises(ValueError, bsp.__add__, asp)
+
+    def test_size_zero_conversions(self):
+        mat = array([])
+        a = mat.reshape((0, 0))
+        b = mat.reshape((0, 5))
+        c = mat.reshape((5, 0))
+
+        for m in [a, b, c]:
+            spm = self.spcreator(m)
+            assert_array_equal(spm.tocoo().toarray(), m)
+            assert_array_equal(spm.tocsr().toarray(), m)
+            assert_array_equal(spm.tocsc().toarray(), m)
+            assert_array_equal(spm.tolil().toarray(), m)
+            assert_array_equal(spm.todok().toarray(), m)
+            assert_array_equal(spm.tobsr().toarray(), m)
+
+    def test_dtype_check(self):
+        a = np.array([[3.5, 0, 1.1], [0, 0, 0]], dtype=np.float16)
+        with assert_raises(ValueError, match="does not support dtype"):
+            self.spcreator(a)
+
+        A32 = self.spcreator(a.astype(np.float32))
+        with assert_raises(ValueError, match="does not support dtype"):
+            self.spcreator(A32, dtype=np.float16)
+
+    def test_pickle(self):
+        import pickle
+        def check():
+            with warnings.catch_warnings():
+                warnings.simplefilter("ignore", SparseEfficiencyWarning)
+                datsp = self.datsp.copy()
+                for protocol in range(pickle.HIGHEST_PROTOCOL):
+                    sploaded = pickle.loads(pickle.dumps(datsp, protocol=protocol))
+                    assert_equal(datsp.shape, sploaded.shape)
+                    assert_array_equal(datsp.toarray(), sploaded.toarray())
+                    assert_equal(datsp.format, sploaded.format)
+                    # Hacky check for class member equality. This assumes that
+                    # all instance variables are one of:
+                    #  1. Plain numpy ndarrays
+                    #  2. Tuples of ndarrays
+                    #  3. Types that support equality comparison with ==
+                    for key, val in datsp.__dict__.items():
+                        if isinstance(val, np.ndarray):
+                            assert_array_equal(val, sploaded.__dict__[key])
+                        elif (isinstance(val, tuple) and val
+                              and isinstance(val[0], np.ndarray)):
+                            assert_array_equal(val, sploaded.__dict__[key])
+                        else:
+                            assert_(val == sploaded.__dict__[key])
+        check()
+
+    def test_unary_ufunc_overrides(self):
+        def check(name):
+            if name == "sign":
+                pytest.skip("sign conflicts with comparison op "
+                            "support on Numpy")
+            if self.datsp.format in ["dok", "lil"]:
+                pytest.skip("Unary ops not implemented for dok/lil")
+            ufunc = getattr(np, name)
+
+            X = self.spcreator(np.arange(20).reshape(4, 5) / 20.)
+            X0 = ufunc(X.toarray())
+
+            X2 = ufunc(X)
+            assert_array_equal(X2.toarray(), X0)
+
+        for name in ["sin", "tan", "arcsin", "arctan", "sinh", "tanh",
+                     "arcsinh", "arctanh", "rint", "sign", "expm1", "log1p",
+                     "deg2rad", "rad2deg", "floor", "ceil", "trunc", "sqrt",
+                     "abs"]:
+            check(name)
+
+    def test_resize(self):
+        # resize(shape) resizes the matrix in-place
+        D = np.array([[1, 0, 3, 4],
+                      [2, 0, 0, 0],
+                      [3, 0, 0, 0]])
+        S = self.spcreator(D)
+        assert_(S.resize((3, 2)) is None)
+        assert_array_equal(S.toarray(), [[1, 0],
+                                         [2, 0],
+                                         [3, 0]])
+        S.resize((2, 2))
+        assert_array_equal(S.toarray(), [[1, 0],
+                                         [2, 0]])
+        S.resize((3, 2))
+        assert_array_equal(S.toarray(), [[1, 0],
+                                         [2, 0],
+                                         [0, 0]])
+        S.resize((3, 3))
+        assert_array_equal(S.toarray(), [[1, 0, 0],
+                                         [2, 0, 0],
+                                         [0, 0, 0]])
+        # test no-op
+        S.resize((3, 3))
+        assert_array_equal(S.toarray(), [[1, 0, 0],
+                                         [2, 0, 0],
+                                         [0, 0, 0]])
+
+        # test *args
+        S.resize(3, 2)
+        assert_array_equal(S.toarray(), [[1, 0],
+                                         [2, 0],
+                                         [0, 0]])
+
+        if self.is_array_test and S.format in ["coo", "csr"]:
+            S.resize(1)
+        else:
+            assert_raises((ValueError, NotImplementedError, IndexError), S.resize, 1)
+
+        for bad_shape in [(-1, 2), (2, -1), (1, 2, 3)]:
+            assert_raises(ValueError, S.resize, bad_shape)
+
+    def test_constructor1_base(self):
+        A = self.datsp
+
+        self_format = A.format
+
+        C = A.__class__(A, copy=False)
+        assert_array_equal_dtype(A.toarray(), C.toarray())
+        if self_format not in NON_ARRAY_BACKED_FORMATS:
+            assert_(sparse_may_share_memory(A, C))
+
+        C = A.__class__(A, dtype=A.dtype, copy=False)
+        assert_array_equal_dtype(A.toarray(), C.toarray())
+        if self_format not in NON_ARRAY_BACKED_FORMATS:
+            assert_(sparse_may_share_memory(A, C))
+
+        C = A.__class__(A, dtype=np.float32, copy=False)
+        assert_array_equal(A.toarray(), C.toarray())
+
+        C = A.__class__(A, copy=True)
+        assert_array_equal_dtype(A.toarray(), C.toarray())
+        assert_(not sparse_may_share_memory(A, C))
+
+        for other_format in ['csr', 'csc', 'coo', 'dia', 'dok', 'lil']:
+            if other_format == self_format:
+                continue
+            B = A.asformat(other_format)
+            C = A.__class__(B, copy=False)
+            assert_array_equal_dtype(A.toarray(), C.toarray())
+
+            C = A.__class__(B, copy=True)
+            assert_array_equal_dtype(A.toarray(), C.toarray())
+            assert_(not sparse_may_share_memory(B, C))
+
+
+class _TestInplaceArithmetic:
+    def test_inplace_dense(self):
+        a = np.ones((3, 4))
+        b = self.spcreator(a)
+
+        x = a.copy()
+        y = a.copy()
+        x += a
+        y += b
+        assert_array_equal(x, y)
+
+        x = a.copy()
+        y = a.copy()
+        x -= a
+        y -= b
+        assert_array_equal(x, y)
+
+        if self.is_array_test:
+            # Elementwise multiply from sparray.__rmul__
+            x = a.copy()
+            y = a.copy()
+            with assert_raises(ValueError, match="inconsistent shapes"):
+                x *= b.T
+            x = x * a
+            y *= b
+            assert_array_equal(x, y.toarray())
+        else:
+            # Matrix multiply from spmatrix.__rmul__
+            x = a.copy()
+            y = a.copy()
+            with assert_raises(ValueError, match="dimension mismatch"):
+                x *= b
+            x = x.dot(a.T)
+            y *= b.T
+            assert_array_equal(x, y)
+
+        # Matrix multiply from __rmatmul__
+        y = a.copy()
+        y @= b.T
+        x = a.copy()
+        y = a.copy()
+        with assert_raises(ValueError, match="dimension mismatch"):
+            x @= b
+        x = x.dot(a.T)
+        y @= b.T
+        assert_array_equal(x, y)
+
+        # Floor division is not supported
+        with assert_raises(TypeError, match="unsupported operand"):
+            x //= b
+
+    def test_imul_scalar(self):
+        def check(dtype):
+            dat = self.dat_dtypes[dtype]
+            datsp = self.datsp_dtypes[dtype]
+
+            # Avoid implicit casting.
+            if np.can_cast(int, dtype, casting='same_kind'):
+                a = datsp.copy()
+                a *= 2
+                b = dat.copy()
+                b *= 2
+                assert_array_equal(b, a.toarray())
+
+            if np.can_cast(float, dtype, casting='same_kind'):
+                a = datsp.copy()
+                a *= 17.3
+                b = dat.copy()
+                b *= 17.3
+                assert_array_equal(b, a.toarray())
+
+        for dtype in self.math_dtypes:
+            check(dtype)
+
+    def test_idiv_scalar(self):
+        def check(dtype):
+            dat = self.dat_dtypes[dtype]
+            datsp = self.datsp_dtypes[dtype]
+
+            if np.can_cast(int, dtype, casting='same_kind'):
+                a = datsp.copy()
+                a /= 2
+                b = dat.copy()
+                b /= 2
+                assert_array_equal(b, a.toarray())
+
+            if np.can_cast(float, dtype, casting='same_kind'):
+                a = datsp.copy()
+                a /= 17.3
+                b = dat.copy()
+                b /= 17.3
+                assert_array_equal(b, a.toarray())
+
+        for dtype in self.math_dtypes:
+            # /= should only be used with float dtypes to avoid implicit
+            # casting.
+            if not np.can_cast(dtype, np.dtype(int)):
+                check(dtype)
+
+    def test_inplace_success(self):
+        # Inplace ops should work even if a specialized version is not
+        # implemented, falling back to x = x <op> y
+        a = self.spcreator(np.eye(5))
+        b = self.spcreator(np.eye(5))
+        bp = self.spcreator(np.eye(5))
+
+        b += a
+        bp = bp + a
+        assert_allclose(b.toarray(), bp.toarray())
+
+        if self.is_array_test:
+            b *= a
+            bp = bp * a
+            assert_allclose(b.toarray(), bp.toarray())
+
+        b @= a
+        bp = bp @ a
+        assert_allclose(b.toarray(), bp.toarray())
+
+        b -= a
+        bp = bp - a
+        assert_allclose(b.toarray(), bp.toarray())
+
+        with assert_raises(TypeError, match="unsupported operand"):
+            a //= b
+
+
+class _TestGetSet:
+    def test_getelement(self):
+        def check(dtype):
+            D = array([[1,0,0],
+                       [4,3,0],
+                       [0,2,0],
+                       [0,0,0]], dtype=dtype)
+            A = self.spcreator(D)
+
+            M,N = D.shape
+
+            for i in range(-M, M):
+                for j in range(-N, N):
+                    assert_equal(A[i,j], D[i,j])
+
+            assert_equal(type(A[1,1]), dtype)
+
+            for ij in [(0,3),(-1,3),(4,0),(4,3),(4,-1), (1, 2, 3)]:
+                assert_raises((IndexError, TypeError), A.__getitem__, ij)
+
+        for dtype in supported_dtypes:
+            check(np.dtype(dtype))
+
+    def test_setelement(self):
+        def check(dtype, scalar_container):
+            A = self.spcreator((3, 4), dtype=dtype)
+            with warnings.catch_warnings():
+                warnings.filterwarnings("ignore", WMSG, SparseEfficiencyWarning)
+                A[0, 0] = scalar_container(dtype.type(0))  # bug 870
+                A[1, 2] = scalar_container(dtype.type(4.0))
+                A[0, 1] = scalar_container(dtype.type(3))
+                A[2, 0] = scalar_container(dtype.type(2.0))
+                A[0, -1] = scalar_container(dtype.type(8))
+                A[-1, -2] = scalar_container(dtype.type(7))
+                A[0, 1] = scalar_container(dtype.type(5))
+
+            if dtype != np.bool_:
+                assert_array_equal(
+                    A.toarray(), [[0, 5, 0, 8], [0, 0, 4, 0], [2, 0, 7, 0]]
+                )
+
+            for ij in [(0, 4), (-1, 4), (3, 0), (3, 4), (3, -1)]:
+                assert_raises(IndexError, A.__setitem__, ij, 123.0)
+
+            for v in [[1, 2, 3], array([1, 2, 3])]:
+                assert_raises(ValueError, A.__setitem__, (0, 0), v)
+
+            if not np.issubdtype(dtype, np.complexfloating) and dtype != np.bool_:
+                for v in [3j]:
+                    assert_raises(TypeError, A.__setitem__, (0, 0), v)
+
+        scalar_containers = [
+            lambda x: csr_array(np.array([[x]])), np.array, lambda x: x
+        ]
+        for scalar_container in scalar_containers:
+            for dtype in supported_dtypes:
+                check(np.dtype(dtype), scalar_container)
+
+    def test_negative_index_assignment(self):
+        # Regression test for GitHub issue 4428.
+
+        def check(dtype):
+            A = self.spcreator((3, 10), dtype=dtype)
+            with warnings.catch_warnings():
+                warnings.filterwarnings("ignore", WMSG, SparseEfficiencyWarning)
+                A[0, -4] = 1
+            assert_equal(A[0, -4], 1)
+
+        for dtype in self.math_dtypes:
+            check(np.dtype(dtype))
+
+    def test_scalar_assign_2(self):
+        n, m = (5, 10)
+
+        def _test_set(i, j, nitems):
+            msg = f"{i!r} ; {j!r} ; {nitems!r}"
+            A = self.spcreator((n, m))
+            with warnings.catch_warnings():
+                warnings.filterwarnings("ignore", WMSG, SparseEfficiencyWarning)
+                A[i, j] = 1
+            assert_almost_equal(A.sum(), nitems, err_msg=msg)
+            assert_almost_equal(A[i, j], 1, err_msg=msg)
+
+        # [i,j]
+        for i, j in [(2, 3), (-1, 8), (-1, -2), (array(-1), -2), (-1, array(-2)),
+                     (array(-1), array(-2))]:
+            _test_set(i, j, 1)
+
+    def test_index_scalar_assign(self):
+        A = self.spcreator((5, 5))
+        B = np.zeros((5, 5))
+        with warnings.catch_warnings():
+            warnings.filterwarnings("ignore", WMSG, SparseEfficiencyWarning)
+            for C in [A, B]:
+                C[0,1] = 1
+                C[3,0] = 4
+                C[3,0] = 9
+        assert_array_equal(A.toarray(), B)
+
+
+@pytest.mark.thread_unsafe(reason="fails in parallel")
+class _TestSolve:
+    def test_solve(self):
+        # Test whether the lu_solve command segfaults, as reported by Nils
+        # Wagner for a 64-bit machine, 02 March 2005 (EJS)
+        n = 20
+        np.random.seed(0)  # make tests repeatable
+        A = zeros((n,n), dtype=complex)
+        x = np.random.rand(n)
+        y = np.random.rand(n-1)+1j*np.random.rand(n-1)
+        r = np.random.rand(n)
+        for i in range(len(x)):
+            A[i,i] = x[i]
+        for i in range(len(y)):
+            A[i,i+1] = y[i]
+            A[i+1,i] = conjugate(y[i])
+        A = self.spcreator(A)
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", "splu converted its input to CSC format",
+                SparseEfficiencyWarning)
+            x = splu(A).solve(r)
+        assert_almost_equal(A @ x,r)
+
+
+class _TestSlicing:
+    def test_dtype_preservation(self):
+        assert_equal(self.spcreator((1,10), dtype=np.int16)[0,1:5].dtype, np.int16)
+        assert_equal(self.spcreator((1,10), dtype=np.int32)[0,1:5].dtype, np.int32)
+        assert_equal(self.spcreator((1,10), dtype=np.float32)[0,1:5].dtype, np.float32)
+        assert_equal(self.spcreator((1,10), dtype=np.float64)[0,1:5].dtype, np.float64)
+
+    def test_dtype_preservation_empty_slice(self):
+        # This should be parametrized with pytest, but something in the parent
+        # class creation used in this file breaks pytest.mark.parametrize.
+        for dt in [np.int16, np.int32, np.float32, np.float64]:
+            A = self.spcreator((3, 2), dtype=dt)
+            assert_equal(A[:, 0:0:2].dtype, dt)
+            assert_equal(A[0:0:2, :].dtype, dt)
+            assert_equal(A[0, 0:0:2].dtype, dt)
+            assert_equal(A[0:0:2, 0].dtype, dt)
+
+    def test_get_horiz_slice(self):
+        B = self.asdense(arange(50.).reshape(5,10))
+        A = self.spcreator(B)
+        r0, r1, r2 = (0, 1, 2) if self.is_array_test else ([0], [1], [2])
+        assert_array_equal(B[r1, :], A[1, :].toarray())
+        assert_array_equal(B[r1, 2:5], A[1, 2:5].toarray())
+
+        C = self.asdense([[1, 2, 1], [4, 0, 6], [0, 0, 0], [0, 0, 1]])
+        D = self.spcreator(C)
+        assert_array_equal(C[r1, 1:3], D[1, 1:3].toarray())
+
+        # Now test slicing when a row contains only zeros
+        E = self.asdense([[1, 2, 1], [4, 0, 0], [0, 0, 0], [0, 0, 1]])
+        F = self.spcreator(E)
+        assert_array_equal(E[r1, 1:3], F[1, 1:3].toarray())
+        assert_array_equal(E[r2, -2:], F[2, -2:].toarray())
+
+        # The following should raise exceptions:
+        assert_raises(IndexError, A.__getitem__, (slice(None), 11))
+        assert_raises(IndexError, A.__getitem__, (6, slice(3, 7)))
+
+    def test_get_vert_slice(self):
+        B = arange(50.).reshape(5, 10)
+        A = self.spcreator(B)
+        c0, c1, c2 = (0, 1, 2) if self.is_array_test else ([0], [1], [2])
+        assert_array_equal(B[2:5, c0], A[2:5, 0].toarray())
+        assert_array_equal(B[:, c1], A[:, 1].toarray())
+
+        C = array([[1, 2, 1], [4, 0, 6], [0, 0, 0], [0, 0, 1]])
+        D = self.spcreator(C)
+        assert_array_equal(C[1:3, c1], D[1:3, 1].toarray())
+        assert_array_equal(C[:, c2], D[:, 2].toarray())
+
+        # Now test slicing when a column contains only zeros
+        E = array([[1, 0, 1], [4, 0, 0], [0, 0, 0], [0, 0, 1]])
+        F = self.spcreator(E)
+        assert_array_equal(E[:, c1], F[:, 1].toarray())
+        assert_array_equal(E[-2:, c2], F[-2:, 2].toarray())
+
+        # The following should raise exceptions:
+        assert_raises(IndexError, A.__getitem__, (slice(None), 11))
+        assert_raises(IndexError, A.__getitem__, (6, slice(3, 7)))
+
+    def test_get_slices(self):
+        B = arange(50.).reshape(5, 10)
+        A = self.spcreator(B)
+        assert_array_equal(A[2:5, 0:3].toarray(), B[2:5, 0:3])
+        assert_array_equal(A[1:, :-1].toarray(), B[1:, :-1])
+        assert_array_equal(A[:-1, 1:].toarray(), B[:-1, 1:])
+
+        # Now test slicing when a column contains only zeros
+        E = array([[1, 0, 1], [4, 0, 0], [0, 0, 0], [0, 0, 1]])
+        F = self.spcreator(E)
+        assert_array_equal(E[1:2, 1:2], F[1:2, 1:2].toarray())
+        assert_array_equal(E[:, 1:], F[:, 1:].toarray())
+
+    def test_non_unit_stride_2d_indexing(self):
+        # Regression test -- used to silently ignore the stride.
+        v0 = np.random.rand(50, 50)
+        try:
+            v = self.spcreator(v0)[0:25:2, 2:30:3]
+        except ValueError:
+            # if unsupported
+            raise pytest.skip("feature not implemented")
+
+        assert_array_equal(v.toarray(), v0[0:25:2, 2:30:3])
+
+    def test_slicing_2(self):
+        B = self.asdense(arange(50).reshape(5,10))
+        A = self.spcreator(B)
+
+        # [i,j]
+        assert_equal(A[2,3], B[2,3])
+        assert_equal(A[-1,8], B[-1,8])
+        assert_equal(A[-1,-2],B[-1,-2])
+        assert_equal(A[array(-1),-2],B[-1,-2])
+        assert_equal(A[-1,array(-2)],B[-1,-2])
+        assert_equal(A[array(-1),array(-2)],B[-1,-2])
+
+        # [i,1:2]
+        assert_equal(A[2, :].toarray(), B[2, :])
+        assert_equal(A[2, 5:-2].toarray(), B[2, 5:-2])
+        assert_equal(A[array(2), 5:-2].toarray(), B[2, 5:-2])
+
+        # [1:2,j]
+        assert_equal(A[:, 2].toarray(), B[:, 2])
+        assert_equal(A[3:4, 9].toarray(), B[3:4, 9])
+        assert_equal(A[1:4, -5].toarray(), B[1:4, -5])
+        assert_equal(A[2:-1, 3].toarray(), B[2:-1, 3])
+        assert_equal(A[2:-1, array(3)].toarray(), B[2:-1, 3])
+
+        # [1:2,1:2]
+        assert_equal(A[1:2, 1:2].toarray(), B[1:2, 1:2])
+        assert_equal(A[4:, 3:].toarray(), B[4:, 3:])
+        assert_equal(A[:4, :5].toarray(), B[:4, :5])
+        assert_equal(A[2:-1, :5].toarray(), B[2:-1, :5])
+
+        # [i]
+        assert_equal(A[1, :].toarray(), B[1, :])
+        assert_equal(A[-2, :].toarray(), B[-2, :])
+        assert_equal(A[array(-2), :].toarray(), B[-2, :])
+
+        # [1:2]
+        assert_equal(A[1:4].toarray(), B[1:4])
+        assert_equal(A[1:-2].toarray(), B[1:-2])
+
+        # Check bug reported by Robert Cimrman:
+        # http://thread.gmane.org/gmane.comp.python.scientific.devel/7986 (dead link)
+        s = slice(int8(2),int8(4),None)
+        assert_equal(A[s, :].toarray(), B[2:4, :])
+        assert_equal(A[:, s].toarray(), B[:, 2:4])
+
+    @pytest.mark.fail_slow(2)
+    def test_slicing_3(self):
+        B = self.asdense(arange(50).reshape(5,10))
+        A = self.spcreator(B)
+
+        s_ = np.s_
+        slices = [s_[:2], s_[1:2], s_[3:], s_[3::2],
+                  s_[15:20], s_[3:2],
+                  s_[8:3:-1], s_[4::-2], s_[:5:-1],
+                  0, 1, s_[:], s_[1:5], -1, -2, -5,
+                  array(-1), np.int8(-3)]
+
+        def check_1(a):
+            x = A[a]
+            y = B[a]
+            if y.shape == ():
+                assert_equal(x, y, repr(a))
+            else:
+                if x.size == 0 and y.size == 0:
+                    pass
+                else:
+                    assert_array_equal(x.toarray(), y, repr(a))
+
+        for j, a in enumerate(slices):
+            check_1(a)
+
+        def check_2(a, b):
+            # Indexing np.matrix with 0-d arrays seems to be broken,
+            # as they seem not to be treated as scalars.
+            # https://github.com/numpy/numpy/issues/3110
+            if isinstance(a, np.ndarray):
+                ai = int(a)
+            else:
+                ai = a
+            if isinstance(b, np.ndarray):
+                bi = int(b)
+            else:
+                bi = b
+
+            x = A[a, b]
+            y = B[ai, bi]
+
+            if y.shape == ():
+                assert_equal(x, y, repr((a, b)))
+            else:
+                if x.size == 0 and y.size == 0:
+                    pass
+                else:
+                    assert_array_equal(x.toarray(), y, repr((a, b)))
+
+        for i, a in enumerate(slices):
+            for j, b in enumerate(slices):
+                check_2(a, b)
+
+        # Check out of bounds etc. systematically
+        extra_slices = []
+        for a, b, c in itertools.product(*([(None, 0, 1, 2, 5, 15,
+                                             -1, -2, 5, -15)]*3)):
+            if c == 0:
+                continue
+            extra_slices.append(slice(a, b, c))
+
+        for a in extra_slices:
+            check_2(a, a)
+            check_2(a, -2)
+            check_2(-2, a)
+
+    def test_None_slicing(self):
+        B = self.asdense(arange(50).reshape(5,10))
+        A = self.spcreator(B)
+
+        assert A[1, 2].ndim == 0
+        assert A[None, 1, 2:4].shape == (1, 2)
+        assert A[None, 1, 2, None].shape == (1, 1)
+
+        # see gh-22458
+        assert A[None, 1].shape == (1, 10)
+        assert A[1, None].shape == (1, 10)
+        assert A[None, 1, :].shape == (1, 10)
+        assert A[1, None, :].shape == (1, 10)
+        assert A[1, :, None].shape == (10, 1)
+
+        assert A[None, 1:3, 2].shape == B[None, 1:3, 2].shape == (1, 2)
+        assert A[1:3, None, 2].shape == B[1:3, None, 2].shape == (2, 1)
+        assert A[1:3, 2, None].shape == B[1:3, 2, None].shape == (2, 1)
+        assert A[None, 1, 2:4].shape == B[None, 1, 2:4].shape == (1, 2)
+        assert A[1, None, 2:4].shape == B[1, None, 2:4].shape == (1, 2)
+        assert A[1, 2:4, None].shape == B[1, 2:4, None].shape == (2, 1)
+
+        # different for spmatrix
+        if self.is_array_test:
+            assert A[1:3, 2].shape == B[1:3, 2].shape == (2,)
+            assert A[1, 2:4].shape == B[1, 2:4].shape == (2,)
+            assert A[None, 1, 2].shape == B[None, 1, 2].shape == (1,)
+            assert A[1, None, 2].shape == B[1, None, 2].shape == (1,)
+            assert A[1, 2, None].shape == B[1, 2, None].shape == (1,)
+        else:
+            assert A[1, 2:4].shape == B[1, 2:4].shape == (1, 2)
+            assert A[1:3, 2].shape == B[1:3, 2].shape == (2, 1)
+            assert A[None, 1, 2].shape == B[None, 1, 2].shape == (1, 1)
+            assert A[1, None, 2].shape == B[1, None, 2].shape == (1, 1)
+            assert A[1, 2, None].shape == B[1, 2, None].shape == (1, 1)
+
+    def test_ellipsis_slicing(self):
+        b = self.asdense(arange(50).reshape(5,10))
+        a = self.spcreator(b)
+
+        assert_array_equal(a[...].toarray(), b[...])
+        assert_array_equal(a[...,].toarray(), b[...,])
+
+        assert_array_equal(a[4, ...].toarray(), b[4, ...])
+        assert_array_equal(a[..., 4].toarray(), b[..., 4])
+        assert_array_equal(a[..., 5].toarray(), b[..., 5])
+        with pytest.raises(IndexError, match='index .5. out of range'):
+            a[5, ...]
+        with pytest.raises(IndexError, match='index .10. out of range'):
+            a[..., 10]
+        with pytest.raises(IndexError, match='index .5. out of range'):
+            a.T[..., 5]
+
+        assert_array_equal(a[1:, ...].toarray(), b[1:, ...])
+        assert_array_equal(a[..., 1:].toarray(), b[..., 1:])
+        assert_array_equal(a[:2, ...].toarray(), b[:2, ...])
+        assert_array_equal(a[..., :2].toarray(), b[..., :2])
+
+        # check slice limit outside range
+        assert_array_equal(a[:5, ...].toarray(), b[:5, ...])
+        assert_array_equal(a[..., :5].toarray(), b[..., :5])
+        assert_array_equal(a[5:, ...].toarray(), b[5:, ...])
+        assert_array_equal(a[..., 5:].toarray(), b[..., 5:])
+        assert_array_equal(a[10:, ...].toarray(), b[10:, ...])
+        assert_array_equal(a[..., 10:].toarray(), b[..., 10:])
+
+        # ellipsis should be ignored
+        assert_array_equal(a[1:, 1, ...].toarray(), b[1:, 1, ...])
+        assert_array_equal(a[1, ..., 1:].toarray(), b[1, ..., 1:])
+        assert_array_equal(a[..., 1, 1:].toarray(), b[1, ..., 1:])
+        assert_array_equal(a[:2, 1, ...].toarray(), b[:2, 1, ...])
+        assert_array_equal(a[1, ..., :2].toarray(), b[1, ..., :2])
+        assert_array_equal(a[..., 1, :2].toarray(), b[1, ..., :2])
+        # These return ints
+        assert_equal(a[1, 1, ...], b[1, 1, ...])
+        assert_equal(a[1, ..., 1], b[1, ..., 1])
+
+    def test_ellipsis_fancy_bool(self):
+        numpy_a = self.asdense(arange(50).reshape(5, 10))
+        a = self.spcreator(numpy_a)
+
+        ix5 = [True, False, True, False, True]
+        ix10 = [False] * 5 + ix5  # same number of True values as ix5
+        ix10_6True = ix5 + ix5  # not same number of True values as ix5
+        full_ix = [ix10] * 5
+
+        assert_array_equal(toarray(a[full_ix, ...]), numpy_a[full_ix, ...])
+        assert_array_equal(toarray(a[..., full_ix]), numpy_a[..., full_ix])
+
+        assert_array_equal(toarray(a[ix5, ...]), numpy_a[ix5, ...])
+        assert_array_equal(toarray(a[..., ix10]), numpy_a[..., ix10])
+
+        assert_array_equal(toarray(a[ix5, ..., ix10]), numpy_a[ix5, ..., ix10])
+        assert_array_equal(toarray(a[..., ix5, ix10]), numpy_a[..., ix5, ix10])
+        assert_array_equal(toarray(a[ix5, ix10, ...]), numpy_a[ix5, ix10, ...])
+
+        with assert_raises(IndexError, match="shape mismatch"):
+            a[ix5, ix10_6True]
+
+    def test_ellipsis_fancy_slicing(self):
+        b = self.asdense(arange(50).reshape(5, 10))
+        a = self.spcreator(b)
+
+        assert_array_equal(a[[4], ...].toarray(), b[[4], ...])
+        assert_array_equal(a[[2, 4], ...].toarray(), b[[2, 4], ...])
+        assert_array_equal(a[..., [4]].toarray(), b[..., [4]])
+        assert_array_equal(a[..., [2, 4]].toarray(), b[..., [2, 4]])
+
+        assert_array_equal(a[[4], 1, ...].toarray(), b[[4], 1, ...])
+        assert_array_equal(a[[2, 4], 1, ...].toarray(), b[[2, 4], 1, ...])
+        assert_array_equal(a[[4], ..., 1].toarray(), b[[4], ..., 1])
+        assert_array_equal(a[..., [4], 1].toarray(), b[..., [4], 1])
+        # fancy index gives dense
+        assert_array_equal(toarray(a[[2, 4], ..., [2, 4]]), b[[2, 4], ..., [2, 4]])
+        assert_array_equal(toarray(a[..., [2, 4], [2, 4]]), b[..., [2, 4], [2, 4]])
+
+    def test_multiple_ellipsis_slicing(self):
+        a = self.spcreator(arange(6).reshape(3, 2))
+
+        with pytest.raises(IndexError,
+                           match='an index can only have a single ellipsis'):
+            a[..., ...]
+        with pytest.raises(IndexError,
+                           match='an index can only have a single ellipsis'):
+            a[..., 1, ...]
+
+
+class _TestSlicingAssign:
+    def test_slice_scalar_assign(self):
+        A = self.spcreator((5, 5))
+        B = np.zeros((5, 5))
+        with warnings.catch_warnings():
+            warnings.filterwarnings("ignore", WMSG, SparseEfficiencyWarning)
+            for C in [A, B]:
+                C[0:1,1] = 1
+                C[3:0,0] = 4
+                C[3:4,0] = 9
+                C[0,4:] = 1
+                C[3::-1,4:] = 9
+        assert_array_equal(A.toarray(), B)
+
+    def test_slice_assign_2(self):
+        n, m = (5, 10)
+
+        def _test_set(i, j):
+            msg = f"i={i!r}; j={j!r}"
+            A = self.spcreator((n, m))
+            with warnings.catch_warnings():
+                warnings.filterwarnings("ignore", WMSG, SparseEfficiencyWarning)
+                A[i, j] = 1
+            B = np.zeros((n, m))
+            B[i, j] = 1
+            assert_array_almost_equal(A.toarray(), B, err_msg=msg)
+        # [i,1:2]
+        for i, j in [(2, slice(3)), (2, slice(None, 10, 4)), (2, slice(5, -2)),
+                     (array(2), slice(5, -2))]:
+            _test_set(i, j)
+
+    def test_self_self_assignment(self):
+        # Tests whether a row of one sparse array can be assigned to another.
+        B = self.spcreator((4,3))
+        with warnings.catch_warnings():
+            warnings.filterwarnings("ignore", WMSG, SparseEfficiencyWarning)
+            B[0,0] = 2
+            B[1,2] = 7
+            B[2,1] = 3
+            B[3,0] = 10
+
+            A = B / 10
+            B[0,:] = A[0,:]
+            assert_array_equal(A[0,:].toarray(), B[0,:].toarray())
+
+            A = B / 10
+            B[:,:] = A[:1,:1]
+            assert_array_equal(np.zeros((4,3)) + A[0,0], B.toarray())
+
+            A = B / 10
+            B[:-1,0] = A[None,0,:].T
+            assert_array_equal(A[0,:].toarray().T, B[:-1,0].toarray())
+
+    def test_slice_assignment(self):
+        B = self.spcreator((4,3))
+        expected = array([[10,0,0],
+                          [0,0,6],
+                          [0,14,0],
+                          [0,0,0]])
+        block = [[1,0],[0,4]]
+
+        with warnings.catch_warnings():
+            warnings.filterwarnings("ignore", WMSG, SparseEfficiencyWarning)
+            B[0,0] = 5
+            B[1,2] = 3
+            B[2,1] = 7
+            B[:,:] = B+B
+            assert_array_equal(B.toarray(), expected)
+
+            B[:2,:2] = self.csc_container(array(block))
+            assert_array_equal(B.toarray()[:2, :2], block)
+
+    def test_sparsity_modifying_assignment(self):
+        B = self.spcreator((4,3))
+        with warnings.catch_warnings():
+            warnings.filterwarnings("ignore", WMSG, SparseEfficiencyWarning)
+            B[0,0] = 5
+            B[1,2] = 3
+            B[2,1] = 7
+            B[3,0] = 10
+            B[:3] = self.csr_container(np.eye(3))
+
+        expected = array([[1,0,0],[0,1,0],[0,0,1],[10,0,0]])
+        assert_array_equal(B.toarray(), expected)
+
+    def test_set_slice(self):
+        A = self.spcreator((5,10))
+        B = array(zeros((5, 10), float))
+        s_ = np.s_
+        slices = [s_[:2], s_[1:2], s_[3:], s_[3::2],
+                  s_[8:3:-1], s_[4::-2], s_[:5:-1],
+                  0, 1, s_[:], s_[1:5], -1, -2, -5,
+                  array(-1), np.int8(-3)]
+
+        with warnings.catch_warnings():
+            warnings.filterwarnings("ignore", WMSG, SparseEfficiencyWarning)
+            for j, a in enumerate(slices):
+                A[a] = j
+                B[a] = j
+                assert_array_equal(A.toarray(), B, repr(a))
+
+            for i, a in enumerate(slices):
+                for j, b in enumerate(slices):
+                    A[a,b] = 10*i + 1000*(j+1)
+                    B[a,b] = 10*i + 1000*(j+1)
+                    assert_array_equal(A.toarray(), B, repr((a, b)))
+
+            A[0, 1:10:2] = range(1, 10, 2)
+            B[0, 1:10:2] = range(1, 10, 2)
+            assert_array_equal(A.toarray(), B)
+            A[1:5:2, 0] = np.arange(1, 5, 2)[:, None]
+            B[1:5:2, 0] = np.arange(1, 5, 2)[:]
+            assert_array_equal(A.toarray(), B)
+
+        # The next commands should raise exceptions
+        assert_raises(ValueError, A.__setitem__, (0, 0), list(range(100)))
+        assert_raises(ValueError, A.__setitem__, (0, 0), arange(100))
+        assert_raises(ValueError, A.__setitem__, (0, slice(None)),
+                      list(range(100)))
+        assert_raises(ValueError, A.__setitem__, (slice(None), 1),
+                      list(range(100)))
+        assert_raises(ValueError, A.__setitem__, (slice(None), 1), A.copy())
+        assert_raises(ValueError, A.__setitem__,
+                      ([[1, 2, 3], [0, 3, 4]], [1, 2, 3]), [1, 2, 3, 4])
+        assert_raises(IndexError, A.__setitem__,
+                      ([[1, 2, 3], [0, 3, 4], [4, 1, 3]],
+                       [[1, 2, 4], [0, 1, 3]]), [2, 3, 4])
+        assert_raises(ValueError, A.__setitem__, (slice(4), 0),
+                      [[1, 2], [3, 4]])
+
+    def test_assign_empty(self):
+        A = self.spcreator(np.ones((2, 3)))
+        B = self.spcreator((1, 2))
+        # Note: This is not like NumPy!! Incoming shape needs to be (2,) for NumPy
+        # we are more lenient to accommodate vectors in 2d format as input
+        A[1, :2] = B
+        assert_array_equal(A.toarray(), [[1, 1, 1], [0, 0, 1]])
+
+    def test_assign_1d_slice(self):
+        A = self.spcreator(np.ones((3, 3)))
+        x = np.zeros(3)
+        A[:, 0] = x
+        A[1, :] = x
+        assert_array_equal(A.toarray(), [[0, 1, 1], [0, 0, 0], [0, 1, 1]])
+
+
+class _TestFancyIndexing:
+    """Tests fancy indexing features.  The tests for any matrix formats
+    that implement these features should derive from this class.
+    """
+
+    def test_dtype_preservation_empty_index(self):
+        # This should be parametrized with pytest, but something in the parent
+        # class creation used in this file breaks pytest.mark.parametrize.
+        for dt in [np.int16, np.int32, np.float32, np.float64]:
+            A = self.spcreator((3, 2), dtype=dt)
+            assert_equal(A[:, [False, False]].dtype, dt)
+            assert_equal(A[[False, False, False], :].dtype, dt)
+            assert_equal(A[:, []].dtype, dt)
+            assert_equal(A[[], :].dtype, dt)
+
+    def test_bad_index(self):
+        A = self.spcreator(np.zeros([5, 5]))
+        assert_raises(IndexError, A.__getitem__, "foo").match('Index dimension')
+        assert_raises(IndexError, A.__getitem__, (2, "foo")).match('Index dimension')
+        idx = ([1, 2, 3], [1, 2, 3, 4])
+        assert_raises(IndexError, A.__getitem__, idx).match('shape mismatch')
+
+    def test_fancy_indexing(self):
+        B = self.asdense(arange(50).reshape(5,10))
+        A = self.spcreator(B)
+
+        # [i]
+        assert_equal(A[[3]].toarray(), B[[3]])
+        assert_equal(A[[1, 3]].toarray(), B[[1, 3]])
+
+        # [i,[1,2]]
+        assert_equal(A[3, [3]].toarray(), B[3, [3]])
+        assert_equal(A[3, [1, 3]].toarray(), B[3, [1, 3]])
+        assert_equal(A[-1, [2, -5]].toarray(), B[-1, [2, -5]])
+        assert_equal(A[array(-1), [2, -5]].toarray(), B[-1, [2, -5]])
+        assert_equal(A[-1, array([2, -5])].toarray(), B[-1, [2, -5]])
+        assert_equal(A[array(-1), array([2, -5])].toarray(), B[-1, [2, -5]])
+
+        # [1:2,[1,2]]
+        assert_equal(A[:, [2, 8, 3, -1]].toarray(), B[:, [2, 8, 3, -1]])
+        assert_equal(A[3:4, [9]].toarray(), B[3:4, [9]])
+        assert_equal(A[1:4, [-1, -5]].toarray(), B[1:4, [-1, -5]])
+        assert_equal(A[1:4, array([-1, -5])].toarray(), B[1:4, [-1, -5]])
+
+        # [[1,2],j]
+        assert_equal(A[[3], 3].toarray(), B[[3], 3])
+        assert_equal(A[[1, 3], 3].toarray(), B[[1, 3], 3])
+        assert_equal(A[[2, -5], -4].toarray(), B[[2, -5], -4])
+        assert_equal(A[array([2, -5]), -4].toarray(), B[[2, -5], -4])
+        assert_equal(A[[2, -5], array(-4)].toarray(), B[[2, -5], -4])
+        assert_equal(A[array([2, -5]), array(-4)].toarray(), B[[2, -5], -4])
+
+        # [[1,2],1:2]
+        assert_equal(A[[3], :].toarray(), B[[3], :])
+        assert_equal(A[[1, 3], :].toarray(), B[[1, 3], :])
+        assert_equal(A[[2, -5], 8:-1].toarray(), B[[2, -5], 8:-1])
+        assert_equal(A[array([2, -5]), 8:-1].toarray(), B[[2, -5], 8:-1])
+
+        # [[1,2],[1,2]]
+        assert_equal(toarray(A[[3], [4]]), B[[3], [4]])
+        assert_equal(toarray(A[[1, 3], [2, 4]]), B[[1, 3], [2, 4]])
+        assert_equal(toarray(A[[-1, -3], [2, -4]]), B[[-1, -3], [2, -4]])
+        assert_equal(
+            toarray(A[array([-1, -3]), [2, -4]]), B[[-1, -3], [2, -4]]
+        )
+        assert_equal(
+            toarray(A[[-1, -3], array([2, -4])]), B[[-1, -3], [2, -4]]
+        )
+        assert_equal(
+            toarray(A[array([-1, -3]), array([2, -4])]), B[[-1, -3], [2, -4]]
+        )
+
+        # [[[1],[2]],[1,2]]
+        assert_equal(A[[[1], [3]], [2, 4]].toarray(), B[[[1], [3]], [2, 4]])
+        assert_equal(
+            A[[[-1], [-3], [-2]], [2, -4]].toarray(),
+            B[[[-1], [-3], [-2]], [2, -4]]
+        )
+        assert_equal(
+            A[array([[-1], [-3], [-2]]), [2, -4]].toarray(),
+            B[[[-1], [-3], [-2]], [2, -4]]
+        )
+        assert_equal(
+            A[[[-1], [-3], [-2]], array([2, -4])].toarray(),
+            B[[[-1], [-3], [-2]], [2, -4]]
+        )
+        assert_equal(
+            A[array([[-1], [-3], [-2]]), array([2, -4])].toarray(),
+            B[[[-1], [-3], [-2]], [2, -4]]
+        )
+
+        # [[1,2]]
+        assert_equal(A[[1, 3]].toarray(), B[[1, 3]])
+        assert_equal(A[[-1, -3]].toarray(), B[[-1, -3]])
+        assert_equal(A[array([-1, -3])].toarray(), B[[-1, -3]])
+
+        # [[1,2],:][:,[1,2]]
+        assert_equal(A[[3], :][:, [4]].toarray(), B[[3], :][:, [4]])
+        assert_equal(
+            A[[1, 3], :][:, [2, 4]].toarray(), B[[1, 3], :][:, [2, 4]]
+        )
+        assert_equal(
+            A[[-1, -3], :][:, [2, -4]].toarray(), B[[-1, -3], :][:, [2, -4]]
+        )
+        assert_equal(
+            A[array([-1, -3]), :][:, array([2, -4])].toarray(),
+            B[[-1, -3], :][:, [2, -4]]
+        )
+
+        assert_equal(
+            A[1, [[1, 3]]][[[0, 0]], 1].toarray(), B[1, [[1, 3]]][[[0, 0]], 1]
+        )
+        assert_equal(
+            A[1, [[-1, -3]]][[[0, -1]], 1].toarray(), B[1, [[-1, -3]]][[[0, -1]], 1]
+        )
+        # leads to 3D result
+        if A.format == "coo":
+            assert_equal(A[:1, [[1, 3]]].toarray(), B[:1, [[1, 3]]])
+            assert_equal(A[[[0, 0]], :1].toarray(), B[[[0, 0]], :1])
+        else:
+            with pytest.raises(IndexError, match="Only 1D or 2D|>2D is not supported"):
+                A[:1, [[1, 3]]]
+            with pytest.raises(IndexError, match="Only 1D or 2D|>2D is not supported"):
+                A[[[0, 0]], :1]
+
+
+        assert_equal(
+            A[:, [1, 3]][[2, 4], :].toarray(), B[:, [1, 3]][[2, 4], :]
+        )
+        assert_equal(
+            A[:, [-1, -3]][[2, -4], :].toarray(), B[:, [-1, -3]][[2, -4], :]
+        )
+        assert_equal(
+            A[:, array([-1, -3])][array([2, -4]), :].toarray(),
+            B[:, [-1, -3]][[2, -4], :]
+        )
+
+        # Check bug reported by Robert Cimrman:
+        # http://thread.gmane.org/gmane.comp.python.scientific.devel/7986 (dead link)
+        s = slice(int8(2),int8(4),None)
+        assert_equal(A[s, :].toarray(), B[2:4, :])
+        assert_equal(A[:, s].toarray(), B[:, 2:4])
+
+        # Regression for gh-4917: index with tuple of 2D arrays
+        i = np.array([[1]], dtype=int)
+        assert_equal(A[i, i].toarray(), B[i, i])
+
+        # Regression for gh-4917: index with tuple of empty nested lists
+        assert_equal(A[[[]], [[]]].toarray(), B[[[]], [[]]])
+
+    def test_fancy_indexing_randomized(self):
+        np.random.seed(1234)  # make runs repeatable
+
+        NUM_SAMPLES = 50
+        M = 6
+        N = 4
+
+        D = self.asdense(np.random.rand(M,N))
+        D = np.multiply(D, D > 0.5)
+
+        I = np.random.randint(-M + 1, M, size=NUM_SAMPLES)
+        J = np.random.randint(-N + 1, N, size=NUM_SAMPLES)
+
+        S = self.spcreator(D)
+
+        SIJ = S[I,J]
+        if issparse(SIJ):
+            SIJ = SIJ.toarray()
+        assert_equal(SIJ, D[I,J])
+
+        I_bad = I + M
+        J_bad = J - N
+
+        assert_raises(IndexError, S.__getitem__, (I_bad,J))
+        assert_raises(IndexError, S.__getitem__, (I,J_bad))
+
+    def test_missized_masking(self):
+        M, N = 5, 10
+
+        B = self.asdense(arange(M * N).reshape(M, N))
+        A = self.spcreator(B)
+
+        # Content of mask shouldn't matter, only its size
+        row_long = np.ones(M + 1, dtype=bool)
+        row_short = np.ones(M - 1, dtype=bool)
+        col_long = np.ones(N + 2, dtype=bool)
+        col_short = np.ones(N - 2, dtype=bool)
+
+        match="bool index .* has shape .* instead of .*"
+        for i, j in itertools.product(
+            (row_long, row_short, slice(None)),
+            (col_long, col_short, slice(None)),
+        ):
+            if isinstance(i, slice) and isinstance(j, slice):
+                continue
+            with pytest.raises(IndexError, match=match):
+                _ = A[i, j]
+
+    def test_fancy_indexing_boolean(self):
+        np.random.seed(1234)  # make runs repeatable
+
+        B = self.asdense(arange(50).reshape(5,10))
+        A = self.spcreator(B)
+
+        I = np.array(np.random.randint(0, 2, size=5), dtype=bool)
+        J = np.array(np.random.randint(0, 2, size=10), dtype=bool)
+        X = np.array(np.random.randint(0, 2, size=(5, 10)), dtype=bool)
+
+        assert_equal(toarray(A[I]), B[I])
+        assert_equal(toarray(A[:, J]), B[:, J])
+        assert_equal(toarray(A[X]), B[X])
+        assert_equal(toarray(A[B > 9]), B[B > 9])
+
+        I = np.array([True, False, True, True, False])
+        J = np.array([False, True, True, False, True,
+                      False, False, False, False, False])
+
+        assert_equal(toarray(A[I, J]), B[I, J])
+
+        Z1 = np.zeros((6, 11), dtype=bool)
+        Z2 = np.zeros((6, 11), dtype=bool)
+        Z2[0,-1] = True
+        Z3 = np.zeros((6, 11), dtype=bool)
+        Z3[-1,0] = True
+
+        assert_raises(IndexError, A.__getitem__, Z1)
+        assert_raises(IndexError, A.__getitem__, Z2)
+        assert_raises(IndexError, A.__getitem__, Z3)
+        assert_raises((IndexError, ValueError), A.__getitem__, (X, 1))
+
+    def test_fancy_indexing_sparse_boolean(self):
+        np.random.seed(1234)  # make runs repeatable
+
+        B = self.asdense(arange(50).reshape(5,10))
+        A = self.spcreator(B)
+
+        X = np.array(np.random.randint(0, 2, size=(5, 10)), dtype=bool)
+
+        Xsp = self.csr_container(X)
+
+        assert_equal(toarray(A[Xsp]), B[X])
+        assert_equal(toarray(A[A > 9]), B[B > 9])
+
+        Z = np.array(np.random.randint(0, 2, size=(5, 11)), dtype=bool)
+        Y = np.array(np.random.randint(0, 2, size=(6, 10)), dtype=bool)
+
+        Zsp = self.csr_container(Z)
+        Ysp = self.csr_container(Y)
+
+        assert_raises(IndexError, A.__getitem__, Zsp)
+        assert_raises(IndexError, A.__getitem__, Ysp)
+        assert_raises((IndexError, ValueError), A.__getitem__, (Xsp, 1))
+
+    def test_fancy_indexing_regression_3087(self):
+        mat = self.spcreator(array([[1, 0, 0], [0,1,0], [1,0,0]]))
+        desired_cols = np.ravel(mat.sum(0)) > 0
+        assert_equal(mat[:, desired_cols].toarray(), [[1, 0], [0, 1], [1, 0]])
+
+    def test_fancy_indexing_seq_assign(self):
+        mat = self.spcreator(array([[1, 0], [0, 1]]))
+        assert_raises(ValueError, mat.__setitem__, (0, 0), np.array([1,2]))
+
+    def test_fancy_indexing_2d_assign(self):
+        # regression test for gh-10695
+        mat = self.spcreator(array([[1, 0], [2, 3]]))
+        with warnings.catch_warnings():
+            warnings.filterwarnings("ignore", WMSG, SparseEfficiencyWarning)
+            mat[[0, 1], [1, 1]] = mat[[1, 0], [0, 0]]
+        assert_equal(toarray(mat), array([[1, 2], [2, 1]]))
+
+    def test_fancy_indexing_empty(self):
+        B = self.asdense(arange(50).reshape(5,10))
+        B[1,:] = 0
+        B[:,2] = 0
+        B[3,6] = 0
+        A = self.spcreator(B)
+
+        K = np.array([False, False, False, False, False])
+        assert_equal(toarray(A[K]), B[K])
+        K = np.array([], dtype=int)
+        assert_equal(toarray(A[K]), B[K])
+        assert_equal(toarray(A[K, K]), B[K, K])
+        J = np.array([0, 1, 2, 3, 4], dtype=int)[:,None]
+        assert_equal(toarray(A[K, J]), B[K, J])
+        assert_equal(toarray(A[J, K]), B[J, K])
+
+
+@contextlib.contextmanager
+def check_remains_sorted(X):
+    """Checks that sorted indices property is retained through an operation
+    """
+    if not hasattr(X, 'has_sorted_indices') or not X.has_sorted_indices:
+        yield
+        return
+    yield
+    indices = X.indices.copy()
+    X.has_sorted_indices = False
+    X.sort_indices()
+    assert_array_equal(indices, X.indices,
+                       'Expected sorted indices, found unsorted')
+
+
+class _TestFancyIndexingAssign:
+    def test_bad_index_assign(self):
+        A = self.spcreator(np.zeros([5, 5]))
+        assert_raises((IndexError, ValueError, TypeError), A.__setitem__, "foo", 2)
+        assert_raises((IndexError, ValueError, TypeError), A.__setitem__, (2, "foo"), 5)
+
+    def test_fancy_indexing_set(self):
+        n, m = (5, 10)
+
+        def _test_set_slice(i, j):
+            A = self.spcreator((n, m))
+            B = self.asdense(np.zeros((n, m)))
+            with warnings.catch_warnings():
+                warnings.filterwarnings("ignore", WMSG, SparseEfficiencyWarning)
+                B[i, j] = 1
+                with check_remains_sorted(A):
+                    A[i, j] = 1
+            assert_array_almost_equal(A.toarray(), B)
+        # [1:2,1:2]
+        for i, j in [((2, 3, 4), slice(None, 10, 4)),
+                     (np.arange(3), slice(5, -2)),
+                     (slice(2, 5), slice(5, -2))]:
+            _test_set_slice(i, j)
+        for i, j in [(np.arange(3), np.arange(3)), ((0, 3, 4), (1, 2, 4))]:
+            _test_set_slice(i, j)
+
+    def test_fancy_assignment_dtypes(self):
+        def check(dtype):
+            A = self.spcreator((5, 5), dtype=dtype)
+            with warnings.catch_warnings():
+                warnings.filterwarnings("ignore", WMSG, SparseEfficiencyWarning)
+                A[[0,1],[0,1]] = dtype.type(1)
+                assert_equal(A.sum(), dtype.type(1)*2)
+                A[0:2,0:2] = dtype.type(1.0)
+                assert_equal(A.sum(), dtype.type(1)*4)
+                A[2,2] = dtype.type(1.0)
+                assert_equal(A.sum(), dtype.type(1)*4 + dtype.type(1))
+
+        for dtype in supported_dtypes:
+            check(np.dtype(dtype))
+
+    def test_sequence_assignment(self):
+        A = self.spcreator((4,3))
+        B = self.spcreator(eye(3,4))
+
+        i0 = [0,1,2]
+        i1 = (0,1,2)
+        i2 = array(i0)
+
+        with warnings.catch_warnings():
+            warnings.filterwarnings("ignore", WMSG, SparseEfficiencyWarning)
+            with check_remains_sorted(A):
+                A[0,i0] = B[i0,0].T
+                A[1,i1] = B[i1,1].T
+                A[2,i2] = B[i2,2].T
+            assert_array_equal(A.toarray(), B.T.toarray())
+
+            # column slice
+            A = self.spcreator((2,3))
+            with check_remains_sorted(A):
+                A[1,1:3] = [10,20]
+            assert_array_equal(A.toarray(), [[0, 0, 0], [0, 10, 20]])
+
+            # row slice
+            A = self.spcreator((3,2))
+            with check_remains_sorted(A):
+                A[1:3,1] = [[10],[20]]
+            assert_array_equal(A.toarray(), [[0, 0], [0, 10], [0, 20]])
+
+            # both slices
+            A = self.spcreator((3,3))
+            B = self.asdense(np.zeros((3,3)))
+            with check_remains_sorted(A):
+                for C in [A, B]:
+                    C[[0,1,2], [0,1,2]] = [4,5,6]
+            assert_array_equal(A.toarray(), B)
+
+            # both slices (2)
+            A = self.spcreator((4, 3))
+            with check_remains_sorted(A):
+                A[(1, 2, 3), (0, 1, 2)] = [1, 2, 3]
+            assert_almost_equal(A.sum(), 6)
+            B = self.asdense(np.zeros((4, 3)))
+            B[(1, 2, 3), (0, 1, 2)] = [1, 2, 3]
+            assert_array_equal(A.toarray(), B)
+
+    def test_fancy_assign_empty(self):
+        B = self.asdense(arange(50).reshape(5,10))
+        B[1,:] = 0
+        B[:,2] = 0
+        B[3,6] = 0
+        A = self.spcreator(B)
+
+        K = np.array([False, False, False, False, False])
+        A[K] = 42
+        assert_equal(toarray(A), B)
+
+        K = np.array([], dtype=int)
+        A[K] = 42
+        assert_equal(toarray(A), B)
+        A[K,K] = 42
+        assert_equal(toarray(A), B)
+
+        J = np.array([0, 1, 2, 3, 4], dtype=int)[:,None]
+        A[K,J] = 42
+        assert_equal(toarray(A), B)
+        A[J,K] = 42
+        assert_equal(toarray(A), B)
+
+
+class _TestFancyMultidim:
+    def test_fancy_indexing_ndarray(self):
+        IandJ = [
+            (np.array([[1], [2], [3]]), np.array([3, 4, 2])),
+            (np.array([[1], [2], [3]]), np.array([[3, 4, 2]])),
+            (np.array([[1, 2, 3]]), np.array([[3], [4], [2]])),
+            (np.array([1, 2, 3]), np.array([[3], [4], [2]])),
+            (np.array([[1, 2, 3], [3, 4, 2]]), np.array([[5, 6, 3], [2, 3, 1]])),
+        ]
+
+        np.random.seed(1234)
+        D = self.asdense(np.random.rand(5, 7))
+        S = self.spcreator(D)
+
+        # These inputs generate 3-D outputs
+        if S.format == 'coo':
+            IandJ.append(
+                (np.array([[[1], [2], [3]], [[3], [4], [2]]]),
+                 np.array([[[5], [6], [3]], [[2], [3], [1]]]))
+            )
+
+        for I, J in IandJ:
+            SIJ = S[I, J]
+            DIJ = D[I, J]
+            assert_equal(toarray(SIJ), DIJ)
+
+            I_bad = I + 5
+            J_bad = J + 7
+
+            assert_raises(IndexError, S.__getitem__, (I_bad, J))
+            assert_raises(IndexError, S.__getitem__, (I, J_bad))
+
+            if S.format != 'coo':
+                assert_raises(IndexError, S.__getitem__, ([I, I], slice(None)))
+                assert_raises(IndexError, S.__getitem__, (slice(None), [J, J]))
+            else:
+                assert_equal(S[[I, I], :].toarray(), D[[I, I], :])
+                assert_equal(S[:, [J, J]].toarray(), D[:, [J, J]])
+
+
+class _TestFancyMultidimAssign:
+    def test_fancy_assign_ndarray(self):
+        np.random.seed(1234)
+
+        D = self.asdense(np.random.rand(5, 7))
+        S = self.spcreator(D)
+        X = np.random.rand(2, 3)
+
+        I = np.array([[1, 2, 3], [3, 4, 2]])
+        J = np.array([[5, 6, 3], [2, 3, 1]])
+
+        with check_remains_sorted(S):
+            S[I,J] = X
+        D[I,J] = X
+        assert_equal(S.toarray(), D)
+
+        I_bad = I + 5
+        J_bad = J + 7
+
+        C = [1, 2, 3]
+
+        with check_remains_sorted(S):
+            S[I,J] = C
+        D[I,J] = C
+        assert_equal(S.toarray(), D)
+
+        with check_remains_sorted(S):
+            S[I,J] = 3
+        D[I,J] = 3
+        assert_equal(S.toarray(), D)
+
+        assert_raises(IndexError, S.__setitem__, (I_bad,J), C)
+        assert_raises(IndexError, S.__setitem__, (I,J_bad), C)
+
+    def test_fancy_indexing_multidim_set(self):
+        n, m = (5, 10)
+
+        def _test_set_slice(i, j):
+            A = self.spcreator((n, m))
+            with check_remains_sorted(A), warnings.catch_warnings():
+                warnings.filterwarnings("ignore", WMSG, SparseEfficiencyWarning)
+                A[i, j] = 1
+            B = self.asdense(np.zeros((n, m)))
+            B[i, j] = 1
+            assert_array_almost_equal(A.toarray(), B)
+        # [[[1, 2], [1, 2]], [1, 2]]
+        for i, j in [(np.array([[1, 2], [1, 3]]), [1, 3]),
+                        (np.array([0, 4]), [[0, 3], [1, 2]]),
+                        ([[1, 2, 3], [0, 2, 4]], [[0, 4, 3], [4, 1, 2]])]:
+            _test_set_slice(i, j)
+
+    def test_fancy_assign_list(self):
+        np.random.seed(1234)
+
+        D = self.asdense(np.random.rand(5, 7))
+        S = self.spcreator(D)
+        X = np.random.rand(2, 3)
+
+        I = [[1, 2, 3], [3, 4, 2]]
+        J = [[5, 6, 3], [2, 3, 1]]
+
+        S[I,J] = X
+        D[I,J] = X
+        assert_equal(S.toarray(), D)
+
+        I_bad = [[ii + 5 for ii in i] for i in I]
+        J_bad = [[jj + 7 for jj in j] for j in J]
+        C = [1, 2, 3]
+
+        S[I,J] = C
+        D[I,J] = C
+        assert_equal(S.toarray(), D)
+
+        S[I,J] = 3
+        D[I,J] = 3
+        assert_equal(S.toarray(), D)
+
+        assert_raises(IndexError, S.__setitem__, (I_bad,J), C)
+        assert_raises(IndexError, S.__setitem__, (I,J_bad), C)
+
+    def test_fancy_assign_slice(self):
+        np.random.seed(1234)
+
+        D = self.asdense(np.random.rand(5, 7))
+        S = self.spcreator(D)
+
+        I = [1, 2, 3, 3, 4, 2]
+        J = [5, 6, 3, 2, 3, 1]
+
+        I_bad = [ii + 5 for ii in I]
+        J_bad = [jj + 7 for jj in J]
+
+        C1 = [1, 2, 3, 4, 5, 6, 7]
+        C2 = np.arange(5)[:, None]
+        assert_raises(IndexError, S.__setitem__, (I_bad, slice(None)), C1)
+        assert_raises(IndexError, S.__setitem__, (slice(None), J_bad), C2)
+
+
+class _TestArithmetic:
+    """
+    Test real/complex arithmetic
+    """
+    def __arith_init(self):
+        # these can be represented exactly in FP (so arithmetic should be exact)
+        __A = array([[-1.5, 6.5, 0, 2.25, 0, 0],
+                          [3.125, -7.875, 0.625, 0, 0, 0],
+                          [0, 0, -0.125, 1.0, 0, 0],
+                          [0, 0, 8.375, 0, 0, 0]], 'float64')
+        __B = array([[0.375, 0, 0, 0, -5, 2.5],
+                          [14.25, -3.75, 0, 0, -0.125, 0],
+                          [0, 7.25, 0, 0, 0, 0],
+                          [18.5, -0.0625, 0, 0, 0, 0]], 'complex128')
+        __B.imag = array([[1.25, 0, 0, 0, 6, -3.875],
+                               [2.25, 4.125, 0, 0, 0, 2.75],
+                               [0, 4.125, 0, 0, 0, 0],
+                               [-0.0625, 0, 0, 0, 0, 0]], 'float64')
+
+        # fractions are all x/16ths
+        assert_array_equal((__A*16).astype('int32'),16*__A)
+        assert_array_equal((__B.real*16).astype('int32'),16*__B.real)
+        assert_array_equal((__B.imag*16).astype('int32'),16*__B.imag)
+
+        __Asp = self.spcreator(__A)
+        __Bsp = self.spcreator(__B)
+        return __A, __B, __Asp, __Bsp
+
+    @pytest.mark.fail_slow(20)
+    def test_add_sub(self):
+        __A, __B, __Asp, __Bsp = self.__arith_init()
+
+        # basic tests
+        assert_array_equal(
+            (__Asp + __Bsp).toarray(), __A + __B
+        )
+
+        # check conversions
+        for x in supported_dtypes:
+            with np.errstate(invalid="ignore"):
+                A = __A.astype(x)
+            Asp = self.spcreator(A)
+            for y in supported_dtypes:
+                if not np.issubdtype(y, np.complexfloating):
+                    with np.errstate(invalid="ignore"):
+                        B = __B.real.astype(y)
+                else:
+                    B = __B.astype(y)
+                Bsp = self.spcreator(B)
+
+                # addition
+                D1 = A + B
+                S1 = Asp + Bsp
+
+                assert_equal(S1.dtype,D1.dtype)
+                assert_array_equal(S1.toarray(), D1)
+                assert_array_equal(Asp + B,D1)          # check sparse + dense
+                assert_array_equal(A + Bsp,D1)          # check dense + sparse
+
+                # subtraction
+                if np.dtype('bool') in [x, y]:
+                    # boolean array subtraction deprecated in 1.9.0
+                    continue
+
+                D1 = A - B
+                S1 = Asp - Bsp
+
+                assert_equal(S1.dtype,D1.dtype)
+                assert_array_equal(S1.toarray(), D1)
+                assert_array_equal(Asp - B,D1)          # check sparse - dense
+                assert_array_equal(A - Bsp,D1)          # check dense - sparse
+
+    def test_mu(self):
+        __A, __B, __Asp, __Bsp = self.__arith_init()
+
+        # basic tests
+        assert_array_equal((__Asp @ __Bsp.T).toarray(),
+                            __A @ __B.T)
+
+        for x in supported_dtypes:
+            with np.errstate(invalid="ignore"):
+                A = __A.astype(x)
+            Asp = self.spcreator(A)
+            for y in supported_dtypes:
+                if np.issubdtype(y, np.complexfloating):
+                    B = __B.astype(y)
+                else:
+                    with np.errstate(invalid="ignore"):
+                        B = __B.real.astype(y)
+                Bsp = self.spcreator(B)
+
+                D1 = A @ B.T
+                S1 = Asp @ Bsp.T
+
+                assert_allclose(S1.toarray(), D1,
+                                atol=1e-14*abs(D1).max())
+                assert_equal(S1.dtype,D1.dtype)
+
+
+class _TestMinMax:
+    def test_minmax(self):
+        for dtype in [np.float32, np.float64, np.int32, np.int64, np.complex128]:
+            D = np.arange(20, dtype=dtype).reshape(5,4)
+
+            X = self.spcreator(D)
+            assert_equal(X.min(), 0)
+            assert_equal(X.max(), 19)
+            assert_equal(X.min().dtype, dtype)
+            assert_equal(X.max().dtype, dtype)
+
+            D *= -1
+            X = self.spcreator(D)
+            assert_equal(X.min(), -19)
+            assert_equal(X.max(), 0)
+
+            D += 5
+            X = self.spcreator(D)
+            assert_equal(X.min(), -14)
+            assert_equal(X.max(), 5)
+
+        # try a fully dense matrix
+        X = self.spcreator(np.arange(1, 10).reshape(3, 3))
+        assert_equal(X.min(), 1)
+        assert_equal(X.min().dtype, X.dtype)
+        assert_equal(X.min(explicit=True), 1)
+
+        X = -X
+        assert_equal(X.max(), -1)
+        assert_equal(X.max(explicit=True), -1)
+
+        # and a fully sparse matrix
+        Z = self.spcreator(np.zeros((1, 1)))
+        assert_equal(Z.min(), 0)
+        assert_equal(Z.max(), 0)
+        assert_equal(Z.max().dtype, Z.dtype)
+
+        # another test
+        D = np.arange(20, dtype=float).reshape(5,4)
+        D[0:2, :] = 0
+        X = self.spcreator(D)
+        assert_equal(X.min(), 0)
+        assert_equal(X.max(), 19)
+
+        # zero-size matrices
+        for D in [np.zeros((0, 0)), np.zeros((0, 10)), np.zeros((10, 0))]:
+            X = self.spcreator(D)
+            assert_raises(ValueError, X.min)
+            assert_raises(ValueError, X.max)
+
+    def test_minmax_axis(self):
+        keep = not self.is_array_test
+        D = np.arange(50).reshape(5, 10)
+        # completely empty rows, leaving some completely full:
+        D[1, :] = 0
+        # empty at end for reduceat:
+        D[:, 9] = 0
+        # partial rows/cols:
+        D[3, 3] = 0
+        # entries on either side of 0:
+        D[2, 2] = -1
+        X = self.spcreator(D)
+
+        axes_even = [0, -2]
+        axes_odd = [1, -1]
+        for axis in axes_odd + axes_even:
+            assert_array_equal(
+                X.max(axis=axis).toarray(), D.max(axis=axis, keepdims=keep)
+            )
+            assert_array_equal(
+                X.min(axis=axis).toarray(), D.min(axis=axis, keepdims=keep)
+            )
+
+        for axis in axes_even:
+            assert_equal(
+                X.max(axis=axis, explicit=True).toarray(),
+                self.asdense([40, 41, 42, 43, 44, 45, 46, 47, 48, 0])
+            )
+            if np.any(X.data == 0):
+                # Noncanonical case
+                expected = self.asdense([20, 1, -1, 3, 4, 5, 0, 7, 8, 0])
+            else:
+                expected = self.asdense([20, 1, -1, 3, 4, 5, 6, 7, 8, 0])
+            assert_equal(X.min(axis=axis, explicit=True).toarray(), expected)
+
+        for axis in axes_odd:
+            expected_max = np.array([8, 0, 28, 38, 48])
+            expected_min = np.array([1, 0, -1, 30, 40])
+            if not self.is_array_test:
+                expected_max = expected_max.reshape((5, 1))
+                expected_min = expected_min.reshape((5, 1))
+            assert_equal(X.max(axis=axis, explicit=True).toarray(), expected_max)
+            assert_equal(X.min(axis=axis, explicit=True).toarray(), expected_min)
+
+        # full matrix
+        D = np.arange(1, 51).reshape(10, 5)
+        X = self.spcreator(D)
+        for axis in axes_odd + axes_even:
+            assert_array_equal(
+                X.max(axis=axis).toarray(), D.max(axis=axis, keepdims=keep)
+            )
+            assert_array_equal(
+                X.min(axis=axis).toarray(), D.min(axis=axis, keepdims=keep)
+            )
+        assert_equal(X.max(axis=(0, 1)), D.max(axis=(0, 1), keepdims=keep))
+
+        for axis in axes_even:
+            expected_max = D[-1, :]
+            expected_min = D[0, :]
+            if not self.is_array_test:
+                expected_max = D[None, -1, :]
+                expected_min = D[None, 0, :]
+            assert_equal(X.max(axis=axis, explicit=True).toarray(), expected_max)
+            assert_equal(X.min(axis=axis, explicit=True).toarray(), expected_min)
+        for axis in axes_odd:
+            expected_max = D[:, -1]
+            expected_min = D[:, 0]
+            if not self.is_array_test:
+                expected_max = D[:, -1, None]
+                expected_min = D[:, 0, None]
+            assert_equal(X.max(axis=axis, explicit=True).toarray(), expected_max)
+            assert_equal(X.min(axis=axis, explicit=True).toarray(), expected_min)
+
+        # empty matrix
+        D = self.asdense(np.zeros((10, 5)))
+        X = self.spcreator(D)
+        for axis in axes_even + axes_odd:
+            assert_equal(X.max(axis=axis, explicit=True).toarray(), D.max(axis=axis))
+            assert_equal(X.min(axis=axis, explicit=True).toarray(), D.min(axis=axis))
+
+        # zero-size matrices
+        D = self.asdense(np.zeros((0, 10)))
+        X = self.spcreator(D)
+        explicit_values = [True, False]
+        even_explicit_pairs = list(itertools.product(axes_even, explicit_values))
+        odd_explicit_pairs = list(itertools.product(axes_odd, explicit_values))
+        for axis, ex in even_explicit_pairs:
+            assert_raises(ValueError, X.min, axis=axis, explicit=ex)
+            assert_raises(ValueError, X.max, axis=axis, explicit=ex)
+        for axis, ex in odd_explicit_pairs:
+            assert_equal(X.max(axis=axis, explicit=ex).toarray(), D.max(axis=axis))
+            assert_equal(X.min(axis=axis, explicit=ex).toarray(), D.min(axis=axis))
+
+        D = self.asdense(np.zeros((10, 0)))
+        X = self.spcreator(D)
+        for axis, ex in odd_explicit_pairs:
+            assert_raises(ValueError, X.min, axis=axis, explicit=ex)
+            assert_raises(ValueError, X.max, axis=axis, explicit=ex)
+        for axis, ex in even_explicit_pairs:
+            assert_equal(X.max(axis=axis, explicit=ex).toarray(), D.max(axis=axis))
+            assert_equal(X.min(axis=axis, explicit=ex).toarray(), D.min(axis=axis))
+
+    def test_minmax_container_type(self):
+        dat = array([[0, 1, 2],
+                     [3, -4, 5],
+                     [-6, 7, 9]])
+        datsp = self.spcreator(dat)
+        matrix_or_array = ndarray if self.is_array_test else np.matrix
+        spmatrix_or_sparray = sparray if self.is_array_test else spmatrix
+
+        assert isscalarlike(datsp.min())
+        assert isinstance(datsp.min(axis=0), spmatrix_or_sparray)
+        assert isinstance(datsp.min(axis=1), spmatrix_or_sparray)
+
+        assert isscalarlike(datsp.max())
+        assert isinstance(datsp.max(axis=0), spmatrix_or_sparray)
+        assert isinstance(datsp.max(axis=1), spmatrix_or_sparray)
+
+        assert isscalarlike(datsp.nanmin())
+        assert isinstance(datsp.nanmin(axis=0), spmatrix_or_sparray)
+        assert isinstance(datsp.nanmin(axis=1), spmatrix_or_sparray)
+
+        assert isscalarlike(datsp.nanmax())
+        assert isinstance(datsp.nanmax(axis=0), spmatrix_or_sparray)
+        assert isinstance(datsp.nanmax(axis=1), spmatrix_or_sparray)
+
+        assert isscalarlike(datsp.argmin())
+        assert isinstance(datsp.argmin(axis=0), matrix_or_array)
+        assert isinstance(datsp.argmin(axis=1), matrix_or_array)
+
+        assert isscalarlike(datsp.argmax())
+        assert isinstance(datsp.argmax(axis=0), matrix_or_array)
+        assert isinstance(datsp.argmax(axis=1), matrix_or_array)
+
+    def test_nanminmax(self):
+        D = self.asdense(np.arange(50).reshape(5,10), dtype=float)
+        D[1, :] = 0
+        D[:, 9] = 0
+        D[3, 3] = 0
+        D[2, 2] = -1
+        D[4, 2] = np.nan
+        D[1, 4] = np.nan
+        X = self.spcreator(D)
+
+        X_nan_maximum = X.nanmax()
+        assert np.isscalar(X_nan_maximum)
+        assert X_nan_maximum == np.nanmax(D)
+
+        X_nan_minimum = X.nanmin()
+        assert np.isscalar(X_nan_minimum)
+        assert X_nan_minimum == np.nanmin(D)
+
+        X_nan_minimum = X.nanmin(axis=(0, 1))
+        assert np.isscalar(X_nan_minimum)
+        assert X_nan_minimum == np.nanmin(D, axis=(0, 1))
+
+        axes = [-2, -1, 0, 1]
+        for axis in axes:
+            X_nan_maxima = X.nanmax(axis=axis)
+            assert_allclose(X_nan_maxima.toarray(), np.nanmax(D, axis=axis))
+            assert isinstance(X_nan_maxima, self.coo_container)
+
+            X_nan_minima = X.nanmin(axis=axis)
+            assert_allclose(X_nan_minima.toarray(), np.nanmin(D, axis=axis))
+            assert isinstance(X_nan_minima, self.coo_container)
+
+    def test_minmax_invalid_params(self):
+        dat = array([[0, 1, 2],
+                     [3, -4, 5],
+                     [-6, 7, 9]])
+        datsp = self.spcreator(dat)
+
+        for fname in ('min', 'max'):
+            datfunc = getattr(dat, fname)
+            func = getattr(datsp, fname)
+            assert_raises(ValueError, func, axis=3)
+            assert_raises(TypeError, func, axis=1.5)
+            assert_raises(ValueError, func, axis=1, out=1)
+            assert_equal(func(axis=(0, 1)), datfunc(axis=(0, 1)))
+
+    def test_numpy_minmax(self):
+        # See gh-5987
+        # xref gh-7460 in 'numpy'
+        from scipy.sparse import _data
+
+        dat = array([[0, 1, 2],
+                     [3, -4, 5],
+                     [-6, 7, 9]])
+        datsp = self.spcreator(dat)
+
+        # We are only testing sparse matrices who have
+        # implemented 'min' and 'max' because they are
+        # the ones with the compatibility issues with
+        # the 'numpy' implementation.
+        if isinstance(datsp, _data._minmax_mixin):
+            assert_array_equal(np.min(datsp), np.min(dat))
+            assert_array_equal(np.max(datsp), np.max(dat))
+
+    def test_argmax(self):
+        from scipy.sparse import _data
+        D1 = np.array([
+            [-1, 5, 2, 3],
+            [0, 0, -1, -2],
+            [-1, -2, -3, -4],
+            [1, 2, 3, 4],
+            [1, 2, 0, 0],
+        ])
+        D2 = D1.transpose()
+        # Non-regression test cases for gh-16929.
+        D3 = np.array([[4, 3], [7, 5]])
+        D4 = np.array([[4, 3], [7, 0]])
+        D5 = np.array([[5, 5, 3], [4, 9, 10], [3, 4, 9]])
+
+        for D in [D1, D2, D3, D4, D5]:
+            D = self.asdense(D)
+            mat = self.spcreator(D)
+            if not isinstance(mat, _data._minmax_mixin):
+                continue
+
+            assert_equal(mat.argmax(), np.argmax(D))
+            assert_equal(mat.argmin(), np.argmin(D))
+
+            assert_equal(mat.argmax(axis=0), np.argmax(D, axis=0))
+            assert_equal(mat.argmin(axis=0), np.argmin(D, axis=0))
+
+            assert_equal(mat.argmax(axis=1), np.argmax(D, axis=1))
+            assert_equal(mat.argmin(axis=1), np.argmin(D, axis=1))
+
+        # full matrix with explicit=True
+        mat = self.spcreator(self.asdense(D5))
+        assert_equal(mat.argmax(explicit=True), 5)
+        assert_equal((-mat).argmax(explicit=True), 2)
+        assert_equal(mat.argmin(explicit=True), 2)
+        assert_equal((-mat).argmin(explicit=True), 5)
+
+        # zero-size matrices
+        D6 = self.spcreator(np.empty((0, 5)))
+        D7 = self.spcreator(np.empty((5, 0)))
+        explicits = [True, False]
+
+        for mat, axis, ex in itertools.product([D6, D7], [None, 0, 1], explicits):
+            if axis is None or mat.shape[axis] == 0:
+                with pytest.raises(ValueError, match="Cannot apply"):
+                    mat.argmax(axis=axis, explicit=ex)
+                with pytest.raises(ValueError, match="Cannot apply"):
+                    mat.argmin(axis=axis, explicit=ex)
+            else:
+                if self.is_array_test:
+                    expected = np.zeros(0)
+                else:
+                    expected = np.zeros((0, 1) if axis == 1 else (1, 0))
+                assert_equal(mat.argmin(axis=axis, explicit=ex), expected)
+                assert_equal(mat.argmax(axis=axis, explicit=ex), expected)
+
+        mat = self.spcreator(D1)
+        assert_equal(mat.argmax(axis=0, explicit=True), self.asdense([3, 0, 3, 3]))
+        assert_equal(mat.argmin(axis=0, explicit=True), self.asdense([0, 2, 2, 2]))
+
+        expected_max = np.array([1, 2, 0, 3, 1])
+        expected_min = np.array([0, 3, 3, 0, 0])
+        if mat.nnz != 16:
+            # Noncanonical case
+            expected_min[-1] = 2
+        if not self.is_array_test:
+            expected_max = expected_max.reshape((5, 1))
+            expected_min = expected_min.reshape((5, 1))
+
+        assert_equal(mat.argmax(axis=1, explicit=True), expected_max)
+        assert_equal(asarray(mat.argmin(axis=1, explicit=True)), expected_min)
+
+        # all zeros
+        D = np.zeros((2, 2))
+        mat = self.spcreator(D)
+        if mat.nnz != 0:
+            # Noncanonical case
+            assert_equal(mat.argmin(axis=None, explicit=True), 0)
+            assert_equal(mat.argmax(axis=None, explicit=True), 0)
+        else:
+            # Canonical case
+            with pytest.raises(ValueError, match="Cannot apply"):
+                mat.argmin(axis=None, explicit=True)
+            with pytest.raises(ValueError, match="Cannot apply"):
+                mat.argmax(axis=None, explicit=True)
+
+
+class _TestGetNnzAxis:
+    def test_getnnz_axis(self):
+        dat = array([[0, 2],
+                     [3, 5],
+                     [-6, 9]])
+        bool_dat = dat.astype(bool)
+        datsp = self.spcreator(dat)
+
+        accepted_return_dtypes = (np.int32, np.int64)
+
+        getnnz = datsp.count_nonzero if self.is_array_test else datsp.getnnz
+        assert_array_equal(bool_dat.sum(axis=None), getnnz(axis=None))
+        assert_array_equal(bool_dat.sum(), getnnz())
+        assert_array_equal(bool_dat.sum(axis=0), getnnz(axis=0))
+        assert_in(getnnz(axis=0).dtype, accepted_return_dtypes)
+        assert_array_equal(bool_dat.sum(axis=1), getnnz(axis=1))
+        assert_in(getnnz(axis=1).dtype, accepted_return_dtypes)
+        assert_array_equal(bool_dat.sum(axis=-2), getnnz(axis=-2))
+        assert_in(getnnz(axis=-2).dtype, accepted_return_dtypes)
+        assert_array_equal(bool_dat.sum(axis=-1), getnnz(axis=-1))
+        assert_in(getnnz(axis=-1).dtype, accepted_return_dtypes)
+
+        assert_raises(ValueError, getnnz, axis=2)
+
+
+#------------------------------------------------------------------------------
+# Tailored base class for generic tests
+#------------------------------------------------------------------------------
+
+def _possibly_unimplemented(cls, require=True):
+    """
+    Construct a class that either runs tests as usual (require=True),
+    or each method skips if it encounters a common error.
+    """
+    if require:
+        return cls
+    else:
+        def wrap(fc):
+            @functools.wraps(fc)
+            def wrapper(*a, **kw):
+                try:
+                    return fc(*a, **kw)
+                except (NotImplementedError, TypeError, ValueError,
+                        IndexError, AttributeError):
+                    raise pytest.skip("feature not implemented")
+
+            return wrapper
+
+        new_dict = dict(cls.__dict__)
+        for name, func in cls.__dict__.items():
+            if name.startswith('test_'):
+                new_dict[name] = wrap(func)
+        return type(cls.__name__ + "NotImplemented",
+                    cls.__bases__,
+                    new_dict)
+
+
+def sparse_test_class(getset=True, slicing=True, slicing_assign=True,
+                      fancy_indexing=True, fancy_assign=True,
+                      fancy_multidim_indexing=True, fancy_multidim_assign=True,
+                      minmax=True, nnz_axis=True):
+    """
+    Construct a base class, optionally converting some of the tests in
+    the suite to check that the feature is not implemented.
+    """
+    bases = (_TestCommon,
+             _possibly_unimplemented(_TestGetSet, getset),
+             _TestSolve,
+             _TestInplaceArithmetic,
+             _TestArithmetic,
+             _possibly_unimplemented(_TestSlicing, slicing),
+             _possibly_unimplemented(_TestSlicingAssign, slicing_assign),
+             _possibly_unimplemented(_TestFancyIndexing, fancy_indexing),
+             _possibly_unimplemented(_TestFancyIndexingAssign,
+                                     fancy_assign),
+             _possibly_unimplemented(_TestFancyMultidim,
+                                     fancy_indexing and fancy_multidim_indexing),
+             _possibly_unimplemented(_TestFancyMultidimAssign,
+                                     fancy_multidim_assign and fancy_assign),
+             _possibly_unimplemented(_TestMinMax, minmax),
+             _possibly_unimplemented(_TestGetNnzAxis, nnz_axis))
+
+    # check that test names do not clash
+    names = {}
+    for cls in bases:
+        for name in cls.__dict__:
+            if not name.startswith('test_'):
+                continue
+            old_cls = names.get(name)
+            if old_cls is not None:
+                raise ValueError(f"Test class {cls.__name__} overloads test "
+                                 f"{name} defined in {old_cls.__name__}")
+            names[name] = cls
+
+    return type("TestBase", bases, {})
+
+
+#------------------------------------------------------------------------------
+# Matrix class based tests
+#------------------------------------------------------------------------------
+
+class _CompressedMixin:
+    def _test_setdiag_sorted(self, D):
+        A = self.spcreator(D)
+        # Force sorted indices
+        A.has_sorted_indices = False
+        A.sort_indices()
+        assert A.has_sorted_indices
+        # Set the diagonal (only 1 new entry / 1002, so _insert_many is used)
+        with check_remains_sorted(A):
+            A.setdiag(5)
+        assert np.all(A.diagonal() == 5)
+
+    def test_setdiag_noconvert(self):
+        # Test small ratio of new elements
+        # see gh-21791 setting mixture of existing and not when new_values < 0.001*nnz
+        # see gh-23644
+        # Create off-main-diagonal elements so that we have multiple elements
+        # per column to see if the indices are sorted or not
+        N = 1002
+        vals = np.arange(1, N + 1)
+        diags = np.c_[[-1, 2, 1]] * vals  # rows are diagonal entries
+        # Remove a small number of  diagonal elements so we have a small ratio
+        # of new ones to force _cs_matrix._setdiag to remain in CSC/CSR format
+        N_new = 3
+        diags[1, -N_new:] = 0.0
+        offsets = [-1, 0, 1]
+        D = self.dia_container((diags, offsets), shape=(N, N))
+        return self._test_setdiag_sorted(D)
+
+    def test_setdiag_cooconvert(self):
+        # Test large ratio of new elements
+        # see gh-23644
+        # Create off-main-diagonal elements so that we have multiple elements
+        # per column to see if the indices are sorted or not
+        N = 1002
+        vals = np.arange(1, N + 1)  # only a few non-zeros
+        diags = np.c_[[-1, 2, 1]] * vals
+        # Remove many entries so we have a large ratio of new entries
+        diags[1, 5:] = 0.0
+        offsets = [-1, 0, 1]
+        D = self.dia_container((diags, offsets), shape=(N, N))
+        return self._test_setdiag_sorted(D)
+
+
+class TestCSR(_CompressedMixin, sparse_test_class()):
+    @classmethod
+    def spcreator(cls, *args, **kwargs):
+        with warnings.catch_warnings():
+            warnings.filterwarnings("ignore", WMSG, SparseEfficiencyWarning)
+            return csr_array(*args, **kwargs)
+    math_dtypes = [np.bool_, np.int_, np.float64, np.complex128]
+
+    def test_constructor1(self):
+        b = array([[0, 4, 0],
+                   [3, 0, 0],
+                   [0, 2, 0]], 'd')
+        bsp = self.csr_container(b)
+        assert_array_almost_equal(bsp.data,[4,3,2])
+        assert_array_equal(bsp.indices,[1,0,1])
+        assert_array_equal(bsp.indptr,[0,1,2,3])
+        assert_equal(bsp.nnz,3)
+        assert_equal(bsp.format,'csr')
+        assert_array_equal(bsp.toarray(), b)
+
+    def test_constructor2(self):
+        b = zeros((6,6),'d')
+        b[3,4] = 5
+        bsp = self.csr_container(b)
+        assert_array_almost_equal(bsp.data,[5])
+        assert_array_equal(bsp.indices,[4])
+        assert_array_equal(bsp.indptr,[0,0,0,0,1,1,1])
+        assert_array_almost_equal(bsp.toarray(), b)
+
+    def test_constructor3(self):
+        b = array([[1, 0],
+                   [0, 2],
+                   [3, 0]], 'd')
+        bsp = self.csr_container(b)
+        assert_array_almost_equal(bsp.data,[1,2,3])
+        assert_array_equal(bsp.indices,[0,1,0])
+        assert_array_equal(bsp.indptr,[0,1,2,3])
+        assert_array_almost_equal(bsp.toarray(), b)
+
+    def test_constructor4(self):
+        # using (data, ij) format
+        row = array([2, 3, 1, 3, 0, 1, 3, 0, 2, 1, 2])
+        col = array([0, 1, 0, 0, 1, 1, 2, 2, 2, 2, 1])
+        data = array([6., 10., 3., 9., 1., 4.,
+                              11., 2., 8., 5., 7.])
+
+        ij = vstack((row,col))
+        csr = self.csr_container((data,ij),(4,3))
+        assert_array_equal(arange(12).reshape(4, 3), csr.toarray())
+
+        # using Python lists and a specified dtype
+        csr = self.csr_container(([2**63 + 1, 1], ([0, 1], [0, 1])), dtype=np.uint64)
+        dense = array([[2**63 + 1, 0], [0, 1]], dtype=np.uint64)
+        assert_array_equal(dense, csr.toarray())
+
+        # with duplicates (should sum the duplicates)
+        csr = self.csr_container(([1,1,1,1], ([0,2,2,0], [0,1,1,0])))
+        assert csr.nnz == 2
+
+    def test_constructor5(self):
+        # infer dimensions from arrays
+        indptr = array([0,1,3,3])
+        indices = array([0,5,1,2])
+        data = array([1,2,3,4])
+        csr = self.csr_container((data, indices, indptr))
+        assert_array_equal(csr.shape,(3,6))
+
+    def test_constructor6(self):
+        # infer dimensions and dtype from lists
+        indptr = [0, 1, 3, 3]
+        indices = [0, 5, 1, 2]
+        data = [1, 2, 3, 4]
+        csr = self.csr_container((data, indices, indptr))
+        assert_array_equal(csr.shape, (3,6))
+        assert_(np.issubdtype(csr.dtype, np.signedinteger))
+
+    def test_constructor_smallcol(self):
+        # int64 indices not required
+        data = arange(6) + 1
+        col = array([1, 2, 1, 0, 0, 2], dtype=np.int64)
+        ptr = array([0, 2, 4, 6], dtype=np.int64)
+
+        a = self.csr_container((data, col, ptr), shape=(3, 3))
+
+        b = array([[0, 1, 2],
+                   [4, 3, 0],
+                   [5, 0, 6]], 'd')
+
+        # sparray is less aggressive in downcasting indices to int32 than spmatrix
+        expected_dtype = np.dtype(np.int64 if self.is_array_test else np.int32)
+        assert_equal(a.indptr.dtype, expected_dtype)
+        assert_equal(a.indices.dtype, expected_dtype)
+        assert_array_equal(a.toarray(), b)
+
+    def test_constructor_largecol(self):
+        # int64 indices required
+        data = arange(6) + 1
+        large = np.iinfo(np.int32).max + 100
+        col = array([0, 1, 2, large, large+1, large+2], dtype=np.int64)
+        ptr = array([0, 2, 4, 6], dtype=np.int64)
+
+        a = self.csr_container((data, col, ptr))
+
+        assert_equal(a.indptr.dtype, np.dtype(np.int64))
+        assert_equal(a.indices.dtype, np.dtype(np.int64))
+        assert_array_equal(a.shape, (3, max(col)+1))
+
+    def test_sort_indices(self):
+        data = arange(5)
+        indices = array([7, 2, 1, 5, 4])
+        indptr = array([0, 3, 5])
+        asp = self.csr_container((data, indices, indptr), shape=(2,10))
+        bsp = asp.copy()
+        asp.sort_indices()
+        assert_array_equal(asp.indices,[1, 2, 7, 4, 5])
+        assert_array_equal(asp.toarray(), bsp.toarray())
+
+    def test_eliminate_zeros(self):
+        data = array([1, 0, 0, 0, 2, 0, 3, 0])
+        indices = array([1, 2, 3, 4, 5, 6, 7, 8])
+        indptr = array([0, 3, 8])
+        asp = self.csr_container((data, indices, indptr), shape=(2,10))
+        bsp = asp.copy()
+        asp.eliminate_zeros()
+        assert_array_equal(asp.nnz, 3)
+        assert_array_equal(asp.data,[1, 2, 3])
+        assert_array_equal(asp.toarray(), bsp.toarray())
+
+    def test_ufuncs(self):
+        X = self.csr_container(np.arange(20).reshape(4, 5) / 20.)
+        for f in ["sin", "tan", "arcsin", "arctan", "sinh", "tanh",
+                  "arcsinh", "arctanh", "rint", "sign", "expm1", "log1p",
+                  "deg2rad", "rad2deg", "floor", "ceil", "trunc", "sqrt"]:
+            assert_equal(hasattr(self.datsp, f), True)
+            X2 = getattr(X, f)()
+            assert_equal(X.shape, X2.shape)
+            assert_array_equal(X.indices, X2.indices)
+            assert_array_equal(X.indptr, X2.indptr)
+            assert_array_equal(X2.toarray(), getattr(np, f)(X.toarray()))
+
+    def test_unsorted_arithmetic(self):
+        data = arange(5)
+        indices = array([7, 2, 1, 5, 4])
+        indptr = array([0, 3, 5])
+        asp = self.csr_container((data, indices, indptr), shape=(2,10))
+        data = arange(6)
+        indices = array([8, 1, 5, 7, 2, 4])
+        indptr = array([0, 2, 6])
+        bsp = self.csr_container((data, indices, indptr), shape=(2,10))
+        assert_equal((asp + bsp).toarray(), asp.toarray() + bsp.toarray())
+
+    def test_fancy_indexing_broadcast(self):
+        # broadcasting indexing mode is supported
+        I = np.array([[1], [2], [3]])
+        J = np.array([3, 4, 2])
+
+        np.random.seed(1234)
+        D = self.asdense(np.random.rand(5, 7))
+        S = self.spcreator(D)
+
+        SIJ = S[I,J]
+        if issparse(SIJ):
+            SIJ = SIJ.toarray()
+        assert_equal(SIJ, D[I,J])
+
+    def test_has_sorted_indices(self):
+        "Ensure has_sorted_indices memoizes sorted state for sort_indices"
+        sorted_inds = np.array([0, 1])
+        unsorted_inds = np.array([1, 0])
+        data = np.array([1, 1])
+        indptr = np.array([0, 2])
+        M = self.csr_container((data, sorted_inds, indptr)).copy()
+        assert_equal(True, M.has_sorted_indices)
+        assert isinstance(M.has_sorted_indices, bool)
+
+        M = self.csr_container((data, unsorted_inds, indptr)).copy()
+        assert_equal(False, M.has_sorted_indices)
+
+        # set by sorting
+        M.sort_indices()
+        assert_equal(True, M.has_sorted_indices)
+        assert_array_equal(M.indices, sorted_inds)
+
+        M = self.csr_container((data, unsorted_inds, indptr)).copy()
+        # set manually (although underlyingly unsorted)
+        M.has_sorted_indices = True
+        assert_equal(True, M.has_sorted_indices)
+        assert_array_equal(M.indices, unsorted_inds)
+
+        # ensure sort bypassed when has_sorted_indices == True
+        M.sort_indices()
+        assert_array_equal(M.indices, unsorted_inds)
+
+    def test_has_canonical_format(self):
+        "Ensure has_canonical_format memoizes state for sum_duplicates"
+
+        info_no_dups = (np.array([2]), np.array([0]), np.array([0, 1]))
+        info_with_dups = (np.array([1, 1]), np.array([0, 0]), np.array([0, 2]))
+
+        M = self.csr_container(info_no_dups)
+        assert_equal(True, M.has_canonical_format)
+
+        M = self.csr_container(info_with_dups).copy()
+        assert_equal(False, M.has_canonical_format)
+        assert isinstance(M.has_canonical_format, bool)
+
+        # set flag by deduplicating
+        M.sum_duplicates()
+        assert_equal(True, M.has_canonical_format)
+        assert_equal(1, len(M.indices))
+
+        # manually set flag True (although underlyingly duplicated)
+        M = self.csr_container(info_with_dups).copy()
+        M.has_canonical_format = True
+        assert_equal(True, M.has_canonical_format)
+        assert_equal(2, len(M.indices))  # unaffected content
+        # ensure deduplication bypassed when has_canonical_format == True
+        M.sum_duplicates()
+        assert_equal(2, len(M.indices))  # still has duplicates!!!!
+        # ensure deduplication reenabled when has_canonical_format == False
+        M.has_canonical_format = False
+        M.sum_duplicates()
+        assert_equal(1, len(M.indices))
+        assert_equal(True, M.has_canonical_format)
+
+        # manually set flag False (although underlyingly canonical)
+        M.has_canonical_format = False
+        assert_equal(False, M.has_canonical_format)
+        Mcheck = self.csr_container((M.data, M.indices, M.indptr))
+        assert_equal(True, Mcheck.has_canonical_format)
+        # sum_duplicates does not complain when no work to do
+        M.sum_duplicates()
+        assert_equal(True, M.has_canonical_format)
+
+        # check assignments maintain canonical format
+        M = self.csr_container((np.array([2]), np.array([2]), np.array([0, 1, 1, 1])))
+        assert_equal(M.shape, (3, 3))
+        with warnings.catch_warnings():
+            warnings.filterwarnings("ignore", WMSG, SparseEfficiencyWarning)
+            M[0, 1] = 2
+            M[1, :] *= 5
+            M[0, 2] = 3
+        assert_equal(True, M.has_canonical_format)
+        Mcheck = self.csr_container((M.data, M.indices, M.indptr))
+        assert_equal(True, Mcheck.has_canonical_format)
+
+        # resetting index arrays before accessing M.has_canonical_format is OK
+        M = self.csr_container(info_no_dups)
+        M.data, M.indices, M.indptr = info_with_dups
+        assert_equal(False, M.has_canonical_format)
+        assert_equal(2, len(M.indices))  # dups and has_canonical_format is False
+
+        # but reset after accessing M.has_canonical_format can break flag
+        M = self.csr_container(info_no_dups)
+        M.has_canonical_format  # underlying attr is set here
+        M.data, M.indices, M.indptr = info_with_dups
+        assert_equal(True, M.has_canonical_format)
+        assert_equal(2, len(M.indices))  # dups but has_canonical_format is True
+        M.sum_duplicates()
+        assert_equal(2, len(M.indices))  # still has duplicates!!!!
+
+    def test_scalar_idx_dtype(self):
+        # Check that index dtype takes into account all parameters
+        # passed to sparsetools, including the scalar ones
+        indptr = np.zeros(2, dtype=np.int32)
+        indices = np.zeros(0, dtype=np.int32)
+        vals = np.zeros(0)
+        a = self.csr_container((vals, indices, indptr), shape=(1, 2**31-1))
+        b = self.csr_container((vals, indices, indptr), shape=(1, 2**31))
+        ij = np.zeros((2, 0), dtype=np.int32)
+        c = self.csr_container((vals, ij), shape=(1, 2**31-1))
+        d = self.csr_container((vals, ij), shape=(1, 2**31))
+        e = self.csr_container((1, 2**31-1))
+        f = self.csr_container((1, 2**31))
+        assert_equal(a.indptr.dtype, np.int32)
+        assert_equal(b.indptr.dtype, np.int64)
+        assert_equal(c.indptr.dtype, np.int32)
+        assert_equal(d.indptr.dtype, np.int64)
+        assert_equal(e.indptr.dtype, np.int32)
+        assert_equal(f.indptr.dtype, np.int64)
+
+        # These shouldn't fail
+        for x in [a, b, c, d, e, f]:
+            x + x
+
+    def test_binop_explicit_zeros(self):
+        # Check that binary ops don't introduce spurious explicit zeros.
+        # See gh-9619 for context.
+        a = self.csr_container([[0, 1, 0]])
+        b = self.csr_container([[1, 1, 0]])
+        assert (a + b).nnz == 2
+        assert a.multiply(b).nnz == 1
+
+
+TestCSR.init_class()
+
+
+class TestCSRMatrix(_MatrixMixin, TestCSR):
+    @classmethod
+    def spcreator(cls, *args, **kwargs):
+        with warnings.catch_warnings():
+            warnings.filterwarnings("ignore", WMSG, SparseEfficiencyWarning)
+            return csr_matrix(*args, **kwargs)
+
+def test_spmatrix_subscriptable():
+    result = csr_matrix[np.int8]
+    assert isinstance(result, GenericAlias)
+    assert result.__origin__ is csr_matrix
+    assert result.__args__ == (np.int8,)
+
+
+TestCSRMatrix.init_class()
+
+
+class TestCSC(_CompressedMixin, sparse_test_class()):
+    @classmethod
+    def spcreator(cls, *args, **kwargs):
+        with warnings.catch_warnings():
+            warnings.filterwarnings("ignore", WMSG, SparseEfficiencyWarning)
+            return csc_array(*args, **kwargs)
+    math_dtypes = [np.bool_, np.int_, np.float64, np.complex128]
+
+    def test_constructor1(self):
+        b = array([[1, 0, 0, 0], [0, 0, 1, 0], [0, 2, 0, 3]], 'd')
+        bsp = self.csc_container(b)
+        assert_array_almost_equal(bsp.data,[1,2,1,3])
+        assert_array_equal(bsp.indices,[0,2,1,2])
+        assert_array_equal(bsp.indptr,[0,1,2,3,4])
+        assert_equal(bsp.nnz,4)
+        assert_equal(bsp.shape,b.shape)
+        assert_equal(bsp.format,'csc')
+
+    def test_constructor2(self):
+        b = zeros((6,6),'d')
+        b[2,4] = 5
+        bsp = self.csc_container(b)
+        assert_array_almost_equal(bsp.data,[5])
+        assert_array_equal(bsp.indices,[2])
+        assert_array_equal(bsp.indptr,[0,0,0,0,0,1,1])
+
+    def test_constructor3(self):
+        b = array([[1, 0], [0, 0], [0, 2]], 'd')
+        bsp = self.csc_container(b)
+        assert_array_almost_equal(bsp.data,[1,2])
+        assert_array_equal(bsp.indices,[0,2])
+        assert_array_equal(bsp.indptr,[0,1,2])
+
+    def test_constructor4(self):
+        # using (data, ij) format
+        row = array([2, 3, 1, 3, 0, 1, 3, 0, 2, 1, 2])
+        col = array([0, 1, 0, 0, 1, 1, 2, 2, 2, 2, 1])
+        data = array([6., 10., 3., 9., 1., 4., 11., 2., 8., 5., 7.])
+
+        ij = vstack((row,col))
+        csc = self.csc_container((data,ij),(4,3))
+        assert_array_equal(arange(12).reshape(4, 3), csc.toarray())
+
+        # with duplicates (should sum the duplicates)
+        csc = self.csc_container(([1,1,1,1], ([0,2,2,0], [0,1,1,0])))
+        assert csc.nnz == 2
+
+    def test_constructor5(self):
+        # infer dimensions from arrays
+        indptr = array([0,1,3,3])
+        indices = array([0,5,1,2])
+        data = array([1,2,3,4])
+        csc = self.csc_container((data, indices, indptr))
+        assert_array_equal(csc.shape,(6,3))
+
+    def test_constructor6(self):
+        # infer dimensions and dtype from lists
+        indptr = [0, 1, 3, 3]
+        indices = [0, 5, 1, 2]
+        data = [1, 2, 3, 4]
+        csc = self.csc_container((data, indices, indptr))
+        assert_array_equal(csc.shape,(6,3))
+        assert_(np.issubdtype(csc.dtype, np.signedinteger))
+
+    def test_eliminate_zeros(self):
+        data = array([1, 0, 0, 0, 2, 0, 3, 0])
+        indices = array([1, 2, 3, 4, 5, 6, 7, 8])
+        indptr = array([0, 3, 8])
+        asp = self.csc_container((data, indices, indptr), shape=(10,2))
+        bsp = asp.copy()
+        asp.eliminate_zeros()
+        assert_array_equal(asp.nnz, 3)
+        assert_array_equal(asp.data,[1, 2, 3])
+        assert_array_equal(asp.toarray(), bsp.toarray())
+
+    def test_sort_indices(self):
+        data = arange(5)
+        row = array([7, 2, 1, 5, 4])
+        ptr = [0, 3, 5]
+        asp = self.csc_container((data, row, ptr), shape=(10,2))
+        bsp = asp.copy()
+        asp.sort_indices()
+        assert_array_equal(asp.indices,[1, 2, 7, 4, 5])
+        assert_array_equal(asp.toarray(), bsp.toarray())
+
+    def test_ufuncs(self):
+        X = self.csc_container(np.arange(21).reshape(7, 3) / 21.)
+        for f in ["sin", "tan", "arcsin", "arctan", "sinh", "tanh",
+                  "arcsinh", "arctanh", "rint", "sign", "expm1", "log1p",
+                  "deg2rad", "rad2deg", "floor", "ceil", "trunc", "sqrt"]:
+            assert_equal(hasattr(self.datsp, f), True)
+            X2 = getattr(X, f)()
+            assert_equal(X.shape, X2.shape)
+            assert_array_equal(X.indices, X2.indices)
+            assert_array_equal(X.indptr, X2.indptr)
+            assert_array_equal(X2.toarray(), getattr(np, f)(X.toarray()))
+
+    def test_unsorted_arithmetic(self):
+        data = arange(5)
+        indices = array([7, 2, 1, 5, 4])
+        indptr = array([0, 3, 5])
+        asp = self.csc_container((data, indices, indptr), shape=(10,2))
+        data = arange(6)
+        indices = array([8, 1, 5, 7, 2, 4])
+        indptr = array([0, 2, 6])
+        bsp = self.csc_container((data, indices, indptr), shape=(10,2))
+        assert_equal((asp + bsp).toarray(), asp.toarray() + bsp.toarray())
+
+    def test_fancy_indexing_broadcast(self):
+        # broadcasting indexing mode is supported
+        I = np.array([[1], [2], [3]])
+        J = np.array([3, 4, 2])
+
+        np.random.seed(1234)
+        D = self.asdense(np.random.rand(5, 7))
+        S = self.spcreator(D)
+
+        SIJ = S[I,J]
+        if issparse(SIJ):
+            SIJ = SIJ.toarray()
+        assert_equal(SIJ, D[I,J])
+
+    def test_scalar_idx_dtype(self):
+        # Check that index dtype takes into account all parameters
+        # passed to sparsetools, including the scalar ones
+        indptr = np.zeros(2, dtype=np.int32)
+        indices = np.zeros(0, dtype=np.int32)
+        vals = np.zeros(0)
+        a = self.csc_container((vals, indices, indptr), shape=(2**31-1, 1))
+        b = self.csc_container((vals, indices, indptr), shape=(2**31, 1))
+        ij = np.zeros((2, 0), dtype=np.int32)
+        c = self.csc_container((vals, ij), shape=(2**31-1, 1))
+        d = self.csc_container((vals, ij), shape=(2**31, 1))
+        e = self.csr_container((1, 2**31-1))
+        f = self.csr_container((1, 2**31))
+        assert_equal(a.indptr.dtype, np.int32)
+        assert_equal(b.indptr.dtype, np.int64)
+        assert_equal(c.indptr.dtype, np.int32)
+        assert_equal(d.indptr.dtype, np.int64)
+        assert_equal(e.indptr.dtype, np.int32)
+        assert_equal(f.indptr.dtype, np.int64)
+
+        # These shouldn't fail
+        for x in [a, b, c, d, e, f]:
+            x + x
+
+
+TestCSC.init_class()
+
+
+class TestCSCMatrix(_MatrixMixin, TestCSC):
+    @classmethod
+    def spcreator(cls, *args, **kwargs):
+        with warnings.catch_warnings():
+            warnings.filterwarnings("ignore", WMSG, SparseEfficiencyWarning)
+            return csc_matrix(*args, **kwargs)
+
+
+TestCSCMatrix.init_class()
+
+
+class TestDOK(sparse_test_class(minmax=False, nnz_axis=False)):
+    spcreator = dok_array
+    math_dtypes = [np.int_, np.float64, np.complex128]
+
+    def test_mult(self):
+        A = self.dok_container((10, 12))
+        A[0, 3] = 10
+        A[5, 6] = 20
+        D = A @ A.T
+        E = A @ A.T.conjugate()
+        assert_array_equal(D.toarray(), E.toarray())
+
+    def test_add_nonzero(self):
+        A = self.spcreator((3,2))
+        A[0,1] = -10
+        A[2,0] = 20
+        A = A + 10
+        B = array([[10, 0], [10, 10], [30, 10]])
+        assert_array_equal(A.toarray(), B)
+
+        A = A + 1j
+        B = B + 1j
+        assert_array_equal(A.toarray(), B)
+
+    def test_dok_divide_scalar(self):
+        A = self.spcreator((3,2))
+        A[0,1] = -10
+        A[2,0] = 20
+
+        assert_array_equal((A/1j).toarray(), A.toarray()/1j)
+        assert_array_equal((A/9).toarray(), A.toarray()/9)
+
+    def test_convert(self):
+        # Test provided by Andrew Straw.  Fails in SciPy <= r1477.
+        (m, n) = (6, 7)
+        a = self.dok_container((m, n))
+
+        # set a few elements, but none in the last column
+        a[2,1] = 1
+        a[0,2] = 2
+        a[3,1] = 3
+        a[1,5] = 4
+        a[4,3] = 5
+        a[4,2] = 6
+
+        # assert that the last column is all zeros
+        assert_array_equal(a.toarray()[:,n-1], zeros(m,))
+
+        # make sure it still works for CSC format
+        csc = a.tocsc()
+        assert_array_equal(csc.toarray()[:,n-1], zeros(m,))
+
+        # now test CSR
+        (m, n) = (n, m)
+        b = a.transpose()
+        assert_equal(b.shape, (m, n))
+        # assert that the last row is all zeros
+        assert_array_equal(b.toarray()[m-1,:], zeros(n,))
+
+        # make sure it still works for CSR format
+        csr = b.tocsr()
+        assert_array_equal(csr.toarray()[m-1,:], zeros(n,))
+
+    def test_ctor(self):
+        # Empty ctor
+        assert_raises(TypeError, self.dok_container)
+
+        # Dense ctor
+        b = array([[1, 0, 0, 0], [0, 0, 1, 0], [0, 2, 0, 3]], 'd')
+        A = self.dok_container(b)
+        assert_equal(b.dtype, A.dtype)
+        assert_equal(A.toarray(), b)
+
+        # Sparse ctor
+        c = self.csr_container(b)
+        assert_equal(A.toarray(), c.toarray())
+
+        data = [[0, 1, 2], [3, 0, 0]]
+        d = self.dok_container(data, dtype=np.float32)
+        assert_equal(d.dtype, np.float32)
+        da = d.toarray()
+        assert_equal(da.dtype, np.float32)
+        assert_array_equal(da, data)
+
+    def test_ticket1160(self):
+        # Regression test for ticket #1160.
+        a = self.dok_container((3,3))
+        a[0,0] = 0
+        # This assert would fail, because the above assignment would
+        # incorrectly call __set_item__ even though the value was 0.
+        assert_((0,0) not in a.keys(), "Unexpected entry (0,0) in keys")
+
+        # Slice assignments were also affected.
+        b = self.dok_container((3,3))
+        b[:,0] = 0
+        assert_(len(b.keys()) == 0, "Unexpected entries in keys")
+
+
+class TestDOKMatrix(_MatrixMixin, TestDOK):
+    spcreator = dok_matrix
+
+
+TestDOK.init_class()
+TestDOKMatrix.init_class()
+
+
+class TestLIL(sparse_test_class(minmax=False)):
+    spcreator = lil_array
+    math_dtypes = [np.int_, np.float64, np.complex128]
+
+    def test_dot(self):
+        A = zeros((10, 10), np.complex128)
+        A[0, 3] = 10
+        A[5, 6] = 20j
+
+        B = self.lil_container((10, 10), dtype=np.complex128)
+        B[0, 3] = 10
+        B[5, 6] = 20j
+
+        # TODO: properly handle this assertion on ppc64le
+        if platform.machine() != 'ppc64le':
+            assert_array_equal(A @ A.T, (B @ B.T).toarray())
+
+        assert_array_equal(A @ A.conjugate().T, (B @ B.conjugate().T).toarray())
+
+    def test_scalar_mul(self):
+        x = self.lil_container((3, 3))
+        x[0, 0] = 2
+
+        x = x*2
+        assert_equal(x[0, 0], 4)
+
+        x = x*0
+        assert_equal(x[0, 0], 0)
+
+    def test_truediv_scalar(self):
+        A = self.spcreator((3, 2))
+        A[0, 1] = -10
+        A[2, 0] = 20
+
+        assert_array_equal((A / 1j).toarray(), A.toarray() / 1j)
+        assert_array_equal((A / 9).toarray(), A.toarray() / 9)
+
+    def test_inplace_ops(self):
+        A = self.lil_container([[0, 2, 3], [4, 0, 6]])
+        B = self.lil_container([[0, 1, 0], [0, 2, 3]])
+
+        data = {'add': (B, A + B),
+                'sub': (B, A - B),
+                'mul': (3, A * 3)}
+
+        for op, (other, expected) in data.items():
+            result = A.copy()
+            getattr(result, f'__i{op}__')(other)
+
+            assert_array_equal(result.toarray(), expected.toarray())
+
+        # Ticket 1604.
+        A = self.lil_container((1, 3), dtype=np.dtype('float64'))
+        B = self.asdense([0.1, 0.1, 0.1])
+        A[0, :] += B
+        assert_array_equal(A[0, :].toarray(), B)
+
+    def test_lil_iteration(self):
+        row_data = [[1, 2, 3], [4, 5, 6]]
+        B = self.lil_container(array(row_data))
+        for r, row in enumerate(B):
+            assert_array_equal(row.toarray(), array(row_data[r], ndmin=row.ndim))
+
+    def test_lil_from_csr(self):
+        # Tests whether a LIL can be constructed from a CSR.
+        B = self.lil_container((10, 10))
+        B[0, 3] = 10
+        B[5, 6] = 20
+        B[8, 3] = 30
+        B[3, 8] = 40
+        B[8, 9] = 50
+        C = B.tocsr()
+        D = self.lil_container(C)
+        assert_array_equal(C.toarray(), D.toarray())
+
+    def test_fancy_indexing_lil(self):
+        M = self.asdense(arange(25).reshape(5, 5))
+        A = self.lil_container(M)
+
+        assert_equal(A[array([1, 2, 3]), 2:3].toarray(),
+                     M[array([1, 2, 3]), 2:3])
+
+    def test_point_wise_multiply(self):
+        l = self.lil_container((4, 3))
+        l[0, 0] = 1
+        l[1, 1] = 2
+        l[2, 2] = 3
+        l[3, 1] = 4
+
+        m = self.lil_container((4, 3))
+        m[0, 0] = 1
+        m[0, 1] = 2
+        m[2, 2] = 3
+        m[3, 1] = 4
+        m[3, 2] = 4
+
+        assert_array_equal(l.multiply(m).toarray(),
+                           m.multiply(l).toarray())
+
+        assert_array_equal(l.multiply(m).toarray(),
+                           [[1, 0, 0],
+                            [0, 0, 0],
+                            [0, 0, 9],
+                            [0, 16, 0]])
+
+    def test_lil_multiply_removal(self):
+        # Ticket #1427.
+        a = self.lil_container(np.ones((3, 3)))
+        a *= 2.
+        a[0, :] = 0
+
+
+class TestLILMatrix(_MatrixMixin, TestLIL):
+    spcreator = lil_matrix
+
+
+TestLIL.init_class()
+TestLILMatrix.init_class()
+
+
+class BaseTestCOO:
+    math_dtypes = [np.int_, np.float64, np.complex128]
+
+    def test_constructor1(self):
+        # unsorted triplet format
+        row = array([2, 3, 1, 3, 0, 1, 3, 0, 2, 1, 2])
+        col = array([0, 1, 0, 0, 1, 1, 2, 2, 2, 2, 1])
+        data = array([6., 10., 3., 9., 1., 4., 11., 2., 8., 5., 7.])
+
+        coo = self.coo_container((data,(row,col)),(4,3))
+        assert_array_equal(arange(12).reshape(4, 3), coo.toarray())
+
+        # using Python lists and a specified dtype
+        coo = self.coo_container(([2**63 + 1, 1], ([0, 1], [0, 1])), dtype=np.uint64)
+        dense = array([[2**63 + 1, 0], [0, 1]], dtype=np.uint64)
+        assert_array_equal(dense, coo.toarray())
+
+    def test_constructor2(self):
+        # unsorted triplet format with duplicates (which are summed)
+        row = array([0,1,2,2,2,2,0,0,2,2])
+        col = array([0,2,0,2,1,1,1,0,0,2])
+        data = array([2,9,-4,5,7,0,-1,2,1,-5])
+        coo = self.coo_container((data,(row,col)),(3,3))
+
+        mat = array([[4, -1, 0], [0, 0, 9], [-3, 7, 0]])
+
+        assert_array_equal(mat, coo.toarray())
+
+    def test_constructor3(self):
+        # empty matrix
+        coo = self.coo_container((4,3))
+
+        assert_array_equal(coo.shape,(4,3))
+        assert_array_equal(coo.row,[])
+        assert_array_equal(coo.col,[])
+        assert_array_equal(coo.data,[])
+        assert_array_equal(coo.toarray(), zeros((4, 3)))
+
+    def test_constructor4(self):
+        # from dense matrix
+        mat = array([[0,1,0,0],
+                     [7,0,3,0],
+                     [0,4,0,0]])
+        coo = self.coo_container(mat)
+        assert_array_equal(coo.toarray(), mat)
+
+        # upgrade rank 1 arrays to row matrix
+        mat = array([0,1,0,0])
+        coo = self.coo_container(mat)
+        expected = mat if self.is_array_test else mat.reshape(1, -1)
+        assert_array_equal(coo.toarray(), expected)
+
+        # error if second arg interpreted as shape (gh-9919)
+        with pytest.raises(TypeError, match=r'object cannot be interpreted'):
+            self.coo_container([0, 11, 22, 33], ([0, 1, 2, 3], [0, 0, 0, 0]))
+
+        # error if explicit shape arg doesn't match the dense matrix
+        with pytest.raises(ValueError, match=r'inconsistent shapes'):
+            self.coo_container([0, 11, 22, 33], shape=(4, 4))
+
+    def test_constructor_data_ij_dtypeNone(self):
+        data = [1]
+        coo = self.coo_container((data, ([0], [0])), dtype=None)
+        assert coo.dtype == np.array(data).dtype
+
+    @pytest.mark.xfail(run=False, reason='COO does not have a __getitem__')
+    def test_iterator(self):
+        pass
+
+    def test_todia_all_zeros(self):
+        zeros = [[0, 0]]
+        dia = self.coo_container(zeros).todia()
+        assert_array_equal(dia.toarray(), zeros)
+
+    def test_sum_duplicates(self):
+        coo = self.coo_container((4,3))
+        coo.sum_duplicates()
+        coo = self.coo_container(([1,2], ([1,0], [1,0])))
+        coo.sum_duplicates()
+        assert_array_equal(coo.toarray(), [[2,0],[0,1]])
+        coo = self.coo_container(([1,2], ([1,1], [1,1])))
+        coo.sum_duplicates()
+        assert_array_equal(coo.toarray(), [[0,0],[0,3]])
+        assert_array_equal(coo.row, [1])
+        assert_array_equal(coo.col, [1])
+        assert_array_equal(coo.data, [3])
+
+    def test_todok_duplicates(self):
+        coo = self.coo_container(([1,1,1,1], ([0,2,2,0], [0,1,1,0])))
+        dok = coo.todok()
+        assert_array_equal(dok.toarray(), coo.toarray())
+
+    def test_tocompressed_duplicates(self):
+        coo = self.coo_container(([1,1,1,1], ([0,2,2,0], [0,1,1,0])))
+        csr = coo.tocsr()
+        assert_equal(csr.nnz + 2, coo.nnz)
+        csc = coo.tocsc()
+        assert_equal(csc.nnz + 2, coo.nnz)
+
+    def test_has_canonical_format(self):
+        "Ensure has_canonical_format memoizes state for sum_duplicates"
+
+        A = self.coo_container((2, 3))
+        assert_equal(A.has_canonical_format, True)
+
+        A_array = np.array([[0, 2, 0]])
+        A_coords_form = (np.array([2]), (np.array([0]), np.array([1])))
+        A_coords_dups = (np.array([1, 1]), (np.array([0, 0]), np.array([1, 1])))
+
+        A = self.coo_container(A_array)
+        assert A.has_canonical_format is True
+        A = self.coo_container(A_coords_form)
+        assert A.has_canonical_format is False
+        A.sum_duplicates()
+        assert A.has_canonical_format is True
+
+        A = self.coo_container(A, copy=True)
+        assert A.has_canonical_format is True
+        A = self.coo_container(A, copy=False)
+        assert A.has_canonical_format is False
+        A.sum_duplicates()
+        assert A.has_canonical_format is True
+
+        A = self.coo_container(A_coords_dups)
+        assert A.has_canonical_format is False
+        assert_equal(A.nnz, 2)  # duplicates
+        A.sum_duplicates()
+        assert A.has_canonical_format is True
+        assert_equal(A.nnz, 1)
+
+        # manually set
+        A.has_canonical_format = False
+        assert_equal(A.has_canonical_format, False)
+        assert_equal(A.nnz, 1)  # incorrectly False
+        A.sum_duplicates()  # check flag updated
+        assert_equal(A.has_canonical_format, True)
+
+        A = self.coo_container(A_coords_dups)
+        A.has_canonical_format = True
+        assert_equal(A.has_canonical_format, True)
+        assert_equal(A.nnz, 2)  # incorrectly True
+        A.sum_duplicates()  # check dups not removed due to flag
+        assert_equal(A.nnz, 2)  # still has duplicates!!!!
+
+    def test_eliminate_zeros(self):
+        data = array([1, 0, 0, 0, 2, 0, 3, 0])
+        row = array([0, 0, 0, 1, 1, 1, 1, 1])
+        col = array([1, 2, 3, 4, 5, 6, 7, 8])
+        asp = self.coo_container((data, (row, col)), shape=(2,10))
+        bsp = asp.copy()
+        asp.eliminate_zeros()
+        assert_((asp.data != 0).all())
+        assert_array_equal(asp.toarray(), bsp.toarray())
+
+    def test_reshape_copy(self):
+        arr = [[0, 10, 0, 0], [0, 0, 0, 0], [0, 20, 30, 40]]
+        new_shape = (2, 6)
+        x = self.coo_container(arr)
+
+        y = x.reshape(new_shape)
+        assert_(y.data is x.data)
+
+        y = x.reshape(new_shape, copy=False)
+        assert_(y.data is x.data)
+
+        y = x.reshape(new_shape, copy=True)
+        assert_(not np.may_share_memory(y.data, x.data))
+
+    def test_large_dimensions_reshape(self):
+        # Test that reshape is immune to integer overflow when number of elements
+        # exceeds 2^31-1
+        mat1 = self.coo_container(([1], ([3000000], [1000])), (3000001, 1001))
+        mat2 = self.coo_container(([1], ([1000], [3000000])), (1001, 3000001))
+
+        # assert_array_equal is slow for big matrices because it expects dense
+        # Using __ne__ and nnz instead
+        assert_((mat1.reshape((1001, 3000001), order='C') != mat2).nnz == 0)
+        assert_((mat2.reshape((3000001, 1001), order='F') != mat1).nnz == 0)
+    
+class TestCOO(BaseTestCOO,
+              sparse_test_class(getset=True,
+                                slicing=True, slicing_assign=True,
+                                fancy_indexing=True, fancy_assign=True)):
+    spcreator = coo_array
+
+class TestCOOMatrix(_MatrixMixin,
+                    BaseTestCOO,
+                    sparse_test_class(getset=False,
+                                      slicing=False, slicing_assign=False,
+                                      fancy_indexing=False, fancy_assign=False)):
+    spcreator = coo_matrix
+
+
+TestCOO.init_class()
+TestCOOMatrix.init_class()
+
+
+def test_sparray_subscriptable():
+    result = coo_array[np.int8, tuple[int]]
+    assert isinstance(result, GenericAlias)
+    assert result.__origin__ is coo_array
+    assert result.__args__ == (np.int8, tuple[int])
+
+    result = coo_array[np.int8]
+    assert isinstance(result, GenericAlias)
+    assert result.__origin__ is coo_array
+    assert result.__args__ == (np.int8,)
+
+
+class TestDIA(sparse_test_class(getset=False, slicing=False, slicing_assign=False,
+                                fancy_indexing=False, fancy_assign=False,
+                                minmax=False, nnz_axis=False)):
+    spcreator = dia_array
+    math_dtypes = [np.int_, np.float64, np.complex128]
+
+    def test_constructor1(self):
+        D = array([[1, 0, 3, 0],
+                   [1, 2, 0, 4],
+                   [0, 2, 3, 0],
+                   [0, 0, 3, 4]])
+        data = np.array([[1,2,3,4]]).repeat(3,axis=0)
+        offsets = np.array([0,-1,2])
+        assert_equal(self.dia_container((data, offsets), shape=(4, 4)).toarray(), D)
+
+    @pytest.mark.xfail(run=False, reason='DIA does not have a __getitem__')
+    def test_iterator(self):
+        pass
+
+    @with_64bit_maxval_limit(3)
+    def test_setdiag_dtype(self):
+        m = self.dia_container(np.eye(3))
+        assert_equal(m.offsets.dtype, np.int32)
+        m.setdiag((3,), k=2)
+        assert_equal(m.offsets.dtype, np.int32)
+
+        m = self.dia_container(np.eye(4))
+        assert_equal(m.offsets.dtype, np.int64)
+        m.setdiag((3,), k=3)
+        assert_equal(m.offsets.dtype, np.int64)
+
+    def ill_cases(self):
+        # Ill-formed inputs and reference 2 x 2 outputs for testing _getnnz()
+        # and tocsr(): list of tuples
+        # (data, offsets, nnz, dense array, case description)
+
+        d1 = [[1]]        # diagonal shorter than width
+        d3 = [[1, 2, 3]]  # diagonal longer than width
+
+        return [(d1, [-1], 1, [[0, 0], [1, 0]],
+                 'shorter diagonal within'),
+                (d1, [1],  0, [[0, 0], [0, 0]],
+                 'shorter diagonal above (but within if full)'),
+                (d1, [3],  0, [[0, 0], [0, 0]],
+                 'shorter diagonal, all elements above'),
+                (d1, [-3], 0, [[0, 0], [0, 0]],
+                 'shorter diagonal, all elements below'),
+                (d3, [-1], 1, [[0, 0], [1, 0]],
+                 'longer diagonal within (only head)'),
+                (d3, [1],  1, [[0, 2], [0, 0]],
+                 'longer diagonal within (only tail)'),
+                (d3, [3],  0, [[0, 0], [0, 0]],
+                 'longer diagonal, all elements above'),
+                (d3, [-3], 0, [[0, 0], [0, 0]],
+                 'longer diagonal, all elements below'),
+                (None, None, 0, [[0, 0], [0, 0]],
+                 'empty input'),
+                ([[0, 0]], [0], 2, [[0, 0], [0, 0]],
+                 'explicit zeros'),
+                (np.arange(1, 1 + 7).reshape((7, 1)),
+                 [0, 1, 2, 3, -1, -2, -3],
+                 2, [[1, 0], [5, 0]],
+                 'overfilled shorter-diagonal, out of order'),
+                (np.arange(1, 1 + 7 * 3).reshape((7, 3)),
+                 [0, 1, 2, 3, -1, -2, -3],
+                 4, [[1, 5], [13, 2]],
+                 'overfilled longer-diagonal, out of order')]
+
+    def test_getnnz(self):
+        for data, ofsets, nnz, ref, case in self.ill_cases():
+            for shape in [(2, 2), (0, 2), (2, 0)]:
+                if data is None:
+                    A = self.dia_container(shape)
+                else:
+                    A = self.dia_container((data, ofsets), shape=shape)
+                if 0 in shape:
+                    nnz = 0
+                assert A._getnnz() == nnz, 'case: ' + case
+
+    @pytest.mark.skip(reason='DIA stores extra zeros')
+    def test_getnnz_axis(self):
+        pass
+
+    def test_tocsr(self):
+        # test bound checks (other pathological cases are tested by
+        # TestConstructUtils::test_spdiags, and normal operation is ensured by
+        # many other tests here using .toarray())
+        for data, ofsets, _, r, case in self.ill_cases():
+            for shape in [(2, 2), (0, 2), (2, 0)]:
+                if data is None:
+                    A = self.dia_container(shape)
+                else:
+                    A = self.dia_container((data, ofsets), shape=shape)
+                B = A.tocsr()
+                ref = np.array(r)[:shape[0], :shape[1]]
+                nnz = np.count_nonzero(ref)
+                assert B.nnz == nnz
+                assert_array_equal(B.toarray(), ref, err_msg='case: ' + case)
+
+    def test_convert_gh14555(self):
+        # regression test for gh-14555
+        m = self.dia_container(([[1, 1, 0]], [-1]), shape=(4, 2))
+        expected = m.toarray()
+        assert_array_equal(m.tocsc().toarray(), expected)
+        assert_array_equal(m.tocsr().toarray(), expected)
+
+    def test_tocoo_gh10050(self):
+        # regression test for gh-10050
+        m = self.dia_container([[1, 2], [3, 4]]).tocoo()
+        flat_inds = np.ravel_multi_index((m.row, m.col), m.shape)
+        inds_are_sorted = np.all(np.diff(flat_inds) > 0)
+        assert m.has_canonical_format == inds_are_sorted
+
+    def test_tocoo_tocsr_tocsc_gh19245(self):
+        # test index_dtype with tocoo, tocsr, tocsc
+        data = np.array([[1, 2, 3, 4]]).repeat(3, axis=0)
+        offsets = np.array([0, -1, 2], dtype=np.int32)
+        dia = sparse.dia_array((data, offsets), shape=(4, 4))
+
+        coo = dia.tocoo()
+        assert coo.col.dtype == np.int32
+        csr = dia.tocsr()
+        assert csr.indices.dtype == np.int32
+        csc = dia.tocsc()
+        assert csc.indices.dtype == np.int32
+
+    def test_add_sparse(self):
+        # test format and cases not covered by common add tests
+        A = diag([1, 2])
+        B = A + diag([3], 1)
+        Asp = self.dia_container(A)
+        Bsp = self.dia_container(B)
+
+        Csp = Asp + Bsp
+        assert isinstance(Csp, self.dia_container)
+        assert_array_equal(Csp.toarray(), A + B)
+
+        Csp = Bsp + Asp
+        assert isinstance(Csp, self.dia_container)
+        assert_array_equal(Csp.toarray(), B + A)
+
+    def test_sub_sparse(self):
+        # test format and cases not covered by common sub tests
+        A = diag([1, 2])
+        B = A + diag([3], 1)
+        Asp = self.dia_container(A)
+        Bsp = self.dia_container(B)
+
+        Csp = Asp - Bsp
+        assert isinstance(Csp, self.dia_container)
+        assert_array_equal(Csp.toarray(), A - B)
+
+        Csp = Bsp - Asp
+        assert isinstance(Csp, self.dia_container)
+        assert_array_equal(Csp.toarray(), B - A)
+
+        Bsp = Bsp.asformat('csr')
+        assert_array_equal((Asp - Bsp).toarray(), A - B)
+        assert_array_equal((Bsp - Asp).toarray(), B - A)
+
+    def test_mul_scalar(self):
+        # repro for gh-20434
+        m = self.dia_container([[1, 2], [0, 4]])
+        res = m * 3
+        assert isinstance(res, m.__class__)
+        assert_array_equal(res.toarray(), [[3, 6], [0, 12]])
+
+        res2 = m.multiply(3)
+        assert isinstance(res2, m.__class__)
+        assert_array_equal(res2.toarray(), [[3, 6], [0, 12]])
+
+    def test_matmul_dia(self):
+        # test DIA structure of DIA @ DIA:
+
+        # that all and only needed elements are used and produced
+        A = array([[1, 2, 3],
+                   [4, 5, 6]])
+        B = array([[11, 12],
+                   [13, 14],
+                   [15, 16]])
+        Asp = self.dia_container(A)
+        Bsp = self.dia_container(B)
+        Asp.data[Asp.data == 0] = -1  # poison outside elements
+        Bsp.data[Bsp.data == 0] = -1
+        assert_array_equal(Asp.toarray(), A)
+        assert_array_equal(Bsp.toarray(), B)
+
+        C = A @ B
+        Csp = Asp @ Bsp
+        assert isinstance(Csp, self.dia_container)
+        assert_array_equal(Csp.toarray(), C)
+        assert_array_equal(Csp.offsets, [-1, 0, 1])
+        assert_array_equal(Csp.data, self.dia_container(C).data)
+
+        C = B @ A
+        Csp = Bsp @ Asp
+        assert isinstance(Csp, self.dia_container)
+        assert_array_equal(Csp.toarray(), C)
+        assert_array_equal(Csp.offsets, [-2, -1, 0, 1, 2])
+        assert_array_equal(Csp.data, self.dia_container(C).data)
+
+        # short data and that order of input offsets doesn't matter
+        Asp = self.dia_container(([[0., 1., 2.], [3., 4., 5.]], [1, -2]), (5, 5))
+        Bsp = self.dia_container(([[6., 7., 8.], [0., 0., 9.]], [-1, 2]), (5, 5))
+
+        Csp = Asp @ Bsp
+        assert_array_equal(Csp.offsets, array([-3, 0]))
+        assert_array_equal(Csp.data, [[24., 35., 0.],
+                                      [6., 14., 27.]])
+
+        Csp = Bsp @ Asp
+        assert_array_equal(Csp.offsets, array([-3, 0]))
+        assert_array_equal(Csp.data, [[24., 0., 0.],
+                                      [27., 6., 14.]])
+
+
+class TestDIAMatrix(_MatrixMixin, TestDIA):
+    spcreator = dia_matrix
+
+
+TestDIA.init_class()
+TestDIAMatrix.init_class()
+
+
+class TestBSR(sparse_test_class(getset=False,
+                                slicing=False, slicing_assign=False,
+                                fancy_indexing=False, fancy_assign=False,
+                                nnz_axis=False)):
+    spcreator = bsr_array
+    math_dtypes = [np.int_, np.float64, np.complex128]
+
+    def test_constructor1(self):
+        # check native BSR format constructor
+        indptr = array([0,2,2,4])
+        indices = array([0,2,2,3])
+        data = zeros((4,2,3))
+
+        data[0] = array([[0, 1, 2],
+                         [3, 0, 5]])
+        data[1] = array([[0, 2, 4],
+                         [6, 0, 10]])
+        data[2] = array([[0, 4, 8],
+                         [12, 0, 20]])
+        data[3] = array([[0, 5, 10],
+                         [15, 0, 25]])
+
+        A = kron([[1,0,2,0],[0,0,0,0],[0,0,4,5]], [[0,1,2],[3,0,5]])
+        Asp = self.bsr_container((data,indices,indptr),shape=(6,12))
+        assert_equal(Asp.toarray(), A)
+
+        # infer shape from arrays
+        Asp = self.bsr_container((data,indices,indptr))
+        assert_equal(Asp.toarray(), A)
+
+    def test_constructor2(self):
+        # construct from dense
+
+        # test zero mats
+        for shape in [(1,1), (5,1), (1,10), (10,4), (3,7), (2,1)]:
+            A = zeros(shape)
+            assert_equal(self.bsr_container(A).toarray(), A)
+        A = zeros((4,6))
+        assert_equal(self.bsr_container(A, blocksize=(2, 2)).toarray(), A)
+        assert_equal(self.bsr_container(A, blocksize=(2, 3)).toarray(), A)
+
+        A = kron([[1,0,2,0],[0,0,0,0],[0,0,4,5]], [[0,1,2],[3,0,5]])
+        assert_equal(self.bsr_container(A).toarray(), A)
+        assert_equal(self.bsr_container(A, shape=(6, 12)).toarray(), A)
+        assert_equal(self.bsr_container(A, blocksize=(1, 1)).toarray(), A)
+        assert_equal(self.bsr_container(A, blocksize=(2, 3)).toarray(), A)
+        assert_equal(self.bsr_container(A, blocksize=(2, 6)).toarray(), A)
+        assert_equal(self.bsr_container(A, blocksize=(2, 12)).toarray(), A)
+        assert_equal(self.bsr_container(A, blocksize=(3, 12)).toarray(), A)
+        assert_equal(self.bsr_container(A, blocksize=(6, 12)).toarray(), A)
+
+        A = kron([[1,0,2,0],[0,1,0,0],[0,0,0,0]], [[0,1,2],[3,0,5]])
+        assert_equal(self.bsr_container(A, blocksize=(2, 3)).toarray(), A)
+
+    def test_constructor3(self):
+        # construct from coo-like (data,(row,col)) format
+        arg = ([1,2,3], ([0,1,1], [0,0,1]))
+        A = array([[1,0],[2,3]])
+        assert_equal(self.bsr_container(arg, blocksize=(2, 2)).toarray(), A)
+
+    def test_constructor4(self):
+        # regression test for gh-6292: self.bsr_matrix((data, indices, indptr)) was
+        #  trying to compare an int to a None
+        n = 8
+        data = np.ones((n, n, 1), dtype=np.int8)
+        indptr = np.array([0, n], dtype=np.int32)
+        indices = np.arange(n, dtype=np.int32)
+        self.bsr_container((data, indices, indptr), blocksize=(n, 1), copy=False)
+
+    def test_constructor5(self):
+        # check for validations introduced in gh-13400
+        n = 8
+        data_1dim = np.ones(n)
+        data = np.ones((n, n, n))
+        indptr = np.array([0, n])
+        indices = np.arange(n)
+
+        with assert_raises(ValueError):
+            # data ndim check
+            self.bsr_container((data_1dim, indices, indptr))
+
+        with assert_raises(ValueError):
+            # invalid blocksize
+            self.bsr_container((data, indices, indptr), blocksize=(1, 1, 1))
+
+        with assert_raises(ValueError):
+            # mismatching blocksize
+            self.bsr_container((data, indices, indptr), blocksize=(1, 1))
+
+    def test_default_dtype(self):
+        # As a numpy array, `values` has shape (2, 2, 1).
+        values = [[[1], [1]], [[1], [1]]]
+        indptr = np.array([0, 2], dtype=np.int32)
+        indices = np.array([0, 1], dtype=np.int32)
+        b = self.bsr_container((values, indices, indptr), blocksize=(2, 1))
+        assert b.dtype == np.array(values).dtype
+
+    def test_bsr_tocsr(self):
+        # check native conversion from BSR to CSR
+        indptr = array([0, 2, 2, 4])
+        indices = array([0, 2, 2, 3])
+        data = zeros((4, 2, 3))
+
+        data[0] = array([[0, 1, 2],
+                         [3, 0, 5]])
+        data[1] = array([[0, 2, 4],
+                         [6, 0, 10]])
+        data[2] = array([[0, 4, 8],
+                         [12, 0, 20]])
+        data[3] = array([[0, 5, 10],
+                         [15, 0, 25]])
+
+        A = kron([[1, 0, 2, 0], [0, 0, 0, 0], [0, 0, 4, 5]],
+                 [[0, 1, 2], [3, 0, 5]])
+        Absr = self.bsr_container((data, indices, indptr), shape=(6, 12))
+        Acsr = Absr.tocsr()
+        Acsr_via_coo = Absr.tocoo().tocsr()
+        assert_equal(Acsr.toarray(), A)
+        assert_equal(Acsr.toarray(), Acsr_via_coo.toarray())
+
+    def test_eliminate_zeros(self):
+        data = kron([1, 0, 0, 0, 2, 0, 3, 0], [[1,1],[1,1]]).T
+        data = data.reshape(-1,2,2)
+        indices = array([1, 2, 3, 4, 5, 6, 7, 8])
+        indptr = array([0, 3, 8])
+        asp = self.bsr_container((data, indices, indptr), shape=(4,20))
+        bsp = asp.copy()
+        asp.eliminate_zeros()
+        assert_array_equal(asp.nnz, 3*4)
+        assert_array_equal(asp.toarray(), bsp.toarray())
+
+    # GitHub issue #9687
+    def test_eliminate_zeros_all_zero(self):
+        np.random.seed(0)
+        m = self.bsr_container(np.random.random((12, 12)), blocksize=(2, 3))
+
+        # eliminate some blocks, but not all
+        m.data[m.data <= 0.9] = 0
+        m.eliminate_zeros()
+        assert_equal(m.nnz, 66)
+        assert_array_equal(m.data.shape, (11, 2, 3))
+
+        # eliminate all remaining blocks
+        m.data[m.data <= 1.0] = 0
+        m.eliminate_zeros()
+        assert_equal(m.nnz, 0)
+        assert_array_equal(m.data.shape, (0, 2, 3))
+        assert_array_equal(m.toarray(), np.zeros((12, 12)))
+
+        # test fast path
+        m.eliminate_zeros()
+        assert_equal(m.nnz, 0)
+        assert_array_equal(m.data.shape, (0, 2, 3))
+        assert_array_equal(m.toarray(), np.zeros((12, 12)))
+
+    def test_has_canonical_format(self):
+        "Ensure has_canonical_format memoizes state for sum_duplicates"
+
+        A = np.array([[2, 3, 2], [0, 2, 1], [-4, 0, 2]])
+        M = self.bsr_container(A)
+        assert_equal(True, M.has_canonical_format)
+
+        indices = np.array([0, 0])  # contains duplicate
+        data = np.array([A, A*0])
+        indptr = np.array([0, 2])
+
+        M = self.bsr_container((data, indices, indptr)).copy()
+        assert_equal(False, M.has_canonical_format)
+        assert isinstance(M.has_canonical_format, bool)
+        # set flag by deduplicating
+        M.sum_duplicates()
+        assert_equal(True, M.has_canonical_format)
+        assert_equal(1, len(M.indices))
+
+        # manually set flag True (although underlyingly duplicated)
+        M = self.bsr_container((data, indices, indptr)).copy()
+        M.has_canonical_format = True
+        assert_equal(True, M.has_canonical_format)
+        assert_equal(2, len(M.indices))  # unaffected content
+        # ensure deduplication bypassed when has_canonical_format == True
+        M.sum_duplicates()
+        assert_equal(2, len(M.indices))  # still has duplicates!!!!
+        # ensure deduplication reenabled when has_canonical_format == False
+        M.has_canonical_format = False
+        M.sum_duplicates()
+        assert_equal(1, len(M.indices))
+        assert_equal(True, M.has_canonical_format)
+
+        # manually set flag False (although underlyingly canonical)
+        M = self.bsr_container(A)
+        M.has_canonical_format = False
+        assert_equal(False, M.has_canonical_format)
+        assert_equal(1, len(M.indices))
+        # sum_duplicates does not complain when no work to do
+        M.sum_duplicates()
+        assert_equal(True, M.has_canonical_format)
+
+        # manually reset index arrays before accessing M.has_canonical_format is OK
+        M = self.bsr_container(A)
+        M.data, M.indices, M.indptr = data, indices, indptr
+        assert_equal(False, M.has_canonical_format)
+        assert_equal(2, len(M.indices))  # dups and has_canonical_format is False
+
+        # but reset after accessing M.has_canonical_format can break flag
+        M = self.bsr_container(A)
+        M.has_canonical_format  # underlying attr is set here
+        M.data, M.indices, M.indptr = data, indices, indptr
+        assert_equal(True, M.has_canonical_format)
+        assert_equal(2, len(M.indices))  # dups but has_canonical_format is True
+        M.sum_duplicates()
+        assert_equal(2, len(M.indices))  # still has duplicates!!!!
+
+    def test_bsr_matvec(self):
+        A = self.bsr_container(arange(2*3*4*5).reshape(2*4,3*5), blocksize=(4,5))
+        x = arange(A.shape[1]).reshape(-1,1)
+        assert_equal(A @ x, A.toarray() @ x)
+
+    def test_bsr_matvecs(self):
+        A = self.bsr_container(arange(2*3*4*5).reshape(2*4,3*5), blocksize=(4,5))
+        x = arange(A.shape[1]*6).reshape(-1,6)
+        assert_equal(A @ x, A.toarray() @ x)
+
+    @pytest.mark.xfail(run=False, reason='BSR does not have a __getitem__')
+    def test_iterator(self):
+        pass
+
+    @pytest.mark.xfail(run=False, reason='BSR does not have a __setitem__')
+    def test_setdiag(self):
+        pass
+
+    def test_resize_blocked(self):
+        # test resize() with non-(1,1) blocksize
+        D = np.array([[1, 0, 3, 4],
+                      [2, 0, 0, 0],
+                      [3, 0, 0, 0]])
+        S = self.spcreator(D, blocksize=(1, 2))
+        assert_(S.resize((3, 2)) is None)
+        assert_array_equal(S.toarray(), [[1, 0],
+                                         [2, 0],
+                                         [3, 0]])
+        S.resize((2, 2))
+        assert_array_equal(S.toarray(), [[1, 0],
+                                         [2, 0]])
+        S.resize((3, 2))
+        assert_array_equal(S.toarray(), [[1, 0],
+                                         [2, 0],
+                                         [0, 0]])
+        S.resize((3, 4))
+        assert_array_equal(S.toarray(), [[1, 0, 0, 0],
+                                         [2, 0, 0, 0],
+                                         [0, 0, 0, 0]])
+        assert_raises(ValueError, S.resize, (2, 3))
+
+    @pytest.mark.xfail(run=False, reason='BSR does not have a __setitem__')
+    def test_setdiag_comprehensive(self):
+        pass
+
+    @pytest.mark.skipif(IS_COLAB, reason="exceeds memory limit")
+    def test_scalar_idx_dtype(self):
+        # Check that index dtype takes into account all parameters
+        # passed to sparsetools, including the scalar ones
+        indptr = np.zeros(2, dtype=np.int32)
+        indices = np.zeros(0, dtype=np.int32)
+        vals = np.zeros((0, 1, 1))
+        a = self.bsr_container((vals, indices, indptr), shape=(1, 2**31-1))
+        b = self.bsr_container((vals, indices, indptr), shape=(1, 2**31))
+        c = self.bsr_container((1, 2**31-1))
+        d = self.bsr_container((1, 2**31))
+        assert_equal(a.indptr.dtype, np.int32)
+        assert_equal(b.indptr.dtype, np.int64)
+        assert_equal(c.indptr.dtype, np.int32)
+        assert_equal(d.indptr.dtype, np.int64)
+
+        try:
+            vals2 = np.zeros((0, 1, 2**31-1))
+            vals3 = np.zeros((0, 1, 2**31))
+            e = self.bsr_container((vals2, indices, indptr), shape=(1, 2**31-1))
+            f = self.bsr_container((vals3, indices, indptr), shape=(1, 2**31))
+            assert_equal(e.indptr.dtype, np.int32)
+            assert_equal(f.indptr.dtype, np.int64)
+        except (MemoryError, ValueError):
+            # May fail on 32-bit Python
+            e = 0
+            f = 0
+
+        # These shouldn't fail
+        for x in [a, b, c, d, e, f]:
+            x + x
+
+
+class TestBSRMatrix(_MatrixMixin, TestBSR):
+    spcreator = bsr_matrix
+
+
+TestBSR.init_class()
+TestBSRMatrix.init_class()
+
+
+#------------------------------------------------------------------------------
+# Tests for non-canonical representations (with duplicates, unsorted indices)
+#------------------------------------------------------------------------------
+
+def _same_sum_duplicate(data, *inds, **kwargs):
+    """Duplicates entries to produce the same matrix"""
+    indptr = kwargs.pop('indptr', None)
+    if np.issubdtype(data.dtype, np.bool_) or \
+       np.issubdtype(data.dtype, np.unsignedinteger):
+        if indptr is None:
+            return (data,) + inds
+        else:
+            return (data,) + inds + (indptr,)
+
+    zeros_pos = (data == 0).nonzero()
+
+    # duplicate data
+    data = data.repeat(2, axis=0)
+    data[::2] -= 1
+    data[1::2] = 1
+
+    # don't spoil all explicit zeros
+    if zeros_pos[0].size > 0:
+        pos = tuple(p[0] for p in zeros_pos)
+        pos1 = (2*pos[0],) + pos[1:]
+        pos2 = (2*pos[0]+1,) + pos[1:]
+        data[pos1] = 0
+        data[pos2] = 0
+
+    inds = tuple(indices.repeat(2) for indices in inds)
+
+    if indptr is None:
+        return (data,) + inds
+    else:
+        return (data,) + inds + (indptr * 2,)
+
+
+class _NonCanonicalMixin:
+    def spcreator(self, D, *args, sorted_indices=False, **kwargs):
+        """Replace D with a non-canonical equivalent: containing
+        duplicate elements and explicit zeros"""
+        construct = super().spcreator
+        M = construct(D, *args, **kwargs)
+
+        zero_pos = (M.toarray() == 0).nonzero()
+        has_zeros = (zero_pos[0].size > 0)
+        if has_zeros:
+            k = zero_pos[0].size//2
+            with warnings.catch_warnings():
+                warnings.filterwarnings("ignore", WMSG, SparseEfficiencyWarning)
+                M = self._insert_explicit_zero(M, zero_pos[0][k], zero_pos[1][k])
+
+        arg1 = self._arg1_for_noncanonical(M, sorted_indices)
+        if 'shape' not in kwargs:
+            kwargs['shape'] = M.shape
+        NC = construct(arg1, **kwargs)
+
+        # check that result is valid
+        if NC.dtype in [np.float32, np.complex64]:
+            # For single-precision floats, the differences between M and NC
+            # that are introduced by the extra operations involved in the
+            # construction of NC necessitate a more lenient tolerance level
+            # than the default.
+            rtol = 1e-05
+        else:
+            rtol = 1e-07
+        assert_allclose(NC.toarray(), M.toarray(), rtol=rtol)
+
+        # check that at least one explicit zero
+        if has_zeros:
+            assert_((NC.data == 0).any())
+        # TODO check that NC has duplicates (which are not explicit zeros)
+
+        return NC
+
+    @pytest.mark.skip(reason='bool(matrix) counts explicit zeros')
+    def test_bool(self):
+        pass
+
+    @pytest.mark.skip(reason='getnnz-axis counts explicit zeros')
+    def test_getnnz_axis(self):
+        pass
+
+    @pytest.mark.skip(reason='nnz counts explicit zeros')
+    def test_empty(self):
+        pass
+
+
+class _NonCanonicalCompressedMixin(_NonCanonicalMixin):
+    def _arg1_for_noncanonical(self, M, sorted_indices=False):
+        """Return non-canonical constructor arg1 equivalent to M"""
+        data, indices, indptr = _same_sum_duplicate(M.data, M.indices,
+                                                    indptr=M.indptr)
+        if not sorted_indices:
+            for start, stop in zip(indptr, indptr[1:]):
+                indices[start:stop] = indices[start:stop][::-1].copy()
+                data[start:stop] = data[start:stop][::-1].copy()
+        return data, indices, indptr
+
+    def _insert_explicit_zero(self, M, i, j):
+        M[i,j] = 0
+        return M
+
+
+class _NonCanonicalCSMixin(_NonCanonicalCompressedMixin):
+    def test_getelement(self):
+        def check(dtype, sorted_indices):
+            D = array([[1,0,0],
+                       [4,3,0],
+                       [0,2,0],
+                       [0,0,0]], dtype=dtype)
+            A = self.spcreator(D, sorted_indices=sorted_indices)
+
+            M,N = D.shape
+
+            for i in range(-M, M):
+                for j in range(-N, N):
+                    assert_equal(A[i,j], D[i,j])
+
+            for ij in [(0,3),(-1,3),(4,0),(4,3),(4,-1), (1, 2, 3)]:
+                assert_raises((IndexError, TypeError), A.__getitem__, ij)
+
+        for dtype in supported_dtypes:
+            for sorted_indices in [False, True]:
+                check(np.dtype(dtype), sorted_indices)
+
+    def test_setitem_sparse(self):
+        D = np.eye(3)
+        A = self.spcreator(D)
+        B = self.spcreator([[1,2,3]])
+
+        D[1,:] = B.toarray()
+        with warnings.catch_warnings():
+            warnings.filterwarnings("ignore", WMSG, SparseEfficiencyWarning)
+            A[1,:] = B
+        assert_array_equal(A.toarray(), D)
+
+        D[:,2] = B.toarray().ravel()
+        with warnings.catch_warnings():
+            warnings.filterwarnings("ignore", WMSG, SparseEfficiencyWarning)
+            A[:,2] = B.T
+        assert_array_equal(A.toarray(), D)
+
+    @pytest.mark.xfail(run=False, reason='inverse broken with non-canonical matrix')
+    def test_inv(self):
+        pass
+
+    @pytest.mark.xfail(run=False, reason='solve broken with non-canonical matrix')
+    def test_solve(self):
+        pass
+
+
+class TestCSRNonCanonical(_NonCanonicalCSMixin, TestCSR):
+    pass
+
+
+class TestCSRNonCanonicalMatrix(TestCSRNonCanonical, TestCSRMatrix):
+    pass
+
+
+class TestCSCNonCanonical(_NonCanonicalCSMixin, TestCSC):
+    pass
+
+
+class TestCSCNonCanonicalMatrix(TestCSCNonCanonical, TestCSCMatrix):
+    pass
+
+
+class TestBSRNonCanonical(_NonCanonicalCompressedMixin, TestBSR):
+    def _insert_explicit_zero(self, M, i, j):
+        x = M.tocsr()
+        x[i,j] = 0
+        return x.tobsr(blocksize=M.blocksize)
+
+    @pytest.mark.xfail(run=False, reason='diagonal broken with non-canonical BSR')
+    def test_diagonal(self):
+        pass
+
+    @pytest.mark.xfail(run=False, reason='expm broken with non-canonical BSR')
+    def test_expm(self):
+        pass
+
+
+class TestBSRNonCanonicalMatrix(TestBSRNonCanonical, TestBSRMatrix):
+    pass
+
+
+class COONonCanonicalMixin(_NonCanonicalMixin):
+    def _arg1_for_noncanonical(self, M, sorted_indices=None):
+        """Return non-canonical constructor arg1 equivalent to M"""
+        data, row, col = _same_sum_duplicate(M.data, M.row, M.col)
+        return data, (row, col)
+
+    def _insert_explicit_zero(self, M, i, j):
+        M.data = np.r_[M.data.dtype.type(0), M.data]
+        M.row = np.r_[M.row.dtype.type(i), M.row]
+        M.col = np.r_[M.col.dtype.type(j), M.col]
+        return M
+
+    def test_setdiag_noncanonical(self):
+        m = self.spcreator(np.eye(3))
+        m.sum_duplicates()
+        m.setdiag([3, 2], k=1)
+        m.sum_duplicates()
+        assert_(np.all(np.diff(m.col) >= 0))
+
+
+class TestCOONonCanonical(COONonCanonicalMixin, TestCOO):
+    pass
+
+
+class TestCOONonCanonicalMatrix(COONonCanonicalMixin, TestCOOMatrix):
+    pass
+
+
+def test_broadcast_to():
+    a = np.array([[1, 0, 2]])
+    b = np.array([[1], [0], [2]])
+    c = np.array([[1, 0, 2], [0, 3, 0]])
+    d = np.array([[7]])
+    e = np.array([[0]])
+    f = np.array([[0,0,0,0]])
+    for container in (csc_matrix, csc_array, csr_matrix, csr_array):
+        res_a = container(a)._broadcast_to((2,3))
+        res_b = container(b)._broadcast_to((3,4))
+        res_c = container(c)._broadcast_to((2,3))
+        res_d = container(d)._broadcast_to((4,4))
+        res_e = container(e)._broadcast_to((5,6))
+        res_f = container(f)._broadcast_to((2,4))
+        assert_array_equal(res_a.toarray(), np.broadcast_to(a, (2,3)))
+        assert_array_equal(res_b.toarray(), np.broadcast_to(b, (3,4)))
+        assert_array_equal(res_c.toarray(), c)
+        assert_array_equal(res_d.toarray(), np.broadcast_to(d, (4,4)))
+        assert_array_equal(res_e.toarray(), np.broadcast_to(e, (5,6)))
+        assert_array_equal(res_f.toarray(), np.broadcast_to(f, (2,4)))
+
+        with pytest.raises(ValueError, match="cannot be broadcast"):
+            container([[1, 2, 0], [3, 0, 1]])._broadcast_to(shape=(2, 1))
+
+        with pytest.raises(ValueError, match="cannot be broadcast"):
+            container([[0, 1, 2]])._broadcast_to(shape=(3, 2))
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_common1d.py b/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_common1d.py
new file mode 100644
index 0000000000000000000000000000000000000000..437af3d839c29d8131672a1e593ddb283608e7e8
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_common1d.py
@@ -0,0 +1,444 @@
+"""Test of 1D aspects of sparse array classes"""
+import warnings
+
+import pytest
+
+import numpy as np
+from numpy.testing import assert_equal, assert_allclose
+from numpy.exceptions import ComplexWarning
+
+from scipy.sparse import (
+        bsr_array, csc_array, dia_array, lil_array,
+        coo_array, csr_array, dok_array,
+    )
+from scipy.sparse._sputils import supported_dtypes, matrix
+
+
+spcreators = [coo_array, csr_array, dok_array]
+math_dtypes = [np.int64, np.float64, np.complex128]
+
+
+@pytest.fixture
+def dat1d():
+    return np.array([3, 0, 1, 0], 'd')
+
+
+@pytest.fixture
+def datsp_math_dtypes(dat1d):
+    dat_dtypes = {dtype: dat1d.astype(dtype) for dtype in math_dtypes}
+    return {
+        spcreator: [(dtype, dat, spcreator(dat)) for dtype, dat in dat_dtypes.items()]
+        for spcreator in spcreators
+    }
+
+
+# Test init with 1D dense input
+# sparrays which do not plan to support 1D
+@pytest.mark.parametrize("spcreator", [bsr_array, csc_array, dia_array, lil_array])
+def test_no_1d_support_in_init(spcreator):
+    with pytest.raises(ValueError, match="arrays don't support 1D input"):
+        spcreator([0, 1, 2, 3])
+
+
+# Test init with nD dense input
+# sparrays which do not yet support nD
+@pytest.mark.parametrize(
+    "spcreator", [csr_array, dok_array, bsr_array, csc_array, dia_array, lil_array]
+)
+def test_no_nd_support_in_init(spcreator):
+    with pytest.raises(ValueError, match="arrays don't.*support 3D"):
+        spcreator(np.ones((3, 2, 4)))
+
+
+# Main tests class
+@pytest.mark.parametrize("spcreator", spcreators)
+class TestCommon1D:
+    """test common functionality shared by 1D sparse formats"""
+
+    def test_create_empty(self, spcreator):
+        assert_equal(spcreator((3,)).toarray(), np.zeros(3))
+        assert_equal(spcreator((3,)).nnz, 0)
+        assert_equal(spcreator((3,)).count_nonzero(), 0)
+
+    def test_invalid_shapes(self, spcreator):
+        with pytest.raises(ValueError, match='elements cannot be negative'):
+            spcreator((-3,))
+
+    def test_repr(self, spcreator, dat1d):
+        repr(spcreator(dat1d))
+
+    def test_str(self, spcreator, dat1d):
+        str(spcreator(dat1d))
+
+    def test_neg(self, spcreator):
+        A = np.array([-1, 0, 17, 0, -5, 0, 1, -4, 0, 0, 0, 0], 'd')
+        assert_equal(-A, (-spcreator(A)).toarray())
+
+    def test_1d_supported_init(self, spcreator):
+        A = spcreator([0, 1, 2, 3])
+        assert A.ndim == 1
+
+    def test_reshape_1d_tofrom_row_or_column(self, spcreator):
+        # add a dimension 1d->2d
+        x = spcreator([1, 0, 7, 0, 0, 0, 0, -3, 0, 0, 0, 5])
+        y = x.reshape(1, 12)
+        desired = [[1, 0, 7, 0, 0, 0, 0, -3, 0, 0, 0, 5]]
+        assert_equal(y.toarray(), desired)
+
+        # remove a size-1 dimension 2d->1d
+        x = spcreator(desired)
+        y = x.reshape(12)
+        assert_equal(y.toarray(), desired[0])
+        y2 = x.reshape((12,))
+        assert y.shape == y2.shape
+
+        # make a 2d column into 1d. 2d->1d
+        y = x.T.reshape(12)
+        assert_equal(y.toarray(), desired[0])
+
+    def test_reshape(self, spcreator):
+        x = spcreator([1, 0, 7, 0, 0, 0, 0, -3, 0, 0, 0, 5])
+        y = x.reshape((4, 3))
+        desired = [[1, 0, 7], [0, 0, 0], [0, -3, 0], [0, 0, 5]]
+        assert_equal(y.toarray(), desired)
+
+        y = x.reshape((12,))
+        assert y is x
+
+        y = x.reshape(12)
+        assert_equal(y.toarray(), x.toarray())
+
+    def test_sum(self, spcreator):
+        np.random.seed(1234)
+        dat_1 = np.array([0, 1, 2, 3, -4, 5, -6, 7, 9])
+        dat_2 = np.random.rand(5)
+        dat_3 = np.array([])
+        dat_4 = np.zeros((40,))
+        arrays = [dat_1, dat_2, dat_3, dat_4]
+
+        for dat in arrays:
+            datsp = spcreator(dat)
+            with np.errstate(over='ignore'):
+                assert np.isscalar(datsp.sum())
+                assert_allclose(dat.sum(), datsp.sum())
+                assert_allclose(dat.sum(axis=None), datsp.sum(axis=None))
+                assert_allclose(dat.sum(axis=0), datsp.sum(axis=0))
+                assert_allclose(dat.sum(axis=-1), datsp.sum(axis=-1))
+
+        # test `out` parameter
+        datsp.sum(axis=0, out=np.zeros(()))
+
+    def test_sum_invalid_params(self, spcreator):
+        out = np.zeros((3,))  # wrong size for out
+        dat = np.array([0, 1, 2])
+        datsp = spcreator(dat)
+
+        with pytest.raises(ValueError, match='axis out of range'):
+            datsp.sum(axis=1)
+        with pytest.raises(ValueError, match='axis out of range'):
+            datsp.sum(axis=(0, 3))
+        with pytest.raises(TypeError, match='axis must be an integer'):
+            datsp.sum(axis=1.5)
+        with pytest.raises(ValueError, match='output parameter.*wrong.*dimension'):
+            datsp.sum(axis=0, out=out)
+
+    def test_numpy_sum(self, spcreator):
+        dat = np.array([0, 1, 2])
+        datsp = spcreator(dat)
+
+        dat_sum = np.sum(dat)
+        datsp_sum = np.sum(datsp)
+
+        assert_allclose(dat_sum, datsp_sum)
+
+    def test_mean(self, spcreator):
+        dat = np.array([0, 1, 2])
+        datsp = spcreator(dat)
+
+        assert_allclose(dat.mean(), datsp.mean())
+        assert np.isscalar(datsp.mean(axis=None))
+        assert_allclose(dat.mean(axis=None), datsp.mean(axis=None))
+        assert_allclose(dat.mean(axis=0), datsp.mean(axis=0))
+        assert_allclose(dat.mean(axis=-1), datsp.mean(axis=-1))
+
+        with pytest.raises(ValueError, match='axis'):
+            datsp.mean(axis=1)
+        with pytest.raises(ValueError, match='axis'):
+            datsp.mean(axis=-2)
+
+    def test_mean_invalid_params(self, spcreator):
+        out = np.asarray(np.zeros((1, 3)))
+        dat = np.array([[0, 1, 2], [3, -4, 5], [-6, 7, 9]])
+
+        datsp = spcreator(dat)
+        with pytest.raises(ValueError, match='axis out of range'):
+            datsp.mean(axis=3)
+        with pytest.raises(ValueError, match='axis out of range'):
+            datsp.mean(axis=(0, 3))
+        with pytest.raises(TypeError, match='axis must be an integer'):
+            datsp.mean(axis=1.5)
+        with pytest.raises(ValueError, match='out.*not match shape'):
+            datsp.mean(axis=1, out=out)
+
+    def test_sum_dtype(self, spcreator):
+        dat = np.array([0, 1, 2])
+        datsp = spcreator(dat)
+
+        for dtype in supported_dtypes:
+            dat_sum = dat.sum(dtype=dtype)
+            datsp_sum = datsp.sum(dtype=dtype)
+
+            assert_allclose(dat_sum, datsp_sum)
+            assert_equal(dat_sum.dtype, datsp_sum.dtype)
+
+    def test_mean_dtype(self, spcreator):
+        dat = np.array([0, 1, 2])
+        datsp = spcreator(dat)
+
+        for dtype in supported_dtypes:
+            dat_mean = dat.mean(dtype=dtype)
+            datsp_mean = datsp.mean(dtype=dtype)
+
+            assert_allclose(dat_mean, datsp_mean)
+            assert_equal(dat_mean.dtype, datsp_mean.dtype)
+
+    def test_mean_out(self, spcreator):
+        dat = np.array([0, 1, 2])
+        datsp = spcreator(dat)
+
+        dat_out = np.array(0)
+        datsp_out = np.array(0)
+
+        dat.mean(out=dat_out)
+        datsp.mean(out=datsp_out)
+        assert_allclose(dat_out, datsp_out)
+
+        dat.mean(axis=0, out=dat_out)
+        datsp.mean(axis=0, out=datsp_out)
+        assert_allclose(dat_out, datsp_out)
+
+        with pytest.raises(ValueError, match="output parameter.*dimension"):
+            datsp.mean(out=np.array([0]))
+        with pytest.raises(ValueError, match="output parameter.*dimension"):
+            datsp.mean(out=np.array([[0]]))
+
+    def test_numpy_mean(self, spcreator):
+        dat = np.array([0, 1, 2])
+        datsp = spcreator(dat)
+
+        dat_mean = np.mean(dat)
+        datsp_mean = np.mean(datsp)
+
+        assert_allclose(dat_mean, datsp_mean)
+        assert_equal(dat_mean.dtype, datsp_mean.dtype)
+
+    def test_from_array(self, spcreator):
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", ComplexWarning)
+            A = np.array([2, 3, 4])
+            assert_equal(spcreator(A).toarray(), A)
+
+            A = np.array([1.0 + 3j, 0, -1])
+            assert_equal(spcreator(A).toarray(), A)
+            assert_equal(spcreator(A, dtype='int16').toarray(), A.astype('int16'))
+
+    def test_from_list(self, spcreator):
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", ComplexWarning)
+            A = [2, 3, 4]
+            assert_equal(spcreator(A).toarray(), A)
+
+            A = [1.0 + 3j, 0, -1]
+            assert_equal(spcreator(A).toarray(), np.array(A))
+            assert_equal(
+                spcreator(A, dtype='int16').toarray(), np.array(A).astype('int16')
+        )
+
+    def test_from_sparse(self, spcreator):
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", ComplexWarning)
+            D = np.array([1, 0, 0])
+            S = coo_array(D)
+            assert_equal(spcreator(S).toarray(), D)
+            S = spcreator(D)
+            assert_equal(spcreator(S).toarray(), D)
+
+            D = np.array([1.0 + 3j, 0, -1])
+            S = coo_array(D)
+            assert_equal(spcreator(S).toarray(), D)
+            assert_equal(spcreator(S, dtype='int16').toarray(), D.astype('int16'))
+            S = spcreator(D)
+            assert_equal(spcreator(S).toarray(), D)
+            assert_equal(spcreator(S, dtype='int16').toarray(), D.astype('int16'))
+
+    def test_toarray(self, spcreator, dat1d):
+        datsp = spcreator(dat1d)
+        # Check C- or F-contiguous (default).
+        chk = datsp.toarray()
+        assert_equal(chk, dat1d)
+        assert chk.flags.c_contiguous == chk.flags.f_contiguous
+
+        # Check C-contiguous (with arg).
+        chk = datsp.toarray(order='C')
+        assert_equal(chk, dat1d)
+        assert chk.flags.c_contiguous
+        assert chk.flags.f_contiguous
+
+        # Check F-contiguous (with arg).
+        chk = datsp.toarray(order='F')
+        assert_equal(chk, dat1d)
+        assert chk.flags.c_contiguous
+        assert chk.flags.f_contiguous
+
+        # Check with output arg.
+        out = np.zeros(datsp.shape, dtype=datsp.dtype)
+        datsp.toarray(out=out)
+        assert_equal(out, dat1d)
+
+        # Check that things are fine when we don't initialize with zeros.
+        out[...] = 1.0
+        datsp.toarray(out=out)
+        assert_equal(out, dat1d)
+
+        # np.dot does not work with sparse matrices (unless scalars)
+        # so this is testing whether dat1d matches datsp.toarray()
+        a = np.array([1.0, 2.0, 3.0, 4.0])
+        dense_dot_dense = np.dot(a, dat1d)
+        check = np.dot(a, datsp.toarray())
+        assert_equal(dense_dot_dense, check)
+
+        b = np.array([1.0, 2.0, 3.0, 4.0])
+        dense_dot_dense = np.dot(dat1d, b)
+        check = np.dot(datsp.toarray(), b)
+        assert_equal(dense_dot_dense, check)
+
+        # Check bool data works.
+        spbool = spcreator(dat1d, dtype=bool)
+        arrbool = dat1d.astype(bool)
+        assert_equal(spbool.toarray(), arrbool)
+
+    def test_add(self, spcreator, datsp_math_dtypes):
+        for dtype, dat, datsp in datsp_math_dtypes[spcreator]:
+            a = dat.copy()
+            a[0] = 2.0
+            b = datsp
+            c = b + a
+            assert_equal(c, b.toarray() + a)
+
+            # test broadcasting
+            # Note: cant add nonzero scalar to sparray. Can add len 1 array
+            c = b + a[0:1]
+            assert_equal(c, b.toarray() + a[0])
+
+    def test_radd(self, spcreator, datsp_math_dtypes):
+        for dtype, dat, datsp in datsp_math_dtypes[spcreator]:
+            a = dat.copy()
+            a[0] = 2.0
+            b = datsp
+            c = a + b
+            assert_equal(c, a + b.toarray())
+
+    def test_rsub(self, spcreator, datsp_math_dtypes):
+        for dtype, dat, datsp in datsp_math_dtypes[spcreator]:
+            if dtype == np.dtype('bool'):
+                # boolean array subtraction deprecated in 1.9.0
+                continue
+
+            assert_equal((dat - datsp), [0, 0, 0, 0])
+            assert_equal((datsp - dat), [0, 0, 0, 0])
+            assert_equal((0 - datsp).toarray(), -dat)
+
+            A = spcreator([1, -4, 0, 2], dtype='d')
+            assert_equal((dat - A), dat - A.toarray())
+            assert_equal((A - dat), A.toarray() - dat)
+            assert_equal(A.toarray() - datsp, A.toarray() - dat)
+            assert_equal(datsp - A.toarray(), dat - A.toarray())
+
+            # test broadcasting
+            assert_equal(dat[:1] - datsp, dat[:1] - dat)
+
+    def test_matmul_basic(self, spcreator):
+        A = np.array([[2, 0, 3.0], [0, 0, 0], [0, 1, 2]])
+        v = np.array([1, 0, 3])
+        Asp = spcreator(A)
+        vsp = spcreator(v)
+
+        # sparse result when both args are sparse and result not scalar
+        assert_equal((Asp @ vsp).toarray(), A @ v)
+        assert_equal(A @ vsp, A @ v)
+        assert_equal(Asp @ v, A @ v)
+        assert_equal((vsp @ Asp).toarray(), v @ A)
+        assert_equal(vsp @ A, v @ A)
+        assert_equal(v @ Asp, v @ A)
+
+        assert_equal(vsp @ vsp, v @ v)
+        assert_equal(v @ vsp, v @ v)
+        assert_equal(vsp @ v, v @ v)
+        assert_equal((Asp @ Asp).toarray(), A @ A)
+        assert_equal(A @ Asp, A @ A)
+        assert_equal(Asp @ A, A @ A)
+
+    def test_matvec(self, spcreator):
+        A = np.array([2, 0, 3.0])
+        Asp = spcreator(A)
+        col = np.array([[1, 2, 3]]).T
+
+        assert_allclose(Asp @ col, Asp.toarray() @ col)
+
+        assert (A @ np.array([1, 2, 3])).shape == ()
+        assert Asp @ np.array([1, 2, 3]) == 11
+        assert (Asp @ np.array([1, 2, 3])).shape == ()
+        assert (Asp @ np.array([[1], [2], [3]])).shape == (1,)
+        # check result type
+        assert isinstance(Asp @ matrix([[1, 2, 3]]).T, np.ndarray)
+
+        # ensure exception is raised for improper dimensions
+        bad_vecs = [np.array([1, 2]), np.array([1, 2, 3, 4]), np.array([[1], [2]])]
+        for x in bad_vecs:
+            with pytest.raises(ValueError, match='dimension mismatch'):
+                Asp @ x
+
+        # The current relationship between sparse matrix products and array
+        # products is as follows:
+        dot_result = np.dot(Asp.toarray(), [1, 2, 3])
+        assert_allclose(Asp @ np.array([1, 2, 3]), dot_result)
+        assert_allclose(Asp @ [[1], [2], [3]], dot_result.T)
+        # Note that the result of Asp @ x is dense if x has a singleton dimension.
+
+    def test_rmatvec(self, spcreator, dat1d):
+        M = spcreator(dat1d)
+        assert_allclose([1, 2, 3, 4] @ M, np.dot([1, 2, 3, 4], M.toarray()))
+        row = np.array([[1, 2, 3, 4]])
+        assert_allclose(row @ M, row @ M.toarray())
+
+    def test_transpose(self, spcreator, dat1d):
+        for A in [dat1d, np.array([])]:
+            B = spcreator(A)
+            assert_equal(B.toarray(), A)
+            assert_equal(B.transpose().toarray(), A)
+            assert_equal(B.dtype, A.dtype)
+
+    def test_add_dense_to_sparse(self, spcreator, datsp_math_dtypes):
+        for dtype, dat, datsp in datsp_math_dtypes[spcreator]:
+            sum1 = dat + datsp
+            assert_equal(sum1, dat + dat)
+            sum2 = datsp + dat
+            assert_equal(sum2, dat + dat)
+
+    def test_iterator(self, spcreator):
+        # test that __iter__ is compatible with NumPy
+        B = np.arange(5)
+        A = spcreator(B)
+
+        if A.format not in ['coo', 'dia', 'bsr']:
+            for x, y in zip(A, B):
+                assert_equal(x, y)
+
+    def test_resize(self, spcreator):
+        # resize(shape) resizes the matrix in-place
+        D = np.array([1, 0, 3, 4])
+        S = spcreator(D)
+        assert S.resize((3,)) is None
+        assert_equal(S.toarray(), [1, 0, 3])
+        S.resize((5,))
+        assert_equal(S.toarray(), [1, 0, 3, 0, 0])
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_construct.py b/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_construct.py
new file mode 100644
index 0000000000000000000000000000000000000000..8f243ad3935e0c7a334bc019999f3f2f3a8c0ddc
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_construct.py
@@ -0,0 +1,1169 @@
+"""test sparse matrix construction functions"""
+
+import numpy as np
+from numpy import array
+from numpy.testing import (assert_equal, assert_,
+        assert_array_equal, assert_array_almost_equal_nulp)
+import pytest
+from pytest import raises as assert_raises
+from scipy._lib._testutils import check_free_memory
+
+from scipy.sparse import (csr_matrix, coo_matrix,
+                          csr_array, coo_array,
+                          csc_array, bsr_array,
+                          dia_array, dok_array,
+                          lil_array, csc_matrix,
+                          bsr_matrix, dia_matrix,
+                          lil_matrix, sparray, spmatrix,
+                          _construct as construct)
+from scipy.sparse._construct import rand as sprand
+
+sparse_formats = ['csr','csc','coo','bsr','dia','lil','dok']
+
+#TODO check whether format=XXX is respected
+
+
+def _sprandn(m, n, density=0.01, format="coo", dtype=None, rng=None):
+    # Helper function for testing.
+    rng = np.random.default_rng(rng)
+    data_rvs = rng.standard_normal
+    return construct.random(m, n, density, format, dtype, rng, data_rvs)
+
+
+def _sprandn_array(m, n, density=0.01, format="coo", dtype=None, rng=None):
+    # Helper function for testing.
+    rng = np.random.default_rng(rng)
+    data_sampler = rng.standard_normal
+    return construct.random_array((m, n), density=density, format=format, dtype=dtype,
+                                  rng=rng, data_sampler=data_sampler)
+
+
+class TestConstructUtils:
+
+    @pytest.mark.parametrize("cls", [
+        csc_array, csr_array, coo_array, bsr_array,
+        dia_array, dok_array, lil_array
+    ])
+    def test_singleton_array_constructor(self, cls):
+        with pytest.raises(
+            ValueError,
+            match=(
+                'scipy sparse array classes do not support '
+                'instantiation from a scalar'
+            )
+        ):
+            cls(0)
+
+    @pytest.mark.parametrize("cls", [
+        csc_matrix, csr_matrix, coo_matrix,
+        bsr_matrix, dia_matrix, lil_matrix
+    ])
+    def test_singleton_matrix_constructor(self, cls):
+        """
+        This test is for backwards compatibility post scipy 1.13.
+        The behavior observed here is what is to be expected
+        with the older matrix classes. This test comes with the
+        exception of dok_matrix, which was not working pre scipy1.12
+        (unlike the rest of these).
+        """
+        assert cls(0).shape == (1, 1)
+
+    def test_spdiags(self):
+        diags1 = array([[1, 2, 3, 4, 5]])
+        diags2 = array([[1, 2, 3, 4, 5],
+                         [6, 7, 8, 9,10]])
+        diags3 = array([[1, 2, 3, 4, 5],
+                         [6, 7, 8, 9,10],
+                         [11,12,13,14,15]])
+
+        cases = []
+        cases.append((diags1, 0, 1, 1, [[1]]))
+        cases.append((diags1, [0], 1, 1, [[1]]))
+        cases.append((diags1, [0], 2, 1, [[1],[0]]))
+        cases.append((diags1, [0], 1, 2, [[1,0]]))
+        cases.append((diags1, [1], 1, 2, [[0,2]]))
+        cases.append((diags1,[-1], 1, 2, [[0,0]]))
+        cases.append((diags1, [0], 2, 2, [[1,0],[0,2]]))
+        cases.append((diags1,[-1], 2, 2, [[0,0],[1,0]]))
+        cases.append((diags1, [3], 2, 2, [[0,0],[0,0]]))
+        cases.append((diags1, [0], 3, 4, [[1,0,0,0],[0,2,0,0],[0,0,3,0]]))
+        cases.append((diags1, [1], 3, 4, [[0,2,0,0],[0,0,3,0],[0,0,0,4]]))
+        cases.append((diags1, [2], 3, 5, [[0,0,3,0,0],[0,0,0,4,0],[0,0,0,0,5]]))
+
+        cases.append((diags2, [0,2], 3, 3, [[1,0,8],[0,2,0],[0,0,3]]))
+        cases.append((diags2, [-1,0], 3, 4, [[6,0,0,0],[1,7,0,0],[0,2,8,0]]))
+        cases.append((diags2, [2,-3], 6, 6, [[0,0,3,0,0,0],
+                                              [0,0,0,4,0,0],
+                                              [0,0,0,0,5,0],
+                                              [6,0,0,0,0,0],
+                                              [0,7,0,0,0,0],
+                                              [0,0,8,0,0,0]]))
+
+        cases.append((diags3, [-1,0,1], 6, 6, [[6,12, 0, 0, 0, 0],
+                                                [1, 7,13, 0, 0, 0],
+                                                [0, 2, 8,14, 0, 0],
+                                                [0, 0, 3, 9,15, 0],
+                                                [0, 0, 0, 4,10, 0],
+                                                [0, 0, 0, 0, 5, 0]]))
+        cases.append((diags3, [-4,2,-1], 6, 5, [[0, 0, 8, 0, 0],
+                                                 [11, 0, 0, 9, 0],
+                                                 [0,12, 0, 0,10],
+                                                 [0, 0,13, 0, 0],
+                                                 [1, 0, 0,14, 0],
+                                                 [0, 2, 0, 0,15]]))
+        cases.append((diags3, [-1, 1, 2], len(diags3[0]), len(diags3[0]),
+                      [[0, 7, 13, 0, 0],
+                       [1, 0, 8, 14, 0],
+                       [0, 2, 0, 9, 15],
+                       [0, 0, 3, 0, 10],
+                       [0, 0, 0, 4, 0]]))
+
+        for d, o, m, n, result in cases:
+            if len(d[0]) == m and m == n:
+                assert_equal(construct.spdiags(d, o).toarray(), result)
+            assert_equal(construct.spdiags(d, o, m, n).toarray(), result)
+            assert_equal(construct.spdiags(d, o, (m, n)).toarray(), result)
+
+    def test_diags(self):
+        a = array([1.0, 2.0, 3.0, 4.0, 5.0])
+        b = array([6.0, 7.0, 8.0, 9.0, 10.0])
+        c = array([11.0, 12.0, 13.0, 14.0, 15.0])
+
+        cases = []
+        cases.append((a[:1], 0, (1, 1), [[1]]))
+        cases.append(([a[:1]], [0], (1, 1), [[1]]))
+        cases.append(([a[:1]], [0], (2, 1), [[1],[0]]))
+        cases.append(([a[:1]], [0], (1, 2), [[1,0]]))
+        cases.append(([a[:1]], [1], (1, 2), [[0,1]]))
+        cases.append(([a[:2]], [0], (2, 2), [[1,0],[0,2]]))
+        cases.append(([a[:1]],[-1], (2, 2), [[0,0],[1,0]]))
+        cases.append(([a[:3]], [0], (3, 4), [[1,0,0,0],[0,2,0,0],[0,0,3,0]]))
+        cases.append(([a[:3]], [1], (3, 4), [[0,1,0,0],[0,0,2,0],[0,0,0,3]]))
+        cases.append(([a[:1]], [-2], (3, 5), [[0,0,0,0,0],[0,0,0,0,0],[1,0,0,0,0]]))
+        cases.append(([a[:2]], [-1], (3, 5), [[0,0,0,0,0],[1,0,0,0,0],[0,2,0,0,0]]))
+        cases.append(([a[:3]], [0], (3, 5), [[1,0,0,0,0],[0,2,0,0,0],[0,0,3,0,0]]))
+        cases.append(([a[:3]], [1], (3, 5), [[0,1,0,0,0],[0,0,2,0,0],[0,0,0,3,0]]))
+        cases.append(([a[:3]], [2], (3, 5), [[0,0,1,0,0],[0,0,0,2,0],[0,0,0,0,3]]))
+        cases.append(([a[:2]], [3], (3, 5), [[0,0,0,1,0],[0,0,0,0,2],[0,0,0,0,0]]))
+        cases.append(([a[:1]], [4], (3, 5), [[0,0,0,0,1],[0,0,0,0,0],[0,0,0,0,0]]))
+        cases.append(([a[:1]], [-4], (5, 3), [[0,0,0],[0,0,0],[0,0,0],[0,0,0],[1,0,0]]))
+        cases.append(([a[:2]], [-3], (5, 3), [[0,0,0],[0,0,0],[0,0,0],[1,0,0],[0,2,0]]))
+        cases.append(([a[:3]], [-2], (5, 3), [[0,0,0],[0,0,0],[1,0,0],[0,2,0],[0,0,3]]))
+        cases.append(([a[:3]], [-1], (5, 3), [[0,0,0],[1,0,0],[0,2,0],[0,0,3],[0,0,0]]))
+        cases.append(([a[:3]], [0], (5, 3), [[1,0,0],[0,2,0],[0,0,3],[0,0,0],[0,0,0]]))
+        cases.append(([a[:2]], [1], (5, 3), [[0,1,0],[0,0,2],[0,0,0],[0,0,0],[0,0,0]]))
+        cases.append(([a[:1]], [2], (5, 3), [[0,0,1],[0,0,0],[0,0,0],[0,0,0],[0,0,0]]))
+
+        cases.append(([a[:3],b[:1]], [0,2], (3, 3), [[1,0,6],[0,2,0],[0,0,3]]))
+        cases.append(([a[:2],b[:3]], [-1,0], (3, 4), [[6,0,0,0],[1,7,0,0],[0,2,8,0]]))
+        cases.append(([a[:4],b[:3]], [2,-3], (6, 6), [[0,0,1,0,0,0],
+                                                     [0,0,0,2,0,0],
+                                                     [0,0,0,0,3,0],
+                                                     [6,0,0,0,0,4],
+                                                     [0,7,0,0,0,0],
+                                                     [0,0,8,0,0,0]]))
+
+        cases.append(([a[:4],b,c[:4]], [-1,0,1], (5, 5), [[6,11, 0, 0, 0],
+                                                            [1, 7,12, 0, 0],
+                                                            [0, 2, 8,13, 0],
+                                                            [0, 0, 3, 9,14],
+                                                            [0, 0, 0, 4,10]]))
+        cases.append(([a[:2],b[:3],c], [-4,2,-1], (6, 5), [[0, 0, 6, 0, 0],
+                                                          [11, 0, 0, 7, 0],
+                                                          [0,12, 0, 0, 8],
+                                                          [0, 0,13, 0, 0],
+                                                          [1, 0, 0,14, 0],
+                                                          [0, 2, 0, 0,15]]))
+
+        # too long arrays are OK
+        cases.append(([a], [0], (1, 1), [[1]]))
+        cases.append(([a[:3],b], [0,2], (3, 3), [[1, 0, 6], [0, 2, 0], [0, 0, 3]]))
+        cases.append((
+            np.array([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]]),
+            [0,-1],
+            (3, 3),
+            [[1, 0, 0], [4, 2, 0], [0, 5, 3]]
+        ))
+
+        # scalar case: broadcasting
+        cases.append(([1.0,-2.0,1.0], [1,0,-1], (3, 3), [[-2, 1, 0],
+                                                         [1, -2, 1],
+                                                         [0, 1, -2]]))
+
+        for d, o, shape, result in cases:
+            err_msg = f"{d!r} {o!r} {shape!r} {result!r}"
+            assert_equal(construct.diags(d, offsets=o, shape=shape).toarray(),
+                         result, err_msg=err_msg)
+
+            if (shape[0] == shape[1]
+                and hasattr(d[0], '__len__')
+                and len(d[0]) <= max(shape)):
+                # should be able to find the shape automatically
+                assert_equal(construct.diags(d, offsets=o).toarray(),
+                             result, err_msg=err_msg)
+
+    def test_diags_default(self):
+        a = array([1.0, 2.0, 3.0, 4.0, 5.0])
+        assert_equal(construct.diags(a).toarray(), np.diag(a))
+
+    def test_diags_default_bad(self):
+        a = array([[1, 2, 3, 4, 5], [2, 3, 4, 5, 6]])
+        assert_raises(ValueError, construct.diags, a)
+
+    def test_diags_bad(self):
+        a = array([1.0, 2.0, 3.0, 4.0, 5.0])
+        b = array([6.0, 7.0, 8.0, 9.0, 10.0])
+        c = array([11.0, 12.0, 13.0, 14.0, 15.0])
+
+        cases = []
+        cases.append(([a[:0]], 0, (1, 1)))
+        cases.append(([a[:4],b,c[:3]], [-1,0,1], (5, 5)))
+        cases.append(([a[:2],c,b[:3]], [-4,2,-1], (6, 5)))
+        cases.append(([a[:2],c,b[:3]], [-4,2,-1], None))
+        cases.append(([], [-4,2,-1], None))
+        cases.append(([1.0], [-5], (4, 4)))
+        cases.append(([a], 0, None))
+
+        for d, o, shape in cases:
+            assert_raises(ValueError, construct.diags, d, offsets=o, shape=shape)
+
+        assert_raises(TypeError, construct.diags, [[None]], offsets=[0])
+
+    def test_diags_vs_diag(self):
+        # Check that
+        #
+        #    diags([a, b, ...], [i, j, ...]) == diag(a, i) + diag(b, j) + ...
+        #
+
+        rng = np.random.RandomState(1234)
+
+        for n_diags in [1, 2, 3, 4, 5, 10]:
+            n = 1 + n_diags//2 + rng.randint(0, 10)
+
+            offsets = np.arange(-n+1, n-1)
+            rng.shuffle(offsets)
+            offsets = offsets[:n_diags]
+
+            diagonals = [rng.rand(n - abs(q)) for q in offsets]
+
+            mat = construct.diags(diagonals, offsets=offsets)
+            dense_mat = sum([np.diag(x, j) for x, j in zip(diagonals, offsets)])
+
+            assert_array_almost_equal_nulp(mat.toarray(), dense_mat)
+
+            if len(offsets) == 1:
+                mat = construct.diags(diagonals[0], offsets=offsets[0])
+                dense_mat = np.diag(diagonals[0], offsets[0])
+                assert_array_almost_equal_nulp(mat.toarray(), dense_mat)
+
+    def test_diags_dtype(self):
+        x = construct.diags([2.2], offsets=[0], shape=(2, 2), dtype=int)
+        assert_equal(x.dtype, int)
+        assert_equal(x.toarray(), [[2, 0], [0, 2]])
+
+    def test_diags_one_diagonal(self):
+        d = [0.0, 1.0, 2.0, 3.0, 4.0]
+        for k in range(-5, 6):
+            assert_equal(construct.diags(d, offsets=k).toarray(),
+                         construct.diags([d], offsets=[k]).toarray())
+
+    def test_diags_empty(self):
+        x = construct.diags([])
+        assert_equal(x.shape, (0, 0))
+
+    @pytest.mark.parametrize("identity", [construct.identity, construct.eye_array])
+    def test_identity(self, identity):
+        assert_equal(identity(1).toarray(), [[1]])
+        assert_equal(identity(2).toarray(), [[1,0],[0,1]])
+
+        I = identity(3, dtype='int8', format='dia')
+        assert_equal(I.dtype, np.dtype('int8'))
+        assert_equal(I.format, 'dia')
+
+        for fmt in sparse_formats:
+            I = identity(3, format=fmt)
+            assert_equal(I.format, fmt)
+            assert_equal(I.toarray(), [[1,0,0],[0,1,0],[0,0,1]])
+
+    @pytest.mark.parametrize("eye", [construct.eye, construct.eye_array])
+    def test_eye(self, eye):
+        assert_equal(eye(1,1).toarray(), [[1]])
+        assert_equal(eye(2,3).toarray(), [[1,0,0],[0,1,0]])
+        assert_equal(eye(3,2).toarray(), [[1,0],[0,1],[0,0]])
+        assert_equal(eye(3,3).toarray(), [[1,0,0],[0,1,0],[0,0,1]])
+
+        assert_equal(eye(3,3,dtype='int16').dtype, np.dtype('int16'))
+
+        for m in [3, 5]:
+            for n in [3, 5]:
+                for k in range(-5,6):
+                    # scipy.sparse.eye deviates from np.eye here. np.eye will
+                    # create arrays of all 0's when the diagonal offset is
+                    # greater than the size of the array. For sparse arrays
+                    # this makes less sense, especially as it results in dia
+                    # arrays with negative diagonals. Therefore sp.sparse.eye
+                    # validates that diagonal offsets fall within the shape of
+                    # the array. See gh-18555.
+                    if (k > 0 and k > n) or (k < 0 and abs(k) > m):
+                        with pytest.raises(
+                            ValueError, match="Offset.*out of bounds"
+                        ):
+                            eye(m, n, k=k)
+
+                    else:
+                        assert_equal(
+                            eye(m, n, k=k).toarray(),
+                            np.eye(m, n, k=k)
+                        )
+                        if m == n:
+                            assert_equal(
+                                eye(m, k=k).toarray(),
+                                np.eye(m, n, k=k)
+                            )
+
+    @pytest.mark.parametrize("eye", [construct.eye, construct.eye_array])
+    def test_eye_one(self, eye):
+        assert_equal(eye(1).toarray(), [[1]])
+        assert_equal(eye(2).toarray(), [[1,0],[0,1]])
+
+        I = eye(3, dtype='int8', format='dia')
+        assert_equal(I.dtype, np.dtype('int8'))
+        assert_equal(I.format, 'dia')
+
+        for fmt in sparse_formats:
+            I = eye(3, format=fmt)
+            assert_equal(I.format, fmt)
+            assert_equal(I.toarray(), [[1,0,0],[0,1,0],[0,0,1]])
+
+    def test_eye_array_vs_matrix(self):
+        assert isinstance(construct.eye_array(3), sparray)
+        assert not isinstance(construct.eye(3), sparray)
+
+    @pytest.mark.parametrize("arr,kw_format,out_format", [
+        ([[0, 0], [0, 1]], None, 'coo'),  # 2D sparse
+        ([[1, 0], [1, 1]], None, 'bsr'),  # 2D dense
+        ([[[1, 0], [1, 1]]], None, 'coo'),  # 3D dense
+    ])
+    def test_kron_output_format(self, arr, kw_format, out_format):
+        sparr = coo_array(arr)
+        assert construct.kron(sparr, sparr, format=kw_format).format == out_format
+        assert construct.kron(sparr, arr, format=kw_format).format == out_format
+        assert construct.kron(arr, sparr, format=kw_format).format == out_format
+
+    def test_kron(self):
+        cases = []
+
+        cases.append(array([[0]]))
+        cases.append(array([[-1]]))
+        cases.append(array([[4]]))
+        cases.append(array([[10]]))
+        cases.append(array([[0], [0]]))
+        cases.append(array([[0, 0]]))
+        cases.append(array([[1, 2], [3, 4]]))
+        cases.append(array([[0, 2], [5, 0]]))
+        cases.append(array([[0, 2, -6], [8, 0, 14]]))
+        cases.append(array([[5, 4], [0, 0], [6, 0]]))
+        cases.append(array([[5, 4, 4], [1, 0, 0], [6, 0, 8]]))
+        cases.append(array([[0, 1, 0, 2, 0, 5, 8]]))
+        cases.append(array([[0.5, 0.125, 0, 3.25], [0, 2.5, 0, 0]]))
+
+        # test all cases with some formats
+        for a in cases:
+            ca = csr_array(a)
+            for b in cases:
+                cb = csr_array(b)
+                expected = np.kron(a, b)
+                for fmt in sparse_formats[1:4]:
+                    result = construct.kron(ca, cb, format=fmt)
+                    assert_equal(result.format, fmt)
+                    assert_array_equal(result.toarray(), expected)
+                    assert isinstance(result, sparray)
+
+        # nD cases
+        cases.append(array([0, 1, 2]))
+        cases.append(array([[[0, 1, 2], [0, 1, 0]]]))
+        cases.append(array([[[0, 1]], [[2, 2]], [[1, 0]], [[2, 0]]]))
+
+        for a in cases:
+            ca = coo_array(a)
+            for b in cases:
+                cb = coo_array(b)
+                expected = np.kron(a, b)
+                result = construct.kron(ca, cb, format="coo")
+                assert_array_equal(result.toarray(), expected)
+
+        # test one case with all formats
+        a = array([[0.5, 0.125, 0, 3.25], [0, 2.5, 0, 0]])
+        b = array([[5, 4, 4], [1, 0, 0], [6, 0, 8]])
+        ca = csr_array(a)
+        cb = csr_array(b)
+
+        expected = np.kron(a, b)
+        for fmt in sparse_formats:
+            result = construct.kron(ca, cb, format=fmt)
+            assert_equal(result.format, fmt)
+            assert_array_equal(result.toarray(), expected)
+            assert isinstance(result, sparray)
+
+        # check that spmatrix returned when both inputs are spmatrix
+        result = construct.kron(csr_matrix(a), csr_matrix(b), format=fmt)
+        assert_equal(result.format, fmt)
+        assert_array_equal(result.toarray(), expected)
+        assert isinstance(result, spmatrix)
+
+    @pytest.mark.filterwarnings("ignore:.*switching.*sparse array:DeprecationWarning")
+    def test_kron_ndim_exceptions(self):
+        # spmatrix is default, so exceptions with 3D unless sparse arrays are input
+        with pytest.raises(TypeError, match='expected 2D array or matrix'):
+            construct.kron([[0], [1]], [[[0, 1]]])
+        with pytest.raises(TypeError, match="expected 2D array or matrix"):
+            construct.kron([[[1, 1]]], [[1], [1]])
+
+        # no exception for 3D if any sparse arrays input
+        construct.kron(coo_array([[[0, 1]]]), [[[0], [1]]])
+        construct.kron([[[0, 1]]], coo_array([[[0], [1]]]))
+
+        # no exception for 1D if either sparray or spmatrix
+        construct.kron([[0], [1]], [0, 1, 0])  # spmatrix b/c lists; 1d-list -> 2d
+        construct.kron([1, 1], [[1], [1]])
+        construct.kron([[0], [1]], coo_array([0, 1, 0]))  # sparray 1d-list -> 1d
+        construct.kron(coo_array([1, 1]), [[1], [1]])
+
+    def test_kron_large(self):
+        n = 2**16
+        a = construct.diags_array([1], shape=(1, n), offsets=n-1, dtype=None)
+        b = construct.diags_array([1], shape=(n, 1), offsets=1-n, dtype=None)
+
+        construct.kron(a, a)
+        construct.kron(b, b)
+
+    def test_kronsum(self):
+        cases = []
+
+        cases.append(array([[0]]))
+        cases.append(array([[-1]]))
+        cases.append(array([[4]]))
+        cases.append(array([[10]]))
+        cases.append(array([[1,2],[3,4]]))
+        cases.append(array([[0,2],[5,0]]))
+        cases.append(array([[0,2,-6],[8,0,14],[0,3,0]]))
+        cases.append(array([[1,0,0],[0,5,-1],[4,-2,8]]))
+
+        # test all cases with default format
+        for a in cases:
+            for b in cases:
+                result = construct.kronsum(csr_array(a), csr_array(b)).toarray()
+                expected = (np.kron(np.eye(b.shape[0]), a)
+                            + np.kron(b, np.eye(a.shape[0])))
+                assert_array_equal(result, expected)
+
+        # check that spmatrix returned when both inputs are spmatrix
+        result = construct.kronsum(csr_matrix(a), csr_matrix(b)).toarray()
+        assert_array_equal(result, expected)
+
+    @pytest.mark.filterwarnings("ignore:.*switching.*sparse array:DeprecationWarning")
+    def test_kronsum_ndim_exceptions(self):
+        with pytest.raises(ValueError, match='requires 2D input'):
+            construct.kronsum([[0], [1]], csr_array([0, 1]))
+        with pytest.raises(ValueError, match='requires 2D input'):
+            construct.kronsum(csr_array([0, 1]), [[0], [1]])
+        # no exception if sparse arrays are not input (spmatrix inferred)
+        construct.kronsum([[0, 1], [1, 0]], [2])
+
+    @pytest.mark.parametrize("coo_cls", [coo_matrix, coo_array])
+    def test_vstack(self, coo_cls):
+        A = coo_cls([[1,2],[3,4]])
+        B = coo_cls([[5,6]])
+
+        expected = array([[1, 2],
+                          [3, 4],
+                          [5, 6]])
+        assert_equal(construct.vstack([A, B]).toarray(), expected)
+        assert_equal(construct.vstack([A, B], dtype=np.float32).dtype,
+                     np.float32)
+
+        assert_equal(construct.vstack([A.todok(), B.todok()]).toarray(), expected)
+
+        assert_equal(construct.vstack([A.tocsr(), B.tocsr()]).toarray(),
+                     expected)
+        result = construct.vstack([A.tocsr(), B.tocsr()],
+                                  format="csr", dtype=np.float32)
+        assert_equal(result.dtype, np.float32)
+        assert_equal(result.indices.dtype, np.int32)
+        assert_equal(result.indptr.dtype, np.int32)
+
+        assert_equal(construct.vstack([A.tocsc(), B.tocsc()]).toarray(),
+                     expected)
+        result = construct.vstack([A.tocsc(), B.tocsc()],
+                                  format="csc", dtype=np.float32)
+        assert_equal(result.dtype, np.float32)
+        assert_equal(result.indices.dtype, np.int32)
+        assert_equal(result.indptr.dtype, np.int32)
+
+    def test_vstack_maintain64bit_idx_dtype(self):
+        # see gh-20389 v/hstack returns int32 idx_dtype with input int64 idx_dtype
+        X = csr_array([[1, 0, 0], [0, 1, 0], [0, 1, 0]])
+        X.indptr = X.indptr.astype(np.int64)
+        X.indices = X.indices.astype(np.int64)
+        assert construct.vstack([X, X]).indptr.dtype == np.int64
+        assert construct.hstack([X, X]).indptr.dtype == np.int64
+
+        X = csc_array([[1, 0, 0], [0, 1, 0], [0, 1, 0]])
+        X.indptr = X.indptr.astype(np.int64)
+        X.indices = X.indices.astype(np.int64)
+        assert construct.vstack([X, X]).indptr.dtype == np.int64
+        assert construct.hstack([X, X]).indptr.dtype == np.int64
+
+        X = coo_array([[1, 0, 0], [0, 1, 0], [0, 1, 0]])
+        X.coords = tuple(co.astype(np.int64) for co in X.coords)
+        assert construct.vstack([X, X]).coords[0].dtype == np.int64
+        assert construct.hstack([X, X]).coords[0].dtype == np.int64
+
+    def test_vstack_matrix_or_array(self):
+        A = [[1,2],[3,4]]
+        B = [[5,6]]
+        assert isinstance(construct.vstack([coo_array(A), coo_array(B)]), sparray)
+        assert isinstance(construct.vstack([coo_array(A), coo_matrix(B)]), sparray)
+        assert isinstance(construct.vstack([coo_matrix(A), coo_array(B)]), sparray)
+        assert isinstance(construct.vstack([coo_matrix(A), coo_matrix(B)]), spmatrix)
+
+    def test_vstack_1d_with_2d(self):
+        # fixes gh-21064
+        arr = csr_array([[1, 0, 0], [0, 1, 0]])
+        arr1d = csr_array([1, 0, 0])
+        arr1dcoo = coo_array([1, 0, 0])
+        assert construct.vstack([arr, np.array([0, 0, 0])]).shape == (3, 3)
+        assert construct.hstack([arr1d, np.array([[0]])]).shape == (1, 4)
+        assert construct.hstack([arr1d, arr1d]).shape == (1, 6)
+        assert construct.vstack([arr1d, arr1d]).shape == (2, 3)
+
+        # check csr specialty stacking code like _stack_along_minor_axis
+        assert construct.hstack([arr, arr]).shape == (2, 6)
+        assert construct.hstack([arr1d, arr1d]).shape == (1, 6)
+
+        assert construct.hstack([arr1d, arr1dcoo]).shape == (1, 6)
+        assert construct.vstack([arr, arr1dcoo]).shape == (3, 3)
+        assert construct.vstack([arr1d, arr1dcoo]).shape == (2, 3)
+
+        with pytest.raises(ValueError, match="incompatible row dimensions"):
+            construct.hstack([arr, np.array([0, 0])])
+        with pytest.raises(ValueError, match="incompatible column dimensions"):
+            construct.vstack([arr, np.array([0, 0])])
+
+    @pytest.mark.parametrize("coo_cls", [coo_matrix, coo_array])
+    def test_hstack(self, coo_cls):
+        A = coo_cls([[1,2],[3,4]])
+        B = coo_cls([[5],[6]])
+
+        expected = array([[1, 2, 5],
+                          [3, 4, 6]])
+        assert_equal(construct.hstack([A, B]).toarray(), expected)
+        assert_equal(construct.hstack([A, B], dtype=np.float32).dtype,
+                     np.float32)
+
+        assert_equal(construct.hstack([A.todok(), B.todok()]).toarray(), expected)
+
+        assert_equal(construct.hstack([A.tocsc(), B.tocsc()]).toarray(),
+                     expected)
+        assert_equal(construct.hstack([A.tocsc(), B.tocsc()],
+                                      dtype=np.float32).dtype,
+                     np.float32)
+        assert_equal(construct.hstack([A.tocsr(), B.tocsr()]).toarray(),
+                     expected)
+        assert_equal(construct.hstack([A.tocsr(), B.tocsr()],
+                                      dtype=np.float32).dtype,
+                     np.float32)
+
+    def test_hstack_matrix_or_array(self):
+        A = [[1,2],[3,4]]
+        B = [[5],[6]]
+        assert isinstance(construct.hstack([coo_array(A), coo_array(B)]), sparray)
+        assert isinstance(construct.hstack([coo_array(A), coo_matrix(B)]), sparray)
+        assert isinstance(construct.hstack([coo_matrix(A), coo_array(B)]), sparray)
+        assert isinstance(construct.hstack([coo_matrix(A), coo_matrix(B)]), spmatrix)
+
+    @pytest.mark.parametrize("block_array", (construct.bmat, construct.block_array))
+    def test_block_creation(self, block_array):
+
+        A = coo_array([[1, 2], [3, 4]])
+        B = coo_array([[5],[6]])
+        C = coo_array([[7]])
+        D = coo_array((0, 0))
+
+        expected = array([[1, 2, 5],
+                          [3, 4, 6],
+                          [0, 0, 7]])
+        assert_equal(block_array([[A, B], [None, C]]).toarray(), expected)
+        E = csr_array((1, 2), dtype=np.int32)
+        assert_equal(block_array([[A.tocsr(), B.tocsr()],
+                                  [E, C.tocsr()]]).toarray(),
+                     expected)
+        assert_equal(block_array([[A.tocsc(), B.tocsc()],
+                                  [E.tocsc(), C.tocsc()]]).toarray(),
+                     expected)
+
+        expected = array([[1, 2, 0],
+                          [3, 4, 0],
+                          [0, 0, 7]])
+        assert_equal(block_array([[A, None], [None, C]]).toarray(), expected)
+        assert_equal(block_array([[A.tocsr(), E.T.tocsr()],
+                                  [E, C.tocsr()]]).toarray(),
+                     expected)
+        assert_equal(block_array([[A.tocsc(), E.T.tocsc()],
+                                  [E.tocsc(), C.tocsc()]]).toarray(),
+                     expected)
+
+        Z = csr_array((1, 1), dtype=np.int32)
+        expected = array([[0, 5],
+                          [0, 6],
+                          [7, 0]])
+        assert_equal(block_array([[None, B], [C, None]]).toarray(), expected)
+        assert_equal(block_array([[E.T.tocsr(), B.tocsr()],
+                                  [C.tocsr(), Z]]).toarray(),
+                     expected)
+        assert_equal(block_array([[E.T.tocsc(), B.tocsc()],
+                                  [C.tocsc(), Z.tocsc()]]).toarray(),
+                     expected)
+
+        expected = np.empty((0, 0))
+        assert_equal(block_array([[None, None]]).toarray(), expected)
+        assert_equal(block_array([[None, D], [D, None]]).toarray(),
+                     expected)
+
+        # test bug reported in gh-5976
+        expected = array([[7]])
+        assert_equal(block_array([[None, D], [C, None]]).toarray(),
+                     expected)
+
+        # test failure cases
+        with assert_raises(ValueError) as excinfo:
+            block_array([[A], [B]])
+        excinfo.match(r'Got blocks\[1,0\]\.shape\[1\] == 1, expected 2')
+
+        with assert_raises(ValueError) as excinfo:
+            block_array([[A.tocsr()], [B.tocsr()]])
+        excinfo.match(r'incompatible dimensions for axis 1')
+
+        with assert_raises(ValueError) as excinfo:
+            block_array([[A.tocsc()], [B.tocsc()]])
+        excinfo.match(r'Mismatching dimensions along axis 1: ({1, 2}|{2, 1})')
+
+        with assert_raises(ValueError) as excinfo:
+            block_array([[A, C]])
+        excinfo.match(r'Got blocks\[0,1\]\.shape\[0\] == 1, expected 2')
+
+        with assert_raises(ValueError) as excinfo:
+            block_array([[A.tocsr(), C.tocsr()]])
+        excinfo.match(r'Mismatching dimensions along axis 0: ({1, 2}|{2, 1})')
+
+        with assert_raises(ValueError) as excinfo:
+            block_array([[A.tocsc(), C.tocsc()]])
+        excinfo.match(r'incompatible dimensions for axis 0')
+
+    def test_block_return_type(self):
+        block = construct.block_array
+
+        # csr format ensures we hit _compressed_sparse_stack
+        # shape of F,G ensure we hit _stack_along_minor_axis
+        # list version ensure we hit the path with neither helper function
+        Fl, Gl = [[1, 2],[3, 4]], [[7], [5]]
+        Fm, Gm = csr_matrix(Fl), csr_matrix(Gl)
+        assert isinstance(block([[None, Fl], [Gl, None]], format="csr"), sparray)
+        assert isinstance(block([[None, Fm], [Gm, None]], format="csr"), sparray)
+        assert isinstance(block([[Fm, Gm]], format="csr"), sparray)
+
+    def test_bmat_return_type(self):
+        """This can be removed after sparse matrix is removed"""
+        bmat = construct.bmat
+        # check return type. if any input _is_array output array, else matrix
+        Fl, Gl = [[1, 2],[3, 4]], [[7], [5]]
+        Fm, Gm = csr_matrix(Fl), csr_matrix(Gl)
+        Fa, Ga = csr_array(Fl), csr_array(Gl)
+        assert isinstance(bmat([[Fa, Ga]], format="csr"), sparray)
+        assert isinstance(bmat([[Fm, Gm]], format="csr"), spmatrix)
+        assert isinstance(bmat([[None, Fa], [Ga, None]], format="csr"), sparray)
+        assert isinstance(bmat([[None, Fm], [Ga, None]], format="csr"), sparray)
+        assert isinstance(bmat([[None, Fm], [Gm, None]], format="csr"), spmatrix)
+        assert isinstance(bmat([[None, Fl], [Gl, None]], format="csr"), spmatrix)
+
+        # type returned by _compressed_sparse_stack (all csr)
+        assert isinstance(bmat([[Ga, Ga]], format="csr"), sparray)
+        assert isinstance(bmat([[Gm, Ga]], format="csr"), sparray)
+        assert isinstance(bmat([[Ga, Gm]], format="csr"), sparray)
+        assert isinstance(bmat([[Gm, Gm]], format="csr"), spmatrix)
+        # shape is 2x2 so no _stack_along_minor_axis
+        assert isinstance(bmat([[Fa, Fm]], format="csr"), sparray)
+        assert isinstance(bmat([[Fm, Fm]], format="csr"), spmatrix)
+
+        # type returned by _compressed_sparse_stack (all csc)
+        assert isinstance(bmat([[Gm.tocsc(), Ga.tocsc()]], format="csc"), sparray)
+        assert isinstance(bmat([[Gm.tocsc(), Gm.tocsc()]], format="csc"), spmatrix)
+        # shape is 2x2 so no _stack_along_minor_axis
+        assert isinstance(bmat([[Fa.tocsc(), Fm.tocsc()]], format="csr"), sparray)
+        assert isinstance(bmat([[Fm.tocsc(), Fm.tocsc()]], format="csr"), spmatrix)
+
+        # type returned when mixed input
+        assert isinstance(bmat([[Gl, Ga]], format="csr"), sparray)
+        assert isinstance(bmat([[Gm.tocsc(), Ga]], format="csr"), sparray)
+        assert isinstance(bmat([[Gm.tocsc(), Gm]], format="csr"), spmatrix)
+        assert isinstance(bmat([[Gm, Gm]], format="csc"), spmatrix)
+
+    @pytest.mark.xslow
+    @pytest.mark.xfail_on_32bit("Can't create large array for test")
+    def test_concatenate_int32_overflow(self):
+        """ test for indptr overflow when concatenating matrices """
+        check_free_memory(30000)
+
+        n = 33000
+        A = csr_array(np.ones((n, n), dtype=bool))
+        B = A.copy()
+        C = construct._compressed_sparse_stack((A, B), axis=0,
+                                               return_spmatrix=False)
+
+        assert_(np.all(np.equal(np.diff(C.indptr), n)))
+        assert_equal(C.indices.dtype, np.int64)
+        assert_equal(C.indptr.dtype, np.int64)
+
+    def test_block_diag_basic(self):
+        """ basic test for block_diag """
+        A = coo_array([[1,2],[3,4]])
+        B = coo_array([[5],[6]])
+        C = coo_array([[7]])
+
+        expected = array([[1, 2, 0, 0],
+                          [3, 4, 0, 0],
+                          [0, 0, 5, 0],
+                          [0, 0, 6, 0],
+                          [0, 0, 0, 7]])
+
+        ABC = construct.block_diag((A, B, C))
+        assert_equal(ABC.toarray(), expected)
+        assert ABC.coords[0].dtype == np.int32
+
+    def test_block_diag_idx_dtype(self):
+        X = coo_array([[1, 0, 0], [0, 1, 0], [0, 1, 0]])
+        X.coords = tuple(co.astype(np.int64) for co in X.coords)
+        assert construct.block_diag([X, X]).coords[0].dtype == np.int64
+
+    @pytest.mark.filterwarnings("ignore:.*switching.*sparse array:DeprecationWarning")
+    def test_block_diag_scalar_1d_args(self):
+        """ block_diag with scalar and 1d arguments """
+        # one 1d matrix and a scalar
+        assert_array_equal(construct.block_diag([[2,3], 4]).toarray(),
+                           [[2, 3, 0], [0, 0, 4]])
+        # 1d sparse arrays
+        A = coo_array([1,0,3])
+        B = coo_array([0,4])
+        assert_array_equal(construct.block_diag([A, B]).toarray(),
+                           [[1, 0, 3, 0, 0], [0, 0, 0, 0, 4]])
+
+    @pytest.mark.filterwarnings("ignore:.*switching.*sparse array:DeprecationWarning")
+    def test_block_diag_1(self):
+        """ block_diag with one matrix """
+        assert_equal(construct.block_diag([[1, 0]]).toarray(),
+                     array([[1, 0]]))
+        assert_equal(construct.block_diag([[[1, 0]]]).toarray(),
+                     array([[1, 0]]))
+        assert_equal(construct.block_diag([[[1], [0]]]).toarray(),
+                     array([[1], [0]]))
+        # just on scalar
+        assert_equal(construct.block_diag([1]).toarray(),
+                     array([[1]]))
+
+    def test_block_diag_sparse_arrays(self):
+        """ block_diag with sparse arrays """
+
+        A = coo_array([[1, 2, 3]], shape=(1, 3))
+        B = coo_array([[4, 5]], shape=(1, 2))
+        assert_equal(construct.block_diag([A, B]).toarray(),
+                     array([[1, 2, 3, 0, 0], [0, 0, 0, 4, 5]]))
+
+        A = coo_array([[1], [2], [3]], shape=(3, 1))
+        B = coo_array([[4], [5]], shape=(2, 1))
+        assert_equal(construct.block_diag([A, B]).toarray(),
+                     array([[1, 0], [2, 0], [3, 0], [0, 4], [0, 5]]))
+
+    def test_block_diag_return_type(self):
+        A, B = coo_array([[1, 2, 3]]), coo_matrix([[2, 3, 4]])
+        assert isinstance(construct.block_diag([A, A]), sparray)
+        assert isinstance(construct.block_diag([A, B]), sparray)
+        assert isinstance(construct.block_diag([B, A]), sparray)
+        assert isinstance(construct.block_diag([B, B]), spmatrix)
+
+    def test_random_sampling(self):
+        # Simple sanity checks for sparse random sampling.
+        for f in sprand, _sprandn:
+            for t in [np.float32, np.float64, np.longdouble,
+                      np.int32, np.int64, np.complex64, np.complex128]:
+                x = f(5, 10, density=0.1, dtype=t)
+                assert_equal(x.dtype, t)
+                assert_equal(x.shape, (5, 10))
+                assert_equal(x.nnz, 5)
+
+            x1 = f(5, 10, density=0.1, rng=4321)
+            assert_equal(x1.dtype, np.float64)
+
+            x2 = f(5, 10, density=0.1, rng=np.random.default_rng(4321))
+
+            assert_array_equal(x1.data, x2.data)
+            assert_array_equal(x1.row, x2.row)
+            assert_array_equal(x1.col, x2.col)
+
+            for density in [0.0, 0.1, 0.5, 1.0]:
+                x = f(5, 10, density=density)
+                assert_equal(x.nnz, int(density * np.prod(x.shape)))
+
+            for fmt in ['coo', 'csc', 'csr', 'lil']:
+                x = f(5, 10, format=fmt)
+                assert_equal(x.format, fmt)
+
+            assert_raises(ValueError, lambda: f(5, 10, 1.1))
+            assert_raises(ValueError, lambda: f(5, 10, -0.1))
+
+    @pytest.mark.parametrize("rng", [None, 4321, np.random.default_rng(4321)])
+    def test_rand(self, rng):
+        # Simple distributional checks for sparse.rand.
+        x = sprand(10, 20, density=0.5, dtype=np.float64, rng=rng)
+        assert_(np.all(np.less_equal(0, x.data)))
+        assert_(np.all(np.less_equal(x.data, 1)))
+
+    @pytest.mark.parametrize("rng", [None, 4321, np.random.default_rng(4321)])
+    def test_randn(self, rng):
+        # Simple distributional checks for sparse.randn.
+        # Statistically, some of these should be negative
+        # and some should be greater than 1.
+        x = _sprandn(10, 20, density=0.5, dtype=np.float64, rng=rng)
+        assert_(np.any(np.less(x.data, 0)))
+        assert_(np.any(np.less(1, x.data)))
+        x = _sprandn_array(10, 20, density=0.5, dtype=np.float64, rng=rng)
+        assert_(np.any(np.less(x.data, 0)))
+        assert_(np.any(np.less(1, x.data)))
+
+    def test_random_accept_str_dtype(self):
+        # anything that np.dtype can convert to a dtype should be accepted
+        # for the dtype
+        construct.random(10, 10, dtype='d')
+        construct.random_array((10, 10), dtype='d')
+        construct.random_array((10, 10, 10), dtype='d')
+        construct.random_array((10, 10, 10, 10, 10), dtype='d')
+
+    def test_random_array_maintains_array_shape(self):
+        # preserve use of old random_state during SPEC 7 transition
+        arr = construct.random_array((0, 4), density=0.3, dtype=int, random_state=0)
+        assert arr.shape == (0, 4)
+
+        arr = construct.random_array((10, 10, 10), density=0.3, dtype=int, rng=0)
+        assert arr.shape == (10, 10, 10)
+
+        arr = construct.random_array((10, 10, 10, 10, 10), density=0.3, dtype=int,
+                                     rng=0)
+        assert arr.shape == (10, 10, 10, 10, 10)
+
+    def test_random_array_idx_dtype(self):
+        A = construct.random_array((10, 10))
+        assert A.coords[0].dtype == np.int32
+
+    def test_random_sparse_matrix_returns_correct_number_of_non_zero_elements(self):
+        # A 10 x 10 matrix, with density of 12.65%, should have 13 nonzero elements.
+        # 10 x 10 x 0.1265 = 12.65, which should be rounded up to 13, not 12.
+        sparse_matrix = construct.random(10, 10, density=0.1265)
+        assert_equal(sparse_matrix.count_nonzero(),13)
+        # check random_array
+        sparse_array = construct.random_array((10, 10), density=0.1265)
+        assert_equal(sparse_array.count_nonzero(),13)
+        assert isinstance(sparse_array, sparray)
+        # check big size
+        shape = (2**33, 2**33)
+        sparse_array = construct.random_array(shape, density=2.7105e-17)
+        assert_equal(sparse_array.count_nonzero(),2000)
+
+        # for n-D
+        # check random_array
+        sparse_array = construct.random_array((10, 10, 10, 10), density=0.12658)
+        assert_equal(sparse_array.count_nonzero(),1266)
+        assert isinstance(sparse_array, sparray)
+        # check big size
+        shape = (2**33, 2**33, 2**33)
+        sparse_array = construct.random_array(shape, density=2.7105e-28)
+        assert_equal(sparse_array.count_nonzero(),172)
+
+
+def test_deprecated_warnings_output_defaults_switch_from_spmatrix():
+    A = B = np.array([[1, 0], [1, 0]])
+    with pytest.deprecated_call(match=".*switching.*sparse array int"):
+        construct.kron(A, B)
+    with pytest.deprecated_call(match=".*switching.*sparse array int"):
+        construct.kronsum(A, B)
+    # Note: vstack hstack and bmat do not support all dense input. So no default.
+    with pytest.deprecated_call(match=".*switching.*sparse array int"):
+        construct.block_diag([A, B])
+
+
+def test_diags_array():
+    """Tests of diags_array that do not rely on diags wrapper."""
+    diag = np.arange(1.0, 5.0)
+
+    assert_array_equal(construct.diags_array(diag, dtype=None).toarray(), np.diag(diag))
+
+    assert_array_equal(
+        construct.diags_array(diag, offsets=2, dtype=None).toarray(), np.diag(diag, k=2)
+    )
+
+    assert_array_equal(
+        construct.diags_array(diag, offsets=2, shape=(4, 4), dtype=None).toarray(),
+        np.diag(diag, k=2)[:4, :4]
+    )
+
+    # Offset outside bounds when shape specified
+    with pytest.raises(ValueError, match=".*out of bounds"):
+        construct.diags(np.arange(1.0, 5.0), 5, shape=(4, 4))
+
+
+@pytest.mark.parametrize('func', (construct.diags_array, construct.diags))
+def test_diags_int(func):
+    d = [[3], [1, 2], [4]]
+    offsets = [-1, 0, 1]
+    # Until the deprecation period is over, `dtype=None` must be given
+    # explicitly to avoid the warning and the cast to an inexact type
+    # in diags_array() (gh-23102).
+    arr = func(d, offsets=offsets, dtype=None)
+    expected = np.array([[1, 4], [3, 2]])
+    assert_array_equal(arr.toarray(), expected, strict=True)
+
+
+@pytest.mark.parametrize('func', (construct.diags_array, construct.diags))
+def test_diags_int_to_float64(func):
+    d = [[3], [1, 2], [4]]
+    offsets = [-1, 0, 1]
+    # Until the deprecation period is over, diags and diag_array will cast
+    # integer inputs to float64 by default.  A warning will be generated
+    # that indicates this behavior is deprecated.
+    # See gh-23102.
+    with pytest.warns(FutureWarning, match="output has been cast to"):
+        arr = func(d, offsets=offsets)
+    expected = np.array([[1.0, 4.0], [3.0, 2.0]])
+    assert_array_equal(arr.toarray(), expected, strict=True)
+
+
+def test_swapaxes():
+    # Borrowed from Numpy swapaxes tests
+    x = np.array([8.375, 7.545, 8.828, 8.5, 1.757, 5.928,
+                  8.43, 7.78, 9.865, 5.878, 8.979, 4.732,
+                  3.012, 6.022, 5.095, 3.116, 5.238, 3.957,
+                  6.04, 9.63, 7.712, 3.382, 4.489, 6.479,
+                  7.189, 9.645, 5.395, 4.961, 9.894, 2.893,
+                  7.357, 9.828, 6.272, 3.758, 6.693, 0.993])
+    sX = coo_array(x).reshape(6, 6)
+    sXswapped = construct.swapaxes(sX, 0, 1)
+    assert_equal(sXswapped[-1].toarray(), sX[:, -1].toarray())
+
+    sXX = sX.reshape(3, 2, 2, 3)
+    sXXswapped = construct.swapaxes(sXX, 0, 2)
+    assert_equal(sXXswapped.shape, (2, 2, 3, 3))
+
+
+def test_3d_swapaxes():
+    tgt = [[[0, 0], [2, 6]], [[1, 5], [0, 7]]]
+    x = np.array([[[0, 1], [2, 0]], [[0, 5], [6, 7]]])
+    A = coo_array(x) #[[[0, 1], [2, 0]], [[0, 5], [6, 7]]])
+    out = construct.swapaxes(A, 0, 2)
+    assert_equal(out.toarray(), tgt)
+    assert_equal(out.toarray(), np.swapaxes(x, 0, 2))
+
+
+@pytest.mark.parametrize("format", sparse_formats)
+def test_sparse_format_swapaxes(format):
+    A = np.array([[2, 0, 1], [3, 5, 0]])
+    SA = coo_array(A).asformat(format)
+
+    out = construct.swapaxes(SA, 1, 0)
+    assert out.format == "coo"
+    assert out.shape == (3, 2)
+    assert_equal(out.toarray(), np.swapaxes(A, 1, 0))
+    assert not out.has_canonical_format
+
+
+def test_axis_swapaxes():
+    A = coo_array([[2, 0], [3, 5]])
+    with assert_raises(ValueError, match="Invalid axis"):
+        construct.swapaxes(A, -4, 0)
+    with assert_raises(ValueError, match="Invalid axis"):
+        construct.swapaxes(A, 0, -4)
+    with assert_raises(ValueError, match="Invalid axis"):
+        construct.swapaxes(A, 3, 0)
+    with assert_raises(ValueError, match="Invalid axis"):
+        construct.swapaxes(A, 0, 3)
+    with assert_raises(ValueError, match="Invalid axis"):
+        construct.swapaxes(A, 1.2, 1)
+    with assert_raises(ValueError, match="Invalid axis"):
+        construct.swapaxes(A, 1, 1.2)
+    assert_equal(construct.swapaxes(A, 0, 0).toarray(), A.toarray())
+    for i in range(2):
+        assert_equal(
+            construct.swapaxes(A, i, 1 - i).toarray(),
+            construct.swapaxes(A, i - 2, -1 - i).toarray()
+        )
+
+
+def test_permute_dims():
+    # Borrowed from Numpy tests.
+    x = np.array([8.375, 7.545, 8.828, 8.5, 1.757, 5.928,
+                  8.43, 7.78, 9.865, 5.878, 8.979, 4.732,
+                  3.012, 6.022, 5.095, 3.116, 5.238, 3.957,
+                  6.04, 9.63, 7.712, 3.382, 4.489, 6.479,
+                  7.189, 9.645, 5.395, 4.961, 9.894, 2.893,
+                  7.357, 9.828, 6.272, 3.758, 6.693, 0.993])
+    npx = x.reshape(6, 6)
+    sX = coo_array(x).reshape(6, 6)
+
+    sXpermuted = construct.permute_dims(sX, axes=(1, 0), copy=True)
+    sXtransposed = sX.transpose(axes=(1, 0))
+    assert_equal(sXpermuted.toarray(), sXtransposed.toarray())
+    assert_equal(sXpermuted[-1].toarray(), sX[:, -1].toarray())
+
+    npxx = npx.reshape(3, 2, 2, 3)
+    sXX = sX.reshape(3, 2, 2, 3)
+    sXXpermuted = construct.permute_dims(sXX, axes=(0, 2, 1, 3), copy=True)
+    assert_equal(sXXpermuted.shape, (3, 2, 2, 3))
+    sXXtransposed = sXX.transpose(axes=(0, 2, 1, 3))
+    assert_equal(sXXtransposed.shape, (3, 2, 2, 3))
+    assert_equal(sXXpermuted.toarray(), sXXtransposed.toarray())
+    # TODO change np.transpose to np.permute_dims when numpy 2 is min supported version
+    assert_equal(sXXpermuted.toarray(), np.transpose(npxx, axes=(0, 2, 1, 3)))
+
+
+def test_3d_permute_dims():
+    tgt = [[[0], [2], [0], [6]], [[1], [0], [5], [7]]]
+    x = np.array([[[0, 1], [2, 0], [0, 5], [6, 7]]])
+    A = coo_array(x)
+
+    out = construct.permute_dims(A, axes=(2, 1, 0))
+    assert_equal(out.shape, (2, 4, 1))
+    assert_equal(out.toarray(), tgt)
+    # TODO change np.transpose to np.permute_dims when numpy 2 is min supported version
+    assert_equal(out.toarray(), np.transpose(x, axes=(2, 1, 0)))
+
+
+def test_canonical_format_permute_dims():
+    A = coo_array([[2, 0, 1], [3, 5, 0]])
+    # identity axes keep has_canoncial_format True after permute_dims.
+    assert construct.permute_dims(A, axes=(0, 1)).has_canonical_format is True
+    assert construct.permute_dims(A, axes=[0, 1]).has_canonical_format is True
+    # order changes set has_canonical_format to False
+    assert construct.permute_dims(A, axes=[1, 0]).has_canonical_format is False
+
+
+def test_axis_permute_dims():
+    A = coo_array([[2, 0, 1], [3, 5, 0]])
+
+    with assert_raises(ValueError, match="Incorrect number of axes"):
+        construct.permute_dims(A, axes=(2, 0, 1))
+    with assert_raises(ValueError, match="duplicate value in axis"):
+        construct.permute_dims(A, axes=(0, 0))
+    with assert_raises(TypeError, match="axis must be an integer/tuple"):
+        construct.permute_dims(A, axes={1, 0})
+
+    with assert_raises(ValueError, match="axis out of range"):
+        construct.permute_dims(A, axes=(-3, 0))
+    with assert_raises(ValueError, match="axis out of range"):
+        construct.permute_dims(A, axes=(0, -3))
+    with assert_raises(ValueError, match="axis out of range"):
+        construct.permute_dims(A, axes=(2, 0))
+    with assert_raises(ValueError, match="axis out of range"):
+        construct.permute_dims(A, axes=(0, 2))
+    with assert_raises(TypeError, match="axis must be an integer"):
+        construct.permute_dims(A, axes=(1.2, 0))
+
+    assert_equal(
+        construct.permute_dims(A, axes=(1, 0), copy=True).toarray(),
+        A.transpose(axes=(1, 0), copy=True).toarray()
+    )
+    # use lists for axes
+    assert_equal(
+        construct.permute_dims(A, axes=[1, 0], copy=True).toarray(),
+        A.transpose(axes=[1, 0], copy=True).toarray()
+    )
+    assert_equal(
+        construct.permute_dims(A, axes=None, copy=True).toarray(),
+        A.transpose(axes=(1, 0), copy=True).toarray()
+    )
+    assert_equal(
+        construct.permute_dims(A, axes=(0, 1), copy=True).toarray(), A.toarray()
+    )
+
+
+@pytest.mark.parametrize("format", sparse_formats)
+def test_sparse_format_permute_dims(format):
+    A = np.array([[2, 0, 1], [3, 5, 0]])
+    SA = coo_array(A).asformat(format)
+
+    out = construct.permute_dims(SA, axes=(1, 0))
+    assert out.format == "coo"
+    assert out.shape == (3, 2)
+    # TODO change np.transpose to np.permute_dims when numpy 2 is min supported version
+    assert_equal(out.toarray(), np.transpose(A, axes=(1, 0)))
+    assert not out.has_canonical_format
+
+
+def test_expand_dims():
+    # Borrowed from Numpy tests.
+    x = np.array([8.375, 7.545, 8.828, 8.5, 1.757, 5.928,
+                  8.43, 7.78, 9.865, 5.878, 8.979, 4.732,
+                  3.012, 6.022, 5.095, 3.116, 5.238, 3.957,
+                  6.04, 9.63, 7.712, 3.382, 4.489, 6.479,
+                  7.189, 9.645, 5.395, 4.961, 9.894, 2.893,
+                  7.357, 9.828, 6.272, 3.758, 6.693, 0.993])
+    npx = x.reshape(6, 6)
+    sX = coo_array(npx)
+
+    npx_expanded = np.expand_dims(npx, axis=1)
+    sXexpanded = construct.expand_dims(sX, axis=1)
+    assert_equal(sXexpanded[-1].toarray(), sX[-1, np.newaxis, :].toarray())
+    assert_equal(sXexpanded.toarray(), npx_expanded)
+
+    npxx = npx.reshape(3, 2, 2, 3)
+    sXX = sX.reshape(3, 2, 2, 3)
+
+    npxx_expanded = np.expand_dims(npxx, axis=2)
+    sXXexpanded = construct.expand_dims(sXX, axis=2)
+    assert_equal(sXXexpanded.shape, (3, 2, 1, 2, 3))
+    assert_equal(sXXexpanded.toarray(), npxx_expanded)
+
+    npxx_expanded = np.expand_dims(npxx, axis=-2)
+    sXXexpanded = construct.expand_dims(sXX, axis=-2)
+    assert_equal(sXXexpanded.shape, (3, 2, 2, 1, 3))
+    assert_equal(sXXexpanded.toarray(), npxx_expanded)
+
+
+def test_3d_expand_dims():
+    tgt = [[[[0, 0], [2, 6]]], [[[1, 5], [0, 7]]]]
+    A = coo_array([[[0, 0], [2, 6]], [[1, 5], [0, 7]]])
+    out = construct.expand_dims(A, axis=1)
+    assert_equal(out.toarray(), tgt)
+
+
+@pytest.mark.parametrize("format", sparse_formats)
+def test_sparse_format_expand_dims(format):
+    A = np.array([[2, 0], [3, 5]])
+    SA = coo_array(A).asformat(format)
+
+    out = construct.expand_dims(SA, axis=1)
+    assert out.format == "coo"
+    assert out.shape == (2, 1, 2)
+    assert_equal(out.toarray(), np.expand_dims(A, axis=1))
+    assert SA.tocoo().has_canonical_format == out.has_canonical_format
+
+
+def test_axis_expand_dims():
+    A = coo_array([[2, 0], [3, 5]])
+    with assert_raises(ValueError, match="Invalid axis"):
+        construct.expand_dims(A, axis=-4)
+    with assert_raises(ValueError, match="Invalid axis"):
+        construct.expand_dims(A, axis=3)
+    with assert_raises(ValueError, match="Invalid axis"):
+        construct.expand_dims(A, axis=1.2)
+    for i in range(3):
+        assert_equal(
+            construct.expand_dims(A, axis=i).toarray(),
+            construct.expand_dims(A, axis=i - 3).toarray()
+        )
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_coo.py b/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_coo.py
new file mode 100644
index 0000000000000000000000000000000000000000..d1d7a58e2599b0719a712a89f126c00fb46cf857
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_coo.py
@@ -0,0 +1,1407 @@
+import math
+import warnings
+
+import numpy as np
+from numpy.testing import assert_equal, assert_allclose
+import pytest
+from scipy.linalg import block_diag
+from scipy.sparse import (
+    coo_array, random_array, SparseEfficiencyWarning, matrix_transpose
+)
+from scipy.sparse._csr import csr_array
+from .._coo import _block_diag, _extract_block_diag
+
+
+def test_shape_constructor():
+    empty1d = coo_array((3,))
+    assert empty1d.shape == (3,)
+    assert_equal(empty1d.toarray(), np.zeros((3,)))
+
+    empty2d = coo_array((3, 2))
+    assert empty2d.shape == (3, 2)
+    assert_equal(empty2d.toarray(), np.zeros((3, 2)))
+
+    empty_nd = coo_array((2,3,4,6,7))
+    assert empty_nd.shape == (2,3,4,6,7)
+    assert_equal(empty_nd.toarray(), np.zeros((2,3,4,6,7)))
+
+
+def test_dense_constructor():
+    # 1d
+    res1d = coo_array([1, 2, 3])
+    assert res1d.shape == (3,)
+    assert_equal(res1d.toarray(), np.array([1, 2, 3]))
+
+    # 2d
+    res2d = coo_array([[1, 2, 3], [4, 5, 6]])
+    assert res2d.shape == (2, 3)
+    assert_equal(res2d.toarray(), np.array([[1, 2, 3], [4, 5, 6]]))
+
+    # 4d
+    arr4d = np.array([[[[3, 7], [1, 0]], [[6, 5], [9, 2]]],
+                      [[[4, 3], [2, 8]], [[7, 5], [1, 6]]],
+                      [[[0, 9], [4, 3]], [[2, 1], [7, 8]]]])
+    res4d = coo_array(arr4d)
+    assert res4d.shape == (3, 2, 2, 2)
+    assert_equal(res4d.toarray(), arr4d)
+
+    # 9d
+    np.random.seed(12)
+    arr9d = np.random.randn(2,3,4,7,6,5,3,2,4)
+    res9d = coo_array(arr9d)
+    assert res9d.shape == (2,3,4,7,6,5,3,2,4)
+    assert_equal(res9d.toarray(), arr9d)
+
+    # storing nan as element of sparse array
+    nan_3d = coo_array([[[1, np.nan]], [[3, 4]], [[5, 6]]])
+    assert nan_3d.shape == (3, 1, 2)
+    assert_equal(nan_3d.toarray(), np.array([[[1, np.nan]], [[3, 4]], [[5, 6]]]))
+
+
+def test_dense_constructor_with_shape():
+    res1d = coo_array([1, 2, 3], shape=(3,))
+    assert res1d.shape == (3,)
+    assert_equal(res1d.toarray(), np.array([1, 2, 3]))
+
+    res2d = coo_array([[1, 2, 3], [4, 5, 6]], shape=(2, 3))
+    assert res2d.shape == (2, 3)
+    assert_equal(res2d.toarray(), np.array([[1, 2, 3], [4, 5, 6]]))
+
+    res3d = coo_array([[[3]], [[4]]], shape=(2, 1, 1))
+    assert res3d.shape == (2, 1, 1)
+    assert_equal(res3d.toarray(), np.array([[[3]], [[4]]]))
+
+    np.random.seed(12)
+    arr7d = np.random.randn(2,4,1,6,5,3,2)
+    res7d = coo_array((arr7d), shape=(2,4,1,6,5,3,2))
+    assert res7d.shape == (2,4,1,6,5,3,2)
+    assert_equal(res7d.toarray(), arr7d)
+
+
+def test_dense_constructor_with_inconsistent_shape():
+    with pytest.raises(ValueError, match='inconsistent shapes'):
+        coo_array([1, 2, 3], shape=(4,))
+
+    with pytest.raises(ValueError, match='inconsistent shapes'):
+        coo_array([1, 2, 3], shape=(3, 1))
+
+    with pytest.raises(ValueError, match='inconsistent shapes'):
+        coo_array([[1, 2, 3]], shape=(3,))
+
+    with pytest.raises(ValueError, match='inconsistent shapes'):
+        coo_array([[[3]], [[4]]], shape=(1, 1, 1))
+
+    with pytest.raises(ValueError,
+                       match='axis 0 index 2 exceeds matrix dimension 2'):
+        coo_array(([1], ([2],)), shape=(2,))
+
+    with pytest.raises(ValueError,
+                       match='axis 1 index 3 exceeds matrix dimension 3'):
+        coo_array(([1,3], ([0, 1], [0, 3], [1, 1])), shape=(2, 3, 2))
+
+    with pytest.raises(ValueError, match='negative axis 0 index: -1'):
+        coo_array(([1], ([-1],)))
+
+    with pytest.raises(ValueError, match='negative axis 2 index: -1'):
+        coo_array(([1], ([0], [2], [-1])))
+
+
+def test_1d_sparse_constructor():
+    empty1d = coo_array((3,))
+    res = coo_array(empty1d)
+    assert res.shape == (3,)
+    assert_equal(res.toarray(), np.zeros((3,)))
+
+
+def test_1d_tuple_constructor():
+    res = coo_array(([9,8], ([1,2],)))
+    assert res.shape == (3,)
+    assert_equal(res.toarray(), np.array([0, 9, 8]))
+
+
+def test_1d_tuple_constructor_with_shape():
+    res = coo_array(([9,8], ([1,2],)), shape=(4,))
+    assert res.shape == (4,)
+    assert_equal(res.toarray(), np.array([0, 9, 8, 0]))
+
+def test_reshape_overflow():
+    # see gh-22353 : new idx_dtype can need to be int64 instead of int32
+    M, N = (1045507, 523266)
+    coords = (np.array([M - 1], dtype='int32'), np.array([N - 1], dtype='int32'))
+    A = coo_array(([3.3], coords), shape=(M, N))
+
+    # need new idx_dtype to not overflow
+    B = A.reshape((M * N, 1))
+    assert B.coords[0].dtype == np.dtype('int64')
+    assert B.coords[0][0] == (M * N) - 1
+
+    # need idx_dtype to stay int32 if before and after can be int32
+    C = A.reshape(N, M)
+    assert C.coords[0].dtype == np.dtype('int32')
+    assert C.coords[0][0] == N - 1
+
+def test_reshape():
+    arr1d = coo_array([1, 0, 3])
+    assert arr1d.shape == (3,)
+
+    col_vec = arr1d.reshape((3, 1))
+    assert col_vec.shape == (3, 1)
+    assert_equal(col_vec.toarray(), np.array([[1], [0], [3]]))
+
+    row_vec = arr1d.reshape((1, 3))
+    assert row_vec.shape == (1, 3)
+    assert_equal(row_vec.toarray(), np.array([[1, 0, 3]]))
+
+    # attempting invalid reshape
+    with pytest.raises(ValueError, match="cannot reshape array"):
+        arr1d.reshape((3,3))
+
+    # attempting reshape with a size 0 dimension
+    with pytest.raises(ValueError, match="cannot reshape array"):
+        arr1d.reshape((3,0))
+
+    arr2d = coo_array([[1, 2, 0], [0, 0, 3]])
+    assert arr2d.shape == (2, 3)
+
+    flat = arr2d.reshape((6,))
+    assert flat.shape == (6,)
+    assert_equal(flat.toarray(), np.array([1, 2, 0, 0, 0, 3]))
+
+    # 2d to 3d
+    to_3d_arr = arr2d.reshape((2, 3, 1))
+    assert to_3d_arr.shape == (2, 3, 1)
+    assert_equal(to_3d_arr.toarray(), np.array([[[1], [2], [0]], [[0], [0], [3]]]))
+
+    # attempting invalid reshape
+    with pytest.raises(ValueError, match="cannot reshape array"):
+        arr2d.reshape((1,3))
+
+
+def test_nnz():
+    arr1d = coo_array([1, 0, 3])
+    assert arr1d.shape == (3,)
+    assert arr1d.nnz == 2
+
+    arr2d = coo_array([[1, 2, 0], [0, 0, 3]])
+    assert arr2d.shape == (2, 3)
+    assert arr2d.nnz == 3
+
+
+def test_transpose():
+    arr1d = coo_array([1, 0, 3]).T
+    assert arr1d.shape == (3,)
+    assert_equal(arr1d.toarray(), np.array([1, 0, 3]))
+
+    arr2d = coo_array([[1, 2, 0], [0, 0, 3]])
+    assert arr2d.T.shape == (3, 2)
+    desired = np.array([[1, 0], [2, 0], [0, 3]])
+    assert_equal(arr2d.T.toarray(), desired)
+    assert_equal(arr2d.mT.toarray(), desired)
+    assert_equal(matrix_transpose(arr2d).toarray(), desired)
+
+
+def test_transpose_with_axis():
+    arr1d = coo_array([1, 0, 3]).transpose(axes=(0,))
+    assert arr1d.shape == (3,)
+    assert_equal(arr1d.toarray(), np.array([1, 0, 3]))
+
+    arr2d = coo_array([[1, 2, 0], [0, 0, 3]]).transpose(axes=(0, 1))
+    assert arr2d.shape == (2, 3)
+    assert_equal(arr2d.toarray(), np.array([[1, 2, 0], [0, 0, 3]]))
+
+    with pytest.raises(ValueError, match="axes don't match matrix dimensions"):
+        coo_array([1, 0, 3]).transpose(axes=(0, 1))
+
+    with pytest.raises(ValueError, match="repeated axis in transpose"):
+        coo_array([[1, 2, 0], [0, 0, 3]]).transpose(axes=(1, 1))
+
+
+def test_1d_row_and_col():
+    res = coo_array([1, -2, -3])
+    assert_equal(res.col, np.array([0, 1, 2]))
+    assert_equal(res.row, np.zeros_like(res.col))
+    assert res.row.dtype == res.col.dtype
+    assert res.row.flags.writeable is False
+
+    res.col = [1, 2, 3]
+    assert len(res.coords) == 1
+    assert_equal(res.col, np.array([1, 2, 3]))
+    assert res.row.dtype == res.col.dtype
+
+    with pytest.raises(ValueError, match="cannot set row attribute"):
+        res.row = [1, 2, 3]
+
+
+def test_1d_toformats():
+    res = coo_array([1, -2, -3])
+    for f in [res.tobsr, res.tocsc, res.todia, res.tolil]:
+        with pytest.raises(ValueError, match='Cannot convert'):
+            f()
+    for f in [res.tocoo, res.tocsr, res.todok]:
+        assert_equal(f().toarray(), res.toarray())
+
+
+@pytest.mark.parametrize('arg', [1, 2, 4, 5, 8])
+def test_1d_resize(arg: int):
+    den = np.array([1, -2, -3])
+    res = coo_array(den)
+    den.resize(arg, refcheck=False)
+    res.resize(arg)
+    assert res.shape == den.shape
+    assert_equal(res.toarray(), den)
+
+
+@pytest.mark.parametrize('arg', list(zip([1, 2, 3, 4], [1, 2, 3, 4])))
+def test_1d_to_2d_resize(arg: tuple[int, int]):
+    den = np.array([1, 0, 3])
+    res = coo_array(den)
+
+    den.resize(arg, refcheck=False)
+    res.resize(arg)
+    assert res.shape == den.shape
+    assert_equal(res.toarray(), den)
+
+
+@pytest.mark.parametrize('arg', [1, 4, 6, 8])
+def test_2d_to_1d_resize(arg: int):
+    den = np.array([[1, 0, 3], [4, 0, 0]])
+    res = coo_array(den)
+    den.resize(arg, refcheck=False)
+    res.resize(arg)
+    assert res.shape == den.shape
+    assert_equal(res.toarray(), den)
+
+
+def test_sum_duplicates():
+    # 1d case
+    arr1d = coo_array(([2, 2, 2], ([1, 0, 1],)))
+    assert arr1d.nnz == 3
+    assert_equal(arr1d.toarray(), np.array([2, 4]))
+    arr1d.sum_duplicates()
+    assert arr1d.nnz == 2
+    assert_equal(arr1d.toarray(), np.array([2, 4]))
+
+    # 4d case
+    arr4d = coo_array(([2, 3, 7], ([1, 0, 1], [0, 2, 0], [1, 2, 1], [1, 0, 1])))
+    assert arr4d.nnz == 3
+    expected = np.array(  # noqa: E501
+        [[[[0, 0], [0, 0], [0, 0]], [[0, 0], [0, 0], [0, 0]], [[0, 0], [0, 0], [3, 0]]],
+         [[[0, 0], [0, 9], [0, 0]], [[0, 0], [0, 0], [0, 0]], [[0, 0], [0, 0], [0, 0]]]]
+    )
+    assert_equal(arr4d.toarray(), expected)
+    arr4d.sum_duplicates()
+    assert arr4d.nnz == 2
+    assert_equal(arr4d.toarray(), expected)
+
+    # when there are no duplicates
+    arr_nodups = coo_array(([1, 2, 3, 4], ([0, 1, 2, 3],)))
+    assert arr_nodups.nnz == 4
+    arr_nodups.sum_duplicates()
+    assert arr_nodups.nnz == 4
+
+
+def test_eliminate_zeros():
+    arr1d = coo_array(([0, 0, 1], ([1, 0, 1],)))
+    assert arr1d.nnz == 3
+    assert arr1d.count_nonzero() == 1
+    assert_equal(arr1d.toarray(), np.array([0, 1]))
+    arr1d.eliminate_zeros()
+    assert arr1d.nnz == 1
+    assert arr1d.count_nonzero() == 1
+    assert_equal(arr1d.toarray(), np.array([0, 1]))
+    assert_equal(arr1d.col, np.array([1]))
+    assert_equal(arr1d.row, np.array([0]))
+
+
+def test_1d_add_dense():
+    den_a = np.array([0, -2, -3, 0])
+    den_b = np.array([0, 1, 2, 3])
+    exp = den_a + den_b
+    res = coo_array(den_a) + den_b
+    assert type(res) is type(exp)
+    assert_equal(res, exp)
+
+
+def test_1d_add_sparse():
+    den_a = np.array([0, -2, -3, 0])
+    den_b = np.array([0, 1, 2, 3])
+    dense_sum = den_a + den_b
+    # this routes through CSR format
+    sparse_sum = coo_array(den_a) + coo_array(den_b)
+    assert_equal(dense_sum, sparse_sum.toarray())
+
+
+def test_1d_matmul_vector():
+    den_a = np.array([0, -2, -3, 0])
+    den_b = np.array([0, 1, 2, 3])
+    exp = den_a @ den_b
+    res = coo_array(den_a) @ den_b
+    assert np.ndim(res) == 0
+    assert_equal(res, exp)
+
+
+def test_1d_matmul_multivector():
+    den = np.array([0, -2, -3, 0])
+    other = np.array([[0, 1, 2, 3], [3, 2, 1, 0]]).T
+    exp = den @ other
+    res = coo_array(den) @ other
+    assert type(res) is type(exp)
+    assert_equal(res, exp)
+
+
+def test_2d_matmul_multivector():
+    # sparse-sparse matmul
+    den = np.array([[0, 1, 2, 3], [3, 2, 1, 0]])
+    arr2d = coo_array(den)
+    exp = den @ den.T
+    res = arr2d @ arr2d.T
+    assert_equal(res.toarray(), exp)
+
+    # sparse-dense matmul for self.ndim = 2
+    den = np.array([[0, 4, 3, 0, 5], [1, 0, 7, 3, 4]])
+    arr2d = coo_array(den)
+    exp = den @ den.T
+    res = arr2d @ den.T
+    assert_equal(res, exp)
+
+    # sparse-dense matmul for self.ndim = 1
+    den_a = np.array([[0, 4, 3, 0, 5], [1, 0, 7, 3, 4]])
+    den_b = np.array([0, 1, 6, 0, 4])
+    arr1d = coo_array(den_b)
+    exp = den_b @ den_a.T
+    res = arr1d @ den_a.T
+    assert_equal(res, exp)
+
+    # sparse-dense matmul for self.ndim = 1 and other.ndim = 2
+    den_a = np.array([1, 0, 2])
+    den_b = np.array([[3], [4], [0]])
+    exp = den_a @ den_b
+    res = coo_array(den_a) @ den_b
+    assert_equal(res, exp)
+    res = coo_array(den_a) @ list(den_b)
+    assert_equal(res, exp)
+
+
+def test_1d_diagonal():
+    den = np.array([0, -2, -3, 0])
+    with pytest.raises(ValueError, match='diagonal requires two dimensions'):
+        coo_array(den).diagonal()
+
+
+@pytest.mark.parametrize('shape', [(0,), (7,), (4,7), (0,0,0), (3,6,2),
+                                   (1,0,3), (7,9,3,2,4,5)])
+def test_nd_todense(shape):
+    np.random.seed(12)
+    arr = np.random.randint(low=0, high=5, size=shape)
+    assert_equal(coo_array(arr).todense(), arr)
+
+
+@pytest.mark.parametrize('shape', [(0,), (7,), (4,7), (0,0,0), (3,6,2),
+                                   (1,0,3), (7,9,3,2,4,5)])
+def test_nd_sparse_constructor(shape):
+    empty_arr = coo_array(shape)
+    res = coo_array(empty_arr)
+    assert res.shape == (shape)
+    assert_equal(res.toarray(), np.zeros(shape))
+
+
+@pytest.mark.parametrize('shape', [(0,), (7,), (4,7), (0,0,0), (3,6,2),
+                                   (1,0,3), (7,9,3,2,4,5)])
+def test_nd_tuple_constructor(shape):
+    np.random.seed(12)
+    arr = np.random.randn(*shape)
+    res = coo_array(arr)
+    assert res.shape == shape
+    assert_equal(res.toarray(), arr)
+
+
+@pytest.mark.parametrize('shape', [(0,), (7,), (4,7), (0,0,0), (3,6,2),
+                                   (1,0,3), (7,9,3,2,4,5)])
+def test_nd_tuple_constructor_with_shape(shape):
+    np.random.seed(12)
+    arr = np.random.randn(*shape)
+    res = coo_array(arr, shape=shape)
+    assert res.shape == shape
+    assert_equal(res.toarray(), arr)
+
+
+def test_tuple_constructor_for_dim_size_zero():
+    # arrays with a dimension of size 0
+    with pytest.raises(ValueError, match='exceeds matrix dimension'):
+        coo_array(([9, 8], ([1, 2], [1, 0], [2, 1])), shape=(3,4,0))
+
+    empty_arr = coo_array(([], ([], [], [], [])), shape=(4,0,2,3))
+    assert_equal(empty_arr.toarray(), np.empty((4,0,2,3)))
+
+
+@pytest.mark.parametrize(('shape', 'new_shape'), [((4,9,6,5), (3,6,15,4)),
+                                                  ((4,9,6,5), (36,30)),
+                                                  ((4,9,6,5), (1080,)),
+                                                  ((4,9,6,5), (2,3,2,2,3,5,3)),])
+def test_nd_reshape(shape, new_shape):
+    # reshaping a 4d sparse array
+    rng = np.random.default_rng(23409823)
+
+    arr4d = random_array(shape, density=0.6, rng=rng, dtype=int)
+    assert arr4d.shape == shape
+    den4d = arr4d.toarray()
+
+    exp_arr = den4d.reshape(new_shape)
+    res_arr = arr4d.reshape(new_shape)
+    assert res_arr.shape == new_shape
+    assert_equal(res_arr.toarray(), exp_arr)
+
+
+@pytest.mark.parametrize('shape', [(0,), (7,), (4,7), (0,0,0), (3,6,2),
+                                   (1,0,3), (7,9,3,2,4,5)])
+def test_nd_nnz(shape):
+    rng = np.random.default_rng(23409823)
+
+    arr = random_array(shape, density=0.6, rng=rng, dtype=int)
+    assert arr.nnz == np.count_nonzero(arr.toarray())
+
+
+@pytest.mark.parametrize('shape', [(0,), (7,), (4,7), (0,0,0), (3,6,2),
+                                   (1,0,3), (7,9,3,2,4,5)])
+def test_nd_transpose(shape):
+    rng = np.random.default_rng(23409823)
+
+    arr = random_array(shape, density=0.6, rng=rng, dtype=int)
+    exp_arr = arr.toarray().T
+    trans_arr = arr.transpose()
+    assert trans_arr.shape == shape[::-1]
+    assert_equal(trans_arr.toarray(), exp_arr)
+
+    if len(shape) >= 2:
+        exp_arr = arr.toarray().mT
+        trans_arr = arr.mT
+        assert trans_arr.shape == exp_arr.shape
+        assert_equal(trans_arr.toarray(), exp_arr)
+    
+        trans_arr = matrix_transpose(arr)
+        assert trans_arr.shape == exp_arr.shape
+        assert_equal(trans_arr.toarray(), exp_arr)
+    else:
+        with pytest.raises(ValueError, match="2-dimensional"):
+            arr.mT
+        with pytest.raises(ValueError, match="2-dimensional"):
+            matrix_transpose(arr)
+
+
+@pytest.mark.parametrize(('shape', 'axis_perm'), [((3,), (0,)),
+                                                  ((2,3), (0,1)),
+                                                  ((2,4,3,6,5,3), (1,2,0,5,3,4)),])
+def test_nd_transpose_with_axis(shape, axis_perm):
+    rng = np.random.default_rng(23409823)
+
+    arr = random_array(shape, density=0.6, rng=rng, dtype=int)
+    trans_arr = arr.transpose(axes=axis_perm)
+    assert_equal(trans_arr.toarray(), np.transpose(arr.toarray(), axes=axis_perm))
+
+
+def test_transpose_with_inconsistent_axis():
+    with pytest.raises(ValueError, match="axes don't match matrix dimensions"):
+        coo_array([1, 0, 3]).transpose(axes=(0, 1))
+
+    with pytest.raises(ValueError, match="repeated axis in transpose"):
+        coo_array([[1, 2, 0], [0, 0, 3]]).transpose(axes=(1, 1))
+
+
+def test_nd_eliminate_zeros():
+    # for 3d sparse arrays
+    arr3d = coo_array(([1, 0, 0, 4], ([0, 1, 1, 2], [0, 1, 0, 1], [1, 1, 2, 0])))
+    assert arr3d.nnz == 4
+    assert arr3d.count_nonzero() == 2
+    assert_equal(arr3d.toarray(), np.array([[[0, 1, 0], [0, 0, 0]],
+                                    [[0, 0, 0], [0, 0, 0]], [[0, 0, 0], [4, 0, 0]]]))
+    arr3d.eliminate_zeros()
+    assert arr3d.nnz == 2
+    assert arr3d.count_nonzero() == 2
+    assert_equal(arr3d.toarray(), np.array([[[0, 1, 0], [0, 0, 0]],
+                                    [[0, 0, 0], [0, 0, 0]], [[0, 0, 0], [4, 0, 0]]]))
+
+    # for a 5d sparse array when all elements of data array are 0
+    coords = ([0, 1, 1, 2], [0, 1, 0, 1], [1, 1, 2, 0], [0, 0, 2, 3], [1, 0, 0, 2])
+    arr5d = coo_array(([0, 0, 0, 0], coords))
+    assert arr5d.nnz == 4
+    assert arr5d.count_nonzero() == 0
+    arr5d.eliminate_zeros()
+    assert arr5d.nnz == 0
+    assert arr5d.count_nonzero() == 0
+    assert_equal(arr5d.col, np.array([]))
+    assert_equal(arr5d.row, np.array([]))
+    assert_equal(arr5d.coords, ([], [], [], [], []))
+
+
+@pytest.mark.parametrize('shape', [(0,), (7,), (4,7), (0,0,0), (3,6,2),
+                                   (1,0,3), (7,9,3,2,4,5)])
+def test_nd_add_dense(shape):
+    rng = np.random.default_rng(23409823)
+    sp_x = random_array(shape, density=0.6, rng=rng, dtype=int)
+    sp_y = random_array(shape, density=0.6, rng=rng, dtype=int)
+    den_x, den_y = sp_x.toarray(), sp_y.toarray()
+    exp = den_x + den_y
+    res = sp_x + den_y
+    assert type(res) is type(exp)
+    assert_equal(res, exp)
+
+
+@pytest.mark.parametrize('shape', [(0,), (7,), (4,7), (0,0,0), (3,6,2),
+                                   (1,0,3), (7,9,3,2,4,5)])
+def test_nd_add_sparse(shape):
+    rng = np.random.default_rng(23409823)
+    sp_x = random_array((shape), density=0.6, rng=rng, dtype=int)
+    sp_y = random_array((shape), density=0.6, rng=rng, dtype=int)
+    den_x, den_y = sp_x.toarray(), sp_y.toarray()
+
+    dense_sum = den_x + den_y
+    sparse_sum = sp_x + sp_y
+    assert_equal(dense_sum, sparse_sum.toarray())
+
+
+def test_add_sparse_with_inf():
+    # addition of sparse arrays with an inf element
+    den_a = np.array([[[0], [np.inf]], [[-3], [0]]])
+    den_b = np.array([[[0], [1]], [[2], [3]]])
+    dense_sum = den_a + den_b
+    sparse_sum = coo_array(den_a) + coo_array(den_b)
+    assert_equal(dense_sum, sparse_sum.toarray())
+
+
+@pytest.mark.parametrize(('a_shape', 'b_shape'), [((7,), (12,)),
+                                                  ((6,4), (6,5)),
+                                                  ((5,9,3,2), (9,5,2,3)),])
+def test_nd_add_sparse_with_inconsistent_shapes(a_shape, b_shape):
+    rng = np.random.default_rng(23409823)
+
+    arr_a = random_array((a_shape), density=0.6, rng=rng, dtype=int)
+    arr_b = random_array((b_shape), density=0.6, rng=rng, dtype=int)
+    with pytest.raises(ValueError, match="inconsistent shapes"):
+        arr_a + arr_b
+
+
+@pytest.mark.parametrize('shape', [(0,), (7,), (4,7), (0,0,0), (3,6,2),
+                                   (1,0,3), (7,9,3,2,4,5)])
+def test_nd_sub_dense(shape):
+    rng = np.random.default_rng(23409823)
+    sp_x = random_array(shape, density=0.6, rng=rng, dtype=int)
+    sp_y = random_array(shape, density=0.6, rng=rng, dtype=int)
+    den_x, den_y = sp_x.toarray(), sp_y.toarray()
+    exp = den_x - den_y
+    res = sp_x - den_y
+    assert type(res) is type(exp)
+    assert_equal(res, exp)
+
+
+@pytest.mark.parametrize('shape', [(0,), (7,), (4,7), (0,0,0), (3,6,2),
+                                   (1,0,3), (7,9,3,2,4,5)])
+def test_nd_sub_sparse(shape):
+    rng = np.random.default_rng(23409823)
+
+    sp_x = random_array(shape, density=0.6, rng=rng, dtype=int)
+    sp_y = random_array(shape, density=0.6, rng=rng, dtype=int)
+    den_x, den_y = sp_x.toarray(), sp_y.toarray()
+
+    dense_sum = den_x - den_y
+    sparse_sum = sp_x - sp_y
+    assert_equal(dense_sum, sparse_sum.toarray())
+
+
+def test_nd_sub_sparse_with_nan():
+    # subtraction of sparse arrays with a nan element
+    den_a = np.array([[[0], [np.nan]], [[-3], [0]]])
+    den_b = np.array([[[0], [1]], [[2], [3]]])
+    dense_sum = den_a - den_b
+    sparse_sum = coo_array(den_a) - coo_array(den_b)
+    assert_equal(dense_sum, sparse_sum.toarray())
+
+
+@pytest.mark.parametrize(('a_shape', 'b_shape'), [((7,), (12,)),
+                                                  ((6,4), (6,5)),
+                                                  ((5,9,3,2), (9,5,2,3)),])
+def test_nd_sub_sparse_with_inconsistent_shapes(a_shape, b_shape):
+    rng = np.random.default_rng(23409823)
+
+    arr_a = random_array((a_shape), density=0.6, rng=rng, dtype=int)
+    arr_b = random_array((b_shape), density=0.6, rng=rng, dtype=int)
+    with pytest.raises(ValueError, match="inconsistent shapes"):
+        arr_a - arr_b
+
+
+mat_vec_shapes = [
+    ((2, 3, 4, 5), (5,)),
+    ((0, 0), (0,)),
+    ((2, 3, 4, 7, 8), (8,)),
+    ((4, 4, 2, 0), (0,)),
+    ((6, 5, 3, 2, 4), (4, 1)),
+    ((2,5), (5,)),
+    ((2, 5), (5, 1)),
+    ((3,), (3, 1)),
+    ((4,), (4,))
+]
+@pytest.mark.parametrize(('mat_shape', 'vec_shape'), mat_vec_shapes)
+def test_nd_matmul_vector(mat_shape, vec_shape):
+    rng = np.random.default_rng(23409823)
+
+    sp_x = random_array(mat_shape, density=0.6, rng=rng, dtype=int)
+    sp_y = random_array(vec_shape, density=0.6, rng=rng, dtype=int)
+    den_x, den_y = sp_x.toarray(), sp_y.toarray()
+    exp = den_x @ den_y
+    res = sp_x @ den_y
+    assert_equal(res,exp)
+    res = sp_x @ list(den_y)
+    assert_equal(res,exp)
+
+
+mat_mat_shapes = [
+    ((2, 3, 4, 5), (2, 3, 5, 7)),
+    ((0, 0), (0,)),
+    ((4, 4, 2, 0), (0,)),
+    ((7, 8, 3), (3,)),
+    ((7, 8, 3), (3, 1)),
+    ((6, 5, 3, 2, 4), (4, 3)),
+    ((1, 3, 2, 4), (6, 5, 1, 4, 3)),
+    ((6, 1, 1, 2, 4), (1, 3, 4, 3)),
+    ((4,), (2, 4, 3)),
+    ((3,), (5, 6, 7, 3, 2)),
+    ((4,), (4, 3)),
+    ((2, 5), (5, 1)),
+]
+@pytest.mark.parametrize(('mat_shape1', 'mat_shape2'), mat_mat_shapes)
+def test_nd_matmul(mat_shape1, mat_shape2):
+    rng = np.random.default_rng(23409823)
+
+    sp_x = random_array(mat_shape1, density=0.6, random_state=rng, dtype=int)
+    sp_y = random_array(mat_shape2, density=0.6, random_state=rng, dtype=int)
+    den_x, den_y = sp_x.toarray(), sp_y.toarray()
+    exp = den_x @ den_y
+    # sparse-sparse
+    res = sp_x @ sp_y
+    assert_equal(res.toarray(), exp)
+    # sparse-dense
+    res = sp_x @ den_y
+    assert_equal(res, exp)
+    res = sp_x @ list(den_y)
+    assert_equal(res, exp)
+
+    # dense-sparse
+    res = den_x @ sp_y
+    assert_equal(res, exp)
+
+
+def test_nd_matmul_sparse_with_inconsistent_arrays():
+    rng = np.random.default_rng(23409823)
+
+    sp_x = random_array((4,5,7,6,3), density=0.6, random_state=rng, dtype=int)
+    sp_y = random_array((1,5,3,2,5), density=0.6, random_state=rng, dtype=int)
+    with pytest.raises(ValueError, match="matmul: dimension mismatch with signature"):
+        sp_x @ sp_y
+    with pytest.raises(ValueError, match="matmul: dimension mismatch with signature"):
+        sp_x @ (sp_y.toarray())
+
+    sp_z = random_array((1,5,3,2), density=0.6, random_state=rng, dtype=int)
+    with pytest.raises(ValueError, match="Batch dimensions are not broadcastable"):
+        sp_x @ sp_z
+    with pytest.raises(ValueError, match="Batch dimensions are not broadcastable"):
+        sp_x @ (sp_z.toarray())
+
+
+def test_dot_1d_1d(): # 1-D inner product
+    a = coo_array([1,2,3])
+    b = coo_array([4,5,6])
+    exp = np.dot(a.toarray(), b.toarray())
+    res = a.dot(b)
+    assert_equal(res, exp)
+    res = a.dot(b.toarray())
+    assert_equal(res, exp)
+
+
+def test_dot_sparse_scalar():
+    a = coo_array([[1, 2], [3, 4], [5, 6]])
+    b = 3
+    res = a.dot(b)
+    exp = np.dot(a.toarray(), b)
+    assert_equal(res.toarray(), exp)
+
+
+def test_dot_with_inconsistent_shapes():
+    arr_a = coo_array([[[1, 2]], [[3, 4]]])
+    arr_b = coo_array([4, 5, 6])
+    with pytest.raises(ValueError, match="not aligned for n-D dot"):
+        arr_a.dot(arr_b)
+
+
+def test_matmul_dot_not_implemented():
+    arr_a = coo_array([[1, 2], [3, 4]])
+    with pytest.raises(TypeError, match="argument not supported type"):
+        arr_a.dot(None)
+    with pytest.raises(TypeError, match="arg not supported type"):
+        arr_a.tensordot(None)
+    with pytest.raises(TypeError, match="unsupported operand type"):
+        arr_a @ None
+    with pytest.raises(TypeError, match="unsupported operand type"):
+        None @ arr_a
+
+
+dot_shapes = [
+    ((3,3), (3,3)), ((4,6), (6,7)), ((1,4), (4,1)), # matrix multiplication 2-D
+    ((3,2,4,7), (7,)), ((5,), (6,3,5,2)), # dot of n-D and 1-D arrays
+    ((3,2,4,7), (7,1)), ((1,5,), (6,3,5,2)),
+    ((4,6), (3,2,6,4)), ((2,8,7), (4,5,7,7,2)), # dot of n-D and m-D arrays
+    ((4,5,7,6), (3,2,6,4)),
+]
+@pytest.mark.parametrize(('a_shape', 'b_shape'), dot_shapes)
+def test_dot_nd(a_shape, b_shape):
+    rng = np.random.default_rng(23409823)
+
+    arr_a = random_array(a_shape, density=0.6, random_state=rng, dtype=int)
+    arr_b = random_array(b_shape, density=0.6, random_state=rng, dtype=int)
+
+    exp = np.dot(arr_a.toarray(), arr_b.toarray())
+    # sparse-dense
+    res = arr_a.dot(arr_b.toarray())
+    assert_equal(res, exp)
+    res = arr_a.dot(list(arr_b.toarray()))
+    assert_equal(res, exp)
+    # sparse-sparse
+    res = arr_a.dot(arr_b)
+    assert_equal(res.toarray(), exp)
+
+
+tensordot_shapes_and_axes = [
+    ((4,6), (6,7), ([1], [0])),
+    ((3,2,4,7), (7,), ([3], [0])),
+    ((5,), (6,3,5,2), ([0], [2])),
+    ((4,5,7,6), (3,2,6,4), ([0, 3], [3, 2])),
+    ((2,8,7), (4,5,7,8,2), ([0, 1, 2], [4, 3, 2])),
+    ((4,5,3,2,6), (3,2,6,7,8), 3),
+    ((4,5,7), (7,3,7), 1),
+    ((2,3,4), (2,3,4), ([0, 1, 2], [0, 1, 2])),
+]
+@pytest.mark.parametrize(('a_shape', 'b_shape', 'axes'), tensordot_shapes_and_axes)
+def test_tensordot(a_shape, b_shape, axes):
+    rng = np.random.default_rng(23409823)
+
+    arr_a = random_array(a_shape, density=0.6, random_state=rng, dtype=int)
+    arr_b = random_array(b_shape, density=0.6, random_state=rng, dtype=int)
+
+    exp = np.tensordot(arr_a.toarray(), arr_b.toarray(), axes=axes)
+
+    # sparse-dense
+    res = arr_a.tensordot(arr_b.toarray(), axes=axes)
+    assert_equal(res, exp)
+    res = arr_a.tensordot(list(arr_b.toarray()), axes=axes)
+    assert_equal(res, exp)
+
+    # sparse-sparse
+    res = arr_a.tensordot(arr_b, axes=axes)
+    if type(res) is coo_array:
+        assert_equal(res.toarray(), exp)
+    else:
+        assert_equal(res, exp)
+
+
+def test_tensordot_with_invalid_args():
+    rng = np.random.default_rng(23409823)
+
+    arr_a = random_array((3,4,5), density=0.6, random_state=rng, dtype=int)
+    arr_b = random_array((3,4,6), density=0.6, random_state=rng, dtype=int)
+
+    axes = ([2], [2]) # sizes of 2nd axes of both shapes do not match
+    with pytest.raises(ValueError, match="sizes of the corresponding axes must match"):
+        arr_a.tensordot(arr_b, axes=axes)
+
+    arr_a = random_array((5,4,2,3,7), density=0.6, random_state=rng, dtype=int)
+    arr_b = random_array((4,6,3,2), density=0.6, random_state=rng, dtype=int)
+
+    axes = ([2,0,1], [1,3]) # lists have different lengths
+    with pytest.raises(ValueError, match="axes lists/tuples must be of the"
+                       " same length"):
+        arr_a.tensordot(arr_b, axes=axes)
+
+
+@pytest.mark.parametrize(('actual_shape', 'broadcast_shape'),
+                         [((1,3,5,4), (2,3,5,4)), ((2,1,5,4), (6,2,3,5,4)),
+                          ((1,1,7,8,9), (4,5,6,7,8,9)), ((1,3), (4,5,3)),
+                          ((7,8,1), (7,8,5)), ((3,1), (3,4)), ((1,), (5,)),
+                          ((1,1,1), (4,5,6)), ((1,3,1,5,4), (8,2,3,9,5,4)),])
+def test_broadcast_to(actual_shape, broadcast_shape):
+    rng = np.random.default_rng(23409823)
+
+    arr = random_array(actual_shape, density=0.6, random_state=rng, dtype=int)
+    res = arr._broadcast_to(broadcast_shape)
+    exp = np.broadcast_to(arr.toarray(), broadcast_shape)
+    assert_equal(res.toarray(), exp)
+
+
+@pytest.mark.parametrize(('shape'), [(4,5,6,7,8), (6,4),
+                                     (5,9,3,2), (9,5,2,3,4),])
+def test_block_diag(shape):
+    rng = np.random.default_rng(23409823)
+    sp_x = random_array(shape, density=0.6, random_state=rng, dtype=int)
+    den_x = sp_x.toarray()
+
+    # converting n-d numpy array to an array of slices of 2-D matrices,
+    # to pass as argument into scipy.linalg.block_diag
+    num_slices = int(np.prod(den_x.shape[:-2]))
+    reshaped_array = den_x.reshape((num_slices,) + den_x.shape[-2:])
+    matrices = [reshaped_array[i, :, :] for i in range(num_slices)]
+    exp = block_diag(*matrices)
+
+    res = _block_diag(sp_x)
+
+    assert_equal(res.toarray(), exp)
+
+
+@pytest.mark.parametrize(('shape'), [(4,5,6,7,8), (6,4),
+                                     (5,9,3,2), (9,5,2,3,4),])
+def test_extract_block_diag(shape):
+    rng = np.random.default_rng(23409823)
+    sp_x = random_array(shape, density=0.6, random_state=rng, dtype=int)
+    res = _extract_block_diag(_block_diag(sp_x), shape)
+
+    assert_equal(res.toarray(), sp_x.toarray())
+
+
+add_sub_shapes = [
+    ((3,4), (3,4)), ((3,4,6), (3,4,6)), ((3,7,5), (3,7,5))
+]
+@pytest.mark.parametrize(('a_shape', 'b_shape'), add_sub_shapes)
+def test_add_no_broadcasting(a_shape, b_shape):
+    rng = np.random.default_rng(23409823)
+    a = random_array(a_shape, density=0.6, random_state=rng, dtype=int)
+    b = random_array(b_shape, density=0.6, random_state=rng, dtype=int)
+
+    res = a + b
+    exp = np.add(a.toarray(), b.toarray())
+    assert_equal(res.toarray(), exp)
+    res = a + b.toarray()
+    assert_equal(res, exp)
+
+
+@pytest.mark.parametrize(('a_shape', 'b_shape'), add_sub_shapes)
+def test_sub_no_broadcasting(a_shape, b_shape):
+    rng = np.random.default_rng(23409823)
+    a = random_array(a_shape, density=0.6, random_state=rng, dtype=int)
+    b = random_array(b_shape, density=0.6, random_state=rng, dtype=int)
+
+    res = a - b
+    exp = np.subtract(a.toarray(), b.toarray())
+    assert_equal(res.toarray(), exp)
+
+    res = a - b.toarray()
+    assert_equal(res, exp)
+
+
+argmax_argmin_shapes_axis = [
+    ((3,), None), ((3,), 0),
+    ((4,6), 1), ((7,3), 0), ((3,5), None),
+    ((2,8,7), 2), ((2,8,7), 0),
+    ((2,0), 0), ((3,0,0,2), 0),
+    ((3,2,4,7), None), ((3,2,4,7), 1), ((3,2,4,7), 0), ((3,2,4,7), 2),
+    ((3,2,4,7), -2), ((4,5,7,8,2), 4), ((4,5,7,8,2), -3),
+]
+
+
+@pytest.mark.parametrize(('shape', 'axis'), argmax_argmin_shapes_axis)
+def test_argmax_argmin(shape, axis):
+    rng = np.random.default_rng(23409823)
+    a = random_array(shape, density=0.6, random_state=rng, dtype=int)
+
+    res = a.argmax(axis=axis)
+    exp = np.argmax(a.toarray(), axis=axis)
+    assert_equal(res, exp)
+
+    res = a.argmin(axis=axis)
+    exp = np.argmin(a.toarray(), axis=axis)
+    assert_equal(res, exp)
+
+
+max_min_shapes_axis = [
+    ((3,), None), ((3,), 0),
+    ((4,6), 1), ((7,3), 0), ((3,5), None),
+    ((2,8,7), 2), ((2,8,7), 0),
+    ((3,2,4,7), None), ((3,2,4,7), 1), ((3,2,4,7), 0), ((3,2,4,7), 2),
+    ((4,5,7,8,2), 4), ((4,5,8,1), 3), ((4,6), (0,)), ((4,6), (0,1)),
+    ((3,0,2), 2), ((3,0,2), (0,2)), ((3,0), 0),
+    ((3,7,8,5), (0,1)), ((3,7,8,5), (2,1)), ((3,7,8,5), (2,0)),
+    ((3,7,8,5), (0,-2)), ((3,7,8,5), (-1,2)), ((3,7,8,5), (3)),
+    ((3,7,8,5), (0,1,2)), ((3,7,8,5), (0,1,2,3)),
+]
+@pytest.mark.parametrize(('shape', 'axis'), max_min_shapes_axis)
+def test_min_max(shape, axis):
+    rng = np.random.default_rng(23409823)
+    a = random_array(shape, density=0.6, random_state=rng, dtype=int)
+
+    res_min = a.min(axis=axis)
+    exp_min = np.min(a.toarray(), axis=axis)
+    res_max = a.max(axis=axis)
+    exp_max = np.max(a.toarray(), axis=axis)
+    res_nanmin = a.nanmin(axis=axis)
+    exp_nanmin = np.nanmin(a.toarray(), axis=axis)
+    res_nanmax = a.nanmax(axis=axis)
+    exp_nanmax = np.nanmax(a.toarray(), axis=axis)
+
+    for res, exp in [(res_min, exp_min), (res_max, exp_max),
+                     (res_nanmin, exp_nanmin), (res_nanmax, exp_nanmax)]:
+        if np.issubdtype(type(res), np.number):
+            assert_equal(res, exp)
+        else:
+            assert_equal(res.toarray(), exp)
+
+
+def test_min_max_full():
+    for a in (coo_array([[[1, 2, 3, 4]]]), coo_array([[1, 2, 3, 4]])):
+        assert a.min() == 1
+        assert (-a).max() == -1
+
+
+sum_mean_params = [
+    ((3,), None, None), ((3,), 0, None),
+    ((4,6), 1, None), ((7,3), 0, None), ((3,5), None, None),
+    ((2,8,7), 2, None), ((2,8,7), 0, np.zeros((8,7))),
+    ((3,2,4,7), None, None), ((3,2,4,7), 1, np.zeros((3,4,7))),
+    ((3,2,4,7), 0, None), ((4,5,7,8,2), 4, None),
+    ((4,5,8,1), 3, None), ((4,6), (0,), None), ((4,6), (0,1), None),
+    ((3,0,2), 2, None), ((3,0,2), (0,2), None), ((3,0), 0, None),
+    ((3,7,8,5), (0,1), np.zeros((8,5))), ((3,7,8,5), (2,1), None),
+    ((3,7,8,5), (0,-2), None), ((3,7,8,5), (-1,2), np.zeros((3,7))),
+    ((3,7,8,5), (3), None), ((3,7,8,5), (0,1,2), np.zeros((5,))),
+    ((3,7,8,5), (0,1,2,3), None),
+]
+@pytest.mark.parametrize(('shape', 'axis', 'out'), sum_mean_params)
+def test_sum(shape, axis, out):
+    rng = np.random.default_rng(23409823)
+    a = random_array(shape, density=0.6, random_state=rng, dtype=int)
+
+    res = a.sum(axis=axis, out=out)
+    exp = np.sum(a.toarray(), axis=axis)
+    assert_equal(res, exp)
+    if out is not None:
+        assert_equal(out, exp)
+        assert id(res) == id(out)
+
+
+@pytest.mark.parametrize(('shape', 'axis', 'out'), sum_mean_params)
+def test_mean(shape, axis, out):
+    rng = np.random.default_rng(23409823)
+    a = random_array(shape, density=0.6, random_state=rng, dtype=int)
+
+    res = a.mean(axis=axis, out=out)
+    exp = np.mean(a.toarray(), axis=axis)
+    assert_allclose(res, exp)
+    if out is not None:
+        assert id(res) == id(out)
+        assert_allclose(out, exp)
+
+
+def test_pow_abs_round():
+    rng = np.random.default_rng(23409823)
+    a = random_array((3,6,5,2,4), density=0.6, random_state=rng, dtype=int)
+    assert_allclose((a**3).toarray(), np.power(a.toarray(), 3))
+    assert_allclose((a**7).toarray(), np.power(a.toarray(), 7))
+    assert_allclose(round(a).toarray(), np.round(a.toarray()))
+    assert_allclose(abs(a).toarray(), np.abs(a.toarray()))
+
+
+#bitwise_op_and_compare_broadcast_shapes = [
+#    ((3,4), (3,4)), ((1,4), (2,1)), ((3,5), (1,)), ((1,), (7,8)),
+#    ((3,4,6), (3,4,6)), ((4,3), (2,1,3)), ((2,1,3), (4,3)),
+#    ((3,5,4), (1,)), ((1,), (7,8,4)), ((16,1,6), (2,6)), ((3,7,5), (3,7,5)),
+#    ((16,2,6), (1,2,6)), ((7,8), (5,7,8)), ((4,5,1), (5,1)),
+#    ((6,8,3), (4,1,1,3)), ((1,1,1), (3,4,2)), ((3,4,2), (1,1,1,1,1)),
+bitwise_op_and_compare_shapes = [
+    ((3,4), (3,4)), ((3,4,6), (3,4,6)), ((3,7,5), (3,7,5)),
+]
+@pytest.mark.parametrize(('a_shape', 'b_shape'), bitwise_op_and_compare_shapes)
+def test_boolean_comparisons(a_shape, b_shape):
+    rng = np.random.default_rng(23409823)
+    a = random_array(a_shape, density=0.6, random_state=rng, dtype=int)
+    b = random_array(b_shape, density=0.6, random_state=rng, dtype=int)
+    with warnings.catch_warnings():
+        warnings.simplefilter("ignore", SparseEfficiencyWarning)
+        assert_equal((a==b).toarray(), a.toarray()==b.toarray())
+        assert_equal((a!=b).toarray(), a.toarray()!=b.toarray())
+        assert_equal((a>=b).toarray(), a.toarray()>=b.toarray())
+        assert_equal((a<=b).toarray(), a.toarray()<=b.toarray())
+        assert_equal((a>b).toarray(), a.toarray()>b.toarray())
+        assert_equal((a<b).toarray(), a.toarray()<b.toarray())
+        assert_equal((a==b).toarray(), np.bitwise_not((a!=b).toarray()))
+        assert_equal((a>=b).toarray(), np.bitwise_not((a<b).toarray()))
+        assert_equal((a<=b).toarray(), np.bitwise_not((a>b).toarray()))
+
+
+def test_boolean_comparisons_with_scalar():
+    rng = np.random.default_rng(23409823)
+    a = random_array((5,4,8,7), density=0.6, random_state=rng, dtype=int)
+    with warnings.catch_warnings():
+        warnings.simplefilter("ignore", SparseEfficiencyWarning)
+        assert_equal((a==0).toarray(), a.toarray()==0)
+        assert_equal((a!=0).toarray(), a.toarray()!=0)
+        assert_equal((a>=1).toarray(), a.toarray()>=1)
+        assert_equal((a<=1).toarray(), a.toarray()<=1)
+        assert_equal((a>0).toarray(), a.toarray()>0)
+        assert_equal((a<0).toarray(), a.toarray()<0)
+
+
+@pytest.mark.parametrize(('a_shape', 'b_shape'), bitwise_op_and_compare_shapes)
+def test_multiply(a_shape, b_shape):
+    rng = np.random.default_rng(23409823)
+    a = random_array(a_shape, density=0.6, random_state=rng, dtype=int)
+    b = random_array(b_shape, density=0.6, random_state=rng, dtype=int)
+    res = a * b
+    exp = np.multiply(a.toarray(), b.toarray())
+    assert_equal(res.toarray(), exp)
+
+
+def test_multiply_with_scalar():
+    rng = np.random.default_rng(23409823)
+    a = random_array((3,5,4), density=0.6, random_state=rng, dtype=int)
+    res = a * 7
+    exp = np.multiply(a.toarray(), 7)
+    assert_equal(res.toarray(), exp)
+
+
+@pytest.mark.parametrize(('a_shape', 'b_shape'), bitwise_op_and_compare_shapes)
+def test_divide(a_shape, b_shape):
+    rng = np.random.default_rng(23409823)
+    a = random_array(a_shape, density=0.6, random_state=rng, dtype=int)
+    b = np.arange(1, 1 + math.prod(b_shape)).reshape(b_shape)
+    res = a / b
+    exp = a.toarray() / b
+    assert_allclose(res.toarray(), exp)
+
+    res = a / b
+    assert_allclose(res.toarray(), exp)
+
+
+def test_divide_with_scalar():
+    rng = np.random.default_rng(23409823)
+    a = random_array((3,5,4), density=0.6, random_state=rng, dtype=int)
+    res = a / 7
+    exp = a.toarray() / 7
+    assert_allclose(res.toarray(), exp)
+
+
+@pytest.mark.parametrize(('a_shape', 'b_shape'), bitwise_op_and_compare_shapes)
+def test_maximum(a_shape, b_shape):
+    rng = np.random.default_rng(23409823)
+    a = random_array(a_shape, density=0.6, random_state=rng, dtype=int)
+    b = random_array(b_shape, density=0.6, random_state=rng, dtype=int)
+    with warnings.catch_warnings():
+        warnings.simplefilter("ignore", SparseEfficiencyWarning)
+        res = a.maximum(b)
+        exp = np.maximum(a.toarray(), b.toarray())
+        assert_equal(res.toarray(), exp)
+
+
+@pytest.mark.parametrize(('a_shape', 'b_shape'), bitwise_op_and_compare_shapes)
+def test_minimum(a_shape, b_shape):
+    rng = np.random.default_rng(23409823)
+    a = random_array(a_shape, density=0.6, random_state=rng, dtype=int)
+    b = random_array(b_shape, density=0.6, random_state=rng, dtype=int)
+    with warnings.catch_warnings():
+        warnings.simplefilter("ignore", SparseEfficiencyWarning)
+        res = a.minimum(b)
+        exp = np.minimum(a.toarray(), b.toarray())
+        assert_equal(res.toarray(), exp)
+
+
+def test_maximum_with_scalar():
+    a = coo_array([0,1,6])
+    b = coo_array([[15, 0], [14, 5], [0, -12]])
+    c = coo_array([[[[3,0], [2,4]], [[8,9], [-3,12]]],
+                   [[[5,2], [3,0]], [[0,7], [0,-6]]]])
+    with warnings.catch_warnings():
+        warnings.simplefilter("ignore", SparseEfficiencyWarning)
+        assert_equal(a.maximum(5).toarray(), np.maximum(a.toarray(), 5))
+        assert_equal(b.maximum(9).toarray(), np.maximum(b.toarray(), 9))
+        assert_equal(c.maximum(5).toarray(), np.maximum(c.toarray(), 5))
+
+
+def test_minimum_with_scalar():
+    a = coo_array([0,1,6])
+    b = coo_array([[15, 0], [14, 5], [0, -12]])
+    c = coo_array([[[[3,0], [2,4]], [[8,9], [-3,12]]],
+                   [[[5,2], [3,0]], [[0,7], [0,-6]]]])
+    with warnings.catch_warnings():
+        warnings.simplefilter("ignore", SparseEfficiencyWarning)
+        assert_equal(a.minimum(5).toarray(), np.minimum(a.toarray(), 5))
+        assert_equal(b.minimum(9).toarray(), np.minimum(b.toarray(), 9))
+        assert_equal(c.minimum(5).toarray(), np.minimum(c.toarray(), 5))
+
+
+def test_1d_coo_get():
+    B = coo_array(np.arange(9))
+
+    assert B[0] == 0
+    assert B[4] == 4
+
+    assert_equal(B[1:3].toarray(), B.toarray()[1:3])
+    assert_equal(B[:3].toarray(), B.toarray()[:3])
+    assert_equal(B[1:].toarray(), B.toarray()[1:])
+    assert_equal(B[1:5:2].toarray(), B.toarray()[1:5:2])
+
+    assert_equal(B[[1, 3, 4]].toarray(), B.toarray()[[1, 3, 4]])
+    assert_equal(B[[3, 4, 1]].toarray(), B.toarray()[[3, 4, 1]])
+
+
+def test_2d_coo_get():
+    B = coo_array(np.arange(4 * 5).reshape((4, 5)))
+
+    assert B[0, 0] == 0
+    assert B[3, 4] == 19
+
+    assert_equal(B[1:3, 0].toarray(), B.toarray()[1:3, 0])
+    assert_equal(B[2, 1:3].toarray(), B.toarray()[2, 1:3])
+    assert_equal(B[:2, 1:5:3].toarray(), B.toarray()[:2, 1:5:3])
+
+    assert_equal(B[[1, 3], 0].toarray(), B.toarray()[[1,3], 0])
+    assert_equal(B[2:, [1, 3]].toarray(), B.toarray()[2:, [1,3]])
+    assert_equal(B[np.array([1, 3]), 0].toarray(), B.toarray()[[1,3], 0])
+    assert_equal(B[2:, np.array([1, 3])].toarray(), B.toarray()[2:, [1,3]])
+
+    assert_equal(B[:, 0].toarray(), B.toarray()[:, 0])
+    assert_equal(B[0, :].toarray(), B.toarray()[0, :])
+
+
+def test_3d_coo_get():
+    A = coo_array(np.arange(4 * 5 * 6).reshape((4, 5, 6)))
+    assert A[0, 0, 0] == 0
+    assert A[3, 4, 5] == 119
+
+    assert_equal(A[0, 1:3, 0].toarray(), A.toarray()[0, 1:3, 0])
+    assert_equal(A[0, 1:3, 3].toarray(), A.toarray()[0, 1:3, 3])
+    assert_equal(A[:3, 1:5:2, 2:].toarray(), A.toarray()[:3, 1:5:2, 2:])
+
+    assert_equal(A[[1, 3], 0, 0].toarray(), A.toarray()[[1, 3], 0, 0])
+    assert_equal(A[:2, 1:3, [1, 3]].toarray(), A.toarray()[:2, 1:3, [1, 3]])
+
+    assert_equal(A[0, :, 0].toarray(), A.toarray()[0, :, 0])
+    assert_equal(A[:, :, 0].toarray(), A.toarray()[:, :, 0])
+
+
+def test_newaxis_get():
+    A = coo_array(np.arange(4 * 5 * 6).reshape((4, 5, 6)))
+    D = A.toarray()
+    assert_equal(A[:5, 3:, 1].toarray(), D[:5, 3:, 1])
+    assert_equal(A[None, :5, 1:3, None, 1].toarray(), D[None, :5, 1:3, None, 1])
+    assert_equal(A[None, :5, 3:, 1, None].toarray(), D[None, :5, 3:, 1, None])
+    assert_equal(A[None, :5, ..., None].toarray(), D[None, :5, ..., None])
+
+
+def test_newaxis_set():
+    D = np.arange(4 * 5 * 6).reshape((4, 5, 6))
+    A = coo_array(D)
+
+    A[None, 3:, 1] = D[None, 3:, 1] = 5
+    assert_equal(A.toarray(), D)
+    A[3:, 1, None] = D[3:, 1, None] = 7
+    assert_equal(A.toarray(), D)
+    A[3:, None, 1] = D[3:, None, 1] = 3
+    assert_equal(A.toarray(), D)
+
+
+def test_1d_coo_set():
+    D = np.arange(9)
+    A = coo_array(D)
+
+    A[0] = D[0] = -1
+    assert_equal(A.toarray(), D)
+    A[4] = D[4] = -2
+    assert_equal(A.toarray(), D)
+
+    A[1:3] = D[1:3] = [-2, -3]
+    assert_equal(A.toarray(), D)
+    A[:3] = D[:3] = [-7, -8, -9]
+    assert_equal(A.toarray(), D)
+    A[1:] = D[1:] = -D[1:]
+    assert_equal(A.toarray(), D)
+    A[1:5:2] = D[1:5:2] = -D[1:5:2]
+    assert_equal(A.toarray(), D)
+
+    A[[1, 3, 4]] = D[[1, 3, 4]] = -D[[1, 3, 4]]
+    assert_equal(A.toarray(), D)
+    A[[3, 4, 1]] = D[[3, 4, 1]] = -D[[1, 2, 3]]
+    assert_equal(A.toarray(), D)
+
+
+D = np.arange(4 * 5).reshape((4, 5))
+A = coo_array(D)
+
+keys = [
+    # all int
+    (1, 3),
+    (-1, -3),
+    # slices and ints
+    (slice(1, 3, None), 0),
+    (2, slice(1, 3, None)),
+    (slice(1, 3, None), slice(1, 5, 3)),
+    (slice(None, None, -1), 2),
+    (1, slice(None)),
+    (Ellipsis,),
+    # array indexing
+    ([1, 3], 0),
+    (2, [1, 2]),
+    (np.array([1, 3]), slice(1, None)),
+    (slice(2), np.array([1, 2, 3])),
+    # fancy array indexing
+    (np.array([1, 3]), np.array([0, 2])),
+]
+
+@pytest.mark.parametrize(["A", "D", "idx"], [(A, D, idx) for idx in keys])
+@pytest.mark.thread_unsafe
+def test_2d_coo_set(A, D, idx):
+    D[idx] = A[idx] = -D[idx]
+    assert_equal(A.toarray(), D)
+
+
+D = np.arange(4 * 5 * 6).reshape((4, 5, 6))
+A = coo_array(D)
+
+keys = [
+    # all ints
+    (0, 0, 0),
+    (3, -4, 5),
+    # slices and ints
+    (0, slice(1, 3), 0),
+    (slice(3, None), 3, slice(2)),
+    (slice(2), slice(1, 5, 2), slice(1, None)),
+    (slice(None, None, -1), slice(None), slice(1, 5, 2)),
+    (Ellipsis),
+    # array indexing
+    (2, [1, 2], slice(3)),
+    (np.array([1, 3]), slice(1, None), 0),
+    (np.array([1, 3]), slice(1, None), [0]),
+    # fancy array indexing
+    (np.array([1, 3]), slice(1, None), np.array([2, 4])),
+    (2, np.array([1, 3]), np.array([2, 4])),
+    (np.array([1, 3]), np.array([2, 4]), 1),
+    (np.array([1, 3]), np.array([2, 4]), [2]),
+]
+
+@pytest.mark.parametrize(["A", "D", "idx"], [(A, D, idx) for idx in keys])
+@pytest.mark.thread_unsafe
+def test_3d_coo_set(A, D, idx):
+    D[idx] = A[idx] = -99
+    assert_equal(A.toarray(), D)
+
+
+@pytest.mark.parametrize(
+    "scalar_container",
+    [lambda x: csr_array(np.array([[x]])), np.array, lambda x: x],
+    ids=["sparse", "dense", "scalar"],
+)
+@pytest.mark.thread_unsafe(reason="fails in parallel")
+def test_3d_coo_singleton(scalar_container):
+    A[(0, 0, 0)] = scalar_container(-99)
+    D[(0, 0, 0)] = -99
+    assert_equal(A.toarray(), D)
+
+
+#D = np.arange(4 * 5 * 6 * 4 * 6).reshape((4, 5, 6, 4, 6))
+D = np.arange(4 * 6 * 6 * 3 * 4).reshape((4, 6, 6, 3, 4))
+A = coo_array(D)
+
+keys = [
+    # multidimensional
+    ("all-ints", (1, 2, 1)),
+    ("ellipsis-first", (..., 0)),
+    ("ellipsis-last", (1, ...)),
+    ("ellipsis-middle", (1, ..., 0)),
+    # slices and ints
+    ("split-ints", (slice(None, 4, None), 2, 1, slice(None, None, None), 1)),
+    ("contiguous-ints-last", (slice(4, None, None), slice(None, None, None), 2, 1, 1)),
+    ("contiguous-ints-first", (2, 1, 1, slice(4, None, None), slice(None, None, None))),
+    ("empty-slice", (slice(4, 4, None), slice(None, None, None), 2, 1, 1)),
+    # slices and arrays and ints
+    ("split-2d-arrays-and-ints",
+        (slice(None, 4, None), [[2, 1, 1], [2, 1, 2]], [[2, 1, 0], [3, 4, 0]],
+         slice(None, None, None), 0)
+    ),
+    ("contiguous-2d-arrays-and-ints",
+        (slice(None, 4, None), [[2, 1, 0], [2, 1, 2]], [[2, 1, 0], [3, 4, 0]],
+         1, slice(None, None, None))
+    ),
+    ("split-1d-arrays-and-ints",
+        (slice(None, 4, None), [2, 1, 0], [2, 1, 0], slice(None, None, None), 1)
+    ),
+    ("split-ints-broadcast-arrays-slice-step-not-1",
+        (0, slice(1, 4, 2), 1, [[2, 1, 0]], [[2], [1], [0]])
+    ),
+    ("contiguous-broadcast-arrays",
+        (slice(None, 3, None), slice(1, 4, 2), 1, [[2, 1, 0]], [[2], [1], [0]])
+    ),
+    ("contiguous-arrays-first",
+        ([[2, 1, 0]], [[2], [1], [0]], 0, slice(1, 4, 2), slice(None, 3, None))
+    ),
+    ("split-arrays-some-first-some-last",
+        ([[2, 1, 0]], slice(1, 4, 2), slice(None, 3, None), 0, [[2], [1], [0]])
+    ),
+    # test we are not creating duplicate entries for duplicate values in array index
+    ("duplicate-array-entries-split-arrays",
+        (slice(None, 4, None), [[2, 1, 0], [2, 1, 1]], [[2, 1, 0], [3, 4, 4]],
+         slice(None, None, None), 1)
+    ),
+    ("duplicate-array-entries-contiguous-broadcast-arrays",
+        (slice(1, 4, 2), 0, 1, [[2, 1, 1]], [[2], [1], [1]])
+    ),
+    ]
+
+@pytest.mark.parametrize(["A", "D", "ix", "msg"], [(A, D, ix, msg) for msg, ix in keys])
+@pytest.mark.thread_unsafe
+def test_5d_coo_set(A, D, ix, msg):
+    D[ix] = A[ix] = -99
+    assert_equal(A.toarray(), D, err_msg=f"\nTest of: {msg}\n")
+
+
+def test_bool_get():
+    D = np.arange(4 * 6 * 6 * 3 * 4).reshape((4, 6, 6, 3, 4))
+    A = coo_array(D)
+
+    assert_equal(A[D > 500].toarray(), D[D > 500])
+    assert_equal(A[D > 5000].toarray(), D[D > 5000])
+    assert_equal(A[D > -1].toarray(), D[D > -1])
+
+    assert_equal(A[A > 500].toarray(), D[D > 500])
+    assert_equal(A[A > 5000].toarray(), D[D > 5000])
+    assert_equal(A[A < -1].toarray(), D[D < -1])
+
+    bi0 = A[:, 0, 0, 0, 0] > 50
+    bi1 = A[0, :, 0, 0, 0] > 50
+
+    idx = (bi0, slice(2, 3, None), [1], slice(None, 2, 2), bi0)
+    idxnp = (bi0.toarray(), slice(2, 3, 1), [1], slice(0, 2, 2), bi0.toarray())
+    result = D[idxnp]
+    assert_equal(A[idx].toarray(), result)
+    assert_equal(A[idxnp].toarray(), result)
+
+    idx = (slice(2, 3, None), bi1, bi1, slice(None, 2, 2), [1])
+    idxnp = (slice(2, 3, None), bi1.toarray(), bi1.toarray(), slice(None, 2, 2), [1])
+    result = D[idxnp]
+    assert_equal(A[idx].toarray(), result)
+
+
+def test_bool_set():
+    D_orig = np.arange(4 * 6 * 6 * 3 * 4).reshape((4, 6, 6, 3, 4))
+    A_orig = coo_array(D_orig)
+
+    A, D = A_orig.copy(), D_orig.copy()
+    D[D > 500] = A[A > 500] = -33
+    assert_equal(A.toarray(), D)
+
+    A, D = A_orig.copy(), D_orig.copy()
+    D[D > 500] = A[A > 500] = -77
+    assert_equal(A.toarray(), D)
+
+    A, D = A_orig.copy(), D_orig.copy()
+    bool0 = A[:, 0, 0, 0, 0] > 50
+    idx = (bool0, slice(2, 3, None), [1], slice(None, 2, 2), bool0)
+    idxnp = (bool0.toarray(), slice(2, 3, 1), [1], slice(0, 2, 2), bool0.toarray())
+
+    D[idxnp] = A[idx] = -55
+    assert_equal(A.toarray(), D)
+
+    A, D = A_orig.copy(), D_orig.copy()
+    D[idxnp] = A[idxnp] = -88
+    assert_equal(A.toarray(), D)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_csc.py b/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_csc.py
new file mode 100644
index 0000000000000000000000000000000000000000..7093a8f1b0dd6b00a554d8df94bf40c0c9e77b86
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_csc.py
@@ -0,0 +1,131 @@
+import operator
+import sys
+import platform
+
+import numpy as np
+from numpy.testing import assert_array_almost_equal, assert_
+from scipy.sparse import csr_matrix, csc_matrix, lil_matrix, csr_array, csc_array
+
+import pytest
+
+
+LINUX_INTEL = (sys.platform == 'linux') and (platform.machine() == 'x86_64')
+
+
+
+def test_csc_getrow():
+    N = 10
+    np.random.seed(0)
+    X = np.random.random((N, N))
+    X[X > 0.7] = 0
+    Xcsc = csc_matrix(X)
+
+    for i in range(N):
+        arr_row = X[i:i + 1, :]
+        csc_row = Xcsc.getrow(i)
+
+        assert_array_almost_equal(arr_row, csc_row.toarray())
+        assert_(type(csc_row) is csr_matrix)
+
+
+def test_csc_getcol():
+    N = 10
+    np.random.seed(0)
+    X = np.random.random((N, N))
+    X[X > 0.7] = 0
+    Xcsc = csc_matrix(X)
+
+    for i in range(N):
+        arr_col = X[:, i:i + 1]
+        csc_col = Xcsc.getcol(i)
+
+        assert_array_almost_equal(arr_col, csc_col.toarray())
+        assert_(type(csc_col) is csc_matrix)
+
+@pytest.mark.parametrize("matrix_input, axis, expected_shape",
+    [(csc_matrix([[1, 0],
+                [0, 0],
+                [0, 2]]),
+      0, (0, 2)),
+     (csc_matrix([[1, 0],
+                [0, 0],
+                [0, 2]]),
+      1, (3, 0)),
+     (csc_matrix([[1, 0],
+                [0, 0],
+                [0, 2]]),
+      'both', (0, 0)),
+     (csc_matrix([[0, 1, 0, 0, 0, 0],
+                [0, 0, 0, 0, 0, 0],
+                [0, 0, 2, 3, 0, 1]]),
+      0, (0, 6))])
+def test_csc_empty_slices(matrix_input, axis, expected_shape):
+    # see gh-11127 for related discussion
+    slice_1 = matrix_input.toarray().shape[0] - 1
+    slice_2 = slice_1
+    slice_3 = slice_2 - 1
+
+    if axis == 0:
+        actual_shape_1 = matrix_input[slice_1:slice_2, :].toarray().shape
+        actual_shape_2 = matrix_input[slice_1:slice_3, :].toarray().shape
+    elif axis == 1:
+        actual_shape_1 = matrix_input[:, slice_1:slice_2].toarray().shape
+        actual_shape_2 = matrix_input[:, slice_1:slice_3].toarray().shape
+    elif axis == 'both':
+        actual_shape_1 = matrix_input[slice_1:slice_2, slice_1:slice_2].toarray().shape
+        actual_shape_2 = matrix_input[slice_1:slice_3, slice_1:slice_3].toarray().shape
+
+    assert actual_shape_1 == expected_shape
+    assert actual_shape_1 == actual_shape_2
+
+
+@pytest.mark.parametrize('ax', (-2, -1, 0, 1, None))
+def test_argmax_overflow(ax):
+    # See gh-13646: Windows integer overflow for large sparse matrices.
+    dim = (100000, 100000)
+    A = lil_matrix(dim)
+    A[-2, -2] = 42
+    A[-3, -3] = 0.1234
+    A = csc_matrix(A)
+    idx = A.argmax(axis=ax)
+
+    if ax is None:
+        # idx is a single flattened index
+        # that we need to convert to a 2d index pair;
+        # can't do this with np.unravel_index because
+        # the dimensions are too large
+        ii = idx % dim[0]
+        jj = idx // dim[0]
+    else:
+        # idx is an array of size of A.shape[ax];
+        # check the max index to make sure no overflows
+        # we encountered
+        assert np.count_nonzero(idx) == A.nnz
+        ii, jj = np.max(idx), np.argmax(idx)
+
+    assert A[ii, jj] == A[-2, -2]
+
+
+@pytest.mark.skipif(not LINUX_INTEL, reason="avoid variations due to OS, see gh-23826")
+@pytest.mark.timeout(2)  # only slow when broken (when spurious conversion occurs)
+@pytest.mark.parametrize("op", (operator.ne, operator.lt, operator.gt,
+                                operator.add, operator.sub, operator.mul,
+                                # truediv, eq, ge, le make dense output so not tested
+                                lambda x, y: x.minimum(y), lambda x, y: x.maximum(y)))
+def test_compressed_rc_conversion_mixup(op):
+    # see gh-23826 for related discussion
+    num_minor_axis = np.iinfo(np.uint32).max + 1
+    minor_axis_index = np.array([num_minor_axis - 1])
+    major_axis_index = np.array([10])
+    row_cols = (minor_axis_index, major_axis_index)
+    col_rows = (major_axis_index, minor_axis_index)
+
+    X = csc_array((np.array([10]), row_cols), shape=(num_minor_axis, 20))
+    X_2 = X.copy()
+    # causes timeout error upon large memory alloc only if conversion to CSR occurs
+    op(X_2, X)
+
+    Z = csr_array((np.array([10]), col_rows), shape=(20, num_minor_axis))
+    Z_2 = Z.copy()
+    # causes timeout error upon large memory alloc only if conversion to CSC occurs
+    op(Z_2, Z)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_csr.py b/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_csr.py
new file mode 100644
index 0000000000000000000000000000000000000000..b7a3f6d980f37870d6683ad465fca9ba9e3c87c0
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_csr.py
@@ -0,0 +1,281 @@
+import warnings
+import numpy as np
+from numpy.testing import assert_array_almost_equal, assert_, assert_array_equal
+from scipy._lib._testutils import check_free_memory
+from scipy.sparse import csr_matrix, csc_matrix, csr_array, csc_array, hstack
+from scipy import sparse
+import pytest
+
+
+def _check_csr_rowslice(i, sl, X, Xcsr):
+    np_slice = X[i, sl]
+    csr_slice = Xcsr[i, sl]
+    assert_array_almost_equal(np_slice, csr_slice.toarray()[0])
+    assert_(type(csr_slice) is csr_matrix)
+
+
+def test_csr_rowslice():
+    N = 10
+    np.random.seed(0)
+    X = np.random.random((N, N))
+    X[X > 0.7] = 0
+    Xcsr = csr_matrix(X)
+
+    slices = [slice(None, None, None),
+              slice(None, None, -1),
+              slice(1, -2, 2),
+              slice(-2, 1, -2)]
+
+    for i in range(N):
+        for sl in slices:
+            _check_csr_rowslice(i, sl, X, Xcsr)
+
+
+def test_csr_getrow():
+    N = 10
+    np.random.seed(0)
+    X = np.random.random((N, N))
+    X[X > 0.7] = 0
+    Xcsr = csr_matrix(X)
+
+    for i in range(N):
+        arr_row = X[i:i + 1, :]
+        csr_row = Xcsr.getrow(i)
+
+        assert_array_almost_equal(arr_row, csr_row.toarray())
+        assert_(type(csr_row) is csr_matrix)
+
+
+def test_csr_getcol():
+    N = 10
+    np.random.seed(0)
+    X = np.random.random((N, N))
+    X[X > 0.7] = 0
+    Xcsr = csr_matrix(X)
+
+    for i in range(N):
+        arr_col = X[:, i:i + 1]
+        csr_col = Xcsr.getcol(i)
+
+        assert_array_almost_equal(arr_col, csr_col.toarray())
+        assert_(type(csr_col) is csr_matrix)
+
+@pytest.mark.parametrize("matrix_input, axis, expected_shape",
+    [(csr_matrix([[1, 0, 0, 0],
+                [0, 0, 0, 0],
+                [0, 2, 3, 0]]),
+      0, (0, 4)),
+     (csr_matrix([[1, 0, 0, 0],
+                [0, 0, 0, 0],
+                [0, 2, 3, 0]]),
+      1, (3, 0)),
+     (csr_matrix([[1, 0, 0, 0],
+                [0, 0, 0, 0],
+                [0, 2, 3, 0]]),
+      'both', (0, 0)),
+     (csr_matrix([[0, 1, 0, 0, 0],
+                [0, 0, 0, 0, 0],
+                [0, 0, 2, 3, 0]]),
+      0, (0, 5))])
+def test_csr_empty_slices(matrix_input, axis, expected_shape):
+    # see gh-11127 for related discussion
+    slice_1 = matrix_input.toarray().shape[0] - 1
+    slice_2 = slice_1
+    slice_3 = slice_2 - 1
+
+    if axis == 0:
+        actual_shape_1 = matrix_input[slice_1:slice_2, :].toarray().shape
+        actual_shape_2 = matrix_input[slice_1:slice_3, :].toarray().shape
+    elif axis == 1:
+        actual_shape_1 = matrix_input[:, slice_1:slice_2].toarray().shape
+        actual_shape_2 = matrix_input[:, slice_1:slice_3].toarray().shape
+    elif axis == 'both':
+        actual_shape_1 = matrix_input[slice_1:slice_2, slice_1:slice_2].toarray().shape
+        actual_shape_2 = matrix_input[slice_1:slice_3, slice_1:slice_3].toarray().shape
+
+    assert actual_shape_1 == expected_shape
+    assert actual_shape_1 == actual_shape_2
+
+
+def test_csr_bool_indexing():
+    data = csr_matrix([[0, 1, 2], [3, 4, 5], [6, 7, 8]])
+    list_indices1 = [False, True, False]
+    array_indices1 = np.array(list_indices1)
+    list_indices2 = [[False, True, False], [False, True, False], [False, True, False]]
+    array_indices2 = np.array(list_indices2)
+    list_indices3 = ([False, True, False], [False, True, False])
+    array_indices3 = (np.array(list_indices3[0]), np.array(list_indices3[1]))
+    slice_list1 = data[list_indices1].toarray()
+    slice_array1 = data[array_indices1].toarray()
+    slice_list2 = data[list_indices2]
+    slice_array2 = data[array_indices2]
+    slice_list3 = data[list_indices3]
+    slice_array3 = data[array_indices3]
+    assert (slice_list1 == slice_array1).all()
+    assert (slice_list2 == slice_array2).all()
+    assert (slice_list3 == slice_array3).all()
+
+
+@pytest.mark.xfail_on_32bit("Can't create large array for test")
+@pytest.mark.timeout(2)  # only slow when broken (conversion to 2d index arrays)
+@pytest.mark.parametrize("cls", [csr_matrix, csr_array, csc_matrix, csc_array])
+def test_fancy_indexing_broadcasts_without_making_dense_2d(cls):
+    # Fixes Issue gh-24339
+    J = np.arange(100_000)
+    I = J.reshape((100_000, 1))
+    S = cls((100_000, 100_000))
+    # checking nnz, but really testing indexing.
+    assert S[I, J].nnz == 0  # 1D row array for columns -> broadcasts to 2D
+    assert S[I, J.reshape(1, -1)].nnz == 0  # 2D row array as index for columns
+
+
+def test_csr_hstack_int64():
+    """
+    Tests if hstack properly promotes to indices and indptr arrays to np.int64
+    when using np.int32 during concatenation would result in either array
+    overflowing.
+    """
+    max_int32 = np.iinfo(np.int32).max
+
+    # First case: indices would overflow with int32
+    data = [1.0]
+    row = [0]
+
+    max_indices_1 = max_int32 - 1
+    max_indices_2 = 3
+
+    # Individual indices arrays are representable with int32
+    col_1 = [max_indices_1 - 1]
+    col_2 = [max_indices_2 - 1]
+
+    X_1 = csr_matrix((data, (row, col_1)))
+    X_2 = csr_matrix((data, (row, col_2)))
+
+    assert max(max_indices_1 - 1, max_indices_2 - 1) < max_int32
+    assert X_1.indices.dtype == X_1.indptr.dtype == np.int32
+    assert X_2.indices.dtype == X_2.indptr.dtype == np.int32
+
+    # ... but when concatenating their CSR matrices, the resulting indices
+    # array can't be represented with int32 and must be promoted to int64.
+    X_hs = hstack([X_1, X_2], format="csr")
+
+    assert X_hs.indices.max() == max_indices_1 + max_indices_2 - 1
+    assert max_indices_1 + max_indices_2 - 1 > max_int32
+    assert X_hs.indices.dtype == X_hs.indptr.dtype == np.int64
+
+    # Even if the matrices are empty, we must account for their size
+    # contribution so that we may safely set the final elements.
+    X_1_empty = csr_matrix(X_1.shape)
+    X_2_empty = csr_matrix(X_2.shape)
+    X_hs_empty = hstack([X_1_empty, X_2_empty], format="csr")
+
+    assert X_hs_empty.shape == X_hs.shape
+    assert X_hs_empty.indices.dtype == np.int64
+
+    # Should be just small enough to stay in int32 after stack. Note that
+    # we theoretically could support indices.max() == max_int32, but due to an
+    # edge-case in the underlying sparsetools code
+    # (namely the `coo_tocsr` routine),
+    # we require that max(X_hs_32.shape) < max_int32 as well.
+    # Hence we can only support max_int32 - 1.
+    col_3 = [max_int32 - max_indices_1 - 1]
+    X_3 = csr_matrix((data, (row, col_3)))
+    X_hs_32 = hstack([X_1, X_3], format="csr")
+    assert X_hs_32.indices.dtype == np.int32
+    assert X_hs_32.indices.max() == max_int32 - 1
+
+@pytest.mark.parametrize("cls", [csr_matrix, csr_array, csc_matrix, csc_array])
+def test_mixed_index_dtype_int_indexing(cls):
+    # https://github.com/scipy/scipy/issues/20182
+    rng = np.random.default_rng(0)
+    base_mtx = cls(sparse.random(50, 50, random_state=rng, density=0.1))
+    indptr_64bit = base_mtx.copy()
+    indices_64bit = base_mtx.copy()
+    indptr_64bit.indptr = base_mtx.indptr.astype(np.int64)
+    indices_64bit.indices = base_mtx.indices.astype(np.int64)
+
+    for mtx in [base_mtx, indptr_64bit, indices_64bit]:
+        np.testing.assert_array_equal(
+            mtx[[1,2], :].toarray(),
+            base_mtx[[1, 2], :].toarray()
+        )
+        np.testing.assert_array_equal(
+            mtx[:, [1, 2]].toarray(),
+            base_mtx[:, [1, 2]].toarray()
+        )
+
+def test_broadcast_to():
+    a = np.array([1, 0, 2])
+    b = np.array([3])
+    e = np.zeros((0,))
+    res_a = csr_array(a)._broadcast_to((2,3))
+    res_b = csr_array(b)._broadcast_to((4,))
+    res_c = csr_array(b)._broadcast_to((2,4))
+    res_d = csr_array(b)._broadcast_to((1,))
+    res_e = csr_array(e)._broadcast_to((4,0))
+    assert_array_equal(res_a.toarray(), np.broadcast_to(a, (2,3)))
+    assert_array_equal(res_b.toarray(), np.broadcast_to(b, (4,)))
+    assert_array_equal(res_c.toarray(), np.broadcast_to(b, (2,4)))
+    assert_array_equal(res_d.toarray(), np.broadcast_to(b, (1,)))
+    assert_array_equal(res_e.toarray(), np.broadcast_to(e, (4,0)))
+
+    with pytest.raises(ValueError, match="cannot be broadcast"):
+        csr_matrix([[1, 2, 0], [3, 0, 1]])._broadcast_to(shape=(2, 1))
+
+    with pytest.raises(ValueError, match="cannot be broadcast"):
+        csr_matrix([[0, 1, 2]])._broadcast_to(shape=(3, 2))
+
+    with pytest.raises(ValueError, match="cannot be broadcast"):
+        csr_array([0, 1, 2])._broadcast_to(shape=(3, 2))
+
+@pytest.mark.xslow
+def test_large_assignments():
+    # When nnz grows bigger than int32 can hold, shift to int64 index arrays
+
+    # This test requires *a lot* of memory!
+    check_free_memory(65536)
+
+    # parametrize puts lots of slow stuff into pytest's collection phase. So dont use it
+    def check(A_info, index, rhs):
+        if A_info is None:
+            A = csr_array((d, d), dtype=np.int32)
+        else:
+            A = csr_array(A_info, shape=(d, d))
+
+        # check that we start small
+        assert A.indices.dtype == np.int32
+        assert A.nnz < 2**31
+        # do the assignment
+        with warnings.catch_warnings():
+            warnings.filterwarnings("ignore", warn_msg, sparse.SparseEfficiencyWarning)
+            A[index[:, None], index] = rhs
+        # check that we end large
+        assert A.indices.dtype == np.int64
+        assert A.nnz > 2**31
+
+    N = 46340  # 46340**2 fits in int32, 46341**2 does not
+    d = 47000  # d**2 > 2**31 with some extra room
+    warn_msg = "Changing the sparsity structure"
+
+    big_data = np.ones((N, N), dtype=np.float32)
+    big_coords = tuple(co.astype(np.int32) for co in big_data.nonzero())
+    big_data = big_data.reshape(-1)
+    big_info = (big_data, big_coords)
+
+    index_N = np.arange(N + 1, dtype=np.int32)
+    index_300 = np.arange(N, N + 300, dtype=np.int32)
+
+    rhs_300 = np.arange(300 * 300, dtype=np.float32).reshape((300, 300))
+    rhs_300_sparse = csr_array(rhs_300)
+
+    # 1: see gh-24915: From empty array, assign 1 to 46341x46341 region")
+    check(None, index_N, 1)
+
+    # 2: From 46340x46340 region filled, assign 1 to new 300x300 region")
+    check(big_info, index_300, 1)
+
+    # 3: From 46340x46340 region filled, assign np.array to new 300x300 region")
+    check(big_info, index_300, rhs_300)
+
+    # 4: From 46340x46340 region filled, assign sparse to new 300x300 region")
+    check(big_info, index_300, rhs_300_sparse)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_dok.py b/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_dok.py
new file mode 100644
index 0000000000000000000000000000000000000000..9b54d3067e8da75b5c8d520e93d480287e364341
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_dok.py
@@ -0,0 +1,225 @@
+import warnings
+
+import pytest
+import numpy as np
+from numpy.testing import assert_equal
+import scipy as sp
+from scipy.sparse import dok_array, dok_matrix
+
+
+pytestmark = pytest.mark.thread_unsafe
+
+
+@pytest.fixture
+def d():
+    return {(0, 1): 1, (0, 2): 2}
+
+@pytest.fixture
+def A():
+    return np.array([[0, 1, 2], [0, 0, 0], [0, 0, 0]])
+
+@pytest.fixture(params=[dok_array, dok_matrix])
+def Asp(request):
+    A = request.param((3, 3))
+    A[(0, 1)] = 1
+    A[(0, 2)] = 2
+    yield A
+
+# Note: __iter__ and comparison dunders act like ndarrays for DOK, not dict.
+# Dunders reversed, or, ror, ior work as dict for dok_matrix, raise for dok_array
+# All other dict methods on DOK format act like dict methods (with extra checks).
+
+# Start of tests
+################
+def test_dict_methods_covered(d, Asp):
+    d_methods = set(dir(d)) - {"__class_getitem__"}
+    asp_methods = set(dir(Asp))
+    assert d_methods < asp_methods
+
+def test_clear(d, Asp):
+    assert d.items() == Asp.items()
+    d.clear()
+    Asp.clear()
+    assert d.items() == Asp.items()
+
+def test_copy(d, Asp):
+    assert d.items() == Asp.items()
+    dd = d.copy()
+    asp = Asp.copy()
+    assert dd.items() == asp.items()
+    assert asp.items() == Asp.items()
+    asp[(0, 1)] = 3
+    assert Asp[(0, 1)] == 1
+
+def test_fromkeys_default():
+    # test with default value
+    edges = [(0, 2), (1, 0), (2, 1)]
+    Xdok = dok_array.fromkeys(edges)
+    X = [[0, 0, 1], [1, 0, 0], [0, 1, 0]]
+    assert_equal(Xdok.toarray(), X)
+
+def test_fromkeys_positional():
+    # test with positional value
+    edges = [(0, 2), (1, 0), (2, 1)]
+    Xdok = dok_array.fromkeys(edges, -1)
+    X = [[0, 0, -1], [-1, 0, 0], [0, -1, 0]]
+    assert_equal(Xdok.toarray(), X)
+
+def test_fromkeys_iterator():
+    it = ((a, a % 2) for a in range(4))
+    Xdok = dok_array.fromkeys(it)
+    X = [[1, 0], [0, 1], [1, 0], [0, 1]]
+    assert_equal(Xdok.toarray(), X)
+
+def test_get(d, Asp):
+    assert Asp.get((0, 1)) == d.get((0, 1))
+    assert Asp.get((0, 0), 99) == d.get((0, 0), 99)
+    with pytest.raises(IndexError, match="out of bounds"):
+        Asp.get((0, 4), 99)
+
+def test_items(d, Asp):
+    assert Asp.items() == d.items()
+
+def test_keys(d, Asp):
+    assert Asp.keys() == d.keys()
+
+def test_pop(d, Asp):
+    assert d.pop((0, 1)) == 1
+    assert Asp.pop((0, 1)) == 1
+    assert d.items() == Asp.items()
+
+    assert Asp.pop((22, 21), None) is None
+    assert Asp.pop((22, 21), "other") == "other"
+    with pytest.raises(KeyError, match="(22, 21)"):
+        Asp.pop((22, 21))
+    msg = "got some positional-only arguments passed as keyword arguments: 'default'"
+    with pytest.raises(TypeError, match=msg):
+        Asp.pop((22, 21), default=5)
+
+def test_popitem(d, Asp):
+    assert d.popitem() == Asp.popitem()
+    assert d.items() == Asp.items()
+
+def test_setdefault(d, Asp):
+    assert Asp.setdefault((0, 1), 4) == 1
+    assert Asp.setdefault((2, 2), 4) == 4
+    d.setdefault((0, 1), 4)
+    d.setdefault((2, 2), 4)
+    assert d.items() == Asp.items()
+
+def test_update(d, Asp):
+    for input in [Asp, Asp._dict, Asp._dict.items()]:
+        Bsp = dok_array(Asp.shape)
+        Bsp.update(input)
+        assert_equal(Bsp.toarray(), Asp.toarray())
+
+    with pytest.raises(ValueError, match="Inexact indices .* not allowed"):
+        Asp.update(np.zeros((2,2)))
+    with pytest.raises(IndexError, match="length needs to match self.shape"):
+        Asp.update({(3, 2, 1, 0): 1.2})
+    with pytest.raises(IndexError, match="integer keys required"):
+        Asp.update({(0.2, 1): 1.2})
+    with pytest.raises(IndexError, match="negative index"):
+        Asp.update({(0, -1): 1.2})
+    with pytest.raises(IndexError, match="index .* is too large"):
+        Asp.update({(0, 3): 1.2})
+
+def test_values(d, Asp):
+    # Note: dict.values are strange: d={1: 1}; d.values() == d.values() is False
+    # Using list(d.values()) makes them comparable.
+    assert list(Asp.values()) == list(d.values())
+
+def test_dunder_getitem(d, Asp):
+    assert Asp[(0, 1)] == d[(0, 1)]
+
+def test_dunder_setitem(d, Asp):
+    Asp[(1, 1)] = 5
+    d[(1, 1)] = 5
+    assert d.items() == Asp.items()
+
+def test_dunder_delitem(d, Asp):
+    del Asp[(0, 1)]
+    del d[(0, 1)]
+    assert d.items() == Asp.items()
+
+def test_dunder_contains(d, Asp):
+    assert ((0, 1) in d) == ((0, 1) in Asp)
+    assert ((0, 0) in d) == ((0, 0) in Asp)
+
+def test_dunder_len(d, Asp):
+    assert len(d) == len(Asp)
+
+# Note: dunders reversed, or, ror, ior work as dict for dok_matrix, raise for dok_array
+def test_dunder_reversed(d, Asp):
+    if isinstance(Asp, dok_array):
+        with pytest.raises(TypeError):
+            list(reversed(Asp))
+    else:
+        assert list(reversed(Asp)) == list(reversed(d))
+
+def test_dunder_ior(d, Asp):
+    if isinstance(Asp, dok_array):
+        with pytest.raises(TypeError):
+            Asp |= Asp
+    else:
+        dd = {(0, 0): 5}
+        Asp |= dd
+        assert Asp[(0, 0)] == 5
+        d |= dd
+        assert d.items() == Asp.items()
+        dd |= Asp
+        assert dd.items() == Asp.items()
+
+def test_dunder_or(d, Asp):
+    if isinstance(Asp, dok_array):
+        with pytest.raises(TypeError):
+            Asp | Asp
+    else:
+        assert d | d == Asp | d
+        assert d | d == Asp | Asp
+
+def test_dunder_ror(d, Asp):
+    if isinstance(Asp, dok_array):
+        with pytest.raises(TypeError):
+            Asp | Asp
+        with pytest.raises(TypeError):
+            d | Asp
+    else:
+        assert Asp.__ror__(d) == Asp.__ror__(Asp)
+        assert d.__ror__(d) == Asp.__ror__(d)
+        assert d | Asp
+
+# Note: comparison dunders, e.g. ==, >=, etc follow np.array not dict
+def test_dunder_eq(A, Asp):
+    with warnings.catch_warnings():
+        warnings.simplefilter("ignore", sp.sparse.SparseEfficiencyWarning)
+        assert (Asp == Asp).toarray().all()
+        assert (A == Asp).all()
+
+def test_dunder_ne(A, Asp):
+    assert not (Asp != Asp).toarray().any()
+    assert not (A != Asp).any()
+
+def test_dunder_lt(A, Asp):
+    assert not (Asp < Asp).toarray().any()
+    assert not (A < Asp).any()
+
+def test_dunder_gt(A, Asp):
+    assert not (Asp > Asp).toarray().any()
+    assert not (A > Asp).any()
+
+def test_dunder_le(A, Asp):
+    with warnings.catch_warnings():
+        warnings.simplefilter("ignore", sp.sparse.SparseEfficiencyWarning)
+        assert (Asp <= Asp).toarray().all()
+        assert (A <= Asp).all()
+
+def test_dunder_ge(A, Asp):
+    with warnings.catch_warnings():
+        warnings.simplefilter("ignore", sp.sparse.SparseEfficiencyWarning)
+        assert (Asp >= Asp).toarray().all()
+        assert (A >= Asp).all()
+
+# Note: iter dunder follows np.array not dict
+def test_dunder_iter(A, Asp):
+    assert all((a == asp).all() for a, asp in zip(A, Asp))
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_extract.py b/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_extract.py
new file mode 100644
index 0000000000000000000000000000000000000000..cfb443890f9cae4955bdec9264d6f1b9afb5007b
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_extract.py
@@ -0,0 +1,61 @@
+"""test sparse matrix construction functions"""
+
+import pytest
+
+from numpy.testing import assert_equal
+from scipy.sparse import csr_matrix, csr_array, sparray
+
+import numpy as np
+from scipy.sparse import _extract
+
+
+class TestExtract:
+    def setup_method(self):
+        self.cases = [
+            csr_array([[1,2]]),
+            csr_array([[1,0]]),
+            csr_array([[0,0]]),
+            csr_array([[1],[2]]),
+            csr_array([[1],[0]]),
+            csr_array([[0],[0]]),
+            csr_array([[1,2],[3,4]]),
+            csr_array([[0,1],[0,0]]),
+            csr_array([[0,0],[1,0]]),
+            csr_array([[0,0],[0,0]]),
+            csr_array([[1,2,0,0,3],[4,5,0,6,7],[0,0,8,9,0]]),
+            csr_array([[1,2,0,0,3],[4,5,0,6,7],[0,0,8,9,0]]).T,
+        ]
+
+    def test_find(self):
+        for A in self.cases:
+            I,J,V = _extract.find(A)
+            B = csr_array((V,(I,J)), shape=A.shape)
+            assert_equal(A.toarray(), B.toarray())
+
+    def test_tril(self):
+        for A in self.cases:
+            B = A.toarray()
+            for k in [-3,-2,-1,0,1,2,3]:
+                assert_equal(_extract.tril(A,k=k).toarray(), np.tril(B,k=k))
+
+    def test_triu(self):
+        for A in self.cases:
+            B = A.toarray()
+            for k in [-3,-2,-1,0,1,2,3]:
+                assert_equal(_extract.triu(A,k=k).toarray(), np.triu(B,k=k))
+
+    def test_array_vs_matrix(self):
+        for A in self.cases:
+            assert isinstance(_extract.tril(A), sparray)
+            assert isinstance(_extract.triu(A), sparray)
+            M = csr_matrix(A)
+            assert not isinstance(_extract.tril(M), sparray)
+            assert not isinstance(_extract.triu(M), sparray)
+
+
+def test_deprecated_warnings_output_defaults_switch_from_spmatrix():
+    A = np.array([[1, 2], [3, 0]])
+    with pytest.deprecated_call(match=".*switching.*sparse array int"):
+        _extract.tril(A)
+    with pytest.deprecated_call(match=".*switching.*sparse array int"):
+        _extract.triu(A)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_indexing1d.py b/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_indexing1d.py
new file mode 100644
index 0000000000000000000000000000000000000000..6b41adc59df59594587b92179e905ebc5bfd9510
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_indexing1d.py
@@ -0,0 +1,611 @@
+import contextlib
+import warnings
+
+import pytest
+import numpy as np
+from numpy.testing import assert_allclose, assert_equal
+
+from scipy.sparse import csr_array, dok_array, SparseEfficiencyWarning
+from .test_arithmetic1d import toarray
+
+
+formats_for_index1d = [csr_array, dok_array]
+
+
+@contextlib.contextmanager
+def check_remains_sorted(X):
+    """Checks that sorted indices property is retained through an operation"""
+    yield
+    if not hasattr(X, 'has_sorted_indices') or not X.has_sorted_indices:
+        return
+    indices = X.indices.copy()
+    X.has_sorted_indices = False
+    X.sort_indices()
+    assert_equal(indices, X.indices, 'Expected sorted indices, found unsorted')
+
+
+@pytest.mark.parametrize("spcreator", formats_for_index1d)
+class TestGetSet1D:
+    def test_None_index(self, spcreator):
+        D = np.array([4, 3, 0])
+        A = spcreator(D)
+
+        N = D.shape[0]
+        for j in range(-N, N):
+            assert_equal(A[j, None].toarray(), D[j, None])
+            assert_equal(A[None, j].toarray(), D[None, j])
+            assert_equal(A[None, None, j].toarray(), D[None, None, j])
+
+    def test_getitem_shape(self, spcreator):
+        A = spcreator(np.arange(3 * 4).reshape(3, 4))
+        assert A[1, 2].ndim == 0
+        assert A[1, 2:3].shape == (1,)
+        assert A[None, 1, 2:3].shape == (1, 1)
+        assert A[None, 1, 2].shape == (1,)
+        assert A[None, 1, 2, None].shape == (1, 1)
+
+        # see gh-22458
+        assert A[None, 1].shape == (1, 4)
+        assert A[1, None].shape == (1, 4)
+        assert A[None, 1, :].shape == (1, 4)
+        assert A[1, None, :].shape == (1, 4)
+        assert A[1, :, None].shape == (4, 1)
+
+        # output is >2D
+        if A.format == "coo":
+            assert A[None, 2, 1, None, None].shape == (1, 1, 1)
+            assert A[None, 0:2, None, 1].shape == (1,2,1)
+            assert A[0:1, 1:, None].shape == (1,3,1)
+            assert A[1:, 1, None, None].shape == (3,1,1)
+
+    def test_getelement(self, spcreator):
+        D = np.array([4, 3, 0])
+        A = spcreator(D)
+
+        N = D.shape[0]
+        for j in range(-N, N):
+            assert_equal(A[j], D[j])
+
+        for ij in [3, -4]:
+            with pytest.raises(IndexError, match='index (.*) out of (range|bounds)'):
+                A.__getitem__(ij)
+
+        # single element tuples unwrapped
+        assert A[(0,)] == 4
+
+        with pytest.raises(IndexError, match='index (.*) out of (range|bounds)'):
+            A.__getitem__((4,))
+
+    @pytest.mark.parametrize(
+        "scalar_container",
+        [lambda x: csr_array(np.array([[x]])), np.array, lambda x: x],
+        ids=["sparse", "dense", "scalar"]
+    )
+    def test_setelement(self, spcreator, scalar_container):
+        dtype = np.float64
+        A = spcreator((12,), dtype=dtype)
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore",
+                "Changing the sparsity structure of .* is expensive",
+                SparseEfficiencyWarning,
+            )
+            A[0] = scalar_container(dtype(0))
+            A[1] = scalar_container(dtype(3))
+            A[8] = scalar_container(dtype(9.0))
+            A[-2] = scalar_container(dtype(7))
+            A[5] = scalar_container(9)
+
+            A[-9,] = scalar_container(dtype(8))
+            A[1,] = scalar_container(dtype(5))  # overwrite using 1-tuple index
+
+            for ij in [13, -14, (13,), (14,)]:
+                with pytest.raises(IndexError, match='out of (range|bounds)'):
+                    A.__setitem__(ij, 123.0)
+
+
+@pytest.mark.parametrize("spcreator", formats_for_index1d)
+class TestSlicingAndFancy1D:
+    #######################
+    #  Int-like Array Index
+    #######################
+    def test_get_array_index(self, spcreator):
+        D = np.array([4, 3, 0])
+        A = spcreator(D)
+
+        assert_equal(A[()].toarray(), D[()])
+        for ij in [(0, 3), (3,)]:
+            with pytest.raises(IndexError, match='out of (range|bounds)|many indices'):
+                A.__getitem__(ij)
+
+    def test_set_array_index(self, spcreator):
+        dtype = np.float64
+        A = spcreator((12,), dtype=dtype)
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore",
+                "Changing the sparsity structure of .* is expensive",
+                SparseEfficiencyWarning,
+            )
+            A[np.array(6)] = dtype(4.0)  # scalar index
+            A[np.array(6)] = dtype(2.0)  # overwrite with scalar index
+            assert_equal(A.toarray(), [0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0])
+
+            for ij in [(13,), (-14,)]:
+                with pytest.raises(IndexError, match='index .* out of (range|bounds)'):
+                    A.__setitem__(ij, 123.0)
+
+            for v in [(), (0, 3), [1, 2, 3], np.array([1, 2, 3])]:
+                msg = 'Trying to assign a sequence to an item'
+                with pytest.raises(ValueError, match=msg):
+                    A.__setitem__(0, v)
+
+    ####################
+    #  1d Slice as index
+    ####################
+    def test_dtype_preservation(self, spcreator):
+        assert_equal(spcreator((10,), dtype=np.int16)[1:5].dtype, np.int16)
+        assert_equal(spcreator((6,), dtype=np.int32)[0:0:2].dtype, np.int32)
+        assert_equal(spcreator((6,), dtype=np.int64)[:].dtype, np.int64)
+
+    def test_get_1d_slice(self, spcreator):
+        B = np.arange(50.)
+        A = spcreator(B)
+        assert_equal(B[:], A[:].toarray())
+        assert_equal(B[2:5], A[2:5].toarray())
+
+        C = np.array([4, 0, 6, 0, 0, 0, 0, 0, 1])
+        D = spcreator(C)
+        assert_equal(C[1:3], D[1:3].toarray())
+
+        # Now test slicing when a row contains only zeros
+        E = np.array([0, 0, 0, 0, 0])
+        F = spcreator(E)
+        assert_equal(E[1:3], F[1:3].toarray())
+        assert_equal(E[-2:], F[-2:].toarray())
+        assert_equal(E[:], F[:].toarray())
+        assert_equal(E[slice(None)], F[slice(None)].toarray())
+
+    def test_slicing_idx_slice(self, spcreator):
+        B = np.arange(50)
+        A = spcreator(B)
+
+        # [i]
+        assert_equal(A[2], B[2])
+        assert_equal(A[-1], B[-1])
+        assert_equal(A[np.array(-2)], B[-2])
+
+        # [1:2]
+        assert_equal(A[:].toarray(), B[:])
+        assert_equal(A[5:-2].toarray(), B[5:-2])
+        assert_equal(A[5:12:3].toarray(), B[5:12:3])
+
+        # int8 slice
+        s = slice(np.int8(2), np.int8(4), None)
+        assert_equal(A[s].toarray(), B[2:4])
+
+        # np.s_
+        s_ = np.s_
+        slices = [s_[:2], s_[1:2], s_[3:], s_[3::2],
+                  s_[15:20], s_[3:2],
+                  s_[8:3:-1], s_[4::-2], s_[:5:-1],
+                  0, 1, s_[:], s_[1:5], -1, -2, -5,
+                  np.array(-1), np.int8(-3)]
+
+        for j, a in enumerate(slices):
+            x = A[a]
+            y = B[a]
+            if y.shape == ():
+                assert_equal(x, y, repr(a))
+            else:
+                if x.size == 0 and y.size == 0:
+                    pass
+                else:
+                    assert_equal(x.toarray(), y, repr(a))
+
+    def test_ellipsis_1d_slicing(self, spcreator):
+        B = np.arange(50)
+        A = spcreator(B)
+        assert_equal(A[...].toarray(), B[...])
+        assert_equal(A[...,].toarray(), B[...,])
+
+    ##########################
+    #  Assignment with Slicing
+    ##########################
+    def test_slice_scalar_assign(self, spcreator):
+        A = spcreator((5,))
+        B = np.zeros((5,))
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore",
+                "Changing the sparsity structure of .* is expensive",
+                SparseEfficiencyWarning,
+            )
+            for C in [A, B]:
+                C[0:1] = 1
+                C[2:0] = 4
+                C[2:3] = 9
+                C[3:] = 1
+                C[3::-1] = 9
+        assert_equal(A.toarray(), B)
+
+    def test_slice_assign_2(self, spcreator):
+        shape = (10,)
+
+        for idx in [slice(3), slice(None, 10, 4), slice(5, -2)]:
+            A = spcreator(shape)
+            with warnings.catch_warnings():
+                warnings.filterwarnings(
+                    "ignore",
+                    "Changing the sparsity structure of .* is expensive",
+                    SparseEfficiencyWarning,
+                )
+                A[idx] = 1
+            B = np.zeros(shape)
+            B[idx] = 1
+            msg = f"idx={idx!r}"
+            assert_allclose(A.toarray(), B, err_msg=msg)
+
+    def test_self_self_assignment(self, spcreator):
+        # Tests whether a row of one lil_matrix can be assigned to another.
+        B = spcreator((5,))
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore",
+                "Changing the sparsity structure of .* is expensive",
+                SparseEfficiencyWarning,
+            )
+            B[0] = 2
+            B[1] = 0
+            B[2] = 3
+            B[3] = 10
+
+            A = B / 10
+            B[:] = A[:]
+            assert_equal(A[:].toarray(), B[:].toarray())
+
+            A = B / 10
+            B[:] = A[:1]
+            assert_equal(np.zeros((5,)) + A[0], B.toarray())
+
+            A = B / 10
+            B[:-1] = A[1:]
+            assert_equal(A[1:].toarray(), B[:-1].toarray())
+
+    def test_slice_assignment(self, spcreator):
+        B = spcreator((4,))
+        expected = np.array([10, 0, 14, 0])
+        block = [2, 1]
+
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore",
+                "Changing the sparsity structure of .* is expensive",
+                SparseEfficiencyWarning,
+            )
+            B[0] = 5
+            B[2] = 7
+            B[:] = B + B
+            assert_equal(B.toarray(), expected)
+
+            B[:2] = csr_array(block)
+            assert_equal(B.toarray()[:2], block)
+
+    def test_set_slice(self, spcreator):
+        A = spcreator((5,))
+        B = np.zeros(5, float)
+        s_ = np.s_
+        slices = [s_[:2], s_[1:2], s_[3:], s_[3::2],
+                  s_[8:3:-1], s_[4::-2], s_[:5:-1],
+                  0, 1, s_[:], s_[1:5], -1, -2, -5,
+                  np.array(-1), np.int8(-3)]
+
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore",
+                "Changing the sparsity structure of .* is expensive",
+                SparseEfficiencyWarning,
+            )
+            for j, a in enumerate(slices):
+                A[a] = j
+                B[a] = j
+                assert_equal(A.toarray(), B, repr(a))
+
+            A[1:10:2] = range(1, 5, 2)
+            B[1:10:2] = range(1, 5, 2)
+            assert_equal(A.toarray(), B)
+
+        # The next commands should raise exceptions
+        toobig = list(range(100))
+        with pytest.raises(ValueError, match='Trying to assign a sequence to an item'):
+            A.__setitem__(0, toobig)
+        with pytest.raises(ValueError, match='could not be broadcast together'):
+            A.__setitem__(slice(None), toobig)
+
+    def test_assign_empty(self, spcreator):
+        A = spcreator(np.ones(3))
+        B = spcreator((2,))
+        A[:2] = B
+        assert_equal(A.toarray(), [0, 0, 1])
+
+    ####################
+    #  1d Fancy Indexing
+    ####################
+    def test_dtype_preservation_empty_index(self, spcreator):
+        A = spcreator((2,), dtype=np.int16)
+        assert_equal(A[[False, False]].dtype, np.int16)
+        assert_equal(A[[]].dtype, np.int16)
+
+    def test_bad_index(self, spcreator):
+        A = spcreator(np.zeros(5))
+        with pytest.raises(IndexError, match='Index dimension must be 1 or 2'):
+            A.__getitem__("foo")
+        with pytest.raises(IndexError, match='tuple index out of range'):
+            A.__getitem__((2, "foo"))
+
+    def test_fancy_indexing_2darray(self, spcreator):
+        B = np.arange(50).reshape((5, 10))
+        A = spcreator(B)
+
+        # [i]
+        assert_equal(A[[1, 3]].toarray(), B[[1, 3]])
+
+        # [i,[1,2]]
+        assert_equal(A[3, [1, 3]].toarray(), B[3, [1, 3]])
+        assert_equal(A[-1, [2, -5]].toarray(), B[-1, [2, -5]])
+        assert_equal(A[np.array(-1), [2, -5]].toarray(), B[-1, [2, -5]])
+        assert_equal(A[-1, np.array([2, -5])].toarray(), B[-1, [2, -5]])
+        assert_equal(A[np.array(-1), np.array([2, -5])].toarray(), B[-1, [2, -5]])
+
+        # [1:2,[1,2]]
+        assert_equal(A[:, [2, 8, 3, -1]].toarray(), B[:, [2, 8, 3, -1]])
+        assert_equal(A[3:4, [9]].toarray(), B[3:4, [9]])
+        assert_equal(A[1:4, [-1, -5]].toarray(), B[1:4, [-1, -5]])
+        assert_equal(A[1:4, np.array([-1, -5])].toarray(), B[1:4, [-1, -5]])
+
+        # [[1,2],j]
+        assert_equal(A[[1, 3], 3].toarray(), B[[1, 3], 3])
+        assert_equal(A[[2, -5], -4].toarray(), B[[2, -5], -4])
+        assert_equal(A[np.array([2, -5]), -4].toarray(), B[[2, -5], -4])
+        assert_equal(A[[2, -5], np.array(-4)].toarray(), B[[2, -5], -4])
+        assert_equal(A[np.array([2, -5]), np.array(-4)].toarray(), B[[2, -5], -4])
+
+        # [[1,2],1:2]
+        assert_equal(A[[1, 3], :].toarray(), B[[1, 3], :])
+        assert_equal(A[[2, -5], 8:-1].toarray(), B[[2, -5], 8:-1])
+        assert_equal(A[np.array([2, -5]), 8:-1].toarray(), B[[2, -5], 8:-1])
+
+        # [[1,2],[1,2]]
+        assert_equal(toarray(A[[1, 3], [2, 4]]), B[[1, 3], [2, 4]])
+        assert_equal(toarray(A[[-1, -3], [2, -4]]), B[[-1, -3], [2, -4]])
+        assert_equal(
+            toarray(A[np.array([-1, -3]), [2, -4]]), B[[-1, -3], [2, -4]]
+        )
+        assert_equal(
+            toarray(A[[-1, -3], np.array([2, -4])]), B[[-1, -3], [2, -4]]
+        )
+        assert_equal(
+            toarray(A[np.array([-1, -3]), np.array([2, -4])]), B[[-1, -3], [2, -4]]
+        )
+
+        # [[[1],[2]],[1,2]]
+        assert_equal(A[[[1], [3]], [2, 4]].toarray(), B[[[1], [3]], [2, 4]])
+        assert_equal(
+            A[[[-1], [-3], [-2]], [2, -4]].toarray(),
+            B[[[-1], [-3], [-2]], [2, -4]]
+        )
+        assert_equal(
+            A[np.array([[-1], [-3], [-2]]), [2, -4]].toarray(),
+            B[[[-1], [-3], [-2]], [2, -4]]
+        )
+        assert_equal(
+            A[[[-1], [-3], [-2]], np.array([2, -4])].toarray(),
+            B[[[-1], [-3], [-2]], [2, -4]]
+        )
+        assert_equal(
+            A[np.array([[-1], [-3], [-2]]), np.array([2, -4])].toarray(),
+            B[[[-1], [-3], [-2]], [2, -4]]
+        )
+
+        # [[1,2]]
+        assert_equal(A[[1, 3]].toarray(), B[[1, 3]])
+        assert_equal(A[[-1, -3]].toarray(), B[[-1, -3]])
+        assert_equal(A[np.array([-1, -3])].toarray(), B[[-1, -3]])
+
+        # [[1,2],:][:,[1,2]]
+        assert_equal(
+            A[[1, 3], :][:, [2, 4]].toarray(), B[[1, 3], :][:, [2, 4]]
+        )
+        assert_equal(
+            A[[-1, -3], :][:, [2, -4]].toarray(), B[[-1, -3], :][:, [2, -4]]
+        )
+        assert_equal(
+            A[np.array([-1, -3]), :][:, np.array([2, -4])].toarray(),
+            B[[-1, -3], :][:, [2, -4]]
+        )
+
+        # [:,[1,2]][[1,2],:]
+        assert_equal(
+            A[:, [1, 3]][[2, 4], :].toarray(), B[:, [1, 3]][[2, 4], :]
+        )
+        assert_equal(
+            A[:, [-1, -3]][[2, -4], :].toarray(), B[:, [-1, -3]][[2, -4], :]
+        )
+        assert_equal(
+            A[:, np.array([-1, -3])][np.array([2, -4]), :].toarray(),
+            B[:, [-1, -3]][[2, -4], :]
+        )
+
+    def test_fancy_indexing(self, spcreator):
+        B = np.arange(50)
+        A = spcreator(B)
+
+        # [i]
+        assert_equal(A[[3]].toarray(), B[[3]])
+
+        # [np.array]
+        assert_equal(A[[1, 3]].toarray(), B[[1, 3]])
+        assert_equal(A[[2, -5]].toarray(), B[[2, -5]])
+        assert_equal(A[np.array(-1)], B[-1])
+        assert_equal(A[np.array([-1, 2])].toarray(), B[[-1, 2]])
+        assert_equal(A[np.array(5)], B[np.array(5)])
+
+        # [[[1],[2]]]
+        ind = np.array([[1], [3]])
+        assert_equal(A[ind].toarray(), B[ind])
+        ind = np.array([[-1], [-3], [-2]])
+        assert_equal(A[ind].toarray(), B[ind])
+
+        # [[1, 2]]
+        assert_equal(A[[1, 3]].toarray(), B[[1, 3]])
+        assert_equal(A[[-1, -3]].toarray(), B[[-1, -3]])
+        assert_equal(A[np.array([-1, -3])].toarray(), B[[-1, -3]])
+
+        # [[1, 2]][[1, 2]]
+        assert_equal(A[[1, 5, 2, 8]][[1, 3]].toarray(),
+                     B[[1, 5, 2, 8]][[1, 3]])
+        assert_equal(A[[-1, -5, 2, 8]][[1, -4]].toarray(),
+                     B[[-1, -5, 2, 8]][[1, -4]])
+
+    def test_fancy_indexing_boolean(self, spcreator):
+        np.random.seed(1234)  # make runs repeatable
+
+        B = np.arange(50)
+        A = spcreator(B)
+
+        I = np.array(np.random.randint(0, 2, size=50), dtype=bool)
+
+        assert_equal(toarray(A[I]), B[I])
+        assert_equal(toarray(A[B > 9]), B[B > 9])
+
+        Z1 = np.zeros(51, dtype=bool)
+        Z2 = np.zeros(51, dtype=bool)
+        Z2[-1] = True
+        Z3 = np.zeros(51, dtype=bool)
+        Z3[0] = True
+
+        msg = 'bool index .* has shape|boolean index did not match'
+        with pytest.raises(IndexError, match=msg):
+            A.__getitem__(Z1)
+        with pytest.raises(IndexError, match=msg):
+            A.__getitem__(Z2)
+        with pytest.raises(IndexError, match=msg):
+            A.__getitem__(Z3)
+
+    def test_fancy_indexing_sparse_boolean(self, spcreator):
+        np.random.seed(1234)  # make runs repeatable
+
+        B = np.arange(20)
+        A = spcreator(B)
+
+        X = np.array(np.random.randint(0, 2, size=20), dtype=bool)
+        Xsp = csr_array(X)
+
+        assert_equal(toarray(A[Xsp]), B[X])
+        assert_equal(toarray(A[A > 9]), B[B > 9])
+
+        Y = np.array(np.random.randint(0, 2, size=60), dtype=bool)
+
+        Ysp = csr_array(Y)
+
+        with pytest.raises(IndexError, match='bool index .* has shape|only integers'):
+            A.__getitem__(Ysp)
+        with pytest.raises(IndexError, match='tuple index out of range|only integers'):
+            A.__getitem__((Xsp, 1))
+
+    def test_fancy_indexing_seq_assign(self, spcreator):
+        mat = spcreator(np.array([1, 0]))
+        with pytest.raises(ValueError, match='Trying to assign a sequence to an item'):
+            mat.__setitem__(0, np.array([1, 2]))
+
+    def test_fancy_indexing_empty(self, spcreator):
+        B = np.arange(50)
+        B[3:9] = 0
+        B[30] = 0
+        A = spcreator(B)
+
+        K = np.array([False] * 50)
+        assert_equal(toarray(A[K]), B[K])
+        K = np.array([], dtype=int)
+        assert_equal(toarray(A[K]), B[K])
+        J = np.array([0, 1, 2, 3, 4], dtype=int)
+        assert_equal(toarray(A[J]), B[J])
+
+    ############################
+    #  1d Fancy Index Assignment
+    ############################
+    def test_bad_index_assign(self, spcreator):
+        A = spcreator(np.zeros(5))
+        msg = 'Index dimension must be 1 or 2|only integers'
+        with pytest.raises((IndexError, ValueError, TypeError), match=msg):
+            A.__setitem__("foo", 2)
+
+    def test_fancy_indexing_set(self, spcreator):
+        M = (5,)
+
+        # [1:2]
+        for j in [[2, 3, 4], slice(None, 10, 4), np.arange(3),
+                     slice(5, -2), slice(2, 5)]:
+            A = spcreator(M)
+            B = np.zeros(M)
+            with warnings.catch_warnings():
+                warnings.filterwarnings(
+                    "ignore",
+                    "Changing the sparsity structure of .* is expensive",
+                    SparseEfficiencyWarning,
+                )
+                B[j] = 1
+                with check_remains_sorted(A):
+                    A[j] = 1
+            assert_allclose(A.toarray(), B)
+
+    def test_sequence_assignment(self, spcreator):
+        A = spcreator((4,))
+        B = spcreator((3,))
+
+        i0 = [0, 1, 2]
+        i1 = (0, 1, 2)
+        i2 = np.array(i0)
+
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore",
+                "Changing the sparsity structure of .* is expensive",
+                SparseEfficiencyWarning,
+            )
+            with check_remains_sorted(A):
+                A[i0] = B[i0]
+                msg = "Too many indices for array|tuple index out of range"
+                with pytest.raises(IndexError, match=msg):
+                    B.__getitem__(i1)
+                A[i2] = B[i2]
+            assert_equal(A[:3].toarray(), B.toarray())
+            assert A.shape == (4,)
+
+            # slice
+            A = spcreator((4,))
+            with check_remains_sorted(A):
+                A[1:3] = [10, 20]
+            assert_equal(A.toarray(), [0, 10, 20, 0])
+
+            # array
+            A = spcreator((4,))
+            B = np.zeros(4)
+            with check_remains_sorted(A):
+                for C in [A, B]:
+                    C[[0, 1, 2]] = [4, 5, 6]
+            assert_equal(A.toarray(), B)
+
+    def test_fancy_assign_empty(self, spcreator):
+        B = np.arange(50)
+        B[2] = 0
+        B[[3, 6]] = 0
+        A = spcreator(B)
+
+        K = np.array([False] * 50)
+        A[K] = 42
+        assert_equal(A.toarray(), B)
+
+        K = np.array([], dtype=int)
+        A[K] = 42
+        assert_equal(A.toarray(), B)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_matrix_io.py b/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_matrix_io.py
new file mode 100644
index 0000000000000000000000000000000000000000..50d97a412125dd59c3fc2717037fa22da72505c6
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_matrix_io.py
@@ -0,0 +1,116 @@
+import os
+import numpy as np
+import tempfile
+
+import pytest
+from pytest import raises as assert_raises
+from numpy.testing import assert_equal, assert_
+
+from scipy.sparse import (sparray, csr_array, coo_array, save_npz, load_npz,
+                          csc_matrix, csr_matrix, bsr_matrix, dia_matrix,
+                          coo_matrix, dok_matrix)
+
+
+DATA_DIR = os.path.join(os.path.dirname(__file__), 'data')
+
+
+def _save_and_load(matrix):
+    fd, tmpfile = tempfile.mkstemp(suffix='.npz')
+    os.close(fd)
+    try:
+        save_npz(tmpfile, matrix)
+        loaded_matrix = load_npz(tmpfile)
+    finally:
+        os.remove(tmpfile)
+    return loaded_matrix
+
+def _check_save_and_load(dense_matrix):
+    for matrix_class in [csc_matrix, csr_matrix, bsr_matrix, dia_matrix, coo_matrix]:
+        matrix = matrix_class(dense_matrix)
+        loaded_matrix = _save_and_load(matrix)
+        assert_(type(loaded_matrix) is matrix_class)
+        assert_(loaded_matrix.shape == dense_matrix.shape)
+        assert_(loaded_matrix.dtype == dense_matrix.dtype)
+        assert_equal(loaded_matrix.toarray(), dense_matrix)
+
+def test_save_and_load_random():
+    N = 10
+    np.random.seed(0)
+    dense_matrix = np.random.random((N, N))
+    dense_matrix[dense_matrix > 0.7] = 0
+    _check_save_and_load(dense_matrix)
+
+def test_save_and_load_empty():
+    dense_matrix = np.zeros((4,6))
+    _check_save_and_load(dense_matrix)
+
+def test_save_and_load_one_entry():
+    dense_matrix = np.zeros((4,6))
+    dense_matrix[1,2] = 1
+    _check_save_and_load(dense_matrix)
+
+def test_sparray_vs_spmatrix():
+    #save/load matrix
+    fd, tmpfile = tempfile.mkstemp(suffix='.npz')
+    os.close(fd)
+    try:
+        save_npz(tmpfile, csr_matrix([[1.2, 0, 0.9], [0, 0.3, 0]]))
+        loaded_matrix = load_npz(tmpfile)
+    finally:
+        os.remove(tmpfile)
+
+    #save/load array
+    fd, tmpfile = tempfile.mkstemp(suffix='.npz')
+    os.close(fd)
+    try:
+        save_npz(tmpfile, csr_array([[1.2, 0, 0.9], [0, 0.3, 0]]))
+        loaded_array = load_npz(tmpfile)
+    finally:
+        os.remove(tmpfile)
+
+    assert not isinstance(loaded_matrix, sparray)
+    assert isinstance(loaded_array, sparray)
+    assert_(loaded_matrix.dtype == loaded_array.dtype)
+    assert_equal(loaded_matrix.toarray(), loaded_array.toarray())
+
+@pytest.mark.parametrize("value", [0, 1.2])
+@pytest.mark.parametrize("ndim", [1, 2, 3])
+def test_nd_coo_format(ndim, value):
+    A = coo_array([value]).reshape((1,) * ndim)
+
+    #save/load array
+    fd, tmpfile = tempfile.mkstemp(suffix='.npz')
+    os.close(fd)
+    try:
+        save_npz(tmpfile, A)
+        loaded_A = load_npz(tmpfile)
+    finally:
+        os.remove(tmpfile)
+
+    assert isinstance(loaded_A, coo_array)
+    assert_(loaded_A.shape == A.shape)
+    assert_equal(A.toarray(), loaded_A.toarray())
+
+def test_malicious_load():
+    class Executor:
+        def __reduce__(self):
+            return (assert_, (False, 'unexpected code execution'))
+
+    fd, tmpfile = tempfile.mkstemp(suffix='.npz')
+    os.close(fd)
+    try:
+        np.savez(tmpfile, format=Executor())
+
+        # Should raise a ValueError, not execute code
+        assert_raises(ValueError, load_npz, tmpfile)
+    finally:
+        os.remove(tmpfile)
+
+def test_implemented_error():
+    # Attempts to save an unsupported type and checks that an
+    # NotImplementedError is raised.
+
+    x = dok_matrix((2,3))
+    x[0,1] = 1
+
+    assert_raises(NotImplementedError, save_npz, 'x.npz', x)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_minmax1d.py b/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_minmax1d.py
new file mode 100644
index 0000000000000000000000000000000000000000..dca3f44fa485070805995c2f76c0c511123ce355
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_minmax1d.py
@@ -0,0 +1,128 @@
+"""Test of min-max 1D features of sparse array classes"""
+
+import pytest
+
+import numpy as np
+
+from numpy.testing import assert_equal, assert_array_equal
+
+from scipy.sparse import coo_array, csr_array, csc_array, bsr_array
+from scipy.sparse import coo_matrix, csr_matrix, csc_matrix, bsr_matrix
+from scipy.sparse._sputils import isscalarlike
+
+
+def toarray(a):
+    if isinstance(a, np.ndarray) or isscalarlike(a):
+        return a
+    return a.toarray()
+
+
+formats_for_minmax = [bsr_array, coo_array, csc_array, csr_array]
+formats_for_minmax_supporting_1d = [coo_array, csr_array]
+
+
+@pytest.mark.parametrize("spcreator", formats_for_minmax_supporting_1d)
+class Test_MinMaxMixin1D:
+    def test_minmax(self, spcreator):
+        D = np.arange(5)
+        X = spcreator(D)
+
+        assert_equal(X.min(), 0)
+        assert_equal(X.max(), 4)
+        assert_equal((-X).min(), -4)
+        assert_equal((-X).max(), 0)
+
+    def test_minmax_axis(self, spcreator):
+        D = np.arange(50)
+        X = spcreator(D)
+
+        for axis in [0, -1]:
+            assert_array_equal(
+                toarray(X.max(axis=axis)), D.max(axis=axis, keepdims=True)
+            )
+            assert_array_equal(
+                toarray(X.min(axis=axis)), D.min(axis=axis, keepdims=True)
+            )
+        for axis in [-2, 1]:
+            with pytest.raises(ValueError, match="axis out of range"):
+                X.min(axis=axis)
+            with pytest.raises(ValueError, match="axis out of range"):
+                X.max(axis=axis)
+
+    def test_numpy_minmax(self, spcreator):
+        dat = np.array([0, 1, 2])
+        datsp = spcreator(dat)
+        assert_array_equal(np.min(datsp), np.min(dat))
+        assert_array_equal(np.max(datsp), np.max(dat))
+
+
+    def test_argmax(self, spcreator):
+        D1 = np.array([-1, 5, 2, 3])
+        D2 = np.array([0, 0, -1, -2])
+        D3 = np.array([-1, -2, -3, -4])
+        D4 = np.array([1, 2, 3, 4])
+        D5 = np.array([1, 2, 0, 0])
+
+        for D in [D1, D2, D3, D4, D5]:
+            mat = spcreator(D)
+
+            assert_equal(mat.argmax(), np.argmax(D))
+            assert_equal(mat.argmin(), np.argmin(D))
+
+            assert_equal(mat.argmax(axis=0), np.argmax(D, axis=0))
+            assert_equal(mat.argmin(axis=0), np.argmin(D, axis=0))
+
+        D6 = np.empty((0,))
+
+        for axis in [None, 0]:
+            mat = spcreator(D6)
+            with pytest.raises(ValueError, match="to an empty matrix"):
+                mat.argmin(axis=axis)
+            with pytest.raises(ValueError, match="to an empty matrix"):
+                mat.argmax(axis=axis)
+
+
+@pytest.mark.parametrize("spcreator", formats_for_minmax)
+class Test_ShapeMinMax2DWithAxis:
+    def test_minmax(self, spcreator):
+        dat = np.array([[-1, 5, 0, 3], [0, 0, -1, -2], [0, 0, 1, 2]])
+        datsp = spcreator(dat)
+
+        for (spminmax, npminmax) in [
+            (datsp.min, np.min),
+            (datsp.max, np.max),
+            (datsp.nanmin, np.nanmin),
+            (datsp.nanmax, np.nanmax),
+        ]:
+            for ax, result_shape in [(0, (4,)), (1, (3,))]:
+                assert_equal(toarray(spminmax(axis=ax)), npminmax(dat, axis=ax))
+                assert_equal(spminmax(axis=ax).shape, result_shape)
+                assert spminmax(axis=ax).format == "coo"
+
+        for spminmax in [datsp.argmin, datsp.argmax]:
+            for ax in [0, 1]:
+                assert isinstance(spminmax(axis=ax), np.ndarray)
+
+        # verify spmatrix behavior
+        spmat_form = {
+            'coo': coo_matrix,
+            'csr': csr_matrix,
+            'csc': csc_matrix,
+            'bsr': bsr_matrix,
+        }
+        datspm = spmat_form[datsp.format](dat)
+
+        for spm, npm in [
+            (datspm.min, np.min),
+            (datspm.max, np.max),
+            (datspm.nanmin, np.nanmin),
+            (datspm.nanmax, np.nanmax),
+        ]:
+            for ax, result_shape in [(0, (1, 4)), (1, (3, 1))]:
+                assert_equal(toarray(spm(axis=ax)), npm(dat, axis=ax, keepdims=True))
+                assert_equal(spm(axis=ax).shape, result_shape)
+                assert spm(axis=ax).format == "coo"
+
+        for spminmax in [datspm.argmin, datspm.argmax]:
+            for ax in [0, 1]:
+                assert isinstance(spminmax(axis=ax), np.ndarray)
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_sparsetools.py b/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_sparsetools.py
new file mode 100644
index 0000000000000000000000000000000000000000..6ac2f2b0efd4de1d9b947dc0bc28b14881bc9db2
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_sparsetools.py
@@ -0,0 +1,340 @@
+import sys
+import os
+import gc
+import threading
+
+import numpy as np
+from numpy.testing import assert_equal, assert_, assert_allclose
+from scipy.sparse import (_sparsetools, coo_matrix, csr_matrix, csc_matrix,
+                          bsr_matrix, dia_matrix)
+from scipy.sparse._sputils import supported_dtypes
+from scipy._lib._testutils import check_free_memory
+
+import pytest
+from pytest import raises as assert_raises
+
+
+def int_to_int8(n):
+    """
+    Wrap an integer to the interval [-128, 127].
+    """
+    return (n + 128) % 256 - 128
+
+
+def test_exception():
+    assert_raises(MemoryError, _sparsetools.test_throw_error)
+
+
+def test_threads():
+    # Smoke test for parallel threaded execution; doesn't actually
+    # check that code runs in parallel, but just that it produces
+    # expected results.
+    nthreads = 10
+    niter = 100
+
+    n = 20
+    a = csr_matrix(np.ones([n, n]))
+    bres = []
+
+    class Worker(threading.Thread):
+        def run(self):
+            b = a.copy()
+            for j in range(niter):
+                _sparsetools.csr_plus_csr(n, n,
+                                          a.indptr, a.indices, a.data,
+                                          a.indptr, a.indices, a.data,
+                                          b.indptr, b.indices, b.data)
+            bres.append(b)
+
+    threads = [Worker() for _ in range(nthreads)]
+    for thread in threads:
+        thread.start()
+    for thread in threads:
+        thread.join()
+
+    for b in bres:
+        assert_(np.all(b.toarray() == 2))
+
+
+def test_regression_std_vector_dtypes():
+    # Regression test for gh-3780, checking the std::vector typemaps
+    # in sparsetools.cxx are complete.
+    for dtype in supported_dtypes:
+        ad = np.array([[1, 2], [3, 4]]).astype(dtype)
+        a = csr_matrix(ad, dtype=dtype)
+
+        # getcol is one function using std::vector typemaps, and should not fail
+        assert_equal(a.getcol(0).toarray(), ad[:, :1])
+
+
+@pytest.mark.slow
+@pytest.mark.xfail_on_32bit("Can't create large array for test")
+def test_nnz_overflow():
+    # Regression test for gh-7230 / gh-7871, checking that coo_toarray
+    # with nnz > int32max doesn't overflow.
+    nnz = np.iinfo(np.int32).max + 1
+    # Ensure ~20 GB of RAM is free to run this test.
+    check_free_memory((4 + 4 + 1) * nnz / 1e6 + 0.5)
+
+    # Use nnz duplicate entries to keep the dense version small.
+    row = np.zeros(nnz, dtype=np.int32)
+    col = np.zeros(nnz, dtype=np.int32)
+    data = np.zeros(nnz, dtype=np.int8)
+    data[-1] = 4
+    s = coo_matrix((data, (row, col)), shape=(1, 1), copy=False)
+    # Sums nnz duplicates to produce a 1x1 array containing 4.
+    d = s.toarray()
+
+    assert_allclose(d, [[4]])
+
+
+@pytest.mark.skipif(
+    not (sys.platform.startswith('linux') and np.dtype(np.intp).itemsize >= 8),
+    reason="test requires 64-bit Linux"
+)
+class TestInt32Overflow:
+    """
+    Some of the sparsetools routines use dense 2D matrices whose
+    total size is not bounded by the nnz of the sparse matrix. These
+    routines used to suffer from int32 wraparounds; here, we try to
+    check that the wraparounds don't occur any more.
+    """
+    # choose n large enough
+    n = 50000
+
+    def setup_method(self):
+        assert self.n**2 > np.iinfo(np.int32).max
+
+        # check there's enough memory even if everything is run at the
+        # same time
+        try:
+            parallel_count = int(os.environ.get('PYTEST_XDIST_WORKER_COUNT', '1'))
+        except ValueError:
+            parallel_count = np.inf
+
+        check_free_memory(3000 * parallel_count)
+
+    def teardown_method(self):
+        gc.collect()
+
+    @pytest.mark.fail_slow(2)  # keep in fast set, only non-slow test
+    def test_coo_todense(self):
+        # Check *_todense routines (cf. gh-2179)
+        #
+        # All of them in the end call coo_matrix.todense
+
+        n = self.n
+
+        i = np.array([0, n-1])
+        j = np.array([0, n-1])
+        data = np.array([1, 2], dtype=np.int8)
+        m = coo_matrix((data, (i, j)))
+
+        r = m.todense()
+        assert_equal(r[0,0], 1)
+        assert_equal(r[-1,-1], 2)
+        del r
+        gc.collect()
+
+    @pytest.mark.slow
+    def test_matvecs(self):
+        # Check *_matvecs routines
+        n = self.n
+
+        i = np.array([0, n-1])
+        j = np.array([0, n-1])
+        data = np.array([1, 2], dtype=np.int8)
+        m = coo_matrix((data, (i, j)))
+
+        b = np.ones((n, n), dtype=np.int8)
+        for sptype in (csr_matrix, csc_matrix, bsr_matrix):
+            m2 = sptype(m)
+            r = m2.dot(b)
+            assert_equal(r[0,0], 1)
+            assert_equal(r[-1,-1], 2)
+            del r
+            gc.collect()
+
+        del b
+        gc.collect()
+
+    @pytest.mark.slow
+    def test_dia_matvec(self):
+        # Check: huge dia_matrix _matvec
+        n = self.n
+        data = np.ones((n, n), dtype=np.int8)
+        offsets = np.arange(n)
+        m = dia_matrix((data, offsets), shape=(n, n))
+        v = np.ones(m.shape[1], dtype=np.int8)
+        r = m.dot(v)
+        assert_equal(r[0], int_to_int8(n))
+        del data, offsets, m, v, r
+        gc.collect()
+
+    _bsr_ops = [pytest.param("matmat", marks=pytest.mark.xslow),
+                pytest.param("matvecs", marks=pytest.mark.xslow),
+                "matvec",
+                "diagonal",
+                "sort_indices",
+                pytest.param("transpose", marks=pytest.mark.xslow)]
+
+    @pytest.mark.slow
+    @pytest.mark.parametrize("op", _bsr_ops)
+    def test_bsr_1_block(self, op):
+        # Check: huge bsr_matrix (1-block)
+        #
+        # The point here is that indices inside a block may overflow.
+
+        def get_matrix():
+            n = self.n
+            data = np.ones((1, n, n), dtype=np.int8)
+            indptr = np.array([0, 1], dtype=np.int32)
+            indices = np.array([0], dtype=np.int32)
+            m = bsr_matrix((data, indices, indptr), blocksize=(n, n), copy=False)
+            del data, indptr, indices
+            return m
+
+        gc.collect()
+        try:
+            getattr(self, "_check_bsr_" + op)(get_matrix)
+        finally:
+            gc.collect()
+
+    @pytest.mark.slow
+    @pytest.mark.parametrize("op", _bsr_ops)
+    def test_bsr_n_block(self, op):
+        # Check: huge bsr_matrix (n-block)
+        #
+        # The point here is that while indices within a block don't
+        # overflow, accumulators across many block may.
+
+        def get_matrix():
+            n = self.n
+            data = np.ones((n, n, 1), dtype=np.int8)
+            indptr = np.array([0, n], dtype=np.int32)
+            indices = np.arange(n, dtype=np.int32)
+            m = bsr_matrix((data, indices, indptr), blocksize=(n, 1), copy=False)
+            del data, indptr, indices
+            return m
+
+        gc.collect()
+        try:
+            getattr(self, "_check_bsr_" + op)(get_matrix)
+        finally:
+            gc.collect()
+
+    def _check_bsr_matvecs(self, m):  # skip name check
+        m = m()
+        n = self.n
+
+        # _matvecs
+        r = m.dot(np.ones((n, 2), dtype=np.int8))
+        assert_equal(r[0, 0], int_to_int8(n))
+
+    def _check_bsr_matvec(self, m):  # skip name check
+        m = m()
+        n = self.n
+
+        # _matvec
+        r = m.dot(np.ones((n,), dtype=np.int8))
+        assert_equal(r[0], int_to_int8(n))
+
+    def _check_bsr_diagonal(self, m):  # skip name check
+        m = m()
+        n = self.n
+
+        # _diagonal
+        r = m.diagonal()
+        assert_equal(r, np.ones(n))
+
+    def _check_bsr_sort_indices(self, m):  # skip name check
+        # _sort_indices
+        m = m()
+        m.sort_indices()
+
+    def _check_bsr_transpose(self, m):  # skip name check
+        # _transpose
+        m = m()
+        m.transpose()
+
+    def _check_bsr_matmat(self, m):  # skip name check
+        m = m()
+        n = self.n
+
+        # _bsr_matmat
+        m2 = bsr_matrix(np.ones((n, 2), dtype=np.int8), blocksize=(m.blocksize[1], 2))
+        m.dot(m2)  # shouldn't SIGSEGV
+        del m2
+
+        # _bsr_matmat
+        m2 = bsr_matrix(np.ones((2, n), dtype=np.int8), blocksize=(2, m.blocksize[0]))
+        m2.dot(m)  # shouldn't SIGSEGV
+
+
+@pytest.mark.skip(reason="64-bit indices in sparse matrices not available")
+def test_csr_matmat_int64_overflow():
+    n = 3037000500
+    assert n**2 > np.iinfo(np.int64).max
+
+    # the test would take crazy amounts of memory
+    check_free_memory(n * (8*2 + 1) * 3 / 1e6)
+
+    # int64 overflow
+    data = np.ones((n,), dtype=np.int8)
+    indptr = np.arange(n+1, dtype=np.int64)
+    indices = np.zeros(n, dtype=np.int64)
+    a = csr_matrix((data, indices, indptr))
+    b = a.T
+
+    assert_raises(RuntimeError, a.dot, b)
+
+
+def test_upcast():
+    a0 = csr_matrix([[np.pi, np.pi*1j], [3, 4]], dtype=complex)
+    b0 = np.array([256+1j, 2**32], dtype=complex)
+
+    for a_dtype in supported_dtypes:
+        for b_dtype in supported_dtypes:
+            msg = f"({a_dtype!r}, {b_dtype!r})"
+
+            if np.issubdtype(a_dtype, np.complexfloating):
+                a = a0.copy().astype(a_dtype)
+            else:
+                a = a0.real.copy().astype(a_dtype)
+
+            if np.issubdtype(b_dtype, np.complexfloating):
+                b = b0.copy().astype(b_dtype)
+            else:
+                with np.errstate(invalid="ignore"):
+                    # Casting a large value (2**32) to int8 causes a warning in
+                    # numpy >1.23
+                    b = b0.real.copy().astype(b_dtype)
+
+            if not (a_dtype == np.bool_ and b_dtype == np.bool_):
+                c = np.zeros((2,), dtype=np.bool_)
+                assert_raises(ValueError, _sparsetools.csr_matvec,
+                              2, 2, a.indptr, a.indices, a.data, b, c)
+
+            if ((np.issubdtype(a_dtype, np.complexfloating) and
+                 not np.issubdtype(b_dtype, np.complexfloating)) or
+                (not np.issubdtype(a_dtype, np.complexfloating) and
+                 np.issubdtype(b_dtype, np.complexfloating))):
+                c = np.zeros((2,), dtype=np.float64)
+                assert_raises(ValueError, _sparsetools.csr_matvec,
+                              2, 2, a.indptr, a.indices, a.data, b, c)
+
+            c = np.zeros((2,), dtype=np.result_type(a_dtype, b_dtype))
+            _sparsetools.csr_matvec(2, 2, a.indptr, a.indices, a.data, b, c)
+            assert_allclose(c, np.dot(a.toarray(), b), err_msg=msg)
+
+
+def test_endianness():
+    d = np.ones((3,4))
+    offsets = [-1,0,1]
+
+    a = dia_matrix((d.astype('<f8'), offsets), (4, 4))
+    b = dia_matrix((d.astype('>f8'), offsets), (4, 4))
+    v = np.arange(4)
+
+    assert_allclose(a.dot(v), [1, 3, 6, 5])
+    assert_allclose(b.dot(v), [1, 3, 6, 5])
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_spfuncs.py b/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_spfuncs.py
new file mode 100644
index 0000000000000000000000000000000000000000..75bc2d92c369be5799a904bc0938617f30321f12
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_spfuncs.py
@@ -0,0 +1,97 @@
+from numpy import array, kron, diag
+from numpy.testing import assert_, assert_equal
+
+from scipy.sparse import _spfuncs as spfuncs
+from scipy.sparse import csr_matrix, csc_matrix, bsr_matrix
+from scipy.sparse._sparsetools import (csr_scale_rows, csr_scale_columns,
+                                       bsr_scale_rows, bsr_scale_columns)
+
+
+class TestSparseFunctions:
+    def test_scale_rows_and_cols(self):
+        D = array([[1, 0, 0, 2, 3],
+                   [0, 4, 0, 5, 0],
+                   [0, 0, 6, 7, 0]])
+
+        #TODO expose through function
+        S = csr_matrix(D)
+        v = array([1,2,3])
+        csr_scale_rows(3,5,S.indptr,S.indices,S.data,v)
+        assert_equal(S.toarray(), diag(v)@D)
+
+        S = csr_matrix(D)
+        v = array([1,2,3,4,5])
+        csr_scale_columns(3,5,S.indptr,S.indices,S.data,v)
+        assert_equal(S.toarray(), D@diag(v))
+
+        # blocks
+        E = kron(D,[[1,2],[3,4]])
+        S = bsr_matrix(E,blocksize=(2,2))
+        v = array([1,2,3,4,5,6])
+        bsr_scale_rows(3,5,2,2,S.indptr,S.indices,S.data,v)
+        assert_equal(S.toarray(), diag(v)@E)
+
+        S = bsr_matrix(E,blocksize=(2,2))
+        v = array([1,2,3,4,5,6,7,8,9,10])
+        bsr_scale_columns(3,5,2,2,S.indptr,S.indices,S.data,v)
+        assert_equal(S.toarray(), E@diag(v))
+
+        E = kron(D,[[1,2,3],[4,5,6]])
+        S = bsr_matrix(E,blocksize=(2,3))
+        v = array([1,2,3,4,5,6])
+        bsr_scale_rows(3,5,2,3,S.indptr,S.indices,S.data,v)
+        assert_equal(S.toarray(), diag(v)@E)
+
+        S = bsr_matrix(E,blocksize=(2,3))
+        v = array([1,2,3,4,5,6,7,8,9,10,11,12,13,14,15])
+        bsr_scale_columns(3,5,2,3,S.indptr,S.indices,S.data,v)
+        assert_equal(S.toarray(), E@diag(v))
+
+    def test_estimate_blocksize(self):
+        mats = []
+        mats.append([[0,1],[1,0]])
+        mats.append([[1,1,0],[0,0,1],[1,0,1]])
+        mats.append([[0],[0],[1]])
+        mats = [array(x) for x in mats]
+
+        blks = []
+        blks.append([[1]])
+        blks.append([[1,1],[1,1]])
+        blks.append([[1,1],[0,1]])
+        blks.append([[1,1,0],[1,0,1],[1,1,1]])
+        blks = [array(x) for x in blks]
+
+        for A in mats:
+            for B in blks:
+                X = kron(A,B)
+                r,c = spfuncs.estimate_blocksize(X)
+                assert_(r >= B.shape[0])
+                assert_(c >= B.shape[1])
+
+    def test_count_blocks(self):
+        def gold(A,bs):
+            R,C = bs
+            I,J = A.nonzero()
+            return len(set(zip(I//R,J//C)))
+
+        mats = []
+        mats.append([[0]])
+        mats.append([[1]])
+        mats.append([[1,0]])
+        mats.append([[1,1]])
+        mats.append([[0,1],[1,0]])
+        mats.append([[1,1,0],[0,0,1],[1,0,1]])
+        mats.append([[0],[0],[1]])
+
+        for A in mats:
+            for B in mats:
+                X = kron(A,B)
+                Y = csr_matrix(X)
+                for R in range(1,6):
+                    for C in range(1,6):
+                        assert_equal(spfuncs.count_blocks(Y, (R, C)), gold(X, (R, C)))
+
+        X = kron([[1,1,0],[0,0,1],[1,0,1]],[[1,1]])
+        Y = csc_matrix(X)
+        assert_equal(spfuncs.count_blocks(X, (1, 2)), gold(X, (1, 2)))
+        assert_equal(spfuncs.count_blocks(Y, (1, 2)), gold(X, (1, 2)))
diff --git a/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_sputils.py b/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_sputils.py
new file mode 100644
index 0000000000000000000000000000000000000000..345f89f8585cb6906794220ae74e172cf1f45cba
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/sparse/tests/test_sputils.py
@@ -0,0 +1,424 @@
+"""unit tests for sparse utility functions"""
+
+import numpy as np
+from numpy.testing import assert_equal
+import pytest
+from pytest import raises as assert_raises
+from scipy.sparse import _sputils as sputils, csr_array, bsr_array, dia_array, coo_array
+from scipy.sparse._sputils import matrix
+
+
+class TestSparseUtils:
+
+    def test_upcast(self):
+        assert_equal(sputils.upcast('intc'), np.intc)
+        assert_equal(sputils.upcast('int32', 'float32'), np.float64)
+        assert_equal(sputils.upcast('bool', complex, float), np.complex128)
+        assert_equal(sputils.upcast('i', 'd'), np.float64)
+
+    def test_getdtype(self):
+        A = np.array([1], dtype='int8')
+
+        assert_equal(sputils.getdtype(None, default=float), float)
+        assert_equal(sputils.getdtype(None, a=A), np.int8)
+
+        with assert_raises(
+            ValueError,
+            match="scipy.sparse does not support dtype object. .*",
+        ):
+            sputils.getdtype("O")
+
+        with assert_raises(
+            ValueError,
+            match="scipy.sparse does not support dtype float16. .*",
+        ):
+            sputils.getdtype(None, default=np.float16)
+
+    def test_isscalarlike(self):
+        assert_equal(sputils.isscalarlike(3.0), True)
+        assert_equal(sputils.isscalarlike(-4), True)
+        assert_equal(sputils.isscalarlike(2.5), True)
+        assert_equal(sputils.isscalarlike(1 + 3j), True)
+        assert_equal(sputils.isscalarlike(np.array(3)), True)
+        assert_equal(sputils.isscalarlike("16"), True)
+
+        assert_equal(sputils.isscalarlike(np.array([3])), False)
+        assert_equal(sputils.isscalarlike([[3]]), False)
+        assert_equal(sputils.isscalarlike((1,)), False)
+        assert_equal(sputils.isscalarlike((1, 2)), False)
+
+    def test_isintlike(self):
+        assert_equal(sputils.isintlike(-4), True)
+        assert_equal(sputils.isintlike(np.array(3)), True)
+        assert_equal(sputils.isintlike(np.array([3])), False)
+        with assert_raises(
+            ValueError,
+            match="Inexact indices into sparse matrices are not allowed"
+        ):
+            sputils.isintlike(3.0)
+
+        assert_equal(sputils.isintlike(2.5), False)
+        assert_equal(sputils.isintlike(1 + 3j), False)
+        assert_equal(sputils.isintlike((1,)), False)
+        assert_equal(sputils.isintlike((1, 2)), False)
+
+    def test_isshape(self):
+        assert_equal(sputils.isshape((1, 2)), True)
+        assert_equal(sputils.isshape((5, 2)), True)
+
+        assert_equal(sputils.isshape((1.5, 2)), False)
+        assert_equal(sputils.isshape((2, 2, 2)), False)
+        assert_equal(sputils.isshape(([2], 2)), False)
+        assert_equal(sputils.isshape((-1, 2), nonneg=False),True)
+        assert_equal(sputils.isshape((2, -1), nonneg=False),True)
+        assert_equal(sputils.isshape((-1, 2), nonneg=True),False)
+        assert_equal(sputils.isshape((2, -1), nonneg=True),False)
+
+        assert_equal(sputils.isshape((1.5, 2), allow_nd=(1, 2)), False)
+        assert_equal(sputils.isshape(([2], 2), allow_nd=(1, 2)), False)
+        assert_equal(sputils.isshape((2, 2, -2), nonneg=True, allow_nd=(1, 2)),
+                     False)
+        assert_equal(sputils.isshape((2,), allow_nd=(1, 2)), True)
+        assert_equal(sputils.isshape((2, 2,), allow_nd=(1, 2)), True)
+        assert_equal(sputils.isshape((2, 2, 2), allow_nd=(1, 2)), False)
+
+    def test_issequence(self):
+        assert_equal(sputils.issequence((1,)), True)
+        assert_equal(sputils.issequence((1, 2, 3)), True)
+        assert_equal(sputils.issequence([1]), True)
+        assert_equal(sputils.issequence([1, 2, 3]), True)
+        assert_equal(sputils.issequence(np.array([1, 2, 3])), True)
+
+        assert_equal(sputils.issequence(np.array([[1], [2], [3]])), False)
+        assert_equal(sputils.issequence(3), False)
+
+    def test_ismatrix(self):
+        assert_equal(sputils.ismatrix(((),)), True)
+        assert_equal(sputils.ismatrix([[1], [2]]), True)
+        assert_equal(sputils.ismatrix(np.arange(3)[None]), True)
+
+        assert_equal(sputils.ismatrix([1, 2]), False)
+        assert_equal(sputils.ismatrix(np.arange(3)), False)
+        assert_equal(sputils.ismatrix([[[1]]]), False)
+        assert_equal(sputils.ismatrix(3), False)
+
+    def test_isdense(self):
+        assert_equal(sputils.isdense(np.array([1])), True)
+        assert_equal(sputils.isdense(matrix([1])), True)
+
+    def test_validateaxis(self):
+        with assert_raises(ValueError, match="does not accept 0D axis"):
+            sputils.validateaxis(())
+
+        for ax in [1.5, (0, 1.5), (1.5, 0)]:
+            with assert_raises(TypeError, match="must be an integer"):
+                sputils.validateaxis(ax)
+        for ax in [(1, 1), (1, -1), (0, -2)]:
+            with assert_raises(ValueError, match="duplicate value in axis"):
+                sputils.validateaxis(ax)
+
+        # ndim 1
+        for ax in [1, -2, (0, 1), (1, -1)]:
+            with assert_raises(ValueError, match="out of range"):
+                sputils.validateaxis(ax, ndim=1)
+        with assert_raises(ValueError, match="duplicate value in axis"):
+            sputils.validateaxis((0, -1), ndim=1)
+        # all valid axis values lead to None when canonical
+        for axis in (0, -1, None, (0,), (-1,)):
+            assert sputils.validateaxis(axis, ndim=1) is None
+
+        # ndim 2
+        for ax in [5, -5, (0, 5), (-5, 0)]:
+            with assert_raises(ValueError, match="out of range"):
+                sputils.validateaxis(ax, ndim=2)
+        for axis in ((0,), (1,), None):
+            assert sputils.validateaxis(axis, ndim=2) == axis
+        axis_2d = {-2: (0,), -1: (1,), 0: (0,), 1: (1,), (0, 1): None, (0, -1): None}
+        for axis, canonical_axis in axis_2d.items():
+            assert sputils.validateaxis(axis, ndim=2) == canonical_axis
+
+        # ndim 4
+        for axis in ((2,), (3,), (2, 3), (2, 1), (0, 3)):
+            assert sputils.validateaxis(axis, ndim=4) == axis
+        axis_4d = {-4: (0,), -3: (1,), 2: (2,), 3: (3,), (3, -4): (3, 0)}
+        for axis, canonical_axis in axis_4d.items():
+            sputils.validateaxis(axis, ndim=4) == canonical_axis
+
+    @pytest.mark.parametrize("container", [csr_array, bsr_array])
+    def test_safely_cast_index_compressed(self, container):
+        # This is slow to test completely as nnz > imax is big
+        # and indptr is big for some shapes
+        # So we don't test large nnz, nor csc_array (same code as csr_array)
+        imax = np.int64(np.iinfo(np.int32).max)
+
+        # Shape 32bit
+        A32 = container((1, imax))
+        # indices big type, small values
+        B32 = A32.copy()
+        B32.indices = B32.indices.astype(np.int64)
+        B32.indptr = B32.indptr.astype(np.int64)
+
+        # Shape 64bit
+        # indices big type, small values
+        A64 = csr_array((1, imax + 1))
+        # indices small type, small values
+        B64 = A64.copy()
+        B64.indices = B64.indices.astype(np.int32)
+        B64.indptr = B64.indptr.astype(np.int32)
+        # indices big type, big values
+        C64 = A64.copy()
+        C64.indices = np.array([imax + 1], dtype=np.int64)
+        C64.indptr = np.array([0, 1], dtype=np.int64)
+        C64.data = np.array([2.2])
+
+        assert (A32.indices.dtype, A32.indptr.dtype) == (np.int32, np.int32)
+        assert (B32.indices.dtype, B32.indptr.dtype) == (np.int64, np.int64)
+        assert (A64.indices.dtype, A64.indptr.dtype) == (np.int64, np.int64)
+        assert (B64.indices.dtype, B64.indptr.dtype) == (np.int32, np.int32)
+        assert (C64.indices.dtype, C64.indptr.dtype) == (np.int64, np.int64)
+
+        for A in [A32, B32, A64, B64]:
+            indices, indptr = sputils.safely_cast_index_arrays(A, np.int32)
+            assert (indices.dtype, indptr.dtype) == (np.int32, np.int32)
+            indices, indptr = sputils.safely_cast_index_arrays(A, np.int64)
+            assert (indices.dtype, indptr.dtype) == (np.int64, np.int64)
+
+            indices, indptr = sputils.safely_cast_index_arrays(A, A.indices.dtype)
+            assert indices is A.indices
+            assert indptr is A.indptr
+
+        with assert_raises(ValueError):
+            sputils.safely_cast_index_arrays(C64, np.int32)
+        indices, indptr = sputils.safely_cast_index_arrays(C64, np.int64)
+        assert indices is C64.indices
+        assert indptr is C64.indptr
+
+    def test_safely_cast_index_coo(self):
+        # This is slow to test completely as nnz > imax is big
+        # So we don't test large nnz
+        imax = np.int64(np.iinfo(np.int32).max)
+
+        # Shape 32bit
+        A32 = coo_array((1, imax))
+        # coords big type, small values
+        B32 = A32.copy()
+        B32.coords = tuple(co.astype(np.int64) for co in B32.coords)
+
+        # Shape 64bit
+        # coords big type, small values
+        A64 = coo_array((1, imax + 1))
+        # coords small type, small values
+        B64 = A64.copy()
+        B64.coords = tuple(co.astype(np.int32) for co in B64.coords)
+        # coords big type, big values
+        C64 = A64.copy()
+        C64.coords = (np.array([imax + 1]), np.array([0]))
+        C64.data = np.array([2.2])
+
+        assert A32.coords[0].dtype == np.int32
+        assert B32.coords[0].dtype == np.int64
+        assert A64.coords[0].dtype == np.int64
+        assert B64.coords[0].dtype == np.int32
+        assert C64.coords[0].dtype == np.int64
+
+        for A in [A32, B32, A64, B64]:
+            coords = sputils.safely_cast_index_arrays(A, np.int32)
+            assert coords[0].dtype == np.int32
+            coords = sputils.safely_cast_index_arrays(A, np.int64)
+            assert coords[0].dtype == np.int64
+
+            coords = sputils.safely_cast_index_arrays(A, A.coords[0].dtype)
+            assert coords[0] is A.coords[0]
+
+        with assert_raises(ValueError):
+            sputils.safely_cast_index_arrays(C64, np.int32)
+        coords = sputils.safely_cast_index_arrays(C64, np.int64)
+        assert coords[0] is C64.coords[0]
+
+    def test_safely_cast_index_dia(self):
+        # This is slow to test completely as nnz > imax is big
+        # So we don't test large nnz
+        imax = np.int64(np.iinfo(np.int32).max)
+
+        # Shape 32bit
+        A32 = dia_array((1, imax))
+        # offsets big type, small values
+        B32 = A32.copy()
+        B32.offsets = B32.offsets.astype(np.int64)
+
+        # Shape 64bit
+        # offsets big type, small values
+        A64 = dia_array((1, imax + 2))
+        # offsets small type, small values
+        B64 = A64.copy()
+        B64.offsets = B64.offsets.astype(np.int32)
+        # offsets big type, big values
+        C64 = A64.copy()
+        C64.offsets = np.array([imax + 1])
+        C64.data = np.array([2.2])
+
+        assert A32.offsets.dtype == np.int32
+        assert B32.offsets.dtype == np.int64
+        assert A64.offsets.dtype == np.int64
+        assert B64.offsets.dtype == np.int32
+        assert C64.offsets.dtype == np.int64
+
+        for A in [A32, B32, A64, B64]:
+            offsets = sputils.safely_cast_index_arrays(A, np.int32)
+            assert offsets.dtype == np.int32
+            offsets = sputils.safely_cast_index_arrays(A, np.int64)
+            assert offsets.dtype == np.int64
+
+            offsets = sputils.safely_cast_index_arrays(A, A.offsets.dtype)
+            assert offsets is A.offsets
+
+        with assert_raises(ValueError):
+            sputils.safely_cast_index_arrays(C64, np.int32)
+        offsets = sputils.safely_cast_index_arrays(C64, np.int64)
+        assert offsets is C64.offsets
+
+    def test_get_index_dtype(self):
+        imax = np.int64(np.iinfo(np.int32).max)
+        too_big = imax + 1
+
+        # Check that uint32's with no values too large doesn't return
+        # int64
+        a1 = np.ones(90, dtype='uint32')
+        a2 = np.ones(90, dtype='uint32')
+        assert_equal(
+            np.dtype(sputils.get_index_dtype((a1, a2), check_contents=True)),
+            np.dtype('int32')
+        )
+
+        # Check that if we can not convert but all values are less than or
+        # equal to max that we can just convert to int32
+        a1[-1] = imax
+        assert_equal(
+            np.dtype(sputils.get_index_dtype((a1, a2), check_contents=True)),
+            np.dtype('int32')
+        )
+
+        # Check that if it can not convert directly and the contents are
+        # too large that we return int64
+        a1[-1] = too_big
+        assert_equal(
+            np.dtype(sputils.get_index_dtype((a1, a2), check_contents=True)),
+            np.dtype('int64')
+        )
+
+        # test that if can not convert and didn't specify to check_contents
+        # we return int64
+        a1 = np.ones(89, dtype='uint32')
+        a2 = np.ones(89, dtype='uint32')
+        assert_equal(
+            np.dtype(sputils.get_index_dtype((a1, a2))),
+            np.dtype('int64')
+        )
+
+        # Check that even if we have arrays that can be converted directly
+        # that if we specify a maxval directly it takes precedence
+        a1 = np.ones(12, dtype='uint32')
+        a2 = np.ones(12, dtype='uint32')
+        assert_equal(
+            np.dtype(sputils.get_index_dtype(
+                (a1, a2), maxval=too_big, check_contents=True
+            )),
+            np.dtype('int64')
+        )
+
+        # Check that an array with a too max size and maxval set
+        # still returns int64
+        a1[-1] = too_big
+        assert_equal(
+            np.dtype(sputils.get_index_dtype((a1, a2), maxval=too_big)),
+            np.dtype('int64')
+        )
+
+    # tests public broadcast_shapes largely from
+    # numpy/numpy/lib/tests/test_stride_tricks.py
+    # first 3 cause np.broadcast to raise index too large, but not sputils
+    @pytest.mark.parametrize("input_shapes,target_shape", [
+        [((6, 5, 1, 4, 1, 1), (1, 2**32), (2**32, 1)), (6, 5, 1, 4, 2**32, 2**32)],
+        [((6, 5, 1, 4, 1, 1), (1, 2**32)), (6, 5, 1, 4, 1, 2**32)],
+        [((1, 2**32), (2**32, 1)), (2**32, 2**32)],
+        [[2, 2, 2], (2,)],
+        [[], ()],
+        [[()], ()],
+        [[(7,)], (7,)],
+        [[(1, 2), (2,)], (1, 2)],
+        [[(2,), (1, 2)], (1, 2)],
+        [[(1, 1)], (1, 1)],
+        [[(1, 1), (3, 4)], (3, 4)],
+        [[(6, 7), (5, 6, 1), (7,), (5, 1, 7)], (5, 6, 7)],
+        [[(5, 6, 1)], (5, 6, 1)],
+        [[(1, 3), (3, 1)], (3, 3)],
+        [[(1, 0), (0, 0)], (0, 0)],
+        [[(0, 1), (0, 0)], (0, 0)],
+        [[(1, 0), (0, 1)], (0, 0)],
+        [[(1, 1), (0, 0)], (0, 0)],
+        [[(1, 1), (1, 0)], (1, 0)],
+        [[(1, 1), (0, 1)], (0, 1)],
+        [[(), (0,)], (0,)],
+        [[(0,), (0, 0)], (0, 0)],
+        [[(0,), (0, 1)], (0, 0)],
+        [[(1,), (0, 0)], (0, 0)],
+        [[(), (0, 0)], (0, 0)],
+        [[(1, 1), (0,)], (1, 0)],
+        [[(1,), (0, 1)], (0, 1)],
+        [[(1,), (1, 0)], (1, 0)],
+        [[(), (1, 0)], (1, 0)],
+        [[(), (0, 1)], (0, 1)],
+        [[(1,), (3,)], (3,)],
+        [[2, (3, 2)], (3, 2)],
+        [[(1, 2)] * 32, (1, 2)],
+        [[(1, 2)] * 100, (1, 2)],
+        [[(2,)] * 32, (2,)],
+    ])
+    def test_broadcast_shapes_successes(self, input_shapes, target_shape):
+        assert_equal(sputils.broadcast_shapes(*input_shapes), target_shape)
+
+    # tests public broadcast_shapes failures
+    @pytest.mark.parametrize("input_shapes", [
+        [(3,), (4,)],
+        [(2, 3), (2,)],
+        [2, (2, 3)],
+        [(3,), (3,), (4,)],
+        [(2, 5), (3, 5)],
+        [(2, 4), (2, 5)],
+        [(1, 3, 4), (2, 3, 3)],
+        [(1, 2), (3, 1), (3, 2), (10, 5)],
+        [(2,)] * 32 + [(3,)] * 32,
+    ])
+    def test_broadcast_shapes_failures(self, input_shapes):
+        with assert_raises(ValueError, match="cannot be broadcast"):
+            sputils.broadcast_shapes(*input_shapes)
+
+    def test_check_shape_overflow(self):
+        new_shape = sputils.check_shape([(10, -1)], (65535, 131070))
+        assert_equal(new_shape, (10, 858967245))
+
+    def test_matrix(self):
+        a = [[1, 2, 3]]
+        b = np.array(a)
+
+        assert isinstance(sputils.matrix(a), np.matrix)
+        assert isinstance(sputils.matrix(b), np.matrix)
+
+        c = sputils.matrix(b)
+        c[:, :] = 123
+        assert_equal(b, a)
+
+        c = sputils.matrix(b, copy=False)
+        c[:, :] = 123
+        assert_equal(b, [[123, 123, 123]])
+
+    def test_asmatrix(self):
+        a = [[1, 2, 3]]
+        b = np.array(a)
+
+        assert isinstance(sputils.asmatrix(a), np.matrix)
+        assert isinstance(sputils.asmatrix(b), np.matrix)
+
+        c = sputils.asmatrix(b)
+        c[:, :] = 123
+        assert_equal(b, [[123, 123, 123]])
diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/__init__.py b/venv/lib/python3.12/site-packages/scipy/spatial/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..d92f89e29c0406c6baf08d192ac0d9e49538ed14
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/__init__.py
@@ -0,0 +1,130 @@
+"""
+=============================================================
+Spatial algorithms and data structures (:mod:`scipy.spatial`)
+=============================================================
+
+.. currentmodule:: scipy.spatial
+
+.. toctree::
+   :hidden:
+
+   spatial.distance
+   spatial.transform
+
+Spatial transformations
+=======================
+
+These are contained in the `scipy.spatial.transform` submodule.
+
+Nearest-neighbor queries
+========================
+.. autosummary::
+   :toctree: generated/
+
+   KDTree      -- class for efficient nearest-neighbor queries
+   cKDTree     -- class for efficient nearest-neighbor queries (faster implementation)
+   Rectangle
+
+Distance metrics
+================
+
+Distance metrics are contained in the :mod:`scipy.spatial.distance` submodule.
+
+Delaunay triangulation, convex hulls, and Voronoi diagrams
+==========================================================
+
+.. autosummary::
+   :toctree: generated/
+
+   Delaunay    -- compute Delaunay triangulation of input points
+   ConvexHull  -- compute a convex hull for input points
+   Voronoi     -- compute a Voronoi diagram hull from input points
+   SphericalVoronoi -- compute a Voronoi diagram from input points on the surface of a sphere
+   HalfspaceIntersection -- compute the intersection points of input halfspaces
+
+Plotting helpers
+================
+
+.. autosummary::
+   :toctree: generated/
+
+   delaunay_plot_2d     -- plot 2-D triangulation
+   convex_hull_plot_2d  -- plot 2-D convex hull
+   voronoi_plot_2d      -- plot 2-D Voronoi diagram
+
+.. seealso:: :ref:`Tutorial <qhulltutorial>`
+
+
+Simplex representation
+======================
+The simplices (triangles, tetrahedra, etc.) appearing in the Delaunay
+tessellation (N-D simplices), convex hull facets, and Voronoi ridges
+(N-1-D simplices) are represented in the following scheme::
+
+    tess = Delaunay(points)
+    hull = ConvexHull(points)
+    voro = Voronoi(points)
+
+    # coordinates of the jth vertex of the ith simplex
+    tess.points[tess.simplices[i, j], :]        # tessellation element
+    hull.points[hull.simplices[i, j], :]        # convex hull facet
+    voro.vertices[voro.ridge_vertices[i, j], :] # ridge between Voronoi cells
+
+For Delaunay triangulations and convex hulls, the neighborhood
+structure of the simplices satisfies the condition:
+``tess.neighbors[i,j]`` is the neighboring simplex of the ith
+simplex, opposite to the ``j``-vertex. It is -1 in case of no neighbor.
+
+Convex hull facets also define a hyperplane equation::
+
+    (hull.equations[i,:-1] * coord).sum() + hull.equations[i,-1] == 0
+
+Similar hyperplane equations for the Delaunay triangulation correspond
+to the convex hull facets on the corresponding N+1-D
+paraboloid.
+
+The Delaunay triangulation objects offer a method for locating the
+simplex containing a given point, and barycentric coordinate
+computations.
+
+Miscellaneous Functions
+=======================
+
+.. autosummary::
+   :toctree: generated/
+
+   tsearch
+   distance_matrix
+   minkowski_distance
+   minkowski_distance_p
+   procrustes
+   geometric_slerp
+
+Warnings / Errors used in :mod:`scipy.spatial`
+==============================================
+.. autosummary::
+   :toctree: generated/
+
+   QhullError
+"""  # noqa: E501
+
+from ._kdtree import *
+from ._ckdtree import *  # type: ignore[import-not-found]
+from ._qhull import *
+from ._spherical_voronoi import SphericalVoronoi
+from ._plotutils import *
+from ._procrustes import procrustes
+from ._geometric_slerp import geometric_slerp
+
+# Deprecated namespaces, to be removed in v2.0.0
+from . import ckdtree, kdtree, qhull
+
+__all__ = [s for s in dir() if not s.startswith('_')]
+
+from . import distance, transform
+
+__all__ += ['distance', 'transform']
+
+from scipy._lib._testutils import PytestTester
+test = PytestTester(__name__)
+del PytestTester
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diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/_geometric_slerp.py b/venv/lib/python3.12/site-packages/scipy/spatial/_geometric_slerp.py
new file mode 100644
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--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/_geometric_slerp.py
@@ -0,0 +1,256 @@
+__all__ = ['geometric_slerp']
+
+import warnings
+from typing import TYPE_CHECKING
+
+import numpy as np
+from scipy.spatial.distance import euclidean
+
+if TYPE_CHECKING:
+    import numpy.typing as npt
+
+
+def _geometric_slerp(start, end, t):
+    # create an orthogonal basis using QR decomposition
+    basis = np.vstack([start, end])
+    Q, R = np.linalg.qr(basis.T)
+    signs = 2 * (np.diag(R) >= 0) - 1
+    Q = Q.T * signs.T[:, np.newaxis]
+    R = R.T * signs.T[:, np.newaxis]
+
+    # calculate the angle between `start` and `end`
+    c = np.dot(start, end)
+    s = np.linalg.det(R)
+    omega = np.arctan2(s, c)
+
+    # interpolate
+    start, end = Q
+    s = np.sin(t * omega)
+    c = np.cos(t * omega)
+    return start * c[:, np.newaxis] + end * s[:, np.newaxis]
+
+
+def geometric_slerp(
+    start: "npt.ArrayLike",
+    end: "npt.ArrayLike",
+    t: "npt.ArrayLike",
+    tol: float = 1e-7,
+) -> np.ndarray:
+    """
+    Geometric spherical linear interpolation.
+
+    The interpolation occurs along a unit-radius
+    great circle arc in arbitrary dimensional space.
+
+    Parameters
+    ----------
+    start : (n_dimensions, ) array-like
+        Single n-dimensional input coordinate in a 1-D array-like
+        object. `n` must be greater than 1.
+    end : (n_dimensions, ) array-like
+        Single n-dimensional input coordinate in a 1-D array-like
+        object. `n` must be greater than 1.
+    t : float or (n_points,) 1D array-like
+        A float or 1D array-like of doubles representing interpolation
+        parameters. A common approach is to generate the array
+        with ``np.linspace(0, 1, n_pts)`` for linearly spaced points.
+        Ascending, descending, and scrambled orders are permitted.
+
+        .. versionchanged:: 1.17.0
+            Extrapolation is permitted, allowing values below `0`
+            and above `1`.
+    tol : float
+        The absolute tolerance for determining if the start and end
+        coordinates are antipodes.
+
+    Returns
+    -------
+    result : (t.size, D)
+        An array of doubles containing the interpolated
+        spherical path and including start and
+        end when 0 and 1 t are used. The
+        interpolated values should correspond to the
+        same sort order provided in the t array. The result
+        may be 1-dimensional if ``t`` is a float.
+
+    Raises
+    ------
+    ValueError
+        If ``start`` or ``end`` are not on the
+        unit n-sphere, or for a variety of degenerate conditions.
+
+    See Also
+    --------
+    scipy.spatial.transform.Slerp : 3-D Slerp that works with quaternions
+
+    Notes
+    -----
+    The implementation is based on the mathematical formula provided in [1]_,
+    and the first known presentation of this algorithm, derived from study of
+    4-D geometry, is credited to Glenn Davis in a footnote of the original
+    quaternion Slerp publication by Ken Shoemake [2]_.
+
+    .. versionadded:: 1.5.0
+
+    References
+    ----------
+    .. [1] https://en.wikipedia.org/wiki/Slerp#Geometric_Slerp
+    .. [2] Ken Shoemake (1985) Animating rotation with quaternion curves.
+           ACM SIGGRAPH Computer Graphics, 19(3): 245-254.
+
+    Examples
+    --------
+    Interpolate four linearly-spaced values on the circumference of
+    a circle spanning 90 degrees:
+
+    >>> import numpy as np
+    >>> from scipy.spatial import geometric_slerp
+    >>> import matplotlib.pyplot as plt
+    >>> fig = plt.figure()
+    >>> ax = fig.add_subplot(111)
+    >>> start = np.array([1, 0])
+    >>> end = np.array([0, 1])
+    >>> t_vals = np.linspace(0, 1, 4)
+    >>> result = geometric_slerp(start,
+    ...                          end,
+    ...                          t_vals)
+
+    The interpolated results should be at 30 degree intervals
+    recognizable on the unit circle:
+
+    >>> ax.scatter(result[...,0], result[...,1], c='k')
+    >>> circle = plt.Circle((0, 0), 1, color='grey')
+    >>> ax.add_artist(circle)
+    >>> ax.set_aspect('equal')
+    >>> plt.show()
+
+    Attempting to interpolate between antipodes on a circle is
+    ambiguous because there are two possible paths, and on a
+    sphere there are infinite possible paths on the geodesic surface.
+    Nonetheless, one of the ambiguous paths is returned along
+    with a warning:
+
+    >>> import warnings
+    >>> opposite_pole = np.array([-1, 0])
+    >>> with warnings.catch_warnings():
+    ...     warnings.simplefilter("ignore", UserWarning)
+    ...     geometric_slerp(start,
+    ...                     opposite_pole,
+    ...                     t_vals)
+    array([[ 1.00000000e+00,  0.00000000e+00],
+           [ 5.00000000e-01,  8.66025404e-01],
+           [-5.00000000e-01,  8.66025404e-01],
+           [-1.00000000e+00,  1.22464680e-16]])
+
+    Extend the original example to a sphere and plot interpolation
+    points in 3D:
+
+    >>> from mpl_toolkits.mplot3d import proj3d
+    >>> fig = plt.figure()
+    >>> ax = fig.add_subplot(111, projection='3d')
+
+    Plot the unit sphere for reference (optional):
+
+    >>> u = np.linspace(0, 2 * np.pi, 100)
+    >>> v = np.linspace(0, np.pi, 100)
+    >>> x = np.outer(np.cos(u), np.sin(v))
+    >>> y = np.outer(np.sin(u), np.sin(v))
+    >>> z = np.outer(np.ones(np.size(u)), np.cos(v))
+    >>> ax.plot_surface(x, y, z, color='y', alpha=0.1)
+
+    Interpolating over a larger number of points
+    may provide the appearance of a smooth curve on
+    the surface of the sphere, which is also useful
+    for discretized integration calculations on a
+    sphere surface:
+
+    >>> start = np.array([1, 0, 0])
+    >>> end = np.array([0, 0, 1])
+    >>> t_vals = np.linspace(0, 1, 200)
+    >>> result = geometric_slerp(start,
+    ...                          end,
+    ...                          t_vals)
+    >>> ax.plot(result[...,0],
+    ...         result[...,1],
+    ...         result[...,2],
+    ...         c='k')
+    >>> plt.show()
+
+    It is also possible to perform extrapolations outside
+    the interpolation interval by using interpolation parameter
+    values below 0 or above 1. For example, the above example
+    may be adjusted to extrapolate to an antipodal position:
+
+    >>> fig = plt.figure()
+    >>> ax = fig.add_subplot(111, projection='3d')
+    >>> ax.plot_surface(x, y, z, color='y', alpha=0.1)
+    >>> start = np.array([1, 0, 0])
+    >>> end = np.array([0, 0, 1])
+    >>> t_vals = np.linspace(0, 2, 400)
+    >>> result = geometric_slerp(start,
+    ...                          end,
+    ...                          t_vals)
+    >>> ax.plot(result[...,0], result[...,1], result[...,2], c='k')
+    >>> plt.show()
+    """
+
+    start = np.asarray(start, dtype=np.float64)
+    end = np.asarray(end, dtype=np.float64)
+    t = np.asarray(t)
+
+    if t.ndim > 1:
+        raise ValueError("The interpolation parameter "
+                         "value must be one dimensional.")
+
+    if start.ndim != 1 or end.ndim != 1:
+        raise ValueError("Start and end coordinates "
+                         "must be one-dimensional")
+
+    if start.size != end.size:
+        raise ValueError("The dimensions of start and "
+                         "end must match (have same size)")
+
+    if start.size < 2 or end.size < 2:
+        raise ValueError("The start and end coordinates must "
+                         "both be in at least two-dimensional "
+                         "space")
+
+    if np.array_equal(start, end):
+        return np.linspace(start, start, t.size)
+
+    # for points that violate equation for n-sphere
+    for coord in [start, end]:
+        if not np.allclose(np.linalg.norm(coord), 1.0,
+                           rtol=1e-9,
+                           atol=0):
+            raise ValueError("start and end are not"
+                             " on a unit n-sphere")
+
+    if not isinstance(tol, float):
+        raise ValueError("tol must be a float")
+    else:
+        tol = np.fabs(tol)
+
+    coord_dist = euclidean(start, end)
+
+    # diameter of 2 within tolerance means antipodes, which is a problem
+    # for all unit n-spheres (even the 0-sphere would have an ambiguous path)
+    if np.allclose(coord_dist, 2.0, rtol=0, atol=tol):
+        warnings.warn("start and end are antipodes "
+                      "using the specified tolerance; "
+                      "this may cause ambiguous slerp paths",
+                      stacklevel=2)
+
+    t = np.asarray(t, dtype=np.float64)
+
+    if t.size == 0:
+        return np.empty((0, start.size))
+
+    if t.ndim == 0:
+        return _geometric_slerp(start,
+                                end,
+                                np.atleast_1d(t)).ravel()
+    else:
+        return _geometric_slerp(start,
+                                end,
+                                t)
diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/_hausdorff.cpython-312-x86_64-linux-gnu.so b/venv/lib/python3.12/site-packages/scipy/spatial/_hausdorff.cpython-312-x86_64-linux-gnu.so
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diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/_kdtree.py b/venv/lib/python3.12/site-packages/scipy/spatial/_kdtree.py
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index 0000000000000000000000000000000000000000..73e46312ab6d3ffbf251575bbb0d318dcb825dad
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+++ b/venv/lib/python3.12/site-packages/scipy/spatial/_kdtree.py
@@ -0,0 +1,1021 @@
+# Copyright Anne M. Archibald 2008
+# Released under the scipy license
+import warnings
+import os
+
+import numpy as np
+from ._ckdtree import cKDTree, cKDTreeNode  # type: ignore[import-not-found]
+from .distance import minkowski
+from scipy._lib._array_api import xp_capabilities
+
+__all__ = ['minkowski_distance_p', 'minkowski_distance',
+           'distance_matrix',
+           'Rectangle', 'KDTree']
+
+
+@xp_capabilities(out_of_scope=True)
+def minkowski_distance_p(x, y, p=2.0):
+    """Compute the pth power of the L**p distance between two arrays.
+
+    For efficiency, this function computes the L**p distance but does
+    not extract the pth root. If `p` is 1 or infinity, this is equal to
+    the actual L**p distance.
+
+    The last dimensions of `x` and `y` must be the same length.  Any
+    other dimensions must be compatible for broadcasting.
+
+    .. deprecated:: 1.18.0
+        This function is deprecated in favor of `scipy.spatial.distance.minkowski`
+        and will be removed in SciPy 1.20.0.
+
+    Parameters
+    ----------
+    x : (..., K) array_like
+        Input array.
+    y : (..., K) array_like
+        Input array.
+    p : float, 1 <= p <= infinity
+        Which Minkowski p-norm to use.
+
+    Returns
+    -------
+    dist : ndarray
+        pth power of the distance between the input arrays.
+
+    Examples
+    --------
+    >>> from scipy.spatial import minkowski_distance_p
+    >>> minkowski_distance_p([[0, 0], [0, 0]], [[1, 1], [0, 1]])
+    array([2., 1.])
+
+    """
+    msg = ("`minkowski_distance_p` is deprecated in favor of "
+           "`scipy.spatial.distance.minkowski` as of SciPy 1.18.0 and will be removed "
+           "in SciPy 1.20.0.")
+    warnings.warn(msg, DeprecationWarning,
+                  skip_file_prefixes=(os.path.dirname(__file__),))
+    x = np.asarray(x)
+    y = np.asarray(y)
+
+    # Find smallest common datatype with float64 (return type of this
+    # function) - addresses #10262.
+    # Don't just cast to float64 for complex input case.
+    common_datatype = np.promote_types(np.promote_types(x.dtype, y.dtype),
+                                       'float64')
+
+    # Make sure x and y are NumPy arrays of correct datatype.
+    x = x.astype(common_datatype)
+    y = y.astype(common_datatype)
+
+    if p == np.inf:
+        return np.amax(np.abs(y-x), axis=-1)
+    elif p == 1:
+        return np.sum(np.abs(y-x), axis=-1)
+    else:
+        return np.sum(np.abs(y-x)**p, axis=-1)
+
+
+@xp_capabilities(out_of_scope=True)
+def minkowski_distance(x, y, p=2.0):
+    """Compute the L**p distance between two arrays.
+
+    The last dimensions of `x` and `y` must be the same length.  Any
+    other dimensions must be compatible for broadcasting.
+
+    .. deprecated:: 1.18.0
+        This function is deprecated in favor of `scipy.spatial.distance.minkowski`
+        and will be removed in SciPy 1.20.0.
+
+    Parameters
+    ----------
+    x : (..., K) array_like
+        Input array.
+    y : (..., K) array_like
+        Input array.
+    p : float, 1 <= p <= infinity
+        Which Minkowski p-norm to use.
+
+    Returns
+    -------
+    dist : ndarray
+        Distance between the input arrays.
+
+    Examples
+    --------
+    >>> from scipy.spatial import minkowski_distance
+    >>> minkowski_distance([[0, 0], [0, 0]], [[1, 1], [0, 1]])
+    array([ 1.41421356,  1.        ])
+
+    """
+    msg = ("`minkowski_distance` is deprecated in favor of "
+           "`scipy.spatial.distance.minkowski` as of SciPy 1.18.0 and will be removed "
+           "in SciPy 1.20.0.")
+    warnings.warn(msg, DeprecationWarning,
+                  skip_file_prefixes=(os.path.dirname(__file__),))
+    x = np.asarray(x)
+    y = np.asarray(y)
+    if p == np.inf or p == 1:
+        return minkowski_distance_p(x, y, p)
+    else:
+        return minkowski_distance_p(x, y, p)**(1./p)
+
+
+class Rectangle:
+    """Hyperrectangle class.
+
+    Represents a Cartesian product of intervals.
+
+    Parameters
+    ----------
+    maxes : array_like of shape (m,)
+        Upper bounds of the hyperrectangle along each dimension.
+    mins : array_like of shape (m,)
+        Lower bounds of the hyperrectangle along each dimension.
+
+    Attributes
+    ----------
+    maxes : ndarray of shape (m,)
+        Upper bounds for each dimension.
+    mins : ndarray of shape (m,)
+        Lower bounds for each dimension.
+    m : int
+        Dimensionality of the hyperrectangle.
+
+    Notes
+    -----
+    If any element of `maxes` is smaller than the corresponding element in `mins`, the
+    values are swapped automatically.
+    """
+    def __init__(self, maxes, mins):
+        """Construct a hyperrectangle."""
+        self.maxes = np.maximum(maxes,mins).astype(float)
+        self.mins = np.minimum(maxes,mins).astype(float)
+        self.m, = self.maxes.shape
+
+    def __repr__(self):
+        return f"<Rectangle {list(zip(self.mins, self.maxes))}>"
+
+    def volume(self):
+        """Compute the total volume of the hyperrectangle.
+
+        Returns
+        -------
+        vol : float
+            Volume of the hyperrectangle.
+        """
+        return np.prod(self.maxes-self.mins)
+
+    def split(self, d, split):
+        """Produce two hyperrectangles by splitting.
+
+        In general, if you need to compute maximum and minimum
+        distances to the children, it can be done more efficiently
+        by updating the maximum and minimum distances to the parent.
+
+        Parameters
+        ----------
+        d : int
+            Axis to split hyperrectangle along.
+        split : float
+            Position along axis `d` to split at.
+
+        Returns
+        -------
+        less : Rectangle
+            Rectangle with `d`-th axis less than `split`.
+        greater : Rectangle
+            Rectangle with `d`-th axis greater than `split`.
+        """
+        mid = np.copy(self.maxes)
+        mid[d] = split
+        less = Rectangle(self.mins, mid)
+        mid = np.copy(self.mins)
+        mid[d] = split
+        greater = Rectangle(mid, self.maxes)
+        return less, greater
+
+    def min_distance_point(self, x, p=2.0):
+        """
+        Return the minimum distance between input and points in the
+        hyperrectangle.
+
+        Parameters
+        ----------
+        x : array_like
+            Input.
+        p : float, optional
+            Input.
+
+        Returns
+        -------
+        dist : ndarray
+            Minimum distance.
+        """
+        delta = np.maximum(0, np.maximum(self.mins - x, x - self.maxes))
+        return minkowski(np.zeros_like(delta), delta, p)
+
+    def max_distance_point(self, x, p=2.0):
+        """
+        Return the maximum distance between input and points in the hyperrectangle.
+
+        Parameters
+        ----------
+        x : array_like
+            Input array.
+        p : float, optional
+            Input.
+
+        Returns
+        -------
+        dist : ndarray
+            Maximum distance.
+        """
+        delta = np.maximum(self.maxes - x, x - self.mins)
+        return minkowski(np.zeros_like(delta), delta, p)
+
+    def min_distance_rectangle(self, other, p=2.0):
+        """
+        Compute the minimum distance between points in the two hyperrectangles.
+
+        Parameters
+        ----------
+        other : hyperrectangle
+            Input.
+        p : float
+            Input.
+
+        Returns
+        -------
+        dist : float
+            Minimum distance between the two hyperrectangles.
+        """
+        delta = np.maximum(0, np.maximum(self.mins - other.maxes,
+                                         other.mins - self.maxes))
+        return minkowski(np.zeros_like(delta), delta, p)
+
+    def max_distance_rectangle(self, other, p=2.0):
+        """
+        Compute the maximum distance between points in the two hyperrectangles.
+
+        Parameters
+        ----------
+        other : hyperrectangle
+            Input.
+        p : float, optional
+            Input.
+
+        Returns
+        -------
+        dist : float
+            Maximum distance between the two hyperrectangles.
+        """
+        delta = np.maximum(self.maxes - other.mins, other.maxes - self.mins)
+        return minkowski(np.zeros_like(delta), delta, p)
+
+
+class KDTree(cKDTree):
+    """
+    kd-tree for quick nearest-neighbor lookup.
+
+    This class provides an index into a set of k-dimensional points
+    which can be used to rapidly look up the nearest neighbors of any
+    point.
+
+    Parameters
+    ----------
+    data : array_like, shape (n,m)
+        The n data points of dimension m to be indexed. This array is
+        not copied unless this is necessary to produce a contiguous
+        array of doubles. The data are also copied if the kd-tree is built
+        with copy_data=True. Concurrently modifying the data while constructing
+        a KDTree is not well-defined and may lead to crashes or data
+        corruption. If no copy happens, modifying the data *after* creating
+        the KDTree may lead to data corruption or incorrect answers when
+        searching the tree.
+    leafsize : positive int, optional
+        The number of points at which the algorithm switches over to
+        brute-force.  Default: 10.
+    compact_nodes : bool, optional
+        If True, the kd-tree is built to shrink the hyperrectangles to
+        the actual data range. This usually gives a more compact tree that
+        is robust against degenerated input data and gives faster queries
+        at the expense of longer build time. Default: True.
+    copy_data : bool, optional
+        If True the data is always copied to protect the kd-tree against
+        data corruption. Default: False.
+    balanced_tree : bool, optional
+        If True, the median is used to split the hyperrectangles instead of
+        the midpoint. This usually gives a more compact tree and
+        faster queries at the expense of longer build time. Default: True.
+    boxsize : array_like or scalar, optional
+        Apply an m-d toroidal topology to the KDTree. The topology is generated
+        by :math:`x_i + n_i L_i` where :math:`n_i` are integers and :math:`L_i`
+        is the boxsize along i-th dimension. The input data shall be wrapped
+        into :math:`[0, L_i)`. A ValueError is raised if any of the data is
+        outside of this bound.
+
+    Attributes
+    ----------
+    data : ndarray, shape (n,m)
+        The n data points of dimension m to be indexed. This array is
+        not copied unless this is necessary to produce a contiguous
+        array of doubles. The data are also copied if the kd-tree is built
+        with ``copy_data=True``.
+    leafsize : positive int
+        The number of points at which the algorithm switches over to
+        brute-force.
+    m : int
+        The dimension of a single data-point.
+    n : int
+        The number of data points.
+    maxes : ndarray, shape (m,)
+        The maximum value in each dimension of the n data points.
+    mins : ndarray, shape (m,)
+        The minimum value in each dimension of the n data points.
+    size : int
+        The number of nodes in the tree.
+    boxsize : None or ndarray, shape (m.)
+        If boxsize is passed to the initializer, this will be set to the bounds
+        of the periodic box. None if no boxsize is passed.
+
+    Notes
+    -----
+    The algorithm used is described in [1]_.
+    The general idea is that the kd-tree is a binary tree, each of whose
+    nodes represents an axis-aligned hyperrectangle. Each node specifies
+    an axis and splits the set of points based on whether their coordinate
+    along that axis is greater than or less than a particular value.
+
+    During construction, the axis and splitting point are chosen by the
+    "sliding midpoint" rule, which ensures that the cells do not all
+    become long and thin.
+
+    The tree can be queried for the r closest neighbors of any given point
+    (optionally returning only those within some maximum distance of the
+    point). It can also be queried, with a substantial gain in efficiency,
+    for the r approximate closest neighbors.
+
+    For large dimensions (20 is already large) do not expect this to run
+    significantly faster than brute force. High-dimensional nearest-neighbor
+    queries are a substantial open problem in computer science.
+
+    References
+    ----------
+    .. [1] S. Maneewongvatana and D.E. Mount, "Analysis of approximate
+           nearest neighbor searching with clustered point sets,"
+           Arxiv e-print, 1999, https://arxiv.org/pdf/cs.CG/9901013
+    """  # numpydoc ignore=SS02
+
+    class node:
+        @staticmethod
+        def _create(ckdtree_node=None):
+            """Create either an inner or leaf node, wrapping a cKDTreeNode instance"""
+            if ckdtree_node is None:
+                return KDTree.node(ckdtree_node)
+            elif ckdtree_node.split_dim == -1:
+                return KDTree.leafnode(ckdtree_node)
+            else:
+                return KDTree.innernode(ckdtree_node)
+
+        def __init__(self, ckdtree_node=None):
+            if ckdtree_node is None:
+                ckdtree_node = cKDTreeNode()
+            self._node = ckdtree_node
+
+        def __lt__(self, other):
+            return id(self) < id(other)
+
+        def __gt__(self, other):
+            return id(self) > id(other)
+
+        def __le__(self, other):
+            return id(self) <= id(other)
+
+        def __ge__(self, other):
+            return id(self) >= id(other)
+
+        def __eq__(self, other):
+            return id(self) == id(other)
+
+    class leafnode(node):
+        @property
+        def idx(self):
+            return self._node.indices
+
+        @property
+        def children(self):
+            return self._node.children
+
+    class innernode(node):
+        def __init__(self, ckdtreenode):
+            assert isinstance(ckdtreenode, cKDTreeNode)
+            super().__init__(ckdtreenode)
+            self.less = KDTree.node._create(ckdtreenode.lesser)
+            self.greater = KDTree.node._create(ckdtreenode.greater)
+
+        @property
+        def split_dim(self):
+            return self._node.split_dim
+
+        @property
+        def split(self):
+            return self._node.split
+
+        @property
+        def children(self):
+            return self._node.children
+
+    @property
+    def tree(self):
+        if not hasattr(self, "_tree"):
+            self._tree = KDTree.node._create(super().tree)
+
+        return self._tree
+
+    def __init__(self, data, leafsize=10, compact_nodes=True, copy_data=False,
+                 balanced_tree=True, boxsize=None):
+        data = np.asarray(data)
+        if data.dtype.kind == 'c':
+            raise TypeError("KDTree does not work with complex data")
+
+        # Note KDTree has different default leafsize from cKDTree
+        super().__init__(data, leafsize, compact_nodes, copy_data,
+                         balanced_tree, boxsize)
+
+    def query(self, x, k=1, eps=0.0, p=2.0, distance_upper_bound=np.inf,
+              workers=1):
+        r"""Query the kd-tree for nearest neighbors.
+
+        Parameters
+        ----------
+        x : array_like, last dimension self.m
+            An array of points to query.
+        k : int or Sequence[int], optional
+            Either the number of nearest neighbors to return, or a list of the
+            k-th nearest neighbors to return, starting from 1.
+        eps : nonnegative float, optional
+            Return approximate nearest neighbors; the kth returned value
+            is guaranteed to be no further than (1+eps) times the
+            distance to the real kth nearest neighbor.
+        p : float, 1<=p<=infinity, optional
+            Which Minkowski p-norm to use.
+            1 is the sum-of-absolute-values distance ("Manhattan" distance).
+            2 is the usual Euclidean distance.
+            infinity is the maximum-coordinate-difference distance.
+            A large, finite p may cause a ValueError if overflow can occur.
+        distance_upper_bound : nonnegative float, optional
+            Return only neighbors within this distance. This is used to prune
+            tree searches, so if you are doing a series of nearest-neighbor
+            queries, it may help to supply the distance to the nearest neighbor
+            of the most recent point.
+        workers : int, optional
+            Number of workers to use for parallel processing. If -1 is given
+            all CPU threads are used. Default: 1.
+
+            .. versionadded:: 1.6.0
+
+        Returns
+        -------
+        d : float or array of floats
+            The distances to the nearest neighbors.
+            If ``x`` has shape ``tuple+(self.m,)``, then ``d`` has shape
+            ``tuple+(k,)``.
+            When k == 1, the last dimension of the output is squeezed.
+            Missing neighbors are indicated with infinite distances.
+            Hits are sorted by distance (nearest first).
+
+            .. versionchanged:: 1.9.0
+               Previously if ``k=None``, then `d` was an object array of
+               shape ``tuple``, containing lists of distances. This behavior
+               has been removed, use `query_ball_point` instead.
+
+        i : int or array of integers
+            The index of each neighbor in ``self.data``.
+            ``i`` is the same shape as d.
+            Missing neighbors are indicated with ``self.n``.
+
+        Examples
+        --------
+
+        >>> import numpy as np
+        >>> from scipy.spatial import KDTree
+        >>> x, y = np.mgrid[0:5, 2:8]
+        >>> tree = KDTree(np.c_[x.ravel(), y.ravel()])
+
+        To query the nearest neighbours and return squeezed result, use
+
+        >>> dd, ii = tree.query([[0, 0], [2.2, 2.9]], k=1)
+        >>> print(dd, ii, sep='\n')
+        [2.         0.2236068]
+        [ 0 13]
+
+        To query the nearest neighbours and return unsqueezed result, use
+
+        >>> dd, ii = tree.query([[0, 0], [2.2, 2.9]], k=[1])
+        >>> print(dd, ii, sep='\n')
+        [[2.        ]
+         [0.2236068]]
+        [[ 0]
+         [13]]
+
+        To query the second nearest neighbours and return unsqueezed result,
+        use
+
+        >>> dd, ii = tree.query([[0, 0], [2.2, 2.9]], k=[2])
+        >>> print(dd, ii, sep='\n')
+        [[2.23606798]
+         [0.80622577]]
+        [[ 6]
+         [19]]
+
+        To query the first and second nearest neighbours, use
+
+        >>> dd, ii = tree.query([[0, 0], [2.2, 2.9]], k=2)
+        >>> print(dd, ii, sep='\n')
+        [[2.         2.23606798]
+         [0.2236068  0.80622577]]
+        [[ 0  6]
+         [13 19]]
+
+        or, be more specific
+
+        >>> dd, ii = tree.query([[0, 0], [2.2, 2.9]], k=[1, 2])
+        >>> print(dd, ii, sep='\n')
+        [[2.         2.23606798]
+         [0.2236068  0.80622577]]
+        [[ 0  6]
+         [13 19]]
+
+        """
+        x = np.asarray(x)
+        if x.dtype.kind == 'c':
+            raise TypeError("KDTree does not work with complex data")
+
+        if k is None:
+            raise ValueError("k must be an integer or a sequence of integers")
+
+        d, i = super().query(x, k, eps, p, distance_upper_bound, workers)
+        if isinstance(i, int):
+            i = np.intp(i)
+        return d, i
+
+    def query_ball_point(self, x, r, p=2.0, eps=0.0, workers=1,
+                         return_sorted=None, return_length=False):
+        """Find all points within distance r of point(s) x.
+
+        Parameters
+        ----------
+        x : array_like, shape tuple + (self.m,)
+            The point or points to search for neighbors of.
+        r : array_like, float
+            The radius of points to return, must broadcast to the length of x.
+        p : float, optional
+            Which Minkowski p-norm to use.  Should be in the range [1, inf].
+            A finite large p may cause a ValueError if overflow can occur.
+        eps : nonnegative float, optional
+            Approximate search. Branches of the tree are not explored if their
+            nearest points are further than ``r / (1 + eps)``, and branches are
+            added in bulk if their furthest points are nearer than
+            ``r * (1 + eps)``.
+        workers : int, optional
+            Number of jobs to schedule for parallel processing. If -1 is given
+            all processors are used. Default: 1.
+
+            .. versionadded:: 1.6.0
+        return_sorted : bool, optional
+            Sorts returned indices if True and does not sort them if False. If
+            None, does not sort single point queries, but does sort
+            multi-point queries which was the behavior before this option
+            was added.
+
+            .. versionadded:: 1.6.0
+        return_length : bool, optional
+            Return the number of points inside the radius instead of a list
+            of the indices.
+
+            .. versionadded:: 1.6.0
+
+        Returns
+        -------
+        results : list or array of lists
+            If `x` is a single point, returns a list of the indices of the
+            neighbors of `x`. If `x` is an array of points, returns an object
+            array of shape tuple containing lists of neighbors.
+
+        Notes
+        -----
+        If you have many points whose neighbors you want to find, you may save
+        substantial amounts of time by putting them in a KDTree and using
+        query_ball_tree.
+
+        Examples
+        --------
+        >>> import numpy as np
+        >>> from scipy import spatial
+        >>> x, y = np.mgrid[0:5, 0:5]
+        >>> points = np.c_[x.ravel(), y.ravel()]
+        >>> tree = spatial.KDTree(points)
+        >>> sorted(tree.query_ball_point([2, 0], 1))
+        [5, 10, 11, 15]
+
+        Query multiple points and plot the results:
+
+        >>> import matplotlib.pyplot as plt
+        >>> points = np.asarray(points)
+        >>> plt.plot(points[:,0], points[:,1], '.')
+        >>> for results in tree.query_ball_point(([2, 0], [3, 3]), 1):
+        ...     nearby_points = points[results]
+        ...     plt.plot(nearby_points[:,0], nearby_points[:,1], 'o')
+        >>> plt.margins(0.1, 0.1)
+        >>> plt.show()
+
+        """
+        x = np.asarray(x)
+        if x.dtype.kind == 'c':
+            raise TypeError("KDTree does not work with complex data")
+        return super().query_ball_point(
+            x, r, p, eps, workers, return_sorted, return_length)
+
+    def query_ball_tree(self, other, r, p=2.0, eps=0.0):
+        """
+        Find all pairs of points between `self` and `other` whose distance is
+        at most r.
+
+        Parameters
+        ----------
+        other : KDTree instance
+            The tree containing points to search against.
+        r : float
+            The maximum distance, has to be positive.
+        p : float, optional
+            Which Minkowski norm to use.  `p` has to meet the condition
+            ``1 <= p <= infinity``.
+        eps : float, optional
+            Approximate search.  Branches of the tree are not explored
+            if their nearest points are further than ``r/(1+eps)``, and
+            branches are added in bulk if their furthest points are nearer
+            than ``r * (1+eps)``.  `eps` has to be non-negative.
+
+        Returns
+        -------
+        results : list of lists
+            For each element ``self.data[i]`` of this tree, ``results[i]`` is a
+            list of the indices of its neighbors in ``other.data``.
+
+        Examples
+        --------
+        You can search all pairs of points between two kd-trees within a distance:
+
+        >>> import matplotlib.pyplot as plt
+        >>> import numpy as np
+        >>> from scipy.spatial import KDTree
+        >>> rng = np.random.default_rng()
+        >>> points1 = rng.random((15, 2))
+        >>> points2 = rng.random((15, 2))
+        >>> plt.figure(figsize=(6, 6))
+        >>> plt.plot(points1[:, 0], points1[:, 1], "xk", markersize=14)
+        >>> plt.plot(points2[:, 0], points2[:, 1], "og", markersize=14)
+        >>> kd_tree1 = KDTree(points1)
+        >>> kd_tree2 = KDTree(points2)
+        >>> indexes = kd_tree1.query_ball_tree(kd_tree2, r=0.2)
+        >>> for i in range(len(indexes)):
+        ...     for j in indexes[i]:
+        ...         plt.plot([points1[i, 0], points2[j, 0]],
+        ...             [points1[i, 1], points2[j, 1]], "-r")
+        >>> plt.show()
+
+        """
+        return super().query_ball_tree(other, r, p, eps)
+
+    def query_pairs(self, r, p=2.0, eps=0.0, output_type='set'):
+        """Find all pairs of points in `self` whose distance is at most r.
+
+        Parameters
+        ----------
+        r : positive float
+            The maximum distance.
+        p : float, optional
+            Which Minkowski norm to use.  `p` has to meet the condition
+            ``1 <= p <= infinity``.
+        eps : float, optional
+            Approximate search.  Branches of the tree are not explored
+            if their nearest points are further than ``r/(1+eps)``, and
+            branches are added in bulk if their furthest points are nearer
+            than ``r * (1+eps)``.  `eps` has to be non-negative.
+        output_type : str, optional
+            Choose the output container, 'set' or 'ndarray'. Default: 'set'
+
+            .. versionadded:: 1.6.0
+
+        Returns
+        -------
+        results : set or ndarray
+            Set of pairs ``(i,j)``, with ``i < j``, for which the corresponding
+            positions are close. If output_type is 'ndarray', an ndarray is
+            returned instead of a set.
+
+        Examples
+        --------
+        You can search all pairs of points in a kd-tree within a distance:
+
+        >>> import matplotlib.pyplot as plt
+        >>> import numpy as np
+        >>> from scipy.spatial import KDTree
+        >>> rng = np.random.default_rng()
+        >>> points = rng.random((20, 2))
+        >>> plt.figure(figsize=(6, 6))
+        >>> plt.plot(points[:, 0], points[:, 1], "xk", markersize=14)
+        >>> kd_tree = KDTree(points)
+        >>> pairs = kd_tree.query_pairs(r=0.2)
+        >>> for (i, j) in pairs:
+        ...     plt.plot([points[i, 0], points[j, 0]],
+        ...             [points[i, 1], points[j, 1]], "-r")
+        >>> plt.show()
+
+        """
+        return super().query_pairs(r, p, eps, output_type)
+
+    def count_neighbors(self, other, r, p=2.0, weights=None, cumulative=True):
+        """Count how many nearby pairs can be formed.
+
+        Count the number of pairs ``(x1,x2)`` can be formed, with ``x1`` drawn
+        from ``self`` and ``x2`` drawn from ``other``, and where
+        ``distance(x1, x2, p) <= r``.
+
+        Data points on ``self`` and ``other`` are optionally weighted by the
+        ``weights`` argument. (See below)
+
+        This is adapted from the "two-point correlation" algorithm described by
+        Gray and Moore [1]_.  See notes for further discussion.
+
+        Parameters
+        ----------
+        other : KDTree
+            The other tree to draw points from, can be the same tree as self.
+        r : float or one-dimensional array of floats
+            The radius to produce a count for. Multiple radii are searched with
+            a single tree traversal.
+            If the count is non-cumulative (``cumulative=False``), ``r``
+            defines the edges of the bins, and must be non-decreasing.
+        p : float, optional
+            1<=p<=infinity.
+            Which Minkowski p-norm to use.
+            Default 2.0.
+            A finite large p may cause a ValueError if overflow can occur.
+        weights : tuple, array_like, or None, optional
+            If None, the pair-counting is unweighted.
+            If given as a tuple, weights[0] is the weights of points in
+            ``self``, and weights[1] is the weights of points in ``other``;
+            either can be None to indicate the points are unweighted.
+            If given as an array_like, weights is the weights of points in
+            ``self`` and ``other``. For this to make sense, ``self`` and
+            ``other`` must be the same tree. If ``self`` and ``other`` are two
+            different trees, a ``ValueError`` is raised.
+            Default: None
+
+            .. versionadded:: 1.6.0
+        cumulative : bool, optional
+            Whether the returned counts are cumulative. When cumulative is set
+            to ``False`` the algorithm is optimized to work with a large number
+            of bins (>10) specified by ``r``. When ``cumulative`` is set to
+            True, the algorithm is optimized to work with a small number of
+            ``r``. Default: True
+
+            .. versionadded:: 1.6.0
+
+        Returns
+        -------
+        result : scalar or 1-D array
+            The number of pairs. For unweighted counts, the result is integer.
+            For weighted counts, the result is float.
+            If cumulative is False, ``result[i]`` contains the counts with
+            ``(-inf if i == 0 else r[i-1]) < R <= r[i]``
+
+        Notes
+        -----
+        Pair-counting is the basic operation used to calculate the two point
+        correlation functions from a data set composed of position of objects.
+
+        Two point correlation function measures the clustering of objects and
+        is widely used in cosmology to quantify the large scale structure
+        in our Universe, but it may be useful for data analysis in other fields
+        where self-similar assembly of objects also occur.
+
+        The Landy-Szalay estimator for the two point correlation function of
+        ``D`` measures the clustering signal in ``D``. [2]_
+
+        For example, given the position of two sets of objects,
+
+        - objects ``D`` (data) contains the clustering signal, and
+
+        - objects ``R`` (random) that contains no signal,
+
+        .. math::
+
+             \\xi(r) = \\frac{<D, D> - 2 f <D, R> + f^2<R, R>}{f^2<R, R>},
+
+        where the brackets represents counting pairs between two data sets
+        in a finite bin around ``r`` (distance), corresponding to setting
+        `cumulative=False`, and ``f = float(len(D)) / float(len(R))`` is the
+        ratio between number of objects from data and random.
+
+        The algorithm implemented here is loosely based on the dual-tree
+        algorithm described in [1]_. We switch between two different
+        pair-cumulation scheme depending on the setting of ``cumulative``.
+        The computing time of the method we use when for
+        ``cumulative == False`` does not scale with the total number of bins.
+        The algorithm for ``cumulative == True`` scales linearly with the
+        number of bins, though it is slightly faster when only
+        1 or 2 bins are used. [5]_.
+
+        As an extension to the naive pair-counting,
+        weighted pair-counting counts the product of weights instead
+        of number of pairs.
+        Weighted pair-counting is used to estimate marked correlation functions
+        ([3]_, section 2.2),
+        or to properly calculate the average of data per distance bin
+        (e.g. [4]_, section 2.1 on redshift).
+
+        .. [1] Gray and Moore,
+               "N-body problems in statistical learning",
+               Mining the sky, 2000,
+               https://arxiv.org/abs/astro-ph/0012333
+
+        .. [2] Landy and Szalay,
+               "Bias and variance of angular correlation functions",
+               The Astrophysical Journal, 1993,
+               http://adsabs.harvard.edu/abs/1993ApJ...412...64L
+
+        .. [3] Sheth, Connolly and Skibba,
+               "Marked correlations in galaxy formation models",
+               Arxiv e-print, 2005,
+               https://arxiv.org/abs/astro-ph/0511773
+
+        .. [4] Hawkins, et al.,
+               "The 2dF Galaxy Redshift Survey: correlation functions,
+               peculiar velocities and the matter density of the Universe",
+               Monthly Notices of the Royal Astronomical Society, 2002,
+               http://adsabs.harvard.edu/abs/2003MNRAS.346...78H
+
+        .. [5] https://github.com/scipy/scipy/pull/5647#issuecomment-168474926
+
+        Examples
+        --------
+        You can count neighbors number between two kd-trees within a distance:
+
+        >>> import numpy as np
+        >>> from scipy.spatial import KDTree
+        >>> rng = np.random.default_rng()
+        >>> points1 = rng.random((5, 2))
+        >>> points2 = rng.random((5, 2))
+        >>> kd_tree1 = KDTree(points1)
+        >>> kd_tree2 = KDTree(points2)
+        >>> kd_tree1.count_neighbors(kd_tree2, 0.2)
+        1
+
+        This number is same as the total pair number calculated by
+        `query_ball_tree`:
+
+        >>> indexes = kd_tree1.query_ball_tree(kd_tree2, r=0.2)
+        >>> sum([len(i) for i in indexes])
+        1
+
+        """
+        return super().count_neighbors(other, r, p, weights, cumulative)
+
+    def sparse_distance_matrix(
+            self, other, max_distance, p=2.0, output_type='dok_matrix'):
+        """Compute a sparse distance matrix.
+
+        Computes a distance matrix between two KDTrees, leaving as zero
+        any distance greater than max_distance.
+
+        Parameters
+        ----------
+        other : KDTree
+            The other `KDTree` to compute distances against.
+        max_distance : positive float
+            Maximum distance within which neighbors are returned. Distances above this
+            value are returned as zero.
+        p : float, 1<=p<=infinity
+            Which Minkowski p-norm to use.
+            A finite large p may cause a ValueError if overflow can occur.
+        output_type : str, optional
+            Which container to use for output data. Options: ``'dok_array'``,
+            ``'coo_array'``, ``'dict'``, or ``'ndarray'``.
+            Legacy options ``'dok_matrix'`` and ``'coo_matrix'`` are still available.
+            Default: ``'dok_matrix'``.
+
+            .. warning:: dok_matrix and coo_matrix are being replaced.
+
+               All new code using scipy sparse should use sparse array
+               types 'dok_array' or 'coo_array'. The default value of
+               `output_type` will be deprecated at v1.19 and switch from
+               'dok_matrix' to 'dok_array' in v1.21.
+               The values 'dok_matrix' and 'coo_matrix' continue
+               to work, but will go away eventually.
+
+            .. versionadded:: 1.6.0
+
+        Returns
+        -------
+        result : dok_array, coo_array, dict or ndarray
+            Sparse matrix representing the results in "dictionary of keys"
+            format. If a dict is returned the keys are ``(i,j)`` tuples of indices.
+            If output_type is ``'ndarray'`` a record array with fields ``'i'``, ``'j'``,
+            and ``'v'`` is returned,
+
+        Examples
+        --------
+        You can compute a sparse distance matrix between two kd-trees:
+
+        >>> import numpy as np
+        >>> from scipy.spatial import KDTree
+        >>> rng = np.random.default_rng()
+        >>> points1 = rng.random((5, 2))
+        >>> points2 = rng.random((5, 2))
+        >>> kdtree1 = KDTree(points1)
+        >>> kdtree2 = KDTree(points2)
+        >>> sdm = kdtree1.sparse_distance_matrix(kdtree2, 0.3, output_type="dok_array")
+        >>> sdm.toarray()
+        array([[0.        , 0.        , 0.12295571, 0.        , 0.        ],
+           [0.        , 0.        , 0.        , 0.        , 0.        ],
+           [0.28942611, 0.        , 0.        , 0.2333084 , 0.        ],
+           [0.        , 0.        , 0.        , 0.        , 0.        ],
+           [0.24617575, 0.29571802, 0.26836782, 0.        , 0.        ]])
+
+        You can check distances above the `max_distance` are zeros:
+
+        >>> from scipy.spatial.distance import cdist
+        >>> cdist(points1, points2)
+        array([[0.56906522, 0.39923701, 0.12295571, 0.8658745 , 0.79428925],
+           [0.37327919, 0.7225693 , 0.87665969, 0.32580855, 0.75679479],
+           [0.28942611, 0.30088013, 0.6395831 , 0.2333084 , 0.33630734],
+           [0.31994999, 0.72658602, 0.71124834, 0.55396483, 0.90785663],
+           [0.24617575, 0.29571802, 0.26836782, 0.57714465, 0.6473269 ]])
+
+        """
+        return super().sparse_distance_matrix(other, max_distance, p, output_type)
+
+
+@xp_capabilities(out_of_scope=True)
+def distance_matrix(x, y, p=2.0, threshold=1000000):
+    """Compute the distance matrix.
+
+    Returns the matrix of all pair-wise distances.
+
+    .. deprecated:: 1.18.0
+        This function is deprecated in favor of `scipy.spatial.distance.cdist`
+        and will be removed in SciPy 1.20.0.
+
+    Parameters
+    ----------
+    x : (M, K) array_like
+        Matrix of M vectors in K dimensions.
+    y : (N, K) array_like
+        Matrix of N vectors in K dimensions.
+    p : float, 1 <= p <= infinity
+        Which Minkowski p-norm to use.
+    threshold : positive int
+        If ``M * N * K`` > `threshold`, algorithm uses a Python loop instead
+        of large temporary arrays.
+
+    Returns
+    -------
+    result : (M, N) ndarray
+        Matrix containing the distance from every vector in `x` to every vector
+        in `y`.
+
+    Examples
+    --------
+    >>> from scipy.spatial import distance_matrix
+    >>> distance_matrix([[0,0],[0,1]], [[1,0],[1,1]])
+    array([[ 1.        ,  1.41421356],
+           [ 1.41421356,  1.        ]])
+
+    """
+    msg = ("`distance_matrix` is deprecated in favor of "
+           "`scipy.spatial.distance.cdist` as of SciPy 1.18.0 and will be removed "
+           "in SciPy 1.20.0.")
+    warnings.warn(msg, DeprecationWarning,
+                  skip_file_prefixes=(os.path.dirname(__file__),))
+    x = np.asarray(x)
+    m, k = x.shape
+    y = np.asarray(y)
+    n, kk = y.shape
+
+    if k != kk:
+        raise ValueError(f"x contains {k}-dimensional vectors but y contains "
+                         f"{kk}-dimensional vectors")
+
+    if m*n*k <= threshold:
+        return minkowski_distance(x[:,np.newaxis,:],y[np.newaxis,:,:],p)
+    else:
+        result = np.empty((m,n),dtype=float)  # FIXME: figure out the best dtype
+        if m < n:
+            for i in range(m):
+                result[i,:] = minkowski_distance(x[i],y,p)
+        else:
+            for j in range(n):
+                result[:,j] = minkowski_distance(x,y[j],p)
+        return result
diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/_plotutils.py b/venv/lib/python3.12/site-packages/scipy/spatial/_plotutils.py
new file mode 100644
index 0000000000000000000000000000000000000000..a6290cde5dd9e37e01ac7c3944758fe59a0952b0
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/_plotutils.py
@@ -0,0 +1,263 @@
+import numpy as np
+
+__all__ = ['delaunay_plot_2d', 'convex_hull_plot_2d', 'voronoi_plot_2d']
+
+
+def _get_axes():
+    import matplotlib.pyplot as plt
+
+    return plt.figure().gca()
+
+
+def _adjust_bounds(ax, points):
+    margin = 0.1 * np.ptp(points, axis=0)
+    xy_min = points.min(axis=0) - margin
+    xy_max = points.max(axis=0) + margin
+    ax.set_xlim(xy_min[0], xy_max[0])
+    ax.set_ylim(xy_min[1], xy_max[1])
+
+
+def delaunay_plot_2d(tri, ax=None):
+    """
+    Plot the given Delaunay triangulation in 2-D.
+
+    Parameters
+    ----------
+    tri : scipy.spatial.Delaunay instance
+        Triangulation to plot
+    ax : matplotlib.axes.Axes instance, optional
+        Axes to plot on
+
+    Returns
+    -------
+    fig : matplotlib.figure.Figure instance
+        Figure for the plot
+
+    See Also
+    --------
+    Delaunay
+    matplotlib.pyplot.triplot
+
+    Notes
+    -----
+    Requires Matplotlib.
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.spatial import Delaunay, delaunay_plot_2d
+
+    The Delaunay triangulation of a set of random points:
+
+    >>> rng = np.random.default_rng()
+    >>> points = rng.random((30, 2))
+    >>> tri = Delaunay(points)
+
+    Plot it:
+
+    >>> _ = delaunay_plot_2d(tri)
+    >>> plt.show()
+
+    """
+    if tri.points.shape[1] != 2:
+        raise ValueError("Delaunay triangulation is not 2-D")
+
+    x, y = tri.points.T
+
+    ax = ax or _get_axes()
+    ax.plot(x, y, 'o')
+    ax.triplot(x, y, tri.simplices.copy())
+
+    _adjust_bounds(ax, tri.points)
+
+    return ax.figure
+
+
+def convex_hull_plot_2d(hull, ax=None):
+    """
+    Plot the given convex hull diagram in 2-D.
+
+    Parameters
+    ----------
+    hull : scipy.spatial.ConvexHull instance
+        Convex hull to plot
+    ax : matplotlib.axes.Axes instance, optional
+        Axes to plot on
+
+    Returns
+    -------
+    fig : matplotlib.figure.Figure instance
+        Figure for the plot
+
+    See Also
+    --------
+    ConvexHull
+
+    Notes
+    -----
+    Requires Matplotlib.
+
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.spatial import ConvexHull, convex_hull_plot_2d
+
+    The convex hull of a random set of points:
+
+    >>> rng = np.random.default_rng()
+    >>> points = rng.random((30, 2))
+    >>> hull = ConvexHull(points)
+
+    Plot it:
+
+    >>> _ = convex_hull_plot_2d(hull)
+    >>> plt.show()
+
+    """
+    from matplotlib.collections import LineCollection
+
+    if hull.points.shape[1] != 2:
+        raise ValueError("Convex hull is not 2-D")
+
+    ax = ax or _get_axes()
+    ax.plot(hull.points[:, 0], hull.points[:, 1], 'o')
+    line_segments = [hull.points[simplex] for simplex in hull.simplices]
+    ax.add_collection(LineCollection(line_segments,
+                                     colors='k',
+                                     linestyle='solid'))
+    _adjust_bounds(ax, hull.points)
+
+    return ax.figure
+
+
+def voronoi_plot_2d(vor, ax=None, **kw):
+    """
+    Plot the given Voronoi diagram in 2-D.
+
+    Parameters
+    ----------
+    vor : scipy.spatial.Voronoi instance
+        Diagram to plot
+    ax : matplotlib.axes.Axes instance, optional
+        Axes to plot on
+    **kw
+        The following options may be passed as keyword arguments:
+
+        show_points : bool, optional
+            Add the Voronoi points to the plot.
+        show_vertices : bool, optional
+            Add the Voronoi vertices to the plot.
+        line_colors : str, optional
+            Specifies the line color for polygon boundaries
+        line_width : float, optional
+            Specifies the line width for polygon boundaries
+        line_alpha : float, optional
+            Specifies the line alpha for polygon boundaries
+        point_size : float, optional
+            Specifies the size of points
+
+    Returns
+    -------
+    fig : matplotlib.figure.Figure instance
+        Figure for the plot
+
+    See Also
+    --------
+    Voronoi
+
+    Notes
+    -----
+    Requires Matplotlib. For degenerate input, including collinearity and
+    other violations of general position, it may be preferable to
+    calculate the Voronoi diagram with Qhull options ``QJ`` for random
+    joggling, or ``Qt`` to enforce triangulated output. Otherwise, some
+    Voronoi regions may not be visible.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.spatial import Voronoi, voronoi_plot_2d
+
+    Create a set of points for the example:
+
+    >>> rng = np.random.default_rng()
+    >>> points = rng.random((10,2))
+
+    Generate the Voronoi diagram for the points:
+
+    >>> vor = Voronoi(points)
+
+    Use `voronoi_plot_2d` to plot the diagram:
+
+    >>> fig = voronoi_plot_2d(vor)
+
+    Use `voronoi_plot_2d` to plot the diagram again, with some settings
+    customized:
+
+    >>> fig = voronoi_plot_2d(vor, show_vertices=False, line_colors='orange',
+    ...                       line_width=2, line_alpha=0.6, point_size=2)
+    >>> plt.show()
+
+    """
+    from matplotlib.collections import LineCollection
+
+    if vor.points.shape[1] != 2:
+        raise ValueError("Voronoi diagram is not 2-D")
+
+    ax = ax or _get_axes()
+
+    if kw.get('show_points', True):
+        point_size = kw.get('point_size', None)
+        ax.plot(vor.points[:, 0], vor.points[:, 1], '.', markersize=point_size)
+    if kw.get('show_vertices', True):
+        ax.plot(vor.vertices[:, 0], vor.vertices[:, 1], 'o')
+
+    line_colors = kw.get('line_colors', 'k')
+    line_width = kw.get('line_width', 1.0)
+    line_alpha = kw.get('line_alpha', 1.0)
+
+    center = vor.points.mean(axis=0)
+    ptp_bound = np.ptp(vor.points, axis=0)
+
+    finite_segments = []
+    infinite_segments = []
+    for pointidx, simplex in zip(vor.ridge_points, vor.ridge_vertices):
+        simplex = np.asarray(simplex)
+        if np.all(simplex >= 0):
+            finite_segments.append(vor.vertices[simplex])
+        else:
+            i = simplex[simplex >= 0][0]  # finite end Voronoi vertex
+
+            t = vor.points[pointidx[1]] - vor.points[pointidx[0]]  # tangent
+            t /= np.linalg.norm(t)
+            n = np.array([-t[1], t[0]])  # normal
+
+            midpoint = vor.points[pointidx].mean(axis=0)
+            direction = np.sign(np.dot(midpoint - center, n)) * n
+            if (vor.furthest_site):
+                direction = -direction
+            aspect_factor = abs(ptp_bound.max() / ptp_bound.min())
+            far_point = vor.vertices[i] + direction * ptp_bound.max() * aspect_factor
+
+            infinite_segments.append([vor.vertices[i], far_point])
+
+    ax.add_collection(LineCollection(finite_segments,
+                                     colors=line_colors,
+                                     lw=line_width,
+                                     alpha=line_alpha,
+                                     linestyle='solid'))
+    ax.add_collection(LineCollection(infinite_segments,
+                                     colors=line_colors,
+                                     lw=line_width,
+                                     alpha=line_alpha,
+                                     linestyle='dashed'))
+
+    _adjust_bounds(ax, vor.points)
+
+    return ax.figure
diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/_procrustes.py b/venv/lib/python3.12/site-packages/scipy/spatial/_procrustes.py
new file mode 100644
index 0000000000000000000000000000000000000000..e3814ab5a8404461b446eb473f5bf96deb9f8c1f
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/_procrustes.py
@@ -0,0 +1,132 @@
+"""
+This module provides functions to perform full Procrustes analysis.
+
+This code was originally written by Justin Kucynski and ported over from
+scikit-bio by Yoshiki Vazquez-Baeza.
+"""
+
+import numpy as np
+from scipy.linalg import orthogonal_procrustes
+
+
+__all__ = ['procrustes']
+
+
+def procrustes(data1, data2):
+    r"""Procrustes analysis, a similarity test for two data sets.
+
+    Each input matrix is a set of points or vectors (the rows of the matrix).
+    The dimension of the space is the number of columns of each matrix. Given
+    two identically sized matrices, procrustes standardizes both such that:
+
+    - :math:`tr(AA^{T}) = 1`.
+
+    - Both sets of points are centered around the origin.
+
+    Procrustes ([1]_, [2]_) then applies the optimal transform to the second
+    matrix (including scaling/dilation, rotations, and reflections) to minimize
+    :math:`M^{2}=\sum(data1-data2)^{2}`, or the sum of the squares of the
+    pointwise differences between the two input datasets.
+
+    This function was not designed to handle datasets with different numbers of
+    datapoints (rows).  If two data sets have different dimensionality
+    (different number of columns), simply add columns of zeros to the smaller
+    of the two.
+
+    Parameters
+    ----------
+    data1 : array_like
+        Matrix, n rows represent points in k (columns) space `data1` is the
+        reference data, after it is standardised, the data from `data2` will be
+        transformed to fit the pattern in `data1` (must have >1 unique points).
+    data2 : array_like
+        n rows of data in k space to be fit to `data1`.  Must be the  same
+        shape ``(numrows, numcols)`` as data1 (must have >1 unique points).
+
+    Returns
+    -------
+    mtx1 : array_like
+        A standardized version of `data1`.
+    mtx2 : array_like
+        The orientation of `data2` that best fits `data1`. Centered, but not
+        necessarily :math:`tr(AA^{T}) = 1`.
+    disparity : float
+        :math:`M^{2}` as defined above.
+
+    Raises
+    ------
+    ValueError
+        If the input arrays are not two-dimensional.
+        If the shape of the input arrays is different.
+        If the input arrays have zero columns or zero rows.
+
+    See Also
+    --------
+    scipy.linalg.orthogonal_procrustes
+    scipy.spatial.distance.directed_hausdorff : Another similarity test
+      for two data sets
+
+    Notes
+    -----
+    - The disparity should not depend on the order of the input matrices, but
+      the output matrices will, as only the first output matrix is guaranteed
+      to be scaled such that :math:`tr(AA^{T}) = 1`.
+
+    - Duplicate data points are generally ok, duplicating a data point will
+      increase its effect on the procrustes fit.
+
+    - The disparity scales as the number of points per input matrix.
+
+    References
+    ----------
+    .. [1] Krzanowski, W. J. (2000). "Principles of Multivariate analysis".
+    .. [2] Gower, J. C. (1975). "Generalized procrustes analysis".
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.spatial import procrustes
+
+    The matrix ``b`` is a rotated, shifted, scaled and mirrored version of
+    ``a`` here:
+
+    >>> a = np.array([[1, 3], [1, 2], [1, 1], [2, 1]], 'd')
+    >>> b = np.array([[4, -2], [4, -4], [4, -6], [2, -6]], 'd')
+    >>> mtx1, mtx2, disparity = procrustes(a, b)
+    >>> round(disparity)
+    0
+
+    """
+    mtx1 = np.array(data1, dtype=np.float64, copy=True)
+    mtx2 = np.array(data2, dtype=np.float64, copy=True)
+
+    if mtx1.ndim != 2 or mtx2.ndim != 2:
+        raise ValueError("Input matrices must be two-dimensional")
+    if mtx1.shape != mtx2.shape:
+        raise ValueError("Input matrices must be of same shape")
+    if mtx1.size == 0:
+        raise ValueError("Input matrices must be >0 rows and >0 cols")
+
+    # translate all the data to the origin
+    mtx1 -= np.mean(mtx1, 0)
+    mtx2 -= np.mean(mtx2, 0)
+
+    norm1 = np.linalg.norm(mtx1)
+    norm2 = np.linalg.norm(mtx2)
+
+    if norm1 == 0 or norm2 == 0:
+        raise ValueError("Input matrices must contain >1 unique points")
+
+    # change scaling of data (in rows) such that trace(mtx*mtx') = 1
+    mtx1 /= norm1
+    mtx2 /= norm2
+
+    # transform mtx2 to minimize disparity
+    R, s = orthogonal_procrustes(mtx1, mtx2)
+    mtx2 = np.dot(mtx2, R.T) * s
+
+    # measure the dissimilarity between the two datasets
+    disparity = np.sum(np.square(mtx1 - mtx2))
+
+    return mtx1, mtx2, disparity
+
diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/_qhull.cpython-312-x86_64-linux-gnu.so b/venv/lib/python3.12/site-packages/scipy/spatial/_qhull.cpython-312-x86_64-linux-gnu.so
new file mode 100644
index 0000000000000000000000000000000000000000..d598bfa3b5a9977e993562a7373b2f8dd3d6bfc0
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/_qhull.cpython-312-x86_64-linux-gnu.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f0ece0e7838e9d1ee5c3126292fed225e740734d99280b0faa3ff1cf726b531a
+size 935776
diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/_qhull.pyi b/venv/lib/python3.12/site-packages/scipy/spatial/_qhull.pyi
new file mode 100644
index 0000000000000000000000000000000000000000..723c28d1ce90ab6cd0657e7587eb1eb6eea2f8d6
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/_qhull.pyi
@@ -0,0 +1,213 @@
+'''
+Static type checking stub file for scipy/spatial/qhull.pyx
+'''
+
+
+import numpy as np
+from numpy.typing import ArrayLike, NDArray
+from typing import final
+
+class QhullError(RuntimeError):
+    ...
+
+@final
+class _Qhull:
+    # Read-only cython attribute that behaves, more or less, like a property
+    @property
+    def ndim(self) -> int: ...
+    mode_option: bytes
+    options: bytes
+    furthest_site: bool
+
+    def __init__(
+        self,
+        mode_option: bytes,
+        points: NDArray[np.float64],
+        options: None | bytes = ...,
+        required_options: None | bytes = ...,
+        furthest_site: bool = ...,
+        incremental: bool = ...,
+        interior_point: None | NDArray[np.float64] = ...,
+    ) -> None: ...
+    def check_active(self) -> None: ...
+    def close(self) -> None: ...
+    def get_points(self) -> NDArray[np.float64]: ...
+    def add_points(
+        self,
+        points: ArrayLike,
+        interior_point: ArrayLike = ...
+    ) -> None: ...
+    def get_paraboloid_shift_scale(self) -> tuple[float, float]: ...
+    def volume_area(self) -> tuple[float, float]: ...
+    def triangulate(self) -> None: ...
+    def get_simplex_facet_array(self) -> tuple[
+        NDArray[np.intc],
+        NDArray[np.intc],
+        NDArray[np.float64],
+        NDArray[np.intc],
+        NDArray[np.intc],
+    ]: ...
+    def get_hull_points(self) -> NDArray[np.float64]: ...
+    def get_hull_facets(self) -> tuple[
+        list[list[int]],
+        NDArray[np.float64],
+    ]: ...
+    def get_voronoi_diagram(self) -> tuple[
+        NDArray[np.float64],
+        NDArray[np.intc],
+        list[list[int]],
+        list[list[int]],
+        NDArray[np.intp],
+    ]: ...
+    def get_extremes_2d(self) -> NDArray[np.intc]: ...
+
+def _get_barycentric_transforms(
+    points: NDArray[np.float64],
+    simplices: NDArray[np.intc],
+    eps: float
+) -> NDArray[np.float64]: ...
+
+class _QhullUser:
+    ndim: int
+    npoints: int
+    min_bound: NDArray[np.float64]
+    max_bound: NDArray[np.float64]
+
+    def __init__(self, qhull: _Qhull, incremental: bool = ...) -> None: ...
+    def close(self) -> None: ...
+    def _update(self, qhull: _Qhull) -> None: ...
+    def _add_points(
+        self,
+        points: ArrayLike,
+        restart: bool = ...,
+        interior_point: ArrayLike = ...
+    ) -> None: ...
+
+class Delaunay(_QhullUser):
+    furthest_site: bool
+    paraboloid_scale: float
+    paraboloid_shift: float
+    simplices: NDArray[np.intc]
+    neighbors: NDArray[np.intc]
+    equations: NDArray[np.float64]
+    coplanar: NDArray[np.intc]
+    good: NDArray[np.intc]
+    nsimplex: int
+    vertices: NDArray[np.intc]
+
+    def __init__(
+        self,
+        points: ArrayLike,
+        furthest_site: bool = ...,
+        incremental: bool = ...,
+        qhull_options: None | str = ...
+    ) -> None: ...
+    def _update(self, qhull: _Qhull) -> None: ...
+    def add_points(
+        self,
+        points: ArrayLike,
+        restart: bool = ...
+    ) -> None: ...
+    @property
+    def points(self) -> NDArray[np.float64]: ...
+    @property
+    def transform(self) -> NDArray[np.float64]: ...
+    @property
+    def vertex_to_simplex(self) -> NDArray[np.intc]: ...
+    @property
+    def vertex_neighbor_vertices(self) -> tuple[
+        NDArray[np.intc],
+        NDArray[np.intc],
+    ]: ...
+    @property
+    def convex_hull(self) -> NDArray[np.intc]: ...
+    def find_simplex(
+        self,
+        xi: ArrayLike,
+        bruteforce: bool = ...,
+        tol: float = ...
+    ) -> NDArray[np.intc]: ...
+    def plane_distance(self, xi: ArrayLike) -> NDArray[np.float64]: ...
+    def lift_points(self, x: ArrayLike) -> NDArray[np.float64]: ...
+
+def tsearch(tri: Delaunay, xi: ArrayLike) -> NDArray[np.intc]: ...
+def _copy_docstr(dst: object, src: object) -> None: ...
+
+class ConvexHull(_QhullUser):
+    simplices: NDArray[np.intc]
+    neighbors: NDArray[np.intc]
+    equations: NDArray[np.float64]
+    coplanar: NDArray[np.intc]
+    good: None | NDArray[np.bool_]
+    volume: float
+    area: float
+    nsimplex: int
+
+    def __init__(
+        self,
+        points: ArrayLike,
+        incremental: bool = ...,
+        qhull_options: None | str = ...
+    ) -> None: ...
+    def _update(self, qhull: _Qhull) -> None: ...
+    def add_points(self, points: ArrayLike,
+                   restart: bool = ...) -> None: ...
+    @property
+    def points(self) -> NDArray[np.float64]: ...
+    @property
+    def vertices(self) -> NDArray[np.intc]: ...
+
+class Voronoi(_QhullUser):
+    vertices: NDArray[np.float64]
+    ridge_points: NDArray[np.intc]
+    ridge_vertices: list[list[int]]
+    regions: list[list[int]]
+    point_region: NDArray[np.intp]
+    furthest_site: bool
+
+    def __init__(
+        self,
+        points: ArrayLike,
+        furthest_site: bool = ...,
+        incremental: bool = ...,
+        qhull_options: None | str = ...
+    ) -> None: ...
+    def _update(self, qhull: _Qhull) -> None: ...
+    def add_points(
+        self,
+        points: ArrayLike,
+        restart: bool = ...
+    ) -> None: ...
+    @property
+    def points(self) -> NDArray[np.float64]: ...
+    @property
+    def ridge_dict(self) -> dict[tuple[int, int], list[int]]: ...
+
+class HalfspaceIntersection(_QhullUser):
+    interior_point: NDArray[np.float64]
+    dual_facets: list[list[int]]
+    dual_equations: NDArray[np.float64]
+    dual_points: NDArray[np.float64]
+    dual_volume: float
+    dual_area: float
+    intersections: NDArray[np.float64]
+    ndim: int
+    nineq: int
+
+    def __init__(
+        self,
+        halfspaces: ArrayLike,
+        interior_point: ArrayLike,
+        incremental: bool = ...,
+        qhull_options: None | str = ...
+    ) -> None: ...
+    def _update(self, qhull: _Qhull) -> None: ...
+    def add_halfspaces(
+        self,
+        halfspaces: ArrayLike,
+        restart: bool = ...
+    ) -> None: ...
+    @property
+    def halfspaces(self) -> NDArray[np.float64]: ...
+    @property
+    def dual_vertices(self) -> NDArray[np.integer]: ...
diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/_spherical_voronoi.py b/venv/lib/python3.12/site-packages/scipy/spatial/_spherical_voronoi.py
new file mode 100644
index 0000000000000000000000000000000000000000..1d4a095ec026fa373759eba3b88b41ec5c896925
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/_spherical_voronoi.py
@@ -0,0 +1,339 @@
+"""
+Spherical Voronoi Code
+
+.. versionadded:: 0.18.0
+
+"""
+#
+# Copyright (C)  Tyler Reddy, Ross Hemsley, Edd Edmondson,
+#                Nikolai Nowaczyk, Joe Pitt-Francis, 2015.
+#
+# Distributed under the same BSD license as SciPy.
+#
+
+import numpy as np
+import scipy
+from . import _voronoi
+from scipy.spatial import cKDTree  # type: ignore[attr-defined]
+
+__all__ = ['SphericalVoronoi']
+
+
+def calculate_solid_angles(R):
+    """Calculates the solid angles of plane triangles. Implements the method of
+    Van Oosterom and Strackee [VanOosterom]_ with some modifications. Assumes
+    that input points have unit norm."""
+    # Original method uses a triple product `R1 . (R2 x R3)` for the numerator.
+    # This is equal to the determinant of the matrix [R1 R2 R3], which can be
+    # computed with better stability.
+    numerator = np.linalg.det(R)
+    denominator = 1 + (np.einsum('ij,ij->i', R[:, 0], R[:, 1]) +
+                       np.einsum('ij,ij->i', R[:, 1], R[:, 2]) +
+                       np.einsum('ij,ij->i', R[:, 2], R[:, 0]))
+    return np.abs(2 * np.arctan2(numerator, denominator))
+
+
+class SphericalVoronoi:
+    """
+    Voronoi diagrams on the surface of a sphere.
+
+    .. versionadded:: 0.18.0
+
+    Parameters
+    ----------
+    points : ndarray of floats, shape (npoints, ndim)
+        Coordinates of points from which to construct a spherical
+        Voronoi diagram.
+    radius : float, optional
+        Radius of the sphere (Default: 1)
+    center : ndarray of floats, shape (ndim,)
+        Center of sphere (Default: origin)
+    threshold : float
+        Threshold for detecting duplicate points and
+        mismatches between points and sphere parameters.
+        (Default: 1e-06)
+
+    Attributes
+    ----------
+    points : double array of shape (npoints, ndim)
+        the points in `ndim` dimensions to generate the Voronoi diagram from
+    radius : double
+        radius of the sphere
+    center : double array of shape (ndim,)
+        center of the sphere
+    vertices : double array of shape (nvertices, ndim)
+        Voronoi vertices corresponding to points
+    regions : list of list of integers of shape (npoints, _ )
+        the n-th entry is a list consisting of the indices
+        of the vertices belonging to the n-th point in points
+
+    Methods
+    -------
+    calculate_areas
+        Calculates the areas of the Voronoi regions. For 2D point sets, the
+        regions are circular arcs. The sum of the areas is ``2 * pi * radius``.
+        For 3D point sets, the regions are spherical polygons. The sum of the
+        areas is ``4 * pi * radius**2``.
+
+    Raises
+    ------
+    ValueError
+        If there are duplicates in `points`.
+        If the provided `radius` is not consistent with `points`.
+
+    See Also
+    --------
+    Voronoi : Conventional Voronoi diagrams in N dimensions.
+
+    Notes
+    -----
+    The spherical Voronoi diagram algorithm proceeds as follows. The Convex
+    Hull of the input points (generators) is calculated, and is equivalent to
+    their Delaunay triangulation on the surface of the sphere [Caroli]_.
+    The Convex Hull neighbour information is then used to
+    order the Voronoi region vertices around each generator. The latter
+    approach is substantially less sensitive to floating point issues than
+    angle-based methods of Voronoi region vertex sorting.
+
+    Empirical assessment of spherical Voronoi algorithm performance suggests
+    quadratic time complexity (loglinear is optimal, but algorithms are more
+    challenging to implement).
+
+    References
+    ----------
+    .. [Caroli] Caroli et al. Robust and Efficient Delaunay triangulations of
+                points on or close to a sphere. Research Report RR-7004, 2009.
+
+    .. [VanOosterom] Van Oosterom and Strackee. The solid angle of a plane
+                     triangle. IEEE Transactions on Biomedical Engineering,
+                     2, 1983, pp 125--126.
+
+    Examples
+    --------
+    Do some imports and take some points on a cube:
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.spatial import SphericalVoronoi, geometric_slerp
+    >>> from mpl_toolkits.mplot3d import proj3d
+    >>> # set input data
+    >>> points = np.array([[0, 0, 1], [0, 0, -1], [1, 0, 0],
+    ...                    [0, 1, 0], [0, -1, 0], [-1, 0, 0], ])
+
+    Calculate the spherical Voronoi diagram:
+
+    >>> radius = 1
+    >>> center = np.array([0, 0, 0])
+    >>> sv = SphericalVoronoi(points, radius, center)
+
+    Generate plot:
+
+    >>> # sort vertices (optional, helpful for plotting)
+    >>> sv.sort_vertices_of_regions()
+    >>> t_vals = np.linspace(0, 1, 2000)
+    >>> fig = plt.figure()
+    >>> ax = fig.add_subplot(111, projection='3d')
+    >>> # plot the unit sphere for reference (optional)
+    >>> u = np.linspace(0, 2 * np.pi, 100)
+    >>> v = np.linspace(0, np.pi, 100)
+    >>> x = np.outer(np.cos(u), np.sin(v))
+    >>> y = np.outer(np.sin(u), np.sin(v))
+    >>> z = np.outer(np.ones(np.size(u)), np.cos(v))
+    >>> ax.plot_surface(x, y, z, color='y', alpha=0.1)
+    >>> # plot generator points
+    >>> ax.scatter(points[:, 0], points[:, 1], points[:, 2], c='b')
+    >>> # plot Voronoi vertices
+    >>> ax.scatter(sv.vertices[:, 0], sv.vertices[:, 1], sv.vertices[:, 2],
+    ...                    c='g')
+    >>> # indicate Voronoi regions (as Euclidean polygons)
+    >>> for region in sv.regions:
+    ...    n = len(region)
+    ...    for i in range(n):
+    ...        start = sv.vertices[region][i]
+    ...        end = sv.vertices[region][(i + 1) % n]
+    ...        result = geometric_slerp(start, end, t_vals)
+    ...        ax.plot(result[..., 0],
+    ...                result[..., 1],
+    ...                result[..., 2],
+    ...                c='k')
+    >>> ax.azim = 10
+    >>> ax.elev = 40
+    >>> _ = ax.set_xticks([])
+    >>> _ = ax.set_yticks([])
+    >>> _ = ax.set_zticks([])
+    >>> fig.set_size_inches(4, 4)
+    >>> plt.show()
+    """
+    def __init__(self, points, radius=1, center=None, threshold=1e-06):
+
+        if radius is None:
+            raise ValueError('`radius` is `None`. '
+                             'Please provide a floating point number '
+                             '(i.e. `radius=1`).')
+
+        self.radius = float(radius)
+        self.points = np.array(points).astype(np.float64)
+        self._dim = self.points.shape[1]
+        if center is None:
+            self.center = np.zeros(self._dim)
+        else:
+            self.center = np.array(center, dtype=float)
+
+        # test degenerate input
+        self._rank = np.linalg.matrix_rank(self.points - self.points[0],
+                                           tol=threshold * self.radius)
+        if self._rank < self._dim:
+            raise ValueError(f"Rank of input points must be at least {self._dim}")
+
+        if cKDTree(self.points).query_pairs(threshold * self.radius):
+            raise ValueError("Duplicate generators present.")
+
+        radii = np.linalg.norm(self.points - self.center, axis=1)
+        max_discrepancy = np.abs(radii - self.radius).max()
+        if max_discrepancy >= threshold * self.radius:
+            raise ValueError("Radius inconsistent with generators.")
+
+        self._calc_vertices_regions()
+
+    def _calc_vertices_regions(self):
+        """
+        Calculates the Voronoi vertices and regions of the generators stored
+        in self.points. The vertices will be stored in self.vertices and the
+        regions in self.regions.
+
+        This algorithm was discussed at PyData London 2015 by
+        Tyler Reddy, Ross Hemsley and Nikolai Nowaczyk
+        """
+        # get Convex Hull
+        conv = scipy.spatial.ConvexHull(self.points)
+        # get circumcenters of Convex Hull triangles from facet equations
+        # for 3D input circumcenters will have shape: (2N-4, 3)
+        self.vertices = self.radius * conv.equations[:, :-1] + self.center
+        self._simplices = conv.simplices
+        # calculate regions from triangulation
+        # for 3D input simplex_indices will have shape: (2N-4,)
+        simplex_indices = np.arange(len(self._simplices))
+        # for 3D input tri_indices will have shape: (6N-12,)
+        tri_indices = np.column_stack([simplex_indices] * self._dim).ravel()
+        # for 3D input point_indices will have shape: (6N-12,)
+        self._point_indices = self._simplices.ravel()
+        # for 3D input indices will have shape: (6N-12,)
+        self._indices = np.argsort(self._point_indices, kind='mergesort')
+        # for 3D input flattened_groups will have shape: (6N-12,)
+        flattened_groups = tri_indices[self._indices].astype(np.intp)
+        # intervals will have shape: (N+1,)
+        self._intervals = np.cumsum(np.bincount(self._point_indices + 1))
+        # split flattened groups to get nested list of unsorted regions
+        groups = [list(flattened_groups[self._intervals[i]:self._intervals[i + 1]])
+                  for i in range(len(self._intervals) - 1)]
+        self.regions = groups
+
+    def sort_vertices_of_regions(self):
+        """Sort indices of the vertices to be (counter-)clockwise ordered.
+
+        Raises
+        ------
+        TypeError
+            If the points are not three-dimensional.
+
+        Notes
+        -----
+        For each region in regions, it sorts the indices of the Voronoi
+        vertices such that the resulting points are in a clockwise or
+        counterclockwise order around the generator point.
+
+        This is done as follows: Recall that the n-th region in regions
+        surrounds the n-th generator in points and that the k-th
+        Voronoi vertex in vertices is the circumcenter of the k-th triangle
+        in self._simplices.  For each region n, we choose the first triangle
+        (=Voronoi vertex) in self._simplices and a vertex of that triangle
+        not equal to the center n. These determine a unique neighbor of that
+        triangle, which is then chosen as the second triangle. The second
+        triangle will have a unique vertex not equal to the current vertex or
+        the center. This determines a unique neighbor of the second triangle,
+        which is then chosen as the third triangle and so forth. We proceed
+        through all the triangles (=Voronoi vertices) belonging to the
+        generator in points and obtain a sorted version of the vertices
+        of its surrounding region.
+        """
+        if self._dim != 3:
+            raise TypeError("Only supported for three-dimensional point sets")
+        _voronoi.sort_vertices_of_regions(self._simplices, self.regions)
+
+    def _calculate_areas_3d(self):
+        self.sort_vertices_of_regions()
+        sizes = np.diff(self._intervals)
+        csizes = np.cumsum(sizes)
+        num_regions = csizes[-1]
+
+        # We create a set of triangles consisting of one point and two Voronoi
+        # vertices. The vertices of each triangle are adjacent in the sorted
+        # regions list.
+        point_indices = self._point_indices[self._indices]
+
+        nbrs1 = np.array([r for region in self.regions for r in region])
+
+        # The calculation of nbrs2 is a vectorized version of:
+        # np.array([r for region in self.regions for r in np.roll(region, 1)])
+        nbrs2 = np.roll(nbrs1, 1)
+        indices = np.roll(csizes, 1)
+        indices[0] = 0
+        nbrs2[indices] = nbrs1[csizes - 1]
+
+        # Normalize points and vertices.
+        pnormalized = (self.points - self.center) / self.radius
+        vnormalized = (self.vertices - self.center) / self.radius
+
+        # Create the complete set of triangles and calculate their solid angles
+        triangles = np.hstack([pnormalized[point_indices],
+                               vnormalized[nbrs1],
+                               vnormalized[nbrs2]
+                               ]).reshape((num_regions, 3, 3))
+        triangle_solid_angles = calculate_solid_angles(triangles)
+
+        # Sum the solid angles of the triangles in each region
+        solid_angles = np.cumsum(triangle_solid_angles)[csizes - 1]
+        solid_angles[1:] -= solid_angles[:-1]
+
+        # Get polygon areas using A = omega * r**2
+        return solid_angles * self.radius**2
+
+    def _calculate_areas_2d(self):
+        # Find start and end points of arcs
+        arcs = self.points[self._simplices] - self.center
+
+        # Calculate the angle subtended by arcs
+        d = np.sum((arcs[:, 1] - arcs[:, 0]) ** 2, axis=1)
+        theta = np.arccos(1 - (d / (2 * (self.radius ** 2))))
+
+        # Get areas using A = r * theta
+        areas = self.radius * theta
+
+        # Correct arcs which go the wrong way (single-hemisphere inputs)
+        indices = np.einsum('ij,ij->i', arcs[:, 0],
+                            self.vertices - self.center) < 0
+        areas[indices] = 2 * np.pi * self.radius - areas[indices]
+        return areas
+
+    def calculate_areas(self):
+        """Calculates the areas of the Voronoi regions.
+
+        For 2D point sets, the regions are circular arcs. The sum of the areas
+        is ``2 * pi * radius``.
+
+        For 3D point sets, the regions are spherical polygons. The sum of the
+        areas is ``4 * pi * radius**2``.
+
+        .. versionadded:: 1.5.0
+
+        Returns
+        -------
+        areas : double array of shape (npoints,)
+            The areas of the Voronoi regions.
+        """
+        if self._dim == 2:
+            return self._calculate_areas_2d()
+        elif self._dim == 3:
+            return self._calculate_areas_3d()
+        else:
+            raise TypeError("Only supported for 2D and 3D point sets")
diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/_voronoi.cpython-312-x86_64-linux-gnu.so b/venv/lib/python3.12/site-packages/scipy/spatial/_voronoi.cpython-312-x86_64-linux-gnu.so
new file mode 100644
index 0000000000000000000000000000000000000000..4284ee93affc8458be4fbe1c325f99c1888ab89c
Binary files /dev/null and b/venv/lib/python3.12/site-packages/scipy/spatial/_voronoi.cpython-312-x86_64-linux-gnu.so differ
diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/_voronoi.pyi b/venv/lib/python3.12/site-packages/scipy/spatial/_voronoi.pyi
new file mode 100644
index 0000000000000000000000000000000000000000..c7c361ff69414d50a6ebcfe2c837025b60083940
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/_voronoi.pyi
@@ -0,0 +1,4 @@
+
+import numpy as np
+
+def sort_vertices_of_regions(simplices: np.ndarray, regions: list[list[int]]) -> None: ...  # noqa: E501
diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/ckdtree.py b/venv/lib/python3.12/site-packages/scipy/spatial/ckdtree.py
new file mode 100644
index 0000000000000000000000000000000000000000..40f524c71bf122ac822626596c2991b19ee0d30e
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/ckdtree.py
@@ -0,0 +1,18 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.spatial` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+
+__all__ = ["cKDTree"]  # noqa: F822
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="spatial", module="ckdtree",
+                                   private_modules=["_ckdtree"], all=__all__,
+                                   attribute=name)
diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/distance.py b/venv/lib/python3.12/site-packages/scipy/spatial/distance.py
new file mode 100644
index 0000000000000000000000000000000000000000..f8602f3faf442881dff5260c4df5652086a7cdb0
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/distance.py
@@ -0,0 +1,2942 @@
+"""
+Distance computations (:mod:`scipy.spatial.distance`)
+=====================================================
+
+.. sectionauthor:: Damian Eads
+
+Function reference
+------------------
+
+Distance matrix computation from a collection of raw observation vectors
+stored in a rectangular array.
+
+.. autosummary::
+   :toctree: generated/
+
+   pdist   -- pairwise distances between observation vectors.
+   cdist   -- distances between two collections of observation vectors
+   squareform -- convert distance matrix to a condensed one and vice versa
+   directed_hausdorff -- directed Hausdorff distance between arrays
+
+Predicates for checking the validity of distance matrices, both
+condensed and redundant. Also contained in this module are functions
+for computing the number of observations in a distance matrix.
+
+.. autosummary::
+   :toctree: generated/
+
+   is_valid_dm -- checks for a valid distance matrix
+   is_valid_y  -- checks for a valid condensed distance matrix
+   num_obs_dm  -- # of observations in a distance matrix
+   num_obs_y   -- # of observations in a condensed distance matrix
+
+Distance functions between two numeric vectors ``u`` and ``v``. Computing
+distances over a large collection of vectors is inefficient for these
+functions. Use ``pdist`` for this purpose.
+
+.. autosummary::
+   :toctree: generated/
+
+   braycurtis       -- the Bray-Curtis distance.
+   canberra         -- the Canberra distance.
+   chebyshev        -- the Chebyshev distance.
+   cityblock        -- the Manhattan distance.
+   correlation      -- the Correlation distance.
+   cosine           -- the Cosine distance.
+   euclidean        -- the Euclidean distance.
+   jensenshannon    -- the Jensen-Shannon distance.
+   mahalanobis      -- the Mahalanobis distance.
+   minkowski        -- the Minkowski distance.
+   seuclidean       -- the normalized Euclidean distance.
+   sqeuclidean      -- the squared Euclidean distance.
+
+Distance functions between two boolean vectors (representing sets) ``u`` and
+``v``.  As in the case of numerical vectors, ``pdist`` is more efficient for
+computing the distances between all pairs.
+
+.. autosummary::
+   :toctree: generated/
+
+   dice             -- the Dice dissimilarity.
+   hamming          -- the Hamming distance.
+   jaccard          -- the Jaccard distance.
+   rogerstanimoto   -- the Rogers-Tanimoto dissimilarity.
+   russellrao       -- the Russell-Rao dissimilarity.
+   sokalsneath      -- the Sokal-Sneath dissimilarity.
+   yule             -- the Yule dissimilarity.
+
+:func:`hamming` also operates over discrete numerical vectors.
+"""
+
+# Copyright (C) Damian Eads, 2007-2008. New BSD License.
+
+__all__ = [
+    'braycurtis',
+    'canberra',
+    'cdist',
+    'chebyshev',
+    'cityblock',
+    'correlation',
+    'cosine',
+    'dice',
+    'directed_hausdorff',
+    'euclidean',
+    'hamming',
+    'is_valid_dm',
+    'is_valid_y',
+    'jaccard',
+    'jensenshannon',
+    'mahalanobis',
+    'minkowski',
+    'num_obs_dm',
+    'num_obs_y',
+    'pdist',
+    'rogerstanimoto',
+    'russellrao',
+    'seuclidean',
+    'sokalsneath',
+    'sqeuclidean',
+    'squareform',
+    'yule'
+]
+
+
+import math
+import warnings
+import dataclasses
+from collections.abc import Callable
+from functools import partial
+
+import numpy as np
+
+from scipy._lib._array_api import _asarray
+from scipy._lib._util import _asarray_validated, _transition_to_rng
+from scipy._external import array_api_extra as xpx
+from scipy.linalg import norm
+from scipy.special import rel_entr
+from . import _hausdorff, _distance_pybind, _distance_wrap
+
+
+def _copy_array_if_base_present(a):
+    """Copy the array if its base points to a parent array."""
+    if a.base is not None:
+        return a.copy()
+    return a
+
+
+def _correlation_cdist_wrap(XA, XB, dm, **kwargs):
+    XA = XA - XA.mean(axis=1, keepdims=True)
+    XB = XB - XB.mean(axis=1, keepdims=True)
+    _distance_wrap.cdist_cosine_double_wrap(XA, XB, dm, **kwargs)
+
+
+def _correlation_pdist_wrap(X, dm, **kwargs):
+    X2 = X - X.mean(axis=1, keepdims=True)
+    _distance_wrap.pdist_cosine_double_wrap(X2, dm, **kwargs)
+
+
+def _convert_to_type(X, out_type):
+    return np.ascontiguousarray(X, dtype=out_type)
+
+
+def _nbool_correspond_all(u, v, w=None):
+    if u.dtype == v.dtype == bool and w is None:
+        not_u = ~u
+        not_v = ~v
+        nff = (not_u & not_v).sum()
+        nft = (not_u & v).sum()
+        ntf = (u & not_v).sum()
+        ntt = (u & v).sum()
+    else:
+        dtype = np.result_type(int, u.dtype, v.dtype)
+        u = u.astype(dtype)
+        v = v.astype(dtype)
+        not_u = 1.0 - u
+        not_v = 1.0 - v
+        if w is not None:
+            not_u = w * not_u
+            u = w * u
+        nff = (not_u * not_v).sum()
+        nft = (not_u * v).sum()
+        ntf = (u * not_v).sum()
+        ntt = (u * v).sum()
+    return (nff, nft, ntf, ntt)
+
+
+def _nbool_correspond_ft_tf(u, v, w=None):
+    if u.dtype == v.dtype == bool and w is None:
+        not_u = ~u
+        not_v = ~v
+        nft = (not_u & v).sum()
+        ntf = (u & not_v).sum()
+    else:
+        dtype = np.result_type(int, u.dtype, v.dtype)
+        u = u.astype(dtype)
+        v = v.astype(dtype)
+        not_u = 1.0 - u
+        not_v = 1.0 - v
+        if w is not None:
+            not_u = w * not_u
+            u = w * u
+        nft = (not_u * v).sum()
+        ntf = (u * not_v).sum()
+    return (nft, ntf)
+
+
+def _validate_cdist_input(XA, XB, mA, mB, n, metric_info, **kwargs):
+    # get supported types
+    types = metric_info.types
+    # choose best type
+    typ = types[types.index(XA.dtype)] if XA.dtype in types else types[0]
+    # validate data
+    XA = _convert_to_type(XA, out_type=typ)
+    XB = _convert_to_type(XB, out_type=typ)
+
+    # validate kwargs
+    _validate_kwargs = metric_info.validator
+    if _validate_kwargs:
+        kwargs = _validate_kwargs((XA, XB), mA + mB, n, **kwargs)
+    return XA, XB, typ, kwargs
+
+
+def _validate_weight_with_size(X, m, n, **kwargs):
+    w = kwargs.pop('w', None)
+    if w is None:
+        return kwargs
+
+    if w.ndim != 1 or w.shape[0] != n:
+        raise ValueError("Weights must have same size as input vector. "
+                         f"{w.shape[0]} vs. {n}")
+
+    kwargs['w'] = _validate_weights(w)
+    return kwargs
+
+
+def _validate_hamming_kwargs(X, m, n, **kwargs):
+    w = kwargs.get('w', np.ones((n,), dtype='double'))
+
+    if w.ndim != 1 or w.shape[0] != n:
+        raise ValueError(f"Weights must have same size as input vector. "
+                         f"{w.shape[0]} vs. {n}")
+
+    kwargs['w'] = _validate_weights(w)
+    return kwargs
+
+
+def _validate_mahalanobis_kwargs(X, m, n, **kwargs):
+    VI = kwargs.pop('VI', None)
+    if VI is None:
+        if m <= n:
+            # There are fewer observations than the dimension of
+            # the observations.
+            raise ValueError(
+                f"The number of observations ({m}) is too small; "
+                f"the covariance matrix is singular. For observations "
+                f"with {n} dimensions, at least {n + 1} observations are required.")
+        if isinstance(X, tuple):
+            X = np.vstack(X)
+        CV = np.atleast_2d(np.cov(X.astype(np.float64, copy=False).T))
+        VI = np.linalg.inv(CV).T.copy()
+    kwargs["VI"] = _convert_to_double(VI)
+    return kwargs
+
+
+def _validate_minkowski_kwargs(X, m, n, **kwargs):
+    kwargs = _validate_weight_with_size(X, m, n, **kwargs)
+    if 'p' not in kwargs:
+        kwargs['p'] = 2.
+    else:
+        if kwargs['p'] <= 0:
+            raise ValueError("p must be greater than 0")
+
+    return kwargs
+
+
+def _validate_pdist_input(X, m, n, metric_info, **kwargs):
+    # get supported types
+    types = metric_info.types
+    # choose best type
+    typ = types[types.index(X.dtype)] if X.dtype in types else types[0]
+    # validate data
+    X = _convert_to_type(X, out_type=typ)
+
+    # validate kwargs
+    _validate_kwargs = metric_info.validator
+    if _validate_kwargs:
+        kwargs = _validate_kwargs(X, m, n, **kwargs)
+    return X, typ, kwargs
+
+
+def _validate_seuclidean_kwargs(X, m, n, **kwargs):
+    V = kwargs.pop('V', None)
+    if V is None:
+        if isinstance(X, tuple):
+            X = np.vstack(X)
+        V = np.var(X.astype(np.float64, copy=False), axis=0, ddof=1)
+    else:
+        V = np.asarray(V, order='c')
+        if len(V.shape) != 1:
+            raise ValueError('Variance vector V must '
+                             'be one-dimensional.')
+        if V.shape[0] != n:
+            raise ValueError('Variance vector V must be of the same '
+                             'dimension as the vectors on which the distances '
+                             'are computed.')
+    kwargs['V'] = _convert_to_double(V)
+    return kwargs
+
+
+def _validate_vector(u, dtype=None):
+    # XXX Is order='c' really necessary?
+    u = np.asarray(u, dtype=dtype, order='c')
+    if u.ndim == 1:
+        return u
+    raise ValueError("Input vector should be 1-D.")
+
+
+def _validate_weights(w, dtype=np.float64):
+    w = _validate_vector(w, dtype=dtype)
+    if np.any(w < 0):
+        raise ValueError("Input weights should be all non-negative")
+    return w
+
+
+@_transition_to_rng('seed', position_num=2, replace_doc=False)
+def directed_hausdorff(u, v, rng=0):
+    """
+    Compute the directed Hausdorff distance between two 2-D arrays.
+
+    Distances between pairs are calculated using a Euclidean metric.
+
+    Parameters
+    ----------
+    u : (M,N) array_like
+        Input array with M points in N dimensions.
+    v : (O,N) array_like
+        Input array with O points in N dimensions.
+    rng : int or `numpy.random.Generator` or None, optional
+        Pseudorandom number generator state. Default is 0 so the
+        shuffling of `u` and `v` is reproducible.
+
+        If `rng` is passed by keyword, types other than `numpy.random.Generator` are
+        passed to `numpy.random.default_rng` to instantiate a ``Generator``.
+        If `rng` is already a ``Generator`` instance, then the provided instance is
+        used.
+
+        If this argument is passed by position or `seed` is passed by keyword,
+        legacy behavior for the argument `seed` applies:
+
+        - If `seed` is None, a new ``RandomState`` instance is used. The state is
+          initialized using data from ``/dev/urandom`` (or the Windows analogue)
+          if available or from the system clock otherwise.
+        - If `seed` is an int, a new ``RandomState`` instance is used,
+          seeded with `seed`.
+        - If `seed` is already a ``Generator`` or ``RandomState`` instance, then
+          that instance is used.
+
+        .. versionchanged:: 1.15.0
+            As part of the `SPEC-007 <https://scientific-python.org/specs/spec-0007/>`_
+            transition from use of `numpy.random.RandomState` to
+            `numpy.random.Generator`, this keyword was changed from `seed` to `rng`.
+            For an interim period, both keywords will continue to work, although only
+            one may be specified at a time. After the interim period, function calls
+            using the `seed` keyword will emit warnings. The behavior of both `seed`
+            and `rng` are outlined above, but only the `rng` keyword should be used in
+            new code.
+
+    Returns
+    -------
+    d : double
+        The directed Hausdorff distance between arrays `u` and `v`,
+
+    index_1 : int
+        index of point contributing to Hausdorff pair in `u`
+
+    index_2 : int
+        index of point contributing to Hausdorff pair in `v`
+
+    Raises
+    ------
+    ValueError
+        An exception is thrown if `u` and `v` do not have
+        the same number of columns.
+
+    See Also
+    --------
+    scipy.spatial.procrustes : Another similarity test for two data sets
+
+    Notes
+    -----
+    Uses the early break technique and the random sampling approach
+    described by [1]_. Although worst-case performance is ``O(m * o)``
+    (as with the brute force algorithm), this is unlikely in practice
+    as the input data would have to require the algorithm to explore
+    every single point interaction, and after the algorithm shuffles
+    the input points at that. The best case performance is ``O(m)``,
+    which is satisfied by selecting an inner loop distance that is
+    less than cmax and leads to an early break as often as possible.
+    The authors have formally shown that the average runtime is
+    closer to ``O(m)``.
+
+    .. versionadded:: 0.19.0
+
+    References
+    ----------
+    .. [1] A. A. Taha and A. Hanbury, "An efficient algorithm for
+           calculating the exact Hausdorff distance." IEEE Transactions On
+           Pattern Analysis And Machine Intelligence, vol. 37, no. 11,
+           pp. 2153-63, 2015. :doi:`10.1109/TPAMI.2015.2408351`.
+
+    Examples
+    --------
+    Find the directed Hausdorff distance between two 2-D arrays of
+    coordinates:
+
+    >>> from scipy.spatial.distance import directed_hausdorff
+    >>> import numpy as np
+    >>> u = np.array([(1.0, 0.0),
+    ...               (0.0, 1.0),
+    ...               (-1.0, 0.0),
+    ...               (0.0, -1.0)])
+    >>> v = np.array([(2.0, 0.0),
+    ...               (0.0, 2.0),
+    ...               (-2.0, 0.0),
+    ...               (0.0, -4.0)])
+
+    >>> directed_hausdorff(u, v)[0]
+    2.23606797749979
+    >>> directed_hausdorff(v, u)[0]
+    3.0
+
+    Find the general (symmetric) Hausdorff distance between two 2-D
+    arrays of coordinates:
+
+    >>> max(directed_hausdorff(u, v)[0], directed_hausdorff(v, u)[0])
+    3.0
+
+    Find the indices of the points that generate the Hausdorff distance
+    (the Hausdorff pair):
+
+    >>> directed_hausdorff(v, u)[1:]
+    (3, 3)
+
+    """
+    u = np.asarray(u, dtype=np.float64, order='c')
+    v = np.asarray(v, dtype=np.float64, order='c')
+    if u.shape[1] != v.shape[1]:
+        raise ValueError('u and v need to have the same '
+                         'number of columns')
+    result = _hausdorff.directed_hausdorff(u, v, rng)
+    return result
+
+
+def minkowski(u, v, p=2, w=None):
+    """
+    Compute the Minkowski distance between two arrays.
+
+    The Minkowski distance between arrays `u` and `v`,
+    is defined as
+
+    .. math::
+
+       {\\|u-v\\|}_p = (\\sum{|u_i - v_i|^p})^{1/p}.
+
+
+       \\left(\\sum{w_i(|(u_i - v_i)|^p)}\\right)^{1/p}.
+
+    Parameters
+    ----------
+    u : (..., N) array_like
+        Input array.
+    v : (..., N) array_like
+        Input array.
+    p : scalar
+        The order of the norm of the difference :math:`{\\|u-v\\|}_p`. Note
+        that for :math:`0 < p < 1`, the triangle inequality only holds with
+        an additional multiplicative factor, i.e. it is only a quasi-metric.
+    w : (N,) array_like, optional
+        The weights for each value in `u` and `v`. Default is None,
+        which gives each value a weight of 1.0
+
+    Returns
+    -------
+    minkowski : float or ndarray
+        The Minkowski distance between vectors `u` and `v`.
+
+    Examples
+    --------
+    >>> from scipy.spatial import distance
+    >>> distance.minkowski([1, 0, 0], [0, 1, 0], 1)
+    2.0
+    >>> distance.minkowski([1, 0, 0], [0, 1, 0], 2)
+    1.4142135623730951
+    >>> distance.minkowski([1, 0, 0], [0, 1, 0], 3)
+    1.2599210498948732
+    >>> distance.minkowski([1, 1, 0], [0, 1, 0], 1)
+    1.0
+    >>> distance.minkowski([1, 1, 0], [0, 1, 0], 2)
+    1.0
+    >>> distance.minkowski([1, 1, 0], [0, 1, 0], 3)
+    1.0
+
+    """
+    u = _asarray(u, order='C')
+    v = _asarray(v, order='C')
+    if p <= 0:
+        raise ValueError("p must be greater than 0")
+    u_v = u - v
+    if w is not None:
+        w = _validate_weights(w)
+        if p == 1:
+            root_w = w
+        elif p == 2:
+            # better precision and speed
+            root_w = np.sqrt(w)
+        elif p == np.inf:
+            root_w = (w != 0)
+        else:
+            root_w = np.power(w, 1/p)
+        u_v = root_w * u_v
+    dist = norm(u_v, ord=p, axis=-1)
+    return dist
+
+
+def euclidean(u, v, w=None):
+    """
+    Computes the Euclidean distance between two arrays.
+
+    The Euclidean distance between arrays `u` and `v`, is defined as
+
+    .. math::
+
+       {\\|u-v\\|}_2
+
+       \\left(\\sum{(w_i |(u_i - v_i)|^2)}\\right)^{1/2}
+
+    Parameters
+    ----------
+    u : (..., N) array_like
+        Input array.
+    v : (..., N) array_like
+        Input array.
+    w : (N,) array_like, optional
+        The weights for each value in `u` and `v`. Default is None,
+        which gives each value a weight of 1.0
+
+    Returns
+    -------
+    euclidean : float or ndarray
+        The Euclidean distance between vectors `u` and `v`.
+
+    Examples
+    --------
+    >>> from scipy.spatial import distance
+    >>> distance.euclidean([1, 0, 0], [0, 1, 0])
+    1.4142135623730951
+    >>> distance.euclidean([1, 1, 0], [0, 1, 0])
+    1.0
+
+    """
+    return minkowski(u, v, p=2, w=w)
+
+
+def sqeuclidean(u, v, w=None):
+    """
+    Compute the squared Euclidean distance between two arrays.
+
+    The squared Euclidean distance between `u` and `v` is defined as
+
+    .. math::
+
+       \\sum_i{w_i |u_i - v_i|^2}
+
+    Parameters
+    ----------
+    u : (..., N) array_like
+        Input array.
+    v : (..., N) array_like
+        Input array.
+    w : (N,) array_like, optional
+        The weights for each value in `u` and `v`. Default is None,
+        which gives each value a weight of 1.0
+
+    Returns
+    -------
+    sqeuclidean : float or ndarray
+        The squared Euclidean distance between vectors `u` and `v`.
+
+    Examples
+    --------
+    >>> from scipy.spatial import distance
+    >>> distance.sqeuclidean([1, 0, 0], [0, 1, 0])
+    2.0
+    >>> distance.sqeuclidean([1, 1, 0], [0, 1, 0])
+    1.0
+
+    """
+    # Preserve float dtypes, but convert everything else to np.float64
+    # for stability.
+    utype, vtype = None, None
+    if not (hasattr(u, "dtype") and np.issubdtype(u.dtype, np.inexact)):
+        utype = np.float64
+    if not (hasattr(v, "dtype") and np.issubdtype(v.dtype, np.inexact)):
+        vtype = np.float64
+
+    u = _asarray(u, dtype=utype, order='C')
+    v = _asarray(v, dtype=vtype, order='C')
+    u_v = u - v
+    u_v_w = u_v  # only want weights applied once
+    if w is not None:
+        w = _validate_weights(w)
+        u_v_w = w * u_v
+    return np.vecdot(u_v, u_v_w)
+
+
+def correlation(u, v, w=None, centered=True):
+    """
+    Compute the correlation distance between two 1-D arrays.
+
+    The correlation distance between `u` and `v`, is
+    defined as
+
+    .. math::
+
+        1 - \\frac{(u - \\bar{u}) \\cdot (v - \\bar{v})}
+                  {{\\|(u - \\bar{u})\\|}_2 {\\|(v - \\bar{v})\\|}_2}
+
+    where :math:`\\bar{u}` is the mean of the elements of `u`
+    and :math:`x \\cdot y` is the dot product of :math:`x` and :math:`y`.
+
+    Parameters
+    ----------
+    u : (N,) array_like of floats
+        Input array.
+    v : (N,) array_like of floats
+        Input array.
+    w : (N,) array_like of floats, optional
+        The weights for each value in `u` and `v`. Default is None,
+        which gives each value a weight of 1.0
+    centered : bool, optional
+        If True, `u` and `v` will be centered. Default is True.
+
+    Returns
+    -------
+    correlation : double
+        The correlation distance between 1-D array `u` and `v`.
+
+    Examples
+    --------
+    Find the correlation between two arrays.
+
+    >>> from scipy.spatial.distance import correlation
+    >>> correlation([1, 0, 1], [1, 1, 0])
+    1.5
+
+    Using a weighting array, the correlation can be calculated as:
+
+    >>> correlation([1, 0, 1], [1, 1, 0], w=[0.9, 0.1, 0.1])
+    1.1
+
+    If centering is not needed, the correlation can be calculated as:
+
+    >>> correlation([1, 0, 1], [1, 1, 0], centered=False)
+    0.5
+    """
+    u = _validate_vector(u)
+    v = _validate_vector(v)
+    if np.iscomplexobj(u) or np.iscomplexobj(v):
+        msg = "`u` and `v` must be real."
+        raise TypeError(msg)
+    if w is not None:
+        w = _validate_weights(w)
+        w = w / w.sum()
+    if centered:
+        if w is not None:
+            umu = np.dot(u, w)
+            vmu = np.dot(v, w)
+        else:
+            umu = np.mean(u)
+            vmu = np.mean(v)
+        u = u - umu
+        v = v - vmu
+    if w is not None:
+        vw = v * w
+        uw = u * w
+    else:
+        vw, uw = v, u
+    uv = np.dot(u, vw)
+    uu = np.dot(u, uw)
+    vv = np.dot(v, vw)
+    dist = 1.0 - uv / math.sqrt(uu * vv)
+    # Clip the result to avoid rounding error
+    return np.clip(dist, 0.0, 2.0)
+
+
+def cosine(u, v, w=None):
+    """
+    Compute the Cosine distance between 1-D arrays.
+
+    The Cosine distance between `u` and `v`, is defined as
+
+    .. math::
+
+        1 - \\frac{u \\cdot v}
+                  {\\|u\\|_2 \\|v\\|_2}.
+
+    where :math:`u \\cdot v` is the dot product of :math:`u` and
+    :math:`v`.
+
+    Parameters
+    ----------
+    u : (N,) array_like of floats
+        Input array.
+    v : (N,) array_like of floats
+        Input array.
+    w : (N,) array_like of floats, optional
+        The weights for each value in `u` and `v`. Default is None,
+        which gives each value a weight of 1.0
+
+    Returns
+    -------
+    cosine : double
+        The Cosine distance between vectors `u` and `v`.
+
+    Examples
+    --------
+    >>> from scipy.spatial import distance
+    >>> distance.cosine([1, 0, 0], [0, 1, 0])
+    1.0
+    >>> distance.cosine([100, 0, 0], [0, 1, 0])
+    1.0
+    >>> distance.cosine([1, 1, 0], [0, 1, 0])
+    0.29289321881345254
+
+    """
+    # cosine distance is also referred to as 'uncentered correlation',
+    #   or 'reflective correlation'
+    return correlation(u, v, w=w, centered=False)
+
+
+def hamming(u, v, w=None):
+    """
+    Compute the Hamming distance between two 1-D arrays.
+
+    The Hamming distance between 1-D arrays `u` and `v`, is simply the
+    proportion of disagreeing components in `u` and `v`. If `u` and `v` are
+    boolean vectors, the Hamming distance is
+
+    .. math::
+
+       \\frac{c_{01} + c_{10}}{n}
+
+    where :math:`c_{ij}` is the number of occurrences of
+    :math:`\\mathtt{u[k]} = i` and :math:`\\mathtt{v[k]} = j` for
+    :math:`k < n`.
+
+    Parameters
+    ----------
+    u : (N,) array_like
+        Input array.
+    v : (N,) array_like
+        Input array.
+    w : (N,) array_like, optional
+        The weights for each value in `u` and `v`. Default is None,
+        which gives each value a weight of 1.0
+
+    Returns
+    -------
+    hamming : double
+        The Hamming distance between vectors `u` and `v`.
+
+    Examples
+    --------
+    >>> from scipy.spatial import distance
+    >>> distance.hamming([1, 0, 0], [0, 1, 0])
+    0.66666666666666663
+    >>> distance.hamming([1, 0, 0], [1, 1, 0])
+    0.33333333333333331
+    >>> distance.hamming([1, 0, 0], [2, 0, 0])
+    0.33333333333333331
+    >>> distance.hamming([1, 0, 0], [3, 0, 0])
+    0.33333333333333331
+
+    """
+    u = _validate_vector(u)
+    v = _validate_vector(v)
+    if u.shape != v.shape:
+        raise ValueError('The 1d arrays must have equal lengths.')
+    u_ne_v = u != v
+    if w is not None:
+        w = _validate_weights(w)
+        if w.shape != u.shape:
+            raise ValueError("'w' should have the same length as 'u' and 'v'.")
+        w = w / w.sum()
+        return np.dot(u_ne_v, w)
+    return np.mean(u_ne_v)
+
+
+def jaccard(u, v, w=None):
+    r"""
+    Compute the Jaccard dissimilarity between two boolean vectors.
+
+    Given boolean vectors :math:`u \equiv (u_1, \cdots, u_n)`
+    and :math:`v \equiv (v_1, \cdots, v_n)` that are not both zero,
+    their *Jaccard dissimilarity* is defined as ([1]_, p. 26)
+
+    .. math::
+
+       d_\textrm{jaccard}(u, v) := \frac{c_{10} + c_{01}}
+                                        {c_{11} + c_{10} + c_{01}}
+
+    where
+
+    .. math::
+
+       c_{ij} := \sum_{1 \le k \le n, u_k=i, v_k=j} 1
+
+    for :math:`i, j \in \{ 0, 1\}`.  If :math:`u` and :math:`v` are both zero,
+    their Jaccard dissimilarity is defined to be zero. [2]_
+
+    If a (non-negative) weight vector :math:`w \equiv (w_1, \cdots, w_n)`
+    is supplied, the *weighted Jaccard dissimilarity* is defined similarly
+    but with :math:`c_{ij}` replaced by
+
+    .. math::
+
+       \tilde{c}_{ij} := \sum_{1 \le k \le n, u_k=i, v_k=j} w_k
+
+    Parameters
+    ----------
+    u : (N,) array_like of bools
+        Input vector.
+    v : (N,) array_like of bools
+        Input vector.
+    w : (N,) array_like of floats, optional
+        Weights for each pair of :math:`(u_k, v_k)`.  Default is ``None``,
+        which gives each pair a weight of ``1.0``.
+
+    Returns
+    -------
+    jaccard : float
+        The Jaccard dissimilarity between vectors `u` and `v`, optionally
+        weighted by `w` if supplied.
+
+    Notes
+    -----
+    The Jaccard dissimilarity satisfies the triangle inequality and is
+    qualified as a metric. [2]_
+
+    The *Jaccard index*, or *Jaccard similarity coefficient*, is equal to
+    one minus the Jaccard dissimilarity. [3]_
+
+    The dissimilarity between general (finite) sets may be computed by
+    encoding them as boolean vectors and computing the dissimilarity
+    between the encoded vectors.
+    For example, subsets :math:`A,B` of :math:`\{ 1, 2, ..., n \}` may be
+    encoded into boolean vectors :math:`u, v` by setting
+    :math:`u_k := 1_{k \in A}`, :math:`v_k := 1_{k \in B}`
+    for :math:`k = 1,2,\cdots,n`.
+
+    .. versionchanged:: 1.2.0
+       Previously, if all (positively weighted) elements in `u` and `v` are
+       zero, the function would return ``nan``.  This was changed to return
+       ``0`` instead.
+
+    .. versionchanged:: 1.15.0
+       Non-0/1 numeric input used to produce an ad hoc result.  Since 1.15.0,
+       numeric input is converted to Boolean before computation.
+
+    References
+    ----------
+    .. [1] Kaufman, L. and Rousseeuw, P. J.  (1990).  "Finding Groups in Data:
+           An Introduction to Cluster Analysis."  John Wiley & Sons, Inc.
+    .. [2] Kosub, S.  (2019).  "A note on the triangle inequality for the
+           Jaccard distance."  *Pattern Recognition Letters*, 120:36-38.
+    .. [3] https://en.wikipedia.org/wiki/Jaccard_index
+
+    Examples
+    --------
+    >>> from scipy.spatial import distance
+
+    Non-zero vectors with no matching 1s have dissimilarity of 1.0:
+
+    >>> distance.jaccard([1, 0, 0], [0, 1, 0])
+    1.0
+
+    Vectors with some matching 1s have dissimilarity less than 1.0:
+
+    >>> distance.jaccard([1, 0, 0, 0], [1, 1, 1, 0])
+    0.6666666666666666
+
+    Identical vectors, including zero vectors, have dissimilarity of 0.0:
+
+    >>> distance.jaccard([1, 0, 0], [1, 0, 0])
+    0.0
+    >>> distance.jaccard([0, 0, 0], [0, 0, 0])
+    0.0
+
+    The following example computes the dissimilarity from a confusion matrix
+    directly by setting the weight vector to the frequency of True Positive,
+    False Negative, False Positive, and True Negative:
+
+    >>> distance.jaccard([1, 1, 0, 0], [1, 0, 1, 0], [31, 41, 59, 26])
+    0.7633587786259542  # (41+59)/(31+41+59)
+
+    """
+    u = _validate_vector(u)
+    v = _validate_vector(v)
+
+    unequal = np.bitwise_xor(u != 0, v != 0)
+    nonzero = np.bitwise_or(u != 0, v != 0)
+    if w is not None:
+        w = _validate_weights(w)
+        unequal = w * unequal
+        nonzero = w * nonzero
+    a = np.float64(unequal.sum())
+    b = np.float64(nonzero.sum())
+    return (a / b) if b != 0 else np.float64(0)
+
+
+def seuclidean(u, v, V):
+    """
+    Return the standardized Euclidean distance between two 1-D arrays.
+
+    The standardized Euclidean distance between two n-vectors `u` and `v` is
+
+    .. math::
+
+       \\sqrt{\\sum\\limits_i \\frac{1}{V_i} \\left(u_i-v_i \\right)^2}
+
+    ``V`` is the variance vector; ``V[I]`` is the variance computed over all the i-th
+    components of the points. If not passed, it is automatically computed.
+
+    Parameters
+    ----------
+    u : (N,) array_like
+        Input array.
+    v : (N,) array_like
+        Input array.
+    V : (N,) array_like
+        `V` is a 1-D array of component variances. It is usually computed
+        among a larger collection of vectors.
+
+    Returns
+    -------
+    seuclidean : double
+        The standardized Euclidean distance between vectors `u` and `v`.
+
+    Examples
+    --------
+    >>> from scipy.spatial import distance
+    >>> distance.seuclidean([1, 0, 0], [0, 1, 0], [0.1, 0.1, 0.1])
+    4.4721359549995796
+    >>> distance.seuclidean([1, 0, 0], [0, 1, 0], [1, 0.1, 0.1])
+    3.3166247903553998
+    >>> distance.seuclidean([1, 0, 0], [0, 1, 0], [10, 0.1, 0.1])
+    3.1780497164141406
+
+    """
+    u = _validate_vector(u)
+    v = _validate_vector(v)
+    V = _validate_vector(V, dtype=np.float64)
+    if V.shape[0] != u.shape[0] or u.shape[0] != v.shape[0]:
+        raise TypeError('V must be a 1-D array of the same dimension '
+                        'as u and v.')
+    return euclidean(u, v, w=1/V)
+
+
+def cityblock(u, v, w=None):
+    """
+    Compute the City Block (Manhattan) distance.
+
+    Computes the Manhattan distance between two 1-D arrays `u` and `v`,
+    which is defined as
+
+    .. math::
+
+       \\sum_i {\\left| u_i - v_i \\right|}.
+
+    Parameters
+    ----------
+    u : (N,) array_like
+        Input array.
+    v : (N,) array_like
+        Input array.
+    w : (N,) array_like, optional
+        The weights for each value in `u` and `v`. Default is None,
+        which gives each value a weight of 1.0
+
+    Returns
+    -------
+    cityblock : double
+        The City Block (Manhattan) distance between vectors `u` and `v`.
+
+    Examples
+    --------
+    >>> from scipy.spatial import distance
+    >>> distance.cityblock([1, 0, 0], [0, 1, 0])
+    2
+    >>> distance.cityblock([1, 0, 0], [0, 2, 0])
+    3
+    >>> distance.cityblock([1, 0, 0], [1, 1, 0])
+    1
+
+    """
+    u = _validate_vector(u)
+    v = _validate_vector(v)
+    l1_diff = abs(u - v)
+    if w is not None:
+        w = _validate_weights(w)
+        l1_diff = w * l1_diff
+    return l1_diff.sum()
+
+
+def mahalanobis(u, v, VI):
+    """
+    Compute the Mahalanobis distance between two 1-D arrays.
+
+    The Mahalanobis distance between 1-D arrays `u` and `v`, is defined as
+
+    .. math::
+
+       \\sqrt{ (u-v) V^{-1} (u-v)^T }
+
+    where ``V`` is the covariance matrix.  Note that the argument `VI`
+    is the inverse of ``V``.
+
+    Parameters
+    ----------
+    u : (N,) array_like
+        Input array.
+    v : (N,) array_like
+        Input array.
+    VI : array_like
+        The inverse of the covariance matrix.
+
+    Returns
+    -------
+    mahalanobis : double
+        The Mahalanobis distance between vectors `u` and `v`.
+
+    Examples
+    --------
+    >>> from scipy.spatial import distance
+    >>> iv = [[1, 0.5, 0.5], [0.5, 1, 0.5], [0.5, 0.5, 1]]
+    >>> distance.mahalanobis([1, 0, 0], [0, 1, 0], iv)
+    1.0
+    >>> distance.mahalanobis([0, 2, 0], [0, 1, 0], iv)
+    1.0
+    >>> distance.mahalanobis([2, 0, 0], [0, 1, 0], iv)
+    1.7320508075688772
+
+    """
+    u = _validate_vector(u)
+    v = _validate_vector(v)
+    VI = np.atleast_2d(VI)
+    delta = u - v
+    m = np.dot(np.dot(delta, VI), delta)
+    return np.sqrt(m)
+
+
+def chebyshev(u, v, w=None):
+    r"""
+    Compute the Chebyshev distance.
+
+    The *Chebyshev distance* between real vectors
+    :math:`u \equiv (u_1, \cdots, u_n)` and
+    :math:`v \equiv (v_1, \cdots, v_n)` is defined as [1]_
+
+    .. math::
+
+       d_\textrm{chebyshev}(u,v) := \max_{1 \le i \le n} |u_i-v_i|
+
+    If a (non-negative) weight vector :math:`w \equiv (w_1, \cdots, w_n)`
+    is supplied, the *weighted Chebyshev distance* is defined to be the
+    weighted Minkowski distance of infinite order; that is,
+
+    .. math::
+
+       \begin{align}
+       d_\textrm{chebyshev}(u,v;w) &:= \lim_{p\rightarrow \infty}
+          \left( \sum_{i=1}^n w_i | u_i-v_i |^p \right)^\frac{1}{p} \\
+        &= \max_{1 \le i \le n} 1_{w_i > 0} | u_i - v_i |
+       \end{align}
+
+    Parameters
+    ----------
+    u : (N,) array_like of floats
+        Input vector.
+    v : (N,) array_like of floats
+        Input vector.
+    w : (N,) array_like of floats, optional
+        Weight vector.  Default is ``None``, which gives all pairs
+        :math:`(u_i, v_i)` the same weight ``1.0``.
+
+    Returns
+    -------
+    chebyshev : float
+        The Chebyshev distance between vectors `u` and `v`, optionally weighted
+        by `w`.
+
+    References
+    ----------
+    .. [1] https://en.wikipedia.org/wiki/Chebyshev_distance
+
+    Examples
+    --------
+    >>> from scipy.spatial import distance
+    >>> distance.chebyshev([1, 0, 0], [0, 1, 0])
+    1
+    >>> distance.chebyshev([1, 1, 0], [0, 1, 0])
+    1
+
+    """
+    u = _validate_vector(u)
+    v = _validate_vector(v)
+    if w is not None:
+        w = _validate_weights(w)
+        return max((w > 0) * abs(u - v))
+    return max(abs(u - v))
+
+
+def braycurtis(u, v, w=None):
+    """
+    Compute the Bray-Curtis distance between two 1-D arrays.
+
+    Bray-Curtis distance is defined as
+
+    .. math::
+
+       \\sum{|u_i-v_i|} / \\sum{|u_i+v_i|}
+
+    The Bray-Curtis distance is in the range [0, 1] if all coordinates are
+    positive, and is undefined if the inputs are of length zero.
+
+    Parameters
+    ----------
+    u : (N,) array_like
+        Input array.
+    v : (N,) array_like
+        Input array.
+    w : (N,) array_like, optional
+        The weights for each value in `u` and `v`. Default is None,
+        which gives each value a weight of 1.0
+
+    Returns
+    -------
+    braycurtis : double
+        The Bray-Curtis distance between 1-D arrays `u` and `v`.
+
+    Examples
+    --------
+    >>> from scipy.spatial import distance
+    >>> distance.braycurtis([1, 0, 0], [0, 1, 0])
+    1.0
+    >>> distance.braycurtis([1, 1, 0], [0, 1, 0])
+    0.33333333333333331
+
+    """
+    u = _validate_vector(u)
+    v = _validate_vector(v, dtype=np.float64)
+    l1_diff = abs(u - v)
+    l1_sum = abs(u + v)
+    if w is not None:
+        w = _validate_weights(w)
+        l1_diff = w * l1_diff
+        l1_sum = w * l1_sum
+    return l1_diff.sum() / l1_sum.sum()
+
+
+def canberra(u, v, w=None):
+    """
+    Compute the Canberra distance between two 1-D arrays.
+
+    The Canberra distance is defined as
+
+    .. math::
+
+         d(u,v) = \\sum_i \\frac{|u_i-v_i|}
+                              {|u_i|+|v_i|}.
+
+    Parameters
+    ----------
+    u : (N,) array_like
+        Input array.
+    v : (N,) array_like
+        Input array.
+    w : (N,) array_like, optional
+        The weights for each value in `u` and `v`. Default is None,
+        which gives each value a weight of 1.0
+
+    Returns
+    -------
+    canberra : double
+        The Canberra distance between vectors `u` and `v`.
+
+    Notes
+    -----
+    When ``u[i]`` and ``v[i]`` are 0 for given i, then the fraction 0/0 = 0 is
+    used in the calculation.
+
+    Examples
+    --------
+    >>> from scipy.spatial import distance
+    >>> distance.canberra([1, 0, 0], [0, 1, 0])
+    2.0
+    >>> distance.canberra([1, 1, 0], [0, 1, 0])
+    1.0
+
+    """
+    u = _validate_vector(u)
+    v = _validate_vector(v, dtype=np.float64)
+    if w is not None:
+        w = _validate_weights(w)
+    with np.errstate(invalid='ignore'):
+        abs_uv = abs(u - v)
+        abs_u = abs(u)
+        abs_v = abs(v)
+        d = abs_uv / (abs_u + abs_v)
+        if w is not None:
+            d = w * d
+        d = np.nansum(d)
+    return d
+
+
+def jensenshannon(p, q, base=None, *, axis=0, keepdims=False):
+    """
+    Compute the Jensen-Shannon distance (metric) between
+    two probability arrays. This is the square root
+    of the Jensen-Shannon divergence.
+
+    The Jensen-Shannon distance between two probability
+    vectors `p` and `q` is defined as,
+
+    .. math::
+
+       \\sqrt{\\frac{D(p \\parallel m) + D(q \\parallel m)}{2}}
+
+    where :math:`m` is the pointwise mean of :math:`p` and :math:`q`
+    and :math:`D` is the Kullback-Leibler divergence.
+
+    This routine will normalize `p` and `q` if they don't sum to 1.0.
+
+    Parameters
+    ----------
+    p : (N,) array_like
+        left probability vector
+    q : (N,) array_like
+        right probability vector
+    base : double, optional
+        the base of the logarithm used to compute the output
+        if not given, then the routine uses the default base of
+        scipy.stats.entropy.
+    axis : int, optional
+        Axis along which the Jensen-Shannon distances are computed. The default
+        is 0.
+
+        .. versionadded:: 1.7.0
+    keepdims : bool, optional
+        If this is set to `True`, the reduced axes are left in the
+        result as dimensions with size one. With this option,
+        the result will broadcast correctly against the input array.
+        Default is False.
+
+        .. versionadded:: 1.7.0
+
+    Returns
+    -------
+    js : double or ndarray
+        The Jensen-Shannon distances between `p` and `q` along the `axis`.
+
+    Notes
+    -----
+
+    .. versionadded:: 1.2.0
+
+    Examples
+    --------
+    >>> from scipy.spatial import distance
+    >>> import numpy as np
+    >>> distance.jensenshannon([1.0, 0.0, 0.0], [0.0, 1.0, 0.0], 2.0)
+    1.0
+    >>> distance.jensenshannon([1.0, 0.0], [0.5, 0.5])
+    0.46450140402245893
+    >>> distance.jensenshannon([1.0, 0.0, 0.0], [1.0, 0.0, 0.0])
+    0.0
+    >>> a = np.array([[1, 2, 3, 4],
+    ...               [5, 6, 7, 8],
+    ...               [9, 10, 11, 12]])
+    >>> b = np.array([[13, 14, 15, 16],
+    ...               [17, 18, 19, 20],
+    ...               [21, 22, 23, 24]])
+    >>> distance.jensenshannon(a, b, axis=0)
+    array([0.1954288, 0.1447697, 0.1138377, 0.0927636])
+    >>> distance.jensenshannon(a, b, axis=1)
+    array([0.1402339, 0.0399106, 0.0201815])
+
+    """
+    p = np.asarray(p)
+    q = np.asarray(q)
+    p = p / np.sum(p, axis=axis, keepdims=True)
+    q = q / np.sum(q, axis=axis, keepdims=True)
+    m = (p + q) / 2.0
+    left = rel_entr(p, m)
+    right = rel_entr(q, m)
+    left_sum = np.sum(left, axis=axis, keepdims=keepdims)
+    right_sum = np.sum(right, axis=axis, keepdims=keepdims)
+    js = left_sum + right_sum
+    if base is not None:
+        js /= np.log(base)
+    return np.sqrt(js / 2.0)
+
+
+def yule(u, v, w=None):
+    """
+    Compute the Yule dissimilarity between two boolean 1-D arrays.
+
+    The Yule dissimilarity is defined as
+
+    .. math::
+
+         \\frac{R}{c_{TT} * c_{FF} + \\frac{R}{2}}
+
+    where :math:`c_{ij}` is the number of occurrences of
+    :math:`\\mathtt{u[k]} = i` and :math:`\\mathtt{v[k]} = j` for
+    :math:`k < n` and :math:`R = 2.0 * c_{TF} * c_{FT}`.
+
+    Parameters
+    ----------
+    u : (N,) array_like, bool
+        Input array.
+    v : (N,) array_like, bool
+        Input array.
+    w : (N,) array_like, optional
+        The weights for each value in `u` and `v`. Default is None,
+        which gives each value a weight of 1.0
+
+    Returns
+    -------
+    yule : double
+        The Yule dissimilarity between vectors `u` and `v`.
+
+    Examples
+    --------
+    >>> from scipy.spatial import distance
+    >>> distance.yule([1, 0, 0], [0, 1, 0])
+    2.0
+    >>> distance.yule([1, 1, 0], [0, 1, 0])
+    0.0
+
+    """
+    u = _validate_vector(u)
+    v = _validate_vector(v)
+    if w is not None:
+        w = _validate_weights(w)
+    (nff, nft, ntf, ntt) = _nbool_correspond_all(u, v, w=w)
+    half_R = ntf * nft
+    if half_R == 0:
+        return 0.0
+    else:
+        return float(2.0 * half_R / (ntt * nff + half_R))
+
+
+def dice(u, v, w=None):
+    """
+    Compute the Dice dissimilarity between two boolean 1-D arrays.
+
+    The Dice dissimilarity between `u` and `v`, is
+
+    .. math::
+
+         \\frac{c_{TF} + c_{FT}}
+              {2c_{TT} + c_{FT} + c_{TF}}
+
+    where :math:`c_{ij}` is the number of occurrences of
+    :math:`\\mathtt{u[k]} = i` and :math:`\\mathtt{v[k]} = j` for
+    :math:`k < n`.
+
+    Parameters
+    ----------
+    u : (N,) array_like, bool
+        Input 1-D array.
+    v : (N,) array_like, bool
+        Input 1-D array.
+    w : (N,) array_like, optional
+        The weights for each value in `u` and `v`. Default is None,
+        which gives each value a weight of 1.0
+
+    Returns
+    -------
+    dice : double
+        The Dice dissimilarity between 1-D arrays `u` and `v`.
+
+    Notes
+    -----
+    This function computes the Dice dissimilarity index. To compute the
+    Dice similarity index, convert one to the other with similarity =
+    1 - dissimilarity.
+
+    Examples
+    --------
+    >>> from scipy.spatial import distance
+    >>> distance.dice([1, 0, 0], [0, 1, 0])
+    1.0
+    >>> distance.dice([1, 0, 0], [1, 1, 0])
+    0.3333333333333333
+    >>> distance.dice([1, 0, 0], [2, 0, 0])
+    -0.3333333333333333
+
+    """
+    u = _validate_vector(u)
+    v = _validate_vector(v)
+    if w is not None:
+        w = _validate_weights(w)
+    if u.dtype == v.dtype == bool and w is None:
+        ntt = (u & v).sum()
+    else:
+        dtype = np.result_type(int, u.dtype, v.dtype)
+        u = u.astype(dtype)
+        v = v.astype(dtype)
+        if w is None:
+            ntt = (u * v).sum()
+        else:
+            ntt = (u * v * w).sum()
+    (nft, ntf) = _nbool_correspond_ft_tf(u, v, w=w)
+    return float((ntf + nft) / np.array(2.0 * ntt + ntf + nft))
+
+
+def rogerstanimoto(u, v, w=None):
+    """
+    Compute the Rogers-Tanimoto dissimilarity between two boolean 1-D arrays.
+
+    The Rogers-Tanimoto dissimilarity between two boolean 1-D arrays
+    `u` and `v`, is defined as
+
+    .. math::
+       \\frac{R}
+            {c_{TT} + c_{FF} + R}
+
+    where :math:`c_{ij}` is the number of occurrences of
+    :math:`\\mathtt{u[k]} = i` and :math:`\\mathtt{v[k]} = j` for
+    :math:`k < n` and :math:`R = 2(c_{TF} + c_{FT})`.
+
+    Parameters
+    ----------
+    u : (N,) array_like, bool
+        Input array.
+    v : (N,) array_like, bool
+        Input array.
+    w : (N,) array_like, optional
+        The weights for each value in `u` and `v`. Default is None,
+        which gives each value a weight of 1.0
+
+    Returns
+    -------
+    rogerstanimoto : double
+        The Rogers-Tanimoto dissimilarity between vectors
+        `u` and `v`.
+
+    Examples
+    --------
+    >>> from scipy.spatial import distance
+    >>> distance.rogerstanimoto([1, 0, 0], [0, 1, 0])
+    0.8
+    >>> distance.rogerstanimoto([1, 0, 0], [1, 1, 0])
+    0.5
+    >>> distance.rogerstanimoto([1, 0, 0], [2, 0, 0])
+    -1.0
+
+    """
+    u = _validate_vector(u)
+    v = _validate_vector(v)
+    if w is not None:
+        w = _validate_weights(w)
+    (nff, nft, ntf, ntt) = _nbool_correspond_all(u, v, w=w)
+    return float(2.0 * (ntf + nft)) / float(ntt + nff + (2.0 * (ntf + nft)))
+
+
+def russellrao(u, v, w=None):
+    """
+    Compute the Russell-Rao dissimilarity between two boolean 1-D arrays.
+
+    The Russell-Rao dissimilarity between two boolean 1-D arrays, `u` and
+    `v`, is defined as
+
+    .. math::
+
+      \\frac{n - c_{TT}}
+           {n}
+
+    where :math:`c_{ij}` is the number of occurrences of
+    :math:`\\mathtt{u[k]} = i` and :math:`\\mathtt{v[k]} = j` for
+    :math:`k < n`.
+
+    Parameters
+    ----------
+    u : (N,) array_like, bool
+        Input array.
+    v : (N,) array_like, bool
+        Input array.
+    w : (N,) array_like, optional
+        The weights for each value in `u` and `v`. Default is None,
+        which gives each value a weight of 1.0
+
+    Returns
+    -------
+    russellrao : double
+        The Russell-Rao dissimilarity between vectors `u` and `v`.
+
+    Examples
+    --------
+    >>> from scipy.spatial import distance
+    >>> distance.russellrao([1, 0, 0], [0, 1, 0])
+    1.0
+    >>> distance.russellrao([1, 0, 0], [1, 1, 0])
+    0.6666666666666666
+    >>> distance.russellrao([1, 0, 0], [2, 0, 0])
+    0.3333333333333333
+
+    """
+    u = _validate_vector(u)
+    v = _validate_vector(v)
+    if u.dtype == v.dtype == bool and w is None:
+        ntt = (u & v).sum()
+        n = float(len(u))
+    elif w is None:
+        ntt = (u * v).sum()
+        n = float(len(u))
+    else:
+        w = _validate_weights(w)
+        ntt = (u * v * w).sum()
+        n = w.sum()
+    return float(n - ntt) / n
+
+
+def sokalsneath(u, v, w=None):
+    """
+    Compute the Sokal-Sneath dissimilarity between two boolean 1-D arrays.
+
+    The Sokal-Sneath dissimilarity between `u` and `v`,
+
+    .. math::
+
+       \\frac{R}
+            {c_{TT} + R}
+
+    where :math:`c_{ij}` is the number of occurrences of
+    :math:`\\mathtt{u[k]} = i` and :math:`\\mathtt{v[k]} = j` for
+    :math:`k < n` and :math:`R = 2(c_{TF} + c_{FT})`.
+
+    Parameters
+    ----------
+    u : (N,) array_like, bool
+        Input array.
+    v : (N,) array_like, bool
+        Input array.
+    w : (N,) array_like, optional
+        The weights for each value in `u` and `v`. Default is None,
+        which gives each value a weight of 1.0
+
+    Returns
+    -------
+    sokalsneath : double
+        The Sokal-Sneath dissimilarity between vectors `u` and `v`.
+
+    Examples
+    --------
+    >>> from scipy.spatial import distance
+    >>> distance.sokalsneath([1, 0, 0], [0, 1, 0])
+    1.0
+    >>> distance.sokalsneath([1, 0, 0], [1, 1, 0])
+    0.66666666666666663
+    >>> distance.sokalsneath([1, 0, 0], [2, 1, 0])
+    0.0
+    >>> distance.sokalsneath([1, 0, 0], [3, 1, 0])
+    -2.0
+
+    """
+    u = _validate_vector(u)
+    v = _validate_vector(v)
+    if u.dtype == v.dtype == bool and w is None:
+        ntt = (u & v).sum()
+    elif w is None:
+        ntt = (u * v).sum()
+    else:
+        w = _validate_weights(w)
+        ntt = (u * v * w).sum()
+    (nft, ntf) = _nbool_correspond_ft_tf(u, v, w=w)
+    denom = np.array(ntt + 2.0 * (ntf + nft))
+    if not denom.any():
+        raise ValueError('Sokal-Sneath dissimilarity is not defined for '
+                         'vectors that are entirely false.')
+    return float(2.0 * (ntf + nft)) / denom
+
+
+_convert_to_double = partial(_convert_to_type, out_type=np.float64)
+_convert_to_bool = partial(_convert_to_type, out_type=bool)
+
+# adding python-only wrappers to _distance_wrap module
+_distance_wrap.pdist_correlation_double_wrap = _correlation_pdist_wrap
+_distance_wrap.cdist_correlation_double_wrap = _correlation_cdist_wrap
+
+
+@dataclasses.dataclass(frozen=True)
+class CDistMetricWrapper:
+    metric_name: str
+
+    def __call__(self, XA, XB, *, out=None, **kwargs):
+        XA = np.ascontiguousarray(XA)
+        XB = np.ascontiguousarray(XB)
+        mA, n = XA.shape
+        mB, _ = XB.shape
+        metric_name = self.metric_name
+        metric_info = _METRICS[metric_name]
+        XA, XB, typ, kwargs = _validate_cdist_input(
+            XA, XB, mA, mB, n, metric_info, **kwargs)
+
+        w = kwargs.pop('w', None)
+        if w is not None:
+            metric = metric_info.dist_func
+            return _cdist_callable(
+                XA, XB, metric=metric, out=out, w=w, **kwargs)
+
+        dm = _prepare_out_argument(out, np.float64, (mA, mB))
+        # get cdist wrapper
+        cdist_fn = getattr(_distance_wrap, f'cdist_{metric_name}_{typ}_wrap')
+        cdist_fn(XA, XB, dm, **kwargs)
+        return dm
+
+
+@dataclasses.dataclass(frozen=True)
+class PDistMetricWrapper:
+    metric_name: str
+
+    def __call__(self, X, *, out=None, **kwargs):
+        X = np.ascontiguousarray(X)
+        m, n = X.shape
+        metric_name = self.metric_name
+        metric_info = _METRICS[metric_name]
+        X, typ, kwargs = _validate_pdist_input(
+            X, m, n, metric_info, **kwargs)
+        out_size = (m * (m - 1)) // 2
+        w = kwargs.pop('w', None)
+        if w is not None:
+            metric = metric_info.dist_func
+            return _pdist_callable(
+                X, metric=metric, out=out, w=w, **kwargs)
+
+        dm = _prepare_out_argument(out, np.float64, (out_size,))
+        # get pdist wrapper
+        pdist_fn = getattr(_distance_wrap, f'pdist_{metric_name}_{typ}_wrap')
+        pdist_fn(X, dm, **kwargs)
+        return dm
+
+
+@dataclasses.dataclass(frozen=True)
+class MetricInfo:
+    # Name of python distance function
+    canonical_name: str
+    # All aliases, including canonical_name
+    aka: set[str]
+    # unvectorized distance function
+    dist_func: Callable
+    # Optimized cdist function
+    cdist_func: Callable
+    # Optimized pdist function
+    pdist_func: Callable
+    # function that checks kwargs and computes default values:
+    # f(X, m, n, **kwargs)
+    validator: Callable | None = None
+    # list of supported types:
+    # X (pdist) and XA (cdist) are used to choose the type. if there is no
+    # match the first type is used. Default double
+    types: list[str] = dataclasses.field(default_factory=lambda: ['double'])
+    # true if out array must be C-contiguous
+    requires_contiguous_out: bool = True
+
+
+# Registry of implemented metrics:
+_METRIC_INFOS = [
+    MetricInfo(
+        canonical_name='braycurtis',
+        aka={'braycurtis'},
+        dist_func=braycurtis,
+        cdist_func=_distance_pybind.cdist_braycurtis,
+        pdist_func=_distance_pybind.pdist_braycurtis,
+    ),
+    MetricInfo(
+        canonical_name='canberra',
+        aka={'canberra'},
+        dist_func=canberra,
+        cdist_func=_distance_pybind.cdist_canberra,
+        pdist_func=_distance_pybind.pdist_canberra,
+    ),
+    MetricInfo(
+        canonical_name='chebyshev',
+        aka={'chebychev', 'chebyshev', 'cheby', 'cheb', 'ch'},
+        dist_func=chebyshev,
+        cdist_func=_distance_pybind.cdist_chebyshev,
+        pdist_func=_distance_pybind.pdist_chebyshev,
+    ),
+    MetricInfo(
+        canonical_name='cityblock',
+        aka={'cityblock', 'cblock', 'cb', 'c'},
+        dist_func=cityblock,
+        cdist_func=_distance_pybind.cdist_cityblock,
+        pdist_func=_distance_pybind.pdist_cityblock,
+    ),
+    MetricInfo(
+        canonical_name='correlation',
+        aka={'correlation', 'co'},
+        dist_func=correlation,
+        cdist_func=CDistMetricWrapper('correlation'),
+        pdist_func=PDistMetricWrapper('correlation'),
+    ),
+    MetricInfo(
+        canonical_name='cosine',
+        aka={'cosine', 'cos'},
+        dist_func=cosine,
+        cdist_func=CDistMetricWrapper('cosine'),
+        pdist_func=PDistMetricWrapper('cosine'),
+    ),
+    MetricInfo(
+        canonical_name='dice',
+        aka={'dice'},
+        types=['bool'],
+        dist_func=dice,
+        cdist_func=_distance_pybind.cdist_dice,
+        pdist_func=_distance_pybind.pdist_dice,
+    ),
+    MetricInfo(
+        canonical_name='euclidean',
+        aka={'euclidean', 'euclid', 'eu', 'e'},
+        dist_func=euclidean,
+        cdist_func=_distance_pybind.cdist_euclidean,
+        pdist_func=_distance_pybind.pdist_euclidean,
+    ),
+    MetricInfo(
+        canonical_name='hamming',
+        aka={'matching', 'hamming', 'hamm', 'ha', 'h'},
+        types=['double', 'bool'],
+        validator=_validate_hamming_kwargs,
+        dist_func=hamming,
+        cdist_func=_distance_pybind.cdist_hamming,
+        pdist_func=_distance_pybind.pdist_hamming,
+    ),
+    MetricInfo(
+        canonical_name='jaccard',
+        aka={'jaccard', 'jacc', 'ja', 'j'},
+        types=['double', 'bool'],
+        dist_func=jaccard,
+        cdist_func=_distance_pybind.cdist_jaccard,
+        pdist_func=_distance_pybind.pdist_jaccard,
+    ),
+    MetricInfo(
+        canonical_name='jensenshannon',
+        aka={'jensenshannon', 'js'},
+        dist_func=jensenshannon,
+        cdist_func=CDistMetricWrapper('jensenshannon'),
+        pdist_func=PDistMetricWrapper('jensenshannon'),
+    ),
+    MetricInfo(
+        canonical_name='mahalanobis',
+        aka={'mahalanobis', 'mahal', 'mah'},
+        validator=_validate_mahalanobis_kwargs,
+        dist_func=mahalanobis,
+        cdist_func=CDistMetricWrapper('mahalanobis'),
+        pdist_func=PDistMetricWrapper('mahalanobis'),
+    ),
+    MetricInfo(
+        canonical_name='minkowski',
+        aka={'minkowski', 'mi', 'm', 'pnorm'},
+        validator=_validate_minkowski_kwargs,
+        dist_func=minkowski,
+        cdist_func=_distance_pybind.cdist_minkowski,
+        pdist_func=_distance_pybind.pdist_minkowski,
+    ),
+    MetricInfo(
+        canonical_name='rogerstanimoto',
+        aka={'rogerstanimoto'},
+        types=['bool'],
+        dist_func=rogerstanimoto,
+        cdist_func=_distance_pybind.cdist_rogerstanimoto,
+        pdist_func=_distance_pybind.pdist_rogerstanimoto,
+    ),
+    MetricInfo(
+        canonical_name='russellrao',
+        aka={'russellrao'},
+        types=['bool'],
+        dist_func=russellrao,
+        cdist_func=_distance_pybind.cdist_russellrao,
+        pdist_func=_distance_pybind.pdist_russellrao,
+    ),
+    MetricInfo(
+        canonical_name='seuclidean',
+        aka={'seuclidean', 'se', 's'},
+        validator=_validate_seuclidean_kwargs,
+        dist_func=seuclidean,
+        cdist_func=CDistMetricWrapper('seuclidean'),
+        pdist_func=PDistMetricWrapper('seuclidean'),
+    ),
+    MetricInfo(
+        canonical_name='sokalsneath',
+        aka={'sokalsneath'},
+        types=['bool'],
+        dist_func=sokalsneath,
+        cdist_func=_distance_pybind.cdist_sokalsneath,
+        pdist_func=_distance_pybind.pdist_sokalsneath,
+    ),
+    MetricInfo(
+        canonical_name='sqeuclidean',
+        aka={'sqeuclidean', 'sqe', 'sqeuclid'},
+        dist_func=sqeuclidean,
+        cdist_func=_distance_pybind.cdist_sqeuclidean,
+        pdist_func=_distance_pybind.pdist_sqeuclidean,
+    ),
+    MetricInfo(
+        canonical_name='yule',
+        aka={'yule'},
+        types=['bool'],
+        dist_func=yule,
+        cdist_func=_distance_pybind.cdist_yule,
+        pdist_func=_distance_pybind.pdist_yule,
+    ),
+]
+
+_METRICS = {info.canonical_name: info for info in _METRIC_INFOS}
+_METRIC_ALIAS = {alias: info
+                     for info in _METRIC_INFOS
+                     for alias in info.aka}
+
+_METRICS_NAMES = list(_METRICS.keys())
+
+_TEST_METRICS = {'test_' + info.canonical_name: info for info in _METRIC_INFOS}
+
+
+def pdist(X, metric='euclidean', *, out=None, **kwargs):
+    """
+    Pairwise distances between observations in n-dimensional space.
+
+    See Notes for common calling conventions.
+
+    Parameters
+    ----------
+    X : array_like
+        An m by n array of m original observations in an
+        n-dimensional space.
+    metric : str or function, optional
+        The distance metric to use. The distance function can
+        be 'braycurtis', 'canberra', 'chebyshev', 'cityblock',
+        'correlation', 'cosine', 'dice', 'euclidean', 'hamming',
+        'jaccard', 'jensenshannon',
+        'mahalanobis', 'matching', 'minkowski', 'rogerstanimoto',
+        'russellrao', 'seuclidean', 'sokalsneath',
+        'sqeuclidean', 'yule'.
+    out : ndarray, optional
+        The output array.
+        If not None, condensed distance matrix Y is stored in this array.
+    **kwargs : dict, optional
+        Extra arguments to `metric`: refer to each metric documentation for a
+        list of all possible arguments.
+
+        Some possible arguments:
+
+        p : scalar
+        The p-norm to apply for Minkowski, weighted and unweighted.
+        Default: 2.
+
+        w : ndarray
+        The weight vector for metrics that support weights (e.g., Minkowski).
+
+        V : ndarray
+        The variance vector for standardized Euclidean.
+        Default: var(X, axis=0, ddof=1)
+
+        VI : ndarray
+        The inverse of the covariance matrix for Mahalanobis.
+        Default: inv(cov(X.T)).T
+
+    Returns
+    -------
+    Y : ndarray
+        Returns a condensed distance matrix Y. For each :math:`i` and :math:`j`
+        (where :math:`i<j<m`),where m is the number of original observations.
+        The metric ``dist(u=X[i], v=X[j])`` is computed and stored in entry ``m
+        * i + j - ((i + 2) * (i + 1)) // 2``.
+
+    See Also
+    --------
+    squareform : converts between condensed distance matrices and
+                 square distance matrices.
+
+    Notes
+    -----
+    See ``squareform`` for information on how to calculate the index of
+    this entry or to convert the condensed distance matrix to a
+    redundant square matrix.
+
+    The following are common calling conventions.
+
+    1. ``Y = pdist(X, 'euclidean')``
+
+       Computes the distance between m points using Euclidean distance
+       (2-norm) as the distance metric between the points. The points
+       are arranged as m n-dimensional row vectors in the matrix X.
+
+    2. ``Y = pdist(X, 'minkowski', p=2.)``
+
+       Computes the distances using the Minkowski distance
+       :math:`\\|u-v\\|_p` (:math:`p`-norm) where :math:`p > 0` (note
+       that this is only a quasi-metric if :math:`0 < p < 1`).
+
+    3. ``Y = pdist(X, 'cityblock')``
+
+       Computes the city block or Manhattan distance between the
+       points.
+
+    4. ``Y = pdist(X, 'seuclidean', V=None)``
+
+       Computes the standardized Euclidean distance. The standardized
+       Euclidean distance between two n-vectors ``u`` and ``v`` is
+
+       .. math::
+
+          \\sqrt{\\sum {(u_i-v_i)^2 / V[x_i]}}
+
+
+       V is the variance vector; V[i] is the variance computed over all
+       the i'th components of the points.  If not passed, it is
+       automatically computed.
+
+    5. ``Y = pdist(X, 'sqeuclidean')``
+
+       Computes the squared Euclidean distance :math:`\\|u-v\\|_2^2` between
+       the vectors.
+
+    6. ``Y = pdist(X, 'cosine')``
+
+       Computes the cosine distance between vectors u and v,
+
+       .. math::
+
+          1 - \\frac{u \\cdot v}
+                   {{\\|u\\|}_2 {\\|v\\|}_2}
+
+       where :math:`\\|*\\|_2` is the 2-norm of its argument ``*``, and
+       :math:`u \\cdot v` is the dot product of ``u`` and ``v``.
+
+    7. ``Y = pdist(X, 'correlation')``
+
+       Computes the correlation distance between vectors u and v. This is
+
+       .. math::
+
+          1 - \\frac{(u - \\bar{u}) \\cdot (v - \\bar{v})}
+                   {{\\|(u - \\bar{u})\\|}_2 {\\|(v - \\bar{v})\\|}_2}
+
+       where :math:`\\bar{v}` is the mean of the elements of vector v,
+       and :math:`x \\cdot y` is the dot product of :math:`x` and :math:`y`.
+
+    8. ``Y = pdist(X, 'hamming')``
+
+       Computes the normalized Hamming distance, or the proportion of
+       those vector elements between two n-vectors ``u`` and ``v``
+       which disagree. To save memory, the matrix ``X`` can be of type
+       boolean.
+
+    9. ``Y = pdist(X, 'jaccard')``
+
+       Computes the Jaccard distance between the points. Given two
+       vectors, ``u`` and ``v``, the Jaccard distance is the
+       proportion of those elements ``u[i]`` and ``v[i]`` that
+       disagree.
+
+    10. ``Y = pdist(X, 'jensenshannon')``
+
+        Computes the Jensen-Shannon distance between two probability arrays.
+        Given two probability vectors, :math:`p` and :math:`q`, the
+        Jensen-Shannon distance is
+
+        .. math::
+
+           \\sqrt{\\frac{D(p \\parallel m) + D(q \\parallel m)}{2}}
+
+        where :math:`m` is the pointwise mean of :math:`p` and :math:`q`
+        and :math:`D` is the Kullback-Leibler divergence.
+
+    11. ``Y = pdist(X, 'chebyshev')``
+
+        Computes the Chebyshev distance between the points. The
+        Chebyshev distance between two n-vectors ``u`` and ``v`` is the
+        maximum norm-1 distance between their respective elements. More
+        precisely, the distance is given by
+
+        .. math::
+
+           d(u,v) = \\max_i {|u_i-v_i|}
+
+    12. ``Y = pdist(X, 'canberra')``
+
+        Computes the Canberra distance between the points. The
+        Canberra distance between two points ``u`` and ``v`` is
+
+        .. math::
+
+          d(u,v) = \\sum_i \\frac{|u_i-v_i|}
+                               {|u_i|+|v_i|}
+
+
+    13. ``Y = pdist(X, 'braycurtis')``
+
+        Computes the Bray-Curtis distance between the points. The
+        Bray-Curtis distance between two points ``u`` and ``v`` is
+
+
+        .. math::
+
+             d(u,v) = \\frac{\\sum_i {|u_i-v_i|}}
+                            {\\sum_i {|u_i+v_i|}}
+
+    14. ``Y = pdist(X, 'mahalanobis', VI=None)``
+
+        Computes the Mahalanobis distance between the points. The
+        Mahalanobis distance between two points ``u`` and ``v`` is
+        :math:`\\sqrt{(u-v)(1/V)(u-v)^T}` where :math:`(1/V)` (the ``VI``
+        variable) is the inverse covariance. If ``VI`` is not None,
+        ``VI`` will be used as the inverse covariance matrix.
+
+    15. ``Y = pdist(X, 'yule')``
+
+        Computes the Yule distance between each pair of boolean
+        vectors. (see yule function documentation)
+
+    16. ``Y = pdist(X, 'matching')``
+
+        Synonym for 'hamming'.
+
+    17. ``Y = pdist(X, 'dice')``
+
+        Computes the Dice distance between each pair of boolean
+        vectors. (see dice function documentation)
+
+
+    18. ``Y = pdist(X, 'rogerstanimoto')``
+
+        Computes the Rogers-Tanimoto distance between each pair of
+        boolean vectors. (see rogerstanimoto function documentation)
+
+    19. ``Y = pdist(X, 'russellrao')``
+
+        Computes the Russell-Rao distance between each pair of
+        boolean vectors. (see russellrao function documentation)
+
+    20. ``Y = pdist(X, 'sokalsneath')``
+
+        Computes the Sokal-Sneath distance between each pair of
+        boolean vectors. (see sokalsneath function documentation)
+
+    21. ``Y = pdist(X, f)``
+
+        Computes the distance between all pairs of vectors in X
+        using the user supplied 2-arity function f. For example,
+        Euclidean distance between the vectors could be computed
+        as follows::
+
+          dm = pdist(X, lambda u, v: np.sqrt(((u-v)**2).sum()))
+
+        Note that you should avoid passing a reference to one of
+        the distance functions defined in this library. For example,::
+
+          dm = pdist(X, sokalsneath)
+
+        would calculate the pair-wise distances between the vectors in
+        X using the Python function sokalsneath. This would result in
+        sokalsneath being called :math:`{n \\choose 2}` times, which
+        is inefficient. Instead, the optimized C version is more
+        efficient, and we call it using the following syntax.::
+
+          dm = pdist(X, 'sokalsneath')
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.spatial.distance import pdist
+
+    ``x`` is an array of five points in three-dimensional space.
+
+    >>> x = np.array([[2, 0, 2], [2, 2, 3], [-2, 4, 5], [0, 1, 9], [2, 2, 4]])
+
+    ``pdist(x)`` with no additional arguments computes the 10 pairwise
+    Euclidean distances:
+
+    >>> pdist(x)
+    array([2.23606798, 6.40312424, 7.34846923, 2.82842712, 4.89897949,
+           6.40312424, 1.        , 5.38516481, 4.58257569, 5.47722558])
+
+    The following computes the pairwise Minkowski distances with ``p = 3.5``:
+
+    >>> pdist(x, metric='minkowski', p=3.5)
+    array([2.04898923, 5.1154929 , 7.02700737, 2.43802731, 4.19042714,
+           6.03956994, 1.        , 4.45128103, 4.10636143, 5.0619695 ])
+
+    The pairwise city block or Manhattan distances:
+
+    >>> pdist(x, metric='cityblock')
+    array([ 3., 11., 10.,  4.,  8.,  9.,  1.,  9.,  7.,  8.])
+
+    """
+    # You can also call this as:
+    #     Y = pdist(X, 'test_abc')
+    # where 'abc' is the metric being tested.  This computes the distance
+    # between all pairs of vectors in X using the distance metric 'abc' but
+    # with a more succinct, verifiable, but less efficient implementation.
+
+    X = _asarray(X)
+    if X.ndim != 2:
+        raise ValueError('A 2-dimensional array must be passed. '
+                         f'(Shape was {X.shape}).')
+
+    n = X.shape[0]
+    return xpx.lazy_apply(_np_pdist, X, out,
+                          # lazy_apply doesn't support Array kwargs
+                          kwargs.pop('w', None),
+                          kwargs.pop('V', None),
+                          kwargs.pop('VI', None),
+                          # See src/distance_pybind.cpp::pdist
+                          shape=((n * (n - 1)) // 2, ), dtype=X.dtype,
+                          as_numpy=True, metric=metric, **kwargs)
+
+
+def _np_pdist(X, out, w, V, VI, metric='euclidean', **kwargs):
+
+    X = _asarray_validated(X, sparse_ok=False, objects_ok=True, mask_ok=True,
+                           check_finite=False)
+    m, n = X.shape
+
+    if w is not None:
+        kwargs["w"] = w
+    if V is not None:
+        kwargs["V"] = V
+    if VI is not None:
+        kwargs["VI"] = VI
+
+    if callable(metric):
+        mstr = getattr(metric, '__name__', 'UnknownCustomMetric')
+        metric_info = _METRIC_ALIAS.get(mstr, None)
+
+        if metric_info is not None:
+            X, typ, kwargs = _validate_pdist_input(
+                X, m, n, metric_info, **kwargs)
+
+        return _pdist_callable(X, metric=metric, out=out, **kwargs)
+    elif isinstance(metric, str):
+        mstr = metric.lower()
+        metric_info = _METRIC_ALIAS.get(mstr, None)
+
+        if metric_info is not None:
+            pdist_fn = metric_info.pdist_func
+            return pdist_fn(X, out=out, **kwargs)
+        elif mstr.startswith("test_"):
+            metric_info = _TEST_METRICS.get(mstr, None)
+            if metric_info is None:
+                raise ValueError(f'Unknown "Test" Distance Metric: {mstr[5:]}')
+            X, typ, kwargs = _validate_pdist_input(
+                X, m, n, metric_info, **kwargs)
+            return _pdist_callable(
+                X, metric=metric_info.dist_func, out=out, **kwargs)
+        else:
+            raise ValueError(f'Unknown Distance Metric: {mstr}')
+    else:
+        raise TypeError('2nd argument metric must be a string identifier '
+                        'or a function.')
+
+
+def squareform(X, force="no", checks=True):
+    """
+    Convert a vector-form distance vector to a square-form distance
+    matrix, and vice-versa.
+
+    Parameters
+    ----------
+    X : array_like
+        Either a condensed or redundant distance matrix.
+    force : str, optional
+        As with MATLAB(TM), if force is equal to ``'tovector'`` or
+        ``'tomatrix'``, the input will be treated as a distance matrix or
+        distance vector respectively.
+    checks : bool, optional
+        If set to False, no checks will be made for matrix
+        symmetry nor zero diagonals. This is useful if it is known that
+        ``X - X.T1`` is small and ``diag(X)`` is close to zero.
+        These values are ignored any way so they do not disrupt the
+        squareform transformation.
+
+    Returns
+    -------
+    Y : ndarray
+        If a condensed distance matrix is passed, a redundant one is
+        returned, or if a redundant one is passed, a condensed distance
+        matrix is returned.
+
+    Notes
+    -----
+    1. ``v = squareform(X)``
+
+       Given a square n-by-n symmetric distance matrix ``X``,
+       ``v = squareform(X)`` returns an ``n * (n-1) / 2``
+       (i.e. binomial coefficient n choose 2) sized vector `v`
+       where :math:`v[{n \\choose 2} - {n-i \\choose 2} + (j-i-1)]`
+       is the distance between distinct points ``i`` and ``j``.
+       If ``X`` is non-square or asymmetric, an error is raised.
+
+    2. ``X = squareform(v)``
+
+       Given an ``n * (n-1) / 2`` sized vector ``v``
+       for some integer ``n >= 1`` encoding distances as described,
+       ``X = squareform(v)`` returns an n-by-n distance matrix ``X``.
+       The ``X[i, j]`` and ``X[j, i]`` values are set to
+       :math:`v[{n \\choose 2} - {n-i \\choose 2} + (j-i-1)]`
+       and all diagonal elements are zero.
+
+    In SciPy 0.19.0, ``squareform`` stopped casting all input types to
+    float64, and started returning arrays of the same dtype as the input.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.spatial.distance import pdist, squareform
+
+    ``x`` is an array of five points in three-dimensional space.
+
+    >>> x = np.array([[2, 0, 2], [2, 2, 3], [-2, 4, 5], [0, 1, 9], [2, 2, 4]])
+
+    ``pdist(x)`` computes the Euclidean distances between each pair of
+    points in ``x``.  The distances are returned in a one-dimensional
+    array with length ``5*(5 - 1)/2 = 10``.
+
+    >>> distvec = pdist(x)
+    >>> distvec
+    array([2.23606798, 6.40312424, 7.34846923, 2.82842712, 4.89897949,
+           6.40312424, 1.        , 5.38516481, 4.58257569, 5.47722558])
+
+    ``squareform(distvec)`` returns the 5x5 distance matrix.
+
+    >>> m = squareform(distvec)
+    >>> m
+    array([[0.        , 2.23606798, 6.40312424, 7.34846923, 2.82842712],
+           [2.23606798, 0.        , 4.89897949, 6.40312424, 1.        ],
+           [6.40312424, 4.89897949, 0.        , 5.38516481, 4.58257569],
+           [7.34846923, 6.40312424, 5.38516481, 0.        , 5.47722558],
+           [2.82842712, 1.        , 4.58257569, 5.47722558, 0.        ]])
+
+    When given a square distance matrix ``m``, ``squareform(m)`` returns
+    the one-dimensional condensed distance vector associated with the
+    matrix.  In this case, we recover ``distvec``.
+
+    >>> squareform(m)
+    array([2.23606798, 6.40312424, 7.34846923, 2.82842712, 4.89897949,
+           6.40312424, 1.        , 5.38516481, 4.58257569, 5.47722558])
+    """
+    X = np.ascontiguousarray(X)
+
+    s = X.shape
+
+    if force.lower() == 'tomatrix':
+        if len(s) != 1:
+            raise ValueError("Forcing 'tomatrix' but input X is not a "
+                             "distance vector.")
+    elif force.lower() == 'tovector':
+        if len(s) != 2:
+            raise ValueError("Forcing 'tovector' but input X is not a "
+                             "distance matrix.")
+
+    # X = squareform(v)
+    if len(s) == 1:
+        if s[0] == 0:
+            return np.zeros((1, 1), dtype=X.dtype)
+
+        # Grab the closest value to the square root of the number
+        # of elements times 2 to see if the number of elements
+        # is indeed a binomial coefficient.
+        d = int(np.ceil(np.sqrt(s[0] * 2)))
+
+        # Check that v is of valid dimensions.
+        if d * (d - 1) != s[0] * 2:
+            raise ValueError('Incompatible vector size. It must be a binomial '
+                             'coefficient n choose 2 for some integer n >= 2.')
+
+        # Allocate memory for the distance matrix.
+        M = np.zeros((d, d), dtype=X.dtype)
+
+        # Since the C code does not support striding using strides.
+        # The dimensions are used instead.
+        X = _copy_array_if_base_present(X)
+
+        # Fill in the values of the distance matrix.
+        _distance_wrap.to_squareform_from_vector_wrap(M, X)
+
+        # Return the distance matrix.
+        return M
+    elif len(s) == 2:
+        if s[0] != s[1]:
+            raise ValueError('The matrix argument must be square.')
+        if checks:
+            is_valid_dm(X, throw=True, name='X')
+
+        # One-side of the dimensions is set here.
+        d = s[0]
+
+        if d <= 1:
+            return np.array([], dtype=X.dtype)
+
+        # Create a vector.
+        v = np.zeros((d * (d - 1)) // 2, dtype=X.dtype)
+
+        # Since the C code does not support striding using strides.
+        # The dimensions are used instead.
+        X = _copy_array_if_base_present(X)
+
+        # Convert the vector to squareform.
+        _distance_wrap.to_vector_from_squareform_wrap(X, v)
+        return v
+    else:
+        raise ValueError("The first argument must be one or two dimensional "
+                         f"array. A {len(s)}-dimensional array is not permitted")
+
+
+def is_valid_dm(D, tol=0.0, throw=False, name="D", warning=False):
+    """
+    Return True if input array satisfies basic distance matrix properties
+    (symmetry and zero diagonal).
+
+    This function checks whether the input is a 2-dimensional square NumPy array
+    with a zero diagonal and symmetry within a specified tolerance. These are
+    necessary properties for a distance matrix but not sufficient -- in particular,
+    this function does **not** check the triangle inequality, which is required
+    for a true metric distance matrix.
+
+    The triangle inequality states that for any three points ``i``, ``j``, and ``k``:
+    ``D[i,k] <= D[i,j] + D[j,k]``
+
+    Parameters
+    ----------
+    D : array_like
+        The candidate object to test for basic distance matrix properties.
+    tol : float, optional
+        The distance matrix is considered symmetric if the absolute difference
+        between entries ``ij`` and ``ji`` is less than or equal to `tol`. The same
+        tolerance is used to determine whether diagonal entries are effectively zero.
+    throw : bool, optional
+        If True, raises an exception when the input is invalid.
+    name : str, optional
+        The name of the variable to check. This is used in exception messages when
+        `throw` is True to identify the offending variable.
+    warning : bool, optional
+        If True, a warning message is raised instead of throwing an exception.
+
+    Returns
+    -------
+    valid : bool
+        True if the input satisfies the symmetry and zero-diagonal conditions.
+
+    Raises
+    ------
+    ValueError
+        If `throw` is True and `D` is not a valid distance matrix.
+    UserWarning
+        If `warning` is True and `D` is not a valid distance matrix.
+
+    Notes
+    -----
+    This function does not check the triangle inequality, which is required for
+    a complete validation of a metric distance matrix. Only structural properties
+    (symmetry and zero diagonal) are verified. Small numerical deviations from symmetry
+    or exact zero diagonal are tolerated within the `tol` parameter.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.spatial.distance import is_valid_dm
+
+    This matrix is a valid distance matrix.
+
+    >>> d = np.array([[0.0, 1.1, 1.2, 1.3],
+    ...               [1.1, 0.0, 1.0, 1.4],
+    ...               [1.2, 1.0, 0.0, 1.5],
+    ...               [1.3, 1.4, 1.5, 0.0]])
+    >>> is_valid_dm(d)
+    True
+
+    In the following examples, the input is not a valid distance matrix.
+
+    Not square:
+
+    >>> is_valid_dm([[0, 2, 2], [2, 0, 2]])
+    False
+
+    Nonzero diagonal element:
+
+    >>> is_valid_dm([[0, 1, 1], [1, 2, 3], [1, 3, 0]])
+    False
+
+    Not symmetric:
+
+    >>> is_valid_dm([[0, 1, 3], [2, 0, 1], [3, 1, 0]])
+    False
+
+    """
+    D = np.asarray(D, order='c')
+    valid = True
+    try:
+        s = D.shape
+        if len(D.shape) != 2:
+            if name:
+                raise ValueError(f"Distance matrix '{name}' must have shape=2 "
+                                 "(i.e. be two-dimensional).")
+            else:
+                raise ValueError('Distance matrix must have shape=2 (i.e. '
+                                 'be two-dimensional).')
+        if tol == 0.0:
+            if not (D == D.T).all():
+                if name:
+                    raise ValueError(f"Distance matrix '{name}' must be symmetric.")
+                else:
+                    raise ValueError('Distance matrix must be symmetric.')
+            if not (D[range(0, s[0]), range(0, s[0])] == 0).all():
+                if name:
+                    raise ValueError(f"Distance matrix '{name}' diagonal must be zero.")
+                else:
+                    raise ValueError('Distance matrix diagonal must be zero.')
+        else:
+            if not (D - D.T <= tol).all():
+                if name:
+                    raise ValueError(f'Distance matrix \'{name}\' must be '
+                                     f'symmetric within tolerance {tol:5.5f}.')
+                else:
+                    raise ValueError('Distance matrix must be symmetric within '
+                                     f'tolerance {tol:5.5f}.')
+            if not (D[range(0, s[0]), range(0, s[0])] <= tol).all():
+                if name:
+                    raise ValueError(f'Distance matrix \'{name}\' diagonal must be '
+                                     f'close to zero within tolerance {tol:5.5f}.')
+                else:
+                    raise ValueError(('Distance matrix \'{}\' diagonal must be close '
+                                      'to zero within tolerance {:5.5f}.').format(*tol))
+    except Exception as e:
+        if throw:
+            raise
+        if warning:
+            warnings.warn(str(e), stacklevel=2)
+        valid = False
+    return valid
+
+
+def is_valid_y(y, warning=False, throw=False, name=None):
+    """
+    Return True if the input array is a valid condensed distance matrix.
+
+    Condensed distance matrices must be 1-dimensional numpy arrays.
+    Their length must be a binomial coefficient :math:`{n \\choose 2}`
+    for some positive integer n.
+
+    Parameters
+    ----------
+    y : array_like
+        The condensed distance matrix.
+    warning : bool, optional
+        Invokes a warning if the variable passed is not a valid
+        condensed distance matrix. The warning message explains why
+        the distance matrix is not valid.  `name` is used when
+        referencing the offending variable.
+    throw : bool, optional
+        Throws an exception if the variable passed is not a valid
+        condensed distance matrix.
+    name : str, optional
+        Used when referencing the offending variable in the
+        warning or exception message.
+
+    Returns
+    -------
+    bool
+        True if the input array is a valid condensed distance matrix,
+        False otherwise.
+
+    Examples
+    --------
+    >>> from scipy.spatial.distance import is_valid_y
+
+    This vector is a valid condensed distance matrix.  The length is 6,
+    which corresponds to ``n = 4``, since ``4*(4 - 1)/2`` is 6.
+
+    >>> v = [1.0, 1.2, 1.0, 0.5, 1.3, 0.9]
+    >>> is_valid_y(v)
+    True
+
+    An input vector with length, say, 7, is not a valid condensed distance
+    matrix.
+
+    >>> is_valid_y([1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7])
+    False
+
+    """
+    y = _asarray(y)
+    name_str = f"'{name}' " if name else ""
+    try:
+        if len(y.shape) != 1:
+            raise ValueError(f"Condensed distance matrix {name_str}must "
+                             "have shape=1 (i.e. be one-dimensional).")
+        n = y.shape[0]
+        d = int(np.ceil(np.sqrt(n * 2)))
+        if (d * (d - 1) / 2) != n:
+            raise ValueError(f"Length n of condensed distance matrix {name_str}"
+                             "must be a binomial coefficient, i.e. "
+                             "there must be a k such that (k \\choose 2)=n)!")
+    except Exception as e:
+        if throw:
+            raise
+        if warning:
+            warnings.warn(str(e), stacklevel=2)
+        return False
+    return True
+
+
+def num_obs_dm(d):
+    """
+    Return the number of original observations that correspond to a
+    square, redundant distance matrix.
+
+    Parameters
+    ----------
+    d : array_like
+        The target distance matrix.
+
+    Returns
+    -------
+    num_obs_dm : int
+        The number of observations in the redundant distance matrix.
+
+    Examples
+    --------
+    Find the number of original observations corresponding
+    to a square redundant distance matrix d.
+
+    >>> from scipy.spatial.distance import num_obs_dm
+    >>> d = [[0, 100, 200], [100, 0, 150], [200, 150, 0]]
+    >>> num_obs_dm(d)
+    3
+    """
+    d = np.asarray(d, order='c')
+    is_valid_dm(d, tol=np.inf, throw=True, name='d')
+    return d.shape[0]
+
+
+def num_obs_y(Y):
+    """
+    Return the number of original observations that correspond to a
+    condensed distance matrix.
+
+    Parameters
+    ----------
+    Y : array_like
+        Condensed distance matrix.
+
+    Returns
+    -------
+    n : int
+        The number of observations in the condensed distance matrix `Y`.
+
+    Examples
+    --------
+    Find the number of original observations corresponding to a
+    condensed distance matrix Y.
+
+    >>> from scipy.spatial.distance import num_obs_y
+    >>> Y = [1, 2, 3.5, 7, 10, 4]
+    >>> num_obs_y(Y)
+    4
+    """
+    Y = _asarray(Y)
+    is_valid_y(Y, throw=True, name='Y')
+    k = Y.shape[0]
+    if k == 0:
+        raise ValueError("The number of observations cannot be determined on "
+                         "an empty distance matrix.")
+    d = int(np.ceil(np.sqrt(k * 2)))
+    if (d * (d - 1) / 2) != k:
+        raise ValueError("Invalid condensed distance matrix passed. Must be "
+                         "some k where k=(n choose 2) for some n >= 2.")
+    return d
+
+
+def _prepare_out_argument(out, dtype, expected_shape):
+    if out is None:
+        return np.empty(expected_shape, dtype=dtype)
+
+    if out.shape != expected_shape:
+        raise ValueError("Output array has incorrect shape.")
+    if not out.flags.c_contiguous:
+        raise ValueError("Output array must be C-contiguous.")
+    if out.dtype != np.float64:
+        raise ValueError("Output array must be double type.")
+    return out
+
+
+def _pdist_callable(X, *, out, metric, **kwargs):
+    n = X.shape[0]
+    out_size = (n * (n - 1)) // 2
+    dm = _prepare_out_argument(out, np.float64, (out_size,))
+    k = 0
+    for i in range(X.shape[0] - 1):
+        for j in range(i + 1, X.shape[0]):
+            dm[k] = metric(X[i], X[j], **kwargs)
+            k += 1
+    return dm
+
+
+def _cdist_callable(XA, XB, *, out, metric, **kwargs):
+    mA = XA.shape[0]
+    mB = XB.shape[0]
+    dm = _prepare_out_argument(out, np.float64, (mA, mB))
+    for i in range(mA):
+        for j in range(mB):
+            dm[i, j] = metric(XA[i], XB[j], **kwargs)
+    return dm
+
+
+def cdist(XA, XB, metric='euclidean', *, out=None, **kwargs):
+    """
+    Compute distance between each pair of the two collections of inputs.
+
+    See Notes for common calling conventions.
+
+    Parameters
+    ----------
+    XA : array_like
+        An :math:`m_A` by :math:`n` array of :math:`m_A`
+        original observations in an :math:`n`-dimensional space.
+        Inputs are converted to float type.
+    XB : array_like
+        An :math:`m_B` by :math:`n` array of :math:`m_B`
+        original observations in an :math:`n`-dimensional space.
+        Inputs are converted to float type.
+    metric : str or callable, optional
+        The distance metric to use. If a string, the distance function can be
+        'braycurtis', 'canberra', 'chebyshev', 'cityblock', 'correlation',
+        'cosine', 'dice', 'euclidean', 'hamming', 'jaccard', 'jensenshannon',
+        'mahalanobis', 'matching', 'minkowski', 'rogerstanimoto', 'russellrao',
+        'seuclidean', 'sokalsneath', 'sqeuclidean', 'yule'.
+    out : ndarray, optional
+        Output array in which to place the result. It must have the same
+        shape as the expected output.
+    **kwargs : dict, optional
+        Extra arguments to `metric`: refer to each metric documentation for a
+        list of all possible arguments.
+
+        Some possible arguments:
+
+        p : scalar
+        The p-norm to apply for Minkowski, weighted and unweighted.
+        Default: 2.
+
+        w : array_like
+        The weight vector for metrics that support weights (e.g., Minkowski).
+
+        V : array_like
+        The variance vector for standardized Euclidean.
+        Default: var(vstack([XA, XB]), axis=0, ddof=1)
+
+        VI : array_like
+        The inverse of the covariance matrix for Mahalanobis.
+        Default: inv(cov(vstack([XA, XB].T))).T
+
+        out : ndarray
+        The output array
+        If not None, the distance matrix Y is stored in this array.
+
+    Returns
+    -------
+    Y : ndarray
+        A :math:`m_A` by :math:`m_B` distance matrix is returned.
+        For each :math:`i` and :math:`j`, the metric
+        ``dist(u=XA[i], v=XB[j])`` is computed and stored in the
+        :math:`ij` th entry.
+
+    Raises
+    ------
+    ValueError
+        An exception is thrown if `XA` and `XB` do not have
+        the same number of columns.
+
+    Notes
+    -----
+    The following are common calling conventions:
+
+    1. ``Y = cdist(XA, XB, 'euclidean')``
+
+       Computes the distance between :math:`m` points using
+       Euclidean distance (2-norm) as the distance metric between the
+       points. The points are arranged as :math:`m`
+       :math:`n`-dimensional row vectors in the matrix X.
+
+    2. ``Y = cdist(XA, XB, 'minkowski', p=2.)``
+
+       Computes the distances using the Minkowski distance
+       :math:`\\|u-v\\|_p` (:math:`p`-norm) where :math:`p > 0` (note
+       that this is only a quasi-metric if :math:`0 < p < 1`).
+
+    3. ``Y = cdist(XA, XB, 'cityblock')``
+
+       Computes the city block or Manhattan distance between the
+       points.
+
+    4. ``Y = cdist(XA, XB, 'seuclidean', V=None)``
+
+       Computes the standardized Euclidean distance. The standardized
+       Euclidean distance between two n-vectors ``u`` and ``v`` is
+
+       .. math::
+
+          \\sqrt{\\sum {(u_i-v_i)^2 / V[x_i]}}.
+
+       V is the variance vector; V[i] is the variance computed over all
+       the i'th components of the points. If not passed, it is
+       automatically computed.
+
+    5. ``Y = cdist(XA, XB, 'sqeuclidean')``
+
+       Computes the squared Euclidean distance :math:`\\|u-v\\|_2^2` between
+       the vectors.
+
+    6. ``Y = cdist(XA, XB, 'cosine')``
+
+       Computes the cosine distance between vectors u and v,
+
+       .. math::
+
+          1 - \\frac{u \\cdot v}
+                   {{\\|u\\|}_2 {\\|v\\|}_2}
+
+       where :math:`\\|*\\|_2` is the 2-norm of its argument ``*``, and
+       :math:`u \\cdot v` is the dot product of :math:`u` and :math:`v`.
+
+    7. ``Y = cdist(XA, XB, 'correlation')``
+
+       Computes the correlation distance between vectors u and v. This is
+
+       .. math::
+
+          1 - \\frac{(u - \\bar{u}) \\cdot (v - \\bar{v})}
+                   {{\\|(u - \\bar{u})\\|}_2 {\\|(v - \\bar{v})\\|}_2}
+
+       where :math:`\\bar{v}` is the mean of the elements of vector v,
+       and :math:`x \\cdot y` is the dot product of :math:`x` and :math:`y`.
+
+
+    8. ``Y = cdist(XA, XB, 'hamming')``
+
+       Computes the normalized Hamming distance, or the proportion of
+       those vector elements between two n-vectors ``u`` and ``v``
+       which disagree. To save memory, the matrix ``X`` can be of type
+       boolean.
+
+    9. ``Y = cdist(XA, XB, 'jaccard')``
+
+       Computes the Jaccard distance between the points. Given two
+       vectors, ``u`` and ``v``, the Jaccard distance is the
+       proportion of those elements ``u[i]`` and ``v[i]`` that
+       disagree where at least one of them is non-zero.
+
+    10. ``Y = cdist(XA, XB, 'jensenshannon')``
+
+        Computes the Jensen-Shannon distance between two probability arrays.
+        Given two probability vectors, :math:`p` and :math:`q`, the
+        Jensen-Shannon distance is
+
+        .. math::
+
+           \\sqrt{\\frac{D(p \\parallel m) + D(q \\parallel m)}{2}}
+
+        where :math:`m` is the pointwise mean of :math:`p` and :math:`q`
+        and :math:`D` is the Kullback-Leibler divergence.
+
+    11. ``Y = cdist(XA, XB, 'chebyshev')``
+
+        Computes the Chebyshev distance between the points. The
+        Chebyshev distance between two n-vectors ``u`` and ``v`` is the
+        maximum norm-1 distance between their respective elements. More
+        precisely, the distance is given by
+
+        .. math::
+
+           d(u,v) = \\max_i {|u_i-v_i|}.
+
+    12. ``Y = cdist(XA, XB, 'canberra')``
+
+        Computes the Canberra distance between the points. The
+        Canberra distance between two points ``u`` and ``v`` is
+
+        .. math::
+
+          d(u,v) = \\sum_i \\frac{|u_i-v_i|}
+                               {|u_i|+|v_i|}.
+
+    13. ``Y = cdist(XA, XB, 'braycurtis')``
+
+        Computes the Bray-Curtis distance between the points. The
+        Bray-Curtis distance between two points ``u`` and ``v`` is
+
+
+        .. math::
+
+             d(u,v) = \\frac{\\sum_i (|u_i-v_i|)}
+                           {\\sum_i (|u_i+v_i|)}
+
+    14. ``Y = cdist(XA, XB, 'mahalanobis', VI=None)``
+
+        Computes the Mahalanobis distance between the points. The
+        Mahalanobis distance between two points ``u`` and ``v`` is
+        :math:`\\sqrt{(u-v)(1/V)(u-v)^T}` where :math:`(1/V)` (the ``VI``
+        variable) is the inverse covariance. If ``VI`` is not None,
+        ``VI`` will be used as the inverse covariance matrix.
+
+    15. ``Y = cdist(XA, XB, 'yule')``
+
+        Computes the Yule distance between the boolean
+        vectors. (see `yule` function documentation)
+
+    16. ``Y = cdist(XA, XB, 'matching')``
+
+        Synonym for 'hamming'.
+
+    17. ``Y = cdist(XA, XB, 'dice')``
+
+        Computes the Dice distance between the boolean vectors. (see
+        `dice` function documentation).
+
+    18. ``Y = cdist(XA, XB, 'rogerstanimoto')``
+
+        Computes the Rogers-Tanimoto distance between the boolean
+        vectors. (see `rogerstanimoto` function documentation)
+
+    19. ``Y = cdist(XA, XB, 'russellrao')``
+
+        Computes the Russell-Rao distance between the boolean
+        vectors. (see `russellrao` function documentation)
+
+    20. ``Y = cdist(XA, XB, 'sokalsneath')``
+
+        Computes the Sokal-Sneath distance between the vectors. (see
+        `sokalsneath` function documentation)
+
+    21. ``Y = cdist(XA, XB, f)``
+
+        Computes the distance between all pairs of vectors in X
+        using the user supplied 2-arity function f. For example,
+        Euclidean distance between the vectors could be computed
+        as follows::
+
+          dm = cdist(XA, XB, lambda u, v: np.sqrt(((u-v)**2).sum()))
+
+        Note that you should avoid passing a reference to one of
+        the distance functions defined in this library. For example,::
+
+          dm = cdist(XA, XB, sokalsneath)
+
+        would calculate the pair-wise distances between the vectors in
+        X using the Python function `sokalsneath`. This would result in
+        sokalsneath being called :math:`{n \\choose 2}` times, which
+        is inefficient. Instead, the optimized C version is more
+        efficient, and we call it using the following syntax::
+
+          dm = cdist(XA, XB, 'sokalsneath')
+
+    Examples
+    --------
+    Find the Euclidean distances between four 2-D coordinates:
+
+    >>> from scipy.spatial import distance
+    >>> import numpy as np
+    >>> coords = [(35.0456, -85.2672),
+    ...           (35.1174, -89.9711),
+    ...           (35.9728, -83.9422),
+    ...           (36.1667, -86.7833)]
+    >>> distance.cdist(coords, coords, 'euclidean')
+    array([[ 0.    ,  4.7044,  1.6172,  1.8856],
+           [ 4.7044,  0.    ,  6.0893,  3.3561],
+           [ 1.6172,  6.0893,  0.    ,  2.8477],
+           [ 1.8856,  3.3561,  2.8477,  0.    ]])
+
+
+    Find the Manhattan distance from a 3-D point to the corners of the unit
+    cube:
+
+    >>> a = np.array([[0, 0, 0],
+    ...               [0, 0, 1],
+    ...               [0, 1, 0],
+    ...               [0, 1, 1],
+    ...               [1, 0, 0],
+    ...               [1, 0, 1],
+    ...               [1, 1, 0],
+    ...               [1, 1, 1]])
+    >>> b = np.array([[ 0.1,  0.2,  0.4]])
+    >>> distance.cdist(a, b, 'cityblock')
+    array([[ 0.7],
+           [ 0.9],
+           [ 1.3],
+           [ 1.5],
+           [ 1.5],
+           [ 1.7],
+           [ 2.1],
+           [ 2.3]])
+
+    """
+    # You can also call this as:
+    #     Y = cdist(XA, XB, 'test_abc')
+    # where 'abc' is the metric being tested.  This computes the distance
+    # between all pairs of vectors in XA and XB using the distance metric 'abc'
+    # but with a more succinct, verifiable, but less efficient implementation.
+
+    XA = np.asarray(XA)
+    XB = np.asarray(XB)
+
+    s = XA.shape
+    sB = XB.shape
+
+    if len(s) != 2:
+        raise ValueError('XA must be a 2-dimensional array.')
+    if len(sB) != 2:
+        raise ValueError('XB must be a 2-dimensional array.')
+    if s[1] != sB[1]:
+        raise ValueError('XA and XB must have the same number of columns '
+                         '(i.e. feature dimension.)')
+
+    mA = s[0]
+    mB = sB[0]
+    n = s[1]
+
+    if callable(metric):
+        mstr = getattr(metric, '__name__', 'Unknown')
+        metric_info = _METRIC_ALIAS.get(mstr, None)
+        if metric_info is not None:
+            XA, XB, typ, kwargs = _validate_cdist_input(
+                XA, XB, mA, mB, n, metric_info, **kwargs)
+        return _cdist_callable(XA, XB, metric=metric, out=out, **kwargs)
+    elif isinstance(metric, str):
+        mstr = metric.lower()
+        metric_info = _METRIC_ALIAS.get(mstr, None)
+        if metric_info is not None:
+            cdist_fn = metric_info.cdist_func
+            return cdist_fn(XA, XB, out=out, **kwargs)
+        elif mstr.startswith("test_"):
+            metric_info = _TEST_METRICS.get(mstr, None)
+            if metric_info is None:
+                raise ValueError(f'Unknown "Test" Distance Metric: {mstr[5:]}')
+            XA, XB, typ, kwargs = _validate_cdist_input(
+                XA, XB, mA, mB, n, metric_info, **kwargs)
+            return _cdist_callable(
+                XA, XB, metric=metric_info.dist_func, out=out, **kwargs)
+        else:
+            raise ValueError(f'Unknown Distance Metric: {mstr}')
+    else:
+        raise TypeError('2nd argument metric must be a string identifier '
+                        'or a function.')
diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/distance.pyi b/venv/lib/python3.12/site-packages/scipy/spatial/distance.pyi
new file mode 100644
index 0000000000000000000000000000000000000000..4846d37e3add466f738f56ab088e9091118e1ca1
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/distance.pyi
@@ -0,0 +1,200 @@
+from typing import (overload, Any, SupportsFloat, Literal, Protocol, SupportsIndex)
+
+import numpy as np
+from numpy.typing import ArrayLike, NDArray
+
+# Anything that can be parsed by `np.float64.__init__` and is thus
+# compatible with `ndarray.__setitem__` (for a float64 array)
+_FloatValue = None | str | bytes | SupportsFloat | SupportsIndex
+
+class _MetricCallback1(Protocol):
+    def __call__(
+        self, __XA: NDArray[Any], __XB: NDArray[Any]
+    ) -> _FloatValue: ...
+
+class _MetricCallback2(Protocol):
+    def __call__(
+        self, __XA: NDArray[Any], __XB: NDArray[Any], **kwargs: Any
+    ) -> _FloatValue: ...
+
+# TODO: Use a single protocol with a parameter specification variable
+# once available (PEP 612)
+_MetricCallback = _MetricCallback1 | _MetricCallback2
+
+_MetricKind = Literal[
+    'braycurtis',
+    'canberra',
+    'chebychev', 'chebyshev', 'cheby', 'cheb', 'ch',
+    'cityblock', 'cblock', 'cb', 'c',
+    'correlation', 'co',
+    'cosine', 'cos',
+    'dice',
+    'euclidean', 'euclid', 'eu', 'e',
+    'hamming', 'hamm', 'ha', 'h',
+    'minkowski', 'mi', 'm', 'pnorm',
+    'jaccard', 'jacc', 'ja', 'j',
+    'jensenshannon', 'js',
+    'mahalanobis', 'mahal', 'mah',
+    'rogerstanimoto',
+    'russellrao',
+    'seuclidean', 'se', 's',
+    'sokalsneath',
+    'sqeuclidean', 'sqe', 'sqeuclid',
+    'yule',
+]
+
+# Function annotations
+
+def braycurtis(
+    u: ArrayLike, v: ArrayLike, w: ArrayLike | None = ...
+) -> np.float64: ...
+
+def canberra(
+    u: ArrayLike, v: ArrayLike, w: ArrayLike | None = ...
+) -> np.float64: ...
+
+# TODO: Add `metric`-specific overloads
+# Returns a float64 or float128 array, depending on the input dtype
+@overload
+def cdist(
+    XA: ArrayLike,
+    XB: ArrayLike,
+    metric: _MetricKind = ...,
+    *,
+    out: None | NDArray[np.floating[Any]] = ...,
+    p: float = ...,
+    w: ArrayLike | None = ...,
+    V: ArrayLike | None = ...,
+    VI: ArrayLike | None = ...,
+) -> NDArray[np.floating[Any]]: ...
+@overload
+def cdist(
+    XA: ArrayLike,
+    XB: ArrayLike,
+    metric: _MetricCallback,
+    *,
+    out: None | NDArray[np.floating[Any]] = ...,
+    **kwargs: Any,
+) -> NDArray[np.floating[Any]]: ...
+
+# TODO: Wait for dtype support; the return type is
+# dependent on the input arrays dtype
+def chebyshev(
+    u: ArrayLike, v: ArrayLike, w: ArrayLike | None = ...
+) -> Any: ...
+
+# TODO: Wait for dtype support; the return type is
+# dependent on the input arrays dtype
+def cityblock(
+    u: ArrayLike, v: ArrayLike, w: ArrayLike | None = ...
+) -> Any: ...
+
+def correlation(
+    u: ArrayLike, v: ArrayLike, w: ArrayLike | None = ..., centered: bool = ...
+) -> np.float64: ...
+
+def cosine(
+    u: ArrayLike, v: ArrayLike, w: ArrayLike | None = ...
+) -> np.float64: ...
+
+def dice(
+    u: ArrayLike, v: ArrayLike, w: ArrayLike | None = ...
+) -> float: ...
+
+def directed_hausdorff(
+    u: ArrayLike, v: ArrayLike, seed: int | None = ...
+) -> tuple[float, int, int]: ...
+
+def euclidean(
+    u: ArrayLike, v: ArrayLike, w: ArrayLike | None = ...
+) -> float: ...
+
+def hamming(
+    u: ArrayLike, v: ArrayLike, w: ArrayLike | None = ...
+) -> np.float64: ...
+
+def is_valid_dm(
+    D: ArrayLike,
+    tol: float = ...,
+    throw: bool = ...,
+    name: str | None = ...,
+    warning: bool = ...,
+) -> bool: ...
+
+def is_valid_y(
+    y: ArrayLike,
+    warning: bool = ...,
+    throw: bool = ...,
+    name: str | None = ...,
+) -> bool: ...
+
+def jaccard(
+    u: ArrayLike, v: ArrayLike, w: ArrayLike | None = ...
+) -> np.float64: ...
+
+def jensenshannon(
+    p: ArrayLike, q: ArrayLike, base: float | None = ...
+) -> np.float64: ...
+
+def mahalanobis(
+    u: ArrayLike, v: ArrayLike, VI: ArrayLike
+) -> np.float64: ...
+
+def minkowski(
+    u: ArrayLike, v: ArrayLike, p: float = ..., w: ArrayLike | None = ...
+) -> float: ...
+
+def num_obs_dm(d: ArrayLike) -> int: ...
+
+def num_obs_y(Y: ArrayLike) -> int: ...
+
+# TODO: Add `metric`-specific overloads
+@overload
+def pdist(
+    X: ArrayLike,
+    metric: _MetricKind = ...,
+    *,
+    out: None | NDArray[np.floating[Any]] = ...,
+    p: float = ...,
+    w: ArrayLike | None = ...,
+    V: ArrayLike | None = ...,
+    VI: ArrayLike | None = ...,
+) -> NDArray[np.floating[Any]]: ...
+@overload
+def pdist(
+    X: ArrayLike,
+    metric: _MetricCallback,
+    *,
+    out: None | NDArray[np.floating[Any]] = ...,
+    **kwargs: Any,
+) -> NDArray[np.floating[Any]]: ...
+
+def seuclidean(
+    u: ArrayLike, v: ArrayLike, V: ArrayLike
+) -> float: ...
+
+def sokalsneath(
+    u: ArrayLike, v: ArrayLike, w: ArrayLike | None = ...
+) -> np.float64: ...
+
+def sqeuclidean(
+    u: ArrayLike, v: ArrayLike, w: ArrayLike | None = ...
+) -> np.float64: ...
+
+def squareform(
+    X: ArrayLike,
+    force: Literal["no", "tomatrix", "tovector"] = ...,
+    checks: bool = ...,
+) -> NDArray[Any]: ...
+
+def rogerstanimoto(
+    u: ArrayLike, v: ArrayLike, w: ArrayLike | None = ...
+) -> float: ...
+
+def russellrao(
+    u: ArrayLike, v: ArrayLike, w: ArrayLike | None = ...
+) -> float: ...
+
+def yule(
+    u: ArrayLike, v: ArrayLike, w: ArrayLike | None = ...
+) -> float: ...
diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/kdtree.py b/venv/lib/python3.12/site-packages/scipy/spatial/kdtree.py
new file mode 100644
index 0000000000000000000000000000000000000000..512205ddc15dc7d427f8df908ee346895295b674
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/kdtree.py
@@ -0,0 +1,25 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.spatial` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+
+__all__ = [  # noqa: F822
+    'KDTree',
+    'Rectangle',
+    'cKDTree',
+    'distance_matrix',
+    'minkowski_distance',
+    'minkowski_distance_p',
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="spatial", module="kdtree",
+                                   private_modules=["_kdtree"], all=__all__,
+                                   attribute=name)
diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/qhull.py b/venv/lib/python3.12/site-packages/scipy/spatial/qhull.py
new file mode 100644
index 0000000000000000000000000000000000000000..a8d51bf239bfe48077e66a36bcbf59f6dbadaf95
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/qhull.py
@@ -0,0 +1,25 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.spatial` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+
+__all__ = [  # noqa: F822
+    'ConvexHull',
+    'Delaunay',
+    'HalfspaceIntersection',
+    'QhullError',
+    'Voronoi',
+    'tsearch',
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="spatial", module="qhull",
+                                   private_modules=["_qhull"], all=__all__,
+                                   attribute=name)
diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/qhull_src/COPYING_QHULL.txt b/venv/lib/python3.12/site-packages/scipy/spatial/qhull_src/COPYING_QHULL.txt
new file mode 100644
index 0000000000000000000000000000000000000000..122a00a4fa9933794601dca8bff713b4ea1459dc
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/qhull_src/COPYING_QHULL.txt
@@ -0,0 +1,39 @@
+                    Qhull, Copyright (c) 1993-2020
+                    
+                            C.B. Barber
+                           Arlington, MA 
+                          
+                               and
+
+       The National Science and Technology Research Center for
+        Computation and Visualization of Geometric Structures
+                        (The Geometry Center)
+                       University of Minnesota
+
+                       email: qhull@qhull.org
+
+This software includes Qhull from C.B. Barber and The Geometry Center.  
+Files derived from Qhull 1.0 are copyrighted by the Geometry Center.  The
+remaining files are copyrighted by C.B. Barber.  Qhull is free software 
+and may be obtained via http from www.qhull.org.  It may be freely copied, 
+modified, and redistributed under the following conditions:
+
+1. All copyright notices must remain intact in all files.
+
+2. A copy of this text file must be distributed along with any copies 
+   of Qhull that you redistribute; this includes copies that you have 
+   modified, or copies of programs or other software products that 
+   include Qhull.
+
+3. If you modify Qhull, you must include a notice giving the
+   name of the person performing the modification, the date of
+   modification, and the reason for such modification.
+
+4. When distributing modified versions of Qhull, or other software 
+   products that include Qhull, you must provide notice that the original 
+   source code may be obtained as noted above.
+
+5. There is no warranty or other guarantee of fitness for Qhull, it is 
+   provided solely "as is".  Bug reports or fixes may be sent to 
+   qhull_bug@qhull.org; the authors may or may not act on them as 
+   they desire.
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diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/cdist-X1.txt b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/cdist-X1.txt
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diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-boolean-inp.txt b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-boolean-inp.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0636cc9f4590f2e960f7136d83a5d2cb07c56536
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-boolean-inp.txt
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diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-chebyshev-ml-iris.txt b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-chebyshev-ml-iris.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0aff1267ca7fd6f41d38c2273540bb771e9cbd0c
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-chebyshev-ml-iris.txt
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2.0000000e-01   1.1000000e+00   6.0000000e-01   4.0000000e-01   4.0000000e-01   4.0000000e-01   4.0000000e-01   4.0000000e-01   3.0000000e-01   1.0000000e-01   3.2000000e+00   3.0000000e+00   3.4000000e+00   2.5000000e+00   3.1000000e+00   3.0000000e+00   3.2000000e+00   1.8000000e+00   3.1000000e+00   2.4000000e+00   2.0000000e+00   2.7000000e+00   2.5000000e+00   3.2000000e+00   2.1000000e+00   2.9000000e+00   3.0000000e+00   2.6000000e+00   3.0000000e+00   2.4000000e+00   3.3000000e+00   2.5000000e+00   3.4000000e+00   3.2000000e+00   2.8000000e+00   2.9000000e+00   3.3000000e+00   3.5000000e+00   3.0000000e+00   2.0000000e+00   2.3000000e+00   2.2000000e+00   2.4000000e+00   3.6000000e+00   3.0000000e+00   3.0000000e+00   3.2000000e+00   2.9000000e+00   2.6000000e+00   2.5000000e+00   2.9000000e+00   3.1000000e+00   2.5000000e+00   1.8000000e+00   2.7000000e+00   2.7000000e+00   2.7000000e+00   2.8000000e+00   1.5000000e+00   2.6000000e+00   4.5000000e+00   3.6000000e+00   4.4000000e+00   4.1000000e+00   4.3000000e+00   5.1000000e+00   3.0000000e+00   4.8000000e+00   4.3000000e+00   4.6000000e+00   3.6000000e+00   3.8000000e+00   4.0000000e+00   3.5000000e+00   3.6000000e+00   3.8000000e+00   4.0000000e+00   5.2000000e+00   5.4000000e+00   3.5000000e+00   4.2000000e+00   3.4000000e+00   5.2000000e+00   3.4000000e+00   4.2000000e+00   4.5000000e+00   3.3000000e+00   3.4000000e+00   4.1000000e+00   4.3000000e+00   4.6000000e+00   4.9000000e+00   4.1000000e+00   3.6000000e+00   4.1000000e+00   4.6000000e+00   4.1000000e+00   4.0000000e+00   3.3000000e+00   3.9000000e+00   4.1000000e+00   3.6000000e+00   3.6000000e+00   4.4000000e+00   4.2000000e+00   3.7000000e+00   3.5000000e+00   3.7000000e+00   3.9000000e+00   3.6000000e+00   5.0000000e-01   1.0000000e+00   5.0000000e-01   4.0000000e-01   3.0000000e-01   1.4000000e+00   1.5000000e+00   1.0000000e+00   7.0000000e-01   1.3000000e+00   9.0000000e-01   1.0000000e+00   8.0000000e-01   7.0000000e-01   7.0000000e-01   5.0000000e-01   6.0000000e-01   6.0000000e-01   8.0000000e-01   8.0000000e-01   3.0000000e-01   4.0000000e-01   1.0000000e+00   1.2000000e+00   1.3000000e+00   5.0000000e-01   6.0000000e-01   1.1000000e+00   5.0000000e-01   1.0000000e-01   7.0000000e-01   6.0000000e-01   6.0000000e-01   3.0000000e-01   6.0000000e-01   9.0000000e-01   4.0000000e-01   9.0000000e-01   3.0000000e-01   9.0000000e-01   6.0000000e-01   3.3000000e+00   3.1000000e+00   3.5000000e+00   2.6000000e+00   3.2000000e+00   3.1000000e+00   3.3000000e+00   1.9000000e+00   3.2000000e+00   2.5000000e+00   2.1000000e+00   2.8000000e+00   2.6000000e+00   3.3000000e+00   2.2000000e+00   3.0000000e+00   3.1000000e+00   2.7000000e+00   3.1000000e+00   2.5000000e+00   3.4000000e+00   2.6000000e+00   3.5000000e+00   3.3000000e+00   2.9000000e+00   3.0000000e+00   3.4000000e+00   3.6000000e+00   3.1000000e+00   2.1000000e+00   2.4000000e+00   2.3000000e+00   2.5000000e+00   3.7000000e+00   3.1000000e+00   3.1000000e+00   3.3000000e+00   3.0000000e+00   2.7000000e+00   2.6000000e+00   3.0000000e+00   3.2000000e+00   2.6000000e+00   1.9000000e+00   2.8000000e+00   2.8000000e+00   2.8000000e+00   2.9000000e+00   1.6000000e+00   2.7000000e+00   4.6000000e+00   3.7000000e+00   4.5000000e+00   4.2000000e+00   4.4000000e+00   5.2000000e+00   3.1000000e+00   4.9000000e+00   4.4000000e+00   4.7000000e+00   3.7000000e+00   3.9000000e+00   4.1000000e+00   3.6000000e+00   3.7000000e+00   3.9000000e+00   4.1000000e+00   5.3000000e+00   5.5000000e+00   3.6000000e+00   4.3000000e+00   3.5000000e+00   5.3000000e+00   3.5000000e+00   4.3000000e+00   4.6000000e+00   3.4000000e+00   3.5000000e+00   4.2000000e+00   4.4000000e+00   4.7000000e+00   5.0000000e+00   4.2000000e+00   3.7000000e+00   4.2000000e+00   4.7000000e+00   4.2000000e+00   4.1000000e+00   3.4000000e+00   4.0000000e+00   4.2000000e+00   3.7000000e+00   3.7000000e+00   4.5000000e+00   4.3000000e+00   3.8000000e+00   3.6000000e+00   3.8000000e+00   4.0000000e+00   3.7000000e+00   6.0000000e-01   3.0000000e-01   1.0000000e-01   6.0000000e-01   9.0000000e-01   1.3000000e+00   8.0000000e-01   4.0000000e-01   8.0000000e-01   7.0000000e-01   5.0000000e-01   6.0000000e-01   5.0000000e-01   4.0000000e-01   4.0000000e-01   1.0000000e-01   3.0000000e-01   4.0000000e-01   3.0000000e-01   2.0000000e-01   1.0000000e-01   5.0000000e-01   1.0000000e+00   1.1000000e+00   0.0000000e+00   3.0000000e-01   6.0000000e-01   0.0000000e+00   5.0000000e-01   3.0000000e-01   4.0000000e-01   8.0000000e-01   5.0000000e-01   5.0000000e-01   7.0000000e-01   2.0000000e-01   7.0000000e-01   3.0000000e-01   6.0000000e-01   2.0000000e-01   3.2000000e+00   3.0000000e+00   3.4000000e+00   2.5000000e+00   3.1000000e+00   3.0000000e+00   3.2000000e+00   1.8000000e+00   3.1000000e+00   2.4000000e+00   2.0000000e+00   2.7000000e+00   2.5000000e+00   3.2000000e+00   2.1000000e+00   2.9000000e+00   3.0000000e+00   2.6000000e+00   3.0000000e+00   2.4000000e+00   3.3000000e+00   2.5000000e+00   3.4000000e+00   3.2000000e+00   2.8000000e+00   2.9000000e+00   3.3000000e+00   3.5000000e+00   3.0000000e+00   2.0000000e+00   2.3000000e+00   2.2000000e+00   2.4000000e+00   3.6000000e+00   3.0000000e+00   3.0000000e+00   3.2000000e+00   2.9000000e+00   2.6000000e+00   2.5000000e+00   2.9000000e+00   3.1000000e+00   2.5000000e+00   1.8000000e+00   2.7000000e+00   2.7000000e+00   2.7000000e+00   2.8000000e+00   1.5000000e+00   2.6000000e+00   4.5000000e+00   3.6000000e+00   4.4000000e+00   4.1000000e+00   4.3000000e+00   5.1000000e+00   3.0000000e+00   4.8000000e+00   4.3000000e+00   4.6000000e+00   3.6000000e+00   3.8000000e+00   4.0000000e+00   3.5000000e+00   3.6000000e+00   3.8000000e+00   4.0000000e+00   5.2000000e+00   5.4000000e+00   3.5000000e+00   4.2000000e+00   3.4000000e+00   5.2000000e+00   3.4000000e+00   4.2000000e+00   4.5000000e+00   3.3000000e+00   3.4000000e+00   4.1000000e+00   4.3000000e+00   4.6000000e+00   4.9000000e+00   4.1000000e+00   3.6000000e+00   4.1000000e+00   4.6000000e+00   4.1000000e+00   4.0000000e+00   3.3000000e+00   3.9000000e+00   4.1000000e+00   3.6000000e+00   3.6000000e+00   4.4000000e+00   4.2000000e+00   3.7000000e+00   3.5000000e+00   3.7000000e+00   3.9000000e+00   3.6000000e+00   6.0000000e-01   7.0000000e-01   1.1000000e+00   4.0000000e-01   7.0000000e-01   2.0000000e-01   3.0000000e-01   3.0000000e-01   3.0000000e-01   3.0000000e-01   3.0000000e-01   8.0000000e-01   4.0000000e-01   6.0000000e-01   7.0000000e-01   4.0000000e-01   2.0000000e-01   3.0000000e-01   7.0000000e-01   6.0000000e-01   3.0000000e-01   4.0000000e-01   5.0000000e-01   6.0000000e-01   5.0000000e-01   2.0000000e-01   6.0000000e-01   1.0000000e+00   3.0000000e-01   4.0000000e-01   1.4000000e+00   1.0000000e+00   4.0000000e-01   4.0000000e-01   7.0000000e-01   3.0000000e-01   8.0000000e-01   1.0000000e-01   4.0000000e-01   3.2000000e+00   3.0000000e+00   3.4000000e+00   2.5000000e+00   3.1000000e+00   3.0000000e+00   3.2000000e+00   1.8000000e+00   3.1000000e+00   2.4000000e+00   2.0000000e+00   2.7000000e+00   2.5000000e+00   3.2000000e+00   2.1000000e+00   2.9000000e+00   3.0000000e+00   2.6000000e+00   3.0000000e+00   2.4000000e+00   3.3000000e+00   2.5000000e+00   3.4000000e+00   3.2000000e+00   2.8000000e+00   2.9000000e+00   3.3000000e+00   3.5000000e+00   3.0000000e+00   2.0000000e+00   2.3000000e+00   2.2000000e+00   2.4000000e+00   3.6000000e+00   3.0000000e+00   3.0000000e+00   3.2000000e+00   2.9000000e+00   2.6000000e+00   2.5000000e+00   2.9000000e+00   3.1000000e+00   2.5000000e+00   1.8000000e+00   2.7000000e+00   2.7000000e+00   2.7000000e+00   2.8000000e+00   1.5000000e+00   2.6000000e+00   4.5000000e+00   3.6000000e+00   4.4000000e+00   4.1000000e+00   4.3000000e+00   5.1000000e+00   3.0000000e+00   4.8000000e+00   4.3000000e+00   4.6000000e+00   3.6000000e+00   3.8000000e+00   4.0000000e+00   3.5000000e+00   3.6000000e+00   3.8000000e+00   4.0000000e+00   5.2000000e+00   5.4000000e+00   3.5000000e+00   4.2000000e+00   3.4000000e+00   5.2000000e+00   3.4000000e+00   4.2000000e+00   4.5000000e+00   3.3000000e+00   3.4000000e+00   4.1000000e+00   4.3000000e+00   4.6000000e+00   4.9000000e+00   4.1000000e+00   3.6000000e+00   4.1000000e+00   4.6000000e+00   4.1000000e+00   4.0000000e+00   3.3000000e+00   3.9000000e+00   4.1000000e+00   3.6000000e+00   3.6000000e+00   4.4000000e+00   4.2000000e+00   3.7000000e+00   3.5000000e+00   3.7000000e+00   3.9000000e+00   3.6000000e+00   4.0000000e-01   5.0000000e-01   1.0000000e+00   1.0000000e+00   6.0000000e-01   3.0000000e-01   9.0000000e-01   4.0000000e-01   6.0000000e-01   3.0000000e-01   6.0000000e-01   3.0000000e-01   3.0000000e-01   4.0000000e-01   2.0000000e-01   4.0000000e-01   4.0000000e-01   2.0000000e-01   3.0000000e-01   6.0000000e-01   7.0000000e-01   8.0000000e-01   3.0000000e-01   4.0000000e-01   7.0000000e-01   3.0000000e-01   4.0000000e-01   3.0000000e-01   3.0000000e-01   1.1000000e+00   4.0000000e-01   4.0000000e-01   4.0000000e-01   4.0000000e-01   4.0000000e-01   2.0000000e-01   5.0000000e-01   2.0000000e-01   3.1000000e+00   2.9000000e+00   3.3000000e+00   2.4000000e+00   3.0000000e+00   2.9000000e+00   3.1000000e+00   1.7000000e+00   3.0000000e+00   2.3000000e+00   1.9000000e+00   2.6000000e+00   2.4000000e+00   3.1000000e+00   2.0000000e+00   2.8000000e+00   2.9000000e+00   2.5000000e+00   2.9000000e+00   2.3000000e+00   3.2000000e+00   2.4000000e+00   3.3000000e+00   3.1000000e+00   2.7000000e+00   2.8000000e+00   3.2000000e+00   3.4000000e+00   2.9000000e+00   1.9000000e+00   2.2000000e+00   2.1000000e+00   2.3000000e+00   3.5000000e+00   2.9000000e+00   2.9000000e+00   3.1000000e+00   2.8000000e+00   2.5000000e+00   2.4000000e+00   2.8000000e+00   3.0000000e+00   2.4000000e+00   1.7000000e+00   2.6000000e+00   2.6000000e+00   2.6000000e+00   2.7000000e+00   1.4000000e+00   2.5000000e+00   4.4000000e+00   3.5000000e+00   4.3000000e+00   4.0000000e+00   4.2000000e+00   5.0000000e+00   2.9000000e+00   4.7000000e+00   4.2000000e+00   4.5000000e+00   3.5000000e+00   3.7000000e+00   3.9000000e+00   3.4000000e+00   3.5000000e+00   3.7000000e+00   3.9000000e+00   5.1000000e+00   5.3000000e+00   3.4000000e+00   4.1000000e+00   3.3000000e+00   5.1000000e+00   3.3000000e+00   4.1000000e+00   4.4000000e+00   3.2000000e+00   3.3000000e+00   4.0000000e+00   4.2000000e+00   4.5000000e+00   4.8000000e+00   4.0000000e+00   3.5000000e+00   4.0000000e+00   4.5000000e+00   4.0000000e+00   3.9000000e+00   3.2000000e+00   3.8000000e+00   4.0000000e+00   3.5000000e+00   3.5000000e+00   4.3000000e+00   4.1000000e+00   3.6000000e+00   3.4000000e+00   3.6000000e+00   3.8000000e+00   3.5000000e+00   5.0000000e-01   1.0000000e+00   1.4000000e+00   9.0000000e-01   5.0000000e-01   9.0000000e-01   8.0000000e-01   6.0000000e-01   7.0000000e-01   6.0000000e-01   4.0000000e-01   5.0000000e-01   2.0000000e-01   4.0000000e-01   5.0000000e-01   4.0000000e-01   2.0000000e-01   2.0000000e-01   6.0000000e-01   1.1000000e+00   1.2000000e+00   1.0000000e-01   2.0000000e-01   7.0000000e-01   1.0000000e-01   4.0000000e-01   4.0000000e-01   5.0000000e-01   7.0000000e-01   4.0000000e-01   5.0000000e-01   8.0000000e-01   2.0000000e-01   8.0000000e-01   2.0000000e-01   7.0000000e-01   3.0000000e-01   3.3000000e+00   3.1000000e+00   3.5000000e+00   2.6000000e+00   3.2000000e+00   3.1000000e+00   3.3000000e+00   1.9000000e+00   3.2000000e+00   2.5000000e+00   2.1000000e+00   2.8000000e+00   2.6000000e+00   3.3000000e+00   2.2000000e+00   3.0000000e+00   3.1000000e+00   2.7000000e+00   3.1000000e+00   2.5000000e+00   3.4000000e+00   2.6000000e+00   3.5000000e+00   3.3000000e+00   2.9000000e+00   3.0000000e+00   3.4000000e+00   3.6000000e+00   3.1000000e+00   2.1000000e+00   2.4000000e+00   2.3000000e+00   2.5000000e+00   3.7000000e+00   3.1000000e+00   3.1000000e+00   3.3000000e+00   3.0000000e+00   2.7000000e+00   2.6000000e+00   3.0000000e+00   3.2000000e+00   2.6000000e+00   1.9000000e+00   2.8000000e+00   2.8000000e+00   2.8000000e+00   2.9000000e+00   1.6000000e+00   2.7000000e+00   4.6000000e+00   3.7000000e+00   4.5000000e+00   4.2000000e+00   4.4000000e+00   5.2000000e+00   3.1000000e+00   4.9000000e+00   4.4000000e+00   4.7000000e+00   3.7000000e+00   3.9000000e+00   4.1000000e+00   3.6000000e+00   3.7000000e+00   3.9000000e+00   4.1000000e+00   5.3000000e+00   5.5000000e+00   3.6000000e+00   4.3000000e+00   3.5000000e+00   5.3000000e+00   3.5000000e+00   4.3000000e+00   4.6000000e+00   3.4000000e+00   3.5000000e+00   4.2000000e+00   4.4000000e+00   4.7000000e+00   5.0000000e+00   4.2000000e+00   3.7000000e+00   4.2000000e+00   4.7000000e+00   4.2000000e+00   4.1000000e+00   3.4000000e+00   4.0000000e+00   4.2000000e+00   3.7000000e+00   3.7000000e+00   4.5000000e+00   4.3000000e+00   3.8000000e+00   3.6000000e+00   3.8000000e+00   4.0000000e+00   3.7000000e+00   1.5000000e+00   1.4000000e+00   1.1000000e+00   8.0000000e-01   1.4000000e+00   8.0000000e-01   1.1000000e+00   8.0000000e-01   6.0000000e-01   8.0000000e-01   8.0000000e-01   7.0000000e-01   7.0000000e-01   9.0000000e-01   9.0000000e-01   5.0000000e-01   5.0000000e-01   1.1000000e+00   1.1000000e+00   1.2000000e+00   6.0000000e-01   7.0000000e-01   1.2000000e+00   6.0000000e-01   2.0000000e-01   8.0000000e-01   7.0000000e-01   7.0000000e-01   2.0000000e-01   7.0000000e-01   8.0000000e-01   5.0000000e-01   8.0000000e-01   3.0000000e-01   1.0000000e+00   7.0000000e-01   3.6000000e+00   3.4000000e+00   3.8000000e+00   2.9000000e+00   3.5000000e+00   3.4000000e+00   3.6000000e+00   2.2000000e+00   3.5000000e+00   2.8000000e+00   2.4000000e+00   3.1000000e+00   2.9000000e+00   3.6000000e+00   2.5000000e+00   3.3000000e+00   3.4000000e+00   3.0000000e+00   3.4000000e+00   2.8000000e+00   3.7000000e+00   2.9000000e+00   3.8000000e+00   3.6000000e+00   3.2000000e+00   3.3000000e+00   3.7000000e+00   3.9000000e+00   3.4000000e+00   2.4000000e+00   2.7000000e+00   2.6000000e+00   2.8000000e+00   4.0000000e+00   3.4000000e+00   3.4000000e+00   3.6000000e+00   3.3000000e+00   3.0000000e+00   2.9000000e+00   3.3000000e+00   3.5000000e+00   2.9000000e+00   2.2000000e+00   3.1000000e+00   3.1000000e+00   3.1000000e+00   3.2000000e+00   1.9000000e+00   3.0000000e+00   4.9000000e+00   4.0000000e+00   4.8000000e+00   4.5000000e+00   4.7000000e+00   5.5000000e+00   3.4000000e+00   5.2000000e+00   4.7000000e+00   5.0000000e+00   4.0000000e+00   4.2000000e+00   4.4000000e+00   3.9000000e+00   4.0000000e+00   4.2000000e+00   4.4000000e+00   5.6000000e+00   5.8000000e+00   3.9000000e+00   4.6000000e+00   3.8000000e+00   5.6000000e+00   3.8000000e+00   4.6000000e+00   4.9000000e+00   3.7000000e+00   3.8000000e+00   4.5000000e+00   4.7000000e+00   5.0000000e+00   5.3000000e+00   4.5000000e+00   4.0000000e+00   4.5000000e+00   5.0000000e+00   4.5000000e+00   4.4000000e+00   3.7000000e+00   4.3000000e+00   4.5000000e+00   4.0000000e+00   4.0000000e+00   4.8000000e+00   4.6000000e+00   4.1000000e+00   3.9000000e+00   4.1000000e+00   4.3000000e+00   4.0000000e+00   4.0000000e-01   4.0000000e-01   7.0000000e-01   5.0000000e-01   7.0000000e-01   6.0000000e-01   7.0000000e-01   1.2000000e+00   7.0000000e-01   1.0000000e+00   1.0000000e+00   8.0000000e-01   6.0000000e-01   6.0000000e-01   1.1000000e+00   1.0000000e+00   6.0000000e-01   6.0000000e-01   3.0000000e-01   9.0000000e-01   8.0000000e-01   5.0000000e-01   9.0000000e-01   1.4000000e+00   7.0000000e-01   8.0000000e-01   1.7000000e+00   1.4000000e+00   8.0000000e-01   7.0000000e-01   1.0000000e+00   7.0000000e-01   1.2000000e+00   5.0000000e-01   8.0000000e-01   3.5000000e+00   3.3000000e+00   3.7000000e+00   2.8000000e+00   3.4000000e+00   3.3000000e+00   3.5000000e+00   2.1000000e+00   3.4000000e+00   2.7000000e+00   2.3000000e+00   3.0000000e+00   2.8000000e+00   3.5000000e+00   2.4000000e+00   3.2000000e+00   3.3000000e+00   2.9000000e+00   3.3000000e+00   2.7000000e+00   3.6000000e+00   2.8000000e+00   3.7000000e+00   3.5000000e+00   3.1000000e+00   3.2000000e+00   3.6000000e+00   3.8000000e+00   3.3000000e+00   2.3000000e+00   2.6000000e+00   2.5000000e+00   2.7000000e+00   3.9000000e+00   3.3000000e+00   3.3000000e+00   3.5000000e+00   3.2000000e+00   2.9000000e+00   2.8000000e+00   3.2000000e+00   3.4000000e+00   2.8000000e+00   2.1000000e+00   3.0000000e+00   3.0000000e+00   3.0000000e+00   3.1000000e+00   1.8000000e+00   2.9000000e+00   4.8000000e+00   3.9000000e+00   4.7000000e+00   4.4000000e+00   4.6000000e+00   5.4000000e+00   3.3000000e+00   5.1000000e+00   4.6000000e+00   4.9000000e+00   3.9000000e+00   4.1000000e+00   4.3000000e+00   3.8000000e+00   3.9000000e+00   4.1000000e+00   4.3000000e+00   5.5000000e+00   5.7000000e+00   3.8000000e+00   4.5000000e+00   3.7000000e+00   5.5000000e+00   3.7000000e+00   4.5000000e+00   4.8000000e+00   3.6000000e+00   3.7000000e+00   4.4000000e+00   4.6000000e+00   4.9000000e+00   5.2000000e+00   4.4000000e+00   3.9000000e+00   4.4000000e+00   4.9000000e+00   4.4000000e+00   4.3000000e+00   3.6000000e+00   4.2000000e+00   4.4000000e+00   3.9000000e+00   3.9000000e+00   4.7000000e+00   4.5000000e+00   4.0000000e+00   3.8000000e+00   4.0000000e+00   4.2000000e+00   3.9000000e+00   5.0000000e-01   9.0000000e-01   6.0000000e-01   6.0000000e-01   1.0000000e+00   7.0000000e-01   1.1000000e+00   1.1000000e+00   1.0000000e+00   1.4000000e+00   1.0000000e+00   9.0000000e-01   1.0000000e+00   1.2000000e+00   1.3000000e+00   1.0000000e+00   5.0000000e-01   2.0000000e-01   1.3000000e+00   1.2000000e+00   9.0000000e-01   1.3000000e+00   1.4000000e+00   1.0000000e+00   9.0000000e-01   2.1000000e+00   1.3000000e+00   9.0000000e-01   6.0000000e-01   1.4000000e+00   6.0000000e-01   1.2000000e+00   7.0000000e-01   1.1000000e+00   3.2000000e+00   3.0000000e+00   3.4000000e+00   2.5000000e+00   3.1000000e+00   3.0000000e+00   3.2000000e+00   2.0000000e+00   3.1000000e+00   2.4000000e+00   2.4000000e+00   2.7000000e+00   2.5000000e+00   3.2000000e+00   2.1000000e+00   2.9000000e+00   3.0000000e+00   2.6000000e+00   3.0000000e+00   2.4000000e+00   3.3000000e+00   2.5000000e+00   3.4000000e+00   3.2000000e+00   2.8000000e+00   2.9000000e+00   3.3000000e+00   3.5000000e+00   3.0000000e+00   2.0000000e+00   2.3000000e+00   2.2000000e+00   2.4000000e+00   3.6000000e+00   3.0000000e+00   3.0000000e+00   3.2000000e+00   2.9000000e+00   2.6000000e+00   2.5000000e+00   2.9000000e+00   3.1000000e+00   2.5000000e+00   2.1000000e+00   2.7000000e+00   2.7000000e+00   2.7000000e+00   2.8000000e+00   1.9000000e+00   2.6000000e+00   4.5000000e+00   3.6000000e+00   4.4000000e+00   4.1000000e+00   4.3000000e+00   5.1000000e+00   3.0000000e+00   4.8000000e+00   4.3000000e+00   4.6000000e+00   3.6000000e+00   3.8000000e+00   4.0000000e+00   3.5000000e+00   3.6000000e+00   3.8000000e+00   4.0000000e+00   5.2000000e+00   5.4000000e+00   3.5000000e+00   4.2000000e+00   3.4000000e+00   5.2000000e+00   3.4000000e+00   4.2000000e+00   4.5000000e+00   3.3000000e+00   3.4000000e+00   4.1000000e+00   4.3000000e+00   4.6000000e+00   4.9000000e+00   4.1000000e+00   3.6000000e+00   4.1000000e+00   4.6000000e+00   4.1000000e+00   4.0000000e+00   3.3000000e+00   3.9000000e+00   4.1000000e+00   3.6000000e+00   3.6000000e+00   4.4000000e+00   4.2000000e+00   3.7000000e+00   3.5000000e+00   3.7000000e+00   3.9000000e+00   3.6000000e+00   4.0000000e-01   4.0000000e-01   3.0000000e-01   5.0000000e-01   3.0000000e-01   8.0000000e-01   6.0000000e-01   6.0000000e-01   9.0000000e-01   5.0000000e-01   4.0000000e-01   5.0000000e-01   7.0000000e-01   8.0000000e-01   5.0000000e-01   3.0000000e-01   3.0000000e-01   8.0000000e-01   7.0000000e-01   4.0000000e-01   8.0000000e-01   1.0000000e+00   5.0000000e-01   4.0000000e-01   1.6000000e+00   1.0000000e+00   4.0000000e-01   6.0000000e-01   9.0000000e-01   3.0000000e-01   8.0000000e-01   2.0000000e-01   6.0000000e-01   3.4000000e+00   3.2000000e+00   3.6000000e+00   2.7000000e+00   3.3000000e+00   3.2000000e+00   3.4000000e+00   2.0000000e+00   3.3000000e+00   2.6000000e+00   2.2000000e+00   2.9000000e+00   2.7000000e+00   3.4000000e+00   2.3000000e+00   3.1000000e+00   3.2000000e+00   2.8000000e+00   3.2000000e+00   2.6000000e+00   3.5000000e+00   2.7000000e+00   3.6000000e+00   3.4000000e+00   3.0000000e+00   3.1000000e+00   3.5000000e+00   3.7000000e+00   3.2000000e+00   2.2000000e+00   2.5000000e+00   2.4000000e+00   2.6000000e+00   3.8000000e+00   3.2000000e+00   3.2000000e+00   3.4000000e+00   3.1000000e+00   2.8000000e+00   2.7000000e+00   3.1000000e+00   3.3000000e+00   2.7000000e+00   2.0000000e+00   2.9000000e+00   2.9000000e+00   2.9000000e+00   3.0000000e+00   1.7000000e+00   2.8000000e+00   4.7000000e+00   3.8000000e+00   4.6000000e+00   4.3000000e+00   4.5000000e+00   5.3000000e+00   3.2000000e+00   5.0000000e+00   4.5000000e+00   4.8000000e+00   3.8000000e+00   4.0000000e+00   4.2000000e+00   3.7000000e+00   3.8000000e+00   4.0000000e+00   4.2000000e+00   5.4000000e+00   5.6000000e+00   3.7000000e+00   4.4000000e+00   3.6000000e+00   5.4000000e+00   3.6000000e+00   4.4000000e+00   4.7000000e+00   3.5000000e+00   3.6000000e+00   4.3000000e+00   4.5000000e+00   4.8000000e+00   5.1000000e+00   4.3000000e+00   3.8000000e+00   4.3000000e+00   4.8000000e+00   4.3000000e+00   4.2000000e+00   3.5000000e+00   4.1000000e+00   4.3000000e+00   3.8000000e+00   3.8000000e+00   4.6000000e+00   4.4000000e+00   3.9000000e+00   3.7000000e+00   3.9000000e+00   4.1000000e+00   3.8000000e+00   6.0000000e-01   3.0000000e-01   3.0000000e-01   2.0000000e-01   5.0000000e-01   3.0000000e-01   5.0000000e-01   5.0000000e-01   2.0000000e-01   1.0000000e-01   1.0000000e-01   4.0000000e-01   4.0000000e-01   3.0000000e-01   6.0000000e-01   7.0000000e-01   4.0000000e-01   3.0000000e-01   4.0000000e-01   4.0000000e-01   7.0000000e-01   1.0000000e-01   1.0000000e-01   1.2000000e+00   7.0000000e-01   3.0000000e-01   5.0000000e-01   5.0000000e-01   3.0000000e-01   5.0000000e-01   2.0000000e-01   2.0000000e-01   3.3000000e+00   3.1000000e+00   3.5000000e+00   2.6000000e+00   3.2000000e+00   3.1000000e+00   3.3000000e+00   1.9000000e+00   3.2000000e+00   2.5000000e+00   2.1000000e+00   2.8000000e+00   2.6000000e+00   3.3000000e+00   2.2000000e+00   3.0000000e+00   3.1000000e+00   2.7000000e+00   3.1000000e+00   2.5000000e+00   3.4000000e+00   2.6000000e+00   3.5000000e+00   3.3000000e+00   2.9000000e+00   3.0000000e+00   3.4000000e+00   3.6000000e+00   3.1000000e+00   2.1000000e+00   2.4000000e+00   2.3000000e+00   2.5000000e+00   3.7000000e+00   3.1000000e+00   3.1000000e+00   3.3000000e+00   3.0000000e+00   2.7000000e+00   2.6000000e+00   3.0000000e+00   3.2000000e+00   2.6000000e+00   1.9000000e+00   2.8000000e+00   2.8000000e+00   2.8000000e+00   2.9000000e+00   1.6000000e+00   2.7000000e+00   4.6000000e+00   3.7000000e+00   4.5000000e+00   4.2000000e+00   4.4000000e+00   5.2000000e+00   3.1000000e+00   4.9000000e+00   4.4000000e+00   4.7000000e+00   3.7000000e+00   3.9000000e+00   4.1000000e+00   3.6000000e+00   3.7000000e+00   3.9000000e+00   4.1000000e+00   5.3000000e+00   5.5000000e+00   3.6000000e+00   4.3000000e+00   3.5000000e+00   5.3000000e+00   3.5000000e+00   4.3000000e+00   4.6000000e+00   3.4000000e+00   3.5000000e+00   4.2000000e+00   4.4000000e+00   4.7000000e+00   5.0000000e+00   4.2000000e+00   3.7000000e+00   4.2000000e+00   4.7000000e+00   4.2000000e+00   4.1000000e+00   3.4000000e+00   4.0000000e+00   4.2000000e+00   3.7000000e+00   3.7000000e+00   4.5000000e+00   4.3000000e+00   3.8000000e+00   3.6000000e+00   3.8000000e+00   4.0000000e+00   3.7000000e+00   6.0000000e-01   4.0000000e-01   6.0000000e-01   1.1000000e+00   6.0000000e-01   9.0000000e-01   8.0000000e-01   7.0000000e-01   5.0000000e-01   5.0000000e-01   1.0000000e+00   9.0000000e-01   4.0000000e-01   5.0000000e-01   4.0000000e-01   8.0000000e-01   7.0000000e-01   4.0000000e-01   8.0000000e-01   1.3000000e+00   6.0000000e-01   7.0000000e-01   1.5000000e+00   1.3000000e+00   7.0000000e-01   6.0000000e-01   9.0000000e-01   6.0000000e-01   1.1000000e+00   4.0000000e-01   7.0000000e-01   3.0000000e+00   2.8000000e+00   3.2000000e+00   2.3000000e+00   2.9000000e+00   2.8000000e+00   3.0000000e+00   1.6000000e+00   2.9000000e+00   2.2000000e+00   1.8000000e+00   2.5000000e+00   2.3000000e+00   3.0000000e+00   1.9000000e+00   2.7000000e+00   2.8000000e+00   2.4000000e+00   2.8000000e+00   2.2000000e+00   3.1000000e+00   2.3000000e+00   3.2000000e+00   3.0000000e+00   2.6000000e+00   2.7000000e+00   3.1000000e+00   3.3000000e+00   2.8000000e+00   1.8000000e+00   2.1000000e+00   2.0000000e+00   2.2000000e+00   3.4000000e+00   2.8000000e+00   2.8000000e+00   3.0000000e+00   2.7000000e+00   2.4000000e+00   2.3000000e+00   2.7000000e+00   2.9000000e+00   2.3000000e+00   1.6000000e+00   2.5000000e+00   2.5000000e+00   2.5000000e+00   2.6000000e+00   1.3000000e+00   2.4000000e+00   4.3000000e+00   3.4000000e+00   4.2000000e+00   3.9000000e+00   4.1000000e+00   4.9000000e+00   2.8000000e+00   4.6000000e+00   4.1000000e+00   4.4000000e+00   3.4000000e+00   3.6000000e+00   3.8000000e+00   3.3000000e+00   3.4000000e+00   3.6000000e+00   3.8000000e+00   5.0000000e+00   5.2000000e+00   3.3000000e+00   4.0000000e+00   3.2000000e+00   5.0000000e+00   3.2000000e+00   4.0000000e+00   4.3000000e+00   3.1000000e+00   3.2000000e+00   3.9000000e+00   4.1000000e+00   4.4000000e+00   4.7000000e+00   3.9000000e+00   3.4000000e+00   3.9000000e+00   4.4000000e+00   3.9000000e+00   3.8000000e+00   3.1000000e+00   3.7000000e+00   3.9000000e+00   3.4000000e+00   3.4000000e+00   4.2000000e+00   4.0000000e+00   3.5000000e+00   3.3000000e+00   3.5000000e+00   3.7000000e+00   3.4000000e+00   4.0000000e-01   1.0000000e-01   5.0000000e-01   5.0000000e-01   4.0000000e-01   8.0000000e-01   4.0000000e-01   3.0000000e-01   4.0000000e-01   6.0000000e-01   7.0000000e-01   4.0000000e-01   3.0000000e-01   4.0000000e-01   7.0000000e-01   6.0000000e-01   4.0000000e-01   7.0000000e-01   8.0000000e-01   4.0000000e-01   3.0000000e-01   1.5000000e+00   7.0000000e-01   3.0000000e-01   4.0000000e-01   8.0000000e-01   1.0000000e-01   6.0000000e-01   2.0000000e-01   5.0000000e-01   3.2000000e+00   3.0000000e+00   3.4000000e+00   2.5000000e+00   3.1000000e+00   3.0000000e+00   3.2000000e+00   1.8000000e+00   3.1000000e+00   2.4000000e+00   2.0000000e+00   2.7000000e+00   2.5000000e+00   3.2000000e+00   2.1000000e+00   2.9000000e+00   3.0000000e+00   2.6000000e+00   3.0000000e+00   2.4000000e+00   3.3000000e+00   2.5000000e+00   3.4000000e+00   3.2000000e+00   2.8000000e+00   2.9000000e+00   3.3000000e+00   3.5000000e+00   3.0000000e+00   2.0000000e+00   2.3000000e+00   2.2000000e+00   2.4000000e+00   3.6000000e+00   3.0000000e+00   3.0000000e+00   3.2000000e+00   2.9000000e+00   2.6000000e+00   2.5000000e+00   2.9000000e+00   3.1000000e+00   2.5000000e+00   1.8000000e+00   2.7000000e+00   2.7000000e+00   2.7000000e+00   2.8000000e+00   1.5000000e+00   2.6000000e+00   4.5000000e+00   3.6000000e+00   4.4000000e+00   4.1000000e+00   4.3000000e+00   5.1000000e+00   3.0000000e+00   4.8000000e+00   4.3000000e+00   4.6000000e+00   3.6000000e+00   3.8000000e+00   4.0000000e+00   3.5000000e+00   3.6000000e+00   3.8000000e+00   4.0000000e+00   5.2000000e+00   5.4000000e+00   3.5000000e+00   4.2000000e+00   3.4000000e+00   5.2000000e+00   3.4000000e+00   4.2000000e+00   4.5000000e+00   3.3000000e+00   3.4000000e+00   4.1000000e+00   4.3000000e+00   4.6000000e+00   4.9000000e+00   4.1000000e+00   3.6000000e+00   4.1000000e+00   4.6000000e+00   4.1000000e+00   4.0000000e+00   3.3000000e+00   3.9000000e+00   4.1000000e+00   3.6000000e+00   3.6000000e+00   4.4000000e+00   4.2000000e+00   3.7000000e+00   3.5000000e+00   3.7000000e+00   3.9000000e+00   3.6000000e+00   3.0000000e-01   8.0000000e-01   3.0000000e-01   6.0000000e-01   4.0000000e-01   4.0000000e-01   2.0000000e-01   3.0000000e-01   7.0000000e-01   6.0000000e-01   2.0000000e-01   7.0000000e-01   8.0000000e-01   5.0000000e-01   5.0000000e-01   4.0000000e-01   5.0000000e-01   1.0000000e+00   3.0000000e-01   4.0000000e-01   1.1000000e+00   1.0000000e+00   4.0000000e-01   4.0000000e-01   6.0000000e-01   4.0000000e-01   8.0000000e-01   3.0000000e-01   4.0000000e-01   3.0000000e+00   2.8000000e+00   3.2000000e+00   2.3000000e+00   2.9000000e+00   2.8000000e+00   3.0000000e+00   1.6000000e+00   2.9000000e+00   2.2000000e+00   1.8000000e+00   2.5000000e+00   2.3000000e+00   3.0000000e+00   1.9000000e+00   2.7000000e+00   2.8000000e+00   2.4000000e+00   2.8000000e+00   2.2000000e+00   3.1000000e+00   2.3000000e+00   3.2000000e+00   3.0000000e+00   2.6000000e+00   2.7000000e+00   3.1000000e+00   3.3000000e+00   2.8000000e+00   1.8000000e+00   2.1000000e+00   2.0000000e+00   2.2000000e+00   3.4000000e+00   2.8000000e+00   2.8000000e+00   3.0000000e+00   2.7000000e+00   2.4000000e+00   2.3000000e+00   2.7000000e+00   2.9000000e+00   2.3000000e+00   1.6000000e+00   2.5000000e+00   2.5000000e+00   2.5000000e+00   2.6000000e+00   1.3000000e+00   2.4000000e+00   4.3000000e+00   3.4000000e+00   4.2000000e+00   3.9000000e+00   4.1000000e+00   4.9000000e+00   2.8000000e+00   4.6000000e+00   4.1000000e+00   4.4000000e+00   3.4000000e+00   3.6000000e+00   3.8000000e+00   3.3000000e+00   3.4000000e+00   3.6000000e+00   3.8000000e+00   5.0000000e+00   5.2000000e+00   3.3000000e+00   4.0000000e+00   3.2000000e+00   5.0000000e+00   3.2000000e+00   4.0000000e+00   4.3000000e+00   3.1000000e+00   3.2000000e+00   3.9000000e+00   4.1000000e+00   4.4000000e+00   4.7000000e+00   3.9000000e+00   3.4000000e+00   3.9000000e+00   4.4000000e+00   3.9000000e+00   3.8000000e+00   3.1000000e+00   3.7000000e+00   3.9000000e+00   3.4000000e+00   3.4000000e+00   4.2000000e+00   4.0000000e+00   3.5000000e+00   3.3000000e+00   3.5000000e+00   3.7000000e+00   3.4000000e+00   5.0000000e-01   4.0000000e-01   4.0000000e-01   7.0000000e-01   3.0000000e-01   2.0000000e-01   3.0000000e-01   5.0000000e-01   6.0000000e-01   3.0000000e-01   4.0000000e-01   5.0000000e-01   6.0000000e-01   5.0000000e-01   4.0000000e-01   6.0000000e-01   7.0000000e-01   3.0000000e-01   2.0000000e-01   1.4000000e+00   7.0000000e-01   2.0000000e-01   4.0000000e-01   7.0000000e-01   2.0000000e-01   5.0000000e-01   2.0000000e-01   4.0000000e-01   3.2000000e+00   3.0000000e+00   3.4000000e+00   2.5000000e+00   3.1000000e+00   3.0000000e+00   3.2000000e+00   1.8000000e+00   3.1000000e+00   2.4000000e+00   2.0000000e+00   2.7000000e+00   2.5000000e+00   3.2000000e+00   2.1000000e+00   2.9000000e+00   3.0000000e+00   2.6000000e+00   3.0000000e+00   2.4000000e+00   3.3000000e+00   2.5000000e+00   3.4000000e+00   3.2000000e+00   2.8000000e+00   2.9000000e+00   3.3000000e+00   3.5000000e+00   3.0000000e+00   2.0000000e+00   2.3000000e+00   2.2000000e+00   2.4000000e+00   3.6000000e+00   3.0000000e+00   3.0000000e+00   3.2000000e+00   2.9000000e+00   2.6000000e+00   2.5000000e+00   2.9000000e+00   3.1000000e+00   2.5000000e+00   1.8000000e+00   2.7000000e+00   2.7000000e+00   2.7000000e+00   2.8000000e+00   1.5000000e+00   2.6000000e+00   4.5000000e+00   3.6000000e+00   4.4000000e+00   4.1000000e+00   4.3000000e+00   5.1000000e+00   3.0000000e+00   4.8000000e+00   4.3000000e+00   4.6000000e+00   3.6000000e+00   3.8000000e+00   4.0000000e+00   3.5000000e+00   3.6000000e+00   3.8000000e+00   4.0000000e+00   5.2000000e+00   5.4000000e+00   3.5000000e+00   4.2000000e+00   3.4000000e+00   5.2000000e+00   3.4000000e+00   4.2000000e+00   4.5000000e+00   3.3000000e+00   3.4000000e+00   4.1000000e+00   4.3000000e+00   4.6000000e+00   4.9000000e+00   4.1000000e+00   3.6000000e+00   4.1000000e+00   4.6000000e+00   4.1000000e+00   4.0000000e+00   3.3000000e+00   3.9000000e+00   4.1000000e+00   3.6000000e+00   3.6000000e+00   4.4000000e+00   4.2000000e+00   3.7000000e+00   3.5000000e+00   3.7000000e+00   3.9000000e+00   3.6000000e+00   7.0000000e-01   9.0000000e-01   6.0000000e-01   6.0000000e-01   6.0000000e-01   6.0000000e-01   6.0000000e-01   6.0000000e-01   8.0000000e-01   6.0000000e-01   9.0000000e-01   5.0000000e-01   4.0000000e-01   9.0000000e-01   5.0000000e-01   6.0000000e-01   5.0000000e-01   4.0000000e-01   1.3000000e+00   4.0000000e-01   6.0000000e-01   9.0000000e-01   6.0000000e-01   6.0000000e-01   4.0000000e-01   7.0000000e-01   4.0000000e-01   3.7000000e+00   3.5000000e+00   3.9000000e+00   3.0000000e+00   3.6000000e+00   3.5000000e+00   3.7000000e+00   2.3000000e+00   3.6000000e+00   2.9000000e+00   2.5000000e+00   3.2000000e+00   3.0000000e+00   3.7000000e+00   2.6000000e+00   3.4000000e+00   3.5000000e+00   3.1000000e+00   3.5000000e+00   2.9000000e+00   3.8000000e+00   3.0000000e+00   3.9000000e+00   3.7000000e+00   3.3000000e+00   3.4000000e+00   3.8000000e+00   4.0000000e+00   3.5000000e+00   2.5000000e+00   2.8000000e+00   2.7000000e+00   2.9000000e+00   4.1000000e+00   3.5000000e+00   3.5000000e+00   3.7000000e+00   3.4000000e+00   3.1000000e+00   3.0000000e+00   3.4000000e+00   3.6000000e+00   3.0000000e+00   2.3000000e+00   3.2000000e+00   3.2000000e+00   3.2000000e+00   3.3000000e+00   2.0000000e+00   3.1000000e+00   5.0000000e+00   4.1000000e+00   4.9000000e+00   4.6000000e+00   4.8000000e+00   5.6000000e+00   3.5000000e+00   5.3000000e+00   4.8000000e+00   5.1000000e+00   4.1000000e+00   4.3000000e+00   4.5000000e+00   4.0000000e+00   4.1000000e+00   4.3000000e+00   4.5000000e+00   5.7000000e+00   5.9000000e+00   4.0000000e+00   4.7000000e+00   3.9000000e+00   5.7000000e+00   3.9000000e+00   4.7000000e+00   5.0000000e+00   3.8000000e+00   3.9000000e+00   4.6000000e+00   4.8000000e+00   5.1000000e+00   5.4000000e+00   4.6000000e+00   4.1000000e+00   4.6000000e+00   5.1000000e+00   4.6000000e+00   4.5000000e+00   3.8000000e+00   4.4000000e+00   4.6000000e+00   4.1000000e+00   4.1000000e+00   4.9000000e+00   4.7000000e+00   4.2000000e+00   4.0000000e+00   4.2000000e+00   4.4000000e+00   4.1000000e+00   3.0000000e-01   3.0000000e-01   1.0000000e-01   3.0000000e-01   3.0000000e-01   4.0000000e-01   3.0000000e-01   3.0000000e-01   8.0000000e-01   9.0000000e-01   4.0000000e-01   5.0000000e-01   4.0000000e-01   4.0000000e-01   7.0000000e-01   3.0000000e-01   4.0000000e-01   1.0000000e+00   7.0000000e-01   2.0000000e-01   5.0000000e-01   3.0000000e-01   5.0000000e-01   5.0000000e-01   4.0000000e-01   3.0000000e-01   3.0000000e+00   2.8000000e+00   3.2000000e+00   2.3000000e+00   2.9000000e+00   2.8000000e+00   3.0000000e+00   1.6000000e+00   2.9000000e+00   2.2000000e+00   1.8000000e+00   2.5000000e+00   2.3000000e+00   3.0000000e+00   1.9000000e+00   2.7000000e+00   2.8000000e+00   2.4000000e+00   2.8000000e+00   2.2000000e+00   3.1000000e+00   2.3000000e+00   3.2000000e+00   3.0000000e+00   2.6000000e+00   2.7000000e+00   3.1000000e+00   3.3000000e+00   2.8000000e+00   1.8000000e+00   2.1000000e+00   2.0000000e+00   2.2000000e+00   3.4000000e+00   2.8000000e+00   2.8000000e+00   3.0000000e+00   2.7000000e+00   2.4000000e+00   2.3000000e+00   2.7000000e+00   2.9000000e+00   2.3000000e+00   1.6000000e+00   2.5000000e+00   2.5000000e+00   2.5000000e+00   2.6000000e+00   1.3000000e+00   2.4000000e+00   4.3000000e+00   3.4000000e+00   4.2000000e+00   3.9000000e+00   4.1000000e+00   4.9000000e+00   2.8000000e+00   4.6000000e+00   4.1000000e+00   4.4000000e+00   3.4000000e+00   3.6000000e+00   3.8000000e+00   3.3000000e+00   3.4000000e+00   3.6000000e+00   3.8000000e+00   5.0000000e+00   5.2000000e+00   3.3000000e+00   4.0000000e+00   3.2000000e+00   5.0000000e+00   3.2000000e+00   4.0000000e+00   4.3000000e+00   3.1000000e+00   3.2000000e+00   3.9000000e+00   4.1000000e+00   4.4000000e+00   4.7000000e+00   3.9000000e+00   3.4000000e+00   3.9000000e+00   4.4000000e+00   3.9000000e+00   3.8000000e+00   3.1000000e+00   3.7000000e+00   3.9000000e+00   3.4000000e+00   3.4000000e+00   4.2000000e+00   4.0000000e+00   3.5000000e+00   3.3000000e+00   3.5000000e+00   3.7000000e+00   3.4000000e+00   4.0000000e-01   3.0000000e-01   4.0000000e-01   5.0000000e-01   3.0000000e-01   3.0000000e-01   6.0000000e-01   7.0000000e-01   8.0000000e-01   4.0000000e-01   7.0000000e-01   7.0000000e-01   4.0000000e-01   6.0000000e-01   4.0000000e-01   6.0000000e-01   1.1000000e+00   6.0000000e-01   4.0000000e-01   4.0000000e-01   5.0000000e-01   4.0000000e-01   5.0000000e-01   5.0000000e-01   5.0000000e-01   2.8000000e+00   2.6000000e+00   3.0000000e+00   2.1000000e+00   2.7000000e+00   2.6000000e+00   2.8000000e+00   1.4000000e+00   2.7000000e+00   2.0000000e+00   1.6000000e+00   2.3000000e+00   2.1000000e+00   2.8000000e+00   1.7000000e+00   2.5000000e+00   2.6000000e+00   2.2000000e+00   2.6000000e+00   2.0000000e+00   2.9000000e+00   2.1000000e+00   3.0000000e+00   2.8000000e+00   2.4000000e+00   2.5000000e+00   2.9000000e+00   3.1000000e+00   2.6000000e+00   1.6000000e+00   1.9000000e+00   1.8000000e+00   2.0000000e+00   3.2000000e+00   2.6000000e+00   2.6000000e+00   2.8000000e+00   2.5000000e+00   2.2000000e+00   2.1000000e+00   2.5000000e+00   2.7000000e+00   2.1000000e+00   1.4000000e+00   2.3000000e+00   2.3000000e+00   2.3000000e+00   2.4000000e+00   1.1000000e+00   2.2000000e+00   4.1000000e+00   3.2000000e+00   4.0000000e+00   3.7000000e+00   3.9000000e+00   4.7000000e+00   2.6000000e+00   4.4000000e+00   3.9000000e+00   4.2000000e+00   3.2000000e+00   3.4000000e+00   3.6000000e+00   3.1000000e+00   3.2000000e+00   3.4000000e+00   3.6000000e+00   4.8000000e+00   5.0000000e+00   3.1000000e+00   3.8000000e+00   3.0000000e+00   4.8000000e+00   3.0000000e+00   3.8000000e+00   4.1000000e+00   2.9000000e+00   3.0000000e+00   3.7000000e+00   3.9000000e+00   4.2000000e+00   4.5000000e+00   3.7000000e+00   3.2000000e+00   3.7000000e+00   4.2000000e+00   3.7000000e+00   3.6000000e+00   2.9000000e+00   3.5000000e+00   3.7000000e+00   3.2000000e+00   3.2000000e+00   4.0000000e+00   3.8000000e+00   3.3000000e+00   3.1000000e+00   3.3000000e+00   3.5000000e+00   3.2000000e+00   4.0000000e-01   5.0000000e-01   4.0000000e-01   3.0000000e-01   2.0000000e-01   4.0000000e-01   1.1000000e+00   1.2000000e+00   1.0000000e-01   4.0000000e-01   5.0000000e-01   1.0000000e-01   6.0000000e-01   4.0000000e-01   5.0000000e-01   7.0000000e-01   6.0000000e-01   5.0000000e-01   8.0000000e-01   2.0000000e-01   8.0000000e-01   4.0000000e-01   7.0000000e-01   3.0000000e-01   3.1000000e+00   2.9000000e+00   3.3000000e+00   2.4000000e+00   3.0000000e+00   2.9000000e+00   3.1000000e+00   1.7000000e+00   3.0000000e+00   2.3000000e+00   1.9000000e+00   2.6000000e+00   2.4000000e+00   3.1000000e+00   2.0000000e+00   2.8000000e+00   2.9000000e+00   2.5000000e+00   2.9000000e+00   2.3000000e+00   3.2000000e+00   2.4000000e+00   3.3000000e+00   3.1000000e+00   2.7000000e+00   2.8000000e+00   3.2000000e+00   3.4000000e+00   2.9000000e+00   1.9000000e+00   2.2000000e+00   2.1000000e+00   2.3000000e+00   3.5000000e+00   2.9000000e+00   2.9000000e+00   3.1000000e+00   2.8000000e+00   2.5000000e+00   2.4000000e+00   2.8000000e+00   3.0000000e+00   2.4000000e+00   1.7000000e+00   2.6000000e+00   2.6000000e+00   2.6000000e+00   2.7000000e+00   1.4000000e+00   2.5000000e+00   4.4000000e+00   3.5000000e+00   4.3000000e+00   4.0000000e+00   4.2000000e+00   5.0000000e+00   2.9000000e+00   4.7000000e+00   4.2000000e+00   4.5000000e+00   3.5000000e+00   3.7000000e+00   3.9000000e+00   3.4000000e+00   3.5000000e+00   3.7000000e+00   3.9000000e+00   5.1000000e+00   5.3000000e+00   3.4000000e+00   4.1000000e+00   3.3000000e+00   5.1000000e+00   3.3000000e+00   4.1000000e+00   4.4000000e+00   3.2000000e+00   3.3000000e+00   4.0000000e+00   4.2000000e+00   4.5000000e+00   4.8000000e+00   4.0000000e+00   3.5000000e+00   4.0000000e+00   4.5000000e+00   4.0000000e+00   3.9000000e+00   3.2000000e+00   3.8000000e+00   4.0000000e+00   3.5000000e+00   3.5000000e+00   4.3000000e+00   4.1000000e+00   3.6000000e+00   3.4000000e+00   3.6000000e+00   3.8000000e+00   3.5000000e+00   2.0000000e-01   2.0000000e-01   3.0000000e-01   3.0000000e-01   4.0000000e-01   7.0000000e-01   8.0000000e-01   3.0000000e-01   4.0000000e-01   5.0000000e-01   3.0000000e-01   6.0000000e-01   2.0000000e-01   3.0000000e-01   1.1000000e+00   6.0000000e-01   2.0000000e-01   4.0000000e-01   4.0000000e-01   4.0000000e-01   4.0000000e-01   3.0000000e-01   2.0000000e-01   3.1000000e+00   2.9000000e+00   3.3000000e+00   2.4000000e+00   3.0000000e+00   2.9000000e+00   3.1000000e+00   1.7000000e+00   3.0000000e+00   2.3000000e+00   1.9000000e+00   2.6000000e+00   2.4000000e+00   3.1000000e+00   2.0000000e+00   2.8000000e+00   2.9000000e+00   2.5000000e+00   2.9000000e+00   2.3000000e+00   3.2000000e+00   2.4000000e+00   3.3000000e+00   3.1000000e+00   2.7000000e+00   2.8000000e+00   3.2000000e+00   3.4000000e+00   2.9000000e+00   1.9000000e+00   2.2000000e+00   2.1000000e+00   2.3000000e+00   3.5000000e+00   2.9000000e+00   2.9000000e+00   3.1000000e+00   2.8000000e+00   2.5000000e+00   2.4000000e+00   2.8000000e+00   3.0000000e+00   2.4000000e+00   1.7000000e+00   2.6000000e+00   2.6000000e+00   2.6000000e+00   2.7000000e+00   1.4000000e+00   2.5000000e+00   4.4000000e+00   3.5000000e+00   4.3000000e+00   4.0000000e+00   4.2000000e+00   5.0000000e+00   2.9000000e+00   4.7000000e+00   4.2000000e+00   4.5000000e+00   3.5000000e+00   3.7000000e+00   3.9000000e+00   3.4000000e+00   3.5000000e+00   3.7000000e+00   3.9000000e+00   5.1000000e+00   5.3000000e+00   3.4000000e+00   4.1000000e+00   3.3000000e+00   5.1000000e+00   3.3000000e+00   4.1000000e+00   4.4000000e+00   3.2000000e+00   3.3000000e+00   4.0000000e+00   4.2000000e+00   4.5000000e+00   4.8000000e+00   4.0000000e+00   3.5000000e+00   4.0000000e+00   4.5000000e+00   4.0000000e+00   3.9000000e+00   3.2000000e+00   3.8000000e+00   4.0000000e+00   3.5000000e+00   3.5000000e+00   4.3000000e+00   4.1000000e+00   3.6000000e+00   3.4000000e+00   3.6000000e+00   3.8000000e+00   3.5000000e+00   1.0000000e-01   5.0000000e-01   4.0000000e-01   2.0000000e-01   6.0000000e-01   7.0000000e-01   4.0000000e-01   3.0000000e-01   3.0000000e-01   4.0000000e-01   8.0000000e-01   1.0000000e-01   2.0000000e-01   1.2000000e+00   8.0000000e-01   4.0000000e-01   4.0000000e-01   5.0000000e-01   3.0000000e-01   6.0000000e-01   2.0000000e-01   2.0000000e-01   3.2000000e+00   3.0000000e+00   3.4000000e+00   2.5000000e+00   3.1000000e+00   3.0000000e+00   3.2000000e+00   1.8000000e+00   3.1000000e+00   2.4000000e+00   2.0000000e+00   2.7000000e+00   2.5000000e+00   3.2000000e+00   2.1000000e+00   2.9000000e+00   3.0000000e+00   2.6000000e+00   3.0000000e+00   2.4000000e+00   3.3000000e+00   2.5000000e+00   3.4000000e+00   3.2000000e+00   2.8000000e+00   2.9000000e+00   3.3000000e+00   3.5000000e+00   3.0000000e+00   2.0000000e+00   2.3000000e+00   2.2000000e+00   2.4000000e+00   3.6000000e+00   3.0000000e+00   3.0000000e+00   3.2000000e+00   2.9000000e+00   2.6000000e+00   2.5000000e+00   2.9000000e+00   3.1000000e+00   2.5000000e+00   1.8000000e+00   2.7000000e+00   2.7000000e+00   2.7000000e+00   2.8000000e+00   1.5000000e+00   2.6000000e+00   4.5000000e+00   3.6000000e+00   4.4000000e+00   4.1000000e+00   4.3000000e+00   5.1000000e+00   3.0000000e+00   4.8000000e+00   4.3000000e+00   4.6000000e+00   3.6000000e+00   3.8000000e+00   4.0000000e+00   3.5000000e+00   3.6000000e+00   3.8000000e+00   4.0000000e+00   5.2000000e+00   5.4000000e+00   3.5000000e+00   4.2000000e+00   3.4000000e+00   5.2000000e+00   3.4000000e+00   4.2000000e+00   4.5000000e+00   3.3000000e+00   3.4000000e+00   4.1000000e+00   4.3000000e+00   4.6000000e+00   4.9000000e+00   4.1000000e+00   3.6000000e+00   4.1000000e+00   4.6000000e+00   4.1000000e+00   4.0000000e+00   3.3000000e+00   3.9000000e+00   4.1000000e+00   3.6000000e+00   3.6000000e+00   4.4000000e+00   4.2000000e+00   3.7000000e+00   3.5000000e+00   3.7000000e+00   3.9000000e+00   3.6000000e+00   5.0000000e-01   4.0000000e-01   2.0000000e-01   7.0000000e-01   8.0000000e-01   3.0000000e-01   2.0000000e-01   3.0000000e-01   3.0000000e-01   8.0000000e-01   1.0000000e-01   2.0000000e-01   1.1000000e+00   8.0000000e-01   4.0000000e-01   5.0000000e-01   4.0000000e-01   4.0000000e-01   6.0000000e-01   3.0000000e-01   2.0000000e-01   3.3000000e+00   3.1000000e+00   3.5000000e+00   2.6000000e+00   3.2000000e+00   3.1000000e+00   3.3000000e+00   1.9000000e+00   3.2000000e+00   2.5000000e+00   2.1000000e+00   2.8000000e+00   2.6000000e+00   3.3000000e+00   2.2000000e+00   3.0000000e+00   3.1000000e+00   2.7000000e+00   3.1000000e+00   2.5000000e+00   3.4000000e+00   2.6000000e+00   3.5000000e+00   3.3000000e+00   2.9000000e+00   3.0000000e+00   3.4000000e+00   3.6000000e+00   3.1000000e+00   2.1000000e+00   2.4000000e+00   2.3000000e+00   2.5000000e+00   3.7000000e+00   3.1000000e+00   3.1000000e+00   3.3000000e+00   3.0000000e+00   2.7000000e+00   2.6000000e+00   3.0000000e+00   3.2000000e+00   2.6000000e+00   1.9000000e+00   2.8000000e+00   2.8000000e+00   2.8000000e+00   2.9000000e+00   1.6000000e+00   2.7000000e+00   4.6000000e+00   3.7000000e+00   4.5000000e+00   4.2000000e+00   4.4000000e+00   5.2000000e+00   3.1000000e+00   4.9000000e+00   4.4000000e+00   4.7000000e+00   3.7000000e+00   3.9000000e+00   4.1000000e+00   3.6000000e+00   3.7000000e+00   3.9000000e+00   4.1000000e+00   5.3000000e+00   5.5000000e+00   3.6000000e+00   4.3000000e+00   3.5000000e+00   5.3000000e+00   3.5000000e+00   4.3000000e+00   4.6000000e+00   3.4000000e+00   3.5000000e+00   4.2000000e+00   4.4000000e+00   4.7000000e+00   5.0000000e+00   4.2000000e+00   3.7000000e+00   4.2000000e+00   4.7000000e+00   4.2000000e+00   4.1000000e+00   3.4000000e+00   4.0000000e+00   4.2000000e+00   3.7000000e+00   3.7000000e+00   4.5000000e+00   4.3000000e+00   3.8000000e+00   3.6000000e+00   3.8000000e+00   4.0000000e+00   3.7000000e+00   1.0000000e-01   7.0000000e-01   9.0000000e-01   1.0000000e+00   2.0000000e-01   4.0000000e-01   8.0000000e-01   2.0000000e-01   3.0000000e-01   4.0000000e-01   3.0000000e-01   9.0000000e-01   3.0000000e-01   4.0000000e-01   6.0000000e-01   2.0000000e-01   6.0000000e-01   2.0000000e-01   6.0000000e-01   3.0000000e-01   3.1000000e+00   2.9000000e+00   3.3000000e+00   2.4000000e+00   3.0000000e+00   2.9000000e+00   3.1000000e+00   1.7000000e+00   3.0000000e+00   2.3000000e+00   1.9000000e+00   2.6000000e+00   2.4000000e+00   3.1000000e+00   2.0000000e+00   2.8000000e+00   2.9000000e+00   2.5000000e+00   2.9000000e+00   2.3000000e+00   3.2000000e+00   2.4000000e+00   3.3000000e+00   3.1000000e+00   2.7000000e+00   2.8000000e+00   3.2000000e+00   3.4000000e+00   2.9000000e+00   1.9000000e+00   2.2000000e+00   2.1000000e+00   2.3000000e+00   3.5000000e+00   2.9000000e+00   2.9000000e+00   3.1000000e+00   2.8000000e+00   2.5000000e+00   2.4000000e+00   2.8000000e+00   3.0000000e+00   2.4000000e+00   1.7000000e+00   2.6000000e+00   2.6000000e+00   2.6000000e+00   2.7000000e+00   1.4000000e+00   2.5000000e+00   4.4000000e+00   3.5000000e+00   4.3000000e+00   4.0000000e+00   4.2000000e+00   5.0000000e+00   2.9000000e+00   4.7000000e+00   4.2000000e+00   4.5000000e+00   3.5000000e+00   3.7000000e+00   3.9000000e+00   3.4000000e+00   3.5000000e+00   3.7000000e+00   3.9000000e+00   5.1000000e+00   5.3000000e+00   3.4000000e+00   4.1000000e+00   3.3000000e+00   5.1000000e+00   3.3000000e+00   4.1000000e+00   4.4000000e+00   3.2000000e+00   3.3000000e+00   4.0000000e+00   4.2000000e+00   4.5000000e+00   4.8000000e+00   4.0000000e+00   3.5000000e+00   4.0000000e+00   4.5000000e+00   4.0000000e+00   3.9000000e+00   3.2000000e+00   3.8000000e+00   4.0000000e+00   3.5000000e+00   3.5000000e+00   4.3000000e+00   4.1000000e+00   3.6000000e+00   3.4000000e+00   3.6000000e+00   3.8000000e+00   3.5000000e+00   6.0000000e-01   1.0000000e+00   1.1000000e+00   1.0000000e-01   4.0000000e-01   7.0000000e-01   1.0000000e-01   4.0000000e-01   3.0000000e-01   4.0000000e-01   8.0000000e-01   4.0000000e-01   4.0000000e-01   7.0000000e-01   2.0000000e-01   7.0000000e-01   2.0000000e-01   6.0000000e-01   2.0000000e-01   3.1000000e+00   2.9000000e+00   3.3000000e+00   2.4000000e+00   3.0000000e+00   2.9000000e+00   3.1000000e+00   1.7000000e+00   3.0000000e+00   2.3000000e+00   1.9000000e+00   2.6000000e+00   2.4000000e+00   3.1000000e+00   2.0000000e+00   2.8000000e+00   2.9000000e+00   2.5000000e+00   2.9000000e+00   2.3000000e+00   3.2000000e+00   2.4000000e+00   3.3000000e+00   3.1000000e+00   2.7000000e+00   2.8000000e+00   3.2000000e+00   3.4000000e+00   2.9000000e+00   1.9000000e+00   2.2000000e+00   2.1000000e+00   2.3000000e+00   3.5000000e+00   2.9000000e+00   2.9000000e+00   3.1000000e+00   2.8000000e+00   2.5000000e+00   2.4000000e+00   2.8000000e+00   3.0000000e+00   2.4000000e+00   1.7000000e+00   2.6000000e+00   2.6000000e+00   2.6000000e+00   2.7000000e+00   1.4000000e+00   2.5000000e+00   4.4000000e+00   3.5000000e+00   4.3000000e+00   4.0000000e+00   4.2000000e+00   5.0000000e+00   2.9000000e+00   4.7000000e+00   4.2000000e+00   4.5000000e+00   3.5000000e+00   3.7000000e+00   3.9000000e+00   3.4000000e+00   3.5000000e+00   3.7000000e+00   3.9000000e+00   5.1000000e+00   5.3000000e+00   3.4000000e+00   4.1000000e+00   3.3000000e+00   5.1000000e+00   3.3000000e+00   4.1000000e+00   4.4000000e+00   3.2000000e+00   3.3000000e+00   4.0000000e+00   4.2000000e+00   4.5000000e+00   4.8000000e+00   4.0000000e+00   3.5000000e+00   4.0000000e+00   4.5000000e+00   4.0000000e+00   3.9000000e+00   3.2000000e+00   3.8000000e+00   4.0000000e+00   3.5000000e+00   3.5000000e+00   4.3000000e+00   4.1000000e+00   3.6000000e+00   3.4000000e+00   3.6000000e+00   3.8000000e+00   3.5000000e+00   7.0000000e-01   8.0000000e-01   5.0000000e-01   4.0000000e-01   2.0000000e-01   5.0000000e-01   1.0000000e+00   3.0000000e-01   4.0000000e-01   1.1000000e+00   1.0000000e+00   4.0000000e-01   4.0000000e-01   6.0000000e-01   4.0000000e-01   8.0000000e-01   3.0000000e-01   4.0000000e-01   3.2000000e+00   3.0000000e+00   3.4000000e+00   2.5000000e+00   3.1000000e+00   3.0000000e+00   3.2000000e+00   1.8000000e+00   3.1000000e+00   2.4000000e+00   2.0000000e+00   2.7000000e+00   2.5000000e+00   3.2000000e+00   2.1000000e+00   2.9000000e+00   3.0000000e+00   2.6000000e+00   3.0000000e+00   2.4000000e+00   3.3000000e+00   2.5000000e+00   3.4000000e+00   3.2000000e+00   2.8000000e+00   2.9000000e+00   3.3000000e+00   3.5000000e+00   3.0000000e+00   2.0000000e+00   2.3000000e+00   2.2000000e+00   2.4000000e+00   3.6000000e+00   3.0000000e+00   3.0000000e+00   3.2000000e+00   2.9000000e+00   2.6000000e+00   2.5000000e+00   2.9000000e+00   3.1000000e+00   2.5000000e+00   1.8000000e+00   2.7000000e+00   2.7000000e+00   2.7000000e+00   2.8000000e+00   1.5000000e+00   2.6000000e+00   4.5000000e+00   3.6000000e+00   4.4000000e+00   4.1000000e+00   4.3000000e+00   5.1000000e+00   3.0000000e+00   4.8000000e+00   4.3000000e+00   4.6000000e+00   3.6000000e+00   3.8000000e+00   4.0000000e+00   3.5000000e+00   3.6000000e+00   3.8000000e+00   4.0000000e+00   5.2000000e+00   5.4000000e+00   3.5000000e+00   4.2000000e+00   3.4000000e+00   5.2000000e+00   3.4000000e+00   4.2000000e+00   4.5000000e+00   3.3000000e+00   3.4000000e+00   4.1000000e+00   4.3000000e+00   4.6000000e+00   4.9000000e+00   4.1000000e+00   3.6000000e+00   4.1000000e+00   4.6000000e+00   4.1000000e+00   4.0000000e+00   3.3000000e+00   3.9000000e+00   4.1000000e+00   3.6000000e+00   3.6000000e+00   4.4000000e+00   4.2000000e+00   3.7000000e+00   3.5000000e+00   3.7000000e+00   3.9000000e+00   3.6000000e+00   3.0000000e-01   1.0000000e+00   9.0000000e-01   6.0000000e-01   1.0000000e+00   1.1000000e+00   7.0000000e-01   6.0000000e-01   1.8000000e+00   9.0000000e-01   6.0000000e-01   4.0000000e-01   1.1000000e+00   3.0000000e-01   9.0000000e-01   4.0000000e-01   8.0000000e-01   3.2000000e+00   3.0000000e+00   3.4000000e+00   2.5000000e+00   3.1000000e+00   3.0000000e+00   3.2000000e+00   1.8000000e+00   3.1000000e+00   2.4000000e+00   2.1000000e+00   2.7000000e+00   2.5000000e+00   3.2000000e+00   2.1000000e+00   2.9000000e+00   3.0000000e+00   2.6000000e+00   3.0000000e+00   2.4000000e+00   3.3000000e+00   2.5000000e+00   3.4000000e+00   3.2000000e+00   2.8000000e+00   2.9000000e+00   3.3000000e+00   3.5000000e+00   3.0000000e+00   2.0000000e+00   2.3000000e+00   2.2000000e+00   2.4000000e+00   3.6000000e+00   3.0000000e+00   3.0000000e+00   3.2000000e+00   2.9000000e+00   2.6000000e+00   2.5000000e+00   2.9000000e+00   3.1000000e+00   2.5000000e+00   1.8000000e+00   2.7000000e+00   2.7000000e+00   2.7000000e+00   2.8000000e+00   1.6000000e+00   2.6000000e+00   4.5000000e+00   3.6000000e+00   4.4000000e+00   4.1000000e+00   4.3000000e+00   5.1000000e+00   3.0000000e+00   4.8000000e+00   4.3000000e+00   4.6000000e+00   3.6000000e+00   3.8000000e+00   4.0000000e+00   3.5000000e+00   3.6000000e+00   3.8000000e+00   4.0000000e+00   5.2000000e+00   5.4000000e+00   3.5000000e+00   4.2000000e+00   3.4000000e+00   5.2000000e+00   3.4000000e+00   4.2000000e+00   4.5000000e+00   3.3000000e+00   3.4000000e+00   4.1000000e+00   4.3000000e+00   4.6000000e+00   4.9000000e+00   4.1000000e+00   3.6000000e+00   4.1000000e+00   4.6000000e+00   4.1000000e+00   4.0000000e+00   3.3000000e+00   3.9000000e+00   4.1000000e+00   3.6000000e+00   3.6000000e+00   4.4000000e+00   4.2000000e+00   3.7000000e+00   3.5000000e+00   3.7000000e+00   3.9000000e+00   3.6000000e+00   1.1000000e+00   1.0000000e+00   7.0000000e-01   1.1000000e+00   1.2000000e+00   8.0000000e-01   7.0000000e-01   1.9000000e+00   1.1000000e+00   7.0000000e-01   5.0000000e-01   1.2000000e+00   4.0000000e-01   1.0000000e+00   5.0000000e-01   9.0000000e-01   3.3000000e+00   3.1000000e+00   3.5000000e+00   2.6000000e+00   3.2000000e+00   3.1000000e+00   3.3000000e+00   1.9000000e+00   3.2000000e+00   2.5000000e+00   2.2000000e+00   2.8000000e+00   2.6000000e+00   3.3000000e+00   2.2000000e+00   3.0000000e+00   3.1000000e+00   2.7000000e+00   3.1000000e+00   2.5000000e+00   3.4000000e+00   2.6000000e+00   3.5000000e+00   3.3000000e+00   2.9000000e+00   3.0000000e+00   3.4000000e+00   3.6000000e+00   3.1000000e+00   2.1000000e+00   2.4000000e+00   2.3000000e+00   2.5000000e+00   3.7000000e+00   3.1000000e+00   3.1000000e+00   3.3000000e+00   3.0000000e+00   2.7000000e+00   2.6000000e+00   3.0000000e+00   3.2000000e+00   2.6000000e+00   1.9000000e+00   2.8000000e+00   2.8000000e+00   2.8000000e+00   2.9000000e+00   1.7000000e+00   2.7000000e+00   4.6000000e+00   3.7000000e+00   4.5000000e+00   4.2000000e+00   4.4000000e+00   5.2000000e+00   3.1000000e+00   4.9000000e+00   4.4000000e+00   4.7000000e+00   3.7000000e+00   3.9000000e+00   4.1000000e+00   3.6000000e+00   3.7000000e+00   3.9000000e+00   4.1000000e+00   5.3000000e+00   5.5000000e+00   3.6000000e+00   4.3000000e+00   3.5000000e+00   5.3000000e+00   3.5000000e+00   4.3000000e+00   4.6000000e+00   3.4000000e+00   3.5000000e+00   4.2000000e+00   4.4000000e+00   4.7000000e+00   5.0000000e+00   4.2000000e+00   3.7000000e+00   4.2000000e+00   4.7000000e+00   4.2000000e+00   4.1000000e+00   3.4000000e+00   4.0000000e+00   4.2000000e+00   3.7000000e+00   3.7000000e+00   4.5000000e+00   4.3000000e+00   3.8000000e+00   3.6000000e+00   3.8000000e+00   4.0000000e+00   3.7000000e+00   3.0000000e-01   6.0000000e-01   0.0000000e+00   5.0000000e-01   3.0000000e-01   4.0000000e-01   8.0000000e-01   5.0000000e-01   5.0000000e-01   7.0000000e-01   2.0000000e-01   7.0000000e-01   3.0000000e-01   6.0000000e-01   2.0000000e-01   3.2000000e+00   3.0000000e+00   3.4000000e+00   2.5000000e+00   3.1000000e+00   3.0000000e+00   3.2000000e+00   1.8000000e+00   3.1000000e+00   2.4000000e+00   2.0000000e+00   2.7000000e+00   2.5000000e+00   3.2000000e+00   2.1000000e+00   2.9000000e+00   3.0000000e+00   2.6000000e+00   3.0000000e+00   2.4000000e+00   3.3000000e+00   2.5000000e+00   3.4000000e+00   3.2000000e+00   2.8000000e+00   2.9000000e+00   3.3000000e+00   3.5000000e+00   3.0000000e+00   2.0000000e+00   2.3000000e+00   2.2000000e+00   2.4000000e+00   3.6000000e+00   3.0000000e+00   3.0000000e+00   3.2000000e+00   2.9000000e+00   2.6000000e+00   2.5000000e+00   2.9000000e+00   3.1000000e+00   2.5000000e+00   1.8000000e+00   2.7000000e+00   2.7000000e+00   2.7000000e+00   2.8000000e+00   1.5000000e+00   2.6000000e+00   4.5000000e+00   3.6000000e+00   4.4000000e+00   4.1000000e+00   4.3000000e+00   5.1000000e+00   3.0000000e+00   4.8000000e+00   4.3000000e+00   4.6000000e+00   3.6000000e+00   3.8000000e+00   4.0000000e+00   3.5000000e+00   3.6000000e+00   3.8000000e+00   4.0000000e+00   5.2000000e+00   5.4000000e+00   3.5000000e+00   4.2000000e+00   3.4000000e+00   5.2000000e+00   3.4000000e+00   4.2000000e+00   4.5000000e+00   3.3000000e+00   3.4000000e+00   4.1000000e+00   4.3000000e+00   4.6000000e+00   4.9000000e+00   4.1000000e+00   3.6000000e+00   4.1000000e+00   4.6000000e+00   4.1000000e+00   4.0000000e+00   3.3000000e+00   3.9000000e+00   4.1000000e+00   3.6000000e+00   3.6000000e+00   4.4000000e+00   4.2000000e+00   3.7000000e+00   3.5000000e+00   3.7000000e+00   3.9000000e+00   3.6000000e+00   5.0000000e-01   3.0000000e-01   6.0000000e-01   3.0000000e-01   3.0000000e-01   9.0000000e-01   6.0000000e-01   4.0000000e-01   7.0000000e-01   2.0000000e-01   6.0000000e-01   4.0000000e-01   5.0000000e-01   2.0000000e-01   3.5000000e+00   3.3000000e+00   3.7000000e+00   2.8000000e+00   3.4000000e+00   3.3000000e+00   3.5000000e+00   2.1000000e+00   3.4000000e+00   2.7000000e+00   2.3000000e+00   3.0000000e+00   2.8000000e+00   3.5000000e+00   2.4000000e+00   3.2000000e+00   3.3000000e+00   2.9000000e+00   3.3000000e+00   2.7000000e+00   3.6000000e+00   2.8000000e+00   3.7000000e+00   3.5000000e+00   3.1000000e+00   3.2000000e+00   3.6000000e+00   3.8000000e+00   3.3000000e+00   2.3000000e+00   2.6000000e+00   2.5000000e+00   2.7000000e+00   3.9000000e+00   3.3000000e+00   3.3000000e+00   3.5000000e+00   3.2000000e+00   2.9000000e+00   2.8000000e+00   3.2000000e+00   3.4000000e+00   2.8000000e+00   2.1000000e+00   3.0000000e+00   3.0000000e+00   3.0000000e+00   3.1000000e+00   1.8000000e+00   2.9000000e+00   4.8000000e+00   3.9000000e+00   4.7000000e+00   4.4000000e+00   4.6000000e+00   5.4000000e+00   3.3000000e+00   5.1000000e+00   4.6000000e+00   4.9000000e+00   3.9000000e+00   4.1000000e+00   4.3000000e+00   3.8000000e+00   3.9000000e+00   4.1000000e+00   4.3000000e+00   5.5000000e+00   5.7000000e+00   3.8000000e+00   4.5000000e+00   3.7000000e+00   5.5000000e+00   3.7000000e+00   4.5000000e+00   4.8000000e+00   3.6000000e+00   3.7000000e+00   4.4000000e+00   4.6000000e+00   4.9000000e+00   5.2000000e+00   4.4000000e+00   3.9000000e+00   4.4000000e+00   4.9000000e+00   4.4000000e+00   4.3000000e+00   3.6000000e+00   4.2000000e+00   4.4000000e+00   3.9000000e+00   3.9000000e+00   4.7000000e+00   4.5000000e+00   4.0000000e+00   3.8000000e+00   4.0000000e+00   4.2000000e+00   3.9000000e+00   6.0000000e-01   1.1000000e+00   4.0000000e-01   5.0000000e-01   1.2000000e+00   1.1000000e+00   5.0000000e-01   6.0000000e-01   7.0000000e-01   4.0000000e-01   9.0000000e-01   2.0000000e-01   5.0000000e-01   3.4000000e+00   3.2000000e+00   3.6000000e+00   2.7000000e+00   3.3000000e+00   3.2000000e+00   3.4000000e+00   2.0000000e+00   3.3000000e+00   2.6000000e+00   2.2000000e+00   2.9000000e+00   2.7000000e+00   3.4000000e+00   2.3000000e+00   3.1000000e+00   3.2000000e+00   2.8000000e+00   3.2000000e+00   2.6000000e+00   3.5000000e+00   2.7000000e+00   3.6000000e+00   3.4000000e+00   3.0000000e+00   3.1000000e+00   3.5000000e+00   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4.1000000e+00   4.3000000e+00   3.8000000e+00   3.8000000e+00   4.6000000e+00   4.4000000e+00   3.9000000e+00   3.7000000e+00   3.9000000e+00   4.1000000e+00   3.8000000e+00   5.0000000e-01   3.0000000e-01   4.0000000e-01   8.0000000e-01   5.0000000e-01   5.0000000e-01   7.0000000e-01   2.0000000e-01   7.0000000e-01   3.0000000e-01   6.0000000e-01   2.0000000e-01   3.2000000e+00   3.0000000e+00   3.4000000e+00   2.5000000e+00   3.1000000e+00   3.0000000e+00   3.2000000e+00   1.8000000e+00   3.1000000e+00   2.4000000e+00   2.0000000e+00   2.7000000e+00   2.5000000e+00   3.2000000e+00   2.1000000e+00   2.9000000e+00   3.0000000e+00   2.6000000e+00   3.0000000e+00   2.4000000e+00   3.3000000e+00   2.5000000e+00   3.4000000e+00   3.2000000e+00   2.8000000e+00   2.9000000e+00   3.3000000e+00   3.5000000e+00   3.0000000e+00   2.0000000e+00   2.3000000e+00   2.2000000e+00   2.4000000e+00   3.6000000e+00   3.0000000e+00   3.0000000e+00   3.2000000e+00   2.9000000e+00   2.6000000e+00   2.5000000e+00   2.9000000e+00   3.1000000e+00   2.5000000e+00   1.8000000e+00   2.7000000e+00   2.7000000e+00   2.7000000e+00   2.8000000e+00   1.5000000e+00   2.6000000e+00   4.5000000e+00   3.6000000e+00   4.4000000e+00   4.1000000e+00   4.3000000e+00   5.1000000e+00   3.0000000e+00   4.8000000e+00   4.3000000e+00   4.6000000e+00   3.6000000e+00   3.8000000e+00   4.0000000e+00   3.5000000e+00   3.6000000e+00   3.8000000e+00   4.0000000e+00   5.2000000e+00   5.4000000e+00   3.5000000e+00   4.2000000e+00   3.4000000e+00   5.2000000e+00   3.4000000e+00   4.2000000e+00   4.5000000e+00   3.3000000e+00   3.4000000e+00   4.1000000e+00   4.3000000e+00   4.6000000e+00   4.9000000e+00   4.1000000e+00   3.6000000e+00   4.1000000e+00   4.6000000e+00   4.1000000e+00   4.0000000e+00   3.3000000e+00   3.9000000e+00   4.1000000e+00   3.6000000e+00   3.6000000e+00   4.4000000e+00   4.2000000e+00   3.7000000e+00   3.5000000e+00   3.7000000e+00   3.9000000e+00   3.6000000e+00   7.0000000e-01   6.0000000e-01   7.0000000e-01   2.0000000e-01   6.0000000e-01   8.0000000e-01   4.0000000e-01   8.0000000e-01   2.0000000e-01   9.0000000e-01   6.0000000e-01   3.4000000e+00   3.2000000e+00   3.6000000e+00   2.7000000e+00   3.3000000e+00   3.2000000e+00   3.4000000e+00   2.0000000e+00   3.3000000e+00   2.6000000e+00   2.2000000e+00   2.9000000e+00   2.7000000e+00   3.4000000e+00   2.3000000e+00   3.1000000e+00   3.2000000e+00   2.8000000e+00   3.2000000e+00   2.6000000e+00   3.5000000e+00   2.7000000e+00   3.6000000e+00   3.4000000e+00   3.0000000e+00   3.1000000e+00   3.5000000e+00   3.7000000e+00   3.2000000e+00   2.2000000e+00   2.5000000e+00   2.4000000e+00   2.6000000e+00   3.8000000e+00   3.2000000e+00   3.2000000e+00   3.4000000e+00   3.1000000e+00   2.8000000e+00   2.7000000e+00   3.1000000e+00   3.3000000e+00   2.7000000e+00   2.0000000e+00   2.9000000e+00   2.9000000e+00   2.9000000e+00   3.0000000e+00   1.7000000e+00   2.8000000e+00   4.7000000e+00   3.8000000e+00   4.6000000e+00   4.3000000e+00   4.5000000e+00   5.3000000e+00   3.2000000e+00   5.0000000e+00   4.5000000e+00   4.8000000e+00   3.8000000e+00   4.0000000e+00   4.2000000e+00   3.7000000e+00   3.8000000e+00   4.0000000e+00   4.2000000e+00   5.4000000e+00   5.6000000e+00   3.7000000e+00   4.4000000e+00   3.6000000e+00   5.4000000e+00   3.6000000e+00   4.4000000e+00   4.7000000e+00   3.5000000e+00   3.6000000e+00   4.3000000e+00   4.5000000e+00   4.8000000e+00   5.1000000e+00   4.3000000e+00   3.8000000e+00   4.3000000e+00   4.8000000e+00   4.3000000e+00   4.2000000e+00   3.5000000e+00   4.1000000e+00   4.3000000e+00   3.8000000e+00   3.8000000e+00   4.6000000e+00   4.4000000e+00   3.9000000e+00   3.7000000e+00   3.9000000e+00   4.1000000e+00   3.8000000e+00   2.0000000e-01   1.1000000e+00   7.0000000e-01   4.0000000e-01   4.0000000e-01   4.0000000e-01   4.0000000e-01   5.0000000e-01   3.0000000e-01   1.0000000e-01   3.2000000e+00   3.0000000e+00   3.4000000e+00   2.5000000e+00   3.1000000e+00   3.0000000e+00   3.2000000e+00   1.8000000e+00   3.1000000e+00   2.4000000e+00   2.0000000e+00   2.7000000e+00   2.5000000e+00   3.2000000e+00   2.1000000e+00   2.9000000e+00   3.0000000e+00   2.6000000e+00   3.0000000e+00   2.4000000e+00   3.3000000e+00   2.5000000e+00   3.4000000e+00   3.2000000e+00   2.8000000e+00   2.9000000e+00   3.3000000e+00   3.5000000e+00   3.0000000e+00   2.0000000e+00   2.3000000e+00   2.2000000e+00   2.4000000e+00   3.6000000e+00   3.0000000e+00   3.0000000e+00   3.2000000e+00   2.9000000e+00   2.6000000e+00   2.5000000e+00   2.9000000e+00   3.1000000e+00   2.5000000e+00   1.8000000e+00   2.7000000e+00   2.7000000e+00   2.7000000e+00   2.8000000e+00   1.5000000e+00   2.6000000e+00   4.5000000e+00   3.6000000e+00   4.4000000e+00   4.1000000e+00   4.3000000e+00   5.1000000e+00   3.0000000e+00   4.8000000e+00   4.3000000e+00   4.6000000e+00   3.6000000e+00   3.8000000e+00   4.0000000e+00   3.5000000e+00   3.6000000e+00   3.8000000e+00   4.0000000e+00   5.2000000e+00   5.4000000e+00   3.5000000e+00   4.2000000e+00   3.4000000e+00   5.2000000e+00   3.4000000e+00   4.2000000e+00   4.5000000e+00   3.3000000e+00   3.4000000e+00   4.1000000e+00   4.3000000e+00   4.6000000e+00   4.9000000e+00   4.1000000e+00   3.6000000e+00   4.1000000e+00   4.6000000e+00   4.1000000e+00   4.0000000e+00   3.3000000e+00   3.9000000e+00   4.1000000e+00   3.6000000e+00   3.6000000e+00   4.4000000e+00   4.2000000e+00   3.7000000e+00   3.5000000e+00   3.7000000e+00   3.9000000e+00   3.6000000e+00   1.2000000e+00   6.0000000e-01   3.0000000e-01   6.0000000e-01   5.0000000e-01   3.0000000e-01   4.0000000e-01   3.0000000e-01   2.0000000e-01   3.4000000e+00   3.2000000e+00   3.6000000e+00   2.7000000e+00   3.3000000e+00   3.2000000e+00   3.4000000e+00   2.0000000e+00   3.3000000e+00   2.6000000e+00   2.2000000e+00   2.9000000e+00   2.7000000e+00   3.4000000e+00   2.3000000e+00   3.1000000e+00   3.2000000e+00   2.8000000e+00   3.2000000e+00   2.6000000e+00   3.5000000e+00   2.7000000e+00   3.6000000e+00   3.4000000e+00   3.0000000e+00   3.1000000e+00   3.5000000e+00   3.7000000e+00   3.2000000e+00   2.2000000e+00   2.5000000e+00   2.4000000e+00   2.6000000e+00   3.8000000e+00   3.2000000e+00   3.2000000e+00   3.4000000e+00   3.1000000e+00   2.8000000e+00   2.7000000e+00   3.1000000e+00   3.3000000e+00   2.7000000e+00   2.0000000e+00   2.9000000e+00   2.9000000e+00   2.9000000e+00   3.0000000e+00   1.7000000e+00   2.8000000e+00   4.7000000e+00   3.8000000e+00   4.6000000e+00   4.3000000e+00   4.5000000e+00   5.3000000e+00   3.2000000e+00   5.0000000e+00   4.5000000e+00   4.8000000e+00   3.8000000e+00   4.0000000e+00   4.2000000e+00   3.7000000e+00   3.8000000e+00   4.0000000e+00   4.2000000e+00   5.4000000e+00   5.6000000e+00   3.7000000e+00   4.4000000e+00   3.6000000e+00   5.4000000e+00   3.6000000e+00   4.4000000e+00   4.7000000e+00   3.5000000e+00   3.6000000e+00   4.3000000e+00   4.5000000e+00   4.8000000e+00   5.1000000e+00   4.3000000e+00   3.8000000e+00   4.3000000e+00   4.8000000e+00   4.3000000e+00   4.2000000e+00   3.5000000e+00   4.1000000e+00   4.3000000e+00   3.8000000e+00   3.8000000e+00   4.6000000e+00   4.4000000e+00   3.9000000e+00   3.7000000e+00   3.9000000e+00   4.1000000e+00   3.8000000e+00   9.0000000e-01   1.2000000e+00   1.5000000e+00   7.0000000e-01   1.5000000e+00   9.0000000e-01   1.4000000e+00   1.0000000e+00   3.4000000e+00   3.2000000e+00   3.6000000e+00   2.7000000e+00   3.3000000e+00   3.2000000e+00   3.4000000e+00   2.0000000e+00   3.3000000e+00   2.6000000e+00   2.2000000e+00   2.9000000e+00   2.7000000e+00   3.4000000e+00   2.3000000e+00   3.1000000e+00   3.2000000e+00   2.8000000e+00   3.2000000e+00   2.6000000e+00   3.5000000e+00   2.7000000e+00   3.6000000e+00   3.4000000e+00   3.0000000e+00   3.1000000e+00   3.5000000e+00   3.7000000e+00   3.2000000e+00   2.2000000e+00   2.5000000e+00   2.4000000e+00   2.6000000e+00   3.8000000e+00   3.2000000e+00   3.2000000e+00   3.4000000e+00   3.1000000e+00   2.8000000e+00   2.7000000e+00   3.1000000e+00   3.3000000e+00   2.7000000e+00   2.0000000e+00   2.9000000e+00   2.9000000e+00   2.9000000e+00   3.0000000e+00   1.7000000e+00   2.8000000e+00   4.7000000e+00   3.8000000e+00   4.6000000e+00   4.3000000e+00   4.5000000e+00   5.3000000e+00   3.2000000e+00   5.0000000e+00   4.5000000e+00   4.8000000e+00   3.8000000e+00   4.0000000e+00   4.2000000e+00   3.7000000e+00   3.8000000e+00   4.0000000e+00   4.2000000e+00   5.4000000e+00   5.6000000e+00   3.7000000e+00   4.4000000e+00   3.6000000e+00   5.4000000e+00   3.6000000e+00   4.4000000e+00   4.7000000e+00   3.5000000e+00   3.6000000e+00   4.3000000e+00   4.5000000e+00   4.8000000e+00   5.1000000e+00   4.3000000e+00   3.8000000e+00   4.3000000e+00   4.8000000e+00   4.3000000e+00   4.2000000e+00   3.5000000e+00   4.1000000e+00   4.3000000e+00   3.8000000e+00   3.8000000e+00   4.6000000e+00   4.4000000e+00   3.9000000e+00   3.7000000e+00   3.9000000e+00   4.1000000e+00   3.8000000e+00   6.0000000e-01   7.0000000e-01   4.0000000e-01   7.0000000e-01   2.0000000e-01   9.0000000e-01   6.0000000e-01   3.4000000e+00   3.2000000e+00   3.6000000e+00   2.7000000e+00   3.3000000e+00   3.2000000e+00   3.4000000e+00   2.0000000e+00   3.3000000e+00   2.6000000e+00   2.2000000e+00   2.9000000e+00   2.7000000e+00   3.4000000e+00   2.3000000e+00   3.1000000e+00   3.2000000e+00   2.8000000e+00   3.2000000e+00   2.6000000e+00   3.5000000e+00   2.7000000e+00   3.6000000e+00   3.4000000e+00   3.0000000e+00   3.1000000e+00   3.5000000e+00   3.7000000e+00   3.2000000e+00   2.2000000e+00   2.5000000e+00   2.4000000e+00   2.6000000e+00   3.8000000e+00   3.2000000e+00   3.2000000e+00   3.4000000e+00   3.1000000e+00   2.8000000e+00   2.7000000e+00   3.1000000e+00   3.3000000e+00   2.7000000e+00   2.0000000e+00   2.9000000e+00   2.9000000e+00   2.9000000e+00   3.0000000e+00   1.7000000e+00   2.8000000e+00   4.7000000e+00   3.8000000e+00   4.6000000e+00   4.3000000e+00   4.5000000e+00   5.3000000e+00   3.2000000e+00   5.0000000e+00   4.5000000e+00   4.8000000e+00   3.8000000e+00   4.0000000e+00   4.2000000e+00   3.7000000e+00   3.8000000e+00   4.0000000e+00   4.2000000e+00   5.4000000e+00   5.6000000e+00   3.7000000e+00   4.4000000e+00   3.6000000e+00   5.4000000e+00   3.6000000e+00   4.4000000e+00   4.7000000e+00   3.5000000e+00   3.6000000e+00   4.3000000e+00   4.5000000e+00   4.8000000e+00   5.1000000e+00   4.3000000e+00   3.8000000e+00   4.3000000e+00   4.8000000e+00   4.3000000e+00   4.2000000e+00   3.5000000e+00   4.1000000e+00   4.3000000e+00   3.8000000e+00   3.8000000e+00   4.6000000e+00   4.4000000e+00   3.9000000e+00   3.7000000e+00   3.9000000e+00   4.1000000e+00   3.8000000e+00   3.0000000e-01   5.0000000e-01   4.0000000e-01   4.0000000e-01   4.0000000e-01   4.0000000e-01   3.1000000e+00   2.9000000e+00   3.3000000e+00   2.4000000e+00   3.0000000e+00   2.9000000e+00   3.1000000e+00   1.7000000e+00   3.0000000e+00   2.3000000e+00   1.9000000e+00   2.6000000e+00   2.4000000e+00   3.1000000e+00   2.0000000e+00   2.8000000e+00   2.9000000e+00   2.5000000e+00   2.9000000e+00   2.3000000e+00   3.2000000e+00   2.4000000e+00   3.3000000e+00   3.1000000e+00   2.7000000e+00   2.8000000e+00   3.2000000e+00   3.4000000e+00   2.9000000e+00   1.9000000e+00   2.2000000e+00   2.1000000e+00   2.3000000e+00   3.5000000e+00   2.9000000e+00   2.9000000e+00   3.1000000e+00   2.8000000e+00   2.5000000e+00   2.4000000e+00   2.8000000e+00   3.0000000e+00   2.4000000e+00   1.7000000e+00   2.6000000e+00   2.6000000e+00   2.6000000e+00   2.7000000e+00   1.4000000e+00   2.5000000e+00   4.4000000e+00   3.5000000e+00   4.3000000e+00   4.0000000e+00   4.2000000e+00   5.0000000e+00   2.9000000e+00   4.7000000e+00   4.2000000e+00   4.5000000e+00   3.5000000e+00   3.7000000e+00   3.9000000e+00   3.4000000e+00   3.5000000e+00   3.7000000e+00   3.9000000e+00   5.1000000e+00   5.3000000e+00   3.4000000e+00   4.1000000e+00   3.3000000e+00   5.1000000e+00   3.3000000e+00   4.1000000e+00   4.4000000e+00   3.2000000e+00   3.3000000e+00   4.0000000e+00   4.2000000e+00   4.5000000e+00   4.8000000e+00   4.0000000e+00   3.5000000e+00   4.0000000e+00   4.5000000e+00   4.0000000e+00   3.9000000e+00   3.2000000e+00   3.8000000e+00   4.0000000e+00   3.5000000e+00   3.5000000e+00   4.3000000e+00   4.1000000e+00   3.6000000e+00   3.4000000e+00   3.6000000e+00   3.8000000e+00   3.5000000e+00   8.0000000e-01   3.0000000e-01   6.0000000e-01   4.0000000e-01   5.0000000e-01   2.8000000e+00   2.6000000e+00   3.0000000e+00   2.1000000e+00   2.7000000e+00   2.6000000e+00   2.8000000e+00   1.4000000e+00   2.7000000e+00   2.0000000e+00   1.8000000e+00   2.3000000e+00   2.1000000e+00   2.8000000e+00   1.7000000e+00   2.5000000e+00   2.6000000e+00   2.2000000e+00   2.6000000e+00   2.0000000e+00   2.9000000e+00   2.1000000e+00   3.0000000e+00   2.8000000e+00   2.4000000e+00   2.5000000e+00   2.9000000e+00   3.1000000e+00   2.6000000e+00   1.6000000e+00   1.9000000e+00   1.8000000e+00   2.0000000e+00   3.2000000e+00   2.6000000e+00   2.6000000e+00   2.8000000e+00   2.5000000e+00   2.2000000e+00   2.1000000e+00   2.5000000e+00   2.7000000e+00   2.1000000e+00   1.5000000e+00   2.3000000e+00   2.3000000e+00   2.3000000e+00   2.4000000e+00   1.3000000e+00   2.2000000e+00   4.1000000e+00   3.2000000e+00   4.0000000e+00   3.7000000e+00   3.9000000e+00   4.7000000e+00   2.6000000e+00   4.4000000e+00   3.9000000e+00   4.2000000e+00   3.2000000e+00   3.4000000e+00   3.6000000e+00   3.1000000e+00   3.2000000e+00   3.4000000e+00   3.6000000e+00   4.8000000e+00   5.0000000e+00   3.1000000e+00   3.8000000e+00   3.0000000e+00   4.8000000e+00   3.0000000e+00   3.8000000e+00   4.1000000e+00   2.9000000e+00   3.0000000e+00   3.7000000e+00   3.9000000e+00   4.2000000e+00   4.5000000e+00   3.7000000e+00   3.2000000e+00   3.7000000e+00   4.2000000e+00   3.7000000e+00   3.6000000e+00   2.9000000e+00   3.5000000e+00   3.7000000e+00   3.2000000e+00   3.2000000e+00   4.0000000e+00   3.8000000e+00   3.3000000e+00   3.1000000e+00   3.3000000e+00   3.5000000e+00   3.2000000e+00   8.0000000e-01   2.0000000e-01   7.0000000e-01   3.0000000e-01   3.3000000e+00   3.1000000e+00   3.5000000e+00   2.6000000e+00   3.2000000e+00   3.1000000e+00   3.3000000e+00   1.9000000e+00   3.2000000e+00   2.5000000e+00   2.1000000e+00   2.8000000e+00   2.6000000e+00   3.3000000e+00   2.2000000e+00   3.0000000e+00   3.1000000e+00   2.7000000e+00   3.1000000e+00   2.5000000e+00   3.4000000e+00   2.6000000e+00   3.5000000e+00   3.3000000e+00   2.9000000e+00   3.0000000e+00   3.4000000e+00   3.6000000e+00   3.1000000e+00   2.1000000e+00   2.4000000e+00   2.3000000e+00   2.5000000e+00   3.7000000e+00   3.1000000e+00   3.1000000e+00   3.3000000e+00   3.0000000e+00   2.7000000e+00   2.6000000e+00   3.0000000e+00   3.2000000e+00   2.6000000e+00   1.9000000e+00   2.8000000e+00   2.8000000e+00   2.8000000e+00   2.9000000e+00   1.6000000e+00   2.7000000e+00   4.6000000e+00   3.7000000e+00   4.5000000e+00   4.2000000e+00   4.4000000e+00   5.2000000e+00   3.1000000e+00   4.9000000e+00   4.4000000e+00   4.7000000e+00   3.7000000e+00   3.9000000e+00   4.1000000e+00   3.6000000e+00   3.7000000e+00   3.9000000e+00   4.1000000e+00   5.3000000e+00   5.5000000e+00   3.6000000e+00   4.3000000e+00   3.5000000e+00   5.3000000e+00   3.5000000e+00   4.3000000e+00   4.6000000e+00   3.4000000e+00   3.5000000e+00   4.2000000e+00   4.4000000e+00   4.7000000e+00   5.0000000e+00   4.2000000e+00   3.7000000e+00   4.2000000e+00   4.7000000e+00   4.2000000e+00   4.1000000e+00   3.4000000e+00   4.0000000e+00   4.2000000e+00   3.7000000e+00   3.7000000e+00   4.5000000e+00   4.3000000e+00   3.8000000e+00   3.6000000e+00   3.8000000e+00   4.0000000e+00   3.7000000e+00   6.0000000e-01   2.0000000e-01   5.0000000e-01   3.1000000e+00   2.9000000e+00   3.3000000e+00   2.4000000e+00   3.0000000e+00   2.9000000e+00   3.1000000e+00   1.7000000e+00   3.0000000e+00   2.3000000e+00   1.9000000e+00   2.6000000e+00   2.4000000e+00   3.1000000e+00   2.0000000e+00   2.8000000e+00   2.9000000e+00   2.5000000e+00   2.9000000e+00   2.3000000e+00   3.2000000e+00   2.4000000e+00   3.3000000e+00   3.1000000e+00   2.7000000e+00   2.8000000e+00   3.2000000e+00   3.4000000e+00   2.9000000e+00   1.9000000e+00   2.2000000e+00   2.1000000e+00   2.3000000e+00   3.5000000e+00   2.9000000e+00   2.9000000e+00   3.1000000e+00   2.8000000e+00   2.5000000e+00   2.4000000e+00   2.8000000e+00   3.0000000e+00   2.4000000e+00   1.7000000e+00   2.6000000e+00   2.6000000e+00   2.6000000e+00   2.7000000e+00   1.4000000e+00   2.5000000e+00   4.4000000e+00   3.5000000e+00   4.3000000e+00   4.0000000e+00   4.2000000e+00   5.0000000e+00   2.9000000e+00   4.7000000e+00   4.2000000e+00   4.5000000e+00   3.5000000e+00   3.7000000e+00   3.9000000e+00   3.4000000e+00   3.5000000e+00   3.7000000e+00   3.9000000e+00   5.1000000e+00   5.3000000e+00   3.4000000e+00   4.1000000e+00   3.3000000e+00   5.1000000e+00   3.3000000e+00   4.1000000e+00   4.4000000e+00   3.2000000e+00   3.3000000e+00   4.0000000e+00   4.2000000e+00   4.5000000e+00   4.8000000e+00   4.0000000e+00   3.5000000e+00   4.0000000e+00   4.5000000e+00   4.0000000e+00   3.9000000e+00   3.2000000e+00   3.8000000e+00   4.0000000e+00   3.5000000e+00   3.5000000e+00   4.3000000e+00   4.1000000e+00   3.6000000e+00   3.4000000e+00   3.6000000e+00   3.8000000e+00   3.5000000e+00   7.0000000e-01   4.0000000e-01   3.3000000e+00   3.1000000e+00   3.5000000e+00   2.6000000e+00   3.2000000e+00   3.1000000e+00   3.3000000e+00   1.9000000e+00   3.2000000e+00   2.5000000e+00   2.1000000e+00   2.8000000e+00   2.6000000e+00   3.3000000e+00   2.2000000e+00   3.0000000e+00   3.1000000e+00   2.7000000e+00   3.1000000e+00   2.5000000e+00   3.4000000e+00   2.6000000e+00   3.5000000e+00   3.3000000e+00   2.9000000e+00   3.0000000e+00   3.4000000e+00   3.6000000e+00   3.1000000e+00   2.1000000e+00   2.4000000e+00   2.3000000e+00   2.5000000e+00   3.7000000e+00   3.1000000e+00   3.1000000e+00   3.3000000e+00   3.0000000e+00   2.7000000e+00   2.6000000e+00   3.0000000e+00   3.2000000e+00   2.6000000e+00   1.9000000e+00   2.8000000e+00   2.8000000e+00   2.8000000e+00   2.9000000e+00   1.6000000e+00   2.7000000e+00   4.6000000e+00   3.7000000e+00   4.5000000e+00   4.2000000e+00   4.4000000e+00   5.2000000e+00   3.1000000e+00   4.9000000e+00   4.4000000e+00   4.7000000e+00   3.7000000e+00   3.9000000e+00   4.1000000e+00   3.6000000e+00   3.7000000e+00   3.9000000e+00   4.1000000e+00   5.3000000e+00   5.5000000e+00   3.6000000e+00   4.3000000e+00   3.5000000e+00   5.3000000e+00   3.5000000e+00   4.3000000e+00   4.6000000e+00   3.4000000e+00   3.5000000e+00   4.2000000e+00   4.4000000e+00   4.7000000e+00   5.0000000e+00   4.2000000e+00   3.7000000e+00   4.2000000e+00   4.7000000e+00   4.2000000e+00   4.1000000e+00   3.4000000e+00   4.0000000e+00   4.2000000e+00   3.7000000e+00   3.7000000e+00   4.5000000e+00   4.3000000e+00   3.8000000e+00   3.6000000e+00   3.8000000e+00   4.0000000e+00   3.7000000e+00   4.0000000e-01   3.2000000e+00   3.0000000e+00   3.4000000e+00   2.5000000e+00   3.1000000e+00   3.0000000e+00   3.2000000e+00   1.8000000e+00   3.1000000e+00   2.4000000e+00   2.0000000e+00   2.7000000e+00   2.5000000e+00   3.2000000e+00   2.1000000e+00   2.9000000e+00   3.0000000e+00   2.6000000e+00   3.0000000e+00   2.4000000e+00   3.3000000e+00   2.5000000e+00   3.4000000e+00   3.2000000e+00   2.8000000e+00   2.9000000e+00   3.3000000e+00   3.5000000e+00   3.0000000e+00   2.0000000e+00   2.3000000e+00   2.2000000e+00   2.4000000e+00   3.6000000e+00   3.0000000e+00   3.0000000e+00   3.2000000e+00   2.9000000e+00   2.6000000e+00   2.5000000e+00   2.9000000e+00   3.1000000e+00   2.5000000e+00   1.8000000e+00   2.7000000e+00   2.7000000e+00   2.7000000e+00   2.8000000e+00   1.5000000e+00   2.6000000e+00   4.5000000e+00   3.6000000e+00   4.4000000e+00   4.1000000e+00   4.3000000e+00   5.1000000e+00   3.0000000e+00   4.8000000e+00   4.3000000e+00   4.6000000e+00   3.6000000e+00   3.8000000e+00   4.0000000e+00   3.5000000e+00   3.6000000e+00   3.8000000e+00   4.0000000e+00   5.2000000e+00   5.4000000e+00   3.5000000e+00   4.2000000e+00   3.4000000e+00   5.2000000e+00   3.4000000e+00   4.2000000e+00   4.5000000e+00   3.3000000e+00   3.4000000e+00   4.1000000e+00   4.3000000e+00   4.6000000e+00   4.9000000e+00   4.1000000e+00   3.6000000e+00   4.1000000e+00   4.6000000e+00   4.1000000e+00   4.0000000e+00   3.3000000e+00   3.9000000e+00   4.1000000e+00   3.6000000e+00   3.6000000e+00   4.4000000e+00   4.2000000e+00   3.7000000e+00   3.5000000e+00   3.7000000e+00   3.9000000e+00   3.6000000e+00   3.3000000e+00   3.1000000e+00   3.5000000e+00   2.6000000e+00   3.2000000e+00   3.1000000e+00   3.3000000e+00   1.9000000e+00   3.2000000e+00   2.5000000e+00   2.1000000e+00   2.8000000e+00   2.6000000e+00   3.3000000e+00   2.2000000e+00   3.0000000e+00   3.1000000e+00   2.7000000e+00   3.1000000e+00   2.5000000e+00   3.4000000e+00   2.6000000e+00   3.5000000e+00   3.3000000e+00   2.9000000e+00   3.0000000e+00   3.4000000e+00   3.6000000e+00   3.1000000e+00   2.1000000e+00   2.4000000e+00   2.3000000e+00   2.5000000e+00   3.7000000e+00   3.1000000e+00   3.1000000e+00   3.3000000e+00   3.0000000e+00   2.7000000e+00   2.6000000e+00   3.0000000e+00   3.2000000e+00   2.6000000e+00   1.9000000e+00   2.8000000e+00   2.8000000e+00   2.8000000e+00   2.9000000e+00   1.6000000e+00   2.7000000e+00   4.6000000e+00   3.7000000e+00   4.5000000e+00   4.2000000e+00   4.4000000e+00   5.2000000e+00   3.1000000e+00   4.9000000e+00   4.4000000e+00   4.7000000e+00   3.7000000e+00   3.9000000e+00   4.1000000e+00   3.6000000e+00   3.7000000e+00   3.9000000e+00   4.1000000e+00   5.3000000e+00   5.5000000e+00   3.6000000e+00   4.3000000e+00   3.5000000e+00   5.3000000e+00   3.5000000e+00   4.3000000e+00   4.6000000e+00   3.4000000e+00   3.5000000e+00   4.2000000e+00   4.4000000e+00   4.7000000e+00   5.0000000e+00   4.2000000e+00   3.7000000e+00   4.2000000e+00   4.7000000e+00   4.2000000e+00   4.1000000e+00   3.4000000e+00   4.0000000e+00   4.2000000e+00   3.7000000e+00   3.7000000e+00   4.5000000e+00   4.3000000e+00   3.8000000e+00   3.6000000e+00   3.8000000e+00   4.0000000e+00   3.7000000e+00   6.0000000e-01   2.0000000e-01   1.5000000e+00   5.0000000e-01   1.3000000e+00   7.0000000e-01   2.1000000e+00   4.0000000e-01   1.8000000e+00   2.0000000e+00   1.1000000e+00   1.0000000e+00   9.0000000e-01   1.4000000e+00   3.0000000e-01   1.4000000e+00   1.2000000e+00   1.0000000e+00   1.4000000e+00   1.1000000e+00   9.0000000e-01   7.0000000e-01   9.0000000e-01   6.0000000e-01   4.0000000e-01   4.0000000e-01   3.0000000e-01   1.0000000e+00   1.3000000e+00   1.5000000e+00   1.5000000e+00   1.2000000e+00   1.0000000e+00   1.6000000e+00   1.0000000e+00   3.0000000e-01   9.0000000e-01   1.4000000e+00   1.5000000e+00   1.5000000e+00   9.0000000e-01   1.2000000e+00   2.0000000e+00   1.4000000e+00   1.3000000e+00   1.3000000e+00   8.0000000e-01   1.9000000e+00   1.3000000e+00   1.3000000e+00   1.2000000e+00   1.2000000e+00   9.0000000e-01   1.1000000e+00   1.9000000e+00   2.1000000e+00   1.6000000e+00   1.1000000e+00   1.4000000e+00   6.0000000e-01   6.0000000e-01   8.0000000e-01   1.3000000e+00   1.2000000e+00   9.0000000e-01   8.0000000e-01   2.0000000e+00   2.2000000e+00   1.0000000e+00   1.0000000e+00   1.4000000e+00   2.0000000e+00   7.0000000e-01   1.0000000e+00   1.3000000e+00   8.0000000e-01   9.0000000e-01   9.0000000e-01   1.1000000e+00   1.4000000e+00   1.7000000e+00   9.0000000e-01   7.0000000e-01   9.0000000e-01   1.4000000e+00   1.0000000e+00   8.0000000e-01   1.0000000e+00   7.0000000e-01   1.0000000e+00   9.0000000e-01   1.2000000e+00   1.2000000e+00   1.1000000e+00   9.0000000e-01   7.0000000e-01   6.0000000e-01   9.0000000e-01   1.1000000e+00   5.0000000e-01   9.0000000e-01   4.0000000e-01   7.0000000e-01   2.0000000e-01   1.5000000e+00   3.0000000e-01   1.2000000e+00   1.4000000e+00   5.0000000e-01   1.0000000e+00   3.0000000e-01   9.0000000e-01   3.0000000e-01   8.0000000e-01   6.0000000e-01   1.0000000e+00   8.0000000e-01   5.0000000e-01   5.0000000e-01   7.0000000e-01   4.0000000e-01   3.0000000e-01   2.0000000e-01   4.0000000e-01   5.0000000e-01   4.0000000e-01   1.0000000e+00   9.0000000e-01   9.0000000e-01   6.0000000e-01   6.0000000e-01   1.0000000e+00   4.0000000e-01   3.0000000e-01   9.0000000e-01   8.0000000e-01   9.0000000e-01   9.0000000e-01   3.0000000e-01   6.0000000e-01   1.4000000e+00   8.0000000e-01   7.0000000e-01   7.0000000e-01   3.0000000e-01   1.5000000e+00   7.0000000e-01   1.5000000e+00   6.0000000e-01   1.4000000e+00   1.1000000e+00   1.3000000e+00   2.1000000e+00   1.5000000e+00   1.8000000e+00   1.3000000e+00   1.6000000e+00   6.0000000e-01   8.0000000e-01   1.0000000e+00   7.0000000e-01   9.0000000e-01   8.0000000e-01   1.0000000e+00   2.2000000e+00   2.4000000e+00   1.0000000e+00   1.2000000e+00   8.0000000e-01   2.2000000e+00   5.0000000e-01   1.2000000e+00   1.5000000e+00   4.0000000e-01   4.0000000e-01   1.1000000e+00   1.3000000e+00   1.6000000e+00   1.9000000e+00   1.1000000e+00   6.0000000e-01   1.1000000e+00   1.6000000e+00   1.1000000e+00   1.0000000e+00   4.0000000e-01   9.0000000e-01   1.1000000e+00   8.0000000e-01   6.0000000e-01   1.4000000e+00   1.2000000e+00   8.0000000e-01   7.0000000e-01   7.0000000e-01   9.0000000e-01   6.0000000e-01   1.4000000e+00   4.0000000e-01   1.2000000e+00   6.0000000e-01   2.0000000e+00   3.0000000e-01   1.7000000e+00   1.9000000e+00   1.0000000e+00   9.0000000e-01   8.0000000e-01   1.3000000e+00   5.0000000e-01   1.3000000e+00   1.1000000e+00   9.0000000e-01   1.3000000e+00   1.0000000e+00   9.0000000e-01   6.0000000e-01   8.0000000e-01   6.0000000e-01   5.0000000e-01   3.0000000e-01   2.0000000e-01   9.0000000e-01   1.4000000e+00   1.4000000e+00   1.4000000e+00   1.1000000e+00   9.0000000e-01   1.5000000e+00   9.0000000e-01   2.0000000e-01   8.0000000e-01   1.3000000e+00   1.4000000e+00   1.4000000e+00   8.0000000e-01   1.1000000e+00   1.9000000e+00   1.3000000e+00   1.2000000e+00   1.2000000e+00   7.0000000e-01   1.9000000e+00   1.2000000e+00   1.1000000e+00   1.1000000e+00   1.0000000e+00   7.0000000e-01   9.0000000e-01   1.7000000e+00   2.0000000e+00   1.4000000e+00   9.0000000e-01   1.2000000e+00   5.0000000e-01   5.0000000e-01   6.0000000e-01   1.2000000e+00   1.1000000e+00   8.0000000e-01   6.0000000e-01   1.8000000e+00   2.0000000e+00   9.0000000e-01   8.0000000e-01   1.3000000e+00   1.8000000e+00   6.0000000e-01   8.0000000e-01   1.1000000e+00   7.0000000e-01   8.0000000e-01   7.0000000e-01   9.0000000e-01   1.2000000e+00   1.5000000e+00   7.0000000e-01   6.0000000e-01   8.0000000e-01   1.2000000e+00   9.0000000e-01   6.0000000e-01   9.0000000e-01   6.0000000e-01   9.0000000e-01   8.0000000e-01   1.1000000e+00   1.0000000e+00   1.0000000e+00   8.0000000e-01   6.0000000e-01   5.0000000e-01   8.0000000e-01   1.0000000e+00   1.0000000e+00   5.0000000e-01   1.0000000e+00   7.0000000e-01   1.1000000e+00   4.0000000e-01   5.0000000e-01   7.0000000e-01   5.0000000e-01   7.0000000e-01   6.0000000e-01   1.2000000e+00   7.0000000e-01   4.0000000e-01   7.0000000e-01   2.0000000e-01   9.0000000e-01   6.0000000e-01   9.0000000e-01   7.0000000e-01   9.0000000e-01   1.1000000e+00   1.3000000e+00   1.2000000e+00   6.0000000e-01   5.0000000e-01   2.0000000e-01   3.0000000e-01   4.0000000e-01   1.1000000e+00   7.0000000e-01   1.1000000e+00   1.2000000e+00   8.0000000e-01   7.0000000e-01   2.0000000e-01   4.0000000e-01   7.0000000e-01   3.0000000e-01   7.0000000e-01   4.0000000e-01   7.0000000e-01   6.0000000e-01   7.0000000e-01   1.0000000e+00   5.0000000e-01   2.0000000e+00   1.1000000e+00   1.9000000e+00   1.6000000e+00   1.8000000e+00   2.6000000e+00   6.0000000e-01   2.3000000e+00   1.8000000e+00   2.1000000e+00   1.1000000e+00   1.3000000e+00   1.5000000e+00   1.0000000e+00   1.1000000e+00   1.3000000e+00   1.5000000e+00   2.7000000e+00   2.9000000e+00   1.0000000e+00   1.7000000e+00   9.0000000e-01   2.7000000e+00   9.0000000e-01   1.7000000e+00   2.0000000e+00   8.0000000e-01   9.0000000e-01   1.6000000e+00   1.8000000e+00   2.1000000e+00   2.4000000e+00   1.6000000e+00   1.1000000e+00   1.6000000e+00   2.2000000e+00   1.6000000e+00   1.5000000e+00   8.0000000e-01   1.4000000e+00   1.6000000e+00   1.4000000e+00   1.1000000e+00   1.9000000e+00   1.7000000e+00   1.2000000e+00   1.0000000e+00   1.2000000e+00   1.4000000e+00   1.1000000e+00   8.0000000e-01   5.0000000e-01   1.6000000e+00   2.0000000e-01   1.3000000e+00   1.5000000e+00   6.0000000e-01   6.0000000e-01   4.0000000e-01   1.0000000e+00   3.0000000e-01   9.0000000e-01   7.0000000e-01   6.0000000e-01   9.0000000e-01   6.0000000e-01   6.0000000e-01   3.0000000e-01   4.0000000e-01   3.0000000e-01   2.0000000e-01   3.0000000e-01   4.0000000e-01   5.0000000e-01   1.1000000e+00   1.0000000e+00   1.0000000e+00   7.0000000e-01   5.0000000e-01   1.1000000e+00   6.0000000e-01   3.0000000e-01   5.0000000e-01   9.0000000e-01   1.0000000e+00   1.0000000e+00   4.0000000e-01   7.0000000e-01   1.5000000e+00   9.0000000e-01   8.0000000e-01   8.0000000e-01   3.0000000e-01   1.6000000e+00   8.0000000e-01   1.4000000e+00   7.0000000e-01   1.3000000e+00   1.0000000e+00   1.2000000e+00   2.0000000e+00   1.6000000e+00   1.7000000e+00   1.2000000e+00   1.5000000e+00   5.0000000e-01   7.0000000e-01   9.0000000e-01   8.0000000e-01   9.0000000e-01   8.0000000e-01   9.0000000e-01   2.1000000e+00   2.3000000e+00   6.0000000e-01   1.1000000e+00   9.0000000e-01   2.1000000e+00   3.0000000e-01   1.1000000e+00   1.4000000e+00   3.0000000e-01   4.0000000e-01   1.0000000e+00   1.2000000e+00   1.5000000e+00   1.8000000e+00   1.0000000e+00   5.0000000e-01   1.0000000e+00   1.5000000e+00   1.0000000e+00   9.0000000e-01   5.0000000e-01   8.0000000e-01   1.0000000e+00   8.0000000e-01   7.0000000e-01   1.3000000e+00   1.1000000e+00   8.0000000e-01   4.0000000e-01   6.0000000e-01   8.0000000e-01   6.0000000e-01   6.0000000e-01   1.2000000e+00   9.0000000e-01   6.0000000e-01   1.0000000e+00   3.0000000e-01   6.0000000e-01   4.0000000e-01   9.0000000e-01   1.0000000e+00   2.0000000e-01   4.0000000e-01   6.0000000e-01   6.0000000e-01   5.0000000e-01   5.0000000e-01   6.0000000e-01   4.0000000e-01   7.0000000e-01   9.0000000e-01   1.1000000e+00   1.0000000e+00   3.0000000e-01   1.0000000e+00   7.0000000e-01   8.0000000e-01   6.0000000e-01   6.0000000e-01   3.0000000e-01   6.0000000e-01   1.0000000e+00   6.0000000e-01   4.0000000e-01   5.0000000e-01   2.0000000e-01   4.0000000e-01   5.0000000e-01   1.2000000e+00   3.0000000e-01   3.0000000e-01   3.0000000e-01   5.0000000e-01   1.5000000e+00   4.0000000e-01   1.5000000e+00   6.0000000e-01   1.4000000e+00   1.1000000e+00   1.3000000e+00   2.1000000e+00   8.0000000e-01   1.8000000e+00   1.3000000e+00   1.6000000e+00   8.0000000e-01   8.0000000e-01   1.1000000e+00   7.0000000e-01   1.1000000e+00   1.0000000e+00   1.0000000e+00   2.2000000e+00   2.4000000e+00   6.0000000e-01   1.2000000e+00   7.0000000e-01   2.2000000e+00   6.0000000e-01   1.2000000e+00   1.5000000e+00   5.0000000e-01   5.0000000e-01   1.1000000e+00   1.5000000e+00   1.7000000e+00   2.2000000e+00   1.1000000e+00   6.0000000e-01   1.1000000e+00   2.0000000e+00   1.1000000e+00   1.0000000e+00   5.0000000e-01   1.2000000e+00   1.1000000e+00   1.2000000e+00   6.0000000e-01   1.4000000e+00   1.2000000e+00   1.0000000e+00   6.0000000e-01   8.0000000e-01   1.0000000e+00   6.0000000e-01   1.4000000e+00   4.0000000e-01   1.1000000e+00   1.3000000e+00   5.0000000e-01   1.1000000e+00   4.0000000e-01   1.1000000e+00   4.0000000e-01   7.0000000e-01   6.0000000e-01   1.1000000e+00   8.0000000e-01   4.0000000e-01   7.0000000e-01   8.0000000e-01   5.0000000e-01   4.0000000e-01   3.0000000e-01   5.0000000e-01   4.0000000e-01   4.0000000e-01   1.2000000e+00   9.0000000e-01   1.0000000e+00   8.0000000e-01   6.0000000e-01   9.0000000e-01   3.0000000e-01   4.0000000e-01   1.0000000e+00   7.0000000e-01   8.0000000e-01   8.0000000e-01   3.0000000e-01   7.0000000e-01   1.4000000e+00   7.0000000e-01   6.0000000e-01   6.0000000e-01   4.0000000e-01   1.7000000e+00   6.0000000e-01   1.3000000e+00   6.0000000e-01   1.2000000e+00   9.0000000e-01   1.1000000e+00   1.9000000e+00   1.4000000e+00   1.6000000e+00   1.1000000e+00   1.4000000e+00   4.0000000e-01   6.0000000e-01   8.0000000e-01   8.0000000e-01   8.0000000e-01   7.0000000e-01   8.0000000e-01   2.0000000e+00   2.2000000e+00   1.1000000e+00   1.0000000e+00   7.0000000e-01   2.0000000e+00   6.0000000e-01   1.0000000e+00   1.3000000e+00   5.0000000e-01   3.0000000e-01   9.0000000e-01   1.1000000e+00   1.4000000e+00   1.7000000e+00   9.0000000e-01   5.0000000e-01   9.0000000e-01   1.4000000e+00   9.0000000e-01   8.0000000e-01   3.0000000e-01   7.0000000e-01   9.0000000e-01   7.0000000e-01   6.0000000e-01   1.2000000e+00   1.0000000e+00   7.0000000e-01   8.0000000e-01   5.0000000e-01   7.0000000e-01   4.0000000e-01   1.7000000e+00   6.0000000e-01   4.0000000e-01   1.0000000e+00   1.1000000e+00   1.4000000e+00   7.0000000e-01   1.8000000e+00   1.2000000e+00   9.0000000e-01   1.3000000e+00   7.0000000e-01   1.5000000e+00   1.2000000e+00   1.6000000e+00   1.4000000e+00   1.5000000e+00   1.7000000e+00   1.9000000e+00   1.8000000e+00   1.2000000e+00   8.0000000e-01   6.0000000e-01   6.0000000e-01   9.0000000e-01   1.8000000e+00   1.2000000e+00   1.2000000e+00   1.8000000e+00   1.4000000e+00   8.0000000e-01   7.0000000e-01   1.1000000e+00   1.3000000e+00   9.0000000e-01   1.0000000e-01   9.0000000e-01   9.0000000e-01   9.0000000e-01   1.3000000e+00   3.0000000e-01   8.0000000e-01   2.7000000e+00   1.8000000e+00   2.6000000e+00   2.3000000e+00   2.5000000e+00   3.3000000e+00   1.2000000e+00   3.0000000e+00   2.5000000e+00   2.8000000e+00   1.8000000e+00   2.0000000e+00   2.2000000e+00   1.7000000e+00   1.8000000e+00   2.0000000e+00   2.2000000e+00   3.4000000e+00   3.6000000e+00   1.7000000e+00   2.4000000e+00   1.6000000e+00   3.4000000e+00   1.6000000e+00   2.4000000e+00   2.7000000e+00   1.5000000e+00   1.6000000e+00   2.3000000e+00   2.5000000e+00   2.8000000e+00   3.1000000e+00   2.3000000e+00   1.8000000e+00   2.3000000e+00   2.8000000e+00   2.3000000e+00   2.2000000e+00   1.5000000e+00   2.1000000e+00   2.3000000e+00   2.0000000e+00   1.8000000e+00   2.6000000e+00   2.4000000e+00   1.9000000e+00   1.7000000e+00   1.9000000e+00   2.1000000e+00   1.8000000e+00   1.4000000e+00   1.6000000e+00   7.0000000e-01   7.0000000e-01   5.0000000e-01   1.0000000e+00   2.0000000e-01   1.0000000e+00   8.0000000e-01   7.0000000e-01   1.0000000e+00   7.0000000e-01   6.0000000e-01   4.0000000e-01   5.0000000e-01   3.0000000e-01   2.0000000e-01   2.0000000e-01   4.0000000e-01   6.0000000e-01   1.1000000e+00   1.1000000e+00   1.1000000e+00   8.0000000e-01   6.0000000e-01   1.2000000e+00   6.0000000e-01   2.0000000e-01   6.0000000e-01   1.0000000e+00   1.1000000e+00   1.1000000e+00   5.0000000e-01   8.0000000e-01   1.6000000e+00   1.0000000e+00   9.0000000e-01   9.0000000e-01   4.0000000e-01   1.6000000e+00   9.0000000e-01   1.4000000e+00   8.0000000e-01   1.3000000e+00   1.0000000e+00   1.2000000e+00   2.0000000e+00   1.7000000e+00   1.7000000e+00   1.2000000e+00   1.5000000e+00   7.0000000e-01   7.0000000e-01   9.0000000e-01   9.0000000e-01   1.1000000e+00   1.0000000e+00   9.0000000e-01   2.1000000e+00   2.3000000e+00   7.0000000e-01   1.1000000e+00   1.0000000e+00   2.1000000e+00   5.0000000e-01   1.1000000e+00   1.4000000e+00   5.0000000e-01   5.0000000e-01   1.0000000e+00   1.2000000e+00   1.5000000e+00   1.8000000e+00   1.0000000e+00   5.0000000e-01   1.0000000e+00   1.5000000e+00   1.1000000e+00   9.0000000e-01   6.0000000e-01   8.0000000e-01   1.1000000e+00   1.0000000e+00   8.0000000e-01   1.3000000e+00   1.2000000e+00   1.0000000e+00   6.0000000e-01   7.0000000e-01   1.0000000e+00   7.0000000e-01   7.0000000e-01   7.0000000e-01   8.0000000e-01   9.0000000e-01   4.0000000e-01   1.5000000e+00   6.0000000e-01   6.0000000e-01   1.0000000e+00   4.0000000e-01   9.0000000e-01   9.0000000e-01   1.1000000e+00   9.0000000e-01   1.2000000e+00   1.4000000e+00   1.6000000e+00   1.5000000e+00   8.0000000e-01   5.0000000e-01   3.0000000e-01   4.0000000e-01   6.0000000e-01   1.2000000e+00   6.0000000e-01   8.0000000e-01   1.5000000e+00   1.1000000e+00   4.0000000e-01   3.0000000e-01   5.0000000e-01   9.0000000e-01   6.0000000e-01   6.0000000e-01   4.0000000e-01   5.0000000e-01   5.0000000e-01   1.0000000e+00   9.0000000e-01   5.0000000e-01   2.1000000e+00   1.2000000e+00   2.0000000e+00   1.7000000e+00   1.9000000e+00   2.7000000e+00   6.0000000e-01   2.4000000e+00   1.9000000e+00   2.2000000e+00   1.3000000e+00   1.4000000e+00   1.6000000e+00   1.1000000e+00   1.2000000e+00   1.4000000e+00   1.6000000e+00   2.8000000e+00   3.0000000e+00   1.1000000e+00   1.8000000e+00   1.0000000e+00   2.8000000e+00   1.1000000e+00   1.8000000e+00   2.1000000e+00   1.0000000e+00   1.0000000e+00   1.7000000e+00   2.0000000e+00   2.2000000e+00   2.7000000e+00   1.7000000e+00   1.2000000e+00   1.7000000e+00   2.5000000e+00   1.7000000e+00   1.6000000e+00   9.0000000e-01   1.7000000e+00   1.7000000e+00   1.7000000e+00   1.2000000e+00   2.0000000e+00   1.8000000e+00   1.5000000e+00   1.1000000e+00   1.3000000e+00   1.5000000e+00   1.2000000e+00   1.0000000e+00   1.0000000e+00   1.2000000e+00   9.0000000e-01   1.7000000e+00   1.0000000e+00   8.0000000e-01   1.2000000e+00   6.0000000e-01   1.3000000e+00   1.1000000e+00   1.4000000e+00   1.2000000e+00   1.4000000e+00   1.6000000e+00   1.8000000e+00   1.7000000e+00   1.0000000e+00   7.0000000e-01   5.0000000e-01   5.0000000e-01   8.0000000e-01   1.6000000e+00   1.0000000e+00   1.4000000e+00   1.7000000e+00   1.3000000e+00   1.0000000e+00   5.0000000e-01   9.0000000e-01   1.1000000e+00   8.0000000e-01   3.0000000e-01   7.0000000e-01   1.0000000e+00   9.0000000e-01   1.2000000e+00   5.0000000e-01   8.0000000e-01   2.5000000e+00   1.6000000e+00   2.4000000e+00   2.1000000e+00   2.3000000e+00   3.1000000e+00   1.0000000e+00   2.8000000e+00   2.3000000e+00   2.6000000e+00   1.6000000e+00   1.8000000e+00   2.0000000e+00   1.5000000e+00   1.6000000e+00   1.8000000e+00   2.0000000e+00   3.2000000e+00   3.4000000e+00   1.5000000e+00   2.2000000e+00   1.4000000e+00   3.2000000e+00   1.4000000e+00   2.2000000e+00   2.5000000e+00   1.3000000e+00   1.4000000e+00   2.1000000e+00   2.3000000e+00   2.6000000e+00   2.9000000e+00   2.1000000e+00   1.6000000e+00   2.1000000e+00   2.7000000e+00   2.1000000e+00   2.0000000e+00   1.3000000e+00   1.9000000e+00   2.1000000e+00   1.9000000e+00   1.6000000e+00   2.4000000e+00   2.2000000e+00   1.7000000e+00   1.5000000e+00   1.7000000e+00   1.9000000e+00   1.6000000e+00   8.0000000e-01   5.0000000e-01   6.0000000e-01   8.0000000e-01   3.0000000e-01   5.0000000e-01   8.0000000e-01   5.0000000e-01   6.0000000e-01   2.0000000e-01   7.0000000e-01   5.0000000e-01   5.0000000e-01   7.0000000e-01   9.0000000e-01   8.0000000e-01   3.0000000e-01   7.0000000e-01   6.0000000e-01   6.0000000e-01   3.0000000e-01   9.0000000e-01   5.0000000e-01   4.0000000e-01   8.0000000e-01   7.0000000e-01   3.0000000e-01   5.0000000e-01   4.0000000e-01   4.0000000e-01   4.0000000e-01   9.0000000e-01   3.0000000e-01   3.0000000e-01   2.0000000e-01   3.0000000e-01   1.2000000e+00   2.0000000e-01   1.8000000e+00   9.0000000e-01   1.7000000e+00   1.4000000e+00   1.6000000e+00   2.4000000e+00   1.0000000e+00   2.1000000e+00   1.6000000e+00   1.9000000e+00   9.0000000e-01   1.1000000e+00   1.3000000e+00   8.0000000e-01   9.0000000e-01   1.1000000e+00   1.3000000e+00   2.5000000e+00   2.7000000e+00   8.0000000e-01   1.5000000e+00   7.0000000e-01   2.5000000e+00   7.0000000e-01   1.5000000e+00   1.8000000e+00   6.0000000e-01   7.0000000e-01   1.4000000e+00   1.6000000e+00   1.9000000e+00   2.2000000e+00   1.4000000e+00   9.0000000e-01   1.4000000e+00   1.9000000e+00   1.4000000e+00   1.3000000e+00   6.0000000e-01   1.2000000e+00   1.4000000e+00   1.0000000e+00   9.0000000e-01   1.7000000e+00   1.5000000e+00   1.0000000e+00   8.0000000e-01   1.0000000e+00   1.2000000e+00   9.0000000e-01   7.0000000e-01   7.0000000e-01   9.0000000e-01   8.0000000e-01   5.0000000e-01   5.0000000e-01   4.0000000e-01   1.0000000e+00   6.0000000e-01   9.0000000e-01   7.0000000e-01   7.0000000e-01   8.0000000e-01   8.0000000e-01   1.0000000e+00   7.0000000e-01   5.0000000e-01   5.0000000e-01   5.0000000e-01   5.0000000e-01   1.1000000e+00   8.0000000e-01   1.2000000e+00   9.0000000e-01   4.0000000e-01   8.0000000e-01   5.0000000e-01   5.0000000e-01   8.0000000e-01   4.0000000e-01   1.0000000e+00   5.0000000e-01   8.0000000e-01   7.0000000e-01   7.0000000e-01   1.0000000e+00   6.0000000e-01   2.0000000e+00   1.1000000e+00   1.9000000e+00   1.6000000e+00   1.8000000e+00   2.6000000e+00   1.1000000e+00   2.3000000e+00   1.8000000e+00   2.1000000e+00   1.1000000e+00   1.3000000e+00   1.5000000e+00   1.0000000e+00   1.4000000e+00   1.3000000e+00   1.5000000e+00   2.7000000e+00   2.9000000e+00   1.0000000e+00   1.7000000e+00   1.0000000e+00   2.7000000e+00   9.0000000e-01   1.7000000e+00   2.0000000e+00   8.0000000e-01   9.0000000e-01   1.6000000e+00   1.8000000e+00   2.1000000e+00   2.4000000e+00   1.6000000e+00   1.1000000e+00   1.6000000e+00   2.1000000e+00   1.6000000e+00   1.5000000e+00   8.0000000e-01   1.4000000e+00   1.6000000e+00   1.3000000e+00   1.1000000e+00   1.9000000e+00   1.7000000e+00   1.3000000e+00   1.0000000e+00   1.2000000e+00   1.4000000e+00   1.1000000e+00   1.1000000e+00   6.0000000e-01   5.0000000e-01   6.0000000e-01   7.0000000e-01   8.0000000e-01   4.0000000e-01   7.0000000e-01   4.0000000e-01   2.0000000e-01   4.0000000e-01   5.0000000e-01   7.0000000e-01   6.0000000e-01   2.0000000e-01   1.2000000e+00   9.0000000e-01   1.0000000e+00   8.0000000e-01   4.0000000e-01   7.0000000e-01   5.0000000e-01   6.0000000e-01   6.0000000e-01   6.0000000e-01   7.0000000e-01   6.0000000e-01   1.0000000e-01   7.0000000e-01   1.4000000e+00   5.0000000e-01   5.0000000e-01   5.0000000e-01   4.0000000e-01   1.7000000e+00   6.0000000e-01   1.3000000e+00   5.0000000e-01   1.2000000e+00   9.0000000e-01   1.1000000e+00   1.9000000e+00   1.2000000e+00   1.6000000e+00   1.1000000e+00   1.4000000e+00   6.0000000e-01   6.0000000e-01   8.0000000e-01   6.0000000e-01   1.0000000e+00   9.0000000e-01   8.0000000e-01   2.0000000e+00   2.2000000e+00   7.0000000e-01   1.0000000e+00   6.0000000e-01   2.0000000e+00   4.0000000e-01   1.0000000e+00   1.3000000e+00   4.0000000e-01   4.0000000e-01   9.0000000e-01   1.1000000e+00   1.4000000e+00   1.8000000e+00   9.0000000e-01   4.0000000e-01   9.0000000e-01   1.6000000e+00   1.0000000e+00   8.0000000e-01   4.0000000e-01   8.0000000e-01   1.0000000e+00   9.0000000e-01   5.0000000e-01   1.2000000e+00   1.1000000e+00   9.0000000e-01   5.0000000e-01   6.0000000e-01   9.0000000e-01   4.0000000e-01   1.1000000e+00   9.0000000e-01   5.0000000e-01   9.0000000e-01   4.0000000e-01   1.2000000e+00   5.0000000e-01   1.3000000e+00   1.1000000e+00   8.0000000e-01   1.0000000e+00   1.2000000e+00   1.4000000e+00   9.0000000e-01   3.0000000e-01   5.0000000e-01   5.0000000e-01   3.0000000e-01   1.5000000e+00   9.0000000e-01   9.0000000e-01   1.1000000e+00   8.0000000e-01   5.0000000e-01   4.0000000e-01   8.0000000e-01   1.0000000e+00   4.0000000e-01   6.0000000e-01   6.0000000e-01   6.0000000e-01   6.0000000e-01   7.0000000e-01   6.0000000e-01   5.0000000e-01   2.4000000e+00   1.5000000e+00   2.3000000e+00   2.0000000e+00   2.2000000e+00   3.0000000e+00   9.0000000e-01   2.7000000e+00   2.2000000e+00   2.5000000e+00   1.5000000e+00   1.7000000e+00   1.9000000e+00   1.4000000e+00   1.5000000e+00   1.7000000e+00   1.9000000e+00   3.1000000e+00   3.3000000e+00   1.4000000e+00   2.1000000e+00   1.3000000e+00   3.1000000e+00   1.3000000e+00   2.1000000e+00   2.4000000e+00   1.2000000e+00   1.3000000e+00   2.0000000e+00   2.2000000e+00   2.5000000e+00   2.8000000e+00   2.0000000e+00   1.5000000e+00   2.0000000e+00   2.5000000e+00   2.0000000e+00   1.9000000e+00   1.2000000e+00   1.8000000e+00   2.0000000e+00   1.5000000e+00   1.5000000e+00   2.3000000e+00   2.1000000e+00   1.6000000e+00   1.4000000e+00   1.6000000e+00   1.8000000e+00   1.5000000e+00   1.1000000e+00   9.0000000e-01   9.0000000e-01   1.1000000e+00   8.0000000e-01   6.0000000e-01   6.0000000e-01   6.0000000e-01   3.0000000e-01   1.0000000e-01   4.0000000e-01   6.0000000e-01   7.0000000e-01   1.0000000e+00   1.2000000e+00   1.2000000e+00   9.0000000e-01   7.0000000e-01   1.3000000e+00   7.0000000e-01   3.0000000e-01   8.0000000e-01   1.1000000e+00   1.2000000e+00   1.2000000e+00   6.0000000e-01   9.0000000e-01   1.7000000e+00   1.1000000e+00   1.0000000e+00   1.0000000e+00   5.0000000e-01   1.6000000e+00   1.0000000e+00   1.6000000e+00   9.0000000e-01   1.5000000e+00   1.2000000e+00   1.4000000e+00   2.2000000e+00   1.8000000e+00   1.9000000e+00   1.4000000e+00   1.7000000e+00   7.0000000e-01   9.0000000e-01   1.1000000e+00   1.0000000e+00   1.0000000e+00   9.0000000e-01   1.1000000e+00   2.3000000e+00   2.5000000e+00   9.0000000e-01   1.3000000e+00   1.1000000e+00   2.3000000e+00   5.0000000e-01   1.3000000e+00   1.6000000e+00   5.0000000e-01   6.0000000e-01   1.2000000e+00   1.4000000e+00   1.7000000e+00   2.0000000e+00   1.2000000e+00   7.0000000e-01   1.2000000e+00   1.7000000e+00   1.2000000e+00   1.1000000e+00   7.0000000e-01   1.0000000e+00   1.2000000e+00   9.0000000e-01   9.0000000e-01   1.5000000e+00   1.3000000e+00   9.0000000e-01   6.0000000e-01   8.0000000e-01   1.0000000e+00   8.0000000e-01   5.0000000e-01   8.0000000e-01   6.0000000e-01   3.0000000e-01   5.0000000e-01   7.0000000e-01   5.0000000e-01   8.0000000e-01   1.0000000e+00   1.2000000e+00   1.1000000e+00   4.0000000e-01   1.0000000e+00   7.0000000e-01   8.0000000e-01   6.0000000e-01   6.0000000e-01   2.0000000e-01   4.0000000e-01   1.1000000e+00   7.0000000e-01   4.0000000e-01   5.0000000e-01   4.0000000e-01   5.0000000e-01   5.0000000e-01   1.2000000e+00   3.0000000e-01   3.0000000e-01   3.0000000e-01   6.0000000e-01   1.5000000e+00   4.0000000e-01   1.5000000e+00   6.0000000e-01   1.5000000e+00   1.1000000e+00   1.3000000e+00   2.1000000e+00   7.0000000e-01   1.8000000e+00   1.3000000e+00   1.6000000e+00   9.0000000e-01   8.0000000e-01   1.2000000e+00   5.0000000e-01   9.0000000e-01   8.0000000e-01   1.0000000e+00   2.2000000e+00   2.4000000e+00   8.0000000e-01   1.3000000e+00   5.0000000e-01   2.2000000e+00   7.0000000e-01   1.2000000e+00   1.6000000e+00   6.0000000e-01   5.0000000e-01   1.1000000e+00   1.6000000e+00   1.8000000e+00   2.3000000e+00   1.1000000e+00   7.0000000e-01   1.1000000e+00   2.1000000e+00   1.1000000e+00   1.0000000e+00   4.0000000e-01   1.3000000e+00   1.1000000e+00   1.3000000e+00   6.0000000e-01   1.4000000e+00   1.2000000e+00   1.1000000e+00   7.0000000e-01   9.0000000e-01   9.0000000e-01   6.0000000e-01   5.0000000e-01   2.0000000e-01   8.0000000e-01   3.0000000e-01   8.0000000e-01   6.0000000e-01   6.0000000e-01   8.0000000e-01   1.0000000e+00   9.0000000e-01   5.0000000e-01   6.0000000e-01   3.0000000e-01   4.0000000e-01   2.0000000e-01   1.0000000e+00   5.0000000e-01   7.0000000e-01   9.0000000e-01   5.0000000e-01   3.0000000e-01   3.0000000e-01   3.0000000e-01   5.0000000e-01   2.0000000e-01   8.0000000e-01   3.0000000e-01   3.0000000e-01   3.0000000e-01   4.0000000e-01   1.1000000e+00   3.0000000e-01   1.9000000e+00   1.0000000e+00   1.8000000e+00   1.5000000e+00   1.7000000e+00   2.5000000e+00   9.0000000e-01   2.2000000e+00   1.7000000e+00   2.0000000e+00   1.0000000e+00   1.2000000e+00   1.4000000e+00   1.0000000e+00   1.4000000e+00   1.3000000e+00   1.4000000e+00   2.6000000e+00   2.8000000e+00   9.0000000e-01   1.6000000e+00   1.0000000e+00   2.6000000e+00   8.0000000e-01   1.6000000e+00   1.9000000e+00   8.0000000e-01   8.0000000e-01   1.5000000e+00   1.7000000e+00   2.0000000e+00   2.3000000e+00   1.5000000e+00   1.0000000e+00   1.5000000e+00   2.0000000e+00   1.5000000e+00   1.4000000e+00   8.0000000e-01   1.3000000e+00   1.5000000e+00   1.3000000e+00   1.0000000e+00   1.8000000e+00   1.6000000e+00   1.3000000e+00   9.0000000e-01   1.1000000e+00   1.3000000e+00   1.0000000e+00   6.0000000e-01   1.0000000e+00   6.0000000e-01   4.0000000e-01   6.0000000e-01   7.0000000e-01   8.0000000e-01   6.0000000e-01   8.0000000e-01   7.0000000e-01   1.0000000e+00   7.0000000e-01   8.0000000e-01   6.0000000e-01   6.0000000e-01   8.0000000e-01   1.2000000e+00   9.0000000e-01   2.0000000e-01   8.0000000e-01   7.0000000e-01   7.0000000e-01   8.0000000e-01   5.0000000e-01   1.2000000e+00   6.0000000e-01   8.0000000e-01   7.0000000e-01   7.0000000e-01   1.5000000e+00   6.0000000e-01   1.5000000e+00   6.0000000e-01   1.4000000e+00   1.1000000e+00   1.3000000e+00   2.1000000e+00   1.3000000e+00   1.8000000e+00   1.3000000e+00   1.6000000e+00   1.0000000e+00   8.0000000e-01   1.0000000e+00   5.0000000e-01   9.0000000e-01   1.0000000e+00   1.0000000e+00   2.2000000e+00   2.4000000e+00   5.0000000e-01   1.2000000e+00   6.0000000e-01   2.2000000e+00   5.0000000e-01   1.2000000e+00   1.5000000e+00   6.0000000e-01   8.0000000e-01   1.1000000e+00   1.3000000e+00   1.6000000e+00   1.9000000e+00   1.1000000e+00   6.0000000e-01   1.1000000e+00   1.6000000e+00   1.2000000e+00   1.0000000e+00   8.0000000e-01   9.0000000e-01   1.1000000e+00   9.0000000e-01   6.0000000e-01   1.4000000e+00   1.2000000e+00   8.0000000e-01   5.0000000e-01   8.0000000e-01   1.2000000e+00   8.0000000e-01   9.0000000e-01   5.0000000e-01   1.0000000e+00   8.0000000e-01   8.0000000e-01   1.0000000e+00   1.2000000e+00   1.1000000e+00   6.0000000e-01   4.0000000e-01   1.0000000e-01   2.0000000e-01   2.0000000e-01   1.2000000e+00   6.0000000e-01   9.0000000e-01   1.1000000e+00   7.0000000e-01   5.0000000e-01   2.0000000e-01   5.0000000e-01   7.0000000e-01   2.0000000e-01   6.0000000e-01   3.0000000e-01   5.0000000e-01   4.0000000e-01   6.0000000e-01   9.0000000e-01   3.0000000e-01   2.1000000e+00   1.2000000e+00   2.0000000e+00   1.7000000e+00   1.9000000e+00   2.7000000e+00   7.0000000e-01   2.4000000e+00   1.9000000e+00   2.2000000e+00   1.2000000e+00   1.4000000e+00   1.6000000e+00   1.1000000e+00   1.3000000e+00   1.4000000e+00   1.6000000e+00   2.8000000e+00   3.0000000e+00   1.1000000e+00   1.8000000e+00   1.0000000e+00   2.8000000e+00   1.0000000e+00   1.8000000e+00   2.1000000e+00   9.0000000e-01   1.0000000e+00   1.7000000e+00   1.9000000e+00   2.2000000e+00   2.5000000e+00   1.7000000e+00   1.2000000e+00   1.7000000e+00   2.2000000e+00   1.7000000e+00   1.6000000e+00   9.0000000e-01   1.5000000e+00   1.7000000e+00   1.3000000e+00   1.2000000e+00   2.0000000e+00   1.8000000e+00   1.3000000e+00   1.1000000e+00   1.3000000e+00   1.5000000e+00   1.2000000e+00   8.0000000e-01   7.0000000e-01   6.0000000e-01   5.0000000e-01   7.0000000e-01   9.0000000e-01   8.0000000e-01   3.0000000e-01   1.3000000e+00   1.0000000e+00   1.1000000e+00   9.0000000e-01   5.0000000e-01   5.0000000e-01   3.0000000e-01   8.0000000e-01   9.0000000e-01   7.0000000e-01   8.0000000e-01   6.0000000e-01   4.0000000e-01   8.0000000e-01   1.5000000e+00   6.0000000e-01   6.0000000e-01   6.0000000e-01   5.0000000e-01   1.8000000e+00   7.0000000e-01   1.2000000e+00   5.0000000e-01   1.2000000e+00   8.0000000e-01   1.0000000e+00   1.8000000e+00   1.0000000e+00   1.5000000e+00   1.0000000e+00   1.3000000e+00   6.0000000e-01   5.0000000e-01   9.0000000e-01   7.0000000e-01   6.0000000e-01   5.0000000e-01   7.0000000e-01   1.9000000e+00   2.1000000e+00   1.0000000e+00   1.0000000e+00   4.0000000e-01   1.9000000e+00   5.0000000e-01   9.0000000e-01   1.3000000e+00   4.0000000e-01   2.0000000e-01   8.0000000e-01   1.3000000e+00   1.5000000e+00   2.0000000e+00   8.0000000e-01   4.0000000e-01   8.0000000e-01   1.8000000e+00   8.0000000e-01   7.0000000e-01   2.0000000e-01   1.0000000e+00   8.0000000e-01   1.0000000e+00   5.0000000e-01   1.1000000e+00   9.0000000e-01   8.0000000e-01   7.0000000e-01   6.0000000e-01   6.0000000e-01   3.0000000e-01   9.0000000e-01   7.0000000e-01   3.0000000e-01   5.0000000e-01   8.0000000e-01   1.0000000e+00   5.0000000e-01   5.0000000e-01   6.0000000e-01   6.0000000e-01   3.0000000e-01   1.1000000e+00   7.0000000e-01   6.0000000e-01   7.0000000e-01   5.0000000e-01   5.0000000e-01   6.0000000e-01   6.0000000e-01   6.0000000e-01   3.0000000e-01   1.1000000e+00   5.0000000e-01   4.0000000e-01   4.0000000e-01   3.0000000e-01   1.0000000e+00   4.0000000e-01   2.0000000e+00   1.1000000e+00   1.9000000e+00   1.6000000e+00   1.8000000e+00   2.6000000e+00   1.2000000e+00   2.3000000e+00   1.8000000e+00   2.1000000e+00   1.1000000e+00   1.3000000e+00   1.5000000e+00   1.0000000e+00   1.1000000e+00   1.3000000e+00   1.5000000e+00   2.7000000e+00   2.9000000e+00   1.0000000e+00   1.7000000e+00   9.0000000e-01   2.7000000e+00   9.0000000e-01   1.7000000e+00   2.0000000e+00   8.0000000e-01   9.0000000e-01   1.6000000e+00   1.8000000e+00   2.1000000e+00   2.4000000e+00   1.6000000e+00   1.1000000e+00   1.6000000e+00   2.1000000e+00   1.6000000e+00   1.5000000e+00   8.0000000e-01   1.4000000e+00   1.6000000e+00   1.1000000e+00   1.1000000e+00   1.9000000e+00   1.7000000e+00   1.2000000e+00   1.0000000e+00   1.2000000e+00   1.4000000e+00   1.1000000e+00   3.0000000e-01   6.0000000e-01   5.0000000e-01   5.0000000e-01   5.0000000e-01   4.0000000e-01   1.4000000e+00   1.1000000e+00   1.2000000e+00   1.0000000e+00   3.0000000e-01   9.0000000e-01   9.0000000e-01   6.0000000e-01   5.0000000e-01   8.0000000e-01   9.0000000e-01   8.0000000e-01   5.0000000e-01   9.0000000e-01   1.6000000e+00   7.0000000e-01   7.0000000e-01   7.0000000e-01   6.0000000e-01   1.9000000e+00   8.0000000e-01   1.1000000e+00   5.0000000e-01   1.0000000e+00   7.0000000e-01   9.0000000e-01   1.7000000e+00   1.4000000e+00   1.4000000e+00   9.0000000e-01   1.2000000e+00   7.0000000e-01   4.0000000e-01   6.0000000e-01   6.0000000e-01   9.0000000e-01   8.0000000e-01   6.0000000e-01   1.8000000e+00   2.0000000e+00   3.0000000e-01   8.0000000e-01   7.0000000e-01   1.8000000e+00   3.0000000e-01   8.0000000e-01   1.1000000e+00   3.0000000e-01   5.0000000e-01   7.0000000e-01   9.0000000e-01   1.2000000e+00   1.6000000e+00   7.0000000e-01   3.0000000e-01   7.0000000e-01   1.4000000e+00   9.0000000e-01   6.0000000e-01   5.0000000e-01   6.0000000e-01   9.0000000e-01   8.0000000e-01   5.0000000e-01   1.0000000e+00   1.0000000e+00   8.0000000e-01   4.0000000e-01   5.0000000e-01   9.0000000e-01   5.0000000e-01   4.0000000e-01   5.0000000e-01   7.0000000e-01   6.0000000e-01   3.0000000e-01   1.2000000e+00   9.0000000e-01   1.0000000e+00   8.0000000e-01   4.0000000e-01   7.0000000e-01   6.0000000e-01   6.0000000e-01   5.0000000e-01   6.0000000e-01   7.0000000e-01   6.0000000e-01   2.0000000e-01   7.0000000e-01   1.4000000e+00   5.0000000e-01   5.0000000e-01   5.0000000e-01   4.0000000e-01   1.7000000e+00   6.0000000e-01   1.3000000e+00   7.0000000e-01   1.2000000e+00   9.0000000e-01   1.1000000e+00   1.9000000e+00   1.2000000e+00   1.6000000e+00   1.1000000e+00   1.4000000e+00   8.0000000e-01   7.0000000e-01   9.0000000e-01   8.0000000e-01   1.2000000e+00   1.1000000e+00   8.0000000e-01   2.0000000e+00   2.2000000e+00   6.0000000e-01   1.1000000e+00   8.0000000e-01   2.0000000e+00   6.0000000e-01   1.0000000e+00   1.3000000e+00   6.0000000e-01   6.0000000e-01   9.0000000e-01   1.1000000e+00   1.4000000e+00   1.8000000e+00   1.0000000e+00   4.0000000e-01   9.0000000e-01   1.6000000e+00   1.2000000e+00   8.0000000e-01   6.0000000e-01   9.0000000e-01   1.2000000e+00   1.1000000e+00   7.0000000e-01   1.2000000e+00   1.3000000e+00   1.1000000e+00   7.0000000e-01   8.0000000e-01   1.1000000e+00   6.0000000e-01   2.0000000e-01   5.0000000e-01   7.0000000e-01   4.0000000e-01   8.0000000e-01   9.0000000e-01   9.0000000e-01   6.0000000e-01   8.0000000e-01   1.0000000e+00   5.0000000e-01   4.0000000e-01   6.0000000e-01   8.0000000e-01   9.0000000e-01   9.0000000e-01   3.0000000e-01   6.0000000e-01   1.4000000e+00   8.0000000e-01   7.0000000e-01   7.0000000e-01   2.0000000e-01   1.3000000e+00   7.0000000e-01   1.7000000e+00   8.0000000e-01   1.6000000e+00   1.3000000e+00   1.5000000e+00   2.3000000e+00   1.5000000e+00   2.0000000e+00   1.5000000e+00   1.8000000e+00   8.0000000e-01   1.0000000e+00   1.2000000e+00   7.0000000e-01   1.1000000e+00   1.0000000e+00   1.2000000e+00   2.4000000e+00   2.6000000e+00   7.0000000e-01   1.4000000e+00   8.0000000e-01   2.4000000e+00   6.0000000e-01   1.4000000e+00   1.7000000e+00   5.0000000e-01   6.0000000e-01   1.3000000e+00   1.5000000e+00   1.8000000e+00   2.1000000e+00   1.3000000e+00   8.0000000e-01   1.3000000e+00   1.8000000e+00   1.3000000e+00   1.2000000e+00   5.0000000e-01   1.1000000e+00   1.3000000e+00   1.0000000e+00   8.0000000e-01   1.6000000e+00   1.4000000e+00   1.0000000e+00   7.0000000e-01   9.0000000e-01   1.1000000e+00   8.0000000e-01   4.0000000e-01   6.0000000e-01   6.0000000e-01   9.0000000e-01   1.1000000e+00   1.1000000e+00   8.0000000e-01   7.0000000e-01   1.2000000e+00   6.0000000e-01   3.0000000e-01   7.0000000e-01   1.0000000e+00   1.1000000e+00   1.1000000e+00   5.0000000e-01   8.0000000e-01   1.6000000e+00   1.0000000e+00   9.0000000e-01   9.0000000e-01   4.0000000e-01   1.5000000e+00   9.0000000e-01   1.6000000e+00   8.0000000e-01   1.5000000e+00   1.2000000e+00   1.4000000e+00   2.2000000e+00   1.7000000e+00   1.9000000e+00   1.4000000e+00   1.7000000e+00   7.0000000e-01   9.0000000e-01   1.1000000e+00   9.0000000e-01   1.0000000e+00   9.0000000e-01   1.1000000e+00   2.3000000e+00   2.5000000e+00   8.0000000e-01   1.3000000e+00   1.0000000e+00   2.3000000e+00   5.0000000e-01   1.3000000e+00   1.6000000e+00   4.0000000e-01   5.0000000e-01   1.2000000e+00   1.4000000e+00   1.7000000e+00   2.0000000e+00   1.2000000e+00   7.0000000e-01   1.2000000e+00   1.7000000e+00   1.2000000e+00   1.1000000e+00   6.0000000e-01   1.0000000e+00   1.2000000e+00   9.0000000e-01   8.0000000e-01   1.5000000e+00   1.3000000e+00   9.0000000e-01   6.0000000e-01   8.0000000e-01   1.0000000e+00   7.0000000e-01   3.0000000e-01   8.0000000e-01   1.3000000e+00   1.3000000e+00   1.3000000e+00   1.0000000e+00   8.0000000e-01   1.4000000e+00   8.0000000e-01   3.0000000e-01   5.0000000e-01   1.2000000e+00   1.3000000e+00   1.3000000e+00   7.0000000e-01   1.0000000e+00   1.8000000e+00   1.2000000e+00   1.1000000e+00   1.1000000e+00   6.0000000e-01   1.8000000e+00   1.1000000e+00   1.2000000e+00   1.0000000e+00   1.1000000e+00   8.0000000e-01   1.0000000e+00   1.8000000e+00   1.9000000e+00   1.5000000e+00   1.0000000e+00   1.3000000e+00   6.0000000e-01   5.0000000e-01   7.0000000e-01   1.1000000e+00   1.0000000e+00   9.0000000e-01   7.0000000e-01   1.9000000e+00   2.1000000e+00   8.0000000e-01   9.0000000e-01   1.2000000e+00   1.9000000e+00   5.0000000e-01   9.0000000e-01   1.2000000e+00   6.0000000e-01   7.0000000e-01   8.0000000e-01   1.0000000e+00   1.3000000e+00   1.6000000e+00   8.0000000e-01   5.0000000e-01   8.0000000e-01   1.3000000e+00   1.0000000e+00   7.0000000e-01   8.0000000e-01   7.0000000e-01   1.0000000e+00   9.0000000e-01   1.0000000e+00   1.1000000e+00   1.1000000e+00   9.0000000e-01   5.0000000e-01   6.0000000e-01   9.0000000e-01   9.0000000e-01   7.0000000e-01   1.5000000e+00   1.2000000e+00   1.3000000e+00   1.1000000e+00   7.0000000e-01   1.3000000e+00   7.0000000e-01   3.0000000e-01   7.0000000e-01   1.1000000e+00   1.2000000e+00   1.2000000e+00   6.0000000e-01   1.0000000e+00   1.7000000e+00   1.1000000e+00   1.0000000e+00   1.0000000e+00   7.0000000e-01   2.0000000e+00   1.0000000e+00   1.0000000e+00   9.0000000e-01   9.0000000e-01   6.0000000e-01   8.0000000e-01   1.6000000e+00   1.8000000e+00   1.3000000e+00   8.0000000e-01   1.1000000e+00   3.0000000e-01   3.0000000e-01   5.0000000e-01   1.0000000e+00   9.0000000e-01   6.0000000e-01   5.0000000e-01   1.7000000e+00   1.9000000e+00   8.0000000e-01   7.0000000e-01   1.1000000e+00   1.7000000e+00   4.0000000e-01   7.0000000e-01   1.0000000e+00   5.0000000e-01   6.0000000e-01   6.0000000e-01   8.0000000e-01   1.1000000e+00   1.4000000e+00   6.0000000e-01   4.0000000e-01   6.0000000e-01   1.1000000e+00   7.0000000e-01   5.0000000e-01   7.0000000e-01   4.0000000e-01   7.0000000e-01   6.0000000e-01   9.0000000e-01   9.0000000e-01   8.0000000e-01   6.0000000e-01   5.0000000e-01   3.0000000e-01   6.0000000e-01   8.0000000e-01   1.0000000e+00   7.0000000e-01   8.0000000e-01   6.0000000e-01   6.0000000e-01   6.0000000e-01   5.0000000e-01   7.0000000e-01   6.0000000e-01   4.0000000e-01   5.0000000e-01   5.0000000e-01   1.0000000e-01   5.0000000e-01   1.2000000e+00   4.0000000e-01   3.0000000e-01   3.0000000e-01   2.0000000e-01   1.5000000e+00   4.0000000e-01   1.5000000e+00   6.0000000e-01   1.4000000e+00   1.1000000e+00   1.3000000e+00   2.1000000e+00   1.1000000e+00   1.8000000e+00   1.3000000e+00   1.6000000e+00   6.0000000e-01   8.0000000e-01   1.0000000e+00   5.0000000e-01   9.0000000e-01   8.0000000e-01   1.0000000e+00   2.2000000e+00   2.4000000e+00   7.0000000e-01   1.2000000e+00   5.0000000e-01   2.2000000e+00   4.0000000e-01   1.2000000e+00   1.5000000e+00   3.0000000e-01   4.0000000e-01   1.1000000e+00   1.3000000e+00   1.6000000e+00   1.9000000e+00   1.1000000e+00   6.0000000e-01   1.1000000e+00   1.7000000e+00   1.1000000e+00   1.0000000e+00   3.0000000e-01   9.0000000e-01   1.1000000e+00   9.0000000e-01   6.0000000e-01   1.4000000e+00   1.2000000e+00   8.0000000e-01   5.0000000e-01   7.0000000e-01   9.0000000e-01   6.0000000e-01   3.0000000e-01   2.0000000e-01   4.0000000e-01   1.6000000e+00   1.0000000e+00   1.0000000e+00   1.2000000e+00   9.0000000e-01   6.0000000e-01   5.0000000e-01   9.0000000e-01   1.1000000e+00   5.0000000e-01   7.0000000e-01   7.0000000e-01   7.0000000e-01   7.0000000e-01   8.0000000e-01   6.0000000e-01   6.0000000e-01   2.5000000e+00   1.6000000e+00   2.4000000e+00   2.1000000e+00   2.3000000e+00   3.1000000e+00   1.0000000e+00   2.8000000e+00   2.3000000e+00   2.6000000e+00   1.6000000e+00   1.8000000e+00   2.0000000e+00   1.5000000e+00   1.6000000e+00   1.8000000e+00   2.0000000e+00   3.2000000e+00   3.4000000e+00   1.5000000e+00   2.2000000e+00   1.4000000e+00   3.2000000e+00   1.4000000e+00   2.2000000e+00   2.5000000e+00   1.3000000e+00   1.4000000e+00   2.1000000e+00   2.3000000e+00   2.6000000e+00   2.9000000e+00   2.1000000e+00   1.6000000e+00   2.1000000e+00   2.6000000e+00   2.1000000e+00   2.0000000e+00   1.3000000e+00   1.9000000e+00   2.1000000e+00   1.6000000e+00   1.6000000e+00   2.4000000e+00   2.2000000e+00   1.7000000e+00   1.5000000e+00   1.7000000e+00   1.9000000e+00   1.6000000e+00   1.0000000e-01   3.0000000e-01   1.3000000e+00   7.0000000e-01   1.0000000e+00   1.2000000e+00   8.0000000e-01   6.0000000e-01   2.0000000e-01   6.0000000e-01   8.0000000e-01   3.0000000e-01   5.0000000e-01   4.0000000e-01   6.0000000e-01   5.0000000e-01   7.0000000e-01   8.0000000e-01   4.0000000e-01   2.2000000e+00   1.3000000e+00   2.1000000e+00   1.8000000e+00   2.0000000e+00   2.8000000e+00   7.0000000e-01   2.5000000e+00   2.0000000e+00   2.3000000e+00   1.3000000e+00   1.5000000e+00   1.7000000e+00   1.2000000e+00   1.3000000e+00   1.5000000e+00   1.7000000e+00   2.9000000e+00   3.1000000e+00   1.2000000e+00   1.9000000e+00   1.1000000e+00   2.9000000e+00   1.1000000e+00   1.9000000e+00   2.2000000e+00   1.0000000e+00   1.1000000e+00   1.8000000e+00   2.0000000e+00   2.3000000e+00   2.6000000e+00   1.8000000e+00   1.3000000e+00   1.8000000e+00   2.3000000e+00   1.8000000e+00   1.7000000e+00   1.0000000e+00   1.6000000e+00   1.8000000e+00   1.4000000e+00   1.3000000e+00   2.1000000e+00   1.9000000e+00   1.4000000e+00   1.2000000e+00   1.4000000e+00   1.6000000e+00   1.3000000e+00   3.0000000e-01   1.4000000e+00   8.0000000e-01   1.0000000e+00   1.2000000e+00   8.0000000e-01   6.0000000e-01   3.0000000e-01   7.0000000e-01   9.0000000e-01   3.0000000e-01   5.0000000e-01   5.0000000e-01   6.0000000e-01   5.0000000e-01   7.0000000e-01   7.0000000e-01   4.0000000e-01   2.3000000e+00   1.4000000e+00   2.2000000e+00   1.9000000e+00   2.1000000e+00   2.9000000e+00   8.0000000e-01   2.6000000e+00   2.1000000e+00   2.4000000e+00   1.4000000e+00   1.6000000e+00   1.8000000e+00   1.3000000e+00   1.4000000e+00   1.6000000e+00   1.8000000e+00   3.0000000e+00   3.2000000e+00   1.3000000e+00   2.0000000e+00   1.2000000e+00   3.0000000e+00   1.2000000e+00   2.0000000e+00   2.3000000e+00   1.1000000e+00   1.2000000e+00   1.9000000e+00   2.1000000e+00   2.4000000e+00   2.7000000e+00   1.9000000e+00   1.4000000e+00   1.9000000e+00   2.4000000e+00   1.9000000e+00   1.8000000e+00   1.1000000e+00   1.7000000e+00   1.9000000e+00   1.4000000e+00   1.4000000e+00   2.2000000e+00   2.0000000e+00   1.5000000e+00   1.3000000e+00   1.5000000e+00   1.7000000e+00   1.4000000e+00   1.2000000e+00   6.0000000e-01   7.0000000e-01   9.0000000e-01   5.0000000e-01   3.0000000e-01   3.0000000e-01   5.0000000e-01   7.0000000e-01   1.0000000e-01   8.0000000e-01   3.0000000e-01   3.0000000e-01   3.0000000e-01   4.0000000e-01   9.0000000e-01   2.0000000e-01   2.1000000e+00   1.2000000e+00   2.0000000e+00   1.7000000e+00   1.9000000e+00   2.7000000e+00   9.0000000e-01   2.4000000e+00   1.9000000e+00   2.2000000e+00   1.2000000e+00   1.4000000e+00   1.6000000e+00   1.1000000e+00   1.2000000e+00   1.4000000e+00   1.6000000e+00   2.8000000e+00   3.0000000e+00   1.1000000e+00   1.8000000e+00   1.0000000e+00   2.8000000e+00   1.0000000e+00   1.8000000e+00   2.1000000e+00   9.0000000e-01   1.0000000e+00   1.7000000e+00   1.9000000e+00   2.2000000e+00   2.5000000e+00   1.7000000e+00   1.2000000e+00   1.7000000e+00   2.2000000e+00   1.7000000e+00   1.6000000e+00   9.0000000e-01   1.5000000e+00   1.7000000e+00   1.2000000e+00   1.2000000e+00   2.0000000e+00   1.8000000e+00   1.3000000e+00   1.1000000e+00   1.3000000e+00   1.5000000e+00   1.2000000e+00   6.0000000e-01   7.0000000e-01   7.0000000e-01   7.0000000e-01   1.0000000e+00   1.1000000e+00   7.0000000e-01   5.0000000e-01   1.1000000e+00   1.8000000e+00   9.0000000e-01   9.0000000e-01   9.0000000e-01   8.0000000e-01   2.1000000e+00   1.0000000e+00   9.0000000e-01   3.0000000e-01   1.1000000e+00   5.0000000e-01   7.0000000e-01   1.6000000e+00   1.1000000e+00   1.3000000e+00   7.0000000e-01   1.2000000e+00   5.0000000e-01   4.0000000e-01   8.0000000e-01   4.0000000e-01   8.0000000e-01   7.0000000e-01   5.0000000e-01   1.7000000e+00   1.8000000e+00   5.0000000e-01   9.0000000e-01   4.0000000e-01   1.7000000e+00   3.0000000e-01   7.0000000e-01   1.2000000e+00   3.0000000e-01   3.0000000e-01   5.0000000e-01   1.2000000e+00   1.4000000e+00   1.9000000e+00   6.0000000e-01   3.0000000e-01   5.0000000e-01   1.7000000e+00   8.0000000e-01   4.0000000e-01   3.0000000e-01   9.0000000e-01   8.0000000e-01   9.0000000e-01   3.0000000e-01   8.0000000e-01   9.0000000e-01   7.0000000e-01   3.0000000e-01   5.0000000e-01   7.0000000e-01   3.0000000e-01   6.0000000e-01   1.3000000e+00   9.0000000e-01   4.0000000e-01   5.0000000e-01   4.0000000e-01   7.0000000e-01   5.0000000e-01   1.2000000e+00   3.0000000e-01   3.0000000e-01   3.0000000e-01   8.0000000e-01   1.5000000e+00   4.0000000e-01   1.5000000e+00   6.0000000e-01   1.7000000e+00   1.1000000e+00   1.3000000e+00   2.2000000e+00   5.0000000e-01   1.9000000e+00   1.3000000e+00   1.8000000e+00   1.1000000e+00   1.0000000e+00   1.4000000e+00   5.0000000e-01   9.0000000e-01   1.0000000e+00   1.1000000e+00   2.3000000e+00   2.4000000e+00   8.0000000e-01   1.5000000e+00   5.0000000e-01   2.3000000e+00   9.0000000e-01   1.3000000e+00   1.8000000e+00   8.0000000e-01   7.0000000e-01   1.1000000e+00   1.8000000e+00   2.0000000e+00   2.5000000e+00   1.1000000e+00   9.0000000e-01   1.1000000e+00   2.3000000e+00   1.1000000e+00   1.0000000e+00   6.0000000e-01   1.5000000e+00   1.3000000e+00   1.5000000e+00   6.0000000e-01   1.4000000e+00   1.3000000e+00   1.3000000e+00   9.0000000e-01   1.1000000e+00   9.0000000e-01   6.0000000e-01   7.0000000e-01   1.1000000e+00   4.0000000e-01   9.0000000e-01   8.0000000e-01   4.0000000e-01   8.0000000e-01   1.2000000e+00   7.0000000e-01   4.0000000e-01   5.0000000e-01   5.0000000e-01   1.5000000e+00   6.0000000e-01   1.5000000e+00   7.0000000e-01   1.4000000e+00   1.1000000e+00   1.3000000e+00   2.1000000e+00   1.1000000e+00   1.8000000e+00   1.3000000e+00   1.6000000e+00   6.0000000e-01   8.0000000e-01   1.0000000e+00   9.0000000e-01   8.0000000e-01   8.0000000e-01   1.0000000e+00   2.2000000e+00   2.4000000e+00   1.2000000e+00   1.2000000e+00   6.0000000e-01   2.2000000e+00   7.0000000e-01   1.2000000e+00   1.5000000e+00   6.0000000e-01   4.0000000e-01   1.1000000e+00   1.3000000e+00   1.6000000e+00   1.9000000e+00   1.1000000e+00   6.0000000e-01   1.1000000e+00   1.7000000e+00   1.1000000e+00   1.0000000e+00   4.0000000e-01   9.0000000e-01   1.1000000e+00   9.0000000e-01   7.0000000e-01   1.4000000e+00   1.2000000e+00   7.0000000e-01   9.0000000e-01   7.0000000e-01   9.0000000e-01   6.0000000e-01   8.0000000e-01   1.1000000e+00   1.2000000e+00   1.2000000e+00   6.0000000e-01   9.0000000e-01   1.7000000e+00   1.1000000e+00   1.0000000e+00   1.0000000e+00   5.0000000e-01   1.7000000e+00   1.0000000e+00   1.3000000e+00   9.0000000e-01   1.2000000e+00   9.0000000e-01   1.1000000e+00   1.9000000e+00   1.8000000e+00   1.6000000e+00   1.1000000e+00   1.4000000e+00   5.0000000e-01   6.0000000e-01   8.0000000e-01   1.0000000e+00   9.0000000e-01   8.0000000e-01   8.0000000e-01   2.0000000e+00   2.2000000e+00   9.0000000e-01   1.0000000e+00   1.1000000e+00   2.0000000e+00   4.0000000e-01   1.0000000e+00   1.3000000e+00   5.0000000e-01   6.0000000e-01   9.0000000e-01   1.1000000e+00   1.4000000e+00   1.7000000e+00   9.0000000e-01   4.0000000e-01   9.0000000e-01   1.4000000e+00   9.0000000e-01   8.0000000e-01   7.0000000e-01   7.0000000e-01   9.0000000e-01   8.0000000e-01   9.0000000e-01   1.2000000e+00   1.0000000e+00   8.0000000e-01   6.0000000e-01   5.0000000e-01   8.0000000e-01   8.0000000e-01   7.0000000e-01   8.0000000e-01   8.0000000e-01   7.0000000e-01   5.0000000e-01   1.3000000e+00   7.0000000e-01   7.0000000e-01   6.0000000e-01   6.0000000e-01   1.4000000e+00   6.0000000e-01   1.6000000e+00   7.0000000e-01   1.5000000e+00   1.2000000e+00   1.4000000e+00   2.2000000e+00   1.4000000e+00   1.9000000e+00   1.4000000e+00   1.7000000e+00   9.0000000e-01   9.0000000e-01   1.1000000e+00   7.0000000e-01   1.1000000e+00   1.0000000e+00   1.1000000e+00   2.3000000e+00   2.5000000e+00   6.0000000e-01   1.3000000e+00   7.0000000e-01   2.3000000e+00   5.0000000e-01   1.3000000e+00   1.6000000e+00   5.0000000e-01   7.0000000e-01   1.2000000e+00   1.4000000e+00   1.7000000e+00   2.0000000e+00   1.2000000e+00   7.0000000e-01   1.2000000e+00   1.7000000e+00   1.2000000e+00   1.1000000e+00   7.0000000e-01   1.0000000e+00   1.2000000e+00   1.0000000e+00   7.0000000e-01   1.5000000e+00   1.3000000e+00   1.0000000e+00   6.0000000e-01   8.0000000e-01   1.1000000e+00   7.0000000e-01   5.0000000e-01   4.0000000e-01   5.0000000e-01   4.0000000e-01   8.0000000e-01   3.0000000e-01   1.0000000e-01   1.0000000e-01   6.0000000e-01   1.1000000e+00   2.0000000e-01   1.9000000e+00   1.0000000e+00   1.8000000e+00   1.5000000e+00   1.7000000e+00   2.5000000e+00   7.0000000e-01   2.2000000e+00   1.7000000e+00   2.0000000e+00   1.0000000e+00   1.2000000e+00   1.4000000e+00   9.0000000e-01   1.1000000e+00   1.2000000e+00   1.4000000e+00   2.6000000e+00   2.8000000e+00   9.0000000e-01   1.6000000e+00   8.0000000e-01   2.6000000e+00   8.0000000e-01   1.6000000e+00   1.9000000e+00   7.0000000e-01   8.0000000e-01   1.5000000e+00   1.7000000e+00   2.0000000e+00   2.3000000e+00   1.5000000e+00   1.0000000e+00   1.5000000e+00   2.1000000e+00   1.5000000e+00   1.4000000e+00   7.0000000e-01   1.3000000e+00   1.5000000e+00   1.3000000e+00   1.0000000e+00   1.8000000e+00   1.6000000e+00   1.1000000e+00   9.0000000e-01   1.1000000e+00   1.3000000e+00   1.0000000e+00   4.0000000e-01   6.0000000e-01   3.0000000e-01   7.0000000e-01   2.0000000e-01   5.0000000e-01   4.0000000e-01   7.0000000e-01   1.0000000e+00   3.0000000e-01   2.0000000e+00   1.1000000e+00   1.9000000e+00   1.6000000e+00   1.8000000e+00   2.6000000e+00   6.0000000e-01   2.3000000e+00   1.8000000e+00   2.1000000e+00   1.1000000e+00   1.3000000e+00   1.5000000e+00   1.0000000e+00   1.1000000e+00   1.3000000e+00   1.5000000e+00   2.7000000e+00   2.9000000e+00   1.0000000e+00   1.7000000e+00   9.0000000e-01   2.7000000e+00   9.0000000e-01   1.7000000e+00   2.0000000e+00   8.0000000e-01   9.0000000e-01   1.6000000e+00   1.8000000e+00   2.1000000e+00   2.4000000e+00   1.6000000e+00   1.1000000e+00   1.6000000e+00   2.2000000e+00   1.6000000e+00   1.5000000e+00   8.0000000e-01   1.4000000e+00   1.6000000e+00   1.4000000e+00   1.1000000e+00   1.9000000e+00   1.7000000e+00   1.2000000e+00   1.0000000e+00   1.2000000e+00   1.4000000e+00   1.1000000e+00   6.0000000e-01   4.0000000e-01   1.1000000e+00   2.0000000e-01   4.0000000e-01   3.0000000e-01   7.0000000e-01   1.4000000e+00   3.0000000e-01   1.6000000e+00   7.0000000e-01   1.6000000e+00   1.2000000e+00   1.4000000e+00   2.2000000e+00   6.0000000e-01   1.9000000e+00   1.4000000e+00   1.7000000e+00   1.0000000e+00   9.0000000e-01   1.3000000e+00   8.0000000e-01   1.2000000e+00   1.1000000e+00   1.1000000e+00   2.3000000e+00   2.5000000e+00   6.0000000e-01   1.4000000e+00   8.0000000e-01   2.3000000e+00   8.0000000e-01   1.3000000e+00   1.7000000e+00   7.0000000e-01   6.0000000e-01   1.2000000e+00   1.7000000e+00   1.9000000e+00   2.4000000e+00   1.2000000e+00   8.0000000e-01   1.2000000e+00   2.2000000e+00   1.2000000e+00   1.1000000e+00   6.0000000e-01   1.4000000e+00   1.2000000e+00   1.4000000e+00   7.0000000e-01   1.5000000e+00   1.3000000e+00   1.2000000e+00   8.0000000e-01   1.0000000e+00   1.1000000e+00   7.0000000e-01   6.0000000e-01   1.3000000e+00   5.0000000e-01   4.0000000e-01   4.0000000e-01   3.0000000e-01   1.6000000e+00   5.0000000e-01   1.4000000e+00   5.0000000e-01   1.3000000e+00   1.0000000e+00   1.2000000e+00   2.0000000e+00   1.2000000e+00   1.7000000e+00   1.2000000e+00   1.5000000e+00   6.0000000e-01   7.0000000e-01   9.0000000e-01   6.0000000e-01   1.0000000e+00   9.0000000e-01   9.0000000e-01   2.1000000e+00   2.3000000e+00   8.0000000e-01   1.1000000e+00   6.0000000e-01   2.1000000e+00   4.0000000e-01   1.1000000e+00   1.4000000e+00   4.0000000e-01   4.0000000e-01   1.0000000e+00   1.2000000e+00   1.5000000e+00   1.8000000e+00   1.0000000e+00   5.0000000e-01   1.0000000e+00   1.6000000e+00   1.0000000e+00   9.0000000e-01   4.0000000e-01   8.0000000e-01   1.0000000e+00   9.0000000e-01   5.0000000e-01   1.3000000e+00   1.1000000e+00   9.0000000e-01   5.0000000e-01   6.0000000e-01   9.0000000e-01   5.0000000e-01   8.0000000e-01   2.0000000e-01   4.0000000e-01   3.0000000e-01   4.0000000e-01   1.0000000e+00   2.0000000e-01   2.0000000e+00   1.1000000e+00   1.9000000e+00   1.6000000e+00   1.8000000e+00   2.6000000e+00   9.0000000e-01   2.3000000e+00   1.8000000e+00   2.1000000e+00   1.1000000e+00   1.3000000e+00   1.5000000e+00   1.0000000e+00   1.2000000e+00   1.3000000e+00   1.5000000e+00   2.7000000e+00   2.9000000e+00   1.0000000e+00   1.7000000e+00   9.0000000e-01   2.7000000e+00   9.0000000e-01   1.7000000e+00   2.0000000e+00   8.0000000e-01   9.0000000e-01   1.6000000e+00   1.8000000e+00   2.1000000e+00   2.4000000e+00   1.6000000e+00   1.1000000e+00   1.6000000e+00   2.1000000e+00   1.6000000e+00   1.5000000e+00   8.0000000e-01   1.4000000e+00   1.6000000e+00   1.1000000e+00   1.1000000e+00   1.9000000e+00   1.7000000e+00   1.2000000e+00   1.0000000e+00   1.2000000e+00   1.4000000e+00   1.1000000e+00   9.0000000e-01   9.0000000e-01   9.0000000e-01   1.2000000e+00   3.0000000e-01   8.0000000e-01   2.7000000e+00   1.8000000e+00   2.6000000e+00   2.3000000e+00   2.5000000e+00   3.3000000e+00   1.2000000e+00   3.0000000e+00   2.5000000e+00   2.8000000e+00   1.8000000e+00   2.0000000e+00   2.2000000e+00   1.7000000e+00   1.8000000e+00   2.0000000e+00   2.2000000e+00   3.4000000e+00   3.6000000e+00   1.7000000e+00   2.4000000e+00   1.6000000e+00   3.4000000e+00   1.6000000e+00   2.4000000e+00   2.7000000e+00   1.5000000e+00   1.6000000e+00   2.3000000e+00   2.5000000e+00   2.8000000e+00   3.1000000e+00   2.3000000e+00   1.8000000e+00   2.3000000e+00   2.8000000e+00   2.3000000e+00   2.2000000e+00   1.5000000e+00   2.1000000e+00   2.3000000e+00   1.9000000e+00   1.8000000e+00   2.6000000e+00   2.4000000e+00   1.9000000e+00   1.7000000e+00   1.9000000e+00   2.1000000e+00   1.8000000e+00   3.0000000e-01   2.0000000e-01   6.0000000e-01   1.2000000e+00   1.0000000e-01   1.8000000e+00   9.0000000e-01   1.7000000e+00   1.4000000e+00   1.6000000e+00   2.4000000e+00   7.0000000e-01   2.1000000e+00   1.6000000e+00   1.9000000e+00   9.0000000e-01   1.1000000e+00   1.3000000e+00   8.0000000e-01   1.1000000e+00   1.1000000e+00   1.3000000e+00   2.5000000e+00   2.7000000e+00   8.0000000e-01   1.5000000e+00   7.0000000e-01   2.5000000e+00   7.0000000e-01   1.5000000e+00   1.8000000e+00   6.0000000e-01   7.0000000e-01   1.4000000e+00   1.6000000e+00   1.9000000e+00   2.3000000e+00   1.4000000e+00   9.0000000e-01   1.4000000e+00   2.1000000e+00   1.4000000e+00   1.3000000e+00   6.0000000e-01   1.3000000e+00   1.4000000e+00   1.3000000e+00   9.0000000e-01   1.7000000e+00   1.5000000e+00   1.1000000e+00   8.0000000e-01   1.0000000e+00   1.2000000e+00   9.0000000e-01   1.0000000e-01   5.0000000e-01   1.2000000e+00   2.0000000e-01   1.8000000e+00   9.0000000e-01   1.7000000e+00   1.4000000e+00   1.6000000e+00   2.4000000e+00   8.0000000e-01   2.1000000e+00   1.6000000e+00   1.9000000e+00   9.0000000e-01   1.1000000e+00   1.3000000e+00   8.0000000e-01   1.2000000e+00   1.1000000e+00   1.3000000e+00   2.5000000e+00   2.7000000e+00   8.0000000e-01   1.5000000e+00   8.0000000e-01   2.5000000e+00   7.0000000e-01   1.5000000e+00   1.8000000e+00   6.0000000e-01   7.0000000e-01   1.4000000e+00   1.6000000e+00   1.9000000e+00   2.2000000e+00   1.4000000e+00   9.0000000e-01   1.4000000e+00   2.0000000e+00   1.4000000e+00   1.3000000e+00   6.0000000e-01   1.2000000e+00   1.4000000e+00   1.2000000e+00   9.0000000e-01   1.7000000e+00   1.5000000e+00   1.1000000e+00   8.0000000e-01   1.0000000e+00   1.2000000e+00   9.0000000e-01   5.0000000e-01   1.2000000e+00   1.0000000e-01   1.8000000e+00   9.0000000e-01   1.7000000e+00   1.4000000e+00   1.6000000e+00   2.4000000e+00   8.0000000e-01   2.1000000e+00   1.6000000e+00   1.9000000e+00   9.0000000e-01   1.1000000e+00   1.3000000e+00   8.0000000e-01   1.1000000e+00   1.1000000e+00   1.3000000e+00   2.5000000e+00   2.7000000e+00   8.0000000e-01   1.5000000e+00   7.0000000e-01   2.5000000e+00   7.0000000e-01   1.5000000e+00   1.8000000e+00   6.0000000e-01   7.0000000e-01   1.4000000e+00   1.6000000e+00   1.9000000e+00   2.2000000e+00   1.4000000e+00   9.0000000e-01   1.4000000e+00   2.0000000e+00   1.4000000e+00   1.3000000e+00   6.0000000e-01   1.2000000e+00   1.4000000e+00   1.2000000e+00   9.0000000e-01   1.7000000e+00   1.5000000e+00   1.0000000e+00   8.0000000e-01   1.0000000e+00   1.2000000e+00   9.0000000e-01   1.3000000e+00   5.0000000e-01   1.7000000e+00   8.0000000e-01   1.6000000e+00   1.3000000e+00   1.5000000e+00   2.3000000e+00   1.3000000e+00   2.0000000e+00   1.5000000e+00   1.8000000e+00   8.0000000e-01   1.0000000e+00   1.2000000e+00   7.0000000e-01   1.1000000e+00   1.0000000e+00   1.2000000e+00   2.4000000e+00   2.6000000e+00   7.0000000e-01   1.4000000e+00   7.0000000e-01   2.4000000e+00   6.0000000e-01   1.4000000e+00   1.7000000e+00   5.0000000e-01   6.0000000e-01   1.3000000e+00   1.5000000e+00   1.8000000e+00   2.1000000e+00   1.3000000e+00   8.0000000e-01   1.3000000e+00   1.8000000e+00   1.3000000e+00   1.2000000e+00   5.0000000e-01   1.1000000e+00   1.3000000e+00   1.0000000e+00   8.0000000e-01   1.6000000e+00   1.4000000e+00   1.0000000e+00   7.0000000e-01   9.0000000e-01   1.1000000e+00   8.0000000e-01   1.1000000e+00   3.0000000e+00   2.1000000e+00   2.9000000e+00   2.6000000e+00   2.8000000e+00   3.6000000e+00   1.5000000e+00   3.3000000e+00   2.8000000e+00   3.1000000e+00   2.1000000e+00   2.3000000e+00   2.5000000e+00   2.0000000e+00   2.1000000e+00   2.3000000e+00   2.5000000e+00   3.7000000e+00   3.9000000e+00   2.0000000e+00   2.7000000e+00   1.9000000e+00   3.7000000e+00   1.9000000e+00   2.7000000e+00   3.0000000e+00   1.8000000e+00   1.9000000e+00   2.6000000e+00   2.8000000e+00   3.1000000e+00   3.4000000e+00   2.6000000e+00   2.1000000e+00   2.6000000e+00   3.1000000e+00   2.6000000e+00   2.5000000e+00   1.8000000e+00   2.4000000e+00   2.6000000e+00   2.1000000e+00   2.1000000e+00   2.9000000e+00   2.7000000e+00   2.2000000e+00   2.0000000e+00   2.2000000e+00   2.4000000e+00   2.1000000e+00   1.9000000e+00   1.0000000e+00   1.8000000e+00   1.5000000e+00   1.7000000e+00   2.5000000e+00   8.0000000e-01   2.2000000e+00   1.7000000e+00   2.0000000e+00   1.0000000e+00   1.2000000e+00   1.4000000e+00   9.0000000e-01   1.1000000e+00   1.2000000e+00   1.4000000e+00   2.6000000e+00   2.8000000e+00   9.0000000e-01   1.6000000e+00   8.0000000e-01   2.6000000e+00   8.0000000e-01   1.6000000e+00   1.9000000e+00   7.0000000e-01   8.0000000e-01   1.5000000e+00   1.7000000e+00   2.0000000e+00   2.3000000e+00   1.5000000e+00   1.0000000e+00   1.5000000e+00   2.0000000e+00   1.5000000e+00   1.4000000e+00   7.0000000e-01   1.3000000e+00   1.5000000e+00   1.2000000e+00   1.0000000e+00   1.8000000e+00   1.6000000e+00   1.1000000e+00   9.0000000e-01   1.1000000e+00   1.3000000e+00   1.0000000e+00   9.0000000e-01   8.0000000e-01   7.0000000e-01   3.0000000e-01   1.3000000e+00   1.5000000e+00   1.0000000e+00   8.0000000e-01   9.0000000e-01   9.0000000e-01   7.0000000e-01   5.0000000e-01   1.0000000e+00   9.0000000e-01   7.0000000e-01   7.0000000e-01   1.4000000e+00   1.4000000e+00   1.1000000e+00   6.0000000e-01   1.1000000e+00   1.4000000e+00   1.1000000e+00   4.0000000e-01   9.0000000e-01   1.2000000e+00   1.1000000e+00   5.0000000e-01   9.0000000e-01   1.1000000e+00   1.6000000e+00   5.0000000e-01   1.0000000e+00   1.1000000e+00   1.4000000e+00   4.0000000e-01   7.0000000e-01   1.2000000e+00   6.0000000e-01   4.0000000e-01   9.0000000e-01   9.0000000e-01   5.0000000e-01   4.0000000e-01   8.0000000e-01   1.0000000e+00   8.0000000e-01   6.0000000e-01   9.0000000e-01   1.3000000e+00   5.0000000e-01   7.0000000e-01   1.8000000e+00   9.0000000e-01   1.5000000e+00   9.0000000e-01   1.4000000e+00   7.0000000e-01   6.0000000e-01   1.0000000e+00   2.0000000e-01   5.0000000e-01   6.0000000e-01   7.0000000e-01   1.9000000e+00   1.9000000e+00   5.0000000e-01   1.1000000e+00   2.0000000e-01   1.9000000e+00   5.0000000e-01   9.0000000e-01   1.4000000e+00   4.0000000e-01   3.0000000e-01   6.0000000e-01   1.4000000e+00   1.6000000e+00   2.1000000e+00   6.0000000e-01   5.0000000e-01   5.0000000e-01   1.9000000e+00   7.0000000e-01   6.0000000e-01   3.0000000e-01   1.1000000e+00   9.0000000e-01   1.1000000e+00   0.0000000e+00   1.0000000e+00   9.0000000e-01   9.0000000e-01   5.0000000e-01   7.0000000e-01   7.0000000e-01   3.0000000e-01   8.0000000e-01   6.0000000e-01   7.0000000e-01   2.2000000e+00   4.0000000e-01   5.0000000e-01   6.0000000e-01   8.0000000e-01   7.0000000e-01   4.0000000e-01   1.4000000e+00   1.3000000e+00   7.0000000e-01   6.0000000e-01   8.0000000e-01   1.0000000e+00   1.1000000e+00   2.0000000e-01   1.5000000e+00   8.0000000e-01   1.0000000e+00   4.0000000e-01   3.0000000e-01   1.1000000e+00   1.0000000e+00   7.0000000e-01   5.0000000e-01   3.0000000e-01   8.0000000e-01   7.0000000e-01   8.0000000e-01   1.0000000e+00   6.0000000e-01   8.0000000e-01   7.0000000e-01   1.1000000e+00   5.0000000e-01   4.0000000e-01   8.0000000e-01   1.3000000e+00   3.0000000e-01   4.0000000e-01   7.0000000e-01   9.0000000e-01   7.0000000e-01   9.0000000e-01   1.2000000e+00   4.0000000e-01   1.3000000e+00   1.4000000e+00   1.0000000e+00   4.0000000e-01   9.0000000e-01   5.0000000e-01   3.0000000e-01   5.0000000e-01   6.0000000e-01   6.0000000e-01   5.0000000e-01   2.0000000e-01   1.4000000e+00   1.4000000e+00   7.0000000e-01   6.0000000e-01   7.0000000e-01   1.4000000e+00   7.0000000e-01   4.0000000e-01   9.0000000e-01   8.0000000e-01   7.0000000e-01   3.0000000e-01   9.0000000e-01   1.1000000e+00   1.6000000e+00   4.0000000e-01   5.0000000e-01   4.0000000e-01   1.4000000e+00   6.0000000e-01   2.0000000e-01   8.0000000e-01   6.0000000e-01   6.0000000e-01   6.0000000e-01   5.0000000e-01   5.0000000e-01   7.0000000e-01   5.0000000e-01   6.0000000e-01   4.0000000e-01   5.0000000e-01   5.0000000e-01   1.1000000e+00   1.6000000e+00   8.0000000e-01   5.0000000e-01   7.0000000e-01   7.0000000e-01   5.0000000e-01   3.0000000e-01   8.0000000e-01   7.0000000e-01   5.0000000e-01   4.0000000e-01   1.2000000e+00   1.2000000e+00   8.0000000e-01   4.0000000e-01   9.0000000e-01   1.2000000e+00   9.0000000e-01   3.0000000e-01   7.0000000e-01   1.0000000e+00   9.0000000e-01   2.0000000e-01   7.0000000e-01   9.0000000e-01   1.4000000e+00   2.0000000e-01   7.0000000e-01   8.0000000e-01   1.2000000e+00   4.0000000e-01   4.0000000e-01   1.0000000e+00   4.0000000e-01   2.0000000e-01   7.0000000e-01   7.0000000e-01   3.0000000e-01   3.0000000e-01   6.0000000e-01   8.0000000e-01   6.0000000e-01   4.0000000e-01   7.0000000e-01   2.7000000e+00   3.0000000e-01   9.0000000e-01   6.0000000e-01   1.5000000e+00   1.3000000e+00   1.1000000e+00   1.9000000e+00   1.8000000e+00   1.3000000e+00   1.1000000e+00   8.0000000e-01   4.0000000e-01   1.6000000e+00   9.0000000e-01   2.0000000e+00   2.0000000e-01   1.7000000e+00   9.0000000e-01   6.0000000e-01   1.8000000e+00   1.7000000e+00   1.2000000e+00   8.0000000e-01   5.0000000e-01   8.0000000e-01   1.2000000e+00   1.5000000e+00   1.5000000e+00   5.0000000e-01   1.3000000e+00   1.2000000e+00   1.8000000e+00   1.2000000e+00   1.0000000e+00   1.5000000e+00   1.8000000e+00   8.0000000e-01   9.0000000e-01   1.4000000e+00   1.6000000e+00   1.4000000e+00   1.4000000e+00   1.7000000e+00   2.4000000e+00   1.8000000e+00   2.3000000e+00   1.6000000e+00   1.5000000e+00   1.9000000e+00   8.0000000e-01   9.0000000e-01   1.5000000e+00   1.6000000e+00   2.8000000e+00   2.8000000e+00   1.1000000e+00   2.0000000e+00   7.0000000e-01   2.8000000e+00   1.4000000e+00   1.8000000e+00   2.3000000e+00   1.3000000e+00   1.2000000e+00   1.5000000e+00   2.3000000e+00   2.5000000e+00   3.0000000e+00   1.5000000e+00   1.4000000e+00   1.2000000e+00   2.8000000e+00   1.4000000e+00   1.5000000e+00   1.1000000e+00   2.0000000e+00   1.8000000e+00   2.0000000e+00   9.0000000e-01   1.9000000e+00   1.8000000e+00   1.8000000e+00   1.4000000e+00   1.6000000e+00   1.3000000e+00   1.0000000e+00   6.0000000e-01   7.0000000e-01   1.2000000e+00   1.0000000e+00   8.0000000e-01   1.6000000e+00   1.5000000e+00   1.0000000e+00   8.0000000e-01   9.0000000e-01   6.0000000e-01   1.3000000e+00   6.0000000e-01   1.7000000e+00   4.0000000e-01   1.4000000e+00   6.0000000e-01   3.0000000e-01   1.5000000e+00   1.4000000e+00   9.0000000e-01   5.0000000e-01   2.0000000e-01   9.0000000e-01   9.0000000e-01   1.2000000e+00   1.2000000e+00   5.0000000e-01   1.0000000e+00   9.0000000e-01   1.5000000e+00   9.0000000e-01   7.0000000e-01   1.2000000e+00   1.5000000e+00   5.0000000e-01   7.0000000e-01   1.1000000e+00   1.3000000e+00   1.1000000e+00   1.1000000e+00   1.4000000e+00   1.1000000e+00   7.0000000e-01   5.0000000e-01   5.0000000e-01   1.0000000e+00   9.0000000e-01   7.0000000e-01   5.0000000e-01   1.3000000e+00   1.1000000e+00   8.0000000e-01   7.0000000e-01   1.1000000e+00   1.0000000e+00   9.0000000e-01   8.0000000e-01   7.0000000e-01   1.0000000e+00   9.0000000e-01   3.0000000e-01   5.0000000e-01   7.0000000e-01   1.3000000e+00   4.0000000e-01   7.0000000e-01   6.0000000e-01   1.0000000e+00   9.0000000e-01   6.0000000e-01   1.0000000e+00   6.0000000e-01   6.0000000e-01   7.0000000e-01   9.0000000e-01   7.0000000e-01   8.0000000e-01   6.0000000e-01   8.0000000e-01   6.0000000e-01   9.0000000e-01   8.0000000e-01   1.0000000e+00   9.0000000e-01   6.0000000e-01   1.5000000e+00   1.4000000e+00   8.0000000e-01   7.0000000e-01   6.0000000e-01   1.0000000e+00   1.4000000e+00   4.0000000e-01   1.6000000e+00   8.0000000e-01   1.2000000e+00   5.0000000e-01   7.0000000e-01   1.3000000e+00   1.2000000e+00   8.0000000e-01   9.0000000e-01   8.0000000e-01   7.0000000e-01   8.0000000e-01   1.0000000e+00   1.1000000e+00   6.0000000e-01   9.0000000e-01   8.0000000e-01   1.3000000e+00   7.0000000e-01   5.0000000e-01   1.0000000e+00   1.4000000e+00   4.0000000e-01   5.0000000e-01   9.0000000e-01   1.1000000e+00   9.0000000e-01   1.0000000e+00   1.3000000e+00   5.0000000e-01   4.0000000e-01   8.0000000e-01   7.0000000e-01   3.0000000e-01   4.0000000e-01   1.6000000e+00   1.8000000e+00   1.0000000e+00   6.0000000e-01   9.0000000e-01   1.6000000e+00   5.0000000e-01   6.0000000e-01   9.0000000e-01   4.0000000e-01   4.0000000e-01   5.0000000e-01   7.0000000e-01   1.0000000e+00   1.4000000e+00   5.0000000e-01   5.0000000e-01   6.0000000e-01   1.2000000e+00   5.0000000e-01   4.0000000e-01   5.0000000e-01   4.0000000e-01   5.0000000e-01   4.0000000e-01   7.0000000e-01   8.0000000e-01   6.0000000e-01   3.0000000e-01   7.0000000e-01   2.0000000e-01   3.0000000e-01   6.0000000e-01   4.0000000e-01   7.0000000e-01   6.0000000e-01   5.0000000e-01   3.0000000e-01   1.4000000e+00   1.6000000e+00   5.0000000e-01   5.0000000e-01   8.0000000e-01   1.4000000e+00   4.0000000e-01   6.0000000e-01   8.0000000e-01   5.0000000e-01   4.0000000e-01   3.0000000e-01   8.0000000e-01   1.0000000e+00   1.5000000e+00   3.0000000e-01   4.0000000e-01   5.0000000e-01   1.3000000e+00   7.0000000e-01   4.0000000e-01   5.0000000e-01   5.0000000e-01   5.0000000e-01   5.0000000e-01   6.0000000e-01   6.0000000e-01   6.0000000e-01   4.0000000e-01   3.0000000e-01   3.0000000e-01   7.0000000e-01   5.0000000e-01   1.1000000e+00   1.0000000e+00   4.0000000e-01   3.0000000e-01   1.2000000e+00   1.4000000e+00   8.0000000e-01   2.0000000e-01   1.2000000e+00   1.2000000e+00   6.0000000e-01   3.0000000e-01   5.0000000e-01   7.0000000e-01   7.0000000e-01   4.0000000e-01   5.0000000e-01   6.0000000e-01   1.1000000e+00   4.0000000e-01   6.0000000e-01   7.0000000e-01   9.0000000e-01   5.0000000e-01   4.0000000e-01   8.0000000e-01   1.0000000e-01   3.0000000e-01   4.0000000e-01   1.0000000e+00   4.0000000e-01   4.0000000e-01   3.0000000e-01   5.0000000e-01   3.0000000e-01   6.0000000e-01   9.0000000e-01   4.0000000e-01   7.0000000e-01   8.0000000e-01   2.0000000e+00   2.0000000e+00   5.0000000e-01   1.2000000e+00   3.0000000e-01   2.0000000e+00   6.0000000e-01   1.0000000e+00   1.5000000e+00   5.0000000e-01   5.0000000e-01   7.0000000e-01   1.5000000e+00   1.7000000e+00   2.2000000e+00   7.0000000e-01   6.0000000e-01   6.0000000e-01   2.0000000e+00   9.0000000e-01   7.0000000e-01   5.0000000e-01   1.2000000e+00   1.0000000e+00   1.2000000e+00   2.0000000e-01   1.1000000e+00   1.0000000e+00   1.0000000e+00   6.0000000e-01   8.0000000e-01   9.0000000e-01   5.0000000e-01   6.0000000e-01   7.0000000e-01   1.9000000e+00   1.9000000e+00   9.0000000e-01   1.1000000e+00   4.0000000e-01   1.9000000e+00   6.0000000e-01   9.0000000e-01   1.4000000e+00   6.0000000e-01   6.0000000e-01   6.0000000e-01   1.4000000e+00   1.6000000e+00   2.1000000e+00   6.0000000e-01   9.0000000e-01   1.0000000e+00   1.9000000e+00   6.0000000e-01   6.0000000e-01   6.0000000e-01   1.1000000e+00   9.0000000e-01   1.1000000e+00   5.0000000e-01   1.0000000e+00   9.0000000e-01   9.0000000e-01   5.0000000e-01   7.0000000e-01   6.0000000e-01   6.0000000e-01   5.0000000e-01   1.4000000e+00   1.6000000e+00   1.0000000e+00   5.0000000e-01   8.0000000e-01   1.4000000e+00   5.0000000e-01   4.0000000e-01   8.0000000e-01   5.0000000e-01   5.0000000e-01   4.0000000e-01   8.0000000e-01   1.0000000e+00   1.5000000e+00   4.0000000e-01   8.0000000e-01   9.0000000e-01   1.3000000e+00   3.0000000e-01   5.0000000e-01   5.0000000e-01   5.0000000e-01   3.0000000e-01   5.0000000e-01   6.0000000e-01   6.0000000e-01   4.0000000e-01   3.0000000e-01   7.0000000e-01   3.0000000e-01   2.0000000e-01   5.0000000e-01   1.2000000e+00   1.4000000e+00   8.0000000e-01   5.0000000e-01   9.0000000e-01   1.2000000e+00   6.0000000e-01   3.0000000e-01   7.0000000e-01   7.0000000e-01   6.0000000e-01   3.0000000e-01   7.0000000e-01   9.0000000e-01   1.4000000e+00   4.0000000e-01   4.0000000e-01   4.0000000e-01   1.2000000e+00   6.0000000e-01   1.0000000e-01   7.0000000e-01   4.0000000e-01   6.0000000e-01   5.0000000e-01   7.0000000e-01   5.0000000e-01   7.0000000e-01   5.0000000e-01   5.0000000e-01   3.0000000e-01   5.0000000e-01   6.0000000e-01   1.2000000e+00   1.7000000e+00   1.0000000e+00   2.1000000e+00   1.0000000e+00   1.8000000e+00   1.0000000e+00   7.0000000e-01   1.9000000e+00   1.8000000e+00   1.3000000e+00   9.0000000e-01   1.0000000e+00   3.0000000e-01   1.3000000e+00   1.6000000e+00   1.6000000e+00   8.0000000e-01   1.4000000e+00   1.3000000e+00   1.9000000e+00   1.3000000e+00   1.1000000e+00   1.6000000e+00   1.9000000e+00   9.0000000e-01   1.0000000e+00   1.5000000e+00   1.7000000e+00   1.5000000e+00   1.5000000e+00   1.8000000e+00   1.9000000e+00   1.2000000e+00   2.1000000e+00   3.0000000e-01   2.0000000e+00   1.2000000e+00   9.0000000e-01   2.1000000e+00   2.0000000e+00   1.3000000e+00   1.1000000e+00   8.0000000e-01   1.2000000e+00   1.3000000e+00   1.8000000e+00   1.6000000e+00   8.0000000e-01   1.4000000e+00   1.4000000e+00   2.1000000e+00   1.5000000e+00   1.3000000e+00   1.8000000e+00   1.9000000e+00   1.0000000e+00   1.2000000e+00   1.7000000e+00   1.9000000e+00   1.7000000e+00   1.5000000e+00   1.8000000e+00   1.0000000e+00   6.0000000e-01   1.7000000e+00   5.0000000e-01   1.1000000e+00   1.2000000e+00   6.0000000e-01   8.0000000e-01   6.0000000e-01   1.2000000e+00   1.4000000e+00   1.9000000e+00   7.0000000e-01   6.0000000e-01   6.0000000e-01   1.7000000e+00   1.2000000e+00   9.0000000e-01   8.0000000e-01   9.0000000e-01   9.0000000e-01   9.0000000e-01   5.0000000e-01   1.0000000e+00   1.1000000e+00   8.0000000e-01   4.0000000e-01   8.0000000e-01   1.2000000e+00   8.0000000e-01   1.3000000e+00   1.0000000e+00   8.0000000e-01   2.0000000e-01   5.0000000e-01   9.0000000e-01   8.0000000e-01   5.0000000e-01   7.0000000e-01   5.0000000e-01   1.0000000e+00   5.0000000e-01   8.0000000e-01   9.0000000e-01   8.0000000e-01   6.0000000e-01   5.0000000e-01   9.0000000e-01   3.0000000e-01   2.0000000e-01   6.0000000e-01   1.1000000e+00   2.0000000e-01   2.0000000e-01   5.0000000e-01   7.0000000e-01   5.0000000e-01   7.0000000e-01   1.0000000e+00   2.1000000e+00   7.0000000e-01   1.1000000e+00   1.6000000e+00   6.0000000e-01   5.0000000e-01   8.0000000e-01   1.6000000e+00   1.8000000e+00   2.3000000e+00   8.0000000e-01   7.0000000e-01   7.0000000e-01   2.1000000e+00   7.0000000e-01   8.0000000e-01   4.0000000e-01   1.3000000e+00   1.1000000e+00   1.3000000e+00   2.0000000e-01   1.2000000e+00   1.1000000e+00   1.1000000e+00   7.0000000e-01   9.0000000e-01   6.0000000e-01   3.0000000e-01   1.8000000e+00   1.0000000e+00   7.0000000e-01   1.9000000e+00   1.8000000e+00   1.3000000e+00   9.0000000e-01   6.0000000e-01   1.0000000e+00   1.3000000e+00   1.6000000e+00   1.6000000e+00   6.0000000e-01   1.4000000e+00   1.3000000e+00   1.9000000e+00   1.3000000e+00   1.1000000e+00   1.6000000e+00   1.9000000e+00   9.0000000e-01   1.0000000e+00   1.5000000e+00   1.7000000e+00   1.5000000e+00   1.5000000e+00   1.8000000e+00   8.0000000e-01   1.1000000e+00   1.0000000e-01   3.0000000e-01   7.0000000e-01   9.0000000e-01   1.2000000e+00   1.6000000e+00   7.0000000e-01   3.0000000e-01   7.0000000e-01   1.4000000e+00   7.0000000e-01   6.0000000e-01   3.0000000e-01   6.0000000e-01   7.0000000e-01   6.0000000e-01   5.0000000e-01   1.0000000e+00   8.0000000e-01   5.0000000e-01   2.0000000e-01   3.0000000e-01   7.0000000e-01   4.0000000e-01   5.0000000e-01   9.0000000e-01   8.0000000e-01   5.0000000e-01   5.0000000e-01   7.0000000e-01   1.2000000e+00   5.0000000e-01   6.0000000e-01   7.0000000e-01   1.0000000e+00   4.0000000e-01   3.0000000e-01   9.0000000e-01   3.0000000e-01   3.0000000e-01   6.0000000e-01   9.0000000e-01   2.0000000e-01   4.0000000e-01   5.0000000e-01   8.0000000e-01   5.0000000e-01   5.0000000e-01   8.0000000e-01   1.2000000e+00   1.1000000e+00   8.0000000e-01   2.0000000e-01   4.0000000e-01   7.0000000e-01   8.0000000e-01   9.0000000e-01   1.1000000e+00   5.0000000e-01   9.0000000e-01   8.0000000e-01   1.2000000e+00   6.0000000e-01   6.0000000e-01   9.0000000e-01   1.4000000e+00   5.0000000e-01   7.0000000e-01   8.0000000e-01   1.0000000e+00   8.0000000e-01   1.0000000e+00   1.3000000e+00   2.0000000e-01   8.0000000e-01   1.0000000e+00   1.3000000e+00   1.7000000e+00   8.0000000e-01   3.0000000e-01   8.0000000e-01   1.5000000e+00   8.0000000e-01   7.0000000e-01   2.0000000e-01   7.0000000e-01   8.0000000e-01   7.0000000e-01   4.0000000e-01   1.1000000e+00   9.0000000e-01   5.0000000e-01   3.0000000e-01   4.0000000e-01   6.0000000e-01   3.0000000e-01   7.0000000e-01   1.1000000e+00   1.3000000e+00   1.8000000e+00   7.0000000e-01   3.0000000e-01   7.0000000e-01   1.6000000e+00   7.0000000e-01   6.0000000e-01   1.0000000e-01   8.0000000e-01   7.0000000e-01   8.0000000e-01   3.0000000e-01   1.0000000e+00   8.0000000e-01   6.0000000e-01   5.0000000e-01   4.0000000e-01   5.0000000e-01   2.0000000e-01   8.0000000e-01   1.0000000e+00   1.5000000e+00   1.0000000e-01   6.0000000e-01   7.0000000e-01   1.3000000e+00   6.0000000e-01   3.0000000e-01   8.0000000e-01   5.0000000e-01   3.0000000e-01   5.0000000e-01   6.0000000e-01   4.0000000e-01   5.0000000e-01   4.0000000e-01   6.0000000e-01   4.0000000e-01   6.0000000e-01   5.0000000e-01   3.0000000e-01   8.0000000e-01   8.0000000e-01   9.0000000e-01   1.1000000e+00   7.0000000e-01   9.0000000e-01   8.0000000e-01   1.2000000e+00   5.0000000e-01   8.0000000e-01   7.0000000e-01   1.4000000e+00   7.0000000e-01   9.0000000e-01   7.0000000e-01   9.0000000e-01   7.0000000e-01   1.0000000e+00   1.3000000e+00   1.0000000e+00   1.0000000e+00   1.1000000e+00   1.3000000e+00   4.0000000e-01   1.1000000e+00   1.0000000e+00   1.4000000e+00   7.0000000e-01   7.0000000e-01   1.0000000e+00   1.6000000e+00   6.0000000e-01   7.0000000e-01   9.0000000e-01   1.1000000e+00   9.0000000e-01   1.2000000e+00   1.5000000e+00   1.5000000e+00   1.6000000e+00   1.8000000e+00   8.0000000e-01   1.6000000e+00   1.5000000e+00   1.9000000e+00   1.0000000e+00   1.2000000e+00   1.3000000e+00   2.1000000e+00   1.1000000e+00   1.2000000e+00   1.2000000e+00   1.6000000e+00   1.4000000e+00   1.7000000e+00   2.0000000e+00   7.0000000e-01   8.0000000e-01   1.3000000e+00   6.0000000e-01   4.0000000e-01   8.0000000e-01   5.0000000e-01   3.0000000e-01   5.0000000e-01   6.0000000e-01   4.0000000e-01   5.0000000e-01   4.0000000e-01   6.0000000e-01   4.0000000e-01   6.0000000e-01   5.0000000e-01   5.0000000e-01   1.4000000e+00   9.0000000e-01   4.0000000e-01   3.0000000e-01   6.0000000e-01   9.0000000e-01   8.0000000e-01   5.0000000e-01   8.0000000e-01   1.0000000e+00   8.0000000e-01   4.0000000e-01   5.0000000e-01   8.0000000e-01   4.0000000e-01   1.6000000e+00   1.0000000e+00   5.0000000e-01   8.0000000e-01   8.0000000e-01   1.0000000e+00   9.0000000e-01   5.0000000e-01   9.0000000e-01   1.1000000e+00   9.0000000e-01   6.0000000e-01   6.0000000e-01   9.0000000e-01   5.0000000e-01   1.4000000e+00   1.3000000e+00   1.7000000e+00   8.0000000e-01   1.0000000e+00   1.0000000e+00   1.9000000e+00   9.0000000e-01   1.0000000e+00   1.0000000e+00   1.4000000e+00   1.2000000e+00   1.5000000e+00   1.8000000e+00   6.0000000e-01   8.0000000e-01   6.0000000e-01   4.0000000e-01   6.0000000e-01   7.0000000e-01   5.0000000e-01   4.0000000e-01   4.0000000e-01   9.0000000e-01   4.0000000e-01   2.0000000e-01   6.0000000e-01   7.0000000e-01   5.0000000e-01   6.0000000e-01   5.0000000e-01   6.0000000e-01   5.0000000e-01   7.0000000e-01   5.0000000e-01   6.0000000e-01   3.0000000e-01   5.0000000e-01   5.0000000e-01   9.0000000e-01   8.0000000e-01   9.0000000e-01   3.0000000e-01   1.1000000e+00   9.0000000e-01   7.0000000e-01   5.0000000e-01   5.0000000e-01   6.0000000e-01   3.0000000e-01   3.0000000e-01   3.0000000e-01   1.1000000e+00   5.0000000e-01   4.0000000e-01   2.0000000e-01   6.0000000e-01   4.0000000e-01   7.0000000e-01   1.0000000e+00   5.0000000e-01   9.0000000e-01   3.0000000e-01   2.0000000e-01   4.0000000e-01   6.0000000e-01   4.0000000e-01   5.0000000e-01   8.0000000e-01   1.1000000e+00   8.0000000e-01   6.0000000e-01   2.0000000e-01   6.0000000e-01   4.0000000e-01   7.0000000e-01   1.0000000e+00   1.0000000e+00   9.0000000e-01   9.0000000e-01   5.0000000e-01   7.0000000e-01   7.0000000e-01   3.0000000e-01   2.0000000e-01   7.0000000e-01   9.0000000e-01   7.0000000e-01   6.0000000e-01   9.0000000e-01   5.0000000e-01   8.0000000e-01   5.0000000e-01   5.0000000e-01   8.0000000e-01   5.0000000e-01   3.0000000e-01   5.0000000e-01   8.0000000e-01   5.0000000e-01   9.0000000e-01   5.0000000e-01   4.0000000e-01   6.0000000e-01   5.0000000e-01
diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-chebyshev-ml.txt b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-chebyshev-ml.txt
new file mode 100644
index 0000000000000000000000000000000000000000..786486295935319c03a60a349f03328c127935b9
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-chebyshev-ml.txt
@@ -0,0 +1 @@
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diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-cityblock-ml-iris.txt b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-cityblock-ml-iris.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6722928a4a4491c74d3fef5205276b532b15dcbf
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-cityblock-ml-iris.txt
@@ -0,0 +1 @@
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8.8000000e+00   6.8000000e+00   1.0700000e+01   7.4000000e+00   8.3000000e+00   8.9000000e+00   7.1000000e+00   6.9000000e+00   8.4000000e+00   8.7000000e+00   9.7000000e+00   1.0400000e+01   8.5000000e+00   7.2000000e+00   7.6000000e+00   1.0200000e+01   8.0000000e+00   7.7000000e+00   6.7000000e+00   8.4000000e+00   8.7000000e+00   8.3000000e+00   7.2000000e+00   8.9000000e+00   8.7000000e+00   8.3000000e+00   7.8000000e+00   7.8000000e+00   7.6000000e+00   6.9000000e+00   1.2000000e+00   5.0000000e-01   7.0000000e-01   3.0000000e-01   8.0000000e-01   1.6000000e+00   1.7000000e+00   1.9000000e+00   1.3000000e+00   4.0000000e-01   1.4000000e+00   6.0000000e-01   6.0000000e-01   6.0000000e-01   1.1000000e+00   7.0000000e-01   6.0000000e-01   5.0000000e-01   3.0000000e-01   3.0000000e-01   3.0000000e-01   6.0000000e-01   6.0000000e-01   6.0000000e-01   1.0000000e+00   1.4000000e+00   5.0000000e-01   5.0000000e-01   8.0000000e-01   5.0000000e-01   1.2000000e+00   1.0000000e-01   4.0000000e-01   1.9000000e+00   1.0000000e+00   6.0000000e-01   1.1000000e+00   8.0000000e-01   6.0000000e-01   7.0000000e-01   6.0000000e-01   2.0000000e-01   6.6000000e+00   5.9000000e+00   6.9000000e+00   5.2000000e+00   6.5000000e+00   5.4000000e+00   6.0000000e+00   3.7000000e+00   6.3000000e+00   4.5000000e+00   4.2000000e+00   5.3000000e+00   5.5000000e+00   6.0000000e+00   4.3000000e+00   6.1000000e+00   5.3000000e+00   4.9000000e+00   6.7000000e+00   4.8000000e+00   6.0000000e+00   5.3000000e+00   6.9000000e+00   5.9000000e+00   5.8000000e+00   6.1000000e+00   6.9000000e+00   7.1000000e+00   5.8000000e+00   4.3000000e+00   4.7000000e+00   4.5000000e+00   4.9000000e+00   6.7000000e+00   5.1000000e+00   5.4000000e+00   6.5000000e+00   6.4000000e+00   4.7000000e+00   5.0000000e+00   5.2000000e+00   5.8000000e+00   5.1000000e+00   3.7000000e+00   5.1000000e+00   4.8000000e+00   5.0000000e+00   5.6000000e+00   3.4000000e+00   5.0000000e+00   8.2000000e+00   6.8000000e+00   8.8000000e+00   7.5000000e+00   8.2000000e+00   1.0000000e+01   5.5000000e+00   9.2000000e+00   8.5000000e+00   9.3000000e+00   7.1000000e+00   7.6000000e+00   8.1000000e+00   6.9000000e+00   7.2000000e+00   7.5000000e+00   7.5000000e+00   1.0300000e+01   1.1000000e+01   7.0000000e+00   8.4000000e+00   6.4000000e+00   1.0300000e+01   7.0000000e+00   7.9000000e+00   8.5000000e+00   6.7000000e+00   6.5000000e+00   8.0000000e+00   8.3000000e+00   9.3000000e+00   1.0000000e+01   8.1000000e+00   6.8000000e+00   7.2000000e+00   9.8000000e+00   7.6000000e+00   7.3000000e+00   6.3000000e+00   8.0000000e+00   8.3000000e+00   7.9000000e+00   6.8000000e+00   8.5000000e+00   8.3000000e+00   7.9000000e+00   7.4000000e+00   7.4000000e+00   7.2000000e+00   6.5000000e+00   9.0000000e-01   1.9000000e+00   1.1000000e+00   6.0000000e-01   6.0000000e-01   2.7000000e+00   3.1000000e+00   2.3000000e+00   1.4000000e+00   2.6000000e+00   1.8000000e+00   1.8000000e+00   1.8000000e+00   1.3000000e+00   1.7000000e+00   1.4000000e+00   9.0000000e-01   1.5000000e+00   1.5000000e+00   1.3000000e+00   8.0000000e-01   8.0000000e-01   1.8000000e+00   2.2000000e+00   2.4000000e+00   9.0000000e-01   1.1000000e+00   1.8000000e+00   9.0000000e-01   2.0000000e-01   1.3000000e+00   1.4000000e+00   9.0000000e-01   4.0000000e-01   1.8000000e+00   2.3000000e+00   6.0000000e-01   1.8000000e+00   5.0000000e-01   1.8000000e+00   1.0000000e+00   7.4000000e+00   6.7000000e+00   7.5000000e+00   5.4000000e+00   6.7000000e+00   5.6000000e+00   7.0000000e+00   3.7000000e+00   6.5000000e+00   4.7000000e+00   4.4000000e+00   5.7000000e+00   5.7000000e+00   6.2000000e+00   4.5000000e+00   6.7000000e+00   5.7000000e+00   5.1000000e+00   6.9000000e+00   5.0000000e+00   6.8000000e+00   5.5000000e+00   7.1000000e+00   6.1000000e+00   6.0000000e+00   6.5000000e+00   7.1000000e+00   7.5000000e+00   6.0000000e+00   4.5000000e+00   4.9000000e+00   4.7000000e+00   5.1000000e+00   6.9000000e+00   5.5000000e+00   6.6000000e+00   7.1000000e+00   6.6000000e+00   5.1000000e+00   5.2000000e+00   5.4000000e+00   6.2000000e+00   5.3000000e+00   3.9000000e+00   5.3000000e+00   5.2000000e+00   5.2000000e+00   5.8000000e+00   3.6000000e+00   5.2000000e+00   9.2000000e+00   7.0000000e+00   9.2000000e+00   7.7000000e+00   8.6000000e+00   1.0400000e+01   5.5000000e+00   9.4000000e+00   8.7000000e+00   1.0500000e+01   7.9000000e+00   7.8000000e+00   8.5000000e+00   7.1000000e+00   7.4000000e+00   8.3000000e+00   7.9000000e+00   1.1500000e+01   1.1200000e+01   7.2000000e+00   9.2000000e+00   6.6000000e+00   1.0500000e+01   7.2000000e+00   8.9000000e+00   9.3000000e+00   6.9000000e+00   6.9000000e+00   8.2000000e+00   8.7000000e+00   9.5000000e+00   1.1200000e+01   8.3000000e+00   7.0000000e+00   7.4000000e+00   1.0200000e+01   8.8000000e+00   7.9000000e+00   6.7000000e+00   8.6000000e+00   8.9000000e+00   8.5000000e+00   7.0000000e+00   9.3000000e+00   9.3000000e+00   8.3000000e+00   7.6000000e+00   7.8000000e+00   8.4000000e+00   6.9000000e+00   1.2000000e+00   6.0000000e-01   3.0000000e-01   1.1000000e+00   2.2000000e+00   2.4000000e+00   1.8000000e+00   9.0000000e-01   1.9000000e+00   1.1000000e+00   1.1000000e+00   1.1000000e+00   1.4000000e+00   1.0000000e+00   9.0000000e-01   4.0000000e-01   8.0000000e-01   8.0000000e-01   8.0000000e-01   5.0000000e-01   3.0000000e-01   1.1000000e+00   1.3000000e+00   1.9000000e+00   0.0000000e+00   6.0000000e-01   1.3000000e+00   0.0000000e+00   9.0000000e-01   6.0000000e-01   9.0000000e-01   1.6000000e+00   9.0000000e-01   1.1000000e+00   1.6000000e+00   5.0000000e-01   1.1000000e+00   6.0000000e-01   1.1000000e+00   5.0000000e-01   6.7000000e+00   6.0000000e+00   6.8000000e+00   5.1000000e+00   6.4000000e+00   5.3000000e+00   6.3000000e+00   3.4000000e+00   6.2000000e+00   4.4000000e+00   4.1000000e+00   5.2000000e+00   5.4000000e+00   5.9000000e+00   4.2000000e+00   6.0000000e+00   5.2000000e+00   4.8000000e+00   6.6000000e+00   4.7000000e+00   6.1000000e+00   5.2000000e+00   6.8000000e+00   5.8000000e+00   5.7000000e+00   6.0000000e+00   6.8000000e+00   7.0000000e+00   5.7000000e+00   4.2000000e+00   4.6000000e+00   4.4000000e+00   4.8000000e+00   6.6000000e+00   5.0000000e+00   5.9000000e+00   6.4000000e+00   6.3000000e+00   4.6000000e+00   4.9000000e+00   5.1000000e+00   5.7000000e+00   5.0000000e+00   3.6000000e+00   5.0000000e+00   4.7000000e+00   4.9000000e+00   5.5000000e+00   3.3000000e+00   4.9000000e+00   8.5000000e+00   6.7000000e+00   8.7000000e+00   7.4000000e+00   8.1000000e+00   9.9000000e+00   5.2000000e+00   9.1000000e+00   8.4000000e+00   9.8000000e+00   7.2000000e+00   7.5000000e+00   8.0000000e+00   6.8000000e+00   7.1000000e+00   7.6000000e+00   7.4000000e+00   1.0800000e+01   1.0900000e+01   6.9000000e+00   8.5000000e+00   6.3000000e+00   1.0200000e+01   6.9000000e+00   8.2000000e+00   8.6000000e+00   6.6000000e+00   6.4000000e+00   7.9000000e+00   8.2000000e+00   9.2000000e+00   1.0500000e+01   8.0000000e+00   6.7000000e+00   7.1000000e+00   9.7000000e+00   8.1000000e+00   7.2000000e+00   6.2000000e+00   7.9000000e+00   8.2000000e+00   7.8000000e+00   6.7000000e+00   8.6000000e+00   8.6000000e+00   7.8000000e+00   7.3000000e+00   7.3000000e+00   7.7000000e+00   6.4000000e+00   1.0000000e+00   1.5000000e+00   2.3000000e+00   1.0000000e+00   1.2000000e+00   6.0000000e-01   7.0000000e-01   7.0000000e-01   5.0000000e-01   5.0000000e-01   5.0000000e-01   1.4000000e+00   1.2000000e+00   1.3000000e+00   1.2000000e+00   1.0000000e+00   4.0000000e-01   6.0000000e-01   1.3000000e+00   1.3000000e+00   5.0000000e-01   7.0000000e-01   7.0000000e-01   1.2000000e+00   1.2000000e+00   5.0000000e-01   1.2000000e+00   1.9000000e+00   6.0000000e-01   9.0000000e-01   2.6000000e+00   1.7000000e+00   1.1000000e+00   1.0000000e+00   1.5000000e+00   5.0000000e-01   1.4000000e+00   1.0000000e-01   9.0000000e-01   6.5000000e+00   5.8000000e+00   6.8000000e+00   5.1000000e+00   6.4000000e+00   5.3000000e+00   5.9000000e+00   4.4000000e+00   6.2000000e+00   4.8000000e+00   4.9000000e+00   5.2000000e+00   5.4000000e+00   5.9000000e+00   4.2000000e+00   6.0000000e+00   5.2000000e+00   4.8000000e+00   6.6000000e+00   4.7000000e+00   5.9000000e+00   5.2000000e+00   6.8000000e+00   5.8000000e+00   5.7000000e+00   6.0000000e+00   6.8000000e+00   7.0000000e+00   5.7000000e+00   4.2000000e+00   4.6000000e+00   4.4000000e+00   4.8000000e+00   6.6000000e+00   5.0000000e+00   5.3000000e+00   6.4000000e+00   6.3000000e+00   4.6000000e+00   4.9000000e+00   5.1000000e+00   5.7000000e+00   5.0000000e+00   4.4000000e+00   5.0000000e+00   4.7000000e+00   4.9000000e+00   5.5000000e+00   3.9000000e+00   4.9000000e+00   8.1000000e+00   6.7000000e+00   8.7000000e+00   7.4000000e+00   8.1000000e+00   9.9000000e+00   6.2000000e+00   9.1000000e+00   8.4000000e+00   8.8000000e+00   7.0000000e+00   7.5000000e+00   8.0000000e+00   6.8000000e+00   7.1000000e+00   7.4000000e+00   7.4000000e+00   9.6000000e+00   1.0900000e+01   6.9000000e+00   8.3000000e+00   6.3000000e+00   1.0200000e+01   6.9000000e+00   7.8000000e+00   8.4000000e+00   6.6000000e+00   6.4000000e+00   7.9000000e+00   8.2000000e+00   9.2000000e+00   9.3000000e+00   8.0000000e+00   6.7000000e+00   7.1000000e+00   9.7000000e+00   7.5000000e+00   7.2000000e+00   6.2000000e+00   7.9000000e+00   8.2000000e+00   7.8000000e+00   6.7000000e+00   8.4000000e+00   8.2000000e+00   7.8000000e+00   7.3000000e+00   7.3000000e+00   7.1000000e+00   6.4000000e+00   7.0000000e-01   1.5000000e+00   2.0000000e+00   2.2000000e+00   1.6000000e+00   7.0000000e-01   1.5000000e+00   9.0000000e-01   7.0000000e-01   9.0000000e-01   1.0000000e+00   8.0000000e-01   3.0000000e-01   6.0000000e-01   4.0000000e-01   6.0000000e-01   6.0000000e-01   3.0000000e-01   3.0000000e-01   9.0000000e-01   1.3000000e+00   1.7000000e+00   6.0000000e-01   8.0000000e-01   1.1000000e+00   6.0000000e-01   1.1000000e+00   4.0000000e-01   7.0000000e-01   1.8000000e+00   9.0000000e-01   7.0000000e-01   1.2000000e+00   7.0000000e-01   7.0000000e-01   6.0000000e-01   9.0000000e-01   5.0000000e-01   6.7000000e+00   6.0000000e+00   7.0000000e+00   5.3000000e+00   6.6000000e+00   5.5000000e+00   6.1000000e+00   3.6000000e+00   6.4000000e+00   4.6000000e+00   4.3000000e+00   5.4000000e+00   5.6000000e+00   6.1000000e+00   4.4000000e+00   6.2000000e+00   5.4000000e+00   5.0000000e+00   6.8000000e+00   4.9000000e+00   6.1000000e+00   5.4000000e+00   7.0000000e+00   6.0000000e+00   5.9000000e+00   6.2000000e+00   7.0000000e+00   7.2000000e+00   5.9000000e+00   4.4000000e+00   4.8000000e+00   4.6000000e+00   5.0000000e+00   6.8000000e+00   5.2000000e+00   5.5000000e+00   6.6000000e+00   6.5000000e+00   4.8000000e+00   5.1000000e+00   5.3000000e+00   5.9000000e+00   5.2000000e+00   3.8000000e+00   5.2000000e+00   4.9000000e+00   5.1000000e+00   5.7000000e+00   3.5000000e+00   5.1000000e+00   8.3000000e+00   6.9000000e+00   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1.1000000e+00   9.0000000e-01   6.0000000e-01   4.0000000e-01   1.4000000e+00   1.6000000e+00   2.0000000e+00   3.0000000e-01   7.0000000e-01   1.4000000e+00   3.0000000e-01   6.0000000e-01   9.0000000e-01   1.0000000e+00   1.3000000e+00   8.0000000e-01   1.4000000e+00   1.9000000e+00   2.0000000e-01   1.4000000e+00   5.0000000e-01   1.4000000e+00   6.0000000e-01   7.0000000e+00   6.3000000e+00   7.1000000e+00   5.2000000e+00   6.5000000e+00   5.4000000e+00   6.6000000e+00   3.5000000e+00   6.3000000e+00   4.5000000e+00   4.2000000e+00   5.3000000e+00   5.5000000e+00   6.0000000e+00   4.3000000e+00   6.3000000e+00   5.3000000e+00   4.9000000e+00   6.7000000e+00   4.8000000e+00   6.4000000e+00   5.3000000e+00   6.9000000e+00   5.9000000e+00   5.8000000e+00   6.1000000e+00   6.9000000e+00   7.1000000e+00   5.8000000e+00   4.3000000e+00   4.7000000e+00   4.5000000e+00   4.9000000e+00   6.7000000e+00   5.1000000e+00   6.2000000e+00   6.7000000e+00   6.4000000e+00   4.7000000e+00   5.0000000e+00   5.2000000e+00   5.8000000e+00   5.1000000e+00   3.7000000e+00   5.1000000e+00   4.8000000e+00   5.0000000e+00   5.6000000e+00   3.4000000e+00   5.0000000e+00   8.8000000e+00   6.8000000e+00   8.8000000e+00   7.5000000e+00   8.2000000e+00   1.0000000e+01   5.3000000e+00   9.2000000e+00   8.5000000e+00   1.0100000e+01   7.5000000e+00   7.6000000e+00   8.1000000e+00   6.9000000e+00   7.2000000e+00   7.9000000e+00   7.5000000e+00   1.1100000e+01   1.1000000e+01   7.0000000e+00   8.8000000e+00   6.4000000e+00   1.0300000e+01   7.0000000e+00   8.5000000e+00   8.9000000e+00   6.7000000e+00   6.5000000e+00   8.0000000e+00   8.3000000e+00   9.3000000e+00   1.0800000e+01   8.1000000e+00   6.8000000e+00   7.2000000e+00   9.8000000e+00   8.4000000e+00   7.5000000e+00   6.3000000e+00   8.2000000e+00   8.5000000e+00   8.1000000e+00   6.8000000e+00   8.9000000e+00   8.9000000e+00   7.9000000e+00   7.4000000e+00   7.4000000e+00   8.0000000e+00   6.5000000e+00   2.7000000e+00   3.5000000e+00   2.5000000e+00   1.8000000e+00   3.0000000e+00   2.2000000e+00   2.2000000e+00   2.2000000e+00   1.1000000e+00   2.1000000e+00   1.8000000e+00   1.3000000e+00   1.9000000e+00   1.9000000e+00   1.7000000e+00   1.2000000e+00   1.2000000e+00   2.2000000e+00   2.4000000e+00   2.8000000e+00   1.1000000e+00   1.1000000e+00   2.0000000e+00   1.1000000e+00   4.0000000e-01   1.7000000e+00   1.6000000e+00   1.3000000e+00   6.0000000e-01   2.2000000e+00   2.7000000e+00   1.0000000e+00   2.2000000e+00   9.0000000e-01   2.2000000e+00   1.4000000e+00   7.8000000e+00   7.1000000e+00   7.9000000e+00   6.0000000e+00   7.3000000e+00   6.2000000e+00   7.4000000e+00   4.3000000e+00   7.1000000e+00   5.3000000e+00   5.0000000e+00   6.1000000e+00   6.3000000e+00   6.8000000e+00   5.1000000e+00   7.1000000e+00   6.1000000e+00   5.7000000e+00   7.5000000e+00   5.6000000e+00   7.2000000e+00   6.1000000e+00   7.7000000e+00   6.7000000e+00   6.6000000e+00   6.9000000e+00   7.7000000e+00   7.9000000e+00   6.6000000e+00   5.1000000e+00   5.5000000e+00   5.3000000e+00   5.7000000e+00   7.5000000e+00   5.9000000e+00   7.0000000e+00   7.5000000e+00   7.2000000e+00   5.5000000e+00   5.8000000e+00   6.0000000e+00   6.6000000e+00   5.9000000e+00   4.5000000e+00   5.9000000e+00   5.6000000e+00   5.8000000e+00   6.4000000e+00   4.2000000e+00   5.8000000e+00   9.6000000e+00   7.6000000e+00   9.6000000e+00   8.3000000e+00   9.0000000e+00   1.0800000e+01   6.1000000e+00   1.0000000e+01   9.3000000e+00   1.0900000e+01   8.3000000e+00   8.4000000e+00   8.9000000e+00   7.7000000e+00   8.0000000e+00   8.7000000e+00   8.3000000e+00   1.1900000e+01   1.1800000e+01   7.8000000e+00   9.6000000e+00   7.2000000e+00   1.1100000e+01   7.8000000e+00   9.3000000e+00   9.7000000e+00   7.5000000e+00   7.3000000e+00   8.8000000e+00   9.1000000e+00   1.0100000e+01   1.1600000e+01   8.9000000e+00   7.6000000e+00   8.0000000e+00   1.0600000e+01   9.2000000e+00   8.3000000e+00   7.1000000e+00   9.0000000e+00   9.3000000e+00   8.9000000e+00   7.6000000e+00   9.7000000e+00   9.7000000e+00   8.7000000e+00   8.2000000e+00   8.2000000e+00   8.8000000e+00   7.3000000e+00   1.0000000e+00   8.0000000e-01   1.5000000e+00   9.0000000e-01   1.3000000e+00   1.5000000e+00   1.5000000e+00   1.8000000e+00   2.2000000e+00   2.3000000e+00   2.2000000e+00   2.0000000e+00   1.4000000e+00   1.4000000e+00   2.3000000e+00   2.3000000e+00   1.5000000e+00   1.1000000e+00   7.0000000e-01   2.2000000e+00   1.6000000e+00   9.0000000e-01   2.2000000e+00   2.5000000e+00   1.6000000e+00   1.5000000e+00   3.2000000e+00   2.3000000e+00   2.1000000e+00   1.8000000e+00   2.3000000e+00   1.3000000e+00   2.2000000e+00   1.1000000e+00   1.7000000e+00   6.7000000e+00   6.0000000e+00   7.0000000e+00   5.9000000e+00   6.6000000e+00   5.7000000e+00   6.1000000e+00   5.4000000e+00   6.4000000e+00   5.8000000e+00   5.9000000e+00   5.4000000e+00   5.6000000e+00   6.1000000e+00   4.8000000e+00   6.2000000e+00   5.8000000e+00   5.0000000e+00   6.8000000e+00   5.3000000e+00   6.1000000e+00   5.4000000e+00   7.0000000e+00   6.0000000e+00   5.9000000e+00   6.2000000e+00   7.0000000e+00   7.2000000e+00   5.9000000e+00   4.6000000e+00   5.4000000e+00   5.2000000e+00   5.0000000e+00   6.8000000e+00   6.0000000e+00   5.5000000e+00   6.6000000e+00   6.5000000e+00   5.2000000e+00   5.7000000e+00   5.9000000e+00   5.9000000e+00   5.2000000e+00   5.4000000e+00   5.6000000e+00   5.1000000e+00   5.3000000e+00   5.7000000e+00   4.9000000e+00   5.3000000e+00   8.3000000e+00   6.9000000e+00   8.9000000e+00   7.6000000e+00   8.3000000e+00   1.0100000e+01   7.2000000e+00   9.3000000e+00   8.6000000e+00   9.0000000e+00   7.2000000e+00   7.7000000e+00   8.2000000e+00   7.2000000e+00   7.3000000e+00   7.6000000e+00   7.6000000e+00   9.6000000e+00   1.1100000e+01   7.1000000e+00   8.5000000e+00   6.9000000e+00   1.0400000e+01   7.1000000e+00   8.0000000e+00   8.6000000e+00   6.8000000e+00   6.6000000e+00   8.1000000e+00   8.4000000e+00   9.4000000e+00   9.3000000e+00   8.2000000e+00   6.9000000e+00   7.3000000e+00   9.9000000e+00   7.7000000e+00   7.4000000e+00   6.4000000e+00   8.1000000e+00   8.4000000e+00   8.0000000e+00   6.9000000e+00   8.6000000e+00   8.4000000e+00   8.0000000e+00   7.5000000e+00   7.5000000e+00   7.3000000e+00   6.6000000e+00   1.0000000e+00   1.7000000e+00   9.0000000e-01   1.3000000e+00   1.7000000e+00   1.3000000e+00   2.6000000e+00   2.0000000e+00   2.5000000e+00   2.4000000e+00   1.8000000e+00   1.6000000e+00   1.8000000e+00   2.5000000e+00   2.5000000e+00   1.3000000e+00   1.1000000e+00   7.0000000e-01   2.4000000e+00   2.4000000e+00   1.5000000e+00   2.4000000e+00   3.1000000e+00   1.8000000e+00   1.9000000e+00   3.6000000e+00   2.9000000e+00   1.9000000e+00   1.6000000e+00   2.5000000e+00   1.5000000e+00   2.6000000e+00   1.3000000e+00   2.1000000e+00   6.7000000e+00   6.0000000e+00   7.0000000e+00   5.7000000e+00   6.6000000e+00   5.5000000e+00   6.1000000e+00   5.2000000e+00   6.4000000e+00   5.6000000e+00   5.7000000e+00   5.4000000e+00   5.6000000e+00   6.1000000e+00   4.6000000e+00   6.2000000e+00   5.6000000e+00   5.0000000e+00   6.8000000e+00   5.1000000e+00   6.1000000e+00   5.4000000e+00   7.0000000e+00   6.0000000e+00   5.9000000e+00   6.2000000e+00   7.0000000e+00   7.2000000e+00   5.9000000e+00   4.4000000e+00   5.2000000e+00   5.0000000e+00   5.0000000e+00   6.8000000e+00   5.8000000e+00   5.5000000e+00   6.6000000e+00   6.5000000e+00   5.0000000e+00   5.5000000e+00   5.7000000e+00   5.9000000e+00   5.2000000e+00   5.2000000e+00   5.4000000e+00   4.9000000e+00   5.1000000e+00   5.7000000e+00   4.7000000e+00   5.1000000e+00   8.3000000e+00   6.9000000e+00   8.9000000e+00   7.6000000e+00   8.3000000e+00   1.0100000e+01   7.0000000e+00   9.3000000e+00   8.6000000e+00   9.0000000e+00   7.2000000e+00   7.7000000e+00   8.2000000e+00   7.0000000e+00   7.3000000e+00   7.6000000e+00   7.6000000e+00   9.6000000e+00   1.1100000e+01   7.1000000e+00   8.5000000e+00   6.7000000e+00   1.0400000e+01   7.1000000e+00   8.0000000e+00   8.6000000e+00   6.8000000e+00   6.6000000e+00   8.1000000e+00   8.4000000e+00   9.4000000e+00   9.3000000e+00   8.2000000e+00   6.9000000e+00   7.3000000e+00   9.9000000e+00   7.7000000e+00   7.4000000e+00   6.4000000e+00   8.1000000e+00   8.4000000e+00   8.0000000e+00   6.9000000e+00   8.6000000e+00   8.4000000e+00   8.0000000e+00   7.5000000e+00   7.5000000e+00   7.3000000e+00   6.6000000e+00   9.0000000e-01   9.0000000e-01   7.0000000e-01   1.1000000e+00   7.0000000e-01   1.6000000e+00   1.4000000e+00   1.9000000e+00   1.8000000e+00   1.2000000e+00   1.0000000e+00   1.0000000e+00   1.9000000e+00   1.9000000e+00   7.0000000e-01   9.0000000e-01   7.0000000e-01   1.8000000e+00   1.4000000e+00   7.0000000e-01   1.8000000e+00   2.1000000e+00   1.2000000e+00   9.0000000e-01   2.6000000e+00   1.9000000e+00   1.3000000e+00   1.0000000e+00   1.7000000e+00   9.0000000e-01   1.8000000e+00   7.0000000e-01   1.3000000e+00   6.7000000e+00   6.0000000e+00   7.0000000e+00   5.3000000e+00   6.6000000e+00   5.5000000e+00   6.1000000e+00   4.6000000e+00   6.4000000e+00   5.0000000e+00   5.1000000e+00   5.4000000e+00   5.6000000e+00   6.1000000e+00   4.4000000e+00   6.2000000e+00   5.4000000e+00   5.0000000e+00   6.8000000e+00   4.9000000e+00   6.1000000e+00   5.4000000e+00   7.0000000e+00   6.0000000e+00   5.9000000e+00   6.2000000e+00   7.0000000e+00   7.2000000e+00   5.9000000e+00   4.4000000e+00   4.8000000e+00   4.6000000e+00   5.0000000e+00   6.8000000e+00   5.2000000e+00   5.5000000e+00   6.6000000e+00   6.5000000e+00   4.8000000e+00   5.1000000e+00   5.3000000e+00   5.9000000e+00   5.2000000e+00   4.6000000e+00   5.2000000e+00   4.9000000e+00   5.1000000e+00   5.7000000e+00   4.1000000e+00   5.1000000e+00   8.3000000e+00   6.9000000e+00   8.9000000e+00   7.6000000e+00   8.3000000e+00   1.0100000e+01   6.4000000e+00   9.3000000e+00   8.6000000e+00   9.0000000e+00   7.2000000e+00   7.7000000e+00   8.2000000e+00   7.0000000e+00   7.3000000e+00   7.6000000e+00   7.6000000e+00   9.6000000e+00   1.1100000e+01   7.1000000e+00   8.5000000e+00   6.5000000e+00   1.0400000e+01   7.1000000e+00   8.0000000e+00   8.6000000e+00   6.8000000e+00   6.6000000e+00   8.1000000e+00   8.4000000e+00   9.4000000e+00   9.3000000e+00   8.2000000e+00   6.9000000e+00   7.3000000e+00   9.9000000e+00   7.7000000e+00   7.4000000e+00   6.4000000e+00   8.1000000e+00   8.4000000e+00   8.0000000e+00   6.9000000e+00   8.6000000e+00   8.4000000e+00   8.0000000e+00   7.5000000e+00   7.5000000e+00   7.3000000e+00   6.6000000e+00   1.2000000e+00   4.0000000e-01   8.0000000e-01   4.0000000e-01   1.1000000e+00   7.0000000e-01   1.0000000e+00   9.0000000e-01   5.0000000e-01   3.0000000e-01   3.0000000e-01   1.0000000e+00   1.0000000e+00   6.0000000e-01   1.0000000e+00   1.2000000e+00   9.0000000e-01   7.0000000e-01   6.0000000e-01   9.0000000e-01   1.4000000e+00   3.0000000e-01   2.0000000e-01   1.9000000e+00   1.2000000e+00   6.0000000e-01   9.0000000e-01   8.0000000e-01   6.0000000e-01   9.0000000e-01   6.0000000e-01   4.0000000e-01   6.6000000e+00   5.9000000e+00   6.9000000e+00   5.2000000e+00   6.5000000e+00   5.4000000e+00   6.0000000e+00   3.9000000e+00   6.3000000e+00   4.5000000e+00   4.4000000e+00   5.3000000e+00   5.5000000e+00   6.0000000e+00   4.3000000e+00   6.1000000e+00   5.3000000e+00   4.9000000e+00   6.7000000e+00   4.8000000e+00   6.0000000e+00   5.3000000e+00   6.9000000e+00   5.9000000e+00   5.8000000e+00   6.1000000e+00   6.9000000e+00   7.1000000e+00   5.8000000e+00   4.3000000e+00   4.7000000e+00   4.5000000e+00   4.9000000e+00   6.7000000e+00   5.1000000e+00   5.4000000e+00   6.5000000e+00   6.4000000e+00   4.7000000e+00   5.0000000e+00   5.2000000e+00   5.8000000e+00   5.1000000e+00   3.9000000e+00   5.1000000e+00   4.8000000e+00   5.0000000e+00   5.6000000e+00   3.4000000e+00   5.0000000e+00   8.2000000e+00   6.8000000e+00   8.8000000e+00   7.5000000e+00   8.2000000e+00   1.0000000e+01   5.7000000e+00   9.2000000e+00   8.5000000e+00   9.1000000e+00   7.1000000e+00   7.6000000e+00   8.1000000e+00   6.9000000e+00   7.2000000e+00   7.5000000e+00   7.5000000e+00   1.0100000e+01   1.1000000e+01   7.0000000e+00   8.4000000e+00   6.4000000e+00   1.0300000e+01   7.0000000e+00   7.9000000e+00   8.5000000e+00   6.7000000e+00   6.5000000e+00   8.0000000e+00   8.3000000e+00   9.3000000e+00   9.8000000e+00   8.1000000e+00   6.8000000e+00   7.2000000e+00   9.8000000e+00   7.6000000e+00   7.3000000e+00   6.3000000e+00   8.0000000e+00   8.3000000e+00   7.9000000e+00   6.8000000e+00   8.5000000e+00   8.3000000e+00   7.9000000e+00   7.4000000e+00   7.4000000e+00   7.2000000e+00   6.5000000e+00   8.0000000e-01   8.0000000e-01   1.0000000e+00   2.1000000e+00   1.3000000e+00   1.6000000e+00   1.7000000e+00   1.3000000e+00   1.1000000e+00   1.3000000e+00   1.8000000e+00   1.8000000e+00   1.0000000e+00   1.2000000e+00   1.0000000e+00   1.9000000e+00   1.9000000e+00   1.0000000e+00   1.9000000e+00   2.6000000e+00   1.3000000e+00   1.4000000e+00   3.1000000e+00   2.4000000e+00   1.4000000e+00   9.0000000e-01   2.0000000e+00   8.0000000e-01   2.1000000e+00   8.0000000e-01   1.6000000e+00   6.0000000e+00   5.3000000e+00   6.3000000e+00   5.0000000e+00   5.9000000e+00   4.8000000e+00   5.4000000e+00   4.5000000e+00   5.7000000e+00   4.9000000e+00   5.0000000e+00   4.7000000e+00   4.9000000e+00   5.4000000e+00   3.9000000e+00   5.5000000e+00   4.9000000e+00   4.3000000e+00   6.1000000e+00   4.4000000e+00   5.4000000e+00   4.7000000e+00   6.3000000e+00   5.3000000e+00   5.2000000e+00   5.5000000e+00   6.3000000e+00   6.5000000e+00   5.2000000e+00   3.7000000e+00   4.5000000e+00   4.3000000e+00   4.3000000e+00   6.1000000e+00   5.1000000e+00   4.8000000e+00   5.9000000e+00   5.8000000e+00   4.3000000e+00   4.8000000e+00   5.0000000e+00   5.2000000e+00   4.5000000e+00   4.5000000e+00   4.7000000e+00   4.2000000e+00   4.4000000e+00   5.0000000e+00   4.0000000e+00   4.4000000e+00   7.6000000e+00   6.2000000e+00   8.2000000e+00   6.9000000e+00   7.6000000e+00   9.4000000e+00   6.3000000e+00   8.6000000e+00   7.9000000e+00   8.3000000e+00   6.5000000e+00   7.0000000e+00   7.5000000e+00   6.3000000e+00   6.6000000e+00   6.9000000e+00   6.9000000e+00   8.9000000e+00   1.0400000e+01   6.4000000e+00   7.8000000e+00   6.0000000e+00   9.7000000e+00   6.4000000e+00   7.3000000e+00   7.9000000e+00   6.1000000e+00   5.9000000e+00   7.4000000e+00   7.7000000e+00   8.7000000e+00   8.6000000e+00   7.5000000e+00   6.2000000e+00   6.6000000e+00   9.2000000e+00   7.0000000e+00   6.7000000e+00   5.7000000e+00   7.4000000e+00   7.7000000e+00   7.3000000e+00   6.2000000e+00   7.9000000e+00   7.7000000e+00   7.3000000e+00   6.8000000e+00   6.8000000e+00   6.6000000e+00   5.9000000e+00   1.0000000e+00   2.0000000e-01   1.3000000e+00   9.0000000e-01   1.2000000e+00   1.1000000e+00   7.0000000e-01   5.0000000e-01   7.0000000e-01   1.2000000e+00   1.2000000e+00   8.0000000e-01   6.0000000e-01   1.0000000e+00   1.1000000e+00   1.1000000e+00   1.0000000e+00   1.1000000e+00   1.8000000e+00   5.0000000e-01   6.0000000e-01   2.3000000e+00   1.6000000e+00   8.0000000e-01   5.0000000e-01   1.2000000e+00   2.0000000e-01   1.3000000e+00   4.0000000e-01   8.0000000e-01   6.8000000e+00   6.1000000e+00   7.1000000e+00   5.4000000e+00   6.7000000e+00   5.6000000e+00   6.2000000e+00   4.1000000e+00   6.5000000e+00   4.7000000e+00   4.6000000e+00   5.5000000e+00   5.7000000e+00   6.2000000e+00   4.5000000e+00   6.3000000e+00   5.5000000e+00   5.1000000e+00   6.9000000e+00   5.0000000e+00   6.2000000e+00   5.5000000e+00   7.1000000e+00   6.1000000e+00   6.0000000e+00   6.3000000e+00   7.1000000e+00   7.3000000e+00   6.0000000e+00   4.5000000e+00   4.9000000e+00   4.7000000e+00   5.1000000e+00   6.9000000e+00   5.3000000e+00   5.6000000e+00   6.7000000e+00   6.6000000e+00   4.9000000e+00   5.2000000e+00   5.4000000e+00   6.0000000e+00   5.3000000e+00   4.1000000e+00   5.3000000e+00   5.0000000e+00   5.2000000e+00   5.8000000e+00   3.6000000e+00   5.2000000e+00   8.4000000e+00   7.0000000e+00   9.0000000e+00   7.7000000e+00   8.4000000e+00   1.0200000e+01   5.9000000e+00   9.4000000e+00   8.7000000e+00   9.1000000e+00   7.3000000e+00   7.8000000e+00   8.3000000e+00   7.1000000e+00   7.4000000e+00   7.7000000e+00   7.7000000e+00   9.7000000e+00   1.1200000e+01   7.2000000e+00   8.6000000e+00   6.6000000e+00   1.0500000e+01   7.2000000e+00   8.1000000e+00   8.7000000e+00   6.9000000e+00   6.7000000e+00   8.2000000e+00   8.5000000e+00   9.5000000e+00   9.4000000e+00   8.3000000e+00   7.0000000e+00   7.4000000e+00   1.0000000e+01   7.8000000e+00   7.5000000e+00   6.5000000e+00   8.2000000e+00   8.5000000e+00   8.1000000e+00   7.0000000e+00   8.7000000e+00   8.5000000e+00   8.1000000e+00   7.6000000e+00   7.6000000e+00   7.4000000e+00   6.7000000e+00   1.0000000e+00   1.7000000e+00   7.0000000e-01   8.0000000e-01   9.0000000e-01   7.0000000e-01   5.0000000e-01   5.0000000e-01   1.0000000e+00   1.0000000e+00   4.0000000e-01   1.2000000e+00   1.2000000e+00   1.1000000e+00   1.1000000e+00   6.0000000e-01   1.1000000e+00   1.8000000e+00   5.0000000e-01   1.0000000e+00   2.5000000e+00   1.6000000e+00   1.0000000e+00   1.1000000e+00   1.4000000e+00   8.0000000e-01   1.3000000e+00   6.0000000e-01   8.0000000e-01   6.0000000e+00   5.3000000e+00   6.3000000e+00   4.6000000e+00   5.9000000e+00   4.8000000e+00   5.4000000e+00   3.9000000e+00   5.7000000e+00   4.3000000e+00   4.4000000e+00   4.7000000e+00   4.9000000e+00   5.4000000e+00   3.7000000e+00   5.5000000e+00   4.7000000e+00   4.3000000e+00   6.1000000e+00   4.2000000e+00   5.4000000e+00   4.7000000e+00   6.3000000e+00   5.3000000e+00   5.2000000e+00   5.5000000e+00   6.3000000e+00   6.5000000e+00   5.2000000e+00   3.7000000e+00   4.1000000e+00   3.9000000e+00   4.3000000e+00   6.1000000e+00   4.5000000e+00   4.8000000e+00   5.9000000e+00   5.8000000e+00   4.1000000e+00   4.4000000e+00   4.6000000e+00   5.2000000e+00   4.5000000e+00   3.9000000e+00   4.5000000e+00   4.2000000e+00   4.4000000e+00   5.0000000e+00   3.4000000e+00   4.4000000e+00   7.6000000e+00   6.2000000e+00   8.2000000e+00   6.9000000e+00   7.6000000e+00   9.4000000e+00   5.7000000e+00   8.6000000e+00   7.9000000e+00   8.7000000e+00   6.5000000e+00   7.0000000e+00   7.5000000e+00   6.3000000e+00   6.6000000e+00   6.9000000e+00   6.9000000e+00   9.7000000e+00   1.0400000e+01   6.4000000e+00   7.8000000e+00   5.8000000e+00   9.7000000e+00   6.4000000e+00   7.3000000e+00   7.9000000e+00   6.1000000e+00   5.9000000e+00   7.4000000e+00   7.7000000e+00   8.7000000e+00   9.4000000e+00   7.5000000e+00   6.2000000e+00   6.6000000e+00   9.2000000e+00   7.0000000e+00   6.7000000e+00   5.7000000e+00   7.4000000e+00   7.7000000e+00   7.3000000e+00   6.2000000e+00   7.9000000e+00   7.7000000e+00   7.3000000e+00   6.8000000e+00   6.8000000e+00   6.6000000e+00   5.9000000e+00   1.3000000e+00   7.0000000e-01   1.2000000e+00   1.1000000e+00   5.0000000e-01   5.0000000e-01   7.0000000e-01   1.2000000e+00   1.2000000e+00   6.0000000e-01   8.0000000e-01   1.2000000e+00   1.1000000e+00   1.1000000e+00   1.0000000e+00   1.1000000e+00   1.8000000e+00   5.0000000e-01   6.0000000e-01   2.3000000e+00   1.6000000e+00   6.0000000e-01   5.0000000e-01   1.2000000e+00   4.0000000e-01   1.3000000e+00   4.0000000e-01   8.0000000e-01   6.6000000e+00   5.9000000e+00   6.9000000e+00   5.2000000e+00   6.5000000e+00   5.4000000e+00   6.0000000e+00   3.9000000e+00   6.3000000e+00   4.5000000e+00   4.4000000e+00   5.3000000e+00   5.5000000e+00   6.0000000e+00   4.3000000e+00   6.1000000e+00   5.3000000e+00   4.9000000e+00   6.7000000e+00   4.8000000e+00   6.0000000e+00   5.3000000e+00   6.9000000e+00   5.9000000e+00   5.8000000e+00   6.1000000e+00   6.9000000e+00   7.1000000e+00   5.8000000e+00   4.3000000e+00   4.7000000e+00   4.5000000e+00   4.9000000e+00   6.7000000e+00   5.1000000e+00   5.4000000e+00   6.5000000e+00   6.4000000e+00   4.7000000e+00   5.0000000e+00   5.2000000e+00   5.8000000e+00   5.1000000e+00   3.9000000e+00   5.1000000e+00   4.8000000e+00   5.0000000e+00   5.6000000e+00   3.4000000e+00   5.0000000e+00   8.2000000e+00   6.8000000e+00   8.8000000e+00   7.5000000e+00   8.2000000e+00   1.0000000e+01   5.7000000e+00   9.2000000e+00   8.5000000e+00   8.9000000e+00   7.1000000e+00   7.6000000e+00   8.1000000e+00   6.9000000e+00   7.2000000e+00   7.5000000e+00   7.5000000e+00   9.7000000e+00   1.1000000e+01   7.0000000e+00   8.4000000e+00   6.4000000e+00   1.0300000e+01   7.0000000e+00   7.9000000e+00   8.5000000e+00   6.7000000e+00   6.5000000e+00   8.0000000e+00   8.3000000e+00   9.3000000e+00   9.4000000e+00   8.1000000e+00   6.8000000e+00   7.2000000e+00   9.8000000e+00   7.6000000e+00   7.3000000e+00   6.3000000e+00   8.0000000e+00   8.3000000e+00   7.9000000e+00   6.8000000e+00   8.5000000e+00   8.3000000e+00   7.9000000e+00   7.4000000e+00   7.4000000e+00   7.2000000e+00   6.5000000e+00   1.8000000e+00   1.3000000e+00   1.6000000e+00   1.4000000e+00   1.2000000e+00   1.2000000e+00   1.1000000e+00   1.3000000e+00   1.7000000e+00   1.7000000e+00   1.9000000e+00   1.4000000e+00   1.0000000e+00   1.3000000e+00   1.4000000e+00   1.1000000e+00   1.2000000e+00   9.0000000e-01   1.8000000e+00   9.0000000e-01   1.5000000e+00   1.8000000e+00   1.3000000e+00   1.3000000e+00   8.0000000e-01   1.3000000e+00   1.1000000e+00   7.7000000e+00   7.0000000e+00   8.0000000e+00   6.3000000e+00   7.6000000e+00   6.5000000e+00   7.1000000e+00   4.6000000e+00   7.4000000e+00   5.6000000e+00   5.3000000e+00   6.4000000e+00   6.6000000e+00   7.1000000e+00   5.4000000e+00   7.2000000e+00   6.4000000e+00   6.0000000e+00   7.8000000e+00   5.9000000e+00   7.1000000e+00   6.4000000e+00   8.0000000e+00   7.0000000e+00   6.9000000e+00   7.2000000e+00   8.0000000e+00   8.2000000e+00   6.9000000e+00   5.4000000e+00   5.8000000e+00   5.6000000e+00   6.0000000e+00   7.8000000e+00   6.2000000e+00   6.5000000e+00   7.6000000e+00   7.5000000e+00   5.8000000e+00   6.1000000e+00   6.3000000e+00   6.9000000e+00   6.2000000e+00   4.8000000e+00   6.2000000e+00   5.9000000e+00   6.1000000e+00   6.7000000e+00   4.5000000e+00   6.1000000e+00   9.3000000e+00   7.9000000e+00   9.9000000e+00   8.6000000e+00   9.3000000e+00   1.1100000e+01   6.4000000e+00   1.0300000e+01   9.6000000e+00   1.0000000e+01   8.2000000e+00   8.7000000e+00   9.2000000e+00   8.0000000e+00   8.3000000e+00   8.6000000e+00   8.6000000e+00   1.1000000e+01   1.2100000e+01   8.1000000e+00   9.5000000e+00   7.5000000e+00   1.1400000e+01   8.1000000e+00   9.0000000e+00   9.6000000e+00   7.8000000e+00   7.6000000e+00   9.1000000e+00   9.4000000e+00   1.0400000e+01   1.0700000e+01   9.2000000e+00   7.9000000e+00   8.3000000e+00   1.0900000e+01   8.7000000e+00   8.4000000e+00   7.4000000e+00   9.1000000e+00   9.4000000e+00   9.0000000e+00   7.9000000e+00   9.6000000e+00   9.4000000e+00   9.0000000e+00   8.5000000e+00   8.5000000e+00   8.3000000e+00   7.6000000e+00   9.0000000e-01   8.0000000e-01   4.0000000e-01   8.0000000e-01   8.0000000e-01   9.0000000e-01   9.0000000e-01   7.0000000e-01   1.5000000e+00   1.9000000e+00   1.0000000e+00   1.0000000e+00   1.3000000e+00   1.0000000e+00   1.7000000e+00   6.0000000e-01   9.0000000e-01   2.2000000e+00   1.5000000e+00   5.0000000e-01   8.0000000e-01   1.1000000e+00   9.0000000e-01   1.2000000e+00   1.1000000e+00   7.0000000e-01   5.9000000e+00   5.2000000e+00   6.2000000e+00   4.5000000e+00   5.8000000e+00   4.7000000e+00   5.3000000e+00   3.2000000e+00   5.6000000e+00   3.8000000e+00   3.7000000e+00   4.6000000e+00   4.8000000e+00   5.3000000e+00   3.6000000e+00   5.4000000e+00   4.6000000e+00   4.2000000e+00   6.0000000e+00   4.1000000e+00   5.3000000e+00   4.6000000e+00   6.2000000e+00   5.2000000e+00   5.1000000e+00   5.4000000e+00   6.2000000e+00   6.4000000e+00   5.1000000e+00   3.6000000e+00   4.0000000e+00   3.8000000e+00   4.2000000e+00   6.0000000e+00   4.4000000e+00   4.9000000e+00   5.8000000e+00   5.7000000e+00   4.0000000e+00   4.3000000e+00   4.5000000e+00   5.1000000e+00   4.4000000e+00   3.2000000e+00   4.4000000e+00   4.1000000e+00   4.3000000e+00   4.9000000e+00   2.7000000e+00   4.3000000e+00   7.5000000e+00   6.1000000e+00   8.1000000e+00   6.8000000e+00   7.5000000e+00   9.3000000e+00   5.0000000e+00   8.5000000e+00   7.8000000e+00   8.8000000e+00   6.4000000e+00   6.9000000e+00   7.4000000e+00   6.2000000e+00   6.5000000e+00   6.8000000e+00   6.8000000e+00   9.8000000e+00   1.0300000e+01   6.3000000e+00   7.7000000e+00   5.7000000e+00   9.6000000e+00   6.3000000e+00   7.2000000e+00   7.8000000e+00   6.0000000e+00   5.8000000e+00   7.3000000e+00   7.6000000e+00   8.6000000e+00   9.5000000e+00   7.4000000e+00   6.1000000e+00   6.5000000e+00   9.1000000e+00   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7.3000000e+00   7.0000000e+00   6.0000000e+00   7.7000000e+00   8.0000000e+00   7.6000000e+00   6.5000000e+00   8.2000000e+00   8.0000000e+00   7.6000000e+00   7.1000000e+00   7.1000000e+00   6.9000000e+00   6.2000000e+00   2.0000000e-01   9.0000000e-01   9.0000000e-01   5.0000000e-01   7.0000000e-01   1.1000000e+00   8.0000000e-01   8.0000000e-01   5.0000000e-01   8.0000000e-01   1.5000000e+00   2.0000000e-01   5.0000000e-01   2.2000000e+00   1.3000000e+00   7.0000000e-01   1.0000000e+00   1.1000000e+00   5.0000000e-01   1.0000000e+00   3.0000000e-01   5.0000000e-01   6.5000000e+00   5.8000000e+00   6.8000000e+00   5.1000000e+00   6.4000000e+00   5.3000000e+00   5.9000000e+00   4.0000000e+00   6.2000000e+00   4.4000000e+00   4.5000000e+00   5.2000000e+00   5.4000000e+00   5.9000000e+00   4.2000000e+00   6.0000000e+00   5.2000000e+00   4.8000000e+00   6.6000000e+00   4.7000000e+00   5.9000000e+00   5.2000000e+00   6.8000000e+00   5.8000000e+00   5.7000000e+00   6.0000000e+00   6.8000000e+00   7.0000000e+00   5.7000000e+00   4.2000000e+00   4.6000000e+00   4.4000000e+00   4.8000000e+00   6.6000000e+00   5.0000000e+00   5.3000000e+00   6.4000000e+00   6.3000000e+00   4.6000000e+00   4.9000000e+00   5.1000000e+00   5.7000000e+00   5.0000000e+00   4.0000000e+00   5.0000000e+00   4.7000000e+00   4.9000000e+00   5.5000000e+00   3.5000000e+00   4.9000000e+00   8.1000000e+00   6.7000000e+00   8.7000000e+00   7.4000000e+00   8.1000000e+00   9.9000000e+00   5.8000000e+00   9.1000000e+00   8.4000000e+00   9.0000000e+00   7.0000000e+00   7.5000000e+00   8.0000000e+00   6.8000000e+00   7.1000000e+00   7.4000000e+00   7.4000000e+00   1.0000000e+01   1.0900000e+01   6.9000000e+00   8.3000000e+00   6.3000000e+00   1.0200000e+01   6.9000000e+00   7.8000000e+00   8.4000000e+00   6.6000000e+00   6.4000000e+00   7.9000000e+00   8.2000000e+00   9.2000000e+00   9.7000000e+00   8.0000000e+00   6.7000000e+00   7.1000000e+00   9.7000000e+00   7.5000000e+00   7.2000000e+00   6.2000000e+00   7.9000000e+00   8.2000000e+00   7.8000000e+00   6.7000000e+00   8.4000000e+00   8.2000000e+00   7.8000000e+00   7.3000000e+00   7.3000000e+00   7.1000000e+00   6.4000000e+00   9.0000000e-01   9.0000000e-01   5.0000000e-01   9.0000000e-01   1.1000000e+00   8.0000000e-01   6.0000000e-01   5.0000000e-01   8.0000000e-01   1.3000000e+00   2.0000000e-01   5.0000000e-01   2.0000000e+00   1.1000000e+00   9.0000000e-01   1.2000000e+00   9.0000000e-01   7.0000000e-01   8.0000000e-01   5.0000000e-01   3.0000000e-01   6.5000000e+00   5.8000000e+00   6.8000000e+00   5.1000000e+00   6.4000000e+00   5.3000000e+00   5.9000000e+00   4.0000000e+00   6.2000000e+00   4.4000000e+00   4.5000000e+00   5.2000000e+00   5.4000000e+00   5.9000000e+00   4.2000000e+00   6.0000000e+00   5.2000000e+00   4.8000000e+00   6.6000000e+00   4.7000000e+00   5.9000000e+00   5.2000000e+00   6.8000000e+00   5.8000000e+00   5.7000000e+00   6.0000000e+00   6.8000000e+00   7.0000000e+00   5.7000000e+00   4.2000000e+00   4.6000000e+00   4.4000000e+00   4.8000000e+00   6.6000000e+00   5.0000000e+00   5.3000000e+00   6.4000000e+00   6.3000000e+00   4.6000000e+00   4.9000000e+00   5.1000000e+00   5.7000000e+00   5.0000000e+00   4.0000000e+00   5.0000000e+00   4.7000000e+00   4.9000000e+00   5.5000000e+00   3.5000000e+00   4.9000000e+00   8.1000000e+00   6.7000000e+00   8.7000000e+00   7.4000000e+00   8.1000000e+00   9.9000000e+00   5.8000000e+00   9.1000000e+00   8.4000000e+00   9.2000000e+00   7.0000000e+00   7.5000000e+00   8.0000000e+00   6.8000000e+00   7.1000000e+00   7.4000000e+00   7.4000000e+00   1.0200000e+01   1.0900000e+01   6.9000000e+00   8.3000000e+00   6.3000000e+00   1.0200000e+01   6.9000000e+00   7.8000000e+00   8.4000000e+00   6.6000000e+00   6.4000000e+00   7.9000000e+00   8.2000000e+00   9.2000000e+00   9.9000000e+00   8.0000000e+00   6.7000000e+00   7.1000000e+00   9.7000000e+00   7.5000000e+00   7.2000000e+00   6.2000000e+00   7.9000000e+00   8.2000000e+00   7.8000000e+00   6.7000000e+00   8.4000000e+00   8.2000000e+00   7.8000000e+00   7.3000000e+00   7.3000000e+00   7.1000000e+00   6.4000000e+00   2.0000000e-01   1.2000000e+00   1.6000000e+00   2.0000000e+00   5.0000000e-01   7.0000000e-01   1.4000000e+00   5.0000000e-01   8.0000000e-01   7.0000000e-01   1.0000000e+00   1.5000000e+00   6.0000000e-01   1.0000000e+00   1.5000000e+00   6.0000000e-01   1.0000000e+00   3.0000000e-01   1.2000000e+00   6.0000000e-01   6.6000000e+00   5.9000000e+00   6.9000000e+00   5.2000000e+00   6.5000000e+00   5.4000000e+00   6.2000000e+00   3.5000000e+00   6.3000000e+00   4.5000000e+00   4.2000000e+00   5.3000000e+00   5.5000000e+00   6.0000000e+00   4.3000000e+00   6.1000000e+00   5.3000000e+00   4.9000000e+00   6.7000000e+00   4.8000000e+00   6.0000000e+00   5.3000000e+00   6.9000000e+00   5.9000000e+00   5.8000000e+00   6.1000000e+00   6.9000000e+00   7.1000000e+00   5.8000000e+00   4.3000000e+00   4.7000000e+00   4.5000000e+00   4.9000000e+00   6.7000000e+00   5.1000000e+00   5.8000000e+00   6.5000000e+00   6.4000000e+00   4.7000000e+00   5.0000000e+00   5.2000000e+00   5.8000000e+00   5.1000000e+00   3.7000000e+00   5.1000000e+00   4.8000000e+00   5.0000000e+00   5.6000000e+00   3.4000000e+00   5.0000000e+00   8.4000000e+00   6.8000000e+00   8.8000000e+00   7.5000000e+00   8.2000000e+00   1.0000000e+01   5.3000000e+00   9.2000000e+00   8.5000000e+00   9.7000000e+00   7.1000000e+00   7.6000000e+00   8.1000000e+00   6.9000000e+00   7.2000000e+00   7.5000000e+00   7.5000000e+00   1.0700000e+01   1.1000000e+01   7.0000000e+00   8.4000000e+00   6.4000000e+00   1.0300000e+01   7.0000000e+00   8.1000000e+00   8.5000000e+00   6.7000000e+00   6.5000000e+00   8.0000000e+00   8.3000000e+00   9.3000000e+00   1.0400000e+01   8.1000000e+00   6.8000000e+00   7.2000000e+00   9.8000000e+00   8.0000000e+00   7.3000000e+00   6.3000000e+00   8.0000000e+00   8.3000000e+00   7.9000000e+00   6.8000000e+00   8.5000000e+00   8.5000000e+00   7.9000000e+00   7.4000000e+00   7.4000000e+00   7.6000000e+00   6.5000000e+00   1.2000000e+00   1.6000000e+00   2.0000000e+00   3.0000000e-01   7.0000000e-01   1.4000000e+00   3.0000000e-01   8.0000000e-01   7.0000000e-01   1.0000000e+00   1.5000000e+00   8.0000000e-01   1.0000000e+00   1.5000000e+00   4.0000000e-01   1.0000000e+00   5.0000000e-01   1.2000000e+00   6.0000000e-01   6.6000000e+00   5.9000000e+00   6.7000000e+00   5.0000000e+00   6.3000000e+00   5.2000000e+00   6.2000000e+00   3.3000000e+00   6.1000000e+00   4.3000000e+00   4.0000000e+00   5.1000000e+00   5.3000000e+00   5.8000000e+00   4.1000000e+00   5.9000000e+00   5.1000000e+00   4.7000000e+00   6.5000000e+00   4.6000000e+00   6.0000000e+00   5.1000000e+00   6.7000000e+00   5.7000000e+00   5.6000000e+00   5.9000000e+00   6.7000000e+00   6.9000000e+00   5.6000000e+00   4.1000000e+00   4.5000000e+00   4.3000000e+00   4.7000000e+00   6.5000000e+00   4.9000000e+00   5.8000000e+00   6.3000000e+00   6.2000000e+00   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1.1200000e+01   7.2000000e+00   8.6000000e+00   6.6000000e+00   1.0500000e+01   7.2000000e+00   8.1000000e+00   8.7000000e+00   6.9000000e+00   6.7000000e+00   8.2000000e+00   8.5000000e+00   9.5000000e+00   9.4000000e+00   8.3000000e+00   7.0000000e+00   7.4000000e+00   1.0000000e+01   7.8000000e+00   7.5000000e+00   6.5000000e+00   8.2000000e+00   8.5000000e+00   8.1000000e+00   7.0000000e+00   8.7000000e+00   8.5000000e+00   8.1000000e+00   7.6000000e+00   7.6000000e+00   7.4000000e+00   6.7000000e+00   1.3000000e+00   5.0000000e-01   6.9000000e+00   6.2000000e+00   7.2000000e+00   5.5000000e+00   6.8000000e+00   5.7000000e+00   6.5000000e+00   3.8000000e+00   6.6000000e+00   4.8000000e+00   4.5000000e+00   5.6000000e+00   5.8000000e+00   6.3000000e+00   4.6000000e+00   6.4000000e+00   5.6000000e+00   5.2000000e+00   7.0000000e+00   5.1000000e+00   6.3000000e+00   5.6000000e+00   7.2000000e+00   6.2000000e+00   6.1000000e+00   6.4000000e+00   7.2000000e+00   7.4000000e+00   6.1000000e+00   4.6000000e+00   5.0000000e+00   4.8000000e+00   5.2000000e+00   7.0000000e+00   5.4000000e+00   6.1000000e+00   6.8000000e+00   6.7000000e+00   5.0000000e+00   5.3000000e+00   5.5000000e+00   6.1000000e+00   5.4000000e+00   4.0000000e+00   5.4000000e+00   5.1000000e+00   5.3000000e+00   5.9000000e+00   3.7000000e+00   5.3000000e+00   8.7000000e+00   7.1000000e+00   9.1000000e+00   7.8000000e+00   8.5000000e+00   1.0300000e+01   5.6000000e+00   9.5000000e+00   8.8000000e+00   1.0000000e+01   7.4000000e+00   7.9000000e+00   8.4000000e+00   7.2000000e+00   7.5000000e+00   7.8000000e+00   7.8000000e+00   1.1000000e+01   1.1300000e+01   7.3000000e+00   8.7000000e+00   6.7000000e+00   1.0600000e+01   7.3000000e+00   8.4000000e+00   8.8000000e+00   7.0000000e+00   6.8000000e+00   8.3000000e+00   8.6000000e+00   9.6000000e+00   1.0700000e+01   8.4000000e+00   7.1000000e+00   7.5000000e+00   1.0100000e+01   8.3000000e+00   7.6000000e+00   6.6000000e+00   8.3000000e+00   8.6000000e+00   8.2000000e+00   7.1000000e+00   8.8000000e+00   8.8000000e+00   8.2000000e+00   7.7000000e+00   7.7000000e+00   7.9000000e+00   6.8000000e+00   8.0000000e-01   6.6000000e+00   5.9000000e+00   6.9000000e+00   5.2000000e+00   6.5000000e+00   5.4000000e+00   6.0000000e+00   4.3000000e+00   6.3000000e+00   4.7000000e+00   4.8000000e+00   5.3000000e+00   5.5000000e+00   6.0000000e+00   4.3000000e+00   6.1000000e+00   5.3000000e+00   4.9000000e+00   6.7000000e+00   4.8000000e+00   6.0000000e+00   5.3000000e+00   6.9000000e+00   5.9000000e+00   5.8000000e+00   6.1000000e+00   6.9000000e+00   7.1000000e+00   5.8000000e+00   4.3000000e+00   4.7000000e+00   4.5000000e+00   4.9000000e+00   6.7000000e+00   5.1000000e+00   5.4000000e+00   6.5000000e+00   6.4000000e+00   4.7000000e+00   5.0000000e+00   5.2000000e+00   5.8000000e+00   5.1000000e+00   4.3000000e+00   5.1000000e+00   4.8000000e+00   5.0000000e+00   5.6000000e+00   3.8000000e+00   5.0000000e+00   8.2000000e+00   6.8000000e+00   8.8000000e+00   7.5000000e+00   8.2000000e+00   1.0000000e+01   6.1000000e+00   9.2000000e+00   8.5000000e+00   8.9000000e+00   7.1000000e+00   7.6000000e+00   8.1000000e+00   6.9000000e+00   7.2000000e+00   7.5000000e+00   7.5000000e+00   9.7000000e+00   1.1000000e+01   7.0000000e+00   8.4000000e+00   6.4000000e+00   1.0300000e+01   7.0000000e+00   7.9000000e+00   8.5000000e+00   6.7000000e+00   6.5000000e+00   8.0000000e+00   8.3000000e+00   9.3000000e+00   9.4000000e+00   8.1000000e+00   6.8000000e+00   7.2000000e+00   9.8000000e+00   7.6000000e+00   7.3000000e+00   6.3000000e+00   8.0000000e+00   8.3000000e+00   7.9000000e+00   6.8000000e+00   8.5000000e+00   8.3000000e+00   7.9000000e+00   7.4000000e+00   7.4000000e+00   7.2000000e+00   6.5000000e+00   6.6000000e+00   5.9000000e+00   6.9000000e+00   5.2000000e+00   6.5000000e+00   5.4000000e+00   6.0000000e+00   3.7000000e+00   6.3000000e+00   4.5000000e+00   4.2000000e+00   5.3000000e+00   5.5000000e+00   6.0000000e+00   4.3000000e+00   6.1000000e+00   5.3000000e+00   4.9000000e+00   6.7000000e+00   4.8000000e+00   6.0000000e+00   5.3000000e+00   6.9000000e+00   5.9000000e+00   5.8000000e+00   6.1000000e+00   6.9000000e+00   7.1000000e+00   5.8000000e+00   4.3000000e+00   4.7000000e+00   4.5000000e+00   4.9000000e+00   6.7000000e+00   5.1000000e+00   5.6000000e+00   6.5000000e+00   6.4000000e+00   4.7000000e+00   5.0000000e+00   5.2000000e+00   5.8000000e+00   5.1000000e+00   3.7000000e+00   5.1000000e+00   4.8000000e+00   5.0000000e+00   5.6000000e+00   3.4000000e+00   5.0000000e+00   8.2000000e+00   6.8000000e+00   8.8000000e+00   7.5000000e+00   8.2000000e+00   1.0000000e+01   5.5000000e+00   9.2000000e+00   8.5000000e+00   9.5000000e+00   7.1000000e+00   7.6000000e+00   8.1000000e+00   6.9000000e+00   7.2000000e+00   7.5000000e+00   7.5000000e+00   1.0500000e+01   1.1000000e+01   7.0000000e+00   8.4000000e+00   6.4000000e+00   1.0300000e+01   7.0000000e+00   7.9000000e+00   8.5000000e+00   6.7000000e+00   6.5000000e+00   8.0000000e+00   8.3000000e+00   9.3000000e+00   1.0200000e+01   8.1000000e+00   6.8000000e+00   7.2000000e+00   9.8000000e+00   7.8000000e+00   7.3000000e+00   6.3000000e+00   8.0000000e+00   8.3000000e+00   7.9000000e+00   6.8000000e+00   8.5000000e+00   8.3000000e+00   7.9000000e+00   7.4000000e+00   7.4000000e+00   7.4000000e+00   6.5000000e+00   9.0000000e-01   5.0000000e-01   3.2000000e+00   1.1000000e+00   2.0000000e+00   1.0000000e+00   4.7000000e+00   9.0000000e-01   3.1000000e+00   4.8000000e+00   1.9000000e+00   3.1000000e+00   1.2000000e+00   2.9000000e+00   7.0000000e-01   1.9000000e+00   2.7000000e+00   2.1000000e+00   3.2000000e+00   1.6000000e+00   2.1000000e+00   1.7000000e+00   1.5000000e+00   1.4000000e+00   9.0000000e-01   7.0000000e-01   1.1000000e+00   1.6000000e+00   3.5000000e+00   3.5000000e+00   3.7000000e+00   2.7000000e+00   2.1000000e+00   2.1000000e+00   1.6000000e+00   5.0000000e-01   2.0000000e+00   2.3000000e+00   3.0000000e+00   2.6000000e+00   1.2000000e+00   2.7000000e+00   4.7000000e+00   2.5000000e+00   2.2000000e+00   2.2000000e+00   1.6000000e+00   4.6000000e+00   2.4000000e+00   3.2000000e+00   2.6000000e+00   2.2000000e+00   2.3000000e+00   2.6000000e+00   3.4000000e+00   3.3000000e+00   2.6000000e+00   2.5000000e+00   3.1000000e+00   1.5000000e+00   2.2000000e+00   1.9000000e+00   2.9000000e+00   3.0000000e+00   2.1000000e+00   1.9000000e+00   4.1000000e+00   4.4000000e+00   2.4000000e+00   2.0000000e+00   2.6000000e+00   3.7000000e+00   1.8000000e+00   2.1000000e+00   1.9000000e+00   1.7000000e+00   1.7000000e+00   2.6000000e+00   1.7000000e+00   2.7000000e+00   3.8000000e+00   2.7000000e+00   1.6000000e+00   2.4000000e+00   3.2000000e+00   2.8000000e+00   1.9000000e+00   1.7000000e+00   1.6000000e+00   2.3000000e+00   1.5000000e+00   2.6000000e+00   2.3000000e+00   2.5000000e+00   1.9000000e+00   2.2000000e+00   1.8000000e+00   2.6000000e+00   2.1000000e+00   1.0000000e+00   2.5000000e+00   6.0000000e-01   1.3000000e+00   5.0000000e-01   4.0000000e+00   8.0000000e-01   2.4000000e+00   4.1000000e+00   1.0000000e+00   2.4000000e+00   9.0000000e-01   2.2000000e+00   6.0000000e-01   1.0000000e+00   2.0000000e+00   1.2000000e+00   2.5000000e+00   1.1000000e+00   1.4000000e+00   1.2000000e+00   1.2000000e+00   7.0000000e-01   6.0000000e-01   1.2000000e+00   1.2000000e+00   7.0000000e-01   2.8000000e+00   2.8000000e+00   3.0000000e+00   2.0000000e+00   1.6000000e+00   1.2000000e+00   7.0000000e-01   6.0000000e-01   1.3000000e+00   1.6000000e+00   2.3000000e+00   1.9000000e+00   7.0000000e-01   2.0000000e+00   4.0000000e+00   1.8000000e+00   1.5000000e+00   1.5000000e+00   9.0000000e-01   3.9000000e+00   1.7000000e+00   2.7000000e+00   2.1000000e+00   2.9000000e+00   1.8000000e+00   2.3000000e+00   4.1000000e+00   2.4000000e+00   3.3000000e+00   2.6000000e+00   3.8000000e+00   1.2000000e+00   1.7000000e+00   2.2000000e+00   2.4000000e+00   2.5000000e+00   1.6000000e+00   1.6000000e+00   4.8000000e+00   5.1000000e+00   1.9000000e+00   2.5000000e+00   2.1000000e+00   4.4000000e+00   1.3000000e+00   2.2000000e+00   2.6000000e+00   1.2000000e+00   1.2000000e+00   2.1000000e+00   2.4000000e+00   3.4000000e+00   4.5000000e+00   2.2000000e+00   1.1000000e+00   2.1000000e+00   3.9000000e+00   2.3000000e+00   1.4000000e+00   1.2000000e+00   2.1000000e+00   2.4000000e+00   2.0000000e+00   2.1000000e+00   2.6000000e+00   2.6000000e+00   2.0000000e+00   1.7000000e+00   1.5000000e+00   2.1000000e+00   1.6000000e+00   3.3000000e+00   1.0000000e+00   2.1000000e+00   1.1000000e+00   4.8000000e+00   1.0000000e+00   3.2000000e+00   4.9000000e+00   1.8000000e+00   3.2000000e+00   1.3000000e+00   3.0000000e+00   8.0000000e-01   1.8000000e+00   2.8000000e+00   2.0000000e+00   3.3000000e+00   1.5000000e+00   2.2000000e+00   1.2000000e+00   1.6000000e+00   1.5000000e+00   1.0000000e+00   6.0000000e-01   6.0000000e-01   1.5000000e+00   3.6000000e+00   3.6000000e+00   3.8000000e+00   2.8000000e+00   1.6000000e+00   2.0000000e+00   1.7000000e+00   4.0000000e-01   2.1000000e+00   2.4000000e+00   3.1000000e+00   2.7000000e+00   1.3000000e+00   2.8000000e+00   4.8000000e+00   2.6000000e+00   2.3000000e+00   2.3000000e+00   1.7000000e+00   4.7000000e+00   2.5000000e+00   2.9000000e+00   2.1000000e+00   1.9000000e+00   1.8000000e+00   2.1000000e+00   3.1000000e+00   3.2000000e+00   2.3000000e+00   2.0000000e+00   3.0000000e+00   1.2000000e+00   1.7000000e+00   1.4000000e+00   2.4000000e+00   2.5000000e+00   1.8000000e+00   1.4000000e+00   4.0000000e+00   4.1000000e+00   1.9000000e+00   1.7000000e+00   2.1000000e+00   3.4000000e+00   1.3000000e+00   1.8000000e+00   1.8000000e+00   1.4000000e+00   1.2000000e+00   2.1000000e+00   1.4000000e+00   2.4000000e+00   3.7000000e+00   2.2000000e+00   1.1000000e+00   2.1000000e+00   2.9000000e+00   2.5000000e+00   1.4000000e+00   1.4000000e+00   1.1000000e+00   1.8000000e+00   1.0000000e+00   2.1000000e+00   2.0000000e+00   2.2000000e+00   1.4000000e+00   1.7000000e+00   1.3000000e+00   2.3000000e+00   1.6000000e+00   2.3000000e+00   1.2000000e+00   2.8000000e+00   1.7000000e+00   2.3000000e+00   9.0000000e-01   1.6000000e+00   1.5000000e+00   9.0000000e-01   2.0000000e+00   1.1000000e+00   2.5000000e+00   1.5000000e+00   1.1000000e+00   1.5000000e+00   6.0000000e-01   2.6000000e+00   1.1000000e+00   2.1000000e+00   1.9000000e+00   1.8000000e+00   2.3000000e+00   2.7000000e+00   3.3000000e+00   1.8000000e+00   1.3000000e+00   5.0000000e-01   7.0000000e-01   9.0000000e-01   2.3000000e+00   1.5000000e+00   2.4000000e+00   2.9000000e+00   1.2000000e+00   9.0000000e-01   2.0000000e-01   8.0000000e-01   2.0000000e+00   7.0000000e-01   1.5000000e+00   7.0000000e-01   1.2000000e+00   1.0000000e+00   1.6000000e+00   1.8000000e+00   8.0000000e-01   5.0000000e+00   2.4000000e+00   5.0000000e+00   3.5000000e+00   4.4000000e+00   6.2000000e+00   1.7000000e+00   5.2000000e+00   3.7000000e+00   6.3000000e+00   3.7000000e+00   3.2000000e+00   4.3000000e+00   2.1000000e+00   3.0000000e+00   4.1000000e+00   3.7000000e+00   7.3000000e+00   6.4000000e+00   1.8000000e+00   5.0000000e+00   2.2000000e+00   6.1000000e+00   2.6000000e+00   4.7000000e+00   5.1000000e+00   2.5000000e+00   2.7000000e+00   3.8000000e+00   4.5000000e+00   5.1000000e+00   7.0000000e+00   3.9000000e+00   2.6000000e+00   2.6000000e+00   6.0000000e+00   4.6000000e+00   3.7000000e+00   2.5000000e+00   4.4000000e+00   4.7000000e+00   4.3000000e+00   2.4000000e+00   5.1000000e+00   5.1000000e+00   4.1000000e+00   2.6000000e+00   3.6000000e+00   4.2000000e+00   2.7000000e+00   1.1000000e+00   9.0000000e-01   3.8000000e+00   4.0000000e-01   2.2000000e+00   3.9000000e+00   1.2000000e+00   2.2000000e+00   7.0000000e-01   2.2000000e+00   8.0000000e-01   1.2000000e+00   1.8000000e+00   1.0000000e+00   2.3000000e+00   1.5000000e+00   1.2000000e+00   8.0000000e-01   8.0000000e-01   7.0000000e-01   6.0000000e-01   6.0000000e-01   1.0000000e+00   7.0000000e-01   2.6000000e+00   2.6000000e+00   2.8000000e+00   1.8000000e+00   1.2000000e+00   1.4000000e+00   1.3000000e+00   6.0000000e-01   1.1000000e+00   1.8000000e+00   2.1000000e+00   1.7000000e+00   7.0000000e-01   1.8000000e+00   3.8000000e+00   1.6000000e+00   1.7000000e+00   1.5000000e+00   9.0000000e-01   3.7000000e+00   1.5000000e+00   3.1000000e+00   1.7000000e+00   2.7000000e+00   1.6000000e+00   2.1000000e+00   3.9000000e+00   2.2000000e+00   2.9000000e+00   2.0000000e+00   4.0000000e+00   1.4000000e+00   1.3000000e+00   2.0000000e+00   2.0000000e+00   2.1000000e+00   2.0000000e+00   1.4000000e+00   5.0000000e+00   4.5000000e+00   1.5000000e+00   2.7000000e+00   1.7000000e+00   3.8000000e+00   9.0000000e-01   2.4000000e+00   2.8000000e+00   8.0000000e-01   1.2000000e+00   1.7000000e+00   2.2000000e+00   2.8000000e+00   4.7000000e+00   1.8000000e+00   7.0000000e-01   1.7000000e+00   3.7000000e+00   2.7000000e+00   1.6000000e+00   1.2000000e+00   2.1000000e+00   2.4000000e+00   2.0000000e+00   1.7000000e+00   2.8000000e+00   2.8000000e+00   1.8000000e+00   1.3000000e+00   1.3000000e+00   2.5000000e+00   1.6000000e+00   1.6000000e+00   2.7000000e+00   1.1000000e+00   1.3000000e+00   2.8000000e+00   9.0000000e-01   1.7000000e+00   8.0000000e-01   1.1000000e+00   1.5000000e+00   5.0000000e-01   9.0000000e-01   1.3000000e+00   1.2000000e+00   1.4000000e+00   9.0000000e-01   1.5000000e+00   7.0000000e-01   1.0000000e+00   1.3000000e+00   1.5000000e+00   2.1000000e+00   6.0000000e-01   1.5000000e+00   1.5000000e+00   1.7000000e+00   9.0000000e-01   1.3000000e+00   7.0000000e-01   1.2000000e+00   1.7000000e+00   1.2000000e+00   7.0000000e-01   1.0000000e+00   6.0000000e-01   8.0000000e-01   9.0000000e-01   2.7000000e+00   5.0000000e-01   6.0000000e-01   4.0000000e-01   8.0000000e-01   2.6000000e+00   4.0000000e-01   3.8000000e+00   1.4000000e+00   3.8000000e+00   2.3000000e+00   3.2000000e+00   5.0000000e+00   1.5000000e+00   4.0000000e+00   3.1000000e+00   5.1000000e+00   2.5000000e+00   2.2000000e+00   3.1000000e+00   1.5000000e+00   1.8000000e+00   2.9000000e+00   2.5000000e+00   6.1000000e+00   5.6000000e+00   1.6000000e+00   3.8000000e+00   1.2000000e+00   4.9000000e+00   1.6000000e+00   3.5000000e+00   3.9000000e+00   1.3000000e+00   1.5000000e+00   2.6000000e+00   3.3000000e+00   3.9000000e+00   5.8000000e+00   2.7000000e+00   1.4000000e+00   1.8000000e+00   4.8000000e+00   3.4000000e+00   2.5000000e+00   1.3000000e+00   3.2000000e+00   3.5000000e+00   3.1000000e+00   1.4000000e+00   3.9000000e+00   3.9000000e+00   2.9000000e+00   2.0000000e+00   2.4000000e+00   3.0000000e+00   1.5000000e+00   4.3000000e+00   1.1000000e+00   2.7000000e+00   4.4000000e+00   1.3000000e+00   2.7000000e+00   8.0000000e-01   2.5000000e+00   1.1000000e+00   1.3000000e+00   2.3000000e+00   1.5000000e+00   2.8000000e+00   8.0000000e-01   1.7000000e+00   1.1000000e+00   1.1000000e+00   1.2000000e+00   1.1000000e+00   1.3000000e+00   1.1000000e+00   1.0000000e+00   3.1000000e+00   3.1000000e+00   3.3000000e+00   2.3000000e+00   1.3000000e+00   1.5000000e+00   6.0000000e-01   7.0000000e-01   1.6000000e+00   1.9000000e+00   2.6000000e+00   2.2000000e+00   8.0000000e-01   2.3000000e+00   4.3000000e+00   2.1000000e+00   1.8000000e+00   1.8000000e+00   1.2000000e+00   4.2000000e+00   2.0000000e+00   2.2000000e+00   1.8000000e+00   2.8000000e+00   1.5000000e+00   2.2000000e+00   4.0000000e+00   2.5000000e+00   3.2000000e+00   2.5000000e+00   3.5000000e+00   1.1000000e+00   1.6000000e+00   2.1000000e+00   2.1000000e+00   2.2000000e+00   1.5000000e+00   1.5000000e+00   4.5000000e+00   5.0000000e+00   1.8000000e+00   2.4000000e+00   1.8000000e+00   4.3000000e+00   1.0000000e+00   1.9000000e+00   2.5000000e+00   9.0000000e-01   9.0000000e-01   2.0000000e+00   2.3000000e+00   3.3000000e+00   4.2000000e+00   2.1000000e+00   1.0000000e+00   2.0000000e+00   3.8000000e+00   1.8000000e+00   1.3000000e+00   9.0000000e-01   2.0000000e+00   2.3000000e+00   1.9000000e+00   1.8000000e+00   2.5000000e+00   2.3000000e+00   1.9000000e+00   1.4000000e+00   1.4000000e+00   1.6000000e+00   1.3000000e+00   3.8000000e+00   1.6000000e+00   7.0000000e-01   3.0000000e+00   2.0000000e+00   3.5000000e+00   1.8000000e+00   4.0000000e+00   3.0000000e+00   2.0000000e+00   3.2000000e+00   1.5000000e+00   4.1000000e+00   2.6000000e+00   3.6000000e+00   3.2000000e+00   3.3000000e+00   3.8000000e+00   4.2000000e+00   4.8000000e+00   3.3000000e+00   1.2000000e+00   1.2000000e+00   1.0000000e+00   2.0000000e+00   3.8000000e+00   2.8000000e+00   3.9000000e+00   4.4000000e+00   2.9000000e+00   2.4000000e+00   1.7000000e+00   2.1000000e+00   3.5000000e+00   2.0000000e+00   2.0000000e-01   2.2000000e+00   2.5000000e+00   2.5000000e+00   3.1000000e+00   7.0000000e-01   2.3000000e+00   6.5000000e+00   3.9000000e+00   6.5000000e+00   5.0000000e+00   5.9000000e+00   7.7000000e+00   2.0000000e+00   6.7000000e+00   5.2000000e+00   7.8000000e+00   5.2000000e+00   4.7000000e+00   5.8000000e+00   3.6000000e+00   4.5000000e+00   5.6000000e+00   5.2000000e+00   8.8000000e+00   7.9000000e+00   3.5000000e+00   6.5000000e+00   3.7000000e+00   7.6000000e+00   4.1000000e+00   6.2000000e+00   6.6000000e+00   4.0000000e+00   4.2000000e+00   5.3000000e+00   6.0000000e+00   6.6000000e+00   8.5000000e+00   5.4000000e+00   4.1000000e+00   4.1000000e+00   7.5000000e+00   6.1000000e+00   5.2000000e+00   4.0000000e+00   5.9000000e+00   6.2000000e+00   5.8000000e+00   3.9000000e+00   6.6000000e+00   6.6000000e+00   5.6000000e+00   4.1000000e+00   5.1000000e+00   5.7000000e+00   4.2000000e+00   2.4000000e+00   3.9000000e+00   1.4000000e+00   2.2000000e+00   7.0000000e-01   2.0000000e+00   6.0000000e-01   1.4000000e+00   1.8000000e+00   1.4000000e+00   2.3000000e+00   1.7000000e+00   1.2000000e+00   1.2000000e+00   8.0000000e-01   5.0000000e-01   4.0000000e-01   6.0000000e-01   1.0000000e+00   9.0000000e-01   2.6000000e+00   2.6000000e+00   2.8000000e+00   1.8000000e+00   1.6000000e+00   1.6000000e+00   1.5000000e+00   6.0000000e-01   1.1000000e+00   1.6000000e+00   2.1000000e+00   1.7000000e+00   7.0000000e-01   1.8000000e+00   3.8000000e+00   1.6000000e+00   1.5000000e+00   1.3000000e+00   7.0000000e-01   3.7000000e+00   1.5000000e+00   3.3000000e+00   2.1000000e+00   2.7000000e+00   1.8000000e+00   2.3000000e+00   3.9000000e+00   2.6000000e+00   2.9000000e+00   2.2000000e+00   4.0000000e+00   1.6000000e+00   1.7000000e+00   2.0000000e+00   2.4000000e+00   2.5000000e+00   2.2000000e+00   1.6000000e+00   5.0000000e+00   4.7000000e+00   1.9000000e+00   2.7000000e+00   2.1000000e+00   4.0000000e+00   1.3000000e+00   2.4000000e+00   2.8000000e+00   1.2000000e+00   1.4000000e+00   2.1000000e+00   2.2000000e+00   3.0000000e+00   4.7000000e+00   2.2000000e+00   1.1000000e+00   1.9000000e+00   3.7000000e+00   2.9000000e+00   1.8000000e+00   1.4000000e+00   2.1000000e+00   2.4000000e+00   2.0000000e+00   2.1000000e+00   2.8000000e+00   2.8000000e+00   1.8000000e+00   1.7000000e+00   1.5000000e+00   2.7000000e+00   1.8000000e+00   1.7000000e+00   1.4000000e+00   1.8000000e+00   1.9000000e+00   1.0000000e+00   2.4000000e+00   1.4000000e+00   1.2000000e+00   2.2000000e+00   9.0000000e-01   2.5000000e+00   1.2000000e+00   2.4000000e+00   2.0000000e+00   1.9000000e+00   2.2000000e+00   2.6000000e+00   3.2000000e+00   1.7000000e+00   1.4000000e+00   1.0000000e+00   1.2000000e+00   8.0000000e-01   2.2000000e+00   1.2000000e+00   2.3000000e+00   2.8000000e+00   2.1000000e+00   1.0000000e+00   7.0000000e-01   1.1000000e+00   1.9000000e+00   1.0000000e+00   1.6000000e+00   8.0000000e-01   1.3000000e+00   1.1000000e+00   1.7000000e+00   1.5000000e+00   9.0000000e-01   4.9000000e+00   2.3000000e+00   4.9000000e+00   3.4000000e+00   4.3000000e+00   6.1000000e+00   1.4000000e+00   5.1000000e+00   4.0000000e+00   6.2000000e+00   3.6000000e+00   3.1000000e+00   4.2000000e+00   2.4000000e+00   2.9000000e+00   4.0000000e+00   3.6000000e+00   7.2000000e+00   6.5000000e+00   2.5000000e+00   4.9000000e+00   2.1000000e+00   6.0000000e+00   2.5000000e+00   4.6000000e+00   5.0000000e+00   2.4000000e+00   2.6000000e+00   3.7000000e+00   4.4000000e+00   5.0000000e+00   6.9000000e+00   3.8000000e+00   2.5000000e+00   2.7000000e+00   5.9000000e+00   4.5000000e+00   3.6000000e+00   2.4000000e+00   4.3000000e+00   4.6000000e+00   4.2000000e+00   2.3000000e+00   5.0000000e+00   5.0000000e+00   4.0000000e+00   2.9000000e+00   3.5000000e+00   4.1000000e+00   2.6000000e+00   3.1000000e+00   1.7000000e+00   3.6000000e+00   1.9000000e+00   4.1000000e+00   3.1000000e+00   2.1000000e+00   2.9000000e+00   1.6000000e+00   4.2000000e+00   2.7000000e+00   3.7000000e+00   3.3000000e+00   3.4000000e+00   3.9000000e+00   4.3000000e+00   4.9000000e+00   3.4000000e+00   1.3000000e+00   1.3000000e+00   1.1000000e+00   2.1000000e+00   3.9000000e+00   2.9000000e+00   4.0000000e+00   4.5000000e+00   2.8000000e+00   2.5000000e+00   1.8000000e+00   2.2000000e+00   3.6000000e+00   2.1000000e+00   5.0000000e-01   2.3000000e+00   2.6000000e+00   2.6000000e+00   3.2000000e+00   1.2000000e+00   2.4000000e+00   6.6000000e+00   4.0000000e+00   6.6000000e+00   5.1000000e+00   6.0000000e+00   7.8000000e+00   2.3000000e+00   6.8000000e+00   5.3000000e+00   7.9000000e+00   5.3000000e+00   4.8000000e+00   5.9000000e+00   3.7000000e+00   4.6000000e+00   5.7000000e+00   5.3000000e+00   8.9000000e+00   8.0000000e+00   3.2000000e+00   6.6000000e+00   3.8000000e+00   7.7000000e+00   4.2000000e+00   6.3000000e+00   6.7000000e+00   4.1000000e+00   4.3000000e+00   5.4000000e+00   6.1000000e+00   6.7000000e+00   8.6000000e+00   5.5000000e+00   4.2000000e+00   4.2000000e+00   7.6000000e+00   6.2000000e+00   5.3000000e+00   4.1000000e+00   6.0000000e+00   6.3000000e+00   5.9000000e+00   4.0000000e+00   6.7000000e+00   6.7000000e+00   5.7000000e+00   4.2000000e+00   5.2000000e+00   5.8000000e+00   4.3000000e+00   1.6000000e+00   9.0000000e-01   1.2000000e+00   1.2000000e+00   6.0000000e-01   1.0000000e+00   1.4000000e+00   1.5000000e+00   1.1000000e+00   8.0000000e-01   1.6000000e+00   1.2000000e+00   9.0000000e-01   1.0000000e+00   1.8000000e+00   1.8000000e+00   5.0000000e-01   1.8000000e+00   1.8000000e+00   2.0000000e+00   1.0000000e+00   1.4000000e+00   8.0000000e-01   9.0000000e-01   1.4000000e+00   1.5000000e+00   6.0000000e-01   1.3000000e+00   1.3000000e+00   7.0000000e-01   1.0000000e+00   3.0000000e+00   8.0000000e-01   5.0000000e-01   5.0000000e-01   7.0000000e-01   2.9000000e+00   7.0000000e-01   3.5000000e+00   1.7000000e+00   3.5000000e+00   2.2000000e+00   2.9000000e+00   4.7000000e+00   2.0000000e+00   3.9000000e+00   3.2000000e+00   4.8000000e+00   2.2000000e+00   2.3000000e+00   2.8000000e+00   2.0000000e+00   2.1000000e+00   2.6000000e+00   2.2000000e+00   5.8000000e+00   5.7000000e+00   1.7000000e+00   3.5000000e+00   1.7000000e+00   5.0000000e+00   1.7000000e+00   3.2000000e+00   3.6000000e+00   1.4000000e+00   1.2000000e+00   2.7000000e+00   3.0000000e+00   4.0000000e+00   5.5000000e+00   2.8000000e+00   1.5000000e+00   2.1000000e+00   4.5000000e+00   3.1000000e+00   2.2000000e+00   1.0000000e+00   2.9000000e+00   3.2000000e+00   2.8000000e+00   1.7000000e+00   3.6000000e+00   3.6000000e+00   2.6000000e+00   2.1000000e+00   2.1000000e+00   2.7000000e+00   1.2000000e+00   1.9000000e+00   1.8000000e+00   2.4000000e+00   2.2000000e+00   8.0000000e-01   1.2000000e+00   9.0000000e-01   2.7000000e+00   1.0000000e+00   2.0000000e+00   1.6000000e+00   1.7000000e+00   2.2000000e+00   2.6000000e+00   3.2000000e+00   1.7000000e+00   1.2000000e+00   1.0000000e+00   1.0000000e+00   1.0000000e+00   2.2000000e+00   2.4000000e+00   2.3000000e+00   2.8000000e+00   1.1000000e+00   1.6000000e+00   1.1000000e+00   1.5000000e+00   1.9000000e+00   8.0000000e-01   1.8000000e+00   1.4000000e+00   1.5000000e+00   1.5000000e+00   1.5000000e+00   2.3000000e+00   1.3000000e+00   4.9000000e+00   2.7000000e+00   4.9000000e+00   3.4000000e+00   4.3000000e+00   6.1000000e+00   2.6000000e+00   5.1000000e+00   3.6000000e+00   6.2000000e+00   3.6000000e+00   3.1000000e+00   4.2000000e+00   2.6000000e+00   3.3000000e+00   4.0000000e+00   3.6000000e+00   7.2000000e+00   6.3000000e+00   1.5000000e+00   4.9000000e+00   2.9000000e+00   6.0000000e+00   2.5000000e+00   4.6000000e+00   5.0000000e+00   2.4000000e+00   2.6000000e+00   3.7000000e+00   4.4000000e+00   5.0000000e+00   6.9000000e+00   3.8000000e+00   2.5000000e+00   2.5000000e+00   5.9000000e+00   4.5000000e+00   3.6000000e+00   2.4000000e+00   4.3000000e+00   4.6000000e+00   4.2000000e+00   2.7000000e+00   5.0000000e+00   5.0000000e+00   4.0000000e+00   2.5000000e+00   3.5000000e+00   4.1000000e+00   2.8000000e+00   1.7000000e+00   1.1000000e+00   9.0000000e-01   1.5000000e+00   1.1000000e+00   2.0000000e+00   1.0000000e+00   9.0000000e-01   9.0000000e-01   3.0000000e-01   8.0000000e-01   9.0000000e-01   9.0000000e-01   1.3000000e+00   4.0000000e-01   2.3000000e+00   2.3000000e+00   2.5000000e+00   1.5000000e+00   9.0000000e-01   1.1000000e+00   1.0000000e+00   9.0000000e-01   1.2000000e+00   1.3000000e+00   1.8000000e+00   1.4000000e+00   2.0000000e-01   1.5000000e+00   3.5000000e+00   1.3000000e+00   1.2000000e+00   1.0000000e+00   6.0000000e-01   3.4000000e+00   1.2000000e+00   3.0000000e+00   1.4000000e+00   3.0000000e+00   1.5000000e+00   2.4000000e+00   4.2000000e+00   2.1000000e+00   3.2000000e+00   2.5000000e+00   4.3000000e+00   1.7000000e+00   1.6000000e+00   2.3000000e+00   1.7000000e+00   1.8000000e+00   2.1000000e+00   1.7000000e+00   5.3000000e+00   5.0000000e+00   1.2000000e+00   3.0000000e+00   1.4000000e+00   4.3000000e+00   1.0000000e+00   2.7000000e+00   3.1000000e+00   7.0000000e-01   7.0000000e-01   2.0000000e+00   2.5000000e+00   3.3000000e+00   5.0000000e+00   2.1000000e+00   8.0000000e-01   1.2000000e+00   4.0000000e+00   2.6000000e+00   1.7000000e+00   7.0000000e-01   2.4000000e+00   2.7000000e+00   2.3000000e+00   1.4000000e+00   3.1000000e+00   3.1000000e+00   2.1000000e+00   1.4000000e+00   1.6000000e+00   2.2000000e+00   1.1000000e+00   2.2000000e+00   1.2000000e+00   1.2000000e+00   2.4000000e+00   9.0000000e-01   2.3000000e+00   1.0000000e+00   2.6000000e+00   1.8000000e+00   1.5000000e+00   2.0000000e+00   2.6000000e+00   3.0000000e+00   1.5000000e+00   8.0000000e-01   1.0000000e+00   1.0000000e+00   8.0000000e-01   2.4000000e+00   1.4000000e+00   2.1000000e+00   2.6000000e+00   2.1000000e+00   6.0000000e-01   9.0000000e-01   1.3000000e+00   1.7000000e+00   1.0000000e+00   1.8000000e+00   8.0000000e-01   9.0000000e-01   7.0000000e-01   1.3000000e+00   1.7000000e+00   7.0000000e-01   4.7000000e+00   2.5000000e+00   4.7000000e+00   3.2000000e+00   4.1000000e+00   5.9000000e+00   2.4000000e+00   4.9000000e+00   4.2000000e+00   6.0000000e+00   3.4000000e+00   3.3000000e+00   4.0000000e+00   2.6000000e+00   2.9000000e+00   3.8000000e+00   3.4000000e+00   7.0000000e+00   6.7000000e+00   2.7000000e+00   4.7000000e+00   2.1000000e+00   6.0000000e+00   2.7000000e+00   4.4000000e+00   4.8000000e+00   2.4000000e+00   2.4000000e+00   3.7000000e+00   4.2000000e+00   5.0000000e+00   6.7000000e+00   3.8000000e+00   2.5000000e+00   2.9000000e+00   5.7000000e+00   4.3000000e+00   3.4000000e+00   2.2000000e+00   4.1000000e+00   4.4000000e+00   4.0000000e+00   2.5000000e+00   4.8000000e+00   4.8000000e+00   3.8000000e+00   3.1000000e+00   3.3000000e+00   3.9000000e+00   2.4000000e+00   1.4000000e+00   2.0000000e+00   1.6000000e+00   2.5000000e+00   1.7000000e+00   1.4000000e+00   1.6000000e+00   1.4000000e+00   7.0000000e-01   2.0000000e-01   8.0000000e-01   1.0000000e+00   1.1000000e+00   2.8000000e+00   2.8000000e+00   3.0000000e+00   2.0000000e+00   2.0000000e+00   1.6000000e+00   1.3000000e+00   4.0000000e-01   1.3000000e+00   1.6000000e+00   2.3000000e+00   1.9000000e+00   9.0000000e-01   2.0000000e+00   4.0000000e+00   1.8000000e+00   1.5000000e+00   1.5000000e+00   9.0000000e-01   3.9000000e+00   1.7000000e+00   3.3000000e+00   2.5000000e+00   2.7000000e+00   2.2000000e+00   2.5000000e+00   3.9000000e+00   2.8000000e+00   3.1000000e+00   2.4000000e+00   3.8000000e+00   1.6000000e+00   2.1000000e+00   2.0000000e+00   2.8000000e+00   2.9000000e+00   2.2000000e+00   1.8000000e+00   4.8000000e+00   4.9000000e+00   2.3000000e+00   2.5000000e+00   2.5000000e+00   4.2000000e+00   1.7000000e+00   2.2000000e+00   2.6000000e+00   1.6000000e+00   1.6000000e+00   2.5000000e+00   2.2000000e+00   3.2000000e+00   4.5000000e+00   2.6000000e+00   1.5000000e+00   2.3000000e+00   3.7000000e+00   2.9000000e+00   1.8000000e+00   1.6000000e+00   1.9000000e+00   2.2000000e+00   1.8000000e+00   2.5000000e+00   2.6000000e+00   2.6000000e+00   1.8000000e+00   2.1000000e+00   1.7000000e+00   2.7000000e+00   2.0000000e+00   1.4000000e+00   1.4000000e+00   1.5000000e+00   1.1000000e+00   1.4000000e+00   1.6000000e+00   1.2000000e+00   1.3000000e+00   1.2000000e+00   1.8000000e+00   1.8000000e+00   5.0000000e-01   2.0000000e+00   1.8000000e+00   2.0000000e+00   1.4000000e+00   1.4000000e+00   2.0000000e-01   9.0000000e-01   1.4000000e+00   1.7000000e+00   6.0000000e-01   1.3000000e+00   9.0000000e-01   7.0000000e-01   1.4000000e+00   3.0000000e+00   8.0000000e-01   7.0000000e-01   7.0000000e-01   1.1000000e+00   2.9000000e+00   9.0000000e-01   3.5000000e+00   1.5000000e+00   3.5000000e+00   2.2000000e+00   2.9000000e+00   4.7000000e+00   1.4000000e+00   3.9000000e+00   3.2000000e+00   4.8000000e+00   2.2000000e+00   2.3000000e+00   2.8000000e+00   1.6000000e+00   1.9000000e+00   2.6000000e+00   2.2000000e+00   5.8000000e+00   5.7000000e+00   1.7000000e+00   3.5000000e+00   1.1000000e+00   5.0000000e+00   1.7000000e+00   3.2000000e+00   3.6000000e+00   1.4000000e+00   1.2000000e+00   2.7000000e+00   3.0000000e+00   4.0000000e+00   5.5000000e+00   2.8000000e+00   1.5000000e+00   2.1000000e+00   4.5000000e+00   3.1000000e+00   2.2000000e+00   1.0000000e+00   2.9000000e+00   3.2000000e+00   2.8000000e+00   1.5000000e+00   3.6000000e+00   3.6000000e+00   2.6000000e+00   2.1000000e+00   2.1000000e+00   2.7000000e+00   1.2000000e+00   1.8000000e+00   7.0000000e-01   2.1000000e+00   8.0000000e-01   2.0000000e+00   1.2000000e+00   1.3000000e+00   1.8000000e+00   2.2000000e+00   2.8000000e+00   1.3000000e+00   8.0000000e-01   1.0000000e+00   1.0000000e+00   4.0000000e-01   1.8000000e+00   1.6000000e+00   1.9000000e+00   2.4000000e+00   1.5000000e+00   8.0000000e-01   9.0000000e-01   9.0000000e-01   1.5000000e+00   4.0000000e-01   2.0000000e+00   6.0000000e-01   7.0000000e-01   7.0000000e-01   1.1000000e+00   2.1000000e+00   5.0000000e-01   4.5000000e+00   1.9000000e+00   4.5000000e+00   3.0000000e+00   3.9000000e+00   5.7000000e+00   2.2000000e+00   4.7000000e+00   3.6000000e+00   5.8000000e+00   3.2000000e+00   2.7000000e+00   3.8000000e+00   2.2000000e+00   2.5000000e+00   3.6000000e+00   3.2000000e+00   6.8000000e+00   6.1000000e+00   2.1000000e+00   4.5000000e+00   2.1000000e+00   5.6000000e+00   2.1000000e+00   4.2000000e+00   4.6000000e+00   2.0000000e+00   2.2000000e+00   3.3000000e+00   4.0000000e+00   4.6000000e+00   6.5000000e+00   3.4000000e+00   2.1000000e+00   2.3000000e+00   5.5000000e+00   4.1000000e+00   3.2000000e+00   2.0000000e+00   3.9000000e+00   4.2000000e+00   3.8000000e+00   1.9000000e+00   4.6000000e+00   4.6000000e+00   3.6000000e+00   2.5000000e+00   3.1000000e+00   3.7000000e+00   2.2000000e+00   1.9000000e+00   1.9000000e+00   1.4000000e+00   8.0000000e-01   1.2000000e+00   1.3000000e+00   1.4000000e+00   1.6000000e+00   2.0000000e+00   9.0000000e-01   2.4000000e+00   2.0000000e+00   2.2000000e+00   1.8000000e+00   1.4000000e+00   1.6000000e+00   1.5000000e+00   1.6000000e+00   5.0000000e-01   2.0000000e+00   1.7000000e+00   1.5000000e+00   1.1000000e+00   1.6000000e+00   3.0000000e+00   1.6000000e+00   1.9000000e+00   1.7000000e+00   1.1000000e+00   3.3000000e+00   1.7000000e+00   3.7000000e+00   1.9000000e+00   3.7000000e+00   2.2000000e+00   3.1000000e+00   4.9000000e+00   1.8000000e+00   3.9000000e+00   2.4000000e+00   5.0000000e+00   2.4000000e+00   1.9000000e+00   3.0000000e+00   1.8000000e+00   2.5000000e+00   2.8000000e+00   2.4000000e+00   6.0000000e+00   5.1000000e+00   7.0000000e-01   3.7000000e+00   2.1000000e+00   4.8000000e+00   1.3000000e+00   3.4000000e+00   3.8000000e+00   1.2000000e+00   1.6000000e+00   2.5000000e+00   3.2000000e+00   3.8000000e+00   5.7000000e+00   2.6000000e+00   1.3000000e+00   1.7000000e+00   4.7000000e+00   3.3000000e+00   2.4000000e+00   1.6000000e+00   3.1000000e+00   3.4000000e+00   3.0000000e+00   1.9000000e+00   3.8000000e+00   3.8000000e+00   2.8000000e+00   1.3000000e+00   2.3000000e+00   2.9000000e+00   2.0000000e+00   2.6000000e+00   1.1000000e+00   2.1000000e+00   1.7000000e+00   1.8000000e+00   2.3000000e+00   2.7000000e+00   3.3000000e+00   1.8000000e+00   7.0000000e-01   3.0000000e-01   5.0000000e-01   5.0000000e-01   2.3000000e+00   1.7000000e+00   2.4000000e+00   2.9000000e+00   1.6000000e+00   9.0000000e-01   4.0000000e-01   8.0000000e-01   2.0000000e+00   5.0000000e-01   1.5000000e+00   7.0000000e-01   1.0000000e+00   1.0000000e+00   1.6000000e+00   1.4000000e+00   8.0000000e-01   5.0000000e+00   2.4000000e+00   5.0000000e+00   3.5000000e+00   4.4000000e+00   6.2000000e+00   1.9000000e+00   5.2000000e+00   3.7000000e+00   6.3000000e+00   3.7000000e+00   3.2000000e+00   4.3000000e+00   2.1000000e+00   3.0000000e+00   4.1000000e+00   3.7000000e+00   7.3000000e+00   6.4000000e+00   2.2000000e+00   5.0000000e+00   2.2000000e+00   6.1000000e+00   2.6000000e+00   4.7000000e+00   5.1000000e+00   2.5000000e+00   2.7000000e+00   3.8000000e+00   4.5000000e+00   5.1000000e+00   7.0000000e+00   3.9000000e+00   2.6000000e+00   2.6000000e+00   6.0000000e+00   4.6000000e+00   3.7000000e+00   2.5000000e+00   4.4000000e+00   4.7000000e+00   4.3000000e+00   2.4000000e+00   5.1000000e+00   5.1000000e+00   4.1000000e+00   2.6000000e+00   3.6000000e+00   4.2000000e+00   2.7000000e+00   1.9000000e+00   1.5000000e+00   1.3000000e+00   1.8000000e+00   1.7000000e+00   1.7000000e+00   1.3000000e+00   1.0000000e+00   2.9000000e+00   2.9000000e+00   3.1000000e+00   2.1000000e+00   1.1000000e+00   1.3000000e+00   8.0000000e-01   1.3000000e+00   2.2000000e+00   1.7000000e+00   2.4000000e+00   2.0000000e+00   1.0000000e+00   2.1000000e+00   4.1000000e+00   1.9000000e+00   1.6000000e+00   1.6000000e+00   1.6000000e+00   4.0000000e+00   1.8000000e+00   2.4000000e+00   1.0000000e+00   2.8000000e+00   1.5000000e+00   2.2000000e+00   4.0000000e+00   2.1000000e+00   3.2000000e+00   2.5000000e+00   3.7000000e+00   1.1000000e+00   1.6000000e+00   2.1000000e+00   1.3000000e+00   1.4000000e+00   1.5000000e+00   1.5000000e+00   4.7000000e+00   5.0000000e+00   1.6000000e+00   2.4000000e+00   1.0000000e+00   4.3000000e+00   1.0000000e+00   2.1000000e+00   2.5000000e+00   7.0000000e-01   5.0000000e-01   2.0000000e+00   2.7000000e+00   3.3000000e+00   4.4000000e+00   2.1000000e+00   1.4000000e+00   2.0000000e+00   3.8000000e+00   2.0000000e+00   1.3000000e+00   3.0000000e-01   2.0000000e+00   2.3000000e+00   1.9000000e+00   1.0000000e+00   2.5000000e+00   2.5000000e+00   1.9000000e+00   1.4000000e+00   1.4000000e+00   1.6000000e+00   5.0000000e-01   1.6000000e+00   8.0000000e-01   7.0000000e-01   1.2000000e+00   1.6000000e+00   2.2000000e+00   9.0000000e-01   1.4000000e+00   1.4000000e+00   1.6000000e+00   6.0000000e-01   1.6000000e+00   1.6000000e+00   1.5000000e+00   1.8000000e+00   1.1000000e+00   8.0000000e-01   9.0000000e-01   1.3000000e+00   9.0000000e-01   6.0000000e-01   2.6000000e+00   8.0000000e-01   9.0000000e-01   7.0000000e-01   5.0000000e-01   2.5000000e+00   5.0000000e-01   3.9000000e+00   2.1000000e+00   3.9000000e+00   2.4000000e+00   3.3000000e+00   5.1000000e+00   2.4000000e+00   4.1000000e+00   3.2000000e+00   5.2000000e+00   2.6000000e+00   2.3000000e+00   3.2000000e+00   2.4000000e+00   2.5000000e+00   3.0000000e+00   2.6000000e+00   6.2000000e+00   5.7000000e+00   1.9000000e+00   3.9000000e+00   2.1000000e+00   5.0000000e+00   1.7000000e+00   3.6000000e+00   4.0000000e+00   1.4000000e+00   1.6000000e+00   2.7000000e+00   3.4000000e+00   4.0000000e+00   5.9000000e+00   2.8000000e+00   1.5000000e+00   1.9000000e+00   4.9000000e+00   3.5000000e+00   2.6000000e+00   1.6000000e+00   3.3000000e+00   3.6000000e+00   3.2000000e+00   2.1000000e+00   4.0000000e+00   4.0000000e+00   3.0000000e+00   2.1000000e+00   2.5000000e+00   3.1000000e+00   2.0000000e+00   1.0000000e+00   1.3000000e+00   1.4000000e+00   1.0000000e+00   1.2000000e+00   1.1000000e+00   2.6000000e+00   2.4000000e+00   2.6000000e+00   2.0000000e+00   8.0000000e-01   1.8000000e+00   1.7000000e+00   1.2000000e+00   9.0000000e-01   2.2000000e+00   1.9000000e+00   1.7000000e+00   1.1000000e+00   1.8000000e+00   3.6000000e+00   1.8000000e+00   2.1000000e+00   1.9000000e+00   1.3000000e+00   3.5000000e+00   1.9000000e+00   2.9000000e+00   1.3000000e+00   2.9000000e+00   1.4000000e+00   2.3000000e+00   4.1000000e+00   2.0000000e+00   3.1000000e+00   1.6000000e+00   4.2000000e+00   1.6000000e+00   1.1000000e+00   2.2000000e+00   1.2000000e+00   1.9000000e+00   2.0000000e+00   1.6000000e+00   5.2000000e+00   4.3000000e+00   7.0000000e-01   2.9000000e+00   1.5000000e+00   4.0000000e+00   5.0000000e-01   2.6000000e+00   3.0000000e+00   8.0000000e-01   1.0000000e+00   1.7000000e+00   2.4000000e+00   3.0000000e+00   4.9000000e+00   1.8000000e+00   5.0000000e-01   1.1000000e+00   3.9000000e+00   2.5000000e+00   1.6000000e+00   1.2000000e+00   2.3000000e+00   2.6000000e+00   2.2000000e+00   1.3000000e+00   3.0000000e+00   3.0000000e+00   2.0000000e+00   5.0000000e-01   1.5000000e+00   2.3000000e+00   1.4000000e+00   9.0000000e-01   1.2000000e+00   1.0000000e+00   1.6000000e+00   7.0000000e-01   2.0000000e+00   2.0000000e+00   2.2000000e+00   1.2000000e+00   1.0000000e+00   1.4000000e+00   1.3000000e+00   1.2000000e+00   1.1000000e+00   1.4000000e+00   1.7000000e+00   1.1000000e+00   5.0000000e-01   1.2000000e+00   3.2000000e+00   1.2000000e+00   1.1000000e+00   1.1000000e+00   7.0000000e-01   3.1000000e+00   1.1000000e+00   3.3000000e+00   1.5000000e+00   3.3000000e+00   1.8000000e+00   2.7000000e+00   4.5000000e+00   2.2000000e+00   3.5000000e+00   2.6000000e+00   4.6000000e+00   2.0000000e+00   1.7000000e+00   2.6000000e+00   1.8000000e+00   1.9000000e+00   2.4000000e+00   2.0000000e+00   5.6000000e+00   5.1000000e+00   1.3000000e+00   3.3000000e+00   1.5000000e+00   4.4000000e+00   1.1000000e+00   3.0000000e+00   3.4000000e+00   8.0000000e-01   1.0000000e+00   2.1000000e+00   2.8000000e+00   3.4000000e+00   5.3000000e+00   2.2000000e+00   9.0000000e-01   1.3000000e+00   4.3000000e+00   2.9000000e+00   2.0000000e+00   1.0000000e+00   2.7000000e+00   3.0000000e+00   2.6000000e+00   1.5000000e+00   3.4000000e+00   3.4000000e+00   2.4000000e+00   1.5000000e+00   1.9000000e+00   2.5000000e+00   1.4000000e+00   5.0000000e-01   1.1000000e+00   1.5000000e+00   8.0000000e-01   2.1000000e+00   2.1000000e+00   2.3000000e+00   1.3000000e+00   1.7000000e+00   1.5000000e+00   1.4000000e+00   1.1000000e+00   8.0000000e-01   1.1000000e+00   1.6000000e+00   1.4000000e+00   8.0000000e-01   1.3000000e+00   3.3000000e+00   1.1000000e+00   1.0000000e+00   8.0000000e-01   2.0000000e-01   3.2000000e+00   1.0000000e+00   3.4000000e+00   2.2000000e+00   3.2000000e+00   1.9000000e+00   2.6000000e+00   4.4000000e+00   2.5000000e+00   3.4000000e+00   2.7000000e+00   4.5000000e+00   1.9000000e+00   1.8000000e+00   2.5000000e+00   2.5000000e+00   2.6000000e+00   2.3000000e+00   1.9000000e+00   5.5000000e+00   5.2000000e+00   2.0000000e+00   3.2000000e+00   2.2000000e+00   4.5000000e+00   1.4000000e+00   2.9000000e+00   3.3000000e+00   1.3000000e+00   1.5000000e+00   2.2000000e+00   2.7000000e+00   3.5000000e+00   5.2000000e+00   2.3000000e+00   1.2000000e+00   2.0000000e+00   4.2000000e+00   3.0000000e+00   1.9000000e+00   1.5000000e+00   2.6000000e+00   2.9000000e+00   2.5000000e+00   2.2000000e+00   3.3000000e+00   3.3000000e+00   2.3000000e+00   1.8000000e+00   1.8000000e+00   2.8000000e+00   1.9000000e+00   8.0000000e-01   1.0000000e+00   9.0000000e-01   2.6000000e+00   2.6000000e+00   2.8000000e+00   1.8000000e+00   1.8000000e+00   1.4000000e+00   1.3000000e+00   6.0000000e-01   1.1000000e+00   1.4000000e+00   2.1000000e+00   1.7000000e+00   7.0000000e-01   1.8000000e+00   3.8000000e+00   1.6000000e+00   1.3000000e+00   1.3000000e+00   7.0000000e-01   3.7000000e+00   1.5000000e+00   3.3000000e+00   2.3000000e+00   2.7000000e+00   2.0000000e+00   2.3000000e+00   3.9000000e+00   2.6000000e+00   3.1000000e+00   2.4000000e+00   4.0000000e+00   1.6000000e+00   1.9000000e+00   2.0000000e+00   2.6000000e+00   2.7000000e+00   2.2000000e+00   1.6000000e+00   5.0000000e+00   4.9000000e+00   2.1000000e+00   2.7000000e+00   2.3000000e+00   4.2000000e+00   1.5000000e+00   2.4000000e+00   2.8000000e+00   1.4000000e+00   1.4000000e+00   2.3000000e+00   2.2000000e+00   3.2000000e+00   4.7000000e+00   2.4000000e+00   1.3000000e+00   2.1000000e+00   3.7000000e+00   2.9000000e+00   1.8000000e+00   1.4000000e+00   2.1000000e+00   2.4000000e+00   2.0000000e+00   2.3000000e+00   2.8000000e+00   2.8000000e+00   1.8000000e+00   1.9000000e+00   1.5000000e+00   2.7000000e+00   1.8000000e+00   8.0000000e-01   1.3000000e+00   3.0000000e+00   3.0000000e+00   3.2000000e+00   2.2000000e+00   1.4000000e+00   2.0000000e+00   1.9000000e+00   6.0000000e-01   1.5000000e+00   2.2000000e+00   2.5000000e+00   2.1000000e+00   1.1000000e+00   2.2000000e+00   4.2000000e+00   2.0000000e+00   2.1000000e+00   1.9000000e+00   1.3000000e+00   4.1000000e+00   1.9000000e+00   3.3000000e+00   1.9000000e+00   2.3000000e+00   1.8000000e+00   2.3000000e+00   3.5000000e+00   2.8000000e+00   2.5000000e+00   1.8000000e+00   3.6000000e+00   1.6000000e+00   1.5000000e+00   1.6000000e+00   2.2000000e+00   2.3000000e+00   2.2000000e+00   1.6000000e+00   4.6000000e+00   4.1000000e+00   1.7000000e+00   2.3000000e+00   1.9000000e+00   3.4000000e+00   1.1000000e+00   2.2000000e+00   2.4000000e+00   1.0000000e+00   1.4000000e+00   1.9000000e+00   1.8000000e+00   2.4000000e+00   4.3000000e+00   2.0000000e+00   9.0000000e-01   1.7000000e+00   3.3000000e+00   2.9000000e+00   1.8000000e+00   1.4000000e+00   1.7000000e+00   2.2000000e+00   1.6000000e+00   1.9000000e+00   2.4000000e+00   2.6000000e+00   1.6000000e+00   1.5000000e+00   1.5000000e+00   2.7000000e+00   1.8000000e+00   1.5000000e+00   3.6000000e+00   3.6000000e+00   3.8000000e+00   2.8000000e+00   1.2000000e+00   2.0000000e+00   1.7000000e+00   6.0000000e-01   2.1000000e+00   2.4000000e+00   3.1000000e+00   2.7000000e+00   1.3000000e+00   2.8000000e+00   4.8000000e+00   2.6000000e+00   2.3000000e+00   2.3000000e+00   1.7000000e+00   4.7000000e+00   2.5000000e+00   2.5000000e+00   1.5000000e+00   1.7000000e+00   1.2000000e+00   1.5000000e+00   2.9000000e+00   2.8000000e+00   2.1000000e+00   1.4000000e+00   3.0000000e+00   8.0000000e-01   1.1000000e+00   1.0000000e+00   1.8000000e+00   1.9000000e+00   1.4000000e+00   8.0000000e-01   4.0000000e+00   3.9000000e+00   1.7000000e+00   1.7000000e+00   1.7000000e+00   3.2000000e+00   9.0000000e-01   1.4000000e+00   1.8000000e+00   1.0000000e+00   8.0000000e-01   1.5000000e+00   1.4000000e+00   2.2000000e+00   3.7000000e+00   1.6000000e+00   9.0000000e-01   1.9000000e+00   2.7000000e+00   2.1000000e+00   1.0000000e+00   1.0000000e+00   1.1000000e+00   1.4000000e+00   1.0000000e+00   1.5000000e+00   1.8000000e+00   1.8000000e+00   8.0000000e-01   1.1000000e+00   7.0000000e-01   1.9000000e+00   1.0000000e+00   2.1000000e+00   2.1000000e+00   2.3000000e+00   1.3000000e+00   9.0000000e-01   7.0000000e-01   6.0000000e-01   1.1000000e+00   1.2000000e+00   1.1000000e+00   1.6000000e+00   1.2000000e+00   4.0000000e-01   1.3000000e+00   3.3000000e+00   1.1000000e+00   1.0000000e+00   8.0000000e-01   6.0000000e-01   3.2000000e+00   1.0000000e+00   3.2000000e+00   1.4000000e+00   3.2000000e+00   1.7000000e+00   2.6000000e+00   4.4000000e+00   1.7000000e+00   3.4000000e+00   2.7000000e+00   4.5000000e+00   1.9000000e+00   1.8000000e+00   2.5000000e+00   1.7000000e+00   1.8000000e+00   2.3000000e+00   1.9000000e+00   5.5000000e+00   5.2000000e+00   1.2000000e+00   3.2000000e+00   1.4000000e+00   4.5000000e+00   1.2000000e+00   2.9000000e+00   3.3000000e+00   9.0000000e-01   9.0000000e-01   2.2000000e+00   2.7000000e+00   3.5000000e+00   5.2000000e+00   2.3000000e+00   1.0000000e+00   1.6000000e+00   4.2000000e+00   2.8000000e+00   1.9000000e+00   7.0000000e-01   2.6000000e+00   2.9000000e+00   2.5000000e+00   1.4000000e+00   3.3000000e+00   3.3000000e+00   2.3000000e+00   1.6000000e+00   1.8000000e+00   2.4000000e+00   1.1000000e+00   8.0000000e-01   6.0000000e-01   8.0000000e-01   2.6000000e+00   2.2000000e+00   2.7000000e+00   3.2000000e+00   2.1000000e+00   1.4000000e+00   1.1000000e+00   1.3000000e+00   2.3000000e+00   8.0000000e-01   1.2000000e+00   1.2000000e+00   1.3000000e+00   1.3000000e+00   1.9000000e+00   1.3000000e+00   1.1000000e+00   5.3000000e+00   2.7000000e+00   5.3000000e+00   3.8000000e+00   4.7000000e+00   6.5000000e+00   2.6000000e+00   5.5000000e+00   4.2000000e+00   6.6000000e+00   4.0000000e+00   3.5000000e+00   4.6000000e+00   2.6000000e+00   3.3000000e+00   4.4000000e+00   4.0000000e+00   7.6000000e+00   6.7000000e+00   2.7000000e+00   5.3000000e+00   2.7000000e+00   6.4000000e+00   2.9000000e+00   5.0000000e+00   5.4000000e+00   2.8000000e+00   3.0000000e+00   4.1000000e+00   4.8000000e+00   5.4000000e+00   7.3000000e+00   4.2000000e+00   2.9000000e+00   2.9000000e+00   6.3000000e+00   4.9000000e+00   4.0000000e+00   2.8000000e+00   4.7000000e+00   5.0000000e+00   4.6000000e+00   2.7000000e+00   5.4000000e+00   5.4000000e+00   4.4000000e+00   3.1000000e+00   3.9000000e+00   4.5000000e+00   3.0000000e+00   2.0000000e-01   8.0000000e-01   2.6000000e+00   1.8000000e+00   2.7000000e+00   3.2000000e+00   1.7000000e+00   1.2000000e+00   5.0000000e-01   9.0000000e-01   2.3000000e+00   8.0000000e-01   1.2000000e+00   1.0000000e+00   1.3000000e+00   1.3000000e+00   1.9000000e+00   1.3000000e+00   1.1000000e+00   5.3000000e+00   2.7000000e+00   5.3000000e+00   3.8000000e+00   4.7000000e+00   6.5000000e+00   2.0000000e+00   5.5000000e+00   4.0000000e+00   6.6000000e+00   4.0000000e+00   3.5000000e+00   4.6000000e+00   2.4000000e+00   3.3000000e+00   4.4000000e+00   4.0000000e+00   7.6000000e+00   6.7000000e+00   2.3000000e+00   5.3000000e+00   2.5000000e+00   6.4000000e+00   2.9000000e+00   5.0000000e+00   5.4000000e+00   2.8000000e+00   3.0000000e+00   4.1000000e+00   4.8000000e+00   5.4000000e+00   7.3000000e+00   4.2000000e+00   2.9000000e+00   2.9000000e+00   6.3000000e+00   4.9000000e+00   4.0000000e+00   2.8000000e+00   4.7000000e+00   5.0000000e+00   4.6000000e+00   2.7000000e+00   5.4000000e+00   5.4000000e+00   4.4000000e+00   2.9000000e+00   3.9000000e+00   4.5000000e+00   3.0000000e+00   1.0000000e+00   2.8000000e+00   2.0000000e+00   2.9000000e+00   3.4000000e+00   1.9000000e+00   1.4000000e+00   7.0000000e-01   1.1000000e+00   2.5000000e+00   1.0000000e+00   1.0000000e+00   1.2000000e+00   1.5000000e+00   1.5000000e+00   2.1000000e+00   1.3000000e+00   1.3000000e+00   5.5000000e+00   2.9000000e+00   5.5000000e+00   4.0000000e+00   4.9000000e+00   6.7000000e+00   2.2000000e+00   5.7000000e+00   4.2000000e+00   6.8000000e+00   4.2000000e+00   3.7000000e+00   4.8000000e+00   2.6000000e+00   3.5000000e+00   4.6000000e+00   4.2000000e+00   7.8000000e+00   6.9000000e+00   2.5000000e+00   5.5000000e+00   2.7000000e+00   6.6000000e+00   3.1000000e+00   5.2000000e+00   5.6000000e+00   3.0000000e+00   3.2000000e+00   4.3000000e+00   5.0000000e+00   5.6000000e+00   7.5000000e+00   4.4000000e+00   3.1000000e+00   3.1000000e+00   6.5000000e+00   5.1000000e+00   4.2000000e+00   3.0000000e+00   4.9000000e+00   5.2000000e+00   4.8000000e+00   2.9000000e+00   5.6000000e+00   5.6000000e+00   4.6000000e+00   3.1000000e+00   4.1000000e+00   4.7000000e+00   3.2000000e+00   1.8000000e+00   1.6000000e+00   1.9000000e+00   2.4000000e+00   1.5000000e+00   8.0000000e-01   7.0000000e-01   9.0000000e-01   1.5000000e+00   2.0000000e-01   2.0000000e+00   6.0000000e-01   7.0000000e-01   7.0000000e-01   1.1000000e+00   1.9000000e+00   5.0000000e-01   4.5000000e+00   1.9000000e+00   4.5000000e+00   3.0000000e+00   3.9000000e+00   5.7000000e+00   2.2000000e+00   4.7000000e+00   3.6000000e+00   5.8000000e+00   3.2000000e+00   2.7000000e+00   3.8000000e+00   2.2000000e+00   2.5000000e+00   3.6000000e+00   3.2000000e+00   6.8000000e+00   6.1000000e+00   2.1000000e+00   4.5000000e+00   2.1000000e+00   5.6000000e+00   2.1000000e+00   4.2000000e+00   4.6000000e+00   2.0000000e+00   2.2000000e+00   3.3000000e+00   4.0000000e+00   4.6000000e+00   6.5000000e+00   3.4000000e+00   2.1000000e+00   2.3000000e+00   5.5000000e+00   4.1000000e+00   3.2000000e+00   2.0000000e+00   3.9000000e+00   4.2000000e+00   3.8000000e+00   1.9000000e+00   4.6000000e+00   4.6000000e+00   3.6000000e+00   2.5000000e+00   3.1000000e+00   3.7000000e+00   2.2000000e+00   1.6000000e+00   1.3000000e+00   1.6000000e+00   1.7000000e+00   2.0000000e+00   2.1000000e+00   1.7000000e+00   1.1000000e+00   1.8000000e+00   3.8000000e+00   1.6000000e+00   1.9000000e+00   1.7000000e+00   1.5000000e+00   3.7000000e+00   1.7000000e+00   2.7000000e+00   5.0000000e-01   2.7000000e+00   1.2000000e+00   2.1000000e+00   3.9000000e+00   2.0000000e+00   2.9000000e+00   1.8000000e+00   4.0000000e+00   1.4000000e+00   9.0000000e-01   2.0000000e+00   1.0000000e+00   1.1000000e+00   1.8000000e+00   1.4000000e+00   5.0000000e+00   4.3000000e+00   7.0000000e-01   2.7000000e+00   1.1000000e+00   3.8000000e+00   7.0000000e-01   2.4000000e+00   2.8000000e+00   8.0000000e-01   8.0000000e-01   1.5000000e+00   2.2000000e+00   2.8000000e+00   4.7000000e+00   1.6000000e+00   5.0000000e-01   9.0000000e-01   3.7000000e+00   2.3000000e+00   1.4000000e+00   8.0000000e-01   2.1000000e+00   2.4000000e+00   2.0000000e+00   5.0000000e-01   2.8000000e+00   2.8000000e+00   1.8000000e+00   9.0000000e-01   1.3000000e+00   1.9000000e+00   6.0000000e-01   1.1000000e+00   1.6000000e+00   1.9000000e+00   8.0000000e-01   1.3000000e+00   9.0000000e-01   9.0000000e-01   1.6000000e+00   2.8000000e+00   1.0000000e+00   9.0000000e-01   9.0000000e-01   1.3000000e+00   2.7000000e+00   1.1000000e+00   3.7000000e+00   1.7000000e+00   3.7000000e+00   2.4000000e+00   3.1000000e+00   4.9000000e+00   1.2000000e+00   4.1000000e+00   3.4000000e+00   5.0000000e+00   2.4000000e+00   2.5000000e+00   3.0000000e+00   1.8000000e+00   2.1000000e+00   2.8000000e+00   2.4000000e+00   6.0000000e+00   5.9000000e+00   1.9000000e+00   3.7000000e+00   1.3000000e+00   5.2000000e+00   1.9000000e+00   3.4000000e+00   3.8000000e+00   1.6000000e+00   1.4000000e+00   2.9000000e+00   3.2000000e+00   4.2000000e+00   5.7000000e+00   3.0000000e+00   1.7000000e+00   2.3000000e+00   4.7000000e+00   3.3000000e+00   2.4000000e+00   1.2000000e+00   3.1000000e+00   3.4000000e+00   3.0000000e+00   1.7000000e+00   3.8000000e+00   3.8000000e+00   2.8000000e+00   2.3000000e+00   2.3000000e+00   2.9000000e+00   1.4000000e+00   1.3000000e+00   1.8000000e+00   1.5000000e+00   2.2000000e+00   1.8000000e+00   8.0000000e-01   1.9000000e+00   3.9000000e+00   1.7000000e+00   1.4000000e+00   1.4000000e+00   1.2000000e+00   3.8000000e+00   1.6000000e+00   2.8000000e+00   1.8000000e+00   3.4000000e+00   2.1000000e+00   2.8000000e+00   4.6000000e+00   2.1000000e+00   3.8000000e+00   3.1000000e+00   3.9000000e+00   1.7000000e+00   2.2000000e+00   2.7000000e+00   2.1000000e+00   2.2000000e+00   2.1000000e+00   2.1000000e+00   4.9000000e+00   5.6000000e+00   1.8000000e+00   3.0000000e+00   1.8000000e+00   4.9000000e+00   1.6000000e+00   2.5000000e+00   3.1000000e+00   1.3000000e+00   1.1000000e+00   2.6000000e+00   2.9000000e+00   3.9000000e+00   4.6000000e+00   2.7000000e+00   1.6000000e+00   2.2000000e+00   4.4000000e+00   2.2000000e+00   1.9000000e+00   9.0000000e-01   2.6000000e+00   2.9000000e+00   2.5000000e+00   1.8000000e+00   3.1000000e+00   2.9000000e+00   2.5000000e+00   2.0000000e+00   2.0000000e+00   1.8000000e+00   1.3000000e+00   1.7000000e+00   2.0000000e+00   2.7000000e+00   2.3000000e+00   9.0000000e-01   2.4000000e+00   4.4000000e+00   2.2000000e+00   1.9000000e+00   1.9000000e+00   1.3000000e+00   4.3000000e+00   2.1000000e+00   2.9000000e+00   2.1000000e+00   2.3000000e+00   1.8000000e+00   2.1000000e+00   3.5000000e+00   2.8000000e+00   2.7000000e+00   2.0000000e+00   3.4000000e+00   1.2000000e+00   1.7000000e+00   1.6000000e+00   2.4000000e+00   2.5000000e+00   1.8000000e+00   1.4000000e+00   4.4000000e+00   4.5000000e+00   1.9000000e+00   2.1000000e+00   2.1000000e+00   3.8000000e+00   1.3000000e+00   1.8000000e+00   2.2000000e+00   1.2000000e+00   1.2000000e+00   2.1000000e+00   1.8000000e+00   2.8000000e+00   4.1000000e+00   2.2000000e+00   1.1000000e+00   2.1000000e+00   3.3000000e+00   2.5000000e+00   1.4000000e+00   1.2000000e+00   1.5000000e+00   1.8000000e+00   1.4000000e+00   2.1000000e+00   2.2000000e+00   2.2000000e+00   1.4000000e+00   1.7000000e+00   1.3000000e+00   2.3000000e+00   1.6000000e+00   1.7000000e+00   1.4000000e+00   1.2000000e+00   1.2000000e+00   1.3000000e+00   2.7000000e+00   1.3000000e+00   1.6000000e+00   1.4000000e+00   8.0000000e-01   3.0000000e+00   1.4000000e+00   3.8000000e+00   2.2000000e+00   3.8000000e+00   2.3000000e+00   3.2000000e+00   5.0000000e+00   2.1000000e+00   4.0000000e+00   2.5000000e+00   5.1000000e+00   2.5000000e+00   2.0000000e+00   3.1000000e+00   2.1000000e+00   2.8000000e+00   2.9000000e+00   2.5000000e+00   6.1000000e+00   5.2000000e+00   1.2000000e+00   3.8000000e+00   2.4000000e+00   4.9000000e+00   1.4000000e+00   3.5000000e+00   3.9000000e+00   1.5000000e+00   1.9000000e+00   2.6000000e+00   3.3000000e+00   3.9000000e+00   5.8000000e+00   2.7000000e+00   1.4000000e+00   1.8000000e+00   4.8000000e+00   3.4000000e+00   2.5000000e+00   1.9000000e+00   3.2000000e+00   3.5000000e+00   3.1000000e+00   2.2000000e+00   3.9000000e+00   3.9000000e+00   2.9000000e+00   1.4000000e+00   2.4000000e+00   3.2000000e+00   2.3000000e+00   7.0000000e-01   9.0000000e-01   1.1000000e+00   8.0000000e-01   2.4000000e+00   4.0000000e-01   3.0000000e-01   3.0000000e-01   9.0000000e-01   2.3000000e+00   3.0000000e-01   4.1000000e+00   2.1000000e+00   4.1000000e+00   2.8000000e+00   3.5000000e+00   5.3000000e+00   2.0000000e+00   4.5000000e+00   3.8000000e+00   5.4000000e+00   2.8000000e+00   2.9000000e+00   3.4000000e+00   2.2000000e+00   2.5000000e+00   3.2000000e+00   2.8000000e+00   6.4000000e+00   6.3000000e+00   2.3000000e+00   4.1000000e+00   1.7000000e+00   5.6000000e+00   2.3000000e+00   3.8000000e+00   4.2000000e+00   2.0000000e+00   1.8000000e+00   3.3000000e+00   3.6000000e+00   4.6000000e+00   6.1000000e+00   3.4000000e+00   2.1000000e+00   2.5000000e+00   5.1000000e+00   3.7000000e+00   2.8000000e+00   1.6000000e+00   3.5000000e+00   3.8000000e+00   3.4000000e+00   2.1000000e+00   4.2000000e+00   4.2000000e+00   3.2000000e+00   2.7000000e+00   2.7000000e+00   3.3000000e+00   1.8000000e+00   6.0000000e-01   1.8000000e+00   5.0000000e-01   1.7000000e+00   5.0000000e-01   1.0000000e+00   8.0000000e-01   1.4000000e+00   1.6000000e+00   6.0000000e-01   4.8000000e+00   2.2000000e+00   4.8000000e+00   3.3000000e+00   4.2000000e+00   6.0000000e+00   1.5000000e+00   5.0000000e+00   3.5000000e+00   6.1000000e+00   3.5000000e+00   3.0000000e+00   4.1000000e+00   1.9000000e+00   2.8000000e+00   3.9000000e+00   3.5000000e+00   7.1000000e+00   6.2000000e+00   2.0000000e+00   4.8000000e+00   2.0000000e+00   5.9000000e+00   2.4000000e+00   4.5000000e+00   4.9000000e+00   2.3000000e+00   2.5000000e+00   3.6000000e+00   4.3000000e+00   4.9000000e+00   6.8000000e+00   3.7000000e+00   2.4000000e+00   2.4000000e+00   5.8000000e+00   4.4000000e+00   3.5000000e+00   2.3000000e+00   4.2000000e+00   4.5000000e+00   4.1000000e+00   2.2000000e+00   4.9000000e+00   4.9000000e+00   3.9000000e+00   2.4000000e+00   3.4000000e+00   4.0000000e+00   2.5000000e+00   1.4000000e+00   7.0000000e-01   2.1000000e+00   5.0000000e-01   8.0000000e-01   8.0000000e-01   1.2000000e+00   2.0000000e+00   8.0000000e-01   4.4000000e+00   1.8000000e+00   4.4000000e+00   2.9000000e+00   3.8000000e+00   5.6000000e+00   1.3000000e+00   4.6000000e+00   3.3000000e+00   5.7000000e+00   3.1000000e+00   2.6000000e+00   3.7000000e+00   1.7000000e+00   2.4000000e+00   3.5000000e+00   3.1000000e+00   6.7000000e+00   5.8000000e+00   1.8000000e+00   4.4000000e+00   1.6000000e+00   5.5000000e+00   2.0000000e+00   4.1000000e+00   4.5000000e+00   1.9000000e+00   2.1000000e+00   3.2000000e+00   3.9000000e+00   4.5000000e+00   6.4000000e+00   3.3000000e+00   2.0000000e+00   2.0000000e+00   5.4000000e+00   4.0000000e+00   3.1000000e+00   1.9000000e+00   3.8000000e+00   4.1000000e+00   3.7000000e+00   1.8000000e+00   4.5000000e+00   4.5000000e+00   3.5000000e+00   2.2000000e+00   3.0000000e+00   3.6000000e+00   2.1000000e+00   1.5000000e+00   3.5000000e+00   1.3000000e+00   1.0000000e+00   1.0000000e+00   6.0000000e-01   3.4000000e+00   1.2000000e+00   3.0000000e+00   1.6000000e+00   3.0000000e+00   1.7000000e+00   2.4000000e+00   4.2000000e+00   2.1000000e+00   3.4000000e+00   2.7000000e+00   4.3000000e+00   1.7000000e+00   1.8000000e+00   2.3000000e+00   1.9000000e+00   2.0000000e+00   2.1000000e+00   1.7000000e+00   5.3000000e+00   5.2000000e+00   1.4000000e+00   3.0000000e+00   1.6000000e+00   4.5000000e+00   1.2000000e+00   2.7000000e+00   3.1000000e+00   9.0000000e-01   7.0000000e-01   2.2000000e+00   2.5000000e+00   3.5000000e+00   5.0000000e+00   2.3000000e+00   1.0000000e+00   1.4000000e+00   4.0000000e+00   2.6000000e+00   1.7000000e+00   7.0000000e-01   2.4000000e+00   2.7000000e+00   2.3000000e+00   1.6000000e+00   3.1000000e+00   3.1000000e+00   2.1000000e+00   1.6000000e+00   1.6000000e+00   2.2000000e+00   1.1000000e+00   2.0000000e+00   6.0000000e-01   7.0000000e-01   7.0000000e-01   1.1000000e+00   1.9000000e+00   5.0000000e-01   4.5000000e+00   1.9000000e+00   4.5000000e+00   3.0000000e+00   3.9000000e+00   5.7000000e+00   2.0000000e+00   4.7000000e+00   3.4000000e+00   5.8000000e+00   3.2000000e+00   2.7000000e+00   3.8000000e+00   2.0000000e+00   2.5000000e+00   3.6000000e+00   3.2000000e+00   6.8000000e+00   5.9000000e+00   1.9000000e+00   4.5000000e+00   2.1000000e+00   5.6000000e+00   2.1000000e+00   4.2000000e+00   4.6000000e+00   2.0000000e+00   2.2000000e+00   3.3000000e+00   4.0000000e+00   4.6000000e+00   6.5000000e+00   3.4000000e+00   2.1000000e+00   2.1000000e+00   5.5000000e+00   4.1000000e+00   3.2000000e+00   2.0000000e+00   3.9000000e+00   4.2000000e+00   3.8000000e+00   1.9000000e+00   4.6000000e+00   4.6000000e+00   3.6000000e+00   2.3000000e+00   3.1000000e+00   3.7000000e+00   2.2000000e+00   2.2000000e+00   2.5000000e+00   2.5000000e+00   3.1000000e+00   7.0000000e-01   2.3000000e+00   6.5000000e+00   3.9000000e+00   6.5000000e+00   5.0000000e+00   5.9000000e+00   7.7000000e+00   2.2000000e+00   6.7000000e+00   5.2000000e+00   7.8000000e+00   5.2000000e+00   4.7000000e+00   5.8000000e+00   3.6000000e+00   4.5000000e+00   5.6000000e+00   5.2000000e+00   8.8000000e+00   7.9000000e+00   3.3000000e+00   6.5000000e+00   3.7000000e+00   7.6000000e+00   4.1000000e+00   6.2000000e+00   6.6000000e+00   4.0000000e+00   4.2000000e+00   5.3000000e+00   6.0000000e+00   6.6000000e+00   8.5000000e+00   5.4000000e+00   4.1000000e+00   4.1000000e+00   7.5000000e+00   6.1000000e+00   5.2000000e+00   4.0000000e+00   5.9000000e+00   6.2000000e+00   5.8000000e+00   3.9000000e+00   6.6000000e+00   6.6000000e+00   5.6000000e+00   4.1000000e+00   5.1000000e+00   5.7000000e+00   4.2000000e+00   5.0000000e-01   3.0000000e-01   9.0000000e-01   2.1000000e+00   3.0000000e-01   4.3000000e+00   1.7000000e+00   4.3000000e+00   2.8000000e+00   3.7000000e+00   5.5000000e+00   1.6000000e+00   4.5000000e+00   3.4000000e+00   5.6000000e+00   3.0000000e+00   2.5000000e+00   3.6000000e+00   1.8000000e+00   2.3000000e+00   3.4000000e+00   3.0000000e+00   6.6000000e+00   5.9000000e+00   1.9000000e+00   4.3000000e+00   1.5000000e+00   5.4000000e+00   1.9000000e+00   4.0000000e+00   4.4000000e+00   1.8000000e+00   2.0000000e+00   3.1000000e+00   3.8000000e+00   4.4000000e+00   6.3000000e+00   3.2000000e+00   1.9000000e+00   2.1000000e+00   5.3000000e+00   3.9000000e+00   3.0000000e+00   1.8000000e+00   3.7000000e+00   4.0000000e+00   3.6000000e+00   1.7000000e+00   4.4000000e+00   4.4000000e+00   3.4000000e+00   2.3000000e+00   2.9000000e+00   3.5000000e+00   2.0000000e+00   2.0000000e-01   8.0000000e-01   2.4000000e+00   4.0000000e-01   4.0000000e+00   2.0000000e+00   4.0000000e+00   2.7000000e+00   3.4000000e+00   5.2000000e+00   2.1000000e+00   4.4000000e+00   3.7000000e+00   5.3000000e+00   2.7000000e+00   2.8000000e+00   3.3000000e+00   2.1000000e+00   2.4000000e+00   3.1000000e+00   2.7000000e+00   6.3000000e+00   6.2000000e+00   2.2000000e+00   4.0000000e+00   1.8000000e+00   5.5000000e+00   2.2000000e+00   3.7000000e+00   4.1000000e+00   1.9000000e+00   1.7000000e+00   3.2000000e+00   3.5000000e+00   4.5000000e+00   6.0000000e+00   3.3000000e+00   2.0000000e+00   2.4000000e+00   5.0000000e+00   3.6000000e+00   2.7000000e+00   1.5000000e+00   3.4000000e+00   3.7000000e+00   3.3000000e+00   2.0000000e+00   4.1000000e+00   4.1000000e+00   3.1000000e+00   2.6000000e+00   2.6000000e+00   3.2000000e+00   1.7000000e+00   6.0000000e-01   2.4000000e+00   2.0000000e-01   4.0000000e+00   1.8000000e+00   4.0000000e+00   2.5000000e+00   3.4000000e+00   5.2000000e+00   1.9000000e+00   4.2000000e+00   3.5000000e+00   5.3000000e+00   2.7000000e+00   2.6000000e+00   3.3000000e+00   1.9000000e+00   2.2000000e+00   3.1000000e+00   2.7000000e+00   6.3000000e+00   6.0000000e+00   2.0000000e+00   4.0000000e+00   1.6000000e+00   5.3000000e+00   2.0000000e+00   3.7000000e+00   4.1000000e+00   1.7000000e+00   1.7000000e+00   3.0000000e+00   3.5000000e+00   4.3000000e+00   6.0000000e+00   3.1000000e+00   1.8000000e+00   2.2000000e+00   5.0000000e+00   3.6000000e+00   2.7000000e+00   1.5000000e+00   3.4000000e+00   3.7000000e+00   3.3000000e+00   1.8000000e+00   4.1000000e+00   4.1000000e+00   3.1000000e+00   2.4000000e+00   2.6000000e+00   3.2000000e+00   1.7000000e+00   3.0000000e+00   8.0000000e-01   3.4000000e+00   2.0000000e+00   3.4000000e+00   1.9000000e+00   2.8000000e+00   4.6000000e+00   2.3000000e+00   3.6000000e+00   2.9000000e+00   4.7000000e+00   2.1000000e+00   2.0000000e+00   2.7000000e+00   2.3000000e+00   2.4000000e+00   2.5000000e+00   2.1000000e+00   5.7000000e+00   5.4000000e+00   1.8000000e+00   3.4000000e+00   2.0000000e+00   4.7000000e+00   1.4000000e+00   3.1000000e+00   3.5000000e+00   1.1000000e+00   1.3000000e+00   2.4000000e+00   2.9000000e+00   3.7000000e+00   5.4000000e+00   2.5000000e+00   1.2000000e+00   1.8000000e+00   4.4000000e+00   3.0000000e+00   2.1000000e+00   1.3000000e+00   2.8000000e+00   3.1000000e+00   2.7000000e+00   2.0000000e+00   3.5000000e+00   3.5000000e+00   2.5000000e+00   1.8000000e+00   2.0000000e+00   2.6000000e+00   1.7000000e+00   2.2000000e+00   6.4000000e+00   3.8000000e+00   6.4000000e+00   4.9000000e+00   5.8000000e+00   7.6000000e+00   2.3000000e+00   6.6000000e+00   5.1000000e+00   7.7000000e+00   5.1000000e+00   4.6000000e+00   5.7000000e+00   3.5000000e+00   4.4000000e+00   5.5000000e+00   5.1000000e+00   8.7000000e+00   7.8000000e+00   3.6000000e+00   6.4000000e+00   3.6000000e+00   7.5000000e+00   4.0000000e+00   6.1000000e+00   6.5000000e+00   3.9000000e+00   4.1000000e+00   5.2000000e+00   5.9000000e+00   6.5000000e+00   8.4000000e+00   5.3000000e+00   4.0000000e+00   4.0000000e+00   7.4000000e+00   6.0000000e+00   5.1000000e+00   3.9000000e+00   5.8000000e+00   6.1000000e+00   5.7000000e+00   3.8000000e+00   6.5000000e+00   6.5000000e+00   5.5000000e+00   4.0000000e+00   5.0000000e+00   5.6000000e+00   4.1000000e+00   4.2000000e+00   1.8000000e+00   4.2000000e+00   2.7000000e+00   3.6000000e+00   5.4000000e+00   1.9000000e+00   4.4000000e+00   3.5000000e+00   5.5000000e+00   2.9000000e+00   2.6000000e+00   3.5000000e+00   1.9000000e+00   2.2000000e+00   3.3000000e+00   2.9000000e+00   6.5000000e+00   6.0000000e+00   2.0000000e+00   4.2000000e+00   1.6000000e+00   5.3000000e+00   2.0000000e+00   3.9000000e+00   4.3000000e+00   1.7000000e+00   1.9000000e+00   3.0000000e+00   3.7000000e+00   4.3000000e+00   6.2000000e+00   3.1000000e+00   1.8000000e+00   2.2000000e+00   5.2000000e+00   3.8000000e+00   2.9000000e+00   1.7000000e+00   3.6000000e+00   3.9000000e+00   3.5000000e+00   1.8000000e+00   4.3000000e+00   4.3000000e+00   3.3000000e+00   2.4000000e+00   2.8000000e+00   3.4000000e+00   1.9000000e+00   2.6000000e+00   1.6000000e+00   1.5000000e+00   1.0000000e+00   2.6000000e+00   4.5000000e+00   2.4000000e+00   2.1000000e+00   1.3000000e+00   1.7000000e+00   2.0000000e+00   1.7000000e+00   2.9000000e+00   2.0000000e+00   1.1000000e+00   1.7000000e+00   2.9000000e+00   3.2000000e+00   3.4000000e+00   1.2000000e+00   2.8000000e+00   3.1000000e+00   2.4000000e+00   1.1000000e+00   1.7000000e+00   2.5000000e+00   2.3000000e+00   1.4000000e+00   2.3000000e+00   2.3000000e+00   3.0000000e+00   1.3000000e+00   2.4000000e+00   2.4000000e+00   2.0000000e+00   6.0000000e-01   1.5000000e+00   2.5000000e+00   1.8000000e+00   1.1000000e+00   1.9000000e+00   2.6000000e+00   9.0000000e-01   7.0000000e-01   1.7000000e+00   2.4000000e+00   1.8000000e+00   1.0000000e+00   2.3000000e+00   2.6000000e+00   1.3000000e+00   2.0000000e+00   3.8000000e+00   1.9000000e+00   3.0000000e+00   1.9000000e+00   3.9000000e+00   1.3000000e+00   8.0000000e-01   1.9000000e+00   5.0000000e-01   6.0000000e-01   1.7000000e+00   1.5000000e+00   4.9000000e+00   4.2000000e+00   1.2000000e+00   2.6000000e+00   6.0000000e-01   3.7000000e+00   8.0000000e-01   2.3000000e+00   2.9000000e+00   9.0000000e-01   9.0000000e-01   1.4000000e+00   2.7000000e+00   2.7000000e+00   4.6000000e+00   1.5000000e+00   1.0000000e+00   1.4000000e+00   3.6000000e+00   2.2000000e+00   1.5000000e+00   9.0000000e-01   2.0000000e+00   2.3000000e+00   1.9000000e+00   0.0000000e+00   2.7000000e+00   2.7000000e+00   1.7000000e+00   8.0000000e-01   1.2000000e+00   1.8000000e+00   5.0000000e-01   1.5000000e+00   8.0000000e-01   1.2000000e+00   4.5000000e+00   1.0000000e+00   1.3000000e+00   1.3000000e+00   1.7000000e+00   1.8000000e+00   7.0000000e-01   2.9000000e+00   2.6000000e+00   1.7000000e+00   1.3000000e+00   2.3000000e+00   2.2000000e+00   3.4000000e+00   8.0000000e-01   2.8000000e+00   1.7000000e+00   2.4000000e+00   9.0000000e-01   7.0000000e-01   2.5000000e+00   2.3000000e+00   1.2000000e+00   7.0000000e-01   9.0000000e-01   2.2000000e+00   1.3000000e+00   2.4000000e+00   2.4000000e+00   1.0000000e+00   1.8000000e+00   1.5000000e+00   2.5000000e+00   8.0000000e-01   1.1000000e+00   1.3000000e+00   2.6000000e+00   7.0000000e-01   1.3000000e+00   1.3000000e+00   2.4000000e+00   1.4000000e+00   2.0000000e+00   2.3000000e+00   9.0000000e-01   2.7000000e+00   3.0000000e+00   1.7000000e+00   1.0000000e+00   2.8000000e+00   1.2000000e+00   7.0000000e-01   1.0000000e+00   1.8000000e+00   1.7000000e+00   1.2000000e+00   4.0000000e-01   3.8000000e+00   3.5000000e+00   1.9000000e+00   1.5000000e+00   1.7000000e+00   2.8000000e+00   9.0000000e-01   1.2000000e+00   1.6000000e+00   1.0000000e+00   1.0000000e+00   5.0000000e-01   1.4000000e+00   1.8000000e+00   3.5000000e+00   6.0000000e-01   9.0000000e-01   9.0000000e-01   2.5000000e+00   1.1000000e+00   4.0000000e-01   1.2000000e+00   1.3000000e+00   1.2000000e+00   1.8000000e+00   1.3000000e+00   1.6000000e+00   1.6000000e+00   1.4000000e+00   1.1000000e+00   9.0000000e-01   1.3000000e+00   1.0000000e+00   2.0000000e+00   3.9000000e+00   1.8000000e+00   1.1000000e+00   1.9000000e+00   1.1000000e+00   1.2000000e+00   7.0000000e-01   2.3000000e+00   1.8000000e+00   9.0000000e-01   7.0000000e-01   2.9000000e+00   2.8000000e+00   2.8000000e+00   8.0000000e-01   2.2000000e+00   2.5000000e+00   1.8000000e+00   7.0000000e-01   1.5000000e+00   1.9000000e+00   1.7000000e+00   6.0000000e-01   1.3000000e+00   1.7000000e+00   3.0000000e+00   5.0000000e-01   1.8000000e+00   1.8000000e+00   1.6000000e+00   1.0000000e+00   9.0000000e-01   1.9000000e+00   1.0000000e+00   7.0000000e-01   1.3000000e+00   2.0000000e+00   7.0000000e-01   9.0000000e-01   9.0000000e-01   1.8000000e+00   8.0000000e-01   1.2000000e+00   1.7000000e+00   5.7000000e+00   1.0000000e+00   2.5000000e+00   1.9000000e+00   2.9000000e+00   3.0000000e+00   1.9000000e+00   4.1000000e+00   3.8000000e+00   2.9000000e+00   2.5000000e+00   1.1000000e+00   1.0000000e+00   4.6000000e+00   2.0000000e+00   4.0000000e+00   5.0000000e-01   3.6000000e+00   2.1000000e+00   1.5000000e+00   3.7000000e+00   3.5000000e+00   2.4000000e+00   1.7000000e+00   1.1000000e+00   1.4000000e+00   2.5000000e+00   3.6000000e+00   3.6000000e+00   8.0000000e-01   3.0000000e+00   2.7000000e+00   3.7000000e+00   2.0000000e+00   2.3000000e+00   2.5000000e+00   3.8000000e+00   1.9000000e+00   2.5000000e+00   2.5000000e+00   3.6000000e+00   2.6000000e+00   3.2000000e+00   3.5000000e+00   4.7000000e+00   3.2000000e+00   5.8000000e+00   3.2000000e+00   2.7000000e+00   3.8000000e+00   1.6000000e+00   2.5000000e+00   3.6000000e+00   3.2000000e+00   6.8000000e+00   5.9000000e+00   2.1000000e+00   4.5000000e+00   1.7000000e+00   5.6000000e+00   2.1000000e+00   4.2000000e+00   4.6000000e+00   2.0000000e+00   2.2000000e+00   3.3000000e+00   4.2000000e+00   4.6000000e+00   6.5000000e+00   3.4000000e+00   2.5000000e+00   2.7000000e+00   5.5000000e+00   4.1000000e+00   3.2000000e+00   2.0000000e+00   3.9000000e+00   4.2000000e+00   3.8000000e+00   1.9000000e+00   4.6000000e+00   4.6000000e+00   3.6000000e+00   2.1000000e+00   3.1000000e+00   3.7000000e+00   2.2000000e+00   1.5000000e+00   1.7000000e+00   2.5000000e+00   2.2000000e+00   1.7000000e+00   3.5000000e+00   3.4000000e+00   2.7000000e+00   1.7000000e+00   2.1000000e+00   1.8000000e+00   3.6000000e+00   1.8000000e+00   3.4000000e+00   1.1000000e+00   2.6000000e+00   1.9000000e+00   7.0000000e-01   2.7000000e+00   2.7000000e+00   2.0000000e+00   9.0000000e-01   5.0000000e-01   1.8000000e+00   2.1000000e+00   2.6000000e+00   2.6000000e+00   1.2000000e+00   2.8000000e+00   1.9000000e+00   2.9000000e+00   1.8000000e+00   2.1000000e+00   2.3000000e+00   3.0000000e+00   1.7000000e+00   2.3000000e+00   2.3000000e+00   2.8000000e+00   2.2000000e+00   3.0000000e+00   2.7000000e+00   2.6000000e+00   1.8000000e+00   1.1000000e+00   1.2000000e+00   2.0000000e+00   2.5000000e+00   2.0000000e+00   1.0000000e+00   3.6000000e+00   2.7000000e+00   2.1000000e+00   1.5000000e+00   2.5000000e+00   2.4000000e+00   1.5000000e+00   1.2000000e+00   1.4000000e+00   1.8000000e+00   2.0000000e+00   1.1000000e+00   1.2000000e+00   1.4000000e+00   3.3000000e+00   1.2000000e+00   1.7000000e+00   1.3000000e+00   2.3000000e+00   2.1000000e+00   1.2000000e+00   2.2000000e+00   1.5000000e+00   1.4000000e+00   2.0000000e+00   1.9000000e+00   1.4000000e+00   1.6000000e+00   1.6000000e+00   1.3000000e+00   1.5000000e+00   2.3000000e+00   2.0000000e+00   2.6000000e+00   3.1000000e+00   2.0000000e+00   4.2000000e+00   3.3000000e+00   2.2000000e+00   2.6000000e+00   1.6000000e+00   2.5000000e+00   4.7000000e+00   1.3000000e+00   4.1000000e+00   2.4000000e+00   3.7000000e+00   1.6000000e+00   1.2000000e+00   3.8000000e+00   3.6000000e+00   2.5000000e+00   1.8000000e+00   1.6000000e+00   1.7000000e+00   2.4000000e+00   3.7000000e+00   3.7000000e+00   1.3000000e+00   1.7000000e+00   2.6000000e+00   3.8000000e+00   1.9000000e+00   1.6000000e+00   2.0000000e+00   3.9000000e+00   1.2000000e+00   1.2000000e+00   2.2000000e+00   3.7000000e+00   2.7000000e+00   2.1000000e+00   3.6000000e+00   9.0000000e-01   1.0000000e+00   1.6000000e+00   1.5000000e+00   6.0000000e-01   8.0000000e-01   3.6000000e+00   3.9000000e+00   2.1000000e+00   1.3000000e+00   1.5000000e+00   3.2000000e+00   1.1000000e+00   1.0000000e+00   1.8000000e+00   1.2000000e+00   1.0000000e+00   1.1000000e+00   2.0000000e+00   2.4000000e+00   3.3000000e+00   1.2000000e+00   1.1000000e+00   2.1000000e+00   2.7000000e+00   1.3000000e+00   8.0000000e-01   1.2000000e+00   9.0000000e-01   1.2000000e+00   8.0000000e-01   1.3000000e+00   1.4000000e+00   1.4000000e+00   8.0000000e-01   1.1000000e+00   3.0000000e-01   1.1000000e+00   1.0000000e+00   1.1000000e+00   1.3000000e+00   1.4000000e+00   9.0000000e-01   7.0000000e-01   4.1000000e+00   3.4000000e+00   1.6000000e+00   1.8000000e+00   1.4000000e+00   2.9000000e+00   6.0000000e-01   1.5000000e+00   2.1000000e+00   9.0000000e-01   1.1000000e+00   6.0000000e-01   1.9000000e+00   1.9000000e+00   3.8000000e+00   7.0000000e-01   8.0000000e-01   1.2000000e+00   2.8000000e+00   1.6000000e+00   7.0000000e-01   1.3000000e+00   1.2000000e+00   1.5000000e+00   1.5000000e+00   8.0000000e-01   1.9000000e+00   1.9000000e+00   1.1000000e+00   6.0000000e-01   6.0000000e-01   1.4000000e+00   1.1000000e+00   2.2000000e+00   1.9000000e+00   1.0000000e+00   6.0000000e-01   3.0000000e+00   2.9000000e+00   2.7000000e+00   7.0000000e-01   2.1000000e+00   2.4000000e+00   1.7000000e+00   6.0000000e-01   1.4000000e+00   1.8000000e+00   1.6000000e+00   7.0000000e-01   1.2000000e+00   1.6000000e+00   2.9000000e+00   8.0000000e-01   1.7000000e+00   1.9000000e+00   1.7000000e+00   1.3000000e+00   8.0000000e-01   1.8000000e+00   3.0000000e-01   6.0000000e-01   8.0000000e-01   1.9000000e+00   8.0000000e-01   1.0000000e+00   6.0000000e-01   1.7000000e+00   7.0000000e-01   1.3000000e+00   1.6000000e+00   9.0000000e-01   2.0000000e+00   2.0000000e+00   5.2000000e+00   4.3000000e+00   1.1000000e+00   2.9000000e+00   5.0000000e-01   4.0000000e+00   1.1000000e+00   2.6000000e+00   3.4000000e+00   1.2000000e+00   1.2000000e+00   1.7000000e+00   3.2000000e+00   3.2000000e+00   4.9000000e+00   1.8000000e+00   1.5000000e+00   1.7000000e+00   3.9000000e+00   2.5000000e+00   2.0000000e+00   1.2000000e+00   2.3000000e+00   2.6000000e+00   2.2000000e+00   5.0000000e-01   3.0000000e+00   3.0000000e+00   2.0000000e+00   7.0000000e-01   1.5000000e+00   2.1000000e+00   1.0000000e+00   1.3000000e+00   1.9000000e+00   4.7000000e+00   4.0000000e+00   1.8000000e+00   2.2000000e+00   8.0000000e-01   3.9000000e+00   1.4000000e+00   2.3000000e+00   3.3000000e+00   1.3000000e+00   1.3000000e+00   1.4000000e+00   3.1000000e+00   3.1000000e+00   4.8000000e+00   1.3000000e+00   1.4000000e+00   2.0000000e+00   3.2000000e+00   1.6000000e+00   1.9000000e+00   1.3000000e+00   2.0000000e+00   1.7000000e+00   1.5000000e+00   6.0000000e-01   2.3000000e+00   2.1000000e+00   1.3000000e+00   1.4000000e+00   1.4000000e+00   1.4000000e+00   9.0000000e-01   1.0000000e+00   3.4000000e+00   3.5000000e+00   2.5000000e+00   9.0000000e-01   1.9000000e+00   3.4000000e+00   1.5000000e+00   1.0000000e+00   2.0000000e+00   1.6000000e+00   1.4000000e+00   9.0000000e-01   2.2000000e+00   2.6000000e+00   3.5000000e+00   8.0000000e-01   1.5000000e+00   2.1000000e+00   2.3000000e+00   7.0000000e-01   8.0000000e-01   1.6000000e+00   9.0000000e-01   8.0000000e-01   8.0000000e-01   1.7000000e+00   1.0000000e+00   1.0000000e+00   6.0000000e-01   1.5000000e+00   7.0000000e-01   5.0000000e-01   1.4000000e+00   3.6000000e+00   3.5000000e+00   2.1000000e+00   1.3000000e+00   1.9000000e+00   2.8000000e+00   1.1000000e+00   1.0000000e+00   1.4000000e+00   1.2000000e+00   1.0000000e+00   7.0000000e-01   1.2000000e+00   1.8000000e+00   3.3000000e+00   8.0000000e-01   1.1000000e+00   1.3000000e+00   2.3000000e+00   1.3000000e+00   2.0000000e-01   1.2000000e+00   9.0000000e-01   1.0000000e+00   1.4000000e+00   1.5000000e+00   1.4000000e+00   1.4000000e+00   1.0000000e+00   1.3000000e+00   5.0000000e-01   1.3000000e+00   1.0000000e+00   1.5000000e+00   5.7000000e+00   2.5000000e+00   5.1000000e+00   1.2000000e+00   4.7000000e+00   2.6000000e+00   2.2000000e+00   4.8000000e+00   4.6000000e+00   3.5000000e+00   2.8000000e+00   2.2000000e+00   7.0000000e-01   3.4000000e+00   4.7000000e+00   4.7000000e+00   1.5000000e+00   3.1000000e+00   3.6000000e+00   4.8000000e+00   2.9000000e+00   3.0000000e+00   3.2000000e+00   4.9000000e+00   2.4000000e+00   2.8000000e+00   3.4000000e+00   4.7000000e+00   3.7000000e+00   3.3000000e+00   4.6000000e+00   4.8000000e+00   2.6000000e+00   4.6000000e+00   7.0000000e-01   4.0000000e+00   3.1000000e+00   2.5000000e+00   4.3000000e+00   4.5000000e+00   3.0000000e+00   2.7000000e+00   1.7000000e+00   2.2000000e+00   2.9000000e+00   4.2000000e+00   3.8000000e+00   1.2000000e+00   3.6000000e+00   3.7000000e+00   4.7000000e+00   3.0000000e+00   2.9000000e+00   3.1000000e+00   4.2000000e+00   2.5000000e+00   3.1000000e+00   3.1000000e+00   3.8000000e+00   3.6000000e+00   3.8000000e+00   4.5000000e+00   3.4000000e+00   1.6000000e+00   4.5000000e+00   1.2000000e+00   3.1000000e+00   3.5000000e+00   1.3000000e+00   1.3000000e+00   2.2000000e+00   2.9000000e+00   3.5000000e+00   5.4000000e+00   2.3000000e+00   1.0000000e+00   1.2000000e+00   4.4000000e+00   3.0000000e+00   2.1000000e+00   1.3000000e+00   2.8000000e+00   3.1000000e+00   2.7000000e+00   1.2000000e+00   3.5000000e+00   3.5000000e+00   2.5000000e+00   1.0000000e+00   2.0000000e+00   2.6000000e+00   1.3000000e+00   2.8000000e+00   2.5000000e+00   2.4000000e+00   5.0000000e-01   1.1000000e+00   2.5000000e+00   2.3000000e+00   1.2000000e+00   1.3000000e+00   1.7000000e+00   2.6000000e+00   1.1000000e+00   2.4000000e+00   2.4000000e+00   1.4000000e+00   1.0000000e+00   1.3000000e+00   2.5000000e+00   6.0000000e-01   5.0000000e-01   7.0000000e-01   2.6000000e+00   3.0000000e-01   5.0000000e-01   9.0000000e-01   2.4000000e+00   1.4000000e+00   1.2000000e+00   2.3000000e+00   3.9000000e+00   1.0000000e+00   2.5000000e+00   3.3000000e+00   9.0000000e-01   9.0000000e-01   1.6000000e+00   3.1000000e+00   3.1000000e+00   4.8000000e+00   1.7000000e+00   1.4000000e+00   2.0000000e+00   3.8000000e+00   2.4000000e+00   1.9000000e+00   9.0000000e-01   2.2000000e+00   2.5000000e+00   2.1000000e+00   6.0000000e-01   2.9000000e+00   2.9000000e+00   1.9000000e+00   1.2000000e+00   1.4000000e+00   2.0000000e+00   9.0000000e-01   3.5000000e+00   2.6000000e+00   1.8000000e+00   3.6000000e+00   3.8000000e+00   2.5000000e+00   2.0000000e+00   1.0000000e+00   1.5000000e+00   2.6000000e+00   3.5000000e+00   3.5000000e+00   1.1000000e+00   3.5000000e+00   3.0000000e+00   4.0000000e+00   2.5000000e+00   2.8000000e+00   3.0000000e+00   3.7000000e+00   2.4000000e+00   3.0000000e+00   3.0000000e+00   3.5000000e+00   2.9000000e+00   3.7000000e+00   3.8000000e+00   2.1000000e+00   2.5000000e+00   3.0000000e-01   5.0000000e-01   1.2000000e+00   2.3000000e+00   2.5000000e+00   4.4000000e+00   1.3000000e+00   6.0000000e-01   1.4000000e+00   3.4000000e+00   2.0000000e+00   1.1000000e+00   7.0000000e-01   1.8000000e+00   2.1000000e+00   1.7000000e+00   8.0000000e-01   2.5000000e+00   2.5000000e+00   1.5000000e+00   4.0000000e-01   1.0000000e+00   1.8000000e+00   9.0000000e-01   1.2000000e+00   2.2000000e+00   2.0000000e+00   9.0000000e-01   1.4000000e+00   1.8000000e+00   2.5000000e+00   1.0000000e+00   2.1000000e+00   2.1000000e+00   1.9000000e+00   9.0000000e-01   1.0000000e+00   2.2000000e+00   7.0000000e-01   6.0000000e-01   1.2000000e+00   2.3000000e+00   6.0000000e-01   4.0000000e-01   1.0000000e+00   2.1000000e+00   1.1000000e+00   1.1000000e+00   2.0000000e+00   2.6000000e+00   2.4000000e+00   1.9000000e+00   6.0000000e-01   8.0000000e-01   1.9000000e+00   2.0000000e+00   2.5000000e+00   2.5000000e+00   1.3000000e+00   2.1000000e+00   1.4000000e+00   2.6000000e+00   1.3000000e+00   1.6000000e+00   1.8000000e+00   2.9000000e+00   1.0000000e+00   1.6000000e+00   2.0000000e+00   2.7000000e+00   1.9000000e+00   2.3000000e+00   2.4000000e+00   4.0000000e-01   1.3000000e+00   2.4000000e+00   2.6000000e+00   4.5000000e+00   1.4000000e+00   7.0000000e-01   1.5000000e+00   3.5000000e+00   2.1000000e+00   1.2000000e+00   4.0000000e-01   1.9000000e+00   2.2000000e+00   1.8000000e+00   9.0000000e-01   2.6000000e+00   2.6000000e+00   1.6000000e+00   7.0000000e-01   1.1000000e+00   1.7000000e+00   8.0000000e-01   1.5000000e+00   2.2000000e+00   2.8000000e+00   4.3000000e+00   1.6000000e+00   9.0000000e-01   1.5000000e+00   3.3000000e+00   1.9000000e+00   1.0000000e+00   2.0000000e-01   1.7000000e+00   2.0000000e+00   1.6000000e+00   9.0000000e-01   2.4000000e+00   2.4000000e+00   1.4000000e+00   9.0000000e-01   9.0000000e-01   1.5000000e+00   4.0000000e-01   1.7000000e+00   1.7000000e+00   3.4000000e+00   1.0000000e-01   1.2000000e+00   1.2000000e+00   2.2000000e+00   1.0000000e+00   7.0000000e-01   1.7000000e+00   1.0000000e+00   9.0000000e-01   1.5000000e+00   1.4000000e+00   1.3000000e+00   1.3000000e+00   1.1000000e+00   1.2000000e+00   8.0000000e-01   1.2000000e+00   1.5000000e+00   1.0000000e+00   2.5000000e+00   1.8000000e+00   1.9000000e+00   1.9000000e+00   1.5000000e+00   2.3000000e+00   1.4000000e+00   2.4000000e+00   1.3000000e+00   1.6000000e+00   1.8000000e+00   2.7000000e+00   1.4000000e+00   1.8000000e+00   1.8000000e+00   2.5000000e+00   1.7000000e+00   2.5000000e+00   2.2000000e+00   1.9000000e+00   1.8000000e+00   2.5000000e+00   2.5000000e+00   9.0000000e-01   2.7000000e+00   2.0000000e+00   3.0000000e+00   1.7000000e+00   2.0000000e+00   2.2000000e+00   2.7000000e+00   1.6000000e+00   2.2000000e+00   2.2000000e+00   2.5000000e+00   2.1000000e+00   2.9000000e+00   2.8000000e+00   3.5000000e+00   4.4000000e+00   4.4000000e+00   1.6000000e+00   3.2000000e+00   3.3000000e+00   4.5000000e+00   2.8000000e+00   3.1000000e+00   3.3000000e+00   4.6000000e+00   2.5000000e+00   2.9000000e+00   3.5000000e+00   4.4000000e+00   3.4000000e+00   3.4000000e+00   4.3000000e+00   1.3000000e+00   1.3000000e+00   2.1000000e+00   9.0000000e-01   8.0000000e-01   1.8000000e+00   1.1000000e+00   8.0000000e-01   1.4000000e+00   1.5000000e+00   1.2000000e+00   1.2000000e+00   1.0000000e+00   1.3000000e+00   9.0000000e-01   1.1000000e+00   1.6000000e+00   1.0000000e+00   3.4000000e+00   2.0000000e+00   1.1000000e+00   1.1000000e+00   1.8000000e+00   2.1000000e+00   1.7000000e+00   1.0000000e+00   2.5000000e+00   2.5000000e+00   1.5000000e+00   8.0000000e-01   1.0000000e+00   1.8000000e+00   9.0000000e-01   3.4000000e+00   2.0000000e+00   1.3000000e+00   1.7000000e+00   2.2000000e+00   2.1000000e+00   2.7000000e+00   1.4000000e+00   2.5000000e+00   2.5000000e+00   2.3000000e+00   1.4000000e+00   1.8000000e+00   2.0000000e+00   1.5000000e+00   2.4000000e+00   2.5000000e+00   3.5000000e+00   1.8000000e+00   1.7000000e+00   1.9000000e+00   3.6000000e+00   1.3000000e+00   1.9000000e+00   1.9000000e+00   3.4000000e+00   2.4000000e+00   2.6000000e+00   3.3000000e+00   1.1000000e+00   2.1000000e+00   1.4000000e+00   7.0000000e-01   1.5000000e+00   2.2000000e+00   1.1000000e+00   7.0000000e-01   1.3000000e+00   2.0000000e+00   1.4000000e+00   4.0000000e-01   1.9000000e+00   1.2000000e+00   9.0000000e-01   1.0000000e+00   1.4000000e+00   1.5000000e+00   1.4000000e+00   1.4000000e+00   1.2000000e+00   1.3000000e+00   7.0000000e-01   1.1000000e+00   1.0000000e+00   1.9000000e+00   2.2000000e+00   1.8000000e+00   9.0000000e-01   2.6000000e+00   2.6000000e+00   1.6000000e+00   1.1000000e+00   1.1000000e+00   1.7000000e+00   4.0000000e-01   7.0000000e-01   5.0000000e-01   2.0000000e+00   9.0000000e-01   1.1000000e+00   7.0000000e-01   1.8000000e+00   8.0000000e-01   1.2000000e+00   1.7000000e+00   8.0000000e-01   2.3000000e+00   6.0000000e-01   4.0000000e-01   6.0000000e-01   2.1000000e+00   1.1000000e+00   1.1000000e+00   2.0000000e+00   1.9000000e+00   1.0000000e+00   1.2000000e+00   4.0000000e-01   1.7000000e+00   9.0000000e-01   1.3000000e+00   1.6000000e+00   2.7000000e+00   2.7000000e+00   1.7000000e+00   8.0000000e-01   1.2000000e+00   1.8000000e+00   5.0000000e-01   6.0000000e-01   1.0000000e+00   2.5000000e+00   1.5000000e+00   1.3000000e+00   2.4000000e+00   1.0000000e+00   2.5000000e+00   1.5000000e+00   1.1000000e+00   2.4000000e+00   1.5000000e+00   5.0000000e-01   1.1000000e+00   1.4000000e+00   1.0000000e+00   1.8000000e+00   1.1000000e+00   1.2000000e+00   9.0000000e-01   1.5000000e+00
diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-cityblock-ml.txt b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-cityblock-ml.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8fb22e62200894f9693010ebf45fb23751f4e3a6
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-cityblock-ml.txt
@@ -0,0 +1 @@
+   3.2420590e+01   3.3246607e+01   3.0526910e+01   3.5166573e+01   3.1868301e+01   3.6025002e+01   3.2513623e+01   3.6557796e+01   3.3752212e+01   3.4422130e+01   3.2526018e+01   3.2581161e+01   3.3743555e+01   3.6960777e+01   3.4225270e+01   3.2965308e+01   3.4591031e+01   3.4204203e+01   3.4678123e+01   3.5728720e+01   3.0830047e+01   3.1550681e+01   3.3304790e+01   3.2676753e+01   3.2742330e+01   3.1684556e+01   3.2830915e+01   3.2956614e+01   2.7365639e+01   3.3207307e+01   3.3420925e+01   3.4357941e+01   2.8280126e+01   3.4523458e+01   3.2705274e+01   3.2455891e+01   3.1636060e+01   3.1594957e+01   3.1805202e+01   3.3886574e+01   3.3438829e+01   3.3330030e+01   3.4168514e+01   3.0637353e+01   4.2149167e+01   3.6340559e+01   2.9315308e+01   3.5778314e+01   3.7693050e+01   3.2598714e+01   3.2990836e+01   3.4967659e+01   3.9748920e+01   3.6745043e+01   2.7117550e+01   3.6014760e+01   2.9367558e+01   3.3845350e+01   3.5477339e+01   3.1513372e+01   3.2517953e+01   2.4755097e+01   3.0229897e+01   3.4799343e+01   3.3371710e+01   2.9600910e+01   3.3275088e+01   3.3567110e+01   3.4527016e+01   3.4942320e+01   3.2359383e+01   3.2607100e+01   3.1467914e+01   2.9032039e+01   3.3122878e+01   2.8496709e+01   2.9908448e+01   2.9962886e+01   3.0345299e+01   3.1737613e+01   2.8551485e+01   3.2610551e+01   3.3082660e+01   3.3719298e+01   3.6434018e+01   3.6589278e+01   3.3889586e+01   3.8036774e+01   3.1483497e+01   3.4196794e+01   3.5154035e+01   3.5488608e+01   3.6143183e+01   3.3473491e+01   3.4686446e+01   2.8687495e+01   3.5725742e+01   3.0188298e+01   3.3084534e+01   3.3538519e+01   3.6226849e+01   2.9052099e+01   3.6032733e+01   3.0811503e+01   3.2616190e+01   3.3888566e+01   3.3074570e+01   2.9683515e+01   3.0600771e+01   3.4345247e+01   3.6983843e+01   3.3692824e+01   3.3762461e+01   3.4024582e+01   3.3698854e+01   3.1238613e+01   3.4978833e+01   3.4991078e+01   3.4577741e+01   3.3749227e+01   3.4982272e+01   3.0487868e+01   3.2317632e+01   3.1125588e+01   3.4413791e+01   3.1881871e+01   3.1373821e+01   3.0416864e+01   3.2066187e+01   3.1128313e+01   3.0240249e+01   3.0125198e+01   3.1343454e+01   3.5479092e+01   3.4450767e+01   3.2953507e+01   3.4456795e+01   3.0136375e+01   3.3462150e+01   2.9894274e+01   3.1367432e+01   3.2839320e+01   3.1440398e+01   2.9400374e+01   3.1106338e+01   3.1242624e+01   3.5537892e+01   3.3056459e+01   2.8610281e+01   3.4296217e+01   3.5819772e+01   3.2503922e+01   3.0963029e+01   3.4762112e+01   3.4796284e+01   2.9645345e+01   3.4468088e+01   2.6975590e+01   3.3738555e+01   2.8825009e+01   3.2663999e+01   3.2547878e+01   3.2308091e+01   3.2489966e+01   3.0868597e+01   3.2974220e+01   3.0866111e+01   3.8197342e+01   3.0609568e+01   3.5478978e+01   2.9249184e+01   3.6185622e+01   3.1948258e+01   3.2649719e+01   3.3305650e+01   3.4643955e+01   3.6566241e+01   3.4968484e+01   3.2632218e+01   3.6741383e+01   3.5700008e+01   3.1962468e+01   3.1410623e+01   3.0412061e+01   3.3749077e+01   3.5649661e+01   3.7649263e+01   3.2832574e+01   3.1783914e+01   2.8264292e+01
diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-correlation-ml-iris.txt b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-correlation-ml-iris.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f297500381fe33428e6725ea3b10ab6191a46fa3
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-correlation-ml-iris.txt
@@ -0,0 +1 @@
+   4.0013388e-03   2.6088954e-05   1.8315482e-03   6.5266850e-04   4.1394685e-04   1.1888069e-03   4.6185289e-04   1.9233577e-03   3.4480388e-03   1.5150632e-05   1.9126718e-03   3.0974734e-03   2.2295833e-04   2.4043394e-03   5.0134320e-03   3.0165570e-03   1.3145239e-04   6.0759419e-04   1.6672981e-03   4.0036132e-03   6.1375191e-04   8.5916540e-03   3.0212269e-03   8.6923503e-03   7.7875235e-03   5.1612907e-04   2.9662451e-04   6.2402983e-04   2.7278440e-03   4.0510347e-03   3.0027154e-03   6.2616145e-03   4.1342211e-03   3.4480388e-03   1.5822510e-03   1.7143312e-03   3.4480388e-03   2.2462074e-04   6.1048465e-04   6.5190641e-04   2.4247873e-02   9.0785596e-04   2.1652052e-04   3.4845573e-03   3.2507646e-03   2.3346511e-03   4.0773355e-04   1.1278223e-04   5.0819669e-04   2.1340893e-01   2.1253858e-01   2.5193073e-01   2.9479565e-01   2.6774348e-01   2.8869785e-01   2.3348217e-01   1.9273490e-01   2.4443270e-01   2.4320510e-01   2.7679421e-01   2.1672263e-01   2.6813840e-01   2.8435705e-01   1.5561363e-01   2.0057173e-01   2.7812139e-01   2.2900256e-01   3.4724680e-01   2.3882260e-01   2.9132931e-01   2.0333645e-01   3.5307051e-01   2.8812452e-01   2.1722530e-01   2.1423111e-01   2.7396952e-01   2.9207940e-01   2.6626182e-01   1.7106032e-01   2.4279706e-01   2.2559055e-01   2.0940857e-01   3.8432412e-01   2.9354670e-01   2.0829958e-01   2.3669414e-01   3.0463326e-01   2.1035851e-01   2.6623117e-01   3.0835417e-01   2.5871089e-01   2.3465249e-01   2.0319416e-01   2.6292582e-01   2.1771735e-01   2.3212816e-01   2.2399387e-01   1.3799316e-01   2.3049526e-01   4.8512087e-01   4.2535066e-01   4.0184471e-01   4.1903049e-01   4.4627199e-01   4.4692268e-01   4.3569888e-01   4.2673251e-01   4.5731950e-01   3.7438176e-01   3.0619251e-01   4.0039114e-01   3.7245195e-01   4.5829878e-01   4.5814844e-01   3.6107062e-01   3.7600936e-01   3.7662883e-01   5.2492832e-01   4.2684428e-01   3.7975064e-01   4.0636707e-01   4.6364339e-01   3.4607190e-01   3.6988036e-01   3.6764668e-01   3.2524634e-01   3.1943549e-01   4.4481193e-01   3.5496498e-01   4.1356534e-01   3.2082320e-01   4.5322964e-01   3.4300770e-01   4.4485158e-01   3.9755578e-01   3.9702418e-01   3.7202285e-01   3.1131344e-01   3.4018064e-01   4.0217537e-01   3.1441868e-01   4.2535066e-01   4.1533176e-01   3.9695242e-01   3.5313531e-01   3.9400199e-01   3.4652657e-01   3.6608320e-01   3.6684161e-01   3.3929143e-03   2.6033698e-03   7.7673212e-03   6.4081099e-03   9.2794464e-03   2.8819447e-03   1.4536586e-03   9.6714455e-04   3.7992387e-03   5.9342609e-03   3.9974031e-04   6.0694735e-03   9.1304628e-03   1.7655983e-02   1.1643899e-02   4.0363794e-03   1.6463709e-03   1.0706739e-02   6.7984475e-04   7.6845878e-03   2.3516587e-02   9.9502337e-05   1.0315881e-02   1.0821735e-03   1.8887942e-03   2.4624674e-03   1.5760536e-03   3.6638868e-03   1.6253664e-03   7.8762517e-04   1.9487010e-02   1.6211862e-02   9.6714455e-04   2.2382105e-03   2.1712385e-03   9.6714455e-04   2.9674185e-03   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4.7707633e-01   3.8217339e-01   3.3708398e-01   3.6131644e-01   4.1712805e-01   3.0571403e-01   3.2625308e-01   3.2419755e-01   2.8563873e-01   2.7883266e-01   3.9884997e-01   3.1256889e-01   3.6952768e-01   2.7953122e-01   4.0726631e-01   3.0093515e-01   3.9702583e-01   3.5566883e-01   3.5181973e-01   3.2782384e-01   2.7114516e-01   3.0000941e-01   3.5891976e-01   2.7762255e-01   3.7954719e-01   3.7024637e-01   3.5327118e-01   3.1362016e-01   3.5214869e-01   3.0546169e-01   3.2226324e-01   3.2277503e-01   1.1668032e-04   8.6044327e-05   1.4968429e-03   3.9691382e-03   6.2388252e-03   7.0588028e-04   1.9691519e-03   6.1279520e-03   1.9660913e-04   2.5761274e-03   2.5168387e-03   2.4029967e-03   9.7429318e-04   2.3122381e-03   2.3682626e-04   7.1643085e-03   1.3128642e-04   5.3939078e-03   6.2992904e-03   9.0353935e-03   1.2266741e-02   2.0706893e-03   1.5408774e-03   2.5522607e-03   3.9522692e-03   6.6899152e-03   6.3980861e-03   2.9039306e-03   1.6942568e-03   6.2388252e-03   3.9336207e-03   4.1533642e-03   6.2388252e-03   1.2180733e-03   2.1518176e-03   8.8270219e-04   3.2743785e-02   7.7572782e-05   1.3417853e-03   2.5322339e-03   6.7844678e-03   8.2761566e-04   8.6236157e-04   3.1792685e-04   2.2579028e-03   2.2976852e-01   2.2800773e-01   2.6917639e-01   3.1391346e-01   2.8619117e-01   3.0434544e-01   2.4844431e-01   2.0773635e-01   2.6148944e-01   2.5886513e-01   2.9555853e-01   2.3241008e-01   2.8723433e-01   3.0077518e-01   1.6999944e-01   2.1692490e-01   2.9290302e-01   2.4423212e-01   3.6894940e-01   2.5556289e-01   3.0695160e-01   2.1997775e-01   3.7292526e-01   3.0427758e-01   2.3385552e-01   2.3106102e-01   2.9243468e-01   3.1048744e-01   2.8298832e-01   1.8662712e-01   2.6007204e-01   2.4232174e-01   2.2560003e-01   4.0265980e-01   3.0762748e-01   2.2151447e-01   2.5355085e-01   3.2493368e-01   2.2408199e-01   2.8382455e-01   3.2448802e-01   2.7442187e-01   2.5162228e-01   2.1940897e-01   2.7915380e-01   2.3127910e-01   2.4702051e-01   2.4019206e-01   1.5301315e-01   2.4619533e-01   5.0391216e-01   4.4483392e-01   4.2228707e-01   4.3731273e-01   4.6617394e-01   4.6750253e-01   4.5367757e-01   4.4636521e-01   4.7842690e-01   3.9329580e-01   3.2434154e-01   4.2091234e-01   3.9272980e-01   4.7962551e-01   4.7998875e-01   3.8052757e-01   3.9422077e-01   3.9365636e-01   5.4778535e-01   4.4784024e-01   3.9985415e-01   4.2545240e-01   4.8476479e-01   3.6622351e-01   3.8794414e-01   3.8577592e-01   3.4462011e-01   3.3712507e-01   4.6543611e-01   3.7346604e-01   4.3442200e-01   3.3762412e-01   4.7437523e-01   3.6087712e-01   4.6258851e-01   4.1954525e-01   4.1507031e-01   3.8935328e-01   3.2880662e-01   3.6009673e-01   4.2314218e-01   3.3549029e-01   4.4483392e-01   4.3505302e-01   4.1710447e-01   3.7450914e-01   4.1581746e-01   3.6597096e-01   3.8346411e-01   3.8386195e-01   2.7739415e-04   8.2117467e-04   2.7843462e-03   4.7394226e-03   3.9365385e-04   1.1964598e-03   4.7400628e-03   2.5527396e-04   3.2634446e-03   3.7103657e-03   3.3188195e-03   8.6302611e-04   1.5635411e-03   6.0189508e-04   5.5859876e-03   3.8282951e-04   7.0925635e-03   5.0273924e-03   7.3470160e-03   1.0223636e-02   1.3503463e-03   9.3049535e-04   1.9663208e-03   2.7155903e-03   5.0798223e-03   5.5875952e-03   3.5987384e-03   2.6550151e-03   4.7394226e-03   3.5923878e-03   3.7937786e-03   4.7394226e-03   6.6480476e-04   1.3814035e-03   1.1581699e-03   3.0091048e-02   1.0888067e-04   1.1634967e-03   1.9052023e-03   5.6332034e-03   7.9034466e-04   3.5005887e-04   1.0179107e-04   1.6076683e-03   2.2018795e-01   2.1841167e-01   2.5888963e-01   3.0298911e-01   2.7568827e-01   2.9345793e-01   2.3845526e-01   1.9853879e-01   2.5133209e-01   2.4870042e-01   2.8491736e-01   2.2273608e-01   2.7678086e-01   2.8993699e-01   1.6165333e-01   2.0762176e-01   2.8220337e-01   2.3432093e-01   3.5743296e-01   2.4549712e-01   2.9602684e-01   2.1063470e-01   3.6116406e-01   2.9338620e-01   2.2421094e-01   2.2149308e-01   2.8182182e-01   2.9956540e-01   2.7243830e-01   1.7796817e-01   2.4995634e-01   2.3251210e-01   2.1609445e-01   3.9047864e-01   2.9675065e-01   2.1202908e-01   2.4353030e-01   3.1395037e-01   2.1453916e-01   2.7329907e-01   3.1330772e-01   2.6399518e-01   2.4164659e-01   2.1003834e-01   2.6865531e-01   2.2160867e-01   2.3705638e-01   2.3039039e-01   1.4523591e-01   2.3625874e-01   4.9071957e-01   4.3219633e-01   4.0993016e-01   4.2475440e-01   4.5332327e-01   4.5465382e-01   4.4096188e-01   4.3371359e-01   4.6548638e-01   3.8123224e-01   3.1318896e-01   4.0857587e-01   3.8073064e-01   4.6668253e-01   4.6707002e-01   3.6864305e-01   3.8213773e-01   3.8159377e-01   5.3428461e-01   4.3521869e-01   3.8775353e-01   4.1301893e-01   4.7176152e-01   3.5457739e-01   3.7593537e-01   3.7379344e-01   3.3323181e-01   3.2577190e-01   4.5261005e-01   3.6164142e-01   4.2194514e-01   3.2625778e-01   4.6147754e-01   3.4920516e-01   4.4979521e-01   4.0734174e-01   4.0275102e-01   3.7733353e-01   3.1756791e-01   3.4852048e-01   4.1080565e-01   3.2443308e-01   4.3219633e-01   4.2252463e-01   4.0479526e-01   3.6286403e-01   4.0364435e-01   3.5428112e-01   3.7151258e-01   3.7191203e-01   2.0478784e-03   4.7860280e-03   7.2727783e-03   1.2329906e-03   2.0550268e-03   7.3066158e-03   5.3810576e-04   3.2245377e-03   2.1674888e-03   2.7856851e-03   1.6387773e-03   3.1323423e-03   6.7307381e-05   8.3332066e-03   3.3954200e-04   4.9119026e-03   7.6276175e-03   8.9240504e-03   1.3851706e-02   2.8347122e-03   2.2069601e-03   3.5278340e-03   4.3892066e-03   7.6179982e-03   7.9398397e-03   2.0003115e-03   1.2885024e-03   7.2727783e-03   5.1809110e-03   5.4327573e-03   7.2727783e-03   1.7938257e-03   2.8924302e-03   1.4132511e-03   3.5877316e-02   5.5425651e-05   2.1070391e-03   2.2246722e-03   8.2675293e-03   4.8309816e-04   1.2152730e-03   6.6498554e-04   3.1323983e-03   2.3387083e-01   2.3171300e-01   2.7340823e-01   3.1873143e-01   2.9087099e-01   3.0765106e-01   2.5178166e-01   2.1138210e-01   2.6568600e-01   2.6244481e-01   3.0032621e-01   2.3618270e-01   2.9221666e-01   3.0443867e-01   1.7368514e-01   2.2112593e-01   2.9589691e-01   2.4771596e-01   3.7467992e-01   2.5965416e-01   3.1023215e-01   2.2429067e-01   3.7775475e-01   3.0780450e-01   2.3805322e-01   2.3537447e-01   2.9708156e-01   3.1499475e-01   2.8689460e-01   1.9071775e-01   2.6437980e-01   2.4650321e-01   2.2965596e-01   4.0666307e-01   3.1024566e-01   2.2426781e-01   2.5770992e-01   3.3024819e-01   2.2703835e-01   2.8812097e-01   3.2789845e-01   2.7792695e-01   2.5584753e-01   2.2352457e-01   2.8285984e-01   2.3411709e-01   2.5033634e-01   2.4414228e-01   1.5718330e-01   2.4987685e-01   5.0772777e-01   4.4916856e-01   4.2715006e-01   4.4114868e-01   4.7061118e-01   4.7223859e-01   4.5731921e-01   4.5076024e-01   4.8335950e-01   3.9759816e-01   3.2864932e-01   4.2581769e-01   3.9765561e-01   4.8465345e-01   4.8525127e-01   3.8513607e-01   3.9820652e-01   3.9712803e-01   5.5326906e-01   4.5284577e-01   4.0466523e-01   4.2968979e-01   4.8967945e-01   3.7122633e-01   3.9189300e-01   3.8976354e-01   3.4937792e-01   3.4115590e-01   4.7020033e-01   3.7767688e-01   4.3942138e-01   3.4125876e-01   4.7934102e-01   3.6486747e-01   4.6609349e-01   4.2514437e-01   4.1889348e-01   3.9297481e-01   3.3279384e-01   3.6502235e-01   4.2824304e-01   3.4111505e-01   4.4916856e-01   4.3953404e-01   4.2185806e-01   3.8004789e-01   4.2135185e-01   3.7064704e-01   3.8713375e-01   3.8737322e-01   5.9378937e-04   1.6263483e-03   3.1194349e-04   8.5089275e-04   1.6365846e-03   1.1579874e-03   4.9430863e-03   7.7957878e-03   5.8209267e-03   9.7423596e-04   2.1559031e-04   2.8280232e-03   2.1261057e-03   1.8496545e-03   1.2342594e-02   1.9347552e-03   5.4995961e-03   5.2624400e-03   1.3773080e-04   7.1496401e-05   7.1145768e-04   9.6706058e-04   1.9028496e-03   3.0842001e-03   7.5087003e-03   6.3709632e-03   1.6263483e-03   2.4219636e-03   2.5416684e-03   1.6263483e-03   4.5881830e-05   1.0508341e-04   2.2101780e-03   2.1711060e-02   1.4779987e-03   1.0004664e-03   2.4029906e-03   2.5527616e-03   2.4859397e-03   1.2918144e-04   4.6388898e-04   3.7292268e-04   1.9674800e-01   1.9551090e-01   2.3384591e-01   2.7581575e-01   2.4956432e-01   2.6852776e-01   2.1529223e-01   1.7652116e-01   2.2659936e-01   2.2483764e-01   2.5838801e-01   1.9958250e-01   2.5031938e-01   2.6459593e-01   1.4127677e-01   1.8459488e-01   2.5809699e-01   2.1110498e-01   3.2773890e-01   2.2109976e-01   2.7105695e-01   1.8736680e-01   3.3227725e-01   2.6813261e-01   2.0050552e-01   1.9777445e-01   2.5552383e-01   2.7284453e-01   2.4733170e-01   1.5638593e-01   2.2514733e-01   2.0849921e-01   1.9287136e-01   3.6191982e-01   2.7281863e-01   1.9071038e-01   2.1912633e-01   2.8593968e-01   1.9281596e-01   2.4768186e-01   2.8763479e-01   2.3971138e-01   2.1723753e-01   1.8699948e-01   2.4393940e-01   1.9979806e-01   2.1397418e-01   2.0672587e-01   1.2529166e-01   2.1270878e-01   4.6033946e-01   4.0222602e-01   3.7977808e-01   3.9565939e-01   4.2276626e-01   4.2367223e-01   4.1181849e-01   4.0362790e-01   4.3403229e-01   3.5248619e-01   2.8628855e-01   3.7840466e-01   3.5121985e-01   4.3508597e-01   4.3518504e-01   3.3982310e-01   3.5380487e-01   3.5403534e-01   5.0086936e-01   4.0431760e-01   3.5820087e-01   3.8360776e-01   4.4020334e-01   3.2567463e-01   3.4780712e-01   3.4566354e-01   3.0520609e-01   2.9886193e-01   4.2163480e-01   3.3351442e-01   3.9135037e-01   2.9988740e-01   4.3006423e-01   3.2170490e-01   4.2068520e-01   3.7643926e-01   3.7416586e-01   3.4964963e-01   2.9095264e-01   3.1987117e-01   3.8035231e-01   2.9582266e-01   4.0222602e-01   3.9256940e-01   3.7489846e-01   3.3318735e-01   3.7289799e-01   3.2576051e-01   3.4389968e-01   3.4452790e-01   2.6022528e-04   1.6357171e-03   1.5776794e-03   3.8821876e-04   3.3383101e-03   8.1348232e-03   1.2673676e-02   9.6454978e-03   2.5951087e-03   4.7710550e-04   5.9640558e-03   5.0935416e-04   4.5005321e-03   1.8295131e-02   8.0881241e-04   4.5548809e-03   2.4342161e-03   4.9437559e-04   7.1285200e-04   1.1827453e-03   5.3640347e-04   3.9274104e-04   2.7126384e-03   1.1795471e-02   1.0834355e-02   2.6022528e-04   3.1798475e-03   3.2407554e-03   2.6022528e-04   8.6271302e-04   3.7982619e-04   4.6816553e-03   1.6563494e-02   3.8583498e-03   2.4190920e-03   3.6876972e-03   1.5540748e-03   4.9548680e-03   1.1822578e-03   2.1020911e-03   7.8943086e-04   1.7690932e-01   1.7592254e-01   2.1244374e-01   2.5265403e-01   2.2738778e-01   2.4651370e-01   1.9514374e-01   1.5780110e-01   2.0549282e-01   2.0415245e-01   2.3585798e-01   1.7978451e-01   2.2802648e-01   2.4243736e-01   1.2428265e-01   1.6526016e-01   2.3669421e-01   1.9101658e-01   3.0265561e-01   2.0025949e-01   2.4898144e-01   1.6786898e-01   3.0733331e-01   2.4595698e-01   1.8046568e-01   1.7781045e-01   2.3314059e-01   2.4991164e-01   2.2560913e-01   1.3845901e-01   2.0404813e-01   1.8812805e-01   1.7322140e-01   3.3666075e-01   2.5129679e-01   1.7201674e-01   1.9833201e-01   2.6229128e-01   1.7386253e-01   2.2573363e-01   2.6492814e-01   2.1852944e-01   1.9648937e-01   1.6758641e-01   2.2246603e-01   1.8066071e-01   1.9389274e-01   1.8653629e-01   1.0911288e-01   1.9242842e-01   4.3299781e-01   3.7574545e-01   3.5353088e-01   3.6969868e-01   3.9574789e-01   3.9644649e-01   3.8564737e-01   3.7707427e-01   4.0646475e-01   3.2727058e-01   2.6301141e-01   3.5217112e-01   3.2569733e-01   4.0744443e-01   4.0742674e-01   3.1477415e-01   3.2876954e-01   3.2939944e-01   4.7166141e-01   3.7739415e-01   3.3254323e-01   3.5763917e-01   4.1251084e-01   3.0085067e-01   3.2295735e-01   3.2084322e-01   2.8110727e-01   2.7535557e-01   3.9443856e-01   3.0887601e-01   3.6474538e-01   2.7663010e-01   4.0256676e-01   2.9754793e-01   3.9443683e-01   3.4998590e-01   3.4873324e-01   3.2500314e-01   2.6771990e-01   2.9525187e-01   3.5397733e-01   2.7178914e-01   3.7574545e-01   3.6622316e-01   3.4883278e-01   3.0797294e-01   3.4655783e-01   3.0107914e-01   3.1936679e-01   3.2010756e-01   3.0868881e-03   2.8691382e-03   1.3643967e-04   5.3429196e-03   1.0581034e-02   1.6459895e-02   1.2551534e-02   4.1576220e-03   1.2160579e-03   8.7064401e-03   5.4418849e-05   6.8214146e-03   2.2732626e-02   5.6586090e-04   4.9831593e-03   1.1314391e-03   1.3090644e-03   1.7262411e-03   1.9770194e-03   1.0389613e-03   9.3641634e-05   2.8067647e-03   1.5471006e-02   1.4411876e-02   0.0000000e+00   4.0251529e-03   4.0402030e-03   0.0000000e+00   2.0104773e-03   1.1579294e-03   6.7733512e-03   1.3328703e-02   6.1195429e-03   3.8280621e-03   5.4471697e-03   1.3203495e-03   7.3930866e-03   2.5511055e-03   3.8011014e-03   1.5935161e-03   1.6488937e-01   1.6420208e-01   1.9946134e-01   2.3841307e-01   2.1377841e-01   2.3352484e-01   1.8323739e-01   1.4660873e-01   1.9269692e-01   1.9183992e-01   2.2200730e-01   1.6791595e-01   2.1423078e-01   2.2922867e-01   1.1407468e-01   1.5349471e-01   2.2418179e-01   1.7908948e-01   2.8692621e-01   1.8765985e-01   2.3596576e-01   1.5596498e-01   2.9203641e-01   2.3278981e-01   1.6829150e-01   1.6563525e-01   2.1942293e-01   2.3592536e-01   2.1256421e-01   1.2755291e-01   1.9121342e-01   1.7576718e-01   1.6132929e-01   3.2148865e-01   2.3885357e-01   1.6118125e-01   1.8573297e-01   2.4757051e-01   1.6279862e-01   2.1240660e-01   2.5149161e-01   2.0595435e-01   1.8389163e-01   1.5580881e-01   2.0964365e-01   1.6953436e-01   1.8203376e-01   1.7437090e-01   9.9184065e-02   1.8031354e-01   4.1664204e-01   3.5971944e-01   3.3744612e-01   3.5416868e-01   3.7936058e-01   3.7982315e-01   3.7006184e-01   3.6098196e-01   3.8956200e-01   3.1201251e-01   2.4889912e-01   3.3607844e-01   3.1002022e-01   3.9046127e-01   3.9028467e-01   2.9949936e-01   3.1373736e-01   3.1479561e-01   4.5355800e-01   3.6085089e-01   3.1682959e-01   3.4195608e-01   3.9553949e-01   2.8555816e-01   3.0804941e-01   3.0593834e-01   2.6633772e-01   2.6121338e-01   3.7782244e-01   2.9399549e-01   3.4839508e-01   2.6278429e-01   3.8569374e-01   2.8303600e-01   3.7885421e-01   3.3349568e-01   3.3352424e-01   3.1033775e-01   2.5375578e-01   2.8011018e-01   3.3772574e-01   2.5671985e-01   3.5971944e-01   3.5022311e-01   3.3289784e-01   2.9224130e-01   3.3016010e-01   2.8599652e-01   3.0475125e-01   3.0561759e-01   1.6232219e-03   2.8110674e-03   3.0992704e-04   2.8009412e-03   5.3859157e-03   3.4428307e-03   2.2389965e-04   4.8865483e-04   1.7600776e-03   3.6417064e-03   7.4576509e-04   9.1296419e-03   2.8123816e-03   8.0068765e-03   7.3379880e-03   3.9579356e-04   1.9713653e-04   6.0194434e-04   2.3367622e-03   3.6239908e-03   3.0185118e-03   6.3202257e-03   4.4046298e-03   3.0868881e-03   1.7141363e-03   1.8461990e-03   3.0868881e-03   1.2729358e-04   4.6571753e-04   8.6393185e-04   2.3903803e-02   9.0441478e-04   3.0528309e-04   3.1648190e-03   3.1223857e-03   2.2339929e-03   2.7724170e-04   9.5102356e-05   4.3913729e-04   2.1061066e-01   2.0964712e-01   2.4888926e-01   2.9163776e-01   2.6471732e-01   2.8522189e-01   2.3035873e-01   1.8998369e-01   2.4143327e-01   2.4006731e-01   2.7373417e-01   2.1381600e-01   2.6519773e-01   2.8097864e-01   1.5319882e-01   1.9790190e-01   2.7464921e-01   2.2594124e-01   3.4406181e-01   2.3583526e-01   2.8783351e-01   2.0067586e-01   3.4959337e-01   2.8469567e-01   2.1442337e-01   2.1148410e-01   2.7089383e-01   2.8885413e-01   2.6304757e-01   1.6861411e-01   2.3983808e-01   2.2272157e-01   2.0662897e-01   3.8050402e-01   2.8992390e-01   2.0524163e-01   2.3373909e-01   3.0156183e-01   2.0732304e-01   2.6311208e-01   3.0478863e-01   2.5545595e-01   2.3172924e-01   2.0047959e-01   2.5968741e-01   2.1460680e-01   2.2900957e-01   2.2107714e-01   1.3590375e-01   2.2746759e-01   4.8087096e-01   4.2142796e-01   3.9814594e-01   4.1502871e-01   4.4228995e-01   4.4300705e-01   4.3159396e-01   4.2281768e-01   4.5341178e-01   3.7067256e-01   3.0283474e-01   3.9670954e-01   3.6890449e-01   4.5441105e-01   4.5432159e-01   3.5749751e-01   3.7222314e-01   3.7273757e-01   5.2092654e-01   4.2307513e-01   3.7613897e-01   4.0250144e-01   4.5970761e-01   3.4267709e-01   3.6611458e-01   3.6389952e-01   3.2189682e-01   3.1593975e-01   4.4091119e-01   3.5132753e-01   4.0985044e-01   3.1723537e-01   4.4934566e-01   3.3938050e-01   4.4068685e-01   3.9407776e-01   3.9311145e-01   3.6818097e-01   3.0785214e-01   3.3679573e-01   3.9853670e-01   3.1138703e-01   4.2142796e-01   4.1148317e-01   3.9324794e-01   3.4985868e-01   3.9052142e-01   3.4304315e-01   3.6227810e-01   3.6300235e-01   3.5297445e-03   2.3993465e-03   8.1469449e-03   8.4116551e-03   8.4748907e-03   3.0443320e-03   1.8587915e-03   2.8140158e-03   3.7033592e-03   2.9317197e-03   1.3265454e-02   4.5015236e-03   2.6265400e-03   7.5415562e-03   1.6353241e-03   1.4046892e-03   3.1172532e-03   6.0159720e-04   2.6265400e-03   7.0517547e-03   5.5270478e-03   6.4518235e-03   2.8691382e-03   6.1014438e-03   6.3013427e-03   2.8691382e-03   1.1615614e-03   1.4498289e-03   4.4069463e-03   2.8268404e-02   1.4610903e-03   3.3082950e-03   4.5136771e-04   5.8170191e-03   1.2876475e-03   5.5964987e-04   1.3152056e-03   2.3446691e-03   1.9624436e-01   1.9365486e-01   2.3272539e-01   2.7570910e-01   2.4962218e-01   2.6341222e-01   2.1161968e-01   1.7505868e-01   2.2555325e-01   2.2171510e-01   2.5853430e-01   1.9783603e-01   2.5146360e-01   2.6075203e-01   1.4121466e-01   1.8483453e-01   2.5221719e-01   2.0803875e-01   3.2980663e-01   2.1983733e-01   2.6580206e-01   1.8792174e-01   3.3096405e-01   2.6375229e-01   2.0022607e-01   1.9799659e-01   2.5530781e-01   2.7170116e-01   2.4472945e-01   1.5721426e-01   2.2453551e-01   2.0791989e-01   1.9232403e-01   3.5721533e-01   2.6541719e-01   1.8583170e-01   2.1815822e-01   2.8740780e-01   1.8853156e-01   2.4642239e-01   2.8243457e-01   2.3594931e-01   2.1655773e-01   1.8685267e-01   2.4074340e-01   1.9492750e-01   2.1026662e-01   2.0538411e-01   1.2769778e-01   2.1026662e-01   4.5350142e-01   3.9795187e-01   3.7769065e-01   3.8983341e-01   4.1851849e-01   4.2042793e-01   4.0510768e-01   3.9953508e-01   4.3130939e-01   3.4895812e-01   2.8413412e-01   3.7648942e-01   3.4987508e-01   4.3267862e-01   4.3359924e-01   3.3758650e-01   3.4918773e-01   3.4772733e-01   4.9915788e-01   4.0231358e-01   3.5632097e-01   3.7931174e-01   4.3732697e-01   3.2511301e-01   3.4317696e-01   3.4120231e-01   3.0420772e-01   2.9548175e-01   4.1851849e-01   3.3003548e-01   3.8954108e-01   2.9516106e-01   4.2751620e-01   3.1771485e-01   4.1340131e-01   3.7704473e-01   3.6865281e-01   3.4390717e-01   2.8759676e-01   3.1915503e-01   3.7909158e-01   2.9821954e-01   3.9795187e-01   3.8894782e-01   3.7251565e-01   3.3442155e-01   3.7333196e-01   3.2403985e-01   3.3841983e-01   3.3852014e-01   4.9713816e-03   9.2903476e-03   1.5944722e-02   1.1386125e-02   3.5402300e-03   9.6201776e-04   8.6911918e-03   9.4953207e-05   6.4447745e-03   2.1940505e-02   1.4660203e-04   6.6774582e-03   1.0681613e-03   1.0987220e-03   1.5397922e-03   1.3925202e-03   1.6744918e-03   4.5493239e-04   1.7274513e-03   1.6063124e-02   1.4167352e-02   1.3643967e-04   2.8974888e-03   2.8893579e-03   1.3643967e-04   1.8844794e-03   1.0195101e-03   5.9835494e-03   1.1907169e-02   6.2144210e-03   3.1461009e-03   6.4603159e-03   6.0804116e-04   7.9398115e-03   2.6608779e-03   3.6611489e-03   1.1878605e-03   1.6827914e-01   1.6808878e-01   2.0330224e-01   2.4208927e-01   2.1725982e-01   2.3901101e-01   1.8791090e-01   1.5022413e-01   1.9646923e-01   1.9636982e-01   2.2550082e-01   1.7178784e-01   2.1730098e-01   2.3423675e-01   1.1690649e-01   1.5652486e-01   2.2988556e-01   1.8351752e-01   2.8999988e-01   1.9148148e-01   2.4151451e-01   1.5889324e-01   2.9641885e-01   2.3800995e-01   1.7162027e-01   1.6875690e-01   2.2303923e-01   2.3997805e-01   2.1702847e-01   1.3016155e-01   1.9481438e-01   1.7925806e-01   1.6471086e-01   3.2723835e-01   2.4516700e-01   1.6613136e-01   1.8943302e-01   2.5069233e-01   1.6755119e-01   2.1637456e-01   2.5710224e-01   2.1080083e-01   1.8747239e-01   1.5900127e-01   2.1430731e-01   1.7454101e-01   1.8671199e-01   1.7813660e-01   1.0093430e-01   1.8452279e-01   4.2348788e-01   3.6545764e-01   3.4229982e-01   3.6044592e-01   3.8515670e-01   3.8525367e-01   3.7671058e-01   3.6665866e-01   3.9483186e-01   3.1729700e-01   2.5339335e-01   3.4086300e-01   3.1448994e-01   3.9561710e-01   3.9513385e-01   3.0425707e-01   3.1942407e-01   3.2109044e-01   4.5863634e-01   3.6575820e-01   3.2152631e-01   3.4763745e-01   4.0088503e-01   2.8963041e-01   3.1371721e-01   3.1153634e-01   2.7048666e-01   2.6621754e-01   3.8319922e-01   2.9918600e-01   3.5318564e-01   2.6828212e-01   3.9088644e-01   2.8836369e-01   3.8573578e-01   3.3732047e-01   3.3961180e-01   3.1641339e-01   2.5871452e-01   2.8421639e-01   3.4227214e-01   2.5952711e-01   3.6545764e-01   3.5568934e-01   3.3784386e-01   2.9565951e-01   3.3403769e-01   2.9050448e-01   3.1070970e-01   3.1176741e-01   1.7225353e-03   3.1252650e-03   1.9141697e-03   3.0572974e-04   1.5621195e-03   7.7657730e-04   6.0730841e-03   9.6969946e-05   6.0804497e-03   4.8728559e-03   1.0019276e-02   1.0630759e-02   1.4028596e-03   1.0008907e-03   1.5106647e-03   3.9425625e-03   5.9922357e-03   4.5089760e-03   4.5296071e-03   2.4544132e-03   5.3429196e-03   2.3927105e-03   2.5658780e-03   5.3429196e-03   8.0759380e-04   1.5345623e-03   3.2653860e-04   2.8784931e-02   4.6959359e-04   5.2961514e-04   3.5529133e-03   5.0787251e-03   1.7528094e-03   7.9750642e-04   1.8469304e-04   1.3949343e-03   2.2601194e-01   2.2489065e-01   2.6538416e-01   3.0933559e-01   2.8173337e-01   3.0217927e-01   2.4601138e-01   2.0461695e-01   2.5772236e-01   2.5608721e-01   2.9099324e-01   2.2920421e-01   2.8227951e-01   2.9802519e-01   1.6660589e-01   2.1294215e-01   2.9118999e-01   2.4154604e-01   3.6304829e-01   2.5194222e-01   3.0483437e-01   2.1582549e-01   3.6852765e-01   3.0175865e-01   2.2996178e-01   2.2696306e-01   2.8805620e-01   3.0640689e-01   2.7978083e-01   1.8266242e-01   2.5611673e-01   2.3849427e-01   2.2189938e-01   3.9968280e-01   3.0655638e-01   2.1989254e-01   2.4981061e-01   3.1957344e-01   2.2214967e-01   2.7998655e-01   3.2222399e-01   2.7182647e-01   2.4776514e-01   2.1557967e-01   2.7625427e-01   2.2956697e-01   2.4461597e-01   2.3673300e-01   1.4870158e-01   2.4319918e-01   5.0146439e-01   4.4143183e-01   4.1797463e-01   4.3468983e-01   4.6265612e-01   4.6350594e-01   4.5140079e-01   4.4286970e-01   4.7413628e-01   3.8981309e-01   3.2063561e-01   4.1652733e-01   3.8823357e-01   4.7518267e-01   4.7516433e-01   3.7651294e-01   3.9124904e-01   3.9150135e-01   5.4273573e-01   4.4336023e-01   3.9556546e-01   4.2215915e-01   4.8051706e-01   3.6152094e-01   3.8501414e-01   3.8277781e-01   3.4024930e-01   3.3391004e-01   4.6138930e-01   3.7007400e-01   4.2991865e-01   3.3504580e-01   4.7002175e-01   3.5780202e-01   4.6054739e-01   4.1401655e-01   4.1241306e-01   3.8694896e-01   3.2563422e-01   3.5550143e-01   4.1844379e-01   3.2964964e-01   4.4143183e-01   4.3139176e-01   4.1295631e-01   3.6894646e-01   4.1038562e-01   3.6180237e-01   3.8096707e-01   3.8161756e-01   2.9059655e-03   2.3706161e-04   1.5622923e-03   4.6985391e-03   3.0899699e-03   1.1144685e-02   1.5452086e-03   4.3912180e-03   8.2378168e-03   1.9894938e-02   1.6022015e-02   4.6248887e-03   4.1434850e-03   3.4955495e-03   1.0239539e-02   1.2012056e-02   5.3911313e-03   8.1025404e-03   3.3141536e-03   1.0581034e-02   2.5128050e-03   2.6447621e-03   1.0581034e-02   4.0444636e-03   5.0265914e-03   5.7591609e-04   3.1111838e-02   3.5439088e-03   1.6935296e-03   1.0096079e-02   7.4536930e-03   6.1909555e-03   4.6446420e-03   2.9301624e-03   3.9714148e-03   2.5068010e-01   2.5098525e-01   2.9216380e-01   3.3638336e-01   3.0774280e-01   3.3430586e-01   2.7479523e-01   2.2946729e-01   2.8415608e-01   2.8467354e-01   3.1719659e-01   2.5534962e-01   3.0706036e-01   3.2874800e-01   1.8820706e-01   2.3625921e-01   3.2370915e-01   2.6954509e-01   3.8903955e-01   2.7840834e-01   3.3718014e-01   2.3890051e-01   3.9852630e-01   3.3314087e-01   2.5453269e-01   2.5085481e-01   3.1457631e-01   3.3452242e-01   3.0863300e-01   2.0400912e-01   2.8201538e-01   2.6372052e-01   2.4645516e-01   4.3401653e-01   3.4099078e-01   2.4885351e-01   2.7587880e-01   3.4510687e-01   2.5062404e-01   3.0740449e-01   3.5503881e-01   3.0161400e-01   2.7344211e-01   2.3943815e-01   3.0560987e-01   2.5890901e-01   2.7338361e-01   2.6272911e-01   1.6653571e-01   2.7061027e-01   5.3996294e-01   4.7622847e-01   4.4996413e-01   4.7092027e-01   4.9784258e-01   4.9765553e-01   4.8884384e-01   4.7750758e-01   5.0792579e-01   4.2270376e-01   3.5026703e-01   4.4829833e-01   4.1874266e-01   5.0865069e-01   5.0773433e-01   4.0771387e-01   4.2529697e-01   4.2723724e-01   5.7654330e-01   4.7578493e-01   4.2683086e-01   4.5657562e-01   5.1458642e-01   3.9050926e-01   4.1892650e-01   4.1646419e-01   3.6916765e-01   3.6521270e-01   4.9536279e-01   4.0243409e-01   4.6185742e-01   3.6775616e-01   5.0354755e-01   3.9037876e-01   4.9872590e-01   4.4290716e-01   4.4784995e-01   4.2202156e-01   3.5667822e-01   3.8450868e-01   4.4953729e-01   3.5436611e-01   4.7622847e-01   4.6530251e-01   4.4515647e-01   3.9606646e-01   4.3939461e-01   3.9207838e-01   4.1563418e-01   4.1682072e-01   1.5609953e-03   4.8490070e-03   9.0958370e-03   1.4989091e-03   1.7813868e-02   2.1261488e-03   5.5450301e-04   1.5694148e-02   1.9384410e-02   2.5209737e-02   8.6954304e-03   7.6213095e-03   8.7105486e-03   1.2654300e-02   1.7334342e-02   1.3883194e-02   2.2522789e-03   1.7443565e-04   1.6459895e-02   9.1718824e-03   9.4916987e-03   1.6459895e-02   6.9918464e-03   8.9833757e-03   2.9662983e-03   4.9266036e-02   2.9055422e-03   5.5731976e-03   8.0889759e-03   1.5739049e-02   3.7597322e-03   6.3200695e-03   4.4644236e-03   8.6395939e-03   2.7692079e-01   2.7499135e-01   3.1941212e-01   3.6719225e-01   3.3760508e-01   3.5656667e-01   2.9687968e-01   2.5298236e-01   3.1115442e-01   3.0819394e-01   3.4760947e-01   2.7976620e-01   3.3861131e-01   3.5300749e-01   2.1161836e-01   2.6294922e-01   3.4413759e-01   2.9242527e-01   4.2523864e-01   3.0477646e-01   3.5931443e-01   2.6623770e-01   4.2973462e-01   3.5665121e-01   2.8133678e-01   2.7828246e-01   3.4429599e-01   3.6357656e-01   3.3414792e-01   2.2982660e-01   3.0962503e-01   2.9049749e-01   2.7240490e-01   4.6073277e-01   3.5937207e-01   2.6744708e-01   3.0261187e-01   3.7874332e-01   2.7038484e-01   3.3511133e-01   3.7800754e-01   3.2481692e-01   3.0053112e-01   2.6567213e-01   3.2997477e-01   2.7805229e-01   2.9533686e-01   2.8819780e-01   1.9246360e-01   2.9461561e-01   5.6604002e-01   5.0500114e-01   4.8160322e-01   4.9684759e-01   5.2728223e-01   5.2878056e-01   5.1374073e-01   5.0662675e-01   5.4019822e-01   4.5105935e-01   3.7828674e-01   4.8016813e-01   4.5059090e-01   5.4146236e-01   5.4186046e-01   4.3772456e-01   4.5187440e-01   4.5090747e-01   6.1216296e-01   5.0833718e-01   4.5807252e-01   4.8471571e-01   5.4678369e-01   4.2264992e-01   4.4526564e-01   4.4301133e-01   3.9982165e-01   3.9174986e-01   5.2663733e-01   4.3017652e-01   4.9431552e-01   3.9206379e-01   5.3598953e-01   4.1681568e-01   5.2288475e-01   4.7864082e-01   4.7360696e-01   4.4651927e-01   3.8292357e-01   4.1618542e-01   4.8251093e-01   3.8978460e-01   5.0500114e-01   4.9485605e-01   4.7615846e-01   4.3123359e-01   4.7475023e-01   4.2239197e-01   4.4037545e-01   4.4066833e-01   2.2696323e-03   5.9674345e-03   2.4448133e-03   1.3335241e-02   1.4550127e-03   2.5899751e-03   1.0462849e-02   2.0483763e-02   1.9016265e-02   5.8048658e-03   5.1341121e-03   4.8749246e-03   1.1285550e-02   1.3907377e-02   7.6337585e-03   6.3180508e-03   2.0267734e-03   1.2551534e-02   4.1078635e-03   4.2919330e-03   1.2551534e-02   4.8854397e-03   6.2043549e-03   8.9134425e-04   3.6466805e-02   3.2782414e-03   2.5696799e-03   9.8307089e-03   9.8120264e-03   5.5450409e-03   5.1728098e-03   3.2838118e-03   5.2555481e-03   2.6123905e-01   2.6103645e-01   3.0329747e-01   3.4864780e-01   3.1958423e-01   3.4458162e-01   2.8459400e-01   2.3921225e-01   2.9516933e-01   2.9488851e-01   3.2923215e-01   2.6553322e-01   3.1926739e-01   3.3946038e-01   1.9751618e-01   2.4678743e-01   3.3347141e-01   2.7948950e-01   4.0283567e-01   2.8923185e-01   3.4744486e-01   2.4959732e-01   4.1128993e-01   3.4370645e-01   2.6525258e-01   2.6168140e-01   3.2643822e-01   3.4638099e-01   3.1949478e-01   2.1402441e-01   2.9314941e-01   2.7451414e-01   2.5691069e-01   4.4594923e-01   3.5036767e-01   2.5760360e-01   2.8676453e-01   3.5805235e-01   2.5967094e-01   3.1875975e-01   3.6562012e-01   3.1188296e-01   2.8438818e-01   2.4989387e-01   3.1618152e-01   2.6787548e-01   2.8314006e-01   2.7321717e-01   1.7615044e-01   2.8082637e-01   5.5224352e-01   4.8885819e-01   4.6311762e-01   4.8285549e-01   5.1073035e-01   5.1093091e-01   5.0061869e-01   4.9022404e-01   5.2151073e-01   4.3495694e-01   3.6199911e-01   4.6149506e-01   4.3176986e-01   5.2236122e-01   5.2173621e-01   4.2026138e-01   4.3714978e-01   4.3841019e-01   5.9117531e-01   4.8927834e-01   4.3976762e-01   4.6895974e-01   5.2818477e-01   4.0343191e-01   4.3068816e-01   4.2826096e-01   3.8162190e-01   3.7670056e-01   5.0866155e-01   4.1442940e-01   4.7525840e-01   3.7873655e-01   5.1715063e-01   4.0199874e-01   5.1036877e-01   4.5693051e-01   4.5962906e-01   4.3336423e-01   3.6804311e-01   3.9729031e-01   4.6298867e-01   3.6775880e-01   4.8885819e-01   4.7805886e-01   4.5813974e-01   4.0968699e-01   4.5331588e-01   4.0460089e-01   4.2699969e-01   4.2797954e-01   8.7894099e-04   2.0541035e-03   4.6305984e-03   6.7282118e-04   8.1166178e-03   3.1872717e-03   1.0880321e-02   8.3605717e-03   8.2577841e-04   6.1811314e-04   5.6936180e-04   3.8806955e-03   4.9821714e-03   2.5043588e-03   7.1844876e-03   4.2468498e-03   4.1576220e-03   9.9353221e-04   1.1055786e-03   4.1576220e-03   5.9733473e-04   9.9247040e-04   3.2081104e-04   2.3598005e-02   1.4307976e-03   3.0934240e-05   4.9322953e-03   3.1299098e-03   3.2877683e-03   9.9769768e-04   4.3968696e-04   6.2770216e-04   2.1786575e-01   2.1746374e-01   2.5686278e-01   2.9961632e-01   2.7235218e-01   2.9521657e-01   2.3917491e-01   1.9737534e-01   2.4929109e-01   2.4877587e-01   2.8142376e-01   2.2163964e-01   2.7235613e-01   2.9042411e-01   1.5945203e-01   2.0466964e-01   2.8483074e-01   2.3445929e-01   3.5153649e-01   2.4372083e-01   2.9790924e-01   2.0734139e-01   3.5860995e-01   2.9439415e-01   2.2162942e-01   2.1843466e-01   2.7871280e-01   2.9725443e-01   2.7179832e-01   1.7471289e-01   2.4749127e-01   2.3015922e-01   2.1385216e-01   3.9117409e-01   3.0083879e-01   2.1421404e-01   2.4147478e-01   3.0893498e-01   2.1609222e-01   2.7129944e-01   3.1500957e-01   2.6459749e-01   2.3931769e-01   2.0744985e-01   2.6864595e-01   2.2369874e-01   2.3782351e-01   2.2882042e-01   1.4076875e-01   2.3574843e-01   4.9305396e-01   4.3221625e-01   4.0786305e-01   4.2639713e-01   4.5320351e-01   4.5351054e-01   4.4342223e-01   4.3354113e-01   4.6376094e-01   3.8078797e-01   3.1179824e-01   4.0634323e-01   3.7808795e-01   4.6463298e-01   4.6419251e-01   3.6697079e-01   3.8279432e-01   3.8398235e-01   5.3121485e-01   4.3292773e-01   3.8560639e-01   4.1316779e-01   4.7015919e-01   3.5131205e-01   3.7664303e-01   3.7434225e-01   3.3054253e-01   3.2553357e-01   4.5134808e-01   3.6126826e-01   4.1953095e-01   3.2738535e-01   4.5959627e-01   3.4943014e-01   4.5279702e-01   4.0259529e-01   4.0419917e-01   3.7916847e-01   3.1736132e-01   3.4544845e-01   4.0790313e-01   3.1842804e-01   4.3221625e-01   4.2193584e-01   4.0305492e-01   3.5775833e-01   3.9908964e-01   3.5217975e-01   3.7311479e-01   3.7405234e-01   4.0128787e-03   1.5082918e-03   2.4327589e-03   1.3749582e-02   9.8644164e-04   7.0275865e-03   4.0509182e-03   9.2137987e-06   8.1954627e-05   2.0221322e-04   1.4919720e-03   1.6918938e-03   1.6810350e-03   9.8366461e-03   7.8161988e-03   1.2160579e-03   1.4072237e-03   1.4774681e-03   1.2160579e-03   1.9402564e-04   2.6249834e-05   2.2527118e-03   1.8043780e-02   2.4914194e-03   7.5228825e-04   4.0311549e-03   1.3209671e-03   4.0483306e-03   6.3837247e-04   9.1866746e-04   4.5668021e-05   1.9279238e-01   1.9221899e-01   2.2979083e-01   2.7088361e-01   2.4479658e-01   2.6610561e-01   2.1267629e-01   1.7326091e-01   2.2258210e-01   2.2184784e-01   2.5349552e-01   1.9619155e-01   2.4503806e-01   2.6157291e-01   1.3780150e-01   1.8042756e-01   2.5616217e-01   2.0823320e-01   3.2136818e-01   2.1724300e-01   2.6868196e-01   1.8301959e-01   3.2745065e-01   2.6534429e-01   1.9640162e-01   1.9346456e-01   2.5082861e-01   2.6843057e-01   2.4386055e-01   1.5229091e-01   2.2093793e-01   2.0444992e-01   1.8898039e-01   3.5852616e-01   2.7153123e-01   1.8897970e-01   2.1514921e-01   2.8018592e-01   1.9075855e-01   2.4355737e-01   2.8508289e-01   2.3688721e-01   2.1314274e-01   1.8298617e-01   2.4079289e-01   1.9795777e-01   2.1138990e-01   2.0306053e-01   1.2090533e-01   2.0951271e-01   4.5737829e-01   3.9834085e-01   3.7497739e-01   3.9259152e-01   4.1873643e-01   4.1914498e-01   4.0909121e-01   3.9964410e-01   4.2918834e-01   3.4857995e-01   2.8224226e-01   3.7353062e-01   3.4626594e-01   4.3008323e-01   4.2978752e-01   3.3538250e-01   3.5042715e-01   3.5150644e-01   4.9516533e-01   3.9931312e-01   3.5345241e-01   3.7985840e-01   4.3539662e-01   3.2054198e-01   3.4448056e-01   3.4226906e-01   3.0044482e-01   2.9530625e-01   4.1705793e-01   3.2972732e-01   3.8633770e-01   2.9699130e-01   4.2515986e-01   3.1826259e-01   4.1819279e-01   3.7038673e-01   3.7108888e-01   3.4686702e-01   2.8745249e-01   3.1485734e-01   3.7515178e-01   2.8956004e-01   3.9834085e-01   3.8842721e-01   3.7027395e-01   3.2715736e-01   3.6694987e-01   3.2117964e-01   3.4102816e-01   3.4191835e-01   9.8460504e-03   4.2097646e-04   3.8720695e-03   8.9609139e-03   1.0271114e-02   1.5759765e-02   3.6853519e-03   2.9640455e-03   4.3261623e-03   5.5313131e-03   9.1074119e-03   8.9974672e-03   1.5687499e-03   7.6879483e-04   8.7064401e-03   5.8625582e-03   6.1329529e-03   8.7064401e-03   2.4949105e-03   3.7729184e-03   1.5387455e-03   3.8489345e-02   2.4427633e-04   2.5870999e-03   2.8098846e-03   9.5472550e-03   6.5811256e-04   1.8465019e-03   1.0925425e-03   3.9557876e-03   2.4136396e-01   2.3914246e-01   2.8140056e-01   3.2726072e-01   2.9909180e-01   3.1587284e-01   2.5940651e-01   2.1853199e-01   2.7358477e-01   2.7023320e-01   3.0865618e-01   2.4367721e-01   3.0046030e-01   3.1269475e-01   1.8026794e-01   2.2845050e-01   3.0393397e-01   2.5531598e-01   3.8377418e-01   2.6747174e-01   3.1847415e-01   2.3166294e-01   3.8684625e-01   3.1607055e-01   2.4560721e-01   2.4289838e-01   3.0537010e-01   3.2346477e-01   2.9500292e-01   1.9758720e-01   2.7227129e-01   2.5416529e-01   2.3708995e-01   4.1588028e-01   3.1833018e-01   2.3144395e-01   2.6550973e-01   3.3890880e-01   2.3429142e-01   2.9628566e-01   3.3633600e-01   2.8587728e-01   2.6362949e-01   2.3087874e-01   2.9089607e-01   2.4143368e-01   2.5794041e-01   2.5175590e-01   1.6347149e-01   2.5753099e-01   5.1758017e-01   4.5875138e-01   4.3664497e-01   4.5058511e-01   4.8035455e-01   4.8203651e-01   4.6682330e-01   4.6036369e-01   4.9325486e-01   4.0679312e-01   3.3723664e-01   4.3530687e-01   4.0692383e-01   4.9456817e-01   4.9519341e-01   3.9426880e-01   4.0735509e-01   4.0616607e-01   5.6363656e-01   4.6254311e-01   4.1397979e-01   4.3911880e-01   4.9961302e-01   3.8027310e-01   4.0098514e-01   3.9884545e-01   3.5820683e-01   3.4982569e-01   4.7998848e-01   3.8669536e-01   4.4902142e-01   3.4986296e-01   4.8921417e-01   3.7374272e-01   4.7562308e-01   4.3467328e-01   4.2816870e-01   4.0201263e-01   3.4137888e-01   3.7400811e-01   4.3776854e-01   3.4988231e-01   4.5875138e-01   4.4907175e-01   4.3130086e-01   3.8919296e-01   4.3084858e-01   3.7966236e-01   3.9613519e-01   3.9634370e-01   7.6697767e-03   2.4232895e-02   4.2497383e-04   5.8645021e-03   7.1697323e-04   1.6459430e-03   2.1472725e-03   2.1701877e-03   1.5644328e-03   2.1493500e-04   2.5540450e-03   1.7185148e-02   1.5785034e-02   5.4418849e-05   4.0402433e-03   4.0294443e-03   5.4418849e-05   2.5045043e-03   1.5070390e-03   7.3845654e-03   1.1685406e-02   7.1165327e-03   4.2192668e-03   6.5870297e-03   1.0764642e-03   8.6213220e-03   3.2147266e-03   4.4993834e-03   1.8554035e-03   1.6163874e-01   1.6124582e-01   1.9600517e-01   2.3441471e-01   2.0995191e-01   2.3066019e-01   1.8049424e-01   1.4375647e-01   1.8928742e-01   1.8888935e-01   2.1809263e-01   1.6489764e-01   2.1018407e-01   2.2610729e-01   1.1131536e-01   1.5021138e-01   2.2157821e-01   1.7624974e-01   2.8213828e-01   1.8434338e-01   2.3311339e-01   1.5259174e-01   2.8788764e-01   2.2976085e-01   1.6495975e-01   1.6222817e-01   2.1560367e-01   2.3216078e-01   2.0930930e-01   1.2444580e-01   1.8772709e-01   1.7242257e-01   1.5812464e-01   3.1788081e-01   2.3649618e-01   1.5894784e-01   1.8237277e-01   2.4318751e-01   1.6040650e-01   2.0886424e-01   2.4850015e-01   2.0301750e-01   1.8048879e-01   1.5257957e-01   2.0654604e-01   1.6721007e-01   1.7931046e-01   1.7120054e-01   9.6139593e-02   1.7732284e-01   4.1297254e-01   3.5577891e-01   3.3316436e-01   3.5061301e-01   3.7530173e-01   3.7554177e-01   3.6661833e-01   3.5699377e-01   3.8511507e-01   3.0820403e-01   2.4524565e-01   3.3176869e-01   3.0575678e-01   3.8594227e-01   3.8559393e-01   2.9549451e-01   3.1016061e-01   3.1160241e-01   4.4857854e-01   3.5641190e-01   3.1263400e-01   3.3812708e-01   3.9109335e-01   2.8129908e-01   3.0451362e-01   3.0237858e-01   2.6230725e-01   2.5773246e-01   3.7352449e-01   2.9029824e-01   3.4398832e-01   2.5959514e-01   3.8123049e-01   2.7952979e-01   3.7549545e-01   3.2868655e-01   3.3002382e-01   3.0704202e-01   2.5032682e-01   2.7592132e-01   3.3326893e-01   2.5208920e-01   3.5577891e-01   3.4619466e-01   3.2870702e-01   2.8757710e-01   3.2540565e-01   2.8197541e-01   3.0143248e-01   3.0241595e-01   4.6779054e-03   6.3405358e-03   1.1072067e-02   1.2740784e-02   2.2273681e-03   1.7042107e-03   2.3469652e-03   4.9562680e-03   7.4940361e-03   5.7695726e-03   3.5981535e-03   1.5844867e-03   6.8214146e-03   3.1957366e-03   3.3967393e-03   6.8214146e-03   1.4289215e-03   2.3814252e-03   3.6906895e-04   3.2052685e-02   4.0942979e-04   9.9039775e-04   3.7975123e-03   6.5400285e-03   1.5831617e-03   1.2837357e-03   4.6903663e-04   2.2256509e-03   2.3440889e-01   2.3310632e-01   2.7431935e-01   3.1898347e-01   2.9103053e-01   3.1107217e-01   2.5431417e-01   2.1253549e-01   2.6655333e-01   2.6462531e-01   3.0042601e-01   2.3750489e-01   2.9168949e-01   3.0705757e-01   1.7397041e-01   2.2119992e-01   2.9980584e-01   2.4986709e-01   3.7353610e-01   2.6066067e-01   3.1374027e-01   2.2416418e-01   3.7874518e-01   3.1076095e-01   2.3844790e-01   2.3545346e-01   2.9741154e-01   3.1590317e-01   2.8873621e-01   1.9043311e-01   2.6497335e-01   2.4708373e-01   2.3022342e-01   4.0978464e-01   3.1511039e-01   2.2757419e-01   2.5853132e-01   3.2950090e-01   2.2996799e-01   2.8911377e-01   3.3136481e-01   2.8050509e-01   2.5648758e-01   2.2384164e-01   2.8507826e-01   2.3741411e-01   2.5289158e-01   2.4520543e-01   1.5591712e-01   2.5163277e-01   5.1215829e-01   4.5200156e-01   4.2861009e-01   4.4496538e-01   4.7341919e-01   4.7441196e-01   4.6168878e-01   4.5347805e-01   4.8519916e-01   3.9997999e-01   3.3019092e-01   4.2716946e-01   3.9865809e-01   4.8629326e-01   4.8637186e-01   3.8670691e-01   4.0127624e-01   4.0126667e-01   5.5444310e-01   4.5424309e-01   4.0600299e-01   4.3254422e-01   4.9161364e-01   3.7174460e-01   3.9497344e-01   3.9273809e-01   3.5018083e-01   3.4346685e-01   4.7229362e-01   3.8003558e-01   4.4070091e-01   3.4442025e-01   4.8107176e-01   3.6755422e-01   4.7082182e-01   4.2490414e-01   4.2252116e-01   3.9675769e-01   3.3509282e-01   3.6564070e-01   4.2918040e-01   3.3977682e-01   4.5200156e-01   4.4195847e-01   4.2350677e-01   3.7942836e-01   4.2122143e-01   3.7189771e-01   3.9075300e-01   3.9132598e-01   2.1401129e-02   2.6296569e-02   3.2566498e-02   1.3297832e-02   1.1999623e-02   1.2969856e-02   1.8466773e-02   2.3873417e-02   1.8518842e-02   4.0273028e-03   1.2616800e-03   2.2732626e-02   1.2827409e-02   1.3181090e-02   2.2732626e-02   1.1261737e-02   1.3701796e-02   5.3984869e-03   5.7610599e-02   5.9941455e-03   8.9691119e-03   1.2694193e-02   2.1144882e-02   7.0627421e-03   1.0543898e-02   8.0308076e-03   1.3063205e-02   2.9989796e-01   2.9808728e-01   3.4381381e-01   3.9275825e-01   3.6234621e-01   3.8238034e-01   3.2086021e-01   2.7526551e-01   3.3529881e-01   3.3248525e-01   3.7261196e-01   3.0300865e-01   3.6317903e-01   3.7865155e-01   2.3211430e-01   2.8532877e-01   3.6963026e-01   3.1621648e-01   4.5177033e-01   3.2875625e-01   3.8520789e-01   2.8867443e-01   4.5697798e-01   3.8242988e-01   3.0442487e-01   3.0118555e-01   3.6926913e-01   3.8920975e-01   3.5915749e-01   2.5088735e-01   3.3365900e-01   3.1393007e-01   2.9523721e-01   4.8898239e-01   3.8528778e-01   2.9050533e-01   3.2648373e-01   4.0430761e-01   2.9352285e-01   3.5998625e-01   4.0438969e-01   3.4965804e-01   3.2429593e-01   2.8821126e-01   3.5492121e-01   3.0147553e-01   3.1927061e-01   3.1166517e-01   2.1164881e-01   3.1841810e-01   5.9626248e-01   5.3406968e-01   5.1001241e-01   5.2586196e-01   5.5673824e-01   5.5816878e-01   5.4309284e-01   5.3570978e-01   5.6971774e-01   4.7901704e-01   4.0442977e-01   5.0852772e-01   4.7828326e-01   5.7096471e-01   5.7126109e-01   4.6526268e-01   4.7993533e-01   4.7902644e-01   6.4260357e-01   5.3722757e-01   4.8599135e-01   5.1340958e-01   5.7642669e-01   4.4962350e-01   4.7318809e-01   4.7087433e-01   4.2633712e-01   4.1835467e-01   5.5597597e-01   4.5768215e-01   5.2292685e-01   4.1877489e-01   5.6541976e-01   4.4406435e-01   5.5240885e-01   5.0657081e-01   5.0216108e-01   4.7452659e-01   4.0930806e-01   4.4303784e-01   5.1082488e-01   4.1541892e-01   5.3406968e-01   5.2368299e-01   5.0449934e-01   4.5807263e-01   5.0263701e-01   4.4952858e-01   4.6823972e-01   4.6855914e-01   8.7198254e-03   1.2902931e-03   1.1684021e-03   1.6341127e-03   1.0742763e-03   2.6208124e-03   1.1173357e-03   8.9620141e-04   1.6960301e-02   1.4197837e-02   5.6586090e-04   2.0157829e-03   1.9836256e-03   5.6586090e-04   2.0413623e-03   1.1637665e-03   5.4511725e-03   1.0718252e-02   6.5990100e-03   2.7263257e-03   7.7966832e-03   1.5754002e-04   8.7922744e-03   3.0619296e-03   3.8030551e-03   1.0550593e-03   1.7203244e-01   1.7235723e-01   2.0751307e-01   2.4611820e-01   2.2109400e-01   2.4491699e-01   1.9298922e-01   1.5421652e-01   2.0061094e-01   2.0129686e-01   2.2934517e-01   1.7603988e-01   2.2070889e-01   2.3964854e-01   1.2009621e-01   1.5990877e-01   2.3601974e-01   1.8834267e-01   2.9339046e-01   1.9567575e-01   2.4748464e-01   1.6217086e-01   3.0116422e-01   2.4364046e-01   1.7530938e-01   1.7223213e-01   2.2701156e-01   2.4439785e-01   2.2188150e-01   1.3311613e-01   1.9877894e-01   1.8311301e-01   1.6845668e-01   3.3339209e-01   2.5192873e-01   1.7150268e-01   1.9350184e-01   2.5414415e-01   1.7271733e-01   2.2071334e-01   2.6313203e-01   2.1605186e-01   1.9141813e-01   1.6255272e-01   2.1936783e-01   1.7996851e-01   1.9179556e-01   1.8227672e-01   1.0300751e-01   1.8912086e-01   4.3075013e-01   3.7158844e-01   3.4752045e-01   3.6713693e-01   3.9134187e-01   3.9105984e-01   3.8378198e-01   3.7272538e-01   4.0046876e-01   3.2297138e-01   2.5826699e-01   3.4601238e-01   3.1932057e-01   4.0113556e-01   4.0033459e-01   3.0938917e-01   3.2551476e-01   3.2781102e-01   4.6405632e-01   3.7102765e-01   3.2659021e-01   3.5371449e-01   4.0659862e-01   2.9405620e-01   3.1978995e-01   3.1753736e-01   2.7499746e-01   2.7161605e-01   3.8895029e-01   3.0476818e-01   3.5833770e-01   2.7419176e-01   3.9644448e-01   2.9409120e-01   3.9304592e-01   3.4147602e-01   3.4611220e-01   3.2290811e-01   2.6406812e-01   2.8867894e-01   3.4717424e-01   2.6265032e-01   3.7158844e-01   3.6154105e-01   3.4316147e-01   2.9940560e-01   3.3824889e-01   2.9538166e-01   3.1708459e-01   3.1834036e-01   8.7316989e-03   6.7615313e-03   6.7580543e-03   9.6081666e-03   2.0657605e-03   3.8371349e-03   1.4271025e-02   1.2184393e-02   1.6084765e-02   4.9831593e-03   1.4699244e-02   1.4912454e-02   4.9831593e-03   6.5028816e-03   6.2489819e-03   1.3726162e-02   3.1411524e-02   7.7445772e-03   1.1141212e-02   2.5000477e-03   1.1143820e-02   6.1604304e-03   5.3711085e-03   7.5849080e-03   8.1835455e-03   1.6688130e-01   1.6291433e-01   2.0003066e-01   2.4149909e-01   2.1722570e-01   2.2445012e-01   1.7758122e-01   1.4623090e-01   1.9343386e-01   1.8753794e-01   2.2568158e-01   1.6690274e-01   2.2030573e-01   2.2323949e-01   1.1699096e-01   1.5725818e-01   2.1323159e-01   1.7489777e-01   2.9532205e-01   1.8786273e-01   2.2655558e-01   1.6049736e-01   2.9226070e-01   2.2550223e-01   1.7083413e-01   1.6938578e-01   2.2221647e-01   2.3649790e-01   2.0956346e-01   1.3266766e-01   1.9299947e-01   1.7760033e-01   1.6320695e-01   3.1350837e-01   2.2421748e-01   1.5253844e-01   1.8664517e-01   2.5447595e-01   1.5560691e-01   2.1266187e-01   2.4223633e-01   2.0012528e-01   1.8549850e-01   1.5864276e-01   2.0519641e-01   1.6093217e-01   1.7628990e-01   1.7435363e-01   1.0801101e-01   1.7763987e-01   4.0351234e-01   3.5280598e-01   3.3582666e-01   3.4348161e-01   3.7251839e-01   3.7541634e-01   3.5722931e-01   3.5450932e-01   3.8642215e-01   3.0688243e-01   2.4703841e-01   3.3487550e-01   3.1018257e-01   3.8808655e-01   3.8990045e-01   2.9749231e-01   3.0596368e-01   3.0291072e-01   4.5287211e-01   3.5944458e-01   3.1570031e-01   3.3498082e-01   3.9202879e-01   2.8759651e-01   3.0023966e-01   2.9853735e-01   2.6729925e-01   2.5639363e-01   3.7372548e-01   2.8896987e-01   3.4745520e-01   2.5469579e-01   3.8297689e-01   2.7675896e-01   3.6463006e-01   3.3839246e-01   3.2358656e-01   2.9982548e-01   2.4898596e-01   2.8176933e-01   3.3810925e-01   2.6587897e-01   3.5280598e-01   3.4488951e-01   3.3055981e-01   2.9862862e-01   3.3464036e-01   2.8522813e-01   2.9487313e-01   2.9445589e-01   4.3312037e-03   5.1674385e-03   4.6600432e-03   4.1032398e-03   1.3249619e-03   3.6837745e-03   2.4877830e-02   2.2958753e-02   1.1314391e-03   6.3769043e-03   6.2810489e-03   1.1314391e-03   5.7702159e-03   4.1635898e-03   1.1902706e-02   7.2040189e-03   1.2293784e-02   7.6706139e-03   1.1339253e-02   1.8296747e-03   1.4280945e-02   6.9429868e-03   8.6587607e-03   4.4388406e-03   1.4462991e-01   1.4494206e-01   1.7756526e-01   2.1378771e-01   1.9031042e-01   2.1286860e-01   1.6419734e-01   1.2822571e-01   1.7113301e-01   1.7185341e-01   1.9804950e-01   1.4833973e-01   1.9005998e-01   2.0775634e-01   9.7105565e-02   1.3348080e-01   2.0467358e-01   1.5981923e-01   2.5874568e-01   1.6653873e-01   2.1530133e-01   1.3558698e-01   2.6575883e-01   2.1156399e-01   1.4766732e-01   1.4484877e-01   1.9583483e-01   2.1211626e-01   1.9101641e-01   1.0897783e-01   1.6943757e-01   1.5488355e-01   1.4132668e-01   2.9650216e-01   2.1994601e-01   1.4455458e-01   1.6451956e-01   2.2152336e-01   1.4555202e-01   1.8989624e-01   2.3000345e-01   1.8566766e-01   1.6258902e-01   1.3589561e-01   1.8870744e-01   1.5235300e-01   1.6309487e-01   1.5410176e-01   8.1942750e-02   1.6048904e-01   3.8999083e-01   3.3294245e-01   3.0988325e-01   3.2882841e-01   3.5187047e-01   3.5156617e-01   3.4487977e-01   3.3402051e-01   3.6059894e-01   2.8649814e-01   2.2516617e-01   3.0844683e-01   2.8301726e-01   3.6124416e-01   3.6050400e-01   2.7355262e-01   2.8899505e-01   2.9139815e-01   4.2192237e-01   3.3236960e-01   2.8992253e-01   3.1585310e-01   3.6648886e-01   2.5905330e-01   2.8355149e-01   2.8139447e-01   2.4097820e-01   2.3780572e-01   3.4954046e-01   2.6919588e-01   3.2022959e-01   2.4036369e-01   3.5673540e-01   2.5910558e-01   3.5384915e-01   3.0430469e-01   3.0871278e-01   2.8664912e-01   2.3068275e-01   2.5394489e-01   3.0958210e-01   2.2970603e-01   3.3294245e-01   3.2329736e-01   3.0571743e-01   2.6432145e-01   3.0120271e-01   2.6026006e-01   2.8107880e-01   2.8234890e-01   3.9333334e-05   2.5761851e-04   1.3896575e-03   1.7536063e-03   1.9216331e-03   9.2702772e-03   7.4022776e-03   1.3090644e-03   1.5444025e-03   1.6252591e-03   1.3090644e-03   1.2151407e-04   1.0618022e-05   2.1493524e-03   1.8833153e-02   2.2172388e-03   7.3253783e-04   3.6800655e-03   1.5497854e-03   3.6733784e-03   4.9421897e-04   7.6664670e-04   7.0183041e-05   1.9407897e-01   1.9337938e-01   2.3114302e-01   2.7244640e-01   2.4629979e-01   2.6718506e-01   2.1373312e-01   1.7438911e-01   2.2391848e-01   2.2298785e-01   2.5503185e-01   1.9737603e-01   2.4663659e-01   2.6276403e-01   1.3891547e-01   1.8173656e-01   2.5713590e-01   2.0933386e-01   3.2324703e-01   2.1854256e-01   2.6975489e-01   1.8436571e-01   3.2904939e-01   2.6649404e-01   1.9772084e-01   1.9481826e-01   2.5232520e-01   2.6989379e-01   2.4511828e-01   1.5354404e-01   2.2230840e-01   2.0576951e-01   1.9024966e-01   3.5987888e-01   2.7239312e-01   1.8983400e-01   2.1646886e-01   2.8191043e-01   1.9167912e-01   2.4493869e-01   2.8620678e-01   2.3801287e-01   2.1448199e-01   1.8427005e-01   2.4198503e-01   1.9884520e-01   2.1243903e-01   2.0430599e-01   1.2215728e-01   2.1067715e-01   4.5871846e-01   3.9981904e-01   3.7661173e-01   3.9390784e-01   4.2025710e-01   4.2076082e-01   4.1035332e-01   4.0114215e-01   4.3087129e-01   3.5002279e-01   2.8365040e-01   3.7517763e-01   3.4790525e-01   4.3179681e-01   4.3157518e-01   3.3691557e-01   3.5177012e-01   3.5268567e-01   4.9705280e-01   4.0100475e-01   3.5505921e-01   3.8129652e-01   4.3707681e-01   3.2219168e-01   3.4580868e-01   3.4360838e-01   3.0200588e-01   2.9663386e-01   4.1868171e-01   3.3113109e-01   3.8802094e-01   2.9819354e-01   4.2685142e-01   3.1959000e-01   4.1941543e-01   3.7225097e-01   3.7239048e-01   3.4809183e-01   2.8876177e-01   3.1647952e-01   3.7686145e-01   2.9138730e-01   3.9981904e-01   3.8994709e-01   3.7187123e-01   3.2897937e-01   3.6879196e-01   3.2272643e-01   3.4226532e-01   3.4310531e-01   3.4181612e-04   1.4644608e-03   2.1632573e-03   2.3231555e-03   8.1286280e-03   6.3818616e-03   1.7262411e-03   1.6624580e-03   1.7631926e-03   1.7262411e-03   2.4569053e-05   5.6859581e-05   1.7551896e-03   2.0541034e-02   1.6702311e-03   5.9025530e-04   3.2341087e-03   2.0408948e-03   3.0131078e-03   2.8888789e-04   4.5924146e-04   1.3293684e-04   1.9862431e-01   1.9776069e-01   2.3600084e-01   2.7779005e-01   2.5142895e-01   2.7187023e-01   2.1810101e-01   1.7860088e-01   2.2871390e-01   2.2752286e-01   2.6024955e-01   2.0181434e-01   2.5187795e-01   2.6758248e-01   1.4283878e-01   1.8622396e-01   2.6161990e-01   2.1373552e-01   3.2920505e-01   2.2325952e-01   2.7444329e-01   1.8891553e-01   3.3470963e-01   2.7127428e-01   2.0233024e-01   1.9944956e-01   2.5748056e-01   2.7510316e-01   2.4993365e-01   1.5775267e-01   2.2713624e-01   2.1043184e-01   1.9474801e-01   3.6534538e-01   2.7678503e-01   1.9377126e-01   2.2119834e-01   2.8749014e-01   1.9572304e-01   2.4991164e-01   2.9104517e-01   2.4261230e-01   2.1922346e-01   1.8874518e-01   2.4669621e-01   2.0288553e-01   2.1678869e-01   2.0886650e-01   1.2608625e-01   2.1517216e-01   4.6449792e-01   4.0560127e-01   3.8251194e-01   3.9944814e-01   4.2616553e-01   4.2679596e-01   4.1587264e-01   4.0695550e-01   4.3702628e-01   3.5557170e-01   2.8885981e-01   3.8108822e-01   3.5369655e-01   4.3799369e-01   4.3786355e-01   3.4252750e-01   3.5719184e-01   3.5788232e-01   5.0366583e-01   4.0706759e-01   3.6083966e-01   3.8695887e-01   4.4324858e-01   3.2788328e-01   3.5118655e-01   3.4899273e-01   3.0749578e-01   3.0179987e-01   4.2472010e-01   3.3655063e-01   3.9402558e-01   3.0319627e-01   4.3300399e-01   3.2485825e-01   4.2490754e-01   3.7841034e-01   3.7783349e-01   3.5333537e-01   2.9386653e-01   3.2211174e-01   3.8285611e-01   2.9712888e-01   4.0560127e-01   3.9574961e-01   3.7770634e-01   3.3490218e-01   3.7491174e-01   3.2829405e-01   3.4750328e-01   3.4827580e-01   2.7893549e-03   2.7277911e-03   9.4108270e-04   1.0799149e-02   7.7770747e-03   1.9770194e-03   5.4325768e-04   5.8945201e-04   1.9770194e-03   5.1514113e-04   3.6478892e-04   1.6876295e-03   1.7172006e-02   2.9808015e-03   3.7816236e-04   5.6735840e-03   1.0535544e-03   5.0675384e-03   1.2248969e-03   1.1742680e-03   5.8878380e-05   1.9840502e-01   1.9840646e-01   2.3601178e-01   2.7699198e-01   2.5062921e-01   2.7429513e-01   2.1981939e-01   1.7908511e-01   2.2870797e-01   2.2884763e-01   2.5935890e-01   2.0237179e-01   2.5038976e-01   2.6920634e-01   1.4261267e-01   1.8559031e-01   2.6457877e-01   2.1508394e-01   3.2684946e-01   2.2341437e-01   2.7694800e-01   1.8806980e-01   3.3447269e-01   2.7322826e-01   2.0195195e-01   1.9876628e-01   2.5683031e-01   2.7497319e-01   2.5083242e-01   1.5688509e-01   2.2686098e-01   2.1020792e-01   1.9457412e-01   3.6717222e-01   2.8066992e-01   1.9637709e-01   2.2117475e-01   2.8566080e-01   1.9793610e-01   2.4995417e-01   2.9345115e-01   2.4428403e-01   2.1902512e-01   1.8834472e-01   2.4798811e-01   2.0544380e-01   2.1853532e-01   2.0913443e-01   1.2439434e-01   2.1611468e-01   4.6739623e-01   4.0702486e-01   3.8261075e-01   4.0188705e-01   4.2751037e-01   4.2749738e-01   4.1883120e-01   4.0825884e-01   4.3736523e-01   3.5667688e-01   2.8932174e-01   3.8108192e-01   3.5341594e-01   4.3812879e-01   4.3747647e-01   3.4285168e-01   3.5898948e-01   3.6076578e-01   5.0317788e-01   4.0703744e-01   3.6087589e-01   3.8845434e-01   4.4366743e-01   3.2719263e-01   3.5301257e-01   3.5071770e-01   3.0715395e-01   3.0299726e-01   4.2534595e-01   3.3768843e-01   3.9391146e-01   3.0525217e-01   4.3324318e-01   3.2636388e-01   4.2820876e-01   3.7681443e-01   3.8013938e-01   3.5586945e-01   2.9507753e-01   3.2153910e-01   3.8242816e-01   2.9467977e-01   4.0702486e-01   3.9678588e-01   3.7800850e-01   3.3305200e-01   3.7343525e-01   3.2833826e-01   3.4988792e-01   3.5099795e-01   7.6889988e-04   5.5936308e-03   9.7548717e-03   1.0412603e-02   1.0389613e-03   5.7781385e-03   5.9052415e-03   1.0389613e-03   1.4340775e-03   1.1584691e-03   6.0259991e-03   2.1726707e-02   3.4598658e-03   3.9021886e-03   1.8160607e-03   3.9104990e-03   3.6199548e-03   1.2013216e-03   2.4248068e-03   2.0560641e-03   1.7726458e-01   1.7519789e-01   2.1239850e-01   2.5350621e-01   2.2831460e-01   2.4335474e-01   1.9301815e-01   1.5733953e-01   2.0548992e-01   2.0248973e-01   2.3687424e-01   1.7915768e-01   2.2981656e-01   2.4028800e-01   1.2483249e-01   1.6617415e-01   2.3289941e-01   1.8936545e-01   3.0533170e-01   2.0007138e-01   2.4571617e-01   1.6904051e-01   3.0733551e-01   2.4338605e-01   1.8100871e-01   1.7874491e-01   2.3386295e-01   2.4993365e-01   2.2441376e-01   1.3976123e-01   2.0438723e-01   1.8845276e-01   1.7353191e-01   3.3400984e-01   2.4631085e-01   1.6886156e-01   1.9837340e-01   2.6441281e-01   1.7118963e-01   2.2560913e-01   2.6174131e-01   2.1639026e-01   1.9675554e-01   1.6819987e-01   2.2078897e-01   1.7753606e-01   1.9173589e-01   1.8624992e-01   1.1156657e-01   1.9127963e-01   4.2879129e-01   3.7350470e-01   3.5299849e-01   3.6620603e-01   3.9355975e-01   3.9506070e-01   3.8147101e-01   3.7498057e-01   4.0550993e-01   3.2554347e-01   2.6225589e-01   3.5177359e-01   3.2570798e-01   4.0674255e-01   4.0737898e-01   3.1405475e-01   3.2617446e-01   3.2545044e-01   4.7160294e-01   3.7696723e-01   3.3214002e-01   3.5535112e-01   4.1144267e-01   3.0143840e-01   3.2034131e-01   3.1835849e-01   2.8130938e-01   2.7364725e-01   3.9315179e-01   3.0715437e-01   3.6445309e-01   2.7384746e-01   4.0174546e-01   2.9539622e-01   3.8981435e-01   3.5158797e-01   3.4545598e-01   3.2149982e-01   2.6601526e-01   2.9570609e-01   3.5410378e-01   2.7466513e-01   3.7350470e-01   3.6448827e-01   3.4805708e-01   3.0999906e-01   3.4801807e-01   3.0074518e-01   3.1606363e-01   3.1638243e-01   3.9211584e-03   1.5428451e-02   1.5051422e-02   9.3641634e-05   5.2251987e-03   5.2564865e-03   9.3641634e-05   2.4059863e-03   1.5411207e-03   7.7716003e-03   1.4517538e-02   6.4009679e-03   4.6963365e-03   4.9429047e-03   2.1131701e-03   7.3135995e-03   2.7662314e-03   4.2415669e-03   2.1979302e-03   1.6154877e-01   1.6047147e-01   1.9568300e-01   2.3468417e-01   2.1025394e-01   2.2838581e-01   1.7884422e-01   1.4313754e-01   1.8898793e-01   1.8753794e-01   2.1845622e-01   1.6418759e-01   2.1103286e-01   2.2447017e-01   1.1131548e-01   1.5046796e-01   2.1889519e-01   1.7489777e-01   2.8359045e-01   1.8392350e-01   2.3077309e-01   1.5301294e-01   2.8765002e-01   2.2785871e-01   1.6499082e-01   1.6250540e-01   2.1577964e-01   2.3190311e-01   2.0826660e-01   1.2493129e-01   1.8764327e-01   1.7232008e-01   1.5800409e-01   3.1597925e-01   2.3306671e-01   1.5663136e-01   1.8209705e-01   2.4426589e-01   1.5839676e-01   2.0849973e-01   2.4621874e-01   2.0137281e-01   1.8035428e-01   1.5264734e-01   2.0519641e-01   1.6491824e-01   1.7763987e-01   1.7071018e-01   9.7334595e-02   1.7628990e-01   4.1013753e-01   3.5415853e-01   3.3261378e-01   3.4819629e-01   3.7372548e-01   3.7447405e-01   3.6377706e-01   3.5546726e-01   3.8432564e-01   3.0688243e-01   2.4450319e-01   3.3130276e-01   3.0553473e-01   3.8531353e-01   3.8537934e-01   2.9480414e-01   3.0829006e-01   3.0887441e-01   4.4839112e-01   3.5594109e-01   3.1215369e-01   3.3646690e-01   3.9023537e-01   2.8142851e-01   3.0262656e-01   3.0057353e-01   2.6218143e-01   2.5639363e-01   3.7251839e-01   2.8896987e-01   3.4359589e-01   2.5757650e-01   3.8052352e-01   2.7792266e-01   3.7237623e-01   3.2948525e-01   3.2773210e-01   3.0459398e-01   2.4898596e-01   2.7596310e-01   3.3313575e-01   2.5365041e-01   3.5415853e-01   3.4488951e-01   3.2799981e-01   2.8862094e-01   3.2611271e-01   2.8152144e-01   2.9910812e-01   2.9982464e-01   1.7874931e-02   1.3166667e-02   2.8067647e-03   5.4483543e-04   4.8491153e-04   2.8067647e-03   2.7932574e-03   2.1120566e-03   4.0283644e-03   1.1006031e-02   7.1968081e-03   1.9824114e-03   1.0903705e-02   3.4373671e-04   1.0364284e-02   4.2441401e-03   4.1832512e-03   1.3456492e-03   1.8893734e-01   1.9027350e-01   2.2602463e-01   2.6493124e-01   2.3909907e-01   2.6731994e-01   2.1287273e-01   1.7119179e-01   2.1885648e-01   2.2106766e-01   2.4751153e-01   1.9400411e-01   2.3783986e-01   2.6104566e-01   1.3465024e-01   1.7581619e-01   2.5867158e-01   2.0765719e-01   3.1157756e-01   2.1392913e-01   2.7004976e-01   1.7791371e-01   3.2221942e-01   2.6551484e-01   1.9215572e-01   1.8858682e-01   2.4539617e-01   2.6396374e-01   2.4190361e-01   1.4753547e-01   2.1663955e-01   2.0044864e-01   1.8527044e-01   3.5759997e-01   2.7597540e-01   1.9143761e-01   2.1146655e-01   2.7190276e-01   1.9231433e-01   2.3971651e-01   2.8607417e-01   2.3671699e-01   2.0909909e-01   1.7885289e-01   2.3973819e-01   2.0020124e-01   2.1166375e-01   2.0015528e-01   1.1482314e-01   2.0802247e-01   4.5814031e-01   3.9622068e-01   3.7010544e-01   3.9277065e-01   4.1629822e-01   4.1528170e-01   4.1031284e-01   3.9724817e-01   4.2445794e-01   3.4613203e-01   2.7894605e-01   3.6843870e-01   3.4078468e-01   4.2489846e-01   4.2345869e-01   3.3131814e-01   3.4950009e-01   3.5299308e-01   4.8820349e-01   3.9397890e-01   3.4860920e-01   3.7803314e-01   4.3080058e-01   3.1437592e-01   3.4366436e-01   3.4124618e-01   2.9521701e-01   2.9351505e-01   4.1304236e-01   3.2750551e-01   3.8091343e-01   2.9709224e-01   4.2023724e-01   3.1695286e-01   4.2011817e-01   3.6184591e-01   3.7113199e-01   3.4760954e-01   2.8576301e-01   3.0899799e-01   3.6912287e-01   2.7985004e-01   3.9622068e-01   3.8552168e-01   3.6588486e-01   3.1841134e-01   3.5869504e-01   3.1661834e-01   3.4148439e-01   3.4312143e-01   1.2983249e-03   1.5471006e-02   1.3470267e-02   1.3877317e-02   1.5471006e-02   7.2739782e-03   9.2612860e-03   6.0792360e-03   5.4160667e-02   2.4574168e-03   8.1477262e-03   3.8451807e-03   1.8194605e-02   1.5067164e-03   5.6792549e-03   4.8846913e-03   1.0004616e-02   2.6108642e-01   2.5718656e-01   3.0162187e-01   3.4990044e-01   3.2118558e-01   3.3212064e-01   2.7586622e-01   2.3634761e-01   2.9366681e-01   2.8770633e-01   3.3110877e-01   2.6200119e-01   3.2383134e-01   3.3046521e-01   1.9829106e-01   2.4860521e-01   3.1887574e-01   2.7240198e-01   4.1018982e-01   2.8711577e-01   3.3461178e-01   2.5228731e-01   4.0944673e-01   3.3325697e-01   2.6572836e-01   2.6351234e-01   3.2731613e-01   3.4479515e-01   3.1382719e-01   2.1730674e-01   2.9282566e-01   2.7420761e-01   2.5662111e-01   4.3493335e-01   3.3165524e-01   2.4546083e-01   2.8544328e-01   3.6363165e-01   2.4916639e-01   3.1676067e-01   3.5299851e-01   3.0301330e-01   2.8384547e-01   2.5066938e-01   3.0887732e-01   2.5579752e-01   2.7431070e-01   2.7082223e-01   1.8355500e-01   2.7545202e-01   5.3566205e-01   4.7913827e-01   4.5930782e-01   4.6887050e-01   5.0113940e-01   5.0408511e-01   4.8425611e-01   4.8100390e-01   5.1611676e-01   4.2712908e-01   3.5770237e-01   4.5815125e-01   4.2990067e-01   5.1783166e-01   5.1944925e-01   4.1592191e-01   4.2634771e-01   4.2297928e-01   5.8870710e-01   4.8576650e-01   4.3645958e-01   4.5912638e-01   5.2238783e-01   4.0361731e-01   4.1983156e-01   4.1785974e-01   3.8054730e-01   3.6909926e-01   5.0215992e-01   4.0667536e-01   4.7224138e-01   3.6745640e-01   5.1222367e-01   3.9280819e-01   4.9246039e-01   4.6045456e-01   4.4643751e-01   4.1946868e-01   3.6048019e-01   3.9703515e-01   4.6143668e-01   3.7590038e-01   4.7913827e-01   4.7009550e-01   4.5350904e-01   4.1479012e-01   4.5636227e-01   4.0162438e-01   4.1380491e-01   4.1334093e-01   1.4411876e-02   8.7935053e-03   9.1184252e-03   1.4411876e-02   5.7453578e-03   7.6054776e-03   2.7409931e-03   4.7624677e-02   1.8780439e-03   4.9746662e-03   5.9684857e-03   1.4534556e-02   2.3601867e-03   4.9286760e-03   3.4466344e-03   7.5341006e-03   2.6746877e-01   2.6516664e-01   3.0921139e-01   3.5673992e-01   3.2754140e-01   3.4481450e-01   2.8624779e-01   2.4359422e-01   3.0108022e-01   2.9756219e-01   3.3745616e-01   2.6990583e-01   3.2887946e-01   3.4163113e-01   2.0331657e-01   2.5392638e-01   3.3233847e-01   2.8201820e-01   4.1489235e-01   2.9472025e-01   3.4749512e-01   2.5726587e-01   4.1828245e-01   3.4508966e-01   2.7189140e-01   2.6903465e-01   3.3406888e-01   3.5284896e-01   3.2333666e-01   2.2149953e-01   2.9970099e-01   2.8083524e-01   2.6300357e-01   4.4804341e-01   3.4702929e-01   2.5691578e-01   2.9267142e-01   3.6866600e-01   2.5996213e-01   3.2467728e-01   3.6599412e-01   3.1379996e-01   2.9070461e-01   2.5648991e-01   3.1904849e-01   2.6736905e-01   2.8471636e-01   2.7833907e-01   1.8530093e-01   2.8435281e-01   5.5199539e-01   4.9206433e-01   4.6946939e-01   4.8356355e-01   5.1418554e-01   5.1595196e-01   5.0010048e-01   4.9372697e-01   5.2743722e-01   4.3877522e-01   3.6710197e-01   4.6809646e-01   4.3893984e-01   5.2878375e-01   5.2942069e-01   4.2592703e-01   4.3928640e-01   4.3789059e-01   5.9924430e-01   4.9601715e-01   4.4619754e-01   4.7193405e-01   5.3393309e-01   4.1149136e-01   4.3273356e-01   4.3054493e-01   3.8875406e-01   3.8007672e-01   5.1386048e-01   4.1809676e-01   4.8216133e-01   3.8002405e-01   5.2330849e-01   4.0472333e-01   5.0903363e-01   4.6735136e-01   4.6059448e-01   4.3368525e-01   3.7134977e-01   4.0504167e-01   4.7061436e-01   3.7989795e-01   4.9206433e-01   4.8217825e-01   4.6398354e-01   4.2055878e-01   4.6343857e-01   4.1088828e-01   4.2766517e-01   4.2782051e-01   4.0251529e-03   4.0402030e-03   0.0000000e+00   2.0104773e-03   1.1579294e-03   6.7733512e-03   1.3328703e-02   6.1195429e-03   3.8280621e-03   5.4471697e-03   1.3203495e-03   7.3930866e-03   2.5511055e-03   3.8011014e-03   1.5935161e-03   1.6488937e-01   1.6420208e-01   1.9946134e-01   2.3841307e-01   2.1377841e-01   2.3352484e-01   1.8323739e-01   1.4660873e-01   1.9269692e-01   1.9183992e-01   2.2200730e-01   1.6791595e-01   2.1423078e-01   2.2922867e-01   1.1407468e-01   1.5349471e-01   2.2418179e-01   1.7908948e-01   2.8692621e-01   1.8765985e-01   2.3596576e-01   1.5596498e-01   2.9203641e-01   2.3278981e-01   1.6829150e-01   1.6563525e-01   2.1942293e-01   2.3592536e-01   2.1256421e-01   1.2755291e-01   1.9121342e-01   1.7576718e-01   1.6132929e-01   3.2148865e-01   2.3885357e-01   1.6118125e-01   1.8573297e-01   2.4757051e-01   1.6279862e-01   2.1240660e-01   2.5149161e-01   2.0595435e-01   1.8389163e-01   1.5580881e-01   2.0964365e-01   1.6953436e-01   1.8203376e-01   1.7437090e-01   9.9184065e-02   1.8031354e-01   4.1664204e-01   3.5971944e-01   3.3744612e-01   3.5416868e-01   3.7936058e-01   3.7982315e-01   3.7006184e-01   3.6098196e-01   3.8956200e-01   3.1201251e-01   2.4889912e-01   3.3607844e-01   3.1002022e-01   3.9046127e-01   3.9028467e-01   2.9949936e-01   3.1373736e-01   3.1479561e-01   4.5355800e-01   3.6085089e-01   3.1682959e-01   3.4195608e-01   3.9553949e-01   2.8555816e-01   3.0804941e-01   3.0593834e-01   2.6633772e-01   2.6121338e-01   3.7782244e-01   2.9399549e-01   3.4839508e-01   2.6278429e-01   3.8569374e-01   2.8303600e-01   3.7885421e-01   3.3349568e-01   3.3352424e-01   3.1033775e-01   2.5375578e-01   2.8011018e-01   3.3772574e-01   2.5671985e-01   3.5971944e-01   3.5022311e-01   3.3289784e-01   2.9224130e-01   3.3016010e-01   2.8599652e-01   3.0475125e-01   3.0561759e-01   3.0700267e-06   4.0251529e-03   1.9467123e-03   1.7971688e-03   1.7301608e-03   1.6293141e-02   4.7718752e-03   6.8454231e-04   9.3235659e-03   1.4106675e-03   7.7429721e-03   3.1097831e-03   2.5391665e-03   9.5764453e-04   2.0739268e-01   2.0836358e-01   2.4589773e-01   2.8656370e-01   2.5981614e-01   2.8739169e-01   2.3131893e-01   1.8849968e-01   2.3845740e-01   2.4007299e-01   2.6857108e-01   2.1230255e-01   2.5877066e-01   2.8137449e-01   1.5046312e-01   1.9386671e-01   2.7809337e-01   2.2610426e-01   3.3523485e-01   2.3325794e-01   2.9016640e-01   1.9614834e-01   3.4542234e-01   2.8580893e-01   2.1082239e-01   2.0722978e-01   2.6628244e-01   2.8528108e-01   2.6193836e-01   1.6431358e-01   2.3627495e-01   2.1939954e-01   2.0354344e-01   3.8077948e-01   2.9536596e-01   2.0839572e-01   2.3078002e-01   2.9414568e-01   2.0957408e-01   2.6009226e-01   3.0679254e-01   2.5613081e-01   2.2839644e-01   1.9694047e-01   2.5948108e-01   2.1757899e-01   2.3004331e-01   2.1886202e-01   1.3010315e-01   2.2671016e-01   4.8309156e-01   4.2059741e-01   3.9446827e-01   4.1650857e-01   4.4118694e-01   4.4046177e-01   4.3416675e-01   4.2171124e-01   4.5001131e-01   3.6938174e-01   3.0049261e-01   3.9280494e-01   3.6453208e-01   4.5055186e-01   4.4930066e-01   3.5453263e-01   3.7247610e-01   3.7543144e-01   5.1540859e-01   4.1899010e-01   3.7243361e-01   4.0192295e-01   4.5645786e-01   3.3753686e-01   3.6646355e-01   3.6403348e-01   3.1765048e-01   3.1516192e-01   4.3820660e-01   3.5021371e-01   4.0564147e-01   3.1837605e-01   4.4574076e-01   3.3915719e-01   4.4399141e-01   3.8666018e-01   3.9439941e-01   3.7011128e-01   3.0715348e-01   3.3195062e-01   3.9368522e-01   3.0254596e-01   4.2059741e-01   4.0983289e-01   3.9004780e-01   3.4211299e-01   3.8338579e-01   3.3953411e-01   3.6390344e-01   3.6538415e-01   4.0402030e-03   2.0647746e-03   1.8810615e-03   1.8744038e-03   1.5904825e-02   5.0089073e-03   7.7718458e-04   9.5962272e-03   1.3536136e-03   8.0354537e-03   3.2683077e-03   2.7053207e-03   1.0204136e-03   2.0663566e-01   2.0767698e-01   2.4509318e-01   2.8563097e-01   2.5892354e-01   2.8672996e-01   2.3068420e-01   1.8783705e-01   2.3766371e-01   2.3938906e-01   2.6765771e-01   2.1160129e-01   2.5782529e-01   2.8065126e-01   1.4982077e-01   1.9310124e-01   2.7749364e-01   2.2544624e-01   3.3411471e-01   2.3248629e-01   2.8950769e-01   1.9536146e-01   3.4445558e-01   2.8510792e-01   2.1004612e-01   2.0643532e-01   2.6539182e-01   2.8440424e-01   2.6118254e-01   1.6358877e-01   2.3546280e-01   2.1862058e-01   2.0279724e-01   3.7994304e-01   2.9482551e-01   2.0788172e-01   2.2999781e-01   2.9312113e-01   2.0902225e-01   2.5926765e-01   3.0610117e-01   2.5545076e-01   2.2760393e-01   1.9618808e-01   2.5876275e-01   2.1704368e-01   2.2941326e-01   2.1812470e-01   1.2939132e-01   2.2601611e-01   4.8224276e-01   4.1968249e-01   3.9347110e-01   4.1568549e-01   4.4024422e-01   4.3946585e-01   4.3337086e-01   4.2078495e-01   4.4897602e-01   3.6849705e-01   2.9964288e-01   3.9180103e-01   3.6353845e-01   4.4949934e-01   4.4820701e-01   3.5360058e-01   3.7164688e-01   3.7469388e-01   5.1424729e-01   4.1795596e-01   3.7145645e-01   4.0103422e-01   4.5542290e-01   3.3654347e-01   3.6564394e-01   3.6320808e-01   3.1671115e-01   3.1435391e-01   4.3720666e-01   3.4935506e-01   4.0461470e-01   3.1763784e-01   4.4470146e-01   3.3834387e-01   4.4321597e-01   3.8553656e-01   3.9358898e-01   3.6934910e-01   3.0635763e-01   3.3097385e-01   3.9264615e-01   3.0146236e-01   4.1968249e-01   4.0889669e-01   3.8907226e-01   3.4102273e-01   3.8227517e-01   3.3859771e-01   3.6313559e-01   3.6464431e-01   2.0104773e-03   1.1579294e-03   6.7733512e-03   1.3328703e-02   6.1195429e-03   3.8280621e-03   5.4471697e-03   1.3203495e-03   7.3930866e-03   2.5511055e-03   3.8011014e-03   1.5935161e-03   1.6488937e-01   1.6420208e-01   1.9946134e-01   2.3841307e-01   2.1377841e-01   2.3352484e-01   1.8323739e-01   1.4660873e-01   1.9269692e-01   1.9183992e-01   2.2200730e-01   1.6791595e-01   2.1423078e-01   2.2922867e-01   1.1407468e-01   1.5349471e-01   2.2418179e-01   1.7908948e-01   2.8692621e-01   1.8765985e-01   2.3596576e-01   1.5596498e-01   2.9203641e-01   2.3278981e-01   1.6829150e-01   1.6563525e-01   2.1942293e-01   2.3592536e-01   2.1256421e-01   1.2755291e-01   1.9121342e-01   1.7576718e-01   1.6132929e-01   3.2148865e-01   2.3885357e-01   1.6118125e-01   1.8573297e-01   2.4757051e-01   1.6279862e-01   2.1240660e-01   2.5149161e-01   2.0595435e-01   1.8389163e-01   1.5580881e-01   2.0964365e-01   1.6953436e-01   1.8203376e-01   1.7437090e-01   9.9184065e-02   1.8031354e-01   4.1664204e-01   3.5971944e-01   3.3744612e-01   3.5416868e-01   3.7936058e-01   3.7982315e-01   3.7006184e-01   3.6098196e-01   3.8956200e-01   3.1201251e-01   2.4889912e-01   3.3607844e-01   3.1002022e-01   3.9046127e-01   3.9028467e-01   2.9949936e-01   3.1373736e-01   3.1479561e-01   4.5355800e-01   3.6085089e-01   3.1682959e-01   3.4195608e-01   3.9553949e-01   2.8555816e-01   3.0804941e-01   3.0593834e-01   2.6633772e-01   2.6121338e-01   3.7782244e-01   2.9399549e-01   3.4839508e-01   2.6278429e-01   3.8569374e-01   2.8303600e-01   3.7885421e-01   3.3349568e-01   3.3352424e-01   3.1033775e-01   2.5375578e-01   2.8011018e-01   3.3772574e-01   2.5671985e-01   3.5971944e-01   3.5022311e-01   3.3289784e-01   2.9224130e-01   3.3016010e-01   2.8599652e-01   3.0475125e-01   3.0561759e-01   1.3213080e-04   1.6348389e-03   2.1958653e-02   1.3024074e-03   6.2459052e-04   2.7868209e-03   2.5128724e-03   2.4948096e-03   1.5213665e-04   2.9312203e-04   2.6269769e-04   2.0119891e-01   2.0014287e-01   2.3871519e-01   2.8086210e-01   2.5438649e-01   2.7419983e-01   2.2034638e-01   1.8091150e-01   2.3139686e-01   2.2990542e-01   2.6326545e-01   2.0423778e-01   2.5497864e-01   2.7008054e-01   1.4507978e-01   1.8881738e-01   2.6377709e-01   2.1604374e-01   3.3279319e-01   2.2588101e-01   2.7676493e-01   1.9156801e-01   3.3788258e-01   2.7371187e-01   2.0495838e-01   2.0212622e-01   2.6043406e-01   2.7802264e-01   2.5251791e-01   1.6022437e-01   2.2986910e-01   2.1306976e-01   1.9729190e-01   3.6816423e-01   2.7878040e-01   1.9567818e-01   2.2384809e-01   2.9081290e-01   1.9773475e-01   2.5268382e-01   2.9345893e-01   2.4498738e-01   2.2190073e-01   1.9130390e-01   2.4917712e-01   2.0485354e-01   2.1902087e-01   2.1139045e-01   1.2850635e-01   2.1757950e-01   4.6735126e-01   4.0863686e-01   3.8577163e-01   4.0223139e-01   4.2927752e-01   4.3005363e-01   4.1858115e-01   4.1002225e-01   4.4039161e-01   3.5852229e-01   2.9170762e-01   3.8436621e-01   3.5694453e-01   4.4140604e-01   4.4138801e-01   3.4560659e-01   3.5999045e-01   3.6042881e-01   5.0737364e-01   4.1042921e-01   3.6404336e-01   3.8992213e-01   4.4661300e-01   3.3112795e-01   3.5395838e-01   3.5178032e-01   3.1059068e-01   3.0453530e-01   4.2798873e-01   3.3942843e-01   3.9736659e-01   3.0574030e-01   4.3638021e-01   3.2761075e-01   4.2755962e-01   3.8201356e-01   3.8058140e-01   3.5594943e-01   2.9656762e-01   3.2531047e-01   3.8623001e-01   3.0061288e-01   4.0863686e-01   3.9884323e-01   3.8090672e-01   3.3841042e-01   3.7847943e-01   3.3138355e-01   3.5013260e-01   3.5082807e-01   2.3963109e-03   1.8894374e-02   2.2439950e-03   9.0594652e-04   3.4335324e-03   1.6224592e-03   3.5937956e-03   4.5783206e-04   8.1747242e-04   1.3119947e-04   1.9231717e-01   1.9150735e-01   2.2920314e-01   2.7047035e-01   2.4441394e-01   2.6481790e-01   2.1164496e-01   1.7262115e-01   2.2200818e-01   2.2091128e-01   2.5312771e-01   1.9549847e-01   2.4484600e-01   2.6050695e-01   1.3741417e-01   1.8008449e-01   2.5474237e-01   2.0730811e-01   3.2133505e-01   2.1663183e-01   2.6736983e-01   1.8273137e-01   3.2682425e-01   2.6418461e-01   1.9596515e-01   1.9311641e-01   2.5039748e-01   2.6783585e-01   2.4301257e-01   1.5205635e-01   2.2044020e-01   2.0395985e-01   1.8849810e-01   3.5730736e-01   2.6984619e-01   1.8774203e-01   2.1458977e-01   2.8004857e-01   1.8962388e-01   2.4294411e-01   2.8377929e-01   2.3583758e-01   2.1263399e-01   1.8257496e-01   2.3984158e-01   1.9672007e-01   2.1035264e-01   2.0243724e-01   1.2095575e-01   2.0869633e-01   4.5579154e-01   3.9719792e-01   3.7421582e-01   3.9117796e-01   4.1759891e-01   4.1818270e-01   4.0752420e-01   3.9853286e-01   4.2831769e-01   3.4756630e-01   2.8146997e-01   3.7279915e-01   3.4563396e-01   4.2926782e-01   4.2911586e-01   3.3459449e-01   3.4922354e-01   3.5000846e-01   4.9447633e-01   3.9856686e-01   3.5272682e-01   3.7871114e-01   4.3449948e-01   3.2004729e-01   3.4327468e-01   3.4109263e-01   2.9987407e-01   2.9431934e-01   4.1611792e-01   3.2872232e-01   3.8562509e-01   2.9576964e-01   4.2431958e-01   3.1716861e-01   4.1652649e-01   3.7009695e-01   3.6972936e-01   3.4546743e-01   2.8647014e-01   3.1433567e-01   3.7453491e-01   2.8958559e-01   3.9719792e-01   3.8739786e-01   3.6946063e-01   3.2697767e-01   3.6662992e-01   3.2048201e-01   3.3967430e-01   3.4047263e-01   2.8241524e-02   1.4713791e-03   4.6823304e-04   6.0296352e-03   5.2071190e-03   3.4182869e-03   1.9529381e-03   9.1025104e-04   1.8441969e-03   2.3388660e-01   2.3348281e-01   2.7404368e-01   3.1787596e-01   2.8991570e-01   3.1331298e-01   2.5580945e-01   2.1274052e-01   2.6625865e-01   2.6571335e-01   2.9921857e-01   2.3779036e-01   2.8985951e-01   3.0846478e-01   1.7343111e-01   2.2024476e-01   3.0259960e-01   2.5097696e-01   3.7082192e-01   2.6053197e-01   3.1606460e-01   2.2298918e-01   3.7823337e-01   3.1251210e-01   2.3776110e-01   2.3444923e-01   2.9645330e-01   3.1548927e-01   2.8938607e-01   1.8922982e-01   2.6439849e-01   2.4655891e-01   2.2974757e-01   4.1142478e-01   3.1887022e-01   2.2998734e-01   2.5821680e-01   3.2732410e-01   2.3197317e-01   2.8887378e-01   3.3359010e-01   2.8195681e-01   2.5599107e-01   2.2312925e-01   2.8613603e-01   2.3977955e-01   2.5441596e-01   2.4519140e-01   1.5385241e-01   2.5232104e-01   5.1493631e-01   4.5323214e-01   4.2845834e-01   4.4724986e-01   4.7457294e-01   4.7489714e-01   4.6451744e-01   4.5458397e-01   4.8531016e-01   4.0086775e-01   3.3039510e-01   4.2690815e-01   3.9810528e-01   4.8619268e-01   4.8572861e-01   3.8678000e-01   4.0288412e-01   4.0400345e-01   5.5371159e-01   4.5396321e-01   4.0578110e-01   4.3384503e-01   4.9180921e-01   3.7075981e-01   3.9660943e-01   3.9426853e-01   3.4955388e-01   3.4443823e-01   4.7269976e-01   3.8095285e-01   4.4033063e-01   3.4628429e-01   4.8107810e-01   3.6885113e-01   4.7400892e-01   4.2299055e-01   4.2466221e-01   3.9913020e-01   3.3607659e-01   3.6477722e-01   4.2848136e-01   3.3695835e-01   4.5323214e-01   4.4278413e-01   4.2356519e-01   3.7724050e-01   4.1943108e-01   3.7167660e-01   3.9296882e-01   3.9389283e-01   3.3787081e-02   2.1999955e-02   3.5606869e-02   9.7919779e-03   3.8730614e-02   2.5164827e-02   2.6849118e-02   1.7903003e-02   1.2662420e-01   1.3061214e-01   1.5776511e-01   1.8787898e-01   1.6611889e-01   2.0099100e-01   1.5292701e-01   1.1474225e-01   1.5177722e-01   1.5820095e-01   1.7289957e-01   1.3332512e-01   1.6306194e-01   1.9266388e-01   8.3782583e-02   1.1475472e-01   1.9583103e-01   1.4727273e-01   2.2350713e-01   1.4824286e-01   2.0360977e-01   1.1578494e-01   2.3876064e-01   1.9766401e-01   1.2872248e-01   1.2487918e-01   1.7184761e-01   1.8912261e-01   1.7398714e-01   9.1697206e-02   1.4908080e-01   1.3596066e-01   1.2380963e-01   2.7656824e-01   2.1428571e-01   1.3903777e-01   1.4563130e-01   1.9085533e-01   1.3814153e-01   1.6927103e-01   2.1683317e-01   1.7245190e-01   1.4312164e-01   1.1792045e-01   1.7357532e-01   1.4591400e-01   1.5204372e-01   1.3733781e-01   6.4362895e-02   1.4610010e-01   3.6994724e-01   3.0922665e-01   2.8172128e-01   3.0981046e-01   3.2683078e-01   3.2376302e-01   3.2734273e-01   3.0972403e-01   3.3079457e-01   2.6398840e-01   2.0377846e-01   2.7991998e-01   2.5479336e-01   3.3054260e-01   3.2764011e-01   2.4845492e-01   2.6936921e-01   2.7648193e-01   3.8578015e-01   3.0244531e-01   2.6262990e-01   2.9337350e-01   3.3673416e-01   2.3057418e-01   2.6437275e-01   2.6189855e-01   2.1511723e-01   2.1874548e-01   3.2151629e-01   2.4786804e-01   2.9060022e-01   2.2492263e-01   3.2669967e-01   2.4001378e-01   3.3739817e-01   2.6941492e-01   2.9020759e-01   2.7043921e-01   2.1216140e-01   2.2627991e-01   2.7921868e-01   1.9599823e-01   3.0922665e-01   2.9841488e-01   2.7865157e-01   2.3076134e-01   2.6697481e-01   2.3479056e-01   2.6453179e-01   2.6724220e-01   1.8463349e-03   1.7603525e-03   7.3051568e-03   4.1015204e-04   7.6986614e-04   4.1505661e-04   2.5516535e-03   2.2715123e-01   2.2501703e-01   2.6621562e-01   3.1107232e-01   2.8349906e-01   3.0014485e-01   2.4486000e-01   2.0495206e-01   2.5858102e-01   2.5538755e-01   2.9285644e-01   2.2943000e-01   2.8485147e-01   2.9693404e-01   1.6780939e-01   2.1457958e-01   2.8854018e-01   2.4083271e-01   3.6655716e-01   2.5261802e-01   3.0270375e-01   2.1770871e-01   3.6954821e-01   3.0027680e-01   2.3128364e-01   2.2864524e-01   2.8964053e-01   3.0736347e-01   2.7955757e-01   1.8460266e-01   2.5729263e-01   2.3962699e-01   2.2298939e-01   3.9825299e-01   3.0280555e-01   2.1772566e-01   2.5069761e-01   3.2250864e-01   2.2044120e-01   2.8076678e-01   3.2019205e-01   2.7070478e-01   2.4885895e-01   2.1694127e-01   2.7557358e-01   2.2744661e-01   2.4343281e-01   2.3729093e-01   1.5163937e-01   2.4296011e-01   4.9867564e-01   4.4043288e-01   4.1855224e-01   4.3250726e-01   4.6172807e-01   4.6333132e-01   4.4859207e-01   4.4201028e-01   4.7437581e-01   3.8923920e-01   3.2088439e-01   4.1722959e-01   3.8928568e-01   4.7566007e-01   4.7625383e-01   3.7686783e-01   3.8986190e-01   3.8884081e-01   5.4387473e-01   4.4406349e-01   3.9623886e-01   4.2109532e-01   4.8065646e-01   3.6308022e-01   3.8359994e-01   3.8148432e-01   3.4142085e-01   3.3328357e-01   4.6130540e-01   3.6948155e-01   4.3073385e-01   3.3341169e-01   4.7038237e-01   3.5679054e-01   4.5732763e-01   4.1658437e-01   4.1040883e-01   3.8470265e-01   3.2499997e-01   3.5692838e-01   4.1963835e-01   3.3330111e-01   4.4043288e-01   4.3085698e-01   4.1330060e-01   3.7185723e-01   4.1281711e-01   3.6250007e-01   3.7890193e-01   3.7915604e-01   5.4235993e-03   2.5998420e-03   3.8677378e-03   1.1491859e-03   6.2877149e-04   4.8332372e-04   2.1486898e-01   2.1467854e-01   2.5369922e-01   2.9604720e-01   2.6891688e-01   2.9246555e-01   2.3653315e-01   1.9467620e-01   2.4616446e-01   2.4597983e-01   2.7792166e-01   2.1880759e-01   2.6876410e-01   2.8748855e-01   1.5684504e-01   2.0165721e-01   2.8227299e-01   2.3174975e-01   3.4738814e-01   2.4066356e-01   2.9516630e-01   2.0426320e-01   3.5491429e-01   2.9152419e-01   2.1857252e-01   2.1532575e-01   2.7527993e-01   2.9385335e-01   2.6877316e-01   1.7184619e-01   2.4431046e-01   2.2708854e-01   2.1089056e-01   3.8786051e-01   2.9845589e-01   2.1195408e-01   2.3838722e-01   3.0508869e-01   2.1371586e-01   2.6806783e-01   3.1216051e-01   2.6180490e-01   2.3620065e-01   2.0447438e-01   2.6573552e-01   2.2136814e-01   2.3519672e-01   2.2587537e-01   1.3797486e-01   2.3292930e-01   4.8968343e-01   4.2865553e-01   4.0406082e-01   4.2311568e-01   4.4955467e-01   4.4970134e-01   4.4022012e-01   4.2994584e-01   4.5983149e-01   3.7733154e-01   3.0847182e-01   4.0252124e-01   3.7430526e-01   4.6065171e-01   4.6008825e-01   3.6337620e-01   3.7950484e-01   3.8097080e-01   5.2689771e-01   4.2900834e-01   3.8187058e-01   4.0969052e-01   4.6622956e-01   3.4753954e-01   3.7338441e-01   3.7106677e-01   3.2693971e-01   3.2232718e-01   4.4752724e-01   3.5789640e-01   4.1563695e-01   3.2438944e-01   4.5565562e-01   3.4619907e-01   4.4965557e-01   3.9841763e-01   4.0096111e-01   3.7608333e-01   3.1419485e-01   3.4172782e-01   4.0397551e-01   3.1440281e-01   4.2865553e-01   4.1831326e-01   3.9931889e-01   3.5369559e-01   3.9495166e-01   3.4857729e-01   3.7001412e-01   3.7103653e-01   9.4891023e-03   8.2375707e-04   1.6686708e-03   2.4475618e-03   4.6565778e-03   2.0491959e-01   2.0139969e-01   2.4160221e-01   2.8586265e-01   2.5951451e-01   2.7003471e-01   2.1844761e-01   1.8272084e-01   2.3436629e-01   2.2908460e-01   2.6861177e-01   2.0572725e-01   2.6206958e-01   2.6821933e-01   1.4908933e-01   1.9377976e-01   2.5813756e-01   2.1522061e-01   3.4200281e-01   2.2841742e-01   2.7236034e-01   1.9712279e-01   3.4101997e-01   2.7089218e-01   2.0911514e-01   2.0716704e-01   2.6510721e-01   2.8112922e-01   2.5280689e-01   1.6599180e-01   2.3361443e-01   2.1674754e-01   2.0090153e-01   3.6527528e-01   2.7043122e-01   1.9136502e-01   2.2690330e-01   2.9871211e-01   1.9453190e-01   2.5541554e-01   2.8925890e-01   2.4310626e-01   2.2546391e-01   1.9558871e-01   2.4836004e-01   2.0063248e-01   2.1704777e-01   2.1367234e-01   1.3678274e-01   2.1790721e-01   4.6096128e-01   4.0671584e-01   3.8773373e-01   3.9744288e-01   4.2748862e-01   4.3009711e-01   4.1223718e-01   4.0843810e-01   4.4142325e-01   3.5773584e-01   2.9306179e-01   3.8663461e-01   3.6011993e-01   4.4301487e-01   4.4448732e-01   3.4710733e-01   3.5722182e-01   3.5456119e-01   5.1046759e-01   4.1264841e-01   3.6628224e-01   3.8788026e-01   4.4738884e-01   3.3559118e-01   3.5113614e-01   3.4925623e-01   3.1415212e-01   3.0373195e-01   4.2825709e-01   3.3863565e-01   3.9988417e-01   3.0248234e-01   4.3771445e-01   3.2582243e-01   4.2019828e-01   3.8883040e-01   3.7626984e-01   3.5109855e-01   2.9576205e-01   3.2946337e-01   3.8969349e-01   3.1023698e-01   4.0671584e-01   3.9807129e-01   3.8231042e-01   3.4615104e-01   3.8497123e-01   3.3374807e-01   3.4573433e-01   3.4546409e-01   9.9827550e-03   3.7862368e-03   4.2584946e-03   1.2265791e-03   1.7617949e-01   1.7703821e-01   2.1212343e-01   2.5052805e-01   2.2530971e-01   2.5127302e-01   1.9850334e-01   1.5861692e-01   2.0515179e-01   2.0665158e-01   2.3356888e-01   1.8070269e-01   2.2448284e-01   2.4549391e-01   1.2367511e-01   1.6367665e-01   2.4261509e-01   1.9359579e-01   2.9712394e-01   2.0027260e-01   2.5390638e-01   1.6582785e-01   3.0629971e-01   2.4971132e-01   1.7938888e-01   1.7609087e-01   2.3136866e-01   2.4921343e-01   2.2715314e-01   1.3644726e-01   2.0313672e-01   1.8736201e-01   1.7259709e-01   3.3997757e-01   2.5916969e-01   1.7732718e-01   1.9796934e-01   2.5795325e-01   1.7832877e-01   2.2545225e-01   2.6961076e-01   2.2173788e-01   1.9575867e-01   1.6649347e-01   2.2485533e-01   1.8584864e-01   1.9731550e-01   1.8682160e-01   1.0543428e-01   1.9413835e-01   4.3845459e-01   3.7813833e-01   3.5313427e-01   3.7426892e-01   3.9794201e-01   3.9726718e-01   3.9130315e-01   3.7920848e-01   4.0649770e-01   3.2906316e-01   2.6354873e-01   3.5155280e-01   3.2453882e-01   4.0704153e-01   4.0591144e-01   3.1492301e-01   3.3203733e-01   3.3498583e-01   4.6984073e-01   3.7668481e-01   3.3204804e-01   3.6021418e-01   4.1270518e-01   2.9886261e-01   3.2629567e-01   3.2396944e-01   2.7989788e-01   2.7743776e-01   3.9510115e-01   3.1077003e-01   3.6387709e-01   2.8054253e-01   4.0239292e-01   3.0024699e-01   4.0081171e-01   3.4598760e-01   3.5305310e-01   3.2985030e-01   2.6984561e-01   2.9352511e-01   3.5245796e-01   2.6611615e-01   3.7813833e-01   3.6780473e-01   3.4887718e-01   3.0350575e-01   3.4281917e-01   3.0065558e-01   3.2390437e-01   3.2536506e-01   1.4872402e-03   1.4261828e-03   4.3370414e-03   2.2707675e-01   2.2400493e-01   2.6569285e-01   3.1123078e-01   2.8378554e-01   2.9683242e-01   2.4257696e-01   2.0422363e-01   2.5811380e-01   2.5348079e-01   2.9319960e-01   2.2849166e-01   2.8589147e-01   2.9450563e-01   1.6807288e-01   2.1502765e-01   2.8470332e-01   2.3897250e-01   3.6819788e-01   2.5200370e-01   2.9929335e-01   2.1837402e-01   3.6884033e-01   2.9747447e-01   2.3136263e-01   2.2907381e-01   2.8973378e-01   3.0680413e-01   2.7799960e-01   1.8547528e-01   2.5712752e-01   2.3949352e-01   2.2288675e-01   3.9517754e-01   2.9790586e-01   2.1461980e-01   2.5028856e-01   3.2375470e-01   2.1774627e-01   2.8014020e-01   3.1681085e-01   2.6834640e-01   2.4865097e-01   2.1711982e-01   2.7360556e-01   2.2434130e-01   2.4112622e-01   2.3662943e-01   1.5362542e-01   2.4153192e-01   4.9407199e-01   4.3763583e-01   4.1728329e-01   4.2863716e-01   4.5893922e-01   4.6123811e-01   4.4410036e-01   4.3933832e-01   4.7263926e-01   3.8698450e-01   3.1961653e-01   4.1608078e-01   3.8854631e-01   4.7414193e-01   4.7530563e-01   3.7551546e-01   3.8685112e-01   3.8465728e-01   5.4280771e-01   4.4284025e-01   3.9512469e-01   4.1829234e-01   4.7881043e-01   3.6289720e-01   3.8058317e-01   3.7858579e-01   3.4094528e-01   3.3115887e-01   4.5930198e-01   3.6727055e-01   4.2965213e-01   3.3035276e-01   4.6876907e-01   3.5423104e-01   4.5243416e-01   4.1718566e-01   4.0676646e-01   3.8091352e-01   3.2289623e-01   3.5664111e-01   4.1894270e-01   3.3518670e-01   4.3763583e-01   4.2851737e-01   4.1182914e-01   3.7291664e-01   4.1330116e-01   3.6151280e-01   3.7529785e-01   3.7518553e-01   2.1466294e-04   8.1135795e-04   2.0395325e-01   2.0232995e-01   2.4147692e-01   2.8429935e-01   2.5773107e-01   2.7550146e-01   2.2191392e-01   1.8311464e-01   2.3414066e-01   2.3177254e-01   2.6670079e-01   2.0650082e-01   2.5876572e-01   2.7190067e-01   1.4755667e-01   1.9178198e-01   2.6468375e-01   2.1783813e-01   3.3738596e-01   2.2849816e-01   2.7802206e-01   1.9468150e-01   3.4113386e-01   2.7532568e-01   2.0783209e-01   2.0518365e-01   2.6370466e-01   2.8101900e-01   2.5475268e-01   1.6319612e-01   2.3278117e-01   2.1587899e-01   1.9999930e-01   3.7014440e-01   2.7911349e-01   1.9654509e-01   2.2657275e-01   2.9494234e-01   1.9887441e-01   2.5547815e-01   2.9483790e-01   2.4668408e-01   2.2473055e-01   1.9413008e-01   2.5114079e-01   2.0579387e-01   2.2056413e-01   2.1387343e-01   1.3181835e-01   2.1964768e-01   4.6883654e-01   4.1098091e-01   3.8893009e-01   4.0388763e-01   4.3171852e-01   4.3291890e-01   4.1992695e-01   4.1244869e-01   4.4351517e-01   3.6095375e-01   2.9436456e-01   3.8758959e-01   3.6027619e-01   4.4466450e-01   4.4498549e-01   3.4851465e-01   3.6196876e-01   3.6168475e-01   5.1115719e-01   4.1372900e-01   3.6718805e-01   3.9217531e-01   4.4969696e-01   3.3465314e-01   3.5590188e-01   3.5378490e-01   3.1382959e-01   3.0675099e-01   4.3089908e-01   3.4178657e-01   4.0069101e-01   3.0739171e-01   4.3956059e-01   3.2969272e-01   4.2869495e-01   3.8625531e-01   3.8227459e-01   3.5742723e-01   2.9874912e-01   3.2874265e-01   3.8973129e-01   3.0516637e-01   4.1098091e-01   4.0141982e-01   3.8392089e-01   3.4269880e-01   3.8263609e-01   3.3443392e-01   3.5169446e-01   3.5216636e-01   9.1517643e-04   2.1524074e-01   2.1387759e-01   2.5373107e-01   2.9714785e-01   2.7003778e-01   2.8920001e-01   2.3426287e-01   1.9410928e-01   2.4622443e-01   2.4423617e-01   2.7915984e-01   2.1812334e-01   2.7081916e-01   2.8531140e-01   1.5727134e-01   2.0260081e-01   2.7829111e-01   2.2998414e-01   3.5056990e-01   2.4050939e-01   2.9179089e-01   2.0549251e-01   3.5521699e-01   2.8889714e-01   2.1915718e-01   2.1632646e-01   2.7619378e-01   2.9404932e-01   2.6759110e-01   1.7313032e-01   2.4473695e-01   2.2745766e-01   2.1120369e-01   3.8534612e-01   2.9320974e-01   2.0849982e-01   2.3847660e-01   3.0758274e-01   2.1079215e-01   2.6804702e-01   3.0890781e-01   2.5958017e-01   2.3652855e-01   2.0509955e-01   2.6402277e-01   2.1797131e-01   2.3288914e-01   2.2557846e-01   1.4040598e-01   2.3171289e-01   4.8566100e-01   4.2666426e-01   4.0387929e-01   4.1975185e-01   4.4765854e-01   4.4867725e-01   4.3614287e-01   4.2811681e-01   4.5929331e-01   3.7580128e-01   3.0785579e-01   4.0248311e-01   3.7465557e-01   4.6038945e-01   4.6053443e-01   3.6291292e-01   3.7703492e-01   3.7702914e-01   5.2744561e-01   4.2898757e-01   3.8178676e-01   4.0761255e-01   4.6557959e-01   3.4846205e-01   3.7087965e-01   3.6870032e-01   3.2740185e-01   3.2070546e-01   4.4660679e-01   3.5633353e-01   4.1573756e-01   3.2160319e-01   4.5525495e-01   3.4414484e-01   4.4510906e-01   4.0053809e-01   3.9779009e-01   3.7261777e-01   3.1255985e-01   3.4249381e-01   4.0450836e-01   3.1773210e-01   4.2666426e-01   4.1685273e-01   3.9886436e-01   3.5618753e-01   3.9691207e-01   3.4850257e-01   3.6675459e-01   3.6731925e-01   1.9628524e-01   1.9595152e-01   2.3363495e-01   2.7477230e-01   2.4851118e-01   2.7084921e-01   2.1685944e-01   1.7678722e-01   2.2636857e-01   2.2599655e-01   2.5724256e-01   1.9993208e-01   2.4854721e-01   2.6607935e-01   1.4078995e-01   1.8369551e-01   2.6097312e-01   2.1228442e-01   3.2508389e-01   2.2103528e-01   2.7346255e-01   1.8624671e-01   3.3183707e-01   2.6996197e-01   1.9987779e-01   1.9682726e-01   2.5462868e-01   2.7249816e-01   2.4805238e-01   1.5523356e-01   2.2463473e-01   2.0803519e-01   1.9245485e-01   3.6364465e-01   2.7666661e-01   1.9319723e-01   2.1887484e-01   2.8382186e-01   1.9489313e-01   2.4750809e-01   2.8994226e-01   2.4123726e-01   2.1680288e-01   1.8634448e-01   2.4506974e-01   2.0223799e-01   2.1557050e-01   2.0677515e-01   1.2326853e-01   2.1346465e-01   4.6321322e-01   4.0354170e-01   3.7970298e-01   3.9803381e-01   4.2400584e-01   4.2423988e-01   4.1474064e-01   4.0481837e-01   4.3422436e-01   3.5345426e-01   2.8656464e-01   3.7821934e-01   3.5073976e-01   4.3506541e-01   4.3461895e-01   3.3997143e-01   3.5549675e-01   3.5686166e-01   5.0021759e-01   4.0411514e-01   3.5805390e-01   3.8499293e-01   4.4048074e-01   3.2475847e-01   3.4952686e-01   3.4727706e-01   3.0464816e-01   2.9991017e-01   4.2212289e-01   3.3451084e-01   3.9105629e-01   3.0183284e-01   4.3015090e-01   3.2308204e-01   4.2396798e-01   3.7459262e-01   3.7639485e-01   3.5210962e-01   2.9201270e-01   3.1907654e-01   3.7972706e-01   2.9306033e-01   4.0354170e-01   3.9347753e-01   3.7503434e-01   3.3106203e-01   3.7117506e-01   3.2561211e-01   3.4620183e-01   3.4718282e-01   5.4794269e-04   1.8595150e-03   7.6486933e-03   3.6709934e-03   1.1297771e-02   3.2211024e-03   9.3536855e-04   1.2319946e-03   2.8277178e-03   4.9162548e-03   4.5756064e-04   4.5051431e-03   8.2041162e-03   5.0174936e-03   3.6228961e-04   1.1821527e-02   2.0977093e-03   2.1132418e-02   9.2067605e-04   1.2006919e-02   4.4257629e-04   2.0287770e-02   9.6871594e-03   3.6190304e-05   1.5767395e-04   4.3807979e-03   7.0604016e-03   4.2468409e-03   2.9914879e-03   1.0695136e-03   1.8996353e-04   2.2349983e-05   3.2007300e-02   1.8626112e-02   5.9280137e-03   7.1455899e-04   1.0704644e-02   4.3625889e-03   3.3835317e-03   1.4689427e-02   5.0222514e-03   5.6899707e-04   1.6818673e-04   4.5805421e-03   5.6585758e-03   3.2371570e-03   3.2354233e-04   1.1207565e-02   1.3610741e-03   7.1737216e-02   4.4570224e-02   3.4818230e-02   4.5037397e-02   5.2043753e-02   5.1252208e-02   5.2740741e-02   4.4819381e-02   5.4844272e-02   2.7492078e-02   9.9689819e-03   3.4289978e-02   2.5632216e-02   5.5069559e-02   5.4817042e-02   2.2717491e-02   2.9451557e-02   3.3085492e-02   8.2968826e-02   4.3268668e-02   2.7878625e-02   3.8225012e-02   5.7392372e-02   1.8533113e-02   2.7752880e-02   2.6863838e-02   1.3522246e-02   1.3720834e-02   5.0366251e-02   2.2136217e-02   3.8620607e-02   1.6104597e-02   5.3184340e-02   1.9805362e-02   5.7449954e-02   3.4065200e-02   3.7316903e-02   3.0490470e-02   1.2067932e-02   1.7032969e-02   3.4772493e-02   1.3995163e-02   4.4570224e-02   4.0370599e-02   3.3379869e-02   2.1584097e-02   3.2788169e-02   1.8689520e-02   2.8313400e-02   2.9690702e-02   2.1810130e-03   9.0584977e-03   5.0419708e-03   8.6169391e-03   1.3497185e-03   5.5621011e-04   1.5626898e-03   1.4715788e-03   6.4159866e-03   2.8759099e-05   6.7456588e-03   6.5333041e-03   5.4642837e-03   1.4108585e-03   8.4463171e-03   6.8795048e-04   2.4580787e-02   1.0388021e-03   9.2286561e-03   1.7639378e-03   2.1069750e-02   7.6032385e-03   7.9175727e-04   1.2932915e-03   5.5725803e-03   7.6219263e-03   3.4673161e-03   4.2795834e-03   1.7380404e-03   7.6483144e-04   5.0584546e-04   3.0216137e-02   1.4096242e-02   2.8861882e-03   1.0548294e-03   1.3430225e-02   1.8234348e-03   3.6876972e-03   1.2061426e-02   3.2511669e-03   1.1268214e-03   9.2690858e-04   3.2976984e-03   2.6938518e-03   1.3276664e-03   2.7368625e-04   1.3465991e-02   4.6822375e-04   6.8703048e-02   4.3340061e-02   3.5237451e-02   4.2511976e-02   5.0937508e-02   5.0961712e-02   4.9575019e-02   4.3743233e-02   5.5024281e-02   2.6603107e-02   9.8022959e-03   3.4840370e-02   2.6494597e-02   5.5508568e-02   5.5916268e-02   2.2800218e-02   2.7686924e-02   2.9943438e-02   8.4266289e-02   4.3880838e-02   2.8349604e-02   3.6881146e-02   5.7478275e-02   1.9879185e-02   2.5944410e-02   2.5180647e-02   1.4399125e-02   1.2641568e-02   5.0169037e-02   2.1180767e-02   3.9323276e-02   1.3938661e-02   5.3485998e-02   1.8367828e-02   5.3859405e-02   3.6620288e-02   3.4933732e-02   2.7786245e-02   1.0959937e-02   1.8222006e-02   3.5858197e-02   1.7515874e-02   4.3340061e-02   3.9619354e-02   3.3535832e-02   2.4403195e-02   3.5188163e-02   1.9107255e-02   2.5791231e-02   2.6740983e-02   2.3644893e-03   7.3259797e-04   5.5696730e-03   2.5707992e-03   4.5988577e-03   6.5028014e-05   1.3580837e-03   1.2238983e-03   1.7109321e-03   1.8714646e-03   2.9944669e-03   1.2905109e-02   3.6725511e-03   6.9487479e-03   1.9516582e-03   1.2369689e-02   2.1307052e-04   6.0423668e-03   3.5751225e-03   1.0028727e-02   4.0861108e-03   1.5902610e-03   2.1378325e-03   8.2628456e-04   1.7251178e-03   8.0406810e-04   9.4788056e-03   1.5999623e-04   8.7509151e-04   2.2560004e-03   1.8732619e-02   1.2379328e-02   7.5803848e-03   2.7223442e-04   5.1089250e-03   5.8562851e-03   2.2798360e-04   7.3027135e-03   2.0605789e-03   3.8651941e-04   3.1125030e-03   1.3286042e-03   6.3896783e-03   2.7088758e-03   9.7424018e-04   2.1879745e-02   1.1792881e-03   5.1158538e-02   2.8393852e-02   2.0746802e-02   2.9099880e-02   3.4416089e-02   3.3763806e-02   3.5540899e-02   2.8575694e-02   3.6757319e-02   1.5144171e-02   3.2315336e-03   2.0363783e-02   1.3898176e-02   3.6986917e-02   3.6943012e-02   1.1630303e-02   1.6809451e-02   2.0213112e-02   6.0723696e-02   2.7441217e-02   1.5470812e-02   2.3398093e-02   3.8846172e-02   9.0112370e-03   1.5570624e-02   1.4874310e-02   5.5171614e-03   5.6710746e-03   3.3048406e-02   1.1270408e-02   2.3776077e-02   7.7482583e-03   3.5413096e-02   9.7831561e-03   3.9569593e-02   2.1047269e-02   2.3004495e-02   1.8015778e-02   4.6822715e-03   7.9260822e-03   2.0880056e-02   7.9428824e-03   2.8393852e-02   2.5015882e-02   1.9595645e-02   1.2073748e-02   1.9972960e-02   8.8353740e-03   1.6316616e-02   1.7585650e-02   7.5921246e-04   7.6581519e-03   8.7602132e-03   1.3285408e-02   3.1081233e-03   6.1183864e-03   3.4258252e-04   8.0693053e-03   1.1527108e-03   4.3989827e-03   2.4770294e-02   1.0297780e-02   1.0716436e-02   8.0921947e-03   4.0468338e-03   3.9682629e-03   8.0100500e-03   9.6963228e-03   3.4263963e-03   5.5915243e-03   6.8271736e-03   7.3405400e-03   4.5375223e-04   3.3086446e-04   2.9090971e-03   1.8954919e-02   3.0536401e-03   5.4665114e-03   8.4934379e-03   1.2174442e-02   1.6139108e-02   1.7445625e-02   4.0248005e-03   8.4214697e-04   1.4968032e-02   1.3210674e-03   7.6674238e-03   5.8292743e-03   4.1363018e-03   9.7236406e-03   4.2254644e-03   1.5250051e-02   9.0649565e-03   6.2807525e-03   3.4303230e-02   6.6673397e-03   3.8666536e-02   1.8227060e-02   1.0732501e-02   2.0722480e-02   2.2627004e-02   2.1137328e-02   2.6644819e-02   1.8156140e-02   2.2956019e-02   8.4429075e-03   1.3075172e-03   1.0338488e-02   5.7120788e-03   2.2877982e-02   2.2249653e-02   5.0348740e-03   1.0858478e-02   1.5670368e-02   4.1328272e-02   1.5415087e-02   7.0760309e-03   1.4735153e-02   2.4690692e-02   2.4709117e-03   1.0136092e-02   9.4846153e-03   1.0671740e-03   3.5238125e-03   2.0483172e-02   6.1432951e-03   1.2637418e-02   6.5903261e-03   2.1786492e-02   6.0819601e-03   3.0486925e-02   9.5174641e-03   1.6103409e-02   1.3353819e-02   3.2356456e-03   1.9926682e-03   1.0243487e-02   2.2538296e-03   1.8227060e-02   1.5108364e-02   1.0188754e-02   3.7627514e-03   8.8362152e-03   3.0791096e-03   1.1920070e-02   1.3588585e-02   8.0203401e-03   5.9881494e-03   7.9998519e-03   1.0330180e-03   3.9563353e-03   9.0962406e-05   4.3155161e-03   3.4798297e-04   4.5913809e-03   1.6934319e-02   5.4778348e-03   1.0415690e-02   5.0724002e-03   7.4143773e-03   1.5625174e-03   8.5090504e-03   5.0363885e-03   7.2978538e-03   5.9687085e-03   3.0800386e-03   3.3854665e-03   6.0369763e-05   9.7766526e-04   2.1106407e-03   1.2150960e-02   8.7050457e-04   2.2450596e-03   4.2656078e-03   1.7573546e-02   1.6541615e-02   1.3010703e-02   1.4863348e-03   2.0318224e-03   1.0715058e-02   5.1959240e-04   9.1091800e-03   4.5577281e-03   1.4679901e-03   5.0882044e-03   3.2208315e-03   1.1416637e-02   6.2084512e-03   2.9761078e-03   2.5010280e-02   3.7556543e-03   4.8641699e-02   2.5613136e-02   1.7022941e-02   2.7738185e-02   3.0983818e-02   2.9540677e-02   3.4381880e-02   2.5612023e-02   3.1832087e-02   1.3388731e-02   2.7364434e-03   1.6556686e-02   1.0555947e-02   3.1795721e-02   3.1144834e-02   9.3248236e-03   1.5850102e-02   2.0586917e-02   5.3133864e-02   2.2885657e-02   1.2291162e-02   2.1220606e-02   3.3851933e-02   5.9611654e-03   1.4821288e-02   1.4065156e-02   3.4935277e-03   5.6486577e-03   2.8790647e-02   1.0114487e-02   1.9481208e-02   8.7344459e-03   3.0476411e-02   9.4253713e-03   3.8601009e-02   1.5492941e-02   2.2081481e-02   1.8082534e-02   4.9261084e-03   5.1866248e-03   1.6531969e-02   3.8794099e-03   2.5613136e-02   2.2037756e-02   1.6246851e-02   7.5034139e-03   1.4652134e-02   6.6254167e-03   1.6367612e-02   1.8037074e-02   3.5963937e-03   1.3253217e-02   6.2726815e-03   2.9800542e-03   8.1679414e-03   8.1170586e-03   1.1643531e-02   4.8148791e-04   2.7366574e-02   1.5666050e-02   3.5602925e-04   4.6080605e-03   1.9717886e-02   6.2846724e-03   1.0858138e-05   1.6108248e-02   9.2526017e-03   1.6342536e-04   1.1289374e-02   1.3182521e-02   7.1086671e-03   4.8107615e-03   2.1505038e-03   2.4867835e-02   7.4585494e-03   9.3457001e-03   1.1859292e-02   8.6506765e-03   1.5825531e-03   7.6287797e-03   7.1464196e-03   1.3469318e-02   7.0587993e-03   4.6011946e-03   3.8423475e-04   1.2933991e-03   8.0463849e-03   1.4044313e-02   1.5554975e-03   5.8246512e-03   3.7445923e-03   7.8179143e-03   4.3383609e-02   5.1292419e-03   3.1208966e-02   1.7106674e-02   1.5590525e-02   1.4711786e-02   2.2118312e-02   2.3677515e-02   1.8355265e-02   1.7620984e-02   2.7322237e-02   8.2125300e-03   3.2025084e-03   1.5673958e-02   1.1993026e-02   2.8215754e-02   3.0043744e-02   8.3225318e-03   7.3692394e-03   7.0283195e-03   5.0297559e-02   2.1175797e-02   1.1957606e-02   1.3050611e-02   2.8749586e-02   1.0337000e-02   6.4346633e-03   6.2339245e-03   7.0135662e-03   2.1302546e-03   2.3356399e-02   5.5096838e-03   1.8637999e-02   1.1462623e-03   2.6577654e-02   3.5495923e-03   2.0668821e-02   2.2280093e-02   1.0461671e-02   6.3164945e-03   1.6640428e-03   9.2261377e-03   1.7584245e-02   1.7910761e-02   1.7106674e-02   1.5703153e-02   1.4029303e-02   1.7152691e-02   2.0996496e-02   7.4959989e-03   5.5175599e-03   5.5902559e-03   3.2004692e-03   2.3419030e-03   2.3799055e-04   7.0894399e-03   1.3013007e-03   8.8089668e-03   2.9046172e-03   1.1317768e-02   5.4246845e-03   3.1331888e-03   1.2023171e-04   2.4596565e-02   1.8369557e-03   3.9714617e-03   5.9789699e-03   1.7350836e-02   3.3069650e-03   3.5250221e-03   4.6752456e-03   5.9850395e-03   6.3682068e-03   1.7841601e-03   1.0289989e-02   3.0278347e-03   2.8250687e-03   3.3130538e-03   2.2020473e-02   6.7612416e-03   1.5121522e-03   2.2413165e-03   1.4397994e-02   9.1427197e-04   3.3482085e-03   6.1881321e-03   7.4537620e-04   2.6935839e-03   4.4237033e-03   1.1678481e-03   9.0068892e-04   2.9616334e-06   1.6314282e-03   2.2817755e-02   4.4730602e-04   5.5111404e-02   3.4158218e-02   2.9021577e-02   3.2043073e-02   4.1089749e-02   4.2083473e-02   3.7707137e-02   3.4692829e-02   4.6329738e-02   1.9906109e-02   6.9820129e-03   2.8847990e-02   2.2051442e-02   4.7099521e-02   4.8343924e-02   1.7860817e-02   1.9868896e-02   2.0488578e-02   7.4490873e-02   3.6906910e-02   2.3107397e-02   2.8319511e-02   4.8426947e-02   1.7182411e-02   1.8331671e-02   1.7811306e-02   1.2023707e-02   8.1012404e-03   4.1487060e-02   1.5227136e-02   3.2990763e-02   8.0392167e-03   4.5098943e-02   1.2350504e-02   4.1149609e-02   3.3318195e-02   2.5517275e-02   1.9030633e-02   6.7530681e-03   1.5581926e-02   3.0469465e-02   1.9100479e-02   3.4158218e-02   3.1415243e-02   2.7190491e-02   2.3321177e-02   3.1828581e-02   1.5212907e-02   1.7498443e-02   1.7919743e-02   3.6042298e-03   3.7468828e-03   9.7768723e-03   7.8664808e-04   9.4997776e-03   1.0849175e-02   2.5690262e-03   9.8725606e-04   1.2645853e-02   2.2464135e-03   3.0594913e-02   2.8398433e-03   1.3996699e-02   1.4253747e-03   2.8011999e-02   1.2147431e-02   1.3365379e-03   1.5899927e-03   8.8722552e-03   1.1913349e-02   6.7897739e-03   2.1135064e-03   3.6254453e-03   1.7898196e-03   6.9240260e-04   3.8891340e-02   1.9082524e-02   3.5297395e-03   2.7024302e-03   1.7766622e-02   2.5342822e-03   6.8092652e-03   1.7593080e-02   6.3527044e-03   2.6240465e-03   7.1495011e-04   6.5371413e-03   3.8357773e-03   3.1136154e-03   1.3436442e-03   8.9702416e-03   2.0253115e-03   8.1348350e-02   5.3552444e-02   4.4248656e-02   5.2648527e-02   6.1923652e-02   6.1838703e-02   6.0414517e-02   5.3985372e-02   6.6201925e-02   3.4742321e-02   1.4883289e-02   4.3767758e-02   3.4228373e-02   6.6672589e-02   6.6939218e-02   3.0219175e-02   3.6020463e-02   3.8455365e-02   9.7619080e-02   5.3827294e-02   3.6463335e-02   4.6373140e-02   6.8906148e-02   2.6398982e-02   3.4032020e-02   3.3159361e-02   2.0120628e-02   1.8469842e-02   6.0950543e-02   2.8524017e-02   4.8737718e-02   1.9976319e-02   6.4489083e-02   2.5275791e-02   6.5080438e-02   4.4969016e-02   4.4191042e-02   3.6066964e-02   1.6430448e-02   2.4524789e-02   4.4743887e-02   2.2062365e-02   5.3552444e-02   4.9370398e-02   4.2403953e-02   3.0850071e-02   4.3434971e-02   2.5846885e-02   3.3807321e-02   3.4832107e-02   1.2988107e-03   1.6703175e-03   1.1675843e-03   2.1414615e-03   3.6300242e-03   1.1143098e-02   2.7878082e-03   7.4699291e-03   1.6417856e-03   1.3833381e-02   5.5119833e-05   6.7870415e-03   2.7321459e-03   1.1691818e-02   4.7830259e-03   1.0265050e-03   1.5056614e-03   1.2372212e-03   2.4522309e-03   1.1336677e-03   8.0050923e-03   5.6870746e-05   4.6915622e-04   1.5562032e-03   2.0887194e-02   1.3125417e-02   6.8837382e-03   7.1162950e-05   5.9522504e-03   5.2043728e-03   5.3649750e-04   8.3200456e-03   2.2696632e-03   1.4322584e-04   2.2876100e-03   1.6070427e-03   5.8684470e-03   2.4558869e-03   5.5570590e-04   1.9651663e-02   8.9172519e-04   5.4659464e-02   3.1114613e-02   2.3119551e-02   3.1736271e-02   3.7415588e-02   3.6761852e-02   3.8397207e-02   3.1313890e-02   3.9883303e-02   1.7150840e-02   4.2007421e-03   2.2713095e-02   1.5842502e-02   4.0120080e-02   4.0057089e-02   1.3428356e-02   1.8845203e-02   2.2251079e-02   6.4673609e-02   3.0152373e-02   1.7530451e-02   2.5859899e-02   4.2056336e-02   1.0552527e-02   1.7518114e-02   1.6789150e-02   6.7575680e-03   6.8601014e-03   3.6016991e-02   1.2994930e-02   2.6303908e-02   8.9623653e-03   3.8482980e-02   1.1333705e-02   4.2542187e-02   2.3287141e-02   2.5337550e-02   1.9991634e-02   5.7451264e-03   9.3841364e-03   2.3239540e-02   8.8973019e-03   3.1114613e-02   2.7595638e-02   2.1905943e-02   1.3658827e-02   2.2169613e-02   1.0410758e-02   1.8207584e-02   1.9484294e-02   4.8008453e-03   1.2650854e-03   6.4006179e-03   1.8900850e-03   1.2501460e-02   5.1363105e-03   3.0955001e-03   2.4385845e-04   2.0020418e-02   1.0205842e-03   3.3467158e-03   5.5033857e-03   1.3788482e-02   2.4101593e-03   2.9461849e-03   4.0056193e-03   3.8916824e-03   4.1559722e-03   7.4799809e-04   1.0679921e-02   1.8732675e-03   2.1213449e-03   3.0477499e-03   1.9047032e-02   6.9834653e-03   2.9438547e-03   1.3758132e-03   1.0992441e-02   2.0426183e-03   1.8183256e-03   5.1275661e-03   3.4870074e-04   1.7800086e-03   4.1941671e-03   4.4278656e-04   2.0594764e-03   2.9165015e-04   1.2452133e-03   2.3762069e-02   2.9165015e-04   5.0966362e-02   3.0166832e-02   2.4694798e-02   2.8788397e-02   3.6671707e-02   3.7274280e-02   3.4472569e-02   3.0604199e-02   4.1125938e-02   1.6692997e-02   4.7977197e-03   2.4489085e-02   1.8077937e-02   4.1761735e-02   4.2713992e-02   1.4455884e-02   1.7039782e-02   1.8322490e-02   6.7670508e-02   3.2041093e-02   1.9169462e-02   2.4724400e-02   4.3157837e-02   1.3510623e-02   1.5640518e-02   1.5102883e-02   8.9767687e-03   6.0642978e-03   3.6671707e-02   1.2419694e-02   2.8323093e-02   6.4935421e-03   3.9910361e-02   1.0006286e-02   3.7967777e-02   2.8141888e-02   2.2594035e-02   1.6734859e-02   4.8977754e-03   1.2095984e-02   2.5839912e-02   1.5166518e-02   3.0166832e-02   2.7378800e-02   2.3072794e-02   1.8885101e-02   2.6783663e-02   1.1941964e-02   1.5226991e-02   1.5844953e-02   5.5898027e-03   3.6211515e-04   4.6884489e-03   1.9469863e-02   6.9494812e-03   1.0856564e-02   6.2070186e-03   5.9174289e-03   2.3319364e-03   8.6215938e-03   6.4261295e-03   5.9157019e-03   6.0481987e-03   4.2268867e-03   4.5610911e-03   4.8970997e-05   6.8799458e-04   2.4420024e-03   1.4255275e-02   1.5079078e-03   3.2366850e-03   5.6006336e-03   1.5957034e-02   1.6871464e-02   1.4787237e-02   2.2762765e-03   1.3333689e-03   1.2378081e-02   7.3736127e-04   8.8932355e-03   5.1508306e-03   2.2779875e-03   6.5293055e-03   3.6737889e-03   1.2985539e-02   7.3417742e-03   4.0613774e-03   2.7837547e-02   4.7997557e-03   4.5639701e-02   2.3278576e-02   1.4877176e-02   2.5663407e-02   2.8314352e-02   2.6769516e-02   3.2135703e-02   2.3238033e-02   2.8854470e-02   1.1827077e-02   2.2644401e-03   1.4421001e-02   8.8429015e-03   2.8776903e-02   2.8063687e-02   7.8778602e-03   1.4365876e-02   1.9273282e-02   4.9067035e-02   2.0328263e-02   1.0496416e-02   1.9196637e-02   3.0789735e-02   4.6457607e-03   1.3443289e-02   1.2708604e-02   2.5804695e-03   5.0424172e-03   2.6041403e-02   8.8829912e-03   1.7122028e-02   8.2367466e-03   2.7547637e-02   8.4529986e-03   3.6274794e-02   1.3225786e-02   2.0335647e-02   1.6784857e-02   4.4669319e-03   3.9860599e-03   1.4316384e-02   2.9523808e-03   2.3278576e-02   1.9803941e-02   1.4205949e-02   5.9492702e-03   1.2454271e-02   5.3895801e-03   1.5143895e-02   1.6858271e-02   5.9387347e-03   5.9571758e-03   6.0526515e-03   1.4146691e-03   8.1320415e-03   6.3420687e-04   2.2943426e-02   7.2217865e-04   8.7156753e-03   1.7123420e-03   1.9617600e-02   7.0385795e-03   6.4044399e-04   1.1390332e-03   4.8019256e-03   6.7384180e-03   2.9679315e-03   4.6026472e-03   1.3268878e-03   5.4152853e-04   4.6516773e-04   2.8772311e-02   1.3783757e-02   3.2459159e-03   7.3821107e-04   1.2234521e-02   2.0992860e-03   3.0774015e-03   1.1372571e-02   2.9352447e-03   8.1022588e-04   9.2842537e-04   2.8855444e-03   2.9418595e-03   1.2977062e-03   1.2869337e-04   1.4124612e-02   3.4246729e-04   6.6626445e-02   4.1505551e-02   3.3416051e-02   4.0874061e-02   4.8928444e-02   4.8860648e-02   4.7883828e-02   4.1881126e-02   5.2796241e-02   2.5141882e-02   8.8605790e-03   3.3017625e-02   2.4870522e-02   5.3247026e-02   5.3590923e-02   2.1349209e-02   2.6308756e-02   2.8721666e-02   8.1439460e-02   4.1842449e-02   2.6703197e-02   3.5208876e-02   5.5212555e-02   1.8433774e-02   2.4622301e-02   2.3863121e-02   1.3181398e-02   1.1675955e-02   4.8074316e-02   1.9890418e-02   3.7380285e-02   1.3082557e-02   5.1276398e-02   1.7233265e-02   5.2150081e-02   3.4634218e-02   3.3454504e-02   2.6550201e-02   1.0070918e-02   1.6842626e-02   3.3968952e-02   1.6166125e-02   4.1505551e-02   3.7811539e-02   3.1780349e-02   2.2766214e-02   3.3244526e-02   1.7747224e-02   2.4583452e-02   2.5577750e-02   7.4058632e-03   1.7632325e-02   5.8672157e-03   1.4554963e-02   7.5139440e-03   6.3063306e-03   2.8227254e-03   1.2216172e-02   5.2171506e-03   8.3411571e-03   9.1198919e-03   3.7613430e-03   3.7527482e-03   5.6979631e-04   2.0412760e-03   4.1677011e-03   1.2238157e-02   1.7043766e-03   3.0984992e-03   5.1374687e-03   2.0730806e-02   2.1628161e-02   1.6669142e-02   2.5627983e-03   1.3966031e-03   1.3985502e-02   1.7150229e-03   1.2743810e-02   7.3773848e-03   2.3644296e-03   5.7186323e-03   5.6669191e-03   1.5046711e-02   9.0550035e-03   4.3221940e-03   2.4177800e-02   5.7926331e-03   5.2977640e-02   2.8412846e-02   1.8464622e-02   3.1548301e-02   3.3726407e-02   3.1637531e-02   3.8729422e-02   2.8292534e-02   3.3574657e-02   1.5809867e-02   4.4178873e-03   1.7890807e-02   1.1580028e-02   3.3334020e-02   3.2156672e-02   1.0943899e-02   1.8967943e-02   2.4791881e-02   5.4103864e-02   2.4225163e-02   1.3643641e-02   2.4071431e-02   3.5681100e-02   6.5373199e-03   1.7959936e-02   1.7099713e-02   4.3929724e-03   8.0887873e-03   3.0809355e-02   1.2543658e-02   2.0721585e-02   1.2037199e-02   3.2114506e-02   1.2207760e-02   4.3300211e-02   1.5218252e-02   2.5733556e-02   2.1932604e-02   7.3680112e-03   5.8739609e-03   1.7443010e-02   2.6299180e-03   2.8412846e-02   2.4437667e-02   1.7887656e-02   6.9159049e-03   1.4494165e-02   7.9434468e-03   2.0060731e-02   2.2068579e-02   2.3875094e-02   1.2000415e-02   1.3948342e-03   3.4546351e-03   1.4939730e-02   3.7950422e-03   6.0175173e-04   1.2211196e-02   7.0052335e-03   9.1256063e-05   8.0336825e-03   9.5484059e-03   3.8945506e-03   2.3206010e-03   7.0732153e-04   2.0727990e-02   4.4889370e-03   6.3258821e-03   8.7927798e-03   9.0069682e-03   3.7952179e-03   7.8092546e-03   4.4335690e-03   9.0550736e-03   6.7946167e-03   2.1531805e-03   9.6426638e-04   7.0770423e-04   5.1150602e-03   1.0670446e-02   5.5187206e-04   6.0114634e-03   3.0771240e-03   5.3655604e-03   3.8039285e-02   3.5100982e-03   3.3392676e-02   1.7228333e-02   1.4023464e-02   1.5984642e-02   2.2267037e-02   2.3075907e-02   2.0330300e-02   1.7609739e-02   2.6354220e-02   7.6657981e-03   1.4938436e-03   1.3975046e-02   9.8087979e-03   2.7013992e-02   2.8227679e-02   6.7815824e-03   7.6426994e-03   8.5739542e-03   4.8734857e-02   1.9601188e-02   1.0188446e-02   1.3147209e-02   2.7911001e-02   7.5145131e-03   6.7053137e-03   6.3732135e-03   4.4764490e-03   1.3642012e-03   2.2654181e-02   4.8866188e-03   1.6888522e-02   1.3930577e-03   2.5469441e-02   3.2860894e-03   2.3095694e-02   1.8694362e-02   1.1451986e-02   7.4272413e-03   8.6465452e-04   6.5073035e-03   1.5400191e-02   1.2824348e-02   1.7228333e-02   1.5313622e-02   1.2672619e-02   1.3006211e-02   1.7530867e-02   5.5400420e-03   6.4187909e-03   6.8900377e-03   3.1968437e-03   2.6175875e-02   9.5689725e-03   4.4766639e-02   9.9845360e-03   2.8418681e-02   3.6870693e-03   4.5253718e-02   2.5815239e-02   5.6468536e-03   5.2271680e-03   1.8578768e-02   2.3906603e-02   1.7414675e-02   6.6309054e-04   1.0701959e-02   7.1563943e-03   4.3943049e-03   6.0754711e-02   3.4699507e-02   9.6990814e-03   9.4374842e-03   2.8881695e-02   8.6238198e-03   1.6549411e-02   3.3492594e-02   1.6963829e-02   8.9575119e-03   3.4839312e-03   1.7214511e-02   1.0985852e-02   1.1115876e-02   7.0774378e-03   2.3223923e-03   9.1191389e-03   1.1169736e-01   7.8250518e-02   6.5808362e-02   7.7763348e-02   8.8114611e-02   8.7449743e-02   8.7215232e-02   7.8675005e-02   9.2203874e-02   5.5132383e-02   2.8794481e-02   6.5100824e-02   5.3025891e-02   9.2531519e-02   9.2220151e-02   4.8731252e-02   5.7186075e-02   6.0580024e-02   1.2745253e-01   7.7174441e-02   5.6198920e-02   6.9678402e-02   9.5449745e-02   4.2538093e-02   5.4722713e-02   5.3576276e-02   3.4860888e-02   3.4291475e-02   8.6329226e-02   4.7343142e-02   7.0978985e-02   3.6695928e-02   9.0088005e-02   4.3430772e-02   9.2828505e-02   6.4239353e-02   6.7481588e-02   5.7536867e-02   3.1542812e-02   4.0297150e-02   6.5753742e-02   3.3241661e-02   7.8250518e-02   7.2933055e-02   6.3794057e-02   4.6178781e-02   6.2571051e-02   4.2843100e-02   5.4666081e-02   5.6027673e-02   1.6139749e-02   3.9412782e-03   2.4265145e-02   2.3891707e-03   1.6498373e-02   4.1418612e-05   2.4988702e-02   1.3783039e-02   4.3146851e-04   2.5122323e-04   6.4815288e-03   1.0052630e-02   7.0587637e-03   1.3669961e-03   2.4020339e-03   9.7331181e-04   2.7171014e-04   3.8783427e-02   2.3881244e-02   7.7285447e-03   2.0010737e-03   1.2962382e-02   6.0316172e-03   5.6775409e-03   1.9642810e-02   8.0347010e-03   1.6772041e-03   5.1201506e-05   7.5139419e-03   7.7685816e-03   5.4104161e-03   1.3577183e-03   7.6646931e-03   3.0214900e-03   8.1621829e-02   5.2182884e-02   4.1040324e-02   5.3055858e-02   6.0133087e-02   5.8980137e-02   6.1457708e-02   5.2397706e-02   6.2608146e-02   3.3589093e-02   1.3750660e-02   4.0409320e-02   3.0837807e-02   6.2732754e-02   6.2152008e-02   2.7986481e-02   3.5988306e-02   4.0227814e-02   9.1799153e-02   5.0051858e-02   3.3478326e-02   4.5393111e-02   6.5357720e-02   2.2750138e-02   3.4139497e-02   3.3132950e-02   1.7367166e-02   1.8328224e-02   5.7997026e-02   2.7720666e-02   4.5013892e-02   2.1236242e-02   6.0787869e-02   2.5266646e-02   6.6573172e-02   3.9086224e-02   4.4693577e-02   3.7322864e-02   1.6444309e-02   2.1159286e-02   4.0674593e-02   1.6113197e-02   5.2182884e-02   4.7503868e-02   3.9598661e-02   2.5231075e-02   3.7795470e-02   2.3382629e-02   3.4903444e-02   3.6481922e-02   4.3266011e-03   2.5120283e-02   7.2104610e-03   3.6362605e-04   1.6818393e-02   1.3224351e-02   8.9751703e-04   1.2039448e-02   1.4078561e-02   9.5477546e-03   7.2983976e-03   3.1999143e-03   2.4639885e-02   8.8187561e-03   1.0207680e-02   1.2236717e-02   1.1661588e-02   8.0001293e-04   5.7297070e-03   8.1532898e-03   1.7517743e-02   5.5505771e-03   6.3202290e-03   1.2261175e-03   1.5275601e-03   9.1326114e-03   1.4417917e-02   2.2056571e-03   4.2297788e-03   3.2218738e-03   8.2583968e-03   4.2679879e-02   5.2144338e-03   3.5325690e-02   2.1286357e-02   2.0340751e-02   1.7932964e-02   2.6773752e-02   2.8858059e-02   2.1473619e-02   2.1925037e-02   3.2987864e-02   1.1596147e-02   5.5679058e-03   2.0475433e-02   1.6418368e-02   3.4058657e-02   3.6285268e-02   1.2036020e-02   1.0227865e-02   8.9974606e-03   5.7847652e-02   2.6531721e-02   1.6295053e-02   1.6788576e-02   3.4473710e-02   1.4498141e-02   9.1389529e-03   8.9727022e-03   1.0441422e-02   4.2212624e-03   2.8555402e-02   8.4473824e-03   2.3791713e-02   2.5698702e-03   3.2242281e-02   5.9266749e-03   2.3676462e-02   2.8216759e-02   1.3343464e-02   8.4809495e-03   3.5554866e-03   1.3166972e-02   2.2745344e-02   2.2629651e-02   2.1286357e-02   1.9992085e-02   1.8520730e-02   2.2324446e-02   2.6771848e-02   1.1107369e-02   7.6788410e-03   7.4852977e-03   2.3512869e-02   1.1702196e-03   5.0486445e-03   4.4067902e-03   1.7493736e-02   4.0658633e-03   2.3529372e-03   3.3047066e-03   5.2094902e-03   6.0430183e-03   1.7805903e-03   8.3604250e-03   2.1645857e-03   1.8214590e-03   2.1737913e-03   2.3530298e-02   8.5714286e-03   1.8444368e-03   1.4565864e-03   1.3243081e-02   1.0630397e-03   2.8808992e-03   7.3652636e-03   1.0835317e-03   1.7933322e-03   3.0961279e-03   1.3436220e-03   1.3043704e-03   1.2482375e-04   8.8034137e-04   2.0043242e-02   1.2482375e-04   5.7954445e-02   3.5775683e-02   2.9742194e-02   3.4149795e-02   4.2824229e-02   4.3477315e-02   4.0214177e-02   3.6256651e-02   4.7605297e-02   2.0950874e-02   7.1042975e-03   2.9499916e-02   2.2329817e-02   4.8271691e-02   4.9230028e-02   1.8375611e-02   2.1296157e-02   2.2492082e-02   7.5802989e-02   3.7751582e-02   2.3617894e-02   2.9827991e-02   4.9792717e-02   1.7017775e-02   1.9724142e-02   1.9131907e-02   1.1873908e-02   8.7349825e-03   4.2824229e-02   1.6130090e-02   3.3687060e-02   9.1410950e-03   4.6289887e-02   1.3350026e-02   4.3904542e-02   3.3071376e-02   2.7381594e-02   2.0813943e-02   7.3233676e-03   1.5432666e-02   3.0904955e-02   1.7682128e-02   3.5775683e-02   3.2747980e-02   2.7982984e-02   2.2571206e-02   3.1620085e-02   1.5454693e-02   1.9154732e-02   1.9759156e-02   1.5625666e-02   2.0014241e-02   2.2906319e-02   3.3689213e-03   1.6561417e-02   1.9555072e-02   1.9724522e-02   6.8229205e-03   6.0996359e-03   1.3507575e-02   3.5744409e-02   1.3348521e-02   1.7651623e-02   2.2506296e-02   1.4148535e-02   3.1413076e-02   3.8119216e-02   1.5501824e-02   1.7783197e-03   3.4445966e-02   9.9745771e-03   1.7822684e-02   1.8993068e-02   1.5436010e-02   2.3911299e-02   1.6070505e-02   3.4793519e-02   2.5109394e-02   1.9730191e-02   5.3384757e-02   2.0981999e-02   3.5016323e-02   1.5808551e-02   7.2216559e-03   2.1250521e-02   1.8323057e-02   1.5289849e-02   2.7077232e-02   1.5342317e-02   1.5450153e-02   9.5719689e-03   7.0769801e-03   6.7142336e-03   3.8618160e-03   1.4833874e-02   1.3052654e-02   5.5299114e-03   1.3477582e-02   2.0871841e-02   2.6745939e-02   9.5407500e-03   5.3018257e-03   1.4058965e-02   1.6863810e-02   2.0380823e-03   1.3353665e-02   1.2655783e-02   3.2775616e-03   9.7625272e-03   1.4632542e-02   9.0437643e-03   7.6711708e-03   1.4740530e-02   1.4381411e-02   1.0907741e-02   3.1026769e-02   2.6758954e-03   1.8148668e-02   1.8095332e-02   1.0256426e-02   2.3444102e-03   5.5327937e-03   1.0086149e-03   1.5808551e-02   1.2612237e-02   7.5482105e-03   2.3261323e-04   2.5482034e-03   4.2287654e-03   1.6814254e-02   1.9242327e-02   6.8098804e-03   2.4185222e-03   1.3095995e-02   4.9100577e-03   8.0319599e-04   1.3085229e-03   1.8113887e-03   3.1306373e-03   1.2541646e-03   7.2250359e-03   1.5182032e-04   3.2471009e-04   1.1793141e-03   2.2134336e-02   1.2798604e-02   5.8036245e-03   2.9068060e-05   7.1481800e-03   4.2574873e-03   8.5847073e-04   8.5715637e-03   2.1039195e-03   1.1389023e-04   1.8746094e-03   1.5895426e-03   4.9316123e-03   1.9257560e-03   2.7708506e-04   1.8515651e-02   5.3986259e-04   5.6637702e-02   3.2886175e-02   2.4967826e-02   3.3187187e-02   3.9414817e-02   3.8923256e-02   3.9880016e-02   3.3128964e-02   4.2231952e-02   1.8470852e-02   4.9097912e-03   2.4570551e-02   1.7467535e-02   4.2525770e-02   4.2580968e-02   1.4790908e-02   2.0011146e-02   2.3142926e-02   6.7845285e-02   3.2285576e-02   1.9161137e-02   2.7420216e-02   4.4447416e-02   1.1980855e-02   1.8611023e-02   1.7883360e-02   7.8729229e-03   7.5466400e-03   3.8175619e-02   1.4096206e-02   2.8321778e-02   9.4496873e-03   4.0815141e-02   1.2211823e-02   4.4024579e-02   2.5465922e-02   2.6596134e-02   2.0925904e-02   6.3340227e-03   1.0720439e-02   2.5211490e-02   1.0333158e-02   3.2886175e-02   2.9360405e-02   2.3656085e-02   1.5413665e-02   2.4285913e-02   1.1678199e-02   1.9116491e-02   2.0313205e-02   1.6950975e-02   9.2576768e-03   2.2830227e-04   1.1996475e-02   1.3943618e-02   7.5471408e-03   5.0950912e-03   2.4447813e-03   2.5903324e-02   8.0139448e-03   9.9879335e-03   1.2585436e-02   8.2754975e-03   1.4174352e-03   8.0478199e-03   7.7042954e-03   1.3901912e-02   7.5078674e-03   4.9957099e-03   2.9997761e-04   1.5395926e-03   8.6362248e-03   1.4833108e-02   1.8222710e-03   6.1957159e-03   4.1238914e-03   8.4102568e-03   4.4734160e-02   5.6076899e-03   3.0288189e-02   1.6597244e-02   1.5336169e-02   1.4117002e-02   2.1529085e-02   2.3159309e-02   1.7633168e-02   1.7119251e-02   2.6802924e-02   7.9632454e-03   3.3472740e-03   1.5438450e-02   1.1914773e-02   2.7716384e-02   2.9607261e-02   8.2241873e-03   7.0346123e-03   6.5727745e-03   4.9604200e-02   2.0828511e-02   1.1808642e-02   1.2615158e-02   2.8194719e-02   1.0429441e-02   6.1245969e-03   5.9452412e-03   7.1618546e-03   2.1261487e-03   2.2855826e-02   5.3452154e-03   1.8357871e-02   1.0397070e-03   2.6087088e-02   3.3990115e-03   1.9871685e-02   2.2251351e-02   9.9773797e-03   5.9192173e-03   1.6976055e-03   9.3317377e-03   1.7391404e-02   1.8375579e-02   1.6597244e-02   1.5280892e-02   1.3772451e-02   1.7356806e-02   2.0968489e-02   7.4978418e-03   5.1634523e-03   5.1963190e-03   2.4233623e-02   1.4077025e-02   4.3787020e-04   1.8512542e-04   6.0477386e-03   9.6703484e-03   7.1488601e-03   1.5477068e-03   2.2742281e-03   9.7171923e-04   3.9271863e-04   3.8509554e-02   2.4774335e-02   8.7360281e-03   1.9891111e-03   1.1995846e-02   6.8973897e-03   5.5019459e-03   1.9965157e-02   8.4152844e-03   1.6247783e-03   1.4531219e-04   7.7480972e-03   8.6972032e-03   5.9824611e-03   1.5176827e-03   7.8567259e-03   3.3493021e-03   8.1204385e-02   5.1575806e-02   4.0135980e-02   5.2803481e-02   5.9400299e-02   5.8042463e-02   6.1291964e-02   5.1745941e-02   6.1508632e-02   3.3138226e-02   1.3469654e-02   3.9479896e-02   2.9967140e-02   6.1565597e-02   6.0825097e-02   2.7361698e-02   3.5748038e-02   4.0333571e-02   9.0138895e-02   4.8984196e-02   3.2667108e-02   4.4902460e-02   6.4253355e-02   2.1894327e-02   3.3940189e-02   3.2913172e-02   1.6731486e-02   1.8202458e-02   5.7045856e-02   2.7382191e-02   4.3985602e-02   2.1375556e-02   5.9676750e-02   2.5108522e-02   6.6474949e-02   3.7689168e-02   4.4508235e-02   3.7339453e-02   1.6368548e-02   2.0371230e-02   3.9606943e-02   1.4908799e-02   5.1575806e-02   4.6824025e-02   3.8781771e-02   2.3989539e-02   3.6452117e-02   2.2748990e-02   3.4902979e-02   3.6586492e-02   7.5459794e-03   1.9125850e-02   2.0310725e-02   6.1222293e-03   3.4447226e-03   8.1418452e-03   3.7867035e-02   1.2077489e-02   1.6567789e-02   2.1605044e-02   3.9038067e-03   1.6430417e-02   2.8689503e-02   1.3569150e-02   4.2181405e-03   2.6167927e-02   7.2610935e-03   7.0630535e-03   1.1392972e-02   1.4088158e-02   2.3849569e-02   9.5566395e-03   2.5308356e-02   1.7804542e-02   1.7150362e-02   5.8921861e-02   1.6182419e-02   2.0027139e-02   6.1819655e-03   2.0410396e-03   8.6030014e-03   8.6357480e-03   7.5787415e-03   1.2598904e-02   6.0656768e-03   8.7139108e-03   1.7031846e-03   2.3331644e-03   1.8821103e-03   3.1682605e-04   8.7160052e-03   8.5600328e-03   2.8826583e-04   3.4529372e-03   7.5176091e-03   2.1668627e-02   4.3875084e-03   6.5654007e-04   4.4940457e-03   9.7914071e-03   1.9831433e-04   3.3391345e-03   2.9870521e-03   6.9985633e-04   2.5162956e-03   7.1853248e-03   1.3860021e-03   2.9754449e-03   4.8339512e-03   8.0121089e-03   2.3142577e-03   1.5373296e-02   2.8512223e-03   6.2399212e-03   5.8796015e-03   3.1092372e-03   2.3415322e-04   1.9852251e-03   5.2321529e-03   6.1819655e-03   4.3274341e-03   1.8113019e-03   1.9110595e-03   2.4033410e-03   9.3130265e-05   5.1498910e-03   6.5356041e-03   9.5659910e-03   1.1252405e-02   5.1556774e-03   3.2048021e-03   1.2695843e-03   2.2856756e-02   5.7848184e-03   7.7211451e-03   1.0283621e-02   8.3602499e-03   2.7615733e-03   7.9786726e-03   5.6505970e-03   1.0691105e-02   7.1332727e-03   3.1295602e-03   5.2401241e-04   9.5266815e-04   6.4319329e-03   1.2318850e-02   9.4872145e-04   6.1326072e-03   3.4758657e-03   6.5333653e-03   4.0853883e-02   4.3049208e-03   3.1649609e-02   1.6528693e-02   1.4101758e-02   1.4838879e-02   2.1483291e-02   2.2597676e-02   1.8841242e-02   1.6959579e-02   2.5991410e-02   7.4250762e-03   1.9970150e-03   1.4113092e-02   1.0250250e-02   2.6744340e-02   2.8212793e-02   6.9997737e-03   7.0607843e-03   7.4739664e-03   4.8397396e-02   1.9593840e-02   1.0430940e-02   1.2525634e-02   2.7473469e-02   8.3209543e-03   6.1476473e-03   5.8775226e-03   5.2455782e-03   1.4265861e-03   2.2224591e-02   4.7507930e-03   1.7000338e-02   1.0369313e-03   2.5178358e-02   3.0495461e-03   2.1392322e-02   1.9628131e-02   1.0500631e-02   6.5204272e-03   9.7357638e-04   7.2933833e-03   1.5732817e-02   1.4704532e-02   1.6528693e-02   1.4858839e-02   1.2681737e-02   1.4339393e-02   1.8427144e-02   5.9852538e-03   5.6194230e-03   5.9265324e-03   8.2461319e-05   3.7688699e-03   6.4113525e-03   4.0576095e-03   3.3120738e-03   8.1782115e-04   1.0911416e-04   1.0750826e-04   3.1097496e-02   1.8955233e-02   6.6951403e-03   5.7580225e-04   9.5785875e-03   5.0095389e-03   2.9949836e-03   1.4512717e-02   5.0859668e-03   4.0940931e-04   2.6323499e-04   4.5146422e-03   6.3221754e-03   3.5606197e-03   3.7002765e-04   1.1722539e-02   1.5048339e-03   7.0395338e-02   4.3268177e-02   3.3370831e-02   4.4028795e-02   5.0578307e-02   4.9629423e-02   5.1746432e-02   4.3478758e-02   5.3066435e-02   2.6481479e-02   9.3392135e-03   3.2828923e-02   2.4313691e-02   5.3237993e-02   5.2867243e-02   2.1623243e-02   2.8596153e-02   3.2496284e-02   8.0563616e-02   4.1614554e-02   2.6578058e-02   3.7074597e-02   5.5590704e-02   1.7323162e-02   2.6950223e-02   2.6053254e-02   1.2554151e-02   1.3157434e-02   4.8740123e-02   2.1279987e-02   3.7040705e-02   1.5739340e-02   5.1410982e-02   1.9129885e-02   5.6480014e-02   3.2271228e-02   3.6432542e-02   2.9847396e-02   1.1573499e-02   1.5895178e-02   3.3202746e-02   1.2659655e-02   4.3268177e-02   3.9046279e-02   3.2014714e-02   2.0067384e-02   3.1045819e-02   1.7642117e-02   2.7677552e-02   2.9133996e-02   4.1910853e-03   7.2076003e-03   5.1147587e-03   2.7507325e-03   1.1620134e-03   3.3310681e-04   2.1458858e-04   3.3405406e-02   2.1499526e-02   8.0088547e-03   9.8332257e-04   9.6892205e-03   6.1744631e-03   3.6704596e-03   1.6544301e-02   6.4217725e-03   7.2111274e-04   2.1270559e-04   5.7183304e-03   7.6981750e-03   4.7117366e-03   8.0177817e-04   1.0442534e-02   2.2910923e-03   7.3784227e-02   4.5661689e-02   3.5029236e-02   4.6823533e-02   5.3065363e-02   5.1836541e-02   5.4866908e-02   4.5828107e-02   5.5174565e-02   2.8408213e-02   1.0505539e-02   3.4430852e-02   2.5609623e-02   5.5260802e-02   5.4654205e-02   2.3114484e-02   3.0836583e-02   3.5207839e-02   8.2686924e-02   4.3372344e-02   2.8064998e-02   3.9380344e-02   5.7772002e-02   1.8254235e-02   2.9162191e-02   2.8206341e-02   1.3497345e-02   1.4745279e-02   5.0900941e-02   2.3090436e-02   3.8677830e-02   1.7710943e-02   5.3450122e-02   2.1019262e-02   5.9801906e-02   3.3130692e-02   3.9030212e-02   3.2379101e-02   1.3108535e-02   1.6839016e-02   3.4625964e-02   1.2551681e-02   4.5661689e-02   4.1207031e-02   3.3732757e-02   2.0513590e-02   3.1937443e-02   1.8908607e-02   3.0105345e-02   3.1711397e-02   5.5341249e-04   1.8100865e-03   1.3685556e-02   1.1595059e-03   2.7733190e-03   5.0259130e-03   1.5582273e-02   1.5303863e-02   1.3216313e-02   1.8061219e-03   1.8483286e-03   1.0961959e-02   4.0632184e-04   7.9419645e-03   4.2030049e-03   1.8572156e-03   5.9964081e-03   2.8843938e-03   1.1487297e-02   6.2195738e-03   3.4171878e-03   2.7328194e-02   3.9549773e-03   4.5323537e-02   2.3233798e-02   1.5194289e-02   2.5226902e-02   2.8389486e-02   2.7075250e-02   3.1585337e-02   2.3242139e-02   2.9332670e-02   1.1663012e-02   1.9950589e-03   1.4768251e-02   9.1566367e-03   2.9330780e-02   2.8799195e-02   7.9264454e-03   1.3962831e-02   1.8481959e-02   5.0115855e-02   2.0802698e-02   1.0733745e-02   1.9041166e-02   3.1266982e-02   4.9760517e-03   1.3001310e-02   1.2292231e-02   2.6877167e-03   4.5798906e-03   2.6364594e-02   8.6153969e-03   1.7566530e-02   7.4744318e-03   2.8043210e-02   7.9969256e-03   3.5640074e-02   1.4109863e-02   1.9847472e-02   1.6098385e-02   3.9587699e-03   4.2468630e-03   1.4818700e-02   3.7268555e-03   2.3233798e-02   1.9851942e-02   1.4429507e-02   6.7117241e-03   1.3281147e-02   5.4664867e-03   1.4483311e-02   1.6079322e-02   1.4644608e-03   1.8793440e-02   2.6529941e-03   4.9386280e-03   7.8423223e-03   1.0293845e-02   1.1871124e-02   1.4064748e-02   3.3517168e-03   2.2145112e-03   1.1983758e-02   7.1285200e-04   4.9198989e-03   3.5944894e-03   3.6244119e-03   9.2640212e-03   2.3814700e-03   1.1959906e-02   6.6391160e-03   5.2659669e-03   3.4768199e-02   5.0225808e-03   3.6096256e-02   1.6893661e-02   1.0608435e-02   1.8369401e-02   2.1445998e-02   2.0588370e-02   2.3840862e-02   1.6945577e-02   2.2798129e-02   7.2320779e-03   4.5716975e-04   1.0311574e-02   5.8475513e-03   2.2922553e-02   2.2802937e-02   4.5367353e-03   8.9750660e-03   1.2721749e-02   4.2209187e-02   1.5508457e-02   6.9302761e-03   1.3261817e-02   2.4477020e-02   2.9037640e-03   8.2014592e-03   7.6405998e-03   1.0779902e-03   2.0077167e-03   2.0000571e-02   4.8259503e-03   1.2764273e-02   4.2375783e-03   2.1711543e-02   4.3575270e-03   2.7378197e-02   1.1026559e-02   1.3799894e-02   1.0731586e-02   1.6733633e-03   2.2875292e-03   1.0634216e-02   4.2659077e-03   1.6893661e-02   1.4117780e-02   9.8480141e-03   5.3491991e-03   1.0216132e-02   2.7977678e-03   9.4220767e-03   1.0761419e-02   1.4255275e-02   1.6372127e-03   2.8542706e-03   4.7214122e-03   1.3332443e-02   7.0444510e-03   6.5532524e-03   1.6174955e-03   6.7559932e-03   5.2389698e-03   5.3640347e-04   3.3171183e-03   5.1283913e-04   2.0296126e-03   6.0950963e-03   1.2744293e-04   5.0948120e-03   1.9318373e-03   2.3608728e-03   2.9089432e-02   1.4755776e-03   4.1865124e-02   2.2429622e-02   1.7100637e-02   2.2021240e-02   2.8022948e-02   2.8179896e-02   2.7393595e-02   2.2729266e-02   3.1385076e-02   1.0928177e-02   1.7748140e-03   1.6893502e-02   1.1535806e-02   3.1856326e-02   3.2502251e-02   8.7863970e-03   1.1670124e-02   1.3706425e-02   5.4822004e-02   2.3316700e-02   1.2494202e-02   1.7833364e-02   3.3214276e-02   7.9216177e-03   1.0562159e-02   1.0054198e-02   4.5572702e-03   2.8793276e-03   2.7614983e-02   7.5454514e-03   2.0103411e-02   3.8323098e-03   3.0272091e-02   5.9246169e-03   3.0771609e-02   1.9772265e-02   1.6666117e-02   1.2065056e-02   2.1106407e-03   6.8455106e-03   1.7918371e-02   1.0155544e-02   2.2429622e-02   1.9803941e-02   1.5812785e-02   1.2351590e-02   1.8630292e-02   6.7616623e-03   1.0713593e-02   1.1544341e-02   7.3852619e-03   4.6030790e-03   2.5842708e-03   5.4300453e-02   3.3576641e-02   1.0668428e-02   6.6015056e-03   2.1814225e-02   9.0913366e-03   1.2584515e-02   3.0243821e-02   1.4861127e-02   6.0467884e-03   1.7442631e-03   1.4568415e-02   1.1492675e-02   1.0173171e-02   5.0439803e-03   2.6472861e-03   7.4513739e-03   1.0326079e-01   7.0098941e-02   5.7127711e-02   7.0823391e-02   7.9250920e-02   7.7946311e-02   8.0298570e-02   7.0363352e-02   8.2049228e-02   4.8294128e-02   2.3708406e-02   5.6369153e-02   4.4949110e-02   8.2157728e-02   8.1370723e-02   4.1592461e-02   5.0974970e-02   5.5456655e-02   1.1462128e-01   6.7593968e-02   4.8172633e-02   6.2189094e-02   8.5184220e-02   3.4981615e-02   4.8742735e-02   4.7569879e-02   2.8345798e-02   2.9430788e-02   7.6817222e-02   4.1186102e-02   6.1732592e-02   3.2638549e-02   7.9961084e-02   3.8043139e-02   8.5993831e-02   5.4182844e-02   6.1100206e-02   5.2203816e-02   2.6988218e-02   3.3049806e-02   5.6579852e-02   2.5305632e-02   7.0098941e-02   6.4715083e-02   5.5458622e-02   3.7374533e-02   5.2731313e-02   3.5938214e-02   4.9377578e-02   5.1061578e-02   3.5870177e-04   1.3937749e-03   2.2192133e-02   1.4887667e-02   7.8001469e-03   8.8171759e-05   5.5216302e-03   5.9793748e-03   7.0276376e-04   9.5746848e-03   3.0437686e-03   8.2181914e-05   2.0068727e-03   2.2506604e-03   6.8090409e-03   3.1469229e-03   6.3301284e-04   1.8528100e-02   1.2625125e-03   5.6704255e-02   3.2399710e-02   2.3806821e-02   3.3394775e-02   3.8737297e-02   3.7833623e-02   4.0310184e-02   3.2556548e-02   4.0845247e-02   1.8140183e-02   4.6897646e-03   2.3353931e-02   1.6279158e-02   4.1004664e-02   4.0734447e-02   1.4064354e-02   2.0110135e-02   2.3937572e-02   6.5512797e-02   3.0871191e-02   1.8117892e-02   2.7110445e-02   4.3069544e-02   1.0732705e-02   1.8772743e-02   1.7996705e-02   7.0003565e-03   7.6876035e-03   3.7052349e-02   1.3928781e-02   2.6945955e-02   1.0128877e-02   3.9392715e-02   1.2368176e-02   4.4616010e-02   2.3284644e-02   2.6871325e-02   2.1527670e-02   6.5473767e-03   9.5899926e-03   2.3719212e-02   8.2529644e-03   3.2399710e-02   2.8696517e-02   2.2657048e-02   1.3399527e-02   2.2203050e-02   1.0884330e-02   1.9665180e-02   2.1074599e-02   3.3845415e-04   2.7555720e-02   1.6677843e-02   6.3795274e-03   1.8362843e-04   8.3039101e-03   4.7168779e-03   1.9845708e-03   1.2200549e-02   3.8746792e-03   1.0179352e-04   6.8781671e-04   3.2951534e-03   5.8068152e-03   2.8838183e-03   1.7929502e-04   1.4079350e-02   1.0261263e-03   6.5064614e-02   3.9139337e-02   2.9910766e-02   3.9801101e-02   4.6137717e-02   4.5316574e-02   4.7159535e-02   3.9352955e-02   4.8674767e-02   2.3254889e-02   7.4636086e-03   2.9417103e-02   2.1432655e-02   4.8877998e-02   4.8632496e-02   1.8795647e-02   2.5200016e-02   2.8886320e-02   7.5371106e-02   3.7782169e-02   2.3498806e-02   3.3236011e-02   5.1084684e-02   1.4998262e-02   2.3652548e-02   2.2813769e-02   1.0515841e-02   1.0877794e-02   4.4476659e-02   1.8379623e-02   3.3440220e-02   1.3262540e-02   4.7104689e-02   1.6362923e-02   5.1690239e-02   2.9302173e-02   3.2587374e-02   2.6378456e-02   9.4404077e-03   1.3645256e-02   2.9862026e-02   1.1376615e-02   3.9139337e-02   3.5158865e-02   2.8588131e-02   1.7920264e-02   2.8103943e-02   1.5132216e-02   2.4337714e-02   2.5719532e-02   3.3433714e-02   1.9092201e-02   5.6820829e-03   9.6311300e-04   1.1687721e-02   4.1741711e-03   3.9152052e-03   1.5429746e-02   5.3660274e-03   8.0766059e-04   9.2937667e-05   4.9943675e-03   5.5161799e-03   3.3131521e-03   4.2533013e-04   1.0435178e-02   1.4826896e-03   7.3827823e-02   4.6346021e-02   3.6506307e-02   4.6683572e-02   5.3981470e-02   5.3241058e-02   5.4467293e-02   4.6614647e-02   5.6933591e-02   2.8894083e-02   1.0839802e-02   3.5973376e-02   2.7110780e-02   5.7179243e-02   5.6957917e-02   2.4065468e-02   3.0813759e-02   3.4360438e-02   8.5582303e-02   4.5156230e-02   2.9396418e-02   3.9850269e-02   5.9522160e-02   1.9818286e-02   2.9063291e-02   2.8164144e-02   1.4610346e-02   1.4656069e-02   5.2344759e-02   2.3377306e-02   4.0412481e-02   1.6984268e-02   5.5250411e-02   2.0918953e-02   5.9213325e-02   3.5814189e-02   3.8804285e-02   3.1759139e-02   1.2931018e-02   1.8261938e-02   3.6495356e-02   1.5089913e-02   4.6346021e-02   4.2098942e-02   3.5016667e-02   2.2986158e-02   3.4503485e-02   1.9934983e-02   2.9546649e-02   3.0900707e-02   1.1335824e-02   3.2301226e-02   2.3277392e-02   1.5629192e-02   3.0795664e-02   1.5041716e-02   5.4315810e-03   1.4713782e-02   2.4451968e-02   3.6761202e-02   1.3762814e-02   2.8473446e-02   2.2472023e-02   2.6736705e-02   8.0230549e-02   2.3341323e-02   8.1067950e-03   1.4485807e-03   2.4486060e-03   1.1703837e-03   3.1310445e-03   3.9732842e-03   2.8350922e-03   1.6242765e-03   5.7101906e-03   4.5289508e-04   6.6077306e-03   2.6813364e-03   3.3571693e-03   6.2840633e-03   7.7260784e-03   2.0715363e-03   5.6385417e-05   8.9610646e-04   1.8073537e-02   3.9621048e-03   2.3604444e-03   4.7560860e-04   6.2480089e-03   5.8573026e-03   1.7069942e-04   2.3254450e-04   6.3902073e-03   3.8624324e-03   3.9083302e-03   1.0347438e-03   3.4531305e-03   3.5564063e-03   5.5040957e-03   1.4887365e-03   4.1720167e-03   8.6822743e-03   2.8448886e-04   5.1458480e-04   4.8536300e-03   5.8397245e-03   3.9827712e-03   1.8058791e-02   1.4485807e-03   1.2408841e-03   1.8448387e-03   1.0796845e-02   8.0405443e-03   3.4808504e-03   5.2754145e-04   8.8520211e-04   8.8923137e-03   1.4043268e-02   2.4126814e-02   9.1698320e-03   1.1327807e-02   1.9771649e-03   4.5360079e-03   1.5317882e-02   2.1762150e-02   5.6097757e-03   7.1877025e-03   6.8496039e-03   1.4100359e-02   5.3810596e-02   9.9629280e-03   3.1307769e-02   2.0553715e-02   2.1937453e-02   1.5991855e-02   2.5676129e-02   2.8613140e-02   1.8469501e-02   2.1322428e-02   3.3003652e-02   1.2471005e-02   8.9752587e-03   2.2249180e-02   1.9221338e-02   3.4330234e-02   3.7274155e-02   1.4283960e-02   1.0136722e-02   7.4549090e-03   5.7532344e-02   2.7732649e-02   1.8492242e-02   1.6393364e-02   3.4241314e-02   1.8497141e-02   9.1551303e-03   9.1767161e-03   1.4470512e-02   6.3039218e-03   2.8459911e-02   9.7413243e-03   2.5409718e-02   3.4719577e-03   3.2484401e-02   7.0164005e-03   2.0017467e-02   3.2249701e-02   1.2084843e-02   7.5073944e-03   5.8227226e-03   1.7146634e-02   2.5055287e-02   2.9865216e-02   2.0553715e-02   2.0008085e-02   1.9953689e-02   2.7764157e-02   3.0721044e-02   1.4086953e-02   7.0439235e-03   6.3871700e-03   6.2932024e-03   2.4881477e-02   1.2570656e-04   9.2318283e-03   1.1425023e-02   3.9781027e-03   6.8287051e-03   6.6316807e-03   5.1943433e-03   1.2253382e-04   1.3842125e-03   4.4535183e-03   2.1436401e-02   2.8241776e-03   6.8828353e-02   4.7091014e-02   4.2520568e-02   4.3241334e-02   5.5155458e-02   5.7042053e-02   4.8981701e-02   4.7857882e-02   6.2261278e-02   3.0649818e-02   1.4761608e-02   4.2406580e-02   3.4493935e-02   6.3340671e-02   6.5239814e-02   2.8920518e-02   2.9750953e-02   2.8851937e-02   9.4568410e-02   5.1830706e-02   3.5536784e-02   4.0198717e-02   6.4555077e-02   2.8697450e-02   2.7846993e-02   2.7347316e-02   2.1934395e-02   1.5675611e-02   5.6443004e-02   2.4878970e-02   4.7356921e-02   1.4503825e-02   6.0963940e-02   2.0840976e-02   5.2367097e-02   4.8672170e-02   3.5784762e-02   2.7656172e-02   1.3836981e-02   2.6623769e-02   4.4650658e-02   3.0852069e-02   4.7091014e-02   4.4370840e-02   4.0176310e-02   3.6600204e-02   4.6858384e-02   2.5835018e-02   2.6019603e-02   2.5994222e-02   6.9728196e-03   4.6608676e-03   9.9835054e-04   9.5223148e-03   2.6272609e-03   2.7884021e-05   1.5635547e-03   2.0372846e-03   5.4615556e-03   2.3300808e-03   2.5698617e-04   1.7457304e-02   7.2996870e-04   5.8453388e-02   3.4095678e-02   2.5737672e-02   3.4628989e-02   4.0687367e-02   4.0032201e-02   4.1519056e-02   3.4313166e-02   4.3287054e-02   1.9386832e-02   5.3532424e-03   2.5306754e-02   1.8013458e-02   4.3531307e-02   4.3448361e-02   1.5446633e-02   2.1111383e-02   2.4519102e-02   6.8935827e-02   3.3123525e-02   1.9821803e-02   2.8570801e-02   4.5547846e-02   1.2302601e-02   1.9692146e-02   1.8929129e-02   8.1934144e-03   8.2421848e-03   3.9256624e-02   1.4936345e-02   2.9083818e-02   1.0370393e-02   4.1828239e-02   1.3093356e-02   4.5785106e-02   2.5766235e-02   2.7913838e-02   2.2194996e-02   6.9953757e-03   1.1047300e-02   2.5843766e-02   1.0033677e-02   3.4095678e-02   3.0429687e-02   2.4458901e-02   1.5454278e-02   2.4603652e-02   1.2196519e-02   2.0322394e-02   2.1606954e-02   2.1763592e-02   3.8778874e-03   1.3140898e-02   1.0973585e-02   6.8570288e-03   1.2689294e-02   8.7227464e-03   2.2446768e-02   1.4768924e-02   9.8837253e-03   3.6594036e-02   1.1176832e-02   4.2371132e-02   2.0489598e-02   1.1322791e-02   2.4620431e-02   2.4482623e-02   2.2010230e-02   3.1108475e-02   2.0217050e-02   2.3141445e-02   1.0944826e-02   3.8599335e-03   1.0791452e-02   6.1542383e-03   2.2743482e-02   2.1333545e-02   6.5515291e-03   1.4388718e-02   2.0852825e-02   3.9383251e-02   1.5461941e-02   7.8878514e-03   1.7372104e-02   2.4911352e-02   2.6880230e-03   1.3798611e-02   1.3025794e-02   2.1193973e-03   6.9838956e-03   2.1270749e-02   8.9787629e-03   1.2743052e-02   1.1335890e-02   2.1877049e-02   9.6533919e-03   3.5351983e-02   7.6384883e-03   2.0107777e-02   1.8067074e-02   6.8413076e-03   2.4741061e-03   1.0039063e-02   3.4670280e-04   2.0489598e-02   1.6923143e-02   1.1154236e-02   2.1521967e-03   7.1850256e-03   4.3898059e-03   1.6491142e-02   1.8665860e-02   7.4245740e-03   1.0715228e-02   3.1685550e-03   5.1120383e-03   5.0451240e-03   4.1323270e-03   1.4489604e-04   8.1318290e-04   3.0839979e-03   1.9714350e-02   1.7947024e-03   6.7440625e-02   4.5128820e-02   3.9916292e-02   4.1909560e-02   5.3040678e-02   5.4550431e-02   4.7872699e-02   4.5818357e-02   5.9509133e-02   2.8778013e-02   1.2927960e-02   3.9749997e-02   3.1835574e-02   6.0466685e-02   6.2068316e-02   2.6673332e-02   2.8274822e-02   2.8015780e-02   9.1028220e-02   4.9020613e-02   3.3018114e-02   3.8378554e-02   6.1817956e-02   2.5959804e-02   2.6422336e-02   2.5876047e-02   1.9520884e-02   1.4184191e-02   5.3918305e-02   2.3137863e-02   4.4568283e-02   1.3507580e-02   5.8174666e-02   1.9385371e-02   5.1416653e-02   4.5132833e-02   3.4491897e-02   2.6637939e-02   1.2404699e-02   2.3988175e-02   4.1744067e-02   2.7329966e-02   4.5128820e-02   4.2235431e-02   3.7715182e-02   3.3171215e-02   4.3405180e-02   2.3512609e-02   2.4946638e-02   2.5117607e-02   5.7451096e-03   2.0181202e-03   1.1916495e-03   5.0056293e-03   1.1565469e-03   7.7131020e-03   3.5313465e-03   2.1072743e-03   2.6393551e-02   2.0670282e-03   4.4935473e-02   2.3639481e-02   1.6646699e-02   2.4503230e-02   2.9137719e-02   2.8488385e-02   3.0530237e-02   2.3788614e-02   3.1241308e-02   1.1731452e-02   1.7654569e-03   1.6307697e-02   1.0602623e-02   3.1457386e-02   3.1449229e-02   8.6094127e-03   1.3341698e-02   1.6740022e-02   5.3656632e-02   2.2705161e-02   1.1958802e-02   1.9130319e-02   3.3171817e-02   6.4720106e-03   1.2268562e-02   1.1633623e-02   3.5425115e-03   3.7925712e-03   2.7828397e-02   8.3873180e-03   1.9384549e-02   5.8220699e-03   3.0002594e-02   7.2263237e-03   3.4339797e-02   1.7195852e-02   1.8977924e-02   1.4659749e-02   3.0403500e-03   5.5430802e-03   1.6804744e-02   6.5028482e-03   2.3639481e-02   2.0526700e-02   1.5612876e-02   9.4514606e-03   1.6202837e-02   6.2323724e-03   1.3120120e-02   1.4374340e-02   2.8180986e-03   1.0509318e-02   1.7897176e-02   2.8798358e-03   9.1928702e-03   6.3970688e-03   1.0746267e-02   5.0496414e-02   7.7981540e-03   2.4751970e-02   1.2458649e-02   1.1686269e-02   1.0356316e-02   1.6774912e-02   1.8282513e-02   1.3498932e-02   1.2919728e-02   2.1579044e-02   5.2962835e-03   2.7725666e-03   1.1818152e-02   9.1091800e-03   2.2436834e-02   2.4265521e-02   5.8512682e-03   4.4398598e-03   4.1822455e-03   4.2435194e-02   1.6425553e-02   8.8184300e-03   9.0473617e-03   2.2804959e-02   8.4055012e-03   3.7245140e-03   3.5955501e-03   5.8501155e-03   1.2261597e-03   1.8027694e-02   3.2889908e-03   1.4332649e-02   2.5252408e-04   2.0964539e-02   1.7865385e-03   1.5552416e-02   1.8549588e-02   6.8429145e-03   3.5948443e-03   1.0694978e-03   7.5092190e-03   1.3665818e-02   1.7252830e-02   1.2458649e-02   1.1370103e-02   1.0296741e-02   1.5007456e-02   1.7383467e-02   5.5463863e-03   2.9922345e-03   3.0734531e-03   3.1960387e-03   6.8662451e-03   1.2966654e-04   2.7649067e-03   8.3427366e-04   2.7984284e-03   2.9822521e-02   1.2731780e-03   4.3416537e-02   2.4875338e-02   2.0714079e-02   2.3200351e-02   3.0852531e-02   3.1753284e-02   2.8200300e-02   2.5332686e-02   3.5512031e-02   1.2989773e-02   3.4785945e-03   2.0603808e-02   1.5135483e-02   3.6226615e-02   3.7456354e-02   1.1531484e-02   1.2959687e-02   1.3737739e-02   6.0763799e-02   2.7435536e-02   1.5849420e-02   1.9923216e-02   3.7336849e-02   1.1567919e-02   1.1725372e-02   1.1300051e-02   7.4803077e-03   3.9656480e-03   3.1244978e-02   9.2703065e-03   2.4126524e-02   3.9496417e-03   3.4455719e-02   7.0383738e-03   3.1302098e-02   2.5203523e-02   1.7680030e-02   1.2436482e-02   3.0466203e-03   1.0266971e-02   2.2126952e-02   1.5206492e-02   2.4875338e-02   2.2550174e-02   1.9125072e-02   1.7383181e-02   2.3878119e-02   9.5944653e-03   1.1168635e-02   1.1615557e-02   1.3151667e-03   2.5320521e-03   6.0366399e-03   2.7823080e-03   2.9364031e-04   1.6476106e-02   9.7247557e-04   6.0284770e-02   3.5334723e-02   2.6546579e-02   3.6095524e-02   4.1987790e-02   4.1172424e-02   4.3178382e-02   3.5527420e-02   4.4374359e-02   2.0339225e-02   5.8436205e-03   2.6082735e-02   1.8603485e-02   4.4570054e-02   4.4351810e-02   1.6144347e-02   2.2244142e-02   2.5921932e-02   7.0056396e-02   3.3998717e-02   2.0524111e-02   2.9752453e-02   4.6679420e-02   1.2673386e-02   2.0806267e-02   2.0008665e-02   8.5632030e-03   8.9793060e-03   4.0369526e-02   1.5814708e-02   2.9884891e-02   1.1327921e-02   4.2874486e-02   1.4012365e-02   4.7563178e-02   2.6115270e-02   2.9259206e-02   2.3493076e-02   7.6990791e-03   1.1423166e-02   2.6517929e-02   9.7961479e-03   3.5334723e-02   3.1531604e-02   2.5300172e-02   1.5549538e-02   2.4969819e-02   1.2759840e-02   2.1558690e-02   2.2929217e-02   6.4418336e-03   6.6136731e-03   4.4102106e-03   9.1481615e-04   8.6358065e-03   2.3009102e-03   7.8700864e-02   5.0063075e-02   3.9499858e-02   5.0635713e-02   5.7926279e-02   5.6986449e-02   5.8777354e-02   5.0310505e-02   6.0682610e-02   3.1865387e-02   1.2666075e-02   3.8913195e-02   2.9597893e-02   6.0871779e-02   6.0471723e-02   2.6606279e-02   3.4024273e-02   3.7905442e-02   8.9816272e-02   4.8416482e-02   3.2086335e-02   4.3354864e-02   6.3371751e-02   2.1811352e-02   3.2202223e-02   3.1242353e-02   1.6436605e-02   1.6909958e-02   5.6040246e-02   2.6101775e-02   4.3480802e-02   1.9524603e-02   5.8918015e-02   2.3597831e-02   6.3733101e-02   3.8161980e-02   4.2440703e-02   3.5140814e-02   1.5073633e-02   2.0215594e-02   3.9313992e-02   1.6000311e-02   5.0063075e-02   4.5569203e-02   3.8016354e-02   2.4659247e-02   3.6849168e-02   2.2186423e-02   3.2805330e-02   3.4269626e-02   3.8467105e-03   1.2875815e-03   2.5072619e-03   2.9525973e-02   1.2875815e-03   4.2282453e-02   2.3357390e-02   1.8646096e-02   2.2313442e-02   2.9124686e-02   2.9658732e-02   2.7480923e-02   2.3735668e-02   3.3135090e-02   1.1714292e-02   2.4574323e-03   1.8489812e-02   1.3106245e-02   3.3729170e-02   3.4672500e-02   9.9345371e-03   1.2062833e-02   1.3461486e-02   5.7431716e-02   2.5093254e-02   1.3932087e-02   1.8599958e-02   3.4955869e-02   9.5459229e-03   1.0897419e-02   1.0433767e-02   5.8375168e-03   3.2324242e-03   2.9124686e-02   8.1819777e-03   2.1845036e-02   3.6925062e-03   3.2054971e-02   6.2644754e-03   3.0710474e-02   2.2249402e-02   1.6897068e-02   1.1997033e-02   2.3970471e-03   8.3620725e-03   1.9766550e-02   1.2536577e-02   2.3357390e-02   2.0894448e-02   1.7210222e-02   1.4675128e-02   2.1017625e-02   7.9709601e-03   1.0694253e-02   1.1329979e-02   8.0862109e-04   3.9488260e-03   2.3216413e-02   2.2109950e-03   6.3313725e-02   4.2461361e-02   3.8219621e-02   3.8832114e-02   5.0144792e-02   5.1966249e-02   4.4333772e-02   4.3192281e-02   5.6977170e-02   2.6944997e-02   1.2389873e-02   3.8126276e-02   3.0729621e-02   5.8026007e-02   5.9897200e-02   2.5415278e-02   2.6079828e-02   2.5293603e-02   8.8103550e-02   4.7063061e-02   3.1649890e-02   3.5923563e-02   5.9166899e-02   2.5434205e-02   2.4297609e-02   2.3831192e-02   1.9112973e-02   1.3083158e-02   5.1398726e-02   2.1557413e-02   4.2826183e-02   1.1968109e-02   5.5744441e-02   1.7792619e-02   4.7600638e-02   4.4377594e-02   3.1768113e-02   2.4143930e-02   1.1416637e-02   2.3484839e-02   4.0313562e-02   2.8205265e-02   4.2461361e-02   3.9889484e-02   3.5980112e-02   3.3161057e-02   4.2633793e-02   2.2600989e-02   2.2605649e-02   2.2606045e-02   1.6651142e-03   2.2593118e-02   4.7494657e-04   5.5766903e-02   3.4735344e-02   2.9594132e-02   3.2557240e-02   4.1723024e-02   4.2746173e-02   3.8238608e-02   3.5278801e-02   4.7033204e-02   2.0363061e-02   7.2717611e-03   2.9420951e-02   2.2560431e-02   4.7813714e-02   4.9078515e-02   1.8314288e-02   2.0299319e-02   2.0869007e-02   7.5386883e-02   3.7549246e-02   2.3623644e-02   2.8844458e-02   4.9142563e-02   1.7633849e-02   1.8744071e-02   1.8222205e-02   1.2402012e-02   8.3988430e-03   4.2147698e-02   1.5629140e-02   3.3602383e-02   8.3018288e-03   4.5796447e-02   1.2702505e-02   4.1687026e-02   3.3943329e-02   2.5980350e-02   1.9415550e-02   7.0260502e-03   1.6012157e-02   3.1063717e-02   1.9520820e-02   3.4735344e-02   3.1983672e-02   2.7741891e-02   2.3833980e-02   3.2440091e-02   1.5637054e-02   1.7874227e-02   1.8281297e-02   1.4972117e-02   3.8328039e-04   6.3723448e-02   3.8719440e-02   3.0384566e-02   3.8629777e-02   4.5827446e-02   4.5472032e-02   4.5653244e-02   3.9023449e-02   4.9116846e-02   2.2930601e-02   7.4083466e-03   2.9962579e-02   2.2100137e-02   4.9469036e-02   4.9598054e-02   1.8997460e-02   2.4379661e-02   2.7279745e-02   7.6566902e-02   3.8413283e-02   2.3958684e-02   3.2715136e-02   5.1484761e-02   1.5886249e-02   2.2794916e-02   2.2023153e-02   1.1094162e-02   1.0331639e-02   4.4681292e-02   1.7978253e-02   3.4097516e-02   1.2099271e-02   4.7608429e-02   1.5662138e-02   4.9957613e-02   3.0977854e-02   3.1455087e-02   2.5013254e-02   8.8604244e-03   1.4432007e-02   3.0714741e-02   1.3426163e-02   3.8719440e-02   3.4992868e-02   2.8902863e-02   1.9656006e-02   2.9684992e-02   1.5494562e-02   2.3064694e-02   2.4203450e-02   1.8836956e-02   1.3755831e-01   9.8685385e-02   8.2425470e-02   1.0000651e-01   1.0925759e-01   1.0726669e-01   1.1120208e-01   9.8918033e-02   1.1167083e-01   7.2661493e-02   4.1665349e-02   8.1426911e-02   6.7501542e-02   1.1159988e-01   1.1014878e-01   6.3989575e-02   7.6224987e-02   8.1835804e-02   1.4773346e-01   9.4587815e-02   7.1696153e-02   8.9447560e-02   1.1534202e-01   5.4876111e-02   7.3538690e-02   7.2081812e-02   4.6952332e-02   4.9385723e-02   1.0589901e-01   6.4038977e-02   8.7644093e-02   5.3625558e-02   1.0917520e-01   6.0322002e-02   1.1787190e-01   7.6918821e-02   8.8499122e-02   7.7885622e-02   4.6255911e-02   5.2612368e-02   8.1239445e-02   4.0019052e-02   9.8685385e-02   9.2131722e-02   8.0633770e-02   5.6243805e-02   7.5363077e-02   5.6811044e-02   7.4440381e-02   7.6512320e-02   5.8097767e-02   3.5211195e-02   2.8463781e-02   3.4215950e-02   4.2147698e-02   4.2414656e-02   4.0542228e-02   3.5615822e-02   4.6295613e-02   2.0363061e-02   6.3798220e-03   2.8163995e-02   2.0925233e-02   4.6838114e-02   4.7487902e-02   1.7368541e-02   2.1117782e-02   2.2967145e-02   7.3810390e-02   3.6316652e-02   2.2375879e-02   2.9367287e-02   4.8511603e-02   1.5463833e-02   1.9583828e-02   1.8938570e-02   1.0601468e-02   8.3988430e-03   4.1723024e-02   1.5629140e-02   3.2244606e-02   9.3153170e-03   4.4933305e-02   1.3111918e-02   4.4412271e-02   3.0809608e-02   2.7438827e-02   2.1093197e-02   7.0260502e-03   1.3969417e-02   2.9313944e-02   1.5218585e-02   3.5211195e-02   3.1983672e-02   2.6841235e-02   2.0313092e-02   2.9439905e-02   1.4332974e-02   1.9364178e-02   2.0170126e-02   3.9924060e-03   1.0538198e-02   3.2148883e-03   2.7366019e-03   4.4621109e-03   1.7397347e-03   4.1425525e-03   5.2723146e-03   1.1136640e-02   2.9112354e-02   1.1160954e-02   1.6541883e-02   6.0336652e-03   8.3590571e-03   1.6026960e-02   9.4770245e-03   8.7523451e-03   9.5282841e-03   8.5487892e-03   1.3900105e-02   5.7309995e-03   4.7773544e-03   2.3853571e-02   1.0495078e-02   1.1045936e-02   2.7111420e-02   2.3076623e-02   4.8207470e-03   1.4681091e-02   1.0141190e-02   2.1316125e-02   5.8141126e-03   1.6474359e-02   1.3064397e-03   2.0347529e-02   5.7992324e-03   9.5368199e-03   2.5369333e-02   2.4565418e-02   1.2896533e-02   4.4389699e-02   3.9924060e-03   5.8442541e-03   1.0341765e-02   2.9771308e-02   2.0024906e-02   2.0168043e-02   1.0668382e-02   1.0461554e-02   1.6977050e-03   8.0038314e-04   3.2736649e-04   7.3247771e-04   1.7861084e-03   1.2199790e-05   1.6168506e-03   2.0903986e-03   1.2529506e-02   1.9650001e-03   4.3150624e-03   2.0139182e-03   3.1759995e-03   4.1258242e-03   2.0323215e-03   3.5878910e-03   9.4977361e-03   1.5488203e-03   3.0112961e-03   2.7909675e-04   1.8152664e-03   8.3701176e-03   2.5714996e-03   2.7148441e-03   1.0520423e-02   9.2964166e-03   7.5284963e-04   3.9888853e-03   1.8331853e-03   9.4586856e-03   1.6039412e-03   5.4889906e-03   2.8052973e-03   7.3341015e-03   1.2316222e-03   3.2601592e-03   1.0868316e-02   8.8162037e-03   2.9210959e-03   2.1963225e-02   0.0000000e+00   1.8230646e-04   1.5254865e-03   1.2273284e-02   6.9788794e-03   6.3577637e-03   3.5631537e-03   4.1101326e-03   4.2047124e-03   2.6033919e-03   1.7916004e-03   6.7524244e-03   1.5279872e-03   2.3303877e-03   1.3468412e-03   7.9573793e-03   9.8329441e-06   8.0754860e-04   2.3639655e-03   2.4986002e-03   1.3799583e-03   2.6729899e-03   6.2996248e-03   1.0853281e-02   4.8574547e-04   3.9201723e-04   1.4418237e-03   2.9002781e-03   3.0725233e-03   3.0407572e-03   2.9093497e-03   5.1175009e-03   6.6599859e-03   1.5926877e-03   2.5889139e-03   1.3713626e-04   8.5117654e-03   1.9829707e-03   4.3442759e-03   8.7298845e-03   2.1325966e-03   3.5994846e-03   5.1472858e-03   7.9423211e-03   3.5289513e-03   2.0294631e-04   1.1925423e-02   1.6977050e-03   7.8274456e-04   4.8500499e-05   4.9289073e-03   1.8879551e-03   2.5218165e-03   4.9495642e-03   6.1589498e-03   1.4775011e-03   2.8508338e-03   3.8437964e-04   1.0082748e-03   4.3870644e-03   2.7766403e-03   1.3317076e-02   4.6107743e-03   7.0365754e-03   5.0970174e-03   7.0294656e-03   5.8145812e-03   1.6991258e-03   1.6190058e-03   1.4192459e-02   4.5311136e-03   5.3518685e-03   7.5607221e-04   4.5347742e-03   1.1372343e-02   2.1219078e-03   2.3903563e-03   1.2745790e-02   9.1602079e-03   2.9606388e-03   4.3905218e-03   4.7897027e-03   8.0493172e-03   4.4779450e-03   5.1908739e-03   9.8295198e-04   1.2281083e-02   3.7969538e-04   1.7665186e-03   1.0605818e-02   1.1571194e-02   6.2101277e-03   2.7119271e-02   8.0038314e-04   1.4492761e-03   3.6743113e-03   1.7056692e-02   1.1710246e-02   8.2821554e-03   2.2240766e-03   2.2684005e-03   3.0380682e-04   2.0343287e-03   2.8037036e-04   8.3123377e-04   3.9939935e-03   1.6647447e-02   2.9061444e-03   6.1278767e-03   1.1769582e-03   2.2926522e-03   6.3717175e-03   3.9793414e-03   5.6921961e-03   6.6386310e-03   1.6577942e-03   4.6178179e-03   1.2108195e-03   8.4773320e-04   1.1017765e-02   4.7223063e-03   4.9236953e-03   1.3900771e-02   1.3046714e-02   3.7972280e-04   6.5335900e-03   2.3480655e-03   1.3286542e-02   9.3142474e-04   8.4820747e-03   2.8343361e-03   8.2403259e-03   2.5815546e-03   5.4537681e-03   1.4900562e-02   1.1670902e-02   3.7659184e-03   2.5593433e-02   3.2736649e-04   7.7091107e-04   2.6079554e-03   1.4611634e-02   8.0055625e-03   9.0564615e-03   5.9260895e-03   6.5055071e-03   3.8779943e-03   5.7015696e-04   1.7303569e-04   4.1690936e-03   1.6322670e-02   1.9974930e-03   5.0009825e-03   3.2570724e-04   9.5057293e-04   5.8304604e-03   4.8059418e-03   7.5457291e-03   5.1241997e-03   6.9111123e-04   3.7782470e-03   1.7092344e-03   2.5698914e-04   9.5453465e-03   5.5846827e-03   5.6938512e-03   1.2788699e-02   1.3393372e-02   7.3809633e-06   6.7682476e-03   1.3200598e-03   1.4442150e-02   1.8441195e-04   9.0822620e-03   4.9911804e-03   5.8437761e-03   3.8589879e-03   6.9829557e-03   1.5273413e-02   1.0318402e-02   2.4584659e-03   2.2525564e-02   7.3247771e-04   8.2385517e-04   1.9942911e-03   1.2041849e-02   5.7258386e-03   8.2738022e-03   7.3225251e-03   8.2204997e-03   2.0515682e-03   5.4510656e-03   5.2217407e-03   1.7964531e-02   7.2742632e-03   1.0588415e-02   6.2949332e-03   8.6345788e-03   9.1795241e-03   3.5876856e-03   2.6991302e-03   1.4376485e-02   6.5862079e-03   8.4804528e-03   2.1372463e-03   5.3927480e-03   1.5896874e-02   4.1394106e-03   4.5375167e-03   1.7523452e-02   1.2909742e-02   4.0941134e-03   7.2891356e-03   7.2227860e-03   1.1126344e-02   5.7124492e-03   8.1126160e-03   1.3907276e-04   1.6260954e-02   1.3854449e-03   3.2122771e-03   1.4553993e-02   1.6151019e-02   9.1578470e-03   3.3857588e-02   1.7861084e-03   2.9619943e-03   6.1829720e-03   2.2326762e-02   1.5680260e-02   1.2223630e-02   3.9245535e-03   3.7050303e-03   1.3686449e-03   2.1603250e-03   1.2649428e-02   1.7801502e-03   4.1458992e-03   1.7278919e-03   2.7991042e-03   4.0888611e-03   2.2218452e-03   3.9716339e-03   8.9665631e-03   1.3013529e-03   2.8806398e-03   3.4594790e-04   1.5677728e-03   8.1916354e-03   2.7802616e-03   2.9107124e-03   1.0452698e-02   9.5134829e-03   5.8171764e-04   4.1098444e-03   1.6001879e-03   9.8257537e-03   1.3468918e-03   5.7037585e-03   3.1132824e-03   6.8805675e-03   1.4645264e-03   3.5912866e-03   1.1107885e-02   8.6722521e-03   2.6587395e-03   2.1561220e-02   1.2199790e-05   1.4772036e-04   1.4023821e-03   1.1878859e-02   6.5538274e-03   6.3060622e-03   3.8811059e-03   4.4873121e-03   5.6719205e-03   1.8601099e-02   2.5037679e-03   5.8026549e-03   3.0990295e-05   3.8568498e-04   7.1301713e-03   6.6581271e-03   9.9891912e-03   3.5467136e-03   7.7986655e-04   4.6294369e-03   2.9226786e-03   3.3006174e-05   1.0560037e-02   7.5497742e-03   7.6393818e-03   1.4326258e-02   1.5841028e-02   1.7171643e-04   8.5994033e-03   1.5671556e-03   1.7334506e-02   1.9316046e-05   1.1306536e-02   6.6195881e-03   5.5794173e-03   5.6606012e-03   9.3044548e-03   1.7865075e-02   1.1490070e-02   2.7178516e-03   2.3185889e-02   1.6168506e-03   1.6521970e-03   2.7157547e-03   1.2355858e-02   5.5768992e-03   9.6617637e-03   9.6558503e-03   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1.1880076e-02   5.1539049e-03   9.7568917e-03   1.0422756e-02   1.1596876e-02   7.5663186e-03   8.6488322e-03   1.3133604e-02   3.0107568e-03   7.9406152e-04   4.7466095e-03   4.5711602e-03   4.9936224e-04   9.9296431e-03   9.5749791e-03   9.5587917e-03   1.4081306e-02   1.7234890e-02   8.7040364e-04   9.9040316e-03   1.5012448e-03   1.9639569e-02   3.0179394e-04   1.3010570e-02   1.0161281e-02   3.9519870e-03   8.1767554e-03   1.2080688e-02   1.9279439e-02   1.0989202e-02   2.3266303e-03   2.0713423e-02   3.1759995e-03   2.8067172e-03   3.1032715e-03   1.0490119e-02   4.0786420e-03   9.8110939e-03   1.2277454e-02   1.3709414e-02   1.7582839e-03   4.9489607e-03   1.9934064e-02   3.5016865e-03   3.4697267e-04   2.6310541e-03   8.0617166e-03   9.6411709e-04   1.7064375e-03   1.4666650e-03   1.4745772e-03   2.1108592e-03   5.5260764e-03   5.1802495e-04   2.3341578e-03   3.7167048e-03   6.5626516e-03   1.3180061e-03   1.1565092e-02   3.6658759e-03   3.8514458e-03   3.6514318e-03   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1.5052125e-02   6.1736712e-04   1.0280118e-04   5.5375454e-03   9.7589612e-03   8.6474768e-03   2.4375316e-02   3.5878910e-03   3.8390770e-03   5.3089764e-03   1.6859170e-02   1.4176552e-02   6.5576789e-03   2.5984028e-04   9.3320862e-05   6.7547274e-03   1.5238284e-02   1.2713534e-02   3.0890016e-03   2.3712664e-02   2.1340343e-02   2.1521507e-02   3.0005294e-02   3.3960619e-02   5.2290080e-03   2.3006673e-02   8.7125215e-03   3.6416136e-02   3.8281789e-03   2.7389250e-02   1.5157530e-02   1.2639929e-02   1.7411617e-02   2.3820503e-02   3.6850697e-02   2.5373970e-02   1.0602298e-02   3.7784525e-02   9.4977361e-03   1.0004799e-02   1.1952848e-02   2.3559319e-02   1.3109247e-02   2.3603108e-02   2.4562463e-02   2.6017612e-02   1.7241949e-03   2.0286689e-03   1.1335916e-03   5.6322483e-03   5.1221157e-03   5.0559971e-03   8.5835151e-03   1.0650923e-02   5.5566853e-04   5.1134826e-03   1.3892193e-04   1.2640034e-02   5.6438567e-04   7.4313522e-03   8.3161300e-03   2.5369950e-03   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1.9179880e-02   2.7909675e-04   2.2008347e-04   1.1064738e-03   1.0688407e-02   6.6082062e-03   4.4435997e-03   1.9606397e-03   2.4773484e-03   1.1763001e-02   8.2259536e-03   8.3480149e-03   1.5692475e-02   1.7083720e-02   2.8355914e-04   9.4960515e-03   2.0536401e-03   1.8469924e-02   1.0092056e-04   1.2279622e-02   6.4441301e-03   6.4046448e-03   6.0274458e-03   9.8857207e-03   1.9188640e-02   1.2736270e-02   3.3492132e-03   2.4941935e-02   1.8152664e-03   1.9865894e-03   3.3071796e-03   1.3641872e-02   6.4197769e-03   1.0769048e-02   1.0309787e-02   1.1341762e-02   5.1119032e-03   4.6662587e-03   4.6505160e-04   3.2269116e-03   9.0774431e-03   2.5215213e-03   4.0057628e-03   6.1199030e-03   9.7447895e-03   3.5360157e-03   1.8995080e-02   2.6805580e-03   8.6582433e-03   8.1342278e-03   3.7198152e-03   3.9443681e-05   2.6670326e-03   3.4016785e-03   8.3701176e-03   6.1426721e-03   2.9189037e-03   1.0083175e-03   2.2713681e-03   3.9595770e-04   7.2341855e-03   8.8447009e-03   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2.3397606e-03   3.5922701e-03   1.1208568e-02   3.9888853e-03   2.9455145e-03   1.9660659e-03   6.5467152e-03   6.1492489e-03   9.3538874e-04   1.2212079e-03   1.9267388e-03   1.0793365e-02   1.2592720e-03   6.0147390e-03   9.1609131e-03   1.8537817e-03   4.5335508e-03   6.6172179e-03   1.0131803e-02   4.6089934e-03   1.7595473e-04   1.2987364e-02   1.8331853e-03   9.7087402e-04   3.3609260e-04   5.4018686e-03   1.7068395e-03   3.6646912e-03   6.4787894e-03   7.7901480e-03   1.6754655e-02   6.9641544e-04   1.3182224e-02   1.4651385e-02   4.9466239e-03   2.3931163e-03   5.9263439e-04   5.4211666e-03   1.0221921e-02   1.4928620e-02   9.4586856e-03   8.3819492e-03   7.3339215e-03   1.2011676e-02   1.3620169e-02   3.6119007e-03   1.8435886e-03   2.0979826e-03   1.0794235e-02   6.9811950e-03   4.9473584e-03   5.5993500e-03   9.1192858e-03   1.7103671e-02   1.0654852e-02   2.2936354e-03   2.1887320e-02   1.6039412e-03   1.5236521e-03   2.3684718e-03   1.1405606e-02   4.9416620e-03   8.9601309e-03   9.4128890e-03   1.0537337e-02   1.0144176e-02   9.3650956e-03   2.8049928e-03   1.4261619e-03   9.6795720e-04   3.1673467e-03   5.6308712e-03   1.2399657e-02   5.4889906e-03   4.4629844e-03   3.5148873e-03   8.2921709e-03   8.5570702e-03   1.5767832e-03   9.7941910e-04   1.5044401e-03   1.9162648e-02   2.3258011e-03   4.3611697e-03   1.7154674e-02   1.9266334e-02   1.1399040e-02   3.8294804e-02   2.8052973e-03   4.2987486e-03   8.1194560e-03   2.5933333e-02   1.8564970e-02   1.4940871e-02   5.2230072e-03   4.8296564e-03   1.1136786e-02   1.2996602e-02   1.1896568e-02   3.3692870e-03   1.0295085e-03   6.7928621e-03   7.3341015e-03   5.3674586e-03   2.6380919e-03   1.7126363e-03   1.9252416e-05   3.9628066e-03   1.2371798e-02   1.4417093e-02   5.5916770e-04   7.0172680e-03   8.6736288e-03   5.5025710e-03   2.2796596e-02   1.2316222e-03   1.4793666e-03   2.9451077e-03   1.4303806e-02   1.0475492e-02   5.7470026e-03   7.8882742e-04   9.0526661e-04   4.3645694e-03   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5.1615257e-03   2.3326030e-03   2.1577255e-03   4.0325048e-03   5.1426622e-03   1.5351757e-03   2.6422594e-03   1.3282600e-02   1.5461999e-02   3.4307479e-03   1.1531055e-02   1.3518551e-02   4.2918744e-03   5.5398788e-03   8.4122900e-05
diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-correlation-ml.txt b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-correlation-ml.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2a17a2a8fb002493fff38c7ed059668867768a7e
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-correlation-ml.txt
@@ -0,0 +1 @@
+   9.2507465e-01   9.6528566e-01   8.7255441e-01   1.1287379e+00   8.7318727e-01   1.0767102e+00   9.1419676e-01   1.1503304e+00   9.8074509e-01   1.0135025e+00   1.0495025e+00   9.4794536e-01   9.6829273e-01   1.1345767e+00   1.1048008e+00   9.2407796e-01   1.0228634e+00   9.3853195e-01   9.9377619e-01   1.0407662e+00   9.5048989e-01   9.0465688e-01   9.8056930e-01   8.9777156e-01   9.6357127e-01   9.3864452e-01   9.9754613e-01   9.7271356e-01   8.4383151e-01   9.6981983e-01   9.7510267e-01   1.0112663e+00   7.8730400e-01   1.0299498e+00   9.9307979e-01   9.0239520e-01   8.5428231e-01   8.8972742e-01   8.5933162e-01   9.6625934e-01   9.4175449e-01   9.9120729e-01   1.0503963e+00   8.8223053e-01   1.3261434e+00   1.1063209e+00   8.4058398e-01   1.0844267e+00   1.1153093e+00   1.0092643e+00   8.9585237e-01   1.0599818e+00   1.2321707e+00   1.1359624e+00   8.3503556e-01   1.1792243e+00   7.9159781e-01   1.0830419e+00   1.2181870e+00   9.9888500e-01   1.0227144e+00   6.8557277e-01   9.6836193e-01   1.1061227e+00   1.0883453e+00   9.5681974e-01   9.9436299e-01   1.0304323e+00   1.1273949e+00   1.0735563e+00   1.0582583e+00   9.6040272e-01   1.0032137e+00   8.4900547e-01   1.1035351e+00   8.7867480e-01   9.6433176e-01   9.1850122e-01   8.9337435e-01   1.0449390e+00   8.9639384e-01   9.6704971e-01   1.0084258e+00   1.0528587e+00   1.1764481e+00   1.0913280e+00   1.0136672e+00   1.2737156e+00   9.5130359e-01   1.0367909e+00   1.1983402e+00   1.1319901e+00   1.1117462e+00   1.0343695e+00   1.0838628e+00   7.5266057e-01   1.0763316e+00   8.8067924e-01   9.6734383e-01   9.8800551e-01   1.2265742e+00   7.8833055e-01   1.0338670e+00   8.6666625e-01   9.9039950e-01   9.7142684e-01   9.3138616e-01   8.5849977e-01   8.5486301e-01   1.0516028e+00   1.1105313e+00   9.5943505e-01   9.8845171e-01   1.0566288e+00   9.9712198e-01   9.5545756e-01   1.1817974e+00   9.9128482e-01   1.0117892e+00   1.0979115e+00   1.0493943e+00   9.1318848e-01   9.3157311e-01   8.7073304e-01   1.2459441e+00   9.3412689e-01   1.0482297e+00   9.4224032e-01   9.5134153e-01   9.0857493e-01   9.7264161e-01   8.2900820e-01   9.3140549e-01   1.1330242e+00   1.0333002e+00   1.0117861e+00   1.2053255e+00   8.5291396e-01   1.0148928e+00   8.6641379e-01   9.7080819e-01   9.5457159e-01   9.5207457e-01   9.3539674e-01   9.0769069e-01   9.5322590e-01   1.1181803e+00   9.9765614e-01   7.5370610e-01   1.0807114e+00   1.0804601e+00   9.0214124e-01   8.7101998e-01   1.0167435e+00   1.2045936e+00   8.7300539e-01   1.1054300e+00   7.9145574e-01   1.0279340e+00   8.7623462e-01   1.0034756e+00   1.0386933e+00   9.3910970e-01   1.0028455e+00   9.9868824e-01   9.8752945e-01   9.8319327e-01   1.3110209e+00   8.6180633e-01   1.0993856e+00   8.5912563e-01   1.1303979e+00   9.8690459e-01   9.6910090e-01   9.1456819e-01   1.1525339e+00   1.1064552e+00   1.1062255e+00   9.7226683e-01   1.1091447e+00   1.1072238e+00   9.6544444e-01   9.6681036e-01   9.3247685e-01   9.6854634e-01   1.1035119e+00   1.1317148e+00   9.5557793e-01   9.8908485e-01   7.4873648e-01
diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-cosine-ml-iris.txt b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-cosine-ml-iris.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8b705b348fc3de5041ad9e3d6a1686af61046b2a
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-cosine-ml-iris.txt
@@ -0,0 +1 @@
+   1.4208365e-03   1.2652718e-05   8.9939315e-04   2.4232332e-04   9.9747033e-04   9.2045721e-04   2.2040648e-04   8.6480051e-04   1.2354911e-03   5.3650090e-06   1.0275886e-03   1.1695784e-03   2.3556571e-04   1.4590172e-03   1.8981327e-03   1.0939621e-03   1.2392314e-04   3.5850877e-04   8.6078038e-04   1.4490833e-03   8.4059347e-04   3.2873982e-03   2.7359832e-03   4.1316044e-03   2.7719149e-03   1.1814143e-03   1.1431285e-04   2.3850299e-04   1.3446247e-03   1.6406549e-03   1.2070654e-03   2.2241257e-03   1.4969348e-03   1.2354911e-03   7.6154552e-04   9.0853884e-04   1.2354911e-03   1.5825612e-04   2.3716586e-04   2.5806020e-04   8.5870759e-03   4.3447170e-04   2.6103416e-03   3.4026094e-03   1.2625429e-03   1.0000714e-03   2.7088099e-04   4.6161202e-05   1.7993015e-04   7.1619641e-02   7.4013940e-02   8.2336355e-02   9.3599031e-02   8.6542298e-02   9.2667602e-02   8.0934616e-02   6.7002415e-02   7.9695318e-02   8.3991107e-02   8.8330128e-02   7.6449243e-02   8.6123390e-02   9.1414445e-02   5.9767596e-02   6.8589764e-02   9.2363748e-02   7.5261304e-02   1.0768528e-01   7.8250149e-02   9.7383870e-02   6.9410330e-02   1.0895936e-01   9.1644587e-02   7.2677910e-02   7.2208930e-02   8.7635618e-02   9.3586395e-02   8.7700193e-02   5.8825053e-02   7.9271072e-02   7.4136423e-02   7.0977606e-02   1.1670751e-01   9.6691498e-02   7.7157266e-02   7.8793137e-02   9.6187418e-02   7.4355610e-02   8.6677009e-02   9.7286808e-02   8.5214421e-02   7.7419803e-02   6.8888638e-02   8.6192502e-02   7.4757686e-02   7.8851331e-02   7.5042247e-02   5.2484298e-02   7.8023694e-02   1.3991867e-01   1.2655756e-01   1.2099780e-01   1.2515784e-01   1.3134370e-01   1.3306336e-01   1.2911903e-01   1.2854613e-01   1.3655327e-01   1.1601604e-01   9.9632498e-02   1.2063863e-01   1.1404742e-01   1.3409335e-01   1.3451976e-01   1.1368563e-01   1.1469397e-01   1.1505768e-01   1.5479411e-01   1.2906390e-01   1.1634186e-01   1.2299625e-01   1.3892070e-01   1.0732534e-01   1.1401190e-01   1.1254699e-01   1.0266168e-01   1.0210743e-01   1.3111378e-01   1.0950615e-01   1.2501276e-01   1.0108759e-01   1.3297245e-01   1.0624129e-01   1.3360037e-01   1.2002867e-01   1.2233784e-01   1.1387071e-01   1.0061412e-01   1.0649150e-01   1.2174429e-01   1.0147290e-01   1.2655756e-01   1.2438709e-01   1.2138109e-01   1.1044406e-01   1.1910000e-01   1.0821359e-01   1.1609070e-01   1.1329724e-01   1.2085473e-03   1.2060695e-03   2.7592041e-03   3.0736184e-03   3.7201033e-03   1.0861043e-03   7.3910902e-04   3.4790667e-04   1.3491546e-03   2.4493052e-03   1.8482587e-04   2.3308566e-03   3.8997403e-03   6.3069928e-03   4.1362617e-03   1.5079538e-03   7.4890015e-04   4.0049414e-03   3.0763412e-04   3.2877725e-03   8.6909088e-03   1.8863199e-03   4.7592122e-03   4.5180751e-04   1.7148301e-03   8.8703626e-04   5.7128783e-04   1.7151033e-03   8.4814176e-04   4.7551630e-04   6.9313334e-03   5.8126778e-03   3.4790667e-04   9.7078221e-04   1.0390338e-03   3.4790667e-04   1.1371495e-03   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1.1385917e-01   1.0708423e-01   1.1221780e-01   1.1844388e-01   1.1798239e-01   1.1767648e-01   1.1356773e-01   1.2073038e-01   1.0467824e-01   8.8441784e-02   1.0671832e-01   1.0091826e-01   1.2051300e-01   1.2244533e-01   1.0247664e-01   1.0203920e-01   1.0334656e-01   1.3764340e-01   1.1314999e-01   1.0390175e-01   1.1148602e-01   1.2274267e-01   9.3929112e-02   1.0239198e-01   9.9372667e-02   9.0109024e-02   9.0770318e-02   1.1749345e-01   9.5509620e-02   1.0956056e-01   8.9331297e-02   1.1936188e-01   9.3207628e-02   1.1935153e-01   1.0516553e-01   1.1204585e-01   1.0191688e-01   8.9582588e-02   9.3806716e-02   1.0922100e-01   8.9087100e-02   1.1385917e-01   1.1193127e-01   1.0978099e-01   9.7766696e-02   1.0448839e-01   9.5849546e-02   1.0619992e-01   1.0212555e-01   7.8301662e-04   3.3186074e-04   9.6097551e-04   9.6384587e-04   1.7160230e-04   7.1714495e-04   1.0915291e-03   1.4406904e-05   9.9431295e-04   1.0280837e-03   3.4520010e-04   1.6070142e-03   2.0814960e-03   1.1810349e-03   9.3270090e-05   2.4892291e-04   9.5000112e-04   1.2447556e-03   8.3736374e-04   3.6303226e-03   2.4141846e-03   3.9965261e-03   2.4688022e-03   1.0115165e-03   6.9871786e-05   1.7487334e-04   1.2251185e-03   1.4398826e-03   9.8199498e-04   2.5137187e-03   1.7466742e-03   1.0915291e-03   7.0690363e-04   8.5846505e-04   1.0915291e-03   1.0992291e-04   1.6427013e-04   2.8562896e-04   8.0123750e-03   5.0490687e-04   2.4076078e-03   3.3222239e-03   1.0270492e-03   1.0987887e-03   2.4862356e-04   7.8815959e-05   1.1120052e-04   7.0071463e-02   7.2494258e-02   8.0694698e-02   9.1816479e-02   8.4823937e-02   9.1055284e-02   7.9406161e-02   6.5540015e-02   7.8075821e-02   8.2418924e-02   8.6586217e-02   7.4908999e-02   8.4375857e-02   8.9771433e-02   5.8365951e-02   6.7055640e-02   9.0792516e-02   7.3755504e-02   1.0570869e-01   7.6652799e-02   9.5758989e-02   6.7858347e-02   1.0707149e-01   9.0015148e-02   7.1111432e-02   7.0634591e-02   8.5909852e-02   9.1841705e-02   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1.3426257e-01   1.1013293e-01   9.8838972e-02   1.0496266e-01   1.1920082e-01   9.0400878e-02   9.6352086e-02   9.4617133e-02   8.6118226e-02   8.5443225e-02   1.1226469e-01   9.1815383e-02   1.0642172e-01   8.4132371e-02   1.1413570e-01   8.8823115e-02   1.1373227e-01   1.0228600e-01   1.0454965e-01   9.5917796e-02   8.4129252e-02   8.9732713e-02   1.0404039e-01   8.5714179e-02   1.0797760e-01   1.0611357e-01   1.0375975e-01   9.3828435e-02   1.0141953e-01   9.1231247e-02   9.8764813e-02   9.5558448e-02   7.0033377e-04   3.9650610e-04   5.3529876e-04   1.4703029e-03   2.2471049e-03   2.6137215e-04   9.1585095e-04   2.3098853e-03   3.2779352e-04   1.7003275e-03   9.5035099e-04   8.4163249e-04   3.6423601e-04   8.6760304e-04   2.6110376e-04   2.4965606e-03   5.0990123e-04   2.2208392e-03   3.4995017e-03   3.9813106e-03   4.2652650e-03   1.4776191e-03   5.3856223e-04   9.6152184e-04   1.6178695e-03   2.4296336e-03   2.2824176e-03   1.0483334e-03   6.6735604e-04   2.2471049e-03   1.7166964e-03   1.9224889e-03   2.2471049e-03   4.4953685e-04   7.5090712e-04   3.1050470e-04   1.1530910e-02   8.0837373e-05   2.6173161e-03   2.7612054e-03   2.3974656e-03   3.9140870e-04   3.5730731e-04   1.1232648e-04   8.0278741e-04   7.4728046e-02   7.6441141e-02   8.5477412e-02   9.7141382e-02   8.9947057e-02   9.5081677e-02   8.2962705e-02   6.9633999e-02   8.3013931e-02   8.6069979e-02   9.2215558e-02   7.8736928e-02   9.0603515e-02   9.4074986e-02   6.2034704e-02   7.1640320e-02   9.4150759e-02   7.8195110e-02   1.1214391e-01   8.1468219e-02   9.9059263e-02   7.2514318e-02   1.1269547e-01   9.4545020e-02   7.5842542e-02   7.5358360e-02   9.1332869e-02   9.6662705e-02   9.0277244e-02   6.2066860e-02   8.2644288e-02   7.7554694e-02   7.3959493e-02   1.1955630e-01   9.8181734e-02   7.8602674e-02   8.1755435e-02   1.0058819e-01   7.6248524e-02   8.9701900e-02   9.9938282e-02   8.7676596e-02   8.0619290e-02   7.1976555e-02   8.8793557e-02   7.6779152e-02   8.1107438e-02   7.7952944e-02   5.5245517e-02   8.0550459e-02   1.4162183e-01   1.2912349e-01   1.2423521e-01   1.2779447e-01   1.3393410e-01   1.3660889e-01   1.3105158e-01   1.3208577e-01   1.4040000e-01   1.1817736e-01   1.0200650e-01   1.2388995e-01   1.1706801e-01   1.3699958e-01   1.3682207e-01   1.1586916e-01   1.1739162e-01   1.1729454e-01   1.5902469e-01   1.3308573e-01   1.1901641e-01   1.2511327e-01   1.4289089e-01   1.1059070e-01   1.1627926e-01   1.1550831e-01   1.0561378e-01   1.0446495e-01   1.3405102e-01   1.1291439e-01   1.2888996e-01   1.0359625e-01   1.3590097e-01   1.0925250e-01   1.3665207e-01   1.2379539e-01   1.2392962e-01   1.1624448e-01   1.0286550e-01   1.0945264e-01   1.2440339e-01   1.0449561e-01   1.2912349e-01   1.2690130e-01   1.2362142e-01   1.1341467e-01   1.2276171e-01   1.1097585e-01   1.1759891e-01   1.1534218e-01   1.3143808e-04   7.3710840e-04   1.1313742e-03   2.6277162e-03   9.9332749e-04   4.8298989e-04   2.9659782e-03   1.8303797e-03   3.9657692e-03   1.4753738e-03   1.6266891e-03   7.0233916e-04   8.0313831e-04   3.4526160e-04   2.3291483e-03   1.3867759e-04   4.2228272e-03   1.6991343e-03   2.3223655e-03   3.8453210e-03   4.2904903e-04   9.9302567e-04   1.7706867e-03   9.4981017e-04   1.8259864e-03   2.0820613e-03   2.1473879e-03   2.0420431e-03   2.6277162e-03   3.0779094e-03   3.4332541e-03   2.6277162e-03   6.3280964e-04   1.0576914e-03   9.5198627e-04   1.0925795e-02   3.7286463e-04   7.9546610e-04   9.1841431e-04   2.1468126e-03   4.9129575e-04   4.3562197e-04   7.5083238e-04   1.3686608e-03   6.3901299e-02   6.4740623e-02   7.3708779e-02   8.4613714e-02   7.7866771e-02   8.2261058e-02   7.0449151e-02   5.8874682e-02   7.1767088e-02   7.3210535e-02   8.0660949e-02   6.6601983e-02   8.0033785e-02   8.1391959e-02   5.1369939e-02   6.0897790e-02   8.0716992e-02   6.7403323e-02   9.9203670e-02   7.0276809e-02   8.4922276e-02   6.1688045e-02   9.9339240e-02   8.2362360e-02   6.4928234e-02   6.4360101e-02   7.9641814e-02   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9.5169428e-02   1.0868349e-01   9.0278091e-02   1.1341836e-01   1.1118524e-01   1.0767597e-01   9.8555096e-02   1.0809822e-01   9.6490550e-02   1.0179914e-01   1.0040847e-01   9.0953179e-04   1.6478123e-03   3.1324421e-03   9.3747882e-04   6.8074049e-04   3.4285457e-03   1.4256139e-03   3.3141786e-03   8.1135619e-04   1.2040955e-03   7.3894006e-04   1.1469835e-03   5.4914496e-05   3.0238895e-03   1.1512346e-04   2.9874978e-03   2.7356591e-03   2.9755481e-03   4.8570629e-03   9.8132331e-04   1.1267736e-03   1.9187302e-03   1.4320892e-03   2.5472569e-03   2.7129147e-03   1.2621760e-03   1.1868918e-03   3.1324421e-03   3.1260816e-03   3.4622842e-03   3.1324421e-03   7.8737454e-04   1.2923124e-03   7.7291736e-04   1.2676988e-02   1.5795155e-04   1.4073300e-03   1.3093851e-03   2.8558230e-03   2.3589004e-04   5.3160641e-04   6.3306680e-04   1.5563919e-03   6.9394652e-02   7.0160248e-02   7.9549278e-02   9.0909253e-02   8.3929778e-02   8.8133516e-02   7.5949213e-02   6.4094635e-02   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1.1052596e-01   1.1587184e-01   1.3530738e-01   1.0320818e-01   1.0775506e-01   1.0806337e-01   9.8123191e-02   9.6541726e-02   1.2533326e-01   1.0616585e-01   1.2166800e-01   9.6181548e-02   1.2699662e-01   1.0216112e-01   1.2885603e-01   1.1626103e-01   1.1421827e-01   1.0807124e-01   9.4882428e-02   1.0171954e-01   1.1554226e-01   9.6763759e-02   1.2029572e-01   1.1801757e-01   1.1438908e-01   1.0525128e-01   1.1515210e-01   1.0301668e-01   1.0810316e-01   1.0676998e-01   2.4407151e-04   6.8243680e-04   1.6882982e-04   4.2217018e-04   8.1245396e-04   8.1915702e-04   2.7980568e-03   2.6783721e-03   2.0076713e-03   3.3526400e-04   9.3506008e-05   1.0407900e-03   7.3148476e-04   9.1895790e-04   4.8425923e-03   1.7878106e-03   2.5638304e-03   1.8092053e-03   6.2482332e-04   4.5470127e-05   3.8680919e-04   4.8577398e-04   7.0932539e-04   1.0773286e-03   2.7081281e-03   2.3916675e-03   6.8243680e-04   1.3234869e-03   1.5152295e-03   6.8243680e-04   1.7279927e-05   4.4719936e-05   7.6774714e-04   7.6386402e-03   5.1509749e-04   2.1386706e-03   2.3673979e-03   8.8641907e-04   8.8317423e-04   5.7646989e-05   1.8767975e-04   1.8238427e-04   6.4591491e-02   6.6891146e-02   7.4787553e-02   8.5653640e-02   7.8909235e-02   8.4481757e-02   7.3468926e-02   6.0165176e-02   7.2232139e-02   7.6459237e-02   8.0572670e-02   6.9287036e-02   7.8547451e-02   8.3338681e-02   5.3514192e-02   6.1787978e-02   8.4336540e-02   6.7840538e-02   9.9351761e-02   7.0839680e-02   8.9318727e-02   6.2598635e-02   1.0029777e-01   8.3444651e-02   6.5618944e-02   6.5228710e-02   7.9886645e-02   8.5622882e-02   7.9922508e-02   5.2526388e-02   7.1863670e-02   6.6948234e-02   6.3994975e-02   1.0763490e-01   8.8479248e-02   6.9931400e-02   7.1440370e-02   8.8224815e-02   6.7118281e-02   7.8968665e-02   8.8858891e-02   7.7432758e-02   7.0109240e-02   6.2023845e-02   7.8396402e-02   6.7393801e-02   7.1380489e-02   6.7813026e-02   4.6767795e-02   7.0645561e-02   1.3044475e-01   1.1734304e-01   1.1197394e-01   1.1577499e-01   1.2198760e-01   1.2346289e-01   1.1982320e-01   1.1899008e-01   1.2683842e-01   1.0736476e-01   9.1564623e-02   1.1164167e-01   1.0538958e-01   1.2475783e-01   1.2551509e-01   1.0524662e-01   1.0574315e-01   1.0607279e-01   1.4459461e-01   1.1962188e-01   1.0766800e-01   1.1407280e-01   1.2909426e-01   9.8905414e-02   1.0524346e-01   1.0359925e-01   9.4433579e-02   9.3820759e-02   1.2176744e-01   1.0065671e-01   1.1574436e-01   9.2625059e-02   1.2364363e-01   9.7538593e-02   1.2367543e-01   1.1121391e-01   1.1355049e-01   1.0493323e-01   9.2419908e-02   9.8167154e-02   1.1298864e-01   9.3668541e-02   1.1734304e-01   1.1533257e-01   1.1267510e-01   1.0222063e-01   1.1031800e-01   9.9779829e-02   1.0752614e-01   1.0448251e-01   3.8330702e-04   7.6710204e-04   5.4934344e-04   6.1141025e-04   1.8880070e-03   4.3782366e-03   4.2558302e-03   3.3445116e-03   9.0730658e-04   1.6460272e-04   1.9935351e-03   2.2277110e-04   1.5935452e-03   7.2001884e-03   1.0201171e-03   1.9163397e-03   8.7300929e-04   4.6754224e-04   3.6671499e-04   7.4258415e-04   2.1567602e-04   1.3361003e-04   9.1168360e-04   4.3156597e-03   4.1158943e-03   3.8330702e-04   1.9019978e-03   2.1146706e-03   3.8330702e-04   3.1982857e-04   2.1854146e-04   1.6719903e-03   5.9155088e-03   1.3110961e-03   2.0595508e-03   2.2774590e-03   5.2912957e-04   1.6598142e-03   4.0619000e-04   8.5702191e-04   4.6128261e-04   5.7335316e-02   5.9791552e-02   6.7034247e-02   7.7315388e-02   7.0912461e-02   7.6541197e-02   6.6231857e-02   5.3290914e-02   6.4524455e-02   6.9096848e-02   7.2330829e-02   6.2164647e-02   7.0266106e-02   7.5359485e-02   4.7211115e-02   5.4717217e-02   7.6724195e-02   6.0437574e-02   9.0217835e-02   6.3227153e-02   8.1624838e-02   5.5479636e-02   9.1272977e-02   7.5343817e-02   5.8299412e-02   5.7952393e-02   7.1727180e-02   7.7451339e-02   7.2165967e-02   4.5880845e-02   6.4164650e-02   5.9464600e-02   5.6817377e-02   9.8638775e-02   8.0838937e-02   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9.1224725e-02   9.9332091e-02   9.5993921e-02   1.1067957e-03   1.4791390e-03   7.1256747e-05   2.0377231e-03   4.3755431e-03   5.9630791e-03   4.4970379e-03   1.5921641e-03   6.4984761e-04   3.3935862e-03   1.2039709e-04   3.0970780e-03   8.3950153e-03   2.1890332e-03   3.1326528e-03   5.0256002e-04   1.6389584e-03   6.4717383e-04   7.1019942e-04   8.9864077e-04   3.8255378e-04   1.2286350e-03   5.5229901e-03   5.1766813e-03   0.0000000e+00   1.5860612e-03   1.6773969e-03   0.0000000e+00   8.4337656e-04   4.6746407e-04   2.4549978e-03   4.7529836e-03   2.3235808e-03   4.0683267e-03   4.3260986e-03   6.7336618e-04   2.8454658e-03   1.0918918e-03   1.3756658e-03   5.7784546e-04   5.9573290e-02   6.3070670e-02   6.9597309e-02   7.9911457e-02   7.3480528e-02   7.9923883e-02   7.0144874e-02   5.5923876e-02   6.6635620e-02   7.3192589e-02   7.4096565e-02   6.5836734e-02   7.1022277e-02   7.8555696e-02   5.0423423e-02   5.7089619e-02   8.1093473e-02   6.2483167e-02   9.2251714e-02   6.5399221e-02   8.6573432e-02   5.7873871e-02   9.3861710e-02   7.7914479e-02   6.0545459e-02   6.0328179e-02   7.3725736e-02   8.0652769e-02   7.5662466e-02   4.7500835e-02   6.6267157e-02   6.1219907e-02   5.9246920e-02   1.0235525e-01   8.5584812e-02   6.7627185e-02   6.6676399e-02   8.1028522e-02   6.3874534e-02   7.4037098e-02   8.3735875e-02   7.3091049e-02   6.4875922e-02   5.7134332e-02   7.3898502e-02   6.3669341e-02   6.7483654e-02   6.3032151e-02   4.3195391e-02   6.6465430e-02   1.2757303e-01   1.1294171e-01   1.0654531e-01   1.1074736e-01   1.1756538e-01   1.1705185e-01   1.1633100e-01   1.1230305e-01   1.1988948e-01   1.0404710e-01   8.7981667e-02   1.0622547e-01   1.0061669e-01   1.2008497e-01   1.2242153e-01   1.0217012e-01   1.0084187e-01   1.0181343e-01   1.3714147e-01   1.1243585e-01   1.0356517e-01   1.1071692e-01   1.2181923e-01   9.3742899e-02   1.0137566e-01   9.8085445e-02   8.9840814e-02   8.9979544e-02   1.1682155e-01   9.4340727e-02   1.0893096e-01   8.8036209e-02   1.1887723e-01   9.1995894e-02   1.1718099e-01   1.0529554e-01   1.1115622e-01   1.0048991e-01   8.8823715e-02   9.3647258e-02   1.0909883e-01   8.9729548e-02   1.1294171e-01   1.1121254e-01   1.0947844e-01   9.8164553e-02   1.0458423e-01   9.5468337e-02   1.0529433e-01   1.0077315e-01   9.3075268e-04   1.0661545e-03   2.6597529e-04   1.6036733e-03   2.0280056e-03   1.2436972e-03   1.5688801e-04   3.1850165e-04   8.9411637e-04   1.3235015e-03   8.8731482e-04   3.4816593e-03   2.6719247e-03   3.9091992e-03   2.6159373e-03   1.1443019e-03   7.9601608e-05   2.3028989e-04   1.2135551e-03   1.4956336e-03   1.2137749e-03   2.2449952e-03   1.5932074e-03   1.1067957e-03   8.0827056e-04   9.5525701e-04   1.1067957e-03   1.2520454e-04   1.8684214e-04   3.3283736e-04   8.4659292e-03   4.3428627e-04   2.6431662e-03   3.3043825e-03   1.2192723e-03   9.6672170e-04   2.2673224e-04   4.0165289e-05   1.5556464e-04   7.0885985e-02   7.3312749e-02   8.1555170e-02   9.2789394e-02   8.5768022e-02   9.1811327e-02   8.0210428e-02   6.6299983e-02   7.8898236e-02   8.3277528e-02   8.7497229e-02   7.5768419e-02   8.5268176e-02   9.0575828e-02   5.9182538e-02   6.7899308e-02   9.1577973e-02   7.4436351e-02   1.0683101e-01   7.7459472e-02   9.6638219e-02   6.8724317e-02   1.0805306e-01   9.0746123e-02   7.1944393e-02   7.1498544e-02   8.6811878e-02   9.2796163e-02   8.6929388e-02   5.8156140e-02   7.8485798e-02   7.3355880e-02   7.0259533e-02   1.1577796e-01   9.5890635e-02   7.6480264e-02   7.8047377e-02   9.5335392e-02   7.3634293e-02   8.5899063e-02   9.6384778e-02   8.4415996e-02   7.6657094e-02   6.8177250e-02   8.5395861e-02   7.3990972e-02   7.8093423e-02   7.4294151e-02   5.1950910e-02   7.7279181e-02   1.3907744e-01   1.2568112e-01   1.2011323e-01   1.2420710e-01   1.3046004e-01   1.3207399e-01   1.2824918e-01   1.2752552e-01   1.3553911e-01   1.1524115e-01   9.8893820e-02   1.1975932e-01   1.1323008e-01   1.3322963e-01   1.3377253e-01   1.1295596e-01   1.1379378e-01   1.1416138e-01   1.5374990e-01   1.2806482e-01   1.1555054e-01   1.2219358e-01   1.3787989e-01   1.0651347e-01   1.1318026e-01   1.1161431e-01   1.0188137e-01   1.0132199e-01   1.3022140e-01   1.0855236e-01   1.2404638e-01   1.0022528e-01   1.3210134e-01   1.0532767e-01   1.3250558e-01   1.1917979e-01   1.2157791e-01   1.1297631e-01   9.9847302e-02   1.0571550e-01   1.2097128e-01   1.0080768e-01   1.2568112e-01   1.2354605e-01   1.2062969e-01   1.0973133e-01   1.1825900e-01   1.0742526e-01   1.1535080e-01   1.1244756e-01   1.9470856e-03   1.8498175e-03   4.7714250e-03   2.8358661e-03   3.0255426e-03   1.1308587e-03   6.7035566e-04   9.3284570e-04   1.3935241e-03   9.8369983e-04   5.6854836e-03   1.9144361e-03   1.0961099e-03   2.6770659e-03   6.7637792e-04   7.3922961e-04   1.6168588e-03   1.9795771e-04   8.8027763e-04   2.3819907e-03   2.3199642e-03   2.7913184e-03   1.4791390e-03   3.2257382e-03   3.5250868e-03   1.4791390e-03   4.9791374e-04   7.0216560e-04   1.6800207e-03   1.0022835e-02   5.5855445e-04   1.9786373e-03   9.4684044e-04   1.9956071e-03   4.5593799e-04   2.5049818e-04   7.2992180e-04   1.1563910e-03   6.0779252e-02   6.2273308e-02   7.0462169e-02   8.1326510e-02   7.4767830e-02   7.8734546e-02   6.8077240e-02   5.6059538e-02   6.8181020e-02   7.1050105e-02   7.6799016e-02   6.4482663e-02   7.5580358e-02   7.7962233e-02   4.9642606e-02   5.8153068e-02   7.8105114e-02   6.3436311e-02   9.5564553e-02   6.6739850e-02   8.2930379e-02   5.9008492e-02   9.5418848e-02   7.8187143e-02   6.1832470e-02   6.1508833e-02   7.5927040e-02   8.0793818e-02   7.4771898e-02   4.9618073e-02   6.7927507e-02   6.3289271e-02   6.0099335e-02   1.0140473e-01   8.1745663e-02   6.4187383e-02   6.7135505e-02   8.4768567e-02   6.1827019e-02   7.4354928e-02   8.3103529e-02   7.2159743e-02   6.6094709e-02   5.8361788e-02   7.3251937e-02   6.2103535e-02   6.6220430e-02   6.3584868e-02   4.3971154e-02   6.5863068e-02   1.2260074e-01   1.1066837e-01   1.0619606e-01   1.0899833e-01   1.1518894e-01   1.1739848e-01   1.1240635e-01   1.1296742e-01   1.2096568e-01   1.0086214e-01   8.5896751e-02   1.0590639e-01   9.9771313e-02   1.1830710e-01   1.1878365e-01   9.8989344e-02   9.9484141e-02   9.9300506e-02   1.3860781e-01   1.1421784e-01   1.0167360e-01   1.0723785e-01   1.2323222e-01   9.3791376e-02   9.8729091e-02   9.7617417e-02   8.9196630e-02   8.7906597e-02   1.1533851e-01   9.5241683e-02   1.1037299e-01   8.6684313e-02   1.1722334e-01   9.1866320e-02   1.1676032e-01   1.0620321e-01   1.0631345e-01   9.8352717e-02   8.6492752e-02   9.2837846e-02   1.0689111e-01   8.8947496e-02   1.1066837e-01   1.0877202e-01   1.0619549e-01   9.7005210e-02   1.0523294e-01   9.4129616e-02   1.0043708e-01   9.7689504e-02   1.8508011e-03   3.7513322e-03   6.0039368e-03   4.2304138e-03   1.5191600e-03   7.2789043e-04   3.6236504e-03   2.5132214e-04   3.2740913e-03   8.1034702e-03   2.4941139e-03   4.0964229e-03   6.0206143e-04   1.9190323e-03   6.6472571e-04   5.1664338e-04   1.3616103e-03   7.0613265e-04   1.0312088e-03   5.8211090e-03   5.1401914e-03   7.1256747e-05   1.1045080e-03   1.1556192e-03   7.1256747e-05   9.3818356e-04   5.1597856e-04   2.2957469e-03   4.3308939e-03   2.5276111e-03   4.3800580e-03   5.1684770e-03   5.8668191e-04   3.2395561e-03   1.2942225e-03   1.4104695e-03   4.9075437e-04   6.2060492e-02   6.5820549e-02   7.2324527e-02   8.2688153e-02   7.6151035e-02   8.3216525e-02   7.3194172e-02   5.8477367e-02   6.9270609e-02   7.6249005e-02   7.6681852e-02   6.8643243e-02   7.3331578e-02   8.1706941e-02   5.2792718e-02   5.9477668e-02   8.4501232e-02   6.5244243e-02   9.4903309e-02   6.8042766e-02   9.0018791e-02   6.0245936e-02   9.6930604e-02   8.1064051e-02   6.3026851e-02   6.2769846e-02   7.6368221e-02   8.3589775e-02   7.8680956e-02   4.9590571e-02   6.8853459e-02   6.3691512e-02   6.1750809e-02   1.0592213e-01   8.9183264e-02   7.0750492e-02   6.9363027e-02   8.3535040e-02   6.6868103e-02   7.6873580e-02   8.7073732e-02   7.6162997e-02   6.7469442e-02   5.9546534e-02   7.6928171e-02   6.6694450e-02   7.0471384e-02   6.5682900e-02   4.5133798e-02   6.9312951e-02   1.3167296e-01   1.1664541e-01   1.0993682e-01   1.1453374e-01   1.2132631e-01   1.2063781e-01   1.2028602e-01   1.1588513e-01   1.2343288e-01   1.0759677e-01   9.1184353e-02   1.0959799e-01   1.0389171e-01   1.2371908e-01   1.2606621e-01   1.0559841e-01   1.0439417e-01   1.0553794e-01   1.4077951e-01   1.1579171e-01   1.0695513e-01   1.1441431e-01   1.2538100e-01   9.6825962e-02   1.0496558e-01   1.0155971e-01   9.2933277e-02   9.3305204e-02   1.2046243e-01   9.7626604e-02   1.1224568e-01   9.1421248e-02   1.2250398e-01   9.5336276e-02   1.2112681e-01   1.0839632e-01   1.1495562e-01   1.0414545e-01   9.2136906e-02   9.6777242e-02   1.1252211e-01   9.2559606e-02   1.1664541e-01   1.1484781e-01   1.1301462e-01   1.0121871e-01   1.0770332e-01   9.8720694e-02   1.0901533e-01   1.0446815e-01   7.8277898e-04   1.7490530e-03   1.0345024e-03   5.6185312e-04   1.1591486e-03   1.1405764e-03   2.5549089e-03   1.4484284e-03   2.2580494e-03   4.5713265e-03   5.6870335e-03   4.1902203e-03   2.4320876e-03   6.0369458e-04   6.2286369e-04   2.4521502e-03   2.9038905e-03   2.2436415e-03   1.7675525e-03   9.5896000e-04   2.0377231e-03   8.9090360e-04   9.7827632e-04   2.0377231e-03   7.4516940e-04   8.4824201e-04   4.3724648e-04   1.0582513e-02   7.1366344e-04   4.1221085e-03   4.7945036e-03   2.3833891e-03   1.3170043e-03   8.5049004e-04   2.9093352e-04   6.7142903e-04   7.9558936e-02   8.2158081e-02   9.0820201e-02   1.0264403e-01   9.5277746e-02   1.0150997e-01   8.9387659e-02   7.4718776e-02   8.7974881e-02   9.2637642e-02   9.6993873e-02   8.4761019e-02   9.4485044e-02   1.0025701e-01   6.7224195e-02   7.6433848e-02   1.0126400e-01   8.3185627e-02   1.1729605e-01   8.6461029e-02   1.0658954e-01   7.7314215e-02   1.1857784e-01   1.0034666e-01   8.0683042e-02   8.0237049e-02   9.6300382e-02   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1.5651711e-01   1.3335007e-01   1.4978001e-01   1.2432862e-01   1.5834992e-01   1.2988375e-01   1.6032290e-01   1.4373178e-01   1.4688056e-01   1.3840222e-01   1.2332107e-01   1.2926358e-01   1.4578293e-01   1.2292671e-01   1.5176730e-01   1.4922075e-01   1.4546636e-01   1.3299550e-01   1.4276363e-01   1.3134387e-01   1.4008961e-01   1.3766630e-01   5.7728358e-04   1.6620505e-03   3.0662753e-03   5.1693417e-04   6.0968463e-03   8.4744633e-04   8.7364721e-04   5.8106642e-03   6.7399476e-03   8.6083103e-03   3.1702748e-03   2.7104978e-03   3.3164143e-03   4.2509190e-03   5.8084215e-03   4.6709776e-03   9.8526568e-04   3.6786909e-04   5.9630791e-03   3.9566796e-03   4.2657824e-03   5.9630791e-03   2.3876668e-03   3.1383576e-03   1.0693622e-03   1.7187016e-02   9.8571152e-04   3.1367899e-03   3.7448988e-03   5.3108404e-03   1.2637202e-03   2.1359423e-03   1.6418787e-03   3.1352541e-03   8.3834616e-02   8.4243676e-02   9.4832859e-02   1.0703873e-01   9.9466934e-02   1.0403376e-01   9.0316788e-02   7.7914871e-02   9.2850027e-02   9.3299365e-02   1.0296391e-01   8.6082003e-02   1.0248600e-01   1.0318273e-01   6.8824902e-02   8.0299100e-02   1.0157055e-01   8.7955506e-02   1.2341155e-01   9.1142100e-02   1.0580332e-01   8.1173197e-02   1.2350931e-01   1.0460831e-01   8.4991511e-02   8.4254332e-02   1.0174542e-01   1.0573929e-01   9.8648070e-02   7.1061471e-02   9.2438015e-02   8.7508516e-02   8.2750270e-02   1.2928539e-01   1.0529438e-01   8.4835976e-02   9.0594121e-02   1.1204138e-01   8.3577196e-02   9.8754999e-02   1.0957368e-01   9.6258171e-02   8.9990776e-02   8.0898906e-02   9.7508458e-02   8.4744426e-02   8.9161769e-02   8.6853262e-02   6.2377571e-02   8.8830405e-02   1.4853162e-01   1.3772455e-01   1.3389458e-01   1.3729951e-01   1.4254710e-01   1.4753124e-01   1.3874272e-01   1.4343376e-01   1.5191156e-01   1.2542851e-01   1.0950060e-01   1.3351960e-01   1.2589032e-01   1.4575308e-01   1.4361388e-01   1.2273259e-01   1.2665814e-01   1.2593062e-01   1.7100462e-01   1.4482556e-01   1.2707776e-01   1.3245591e-01   1.5480441e-01   1.1982038e-01   1.2429326e-01   1.2550864e-01   1.1421155e-01   1.1236837e-01   1.4320023e-01   1.2379599e-01   1.4017288e-01   1.1252737e-01   1.4478118e-01   1.1925773e-01   1.4807486e-01   1.3379535e-01   1.3019772e-01   1.2505772e-01   1.1047444e-01   1.1793234e-01   1.3214851e-01   1.1203286e-01   1.3772455e-01   1.3511133e-01   1.3062456e-01   1.2117415e-01   1.3256036e-01   1.1928977e-01   1.2368263e-01   1.2328316e-01   7.8697050e-04   2.0732289e-03   9.4315564e-04   4.6001401e-03   8.4240364e-04   1.3015708e-03   4.6297460e-03   7.5292997e-03   6.5572401e-03   2.5566943e-03   1.7941741e-03   1.8226799e-03   3.9920133e-03   4.8070278e-03   2.6490734e-03   2.2737423e-03   8.3198965e-04   4.4970379e-03   1.8707122e-03   2.0801746e-03   4.4970379e-03   1.6864362e-03   2.1518496e-03   3.0908897e-04   1.2802000e-02   1.1444166e-03   2.7605116e-03   4.8428825e-03   3.3840997e-03   1.9469936e-03   1.7958172e-03   1.1565833e-03   1.8697862e-03   8.2127567e-02   8.3518119e-02   9.3314949e-02   1.0506408e-01   9.7541782e-02   1.0397584e-01   9.0341739e-02   7.6817337e-02   9.1083710e-02   9.3231274e-02   1.0048418e-01   8.5524503e-02   9.9112893e-02   1.0267345e-01   6.7846626e-02   7.8515797e-02   1.0225403e-01   8.6849217e-02   1.2022955e-01   8.9502113e-02   1.0655817e-01   7.9297559e-02   1.2165144e-01   1.0391861e-01   8.3203942e-02   8.2410584e-02   9.9528824e-02   1.0443382e-01   9.8019721e-02   6.8818975e-02   9.0543610e-02   8.5485551e-02   8.1186134e-02   1.2894588e-01   1.0651601e-01   8.5580315e-02   8.9213768e-02   1.0886353e-01   8.3754339e-02   9.7441118e-02   1.0932583e-01   9.5882843e-02   8.8282134e-02   7.9128322e-02   9.6917266e-02   8.4873719e-02   8.8927957e-02   8.5532654e-02   6.0384203e-02   8.8123284e-02   1.4980593e-01   1.3770759e-01   1.3282368e-01   1.3741111e-01   1.4254251e-01   1.4639384e-01   1.3970199e-01   1.4238069e-01   1.5040197e-01   1.2563911e-01   1.0916002e-01   1.3240724e-01   1.2489275e-01   1.4520334e-01   1.4360899e-01   1.2274102e-01   1.2644577e-01   1.2642535e-01   1.6908994e-01   1.4294672e-01   1.2654652e-01   1.3286867e-01   1.5320101e-01   1.1837980e-01   1.2451917e-01   1.2497748e-01   1.1312705e-01   1.1222677e-01   1.4268257e-01   1.2261254e-01   1.3839073e-01   1.1239899e-01   1.4421566e-01   1.1854547e-01   1.4805458e-01   1.3176737e-01   1.3127552e-01   1.2532607e-01   1.1042618e-01   1.1684289e-01   1.3160924e-01   1.1043724e-01   1.3770759e-01   1.3504379e-01   1.3066174e-01   1.1987723e-01   1.3066578e-01   1.1856367e-01   1.2478710e-01   1.2391087e-01   3.0983409e-04   7.5828890e-04   1.5917755e-03   4.8958816e-04   3.3744944e-03   2.1101097e-03   4.2400870e-03   2.8698866e-03   7.9583168e-04   2.4610899e-04   3.6436132e-04   1.4311801e-03   1.7294514e-03   8.6738167e-04   2.6111809e-03   1.6704106e-03   1.5921641e-03   8.6161593e-04   1.0547029e-03   1.5921641e-03   2.0427868e-04   3.5845705e-04   1.2194863e-04   8.2981219e-03   4.9180195e-04   1.7380522e-03   3.0734607e-03   1.0728608e-03   1.1397310e-03   3.4603128e-04   1.9200118e-04   2.8845040e-04   6.9779438e-02   7.1836392e-02   8.0319868e-02   9.1354890e-02   8.4353236e-02   9.0635736e-02   7.8599311e-02   6.5140986e-02   7.7899100e-02   8.1486701e-02   8.6472565e-02   7.4062042e-02   8.4619349e-02   8.9336326e-02   5.7575298e-02   6.6635212e-02   8.9946961e-02   7.3779929e-02   1.0532587e-01   7.6464940e-02   9.4587006e-02   6.7402630e-02   1.0673169e-01   8.9925800e-02   7.0797999e-02   7.0219100e-02   8.5721997e-02   9.1187854e-02   8.5377890e-02   5.7235173e-02   7.7431768e-02   7.2498793e-02   6.9063158e-02   1.1428266e-01   9.4218471e-02   7.4725647e-02   7.6703845e-02   9.4228329e-02   7.2261001e-02   8.4462132e-02   9.5360997e-02   8.3133678e-02   7.5506963e-02   6.7041127e-02   8.4070372e-02   7.2903149e-02   7.6784460e-02   7.3115143e-02   5.0413571e-02   7.5926129e-02   1.3636539e-01   1.2353657e-01   1.1821263e-01   1.2258303e-01   1.2822457e-01   1.3051322e-01   1.2599517e-01   1.2631512e-01   1.3406707e-01   1.1278003e-01   9.6722933e-02   1.1783731e-01   1.1110860e-01   1.3080317e-01   1.3063996e-01   1.1029647e-01   1.1216341e-01   1.1248813e-01   1.5199693e-01   1.2674108e-01   1.1318561e-01   1.1969790e-01   1.3653036e-01   1.0458853e-01   1.1112582e-01   1.1028100e-01   9.9890110e-02   9.9356661e-02   1.2805612e-01   1.0750038e-01   1.2261289e-01   9.8791075e-02   1.2975191e-01   1.0408196e-01   1.3162969e-01   1.1713290e-01   1.1886116e-01   1.1132823e-01   9.7814075e-02   1.0357451e-01   1.1833994e-01   9.8179977e-02   1.2353657e-01   1.2124412e-01   1.1787602e-01   1.0709455e-01   1.1618054e-01   1.0529428e-01   1.1269702e-01   1.1053049e-01   1.3650135e-03   5.3926014e-04   9.6875216e-04   5.5085642e-03   1.1951469e-03   2.8096772e-03   1.4033998e-03   3.8702395e-04   1.0970323e-04   3.3218009e-04   5.6326785e-04   5.8024795e-04   5.6723773e-04   3.5935032e-03   3.0059920e-03   6.4984761e-04   1.1677062e-03   1.3673782e-03   6.4984761e-04   7.6378345e-05   6.3488092e-05   8.1586688e-04   6.3954323e-03   8.4458294e-04   1.6959745e-03   2.5316364e-03   4.4648839e-04   1.3649198e-03   2.1646092e-04   4.0910219e-04   1.5323026e-04   6.2114649e-02   6.4461203e-02   7.2168083e-02   8.2712554e-02   7.6067484e-02   8.2127836e-02   7.1085856e-02   5.7869953e-02   6.9689694e-02   7.3941980e-02   7.7755077e-02   6.6772898e-02   7.5730146e-02   8.0858032e-02   5.1159438e-02   5.9263906e-02   8.1982206e-02   6.5662191e-02   9.5957099e-02   6.8346124e-02   8.6755825e-02   6.0017643e-02   9.7272303e-02   8.1103209e-02   6.3092478e-02   6.2637310e-02   7.7107544e-02   8.2765719e-02   7.7320565e-02   5.0179546e-02   6.9272103e-02   6.4477670e-02   6.1520691e-02   1.0482403e-01   8.6201836e-02   6.7723532e-02   6.8849001e-02   8.5128110e-02   6.4954612e-02   7.6260237e-02   8.6474261e-02   7.5037042e-02   6.7540885e-02   5.9554295e-02   7.5917230e-02   6.5334858e-02   6.9084098e-02   6.5352935e-02   4.4308417e-02   6.8222624e-02   1.2733314e-01   1.1424612e-01   1.0876932e-01   1.1294180e-01   1.1881213e-01   1.2027633e-01   1.1690957e-01   1.1601884e-01   1.2357066e-01   1.0430113e-01   8.8647048e-02   1.0842142e-01   1.0217893e-01   1.2134270e-01   1.2195833e-01   1.0207761e-01   1.0292571e-01   1.0341320e-01   1.4095409e-01   1.1639921e-01   1.0445121e-01   1.1097871e-01   1.2583780e-01   9.5736690e-02   1.0236688e-01   1.0085185e-01   9.1372067e-02   9.1009848e-02   1.1849408e-01   9.7905297e-02   1.1253291e-01   9.0050809e-02   1.2026601e-01   9.4848068e-02   1.2106318e-01   1.0772883e-01   1.1055160e-01   1.0223795e-01   8.9621067e-02   9.5003079e-02   1.0961118e-01   9.0242843e-02   1.1424612e-01   1.1217935e-01   1.0939970e-01   9.8767943e-02   1.0686010e-01   9.6691216e-02   1.0462140e-01   1.0177309e-01   3.4212913e-03   2.0350185e-04   2.2645835e-03   3.4346676e-03   3.6178579e-03   5.4115677e-03   1.4013939e-03   1.2010586e-03   1.9342083e-03   1.8303919e-03   3.0241355e-03   3.0182648e-03   8.7783530e-04   7.3200159e-04   3.3935862e-03   3.0016113e-03   3.3110105e-03   3.3935862e-03   9.0468402e-04   1.4291912e-03   6.5529771e-04   1.3482371e-02   1.1883350e-04   1.9129351e-03   1.8189821e-03   3.2224845e-03   2.2840556e-04   6.5009173e-04   5.8224397e-04   1.6275063e-03   7.3184911e-02   7.4026716e-02   8.3609924e-02   9.5240271e-02   8.8102740e-02   9.2390529e-02   7.9966102e-02   6.7767341e-02   8.1513618e-02   8.2938634e-02   9.0997666e-02   7.6011769e-02   9.0234918e-02   9.1578032e-02   5.9804069e-02   7.0034281e-02   9.0682677e-02   7.6686753e-02   1.1071727e-01   7.9918092e-02   9.5151478e-02   7.0899518e-02   1.1069472e-01   9.2509702e-02   7.4297007e-02   7.3732579e-02   8.9920224e-02   9.4250688e-02   8.7608739e-02   6.1121885e-02   8.1169501e-02   7.6375843e-02   7.2267735e-02   1.1652820e-01   9.4360734e-02   7.5150369e-02   7.9755441e-02   9.9609504e-02   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2.8709378e-03   9.0791333e-03   1.3407674e-03   2.7138923e-03   2.4677711e-04   1.1444972e-03   7.6121265e-04   8.8810957e-04   7.0009018e-04   1.4757411e-04   9.0393445e-04   6.0883361e-03   5.6961877e-03   1.2039709e-04   1.8816976e-03   2.0265121e-03   1.2039709e-04   8.6239061e-04   5.2686780e-04   2.5538294e-03   4.1367540e-03   2.4461852e-03   3.1968429e-03   3.7345867e-03   3.8813913e-04   2.9749715e-03   1.1153685e-03   1.5845430e-03   6.9221070e-04   5.5493017e-02   5.8687008e-02   6.5182775e-02   7.5153394e-02   6.8882837e-02   7.5289957e-02   6.5516107e-02   5.1904720e-02   6.2434251e-02   6.8395322e-02   6.9725101e-02   6.1264247e-02   6.7000659e-02   7.3915045e-02   4.6337454e-02   5.2993228e-02   7.6203506e-02   5.8574285e-02   8.7235787e-02   6.1228310e-02   8.1349394e-02   5.3727422e-02   8.8860415e-02   7.3529860e-02   5.6419133e-02   5.6136434e-02   6.9314277e-02   7.5768587e-02   7.0921131e-02   4.3887190e-02   6.2047408e-02   5.7247874e-02   5.5122668e-02   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1.1928692e-01   1.2425009e-01   1.1675840e-01   8.5744895e-02   1.0931412e-01   1.0376332e-01   9.9002718e-02   1.4971116e-01   1.2434000e-01   1.0215677e-01   1.0769100e-01   1.2998610e-01   1.0050022e-01   1.1660891e-01   1.2830083e-01   1.1408155e-01   1.0679553e-01   9.6866698e-02   1.1540492e-01   1.0158690e-01   1.0644304e-01   1.0354221e-01   7.6665035e-02   1.0598765e-01   1.7102185e-01   1.5912057e-01   1.5467066e-01   1.5843570e-01   1.6430112e-01   1.6898961e-01   1.6040927e-01   1.6442765e-01   1.7347908e-01   1.4613872e-01   1.2882261e-01   1.5426961e-01   1.4623773e-01   1.6767510e-01   1.6569930e-01   1.4326884e-01   1.4700928e-01   1.4639344e-01   1.9375995e-01   1.6572948e-01   1.4772209e-01   1.5370280e-01   1.7644069e-01   1.3951457e-01   1.4477511e-01   1.4552738e-01   1.3362833e-01   1.3186831e-01   1.6485780e-01   1.4332228e-01   1.6088049e-01   1.3176893e-01   1.6660706e-01   1.3873049e-01   1.6938110e-01   1.5434218e-01   1.5143663e-01   1.4540553e-01   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4.9289042e-02   4.8703396e-02   6.2029842e-02   6.6459215e-02   6.1626890e-02   3.8139914e-02   5.4977441e-02   5.0955269e-02   4.7810568e-02   8.6879401e-02   6.9864176e-02   5.2960539e-02   5.4195866e-02   6.9397405e-02   5.0805294e-02   6.0771100e-02   7.0699543e-02   5.9928918e-02   5.3277849e-02   4.6137567e-02   6.0647902e-02   5.1507184e-02   5.4535520e-02   5.1271651e-02   3.2182295e-02   5.3653922e-02   1.0655841e-01   9.4809862e-02   8.9943103e-02   9.4257768e-02   9.8930460e-02   1.0102907e-01   9.7318001e-02   9.7573045e-02   1.0420091e-01   8.5339961e-02   7.1237738e-02   8.9593643e-02   8.3615246e-02   1.0099568e-01   1.0093948e-01   8.3072610e-02   8.4968711e-02   8.5464008e-02   1.2001752e-01   9.7755169e-02   8.5475001e-02   9.1482164e-02   1.0648093e-01   7.7912530e-02   8.4002788e-02   8.3421922e-02   7.3855173e-02   7.3645673e-02   9.8656580e-02   8.1073912e-02   9.4018658e-02   7.3420060e-02   1.0008227e-01   7.8012093e-02   1.0282145e-01   8.8787179e-02   9.1014600e-02   8.4377747e-02   7.2315249e-02   7.7005472e-02   8.9946277e-02   7.2132565e-02   9.4809862e-02   9.2717682e-02   8.9711332e-02   7.9921256e-02   8.7947099e-02   7.8589830e-02   8.5634568e-02   8.3685774e-02   3.6322977e-03   2.1046334e-03   3.2662345e-03   4.7576391e-03   8.8436254e-04   1.6169936e-03   5.0909036e-03   5.3937261e-03   6.9592372e-03   3.1326528e-03   7.3963134e-03   7.8155750e-03   3.1326528e-03   2.8162695e-03   2.9888005e-03   5.3841195e-03   1.1640832e-02   3.1058623e-03   3.5268449e-03   8.9518404e-04   4.1579453e-03   2.4418843e-03   2.3174283e-03   3.5804624e-03   3.9289766e-03   4.8779386e-02   4.9807262e-02   5.7295117e-02   6.7429274e-02   6.1528729e-02   6.3805672e-02   5.4672352e-02   4.4305273e-02   5.5263563e-02   5.7527840e-02   6.3439356e-02   5.1886311e-02   6.2844358e-02   6.3392021e-02   3.9105833e-02   4.6659036e-02   6.3315061e-02   5.0431450e-02   8.1151197e-02   5.3901750e-02   6.8036856e-02   4.7518043e-02   7.9948453e-02   6.3397617e-02   4.9788208e-02   4.9648688e-02   6.2516012e-02   6.6678586e-02   6.0874148e-02   3.9322135e-02   5.5164136e-02   5.1029588e-02   4.8159012e-02   8.4641068e-02   6.6410487e-02   5.1100232e-02   5.4352465e-02   7.1152366e-02   4.8870866e-02   6.0790663e-02   6.7705030e-02   5.8185400e-02   5.3489810e-02   4.6729049e-02   5.9304859e-02   4.8888831e-02   5.2875044e-02   5.1050585e-02   3.4854587e-02   5.2844524e-02   1.0451993e-01   9.3506986e-02   8.9732041e-02   9.1442484e-02   9.7717353e-02   9.9707944e-02   9.4802947e-02   9.5351404e-02   1.0312713e-01   8.4850971e-02   7.1294232e-02   8.9511382e-02   8.4075688e-02   1.0102482e-01   1.0205801e-01   8.3487981e-02   8.2948462e-02   8.2499658e-02   1.1982484e-01   9.7067919e-02   8.5815629e-02   9.0584285e-02   1.0517734e-01   7.8728615e-02   8.2465362e-02   8.1175179e-02   7.4451161e-02   7.2780961e-02   9.8027119e-02   7.9186352e-02   9.3572539e-02   7.1178913e-02   9.9960717e-02   7.6001190e-02   9.8069469e-02   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5.7546133e-02   5.6993841e-02   7.1300530e-02   7.5820775e-02   7.0342915e-02   4.5615196e-02   6.3638314e-02   5.9296597e-02   5.5885275e-02   9.6910282e-02   7.8117499e-02   6.0390425e-02   6.2700176e-02   7.9484269e-02   5.8304382e-02   6.9718471e-02   7.9589842e-02   6.8316048e-02   6.1785991e-02   5.4151233e-02   6.9205713e-02   5.8981505e-02   6.2496988e-02   5.9482310e-02   3.9268283e-02   6.1808750e-02   1.1700097e-01   1.0528100e-01   1.0062122e-01   1.0448643e-01   1.0962576e-01   1.1218593e-01   1.0740486e-01   1.0838294e-01   1.1564442e-01   9.5242357e-02   8.0565058e-02   1.0027898e-01   9.3976493e-02   1.1211413e-01   1.1185843e-01   9.2981806e-02   9.4878465e-02   9.5039709e-02   1.3246555e-01   1.0898490e-01   9.5760022e-02   1.0161372e-01   1.1802422e-01   8.8109745e-02   9.3746381e-02   9.3301915e-02   8.3669649e-02   8.2970713e-02   1.0958444e-01   9.1015393e-02   1.0506496e-01   8.2570171e-02   1.1114727e-01   8.7646381e-02   1.1324005e-01   9.9872205e-02   1.0076379e-01   9.4009317e-02   8.1526386e-02   8.7041367e-02   1.0052094e-01   8.2193042e-02   1.0528100e-01   1.0314067e-01   9.9984788e-02   9.0308392e-02   9.8939123e-02   8.8538901e-02   9.5061969e-02   9.3157351e-02   1.7227462e-04   7.9314599e-04   8.9844173e-04   8.9518090e-04   2.8880348e-03   2.3244520e-03   6.4717383e-04   8.8327223e-04   1.0385020e-03   6.4717383e-04   4.2082433e-05   2.2535838e-05   6.1632160e-04   7.2421116e-03   6.3599645e-04   2.4204146e-03   3.0244507e-03   7.7555952e-04   1.1490838e-03   1.6721205e-04   1.6116507e-04   5.3985478e-05   6.6593275e-02   6.9140456e-02   7.6991415e-02   8.7909276e-02   8.1079796e-02   8.7140283e-02   7.5972851e-02   6.2229264e-02   7.4340995e-02   7.8983123e-02   8.2638003e-02   7.1602020e-02   8.0355120e-02   8.5886853e-02   5.5471847e-02   6.3724100e-02   8.7131187e-02   7.0026001e-02   1.0150375e-01   7.2956045e-02   9.2179245e-02   6.4526163e-02   1.0277569e-01   8.5954479e-02   6.7618774e-02   6.7207904e-02   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9.5167233e-02   1.0076949e-01   1.1586910e-01   9.6070623e-02   1.2040855e-01   1.1835687e-01   1.1566030e-01   1.0480317e-01   1.1289922e-01   1.0248125e-01   1.1065853e-01   1.0752770e-01   1.5518070e-03   1.3360426e-03   6.1855325e-04   3.8684575e-03   2.7981409e-03   7.1019942e-04   2.9249692e-04   3.8108588e-04   7.1019942e-04   3.4811331e-04   2.0628507e-04   6.8481588e-04   6.1413327e-03   1.2640084e-03   3.0810810e-03   4.5162171e-03   6.1490495e-04   2.0823475e-03   6.6391763e-04   4.5940617e-04   4.0824218e-05   6.8980444e-02   7.2049409e-02   7.9659630e-02   9.0518795e-02   8.3601945e-02   9.0707158e-02   7.9362725e-02   6.4838475e-02   7.6843708e-02   8.2367370e-02   8.4912050e-02   7.4621958e-02   8.2116380e-02   8.9210086e-02   5.7968714e-02   6.6009408e-02   9.1025554e-02   7.2793579e-02   1.0368926e-01   7.5498978e-02   9.6154006e-02   6.6776572e-02   1.0567953e-01   8.9202124e-02   6.9982422e-02   6.9528749e-02   8.4404562e-02   9.0968518e-02   8.5580442e-02   5.6059636e-02   7.6365493e-02   7.1188605e-02   6.8464233e-02   1.1430428e-01   9.5645657e-02   7.6165252e-02   7.6295454e-02   9.2254316e-02   7.2920975e-02   8.4113452e-02   9.5088632e-02   8.3209827e-02   7.4687466e-02   6.6271074e-02   8.4049660e-02   7.3195324e-02   7.7054222e-02   7.2597553e-02   5.0198701e-02   7.5958466e-02   1.3864088e-01   1.2443023e-01   1.1820696e-01   1.2296103e-01   1.2918980e-01   1.2996108e-01   1.2761885e-01   1.2545185e-01   1.3315049e-01   1.1429516e-01   9.7708479e-02   1.1783417e-01   1.1147502e-01   1.3162480e-01   1.3265015e-01   1.1194384e-01   1.1244164e-01   1.1326233e-01   1.5100180e-01   1.2549100e-01   1.1411167e-01   1.2131599e-01   1.3539430e-01   1.0451333e-01   1.1218678e-01   1.1003412e-01   1.0016268e-01   1.0019858e-01   1.2861591e-01   1.0655136e-01   1.2158527e-01   9.9029274e-02   1.3048234e-01   1.0368193e-01   1.3098775e-01   1.1671318e-01   1.2117898e-01   1.1194010e-01   9.8811276e-02   1.0398171e-01   1.1952683e-01   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9.5419957e-02   7.7143847e-02   6.0075763e-02   6.1882505e-02   7.8193894e-02   5.7405077e-02   6.8884889e-02   7.7590521e-02   6.7073564e-02   6.0698980e-02   5.3256477e-02   6.8055547e-02   5.7544133e-02   6.1428351e-02   5.8436070e-02   3.9618229e-02   6.0914936e-02   1.1719371e-01   1.0478727e-01   9.9928933e-02   1.0301520e-01   1.0921839e-01   1.1065431e-01   1.0694189e-01   1.0626748e-01   1.1395294e-01   9.5522682e-02   8.0692317e-02   9.9640584e-02   9.3821909e-02   1.1210560e-01   1.1313776e-01   9.3722341e-02   9.3659306e-02   9.3792773e-02   1.3107147e-01   1.0721381e-01   9.5955259e-02   1.0180084e-01   1.1608360e-01   8.7786080e-02   9.3279943e-02   9.1618132e-02   8.3505928e-02   8.2622852e-02   1.0912386e-01   8.8978076e-02   1.0355009e-01   8.1236966e-02   1.1101306e-01   8.5950464e-02   1.1026035e-01   9.9640402e-02   1.0131013e-01   9.2768985e-02   8.1325904e-02   8.7087186e-02   1.0113076e-01   8.3368795e-02   1.0478727e-01   1.0299507e-01   1.0075649e-01   9.1267488e-02   9.8760345e-02   8.8473047e-02   9.5602739e-02   9.2388034e-02   1.3192990e-03   5.6049942e-03   5.6260410e-03   3.8255378e-04   2.7098321e-03   2.9260165e-03   3.8255378e-04   8.5873923e-04   6.4551657e-04   2.7466704e-03   5.2436473e-03   2.1741200e-03   2.6488612e-03   2.5599967e-03   7.2546074e-04   2.4454411e-03   9.4817109e-04   1.6251073e-03   9.8969141e-04   5.2867682e-02   5.5519966e-02   6.2241614e-02   7.2187515e-02   6.6023504e-02   7.1524895e-02   6.1872329e-02   4.9090525e-02   5.9694897e-02   6.4712456e-02   6.7154795e-02   5.7947928e-02   6.4972194e-02   7.0357979e-02   4.3573654e-02   5.0441816e-02   7.2068579e-02   5.5680796e-02   8.4591184e-02   5.8459303e-02   7.7051055e-02   5.1193288e-02   8.5601942e-02   7.0117829e-02   5.3803216e-02   5.3535941e-02   6.6621467e-02   7.2473708e-02   6.7439009e-02   4.1816308e-02   5.9366143e-02   5.4760331e-02   5.2431175e-02   9.2978431e-02   7.6152091e-02   5.9131458e-02   5.9321453e-02   7.4096463e-02   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3.2948907e-03   2.1817756e-03   1.9232390e-02   1.0060949e-03   5.2893888e-03   3.6565664e-03   6.4838776e-03   7.5722530e-04   2.1347736e-03   1.7405562e-03   3.5508478e-03   8.4906111e-02   8.5684875e-02   9.5941240e-02   1.0863973e-01   1.0110388e-01   1.0421406e-01   9.1634377e-02   7.8911086e-02   9.3575504e-02   9.5023267e-02   1.0394314e-01   8.7940160e-02   1.0307352e-01   1.0372095e-01   7.0927620e-02   8.1814584e-02   1.0248405e-01   8.7682138e-02   1.2553590e-01   9.1822634e-02   1.0758552e-01   8.2848043e-02   1.2459059e-01   1.0427303e-01   8.6172494e-02   8.5771372e-02   1.0276107e-01   1.0743739e-01   1.0000507e-01   7.2180344e-02   9.3352407e-02   8.8118179e-02   8.3972299e-02   1.2999219e-01   1.0601815e-01   8.6245777e-02   9.1942699e-02   1.1341937e-01   8.4389659e-02   1.0016617e-01   1.0942619e-01   9.6927434e-02   9.1068024e-02   8.2112078e-02   9.8354950e-02   8.4918144e-02   8.9929197e-02   8.7860129e-02   6.4913483e-02   8.9916257e-02   1.5108513e-01   1.3966025e-01   1.3579363e-01   1.3800221e-01   1.4462965e-01   1.4853849e-01   1.4049017e-01   1.4366186e-01   1.5284247e-01   1.2813521e-01   1.1198929e-01   1.3549048e-01   1.2835377e-01   1.4847864e-01   1.4775011e-01   1.2601872e-01   1.2764409e-01   1.2670935e-01   1.7255531e-01   1.4567287e-01   1.2987249e-01   1.3506836e-01   1.5547286e-01   1.2211481e-01   1.2607603e-01   1.2598262e-01   1.1656479e-01   1.1426125e-01   1.4534374e-01   1.2395854e-01   1.4127350e-01   1.1320894e-01   1.4734853e-01   1.1969377e-01   1.4703899e-01   1.3646872e-01   1.3305975e-01   1.2588961e-01   1.1250545e-01   1.2058130e-01   1.3549735e-01   1.1610735e-01   1.3966025e-01   1.3745925e-01   1.3401818e-01   1.2501338e-01   1.3525796e-01   1.2173379e-01   1.2646805e-01   1.2458940e-01   5.1766813e-03   3.3038909e-03   3.5089109e-03   5.1766813e-03   2.1988415e-03   2.7782772e-03   1.0688451e-03   1.7030893e-02   8.9726872e-04   4.6231995e-03   4.6736672e-03   5.3382818e-03   1.1647725e-03   1.9758755e-03   1.2750935e-03   2.7128598e-03   8.7833448e-02   8.9010914e-02   9.9253982e-02   1.1183035e-01   1.0412107e-01   1.0885582e-01   9.5547284e-02   8.2028755e-02   9.6837094e-02   9.8811318e-02   1.0697473e-01   9.1242752e-02   1.0570232e-01   1.0798221e-01   7.3423587e-02   8.4439842e-02   1.0715501e-01   9.1521191e-02   1.2824419e-01   9.5124610e-02   1.1205287e-01   8.5389026e-02   1.2841576e-01   1.0878552e-01   8.9048303e-02   8.8474213e-02   1.0589810e-01   1.1091852e-01   1.0379001e-01   7.4413565e-02   9.6465402e-02   9.1132676e-02   8.6893608e-02   1.3487393e-01   1.1110410e-01   9.0320856e-02   9.5130800e-02   1.1613190e-01   8.8387927e-02   1.0357744e-01   1.1422195e-01   1.0103671e-01   9.4160592e-02   8.4870839e-02   1.0232030e-01   8.9160088e-02   9.3889889e-02   9.1104413e-02   6.6493231e-02   9.3508454e-02   1.5639991e-01   1.4440871e-01   1.3995325e-01   1.4327783e-01   1.4942424e-01   1.5327636e-01   1.4579380e-01   1.4864466e-01   1.5749945e-01   1.3242397e-01   1.1574188e-01   1.3959357e-01   1.3216131e-01   1.5281767e-01   1.5172347e-01   1.2991524e-01   1.3242882e-01   1.3190251e-01   1.7712896e-01   1.5002220e-01   1.3380600e-01   1.3964037e-01   1.6023126e-01   1.2562692e-01   1.3071698e-01   1.3077115e-01   1.2010966e-01   1.1841338e-01   1.4987755e-01   1.2848062e-01   1.4548859e-01   1.1783301e-01   1.5172346e-01   1.2426441e-01   1.5309487e-01   1.3983154e-01   1.3778354e-01   1.3093423e-01   1.1660453e-01   1.2409289e-01   1.3931059e-01   1.1865130e-01   1.4440871e-01   1.4196632e-01   1.3805465e-01   1.2801436e-01   1.3865562e-01   1.2553921e-01   1.3109454e-01   1.2958547e-01   1.5860612e-03   1.6773969e-03   0.0000000e+00   8.4337656e-04   4.6746407e-04   2.4549978e-03   4.7529836e-03   2.3235808e-03   4.0683267e-03   4.3260986e-03   6.7336618e-04   2.8454658e-03   1.0918918e-03   1.3756658e-03   5.7784546e-04   5.9573290e-02   6.3070670e-02   6.9597309e-02   7.9911457e-02   7.3480528e-02   7.9923883e-02   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1.3714147e-01   1.1243585e-01   1.0356517e-01   1.1071692e-01   1.2181923e-01   9.3742899e-02   1.0137566e-01   9.8085445e-02   8.9840814e-02   8.9979544e-02   1.1682155e-01   9.4340727e-02   1.0893096e-01   8.8036209e-02   1.1887723e-01   9.1995894e-02   1.1718099e-01   1.0529554e-01   1.1115622e-01   1.0048991e-01   8.8823715e-02   9.3647258e-02   1.0909883e-01   8.9729548e-02   1.1294171e-01   1.1121254e-01   1.0947844e-01   9.8164553e-02   1.0458423e-01   9.5468337e-02   1.0529433e-01   1.0077315e-01   1.0959804e-05   1.5860612e-03   1.2066237e-03   9.8801305e-04   9.8752232e-04   6.0992006e-03   2.3026455e-03   4.3295194e-03   6.8464966e-03   1.1467011e-03   3.5017117e-03   1.7326793e-03   1.1803657e-03   5.4725577e-04   7.4912594e-02   7.8462634e-02   8.6080465e-02   9.7055695e-02   8.9913940e-02   9.8246196e-02   8.6359614e-02   7.0875411e-02   8.3096610e-02   8.9373603e-02   9.1095332e-02   8.1132274e-02   8.7784959e-02   9.6471287e-02   6.3584445e-02   7.1727351e-02   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1.3685139e-01   1.1414077e-01   1.2924282e-01   1.0675126e-01   1.3867943e-01   1.1135088e-01   1.3991357e-01   1.2389778e-01   1.2963231e-01   1.2019755e-01   1.0634263e-01   1.1117491e-01   1.2727853e-01   1.0546335e-01   1.3277361e-01   1.3050496e-01   1.2753116e-01   1.1493738e-01   1.2310368e-01   1.1333277e-01   1.2330887e-01   1.1999903e-01   1.6773969e-03   1.4044930e-03   1.1476188e-03   1.1728210e-03   6.0850239e-03   2.5611449e-03   4.7720148e-03   7.3487783e-03   1.2981958e-03   3.8044610e-03   1.9624179e-03   1.3573639e-03   6.7050163e-04   7.5875383e-02   7.9591742e-02   8.7130965e-02   9.8136915e-02   9.0968214e-02   9.9474916e-02   8.7612410e-02   7.1886206e-02   8.4072967e-02   9.0657173e-02   9.2037661e-02   8.2322796e-02   8.8559519e-02   9.7661149e-02   6.4636714e-02   7.2692172e-02   1.0010765e-01   8.0266168e-02   1.1103798e-01   8.2745924e-02   1.0537406e-01   7.3430328e-02   1.1396572e-01   9.7599809e-02   7.6869874e-02   7.6340270e-02   9.1668858e-02   9.8974404e-02   9.3760611e-02   6.2005453e-02   8.3489209e-02   7.8020463e-02   7.5407355e-02   1.2375637e-01   1.0517097e-01   8.4594299e-02   8.3682974e-02   9.9214366e-02   8.1008204e-02   9.1862911e-02   1.0394615e-01   9.1478420e-02   8.1837398e-02   7.2994499e-02   9.2227696e-02   8.1322109e-02   8.5126430e-02   7.9879628e-02   5.5860810e-02   8.3714500e-02   1.4946173e-01   1.3427629e-01   1.2730802e-01   1.3293539e-01   1.3918009e-01   1.3947497e-01   1.3805161e-01   1.3491280e-01   1.4255824e-01   1.2381647e-01   1.0639120e-01   1.2689399e-01   1.2032986e-01   1.4134878e-01   1.4247553e-01   1.2120787e-01   1.2187456e-01   1.2309328e-01   1.6066767e-01   1.3444738e-01   1.2325830e-01   1.3118369e-01   1.4483072e-01   1.1290137e-01   1.2175315e-01   1.1925251e-01   1.0857610e-01   1.0914142e-01   1.3832403e-01   1.1530308e-01   1.3045824e-01   1.0804612e-01   1.4018015e-01   1.1257905e-01   1.4124338e-01   1.2516443e-01   1.3130183e-01   1.2160995e-01   1.0773181e-01   1.1250108e-01   1.2878318e-01   1.0678720e-01   1.3427629e-01   1.3201801e-01   1.2910620e-01   1.1632723e-01   1.2438544e-01   1.1469977e-01   1.2494953e-01   1.2148287e-01   8.4337656e-04   4.6746407e-04   2.4549978e-03   4.7529836e-03   2.3235808e-03   4.0683267e-03   4.3260986e-03   6.7336618e-04   2.8454658e-03   1.0918918e-03   1.3756658e-03   5.7784546e-04   5.9573290e-02   6.3070670e-02   6.9597309e-02   7.9911457e-02   7.3480528e-02   7.9923883e-02   7.0144874e-02   5.5923876e-02   6.6635620e-02   7.3192589e-02   7.4096565e-02   6.5836734e-02   7.1022277e-02   7.8555696e-02   5.0423423e-02   5.7089619e-02   8.1093473e-02   6.2483167e-02   9.2251714e-02   6.5399221e-02   8.6573432e-02   5.7873871e-02   9.3861710e-02   7.7914479e-02   6.0545459e-02   6.0328179e-02   7.3725736e-02   8.0652769e-02   7.5662466e-02   4.7500835e-02   6.6267157e-02   6.1219907e-02   5.9246920e-02   1.0235525e-01   8.5584812e-02   6.7627185e-02   6.6676399e-02   8.1028522e-02   6.3874534e-02   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5.7500583e-04   7.7277880e-03   4.4752900e-04   1.9151463e-03   2.3881652e-03   8.6221368e-04   8.6997251e-04   5.7712764e-05   1.4261239e-04   1.6337476e-04   6.5357511e-02   6.7564930e-02   7.5599895e-02   8.6482524e-02   7.9693502e-02   8.5392044e-02   7.4152863e-02   6.0880360e-02   7.3094884e-02   7.7108408e-02   8.1483729e-02   6.9905750e-02   7.9537736e-02   8.4220614e-02   5.4020845e-02   6.2478782e-02   8.5095725e-02   6.8776984e-02   1.0023818e-01   7.1693803e-02   8.9974847e-02   6.3277271e-02   1.0126704e-01   8.4456284e-02   6.6380508e-02   6.5944304e-02   8.0776371e-02   8.6401760e-02   8.0678654e-02   5.3232214e-02   7.2705055e-02   6.7807498e-02   6.4728976e-02   1.0860574e-01   8.9250516e-02   7.0532132e-02   7.2192370e-02   8.9155393e-02   6.7825786e-02   7.9751674e-02   8.9848634e-02   7.8255825e-02   7.0908403e-02   6.2757363e-02   7.9213209e-02   6.8195297e-02   7.2146158e-02   6.8587288e-02   4.7220467e-02   7.1390990e-02   1.3114639e-01   1.1816523e-01   1.1284157e-01   1.1675611e-01   1.2280854e-01   1.2450964e-01   1.2061835e-01   1.2011904e-01   1.2793055e-01   1.0801409e-01   9.2203467e-02   1.1250005e-01   1.0614185e-01   1.2553294e-01   1.2604996e-01   1.0581394e-01   1.0665851e-01   1.0697400e-01   1.4569576e-01   1.2071369e-01   1.0835453e-01   1.1475367e-01   1.3023667e-01   9.9676180e-02   1.0601570e-01   1.0459446e-01   9.5152798e-02   9.4544535e-02   1.2261107e-01   1.0171679e-01   1.1677938e-01   9.3513090e-02   1.2443770e-01   9.8519974e-02   1.2493623e-01   1.1202254e-01   1.1414514e-01   1.0583616e-01   9.3110547e-02   9.8863035e-02   1.1361961e-01   9.4163495e-02   1.1816523e-01   1.1608967e-01   1.1325987e-01   1.0277556e-01   1.1111172e-01   1.0049112e-01   1.0810161e-01   1.0529258e-01   8.3201047e-04   6.6553558e-03   8.0817319e-04   2.3666253e-03   2.9401972e-03   6.0430641e-04   1.3109323e-03   2.0042209e-04   2.9042771e-04   6.4823857e-05   6.4369752e-02   6.6980839e-02   7.4622998e-02   8.5371818e-02   7.8644884e-02   8.4714120e-02   7.3778054e-02   6.0124143e-02   7.1976215e-02   7.6757894e-02   8.0112003e-02   6.9445381e-02   7.7800626e-02   8.3451231e-02   5.3558729e-02   6.1563285e-02   8.4824350e-02   6.7739660e-02   9.8727492e-02   7.0619990e-02   8.9865595e-02   6.2353086e-02   1.0002589e-01   8.3464224e-02   6.5377675e-02   6.4985443e-02   7.9506921e-02   8.5546781e-02   8.0035925e-02   5.2147031e-02   7.1577598e-02   6.6610625e-02   6.3822994e-02   1.0780225e-01   8.9119904e-02   7.0461434e-02   7.1328305e-02   8.7570443e-02   6.7451743e-02   7.8878318e-02   8.9018945e-02   7.7592264e-02   6.9886540e-02   6.1789581e-02   7.8498655e-02   6.7684600e-02   7.1587759e-02   6.7704325e-02   4.6526712e-02   7.0724596e-02   1.3117528e-01   1.1766016e-01   1.1197322e-01   1.1607657e-01   1.2231416e-01   1.2340084e-01   1.2042522e-01   1.1891967e-01   1.2666041e-01   1.0778594e-01   9.1812847e-02   1.1163169e-01   1.0543690e-01   1.2494830e-01   1.2593147e-01   1.0563286e-01   1.0596141e-01   1.0649455e-01   1.4431904e-01   1.1933022e-01   1.0786987e-01   1.1454955e-01   1.2887601e-01   9.8812977e-02   1.0562884e-01   1.0369928e-01   9.4451580e-02   9.4102215e-02   1.2194237e-01   1.0054711e-01   1.1549365e-01   9.2857172e-02   1.2382256e-01   9.7583400e-02   1.2385907e-01   1.1095947e-01   1.1423829e-01   1.0528942e-01   9.2735747e-02   9.8196145e-02   1.1321168e-01   9.3608756e-02   1.1766016e-01   1.1565299e-01   1.1307354e-01   1.0223904e-01   1.1010492e-01   9.9908851e-02   1.0821954e-01   1.0496782e-01   9.9295890e-03   5.3473138e-04   2.1693539e-03   3.7076821e-03   1.8222092e-03   1.2380588e-03   7.0429726e-04   3.2576994e-04   6.7027380e-04   7.5169669e-02   7.7062740e-02   8.6033367e-02   9.7417771e-02   9.0184218e-02   9.6534643e-02   8.3912481e-02   7.0270670e-02   8.3626528e-02   8.6844061e-02   9.2545497e-02   7.9257265e-02   9.0777176e-02   9.5235076e-02   6.2208659e-02   7.1858472e-02   9.5535449e-02   7.9390740e-02   1.1189093e-01   8.2130752e-02   1.0013922e-01   7.2643917e-02   1.1330079e-01   9.5998078e-02   7.6221141e-02   7.5580594e-02   9.1730689e-02   9.7114882e-02   9.1048046e-02   6.2224749e-02   8.3137120e-02   7.8094271e-02   7.4382594e-02   1.2083561e-01   9.9831872e-02   7.9711043e-02   8.2237066e-02   1.0057287e-01   7.7408745e-02   9.0227459e-02   1.0148848e-01   8.8790024e-02   8.1095637e-02   7.2322440e-02   8.9773416e-02   7.8184960e-02   8.2186791e-02   7.8567440e-02   5.4863235e-02   8.1347337e-02   1.4275245e-01   1.3005259e-01   1.2482271e-01   1.2925722e-01   1.3482920e-01   1.3759096e-01   1.3236924e-01   1.3338627e-01   1.4130888e-01   1.1880967e-01   1.0247320e-01   1.2443347e-01   1.1741517e-01   1.3747488e-01   1.3688510e-01   1.1618864e-01   1.1858835e-01   1.1879679e-01   1.5963135e-01   1.3387511e-01   1.1938532e-01   1.2588037e-01   1.4388488e-01   1.1083228e-01   1.1728514e-01   1.1680010e-01   1.0591970e-01   1.0525056e-01   1.3476053e-01   1.1410719e-01   1.2959057e-01   1.0487194e-01   1.3643100e-01   1.1046993e-01   1.3880755e-01   1.2375874e-01   1.2479172e-01   1.1764923e-01   1.0361548e-01   1.0965651e-01   1.2456830e-01   1.0392711e-01   1.3005259e-01   1.2763609e-01   1.2394348e-01   1.1308481e-01   1.2275352e-01   1.1138648e-01   1.1846972e-01   1.1666230e-01   1.1839370e-02   9.5901133e-03   1.3740734e-02   3.5338001e-03   1.3550011e-02   8.8526707e-03   9.4699409e-03   6.3350154e-03   4.8467987e-02   5.3749987e-02   5.7717889e-02   6.5676566e-02   6.0050880e-02   7.0693363e-02   6.1877604e-02   4.6729706e-02   5.4665912e-02   6.4242849e-02   5.9590174e-02   5.6493218e-02   5.5132102e-02   6.8254515e-02   4.1974046e-02   4.5979775e-02   7.3375693e-02   5.2912711e-02   7.3889063e-02   5.3879214e-02   7.8254066e-02   4.6403740e-02   7.8645675e-02   6.7578949e-02   4.9098308e-02   4.8671019e-02   5.9827034e-02   6.7861186e-02   6.5136324e-02   3.6759287e-02   5.3980965e-02   4.9365653e-02   4.8462917e-02   9.0010105e-02   7.8830145e-02   6.1496889e-02   5.5380536e-02   6.4107134e-02   5.6871111e-02   6.2034296e-02   7.3759034e-02   6.3674900e-02   5.3119604e-02   4.6143136e-02   6.3811294e-02   5.6759011e-02   5.9030859e-02   5.2419966e-02   3.3258744e-02   5.6880106e-02   1.1655832e-01   1.0005043e-01   9.1684275e-02   9.8727002e-02   1.0425490e-01   1.0138126e-01   1.0565129e-01   9.7538138e-02   1.0314095e-01   9.2386824e-02   7.6571607e-02   9.1274575e-02   8.6336607e-02   1.0505203e-01   1.0829773e-01   9.0077109e-02   8.8858206e-02   9.1549427e-02   1.1781623e-01   9.5530481e-02   9.0068051e-02   9.8963246e-02   1.0479240e-01   7.9118056e-02   9.0207341e-02   8.5766485e-02   7.6442113e-02   7.8991975e-02   1.0229780e-01   8.0971468e-02   9.2462279e-02   7.7616682e-02   1.0394880e-01   7.9854175e-02   1.0493060e-01   8.8086863e-02   1.0105189e-01   8.9771099e-02   7.8157448e-02   7.9782471e-02   9.4953430e-02   7.4768636e-02   1.0005043e-01   9.8253215e-02   9.6744777e-02   8.3113340e-02   8.7744069e-02   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1.1978148e-01   1.2301688e-01   1.2902659e-01   1.3200226e-01   1.2597225e-01   1.2757685e-01   1.3584109e-01   1.1348127e-01   9.7761057e-02   1.1945082e-01   1.1270375e-01   1.3215934e-01   1.3182973e-01   1.1125522e-01   1.1287096e-01   1.1260483e-01   1.5425448e-01   1.2876341e-01   1.1448536e-01   1.2024528e-01   1.3833407e-01   1.0647529e-01   1.1163750e-01   1.1113351e-01   1.0149473e-01   1.0013701e-01   1.2927004e-01   1.0879101e-01   1.2459621e-01   9.9330508e-02   1.3108770e-01   1.0504760e-01   1.3186075e-01   1.1958837e-01   1.1892921e-01   1.1162833e-01   9.8541878e-02   1.0525098e-01   1.1976536e-01   1.0049727e-01   1.2430643e-01   1.2212353e-01   1.1885667e-01   1.0916600e-01   1.1853397e-01   1.0665478e-01   1.1270995e-01   1.1063603e-01   1.5750019e-03   2.3061943e-03   2.5267586e-03   1.8816551e-03   2.4916769e-03   2.6490348e-03   5.6749564e-02   5.7171493e-02   6.5939847e-02   7.5932398e-02   6.9508351e-02   7.4656451e-02   6.2624290e-02   5.2024188e-02   6.4437230e-02   6.4937043e-02   7.2745199e-02   5.8611781e-02   7.2652586e-02   7.3573688e-02   4.4171072e-02   5.3594578e-02   7.2641168e-02   6.1050608e-02   8.9566976e-02   6.3051224e-02   7.6010398e-02   5.4225638e-02   9.0321512e-02   7.5195114e-02   5.7639533e-02   5.6852233e-02   7.1710391e-02   7.4949900e-02   6.9318916e-02   4.6230253e-02   6.3971485e-02   6.0026157e-02   5.5798348e-02   9.5989279e-02   7.6232404e-02   5.8444003e-02   6.2302257e-02   8.0224536e-02   5.7278169e-02   6.9150783e-02   7.9467477e-02   6.7704503e-02   6.1864652e-02   5.4241616e-02   6.8592620e-02   5.8516944e-02   6.1759106e-02   5.9360348e-02   3.8591759e-02   6.1151978e-02   1.1324556e-01   1.0303819e-01   9.9201558e-02   1.0318500e-01   1.0721879e-01   1.1147036e-01   1.0460948e-01   1.0828938e-01   1.1523751e-01   9.2280249e-02   7.8300492e-02   9.8832112e-02   9.2088327e-02   1.0954453e-01   1.0774163e-01   8.9704304e-02   9.3649245e-02   9.3477002e-02   1.3171389e-01   1.0896793e-01   9.3248418e-02   9.8534682e-02   1.1788866e-01   8.6730988e-02   9.1550165e-02   9.2743651e-02   8.2023117e-02   8.1036634e-02   1.0749375e-01   9.1211084e-02   1.0479473e-01   8.1639608e-02   1.0872731e-01   8.7298316e-02   1.1342725e-01   9.8507274e-02   9.7018335e-02   9.2572028e-02   7.9424005e-02   8.5123740e-02   9.7519007e-02   7.9504622e-02   1.0303819e-01   1.0060889e-01   9.6540999e-02   8.7528391e-02   9.7464514e-02   8.6517419e-02   9.1407615e-02   9.1076579e-02   4.2759888e-03   1.3998823e-03   1.8495751e-03   2.8301386e-03   3.7334484e-03   5.5009109e-02   5.4964037e-02   6.3820777e-02   7.4331569e-02   6.8062522e-02   7.0406681e-02   5.9595322e-02   4.9880526e-02   6.2237804e-02   6.2265151e-02   7.1113130e-02   5.6594278e-02   7.1451534e-02   6.9994053e-02   4.3126676e-02   5.2381128e-02   6.8520339e-02   5.7597897e-02   8.9058557e-02   6.0751652e-02   7.2510768e-02   5.3201106e-02   8.7849614e-02   7.0985642e-02   5.6028788e-02   5.5591108e-02   6.9920676e-02   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7.7301298e-02   6.5155686e-02   7.8476830e-02   8.0402665e-02   8.7884855e-02   7.3650267e-02   8.6974315e-02   8.8299731e-02   5.7895678e-02   6.7595783e-02   8.7665774e-02   7.3314500e-02   1.0776923e-01   7.6895020e-02   9.2474273e-02   6.8514181e-02   1.0728576e-01   8.8812805e-02   7.1614033e-02   7.1214401e-02   8.6845407e-02   9.1428310e-02   8.4778392e-02   5.8702706e-02   7.8223013e-02   7.3389903e-02   6.9650470e-02   1.1290739e-01   9.1229062e-02   7.2678536e-02   7.7045799e-02   9.6518176e-02   7.0683794e-02   8.4677029e-02   9.3753287e-02   8.2039996e-02   7.6152676e-02   6.7885263e-02   8.3273481e-02   7.1166737e-02   7.5618620e-02   7.3311647e-02   5.2129744e-02   7.5414559e-02   1.3361288e-01   1.2212885e-01   1.1803753e-01   1.2062983e-01   1.2681873e-01   1.3003785e-01   1.2339855e-01   1.2552093e-01   1.3397302e-01   1.1145011e-01   9.6072866e-02   1.1773621e-01   1.1108813e-01   1.3021606e-01   1.2991222e-01   1.0941117e-01   1.1074904e-01   1.1019635e-01   1.5245649e-01   1.2709803e-01   1.1272646e-01   1.1805571e-01   1.3644429e-01   1.0507143e-01   1.0948152e-01   1.0908044e-01   1.0002018e-01   9.8259510e-02   1.2725753e-01   1.0697349e-01   1.2296793e-01   9.7285465e-02   1.2913723e-01   1.0312519e-01   1.2920697e-01   1.1832381e-01   1.1655849e-01   1.0932054e-01   9.6669076e-02   1.0377916e-01   1.1803847e-01   9.9488230e-02   1.2212885e-01   1.2004765e-01   1.1693776e-01   1.0790940e-01   1.1723226e-01   1.0500092e-01   1.1038445e-01   1.0827603e-01   1.5232780e-04   4.0007181e-04   6.5289213e-02   6.7204649e-02   7.5443787e-02   8.6444762e-02   7.9660759e-02   8.4749914e-02   7.3546883e-02   6.0641799e-02   7.3012359e-02   7.6531840e-02   8.1598668e-02   6.9499172e-02   7.9923854e-02   8.3724381e-02   5.3799024e-02   6.2453508e-02   8.4253942e-02   6.8486788e-02   1.0054294e-01   7.1576362e-02   8.9122210e-02   6.3281093e-02   1.0114322e-01   8.3993466e-02   6.6335786e-02   6.5925957e-02   8.0814161e-02   8.6165539e-02   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1.2553252e-01   1.2026484e-01   1.2407451e-01   1.3030382e-01   1.3228892e-01   1.2783055e-01   1.2774776e-01   1.3586522e-01   1.1498861e-01   9.8800101e-02   1.1991948e-01   1.1333278e-01   1.3320266e-01   1.3352807e-01   1.1273476e-01   1.1373642e-01   1.1391093e-01   1.5417322e-01   1.2849633e-01   1.1550662e-01   1.2189074e-01   1.3824515e-01   1.0674666e-01   1.1296262e-01   1.1166908e-01   1.0200786e-01   1.0119861e-01   1.3020916e-01   1.0880524e-01   1.2443747e-01   1.0015009e-01   1.3208523e-01   1.0543261e-01   1.3248948e-01   1.1957063e-01   1.2107326e-01   1.1278773e-01   9.9690412e-02   1.0583253e-01   1.2090813e-01   1.0100447e-01   1.2553252e-01   1.2339293e-01   1.2039941e-01   1.0985773e-01   1.1861026e-01   1.0744824e-01   1.1483872e-01   1.1213527e-01   6.6878313e-02   6.9715409e-02   7.7364528e-02   8.8171063e-02   8.1336125e-02   8.7984980e-02   7.6788970e-02   6.2680317e-02   7.4638540e-02   7.9773718e-02   8.2744330e-02   7.2225777e-02   8.0191157e-02   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1.0716280e-01   9.7527876e-02   9.7386912e-02   1.2555051e-01   1.0384747e-01   1.1883003e-01   9.6216108e-02   1.2741273e-01   1.0091958e-01   1.2779606e-01   1.1407020e-01   1.1794445e-01   1.0890370e-01   9.6003260e-02   1.0130628e-01   1.1658801e-01   9.6417670e-02   1.2131760e-01   1.1923852e-01   1.1654354e-01   1.0526503e-01   1.1322934e-01   1.0313209e-01   1.1184758e-01   1.0860395e-01   7.4548764e-04   4.1909104e-04   1.5729317e-03   7.9277531e-04   2.5985333e-03   2.1157871e-03   2.6363318e-04   2.7214324e-04   2.5006701e-03   1.1999234e-03   1.3641574e-03   2.4228657e-03   1.9193080e-03   1.5580763e-03   9.1547441e-05   4.2498838e-03   5.1587623e-04   4.4451535e-03   1.9710136e-04   5.9468529e-03   1.1637586e-04   4.0879090e-03   1.9577278e-03   7.5438506e-06   5.1321994e-05   9.5746588e-04   1.8362275e-03   1.6353958e-03   8.5567943e-04   2.3534169e-04   2.0155706e-04   2.8744085e-05   6.6464816e-03   6.0500135e-03   3.7609984e-03   3.0183871e-04   2.6908058e-03   1.8208811e-03   9.2994693e-04   3.0287331e-03   1.4489077e-03   1.1766146e-04   3.4058119e-05   1.3255619e-03   1.5104843e-03   1.2375803e-03   1.2042792e-04   2.2770079e-03   7.0925866e-04   1.7863102e-02   1.0250835e-02   7.3485693e-03   9.3316539e-03   1.1683662e-02   1.0169272e-02   1.2909901e-02   9.0217168e-03   1.1005819e-02   9.1383359e-03   4.6331293e-03   7.2658380e-03   6.2625155e-03   1.2163934e-02   1.5604510e-02   9.0849374e-03   6.4499430e-03   7.6430735e-03   1.6734199e-02   8.8633570e-03   7.8095179e-03   1.1083442e-02   1.1720144e-02   4.3192019e-03   7.6217573e-03   5.4833250e-03   3.8602370e-03   4.7396014e-03   1.0813609e-02   4.4772013e-03   7.7667524e-03   3.8237256e-03   1.1654961e-02   4.0471444e-03   1.1640132e-02   6.9842505e-03   1.3199398e-02   6.9808241e-03   4.8195688e-03   4.8204301e-03   9.7963275e-03   5.3012133e-03   1.0250835e-02   1.0025463e-02   1.1016974e-02   6.8718627e-03   6.8391566e-03   5.4173007e-03   1.1780352e-02   7.9156890e-03   7.3587704e-04   1.9839586e-03   1.2219042e-03   1.5405721e-03   4.1726993e-04   3.7297590e-04   1.1835574e-03   6.1737386e-04   2.7177989e-03   1.1395438e-04   5.3634867e-03   1.2095802e-03   9.5552631e-04   7.0211590e-04   1.8297765e-03   1.3098829e-03   5.8522900e-03   1.0011765e-03   2.8317516e-03   7.2859483e-04   4.4710316e-03   2.0244176e-03   7.6733040e-04   6.7685529e-04   2.1301657e-03   1.3518842e-03   6.1205846e-04   2.4644310e-03   1.1938153e-03   1.5975309e-03   5.1076446e-04   5.2791382e-03   3.0339660e-03   1.1907842e-03   3.5011674e-04   4.7257393e-03   3.5465173e-04   7.3647426e-04   2.3478030e-03   5.8214999e-04   7.6861523e-04   8.1449121e-04   5.9893306e-04   4.9750178e-04   2.3193980e-04   3.6882491e-04   2.8017975e-03   9.9802686e-05   1.3102890e-02   7.5969761e-03   6.0828162e-03   7.3064415e-03   8.8657957e-03   9.3996859e-03   9.1529212e-03   8.6958624e-03   1.0707084e-02   5.8653516e-03   2.3848099e-03   6.0110419e-03   4.6435179e-03   9.5841132e-03   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3.6015682e-03   4.5184530e-03   5.0362911e-03   2.3873447e-03   2.3916463e-03   2.1166084e-03   5.8005881e-03   9.3326086e-03   5.1921662e-03   2.5583136e-03   3.9040792e-03   8.1942534e-03   3.2098756e-03   3.4610228e-03   6.2351763e-03   5.0378736e-03   9.3974884e-04   3.8135545e-03   1.8905878e-03   1.0935023e-03   2.2739982e-03   4.8352649e-03   1.2660181e-03   2.5068904e-03   1.6511455e-03   5.4229770e-03   1.1989559e-03   6.1054655e-03   2.0081796e-03   8.6788304e-03   3.3159020e-03   2.5546078e-03   1.5534900e-03   4.7975700e-03   2.5264412e-03   4.9138585e-03   4.8875866e-03   6.2264786e-03   3.0375207e-03   1.9750388e-03   2.0217929e-03   8.0063599e-03   4.3571190e-03   1.6611913e-03   2.0167984e-03   1.5438876e-03   3.6494229e-04   2.0217253e-03   4.6462511e-04   1.5312613e-03   2.1707116e-03   9.6955753e-04   3.3920004e-03   1.0848877e-03   3.2679078e-03   1.3217642e-03   1.7681092e-03   4.3634818e-04   4.3762590e-03   9.8982281e-04   1.4702047e-03   1.2309511e-03   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9.4645289e-03   4.1075164e-03   2.7837137e-03   2.0667492e-03   5.7442304e-03   2.7416306e-03   6.1088154e-03   5.9744542e-03   7.0784056e-03   3.5969994e-03   3.0144395e-03   2.5834027e-03   8.5675229e-03   5.0446428e-03   9.3410747e-04   2.6108336e-03   1.8631164e-03   1.0514258e-03   2.7757095e-03   1.6027319e-03   5.9009151e-03   9.3507643e-05   4.8585250e-03   3.2279691e-03   7.0814372e-04   1.8064210e-03   4.7021523e-03   1.7906187e-03   1.7438865e-03   3.2726931e-03   2.1092470e-03   4.4199215e-04   2.5742583e-03   2.7576288e-03   2.1865740e-03   8.5954487e-04   4.3875130e-04   6.2385517e-03   2.0706463e-03   2.9895922e-03   2.4900150e-03   1.5452115e-03   1.2972442e-03   2.2089282e-03   1.3825902e-03   4.4047937e-03   1.3378707e-03   8.5528525e-04   1.4287812e-04   2.3200710e-04   1.9018574e-03   3.1193134e-03   2.7835858e-04   1.0440284e-03   6.7774868e-04   1.6434489e-03   8.2787646e-03   9.1805293e-04   8.2830461e-03   3.6334874e-03   2.7936555e-03   2.6701226e-03   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2.0616206e-03   2.1327263e-03   2.0380999e-03   3.2539726e-03   1.3598045e-03   3.9670027e-04   4.8634117e-03   2.4197901e-03   3.2204932e-03   1.7622064e-03   3.8856461e-03   1.2334789e-03   4.0452577e-04   1.0887743e-03   6.2435560e-03   2.0292084e-04   1.0829901e-03   1.7786841e-03   4.1228310e-04   1.8859956e-03   2.3286589e-03   5.1772577e-04   4.9172870e-04   2.0007065e-04   1.2918676e-03   5.0330599e-03   3.9898095e-04   9.4287570e-03   5.3866372e-03   4.8647393e-03   5.2819054e-03   6.4598280e-03   8.0073865e-03   6.1852254e-03   7.5566712e-03   9.5128884e-03   3.7267827e-03   1.2843714e-03   4.8237356e-03   3.5085400e-03   7.3800011e-03   8.6672418e-03   3.7373665e-03   3.3006522e-03   3.2553459e-03   1.4768796e-02   8.5372346e-03   3.7597131e-03   5.0208833e-03   1.0540608e-02   2.9216135e-03   2.9987594e-03   3.5026889e-03   1.9346800e-03   1.3415748e-03   6.5619943e-03   4.2356898e-03   7.2096387e-03   1.4370251e-03   7.0771420e-03   2.7742326e-03   8.9575949e-03   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1.1788899e-02   1.2850999e-02   1.0630699e-02   1.2964118e-02   9.0438994e-03   4.5288546e-03   8.3580766e-03   6.9988358e-03   1.3044370e-02   1.5771615e-02   8.9276151e-03   7.0025139e-03   7.7681345e-03   1.9248623e-02   1.0890288e-02   8.2148016e-03   1.1050411e-02   1.3845989e-02   5.2067991e-03   7.6819868e-03   6.2976924e-03   4.3733262e-03   4.7066273e-03   1.1733076e-02   5.6953630e-03   9.5825887e-03   4.0184455e-03   1.2555508e-02   4.8201445e-03   1.2938333e-02   8.5012649e-03   1.2613331e-02   7.2187981e-03   4.6491251e-03   5.3739269e-03   1.0213138e-02   5.7106829e-03   1.0764587e-02   1.0424589e-02   1.1013685e-02   7.3861586e-03   8.2413252e-03   5.8213434e-03   1.1031181e-02   7.7860554e-03   2.6482878e-03   4.2794287e-04   1.8319104e-03   1.5871773e-03   1.2340260e-03   2.9761573e-03   6.4181441e-04   3.9337040e-03   3.6570436e-04   2.9155752e-03   1.3382816e-05   5.6692471e-03   6.4631376e-04   2.4262663e-03   1.0063227e-03   2.3414789e-04   3.8352406e-04   2.6670153e-04   1.1841642e-03   1.3362953e-03   1.8214422e-03   1.1939941e-05   1.6841308e-04   4.0205285e-04   4.8423454e-03   5.6256276e-03   4.4224155e-03   3.0861840e-04   1.5326607e-03   2.2893524e-03   5.4845532e-04   1.9363566e-03   1.1483728e-03   6.7060376e-05   4.8890125e-04   9.7136579e-04   1.7676633e-03   1.3375465e-03   2.5372175e-04   4.0846507e-03   8.2917869e-04   1.6077651e-02   8.4460632e-03   5.5177458e-03   7.2638972e-03   9.7215743e-03   7.5597148e-03   1.1218034e-02   6.4234899e-03   8.1582316e-03   8.1119193e-03   4.1520915e-03   5.4624397e-03   4.9276011e-03   1.0142169e-02   1.4194600e-02   8.3023965e-03   4.8434975e-03   6.1466052e-03   1.3239048e-02   6.2447391e-03   6.5902144e-03   9.7724034e-03   8.6919298e-03   3.1454944e-03   6.3952659e-03   3.7622934e-03   3.0039560e-03   4.0045050e-03   8.7466217e-03   2.6847018e-03   5.4026497e-03   2.7900002e-03   9.6269482e-03   2.5687827e-03   8.7444600e-03   5.2241473e-03   1.2215015e-02   5.4919656e-03   4.2251052e-03   3.8716574e-03   8.5147448e-03   4.9424074e-03   8.4460632e-03   8.4294916e-03   9.9304629e-03   6.0757927e-03   5.1533590e-03   4.4115457e-03   1.1061881e-02   6.6918878e-03   4.2077380e-03   2.8084601e-04   8.0255307e-03   1.0009734e-03   2.4531898e-03   2.5259126e-03   4.7784400e-04   2.9272193e-03   6.4204523e-03   2.4613181e-03   8.1446100e-04   2.5131313e-03   4.2288269e-03   2.3479589e-03   2.4787654e-03   2.3219118e-03   3.4016339e-03   1.1923522e-03   3.6609993e-04   5.5309499e-03   2.7130308e-03   3.6876750e-03   2.1157012e-03   3.5197143e-03   1.1211667e-03   5.0040735e-04   1.2581494e-03   6.2453424e-03   4.9316252e-04   1.0956505e-03   1.9034882e-03   5.6262931e-04   2.1623642e-03   2.7381233e-03   6.2275542e-04   9.1647472e-04   4.3469066e-04   1.6016964e-03   5.5073116e-03   6.0170029e-04   8.2861929e-03   4.5965840e-03   4.2124912e-03   4.7715416e-03   5.5699315e-03   7.3813594e-03   5.3659110e-03   7.1660104e-03   8.8786575e-03   2.9267242e-03   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2.0584975e-03   2.4845352e-03   1.6034070e-03   3.3059261e-04   1.8671770e-03   2.0088877e-03   1.4284810e-03   4.3098388e-04   2.3514979e-04   5.2698749e-03   1.3824059e-03   2.2360501e-03   1.8501267e-03   1.6468815e-03   1.8319470e-03   2.4154150e-03   8.5423988e-04   3.3259702e-03   1.3633177e-03   3.9750527e-04   2.1357310e-04   1.4089375e-04   1.2605369e-03   2.3906980e-03   1.0696291e-04   1.0906412e-03   5.9076498e-04   1.1304618e-03   7.2732511e-03   6.4012947e-04   8.9598694e-03   3.8314732e-03   2.5915433e-03   2.9763427e-03   4.7600376e-03   4.3053173e-03   5.3266981e-03   3.6190516e-03   5.2272723e-03   3.6549051e-03   1.5047575e-03   2.5888356e-03   2.1634980e-03   5.5055672e-03   8.5050147e-03   4.0885074e-03   1.5151975e-03   1.9844585e-03   9.6042351e-03   4.2899092e-03   2.9941597e-03   4.6609860e-03   5.8520656e-03   1.4443089e-03   2.3092039e-03   1.1621771e-03   1.1296414e-03   1.1169479e-03   4.4204603e-03   1.2641450e-03   3.4620250e-03   3.4971048e-04   5.1226200e-03   6.2752047e-04   4.7853928e-03   3.3731886e-03   6.3070664e-03   1.6662334e-03   1.2828407e-03   1.6597311e-03   4.4397739e-03   3.3292201e-03   3.8314732e-03   3.8867782e-03   5.1669823e-03   3.5417199e-03   3.1734550e-03   1.6842820e-03   5.5385508e-03   2.3108610e-03   1.0105990e-03   4.7523926e-03   2.9847642e-03   9.7105522e-03   2.6675945e-03   5.8410645e-03   1.0628436e-03   8.9773521e-03   5.4199214e-03   1.6519449e-03   1.3847497e-03   4.5932482e-03   4.2245140e-03   3.0278103e-03   1.7095869e-03   2.8675709e-03   2.8000554e-03   1.2095222e-03   1.0633409e-02   6.3588443e-03   2.3146826e-03   1.8579783e-03   7.7501487e-03   1.5279559e-03   3.0361588e-03   6.2292475e-03   2.9996444e-03   2.2092276e-03   1.2670329e-03   3.0585508e-03   1.9631739e-03   1.9448597e-03   1.6026176e-03   7.3057463e-04   1.6268750e-03   1.9360609e-02   1.3271536e-02   1.1367917e-02   1.3356276e-02   1.4871782e-02   1.6028245e-02   1.4980963e-02   1.5218503e-02   1.7630002e-02   1.0242398e-02   5.4451367e-03   1.1236806e-02   9.0841292e-03   1.5577818e-02   1.6739427e-02   9.6435556e-03   9.8426714e-03   1.0341095e-02   2.4442578e-02   1.5482723e-02   9.8424496e-03   1.2530745e-02   1.8870958e-02   7.3605563e-03   9.5556413e-03   9.6316193e-03   6.0281749e-03   6.1257342e-03   1.4596779e-02   9.4938425e-03   1.3739836e-02   6.3629397e-03   1.5181016e-02   7.9755348e-03   1.8111593e-02   1.1305790e-02   1.3376686e-02   9.8378125e-03   5.8135644e-03   6.9819428e-03   1.1631750e-02   6.1445613e-03   1.3271536e-02   1.2517306e-02   1.1992997e-02   8.3045136e-03   1.0906252e-02   7.4644491e-03   1.1536762e-02   9.7524154e-03   4.5852486e-03   9.8595493e-04   5.1231602e-03   5.3641159e-04   6.1291344e-03   9.0289414e-06   4.9719488e-03   2.7623691e-03   1.0135570e-04   4.9630072e-05   1.4573369e-03   2.2050307e-03   1.9067713e-03   6.5935996e-04   5.5655703e-04   4.9349156e-04   5.3910141e-05   7.6334144e-03   6.4541501e-03   3.6168243e-03   4.5600228e-04   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8.5614846e-03   3.8688652e-03   7.5179133e-03   3.7407669e-03   3.1676786e-04   4.6173801e-03   4.2799166e-03   2.2501511e-03   4.2413983e-03   4.2204030e-03   4.6109813e-03   1.7937707e-03   8.2328963e-04   8.3021324e-03   4.1326900e-03   5.3767829e-03   3.8579826e-03   2.3734756e-03   1.6523409e-04   8.8835369e-04   2.5288831e-03   7.6911436e-03   1.1035999e-03   1.9572002e-03   1.3626197e-03   8.4501724e-04   3.6117590e-03   4.7013989e-03   1.0056440e-03   1.3674472e-03   9.9055737e-04   2.9505217e-03   8.8795046e-03   1.5067108e-03   6.0099517e-03   3.2148697e-03   3.5475051e-03   3.0620571e-03   4.0315627e-03   6.0415844e-03   3.4044063e-03   5.7826017e-03   7.5784861e-03   2.1065729e-03   8.8233953e-04   3.5528527e-03   2.5792431e-03   5.1245213e-03   6.2842876e-03   2.4095844e-03   1.8446522e-03   1.4167723e-03   1.2151930e-02   7.2262167e-03   2.4839286e-03   2.9019075e-03   8.5383029e-03   2.6181282e-03   1.4064800e-03   2.3288946e-03   1.7187301e-03   6.4203056e-04   4.4078979e-03   3.6116427e-03   6.0606537e-03   7.3312980e-04   4.8772717e-03   2.0701887e-03   6.3495233e-03   5.1782781e-03   3.3738477e-03   1.3922890e-03   5.6378115e-04   2.0528392e-03   3.5526857e-03   3.4142665e-03   3.2148697e-03   3.0384066e-03   3.3899600e-03   3.3852248e-03   4.7610217e-03   1.6939002e-03   2.6027995e-03   1.1563987e-03   4.9937739e-03   2.8043563e-04   6.0192505e-03   1.1047123e-03   3.7340869e-03   9.3891763e-04   5.7693223e-04   8.5742923e-04   1.1063653e-03   2.1518410e-03   1.7873418e-03   1.8443813e-03   4.7874237e-04   4.0562362e-04   6.3806313e-04   5.6896950e-03   5.3990383e-03   4.0838955e-03   7.6270784e-04   3.0255235e-03   1.8702287e-03   1.2256654e-03   1.9416278e-03   1.1863062e-03   4.8488269e-04   7.2384993e-04   1.1782779e-03   1.1397261e-03   1.1824844e-03   4.5012569e-04   4.3416102e-03   9.3532010e-04   1.7514227e-02   9.8600607e-03   7.1630436e-03   8.1480968e-03   1.1292909e-02   9.1710206e-03   1.2255610e-02   7.6051240e-03   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2.0117915e-03   1.4112028e-03   1.1968526e-02   7.9088029e-03   1.7082776e-03   1.7239090e-03   9.0238817e-03   2.6874577e-03   9.4975956e-04   2.9722514e-03   1.7009640e-03   5.1343341e-04   3.7130353e-03   4.7806054e-03   6.6267337e-03   1.3220831e-03   3.9245747e-03   2.9403206e-03   7.2757164e-03   5.0266602e-03   1.8157078e-03   1.4701768e-03   3.5054511e-04   1.7883207e-03   2.3616946e-03   2.6617941e-03   2.5222817e-03   2.1723972e-03   1.9530095e-03   2.4533627e-03   4.5559375e-03   1.3609168e-03   1.2016297e-03   8.2861882e-04   4.8139327e-03   2.8209366e-03   1.1052349e-04   3.7194090e-05   1.3880093e-03   2.0960687e-03   1.8746430e-03   7.3307377e-04   5.4600497e-04   5.2531656e-04   7.7399437e-05   7.5260309e-03   6.5039124e-03   3.6958100e-03   4.3794778e-04   3.1691974e-03   1.9589162e-03   1.1747018e-03   3.8950000e-03   1.8610625e-03   3.3531102e-04   5.6607375e-05   1.7087501e-03   1.8728452e-03   1.4997100e-03   3.0123700e-04   1.5391826e-03   8.8147902e-04   1.8294246e-02   1.0829571e-02   7.9341800e-03   1.0299926e-02   1.2275737e-02   1.1220530e-02   1.3508784e-02   1.0262914e-02   1.2147087e-02   9.2823036e-03   4.6531594e-03   7.8245831e-03   6.5524640e-03   1.2610156e-02   1.5512672e-02   9.0061844e-03   7.1992659e-03   8.4158356e-03   1.7921554e-02   9.9492079e-03   7.9854978e-03   1.1342596e-02   1.2982212e-02   4.5954373e-03   8.0580657e-03   6.3922041e-03   4.0251341e-03   4.9895677e-03   1.1418706e-02   5.4787432e-03   8.7107499e-03   4.4679304e-03   1.2142235e-02   4.8867636e-03   1.3297934e-02   7.3458933e-03   1.3299484e-02   7.7358341e-03   4.9917221e-03   4.9413674e-03   9.8545070e-03   4.8770063e-03   1.0829571e-02   1.0435652e-02   1.1007902e-02   6.6474718e-03   7.1727397e-03   5.6106947e-03   1.1815640e-02   8.4729744e-03   1.5166983e-03   3.8470717e-03   4.0414722e-03   1.3464004e-03   1.0521554e-03   2.2256122e-03   8.2355212e-03   2.4972654e-03   3.6758320e-03   4.2952040e-03   1.2466978e-03   5.4237685e-03   7.4233145e-03   2.7434894e-03   1.3920410e-03   5.6705580e-03   1.6006987e-03   1.4795623e-03   2.5504964e-03   2.8217649e-03   4.8039535e-03   2.1716992e-03   5.1387834e-03   3.8511647e-03   3.4066344e-03   1.1638730e-02   3.4223746e-03   9.4998939e-03   3.3659956e-03   1.1438717e-03   2.4828929e-03   3.9653407e-03   1.5796312e-03   5.9993003e-03   1.2126234e-03   1.7377370e-03   4.6402796e-03   3.0884931e-03   1.1351744e-03   1.5562166e-03   3.9244608e-03   8.1556610e-03   5.1855221e-03   1.5226783e-03   2.8914073e-03   4.3431210e-03   9.2550137e-04   2.9272754e-03   5.3162687e-03   2.0104865e-03   7.9177243e-04   3.1975522e-03   8.1317449e-04   1.3785091e-03   2.5714969e-03   2.9511423e-03   2.8161529e-04   5.9442405e-04   1.5991249e-03   3.5615321e-03   5.8433150e-04   3.1011353e-03   9.7656296e-04   8.0983113e-03   2.3700003e-03   3.0461348e-03   1.6450583e-03   4.0872867e-03   3.5603497e-03   3.3659956e-03   3.6518311e-03   5.6844228e-03   3.2852236e-03   1.0303385e-03   1.9470044e-03   7.8778855e-03   3.7000111e-03   1.9300708e-03   2.2574717e-03   1.1284358e-03   1.0646979e-03   1.0312076e-03   5.0621817e-03   1.2060164e-03   1.8000639e-03   2.0650564e-03   2.1487796e-03   3.2333878e-03   4.0195479e-03   1.2411974e-03   2.7183002e-03   2.2726383e-03   8.5094120e-04   2.4056963e-04   6.3782113e-04   1.2937611e-03   2.4889893e-03   5.9722053e-04   1.5621785e-03   1.2375553e-03   1.3358412e-03   8.1240216e-03   1.2311022e-03   1.1517636e-02   5.2909227e-03   3.4509195e-03   3.7153220e-03   6.3154320e-03   4.5407961e-03   7.2027738e-03   3.4054800e-03   5.2043334e-03   5.7490488e-03   3.1731637e-03   3.4719309e-03   3.4347027e-03   7.1701181e-03   1.1379612e-02   6.4467389e-03   2.2692649e-03   2.9960956e-03   9.7363741e-03   4.0178908e-03   4.7338729e-03   6.7982603e-03   5.6061060e-03   2.3699712e-03   3.8192855e-03   1.4133848e-03   2.2956056e-03   2.5088406e-03   5.7314562e-03   9.5862581e-04   3.4107092e-03   9.7091810e-04   6.6778472e-03   7.6184177e-04   4.3247639e-03   4.2032521e-03   8.9746527e-03   2.5881501e-03   2.8171688e-03   3.0086239e-03   6.5256052e-03   5.3225794e-03   5.2909227e-03   5.5860698e-03   7.6013097e-03   5.5376614e-03   4.0938335e-03   3.1000848e-03   8.1789436e-03   3.7376243e-03   3.2267663e-05   8.3707549e-04   1.6905622e-03   1.5718936e-03   9.3681209e-04   1.8762095e-04   1.9684682e-04   4.1277465e-05   6.4440482e-03   6.0518000e-03   3.8422414e-03   2.6274935e-04   2.4665214e-03   1.9088192e-03   8.3864343e-04   2.9786928e-03   1.4388393e-03   8.3975474e-05   5.3416679e-05   1.2919166e-03   1.6159093e-03   1.2740163e-03   1.2266042e-04   2.3692761e-03   7.1636545e-04   1.7563748e-02   9.9676420e-03   7.0439691e-03   9.1049407e-03   1.1370346e-02   9.8276989e-03   1.2673450e-02   8.7383729e-03   1.0632094e-02   8.9036592e-03   4.4721835e-03   6.9588127e-03   5.9822651e-03   1.1786793e-02   1.5215597e-02   8.8361414e-03   6.2553172e-03   7.4909328e-03   1.6226352e-02   8.5173085e-03   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1.0920912e-02   8.6425556e-03   4.2412792e-03   6.9624194e-03   5.8567924e-03   1.1639501e-02   1.4739829e-02   8.4651679e-03   6.3684651e-03   7.5923014e-03   1.6475338e-02   8.8252851e-03   7.3097093e-03   1.0588424e-02   1.1694482e-02   3.9807447e-03   7.3452100e-03   5.5353092e-03   3.5104587e-03   4.4753907e-03   1.0430724e-02   4.6273816e-03   7.6755144e-03   3.8450588e-03   1.1170257e-02   4.1281664e-03   1.1986478e-02   6.5423939e-03   1.2634016e-02   6.9257811e-03   4.5247923e-03   4.3922796e-03   9.1553155e-03   4.5676871e-03   9.9147481e-03   9.5995789e-03   1.0353234e-02   6.1627903e-03   6.3902007e-03   5.0235520e-03   1.1247115e-02   7.7428181e-03   9.7824889e-04   1.6624661e-03   3.0059873e-03   2.5249972e-04   6.2343657e-04   1.1719366e-03   4.0275459e-03   6.3575546e-03   5.8712921e-03   7.5872446e-04   5.6741436e-04   3.5908637e-03   6.4996051e-04   1.9776689e-03   1.6840088e-03   4.6219818e-04   1.2917587e-03   1.3743184e-03   3.0187893e-03   2.2373182e-03   9.0828703e-04   5.7426890e-03   1.5775049e-03   1.5168309e-02   7.4080646e-03   4.2538993e-03   6.3033105e-03   8.5100385e-03   5.7899432e-03   1.0520014e-02   4.8624768e-03   6.1169570e-03   7.6384090e-03   4.1091153e-03   4.1981402e-03   3.9923041e-03   8.6172736e-03   1.2997087e-02   7.8717119e-03   4.1667776e-03   5.7584992e-03   1.0387455e-02   4.3546484e-03   5.7746712e-03   9.1054055e-03   6.5301937e-03   2.3054088e-03   5.9614728e-03   3.0379183e-03   2.5067124e-03   3.9126904e-03   7.3239330e-03   1.8370981e-03   3.7021481e-03   2.7152943e-03   8.1304066e-03   2.0347479e-03   7.4172182e-03   3.6502880e-03   1.1915038e-02   5.0530642e-03   4.2458688e-03   3.2213237e-03   7.5116191e-03   4.3860606e-03   7.4080646e-03   7.4726409e-03   9.2071058e-03   5.2421868e-03   3.6675370e-03   3.8308993e-03   1.1024145e-02   6.4520833e-03   3.0133930e-04   5.1037905e-03   1.2017859e-03   2.1951761e-03   1.7686888e-03   1.8224411e-03   2.8788865e-03   3.1740291e-03   7.0420689e-04   2.2350252e-03   2.1605967e-03   1.6074282e-04   9.9312132e-04   6.3910600e-04   1.1068342e-03   2.2522084e-03   4.2563220e-04   2.1383582e-03   1.1781524e-03   1.1965920e-03   6.6826197e-03   8.9701315e-04   8.8374021e-03   3.5249181e-03   1.9006375e-03   3.2674819e-03   4.3522253e-03   3.8602822e-03   5.5032387e-03   3.5903574e-03   4.6280025e-03   3.2207897e-03   1.0860964e-03   1.8528751e-03   1.3287556e-03   4.5637650e-03   7.2040689e-03   3.3452381e-03   1.6438459e-03   2.5042800e-03   8.4078534e-03   3.6412189e-03   2.1968551e-03   4.2884610e-03   5.3072049e-03   5.5962180e-04   2.2924485e-03   1.3972917e-03   4.1775124e-04   1.0120628e-03   3.7672964e-03   1.3901921e-03   2.7802443e-03   7.8074497e-04   4.2513803e-03   8.6439557e-04   5.7017672e-03   1.9558095e-03   6.1305769e-03   2.0764524e-03   1.1750038e-03   7.8121442e-04   3.3536027e-03   1.6840705e-03   3.5249181e-03   3.4031938e-03   4.3169071e-03   2.0323666e-03   1.8104373e-03   1.0313169e-03   5.4663596e-03   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3.9767727e-03   3.0148559e-03   4.1087786e-03   8.8891438e-03   2.8692574e-03   5.5219515e-03   2.9822205e-03   9.7392578e-03   2.7559926e-03   9.1569917e-03   5.1978118e-03   1.2376315e-02   5.7353587e-03   4.3202502e-03   3.8711781e-03   8.5388416e-03   4.7844327e-03   8.6239000e-03   8.5671038e-03   9.9856257e-03   5.9819812e-03   5.1316831e-03   4.4550423e-03   1.1213210e-02   6.9205612e-03   3.8131057e-04   6.7888158e-03   7.3363003e-03   5.3694436e-03   6.8516623e-04   1.8924051e-03   2.8895525e-03   1.2584203e-03   3.1106561e-03   1.9851820e-03   2.2993360e-04   3.0705767e-04   1.8065799e-03   2.2681792e-03   1.9895114e-03   4.4561501e-04   3.2950230e-03   1.3536253e-03   1.9442033e-02   1.0986408e-02   7.5586116e-03   9.6139706e-03   1.2432885e-02   9.8077912e-03   1.4077548e-02   8.4254038e-03   1.0370813e-02   1.0478515e-02   5.7856689e-03   7.4894276e-03   6.8497491e-03   1.2864462e-02   1.7242156e-02   1.0603978e-02   6.8089917e-03   8.2980029e-03   1.5941696e-02   8.0862824e-03   8.7712331e-03   1.2406133e-02   1.0894930e-02   4.6791769e-03   8.5829625e-03   5.4740472e-03   4.5017704e-03   5.7029968e-03   1.1309070e-02   4.0232333e-03   7.1989285e-03   4.2761837e-03   1.2289743e-02   4.0060693e-03   1.1002553e-02   7.0316526e-03   1.5021687e-02   7.5484658e-03   5.9167328e-03   5.5390768e-03   1.0934157e-02   6.4525090e-03   1.0986408e-02   1.0943118e-02   1.2502015e-02   7.9589531e-03   6.9802991e-03   6.2208864e-03   1.3663387e-02   8.8999016e-03   6.6062542e-03   5.5827314e-03   3.2137911e-03   2.4648342e-04   3.0882054e-03   1.4855278e-03   8.8238305e-04   3.0312113e-03   1.3048774e-03   1.7074342e-04   4.2409993e-05   1.2055084e-03   1.2882692e-03   1.0204762e-03   8.9780466e-05   2.0467514e-03   5.4370125e-04   1.7241595e-02   9.9776023e-03   7.2970604e-03   9.2205394e-03   1.1400153e-02   1.0313298e-02   1.2454804e-02   9.2538420e-03   1.1254653e-02   8.6534668e-03   4.2479840e-03   7.2108683e-03   6.0807502e-03   1.1908599e-02   1.4998922e-02   8.5435101e-03   6.3304436e-03   7.3992448e-03   1.7031719e-02   9.1810782e-03   7.4786833e-03   1.0592315e-02   1.2037933e-02   4.2382770e-03   7.2750145e-03   5.5074473e-03   3.6741461e-03   4.4146887e-03   1.0634443e-02   4.6823366e-03   8.0104480e-03   3.6842552e-03   1.1424845e-02   4.0945647e-03   1.1857190e-02   7.0169427e-03   1.2513676e-02   6.7752703e-03   4.4459599e-03   4.6022279e-03   9.3965771e-03   4.9465269e-03   9.9776023e-03   9.6902181e-03   1.0478640e-02   6.5221232e-03   6.8355801e-03   5.1573625e-03   1.1079009e-02   7.5518079e-03   2.6192775e-03   5.9216859e-03   4.3727502e-03   5.1296754e-03   5.3199310e-03   2.7670517e-03   1.1371035e-03   2.6020928e-03   5.1188394e-03   7.5382072e-03   2.4476107e-03   5.0616317e-03   3.9293810e-03   5.2302586e-03   1.5095801e-02   4.1435464e-03   4.4658108e-03   8.7058429e-04   4.4660793e-04   2.5555941e-04   1.2381894e-03   8.7244097e-04   2.0362511e-03   8.1311609e-04   1.5164656e-03   1.9481959e-03   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6.2404178e-03   8.0807935e-03   1.9416596e-03   1.3024398e-03   4.0245181e-03   3.0697725e-03   5.0283287e-03   5.8270256e-03   2.3505477e-03   2.0375391e-03   1.2652208e-03   1.2527532e-02   8.0556250e-03   2.6750700e-03   2.5225228e-03   9.0764566e-03   3.4699713e-03   1.3308823e-03   2.7664696e-03   2.4678015e-03   9.5729618e-04   4.3858320e-03   4.4729680e-03   6.8828714e-03   1.1547480e-03   4.8183810e-03   2.7179325e-03   6.3087897e-03   6.0843336e-03   2.6715726e-03   1.3701564e-03   8.5085504e-04   2.7129190e-03   3.6187454e-03   4.3357364e-03   3.0323131e-03   2.8888833e-03   3.1752051e-03   4.0026050e-03   5.6110347e-03   2.1520192e-03   2.0021167e-03   9.3001678e-04   2.6139835e-03   9.7625461e-03   4.3820793e-04   2.7906691e-03   3.4740135e-03   1.5471352e-03   3.7324822e-03   3.8774805e-03   1.8049144e-03   1.0166909e-03   9.6586952e-04   2.7620874e-03   5.6379477e-03   1.4267399e-03   9.9420936e-03   6.9534902e-03   7.2046628e-03   7.1611325e-03   8.0864542e-03   1.1050679e-02   7.0236664e-03   1.0684883e-02   1.2982713e-02   4.4982901e-03   2.1523458e-03   7.1621069e-03   5.3786825e-03   9.3055499e-03   9.5487861e-03   4.3879387e-03   5.0693092e-03   4.4931267e-03   1.8805226e-02   1.2143973e-02   5.1616364e-03   5.8432704e-03   1.4239876e-02   5.0396297e-03   4.0643450e-03   5.6688069e-03   3.5911389e-03   2.3422208e-03   8.6067938e-03   6.9700590e-03   1.0540875e-02   2.8498735e-03   9.0488233e-03   4.9258801e-03   1.1781603e-02   8.6822745e-03   5.8089260e-03   4.4337196e-03   2.0267056e-03   4.1354243e-03   6.4148025e-03   4.4976834e-03   6.9534902e-03   6.4275292e-03   5.9584428e-03   5.3006657e-03   8.1437729e-03   3.9023880e-03   4.5299634e-03   3.7988456e-03   2.5123066e-03   1.1946309e-03   2.0097566e-04   1.7928786e-03   5.7143349e-04   1.2667176e-04   4.6644872e-04   4.4712161e-04   1.0683378e-03   5.7468992e-04   7.6554900e-05   3.3664265e-03   2.0582490e-04   1.3553574e-02   7.1051776e-03   4.8941009e-03   6.5257957e-03   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9.6551734e-03   5.6073015e-03   1.2632980e-02   4.7967985e-03   5.4595549e-03   9.6779905e-03   6.1919843e-03   4.6437798e-03   4.8811137e-03   9.2634464e-03   1.4470481e-02   9.9239882e-03   5.5116951e-03   7.7393895e-03   8.8498403e-03   3.6104684e-03   7.0913900e-03   1.1068993e-02   5.6668826e-03   3.0002631e-03   7.9032607e-03   4.0760726e-03   3.7279027e-03   5.9729084e-03   7.9919733e-03   2.3383845e-03   3.2272638e-03   4.6096764e-03   8.7690968e-03   3.1364844e-03   7.9578373e-03   3.3962632e-03   1.4631125e-02   6.8663759e-03   6.4834920e-03   4.3461235e-03   8.7377082e-03   5.5255283e-03   8.6823566e-03   8.8561968e-03   1.1024987e-02   6.2645608e-03   3.5745084e-03   5.1960404e-03   1.3983177e-02   8.7265781e-03   1.5360474e-03   2.2738132e-03   6.3957013e-04   1.8470485e-03   1.9436948e-03   8.2753134e-04   1.4870044e-04   1.8575051e-04   1.1511457e-03   4.1570185e-03   4.2481246e-04   1.2022631e-02   7.4558885e-03   6.7319225e-03   7.0097246e-03   8.7236579e-03   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3.7014773e-03   2.9064840e-03   2.5951953e-04   1.5239927e-02   8.3975944e-03   6.0152535e-03   7.5736149e-03   9.7205279e-03   8.7194769e-03   1.0665619e-02   7.7107157e-03   9.6513260e-03   7.3495285e-03   3.4129734e-03   5.9493098e-03   4.9891659e-03   1.0300134e-02   1.3429483e-02   7.3762928e-03   4.9967161e-03   5.9349958e-03   1.5151045e-02   7.8143476e-03   6.2821596e-03   9.0873094e-03   1.0390318e-02   3.3768176e-03   5.9427925e-03   4.2522990e-03   2.8707879e-03   3.4399883e-03   9.0442431e-03   3.6087055e-03   6.7269934e-03   2.6557188e-03   9.8316941e-03   3.0241465e-03   9.9672648e-03   5.9844482e-03   1.0964814e-02   5.3765757e-03   3.5060112e-03   3.7251338e-03   8.1205003e-03   4.4033527e-03   8.3975944e-03   8.1986819e-03   9.1329776e-03   5.6810271e-03   5.8010063e-03   4.1618459e-03   9.6695634e-03   6.1457695e-03   3.7030792e-03   2.6425725e-02   1.8599298e-02   1.5467357e-02   1.8635118e-02   2.0442342e-02   2.0541696e-02   2.1259986e-02   1.9510831e-02   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4.7474248e-03   6.8472012e-03   9.8808760e-03   2.7678758e-03   4.1999833e-03   3.4360629e-03   2.0712504e-03   2.1185414e-03   7.4497841e-03   3.4016631e-03   6.4264729e-03   1.6858980e-03   8.1251590e-03   2.4514173e-03   8.9161864e-03   5.4840504e-03   8.2209587e-03   3.8745808e-03   2.1076714e-03   2.7824071e-03   6.3561971e-03   3.5186798e-03   6.5819636e-03   6.3377454e-03   6.9667686e-03   4.4964760e-03   5.2124475e-03   2.9917795e-03   7.0285944e-03   4.2716151e-03   1.5675754e-03   4.2437140e-03   2.9528525e-03   1.2801911e-03   5.5300675e-03   5.2313183e-04   7.0373258e-03   7.0028853e-03   1.5817688e-03   4.6017698e-03   4.2905415e-03   3.9763653e-03   1.7507004e-03   9.8088526e-04   2.0205251e-03   3.8651167e-03   2.8498196e-03   8.0083780e-03   8.7219602e-03   2.5429883e-03   8.6090275e-04   7.9906965e-03   6.1518285e-03   2.2097973e-03   5.7963314e-03   5.7460009e-03   4.2262969e-03   2.1872477e-03   8.9731860e-03   7.8793225e-03   5.8991938e-03   1.8999235e-03   7.1341168e-03   7.0170212e-03   6.4409068e-03   6.9062404e-04   3.2402506e-03   4.2346770e-03   4.9489360e-03   1.9844891e-03   6.6121605e-03   1.5675754e-03   1.4409377e-03   1.2937675e-03   4.5154908e-03   6.0031850e-03   4.0189646e-03   1.2526895e-03   2.2326743e-03   6.7976748e-04   4.4251056e-04   5.1964468e-05   1.5314410e-03   4.7093005e-04   2.2872076e-03   2.4409680e-03   6.1996952e-04   1.8531872e-03   7.0675084e-04   7.4672595e-04   2.9977980e-04   1.6320684e-03   1.1279305e-03   6.4871929e-04   6.2074215e-04   4.0109945e-03   3.1610099e-03   4.6600326e-04   4.3207236e-04   3.1187047e-03   1.7495883e-03   3.8892953e-04   1.4972893e-03   1.7881991e-03   1.3932149e-03   1.6264024e-04   3.1616233e-03   2.5553184e-03   1.9652949e-03   2.4129313e-04   2.2301817e-03   3.0218268e-03   1.9168834e-03   1.5054952e-03   6.4024254e-04   1.6084351e-03   1.4082859e-03   5.9336508e-04   3.2376306e-03   1.1102230e-16   6.3653022e-05   8.5949029e-04   1.8263557e-03   1.6881339e-03   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1.7461140e-03   1.4560452e-03   1.4920651e-03   2.5772801e-03   1.7019143e-03   1.0341988e-03   4.0085546e-03   3.6492138e-03   7.4340196e-03   7.9703529e-03   1.4966880e-03   7.8440192e-04   7.7789554e-03   4.4532033e-03   2.2360209e-03   5.9110335e-03   4.1723764e-03   3.6115483e-03   1.8645164e-03   8.6587941e-03   6.9790025e-03   5.9223579e-03   1.3508421e-03   6.9679643e-03   8.8100022e-03   4.3884451e-03   9.3956602e-04   3.8113149e-03   3.5744927e-03   3.3082295e-03   7.5316334e-04   3.6491972e-03   1.6320684e-03   1.1884181e-03   4.5803930e-04   2.1497659e-03   4.0210128e-03   2.8148066e-03   1.4099016e-03   2.8014283e-03   2.0075866e-03   1.7351697e-03   8.4094224e-03   6.5677927e-03   3.9418601e-04   3.5055970e-04   7.1718250e-03   2.0973679e-03   6.4851765e-04   3.3744442e-03   1.5292791e-03   9.4071576e-04   1.7144529e-03   5.4753391e-03   5.4188405e-03   2.5828658e-03   1.5301373e-03   3.8027206e-03   7.3328244e-03   3.1192913e-03   6.2731613e-04   1.7741918e-03   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1.0485877e-03   2.7784351e-03   1.1708179e-03   5.9587066e-04   1.2049026e-03   1.1592978e-03   4.9960727e-04   2.5830270e-03   2.2390567e-03   9.5053595e-04   5.2396832e-03   2.8622802e-03   2.1952710e-03   8.7416055e-04   1.1307517e-03
diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-cosine-ml.txt b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-cosine-ml.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7c6b67fa43c5fef11101d28dd46f4c1b325b65ee
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-cosine-ml.txt
@@ -0,0 +1 @@
+   2.5695885e-01   2.6882042e-01   2.3470353e-01   2.9299329e-01   2.2742702e-01   3.1253572e-01   2.4986352e-01   3.0770122e-01   2.5191977e-01   2.7931567e-01   2.8133743e-01   2.6316239e-01   2.6067201e-01   3.2982339e-01   2.8993002e-01   2.5506356e-01   2.8728051e-01   2.4952121e-01   2.8613379e-01   2.6894157e-01   2.3606353e-01   2.1670935e-01   2.3470242e-01   2.4294172e-01   2.4376454e-01   2.3228195e-01   2.3554918e-01   2.4851241e-01   2.0917546e-01   2.4971488e-01   2.4264224e-01   2.7405461e-01   1.9086415e-01   2.6346574e-01   2.5908801e-01   2.2138495e-01   2.2910721e-01   2.2169919e-01   2.0660065e-01   2.3207102e-01   2.5554688e-01   2.5153751e-01   2.6073682e-01   2.0919640e-01   3.3984433e-01   2.7503792e-01   2.1709889e-01   2.7068095e-01   3.0307041e-01   2.4529612e-01   2.2987015e-01   2.7736967e-01   3.0310708e-01   3.0544316e-01   1.9205388e-01   2.7098021e-01   2.0722466e-01   2.6387343e-01   2.8998308e-01   2.2633010e-01   2.5177075e-01   1.6347011e-01   2.4036389e-01   2.6485871e-01   2.8491965e-01   2.2273619e-01   2.4511873e-01   2.5930533e-01   2.6589995e-01   2.7797191e-01   2.3357373e-01   2.4279909e-01   2.3544532e-01   1.9447286e-01   2.3993534e-01   2.0856243e-01   2.2125251e-01   2.1988206e-01   2.0590152e-01   2.6441952e-01   2.0052739e-01   2.2978496e-01   2.4483670e-01   2.3879510e-01   2.9398425e-01   2.7541852e-01   2.3777469e-01   2.9151131e-01   2.0672752e-01   2.4584031e-01   2.7475025e-01   2.7064343e-01   2.5603684e-01   2.6165327e-01   2.4233155e-01   1.7892657e-01   2.6111203e-01   1.9965682e-01   2.4201634e-01   2.6281353e-01   3.1928221e-01   1.9731963e-01   2.7752862e-01   2.2633080e-01   2.6783167e-01   2.5447186e-01   2.6424243e-01   2.1960672e-01   2.2984242e-01   2.8788736e-01   2.8681630e-01   2.6949787e-01   2.3993685e-01   2.4440073e-01   2.5010397e-01   2.3230769e-01   2.9879682e-01   2.4200592e-01   2.6957748e-01   2.6073240e-01   2.6355347e-01   2.3403674e-01   2.2411413e-01   2.2956729e-01   2.8105976e-01   2.2913304e-01   2.4898608e-01   2.3304000e-01   2.2692988e-01   2.3728251e-01   2.2552243e-01   2.0364084e-01   2.3359511e-01   2.6619167e-01   2.6666588e-01   2.3666880e-01   2.7239113e-01   2.0146697e-01   2.3045559e-01   2.1695523e-01   2.1387991e-01   2.2366404e-01   2.2809635e-01   2.0901297e-01   2.2441100e-01   2.3418882e-01   2.8552218e-01   2.4609015e-01   2.0282492e-01   2.5940295e-01   2.7407006e-01   2.3344890e-01   2.1179142e-01   2.7047821e-01   2.9832768e-01   2.0859082e-01   2.8881331e-01   1.8384598e-01   2.5286491e-01   2.2012615e-01   2.3615775e-01   2.6845565e-01   2.3356355e-01   2.7164193e-01   2.4179380e-01   2.5247973e-01   2.5637548e-01   3.2126483e-01   2.3100774e-01   2.8832546e-01   2.0043257e-01   2.7918333e-01   2.4884522e-01   2.2904723e-01   2.3738940e-01   2.9461278e-01   2.9782005e-01   3.0332073e-01   2.5175971e-01   3.1203784e-01   2.6611535e-01   2.3713507e-01   2.2203585e-01   2.3602325e-01   2.5093670e-01   2.6860434e-01   3.0137874e-01   2.3759606e-01   2.6840346e-01   1.9200556e-01
diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-double-inp.txt b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-double-inp.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7a77021775ddb61d226aa8c4ba60f0af013e4a6c
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-double-inp.txt
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diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-euclidean-ml-iris.txt b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-euclidean-ml-iris.txt
new file mode 100644
index 0000000000000000000000000000000000000000..86de3c7592893bdb4438c9a0e7e60b2e7e5e1727
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-euclidean-ml-iris.txt
@@ -0,0 +1 @@
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1.0099505e+00   5.1961524e-01   1.2369317e+00   7.5498344e-01   8.3066239e-01   7.0000000e-01   5.0990195e-01   6.4807407e-01   6.4031242e-01   4.6904158e-01   5.0990195e-01   6.1644140e-01   5.4772256e-01   3.0000000e-01   3.3166248e-01   7.8102497e-01   1.0535654e+00   1.2845233e+00   3.1622777e-01   3.1622777e-01   8.5440037e-01   3.1622777e-01   3.6055513e-01   4.8989795e-01   4.3588989e-01   9.2736185e-01   3.0000000e-01   6.5574385e-01   9.5916630e-01   2.6457513e-01   7.8102497e-01   1.4142136e-01   8.0622577e-01   3.3166248e-01   4.2766810e+00   3.8496753e+00   4.4158804e+00   3.1543621e+00   3.9974992e+00   3.5510562e+00   4.0112342e+00   2.3065125e+00   3.9749214e+00   2.9495762e+00   2.6476405e+00   3.4029399e+00   3.2588341e+00   3.8794329e+00   2.7202941e+00   3.8807216e+00   3.5749126e+00   3.1527766e+00   3.8961519e+00   2.9782545e+00   4.0311289e+00   3.2588341e+00   4.2071368e+00   3.8314488e+00   3.6318040e+00   3.8340579e+00   4.2731721e+00   4.4698993e+00   3.7027017e+00   2.6153394e+00   2.8879058e+00   2.7712813e+00   3.0364453e+00   4.2825226e+00   3.5298725e+00   3.7322915e+00   4.1545156e+00   3.7669616e+00   3.1464265e+00   3.1032241e+00   3.4073450e+00   3.7854986e+00   3.1400637e+00   2.3537205e+00   3.2680269e+00   3.2326460e+00   3.2726136e+00   3.5425979e+00   2.0856654e+00   3.1953091e+00   5.4726593e+00   4.3347434e+00   5.5290144e+00   4.8682646e+00   5.2469038e+00   6.3364028e+00   3.6083237e+00   5.8660038e+00   5.2249402e+00   5.8940648e+00   4.5738387e+00   4.6936127e+00   5.0695167e+00   4.2918527e+00   4.5442271e+00   4.8270074e+00   4.8456166e+00   6.5207362e+00   6.7178866e+00   4.2508823e+00   5.3488316e+00   4.1436699e+00   6.4467046e+00   4.2813549e+00   5.1942276e+00   5.5587768e+00   4.1496988e+00   4.1856899e+00   5.0149776e+00   5.3385391e+00   5.7775427e+00   6.3126856e+00   5.0537115e+00   4.3416587e+00   4.7169906e+00   6.0406953e+00   5.0921508e+00   4.8062459e+00   4.0669399e+00   5.0269275e+00   5.2287666e+00   4.8682646e+00   4.3347434e+00   5.4753995e+00   5.3535035e+00   4.8641546e+00   4.4305756e+00   4.6615448e+00   4.8487112e+00   4.2988371e+00   6.4807407e-01   1.1661904e+00   3.3166248e-01   5.0000000e-01   3.0000000e-01   3.1622777e-01   1.0000000e+00   3.7416574e-01   2.6457513e-01   5.1961524e-01   1.5297059e+00   1.7146428e+00   1.1661904e+00   6.5574385e-01   1.3228757e+00   8.6602540e-01   8.7749644e-01   8.0622577e-01   7.0710678e-01   6.4807407e-01   5.3851648e-01   4.2426407e-01   5.4772256e-01   7.2111026e-01   6.7823300e-01   1.7320508e-01   2.2360680e-01   8.7749644e-01   1.1704700e+00   1.4247807e+00   3.1622777e-01   5.0990195e-01   1.0049876e+00   3.1622777e-01   3.0000000e-01   5.8309519e-01   6.0827625e-01   8.3666003e-01   3.0000000e-01   7.0000000e-01   9.6953597e-01   2.6457513e-01   8.6602540e-01   1.4142136e-01   9.2195445e-01   4.5825757e-01   4.1773197e+00   3.7336309e+00   4.3058100e+00   2.9849623e+00   3.8729833e+00   3.3926391e+00   3.8897301e+00   2.1118712e+00   3.8548671e+00   2.7784888e+00   2.4515301e+00   3.2680269e+00   3.1080541e+00   3.7376463e+00   2.5806976e+00   3.7762415e+00   3.4205263e+00   3.0000000e+00   3.7496667e+00   2.8160256e+00   3.8923001e+00   3.1304952e+00   4.0620192e+00   3.6851052e+00   3.5114100e+00   3.7229021e+00   4.1545156e+00   4.3497126e+00   3.5623026e+00   2.4698178e+00   2.7202941e+00   2.6038433e+00   2.8913665e+00   4.1279535e+00   3.3674916e+00   3.6069378e+00   4.0422766e+00   3.6262929e+00   2.9966648e+00   2.9376862e+00   3.2357379e+00   3.6482873e+00   2.9899833e+00   2.1633308e+00   3.1080541e+00   3.0838288e+00   3.1224990e+00   3.4132096e+00   1.9157244e+00   3.0446675e+00   5.3357286e+00   4.1773197e+00   5.4064776e+00   4.7222876e+00   5.1097945e+00   6.2153037e+00   3.4205263e+00   5.7384667e+00   5.0813384e+00   5.7844619e+00   4.4519659e+00   4.5530210e+00   4.9457052e+00   4.1303753e+00   4.3965896e+00   4.7010637e+00   4.7095647e+00   6.4140471e+00   6.5901442e+00   4.0877867e+00   5.2297227e+00   3.9862263e+00   6.3229740e+00   4.1436699e+00   5.0695167e+00   5.4387499e+00   4.0124805e+00   4.0472213e+00   4.8733972e+00   5.2172790e+00   5.6550862e+00   6.2153037e+00   4.9132474e+00   4.1988094e+00   4.5552168e+00   5.9321160e+00   4.9628621e+00   4.6690470e+00   3.9268308e+00   4.9101935e+00   5.1048996e+00   4.7602521e+00   4.1773197e+00   5.3497664e+00   5.2325902e+00   4.7455242e+00   4.2883563e+00   4.5332108e+00   4.7191101e+00   4.1496988e+00   6.1644140e-01   4.5825757e-01   2.2360680e-01   9.2195445e-01   5.2915026e-01   4.2426407e-01   3.4641016e-01   6.4031242e-01   9.7467943e-01   9.1651514e-01   1.0862780e+00   5.4772256e-01   1.7320508e-01   7.9372539e-01   2.6457513e-01   5.3851648e-01   2.6457513e-01   5.6568542e-01   5.2915026e-01   5.7445626e-01   6.3245553e-01   3.4641016e-01   2.4494897e-01   2.8284271e-01   5.3851648e-01   5.7445626e-01   5.0000000e-01   5.5677644e-01   7.8102497e-01   5.2915026e-01   4.4721360e-01   5.1961524e-01   5.2915026e-01   8.5440037e-01   2.4494897e-01   1.7320508e-01   1.4000000e+00   7.2801099e-01   4.5825757e-01   5.8309519e-01   6.4031242e-01   3.0000000e-01   5.6568542e-01   3.3166248e-01   3.0000000e-01   4.0607881e+00   3.6633318e+00   4.2190046e+00   3.1480152e+00   3.8496753e+00   3.4568772e+00   3.8249183e+00   2.3874673e+00   3.8078866e+00   2.9223278e+00   2.7586228e+00   3.2710854e+00   3.2186954e+00   3.7456642e+00   2.6267851e+00   3.6851052e+00   3.4669872e+00   3.0626786e+00   3.8340579e+00   2.9376862e+00   3.8845849e+00   3.1336879e+00   4.1036569e+00   3.7067506e+00   3.4741906e+00   3.6551334e+00   4.1085277e+00   4.2965102e+00   3.5763109e+00   2.5573424e+00   2.8740216e+00   2.7604347e+00   2.9495762e+00   4.1785165e+00   3.4380227e+00   3.5510562e+00   3.9648455e+00   3.6864617e+00   3.0364453e+00   3.0708305e+00   3.3541020e+00   3.6400549e+00   3.0659419e+00   2.4372115e+00   3.1968735e+00   3.1128765e+00   3.1670175e+00   3.3985291e+00   2.1424285e+00   3.1032241e+00   5.3131911e+00   4.2461747e+00   5.3507009e+00   4.7307505e+00   5.0960769e+00   6.1457302e+00   3.6166283e+00   5.6877060e+00   5.1009803e+00   5.6762664e+00   4.3977267e+00   4.5683695e+00   4.9010203e+00   4.2308392e+00   4.4508426e+00   4.6626173e+00   4.6882833e+00   6.2785349e+00   6.5536250e+00   4.1964271e+00   5.1643005e+00   4.0607881e+00   6.2657801e+00   4.1605288e+00   5.0079936e+00   5.3591044e+00   4.0249224e+00   4.0472213e+00   4.8836462e+00   5.1497573e+00   5.6017854e+00   6.0572271e+00   4.9234135e+00   4.2083251e+00   4.6141088e+00   5.8438001e+00   4.9203658e+00   4.6454279e+00   3.9344631e+00   4.8445846e+00   5.0616203e+00   4.6861498e+00   4.2461747e+00   5.2971691e+00   5.1730069e+00   4.7010637e+00   4.3301270e+00   4.5044423e+00   4.6786750e+00   4.1737274e+00   9.9498744e-01   7.0000000e-01   1.4594520e+00   1.0099505e+00   3.4641016e-01   8.1240384e-01   1.1618950e+00   1.5716234e+00   6.7823300e-01   6.1644140e-01   4.0000000e-01   5.9160798e-01   3.3166248e-01   3.8729833e-01   5.3851648e-01   4.1231056e-01   1.1224972e+00   6.7823300e-01   8.3066239e-01   1.0099505e+00   6.4807407e-01   5.2915026e-01   6.4807407e-01   1.0148892e+00   1.0246951e+00   5.3851648e-01   4.5825757e-01   4.7958315e-01   1.0099505e+00   9.6953597e-01   6.0827625e-01   1.0099505e+00   1.4177447e+00   6.4807407e-01   7.0000000e-01   1.8814888e+00   1.3000000e+00   6.0827625e-01   3.7416574e-01   1.1269428e+00   3.8729833e-01   1.1224972e+00   3.6055513e-01   8.0622577e-01   3.6124784e+00   3.2465366e+00   3.7868192e+00   2.9444864e+00   3.4698703e+00   3.1543621e+00   3.4073450e+00   2.3280893e+00   3.4146742e+00   2.7055499e+00   2.7147744e+00   2.9189039e+00   2.9832868e+00   3.3896903e+00   2.3366643e+00   3.2588341e+00   3.1464265e+00   2.7784888e+00   3.5468296e+00   2.7073973e+00   3.5085610e+00   2.7928480e+00   3.7709415e+00   3.3674916e+00   3.0935417e+00   3.2465366e+00   3.7121422e+00   3.8832976e+00   3.2264532e+00   2.3194827e+00   2.6758176e+00   2.5729361e+00   2.6608269e+00   3.8470768e+00   3.1400637e+00   3.1448370e+00   3.5411862e+00   3.3867388e+00   2.7239677e+00   2.8407745e+00   3.1032241e+00   3.2726136e+00   2.7892651e+00   2.3748684e+00   2.9223278e+00   2.7910571e+00   2.8548205e+00   3.0347982e+00   2.0566964e+00   2.8053520e+00   4.9061186e+00   3.9255573e+00   4.9223978e+00   4.3566042e+00   4.6978719e+00   5.7052607e+00   3.4263683e+00   5.2659282e+00   4.7349762e+00   5.2057660e+00   3.9774364e+00   4.2011903e+00   4.4833024e+00   3.9370039e+00   4.1146081e+00   4.2497059e+00   4.2918527e+00   5.7913729e+00   6.1343296e+00   3.9179076e+00   4.7275787e+00   3.7483330e+00   5.8360946e+00   3.8013156e+00   4.5760245e+00   4.9173163e+00   3.6633318e+00   3.6742346e+00   4.5066617e+00   4.7222876e+00   5.1788030e+00   5.5596762e+00   4.5453273e+00   3.8457769e+00   4.2883563e+00   5.3916602e+00   4.5022217e+00   4.2473521e+00   3.5693137e+00   4.4124823e+00   4.6411206e+00   4.2497059e+00   3.9255573e+00   4.8682646e+00   4.7391982e+00   4.2848571e+00   3.9887341e+00   4.1024383e+00   4.2649736e+00   3.8183766e+00   4.2426407e-01   5.4772256e-01   4.7958315e-01   8.6602540e-01   3.0000000e-01   4.8989795e-01   6.1644140e-01   1.3601471e+00   1.4933185e+00   9.5393920e-01   5.0990195e-01   1.2083046e+00   6.4807407e-01   8.6023253e-01   6.0000000e-01   4.5825757e-01   6.2449980e-01   5.4772256e-01   6.0827625e-01   4.5825757e-01   6.2449980e-01   6.0827625e-01   3.1622777e-01   4.2426407e-01   8.1240384e-01   9.4868330e-01   1.2083046e+00   4.7958315e-01   5.0000000e-01   9.1651514e-01   4.7958315e-01   4.6904158e-01   5.1961524e-01   4.2426407e-01   1.1090537e+00   3.1622777e-01   5.4772256e-01   8.1853528e-01   4.4721360e-01   6.7823300e-01   2.2360680e-01   7.7459667e-01   4.2426407e-01   4.2308392e+00   3.7854986e+00   4.3669211e+00   3.1272992e+00   3.9560081e+00   3.4899857e+00   3.9344631e+00   2.2781571e+00   3.9357337e+00   2.8827071e+00   2.6495283e+00   3.3361655e+00   3.2634338e+00   3.8209946e+00   2.6627054e+00   3.8353618e+00   3.4942810e+00   3.1160873e+00   3.8794329e+00   2.9495762e+00   3.9420807e+00   3.2202484e+00   4.1701319e+00   3.7828561e+00   3.5916570e+00   3.7907783e+00   4.2391037e+00   4.4147480e+00   3.6414283e+00   2.5980762e+00   2.8653098e+00   2.7549955e+00   2.9983329e+00   4.2225585e+00   3.4423829e+00   3.6414283e+00   4.1024383e+00   3.7549967e+00   3.0740852e+00   3.0626786e+00   3.3555923e+00   3.7229021e+00   3.1064449e+00   2.3388031e+00   3.2140317e+00   3.1654384e+00   3.2093613e+00   3.4957117e+00   2.0639767e+00   3.1400637e+00   5.3758720e+00   4.2638011e+00   5.4680892e+00   4.7989582e+00   5.1710734e+00   6.2801274e+00   3.5312887e+00   5.8137767e+00   5.1797683e+00   5.8077534e+00   4.4977772e+00   4.6368092e+00   5.0049975e+00   4.2272923e+00   4.4609416e+00   4.7423623e+00   4.7780749e+00   6.4397205e+00   6.6708320e+00   4.2190046e+00   5.2744668e+00   4.0620192e+00   6.3992187e+00   4.2284749e+00   5.1137071e+00   5.4963624e+00   4.0902323e+00   4.1121770e+00   4.9477268e+00   5.2886671e+00   5.7314920e+00   6.2401923e+00   4.9849774e+00   4.2871902e+00   4.6626173e+00   5.9883220e+00   4.9939964e+00   4.7318073e+00   3.9912404e+00   4.9618545e+00   5.1526692e+00   4.8031240e+00   4.2638011e+00   5.3972215e+00   5.2678269e+00   4.7968740e+00   4.3840620e+00   4.5934736e+00   4.7497368e+00   4.2178193e+00   7.8740079e-01   3.3166248e-01   5.0000000e-01   2.2360680e-01   4.6904158e-01   9.0553851e-01   1.0440307e+00   1.2369317e+00   7.0000000e-01   2.0000000e-01   8.3666003e-01   4.2426407e-01   4.4721360e-01   3.7416574e-01   6.7082039e-01   3.8729833e-01   4.4721360e-01   4.1231056e-01   2.2360680e-01   2.2360680e-01   2.2360680e-01   3.7416574e-01   3.7416574e-01   4.4721360e-01   7.3484692e-01   9.4868330e-01   3.3166248e-01   3.6055513e-01   5.4772256e-01   3.3166248e-01   7.4833148e-01   1.0000000e-01   2.4494897e-01   1.2288206e+00   6.6332496e-01   4.2426407e-01   6.0827625e-01   4.6904158e-01   4.2426407e-01   4.5825757e-01   4.2426407e-01   1.4142136e-01   3.9648455e+00   3.5623026e+00   4.1170378e+00   2.9866369e+00   3.7296112e+00   3.3256578e+00   3.7282704e+00   2.2113344e+00   3.6918830e+00   2.7802878e+00   2.5690465e+00   3.1543621e+00   3.0545049e+00   3.6249138e+00   2.4959968e+00   3.5818989e+00   3.3481338e+00   2.9206164e+00   3.6837481e+00   2.7820855e+00   3.7815341e+00   3.0049958e+00   3.9686270e+00   3.5791060e+00   3.3555923e+00   3.5454196e+00   3.9912404e+00   4.1892720e+00   3.4554305e+00   2.4020824e+00   2.7110883e+00   2.5942244e+00   2.8089144e+00   4.0509258e+00   3.3181320e+00   3.4583233e+00   3.8613469e+00   3.5383612e+00   2.9137605e+00   2.9189039e+00   3.2093613e+00   3.5242020e+00   2.9206164e+00   2.2561028e+00   3.0577770e+00   2.9899833e+00   3.0397368e+00   3.2771939e+00   1.9697716e+00   2.9698485e+00   5.2191953e+00   4.1206796e+00   5.2478567e+00   4.6162756e+00   4.9899900e+00   6.0448325e+00   3.4741906e+00   5.5803226e+00   4.9749372e+00   5.5973208e+00   4.3000000e+00   4.4474712e+00   4.7968740e+00   4.0975602e+00   4.3358967e+00   4.5661800e+00   4.5793013e+00   6.2040309e+00   6.4420494e+00   4.0472213e+00   5.0695167e+00   3.9395431e+00   6.1587336e+00   4.0373258e+00   4.9142650e+00   5.2621288e+00   3.9051248e+00   3.9357337e+00   4.7686476e+00   5.0447993e+00   5.4927225e+00   5.9849812e+00   4.8093659e+00   4.0865633e+00   4.4833024e+00   5.7463032e+00   4.8311489e+00   4.5398238e+00   3.8223030e+00   4.7455242e+00   4.9628621e+00   4.5902070e+00   4.1206796e+00   5.2009614e+00   5.0823223e+00   4.5989129e+00   4.2000000e+00   4.3977267e+00   4.5891176e+00   4.0607881e+00   5.5677644e-01   1.2845233e+00   6.7082039e-01   4.2426407e-01   3.4641016e-01   1.7916473e+00   1.9974984e+00   1.4317821e+00   9.2736185e-01   1.6124515e+00   1.1489125e+00   1.1575837e+00   1.0862780e+00   8.3066239e-01   9.1104336e-01   8.1240384e-01   6.4031242e-01   8.3066239e-01   1.0049876e+00   9.4339811e-01   4.6904158e-01   4.8989795e-01   1.1401754e+00   1.4491377e+00   1.7029386e+00   5.5677644e-01   7.0000000e-01   1.2569805e+00   5.5677644e-01   1.4142136e-01   8.6602540e-01   8.6023253e-01   6.2449980e-01   3.1622777e-01   9.5916630e-01   1.2609520e+00   4.2426407e-01   1.1575837e+00   3.6055513e-01   1.2083046e+00   7.2111026e-01   4.3794977e+00   3.9230090e+00   4.4977772e+00   3.0886890e+00   4.0435133e+00   3.5383612e+00   4.0767634e+00   2.1794495e+00   4.0360872e+00   2.8930952e+00   2.4939928e+00   3.4336569e+00   3.2326460e+00   3.9012818e+00   2.7367864e+00   3.9711459e+00   3.5707142e+00   3.1511903e+00   3.8768544e+00   2.9427878e+00   4.0570926e+00   3.2969683e+00   4.2083251e+00   3.8457769e+00   3.6905284e+00   3.9102430e+00   4.3324358e+00   4.5287967e+00   3.7229021e+00   2.6134269e+00   2.8337255e+00   2.7184554e+00   3.0413813e+00   4.2720019e+00   3.5085610e+00   3.7920970e+00   4.2320208e+00   3.7656341e+00   3.1543621e+00   3.0561414e+00   3.3615473e+00   3.8183766e+00   3.1320920e+00   2.2293497e+00   3.2449961e+00   3.2465366e+00   3.2771939e+00   3.5860842e+00   2.0049938e+00   3.1937439e+00   5.4972721e+00   4.3104524e+00   5.5821143e+00   4.8795492e+00   5.2706736e+00   6.3953108e+00   3.5028560e+00   5.9143892e+00   5.2316345e+00   5.9757845e+00   4.6292548e+00   4.7053161e+00   5.1176166e+00   4.2485292e+00   4.5276926e+00   4.8692915e+00   4.8774994e+00   6.6174013e+00   6.7557383e+00   4.2071368e+00   5.4074023e+00   4.1158231e+00   6.4984614e+00   4.2965102e+00   5.2488094e+00   5.6258333e+00   4.1677332e+00   4.2083251e+00   5.0259327e+00   5.4009258e+00   5.8300943e+00   6.4265076e+00   5.0645829e+00   4.3588989e+00   4.6968074e+00   6.1155539e+00   5.1322510e+00   4.8383882e+00   4.0853396e+00   5.0892043e+00   5.2735187e+00   4.9386233e+00   4.3104524e+00   5.5235858e+00   5.4064776e+00   4.9142650e+00   4.4294469e+00   4.7010637e+00   4.8887626e+00   4.3023250e+00   7.8740079e-01   3.4641016e-01   1.7320508e-01   7.2801099e-01   1.3114877e+00   1.5556349e+00   1.0099505e+00   5.0000000e-01   1.1000000e+00   7.5498344e-01   6.2449980e-01   7.0000000e-01   7.7459667e-01   5.2915026e-01   5.1961524e-01   2.0000000e-01   4.4721360e-01   5.0990195e-01   4.4721360e-01   2.6457513e-01   1.7320508e-01   6.5574385e-01   1.0440307e+00   1.2609520e+00   0.0000000e+00   3.4641016e-01   7.5498344e-01   0.0000000e+00   5.5677644e-01   3.7416574e-01   5.0000000e-01   9.3808315e-01   5.5677644e-01   6.5574385e-01   8.8317609e-01   2.6457513e-01   7.4161985e-01   3.4641016e-01   7.2801099e-01   2.6457513e-01   4.0435133e+00   3.6359318e+00   4.1856899e+00   2.9478806e+00   3.7709415e+00   3.3421550e+00   3.8065733e+00   2.1307276e+00   3.7389838e+00   2.7748874e+00   2.4556058e+00   3.2031235e+00   3.0133038e+00   3.6619667e+00   2.5258662e+00   3.6523965e+00   3.3852622e+00   2.9223278e+00   3.6687873e+00   2.7586228e+00   3.8457769e+00   3.0364453e+00   3.9799497e+00   3.6027767e+00   3.4014703e+00   3.6055513e+00   4.0348482e+00   4.2497059e+00   3.4942810e+00   2.3874673e+00   2.6720778e+00   2.5495098e+00   2.8178006e+00   4.0718546e+00   3.3496268e+00   3.5425979e+00   3.9293765e+00   3.5284558e+00   2.9495762e+00   2.9000000e+00   3.1984371e+00   3.5707142e+00   2.9189039e+00   2.1679483e+00   3.0626786e+00   3.0248967e+00   3.0675723e+00   3.3181320e+00   1.9104973e+00   2.9883106e+00   5.2924474e+00   4.1436699e+00   5.3113087e+00   4.6583259e+00   5.0467812e+00   6.1081912e+00   3.4525353e+00   5.6329388e+00   4.9979996e+00   5.6973678e+00   4.3749286e+00   4.4821870e+00   4.8600412e+00   4.1060930e+00   4.3760713e+00   4.6411206e+00   4.6324939e+00   6.3071388e+00   6.4876806e+00   4.0286474e+00   5.1468437e+00   3.9686270e+00   6.2112801e+00   4.0706265e+00   4.9919936e+00   5.3329167e+00   3.9446166e+00   3.9874804e+00   4.8114447e+00   5.1029403e+00   5.5443665e+00   6.0917978e+00   4.8538644e+00   4.1194660e+00   4.4933284e+00   5.8180753e+00   4.9142650e+00   4.5978256e+00   3.8729833e+00   4.8176758e+00   5.0338852e+00   4.6690470e+00   4.1436699e+00   5.2744668e+00   5.1652686e+00   4.6669048e+00   4.2201896e+00   4.4575778e+00   4.6722586e+00   4.1060930e+00   6.7823300e-01   9.3273791e-01   1.3674794e+00   5.8309519e-01   7.8740079e-01   3.4641016e-01   3.8729833e-01   3.8729833e-01   3.3166248e-01   3.6055513e-01   3.6055513e-01   9.4868330e-01   6.1644140e-01   7.8102497e-01   8.1240384e-01   5.4772256e-01   2.8284271e-01   3.7416574e-01   8.6602540e-01   8.5440037e-01   3.6055513e-01   4.5825757e-01   5.1961524e-01   7.8740079e-01   7.0710678e-01   3.0000000e-01   7.8740079e-01   1.2369317e+00   4.2426407e-01   5.0000000e-01   1.6792856e+00   1.1357817e+00   6.0827625e-01   5.4772256e-01   9.3273791e-01   3.3166248e-01   9.4868330e-01   1.0000000e-01   5.7445626e-01   3.8065733e+00   3.4554305e+00   3.9824616e+00   3.0708305e+00   3.6496575e+00   3.3331667e+00   3.6290495e+00   2.4124676e+00   3.5916570e+00   2.8705400e+00   2.7730849e+00   3.1176915e+00   3.0822070e+00   3.5791060e+00   2.5099801e+00   3.4496377e+00   3.3496268e+00   2.9257478e+00   3.6851052e+00   2.8372522e+00   3.7349699e+00   2.9597297e+00   3.9370039e+00   3.5411862e+00   3.2695565e+00   3.4322005e+00   3.8858718e+00   4.0841156e+00   3.4190642e+00   2.4372115e+00   2.7928480e+00   2.6795522e+00   2.8142495e+00   4.0348482e+00   3.3436507e+00   3.3778692e+00   3.7389838e+00   3.5199432e+00   2.9154759e+00   2.9849623e+00   3.2603681e+00   3.4684290e+00   2.9359837e+00   2.4494897e+00   3.0886890e+00   2.9782545e+00   3.0380915e+00   3.2140317e+00   2.1424285e+00   2.9782545e+00   5.1487863e+00   4.1243181e+00   5.1332251e+00   4.5628938e+00   4.9183331e+00   5.9118525e+00   3.5972211e+00   5.4635154e+00   4.9173163e+00   5.4497706e+00   4.2023803e+00   4.3965896e+00   4.6968074e+00   4.1255303e+00   4.3324358e+00   4.4833024e+00   4.5011110e+00   6.0282667e+00   6.3300869e+00   4.0681691e+00   4.9547957e+00   3.9560081e+00   6.0315835e+00   3.9912404e+00   4.8062459e+00   5.1283526e+00   3.8600518e+00   3.8858718e+00   4.7148701e+00   4.9173163e+00   5.3721504e+00   5.7887823e+00   4.7560488e+00   4.0336088e+00   4.4665423e+00   5.5991071e+00   4.7486840e+00   4.4631827e+00   3.7815341e+00   4.6292548e+00   4.8682646e+00   4.4698993e+00   4.1243181e+00   5.0970580e+00   4.9779514e+00   4.5033321e+00   4.1701319e+00   4.3162484e+00   4.5110974e+00   4.0323690e+00   4.5825757e-01   8.1853528e-01   1.2328828e+00   1.3638182e+00   8.6023253e-01   3.8729833e-01   9.9498744e-01   5.1961524e-01   6.0827625e-01   4.7958315e-01   6.6332496e-01   4.4721360e-01   3.0000000e-01   4.4721360e-01   2.8284271e-01   4.2426407e-01   4.4721360e-01   2.2360680e-01   3.0000000e-01   6.4031242e-01   8.1853528e-01   1.0816654e+00   3.4641016e-01   4.8989795e-01   7.6811457e-01   3.4641016e-01   6.4031242e-01   3.1622777e-01   3.8729833e-01   1.1832160e+00   5.3851648e-01   4.5825757e-01   6.1644140e-01   4.5825757e-01   5.0000000e-01   3.4641016e-01   5.9160798e-01   3.0000000e-01   3.9912404e+00   3.5637059e+00   4.1327957e+00   2.9444864e+00   3.7336309e+00   3.2848135e+00   3.7188708e+00   2.1307276e+00   3.7013511e+00   2.7166155e+00   2.5000000e+00   3.1336879e+00   3.0463092e+00   3.6041643e+00   2.4698178e+00   3.6027767e+00   3.3015148e+00   2.8948230e+00   3.6742346e+00   2.7477263e+00   3.7483330e+00   3.0033315e+00   3.9547440e+00   3.5580894e+00   3.3630343e+00   3.5608988e+00   4.0049969e+00   4.1928511e+00   3.4336569e+00   2.3874673e+00   2.6720778e+00   2.5573424e+00   2.7892651e+00   4.0174619e+00   3.2588341e+00   3.4365681e+00   3.8729833e+00   3.5369478e+00   2.8740216e+00   2.8757608e+00   3.1575307e+00   3.5057096e+00   2.8982753e+00   2.1863211e+00   3.0166206e+00   2.9546573e+00   3.0049958e+00   3.2726136e+00   1.9157244e+00   2.9376862e+00   5.1874849e+00   4.0779897e+00   5.2488094e+00   4.5891176e+00   4.9689033e+00   6.0506198e+00   3.3882149e+00   5.5812185e+00   4.9618545e+00   5.5982140e+00   4.2918527e+00   4.4305756e+00   4.7937459e+00   4.0521599e+00   4.2953463e+00   4.5497253e+00   4.5628938e+00   6.2112801e+00   6.4459289e+00   4.0162171e+00   5.0665570e+00   3.8897301e+00   6.1660360e+00   4.0236799e+00   4.9030603e+00   5.2649786e+00   3.8884444e+00   3.9115214e+00   4.7465777e+00   5.0517324e+00   5.5009090e+00   6.0041652e+00   4.7874837e+00   4.0681691e+00   4.4463468e+00   5.7645468e+00   4.8052055e+00   4.5188494e+00   3.7947332e+00   4.7486840e+00   4.9537864e+00   4.6000000e+00   4.0779897e+00   5.1903757e+00   5.0714889e+00   4.5978256e+00   4.1844952e+00   4.3874822e+00   4.5617979e+00   4.0224371e+00   5.8309519e-01   1.4317821e+00   1.6941074e+00   1.1269428e+00   6.1644140e-01   1.2569805e+00   8.8317609e-01   7.8740079e-01   8.2462113e-01   7.5498344e-01   6.5574385e-01   6.4807407e-01   3.0000000e-01   5.7445626e-01   6.5574385e-01   5.7445626e-01   3.1622777e-01   2.4494897e-01   7.8740079e-01   1.1747340e+00   1.3928388e+00   1.7320508e-01   3.6055513e-01   8.7177979e-01   1.7320508e-01   4.2426407e-01   5.1961524e-01   5.8309519e-01   7.9372539e-01   4.6904158e-01   7.6157731e-01   1.0344080e+00   2.0000000e-01   8.8317609e-01   3.0000000e-01   8.7177979e-01   3.7416574e-01   4.1785165e+00   3.7643060e+00   4.3162484e+00   3.0298515e+00   3.8897301e+00   3.4496377e+00   3.9344631e+00   2.1886069e+00   3.8639358e+00   2.8618176e+00   2.5019992e+00   3.3181320e+00   3.1064449e+00   3.7788887e+00   2.6324893e+00   3.7828561e+00   3.4942810e+00   3.0315013e+00   3.7643060e+00   2.8530685e+00   3.9623226e+00   3.1511903e+00   4.0877867e+00   3.7188708e+00   3.5242020e+00   3.7322915e+00   4.1581246e+00   4.3737855e+00   3.6083237e+00   2.4879711e+00   2.7586228e+00   2.6362853e+00   2.9240383e+00   4.1797129e+00   3.4539832e+00   3.6687873e+00   4.0583248e+00   3.6304270e+00   3.0610456e+00   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6.3253458e+00   4.2883563e+00   4.9122296e+00   4.0853396e+00   6.0133186e+00   4.0951190e+00   4.7686476e+00   5.0892043e+00   3.9572718e+00   3.9547440e+00   4.7696960e+00   4.9132474e+00   5.3721504e+00   5.6364883e+00   4.8062459e+00   4.1340053e+00   4.6054316e+00   5.5434646e+00   4.7085029e+00   4.4877611e+00   3.8600518e+00   4.6076024e+00   4.8476799e+00   4.4384682e+00   4.2555846e+00   5.0616203e+00   4.9254441e+00   4.5011110e+00   4.2976738e+00   4.3416587e+00   4.4799554e+00   4.1133928e+00   5.1961524e-01   5.1961524e-01   3.8729833e-01   6.7082039e-01   4.1231056e-01   9.2736185e-01   7.8740079e-01   1.0049876e+00   1.0488088e+00   7.0710678e-01   5.2915026e-01   5.8309519e-01   1.0535654e+00   1.0630146e+00   5.3851648e-01   4.5825757e-01   3.8729833e-01   1.0099505e+00   8.3666003e-01   4.5825757e-01   1.0099505e+00   1.3601471e+00   6.4807407e-01   5.7445626e-01   1.8384776e+00   1.2369317e+00   6.7082039e-01   6.7823300e-01   1.0908712e+00   4.7958315e-01   1.0862780e+00   3.6055513e-01   7.5498344e-01   3.9509493e+00   3.5972211e+00   4.1303753e+00   3.2664966e+00   3.8105118e+00   3.5142567e+00   3.7643060e+00   2.6191602e+00   3.7603191e+00   3.0397368e+00   2.9949958e+00   3.2680269e+00   3.3015148e+00   3.7483330e+00   2.6720778e+00   3.5972211e+00   3.5071356e+00   3.1304952e+00   3.8704005e+00   3.0413813e+00   3.8665230e+00   3.1304952e+00   4.1158231e+00   3.7282704e+00   3.4365681e+00   3.5860842e+00   4.0521599e+00   4.2284749e+00   3.5791060e+00   2.6419690e+00   3.0000000e+00   2.8948230e+00   3.0000000e+00   4.2047592e+00   3.5014283e+00   3.5057096e+00   3.8858718e+00   3.7134889e+00   3.0822070e+00   3.1733263e+00   3.4568772e+00   3.6318040e+00   3.1272992e+00   2.6608269e+00   3.2710854e+00   3.1543621e+00   3.2109189e+00   3.3837849e+00   2.3302360e+00   3.1543621e+00   5.2602281e+00   4.2766810e+00   5.2678269e+00   4.7180504e+00   5.0507425e+00   6.0522723e+00   3.7603191e+00   5.6187187e+00   5.0852729e+00   5.5479726e+00   4.3243497e+00   4.5486262e+00   4.8270074e+00   4.2778499e+00   4.4508426e+00   4.5934736e+00   4.6497312e+00   6.1400326e+00   6.4768820e+00   4.2602817e+00   5.0705029e+00   4.0951190e+00   6.1822326e+00   4.1436699e+00   4.9295030e+00   5.2706736e+00   4.0074930e+00   4.0274061e+00   4.8569538e+00   5.0734604e+00   5.5226805e+00   5.9016947e+00   4.8928519e+00   4.2035699e+00   4.6551047e+00   5.7227616e+00   4.8528342e+00   4.6086874e+00   3.9217343e+00   4.7528939e+00   4.9819675e+00   4.5760245e+00   4.2766810e+00   5.2172790e+00   5.0813384e+00   4.6173586e+00   4.3255058e+00   4.4485953e+00   4.6162756e+00   4.1785165e+00   7.3484692e-01   3.1622777e-01   4.4721360e-01   2.4494897e-01   6.5574385e-01   4.1231056e-01   6.0000000e-01   5.5677644e-01   2.6457513e-01   1.7320508e-01   1.7320508e-01   5.4772256e-01   5.4772256e-01   3.4641016e-01   6.4807407e-01   8.1240384e-01   5.0000000e-01   3.8729833e-01   4.2426407e-01   5.0000000e-01   8.7177979e-01   1.7320508e-01   1.4142136e-01   1.3453624e+00   7.7459667e-01   3.7416574e-01   5.9160798e-01   5.8309519e-01   3.7416574e-01   5.9160798e-01   3.1622777e-01   2.4494897e-01   3.9749214e+00   3.5818989e+00   4.1340053e+00   3.0594117e+00   3.7589892e+00   3.3852622e+00   3.7496667e+00   2.3130067e+00   3.7215588e+00   2.8478062e+00   2.6758176e+00   3.1890437e+00   3.1224990e+00   3.6687873e+00   2.5396850e+00   3.5958309e+00   3.3985291e+00   2.9849623e+00   3.7349699e+00   2.8530685e+00   3.8131352e+00   3.0413813e+00   4.0162171e+00   3.6318040e+00   3.3852622e+00   3.5651087e+00   4.0187063e+00   4.2107007e+00   3.4957117e+00   2.4637370e+00   2.7874720e+00   2.6739484e+00   2.8618176e+00   4.1024383e+00   3.3749074e+00   3.4813790e+00   3.8794329e+00   3.5888717e+00   2.9647934e+00   2.9866369e+00   3.2832910e+00   3.5637059e+00   2.9782545e+00   2.3558438e+00   3.1192948e+00   3.0430248e+00   3.0919250e+00   3.3136083e+00   2.0493902e+00   3.0232433e+00   5.2421370e+00   4.1689327e+00   5.2668776e+00   4.6572524e+00   5.0179677e+00   6.0646517e+00   3.5510562e+00   5.6089215e+00   5.0169712e+00   5.5991071e+00   4.3162484e+00   4.4833024e+00   4.8155997e+00   4.1484937e+00   4.3680659e+00   4.5814845e+00   4.6119410e+00   6.2088646e+00   6.4668385e+00   4.1109610e+00   5.0813384e+00   3.9849718e+00   6.1830413e+00   4.0718546e+00   4.9325450e+00   5.2829916e+00   3.9382737e+00   3.9686270e+00   4.8020829e+00   5.0705029e+00   5.5163394e+00   5.9849812e+00   4.8404545e+00   4.1303753e+00   4.5453273e+00   5.7532599e+00   4.8476799e+00   4.5727453e+00   3.8561639e+00   4.7581509e+00   4.9769469e+00   4.5923850e+00   4.1689327e+00   5.2182373e+00   5.0921508e+00   4.6097722e+00   4.2379240e+00   4.4204072e+00   4.6065171e+00   4.1024383e+00   6.3245553e-01   5.0990195e-01   6.4807407e-01   1.3228757e+00   8.0622577e-01   1.0099505e+00   1.0723805e+00   8.1853528e-01   6.2449980e-01   7.1414284e-01   1.1747340e+00   1.1489125e+00   5.4772256e-01   6.4807407e-01   5.4772256e-01   1.1000000e+00   1.0535654e+00   5.4772256e-01   1.1000000e+00   1.5811388e+00   7.5498344e-01   8.6023253e-01   1.9621417e+00   1.4899664e+00   8.2462113e-01   6.4031242e-01   1.2409674e+00   6.1644140e-01   1.2922848e+00   4.6904158e-01   9.1651514e-01   3.5014283e+00   3.1827661e+00   3.6891733e+00   2.9291637e+00   3.3896903e+00   3.1368774e+00   3.3615473e+00   2.3769729e+00   3.3211444e+00   2.7404379e+00   2.7313001e+00   2.8930952e+00   2.9034462e+00   3.3436507e+00   2.3302360e+00   3.1606961e+00   3.1511903e+00   2.7331301e+00   3.4770677e+00   2.6795522e+00   3.5014283e+00   2.7294688e+00   3.7054015e+00   3.3120990e+00   3.0099834e+00   3.1543621e+00   3.6097091e+00   3.8065733e+00   3.1906112e+00   2.2737634e+00   2.6551836e+00   2.5475478e+00   2.6210685e+00   3.8144462e+00   3.1638584e+00   3.1272992e+00   3.4539832e+00   3.3015148e+00   2.7221315e+00   2.8319605e+00   3.0951575e+00   3.2280025e+00   2.7477263e+00   2.4062419e+00   2.9103264e+00   2.7748874e+00   2.8390139e+00   2.9698485e+00   2.0928450e+00   2.7856777e+00   4.8928519e+00   3.9166312e+00   4.8456166e+00   4.3162484e+00   4.6583259e+00   5.6124861e+00   3.4828150e+00   5.1749396e+00   4.6636895e+00   5.1468437e+00   3.9306488e+00   4.1496988e+00   4.4192760e+00   3.9331921e+00   4.1206796e+00   4.2201896e+00   4.2391037e+00   5.7105166e+00   6.0398675e+00   3.8704005e+00   4.6690470e+00   3.7603191e+00   5.7349804e+00   3.7496667e+00   4.5265881e+00   4.8321838e+00   3.6207734e+00   3.6455452e+00   4.4654227e+00   4.6249324e+00   5.0803543e+00   5.4607692e+00   4.5066617e+00   3.7894591e+00   4.2449971e+00   5.2915026e+00   4.4877611e+00   4.2035699e+00   3.5482390e+00   4.3428102e+00   4.5945620e+00   4.1821047e+00   3.9166312e+00   4.8176758e+00   4.7000000e+00   4.2296572e+00   3.9370039e+00   4.0521599e+00   4.2544095e+00   3.8065733e+00   5.4772256e-01   1.4142136e-01   7.4161985e-01   5.7445626e-01   6.4807407e-01   8.1853528e-01   4.3588989e-01   3.3166248e-01   4.3588989e-01   7.3484692e-01   7.7459667e-01   5.0990195e-01   3.7416574e-01   5.8309519e-01   7.5498344e-01   6.8556546e-01   5.4772256e-01   7.5498344e-01   1.0862780e+00   4.1231056e-01   3.7416574e-01   1.6278821e+00   9.4868330e-01   4.4721360e-01   4.1231056e-01   8.6023253e-01   1.4142136e-01   7.9372539e-01   2.4494897e-01   5.2915026e-01   3.9268308e+00   3.5341194e+00   4.0902323e+00   3.1080541e+00   3.7429935e+00   3.3704599e+00   3.6905284e+00   2.3937418e+00   3.6972963e+00   2.8618176e+00   2.7820855e+00   3.1638584e+00   3.1796226e+00   3.6414283e+00   2.5436195e+00   3.5594943e+00   3.3660065e+00   2.9916551e+00   3.7696154e+00   2.8879058e+00   3.7603191e+00   3.0413813e+00   4.0162171e+00   3.6124784e+00   3.3674916e+00   3.5369478e+00   3.9987498e+00   4.1725292e+00   3.4727511e+00   2.5079872e+00   2.8372522e+00   2.7294688e+00   2.8757608e+00   4.0828911e+00   3.3421550e+00   3.4146742e+00   3.8379682e+00   3.6193922e+00   2.9410882e+00   3.0166206e+00   3.2893768e+00   3.5298725e+00   2.9983329e+00   2.4474477e+00   3.1224990e+00   3.0166206e+00   3.0757113e+00   3.2954514e+00   2.1400935e+00   3.0199338e+00   5.1749396e+00   4.1496988e+00   5.2191953e+00   4.6162756e+00   4.9699095e+00   6.0116553e+00   3.5623026e+00   5.5623736e+00   4.9989999e+00   5.5181519e+00   4.2626283e+00   4.4609416e+00   4.7717921e+00   4.1460825e+00   4.3428102e+00   4.5265881e+00   4.5661800e+00   6.1163715e+00   6.4311741e+00   4.1303753e+00   5.0239427e+00   3.9623226e+00   6.1392182e+00   4.0570926e+00   4.8672374e+00   5.2220686e+00   3.9179076e+00   3.9306488e+00   4.7686476e+00   5.0229473e+00   5.4781384e+00   5.8940648e+00   4.8072861e+00   4.1036569e+00   4.5232732e+00   5.7061370e+00   4.7770284e+00   4.5199558e+00   3.8196859e+00   4.7095647e+00   4.9264592e+00   4.5486262e+00   4.1496988e+00   5.1584882e+00   5.0289164e+00   4.5705580e+00   4.2355637e+00   4.3794977e+00   4.5365185e+00   4.0607881e+00   5.0990195e-01   1.0816654e+00   4.3588989e-01   6.3245553e-01   5.7445626e-01   4.5825757e-01   3.0000000e-01   3.6055513e-01   7.3484692e-01   6.7823300e-01   2.8284271e-01   7.6157731e-01   8.6023253e-01   6.2449980e-01   6.7082039e-01   4.2426407e-01   6.2449980e-01   1.1489125e+00   3.6055513e-01   5.8309519e-01   1.4798649e+00   1.0954451e+00   5.8309519e-01   5.7445626e-01   7.8740079e-01   5.0990195e-01   8.7749644e-01   3.7416574e-01   5.0990195e-01   3.6110940e+00   3.2511536e+00   3.7775654e+00   2.7784888e+00   3.4161382e+00   3.0822070e+00   3.4322005e+00   2.1095023e+00   3.3630343e+00   2.6095977e+00   2.4494897e+00   2.8896367e+00   2.7802878e+00   3.3436507e+00   2.2605309e+00   3.2419130e+00   3.1192948e+00   2.6551836e+00   3.4073450e+00   2.5495098e+00   3.5298725e+00   2.7110883e+00   3.6810325e+00   3.2939338e+00   3.0364453e+00   3.2140317e+00   3.6565011e+00   3.8716921e+00   3.1843367e+00   2.1470911e+00   2.4959968e+00   2.3769729e+00   2.5475478e+00   3.7907783e+00   3.1128765e+00   3.1874755e+00   3.5312887e+00   3.2434549e+00   2.6776856e+00   2.7055499e+00   2.9899833e+00   3.2403703e+00   2.6627054e+00   2.1377558e+00   2.8266588e+00   2.7386128e+00   2.7928480e+00   2.9765752e+00   1.8439089e+00   2.7239677e+00   4.9598387e+00   3.8858718e+00   4.9295030e+00   4.3393548e+00   4.7095647e+00   5.7113921e+00   3.3391616e+00   5.2516664e+00   4.6765372e+00   5.2848841e+00   4.0062451e+00   4.1641326e+00   4.4911023e+00   3.8768544e+00   4.1133928e+00   4.2906876e+00   4.2860238e+00   5.8694122e+00   6.1139185e+00   3.7920970e+00   4.7644517e+00   3.7255872e+00   5.8215118e+00   3.7549967e+00   4.6162756e+00   4.9325450e+00   3.6290495e+00   3.6674242e+00   4.4922155e+00   4.7085029e+00   5.1584882e+00   5.6338264e+00   4.5354162e+00   3.7973675e+00   4.2166337e+00   5.4055527e+00   4.5672749e+00   4.2532341e+00   3.5623026e+00   4.4317040e+00   4.6722586e+00   4.2790186e+00   3.8858718e+00   4.9040799e+00   4.7947888e+00   4.3023250e+00   3.9242834e+00   4.1060930e+00   4.3289722e+00   3.8118237e+00   7.4161985e-01   4.5825757e-01   6.1644140e-01   7.4161985e-01   3.3166248e-01   3.0000000e-01   3.8729833e-01   6.7823300e-01   7.0710678e-01   4.2426407e-01   5.0990195e-01   6.7823300e-01   7.0000000e-01   6.2449980e-01   5.2915026e-01   7.0000000e-01   1.0295630e+00   3.6055513e-01   3.1622777e-01   1.5394804e+00   9.0553851e-01   3.1622777e-01   4.1231056e-01   7.7459667e-01   2.4494897e-01   7.4161985e-01   2.8284271e-01   4.6904158e-01   3.8858718e+00   3.4856850e+00   4.0459857e+00   3.0298515e+00   3.6864617e+00   3.3136083e+00   3.6441734e+00   2.3086793e+00   3.6482873e+00   2.7874720e+00   2.6944387e+00   3.1032241e+00   3.1096624e+00   3.5888717e+00   2.4718414e+00   3.5114100e+00   3.3090784e+00   2.9342802e+00   3.6972963e+00   2.8178006e+00   3.7067506e+00   2.9782545e+00   3.9560081e+00   3.5623026e+00   3.3136083e+00   3.4856850e+00   3.9484174e+00   4.1218928e+00   3.4146742e+00   2.4351591e+00   2.7622455e+00   2.6551836e+00   2.8089144e+00   4.0261644e+00   3.2848135e+00   3.3674916e+00   3.7907783e+00   3.5524639e+00   2.8827071e+00   2.9427878e+00   3.2280025e+00   3.4785054e+00   2.9308702e+00   2.3600847e+00   3.0577770e+00   2.9631065e+00   3.0166206e+00   3.2403703e+00   2.0445048e+00   2.9563491e+00   5.1244512e+00   4.0865633e+00   5.1710734e+00   4.5661800e+00   4.9173163e+00   5.9699246e+00   3.4885527e+00   5.5208695e+00   4.9446941e+00   5.4763126e+00   4.2107007e+00   4.4022721e+00   4.7191101e+00   4.0755368e+00   4.2731721e+00   4.4710178e+00   4.5177428e+00   6.0868711e+00   6.3827894e+00   4.0644803e+00   4.9739320e+00   3.8961519e+00   6.0967204e+00   3.9949969e+00   4.8218254e+00   5.1836281e+00   3.8561639e+00   3.8742741e+00   4.7116876e+00   4.9829710e+00   5.4323107e+00   5.8668561e+00   4.7486840e+00   4.0521599e+00   4.4743715e+00   5.6586217e+00   4.7265209e+00   4.4732538e+00   3.7616486e+00   4.6583259e+00   4.8713448e+00   4.4911023e+00   4.0865633e+00   5.1097945e+00   4.9769469e+00   4.5110974e+00   4.1689327e+00   4.3243497e+00   4.4855323e+00   4.0062451e+00   9.5916630e-01   9.4339811e-01   9.3808315e-01   7.7459667e-01   7.8740079e-01   7.4833148e-01   7.2801099e-01   8.0622577e-01   9.8488578e-01   9.3273791e-01   1.1532563e+00   7.7459667e-01   6.0000000e-01   9.5393920e-01   7.7459667e-01   7.0000000e-01   7.3484692e-01   5.1961524e-01   1.3416408e+00   5.3851648e-01   8.3066239e-01   1.0677078e+00   7.5498344e-01   8.0622577e-01   5.6568542e-01   8.6602540e-01   6.4031242e-01   4.5880279e+00   4.1641326e+00   4.7370877e+00   3.5651087e+00   4.3474130e+00   3.9127995e+00   4.3162484e+00   2.7313001e+00   4.3197222e+00   3.3196385e+00   3.1000000e+00   3.7389838e+00   3.6823905e+00   4.2272923e+00   3.0757113e+00   4.2023803e+00   3.9115214e+00   3.5355339e+00   4.2965102e+00   3.3808283e+00   4.3416587e+00   3.6193922e+00   4.5825757e+00   4.1928511e+00   3.9786933e+00   4.1665333e+00   4.6216880e+00   4.7979162e+00   4.0484565e+00   3.0166206e+00   3.3015148e+00   3.1906112e+00   3.4146742e+00   4.6411206e+00   3.8652296e+00   4.0261644e+00   4.4766059e+00   4.1653331e+00   3.4899857e+00   3.4971417e+00   3.7907783e+00   4.1243181e+00   3.5270384e+00   2.7892651e+00   3.6414283e+00   3.5791060e+00   3.6262929e+00   3.8923001e+00   2.5039968e+00   3.5594943e+00   5.7680153e+00   4.6850827e+00   5.8506410e+00   5.2057660e+00   5.5686623e+00   6.6580778e+00   3.9749214e+00   6.1991935e+00   5.5874860e+00   6.1692787e+00   4.8805737e+00   5.0428167e+00   5.3907328e+00   4.6540305e+00   4.8713448e+00   5.1283526e+00   5.1749396e+00   6.7926431e+00   7.0590368e+00   4.6486557e+00   5.6524331e+00   4.4821870e+00   6.7808554e+00   4.6335731e+00   5.4954527e+00   5.8719673e+00   4.4944410e+00   4.5144213e+00   5.3525695e+00   5.6674509e+00   6.1139185e+00   6.5825527e+00   5.3888774e+00   4.6936127e+00   5.0842895e+00   6.3553127e+00   5.3786615e+00   5.1283526e+00   4.3954522e+00   5.3394756e+00   5.5371473e+00   5.1730069e+00   4.6850827e+00   5.7810034e+00   5.6462377e+00   5.1788030e+00   4.7947888e+00   4.9849774e+00   5.1351728e+00   4.6281746e+00   4.7958315e-01   4.4721360e-01   2.0000000e-01   4.2426407e-01   4.4721360e-01   5.1961524e-01   4.7958315e-01   3.8729833e-01   9.2195445e-01   1.0723805e+00   5.2915026e-01   6.0000000e-01   6.7082039e-01   5.2915026e-01   9.1104336e-01   3.7416574e-01   5.0000000e-01   1.2489996e+00   8.6602540e-01   2.6457513e-01   5.4772256e-01   5.5677644e-01   5.9160798e-01   6.6332496e-01   5.7445626e-01   4.3588989e-01   3.6646964e+00   3.2465366e+00   3.8105118e+00   2.6627054e+00   3.4088121e+00   3.0149627e+00   3.4132096e+00   1.9131126e+00   3.3852622e+00   2.4535688e+00   2.2781571e+00   2.8248894e+00   2.7495454e+00   3.3120990e+00   2.1587033e+00   3.2710854e+00   3.0298515e+00   2.6191602e+00   3.3555923e+00   2.4677925e+00   3.4568772e+00   2.6795522e+00   3.6496575e+00   3.2771939e+00   3.0413813e+00   3.2310989e+00   3.6823905e+00   3.8704005e+00   3.1320920e+00   2.0832667e+00   2.3958297e+00   2.2847319e+00   2.4859606e+00   3.7336309e+00   3.0033315e+00   3.1416556e+00   3.5496479e+00   3.2202484e+00   2.5961510e+00   2.5942244e+00   2.9034462e+00   3.2109189e+00   2.6000000e+00   1.9544820e+00   2.7386128e+00   2.6814175e+00   2.7221315e+00   2.9614186e+00   1.6401219e+00   2.6476405e+00   4.8918299e+00   3.7907783e+00   4.9284886e+00   4.3011626e+00   4.6636895e+00   5.7367238e+00   3.1559468e+00   5.2773099e+00   4.6583259e+00   5.2782573e+00   3.9724048e+00   4.1194660e+00   4.4698993e+00   3.7603191e+00   3.9887341e+00   4.2308392e+00   4.2638011e+00   5.9076222e+00   6.1261734e+00   3.7296112e+00   4.7423623e+00   3.6041643e+00   5.8532043e+00   3.7054015e+00   4.5956501e+00   4.9598387e+00   3.5721142e+00   3.6083237e+00   4.4395946e+00   4.7455242e+00   5.1826634e+00   5.6947344e+00   4.4766059e+00   3.7749172e+00   4.1844952e+00   5.4267854e+00   4.5022217e+00   4.2261093e+00   3.4928498e+00   4.4192760e+00   4.6281746e+00   4.2520583e+00   3.7907783e+00   4.8764741e+00   4.7497368e+00   4.2591079e+00   3.8639358e+00   4.0681691e+00   4.2602817e+00   3.7389838e+00   5.3851648e-01   4.1231056e-01   5.7445626e-01   6.4031242e-01   3.7416574e-01   4.2426407e-01   7.4833148e-01   9.0553851e-01   1.1747340e+00   5.1961524e-01   7.5498344e-01   9.2736185e-01   5.1961524e-01   8.2462113e-01   5.0000000e-01   6.4807407e-01   1.2922848e+00   7.4833148e-01   5.4772256e-01   5.3851648e-01   6.4807407e-01   5.8309519e-01   5.7445626e-01   7.0710678e-01   5.4772256e-01   3.7629775e+00   3.3241540e+00   3.8974351e+00   2.7055499e+00   3.4971417e+00   3.0232433e+00   3.4727511e+00   1.9000000e+00   3.4626579e+00   2.4677925e+00   2.2803509e+00   2.8896367e+00   2.8160256e+00   3.3496268e+00   2.2338308e+00   3.3749074e+00   3.0413813e+00   2.6400758e+00   3.4423829e+00   2.5019992e+00   3.4957117e+00   2.7694765e+00   3.7080992e+00   3.3000000e+00   3.1272992e+00   3.3301652e+00   3.7696154e+00   3.9534795e+00   3.1843367e+00   2.1563859e+00   2.4310492e+00   2.3173260e+00   2.5475478e+00   3.7589892e+00   2.9949958e+00   3.1874755e+00   3.6373067e+00   3.3045423e+00   2.6172505e+00   2.6305893e+00   2.8948230e+00   3.2526912e+00   2.6551836e+00   1.9621417e+00   2.7622455e+00   2.6944387e+00   2.7495454e+00   3.0298515e+00   1.7088007e+00   2.6870058e+00   4.9355851e+00   3.8236109e+00   5.0059964e+00   4.3301270e+00   4.7180504e+00   5.8051701e+00   3.1352831e+00   5.3310412e+00   4.7106263e+00   5.3600373e+00   4.0509258e+00   4.1833001e+00   4.5530210e+00   3.8039453e+00   4.0546270e+00   4.3092923e+00   4.3092923e+00   5.9674115e+00   6.2016127e+00   3.7656341e+00   4.8270074e+00   3.6386811e+00   5.9203040e+00   3.7815341e+00   4.6551047e+00   5.0169712e+00   3.6455452e+00   3.6619667e+00   4.4966654e+00   4.8052055e+00   5.2583267e+00   5.7671483e+00   4.5398238e+00   3.8131352e+00   4.1785165e+00   5.5335341e+00   4.5585085e+00   4.2626283e+00   3.5454196e+00   4.5122057e+00   4.7148701e+00   4.3760713e+00   3.8236109e+00   4.9446941e+00   4.8321838e+00   4.3669211e+00   3.9446166e+00   4.1448764e+00   4.3150898e+00   3.7643060e+00   4.4721360e-01   5.4772256e-01   4.8989795e-01   3.6055513e-01   2.2360680e-01   6.0827625e-01   1.1269428e+00   1.3152946e+00   2.0000000e-01   4.4721360e-01   7.6811457e-01   2.0000000e-01   6.7082039e-01   4.2426407e-01   5.9160798e-01   9.1651514e-01   7.0000000e-01   6.4031242e-01   8.8317609e-01   3.0000000e-01   8.0622577e-01   4.8989795e-01   7.6811457e-01   3.6055513e-01   3.8845849e+00   3.4785054e+00   4.0249224e+00   2.7766887e+00   3.6027767e+00   3.1859065e+00   3.6537652e+00   1.9748418e+00   3.5749126e+00   2.6191602e+00   2.2912878e+00   3.0430248e+00   2.8354894e+00   3.5028560e+00   2.3622024e+00   3.4899857e+00   3.2341923e+00   2.7604347e+00   3.4899857e+00   2.5903668e+00   3.6945906e+00   2.8670542e+00   3.8105118e+00   3.4438351e+00   3.2357379e+00   3.4409301e+00   3.8678159e+00   4.0865633e+00   3.3331667e+00   2.2135944e+00   2.5019992e+00   2.3790755e+00   2.6495283e+00   3.9115214e+00   3.2031235e+00   3.3955854e+00   3.7682887e+00   3.3511192e+00   2.7964263e+00   2.7331301e+00   3.0413813e+00   3.4132096e+00   2.7495454e+00   2.0049938e+00   2.9017236e+00   2.8722813e+00   2.9103264e+00   3.1543621e+00   1.7406895e+00   2.8266588e+00   5.1410116e+00   3.9837169e+00   5.1487863e+00   4.5011110e+00   4.8877398e+00   5.9472683e+00   3.3045423e+00   5.4726593e+00   4.8311489e+00   5.5443665e+00   4.2166337e+00   4.3162484e+00   4.6968074e+00   3.9420807e+00   4.2154478e+00   4.4833024e+00   4.4743715e+00   6.1595454e+00   6.3206012e+00   3.8587563e+00   4.9869831e+00   3.8118237e+00   6.0481402e+00   3.9025633e+00   4.8373546e+00   5.1768716e+00   3.7788887e+00   3.8288379e+00   4.6486557e+00   4.9436828e+00   5.3795911e+00   5.9439044e+00   4.6904158e+00   3.9585351e+00   4.3370497e+00   5.6524331e+00   4.7634021e+00   4.4429720e+00   3.7148351e+00   4.6551047e+00   4.8723711e+00   4.5033321e+00   3.9837169e+00   5.1166395e+00   5.0079936e+00   4.5011110e+00   4.0484565e+00   4.2953463e+00   4.5221676e+00   3.9522146e+00   3.1622777e-01   3.4641016e-01   4.1231056e-01   4.1231056e-01   4.1231056e-01   7.9372539e-01   9.8488578e-01   4.4721360e-01   4.8989795e-01   6.2449980e-01   4.4721360e-01   8.0622577e-01   2.4494897e-01   3.3166248e-01   1.2489996e+00   7.2801099e-01   2.2360680e-01   5.0990195e-01   5.0000000e-01   4.5825757e-01   5.2915026e-01   4.7958315e-01   3.0000000e-01   3.8275318e+00   3.4088121e+00   3.9749214e+00   2.8337255e+00   3.5805028e+00   3.1733263e+00   3.5707142e+00   2.0639767e+00   3.5524639e+00   2.6115130e+00   2.4351591e+00   2.9899833e+00   2.9257478e+00   3.4741906e+00   2.3280893e+00   3.4380227e+00   3.1843367e+00   2.7820855e+00   3.5355339e+00   2.6362853e+00   3.6124784e+00   2.8530685e+00   3.8209946e+00   3.4380227e+00   3.2109189e+00   3.4000000e+00   3.8522721e+00   4.0373258e+00   3.2969683e+00   2.2583180e+00   2.5651511e+00   2.4535688e+00   2.6570661e+00   3.8961519e+00   3.1527766e+00   3.2939338e+00   3.7148351e+00   3.3985291e+00   2.7531800e+00   2.7622455e+00   3.0610456e+00   3.3719431e+00   2.7712813e+00   2.1118712e+00   2.9017236e+00   2.8372522e+00   2.8827071e+00   3.1288976e+00   1.8083141e+00   2.8124722e+00   5.0467812e+00   3.9534795e+00   5.0941143e+00   4.4609416e+00   4.8259714e+00   5.9000000e+00   3.3045423e+00   5.4396691e+00   4.8270074e+00   5.4350713e+00   4.1352146e+00   4.2883563e+00   4.6368092e+00   3.9268308e+00   4.1533119e+00   4.3931765e+00   4.4249294e+00   6.0580525e+00   6.2952363e+00   3.9000000e+00   4.9061186e+00   3.7643060e+00   6.0183054e+00   3.8768544e+00   4.7539457e+00   5.1185936e+00   3.7416574e+00   3.7709415e+00   4.6054316e+00   4.9071377e+00   5.3497664e+00   5.8455111e+00   4.6432747e+00   3.9382737e+00   4.3416587e+00   5.5955339e+00   4.6572524e+00   4.3840620e+00   3.6551334e+00   4.5858478e+00   4.7937459e+00   4.4226689e+00   3.9534795e+00   5.0378567e+00   4.9112117e+00   4.4294469e+00   4.0385641e+00   4.2343831e+00   4.4147480e+00   3.8961519e+00   1.4142136e-01   5.9160798e-01   5.7445626e-01   3.0000000e-01   6.0827625e-01   7.6811457e-01   5.0990195e-01   4.6904158e-01   3.6055513e-01   5.0990195e-01   9.6436508e-01   1.4142136e-01   3.0000000e-01   1.4071247e+00   8.7749644e-01   4.5825757e-01   5.4772256e-01   6.5574385e-01   3.3166248e-01   6.7823300e-01   2.2360680e-01   3.0000000e-01   3.8742741e+00   3.4957117e+00   4.0373258e+00   2.9983329e+00   3.6715120e+00   3.3090784e+00   3.6674242e+00   2.2759613e+00   3.6249138e+00   2.8000000e+00   2.6324893e+00   3.1176915e+00   3.0364453e+00   3.5846897e+00   2.4779023e+00   3.5014283e+00   3.3316662e+00   2.8982753e+00   3.6578682e+00   2.7802878e+00   3.7456642e+00   2.9597297e+00   3.9319207e+00   3.5411862e+00   3.2939338e+00   3.4727511e+00   3.9217343e+00   4.1231056e+00   3.4190642e+00   2.3874673e+00   2.7202941e+00   2.6038433e+00   2.7856777e+00   4.0249224e+00   3.3136083e+00   3.4073450e+00   3.7868192e+00   3.5028560e+00   2.8948230e+00   2.9240383e+00   3.2109189e+00   3.4799425e+00   2.9017236e+00   2.3151674e+00   3.0495901e+00   2.9647934e+00   3.0182777e+00   3.2264532e+00   2.0174241e+00   2.9512709e+00   5.1759057e+00   4.1048752e+00   5.1797683e+00   4.5760245e+00   4.9426713e+00   5.9690870e+00   3.5128336e+00   5.5108983e+00   4.9295030e+00   5.5190579e+00   4.2402830e+00   4.4056782e+00   4.7349762e+00   4.0914545e+00   4.3185646e+00   4.5144213e+00   4.5276926e+00   6.1139185e+00   6.3741666e+00   4.0336088e+00   5.0029991e+00   3.9306488e+00   6.0844063e+00   3.9962482e+00   4.8518038e+00   5.1865210e+00   3.8652296e+00   3.8961519e+00   4.7275787e+00   4.9699095e+00   5.4203321e+00   5.8847260e+00   4.7686476e+00   4.0435133e+00   4.4575778e+00   5.6630381e+00   4.7822589e+00   4.4899889e+00   3.7868192e+00   4.6765372e+00   4.9050994e+00   4.5188494e+00   4.1048752e+00   5.1400389e+00   5.0219518e+00   4.5387223e+00   4.1653331e+00   4.3439613e+00   4.5420260e+00   4.0323690e+00   5.7445626e-01   5.3851648e-01   3.0000000e-01   7.1414284e-01   8.5440037e-01   4.4721360e-01   3.4641016e-01   3.3166248e-01   4.4721360e-01   9.0000000e-01   1.4142136e-01   2.6457513e-01   1.3114877e+00   8.3066239e-01   5.0000000e-01   6.7823300e-01   5.7445626e-01   4.5825757e-01   6.3245553e-01   3.3166248e-01   2.2360680e-01   3.9509493e+00   3.5749126e+00   4.1133928e+00   3.0446675e+00   3.7389838e+00   3.3808283e+00   3.7509999e+00   2.3108440e+00   3.6959437e+00   2.8600699e+00   2.6551836e+00   3.1906112e+00   3.0789609e+00   3.6592349e+00   2.5416530e+00   3.5749126e+00   3.4088121e+00   2.9631065e+00   3.7067506e+00   2.8337255e+00   3.8275318e+00   3.0232433e+00   3.9949969e+00   3.6138622e+00   3.3630343e+00   3.5440090e+00   3.9899875e+00   4.1976184e+00   3.4914181e+00   2.4372115e+00   2.7676705e+00   2.6495283e+00   2.8460499e+00   4.0963398e+00   3.3911650e+00   3.4942810e+00   3.8626416e+00   3.5538711e+00   2.9698485e+00   2.9782545e+00   3.2756679e+00   3.5566838e+00   2.9597297e+00   2.3452079e+00   3.1144823e+00   3.0413813e+00   3.0903074e+00   3.2969683e+00   2.0469489e+00   3.0182777e+00   5.2602281e+00   4.1749251e+00   5.2564246e+00   4.6540305e+00   5.0209561e+00   6.0473135e+00   3.5721142e+00   5.5883808e+00   4.9979996e+00   5.6053546e+00   4.3197222e+00   4.4754888e+00   4.8104054e+00   4.1545156e+00   4.3874822e+00   4.5934736e+00   4.6065171e+00   6.2048368e+00   6.4459289e+00   4.0902323e+00   5.0823223e+00   4.0012498e+00   6.1595454e+00   4.0632499e+00   4.9355851e+00   5.2687759e+00   3.9344631e+00   3.9724048e+00   4.8010416e+00   5.0477718e+00   5.4936327e+00   5.9741108e+00   4.8414874e+00   4.1170378e+00   4.5310043e+00   5.7367238e+00   4.8672374e+00   4.5716518e+00   3.8626416e+00   4.7528939e+00   4.9819675e+00   4.5912961e+00   4.1749251e+00   5.2211110e+00   5.1029403e+00   4.6108568e+00   4.2272923e+00   4.4192760e+00   4.6270941e+00   4.1109610e+00   1.4142136e-01   7.6157731e-01   1.0392305e+00   1.2961481e+00   2.6457513e-01   5.0000000e-01   9.0553851e-01   2.6457513e-01   4.6904158e-01   4.5825757e-01   5.2915026e-01   9.7467943e-01   4.2426407e-01   5.8309519e-01   8.0622577e-01   3.1622777e-01   7.2111026e-01   2.2360680e-01   7.8740079e-01   3.7416574e-01   4.0422766e+00   3.6041643e+00   4.1749251e+00   2.9017236e+00   3.7536649e+00   3.2832910e+00   3.7603191e+00   2.0518285e+00   3.7296112e+00   2.6888659e+00   2.4041631e+00   3.1511903e+00   3.0149627e+00   3.6193922e+00   2.4718414e+00   3.6455452e+00   3.3090784e+00   2.8896367e+00   3.6537652e+00   2.7202941e+00   3.7735925e+00   3.0149627e+00   3.9534795e+00   3.5679126e+00   3.3882149e+00   3.5958309e+00   4.0311289e+00   4.2249260e+00   3.4467376e+00   2.3685439e+00   2.6324893e+00   2.5159491e+00   2.7838822e+00   4.0187063e+00   3.2603681e+00   3.4785054e+00   3.9127995e+00   3.5242020e+00   2.8827071e+00   2.8460499e+00   3.1368774e+00   3.5270384e+00   2.8861739e+00   2.1047565e+00   3.0049958e+00   2.9664794e+00   3.0099834e+00   3.2924155e+00   1.8493242e+00   2.9359837e+00   5.2172790e+00   4.0743098e+00   5.2820451e+00   4.6054316e+00   4.9919936e+00   6.0876925e+00   3.3451457e+00   5.6124861e+00   4.9689033e+00   5.6524331e+00   4.3278170e+00   4.4407207e+00   4.8238988e+00   4.0360872e+00   4.2965102e+00   4.5814845e+00   4.5880279e+00   6.2745518e+00   6.4699304e+00   3.9924930e+00   5.1048996e+00   3.8858718e+00   6.1975802e+00   4.0323690e+00   4.9426713e+00   5.3075418e+00   3.9000000e+00   3.9306488e+00   4.7602521e+00   5.0882217e+00   5.5308227e+00   6.0728906e+00   4.8010416e+00   4.0816663e+00   4.4452222e+00   5.8051701e+00   4.8414874e+00   4.5464272e+00   3.8118237e+00   4.7853944e+00   4.9849774e+00   4.6378875e+00   4.0743098e+00   5.2258971e+00   5.1097945e+00   4.6270941e+00   4.1833001e+00   4.4136153e+00   4.5978256e+00   4.0360872e+00   7.0710678e-01   1.0862780e+00   1.3190906e+00   1.7320508e-01   4.5825757e-01   8.6023253e-01   1.7320508e-01   5.0990195e-01   4.3588989e-01   5.4772256e-01   9.1104336e-01   5.0990195e-01   6.0000000e-01   8.4261498e-01   2.4494897e-01   7.6157731e-01   3.0000000e-01   7.8740079e-01   3.4641016e-01   3.9874804e+00   3.5594943e+00   4.1218928e+00   2.8460499e+00   3.6972963e+00   3.2434549e+00   3.7229021e+00   2.0074860e+00   3.6728735e+00   2.6551836e+00   2.3452079e+00   3.1096624e+00   2.9410882e+00   3.5749126e+00   2.4269322e+00   3.5902646e+00   3.2787193e+00   2.8372522e+00   3.5874782e+00   2.6645825e+00   3.7443290e+00   2.9580399e+00   3.8974351e+00   3.5199432e+00   3.3316662e+00   3.5397740e+00   3.9711459e+00   4.1749251e+00   3.4029399e+00   2.3043437e+00   2.5748786e+00   2.4556058e+00   2.7294688e+00   3.9761791e+00   3.2357379e+00   3.4496377e+00   3.8613469e+00   3.4554305e+00   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7.8740079e-01   8.3666003e-01   6.5574385e-01   5.7445626e-01   3.1622777e-01   6.5574385e-01   1.1135529e+00   3.6055513e-01   4.6904158e-01   1.4387495e+00   1.0583005e+00   4.6904158e-01   6.4031242e-01   7.3484692e-01   5.4772256e-01   8.5440037e-01   3.7416574e-01   4.6904158e-01   3.7202150e+00   3.3541020e+00   3.8871583e+00   2.8774989e+00   3.5199432e+00   3.2031235e+00   3.5355339e+00   2.2022716e+00   3.4799425e+00   2.7000000e+00   2.5455844e+00   2.9849623e+00   2.9000000e+00   3.4612137e+00   2.3473389e+00   3.3451457e+00   3.2264532e+00   2.7874720e+00   3.5057096e+00   2.6645825e+00   3.6249138e+00   2.8124722e+00   3.7934153e+00   3.4249088e+00   3.1464265e+00   3.3181320e+00   3.7696154e+00   3.9736633e+00   3.2893768e+00   2.2561028e+00   2.6057628e+00   2.4919872e+00   2.6551836e+00   3.9051248e+00   3.2202484e+00   3.2863353e+00   3.6373067e+00   3.3526109e+00   2.7874720e+00   2.8071338e+00   3.1144823e+00   3.3555923e+00   2.7730849e+00   2.2293497e+00   2.9376862e+00   2.8600699e+00   2.9051678e+00   3.0886890e+00   1.9078784e+00   2.8319605e+00   5.0477718e+00   3.9824616e+00   5.0299105e+00   4.4530888e+00   4.8062459e+00   5.8223707e+00   3.4278273e+00   5.3721504e+00   4.7906158e+00   5.3712196e+00   4.0951190e+00   4.2638011e+00   4.5836667e+00   3.9635842e+00   4.1809090e+00   4.3692105e+00   4.3965896e+00   5.9774577e+00   6.2209324e+00   3.9064050e+00   4.8518038e+00   3.8105118e+00   5.9371710e+00   3.8496753e+00   4.7148701e+00   5.0487622e+00   3.7215588e+00   3.7643060e+00   4.5891176e+00   4.8301139e+00   5.2697249e+00   5.7428216e+00   4.6270941e+00   3.9166312e+00   4.3520110e+00   5.4972721e+00   4.6497312e+00   4.3646306e+00   3.6565011e+00   4.5210618e+00   4.7528939e+00   4.3485630e+00   3.9824616e+00   4.9969991e+00   4.8733972e+00   4.3760713e+00   4.0149720e+00   4.1976184e+00   4.4113490e+00   3.9153544e+00   3.4641016e-01   1.0440307e+00   9.7467943e-01   7.0710678e-01   1.0440307e+00   1.3784049e+00   7.1414284e-01   6.9282032e-01   1.9519221e+00   1.2247449e+00   8.1240384e-01   5.9160798e-01   1.1916375e+00   3.4641016e-01   1.0908712e+00   4.2426407e-01   8.3666003e-01   3.9974992e+00   3.6345564e+00   4.1725292e+00   3.3196385e+00   3.8665230e+00   3.5185224e+00   3.7868192e+00   2.6514147e+00   3.8013156e+00   3.0675723e+00   3.0430248e+00   3.3090784e+00   3.3630343e+00   3.7656341e+00   2.7294688e+00   3.6537652e+00   3.5114100e+00   3.1448370e+00   3.9458839e+00   3.0789609e+00   3.8832976e+00   3.1921779e+00   4.1581246e+00   3.7349699e+00   3.4871192e+00   3.6428011e+00   4.1024383e+00   4.2743421e+00   3.6110940e+00   2.7037012e+00   3.0446675e+00   2.9376862e+00   3.0479501e+00   4.2201896e+00   3.4942810e+00   3.5185224e+00   3.9306488e+00   3.7815341e+00   3.0935417e+00   3.2155870e+00   3.4583233e+00   3.6496575e+00   3.1733263e+00   2.7073973e+00   3.2939338e+00   3.1559468e+00   3.2280025e+00   3.4234486e+00   2.4124676e+00   3.1843367e+00   5.2782573e+00   4.3034870e+00   5.3084838e+00   4.7275787e+00   5.0793700e+00   6.0811183e+00   3.7696154e+00   5.6373753e+00   5.1176166e+00   5.5830099e+00   4.3669211e+00   4.5912961e+00   4.8754487e+00   4.3208795e+00   4.5055521e+00   4.6400431e+00   4.6679760e+00   6.1473572e+00   6.5192024e+00   4.2965102e+00   5.1166395e+00   4.1255303e+00   6.2120850e+00   4.1976184e+00   4.9527770e+00   5.2867760e+00   4.0583248e+00   4.0583248e+00   4.8928519e+00   5.0941143e+00   5.5614746e+00   5.9160798e+00   4.9345719e+00   4.2213742e+00   4.6432747e+00   5.7844619e+00   4.8785244e+00   4.6184413e+00   3.9534795e+00   4.8062459e+00   5.0348784e+00   4.6572524e+00   4.3034870e+00   5.2507142e+00   5.1273775e+00   4.6893496e+00   4.3886217e+00   4.4944410e+00   4.6411206e+00   4.1892720e+00   1.2609520e+00   1.1357817e+00   7.0710678e-01   1.2609520e+00   1.6309506e+00   9.0000000e-01   8.7177979e-01   2.1517435e+00   1.4899664e+00   9.6953597e-01   7.8102497e-01   1.3928388e+00   6.0000000e-01   1.3453624e+00   5.4772256e-01   1.0295630e+00   3.9471509e+00   3.6207734e+00   4.1364236e+00   3.4029399e+00   3.8587563e+00   3.5805028e+00   3.7815341e+00   2.8017851e+00   3.7881394e+00   3.1670175e+00   3.1843367e+00   3.3361655e+00   3.4132096e+00   3.7920970e+00   2.7838822e+00   3.6180105e+00   3.5707142e+00   3.2046841e+00   3.9736633e+00   3.1559468e+00   3.9089641e+00   3.2078030e+00   4.1797129e+00   3.7696154e+00   3.4813790e+00   3.6180105e+00   4.0804412e+00   4.2532341e+00   3.6386811e+00   2.7658633e+00   3.1320920e+00   3.0282008e+00   3.0967725e+00   4.2602817e+00   3.5707142e+00   3.5298725e+00   3.9025633e+00   3.8026307e+00   3.1543621e+00   3.2954514e+00   3.5440090e+00   3.6715120e+00   3.2264532e+00   2.8478062e+00   3.3630343e+00   3.2124757e+00   3.2832910e+00   3.4351128e+00   2.5337719e+00   3.2403703e+00   5.2820451e+00   4.3497126e+00   5.2782573e+00   4.7465777e+00   5.0793700e+00   6.0415230e+00   3.8871583e+00   5.6124861e+00   5.1234754e+00   5.5344376e+00   4.3508620e+00   4.6000000e+00   4.8528342e+00   4.3737855e+00   4.5365185e+00   4.6292548e+00   4.6701178e+00   6.0901560e+00   6.4853681e+00   4.3474130e+00   5.0852729e+00   4.1785165e+00   6.1749494e+00   4.2071368e+00   4.9345719e+00   5.2545219e+00   4.0706265e+00   4.0755368e+00   4.9010203e+00   5.0645829e+00   5.5272054e+00   5.8446557e+00   4.9406477e+00   4.2402830e+00   4.6904158e+00   5.7253821e+00   4.8744230e+00   4.6249324e+00   3.9761791e+00   4.7728398e+00   5.0129831e+00   4.6119410e+00   4.3497126e+00   5.2297227e+00   5.1019604e+00   4.6615448e+00   4.4022721e+00   4.4855323e+00   4.6411206e+00   4.2249260e+00   3.4641016e-01   7.5498344e-01   0.0000000e+00   5.5677644e-01   3.7416574e-01   5.0000000e-01   9.3808315e-01   5.5677644e-01   6.5574385e-01   8.8317609e-01   2.6457513e-01   7.4161985e-01   3.4641016e-01   7.2801099e-01   2.6457513e-01   4.0435133e+00   3.6359318e+00   4.1856899e+00   2.9478806e+00   3.7709415e+00   3.3421550e+00   3.8065733e+00   2.1307276e+00   3.7389838e+00   2.7748874e+00   2.4556058e+00   3.2031235e+00   3.0133038e+00   3.6619667e+00   2.5258662e+00   3.6523965e+00   3.3852622e+00   2.9223278e+00   3.6687873e+00   2.7586228e+00   3.8457769e+00   3.0364453e+00   3.9799497e+00   3.6027767e+00   3.4014703e+00   3.6055513e+00   4.0348482e+00   4.2497059e+00   3.4942810e+00   2.3874673e+00   2.6720778e+00   2.5495098e+00   2.8178006e+00   4.0718546e+00   3.3496268e+00   3.5425979e+00   3.9293765e+00   3.5284558e+00   2.9495762e+00   2.9000000e+00   3.1984371e+00   3.5707142e+00   2.9189039e+00   2.1679483e+00   3.0626786e+00   3.0248967e+00   3.0675723e+00   3.3181320e+00   1.9104973e+00   2.9883106e+00   5.2924474e+00   4.1436699e+00   5.3113087e+00   4.6583259e+00   5.0467812e+00   6.1081912e+00   3.4525353e+00   5.6329388e+00   4.9979996e+00   5.6973678e+00   4.3749286e+00   4.4821870e+00   4.8600412e+00   4.1060930e+00   4.3760713e+00   4.6411206e+00   4.6324939e+00   6.3071388e+00   6.4876806e+00   4.0286474e+00   5.1468437e+00   3.9686270e+00   6.2112801e+00   4.0706265e+00   4.9919936e+00   5.3329167e+00   3.9446166e+00   3.9874804e+00   4.8114447e+00   5.1029403e+00   5.5443665e+00   6.0917978e+00   4.8538644e+00   4.1194660e+00   4.4933284e+00   5.8180753e+00   4.9142650e+00   4.5978256e+00   3.8729833e+00   4.8176758e+00   5.0338852e+00   4.6690470e+00   4.1436699e+00   5.2744668e+00   5.1652686e+00   4.6669048e+00   4.2201896e+00   4.4575778e+00   4.6722586e+00   4.1060930e+00   5.9160798e-01   3.4641016e-01   6.4031242e-01   3.7416574e-01   3.3166248e-01   1.0392305e+00   6.0827625e-01   6.4031242e-01   9.4868330e-01   3.6055513e-01   7.2801099e-01   4.4721360e-01   6.5574385e-01   2.2360680e-01   4.2059482e+00   3.8131352e+00   4.3588989e+00   3.1796226e+00   3.9572718e+00   3.5707142e+00   3.9887341e+00   2.3874673e+00   3.9268308e+00   3.0033315e+00   2.7147744e+00   3.3970576e+00   3.2372828e+00   3.8716921e+00   2.7239677e+00   3.8183766e+00   3.6027767e+00   3.1527766e+00   3.8755645e+00   2.9916551e+00   4.0410395e+00   3.2280025e+00   4.1904654e+00   3.8236109e+00   3.5874782e+00   3.7788887e+00   4.2190046e+00   4.4294469e+00   3.6972963e+00   2.6038433e+00   2.9086079e+00   2.7892651e+00   3.0298515e+00   4.2918527e+00   3.5749126e+00   3.7269290e+00   4.1036569e+00   3.7349699e+00   3.1654384e+00   3.1288976e+00   3.4423829e+00   3.7749172e+00   3.1368774e+00   2.4207437e+00   3.2893768e+00   3.2449961e+00   3.2848135e+00   3.5142567e+00   2.1330729e+00   3.2046841e+00   5.4799635e+00   4.3577517e+00   5.4909016e+00   4.8682646e+00   5.2392748e+00   6.2904690e+00   3.6932371e+00   5.8266629e+00   5.2057660e+00   5.8566202e+00   4.5497253e+00   4.6808119e+00   5.0378567e+00   4.3197222e+00   4.5661800e+00   4.8145612e+00   4.8311489e+00   6.4730209e+00   6.6745786e+00   4.2579338e+00   5.3169540e+00   4.1773197e+00   6.3984373e+00   4.2649736e+00   5.1730069e+00   5.5172457e+00   4.1376322e+00   4.1833001e+00   5.0089919e+00   5.2915026e+00   5.7288742e+00   6.2489999e+00   5.0477718e+00   4.3301270e+00   4.7296934e+00   5.9791304e+00   5.0921508e+00   4.7979162e+00   4.0693980e+00   4.9869831e+00   5.2057660e+00   4.8207883e+00   4.3577517e+00   5.4534393e+00   5.3329167e+00   4.8311489e+00   4.4170126e+00   4.6400431e+00   4.8507731e+00   4.3150898e+00   7.5498344e-01   1.2083046e+00   4.5825757e-01   5.0990195e-01   1.5652476e+00   1.1401754e+00   7.0710678e-01   8.0622577e-01   8.7177979e-01   5.8309519e-01   9.5393920e-01   3.4641016e-01   5.4772256e-01   3.9166312e+00   3.5818989e+00   4.0951190e+00   3.1527766e+00   3.7509999e+00   3.4612137e+00   3.7682887e+00   2.4919872e+00   3.6972963e+00   2.9883106e+00   2.8248894e+00   3.2419130e+00   3.1416556e+00   3.7040518e+00   2.6210685e+00   3.5566838e+00   3.4914181e+00   3.0347982e+00   3.7563280e+00   2.9291637e+00   3.8807216e+00   3.0577770e+00   4.0360872e+00   3.6619667e+00   3.3734256e+00   3.5369478e+00   3.9837169e+00   4.1988094e+00   3.5411862e+00   2.5159491e+00   2.8757608e+00   2.7586228e+00   2.9137605e+00   4.1581246e+00   3.4914181e+00   3.5298725e+00   3.8535698e+00   3.5916570e+00   3.0512293e+00   3.0822070e+00   3.3793490e+00   3.5972211e+00   3.0315013e+00   2.5159491e+00   3.2046841e+00   3.1144823e+00   3.1654384e+00   3.3256578e+00   2.2045408e+00   3.0951575e+00   5.2971691e+00   4.2497059e+00   5.2516664e+00   4.6957428e+00   5.0497525e+00   6.0299254e+00   3.7215588e+00   5.5821143e+00   5.0249378e+00   5.5883808e+00   4.3324358e+00   4.5099889e+00   4.8155997e+00   4.2391037e+00   4.4564560e+00   4.6162756e+00   4.6314145e+00   6.1717096e+00   6.4358372e+00   4.1617304e+00   5.0813384e+00   4.0865633e+00   6.1424751e+00   4.0987803e+00   4.9446941e+00   5.2564246e+00   3.9736633e+00   4.0162171e+00   4.8373546e+00   5.0348784e+00   5.4799635e+00   5.9245253e+00   4.8774994e+00   4.1545156e+00   4.5934736e+00   5.7043843e+00   4.8969378e+00   4.6010868e+00   3.9127995e+00   4.7476310e+00   4.9929951e+00   4.5793013e+00   4.2497059e+00   5.2297227e+00   5.1117512e+00   4.6162756e+00   4.2684892e+00   4.4384682e+00   4.6604721e+00   4.1725292e+00   5.5677644e-01   3.7416574e-01   5.0000000e-01   9.3808315e-01   5.5677644e-01   6.5574385e-01   8.8317609e-01   2.6457513e-01   7.4161985e-01   3.4641016e-01   7.2801099e-01   2.6457513e-01   4.0435133e+00   3.6359318e+00   4.1856899e+00   2.9478806e+00   3.7709415e+00   3.3421550e+00   3.8065733e+00   2.1307276e+00   3.7389838e+00   2.7748874e+00   2.4556058e+00   3.2031235e+00   3.0133038e+00   3.6619667e+00   2.5258662e+00   3.6523965e+00   3.3852622e+00   2.9223278e+00   3.6687873e+00   2.7586228e+00   3.8457769e+00   3.0364453e+00   3.9799497e+00   3.6027767e+00   3.4014703e+00   3.6055513e+00   4.0348482e+00   4.2497059e+00   3.4942810e+00   2.3874673e+00   2.6720778e+00   2.5495098e+00   2.8178006e+00   4.0718546e+00   3.3496268e+00   3.5425979e+00   3.9293765e+00   3.5284558e+00   2.9495762e+00   2.9000000e+00   3.1984371e+00   3.5707142e+00   2.9189039e+00   2.1679483e+00   3.0626786e+00   3.0248967e+00   3.0675723e+00   3.3181320e+00   1.9104973e+00   2.9883106e+00   5.2924474e+00   4.1436699e+00   5.3113087e+00   4.6583259e+00   5.0467812e+00   6.1081912e+00   3.4525353e+00   5.6329388e+00   4.9979996e+00   5.6973678e+00   4.3749286e+00   4.4821870e+00   4.8600412e+00   4.1060930e+00   4.3760713e+00   4.6411206e+00   4.6324939e+00   6.3071388e+00   6.4876806e+00   4.0286474e+00   5.1468437e+00   3.9686270e+00   6.2112801e+00   4.0706265e+00   4.9919936e+00   5.3329167e+00   3.9446166e+00   3.9874804e+00   4.8114447e+00   5.1029403e+00   5.5443665e+00   6.0917978e+00   4.8538644e+00   4.1194660e+00   4.4933284e+00   5.8180753e+00   4.9142650e+00   4.5978256e+00   3.8729833e+00   4.8176758e+00   5.0338852e+00   4.6690470e+00   4.1436699e+00   5.2744668e+00   5.1652686e+00   4.6669048e+00   4.2201896e+00   4.4575778e+00   4.6722586e+00   4.1060930e+00   8.3066239e-01   7.8740079e-01   7.1414284e-01   2.0000000e-01   9.2736185e-01   1.2369317e+00   4.2426407e-01   1.1045361e+00   3.0000000e-01   1.1575837e+00   6.7823300e-01   4.4497191e+00   3.9962482e+00   4.5727453e+00   3.1937439e+00   4.1267421e+00   3.6304270e+00   4.1496988e+00   2.2912878e+00   4.1170378e+00   2.9883106e+00   2.6153394e+00   3.5142567e+00   3.3361655e+00   3.9874804e+00   2.8195744e+00   4.0435133e+00   3.6565011e+00   3.2449961e+00   3.9761791e+00   3.0430248e+00   4.1352146e+00   3.3808283e+00   4.3023250e+00   3.9357337e+00   3.7709415e+00   3.9862263e+00   4.4147480e+00   4.6076024e+00   3.8078866e+00   2.7073973e+00   2.9376862e+00   2.8231188e+00   3.1320920e+00   4.3646306e+00   3.5958309e+00   3.8626416e+00   4.3069711e+00   3.8626416e+00   3.2388269e+00   3.1559468e+00   3.4612137e+00   3.9012818e+00   3.2264532e+00   2.3430749e+00   3.3391616e+00   3.3316662e+00   3.3645208e+00   3.6687873e+00   2.1071308e+00   3.2832910e+00   5.5749439e+00   4.4022721e+00   5.6621551e+00   4.9668904e+00   5.3535035e+00   6.4761099e+00   3.6041643e+00   5.9983331e+00   5.3244718e+00   6.0440053e+00   4.7042534e+00   4.7937459e+00   5.1971146e+00   4.3439613e+00   4.6130250e+00   4.9446941e+00   4.9608467e+00   6.6850580e+00   6.8425142e+00   4.3104524e+00   5.4827001e+00   4.2047592e+00   6.5825527e+00   4.3840620e+00   5.3244718e+00   5.7035077e+00   4.2532341e+00   4.2906876e+00   5.1127292e+00   5.4817880e+00   5.9135438e+00   6.4915329e+00   5.1507281e+00   4.4474712e+00   4.7937459e+00   6.1919302e+00   5.2057660e+00   4.9203658e+00   4.1677332e+00   5.1652686e+00   5.3507009e+00   5.0109879e+00   4.4022721e+00   5.6008928e+00   5.4799635e+00   4.9909919e+00   4.5210618e+00   4.7812132e+00   4.9618545e+00   4.3874822e+00   2.6457513e-01   1.2727922e+00   7.5498344e-01   4.3588989e-01   6.0000000e-01   5.1961524e-01   4.1231056e-01   5.4772256e-01   3.6055513e-01   1.7320508e-01   3.9153544e+00   3.5242020e+00   4.0718546e+00   2.9715316e+00   3.6905284e+00   3.3060551e+00   3.6945906e+00   2.2181073e+00   3.6496575e+00   2.7748874e+00   2.5709920e+00   3.1272992e+00   3.0232433e+00   3.5958309e+00   2.4738634e+00   3.5355339e+00   3.3316662e+00   2.8948230e+00   3.6523965e+00   2.7622455e+00   3.7589892e+00   2.9698485e+00   3.9370039e+00   3.5496479e+00   3.3151169e+00   3.5014283e+00   3.9471509e+00   4.1496988e+00   3.4278273e+00   2.3748684e+00   2.6944387e+00   2.5768197e+00   2.7820855e+00   4.0274061e+00   3.3075671e+00   3.4307434e+00   3.8183766e+00   3.5028560e+00   2.8948230e+00   2.9034462e+00   3.1953091e+00   3.4942810e+00   2.8948230e+00   2.2583180e+00   3.0397368e+00   2.9681644e+00   3.0182777e+00   3.2419130e+00   1.9672316e+00   2.9478806e+00   5.1951901e+00   4.1024383e+00   5.2086467e+00   4.5891176e+00   4.9608467e+00   6.0024995e+00   3.4785054e+00   5.5398556e+00   4.9416596e+00   5.5587768e+00   4.2661458e+00   4.4170126e+00   4.7602521e+00   4.0816663e+00   4.3185646e+00   4.5365185e+00   4.5475268e+00   6.1611687e+00   6.4007812e+00   4.0236799e+00   5.0328918e+00   3.9255573e+00   6.1155539e+00   4.0062451e+00   4.8805737e+00   5.2211110e+00   3.8755645e+00   3.9089641e+00   4.7402532e+00   5.0019996e+00   5.4497706e+00   5.9371710e+00   4.7812132e+00   4.0558600e+00   4.4598206e+00   5.7000000e+00   4.8052055e+00   4.5099889e+00   3.7973675e+00   4.7063787e+00   4.9295030e+00   4.5497253e+00   4.1024383e+00   5.1672043e+00   5.0497525e+00   4.5628938e+00   4.1701319e+00   4.3646306e+00   4.5639895e+00   4.0398020e+00   1.3000000e+00   6.7823300e-01   4.2426407e-01   6.8556546e-01   5.4772256e-01   4.4721360e-01   5.1961524e-01   4.2426407e-01   2.4494897e-01   4.1060930e+00   3.7054015e+00   4.2626283e+00   3.1591138e+00   3.8820098e+00   3.4957117e+00   3.8704005e+00   2.3895606e+00   3.8483763e+00   2.9410882e+00   2.7531800e+00   3.3030289e+00   3.2357379e+00   3.7868192e+00   2.6476405e+00   3.7242449e+00   3.5057096e+00   3.1000000e+00   3.8483763e+00   2.9597297e+00   3.9242834e+00   3.1606961e+00   4.1340053e+00   3.7509999e+00   3.5099858e+00   3.6918830e+00   4.1460825e+00   4.3347434e+00   3.6110940e+00   2.5748786e+00   2.8896367e+00   2.7766887e+00   2.9748950e+00   4.2154478e+00   3.4770677e+00   3.5972211e+00   4.0062451e+00   3.7067506e+00   3.0740852e+00   3.0886890e+00   3.3882149e+00   3.6823905e+00   3.0903074e+00   2.4351591e+00   3.2264532e+00   3.1559468e+00   3.2031235e+00   3.4351128e+00   2.1307276e+00   3.1336879e+00   5.3535035e+00   4.2755117e+00   5.3907328e+00   4.7738873e+00   5.1341991e+00   6.1919302e+00   3.6345564e+00   5.7358522e+00   5.1371198e+00   5.7210139e+00   4.4350874e+00   4.6000000e+00   4.9365980e+00   4.2508823e+00   4.4698993e+00   4.6957428e+00   4.7318073e+00   6.3364028e+00   6.5924199e+00   4.2213742e+00   5.2019227e+00   4.0865633e+00   6.3111013e+00   4.1880783e+00   5.0527220e+00   5.4101756e+00   4.0533936e+00   4.0828911e+00   4.9173163e+00   5.1990384e+00   5.6435804e+00   6.1155539e+00   4.9547957e+00   4.2497059e+00   4.6604721e+00   5.8804762e+00   4.9598387e+00   4.6914816e+00   3.9686270e+00   4.8805737e+00   5.0941143e+00   4.7127487e+00   4.2755117e+00   5.3376025e+00   5.2086467e+00   4.7275787e+00   4.3520110e+00   4.5387223e+00   4.7180504e+00   4.2130749e+00   9.1104336e-01   1.3674794e+00   1.7262677e+00   7.6811457e-01   1.6462078e+00   9.1651514e-01   1.6278821e+00   1.1269428e+00   4.4530888e+00   4.0124805e+00   4.5607017e+00   3.0479501e+00   4.0718546e+00   3.5958309e+00   4.1821047e+00   2.1587033e+00   4.0816663e+00   2.9359837e+00   2.3811762e+00   3.5071356e+00   3.1685959e+00   3.9610605e+00   2.8035692e+00   4.0373258e+00   3.6578682e+00   3.1906112e+00   3.8183766e+00   2.9410882e+00   4.1557190e+00   3.3316662e+00   4.2047592e+00   3.8961519e+00   3.7376463e+00   3.9648455e+00   4.3588989e+00   4.5803930e+00   3.7802116e+00   2.6191602e+00   2.8106939e+00   2.6944387e+00   3.0692019e+00   4.3058100e+00   3.6027767e+00   3.9230090e+00   4.2988371e+00   3.7215588e+00   3.2465366e+00   3.0545049e+00   3.3926391e+00   3.8923001e+00   3.1432467e+00   2.1771541e+00   3.2832910e+00   3.3391616e+00   3.3481338e+00   3.6400549e+00   1.9824228e+00   3.2449961e+00   5.5830099e+00   4.3416587e+00   5.6258333e+00   4.9335586e+00   5.3244718e+00   6.4366140e+00   3.5213634e+00   5.9539903e+00   5.2325902e+00   6.0712437e+00   4.7053161e+00   4.7254629e+00   5.1633323e+00   4.2497059e+00   4.5596052e+00   4.9416596e+00   4.9376108e+00   6.7275553e+00   6.7594378e+00   4.1701319e+00   5.4708317e+00   4.1605288e+00   6.5222695e+00   4.3139309e+00   5.3329167e+00   5.6956123e+00   4.2000000e+00   4.2731721e+00   5.0586559e+00   5.4516053e+00   5.8532043e+00   6.5352888e+00   5.0950957e+00   4.4011362e+00   4.7275787e+00   6.1457302e+00   5.2297227e+00   4.9132474e+00   4.1521079e+00   5.1429563e+00   5.3272882e+00   4.9839743e+00   4.3416587e+00   5.5910643e+00   5.4808758e+00   4.9537864e+00   4.4192760e+00   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3.7013511e+00   2.5632011e+00   3.6565011e+00   3.4278273e+00   2.9883106e+00   3.7349699e+00   2.8390139e+00   3.8652296e+00   3.0708305e+00   4.0336088e+00   3.6537652e+00   3.4263683e+00   3.6180105e+00   4.0607881e+00   4.2649736e+00   3.5298725e+00   2.4556058e+00   2.7622455e+00   2.6438608e+00   2.8722813e+00   4.1243181e+00   3.3985291e+00   3.5468296e+00   3.9382737e+00   3.5916570e+00   2.9916551e+00   2.9765752e+00   3.2771939e+00   3.6027767e+00   2.9816103e+00   2.2912878e+00   3.1256999e+00   3.0692019e+00   3.1144823e+00   3.3496268e+00   2.0049938e+00   3.0397368e+00   5.3047149e+00   4.1928511e+00   5.3254108e+00   4.6957428e+00   5.0695167e+00   6.1237244e+00   3.5369478e+00   5.6586217e+00   5.0447993e+00   5.6841886e+00   4.3806392e+00   4.5188494e+00   4.8733972e+00   4.1629317e+00   4.4068129e+00   4.6465041e+00   4.6593991e+00   6.2952363e+00   6.5145990e+00   4.1060930e+00   5.1497573e+00   4.0124805e+00   6.2345810e+00   4.1060930e+00   4.9989999e+00   5.3450912e+00   3.9761791e+00   4.0137264e+00   4.8435524e+00   5.1234754e+00   5.5668663e+00   6.0745370e+00   4.8836462e+00   4.1617304e+00   4.5585085e+00   5.8206529e+00   4.9173163e+00   4.6227697e+00   3.9000000e+00   4.8228622e+00   5.0408333e+00   4.6636895e+00   4.1928511e+00   5.2829916e+00   5.1643005e+00   4.6722586e+00   4.2638011e+00   4.4743715e+00   4.6754679e+00   4.1412558e+00   6.4031242e-01   2.6457513e-01   1.8867962e+00   6.5574385e-01   1.3784049e+00   7.3484692e-01   2.6776856e+00   5.1961524e-01   2.0322401e+00   2.6532998e+00   1.2288206e+00   1.6278821e+00   9.4868330e-01   1.8083141e+00   4.3588989e-01   1.4317821e+00   1.4866069e+00   1.3000000e+00   1.7832555e+00   1.1747340e+00   1.2124356e+00   1.0148892e+00   1.0049876e+00   7.8740079e-01   5.3851648e-01   4.5825757e-01   5.5677644e-01   1.0677078e+00   1.9104973e+00   1.9467922e+00   2.0124612e+00   1.5394804e+00   1.2041595e+00   1.6278821e+00   1.0583005e+00   3.3166248e-01   1.1832160e+00   1.5394804e+00   1.8000000e+00   1.6552945e+00   9.2736185e-01   1.5264338e+00   2.6324893e+00   1.5716234e+00   1.4212670e+00   1.4282857e+00   9.4868330e-01   2.6608269e+00   1.4899664e+00   1.8439089e+00   1.4491377e+00   1.4071247e+00   1.2449900e+00   1.4628739e+00   2.1213203e+00   2.2427661e+00   1.7029386e+00   1.3964240e+00   1.8357560e+00   8.7749644e-01   1.1045361e+00   1.1000000e+00   1.6217275e+00   1.6613248e+00   1.2369317e+00   1.0440307e+00   2.3430749e+00   2.5495098e+00   1.4491377e+00   1.3490738e+00   1.5874508e+00   2.2383029e+00   9.6953597e-01   1.2609520e+00   1.3747727e+00   9.8488578e-01   1.0246951e+00   1.3490738e+00   1.1532563e+00   1.5905974e+00   2.1023796e+00   1.4035669e+00   9.0553851e-01   1.4071247e+00   1.8165902e+00   1.5297059e+00   1.0816654e+00   1.1000000e+00   1.0000000e+00   1.3820275e+00   9.9498744e-01   1.4491377e+00   1.5132746e+00   1.5198684e+00   1.0908712e+00   1.1489125e+00   9.4868330e-01   1.4071247e+00   1.2529964e+00   6.4807407e-01   1.3820275e+00   4.2426407e-01   8.3066239e-01   2.6457513e-01   2.1400935e+00   4.2426407e-01   1.4352700e+00   2.1563859e+00   6.1644140e-01   1.2884099e+00   4.7958315e-01   1.2569805e+00   3.4641016e-01   8.2462113e-01   1.0099505e+00   1.0198039e+00   1.2845233e+00   6.5574385e-01   7.3484692e-01   8.1240384e-01   6.1644140e-01   4.1231056e-01   3.1622777e-01   6.4807407e-01   6.4807407e-01   5.0000000e-01   1.4491377e+00   1.4491377e+00   1.5297059e+00   1.0295630e+00   8.8317609e-01   1.0198039e+00   4.5825757e-01   3.7416574e-01   9.3273791e-01   9.3808315e-01   1.2609520e+00   1.1269428e+00   3.8729833e-01   1.0295630e+00   2.1118712e+00   1.0099505e+00   8.4261498e-01   8.4261498e-01   4.5825757e-01   2.1424285e+00   9.2195445e-01   1.8083141e+00   1.0630146e+00   1.6881943e+00   1.1832160e+00   1.4933185e+00   2.5000000e+00   1.6673332e+00   2.0566964e+00   1.5362291e+00   2.0880613e+00   7.8740079e-01   1.0246951e+00   1.2489996e+00   1.2165525e+00   1.3000000e+00   1.1313708e+00   1.0677078e+00   2.7166155e+00   2.9068884e+00   1.1874342e+00   1.5264338e+00   1.1000000e+00   2.6343880e+00   7.1414284e-01   1.3784049e+00   1.7262677e+00   6.1644140e-01   6.1644140e-01   1.3152946e+00   1.5427249e+00   1.9697716e+00   2.5436195e+00   1.3638182e+00   7.2801099e-01   1.2922848e+00   2.2203603e+00   1.4387495e+00   1.0488088e+00   6.1644140e-01   1.1958261e+00   1.4560220e+00   1.1224972e+00   1.0630146e+00   1.6613248e+00   1.5937377e+00   1.1224972e+00   9.5393920e-01   8.8881944e-01   1.2369317e+00   8.6023253e-01   1.8574176e+00   5.8309519e-01   1.3152946e+00   6.7082039e-01   2.7018512e+00   5.0990195e-01   2.0149442e+00   2.6514147e+00   1.2247449e+00   1.6370706e+00   8.5440037e-01   1.8601075e+00   5.4772256e-01   1.3638182e+00   1.5033296e+00   1.2083046e+00   1.7916473e+00   1.0535654e+00   1.2569805e+00   8.4852814e-01   9.2736185e-01   8.3066239e-01   6.0000000e-01   3.4641016e-01   3.1622777e-01   1.0049876e+00   1.9748418e+00   1.9544820e+00   2.0346990e+00   1.5684387e+00   1.0099505e+00   1.5556349e+00   1.0344080e+00   2.8284271e-01   1.1357817e+00   1.5427249e+00   1.7804494e+00   1.5968719e+00   8.6602540e-01   1.5362291e+00   2.6570661e+00   1.5427249e+00   1.4247807e+00   1.4177447e+00   9.6436508e-01   2.7147744e+00   1.4866069e+00   1.6155494e+00   1.2529964e+00   1.1874342e+00   9.8994949e-01   1.2124356e+00   1.9364917e+00   2.1354157e+00   1.5000000e+00   1.1401754e+00   1.6673332e+00   6.7823300e-01   8.5440037e-01   8.6023253e-01   1.4352700e+00   1.4662878e+00   1.0295630e+00   7.8740079e-01   2.2045408e+00   2.3515952e+00   1.2767145e+00   1.1357817e+00   1.4247807e+00   2.0542639e+00   7.8102497e-01   1.0392305e+00   1.1832160e+00   8.2462113e-01   8.6023253e-01   1.0908712e+00   9.5916630e-01   1.3928388e+00   1.9974984e+00   1.1489125e+00   7.0000000e-01   1.1789826e+00   1.6522712e+00   1.3228757e+00   8.3666003e-01   9.5916630e-01   7.8102497e-01   1.1575837e+00   8.2462113e-01   1.2529964e+00   1.2884099e+00   1.3114877e+00   8.8317609e-01   9.4339811e-01   7.1414284e-01   1.2124356e+00   1.0677078e+00   1.2845233e+00   7.3484692e-01   1.4899664e+00   9.7467943e-01   1.3892444e+00   5.1961524e-01   8.2462113e-01   8.5440037e-01   5.9160798e-01   1.1045361e+00   7.2801099e-01   1.5000000e+00   8.8881944e-01   5.9160798e-01   8.8881944e-01   3.1622777e-01   1.3638182e+00   7.8102497e-01   1.2369317e+00   1.0535654e+00   1.1224972e+00   1.3674794e+00   1.6093477e+00   1.7578396e+00   9.4868330e-01   6.8556546e-01   3.0000000e-01   4.3588989e-01   5.1961524e-01   1.3076697e+00   8.8881944e-01   1.3416408e+00   1.6155494e+00   8.9442719e-01   7.1414284e-01   2.0000000e-01   5.0990195e-01   1.1045361e+00   4.3588989e-01   9.1104336e-01   4.5825757e-01   7.6157731e-01   6.6332496e-01   9.6953597e-01   1.1135529e+00   5.4772256e-01   2.6608269e+00   1.3490738e+00   2.7018512e+00   1.9519221e+00   2.3537205e+00   3.5071356e+00   9.0000000e-01   3.0232433e+00   2.2293497e+00   3.2295511e+00   1.8734994e+00   1.7378147e+00   2.2516660e+00   1.2529964e+00   1.6613248e+00   2.0760539e+00   1.9974984e+00   3.8974351e+00   3.7868192e+00   1.1401754e+00   2.5806976e+00   1.2489996e+00   3.5874782e+00   1.3638182e+00   2.4433583e+00   2.8195744e+00   1.2767145e+00   1.3820275e+00   2.0639767e+00   2.5903668e+00   2.9376862e+00   3.7762415e+00   2.1047565e+00   1.4628739e+00   1.7378147e+00   3.2771939e+00   2.3706539e+00   1.9874607e+00   1.2767145e+00   2.2803509e+00   2.4186773e+00   2.1931712e+00   1.3490738e+00   2.6664583e+00   2.6019224e+00   2.0904545e+00   1.4282857e+00   1.8493242e+00   2.1587033e+00   1.4525839e+00   8.3066239e-01   5.5677644e-01   2.1587033e+00   2.4494897e-01   1.4832397e+00   2.0856654e+00   7.4833148e-01   1.1045361e+00   4.3588989e-01   1.3638182e+00   4.2426407e-01   9.2736185e-01   1.0000000e+00   6.7823300e-01   1.2449900e+00   8.0622577e-01   7.4833148e-01   4.6904158e-01   5.0990195e-01   3.8729833e-01   3.1622777e-01   3.7416574e-01   5.2915026e-01   5.1961524e-01   1.4628739e+00   1.4000000e+00   1.4899664e+00   1.0392305e+00   7.2111026e-01   1.1224972e+00   7.9372539e-01   3.7416574e-01   6.0827625e-01   1.0677078e+00   1.2206556e+00   1.0816654e+00   4.5825757e-01   9.8994949e-01   2.1071308e+00   1.0099505e+00   9.6436508e-01   9.2195445e-01   4.7958315e-01   2.1840330e+00   9.6436508e-01   1.8027756e+00   9.5393920e-01   1.5652476e+00   1.0677078e+00   1.4035669e+00   2.3685439e+00   1.6431677e+00   1.9052559e+00   1.2884099e+00   2.0928450e+00   8.1240384e-01   8.1853528e-01   1.1401754e+00   1.0677078e+00   1.2449900e+00   1.1401754e+00   9.6953597e-01   2.7092434e+00   2.7221315e+00   8.7749644e-01   1.4730920e+00   1.0723805e+00   2.4698178e+00   4.7958315e-01   1.3638182e+00   1.6431677e+00   4.6904158e-01   6.1644140e-01   1.1704700e+00   1.4071247e+00   1.7944358e+00   2.5396850e+00   1.2247449e+00   5.3851648e-01   1.1000000e+00   2.0904545e+00   1.4866069e+00   1.0000000e+00   6.4807407e-01   1.1180340e+00   1.3928388e+00   1.0677078e+00   9.5393920e-01   1.6062378e+00   1.5811388e+00   1.0392305e+00   6.7082039e-01   8.0622577e-01   1.3152946e+00   8.6023253e-01   8.6023253e-01   1.5264338e+00   9.1104336e-01   7.9372539e-01   1.4899664e+00   4.5825757e-01   8.8881944e-01   4.6904158e-01   9.1104336e-01   1.0535654e+00   3.0000000e-01   5.1961524e-01   8.0622577e-01   7.0710678e-01   7.3484692e-01   6.4031242e-01   8.0622577e-01   4.5825757e-01   7.3484692e-01   9.3273791e-01   1.1445523e+00   1.2041595e+00   3.7416574e-01   1.0630146e+00   8.5440037e-01   9.6436508e-01   6.2449980e-01   7.4161985e-01   4.1231056e-01   7.3484692e-01   1.0816654e+00   7.8740079e-01   4.5825757e-01   6.1644140e-01   3.1622777e-01   4.6904158e-01   5.5677644e-01   1.5066519e+00   3.3166248e-01   3.7416574e-01   3.1622777e-01   5.4772256e-01   1.6552945e+00   4.0000000e-01   2.0736441e+00   8.6023253e-01   2.1447611e+00   1.3527749e+00   1.7832555e+00   2.9495762e+00   9.4339811e-01   2.4617067e+00   1.7406895e+00   2.6248809e+00   1.2845233e+00   1.2247449e+00   1.7000000e+00   9.1104336e-01   1.2569805e+00   1.5132746e+00   1.3892444e+00   3.2634338e+00   3.2863353e+00   8.6023253e-01   2.0099751e+00   8.1240384e-01   3.0545049e+00   8.8317609e-01   1.8248288e+00   2.2158520e+00   7.6811457e-01   7.8102497e-01   1.5297059e+00   2.0174241e+00   2.4103942e+00   3.1527766e+00   1.5842980e+00   8.7177979e-01   1.1916375e+00   2.7568098e+00   1.7720045e+00   1.3527749e+00   6.8556546e-01   1.7262677e+00   1.8734994e+00   1.7000000e+00   8.6023253e-01   2.0808652e+00   2.0322401e+00   1.5905974e+00   1.0295630e+00   1.2884099e+00   1.5556349e+00   8.3066239e-01   2.2561028e+00   5.9160798e-01   1.5000000e+00   2.2759613e+00   7.1414284e-01   1.4662878e+00   4.8989795e-01   1.3964240e+00   5.7445626e-01   7.9372539e-01   1.1532563e+00   1.1269428e+00   1.4212670e+00   4.6904158e-01   9.3273791e-01   8.3066239e-01   6.7082039e-01   6.4807407e-01   5.5677644e-01   7.4161985e-01   5.9160798e-01   5.4772256e-01   1.6278821e+00   1.5842980e+00   1.6763055e+00   1.1874342e+00   7.8102497e-01   9.7467943e-01   3.7416574e-01   4.5825757e-01   1.0862780e+00   1.0148892e+00   1.3638182e+00   1.1747340e+00   4.2426407e-01   1.1789826e+00   2.2383029e+00   1.0908712e+00   9.2736185e-01   9.2736185e-01   6.4807407e-01   2.2847319e+00   1.0295630e+00   1.5811388e+00   9.2736185e-01   1.5556349e+00   1.0049876e+00   1.3038405e+00   2.3748684e+00   1.6278821e+00   1.9390719e+00   1.4317821e+00   1.9157244e+00   6.0827625e-01   9.0553851e-01   1.1090537e+00   1.1180340e+00   1.1401754e+00   9.3273791e-01   9.0000000e-01   2.5632011e+00   2.7892651e+00   1.1832160e+00   1.3638182e+00   9.6953597e-01   2.5238859e+00   6.6332496e-01   1.1874342e+00   1.5968719e+00   5.5677644e-01   4.5825757e-01   1.1489125e+00   1.4525839e+00   1.8734994e+00   2.4207437e+00   1.1958261e+00   6.4807407e-01   1.1747340e+00   2.1213203e+00   1.2083046e+00   8.5440037e-01   4.7958315e-01   1.0677078e+00   1.2845233e+00   1.0246951e+00   9.2736185e-01   1.4798649e+00   1.4035669e+00   9.9498744e-01   9.0553851e-01   7.3484692e-01   1.0000000e+00   6.7082039e-01   2.2181073e+00   8.3666003e-01   4.5825757e-01   1.5556349e+00   1.3190906e+00   1.9519221e+00   9.5916630e-01   2.2583180e+00   1.5937377e+00   1.2409674e+00   1.8493242e+00   9.3273791e-01   2.1283797e+00   1.4764823e+00   2.1863211e+00   1.8973666e+00   1.8947295e+00   2.1494185e+00   2.4859606e+00   2.6419690e+00   1.7748239e+00   8.4852814e-01   7.8740079e-01   7.2111026e-01   1.1401754e+00   2.2135944e+00   1.5165751e+00   2.0024984e+00   2.4372115e+00   1.8083141e+00   1.2569805e+00   9.7467943e-01   1.2845233e+00   1.9104973e+00   1.1747340e+00   1.4142136e-01   1.2165525e+00   1.3601471e+00   1.3379088e+00   1.7406895e+00   3.8729833e-01   1.2369317e+00   3.5085610e+00   2.2248595e+00   3.6290495e+00   2.8530685e+00   3.2572995e+00   4.4440972e+00   1.3928388e+00   3.9560081e+00   3.1843367e+00   4.1012193e+00   2.7276363e+00   2.6739484e+00   3.1654384e+00   2.1307276e+00   2.4839485e+00   2.9291637e+00   2.8982753e+00   4.7749346e+00   4.7465777e+00   2.0952327e+00   3.4770677e+00   2.0518285e+00   4.5343136e+00   2.2912878e+00   3.3196385e+00   3.7229021e+00   2.1771541e+00   2.2360680e+00   2.9849623e+00   3.5014283e+00   3.8807216e+00   4.6443514e+00   3.0232433e+00   2.3685439e+00   2.6324893e+00   4.2107007e+00   3.1953091e+00   2.8670542e+00   2.1118712e+00   3.1796226e+00   3.3136083e+00   3.0692019e+00   2.2248595e+00   3.5637059e+00   3.4727511e+00   2.9832868e+00   2.3811762e+00   2.7440845e+00   2.9647934e+00   2.2891046e+00   1.5811388e+00   2.1610183e+00   8.3666003e-01   1.1401754e+00   5.1961524e-01   1.4142136e+00   3.1622777e-01   1.0295630e+00   1.0099505e+00   8.3666003e-01   1.3000000e+00   9.3273791e-01   7.8740079e-01   6.1644140e-01   5.2915026e-01   3.6055513e-01   2.4494897e-01   3.1622777e-01   5.8309519e-01   6.4031242e-01   1.4832397e+00   1.4628739e+00   1.5362291e+00   1.0862780e+00   8.6023253e-01   1.2247449e+00   8.4261498e-01   3.1622777e-01   7.0000000e-01   1.1224972e+00   1.3152946e+00   1.1618950e+00   5.1961524e-01   1.0488088e+00   2.1679483e+00   1.0954451e+00   9.9498744e-01   9.8488578e-01   5.0000000e-01   2.2383029e+00   1.0344080e+00   1.9104973e+00   1.1357817e+00   1.6093477e+00   1.1575837e+00   1.5066519e+00   2.3769729e+00   1.7944358e+00   1.9052559e+00   1.3638182e+00   2.1307276e+00   9.1651514e-01   9.6436508e-01   1.2247449e+00   1.2727922e+00   1.4525839e+00   1.2727922e+00   1.0392305e+00   2.6907248e+00   2.7549955e+00   1.0246951e+00   1.5459625e+00   1.2609520e+00   2.4738634e+00   6.8556546e-01   1.4212670e+00   1.6309506e+00   6.7823300e-01   7.7459667e-01   1.3000000e+00   1.3784049e+00   1.8055470e+00   2.4959968e+00   1.3638182e+00   6.2449980e-01   1.1618950e+00   2.1142375e+00   1.5968719e+00   1.0677078e+00   8.1240384e-01   1.1874342e+00   1.5033296e+00   1.1747340e+00   1.1357817e+00   1.6792856e+00   1.6792856e+00   1.1747340e+00   8.7749644e-01   9.3273791e-01   1.4317821e+00   1.0000000e+00   9.2195445e-01   8.2462113e-01   1.0295630e+00   1.2206556e+00   5.4772256e-01   1.6309506e+00   7.8740079e-01   7.4833148e-01   1.2727922e+00   5.3851648e-01   1.3076697e+00   9.1651514e-01   1.5033296e+00   1.2247449e+00   1.2845233e+00   1.5165751e+00   1.8384776e+00   1.9078784e+00   1.0246951e+00   7.6157731e-01   5.2915026e-01   6.1644140e-01   6.3245553e-01   1.4560220e+00   7.0710678e-01   1.2369317e+00   1.7492856e+00   1.2767145e+00   5.4772256e-01   3.8729833e-01   6.2449980e-01   1.1789826e+00   6.4807407e-01   8.4852814e-01   5.0990195e-01   6.8556546e-01   6.2449980e-01   1.1000000e+00   9.7467943e-01   5.5677644e-01   2.6814175e+00   1.4317821e+00   2.8618176e+00   2.0736441e+00   2.4556058e+00   3.6918830e+00   7.6157731e-01   3.2202484e+00   2.4617067e+00   3.2954514e+00   1.9339080e+00   1.9104973e+00   2.3874673e+00   1.3638182e+00   1.6763055e+00   2.1118712e+00   2.1213203e+00   3.9924930e+00   4.0087405e+00   1.4525839e+00   2.6814175e+00   1.2369317e+00   3.8026307e+00   1.5394804e+00   2.5179357e+00   2.9698485e+00   1.4071247e+00   1.4352700e+00   2.1977261e+00   2.7820855e+00   3.1527766e+00   3.8871583e+00   2.2315914e+00   1.6340135e+00   1.9261360e+00   3.4626579e+00   2.3643181e+00   2.0784610e+00   1.3038405e+00   2.4062419e+00   2.5099801e+00   2.3021729e+00   1.4317821e+00   2.7604347e+00   2.6570661e+00   2.2000000e+00   1.6462078e+00   1.9570386e+00   2.1330729e+00   1.4764823e+00   1.5968719e+00   1.1357817e+00   1.9026298e+00   1.1269428e+00   2.2516660e+00   1.6155494e+00   1.2206556e+00   1.6522712e+00   8.8317609e-01   2.1400935e+00   1.4798649e+00   2.0371549e+00   1.8248288e+00   1.8708287e+00   2.1283797e+00   2.3937418e+00   2.5748786e+00   1.7492856e+00   9.2195445e-01   7.1414284e-01   6.7082039e-01   1.1532563e+00   2.1000000e+00   1.5524175e+00   2.0784610e+00   2.4062419e+00   1.6370706e+00   1.3453624e+00   9.1651514e-01   1.2083046e+00   1.8920888e+00   1.1357817e+00   3.6055513e-01   1.1958261e+00   1.4212670e+00   1.3711309e+00   1.7262677e+00   7.2111026e-01   1.2569805e+00   3.4467376e+00   2.1213203e+00   3.5185224e+00   2.7477263e+00   3.1591138e+00   4.3104524e+00   1.3228757e+00   3.8183766e+00   3.0116441e+00   4.0509258e+00   2.6925824e+00   2.5495098e+00   3.0740852e+00   1.9974984e+00   2.4083189e+00   2.8861739e+00   2.8089144e+00   4.7127487e+00   4.5716518e+00   1.8814888e+00   3.4029399e+00   1.9899749e+00   4.3783559e+00   2.1863211e+00   3.2603681e+00   3.6290495e+00   2.1000000e+00   2.1931712e+00   2.8670542e+00   3.3896903e+00   3.7376463e+00   4.5891176e+00   2.9068884e+00   2.2671568e+00   2.4779023e+00   4.0914545e+00   3.1654384e+00   2.7946377e+00   2.0808652e+00   3.1048349e+00   3.2357379e+00   3.0116441e+00   2.1213203e+00   3.4828150e+00   3.4161382e+00   2.9103264e+00   2.2360680e+00   2.6720778e+00   2.9495762e+00   2.2383029e+00   9.6953597e-01   5.5677644e-01   7.0710678e-01   8.3666003e-01   4.2426407e-01   6.0000000e-01   9.0553851e-01   7.6811457e-01   7.0000000e-01   4.0000000e-01   9.4868330e-01   6.4807407e-01   5.5677644e-01   7.3484692e-01   1.1045361e+00   1.1489125e+00   3.3166248e-01   9.6953597e-01   9.1651514e-01   1.0099505e+00   5.2915026e-01   9.5916630e-01   5.8309519e-01   5.1961524e-01   9.4868330e-01   8.5440037e-01   3.7416574e-01   7.0000000e-01   6.7082039e-01   4.5825757e-01   5.4772256e-01   1.5362291e+00   4.6904158e-01   3.6055513e-01   3.0000000e-01   3.8729833e-01   1.5779734e+00   3.6055513e-01   2.1189620e+00   1.0344080e+00   2.1656408e+00   1.4899664e+00   1.8466185e+00   3.0016662e+00   1.1747340e+00   2.5436195e+00   1.8814888e+00   2.5806976e+00   1.2083046e+00   1.3076697e+00   1.6911535e+00   1.0862780e+00   1.2922848e+00   1.4628739e+00   1.4628739e+00   3.2588341e+00   3.3660065e+00   1.1357817e+00   1.9824228e+00   9.3273791e-01   3.1272992e+00   9.1104336e-01   1.8275667e+00   2.2494444e+00   7.6157731e-01   7.8740079e-01   1.6155494e+00   2.0639767e+00   2.4617067e+00   3.1192948e+00   1.6552945e+00   1.0049876e+00   1.4730920e+00   2.7367864e+00   1.7578396e+00   1.4282857e+00   6.7823300e-01   1.6763055e+00   1.8493242e+00   1.5684387e+00   1.0344080e+00   2.0928450e+00   1.9949937e+00   1.5099669e+00   1.1000000e+00   1.2688578e+00   1.5264338e+00   9.4868330e-01   1.0723805e+00   9.4868330e-01   1.2727922e+00   1.1401754e+00   5.4772256e-01   7.3484692e-01   5.1961524e-01   1.5132746e+00   6.7823300e-01   1.1135529e+00   9.4868330e-01   9.1104336e-01   1.1489125e+00   1.3416408e+00   1.6186414e+00   9.9498744e-01   7.0710678e-01   5.8309519e-01   6.1644140e-01   5.8309519e-01   1.3490738e+00   1.2247449e+00   1.4317821e+00   1.4282857e+00   5.9160798e-01   9.4868330e-01   6.5574385e-01   7.8102497e-01   1.0816654e+00   4.8989795e-01   1.2247449e+00   7.3484692e-01   9.0000000e-01   8.4261498e-01   8.4261498e-01   1.3820275e+00   7.4161985e-01   2.7477263e+00   1.5198684e+00   2.5826343e+00   1.9442222e+00   2.3600847e+00   3.3421550e+00   1.4282857e+00   2.8478062e+00   2.1118712e+00   3.1717503e+00   1.8601075e+00   1.7058722e+00   2.1771541e+00   1.4764823e+00   1.8894444e+00   2.1307276e+00   1.9442222e+00   3.7656341e+00   3.6262929e+00   1.1180340e+00   2.5278449e+00   1.5264338e+00   3.3970576e+00   1.3379088e+00   2.4083189e+00   2.6608269e+00   1.2961481e+00   1.4491377e+00   2.0712315e+00   2.3832751e+00   2.7459060e+00   3.5958309e+00   2.1260292e+00   1.3820275e+00   1.7000000e+00   3.1032241e+00   2.4596748e+00   1.9646883e+00   1.3856406e+00   2.1886069e+00   2.4124676e+00   2.1260292e+00   1.5198684e+00   2.6343880e+00   2.6153394e+00   2.0639767e+00   1.4106736e+00   1.8248288e+00   2.2649503e+00   1.5811388e+00   1.2124356e+00   7.0000000e-01   5.5677644e-01   8.0622577e-01   7.4161985e-01   1.0677078e+00   5.4772256e-01   7.1414284e-01   5.0000000e-01   2.2360680e-01   5.0990195e-01   5.9160798e-01   7.1414284e-01   7.4161985e-01   2.4494897e-01   1.3601471e+00   1.2288206e+00   1.3304135e+00   9.0000000e-01   5.0000000e-01   7.4161985e-01   5.8309519e-01   6.4031242e-01   7.0710678e-01   7.9372539e-01   1.0099505e+00   7.6157731e-01   1.4142136e-01   8.4261498e-01   1.9209373e+00   7.4161985e-01   6.7823300e-01   6.4807407e-01   4.2426407e-01   2.0346990e+00   7.3484692e-01   1.7606817e+00   7.3484692e-01   1.7146428e+00   1.0049876e+00   1.4212670e+00   2.5219040e+00   1.3152946e+00   2.0396078e+00   1.3747727e+00   2.2068076e+00   8.7749644e-01   8.6023253e-01   1.2767145e+00   8.7749644e-01   1.1224972e+00   1.1618950e+00   9.8488578e-01   2.8301943e+00   2.8809721e+00   7.7459667e-01   1.5937377e+00   8.1240384e-01   2.6324893e+00   5.2915026e-01   1.4177447e+00   1.7748239e+00   4.3588989e-01   4.5825757e-01   1.1832160e+00   1.5716234e+00   1.9773720e+00   2.7018512e+00   1.2449900e+00   4.6904158e-01   9.4868330e-01   2.3108440e+00   1.4491377e+00   9.6436508e-01   4.3588989e-01   1.2884099e+00   1.4866069e+00   1.2845233e+00   7.3484692e-01   1.6822604e+00   1.6522712e+00   1.1958261e+00   7.3484692e-01   8.8317609e-01   1.2489996e+00   6.0827625e-01   1.3784049e+00   9.2736185e-01   6.4807407e-01   1.3038405e+00   5.3851648e-01   1.3674794e+00   6.4807407e-01   1.5427249e+00   1.2165525e+00   1.0630146e+00   1.2884099e+00   1.7029386e+00   1.8275667e+00   1.0049876e+00   4.4721360e-01   5.8309519e-01   6.0000000e-01   4.2426407e-01   1.5937377e+00   9.4868330e-01   1.1445523e+00   1.5811388e+00   1.2206556e+00   5.0990195e-01   5.7445626e-01   8.6602540e-01   1.1269428e+00   5.4772256e-01   9.4868330e-01   6.3245553e-01   6.2449980e-01   6.0827625e-01   9.2195445e-01   9.0000000e-01   5.1961524e-01   2.8017851e+00   1.6401219e+00   2.8618176e+00   2.1771541e+00   2.5436195e+00   3.6945906e+00   1.2727922e+00   3.2295511e+00   2.5416530e+00   3.2771939e+00   1.9078784e+00   1.9824228e+00   2.3874673e+00   1.6186414e+00   1.8734994e+00   2.1494185e+00   2.1633308e+00   3.9547440e+00   4.0484565e+00   1.6278821e+00   2.6814175e+00   1.4798649e+00   3.8105118e+00   1.5716234e+00   2.5337719e+00   2.9427878e+00   1.4352700e+00   1.4832397e+00   2.3000000e+00   2.7386128e+00   3.1400637e+00   3.7986840e+00   2.3366643e+00   1.6703293e+00   2.0856654e+00   3.4161382e+00   2.4392622e+00   2.1307276e+00   1.3638182e+00   2.3685439e+00   2.5416530e+00   2.2315914e+00   1.6401219e+00   2.7964263e+00   2.6870058e+00   2.1863211e+00   1.7233688e+00   1.9672316e+00   2.2022716e+00   1.6124515e+00   1.1135529e+00   1.1045361e+00   1.0392305e+00   1.3820275e+00   9.8488578e-01   7.8740079e-01   8.8317609e-01   7.6157731e-01   3.8729833e-01   1.4142136e-01   5.0990195e-01   6.7823300e-01   7.4161985e-01   1.4899664e+00   1.5427249e+00   1.6062378e+00   1.1224972e+00   1.0862780e+00   1.3114877e+00   7.9372539e-01   3.1622777e-01   9.0000000e-01   1.1489125e+00   1.4035669e+00   1.3152946e+00   6.4031242e-01   1.1224972e+00   2.2135944e+00   1.1916375e+00   1.0440307e+00   1.0440307e+00   5.5677644e-01   2.2293497e+00   1.0908712e+00   1.9924859e+00   1.3076697e+00   1.7058722e+00   1.3416408e+00   1.6278821e+00   2.4799194e+00   1.9235384e+00   2.0420578e+00   1.5748016e+00   2.1447611e+00   9.4868330e-01   1.1445523e+00   1.3114877e+00   1.4422205e+00   1.5459625e+00   1.3114877e+00   1.1916375e+00   2.7239677e+00   2.8827071e+00   1.2922848e+00   1.5968719e+00   1.3820275e+00   2.5961510e+00   8.5440037e-01   1.4899664e+00   1.7262677e+00   8.1240384e-01   8.8317609e-01   1.4525839e+00   1.5033296e+00   1.9287302e+00   2.5079872e+00   1.5033296e+00   8.6602540e-01   1.4317821e+00   2.1702534e+00   1.6401219e+00   1.2083046e+00   9.0553851e-01   1.2369317e+00   1.5620499e+00   1.1575837e+00   1.3076697e+00   1.7549929e+00   1.7146428e+00   1.2083046e+00   1.0630146e+00   1.0246951e+00   1.4662878e+00   1.1401754e+00   7.3484692e-01   1.0000000e+00   8.7749644e-01   5.5677644e-01   7.6157731e-01   9.4868330e-01   6.4807407e-01   8.5440037e-01   1.0099505e+00   1.2569805e+00   1.2247449e+00   4.1231056e-01   1.1916375e+00   1.0099505e+00   1.1224972e+00   7.6157731e-01   7.8740079e-01   2.0000000e-01   5.7445626e-01   1.1224972e+00   1.0148892e+00   4.4721360e-01   7.4161985e-01   5.1961524e-01   5.1961524e-01   7.3484692e-01   1.5937377e+00   4.6904158e-01   4.3588989e-01   3.8729833e-01   6.7082039e-01   1.7058722e+00   5.0000000e-01   1.9570386e+00   8.0622577e-01   2.1377558e+00   1.3416408e+00   1.7291616e+00   2.9614186e+00   8.8317609e-01   2.4959968e+00   1.8000000e+00   2.5455844e+00   1.2083046e+00   1.2369317e+00   1.6733201e+00   8.7177979e-01   1.1180340e+00   1.4000000e+00   1.3784049e+00   3.2218007e+00   3.3120990e+00   1.0246951e+00   1.9519221e+00   6.7082039e-01   3.0886890e+00   9.1104336e-01   1.7606817e+00   2.2226111e+00   7.6157731e-01   7.0710678e-01   1.5000000e+00   2.0639767e+00   2.4494897e+00   3.1288976e+00   1.5427249e+00   9.4339811e-01   1.2767145e+00   2.7586228e+00   1.6340135e+00   1.3190906e+00   5.8309519e-01   1.6941074e+00   1.8000000e+00   1.6431677e+00   8.0622577e-01   2.0199010e+00   1.9339080e+00   1.5297059e+00   1.0723805e+00   1.2449900e+00   1.4035669e+00   7.3484692e-01   9.0553851e-01   3.6055513e-01   1.1789826e+00   4.4721360e-01   1.0862780e+00   7.0710678e-01   7.2801099e-01   9.8994949e-01   1.2884099e+00   1.4832397e+00   7.0000000e-01   6.1644140e-01   5.2915026e-01   5.8309519e-01   2.8284271e-01   1.1832160e+00   8.1240384e-01   1.0246951e+00   1.2569805e+00   7.6811457e-01   4.6904158e-01   4.7958315e-01   4.7958315e-01   7.6811457e-01   2.4494897e-01   1.2000000e+00   3.7416574e-01   3.8729833e-01   3.8729833e-01   5.7445626e-01   1.3228757e+00   3.3166248e-01   2.5436195e+00   1.3453624e+00   2.4959968e+00   1.7832555e+00   2.2158520e+00   3.2848135e+00   1.2247449e+00   2.7874720e+00   2.0928450e+00   3.0033315e+00   1.6552945e+00   1.6155494e+00   2.0639767e+00   1.3638182e+00   1.7233688e+00   1.9339080e+00   1.7832555e+00   3.6083237e+00   3.6262929e+00   1.1618950e+00   2.3895606e+00   1.3000000e+00   3.3734256e+00   1.2369317e+00   2.2226111e+00   2.5416530e+00   1.1401754e+00   1.2083046e+00   1.9570386e+00   2.3021729e+00   2.7166155e+00   3.4510868e+00   2.0149442e+00   1.2288206e+00   1.5842980e+00   3.0643107e+00   2.2248595e+00   1.7663522e+00   1.1224972e+00   2.0663978e+00   2.2759613e+00   2.0149442e+00   1.3453624e+00   2.4859606e+00   2.4454039e+00   1.9493589e+00   1.3820275e+00   1.6703293e+00   2.0074860e+00   1.3190906e+00   9.8488578e-01   1.1269428e+00   8.1240384e-01   5.0990195e-01   7.0710678e-01   7.8102497e-01   9.0553851e-01   9.0553851e-01   1.0862780e+00   7.2801099e-01   1.2884099e+00   1.0862780e+00   1.1916375e+00   9.2736185e-01   8.1240384e-01   1.1313708e+00   1.2206556e+00   1.0488088e+00   2.6457513e-01   1.0954451e+00   9.3273791e-01   8.6602540e-01   8.1853528e-01   8.1240384e-01   1.7720045e+00   8.6023253e-01   1.0344080e+00   9.3273791e-01   7.5498344e-01   1.9261360e+00   9.0000000e-01   2.1142375e+00   9.6436508e-01   1.9416488e+00   1.3416408e+00   1.7058722e+00   2.7147744e+00   1.3490738e+00   2.2427661e+00   1.4560220e+00   2.5534291e+00   1.3038405e+00   1.0440307e+00   1.5362291e+00   9.1651514e-01   1.3000000e+00   1.5231546e+00   1.3490738e+00   3.1843367e+00   2.9681644e+00   5.3851648e-01   1.8894444e+00   1.0630146e+00   2.7748874e+00   7.1414284e-01   1.8055470e+00   2.0832667e+00   7.3484692e-01   9.4868330e-01   1.4035669e+00   1.8275667e+00   2.1260292e+00   3.0512293e+00   1.4491377e+00   8.5440037e-01   1.1789826e+00   2.4677925e+00   1.8627936e+00   1.3928388e+00   9.2736185e-01   1.5716234e+00   1.7549929e+00   1.5165751e+00   9.6436508e-01   1.9899749e+00   1.9748418e+00   1.4212670e+00   7.1414284e-01   1.2124356e+00   1.7000000e+00   1.0862780e+00   1.3711309e+00   6.2449980e-01   1.2845233e+00   9.9498744e-01   1.0000000e+00   1.2609520e+00   1.5588457e+00   1.7406895e+00   9.1651514e-01   4.3588989e-01   1.7320508e-01   2.6457513e-01   3.0000000e-01   1.3747727e+00   9.0000000e-01   1.2569805e+00   1.5394804e+00   9.0553851e-01   5.7445626e-01   2.4494897e-01   5.2915026e-01   1.0392305e+00   2.6457513e-01   8.7749644e-01   4.1231056e-01   6.0000000e-01   5.4772256e-01   8.4852814e-01   1.0295630e+00   4.2426407e-01   2.7386128e+00   1.4696938e+00   2.7386128e+00   2.0074860e+00   2.4248711e+00   3.5411862e+00   1.1000000e+00   3.0495901e+00   2.3043437e+00   3.2511536e+00   1.8841444e+00   1.8110770e+00   2.2912878e+00   1.4247807e+00   1.8055470e+00   2.1283797e+00   2.0273135e+00   3.8923001e+00   3.8548671e+00   1.2727922e+00   2.6191602e+00   1.3784049e+00   3.6262929e+00   1.4212670e+00   2.4677925e+00   2.8195744e+00   1.3228757e+00   1.4106736e+00   2.1494185e+00   2.5826343e+00   2.9681644e+00   3.7469988e+00   2.1977261e+00   1.4764823e+00   1.8000000e+00   3.3075671e+00   2.4248711e+00   2.0124612e+00   1.3076697e+00   2.3021729e+00   2.4799194e+00   2.2203603e+00   1.4696938e+00   2.7147744e+00   2.6551836e+00   2.1424285e+00   1.5297059e+00   1.8867962e+00   2.2045408e+00   1.5066519e+00   1.0440307e+00   8.6602540e-01   7.5498344e-01   9.1651514e-01   9.2195445e-01   1.0630146e+00   8.5440037e-01   5.2915026e-01   1.6522712e+00   1.5132746e+00   1.6278821e+00   1.1958261e+00   6.2449980e-01   6.8556546e-01   4.2426407e-01   8.6602540e-01   1.1747340e+00   9.3273791e-01   1.2409674e+00   1.0198039e+00   5.2915026e-01   1.1704700e+00   2.1236761e+00   9.7467943e-01   8.9442719e-01   8.6023253e-01   8.2462113e-01   2.2045408e+00   9.6953597e-01   1.4491377e+00   6.0000000e-01   1.6673332e+00   9.4339811e-01   1.2489996e+00   2.5019992e+00   1.2609520e+00   2.0736441e+00   1.4594520e+00   2.0074860e+00   7.0000000e-01   8.7177979e-01   1.1958261e+00   7.8102497e-01   7.8740079e-01   8.6602540e-01   9.4339811e-01   2.7147744e+00   2.8740216e+00   1.0677078e+00   1.4352700e+00   5.4772256e-01   2.6551836e+00   6.4807407e-01   1.2449900e+00   1.7691806e+00   5.0000000e-01   3.0000000e-01   1.0677078e+00   1.6643317e+00   2.0273135e+00   2.6381812e+00   1.1000000e+00   7.0710678e-01   1.0954451e+00   2.2847319e+00   1.0954451e+00   8.6602540e-01   2.2360680e-01   1.2083046e+00   1.2845233e+00   1.1618950e+00   6.0000000e-01   1.5066519e+00   1.3964240e+00   1.0440307e+00   8.3666003e-01   7.7459667e-01   8.6023253e-01   3.6055513e-01   9.8994949e-01   7.0710678e-01   4.3588989e-01   6.7823300e-01   1.0677078e+00   1.2489996e+00   5.5677644e-01   7.3484692e-01   7.7459667e-01   8.3666003e-01   3.4641016e-01   1.1489125e+00   9.0553851e-01   8.4261498e-01   9.8994949e-01   6.7082039e-01   5.4772256e-01   6.7082039e-01   7.5498344e-01   6.4031242e-01   3.7416574e-01   1.4282857e+00   5.4772256e-01   5.0000000e-01   4.5825757e-01   3.3166248e-01   1.4594520e+00   4.1231056e-01   2.3937418e+00   1.2922848e+00   2.3000000e+00   1.6911535e+00   2.0615528e+00   3.1128765e+00   1.3928388e+00   2.6438608e+00   1.9849433e+00   2.7748874e+00   1.4212670e+00   1.4662878e+00   1.8493242e+00   1.3190906e+00   1.5842980e+00   1.7146428e+00   1.6431677e+00   3.4146742e+00   3.4655447e+00   1.1874342e+00   2.1656408e+00   1.2449900e+00   3.2155870e+00   1.0535654e+00   2.0346990e+00   2.3706539e+00   9.4868330e-01   1.0488088e+00   1.8138357e+00   2.1400935e+00   2.5416530e+00   3.2388269e+00   1.8601075e+00   1.1357817e+00   1.6155494e+00   2.8301943e+00   2.0420578e+00   1.6370706e+00   9.6953597e-01   1.8248288e+00   2.0542639e+00   1.7146428e+00   1.2922848e+00   2.2934690e+00   2.2226111e+00   1.6852300e+00   1.2206556e+00   1.4594520e+00   1.8248288e+00   1.2409674e+00   5.0990195e-01   7.5498344e-01   7.7459667e-01   6.0000000e-01   6.7823300e-01   6.4031242e-01   1.6062378e+00   1.4212670e+00   1.5297059e+00   1.1747340e+00   4.2426407e-01   1.1045361e+00   1.0344080e+00   7.4833148e-01   5.7445626e-01   1.1916375e+00   1.2206556e+00   9.9498744e-01   6.2449980e-01   1.0770330e+00   2.1307276e+00   1.0295630e+00   1.0908712e+00   1.0246951e+00   7.5498344e-01   2.2825424e+00   1.0630146e+00   1.6881943e+00   7.0000000e-01   1.5000000e+00   8.6023253e-01   1.2609520e+00   2.2781571e+00   1.4696938e+00   1.7916473e+00   1.0295630e+00   2.1118712e+00   9.0553851e-01   6.0827625e-01   1.1045361e+00   7.8740079e-01   1.0908712e+00   1.1401754e+00   8.6023253e-01   2.7166155e+00   2.5709920e+00   4.3588989e-01   1.4594520e+00   9.1104336e-01   2.3537205e+00   3.6055513e-01   1.3416408e+00   1.6124515e+00   4.4721360e-01   6.1644140e-01   9.7467943e-01   1.3711309e+00   1.7029386e+00   2.5980762e+00   1.0392305e+00   3.6055513e-01   7.4161985e-01   2.0712315e+00   1.4525839e+00   9.0553851e-01   6.6332496e-01   1.1532563e+00   1.3490738e+00   1.1832160e+00   7.0000000e-01   1.5427249e+00   1.5620499e+00   1.0677078e+00   4.1231056e-01   7.9372539e-01   1.3076697e+00   7.3484692e-01   5.1961524e-01   6.4807407e-01   7.3484692e-01   8.6023253e-01   3.8729833e-01   1.2961481e+00   1.1575837e+00   1.2489996e+00   8.6023253e-01   5.8309519e-01   8.1240384e-01   7.5498344e-01   7.3484692e-01   6.2449980e-01   8.1240384e-01   9.7467943e-01   7.0000000e-01   3.0000000e-01   7.8740079e-01   1.8601075e+00   7.2111026e-01   6.7082039e-01   6.5574385e-01   4.3588989e-01   1.9974984e+00   7.2801099e-01   1.9157244e+00   8.6602540e-01   1.8138357e+00   1.1045361e+00   1.5524175e+00   2.5903668e+00   1.3490738e+00   2.0904545e+00   1.4212670e+00   2.3452079e+00   1.0583005e+00   9.7467943e-01   1.4071247e+00   9.8994949e-01   1.3000000e+00   1.3490738e+00   1.0954451e+00   2.9257478e+00   2.9410882e+00   7.4161985e-01   1.7349352e+00   9.6436508e-01   2.6832816e+00   6.7082039e-01   1.5556349e+00   1.8493242e+00   6.1644140e-01   6.6332496e-01   1.3076697e+00   1.6186414e+00   2.0346990e+00   2.7874720e+00   1.3784049e+00   5.3851648e-01   9.4339811e-01   2.4020824e+00   1.6278821e+00   1.0862780e+00   6.4807407e-01   1.4247807e+00   1.6431677e+00   1.4491377e+00   8.6602540e-01   1.8165902e+00   1.8165902e+00   1.3638182e+00   8.4261498e-01   1.0440307e+00   1.4387495e+00   7.7459667e-01   2.6457513e-01   6.5574385e-01   8.6602540e-01   4.8989795e-01   1.1445523e+00   1.1618950e+00   1.2288206e+00   7.5498344e-01   9.6436508e-01   1.0440307e+00   7.3484692e-01   5.7445626e-01   6.1644140e-01   8.3066239e-01   1.0295630e+00   9.5916630e-01   4.4721360e-01   7.4161985e-01   1.8466185e+00   8.3066239e-01   7.2111026e-01   7.0710678e-01   2.0000000e-01   1.8920888e+00   7.3484692e-01   2.1213203e+00   1.1832160e+00   1.9235384e+00   1.3964240e+00   1.7549929e+00   2.7166155e+00   1.6155494e+00   2.2494444e+00   1.6583124e+00   2.4103942e+00   1.1090537e+00   1.1832160e+00   1.5000000e+00   1.2767145e+00   1.4899664e+00   1.4456832e+00   1.3076697e+00   3.0116441e+00   3.0886890e+00   1.0862780e+00   1.8165902e+00   1.2247449e+00   2.8195744e+00   8.1240384e-01   1.6881943e+00   1.9672316e+00   7.4161985e-01   8.4261498e-01   1.5297059e+00   1.7291616e+00   2.1470911e+00   2.8213472e+00   1.5842980e+00   8.3666003e-01   1.3711309e+00   2.4372115e+00   1.7776389e+00   1.3152946e+00   8.1853528e-01   1.4628739e+00   1.7406895e+00   1.3892444e+00   1.1832160e+00   1.9519221e+00   1.9104973e+00   1.3820275e+00   1.0099505e+00   1.1489125e+00   1.5811388e+00   1.0723805e+00   4.8989795e-01   6.7823300e-01   6.2449980e-01   1.3928388e+00   1.4212670e+00   1.4899664e+00   1.0099505e+00   9.8994949e-01   1.2083046e+00   7.5498344e-01   3.4641016e-01   7.6811457e-01   1.0488088e+00   1.2767145e+00   1.1874342e+00   5.3851648e-01   1.0000000e+00   2.1023796e+00   1.0677078e+00   9.4339811e-01   9.3273791e-01   4.3588989e-01   2.1330729e+00   9.7467943e-01   1.9874607e+00   1.2124356e+00   1.7291616e+00   1.3038405e+00   1.6155494e+00   2.5159491e+00   1.8000000e+00   2.0663978e+00   1.5427249e+00   2.1954498e+00   9.4868330e-01   1.0908712e+00   1.3190906e+00   1.3341664e+00   1.4730920e+00   1.3038405e+00   1.1747340e+00   2.7892651e+00   2.9034462e+00   1.1704700e+00   1.6217275e+00   1.2845233e+00   2.6267851e+00   7.6811457e-01   1.5099669e+00   1.7663522e+00   7.2111026e-01   8.1240384e-01   1.4177447e+00   1.5362291e+00   1.9544820e+00   2.5865034e+00   1.4696938e+00   7.9372539e-01   1.3601471e+00   2.2158520e+00   1.6401219e+00   1.1916375e+00   8.2462113e-01   1.2609520e+00   1.5684387e+00   1.1832160e+00   1.2124356e+00   1.7720045e+00   1.7320508e+00   1.2083046e+00   9.7467943e-01   1.0049876e+00   1.4594520e+00   1.0677078e+00   4.2426407e-01   8.6602540e-01   1.7606817e+00   1.7146428e+00   1.7944358e+00   1.3638182e+00   8.8317609e-01   1.4491377e+00   1.0630146e+00   3.4641016e-01   8.1853528e-01   1.4071247e+00   1.5588457e+00   1.3892444e+00   7.5498344e-01   1.3114877e+00   2.4289916e+00   1.3490738e+00   1.2845233e+00   1.2609520e+00   7.9372539e-01   2.5119713e+00   1.3076697e+00   1.7748239e+00   1.1618950e+00   1.3527749e+00   1.0295630e+00   1.3304135e+00   2.1000000e+00   1.9697716e+00   1.6340135e+00   1.1224972e+00   1.9235384e+00   8.3666003e-01   8.1853528e-01   1.0099505e+00   1.3038405e+00   1.4456832e+00   1.1747340e+00   8.8317609e-01   2.4617067e+00   2.4637370e+00   1.0246951e+00   1.3379088e+00   1.3453624e+00   2.1863211e+00   6.5574385e-01   1.2489996e+00   1.3856406e+00   7.2111026e-01   8.3666003e-01   1.1357817e+00   1.1135529e+00   1.5165751e+00   2.2649503e+00   1.2000000e+00   5.9160798e-01   1.0816654e+00   1.8303005e+00   1.5000000e+00   9.4868330e-01   9.1651514e-01   9.7467943e-01   1.3190906e+00   1.0000000e+00   1.1618950e+00   1.4764823e+00   1.5099669e+00   1.0099505e+00   7.9372539e-01   8.0622577e-01   1.3747727e+00   1.0488088e+00   8.8881944e-01   1.9748418e+00   1.8973666e+00   1.9949937e+00   1.5362291e+00   7.7459667e-01   1.4071247e+00   9.5393920e-01   3.7416574e-01   1.0816654e+00   1.4764823e+00   1.6881943e+00   1.4866069e+00   7.8102497e-01   1.4899664e+00   2.6000000e+00   1.4491377e+00   1.3747727e+00   1.3453624e+00   9.5393920e-01   2.6776856e+00   1.4177447e+00   1.3747727e+00   9.7467943e-01   1.0630146e+00   7.3484692e-01   9.6436508e-01   1.8788294e+00   1.9339080e+00   1.4387495e+00   9.4868330e-01   1.5684387e+00   4.2426407e-01   5.5677644e-01   6.4807407e-01   1.1575837e+00   1.1618950e+00   7.6157731e-01   5.4772256e-01   2.1863211e+00   2.2649503e+00   1.0816654e+00   9.6436508e-01   1.1618950e+00   2.0049938e+00   5.1961524e-01   8.6023253e-01   1.1401754e+00   5.8309519e-01   6.1644140e-01   8.0622577e-01   9.4868330e-01   1.3341664e+00   2.0322401e+00   8.6023253e-01   5.0000000e-01   9.8488578e-01   1.6031220e+00   1.0816654e+00   6.0000000e-01   7.3484692e-01   6.0827625e-01   9.2736185e-01   6.4807407e-01   9.7467943e-01   1.1045361e+00   1.1045361e+00   6.3245553e-01   6.7082039e-01   4.1231056e-01   9.6436508e-01   8.1240384e-01   1.1958261e+00   1.0723805e+00   1.1789826e+00   7.2801099e-01   6.4031242e-01   6.0827625e-01   5.0990195e-01   7.5498344e-01   7.0710678e-01   6.0827625e-01   8.3666003e-01   6.6332496e-01   2.0000000e-01   6.8556546e-01   1.7464249e+00   5.7445626e-01   5.2915026e-01   4.6904158e-01   3.4641016e-01   1.8384776e+00   5.4772256e-01   1.8708287e+00   7.7459667e-01   1.8814888e+00   1.1789826e+00   1.5620499e+00   2.7092434e+00   1.1874342e+00   2.2405357e+00   1.5588457e+00   2.3430749e+00   9.7467943e-01   1.0000000e+00   1.4177447e+00   8.6602540e-01   1.1045361e+00   1.2369317e+00   1.1618950e+00   3.0049958e+00   3.0626786e+00   8.6023253e-01   1.7262677e+00   7.6157731e-01   2.8266588e+00   6.1644140e-01   1.5652476e+00   1.9672316e+00   4.7958315e-01   5.1961524e-01   1.3190906e+00   1.7748239e+00   2.1656408e+00   2.8774989e+00   1.3674794e+00   6.7823300e-01   1.1489125e+00   2.4698178e+00   1.5362291e+00   1.1357817e+00   4.3588989e-01   1.4212670e+00   1.5968719e+00   1.3601471e+00   7.7459667e-01   1.8248288e+00   1.7578396e+00   1.2767145e+00   8.1240384e-01   1.0000000e+00   1.3190906e+00   6.8556546e-01   4.2426407e-01   3.4641016e-01   4.6904158e-01   1.7378147e+00   1.2247449e+00   1.4456832e+00   1.7146428e+00   1.1618950e+00   7.8740079e-01   6.2449980e-01   9.4339811e-01   1.3000000e+00   5.4772256e-01   7.8740079e-01   7.7459667e-01   8.3066239e-01   8.1853528e-01   1.0344080e+00   7.9372539e-01   7.0000000e-01   3.0577770e+00   1.8411953e+00   3.0149627e+00   2.3452079e+00   2.7440845e+00   3.8196859e+00   1.4628739e+00   3.3361655e+00   2.6343880e+00   3.5014283e+00   2.1354157e+00   2.1330729e+00   2.5651511e+00   1.8055470e+00   2.1377558e+00   2.4041631e+00   2.3323808e+00   4.1376322e+00   4.1533119e+00   1.6583124e+00   2.8861739e+00   1.7349352e+00   3.9089641e+00   1.7233688e+00   2.7459060e+00   3.0822070e+00   1.6186414e+00   1.7088007e+00   2.4799194e+00   2.8390139e+00   3.2403703e+00   3.9610605e+00   2.5258662e+00   1.7916473e+00   2.1748563e+00   3.5510562e+00   2.7147744e+00   2.3194827e+00   1.6062378e+00   2.5514702e+00   2.7604347e+00   2.4372115e+00   1.8411953e+00   3.0033315e+00   2.9291637e+00   2.3958297e+00   1.8520259e+00   2.1656408e+00   2.4879711e+00   1.8439089e+00   1.4142136e-01   4.4721360e-01   1.5099669e+00   1.0099505e+00   1.4106736e+00   1.7029386e+00   1.0246951e+00   7.0710678e-01   3.0000000e-01   6.4031242e-01   1.2041595e+00   4.2426407e-01   7.2111026e-01   5.4772256e-01   7.5498344e-01   7.0000000e-01   1.0148892e+00   9.0000000e-01   5.7445626e-01   2.8722813e+00   1.5842980e+00   2.8861739e+00   2.1494185e+00   2.5632011e+00   3.6891733e+00   1.1045361e+00   3.1984371e+00   2.4372115e+00   3.4029399e+00   2.0346990e+00   1.9467922e+00   2.4372115e+00   1.5165751e+00   1.9052559e+00   2.2671568e+00   2.1771541e+00   4.0521599e+00   3.9912404e+00   1.3747727e+00   2.7658633e+00   1.4798649e+00   3.7709415e+00   1.5588457e+00   2.6191602e+00   2.9765752e+00   1.4628739e+00   1.5556349e+00   2.2825424e+00   2.7386128e+00   3.1144823e+00   3.9102430e+00   2.3280893e+00   1.6278821e+00   1.9313208e+00   3.4539832e+00   2.5632011e+00   2.1633308e+00   1.4491377e+00   2.4515301e+00   2.6191602e+00   2.3622024e+00   1.5842980e+00   2.8600699e+00   2.7964263e+00   2.2803509e+00   1.6522712e+00   2.0322401e+00   2.3430749e+00   1.6431677e+00   5.0990195e-01   1.6309506e+00   1.1224972e+00   1.5000000e+00   1.7832555e+00   1.1090537e+00   7.8740079e-01   4.3588989e-01   7.5498344e-01   1.3000000e+00   5.0990195e-01   6.4807407e-01   6.6332496e-01   8.3066239e-01   7.9372539e-01   1.0908712e+00   8.1853528e-01   6.7082039e-01   2.9983329e+00   1.7175564e+00   2.9949958e+00   2.2671568e+00   2.6851443e+00   3.7934153e+00   1.2247449e+00   3.3000000e+00   2.5495098e+00   3.5128336e+00   2.1447611e+00   2.0663978e+00   2.5495098e+00   1.6552945e+00   2.0420578e+00   2.3874673e+00   2.2891046e+00   4.1521079e+00   4.1000000e+00   1.4933185e+00   2.8792360e+00   1.6155494e+00   3.8729833e+00   1.6763055e+00   2.7313001e+00   3.0757113e+00   1.5811388e+00   1.6733201e+00   2.4062419e+00   2.8319605e+00   3.2155870e+00   4.0012498e+00   2.4535688e+00   1.7349352e+00   2.0420578e+00   3.5566838e+00   2.6851443e+00   2.2759613e+00   1.5684387e+00   2.5592968e+00   2.7386128e+00   2.4698178e+00   1.7175564e+00   2.9765752e+00   2.9154759e+00   2.3958297e+00   1.7748239e+00   2.1470911e+00   2.4637370e+00   1.7663522e+00   1.2806248e+00   8.3666003e-01   1.0246951e+00   1.3038405e+00   8.1853528e-01   4.2426407e-01   3.8729833e-01   5.9160798e-01   8.4261498e-01   1.4142136e-01   1.0954451e+00   3.7416574e-01   4.3588989e-01   3.8729833e-01   6.0827625e-01   1.1618950e+00   2.6457513e-01   2.5903668e+00   1.3892444e+00   2.5670995e+00   1.8814888e+00   2.2781571e+00   3.3808283e+00   1.2083046e+00   2.9000000e+00   2.1954498e+00   3.0495901e+00   1.6792856e+00   1.6763055e+00   2.1118712e+00   1.3784049e+00   1.7000000e+00   1.9442222e+00   1.8708287e+00   3.6959437e+00   3.7188708e+00   1.2609520e+00   2.4310492e+00   1.3000000e+00   3.4785054e+00   1.2688578e+00   2.2847319e+00   2.6419690e+00   1.1575837e+00   1.2409674e+00   2.0174241e+00   2.4124676e+00   2.8106939e+00   3.5369478e+00   2.0639767e+00   1.3379088e+00   1.7406895e+00   3.1224990e+00   2.2516660e+00   1.8547237e+00   1.1401754e+00   2.1047565e+00   2.3021729e+00   2.0049938e+00   1.3892444e+00   2.5416530e+00   2.4698178e+00   1.9493589e+00   1.4106736e+00   1.7058722e+00   2.0273135e+00   1.3784049e+00   9.0553851e-01   9.2195445e-01   9.0553851e-01   9.1104336e-01   1.1575837e+00   1.2609520e+00   9.5393920e-01   6.2449980e-01   1.1916375e+00   2.1817424e+00   1.0295630e+00   1.0723805e+00   1.0148892e+00   9.0000000e-01   2.3473389e+00   1.0908712e+00   1.4387495e+00   3.6055513e-01   1.4798649e+00   6.4807407e-01   1.0908712e+00   2.2693611e+00   1.2727922e+00   1.7916473e+00   1.0295630e+00   2.0149442e+00   8.1240384e-01   5.3851648e-01   1.0677078e+00   5.4772256e-01   8.3066239e-01   9.6953597e-01   7.3484692e-01   2.6495283e+00   2.5748786e+00   5.1961524e-01   1.3820275e+00   6.0827625e-01   2.3706539e+00   4.1231056e-01   1.2083046e+00   1.5937377e+00   4.2426407e-01   4.2426407e-01   8.1853528e-01   1.4212670e+00   1.7492856e+00   2.5826343e+00   8.8317609e-01   3.3166248e-01   5.5677644e-01   2.1142375e+00   1.2124356e+00   7.2111026e-01   4.6904158e-01   1.1445523e+00   1.2409674e+00   1.2083046e+00   3.6055513e-01   1.4212670e+00   1.4212670e+00   1.0392305e+00   4.7958315e-01   7.1414284e-01   1.0535654e+00   3.7416574e-01   7.2801099e-01   1.3190906e+00   1.1618950e+00   4.8989795e-01   7.4161985e-01   5.1961524e-01   7.1414284e-01   8.1240384e-01   1.5297059e+00   5.0990195e-01   5.1961524e-01   4.7958315e-01   8.5440037e-01   1.6583124e+00   5.7445626e-01   2.0371549e+00   8.7749644e-01   2.2825424e+00   1.4560220e+00   1.8411953e+00   3.1000000e+00   7.3484692e-01   2.6362853e+00   1.9287302e+00   2.6758176e+00   1.3638182e+00   1.3747727e+00   1.8220867e+00   9.1651514e-01   1.1704700e+00   1.5231546e+00   1.5165751e+00   3.3555923e+00   3.4423829e+00   1.1180340e+00   2.0904545e+00   7.0000000e-01   3.2280025e+00   1.0723805e+00   1.8920888e+00   2.3706539e+00   9.2736185e-01   8.6023253e-01   1.6155494e+00   2.2226111e+00   2.6000000e+00   3.2787193e+00   1.6552945e+00   1.1000000e+00   1.3674794e+00   2.9137605e+00   1.7291616e+00   1.4491377e+00   7.3484692e-01   1.8520259e+00   1.9287302e+00   1.8055470e+00   8.7749644e-01   2.1447611e+00   2.0542639e+00   1.6792856e+00   1.2124356e+00   1.3964240e+00   1.5000000e+00   8.3666003e-01   7.9372539e-01   1.1832160e+00   7.5498344e-01   1.1832160e+00   1.0295630e+00   4.6904158e-01   1.0440307e+00   2.0024984e+00   9.1104336e-01   7.0710678e-01   7.2111026e-01   6.4807407e-01   2.0297783e+00   8.3666003e-01   1.7776389e+00   9.8994949e-01   1.8920888e+00   1.2609520e+00   1.5684387e+00   2.7166155e+00   1.4247807e+00   2.2847319e+00   1.7406895e+00   2.2022716e+00   9.0000000e-01   1.1747340e+00   1.4317821e+00   1.1445523e+00   1.1832160e+00   1.1532563e+00   1.2041595e+00   2.8722813e+00   3.1272992e+00   1.3038405e+00   1.6673332e+00   9.1651514e-01   2.8722813e+00   8.8317609e-01   1.4798649e+00   1.9416488e+00   7.2801099e-01   6.0827625e-01   1.4071247e+00   1.8138357e+00   2.2293497e+00   2.7459060e+00   1.4456832e+00   9.0553851e-01   1.3784049e+00   2.4698178e+00   1.3928388e+00   1.1357817e+00   5.3851648e-01   1.4000000e+00   1.5588457e+00   1.3228757e+00   9.8994949e-01   1.7691806e+00   1.6583124e+00   1.2767145e+00   1.1135529e+00   1.0295630e+00   1.1575837e+00   7.5498344e-01   9.6436508e-01   1.2727922e+00   1.5264338e+00   1.3674794e+00   6.2449980e-01   1.2806248e+00   2.3958297e+00   1.2884099e+00   1.1618950e+00   1.1532563e+00   7.0000000e-01   2.4433583e+00   1.2206556e+00   1.7000000e+00   1.1357817e+00   1.4035669e+00   1.0488088e+00   1.3228757e+00   2.1886069e+00   1.9183326e+00   1.7464249e+00   1.2884099e+00   1.8601075e+00   6.7823300e-01   8.7749644e-01   1.0099505e+00   1.3038405e+00   1.3674794e+00   1.0488088e+00   8.8317609e-01   2.4454039e+00   2.5942244e+00   1.1789826e+00   1.3000000e+00   1.2609520e+00   2.3108440e+00   6.7082039e-01   1.1832160e+00   1.4282857e+00   6.6332496e-01   7.0710678e-01   1.1618950e+00   1.2165525e+00   1.6431677e+00   2.2516660e+00   1.2165525e+00   6.4031242e-01   1.1958261e+00   1.9000000e+00   1.3674794e+00   9.0553851e-01   7.7459667e-01   9.4339811e-01   1.2727922e+00   9.1651514e-01   1.1357817e+00   1.4491377e+00   1.4282857e+00   9.4868330e-01   8.7749644e-01   7.4161985e-01   1.2124356e+00   9.4868330e-01   1.0344080e+00   9.1651514e-01   8.6023253e-01   7.6157731e-01   7.1414284e-01   1.7291616e+00   8.3066239e-01   9.4868330e-01   8.7177979e-01   6.1644140e-01   1.8654758e+00   8.3666003e-01   2.2360680e+00   1.1224972e+00   2.0049938e+00   1.4317821e+00   1.8165902e+00   2.7676705e+00   1.4730920e+00   2.2847319e+00   1.5524175e+00   2.6134269e+00   1.3527749e+00   1.1575837e+00   1.6093477e+00   1.1180340e+00   1.4832397e+00   1.6217275e+00   1.4106736e+00   3.2109189e+00   3.0495901e+00   7.0710678e-01   1.9646883e+00   1.2165525e+00   2.8266588e+00   8.1240384e-01   1.8681542e+00   2.1047565e+00   8.1853528e-01   1.0148892e+00   1.5297059e+00   1.8303005e+00   2.1702534e+00   3.0495901e+00   1.5842980e+00   8.8317609e-01   1.2569805e+00   2.5179357e+00   1.9646883e+00   1.4525839e+00   9.9498744e-01   1.6248077e+00   1.8574176e+00   1.5779734e+00   1.1224972e+00   2.0760539e+00   2.0712315e+00   1.5132746e+00   8.7177979e-01   1.2884099e+00   1.7944358e+00   1.1789826e+00   5.1961524e-01   5.1961524e-01   7.1414284e-01   4.6904158e-01   1.2569805e+00   3.1622777e-01   1.7320508e-01   1.7320508e-01   6.4031242e-01   1.3228757e+00   2.2360680e-01   2.3727621e+00   1.2206556e+00   2.4758837e+00   1.7320508e+00   2.1236761e+00   3.3000000e+00   1.0295630e+00   2.8266588e+00   2.1447611e+00   2.8913665e+00   1.5297059e+00   1.5905974e+00   2.0099751e+00   1.2489996e+00   1.5132746e+00   1.7663522e+00   1.7378147e+00   3.5524639e+00   3.6619667e+00   1.2845233e+00   2.3000000e+00   1.0816654e+00   3.4205263e+00   1.2124356e+00   2.1213203e+00   2.5416530e+00   1.0677078e+00   1.0677078e+00   1.8894444e+00   2.3537205e+00   2.7640550e+00   3.4219877e+00   1.9339080e+00   1.2529964e+00   1.6340135e+00   3.0675723e+00   2.0273135e+00   1.6911535e+00   9.4868330e-01   2.0074860e+00   2.1633308e+00   1.9235384e+00   1.2206556e+00   2.3916521e+00   2.3021729e+00   1.8493242e+00   1.3820275e+00   1.5842980e+00   1.7916473e+00   1.1575837e+00   4.2426407e-01   9.8994949e-01   3.3166248e-01   9.3273791e-01   3.0000000e-01   5.8309519e-01   4.8989795e-01   8.6023253e-01   1.0954451e+00   3.7416574e-01   2.5922963e+00   1.3038405e+00   2.6570661e+00   1.9000000e+00   2.3021729e+00   3.4727511e+00   8.7749644e-01   2.9899833e+00   2.2203603e+00   3.1543621e+00   1.7860571e+00   1.7029386e+00   2.1977261e+00   1.2369317e+00   1.6124515e+00   1.9974984e+00   1.9364917e+00   3.8249183e+00   3.7762415e+00   1.1747340e+00   2.5179357e+00   1.1832160e+00   3.5651087e+00   1.3190906e+00   2.3685439e+00   2.7622455e+00   1.2124356e+00   1.2922848e+00   2.0248457e+00   2.5436195e+00   2.9103264e+00   3.7013511e+00   2.0663978e+00   1.4071247e+00   1.7146428e+00   3.2403703e+00   2.2847319e+00   1.9157244e+00   1.1789826e+00   2.2181073e+00   2.3600847e+00   2.1283797e+00   1.3038405e+00   2.6057628e+00   2.5317978e+00   2.0322401e+00   1.4142136e+00   1.7832555e+00   2.0639767e+00   1.3674794e+00   7.7459667e-01   5.0000000e-01   1.2609520e+00   2.6457513e-01   4.8989795e-01   4.2426407e-01   7.7459667e-01   1.4628739e+00   4.2426407e-01   2.3194827e+00   1.0392305e+00   2.4041631e+00   1.5905974e+00   2.0297783e+00   3.1968735e+00   7.9372539e-01   2.7018512e+00   1.9416488e+00   2.9103264e+00   1.5779734e+00   1.4560220e+00   1.9672316e+00   1.0246951e+00   1.4352700e+00   1.7860571e+00   1.6522712e+00   3.5454196e+00   3.5071356e+00   9.2736185e-01   2.2847319e+00   9.6953597e-01   3.2878564e+00   1.1224972e+00   2.1047565e+00   2.4839485e+00   1.0246951e+00   1.0630146e+00   1.7606817e+00   2.2737634e+00   2.6514147e+00   3.4409301e+00   1.8138357e+00   1.1224972e+00   1.3564660e+00   3.0166206e+00   2.0396078e+00   1.6217275e+00   9.6436508e-01   2.0049938e+00   2.1377558e+00   1.9773720e+00   1.0392305e+00   2.3473389e+00   2.3043437e+00   1.8574176e+00   1.2247449e+00   1.5620499e+00   1.8275667e+00   1.0816654e+00   8.0622577e-01   1.8841444e+00   7.1414284e-01   6.0000000e-01   5.8309519e-01   3.4641016e-01   1.9748418e+00   6.7823300e-01   1.8165902e+00   8.2462113e-01   1.7832555e+00   1.1000000e+00   1.4966630e+00   2.5961510e+00   1.3379088e+00   2.1213203e+00   1.4866069e+00   2.2427661e+00   9.0000000e-01   9.5916630e-01   1.3379088e+00   9.6436508e-01   1.1747340e+00   1.1958261e+00   1.0630146e+00   2.8722813e+00   2.9698485e+00   9.0553851e-01   1.6431677e+00   8.6023253e-01   2.7147744e+00   6.1644140e-01   1.4662878e+00   1.8357560e+00   5.0000000e-01   5.0000000e-01   1.2727922e+00   1.6401219e+00   2.0566964e+00   2.7349589e+00   1.3304135e+00   5.8309519e-01   1.0770330e+00   2.3706539e+00   1.4832397e+00   1.0344080e+00   4.5825757e-01   1.3341664e+00   1.5394804e+00   1.3076697e+00   8.2462113e-01   1.7406895e+00   1.6941074e+00   1.2369317e+00   8.3666003e-01   9.3808315e-01   1.2727922e+00   6.7082039e-01   1.1224972e+00   3.1622777e-01   4.5825757e-01   3.8729833e-01   5.9160798e-01   1.2288206e+00   2.6457513e-01   2.5357445e+00   1.3076697e+00   2.5039968e+00   1.8055470e+00   2.2113344e+00   3.3120990e+00   1.1489125e+00   2.8266588e+00   2.1023796e+00   3.0099834e+00   1.6431677e+00   1.5968719e+00   2.0542639e+00   1.2884099e+00   1.6401219e+00   1.9026298e+00   1.8055470e+00   3.6523965e+00   3.6373067e+00   1.1357817e+00   2.3811762e+00   1.2369317e+00   3.4029399e+00   1.1958261e+00   2.2360680e+00   2.5845696e+00   1.0954451e+00   1.1916375e+00   1.9416488e+00   2.3494680e+00   2.7386128e+00   3.5000000e+00   1.9899749e+00   1.2609520e+00   1.6401219e+00   3.0643107e+00   2.2113344e+00   1.7944358e+00   1.0954451e+00   2.0566964e+00   2.2494444e+00   1.9697716e+00   1.3076697e+00   2.4859606e+00   2.4248711e+00   1.9026298e+00   1.3228757e+00   1.6522712e+00   1.9924859e+00   1.3190906e+00   1.1916375e+00   1.3527749e+00   1.3228757e+00   1.7000000e+00   3.8729833e-01   1.2124356e+00   3.4971417e+00   2.2022716e+00   3.5874782e+00   2.8248894e+00   3.2295511e+00   4.3988635e+00   1.4071247e+00   3.9102430e+00   3.1336879e+00   4.0767634e+00   2.7018512e+00   2.6324893e+00   3.1272992e+00   2.1023796e+00   2.4677925e+00   2.9086079e+00   2.8670542e+00   4.7476310e+00   4.6936127e+00   2.0371549e+00   3.4452866e+00   2.0420578e+00   4.4833024e+00   2.2472205e+00   3.2954514e+00   3.6851052e+00   2.1400935e+00   2.2135944e+00   2.9512709e+00   3.4554305e+00   3.8288379e+00   4.6119410e+00   2.9899833e+00   2.3302360e+00   2.5980762e+00   4.1605288e+00   3.1859065e+00   2.8425341e+00   2.0928450e+00   3.1416556e+00   3.2832910e+00   3.0298515e+00   2.2022716e+00   3.5355339e+00   3.4496377e+00   2.9461840e+00   2.3302360e+00   2.7110883e+00   2.9580399e+00   2.2759613e+00   3.3166248e-01   2.2360680e-01   6.4031242e-01   1.3304135e+00   1.7320508e-01   2.3515952e+00   1.1000000e+00   2.4228083e+00   1.6552945e+00   2.0663978e+00   3.2388269e+00   8.8317609e-01   2.7549955e+00   2.0149442e+00   2.9017236e+00   1.5362291e+00   1.4866069e+00   1.9646883e+00   1.0862780e+00   1.4387495e+00   1.7606817e+00   1.6852300e+00   3.5608988e+00   3.5651087e+00   1.0440307e+00   2.2781571e+00   9.9498744e-01   3.3406586e+00   1.1090537e+00   2.1118712e+00   2.5099801e+00   9.8994949e-01   1.0392305e+00   1.8027756e+00   2.3021729e+00   2.6870058e+00   3.4394767e+00   1.8493242e+00   1.1618950e+00   1.4933185e+00   3.0182777e+00   2.0371549e+00   1.6552945e+00   9.2736185e-01   1.9824228e+00   2.1307276e+00   1.9131126e+00   1.1000000e+00   2.3622024e+00   2.2934690e+00   1.8165902e+00   1.2369317e+00   1.5459625e+00   1.8138357e+00   1.1135529e+00   1.4142136e-01   5.2915026e-01   1.4352700e+00   2.4494897e-01   2.3194827e+00   1.1832160e+00   2.3790755e+00   1.6401219e+00   2.0493902e+00   3.1906112e+00   1.1090537e+00   2.7092434e+00   2.0420578e+00   2.8124722e+00   1.4594520e+00   1.5099669e+00   1.9261360e+00   1.2369317e+00   1.5165751e+00   1.7175564e+00   1.6401219e+00   3.4481879e+00   3.5580894e+00   1.2083046e+00   2.2226111e+00   1.0862780e+00   3.3060551e+00   1.1401754e+00   2.0371549e+00   2.4269322e+00   1.0049876e+00   1.0049876e+00   1.8165902e+00   2.2293497e+00   2.6514147e+00   3.3105891e+00   1.8681542e+00   1.1401754e+00   1.5231546e+00   2.9698485e+00   1.9798990e+00   1.5968719e+00   9.0000000e-01   1.9235384e+00   2.1000000e+00   1.8627936e+00   1.1832160e+00   2.3130067e+00   2.2427661e+00   1.7916473e+00   1.3190906e+00   1.5099669e+00   1.7492856e+00   1.1000000e+00   5.0990195e-01   1.4142136e+00   1.4142136e-01   2.2803509e+00   1.1045361e+00   2.3452079e+00   1.6031220e+00   2.0049938e+00   3.1654384e+00   1.0246951e+00   2.6870058e+00   1.9924859e+00   2.7910571e+00   1.4247807e+00   1.4491377e+00   1.8841444e+00   1.1357817e+00   1.4282857e+00   1.6703293e+00   1.6093477e+00   3.4452866e+00   3.5185224e+00   1.1224972e+00   2.1863211e+00   1.0000000e+00   3.2787193e+00   1.0677078e+00   2.0124612e+00   2.4145393e+00   9.3273791e-01   9.5393920e-01   1.7606817e+00   2.2158520e+00   2.6210685e+00   3.3136083e+00   1.8083141e+00   1.1045361e+00   1.4899664e+00   2.9359837e+00   1.9442222e+00   1.5716234e+00   8.4261498e-01   1.8867962e+00   2.0518285e+00   1.8138357e+00   1.1045361e+00   2.2781571e+00   2.2022716e+00   1.7349352e+00   1.2328828e+00   1.4628739e+00   1.7146428e+00   1.0535654e+00   1.7606817e+00   5.4772256e-01   2.1213203e+00   1.0954451e+00   2.0049938e+00   1.3964240e+00   1.7776389e+00   2.8106939e+00   1.4317821e+00   2.3366643e+00   1.7058722e+00   2.4839485e+00   1.1445523e+00   1.2000000e+00   1.5652476e+00   1.1789826e+00   1.4212670e+00   1.4594520e+00   1.3379088e+00   3.1032241e+00   3.1780497e+00   1.0295630e+00   1.8814888e+00   1.1045361e+00   2.9171904e+00   8.1240384e-01   1.7349352e+00   2.0566964e+00   7.1414284e-01   7.9372539e-01   1.5427249e+00   1.8303005e+00   2.2472205e+00   2.9325757e+00   1.5968719e+00   8.3666003e-01   1.3416408e+00   2.5495098e+00   1.7776389e+00   1.3304135e+00   7.4161985e-01   1.5427249e+00   1.7860571e+00   1.4730920e+00   1.0954451e+00   2.0024984e+00   1.9519221e+00   1.4387495e+00   1.0099505e+00   1.1832160e+00   1.5684387e+00   9.9498744e-01   1.3038405e+00   3.6110940e+00   2.3622024e+00   3.6959437e+00   2.9748950e+00   3.3555923e+00   4.5232732e+00   1.6278821e+00   4.0472213e+00   3.3000000e+00   4.1460825e+00   2.7694765e+00   2.7676705e+00   3.2233523e+00   2.2737634e+00   2.5845696e+00   2.9849623e+00   2.9916551e+00   4.8321838e+00   4.8394215e+00   2.2494444e+00   3.5298725e+00   2.1817424e+00   4.6206060e+00   2.3622024e+00   3.3896903e+00   3.7934153e+00   2.2427661e+00   2.3130067e+00   3.0886890e+00   3.5707142e+00   3.9534795e+00   4.6797436e+00   3.1224990e+00   2.4698178e+00   2.8035692e+00   4.2497059e+00   3.2710854e+00   2.9647934e+00   2.1886069e+00   3.2186954e+00   3.3719431e+00   3.0740852e+00   2.3622024e+00   3.6373067e+00   3.5284558e+00   3.0149627e+00   2.4657656e+00   2.8035692e+00   3.0364453e+00   2.4062419e+00   2.3790755e+00   1.1747340e+00   2.4248711e+00   1.6941074e+00   2.0928450e+00   3.2465366e+00   1.0246951e+00   2.7676705e+00   2.0566964e+00   2.8861739e+00   1.5132746e+00   1.5165751e+00   1.9621417e+00   1.1789826e+00   1.4899664e+00   1.7578396e+00   1.7000000e+00   3.5454196e+00   3.5888717e+00   1.1401754e+00   2.2715633e+00   1.0677078e+00   3.3541020e+00   1.1224972e+00   2.1095023e+00   2.5039968e+00   9.9498744e-01   1.0440307e+00   1.8384776e+00   2.2956481e+00   2.6925824e+00   3.4088121e+00   1.8841444e+00   1.1832160e+00   1.5684387e+00   3.0066593e+00   2.0445048e+00   1.6703293e+00   9.3273791e-01   1.9646883e+00   2.1330729e+00   1.8788294e+00   1.1747340e+00   2.3685439e+00   2.2912878e+00   1.8027756e+00   1.2727922e+00   1.5427249e+00   1.8165902e+00   1.1532563e+00   1.3341664e+00   9.4868330e-01   9.0000000e-01   5.0990195e-01   1.5165751e+00   2.3430749e+00   1.3190906e+00   1.1532563e+00   9.5393920e-01   1.0535654e+00   1.1045361e+00   8.6602540e-01   1.5000000e+00   1.1489125e+00   7.4161985e-01   9.3273791e-01   1.6703293e+00   1.8165902e+00   1.8165902e+00   7.0710678e-01   1.4832397e+00   1.7175564e+00   1.4352700e+00   6.4031242e-01   1.1445523e+00   1.4798649e+00   1.3527749e+00   7.6157731e-01   1.3228757e+00   1.3527749e+00   1.7944358e+00   7.1414284e-01   1.4352700e+00   1.3784049e+00   1.4491377e+00   4.2426407e-01   8.8881944e-01   1.4525839e+00   9.5916630e-01   6.0827625e-01   1.1180340e+00   1.3341664e+00   5.5677644e-01   5.0000000e-01   9.6436508e-01   1.4142136e+00   1.0099505e+00   6.4807407e-01   1.2449900e+00   1.5684387e+00   7.4161985e-01   1.0770330e+00   2.3706539e+00   1.1180340e+00   1.9339080e+00   1.1618950e+00   2.0322401e+00   8.6602540e-01   6.3245553e-01   1.1357817e+00   2.6457513e-01   5.0990195e-01   9.0000000e-01   8.6602540e-01   2.7331301e+00   2.6495283e+00   6.7823300e-01   1.4071247e+00   3.1622777e-01   2.4879711e+00   5.4772256e-01   1.2529964e+00   1.7406895e+00   5.1961524e-01   4.7958315e-01   8.1240384e-01   1.6217275e+00   1.8894444e+00   2.7055499e+00   8.4261498e-01   6.4807407e-01   7.7459667e-01   2.2045408e+00   1.1135529e+00   8.3066239e-01   4.7958315e-01   1.2247449e+00   1.2124356e+00   1.2369317e+00   0.0000000e+00   1.4317821e+00   1.3747727e+00   1.0344080e+00   5.4772256e-01   7.7459667e-01   9.4868330e-01   3.3166248e-01   9.1104336e-01   6.1644140e-01   8.6023253e-01   2.6851443e+00   5.4772256e-01   7.1414284e-01   7.5498344e-01   1.0246951e+00   9.8994949e-01   5.0000000e-01   1.7406895e+00   1.5684387e+00   9.6436508e-01   7.8102497e-01   1.2845233e+00   1.2489996e+00   1.7378147e+00   4.0000000e-01   1.8165902e+00   1.0246951e+00   1.3490738e+00   5.3851648e-01   3.8729833e-01   1.4662878e+00   1.4456832e+00   7.8740079e-01   5.1961524e-01   4.5825757e-01   1.2409674e+00   7.9372539e-01   1.2961481e+00   1.3190906e+00   6.6332496e-01   9.8994949e-01   8.6602540e-01   1.5842980e+00   5.4772256e-01   5.9160798e-01   8.5440037e-01   1.5684387e+00   4.1231056e-01   6.7082039e-01   8.3066239e-01   1.3190906e+00   9.2736185e-01   1.1224972e+00   1.4730920e+00   5.0000000e-01   1.6703293e+00   1.8275667e+00   1.2206556e+00   6.0000000e-01   1.4282857e+00   6.4807407e-01   3.8729833e-01   6.0000000e-01   9.5916630e-01   9.3273791e-01   6.6332496e-01   2.4494897e-01   2.0346990e+00   1.9974984e+00   1.0148892e+00   8.4261498e-01   1.0148892e+00   1.7944358e+00   7.2801099e-01   6.4807407e-01   1.0295630e+00   8.1240384e-01   7.3484692e-01   3.3166248e-01   9.4868330e-01   1.2165525e+00   2.0124612e+00   4.2426407e-01   5.9160798e-01   5.3851648e-01   1.5716234e+00   7.8102497e-01   2.4494897e-01   8.6023253e-01   7.2801099e-01   7.4833148e-01   9.4868330e-01   7.4161985e-01   8.2462113e-01   9.0553851e-01   7.6157731e-01   7.2801099e-01   5.0000000e-01   7.4161985e-01   6.4807407e-01   1.3638182e+00   2.1794495e+00   1.0295630e+00   6.7082039e-01   1.0148892e+00   7.5498344e-01   6.6332496e-01   4.3588989e-01   1.2529964e+00   1.0295630e+00   5.5677644e-01   5.0000000e-01   1.7000000e+00   1.6792856e+00   1.4212670e+00   4.6904158e-01   1.3038405e+00   1.5264338e+00   1.0488088e+00   3.8729833e-01   8.5440037e-01   1.1357817e+00   1.0630146e+00   3.1622777e-01   9.2195445e-01   1.0148892e+00   1.7320508e+00   3.0000000e-01   1.0295630e+00   1.0000000e+00   1.2409674e+00   5.2915026e-01   5.1961524e-01   1.1874342e+00   5.8309519e-01   3.6055513e-01   8.1853528e-01   1.0770330e+00   3.8729833e-01   4.7958315e-01   6.4031242e-01   1.0099505e+00   6.3245553e-01   6.4807407e-01   1.0049876e+00   3.4799425e+00   5.2915026e-01   1.3379088e+00   9.6436508e-01   1.8734994e+00   1.8055470e+00   1.3601471e+00   2.5357445e+00   2.3706539e+00   1.7916473e+00   1.5842980e+00   8.1853528e-01   5.4772256e-01   2.4738634e+00   1.1747340e+00   2.6343880e+00   2.6457513e-01   2.1817424e+00   1.3076697e+00   8.0622577e-01   2.3086793e+00   2.2869193e+00   1.5748016e+00   1.0246951e+00   6.0827625e-01   8.8317609e-01   1.5779734e+00   2.0832667e+00   1.9748418e+00   5.4772256e-01   1.7146428e+00   1.6583124e+00   2.4269322e+00   1.3928388e+00   1.3820275e+00   1.6703293e+00   2.3706539e+00   1.1000000e+00   1.3674794e+00   1.6763055e+00   2.1307276e+00   1.7832555e+00   1.8973666e+00   2.2869193e+00   3.0282008e+00   2.2226111e+00   3.1144823e+00   1.8708287e+00   1.7233688e+00   2.2405357e+00   9.8994949e-01   1.3228757e+00   1.9339080e+00   1.9544820e+00   3.8236109e+00   3.7376463e+00   1.2609520e+00   2.5079872e+00   9.1104336e-01   3.5860842e+00   1.4730920e+00   2.3409400e+00   2.8354894e+00   1.3711309e+00   1.3638182e+00   1.9261360e+00   2.6907248e+00   2.9899833e+00   3.7934153e+00   1.9493589e+00   1.5652476e+00   1.6583124e+00   3.3181320e+00   2.1142375e+00   1.9026298e+00   1.2489996e+00   2.3086793e+00   2.3021729e+00   2.2538855e+00   1.1180340e+00   2.5337719e+00   2.4413111e+00   2.0832667e+00   1.5000000e+00   1.8411953e+00   1.9157244e+00   1.2727922e+00   8.7749644e-01   1.0148892e+00   1.4866069e+00   1.3638182e+00   9.9498744e-01   2.1095023e+00   2.0149442e+00   1.4662878e+00   1.1357817e+00   1.1357817e+00   9.2736185e-01   1.9899749e+00   9.2736185e-01   2.2135944e+00   6.0827625e-01   1.7320508e+00   9.8488578e-01   4.3588989e-01   1.8627936e+00   1.8466185e+00   1.1832160e+00   5.5677644e-01   2.6457513e-01   1.1045361e+00   1.2124356e+00   1.5937377e+00   1.4764823e+00   6.7823300e-01   1.4491377e+00   1.2206556e+00   1.9874607e+00   1.0488088e+00   1.1180340e+00   1.3747727e+00   1.9339080e+00   8.6602540e-01   1.1704700e+00   1.3527749e+00   1.6911535e+00   1.3784049e+00   1.5874508e+00   1.8466185e+00   1.4282857e+00   1.0295630e+00   6.2449980e-01   6.6332496e-01   1.2961481e+00   1.3228757e+00   1.0392305e+00   6.1644140e-01   1.9131126e+00   1.5716234e+00   1.1445523e+00   8.8881944e-01   1.4662878e+00   1.3928388e+00   1.0049876e+00   8.6023253e-01   8.8317609e-01   1.1575837e+00   1.1916375e+00   5.5677644e-01   7.3484692e-01   8.2462113e-01   1.8788294e+00   6.1644140e-01   9.1104336e-01   7.5498344e-01   1.2609520e+00   1.1704700e+00   7.3484692e-01   1.3190906e+00   8.0622577e-01   8.7177979e-01   1.0677078e+00   1.1618950e+00   8.7177979e-01   1.0677078e+00   9.2736185e-01   9.0000000e-01   8.3066239e-01   1.2124356e+00   1.1747340e+00   1.3784049e+00   1.5652476e+00   1.0198039e+00   2.2181073e+00   1.9000000e+00   1.2165525e+00   1.3038405e+00   8.6023253e-01   1.3892444e+00   2.3685439e+00   6.7082039e-01   2.2113344e+00   1.2247449e+00   1.8841444e+00   8.1240384e-01   8.1240384e-01   1.9544820e+00   1.8708287e+00   1.3000000e+00   1.1224972e+00   1.0198039e+00   9.3273791e-01   1.2727922e+00   1.8574176e+00   1.9157244e+00   8.0622577e-01   1.0535654e+00   1.3190906e+00   1.9949937e+00   9.9498744e-01   8.7177979e-01   1.1747340e+00   2.0322401e+00   6.3245553e-01   7.0710678e-01   1.2083046e+00   1.8947295e+00   1.3820275e+00   1.2529964e+00   1.8814888e+00   5.5677644e-01   5.4772256e-01   1.0677078e+00   9.0000000e-01   3.7416574e-01   4.8989795e-01   2.0976177e+00   2.2649503e+00   1.2288206e+00   7.8102497e-01   1.0049876e+00   2.0396078e+00   6.0827625e-01   6.4807407e-01   1.1575837e+00   6.1644140e-01   5.2915026e-01   6.5574385e-01   1.0862780e+00   1.4071247e+00   2.0024984e+00   6.7823300e-01   6.7082039e-01   1.0630146e+00   1.6031220e+00   7.0000000e-01   4.6904158e-01   6.4807407e-01   5.1961524e-01   6.7823300e-01   5.0990195e-01   8.6602540e-01   9.0553851e-01   8.1240384e-01   4.2426407e-01   7.4161985e-01   2.2360680e-01   5.5677644e-01   6.6332496e-01   5.7445626e-01   7.9372539e-01   8.1240384e-01   6.4031242e-01   3.8729833e-01   2.2248595e+00   2.1023796e+00   8.1240384e-01   9.0553851e-01   9.0553851e-01   1.9157244e+00   4.2426407e-01   8.0622577e-01   1.1789826e+00   5.5677644e-01   5.9160798e-01   3.7416574e-01   1.0344080e+00   1.2845233e+00   2.1633308e+00   4.3588989e-01   4.6904158e-01   6.6332496e-01   1.6062378e+00   9.1651514e-01   4.5825757e-01   7.1414284e-01   6.7823300e-01   7.6811457e-01   7.8102497e-01   6.3245553e-01   9.6436508e-01   9.8488578e-01   5.9160798e-01   3.7416574e-01   3.4641016e-01   8.3666003e-01   6.2449980e-01   1.3114877e+00   1.1357817e+00   5.2915026e-01   4.2426407e-01   1.7029386e+00   1.7233688e+00   1.3747727e+00   3.6055513e-01   1.3601471e+00   1.5165751e+00   8.8881944e-01   3.7416574e-01   7.3484692e-01   9.8994949e-01   9.6953597e-01   4.5825757e-01   7.0710678e-01   8.9442719e-01   1.6340135e+00   4.6904158e-01   9.0000000e-01   1.0723805e+00   1.1000000e+00   7.1414284e-01   5.0990195e-01   1.1045361e+00   1.7320508e-01   3.4641016e-01   4.6904158e-01   1.1357817e+00   4.8989795e-01   5.4772256e-01   3.7416574e-01   8.8881944e-01   4.3588989e-01   7.5498344e-01   1.0295630e+00   5.1961524e-01   1.0770330e+00   1.0862780e+00   2.9359837e+00   2.7766887e+00   6.5574385e-01   1.5842980e+00   3.3166248e-01   2.6419690e+00   6.7082039e-01   1.4628739e+00   1.9442222e+00   6.4807407e-01   6.7823300e-01   9.7467943e-01   1.8165902e+00   2.0493902e+00   2.9137605e+00   9.8994949e-01   8.4261498e-01   9.4339811e-01   2.3558438e+00   1.3000000e+00   1.0677078e+00   6.4807407e-01   1.4035669e+00   1.3711309e+00   1.3784049e+00   2.6457513e-01   1.6124515e+00   1.5427249e+00   1.1747340e+00   6.0827625e-01   9.6436508e-01   1.1445523e+00   5.8309519e-01   7.5498344e-01   1.0246951e+00   2.6851443e+00   2.6267851e+00   1.1045361e+00   1.3190906e+00   4.8989795e-01   2.5159491e+00   8.1240384e-01   1.2288206e+00   1.8138357e+00   7.8102497e-01   7.2801099e-01   8.3666003e-01   1.7691806e+00   1.9519221e+00   2.6944387e+00   8.0622577e-01   1.0295630e+00   1.1747340e+00   2.1587033e+00   9.2736185e-01   9.8488578e-01   7.2801099e-01   1.2165525e+00   1.0723805e+00   1.1445523e+00   5.0990195e-01   1.3453624e+00   1.1958261e+00   9.3273791e-01   7.7459667e-01   8.3666003e-01   7.8740079e-01   6.4031242e-01   5.8309519e-01   2.0049938e+00   2.1470911e+00   1.3747727e+00   6.4031242e-01   1.0246951e+00   1.9748418e+00   8.1853528e-01   5.4772256e-01   1.1747340e+00   8.3666003e-01   7.3484692e-01   5.3851648e-01   1.1916375e+00   1.4000000e+00   1.9773720e+00   5.0990195e-01   9.2195445e-01   1.1618950e+00   1.5394804e+00   3.8729833e-01   5.4772256e-01   8.3666003e-01   5.5677644e-01   4.4721360e-01   5.4772256e-01   9.0000000e-01   7.2111026e-01   5.4772256e-01   3.7416574e-01   8.6602540e-01   3.8729833e-01   3.0000000e-01   7.6157731e-01   1.9183326e+00   1.9519221e+00   1.1090537e+00   7.0000000e-01   1.1180340e+00   1.7204651e+00   7.0000000e-01   5.0990195e-01   8.8317609e-01   7.8740079e-01   7.2111026e-01   3.8729833e-01   7.8740079e-01   1.1045361e+00   1.8574176e+00   4.6904158e-01   5.7445626e-01   7.0000000e-01   1.4317821e+00   7.5498344e-01   1.4142136e-01   8.6023253e-01   5.1961524e-01   6.4807407e-01   7.6157731e-01   8.6602540e-01   7.3484692e-01   8.1240384e-01   6.1644140e-01   7.4161985e-01   3.6055513e-01   7.1414284e-01   7.2111026e-01   1.2206556e+00   2.9715316e+00   1.4177447e+00   2.9478806e+00   1.0198039e+00   2.5632011e+00   1.5033296e+00   1.1224972e+00   2.6495283e+00   2.5690465e+00   1.9773720e+00   1.4352700e+00   1.2409674e+00   4.1231056e-01   1.9748418e+00   2.4515301e+00   2.4186773e+00   1.0049876e+00   1.8357560e+00   1.9442222e+00   2.7018512e+00   1.6822604e+00   1.6552945e+00   1.9235384e+00   2.7331301e+00   1.3490738e+00   1.5297059e+00   1.9748418e+00   2.5748786e+00   2.0904545e+00   2.0273135e+00   2.5690465e+00   2.7018512e+00   1.5620499e+00   2.9223278e+00   4.1231056e-01   2.4939928e+00   1.7233688e+00   1.2922848e+00   2.6362853e+00   2.6400758e+00   1.8601075e+00   1.4525839e+00   9.6436508e-01   1.3490738e+00   1.8520259e+00   2.4248711e+00   2.2494444e+00   8.9442719e-01   2.0736441e+00   2.0371549e+00   2.7766887e+00   1.7832555e+00   1.7175564e+00   2.0322401e+00   2.6495283e+00   1.4730920e+00   1.7233688e+00   2.0124612e+00   2.3958297e+00   2.1400935e+00   2.2671568e+00   2.6248809e+00   1.7146428e+00   8.8317609e-01   2.5278449e+00   6.6332496e-01   1.5968719e+00   1.8788294e+00   7.2801099e-01   8.6602540e-01   1.1135529e+00   1.6522712e+00   1.9209373e+00   2.8948230e+00   1.1704700e+00   6.7823300e-01   7.3484692e-01   2.3194827e+00   1.6431677e+00   1.1445523e+00   8.7749644e-01   1.4628739e+00   1.5716234e+00   1.5066519e+00   6.7823300e-01   1.7578396e+00   1.7860571e+00   1.3453624e+00   5.8309519e-01   1.0862780e+00   1.5099669e+00   8.6602540e-01   1.6062378e+00   1.3747727e+00   1.2247449e+00   3.0000000e-01   6.5574385e-01   1.3076697e+00   1.2529964e+00   6.7823300e-01   7.9372539e-01   8.5440037e-01   1.3928388e+00   6.5574385e-01   1.2328828e+00   1.3490738e+00   9.1651514e-01   6.4807407e-01   7.4161985e-01   1.3820275e+00   3.7416574e-01   2.6457513e-01   6.0827625e-01   1.4071247e+00   2.2360680e-01   3.0000000e-01   5.7445626e-01   1.2247449e+00   7.3484692e-01   7.8740079e-01   1.2845233e+00   2.7658633e+00   7.3484692e-01   1.4525839e+00   1.9924859e+00   6.4031242e-01   5.7445626e-01   1.0677078e+00   1.8894444e+00   2.1656408e+00   2.9223278e+00   1.0816654e+00   8.8317609e-01   1.0677078e+00   2.4454039e+00   1.2247449e+00   1.0630146e+00   5.0000000e-01   1.4282857e+00   1.3964240e+00   1.3820275e+00   3.1622777e-01   1.6401219e+00   1.5329710e+00   1.1958261e+00   7.7459667e-01   9.6953597e-01   1.0295630e+00   4.5825757e-01   2.2912878e+00   1.5033296e+00   9.6953597e-01   2.4289916e+00   2.4248711e+00   1.7058722e+00   1.1224972e+00   6.7823300e-01   1.0630146e+00   1.7146428e+00   2.1840330e+00   2.0420578e+00   7.0000000e-01   1.9209373e+00   1.8055470e+00   2.5651511e+00   1.5588457e+00   1.5684387e+00   1.8384776e+00   2.4879711e+00   1.3038405e+00   1.5811388e+00   1.8384776e+00   2.2248595e+00   1.9313208e+00   2.0952327e+00   2.4248711e+00   1.1180340e+00   1.5066519e+00   1.7320508e-01   3.6055513e-01   7.7459667e-01   1.3228757e+00   1.6340135e+00   2.4617067e+00   8.1853528e-01   3.7416574e-01   8.3666003e-01   1.9339080e+00   1.1575837e+00   7.2801099e-01   4.3588989e-01   9.2736185e-01   1.0816654e+00   9.0000000e-01   5.4772256e-01   1.3228757e+00   1.2845233e+00   7.6811457e-01   2.4494897e-01   5.0990195e-01   1.0000000e+00   5.3851648e-01   6.6332496e-01   1.1832160e+00   1.0862780e+00   5.9160798e-01   7.7459667e-01   9.6953597e-01   1.4798649e+00   6.0000000e-01   1.0630146e+00   1.1618950e+00   1.1357817e+00   5.1961524e-01   5.0990195e-01   1.2165525e+00   4.1231056e-01   3.7416574e-01   6.9282032e-01   1.2529964e+00   3.1622777e-01   4.0000000e-01   6.1644140e-01   1.1532563e+00   6.2449980e-01   6.2449980e-01   1.0862780e+00   1.6124515e+00   1.5684387e+00   1.0246951e+00   3.4641016e-01   4.6904158e-01   1.0246951e+00   1.0583005e+00   1.3674794e+00   1.3747727e+00   7.4161985e-01   1.1704700e+00   9.4868330e-01   1.7088007e+00   7.4161985e-01   8.8317609e-01   1.0770330e+00   1.7406895e+00   6.4807407e-01   9.1651514e-01   1.0862780e+00   1.5198684e+00   1.1000000e+00   1.2845233e+00   1.5937377e+00   2.4494897e-01   8.7749644e-01   1.4422205e+00   1.7720045e+00   2.5475478e+00   9.1651514e-01   4.3588989e-01   9.2195445e-01   2.0566964e+00   1.1704700e+00   7.8740079e-01   2.8284271e-01   1.0148892e+00   1.1575837e+00   9.5916630e-01   5.1961524e-01   1.4071247e+00   1.3416408e+00   8.3666003e-01   3.8729833e-01   5.7445626e-01   9.8488578e-01   4.6904158e-01   8.4261498e-01   1.4352700e+00   1.7832555e+00   2.4839485e+00   8.8317609e-01   4.5825757e-01   9.0000000e-01   2.0615528e+00   1.0246951e+00   6.7823300e-01   1.4142136e-01   9.9498744e-01   1.1045361e+00   9.6953597e-01   4.7958315e-01   1.3341664e+00   1.2569805e+00   8.3666003e-01   5.5677644e-01   5.3851648e-01   8.1853528e-01   2.8284271e-01   9.8488578e-01   1.1357817e+00   1.9748418e+00   1.0000000e-01   7.8740079e-01   7.8740079e-01   1.4212670e+00   6.7823300e-01   4.3588989e-01   9.6436508e-01   6.1644140e-01   5.1961524e-01   7.9372539e-01   8.1240384e-01   6.7082039e-01   7.1414284e-01   5.7445626e-01   7.0710678e-01   4.6904158e-01   6.9282032e-01   7.9372539e-01   5.0990195e-01   1.2845233e+00   1.0392305e+00   1.1618950e+00   1.2041595e+00   9.1104336e-01   1.2845233e+00   8.8317609e-01   1.5748016e+00   7.1414284e-01   9.6953597e-01   1.0392305e+00   1.6217275e+00   8.3666003e-01   1.0770330e+00   1.0488088e+00   1.3379088e+00   1.0049876e+00   1.3453624e+00   1.4899664e+00   1.1618950e+00   1.1575837e+00   1.5394804e+00   1.4933185e+00   5.3851648e-01   1.4387495e+00   1.2083046e+00   1.9235384e+00   9.3273791e-01   1.0392305e+00   1.2247449e+00   1.8894444e+00   8.4852814e-01   1.1224972e+00   1.2247449e+00   1.5842980e+00   1.2922848e+00   1.5652476e+00   1.8165902e+00   1.9824228e+00   2.3452079e+00   2.3832751e+00   9.2736185e-01   1.8761663e+00   1.8947295e+00   2.6172505e+00   1.5811388e+00   1.6522712e+00   1.8083141e+00   2.7055499e+00   1.3820275e+00   1.5588457e+00   1.9000000e+00   2.4939928e+00   2.0099751e+00   2.0346990e+00   2.5238859e+00   8.6602540e-01   8.7749644e-01   1.4106736e+00   6.4031242e-01   5.0990195e-01   1.0000000e+00   6.2449980e-01   4.6904158e-01   7.7459667e-01   8.4261498e-01   6.4807407e-01   6.6332496e-01   5.4772256e-01   7.4161985e-01   5.0000000e-01   6.7082039e-01   8.3666003e-01   5.8309519e-01   1.9078784e+00   1.1916375e+00   5.9160798e-01   5.5677644e-01   9.4868330e-01   1.1445523e+00   1.0440307e+00   6.4807407e-01   1.3000000e+00   1.3304135e+00   9.2195445e-01   5.0990195e-01   5.8309519e-01   1.0488088e+00   5.3851648e-01   1.9442222e+00   1.2961481e+00   7.1414284e-01   9.8488578e-01   1.1916375e+00   1.2688578e+00   1.3964240e+00   7.7459667e-01   1.3228757e+00   1.4387495e+00   1.2206556e+00   8.1240384e-01   9.1651514e-01   1.2247449e+00   7.8102497e-01   1.5427249e+00   1.5198684e+00   2.1977261e+00   1.0862780e+00   1.1269428e+00   1.2845233e+00   2.2045408e+00   9.4339811e-01   1.1357817e+00   1.3453624e+00   1.8920888e+00   1.5297059e+00   1.7029386e+00   2.1189620e+00   6.8556546e-01   1.1180340e+00   7.6157731e-01   5.0000000e-01   8.4261498e-01   1.1135529e+00   6.2449980e-01   4.3588989e-01   7.0000000e-01   1.1916375e+00   7.2111026e-01   2.4494897e-01   9.6436508e-01   8.1240384e-01   5.9160798e-01   6.7823300e-01   8.1240384e-01   8.3066239e-01   7.6157731e-01   8.1240384e-01   6.6332496e-01   7.9372539e-01   3.8729833e-01   6.2449980e-01   6.4807407e-01   1.1269428e+00   1.2247449e+00   1.0770330e+00   4.7958315e-01   1.4628739e+00   1.3711309e+00   9.4868330e-01   6.2449980e-01   6.7082039e-01   9.0000000e-01   3.1622777e-01   4.1231056e-01   3.6055513e-01   1.2247449e+00   5.5677644e-01   5.7445626e-01   3.6055513e-01   9.5916630e-01   4.6904158e-01   7.8740079e-01   1.0908712e+00   5.4772256e-01   1.2124356e+00   3.4641016e-01   2.4494897e-01   4.2426407e-01   1.0630146e+00   6.0827625e-01   6.2449980e-01   1.1224972e+00   1.2369317e+00   8.1240384e-01   6.9282032e-01   2.4494897e-01   9.4339811e-01   5.1961524e-01   8.1853528e-01   1.1224972e+00   1.4317821e+00   1.3747727e+00   1.0344080e+00   5.4772256e-01   7.7459667e-01   9.4868330e-01   3.3166248e-01   3.1622777e-01   7.3484692e-01   1.3076697e+00   8.4261498e-01   8.0622577e-01   1.3190906e+00   6.1644140e-01   1.2845233e+00   7.9372539e-01   6.2449980e-01   1.2569805e+00   7.8102497e-01   3.6055513e-01   6.7082039e-01   9.4868330e-01   5.8309519e-01   1.0677078e+00   6.5574385e-01   6.1644140e-01   6.4031242e-01   7.6811457e-01
diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-euclidean-ml.txt b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-euclidean-ml.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1b7552021bf9a0606c36628f9432e8f0afe8d765
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-euclidean-ml.txt
@@ -0,0 +1 @@
+   4.0515260e+00   4.2121458e+00   3.7357405e+00   4.2313317e+00   3.9136009e+00   4.3843298e+00   3.9811426e+00   4.3624182e+00   4.0642508e+00   4.2105933e+00   4.0747226e+00   3.9068586e+00   4.1637004e+00   4.4303203e+00   4.1841564e+00   4.1063279e+00   4.1862390e+00   4.0719925e+00   4.2227579e+00   4.3173531e+00   3.8811067e+00   3.7577567e+00   4.0623722e+00   3.9882453e+00   4.0432671e+00   3.9085109e+00   4.0283414e+00   4.0846110e+00   3.6459235e+00   3.9544001e+00   4.1134244e+00   4.1805752e+00   3.5121011e+00   4.2747789e+00   4.1048323e+00   3.9269426e+00   3.8932032e+00   3.8281172e+00   3.7288430e+00   4.0863477e+00   4.1527428e+00   4.1646409e+00   4.2027433e+00   3.8441594e+00   4.8419117e+00   4.2455384e+00   3.7622220e+00   4.3967923e+00   4.4663183e+00   4.0435853e+00   4.0421692e+00   4.3124625e+00   4.6499961e+00   4.5595743e+00   3.4230430e+00   4.2612266e+00   3.5676603e+00   4.0866580e+00   4.2307103e+00   3.8521940e+00   3.9951183e+00   3.1022409e+00   3.7290193e+00   4.1931517e+00   4.1127027e+00   3.6633651e+00   4.0235815e+00   3.9729858e+00   4.1980132e+00   4.1579993e+00   3.9948955e+00   3.9081966e+00   3.9031152e+00   3.5069036e+00   4.0015727e+00   3.6763496e+00   3.6614339e+00   3.6227109e+00   3.7357992e+00   4.0170026e+00   3.5216829e+00   3.9322227e+00   3.9094621e+00   4.0170286e+00   4.3264246e+00   4.3435483e+00   4.0788635e+00   4.4761765e+00   3.8468186e+00   4.1490333e+00   4.2800007e+00   4.2260191e+00   4.3031858e+00   4.1897413e+00   4.0530244e+00   3.5893641e+00   4.2186615e+00   3.7979503e+00   4.0915473e+00   4.1343073e+00   4.5063851e+00   3.6394889e+00   4.2508448e+00   3.7160826e+00   4.0105262e+00   4.1578269e+00   4.0290590e+00   3.6971819e+00   3.9414087e+00   4.2522313e+00   4.4091714e+00   4.1542292e+00   3.9594691e+00   4.0923600e+00   4.0855497e+00   3.8253075e+00   4.3034717e+00   4.0976731e+00   4.1316523e+00   4.0872717e+00   4.2643353e+00   3.8887280e+00   3.9411273e+00   3.8848001e+00   4.3481996e+00   3.8716733e+00   3.9084684e+00   3.7546361e+00   3.9354816e+00   3.8293694e+00   3.7568515e+00   3.7184961e+00   3.8404278e+00   4.2570811e+00   4.1423777e+00   4.0291411e+00   4.2094682e+00   3.6127418e+00   4.0459839e+00   3.7737985e+00   3.7647653e+00   3.9762006e+00   3.8999512e+00   3.8509090e+00   3.8975941e+00   3.8432839e+00   4.2109046e+00   4.1339124e+00   3.5898873e+00   4.0794519e+00   4.3504966e+00   3.8862612e+00   3.8332931e+00   4.2190310e+00   4.1366595e+00   3.7220268e+00   4.1250795e+00   3.3169452e+00   4.0757181e+00   3.6487114e+00   3.9513724e+00   4.0735549e+00   3.9137880e+00   3.9656942e+00   3.7724953e+00   4.0505153e+00   3.9062302e+00   4.5671852e+00   3.7542175e+00   4.3731708e+00   3.6733907e+00   4.4667545e+00   4.1004635e+00   4.0530038e+00   4.0346958e+00   4.2145752e+00   4.4298637e+00   4.2982360e+00   4.0878239e+00   4.4061563e+00   4.2115971e+00   3.8263277e+00   3.8603258e+00   3.8572375e+00   4.1051910e+00   4.3787786e+00   4.5309659e+00   4.0047055e+00   4.1308854e+00   3.6283561e+00
diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-hamming-ml.txt b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-hamming-ml.txt
new file mode 100644
index 0000000000000000000000000000000000000000..bc4e1ddcb6e1e8699570ecc410e2cb0cfdba2507
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-hamming-ml.txt
@@ -0,0 +1 @@
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diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-jaccard-ml.txt b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-jaccard-ml.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a7570d8c3fbdf63bb2240c964941d9e48bc2ad3c
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-jaccard-ml.txt
@@ -0,0 +1 @@
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diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-jensenshannon-ml-iris.txt b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-jensenshannon-ml-iris.txt
new file mode 100644
index 0000000000000000000000000000000000000000..da698cf511e6983e1db1bbed6e2974f3480a6903
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-jensenshannon-ml-iris.txt
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diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-jensenshannon-ml.txt b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-jensenshannon-ml.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8ed5b9653f4ed88e146d2d5dc5b032537b426f8b
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-jensenshannon-ml.txt
@@ -0,0 +1 @@
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diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-minkowski-3.2-ml-iris.txt b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-minkowski-3.2-ml-iris.txt
new file mode 100644
index 0000000000000000000000000000000000000000..dc396c8c16032b9657101532f7e08e6aa04b2aea
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-minkowski-3.2-ml-iris.txt
@@ -0,0 +1 @@
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5.3588338e-01   4.0000000e-01   4.8135521e-01   3.0546431e-01   3.2816937e-01   5.0817745e-01   3.4378533e-01   9.4558103e-01   6.2024833e-01   6.9728513e-01   9.2288144e-01   5.6700421e-01   4.3691963e-01   5.4292906e-01   8.7202528e-01   8.9095811e-01   5.0817745e-01   3.6171588e-01   3.8934542e-01   8.6361309e-01   7.9878917e-01   5.0592043e-01   8.6361309e-01   1.1959482e+00   5.4292906e-01   5.6454040e-01   1.6807352e+00   1.1055064e+00   5.0592043e-01   3.2586371e-01   9.7779835e-01   3.2816937e-01   9.4558103e-01   2.8507955e-01   6.6827038e-01   3.1533911e+00   2.8840079e+00   3.3274872e+00   2.5335921e+00   3.0169509e+00   2.8661222e+00   3.0732956e+00   1.9492232e+00   3.0013391e+00   2.3437032e+00   2.3116343e+00   2.5873149e+00   2.5591371e+00   3.0631725e+00   2.0220740e+00   2.8270253e+00   2.8656468e+00   2.4892190e+00   3.0178921e+00   2.3656538e+00   3.1846482e+00   2.4132559e+00   3.3163294e+00   3.0590735e+00   2.6993871e+00   2.8174914e+00   3.2310326e+00   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2.1269358e-01   1.1283882e+00   6.1092863e-01   4.0293660e-01   5.0592043e-01   4.1586001e-01   4.0293660e-01   4.1449626e-01   3.7255734e-01   1.2418578e-01   3.4445326e+00   3.1392617e+00   3.6011035e+00   2.6118700e+00   3.2516941e+00   3.0511838e+00   3.3218097e+00   1.9189245e+00   3.2468925e+00   2.4924452e+00   2.2081024e+00   2.8038661e+00   2.6291264e+00   3.2767369e+00   2.1964719e+00   3.1025274e+00   3.0696611e+00   2.6485861e+00   3.1554034e+00   2.4715204e+00   3.4135983e+00   2.6151245e+00   3.5092032e+00   3.2604423e+00   2.9354140e+00   3.0782101e+00   3.4818889e+00   3.6726568e+00   3.0922811e+00   2.0843471e+00   2.3874354e+00   2.2845234e+00   2.4794505e+00   3.6775470e+00   3.0659000e+00   3.1055388e+00   3.3775462e+00   3.0430948e+00   2.6597612e+00   2.5873149e+00   2.9471553e+00   3.1807044e+00   2.5795723e+00   1.9450499e+00   2.7640668e+00   2.7473221e+00   2.7611864e+00   2.9015702e+00   1.6626642e+00   2.6693888e+00   4.6823704e+00   3.7130994e+00   4.6117428e+00   4.1946425e+00   4.4565357e+00   5.3399939e+00   3.1168466e+00   4.9805386e+00   4.4303862e+00   4.8738189e+00   3.7806643e+00   3.9387918e+00   4.2018804e+00   3.6441274e+00   3.8290120e+00   4.0132700e+00   4.1177139e+00   5.4615788e+00   5.6559440e+00   3.5983434e+00   4.4321573e+00   3.5405803e+00   5.4429455e+00   3.5441556e+00   4.3687483e+00   4.6853394e+00   3.4399664e+00   3.5203203e+00   4.2473048e+00   4.4861009e+00   4.8281381e+00   5.2242271e+00   4.2652659e+00   3.6876909e+00   4.1503255e+00   4.9488209e+00   4.2966585e+00   4.1071698e+00   3.4205830e+00   4.1292490e+00   4.3363292e+00   3.9150359e+00   3.7130994e+00   4.5977729e+00   4.4473292e+00   3.9643224e+00   3.6603913e+00   3.8715927e+00   4.0861975e+00   3.6954796e+00   5.0991930e-01   1.1327825e+00   5.7257017e-01   4.0293660e-01   3.0811765e-01   1.5771666e+00   1.7488874e+00   1.2431040e+00   8.1273630e-01   1.4170618e+00   1.0106392e+00   1.0389435e+00   9.3824087e-01   7.3813096e-01   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4.0656969e+00   4.2413113e+00   3.8376713e+00   6.8961791e-01   3.0811765e-01   1.4096146e-01   6.4755655e-01   1.1229906e+00   1.3835747e+00   8.6361309e-01   4.2667565e-01   9.4009473e-01   7.0784540e-01   5.3665999e-01   6.2482915e-01   6.3977563e-01   4.3691963e-01   4.4651726e-01   1.5422108e-01   3.7598397e-01   4.4535192e-01   3.7598397e-01   2.1845981e-01   1.4096146e-01   5.5419992e-01   1.0065841e+00   1.1474460e+00   0.0000000e+00   3.0811765e-01   6.5223271e-01   0.0000000e+00   5.0991930e-01   3.2586371e-01   4.2667565e-01   8.3172002e-01   5.0991930e-01   5.6769031e-01   7.5082357e-01   2.1845981e-01   7.0479928e-01   3.0811765e-01   6.4755655e-01   2.1845981e-01   3.4865562e+00   3.1726595e+00   3.6377960e+00   2.5987470e+00   3.2814045e+00   3.0627375e+00   3.3515846e+00   1.8841865e+00   3.2769379e+00   2.5038079e+00   2.1311468e+00   2.8311678e+00   2.6104387e+00   3.2962520e+00   2.2214438e+00   3.1433122e+00   3.0878634e+00   2.6552472e+00   3.1570103e+00   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4.0892044e+00   5.3882212e+00   5.5946413e+00   3.6180819e+00   4.3839191e+00   3.5469476e+00   5.3734444e+00   3.5262672e+00   4.3306501e+00   4.6237863e+00   3.4237160e+00   3.5051302e+00   4.2288456e+00   4.4201622e+00   4.7609637e+00   5.1280035e+00   4.2469785e+00   3.6684143e+00   4.1480002e+00   4.8602572e+00   4.2765700e+00   4.0824098e+00   3.4092877e+00   4.0737132e+00   4.2991233e+00   3.8524190e+00   3.7173526e+00   4.5590471e+00   4.4107160e+00   3.9202843e+00   3.6509512e+00   3.8388884e+00   4.0680120e+00   3.6894983e+00   4.1449626e-01   6.6539428e-01   1.0717668e+00   1.1847335e+00   7.0776547e-01   3.2816937e-01   9.2095040e-01   4.4651726e-01   6.0060595e-01   3.8934542e-01   6.1092863e-01   3.7598397e-01   3.0000000e-01   4.1312257e-01   2.4837156e-01   4.0293660e-01   4.1312257e-01   2.0656129e-01   3.0000000e-01   6.0611244e-01   7.3535471e-01   9.3801395e-01   3.0811765e-01   4.2538717e-01   7.1462831e-01   3.0811765e-01   5.2574978e-01   3.0275928e-01   3.2816937e-01   1.1107977e+00   4.5470518e-01   4.1449626e-01   4.8927739e-01   4.1449626e-01   4.4417983e-01   2.8192292e-01   5.2942799e-01   2.5251796e-01   3.4297053e+00   3.0906838e+00   3.5704156e+00   2.5301680e+00   3.2062204e+00   2.9663489e+00   3.2615889e+00   1.8330979e+00   3.2074600e+00   2.4030878e+00   2.1292724e+00   2.7344480e+00   2.5716369e+00   3.2053511e+00   2.1242643e+00   3.0798277e+00   2.9831836e+00   2.5729378e+00   3.0964590e+00   2.3917863e+00   3.3353616e+00   2.5635110e+00   3.4441347e+00   3.1882407e+00   2.8938821e+00   3.0477086e+00   3.4484194e+00   3.6265826e+00   3.0209783e+00   2.0203134e+00   2.3063579e+00   2.2046610e+00   2.4100833e+00   3.5972040e+00   2.9748436e+00   3.0349291e+00   3.3414931e+00   2.9918962e+00   2.5764694e+00   2.5038051e+00   2.8573838e+00   3.1113597e+00   2.5079404e+00   1.8623849e+00   2.6799601e+00   2.6656374e+00   2.6804452e+00   2.8458006e+00   1.5870088e+00   2.5906376e+00   4.6056614e+00   3.6293396e+00   4.5625120e+00   4.1184849e+00   4.3862724e+00   5.2957861e+00   3.0253131e+00   4.9300368e+00   4.3656957e+00   4.8256905e+00   3.7228356e+00   3.8717400e+00   4.1487889e+00   3.5605424e+00   3.7509165e+00   3.9489970e+00   4.0502806e+00   5.4193574e+00   5.6096505e+00   3.5201263e+00   4.3797165e+00   3.4555095e+00   5.4004015e+00   3.4805320e+00   4.3069452e+00   4.6373516e+00   3.3738930e+00   3.4478147e+00   4.1762321e+00   4.4428877e+00   4.7870294e+00   5.1982218e+00   4.1948678e+00   3.6180819e+00   4.0668114e+00   4.9227056e+00   4.2245318e+00   4.0358897e+00   3.3459883e+00   4.0835979e+00   4.2783731e+00   3.8797354e+00   3.6293396e+00   4.5370189e+00   4.3879553e+00   3.9155334e+00   3.5955337e+00   3.8113970e+00   4.0131848e+00   3.6132595e+00   5.2862779e-01   1.2431040e+00   1.5013525e+00   9.7779835e-01   5.3588338e-01   1.0669582e+00   8.1385214e-01   6.6432544e-01   7.2823007e-01   6.5223271e-01   5.1138698e-01   5.6700421e-01   2.5251796e-01   4.6472023e-01   5.6769031e-01   4.9766035e-01   2.5651975e-01   2.1269358e-01   6.6432544e-01   1.1134787e+00   1.2632199e+00   1.4096146e-01   2.8507955e-01   7.6787403e-01   1.4096146e-01   4.0293660e-01   4.4651726e-01   5.1691876e-01   7.1840099e-01   4.1586001e-01   6.3108414e-01   8.7021234e-01   2.0000000e-01   8.1385214e-01   2.5251796e-01   7.6787403e-01   3.2586371e-01   3.6025735e+00   3.2810515e+00   3.7511944e+00   2.6894009e+00   3.3904673e+00   3.1636869e+00   3.4574937e+00   1.9666356e+00   3.3893691e+00   2.5954173e+00   2.1997395e+00   2.9322283e+00   2.7092568e+00   3.4012145e+00   2.3186758e+00   3.2568914e+00   3.1861493e+00   2.7595194e+00   3.2561045e+00   2.5646808e+00   3.5381764e+00   2.7476411e+00   3.6278993e+00   3.3809159e+00   3.0768226e+00   3.2277675e+00   3.6265617e+00   3.8150532e+00   3.2176230e+00   2.1864840e+00   2.4668912e+00   2.3596992e+00   2.5949561e+00   3.7935487e+00   3.1789378e+00   3.2360886e+00   3.5252258e+00   3.1522058e+00   2.7777040e+00   2.6819136e+00   3.0473722e+00   3.3079290e+00   2.6886547e+00   1.9757309e+00   2.8726212e+00   2.8654680e+00   2.8788483e+00   3.0349462e+00   1.7160413e+00   2.7852734e+00   4.8087107e+00   3.8282466e+00   4.7531334e+00   4.3176393e+00   4.5857287e+00   5.4831923e+00   3.2147850e+00   5.1185883e+00   4.5544260e+00   5.0194259e+00   3.9185849e+00   4.0655452e+00   4.3416283e+00   3.7535680e+00   3.9509795e+00   4.1478442e+00   4.2472736e+00   5.6096505e+00   5.7957776e+00   3.6945993e+00   4.5734622e+00   3.6568202e+00   5.5854254e+00   3.6720840e+00   4.5038991e+00   4.8262859e+00   3.5684917e+00   3.6474985e+00   4.3740189e+00   4.6282931e+00   4.9713928e+00   5.3806679e+00   4.3928114e+00   3.8121990e+00   4.2612863e+00   5.1032991e+00   4.4267055e+00   4.2347444e+00   3.5464871e+00   4.2738510e+00   4.4745238e+00   4.0663411e+00   3.8282466e+00   4.7338066e+00   4.5852690e+00   4.1075310e+00   3.7823897e+00   4.0070636e+00   4.2156933e+00   3.8157950e+00   1.6177449e+00   1.7454671e+00   1.2604558e+00   8.6361309e-01   1.4955532e+00   1.0118409e+00   1.1594648e+00   9.6204649e-01   6.2081167e-01   9.1750357e-01   8.7504951e-01   7.6752131e-01   8.0660588e-01   9.5965467e-01   9.2859317e-01   5.7324170e-01   6.2205176e-01   1.1313840e+00   1.2653669e+00   1.4930627e+00   6.4755655e-01   7.0479928e-01   1.2236003e+00   6.4755655e-01   2.1269358e-01   8.5105559e-01   7.7360126e-01   7.1169738e-01   2.5651975e-01   8.7229670e-01   1.1327578e+00   5.3588338e-01   1.0269295e+00   3.8934542e-01   1.1042097e+00   7.2823007e-01   4.0317004e+00   3.6659830e+00   4.1618561e+00   3.0123702e+00   3.7804276e+00   3.4970843e+00   3.8244351e+00   2.2591077e+00   3.7930789e+00   2.8953397e+00   2.4889124e+00   3.2809188e+00   3.0866488e+00   3.7578933e+00   2.6595288e+00   3.6754272e+00   3.5073435e+00   3.1173742e+00   3.6212723e+00   2.9065572e+00   3.8667462e+00   3.1302383e+00   3.9918403e+00   3.7416229e+00   3.4760444e+00   3.6375992e+00   4.0358101e+00   4.2016915e+00   3.5683934e+00   2.5569968e+00   2.8007817e+00   2.6989368e+00   2.9539253e+00   4.1306024e+00   3.4882801e+00   3.5831257e+00   3.9280671e+00   3.5362697e+00   3.1099883e+00   3.0065416e+00   3.3706887e+00   3.6672620e+00   3.0442126e+00   2.2719663e+00   3.2032390e+00   3.2071637e+00   3.2176230e+00   3.4155491e+00   2.0139971e+00   3.1260028e+00   5.1310217e+00   4.1456639e+00   5.1323742e+00   4.6609614e+00   4.9284761e+00   5.8739676e+00   3.4984873e+00   5.5048216e+00   4.9175276e+00   5.3898806e+00   4.2781762e+00   4.4176533e+00   4.7107211e+00   4.0621414e+00   4.2494597e+00   4.4865569e+00   4.6045396e+00   6.0012333e+00   6.1816086e+00   4.0339598e+00   4.9390284e+00   3.9601358e+00   5.9803696e+00   4.0277694e+00   4.8626276e+00   5.2147981e+00   3.9185849e+00   3.9887029e+00   4.7161140e+00   5.0257341e+00   5.3673499e+00   5.7939320e+00   4.7320534e+00   4.1713411e+00   4.5995433e+00   5.5085511e+00   4.7536729e+00   4.5857356e+00   3.8819510e+00   4.6519178e+00   4.8256399e+00   4.4430890e+00   4.1456639e+00   5.0898961e+00   4.9316646e+00   4.4680158e+00   4.1325542e+00   4.3648035e+00   4.5412859e+00   4.1418557e+00   4.5581864e-01   4.1586001e-01   7.7074935e-01   5.0991930e-01   7.1840099e-01   7.2486328e-01   7.3145860e-01   1.2122249e+00   9.2112464e-01   1.1384810e+00   1.1451403e+00   9.1163729e-01   7.0386584e-01   7.4855857e-01   1.2220203e+00   1.1947245e+00   6.6827038e-01   6.2081167e-01   3.4378533e-01   1.1229906e+00   9.9348625e-01   5.2942799e-01   1.1229906e+00   1.5344133e+00   8.2275389e-01   8.5233811e-01   1.8985661e+00   1.4692412e+00   8.9653332e-01   8.7420176e-01   1.2431040e+00   7.3813096e-01   1.2951131e+00   5.5419992e-01   9.3801395e-01   3.5789198e+00   3.3663244e+00   3.7753619e+00   3.0049442e+00   3.4909841e+00   3.3695525e+00   3.5654259e+00   2.3989172e+00   3.4663502e+00   2.8427326e+00   2.7185849e+00   3.0894572e+00   3.0108764e+00   3.5617386e+00   2.5173832e+00   3.2758681e+00   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5.7257017e-01   5.2655962e-01   4.3456114e-01   6.2660376e-01   4.8135521e-01   4.5581864e-01   1.3318128e+00   1.2468939e+00   1.3144065e+00   9.4935318e-01   6.6384020e-01   9.1075311e-01   3.2586371e-01   4.1449626e-01   1.0130748e+00   8.3280511e-01   1.0906119e+00   9.6204649e-01   3.4583729e-01   9.3296062e-01   1.7901543e+00   8.7170815e-01   7.3805807e-01   7.3805807e-01   5.2655962e-01   1.9041928e+00   8.1521713e-01   1.4138821e+00   7.3805807e-01   1.3166957e+00   9.2264612e-01   1.1533602e+00   2.0690479e+00   1.4700179e+00   1.7092525e+00   1.2231847e+00   1.5870088e+00   5.0592043e-01   7.5791688e-01   9.0575661e-01   9.1750357e-01   9.1802948e-01   8.1304731e-01   8.1638392e-01   2.1978861e+00   2.3802944e+00   1.1107977e+00   1.1386292e+00   7.9878917e-01   2.1900222e+00   6.1092863e-01   1.0480665e+00   1.4148192e+00   5.0991930e-01   3.6171588e-01   9.7825559e-01   1.2593659e+00   1.5912764e+00   2.0615043e+00   1.0056742e+00   5.6700421e-01   1.0137836e+00   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3.7921012e+00   1.2632199e+00   3.4105293e+00   2.7619926e+00   3.3261421e+00   2.2045198e+00   2.2598424e+00   2.6204307e+00   1.8330979e+00   2.0701646e+00   2.3622531e+00   2.4525409e+00   3.9619101e+00   4.0743074e+00   1.8315269e+00   2.8475224e+00   1.7388184e+00   3.9054939e+00   1.9111264e+00   2.7377517e+00   3.1510494e+00   1.7964653e+00   1.8350071e+00   2.5277506e+00   2.9970778e+00   3.3196868e+00   3.8532018e+00   2.5453122e+00   2.0312250e+00   2.3887539e+00   3.5269824e+00   2.5986705e+00   2.4210417e+00   1.7228354e+00   2.6125646e+00   2.7062349e+00   2.4839132e+00   1.9158303e+00   2.9502077e+00   2.8139128e+00   2.4180244e+00   1.9947426e+00   2.2550764e+00   2.3956104e+00   1.9332869e+00   1.4468211e+00   1.8027242e+00   7.3851529e-01   9.0658670e-01   5.0180477e-01   1.2418578e+00   2.5651975e-01   1.0022010e+00   8.6361309e-01   7.3851529e-01   1.1055064e+00   7.8197925e-01   6.8961791e-01   4.8927739e-01   5.0270183e-01   3.2352160e-01   2.1269358e-01   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6.9369532e-01   1.0019724e+00   1.3083079e+00   1.0406064e+00   9.3238528e-01   1.4580335e+00   1.4387122e+00   1.0576043e+00   7.0233835e-01   8.1304731e-01   1.1697902e+00   8.2372435e-01   7.6914805e-01   7.2823007e-01   8.7504951e-01   1.0611732e+00   4.5581864e-01   1.5204521e+00   6.6432544e-01   6.5172743e-01   1.0866092e+00   4.5470518e-01   1.0573285e+00   9.0074515e-01   1.3083079e+00   1.0613462e+00   1.2123540e+00   1.4190961e+00   1.6754036e+00   1.6596797e+00   8.9095811e-01   6.1947990e-01   4.2418962e-01   4.8927739e-01   6.0551856e-01   1.2951131e+00   6.2538346e-01   1.0030700e+00   1.5663312e+00   1.1396406e+00   4.5581864e-01   3.2816937e-01   5.3665999e-01   1.0166932e+00   6.0670504e-01   6.9167458e-01   4.4535192e-01   5.6075294e-01   5.3665999e-01   1.0182895e+00   9.1075311e-01   5.0991930e-01   2.2632657e+00   1.2601890e+00   2.4384530e+00   1.8269304e+00   2.0927845e+00   3.1870761e+00   6.4290921e-01   2.8096725e+00   2.1462316e+00   2.6900593e+00   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1.7518264e+00   1.2724737e+00   1.6669115e+00   1.9675324e+00   1.4200435e+00   1.1136605e+00   7.1881659e-01   1.0072663e+00   1.5134954e+00   9.3238528e-01   3.2352160e-01   9.5222919e-01   1.1681971e+00   1.1043332e+00   1.4120836e+00   6.2205176e-01   1.0078327e+00   2.8028143e+00   1.7525933e+00   2.8815987e+00   2.2944257e+00   2.5825907e+00   3.6132031e+00   1.1179743e+00   3.2286633e+00   2.5673494e+00   3.2133201e+00   2.1127170e+00   2.0867931e+00   2.4721080e+00   1.6626615e+00   1.9456450e+00   2.2607446e+00   2.2983453e+00   3.8335668e+00   3.8818411e+00   1.6299374e+00   2.7127377e+00   1.6132118e+00   3.7182722e+00   1.7559391e+00   2.6123294e+00   2.9966900e+00   1.6625128e+00   1.7303440e+00   2.3560577e+00   2.8340159e+00   3.1407514e+00   3.7366777e+00   2.3765195e+00   1.8701780e+00   2.1933937e+00   3.3657099e+00   2.5066503e+00   2.2797241e+00   1.6331631e+00   2.4808010e+00   2.5698271e+00   2.3770285e+00   1.7525933e+00   2.8053367e+00   2.6963680e+00   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5.8914551e-01   8.5462626e-01   8.7848692e-01   1.4517959e+00   7.3851529e-01   9.4854455e-01   8.6263408e-01   1.0941064e+00   8.3783744e-01   1.1172689e+00   1.3545005e+00   1.0391247e+00   1.0389435e+00   1.3163598e+00   1.3379696e+00   4.5470518e-01   1.1951875e+00   1.0632598e+00   1.6796759e+00   7.8197925e-01   8.3345577e-01   1.0540105e+00   1.7036156e+00   6.9167458e-01   8.8503502e-01   1.0279631e+00   1.3693737e+00   1.1192426e+00   1.3077572e+00   1.6183051e+00   1.6694974e+00   1.9094934e+00   1.9895190e+00   8.2384013e-01   1.6634400e+00   1.6218244e+00   2.2178691e+00   1.3008161e+00   1.3567326e+00   1.4994715e+00   2.3021295e+00   1.1763719e+00   1.3024224e+00   1.5535909e+00   2.0373882e+00   1.6756749e+00   1.7981158e+00   2.1739455e+00   7.6752131e-01   8.1354181e-01   1.3198846e+00   6.0611244e-01   4.4535192e-01   8.5335130e-01   5.3665999e-01   3.8776762e-01   6.3977563e-01   7.0429250e-01   5.2655962e-01   5.5492130e-01   4.5581864e-01   6.3861009e-01   4.2667565e-01   6.1151102e-01   6.6932542e-01   5.1691876e-01   1.5922648e+00   1.0054794e+00   4.8135521e-01   4.3456114e-01   7.6955924e-01   9.6664346e-01   8.9687438e-01   5.6700421e-01   1.0421979e+00   1.1001291e+00   8.2929029e-01   4.4535192e-01   5.1691876e-01   8.9712482e-01   4.5470518e-01   1.6914476e+00   1.1340084e+00   5.8914551e-01   8.5105559e-01   9.7548738e-01   1.0864449e+00   1.1160770e+00   6.3977563e-01   1.0720678e+00   1.2163831e+00   1.0047836e+00   6.9369532e-01   7.2343175e-01   1.0613462e+00   6.2407309e-01   1.4238090e+00   1.3511716e+00   1.9067300e+00   9.3824087e-01   1.0331736e+00   1.1327825e+00   1.9782093e+00   9.0454394e-01   1.0244319e+00   1.1833480e+00   1.5948732e+00   1.3360558e+00   1.5461469e+00   1.8900319e+00   6.2081167e-01   9.1750357e-01   6.4290921e-01   4.4417983e-01   7.0429250e-01   8.7229670e-01   5.3665999e-01   4.0438741e-01   5.6454040e-01   1.0054794e+00   5.7015910e-01   2.1269358e-01   7.5705927e-01   7.3496673e-01   5.2942799e-01   6.2024833e-01   6.6491075e-01   6.8801986e-01   6.1947990e-01   7.2172678e-01   5.5492130e-01   6.9006418e-01   3.2816937e-01   5.3665999e-01   5.6700421e-01   9.7779835e-01   1.0014633e+00   9.4854455e-01   3.8934542e-01   1.2342162e+00   1.1043332e+00   7.9580667e-01   5.3665999e-01   5.7257017e-01   7.2852070e-01   3.0275928e-01   3.4378533e-01   3.2352160e-01   1.1199472e+00   5.0991930e-01   4.6472023e-01   2.8507955e-01   7.7869083e-01   4.1586001e-01   7.1799256e-01   1.0132664e+00   5.0905001e-01   9.9519977e-01   3.0811765e-01   2.1269358e-01   4.0293660e-01   8.3060013e-01   5.0592043e-01   5.3665999e-01   9.3049742e-01   1.1263042e+00   8.0064372e-01   6.1623531e-01   2.1269358e-01   7.7588000e-01   4.4651726e-01   7.2783368e-01   1.0329901e+00   1.1697902e+00   1.0851476e+00   9.2859317e-01   5.0905001e-01   7.1504098e-01   7.7763126e-01   3.0546431e-01   2.5651975e-01   7.0437330e-01   1.0573285e+00   7.3145860e-01   6.9325418e-01   1.0901359e+00   5.3588338e-01   1.0175773e+00   6.4405773e-01   5.3665999e-01   1.0078327e+00   6.2407309e-01   3.2352160e-01   5.7257017e-01   8.5205778e-01   5.1691876e-01   9.4022486e-01   5.6769031e-01   4.8927739e-01   6.0611244e-01   6.0900723e-01
diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-minkowski-3.2-ml.txt b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-minkowski-3.2-ml.txt
new file mode 100644
index 0000000000000000000000000000000000000000..daa81110a2be1a670f6163a8b255b2c6ecd5ccaa
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-minkowski-3.2-ml.txt
@@ -0,0 +1 @@
+   2.0215050e+00   2.0988154e+00   1.8614681e+00   2.0510161e+00   1.9210911e+00   2.1323516e+00   1.9565454e+00   2.1029889e+00   1.9617871e+00   2.0544792e+00   2.0357408e+00   1.8811414e+00   2.0694693e+00   2.1245977e+00   2.0632165e+00   2.0452823e+00   2.0249330e+00   1.9635489e+00   2.0508580e+00   2.0838578e+00   1.9324052e+00   1.8224609e+00   1.9795343e+00   1.9536534e+00   1.9694910e+00   1.9075569e+00   1.9590397e+00   2.0022087e+00   1.8814000e+00   1.8884208e+00   1.9961121e+00   2.0215351e+00   1.7515769e+00   2.0756437e+00   2.0109476e+00   1.9234849e+00   1.9160076e+00   1.8550862e+00   1.7733640e+00   2.0071906e+00   2.0209542e+00   2.0616569e+00   2.0565503e+00   1.9083573e+00   2.2732431e+00   1.9975503e+00   1.9080072e+00   2.1437809e+00   2.1296295e+00   1.9739085e+00   1.9834166e+00   2.1078664e+00   2.2016840e+00   2.2080962e+00   1.7340579e+00   2.0549287e+00   1.7331748e+00   1.9559688e+00   2.0343364e+00   1.8736929e+00   1.9730416e+00   1.5308944e+00   1.8421831e+00   2.0174240e+00   2.0137378e+00   1.7956151e+00   1.9606596e+00   1.9074857e+00   2.0413879e+00   2.0070305e+00   1.9584677e+00   1.8977851e+00   1.9176239e+00   1.7067419e+00   1.9461927e+00   1.8431700e+00   1.8284576e+00   1.7778704e+00   1.8350329e+00   2.0175415e+00   1.7459063e+00   1.9242505e+00   1.8757370e+00   1.9312506e+00   2.0574808e+00   2.0894636e+00   1.9780203e+00   2.1374036e+00   1.8900436e+00   2.0273032e+00   2.0681953e+00   2.0234699e+00   2.0666449e+00   2.0663485e+00   1.9281402e+00   1.7846314e+00   2.0372479e+00   1.8831230e+00   2.0186015e+00   2.0193231e+00   2.2022665e+00   1.8145737e+00   2.0466545e+00   1.8092421e+00   1.9600687e+00   2.0322961e+00   1.9556364e+00   1.8266422e+00   1.9950345e+00   2.1038429e+00   2.1164145e+00   2.0188062e+00   1.8863331e+00   2.0006971e+00   1.9971068e+00   1.8771862e+00   2.1148855e+00   1.9570638e+00   1.9859615e+00   2.0030854e+00   2.0737344e+00   1.9739259e+00   1.9266524e+00   1.9200535e+00   2.1376689e+00   1.8944425e+00   1.9330553e+00   1.8561590e+00   1.9422954e+00   1.8874178e+00   1.8624808e+00   1.8265563e+00   1.8840519e+00   2.0515092e+00   2.0174226e+00   1.9771196e+00   2.0635988e+00   1.7334466e+00   1.9912604e+00   1.8915711e+00   1.8262636e+00   1.9369173e+00   1.9560446e+00   1.9549934e+00   1.9279230e+00   1.9021073e+00   2.0113391e+00   2.0305786e+00   1.8066806e+00   1.9656739e+00   2.1219217e+00   1.8820250e+00   1.8936826e+00   2.0565131e+00   1.9839441e+00   1.8553479e+00   1.9923760e+00   1.6393276e+00   1.9786440e+00   1.8274394e+00   1.9322611e+00   2.0404318e+00   1.9216532e+00   1.9361171e+00   1.8401373e+00   1.9908059e+00   1.9495117e+00   2.1975655e+00   1.8413913e+00   2.1528773e+00   1.8434374e+00   2.1668863e+00   2.0429273e+00   1.9980016e+00   1.9790129e+00   2.0264829e+00   2.1478843e+00   2.0899600e+00   2.0280670e+00   2.1210881e+00   1.9993891e+00   1.8646871e+00   1.9099983e+00   1.9263353e+00   2.0042495e+00   2.1365919e+00   2.1830279e+00   1.9631961e+00   2.0880004e+00   1.8348369e+00
diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-minkowski-5.8-ml-iris.txt b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-minkowski-5.8-ml-iris.txt
new file mode 100644
index 0000000000000000000000000000000000000000..aa26b0439f568f97c95bee1b04204f24c9a1f3e0
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-minkowski-5.8-ml-iris.txt
@@ -0,0 +1 @@
+   5.0042326e-01   4.1210927e-01   5.2133179e-01   1.1269424e-01   4.2362917e-01   5.0001522e-01   1.2085435e-01   7.4262850e-01   4.0127250e-01   3.0482299e-01   3.0482299e-01   5.0436965e-01   8.0923926e-01   7.1629168e-01   9.1424701e-01   4.1317535e-01   1.0000000e-01   6.0366256e-01   3.0017653e-01   3.3813251e-01   2.2573593e-01   5.2133179e-01   3.4080442e-01   5.0436965e-01   5.0043084e-01   2.2608083e-01   1.1269424e-01   1.1269424e-01   4.1315633e-01   4.1315633e-01   3.0490481e-01   6.0000952e-01   7.0462550e-01   4.0127250e-01   3.0482299e-01   4.0002221e-01   4.0127250e-01   7.1621748e-01   1.1269424e-01   1.2085435e-01   1.2036864e+00   7.0088477e-01   4.0125062e-01   5.0476836e-01   5.0436965e-01   3.0474106e-01   5.0436235e-01   2.2573593e-01   2.0061436e-01   3.3243227e+00   3.1068812e+00   3.5145413e+00   2.6080595e+00   3.2075731e+00   3.1014454e+00   3.3055260e+00   1.9156198e+00   3.2079238e+00   2.5066441e+00   2.1498493e+00   2.8059664e+00   2.6093989e+00   3.3021953e+00   2.2070266e+00   3.0158454e+00   3.1034764e+00   2.7009878e+00   3.1081779e+00   2.5032992e+00   3.4074959e+00   2.6050088e+00   3.5035589e+00   3.3011884e+00   2.9065890e+00   3.0117336e+00   3.4118782e+00   3.6094426e+00   3.1038958e+00   2.1042326e+00   2.4058620e+00   2.3063407e+00   2.5029614e+00   3.7025335e+00   3.1034636e+00   3.1057006e+00   3.3110189e+00   3.0065909e+00   2.7025941e+00   2.6047974e+00   3.0013665e+00   3.2025221e+00   2.6029242e+00   1.9242109e+00   2.8024935e+00   2.8013151e+00   2.8022622e+00   2.9036582e+00   1.6267693e+00   2.7028014e+00   4.6144526e+00   3.7071079e+00   4.5121787e+00   4.2031939e+00   4.4087839e+00   5.2153194e+00   3.1086291e+00   4.9093646e+00   4.4044245e+00   4.7202040e+00   3.7119486e+00   3.9066365e+00   4.1123628e+00   3.6114402e+00   3.7307413e+00   3.9194642e+00   4.1043951e+00   5.3177489e+00   5.5157728e+00   3.6035661e+00   4.3162097e+00   3.5127031e+00   5.3163123e+00   3.5077296e+00   4.3088507e+00   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4.0125062e-01   5.0002283e-01   7.0462844e-01   5.0043084e-01   5.2167829e-01   8.0888055e-01   1.1269424e-01   8.0008884e-01   3.0474106e-01   7.0462697e-01   3.0008832e-01   3.3416860e+00   3.1112912e+00   3.5249966e+00   2.6033557e+00   3.2127499e+00   3.1015178e+00   3.3078313e+00   1.9025708e+00   3.2150318e+00   2.5060738e+00   2.1061951e+00   2.8068283e+00   2.6040016e+00   3.3032134e+00   2.2072454e+00   3.0286102e+00   3.1035443e+00   2.7011973e+00   3.1070853e+00   2.5014549e+00   3.4078435e+00   2.6080511e+00   3.5048916e+00   3.3021665e+00   2.9125999e+00   3.0213627e+00   3.4211337e+00   3.6148618e+00   3.1047537e+00   2.1027003e+00   2.4016639e+00   2.3011929e+00   2.5032633e+00   3.7028303e+00   3.1034629e+00   3.1065984e+00   3.3192072e+00   3.0078209e+00   2.7027260e+00   2.6031664e+00   3.0009332e+00   3.2037232e+00   2.6027120e+00   1.9031578e+00   2.8022915e+00   2.8015662e+00   2.8024715e+00   2.9065359e+00   1.6099792e+00   2.7029416e+00   4.6149181e+00   3.7071538e+00   4.5172866e+00   4.2039132e+00   4.4099272e+00   5.2224057e+00   3.1078968e+00   4.9146298e+00   4.4063795e+00   4.7253524e+00   3.7145622e+00   3.9080413e+00   4.1161770e+00   3.6111646e+00   3.7308314e+00   3.9209137e+00   4.1060063e+00   5.3254977e+00   5.5222404e+00   3.6024247e+00   4.3201293e+00   3.5126957e+00   5.3240486e+00   3.5093499e+00   4.3111749e+00   4.6158382e+00   3.4095576e+00   3.5076152e+00   4.2090727e+00   4.4184242e+00   4.7227808e+00   5.0458491e+00   4.2115634e+00   3.7037441e+00   4.2010125e+00   4.7466313e+00   4.2180733e+00   4.1050714e+00   3.4081972e+00   4.0212972e+00   4.2220584e+00   3.7407842e+00   3.7071538e+00   4.5144444e+00   4.3240980e+00   3.8290678e+00   3.6105228e+00   3.8128297e+00   4.0172657e+00   3.7052380e+00   2.0121983e-01   4.1210927e-01   7.9153339e-01   2.0181667e-01   3.0915245e-01   3.3813251e-01   2.2608083e-01   7.1629168e-01   3.0482299e-01   2.0181667e-01   4.0246123e-01   1.1281267e+00   1.2633045e+00   7.8890721e-01   4.1212852e-01   1.0095370e+00   6.0964891e-01   7.0470720e-01   5.2201750e-01   4.1210927e-01   4.5784410e-01   6.0017982e-01   3.4080442e-01   3.4342562e-01   5.0476836e-01   5.0043084e-01   3.0000000e-01   3.0017653e-01   7.0025283e-01   9.0508756e-01   1.0426513e+00   2.2608083e-01   3.0008832e-01   8.0046605e-01   2.2608083e-01   3.0474106e-01   4.0243965e-01   3.3813251e-01   9.0002570e-01   3.0000000e-01   4.3213914e-01   6.8170466e-01   2.0181667e-01   6.1119267e-01   1.1269424e-01   6.3178534e-01   3.0017653e-01   3.4595765e+00   3.2168311e+00   3.6364650e+00   2.7037323e+00   3.3192099e+00   3.2017763e+00   3.4107328e+00   2.0033798e+00   3.3237063e+00   2.6050967e+00   2.2121910e+00   2.9077087e+00   2.7085154e+00   3.4047917e+00   2.3071665e+00   3.1428042e+00   3.2033135e+00   2.8024935e+00   3.2103481e+00   2.6021247e+00   3.5076152e+00   2.7127272e+00   3.6073242e+00   3.4038884e+00   3.0203881e+00   3.1325879e+00   3.5317021e+00   3.7210979e+00   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3.2183845e+00   1.8040969e+00   3.1419971e+00   2.4075162e+00   2.0123013e+00   2.7132680e+00   2.5163999e+00   3.2086215e+00   2.1132077e+00   2.9750754e+00   3.0049127e+00   2.6055197e+00   3.0177719e+00   2.4040962e+00   3.3110162e+00   2.5253371e+00   3.4126529e+00   3.2074182e+00   2.8380954e+00   2.9580787e+00   3.3536443e+00   3.5347730e+00   3.0101869e+00   2.0123796e+00   2.3038195e+00   2.2036797e+00   2.4099203e+00   3.6051707e+00   3.0042758e+00   3.0123228e+00   3.2490712e+00   2.9241808e+00   2.6047889e+00   2.5049231e+00   2.9016211e+00   3.1100277e+00   2.5081992e+00   1.8056342e+00   2.7040060e+00   2.7039988e+00   2.7050721e+00   2.8205713e+00   1.5147271e+00   2.6060742e+00   4.5183778e+00   3.6090052e+00   4.4337691e+00   4.1072664e+00   4.3151164e+00   5.1425125e+00   3.0092613e+00   4.8303615e+00   4.3139066e+00   4.6422789e+00   3.6259317e+00   3.8146285e+00   4.0301568e+00   3.5133848e+00   3.6358680e+00   3.8290678e+00   4.0124919e+00   5.2471177e+00   5.4403962e+00   3.5051114e+00   4.2343452e+00   3.4149831e+00   5.2455706e+00   3.4177035e+00   4.2200398e+00   4.5335328e+00   3.3168776e+00   3.4123846e+00   4.1140176e+00   4.3402553e+00   4.6459028e+00   4.9843016e+00   4.1167964e+00   3.6096226e+00   4.1026403e+00   4.6849407e+00   4.1230798e+00   4.0100505e+00   3.3123688e+00   3.9407837e+00   4.1330547e+00   3.6700537e+00   3.6090052e+00   4.4237036e+00   4.2343452e+00   3.7463488e+00   3.5181052e+00   3.7227931e+00   3.9220791e+00   3.6072781e+00   4.2362917e-01   4.0125062e-01   2.0061436e-01   7.4262850e-01   5.0002283e-01   4.0004442e-01   2.4170870e-01   6.0017982e-01   7.4329527e-01   8.0250123e-01   8.5406674e-01   4.1317535e-01   1.2085435e-01   7.0096858e-01   2.0181667e-01   4.1315633e-01   2.0181667e-01   4.5077696e-01   3.6259865e-01   5.0084481e-01   6.0017665e-01   2.4170870e-01   2.0121983e-01   2.2538848e-01   4.1315633e-01   5.0084481e-01   4.0246123e-01   5.0043842e-01   6.3164729e-01   5.0002283e-01   4.0122873e-01   5.0001522e-01   5.0002283e-01   6.7616723e-01   2.0121983e-01   1.2085435e-01   1.3008771e+00   6.0948506e-01   4.0125062e-01   5.0085236e-01   6.0017982e-01   2.2573593e-01   4.5077696e-01   3.0017653e-01   3.0000000e-01   3.3320240e+00   3.1087192e+00   3.5191371e+00   2.6110181e+00   3.2098845e+00   3.1016129e+00   3.3064697e+00   1.9242109e+00   3.2110200e+00   2.5072065e+00   2.1702438e+00   2.8063347e+00   2.6144115e+00   3.3026483e+00   2.2074446e+00   3.0213781e+00   3.1035271e+00   2.7015967e+00   3.1108570e+00   2.5049231e+00   3.4076266e+00   2.6065485e+00   3.5045818e+00   3.3016829e+00   2.9091905e+00   3.0158857e+00   3.4160038e+00   3.6117923e+00   3.1042949e+00   2.1068047e+00   2.4087956e+00   2.3099309e+00   2.5038387e+00   3.7027671e+00   3.1034919e+00   3.1060428e+00   3.3145595e+00   3.0095593e+00   2.7026925e+00   2.6061038e+00   3.0017811e+00   3.2030205e+00   2.6039803e+00   1.9366876e+00   2.8028640e+00   2.8014482e+00   2.8024453e+00   2.9049136e+00   1.6388635e+00   2.7031257e+00   4.6146430e+00   3.7072412e+00   4.5144508e+00   4.2035048e+00   4.4092709e+00   5.2185448e+00   3.1091788e+00   4.9117351e+00   4.4054277e+00   4.7224997e+00   3.7130507e+00   3.9073151e+00   4.1140274e+00   3.6117351e+00   3.7308330e+00   3.9200674e+00   4.1050815e+00   5.3212796e+00   5.5187578e+00   3.6046347e+00   4.3179262e+00   3.5127783e+00   5.3198559e+00   3.5085510e+00   4.3098508e+00   4.6126513e+00   3.4088749e+00   3.5071604e+00   4.2085176e+00   4.4144980e+00   4.7185095e+00   5.0381903e+00   4.2110099e+00   3.7030413e+00   4.2009868e+00   4.7393218e+00   4.2176488e+00   4.1043951e+00   3.4078683e+00   4.0181902e+00   4.2205976e+00   3.7363838e+00   3.7072412e+00   4.5130595e+00   4.3227928e+00   3.8267408e+00   3.6102542e+00   3.8115096e+00   4.0168944e+00   3.7051079e+00   8.0923926e-01   5.2201750e-01   1.1270411e+00   8.0928056e-01   2.4170870e-01   6.3178782e-01   9.1471442e-01   1.1573074e+00   5.2167829e-01   5.0476836e-01   4.0000000e-01   4.2270142e-01   3.0017653e-01   3.0490481e-01   5.0042326e-01   3.0915245e-01   8.5440680e-01   6.0184622e-01   6.3192325e-01   9.0142681e-01   5.2133179e-01   4.0363334e-01   5.0517282e-01   7.8890806e-01   8.2421923e-01   5.0042326e-01   3.1328089e-01   3.4085233e-01   8.0928056e-01   7.2044167e-01   4.5148429e-01   8.0928056e-01   1.0782211e+00   5.0517282e-01   4.8342635e-01   1.6097492e+00   1.0215068e+00   4.5148429e-01   3.0482299e-01   9.1446938e-01   3.0490481e-01   8.5440680e-01   2.4195741e-01   6.1135434e-01   3.0143288e+00   2.8035152e+00   3.2080663e+00   2.3476141e+00   2.9053991e+00   2.8028019e+00   3.0030626e+00   1.7519158e+00   2.9045816e+00   2.2149484e+00   2.0887699e+00   2.5048522e+00   2.3645147e+00   3.0018766e+00   1.9120303e+00   2.7085154e+00   2.8028008e+00   2.4075162e+00   2.8284908e+00   2.2272457e+00   3.1054022e+00   2.3075573e+00   3.2060163e+00   3.0018874e+00   2.6044486e+00   2.7064438e+00   3.1073418e+00   3.3054063e+00   2.8034238e+00   1.8447840e+00   2.1492024e+00   2.0607272e+00   2.2122063e+00   3.4028104e+00   2.8028007e+00   2.8036182e+00   3.0057998e+00   2.7234787e+00   2.4027927e+00   2.3234132e+00   2.7070699e+00   2.9017335e+00   2.3151346e+00   1.8036834e+00   2.5072065e+00   2.5017313e+00   2.5032633e+00   2.6031823e+00   1.5292174e+00   2.4058519e+00   4.3116266e+00   3.4064593e+00   4.2076930e+00   3.9021503e+00   4.1063936e+00   4.9099401e+00   2.8141516e+00   4.6055969e+00   4.1036742e+00   4.4145324e+00   3.4082578e+00   3.6052799e+00   3.8082804e+00   3.3123693e+00   3.4273179e+00   3.6154977e+00   3.8026444e+00   5.0117750e+00   5.2107474e+00   3.3130198e+00   4.0114753e+00   3.2109395e+00   5.0107787e+00   3.2067490e+00   4.0058313e+00   4.3058539e+00   3.1067996e+00   3.2049797e+00   3.9061098e+00   4.1066170e+00   4.4095056e+00   4.7221364e+00   3.9082316e+00   3.4019453e+00   3.9014304e+00   4.4232188e+00   3.9139973e+00   3.8023591e+00   3.1057392e+00   3.7104219e+00   3.9150553e+00   3.4248402e+00   3.4064593e+00   4.2084919e+00   4.0172759e+00   3.5193527e+00   3.3100431e+00   3.5073655e+00   3.7133435e+00   3.4036743e+00   4.0004442e-01   5.0043084e-01   3.4085233e-01   8.0046764e-01   2.2573593e-01   4.0243965e-01   4.2362917e-01   1.2036925e+00   1.1896595e+00   8.0879776e-01   5.0000761e-01   1.1006371e+00   5.2133179e-01   8.0046685e-01   5.0437695e-01   4.0125062e-01   5.0477564e-01   5.0043084e-01   4.5148429e-01   4.0125062e-01   6.0000952e-01   6.0000317e-01   2.2608083e-01   3.0922892e-01   8.0000160e-01   7.4269314e-01   9.6572569e-01   3.4085233e-01   4.0246123e-01   9.0000136e-01   3.4085233e-01   4.0127250e-01   5.0001522e-01   4.0004442e-01   1.1000003e+00   2.2608083e-01   4.1317535e-01   5.7609230e-01   4.0122873e-01   5.2167829e-01   2.0061436e-01   7.0088627e-01   4.0004442e-01   3.3852404e+00   3.1245391e+00   3.5521657e+00   2.6057331e+00   3.2281303e+00   3.1021033e+00   3.3145497e+00   1.9088256e+00   3.2358110e+00   2.5040476e+00   2.1337832e+00   2.8091158e+00   2.6173653e+00   3.3068237e+00   2.2078368e+00   3.0635687e+00   3.1029264e+00   2.7045714e+00   3.1156892e+00   2.5038387e+00   3.4072735e+00   2.6199287e+00   3.5105217e+00   3.3061800e+00   2.9316687e+00   3.0488379e+00   3.4462681e+00   3.6292576e+00   3.1074604e+00   2.1103491e+00   2.4046650e+00   2.3052527e+00   2.5074705e+00   3.7037846e+00   3.1023805e+00   3.1087156e+00   3.3416864e+00   3.0212423e+00   2.7029308e+00   2.6036513e+00   3.0012006e+00   3.2078939e+00   2.6064541e+00   1.9145304e+00   2.8026114e+00   2.8028068e+00   2.8033825e+00   2.9167099e+00   1.6147493e+00   2.7040740e+00   4.6133719e+00   3.7058811e+00   4.5290217e+00   4.2056470e+00   4.4115634e+00   5.2381327e+00   3.1057013e+00   4.9271590e+00   4.4118721e+00   4.7354168e+00   3.7201124e+00   3.9113698e+00   4.1247181e+00   3.6087856e+00   3.7244383e+00   3.9212835e+00   4.1101783e+00   5.3422962e+00   5.5362181e+00   3.6046999e+00   4.3279835e+00   3.5095358e+00   5.3412086e+00   3.5135120e+00   4.3162096e+00   4.6297141e+00   3.4124092e+00   3.5088081e+00   4.2105763e+00   4.4358170e+00   4.7408876e+00   5.0762364e+00   4.2125085e+00   3.7079173e+00   4.2021973e+00   4.7752666e+00   4.2166536e+00   4.1080028e+00   3.4084548e+00   4.0338654e+00   4.2256165e+00   3.7563734e+00   3.7058811e+00   4.5190617e+00   4.3264209e+00   3.8360186e+00   3.6136974e+00   3.8177300e+00   4.0156240e+00   3.7048582e+00   6.3164977e-01   3.0017653e-01   4.1209001e-01   2.0061436e-01   4.0127250e-01   7.0911112e-01   8.2458409e-01   1.0207396e+00   5.2201750e-01   1.2699992e-01   7.0470867e-01   4.0004442e-01   4.0122873e-01   3.0482299e-01   5.2167208e-01   3.0490481e-01   4.0122873e-01   4.0002221e-01   2.0061436e-01   2.0061436e-01   2.0061436e-01   3.0482299e-01   3.0482299e-01   4.0122873e-01   7.0008584e-01   8.0879701e-01   3.0017653e-01   3.0474106e-01   5.0043084e-01   3.0017653e-01   6.0964597e-01   1.0000000e-01   2.0121983e-01   1.1019599e+00   6.0035305e-01   4.0004442e-01   4.5148429e-01   4.0127250e-01   4.0004442e-01   4.0125062e-01   3.3808272e-01   1.1269424e-01   3.2369541e+00   3.0101869e+00   3.4219340e+00   2.5073576e+00   3.1113295e+00   3.0016913e+00   3.2074921e+00   1.8128536e+00   3.1127326e+00   2.4076937e+00   2.0429861e+00   2.7074657e+00   2.5087337e+00   3.2029987e+00   2.1087640e+00   2.9250474e+00   3.0040848e+00   2.6011837e+00   3.0090716e+00   2.4029250e+00   3.3087901e+00   2.5074281e+00   3.4046875e+00   3.2018065e+00   2.8107271e+00   2.9185950e+00   3.3183094e+00   3.5134617e+00   3.0049285e+00   2.0041542e+00   2.3049133e+00   2.2050331e+00   2.4035997e+00   3.6030023e+00   3.0040438e+00   3.0070658e+00   3.2168317e+00   2.9083216e+00   2.6031436e+00   2.5048522e+00   2.9013423e+00   3.1034810e+00   2.5032729e+00   1.8201043e+00   2.7028014e+00   2.7016556e+00   2.7027522e+00   2.8056775e+00   1.5256523e+00   2.6033557e+00   4.5162553e+00   3.6081006e+00   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3.8290678e+00   4.0228342e+00   3.7082809e+00   6.3164977e-01   3.0026460e-01   1.2085435e-01   6.0948506e-01   1.0143978e+00   1.3131369e+00   8.0928056e-01   4.0246123e-01   8.5409862e-01   7.0016860e-01   5.0477564e-01   6.0201716e-01   5.6595908e-01   4.0363334e-01   4.1212852e-01   1.2699992e-01   3.3818226e-01   4.1210927e-01   3.3818226e-01   2.0181667e-01   1.2085435e-01   5.0855077e-01   1.0001598e+00   1.1055707e+00   0.0000000e+00   3.0026460e-01   6.0964891e-01   0.0000000e+00   5.0043842e-01   3.0482299e-01   4.0246123e-01   8.0254500e-01   5.0043842e-01   5.2133802e-01   7.0556260e-01   2.0181667e-01   7.0008735e-01   3.0026460e-01   6.0948506e-01   2.0181667e-01   3.2490712e+00   3.0153168e+00   3.4297841e+00   2.5067523e+00   3.1166337e+00   3.0027816e+00   3.2112793e+00   1.8068048e+00   3.1183051e+00   2.4116924e+00   2.0138832e+00   2.7116615e+00   2.5059537e+00   3.2048192e+00   2.1144760e+00   2.9351753e+00   3.0063019e+00   2.6019122e+00   3.0106587e+00   2.4030297e+00   3.3125861e+00   2.5120719e+00   3.4068163e+00   3.2029877e+00   2.8162444e+00   2.9267417e+00   3.3252407e+00   3.5189464e+00   3.0077107e+00   2.0051350e+00   2.3037132e+00   2.2028146e+00   2.4058620e+00   3.6044981e+00   3.0062070e+00   3.0107283e+00   3.2237456e+00   2.9105093e+00   2.6052541e+00   2.5062865e+00   2.9018772e+00   3.1056084e+00   2.5048522e+00   1.8082911e+00   2.7043948e+00   2.7029415e+00   2.7046027e+00   2.8091099e+00   1.5248852e+00   2.6055127e+00   4.5209020e+00   3.6112573e+00   4.4212031e+00   4.1056541e+00   4.3138986e+00   5.1255338e+00   3.0133997e+00   4.8167235e+00   4.3081273e+00   4.6319211e+00   3.6205854e+00   3.8114965e+00   4.0212972e+00   3.5173798e+00   3.6449970e+00   3.8299342e+00   4.0081754e+00   5.2290121e+00   5.4254411e+00   3.5039202e+00   4.2264145e+00   3.4198378e+00   5.2270034e+00   3.4138008e+00   4.2149806e+00   4.5183778e+00   3.3145502e+00   3.4118179e+00   4.1129687e+00   4.3210760e+00   4.6261633e+00   4.9512603e+00   4.1165035e+00   3.6051692e+00   4.1014742e+00   4.6540056e+00   4.1257291e+00   4.0071257e+00   3.3129914e+00   3.9274863e+00   4.1301604e+00   3.6542046e+00   3.6112573e+00   4.4192311e+00   4.2328883e+00   3.7399948e+00   3.5155767e+00   3.7180846e+00   3.9250546e+00   3.6083191e+00   6.0184622e-01   7.4263078e-01   1.1138955e+00   4.2268438e-01   7.0096708e-01   2.4170870e-01   3.0490481e-01   3.0490481e-01   3.0017653e-01   3.0474106e-01   3.0474106e-01   8.0879701e-01   4.2362917e-01   6.1119267e-01   7.0462697e-01   4.1317535e-01   2.2538848e-01   3.0482299e-01   7.1621748e-01   6.7616723e-01   3.0474106e-01   4.0125062e-01   5.0001522e-01   6.3164977e-01   5.2491131e-01   2.2573593e-01   6.3164977e-01   1.0207396e+00   3.3808272e-01   4.0246123e-01   1.4180463e+00   1.0030868e+00   4.5148429e-01   4.1317535e-01   7.4263078e-01   3.0017653e-01   8.0879701e-01   1.0000000e-01   4.5078948e-01   3.2116783e+00   3.0049285e+00   3.4072983e+00   2.5182898e+00   3.1051604e+00   3.0020136e+00   3.2049016e+00   1.8469618e+00   3.1036832e+00   2.4099081e+00   2.1180493e+00   2.7068820e+00   2.5224740e+00   3.2021231e+00   2.1097449e+00   2.9077617e+00   3.0041462e+00   2.6022422e+00   3.0134290e+00   2.4087504e+00   3.3085101e+00   2.5050799e+00   3.4038679e+00   3.2010814e+00   2.8036959e+00   2.9060895e+00   3.3058271e+00   3.5063866e+00   3.0043212e+00   2.0122773e+00   2.3159426e+00   2.2186306e+00   2.4051454e+00   3.6029749e+00   3.0041461e+00   3.0062373e+00   3.2059465e+00   2.9096170e+00   2.6032656e+00   2.5097004e+00   2.9028411e+00   3.1023606e+00   2.5057847e+00   1.8685354e+00   2.7039990e+00   2.7016498e+00   2.7029428e+00   2.8028074e+00   1.5747520e+00   2.6039937e+00   4.5157550e+00   3.6083209e+00   4.4088451e+00   4.1031691e+00   4.3089952e+00   5.1095334e+00   3.0117336e+00   4.8052574e+00   4.3035619e+00   4.6175091e+00   3.6116958e+00   3.8067089e+00   4.0107159e+00   3.5138361e+00   3.6350483e+00   3.8210210e+00   4.0037985e+00   5.2113565e+00   5.4105254e+00   3.5063553e+00   4.2147222e+00   3.4147657e+00   5.2097995e+00   3.4081036e+00   4.2080425e+00   4.5057296e+00   3.3089414e+00   3.4074852e+00   4.1084282e+00   4.3058539e+00   4.6088153e+00   4.9193995e+00   4.1112251e+00   3.6020843e+00   4.1009356e+00   4.6223848e+00   4.1190046e+00   4.0036188e+00   3.3085886e+00   3.9129256e+00   4.1197933e+00   3.6305006e+00   3.6083209e+00   4.4113183e+00   4.2225427e+00   3.7249938e+00   3.5105217e+00   3.7103007e+00   3.9184088e+00   3.6056580e+00   4.0125062e-01   5.7609230e-01   1.0095367e+00   1.0776296e+00   6.3322667e-01   3.0490481e-01   9.0140221e-01   4.1212852e-01   6.0000317e-01   3.4085233e-01   6.0035305e-01   3.3818226e-01   3.0000000e-01   4.0122873e-01   2.2538848e-01   4.0004442e-01   4.0122873e-01   2.0061436e-01   3.0000000e-01   6.0017982e-01   7.0462844e-01   8.5406616e-01   3.0026460e-01   4.0243965e-01   7.0088477e-01   3.0026460e-01   4.5783248e-01   3.0008832e-01   3.0490481e-01   1.1002025e+00   4.1315633e-01   4.0125062e-01   4.2362917e-01   4.0125062e-01   4.1209001e-01   2.4170870e-01   5.0436965e-01   2.2573593e-01   3.1712557e+00   2.9203034e+00   3.3425817e+00   2.4092081e+00   3.0228582e+00   2.9024211e+00   3.1131137e+00   1.7168003e+00   3.0276611e+00   2.3094323e+00   1.9540727e+00   2.6109956e+00   2.4153242e+00   3.1056218e+00   2.0123796e+00   2.8520945e+00   2.9050328e+00   2.5029614e+00   2.9148948e+00   2.3042831e+00   3.2109395e+00   2.4161682e+00   3.3086859e+00   3.1042389e+00   2.7244207e+00   2.8394157e+00   3.2369857e+00   3.4247142e+00   2.9077271e+00   1.9085444e+00   2.2064916e+00   2.1068047e+00   2.3066817e+00   3.5042241e+00   2.9048033e+00   2.9102290e+00   3.1338090e+00   2.8169587e+00   2.5042601e+00   2.4061715e+00   2.8017212e+00   3.0065627e+00   2.4058322e+00   1.7261843e+00   2.6037439e+00   2.6027120e+00   2.6040234e+00   2.7127458e+00   1.4350761e+00   2.5049231e+00   4.4189015e+00   3.5095669e+00   4.3257995e+00   4.0057109e+00   4.2135057e+00   5.0324952e+00   2.9113810e+00   4.7221382e+00   4.2099962e+00   4.5353918e+00   3.5215862e+00   3.7118930e+00   3.9240025e+00   3.4150232e+00   3.5401623e+00   3.7282910e+00   3.9092259e+00   5.1365012e+00   5.3314853e+00   3.4049933e+00   4.1286955e+00   3.3168890e+00   5.1347989e+00   3.3143385e+00   4.1161770e+00   4.4243750e+00   3.2143454e+00   3.3110189e+00   4.0125032e+00   4.2289520e+00   4.5343227e+00   4.8661173e+00   4.0156353e+00   3.5063553e+00   4.0017163e+00   4.5675364e+00   4.0235140e+00   3.9076272e+00   3.2116700e+00   3.8321139e+00   4.0301570e+00   3.5598557e+00   3.5095669e+00   4.3201293e+00   4.1322798e+00   3.6413292e+00   3.4157005e+00   3.6188994e+00   3.8226858e+00   3.5071409e+00   5.0436235e-01   1.1269511e+00   1.4180734e+00   9.1446938e-01   5.0476836e-01   9.6593231e-01   8.0051115e-01   6.1119558e-01   7.0176271e-01   6.0964891e-01   4.3213914e-01   5.2133179e-01   2.2573593e-01   4.1420960e-01   5.2133802e-01   4.5078948e-01   2.2608083e-01   2.0121983e-01   6.1119558e-01   1.1005364e+00   1.2089192e+00   1.2085435e-01   2.4195741e-01   7.1621884e-01   1.2085435e-01   4.0004442e-01   4.1212852e-01   5.0085236e-01   7.0096858e-01   4.0127250e-01   5.6394820e-01   8.0967961e-01   2.0000000e-01   8.0051115e-01   2.2573593e-01   7.1621884e-01   3.0482299e-01   3.3545239e+00   3.1166331e+00   3.5333785e+00   2.6054739e+00   3.2183845e+00   3.1025789e+00   3.3116521e+00   1.9046783e+00   3.2211369e+00   2.5096353e+00   2.1074907e+00   2.8107054e+00   2.6064541e+00   3.3051050e+00   2.2121875e+00   3.0393610e+00   3.1054994e+00   2.7022579e+00   3.1107490e+00   2.5027328e+00   3.4112739e+00   2.6129479e+00   3.5073688e+00   3.3035252e+00   2.9185900e+00   3.0300451e+00   3.4286400e+00   3.6205854e+00   3.1074470e+00   2.1053074e+00   2.4030297e+00   2.3022754e+00   2.5057763e+00   3.7043108e+00   3.1053329e+00   3.1100313e+00   3.3265652e+00   3.0118276e+00   2.7046025e+00   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9.2867113e-01   9.0155393e-01   1.0001753e+00   2.2182690e+00   2.4124980e+00   1.0039060e+00   1.2201577e+00   8.1343016e-01   2.2176846e+00   5.2491734e-01   1.2037520e+00   1.5066999e+00   4.2362917e-01   4.2362917e-01   1.1060937e+00   1.3130978e+00   1.6177611e+00   1.9760242e+00   1.1138953e+00   6.0948506e-01   1.1056693e+00   1.6779798e+00   1.1527746e+00   1.0001601e+00   4.2362917e-01   9.1892454e-01   1.1528477e+00   8.3183672e-01   6.9987517e-01   1.4094144e+00   1.2633467e+00   8.5440680e-01   7.2036951e-01   7.1629303e-01   9.6576136e-01   6.3322667e-01   1.4267554e+00   4.2268438e-01   1.2004262e+00   6.0035621e-01   2.0860325e+00   3.4342562e-01   1.7133162e+00   1.9641993e+00   1.0207260e+00   1.0897469e+00   8.0008964e-01   1.4650300e+00   5.0043084e-01   1.3002407e+00   1.1303267e+00   9.3424659e-01   1.3473688e+00   1.0001604e+00   9.6593231e-01   6.7616545e-01   8.0097499e-01   6.3192325e-01   5.0437695e-01   3.0026460e-01   2.2608083e-01   9.0142636e-01   1.4861824e+00   1.4580174e+00   1.4889602e+00   1.1900969e+00   9.0142681e-01   1.5001212e+00   9.0166476e-01   2.2538848e-01   8.3187290e-01   1.3130978e+00   1.4197078e+00   1.4012600e+00   8.0046764e-01   1.1544060e+00   2.0075255e+00   1.3063533e+00   1.2089835e+00   1.2089313e+00   7.4275547e-01   2.0887699e+00   1.2190319e+00   1.1935069e+00   1.1010807e+00   1.0087396e+00   7.4335736e-01   9.3424697e-01   1.7023957e+00   2.0003507e+00   1.4002035e+00   9.1449234e-01   1.2643523e+00   5.2167829e-01   5.5450500e-01   6.7616902e-01   1.2049541e+00   1.1528553e+00   8.1112984e-01   6.1119558e-01   1.8053679e+00   2.0034894e+00   1.0142484e+00   9.0155438e-01   1.3009222e+00   1.8029948e+00   6.1119267e-01   8.2425704e-01   1.1002025e+00   7.0176271e-01   8.0046685e-01   7.5564478e-01   9.0026588e-01   1.2017042e+00   1.5269837e+00   7.9871893e-01   6.0201716e-01   8.6051471e-01   1.2366099e+00   9.4532171e-01   6.3309012e-01   9.0026588e-01   6.3164729e-01   9.3308853e-01   8.0004443e-01   1.1010807e+00   1.0426516e+00   1.0426760e+00   8.0051115e-01   6.8161057e-01   5.2491734e-01   8.6084272e-01   1.0001753e+00   1.0116865e+00   5.6370994e-01   1.0599087e+00   7.4329527e-01   1.1110092e+00   4.1212852e-01   5.6838732e-01   7.0478886e-01   5.0436965e-01   7.7598796e-01   6.0948506e-01   1.2192920e+00   7.1629303e-01   4.2270142e-01   7.1629303e-01   2.2608083e-01   9.7033357e-01   6.3164729e-01   9.6576136e-01   7.5503094e-01   9.1446896e-01   1.1138955e+00   1.3139296e+00   1.2705641e+00   6.5724028e-01   5.0894102e-01   2.2573593e-01   3.3813251e-01   4.1212852e-01   1.1025819e+00   7.1629303e-01   1.1039833e+00   1.2272550e+00   8.0245746e-01   7.0000303e-01   2.0000000e-01   4.1210927e-01   7.7598796e-01   3.3813251e-01   7.1700774e-01   4.0125062e-01   7.0017011e-01   6.0035305e-01   7.4329414e-01   1.0008768e+00   5.0043084e-01   2.0249458e+00   1.1061923e+00   2.0081838e+00   1.6061519e+00   1.8167511e+00   2.7171724e+00   6.3925756e-01   2.3875202e+00   1.8286180e+00   2.2239101e+00   1.2353587e+00   1.3278587e+00   1.6038059e+00   1.0207533e+00   1.2407946e+00   1.3868868e+00   1.5269837e+00   2.8396169e+00   2.9941208e+00   1.0030871e+00   1.8005082e+00   9.3733589e-01   2.8269381e+00   9.7033357e-01   1.7520952e+00   2.1193712e+00   8.6676847e-01   9.4912864e-01   1.6147493e+00   1.9768316e+00   2.2674825e+00   2.7199050e+00   1.6193612e+00   1.1298636e+00   1.6009488e+00   2.4288142e+00   1.6617386e+00   1.5199103e+00   8.6676847e-01   1.5881447e+00   1.6785116e+00   1.4886759e+00   1.1061923e+00   1.9457481e+00   1.7813291e+00   1.3946348e+00   1.0498347e+00   1.2771155e+00   1.4848797e+00   1.1157320e+00   8.0004523e-01   5.0043842e-01   1.6743483e+00   2.0121983e-01   1.3061139e+00   1.5464046e+00   6.0964597e-01   7.1183012e-01   4.0006662e-01   1.0776296e+00   3.0922892e-01   9.0002570e-01   7.3084171e-01   6.0184622e-01   9.3446811e-01   6.1135434e-01   6.0964597e-01   3.4080442e-01   4.1210927e-01   3.0490481e-01   2.2608083e-01   3.0482299e-01   4.0363334e-01   5.0001522e-01   1.1298636e+00   1.0440350e+00   1.0803561e+00   7.8935898e-01   5.6347978e-01   1.1000098e+00   6.3165225e-01   3.0482299e-01   5.0126466e-01   9.0511169e-01   1.0088926e+00   1.0001903e+00   4.0125062e-01   7.4335736e-01   1.5972311e+00   9.0142681e-01   8.0296037e-01   8.0250202e-01   3.4085233e-01   1.7081446e+00   8.0883841e-01   1.4329858e+00   7.2036951e-01   1.3050153e+00   1.0001753e+00   1.2089252e+00   2.0109333e+00   1.6000184e+00   1.7036944e+00   1.2001396e+00   1.5327217e+00   5.7608844e-01   7.0462844e-01   9.1449234e-01   8.1156529e-01   9.3733552e-01   8.5583415e-01   9.0029018e-01   2.1191883e+00   2.3098756e+00   6.3912709e-01   1.1290757e+00   9.0532049e-01   2.1139617e+00   3.4085233e-01   1.1074834e+00   1.4044980e+00   3.4080442e-01   4.2362917e-01   1.0087250e+00   1.2089253e+00   1.5132032e+00   1.8748226e+00   1.0207260e+00   5.0042326e-01   1.0008620e+00   1.5694554e+00   1.0837679e+00   9.0053003e-01   5.0517282e-01   8.2671175e-01   1.0777411e+00   8.1156529e-01   7.2036951e-01   1.3133662e+00   1.1910068e+00   8.2425704e-01   4.5847767e-01   6.3178534e-01   9.1590889e-01   6.3322667e-01   6.3322667e-01   1.2193537e+00   9.0000091e-01   6.3165225e-01   1.0599087e+00   3.1328089e-01   6.3451734e-01   4.0127250e-01   9.0000091e-01   1.0001604e+00   2.2573593e-01   4.1212852e-01   6.3178534e-01   6.0202028e-01   5.2524663e-01   5.2132556e-01   6.1135434e-01   4.0125062e-01   7.0008584e-01   9.0002615e-01   1.1001014e+00   1.0039209e+00   3.0482299e-01   1.0001751e+00   7.0478886e-01   8.0296037e-01   6.0000952e-01   6.0366256e-01   3.0915245e-01   6.0365948e-01   1.0001903e+00   6.3164977e-01   4.0125062e-01   5.0476836e-01   2.2608083e-01   4.0127250e-01   5.0043842e-01   1.2102248e+00   3.0017653e-01   3.0482299e-01   3.0008832e-01   5.0043084e-01   1.5012947e+00   4.0000000e-01   1.5653766e+00   6.7616902e-01   1.5829749e+00   1.1074742e+00   1.3373141e+00   2.2681751e+00   8.0291671e-01   1.9315820e+00   1.3458100e+00   1.7862938e+00   8.7372177e-01   8.7209348e-01   1.2093969e+00   7.1700774e-01   1.1055705e+00   1.0604287e+00   1.0451812e+00   2.3834499e+00   2.5286011e+00   6.3322667e-01   1.3903623e+00   7.0462697e-01   2.3796582e+00   6.3912943e-01   1.2792049e+00   1.6907308e+00   5.6595488e-01   5.3943256e-01   1.1400339e+00   1.5965952e+00   1.8639835e+00   2.3424496e+00   1.1635325e+00   6.7626502e-01   1.1005460e+00   2.0903382e+00   1.2459141e+00   1.0236548e+00   5.0894102e-01   1.2528590e+00   1.2949162e+00   1.2662318e+00   6.7616902e-01   1.4817248e+00   1.3908238e+00   1.1389163e+00   6.9600743e-01   8.9540816e-01   1.0858512e+00   6.3192325e-01   1.5890088e+00   4.2270142e-01   1.1330776e+00   1.5368468e+00   5.2491734e-01   1.1187430e+00   4.0243965e-01   1.1139906e+00   4.1420960e-01   7.0096858e-01   7.3895268e-01   1.1000100e+00   9.3861512e-01   4.0127250e-01   7.1708289e-01   8.0004523e-01   5.2167208e-01   4.5784410e-01   3.6452132e-01   5.6371422e-01   4.2270142e-01   4.1317535e-01   1.2159868e+00   1.0567817e+00   1.1138092e+00   8.3387677e-01   6.1119267e-01   9.0029064e-01   3.0482299e-01   4.0125062e-01   1.0003196e+00   7.4395693e-01   9.3459651e-01   8.5617086e-01   3.0922892e-01   8.0073117e-01   1.5493206e+00   7.5564478e-01   6.4049114e-01   6.4049114e-01   4.5784410e-01   1.7404389e+00   6.9600743e-01   1.3253457e+00   6.4049114e-01   1.2202193e+00   9.0142636e-01   1.1056785e+00   1.9348400e+00   1.4092540e+00   1.6176783e+00   1.1286101e+00   1.4350761e+00   4.5148429e-01   6.7720957e-01   8.1757693e-01   8.2671175e-01   8.1937731e-01   7.4263078e-01   8.0055465e-01   2.0418418e+00   2.2277117e+00   1.1002025e+00   1.0286508e+00   7.2044167e-01   2.0415798e+00   6.0035305e-01   1.0039060e+00   1.3253497e+00   5.0043842e-01   3.1328089e-01   9.0999313e-01   1.1528476e+00   1.4548293e+00   1.8637334e+00   9.1892454e-01   5.2133179e-01   9.3310976e-01   1.5801693e+00   9.6572569e-01   8.0008964e-01   3.4085233e-01   7.5508853e-01   9.6674360e-01   7.4618926e-01   6.4049114e-01   1.2101609e+00   1.0782105e+00   7.2113820e-01   8.0093081e-01   5.2524663e-01   7.8886139e-01   4.5847767e-01   1.7572657e+00   6.1288055e-01   4.0125062e-01   1.0858512e+00   1.1133984e+00   1.4858469e+00   7.1779518e-01   1.8187119e+00   1.2137020e+00   9.6591433e-01   1.4146346e+00   7.4263078e-01   1.5359852e+00   1.2093243e+00   1.7083042e+00   1.4853863e+00   1.5241361e+00   1.7234436e+00   1.9756319e+00   1.9771636e+00   1.3035495e+00   8.0008884e-01   6.3164977e-01   6.0948212e-01   9.1449234e-01   1.8179429e+00   1.2062153e+00   1.3486924e+00   1.8673780e+00   1.4543172e+00   8.7240114e-01   7.4329527e-01   1.1055892e+00   1.4158897e+00   9.3310976e-01   1.1269424e-01   9.3351278e-01   9.7600992e-01   9.6953662e-01   1.3458100e+00   3.0490481e-01   9.0320459e-01   2.7259033e+00   1.8109877e+00   2.7506971e+00   2.3226569e+00   2.5372438e+00   3.4590995e+00   1.2089192e+00   3.1281646e+00   2.5610212e+00   2.9500632e+00   1.9406671e+00   2.0633570e+00   2.3443688e+00   1.7168003e+00   1.8708330e+00   2.0857354e+00   2.2573821e+00   3.5725062e+00   3.7336869e+00   1.7229558e+00   2.5362836e+00   1.6198349e+00   3.5690915e+00   1.7116793e+00   2.4776152e+00   2.8599555e+00   1.6016303e+00   1.6534235e+00   2.3372717e+00   2.7159844e+00   3.0094888e+00   3.4430661e+00   2.3406025e+00   1.8663319e+00   2.3090404e+00   3.1586433e+00   2.3454995e+00   2.2408459e+00   1.5471213e+00   2.3192230e+00   2.4059451e+00   2.1751377e+00   1.8109877e+00   2.6757243e+00   2.4966678e+00   2.1111734e+00   1.7901165e+00   2.0121175e+00   2.1471399e+00   1.8133657e+00   1.4043036e+00   1.6388784e+00   7.0470867e-01   7.7652636e-01   5.0001522e-01   1.1269424e+00   2.2608083e-01   1.0000158e+00   8.0928056e-01   7.0470867e-01   1.0215068e+00   7.1708289e-01   6.3164977e-01   4.2362917e-01   5.0002283e-01   3.0474106e-01   2.0121983e-01   2.2608083e-01   4.5080200e-01   6.0017982e-01   1.1529284e+00   1.1298636e+00   1.1544060e+00   8.5406674e-01   6.3322667e-01   1.2000066e+00   6.3309258e-01   2.2608083e-01   6.0201716e-01   1.0030721e+00   1.1060937e+00   1.1001110e+00   5.0001522e-01   8.2458478e-01   1.6747799e+00   1.0008617e+00   9.0140221e-01   9.0140131e-01   4.1209001e-01   1.7511598e+00   9.0506299e-01   1.4854079e+00   8.3187290e-01   1.3139296e+00   1.0032293e+00   1.2362702e+00   2.0078120e+00   1.7001329e+00   1.7019430e+00   1.2016381e+00   1.5675442e+00   7.1700909e-01   7.4275547e-01   9.6574369e-01   9.3541878e-01   1.1298552e+00   1.0208844e+00   9.0506343e-01   2.1136134e+00   2.3085898e+00   7.4618926e-01   1.1897982e+00   1.0208709e+00   2.1090362e+00   5.0894102e-01   1.1286018e+00   1.4024091e+00   5.2167829e-01   5.6595908e-01   1.0426638e+00   1.2037520e+00   1.5079206e+00   1.8503663e+00   1.0776296e+00   5.0477564e-01   1.0032296e+00   1.5611241e+00   1.1910693e+00   9.0511169e-01   6.3178782e-01   9.0184172e-01   1.1896660e+00   1.0032443e+00   8.3187290e-01   1.3450688e+00   1.3020492e+00   1.0087252e+00   6.1990228e-01   7.4263078e-01   1.0458540e+00   7.3084171e-01   7.0918894e-01   7.0176271e-01   8.1112984e-01   9.6574336e-01   4.1317535e-01   1.5005626e+00   6.1119558e-01   6.0964597e-01   1.0116724e+00   4.1315633e-01   9.3848935e-01   9.0000136e-01   1.1896660e+00   9.6574369e-01   1.2003597e+00   1.4006465e+00   1.6096629e+00   1.5401713e+00   8.2421923e-01   5.3914287e-01   3.6259865e-01   4.2362917e-01   6.0017665e-01   1.2189701e+00   6.0202028e-01   8.7212232e-01   1.5067961e+00   1.1024820e+00   4.1317535e-01   3.0490481e-01   5.0477564e-01   9.3329017e-01   6.0018299e-01   6.1845783e-01   4.1210927e-01   5.0894102e-01   5.0477564e-01   1.0008620e+00   9.0029064e-01   5.0043842e-01   2.1169442e+00   1.2049539e+00   2.2014913e+00   1.7227908e+00   1.9366943e+00   2.8973091e+00   6.0383105e-01   2.5621105e+00   1.9756002e+00   2.3854144e+00   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1.0797700e+00   1.1139044e+00   1.4000349e+00   4.0004442e-01   7.1629303e-01   1.2090477e+00   6.8170466e-01   4.5148429e-01   9.1427000e-01   9.3184922e-01   5.0043842e-01   4.1209001e-01   8.0296037e-01   1.0498226e+00   8.0928056e-01   6.0018299e-01   9.3446811e-01   1.3131410e+00   5.6371422e-01   7.8985507e-01   1.8949500e+00   9.1427000e-01   1.5639785e+00   9.3308891e-01   1.4501583e+00   7.1621748e-01   6.0017665e-01   1.0010209e+00   2.0181667e-01   5.0000761e-01   6.3925756e-01   7.0548283e-01   2.0162299e+00   2.0885102e+00   5.2167829e-01   1.1079931e+00   2.2608083e-01   2.0057464e+00   5.0043084e-01   9.2747919e-01   1.4186217e+00   4.1212852e-01   3.4085233e-01   6.3178782e-01   1.4043632e+00   1.6175925e+00   2.1298991e+00   6.3309258e-01   5.2133179e-01   5.6595908e-01   1.9078843e+00   7.4418186e-01   6.1830764e-01   3.4085233e-01   1.1006468e+00   9.1132198e-01   1.1010711e+00   0.0000000e+00   1.0458540e+00   9.3984267e-01   9.0166476e-01   5.0043084e-01   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2.0121983e-01   1.4695463e+00   1.5267750e+00   7.4395693e-01   6.3309258e-01   7.8890806e-01   1.4542932e+00   7.0008432e-01   4.5784410e-01   9.0166431e-01   8.0000160e-01   7.0008584e-01   3.0017653e-01   9.0005094e-01   1.1019505e+00   1.6144405e+00   4.0004442e-01   5.0436965e-01   4.1315633e-01   1.4012283e+00   6.3164729e-01   2.0121983e-01   8.0046685e-01   6.0219099e-01   6.0964597e-01   6.5724028e-01   5.6371422e-01   5.6838732e-01   7.0911112e-01   5.3914287e-01   6.0948506e-01   4.0246123e-01   5.6371422e-01   5.2133179e-01   1.1281267e+00   1.6745375e+00   8.1112984e-01   5.2167208e-01   7.4395693e-01   7.0016860e-01   5.0855778e-01   3.3813251e-01   9.0659977e-01   7.8895472e-01   5.0043842e-01   4.1209001e-01   1.2528048e+00   1.3020492e+00   9.3861512e-01   4.0127250e-01   1.0142766e+00   1.2362810e+00   9.0168933e-01   3.0490481e-01   7.0478886e-01   1.0010209e+00   9.0279223e-01   2.2608083e-01   7.4262850e-01   9.0055475e-01   1.4109657e+00   2.2573593e-01   7.8895472e-01   8.0492246e-01   1.2000668e+00   4.0363334e-01   4.1212852e-01   1.0039060e+00   4.5080200e-01   2.4195741e-01   7.0462844e-01   7.8985507e-01   3.0490481e-01   3.4085233e-01   6.0017982e-01   8.0928056e-01   6.0017665e-01   4.5784410e-01   7.4612718e-01   2.7992301e+00   3.6259865e-01   9.6953662e-01   6.4620889e-01   1.5401330e+00   1.4140789e+00   1.1281265e+00   2.0058560e+00   1.8949500e+00   1.4140515e+00   1.2396937e+00   8.0000239e-01   4.1317535e-01   1.8064092e+00   9.3310976e-01   2.1167364e+00   2.0181667e-01   1.7570696e+00   1.0143975e+00   6.1135434e-01   1.8661434e+00   1.8197089e+00   1.2632995e+00   8.1112909e-01   5.0126466e-01   8.0051115e-01   1.2632996e+00   1.5975200e+00   1.5266891e+00   5.0043084e-01   1.3452695e+00   1.3018553e+00   1.9314575e+00   1.2089192e+00   1.0777307e+00   1.5030978e+00   1.8949500e+00   8.5409862e-01   1.0151880e+00   1.4180463e+00   1.6742781e+00   1.4542907e+00   1.4853863e+00   1.8197089e+00   2.4725511e+00   1.8443040e+00   2.3518103e+00   1.6032169e+00   1.5066818e+00   1.9080163e+00   8.0923851e-01   9.4532171e-01   1.5109394e+00   1.6179000e+00   2.9132779e+00   2.9705619e+00   1.1020600e+00   2.0185049e+00   7.0633229e-01   2.9085831e+00   1.4001717e+00   1.8310931e+00   2.3325127e+00   1.3000908e+00   1.2016381e+00   1.5402579e+00   2.3143334e+00   2.5314248e+00   3.0393618e+00   1.5405402e+00   1.4018011e+00   1.3018553e+00   2.8185850e+00   1.4728279e+00   1.5248833e+00   1.1020506e+00   2.0036931e+00   1.8191683e+00   2.0009584e+00   9.1427000e-01   1.9534067e+00   1.8336293e+00   1.8020058e+00   1.4006178e+00   1.6026130e+00   1.3506710e+00   1.0116724e+00   6.3912709e-01   7.8890806e-01   1.2190319e+00   1.0776296e+00   8.0923926e-01   1.6740888e+00   1.5650163e+00   1.0798806e+00   9.0155438e-01   9.0417295e-01   6.4049114e-01   1.4685147e+00   6.4049114e-01   1.7843537e+00   4.5148429e-01   1.4324350e+00   6.8261201e-01   3.3813251e-01   1.5401311e+00   1.4852570e+00   9.3329055e-01   5.0043842e-01   2.0181667e-01   9.1424701e-01   9.3424697e-01   1.2633467e+00   1.2093243e+00   5.2167829e-01   1.0313359e+00   9.6574336e-01   1.5965767e+00   9.0168933e-01   7.7603846e-01   1.2016443e+00   1.5639785e+00   5.7832449e-01   7.7882758e-01   1.1074742e+00   1.3452311e+00   1.1281352e+00   1.1558746e+00   1.4852570e+00   1.1153247e+00   7.8895472e-01   5.0477564e-01   5.0855778e-01   1.0426636e+00   9.4532171e-01   7.3155911e-01   5.0476836e-01   1.3669148e+00   1.1910003e+00   8.5471446e-01   7.1629303e-01   1.1528553e+00   1.0777411e+00   9.0142636e-01   8.0046685e-01   7.1629168e-01   1.0032293e+00   9.1892413e-01   3.6452132e-01   5.6370994e-01   7.0176271e-01   1.4157327e+00   4.2362917e-01   7.0633229e-01   6.0964891e-01   1.0062544e+00   9.1554656e-01   6.0365948e-01   1.0235118e+00   6.1135434e-01   6.7626502e-01   7.5508853e-01   9.3308891e-01   7.1621884e-01   8.5403428e-01   6.5712608e-01   8.0245824e-01   6.3192325e-01   9.1132198e-01   8.6051414e-01   1.0242692e+00   1.0232576e+00   6.8685125e-01   1.5761415e+00   1.4407364e+00   9.0296858e-01   8.3689956e-01   6.3322667e-01   1.0451812e+00   1.5490134e+00   4.5847767e-01   1.6529028e+00   8.3916809e-01   1.2749306e+00   5.4219811e-01   7.0462697e-01   1.3611955e+00   1.3103292e+00   9.0792879e-01   9.1446896e-01   8.2421853e-01   7.1708289e-01   9.0683128e-01   1.1954899e+00   1.2957636e+00   6.3178534e-01   9.0508756e-01   8.7796615e-01   1.4198077e+00   7.2113820e-01   6.0427481e-01   1.0032443e+00   1.4501583e+00   4.5216167e-01   5.2491131e-01   9.1894698e-01   1.2738390e+00   9.4912864e-01   1.0207533e+00   1.3523292e+00   5.0043842e-01   4.1317535e-01   8.5403428e-01   7.0910969e-01   3.0482299e-01   4.0243965e-01   1.6491696e+00   1.8289467e+00   1.0060994e+00   6.1119267e-01   9.0142636e-01   1.6484371e+00   5.0126466e-01   6.0018299e-01   9.3308853e-01   4.2362917e-01   4.0363334e-01   5.2133802e-01   7.9153339e-01   1.0782107e+00   1.5275160e+00   5.2167829e-01   5.2167208e-01   6.9987517e-01   1.2633516e+00   5.2201750e-01   4.0127250e-01   5.0517282e-01   4.1212852e-01   5.2167829e-01   4.1210927e-01   7.1621748e-01   8.0093081e-01   6.3178782e-01   3.0922892e-01   7.0008735e-01   2.0061436e-01   3.6452132e-01   6.0035305e-01   4.1420960e-01   7.0096858e-01   6.3178782e-01   5.2132556e-01   3.0490481e-01   1.5634961e+00   1.6740875e+00   5.4219811e-01   5.8750389e-01   8.0245903e-01   1.5263478e+00   4.0004442e-01   6.1135434e-01   8.6051471e-01   5.0043842e-01   4.2270142e-01   3.0482299e-01   8.0967961e-01   1.0426513e+00   1.5757929e+00   3.3813251e-01   4.0127250e-01   5.0855778e-01   1.3133662e+00   7.1700909e-01   4.0125062e-01   5.2491734e-01   5.2167829e-01   5.2838320e-01   5.3943256e-01   6.0017665e-01   6.4620889e-01   6.8261201e-01   4.2270142e-01   3.0482299e-01   3.0026460e-01   7.0470867e-01   5.0477564e-01   1.1038840e+00   1.0010209e+00   4.0363334e-01   3.3808272e-01   1.2528049e+00   1.4182049e+00   9.2033101e-01   2.4195741e-01   1.2036925e+00   1.2362756e+00   6.3451734e-01   3.0482299e-01   5.2524663e-01   7.4335736e-01   7.4329414e-01   4.0125062e-01   5.2491131e-01   6.7636452e-01   1.1755449e+00   4.0127250e-01   6.3925756e-01   7.9148746e-01   9.1424659e-01   5.2491734e-01   4.1210927e-01   8.5437440e-01   1.2085435e-01   3.0026460e-01   4.0127250e-01   1.0010209e+00   4.0243965e-01   4.1317535e-01   3.0482299e-01   6.0444249e-01   3.3813251e-01   6.0964891e-01   9.0166431e-01   4.1212852e-01   7.8985507e-01   8.1719606e-01   2.1378157e+00   2.2009978e+00   5.0855077e-01   1.2175952e+00   3.0017653e-01   2.1167404e+00   6.0035621e-01   1.0597879e+00   1.5265797e+00   5.0517282e-01   5.2167829e-01   7.4329527e-01   1.5072282e+00   1.7227391e+00   2.2434054e+00   7.4335736e-01   6.3309258e-01   6.8161057e-01   2.0107350e+00   9.2867113e-01   7.5508853e-01   5.0517282e-01   1.2040344e+00   1.0178820e+00   1.2037520e+00   2.0181667e-01   1.1636098e+00   1.0621172e+00   1.0032443e+00   6.0000317e-01   8.0883841e-01   9.0668287e-01   5.0085236e-01   6.0964891e-01   7.4618926e-01   2.0118073e+00   2.0884859e+00   9.1424701e-01   1.1060939e+00   4.0243965e-01   2.0057764e+00   6.3178782e-01   9.1916394e-01   1.4198627e+00   6.1119267e-01   6.0219099e-01   6.3309012e-01   1.4134218e+00   1.6179000e+00   2.1265315e+00   6.3178534e-01   9.0506254e-01   1.0032443e+00   1.9078396e+00   6.5712608e-01   6.8261201e-01   6.0219099e-01   1.1003034e+00   9.0532049e-01   1.1001014e+00   5.0000761e-01   1.0433444e+00   9.1892454e-01   9.0002615e-01   5.6595908e-01   7.0470867e-01   6.1119558e-01   6.0017982e-01   5.0085236e-01   1.5275160e+00   1.6747664e+00   1.0434746e+00   5.2132556e-01   8.0533198e-01   1.5264802e+00   5.7609230e-01   4.1317535e-01   8.6051414e-01   5.7630313e-01   5.2524663e-01   4.1315633e-01   8.6054545e-01   1.0440350e+00   1.5412701e+00   4.1210927e-01   8.0250202e-01   9.1471442e-01   1.3130978e+00   3.0490481e-01   5.0043084e-01   5.7630313e-01   5.0043842e-01   3.3818226e-01   5.0043084e-01   6.3925756e-01   6.0948212e-01   4.1317535e-01   3.0482299e-01   7.0548283e-01   3.0490481e-01   2.2573593e-01   5.6394820e-01   1.3634093e+00   1.4858469e+00   8.1757693e-01   5.2201750e-01   9.1427000e-01   1.3523380e+00   6.0201716e-01   3.4342562e-01   7.1629168e-01   7.0096708e-01   6.0948212e-01   3.0490481e-01   7.0096708e-01   9.1424701e-01   1.4267554e+00   4.0127250e-01   4.1420960e-01   4.8342635e-01   1.2049539e+00   6.0964891e-01   1.1269424e-01   7.1621613e-01   4.1212852e-01   6.0018299e-01   5.3914287e-01   7.0548283e-01   5.2524663e-01   7.0105084e-01   5.0476836e-01   5.6371422e-01   3.0474106e-01   5.2491734e-01   6.0948212e-01   1.2000065e+00   2.0187441e+00   1.0498228e+00   2.2315584e+00   1.0000152e+00   1.8808952e+00   1.1286798e+00   7.5826453e-01   1.9821126e+00   1.9334872e+00   1.4094023e+00   9.7944085e-01   1.0090312e+00   3.0915245e-01   1.4094022e+00   1.7226330e+00   1.6785116e+00   8.2418071e-01   1.4544336e+00   1.4183053e+00   2.0448570e+00   1.3189240e+00   1.1989547e+00   1.6071563e+00   2.0162299e+00   9.7599312e-01   1.1287691e+00   1.5299044e+00   1.8304280e+00   1.5694554e+00   1.5966664e+00   1.9334872e+00   2.0448570e+00   1.2223853e+00   2.3135239e+00   3.0915245e-01   2.0415522e+00   1.2703001e+00   9.2351241e-01   2.1487275e+00   2.0854181e+00   1.4650300e+00   1.1157320e+00   8.0296037e-01   1.2013591e+00   1.4650276e+00   1.8684939e+00   1.6818191e+00   8.0245746e-01   1.5324961e+00   1.5271597e+00   2.1953922e+00   1.5071120e+00   1.3457716e+00   1.8029854e+00   2.0885102e+00   1.0837575e+00   1.2703001e+00   1.7133162e+00   1.9522053e+00   1.7369702e+00   1.6941963e+00   2.0286286e+00   1.1213597e+00   6.3912943e-01   1.9163315e+00   5.0855778e-01   1.1310337e+00   1.3142952e+00   6.0219099e-01   8.0046764e-01   7.2904264e-01   1.2366099e+00   1.4559030e+00   2.0467625e+00   7.7882758e-01   6.0184622e-01   6.0948800e-01   1.7296063e+00   1.2395260e+00   9.0668287e-01   8.0051036e-01   1.0231745e+00   1.0411548e+00   1.0543951e+00   5.2167829e-01   1.1356187e+00   1.2079042e+00   9.3439622e-01   4.2268438e-01   8.1719606e-01   1.2192978e+00   8.0046764e-01   1.3133662e+00   1.0434746e+00   8.3916809e-01   2.2573593e-01   5.0855077e-01   9.3848935e-01   9.0659977e-01   5.2167829e-01   7.0096858e-01   5.5450500e-01   1.0287902e+00   5.2133802e-01   8.4725834e-01   9.7599312e-01   8.0250123e-01   6.0018299e-01   5.6371422e-01   1.0171340e+00   3.0482299e-01   2.0181667e-01   6.0000317e-01   1.1079931e+00   2.0061436e-01   2.2573593e-01   5.0084481e-01   8.1683095e-01   5.2524663e-01   7.0096708e-01   1.0116865e+00   2.2278855e+00   7.0008584e-01   1.1298552e+00   1.6300950e+00   6.0017982e-01   5.0084481e-01   8.5403428e-01   1.6097507e+00   1.8284464e+00   2.3350903e+00   8.5406616e-01   7.1629168e-01   7.5508853e-01   2.1138813e+00   8.1683095e-01   8.2462252e-01   4.0246123e-01   1.3009222e+00   1.1139906e+00   1.3000951e+00   2.2608083e-01   1.2636227e+00   1.1315710e+00   1.1002119e+00   7.0088627e-01   9.0029018e-01   6.9600743e-01   3.1328089e-01   1.8661354e+00   1.1286798e+00   7.2044167e-01   1.9755679e+00   1.9314520e+00   1.3741466e+00   9.0645118e-01   6.0184622e-01   1.0001751e+00   1.3741498e+00   1.7083042e+00   1.6308665e+00   6.0201716e-01   1.4559030e+00   1.4140789e+00   2.0433026e+00   1.3131370e+00   1.1900969e+00   1.6049479e+00   2.0057464e+00   9.6691372e-01   1.1304042e+00   1.5237285e+00   1.7843627e+00   1.5639785e+00   1.5975352e+00   1.9314520e+00   8.2671175e-01   1.1543257e+00   1.2085435e-01   3.0474106e-01   7.0088627e-01   1.0144117e+00   1.3018103e+00   1.7709153e+00   7.0462844e-01   3.0482299e-01   7.0470867e-01   1.4857440e+00   8.1457587e-01   6.0948506e-01   3.3813251e-01   6.4049114e-01   7.4954884e-01   6.3925756e-01   5.0043084e-01   1.0090834e+00   8.7372177e-01   5.2838320e-01   2.0121983e-01   3.4342562e-01   7.3084171e-01   4.1315633e-01   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5.0476836e-01   8.7372177e-01   5.6618864e-01   5.0477564e-01   8.7240114e-01   5.3943256e-01   3.0474106e-01   5.2167208e-01   8.0879701e-01   5.0085236e-01   9.0279268e-01   5.2133802e-01   4.2362917e-01   6.0017982e-01   5.2838320e-01
diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-seuclidean-ml-iris.txt b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-seuclidean-ml-iris.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3e2759df30c14c1503818cc6a400a370e8fd8e89
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-seuclidean-ml-iris.txt
@@ -0,0 +1 @@
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diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-seuclidean-ml.txt b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-seuclidean-ml.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ce80cb1ead3f88bec0fbaf6d48cb4fc584e52168
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-seuclidean-ml.txt
@@ -0,0 +1 @@
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diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-spearman-ml.txt b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-spearman-ml.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b50fe3af1912d20aaa737eedc1b6e096a7005876
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/pdist-spearman-ml.txt
@@ -0,0 +1 @@
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diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/random-bool-data.txt b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/random-bool-data.txt
new file mode 100644
index 0000000000000000000000000000000000000000..df0d838f517f6c0afd8954ad87bc83886e0e3de4
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/random-bool-data.txt
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diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/random-double-data.txt b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/random-double-data.txt
new file mode 100644
index 0000000000000000000000000000000000000000..039ac506f5590f953ffc6598c11197d3fade2bbd
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/random-double-data.txt
@@ -0,0 +1,100 @@
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diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/random-int-data.txt b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/random-int-data.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4fd11b7509e65b01393a6af6125d1b304d524bd7
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/random-int-data.txt
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diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/random-uint-data.txt b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/random-uint-data.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c1ec7a5d64e540428507ee5a3358743b6c034ebc
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/random-uint-data.txt
@@ -0,0 +1,100 @@
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diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/selfdual-4d-polytope.txt b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/selfdual-4d-polytope.txt
new file mode 100644
index 0000000000000000000000000000000000000000..47ce4a7ae522fc2a2bbaa9d8ca285913b8ef0712
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/tests/data/selfdual-4d-polytope.txt
@@ -0,0 +1,27 @@
+# The facets of a self-dual 4-dim regular polytope
+# with 24 octahedron facets. Taken from cddlib.
+# Format b + Ax >= 0
+ 1  1  1  1  1
+ 1  1  1  1 -1
+ 1  1  1 -1  1
+ 1  1  1 -1 -1
+ 1  1 -1  1  1
+ 1  1 -1  1 -1
+ 1  1 -1 -1  1
+ 1  1 -1 -1 -1
+ 1 -1  1  1  1
+ 1 -1  1  1 -1
+ 1 -1  1 -1  1
+ 1 -1  1 -1 -1
+ 1 -1 -1  1  1
+ 1 -1 -1  1 -1
+ 1 -1 -1 -1  1
+ 1 -1 -1 -1 -1
+ 1  2  0  0  0
+ 1  0  2  0  0
+ 1  0  0  2  0
+ 1  0  0  0  2
+ 1 -2  0  0  0
+ 1  0 -2  0  0
+ 1  0  0 -2  0
+ 1  0  0  0 -2
diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/tests/test__plotutils.py b/venv/lib/python3.12/site-packages/scipy/spatial/tests/test__plotutils.py
new file mode 100644
index 0000000000000000000000000000000000000000..0e2553bf7ad56e97b567e5b334ccf17921f7f7f3
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/tests/test__plotutils.py
@@ -0,0 +1,91 @@
+import pytest
+import numpy as np
+from numpy.testing import assert_, assert_array_equal, assert_allclose
+
+try:
+    import matplotlib
+    matplotlib.rcParams['backend'] = 'Agg'
+    import matplotlib.pyplot as plt
+    has_matplotlib = True
+except Exception:
+    has_matplotlib = False
+
+from scipy.spatial import \
+     delaunay_plot_2d, voronoi_plot_2d, convex_hull_plot_2d, \
+     Delaunay, Voronoi, ConvexHull
+
+
+@pytest.mark.skipif(not has_matplotlib, reason="Matplotlib not available")
+class TestPlotting:
+    points = [(0,0), (0,1), (1,0), (1,1)]
+
+    def test_delaunay(self):
+        # Smoke test
+        fig = plt.figure()
+        obj = Delaunay(self.points)
+        s_before = obj.simplices.copy()
+        r = delaunay_plot_2d(obj, ax=fig.gca())
+        assert_array_equal(obj.simplices, s_before)  # shouldn't modify
+        assert_(r is fig)
+        delaunay_plot_2d(obj, ax=fig.gca())
+
+    def test_voronoi(self):
+        # Smoke test
+        fig = plt.figure()
+        obj = Voronoi(self.points)
+        r = voronoi_plot_2d(obj, ax=fig.gca())
+        assert_(r is fig)
+        voronoi_plot_2d(obj)
+        voronoi_plot_2d(obj, show_vertices=False)
+
+    def test_convex_hull(self):
+        # Smoke test
+        fig = plt.figure()
+        tri = ConvexHull(self.points)
+        r = convex_hull_plot_2d(tri, ax=fig.gca())
+        assert_(r is fig)
+        convex_hull_plot_2d(tri)
+
+    def test_gh_19653(self):
+        # aspect ratio sensitivity of voronoi_plot_2d
+        # infinite Voronoi edges
+        points = np.array([[245.059986986012, 10.971011721360075],
+                           [320.49044143557785, 10.970258360366753],
+                           [239.79023081978914, 13.108487516946218],
+                           [263.38325791238833, 12.93241352743668],
+                           [219.53334398353175, 13.346107628161008]])
+        vor = Voronoi(points)
+        fig = voronoi_plot_2d(vor)
+        ax = fig.gca()
+        infinite_segments = ax.collections[1].get_segments()
+        expected_segments = np.array([[[282.77256, -254.76904],
+                                       [282.729714, -4544.744698]],
+                                      [[282.77256014, -254.76904029],
+                                       [430.08561382, 4032.67658742]],
+                                      [[229.26733285,  -20.39957514],
+                                       [-168.17167404, -4291.92545966]],
+                                      [[289.93433364, 5151.40412217],
+                                       [330.40553385, 9441.18887532]]])
+        assert_allclose(infinite_segments, expected_segments)
+
+    def test_gh_19653_smaller_aspect(self):
+        # reasonable behavior for less extreme aspect
+        # ratio
+        points = np.array([[24.059986986012, 10.971011721360075],
+                           [32.49044143557785, 10.970258360366753],
+                           [23.79023081978914, 13.108487516946218],
+                           [26.38325791238833, 12.93241352743668],
+                           [21.53334398353175, 13.346107628161008]])
+        vor = Voronoi(points)
+        fig = voronoi_plot_2d(vor)
+        ax = fig.gca()
+        infinite_segments = ax.collections[1].get_segments()
+        expected_segments = np.array([[[28.274979, 8.335027],
+                                       [28.270463, -42.19763338]],
+                                      [[28.27497869, 8.33502697],
+                                       [43.73223829, 56.44555501]],
+                                      [[22.51805823, 11.8621754],
+                                       [-12.09266506, -24.95694485]],
+                                      [[29.53092448, 78.46952378],
+                                       [33.82572726, 128.81934455]]])
+        assert_allclose(infinite_segments, expected_segments)
diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/tests/test__procrustes.py b/venv/lib/python3.12/site-packages/scipy/spatial/tests/test__procrustes.py
new file mode 100644
index 0000000000000000000000000000000000000000..42a3c4d35bd55e2ffecefb691c805f517c56d6ca
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/tests/test__procrustes.py
@@ -0,0 +1,116 @@
+import numpy as np
+from numpy.testing import assert_allclose, assert_equal, assert_almost_equal
+from pytest import raises as assert_raises
+
+from scipy.spatial import procrustes
+
+
+class TestProcrustes:
+    def setup_method(self):
+        """creates inputs"""
+        # an L
+        self.data1 = np.array([[1, 3], [1, 2], [1, 1], [2, 1]], 'd')
+
+        # a larger, shifted, mirrored L
+        self.data2 = np.array([[4, -2], [4, -4], [4, -6], [2, -6]], 'd')
+
+        # an L shifted up 1, right 1, and with point 4 shifted an extra .5
+        # to the right
+        # pointwise distance disparity with data1: 3*(2) + (1 + 1.5^2)
+        self.data3 = np.array([[2, 4], [2, 3], [2, 2], [3, 2.5]], 'd')
+
+        # data4, data5 are standardized (trace(A*A') = 1).
+        # procrustes should return an identical copy if they are used
+        # as the first matrix argument.
+        shiftangle = np.pi / 8
+        self.data4 = np.array([[1, 0], [0, 1], [-1, 0],
+                              [0, -1]], 'd') / np.sqrt(4)
+        self.data5 = np.array([[np.cos(shiftangle), np.sin(shiftangle)],
+                              [np.cos(np.pi / 2 - shiftangle),
+                               np.sin(np.pi / 2 - shiftangle)],
+                              [-np.cos(shiftangle),
+                               -np.sin(shiftangle)],
+                              [-np.cos(np.pi / 2 - shiftangle),
+                               -np.sin(np.pi / 2 - shiftangle)]],
+                              'd') / np.sqrt(4)
+
+    def test_procrustes(self):
+        # tests procrustes' ability to match two matrices.
+        #
+        # the second matrix is a rotated, shifted, scaled, and mirrored version
+        # of the first, in two dimensions only
+        #
+        # can shift, mirror, and scale an 'L'?
+        a, b, disparity = procrustes(self.data1, self.data2)
+        assert_allclose(b, a)
+        assert_almost_equal(disparity, 0.)
+
+        # if first mtx is standardized, leaves first mtx unchanged?
+        m4, m5, disp45 = procrustes(self.data4, self.data5)
+        assert_equal(m4, self.data4)
+
+        # at worst, data3 is an 'L' with one point off by .5
+        m1, m3, disp13 = procrustes(self.data1, self.data3)
+        #assert_(disp13 < 0.5 ** 2)
+
+    def test_procrustes2(self):
+        # procrustes disparity should not depend on order of matrices
+        m1, m3, disp13 = procrustes(self.data1, self.data3)
+        m3_2, m1_2, disp31 = procrustes(self.data3, self.data1)
+        assert_almost_equal(disp13, disp31)
+
+        # try with 3d, 8 pts per
+        rand1 = np.array([[2.61955202, 0.30522265, 0.55515826],
+                         [0.41124708, -0.03966978, -0.31854548],
+                         [0.91910318, 1.39451809, -0.15295084],
+                         [2.00452023, 0.50150048, 0.29485268],
+                         [0.09453595, 0.67528885, 0.03283872],
+                         [0.07015232, 2.18892599, -1.67266852],
+                         [0.65029688, 1.60551637, 0.80013549],
+                         [-0.6607528, 0.53644208, 0.17033891]])
+
+        rand3 = np.array([[0.0809969, 0.09731461, -0.173442],
+                         [-1.84888465, -0.92589646, -1.29335743],
+                         [0.67031855, -1.35957463, 0.41938621],
+                         [0.73967209, -0.20230757, 0.52418027],
+                         [0.17752796, 0.09065607, 0.29827466],
+                         [0.47999368, -0.88455717, -0.57547934],
+                         [-0.11486344, -0.12608506, -0.3395779],
+                         [-0.86106154, -0.28687488, 0.9644429]])
+        res1, res3, disp13 = procrustes(rand1, rand3)
+        res3_2, res1_2, disp31 = procrustes(rand3, rand1)
+        assert_almost_equal(disp13, disp31)
+
+    def test_procrustes_shape_mismatch(self):
+        assert_raises(ValueError, procrustes,
+                      np.array([[1, 2], [3, 4]]),
+                      np.array([[5, 6, 7], [8, 9, 10]]))
+
+    def test_procrustes_empty_rows_or_cols(self):
+        empty = np.array([[]])
+        assert_raises(ValueError, procrustes, empty, empty)
+
+    def test_procrustes_no_variation(self):
+        assert_raises(ValueError, procrustes,
+                      np.array([[42, 42], [42, 42]]),
+                      np.array([[45, 45], [45, 45]]))
+
+    def test_procrustes_bad_number_of_dimensions(self):
+        # fewer dimensions in one dataset
+        assert_raises(ValueError, procrustes,
+                      np.array([1, 1, 2, 3, 5, 8]),
+                      np.array([[1, 2], [3, 4]]))
+
+        # fewer dimensions in both datasets
+        assert_raises(ValueError, procrustes,
+                      np.array([1, 1, 2, 3, 5, 8]),
+                      np.array([1, 1, 2, 3, 5, 8]))
+
+        # zero dimensions
+        assert_raises(ValueError, procrustes, np.array(7), np.array(11))
+
+        # extra dimensions
+        assert_raises(ValueError, procrustes,
+                      np.array([[[11], [7]]]),
+                      np.array([[[5, 13]]]))
+
diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/tests/test_distance.py b/venv/lib/python3.12/site-packages/scipy/spatial/tests/test_distance.py
new file mode 100644
index 0000000000000000000000000000000000000000..6634d2c695d587cc9568a6184200dc077b0355e5
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/tests/test_distance.py
@@ -0,0 +1,2297 @@
+#
+# Author: Damian Eads
+# Date: April 17, 2008
+#
+# Copyright (C) 2008 Damian Eads
+#
+# Redistribution and use in source and binary forms, with or without
+# modification, are permitted provided that the following conditions
+# are met:
+#
+# 1. Redistributions of source code must retain the above copyright
+#    notice, this list of conditions and the following disclaimer.
+#
+# 2. Redistributions in binary form must reproduce the above
+#    copyright notice, this list of conditions and the following
+#    disclaimer in the documentation and/or other materials provided
+#    with the distribution.
+#
+# 3. The name of the author may not be used to endorse or promote
+#    products derived from this software without specific prior
+#    written permission.
+#
+# THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS
+# OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+# WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+# ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
+# DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+# DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE
+# GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+# INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY,
+# WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+# NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+# SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+from functools import wraps, partial
+import os.path
+import sys
+import sysconfig
+import warnings
+import weakref
+
+import numpy as np
+from numpy.linalg import norm
+from numpy.testing import (verbose, assert_,
+                           assert_array_equal, assert_equal,
+                           assert_almost_equal, assert_allclose)
+import pytest
+
+import scipy.spatial.distance
+
+from scipy.spatial.distance import (
+    squareform, pdist, cdist, num_obs_y, num_obs_dm, is_valid_dm, is_valid_y,
+    _validate_vector, _METRICS_NAMES)
+
+# these were missing: chebyshev cityblock
+# jensenshannon  and seuclidean are referenced by string name.
+from scipy.spatial.distance import (braycurtis, canberra, chebyshev, cityblock,
+                                    correlation, cosine, dice, euclidean,
+                                    hamming, jaccard, jensenshannon, mahalanobis,
+                                    minkowski, rogerstanimoto,
+                                    russellrao, seuclidean,  # noqa: F401
+                                    sokalsneath, sqeuclidean, yule)
+from scipy._lib._util import _apply_over_batch
+from scipy.conftest import skip_xp_invalid_arg
+
+
+@pytest.fixture(params=_METRICS_NAMES, scope="session")
+def metric(request):
+    """
+    Fixture for all metrics in scipy.spatial.distance
+    """
+    return request.param
+
+
+_filenames = [
+              "cdist-X1.txt",
+              "cdist-X2.txt",
+              "iris.txt",
+              "pdist-boolean-inp.txt",
+              "pdist-chebyshev-ml-iris.txt",
+              "pdist-chebyshev-ml.txt",
+              "pdist-cityblock-ml-iris.txt",
+              "pdist-cityblock-ml.txt",
+              "pdist-correlation-ml-iris.txt",
+              "pdist-correlation-ml.txt",
+              "pdist-cosine-ml-iris.txt",
+              "pdist-cosine-ml.txt",
+              "pdist-double-inp.txt",
+              "pdist-euclidean-ml-iris.txt",
+              "pdist-euclidean-ml.txt",
+              "pdist-hamming-ml.txt",
+              "pdist-jaccard-ml.txt",
+              "pdist-jensenshannon-ml-iris.txt",
+              "pdist-jensenshannon-ml.txt",
+              "pdist-minkowski-3.2-ml-iris.txt",
+              "pdist-minkowski-3.2-ml.txt",
+              "pdist-minkowski-5.8-ml-iris.txt",
+              "pdist-seuclidean-ml-iris.txt",
+              "pdist-seuclidean-ml.txt",
+              "pdist-spearman-ml.txt",
+              "random-bool-data.txt",
+              "random-double-data.txt",
+              "random-int-data.txt",
+              "random-uint-data.txt",
+              ]
+
+_tdist = np.array([[0, 662, 877, 255, 412, 996],
+                      [662, 0, 295, 468, 268, 400],
+                      [877, 295, 0, 754, 564, 138],
+                      [255, 468, 754, 0, 219, 869],
+                      [412, 268, 564, 219, 0, 669],
+                      [996, 400, 138, 869, 669, 0]], dtype='double')
+
+_ytdist = squareform(_tdist)
+
+# A hashmap of expected output arrays for the tests. These arrays
+# come from a list of text files, which are read prior to testing.
+# Each test loads inputs and outputs from this dictionary.
+eo = {}
+
+
+def load_testing_files():
+    for fn in _filenames:
+        name = fn.replace(".txt", "").replace("-ml", "")
+        fqfn = os.path.join(os.path.dirname(__file__), 'data', fn)
+        fp = open(fqfn)
+        eo[name] = np.loadtxt(fp)
+        fp.close()
+    eo['pdist-boolean-inp'] = np.bool_(eo['pdist-boolean-inp'])
+    eo['random-bool-data'] = np.bool_(eo['random-bool-data'])
+    eo['random-float32-data'] = np.float32(eo['random-double-data'])
+    eo['random-int-data'] = np.long(eo['random-int-data'])
+    eo['random-uint-data'] = np.ulong(eo['random-uint-data'])
+
+
+load_testing_files()
+
+
+def _is_32bit():
+    return np.intp(0).itemsize < 8
+
+
+def _chk_asarrays(arrays, axis=None):
+    arrays = [np.asanyarray(a) for a in arrays]
+    if axis is None:
+        # np < 1.10 ravel removes subclass from arrays
+        arrays = [np.ravel(a) if a.ndim != 1 else a
+                  for a in arrays]
+        axis = 0
+    arrays = tuple(np.atleast_1d(a) for a in arrays)
+    if axis < 0:
+        if not all(a.ndim == arrays[0].ndim for a in arrays):
+            raise ValueError("array ndim must be the same for neg axis")
+        axis = range(arrays[0].ndim)[axis]
+    return arrays + (axis,)
+
+
+def _chk_weights(arrays, weights=None, axis=None,
+                 force_weights=False, simplify_weights=True,
+                 pos_only=False, neg_check=False,
+                 nan_screen=False, mask_screen=False,
+                 ddof=None):
+    chked = _chk_asarrays(arrays, axis=axis)
+    arrays, axis = chked[:-1], chked[-1]
+
+    simplify_weights = simplify_weights and not force_weights
+    if not force_weights and mask_screen:
+        force_weights = any(np.ma.getmask(a) is not np.ma.nomask for a in arrays)
+
+    if nan_screen:
+        has_nans = [np.isnan(np.sum(a)) for a in arrays]
+        if any(has_nans):
+            mask_screen = True
+            force_weights = True
+            arrays = tuple(np.ma.masked_invalid(a) if has_nan else a
+                           for a, has_nan in zip(arrays, has_nans))
+
+    if weights is not None:
+        weights = np.asanyarray(weights)
+    elif force_weights:
+        weights = np.ones(arrays[0].shape[axis])
+    else:
+        return arrays + (weights, axis)
+
+    if ddof:
+        weights = _freq_weights(weights)
+
+    if mask_screen:
+        weights = _weight_masked(arrays, weights, axis)
+
+    if not all(weights.shape == (a.shape[axis],) for a in arrays):
+        raise ValueError("weights shape must match arrays along axis")
+    if neg_check and (weights < 0).any():
+        raise ValueError("weights cannot be negative")
+
+    if pos_only:
+        pos_weights = np.nonzero(weights > 0)[0]
+        if pos_weights.size < weights.size:
+            arrays = tuple(np.take(a, pos_weights, axis=axis) for a in arrays)
+            weights = weights[pos_weights]
+    if simplify_weights and (weights == 1).all():
+        weights = None
+    return arrays + (weights, axis)
+
+
+def _freq_weights(weights):
+    if weights is None:
+        return weights
+    int_weights = weights.astype(int)
+    if (weights != int_weights).any():
+        raise ValueError(f"frequency (integer count-type) weights required {weights}")
+    return int_weights
+
+
+def _weight_masked(arrays, weights, axis):
+    if axis is None:
+        axis = 0
+    weights = np.asanyarray(weights)
+    for a in arrays:
+        axis_mask = np.ma.getmask(a)
+        if axis_mask is np.ma.nomask:
+            continue
+        if a.ndim > 1:
+            not_axes = tuple(i for i in range(a.ndim) if i != axis)
+            axis_mask = axis_mask.any(axis=not_axes)
+        weights *= 1 - axis_mask.astype(int)
+    return weights
+
+
+def _rand_split(arrays, weights, axis, split_per, seed=None):
+    # Coerce `arrays` to float64 if integer, to avoid nan-to-integer issues
+    arrays = [arr.astype(np.float64) if np.issubdtype(arr.dtype, np.integer)
+              else arr for arr in arrays]
+
+    # inverse operation for stats.collapse_weights
+    weights = np.array(weights, dtype=np.float64)  # modified inplace; need a copy
+    seeded_rand = np.random.RandomState(seed)
+
+    def mytake(a, ix, axis):
+        record = np.asanyarray(np.take(a, ix, axis=axis))
+        return record.reshape([a.shape[i] if i != axis else 1
+                               for i in range(a.ndim)])
+
+    n_obs = arrays[0].shape[axis]
+    assert all(a.shape[axis] == n_obs for a in arrays), \
+           "data must be aligned on sample axis"
+    for i in range(int(split_per) * n_obs):
+        split_ix = seeded_rand.randint(n_obs + i)
+        prev_w = weights[split_ix]
+        q = seeded_rand.rand()
+        weights[split_ix] = q * prev_w
+        weights = np.append(weights, (1. - q) * prev_w)
+        arrays = [np.append(a, mytake(a, split_ix, axis=axis),
+                            axis=axis) for a in arrays]
+    return arrays, weights
+
+
+assert_allclose_forgiving = partial(assert_allclose, atol=1e-5)
+
+
+def _rough_check(a, b, compare_assert=assert_allclose_forgiving,
+                  key=lambda x: x, w=None):
+    check_a = key(a)
+    check_b = key(b)
+    try:
+        if np.array(check_a != check_b).any():  # try strict equality for string types
+            compare_assert(check_a, check_b)
+    except AttributeError:  # masked array
+        compare_assert(check_a, check_b)
+    except (TypeError, ValueError):  # nested data structure
+        for a_i, b_i in zip(check_a, check_b):
+            _rough_check(a_i, b_i, compare_assert=compare_assert)
+
+# diff from test_stats:
+#  n_args=2, weight_arg='w', default_axis=None
+#  ma_safe = False, nan_safe = False
+def _weight_checked(fn, n_args=2, default_axis=None, key=lambda x: x, weight_arg='w',
+                    squeeze=True, silent=False,
+                    ones_test=True, const_test=True, dup_test=True,
+                    split_test=True, dud_test=True, ma_safe=False, ma_very_safe=False,
+                    nan_safe=False, split_per=1.0, seed=0,
+                    compare_assert=assert_allclose_forgiving):
+    """runs fn on its arguments 2 or 3 ways, checks that the results are the same,
+       then returns the same thing it would have returned before"""
+    @wraps(fn)
+    def wrapped(*args, **kwargs):
+        result = fn(*args, **kwargs)
+
+        arrays = args[:n_args]
+        rest = args[n_args:]
+        weights = kwargs.get(weight_arg, None)
+        axis = kwargs.get('axis', default_axis)
+
+        chked = _chk_weights(arrays, weights=weights, axis=axis,
+                             force_weights=True, mask_screen=True)
+        arrays, weights, axis = chked[:-2], chked[-2], chked[-1]
+        if squeeze:
+            arrays = [np.atleast_1d(a.squeeze()) for a in arrays]
+
+        try:
+            # WEIGHTS CHECK 1: EQUAL WEIGHTED OBSERVATIONS
+            args = tuple(arrays) + rest
+            if ones_test:
+                kwargs[weight_arg] = weights
+                _rough_check(result, fn(*args, **kwargs), key=key)
+            if const_test:
+                kwargs[weight_arg] = weights * 101.0
+                _rough_check(result, fn(*args, **kwargs), key=key)
+                kwargs[weight_arg] = weights * 0.101
+                try:
+                    _rough_check(result, fn(*args, **kwargs), key=key)
+                except Exception as e:
+                    raise type(e)((e, arrays, weights)) from e
+
+            # WEIGHTS CHECK 2: ADDL 0-WEIGHTED OBS
+            if dud_test:
+                # add randomly resampled rows, weighted at 0
+                dud_arrays, dud_weights = _rand_split(arrays, weights, axis,
+                                                      split_per=split_per, seed=seed)
+                dud_weights[:weights.size] = weights # not exactly 1 because of masked arrays  # noqa: E501
+                dud_weights[weights.size:] = 0
+                dud_args = tuple(dud_arrays) + rest
+                kwargs[weight_arg] = dud_weights
+                _rough_check(result, fn(*dud_args, **kwargs), key=key)
+                # increase the value of those 0-weighted rows
+                for a in dud_arrays:
+                    indexer = [slice(None)] * a.ndim
+                    indexer[axis] = slice(weights.size, None)
+                    indexer = tuple(indexer)
+                    a[indexer] = a[indexer] * 101
+                dud_args = tuple(dud_arrays) + rest
+                _rough_check(result, fn(*dud_args, **kwargs), key=key)
+                # set those 0-weighted rows to NaNs
+                for a in dud_arrays:
+                    indexer = [slice(None)] * a.ndim
+                    indexer[axis] = slice(weights.size, None)
+                    indexer = tuple(indexer)
+                    a[indexer] = a[indexer] * np.nan
+                if kwargs.get("nan_policy", None) == "omit" and nan_safe:
+                    dud_args = tuple(dud_arrays) + rest
+                    _rough_check(result, fn(*dud_args, **kwargs), key=key)
+                # mask out those nan values
+                if ma_safe:
+                    dud_arrays = [np.ma.masked_invalid(a) for a in dud_arrays]
+                    dud_args = tuple(dud_arrays) + rest
+                    _rough_check(result, fn(*dud_args, **kwargs), key=key)
+                    if ma_very_safe:
+                        kwargs[weight_arg] = None
+                        _rough_check(result, fn(*dud_args, **kwargs), key=key)
+                del dud_arrays, dud_args, dud_weights
+
+            # WEIGHTS CHECK 3: DUPLICATE DATA (DUMB SPLITTING)
+            if dup_test:
+                dup_arrays = [np.append(a, a, axis=axis) for a in arrays]
+                dup_weights = np.append(weights, weights) / 2.0
+                dup_args = tuple(dup_arrays) + rest
+                kwargs[weight_arg] = dup_weights
+                _rough_check(result, fn(*dup_args, **kwargs), key=key)
+                del dup_args, dup_arrays, dup_weights
+
+            # WEIGHT CHECK 3: RANDOM SPLITTING
+            if split_test and split_per > 0:
+                split = _rand_split(arrays, weights, axis,
+                                    split_per=split_per, seed=seed)
+                split_arrays, split_weights = split
+                split_args = tuple(split_arrays) + rest
+                kwargs[weight_arg] = split_weights
+                _rough_check(result, fn(*split_args, **kwargs), key=key)
+        except NotImplementedError as e:
+            # when some combination of arguments makes weighting impossible,
+            #  this is the desired response
+            if not silent:
+                warnings.warn(f"{fn.__name__} NotImplemented weights: {e}",
+                              stacklevel=3)
+        return result
+    return wrapped
+
+
+wcdist = _weight_checked(cdist, default_axis=1, squeeze=False)
+wcdist_no_const = _weight_checked(cdist, default_axis=1,
+                                  squeeze=False, const_test=False)
+wpdist = _weight_checked(pdist, default_axis=1, squeeze=False, n_args=1)
+wpdist_no_const = _weight_checked(pdist, default_axis=1, squeeze=False,
+                                  const_test=False, n_args=1)
+wrogerstanimoto = _weight_checked(rogerstanimoto)
+wmatching = whamming = _weight_checked(hamming, dud_test=False)
+wyule = _weight_checked(yule)
+wdice = _weight_checked(dice)
+wcityblock = _weight_checked(cityblock)
+wchebyshev = _weight_checked(chebyshev)
+wcosine = _weight_checked(cosine)
+wcorrelation = _weight_checked(correlation)
+wjaccard = _weight_checked(jaccard)
+weuclidean = _weight_checked(euclidean, const_test=False)
+wsqeuclidean = _weight_checked(sqeuclidean, const_test=False)
+wbraycurtis = _weight_checked(braycurtis)
+wcanberra = _weight_checked(canberra, const_test=False)
+wsokalsneath = _weight_checked(sokalsneath)
+wrussellrao = _weight_checked(russellrao)
+
+
+class TestCdist:
+
+    def setup_method(self):
+        self.rnd_eo_names = ['random-float32-data', 'random-int-data',
+                             'random-uint-data', 'random-double-data',
+                             'random-bool-data']
+        self.valid_upcasts = {'bool': [np.ulong, np.long, np.float32, np.float64],
+                              'uint': [np.long, np.float32, np.float64],
+                              'int': [np.float32, np.float64],
+                              'float32': [np.float64]}
+
+    def test_cdist_extra_args(self, metric):
+        # Tests that args and kwargs are correctly handled
+
+        X1 = [[1., 2., 3.], [1.2, 2.3, 3.4], [2.2, 2.3, 4.4]]
+        X2 = [[7., 5., 8.], [7.5, 5.8, 8.4], [5.5, 5.8, 4.4]]
+        kwargs = {"N0tV4l1D_p4raM": 3.14, "w": np.arange(3)}
+        args = [3.14] * 200
+
+        with pytest.raises(TypeError):
+            cdist(X1, X2, metric=metric, **kwargs)
+        with pytest.raises(TypeError):
+            cdist(X1, X2, metric=eval(metric), **kwargs)
+        with pytest.raises(TypeError):
+            cdist(X1, X2, metric="test_" + metric, **kwargs)
+        with pytest.raises(TypeError):
+            cdist(X1, X2, metric=metric, *args)
+        with pytest.raises(TypeError):
+            cdist(X1, X2, metric=eval(metric), *args)
+        with pytest.raises(TypeError):
+            cdist(X1, X2, metric="test_" + metric, *args)
+
+    def test_cdist_extra_args_custom(self):
+        # Tests that args and kwargs are correctly handled
+        # also for custom metric
+        def _my_metric(x, y, arg, kwarg=1, kwarg2=2):
+            return arg + kwarg + kwarg2
+
+        X1 = [[1., 2., 3.], [1.2, 2.3, 3.4], [2.2, 2.3, 4.4]]
+        X2 = [[7., 5., 8.], [7.5, 5.8, 8.4], [5.5, 5.8, 4.4]]
+        kwargs = {"N0tV4l1D_p4raM": 3.14, "w": np.arange(3)}
+        args = [3.14] * 200
+
+        with pytest.raises(TypeError):
+            cdist(X1, X2, _my_metric)
+        with pytest.raises(TypeError):
+            cdist(X1, X2, _my_metric, *args)
+        with pytest.raises(TypeError):
+            cdist(X1, X2, _my_metric, **kwargs)
+        with pytest.raises(TypeError):
+            cdist(X1, X2, _my_metric, kwarg=2.2, kwarg2=3.3)
+        with pytest.raises(TypeError):
+            cdist(X1, X2, _my_metric, 1, 2, kwarg=2.2)
+        with pytest.raises(TypeError):
+            cdist(X1, X2, _my_metric, 1, 2, kwarg=2.2)
+        with pytest.raises(TypeError):
+            cdist(X1, X2, _my_metric, 1.1, 2.2, 3.3)
+        with pytest.raises(TypeError):
+            cdist(X1, X2, _my_metric, 1.1, 2.2)
+        with pytest.raises(TypeError):
+            cdist(X1, X2, _my_metric, 1.1)
+        with pytest.raises(TypeError):
+            cdist(X1, X2, _my_metric, 1.1, kwarg=2.2, kwarg2=3.3)
+
+        # this should work
+        assert_allclose(cdist(X1, X2, metric=_my_metric,
+                              arg=1.1, kwarg2=3.3), 5.4)
+
+    def test_cdist_euclidean_random_unicode(self):
+        eps = 1e-15
+        X1 = eo['cdist-X1']
+        X2 = eo['cdist-X2']
+        Y1 = wcdist_no_const(X1, X2, 'euclidean')
+        Y2 = wcdist_no_const(X1, X2, 'test_euclidean')
+        assert_allclose(Y1, Y2, rtol=eps, verbose=verbose > 2)
+
+    @pytest.mark.parametrize("p", [0.1, 0.25, 1.0, 1.23,
+                                   2.0, 3.8, 4.6, np.inf])
+    def test_cdist_minkowski_random(self, p):
+        eps = 1e-13
+        X1 = eo['cdist-X1']
+        X2 = eo['cdist-X2']
+        Y1 = wcdist_no_const(X1, X2, 'minkowski', p=p)
+        Y2 = wcdist_no_const(X1, X2, 'test_minkowski', p=p)
+        assert_allclose(Y1, Y2, atol=0, rtol=eps, verbose=verbose > 2)
+
+    def test_cdist_cosine_random(self):
+        eps = 1e-14
+        X1 = eo['cdist-X1']
+        X2 = eo['cdist-X2']
+        Y1 = wcdist(X1, X2, 'cosine')
+
+        # Naive implementation
+        def norms(X):
+            return np.linalg.norm(X, axis=1).reshape(-1, 1)
+
+        Y2 = 1 - np.dot((X1 / norms(X1)), (X2 / norms(X2)).T)
+
+        assert_allclose(Y1, Y2, rtol=eps, verbose=verbose > 2)
+
+    def test_cdist_mahalanobis(self):
+        # 1-dimensional observations
+        x1 = np.array([[2], [3]])
+        x2 = np.array([[2], [5]])
+        dist = cdist(x1, x2, metric='mahalanobis')
+        assert_allclose(dist, [[0.0, np.sqrt(4.5)], [np.sqrt(0.5), np.sqrt(2)]])
+
+        # 2-dimensional observations
+        x1 = np.array([[0, 0], [-1, 0]])
+        x2 = np.array([[0, 2], [1, 0], [0, -2]])
+        dist = cdist(x1, x2, metric='mahalanobis')
+        rt2 = np.sqrt(2)
+        assert_allclose(dist, [[rt2, rt2, rt2], [2, 2 * rt2, 2]])
+
+        # Too few observations
+        with pytest.raises(ValueError):
+            cdist([[0, 1]], [[2, 3]], metric='mahalanobis')
+
+    def test_cdist_custom_notdouble(self):
+        class myclass:
+            pass
+
+        def _my_metric(x, y):
+            if not isinstance(x[0], myclass) or not isinstance(y[0], myclass):
+                raise ValueError("Type has been changed")
+            return 1.123
+        data = np.array([[myclass()]], dtype=object)
+        cdist_y = cdist(data, data, metric=_my_metric)
+        right_y = 1.123
+        assert_equal(cdist_y, right_y, verbose=verbose > 2)
+
+    def _check_calling_conventions(self, X1, X2, metric, eps=1e-07, **kwargs):
+        # helper function for test_cdist_calling_conventions
+        try:
+            y1 = cdist(X1, X2, metric=metric, **kwargs)
+            y2 = cdist(X1, X2, metric=eval(metric), **kwargs)
+            y3 = cdist(X1, X2, metric="test_" + metric, **kwargs)
+        except Exception as e:
+            e_cls = e.__class__
+            if verbose > 2:
+                print(e_cls.__name__)
+                print(e)
+            with pytest.raises(e_cls):
+                cdist(X1, X2, metric=metric, **kwargs)
+            with pytest.raises(e_cls):
+                cdist(X1, X2, metric=eval(metric), **kwargs)
+            with pytest.raises(e_cls):
+                cdist(X1, X2, metric="test_" + metric, **kwargs)
+        else:
+            assert_allclose(y1, y2, rtol=eps, verbose=verbose > 2)
+            assert_allclose(y1, y3, rtol=eps, verbose=verbose > 2)
+
+    def test_cdist_calling_conventions(self, metric):
+        # Ensures that specifying the metric with a str or scipy function
+        # gives the same behaviour (i.e. same result or same exception).
+        # NOTE: The correctness should be checked within each metric tests.
+        for eo_name in self.rnd_eo_names:
+            # subsampling input data to speed-up tests
+            # NOTE: num samples needs to be > than dimensions for mahalanobis
+            X1 = eo[eo_name][::5, ::-2]
+            X2 = eo[eo_name][1::5, ::2]
+            if verbose > 2:
+                print("testing: ", metric, " with: ", eo_name)
+            if (metric in {'dice', 'yule', 'rogerstanimoto', 'russellrao',
+                           'sokalsneath'}
+                and 'bool' not in eo_name):
+                # python version permits non-bools e.g. for fuzzy logic
+                continue
+            self._check_calling_conventions(X1, X2, metric)
+
+            # Testing built-in metrics with extra args
+            if metric == "seuclidean":
+                X12 = np.vstack([X1, X2]).astype(np.float64)
+                V = np.var(X12, axis=0, ddof=1)
+                self._check_calling_conventions(X1, X2, metric, V=V)
+            elif metric == "mahalanobis":
+                X12 = np.vstack([X1, X2]).astype(np.float64)
+                V = np.atleast_2d(np.cov(X12.T))
+                VI = np.array(np.linalg.inv(V).T)
+                self._check_calling_conventions(X1, X2, metric, VI=VI)
+
+    def test_cdist_dtype_equivalence(self, metric):
+        # Tests that the result is not affected by type up-casting
+        eps = 1e-07
+        tests = [(eo['random-bool-data'], self.valid_upcasts['bool']),
+                 (eo['random-uint-data'], self.valid_upcasts['uint']),
+                 (eo['random-int-data'], self.valid_upcasts['int']),
+                 (eo['random-float32-data'], self.valid_upcasts['float32'])]
+        for test in tests:
+            X1 = test[0][::5, ::-2]
+            X2 = test[0][1::5, ::2]
+            try:
+                y1 = cdist(X1, X2, metric=metric)
+            except Exception as e:
+                e_cls = e.__class__
+                if verbose > 2:
+                    print(e_cls.__name__)
+                    print(e)
+                for new_type in test[1]:
+                    X1new = new_type(X1)
+                    X2new = new_type(X2)
+                    with pytest.raises(e_cls):
+                        cdist(X1new, X2new, metric=metric)
+            else:
+                for new_type in test[1]:
+                    y2 = cdist(new_type(X1), new_type(X2), metric=metric)
+                    assert_allclose(y1, y2, rtol=eps, verbose=verbose > 2)
+
+    @pytest.mark.skipif(sysconfig.get_platform() == 'win-arm64', reason="numpy#29442")
+    def test_cdist_out(self, metric):
+        # Test that out parameter works properly
+        eps = 1e-15
+        X1 = eo['cdist-X1']
+        X2 = eo['cdist-X2']
+        out_r, out_c = X1.shape[0], X2.shape[0]
+
+        kwargs = dict()
+        if metric == 'minkowski':
+            kwargs['p'] = 1.23
+        out1 = np.empty((out_r, out_c), dtype=np.float64)
+        Y1 = cdist(X1, X2, metric, **kwargs)
+        Y2 = cdist(X1, X2, metric, out=out1, **kwargs)
+
+        # test that output is numerically equivalent
+        assert_allclose(Y1, Y2, rtol=eps, verbose=verbose > 2)
+
+        # test that Y_test1 and out1 are the same object
+        assert_(Y2 is out1)
+
+        # test for incorrect shape
+        out2 = np.empty((out_r-1, out_c+1), dtype=np.float64)
+        with pytest.raises(ValueError):
+            cdist(X1, X2, metric, out=out2, **kwargs)
+
+        # test for C-contiguous order
+        out3 = np.empty(
+            (2 * out_r, 2 * out_c), dtype=np.float64)[::2, ::2]
+        out4 = np.empty((out_r, out_c), dtype=np.float64, order='F')
+        with pytest.raises(ValueError):
+            cdist(X1, X2, metric, out=out3, **kwargs)
+        with pytest.raises(ValueError):
+            cdist(X1, X2, metric, out=out4, **kwargs)
+
+        # test for incorrect dtype
+        out5 = np.empty((out_r, out_c), dtype=np.int64)
+        with pytest.raises(ValueError):
+            cdist(X1, X2, metric, out=out5, **kwargs)
+
+    def test_striding(self, metric):
+        # test that striding is handled correct with calls to
+        # _copy_array_if_base_present
+        eps = 1e-15
+        X1 = eo['cdist-X1'][::2, ::2]
+        X2 = eo['cdist-X2'][::2, ::2]
+        X1_copy = X1.copy()
+        X2_copy = X2.copy()
+
+        # confirm equivalence
+        assert_equal(X1, X1_copy)
+        assert_equal(X2, X2_copy)
+        # confirm contiguity
+        assert_(not X1.flags.c_contiguous)
+        assert_(not X2.flags.c_contiguous)
+        assert_(X1_copy.flags.c_contiguous)
+        assert_(X2_copy.flags.c_contiguous)
+
+        kwargs = dict()
+        if metric == 'minkowski':
+            kwargs['p'] = 1.23
+        Y1 = cdist(X1, X2, metric, **kwargs)
+        Y2 = cdist(X1_copy, X2_copy, metric, **kwargs)
+        # test that output is numerically equivalent
+        assert_allclose(Y1, Y2, rtol=eps, verbose=verbose > 2)
+
+    def test_cdist_refcount(self, metric):
+        x1 = np.random.rand(10, 10)
+        x2 = np.random.rand(10, 10)
+
+        kwargs = dict()
+        if metric == 'minkowski':
+            kwargs['p'] = 1.23
+
+        out = cdist(x1, x2, metric=metric, **kwargs)
+
+        # Check reference counts aren't messed up. If we only hold weak
+        # references, the arrays should be deallocated.
+        weak_refs = [weakref.ref(v) for v in (x1, x2, out)]
+        del x1, x2, out
+
+        assert all(weak_ref() is None for weak_ref in weak_refs)
+
+
+class TestPdist:
+
+    def setup_method(self):
+        self.rnd_eo_names = ['random-float32-data', 'random-int-data',
+                             'random-uint-data', 'random-double-data',
+                             'random-bool-data']
+        self.valid_upcasts = {'bool': [np.ulong, np.long, np.float32, np.float64],
+                              'uint': [np.long, np.float32, np.float64],
+                              'int': [np.float32, np.float64],
+                              'float32': [np.float64]}
+
+    def test_pdist_extra_args(self, metric):
+        # Tests that args and kwargs are correctly handled
+        X1 = [[1., 2.], [1.2, 2.3], [2.2, 2.3]]
+        kwargs = {"N0tV4l1D_p4raM": 3.14, "w": np.arange(2)}
+        args = [3.14] * 200
+
+        with pytest.raises(TypeError):
+            pdist(X1, metric=metric, **kwargs)
+        with pytest.raises(TypeError):
+            pdist(X1, metric=eval(metric), **kwargs)
+        with pytest.raises(TypeError):
+            pdist(X1, metric="test_" + metric, **kwargs)
+        with pytest.raises(TypeError):
+            pdist(X1, metric=metric, *args)
+        with pytest.raises(TypeError):
+            pdist(X1, metric=eval(metric), *args)
+        with pytest.raises(TypeError):
+            pdist(X1, metric="test_" + metric, *args)
+
+    def test_pdist_extra_args_custom(self):
+        # Tests that args and kwargs are correctly handled
+        # also for custom metric
+        def _my_metric(x, y, arg, kwarg=1, kwarg2=2):
+            return arg + kwarg + kwarg2
+
+        X1 = [[1., 2.], [1.2, 2.3], [2.2, 2.3]]
+        kwargs = {"N0tV4l1D_p4raM": 3.14, "w": np.arange(2)}
+        args = [3.14] * 200
+
+        with pytest.raises(TypeError):
+            pdist(X1, _my_metric)
+        with pytest.raises(TypeError):
+            pdist(X1, _my_metric, *args)
+        with pytest.raises(TypeError):
+            pdist(X1, _my_metric, **kwargs)
+        with pytest.raises(TypeError):
+            pdist(X1, _my_metric, kwarg=2.2, kwarg2=3.3)
+        with pytest.raises(TypeError):
+            pdist(X1, _my_metric, 1, 2, kwarg=2.2)
+        with pytest.raises(TypeError):
+            pdist(X1, _my_metric, 1, 2, kwarg=2.2)
+        with pytest.raises(TypeError):
+            pdist(X1, _my_metric, 1.1, 2.2, 3.3)
+        with pytest.raises(TypeError):
+            pdist(X1, _my_metric, 1.1, 2.2)
+        with pytest.raises(TypeError):
+            pdist(X1, _my_metric, 1.1)
+        with pytest.raises(TypeError):
+            pdist(X1, _my_metric, 1.1, kwarg=2.2, kwarg2=3.3)
+
+        # these should work
+        assert_allclose(pdist(X1, metric=_my_metric,
+                              arg=1.1, kwarg2=3.3), 5.4)
+
+    def test_pdist_euclidean_random(self):
+        eps = 1e-07
+        X = eo['pdist-double-inp']
+        Y_right = eo['pdist-euclidean']
+        Y_test1 = wpdist_no_const(X, 'euclidean')
+        assert_allclose(Y_test1, Y_right, rtol=eps)
+
+    def test_pdist_euclidean_random_u(self):
+        eps = 1e-07
+        X = eo['pdist-double-inp']
+        Y_right = eo['pdist-euclidean']
+        Y_test1 = wpdist_no_const(X, 'euclidean')
+        assert_allclose(Y_test1, Y_right, rtol=eps)
+
+    def test_pdist_euclidean_random_float32(self):
+        eps = 1e-07
+        X = np.float32(eo['pdist-double-inp'])
+        Y_right = eo['pdist-euclidean']
+        Y_test1 = wpdist_no_const(X, 'euclidean')
+        assert_allclose(Y_test1, Y_right, rtol=eps)
+
+    def test_pdist_euclidean_random_nonC(self):
+        eps = 1e-07
+        X = eo['pdist-double-inp']
+        Y_right = eo['pdist-euclidean']
+        Y_test2 = wpdist_no_const(X, 'test_euclidean')
+        assert_allclose(Y_test2, Y_right, rtol=eps)
+
+    @pytest.mark.slow
+    def test_pdist_euclidean_iris_double(self):
+        eps = 1e-7
+        X = eo['iris']
+        Y_right = eo['pdist-euclidean-iris']
+        Y_test1 = wpdist_no_const(X, 'euclidean')
+        assert_allclose(Y_test1, Y_right, rtol=eps)
+
+    @pytest.mark.slow
+    def test_pdist_euclidean_iris_float32(self):
+        eps = 1e-5
+        X = np.float32(eo['iris'])
+        Y_right = eo['pdist-euclidean-iris']
+        Y_test1 = wpdist_no_const(X, 'euclidean')
+        assert_allclose(Y_test1, Y_right, rtol=eps, verbose=verbose > 2)
+
+    @pytest.mark.slow
+    def test_pdist_euclidean_iris_nonC(self):
+        # Test pdist(X, 'test_euclidean') [the non-C implementation] on the
+        # Iris data set.
+        eps = 1e-7
+        X = eo['iris']
+        Y_right = eo['pdist-euclidean-iris']
+        Y_test2 = wpdist_no_const(X, 'test_euclidean')
+        assert_allclose(Y_test2, Y_right, rtol=eps)
+
+    def test_pdist_seuclidean_random(self):
+        eps = 1e-7
+        X = eo['pdist-double-inp']
+        Y_right = eo['pdist-seuclidean']
+        Y_test1 = pdist(X, 'seuclidean')
+        assert_allclose(Y_test1, Y_right, rtol=eps)
+
+    def test_pdist_seuclidean_random_float32(self):
+        eps = 1e-7
+        X = np.float32(eo['pdist-double-inp'])
+        Y_right = eo['pdist-seuclidean']
+        Y_test1 = pdist(X, 'seuclidean')
+        assert_allclose(Y_test1, Y_right, rtol=eps)
+
+        # Check no error is raise when V has float32 dtype (#11171).
+        V = np.var(X, axis=0, ddof=1)
+        Y_test2 = pdist(X, 'seuclidean', V=V)
+        assert_allclose(Y_test2, Y_right, rtol=eps)
+
+    def test_pdist_seuclidean_random_nonC(self):
+        # Test pdist(X, 'test_sqeuclidean') [the non-C implementation]
+        eps = 1e-07
+        X = eo['pdist-double-inp']
+        Y_right = eo['pdist-seuclidean']
+        Y_test2 = pdist(X, 'test_seuclidean')
+        assert_allclose(Y_test2, Y_right, rtol=eps)
+
+    def test_pdist_seuclidean_iris(self):
+        eps = 1e-7
+        X = eo['iris']
+        Y_right = eo['pdist-seuclidean-iris']
+        Y_test1 = pdist(X, 'seuclidean')
+        assert_allclose(Y_test1, Y_right, rtol=eps)
+
+    def test_pdist_seuclidean_iris_float32(self):
+        # Tests pdist(X, 'seuclidean') on the Iris data set (float32).
+        eps = 1e-5
+        X = np.float32(eo['iris'])
+        Y_right = eo['pdist-seuclidean-iris']
+        Y_test1 = pdist(X, 'seuclidean')
+        assert_allclose(Y_test1, Y_right, rtol=eps)
+
+    def test_pdist_seuclidean_iris_nonC(self):
+        # Test pdist(X, 'test_seuclidean') [the non-C implementation] on the
+        # Iris data set.
+        eps = 1e-7
+        X = eo['iris']
+        Y_right = eo['pdist-seuclidean-iris']
+        Y_test2 = pdist(X, 'test_seuclidean')
+        assert_allclose(Y_test2, Y_right, rtol=eps)
+
+    def test_pdist_cosine_random(self):
+        eps = 1e-7
+        X = eo['pdist-double-inp']
+        Y_right = eo['pdist-cosine']
+        Y_test1 = wpdist(X, 'cosine')
+        assert_allclose(Y_test1, Y_right, rtol=eps)
+
+    def test_pdist_cosine_random_float32(self):
+        eps = 1e-7
+        X = np.float32(eo['pdist-double-inp'])
+        Y_right = eo['pdist-cosine']
+        Y_test1 = wpdist(X, 'cosine')
+        assert_allclose(Y_test1, Y_right, rtol=eps)
+
+    def test_pdist_cosine_random_nonC(self):
+        # Test pdist(X, 'test_cosine') [the non-C implementation]
+        eps = 1e-7
+        X = eo['pdist-double-inp']
+        Y_right = eo['pdist-cosine']
+        Y_test2 = wpdist(X, 'test_cosine')
+        assert_allclose(Y_test2, Y_right, rtol=eps)
+
+    @pytest.mark.slow
+    def test_pdist_cosine_iris(self):
+        eps = 1e-05
+        X = eo['iris']
+        Y_right = eo['pdist-cosine-iris']
+        Y_test1 = wpdist(X, 'cosine')
+        assert_allclose(Y_test1, Y_right, atol=eps)
+
+    @pytest.mark.slow
+    def test_pdist_cosine_iris_float32(self):
+        eps = 1e-05
+        X = np.float32(eo['iris'])
+        Y_right = eo['pdist-cosine-iris']
+        Y_test1 = wpdist(X, 'cosine')
+        assert_allclose(Y_test1, Y_right, atol=eps, verbose=verbose > 2)
+
+    @pytest.mark.slow
+    def test_pdist_cosine_iris_nonC(self):
+        eps = 1e-05
+        X = eo['iris']
+        Y_right = eo['pdist-cosine-iris']
+        Y_test2 = wpdist(X, 'test_cosine')
+        assert_allclose(Y_test2, Y_right, atol=eps)
+
+    def test_pdist_cosine_bounds(self):
+        # Test adapted from @joernhees's example at gh-5208: case where
+        # cosine distance used to be negative. XXX: very sensitive to the
+        # specific norm computation.
+        x = np.abs(np.random.RandomState(1337).rand(91))
+        X = np.vstack([x, x])
+        assert_(wpdist(X, 'cosine')[0] >= 0,
+                msg='cosine distance should be non-negative')
+
+    def test_pdist_cityblock_random(self):
+        eps = 1e-7
+        X = eo['pdist-double-inp']
+        Y_right = eo['pdist-cityblock']
+        Y_test1 = wpdist_no_const(X, 'cityblock')
+        assert_allclose(Y_test1, Y_right, rtol=eps)
+
+    def test_pdist_cityblock_random_float32(self):
+        eps = 1e-7
+        X = np.float32(eo['pdist-double-inp'])
+        Y_right = eo['pdist-cityblock']
+        Y_test1 = wpdist_no_const(X, 'cityblock')
+        assert_allclose(Y_test1, Y_right, rtol=eps)
+
+    def test_pdist_cityblock_random_nonC(self):
+        eps = 1e-7
+        X = eo['pdist-double-inp']
+        Y_right = eo['pdist-cityblock']
+        Y_test2 = wpdist_no_const(X, 'test_cityblock')
+        assert_allclose(Y_test2, Y_right, rtol=eps)
+
+    @pytest.mark.slow
+    def test_pdist_cityblock_iris(self):
+        eps = 1e-14
+        X = eo['iris']
+        Y_right = eo['pdist-cityblock-iris']
+        Y_test1 = wpdist_no_const(X, 'cityblock')
+        assert_allclose(Y_test1, Y_right, rtol=eps)
+
+    @pytest.mark.slow
+    def test_pdist_cityblock_iris_float32(self):
+        eps = 1e-5
+        X = np.float32(eo['iris'])
+        Y_right = eo['pdist-cityblock-iris']
+        Y_test1 = wpdist_no_const(X, 'cityblock')
+        assert_allclose(Y_test1, Y_right, rtol=eps, verbose=verbose > 2)
+
+    @pytest.mark.slow
+    def test_pdist_cityblock_iris_nonC(self):
+        # Test pdist(X, 'test_cityblock') [the non-C implementation] on the
+        # Iris data set.
+        eps = 1e-14
+        X = eo['iris']
+        Y_right = eo['pdist-cityblock-iris']
+        Y_test2 = wpdist_no_const(X, 'test_cityblock')
+        assert_allclose(Y_test2, Y_right, rtol=eps)
+
+    def test_pdist_correlation_random(self):
+        eps = 1e-7
+        X = eo['pdist-double-inp']
+        Y_right = eo['pdist-correlation']
+        Y_test1 = wpdist(X, 'correlation')
+        assert_allclose(Y_test1, Y_right, rtol=eps)
+
+    def test_pdist_correlation_random_float32(self):
+        eps = 1e-7
+        X = np.float32(eo['pdist-double-inp'])
+        Y_right = eo['pdist-correlation']
+        Y_test1 = wpdist(X, 'correlation')
+        assert_allclose(Y_test1, Y_right, rtol=eps)
+
+    def test_pdist_correlation_random_nonC(self):
+        eps = 1e-7
+        X = eo['pdist-double-inp']
+        Y_right = eo['pdist-correlation']
+        Y_test2 = wpdist(X, 'test_correlation')
+        assert_allclose(Y_test2, Y_right, rtol=eps)
+
+    @pytest.mark.slow
+    def test_pdist_correlation_iris(self):
+        eps = 1e-7
+        X = eo['iris']
+        Y_right = eo['pdist-correlation-iris']
+        Y_test1 = wpdist(X, 'correlation')
+        assert_allclose(Y_test1, Y_right, rtol=eps)
+
+    @pytest.mark.slow
+    def test_pdist_correlation_iris_float32(self):
+        eps = 1e-7
+        X = eo['iris']
+        Y_right = np.float32(eo['pdist-correlation-iris'])
+        Y_test1 = wpdist(X, 'correlation')
+        assert_allclose(Y_test1, Y_right, rtol=eps, verbose=verbose > 2)
+
+    @pytest.mark.slow
+    def test_pdist_correlation_iris_nonC(self):
+        if sys.maxsize > 2**32:
+            eps = 1e-7
+        else:
+            pytest.skip("see gh-16456")
+        X = eo['iris']
+        Y_right = eo['pdist-correlation-iris']
+        Y_test2 = wpdist(X, 'test_correlation')
+        assert_allclose(Y_test2, Y_right, rtol=eps)
+
+    @pytest.mark.parametrize("p", [0.1, 0.25, 1.0, 2.0, 3.2, np.inf])
+    def test_pdist_minkowski_random_p(self, p):
+        eps = 1e-13
+        X = eo['pdist-double-inp']
+        Y1 = wpdist_no_const(X, 'minkowski', p=p)
+        Y2 = wpdist_no_const(X, 'test_minkowski', p=p)
+        assert_allclose(Y1, Y2, atol=0, rtol=eps)
+
+    def test_pdist_minkowski_random(self):
+        eps = 1e-7
+        X = eo['pdist-double-inp']
+        Y_right = eo['pdist-minkowski-3.2']
+        Y_test1 = wpdist_no_const(X, 'minkowski', p=3.2)
+        assert_allclose(Y_test1, Y_right, rtol=eps)
+
+    def test_pdist_minkowski_random_float32(self):
+        eps = 1e-7
+        X = np.float32(eo['pdist-double-inp'])
+        Y_right = eo['pdist-minkowski-3.2']
+        Y_test1 = wpdist_no_const(X, 'minkowski', p=3.2)
+        assert_allclose(Y_test1, Y_right, rtol=eps)
+
+    def test_pdist_minkowski_random_nonC(self):
+        eps = 1e-7
+        X = eo['pdist-double-inp']
+        Y_right = eo['pdist-minkowski-3.2']
+        Y_test2 = wpdist_no_const(X, 'test_minkowski', p=3.2)
+        assert_allclose(Y_test2, Y_right, rtol=eps)
+
+    @pytest.mark.slow
+    def test_pdist_minkowski_3_2_iris(self):
+        eps = 1e-7
+        X = eo['iris']
+        Y_right = eo['pdist-minkowski-3.2-iris']
+        Y_test1 = wpdist_no_const(X, 'minkowski', p=3.2)
+        assert_allclose(Y_test1, Y_right, rtol=eps)
+
+    @pytest.mark.slow
+    def test_pdist_minkowski_3_2_iris_float32(self):
+        eps = 1e-5
+        X = np.float32(eo['iris'])
+        Y_right = eo['pdist-minkowski-3.2-iris']
+        Y_test1 = wpdist_no_const(X, 'minkowski', p=3.2)
+        assert_allclose(Y_test1, Y_right, rtol=eps)
+
+    @pytest.mark.slow
+    def test_pdist_minkowski_3_2_iris_nonC(self):
+        eps = 1e-7
+        X = eo['iris']
+        Y_right = eo['pdist-minkowski-3.2-iris']
+        Y_test2 = wpdist_no_const(X, 'test_minkowski', p=3.2)
+        assert_allclose(Y_test2, Y_right, rtol=eps)
+
+    @pytest.mark.slow
+    def test_pdist_minkowski_5_8_iris(self):
+        eps = 1e-7
+        X = eo['iris']
+        Y_right = eo['pdist-minkowski-5.8-iris']
+        Y_test1 = wpdist_no_const(X, 'minkowski', p=5.8)
+        assert_allclose(Y_test1, Y_right, rtol=eps)
+
+    @pytest.mark.slow
+    def test_pdist_minkowski_5_8_iris_float32(self):
+        eps = 1e-5
+        X = np.float32(eo['iris'])
+        Y_right = eo['pdist-minkowski-5.8-iris']
+        Y_test1 = wpdist_no_const(X, 'minkowski', p=5.8)
+        assert_allclose(Y_test1, Y_right, rtol=eps, verbose=verbose > 2)
+
+    @pytest.mark.slow
+    def test_pdist_minkowski_5_8_iris_nonC(self):
+        eps = 1e-7
+        X = eo['iris']
+        Y_right = eo['pdist-minkowski-5.8-iris']
+        Y_test2 = wpdist_no_const(X, 'test_minkowski', p=5.8)
+        assert_allclose(Y_test2, Y_right, rtol=eps)
+
+    def test_pdist_mahalanobis(self):
+        # 1-dimensional observations
+        x = np.array([2.0, 2.0, 3.0, 5.0]).reshape(-1, 1)
+        dist = pdist(x, metric='mahalanobis')
+        assert_allclose(dist, [0.0, np.sqrt(0.5), np.sqrt(4.5),
+                               np.sqrt(0.5), np.sqrt(4.5), np.sqrt(2.0)])
+
+        # 2-dimensional observations
+        x = np.array([[0, 0], [-1, 0], [0, 2], [1, 0], [0, -2]])
+        dist = pdist(x, metric='mahalanobis')
+        rt2 = np.sqrt(2)
+        assert_allclose(dist, [rt2, rt2, rt2, rt2, 2, 2 * rt2, 2, 2, 2 * rt2, 2])
+
+        # Too few observations
+        with pytest.raises(ValueError):
+            wpdist([[0, 1], [2, 3]], metric='mahalanobis')
+
+    def test_pdist_hamming_random(self):
+        eps = 1e-15
+        X = eo['pdist-boolean-inp']
+        Y_right = eo['pdist-hamming']
+        Y_test1 = wpdist(X, 'hamming')
+        assert_allclose(Y_test1, Y_right, rtol=eps)
+
+    def test_pdist_hamming_random_float32(self):
+        eps = 1e-15
+        X = np.float32(eo['pdist-boolean-inp'])
+        Y_right = eo['pdist-hamming']
+        Y_test1 = wpdist(X, 'hamming')
+        assert_allclose(Y_test1, Y_right, rtol=eps)
+
+    def test_pdist_hamming_random_nonC(self):
+        eps = 1e-15
+        X = eo['pdist-boolean-inp']
+        Y_right = eo['pdist-hamming']
+        Y_test2 = wpdist(X, 'test_hamming')
+        assert_allclose(Y_test2, Y_right, rtol=eps)
+
+    def test_pdist_dhamming_random(self):
+        eps = 1e-15
+        X = np.float64(eo['pdist-boolean-inp'])
+        Y_right = eo['pdist-hamming']
+        Y_test1 = wpdist(X, 'hamming')
+        assert_allclose(Y_test1, Y_right, rtol=eps)
+
+    def test_pdist_dhamming_random_float32(self):
+        eps = 1e-15
+        X = np.float32(eo['pdist-boolean-inp'])
+        Y_right = eo['pdist-hamming']
+        Y_test1 = wpdist(X, 'hamming')
+        assert_allclose(Y_test1, Y_right, rtol=eps)
+
+    def test_pdist_dhamming_random_nonC(self):
+        eps = 1e-15
+        X = np.float64(eo['pdist-boolean-inp'])
+        Y_right = eo['pdist-hamming']
+        Y_test2 = wpdist(X, 'test_hamming')
+        assert_allclose(Y_test2, Y_right, rtol=eps)
+
+    def test_pdist_jensenshannon_random(self):
+        eps = 1e-11
+        X = eo['pdist-double-inp']
+        Y_right = eo['pdist-jensenshannon']
+        Y_test1 = pdist(X, 'jensenshannon')
+        assert_allclose(Y_test1, Y_right, rtol=eps)
+
+    def test_pdist_jensenshannon_random_float32(self):
+        eps = 1e-8
+        X = np.float32(eo['pdist-double-inp'])
+        Y_right = eo['pdist-jensenshannon']
+        Y_test1 = pdist(X, 'jensenshannon')
+        assert_allclose(Y_test1, Y_right, rtol=eps, verbose=verbose > 2)
+
+    def test_pdist_jensenshannon_random_nonC(self):
+        eps = 1e-11
+        X = eo['pdist-double-inp']
+        Y_right = eo['pdist-jensenshannon']
+        Y_test2 = pdist(X, 'test_jensenshannon')
+        assert_allclose(Y_test2, Y_right, rtol=eps)
+
+    def test_pdist_jensenshannon_iris(self):
+        if _is_32bit():
+            # Test failing on 32-bit Linux on Azure otherwise, see gh-12810
+            eps = 2.5e-10
+        else:
+            eps = 1e-12
+
+        X = eo['iris']
+        Y_right = eo['pdist-jensenshannon-iris']
+        Y_test1 = pdist(X, 'jensenshannon')
+        assert_allclose(Y_test1, Y_right, atol=eps)
+
+    def test_pdist_jensenshannon_iris_float32(self):
+        eps = 1e-06
+        X = np.float32(eo['iris'])
+        Y_right = eo['pdist-jensenshannon-iris']
+        Y_test1 = pdist(X, 'jensenshannon')
+        assert_allclose(Y_test1, Y_right, atol=eps, verbose=verbose > 2)
+
+    def test_pdist_jensenshannon_iris_nonC(self):
+        eps = 5e-5
+        X = eo['iris']
+        Y_right = eo['pdist-jensenshannon-iris']
+        Y_test2 = pdist(X, 'test_jensenshannon')
+        assert_allclose(Y_test2, Y_right, rtol=eps)
+
+    def test_pdist_matching_mtica1(self):
+        # Test matching(*,*) with mtica example #1 (nums).
+        m = wmatching(np.array([1, 0, 1, 1, 0]),
+                      np.array([1, 1, 0, 1, 1]))
+        m2 = wmatching(np.array([1, 0, 1, 1, 0], dtype=bool),
+                       np.array([1, 1, 0, 1, 1], dtype=bool))
+        assert_allclose(m, 0.6, rtol=0, atol=1e-10)
+        assert_allclose(m2, 0.6, rtol=0, atol=1e-10)
+
+    def test_pdist_matching_mtica2(self):
+        # Test matching(*,*) with mtica example #2.
+        m = wmatching(np.array([1, 0, 1]),
+                     np.array([1, 1, 0]))
+        m2 = wmatching(np.array([1, 0, 1], dtype=bool),
+                      np.array([1, 1, 0], dtype=bool))
+        assert_allclose(m, 2 / 3, rtol=0, atol=1e-10)
+        assert_allclose(m2, 2 / 3, rtol=0, atol=1e-10)
+
+    def test_pdist_yule_mtica1(self):
+        m = wyule(np.array([1, 0, 1, 1, 0]),
+                  np.array([1, 1, 0, 1, 1]))
+        m2 = wyule(np.array([1, 0, 1, 1, 0], dtype=bool),
+                   np.array([1, 1, 0, 1, 1], dtype=bool))
+        if verbose > 2:
+            print(m)
+        assert_allclose(m, 2, rtol=0, atol=1e-10)
+        assert_allclose(m2, 2, rtol=0, atol=1e-10)
+
+    def test_pdist_yule_mtica2(self):
+        m = wyule(np.array([1, 0, 1]),
+                  np.array([1, 1, 0]))
+        m2 = wyule(np.array([1, 0, 1], dtype=bool),
+                   np.array([1, 1, 0], dtype=bool))
+        if verbose > 2:
+            print(m)
+        assert_allclose(m, 2, rtol=0, atol=1e-10)
+        assert_allclose(m2, 2, rtol=0, atol=1e-10)
+
+    def test_pdist_dice_mtica1(self):
+        m = wdice(np.array([1, 0, 1, 1, 0]),
+                  np.array([1, 1, 0, 1, 1]))
+        m2 = wdice(np.array([1, 0, 1, 1, 0], dtype=bool),
+                   np.array([1, 1, 0, 1, 1], dtype=bool))
+        if verbose > 2:
+            print(m)
+        assert_allclose(m, 3 / 7, rtol=0, atol=1e-10)
+        assert_allclose(m2, 3 / 7, rtol=0, atol=1e-10)
+
+    def test_pdist_dice_mtica2(self):
+        m = wdice(np.array([1, 0, 1]),
+                  np.array([1, 1, 0]))
+        m2 = wdice(np.array([1, 0, 1], dtype=bool),
+                   np.array([1, 1, 0], dtype=bool))
+        if verbose > 2:
+            print(m)
+        assert_allclose(m, 0.5, rtol=0, atol=1e-10)
+        assert_allclose(m2, 0.5, rtol=0, atol=1e-10)
+
+    def test_pdist_sokalsneath_mtica1(self):
+        m = sokalsneath(np.array([1, 0, 1, 1, 0]),
+                        np.array([1, 1, 0, 1, 1]))
+        m2 = sokalsneath(np.array([1, 0, 1, 1, 0], dtype=bool),
+                         np.array([1, 1, 0, 1, 1], dtype=bool))
+        if verbose > 2:
+            print(m)
+        assert_allclose(m, 3 / 4, rtol=0, atol=1e-10)
+        assert_allclose(m2, 3 / 4, rtol=0, atol=1e-10)
+
+    def test_pdist_sokalsneath_mtica2(self):
+        m = wsokalsneath(np.array([1, 0, 1]),
+                         np.array([1, 1, 0]))
+        m2 = wsokalsneath(np.array([1, 0, 1], dtype=bool),
+                          np.array([1, 1, 0], dtype=bool))
+        if verbose > 2:
+            print(m)
+        assert_allclose(m, 4 / 5, rtol=0, atol=1e-10)
+        assert_allclose(m2, 4 / 5, rtol=0, atol=1e-10)
+
+    def test_pdist_rogerstanimoto_mtica1(self):
+        m = wrogerstanimoto(np.array([1, 0, 1, 1, 0]),
+                            np.array([1, 1, 0, 1, 1]))
+        m2 = wrogerstanimoto(np.array([1, 0, 1, 1, 0], dtype=bool),
+                             np.array([1, 1, 0, 1, 1], dtype=bool))
+        if verbose > 2:
+            print(m)
+        assert_allclose(m, 3 / 4, rtol=0, atol=1e-10)
+        assert_allclose(m2, 3 / 4, rtol=0, atol=1e-10)
+
+    def test_pdist_rogerstanimoto_mtica2(self):
+        m = wrogerstanimoto(np.array([1, 0, 1]),
+                            np.array([1, 1, 0]))
+        m2 = wrogerstanimoto(np.array([1, 0, 1], dtype=bool),
+                             np.array([1, 1, 0], dtype=bool))
+        if verbose > 2:
+            print(m)
+        assert_allclose(m, 4 / 5, rtol=0, atol=1e-10)
+        assert_allclose(m2, 4 / 5, rtol=0, atol=1e-10)
+
+    def test_pdist_russellrao_mtica1(self):
+        m = wrussellrao(np.array([1, 0, 1, 1, 0]),
+                        np.array([1, 1, 0, 1, 1]))
+        m2 = wrussellrao(np.array([1, 0, 1, 1, 0], dtype=bool),
+                         np.array([1, 1, 0, 1, 1], dtype=bool))
+        if verbose > 2:
+            print(m)
+        assert_allclose(m, 3 / 5, rtol=0, atol=1e-10)
+        assert_allclose(m2, 3 / 5, rtol=0, atol=1e-10)
+
+    def test_pdist_russellrao_mtica2(self):
+        m = wrussellrao(np.array([1, 0, 1]),
+                        np.array([1, 1, 0]))
+        m2 = wrussellrao(np.array([1, 0, 1], dtype=bool),
+                         np.array([1, 1, 0], dtype=bool))
+        if verbose > 2:
+            print(m)
+        assert_allclose(m, 2 / 3, rtol=0, atol=1e-10)
+        assert_allclose(m2, 2 / 3, rtol=0, atol=1e-10)
+
+    @pytest.mark.slow
+    def test_pdist_canberra_match(self):
+        D = eo['iris']
+        if verbose > 2:
+            print(D.shape, D.dtype)
+        eps = 1e-15
+        y1 = wpdist_no_const(D, "canberra")
+        y2 = wpdist_no_const(D, "test_canberra")
+        assert_allclose(y1, y2, rtol=eps, verbose=verbose > 2)
+
+    def test_pdist_canberra_ticket_711(self):
+        # Test pdist(X, 'canberra') to see if Canberra gives the right result
+        # as reported on gh-1238.
+        eps = 1e-8
+        pdist_y = wpdist_no_const(([3.3], [3.4]), "canberra")
+        right_y = 0.01492537
+        assert_allclose(pdist_y, right_y, atol=eps, verbose=verbose > 2)
+
+    @skip_xp_invalid_arg
+    def test_pdist_custom_notdouble(self):
+        # tests that when using a custom metric the data type is not altered
+        class myclass:
+            pass
+
+        def _my_metric(x, y):
+            if not isinstance(x[0], myclass) or not isinstance(y[0], myclass):
+                raise ValueError("Type has been changed")
+            return 1.123
+        data = np.array([[myclass()], [myclass()]], dtype=object)
+        pdist_y = pdist(data, metric=_my_metric)
+        right_y = 1.123
+        assert_equal(pdist_y, right_y, verbose=verbose > 2)
+
+    def _check_calling_conventions(self, X, metric, eps=1e-07, **kwargs):
+        # helper function for test_pdist_calling_conventions
+        try:
+            y1 = pdist(X, metric=metric, **kwargs)
+            y2 = pdist(X, metric=eval(metric), **kwargs)
+            y3 = pdist(X, metric="test_" + metric, **kwargs)
+        except Exception as e:
+            e_cls = e.__class__
+            if verbose > 2:
+                print(e_cls.__name__)
+                print(e)
+            with pytest.raises(e_cls):
+                pdist(X, metric=metric, **kwargs)
+            with pytest.raises(e_cls):
+                pdist(X, metric=eval(metric), **kwargs)
+            with pytest.raises(e_cls):
+                pdist(X, metric="test_" + metric, **kwargs)
+        else:
+            assert_allclose(y1, y2, rtol=eps, verbose=verbose > 2)
+            assert_allclose(y1, y3, rtol=eps, verbose=verbose > 2)
+
+    def test_pdist_calling_conventions(self, metric):
+        # Ensures that specifying the metric with a str or scipy function
+        # gives the same behaviour (i.e. same result or same exception).
+        # NOTE: The correctness should be checked within each metric tests.
+        # NOTE: Extra args should be checked with a dedicated test
+        for eo_name in self.rnd_eo_names:
+            # subsampling input data to speed-up tests
+            # NOTE: num samples needs to be > than dimensions for mahalanobis
+            X = eo[eo_name][::5, ::2]
+            if verbose > 2:
+                print("testing: ", metric, " with: ", eo_name)
+            if metric in {'dice', 'yule', 'matching', 'rogerstanimoto', 'russellrao',
+                          'sokalsneath'} and 'bool' not in eo_name:
+                # python version permits non-bools e.g. for fuzzy logic
+                continue
+            self._check_calling_conventions(X, metric)
+
+            # Testing built-in metrics with extra args
+            if metric == "seuclidean":
+                V = np.var(X.astype(np.float64), axis=0, ddof=1)
+                self._check_calling_conventions(X, metric, V=V)
+            elif metric == "mahalanobis":
+                V = np.atleast_2d(np.cov(X.astype(np.float64).T))
+                VI = np.array(np.linalg.inv(V).T)
+                self._check_calling_conventions(X, metric, VI=VI)
+
+    def test_pdist_dtype_equivalence(self, metric):
+        # Tests that the result is not affected by type up-casting
+        eps = 1e-07
+        tests = [(eo['random-bool-data'], self.valid_upcasts['bool']),
+                 (eo['random-uint-data'], self.valid_upcasts['uint']),
+                 (eo['random-int-data'], self.valid_upcasts['int']),
+                 (eo['random-float32-data'], self.valid_upcasts['float32'])]
+        for test in tests:
+            X1 = test[0][::5, ::2]
+            try:
+                y1 = pdist(X1, metric=metric)
+            except Exception as e:
+                e_cls = e.__class__
+                if verbose > 2:
+                    print(e_cls.__name__)
+                    print(e)
+                for new_type in test[1]:
+                    X2 = new_type(X1)
+                    with pytest.raises(e_cls):
+                        pdist(X2, metric=metric)
+            else:
+                for new_type in test[1]:
+                    y2 = pdist(new_type(X1), metric=metric)
+                    assert_allclose(y1, y2, rtol=eps, verbose=verbose > 2)
+
+    def test_pdist_out(self, metric):
+        # Test that out parameter works properly
+        eps = 1e-15
+        X = eo['random-float32-data'][::5, ::2]
+        out_size = int((X.shape[0] * (X.shape[0] - 1)) / 2)
+
+        kwargs = dict()
+        if metric == 'minkowski':
+            kwargs['p'] = 1.23
+        out1 = np.empty(out_size, dtype=np.float64)
+        Y_right = pdist(X, metric, **kwargs)
+        Y_test1 = pdist(X, metric, out=out1, **kwargs)
+
+        # test that output is numerically equivalent
+        assert_allclose(Y_test1, Y_right, rtol=eps)
+
+        # test that Y_test1 and out1 are the same object
+        assert_(Y_test1 is out1)
+
+        # test for incorrect shape
+        out2 = np.empty(out_size + 3, dtype=np.float64)
+        with pytest.raises(ValueError):
+            pdist(X, metric, out=out2, **kwargs)
+
+        # test for (C-)contiguous output
+        out3 = np.empty(2 * out_size, dtype=np.float64)[::2]
+        with pytest.raises(ValueError):
+            pdist(X, metric, out=out3, **kwargs)
+
+        # test for incorrect dtype
+        out5 = np.empty(out_size, dtype=np.int64)
+        with pytest.raises(ValueError):
+            pdist(X, metric, out=out5, **kwargs)
+
+    def test_striding(self, metric):
+        # test that striding is handled correct with calls to
+        # _copy_array_if_base_present
+        eps = 1e-15
+        X = eo['random-float32-data'][::5, ::2]
+        X_copy = X.copy()
+
+        # confirm contiguity
+        assert_(not X.flags.c_contiguous)
+        assert_(X_copy.flags.c_contiguous)
+
+        kwargs = dict()
+        if metric == 'minkowski':
+            kwargs['p'] = 1.23
+        Y1 = pdist(X, metric, **kwargs)
+        Y2 = pdist(X_copy, metric, **kwargs)
+        # test that output is numerically equivalent
+        assert_allclose(Y1, Y2, rtol=eps, verbose=verbose > 2)
+
+class TestSomeDistanceFunctions:
+
+    def setup_method(self):
+        # 1D arrays
+        x = np.array([1.0, 2.0, 3.0])
+        y = np.array([1.0, 1.0, 5.0])
+
+        self.cases = [(x, y)]
+
+    def test_minkowski(self):
+        for x, y in self.cases:
+            dist1 = minkowski(x, y, p=1)
+            assert_almost_equal(dist1, 3.0)
+            dist1p5 = minkowski(x, y, p=1.5)
+            assert_almost_equal(dist1p5, (1.0 + 2.0**1.5)**(2. / 3))
+            dist2 = minkowski(x, y, p=2)
+            assert_almost_equal(dist2, 5.0 ** 0.5)
+            dist0p25 = minkowski(x, y, p=0.25)
+            assert_almost_equal(dist0p25, (1.0 + 2.0 ** 0.25) ** 4)
+
+        # Check that casting input to minimum scalar type doesn't affect result
+        # (issue #10262). This could be extended to more test inputs with
+        # np.min_scalar_type(np.max(input_matrix)).
+        a = np.array([352, 916])
+        b = np.array([350, 660])
+        assert_equal(minkowski(a, b),
+                     minkowski(a.astype('uint16'), b.astype('uint16')))
+
+    def test_euclidean(self):
+        for x, y in self.cases:
+            dist = weuclidean(x, y)
+            assert_almost_equal(dist, np.sqrt(5))
+
+    def test_sqeuclidean(self):
+        for x, y in self.cases:
+            dist = wsqeuclidean(x, y)
+            assert_almost_equal(dist, 5.0)
+
+    def test_cosine(self):
+        for x, y in self.cases:
+            dist = wcosine(x, y)
+            assert_almost_equal(dist, 1.0 - 18.0 / (np.sqrt(14) * np.sqrt(27)))
+
+    def test_cosine_output_dtype(self):
+        # Regression test for gh-19541
+        assert isinstance(wcorrelation([1, 1], [1, 1], centered=False), float)
+        assert isinstance(wcosine([1, 1], [1, 1]), float)
+
+    def test_correlation(self):
+        xm = np.array([-1.0, 0, 1.0])
+        ym = np.array([-4.0 / 3, -4.0 / 3, 5.0 - 7.0 / 3])
+        for x, y in self.cases:
+            dist = wcorrelation(x, y)
+            assert_almost_equal(dist, 1.0 - np.dot(xm, ym) / (norm(xm) * norm(ym)))
+
+    def test_correlation_positive(self):
+        # Regression test for gh-12320 (negative return value due to rounding
+        x = np.array([0., 0., 0., 0., 0., 0., -2., 0., 0., 0., -2., -2., -2.,
+                      0., -2., 0., -2., 0., 0., -1., -2., 0., 1., 0., 0., -2.,
+                      0., 0., -2., 0., -2., -2., -2., -2., -2., -2., 0.])
+        y = np.array([1., 1., 1., 1., 1., 1., -1., 1., 1., 1., -1., -1., -1.,
+                      1., -1., 1., -1., 1., 1., 0., -1., 1., 2., 1., 1., -1.,
+                      1., 1., -1., 1., -1., -1., -1., -1., -1., -1., 1.])
+        dist = correlation(x, y)
+        assert 0 <= dist <= 10 * np.finfo(np.float64).eps
+
+    @pytest.mark.filterwarnings('ignore:Casting complex')
+    @pytest.mark.parametrize("func", [correlation, cosine])
+    def test_corr_dep_complex(self, func):
+        x = [1+0j, 2+0j]
+        y = [3+0j, 4+0j]
+        with pytest.raises(TypeError, match="real"):
+            func(x, y)
+
+    def test_mahalanobis(self):
+        x = np.array([1.0, 2.0, 3.0])
+        y = np.array([1.0, 1.0, 5.0])
+        vi = np.array([[2.0, 1.0, 0.0], [1.0, 2.0, 1.0], [0.0, 1.0, 2.0]])
+        for x, y in self.cases:
+            dist = mahalanobis(x, y, vi)
+            assert_almost_equal(dist, np.sqrt(6.0))
+
+
+class TestSquareForm:
+    checked_dtypes = [np.float64, np.float32, np.int32, np.int8, bool]
+
+    def test_squareform_matrix(self):
+        for dtype in self.checked_dtypes:
+            self.check_squareform_matrix(dtype)
+
+    def test_squareform_vector(self):
+        for dtype in self.checked_dtypes:
+            self.check_squareform_vector(dtype)
+
+    def check_squareform_matrix(self, dtype):
+        A = np.zeros((0, 0), dtype=dtype)
+        rA = squareform(A)
+        assert_equal(rA.shape, (0,))
+        assert_equal(rA.dtype, dtype)
+
+        A = np.zeros((1, 1), dtype=dtype)
+        rA = squareform(A)
+        assert_equal(rA.shape, (0,))
+        assert_equal(rA.dtype, dtype)
+
+        A = np.array([[0, 4.2], [4.2, 0]], dtype=dtype)
+        rA = squareform(A)
+        assert_equal(rA.shape, (1,))
+        assert_equal(rA.dtype, dtype)
+        assert_array_equal(rA, np.array([4.2], dtype=dtype))
+
+    def check_squareform_vector(self, dtype):
+        v = np.zeros((0,), dtype=dtype)
+        rv = squareform(v)
+        assert_equal(rv.shape, (1, 1))
+        assert_equal(rv.dtype, dtype)
+        assert_array_equal(rv, [[0]])
+
+        v = np.array([8.3], dtype=dtype)
+        rv = squareform(v)
+        assert_equal(rv.shape, (2, 2))
+        assert_equal(rv.dtype, dtype)
+        assert_array_equal(rv, np.array([[0, 8.3], [8.3, 0]], dtype=dtype))
+
+    def test_squareform_multi_matrix(self):
+        for n in range(2, 5):
+            self.check_squareform_multi_matrix(n)
+
+    def check_squareform_multi_matrix(self, n):
+        X = np.random.rand(n, 4)
+        Y = wpdist_no_const(X)
+        assert_equal(len(Y.shape), 1)
+        A = squareform(Y)
+        Yr = squareform(A)
+        s = A.shape
+        k = 0
+        if verbose >= 3:
+            print(A.shape, Y.shape, Yr.shape)
+        assert_equal(len(s), 2)
+        assert_equal(len(Yr.shape), 1)
+        assert_equal(s[0], s[1])
+        for i in range(0, s[0]):
+            for j in range(i + 1, s[1]):
+                if i != j:
+                    assert_equal(A[i, j], Y[k])
+                    k += 1
+                else:
+                    assert_equal(A[i, j], 0)
+
+
+class TestNumObsY:
+
+    def test_num_obs_y_multi_matrix(self):
+        for n in range(2, 10):
+            X = np.random.rand(n, 4)
+            Y = wpdist_no_const(X)
+            assert_equal(num_obs_y(Y), n)
+
+    def test_num_obs_y_1(self):
+        # Tests num_obs_y(y) on a condensed distance matrix over 1
+        # observations. Expecting exception.
+        with pytest.raises(ValueError):
+            self.check_y(1)
+
+    def test_num_obs_y_2(self):
+        # Tests num_obs_y(y) on a condensed distance matrix over 2
+        # observations.
+        assert_(self.check_y(2))
+
+    def test_num_obs_y_3(self):
+        assert_(self.check_y(3))
+
+    def test_num_obs_y_4(self):
+        assert_(self.check_y(4))
+
+    def test_num_obs_y_5_10(self):
+        for i in range(5, 16):
+            self.minit(i)
+
+    def test_num_obs_y_2_100(self):
+        # Tests num_obs_y(y) on 100 improper condensed distance matrices.
+        # Expecting exception.
+        a = set()
+        for n in range(2, 16):
+            a.add(n * (n - 1) / 2)
+        for i in range(5, 105):
+            if i not in a:
+                with pytest.raises(ValueError):
+                    self.bad_y(i)
+
+    def minit(self, n):
+        assert_(self.check_y(n))
+
+    def bad_y(self, n):
+        y = np.random.rand(n)
+        return num_obs_y(y)
+
+    def check_y(self, n):
+        return num_obs_y(self.make_y(n)) == n
+
+    def make_y(self, n):
+        return np.random.rand((n * (n - 1)) // 2)
+
+
+class TestNumObsDM:
+
+    def test_num_obs_dm_multi_matrix(self):
+        for n in range(1, 10):
+            X = np.random.rand(n, 4)
+            Y = wpdist_no_const(X)
+            A = squareform(Y)
+            if verbose >= 3:
+                print(A.shape, Y.shape)
+            assert_equal(num_obs_dm(A), n)
+
+    def test_num_obs_dm_0(self):
+        # Tests num_obs_dm(D) on a 0x0 distance matrix. Expecting exception.
+        assert_(self.check_D(0))
+
+    def test_num_obs_dm_1(self):
+        # Tests num_obs_dm(D) on a 1x1 distance matrix.
+        assert_(self.check_D(1))
+
+    def test_num_obs_dm_2(self):
+        assert_(self.check_D(2))
+
+    def test_num_obs_dm_3(self):
+        assert_(self.check_D(2))
+
+    def test_num_obs_dm_4(self):
+        assert_(self.check_D(4))
+
+    def check_D(self, n):
+        return num_obs_dm(self.make_D(n)) == n
+
+    def make_D(self, n):
+        return np.random.rand(n, n)
+
+
+def is_valid_dm_throw(D):
+    return is_valid_dm(D, throw=True)
+
+
+class TestIsValidDM:
+
+    def test_is_valid_dm_improper_shape_1D_E(self):
+        D = np.zeros((5,), dtype=np.float64)
+        with pytest.raises(ValueError):
+            is_valid_dm_throw(D)
+
+    def test_is_valid_dm_improper_shape_1D_F(self):
+        D = np.zeros((5,), dtype=np.float64)
+        assert_equal(is_valid_dm(D), False)
+
+    def test_is_valid_dm_improper_shape_3D_E(self):
+        D = np.zeros((3, 3, 3), dtype=np.float64)
+        with pytest.raises(ValueError):
+            is_valid_dm_throw(D)
+
+    def test_is_valid_dm_improper_shape_3D_F(self):
+        D = np.zeros((3, 3, 3), dtype=np.float64)
+        assert_equal(is_valid_dm(D), False)
+
+    def test_is_valid_dm_nonzero_diagonal_E(self):
+        y = np.random.rand(10)
+        D = squareform(y)
+        for i in range(0, 5):
+            D[i, i] = 2.0
+        with pytest.raises(ValueError):
+            is_valid_dm_throw(D)
+
+    def test_is_valid_dm_nonzero_diagonal_F(self):
+        y = np.random.rand(10)
+        D = squareform(y)
+        for i in range(0, 5):
+            D[i, i] = 2.0
+        assert_equal(is_valid_dm(D), False)
+
+    def test_is_valid_dm_asymmetric_E(self):
+        y = np.random.rand(10)
+        D = squareform(y)
+        D[1, 3] = D[3, 1] + 1
+        with pytest.raises(ValueError):
+            is_valid_dm_throw(D)
+
+    def test_is_valid_dm_asymmetric_F(self):
+        y = np.random.rand(10)
+        D = squareform(y)
+        D[1, 3] = D[3, 1] + 1
+        assert_equal(is_valid_dm(D), False)
+
+    def test_is_valid_dm_correct_1_by_1(self):
+        D = np.zeros((1, 1), dtype=np.float64)
+        assert_equal(is_valid_dm(D), True)
+
+    def test_is_valid_dm_correct_2_by_2(self):
+        y = np.random.rand(1)
+        D = squareform(y)
+        assert_equal(is_valid_dm(D), True)
+
+    def test_is_valid_dm_correct_3_by_3(self):
+        y = np.random.rand(3)
+        D = squareform(y)
+        assert_equal(is_valid_dm(D), True)
+
+    def test_is_valid_dm_correct_4_by_4(self):
+        y = np.random.rand(6)
+        D = squareform(y)
+        assert_equal(is_valid_dm(D), True)
+
+    def test_is_valid_dm_correct_5_by_5(self):
+        y = np.random.rand(10)
+        D = squareform(y)
+        assert_equal(is_valid_dm(D), True)
+
+
+def is_valid_y_throw(y):
+    return is_valid_y(y, throw=True)
+
+
+class TestIsValidY:
+    # If test case name ends on "_E" then an exception is expected for the
+    # given input, if it ends in "_F" then False is expected for the is_valid_y
+    # check.  Otherwise the input is expected to be valid.
+
+    def test_is_valid_y_improper_shape_2D_E(self):
+        y = np.zeros((3, 3,), dtype=np.float64)
+        with pytest.raises(ValueError):
+            is_valid_y_throw(y)
+
+    def test_is_valid_y_improper_shape_2D_F(self):
+        y = np.zeros((3, 3,), dtype=np.float64)
+        assert_equal(is_valid_y(y), False)
+
+    def test_is_valid_y_improper_shape_3D_E(self):
+        y = np.zeros((3, 3, 3), dtype=np.float64)
+        with pytest.raises(ValueError):
+            is_valid_y_throw(y)
+
+    def test_is_valid_y_improper_shape_3D_F(self):
+        y = np.zeros((3, 3, 3), dtype=np.float64)
+        assert_equal(is_valid_y(y), False)
+
+    def test_is_valid_y_correct_2_by_2(self):
+        y = self.correct_n_by_n(2)
+        assert_equal(is_valid_y(y), True)
+
+    def test_is_valid_y_correct_3_by_3(self):
+        y = self.correct_n_by_n(3)
+        assert_equal(is_valid_y(y), True)
+
+    def test_is_valid_y_correct_4_by_4(self):
+        y = self.correct_n_by_n(4)
+        assert_equal(is_valid_y(y), True)
+
+    def test_is_valid_y_correct_5_by_5(self):
+        y = self.correct_n_by_n(5)
+        assert_equal(is_valid_y(y), True)
+
+    def test_is_valid_y_2_100(self):
+        a = set()
+        for n in range(2, 16):
+            a.add(n * (n - 1) / 2)
+        for i in range(5, 105):
+            if i not in a:
+                with pytest.raises(ValueError):
+                    self.bad_y(i)
+
+    def bad_y(self, n):
+        y = np.random.rand(n)
+        return is_valid_y(y, throw=True)
+
+    def correct_n_by_n(self, n):
+        y = np.random.rand((n * (n - 1)) // 2)
+        return y
+
+
+@pytest.mark.parametrize("p", [-10.0, -0.5, 0.0])
+def test_bad_p(p):
+    # Raise ValueError if p <=0.
+    with pytest.raises(ValueError):
+        minkowski([1, 2], [3, 4], p)
+    with pytest.raises(ValueError):
+        minkowski([1, 2], [3, 4], p, [1, 1])
+
+
+def test_sokalsneath_all_false():
+    # Regression test for ticket #876
+    with pytest.raises(ValueError):
+        sokalsneath([False, False, False], [False, False, False])
+
+
+def test_canberra():
+    # Regression test for ticket #1430.
+    assert_equal(wcanberra([1, 2, 3], [2, 4, 6]), 1)
+    assert_equal(wcanberra([1, 1, 0, 0], [1, 0, 1, 0]), 2)
+
+
+def test_braycurtis():
+    # Regression test for ticket #1430.
+    assert_almost_equal(wbraycurtis([1, 2, 3], [2, 4, 6]), 1. / 3, decimal=15)
+    assert_almost_equal(wbraycurtis([1, 1, 0, 0], [1, 0, 1, 0]), 0.5, decimal=15)
+
+
+def test_euclideans():
+    # Regression test for ticket #1328.
+    x1 = np.array([1, 1, 1])
+    x2 = np.array([0, 0, 0])
+
+    # Basic test of the calculation.
+    assert_almost_equal(wsqeuclidean(x1, x2), 3.0, decimal=14)
+    assert_almost_equal(weuclidean(x1, x2), np.sqrt(3), decimal=14)
+
+    # Another check, with random data.
+    rs = np.random.RandomState(1234567890)
+    x = rs.rand(10)
+    y = rs.rand(10)
+    d1 = weuclidean(x, y)
+    d2 = wsqeuclidean(x, y)
+    assert_almost_equal(d1**2, d2, decimal=14)
+
+
+def test_hamming_unequal_length():
+    # Regression test for gh-4290.
+    x = [0, 0, 1]
+    y = [1, 0, 1, 0]
+    # Used to give an AttributeError from ndarray.mean called on bool
+    with pytest.raises(ValueError):
+        whamming(x, y)
+
+
+def test_hamming_unequal_length_with_w():
+    u = [0, 0, 1]
+    v = [0, 0, 1]
+    w = [1, 0, 1, 0]
+    msg = "'w' should have the same length as 'u' and 'v'."
+    with pytest.raises(ValueError, match=msg):
+        whamming(u, v, w)
+
+
+def test_hamming_string_array():
+    # https://github.com/scikit-learn/scikit-learn/issues/4014
+    a = np.array(['eggs', 'spam', 'spam', 'eggs', 'spam', 'spam', 'spam',
+                  'spam', 'spam', 'spam', 'spam', 'eggs', 'eggs', 'spam',
+                  'eggs', 'eggs', 'eggs', 'eggs', 'eggs', 'spam'],
+                  dtype='|S4')
+    b = np.array(['eggs', 'spam', 'spam', 'eggs', 'eggs', 'spam', 'spam',
+                  'spam', 'spam', 'eggs', 'spam', 'eggs', 'spam', 'eggs',
+                  'spam', 'spam', 'eggs', 'spam', 'spam', 'eggs'],
+                  dtype='|S4')
+    desired = 0.45
+    assert_allclose(whamming(a, b), desired)
+
+
+def test_minkowski_w():
+    # Regression test for gh-8142.
+    arr_in = np.array([[83.33333333, 100., 83.33333333, 100., 36.,
+                        60., 90., 150., 24., 48.],
+                       [83.33333333, 100., 83.33333333, 100., 36.,
+                        60., 90., 150., 24., 48.]])
+    p0 = pdist(arr_in, metric='minkowski', p=1, w=None)
+    c0 = cdist(arr_in, arr_in, metric='minkowski', p=1, w=None)
+    p1 = pdist(arr_in, metric='minkowski', p=1)
+    c1 = cdist(arr_in, arr_in, metric='minkowski', p=1)
+
+    assert_allclose(p0, p1, rtol=1e-15)
+    assert_allclose(c0, c1, rtol=1e-15)
+
+
+def test_sqeuclidean_dtypes():
+    # Assert that sqeuclidean returns the right types of values.
+    # Integer types should be converted to floating for stability.
+    # Floating point types should be the same as the input.
+    x = [1, 2, 3]
+    y = [4, 5, 6]
+
+    for dtype in [np.int8, np.int16, np.int32, np.int64]:
+        d = wsqeuclidean(np.asarray(x, dtype=dtype), np.asarray(y, dtype=dtype))
+        assert_(np.issubdtype(d.dtype, np.floating))
+
+    for dtype in [np.uint8, np.uint16, np.uint32, np.uint64]:
+        umax = np.iinfo(dtype).max
+        d1 = wsqeuclidean([0], np.asarray([umax], dtype=dtype))
+        d2 = wsqeuclidean(np.asarray([umax], dtype=dtype), [0])
+
+        assert_equal(d1, d2)
+        assert_equal(d1, np.float64(umax)**2)
+
+    dtypes = [np.float32, np.float64, np.complex64, np.complex128]
+    for dtype in ['float16', 'float128']:
+        # These aren't present in older numpy versions; float128 may also not
+        # be present on all platforms.
+        if hasattr(np, dtype):
+            dtypes.append(getattr(np, dtype))
+
+    for dtype in dtypes:
+        d = wsqeuclidean(np.asarray(x, dtype=dtype), np.asarray(y, dtype=dtype))
+        assert_equal(d.dtype, dtype)
+
+
+def test_modifies_input(metric):
+    # test whether cdist or pdist modifies input arrays
+    X1 = np.asarray([[1., 2., 3.],
+                     [1.2, 2.3, 3.4],
+                     [2.2, 2.3, 4.4],
+                     [22.2, 23.3, 44.4]])
+    X1_copy = X1.copy()
+    cdist(X1, X1, metric)
+    pdist(X1, metric)
+    assert_array_equal(X1, X1_copy)
+
+
+def test_Xdist_deprecated_args(metric):
+    # testing both cdist and pdist deprecated warnings
+    X1 = np.asarray([[1., 2., 3.],
+                     [1.2, 2.3, 3.4],
+                     [2.2, 2.3, 4.4],
+                     [22.2, 23.3, 44.4]])
+
+    with pytest.raises(TypeError):
+        cdist(X1, X1, metric, 2.)
+
+    with pytest.raises(TypeError):
+        pdist(X1, metric, 2.)
+
+    for arg in ["p", "V", "VI"]:
+        kwargs = {arg: np.asarray(1.)}
+
+        if ((arg == "V" and metric == "seuclidean")
+                or (arg == "VI" and metric == "mahalanobis")
+                or (arg == "p" and metric == "minkowski")):
+            continue
+
+        with pytest.raises(TypeError):
+            cdist(X1, X1, metric, **kwargs)
+
+        with pytest.raises(TypeError):
+            pdist(X1, metric, **kwargs)
+
+
+def test_Xdist_non_negative_weights(metric):
+    X = eo['random-float32-data'][::5, ::2]
+    w = np.ones(X.shape[1])
+    w[::5] = -w[::5]
+
+    if metric in ['seuclidean', 'mahalanobis', 'jensenshannon']:
+        pytest.skip("not applicable")
+
+    for m in [metric, eval(metric), "test_" + metric]:
+        with pytest.raises(ValueError):
+            pdist(X, m, w=w)
+        with pytest.raises(ValueError):
+            cdist(X, X, m, w=w)
+
+
+def test__validate_vector():
+    x = [1, 2, 3]
+    y = _validate_vector(x)
+    assert_array_equal(y, x)
+
+    y = _validate_vector(x, dtype=np.float64)
+    assert_array_equal(y, x)
+    assert_equal(y.dtype, np.float64)
+
+    x = [1]
+    y = _validate_vector(x)
+    assert_equal(y.ndim, 1)
+    assert_equal(y, x)
+
+    x = 1
+    with pytest.raises(ValueError, match="Input vector should be 1-D"):
+        _validate_vector(x)
+
+    x = np.arange(5).reshape(1, -1, 1)
+    with pytest.raises(ValueError, match="Input vector should be 1-D"):
+        _validate_vector(x)
+
+    x = [[1, 2], [3, 4]]
+    with pytest.raises(ValueError, match="Input vector should be 1-D"):
+        _validate_vector(x)
+
+def test_yule_all_same():
+    # Test yule avoids a divide by zero when exactly equal
+    x = np.ones((2, 6), dtype=bool)
+    d = wyule(x[0], x[0])
+    assert d == 0.0
+
+    d = pdist(x, 'yule')
+    assert_equal(d, [0.0])
+
+    d = cdist(x[:1], x[:1], 'yule')
+    assert_equal(d, [[0.0]])
+
+
+def test_jensenshannon():
+    assert_almost_equal(jensenshannon([1.0, 0.0, 0.0], [0.0, 1.0, 0.0], 2.0),
+                        1.0)
+    assert_almost_equal(jensenshannon([1.0, 0.0], [0.5, 0.5]),
+                        0.46450140402245893)
+    assert_almost_equal(jensenshannon([1.0, 0.0, 0.0], [1.0, 0.0, 0.0]), 0.0)
+
+    assert_almost_equal(jensenshannon([[1.0, 2.0]], [[0.5, 1.5]], axis=0),
+                        [0.0, 0.0])
+    assert_almost_equal(jensenshannon([[1.0, 2.0]], [[0.5, 1.5]], axis=1),
+                        [0.0649045])
+    assert_almost_equal(jensenshannon([[1.0, 2.0]], [[0.5, 1.5]], axis=0,
+                                      keepdims=True), [[0.0, 0.0]])
+    assert_almost_equal(jensenshannon([[1.0, 2.0]], [[0.5, 1.5]], axis=1,
+                                      keepdims=True), [[0.0649045]])
+
+    a = np.array([[1, 2, 3, 4],
+                  [5, 6, 7, 8],
+                  [9, 10, 11, 12]])
+    b = np.array([[13, 14, 15, 16],
+                  [17, 18, 19, 20],
+                  [21, 22, 23, 24]])
+
+    assert_almost_equal(jensenshannon(a, b, axis=0),
+                        [0.1954288, 0.1447697, 0.1138377, 0.0927636])
+    assert_almost_equal(jensenshannon(a, b, axis=1),
+                        [0.1402339, 0.0399106, 0.0201815])
+
+
+def test_gh_17703():
+    arr_1 = np.array([1, 0, 0])
+    arr_2 = np.array([2, 0, 0])
+    expected = dice(arr_1, arr_2)
+    actual = pdist([arr_1, arr_2], metric='dice')
+    assert_allclose(actual, expected)
+    actual = cdist(np.atleast_2d(arr_1),
+                   np.atleast_2d(arr_2), metric='dice')
+    assert_allclose(actual, expected)
+
+
+def test_immutable_input(metric):
+    if metric in ("jensenshannon", "mahalanobis", "seuclidean"):
+        pytest.skip("not applicable")
+    x = np.arange(10, dtype=np.float64)
+    x.setflags(write=False)
+    getattr(scipy.spatial.distance, metric)(x, x, w=x)
+
+
+def test_gh_23109():
+    a = np.array([0, 0, 1, 1])
+    b = np.array([0, 1, 1, 0])
+    w = np.asarray([1.5, 1.2, 0.7, 1.3])
+    expected = yule(a, b, w=w)
+    assert_allclose(expected, 1.1954022988505748)
+    actual = cdist(np.atleast_2d(a),
+                   np.atleast_2d(b),
+                   metric='yule', w=w)
+    assert_allclose(actual, expected)
+
+
+class TestJaccard:
+
+    def test_pdist_jaccard_random(self):
+        eps = 1e-8
+        X = eo['pdist-boolean-inp']
+        Y_right = eo['pdist-jaccard']
+        Y_test1 = wpdist(X, 'jaccard')
+        assert_allclose(Y_test1, Y_right, rtol=eps)
+
+    def test_pdist_jaccard_random_float32(self):
+        eps = 1e-8
+        X = np.float32(eo['pdist-boolean-inp'])
+        Y_right = eo['pdist-jaccard']
+        Y_test1 = wpdist(X, 'jaccard')
+        assert_allclose(Y_test1, Y_right, rtol=eps)
+
+    def test_pdist_jaccard_random_nonC(self):
+        eps = 1e-8
+        X = eo['pdist-boolean-inp']
+        Y_right = eo['pdist-jaccard']
+        Y_test2 = wpdist(X, 'test_jaccard')
+        assert_allclose(Y_test2, Y_right, rtol=eps)
+
+    def test_pdist_djaccard_random(self):
+        eps = 1e-8
+        X = np.float64(eo['pdist-boolean-inp'])
+        Y_right = eo['pdist-jaccard']
+        Y_test1 = wpdist(X, 'jaccard')
+        assert_allclose(Y_test1, Y_right, rtol=eps)
+
+    def test_pdist_djaccard_random_float32(self):
+        eps = 1e-8
+        X = np.float32(eo['pdist-boolean-inp'])
+        Y_right = eo['pdist-jaccard']
+        Y_test1 = wpdist(X, 'jaccard')
+        assert_allclose(Y_test1, Y_right, rtol=eps)
+
+    def test_pdist_djaccard_allzeros(self):
+        eps = 1e-15
+        Y = pdist(np.zeros((5, 3)), 'jaccard')
+        assert_allclose(np.zeros(10), Y, rtol=eps)
+
+    def test_pdist_djaccard_random_nonC(self):
+        eps = 1e-8
+        X = np.float64(eo['pdist-boolean-inp'])
+        Y_right = eo['pdist-jaccard']
+        Y_test2 = wpdist(X, 'test_jaccard')
+        assert_allclose(Y_test2, Y_right, rtol=eps)
+
+    def test_pdist_djaccard_allzeros_nonC(self):
+        eps = 1e-15
+        Y = pdist(np.zeros((5, 3)), 'test_jaccard')
+        assert_allclose(np.zeros(10), Y, rtol=eps)
+
+    def test_pdist_jaccard_mtica1(self):
+        m = wjaccard(np.array([1, 0, 1, 1, 0]),
+                     np.array([1, 1, 0, 1, 1]))
+        m2 = wjaccard(np.array([1, 0, 1, 1, 0], dtype=bool),
+                      np.array([1, 1, 0, 1, 1], dtype=bool))
+        assert_allclose(m, 0.6, rtol=0, atol=1e-10)
+        assert_allclose(m2, 0.6, rtol=0, atol=1e-10)
+
+    def test_pdist_jaccard_mtica2(self):
+        m = wjaccard(np.array([1, 0, 1]),
+                     np.array([1, 1, 0]))
+        m2 = wjaccard(np.array([1, 0, 1], dtype=bool),
+                      np.array([1, 1, 0], dtype=bool))
+        assert_allclose(m, 2 / 3, rtol=0, atol=1e-10)
+        assert_allclose(m2, 2 / 3, rtol=0, atol=1e-10)
+
+    def test_non_01_input(self):
+        # Non-0/1 numeric input should be cast to bool before computation.
+        # See gh-21176.
+        x = np.array([-10, 2.5, 0])  # [True, True, False]
+        y = np.array([ 2,   -5, 2])  # [True, True, True]
+        eps = np.finfo(float).eps
+        assert_allclose(jaccard(x, y), 1/3, rtol=eps)
+        assert_allclose(cdist([x], [y], 'jaccard'), [[1/3]])
+        assert_allclose(pdist([x, y], 'jaccard'), [1/3])
+
+
+class TestChebyshev:
+
+    def test_pdist_chebyshev_random(self):
+        eps = 1e-8
+        X = eo['pdist-double-inp']
+        Y_right = eo['pdist-chebyshev']
+        Y_test1 = pdist(X, 'chebyshev')
+        assert_allclose(Y_test1, Y_right, rtol=eps)
+
+    def test_pdist_chebyshev_random_float32(self):
+        eps = 1e-7
+        X = np.float32(eo['pdist-double-inp'])
+        Y_right = eo['pdist-chebyshev']
+        Y_test1 = pdist(X, 'chebyshev')
+        assert_allclose(Y_test1, Y_right, rtol=eps, verbose=verbose > 2)
+
+    def test_pdist_chebyshev_random_nonC(self):
+        eps = 1e-8
+        X = eo['pdist-double-inp']
+        Y_right = eo['pdist-chebyshev']
+        Y_test2 = pdist(X, 'test_chebyshev')
+        assert_allclose(Y_test2, Y_right, rtol=eps)
+
+    def test_pdist_chebyshev_iris(self):
+        eps = 1e-14
+        X = eo['iris']
+        Y_right = eo['pdist-chebyshev-iris']
+        Y_test1 = pdist(X, 'chebyshev')
+        assert_allclose(Y_test1, Y_right, rtol=eps)
+
+    def test_pdist_chebyshev_iris_float32(self):
+        eps = 1e-5
+        X = np.float32(eo['iris'])
+        Y_right = eo['pdist-chebyshev-iris']
+        Y_test1 = pdist(X, 'chebyshev')
+        assert_allclose(Y_test1, Y_right, rtol=eps, verbose=verbose > 2)
+
+    def test_pdist_chebyshev_iris_nonC(self):
+        eps = 1e-14
+        X = eo['iris']
+        Y_right = eo['pdist-chebyshev-iris']
+        Y_test2 = pdist(X, 'test_chebyshev')
+        assert_allclose(Y_test2, Y_right, rtol=eps)
+
+    def test_weighted(self):
+        # Basic test for weighted Chebyshev.  Only components with non-zero
+        # weight participate in the 'max'.
+        x = [1, 2, 3]
+        y = [6, 5, 4]
+        w = [0, 1, 5]
+        assert_equal(chebyshev(x, y, w), 3)
+        assert_equal(pdist([x, y], 'chebyshev', w=w), [3])
+        assert_equal(cdist([x], [y], 'chebyshev', w=w), [[3]])
+
+    def test_zero_weight(self):
+        # If the weight is identically zero, the distance should be zero.
+        x = [1, 2, 3]
+        y = [6, 5, 4]
+        w = [0, 0, 0]
+        assert_equal(chebyshev(x, y, w), 0)
+        assert_equal(pdist([x, y], 'chebyshev', w=w), [0])
+        assert_equal(cdist([x], [y], 'chebyshev', w=w), [[0]])
+
+
+@pytest.mark.parametrize(
+    "func,p",
+    [
+        (minkowski, 1),
+        (minkowski, 2),
+        (minkowski, 3.5),
+        (minkowski, np.inf),
+        (euclidean, None),
+        (sqeuclidean, None),
+    ],
+)
+@pytest.mark.parametrize("weights", [True, False])
+def test_distance_nd(func, p, weights):
+    #  check that inputs broadcast correctly against a reference implementation
+    rng = np.random.default_rng(6738657865438)
+    ref_func = _apply_over_batch(('u', 1), ('v', 1), ('p', 1), ('w', 1))(func)
+
+    u = rng.random((5, 2, 4))
+    v = rng.random((2, 4))
+    w = rng.random(4) if weights else None
+    kwargs = {'w': w} if p is None else {'p': p, 'w': w}
+
+    res = func(u, v, **kwargs)
+    ref = ref_func(u, v, **kwargs)
+
+    assert_allclose(res, ref)
diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/tests/test_hausdorff.py b/venv/lib/python3.12/site-packages/scipy/spatial/tests/test_hausdorff.py
new file mode 100644
index 0000000000000000000000000000000000000000..45d89e868c8c2daca6e9c30973399fbbfc5d52fd
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/tests/test_hausdorff.py
@@ -0,0 +1,199 @@
+import numpy as np
+from numpy.testing import (assert_allclose,
+                           assert_array_equal,
+                           assert_equal)
+import pytest
+from scipy.spatial.distance import directed_hausdorff
+from scipy.spatial import distance
+from scipy._lib._util import check_random_state
+
+
+class TestHausdorff:
+    # Test various properties of the directed Hausdorff code.
+
+    def setup_method(self):
+        np.random.seed(1234)
+        random_angles = np.random.random(100) * np.pi * 2
+        random_columns = np.column_stack(
+            (random_angles, random_angles, np.zeros(100)))
+        random_columns[..., 0] = np.cos(random_columns[..., 0])
+        random_columns[..., 1] = np.sin(random_columns[..., 1])
+        random_columns_2 = np.column_stack(
+            (random_angles, random_angles, np.zeros(100)))
+        random_columns_2[1:, 0] = np.cos(random_columns_2[1:, 0]) * 2.0
+        random_columns_2[1:, 1] = np.sin(random_columns_2[1:, 1]) * 2.0
+        # move one point farther out so we don't have two perfect circles
+        random_columns_2[0, 0] = np.cos(random_columns_2[0, 0]) * 3.3
+        random_columns_2[0, 1] = np.sin(random_columns_2[0, 1]) * 3.3
+        self.path_1 = random_columns
+        self.path_2 = random_columns_2
+        self.path_1_4d = np.insert(self.path_1, 3, 5, axis=1)
+        self.path_2_4d = np.insert(self.path_2, 3, 27, axis=1)
+
+    def test_symmetry(self):
+        # Ensure that the directed (asymmetric) Hausdorff distance is
+        # actually asymmetric
+
+        forward = directed_hausdorff(self.path_1, self.path_2)[0]
+        reverse = directed_hausdorff(self.path_2, self.path_1)[0]
+        assert forward != reverse
+
+    def test_brute_force_comparison_forward(self):
+        # Ensure that the algorithm for directed_hausdorff gives the
+        # same result as the simple / brute force approach in the
+        # forward direction.
+        actual = directed_hausdorff(self.path_1, self.path_2)[0]
+        # brute force over rows:
+        expected = max(np.amin(distance.cdist(self.path_1, self.path_2),
+                               axis=1))
+        assert_allclose(actual, expected)
+
+    def test_brute_force_comparison_reverse(self):
+        # Ensure that the algorithm for directed_hausdorff gives the
+        # same result as the simple / brute force approach in the
+        # reverse direction.
+        actual = directed_hausdorff(self.path_2, self.path_1)[0]
+        # brute force over columns:
+        expected = max(np.amin(distance.cdist(self.path_1, self.path_2),
+                               axis=0))
+        assert_allclose(actual, expected)
+
+    def test_degenerate_case(self):
+        # The directed Hausdorff distance must be zero if both input
+        # data arrays match.
+        actual = directed_hausdorff(self.path_1, self.path_1)[0]
+        assert_allclose(actual, 0.0)
+
+    def test_2d_data_forward(self):
+        # Ensure that 2D data is handled properly for a simple case
+        # relative to brute force approach.
+        actual = directed_hausdorff(self.path_1[..., :2],
+                                    self.path_2[..., :2])[0]
+        expected = max(np.amin(distance.cdist(self.path_1[..., :2],
+                                              self.path_2[..., :2]),
+                               axis=1))
+        assert_allclose(actual, expected)
+
+    def test_4d_data_reverse(self):
+        # Ensure that 4D data is handled properly for a simple case
+        # relative to brute force approach.
+        actual = directed_hausdorff(self.path_2_4d, self.path_1_4d)[0]
+        # brute force over columns:
+        expected = max(np.amin(distance.cdist(self.path_1_4d, self.path_2_4d),
+                               axis=0))
+        assert_allclose(actual, expected)
+
+    def test_indices(self):
+        # Ensure that correct point indices are returned -- they should
+        # correspond to the Hausdorff pair
+        path_simple_1 = np.array([[-1,-12],[0,0], [1,1], [3,7], [1,2]])
+        path_simple_2 = np.array([[0,0], [1,1], [4,100], [10,9]])
+        actual = directed_hausdorff(path_simple_2, path_simple_1)[1:]
+        expected = (2, 3)
+        assert_array_equal(actual, expected)
+
+    def test_random_state(self):
+        # ensure that the global random state is not modified because
+        # the directed Hausdorff algorithm uses randomization
+        rs = check_random_state(None)
+        old_global_state = rs.get_state()
+        directed_hausdorff(self.path_1, self.path_2)
+        rs2 = check_random_state(None)
+        new_global_state = rs2.get_state()
+        assert_equal(new_global_state, old_global_state)
+
+    @pytest.mark.parametrize("seed", [None, 27870671, np.random.default_rng(177)])
+    def test_random_state_None_int(self, seed):
+        # check that seed values of None or int do not alter global
+        # random state
+        rs = check_random_state(None)
+        old_global_state = rs.get_state()
+        directed_hausdorff(self.path_1, self.path_2, seed)
+        rs2 = check_random_state(None)
+        new_global_state = rs2.get_state()
+        assert_equal(new_global_state, old_global_state)
+
+    def test_invalid_dimensions(self):
+        # Ensure that a ValueError is raised when the number of columns
+        # is not the same
+        rng = np.random.default_rng(189048172503940875434364128139223470523)
+        A = rng.random((3, 2))
+        B = rng.random((3, 5))
+        msg = r"need to have the same number of columns"
+        with pytest.raises(ValueError, match=msg):
+            directed_hausdorff(A, B)
+
+    # preserve use of legacy keyword `seed` during SPEC 7 transition
+    @pytest.mark.parametrize("A, B, seed, expected", [
+        # the two cases from gh-11332
+        ([(0,0)],
+         [(0,1), (0,0)],
+         np.int64(0),
+         (0.0, 0, 1)),
+        ([(0,0)],
+         [(0,1), (0,0)],
+         1,
+         (0.0, 0, 1)),
+        # gh-11332 cases with a Generator
+        ([(0,0)],
+         [(0,1), (0,0)],
+         np.random.default_rng(0),
+         (0.0, 0, 1)),
+        ([(0,0)],
+         [(0,1), (0,0)],
+         np.random.default_rng(1),
+         (0.0, 0, 1)),
+        # slightly more complex case
+        ([(-5, 3), (0,0)],
+         [(0,1), (0,0), (-5, 3)],
+         77098,
+         # the maximum minimum distance will
+         # be the last one found, but a unique
+         # solution is not guaranteed more broadly
+         (0.0, 1, 1)),
+        # repeated with Generator seeding
+        ([(-5, 3), (0,0)],
+         [(0,1), (0,0), (-5, 3)],
+         np.random.default_rng(77098),
+         # NOTE: using a Generator changes the
+         # indices but not the distance (unique solution
+         # not guaranteed)
+         (0.0, 0, 2)),
+    ])
+    def test_subsets(self, A, B, seed, expected, num_parallel_threads):
+        # verify fix for gh-11332
+        actual = directed_hausdorff(u=A, v=B, seed=seed)
+        # check distance
+        assert_allclose(actual[0], expected[0])
+        starting_seed = seed
+        if hasattr(seed, 'bit_generator'):
+            starting_seed = seed.bit_generator._seed_seq.entropy
+        # check indices
+        if num_parallel_threads == 1 or starting_seed != 77098:
+            assert actual[1:] == expected[1:]
+
+        if not isinstance(seed, np.random.RandomState):
+            # Check that new `rng` keyword is also accepted
+            actual = directed_hausdorff(u=A, v=B, rng=seed)
+            assert_allclose(actual[0], expected[0])
+
+
+@pytest.mark.xslow
+def test_massive_arr_overflow():
+    # on 64-bit systems we should be able to
+    # handle arrays that exceed the indexing
+    # size of a 32-bit signed integer
+    try:
+        import psutil
+    except ModuleNotFoundError:
+        pytest.skip("psutil required to check available memory")
+    if psutil.virtual_memory().available < 80*2**30:
+        # Don't run the test if there is less than 80 gig of RAM available.
+        pytest.skip('insufficient memory available to run this test')
+    size = int(3e9)
+    arr1 = np.zeros(shape=(size, 2))
+    arr2 = np.zeros(shape=(3, 2))
+    arr1[size - 1] = [5, 5]
+    actual = directed_hausdorff(u=arr1, v=arr2)
+    assert_allclose(actual[0], 7.0710678118654755)
+    assert_allclose(actual[1], size - 1)
diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/tests/test_kdtree.py b/venv/lib/python3.12/site-packages/scipy/spatial/tests/test_kdtree.py
new file mode 100644
index 0000000000000000000000000000000000000000..e86456e781f65adb9e43f0104a4ae92627f2109c
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/tests/test_kdtree.py
@@ -0,0 +1,1636 @@
+# Copyright Anne M. Archibald 2008
+# Released under the scipy license
+
+import itertools
+import os
+
+from numpy.testing import (assert_equal, assert_array_equal, assert_,
+                           assert_almost_equal, assert_array_almost_equal,
+                           assert_allclose)
+from pytest import raises as assert_raises
+import pytest
+import numpy as np
+from scipy._lib._testutils import _run_concurrent_barrier
+from scipy.spatial import KDTree, Rectangle, distance_matrix, cKDTree
+from scipy.spatial._ckdtree import cKDTreeNode
+from scipy.spatial import minkowski_distance, minkowski_distance_p
+from scipy.spatial.distance import cdist, minkowski
+from scipy.sparse import dok_array, coo_array, dok_matrix, coo_matrix
+
+
+@pytest.fixture(params=[KDTree, cKDTree])
+def kdtree_type(request):
+    return request.param
+
+
+def KDTreeTest(kls):
+    """Class decorator to create test cases for KDTree and cKDTree
+
+    Tests use the class variable ``kdtree_type`` as the tree constructor.
+    """
+    if not kls.__name__.startswith('_Test'):
+        raise RuntimeError("Expected a class name starting with _Test")
+
+    for tree in (KDTree, cKDTree):
+        test_name = kls.__name__[1:] + '_' + tree.__name__
+
+        if test_name in globals():
+            raise RuntimeError("Duplicated test name: " + test_name)
+
+        # Create a new sub-class with kdtree_type defined
+        test_case = type(test_name, (kls,), {'kdtree_type': tree})
+        globals()[test_name] = test_case
+    return kls
+
+
+def distance_box(a, b, p, boxsize):
+    diff = a - b
+    diff[diff > 0.5 * boxsize] -= boxsize
+    diff[diff < -0.5 * boxsize] += boxsize
+    d = minkowski(diff, 0, p)
+    return d
+
+class ConsistencyTests:
+    def distance(self, a, b, p):
+        return minkowski(a, b, p)
+
+    def test_nearest(self):
+        x = self.x
+        d, i = self.kdtree.query(x, 1)
+        assert_almost_equal(d**2, np.sum((x-self.data[i])**2))
+        eps = 1e-8
+        assert_(np.all(np.sum((self.data-x[np.newaxis, :])**2, axis=1) > d**2-eps))
+
+    def test_m_nearest(self):
+        x = self.x
+        m = self.m
+        dd, ii = self.kdtree.query(x, m)
+        d = np.amax(dd)
+        i = ii[np.argmax(dd)]
+        assert_almost_equal(d**2, np.sum((x-self.data[i])**2))
+        eps = 1e-8
+        assert_equal(
+            np.sum(np.sum((self.data-x[np.newaxis, :])**2, axis=1) < d**2+eps),
+            m,
+        )
+
+    def test_points_near(self):
+        x = self.x
+        d = self.d
+        dd, ii = self.kdtree.query(x, k=self.kdtree.n, distance_upper_bound=d)
+        eps = 1e-8
+        hits = 0
+        for near_d, near_i in zip(dd, ii):
+            if near_d == np.inf:
+                continue
+            hits += 1
+            assert_almost_equal(near_d**2, np.sum((x-self.data[near_i])**2))
+            assert_(near_d < d+eps, f"near_d={near_d:g} should be less than {d:g}")
+        assert_equal(np.sum(self.distance(self.data, x, 2) < d**2+eps), hits)
+
+    def test_points_near_l1(self):
+        x = self.x
+        d = self.d
+        dd, ii = self.kdtree.query(x, k=self.kdtree.n, p=1, distance_upper_bound=d)
+        eps = 1e-8
+        hits = 0
+        for near_d, near_i in zip(dd, ii):
+            if near_d == np.inf:
+                continue
+            hits += 1
+            assert_almost_equal(near_d, self.distance(x, self.data[near_i], 1))
+            assert_(near_d < d+eps, f"near_d={near_d:g} should be less than {d:g}")
+        assert_equal(np.sum(self.distance(self.data, x, 1) < d+eps), hits)
+
+    def test_points_near_linf(self):
+        x = self.x
+        d = self.d
+        dd, ii = self.kdtree.query(x, k=self.kdtree.n, p=np.inf, distance_upper_bound=d)
+        eps = 1e-8
+        hits = 0
+        for near_d, near_i in zip(dd, ii):
+            if near_d == np.inf:
+                continue
+            hits += 1
+            assert_almost_equal(near_d, self.distance(x, self.data[near_i], np.inf))
+            assert_(near_d < d+eps, f"near_d={near_d:g} should be less than {d:g}")
+        assert_equal(np.sum(self.distance(self.data, x, np.inf) < d+eps), hits)
+
+    def test_approx(self):
+        x = self.x
+        k = self.k
+        eps = 0.1
+        d_real, i_real = self.kdtree.query(x, k)
+        d, i = self.kdtree.query(x, k, eps=eps)
+        assert_(np.all(d <= d_real*(1+eps)))
+
+
+@KDTreeTest
+class _Test_random(ConsistencyTests):
+    def setup_method(self):
+        self.n = 100
+        self.m = 4
+        np.random.seed(1234)
+        self.data = np.random.randn(self.n, self.m)
+        self.kdtree = self.kdtree_type(self.data, leafsize=2)
+        self.x = np.random.randn(self.m)
+        self.d = 0.2
+        self.k = 10
+
+
+@KDTreeTest
+class _Test_random_far(_Test_random):
+    def setup_method(self):
+        super().setup_method()
+        self.x = np.random.randn(self.m)+10
+
+
+@KDTreeTest
+class _Test_small(ConsistencyTests):
+    def setup_method(self):
+        self.data = np.array([[0, 0, 0],
+                              [0, 0, 1],
+                              [0, 1, 0],
+                              [0, 1, 1],
+                              [1, 0, 0],
+                              [1, 0, 1],
+                              [1, 1, 0],
+                              [1, 1, 1]])
+        self.kdtree = self.kdtree_type(self.data)
+        self.n = self.kdtree.n
+        self.m = self.kdtree.m
+        np.random.seed(1234)
+        self.x = np.random.randn(3)
+        self.d = 0.5
+        self.k = 4
+
+    def test_nearest(self):
+        assert_array_equal(
+                self.kdtree.query((0, 0, 0.1), 1),
+                (0.1, 0))
+
+    def test_nearest_two(self):
+        assert_array_equal(
+                self.kdtree.query((0, 0, 0.1), 2),
+                ([0.1, 0.9], [0, 1]))
+
+
+@KDTreeTest
+class _Test_small_nonleaf(_Test_small):
+    def setup_method(self):
+        super().setup_method()
+        self.kdtree = self.kdtree_type(self.data, leafsize=1)
+
+
+class Test_vectorization_KDTree:
+    def setup_method(self):
+        self.data = np.array([[0, 0, 0],
+                              [0, 0, 1],
+                              [0, 1, 0],
+                              [0, 1, 1],
+                              [1, 0, 0],
+                              [1, 0, 1],
+                              [1, 1, 0],
+                              [1, 1, 1]])
+        self.kdtree = KDTree(self.data)
+
+    def test_single_query(self):
+        d, i = self.kdtree.query(np.array([0, 0, 0]))
+        assert_(isinstance(d, float))
+        assert_(np.issubdtype(i, np.signedinteger))
+
+    def test_vectorized_query(self):
+        d, i = self.kdtree.query(np.zeros((2, 4, 3)))
+        assert_equal(np.shape(d), (2, 4))
+        assert_equal(np.shape(i), (2, 4))
+
+    def test_single_query_multiple_neighbors(self):
+        s = 23
+        kk = self.kdtree.n+s
+        d, i = self.kdtree.query(np.array([0, 0, 0]), k=kk)
+        assert_equal(np.shape(d), (kk,))
+        assert_equal(np.shape(i), (kk,))
+        assert_(np.all(~np.isfinite(d[-s:])))
+        assert_(np.all(i[-s:] == self.kdtree.n))
+
+    def test_vectorized_query_multiple_neighbors(self):
+        s = 23
+        kk = self.kdtree.n+s
+        d, i = self.kdtree.query(np.zeros((2, 4, 3)), k=kk)
+        assert_equal(np.shape(d), (2, 4, kk))
+        assert_equal(np.shape(i), (2, 4, kk))
+        assert_(np.all(~np.isfinite(d[:, :, -s:])))
+        assert_(np.all(i[:, :, -s:] == self.kdtree.n))
+
+    def test_query_raises_for_k_none(self):
+        x = 1.0
+        with pytest.raises(ValueError, match="k must be an integer or*"):
+            self.kdtree.query(x, k=None)
+
+class Test_vectorization_cKDTree:
+    def setup_method(self):
+        self.data = np.array([[0, 0, 0],
+                              [0, 0, 1],
+                              [0, 1, 0],
+                              [0, 1, 1],
+                              [1, 0, 0],
+                              [1, 0, 1],
+                              [1, 1, 0],
+                              [1, 1, 1]])
+        self.kdtree = cKDTree(self.data)
+
+    def test_single_query(self):
+        d, i = self.kdtree.query([0, 0, 0])
+        assert_(isinstance(d, float))
+        assert_(isinstance(i, int))
+
+    def test_vectorized_query(self):
+        d, i = self.kdtree.query(np.zeros((2, 4, 3)))
+        assert_equal(np.shape(d), (2, 4))
+        assert_equal(np.shape(i), (2, 4))
+
+    def test_vectorized_query_noncontiguous_values(self):
+        np.random.seed(1234)
+        qs = np.random.randn(3, 1000).T
+        ds, i_s = self.kdtree.query(qs)
+        for q, d, i in zip(qs, ds, i_s):
+            assert_equal(self.kdtree.query(q), (d, i))
+
+    def test_single_query_multiple_neighbors(self):
+        s = 23
+        kk = self.kdtree.n+s
+        d, i = self.kdtree.query([0, 0, 0], k=kk)
+        assert_equal(np.shape(d), (kk,))
+        assert_equal(np.shape(i), (kk,))
+        assert_(np.all(~np.isfinite(d[-s:])))
+        assert_(np.all(i[-s:] == self.kdtree.n))
+
+    def test_vectorized_query_multiple_neighbors(self):
+        s = 23
+        kk = self.kdtree.n+s
+        d, i = self.kdtree.query(np.zeros((2, 4, 3)), k=kk)
+        assert_equal(np.shape(d), (2, 4, kk))
+        assert_equal(np.shape(i), (2, 4, kk))
+        assert_(np.all(~np.isfinite(d[:, :, -s:])))
+        assert_(np.all(i[:, :, -s:] == self.kdtree.n))
+
+class ball_consistency:
+    tol = 0.0
+
+    def distance(self, a, b, p):
+        return minkowski(a * 1.0, b * 1.0, p)
+
+    def test_in_ball(self):
+        x = np.atleast_2d(self.x)
+        d = np.broadcast_to(self.d, x.shape[:-1])
+        l = self.T.query_ball_point(x, self.d, p=self.p, eps=self.eps)
+        for i, ind in enumerate(l):
+            dist = self.distance(self.data[ind], x[i], self.p) - d[i]*(1.+self.eps)
+            norm = self.distance(self.data[ind], x[i], self.p) + d[i]*(1.+self.eps)
+            assert_array_equal(dist < self.tol * norm, True)
+
+    def test_found_all(self):
+        x = np.atleast_2d(self.x)
+        d = np.broadcast_to(self.d, x.shape[:-1])
+        l = self.T.query_ball_point(x, self.d, p=self.p, eps=self.eps)
+        for i, ind in enumerate(l):
+            c = np.ones(self.T.n, dtype=bool)
+            c[ind] = False
+            dist = self.distance(self.data[c], x[i], self.p) - d[i]/(1.+self.eps)
+            norm = self.distance(self.data[c], x[i], self.p) + d[i]/(1.+self.eps)
+            assert_array_equal(dist > -self.tol * norm, True)
+
+@KDTreeTest
+class _Test_random_ball(ball_consistency):
+    def setup_method(self):
+        n = 100
+        m = 4
+        np.random.seed(1234)
+        self.data = np.random.randn(n, m)
+        self.T = self.kdtree_type(self.data, leafsize=2)
+        self.x = np.random.randn(m)
+        self.p = 2.
+        self.eps = 0
+        self.d = 0.2
+
+
+@KDTreeTest
+class _Test_random_ball_periodic(ball_consistency):
+    def distance(self, a, b, p):
+        return distance_box(a, b, p, 1.0)
+
+    def setup_method(self):
+        n = 10000
+        m = 4
+        np.random.seed(1234)
+        self.data = np.random.uniform(size=(n, m))
+        self.T = self.kdtree_type(self.data, leafsize=2, boxsize=1)
+        self.x = np.full(m, 0.1)
+        self.p = 2.
+        self.eps = 0
+        self.d = 0.2
+
+    def test_in_ball_outside(self):
+        l = self.T.query_ball_point(self.x + 1.0, self.d, p=self.p, eps=self.eps)
+        for i in l:
+            assert_(self.distance(self.data[i], self.x, self.p) <= self.d*(1.+self.eps))
+        l = self.T.query_ball_point(self.x - 1.0, self.d, p=self.p, eps=self.eps)
+        for i in l:
+            assert_(self.distance(self.data[i], self.x, self.p) <= self.d*(1.+self.eps))
+
+    def test_found_all_outside(self):
+        c = np.ones(self.T.n, dtype=bool)
+        l = self.T.query_ball_point(self.x + 1.0, self.d, p=self.p, eps=self.eps)
+        c[l] = False
+        assert np.all(
+            self.distance(self.data[c], self.x, self.p) >= self.d/(1.+self.eps)
+        )
+
+        l = self.T.query_ball_point(self.x - 1.0, self.d, p=self.p, eps=self.eps)
+        c[l] = False
+        assert np.all(
+            self.distance(self.data[c], self.x, self.p) >= self.d/(1.+self.eps)
+        )
+
+
+@KDTreeTest
+class _Test_random_ball_largep_issue9890(ball_consistency):
+
+    # allow some roundoff errors due to numerical issues
+    tol = 1e-13
+
+    def setup_method(self):
+        n = 1000
+        m = 2
+        np.random.seed(123)
+        self.data = np.random.randint(100, 1000, size=(n, m))
+        self.T = self.kdtree_type(self.data)
+        self.x = self.data
+        self.p = 100
+        self.eps = 0
+        self.d = 10
+
+
+@KDTreeTest
+class _Test_random_ball_approx(_Test_random_ball):
+
+    def setup_method(self):
+        super().setup_method()
+        self.eps = 0.1
+
+
+@KDTreeTest
+class _Test_random_ball_approx_periodic(_Test_random_ball):
+
+    def setup_method(self):
+        super().setup_method()
+        self.eps = 0.1
+
+
+@KDTreeTest
+class _Test_random_ball_far(_Test_random_ball):
+
+    def setup_method(self):
+        super().setup_method()
+        self.d = 2.
+
+@KDTreeTest
+class _Test_random_ball_far_periodic(_Test_random_ball_periodic):
+
+    def setup_method(self):
+        super().setup_method()
+        self.d = 2.
+
+
+@KDTreeTest
+class _Test_random_ball_l1(_Test_random_ball):
+
+    def setup_method(self):
+        super().setup_method()
+        self.p = 1
+
+
+@KDTreeTest
+class _Test_random_ball_linf(_Test_random_ball):
+
+    def setup_method(self):
+        super().setup_method()
+        self.p = np.inf
+
+
+def test_random_ball_vectorized(kdtree_type):
+    n = 20
+    m = 5
+    np.random.seed(1234)
+    T = kdtree_type(np.random.randn(n, m))
+
+    r = T.query_ball_point(np.random.randn(2, 3, m), 1)
+    assert_equal(r.shape, (2, 3))
+    assert_(isinstance(r[0, 0], list))
+
+
+@pytest.mark.thread_unsafe(reason="Test spawns worker threads")
+@pytest.mark.fail_slow(5)
+def test_query_ball_point_multithreaded_workers(kdtree_type):
+    np.random.seed(0)
+    n = 5000
+    k = 2
+    points = np.random.randn(n, k)
+    T = kdtree_type(points)
+    l1 = T.query_ball_point(points, 0.003, workers=1)
+    l2 = T.query_ball_point(points, 0.003, workers=64)
+    l3 = T.query_ball_point(points, 0.003, workers=-1)
+
+    for i in range(n):
+        if l1[i] or l2[i]:
+            assert_array_equal(l1[i], l2[i])
+
+    for i in range(n):
+        if l1[i] or l3[i]:
+            assert_array_equal(l1[i], l3[i])
+
+
+@pytest.mark.thread_unsafe(reason="Test spawns worker threads")
+@pytest.mark.fail_slow(5)
+def test_query_ball_point_multithreaded_explicit(kdtree_type):
+    rng = np.random.RandomState(3819232613)
+    n = 10000
+    k = 2
+
+    points = rng.randn(n, k)
+    tree = kdtree_type(points)
+    max_workers = 10
+    assert(n//max_workers * max_workers == n)
+    search_points = rng.randn(max_workers, n//max_workers, k)
+    all_search_points = np.reshape(search_points, (n, k))
+    radius = 0.3
+
+    def worker_func(i, tree, search_points):
+        return tree.query_ball_point(search_points[i], radius)
+
+    results = _run_concurrent_barrier(
+        max_workers, worker_func, tree, search_points)
+
+    serial_results = tree.query_ball_point(all_search_points, radius)
+    # the results from concurrent searching the tree should match the results
+    # from searching the same set of points in one thread
+    assert_array_equal(np.sort(np.concatenate(results)), np.sort(serial_results))
+
+
+class two_trees_consistency:
+
+    def distance(self, a, b, p):
+        return minkowski(a, b, p)
+
+    def test_all_in_ball(self):
+        r = self.T1.query_ball_tree(self.T2, self.d, p=self.p, eps=self.eps)
+        for i, l in enumerate(r):
+            for j in l:
+                assert (self.distance(self.data1[i], self.data2[j], self.p)
+                        <= self.d*(1.+self.eps))
+
+    def test_found_all(self):
+        r = self.T1.query_ball_tree(self.T2, self.d, p=self.p, eps=self.eps)
+        for i, l in enumerate(r):
+            c = np.ones(self.T2.n, dtype=bool)
+            c[l] = False
+            assert np.all(self.distance(self.data2[c], self.data1[i], self.p)
+                          >= self.d/(1.+self.eps))
+
+
+@KDTreeTest
+class _Test_two_random_trees(two_trees_consistency):
+
+    def setup_method(self):
+        n = 50
+        m = 4
+        np.random.seed(1234)
+        self.data1 = np.random.randn(n, m)
+        self.T1 = self.kdtree_type(self.data1, leafsize=2)
+        self.data2 = np.random.randn(n, m)
+        self.T2 = self.kdtree_type(self.data2, leafsize=2)
+        self.p = 2.
+        self.eps = 0
+        self.d = 0.2
+
+
+@KDTreeTest
+class _Test_two_random_trees_periodic(two_trees_consistency):
+    def distance(self, a, b, p):
+        return distance_box(a, b, p, 1.0)
+
+    def setup_method(self):
+        n = 50
+        m = 4
+        np.random.seed(1234)
+        self.data1 = np.random.uniform(size=(n, m))
+        self.T1 = self.kdtree_type(self.data1, leafsize=2, boxsize=1.0)
+        self.data2 = np.random.uniform(size=(n, m))
+        self.T2 = self.kdtree_type(self.data2, leafsize=2, boxsize=1.0)
+        self.p = 2.
+        self.eps = 0
+        self.d = 0.2
+
+
+@KDTreeTest
+class _Test_two_random_trees_far(_Test_two_random_trees):
+
+    def setup_method(self):
+        super().setup_method()
+        self.d = 2
+
+
+@KDTreeTest
+class _Test_two_random_trees_far_periodic(_Test_two_random_trees_periodic):
+
+    def setup_method(self):
+        super().setup_method()
+        self.d = 2
+
+
+@KDTreeTest
+class _Test_two_random_trees_linf(_Test_two_random_trees):
+
+    def setup_method(self):
+        super().setup_method()
+        self.p = np.inf
+
+
+@KDTreeTest
+class _Test_two_random_trees_linf_periodic(_Test_two_random_trees_periodic):
+
+    def setup_method(self):
+        super().setup_method()
+        self.p = np.inf
+
+
+class Test_rectangle:
+
+    def setup_method(self):
+        self.rect = Rectangle([0, 0], [1, 1])
+
+    def test_min_inside(self):
+        assert_almost_equal(self.rect.min_distance_point([0.5, 0.5]), 0)
+
+    def test_min_one_side(self):
+        assert_almost_equal(self.rect.min_distance_point([0.5, 1.5]), 0.5)
+
+    def test_min_two_sides(self):
+        assert_almost_equal(self.rect.min_distance_point([2, 2]), np.sqrt(2))
+
+    def test_max_inside(self):
+        assert_almost_equal(self.rect.max_distance_point([0.5, 0.5]), 1/np.sqrt(2))
+
+    def test_max_one_side(self):
+        assert_almost_equal(self.rect.max_distance_point([0.5, 1.5]),
+                            np.hypot(0.5, 1.5))
+
+    def test_max_two_sides(self):
+        assert_almost_equal(self.rect.max_distance_point([2, 2]), 2*np.sqrt(2))
+
+    def test_split(self):
+        less, greater = self.rect.split(0, 0.1)
+        assert_array_equal(less.maxes, [0.1, 1])
+        assert_array_equal(less.mins, [0, 0])
+        assert_array_equal(greater.maxes, [1, 1])
+        assert_array_equal(greater.mins, [0.1, 0])
+
+
+def test_distance_l2():
+    with pytest.deprecated_call(match="1.20.0"):
+        assert_almost_equal(minkowski_distance([0, 0], [1, 1], 2), np.sqrt(2))
+    with pytest.deprecated_call(match="1.20.0"):
+        assert_almost_equal(minkowski_distance_p([0, 0], [1, 1], 2), 2)
+
+
+def test_distance_l1():
+    with pytest.deprecated_call(match="1.20.0"):
+        assert_almost_equal(minkowski_distance([0, 0], [1, 1], 1), 2)
+
+
+def test_distance_linf():
+    with pytest.deprecated_call(match="1.20.0"):
+        assert_almost_equal(minkowski_distance([0, 0], [1, 1], np.inf), 1)
+
+
+def test_distance_vectorization():
+    np.random.seed(1234)
+    x = np.random.randn(10, 1, 3)
+    y = np.random.randn(1, 7, 3)
+    with pytest.deprecated_call(match="1.20.0"):
+        assert_equal(minkowski_distance(x, y).shape, (10, 7))
+
+
+class count_neighbors_consistency:
+    def test_one_radius(self):
+        r = 0.2
+        assert_equal(self.T1.count_neighbors(self.T2, r),
+                np.sum([len(l) for l in self.T1.query_ball_tree(self.T2, r)]))
+
+    def test_large_radius(self):
+        r = 1000
+        assert_equal(self.T1.count_neighbors(self.T2, r),
+                np.sum([len(l) for l in self.T1.query_ball_tree(self.T2, r)]))
+
+    def test_multiple_radius(self):
+        rs = np.exp(np.linspace(np.log(0.01), np.log(10), 3))
+        results = self.T1.count_neighbors(self.T2, rs)
+        assert_(np.all(np.diff(results) >= 0))
+        for r, result in zip(rs, results):
+            assert_equal(self.T1.count_neighbors(self.T2, r), result)
+
+@KDTreeTest
+class _Test_count_neighbors(count_neighbors_consistency):
+    def setup_method(self):
+        n = 50
+        m = 2
+        np.random.seed(1234)
+        self.T1 = self.kdtree_type(np.random.randn(n, m), leafsize=2)
+        self.T2 = self.kdtree_type(np.random.randn(n, m), leafsize=2)
+
+
+class sparse_distance_matrix_consistency:
+
+    def distance(self, a, b, p):
+        return minkowski(a, b, p)
+
+    def test_consistency_with_neighbors(self):
+        M = self.T1.sparse_distance_matrix(self.T2, self.r, output_type='dok_array')
+        r = self.T1.query_ball_tree(self.T2, self.r)
+        for i, l in enumerate(r):
+            for j in l:
+                assert_almost_equal(
+                    M[i, j],
+                    self.distance(self.T1.data[i], self.T2.data[j], self.p),
+                    decimal=14
+                )
+        for ((i, j), d) in M.items():
+            assert_(j in r[i])
+
+    def test_zero_distance(self):
+        # raises an exception for bug 870 (FIXME: Does it?)
+        self.T1.sparse_distance_matrix(self.T1, self.r, output_type='dok_array')
+
+    def test_consistency(self):
+        # Test consistency with a distance_matrix
+        M1 = self.T1.sparse_distance_matrix(self.T2, self.r, output_type='dok_array')
+        expected = cdist(self.T1.data, self.T2.data)
+        expected[expected > self.r] = 0
+        assert_array_almost_equal(M1.toarray(), expected, decimal=14)
+
+    def test_against_logic_error_regression(self):
+        # regression test for gh-5077 logic error
+        np.random.seed(0)
+        too_many = np.array(np.random.randn(18, 2), dtype=int)
+        tree = self.kdtree_type(
+            too_many, balanced_tree=False, compact_nodes=False)
+        d = tree.sparse_distance_matrix(tree, 3, output_type='dok_array').toarray()
+        assert_array_almost_equal(d, d.T, decimal=14)
+
+    def test_ckdtree_return_types(self):
+        # brute-force reference
+        ref = np.zeros((self.n, self.n))
+        for i in range(self.n):
+            for j in range(self.n):
+                v = self.data1[i, :] - self.data2[j, :]
+                ref[i, j] = np.dot(v, v)
+        ref = np.sqrt(ref)
+        ref[ref > self.r] = 0.
+        # test return type 'dict'
+        dist = np.zeros((self.n, self.n))
+        r = self.T1.sparse_distance_matrix(self.T2, self.r, output_type='dict')
+        for i, j in r.keys():
+            dist[i, j] = r[(i, j)]
+        assert_array_almost_equal(ref, dist, decimal=14)
+        # test return type 'ndarray'
+        dist = np.zeros((self.n, self.n))
+        r = self.T1.sparse_distance_matrix(self.T2, self.r,
+            output_type='ndarray')
+        for k in range(r.shape[0]):
+            i = r['i'][k]
+            j = r['j'][k]
+            v = r['v'][k]
+            dist[i, j] = v
+        assert_array_almost_equal(ref, dist, decimal=14)
+        # test return type 'dok_array'
+        r = self.T1.sparse_distance_matrix(self.T2, self.r,
+            output_type='dok_array')
+        assert_array_almost_equal(ref, r.toarray(), decimal=14)
+        assert isinstance(r, dok_array)
+        # test return type 'dok_matrix'
+        r = self.T1.sparse_distance_matrix(self.T2, self.r,
+            output_type='dok_matrix')
+        assert_array_almost_equal(ref, r.toarray(), decimal=14)
+        assert isinstance(r, dok_matrix)
+        # test return type 'coo_array'
+        r = self.T1.sparse_distance_matrix(self.T2, self.r,
+            output_type='coo_array')
+        assert_array_almost_equal(ref, r.toarray(), decimal=14)
+        assert isinstance(r, coo_array)
+        # test return type 'coo_matrix'
+        r = self.T1.sparse_distance_matrix(self.T2, self.r,
+            output_type='coo_matrix')
+        assert_array_almost_equal(ref, r.toarray(), decimal=14)
+        assert isinstance(r, coo_matrix)
+        # test default return type 'dok_matrix'
+        r = self.T1.sparse_distance_matrix(self.T2, self.r)
+        assert isinstance(r, dok_matrix)
+
+
+@KDTreeTest
+class _Test_sparse_distance_matrix(sparse_distance_matrix_consistency):
+    def setup_method(self):
+        n = 50
+        m = 4
+        np.random.seed(1234)
+        data1 = np.random.randn(n, m)
+        data2 = np.random.randn(n, m)
+        self.T1 = self.kdtree_type(data1, leafsize=2)
+        self.T2 = self.kdtree_type(data2, leafsize=2)
+        self.r = 0.5
+        self.p = 2
+        self.data1 = data1
+        self.data2 = data2
+        self.n = n
+        self.m = m
+
+
+def test_distance_matrix():
+    m = 10
+    n = 11
+    k = 4
+    np.random.seed(1234)
+    xs = np.random.randn(m, k)
+    ys = np.random.randn(n, k)
+    with pytest.deprecated_call(match="1.20.0"):
+        ds = distance_matrix(xs, ys)
+    assert_equal(ds.shape, (m, n))
+    for i in range(m):
+        for j in range(n):
+            with pytest.deprecated_call(match="1.20.0"):
+                assert_almost_equal(minkowski_distance(xs[i], ys[j]), ds[i, j])
+
+
+def test_distance_matrix_looping():
+    m = 10
+    n = 11
+    k = 4
+    np.random.seed(1234)
+    xs = np.random.randn(m, k)
+    ys = np.random.randn(n, k)
+    with pytest.deprecated_call(match="1.20.0"):
+        ds = distance_matrix(xs, ys)
+    with pytest.deprecated_call(match="1.20.0"):
+        dsl = distance_matrix(xs, ys, threshold=1)
+    assert_equal(ds, dsl)
+
+
+def check_onetree_query(T, d):
+    r = T.query_ball_tree(T, d)
+    s = set()
+    for i, l in enumerate(r):
+        for j in l:
+            if i < j:
+                s.add((i, j))
+
+    assert_(s == T.query_pairs(d))
+
+def test_onetree_query(kdtree_type):
+    np.random.seed(0)
+    n = 50
+    k = 4
+    points = np.random.randn(n, k)
+    T = kdtree_type(points)
+    check_onetree_query(T, 0.1)
+
+    points = np.random.randn(3*n, k)
+    points[:n] *= 0.001
+    points[n:2*n] += 2
+    T = kdtree_type(points)
+    check_onetree_query(T, 0.1)
+    check_onetree_query(T, 0.001)
+    check_onetree_query(T, 0.00001)
+    check_onetree_query(T, 1e-6)
+
+
+def test_query_pairs_single_node(kdtree_type):
+    tree = kdtree_type([[0, 1]])
+    assert_equal(tree.query_pairs(0.5), set())
+
+
+def test_kdtree_query_pairs(kdtree_type):
+    np.random.seed(0)
+    n = 50
+    k = 2
+    r = 0.1
+    r2 = r**2
+    points = np.random.randn(n, k)
+    T = kdtree_type(points)
+    # brute force reference
+    brute = set()
+    for i in range(n):
+        for j in range(i+1, n):
+            v = points[i, :] - points[j, :]
+            if np.dot(v, v) <= r2:
+                brute.add((i, j))
+    l0 = sorted(brute)
+    # test default return type
+    s = T.query_pairs(r)
+    l1 = sorted(s)
+    assert_array_equal(l0, l1)
+    # test return type 'set'
+    s = T.query_pairs(r, output_type='set')
+    l1 = sorted(s)
+    assert_array_equal(l0, l1)
+    # test return type 'ndarray'
+    s = set()
+    arr = T.query_pairs(r, output_type='ndarray')
+    for i in range(arr.shape[0]):
+        s.add((int(arr[i, 0]), int(arr[i, 1])))
+    l2 = sorted(s)
+    assert_array_equal(l0, l2)
+
+
+def test_query_pairs_eps(kdtree_type):
+    spacing = np.sqrt(2)
+    # irrational spacing to have potential rounding errors
+    x_range = np.linspace(0, 3 * spacing, 4)
+    y_range = np.linspace(0, 3 * spacing, 4)
+    xy_array = [(xi, yi) for xi in x_range for yi in y_range]
+    tree = kdtree_type(xy_array)
+    pairs_eps = tree.query_pairs(r=spacing, eps=.1)
+    # result: 24 with eps, 16 without due to rounding
+    pairs = tree.query_pairs(r=spacing * 1.01)
+    # result: 24
+    assert_equal(pairs, pairs_eps)
+
+
+def test_ball_point_ints(kdtree_type):
+    # Regression test for #1373.
+    x, y = np.mgrid[0:4, 0:4]
+    points = list(zip(x.ravel(), y.ravel()))
+    tree = kdtree_type(points)
+    assert_equal(sorted([4, 8, 9, 12]),
+                 sorted(tree.query_ball_point((2, 0), 1)))
+    points = np.asarray(points, dtype=float)
+    tree = kdtree_type(points)
+    assert_equal(sorted([4, 8, 9, 12]),
+                 sorted(tree.query_ball_point((2, 0), 1)))
+
+
+def test_kdtree_comparisons():
+    # Regression test: node comparisons were done wrong in 0.12 w/Py3.
+    nodes = [KDTree.node() for _ in range(3)]
+    assert_equal(sorted(nodes), sorted(nodes[::-1]))
+
+
+def test_kdtree_build_modes(kdtree_type):
+    # check if different build modes for KDTree give similar query results
+    np.random.seed(0)
+    n = 5000
+    k = 4
+    points = np.random.randn(n, k)
+    T1 = kdtree_type(points).query(points, k=5)[-1]
+    T2 = kdtree_type(points, compact_nodes=False).query(points, k=5)[-1]
+    T3 = kdtree_type(points, balanced_tree=False).query(points, k=5)[-1]
+    T4 = kdtree_type(points, compact_nodes=False,
+                     balanced_tree=False).query(points, k=5)[-1]
+    assert_array_equal(T1, T2)
+    assert_array_equal(T1, T3)
+    assert_array_equal(T1, T4)
+
+def test_kdtree_pickle(kdtree_type):
+    # test if it is possible to pickle a KDTree
+    import pickle
+    np.random.seed(0)
+    n = 50
+    k = 4
+    points = np.random.randn(n, k)
+    T1 = kdtree_type(points)
+    tmp = pickle.dumps(T1)
+    T2 = pickle.loads(tmp)
+    T1 = T1.query(points, k=5)[-1]
+    T2 = T2.query(points, k=5)[-1]
+    assert_array_equal(T1, T2)
+
+def test_kdtree_pickle_boxsize(kdtree_type):
+    # test if it is possible to pickle a periodic KDTree
+    import pickle
+    np.random.seed(0)
+    n = 50
+    k = 4
+    points = np.random.uniform(size=(n, k))
+    T1 = kdtree_type(points, boxsize=1.0)
+    tmp = pickle.dumps(T1)
+    T2 = pickle.loads(tmp)
+    T1 = T1.query(points, k=5)[-1]
+    T2 = T2.query(points, k=5)[-1]
+    assert_array_equal(T1, T2)
+
+def test_kdtree_copy_data(kdtree_type):
+    # check if copy_data=True makes the kd-tree
+    # impervious to data corruption by modification of
+    # the data arrray
+    np.random.seed(0)
+    n = 5000
+    k = 4
+    points = np.random.randn(n, k)
+    T = kdtree_type(points, copy_data=True)
+    q = points.copy()
+    T1 = T.query(q, k=5)[-1]
+    points[...] = np.random.randn(n, k)
+    T2 = T.query(q, k=5)[-1]
+    assert_array_equal(T1, T2)
+
+def test_ckdtree_parallel(kdtree_type, monkeypatch):
+    # check if parallel=True also generates correct query results
+    np.random.seed(0)
+    n = 5000
+    k = 4
+    points = np.random.randn(n, k)
+    T = kdtree_type(points)
+    T1 = T.query(points, k=5, workers=64)[-1]
+    T2 = T.query(points, k=5, workers=-1)[-1]
+    T3 = T.query(points, k=5)[-1]
+    assert_array_equal(T1, T2)
+    assert_array_equal(T1, T3)
+
+    monkeypatch.setattr(os, 'cpu_count', lambda: None)
+    with pytest.raises(NotImplementedError, match="Cannot determine the"):
+        T.query(points, 1, workers=-1)
+
+
+def test_ckdtree_view():
+    # Check that the nodes can be correctly viewed from Python.
+    # This test also sanity checks each node in the cKDTree, and
+    # thus verifies the internal structure of the kd-tree.
+    np.random.seed(0)
+    n = 100
+    k = 4
+    points = np.random.randn(n, k)
+    kdtree = cKDTree(points)
+
+    # walk the whole kd-tree and sanity check each node
+    def recurse_tree(n):
+        assert_(isinstance(n, cKDTreeNode))
+        if n.split_dim == -1:
+            assert_(n.lesser is None)
+            assert_(n.greater is None)
+            assert_(n.indices.shape[0] <= kdtree.leafsize)
+        else:
+            recurse_tree(n.lesser)
+            recurse_tree(n.greater)
+            x = n.lesser.data_points[:, n.split_dim]
+            y = n.greater.data_points[:, n.split_dim]
+            assert_(x.max() < y.min())
+
+    recurse_tree(kdtree.tree)
+    # check that indices are correctly retrieved
+    n = kdtree.tree
+    assert_array_equal(np.sort(n.indices), range(100))
+    # check that data_points are correctly retrieved
+    assert_array_equal(kdtree.data[n.indices, :], n.data_points)
+
+# KDTree is specialized to type double points, so no need to make
+# a unit test corresponding to test_ball_point_ints()
+
+def test_kdtree_list_k(kdtree_type):
+    # check kdtree periodic boundary
+    n = 200
+    m = 2
+    klist = [1, 2, 3]
+    kint = 3
+
+    np.random.seed(1234)
+    data = np.random.uniform(size=(n, m))
+    kdtree = kdtree_type(data, leafsize=1)
+
+    # check agreement between arange(1, k+1) and k
+    dd, ii = kdtree.query(data, klist)
+    dd1, ii1 = kdtree.query(data, kint)
+    assert_equal(dd, dd1)
+    assert_equal(ii, ii1)
+
+    # now check skipping one element
+    klist = np.array([1, 3])
+    kint = 3
+    dd, ii = kdtree.query(data, kint)
+    dd1, ii1 = kdtree.query(data, klist)
+    assert_equal(dd1, dd[..., klist - 1])
+    assert_equal(ii1, ii[..., klist - 1])
+
+    # check k == 1 special case
+    # and k == [1] non-special case
+    dd, ii = kdtree.query(data, 1)
+    dd1, ii1 = kdtree.query(data, [1])
+    assert_equal(len(dd.shape), 1)
+    assert_equal(len(dd1.shape), 2)
+    assert_equal(dd, np.ravel(dd1))
+    assert_equal(ii, np.ravel(ii1))
+
+@pytest.mark.fail_slow(10)
+def test_kdtree_box(kdtree_type):
+    # check ckdtree periodic boundary
+    n = 2000
+    m = 3
+    k = 3
+    np.random.seed(1234)
+    data = np.random.uniform(size=(n, m))
+    kdtree = kdtree_type(data, leafsize=1, boxsize=1.0)
+
+    # use the standard python KDTree for the simulated periodic box
+    kdtree2 = kdtree_type(data, leafsize=1)
+
+    for p in [1, 2, 3.0, np.inf]:
+        dd, ii = kdtree.query(data, k, p=p)
+
+        dd1, ii1 = kdtree.query(data + 1.0, k, p=p)
+        assert_almost_equal(dd, dd1)
+        assert_equal(ii, ii1)
+
+        dd1, ii1 = kdtree.query(data - 1.0, k, p=p)
+        assert_almost_equal(dd, dd1)
+        assert_equal(ii, ii1)
+
+        dd2, ii2 = simulate_periodic_box(kdtree2, data, k, boxsize=1.0, p=p)
+        assert_almost_equal(dd, dd2)
+        assert_equal(ii, ii2)
+
+def test_kdtree_box_0boxsize(kdtree_type):
+    # check ckdtree periodic boundary that mimics non-periodic
+    n = 2000
+    m = 2
+    k = 3
+    np.random.seed(1234)
+    data = np.random.uniform(size=(n, m))
+    kdtree = kdtree_type(data, leafsize=1, boxsize=0.0)
+
+    # use the standard python KDTree for the simulated periodic box
+    kdtree2 = kdtree_type(data, leafsize=1)
+
+    for p in [1, 2, np.inf]:
+        dd, ii = kdtree.query(data, k, p=p)
+
+        dd1, ii1 = kdtree2.query(data, k, p=p)
+        assert_almost_equal(dd, dd1)
+        assert_equal(ii, ii1)
+
+def test_kdtree_box_upper_bounds(kdtree_type):
+    data = np.linspace(0, 2, 10).reshape(-1, 2)
+    data[:, 1] += 10
+    with pytest.raises(ValueError):
+        kdtree_type(data, leafsize=1, boxsize=1.0)
+    with pytest.raises(ValueError):
+        kdtree_type(data, leafsize=1, boxsize=(0.0, 2.0))
+    # skip a dimension.
+    kdtree_type(data, leafsize=1, boxsize=(2.0, 0.0))
+
+def test_kdtree_box_lower_bounds(kdtree_type):
+    data = np.linspace(-1, 1, 10)
+    assert_raises(ValueError, kdtree_type, data, leafsize=1, boxsize=1.0)
+
+def simulate_periodic_box(kdtree, data, k, boxsize, p):
+    dd = []
+    ii = []
+    x = np.arange(3 ** data.shape[1])
+    nn = np.array(np.unravel_index(x, [3] * data.shape[1])).T
+    nn = nn - 1.0
+    for n in nn:
+        image = data + n * 1.0 * boxsize
+        dd2, ii2 = kdtree.query(image, k, p=p)
+        dd2 = dd2.reshape(-1, k)
+        ii2 = ii2.reshape(-1, k)
+        dd.append(dd2)
+        ii.append(ii2)
+    dd = np.concatenate(dd, axis=-1)
+    ii = np.concatenate(ii, axis=-1)
+
+    result = np.empty([len(data), len(nn) * k], dtype=[
+            ('ii', 'i8'),
+            ('dd', 'f8')])
+    result['ii'][:] = ii
+    result['dd'][:] = dd
+    result.sort(order='dd')
+    return result['dd'][:, :k], result['ii'][:, :k]
+
+
+@pytest.mark.fail_asan
+def test_ckdtree_memuse():
+    # unit test adaptation of gh-5630
+
+    # NOTE: this will fail when run via valgrind,
+    # because rss is no longer a reliable memory usage indicator.
+    # It was also observed to be flaky under ASan.
+
+    try:
+        import resource
+    except ImportError:
+        # resource is not available on Windows
+        return
+    # Make some data
+    dx, dy = 0.05, 0.05
+    y, x = np.mgrid[slice(1, 5 + dy, dy),
+                    slice(1, 5 + dx, dx)]
+    z = np.sin(x)**10 + np.cos(10 + y*x) * np.cos(x)
+    z_copy = np.empty_like(z)
+    z_copy[:] = z
+    # Place FILLVAL in z_copy at random number of random locations
+    FILLVAL = 99.
+    mask = np.random.randint(0, z.size, np.random.randint(50) + 5)
+    z_copy.flat[mask] = FILLVAL
+    igood = np.vstack(np.nonzero(x != FILLVAL)).T
+    ibad = np.vstack(np.nonzero(x == FILLVAL)).T
+    mem_use = resource.getrusage(resource.RUSAGE_SELF).ru_maxrss
+    # burn-in
+    for i in range(10):
+        tree = cKDTree(igood)
+    # count memleaks while constructing and querying cKDTree
+    num_leaks = 0
+    for i in range(100):
+        mem_use = resource.getrusage(resource.RUSAGE_SELF).ru_maxrss
+        tree = cKDTree(igood)
+        dist, iquery = tree.query(ibad, k=4, p=2)
+        new_mem_use = resource.getrusage(resource.RUSAGE_SELF).ru_maxrss
+        if new_mem_use > mem_use:
+            num_leaks += 1
+    # ideally zero leaks, but errors might accidentally happen
+    # outside cKDTree
+    assert_(num_leaks < 10)
+
+def test_kdtree_weights(kdtree_type):
+
+    data = np.linspace(0, 1, 4).reshape(-1, 1)
+    tree1 = kdtree_type(data, leafsize=1)
+    weights = np.ones(len(data), dtype='f4')
+
+    nw = tree1._build_weights(weights)
+    assert_array_equal(nw, [4, 2, 1, 1, 2, 1, 1])
+
+    assert_raises(ValueError, tree1._build_weights, weights[:-1])
+
+    for i in range(10):
+        # since weights are uniform, these shall agree:
+        c1 = tree1.count_neighbors(tree1, np.linspace(0, 10, i))
+        c2 = tree1.count_neighbors(tree1, np.linspace(0, 10, i),
+                weights=(weights, weights))
+        c3 = tree1.count_neighbors(tree1, np.linspace(0, 10, i),
+                weights=(weights, None))
+        c4 = tree1.count_neighbors(tree1, np.linspace(0, 10, i),
+                weights=(None, weights))
+        tree1.count_neighbors(tree1, np.linspace(0, 10, i),
+                weights=weights)
+
+        assert_array_equal(c1, c2)
+        assert_array_equal(c1, c3)
+        assert_array_equal(c1, c4)
+
+    for i in range(len(data)):
+        # this tests removal of one data point by setting weight to 0
+        w1 = weights.copy()
+        w1[i] = 0
+        data2 = data[w1 != 0]
+        tree2 = kdtree_type(data2)
+
+        c1 = tree1.count_neighbors(tree1, np.linspace(0, 10, 100),
+                weights=(w1, w1))
+        # "c2 is correct"
+        c2 = tree2.count_neighbors(tree2, np.linspace(0, 10, 100))
+
+        assert_array_equal(c1, c2)
+
+        #this asserts for two different trees, singular weights
+        # crashes
+        assert_raises(ValueError, tree1.count_neighbors,
+            tree2, np.linspace(0, 10, 100), weights=w1)
+
+@pytest.mark.fail_slow(10)
+def test_kdtree_count_neighbous_multiple_r(kdtree_type):
+    n = 2000
+    m = 2
+    np.random.seed(1234)
+    data = np.random.normal(size=(n, m))
+    kdtree = kdtree_type(data, leafsize=1)
+    r0 = [0, 0.01, 0.01, 0.02, 0.05]
+    i0 = np.arange(len(r0))
+    n0 = kdtree.count_neighbors(kdtree, r0)
+    nnc = kdtree.count_neighbors(kdtree, r0, cumulative=False)
+    assert_equal(n0, nnc.cumsum())
+
+    for i, r in zip(itertools.permutations(i0),
+                    itertools.permutations(r0)):
+        # permute n0 by i and it shall agree
+        n = kdtree.count_neighbors(kdtree, r)
+        assert_array_equal(n, n0[list(i)])
+
+def test_len0_arrays(kdtree_type):
+    # make sure len-0 arrays are handled correctly
+    # in range queries (gh-5639)
+    rng = np.random.RandomState(1234)
+    X = rng.rand(10, 2)
+    Y = rng.rand(10, 2)
+    tree = kdtree_type(X)
+    # query_ball_point (single)
+    d, i = tree.query([.5, .5], k=1)
+    z = tree.query_ball_point([.5, .5], 0.1*d)
+    assert_array_equal(z, [])
+    # query_ball_point (multiple)
+    d, i = tree.query(Y, k=1)
+    mind = d.min()
+    z = tree.query_ball_point(Y, 0.1*mind)
+    y = np.empty(shape=(10, ), dtype=object)
+    y.fill([])
+    assert_array_equal(y, z)
+    # query_ball_tree
+    other = kdtree_type(Y)
+    y = tree.query_ball_tree(other, 0.1*mind)
+    assert_array_equal(10*[[]], y)
+    # count_neighbors
+    y = tree.count_neighbors(other, 0.1*mind)
+    assert_(y == 0)
+    # sparse_distance_matrix
+    y = tree.sparse_distance_matrix(other, 0.1*mind, output_type='dok_array')
+    assert_array_equal(y == np.zeros((10, 10)), True)
+    y = tree.sparse_distance_matrix(other, 0.1*mind, output_type='coo_array')
+    assert_array_equal(y == np.zeros((10, 10)), True)
+    y = tree.sparse_distance_matrix(other, 0.1*mind, output_type='dict')
+    assert_equal(y, {})
+    y = tree.sparse_distance_matrix(other, 0.1*mind, output_type='ndarray')
+    _dtype = [('i', np.intp), ('j', np.intp), ('v', np.float64)]
+    res_dtype = np.dtype(_dtype, align=True)
+    z = np.empty(shape=(0, ), dtype=res_dtype)
+    assert_array_equal(y, z)
+    # query_pairs
+    d, i = tree.query(X, k=2)
+    mind = d[:, -1].min()
+    y = tree.query_pairs(0.1*mind, output_type='set')
+    assert_equal(y, set())
+    y = tree.query_pairs(0.1*mind, output_type='ndarray')
+    z = np.empty(shape=(0, 2), dtype=np.intp)
+    assert_array_equal(y, z)
+
+def test_kdtree_duplicated_inputs(kdtree_type):
+    # check kdtree with duplicated inputs
+    n = 1024
+    for m in range(1, 8):
+        data = np.ones((n, m))
+        data[n//2:] = 2
+
+        for balanced, compact in itertools.product((False, True), repeat=2):
+            kdtree = kdtree_type(data, balanced_tree=balanced,
+                                 compact_nodes=compact, leafsize=1)
+            assert kdtree.size == 3
+
+            tree = (kdtree.tree if kdtree_type is cKDTree else
+                    kdtree.tree._node)
+
+            assert_equal(
+                np.sort(tree.lesser.indices),
+                np.arange(0, n // 2))
+            assert_equal(
+                np.sort(tree.greater.indices),
+                np.arange(n // 2, n))
+
+
+def test_kdtree_noncumulative_nondecreasing(kdtree_type):
+    # check kdtree with duplicated inputs
+
+    # it shall not divide more than 3 nodes.
+    # root left (1), and right (2)
+    kdtree = kdtree_type([[0]], leafsize=1)
+
+    assert_raises(ValueError, kdtree.count_neighbors,
+        kdtree, [0.1, 0], cumulative=False)
+
+def test_short_knn(kdtree_type):
+
+    # The test case is based on github: #6425 by @SteveDoyle2
+
+    xyz = np.array([
+        [0., 0., 0.],
+        [1.01, 0., 0.],
+        [0., 1., 0.],
+        [0., 1.01, 0.],
+        [1., 0., 0.],
+        [1., 1., 0.]],
+    dtype='float64')
+
+    ckdt = kdtree_type(xyz)
+
+    deq, ieq = ckdt.query(xyz, k=4, distance_upper_bound=0.2)
+
+    assert_array_almost_equal(deq,
+            [[0., np.inf, np.inf, np.inf],
+            [0., 0.01, np.inf, np.inf],
+            [0., 0.01, np.inf, np.inf],
+            [0., 0.01, np.inf, np.inf],
+            [0., 0.01, np.inf, np.inf],
+            [0., np.inf, np.inf, np.inf]])
+
+def test_query_ball_point_vector_r(kdtree_type):
+
+    np.random.seed(1234)
+    data = np.random.normal(size=(100, 3))
+    query = np.random.normal(size=(100, 3))
+    tree = kdtree_type(data)
+    d = np.random.uniform(0, 0.3, size=len(query))
+
+    rvector = tree.query_ball_point(query, d)
+    rscalar = [tree.query_ball_point(qi, di) for qi, di in zip(query, d)]
+    for a, b in zip(rvector, rscalar):
+        assert_array_equal(sorted(a), sorted(b))
+
+def test_query_ball_point_length(kdtree_type):
+
+    np.random.seed(1234)
+    data = np.random.normal(size=(100, 3))
+    query = np.random.normal(size=(100, 3))
+    tree = kdtree_type(data)
+    d = 0.3
+
+    length = tree.query_ball_point(query, d, return_length=True)
+    length2 = [len(ind) for ind in tree.query_ball_point(query, d, return_length=False)]
+    length3 = [len(tree.query_ball_point(qi, d)) for qi in query]
+    length4 = [tree.query_ball_point(qi, d, return_length=True) for qi in query]
+    assert_array_equal(length, length2)
+    assert_array_equal(length, length3)
+    assert_array_equal(length, length4)
+
+def test_discontiguous(kdtree_type):
+
+    np.random.seed(1234)
+    data = np.random.normal(size=(100, 3))
+    d_contiguous = np.arange(100) * 0.04
+    d_discontiguous = np.ascontiguousarray(
+                          np.arange(100)[::-1] * 0.04)[::-1]
+    query_contiguous = np.random.normal(size=(100, 3))
+    query_discontiguous = np.ascontiguousarray(query_contiguous.T).T
+    assert query_discontiguous.strides[-1] != query_contiguous.strides[-1]
+    assert d_discontiguous.strides[-1] != d_contiguous.strides[-1]
+
+    tree = kdtree_type(data)
+
+    length1 = tree.query_ball_point(query_contiguous,
+                                    d_contiguous, return_length=True)
+    length2 = tree.query_ball_point(query_discontiguous,
+                                    d_discontiguous, return_length=True)
+
+    assert_array_equal(length1, length2)
+
+    d1, i1 = tree.query(query_contiguous, 1)
+    d2, i2 = tree.query(query_discontiguous, 1)
+
+    assert_array_equal(d1, d2)
+    assert_array_equal(i1, i2)
+
+
+@pytest.mark.parametrize("balanced_tree, compact_nodes",
+    [(True, False),
+     (True, True),
+     (False, False),
+     (False, True)])
+def test_kdtree_empty_input(kdtree_type, balanced_tree, compact_nodes):
+    # https://github.com/scipy/scipy/issues/5040
+    np.random.seed(1234)
+    empty_v3 = np.empty(shape=(0, 3))
+    query_v3 = np.ones(shape=(1, 3))
+    query_v2 = np.ones(shape=(2, 3))
+
+    tree = kdtree_type(empty_v3, balanced_tree=balanced_tree,
+                       compact_nodes=compact_nodes)
+    length = tree.query_ball_point(query_v3, 0.3, return_length=True)
+    assert length == 0
+
+    dd, ii = tree.query(query_v2, 2)
+    assert ii.shape == (2, 2)
+    assert dd.shape == (2, 2)
+    assert np.isinf(dd).all()
+
+    N = tree.count_neighbors(tree, [0, 1])
+    assert_array_equal(N, [0, 0])
+
+    M = tree.sparse_distance_matrix(tree, 0.3, output_type='dok_array')
+    assert M.shape == (0, 0)
+
+@KDTreeTest
+class _Test_sorted_query_ball_point:
+    def setup_method(self):
+        np.random.seed(1234)
+        self.x = np.random.randn(100, 1)
+        self.ckdt = self.kdtree_type(self.x)
+
+    def test_return_sorted_True(self):
+        idxs_list = self.ckdt.query_ball_point(self.x, 1., return_sorted=True)
+        for idxs in idxs_list:
+            assert_array_equal(idxs, sorted(idxs))
+
+        for xi in self.x:
+            idxs = self.ckdt.query_ball_point(xi, 1., return_sorted=True)
+            assert_array_equal(idxs, sorted(idxs))
+
+    def test_return_sorted_None(self):
+        """Previous behavior was to sort the returned indices if there were
+        multiple points per query but not sort them if there was a single point
+        per query."""
+        idxs_list = self.ckdt.query_ball_point(self.x, 1.)
+        for idxs in idxs_list:
+            assert_array_equal(idxs, sorted(idxs))
+
+        idxs_list_single = [self.ckdt.query_ball_point(xi, 1.) for xi in self.x]
+        idxs_list_False = self.ckdt.query_ball_point(self.x, 1., return_sorted=False)
+        for idxs0, idxs1 in zip(idxs_list_False, idxs_list_single):
+            assert_array_equal(idxs0, idxs1)
+
+
+def test_kdtree_complex_data():
+    # Test that KDTree rejects complex input points (gh-9108)
+    points = np.random.rand(10, 2).view(complex)
+
+    with pytest.raises(TypeError, match="complex data"):
+        t = KDTree(points)
+
+    t = KDTree(points.real)
+
+    with pytest.raises(TypeError, match="complex data"):
+        t.query(points)
+
+    with pytest.raises(TypeError, match="complex data"):
+        t.query_ball_point(points, r=1)
+
+
+def visit_tree(i, t, points):
+    root = t.tree
+
+    assert isinstance(root, KDTree.innernode)
+    assert root.children == points.shape[0]
+
+    # Visit the tree and assert some basic properties for each node
+    nodes = [root]
+
+    while nodes:
+        n = nodes.pop(-1)
+
+        if isinstance(n, KDTree.leafnode):
+            assert isinstance(n.children, int)
+            assert n.children == len(n.idx)
+            assert_array_equal(points[n.idx], n._node.data_points)
+        else:
+            assert isinstance(n, KDTree.innernode)
+            assert isinstance(n.split_dim, int)
+            assert 0 <= n.split_dim < t.m
+            assert isinstance(n.split, float)
+            assert isinstance(n.children, int)
+            assert n.children == n.less.children + n.greater.children
+            nodes.append(n.greater)
+            nodes.append(n.less)
+
+
+
+def test_kdtree_tree_access():
+    # Test KDTree.tree can be used to traverse the KDTree
+    np.random.seed(1234)
+    points = np.random.rand(100, 4)
+    t = KDTree(points)
+    visit_tree(0, t, points)
+
+
+@pytest.mark.thread_unsafe(reason="Spawns worker threads")
+def test_multithreaded_tree_access():
+    # Test that lazily generating KDTree.tree works when tree generation
+    # is reqested from multiple threads
+    rng = np.random.RandomState(3116978525)
+    points = rng.rand(100, 4)
+    t = KDTree(points)
+    _run_concurrent_barrier(10, visit_tree, t, points)
+
+
+def test_kdtree_attributes():
+    # Test KDTree's attributes are available
+    np.random.seed(1234)
+    points = np.random.rand(100, 4)
+    t = KDTree(points)
+
+    assert isinstance(t.m, int)
+    assert t.n == points.shape[0]
+
+    assert isinstance(t.n, int)
+    assert t.m == points.shape[1]
+
+    assert isinstance(t.leafsize, int)
+    assert t.leafsize == 10
+
+    assert_array_equal(t.maxes, np.amax(points, axis=0))
+    assert_array_equal(t.mins, np.amin(points, axis=0))
+    assert t.data.base is points
+
+
+@pytest.mark.parametrize("kdtree_class", [KDTree, cKDTree])
+def test_kdtree_count_neighbors_weighted(kdtree_class):
+    rng = np.random.RandomState(1234)
+    r = np.arange(0.05, 1, 0.05)
+
+    A = rng.random(21).reshape((7,3))
+    B = rng.random(45).reshape((15,3))
+
+    wA = rng.random(7)
+    wB = rng.random(15)
+
+    kdA = kdtree_class(A)
+    kdB = kdtree_class(B)
+
+    nAB = kdA.count_neighbors(kdB, r, cumulative=False, weights=(wA,wB))
+
+    # Compare against brute-force
+    weights = wA[None, :] * wB[:, None]
+    dist = np.linalg.norm(A[None, :, :] - B[:, None, :], axis=-1)
+    expect = [np.sum(weights[(prev_radius < dist) & (dist <= radius)])
+              for prev_radius, radius in zip(itertools.chain([0], r[:-1]), r)]
+    assert_allclose(nAB, expect)
+
+
+def test_kdtree_nan():
+    vals = [1, 5, -10, 7, -4, -16, -6, 6, 3, -11]
+    n = len(vals)
+    data = np.concatenate([vals, np.full(n, np.nan)])[:, None]
+    with pytest.raises(ValueError, match="must be finite"):
+        KDTree(data)
+
+
+def test_nonfinite_inputs_gh_18223():
+    rng = np.random.default_rng(12345)
+    coords = rng.uniform(size=(100, 3), low=0.0, high=0.1)
+    t = KDTree(coords, balanced_tree=False, compact_nodes=False)
+    bad_coord = [np.nan for _ in range(3)]
+
+    with pytest.raises(ValueError, match="must be finite"):
+        t.query(bad_coord)
+    with pytest.raises(ValueError, match="must be finite"):
+        t.query_ball_point(bad_coord, 1)
+
+    coords[0, :] = np.nan
+    with pytest.raises(ValueError, match="must be finite"):
+        KDTree(coords, balanced_tree=True, compact_nodes=False)
+    with pytest.raises(ValueError, match="must be finite"):
+        KDTree(coords, balanced_tree=False, compact_nodes=True)
+    with pytest.raises(ValueError, match="must be finite"):
+        KDTree(coords, balanced_tree=True, compact_nodes=True)
+    with pytest.raises(ValueError, match="must be finite"):
+        KDTree(coords, balanced_tree=False, compact_nodes=False)
+
+
+@pytest.mark.parametrize("incantation", [cKDTree, KDTree])
+def test_gh_18800(incantation):
+    # our prohibition on non-finite values
+    # in kd-tree workflows means we need
+    # coercion to NumPy arrays enforced
+
+    class ArrLike(np.ndarray):
+        def __new__(cls, input_array):
+            obj = np.asarray(input_array).view(cls)
+            # we override all() to mimic the problem
+            # pandas DataFrames encountered in gh-18800
+            obj.all = None
+            return obj
+
+        def __array_finalize__(self, obj):
+            if obj is None:
+                return
+            self.all = getattr(obj, 'all', None)
+
+    points = [
+        [66.22, 32.54],
+        [22.52, 22.39],
+        [31.01, 81.21],
+        ]
+    arr = np.array(points)
+    arr_like = ArrLike(arr)
+    tree = incantation(points, 10)
+    tree.query(arr_like, 1)
+    tree.query_ball_point(arr_like, 200)
+
+
+def test_immutable(kdtree_type):
+    rng = np.random.RandomState(3965682946)
+    n = 1000
+    k = 2
+    points = rng.rand(n, k)
+    T = kdtree_type(points, boxsize=1)
+    object_attrs = {
+        'm': 3,
+        'n': 3,
+        'size': 100,
+        'leafsize': 12,
+        'tree': None,
+    }
+    for attr, attr_val in object_attrs.items():
+        with pytest.raises(AttributeError, match="(is not writable|has no setter)"):
+            setattr(T, attr, attr_val)
+    array_attrs = {
+        'data': np.array([0, 0], dtype=np.float64),
+        'indices': 7,
+        'boxsize': 4,
+        'maxes': 1.5,
+        'mins': 1.5,
+    }
+    for attr, attr_val in array_attrs.items():
+        with pytest.raises(ValueError, match="destination is read-only"):
+            getattr(T, attr)[:] = attr_val
diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/tests/test_qhull.py b/venv/lib/python3.12/site-packages/scipy/spatial/tests/test_qhull.py
new file mode 100644
index 0000000000000000000000000000000000000000..b6ca304228083fd060adc4f15e64655021bf28f2
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/tests/test_qhull.py
@@ -0,0 +1,1312 @@
+import os
+import copy
+
+import numpy as np
+from numpy.testing import (assert_equal, assert_almost_equal,
+                           assert_, assert_allclose, assert_array_equal)
+import pytest
+from pytest import raises as assert_raises
+
+import scipy.spatial._qhull as qhull
+from scipy.spatial import cKDTree as KDTree  # type: ignore[attr-defined]
+from scipy.spatial import Voronoi
+
+import itertools
+
+def sorted_tuple(x):
+    return tuple(sorted(x))
+
+
+def assert_unordered_tuple_list_equal(a, b, tpl=tuple):
+    if isinstance(a, np.ndarray):
+        a = a.tolist()
+    if isinstance(b, np.ndarray):
+        b = b.tolist()
+    a = list(map(tpl, a))
+    a.sort()
+    b = list(map(tpl, b))
+    b.sort()
+    assert_equal(a, b)
+
+
+np.random.seed(1234)
+
+points = [(0,0), (0,1), (1,0), (1,1), (0.5, 0.5), (0.5, 1.5)]
+
+pathological_data_1 = np.array([
+    [-3.14,-3.14], [-3.14,-2.36], [-3.14,-1.57], [-3.14,-0.79],
+    [-3.14,0.0], [-3.14,0.79], [-3.14,1.57], [-3.14,2.36],
+    [-3.14,3.14], [-2.36,-3.14], [-2.36,-2.36], [-2.36,-1.57],
+    [-2.36,-0.79], [-2.36,0.0], [-2.36,0.79], [-2.36,1.57],
+    [-2.36,2.36], [-2.36,3.14], [-1.57,-0.79], [-1.57,0.79],
+    [-1.57,-1.57], [-1.57,0.0], [-1.57,1.57], [-1.57,-3.14],
+    [-1.57,-2.36], [-1.57,2.36], [-1.57,3.14], [-0.79,-1.57],
+    [-0.79,1.57], [-0.79,-3.14], [-0.79,-2.36], [-0.79,-0.79],
+    [-0.79,0.0], [-0.79,0.79], [-0.79,2.36], [-0.79,3.14],
+    [0.0,-3.14], [0.0,-2.36], [0.0,-1.57], [0.0,-0.79], [0.0,0.0],
+    [0.0,0.79], [0.0,1.57], [0.0,2.36], [0.0,3.14], [0.79,-3.14],
+    [0.79,-2.36], [0.79,-0.79], [0.79,0.0], [0.79,0.79],
+    [0.79,2.36], [0.79,3.14], [0.79,-1.57], [0.79,1.57],
+    [1.57,-3.14], [1.57,-2.36], [1.57,2.36], [1.57,3.14],
+    [1.57,-1.57], [1.57,0.0], [1.57,1.57], [1.57,-0.79],
+    [1.57,0.79], [2.36,-3.14], [2.36,-2.36], [2.36,-1.57],
+    [2.36,-0.79], [2.36,0.0], [2.36,0.79], [2.36,1.57],
+    [2.36,2.36], [2.36,3.14], [3.14,-3.14], [3.14,-2.36],
+    [3.14,-1.57], [3.14,-0.79], [3.14,0.0], [3.14,0.79],
+    [3.14,1.57], [3.14,2.36], [3.14,3.14],
+])
+
+pathological_data_2 = np.array([
+    [-1, -1], [-1, 0], [-1, 1],
+    [0, -1], [0, 0], [0, 1],
+    [1, -1 - np.finfo(np.float64).eps], [1, 0], [1, 1],
+])
+
+bug_2850_chunks = [np.random.rand(10, 2),
+                   np.array([[0,0], [0,1], [1,0], [1,1]])  # add corners
+                   ]
+
+# same with some additional chunks
+bug_2850_chunks_2 = (bug_2850_chunks +
+                     [np.random.rand(10, 2),
+                      0.25 + np.array([[0,0], [0,1], [1,0], [1,1]])])
+
+DATASETS = {
+    'some-points': np.asarray(points),
+    'random-2d': np.random.rand(30, 2),
+    'random-3d': np.random.rand(30, 3),
+    'random-4d': np.random.rand(30, 4),
+    'random-5d': np.random.rand(30, 5),
+    'random-6d': np.random.rand(10, 6),
+    'random-7d': np.random.rand(10, 7),
+    'random-8d': np.random.rand(10, 8),
+    'pathological-1': pathological_data_1,
+    'pathological-2': pathological_data_2
+}
+
+INCREMENTAL_DATASETS = {
+    'bug-2850': (bug_2850_chunks, None),
+    'bug-2850-2': (bug_2850_chunks_2, None),
+}
+
+
+def _add_inc_data(name, chunksize):
+    """
+    Generate incremental datasets from basic data sets
+    """
+    points = DATASETS[name]
+    ndim = points.shape[1]
+
+    opts = None
+    nmin = ndim + 2
+
+    if name == 'some-points':
+        # since Qz is not allowed, use QJ
+        opts = 'QJ Pp'
+    elif name == 'pathological-1':
+        # include enough points so that we get different x-coordinates
+        nmin = 12
+
+    chunks = [points[:nmin]]
+    for j in range(nmin, len(points), chunksize):
+        chunks.append(points[j:j+chunksize])
+
+    new_name = f"{name}-chunk-{chunksize}"
+    assert new_name not in INCREMENTAL_DATASETS
+    INCREMENTAL_DATASETS[new_name] = (chunks, opts)
+
+
+for name in DATASETS:
+    for chunksize in 1, 4, 16:
+        _add_inc_data(name, chunksize)
+
+
+class Test_Qhull:
+    def test_swapping(self):
+        # Check that Qhull state swapping works
+
+        x = qhull._Qhull(b'v',
+                         np.array([[0,0],[0,1],[1,0],[1,1.],[0.5,0.5]]),
+                         b'Qz')
+        xd = copy.deepcopy(x.get_voronoi_diagram())
+
+        y = qhull._Qhull(b'v',
+                         np.array([[0,0],[0,1],[1,0],[1,2.]]),
+                         b'Qz')
+        yd = copy.deepcopy(y.get_voronoi_diagram())
+
+        xd2 = copy.deepcopy(x.get_voronoi_diagram())
+        x.close()
+        yd2 = copy.deepcopy(y.get_voronoi_diagram())
+        y.close()
+
+        assert_raises(RuntimeError, x.get_voronoi_diagram)
+        assert_raises(RuntimeError, y.get_voronoi_diagram)
+
+        assert_allclose(xd[0], xd2[0])
+        assert_unordered_tuple_list_equal(xd[1], xd2[1], tpl=sorted_tuple)
+        assert_unordered_tuple_list_equal(xd[2], xd2[2], tpl=sorted_tuple)
+        assert_unordered_tuple_list_equal(xd[3], xd2[3], tpl=sorted_tuple)
+        assert_array_equal(xd[4], xd2[4])
+
+        assert_allclose(yd[0], yd2[0])
+        assert_unordered_tuple_list_equal(yd[1], yd2[1], tpl=sorted_tuple)
+        assert_unordered_tuple_list_equal(yd[2], yd2[2], tpl=sorted_tuple)
+        assert_unordered_tuple_list_equal(yd[3], yd2[3], tpl=sorted_tuple)
+        assert_array_equal(yd[4], yd2[4])
+
+        x.close()
+        assert_raises(RuntimeError, x.get_voronoi_diagram)
+        y.close()
+        assert_raises(RuntimeError, y.get_voronoi_diagram)
+
+    def test_issue_8051(self):
+        points = np.array(
+            [[0, 0], [0, 1], [0, 2], [1, 0], [1, 1], [1, 2],[2, 0], [2, 1], [2, 2]]
+        )
+        Voronoi(points)
+
+
+class TestUtilities:
+    """
+    Check that utility functions work.
+
+    """
+
+    def test_find_simplex(self):
+        # Simple check that simplex finding works
+        points = np.array([(0,0), (0,1), (1,1), (1,0)], dtype=np.float64)
+        tri = qhull.Delaunay(points)
+
+        # +---+
+        # |\ 0|
+        # | \ |
+        # |1 \|
+        # +---+
+
+        assert_equal(tri.simplices, [[1, 3, 2], [3, 1, 0]])
+
+        for p in [(0.25, 0.25, 1),
+                  (0.75, 0.75, 0),
+                  (0.3, 0.2, 1)]:
+            i = tri.find_simplex(p[:2])
+            assert_equal(i, p[2], err_msg=f'{p!r}')
+            with pytest.warns(DeprecationWarning, match="`tsearch` is deprecated"):
+                j = qhull.tsearch(tri, p[:2])
+            assert_equal(i, j)
+
+    def test_plane_distance(self):
+        # Compare plane distance from hyperplane equations obtained from Qhull
+        # to manually computed plane equations
+        x = np.array([(0,0), (1, 1), (1, 0), (0.99189033, 0.37674127),
+                      (0.99440079, 0.45182168)], dtype=np.float64)
+        p = np.array([0.99966555, 0.15685619], dtype=np.float64)
+
+        tri = qhull.Delaunay(x)
+
+        z = tri.lift_points(x)
+        pz = tri.lift_points(p)
+
+        dist = tri.plane_distance(p)
+
+        for j, v in enumerate(tri.simplices):
+            x1 = z[v[0]]
+            x2 = z[v[1]]
+            x3 = z[v[2]]
+
+            n = np.cross(x1 - x3, x2 - x3)
+            n /= np.sqrt(np.dot(n, n))
+            n *= -np.sign(n[2])
+
+            d = np.dot(n, pz - x3)
+
+            assert_almost_equal(dist[j], d)
+
+    def test_convex_hull(self):
+        # Simple check that the convex hull seems to works
+        points = np.array([(0,0), (0,1), (1,1), (1,0)], dtype=np.float64)
+        tri = qhull.Delaunay(points)
+
+        # +---+
+        # |\ 0|
+        # | \ |
+        # |1 \|
+        # +---+
+
+        assert_equal(tri.convex_hull, [[3, 2], [1, 2], [1, 0], [3, 0]])
+
+    def test_volume_area(self):
+        #Basic check that we get back the correct volume and area for a cube
+        points = np.array([(0, 0, 0), (0, 1, 0), (1, 0, 0), (1, 1, 0),
+                           (0, 0, 1), (0, 1, 1), (1, 0, 1), (1, 1, 1)])
+        hull = qhull.ConvexHull(points)
+
+        assert_allclose(hull.volume, 1., rtol=1e-14,
+                        err_msg="Volume of cube is incorrect")
+        assert_allclose(hull.area, 6., rtol=1e-14,
+                        err_msg="Area of cube is incorrect")
+
+    def test_random_volume_area(self):
+        #Test that the results for a random 10-point convex are
+        #coherent with the output of qconvex Qt s FA
+        points = np.array([(0.362568364506, 0.472712355305, 0.347003084477),
+                           (0.733731893414, 0.634480295684, 0.950513180209),
+                           (0.511239955611, 0.876839441267, 0.418047827863),
+                           (0.0765906233393, 0.527373281342, 0.6509863541),
+                           (0.146694972056, 0.596725793348, 0.894860986685),
+                           (0.513808585741, 0.069576205858, 0.530890338876),
+                           (0.512343805118, 0.663537132612, 0.037689295973),
+                           (0.47282965018, 0.462176697655, 0.14061843691),
+                           (0.240584597123, 0.778660020591, 0.722913476339),
+                           (0.951271745935, 0.967000673944, 0.890661319684)])
+
+        hull = qhull.ConvexHull(points)
+        assert_allclose(hull.volume, 0.14562013, rtol=1e-07,
+                        err_msg="Volume of random polyhedron is incorrect")
+        assert_allclose(hull.area, 1.6670425, rtol=1e-07,
+                        err_msg="Area of random polyhedron is incorrect")
+
+    def test_incremental_volume_area_random_input(self):
+        """Test that incremental mode gives the same volume/area as
+        non-incremental mode and incremental mode with restart"""
+        nr_points = 20
+        dim = 3
+        points = np.random.random((nr_points, dim))
+        inc_hull = qhull.ConvexHull(points[:dim+1, :], incremental=True)
+        inc_restart_hull = qhull.ConvexHull(points[:dim+1, :], incremental=True)
+        for i in range(dim+1, nr_points):
+            hull = qhull.ConvexHull(points[:i+1, :])
+            inc_hull.add_points(points[i:i+1, :])
+            inc_restart_hull.add_points(points[i:i+1, :], restart=True)
+            assert_allclose(hull.volume, inc_hull.volume, rtol=1e-7)
+            assert_allclose(hull.volume, inc_restart_hull.volume, rtol=1e-7)
+            assert_allclose(hull.area, inc_hull.area, rtol=1e-7)
+            assert_allclose(hull.area, inc_restart_hull.area, rtol=1e-7)
+
+    def _check_barycentric_transforms(self, tri, err_msg="",
+                                      unit_cube=False,
+                                      unit_cube_tol=0):
+        """Check that a triangulation has reasonable barycentric transforms"""
+        vertices = tri.points[tri.simplices]
+        sc = 1/(tri.ndim + 1.0)
+        centroids = vertices.sum(axis=1) * sc
+
+        # Either: (i) the simplex has a `nan` barycentric transform,
+        # or, (ii) the centroid is in the simplex
+
+        def barycentric_transform(tr, x):
+            r = tr[:,-1,:]
+            Tinv = tr[:,:-1,:]
+            return np.einsum('ijk,ik->ij', Tinv, x - r)
+
+        eps = np.finfo(float).eps
+
+        c = barycentric_transform(tri.transform, centroids)
+        with np.errstate(invalid="ignore"):
+            ok = np.isnan(c).all(axis=1) | (abs(c - sc)/sc < 0.1).all(axis=1)
+
+        assert_(ok.all(), f"{err_msg} {np.nonzero(~ok)}")
+
+        # Invalid simplices must be (nearly) zero volume
+        q = vertices[:,:-1,:] - vertices[:,-1,None,:]
+        volume = np.array([np.linalg.det(q[k,:,:])
+                           for k in range(tri.nsimplex)])
+        ok = np.isfinite(tri.transform[:,0,0]) | (volume < np.sqrt(eps))
+        assert_(ok.all(), f"{err_msg} {np.nonzero(~ok)}")
+
+        # Also, find_simplex for the centroid should end up in some
+        # simplex for the non-degenerate cases
+        j = tri.find_simplex(centroids)
+        ok = (j != -1) | np.isnan(tri.transform[:,0,0])
+        assert_(ok.all(), f"{err_msg} {np.nonzero(~ok)}")
+
+        if unit_cube:
+            # If in unit cube, no interior point should be marked out of hull
+            at_boundary = (centroids <= unit_cube_tol).any(axis=1)
+            at_boundary |= (centroids >= 1 - unit_cube_tol).any(axis=1)
+
+            ok = (j != -1) | at_boundary
+            assert_(ok.all(), f"{err_msg} {np.nonzero(~ok)}")
+
+    @pytest.mark.fail_slow(10)
+    def test_degenerate_barycentric_transforms(self):
+        # The triangulation should not produce invalid barycentric
+        # transforms that stump the simplex finding
+        data = np.load(os.path.join(os.path.dirname(__file__), 'data',
+                                    'degenerate_pointset.npz'))
+        points = data['c']
+        data.close()
+
+        tri = qhull.Delaunay(points)
+
+        # Check that there are not too many invalid simplices
+        bad_count = np.isnan(tri.transform[:,0,0]).sum()
+        assert_(bad_count < 23, bad_count)
+
+        # Check the transforms
+        self._check_barycentric_transforms(tri)
+
+    @pytest.mark.slow
+    @pytest.mark.fail_slow(20)
+    # OK per https://github.com/scipy/scipy/pull/20487#discussion_r1572684869
+    def test_more_barycentric_transforms(self):
+        # Triangulate some "nasty" grids
+
+        eps = np.finfo(float).eps
+
+        npoints = {2: 70, 3: 11, 4: 5, 5: 3}
+
+        for ndim in range(2, 6):
+            # Generate a uniform grid in n-d unit cube
+            x = np.linspace(0, 1, npoints[ndim])
+            grid = np.c_[
+                list(map(np.ravel, np.broadcast_arrays(*np.ix_(*([x]*ndim)))))
+            ].T
+
+            err_msg = f"ndim={ndim}"
+
+            # Check using regular grid
+            tri = qhull.Delaunay(grid)
+            self._check_barycentric_transforms(tri, err_msg=err_msg,
+                                               unit_cube=True)
+
+            # Check with eps-perturbations
+            np.random.seed(1234)
+            m = (np.random.rand(grid.shape[0]) < 0.2)
+            grid[m,:] += 2*eps*(np.random.rand(*grid[m,:].shape) - 0.5)
+
+            tri = qhull.Delaunay(grid)
+            self._check_barycentric_transforms(tri, err_msg=err_msg,
+                                               unit_cube=True,
+                                               unit_cube_tol=2*eps)
+
+            # Check with duplicated data
+            tri = qhull.Delaunay(np.r_[grid, grid])
+            self._check_barycentric_transforms(tri, err_msg=err_msg,
+                                               unit_cube=True,
+                                               unit_cube_tol=2*eps)
+
+
+class TestVertexNeighborVertices:
+    def _check(self, tri):
+        expected = [set() for j in range(tri.points.shape[0])]
+        for s in tri.simplices:
+            for a in s:
+                for b in s:
+                    if a != b:
+                        expected[a].add(b)
+
+        indptr, indices = tri.vertex_neighbor_vertices
+
+        got = [set(map(int, indices[indptr[j]:indptr[j+1]]))
+               for j in range(tri.points.shape[0])]
+
+        assert_equal(got, expected, err_msg=f"{got!r} != {expected!r}")
+
+    def test_triangle(self):
+        points = np.array([(0,0), (0,1), (1,0)], dtype=np.float64)
+        tri = qhull.Delaunay(points)
+        self._check(tri)
+
+    def test_rectangle(self):
+        points = np.array([(0,0), (0,1), (1,1), (1,0)], dtype=np.float64)
+        tri = qhull.Delaunay(points)
+        self._check(tri)
+
+    def test_complicated(self):
+        points = np.array([(0,0), (0,1), (1,1), (1,0),
+                           (0.5, 0.5), (0.9, 0.5)], dtype=np.float64)
+        tri = qhull.Delaunay(points)
+        self._check(tri)
+
+
+class TestDelaunay:
+    """
+    Check that triangulation works.
+
+    """
+    def test_masked_array_fails(self):
+        masked_array = np.ma.masked_all(1)
+        assert_raises(ValueError, qhull.Delaunay, masked_array)
+
+    # Shouldn't be inherently unsafe; retry with cpython 3.14 once traceback
+    # thread safety issues are fixed (also goes for other test with same name
+    # further down)
+    def test_array_with_nans_fails(self):
+        points_with_nan = np.array([(0,0), (0,1), (1,1), (1,np.nan)], dtype=np.float64)
+        assert_raises(ValueError, qhull.Delaunay, points_with_nan)
+
+    def test_nd_simplex(self):
+        # simple smoke test: triangulate a n-dimensional simplex
+        for nd in range(2, 8):
+            points = np.zeros((nd+1, nd))
+            for j in range(nd):
+                points[j,j] = 1.0
+            points[-1,:] = 1.0
+
+            tri = qhull.Delaunay(points)
+
+            tri.simplices.sort()
+
+            assert_equal(tri.simplices, np.arange(nd+1, dtype=int)[None, :])
+            assert_equal(tri.neighbors, -1 + np.zeros((nd+1), dtype=int)[None,:])
+
+    def test_2d_square(self):
+        # simple smoke test: 2d square
+        points = np.array([(0,0), (0,1), (1,1), (1,0)], dtype=np.float64)
+        tri = qhull.Delaunay(points)
+
+        assert_equal(tri.simplices, [[1, 3, 2], [3, 1, 0]])
+        assert_equal(tri.neighbors, [[-1, -1, 1], [-1, -1, 0]])
+
+    def test_duplicate_points(self):
+        x = np.array([0, 1, 0, 1], dtype=np.float64)
+        y = np.array([0, 0, 1, 1], dtype=np.float64)
+
+        xp = np.r_[x, x]
+        yp = np.r_[y, y]
+
+        # shouldn't fail on duplicate points
+        qhull.Delaunay(np.c_[x, y])
+        qhull.Delaunay(np.c_[xp, yp])
+
+    def test_pathological(self):
+        # both should succeed
+        points = DATASETS['pathological-1']
+        tri = qhull.Delaunay(points)
+        assert_equal(tri.points[tri.simplices].max(), points.max())
+        assert_equal(tri.points[tri.simplices].min(), points.min())
+
+        points = DATASETS['pathological-2']
+        tri = qhull.Delaunay(points)
+        assert_equal(tri.points[tri.simplices].max(), points.max())
+        assert_equal(tri.points[tri.simplices].min(), points.min())
+
+    def test_joggle(self):
+        # Check that the option QJ indeed guarantees that all input points
+        # occur as vertices of the triangulation
+
+        points = np.random.rand(10, 2)
+        points = np.r_[points, points]  # duplicate input data
+
+        tri = qhull.Delaunay(points, qhull_options="QJ Qbb Pp")
+        assert_array_equal(np.unique(tri.simplices.ravel()),
+                           np.arange(len(points)))
+
+    def test_coplanar(self):
+        # Check that the coplanar point output option indeed works
+        points = np.random.rand(10, 2)
+        points = np.r_[points, points]  # duplicate input data
+
+        tri = qhull.Delaunay(points)
+
+        assert_(len(np.unique(tri.simplices.ravel())) == len(points)//2)
+        assert_(len(tri.coplanar) == len(points)//2)
+
+        assert_(len(np.unique(tri.coplanar[:,2])) == len(points)//2)
+
+        assert_(np.all(tri.vertex_to_simplex >= 0))
+
+    def test_furthest_site(self):
+        points = [(0, 0), (0, 1), (1, 0), (0.5, 0.5), (1.1, 1.1)]
+        tri = qhull.Delaunay(points, furthest_site=True)
+
+        expected = np.array([(1, 4, 0), (4, 2, 0)])  # from Qhull
+        assert_array_equal(tri.simplices, expected)
+
+    @pytest.mark.parametrize("name", sorted(INCREMENTAL_DATASETS))
+    def test_incremental(self, name):
+        # Test incremental construction of the triangulation
+
+        chunks, opts = INCREMENTAL_DATASETS[name]
+        points = np.concatenate(chunks, axis=0)
+
+        obj = qhull.Delaunay(chunks[0], incremental=True,
+                             qhull_options=opts)
+        for chunk in chunks[1:]:
+            obj.add_points(chunk)
+
+        obj2 = qhull.Delaunay(points)
+
+        obj3 = qhull.Delaunay(chunks[0], incremental=True,
+                              qhull_options=opts)
+        if len(chunks) > 1:
+            obj3.add_points(np.concatenate(chunks[1:], axis=0),
+                            restart=True)
+
+        # Check that the incremental mode agrees with upfront mode
+        if name.startswith('pathological'):
+            # XXX: These produce valid but different triangulations.
+            #      They look OK when plotted, but how to check them?
+
+            assert_array_equal(np.unique(obj.simplices.ravel()),
+                               np.arange(points.shape[0]))
+            assert_array_equal(np.unique(obj2.simplices.ravel()),
+                               np.arange(points.shape[0]))
+        else:
+            assert_unordered_tuple_list_equal(obj.simplices, obj2.simplices,
+                                              tpl=sorted_tuple)
+
+        assert_unordered_tuple_list_equal(obj2.simplices, obj3.simplices,
+                                          tpl=sorted_tuple)
+
+
+def assert_hulls_equal(points, facets_1, facets_2):
+    # Check that two convex hulls constructed from the same point set
+    # are equal
+
+    facets_1 = set(map(sorted_tuple, facets_1))
+    facets_2 = set(map(sorted_tuple, facets_2))
+
+    if facets_1 != facets_2 and points.shape[1] == 2:
+        # The direct check fails for the pathological cases
+        # --- then the convex hull from Delaunay differs (due
+        # to rounding error etc.) from the hull computed
+        # otherwise, by the question whether (tricoplanar)
+        # points that lie almost exactly on the hull are
+        # included as vertices of the hull or not.
+        #
+        # So we check the result, and accept it if the Delaunay
+        # hull line segments are a subset of the usual hull.
+
+        eps = 1000 * np.finfo(float).eps
+
+        for a, b in facets_1:
+            for ap, bp in facets_2:
+                t = points[bp] - points[ap]
+                t /= np.linalg.norm(t)       # tangent
+                n = np.array([-t[1], t[0]])  # normal
+
+                # check that the two line segments are parallel
+                # to the same line
+                c1 = np.dot(n, points[b] - points[ap])
+                c2 = np.dot(n, points[a] - points[ap])
+                if not np.allclose(np.dot(c1, n), 0):
+                    continue
+                if not np.allclose(np.dot(c2, n), 0):
+                    continue
+
+                # Check that the segment (a, b) is contained in (ap, bp)
+                c1 = np.dot(t, points[a] - points[ap])
+                c2 = np.dot(t, points[b] - points[ap])
+                c3 = np.dot(t, points[bp] - points[ap])
+                if c1 < -eps or c1 > c3 + eps:
+                    continue
+                if c2 < -eps or c2 > c3 + eps:
+                    continue
+
+                # OK:
+                break
+            else:
+                raise AssertionError("comparison fails")
+
+        # it was OK
+        return
+
+    assert_equal(facets_1, facets_2)
+
+
+class TestConvexHull:
+    def test_masked_array_fails(self):
+        masked_array = np.ma.masked_all(1)
+        assert_raises(ValueError, qhull.ConvexHull, masked_array)
+
+    def test_array_with_nans_fails(self):
+        points_with_nan = np.array([(0,0), (1,1), (2,np.nan)], dtype=np.float64)
+        assert_raises(ValueError, qhull.ConvexHull, points_with_nan)
+
+    @pytest.mark.parametrize("name", sorted(DATASETS))
+    def test_hull_consistency_tri(self, name):
+        # Check that a convex hull returned by qhull in ndim
+        # and the hull constructed from ndim delaunay agree
+        points = DATASETS[name]
+
+        tri = qhull.Delaunay(points)
+        hull = qhull.ConvexHull(points)
+
+        assert_hulls_equal(points, tri.convex_hull, hull.simplices)
+
+        # Check that the hull extremes are as expected
+        if points.shape[1] == 2:
+            assert_equal(np.unique(hull.simplices), np.sort(hull.vertices))
+        else:
+            assert_equal(np.unique(hull.simplices), hull.vertices)
+
+    @pytest.mark.parametrize("name", sorted(INCREMENTAL_DATASETS))
+    def test_incremental(self, name):
+        # Test incremental construction of the convex hull
+        chunks, _ = INCREMENTAL_DATASETS[name]
+        points = np.concatenate(chunks, axis=0)
+
+        obj = qhull.ConvexHull(chunks[0], incremental=True)
+        for chunk in chunks[1:]:
+            obj.add_points(chunk)
+
+        obj2 = qhull.ConvexHull(points)
+
+        obj3 = qhull.ConvexHull(chunks[0], incremental=True)
+        if len(chunks) > 1:
+            obj3.add_points(np.concatenate(chunks[1:], axis=0),
+                            restart=True)
+
+        # Check that the incremental mode agrees with upfront mode
+        assert_hulls_equal(points, obj.simplices, obj2.simplices)
+        assert_hulls_equal(points, obj.simplices, obj3.simplices)
+
+    def test_vertices_2d(self):
+        # The vertices should be in counterclockwise order in 2-D
+        np.random.seed(1234)
+        points = np.random.rand(30, 2)
+
+        hull = qhull.ConvexHull(points)
+        assert_equal(np.unique(hull.simplices), np.sort(hull.vertices))
+
+        # Check counterclockwiseness
+        x, y = hull.points[hull.vertices].T
+        angle = np.arctan2(y - y.mean(), x - x.mean())
+        assert_(np.all(np.diff(np.unwrap(angle)) > 0))
+
+    def test_volume_area(self):
+        # Basic check that we get back the correct volume and area for a cube
+        points = np.array([(0, 0, 0), (0, 1, 0), (1, 0, 0), (1, 1, 0),
+                           (0, 0, 1), (0, 1, 1), (1, 0, 1), (1, 1, 1)])
+        tri = qhull.ConvexHull(points)
+
+        assert_allclose(tri.volume, 1., rtol=1e-14)
+        assert_allclose(tri.area, 6., rtol=1e-14)
+
+    @pytest.mark.parametrize("incremental", [False, True])
+    def test_good2d(self, incremental):
+        # Make sure the QGn option gives the correct value of "good".
+        points = np.array([[0.2, 0.2],
+                           [0.2, 0.4],
+                           [0.4, 0.4],
+                           [0.4, 0.2],
+                           [0.3, 0.6]])
+        hull = qhull.ConvexHull(points=points,
+                                incremental=incremental,
+                                qhull_options='QG4')
+        expected = np.array([False, True, False, False], dtype=bool)
+        actual = hull.good
+        assert_equal(actual, expected)
+
+    @pytest.mark.parametrize("visibility", [
+                              "QG4",  # visible=True
+                              "QG-4",  # visible=False
+                              ])
+    @pytest.mark.parametrize("new_gen, expected", [
+        # add generator that places QG4 inside hull
+        # so all facets are invisible
+        (np.array([[0.3, 0.7]]),
+         np.array([False, False, False, False, False], dtype=bool)),
+        # adding a generator on the opposite side of the square
+        # should preserve the single visible facet & add one invisible
+        # facet
+        (np.array([[0.3, -0.7]]),
+         np.array([False, True, False, False, False], dtype=bool)),
+        # split the visible facet on top of the square into two
+        # visible facets, with visibility at the end of the array
+        # because add_points concatenates
+        (np.array([[0.3, 0.41]]),
+         np.array([False, False, False, True, True], dtype=bool)),
+        # with our current Qhull options, coplanarity will not count
+        # for visibility; this case shifts one visible & one invisible
+        # facet & adds a coplanar facet
+        # simplex at index position 2 is the shifted visible facet
+        # the final simplex is the coplanar facet
+        (np.array([[0.5, 0.6], [0.6, 0.6]]),
+         np.array([False, False, True, False, False], dtype=bool)),
+        # place the new generator such that it envelops the query
+        # point within the convex hull, but only just barely within
+        # the double precision limit
+        # NOTE: testing exact degeneracy is less predictable than this
+        # scenario, perhaps because of the default Qt option we have
+        # enabled for Qhull to handle precision matters
+        (np.array([[0.3, 0.6 + 1e-16]]),
+         np.array([False, False, False, False, False], dtype=bool)),
+        ])
+    def test_good2d_incremental_changes(self, new_gen, expected,
+                                        visibility):
+        # use the usual square convex hull
+        # generators from test_good2d
+        points = np.array([[0.2, 0.2],
+                           [0.2, 0.4],
+                           [0.4, 0.4],
+                           [0.4, 0.2],
+                           [0.3, 0.6]])
+        hull = qhull.ConvexHull(points=points,
+                                incremental=True,
+                                qhull_options=visibility)
+        hull.add_points(new_gen)
+        actual = hull.good
+        if '-' in visibility:
+            expected = np.invert(expected)
+        assert_equal(actual, expected)
+
+    @pytest.mark.parametrize("incremental", [False, True])
+    def test_good2d_no_option(self, incremental):
+        # handle case where good attribute doesn't exist
+        # because Qgn or Qg-n wasn't specified
+        points = np.array([[0.2, 0.2],
+                           [0.2, 0.4],
+                           [0.4, 0.4],
+                           [0.4, 0.2],
+                           [0.3, 0.6]])
+        hull = qhull.ConvexHull(points=points,
+                                incremental=incremental)
+        actual = hull.good
+        assert actual is None
+        # preserve None after incremental addition
+        if incremental:
+            hull.add_points(np.zeros((1, 2)))
+            actual = hull.good
+            assert actual is None
+
+    @pytest.mark.parametrize("incremental", [False, True])
+    def test_good2d_inside(self, incremental):
+        # Make sure the QGn option gives the correct value of "good".
+        # When point n is inside the convex hull of the rest, good is
+        # all False.
+        points = np.array([[0.2, 0.2],
+                           [0.2, 0.4],
+                           [0.4, 0.4],
+                           [0.4, 0.2],
+                           [0.3, 0.3]])
+        hull = qhull.ConvexHull(points=points,
+                                incremental=incremental,
+                                qhull_options='QG4')
+        expected = np.array([False, False, False, False], dtype=bool)
+        actual = hull.good
+        assert_equal(actual, expected)
+
+    @pytest.mark.parametrize("incremental", [False, True])
+    def test_good3d(self, incremental):
+        # Make sure the QGn option gives the correct value of "good"
+        # for a 3d figure
+        points = np.array([[0.0, 0.0, 0.0],
+                           [0.90029516, -0.39187448, 0.18948093],
+                           [0.48676420, -0.72627633, 0.48536925],
+                           [0.57651530, -0.81179274, -0.09285832],
+                           [0.67846893, -0.71119562, 0.18406710]])
+        hull = qhull.ConvexHull(points=points,
+                                incremental=incremental,
+                                qhull_options='QG0')
+        expected = np.array([True, False, False, False], dtype=bool)
+        assert_equal(hull.good, expected)
+
+class TestVoronoi:
+
+    @pytest.mark.parametrize("qhull_opts, extra_pts", [
+        # option Qz (default for SciPy) will add
+        # an extra point at infinity
+        ("Qbb Qc Qz", 1),
+        ("Qbb Qc", 0),
+    ])
+    @pytest.mark.parametrize("n_pts", [50, 100])
+    @pytest.mark.parametrize("ndim", [2, 3])
+    def test_point_region_structure(self,
+                                    qhull_opts,
+                                    n_pts,
+                                    extra_pts,
+                                    ndim):
+        # see gh-16773
+        rng = np.random.default_rng(7790)
+        points = rng.random((n_pts, ndim))
+        vor = Voronoi(points, qhull_options=qhull_opts)
+        pt_region = vor.point_region
+        assert pt_region.max() == n_pts - 1 + extra_pts
+        assert pt_region.size == len(vor.regions) - extra_pts
+        assert len(vor.regions) == n_pts + extra_pts
+        assert vor.points.shape[0] == n_pts
+        # if there is an empty sublist in the Voronoi
+        # regions data structure, it should never be
+        # indexed because it corresponds to an internally
+        # added point at infinity and is not a member of the
+        # generators (input points)
+        if extra_pts:
+            sublens = [len(x) for x in vor.regions]
+            # only one point at infinity (empty region)
+            # is allowed
+            assert sublens.count(0) == 1
+            assert sublens.index(0) not in pt_region
+
+    def test_masked_array_fails(self):
+        masked_array = np.ma.masked_all(1)
+        assert_raises(ValueError, qhull.Voronoi, masked_array)
+
+    def test_simple(self):
+        # Simple case with known Voronoi diagram
+        points = [(0, 0), (0, 1), (0, 2),
+                  (1, 0), (1, 1), (1, 2),
+                  (2, 0), (2, 1), (2, 2)]
+
+        # qhull v o Fv Qbb Qc Qz < dat
+        output = """
+        2
+        5 10 1
+        -10.101 -10.101
+           0.5    0.5
+           0.5    1.5
+           1.5    0.5
+           1.5    1.5
+        2 0 1
+        3 2 0 1
+        2 0 2
+        3 3 0 1
+        4 1 2 4 3
+        3 4 0 2
+        2 0 3
+        3 4 0 3
+        2 0 4
+        0
+        12
+        4 0 3 0 1
+        4 0 1 0 1
+        4 1 4 1 2
+        4 1 2 0 2
+        4 2 5 0 2
+        4 3 4 1 3
+        4 3 6 0 3
+        4 4 5 2 4
+        4 4 7 3 4
+        4 5 8 0 4
+        4 6 7 0 3
+        4 7 8 0 4
+        """
+        self._compare_qvoronoi(points, output)
+
+    def _compare_qvoronoi(self, points, output, **kw):
+        """Compare to output from 'qvoronoi o Fv < data' to Voronoi()"""
+
+        # Parse output
+        output = [list(map(float, x.split())) for x in output.strip().splitlines()]
+        nvertex = int(output[1][0])
+        vertices = list(map(tuple, output[3:2+nvertex]))  # exclude inf
+        nregion = int(output[1][1])
+        regions = [[int(y)-1 for y in x[1:]]
+                   for x in output[2+nvertex:2+nvertex+nregion]]
+        ridge_points = [[int(y) for y in x[1:3]]
+                        for x in output[3+nvertex+nregion:]]
+        ridge_vertices = [[int(y)-1 for y in x[3:]]
+                          for x in output[3+nvertex+nregion:]]
+
+        # Compare results
+        vor = qhull.Voronoi(points, **kw)
+
+        def sorttuple(x):
+            return tuple(sorted(x))
+
+        assert_allclose(vor.vertices, vertices)
+        assert_equal(set(map(tuple, vor.regions)),
+                     set(map(tuple, regions)))
+
+        p1 = list(zip(list(map(sorttuple, ridge_points)),
+                      list(map(sorttuple, ridge_vertices))))
+        p2 = list(zip(list(map(sorttuple, vor.ridge_points.tolist())),
+                      list(map(sorttuple, vor.ridge_vertices))))
+        p1.sort()
+        p2.sort()
+
+        assert_equal(p1, p2)
+
+    @pytest.mark.parametrize("name", sorted(DATASETS))
+    def test_ridges(self, name):
+        # Check that the ridges computed by Voronoi indeed separate
+        # the regions of nearest neighborhood, by comparing the result
+        # to KDTree.
+
+        points = DATASETS[name]
+
+        tree = KDTree(points)
+        vor = qhull.Voronoi(points)
+
+        for p, v in vor.ridge_dict.items():
+            # consider only finite ridges
+            if not np.all(np.asarray(v) >= 0):
+                continue
+
+            ridge_midpoint = vor.vertices[v].mean(axis=0)
+            d = 1e-6 * (points[p[0]] - ridge_midpoint)
+
+            dist, k = tree.query(ridge_midpoint + d, k=1)
+            assert_equal(k, p[0])
+
+            dist, k = tree.query(ridge_midpoint - d, k=1)
+            assert_equal(k, p[1])
+
+    def test_furthest_site(self):
+        points = [(0, 0), (0, 1), (1, 0), (0.5, 0.5), (1.1, 1.1)]
+
+        # qhull v o Fv Qbb Qc Qu < dat
+        output = """
+        2
+        3 5 1
+        -10.101 -10.101
+        0.6000000000000001    0.5
+           0.5 0.6000000000000001
+        3 0 2 1
+        2 0 1
+        2 0 2
+        0
+        3 0 2 1
+        5
+        4 0 2 0 2
+        4 0 4 1 2
+        4 0 1 0 1
+        4 1 4 0 1
+        4 2 4 0 2
+        """
+        self._compare_qvoronoi(points, output, furthest_site=True)
+
+    def test_furthest_site_flag(self):
+        points = [(0, 0), (0, 1), (1, 0), (0.5, 0.5), (1.1, 1.1)]
+
+        vor = Voronoi(points)
+        assert_equal(vor.furthest_site,False)
+        vor = Voronoi(points,furthest_site=True)
+        assert_equal(vor.furthest_site,True)
+
+    @pytest.mark.fail_slow(10)
+    @pytest.mark.parametrize("name", sorted(INCREMENTAL_DATASETS))
+    def test_incremental(self, name):
+        # Test incremental construction of the triangulation
+
+        if INCREMENTAL_DATASETS[name][0][0].shape[1] > 3:
+            # too slow (testing of the result --- qhull is still fast)
+            return
+
+        chunks, opts = INCREMENTAL_DATASETS[name]
+        points = np.concatenate(chunks, axis=0)
+
+        obj = qhull.Voronoi(chunks[0], incremental=True,
+                             qhull_options=opts)
+        for chunk in chunks[1:]:
+            obj.add_points(chunk)
+
+        obj2 = qhull.Voronoi(points)
+
+        obj3 = qhull.Voronoi(chunks[0], incremental=True,
+                             qhull_options=opts)
+        if len(chunks) > 1:
+            obj3.add_points(np.concatenate(chunks[1:], axis=0),
+                            restart=True)
+
+        # -- Check that the incremental mode agrees with upfront mode
+        assert_equal(len(obj.point_region), len(obj2.point_region))
+        assert_equal(len(obj.point_region), len(obj3.point_region))
+
+        # The vertices may be in different order or duplicated in
+        # the incremental map
+        for objx in obj, obj3:
+            vertex_map = {-1: -1}
+            for i, v in enumerate(objx.vertices):
+                for j, v2 in enumerate(obj2.vertices):
+                    if np.allclose(v, v2):
+                        vertex_map[i] = j
+
+            def remap(x):
+                if hasattr(x, '__len__'):
+                    return tuple({remap(y) for y in x})
+                try:
+                    return vertex_map[x]
+                except KeyError as e:
+                    message = (f"incremental result has spurious vertex "
+                               f"at {objx.vertices[x]!r}")
+                    raise AssertionError(message) from e
+
+            def simplified(x):
+                items = set(map(sorted_tuple, x))
+                if () in items:
+                    items.remove(())
+                items = [x for x in items if len(x) > 1]
+                items.sort()
+                return items
+
+            assert_equal(
+                simplified(remap(objx.regions)),
+                simplified(obj2.regions)
+                )
+            assert_equal(
+                simplified(remap(objx.ridge_vertices)),
+                simplified(obj2.ridge_vertices)
+                )
+
+            # XXX: compare ridge_points --- not clear exactly how to do this
+
+
+class Test_HalfspaceIntersection:
+    def assert_unordered_allclose(self, arr1, arr2, rtol=1e-7):
+        """Check that every line in arr1 is only once in arr2"""
+        assert_equal(arr1.shape, arr2.shape)
+
+        truths = np.zeros((arr1.shape[0],), dtype=bool)
+        for l1 in arr1:
+            indexes = np.nonzero((abs(arr2 - l1) < rtol).all(axis=1))[0]
+            assert_equal(indexes.shape, (1,))
+            truths[indexes[0]] = True
+        assert_(truths.all())
+
+    @pytest.mark.parametrize("dt", [np.float64, int])
+    def test_cube_halfspace_intersection(self, dt):
+        halfspaces = np.array([[-1, 0, 0],
+                               [0, -1, 0],
+                               [1, 0, -2],
+                               [0, 1, -2]], dtype=dt)
+        feasible_point = np.array([1, 1], dtype=dt)
+
+        points = np.array([[0.0, 0.0], [2.0, 0.0], [0.0, 2.0], [2.0, 2.0]])
+
+        hull = qhull.HalfspaceIntersection(halfspaces, feasible_point)
+
+        assert_allclose(hull.intersections, points)
+
+    def test_self_dual_polytope_intersection(self):
+        fname = os.path.join(os.path.dirname(__file__), 'data',
+                             'selfdual-4d-polytope.txt')
+        ineqs = np.genfromtxt(fname)
+        halfspaces = -np.hstack((ineqs[:, 1:], ineqs[:, :1]))
+
+        feas_point = np.array([0., 0., 0., 0.])
+        hs = qhull.HalfspaceIntersection(halfspaces, feas_point)
+
+        assert_equal(hs.intersections.shape, (24, 4))
+
+        assert_almost_equal(hs.dual_volume, 32.0)
+        assert_equal(len(hs.dual_facets), 24)
+        for facet in hs.dual_facets:
+            assert_equal(len(facet), 6)
+
+        dists = halfspaces[:, -1] + halfspaces[:, :-1].dot(feas_point)
+        self.assert_unordered_allclose((halfspaces[:, :-1].T/dists).T, hs.dual_points)
+
+        points = itertools.permutations([0., 0., 0.5, -0.5])
+        for point in points:
+            assert_equal(np.sum((hs.intersections == point).all(axis=1)), 1)
+
+    def test_wrong_feasible_point(self):
+        halfspaces = np.array([[-1.0, 0.0, 0.0],
+                               [0.0, -1.0, 0.0],
+                               [1.0, 0.0, -1.0],
+                               [0.0, 1.0, -1.0]])
+        feasible_point = np.array([0.5, 0.5, 0.5])
+        #Feasible point is (ndim,) instead of (ndim-1,)
+        assert_raises(ValueError,
+                      qhull.HalfspaceIntersection, halfspaces, feasible_point)
+        feasible_point = np.array([[0.5], [0.5]])
+        #Feasible point is (ndim-1, 1) instead of (ndim-1,)
+        assert_raises(ValueError,
+                      qhull.HalfspaceIntersection, halfspaces, feasible_point)
+        feasible_point = np.array([[0.5, 0.5]])
+        #Feasible point is (1, ndim-1) instead of (ndim-1,)
+        assert_raises(ValueError,
+                      qhull.HalfspaceIntersection, halfspaces, feasible_point)
+
+        feasible_point = np.array([-0.5, -0.5])
+        #Feasible point is outside feasible region
+        assert_raises(qhull.QhullError,
+                      qhull.HalfspaceIntersection, halfspaces, feasible_point)
+
+    def test_incremental(self):
+        #Cube
+        halfspaces = np.array([[0., 0., -1., -0.5],
+                               [0., -1., 0., -0.5],
+                               [-1., 0., 0., -0.5],
+                               [1., 0., 0., -0.5],
+                               [0., 1., 0., -0.5],
+                               [0., 0., 1., -0.5]])
+        #Cut each summit
+        extra_normals = np.array([[1., 1., 1.],
+                                  [1., 1., -1.],
+                                  [1., -1., 1.],
+                                  [1, -1., -1.]])
+        offsets = np.array([[-1.]]*8)
+        extra_halfspaces = np.hstack((np.vstack((extra_normals, -extra_normals)),
+                                      offsets))
+
+        feas_point = np.array([0., 0., 0.])
+
+        inc_hs = qhull.HalfspaceIntersection(halfspaces, feas_point, incremental=True)
+
+        inc_res_hs = qhull.HalfspaceIntersection(halfspaces, feas_point,
+                                                 incremental=True)
+
+        for i, ehs in enumerate(extra_halfspaces):
+            inc_hs.add_halfspaces(ehs[np.newaxis, :])
+
+            inc_res_hs.add_halfspaces(ehs[np.newaxis, :], restart=True)
+
+            total = np.vstack((halfspaces, extra_halfspaces[:i+1, :]))
+
+            hs = qhull.HalfspaceIntersection(total, feas_point)
+
+            assert_allclose(inc_hs.halfspaces, inc_res_hs.halfspaces)
+            assert_allclose(inc_hs.halfspaces, hs.halfspaces)
+
+            #Direct computation and restart should have points in same order
+            assert_allclose(hs.intersections, inc_res_hs.intersections)
+            #Incremental will have points in different order than direct computation
+            self.assert_unordered_allclose(inc_hs.intersections, hs.intersections)
+
+        inc_hs.close()
+
+    def test_cube(self):
+        # Halfspaces of the cube:
+        halfspaces = np.array([[-1., 0., 0., 0.],  # x >= 0
+                               [1., 0., 0., -1.],  # x <= 1
+                               [0., -1., 0., 0.],  # y >= 0
+                               [0., 1., 0., -1.],  # y <= 1
+                               [0., 0., -1., 0.],  # z >= 0
+                               [0., 0., 1., -1.]])  # z <= 1
+        point = np.array([0.5, 0.5, 0.5])
+
+        hs = qhull.HalfspaceIntersection(halfspaces, point)
+
+        # qhalf H0.5,0.5,0.5 o < input.txt
+        qhalf_points = np.array([
+            [-2, 0, 0],
+            [2, 0, 0],
+            [0, -2, 0],
+            [0, 2, 0],
+            [0, 0, -2],
+            [0, 0, 2]])
+        qhalf_facets = [
+            [2, 4, 0],
+            [4, 2, 1],
+            [5, 2, 0],
+            [2, 5, 1],
+            [3, 4, 1],
+            [4, 3, 0],
+            [5, 3, 1],
+            [3, 5, 0]]
+
+        assert len(qhalf_facets) == len(hs.dual_facets)
+        for a, b in zip(qhalf_facets, hs.dual_facets):
+            assert set(a) == set(b)  # facet orientation can differ
+
+        assert_allclose(hs.dual_points, qhalf_points)
+
+    @pytest.mark.parametrize("k", range(1,4))
+    def test_halfspace_batch(self, k):
+        # Test that we can add halfspaces a few at a time
+        big_square = np.array([[ 1.,  0., -2.],
+                               [-1.,  0., -2.],
+                               [ 0.,  1., -2.],
+                               [ 0., -1., -2.]])
+
+        small_square = np.array([[ 1.,  0., -1.],
+                                 [-1.,  0., -1.],
+                                 [ 0.,  1., -1.],
+                                 [ 0., -1., -1.]])
+
+        hs = qhull.HalfspaceIntersection(big_square,
+                                         np.array([0.3141, 0.2718]),
+                                         incremental=True)
+
+        hs.add_halfspaces(small_square[0:k,:])
+        hs.add_halfspaces(small_square[k:4,:])
+        hs.close()
+
+        # Check the intersections are correct (they are the corners of the small square)
+        expected_intersections = np.array([[1., 1.],
+                                           [1., -1.],
+                                           [-1., 1.],
+                                           [-1., -1.]])
+        actual_intersections = hs.intersections
+        # They may be in any order, so just check that under some permutation 
+        # expected=actual.
+
+        ind1 = np.lexsort((actual_intersections[:, 1], actual_intersections[:, 0]))
+        ind2 = np.lexsort((expected_intersections[:, 1], expected_intersections[:, 0]))
+        assert_allclose(actual_intersections[ind1], expected_intersections[ind2])
+
+
+    @pytest.mark.parametrize("halfspaces", [
+    (np.array([-0.70613882, -0.45589431, 0.04178256])),
+    (np.array([[-0.70613882, -0.45589431,  0.04178256],
+               [0.70807342, -0.45464871, -0.45969769],
+               [0.,  0.76515026, -0.35614825]])),
+    ])
+    def test_gh_19865(self, halfspaces):
+        # starting off with a feasible interior point and
+        # adding halfspaces for which it is no longer feasible
+        # should result in an error rather than a problematic
+        # intersection polytope
+        initial_square =  np.array(
+                    [[1, 0, -1], [0, 1, -1], [-1, 0, -1], [0, -1, -1]]
+                )
+        incremental_intersector = qhull.HalfspaceIntersection(initial_square,
+                                                              np.zeros(2),
+                                                              incremental=True)
+        with pytest.raises(qhull.QhullError, match="feasible.*-0.706.*"):
+            incremental_intersector.add_halfspaces(halfspaces)
+
+
+    def test_gh_19865_3d(self):
+        # 3d case where closed half space is enforced for
+        # feasibility
+        halfspaces = np.array([[1, 1, 1, -1], # doesn't exclude origin
+                               [-1, -1, -1, -1], # doesn't exclude origin
+                               [1, 0, 0, 0]]) # the origin is on the line
+        initial_cube = np.array([[1, 0, 0, -1],
+                                 [-1, 0, 0, -1],
+                                 [0, 1, 0, -1],
+                                 [0, -1, 0, -1],
+                                 [0, 0, 1, -1],
+                                 [0, 0, -1, -1]])
+        incremental_intersector = qhull.HalfspaceIntersection(initial_cube,
+                                                              np.zeros(3),
+                                                              incremental=True)
+        with pytest.raises(qhull.QhullError, match="feasible.*[1 0 0 0]"):
+            incremental_intersector.add_halfspaces(halfspaces)
+
+
+    def test_2d_add_halfspace_input(self):
+        # incrementally added halfspaces should respect the 2D
+        # array shape requirement
+        initial_square =  np.array(
+                    [[1, 0, -1], [0, 1, -1], [-1, 0, -1], [0, -1, -1]]
+                )
+        incremental_intersector = qhull.HalfspaceIntersection(initial_square,
+                                                              np.zeros(2),
+                                                              incremental=True)
+        with pytest.raises(ValueError, match="2D array"):
+            incremental_intersector.add_halfspaces(np.ones((4, 4, 4)))
+
+    def test_1d_add_halfspace_input(self):
+        # we do allow 1D `halfspaces` input to add_halfspaces()
+        initial_square =  np.array(
+                    [[1, 0, -1], [0, 1, -1], [-1, 0, -1], [0, -1, -1]]
+                )
+        incremental_intersector = qhull.HalfspaceIntersection(initial_square,
+                                                              np.zeros(2),
+                                                              incremental=True)
+        assert_allclose(incremental_intersector.dual_vertices, np.arange(4))
+        incremental_intersector.add_halfspaces(np.array([2, 2, -1]))
+        assert_allclose(incremental_intersector.dual_vertices, np.arange(5))
+
+
+@pytest.mark.parametrize("diagram_type", [Voronoi, qhull.Delaunay])
+def test_gh_20623(diagram_type):
+    rng = np.random.default_rng(123)
+    invalid_data = rng.random((4, 10, 3))
+    with pytest.raises(ValueError, match="dimensions"):
+        diagram_type(invalid_data)
+
+
+def test_gh_21286():
+    generators = np.array([[0, 0], [0, 1.1], [1, 0], [1, 1]])
+    tri = qhull.Delaunay(generators)
+    # verify absence of segfault reported in ticket:
+    with pytest.raises(IndexError):
+        tri.find_simplex(1)
+    with pytest.raises(IndexError):
+        # strikingly, Delaunay object has shape
+        # () just like np.asanyarray(1) above
+        tri.find_simplex(tri)
+
+
+def test_find_simplex_ndim_err():
+    generators = np.array([[0, 0], [0, 1.1], [1, 0], [1, 1]])
+    tri = qhull.Delaunay(generators)
+    with pytest.raises(ValueError):
+        tri.find_simplex([2, 2, 2])
diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/tests/test_slerp.py b/venv/lib/python3.12/site-packages/scipy/spatial/tests/test_slerp.py
new file mode 100644
index 0000000000000000000000000000000000000000..001701e8e85f275e61e10c59086065385cc2e516
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/tests/test_slerp.py
@@ -0,0 +1,465 @@
+import math
+import warnings
+
+import numpy as np
+from numpy.testing import assert_allclose
+
+import pytest
+from scipy.spatial import geometric_slerp
+
+
+def _generate_spherical_points(ndim=3, n_pts=2):
+    # generate uniform points on sphere
+    # see: https://stackoverflow.com/a/23785326
+    # tentatively extended to arbitrary dims
+    # for 0-sphere it will always produce antipodes
+    np.random.seed(123)
+    points = np.random.normal(size=(n_pts, ndim))
+    points /= np.linalg.norm(points, axis=1)[:, np.newaxis]
+    return points[0], points[1]
+
+
+class TestGeometricSlerp:
+    # Test various properties of the geometric slerp code
+
+    @pytest.mark.parametrize("n_dims", [2, 3, 5, 7, 9])
+    @pytest.mark.parametrize("n_pts", [0, 3, 17])
+    def test_shape_property(self, n_dims, n_pts):
+        # geometric_slerp output shape should match
+        # input dimensionality & requested number
+        # of interpolation points
+        start, end = _generate_spherical_points(n_dims, 2)
+
+        actual = geometric_slerp(start=start,
+                                 end=end,
+                                 t=np.linspace(0, 1, n_pts))
+
+        assert actual.shape == (n_pts, n_dims)
+
+    @pytest.mark.parametrize("n_dims", [2, 3, 5, 7, 9])
+    @pytest.mark.parametrize("n_pts", [3, 17])
+    def test_include_ends(self, n_dims, n_pts):
+        # geometric_slerp should return a data structure
+        # that includes the start and end coordinates
+        # when t includes 0 and 1 ends
+        # this is convenient for plotting surfaces represented
+        # by interpolations for example
+
+        # the generator doesn't work so well for the unit
+        # sphere (it always produces antipodes), so use
+        # custom values there
+        start, end = _generate_spherical_points(n_dims, 2)
+
+        actual = geometric_slerp(start=start,
+                                 end=end,
+                                 t=np.linspace(0, 1, n_pts))
+
+        assert_allclose(actual[0], start)
+        assert_allclose(actual[-1], end)
+
+    @pytest.mark.parametrize("start, end", [
+        # both arrays are not flat
+        (np.zeros((1, 3)), np.ones((1, 3))),
+        # only start array is not flat
+        (np.zeros((1, 3)), np.ones(3)),
+        # only end array is not flat
+        (np.zeros(1), np.ones((3, 1))),
+        ])
+    def test_input_shape_flat(self, start, end):
+        # geometric_slerp should handle input arrays that are
+        # not flat appropriately
+        with pytest.raises(ValueError, match='one-dimensional'):
+            geometric_slerp(start=start,
+                            end=end,
+                            t=np.linspace(0, 1, 10))
+
+    @pytest.mark.parametrize("start, end", [
+        # 7-D and 3-D ends
+        (np.zeros(7), np.ones(3)),
+        # 2-D and 1-D ends
+        (np.zeros(2), np.ones(1)),
+        # empty, "3D" will also get caught this way
+        (np.array([]), np.ones(3)),
+        ])
+    def test_input_dim_mismatch(self, start, end):
+        # geometric_slerp must appropriately handle cases where
+        # an interpolation is attempted across two different
+        # dimensionalities
+        with pytest.raises(ValueError, match='dimensions'):
+            geometric_slerp(start=start,
+                            end=end,
+                            t=np.linspace(0, 1, 10))
+
+    @pytest.mark.parametrize("start, end", [
+        # both empty
+        (np.array([]), np.array([])),
+        ])
+    def test_input_at_least1d(self, start, end):
+        # empty inputs to geometric_slerp must
+        # be handled appropriately when not detected
+        # by mismatch
+        with pytest.raises(ValueError, match='at least two-dim'):
+            geometric_slerp(start=start,
+                            end=end,
+                            t=np.linspace(0, 1, 10))
+
+    @pytest.mark.parametrize("start, end, expected", [
+        # North and South Poles are definitely antipodes
+        # but should be handled gracefully now
+        (np.array([0, 0, 1.0]), np.array([0, 0, -1.0]), "warning"),
+        # this case will issue a warning & be handled
+        # gracefully as well;
+        # North Pole was rotated very slightly
+        # using r = R.from_euler('x', 0.035, degrees=True)
+        # to achieve Euclidean distance offset from diameter by
+        # 9.328908379124812e-08, within the default tol
+        (np.array([0.00000000e+00,
+                  -6.10865200e-04,
+                  9.99999813e-01]), np.array([0, 0, -1.0]), "warning"),
+        # this case should succeed without warning because a
+        # sufficiently large
+        # rotation was applied to North Pole point to shift it
+        # to a Euclidean distance of 2.3036691931821451e-07
+        # from South Pole, which is larger than tol
+        (np.array([0.00000000e+00,
+                  -9.59930941e-04,
+                  9.99999539e-01]), np.array([0, 0, -1.0]), "success"),
+        ])
+    def test_handle_antipodes(self, start, end, expected):
+        # antipodal points must be handled appropriately;
+        # there are an infinite number of possible geodesic
+        # interpolations between them in higher dims
+        if expected == "warning":
+            with pytest.warns(UserWarning, match='antipodes'):
+                res = geometric_slerp(start=start,
+                                      end=end,
+                                      t=np.linspace(0, 1, 10))
+        else:
+            res = geometric_slerp(start=start,
+                                  end=end,
+                                  t=np.linspace(0, 1, 10))
+
+        # antipodes or near-antipodes should still produce
+        # slerp paths on the surface of the sphere (but they
+        # may be ambiguous):
+        assert_allclose(np.linalg.norm(res, axis=1), 1.0)
+
+    @pytest.mark.parametrize("start, end, expected", [
+        # 2-D with n_pts=4 (two new interpolation points)
+        # this is an actual circle
+        (np.array([1, 0]),
+         np.array([0, 1]),
+         np.array([[1, 0],
+                   [np.sqrt(3) / 2, 0.5],  # 30 deg on unit circle
+                   [0.5, np.sqrt(3) / 2],  # 60 deg on unit circle
+                   [0, 1]])),
+        # likewise for 3-D (add z = 0 plane)
+        # this is an ordinary sphere
+        (np.array([1, 0, 0]),
+         np.array([0, 1, 0]),
+         np.array([[1, 0, 0],
+                   [np.sqrt(3) / 2, 0.5, 0],
+                   [0.5, np.sqrt(3) / 2, 0],
+                   [0, 1, 0]])),
+        # for 5-D, pad more columns with constants
+        # zeros are easiest--non-zero values on unit
+        # circle are more difficult to reason about
+        # at higher dims
+        (np.array([1, 0, 0, 0, 0]),
+         np.array([0, 1, 0, 0, 0]),
+         np.array([[1, 0, 0, 0, 0],
+                   [np.sqrt(3) / 2, 0.5, 0, 0, 0],
+                   [0.5, np.sqrt(3) / 2, 0, 0, 0],
+                   [0, 1, 0, 0, 0]])),
+
+    ])
+    def test_straightforward_examples(self, start, end, expected):
+        # some straightforward interpolation tests, sufficiently
+        # simple to use the unit circle to deduce expected values;
+        # for larger dimensions, pad with constants so that the
+        # data is N-D but simpler to reason about
+        actual = geometric_slerp(start=start,
+                                 end=end,
+                                 t=np.linspace(0, 1, 4))
+        assert_allclose(actual, expected, atol=1e-16)
+
+    @pytest.mark.parametrize("start, end", [
+        (np.array([1]),
+         np.array([0])),
+        (np.array([0]),
+         np.array([1])),
+        (np.array([-17.7]),
+         np.array([165.9])),
+     ])
+    def test_0_sphere_handling(self, start, end):
+        # it does not make sense to interpolate the set of
+        # two points that is the 0-sphere
+        with pytest.raises(ValueError, match='at least two-dim'):
+            _ = geometric_slerp(start=start,
+                                end=end,
+                                t=np.linspace(0, 1, 4))
+
+    @pytest.mark.parametrize("tol", [
+        # an integer currently raises
+        5,
+        # string raises
+        "7",
+        # list and arrays also raise
+        [5, 6, 7], np.array(9.0),
+        ])
+    def test_tol_type(self, tol):
+        # geometric_slerp() should raise if tol is not
+        # a suitable float type
+        with pytest.raises(ValueError, match='must be a float'):
+            _ = geometric_slerp(start=np.array([1, 0]),
+                                end=np.array([0, 1]),
+                                t=np.linspace(0, 1, 5),
+                                tol=tol)
+
+    @pytest.mark.parametrize("tol", [
+        -5e-6,
+        -7e-10,
+        ])
+    def test_tol_sign(self, tol):
+        # geometric_slerp() currently handles negative
+        # tol values, as long as they are floats
+        _ = geometric_slerp(start=np.array([1, 0]),
+                            end=np.array([0, 1]),
+                            t=np.linspace(0, 1, 5),
+                            tol=tol)
+
+    @pytest.mark.parametrize("start, end", [
+        # 1-sphere (circle) with one point at origin
+        # and the other on the circle
+        (np.array([1, 0]), np.array([0, 0])),
+        # 2-sphere (normal sphere) with both points
+        # just slightly off sphere by the same amount
+        # in different directions
+        (np.array([1 + 1e-6, 0, 0]),
+         np.array([0, 1 - 1e-6, 0])),
+        # same thing in 4-D
+        (np.array([1 + 1e-6, 0, 0, 0]),
+         np.array([0, 1 - 1e-6, 0, 0])),
+        ])
+    def test_unit_sphere_enforcement(self, start, end):
+        # geometric_slerp() should raise on input that clearly
+        # cannot be on an n-sphere of radius 1
+        with pytest.raises(ValueError, match='unit n-sphere'):
+            geometric_slerp(start=start,
+                            end=end,
+                            t=np.linspace(0, 1, 5))
+
+    @pytest.mark.parametrize("start, end", [
+        # 1-sphere 45 degree case
+        (np.array([1, 0]),
+         np.array([np.sqrt(2) / 2.,
+                   np.sqrt(2) / 2.])),
+        # 2-sphere 135 degree case
+        (np.array([1, 0]),
+         np.array([-np.sqrt(2) / 2.,
+                   np.sqrt(2) / 2.])),
+        ])
+    @pytest.mark.parametrize("t_func", [
+        np.linspace, np.logspace])
+    def test_order_handling(self, start, end, t_func):
+        # geometric_slerp() should handle scenarios with
+        # ascending and descending t value arrays gracefully;
+        # results should simply be reversed
+
+        # for scrambled / unsorted parameters, the same values
+        # should be returned, just in scrambled order
+
+        num_t_vals = 20
+        np.random.seed(789)
+        forward_t_vals = t_func(0, 10, num_t_vals)
+        # normalize to max of 1
+        forward_t_vals /= forward_t_vals.max()
+        reverse_t_vals = np.flipud(forward_t_vals)
+        shuffled_indices = np.arange(num_t_vals)
+        np.random.shuffle(shuffled_indices)
+        scramble_t_vals = forward_t_vals.copy()[shuffled_indices]
+
+        forward_results = geometric_slerp(start=start,
+                                          end=end,
+                                          t=forward_t_vals)
+        reverse_results = geometric_slerp(start=start,
+                                          end=end,
+                                          t=reverse_t_vals)
+        scrambled_results = geometric_slerp(start=start,
+                                            end=end,
+                                            t=scramble_t_vals)
+
+        # check fidelity to input order
+        assert_allclose(forward_results, np.flipud(reverse_results))
+        assert_allclose(forward_results[shuffled_indices],
+                        scrambled_results)
+
+    @pytest.mark.parametrize("t", [
+        # string:
+        "15, 5, 7",
+        # complex numbers currently produce a warning
+        # but not sure we need to worry about it too much:
+        # [3 + 1j, 5 + 2j],
+        ])
+    def test_t_values_conversion(self, t):
+        with pytest.raises(ValueError):
+            _ = geometric_slerp(start=np.array([1]),
+                                end=np.array([0]),
+                                t=t)
+
+    def test_accept_arraylike(self):
+        # array-like support requested by reviewer
+        # in gh-10380
+        actual = geometric_slerp([1, 0], [0, 1], [0, 1/3, 0.5, 2/3, 1])
+
+        # expected values are based on visual inspection
+        # of the unit circle for the progressions along
+        # the circumference provided in t
+        expected = np.array([[1, 0],
+                             [np.sqrt(3) / 2, 0.5],
+                             [np.sqrt(2) / 2,
+                              np.sqrt(2) / 2],
+                             [0.5, np.sqrt(3) / 2],
+                             [0, 1]], dtype=np.float64)
+        # Tyler's original Cython implementation of geometric_slerp
+        # can pass at atol=0 here, but on balance we will accept
+        # 1e-16 for an implementation that avoids Cython and
+        # makes up accuracy ground elsewhere
+        assert_allclose(actual, expected, atol=1e-16)
+
+    def test_scalar_t(self):
+        # when t is a scalar, return value is a single
+        # interpolated point of the appropriate dimensionality
+        # requested by reviewer in gh-10380
+        actual = geometric_slerp([1, 0], [0, 1], 0.5)
+        expected = np.array([np.sqrt(2) / 2,
+                             np.sqrt(2) / 2], dtype=np.float64)
+        assert actual.shape == (2,)
+        assert_allclose(actual, expected)
+
+    @pytest.mark.parametrize('start', [
+        np.array([1, 0, 0]),
+        np.array([0, 1]),
+    ])
+    @pytest.mark.parametrize('t', [
+        np.array(1),
+        np.array([1]),
+        np.array([[1]]),
+        np.array([[[1]]]),
+        np.array([]),
+        np.linspace(0, 1, 5),
+    ])
+    def test_degenerate_input(self, start, t):
+        if np.asarray(t).ndim > 1:
+            with pytest.raises(ValueError):
+                geometric_slerp(start=start, end=start, t=t)
+        else:
+
+            shape = (t.size,) + start.shape
+            expected = np.full(shape, start)
+
+            actual = geometric_slerp(start=start, end=start, t=t)
+            assert_allclose(actual, expected)
+
+            # Check that degenerate and non-degenerate
+            # inputs yield the same size
+            non_degenerate = geometric_slerp(start=start, end=start[::-1], t=t)
+            assert actual.size == non_degenerate.size
+
+    @pytest.mark.parametrize('k', np.logspace(-10, -1, 10))
+    def test_numerical_stability_pi(self, k):
+        # geometric_slerp should have excellent numerical
+        # stability for angles approaching pi between
+        # the start and end points
+        angle = np.pi - k
+        ts = np.linspace(0, 1, 100)
+        P = np.array([1, 0, 0, 0])
+        Q = np.array([np.cos(angle), np.sin(angle), 0, 0])
+        # the test should only be enforced for cases where
+        # geometric_slerp determines that the input is actually
+        # on the unit sphere
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", UserWarning)
+            result = geometric_slerp(P, Q, ts, 1e-18)
+            norms = np.linalg.norm(result, axis=1)
+            error = np.max(np.abs(norms - 1))
+            assert error < 4e-15
+
+    @pytest.mark.parametrize('t', [
+     [[0, 0.5]],
+     [[[[[[[[[0, 0.5]]]]]]]]],
+    ])
+    def test_interpolation_param_ndim(self, t):
+        # regression test for gh-14465
+        arr1 = np.array([0, 1])
+        arr2 = np.array([1, 0])
+
+        with pytest.raises(ValueError):
+            geometric_slerp(start=arr1,
+                            end=arr2,
+                            t=t)
+
+        with pytest.raises(ValueError):
+            geometric_slerp(start=arr1,
+                            end=arr1,
+                            t=t)
+
+
+    @pytest.mark.parametrize("start, end, t, expected", [
+        # verify intuitive cases for t > 1 or < 0 (extrapolation)
+
+        # quarter way around the unit circle, doubling to
+        # half way around (allowed antipode since non-ambiguous
+        # geodesic):
+        ([0, 1], [1, 0], 2, [0, -1]),
+        # 1/8 way around the unit circle, quadrupling to half way
+        # (another allowed non-ambiguous antipode)
+        ([0, 1], [math.sqrt(2)/2, math.sqrt(2)/2], 4, [0, -1]),
+        # 1/8 way around the unit circle, 6x to 3/4 way around (270 deg)
+        ([0, 1], [math.sqrt(2)/2, math.sqrt(2)/2], 6, [-1, 0]),
+        # 1/8 way around the unit circle, 7x to 315 deg
+        ([0, 1], [math.sqrt(2)/2, math.sqrt(2)/2], 7,
+         [-math.sqrt(2)/2, math.sqrt(2)/2]),
+        # the above three extrapolations in reverse order should be returned
+        # in that same order:
+        ([0, 1],
+         [math.sqrt(2)/2, math.sqrt(2)/2],
+         [7, 6, 4],
+         [[-math.sqrt(2)/2, math.sqrt(2)/2],
+          [-1, 0],
+          [0, -1]]),
+        # same case in 3d (sphere), in the xy plane:
+        ([0, 1, 0],
+         [math.sqrt(2)/2, math.sqrt(2)/2, 0],
+         [7, 6, 4],
+         [[-math.sqrt(2)/2, math.sqrt(2)/2, 0],
+          [-1, 0, 0],
+          [0, -1, 0]]),
+        # 1/8 way around the unit circle, moving 300 deg backwards
+        # should end up at pi/6 (since there is no forward travel with
+        # negative extrapolation)
+        ([0, 1], [math.sqrt(2)/2, math.sqrt(2)/2], (-300/45), [math.sqrt(3)/2, 0.5]),
+    ])
+    def test_extrapolation_basic(self, start, end, t, expected):
+        actual_path = geometric_slerp(start=start,
+                                      end=end,
+                                      t=t)
+        assert_allclose(actual_path, expected, atol=2e-16)
+
+    @pytest.mark.parametrize("start, end, t, expected", [
+    # cases where start and end proper are antipodes
+    # and t > 1 or < 0; these cases should issue a warning due to
+    # geodesic ambiguity
+
+    # North to South on unit sphere, then back to North again;
+    # there are an infinite number of possible routes, but they all
+    # return back to North
+    ([0, 0, 1], [0, 0, -1], -2, [0, 0, 1]),
+    # move "backwards" to South pole via an infinite number
+    # of possible routes
+    ([0, 0, 1], [0, 0, -1], -1, [0, 0, -1]),
+    ])
+    def test_extrapolation_antipodes(self, start, end, t, expected):
+        with pytest.warns(UserWarning, match='antipodes'):
+            actual_path = geometric_slerp(start=start, end=end, t=t)
+        assert_allclose(actual_path, expected, atol=2.8e-16)
diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/tests/test_spherical_voronoi.py b/venv/lib/python3.12/site-packages/scipy/spatial/tests/test_spherical_voronoi.py
new file mode 100644
index 0000000000000000000000000000000000000000..8bf4764e9e37312d08f25870327457107b9dcd91
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/tests/test_spherical_voronoi.py
@@ -0,0 +1,358 @@
+import numpy as np
+import itertools
+from numpy.testing import (assert_equal,
+                           assert_almost_equal,
+                           assert_array_equal,
+                           assert_array_almost_equal)
+import pytest
+from pytest import raises as assert_raises
+from scipy.spatial import SphericalVoronoi, distance
+from scipy.optimize import linear_sum_assignment
+from scipy.constants import golden as phi
+from scipy.special import gamma
+
+
+TOL = 1E-10
+
+
+def _generate_tetrahedron():
+    return np.array([[1, 1, 1], [1, -1, -1], [-1, 1, -1], [-1, -1, 1]])
+
+
+def _generate_cube():
+    return np.array(list(itertools.product([-1, 1.], repeat=3)))
+
+
+def _generate_octahedron():
+    return np.array([[-1, 0, 0], [+1, 0, 0], [0, -1, 0],
+                     [0, +1, 0], [0, 0, -1], [0, 0, +1]])
+
+
+def _generate_dodecahedron():
+
+    x1 = _generate_cube()
+    x2 = np.array([[0, -phi, -1 / phi],
+                   [0, -phi, +1 / phi],
+                   [0, +phi, -1 / phi],
+                   [0, +phi, +1 / phi]])
+    x3 = np.array([[-1 / phi, 0, -phi],
+                   [+1 / phi, 0, -phi],
+                   [-1 / phi, 0, +phi],
+                   [+1 / phi, 0, +phi]])
+    x4 = np.array([[-phi, -1 / phi, 0],
+                   [-phi, +1 / phi, 0],
+                   [+phi, -1 / phi, 0],
+                   [+phi, +1 / phi, 0]])
+    return np.concatenate((x1, x2, x3, x4))
+
+
+def _generate_icosahedron():
+    x = np.array([[0, -1, -phi],
+                  [0, -1, +phi],
+                  [0, +1, -phi],
+                  [0, +1, +phi]])
+    return np.concatenate([np.roll(x, i, axis=1) for i in range(3)])
+
+
+def _generate_polytope(name):
+    polygons = ["triangle", "square", "pentagon", "hexagon", "heptagon",
+                "octagon", "nonagon", "decagon", "undecagon", "dodecagon"]
+    polyhedra = ["tetrahedron", "cube", "octahedron", "dodecahedron",
+                 "icosahedron"]
+    if name not in polygons and name not in polyhedra:
+        raise ValueError("unrecognized polytope")
+
+    if name in polygons:
+        n = polygons.index(name) + 3
+        thetas = np.linspace(0, 2 * np.pi, n, endpoint=False)
+        p = np.vstack([np.cos(thetas), np.sin(thetas)]).T
+    elif name == "tetrahedron":
+        p = _generate_tetrahedron()
+    elif name == "cube":
+        p = _generate_cube()
+    elif name == "octahedron":
+        p = _generate_octahedron()
+    elif name == "dodecahedron":
+        p = _generate_dodecahedron()
+    elif name == "icosahedron":
+        p = _generate_icosahedron()
+
+    return p / np.linalg.norm(p, axis=1, keepdims=True)
+
+
+def _hypersphere_area(dim, radius):
+    # https://en.wikipedia.org/wiki/N-sphere#Closed_forms
+    return 2 * np.pi**(dim / 2) / gamma(dim / 2) * radius**(dim - 1)
+
+
+def _sample_sphere(n, dim, seed=None):
+    # Sample points uniformly at random from the hypersphere
+    rng = np.random.RandomState(seed=seed)
+    points = rng.randn(n, dim)
+    points /= np.linalg.norm(points, axis=1, keepdims=True)
+    return points
+
+
+class TestSphericalVoronoi:
+
+    def setup_method(self):
+        self.points = np.array([
+            [-0.78928481, -0.16341094, 0.59188373],
+            [-0.66839141, 0.73309634, 0.12578818],
+            [0.32535778, -0.92476944, -0.19734181],
+            [-0.90177102, -0.03785291, -0.43055335],
+            [0.71781344, 0.68428936, 0.12842096],
+            [-0.96064876, 0.23492353, -0.14820556],
+            [0.73181537, -0.22025898, -0.6449281],
+            [0.79979205, 0.54555747, 0.25039913]]
+        )
+
+    def test_constructor(self):
+        center = np.array([1, 2, 3])
+        radius = 2
+        s1 = SphericalVoronoi(self.points)
+        # user input checks in SphericalVoronoi now require
+        # the radius / center to match the generators so adjust
+        # accordingly here
+        s2 = SphericalVoronoi(self.points * radius, radius)
+        s3 = SphericalVoronoi(self.points + center, center=center)
+        s4 = SphericalVoronoi(self.points * radius + center, radius, center)
+        assert_array_equal(s1.center, np.array([0, 0, 0]))
+        assert_equal(s1.radius, 1)
+        assert_array_equal(s2.center, np.array([0, 0, 0]))
+        assert_equal(s2.radius, 2)
+        assert_array_equal(s3.center, center)
+        assert_equal(s3.radius, 1)
+        assert_array_equal(s4.center, center)
+        assert_equal(s4.radius, radius)
+
+        # Test a non-sequence/-ndarray based array-like
+        s5 = SphericalVoronoi(memoryview(self.points))  # type: ignore[arg-type]
+        assert_array_equal(s5.center, np.array([0, 0, 0]))
+        assert_equal(s5.radius, 1)
+
+    def test_vertices_regions_translation_invariance(self):
+        sv_origin = SphericalVoronoi(self.points)
+        center = np.array([1, 1, 1])
+        sv_translated = SphericalVoronoi(self.points + center, center=center)
+        assert_equal(sv_origin.regions, sv_translated.regions)
+        assert_array_almost_equal(sv_origin.vertices + center,
+                                  sv_translated.vertices)
+
+    def test_vertices_regions_scaling_invariance(self):
+        sv_unit = SphericalVoronoi(self.points)
+        sv_scaled = SphericalVoronoi(self.points * 2, 2)
+        assert_equal(sv_unit.regions, sv_scaled.regions)
+        assert_array_almost_equal(sv_unit.vertices * 2,
+                                  sv_scaled.vertices)
+
+    def test_old_radius_api_error(self):
+        with pytest.raises(ValueError, match='`radius` is `None`. *'):
+            SphericalVoronoi(self.points, radius=None)
+
+    def test_sort_vertices_of_regions(self):
+        sv = SphericalVoronoi(self.points)
+        unsorted_regions = sv.regions
+        sv.sort_vertices_of_regions()
+        assert_equal(sorted(sv.regions), sorted(unsorted_regions))
+
+    def test_sort_vertices_of_regions_flattened(self):
+        expected = sorted([[0, 6, 5, 2, 3], [2, 3, 10, 11, 8, 7], [0, 6, 4, 1],
+                           [4, 8, 7, 5, 6], [9, 11, 10], [2, 7, 5],
+                           [1, 4, 8, 11, 9], [0, 3, 10, 9, 1]])
+        expected = list(itertools.chain(*sorted(expected)))  # type: ignore
+        sv = SphericalVoronoi(self.points)
+        sv.sort_vertices_of_regions()
+        actual = list(itertools.chain(*sorted(sv.regions)))
+        assert_array_equal(actual, expected)
+
+    def test_sort_vertices_of_regions_dimensionality(self):
+        points = np.array([[1, 0, 0, 0],
+                           [0, 1, 0, 0],
+                           [0, 0, 1, 0],
+                           [0, 0, 0, 1],
+                           [0.5, 0.5, 0.5, 0.5]])
+        with pytest.raises(TypeError, match="three-dimensional"):
+            sv = SphericalVoronoi(points)
+            sv.sort_vertices_of_regions()
+
+    def test_num_vertices(self):
+        # for any n >= 3, a spherical Voronoi diagram has 2n - 4
+        # vertices; this is a direct consequence of Euler's formula
+        # as explained by Dinis and Mamede (2010) Proceedings of the
+        # 2010 International Symposium on Voronoi Diagrams in Science
+        # and Engineering
+        sv = SphericalVoronoi(self.points)
+        expected = self.points.shape[0] * 2 - 4
+        actual = sv.vertices.shape[0]
+        assert_equal(actual, expected)
+
+    def test_voronoi_circles(self):
+        sv = SphericalVoronoi(self.points)
+        for vertex in sv.vertices:
+            distances = distance.cdist(sv.points, np.array([vertex]))
+            closest = np.array(sorted(distances)[0:3])
+            assert_almost_equal(closest[0], closest[1], 7, str(vertex))
+            assert_almost_equal(closest[0], closest[2], 7, str(vertex))
+
+    def test_duplicate_point_handling(self):
+        # an exception should be raised for degenerate generators
+        # related to Issue# 7046
+        self.degenerate = np.concatenate((self.points, self.points))
+        with assert_raises(ValueError):
+            SphericalVoronoi(self.degenerate)
+
+    def test_incorrect_radius_handling(self):
+        # an exception should be raised if the radius provided
+        # cannot possibly match the input generators
+        with assert_raises(ValueError):
+            SphericalVoronoi(self.points, radius=0.98)
+
+    def test_incorrect_center_handling(self):
+        # an exception should be raised if the center provided
+        # cannot possibly match the input generators
+        with assert_raises(ValueError):
+            SphericalVoronoi(self.points, center=[0.1, 0, 0])
+
+    @pytest.mark.parametrize("dim", range(2, 6))
+    @pytest.mark.parametrize("shift", [False, True])
+    def test_single_hemisphere_handling(self, dim, shift):
+        n = 10
+        points = _sample_sphere(n, dim, seed=0)
+        points[:, 0] = np.abs(points[:, 0])
+        center = (np.arange(dim) + 1) * shift
+        sv = SphericalVoronoi(points + center, center=center)
+        dots = np.einsum('ij,ij->i', sv.vertices - center,
+                                     sv.points[sv._simplices[:, 0]] - center)
+        circumradii = np.arccos(np.clip(dots, -1, 1))
+        assert np.max(circumradii) > np.pi / 2
+
+    @pytest.mark.parametrize("n", [1, 2, 10])
+    @pytest.mark.parametrize("dim", range(2, 6))
+    @pytest.mark.parametrize("shift", [False, True])
+    def test_rank_deficient(self, n, dim, shift):
+        center = (np.arange(dim) + 1) * shift
+        points = _sample_sphere(n, dim - 1, seed=0)
+        points = np.hstack([points, np.zeros((n, 1))])
+        with pytest.raises(ValueError, match="Rank of input points"):
+            SphericalVoronoi(points + center, center=center)
+
+    @pytest.mark.parametrize("dim", range(2, 6))
+    def test_higher_dimensions(self, dim):
+        n = 100
+        points = _sample_sphere(n, dim, seed=0)
+        sv = SphericalVoronoi(points)
+        assert sv.vertices.shape[1] == dim
+        assert len(sv.regions) == n
+
+        # verify Euler characteristic
+        cell_counts = []
+        simplices = np.sort(sv._simplices)
+        for i in range(1, dim + 1):
+            cells = []
+            for indices in itertools.combinations(range(dim), i):
+                cells.append(simplices[:, list(indices)])
+            cells = np.unique(np.concatenate(cells), axis=0)
+            cell_counts.append(len(cells))
+        expected_euler = 1 + (-1)**(dim-1)
+        actual_euler = sum([(-1)**i * e for i, e in enumerate(cell_counts)])
+        assert expected_euler == actual_euler
+
+    @pytest.mark.parametrize("dim", range(2, 6))
+    def test_cross_polytope_regions(self, dim):
+        # The hypercube is the dual of the cross-polytope, so the voronoi
+        # vertices of the cross-polytope lie on the points of the hypercube.
+
+        # generate points of the cross-polytope
+        points = np.concatenate((-np.eye(dim), np.eye(dim)))
+        sv = SphericalVoronoi(points)
+        assert all([len(e) == 2**(dim - 1) for e in sv.regions])
+
+        # generate points of the hypercube
+        expected = np.vstack(list(itertools.product([-1, 1], repeat=dim)))
+        expected = expected.astype(np.float64) / np.sqrt(dim)
+
+        # test that Voronoi vertices are correctly placed
+        dist = distance.cdist(sv.vertices, expected)
+        res = linear_sum_assignment(dist)
+        assert dist[res].sum() < TOL
+
+    @pytest.mark.parametrize("dim", range(2, 6))
+    def test_hypercube_regions(self, dim):
+        # The cross-polytope is the dual of the hypercube, so the voronoi
+        # vertices of the hypercube lie on the points of the cross-polytope.
+
+        # generate points of the hypercube
+        points = np.vstack(list(itertools.product([-1, 1], repeat=dim)))
+        points = points.astype(np.float64) / np.sqrt(dim)
+        sv = SphericalVoronoi(points)
+
+        # generate points of the cross-polytope
+        expected = np.concatenate((-np.eye(dim), np.eye(dim)))
+
+        # test that Voronoi vertices are correctly placed
+        dist = distance.cdist(sv.vertices, expected)
+        res = linear_sum_assignment(dist)
+        assert dist[res].sum() < TOL
+
+    @pytest.mark.parametrize("n", [10, 500])
+    @pytest.mark.parametrize("dim", [2, 3])
+    @pytest.mark.parametrize("radius", [0.5, 1, 2])
+    @pytest.mark.parametrize("shift", [False, True])
+    @pytest.mark.parametrize("single_hemisphere", [False, True])
+    def test_area_reconstitution(self, n, dim, radius, shift,
+                                 single_hemisphere):
+        points = _sample_sphere(n, dim, seed=0)
+
+        # move all points to one side of the sphere for single-hemisphere test
+        if single_hemisphere:
+            points[:, 0] = np.abs(points[:, 0])
+
+        center = (np.arange(dim) + 1) * shift
+        points = radius * points + center
+
+        sv = SphericalVoronoi(points, radius=radius, center=center)
+        areas = sv.calculate_areas()
+        assert_almost_equal(areas.sum(), _hypersphere_area(dim, radius))
+
+    @pytest.mark.parametrize("poly", ["triangle", "dodecagon",
+                                      "tetrahedron", "cube", "octahedron",
+                                      "dodecahedron", "icosahedron"])
+    def test_equal_area_reconstitution(self, poly):
+        points = _generate_polytope(poly)
+        n, dim = points.shape
+        sv = SphericalVoronoi(points)
+        areas = sv.calculate_areas()
+        assert_almost_equal(areas, _hypersphere_area(dim, 1) / n)
+
+    def test_area_unsupported_dimension(self):
+        dim = 4
+        points = np.concatenate((-np.eye(dim), np.eye(dim)))
+        sv = SphericalVoronoi(points)
+        with pytest.raises(TypeError, match="Only supported"):
+            sv.calculate_areas()
+
+    @pytest.mark.parametrize("radius", [1, 1.])
+    @pytest.mark.parametrize("center", [None, (1, 2, 3), (1., 2., 3.)])
+    def test_attribute_types(self, radius, center):
+        points = radius * self.points
+        if center is not None:
+            points += center
+
+        sv = SphericalVoronoi(points, radius=radius, center=center)
+        assert sv.points.dtype is np.dtype(np.float64)
+        assert sv.center.dtype is np.dtype(np.float64)
+        assert isinstance(sv.radius, float)
+
+    def test_region_types(self):
+        # Tests that region integer type does not change
+        # See Issue #13412
+        sv = SphericalVoronoi(self.points)
+        dtype = type(sv.regions[0][0])
+        # also enforce nested list type per gh-19177
+        for region in sv.regions:
+            assert isinstance(region, list)
+        sv.sort_vertices_of_regions()
+        assert isinstance(sv.regions[0][0], dtype)
+        sv.sort_vertices_of_regions()
+        assert isinstance(sv.regions[0][0], dtype)
diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/transform/__init__.py b/venv/lib/python3.12/site-packages/scipy/spatial/transform/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..1490a18e2ef0b0435fdada41f6f083aa89a3d859
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/transform/__init__.py
@@ -0,0 +1,31 @@
+"""
+Spatial Transformations (:mod:`scipy.spatial.transform`)
+========================================================
+
+.. currentmodule:: scipy.spatial.transform
+
+This package implements various spatial transformations. For now, rotations
+and rigid transforms (rotations and translations) are supported.
+
+Rotations in 3 dimensions
+-------------------------
+.. autosummary::
+   :toctree: generated/
+
+   RigidTransform
+   Rotation
+   Slerp
+   RotationSpline
+"""
+from ._rotation import Rotation, Slerp
+from ._rigid_transform import RigidTransform
+from ._rotation_spline import RotationSpline
+
+# Deprecated namespaces, to be removed in v2.0.0
+from . import rotation
+
+__all__ = ['Rotation', 'Slerp', 'RotationSpline', 'RigidTransform']
+
+from scipy._lib._testutils import PytestTester
+test = PytestTester(__name__)
+del PytestTester
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new file mode 100644
index 0000000000000000000000000000000000000000..0a06f86af379ce6999dd0af04e74969e3a0a4094
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/transform/__pycache__/_rotation.cpython-312.pyc
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
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+++ b/venv/lib/python3.12/site-packages/scipy/spatial/transform/_rigid_transform.py
@@ -0,0 +1,1975 @@
+from __future__ import annotations
+
+from collections.abc import Iterable, Iterator
+from types import EllipsisType, GenericAlias, ModuleType, NotImplementedType
+from collections.abc import Callable
+
+import numpy as np
+
+from scipy._lib._array_api import (
+    array_namespace,
+    is_numpy,
+    ArrayLike,
+    Array,
+    xp_capabilities,
+)
+from scipy.spatial.transform import Rotation
+from scipy.spatial.transform._rotation import _promote
+import scipy.spatial.transform._rigid_transform_cy as cython_backend
+import scipy.spatial.transform._rigid_transform_xp as xp_backend
+import scipy._external.array_api_extra as xpx
+from scipy._external.array_api_compat import device
+from scipy._lib._array_api import xp_promote
+from scipy._lib._util import broadcastable
+
+
+__all__ = ["RigidTransform"]
+
+backend_registry = {array_namespace(np.empty(0)): cython_backend}
+
+
+def select_backend(xp: ModuleType, cython_compatible: bool):
+    """Select the backend for the given array library.
+
+    We need this selection function because the Cython backend for numpy does not
+    support quaternions of arbitrary dimensions. We therefore only use the Array API
+    backend for numpy if we are dealing with rotations of more than one leading
+    dimension.
+    """
+    if is_numpy(xp) and not cython_compatible:
+        return xp_backend
+    return backend_registry.get(xp, xp_backend)
+
+
+@xp_capabilities()
+def normalize_dual_quaternion(dual_quat: ArrayLike) -> Array:
+    """Normalize dual quaternion."""
+    xp = array_namespace(dual_quat)
+    dual_quat = _promote(dual_quat, xp=xp)
+    single = dual_quat.ndim == 1 and is_numpy(xp)
+    if single:
+        dual_quat = xpx.atleast_nd(dual_quat, ndim=2, xp=xp)
+    cython_compatible = dual_quat.ndim < 3
+    dq = select_backend(xp, cython_compatible).normalize_dual_quaternion(dual_quat)
+    if single:
+        return dq[0]
+    return dq
+
+
+rigid_transform_extra_note = (
+    """The method ``apply`` is not supported with cupy<14.*.
+
+    """)
+
+
+@xp_capabilities(
+    skip_backends=[("dask.array", "missing linalg.cross/det functions")],
+    method_capabilities={
+        "__init__": dict(
+            jax_jit=False,
+            skip_backends=[("dask.array", "missing linalg.cross/det functions")],
+        ),
+        "from_matrix": dict(
+            jax_jit=False,
+            skip_backends=[("dask.array", "missing linalg.cross/det functions")],
+        ),
+        "__getitem__": dict(
+            jax_jit=False,
+            skip_backends=[
+                ("dask.array", "cannot handle zero-length rigid transforms")
+            ],
+        ),
+        "__setitem__": dict(
+            jax_jit=False,
+            skip_backends=[
+                ("dask.array", "cannot handle zero-length rigid transforms")
+            ],
+        ),
+        "apply": dict(
+            skip_backends=[
+                ("dask.array", "missing linalg.cross/det functions"),
+                ("cupy", "missing .mT attribute in cupy<14.*"),
+            ],
+        ),
+    },
+    extra_note=rigid_transform_extra_note,
+)
+class RigidTransform:
+    """
+    Rigid transform in 3 dimensions.
+
+    This class provides an interface to initialize from and represent rigid
+    transforms (rotation and translation) in 3D space. In different fields,
+    this type of transform may be referred to as "*pose*" (especially in
+    robotics), "*extrinsic parameters*", or the "*model matrix*" (especially in
+    computer graphics), but the core concept is the same: a rotation and
+    translation describing the orientation of one 3D coordinate frame relative
+    to another. Mathematically, these transforms belong to the Special
+    Euclidean group SE(3), which encodes rotation (SO(3)) plus translation.
+
+    The following operations on rigid transforms are supported:
+
+    - Application on vectors
+    - Transformation composition
+    - Transformation inversion
+    - Transformation indexing
+
+    Note that coordinate systems must be right-handed. Because of this, this
+    class more precisely represents *proper* rigid transformations in SE(3)
+    rather than rigid transforms in E(3) more generally [1]_.
+
+    Indexing within a transform is supported since multiple transforms can be
+    stored within a single `RigidTransform` instance.
+
+    Multiple transforms can be stored in a single `RigidTransform` object, which can be
+    initialized using N-dimensional arrays and supports broadcasting for all
+    operations.
+
+    To create `RigidTransform` objects use ``from_...`` methods (see examples
+    below). ``RigidTransform(...)`` is not supposed to be instantiated directly.
+
+    For rigorous introductions to rigid transforms, see [2]_, [3]_, and [4]_.
+
+    Parameters
+    ----------
+    matrix : array_like, shape (..., 4, 4)
+        A single transformation matrix or a stack of transformation
+        matrices.
+    normalize : bool, optional
+        If True, orthonormalize the rotation matrix using singular value
+        decomposition. If False, the rotation matrix is not checked for
+        orthogonality or right-handedness.
+    copy : bool, optional
+        If True, copy the input matrix. If False, a reference to the input
+        matrix is used. If normalize is True, the input matrix is always
+        copied regardless of the value of copy.
+
+    Attributes
+    ----------
+    single
+    rotation
+    translation
+
+    Methods
+    -------
+    __len__
+    __getitem__
+    __mul__
+    __pow__
+    from_matrix
+    from_rotation
+    from_translation
+    from_components
+    from_exp_coords
+    from_dual_quat
+    as_matrix
+    as_components
+    as_exp_coords
+    as_dual_quat
+    concatenate
+    mean
+    apply
+    inv
+    identity
+
+    Notes
+    -----
+    .. versionadded:: 1.16.0
+
+    References
+    ----------
+    .. [1] https://en.wikipedia.org/wiki/Rigid_transformation
+    .. [2] https://motion.cs.illinois.edu/RoboticSystems/CoordinateTransformations.html
+    .. [3] https://www.brainvoyager.com/bv/doc/UsersGuide/CoordsAndTransforms/SpatialTransformationMatrices.html
+    .. [4] Kevin M. Lynch and Frank C. Park, "Modern Robotics: Mechanics,
+           Planning, and Control" Chapter 3.3, 2017, Cambridge University Press.
+           https://hades.mech.northwestern.edu/images/2/25/MR-v2.pdf#page=107.31
+    .. [5] Paul Furgale, "Representing Robot Pose: The good, the bad, and the
+           ugly", June 9, 2014.
+           https://rpg.ifi.uzh.ch/docs/teaching/2024/FurgaleTutorial.pdf
+
+    Examples
+    --------
+    A `RigidTransform` instance can be initialized in any of the above formats
+    and converted to any of the others. The underlying object is independent of
+    the representation used for initialization.
+
+    **Notation Conventions and Composition**
+
+    The notation here largely follows the convention defined in [5]_. When we
+    name transforms, we read the subscripts from right to left. So ``tf_A_B``
+    represents a transform A <- B and can be interpreted as:
+
+    - the coordinates and orientation of B relative to A
+    - the transformation of points from B to A
+    - the pose of B described in A's coordinate system
+
+    .. parsed-literal::
+        :class: highlight-none
+
+        tf_A_B
+           ^ ^
+           | |
+           | --- from B
+           |
+           ----- to A
+
+    When composing transforms, the order is important. Transforms are not
+    commutative, so in general ``tf_A_B * tf_B_C`` is not the same as
+    ``tf_B_C * tf_A_B``. Transforms are composed and applied to vectors
+    right-to-left. So ``(tf_A_B * tf_B_C).apply(p_C)`` is the same as
+    ``tf_A_B.apply(tf_B_C.apply(p_C))``.
+
+    When composed, transforms should be ordered such that the multiplication
+    operator is surrounded by a single frame, so the frame "cancels out" and
+    the outside frames are left. In the example below, B cancels out and the
+    outside frames A and C are left. Or to put it another way, A <- C is the
+    same as A <- B <- C.
+
+    .. parsed-literal::
+        :class: highlight-none
+
+                      ----------- B cancels out
+                      |      |
+                      v      v
+        tf_A_C = tf_A_B * tf_B_C
+                    ^          ^
+                    |          |
+                    ------------ to A, from C are left
+
+    When we notate vectors, we write the subscript of the frame that the vector
+    is defined in. So ``p_B`` means the point ``p`` defined in frame B. To
+    transform this point from frame B to coordinates in frame A, we apply the
+    transform ``tf_A_B`` to the vector, lining things up such that the notated
+    B frames are next to each other and "cancel out".
+
+    .. parsed-literal::
+        :class: highlight-none
+
+                   ------------ B cancels out
+                   |         |
+                   v         v
+        p_A = tf_A_B.apply(p_B)
+                 ^
+                 |
+                 -------------- A is left
+
+    **Visualization**
+
+    >>> from scipy.spatial.transform import RigidTransform as Tf
+    >>> from scipy.spatial.transform import Rotation as R
+    >>> import numpy as np
+
+    The following function can be used to plot transforms with Matplotlib
+    by showing how they transform the standard x, y, z coordinate axes:
+
+    >>> import matplotlib.pyplot as plt
+    >>> colors = ("#FF6666", "#005533", "#1199EE")  # Colorblind-safe RGB
+    >>> def plot_transformed_axes(ax, tf, name=None, scale=1):
+    ...     r = tf.rotation
+    ...     t = tf.translation
+    ...     loc = np.array([t, t])
+    ...     for i, (axis, c) in enumerate(zip((ax.xaxis, ax.yaxis, ax.zaxis),
+    ...                                       colors)):
+    ...         axlabel = axis.axis_name
+    ...         axis.set_label_text(axlabel)
+    ...         axis.label.set_color(c)
+    ...         axis.line.set_color(c)
+    ...         axis.set_tick_params(colors=c)
+    ...         line = np.zeros((2, 3))
+    ...         line[1, i] = scale
+    ...         line_rot = r.apply(line)
+    ...         line_plot = line_rot + loc
+    ...         ax.plot(line_plot[:, 0], line_plot[:, 1], line_plot[:, 2], c)
+    ...         text_loc = line[1]*1.2
+    ...         text_loc_rot = r.apply(text_loc)
+    ...         text_plot = text_loc_rot + t
+    ...         ax.text(*text_plot, axlabel.upper(), color=c,
+    ...                 va="center", ha="center")
+    ...     ax.text(*tf.translation, name, color="k", va="center", ha="center",
+    ...             bbox={"fc": "w", "alpha": 0.8, "boxstyle": "circle"})
+
+    **Defining Frames**
+
+    Let's work through an example.
+
+    First, define the "world frame" A, also called the "base frame".
+    All frames are the identity transform from their own perspective.
+
+    >>> tf_A = Tf.identity()
+
+    We will visualize a new frame B in A's coordinate system. So we need to
+    define the transform that converts coordinates from frame B to frame A
+    (A <- B).
+
+    Physically, let's imagine constructing B from A by:
+
+    1) Rotating A by +90 degrees around its x-axis.
+    2) Translating the rotated frame 2 units in A's -x direction.
+
+    From A's perspective, B is at [-2, 0, 0] and rotated +90 degrees about the
+    x-axis, which is exactly the transform A <- B.
+
+    >>> t_A_B = np.array([-2, 0, 0])
+    >>> r_A_B = R.from_euler('xyz', [90, 0, 0], degrees=True)
+    >>> tf_A_B = Tf.from_components(t_A_B, r_A_B)
+
+    Let's plot these frames.
+
+    >>> fig, ax = plt.subplots(subplot_kw={"projection": "3d"})
+    >>> plot_transformed_axes(ax, tf_A, name="tfA")     # A plotted in A
+    >>> plot_transformed_axes(ax, tf_A_B, name="tfAB")  # B plotted in A
+    >>> ax.set_title("A, B frames with respect to A")
+    >>> ax.set_aspect("equal")
+    >>> ax.figure.set_size_inches(6, 5)
+    >>> plt.show()
+
+    Now let's visualize a new frame C in B's coordinate system.
+    Let's imagine constructing C from B by:
+
+    1) Translating B by 2 units in its +z direction.
+    2) Rotating B by +30 degrees around its z-axis.
+
+    >>> t_B_C = np.array([0, 0, 2])
+    >>> r_B_C = R.from_euler('xyz', [0, 0, 30], degrees=True)
+    >>> tf_B_C = Tf.from_components(t_B_C, r_B_C)
+
+    In order to plot these frames from a consistent perspective, we need to
+    calculate the transform between A and C. Note that we do not make this
+    transform directly, but instead compose intermediate transforms that let us
+    get from C to A:
+
+    >>> tf_A_C = tf_A_B * tf_B_C  # A <- B <- C
+
+    Now we can plot these three frames from A's perspective.
+
+    >>> fig, ax = plt.subplots(subplot_kw={"projection": "3d"})
+    >>> plot_transformed_axes(ax, tf_A, name="tfA")     # A plotted in A
+    >>> plot_transformed_axes(ax, tf_A_B, name="tfAB")  # B plotted in A
+    >>> plot_transformed_axes(ax, tf_A_C, name="tfAC")  # C plotted in A
+    >>> ax.set_title("A, B, C frames with respect to A")
+    >>> ax.set_aspect("equal")
+    >>> ax.figure.set_size_inches(6, 5)
+    >>> plt.show()
+
+    **Transforming Vectors**
+
+    Let's transform a vector from A, to B and C. To do this, we will first
+    invert the transforms we already have from B and C, to A.
+
+    >>> tf_B_A = tf_A_B.inv()  # B <- A
+    >>> tf_C_A = tf_A_C.inv()  # C <- A
+
+    Now we can define a point in A and use the above transforms to get its
+    coordinates in B and C:
+
+    >>> p1_A = np.array([1, 0, 0])  # +1 in x_A direction
+    >>> p1_B = tf_B_A.apply(p1_A)
+    >>> p1_C = tf_C_A.apply(p1_A)
+    >>> print(p1_A)  # Original point 1 in A
+    [1 0 0]
+    >>> print(p1_B)  # Point 1 in B
+    [3. 0. 0.]
+    >>> print(p1_C)  # Point 1 in C
+    [ 2.59807621 -1.5       -2.        ]
+
+    We can also do the reverse. We define a point in C and transform it to A:
+
+    >>> p2_C = np.array([0, 1, 0])  # +1 in y_C direction
+    >>> p2_A = tf_A_C.apply(p2_C)
+    >>> print(p2_C)  # Original point 2 in C
+    [0 1 0]
+    >>> print(p2_A)  # Point 2 in A
+    [-2.5       -2.         0.8660254]
+
+    Plot the frames with respect to A again, but also plot these two points:
+
+    >>> fig, ax = plt.subplots(subplot_kw={"projection": "3d"})
+    >>> plot_transformed_axes(ax, tf_A, name="tfA")     # A plotted in A
+    >>> plot_transformed_axes(ax, tf_A_B, name="tfAB")  # B plotted in A
+    >>> plot_transformed_axes(ax, tf_A_C, name="tfAC")  # C plotted in A
+    >>> ax.scatter(p1_A[0], p1_A[1], p1_A[2], color=colors[0])  # +1 x_A
+    >>> ax.scatter(p2_A[0], p2_A[1], p2_A[2], color=colors[1])  # +1 y_C
+    >>> ax.set_title("A, B, C frames and points with respect to A")
+    >>> ax.set_aspect("equal")
+    >>> ax.figure.set_size_inches(6, 5)
+    >>> plt.show()
+
+    **Switching Base Frames**
+
+    Up to this point, we have been visualizing frames from A's perspective.
+    Let's use the transforms we defined to visualize the frames from C's
+    perspective.
+
+    Now C is the "base frame" or "world frame". All frames are the identity
+    transform from their own perspective.
+
+    >>> tf_C = Tf.identity()
+
+    We've already defined the transform C <- A, and can obtain C <- B by
+    inverting the existing transform B <- C.
+
+    >>> tf_C_B = tf_B_C.inv()  # C <- B
+
+    This lets us plot everything from C's perspective:
+
+    >>> fig, ax = plt.subplots(subplot_kw={"projection": "3d"})
+    >>> plot_transformed_axes(ax, tf_C, name="tfC")     # C plotted in C
+    >>> plot_transformed_axes(ax, tf_C_B, name="tfCB")  # B plotted in C
+    >>> plot_transformed_axes(ax, tf_C_A, name="tfCA")  # A plotted in C
+    >>> ax.scatter(p1_C[0], p1_C[1], p1_C[2], color=colors[0])
+    >>> ax.scatter(p2_C[0], p2_C[1], p2_C[2], color=colors[1])
+    >>> ax.set_title("A, B, C frames and points with respect to C")
+    >>> ax.set_aspect("equal")
+    >>> ax.figure.set_size_inches(6, 5)
+    >>> plt.show()
+    """
+
+    # generic type compatibility with scipy-stubs
+    __class_getitem__: classmethod = classmethod(GenericAlias)
+
+    def __init__(self, matrix: ArrayLike, normalize: bool = True, copy: bool = True):
+        """Initialize from a 4x4 transformation matrix.
+
+        Rotations are not meant to be initialized directly. Please use one of
+        the `from_...` methods instead.
+
+        Parameters
+        ----------
+        matrix : array_like, shape (..., 4, 4)
+            A single transformation matrix or a stack of transformation
+            matrices.
+        normalize : bool, optional
+            If True, orthonormalize the rotation matrix using singular value
+            decomposition. If False, the rotation matrix is not checked for
+            orthogonality or right-handedness.
+        copy : bool, optional
+            If True, copy the input matrix. If False, a reference to the input
+            matrix is used. If normalize is True, the input matrix is always
+            copied regardless of the value of copy.
+
+        Returns
+        -------
+        transform : `RigidTransform` instance
+        """
+        xp = array_namespace(matrix)
+        self._xp = xp
+        matrix = _promote(matrix, xp=xp)
+        if matrix.shape[-2:] != (4, 4):
+            raise ValueError(
+                f"Expected `matrix` to have shape (..., 4, 4), got {matrix.shape}."
+            )
+        # We only need the _single flag for the cython backend. The Array API backend
+        # uses broadcasting by default and hence returns the correct shape without
+        # additional _single logic
+        self._single = matrix.ndim == 2 and is_numpy(xp)
+        if self._single:
+            matrix = xpx.atleast_nd(matrix, ndim=3, xp=xp)
+
+        self._backend = select_backend(xp, matrix.ndim < 4)
+        self._matrix = self._backend.from_matrix(matrix, normalize, copy)
+
+    def __repr__(self):
+        m = f"{self.as_matrix()!r}".splitlines()
+        # bump indent (+27 characters)
+        m[1:] = [" " * 27 + m[i] for i in range(1, len(m))]
+        return "RigidTransform.from_matrix(" + "\n".join(m) + ")"
+
+    @staticmethod
+    def from_matrix(matrix: ArrayLike) -> RigidTransform:
+        """Initialize from a 4x4 transformation matrix.
+
+        Parameters
+        ----------
+        matrix : array_like, shape (..., 4, 4)
+            Transformation matrices. Each matrix[..., :, :] represents a 4x4
+            transformation matrix.
+
+        Returns
+        -------
+        transform : `RigidTransform` instance
+            Object containing the rigid transform represented by the input matrix.
+
+        Notes
+        -----
+        4x4 rigid transformation matrices are of the form::
+
+            [       tx]
+            [   R   ty]
+            [       tz]
+            [ 0 0 0  1]
+
+        where ``R`` is a 3x3 rotation matrix and ``t = [tx, ty, tz]`` is a 3x1
+        translation vector. As rotation matrices must be proper orthogonal, the
+        rotation component is orthonormalized using singular value decomposition
+        before initialization.
+
+        Examples
+        --------
+        >>> from scipy.spatial.transform import RigidTransform as Tf
+        >>> import numpy as np
+
+        Creating a transform from a single matrix:
+
+        >>> m = np.array([[0, 1, 0, 2],
+        ...               [0, 0, 1, 3],
+        ...               [1, 0, 0, 4],
+        ...               [0, 0, 0, 1]])
+        >>> tf = Tf.from_matrix(m)
+        >>> tf.as_matrix()
+        array([[0., 1., 0., 2.],
+               [0., 0., 1., 3.],
+               [1., 0., 0., 4.],
+               [0., 0., 0., 1.]])
+        >>> tf.single
+        True
+
+        Creating a transform from an N-dimensional array of matrices:
+
+        >>> m = np.tile(np.eye(4), (2, 5, 1, 1))  # Shape (2, 5, 4, 4)
+        >>> tf = Tf.from_matrix(m)
+        >>> tf.shape
+        (2, 5)
+        >>> tf.single
+        False
+        >>> len(tf)
+        2
+
+        Matrices with a rotation component that is not proper orthogonal are
+        orthogonalized using singular value decomposition before initialization:
+
+        >>> tf = Tf.from_matrix(np.diag([2, 2, 2, 1]))
+        >>> tf.as_matrix()
+        array([[1., 0., 0., 0.],
+               [0., 1., 0., 0.],
+               [0., 0., 1., 0.],
+               [0., 0., 0., 1.]])
+        """
+        return RigidTransform(matrix, normalize=True, copy=True)
+
+    @staticmethod
+    def from_rotation(rotation: Rotation) -> RigidTransform:
+        """Initialize from a rotation, without a translation.
+
+        When applying this transform to a vector ``v``, the result is the
+        same as if the rotation was applied to the vector.
+        ``Tf.from_rotation(r).apply(v) == r.apply(v)``
+
+        Parameters
+        ----------
+        rotation : `Rotation` instance
+            A single rotation or a rotation with N leading dimensions.
+
+        Returns
+        -------
+        transform : `RigidTransform` instance
+            Object containing the rigid transform represented by the input rotation.
+
+        Examples
+        --------
+        >>> from scipy.spatial.transform import RigidTransform as Tf
+        >>> from scipy.spatial.transform import Rotation as R
+        >>> import numpy as np
+
+        Creating a transform from a single rotation:
+
+        >>> r = R.from_euler("ZYX", [90, 30, 0], degrees=True)
+        >>> r.apply([1, 0, 0])
+        array([0.       , 0.8660254, -0.5     ])
+        >>> tf = Tf.from_rotation(r)
+        >>> tf.apply([1, 0, 0])
+        array([0.       , 0.8660254, -0.5     ])
+        >>> tf.single
+        True
+
+        The upper 3x3 submatrix of the transformation matrix is the rotation
+        matrix:
+
+        >>> np.allclose(tf.as_matrix()[:3, :3], r.as_matrix(), atol=1e-12)
+        True
+
+        Creating multiple transforms from a rotation with N leading dimensions:
+
+        >>> r = R.from_euler("ZYX", [[90, 30, 0], [45, 30, 60]], degrees=True)
+        >>> r.apply([1, 0, 0])
+        array([[0.        , 0.8660254 , -0.5       ],
+               [0.61237244, 0.61237244, -0.5       ]])
+        >>> tf = Tf.from_rotation(r)
+        >>> tf.apply([1, 0, 0])
+        array([[0.        , 0.8660254 , -0.5       ],
+               [0.61237244, 0.61237244, -0.5       ]])
+        >>> tf.single
+        False
+        >>> len(tf)
+        2
+        """
+        if not isinstance(rotation, Rotation):
+            raise TypeError(
+                "Expected `rotation` to be a `Rotation` instance, "
+                f"got {type(rotation)}."
+            )
+        quat = rotation.as_quat()
+        xp = array_namespace(quat)
+        backend = select_backend(xp, quat.ndim < 3)
+        matrix = backend.from_rotation(quat)
+        return RigidTransform._from_raw_matrix(matrix, xp, backend)
+
+    @staticmethod
+    def from_translation(translation: ArrayLike) -> RigidTransform:
+        """Initialize from a translation numpy array, without a rotation.
+
+        When applying this transform to a vector ``v``, the result is the same
+        as if the translation and vector were added together. If ``t`` is the
+        displacement vector of the translation, then:
+
+        ``Tf.from_translation(t).apply(v) == t + v``
+
+        Parameters
+        ----------
+        translation : array_like, shape (..., 3)
+            Translation vectors. Each translation[..., :] represents a 3D
+            translation vector.
+
+        Returns
+        -------
+        transform : `RigidTransform` instance
+            Object containing the rigid transform represented by the input translation.
+
+        Examples
+        --------
+        >>> from scipy.spatial.transform import RigidTransform as Tf
+        >>> import numpy as np
+
+        Creating a transform from a single translation vector:
+
+        >>> t = np.array([2, 3, 4])
+        >>> t + np.array([1, 0, 0])
+        array([3, 3, 4])
+        >>> tf = Tf.from_translation(t)
+        >>> tf.apply([1, 0, 0])
+        array([3., 3., 4.])
+        >>> tf.single
+        True
+
+        The top 3x1 points in the rightmost column of the transformation matrix
+        is the translation vector:
+
+        >>> tf.as_matrix()
+        array([[1., 0., 0., 2.],
+               [0., 1., 0., 3.],
+               [0., 0., 1., 4.],
+               [0., 0., 0., 1.]])
+        >>> np.allclose(tf.as_matrix()[:3, 3], t)
+        True
+
+        Creating multiple transforms from an N-dimensional array of translation
+        vectors:
+
+        >>> t = np.array([[2, 3, 4], [1, 0, 0]])
+        >>> t + np.array([1, 0, 0])
+        array([[3, 3, 4],
+               [2, 0, 0]])
+        >>> tf = Tf.from_translation(t)
+        >>> tf.apply([1, 0, 0])
+        array([[3., 3., 4.],
+               [2., 0., 0.]])
+        >>> np.allclose(tf.as_matrix()[:, :3, 3], t)
+        True
+        >>> tf.single
+        False
+        >>> len(tf)
+        2
+        """
+        xp = array_namespace(translation)
+        translation = _promote(translation, xp=xp)
+        backend = select_backend(xp, translation.ndim < 3)
+        matrix = backend.from_translation(translation)
+        return RigidTransform._from_raw_matrix(matrix, xp, backend)
+
+    @staticmethod
+    def from_components(translation: ArrayLike, rotation: Rotation) -> RigidTransform:
+        """Initialize a rigid transform from translation and rotation
+        components.
+
+        When creating a rigid transform from a translation and rotation, the
+        translation is applied after the rotation, such that
+        ``tf = Tf.from_components(translation, rotation)``
+        is equivalent to
+        ``tf = Tf.from_translation(translation) * Tf.from_rotation(rotation)``.
+
+        When applying a transform to a vector ``v``, the result is the
+        same as if the transform was applied to the vector in the
+        following way: ``tf.apply(v) == translation + rotation.apply(v)``
+
+        Parameters
+        ----------
+        translation : array_like, shape (..., 3)
+            Translation vectors. Each translation[..., :] represents a 3D
+            translation vector.
+        rotation : `Rotation` instance
+            Rotation objects. The shape must be broadcastable with the
+            translation shape.
+
+        Returns
+        -------
+        transform : `RigidTransform` instance
+            Rigid transform objects. The shape is determined by broadcasting
+            the translation and rotation shapes together.
+
+        Examples
+        --------
+        >>> from scipy.spatial.transform import RigidTransform as Tf
+        >>> from scipy.spatial.transform import Rotation as R
+        >>> import numpy as np
+
+        Creating from a single rotation and translation:
+
+        >>> t = np.array([2, 3, 4])
+        >>> r = R.from_euler("ZYX", [90, 30, 0], degrees=True)
+        >>> r.as_matrix()
+        array([[ 0.       , -1.,  0.        ],
+               [ 0.8660254,  0.,  0.5       ],
+               [-0.5      ,  0.,  0.8660254 ]])
+        >>> tf = Tf.from_components(t, r)
+        >>> tf.rotation.as_matrix()
+        array([[ 0.       , -1.,  0.        ],
+               [ 0.8660254,  0.,  0.5       ],
+               [-0.5      ,  0.,  0.8660254 ]])
+        >>> tf.translation
+        array([2., 3., 4.])
+        >>> tf.single
+        True
+
+        When applying a transform to a vector ``v``, the result is the same as
+        if the transform was applied to the vector in the following way:
+        ``tf.apply(v) == translation + rotation.apply(v)``
+
+        >>> r.apply([1, 0, 0])
+        array([0.       , 0.8660254, -0.5     ])
+        >>> t + r.apply([1, 0, 0])
+        array([2.       , 3.8660254,  3.5     ])
+        >>> tf.apply([1, 0, 0])
+        array([2.       , 3.8660254,  3.5     ])
+        """
+        rotation_tf = RigidTransform.from_rotation(rotation)
+        return RigidTransform.from_translation(translation) * rotation_tf
+
+    @staticmethod
+    def from_exp_coords(exp_coords: ArrayLike) -> RigidTransform:
+        r"""Initialize from exponential coordinates of transform.
+
+        This implements the exponential map that converts 6-dimensional real
+        vectors to SE(3).
+
+        An exponential coordinate vector consists of 6 elements
+        ``[rx, ry, rz, vx, vy, vz]``. The first 3 encode rotation (and form a
+        rotation vector used in `Rotation.from_rotvec`) and the last 3 encode
+        translation (and form a translation vector for pure translations).
+        The exponential mapping can be expressed as matrix exponential
+        ``T = exp(tau)``, where ``T`` is a 4x4 matrix representing a rigid
+        transform and ``tau`` is a 4x4 matrix formed from the elements of an
+        exponential coordinate vector::
+
+            tau = [  0 -rz  ry vx]
+                  [ rz   0 -rx vy]
+                  [-ry  rx   0 vz]
+                  [  0   0   0  1]
+
+        Parameters
+        ----------
+        exp_coords : array_like, shape (..., 6)
+            Exponential coordinate vectors. Each exp_coords[..., :] represents
+            a 6D exponential coordinate vector with the expected order of
+            components ``[rx, ry, rz, vx, vy, vz]``. The first 3 components
+            encode rotation and the last 3 encode translation.
+
+        Returns
+        -------
+        transform : `RigidTransform` instance
+            Rigid transform objects with the same leading dimensions as the input.
+
+        Examples
+        --------
+        >>> from scipy.spatial.transform import RigidTransform as Tf
+        >>> import numpy as np
+
+        Creating from a single 6d vector of exponential coordinates:
+
+        >>> tf = Tf.from_exp_coords([
+        ...     -2.01041204, -0.52983629, 0.65773501,
+        ...     0.10386614, 0.05855009, 0.54959179])
+        >>> tf.as_matrix()
+        array([[0.76406621, 0.10504613, -0.63652819, -0.10209961],
+               [0.59956454, -0.47987325, 0.64050295, 0.40158789],
+               [-0.2381705, -0.87102639, -0.42963687, 0.19637636],
+               [0., 0., 0., 1.]])
+        >>> tf.single
+        True
+
+        A vector of zeros represents the identity transform:
+
+        >>> tf = Tf.from_exp_coords(np.zeros(6))
+        >>> tf.as_matrix()
+        array([[1., 0., 0., 0.],
+               [0., 1., 0., 0.],
+               [0., 0., 1., 0.],
+               [0., 0., 0., 1.]])
+
+        The last three numbers encode translation. If the first three numbers
+        are zero, the last three components can be interpreted as the
+        translation:
+
+        >>> tf_trans = Tf.from_exp_coords([0, 0, 0, 4.3, -2, 3.4])
+        >>> tf_trans.translation
+        array([4.3, -2., 3.4])
+
+        The first three numbers encode rotation as a rotation vector:
+
+        >>> tf_rot = Tf.from_exp_coords([0.5, 0.3, 0.1, 0, 0, 0])
+        >>> tf_rot.rotation.as_rotvec()
+        array([0.5, 0.3, 0.1])
+
+        Combining translation and rotation preserves the rotation vector,
+        but changes the last three components as they encode translation and
+        rotation:
+
+        >>> (tf_trans * tf_rot).as_exp_coords()
+        array([0.5, 0.3, 0.1, 3.64305882, -1.25879559, 4.46109265])
+        """
+        xp = array_namespace(exp_coords)
+        exp_coords = xp_promote(exp_coords, force_floating=True, xp=xp)
+        if exp_coords.shape[-1] != 6:
+            raise ValueError(
+                f"Expected `exp_coords` to have shape (..., 6), got {exp_coords.shape}."
+            )
+        backend = select_backend(xp, cython_compatible=exp_coords.ndim < 3)
+        matrix = backend.from_exp_coords(exp_coords)
+        return RigidTransform._from_raw_matrix(matrix, xp, backend)
+
+    @staticmethod
+    def from_dual_quat(
+        dual_quat: ArrayLike, *, scalar_first: bool = False
+    ) -> RigidTransform:
+        """Initialize from a unit dual quaternion.
+
+        Unit dual quaternions encode orientation in a real unit quaternion
+        and translation in a dual quaternion. There is a double cover, i.e.,
+        the unit dual quaternions q and -q represent the same transform.
+
+        Unit dual quaternions must have a real quaternion with unit norm and
+        a dual quaternion that is orthogonal to the real quaternion to satisfy
+        the unit norm constraint. This function will enforce both properties
+        through normalization.
+
+        Parameters
+        ----------
+        dual_quat : array_like, shape (..., 8)
+            Unit dual quaternions. Each dual_quat[..., :] represents a unit
+            dual quaternion. The real part is stored in the first four
+            components and the dual part in the last four components.
+        scalar_first : bool, optional
+            Whether the scalar component goes first or last in the two
+            individual quaternions that represent the real and the dual part.
+            Default is False, i.e. the scalar-last order is used.
+
+        Returns
+        -------
+        transform : `RigidTransform` instance
+            Rigid transform objects with the same leading dimensions as the input.
+
+        Examples
+        --------
+        >>> from scipy.spatial.transform import RigidTransform as Tf
+        >>> import numpy as np
+
+        Creating from a single unit dual quaternion:
+
+        >>> tf = Tf.from_dual_quat([
+        ...     0.0617101, -0.06483886, 0.31432811, 0.94508498,
+        ...     0.04985168, -0.26119618, 0.1691491, -0.07743254])
+        >>> tf.as_matrix()
+        array([[0.79398752, -0.60213598, -0.08376202, 0.24605262],
+               [0.58613113, 0.79477941, -0.15740392, -0.4932833],
+               [0.16135089, 0.07588122, 0.98397557, 0.34262676],
+               [0., 0., 0., 1.]])
+        >>> tf.single
+        True
+        """
+        xp = array_namespace(dual_quat)
+        dual_quat = _promote(dual_quat, xp=xp)
+        backend = select_backend(xp, dual_quat.ndim < 3)
+        matrix = backend.from_dual_quat(dual_quat, scalar_first=scalar_first)
+        return RigidTransform._from_raw_matrix(matrix, xp, backend)
+
+    @staticmethod
+    def identity(
+        num: int | None = None, *, shape: int | tuple[int, ...] | None = None
+    ) -> RigidTransform:
+        """Initialize an identity transform.
+
+        Composition with the identity transform has no effect, and
+        applying the identity transform to a vector has no effect.
+
+        Parameters
+        ----------
+        num : int, optional
+            Number of identity transforms to generate. If None (default),
+            then a single transform is generated.
+        shape : int or tuple of ints, optional
+            Shape of the identity transforms. If specified, `num` must
+            be None.
+
+        Returns
+        -------
+        transform : `RigidTransform` instance
+            The identity transform.
+
+        Examples
+        --------
+        >>> from scipy.spatial.transform import RigidTransform as Tf
+        >>> from scipy.spatial.transform import Rotation as R
+        >>> import numpy as np
+
+        Creating a single identity transform:
+
+        >>> tf = Tf.identity()
+        >>> tf.as_matrix()
+        array([[1., 0., 0., 0.],
+               [0., 1., 0., 0.],
+               [0., 0., 1., 0.],
+               [0., 0., 0., 1.]])
+        >>> tf.single
+        True
+
+        The identity transform can be applied to a vector without effect:
+
+        >>> tf.apply([1, 2, 3])
+        array([1., 2., 3.])
+
+        The identity transform when composed with another transform has no
+        effect:
+
+        >>> rng = np.random.default_rng(123)
+        >>> t = rng.random(3)
+        >>> r = R.random(rng=rng)
+        >>> tf = Tf.from_components(t, r)
+        >>> np.allclose((Tf.identity() * tf).as_matrix(),
+        ...             tf.as_matrix(), atol=1e-12)
+        True
+
+        Multiple identity transforms can be generated at once:
+
+        >>> tf = Tf.identity(2)
+        >>> tf.as_matrix()
+        array([[[1., 0., 0., 0.],
+                [0., 1., 0., 0.],
+                [0., 0., 1., 0.],
+                [0., 0., 0., 1.]],
+               [[1., 0., 0., 0.],
+                [0., 1., 0., 0.],
+                [0., 0., 1., 0.],
+                [0., 0., 0., 1.]]])
+        >>> tf.single
+        False
+        >>> len(tf)
+        2
+        """
+        if num is not None and shape is not None:
+            raise ValueError("Only one of `num` and `shape` can be specified.")
+        if num is None and shape is None:
+            shape = ()
+        elif num is not None:
+            shape = (num,)
+        elif isinstance(shape, int):
+            shape = (shape,)
+        elif not isinstance(shape, tuple):
+            raise ValueError("`shape` must be an int or a tuple of ints or None.")
+        matrix = np.tile(np.eye(4), shape + (1, 1))
+        # No need for a backend call here since identity is easy to construct and we are
+        # currently not offering a backend-specific identity matrix
+        return RigidTransform._from_raw_matrix(matrix, array_namespace(matrix))
+
+    @staticmethod
+    def concatenate(
+        transforms: RigidTransform | Iterable[RigidTransform],
+    ) -> RigidTransform:
+        """
+        Concatenate a sequence of `RigidTransform` objects into a
+        single object.
+
+        Parameters
+        ----------
+        transforms : sequence of `RigidTransform`
+            If a single `RigidTransform` instance is passed in, a copy of
+            it is returned.
+
+        Returns
+        -------
+        transform : `RigidTransform` instance
+            The concatenated transform.
+
+        Examples
+        --------
+        >>> from scipy.spatial.transform import RigidTransform as Tf
+        >>> tf1 = Tf.from_translation([1, 0, 0])
+        >>> tf2 = Tf.from_translation([[2, 0, 0], [3, 0, 0]])
+        >>> Tf.concatenate([tf1, tf2]).translation
+        array([[1., 0., 0.],
+               [2., 0., 0.],
+               [3., 0., 0.]])
+        """
+        if isinstance(transforms, RigidTransform):
+            return RigidTransform._from_raw_matrix(
+                transforms.as_matrix(), transforms._xp
+            )
+        if not all(isinstance(x, RigidTransform) for x in transforms):
+            raise TypeError("input must contain RigidTransform objects only")
+
+        xp = array_namespace(transforms[0].as_matrix())  # type:ignore[index]
+        matrix = xp.concat(
+            [xpx.atleast_nd(x.as_matrix(), ndim=3, xp=xp) for x in transforms]
+        )
+        return RigidTransform._from_raw_matrix(matrix, xp, None)
+
+    def mean(self,
+        weights: ArrayLike | None = None,
+        axis: None | int | tuple[int, ...] = None
+    ) -> RigidTransform:
+        """Get the mean of the transforms.
+
+        The mean of a set of transforms is the same as the mean of its
+        rotation and translation components.
+
+        The mean used for the rotation component is the chordal L2 mean (also
+        called the projected or induced arithmetic mean) [1]_. If ``A`` is a
+        set of rotation matrices, then the mean ``M`` is the rotation matrix
+        that minimizes the following loss function:
+
+        .. math::
+
+            L(M) = \\sum_{i = 1}^{n} w_i \\lVert \\mathbf{A}_i -
+            \\mathbf{M} \\rVert^2 ,
+
+        where :math:`w_i`'s are the `weights` corresponding to each matrix.
+
+        Parameters
+        ----------
+        weights : array_like shape (..., N), optional
+            Weights describing the relative importance of the transforms. If
+            None (default), then all values in `weights` are assumed to be
+            equal. If given, the shape of `weights` must be broadcastable to
+            the transform shape. Weights must be non-negative.
+        axis : None, int, or tuple of ints, optional
+            Axis or axes along which the means are computed. The default is to
+            compute the mean of all transforms.
+
+        Returns
+        -------
+        mean : `RigidTransform` instance
+            Single transform containing the mean of the transforms in the
+            current instance.
+
+        References
+        ----------
+        .. [1] Hartley, Richard, et al.,
+                "Rotation Averaging", International Journal of Computer Vision
+                103, 2013, pp. 267-305.
+
+        Examples
+        --------
+        >>> import numpy as np
+        >>> from scipy.spatial.transform import RigidTransform as Tf
+        >>> from scipy.spatial.transform import Rotation as R
+        >>> rng = np.random.default_rng(seed=123)
+
+        The mean of a set of transforms is the same as the mean of the
+        translation and rotation components:
+
+        >>> t = rng.random((4, 3))
+        >>> r = R.random(4, rng=rng)
+        >>> tf = Tf.from_components(t, r)
+        >>> tf.mean().as_matrix()
+        array([[ 0.61593485, -0.74508342,  0.25588075,  0.66999034],
+               [-0.59353615, -0.65246765, -0.47116962,  0.25481794],
+               [ 0.51801458,  0.13833531, -0.84411151,  0.52429339],
+               [0., 0., 0., 1.]])
+        >>> Tf.from_components(t.mean(axis=0), r.mean()).as_matrix()
+        array([[ 0.61593485, -0.74508342,  0.25588075,  0.66999034],
+               [-0.59353615, -0.65246765, -0.47116962,  0.25481794],
+               [ 0.51801458,  0.13833531, -0.84411151,  0.52429339],
+               [0., 0., 0., 1.]])
+        """
+        mean = self._backend.mean(self._matrix, weights=weights, axis=axis)
+        return RigidTransform._from_raw_matrix(mean, xp=self._xp,
+                                               backend=self._backend)
+
+    def as_matrix(self) -> Array:
+        """Return a copy of the matrix representation of the transform.
+
+        4x4 rigid transformation matrices are of the form::
+
+            [       tx]
+            [   R   ty]
+            [       tz]
+            [ 0 0 0  1]
+
+        where ``R`` is a 3x3 orthonormal rotation matrix and
+        ``t = [tx, ty, tz]`` is a 3x1 translation vector.
+
+        Returns
+        -------
+        matrix : numpy.ndarray, shape (..., 4, 4)
+            Transformation matrices with the same leading dimensions as the transform.
+
+        Examples
+        --------
+        >>> from scipy.spatial.transform import RigidTransform as Tf
+        >>> from scipy.spatial.transform import Rotation as R
+        >>> import numpy as np
+
+        A transformation matrix is a 4x4 matrix formed from a 3x3 rotation
+        matrix and a 3x1 translation vector:
+
+        >>> t = np.array([2, 3, 4])
+        >>> r = R.from_matrix([[0, 0, 1],
+        ...                    [1, 0, 0],
+        ...                    [0, 1, 0]])
+        >>> tf = Tf.from_components(t, r)
+        >>> tf.as_matrix()
+        array([[ 0., 0., 1., 2.],
+               [ 1., 0., 0., 3.],
+               [ 0., 1., 0., 4.],
+               [ 0., 0., 0., 1.]])
+
+        >>> Tf.identity(2).as_matrix()
+        array([[[1., 0., 0., 0.],
+                [0., 1., 0., 0.],
+                [0., 0., 1., 0.],
+                [0., 0., 0., 1.]],
+               [[1., 0., 0., 0.],
+                [0., 1., 0., 0.],
+                [0., 0., 1., 0.],
+                [0., 0., 0., 1.]]])
+        """
+        matrix = self._xp.asarray(self._matrix, copy=True)
+        if self._single:
+            return matrix[0, ...]
+        return matrix
+
+    def as_components(self) -> tuple[Array, Rotation]:
+        """Return the translation and rotation components of the transform,
+        where the rotation is applied first, followed by the translation.
+
+        4x4 rigid transformation matrices are of the form::
+
+            [       tx]
+            [   R   ty]
+            [       tz]
+            [ 0 0 0  1]
+
+        Where ``R`` is a 3x3 orthonormal rotation matrix and
+        ``t = [tx, ty, tz]`` is a 3x1 translation vector. This function
+        returns the rotation corresponding to this rotation matrix
+        ``r = Rotation.from_matrix(R)`` and the translation vector ``t``.
+
+        When applying a transform ``tf`` to a vector ``v``, the result is the same
+        as if the rotation and translation components were applied to the vector
+        with the following operation:
+        ``tf.apply(v) == translation + rotation.apply(v)``.
+
+        Returns
+        -------
+        translation : numpy.ndarray, shape (..., 3)
+            The translation of the transform.
+        rotation : `Rotation` instance
+            The rotation of the transform.
+
+        Examples
+        --------
+        >>> from scipy.spatial.transform import RigidTransform as Tf
+        >>> from scipy.spatial.transform import Rotation as R
+        >>> import numpy as np
+
+        Recover the rotation and translation from a transform:
+
+        >>> t = np.array([2, 3, 4])
+        >>> r = R.from_matrix([[0, 0, 1],
+        ...                    [1, 0, 0],
+        ...                    [0, 1, 0]])
+        >>> tf = Tf.from_components(t, r)
+        >>> t, r = tf.as_components()
+        >>> t
+        array([2., 3., 4.])
+        >>> r.as_matrix()
+        array([[0., 0., 1.],
+               [1., 0., 0.],
+               [0., 1., 0.]])
+
+        The transform applied to a vector is equivalent to the rotation applied
+        to the vector, followed by the translation:
+
+        >>> t + r.apply([1, 0, 0])
+        array([2., 4., 4.])
+        >>> tf.apply([1, 0, 0])
+        array([2., 4., 4.])
+        """
+        return self.translation, self.rotation
+
+    def as_exp_coords(self) -> Array:
+        """Return the exponential coordinates of the transform.
+
+        This implements the logarithmic map that converts SE(3) to 6-dimensional
+        real vectors.
+
+        This is an inverse of `from_exp_coords` where details on the mapping can
+        be found.
+
+        Returns
+        -------
+        exp_coords : numpy.ndarray, shape (..., 6)
+            Exponential coordinate vectors with the same leading dimensions as the
+            transform. The first three components define the rotation and the last
+            three components define the translation.
+
+        Examples
+        --------
+        >>> from scipy.spatial.transform import RigidTransform as Tf
+        >>> import numpy as np
+
+        Get exponential coordinates of the identity matrix:
+
+        >>> Tf.identity().as_exp_coords()
+        array([0., 0., 0., 0., 0., 0.])
+        """
+        exp_coords = self._backend.as_exp_coords(self._matrix)
+        if self._single:
+            exp_coords = exp_coords[0, ...]
+        return exp_coords
+
+    def as_dual_quat(self, *, scalar_first: bool = False) -> Array:
+        """Return the dual quaternion representation of the transform.
+
+        Unit dual quaternions encode orientation in a real unit quaternion
+        and translation in a dual quaternion. There is a double cover, i.e.,
+        the unit dual quaternions q and -q represent the same transform.
+
+        Parameters
+        ----------
+        scalar_first : bool, optional
+            Whether the scalar component goes first or last in the two
+            individual quaternions that represent the real and the dual part.
+            Default is False, i.e. the scalar-last order is used.
+
+        Returns
+        -------
+        dual_quat : numpy.ndarray, shape (..., 8)
+            Unit dual quaternion vectors with the same leading dimensions as the
+            transform. The real part is stored in the first four components and the
+            dual part in the last four components.
+
+        Examples
+        --------
+        >>> from scipy.spatial.transform import RigidTransform as Tf
+        >>> import numpy as np
+
+        Get identity dual quaternion (we use scalar-last by default):
+
+        >>> Tf.identity().as_dual_quat()
+        array([0., 0., 0., 1., 0., 0., 0., 0.])
+
+        When we want to use the scalar-first convention, we use the argument:
+
+        >>> Tf.identity().as_dual_quat(scalar_first=True)
+        array([1., 0., 0., 0., 0., 0., 0., 0.])
+        """
+        dual_quat = self._backend.as_dual_quat(self._matrix, scalar_first=scalar_first)
+        if self._single:
+            dual_quat = dual_quat[0]
+        return dual_quat
+
+    def __len__(self) -> int:
+        """Return the length of the leading transform dimension.
+
+        A transform can store an N-dimensional array of transforms. The length is the
+        size of the first dimension of this array. If the transform is a single
+        transform, the length is not defined and an error is raised.
+
+        Returns
+        -------
+        length : int
+            The number of transforms in this object.
+
+        Raises
+        ------
+        TypeError
+            If the transform is a single transform.
+
+        Examples
+        --------
+        >>> from scipy.spatial.transform import RigidTransform as Tf
+        >>> import numpy as np
+        >>> tf = Tf.identity(3)
+        >>> len(tf)
+        3
+
+        An N-dimensional array of transforms returns its first dimension size:
+
+        >>> t = np.ones((5, 2, 3, 1, 3))
+        >>> tf = Tf.from_translation(t)
+        >>> len(tf)
+        5
+
+        A single transform has no length:
+
+        >>> tf = Tf.from_translation([1, 0, 0])
+        >>> len(tf)  # doctest: +IGNORE_EXCEPTION_DETAIL
+        Traceback (most recent call last):
+            ...
+        TypeError: Single transform has no len().
+        """
+        # We don't use self._single here because we also want to raise an error for
+        # Array API backends that call len() on single RigidTransform objects.
+        if self.single:
+            raise TypeError("Single transform has no len")
+        return self._matrix.shape[0]
+
+    def __getitem__(
+        self, indexer: int | slice | EllipsisType | None | ArrayLike
+    ) -> RigidTransform:
+        """Extract transform(s) at given index(es) from this object.
+
+        Creates a new `RigidTransform` instance containing a subset of
+        transforms stored in this object.
+
+        Parameters
+        ----------
+        indexer : int or slice or array_like
+            Specifies which transform(s) to extract. A single indexer must be
+            specified, i.e. as if indexing a 1 dimensional array or list.
+
+        Returns
+        -------
+        transform : `RigidTransform` instance
+            Contains
+                - a single transform, if `indexer` is a single index
+                - a stack of transform(s), if `indexer` is a slice, or an index
+                  array.
+
+        Raises
+        ------
+        TypeError
+            If the transform is a single transform.
+
+        Examples
+        --------
+        >>> from scipy.spatial.transform import RigidTransform as Tf
+        >>> t = [[0, 0, 0], [1, 0, 0], [2, 0, 0]]  # 3 translations
+        >>> tf = Tf.from_translation(t)
+
+        A single index returns a single transform:
+
+        >>> tf[0].as_matrix()
+        array([[1., 0., 0., 0.],
+               [0., 1., 0., 0.],
+               [0., 0., 1., 0.],
+               [0., 0., 0., 1.]])
+
+        A slice returns a stack of transforms:
+
+        >>> tf[1:3].translation
+        array([[1., 0., 0.],
+               [2., 0., 0.]])
+
+        An index array returns a stack of transforms:
+
+        >>> tf[[0, 2]].translation
+        array([[0., 0., 0.],
+               [2., 0., 0.]])
+        """
+        if self.single:
+            raise TypeError("Single transform is not subscriptable.")
+
+        is_array = isinstance(indexer, type(self._matrix))
+        xp = self._xp
+        # Masking is only specified in the Array API when the array is the sole index
+        # This special case handling is necessary to support boolean indexing and
+        # integer array indexing with take (see
+        # https://github.com/data-apis/array-api/pull/900#issuecomment-2674432480)
+        # Ideally we would converge to [indexer, ...] indexing, but this is not
+        # supported for now.
+        if is_array and indexer.dtype == xp.bool:  # type:ignore[union-attr]
+            return RigidTransform(self._matrix[indexer], normalize=False)
+        if is_array and xp.isdtype(indexer.dtype, "integral"):  # type:ignore[union-attr]
+            if self._matrix.shape[0] == 0:
+                raise IndexError("cannot take from an empty array")
+            return RigidTransform(
+                xp.take(self._matrix, indexer, axis=0), normalize=False
+            )
+        return RigidTransform(self._matrix[indexer, ...], normalize=False)
+
+    def __setitem__(
+        self,
+        indexer: int | slice | EllipsisType | None | ArrayLike,
+        value: RigidTransform,
+    ):
+        """Set transform(s) at given index(es) in this object.
+
+        Parameters
+        ----------
+        indexer : int or slice or array_like
+            Specifies which transform(s) to replace. A single indexer must be
+            specified, i.e. as if indexing a 1 dimensional array or list.
+
+        value : `RigidTransform` instance
+            The transform(s) to set.
+
+        Raises
+        ------
+        TypeError
+            If the transform is a single transform.
+
+        Examples
+        --------
+        >>> from scipy.spatial.transform import RigidTransform as Tf
+        >>> t = [[0, 0, 0], [1, 0, 0], [2, 0, 0]]  # 3 translations
+        >>> tf = Tf.from_translation(t)
+
+        Set a single transform:
+
+        >>> tf[0] = Tf.from_translation([9, 9, 9])
+        >>> tf.translation
+        array([[9., 9., 9.],
+               [1., 0., 0.],
+               [2., 0., 0.]])
+        """
+        if self.single:
+            raise TypeError("Single transform is not subscriptable.")
+
+        if not isinstance(value, RigidTransform):
+            raise TypeError("value must be a RigidTransform object")
+
+        self._matrix = self._backend.setitem(self._matrix, indexer, value.as_matrix())
+
+    def __mul__(
+        self, other: RigidTransform | Rotation
+    ) -> RigidTransform | NotImplementedType:
+        """Compose this transform with the other.
+
+        If ``p`` and ``q`` are two transforms, then the composition of '``q``
+        followed by ``p``' is equivalent to ``p * q``. In terms of
+        transformation matrices, the composition can be expressed as
+        ``p.as_matrix() @ q.as_matrix()``.
+
+        In terms of translations and rotations, the composition when applied to
+        a vector ``v`` is equivalent to
+        ``p.translation + p.rotation.apply(q.translation)
+        + (p.rotation * q.rotation).apply(v)``.
+
+        This function supports composition of multiple transforms at a time using
+        broadcasting rules. The resulting shape for two `RigidTransform` instances
+        ``p`` and ``q`` is `np.broadcast_shapes(p.shape, q.shape)`.
+
+        If ``other`` is a `Rotation`, it is automatically promoted to a
+        `RigidTransform` with zero translation.
+
+        Parameters
+        ----------
+        other : `RigidTransform` or `Rotation` instance
+            Transform(s) or rotation(s) to be composed with this one. The shapes
+            must be broadcastable.
+
+        Returns
+        -------
+        `RigidTransform` instance
+            The composed transform.
+
+        Examples
+        --------
+        >>> from scipy.spatial.transform import RigidTransform as Tf
+        >>> from scipy.spatial.transform import Rotation as R
+        >>> import numpy as np
+
+        Compose two transforms:
+
+        >>> tf1 = Tf.from_translation([1, 0, 0])
+        >>> tf2 = Tf.from_translation([0, 1, 0])
+        >>> tf = tf1 * tf2
+        >>> tf.translation
+        array([1., 1., 0.])
+        >>> tf.single
+        True
+
+        When applied to a vector, the composition of two transforms is applied
+        in right-to-left order.
+
+        >>> t1, r1 = [1, 2, 3], R.from_euler('z', 60, degrees=True)
+        >>> t2, r2 = [0, 1, 0], R.from_euler('x', 30, degrees=True)
+        >>> tf1 = Tf.from_components(t1, r1)
+        >>> tf2 = Tf.from_components(t2, r2)
+        >>> tf = tf1 * tf2
+        >>> tf.apply([1, 0, 0])
+        array([0.6339746, 3.3660254, 3.       ])
+        >>> tf1.apply(tf2.apply([1, 0, 0]))
+        array([0.6339746, 3.3660254, 3.       ])
+
+        When at least one of the transforms is not single, the result is a stack
+        of transforms.
+
+        >>> tf1 = Tf.from_translation([1, 0, 0])
+        >>> tf2 = Tf.from_translation([[0, 2, 0], [0, 0, 3]])
+        >>> tf = tf1 * tf2
+        >>> tf.translation
+        array([[1., 2., 0.],
+               [1., 0., 3.]])
+        >>> tf.single
+        False
+        >>> len(tf)
+        2
+
+        Broadcasting rules apply when composing multiple transforms at a time.
+
+        >>> tf1 = Tf.from_translation(np.ones((5, 1, 3)))  # Shape (5, 1, 3)
+        >>> tf2 = Tf.from_translation(np.ones((1, 4, 3)))  # Shape (1, 4, 3)
+        >>> tf = tf1 * tf2  # Shape (5, 4, 3)
+        >>> tf.translation.shape
+        (5, 4, 3)
+        """
+        if isinstance(other, Rotation):
+            other = RigidTransform.from_rotation(other)
+        elif not isinstance(other, RigidTransform):
+            # If other is not a RigidTransform, we return NotImplemented to allow other
+            # types to implement __rmul__
+            return NotImplemented
+        if not broadcastable(self._matrix.shape, other._matrix.shape):
+            raise ValueError(
+                f"Cannot broadcast {self._matrix.shape[:-2]} transforms in "
+                f"first to {other._matrix.shape[:-2]} transforms in second object."
+            )
+        cython_compatible = self._matrix.ndim < 4 and other._matrix.ndim < 4
+        backend = select_backend(self._xp, cython_compatible=cython_compatible)
+        matrix = backend.compose_transforms(self._matrix, other._matrix)
+        # Only necessary for cython. Array API broadcasting handles this by default
+        if self._single and other._single:
+            matrix = matrix[0, ...]
+        return RigidTransform(matrix, normalize=True, copy=False)
+
+    def __rmul__(self, other: Rotation) -> RigidTransform | NotImplementedType:
+        """Compose a rotation with this transform (rotation applied second).
+
+        See `__mul__` for more details.
+
+        Parameters
+        ----------
+        other : `Rotation` instance
+            The rotation to compose with this transform. The shapes must be
+            broadcastable.
+
+        Returns
+        -------
+        `RigidTransform` instance
+            The composed transform.
+        """
+        if isinstance(other, Rotation):
+            return RigidTransform.from_rotation(other) * self
+        # When other is a RigidTransform __mul__ is called, so we don't handle it here
+        return NotImplemented
+
+    def __pow__(self, n: float) -> RigidTransform:
+        """Compose this transform with itself `n` times.
+
+        A rigid transform `p` when raised to non-integer powers can be thought
+        of as finding a fraction of the transformation. For example, a power of
+        0.5 finds a "halfway" transform from the identity to `p`.
+
+        This is implemented by applying screw linear interpolation (ScLERP)
+        between `p` and the identity transform, where the angle of the rotation
+        component is scaled by `n`, and the translation is proportionally
+        adjusted along the screw axis.
+
+        ``q = p ** n`` can also be expressed as
+        ``q = RigidTransform.from_exp_coords(p.as_exp_coords() * n)``.
+
+        If `n` is negative, then the transform is inverted before the power
+        is applied. In other words, ``p ** -abs(n) == p.inv() ** abs(n)``.
+
+        Parameters
+        ----------
+        n : float
+            The number of times to compose the transform with itself.
+
+        Returns
+        -------
+        `RigidTransform` instance
+            If the input Rotation `p` contains `N` multiple rotations, then
+            the output will contain `N` rotations where the `i` th rotation
+            is equal to ``p[i] ** n``.
+
+        Notes
+        -----
+        There are three notable cases: if ``n == 1`` then a copy of the original
+        transform is returned, if ``n == 0`` then the identity transform is
+        returned, and if ``n == -1`` then the inverse transform is returned.
+
+        Note that fractional powers ``n`` which effectively take a root of
+        rotation, do so using the shortest path smallest representation of that
+        angle (the principal root). This means that powers of ``n`` and ``1/n``
+        are not necessarily inverses of each other. For example, a 0.5 power of
+        a +240 degree rotation will be calculated as the 0.5 power of a -120
+        degree rotation, with the result being a rotation of -60 rather than
+        +120 degrees.
+
+        Examples
+        --------
+        >>> from scipy.spatial.transform import RigidTransform as Tf
+        >>> import numpy as np
+
+        A power of 2 returns the transform composed with itself:
+
+        >>> tf = Tf.from_translation([1, 2, 3])
+        >>> (tf ** 2).translation
+        array([2., 4., 6.])
+        >>> (tf ** 2).as_matrix()
+        array([[1., 0., 0., 2.],
+               [0., 1., 0., 4.],
+               [0., 0., 1., 6.],
+               [0., 0., 0., 1.]])
+
+        A negative power returns the inverse of the transform raised to the
+        absolute value of `n`:
+
+        >>> (tf ** -2).translation
+        array([-2., -4., -6.])
+        >>> np.allclose((tf ** -2).as_matrix(), (tf.inv() ** 2).as_matrix(),
+        ...             atol=1e-12)
+        True
+
+        A power of 0 returns the identity transform:
+
+        >>> (tf ** 0).as_matrix()
+        array([[1., 0., 0., 0.],
+               [0., 1., 0., 0.],
+               [0., 0., 1., 0.],
+               [0., 0., 0., 1.]])
+
+        A power of 1 returns a copy of the original transform:
+
+        >>> (tf ** 1).as_matrix()
+        array([[1., 0., 0., 1.],
+               [0., 1., 0., 2.],
+               [0., 0., 1., 3.],
+               [0., 0., 0., 1.]])
+
+        A fractional power returns a transform with a scaled rotation and
+        translated along the screw axis. Here we take the square root of the
+        transform, which when squared recovers the original transform:
+
+        >>> tf_half = (tf ** 0.5)
+        >>> tf_half.translation
+        array([0.5, 1., 1.5])
+        >>> (tf_half ** 2).as_matrix()
+        array([[1., 0., 0., 1.],
+               [0., 1., 0., 2.],
+               [0., 0., 1., 3.],
+               [0., 0., 0., 1.]])
+        """
+        matrix = self._backend.pow(self._matrix, n)
+        if self._single:
+            matrix = matrix[0, ...]
+        return RigidTransform._from_raw_matrix(matrix, self._xp, self._backend)
+
+    def inv(self) -> RigidTransform:
+        """Invert this transform.
+
+        Composition of a transform with its inverse results in an identity
+        transform.
+
+        A rigid transform is a composition of a rotation and a translation,
+        where the rotation is applied first, followed by the translation. So the
+        inverse transform is equivalent to the inverse translation followed by
+        the inverse rotation.
+
+        Returns
+        -------
+        `RigidTransform` instance
+            The inverse of this transform.
+
+        Examples
+        --------
+        >>> from scipy.spatial.transform import RigidTransform as Tf
+        >>> from scipy.spatial.transform import Rotation as R
+        >>> import numpy as np
+
+        A transform composed with its inverse results in an identity transform:
+
+        >>> rng = np.random.default_rng(seed=123)
+        >>> t = rng.random(3)
+        >>> r = R.random(rng=rng)
+        >>> tf = Tf.from_components(t, r)
+        >>> tf.as_matrix()
+        array([[-0.45431291,  0.67276178, -0.58394466,  0.68235186],
+               [-0.23272031,  0.54310598,  0.80676958,  0.05382102],
+               [ 0.85990758,  0.50242162, -0.09017473,  0.22035987],
+               [ 0.        ,  0.        ,  0.        ,  1.        ]])
+
+        >>> (tf.inv() * tf).as_matrix()
+        array([[[1., 0., 0., 0.],
+                [0., 1., 0., 0.],
+                [0., 0., 1., 0.],
+                [0., 0., 0., 1.]]])
+
+        The inverse rigid transform is the same as the inverse translation
+        followed by the inverse rotation:
+
+        >>> t, r = tf.as_components()
+        >>> r_inv = r.inv()  # inverse rotation
+        >>> t_inv = -t  # inverse translation
+        >>> tf_r_inv = Tf.from_rotation(r_inv)
+        >>> tf_t_inv = Tf.from_translation(t_inv)
+        >>> np.allclose((tf_r_inv * tf_t_inv).as_matrix(),
+        ...             tf.inv().as_matrix(),
+        ...             atol=1e-12)
+        True
+        >>> (tf_r_inv * tf_t_inv * tf).as_matrix()
+        array([[[1., 0., 0., 0.],
+                [0., 1., 0., 0.],
+                [0., 0., 1., 0.],
+                [0., 0., 0., 1.]]])
+        """
+        matrix = self._backend.inv(self._matrix)
+        if self._single:
+            matrix = matrix[0, ...]
+        return RigidTransform._from_raw_matrix(matrix, self._xp, self._backend)
+
+    def apply(self, vector: ArrayLike, inverse: bool = False) -> Array:
+        """Apply the transform to a vector.
+
+        If the original frame transforms to the final frame by this transform,
+        then its application to a vector can be seen in two ways:
+
+            - As a projection of vector components expressed in the final frame
+              to the original frame.
+            - As the physical transformation of a vector being glued to the
+              original frame as it transforms. In this case the vector
+              components are expressed in the original frame before and after
+              the transformation.
+
+        In terms of the rotation matrix and translation,
+        this application is the same as
+        ``self.translation + (mat @ vector[..., np.newaxis])[..., 0]``,
+        where ``mat = self.rotation.as_matrix()``.
+
+        For a single transform, this is the same as
+        ``self.translation + vector @ self.rotation.as_matrix().T``.
+
+        Parameters
+        ----------
+        vector : array_like, shape (..., 3)
+            Vector(s) to be transformed. Each vector[..., :] represents a 3D
+            vector.
+        inverse : bool, optional
+            If True, the inverse of the transform is applied to the vector.
+
+        Returns
+        -------
+        transformed_vector : numpy.ndarray, shape (..., 3)
+            The transformed vector(s) with shape determined by broadcasting
+            the transform and vector shapes together.
+
+        Examples
+        --------
+        >>> from scipy.spatial.transform import RigidTransform as Tf
+        >>> from scipy.spatial.transform import Rotation as R
+        >>> import numpy as np
+
+        Apply a single transform to a vector. Here the transform is just a
+        translation, so the result is the vector added to the translation
+        vector.
+
+        >>> t = np.array([1, 2, 3])
+        >>> tf = Tf.from_translation(t)
+        >>> t + np.array([1, 0, 0])
+        array([2, 2, 3])
+        >>> tf.apply([1, 0, 0])
+        array([2., 2., 3.])
+
+        Apply a single transform to a stack of vectors:
+
+        >>> tf.apply([[1, 0, 0], [0, 1, 0]])
+        array([[2., 2., 3.],
+               [1., 3., 3.]])
+
+        Apply the inverse of a transform to a vector, so the result is the
+        negative of the translation vector added to the vector.
+
+        >>> -t + np.array([1, 0, 0])
+        array([0, -2, -3])
+        >>> tf.apply([1, 0, 0], inverse=True)
+        array([0., -2., -3.])
+
+        Broadcasting is supported when applying multiple transforms to an N-dimensional
+        array of vectors.
+
+        >>> tf = Tf.from_translation(np.ones((4, 5, 1, 3)))
+        >>> vectors = np.zeros((2, 3))
+        >>> tf.apply(vectors).shape
+        (4, 5, 2, 3)
+
+        For transforms which are not just pure translations, applying it to a
+        vector is the same as applying the rotation component to the vector and
+        then adding the translation component.
+
+        >>> r = R.from_euler('z', 60, degrees=True)
+        >>> tf = Tf.from_components(t, r)
+        >>> t + r.apply([1, 0, 0])
+        array([1.5,       2.8660254, 3.       ])
+        >>> tf.apply([1, 0, 0])
+        array([1.5,       2.8660254, 3.       ])
+
+        When applying the inverse of a transform, the result is the negative of
+        the translation vector added to the vector, and then rotated by the
+        inverse rotation.
+
+        >>> r.inv().apply(-t + np.array([1, 0, 0]))
+        array([-1.73205081, -1.        , -3.        ])
+        >>> tf.apply([1, 0, 0], inverse=True)
+        array([-1.73205081, -1.        , -3.        ])
+        """
+        # We do not use the cached xp here to catch cases where matrix and vector have
+        # different xp instances.
+        xp = array_namespace(self._matrix, vector)
+        vector = xp.asarray(
+            vector, dtype=self._matrix.dtype, device=device(self._matrix)
+        )
+        cython_compatible = self._matrix.ndim < 4 and vector.ndim < 3
+        backend = select_backend(xp, cython_compatible=cython_compatible)
+        result = backend.apply(self._matrix, vector, inverse)
+        if self._single and vector.ndim == 1:
+            result = result[0, ...]
+        return result
+
+    @property
+    def rotation(self) -> Rotation:
+        """Return the rotation component of the transform.
+
+        A transform is a composition of a rotation and a translation, such that
+        when applied to a vector, the vector is first rotated and then
+        translated. This property returns the rotation part of the transform.
+
+        Returns
+        -------
+        rotation : `Rotation` instance
+            A single rotation or a stack of rotations.
+
+        Examples
+        --------
+        >>> from scipy.spatial.transform import RigidTransform as Tf
+        >>> from scipy.spatial.transform import Rotation as R
+        >>> import numpy as np
+
+        The rotation component is extracted from the transform:
+
+        >>> t = np.array([1, 0, 0])
+        >>> r = R.random(3)
+        >>> tf = Tf.from_components(t, r)
+        >>> np.allclose(tf.rotation.as_matrix(), r.as_matrix())
+        True
+        """
+        if self._single:
+            return Rotation.from_matrix(self._matrix[0, :3, :3])
+        return Rotation.from_matrix(self._matrix[..., :3, :3])
+
+    @property
+    def translation(self) -> Array:
+        """Return the translation component of the transform.
+
+        A transform is a composition of a rotation and a translation, such that
+        when applied to a vector, the vector is first rotated and then
+        translated. This property returns the translation part of the transform.
+
+        Returns
+        -------
+        translation : numpy.ndarray, shape (..., 3)
+            Translation vectors with the same leading dimensions as the transform.
+
+        Examples
+        --------
+        >>> from scipy.spatial.transform import RigidTransform as Tf
+        >>> from scipy.spatial.transform import Rotation as R
+        >>> import numpy as np
+
+        The translation component is extracted from the transform:
+
+        >>> t = np.array([[1, 0, 0], [2, 0, 0], [3, 0, 0]])
+        >>> r = R.random()
+        >>> tf = Tf.from_components(t, r)
+        >>> np.allclose(tf.translation, t)
+        True
+        """
+        if self._single:
+            return self._xp.asarray(self._matrix[0, :3, 3], copy=True)
+        return self._xp.asarray(self._matrix[..., :3, 3], copy=True)
+
+    @property
+    def single(self) -> bool:
+        """Whether this instance represents a single transform.
+
+        Single transforms are not subscriptable, and do not have a length.
+
+        Returns
+        -------
+        single : bool
+            True if this instance represents a single transform, False
+            otherwise.
+        """
+        return self._single or self._matrix.ndim == 2
+
+    @property
+    def shape(self) -> tuple[int, ...]:
+        """The shape of the transform's leading dimensions."""
+        if self._single or self._matrix.ndim == 2:
+            return ()
+        return self._matrix.shape[:-2]
+
+    def __reduce__(self) -> tuple[Callable, tuple]:
+        """Reduce the RigidTransform for pickling.
+
+        We store modules inside RigidTransforms which cannot be pickled. To circumvent
+        this, we pickle only the matrix and restore the cached modules from the matrix
+        type in `from_matrix`.
+        """
+        matrix = self._matrix
+        if self._single:
+            matrix = matrix[0, ...]
+        return (self.__class__.from_matrix, (matrix,))
+
+    def __iter__(self) -> Iterator[RigidTransform]:
+        """Iterate over transforms."""
+        if self._single or self._matrix.ndim == 2:
+            raise TypeError("Single transform is not iterable.")
+        # We return a generator that yields a new RigidTransform object for each
+        # transform in the current object. We cannot rely on the default implementation
+        # because jax will not raise an IndexError for out-of-bounds indices.
+        for i in range(self._matrix.shape[0]):
+            yield RigidTransform._from_raw_matrix(
+                self._matrix[i, ...], self._xp, self._backend
+            )
+
+    @staticmethod
+    def _from_raw_matrix(
+        matrix: Array, xp: ModuleType, backend: ModuleType | None = None
+    ) -> RigidTransform:
+        """Create a RigidTransform skipping all sanitization steps.
+
+        This method is is intended for internal, performant creation of RigidTransforms
+        with matrices that are guaranteed to be valid.
+        """
+        tf = RigidTransform.__new__(RigidTransform)
+        tf._single = matrix.ndim == 2 and is_numpy(xp)
+        if tf._single:
+            matrix = xpx.atleast_nd(matrix, ndim=3, xp=xp)
+        tf._matrix = matrix
+        tf._xp = xp
+        if backend is None:
+            backend = select_backend(xp, matrix.ndim < 4)
+        tf._backend = backend
+        return tf
diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/transform/_rigid_transform_cy.cpython-312-x86_64-linux-gnu.so b/venv/lib/python3.12/site-packages/scipy/spatial/transform/_rigid_transform_cy.cpython-312-x86_64-linux-gnu.so
new file mode 100644
index 0000000000000000000000000000000000000000..65a12dca031bbdc89b6c9ec6de629df1efefb730
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/transform/_rigid_transform_cy.cpython-312-x86_64-linux-gnu.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:8d025603d3b079716af5331e0b4cf7a3fa3020d56ec106200d9258e07960c862
+size 245720
diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/transform/_rigid_transform_xp.py b/venv/lib/python3.12/site-packages/scipy/spatial/transform/_rigid_transform_xp.py
new file mode 100644
index 0000000000000000000000000000000000000000..8700f3065283dcfdeece75c7ef1f4c18388d2757
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/transform/_rigid_transform_xp.py
@@ -0,0 +1,448 @@
+from types import EllipsisType
+
+from scipy._lib._array_api import (
+    array_namespace,
+    Array,
+    ArrayLike,
+    is_lazy_array,
+    xp_vector_norm,
+    xp_result_type,
+    xp_promote,
+    is_array_api_obj,
+)
+import scipy._external.array_api_extra as xpx
+from scipy.spatial.transform._rotation_xp import (
+    as_matrix as quat_as_matrix,
+    from_matrix as quat_from_matrix,
+    _from_matrix_orthogonal as quat_from_matrix_orthogonal,
+    from_rotvec as quat_from_rotvec,
+    as_rotvec as quat_as_rotvec,
+    compose_quat,
+    from_quat,
+    inv as quat_inv,
+    mean as quat_mean,
+)
+from scipy._external.array_api_compat import device as xp_device
+from scipy._lib._util import broadcastable
+
+
+def from_matrix(matrix: Array, normalize: bool = True, copy: bool = True) -> Array:
+    xp = array_namespace(matrix)
+    # Shape check should be done before calling this function
+    if normalize or copy:
+        matrix = xp.asarray(matrix, copy=True)
+
+    last_row_ok = xp.all(
+        matrix[..., 3, :] == xp.asarray([0, 0, 0, 1.0], device=xp_device(matrix)),
+        axis=-1,
+    )
+    lazy = is_lazy_array(matrix)
+    # We delay lazy branch checks until after normalization to avoid overwriting nans
+    # with the rotation matrix
+    if not lazy and xp.any(~last_row_ok):
+        if last_row_ok.shape == ():
+            idx = ()
+        else:
+            idx = tuple(int(i[0]) for i in xp.nonzero(~last_row_ok))
+        vals = matrix[idx + (3, ...)]
+        raise ValueError(
+            f"Expected last row of transformation matrix {idx} to be "
+            f"exactly [0, 0, 0, 1], got {vals}"
+        )
+
+    # The quat_from_matrix() method orthogonalizes the rotation
+    # component of the transformation matrix. While this does have some
+    # overhead in converting a rotation matrix to a quaternion and back, it
+    # allows for skipping singular value decomposition for near-orthogonal
+    # matrices, which is a computationally expensive operation.
+    if normalize:
+        rotmat = quat_as_matrix(quat_from_matrix(matrix[..., :3, :3]))
+        matrix = xpx.at(matrix)[..., :3, :3].set(rotmat)
+    # Lazy branch matrix invalidation
+    if lazy:
+        matrix = xp.where(last_row_ok[..., None, None], matrix, xp.nan)
+    return matrix
+
+
+def from_rotation(quat: Array) -> Array:
+    xp = array_namespace(quat)
+    rotmat = quat_as_matrix(quat)
+    matrix = xp.zeros(
+        (*rotmat.shape[:-2], 4, 4), dtype=quat.dtype, device=xp_device(quat)
+    )
+    matrix = xpx.at(matrix)[..., :3, :3].set(rotmat)
+    matrix = xpx.at(matrix)[..., 3, 3].set(1)
+    return matrix
+
+
+def from_translation(translation: Array) -> Array:
+    xp = array_namespace(translation)
+
+    if translation.shape[-1] != 3:
+        raise ValueError(
+            f"Expected `translation` to have shape (..., 3), got {translation.shape}."
+        )
+    device = xp_device(translation)
+    dtype = xp_result_type(translation, force_floating=True, xp=xp)
+    eye = xp.eye(4, dtype=dtype, device=device)
+
+    matrix = xpx.atleast_nd(eye, ndim=translation.ndim + 1, xp=xp)
+    matrix = xp.zeros(
+        (*translation.shape[:-1], 4, 4),
+        dtype=dtype,
+        device=device,
+    )
+    matrix = xpx.at(matrix)[...].set(xp.eye(4, dtype=dtype, device=device))
+    matrix = xpx.at(matrix)[..., :3, 3].set(
+        xp_promote(translation, force_floating=True, xp=xp)
+    )
+    return matrix
+
+
+def from_components(translation: Array, quat: Array) -> Array:
+    return compose_transforms(from_translation(translation), from_rotation(quat))
+
+
+def from_exp_coords(exp_coords: Array) -> Array:
+    rot_vec = exp_coords[..., :3]
+    rot_matrix = quat_as_matrix(quat_from_rotvec(rot_vec))
+    translation_transform = _compute_se3_exp_translation_transform(rot_vec)
+    translations = (translation_transform @ exp_coords[..., 3:, None])[..., 0]
+    return _create_transformation_matrix(translations, rot_matrix)
+
+
+def from_dual_quat(dual_quat: Array, *, scalar_first: bool = False) -> Array:
+    xp = array_namespace(dual_quat)
+
+    if dual_quat.shape[-1] != 8:
+        raise ValueError(
+            f"Expected `dual_quat` to have shape (..., 8), got {dual_quat.shape}."
+        )
+
+    real_part = dual_quat[..., :4]
+    dual_part = dual_quat[..., 4:]
+    if scalar_first:
+        real_part = xp.roll(real_part, -1, axis=-1)
+        dual_part = xp.roll(dual_part, -1, axis=-1)
+
+    real_part, dual_part = _normalize_dual_quaternion(real_part, dual_part)
+
+    rot_quat = from_quat(real_part)
+
+    translation = 2.0 * compose_quat(dual_part, quat_inv(rot_quat))[..., :3]
+    matrix = _create_transformation_matrix(translation, quat_as_matrix(rot_quat))
+
+    return matrix
+
+
+def as_exp_coords(matrix: Array) -> Array:
+    xp = array_namespace(matrix)
+    rot_vec = quat_as_rotvec(quat_from_matrix_orthogonal(matrix[..., :3, :3]))
+    translation_transform = _compute_se3_log_translation_transform(rot_vec)
+    translations = (translation_transform @ matrix[..., :3, 3][..., None])[..., 0]
+    exp_coords = xp.concat([rot_vec, translations], axis=-1)
+    return exp_coords
+
+
+def as_dual_quat(matrix: Array, *, scalar_first: bool = False) -> Array:
+    xp = array_namespace(matrix)
+    real_parts = quat_from_matrix_orthogonal(matrix[..., :3, :3])
+
+    pure_translation_quats = xp.empty(
+        (*matrix.shape[:-2], 4), dtype=matrix.dtype, device=xp_device(matrix)
+    )
+    pure_translation_quats = xpx.at(pure_translation_quats)[..., :3].set(
+        matrix[..., :3, 3]
+    )
+    pure_translation_quats = xpx.at(pure_translation_quats)[..., 3].set(0.0)
+
+    dual_parts = 0.5 * compose_quat(pure_translation_quats, real_parts)
+
+    if scalar_first:
+        real_parts = xp.roll(real_parts, 1, axis=-1)
+        dual_parts = xp.roll(dual_parts, 1, axis=-1)
+
+    dual_quats = xp.concat([real_parts, dual_parts], axis=-1)
+    return dual_quats
+
+
+def compose_transforms(tf_matrix: Array, other_tf_matrix: Array) -> Array:
+    if not broadcastable(tf_matrix.shape, other_tf_matrix.shape):
+        len_a = tf_matrix.shape[0] if tf_matrix.ndim == 3 else 1
+        len_b = other_tf_matrix.shape[0] if other_tf_matrix.ndim == 3 else 1
+        raise ValueError(
+            "Expected equal number of transforms in both or a "
+            "single transform in either object, got "
+            f"{len_a} transforms in first and {len_b}"
+            "transforms in second object."
+        )
+    return tf_matrix @ other_tf_matrix
+
+
+def inv(matrix: Array) -> Array:
+    xp = array_namespace(matrix)
+    r_inv = xp.matrix_transpose(matrix[..., :3, :3])
+    # Matrix multiplication of r_inv and translation vector
+    t_inv = -(r_inv @ matrix[..., :3, 3][..., None])[..., 0]
+    matrix = xp.zeros(
+        (*matrix.shape[:-2], 4, 4), dtype=matrix.dtype, device=xp_device(matrix)
+    )
+    matrix = xpx.at(matrix)[..., :3, :3].set(r_inv)
+    matrix = xpx.at(matrix)[..., :3, 3].set(t_inv)
+    matrix = xpx.at(matrix)[..., 3, 3].set(1)
+    return matrix
+
+
+def apply(matrix: Array, vector: Array, inverse: bool = False) -> Array:
+    xp = array_namespace(matrix)
+    if vector.shape[-1] != 3:
+        raise ValueError(f"Expected vector to have shape (..., 3), got {vector.shape}.")
+    vec = xp.empty(
+        (*vector.shape[:-1], 4), dtype=vector.dtype, device=xp_device(vector)
+    )
+    vec = xpx.at(vec)[..., :3].set(vector)
+    vec = xpx.at(vec)[..., 3].set(1)
+    vec = vec[..., None]
+
+    if inverse:
+        matrix = inv(matrix)
+
+    # We raise a ValueError manually here because letting the function run its course
+    # would raise heterogeneous error types and messages for different frameworks.
+    # However, the error only mimics numpy's error message and does not provide the
+    # same amount of context.
+    if not broadcastable(matrix.shape, vec.shape):  # type:ignore[arg-type]
+        raise ValueError("operands could not be broadcast together")
+    return (matrix @ vec)[..., :3, 0]
+
+
+def pow(matrix: Array, n: float | Array) -> Array:
+    xp = array_namespace(matrix)
+    device = xp_device(matrix)
+    # If n is an array, we sanitize it to a scalar and promote quat and n to
+    # the same dtype.
+    if is_array_api_obj(n):
+        if n.shape == (1,):  # type:ignore[union-attr]
+            n = n[0]  # type:ignore[index]
+        elif n.ndim != 0:  # type:ignore[union-attr]
+            raise ValueError("Array exponent must be a scalar")
+        matrix, n = xp_promote(matrix, n, force_floating=True, xp=xp)
+
+    # If n is a lazy array, we cannot take fast paths for special cases.
+    if is_lazy_array(n):
+        # Lazy execution. We compute all special cases and the general case
+        result = from_exp_coords(as_exp_coords(matrix) * n)
+        identity = xp.eye(4, dtype=matrix.dtype, device=device)
+        result = xp.where(n == 0, identity, result)
+        result = xp.where(n == -1, inv(matrix), result)
+        result = xp.where(n == 1, matrix, result)
+        return result
+    if n == 0:
+        identity = xp.eye(4, dtype=matrix.dtype, device=device)
+        identity = xpx.atleast_nd(identity, ndim=matrix.ndim, xp=xp)
+        return xp.tile(identity, (*matrix.shape[:-2], 1, 1))
+    elif n == -1:
+        return inv(matrix)
+    elif n == 1:
+        return matrix
+    return from_exp_coords(as_exp_coords(matrix) * n)
+
+
+def mean(
+    matrix: Array,
+    weights: ArrayLike | None = None,
+    axis: None | int | tuple[int, ...] = None
+) -> Array:
+    xp = array_namespace(matrix)
+    if matrix.shape[0] == 0:
+        raise ValueError("Mean of an empty rotation set is undefined.")
+    # Axis logic: For None, we reduce over all axes. For int, we only reduce over that
+    # axis. For tuple, we reduce over all specified axes.
+    all_axes = tuple(range(matrix.ndim - 2))
+    if axis is None:
+        axis = all_axes
+    elif isinstance(axis, int):
+        axis = (axis,)
+    if not isinstance(axis, tuple):
+        raise ValueError("`axis` must be None, int, or tuple of ints.")
+    # Ensure all axes are within bounds
+    if (axis != () and
+       (min(axis) < -(matrix.ndim - 2) or max(axis) > (matrix.ndim - 3))
+    ):
+        raise ValueError(
+            f"axis {axis} is out of bounds for transform with shape "
+            f"{matrix.shape[:-2]}."
+        )
+    # Ensure all axes are positive and unique
+    axis = tuple(sorted(set(x % (matrix.ndim - 2) for x in axis)))
+
+    lazy = is_lazy_array(matrix)
+    quats = quat_from_matrix_orthogonal(matrix[..., :3, :3])
+    if weights is None:
+        quats_mean = quat_mean(quats, axis=axis)
+    else:
+        neg_weights = weights < 0  # type:ignore[operator]
+        any_neg_weights = xp.any(neg_weights)
+        if not lazy and any_neg_weights:
+            raise ValueError("`weights` must be non-negative.")
+        if weights.shape != matrix.shape[:-2]:  # type:ignore[union-attr]
+            raise ValueError(
+                f"Expected `weights` to match transform shape, got shape "
+                f"{weights.shape} for {matrix.shape[:-2]} transformations."  # type:ignore[union-attr]
+            )
+        quats_mean = quat_mean(quats, weights=weights, axis=axis)
+    r_mean = quat_as_matrix(quats_mean)
+
+    t = matrix[..., :3, 3]
+    if weights is None:
+        t_mean = xp.mean(t, axis=axis)
+    else:
+        norm = xp.sum(weights[..., None], axis=axis)  # type:ignore[index]
+        wsum = xp.sum(t * weights[..., None], axis=axis)  # type:ignore[index]
+        t_mean = wsum / norm
+
+    tf = _create_transformation_matrix(t_mean, r_mean)
+    if weights is not None and lazy:
+        # We cannot raise on negative weights because jit code needs to be
+        # non-branching. We return NaN instead
+        mask = xp.where(any_neg_weights, xp.nan, 1.0)  # pyrefly:ignore[unbound-name]
+        tf = mask * tf
+    return tf
+
+
+def setitem(
+    matrix: Array,
+    indexer: Array | int | tuple | slice | EllipsisType | None,
+    value: Array,
+) -> Array:
+    xp = array_namespace(matrix)
+    if isinstance(indexer, EllipsisType):
+        return xpx.at(matrix)[indexer].set(value)
+    if is_array_api_obj(indexer) and indexer.dtype == xp.bool:  # type:ignore[union-attr]
+        return xpx.at(matrix)[indexer].set(value)  # type:ignore[index]
+    return xpx.at(matrix)[indexer, ...].set(value)  # type:ignore[index]
+
+
+def normalize_dual_quaternion(dual_quat: Array) -> Array:
+    """Normalize dual quaternion."""
+    xp = array_namespace(dual_quat)
+    real, dual = _normalize_dual_quaternion(dual_quat[..., :4], dual_quat[..., 4:])
+    return xp.concat((real, dual), axis=-1)
+
+
+def _create_transformation_matrix(
+    translations: Array, rotation_matrices: Array
+) -> Array:
+    if not translations.shape[:-1] == rotation_matrices.shape[:-2]:
+        raise ValueError(
+            "The number of rotation matrices and translations must be the same."
+        )
+    xp = array_namespace(translations)
+    matrix = xp.empty(
+        (*translations.shape[:-1], 4, 4),
+        dtype=translations.dtype,
+        device=xp_device(translations),
+    )
+    matrix = xpx.at(matrix)[..., :3, :3].set(rotation_matrices)
+    matrix = xpx.at(matrix)[..., :3, 3].set(translations)
+    matrix = xpx.at(matrix)[..., 3, :3].set(0)
+    matrix = xpx.at(matrix)[..., 3, 3].set(1)
+    return matrix
+
+
+def _compute_se3_exp_translation_transform(rot_vec: Array) -> Array:
+    """Compute the transformation matrix from the se3 translation part to SE3
+    translation.
+
+    The transformation matrix depends on the rotation vector.
+    """
+    xp = array_namespace(rot_vec)
+    device = xp_device(rot_vec)
+    dtype = rot_vec.dtype
+    angle = xp_vector_norm(rot_vec, axis=-1, keepdims=True, xp=xp)
+    small_scale = angle < 1e-3
+
+    k1_small = 0.5 - angle**2 / 24 + angle**4 / 720
+    # Avoid division by zero for non-branching computations. The value will get
+    # discarded in the xp.where selection.
+    safe_angle = angle + xp.asarray(small_scale, dtype=dtype, device=device)
+    k1 = (1.0 - xp.cos(angle)) / safe_angle**2
+    k1 = xp.where(small_scale, k1_small, k1)
+
+    k2_small = 1 / 6 - angle**2 / 120 + angle**4 / 5040
+    # Again, avoid division by zero by adding one to all near-zero angles.
+    safe_angle = angle + xp.asarray(small_scale, dtype=dtype, device=device)
+    k2 = (angle - xp.sin(angle)) / safe_angle**3
+    k2 = xp.where(small_scale, k2_small, k2)
+
+    s = _create_skew_matrix(rot_vec)
+    eye = xp.eye(3, dtype=dtype, device=device)
+
+    return eye + k1[..., None] * s + k2[..., None] * s @ s
+
+
+def _compute_se3_log_translation_transform(rot_vec: Array) -> Array:
+    """Compute the transformation matrix from SE3 translation to the se3
+    translation part.
+
+    It is the inverse of `_compute_se3_exp_translation_transform` in a closed
+    analytical form.
+    """
+    xp = array_namespace(rot_vec)
+    dtype = rot_vec.dtype
+    device = xp_device(rot_vec)
+    angle = xp_vector_norm(rot_vec, axis=-1, keepdims=True, xp=xp)
+    mask = angle < 1e-3
+
+    k_small = 1 / 12 + angle**2 / 720 + angle**4 / 30240
+    safe_angle = angle + xp.asarray(mask, dtype=dtype, device=device)
+    k = (1 - 0.5 * angle / xp.tan(0.5 * safe_angle)) / safe_angle**2
+    k = xp.where(mask, k_small, k)
+
+    s = _create_skew_matrix(rot_vec)
+
+    return xp.eye(3, dtype=dtype, device=device) - 0.5 * s + k[..., None] * s @ s
+
+
+def _create_skew_matrix(vec: Array) -> Array:
+    """Create skew-symmetric (aka cross-product) matrix for stack of vectors."""
+    xp = array_namespace(vec)
+    result = xp.zeros((*vec.shape[:-1], 3, 3), dtype=vec.dtype, device=xp_device(vec))
+    result = xpx.at(result)[..., 0, 1].set(-vec[..., 2])
+    result = xpx.at(result)[..., 0, 2].set(vec[..., 1])
+    result = xpx.at(result)[..., 1, 0].set(vec[..., 2])
+    result = xpx.at(result)[..., 1, 2].set(-vec[..., 0])
+    result = xpx.at(result)[..., 2, 0].set(-vec[..., 1])
+    result = xpx.at(result)[..., 2, 1].set(vec[..., 0])
+    return result
+
+
+def _normalize_dual_quaternion(
+    real_part: Array, dual_part: Array
+) -> tuple[Array, Array]:
+    """Ensure that the dual quaternion has unit norm.
+
+    The norm is a dual number and must be 1 + 0 * epsilon, which means that
+    the real quaternion must have unit norm and the dual quaternion must be
+    orthogonal to the real quaternion.
+    """
+    xp = array_namespace(real_part)
+
+    real_norm = xp_vector_norm(real_part, axis=-1, keepdims=True, xp=xp)
+
+    # special case: real quaternion is 0, we set it to identity
+    zero_real_mask = real_norm == 0.0
+    unit_quat = xp.asarray(
+        [0.0, 0.0, 0.0, 1.0], dtype=real_part.dtype, device=xp_device(real_part)
+    )
+    real_part = xp.where(zero_real_mask, unit_quat, real_part)
+    real_norm = xp.where(zero_real_mask, 1.0, real_norm)
+
+    # 1. ensure unit real quaternion
+    real_part = real_part / real_norm
+    dual_part = dual_part / real_norm
+
+    # 2. ensure orthogonality of real and dual quaternion
+    dual_part -= xp.sum(real_part * dual_part, axis=-1, keepdims=True) * real_part
+
+    return real_part, dual_part
diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/transform/_rotation.py b/venv/lib/python3.12/site-packages/scipy/spatial/transform/_rotation.py
new file mode 100644
index 0000000000000000000000000000000000000000..6765df1d79ffc6e8288d184c85dae7307052d06a
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/transform/_rotation.py
@@ -0,0 +1,2856 @@
+from __future__ import annotations
+
+from collections.abc import Iterator, Sequence
+from types import EllipsisType, GenericAlias, ModuleType, NotImplementedType
+
+import numpy as np
+
+import scipy.spatial.transform._rotation_cy as cython_backend
+import scipy.spatial.transform._rotation_xp as xp_backend
+from scipy.spatial.transform._rotation_groups import create_group
+from scipy._lib._array_api import (
+    array_namespace,
+    Array,
+    is_numpy,
+    ArrayLike,
+    is_lazy_array,
+    xp_capabilities,
+    xp_promote,
+)
+from scipy._external.array_api_compat import device as xp_device
+import scipy._external.array_api_extra as xpx
+from scipy._lib._util import _transition_to_rng, broadcastable
+
+backend_registry = {array_namespace(np.empty(0)): cython_backend}
+
+
+def select_backend(xp: ModuleType, cython_compatible: bool):
+    """Select the backend for the given array library.
+
+    We need this selection function because the Cython backend for numpy does not
+    support quaternions of arbitrary dimensions. We therefore only use the Array API
+    backend for numpy if we are dealing with rotations of more than one leading
+    dimension.
+    """
+    if is_numpy(xp) and not cython_compatible:
+        return xp_backend
+    return backend_registry.get(xp, xp_backend)
+
+
+def _promote(*args: ArrayLike, xp: ModuleType) -> Array:
+    """Promote arrays to float64 for numpy, else according to the Array API spec.
+
+    The return array dtype follows the following rules:
+    - If quat is an ArrayLike or NumPy array, we always promote to float64
+    - If quat is an Array from frameworks other than NumPy, we preserve the precision
+      of the input array dtype.
+
+    The first rule is required by the cython backend signatures that expect
+    cython.double views. The second rule is necessary to promote non-floating arrays
+    to the correct type in frameworks that may not support double precision (e.g.
+    jax by default).
+    """
+    if is_numpy(xp):
+        args += (np.empty(0, dtype=np.float64),)  # Force float64 conversion
+        out = xp_promote(*args, force_floating=True, xp=xp)
+        if len(args) == 2:  # One argument was passed  + the added empty array
+            return out[0]
+        return out[:-1]
+    return xp_promote(*args, force_floating=True, xp=xp)
+
+
+rotation_extra_note = """The methods ``as_davenport``, ``apply``, and ``align_vectors``
+    are not supported with cupy<14.*.
+
+    """
+
+
+@xp_capabilities(
+    skip_backends=[("dask.array", "missing linalg.cross/det functions")],
+    method_capabilities={
+        "__init__": dict(
+            jax_jit=False,
+            skip_backends=[("dask.array", "dask not supported")],
+        ),
+        "as_davenport": dict(
+            skip_backends=[
+                ("dask.array", "missing linalg.cross/det functions and .mT attribute"),
+                ("cupy", "missing .mT attribute in cupy<14.*"),
+            ]
+        ),
+        "apply": dict(
+            skip_backends=[
+                ("dask.array", "missing linalg.cross/det functions and .mT attribute"),
+                ("cupy", "missing .mT attribute in cupy<14.*"),
+            ],
+        ),
+        "__getitem__": dict(
+            jax_jit=False,
+            skip_backends=[("dask.array", "cannot handle zero-length rotations")],
+        ),
+        "__setitem__": dict(
+            jax_jit=False,
+            skip_backends=[("dask.array", "cannot handle zero-length rotations")],
+        ),
+        "align_vectors": dict(
+            skip_backends=[
+                ("dask.array", "missing linalg.cross/det functions and .mT attribute"),
+                ("cupy", "missing .mT attribute in cupy<14.*"),
+            ],
+        ),
+    },
+    extra_note=rotation_extra_note,
+)
+class Rotation:
+    """Rotation in 3 dimensions.
+
+    This class provides an interface to initialize from and represent rotations
+    with:
+
+    - Quaternions
+    - Rotation Matrices
+    - Rotation Vectors
+    - Modified Rodrigues Parameters
+    - Euler Angles
+    - Davenport Angles (Generalized Euler Angles)
+
+    The following operations on rotations are supported:
+
+    - Application on vectors
+    - Rotation Composition
+    - Rotation Inversion
+    - Rotation Indexing
+
+    A `Rotation` instance can contain a single rotation transform or rotations of
+    multiple leading dimensions. E.g., it is possible to have an N-dimensional array of
+    (N, M, K) rotations. When applied to other rotations or vectors, standard
+    broadcasting rules apply.
+
+    Indexing within a rotation is supported to access a subset of the rotations stored
+    in a `Rotation` instance.
+
+    To create `Rotation` objects use ``from_...`` methods (see examples below).
+    ``Rotation(...)`` is not supposed to be instantiated directly.
+
+    Parameters
+    ----------
+    quat : array_like, shape (..., 4)
+        Quaternion representing the rotation.
+    normalize : bool, optional
+        If True, orthonormalize the rotation matrix using singular value
+        decomposition. If False, the rotation matrix is not checked for
+        orthogonality or right-handedness.
+    copy : bool, optional
+        If True, copy the input matrix. If False, a reference to the input
+        matrix is used. If normalize is True, the input matrix is always
+        copied regardless of the value of copy.
+    scalar_first : bool, optional
+        If ``True`` then `quat` is expect in scalar-first format otherwise it is
+        expected in scalar-last format. Defaults to ``False``.
+
+    Attributes
+    ----------
+    single
+
+    Methods
+    -------
+    __len__
+    from_quat
+    from_matrix
+    from_rotvec
+    from_mrp
+    from_euler
+    from_davenport
+    as_quat
+    as_matrix
+    as_rotvec
+    as_mrp
+    as_euler
+    as_davenport
+    concatenate
+    apply
+    __mul__
+    __pow__
+    inv
+    magnitude
+    approx_equal
+    mean
+    reduce
+    create_group
+    __getitem__
+    identity
+    random
+    align_vectors
+
+    See Also
+    --------
+    Slerp
+
+    Notes
+    -----
+    .. versionadded:: 1.2.0
+
+    Examples
+    --------
+    >>> from scipy.spatial.transform import Rotation as R
+    >>> import numpy as np
+
+    A `Rotation` instance can be initialized in any of the above formats and
+    converted to any of the others. The underlying object is independent of the
+    representation used for initialization.
+
+    Consider a counter-clockwise rotation of 90 degrees about the z-axis. This
+    corresponds to the following quaternion (in scalar-last format):
+
+    >>> r = R.from_quat([0, 0, np.sin(np.pi/4), np.cos(np.pi/4)])
+
+    The rotation can be expressed in any of the other formats:
+
+    >>> r.as_matrix()
+    array([[ 2.22044605e-16, -1.00000000e+00,  0.00000000e+00],
+    [ 1.00000000e+00,  2.22044605e-16,  0.00000000e+00],
+    [ 0.00000000e+00,  0.00000000e+00,  1.00000000e+00]])
+    >>> r.as_rotvec()
+    array([0.        , 0.        , 1.57079633])
+    >>> r.as_euler('zyx', degrees=True)
+    array([90.,  0.,  0.])
+
+    The same rotation can be initialized using a rotation matrix:
+
+    >>> r = R.from_matrix([[0, -1, 0],
+    ...                    [1, 0, 0],
+    ...                    [0, 0, 1]])
+
+    Representation in other formats:
+
+    >>> r.as_quat()
+    array([0.        , 0.        , 0.70710678, 0.70710678])
+    >>> r.as_rotvec()
+    array([0.        , 0.        , 1.57079633])
+    >>> r.as_euler('zyx', degrees=True)
+    array([90.,  0.,  0.])
+
+    The rotation vector corresponding to this rotation is given by:
+
+    >>> r = R.from_rotvec(np.pi/2 * np.array([0, 0, 1]))
+
+    Representation in other formats:
+
+    >>> r.as_quat()
+    array([0.        , 0.        , 0.70710678, 0.70710678])
+    >>> r.as_matrix()
+    array([[ 2.22044605e-16, -1.00000000e+00,  0.00000000e+00],
+           [ 1.00000000e+00,  2.22044605e-16,  0.00000000e+00],
+           [ 0.00000000e+00,  0.00000000e+00,  1.00000000e+00]])
+    >>> r.as_euler('zyx', degrees=True)
+    array([90.,  0.,  0.])
+
+    The ``from_euler`` method is quite flexible in the range of input formats
+    it supports. Here we initialize a single rotation about a single axis:
+
+    >>> r = R.from_euler('z', 90, degrees=True)
+
+    Again, the object is representation independent and can be converted to any
+    other format:
+
+    >>> r.as_quat()
+    array([0.        , 0.        , 0.70710678, 0.70710678])
+    >>> r.as_matrix()
+    array([[ 2.22044605e-16, -1.00000000e+00,  0.00000000e+00],
+           [ 1.00000000e+00,  2.22044605e-16,  0.00000000e+00],
+           [ 0.00000000e+00,  0.00000000e+00,  1.00000000e+00]])
+    >>> r.as_rotvec()
+    array([0.        , 0.        , 1.57079633])
+
+    It is also possible to initialize multiple rotations in a single instance
+    using any of the ``from_...`` functions. Here we initialize a stack of 3
+    rotations using the ``from_euler`` method:
+
+    >>> r = R.from_euler('zyx', [
+    ... [90, 0, 0],
+    ... [0, 45, 0],
+    ... [45, 60, 30]], degrees=True)
+
+    The other representations also now return a stack of 3 rotations. For
+    example:
+
+    >>> r.as_quat()
+    array([[0.        , 0.        , 0.70710678, 0.70710678],
+           [0.        , 0.38268343, 0.        , 0.92387953],
+           [0.39190384, 0.36042341, 0.43967974, 0.72331741]])
+
+    Applying the above rotations onto a vector:
+
+    >>> v = [1, 2, 3]
+    >>> r.apply(v)
+    array([[-2.        ,  1.        ,  3.        ],
+           [ 2.82842712,  2.        ,  1.41421356],
+           [ 2.24452282,  0.78093109,  2.89002836]])
+
+    A `Rotation` instance can be indexed and sliced as if it were an ND array:
+
+    >>> r.as_quat()
+    array([[0.        , 0.        , 0.70710678, 0.70710678],
+           [0.        , 0.38268343, 0.        , 0.92387953],
+           [0.39190384, 0.36042341, 0.43967974, 0.72331741]])
+    >>> p = r[0]
+    >>> p.as_matrix()
+    array([[ 2.22044605e-16, -1.00000000e+00,  0.00000000e+00],
+           [ 1.00000000e+00,  2.22044605e-16,  0.00000000e+00],
+           [ 0.00000000e+00,  0.00000000e+00,  1.00000000e+00]])
+    >>> q = r[1:3]
+    >>> q.as_quat()
+    array([[0.        , 0.38268343, 0.        , 0.92387953],
+           [0.39190384, 0.36042341, 0.43967974, 0.72331741]])
+
+    In fact it can be converted to numpy.array:
+
+    >>> r_array = np.asarray(r)
+    >>> r_array.shape
+    (3,)
+    >>> r_array[0].as_matrix()
+    array([[ 2.22044605e-16, -1.00000000e+00,  0.00000000e+00],
+           [ 1.00000000e+00,  2.22044605e-16,  0.00000000e+00],
+           [ 0.00000000e+00,  0.00000000e+00,  1.00000000e+00]])
+
+    Multiple rotations can be composed using the ``*`` operator:
+
+    >>> r1 = R.from_euler('z', 90, degrees=True)
+    >>> r2 = R.from_rotvec([np.pi/4, 0, 0])
+    >>> v = [1, 2, 3]
+    >>> r2.apply(r1.apply(v))
+    array([-2.        , -1.41421356,  2.82842712])
+    >>> r3 = r2 * r1 # Note the order
+    >>> r3.apply(v)
+    array([-2.        , -1.41421356,  2.82842712])
+
+    A rotation can be composed with itself using the ``**`` operator:
+
+    >>> p = R.from_rotvec([1, 0, 0])
+    >>> q = p ** 2
+    >>> q.as_rotvec()
+    array([2., 0., 0.])
+
+    Finally, it is also possible to invert rotations:
+
+    >>> r1 = R.from_euler('z', [[90], [45]], degrees=True)
+    >>> r2 = r1.inv()
+    >>> r2.as_euler('zyx', degrees=True)
+    array([[-90.,   0.,   0.],
+           [-45.,   0.,   0.]])
+
+    The following function can be used to plot rotations with Matplotlib by
+    showing how they transform the standard x, y, z coordinate axes:
+
+    >>> import matplotlib.pyplot as plt
+
+    >>> def plot_rotated_axes(ax, r, name=None, offset=(0, 0, 0), scale=1):
+    ...     colors = ("#FF6666", "#005533", "#1199EE")  # Colorblind-safe RGB
+    ...     loc = np.array([offset, offset])
+    ...     for i, (axis, c) in enumerate(zip((ax.xaxis, ax.yaxis, ax.zaxis),
+    ...                                       colors)):
+    ...         axlabel = axis.axis_name
+    ...         axis.set_label_text(axlabel)
+    ...         axis.label.set_color(c)
+    ...         axis.line.set_color(c)
+    ...         axis.set_tick_params(colors=c)
+    ...         line = np.zeros((2, 3))
+    ...         line[1, i] = scale
+    ...         line_rot = r.apply(line)
+    ...         line_plot = line_rot + loc
+    ...         ax.plot(line_plot[:, 0], line_plot[:, 1], line_plot[:, 2], c)
+    ...         text_loc = line[1]*1.2
+    ...         text_loc_rot = r.apply(text_loc)
+    ...         text_plot = text_loc_rot + loc[0]
+    ...         ax.text(*text_plot, axlabel.upper(), color=c,
+    ...                 va="center", ha="center")
+    ...     ax.text(*offset, name, color="k", va="center", ha="center",
+    ...             bbox={"fc": "w", "alpha": 0.8, "boxstyle": "circle"})
+
+    Create three rotations - the identity and two Euler rotations using
+    intrinsic and extrinsic conventions:
+
+    >>> r0 = R.identity()
+    >>> r1 = R.from_euler("ZYX", [90, -30, 0], degrees=True)  # intrinsic
+    >>> r2 = R.from_euler("zyx", [90, -30, 0], degrees=True)  # extrinsic
+
+    Add all three rotations to a single plot:
+
+    >>> ax = plt.figure().add_subplot(projection="3d", proj_type="ortho")
+    >>> plot_rotated_axes(ax, r0, name="r0", offset=(0, 0, 0))
+    >>> plot_rotated_axes(ax, r1, name="r1", offset=(3, 0, 0))
+    >>> plot_rotated_axes(ax, r2, name="r2", offset=(6, 0, 0))
+    >>> _ = ax.annotate(
+    ...     "r0: Identity Rotation\\n"
+    ...     "r1: Intrinsic Euler Rotation (ZYX)\\n"
+    ...     "r2: Extrinsic Euler Rotation (zyx)",
+    ...     xy=(0.6, 0.7), xycoords="axes fraction", ha="left"
+    ... )
+    >>> ax.set(xlim=(-1.25, 7.25), ylim=(-1.25, 1.25), zlim=(-1.25, 1.25))
+    >>> ax.set(xticks=range(-1, 8), yticks=[-1, 0, 1], zticks=[-1, 0, 1])
+    >>> ax.set_aspect("equal", adjustable="box")
+    >>> ax.figure.set_size_inches(6, 5)
+    >>> plt.tight_layout()
+
+    Show the plot:
+
+    >>> plt.show()
+
+    These examples serve as an overview into the `Rotation` class and highlight
+    major functionalities. For more thorough examples of the range of input and
+    output formats supported, consult the individual method's examples.
+
+    """
+
+    # generic type compatibility with scipy-stubs
+    __class_getitem__: classmethod = classmethod(GenericAlias)
+
+    def __init__(
+        self,
+        quat: ArrayLike,
+        normalize: bool = True,
+        copy: bool = True,
+        scalar_first: bool = False,
+    ):
+        xp = array_namespace(quat)
+        self._xp = xp
+        quat = _promote(quat, xp=xp)
+        if quat.shape[-1] != 4:
+            raise ValueError(
+                f"Expected `quat` to have shape (..., 4), got {quat.shape}."
+            )
+        # Single NumPy quats or list of quats are accelerated by the cython backend.
+        # This backend needs inputs with fixed ndim, so we always expand to 2D and
+        # select the 0th element if quat was single to get the correct shape. For other
+        # frameworks and quaternion tensors we use the generic array API backend.
+        self._single = quat.ndim == 1 and is_numpy(xp)
+        if self._single:
+            quat = xpx.atleast_nd(quat, ndim=2, xp=xp)
+        self._backend = select_backend(xp, cython_compatible=quat.ndim < 3)
+        self._quat: Array = self._backend.from_quat(
+            quat, normalize=normalize, copy=copy, scalar_first=scalar_first
+        )
+
+    @staticmethod
+    def from_quat(quat: ArrayLike, *, scalar_first: bool = False) -> Rotation:
+        """Initialize from quaternions.
+
+        Rotations in 3 dimensions can be represented using unit norm
+        quaternions [1]_.
+
+        The 4 components of a quaternion are divided into a scalar part ``w``
+        and a vector part ``(x, y, z)`` and can be expressed from the angle
+        ``theta`` and the axis ``n`` of a rotation as follows::
+
+            w = cos(theta / 2)
+            x = sin(theta / 2) * n_x
+            y = sin(theta / 2) * n_y
+            z = sin(theta / 2) * n_z
+
+        There are 2 conventions to order the components in a quaternion:
+
+        - scalar-first order -- ``(w, x, y, z)``
+        - scalar-last order -- ``(x, y, z, w)``
+
+        The choice is controlled by `scalar_first` argument.
+        By default, it is False and the scalar-last order is assumed.
+
+        Advanced users may be interested in the "double cover" of 3D space by
+        the quaternion representation [2]_. As of version 1.11.0, the
+        following subset (and only this subset) of operations on a `Rotation`
+        ``r`` corresponding to a quaternion ``q`` are guaranteed to preserve
+        the double cover property: ``r = Rotation.from_quat(q)``,
+        ``r.as_quat(canonical=False)``, ``r.inv()``, and composition using the
+        ``*`` operator such as ``r*r``.
+
+        Parameters
+        ----------
+        quat : array_like, shape (..., 4)
+            Each row is a (possibly non-unit norm) quaternion representing an
+            active rotation. Each quaternion will be normalized to unit norm.
+        scalar_first : bool, optional
+            Whether the scalar component goes first or last.
+            Default is False, i.e. the scalar-last order is assumed.
+
+        Returns
+        -------
+        rotation : `Rotation` instance
+            Object containing the rotations represented by input quaternions.
+
+        References
+        ----------
+        .. [1] https://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation
+        .. [2] Hanson, Andrew J. "Visualizing quaternions."
+            Morgan Kaufmann Publishers Inc., San Francisco, CA. 2006.
+
+        Examples
+        --------
+        >>> from scipy.spatial.transform import Rotation as R
+
+        A rotation can be initialized from a quaternion with the scalar-last
+        (default) or scalar-first component order as shown below:
+
+        >>> r = R.from_quat([0, 0, 0, 1])
+        >>> r.as_matrix()
+        array([[1., 0., 0.],
+               [0., 1., 0.],
+               [0., 0., 1.]])
+        >>> r = R.from_quat([1, 0, 0, 0], scalar_first=True)
+        >>> r.as_matrix()
+        array([[1., 0., 0.],
+               [0., 1., 0.],
+               [0., 0., 1.]])
+
+        It is possible to initialize multiple rotations in a single object by
+        passing an N-dimensional array:
+
+        >>> r = R.from_quat([[
+        ... [1, 0, 0, 0],
+        ... [0, 0, 0, 1]
+        ... ]])
+        >>> r.as_quat()
+        array([[[1., 0., 0., 0.],
+                [0., 0., 0., 1.]]])
+        >>> r.as_quat().shape
+        (1, 2, 4)
+
+        It is also possible to have a stack of a single rotation:
+
+        >>> r = R.from_quat([[0, 0, 0, 1]])
+        >>> r.as_quat()
+        array([[0., 0., 0., 1.]])
+        >>> r.as_quat().shape
+        (1, 4)
+
+        Quaternions are normalized before initialization.
+
+        >>> r = R.from_quat([0, 0, 1, 1])
+        >>> r.as_quat()
+        array([0.        , 0.        , 0.70710678, 0.70710678])
+        """
+        return Rotation(quat, normalize=True, scalar_first=scalar_first)
+
+    @staticmethod
+    def from_matrix(matrix: ArrayLike, *, assume_valid: bool = False) -> Rotation:
+        """Initialize from rotation matrix.
+
+        Rotations in 3 dimensions can be represented with 3 x 3 orthogonal
+        matrices [1]_. If the input is not orthogonal, an approximation is
+        created by orthogonalizing the input matrix using the method described
+        in [2]_, and then converting the orthogonal rotation matrices to
+        quaternions using the algorithm described in [3]_. Matrices must be
+        right-handed.
+
+        Parameters
+        ----------
+        matrix : array_like, shape (..., 3, 3)
+            A single matrix or an ND array of matrices, where the last two dimensions
+            contain the rotation matrices.
+        assume_valid : bool, optional
+            Must be False unless users can guarantee the input is a valid rotation
+            matrix, i.e. it is orthogonal, rows and columns have unit norm and the
+            determinant is 1. Setting this to True without ensuring these properties
+            is unsafe and will silently lead to incorrect results. If True,
+            normalization steps are skipped, which can improve runtime performance.
+            Default is False.
+
+        Returns
+        -------
+        rotation : `Rotation` instance
+            Object containing the rotations represented by the rotation
+            matrices.
+
+        Notes
+        -----
+        This function was called from_dcm before.
+
+        .. versionadded:: 1.4.0
+
+        References
+        ----------
+        .. [1] https://en.wikipedia.org/wiki/Rotation_matrix#In_three_dimensions
+        .. [2] https://en.wikipedia.org/wiki/Orthogonal_Procrustes_problem
+        .. [3] F. Landis Markley, "Unit Quaternion from Rotation Matrix",
+               Journal of guidance, control, and dynamics vol. 31.2, pp.
+               440-442, 2008.
+
+        Examples
+        --------
+        >>> from scipy.spatial.transform import Rotation as R
+        >>> import numpy as np
+
+        Initialize a single rotation:
+
+        >>> r = R.from_matrix([
+        ... [0, -1, 0],
+        ... [1, 0, 0],
+        ... [0, 0, 1]])
+        >>> r.single
+        True
+        >>> r.as_matrix().shape
+        (3, 3)
+
+        Initialize multiple rotations in a single object:
+
+        >>> r = R.from_matrix([
+        ... [
+        ...     [0, -1, 0],
+        ...     [1, 0, 0],
+        ...     [0, 0, 1],
+        ... ],
+        ... [
+        ...     [1, 0, 0],
+        ...     [0, 0, -1],
+        ...     [0, 1, 0],
+        ... ]])
+        >>> r.as_matrix().shape
+        (2, 3, 3)
+        >>> r.single
+        False
+        >>> len(r)
+        2
+
+        If input matrices are not special orthogonal (orthogonal with
+        determinant equal to +1), then a special orthogonal estimate is stored:
+
+        >>> a = np.array([
+        ... [0, -0.5, 0],
+        ... [0.5, 0, 0],
+        ... [0, 0, 0.5]])
+        >>> np.linalg.det(a)
+        0.125
+        >>> r = R.from_matrix(a)
+        >>> matrix = r.as_matrix()
+        >>> matrix
+        array([[ 0., -1.,  0.],
+               [ 1.,  0.,  0.],
+               [ 0.,  0.,  1.]])
+        >>> np.linalg.det(matrix)
+        1.0
+
+        It is also possible to have a stack containing a single rotation:
+
+        >>> r = R.from_matrix([[
+        ... [0, -1, 0],
+        ... [1, 0, 0],
+        ... [0, 0, 1]]])
+        >>> r.as_matrix()
+        array([[[ 0., -1.,  0.],
+                [ 1.,  0.,  0.],
+                [ 0.,  0.,  1.]]])
+        >>> r.as_matrix().shape
+        (1, 3, 3)
+
+        We can also create an N-dimensional array of rotations:
+
+        >>> r = R.from_matrix(np.tile(np.eye(3), (2, 3, 1, 1)))
+        >>> r.shape
+        (2, 3)
+
+        """
+        xp = array_namespace(matrix)
+        matrix = _promote(matrix, xp=xp)
+        # Resulting quat will have 1 less dimension than matrix
+        backend = select_backend(xp, cython_compatible=matrix.ndim < 4)
+        quat = backend.from_matrix(matrix, assume_valid=assume_valid)
+        return Rotation._from_raw_quat(quat, xp=xp, backend=backend)
+
+    @staticmethod
+    def from_rotvec(rotvec: ArrayLike, degrees: bool = False) -> Rotation:
+        """Initialize from rotation vectors.
+
+        A rotation vector is a 3 dimensional vector which is co-directional to
+        the axis of rotation and whose norm gives the angle of rotation [1]_.
+
+        Parameters
+        ----------
+        rotvec : array_like, shape (..., 3)
+            A single vector or an ND array of vectors, where the last dimension
+            contains the rotation vectors.
+        degrees : bool, optional
+            If True, then the given magnitudes are assumed to be in degrees.
+            Default is False.
+
+            .. versionadded:: 1.7.0
+
+        Returns
+        -------
+        rotation : `Rotation` instance
+            Object containing the rotations represented by input rotation
+            vectors.
+
+        References
+        ----------
+        .. [1] https://en.wikipedia.org/wiki/Axis%E2%80%93angle_representation#Rotation_vector
+
+        Examples
+        --------
+        >>> from scipy.spatial.transform import Rotation as R
+        >>> import numpy as np
+
+        Initialize a single rotation:
+
+        >>> r = R.from_rotvec(np.pi/2 * np.array([0, 0, 1]))
+        >>> r.as_rotvec()
+        array([0.        , 0.        , 1.57079633])
+        >>> r.as_rotvec().shape
+        (3,)
+
+        Initialize a rotation in degrees, and view it in degrees:
+
+        >>> r = R.from_rotvec(45 * np.array([0, 1, 0]), degrees=True)
+        >>> r.as_rotvec(degrees=True)
+        array([ 0., 45.,  0.])
+
+        Initialize multiple rotations in one object:
+
+        >>> r = R.from_rotvec([
+        ... [0, 0, np.pi/2],
+        ... [np.pi/2, 0, 0]])
+        >>> r.as_rotvec()
+        array([[0.        , 0.        , 1.57079633],
+               [1.57079633, 0.        , 0.        ]])
+        >>> r.as_rotvec().shape
+        (2, 3)
+
+        It is also possible to have a stack of a single rotation:
+
+        >>> r = R.from_rotvec([[0, 0, np.pi/2]])
+        >>> r.as_rotvec().shape
+        (1, 3)
+
+        """
+        xp = array_namespace(rotvec)
+        rotvec = _promote(rotvec, xp=xp)
+        backend = select_backend(xp, cython_compatible=rotvec.ndim < 3)
+        quat = backend.from_rotvec(rotvec, degrees=degrees)
+        return Rotation._from_raw_quat(quat, xp=xp, backend=backend)
+
+    @staticmethod
+    def from_euler(seq: str, angles: ArrayLike, degrees: bool = False) -> Rotation:
+        """Initialize from Euler angles.
+
+        Rotations in 3-D can be represented by a sequence of 3
+        rotations around a sequence of axes. In theory, any three axes spanning
+        the 3-D Euclidean space are enough. In practice, the axes of rotation are
+        chosen to be the basis vectors.
+
+        The three rotations can either be in a global frame of reference
+        (extrinsic) or in a body centred frame of reference (intrinsic), which
+        is attached to, and moves with, the object under rotation [1]_.
+
+        Parameters
+        ----------
+        seq : str
+            Specifies sequence of axes for rotations. Up to 3 characters
+            belonging to the set {'X', 'Y', 'Z'} for intrinsic rotations, or
+            {'x', 'y', 'z'} for extrinsic rotations. Extrinsic and intrinsic
+            rotations cannot be mixed in one function call.
+        angles : float or array_like, shape (...,  [1 or 2 or 3])
+            Euler angles specified in radians (`degrees` is False) or degrees
+            (`degrees` is True).
+            Each character in `seq` defines one axis around which `angles` turns.
+            The resulting rotation has the shape np.atleast_1d(angles).shape[:-1].
+            Dimensionless angles are thus only valid for single character `seq`.
+
+        degrees : bool, optional
+            If True, then the given angles are assumed to be in degrees.
+            Default is False.
+
+        Returns
+        -------
+        rotation : `Rotation` instance
+            Object containing the rotation represented by the sequence of
+            rotations around given axes with given angles.
+
+        References
+        ----------
+        .. [1] https://en.wikipedia.org/wiki/Euler_angles#Definition_by_intrinsic_rotations
+
+        Examples
+        --------
+        >>> from scipy.spatial.transform import Rotation as R
+
+        Initialize a single rotation along a single axis:
+
+        >>> r = R.from_euler('x', 90, degrees=True)
+        >>> r.as_quat().shape
+        (4,)
+
+        Initialize a single rotation with a given axis sequence:
+
+        >>> r = R.from_euler('zyx', [90, 45, 30], degrees=True)
+        >>> r.as_quat().shape
+        (4,)
+
+        Initialize a stack with a single rotation around a single axis:
+
+        >>> r = R.from_euler('x', [[90]], degrees=True)
+        >>> r.as_quat().shape
+        (1, 4)
+
+        Initialize a stack with a single rotation with an axis sequence:
+
+        >>> r = R.from_euler('zyx', [[90, 45, 30]], degrees=True)
+        >>> r.as_quat().shape
+        (1, 4)
+
+        Initialize multiple elementary rotations in one object:
+
+        >>> r = R.from_euler('x', [[90], [45], [30]], degrees=True)
+        >>> r.as_quat().shape
+        (3, 4)
+
+        Initialize multiple rotations in one object:
+
+        >>> r = R.from_euler('zyx', [[90, 45, 30], [35, 45, 90]], degrees=True)
+        >>> r.as_quat().shape
+        (2, 4)
+
+        """
+        xp = array_namespace(angles)
+        angles = _promote(angles, xp=xp)
+        backend = select_backend(xp, cython_compatible=angles.ndim < 3)
+        quat = backend.from_euler(seq, angles, degrees=degrees)
+        return Rotation._from_raw_quat(quat, xp=xp, backend=backend)
+
+    @staticmethod
+    def from_davenport(
+        axes: ArrayLike,
+        order: str,
+        angles: ArrayLike | float,
+        degrees: bool = False,
+    ) -> Rotation:
+        """Initialize from Davenport angles.
+
+        Rotations in 3-D can be represented by a sequence of 3
+        rotations around a sequence of axes.
+
+        The three rotations can either be in a global frame of reference
+        (extrinsic) or in a body centred frame of reference (intrinsic), which
+        is attached to, and moves with, the object under rotation [1]_.
+
+        For both Euler angles and Davenport angles, consecutive axes must
+        be are orthogonal (``axis2`` is orthogonal to both ``axis1`` and
+        ``axis3``). For Euler angles, there is an additional relationship
+        between ``axis1`` or ``axis3``, with two possibilities:
+
+            - ``axis1`` and ``axis3`` are also orthogonal (asymmetric sequence)
+            - ``axis1 == axis3`` (symmetric sequence)
+
+        For Davenport angles, this last relationship is relaxed [2]_, and only
+        the consecutive orthogonal axes requirement is maintained.
+
+        Parameters
+        ----------
+        axes : array_like, shape (3,) or (..., [1 or 2 or 3], 3)
+            Axis of rotation, if one dimensional. If two or more dimensional, describes
+            the sequence of axes for rotations, where each axes[..., i, :] is the ith
+            axis. If more than one axis is given, then the second axis must be
+            orthogonal to both the first and third axes.
+        order : str
+            If it is equal to 'e' or 'extrinsic', the sequence will be
+            extrinsic. If it is equal to 'i' or 'intrinsic', sequence
+            will be treated as intrinsic.
+        angles : float or array_like, shape (..., [1 or 2 or 3])
+            Angles specified in radians (`degrees` is False) or degrees
+            (`degrees` is True).
+            Each angle i in the last dimension of `angles` turns around the corresponding
+            axis axis[..., i, :]. The resulting rotation has the shape
+            np.broadcast_shapes(np.atleast_2d(axes).shape[:-2], np.atleast_1d(angles).shape[:-1])
+            Dimensionless angles are thus only valid for a single axis.
+
+        degrees : bool, optional
+            If True, then the given angles are assumed to be in degrees.
+            Default is False.
+
+        Returns
+        -------
+        rotation : `Rotation` instance
+            Object containing the rotation represented by the sequence of
+            rotations around given axes with given angles.
+
+        References
+        ----------
+        .. [1] https://en.wikipedia.org/wiki/Euler_angles#Definition_by_intrinsic_rotations
+        .. [2] Shuster, Malcolm & Markley, Landis. (2003). Generalization of
+               the Euler Angles. Journal of the Astronautical Sciences. 51. 123-132.
+               10.1007/BF03546304.
+
+        Examples
+        --------
+        >>> from scipy.spatial.transform import Rotation as R
+
+        Davenport angles are a generalization of Euler angles, when we use the
+        canonical basis axes:
+
+        >>> ex = [1, 0, 0]
+        >>> ey = [0, 1, 0]
+        >>> ez = [0, 0, 1]
+
+        Initialize a single rotation with a given axis sequence:
+
+        >>> axes = [ez, ey, ex]
+        >>> r = R.from_davenport(axes, 'extrinsic', [90, 0, 0], degrees=True)
+        >>> r.as_quat().shape
+        (4,)
+
+        It is equivalent to Euler angles in this case:
+
+        >>> r.as_euler('zyx', degrees=True)
+        array([90.,  0., -0.])
+
+        Initialize multiple rotations in one object:
+
+        >>> r = R.from_davenport(axes, 'extrinsic', [[90, 45, 30], [35, 45, 90]], degrees=True)
+        >>> r.as_quat().shape
+        (2, 4)
+
+        Using only one or two axes is also possible:
+
+        >>> r = R.from_davenport([ez, ex], 'extrinsic', [[90, 45], [35, 45]], degrees=True)
+        >>> r.as_quat().shape
+        (2, 4)
+
+        Non-canonical axes are possible, and they do not need to be normalized,
+        as long as consecutive axes are orthogonal:
+
+        >>> e1 = [2, 0, 0]
+        >>> e2 = [0, 1, 0]
+        >>> e3 = [1, 0, 1]
+        >>> axes = [e1, e2, e3]
+        >>> r = R.from_davenport(axes, 'extrinsic', [90, 45, 30], degrees=True)
+        >>> r.as_quat()
+        [ 0.701057,  0.430459, -0.092296,  0.560986]
+        """  # noqa: E501
+        xp = array_namespace(axes)
+        axes, angles = _promote(axes, angles, xp=xp)
+        cython_compatible = axes.ndim < 3 and angles.ndim < 2  # type:ignore[union-attr]
+        backend = select_backend(xp, cython_compatible=cython_compatible)
+        quat = backend.from_davenport(axes, order, angles, degrees)
+        return Rotation._from_raw_quat(quat, xp=xp, backend=backend)
+
+    @staticmethod
+    def from_mrp(mrp: ArrayLike) -> Rotation:
+        """Initialize from Modified Rodrigues Parameters (MRPs).
+
+        MRPs are a 3 dimensional vector co-directional to the axis of rotation and whose
+        magnitude is equal to ``tan(theta / 4)``, where ``theta`` is the angle of
+        rotation (in radians) [1]_.
+
+        MRPs have a singularity at 360 degrees which can be avoided by ensuring the
+        angle of rotation does not exceed 180 degrees, i.e. switching the direction of
+        the rotation when it is past 180 degrees.
+
+        Parameters
+        ----------
+        mrp : array_like, shape (..., 3)
+            A single vector or an ND array of vectors, where the last dimension
+            contains the rotation parameters.
+
+        Returns
+        -------
+        rotation : `Rotation` instance
+            Object containing the rotations represented by input MRPs.
+
+        Notes
+        -----
+
+        .. versionadded:: 1.6.0
+
+        References
+        ----------
+        .. [1] Shuster, M. D. "A Survey of Attitude Representations",
+               The Journal of Astronautical Sciences, Vol. 41, No.4, 1993,
+               pp. 475-476
+
+        Examples
+        --------
+        >>> from scipy.spatial.transform import Rotation as R
+        >>> import numpy as np
+
+        Initialize a single rotation:
+
+        >>> r = R.from_mrp([0, 0, 1])
+        >>> r.as_euler('xyz', degrees=True)
+        array([0.        , 0.        , 180.      ])
+        >>> r.as_euler('xyz').shape
+        (3,)
+
+        Initialize multiple rotations in one object:
+
+        >>> r = R.from_mrp([
+        ... [0, 0, 1],
+        ... [1, 0, 0]])
+        >>> r.as_euler('xyz', degrees=True)
+        array([[0.        , 0.        , 180.      ],
+               [180.0     , 0.        , 0.        ]])
+        >>> r.as_euler('xyz').shape
+        (2, 3)
+
+        It is also possible to have a stack of a single rotation:
+
+        >>> r = R.from_mrp([[0, 0, np.pi/2]])
+        >>> r.as_euler('xyz').shape
+        (1, 3)
+
+        """
+        xp = array_namespace(mrp)
+        mrp = _promote(mrp, xp=xp)
+        backend = select_backend(xp, cython_compatible=mrp.ndim < 3)
+        quat = backend.from_mrp(mrp)
+        return Rotation._from_raw_quat(quat, xp=xp, backend=backend)
+
+    def as_quat(self, canonical: bool = False, *, scalar_first: bool = False) -> Array:
+        """Represent as quaternions.
+
+        Rotations in 3 dimensions can be represented using unit norm
+        quaternions [1]_.
+
+        The 4 components of a quaternion are divided into a scalar part ``w``
+        and a vector part ``(x, y, z)`` and can be expressed from the angle
+        ``theta`` and the axis ``n`` of a rotation as follows::
+
+            w = cos(theta / 2)
+            x = sin(theta / 2) * n_x
+            y = sin(theta / 2) * n_y
+            z = sin(theta / 2) * n_z
+
+        There are 2 conventions to order the components in a quaternion:
+
+        - scalar-first order -- ``(w, x, y, z)``
+        - scalar-last order -- ``(x, y, z, w)``
+
+        The choice is controlled by `scalar_first` argument.
+        By default, it is False and the scalar-last order is used.
+
+        The mapping from quaternions to rotations is
+        two-to-one, i.e. quaternions ``q`` and ``-q``, where ``-q`` simply
+        reverses the sign of each component, represent the same spatial
+        rotation.
+
+        Parameters
+        ----------
+        canonical : `bool`, default False
+            Whether to map the redundant double cover of rotation space to a
+            unique "canonical" single cover. If True, then the quaternion is
+            chosen from {q, -q} such that the w term is positive. If the w term
+            is 0, then the quaternion is chosen such that the first nonzero
+            term of the x, y, and z terms is positive.
+        scalar_first : bool, optional
+            Whether the scalar component goes first or last.
+            Default is False, i.e. the scalar-last order is used.
+
+        Returns
+        -------
+        quat : `numpy.ndarray`, shape (..., 4)
+            Shape depends on shape of inputs used for initialization.
+
+        References
+        ----------
+        .. [1] https://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation
+
+        Examples
+        --------
+        >>> from scipy.spatial.transform import Rotation as R
+        >>> import numpy as np
+
+        A rotation can be represented as a quaternion with either scalar-last
+        (default) or scalar-first component order.
+        This is shown for a single rotation:
+
+        >>> r = R.from_matrix(np.eye(3))
+        >>> r.as_quat()
+        array([0., 0., 0., 1.])
+        >>> r.as_quat(scalar_first=True)
+        array([1., 0., 0., 0.])
+
+        The resulting shape of the quaternion is always the shape of the Rotation
+        object with an added last dimension of size 4. E.g. when the `Rotation` object
+        contains an N-dimensional array (N, M, K) of rotations, the result will be a
+        4-dimensional array:
+
+        >>> r = R.from_rotvec(np.ones((2, 3, 4, 3)))
+        >>> r.as_quat().shape
+        (2, 3, 4, 4)
+
+        Quaternions can be mapped from a redundant double cover of the
+        rotation space to a canonical representation with a positive w term.
+
+        >>> r = R.from_quat([0, 0, 0, -1])
+        >>> r.as_quat()
+        array([0. , 0. , 0. , -1.])
+        >>> r.as_quat(canonical=True)
+        array([0. , 0. , 0. , 1.])
+        """
+        quat = self._backend.as_quat(
+            self._quat, canonical=canonical, scalar_first=scalar_first
+        )
+        if self._single:
+            return quat[0, ...]
+        return quat
+
+    def as_matrix(self) -> Array:
+        """Represent as rotation matrix.
+
+        3D rotations can be represented using rotation matrices, which
+        are 3 x 3 real orthogonal matrices with determinant equal to +1 [1]_.
+
+        Returns
+        -------
+        matrix : ndarray, shape (..., 3)
+            Shape depends on shape of inputs used for initialization.
+
+        Notes
+        -----
+        This function was called as_dcm before.
+
+        .. versionadded:: 1.4.0
+
+        References
+        ----------
+        .. [1] https://en.wikipedia.org/wiki/Rotation_matrix#In_three_dimensions
+
+        Examples
+        --------
+        >>> from scipy.spatial.transform import Rotation as R
+        >>> import numpy as np
+
+        Represent a single rotation:
+
+        >>> r = R.from_rotvec([0, 0, np.pi/2])
+        >>> r.as_matrix()
+        array([[ 2.22044605e-16, -1.00000000e+00,  0.00000000e+00],
+               [ 1.00000000e+00,  2.22044605e-16,  0.00000000e+00],
+               [ 0.00000000e+00,  0.00000000e+00,  1.00000000e+00]])
+        >>> r.as_matrix().shape
+        (3, 3)
+
+        Represent a stack with a single rotation:
+
+        >>> r = R.from_quat([[1, 1, 0, 0]])
+        >>> r.as_matrix()
+        array([[[ 0.,  1.,  0.],
+                [ 1.,  0.,  0.],
+                [ 0.,  0., -1.]]])
+        >>> r.as_matrix().shape
+        (1, 3, 3)
+
+        Represent multiple rotations:
+
+        >>> r = R.from_rotvec([[np.pi/2, 0, 0], [0, 0, np.pi/2]])
+        >>> r.as_matrix()
+        array([[[ 1.00000000e+00,  0.00000000e+00,  0.00000000e+00],
+                [ 0.00000000e+00,  2.22044605e-16, -1.00000000e+00],
+                [ 0.00000000e+00,  1.00000000e+00,  2.22044605e-16]],
+               [[ 2.22044605e-16, -1.00000000e+00,  0.00000000e+00],
+                [ 1.00000000e+00,  2.22044605e-16,  0.00000000e+00],
+                [ 0.00000000e+00,  0.00000000e+00,  1.00000000e+00]]])
+        >>> r.as_matrix().shape
+        (2, 3, 3)
+
+        """
+        matrix = self._backend.as_matrix(self._quat)
+        if self._single:
+            return matrix[0, ...]
+        return matrix
+
+    def as_rotvec(self, degrees: bool = False) -> Array:
+        """Represent as rotation vectors.
+
+        A rotation vector is a 3 dimensional vector which is co-directional to
+        the axis of rotation and whose norm gives the angle of rotation [1]_.
+
+        Parameters
+        ----------
+        degrees : bool, optional
+            Returned magnitudes are in degrees if this flag is True, else they are
+            in radians. Default is False.
+
+            .. versionadded:: 1.7.0
+
+        Returns
+        -------
+        rotvec : ndarray, shape (..., 3)
+            Shape depends on shape of inputs used for initialization.
+
+        References
+        ----------
+        .. [1] https://en.wikipedia.org/wiki/Axis%E2%80%93angle_representation#Rotation_vector
+
+        Examples
+        --------
+        >>> from scipy.spatial.transform import Rotation as R
+        >>> import numpy as np
+
+        Represent a single rotation:
+
+        >>> r = R.from_euler('z', 90, degrees=True)
+        >>> r.as_rotvec()
+        array([0.        , 0.        , 1.57079633])
+        >>> r.as_rotvec().shape
+        (3,)
+
+        Represent a rotation in degrees:
+
+        >>> r = R.from_euler('YX', (-90, -90), degrees=True)
+        >>> s = r.as_rotvec(degrees=True)
+        >>> s
+        array([-69.2820323, -69.2820323, -69.2820323])
+        >>> np.linalg.norm(s)
+        120.00000000000001
+
+        Represent a stack with a single rotation:
+
+        >>> r = R.from_quat([[0, 0, 1, 1]])
+        >>> r.as_rotvec()
+        array([[0.        , 0.        , 1.57079633]])
+        >>> r.as_rotvec().shape
+        (1, 3)
+
+        Represent multiple rotations in a single object:
+
+        >>> r = R.from_quat([[0, 0, 1, 1], [1, 1, 0, 1]])
+        >>> r.as_rotvec()
+        array([[0.        , 0.        , 1.57079633],
+               [1.35102172, 1.35102172, 0.        ]])
+        >>> r.as_rotvec().shape
+        (2, 3)
+
+        """
+        rotvec = self._backend.as_rotvec(self._quat, degrees=degrees)
+        if self._single:
+            return rotvec[0, ...]
+        return rotvec
+
+    def as_euler(
+        self, seq: str, degrees: bool = False, *, suppress_warnings: bool = False
+    ) -> Array:
+        """Represent as Euler angles.
+
+        Any orientation can be expressed as a composition of 3 elementary
+        rotations. Once the axis sequence has been chosen, Euler angles define
+        the angle of rotation around each respective axis [1]_.
+
+        The algorithm from [2]_ has been used to calculate Euler angles for the
+        rotation about a given sequence of axes.
+
+        Euler angles suffer from the problem of gimbal lock [3]_, where the
+        representation loses a degree of freedom and it is not possible to
+        determine the first and third angles uniquely. In this case,
+        a warning is raised (unless the ``suppress_warnings`` option is used),
+        and the third angle is set to zero. Note however that the returned
+        angles still represent the correct rotation.
+
+        Parameters
+        ----------
+        seq : str, length 3
+            3 characters belonging to the set {'X', 'Y', 'Z'} for intrinsic
+            rotations, or {'x', 'y', 'z'} for extrinsic rotations [1]_.
+            Adjacent axes cannot be the same.
+            Extrinsic and intrinsic rotations cannot be mixed in one function
+            call.
+        degrees : bool, optional
+            Returned angles are in degrees if this flag is True, else they are
+            in radians. Default is False.
+        suppress_warnings : bool, optional
+            Disable warnings about gimbal lock. Default is False.
+
+        Returns
+        -------
+        angles : ndarray, shape (..., 3)
+            Shape depends on shape of inputs used to initialize object.
+            The returned angles are in the range:
+
+            - First angle belongs to [-180, 180] degrees (both inclusive)
+            - Third angle belongs to [-180, 180] degrees (both inclusive)
+            - Second angle belongs to:
+
+                - [-90, 90] degrees if all axes are different (like xyz)
+                - [0, 180] degrees if first and third axes are the same
+                  (like zxz)
+
+        References
+        ----------
+        .. [1] https://en.wikipedia.org/wiki/Euler_angles#Definition_by_intrinsic_rotations
+        .. [2] Bernardes E, Viollet S (2022) Quaternion to Euler angles
+               conversion: A direct, general and computationally efficient
+               method. PLoS ONE 17(11): e0276302.
+               :doi:`10.1371/journal.pone.0276302`.
+        .. [3] https://en.wikipedia.org/wiki/Gimbal_lock#In_applied_mathematics
+
+        Examples
+        --------
+        >>> from scipy.spatial.transform import Rotation as R
+        >>> import numpy as np
+
+        Represent a single rotation:
+
+        >>> r = R.from_rotvec([0, 0, np.pi/2])
+        >>> r.as_euler('zxy', degrees=True)
+        array([90.,  0.,  0.])
+        >>> r.as_euler('zxy', degrees=True).shape
+        (3,)
+
+        Represent a stack of single rotation:
+
+        >>> r = R.from_rotvec([[0, 0, np.pi/2]])
+        >>> r.as_euler('zxy', degrees=True)
+        array([[90.,  0.,  0.]])
+        >>> r.as_euler('zxy', degrees=True).shape
+        (1, 3)
+
+        Represent multiple rotations in a single object:
+
+        >>> r = R.from_rotvec([
+        ... [0, 0, np.pi/2],
+        ... [0, -np.pi/3, 0],
+        ... [np.pi/4, 0, 0]])
+        >>> r.as_euler('zxy', degrees=True)
+        array([[ 90.,   0.,   0.],
+               [  0.,   0., -60.],
+               [  0.,  45.,   0.]])
+        >>> r.as_euler('zxy', degrees=True).shape
+        (3, 3)
+
+        """
+        euler = self._backend.as_euler(
+            self._quat, seq, degrees=degrees, suppress_warnings=suppress_warnings
+        )
+        if self._single:
+            return euler[0, ...]
+        return euler
+
+    def as_davenport(
+        self,
+        axes: ArrayLike,
+        order: str,
+        degrees: bool = False,
+        *,
+        suppress_warnings: bool = False,
+    ) -> Array:
+        """Represent as Davenport angles.
+
+        Any orientation can be expressed as a composition of 3 elementary
+        rotations.
+
+        For both Euler angles and Davenport angles, consecutive axes must
+        be are orthogonal (``axis2`` is orthogonal to both ``axis1`` and
+        ``axis3``). For Euler angles, there is an additional relationship
+        between ``axis1`` or ``axis3``, with two possibilities:
+
+            - ``axis1`` and ``axis3`` are also orthogonal (asymmetric sequence)
+            - ``axis1 == axis3`` (symmetric sequence)
+
+        For Davenport angles, this last relationship is relaxed [1]_, and only
+        the consecutive orthogonal axes requirement is maintained.
+
+        A slightly modified version of the algorithm from [2]_ has been used to
+        calculate Davenport angles for the rotation about a given sequence of
+        axes.
+
+        Davenport angles, just like Euler angles, suffer from the problem of
+        gimbal lock [3]_, where the representation loses a degree of freedom
+        and it is not possible to determine the first and third angles
+        uniquely. In this case, a warning is raised (unless the
+        ``suppress_warnings`` option is used), and the third angle is set
+        to zero. Note however that the returned angles still represent the
+        correct rotation.
+
+        Parameters
+        ----------
+        axes : array_like, shape (..., [1 or 2 or 3], 3) or (..., 3)
+            Axis of rotation, if one dimensional. If N dimensional, describes the
+            sequence of axes for rotations, where each axes[..., i, :] is the ith
+            axis. If more than one axis is given, then the second axis must be
+            orthogonal to both the first and third axes.
+        order : str
+            If it belongs to the set {'e', 'extrinsic'}, the sequence will be
+            extrinsic. If it belongs to the set {'i', 'intrinsic'}, sequence
+            will be treated as intrinsic.
+        degrees : bool, optional
+            Returned angles are in degrees if this flag is True, else they are
+            in radians. Default is False.
+        suppress_warnings : bool, optional
+            Disable warnings about gimbal lock. Default is False.
+
+        Returns
+        -------
+        angles : ndarray, shape (..., 3)
+            Shape depends on shape of inputs used to initialize object.
+            The returned angles are in the range:
+
+            - First angle belongs to [-180, 180] degrees (both inclusive)
+            - Third angle belongs to [-180, 180] degrees (both inclusive)
+            - Second angle belongs to a set of size 180 degrees,
+              given by: ``[-abs(lambda), 180 - abs(lambda)]``, where ``lambda``
+              is the angle between the first and third axes.
+
+        References
+        ----------
+        .. [1] Shuster, Malcolm & Markley, Landis. (2003). Generalization of
+               the Euler Angles. Journal of the Astronautical Sciences. 51. 123-132.
+               10.1007/BF03546304.
+        .. [2] Bernardes E, Viollet S (2022) Quaternion to Euler angles
+               conversion: A direct, general and computationally efficient method.
+               PLoS ONE 17(11): e0276302. 10.1371/journal.pone.0276302
+        .. [3] https://en.wikipedia.org/wiki/Gimbal_lock#In_applied_mathematics
+
+        Examples
+        --------
+        >>> from scipy.spatial.transform import Rotation as R
+        >>> import numpy as np
+
+        Davenport angles are a generalization of Euler angles, when we use the
+        canonical basis axes:
+
+        >>> ex = [1, 0, 0]
+        >>> ey = [0, 1, 0]
+        >>> ez = [0, 0, 1]
+
+        Represent a single rotation:
+
+        >>> r = R.from_rotvec([0, 0, np.pi/2])
+        >>> r.as_davenport([ez, ex, ey], 'extrinsic', degrees=True)
+        array([90.,  0.,  0.])
+        >>> r.as_euler('zxy', degrees=True)
+        array([90.,  0.,  0.])
+        >>> r.as_davenport([ez, ex, ey], 'extrinsic', degrees=True).shape
+        (3,)
+
+        Represent a stack of single rotation:
+
+        >>> r = R.from_rotvec([[0, 0, np.pi/2]])
+        >>> r.as_davenport([ez, ex, ey], 'extrinsic', degrees=True)
+        array([[90.,  0.,  0.]])
+        >>> r.as_davenport([ez, ex, ey], 'extrinsic', degrees=True).shape
+        (1, 3)
+
+        Represent multiple rotations in a single object:
+
+        >>> r = R.from_rotvec([
+        ... [0, 0, 90],
+        ... [45, 0, 0]], degrees=True)
+        >>> r.as_davenport([ez, ex, ey], 'extrinsic', degrees=True)
+        array([[90.,  0.,  0.],
+               [ 0., 45.,  0.]])
+        >>> r.as_davenport([ez, ex, ey], 'extrinsic', degrees=True).shape
+        (2, 3)
+        """
+        axes = self._xp.asarray(
+            axes, dtype=self._quat.dtype, device=xp_device(self._quat)
+        )
+        davenport = self._backend.as_davenport(
+            self._quat, axes, order, degrees, suppress_warnings=suppress_warnings
+        )
+        if self._single:
+            return davenport[0, ...]
+        return davenport
+
+    def as_mrp(self) -> Array:
+        """Represent as Modified Rodrigues Parameters (MRPs).
+
+        MRPs are a 3 dimensional vector co-directional to the axis of rotation and whose
+        magnitude is equal to ``tan(theta / 4)``, where ``theta`` is the angle of
+        rotation (in radians) [1]_.
+
+        MRPs have a singularity at 360 degrees which can be avoided by ensuring the
+        angle of rotation does not exceed 180 degrees, i.e. switching the direction of
+        the rotation when it is past 180 degrees. This function will always return MRPs
+        corresponding to a rotation of less than or equal to 180 degrees.
+
+        Returns
+        -------
+        mrps : ndarray, shape (..., 3)
+            Shape depends on shape of inputs used for initialization.
+
+        Notes
+        -----
+
+        .. versionadded:: 1.6.0
+
+        References
+        ----------
+        .. [1] Shuster, M. D. "A Survey of Attitude Representations",
+               The Journal of Astronautical Sciences, Vol. 41, No.4, 1993,
+               pp. 475-476
+
+        Examples
+        --------
+        >>> from scipy.spatial.transform import Rotation as R
+        >>> import numpy as np
+
+        Represent a single rotation:
+
+        >>> r = R.from_rotvec([0, 0, np.pi])
+        >>> r.as_mrp()
+        array([0.        , 0.        , 1.         ])
+        >>> r.as_mrp().shape
+        (3,)
+
+        Represent a stack with a single rotation:
+
+        >>> r = R.from_euler('xyz', [[180, 0, 0]], degrees=True)
+        >>> r.as_mrp()
+        array([[1.       , 0.        , 0.         ]])
+        >>> r.as_mrp().shape
+        (1, 3)
+
+        Represent multiple rotations:
+
+        >>> r = R.from_rotvec([[np.pi/2, 0, 0], [0, 0, np.pi/2]])
+        >>> r.as_mrp()
+        array([[0.41421356, 0.        , 0.        ],
+               [0.        , 0.        , 0.41421356]])
+        >>> r.as_mrp().shape
+        (2, 3)
+
+        """
+        mrp = self._backend.as_mrp(self._quat)
+        if self._single:
+            return mrp[0, ...]
+        return mrp
+
+    @staticmethod
+    def concatenate(rotations: Rotation | Sequence[Rotation]) -> Rotation:
+        """Concatenate a sequence of `Rotation` objects into a single object.
+
+        This is useful if you want to, for example, take the mean of a set of
+        rotations and need to pack them into a single object to do so.
+
+        Parameters
+        ----------
+        rotations : sequence of `Rotation` objects
+            The rotations to concatenate. If a single `Rotation` object is
+            passed in, a copy is returned.
+
+        Returns
+        -------
+        concatenated : `Rotation` instance
+            The concatenated rotations.
+
+        Notes
+        -----
+        .. versionadded:: 1.8.0
+
+        Examples
+        --------
+        >>> from scipy.spatial.transform import Rotation as R
+        >>> r1 = R.from_rotvec([0, 0, 1])
+        >>> r2 = R.from_rotvec([0, 0, 2])
+        >>> rc = R.concatenate([r1, r2])
+        >>> rc.as_rotvec()
+        array([[0., 0., 1.],
+               [0., 0., 2.]])
+        >>> rc.mean().as_rotvec()
+        array([0., 0., 1.5])
+
+        Concatenation of a split rotation recovers the original object.
+
+        >>> rs = [r for r in rc]
+        >>> R.concatenate(rs).as_rotvec()
+        array([[0., 0., 1.],
+               [0., 0., 2.]])
+
+        Note that it may be simpler to create the desired rotations by passing
+        in a single list of the data during initialization, rather then by
+        concatenating:
+
+        >>> R.from_rotvec([[0, 0, 1], [0, 0, 2]]).as_rotvec()
+        array([[0., 0., 1.],
+               [0., 0., 2.]])
+
+        """
+        if isinstance(rotations, Rotation):
+            return Rotation(rotations.as_quat(), normalize=False, copy=True)
+        if not all(isinstance(x, Rotation) for x in rotations):
+            raise TypeError("input must contain Rotation objects only")
+
+        xp = array_namespace(rotations[0].as_quat())
+        quats = xp.concat(
+            [xpx.atleast_nd(x.as_quat(), ndim=2, xp=xp) for x in rotations]
+        )
+        return Rotation._from_raw_quat(quats, xp=xp)
+
+    def apply(self, vectors: ArrayLike, inverse: bool = False) -> Array:
+        """Apply this rotation to a set of vectors.
+
+        If the original frame rotates to the final frame by this rotation, then
+        its application to a vector can be seen in two ways:
+
+            - As a projection of vector components expressed in the final frame
+              to the original frame.
+            - As the physical rotation of a vector being glued to the original
+              frame as it rotates. In this case the vector components are
+              expressed in the original frame before and after the rotation.
+
+        In terms of rotation matrices, this application is the same as
+        ``(self.as_matrix() @ vectors[..., np.newaxis])[..., 0]``.
+        For a single rotation, this is the same as
+        ``vectors @ self.as_matrix().T``.
+
+        Parameters
+        ----------
+        vectors : array_like, shape (..., 3)
+            Each `vectors[..., :]` represents a vector in 3D space. The shape of
+            rotations and shape of vectors given must follow standard numpy
+            broadcasting rules: either one of them equals unity or they both
+            equal each other.
+        inverse : bool, optional
+            If True then the inverse of the rotation(s) is applied to the input
+            vectors. Default is False.
+
+        Returns
+        -------
+        rotated_vectors : ndarray, shape (..., 3)
+            Result of applying rotation on input vectors.
+            Shape is determined according to numpy broadcasting rules. I.e., the result
+            will have the shape `np.broadcast_shapes(r.shape, v.shape[:-1]) + (3,)`
+
+        Examples
+        --------
+        >>> from scipy.spatial.transform import Rotation as R
+        >>> import numpy as np
+
+        Single rotation applied on a single vector:
+
+        >>> vector = np.array([1, 0, 0])
+        >>> r = R.from_rotvec([0, 0, np.pi/2])
+        >>> r.as_matrix()
+        array([[ 2.22044605e-16, -1.00000000e+00,  0.00000000e+00],
+               [ 1.00000000e+00,  2.22044605e-16,  0.00000000e+00],
+               [ 0.00000000e+00,  0.00000000e+00,  1.00000000e+00]])
+        >>> r.apply(vector)
+        array([2.22044605e-16, 1.00000000e+00, 0.00000000e+00])
+        >>> r.apply(vector).shape
+        (3,)
+
+        Single rotation applied on multiple vectors:
+
+        >>> vectors = np.array([
+        ... [1, 0, 0],
+        ... [1, 2, 3]])
+        >>> r = R.from_rotvec([0, 0, np.pi/4])
+        >>> r.as_matrix()
+        array([[ 0.70710678, -0.70710678,  0.        ],
+               [ 0.70710678,  0.70710678,  0.        ],
+               [ 0.        ,  0.        ,  1.        ]])
+        >>> r.apply(vectors)
+        array([[ 0.70710678,  0.70710678,  0.        ],
+               [-0.70710678,  2.12132034,  3.        ]])
+        >>> r.apply(vectors).shape
+        (2, 3)
+
+        Multiple rotations on a single vector:
+
+        >>> r = R.from_rotvec([[0, 0, np.pi/4], [np.pi/2, 0, 0]])
+        >>> vector = np.array([1,2,3])
+        >>> r.as_matrix()
+        array([[[ 7.07106781e-01, -7.07106781e-01,  0.00000000e+00],
+                [ 7.07106781e-01,  7.07106781e-01,  0.00000000e+00],
+                [ 0.00000000e+00,  0.00000000e+00,  1.00000000e+00]],
+               [[ 1.00000000e+00,  0.00000000e+00,  0.00000000e+00],
+                [ 0.00000000e+00,  2.22044605e-16, -1.00000000e+00],
+                [ 0.00000000e+00,  1.00000000e+00,  2.22044605e-16]]])
+        >>> r.apply(vector)
+        array([[-0.70710678,  2.12132034,  3.        ],
+               [ 1.        , -3.        ,  2.        ]])
+        >>> r.apply(vector).shape
+        (2, 3)
+
+        Multiple rotations on multiple vectors. Each rotation is applied on the
+        corresponding vector:
+
+        >>> r = R.from_euler('zxy', [
+        ... [0, 0, 90],
+        ... [45, 30, 60]], degrees=True)
+        >>> vectors = [
+        ... [1, 2, 3],
+        ... [1, 0, -1]]
+        >>> r.apply(vectors)
+        array([[ 3.        ,  2.        , -1.        ],
+               [-0.09026039,  1.11237244, -0.86860844]])
+        >>> r.apply(vectors).shape
+        (2, 3)
+
+        Broadcasting rules apply:
+
+        >>> r = R.from_rotvec(np.tile([0, 0, np.pi/4], (5, 1, 4, 1)))
+        >>> vectors = np.ones((3, 4, 3))
+        >>> r.shape, vectors.shape
+        ((5, 1, 4), (3, 4, 3))
+        >>> r.apply(vectors).shape
+        (5, 3, 4, 3)
+
+        It is also possible to apply the inverse rotation:
+
+        >>> r = R.from_euler('zxy', [
+        ... [0, 0, 90],
+        ... [45, 30, 60]], degrees=True)
+        >>> vectors = [
+        ... [1, 2, 3],
+        ... [1, 0, -1]]
+        >>> r.apply(vectors, inverse=True)
+        array([[-3.        ,  2.        ,  1.        ],
+               [ 1.09533535, -0.8365163 ,  0.3169873 ]])
+
+        """
+        vectors = self._xp.asarray(
+            vectors, device=xp_device(self._quat), dtype=self._quat.dtype
+        )
+        single_vector = vectors.ndim == 1
+        # Numpy optimization: The Cython backend typing requires us to have fixed
+        # dimensions, so for the Numpy case we always broadcast the vector to 2D.
+        if vectors.shape[-1] != 3:
+            raise ValueError(f"Expected input of shape (..., 3), got {vectors.shape}.")
+        if is_numpy(self._xp):
+            vectors = xpx.atleast_nd(vectors, ndim=2, xp=self._xp)
+        cython_compatible = self._quat.ndim < 3 and vectors.ndim < 3
+        backend = select_backend(self._xp, cython_compatible=cython_compatible)
+        result = backend.apply(self._quat, vectors, inverse=inverse)
+        if self._single and single_vector:
+            return result[0, ...]
+        return result
+
+    def __mul__(self, other: Rotation) -> Rotation | NotImplementedType:
+        """Compose this rotation with the other.
+
+        If `p` and `q` are two rotations, then the composition of 'q followed
+        by p' is equivalent to `p * q`. In terms of rotation matrices,
+        the composition can be expressed as
+        ``p.as_matrix() @ q.as_matrix()``.
+
+        Parameters
+        ----------
+        other : `Rotation` instance
+            Object containing the rotations to be composed with this one. Note
+            that rotation compositions are not commutative, so ``p * q`` is
+            generally different from ``q * p``.
+
+        Returns
+        -------
+        composition : `Rotation` instance
+            This function supports composition of multiple rotations at a time.
+            Composition follows standard numpy broadcasting rules. The resulting
+            `Rotation` object will have the shape
+            `np.broadcast_shapes(p.shape, q.shape)`. In dimensions with size > 1,
+            rotations are composed with matching indices. In dimensions with only
+            one rotation, the single rotation is composed with each rotation in the
+            other object.
+
+        Examples
+        --------
+        >>> from scipy.spatial.transform import Rotation as R
+        >>> import numpy as np
+
+        Composition of two single rotations:
+
+        >>> p = R.from_quat([0, 0, 1, 1])
+        >>> q = R.from_quat([1, 0, 0, 1])
+        >>> p.as_matrix()
+        array([[ 0., -1.,  0.],
+               [ 1.,  0.,  0.],
+               [ 0.,  0.,  1.]])
+        >>> q.as_matrix()
+        array([[ 1.,  0.,  0.],
+               [ 0.,  0., -1.],
+               [ 0.,  1.,  0.]])
+        >>> r = p * q
+        >>> r.as_matrix()
+        array([[0., 0., 1.],
+               [1., 0., 0.],
+               [0., 1., 0.]])
+
+        Composition of two objects containing equal number of rotations:
+
+        >>> p = R.from_quat([[0, 0, 1, 1], [1, 0, 0, 1]])
+        >>> q = R.from_rotvec([[np.pi/4, 0, 0], [-np.pi/4, 0, np.pi/4]])
+        >>> p.as_quat()
+        array([[0.        , 0.        , 0.70710678, 0.70710678],
+               [0.70710678, 0.        , 0.        , 0.70710678]])
+        >>> q.as_quat()
+        array([[ 0.38268343,  0.        ,  0.        ,  0.92387953],
+               [-0.37282173,  0.        ,  0.37282173,  0.84971049]])
+        >>> r = p * q
+        >>> r.as_quat()
+        array([[ 0.27059805,  0.27059805,  0.65328148,  0.65328148],
+               [ 0.33721128, -0.26362477,  0.26362477,  0.86446082]])
+
+        Broadcasting rules apply:
+        >>> p = R.from_quat(np.tile(np.array([0, 0, 1, 1]), (5, 1, 1)))
+        >>> q = R.from_quat(np.tile(np.array([1, 0, 0, 1]), (1, 6, 1)))
+        >>> p.shape, q.shape
+        ((5, 1), (1, 6))
+        >>> r = p * q
+        >>> r.shape
+        (5, 6)
+        """
+        # Check that other is a Rotation object. We want to return NotImplemented
+        # instead of raising an error to allow other types to implement __rmul__.
+        # Python will then automatically try to delegate the multiplication to the
+        # other type.
+        # See https://github.com/scipy/scipy/issues/21541
+        if not isinstance(other, Rotation):
+            return NotImplemented
+        if not broadcastable(self._quat.shape, other._quat.shape):
+            raise ValueError(
+                f"Cannot broadcast {self._quat.shape[:-1]} rotations in "
+                f"first to {other._quat.shape[:-1]} rotations in second object."
+            )
+        cython_compatible = self._quat.ndim < 3 and other._quat.ndim < 3
+        backend = select_backend(self._xp, cython_compatible=cython_compatible)
+        quat = backend.compose_quat(self._quat, other._quat)
+        if self._single and other._single:
+            quat = quat[0]
+        return Rotation(quat, normalize=True, copy=False)
+
+    def __pow__(self, n: float | Array, modulus: None = None) -> Rotation:
+        """Compose this rotation with itself `n` times.
+
+        Composition of a rotation ``p`` with itself can be extended to
+        non-integer ``n`` by considering the power ``n`` to be a scale factor
+        applied to the angle of rotation about the rotation's fixed axis. The
+        expression ``q = p ** n`` can also be expressed as
+        ``q = Rotation.from_rotvec(n * p.as_rotvec())``.
+
+        If ``n`` is negative, then the rotation is inverted before the power
+        is applied. In other words, ``p ** -abs(n) == p.inv() ** abs(n)``.
+
+        Parameters
+        ----------
+        n : float | Array
+            The number of times to compose the rotation with itself. If `n` is
+            an array, then it must be 0d or 1d with shape (1,).
+        modulus : None
+            This overridden argument is not applicable to Rotations and must be
+            ``None``.
+
+        Returns
+        -------
+        power : `Rotation` instance
+            The resulting rotation will be of the same shape as the original rotation
+            object. Each element of the output is the corresponding element of the
+            input rotation raised to the power of ``n``.
+
+        Notes
+        -----
+        For example, a power of 2 will double the angle of rotation, and a
+        power of 0.5 will halve the angle. There are three notable cases: if
+        ``n == 1`` then the original rotation is returned, if ``n == 0``
+        then the identity rotation is returned, and if ``n == -1`` then
+        ``p.inv()`` is returned.
+
+        Note that fractional powers ``n`` which effectively take a root of
+        rotation, do so using the shortest path smallest representation of that
+        angle (the principal root). This means that powers of ``n`` and ``1/n``
+        are not necessarily inverses of each other. For example, a 0.5 power of
+        a +240 degree rotation will be calculated as the 0.5 power of a -120
+        degree rotation, with the result being a rotation of -60 rather than
+        +120 degrees.
+
+        Examples
+        --------
+        >>> from scipy.spatial.transform import Rotation as R
+
+        Raising a rotation to a power:
+
+        >>> p = R.from_rotvec([1, 0, 0])
+        >>> q = p ** 2
+        >>> q.as_rotvec()
+        array([2., 0., 0.])
+        >>> r = p ** 0.5
+        >>> r.as_rotvec()
+        array([0.5, 0., 0.])
+
+        Inverse powers do not necessarily cancel out:
+
+        >>> p = R.from_rotvec([0, 0, 120], degrees=True)
+        >>> ((p ** 2) ** 0.5).as_rotvec(degrees=True)
+        array([  -0.,   -0., -60.])
+
+        """
+        if modulus is not None:
+            raise NotImplementedError("modulus not supported")
+        quat = self._backend.pow(self._quat, n)
+        if self._single:
+            quat = quat[0]
+        return Rotation._from_raw_quat(quat, xp=self._xp, backend=self._backend)
+
+    def inv(self) -> Rotation:
+        """Invert this rotation.
+
+        Composition of a rotation with its inverse results in an identity
+        transformation.
+
+        Returns
+        -------
+        inverse : `Rotation` instance
+            Object containing inverse of the rotations in the current instance.
+
+        Examples
+        --------
+        >>> from scipy.spatial.transform import Rotation as R
+        >>> import numpy as np
+
+        Inverting a single rotation:
+
+        >>> p = R.from_euler('z', 45, degrees=True)
+        >>> q = p.inv()
+        >>> q.as_euler('zyx', degrees=True)
+        array([-45.,   0.,   0.])
+
+        Inverting multiple rotations:
+
+        >>> p = R.from_rotvec([[0, 0, np.pi/3], [-np.pi/4, 0, 0]])
+        >>> q = p.inv()
+        >>> q.as_rotvec()
+        array([[-0.        , -0.        , -1.04719755],
+               [ 0.78539816, -0.        , -0.        ]])
+
+        """
+        q_inv = self._backend.inv(self._quat)
+        if self._single:
+            q_inv = q_inv[0, ...]
+        return Rotation._from_raw_quat(q_inv, xp=self._xp, backend=self._backend)
+
+    def magnitude(self) -> Array:
+        """Get the magnitude(s) of the rotation(s).
+
+        Returns
+        -------
+        magnitude : ndarray or float
+            Angle(s) in radians, float if object contains a single rotation
+            and ndarray if object contains ND rotations. The magnitude
+            will always be in the range [0, pi].
+
+        Examples
+        --------
+        >>> from scipy.spatial.transform import Rotation as R
+        >>> import numpy as np
+        >>> r = R.from_quat(np.eye(4))
+        >>> r.as_quat()
+        array([[ 1., 0., 0., 0.],
+               [ 0., 1., 0., 0.],
+               [ 0., 0., 1., 0.],
+               [ 0., 0., 0., 1.]])
+        >>> r.magnitude()
+        array([3.14159265, 3.14159265, 3.14159265, 0.        ])
+
+        Magnitude of a single rotation:
+
+        >>> r[0].magnitude()
+        3.141592653589793
+        """
+        magnitude = self._backend.magnitude(self._quat)
+        if self._single:
+            # Special handling for numpy and single rotations. self._single is only set
+            # if xp is numpy. We therefore know that magnitude is a numpy array and
+            # that it contains a single element. Previously this code returned a Python
+            # float in that case. Here we return a numpy float64 scalar. All other
+            # Array API libraries return 0d arrays instead.
+            # See https://github.com/scipy/scipy/pull/23198#issuecomment-3003757848
+            return magnitude[0]
+        return magnitude
+
+    def approx_equal(
+        self, other: Rotation, atol: float | None = None, degrees: bool = False
+    ) -> Array | np.bool:
+        """Determine if another rotation is approximately equal to this one.
+
+        Equality is measured by calculating the smallest angle between the
+        rotations, and checking to see if it is smaller than `atol`.
+
+        Parameters
+        ----------
+        other : `Rotation` instance
+            Object containing the rotations to measure against this one.
+        atol : float, optional
+            The absolute angular tolerance, below which the rotations are
+            considered equal. If not given, then set to 1e-8 radians by
+            default.
+        degrees : bool, optional
+            If True and `atol` is given, then `atol` is measured in degrees. If
+            False (default), then atol is measured in radians.
+
+        Returns
+        -------
+        approx_equal : Array or `numpy.bool`
+            Whether the rotations are approximately equal, `numpy.bool` if object
+            contains a single numpy rotation and Array if object contains multiple
+            rotations or is from another library.
+
+        Examples
+        --------
+        >>> from scipy.spatial.transform import Rotation as R
+        >>> import numpy as np
+        >>> p = R.from_quat([0, 0, 0, 1])
+        >>> q = R.from_quat(np.eye(4))
+        >>> p.approx_equal(q)
+        array([False, False, False, True])
+
+        Approximate equality for a single rotation:
+
+        >>> p.approx_equal(q[0])
+        np.False_
+        """
+        cython_compatible = self._quat.ndim < 3 and other._quat.ndim < 3
+        backend = select_backend(self._xp, cython_compatible=cython_compatible)
+        approx_equal = backend.approx_equal(
+            self._quat, other._quat, atol=atol, degrees=degrees
+        )
+        if self._single and other._single:
+            return approx_equal[0]
+        return approx_equal
+
+    def mean(
+        self,
+        weights: ArrayLike | None = None,
+        axis: None | int | tuple[int, ...] = None,
+    ) -> Rotation:
+        """Get the mean of the rotations.
+
+        The mean used is the chordal L2 mean (also called the projected or
+        induced arithmetic mean) [1]_. If ``A`` is a set of rotation matrices,
+        then the mean ``M`` is the rotation matrix that minimizes the
+        following loss function:
+
+        .. math::
+
+            L(M) = \\sum_{i = 1}^{n} w_i \\lVert \\mathbf{A}_i -
+            \\mathbf{M} \\rVert^2 ,
+
+        where :math:`w_i`'s are the `weights` corresponding to each matrix.
+
+        Parameters
+        ----------
+        weights : array_like shape (..., N), optional
+            Weights describing the relative importance of the rotations. If
+            None (default), then all values in `weights` are assumed to be
+            equal. If given, the shape of `weights` must be broadcastable to
+            the rotation shape. Weights must be non-negative.
+        axis : None, int, or tuple of ints, optional
+            Axis or axes along which the means are computed. The default is to
+            compute the mean of all rotations.
+
+        Returns
+        -------
+        mean : `Rotation` instance
+            Single rotation containing the mean of the rotations in the
+            current instance.
+
+        References
+        ----------
+        .. [1] Hartley, Richard, et al.,
+                "Rotation Averaging", International Journal of Computer Vision
+                103, 2013, pp. 267-305.
+
+        Examples
+        --------
+        >>> from scipy.spatial.transform import Rotation as R
+        >>> r = R.from_euler('zyx', [[0, 0, 0],
+        ...                          [1, 0, 0],
+        ...                          [0, 1, 0],
+        ...                          [0, 0, 1]], degrees=True)
+        >>> r.mean().as_euler('zyx', degrees=True)
+        array([0.24945696, 0.25054542, 0.24945696])
+        """
+        mean = self._backend.mean(self._quat, weights=weights, axis=axis)
+        return Rotation._from_raw_quat(mean, xp=self._xp, backend=self._backend)
+
+    def reduce(
+        self,
+        left: Rotation | None = None,
+        right: Rotation | None = None,
+        return_indices: bool = False,
+    ) -> Rotation | tuple[Rotation, Array, Array]:
+        """Reduce this rotation with the provided rotation groups.
+
+        Reduction of a rotation ``p`` is a transformation of the form
+        ``q = l * p * r``, where ``l`` and ``r`` are chosen from `left` and
+        `right` respectively, such that rotation ``q`` has the smallest
+        magnitude.
+
+        If `left` and `right` are rotation groups representing symmetries of
+        two objects rotated by ``p``, then ``q`` is the rotation of the
+        smallest magnitude to align these objects considering their symmetries.
+
+        Parameters
+        ----------
+        left : `Rotation` instance, optional
+            Object containing the left rotation(s). Default value (None)
+            corresponds to the identity rotation.
+        right : `Rotation` instance, optional
+            Object containing the right rotation(s). Default value (None)
+            corresponds to the identity rotation.
+        return_indices : bool, optional
+            Whether to return the indices of the rotations from `left` and
+            `right` used for reduction.
+
+        Returns
+        -------
+        reduced : `Rotation` instance
+            Object containing reduced rotations.
+        left_best, right_best: int ndarray
+            Indices of elements from `left` and `right` used for reduction.
+        """
+        left = left.as_quat() if left is not None else None
+        right = right.as_quat() if right is not None else None
+        reduced, left_idx, right_idx = self._backend.reduce(
+            self._quat, left=left, right=right
+        )
+        if self._single:
+            reduced = reduced[0, ...]
+        rot = Rotation._from_raw_quat(reduced, xp=self._xp, backend=self._backend)
+        if return_indices:
+            left_idx = left_idx if left is not None else None
+            right_idx = right_idx if right is not None else None
+            return rot, left_idx, right_idx
+        return rot
+
+    @classmethod
+    def create_group(cls, group: str, axis: str = "Z") -> Rotation:
+        """Create a 3D rotation group.
+
+        Parameters
+        ----------
+        group : str
+            The name of the group. Must be one of 'I', 'O', 'T', 'Dn', 'Cn',
+            where `n` is a positive integer. The groups are:
+
+                * I: Icosahedral group
+                * O: Octahedral group
+                * T: Tetrahedral group
+                * D: Dicyclic group
+                * C: Cyclic group
+
+        axis : int
+            The cyclic rotation axis. Must be one of ['X', 'Y', 'Z'] (or
+            lowercase). Default is 'Z'. Ignored for groups 'I', 'O', and 'T'.
+
+        Returns
+        -------
+        rotation : `Rotation` instance
+            Object containing the elements of the rotation group.
+
+        Notes
+        -----
+        This method generates rotation groups only. The full 3-dimensional
+        point groups [PointGroups]_ also contain reflections.
+
+        References
+        ----------
+        .. [PointGroups] `Point groups
+           <https://en.wikipedia.org/wiki/Point_groups_in_three_dimensions>`_
+           on Wikipedia.
+        """
+        # TODO: We defer the implementation of groups for arbitrary Array API frameworks
+        # to the follow-up PR that adds general Array API support for Rotations.
+        return create_group(cls, group, axis=axis)
+
+    def __getitem__(
+        self, indexer: int | slice | EllipsisType | Array | None
+    ) -> Rotation:
+        """Extract rotation(s) at given index(es) from object.
+
+        Create a new `Rotation` instance containing a subset of rotations
+        stored in this object.
+
+        Parameters
+        ----------
+        indexer : index, slice, or index array
+            Specifies which rotation(s) to extract. A single indexer must be
+            specified, i.e. as if indexing a 1 dimensional array or list.
+
+        Returns
+        -------
+        rotation : `Rotation` instance
+            Contains
+                - a single rotation, if `indexer` is a single index
+                - a stack of rotation(s), if `indexer` is a slice, or and index
+                  array.
+
+        Raises
+        ------
+        TypeError if the instance was created as a single rotation.
+
+        Examples
+        --------
+        >>> from scipy.spatial.transform import Rotation as R
+        >>> rs = R.from_quat([
+        ... [1, 1, 0, 0],
+        ... [0, 1, 0, 1],
+        ... [1, 1, -1, 0]])  # These quats are normalized
+        >>> rs.as_quat()
+        array([[ 0.70710678,  0.70710678,  0.        ,  0.        ],
+               [ 0.        ,  0.70710678,  0.        ,  0.70710678],
+               [ 0.57735027,  0.57735027, -0.57735027,  0.        ]])
+
+        Indexing using a single index:
+
+        >>> a = rs[0]
+        >>> a.as_quat()
+        array([0.70710678, 0.70710678, 0.        , 0.        ])
+
+        Array slicing:
+
+        >>> b = rs[1:3]
+        >>> b.as_quat()
+        array([[ 0.        ,  0.70710678,  0.        ,  0.70710678],
+               [ 0.57735027,  0.57735027, -0.57735027,  0.        ]])
+
+        List comprehension to split each rotation into its own object:
+
+        >>> c = [r for r in rs]
+        >>> print([r.as_quat() for r in c])
+        [array([ 0.70710678,  0.70710678,  0.        ,  0.        ]),
+         array([ 0.        ,  0.70710678,  0.        ,  0.70710678]),
+         array([ 0.57735027,  0.57735027, -0.57735027,  0.        ])]
+
+        Concatenation of split rotations will recover the original object:
+
+        >>> R.concatenate([a, b]).as_quat()
+        array([[ 0.70710678,  0.70710678,  0.        ,  0.        ],
+               [ 0.        ,  0.70710678,  0.        ,  0.70710678],
+               [ 0.57735027,  0.57735027, -0.57735027,  0.        ]])
+        """
+        if self._single or self._quat.ndim == 1:
+            raise TypeError("Single rotation is not subscriptable.")
+        is_array = isinstance(indexer, type(self._quat))
+        # Masking is only specified in the Array API when the array is the sole index
+        # TODO: This special case handling is mainly a result of Array API limitations.
+        # Ideally we would get rid of them altogether and converge to [indexer, ...]
+        # indexing.
+        if is_array and indexer.dtype == self._xp.bool:  # type:ignore[union-attr]
+            return Rotation(self._quat[indexer], normalize=False)
+        if is_array and self._xp.isdtype(indexer.dtype, "integral"):  # type:ignore[union-attr]
+            # xp.take is implementation-defined for zero-dim arrays, hence we raise
+            # pre-emptively to have consistent behavior across frameworks.
+            if self._quat.shape[0] == 0:
+                raise IndexError("cannot do a non-empty take from an empty axes.")
+            return Rotation(self._xp.take(self._quat, indexer, axis=0), normalize=False)
+        return Rotation(self._quat[indexer, ...], normalize=False)
+
+    def __setitem__(self, indexer: int | slice | EllipsisType | None, value: Rotation):
+        """Set rotation(s) at given index(es) from object.
+
+        Parameters
+        ----------
+        indexer : index, slice, or index array
+            Specifies which rotation(s) to replace. A single indexer must be
+            specified, i.e. as if indexing a 1 dimensional array or list.
+
+        value : `Rotation` instance
+            The rotations to set.
+
+        Raises
+        ------
+        TypeError if the instance was created as a single rotation.
+
+        Notes
+        -----
+
+        .. versionadded:: 1.8.0
+        """
+        if self._single or self._quat.ndim == 1:
+            raise TypeError("Single rotation is not subscriptable.")
+
+        if not isinstance(value, Rotation):
+            raise TypeError("value must be a Rotation object")
+
+        self._quat = self._backend.setitem(self._quat, value.as_quat(), indexer)
+
+    @staticmethod
+    def identity(
+        num: int | None = None, *, shape: int | tuple[int, ...] | None = None
+    ) -> Rotation:
+        """Get identity rotation(s).
+
+        Composition with the identity rotation has no effect.
+
+        Parameters
+        ----------
+        num : int or None, optional
+            Number of identity rotations to generate. If None (default), then a
+            single rotation is generated.
+        shape : int or tuple of ints, optional
+            Shape of identity rotations to generate. If specified, `num` must
+            be None.
+
+        Returns
+        -------
+        identity : Rotation object
+            The identity rotation.
+        """
+        # TODO: We should move to one single way of specifying the output shape and
+        # deprecate `num`.
+        if num is not None and shape is not None:
+            raise ValueError("Only one of `num` or `shape` can be specified.")
+        quat = cython_backend.identity(num, shape=shape)
+        return Rotation._from_raw_quat(quat, xp=array_namespace(quat))
+
+    @staticmethod
+    @_transition_to_rng("random_state", position_num=2)
+    def random(
+        num: int | None = None,
+        rng: np.random.Generator | None = None,
+        *,
+        shape: tuple[int, ...] | None = None,
+    ) -> Rotation:
+        r"""Generate rotations that are uniformly distributed on a sphere.
+
+        Formally, the rotations follow the Haar-uniform distribution over the SO(3)
+        group.
+
+        Parameters
+        ----------
+        num : int or None, optional
+            Number of random rotations to generate. If None (default), then a
+            single rotation is generated.
+        rng : `numpy.random.Generator`, optional
+            Pseudorandom number generator state. When `rng` is None, a new
+            `numpy.random.Generator` is created using entropy from the
+            operating system. Types other than `numpy.random.Generator` are
+            passed to `numpy.random.default_rng` to instantiate a `Generator`.
+        shape : tuple of ints, optional
+            Shape of random rotations to generate. If specified, `num` must be None.
+
+        Returns
+        -------
+        random_rotation : `Rotation` instance
+            Contains a single rotation if `num` is None. Otherwise contains a
+            stack of `num` rotations.
+
+        Notes
+        -----
+        This function is optimized for efficiently sampling random rotation
+        matrices in three dimensions. For generating random rotation matrices
+        in higher dimensions, see `scipy.stats.special_ortho_group`.
+
+        Examples
+        --------
+        >>> from scipy.spatial.transform import Rotation as R
+
+        Sample a single rotation:
+
+        >>> R.random().as_euler('zxy', degrees=True)
+        array([-110.5976185 ,   55.32758512,   76.3289269 ])  # random
+
+        Sample a stack of rotations:
+
+        >>> R.random(5).as_euler('zxy', degrees=True)
+        array([[-110.5976185 ,   55.32758512,   76.3289269 ],  # random
+               [ -91.59132005,  -14.3629884 ,  -93.91933182],
+               [  25.23835501,   45.02035145, -121.67867086],
+               [ -51.51414184,  -15.29022692, -172.46870023],
+               [ -81.63376847,  -27.39521579,    2.60408416]])
+
+        See Also
+        --------
+        scipy.stats.special_ortho_group
+
+        """
+        # TODO: We should move to one single way of specifying the output shape and
+        # deprecate `num`.
+        if num is not None and shape is not None:
+            raise ValueError("Only one of `num` or `shape` can be specified.")
+        sample = cython_backend.random(num, rng, shape=shape)
+        return Rotation(sample, normalize=True, copy=False)
+
+    @staticmethod
+    def align_vectors(
+        a: ArrayLike,
+        b: ArrayLike,
+        weights: ArrayLike | None = None,
+        return_sensitivity: bool = False,
+    ) -> tuple[Rotation, float] | tuple[Rotation, float, Array]:
+        """Estimate a rotation to optimally align two sets of vectors.
+
+        Find a rotation between frames A and B which best aligns a set of
+        vectors `a` and `b` observed in these frames. The following loss
+        function is minimized to solve for the rotation matrix
+        :math:`C`:
+
+        .. math::
+
+            L(C) = \\frac{1}{2} \\sum_{i = 1}^{n} w_i \\lVert \\mathbf{a}_i -
+            C \\mathbf{b}_i \\rVert^2 ,
+
+        where :math:`w_i`'s are the `weights` corresponding to each vector.
+
+        The rotation is estimated with Kabsch algorithm [1]_, and solves what
+        is known as the "pointing problem", or "Wahba's problem" [2]_.
+
+        Note that the length of each vector in this formulation acts as an
+        implicit weight. So for use cases where all vectors need to be
+        weighted equally, you should normalize them to unit length prior to
+        calling this method.
+
+        There are two special cases. The first is if a single vector is given
+        for `a` and `b`, in which the shortest distance rotation that aligns
+        `b` to `a` is returned.
+
+        The second is when one of the weights is infinity. In this case, the
+        shortest distance rotation between the primary infinite weight vectors
+        is calculated as above. Then, the rotation about the aligned primary
+        vectors is calculated such that the secondary vectors are optimally
+        aligned per the above loss function. The result is the composition
+        of these two rotations. The result via this process is the same as the
+        Kabsch algorithm as the corresponding weight approaches infinity in
+        the limit. For a single secondary vector this is known as the
+        "align-constrain" algorithm [3]_.
+
+        For both special cases (single vectors or an infinite weight), the
+        sensitivity matrix does not have physical meaning and an error will be
+        raised if it is requested. For an infinite weight, the primary vectors
+        act as a constraint with perfect alignment, so their contribution to
+        `rssd` will be forced to 0 even if they are of different lengths.
+
+        Parameters
+        ----------
+        a : array_like, shape (3,) or (N, 3)
+            Vector components observed in initial frame A. Each row of `a`
+            denotes a vector.
+        b : array_like, shape (3,) or (N, 3)
+            Vector components observed in another frame B. Each row of `b`
+            denotes a vector.
+        weights : array_like shape (N,), optional
+            Weights describing the relative importance of the vector
+            observations. If None (default), then all values in `weights` are
+            assumed to be 1. One and only one weight may be infinity, and
+            weights must be positive.
+        return_sensitivity : bool, optional
+            Whether to return the sensitivity matrix. See Notes for details.
+            Default is False.
+
+        Returns
+        -------
+        rotation : `Rotation` instance
+            Best estimate of the rotation that transforms `b` to `a`.
+        rssd : float
+            Stands for "root sum squared distance". Square root of the weighted
+            sum of the squared distances between the given sets of vectors
+            after alignment. It is equal to ``sqrt(2 * minimum_loss)``, where
+            ``minimum_loss`` is the loss function evaluated for the found
+            optimal rotation.
+            Note that the result will also be weighted by the vectors'
+            magnitudes, so perfectly aligned vector pairs will have nonzero
+            `rssd` if they are not of the same length. This can be avoided by
+            normalizing them to unit length prior to calling this method,
+            though note that doing this will change the resulting rotation.
+        sensitivity_matrix : ndarray, shape (3, 3)
+            Sensitivity matrix of the estimated rotation estimate as explained
+            in Notes. Returned only when `return_sensitivity` is True. Not
+            valid if aligning a single pair of vectors or if there is an
+            infinite weight, in which cases an error will be raised.
+
+        Notes
+        -----
+        The sensitivity matrix gives the sensitivity of the estimated rotation
+        to small perturbations of the vector measurements. Specifically we
+        consider the rotation estimate error as a small rotation vector of
+        frame A. The sensitivity matrix is proportional to the covariance of
+        this rotation vector assuming that the vectors in `a` was measured with
+        errors significantly less than their lengths. To get the true
+        covariance matrix, the returned sensitivity matrix must be multiplied
+        by harmonic mean [4]_ of variance in each observation. Note that
+        `weights` are supposed to be inversely proportional to the observation
+        variances to get consistent results. For example, if all vectors are
+        measured with the same accuracy of 0.01 (`weights` must be all equal),
+        then you should multiple the sensitivity matrix by 0.01**2 to get the
+        covariance.
+
+        Refer to [5]_ for more rigorous discussion of the covariance
+        estimation. See [6]_ for more discussion of the pointing problem and
+        minimal proper pointing.
+
+        This function does not support broadcasting or ND arrays with N > 2.
+
+        References
+        ----------
+        .. [1] https://en.wikipedia.org/wiki/Kabsch_algorithm
+        .. [2] https://en.wikipedia.org/wiki/Wahba%27s_problem
+        .. [3] Magner, Robert,
+                "Extending target tracking capabilities through trajectory and
+                momentum setpoint optimization." Small Satellite Conference,
+                2018.
+        .. [4] https://en.wikipedia.org/wiki/Harmonic_mean
+        .. [5] F. Landis Markley,
+                "Attitude determination using vector observations: a fast
+                optimal matrix algorithm", Journal of Astronautical Sciences,
+                Vol. 41, No.2, 1993, pp. 261-280.
+        .. [6] Bar-Itzhack, Itzhack Y., Daniel Hershkowitz, and Leiba Rodman,
+                "Pointing in Real Euclidean Space", Journal of Guidance,
+                Control, and Dynamics, Vol. 20, No. 5, 1997, pp. 916-922.
+
+        Examples
+        --------
+        >>> import numpy as np
+        >>> from scipy.spatial.transform import Rotation as R
+
+        Here we run the baseline Kabsch algorithm to best align two sets of
+        vectors, where there is noise on the last two vector measurements of
+        the ``b`` set:
+
+        >>> a = [[0, 1, 0], [0, 1, 1], [0, 1, 1]]
+        >>> b = [[1, 0, 0], [1, 1.1, 0], [1, 0.9, 0]]
+        >>> rot, rssd, sens = R.align_vectors(a, b, return_sensitivity=True)
+        >>> rot.as_matrix()
+        array([[0., 0., 1.],
+               [1., 0., 0.],
+               [0., 1., 0.]])
+
+        When we apply the rotation to ``b``, we get vectors close to ``a``:
+
+        >>> rot.apply(b)
+        array([[0. , 1. , 0. ],
+               [0. , 1. , 1.1],
+               [0. , 1. , 0.9]])
+
+        The error for the first vector is 0, and for the last two the error is
+        magnitude 0.1. The `rssd` is the square root of the sum of the
+        weighted squared errors, and the default weights are all 1, so in this
+        case the `rssd` is calculated as
+        ``sqrt(1 * 0**2 + 1 * 0.1**2 + 1 * (-0.1)**2) = 0.141421356237308``
+
+        >>> a - rot.apply(b)
+        array([[ 0., 0.,  0. ],
+               [ 0., 0., -0.1],
+               [ 0., 0.,  0.1]])
+        >>> np.sqrt(np.sum(np.ones(3) @ (a - rot.apply(b))**2))
+        0.141421356237308
+        >>> rssd
+        0.141421356237308
+
+        The sensitivity matrix for this example is as follows:
+
+        >>> sens
+        array([[0.2, 0. , 0.],
+               [0. , 1.5, 1.],
+               [0. , 1. , 1.]])
+
+        Special case 1: Find a minimum rotation between single vectors:
+
+        >>> a = [1, 0, 0]
+        >>> b = [0, 1, 0]
+        >>> rot, _ = R.align_vectors(a, b)
+        >>> rot.as_matrix()
+        array([[0., 1., 0.],
+               [-1., 0., 0.],
+               [0., 0., 1.]])
+        >>> rot.apply(b)
+        array([1., 0., 0.])
+
+        Special case 2: One infinite weight. Here we find a rotation between
+        primary and secondary vectors that can align exactly:
+
+        >>> a = [[0, 1, 0], [0, 1, 1]]
+        >>> b = [[1, 0, 0], [1, 1, 0]]
+        >>> rot, _ = R.align_vectors(a, b, weights=[np.inf, 1])
+        >>> rot.as_matrix()
+        array([[0., 0., 1.],
+               [1., 0., 0.],
+               [0., 1., 0.]])
+        >>> rot.apply(b)
+        array([[0., 1., 0.],
+               [0., 1., 1.]])
+
+        Here the secondary vectors must be best-fit:
+
+        >>> a = [[0, 1, 0], [0, 1, 1]]
+        >>> b = [[1, 0, 0], [1, 2, 0]]
+        >>> rot, _ = R.align_vectors(a, b, weights=[np.inf, 1])
+        >>> rot.as_matrix()
+        array([[0., 0., 1.],
+               [1., 0., 0.],
+               [0., 1., 0.]])
+        >>> rot.apply(b)
+        array([[0., 1., 0.],
+               [0., 1., 2.]])
+        """
+        xp = array_namespace(a)
+        a, b, weights = _promote(a, b, weights, xp=xp)
+        cython_compatible = (
+            (a.ndim < 3) & (b.ndim < 3) & (weights is None or weights.ndim < 2)  # type:ignore[union-attr]
+        )
+        backend = select_backend(xp, cython_compatible=cython_compatible)
+        q, rssd, sensitivity = backend.align_vectors(a, b, weights, return_sensitivity)
+        if return_sensitivity:
+            return Rotation._from_raw_quat(q, xp=xp, backend=backend), rssd, sensitivity
+        return Rotation._from_raw_quat(q, xp=xp, backend=backend), rssd
+
+    def __getstate__(self) -> tuple[Array, bool]:
+        return (self._quat, self._single)
+
+    def __setstate__(self, state: tuple[Array, bool]):
+        quat, single = state
+        xp = array_namespace(quat)
+        self._xp = xp
+        self._quat = xp.asarray(quat, copy=True)
+        self._backend = select_backend(xp, cython_compatible=self._quat.ndim < 3)
+        self._single = single
+
+    @property
+    def single(self) -> bool:
+        """Whether this instance represents a single rotation."""
+        return self._single or self._quat.ndim == 1
+
+    @property
+    def shape(self) -> tuple[int, ...]:
+        """The shape of the rotation's leading dimensions."""
+        if self._single:
+            return ()
+        return self._quat.shape[:-1]
+
+    def __bool__(self) -> bool:
+        """Comply with Python convention for objects to be True.
+
+        Required because `Rotation.__len__()` is defined and not always truthy.
+        """
+        return True
+
+    def __len__(self) -> int:
+        """Number of rotations contained in this object.
+
+        Multiple rotations can be stored in a single instance.
+
+        Returns
+        -------
+        length : int
+            Number of rotations stored in object.
+
+        Raises
+        ------
+        TypeError if the instance was created as a single rotation.
+        """
+        if self._single or self._quat.ndim == 1:
+            raise TypeError("Single rotation has no len().")
+        return self._quat.shape[0]
+
+    def __repr__(self) -> str:
+        m = f"{self.as_matrix()!r}".splitlines()
+        # bump indent (+21 characters)
+        m[1:] = [" " * 21 + m[i] for i in range(1, len(m))]
+        return "Rotation.from_matrix(" + "\n".join(m) + ")"
+
+    def __iter__(self) -> Iterator[Rotation]:
+        """Iterate over rotations."""
+        if self._single or self._quat.ndim == 1:
+            raise TypeError("Single rotation is not iterable.")
+        # We return a generator that yields a new Rotation object for each rotation
+        # in the current object. We cannot rely on the default implementation using
+        # __getitem__ because jax will not raise an IndexError for out-of-bounds
+        # indices.
+        for i in range(self._quat.shape[0]):
+            yield Rotation(self._quat[i, ...], normalize=False, copy=False)
+
+    @staticmethod
+    def _from_raw_quat(
+        quat: Array, xp: ModuleType, backend: ModuleType | None = None
+    ) -> Rotation:
+        """Create a Rotation skipping all sanitization steps.
+
+        This method is intended for internal, performant creation of Rotations with
+        quaternions that are guaranteed to be valid.
+        """
+        rot = Rotation.__new__(Rotation)
+        rot._single = quat.ndim == 1 and is_numpy(xp)
+        if rot._single:
+            quat = xpx.atleast_nd(quat, ndim=2, xp=xp)
+        rot._quat = quat
+        rot._xp = xp
+        if backend is None:
+            backend = select_backend(xp, cython_compatible=quat.ndim < 3)
+        rot._backend = backend
+        return rot
+
+
+@xp_capabilities(
+    skip_backends=[("dask.array", "missing linalg.cross function")],
+    method_capabilities={
+        "__init__": dict(
+            jax_jit=False,
+            skip_backends=[("dask.array", "missing linalg.cross function")],
+        ),
+    },
+)
+class Slerp:
+    """Spherical Linear Interpolation of Rotations.
+
+    The interpolation between consecutive rotations is performed as a rotation
+    around a fixed axis with a constant angular velocity [1]_. This ensures
+    that the interpolated rotations follow the shortest path between initial
+    and final orientations.
+
+    Parameters
+    ----------
+    times : array_like, shape (N,)
+        Times of the known rotations. At least 2 times must be specified.
+    rotations : `Rotation` instance
+        Rotations to perform the interpolation between. Must contain N
+        rotations.
+
+    Methods
+    -------
+    __call__
+
+    See Also
+    --------
+    Rotation
+
+    Notes
+    -----
+    This class only supports interpolation of rotations with a single leading
+    dimension.
+
+    .. versionadded:: 1.2.0
+
+    References
+    ----------
+    .. [1] https://en.wikipedia.org/wiki/Slerp#Quaternion_Slerp
+
+    Examples
+    --------
+    >>> from scipy.spatial.transform import Rotation as R
+    >>> from scipy.spatial.transform import Slerp
+
+    Setup the fixed keyframe rotations and times:
+
+    >>> key_rots = R.random(5, random_state=2342345)
+    >>> key_times = [0, 1, 2, 3, 4]
+
+    Create the interpolator object:
+
+    >>> slerp = Slerp(key_times, key_rots)
+
+    Interpolate the rotations at the given times:
+
+    >>> times = [0, 0.5, 0.25, 1, 1.5, 2, 2.75, 3, 3.25, 3.60, 4]
+    >>> interp_rots = slerp(times)
+
+    The keyframe rotations expressed as Euler angles:
+
+    >>> key_rots.as_euler('xyz', degrees=True)
+    array([[ 14.31443779, -27.50095894,  -3.7275787 ],
+           [ -1.79924227, -24.69421529, 164.57701743],
+           [146.15020772,  43.22849451, -31.34891088],
+           [ 46.39959442,  11.62126073, -45.99719267],
+           [-88.94647804, -49.64400082, -65.80546984]])
+
+    The interpolated rotations expressed as Euler angles. These agree with the
+    keyframe rotations at both endpoints of the range of keyframe times.
+
+    >>> interp_rots.as_euler('xyz', degrees=True)
+    array([[  14.31443779,  -27.50095894,   -3.7275787 ],
+           [   4.74588574,  -32.44683966,   81.25139984],
+           [  10.71094749,  -31.56690154,   38.06896408],
+           [  -1.79924227,  -24.69421529,  164.57701743],
+           [  11.72796022,   51.64207311, -171.7374683 ],
+           [ 146.15020772,   43.22849451,  -31.34891088],
+           [  68.10921869,   20.67625074,  -48.74886034],
+           [  46.39959442,   11.62126073,  -45.99719267],
+           [  12.35552615,    4.21525086,  -64.89288124],
+           [ -30.08117143,  -19.90769513,  -78.98121326],
+           [ -88.94647804,  -49.64400082,  -65.80546984]])
+
+    """
+
+    def __init__(self, times: ArrayLike, rotations: Rotation):
+        if not isinstance(rotations, Rotation):
+            raise TypeError("`rotations` must be a `Rotation` instance.")
+
+        if rotations.single or len(rotations) <= 1:
+            raise ValueError("`rotations` must be a sequence of at least 2 rotations.")
+
+        q = rotations.as_quat()
+        if q.ndim > 2:
+            raise ValueError(
+                "Rotations with more than 1 leading dimension are not supported."
+            )
+
+        xp = array_namespace(q)
+        times = xp.asarray(times, device=xp_device(q), dtype=q.dtype)
+        if times.ndim != 1:
+            raise ValueError(
+                "Expected times to be specified in a 1 dimensional array, got "
+                f"{times.ndim} dimensions."
+            )
+
+        if times.shape[0] != len(rotations):
+            raise ValueError(
+                "Expected number of rotations to be equal to number of timestamps "
+                f"given, got {len(rotations)} rotations and {times.shape[0]} "
+                "timestamps."
+            )
+        self.times = times
+        self.timedelta = xp.diff(times)
+
+        # We cannot check for values for lazy backends, so we cannot raise an error on
+        # timedelta < 0 for lazy backends. Instead, we set timedelta to nans
+        neg_mask = xp.any(self.timedelta <= 0)
+        if is_lazy_array(neg_mask):
+            self.timedelta = xp.where(neg_mask, xp.nan, self.timedelta)
+            self.times = xp.where(neg_mask, xp.nan, self.times)
+        elif xp.any(neg_mask):
+            raise ValueError("Times must be in strictly increasing order.")
+
+        self.rotations = rotations[:-1]
+        self.rotvecs = (self.rotations.inv() * rotations[1:]).as_rotvec()
+
+    def __call__(self, times: ArrayLike) -> Rotation:
+        """Interpolate rotations.
+
+        Compute the interpolated rotations at the given `times`.
+
+        Parameters
+        ----------
+        times : array_like
+            Times to compute the interpolations at. Can be a scalar or
+            1-dimensional.
+
+        Returns
+        -------
+        interpolated_rotation : `Rotation` instance
+            Object containing the rotations computed at given `times`.
+
+        """
+        xp = array_namespace(self.times)
+        device = xp_device(self.times)
+        # Clearly differentiate from self.times property
+        compute_times = xp.asarray(times, device=device, dtype=self.times.dtype)
+        if compute_times.ndim > 1:
+            raise ValueError("`times` must be at most 1-dimensional.")
+
+        single_time = compute_times.ndim == 0
+        compute_times = xpx.atleast_nd(compute_times, ndim=1, xp=xp)
+
+        # side = 'left' (default) excludes t_min.
+        ind = xp.searchsorted(self.times, compute_times) - 1
+        # Include t_min. Without this step, index for t_min equals -1
+        ind = xpx.at(ind, compute_times == self.times[0]).set(0)
+        # We cannot error out on invalid indices for jit compiled code. To not produce
+        # an index error, we set the index to 0 in case it is out of bounds, and later
+        # set the result to nan.
+        invalid_ind: Array = (ind < 0) | (ind > len(self.rotations) - 1)
+        if is_lazy_array(invalid_ind):
+            ind = xpx.at(ind, invalid_ind).set(0)
+        elif xp.any(invalid_ind):
+            raise ValueError(
+                f"Interpolation times must be within the range [{self.times[0]}, "
+                f"{self.times[-1]}], both inclusive."
+            )
+
+        alpha = (compute_times - self.times[ind]) / self.timedelta[ind]
+        alpha = xpx.at(alpha, invalid_ind).set(xp.nan)
+
+        # The array API does not support integer arrays + ellipsis indexing and won't
+        # stabilize this feature due to blockers in PyTorch. Therefore we need to
+        # construct the index for the last dimension manually.
+        # See https://github.com/scipy/scipy/pull/23249#discussion_r2198363047
+        result = self.rotations[ind] * Rotation.from_rotvec(
+            self.rotvecs[ind[:, None], xp.arange(3, device=device)] * alpha[:, None]
+        )
+
+        if single_time:
+            result = result[0]
+
+        return result
diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/transform/_rotation_cy.cpython-312-x86_64-linux-gnu.so b/venv/lib/python3.12/site-packages/scipy/spatial/transform/_rotation_cy.cpython-312-x86_64-linux-gnu.so
new file mode 100644
index 0000000000000000000000000000000000000000..e37b078b30a703fbf18b1866728a0d53144c5ed5
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/transform/_rotation_cy.cpython-312-x86_64-linux-gnu.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:bdb2a72c5d97e35e0a3cbf64d20c86c9fa7e81bcb1ddf8208cd7832daa3e9b39
+size 573960
diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/transform/_rotation_groups.py b/venv/lib/python3.12/site-packages/scipy/spatial/transform/_rotation_groups.py
new file mode 100644
index 0000000000000000000000000000000000000000..870e9b9e2b44bff56b8228a70607e29f8173accc
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/transform/_rotation_groups.py
@@ -0,0 +1,140 @@
+import numpy as np
+from scipy.constants import golden as phi
+
+
+def icosahedral(cls):
+    g1 = tetrahedral(cls).as_quat()
+    a = 0.5
+    b = 0.5 / phi
+    c = phi / 2
+    g2 = np.array([[+a, +b, +c, 0],
+                   [+a, +b, -c, 0],
+                   [+a, +c, 0, +b],
+                   [+a, +c, 0, -b],
+                   [+a, -b, +c, 0],
+                   [+a, -b, -c, 0],
+                   [+a, -c, 0, +b],
+                   [+a, -c, 0, -b],
+                   [+a, 0, +b, +c],
+                   [+a, 0, +b, -c],
+                   [+a, 0, -b, +c],
+                   [+a, 0, -b, -c],
+                   [+b, +a, 0, +c],
+                   [+b, +a, 0, -c],
+                   [+b, +c, +a, 0],
+                   [+b, +c, -a, 0],
+                   [+b, -a, 0, +c],
+                   [+b, -a, 0, -c],
+                   [+b, -c, +a, 0],
+                   [+b, -c, -a, 0],
+                   [+b, 0, +c, +a],
+                   [+b, 0, +c, -a],
+                   [+b, 0, -c, +a],
+                   [+b, 0, -c, -a],
+                   [+c, +a, +b, 0],
+                   [+c, +a, -b, 0],
+                   [+c, +b, 0, +a],
+                   [+c, +b, 0, -a],
+                   [+c, -a, +b, 0],
+                   [+c, -a, -b, 0],
+                   [+c, -b, 0, +a],
+                   [+c, -b, 0, -a],
+                   [+c, 0, +a, +b],
+                   [+c, 0, +a, -b],
+                   [+c, 0, -a, +b],
+                   [+c, 0, -a, -b],
+                   [0, +a, +c, +b],
+                   [0, +a, +c, -b],
+                   [0, +a, -c, +b],
+                   [0, +a, -c, -b],
+                   [0, +b, +a, +c],
+                   [0, +b, +a, -c],
+                   [0, +b, -a, +c],
+                   [0, +b, -a, -c],
+                   [0, +c, +b, +a],
+                   [0, +c, +b, -a],
+                   [0, +c, -b, +a],
+                   [0, +c, -b, -a]])
+    return cls.from_quat(np.concatenate((g1, g2)))
+
+
+def octahedral(cls):
+    g1 = tetrahedral(cls).as_quat()
+    c = np.sqrt(2) / 2
+    g2 = np.array([[+c, 0, 0, +c],
+                   [0, +c, 0, +c],
+                   [0, 0, +c, +c],
+                   [0, 0, -c, +c],
+                   [0, -c, 0, +c],
+                   [-c, 0, 0, +c],
+                   [0, +c, +c, 0],
+                   [0, -c, +c, 0],
+                   [+c, 0, +c, 0],
+                   [-c, 0, +c, 0],
+                   [+c, +c, 0, 0],
+                   [-c, +c, 0, 0]])
+    return cls.from_quat(np.concatenate((g1, g2)))
+
+
+def tetrahedral(cls):
+    g1 = np.eye(4)
+    c = 0.5
+    g2 = np.array([[c, -c, -c, +c],
+                   [c, -c, +c, +c],
+                   [c, +c, -c, +c],
+                   [c, +c, +c, +c],
+                   [c, -c, -c, -c],
+                   [c, -c, +c, -c],
+                   [c, +c, -c, -c],
+                   [c, +c, +c, -c]])
+    return cls.from_quat(np.concatenate((g1, g2)))
+
+
+def dicyclic(cls, n, axis=2):
+    g1 = cyclic(cls, n, axis).as_rotvec()
+
+    thetas = np.linspace(0, np.pi, n, endpoint=False)
+    rv = np.pi * np.vstack([np.zeros(n), np.cos(thetas), np.sin(thetas)]).T
+    g2 = np.roll(rv, axis, axis=1)
+    return cls.from_rotvec(np.concatenate((g1, g2)))
+
+
+def cyclic(cls, n, axis=2):
+    thetas = np.linspace(0, 2 * np.pi, n, endpoint=False)
+    rv = np.vstack([thetas, np.zeros(n), np.zeros(n)]).T
+    return cls.from_rotvec(np.roll(rv, axis, axis=1))
+
+
+def create_group(cls, group, axis='Z'):
+    if not isinstance(group, str):
+        raise ValueError("`group` argument must be a string")
+
+    permitted_axes = ['x', 'y', 'z', 'X', 'Y', 'Z']
+    if axis not in permitted_axes:
+        raise ValueError("`axis` must be one of " + ", ".join(permitted_axes))
+
+    if group in ['I', 'O', 'T']:
+        symbol = group
+        order = 1
+    elif group[:1] in ['C', 'D'] and group[1:].isdigit():
+        symbol = group[:1]
+        order = int(group[1:])
+    else:
+        raise ValueError("`group` must be one of 'I', 'O', 'T', 'Dn', 'Cn'")
+
+    if order < 1:
+        raise ValueError("Group order must be positive")
+
+    axis = 'xyz'.index(axis.lower())
+    if symbol == 'I':
+        return icosahedral(cls)
+    elif symbol == 'O':
+        return octahedral(cls)
+    elif symbol == 'T':
+        return tetrahedral(cls)
+    elif symbol == 'D':
+        return dicyclic(cls, order, axis=axis)
+    elif symbol == 'C':
+        return cyclic(cls, order, axis=axis)
+    else:
+        assert False
diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/transform/_rotation_spline.py b/venv/lib/python3.12/site-packages/scipy/spatial/transform/_rotation_spline.py
new file mode 100644
index 0000000000000000000000000000000000000000..9d6b99a5af898bff9ee9148b8712f861c54740fd
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/transform/_rotation_spline.py
@@ -0,0 +1,465 @@
+import numpy as np
+from scipy.linalg import solve_banded
+from ._rotation import Rotation
+
+
+def _create_skew_matrix(x):
+    """Create skew-symmetric matrices corresponding to vectors.
+
+    Parameters
+    ----------
+    x : ndarray, shape (n, 3)
+        Set of vectors.
+
+    Returns
+    -------
+    ndarray, shape (n, 3, 3)
+    """
+    result = np.zeros((len(x), 3, 3))
+    result[:, 0, 1] = -x[:, 2]
+    result[:, 0, 2] = x[:, 1]
+    result[:, 1, 0] = x[:, 2]
+    result[:, 1, 2] = -x[:, 0]
+    result[:, 2, 0] = -x[:, 1]
+    result[:, 2, 1] = x[:, 0]
+    return result
+
+
+def _matrix_vector_product_of_stacks(A, b):
+    """Compute the product of stack of matrices and vectors."""
+    return np.einsum("ijk,ik->ij", A, b)
+
+
+def _angular_rate_to_rotvec_dot_matrix(rotvecs):
+    """Compute matrices to transform angular rates to rot. vector derivatives.
+
+    The matrices depend on the current attitude represented as a rotation
+    vector.
+
+    Parameters
+    ----------
+    rotvecs : ndarray, shape (n, 3)
+        Set of rotation vectors.
+
+    Returns
+    -------
+    ndarray, shape (n, 3, 3)
+    """
+    norm = np.linalg.norm(rotvecs, axis=1)
+    k = np.empty_like(norm)
+
+    mask = norm > 1e-4
+    nm = norm[mask]
+    k[mask] = (1 - 0.5 * nm / np.tan(0.5 * nm)) / nm**2
+    mask = ~mask
+    nm = norm[mask]
+    k[mask] = 1/12 + 1/720 * nm**2
+
+    skew = _create_skew_matrix(rotvecs)
+
+    result = np.empty((len(rotvecs), 3, 3))
+    result[:] = np.identity(3)
+    result[:] += 0.5 * skew
+    result[:] += k[:, None, None] * np.matmul(skew, skew)
+
+    return result
+
+
+def _rotvec_dot_to_angular_rate_matrix(rotvecs):
+    """Compute matrices to transform rot. vector derivatives to angular rates.
+
+    The matrices depend on the current attitude represented as a rotation
+    vector.
+
+    Parameters
+    ----------
+    rotvecs : ndarray, shape (n, 3)
+        Set of rotation vectors.
+
+    Returns
+    -------
+    ndarray, shape (n, 3, 3)
+    """
+    norm = np.linalg.norm(rotvecs, axis=1)
+    k1 = np.empty_like(norm)
+    k2 = np.empty_like(norm)
+
+    mask = norm > 1e-4
+    nm = norm[mask]
+    k1[mask] = (1 - np.cos(nm)) / nm ** 2
+    k2[mask] = (nm - np.sin(nm)) / nm ** 3
+
+    mask = ~mask
+    nm = norm[mask]
+    k1[mask] = 0.5 - nm ** 2 / 24
+    k2[mask] = 1 / 6 - nm ** 2 / 120
+
+    skew = _create_skew_matrix(rotvecs)
+
+    result = np.empty((len(rotvecs), 3, 3))
+    result[:] = np.identity(3)
+    result[:] -= k1[:, None, None] * skew
+    result[:] += k2[:, None, None] * np.matmul(skew, skew)
+
+    return result
+
+
+def _angular_acceleration_nonlinear_term(rotvecs, rotvecs_dot):
+    """Compute the non-linear term in angular acceleration.
+
+    The angular acceleration contains a quadratic term with respect to
+    the derivative of the rotation vector. This function computes that.
+
+    Parameters
+    ----------
+    rotvecs : ndarray, shape (n, 3)
+        Set of rotation vectors.
+    rotvecs_dot : ndarray, shape (n, 3)
+        Set of rotation vector derivatives.
+
+    Returns
+    -------
+    ndarray, shape (n, 3)
+    """
+    norm = np.linalg.norm(rotvecs, axis=1)
+    dp = np.sum(rotvecs * rotvecs_dot, axis=1)
+    cp = np.cross(rotvecs, rotvecs_dot)
+    ccp = np.cross(rotvecs, cp)
+    dccp = np.cross(rotvecs_dot, cp)
+
+    k1 = np.empty_like(norm)
+    k2 = np.empty_like(norm)
+    k3 = np.empty_like(norm)
+
+    mask = norm > 1e-4
+    nm = norm[mask]
+    k1[mask] = (-nm * np.sin(nm) - 2 * (np.cos(nm) - 1)) / nm ** 4
+    k2[mask] = (-2 * nm + 3 * np.sin(nm) - nm * np.cos(nm)) / nm ** 5
+    k3[mask] = (nm - np.sin(nm)) / nm ** 3
+
+    mask = ~mask
+    nm = norm[mask]
+    k1[mask] = 1/12 - nm ** 2 / 180
+    k2[mask] = -1/60 + nm ** 2 / 12604
+    k3[mask] = 1/6 - nm ** 2 / 120
+
+    dp = dp[:, None]
+    k1 = k1[:, None]
+    k2 = k2[:, None]
+    k3 = k3[:, None]
+
+    return dp * (k1 * cp + k2 * ccp) + k3 * dccp
+
+
+def _compute_angular_rate(rotvecs, rotvecs_dot):
+    """Compute angular rates given rotation vectors and its derivatives.
+
+    Parameters
+    ----------
+    rotvecs : ndarray, shape (n, 3)
+        Set of rotation vectors.
+    rotvecs_dot : ndarray, shape (n, 3)
+        Set of rotation vector derivatives.
+
+    Returns
+    -------
+    ndarray, shape (n, 3)
+    """
+    return _matrix_vector_product_of_stacks(
+        _rotvec_dot_to_angular_rate_matrix(rotvecs), rotvecs_dot)
+
+
+def _compute_angular_acceleration(rotvecs, rotvecs_dot, rotvecs_dot_dot):
+    """Compute angular acceleration given rotation vector and its derivatives.
+
+    Parameters
+    ----------
+    rotvecs : ndarray, shape (n, 3)
+        Set of rotation vectors.
+    rotvecs_dot : ndarray, shape (n, 3)
+        Set of rotation vector derivatives.
+    rotvecs_dot_dot : ndarray, shape (n, 3)
+        Set of rotation vector second derivatives.
+
+    Returns
+    -------
+    ndarray, shape (n, 3)
+    """
+    return (_compute_angular_rate(rotvecs, rotvecs_dot_dot) +
+            _angular_acceleration_nonlinear_term(rotvecs, rotvecs_dot))
+
+
+def _create_block_3_diagonal_matrix(A, B, d):
+    """Create a 3-diagonal block matrix as banded.
+
+    The matrix has the following structure:
+
+        DB...
+        ADB..
+        .ADB.
+        ..ADB
+        ...AD
+
+    The blocks A, B and D are 3-by-3 matrices. The D matrices has the form
+    d * I.
+
+    Parameters
+    ----------
+    A : ndarray, shape (n, 3, 3)
+        Stack of A blocks.
+    B : ndarray, shape (n, 3, 3)
+        Stack of B blocks.
+    d : ndarray, shape (n + 1,)
+        Values for diagonal blocks.
+
+    Returns
+    -------
+    ndarray, shape (11, 3 * (n + 1))
+        Matrix in the banded form as used by `scipy.linalg.solve_banded`.
+    """
+    ind = np.arange(3)
+    ind_blocks = np.arange(len(A))
+
+    A_i = np.empty_like(A, dtype=int)
+    A_i[:] = ind[:, None]
+    A_i += 3 * (1 + ind_blocks[:, None, None])
+
+    A_j = np.empty_like(A, dtype=int)
+    A_j[:] = ind
+    A_j += 3 * ind_blocks[:, None, None]
+
+    B_i = np.empty_like(B, dtype=int)
+    B_i[:] = ind[:, None]
+    B_i += 3 * ind_blocks[:, None, None]
+
+    B_j = np.empty_like(B, dtype=int)
+    B_j[:] = ind
+    B_j += 3 * (1 + ind_blocks[:, None, None])
+
+    diag_i = diag_j = np.arange(3 * len(d))
+    i = np.hstack((A_i.ravel(), B_i.ravel(), diag_i))
+    j = np.hstack((A_j.ravel(), B_j.ravel(), diag_j))
+    values = np.hstack((A.ravel(), B.ravel(), np.repeat(d, 3)))
+
+    u = 5
+    l = 5
+    result = np.zeros((u + l + 1, 3 * len(d)))
+    result[u + i - j, j] = values
+    return result
+
+
+class RotationSpline:
+    """Interpolate rotations with continuous angular rate and acceleration.
+
+    The rotation vectors between each consecutive orientation are cubic
+    functions of time and it is guaranteed that angular rate and acceleration
+    are continuous. Such interpolation are analogous to cubic spline
+    interpolation.
+
+    Refer to [1]_ for math and implementation details.
+
+    Parameters
+    ----------
+    times : array_like, shape (N,)
+        Times of the known rotations. At least 2 times must be specified.
+    rotations : `Rotation` instance
+        Rotations to perform the interpolation between. Must contain N
+        rotations.
+
+    Methods
+    -------
+    __call__
+
+    References
+    ----------
+    .. [1] `Smooth Attitude Interpolation
+            <https://github.com/scipy/scipy/files/2932755/attitude_interpolation.pdf>`_
+
+    Examples
+    --------
+    >>> from scipy.spatial.transform import Rotation, RotationSpline
+    >>> import numpy as np
+
+    Define the sequence of times and rotations from the Euler angles:
+
+    >>> times = [0, 10, 20, 40]
+    >>> angles = [[-10, 20, 30], [0, 15, 40], [-30, 45, 30], [20, 45, 90]]
+    >>> rotations = Rotation.from_euler('XYZ', angles, degrees=True)
+
+    Create the interpolator object:
+
+    >>> spline = RotationSpline(times, rotations)
+
+    Interpolate the Euler angles, angular rate and acceleration:
+
+    >>> angular_rate = np.rad2deg(spline(times, 1))
+    >>> angular_acceleration = np.rad2deg(spline(times, 2))
+    >>> times_plot = np.linspace(times[0], times[-1], 100)
+    >>> angles_plot = spline(times_plot).as_euler('XYZ', degrees=True)
+    >>> angular_rate_plot = np.rad2deg(spline(times_plot, 1))
+    >>> angular_acceleration_plot = np.rad2deg(spline(times_plot, 2))
+
+    On this plot you see that Euler angles are continuous and smooth:
+
+    >>> import matplotlib.pyplot as plt
+    >>> plt.plot(times_plot, angles_plot)
+    >>> plt.plot(times, angles, 'x')
+    >>> plt.title("Euler angles")
+    >>> plt.show()
+
+    The angular rate is also smooth:
+
+    >>> plt.plot(times_plot, angular_rate_plot)
+    >>> plt.plot(times, angular_rate, 'x')
+    >>> plt.title("Angular rate")
+    >>> plt.show()
+
+    The angular acceleration is continuous, but not smooth. Also note that
+    the angular acceleration is not a piecewise-linear function, because
+    it is different from the second derivative of the rotation vector (which
+    is a piecewise-linear function as in the cubic spline).
+
+    >>> plt.plot(times_plot, angular_acceleration_plot)
+    >>> plt.plot(times, angular_acceleration, 'x')
+    >>> plt.title("Angular acceleration")
+    >>> plt.show()
+    """
+    # Parameters for the solver for angular rate.
+    MAX_ITER = 10
+    TOL = 1e-9
+
+    def _solve_for_angular_rates(self, dt, angular_rates, rotvecs):
+        angular_rate_first = angular_rates[0].copy()
+
+        A = _angular_rate_to_rotvec_dot_matrix(rotvecs)
+        A_inv = _rotvec_dot_to_angular_rate_matrix(rotvecs)
+        M = _create_block_3_diagonal_matrix(
+            2 * A_inv[1:-1] / dt[1:-1, None, None],
+            2 * A[1:-1] / dt[1:-1, None, None],
+            4 * (1 / dt[:-1] + 1 / dt[1:]))
+
+        b0 = 6 * (rotvecs[:-1] * dt[:-1, None] ** -2 +
+                  rotvecs[1:] * dt[1:, None] ** -2)
+        b0[0] -= 2 / dt[0] * A_inv[0].dot(angular_rate_first)
+        b0[-1] -= 2 / dt[-1] * A[-1].dot(angular_rates[-1])
+
+        for iteration in range(self.MAX_ITER):
+            rotvecs_dot = _matrix_vector_product_of_stacks(A, angular_rates)
+            delta_beta = _angular_acceleration_nonlinear_term(
+                rotvecs[:-1], rotvecs_dot[:-1])
+            b = b0 - delta_beta
+            angular_rates_new = solve_banded((5, 5), M, b.ravel())
+            angular_rates_new = angular_rates_new.reshape((-1, 3))
+
+            delta = np.abs(angular_rates_new - angular_rates[:-1])
+            angular_rates[:-1] = angular_rates_new
+            if np.all(delta < self.TOL * (1 + np.abs(angular_rates_new))):
+                break
+
+        rotvecs_dot = _matrix_vector_product_of_stacks(A, angular_rates)
+        angular_rates = np.vstack((angular_rate_first, angular_rates[:-1]))
+
+        return angular_rates, rotvecs_dot
+
+    def __init__(self, times, rotations):
+        from scipy.interpolate import PPoly
+
+        if rotations.single:
+            raise ValueError("`rotations` must be a sequence of rotations.")
+
+        if rotations.as_quat().ndim > 2:
+            raise ValueError(
+                "Rotations with more than 1 leading dimension are not supported."
+            )
+
+        if len(rotations) == 1:
+            raise ValueError("`rotations` must contain at least 2 rotations.")
+
+        times = np.asarray(times, dtype=float)
+        if times.ndim != 1:
+            raise ValueError("`times` must be 1-dimensional.")
+
+        if len(times) != len(rotations):
+            raise ValueError("Expected number of rotations to be equal to "
+                             "number of timestamps given, "
+                             f"got {len(rotations)} rotations "
+                             f"and {len(times)} timestamps.")
+
+        dt = np.diff(times)
+        if np.any(dt <= 0):
+            raise ValueError("Values in `times` must be in a strictly "
+                             "increasing order.")
+
+        rotvecs = (rotations[:-1].inv() * rotations[1:]).as_rotvec()
+        angular_rates = rotvecs / dt[:, None]
+
+        if len(rotations) == 2:
+            rotvecs_dot = angular_rates
+        else:
+            angular_rates, rotvecs_dot = self._solve_for_angular_rates(
+                dt, angular_rates, rotvecs)
+
+        dt = dt[:, None]
+        coeff = np.empty((4, len(times) - 1, 3))
+        coeff[0] = (-2 * rotvecs + dt * angular_rates
+                    + dt * rotvecs_dot) / dt ** 3
+        coeff[1] = (3 * rotvecs - 2 * dt * angular_rates
+                    - dt * rotvecs_dot) / dt ** 2
+        coeff[2] = angular_rates
+        coeff[3] = 0
+
+        self.times = times
+        self.rotations = rotations
+        self.interpolator = PPoly(coeff, times)
+
+    def __call__(self, times, order=0):
+        """Compute interpolated values.
+
+        Parameters
+        ----------
+        times : float or array_like
+            Times of interest.
+        order : {0, 1, 2}, optional
+            Order of differentiation:
+
+                * 0 (default) : return Rotation
+                * 1 : return the angular rate in rad/sec
+                * 2 : return the angular acceleration in rad/sec/sec
+
+        Returns
+        -------
+        Interpolated Rotation, angular rate or acceleration.
+        """
+        if order not in [0, 1, 2]:
+            raise ValueError("`order` must be 0, 1 or 2.")
+
+        times = np.asarray(times, dtype=float)
+        if times.ndim > 1:
+            raise ValueError("`times` must be at most 1-dimensional.")
+
+        singe_time = times.ndim == 0
+        times = np.atleast_1d(times)
+
+        rotvecs = self.interpolator(times)
+        if order == 0:
+            index = np.searchsorted(self.times, times, side='right')
+            index -= 1
+            index[index < 0] = 0
+            n_segments = len(self.times) - 1
+            index[index > n_segments - 1] = n_segments - 1
+            result = self.rotations[index] * Rotation.from_rotvec(rotvecs)
+        elif order == 1:
+            rotvecs_dot = self.interpolator(times, 1)
+            result = _compute_angular_rate(rotvecs, rotvecs_dot)
+        elif order == 2:
+            rotvecs_dot = self.interpolator(times, 1)
+            rotvecs_dot_dot = self.interpolator(times, 2)
+            result = _compute_angular_acceleration(rotvecs, rotvecs_dot,
+                                                   rotvecs_dot_dot)
+        else:
+            assert False
+
+        if singe_time:
+            result = result[0]
+
+        return result
diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/transform/_rotation_xp.py b/venv/lib/python3.12/site-packages/scipy/spatial/transform/_rotation_xp.py
new file mode 100644
index 0000000000000000000000000000000000000000..5eea00637acab3d8d914ae3bbd3bdae2a87eb9c8
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/transform/_rotation_xp.py
@@ -0,0 +1,1140 @@
+"""Array API backend for the `Rotation` class.
+
+This module provides generic, functional implementations of the `Rotation` class methods
+that work with any Array API-compatible backend.
+"""
+
+# Parts of the implementation are adapted from the cython backend and
+# https://github.com/jax-ml/jax/blob/d695aa4c63ffcebefce52794427c46bad576680c/jax/_src/scipy/spatial/transform.py.
+import re
+import warnings
+from types import EllipsisType
+
+import numpy as np
+from scipy._lib._array_api import (
+    array_namespace,
+    Array,
+    ArrayLike,
+    is_lazy_array,
+    xp_vector_norm,
+    xp_result_type,
+    xp_promote,
+    is_jax,
+)
+from scipy._lib._util import broadcastable
+from scipy._external.array_api_compat import device as xp_device
+from scipy._external.array_api_compat import is_array_api_obj
+import scipy._external.array_api_extra as xpx
+
+# mypy: disable-error-code=index
+# mypy: disable-error-code=operator
+# mypy: disable-error-code=union-attr
+
+def from_quat(
+    quat: Array,
+    normalize: bool = True,
+    copy: bool = True,
+    *,
+    scalar_first: bool = False,
+) -> Array:
+    xp = array_namespace(quat)
+    if scalar_first:
+        quat = xp.roll(quat, -1, axis=-1)
+    # Normalize will always copy, so we avoid the extra copy if we normalize
+    if copy and not normalize:
+        quat = xp.asarray(quat, copy=True)
+    if normalize:
+        quat = _normalize_quaternion(quat)
+    return quat
+
+
+def from_matrix(matrix: Array, assume_valid: bool = False) -> Array:
+    xp = array_namespace(matrix)
+    device = xp_device(matrix)
+
+    if not assume_valid:
+        mask = xp.linalg.det(matrix) <= 0
+        lazy = is_lazy_array(mask)
+        # Only non-lazy backends raise an error for non-positive determinants.
+        if not lazy and xp.any(mask):
+            ind = int(xp.nonzero(xpx.atleast_nd(mask, ndim=1, xp=xp))[0][0])
+            raise ValueError(
+                "Non-positive determinant (left-handed or null coordinate frame) in "
+                f"rotation matrix {ind}: {matrix[ind, ...]}."
+            )
+        elif lazy:
+            matrix = xp.where(mask[..., None, None], xp.nan, matrix)
+
+        gramians = matrix @ xp.matrix_transpose(matrix)
+        eye = xp.eye(3, dtype=matrix.dtype, device=device)
+        is_orthogonal = xp.all(
+            xpx.isclose(gramians, eye, atol=1e-12, xp=xp), axis=(-2, -1)
+        )
+
+        if lazy:
+            # Lazy backends do not support non-concrete boolean indexing or any form of
+            # computation without statically known shapes, so we always compute SVD and
+            # use xp.where to select the result.
+            U, _, Vt = xp.linalg.svd(matrix, full_matrices=False)
+            matrix = xp.where(is_orthogonal[..., None, None], matrix, U @ Vt)
+        elif not xp.all(is_orthogonal):
+            # For eager frameworks, only compute SVD if needed.
+            is_not_orthogonal = ~is_orthogonal
+            U, _, Vt = xp.linalg.svd(matrix[is_not_orthogonal], full_matrices=False)
+            matrix = xpx.at(matrix)[is_not_orthogonal].set(U @ Vt)
+
+    return _from_matrix_orthogonal(matrix)
+
+
+def _from_matrix_orthogonal(matrix: Array) -> Array:
+    """Convert known orthogonal rotation matrix to quaternion"""
+    xp = array_namespace(matrix)
+    device = xp_device(matrix)
+
+    matrix_trace = matrix[..., 0, 0] + matrix[..., 1, 1] + matrix[..., 2, 2]
+    decision = xp.stack(
+        [matrix[..., 0, 0], matrix[..., 1, 1], matrix[..., 2, 2], matrix_trace],
+        axis=-1,
+    )
+    choice = xp.argmax(decision, axis=-1, keepdims=True)
+    quat = xp.empty((*matrix.shape[:-2], 4), dtype=matrix.dtype, device=device)
+
+    # The Array API does not support mixing integer indexing with ellipsis, so we cannot
+    # follow the same pattern as the cython backend. Instead, we compute each case
+    # explicitly and assemble the final result with `xp.where`.
+    # TODO: Revisit this implementation if the array API supports mixed integer and
+    # ellipsis indexing.
+
+    # Case 0
+    quat_0 = xp.stack(
+        [
+            1 - matrix_trace[...] + 2 * matrix[..., 0, 0],
+            matrix[..., 1, 0] + matrix[..., 0, 1],
+            matrix[..., 2, 0] + matrix[..., 0, 2],
+            matrix[..., 2, 1] - matrix[..., 1, 2],
+        ],
+        axis=-1,
+    )
+    quat = xp.where(choice == 0, quat_0, quat)
+
+    # Case 1
+    quat_1 = xp.stack(
+        [
+            matrix[..., 1, 0] + matrix[..., 0, 1],
+            1 - matrix_trace[...] + 2 * matrix[..., 1, 1],
+            matrix[..., 2, 1] + matrix[..., 1, 2],
+            matrix[..., 0, 2] - matrix[..., 2, 0],
+        ],
+        axis=-1,
+    )
+    quat = xp.where(choice == 1, quat_1, quat)
+
+    # Case 2
+    quat_2 = xp.stack(
+        [
+            matrix[..., 2, 0] + matrix[..., 0, 2],
+            matrix[..., 2, 1] + matrix[..., 1, 2],
+            1 - matrix_trace[...] + 2 * matrix[..., 2, 2],
+            matrix[..., 1, 0] - matrix[..., 0, 1],
+        ],
+        axis=-1,
+    )
+    quat = xp.where(choice == 2, quat_2, quat)
+
+    # Case 3
+    quat_3 = xp.stack(
+        [
+            matrix[..., 2, 1] - matrix[..., 1, 2],
+            matrix[..., 0, 2] - matrix[..., 2, 0],
+            matrix[..., 1, 0] - matrix[..., 0, 1],
+            1 + matrix_trace[...],
+        ],
+        axis=-1,
+    )
+    quat = xp.where(choice == 3, quat_3, quat)
+
+    return _normalize_quaternion(quat)
+
+
+def from_rotvec(rotvec: Array, degrees: bool = False) -> Array:
+    xp = array_namespace(rotvec)
+    if rotvec.shape[-1] != 3:
+        raise ValueError(
+            f"Expected `rot_vec` to have shape (..., 3), got {rotvec.shape}"
+        )
+    rotvec = _deg2rad(rotvec) if degrees else rotvec
+
+    angle = xp_vector_norm(rotvec, axis=-1, keepdims=True, xp=xp)
+    small_angle = angle <= 1e-3
+    angle2 = angle**2
+    small_scale = 0.5 - angle2 / 48 + angle2**2 / 3840
+    # We need to handle the case where angle is 0 to avoid division by zero. We use the
+    # value of the Taylor series approximation, but non-branching operations require
+    # that we still divide by the angle. Since we do not use the result where the angle
+    # is close to 0, this is safe.
+    div_angle = angle + xp.asarray(small_angle, dtype=angle.dtype)
+    large_scale = xp.sin(angle / 2) / div_angle
+    scale = xp.where(small_angle, small_scale, large_scale)
+    quat = xp.concat([rotvec * scale, xp.cos(angle / 2)], axis=-1)
+    return quat
+
+
+def from_mrp(mrp: Array) -> Array:
+    xp = array_namespace(mrp)
+    if mrp.shape[-1] != 3:
+        raise ValueError(f"Expected `mrp` to have shape (..., 3), got {mrp.shape}")
+    mrp2_plus_1 = xp.linalg.vecdot(mrp, mrp, axis=-1)[..., None] + 1
+    q_no_norm = xp.concat([2 * mrp[..., :3], (2 - mrp2_plus_1)], axis=-1)
+    quat = q_no_norm / mrp2_plus_1
+    return quat
+
+
+def from_euler(seq: str, angles: Array, degrees: bool = False) -> Array:
+    xp = array_namespace(angles)
+    num_axes = len(seq)
+    if num_axes < 1 or num_axes > 3:
+        raise ValueError(
+            "Expected axis specification to be a non-empty "
+            f"string of up to 3 characters, got {seq}"
+        )
+
+    intrinsic = re.match(r"^[XYZ]{1,3}$", seq) is not None
+    extrinsic = re.match(r"^[xyz]{1,3}$", seq) is not None
+    if not (intrinsic or extrinsic):
+        raise ValueError(
+            "Expected axes from `seq` to be from ['x', 'y', "
+            f"'z'] or ['X', 'Y', 'Z'], got {seq}"
+        )
+
+    if any(seq[i] == seq[i + 1] for i in range(num_axes - 1)):
+        raise ValueError(f"Expected consecutive axes to be different, got {seq}")
+
+    if degrees:
+        angles = _deg2rad(angles)
+
+    angles = xpx.atleast_nd(angles, ndim=1, xp=xp)
+
+    if angles.shape[-1] != num_axes:
+        raise ValueError(
+            "Expected last dimension of `angles` to match number of sequence axes "
+            f"specified, got {angles.shape[-1]}."
+        )
+    axes = [_elementary_basis_index(x) for x in seq.lower()]
+    q = _elementary_quat_compose(axes, angles, intrinsic)
+    return q
+
+
+def from_davenport(
+    axes: Array, order: str, angles: Array, degrees: bool = False
+) -> Array:
+    xp = array_namespace(axes)
+    device = xp_device(axes)
+    if order in ["e", "extrinsic"]:  # Must be static, cannot be jitted
+        extrinsic = True
+    elif order in ["i", "intrinsic"]:
+        extrinsic = False
+    else:
+        raise ValueError(
+            "order should be 'e'/'extrinsic' for extrinsic sequences or 'i'/"
+            f"'intrinsic' for intrinsic sequences, got {order}"
+        )
+
+    if axes.shape[-1] != 3:
+        raise ValueError("Axes must be vectors of length 3.")
+
+    axes = xpx.atleast_nd(axes, ndim=2, xp=xp)
+    angles = xpx.atleast_nd(angles, ndim=1, xp=xp) 
+    num_axes = axes.shape[-2]
+    if num_axes < 1 or num_axes > 3:
+        raise ValueError(f"Expected up to 3 axes, got {num_axes}")
+
+    axes = axes / xp_vector_norm(axes, axis=-1, keepdims=True, xp=xp)
+
+    # Check if axes are orthogonal. Shape checks also work for lazy backends.
+    axes_not_orthogonal = xp.zeros(axes.shape[:-2], dtype=xp.bool, device=device)
+    if num_axes > 1:
+        # Cannot be True yet, so we do not need to use xp.logical_or
+        axes_not_orthogonal = axes_not_orthogonal | (
+            xp.abs(xp.vecdot(axes[..., 0, :], axes[..., 1, :])) > 1e-7
+        )
+    if num_axes > 2:
+        axes_not_orthogonal = axes_not_orthogonal | (
+            xp.abs(xp.vecdot(axes[..., 1, :], axes[..., 2, :])) > 1e-7
+        )
+    if not is_lazy_array(axes_not_orthogonal) and xp.any(axes_not_orthogonal):
+        raise ValueError("Consecutive axes must be orthogonal.")
+    else:
+        axes = xp.where(axes_not_orthogonal[..., None, None], xp.nan, axes)
+
+    if degrees:
+        angles = _deg2rad(angles)
+
+    if (
+        not broadcastable(axes.shape[:-1], angles.shape)
+        or axes.shape[-2] != angles.shape[-1]
+    ):
+        raise ValueError(
+            f"Expected `angles` to match number of axes, got {angles.shape} angles "
+            f"and {axes.shape} axes."
+        )
+
+    q_shape = angles.shape[:-1] + (4,)
+    q = xp.zeros(q_shape, dtype=angles.dtype, device=xp_device(angles))
+    q = xpx.at(q)[..., 3].set(1)
+
+    for i in range(num_axes):
+        qi = from_rotvec(angles[..., i, None] * axes[..., i, :])
+        q = compose_quat(qi, q) if extrinsic else compose_quat(q, qi)
+    return q
+
+
+def as_quat(
+    quat: Array, canonical: bool = False, *, scalar_first: bool = False
+) -> Array:
+    xp = array_namespace(quat)
+    if canonical:
+        quat = _quat_canonical(quat)
+    if scalar_first:
+        quat = xp.roll(quat, 1, axis=-1)
+    return quat
+
+
+def as_matrix(quat: Array) -> Array:
+    xp = array_namespace(quat)
+    x = quat[..., 0]
+    y = quat[..., 1]
+    z = quat[..., 2]
+    w = quat[..., 3]
+
+    x2 = x * x
+    y2 = y * y
+    z2 = z * z
+    w2 = w * w
+
+    xy = x * y
+    zw = z * w
+    xz = x * z
+    yw = y * w
+    yz = y * z
+    xw = x * w
+
+    matrix_elements = [
+        x2 - y2 - z2 + w2,
+        2 * (xy - zw),
+        2 * (xz + yw),
+        2 * (xy + zw),
+        -x2 + y2 - z2 + w2,
+        2 * (yz - xw),
+        2 * (xz - yw),
+        2 * (yz + xw),
+        -x2 - y2 + z2 + w2,
+    ]
+    matrix = xp.reshape(xp.stack(matrix_elements, axis=-1), (*quat.shape[:-1], 3, 3))
+    return matrix
+
+
+def as_rotvec(quat: Array, degrees: bool = False) -> Array:
+    xp = array_namespace(quat)
+    quat = _quat_canonical(quat)
+    ax_norm = xp_vector_norm(quat[..., :3], axis=-1, keepdims=True, xp=xp)
+    angle = 2 * xp.atan2(ax_norm, quat[..., 3][..., None])
+    small_angle = angle <= 1e-3
+    angle2 = angle**2
+    small_scale = 2 + angle2 / 12 + 7 * angle2**2 / 2880
+    # We need to handle the case where sin(angle/2) is 0 to avoid division by zero. We
+    # use the value of the Taylor series approximation, but non-branching operations
+    # require that we still divide by the sin. Since we do not use the result where the
+    # angle is close to 0, adding one to the sin where we discard the result is safe.
+    div_sin = xp.sin(angle / 2.0) + xp.asarray(small_angle, dtype=angle.dtype)
+    large_scale = angle / div_sin
+    scale = xp.where(small_angle, small_scale, large_scale)
+    if degrees:
+        scale = _rad2deg(scale)
+    rotvec = scale * quat[..., :3]
+    return rotvec
+
+
+def as_mrp(quat: Array) -> Array:
+    xp = array_namespace(quat)
+    one = xp.asarray(1.0, device=xp_device(quat), dtype=quat.dtype)
+    sign = xp.where(quat[..., 3, None] < 0, -1, one)
+    denominator = 1.0 + sign * quat[..., 3, None]
+    return sign * quat[..., :3] / denominator
+
+
+def as_euler(
+    quat: Array, seq: str, degrees: bool = False, *, suppress_warnings: bool = False
+) -> Array:
+    xp = array_namespace(quat)
+
+    # Sanitize the sequence
+    if len(seq) != 3:
+        raise ValueError(f"Expected 3 axes, got {seq}.")
+    intrinsic = re.match(r"^[XYZ]{1,3}$", seq) is not None
+    extrinsic = re.match(r"^[xyz]{1,3}$", seq) is not None
+    if not (intrinsic or extrinsic):
+        raise ValueError(
+            "Expected axes from `seq` to be from ['x', 'y', 'z'] or ['X', 'Y', 'Z'], "
+            f"got {seq}"
+        )
+    if any(seq[i] == seq[i + 1] for i in range(2)):
+        raise ValueError(f"Expected consecutive axes to be different, got {seq}")
+
+    device = xp_device(quat)
+    axes = [_elementary_basis_index(x) for x in seq.lower()]
+    axes = axes if extrinsic else axes[::-1]
+    i, j, k = axes
+    symmetric = i == k
+    k = 3 - i - j if symmetric else k
+
+    mask = xp.asarray(symmetric, device=device)
+    sign = xp.asarray((i - j) * (j - k) * (k - i) // 2, dtype=quat.dtype, device=device)
+    # Permute quaternion elements
+    a = xp.where(mask, quat[..., 3], quat[..., 3] - quat[..., j])
+    b = xp.where(mask, quat[..., i], quat[..., i] + quat[..., k] * sign)
+    c = xp.where(mask, quat[..., j], quat[..., j] + quat[..., 3])
+    d = xp.where(mask, quat[..., k] * sign, quat[..., k] * sign - quat[..., i])
+
+    angles = _get_angles(
+        extrinsic, symmetric, sign, xp.pi / 2, a, b, c, d, suppress_warnings
+    )
+    return _rad2deg(angles) if degrees else angles
+
+
+def as_davenport(
+    quat: Array,
+    axes: Array,
+    order: str,
+    degrees: bool = False,
+    *,
+    suppress_warnings: bool = False,
+) -> Array:
+    xp = array_namespace(quat)
+
+    # Check argument validity
+    if order in ["e", "extrinsic"]:
+        extrinsic = True
+    elif order in ["i", "intrinsic"]:
+        extrinsic = False
+    else:
+        raise ValueError(
+            "order should be 'e'/'extrinsic' for extrinsic sequences or 'i'/'intrinsic'"
+            f" for intrinsic sequences, got {order}"
+        )
+    if axes.shape[-2] != 3:
+        raise ValueError(f"Expected 3 axes, got {axes.shape}.")
+    if axes.shape[-1] != 3:
+        raise ValueError("Axes must be vectors of length 3.")
+    if not broadcastable(axes.shape[:-2], quat.shape[:-1]):
+        raise ValueError(
+            f"Expected `axes` to match number of rotations, got {axes.shape} axes "
+            f"and {quat.shape} rotations."
+        )
+
+    # normalize axes
+    axes = axes / xp_vector_norm(axes, axis=-1, keepdims=True, xp=xp)
+    vdot_ax0_ax1 = xp.vecdot(axes[..., 0, :], axes[..., 1, :])
+    vdot_ax1_ax2 = xp.vecdot(axes[..., 1, :], axes[..., 2, :])
+    is_invalid = (vdot_ax0_ax1 >= 1e-7) | (vdot_ax1_ax2 >= 1e-7)
+    if is_lazy_array(is_invalid):
+        axes = xp.where(is_invalid[..., None, None], xp.nan, axes)
+    elif xp.any(is_invalid):
+        raise ValueError("Consecutive axes must be orthogonal.")
+
+    angles = _compute_davenport_from_quat(
+        quat,
+        axes[..., 0, :],
+        axes[..., 1, :],
+        axes[..., 2, :],
+        extrinsic,
+        suppress_warnings,
+    )
+    if degrees:
+        angles = _rad2deg(angles)
+    return angles
+
+
+def inv(quat: Array) -> Array:
+    return xpx.at(quat)[..., :3].multiply(-1, copy=True)
+
+
+def magnitude(quat: Array) -> Array:
+    xp = array_namespace(quat)
+    sin_q = xp_vector_norm(quat[..., :3], axis=-1, xp=xp)
+    cos_q = xp.abs(quat[..., 3])
+    angles = 2 * xp.atan2(sin_q, cos_q)
+    return angles
+
+
+def approx_equal(
+    quat: Array, other: Array, atol: float | None = None, degrees: bool = False
+) -> Array:
+    if atol is None:
+        if degrees:
+            warnings.warn(
+                "atol must be set to use the degrees flag, defaulting to 1e-8 radians.",
+                stacklevel=2,
+            )
+        atol = 1e-8
+    elif degrees:
+        atol = _deg2rad(atol)
+
+    if not broadcastable(quat.shape, other.shape):
+        raise ValueError(
+            f"Expected broadcastable shapes in both rotations, got {quat.shape[:-1]} "
+            f"rotations in first and {other.shape[:-1]} rotations in second object."
+        )
+
+    quat_result = compose_quat(other, inv(quat))
+    angles = magnitude(quat_result)
+    return angles < atol
+
+
+def mean(
+    quat: Array,
+    weights: ArrayLike | None = None,
+    axis: None | int | tuple[int, ...] = None,
+) -> Array:
+    xp = array_namespace(quat)
+    device = xp_device(quat)
+    dtype = xp_result_type(quat, force_floating=True, xp=xp)
+    if quat.shape[0] == 0:
+        raise ValueError("Mean of an empty rotation set is undefined.")
+    # Axis logic: For None, we reduce over all axes. For int, we only reduce over that
+    # axis. For tuple, we reduce over all specified axes.
+    all_axes = tuple(range(quat.ndim - 1))
+    if axis is None:
+        axis = all_axes
+    elif isinstance(axis, int):
+        axis = (axis,)
+    if not isinstance(axis, tuple):
+        raise ValueError("`axis` must be None, int, or tuple of ints.")
+    # Ensure all axes are within bounds
+    if axis != () and (min(axis) < -(quat.ndim - 1) or max(axis) > (quat.ndim - 2)):
+        raise ValueError(
+            f"axis {axis} is out of bounds for rotation with shape {quat.shape[:-1]}."
+        )
+    # Ensure all axes are positive and unique
+    axis = tuple(sorted(set(x % (quat.ndim - 1) for x in axis)))
+
+    lazy = is_lazy_array(quat)
+    # Branching code is okay for checks that include meta info such as shapes and types
+    quat_expand = quat[..., None, :]
+    if weights is None:
+        K = xp.matrix_transpose(quat_expand) @ quat_expand
+    else:
+        weights = xp.asarray(weights, dtype=dtype, device=device)
+        neg_weights = weights < 0
+        if not lazy and xp.any(neg_weights):
+            raise ValueError("`weights` must be non-negative.")
+        elif lazy:
+            # We cannot check for negative weights because jit code needs to be
+            # non-branching. We return NaN instead
+            weights = xp.where(neg_weights, xp.nan, weights)
+
+        if not broadcastable(quat.shape[:-1], weights.shape):
+            raise ValueError(
+                "Expected `weights` to be broadcastable to rotation shape, got shape "
+                f"{weights.shape} for {quat.shape[:-1]} rotations."
+            )
+
+        # Make sure we can transpose quat
+        weighted_quat = weights[..., None, None] * quat_expand
+        K = xp.matrix_transpose(weighted_quat) @ quat_expand
+
+    # Move reduction axes to the end
+    keep_axes = tuple(i for i in all_axes if i not in axis)
+    axes_order = keep_axes + axis
+    K_reordered = xp.moveaxis(K, axes_order, all_axes)
+    # Reshape to flatten reduction axes
+    new_shape = K_reordered.shape[: len(keep_axes)] + (-1, 4, 4)
+    K = xp.mean(xp.reshape(K_reordered, new_shape), axis=-3)
+    _, v = xp.linalg.eigh(K)
+    return v[..., -1]
+
+
+def reduce(
+    quat: Array,
+    left: Array | None = None,
+    right: Array | None = None,
+) -> tuple[Array, Array | None, Array | None]:
+    if left is None and right is None:
+        return quat, None, None
+    # DECISION: We cannot have variable number of return arguments for jit compiled
+    # functions. We therefore always return the indices, and filter out later.
+    # TOOD: Properly support broadcasting.
+    xp = array_namespace(quat)
+    quat = xpx.atleast_nd(quat, ndim=2, xp=xp)
+    if left is None:
+        left = xp.ones_like(quat)
+    if right is None:
+        right = xp.ones_like(quat)
+
+    # We want to calculate the real components of q = l * p * r. It can
+    # be shown that:
+    #     qs = ls * ps * rs - ls * dot(pv, rv) - ps * dot(lv, rv)
+    #          - rs * dot(lv, pv) - dot(cross(lv, pv), rv)
+    # where ls and lv denote the scalar and vector components of l.
+
+    p = quat
+    ps, pv = _split_rotation(p, xp)
+    ls, lv = _split_rotation(left, xp)
+    rs, rv = _split_rotation(right, xp)
+
+    # Compute each term without einsum (not accessible in the Array API)
+    # First term: np.einsum("i,j,k", ls, ps, rs)
+    term1 = ls[..., :, None, None] * ps[..., None, :, None] * rs[..., None, None, :]
+    # Second term: np.einsum('i,jx,kx', ls, pv, rv)
+    prv = xp.sum(pv[..., :, None, :] * rv[..., None, :, :], axis=-1)
+    term2 = ls[..., :, None, None] * prv[..., None, :, :]
+    # Third term: np.einsum('ix,j,kx', lv, ps, rv)
+    lrv = xp.sum(lv[..., :, None, :] * rv[..., None, :, :], axis=-1)
+    term3 = ps[..., None, :, None] * lrv[..., :, None, :]
+    # Fourth term: np.einsum('ix,jx,k', lv, pv, rs)
+    lpv = xp.sum(lv[..., :, None, :] * pv[..., None, :, :], axis=-1)
+    term4 = rs[..., None, None, :] * lpv[..., :, :, None]
+    # Fifth term: np.einsum('xyz,ix,jy,kz', e, lv, pv, rv). We want to avoid expanding
+    # the einsum into a 6D tensor to avoid excessive memory usage. Instead, we compute
+    # the cross product between lv and pv and then compute the dot product with rv.
+    # First compute cross products between lv and pv
+    lv_expanded = lv[..., :, None, :]
+    pv_expanded = pv[..., None, :, :]
+    cross_lp = xp.linalg.cross(lv_expanded, pv_expanded)
+    # Then compute dot product with rv
+    term5 = xp.sum(cross_lp[..., :, :, None, :] * rv[..., None, None, :, :], axis=-1)
+    # Combine all terms with proper shape alignment
+    qs = xp.abs(term1 - term2 - term3 - term4 - term5)
+    qs = xp.reshape(xp.moveaxis(qs, 1, 0), (qs.shape[1], -1))
+
+    # Find best indices from scalar components
+    max_ind = xp.argmax(xp.reshape(qs, (qs.shape[0], -1)), axis=1)
+    left_best = max_ind // rv.shape[0]
+    right_best = max_ind % rv.shape[0]
+    # Array API limitation: Integer index arrays are only allowed with integer indices
+    # TODO: Can we somehow avoid this?
+    all_idx = xp.reshape(xp.arange(left.shape[-1]), (1, -1))
+    left_idx = xp.reshape(left_best, (-1, 1))
+    left = left[left_idx, all_idx]
+    right_idx = xp.reshape(right_best, (-1, 1))
+    right = right[right_idx, all_idx]
+
+    # Reduce the rotation using the best indices
+    reduced = compose_quat(left, compose_quat(p, right))
+
+    if left is None:
+        left_best = None
+    if right is None:
+        right_best = None
+    return reduced, left_best, right_best
+
+
+def apply(quat: Array, points: Array, inverse: bool = False) -> Array:
+    xp = array_namespace(quat)
+    mat = as_matrix(quat)
+    # We do not have access to einsum. To avoid broadcasting issues, we add a singleton
+    # dimension to the points array and remove it after the operation.
+    points = points[..., None]
+    if not broadcastable(mat.shape, points.shape):
+        raise ValueError(
+            f"Cannot broadcast {quat.shape[:-1]} rotations to {points.shape[:-1]} "
+            "vectors."
+        )
+    if inverse:
+        # TODO: Replace with .mT once numpy 2.0 is the minimum supported version
+        return (xp.matrix_transpose(mat) @ points)[..., 0]
+    return (mat @ points)[..., 0]
+
+
+def setitem(
+    quat: Array, value: Array, indexer: int | slice | EllipsisType | None
+) -> Array:
+    return xpx.at(quat)[indexer, ...].set(value)
+
+
+def align_vectors(
+    a: Array, b: Array, weights: Array | None = None, return_sensitivity: bool = False
+) -> tuple[Array, Array, Array]:
+    xp = array_namespace(a)
+    # Check input vectors
+    dtype = xp_result_type(a, b, force_floating=True, xp=xp)
+    a_original = xp.asarray(a, dtype=dtype)
+    b_original = xp.asarray(b, dtype=dtype)
+    a = xpx.atleast_nd(a_original, ndim=2, xp=xp)
+    b = xpx.atleast_nd(b_original, ndim=2, xp=xp)
+    if a.shape[-1] != 3:
+        raise ValueError(
+            f"Expected input `a` to have shape (3,) or (N, 3), got {a_original.shape}"
+        )
+    if b.shape[-1] != 3:
+        raise ValueError(
+            f"Expected input `b` to have shape (3,) or (N, 3), got {b_original.shape}"
+        )
+    if a.shape != b.shape:
+        raise ValueError(
+            "Expected inputs `a` and `b` to have same shapes"
+            f", got {a_original.shape} and {b_original.shape} respectively."
+        )
+    if a.ndim > 2 or b.ndim > 2:  # This function does not support broadcasting
+        raise ValueError(
+            "Expected inputs `a` and `b` to have shape (3,) or (N, 3), got "
+            f"{a_original.shape} and {b_original.shape} respectively."
+        )
+    N = a.shape[0]
+
+    # Check weights
+    if weights is None:
+        weights = xp.ones(N, device=xp_device(a), dtype=a.dtype)
+    else:
+        weights = xp.asarray(weights, device=xp_device(a), dtype=a.dtype)
+        if weights.ndim != 1:
+            raise ValueError(
+                f"Expected `weights` to be 1 dimensional, got shape {weights.shape}."
+            )
+        if N > 1 and (weights.shape[0] != N):
+            raise ValueError(
+                "Expected `weights` to have number of values equal to number of input "
+                f"vectors, got {weights.shape[0]} values and {N} vectors."
+            )
+        # We can only check for negative weights in eager execution models. Lazy
+        # backends will return NaNs instead.
+        negative_weights = weights < 0
+        if not is_lazy_array(negative_weights) and xp.any(negative_weights):
+            raise ValueError("`weights` may not contain negative values")
+        weights = xp.where(negative_weights, xp.nan, weights)
+
+    # For the special case of a single vector pair, we use the infinite
+    # weight code path
+    weight_is_inf = xp.asarray([True]) if N == 1 else weights == xp.inf
+    n_inf = xp.sum(xp.astype(weight_is_inf, a.dtype))
+    # We can only error out on multiple infinite weights or sensitivity return with
+    # infinite weights in eager execution models. Lazy backends will return NaNs.
+    if not is_lazy_array(n_inf):
+        if n_inf > 1:
+            raise ValueError("Only one infinite weight is allowed")
+        if n_inf == 1 and return_sensitivity:
+            raise ValueError(
+                "Cannot return sensitivity matrix with an "
+                "infinite weight or one vector pair"
+            )
+
+    weights = xp.where(n_inf > 1, xp.nan, weights)
+
+    inf_branch = xp.any(weight_is_inf, axis=-1)
+    # DECISION: We cannot compute both branches for all frameworks. There are two main
+    # reasons:
+    # 1. Computing both for eager execution models is expensive.
+    # 2. Some operations will fail when running the unused branch because of numerical
+    # and algorithmical issues. Numpy e.g. will raise an exception when trying to
+    # compute the svd of a matrix with infinite weights. To prevent this, we only
+    # compute the branch that is needed. Lazy backends however require us to take the
+    # full compute graph. Therefore, we use xp.where for lazy backends and a branching
+    # version for eager frameworks.
+    #
+    # Note that we could also solve this by exploiting the externals of xpx.apply_where.
+    # However, we'd have to rely on the implementation details of apply_where, which is
+    # something we should avoid.
+    # See https://github.com/scipy/scipy/pull/22777#discussion_r2028868364
+    if is_lazy_array(inf_branch):
+        q_opt, rssd, sensitivity = _align_vectors(a, b, weights)
+        q_opt_inf, rssd_inf, sensitivity_inf = _align_vectors_fixed(a, b, weights)
+        q_opt = xp.where(inf_branch, q_opt_inf, q_opt)
+        rssd = xp.where(inf_branch, rssd_inf, rssd)
+        sensitivity = xp.where(inf_branch, sensitivity_inf, sensitivity)
+    else:
+        if xp.any(inf_branch):
+            q_opt, rssd, sensitivity = _align_vectors_fixed(a, b, weights)
+        else:
+            q_opt, rssd, sensitivity = _align_vectors(a, b, weights)
+    return q_opt, rssd, sensitivity
+
+
+def _align_vectors(a: Array, b: Array, weights: Array) -> tuple[Array, Array, Array]:
+    xp = array_namespace(a)
+    device = xp_device(a)
+    B = (weights[:, None] * a).mT @ b
+    u, s, vh = xp.linalg.svd(B)
+
+    # Correct improper rotation if necessary (as in Kabsch algorithm)
+    neg_det = xp.linalg.det(u @ vh) < 0
+    s = xpx.at(s)[..., -1].set(xp.where(neg_det, -s[..., -1], s[..., -1]))
+    u = xpx.at(u)[..., :, -1].set(xp.where(neg_det, -u[..., :, -1], u[..., :, -1]))
+
+    C = u @ vh
+
+    # DECISION: We cannot branch on the condition because jit code needs to be
+    # non-branching. Hence, we omit the check for uniqueness
+    # (s[1] + s[2] < 1e-16 * s[0])
+    ssd = xp.sum(weights * xp.sum(b**2 + a**2, axis=-1), axis=-1) - 2 * xp.sum(
+        s, axis=-1
+    )
+    rssd = xp.sqrt(xp.maximum(ssd, xp.zeros(1, device=device)))[..., 0]
+
+    # TODO: We currently need to always compute the sensitivity matrix because lazy code
+    # needs to be non-branching. We should check if compilers can optimize the where
+    # statement (e.g. in jax) and check if we can have an eager version that only
+    # evaluates the branch that is needed.
+    # See xpx.apply_where, issue: https://github.com/data-apis/array-api-extra/pull/141
+    zeta = (s[..., 0] + s[..., 1]) * (s[..., 1] + s[..., 2]) * (s[..., 2] + s[..., 0])
+    kappa = s[..., 0] * s[..., 1] + s[..., 1] * s[..., 2] + s[..., 2] * s[..., 0]
+    eye = xp.eye(3, dtype=a.dtype, device=device)
+    sensitivity = xp.mean(weights) / zeta * (kappa * eye + B @ B.mT)
+    q_opt = _from_matrix_orthogonal(C)
+    return q_opt, rssd, sensitivity
+
+
+def _align_vectors_fixed(
+    a: Array, b: Array, weights: Array
+) -> tuple[Array, Array, Array]:
+    xp = array_namespace(a)
+    device = xp_device(a)
+    N = a.shape[0]
+    weight_is_inf = xp.asarray([True], device=device) if N == 1 else weights == xp.inf
+    # We cannot use boolean masks for indexing because of jax. For the same reason, we
+    # also cannot use dynamic slices. As a workaround, we roll the array so that the
+    # infinitely weighted vector is at index 0. We then use static slices to get the
+    # primary and secondary vectors.
+    #
+    # Note that argmax fulfils a secondary purpose here:
+    # When we trace this function with jax, this function might get executed even if
+    # weight_is_inf does not have a single valid entry. Argmax will still give us a
+    # valid index which allows us to proceed with the function (the results are
+    # discarded anyways), whereas boolean indexing would result in invalid, zero-shaped
+    # arrays.
+
+    inf_idx = xp.argmax(xp.astype(weight_is_inf, xp.uint8))
+    # xp.argmax returns an Array, but the specification of xp.roll does not support
+    # Arrays as shifts. For lazy execution models we cannot convert to int because this
+    # raises a concretization error. However, jax does accept Arrays as shifts which
+    # allows jit compiling the function. Hence we do not convert to int for jax.
+    # See https://github.com/data-apis/array-api/issues/914#issuecomment-2918959918
+    if not is_jax(xp):
+        inf_idx = int(inf_idx)
+    a_sorted = xp.roll(a, shift=-inf_idx, axis=0)
+    b_sorted = xp.roll(b, shift=-inf_idx, axis=0)
+    weights_sorted = xp.roll(weights, shift=-inf_idx, axis=0)
+
+    a_pri = a_sorted[0, ...][None, ...]  # Effectively [[0], ...]
+    b_pri = b_sorted[0, ...][None, ...]
+    a_pri_norm = xp_vector_norm(a_pri, axis=-1, keepdims=True, xp=xp)
+    b_pri_norm = xp_vector_norm(b_pri, axis=-1, keepdims=True, xp=xp)
+    if not is_lazy_array(a_pri_norm):
+        if xp.any(a_pri_norm == 0) or xp.any(b_pri_norm == 0):
+            raise ValueError("Cannot align zero length primary vectors")
+
+    # We cannot error out on zero length vectors. We set the norm to NaN to avoid
+    # division by zero and mark the result as invalid.
+    a_pri_norm = xpx.at(a_pri_norm)[a_pri_norm == 0].set(xp.nan)
+    b_pri_norm = xpx.at(b_pri_norm)[b_pri_norm == 0].set(xp.nan)
+
+    a_pri = a_pri / a_pri_norm
+    b_pri = b_pri / b_pri_norm
+
+    # We first find the minimum angle rotation between the primary
+    # vectors.
+    cross = xp.linalg.cross(b_pri[..., 0, :], a_pri[..., 0, :])
+    cross_norm = xp_vector_norm(cross, axis=-1, xp=xp)
+    theta = xp.atan2(cross_norm, xp.sum(a_pri[..., 0, :] * b_pri[..., 0, :], axis=-1))
+    tolerance = 1e-3  # tolerance for small angle approximation (rad)
+    q_flip = xp.asarray([0.0, 0.0, 0.0, 1.0], dtype=a_pri.dtype, device=device)
+
+    # Near pi radians, the Taylor series approximation of x/sin(x) diverges, so for
+    # numerical stability we flip pi and then rotate back by the small angle pi - theta
+    flip = xp.pi - theta < tolerance
+    # For antiparallel vectors, cross = [0, 0, 0] so we need to manually set an
+    # arbitrary orthogonal axis of rotation
+    i = xp.argmin(xp.abs(a_pri[..., 0, :]))
+    # TODO: Array API does not support fancy indexing __setitem__. The code is
+    # equivalent to doing the following:
+    # r_components = xp.zeros(3)
+    # r_components = xpx.at(r_components)[i - 1].set(a_pri[0, i - 2])
+    # r_components = xpx.at(r_components)[i - 2].set(-a_pri[0, i - 1])
+    r_components = xp.stack(
+        [
+            xp.where(i == 1, a_pri[0, 2], xp.where(i == 2, -a_pri[0, 1], 0)),
+            xp.where(i == 2, a_pri[0, 0], xp.where(i == 0, -a_pri[0, 2], 0)),
+            xp.where(i == 0, a_pri[0, 1], xp.where(i == 1, -a_pri[0, 0], 0)),
+        ]
+    )
+    r = xp.where(cross_norm == 0, r_components, cross)
+
+    q_flip = xp.where(flip, from_rotvec(r / xp_vector_norm(r, xp=xp) * xp.pi), q_flip)
+    theta = xp.where(flip, xp.pi - theta, theta)
+    cross = xp.where(flip, -cross, cross)
+
+    # Small angle Taylor series approximation for numerical stability
+    theta2 = theta * theta
+    small_scale = xp.abs(theta) < tolerance
+    r_small_scale = cross * (1 + theta2 / 6 + theta2 * theta2 * 7 / 360)
+    # We need to handle the case where theta is 0 to avoid division by zero. We use the
+    # value of the Taylor series approximation, but non-branching operations require
+    # that we still divide by the angle. Since we do not use the result where the angle
+    # is close to 0, this is safe.
+    theta = theta + xp.asarray(small_scale, dtype=theta.dtype)
+    r_large_scale = cross * theta / xp.sin(theta)
+    r = xp.where(small_scale, r_small_scale, r_large_scale)
+    q_pri = compose_quat(from_rotvec(r), q_flip)
+
+    # Case 1): No secondary vectors, q_opt is q_pri -> Immediately done
+    # Case 2): Secondary vectors exist
+    # We cannot use boolean masks here because of jax
+    a_sec = a_sorted[1:, ...]
+    b_sec = b_sorted[1:, ...]
+    weights_sec = weights_sorted[1:]
+
+    # We apply the first rotation to the b vectors to align the
+    # primary vectors, resulting in vectors c. The secondary
+    # vectors must now be rotated about that primary vector to best
+    # align c to a.
+    c_sec = apply(q_pri, b_sec)
+
+    # Calculate vector components for the angle calculation. The
+    # angle phi to rotate a single 2D vector C to align to 2D
+    # vector A in the xy plane can be found with the equation
+    # phi = atan2(cross(C, A), dot(C, A))
+    #     = atan2(|C|*|A|*sin(phi), |C|*|A|*cos(phi))
+    # The below equations perform the same operation, but with the
+    # 3D rotation restricted to the 2D plane normal to a_pri, where
+    # the secondary vectors are projected into that plane. We then
+    # find the composite angle from the weighted sum of the
+    # axial components in that plane, minimizing the 2D alignment
+    # problem.
+    sin_term = xp.linalg.vecdot(xp.linalg.cross(c_sec, a_sec), a_pri)
+    cos_term = xp.linalg.vecdot(c_sec, a_sec) - (
+        xp.linalg.vecdot(c_sec, a_pri) * xp.linalg.vecdot(a_sec, a_pri)
+    )
+    phi = xp.atan2(xp.sum(weights_sec * sin_term), xp.sum(weights_sec * cos_term))
+    q_sec = from_rotvec(phi * a_pri[0, ...])
+
+    # Compose these to get the optimal rotation
+    q_opt = q_pri if N == 1 else compose_quat(q_sec, q_pri)
+
+    # Calculate the root sum squared distance. We force the error to
+    # be zero for the infinite weight vectors since they will align
+    # exactly.
+    mask = ((N > 1) | (weights[0] == xp.inf)) & weight_is_inf
+    # Skip non-infinite weight single vectors pairs, we used the
+    # infinite weight code path but don't want to zero that weight
+    weights_inf_zero = xpx.at(weights, mask).set(0, copy=True, xp=xp)
+    a_est = apply(q_opt, b)
+    rssd = xp.sqrt(xp.sum(weights_inf_zero @ (a - a_est) ** 2))
+
+    mask = xp.any(xp.isnan(weights), axis=-1)
+    q_opt = xp.where(mask, xp.nan, q_opt)
+    return q_opt, rssd, xp.asarray(xp.nan, device=device)
+
+
+def pow(quat: Array, n: float | Array) -> Array:
+    xp = array_namespace(quat)
+    device = xp_device(quat)
+    # If n is an array, we sanitize it to a scalar and promote quat and n to
+    # the same dtype.
+    if is_array_api_obj(n):
+        if n.shape == (1,):  # pyrefly:ignore[missing-attribute]
+            n = n[0]  # pyrefly:ignore[bad-index]
+        elif n.ndim != 0:  # pyrefly:ignore[missing-attribute]
+            raise ValueError("Array exponent must be a scalar")
+        quat, n = xp_promote(quat, n, force_floating=True, xp=xp)
+
+    # If n is a lazy array, we cannot take fast paths for special cases.
+    if is_lazy_array(n):
+        result = from_rotvec(n * as_rotvec(quat))  # general scaling of rotation angle
+        # Special cases 0 -> identity, -1 -> inv, 1 -> copy
+        identity = xp.zeros((*quat.shape[:-1], 4), dtype=quat.dtype, device=device)
+        identity = xpx.at(identity)[..., 3].set(1)
+        result = xp.where(n == 0, identity, result)
+        result = xp.where(n == -1, inv(quat), result)
+        result = xp.where(n == 1, quat, result)
+        return result
+    if n == 0:
+        identity = xp.zeros((*quat.shape[:-1], 4), dtype=quat.dtype, device=device)
+        return xpx.at(identity)[..., 3].set(1)
+    if n == -1:
+        return inv(quat)
+    if n == 1:
+        return quat
+    return from_rotvec(n * as_rotvec(quat))
+
+
+def _normalize_quaternion(quat: Array) -> Array:
+    xp = array_namespace(quat)
+    quat_norm = xp_vector_norm(quat, axis=-1, keepdims=True, xp=xp)
+    zero_norm = quat_norm == 0
+    if is_lazy_array(quat_norm):
+        quat = xp.where(zero_norm, xp.nan, quat)
+    elif xp.any(zero_norm):
+        raise ValueError("Found zero norm quaternions in `quat`.")
+    return quat / quat_norm
+
+
+def _quat_canonical(quat: Array) -> Array:
+    xp = array_namespace(quat)
+    mask = quat[..., 3] < 0
+    zero_w = quat[..., 3] == 0
+    mask = mask | (zero_w & (quat[..., 0] < 0))
+    zero_wx = zero_w & (quat[..., 0] == 0)
+    mask = mask | (zero_wx & (quat[..., 1] < 0))
+    zero_wxy = zero_wx & (quat[..., 1] == 0)
+    mask = mask | (zero_wxy & (quat[..., 2] < 0))
+    return xp.where(mask[..., None], -quat, quat)
+
+
+def _elementary_basis_index(axis: str) -> int:
+    if axis == "x":
+        return 0
+    elif axis == "y":
+        return 1
+    elif axis == "z":
+        return 2
+    raise ValueError(f"Expected axis to be from ['x', 'y', 'z'], got {axis}")
+
+
+def _compute_davenport_from_quat(
+    quat: Array,
+    n1: Array,
+    n2: Array,
+    n3: Array,
+    extrinsic: bool,
+    suppress_warnings: bool,
+) -> Array:
+    # The algorithm assumes extrinsic frame transformations. The algorithm
+    # in the paper is formulated for rotation quaternions, which are stored
+    # directly by Rotation.
+    # Adapt the algorithm for our case by reversing both axis sequence and
+    # angles for intrinsic rotations when needed
+    xp = array_namespace(quat)
+    n1, n3 = (n1, n3) if extrinsic else (n3, n1)
+
+    n_cross = xp.linalg.cross(n1, n2)
+    lamb = xp.atan2(xp.vecdot(n3, n_cross), xp.vecdot(n3, n1))
+
+    # alternative set of angles compatible with as_euler implementation
+    mask = lamb < 0
+    n2 = xp.where(mask[..., None], -n2, n2)
+    lamb = xp.where(mask, -lamb, lamb)
+    n_cross = xp.where(mask[..., None], -n_cross, n_cross)
+    correct_set = mask
+
+    quat_lamb = xp.concat(
+        (xp.sin(lamb / 2)[..., None] * n2, xp.cos(lamb / 2)[..., None]), axis=-1
+    )
+
+    q_trans = compose_quat(quat_lamb, quat)
+    a = q_trans[..., 3]
+    b = xp.linalg.vecdot(q_trans[..., :3], n1)
+    c = xp.linalg.vecdot(q_trans[..., :3], n2)
+    d = xp.linalg.vecdot(q_trans[..., :3], n_cross)
+
+    angles = _get_angles(extrinsic, False, 1, lamb, a, b, c, d, suppress_warnings)
+    angles = xpx.at(angles)[..., 1].set(
+        xp.where(correct_set, -angles[..., 1], angles[..., 1])
+    )
+
+    return angles
+
+
+def _elementary_quat_compose(axes: list[int], angles: Array, intrinsic: bool) -> Array:
+    xp = array_namespace(angles)
+    device = xp_device(angles)
+    quat = _make_elementary_quat(axes[0], angles[..., 0], device=device, xp=xp)
+    for i in range(1, len(axes)):
+        ax_quat = _make_elementary_quat(axes[i], angles[..., i], device=device, xp=xp)
+        quat = compose_quat(quat, ax_quat) if intrinsic else compose_quat(ax_quat, quat)
+    return quat
+
+
+def _make_elementary_quat(axis: int, angle: Array, device, xp) -> Array:
+    quat = xp.zeros((*angle.shape, 4), dtype=angle.dtype, device=device)
+    quat = xpx.at(quat)[..., 3].set(xp.cos(angle / 2.0))
+    quat = xpx.at(quat)[..., axis].set(xp.sin(angle / 2.0))
+    return quat
+
+
+def _get_angles(
+    extrinsic: bool,
+    symmetric: bool,
+    sign: int,
+    lamb: float,
+    a: Array,
+    b: Array,
+    c: Array,
+    d: Array,
+    suppress_warnings: bool,
+) -> Array:
+    xp = array_namespace(a)
+    device = xp_device(a)
+    eps = 1e-7
+    half_sum = xp.atan2(b, a)
+    half_diff = xp.atan2(d, c)
+    # We zero-initialize to automatically cover singular cases where the second angle is
+    # not defined uniquely.
+    angles = xp.zeros((*a.shape, 3), dtype=a.dtype, device=device)
+
+    angles = xpx.at(angles)[..., 1].set(2 * xp.atan2(xp.hypot(c, d), xp.hypot(a, b)))
+
+    angle_first = 0 if extrinsic else 2
+    angle_third = 2 if extrinsic else 0
+
+    # Check if the second angle is close to 0 or pi, causing a singularity.
+    # - Case 0: Second angle is neither close to 0 nor pi.
+    # - Case 1: Second angle is close to 0.
+    # - Case 2: Second angle is close to pi.
+    case1 = xp.abs(angles[..., 1]) <= eps
+    case2 = xp.abs(angles[..., 1] - xp.pi) <= eps
+    case0 = ~(case1 | case2)
+    if not suppress_warnings and not is_lazy_array(case0) and xp.any(~case0):
+        warnings.warn(
+            "Gimbal lock detected. Setting third angle to zero "
+            "since it is not possible to uniquely determine "
+            "all angles.",
+            stacklevel=3,
+        )
+
+    # This writes case1 into a0 where True and case2 everywhere else. This is sound
+    # because we later overwrite any values without singularity with the regular value
+    # of case0. The second angle is covered by default since we zero-initialized the
+    # second dimension.
+    a0 = xp.where(case1, 2 * half_sum, 2 * half_diff * (-1 if extrinsic else 1))
+    angles = xpx.at(angles)[..., 0].set(a0)
+
+    # We overwrite the values of angles without singularities (case0)
+    a1 = xp.where(case0, half_sum - half_diff, angles[..., angle_first])
+    angles = xpx.at(angles)[..., angle_first].set(a1)
+
+    # Same as above but for the third angle. We overwrite the non-singular case0 values
+    a3 = xp.where(case0, half_sum + half_diff, angles[..., angle_third])
+    if not symmetric:
+        a3 = a3 * sign
+        angles = xpx.at(angles)[..., 1].set(angles[..., 1] - lamb)
+    angles = xpx.at(angles)[..., angle_third].set(a3)
+
+    angles = (angles + xp.pi) % (2 * xp.pi) - xp.pi
+    return angles
+
+
+def compose_quat(p: Array, q: Array) -> Array:
+    xp = array_namespace(p)
+    cross = xp.linalg.cross(p[..., :3], q[..., :3])
+    qx = p[..., 3] * q[..., 0] + q[..., 3] * p[..., 0] + cross[..., 0]
+    qy = p[..., 3] * q[..., 1] + q[..., 3] * p[..., 1] + cross[..., 1]
+    qz = p[..., 3] * q[..., 2] + q[..., 3] * p[..., 2] + cross[..., 2]
+    qw = (
+        p[..., 3] * q[..., 3]
+        - p[..., 0] * q[..., 0]
+        - p[..., 1] * q[..., 1]
+        - p[..., 2] * q[..., 2]
+    )
+    quat = xp.stack([qx, qy, qz, qw], axis=-1)
+    return quat
+
+
+def _split_rotation(q: Array, xp) -> tuple[Array, Array]:
+    q = xpx.atleast_nd(q, ndim=2, xp=xp)
+    return q[..., -1], q[..., :-1]
+
+
+def _deg2rad(angles: Array) -> Array:
+    return angles * (np.pi / 180.0)
+
+
+def _rad2deg(angles: Array) -> Array:
+    return angles * (180.0 / np.pi)
diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/transform/rotation.py b/venv/lib/python3.12/site-packages/scipy/spatial/transform/rotation.py
new file mode 100644
index 0000000000000000000000000000000000000000..a719437415124f4afc842b98c708836c1fe68f22
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/transform/rotation.py
@@ -0,0 +1,21 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.spatial` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+
+__all__ = [  # noqa: F822
+    'Rotation',
+    'Slerp',
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="spatial.transform", module="rotation",
+                                   private_modules=["_rotation"], all=__all__,
+                                   attribute=name)
diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/transform/tests/__init__.py b/venv/lib/python3.12/site-packages/scipy/spatial/transform/tests/__init__.py
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diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/transform/tests/__pycache__/test_rotation.cpython-312.pyc b/venv/lib/python3.12/site-packages/scipy/spatial/transform/tests/__pycache__/test_rotation.cpython-312.pyc
new file mode 100644
index 0000000000000000000000000000000000000000..dc8fcaec8997fb57ff8db4f92fda6b0286d33174
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/transform/tests/__pycache__/test_rotation.cpython-312.pyc
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
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+size 200207
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diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/transform/tests/test_rigid_transform.py b/venv/lib/python3.12/site-packages/scipy/spatial/transform/tests/test_rigid_transform.py
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index 0000000000000000000000000000000000000000..23d38c12987415a366533f160910ab3006031564
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+++ b/venv/lib/python3.12/site-packages/scipy/spatial/transform/tests/test_rigid_transform.py
@@ -0,0 +1,1531 @@
+import pickle
+from itertools import product
+
+import pytest
+
+import numpy as np
+from scipy.spatial.transform import Rotation, RigidTransform
+from scipy.spatial.transform._rigid_transform import normalize_dual_quaternion
+from scipy._lib._array_api import (
+    is_lazy_array,
+    xp_vector_norm,
+    is_numpy,
+    xp_assert_close,
+    make_xp_test_case,
+    xp_assert_equal,
+    xp_promote
+)
+import scipy._external.array_api_extra as xpx
+
+
+def rotation_to_xp(r: Rotation, xp):
+    dtype = xpx.default_dtype(xp)
+    return Rotation.from_quat(xp.asarray(r.as_quat(), dtype=dtype))
+
+
+def rigid_transform_to_xp(r: RigidTransform, xp):
+    dtype = xpx.default_dtype(xp)
+    return RigidTransform.from_matrix(xp.asarray(r.as_matrix(), dtype=dtype))
+
+
+@make_xp_test_case((RigidTransform, "as_matrix"))
+def test_repr(xp):
+    actual = repr(RigidTransform.from_matrix(xp.eye(4)))
+    expected = """\
+RigidTransform.from_matrix(array([[1., 0., 0., 0.],
+                                  [0., 1., 0., 0.],
+                                  [0., 0., 1., 0.],
+                                  [0., 0., 0., 1.]]))"""
+    if is_numpy(xp):
+        assert actual == expected
+    else:
+        assert actual.startswith("RigidTransform.from_matrix(")
+
+    tf = RigidTransform.from_matrix(xp.asarray(RigidTransform.identity(2).as_matrix()))
+    actual = repr(tf)
+    expected = """\
+RigidTransform.from_matrix(array([[[1., 0., 0., 0.],
+                                   [0., 1., 0., 0.],
+                                   [0., 0., 1., 0.],
+                                   [0., 0., 0., 1.]],
+                           
+                                  [[1., 0., 0., 0.],
+                                   [0., 1., 0., 0.],
+                                   [0., 0., 1., 0.],
+                                   [0., 0., 0., 1.]]]))"""
+    if is_numpy(xp):
+        assert actual == expected
+    else:
+        assert actual.startswith("RigidTransform.from_matrix(")
+
+
+@make_xp_test_case((RigidTransform, "from_rotation"))
+@pytest.mark.parametrize("ndim", range(1, 4))
+def test_from_rotation(xp, ndim: int):
+    atol = 1e-12
+    rng = np.random.default_rng(0)
+    shape = (ndim,) * (ndim - 1) + (4,)
+    r = rotation_to_xp(Rotation.from_quat(rng.normal(size=shape)), xp=xp)
+    tf = RigidTransform.from_rotation(r)
+    xp_assert_close(tf.as_matrix()[..., :3, :3], r.as_matrix(), atol=atol)
+    xp_assert_close(tf.as_matrix()[..., :3, 3], xp.zeros(shape[:-1] + (3,)), atol=atol)
+    xp_assert_close(tf.as_matrix()[..., 3, :3], xp.zeros(shape[:-1] + (3,)), atol=atol)
+    xp_assert_close(tf.as_matrix()[..., 3, 3], xp.ones(shape[:-1]), atol=atol)
+    assert tf.single == (ndim == 1)
+
+
+@make_xp_test_case((RigidTransform, "from_translation"))
+@pytest.mark.parametrize("ndim", range(1, 4))
+def test_from_translation(xp, ndim: int):
+    shape = (ndim,) * (ndim - 1)
+    t = xp.reshape(xp.arange(ndim ** (ndim-1) * 3), shape + (3,))
+    tf = RigidTransform.from_translation(t)
+
+    expected = xp.tile(xp.eye(4), shape + (1, 1))
+    t_float = xp_promote(t, force_floating=True, xp=xp)
+    expected = xpx.at(expected)[..., :3, 3].set(t_float)
+    xp_assert_close(tf.as_matrix(), expected)
+    assert tf.single == (ndim == 1)
+
+
+def test_from_translation_array_like():
+    # Test single translation
+    t = [1, 2, 3]
+    tf = RigidTransform.from_translation(t)
+    tf_expected = RigidTransform.from_translation(np.array(t))
+    xp_assert_close(tf.as_matrix(), tf_expected.as_matrix())
+    assert tf.single
+
+    # Test multiple translations
+    t = [[1, 2, 3], [4, 5, 6]]
+    tf = RigidTransform.from_translation(t)
+    tf_expected = RigidTransform.from_translation(np.array(t))
+    xp_assert_close(tf.as_matrix(), tf_expected.as_matrix())
+    assert not tf.single
+
+
+@make_xp_test_case((RigidTransform, "from_matrix"), (RigidTransform, "as_matrix"))
+@pytest.mark.parametrize("ndim", range(1, 4))
+def test_from_matrix(xp, ndim: int):
+    atol = 1e-12
+    shape = (ndim,) * (ndim - 1) + (4, 4)
+    dtype = xpx.default_dtype(xp)
+
+    matrix = xp.tile(xp.eye(4), shape[:-2] + (1, 1))
+    t = xp.reshape(xp.arange(ndim ** (ndim-1) * 3, dtype=dtype), shape[:-2] + (3,))
+    matrix = xpx.at(matrix)[..., :3, 3].set(t)
+
+    tf = RigidTransform.from_matrix(matrix)
+    xp_assert_close(tf.as_matrix(), matrix, atol=atol)
+    assert tf.single == (ndim == 1)
+
+    # Test non-1 determinant
+    matrix = xp.tile(xp.eye(4), shape[:-2] + (1, 1))
+    matrix = xpx.at(matrix)[..., :3, :3].set(xp.eye(3) * 2.0)
+    tf = RigidTransform.from_matrix(matrix)
+    expected = xp.tile(xp.eye(4), shape[:-2] + (1, 1))
+    xp_assert_close(tf.as_matrix(), expected, atol=atol)
+
+    # Test non-orthogonal rotation matrix
+    matrix = xp.tile(xp.eye(4), shape[:-2] + (1, 1))
+    # matrix is equivalent to [[1, 1, 0, 0],
+    #                          [0, 1, 0, 0],
+    #                          [0, 0, 1, 0],
+    #                          [0, 0, 0, 1]]
+    matrix = xpx.at(matrix)[..., 0, 1].set(1.0)
+    tf = RigidTransform.from_matrix(matrix)
+    expected = xp.tile(xp.eye(4), shape[:-2] + (1, 1))
+    expected = xpx.at(expected)[..., 0, 0].set(0.894427)
+    expected = xpx.at(expected)[..., 0, 1].set(0.447214)
+    expected = xpx.at(expected)[..., 1, 0].set(-0.447214)
+    expected = xpx.at(expected)[..., 1, 1].set(0.894427)
+    xp_assert_close(tf.as_matrix(), expected, atol=1e-6)
+
+    # Test invalid matrix
+    invalid = xp.tile(xp.eye(4), shape[:-2] + (1, 1))
+    invalid = xpx.at(invalid)[..., 3, 3].set(2)  # Invalid last row
+    if is_lazy_array(invalid):
+        tf = RigidTransform.from_matrix(invalid)
+        assert xp.all(xp.isnan(tf.as_matrix()))
+    else:
+        with pytest.raises(ValueError):
+            RigidTransform.from_matrix(invalid)
+
+
+def test_from_matrix_array_like():
+    # Test single transform matrix
+    matrix = [[1, 0, 0, 0],
+              [0, 1, 0, 0],
+              [0, 0, 1, 0],
+              [0, 0, 0, 1]]
+    expected = np.eye(4)
+    tf = RigidTransform.from_matrix(matrix)
+    xp_assert_close(tf.as_matrix(), expected)
+    assert tf.single
+
+    # Test multiple transform matrices
+    matrices = [matrix, matrix]
+    tf = RigidTransform.from_matrix(matrices)
+    for i in range(len(matrices)):
+        xp_assert_close(tf.as_matrix()[i, ...], expected)
+    assert not tf.single
+
+
+@make_xp_test_case((RigidTransform, "from_components"))
+@pytest.mark.parametrize("r_ndim", range(1, 3))
+@pytest.mark.parametrize("t_ndim", range(1, 3))
+def test_from_components(xp, r_ndim: int, t_ndim: int):
+    atol = 1e-12
+    dims = (6, 5, 4, 3)  # Common shape
+    q_shape = dims[:r_ndim - 1][::-1] + (4,)
+    t_shape = dims[:t_ndim - 1][::-1] + (3,)
+    tf_shape = np.broadcast_shapes(q_shape[:-1], t_shape[:-1]) + (4, 4)
+    rng = np.random.default_rng(0)
+
+    t = xp.reshape(xp.arange(np.prod(t_shape[:-1]) * 3), t_shape)
+    r = rotation_to_xp(Rotation.from_quat(rng.random(size=q_shape)), xp=xp)
+    tf = RigidTransform.from_components(t, r)
+
+    expected = xp.zeros(tf_shape)
+    expected = xpx.at(expected)[..., :3, :3].set(r.as_matrix())
+    t_float = xp_promote(t, force_floating=True, xp=xp)
+    expected = xpx.at(expected)[..., :3, 3].set(t_float)
+    expected = xpx.at(expected)[..., 3, 3].set(1)
+    xp_assert_close(tf.as_matrix(), expected, atol=atol)
+    assert tf.single == (r_ndim == 1 and t_ndim == 1)
+
+
+def test_from_components_array_like():
+    rng = np.random.default_rng(123)
+    # Test single rotation and translation
+    t = [1, 2, 3]
+    r = Rotation.random(rng=rng)
+    tf = RigidTransform.from_components(t, r)
+    tf_expected = RigidTransform.from_components(np.array(t), r)
+    xp_assert_close(tf.as_matrix(), tf_expected.as_matrix(), atol=1e-12)
+    assert tf.single
+
+    # Test multiple rotations and translations
+    t = [[1, 2, 3], [4, 5, 6]]
+    r = Rotation.random(len(t), rng=rng)
+    tf = RigidTransform.from_components(t, r)
+    tf_expected = RigidTransform.from_components(np.array(t), r)
+    xp_assert_close(tf.as_matrix(), tf_expected.as_matrix(), atol=1e-12)
+    assert not tf.single
+
+
+@make_xp_test_case((RigidTransform, "as_components"))
+@pytest.mark.parametrize("ndim", range(1, 4))
+def test_as_components(xp, ndim):
+    dtype = xpx.default_dtype(xp)
+    atol = 1e-12 if dtype == xp.float64 else 1e-6
+    shape = (ndim,) * (ndim - 1)
+    rng = np.random.default_rng(123)
+    t = xp.asarray(rng.normal(size=shape + (3,)), dtype=dtype)
+    r = rotation_to_xp(Rotation.from_quat(rng.random(shape + (4,))), xp=xp)
+    tf = RigidTransform.from_components(t, r)
+    new_t, new_r = tf.as_components()
+    assert xp.all(new_r.approx_equal(r, atol=atol))
+    xp_assert_close(new_t, t, atol=atol)
+
+
+@make_xp_test_case((RigidTransform, "from_exp_coords"))
+@pytest.mark.parametrize("dim", range(1, 4))
+def test_from_exp_coords(xp, dim: int):
+    shape = (dim,) * (dim - 1)
+    # example from 3.3 of
+    # https://hades.mech.northwestern.edu/images/2/25/MR-v2.pdf
+    dtype = xpx.default_dtype(xp)
+    angle1 = np.deg2rad(30.0)
+    mat = xp.asarray([
+        [np.cos(angle1), -np.sin(angle1), 0.0, 1.0],
+        [np.sin(angle1), np.cos(angle1), 0.0, 2.0],
+        [0.0, 0.0, 1.0, 0.0],
+        [0.0, 0.0, 0.0, 1.0]
+    ], dtype=dtype)
+    mat = xp.tile(mat, shape + (1, 1))
+    tf1 = RigidTransform.from_matrix(mat)
+    angle2 = np.deg2rad(60.0)
+    mat = xp.asarray([
+        [np.cos(angle2), -np.sin(angle2), 0.0, 2.0],
+        [np.sin(angle2), np.cos(angle2), 0.0, 1.0],
+        [0.0, 0.0, 1.0, 0.0],
+        [0.0, 0.0, 0.0, 1.0]
+    ], dtype=dtype)
+    mat = xp.tile(mat, shape + (1, 1))
+    tf2 = RigidTransform.from_matrix(mat)
+    expected = tf2 * tf1.inv()
+    deg2rag = xp.asarray(np.deg2rad(30.0))
+    exp_coords = deg2rag * xp.asarray([0.0, 0.0, 1.0, 3.37, -3.37, 0.0])
+    exp_coords = xp.tile(exp_coords, shape + (1,))
+    actual = RigidTransform.from_exp_coords(exp_coords)
+    xp_assert_close(actual.as_matrix(), expected.as_matrix(), atol=1e-2)
+
+    # test cases generated by comparison to pytransform3d
+    exp_coords = xp.asarray([
+        [-2.01041204, -0.52983629, 0.65773501,
+         0.10386614, 0.05855009, 0.54959179],
+        [-0.22537438, -0.24132627, -2.4747121,
+         -0.09158594,  1.88075832, -0.03197204]
+    ])
+    exp_coords = xp.tile(exp_coords, shape + (1,))
+    expected_matrix = xp.asarray([
+        [[0.76406621, 0.10504613, -0.63652819, -0.10209961],
+         [0.59956454, -0.47987325, 0.64050295, 0.40158789],
+         [-0.2381705, -0.87102639, -0.42963687, 0.19637636],
+         [0., 0., 0., 1.]],
+        [[-0.78446989, 0.61157488, 0.10287448, 1.33330055],
+         [-0.58017785, -0.78232107, 0.22664378, 0.52660831],
+         [0.21909052, 0.11810973, 0.96852952, -0.02968529],
+         [0., 0., 0., 1.]]
+    ])
+    expected_matrix = xp.tile(expected_matrix, shape + (1, 1))
+    xp_assert_close(
+        RigidTransform.from_exp_coords(exp_coords).as_matrix(),
+        expected_matrix, atol=1e-8)
+
+    # identity
+    expected_matrix = xp.tile(xp.eye(4), shape + (1, 1))
+    exp_coords = xp.zeros(shape + (6,), dtype=dtype)
+    xp_assert_close(
+        RigidTransform.from_exp_coords(exp_coords).as_matrix(),
+        expected_matrix, atol=1e-12)
+
+    # only translation
+    expected_matrix = xp.asarray([
+        [[1.0, 0.0, 0.0, 3.0],
+         [0.0, 1.0, 0.0, -5.4],
+         [0.0, 0.0, 1.0, 100.2],
+         [0.0, 0.0, 0.0, 1.0]],
+        [[1.0, 0.0, 0.0, -3.0],
+         [0.0, 1.0, 0.0, 13.3],
+         [0.0, 0.0, 1.0, 1.3],
+         [0.0, 0.0, 0.0, 1.0]]
+    ])
+    expected_matrix = xp.tile(expected_matrix, shape + (1, 1, 1))
+    exp_coords = xp.asarray([
+        [0.0, 0.0, 0.0, 3.0, -5.4, 100.2],
+        [0.0, 0.0, 0.0, -3.0, 13.3, 1.3],
+    ])
+    exp_coords = xp.tile(exp_coords, shape + (1, 1))
+    actual = RigidTransform.from_exp_coords(exp_coords)
+    xp_assert_close(actual.as_matrix(), expected_matrix, atol=1e-12)
+
+    # only rotation
+    angles = xp.asarray([[34, -12, 0.5], [-102, -55, 30]])
+    angles = xp.tile(angles, shape + (1, 1))
+    rot = Rotation.from_euler('zyx', angles, degrees=True)
+    rotvec = rot.as_rotvec()
+    expected_matrix = xp.tile(xp.eye(4), shape + (2, 1, 1))
+    expected_matrix = xpx.at(expected_matrix)[..., :3, :3].set(rot.as_matrix())
+    exp_coords = xp.concat((rotvec, xp.zeros_like(rotvec)), axis=-1)
+    actual = RigidTransform.from_exp_coords(exp_coords)
+    xp_assert_close(actual.as_matrix(), expected_matrix, atol=1e-12)
+
+
+def test_from_exp_coords_array_like():
+    rng = np.random.default_rng(123)
+    # Test single transform
+    t = np.array([1, 2, 3])
+    r = Rotation.random(rng=rng)
+    tf_expected = RigidTransform.from_components(t, r)
+    exp_coords = tf_expected.as_exp_coords().tolist()
+    assert isinstance(exp_coords, list)
+    tf = RigidTransform.from_exp_coords(exp_coords)
+    xp_assert_close(tf.as_matrix(), tf_expected.as_matrix(), atol=1e-12)
+
+    # Test multiple transforms
+    t = [[1, 2, 3], [4, 5, 6]]
+    r = Rotation.random(len(t), rng=rng)
+    tf_expected = RigidTransform.from_components(t, r)
+    exp_coords = tf_expected.as_exp_coords().tolist()
+    assert isinstance(exp_coords, list)
+    tf = RigidTransform.from_exp_coords(exp_coords)
+    xp_assert_close(tf.as_matrix(), tf_expected.as_matrix(), atol=1e-12)
+
+
+@make_xp_test_case((RigidTransform, "as_exp_coords"))
+@pytest.mark.parametrize("ndim", range(1, 4))
+def test_as_exp_coords(xp, ndim: int):
+    shape = (ndim,) * (ndim - 1)
+    # identity
+    expected = xp.zeros(shape + (6,))
+    actual = RigidTransform.from_exp_coords(expected).as_exp_coords()
+    xp_assert_close(actual, expected, atol=1e-12)
+
+    rng = np.random.default_rng(10)
+
+    # pure rotation
+    rot_vec = xp.asarray(rng.normal(scale=0.1, size=shape + (1000, 3)))
+    tf = RigidTransform.from_rotation(Rotation.from_rotvec(rot_vec))
+    exp_coords = tf.as_exp_coords()
+    xp_assert_close(exp_coords[..., :3], rot_vec, atol=1e-12)
+    expected = xp.zeros_like(rot_vec)
+    xp_assert_close(exp_coords[..., 3:], expected, atol=1e-16)
+
+    # pure translation
+    translation = xp.asarray(rng.normal(scale=100.0, size=shape + (1000, 3)))
+    tf = RigidTransform.from_translation(translation)
+    exp_coords = tf.as_exp_coords()
+    xp_assert_close(exp_coords[..., :3], expected, atol=1e-16)
+    xp_assert_close(exp_coords[..., 3:], translation, atol=1e-15)
+
+
+@make_xp_test_case((RigidTransform, "from_dual_quat"))
+@pytest.mark.parametrize("ndim", range(1, 4))
+def test_from_dual_quat(xp, ndim: int):
+    dtype = xpx.default_dtype(xp)
+    atol = 1e-12 if dtype == xp.float64 else 1e-7
+    shape = (ndim,) * (ndim - 1)
+
+    # identity
+    dq = xp.asarray([0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0], dtype=dtype)
+    dq = xp.tile(dq, shape + (1,))
+    expected = xp.tile(xp.eye(4), shape + (1, 1))
+    xp_assert_close(RigidTransform.from_dual_quat(dq).as_matrix(), expected, atol=atol)
+    dq = xp.asarray([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], dtype=dtype)
+    dq = xp.tile(dq, shape + (1,))
+    xp_assert_close(RigidTransform.from_dual_quat(dq, scalar_first=True).as_matrix(),
+                    expected, atol=atol)
+
+    # only translation
+    dq = xp.asarray([0, 0, 0, 1, 0.25, 0.15, -0.7, 0], dtype=dtype)
+    dq = xp.tile(dq, shape + (1,))
+    actual = RigidTransform.from_dual_quat(dq)
+    expected_matrix = xp.asarray([
+        [1, 0, 0, 0.5],
+        [0, 1, 0, 0.3],
+        [0, 0, 1, -1.4],
+        [0, 0, 0, 1]
+    ])
+    expected_matrix = xp.tile(expected_matrix, shape + (1, 1))
+    xp_assert_close(actual.as_matrix(), expected_matrix, atol=atol)
+    dq = xp.asarray([1, 0, 0, 0, 0, 0.25, 0.15, -0.7], dtype=dtype)
+    dq = xp.tile(dq, shape + (1,))
+    actual = RigidTransform.from_dual_quat(dq, scalar_first=True)
+    xp_assert_close(actual.as_matrix(), expected_matrix, atol=atol)
+
+    # only rotation
+    angles = xp.asarray([65, -13, 90], dtype=dtype)
+    angles = xp.tile(angles, shape + (1,))
+    actual_rot = Rotation.from_euler("xyz", angles, degrees=True)
+    qrot = actual_rot.as_quat()
+    dq = xp.concat((qrot, xp.zeros_like(qrot)), axis=-1)
+    actual = RigidTransform.from_dual_quat(dq)
+    expected_matrix = xp.tile(xp.eye(4), shape + (1, 1))
+    expected_matrix = xpx.at(expected_matrix)[..., :3, :3].set(actual_rot.as_matrix())
+    xp_assert_close(actual.as_matrix(), expected_matrix, atol=atol)
+
+    qrot = actual_rot.as_quat(scalar_first=True)
+    dq = xp.concat((qrot, xp.zeros_like(qrot)), axis=-1)
+    actual = RigidTransform.from_dual_quat(dq, scalar_first=True)
+    expected_matrix = xp.tile(xp.eye(4), shape + (1, 1))
+    expected_matrix = xpx.at(expected_matrix)[..., :3, :3].set(actual_rot.as_matrix())
+    xp_assert_close(actual.as_matrix(), expected_matrix, atol=atol)
+
+    # rotation and translation
+    # rtol is set to 1e-7 because xp_assert_close deviates from
+    # np.testing.assert_allclose in that it does not automatically default to 1e-7 for
+    # floating point inputs.
+    # See https://numpy.org/doc/2.2/reference/generated/numpy.testing.assert_allclose.html
+    dq = xp.asarray(
+        [[0.0617101, -0.06483886, 0.31432811, 0.94508498,
+          0.04985168, -0.26119618, 0.1691491, -0.07743254],
+         [0.19507259, 0.49404931, -0.06091285, 0.8450749,
+          0.65049656, -0.30782513, 0.16566752, 0.04174544]])
+    dq = xp.tile(dq, shape + (1, 1))
+    actual = RigidTransform.from_dual_quat(dq)
+    expected_matrix = xp.asarray(
+        [[[0.79398752, -0.60213598, -0.08376202, 0.24605262],
+          [0.58613113, 0.79477941, -0.15740392, -0.4932833],
+          [0.16135089, 0.07588122, 0.98397557, 0.34262676],
+          [0., 0., 0., 1.]],
+         [[0.50440981, 0.2957028, 0.81125249, 1.20934468],
+          [0.08979911, 0.91647262, -0.3898898, -0.70540077],
+          [-0.8587822, 0.26951399, 0.43572393, -0.47776265],
+          [0., 0., 0., 1.]]])
+    expected_matrix = xp.tile(expected_matrix, shape + (1, 1, 1))
+    xp_assert_close(actual.as_matrix(), expected_matrix, atol=atol, rtol=1e-7)
+
+    dq = xp.asarray(
+        [[0.94508498, 0.0617101, -0.06483886, 0.31432811,
+          -0.07743254, 0.04985168, -0.26119618, 0.1691491],
+         [0.8450749, 0.19507259, 0.49404931, -0.06091285,
+          0.04174544, 0.65049656, -0.30782513, 0.16566752]])
+    dq = xp.tile(dq, shape + (1, 1))
+    actual = RigidTransform.from_dual_quat(dq, scalar_first=True)
+    xp_assert_close(actual.as_matrix(), expected_matrix, atol=atol, rtol=1e-7)
+
+    # unnormalized dual quaternions
+
+    # invalid real quaternion with norm 0
+    dq = xp.zeros(shape + (8,))
+    actual = RigidTransform.from_dual_quat(dq)
+    expected = xp.tile(xp.eye(4), shape + (1, 1))
+    xp_assert_close(actual.as_matrix(), expected, atol=atol)
+
+    # real quaternion with norm != 1
+    unnormalized_dual_quat = xp.asarray(
+        [-0.2547655, 1.23506123, 0.20230088, 0.24247194,  # norm 1.3
+         0.38559628, 0.08184063, 0.1755943, -0.1582222]  # orthogonal
+    )
+    xp_assert_close(xp_vector_norm(unnormalized_dual_quat[:4]), xp.asarray(1.3)[()],
+                    atol=atol)
+    xp_assert_close(xp.vecdot(unnormalized_dual_quat[:4],
+                              unnormalized_dual_quat[4:])[()],
+                    xp.asarray(0.0)[()], atol=1e-8)
+
+    dq = xp.tile(unnormalized_dual_quat, shape + (1,))
+    dual_quat = RigidTransform.from_dual_quat(dq).as_dual_quat()
+
+    expected_ones = xp.ones(shape) if shape != () else xp.asarray(1.0)[()]
+    expected_zeros = xp.zeros(shape) if shape != () else xp.asarray(0.0)[()]
+    xp_assert_close(xp_vector_norm(dual_quat[..., :4], axis=-1), expected_ones,
+                    atol=1e-12)
+    vecdot = xp.vecdot(dual_quat[..., :4], dual_quat[..., 4:])
+    vecdot = vecdot[()] if vecdot.shape == () else vecdot
+    xp_assert_close(vecdot, expected_zeros, atol=atol)
+
+    # real and dual quaternion are not orthogonal
+    unnormalized_dual_quat = xp.asarray(
+        [0.20824458, 0.75098079, 0.54542913, -0.30849493,  # unit norm
+         -0.16051025, 0.10742978, 0.21277201, 0.20596935]  # not orthogonal
+    )
+    xp_assert_close(xp_vector_norm(unnormalized_dual_quat[:4]), xp.asarray(1.0)[()],
+                    atol=atol)
+    assert xp.vecdot(unnormalized_dual_quat[:4], unnormalized_dual_quat[4:]) != 0.0
+    dq = xp.tile(unnormalized_dual_quat, shape + (1,))
+    dual_quat = RigidTransform.from_dual_quat(dq).as_dual_quat()
+
+    xp_assert_close(xp_vector_norm(dual_quat[..., :4], axis=-1), expected_ones,
+                    atol=1e-12)
+    vecdot = xp.vecdot(dual_quat[..., :4], dual_quat[..., 4:])
+    vecdot = vecdot[()] if vecdot.shape == () else vecdot
+    xp_assert_close(vecdot, expected_zeros, atol=atol)
+
+    # invalid real quaternion with norm 0, non-orthogonal dual quaternion
+    unnormalized_dual_quat = xp.asarray(
+        [0.0, 0.0, 0.0, 0.0, -0.16051025, 0.10742978, 0.21277201, 0.20596935])
+    assert xp.vecdot(xp.asarray([0.0, 0, 0, 1]), unnormalized_dual_quat[4:]) != 0.0
+    dq = xp.tile(unnormalized_dual_quat, shape + (1,))
+    dual_quat = RigidTransform.from_dual_quat(dq).as_dual_quat()
+
+    xp_assert_close(xp_vector_norm(dual_quat[..., :4], axis=-1), expected_ones,
+                    atol=1e-12)
+    vecdot = xp.vecdot(dual_quat[..., :4], dual_quat[..., 4:])
+    vecdot = vecdot[()] if vecdot.shape == () else vecdot
+    xp_assert_close(vecdot, expected_zeros, atol=atol)
+
+    # compensation for precision loss in real quaternion
+    rng = np.random.default_rng(1000)
+    t = xp.asarray(rng.normal(size=shape + (3,)), dtype=dtype)
+    q = xp.asarray(rng.normal(size=shape + (4,)), dtype=dtype)
+    r = Rotation.from_quat(q)
+    random_dual_quats = RigidTransform.from_components(t, r).as_dual_quat()
+
+    # ensure that random quaternions are not normalized
+    random_dual_quats = xpx.at(random_dual_quats)[..., :4].add(0.01)
+    assert not xp.any(xpx.isclose(xp_vector_norm(random_dual_quats[..., :4], axis=-1),
+                                  1.0, atol=0.0001))
+    dual_quat_norm = RigidTransform.from_dual_quat(
+        random_dual_quats).as_dual_quat()
+    xp_assert_close(xp_vector_norm(dual_quat_norm[..., :4], axis=-1), expected_ones,
+                    atol=atol)
+
+    # compensation for precision loss in dual quaternion, results in violation
+    # of orthogonality constraint
+    t = xp.asarray(rng.normal(size=shape + (3,)), dtype=dtype)
+    q = xp.asarray(rng.normal(size=shape + (4,)), dtype=dtype)
+    r = Rotation.from_quat(q)
+    random_dual_quats = RigidTransform.from_components(t, r).as_dual_quat()
+
+    # ensure that random quaternions are not normalized
+    random_dual_quats = xpx.at(random_dual_quats)[..., 4:].add(0.1)
+    q_norm = xp.vecdot(random_dual_quats[..., :4], random_dual_quats[..., 4:])
+    assert not xp.any(xpx.isclose(q_norm, 0.0, atol=0.0001))
+    dual_quat_norm = RigidTransform.from_dual_quat(
+        random_dual_quats).as_dual_quat()
+    vecdot = xp.vecdot(dual_quat[..., :4], dual_quat[..., 4:])
+    vecdot = vecdot[()] if vecdot.shape == () else vecdot
+    xp_assert_close(vecdot, expected_zeros, atol=atol)
+    xp_assert_close(random_dual_quats[..., :4], dual_quat_norm[..., :4], atol=atol)
+
+
+def test_from_dual_quat_array_like():
+    rng = np.random.default_rng(123)
+    # Test single transform
+    t = np.array([1, 2, 3])
+    r = Rotation.random(rng=rng)
+    tf_expected = RigidTransform.from_components(t, r)
+    dual_quat = tf_expected.as_dual_quat().tolist()
+    assert isinstance(dual_quat, list)
+    tf = RigidTransform.from_dual_quat(dual_quat)
+    xp_assert_close(tf.as_matrix(), tf_expected.as_matrix(), atol=1e-12)
+
+    # Test multiple transforms
+    t = [[1, 2, 3], [4, 5, 6]]
+    r = Rotation.random(len(t), rng=rng)
+    tf_expected = RigidTransform.from_components(t, r)
+    dual_quat = tf_expected.as_dual_quat().tolist()
+    assert isinstance(dual_quat, list)
+    tf = RigidTransform.from_dual_quat(dual_quat)
+    xp_assert_close(tf.as_matrix(), tf_expected.as_matrix(), atol=1e-12)
+
+
+@make_xp_test_case((RigidTransform, "as_dual_quat"))
+@pytest.mark.parametrize("ndim", range(1, 4))
+def test_as_dual_quat(xp, ndim: int):
+    dtype = xpx.default_dtype(xp)
+    shape = (ndim,) * (ndim - 1)
+    # identity
+    expected = xp.asarray([0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0], dtype=dtype)
+    actual = rigid_transform_to_xp(RigidTransform.identity(), xp).as_dual_quat()
+    xp_assert_close(actual, expected, atol=1e-12)
+
+    expected = xp.asarray([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0])
+    tf = rigid_transform_to_xp(RigidTransform.identity(), xp)
+    actual = tf.as_dual_quat(scalar_first=True)
+    xp_assert_close(actual, expected, atol=1e-12)
+
+    rng = np.random.default_rng(10)
+
+    # only rotation
+    for _ in range(10):
+        q = xp.asarray(rng.normal(size=shape + (4,)), dtype=dtype)
+        real_part = Rotation.from_quat(q).as_quat()
+        dual_part = xp.zeros_like(real_part)
+        expected = xp.concat((real_part, dual_part), axis=-1)
+        actual = RigidTransform.from_dual_quat(expected).as_dual_quat()
+        # because of double cover:
+        actual = actual * xp.sign(actual[..., 0, None])
+        expected = expected * xp.sign(expected[..., 0, None])
+        xp_assert_close(actual, expected, atol=1e-12)
+
+    # only translation
+    for _ in range(10):
+        tf = 0.5 * xp.asarray(rng.normal(size=shape + (3,)), dtype=dtype)
+        expected = xp.zeros(shape + (8,), dtype=dtype)
+        expected = xpx.at(expected)[..., 3].set(1.0)
+        expected = xpx.at(expected)[..., 4:7].set(tf)
+        actual = RigidTransform.from_dual_quat(expected).as_dual_quat()
+        # because of double cover:
+        actual = actual * xp.sign(actual[..., 0, None])
+        expected = expected * xp.sign(expected[..., 0, None])
+        xp_assert_close(actual, expected, atol=1e-12)
+
+    # rotation and translation
+    for _ in range(10):
+        t = xp.asarray(rng.normal(size=shape + (3,)), dtype=dtype)
+        r = Rotation.from_quat(xp.asarray(rng.normal(size=shape + (4,)), dtype=dtype))
+        expected = RigidTransform.from_components(t, r).as_dual_quat()
+        actual = RigidTransform.from_dual_quat(expected).as_dual_quat()
+        # because of double cover:
+        actual = actual * xp.sign(actual[..., 0, None])
+        expected = expected * xp.sign(expected[..., 0, None])
+        xp_assert_close(actual, expected, atol=1e-12)
+
+
+@make_xp_test_case(
+    (RigidTransform, "from_components"), (RigidTransform, "as_components"),
+    (RigidTransform, "from_exp_coords"), (RigidTransform, "as_exp_coords"),
+    (RigidTransform, "from_matrix"), (RigidTransform, "as_matrix"),
+    (RigidTransform, "from_dual_quat"), (RigidTransform, "as_dual_quat")
+)
+@pytest.mark.parametrize("ndim", range(1, 4))
+def test_from_as_internal_consistency(xp, ndim: int):
+    dtype = xpx.default_dtype(xp)
+    atol = 1e-12
+    n = 10
+    rng = np.random.default_rng(10)
+    shape = (n,) + (ndim,) * (ndim - 1)
+
+    t = xp.asarray(rng.normal(size=shape + (3,)), dtype=dtype)
+    r = Rotation.from_quat(xp.asarray(rng.normal(size=shape + (4,)), dtype=dtype))
+    tf0 = RigidTransform.from_components(t, r)
+
+    tf1 = RigidTransform.from_components(*tf0.as_components())
+    xp_assert_close(tf0.as_matrix(), tf1.as_matrix(), atol=atol)
+
+    tf1 = RigidTransform.from_components(tf0.translation, tf0.rotation)
+    xp_assert_close(tf0.as_matrix(), tf1.as_matrix(), atol=atol)
+
+    tf1 = RigidTransform.from_exp_coords(tf0.as_exp_coords())
+    xp_assert_close(tf0.as_matrix(), tf1.as_matrix(), atol=atol)
+
+    tf1 = RigidTransform.from_matrix(tf0.as_matrix())
+    xp_assert_close(tf0.as_matrix(), tf1.as_matrix(), atol=atol)
+
+    tf1 = RigidTransform.from_dual_quat(tf0.as_dual_quat())
+    xp_assert_close(tf0.as_matrix(), tf1.as_matrix(), atol=atol)
+
+    # exp_coords small rotation
+    t = xp.asarray(rng.normal(scale=1000.0, size=shape + (3,)), dtype=dtype)
+    rotvec = xp.asarray(rng.normal(scale=1e-10, size=shape + (3,)), dtype=dtype)
+    r = Rotation.from_rotvec(rotvec)
+    tf0 = RigidTransform.from_components(t, r)
+    tf1 = RigidTransform.from_exp_coords(tf0.as_exp_coords())
+    xp_assert_close(tf0.as_matrix(), tf1.as_matrix(), atol=atol)
+
+
+def test_identity():
+    # We do not use xp here because identity always returns numpy arrays
+    atol = 1e-12
+    # Test single identity
+    tf = RigidTransform.identity()
+    xp_assert_close(tf.as_matrix(), np.eye(4), atol=atol)
+    # Test multiple identities
+    tf = RigidTransform.identity(5)
+    xp_assert_close(tf.as_matrix(), np.array([np.eye(4)] * 5), atol=atol)
+    # Test shape
+    tf = RigidTransform.identity(shape=3)
+    expected = np.tile(np.eye(4), (3, 1, 1))
+    xp_assert_close(tf.as_matrix(), expected, atol=atol)
+    tf = RigidTransform.identity(shape=(2, 3))
+    expected = np.tile(np.eye(4), (2, 3, 1, 1))
+    xp_assert_close(tf.as_matrix(), expected, atol=atol)
+    # Test errors
+    with pytest.raises(ValueError, match="Only one of `num` and `shape` can be."):
+        RigidTransform.identity(10, shape=(2, 3))
+    with pytest.raises(TypeError, match="takes from 0 to 1 positional arguments"):
+        RigidTransform.identity(None, (-1, 3))  # Shape is kwarg only
+    with pytest.raises(ValueError, match="`shape` must be an int or a tuple of ints"):
+        RigidTransform.identity(shape="invalid")
+
+
+@make_xp_test_case((RigidTransform, "apply"))
+def test_apply(xp):
+    atol = 1e-12
+    # Broadcast shape: (6, 5, 4, 2) ( + (3,) for vectors, + (4,) for rotations)
+    vector_shapes = [(), (1,), (2,), (1, 2), (5, 1, 2)]
+    tf_shapes = [(), (1,), (2,), (1, 2), (4, 2), (1, 4, 2), (5, 4, 2), (6, 5, 4, 2)]
+    rng = np.random.default_rng(123)
+
+    for tf_shape, v_shape in product(tf_shapes, vector_shapes):
+        # Random rotation and translation
+        t = xp.asarray(rng.normal(size=tf_shape + (3,)))
+        q = xp.asarray(rng.normal(size=tf_shape + (4,)))
+        r = Rotation.from_quat(q)
+        tf = RigidTransform.from_components(t, r)
+
+        vecs = xp.asarray(rng.normal(size=v_shape + (3,)))
+        expected = t + r.apply(vecs)
+        res = tf.apply(vecs)
+        assert res.shape == np.broadcast_shapes(tf_shape, v_shape) + (3,)
+        xp_assert_close(res, expected, atol=atol)
+
+
+def test_apply_array_like():
+    rng = np.random.default_rng(123)
+    # Single vector
+    t = np.array([1, 2, 3])
+    r = Rotation.random(rng=rng)
+    tf = RigidTransform.from_components(t, r)
+    vec = [1, 0, 0]
+    expected = t + r.apply(vec)
+    xp_assert_close(tf.apply(vec), expected, atol=1e-12)
+
+    # Multiple vectors
+    t = np.array([[1, 2, 3], [4, 5, 6]])
+    r = Rotation.random(len(t), rng=rng)
+    tf = RigidTransform.from_components(t, r)
+    vec = [[1, 0, 0], [0, 1, 0]]
+    expected = t + r.apply(vec)
+    xp_assert_close(tf.apply(vec), expected, atol=1e-12)
+
+
+def test_apply_matrix_equivalence():
+    """Test documented equivalence for single transform:
+    `apply(vector) == translation + vector @ rotation.as_matrix().T.`"""
+    t = np.array([1.0, 2.0, 3.0])
+    r = Rotation.from_rotvec([0, 0, 1])
+    tf = RigidTransform.from_components(t, r)
+    # Single vector (3,)
+    v = np.array([1.0, 0.0, 0.0])
+    xp_assert_close(tf.apply(v), t + v @ r.as_matrix().T)
+    # Multiple vectors (P, 3)
+    arr = np.array([[1, 0, 0], [0, 1, 0]], dtype=float)
+    xp_assert_close(tf.apply(arr), t + arr @ r.as_matrix().T)
+
+
+@make_xp_test_case((RigidTransform, "apply"))
+def test_inverse_apply(xp):
+    atol = 1e-12
+    # Broadcast shape: (6, 5, 4, 2) ( + (3,) for vectors, + (4,) for rotations)
+    vector_shapes = [(), (1,), (2,), (1, 2), (5, 1, 2)]
+    tf_shapes = [(), (1,), (2,), (1, 2), (4, 2), (1, 4, 2), (5, 4, 2), (6, 5, 4, 2)]
+    rng = np.random.default_rng(123)
+
+    for tf_shape, v_shape in product(tf_shapes, vector_shapes):
+        # Random rotation and translation
+        t = xp.asarray(rng.normal(size=tf_shape + (3,)))
+        q = xp.asarray(rng.normal(size=tf_shape + (4,)))
+        r = Rotation.from_quat(q)
+        tf = RigidTransform.from_components(t, r)
+
+        vecs = xp.asarray(rng.normal(size=v_shape + (3,)))
+        expected = tf.inv().apply(vecs)
+        res = tf.apply(vecs, inverse=True)
+        assert res.shape == np.broadcast_shapes(tf_shape, v_shape) + (3,)
+        xp_assert_close(res, expected, atol=atol)
+
+
+@make_xp_test_case((RigidTransform, "apply"))
+def test_rotation_alone(xp):
+    atol = 1e-12
+
+    r = Rotation.from_euler('z', xp.asarray(90), degrees=True)
+    tf = RigidTransform.from_rotation(r)
+    vec = xp.asarray([1, 0, 0])
+    expected = r.apply(vec)
+    xp_assert_close(tf.apply(vec), expected, atol=atol)
+
+
+@make_xp_test_case((RigidTransform, "apply"))
+def test_translation_alone(xp):
+    atol = 1e-12
+    t = xp.asarray([1.0, 2, 3])
+    tf = RigidTransform.from_translation(t)
+    vec = xp.asarray([5.0, 6, 7])
+    expected = t + vec
+    xp_assert_close(tf.apply(vec), expected, atol=atol)
+
+
+@make_xp_test_case((RigidTransform, "apply"), (RigidTransform, "__mul__"))
+def test_composition(xp):
+    atol = 1e-12
+    tf_shapes = [(), (1,), (2,), (1, 2), (4, 2), (5, 4, 2)]
+    dtype = xpx.default_dtype(xp)
+    rng = np.random.default_rng(123)
+
+    for tf_shape1, tf_shape2 in product(tf_shapes, repeat=2):
+        # Random rotation and translation
+        t1 = xp.asarray(rng.normal(size=tf_shape1 + (3,)))
+        q1 = xp.asarray(rng.normal(size=tf_shape1 + (4,)))
+        r1 = Rotation.from_quat(q1)
+        tf1 = RigidTransform.from_components(t1, r1)
+
+        t2 = xp.asarray(rng.normal(size=tf_shape2 + (3,)))
+        q2 = xp.asarray(rng.normal(size=tf_shape2 + (4,)))
+        r2 = Rotation.from_quat(q2)
+        tf2 = RigidTransform.from_components(t2, r2)
+
+        composed = tf2 * tf1
+        vec = xp.asarray(rng.normal(size=(3,)), dtype=dtype)
+        expected = tf2.apply(tf1.apply(vec))
+        res = composed.apply(vec)
+        assert res.shape == np.broadcast_shapes(tf_shape1, tf_shape2) + (3,)
+        xp_assert_close(res, expected, atol=atol)
+
+        expected = t2 + r2.apply(t1 + r1.apply(vec))
+        xp_assert_close(composed.apply(vec), expected, atol=atol)
+        assert composed.single == (tf1.single and tf2.single)
+
+
+@make_xp_test_case((RigidTransform, "__pow__"), (RigidTransform, "__mul__"))
+@pytest.mark.parametrize("ndim", range(1, 4))
+def test_pow(xp, ndim: int):
+    dtype = xpx.default_dtype(xp)
+    atol = 1e-12 if dtype == xp.float64 else 1e-6
+    num = 10
+    rng = np.random.default_rng(100)
+    shape = (num,) + (ndim,) * (ndim - 1)
+    t = xp.asarray(rng.normal(size=shape + (3,)), dtype=dtype)
+    q = xp.asarray(rng.normal(size=shape + (4,)), dtype=dtype)
+    r = Rotation.from_quat(q)
+    p = RigidTransform.from_components(t, r)
+    p_inv = p.inv()
+
+    # Test the short-cuts and other integers
+    for n in [-5, -2, -1, 0, 1, 2, 5]:
+        q = p**n
+        # Regression test for gh-24436
+        assert isinstance(q._matrix, type(p._matrix))
+        r = RigidTransform.from_matrix(xp.tile(xp.eye(4), shape + (1, 1)))
+        for _ in range(abs(n)):
+            if n > 0:
+                r = r * p
+            else:
+                r = r * p_inv
+        xp_assert_close(q.as_matrix(), r.as_matrix(), atol=atol)
+
+    # Test shape preservation of single
+    single_tf = RigidTransform.identity()
+    assert (single_tf**n).as_matrix().shape == (4, 4)
+
+    # Test fractional powers
+    q = p**0.5
+    xp_assert_close((q * q).as_matrix(), p.as_matrix(), atol=atol)
+    q = p**-0.5
+    xp_assert_close((q * q).as_matrix(), p.inv().as_matrix(), atol=atol)
+    q = p** 1.5
+    xp_assert_close((q * q).as_matrix(), (p**3).as_matrix(), atol=atol)
+    q = p** -1.5
+    xp_assert_close((q * q).as_matrix(), (p**-3).as_matrix(), atol=atol)
+
+    # pow function
+    tf = pow(RigidTransform.from_matrix(xp.eye(4)), 2)
+    xp_assert_close(tf.as_matrix(), xp.eye(4), atol=atol)
+
+
+@make_xp_test_case((RigidTransform, "__pow__"))
+@pytest.mark.parametrize("ndim", range(1, 4))
+def test_pow_equivalence_with_rotation(xp, ndim: int):
+    atol = 1e-12
+    num = 10
+    rng = np.random.default_rng(100)
+    dtype = xpx.default_dtype(xp)
+    shape = (num,) + (ndim,) * (ndim - 1)
+
+    r = Rotation.from_quat(xp.asarray(rng.normal(size=shape + (4,)), dtype=dtype))
+    p = RigidTransform.from_rotation(r)
+    for n in [-5, -2, -1.5, -1, -0.5, 0.0, 0.5, 1, 1.5, 2, 5]:
+        xp_assert_close((p**n).rotation.as_matrix(), (r**n).as_matrix(), atol=atol)
+
+
+@make_xp_test_case((RigidTransform, "inv"), (RigidTransform, "__mul__"))
+@pytest.mark.parametrize("ndim", range(1, 4))
+def test_inverse(xp, ndim: int):
+    dtype = xpx.default_dtype(xp)
+    atol = 1e-12 if dtype == xp.float64 else 1e-6
+    rng = np.random.default_rng(100)
+    shape = (ndim,) * (ndim - 1)
+
+    # Test inverse transform
+    r = Rotation.from_quat(xp.asarray(rng.normal(size=shape + (4,)), dtype=dtype))
+    t = xp.asarray(rng.normal(size=shape + (3,)), dtype=dtype)
+    tf = RigidTransform.from_components(t, r)
+
+    # Test that tf * tf.inv() equals identity
+    tf_inv = tf.inv()
+    composed = tf * tf_inv
+    expected = xp.tile(xp.eye(4), shape + (1, 1))
+    xp_assert_close(composed.as_matrix(), expected, atol=atol)
+
+
+@make_xp_test_case((RigidTransform, "as_matrix"))
+@pytest.mark.parametrize("ndim", range(1, 4))
+def test_properties(xp, ndim: int):
+    atol = 1e-12 if xpx.default_dtype(xp) == xp.float64 else 1e-6
+    shape = (ndim,) * (ndim - 1)
+    dtype = xpx.default_dtype(xp)
+    rng = np.random.default_rng(100)
+
+    # Test rotation and translation properties
+    r = Rotation.from_quat(xp.asarray(rng.normal(size=shape + (4,)), dtype=dtype))
+    t = xp.asarray(rng.normal(size=shape + (3,)), dtype=dtype)
+    tf = RigidTransform.from_components(t, r)
+
+    xp_assert_close(tf.rotation.as_matrix(), r.as_matrix(), atol=atol)
+    assert xp.all(tf.rotation.approx_equal(r, atol=atol))
+    xp_assert_close(tf.translation, t, atol=atol)
+    # Test that we don't return views that would modify the original array
+    xpx.at(tf.translation)[..., 0].set(0.0)
+    xp_assert_close(tf.translation, t, atol=atol)
+    assert tf.single == (shape == ())
+
+
+@make_xp_test_case((RigidTransform, "__getitem__"))
+def test_indexing(xp):
+    atol = 1e-12
+
+    # Test indexing for multiple transforms
+    r = Rotation.from_euler('zyx', xp.asarray([[90, 0, 0], [0, 90, 0]]), degrees=True)
+    t = xp.asarray([[1.0, 2, 3], [4, 5, 6]])
+    tf = RigidTransform.from_components(t, r)
+
+    # Test single index
+    xp_assert_close(tf[0].as_matrix()[:3, :3], r[0].as_matrix(), atol=atol)
+    xp_assert_close(tf[0].as_matrix()[:3, 3], t[0, ...], atol=atol)
+
+    # Test slice
+    tf_slice = tf[0:2]
+    xp_assert_close(tf_slice.as_matrix()[:, :3, :3], r[0:2].as_matrix(), atol=atol)
+    xp_assert_close(tf_slice.as_matrix()[:, :3, 3], t[0:2, ...], atol=atol)
+
+    # Test boolean indexing
+    tf_masked = tf[xp.asarray([True, True])]
+    xp_assert_close(tf_masked.as_matrix()[:, :3, :3], r.as_matrix(), atol=atol)
+    xp_assert_close(tf_masked.as_matrix()[:, :3, 3], t, atol=atol)
+
+    tf_masked = tf[xp.asarray([False, True])]
+    xp_assert_close(tf_masked.as_matrix()[:, :3, :3],
+                    r[xp.asarray([False, True])].as_matrix(), atol=atol)
+    xp_assert_close(tf_masked.as_matrix()[:, :3, 3], t[xp.asarray([False, True])],
+                    atol=atol)
+
+    tf_masked = tf[xp.asarray([False, False])]
+    assert len(tf_masked) == 0
+
+    # Test integer array indexing
+    idx = xp.asarray([0, 1])
+    xp_assert_close(tf[idx].as_matrix()[:, :3, :3], r[idx].as_matrix(), atol=atol)
+    xp_assert_close(tf[idx].as_matrix()[:, :3, 3], t, atol=atol)
+
+
+def test_indexing_array_like():
+    atol = 1e-12
+
+    r = Rotation.from_euler('zyx', np.array([[90, 0, 0], [0, 90, 0]]), degrees=True)
+    t = np.array([[1.0, 2, 3], [4, 5, 6]])
+    tf = RigidTransform.from_components(t, r)
+
+    tf_masked = tf[[False, True]]
+    xp_assert_close(tf_masked.as_matrix()[:, :3, :3], r[[False, True]].as_matrix(),
+                    atol=atol)
+    xp_assert_close(tf_masked.as_matrix()[:, :3, 3], t[[False, True]], atol=atol)
+    tf_masked = tf[[False, False]]
+    assert len(tf_masked) == 0
+
+
+@make_xp_test_case((RigidTransform, "concatenate"))
+def test_concatenate(xp):
+    atol = 1e-12
+
+    # Test concatenation of transforms
+    t1 = xp.asarray([1, 0, 0])
+    r1 = Rotation.from_euler('z', xp.asarray(90), degrees=True)
+    tf1 = RigidTransform.from_components(t1, r1)
+
+    t2 = xp.asarray([0, 1, 0])
+    r2 = Rotation.from_euler('x', xp.asarray(90), degrees=True)
+    tf2 = RigidTransform.from_components(t2, r2)
+
+    # Concatenate single transforms
+    concatenated1 = RigidTransform.concatenate([tf1, tf2])
+    xp_assert_close(concatenated1[0].as_matrix(), tf1.as_matrix(), atol=atol)
+    xp_assert_close(concatenated1[1].as_matrix(), tf2.as_matrix(), atol=atol)
+
+    # Concatenate multiple transforms
+    concatenated2 = RigidTransform.concatenate([tf1, concatenated1])
+    xp_assert_close(concatenated2[0].as_matrix(), tf1.as_matrix(), atol=atol)
+    xp_assert_close(concatenated2[1].as_matrix(), tf1.as_matrix(), atol=atol)
+    xp_assert_close(concatenated2[2].as_matrix(), tf2.as_matrix(), atol=atol)
+
+    # Test ND concatenation
+    tf3 = RigidTransform.from_translation(xp.reshape(xp.arange(18), (3, 2, 3)))
+    tf4 = RigidTransform.from_translation(xp.reshape(xp.arange(18) + 18, (3, 2, 3)))
+    concatenated3 = RigidTransform.concatenate([tf3, tf4])
+    xp_assert_close(concatenated3.as_matrix()[:3, ...], tf3.as_matrix(), atol=atol)
+    xp_assert_close(concatenated3.as_matrix()[3:, ...], tf4.as_matrix(), atol=atol)
+
+
+@make_xp_test_case((RigidTransform, "from_matrix"))
+def test_input_validation(xp):
+    # Test invalid matrix shapes
+    inputs = [xp.eye(3), xp.zeros((4, 3)), []]
+    for input in inputs:
+        with pytest.raises(ValueError, match="Expected `matrix` to have shape"):
+            RigidTransform.from_matrix(input)
+
+    # Test invalid last row
+    for ndim in range(3):
+        shape = (ndim,) * (ndim - 1)
+        matrix = xp.zeros(shape + (4, 4))
+        matrix = xpx.at(matrix)[...].set(xp.eye(4))
+        matrix = xpx.at(matrix)[..., 3, :].set(xp.asarray([1.0, 0, 0, 1]))
+        if is_lazy_array(matrix):
+            matrix = RigidTransform.from_matrix(matrix).as_matrix()
+            assert xp.all(xp.isnan(matrix[..., 3, :]))
+        else:
+            with pytest.raises(ValueError, match="last row of transformation matrix"):
+                RigidTransform.from_matrix(matrix)
+
+    # Test left handed rotation matrix
+    matrix = xp.eye(4)
+    matrix = xpx.at(matrix)[0, 0].set(-1)
+    if is_lazy_array(matrix):
+        matrix = RigidTransform.from_matrix(matrix).as_matrix()
+        assert xp.all(xp.isnan(matrix[..., :3, :3]))
+    else:
+        with pytest.raises(ValueError, match="Non-positive determinant"):
+            RigidTransform(matrix, normalize=True)
+
+    # Test non-Rotation input
+    with pytest.raises(TypeError,
+                       match="Expected `rotation` to be a `Rotation` instance"):
+        RigidTransform.from_rotation(xp.eye(3))
+
+
+@make_xp_test_case((RigidTransform, "mean"))
+@pytest.mark.parametrize("ndim", range(1, 4))
+def test_mean(xp, ndim: int):
+    atol = 1e-12
+    rng = np.random.default_rng(123)
+
+    dtype = xpx.default_dtype(xp)
+    t = xp.asarray(rng.normal(size=(ndim,) * (ndim - 1) + (3,)), dtype=dtype)
+    q = xp.asarray(rng.normal(size=(ndim,) * (ndim - 1) + (4,)), dtype=dtype)
+    r = Rotation.from_quat(q)
+    tf = RigidTransform.from_components(t, r)
+
+    # Unweighted mean
+    axis = tuple(range(t.ndim - 1))
+    t_mean = xp.mean(t, axis=axis)
+    r_mean = r.mean()
+    tf_mean = tf.mean()
+    assert tf_mean.shape == ()
+    xp_assert_close(tf_mean.as_matrix(),
+                    RigidTransform.from_components(t_mean, r_mean).as_matrix(),
+                    atol=atol)
+
+    # Weighted mean
+    if ndim == 1:
+        weights = None
+        t_mean = t
+    else:
+        weights = xp.asarray(rng.random(size=(ndim,) * (ndim - 1)), dtype=dtype)
+        norm = xp.sum(weights[..., None], axis=axis)
+        wsum = xp.sum(t * weights[..., None], axis=axis)
+        t_mean = wsum/norm
+    r_mean = r.mean(weights=weights)
+    tf_mean = tf.mean(weights=weights)
+    assert tf_mean.shape == ()
+    xp_assert_close(tf_mean.as_matrix(),
+                    RigidTransform.from_components(t_mean, r_mean).as_matrix(),
+                    atol=atol)
+
+
+@make_xp_test_case(
+    (RigidTransform, "from_rotation"), (RigidTransform, "mean"), (Rotation, "magnitude")
+)
+@pytest.mark.parametrize("ndim", range(1, 5))
+def test_mean_axis(xp, ndim: int):
+    axes = xp.tile(xp.concat((-xp.eye(3), xp.eye(3))), (3,) * (ndim - 1) + (1, 1))
+    theta = xp.pi / 4
+    r = Rotation.from_rotvec(theta * axes)
+    tf = RigidTransform.from_rotation(r)
+
+    # Test mean over last axis
+    desired = xp.full(axes.shape[:-2], 0.0)
+    if ndim == 1:
+        desired = desired[()]
+    atol = 1e-6 if xpx.default_dtype(xp) is xp.float32 else 1e-10
+    xp_assert_close(tf.mean(axis=-1).rotation.magnitude(), desired, atol=atol)
+
+    # Test tuple axes
+    desired = xp.full(axes.shape[1:-2], 0.0)
+    if ndim < 3:
+        desired = desired[()]
+    xp_assert_close(tf.mean(axis=(0, -1)).rotation.magnitude(), desired, atol=atol)
+
+    # Empty axis tuple should return RigidTransform unchanged
+    tf_mean = tf.mean(axis=())
+    xp_assert_close(tf_mean.as_matrix(), tf.as_matrix(), atol=atol)
+
+
+@make_xp_test_case((RigidTransform, "mean"), (Rotation, "magnitude"))
+def test_mean_compare_axis(xp):
+    # Create a random set of transforms and compare the mean over an axis with
+    # the mean without axis of the sliced transform
+    atol = 1e-10 if xpx.default_dtype(xp) == xp.float64 else 1e-6
+    rng = np.random.default_rng(0)
+    q = xp.asarray(rng.normal(size=(4, 5, 6, 4)), dtype=xpx.default_dtype(xp))
+    r = Rotation.from_quat(q)
+    t = xp.asarray(rng.normal(size=(4, 5, 6, 3)), dtype=xpx.default_dtype(xp))
+    tf = RigidTransform.from_components(t, r)
+
+    mean_0 = tf.mean(axis=0)
+    for i in range(q.shape[1]):
+        for j in range(q.shape[2]):
+            r_slice = Rotation.from_quat(q[:, i, j, ...])
+            t_slice = t[:, i, j, ...]
+            mean_slice_tf = RigidTransform.from_components(t_slice, r_slice).mean()
+            xp_assert_close(
+                (mean_0[i][j].rotation * mean_slice_tf.rotation.inv()).magnitude(),
+                xp.asarray(0.0)[()], atol=atol,
+            )
+            xp_assert_close(
+                mean_0[i][j].translation, mean_slice_tf.translation, atol=atol,
+            )
+    mean_1_2 = tf.mean(axis=(1, 2))
+    for i in range(q.shape[0]):
+        r_slice = Rotation.from_quat(q[i, ...])
+        t_slice = t[i, ...]
+        mean_slice_tf = RigidTransform.from_components(t_slice, r_slice).mean()
+        xp_assert_close(
+            (mean_1_2[i].rotation * mean_slice_tf.rotation.inv()).magnitude(),
+            xp.asarray(0.0)[()], atol=atol,
+        )
+        xp_assert_close(
+            mean_1_2[i].translation, mean_slice_tf.translation, atol=atol,
+        )
+
+
+@make_xp_test_case((RigidTransform, "mean"))
+def test_mean_invalid_weights(xp):
+    tf = RigidTransform.from_matrix(xp.tile(xp.eye(4), (4, 1, 1)))
+    if is_lazy_array(tf.as_matrix()):
+        m = tf.mean(weights=-xp.ones(4))
+        assert xp.all(xp.isnan(m.as_matrix()))
+    else:
+        with pytest.raises(ValueError, match="non-negative"):
+            tf.mean(weights=-xp.ones(4))
+
+    # Test weight shape mismatch
+    tf = RigidTransform.from_matrix(xp.eye(4))
+    with pytest.raises(ValueError, match="Expected `weights` to"):
+        tf.mean(weights=xp.ones((2,)))
+    tf = RigidTransform.from_matrix(xp.tile(xp.eye(4), (3, 2, 1, 1, 1)))
+    with pytest.raises(ValueError, match="Expected `weights` to"):
+        tf.mean(weights=xp.ones((2, 1)))
+
+
+@make_xp_test_case((RigidTransform, "from_translation"))
+def test_translation_validation(xp):
+    # Test invalid translation shapes
+    with pytest.raises(ValueError, match="Expected `translation` to have shape"):
+        RigidTransform.from_translation(xp.asarray([1, 2]))
+
+    with pytest.raises(ValueError, match="Expected `translation` to have shape"):
+        RigidTransform.from_translation(xp.zeros((2, 2)))
+
+
+@make_xp_test_case((RigidTransform, "apply"))
+def test_vector_validation(xp):
+    tf = rigid_transform_to_xp(RigidTransform.identity(2), xp=xp)
+
+    # Test invalid vector shapes
+    with pytest.raises(ValueError, match="Expected vector to have shape"):
+        tf.apply(xp.asarray([1, 2]))
+
+    with pytest.raises(ValueError, match="Expected vector to have shape"):
+        tf.apply(xp.zeros((2, 2)))
+
+    with pytest.raises(ValueError, match="operands could not be broadcast"):
+        tf.apply(xp.zeros((1, 4, 3)))
+
+
+@make_xp_test_case((RigidTransform, "__getitem__"))
+def test_indexing_validation(xp):
+    tf = RigidTransform.from_matrix(xp.eye(4))
+
+    # Test indexing on single transform
+    with pytest.raises(TypeError, match="Single transform is not subscriptable"):
+        tf[0]
+
+    with pytest.raises(TypeError, match="Single transform is not subscriptable"):
+        tf[0:1]
+
+    # Test length on single transform
+    with pytest.raises(TypeError, match="Single transform has no len"):
+        len(tf)
+
+
+@make_xp_test_case((RigidTransform, "__mul__"))
+def test_composition_validation(xp):
+    tf2 = RigidTransform.from_translation(xp.asarray([[1, 2, 3], [4, 5, 6]]))
+    tf3 = RigidTransform.from_translation(xp.asarray([[1, 2, 3], [4, 5, 6], [7, 8, 9]]))
+
+    # Test incompatible shapes
+    with pytest.raises(ValueError, match="Cannot broadcast"):
+        tf2 * tf3
+
+    tf4 = RigidTransform.from_matrix(xp.tile(xp.eye(4), (1, 4, 1, 1)))
+    # Test invalid broadcasting shape
+    with pytest.raises(ValueError, match="Cannot broadcast"):
+        tf2 * tf4
+
+
+@make_xp_test_case((RigidTransform, "__mul__"), (RigidTransform, "__rmul__"))
+def test_rotation_promotion(xp):
+    """Test that Rotation is promoted to RigidTransform in composition."""
+    atol = 1e-12
+    dtype = xpx.default_dtype(xp)
+    rng = np.random.default_rng(0)
+
+    t = xp.asarray(rng.normal(size=(3,)), dtype=dtype)
+    r1 = rotation_to_xp(Rotation.random(rng=rng), xp)
+    r2 = rotation_to_xp(Rotation.random(rng=rng), xp)
+    tf = RigidTransform.from_components(t, r2)
+
+    # RigidTransform * Rotation
+    result = tf * r1
+    expected = tf * RigidTransform.from_rotation(r1)
+    assert isinstance(result, RigidTransform)
+    xp_assert_close(result.as_matrix(), expected.as_matrix(), atol=atol)
+
+    # Rotation * RigidTransform
+    result = r1 * tf
+    expected = RigidTransform.from_rotation(r1) * tf
+    assert isinstance(result, RigidTransform)
+    xp_assert_close(result.as_matrix(), expected.as_matrix(), atol=atol)
+
+
+@make_xp_test_case((RigidTransform, "concatenate"))
+def test_concatenate_validation(xp):
+    tf = RigidTransform.from_matrix(xp.eye(4))
+
+    # Test invalid inputs
+    with pytest.raises(TypeError,
+                       match="input must contain RigidTransform objects"):
+        RigidTransform.concatenate([tf, xp.eye(4)])
+
+    # Test incompatible shapes
+    tf2 = RigidTransform.from_translation(xp.ones((1, 1, 1, 3)))
+    # Frameworks have a highly heterogeneous way of reporting errors for this case
+    with pytest.raises((ValueError, TypeError, RuntimeError)):
+        RigidTransform.concatenate([tf, tf2])
+
+
+@make_xp_test_case((RigidTransform, "__setitem__"))
+def test_setitem(xp):
+    tf = RigidTransform.from_translation(xp.asarray([[1, 2, 3], [4, 5, 6], [7, 8, 9]]))
+    single = RigidTransform.from_translation(xp.asarray([1, 1, 1]))
+    double = RigidTransform.from_translation(xp.asarray([[2, 2, 2], [3, 3, 3]]))
+    triple = RigidTransform.from_translation(xp.asarray([[3, 3, 3],
+                                                         [4, 4, 4],
+                                                         [5, 5, 5]]))
+
+    # Test indexing with integer index
+    tf[0] = single
+    xp_assert_close(tf.translation, xp.asarray([[1.0, 1, 1], [4, 5, 6], [7, 8, 9]]))
+
+    # Test indexing with slice
+    tf = RigidTransform.from_translation(xp.asarray([[1, 2, 3], [4, 5, 6], [7, 8, 9]]))
+    tf[:2] = double
+    xp_assert_close(tf.translation, xp.asarray([[2.0, 2, 2], [3, 3, 3], [7, 8, 9]]))
+
+    # Test indexing with ellipsis
+    tf = RigidTransform.from_translation(xp.asarray([[1, 2, 3], [4, 5, 6], [7, 8, 9]]))
+    tf[...] = triple
+    xp_assert_close(tf.translation, xp.asarray([[3.0, 3, 3], [4, 4, 4], [5, 5, 5]]))
+
+    # Test indexing with boolean array
+    tf = RigidTransform.from_translation(xp.asarray([[1, 2, 3], [4, 5, 6], [7, 8, 9]]))
+    mask = xp.asarray([True, False, True])
+    tf[mask] = double
+    xp_assert_close(tf.translation, xp.asarray([[2.0, 2, 2], [4, 5, 6], [3, 3, 3]]))
+
+
+@make_xp_test_case((RigidTransform, "__setitem__"))
+@pytest.mark.skip_xp_backends("array_api_strict",
+                              reason="doesn't support fancy indexing __setitem__")
+def test_setitem_fancy_indexing(xp):
+    double = RigidTransform.from_translation(xp.asarray([[2, 2, 2], [3, 3, 3]]))
+    tf = RigidTransform.from_translation(xp.asarray([[1, 2, 3], [4, 5, 6], [7, 8, 9]]))
+    idx = xp.asarray([0, 2])
+    tf[idx] = double
+    xp_assert_close(tf.translation, xp.asarray([[2.0, 2, 2], [4, 5, 6], [3, 3, 3]]))
+
+
+@make_xp_test_case((RigidTransform, "__setitem__"))
+def test_setitem_validation(xp):
+    tf = RigidTransform.from_translation(xp.asarray([[1, 2, 3], [4, 5, 6]]))
+    single = RigidTransform.from_matrix(xp.eye(4))
+
+    # Test setting item on single transform
+    with pytest.raises(TypeError, match="Single transform is not subscriptable"):
+        single[0] = tf
+
+    # Test invalid value type
+    with pytest.raises(TypeError, match="value must be a RigidTransform"):
+        tf[0] = xp.eye(4)
+
+
+@pytest.mark.skip_xp_backends("jax.numpy",
+                              reason="JAX does not support memory sharing")
+@make_xp_test_case((RigidTransform, "as_matrix"))
+def test_copy_flag(xp):
+    # Test that copy=True creates new memory
+    matrix = xp.eye(4)
+    tf = RigidTransform(matrix, normalize=False, copy=True)
+    matrix[0, 0] = 2
+    assert tf.as_matrix()[0, 0] == 1
+
+    # Test that copy=False shares memory
+    matrix = xp.eye(4)
+    tf = RigidTransform(matrix, normalize=False, copy=False)
+    matrix[0, 0] = 2
+    assert tf.as_matrix()[0, 0] == 2
+
+
+@make_xp_test_case(normalize_dual_quaternion)
+@pytest.mark.parametrize("ndim", range(1, 4))
+def test_normalize_dual_quaternion(xp, ndim: int):
+    dtype = xpx.default_dtype(xp)
+    atol = 1e-12 if dtype == xp.float64 else 1e-6
+    rng = np.random.default_rng(100)
+    shape = (ndim,) * (ndim - 1)
+
+    dual_quat = normalize_dual_quaternion(xp.zeros((1, 8)))
+    xp_assert_close(xp_vector_norm(dual_quat[0, :4], axis=-1), xp.asarray(1.0)[()],
+                    atol=1e-12)
+    xp_assert_close(xp.vecdot(dual_quat[0, :4], dual_quat[0, 4:])[()],
+                    xp.asarray(0.0)[()], atol=1e-12)
+
+    dual_quat = xp.asarray(rng.normal(size=shape + (8,)), dtype=dtype)
+    dual_quat = normalize_dual_quaternion(dual_quat)
+    expected = xp.ones(shape) if shape != () else xp.asarray(1.0)[()]
+    xp_assert_close(xp_vector_norm(dual_quat[..., :4], axis=-1), expected, atol=atol)
+    expected = xp.zeros(shape) if shape != () else xp.asarray(0.0)[()]
+    vecdot = xp.vecdot(dual_quat[..., :4], dual_quat[..., 4:])
+    vecdot = vecdot[()] if vecdot.shape == () else vecdot
+    xp_assert_close(vecdot, expected, atol=atol)
+
+
+@make_xp_test_case(
+    (RigidTransform, "from_matrix"), (RigidTransform, "from_rotation"),
+    (RigidTransform, "from_translation"), (RigidTransform, "from_components"),
+    (RigidTransform, "from_exp_coords"), (RigidTransform, "from_dual_quat")
+)
+def test_empty_transform_construction(xp):
+    tf = RigidTransform.from_matrix(xp.empty((0, 4, 4)))
+    assert len(tf) == 0
+    assert not tf.single
+
+    tf = RigidTransform.from_rotation(Rotation.from_quat(xp.zeros((0, 4))))
+    assert len(tf) == 0
+    assert not tf.single
+
+    tf = RigidTransform.from_translation(xp.empty((0, 3)))
+    assert len(tf) == 0
+    assert not tf.single
+
+    empty_rot = Rotation.from_quat(xp.zeros((0, 4)))
+    tf = RigidTransform.from_components(xp.empty((0, 3)), empty_rot)
+    assert len(tf) == 0
+    assert not tf.single
+
+    tf = RigidTransform.from_exp_coords(xp.empty((0, 6)))
+    assert len(tf) == 0
+    assert not tf.single
+
+    tf = RigidTransform.from_dual_quat(xp.empty((0, 8)))
+    assert len(tf) == 0
+    assert not tf.single
+
+    tf = RigidTransform.identity(0)
+    assert len(tf) == 0
+    assert not tf.single
+
+
+@make_xp_test_case((RigidTransform, "from_matrix"), (RigidTransform, "as_components"),
+                   (RigidTransform, "as_exp_coords"), (RigidTransform, "as_dual_quat"))
+def test_empty_transform_representation(xp):
+    tf = RigidTransform.from_matrix(xp.empty((0, 4, 4)))
+
+    assert len(tf.rotation) == 0
+    assert tf.translation.shape == (0, 3)
+
+    t, r = tf.as_components()
+    assert t.shape == (0, 3)
+    assert len(r) == 0
+
+    assert tf.as_matrix().shape == (0, 4, 4)
+    assert tf.as_exp_coords().shape == (0, 6)
+    assert tf.as_dual_quat().shape == (0, 8)
+
+
+@make_xp_test_case((RigidTransform, "from_matrix"), (RigidTransform, "apply"))
+def test_empty_transform_application(xp):
+    tf = RigidTransform.from_matrix(xp.empty((0, 4, 4)))
+
+    assert tf.apply(xp.zeros((3,))).shape == (0, 3)
+    assert tf.apply(xp.empty((0, 3))).shape == (0, 3)
+
+    with pytest.raises(ValueError, match="operands could not be broadcast together"):
+        tf.apply(xp.zeros((2, 3)))
+
+
+@make_xp_test_case((RigidTransform, "from_matrix"), (RigidTransform, "__mul__"))
+def test_empty_transform_composition(xp):
+    tf_empty = RigidTransform.from_matrix(xp.empty((0, 4, 4)))
+    tf_single = RigidTransform.from_matrix(xp.eye(4))
+    tf_many = rigid_transform_to_xp(RigidTransform.identity(3), xp=xp)
+
+    assert len(tf_empty * tf_empty) == 0
+    assert len(tf_empty * tf_single) == 0
+    assert len(tf_single * tf_empty) == 0
+
+    with pytest.raises(ValueError, match="Cannot broadcast"):
+        tf_many * tf_empty
+
+    with pytest.raises(ValueError, match="Cannot broadcast"):
+        tf_empty * tf_many
+
+
+@make_xp_test_case((RigidTransform, "from_matrix"), (RigidTransform, "concatenate"))
+def test_empty_transform_concatenation(xp):
+    tf_empty = RigidTransform.from_matrix(xp.empty((0, 4, 4)))
+    tf_single = RigidTransform.from_matrix(xp.eye(4))
+    tf_many = rigid_transform_to_xp(RigidTransform.identity(2), xp=xp)
+
+    assert len(RigidTransform.concatenate([tf_empty, tf_empty])) == 0
+    assert len(RigidTransform.concatenate([tf_empty, tf_single])) == 1
+    assert len(RigidTransform.concatenate([tf_single, tf_empty])) == 1
+    assert len(RigidTransform.concatenate([tf_empty, tf_many])) == 2
+    assert len(RigidTransform.concatenate([tf_many, tf_empty])) == 2
+    assert len(RigidTransform.concatenate([tf_many, tf_empty, tf_single])) == 3
+
+
+@make_xp_test_case((RigidTransform, "from_matrix"), (RigidTransform, "inv"),
+                   (RigidTransform, "__pow__"))
+def test_empty_transform_inv_and_pow(xp):
+    tf = RigidTransform.from_matrix(xp.empty((0, 4, 4)))
+    assert len(tf.inv()) == 0
+    assert len(tf ** 0) == 0
+    assert len(tf ** 1) == 0
+    assert len(tf ** -1) == 0
+    assert len(tf ** 0.5) == 0
+
+
+@make_xp_test_case((RigidTransform, "__getitem__"))
+def test_empty_transform_indexing(xp):
+    tf_many = rigid_transform_to_xp(RigidTransform.identity(3), xp=xp)
+    tf_zero = tf_many[xp.asarray([], dtype=xp.int32)]
+    assert len(tf_zero) == 0
+
+    # Array API does not specify out-of-bounds indexing. Only check for numpy.
+    if is_numpy(xp):
+        assert len(tf_zero[:5]) == 0  # Slices can go out of bounds.
+
+    with pytest.raises(IndexError):
+        tf_zero[0]
+
+    with pytest.raises(IndexError):
+        tf_zero[xp.asarray([0, 2])]
+
+    with pytest.raises(IndexError):
+        tf_zero[xp.asarray([False, True])]
+
+
+@make_xp_test_case((RigidTransform, "from_matrix"))
+@pytest.mark.skip_xp_backends("array_api_strict",
+                              reason="array API doesn't support pickling")
+def test_pickling(xp):
+    # Note: Array API makes no provision for arrays to be pickleable, so
+    # it's OK to skip this test for the backends that don't support it
+    mat = xp.eye(4)
+    mat = xpx.at(mat)[0, 3].set(2.0)
+    tf = RigidTransform.from_matrix(mat)
+    pkl = pickle.dumps(tf)
+    unpickled = pickle.loads(pkl)
+    xp_assert_close(tf.as_matrix(), unpickled.as_matrix(), atol=1e-15)
+
+
+@make_xp_test_case(
+    (RigidTransform, "as_matrix"),
+    (RigidTransform, "__iter__"),
+    (RigidTransform, "identity"),
+)
+def test_rigid_transform_iter(xp):
+    r = rigid_transform_to_xp(RigidTransform.identity(3), xp)
+    for i, r_i in enumerate(r):
+        assert isinstance(r_i, RigidTransform)
+        xp_assert_equal(r_i.as_matrix(), r[i].as_matrix())
+        if i > len(r):
+            raise RuntimeError("Iteration exceeded length of transforms")
+
+
+@make_xp_test_case((RigidTransform, "from_translation"))
+@pytest.mark.parametrize("dim", range(1, 5))
+def test_shape_property(xp, dim: int):
+    shape = (dim,) * (dim - 1)
+    tf = RigidTransform.from_translation(xp.zeros(shape + (3,)))
+    assert tf.shape == shape
+
+
+def test_non_writeable():
+    mat = np.eye(4)
+    mat.flags.writeable = False
+    RigidTransform.from_matrix(mat)  # Regression test against gh-24378
diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/transform/tests/test_rotation.py b/venv/lib/python3.12/site-packages/scipy/spatial/transform/tests/test_rotation.py
new file mode 100644
index 0000000000000000000000000000000000000000..b2f96b93c20e41389ef64912285147e77a52cddd
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/transform/tests/test_rotation.py
@@ -0,0 +1,3223 @@
+import math
+
+import pytest
+
+import numpy as np
+from numpy.testing import assert_equal
+from scipy.spatial.transform import Rotation, Slerp
+import scipy.spatial.transform._rotation_cy as cython_backend
+import scipy.spatial.transform._rotation_xp as xp_backend
+from scipy.stats import special_ortho_group
+from itertools import permutations, product
+from contextlib import contextmanager
+import warnings
+from scipy._lib._array_api import (
+    xp_assert_equal,
+    array_namespace,
+    is_numpy,
+    is_lazy_array,
+    xp_vector_norm,
+    xp_assert_close,
+    eager_warns,
+    xp_default_dtype,
+    make_xp_test_case,
+    make_xp_pytest_marks,
+    xp_device_type,
+)
+import scipy._external.array_api_extra as xpx
+
+import pickle
+import copy
+
+
+# from_quat and as_quat are used in almost all tests, so we mark them module-wide
+pytestmark = make_xp_pytest_marks((Rotation, "as_quat"), (Rotation, "from_quat"))
+
+
+def basis_vec(axis):
+    if axis == 'x':
+        return [1, 0, 0]
+    elif axis == 'y':
+        return [0, 1, 0]
+    elif axis == 'z':
+        return [0, 0, 1]
+
+
+def rotation_to_xp(r: Rotation, xp):
+    dtype = xpx.default_dtype(xp)
+    return Rotation.from_quat(xp.asarray(r.as_quat(), dtype=dtype))
+
+
+def test_init_non_array():
+    Rotation((0, 0, 0, 1))
+    Rotation([0, 0, 0, 1])
+    Rotation([[[0, 0, 0, 1]]])
+
+
+def test_cython_backend_selection():
+    r = Rotation.from_quat(np.array([0, 0, 0, 1]))
+    assert r._backend is cython_backend
+    r = Rotation.from_quat(np.array([[0, 0, 0, 1]]))
+    assert r._backend is cython_backend
+    r = Rotation.from_quat(np.array([[[0, 0, 0, 1]]]))
+    assert r._backend is xp_backend
+
+
+def test_numpy_float32_inputs():
+    Rotation.from_quat(np.array([1, 0, 0, 0], dtype=np.float32))
+
+
+def test_generic_quat_matrix(xp):
+    x = xp.asarray([[3.0, 4, 0, 0], [5, 12, 0, 0]])
+    r = Rotation.from_quat(x)
+    expected_quat = x / xp.asarray([[5.0], [13.0]])
+    xp_assert_close(r.as_quat(), expected_quat)
+
+
+@pytest.mark.parametrize("ndim", list(range(1, 6)))
+def test_from_single_nd_quaternion(xp, ndim: int):
+    x = xp.asarray([3.0, 4, 0, 0])
+    x = xp.reshape(x, (1,) * (ndim - 1) + (4,))
+    r = Rotation.from_quat(x)
+    expected_quat = x / 5
+    xp_assert_close(r.as_quat(), expected_quat)
+
+
+@make_xp_test_case((Rotation, "as_matrix"))
+def test_from_quat_scalar_first(xp):
+    rng = np.random.RandomState(0)
+
+    r = Rotation.from_quat(xp.asarray([1, 0, 0, 0]), scalar_first=True)
+    xp_assert_close(r.as_matrix(), xp.eye(3), rtol=1e-15, atol=1e-16)
+
+    q = xp.tile(xp.asarray([1, 0, 0, 0]), (10, 1))
+    r = Rotation.from_quat(q, scalar_first=True)
+    xp_assert_close(
+        r.as_matrix(), xp.tile(xp.eye(3), (10, 1, 1)), rtol=1e-15, atol=1e-16
+    )
+
+    q = xp.asarray(rng.randn(100, 4))
+    q /= xp_vector_norm(q, axis=1)[:, None]
+    for i in range(q.shape[0]):  # Array API conforming loop
+        qi = q[i, ...]
+        r = Rotation.from_quat(qi, scalar_first=True)
+        xp_assert_close(xp.roll(r.as_quat(), 1), qi, rtol=1e-15)
+
+    r = Rotation.from_quat(q, scalar_first=True)
+    xp_assert_close(xp.roll(r.as_quat(), 1, axis=1), q, rtol=1e-15)
+
+
+def test_from_quat_array_like():
+    rng = np.random.default_rng(123)
+    # Single rotation
+    r_expected = Rotation.random(rng=rng)
+    r = Rotation.from_quat(r_expected.as_quat().tolist())
+    assert r_expected.approx_equal(r, atol=1e-12)
+
+    # Multiple rotations
+    r_expected = Rotation.random(3, rng=rng)
+    r = Rotation.from_quat(r_expected.as_quat().tolist())
+    assert np.all(r_expected.approx_equal(r, atol=1e-12))
+
+    # Tensor of rotations
+    q = rng.normal(size=(3, 4, 5, 4))
+    q /= xp_vector_norm(q, axis=-1)[..., None]
+    r_expected = Rotation.from_quat(q)
+    r = Rotation.from_quat(q)
+    assert np.all(r_expected.approx_equal(r, atol=1e-12))
+
+
+def test_from_quat_int_dtype(xp):
+    r = Rotation.from_quat(xp.asarray([1, 0, 0, 0]))
+    assert r.as_quat().dtype == xp_default_dtype(xp)
+
+
+def test_quat_canonical(xp):
+    # Case 0: w < 0
+    q = xp.asarray([0.0, 0, 0, -1])
+    xp_assert_close(Rotation.from_quat(q).as_quat(canonical=True), -q)
+    # Case 1: w == 0, x < 0
+    q = xp.asarray([-1.0, 0, 0, 0])
+    xp_assert_close(Rotation.from_quat(q).as_quat(canonical=True), -q)
+    # Case 2: w == 0, x == 0, y < 0
+    q = xp.asarray([0.0, -1, 0, 0])
+    xp_assert_close(Rotation.from_quat(q).as_quat(canonical=True), -q)
+    # Case 3: w == 0, x == 0, y == 0, z < 0
+    q = xp.asarray([0.0, 0, -1, 0])
+    xp_assert_close(Rotation.from_quat(q).as_quat(canonical=True), -q)
+    # Other cases: w > 0, y < 0
+    q = xp.asarray([0.0, -0.1, 0, 0.9])
+    q = q / xp_vector_norm(q)
+    xp_assert_close(Rotation.from_quat(q).as_quat(canonical=True), q)
+    # Other cases: w > 0, z < 0
+    q = xp.asarray([0.0, 0.0, -0.1, 0.9])
+    q = q / xp_vector_norm(q)
+    xp_assert_close(Rotation.from_quat(q).as_quat(canonical=True), q)
+
+
+@make_xp_test_case((Rotation, "from_euler"))
+def test_as_quat_scalar_first(xp):
+    rng = np.random.RandomState(0)
+
+    r = Rotation.from_euler('xyz', xp.zeros(3))
+    xp_assert_close(r.as_quat(scalar_first=True), xp.asarray([1.0, 0, 0, 0]),
+                    rtol=1e-15, atol=1e-16)
+
+    r = Rotation.from_euler('xyz', xp.zeros((10, 3)))
+    xp_assert_close(r.as_quat(scalar_first=True),
+                    xp.tile(xp.asarray([1.0, 0, 0, 0]), (10, 1)),
+                    rtol=1e-15, atol=1e-16)
+
+    q = xp.asarray(rng.randn(100, 4))
+    q /= xp_vector_norm(q, axis=1)[:, None]
+    for i in range(q.shape[0]):  # Array API conforming loop
+        qi = q[i, ...]
+        r = Rotation.from_quat(qi)
+        xp_assert_close(r.as_quat(scalar_first=True), xp.roll(qi, 1),
+                        rtol=1e-15)
+
+        xp_assert_close(r.as_quat(canonical=True, scalar_first=True),
+                        xp.roll(r.as_quat(canonical=True), 1),
+                        rtol=1e-15)
+
+    r = Rotation.from_quat(q)
+    xp_assert_close(r.as_quat(scalar_first=True), xp.roll(q, 1, axis=1),
+                    rtol=1e-15)
+
+    xp_assert_close(r.as_quat(canonical=True, scalar_first=True),
+                    xp.roll(r.as_quat(canonical=True), 1, axis=1), rtol=1e-15)
+
+
+def test_from_square_quat_matrix(xp):
+    # Ensure proper norm array broadcasting
+    x = xp.asarray([
+        [3.0, 0, 0, 4],
+        [5, 0, 12, 0],
+        [0, 0, 0, 1],
+        [-1, -1, -1, 1],
+        [0, 0, 0, -1],  # Check double cover
+        [-1, -1, -1, -1]  # Check double cover
+        ])
+    r = Rotation.from_quat(x)
+    expected_quat = x / xp.asarray([[5.0], [13], [1], [2], [1], [2]])
+    xp_assert_close(r.as_quat(), expected_quat)
+
+
+def test_quat_double_to_canonical_single_cover(xp):
+    x = xp.asarray([
+        [-1.0, 0, 0, 0],
+        [0, -1, 0, 0],
+        [0, 0, -1, 0],
+        [0, 0, 0, -1],
+        [-1, -1, -1, -1]
+        ])
+    r = Rotation.from_quat(x)
+    expected_quat = xp.abs(x) / xp_vector_norm(x, axis=1)[:, None]
+    xp_assert_close(r.as_quat(canonical=True), expected_quat)
+
+
+@make_xp_test_case((Rotation, "inv"), (Rotation, "__mul__"))
+def test_quat_double_cover(xp):
+    # See the Rotation.from_quat() docstring for scope of the quaternion
+    # double cover property.
+    # Check from_quat and as_quat(canonical=False)
+    q = xp.asarray([0.0, 0, 0, -1])
+    r = Rotation.from_quat(q)
+    xp_assert_equal(q, r.as_quat(canonical=False))
+    # Check composition and inverse
+    q = xp.asarray([1.0, 0, 0, 1])/math.sqrt(2)  # 90 deg rotation about x
+    r = Rotation.from_quat(q)
+    r3 = r*r*r
+    xp_assert_close(r.as_quat(canonical=False)*math.sqrt(2),
+                    xp.asarray([1.0, 0, 0, 1]))
+    xp_assert_close(r.inv().as_quat(canonical=False)*math.sqrt(2),
+                    xp.asarray([-1.0, 0, 0, 1]))
+    xp_assert_close(r3.as_quat(canonical=False)*math.sqrt(2),
+                    xp.asarray([1.0, 0, 0, -1]))
+    xp_assert_close(r3.inv().as_quat(canonical=False)*math.sqrt(2),
+                    xp.asarray([-1.0, 0, 0, -1]))
+
+    # More sanity checks
+    xp_assert_close((r*r.inv()).as_quat(canonical=False),
+                    xp.asarray([0.0, 0, 0, 1]), atol=2e-16)
+    xp_assert_close((r3*r3.inv()).as_quat(canonical=False),
+                    xp.asarray([0.0, 0, 0, 1]), atol=2e-16)
+    xp_assert_close((r*r3).as_quat(canonical=False),
+                    xp.asarray([0.0, 0, 0, -1]), atol=2e-16)
+    xp_assert_close((r.inv() * r3.inv()).as_quat(canonical=False),
+                    xp.asarray([0.0, 0, 0, -1]), atol=2e-16)
+
+
+@pytest.mark.parametrize("ndim", list(range(1, 6)))
+def test_from_quat_wrong_shape(xp, ndim: int):
+    quat = xp.zeros((*((1,) * ndim), 5))
+    with pytest.raises(ValueError, match="Expected `quat` to have shape"):
+        Rotation.from_quat(quat)
+
+
+def test_zero_norms_from_quat(xp):
+    x = xp.asarray([
+            [3, 4, 0, 0],
+            [0, 0, 0, 0],
+            [5, 0, 12, 0]
+            ])
+    if is_lazy_array(x):
+        assert xp.all(xp.isnan(Rotation.from_quat(x).as_quat()[1, ...]))
+    else:
+        with pytest.raises(ValueError):
+            Rotation.from_quat(x)
+
+
+@make_xp_test_case((Rotation, "as_matrix"))
+@pytest.mark.parametrize("ndim", list(range(1, 6)))
+def test_as_matrix_single_nd_quaternion(xp, ndim: int):
+    quat = xp.asarray([0, 0, 1, 1])
+    quat = xp.reshape(quat, (1,) * (ndim - 1) + (4,))
+    mat = Rotation.from_quat(quat).as_matrix()
+    expected_mat = xp.asarray([
+        [0.0, -1, 0],
+        [1, 0, 0],
+        [0, 0, 1]
+        ])
+    expected_mat = xp.reshape(expected_mat, (1,) * (ndim - 1) + (3, 3))
+    xp_assert_close(mat, expected_mat, atol=1e-16)
+
+
+@make_xp_test_case((Rotation, "as_matrix"))
+def test_as_matrix_from_square_input(xp):
+    quats = xp.asarray([
+            [0, 0, 1, 1],
+            [0, 1, 0, 1],
+            [0, 0, 0, 1],
+            [0, 0, 0, -1]
+            ])
+    mat = Rotation.from_quat(quats).as_matrix()
+    assert_equal(mat.shape, (4, 3, 3))
+
+    expected0 = xp.asarray([
+        [0.0, -1, 0],
+        [1, 0, 0],
+        [0, 0, 1]
+        ])
+    xp_assert_close(mat[0, ...], expected0, atol=1e-16)
+
+    expected1 = xp.asarray([
+        [0.0, 0, 1],
+        [0, 1, 0],
+        [-1, 0, 0]
+        ])
+    xp_assert_close(mat[1, ...], expected1, atol=1e-16)
+    xp_assert_close(mat[2, ...], xp.eye(3))
+    xp_assert_close(mat[3, ...], xp.eye(3))
+
+
+@make_xp_test_case((Rotation, "as_matrix"))
+def test_as_matrix_from_generic_input(xp):
+    quats = xp.asarray([
+            [0, 0, 1, 1],
+            [0, 1, 0, 1],
+            [1, 2, 3, 4]
+            ])
+    mat = Rotation.from_quat(quats).as_matrix()
+    assert_equal(mat.shape, (3, 3, 3))
+
+    expected0 = xp.asarray([
+        [0.0, -1, 0],
+        [1, 0, 0],
+        [0, 0, 1]
+        ])
+    xp_assert_close(mat[0, ...], expected0, atol=1e-16)
+
+    expected1 = xp.asarray([
+        [0.0, 0, 1],
+        [0, 1, 0],
+        [-1, 0, 0]
+        ])
+    xp_assert_close(mat[1, ...], expected1, atol=1e-16)
+
+    expected2 = xp.asarray([
+        [0.4, -2, 2.2],
+        [2.8, 1, 0.4],
+        [-1, 2, 2]
+        ]) / 3
+    xp_assert_close(mat[2, ...], expected2)
+
+
+@make_xp_test_case((Rotation, "from_matrix"))
+@pytest.mark.parametrize("ndim", list(range(1, 6)))
+def test_from_single_nd_matrix(xp, ndim: int):
+    mat = xp.asarray([
+            [0, 0, 1],
+            [1, 0, 0],
+            [0, 1, 0]
+            ])
+    mat = xp.reshape(mat, (1,) * (ndim - 1) + (3, 3))
+    expected_quat = xp.asarray([0.5, 0.5, 0.5, 0.5])
+    expected_quat = xp.reshape(expected_quat, (1,) * (ndim - 1) + (4,))
+    xp_assert_close(Rotation.from_matrix(mat).as_quat(), expected_quat)
+
+
+@make_xp_test_case((Rotation, "from_matrix"))
+def test_from_matrix_calculation(xp):
+    atol = 1e-8
+    expected_quat = xp.asarray([1.0, 1, 6, 1]) / math.sqrt(39)
+    mat = xp.asarray([
+            [-0.8974359, -0.2564103, 0.3589744],
+            [0.3589744, -0.8974359, 0.2564103],
+            [0.2564103, 0.3589744, 0.8974359]
+            ])
+    xp_assert_close(Rotation.from_matrix(mat).as_quat(), expected_quat, atol=atol)
+    xp_assert_close(Rotation.from_matrix(xp.reshape(mat, (1, 3, 3))).as_quat(),
+                    xp.reshape(expected_quat, (1, 4)),
+                    atol=atol)
+
+
+@make_xp_test_case((Rotation, "from_matrix"), (Rotation, "as_matrix"))
+def test_matrix_calculation_pipeline(xp):
+    mat = xp.asarray(special_ortho_group.rvs(3, size=10, random_state=0))
+    xp_assert_close(Rotation.from_matrix(mat).as_matrix(), mat)
+
+
+@make_xp_test_case((Rotation, "from_matrix"), (Rotation, "as_matrix"))
+def test_from_matrix_ortho_output(xp):
+    dtype = xpx.default_dtype(xp)
+    atol = 1e-12 if dtype == xp.float64 else 1e-6
+    rnd = np.random.RandomState(0)
+    mat = xp.asarray(rnd.random_sample((100, 3, 3)), dtype=dtype)
+    dets = xp.linalg.det(mat)
+    for i in range(dets.shape[0]):
+        # Make sure we have a right-handed rotation matrix
+        if dets[i] < 0:
+            mat = xpx.at(mat)[i, ...].set(-mat[i, ...])
+    ortho_mat = Rotation.from_matrix(mat).as_matrix()
+
+    mult_result = xp.matmul(ortho_mat, xp.matrix_transpose(ortho_mat))
+
+    eye3d = xp.zeros((100, 3, 3)) + xp.eye(3)
+    xp_assert_close(mult_result, eye3d, atol=atol)
+
+
+@make_xp_test_case((Rotation, "from_matrix"), (Rotation, "as_matrix"))
+def test_from_matrix_normalize(xp):
+    mat = xp.asarray([
+        [1, 1, 0],
+        [0, 1, 0],
+        [0, 0, 1]])
+    expected = xp.asarray([[ 0.894427, 0.447214, 0.0],
+                           [-0.447214, 0.894427, 0.0],
+                           [ 0.0,      0.0,      1.0]])
+    xp_assert_close(Rotation.from_matrix(mat).as_matrix(), expected, atol=1e-6)
+
+    mat = xp.asarray([
+        [0,  -0.5, 0  ],
+        [0.5, 0  , 0  ],
+        [0,   0  , 0.5]])
+    expected = xp.asarray([[0.0, -1, 0],
+                           [  1,  0, 0],
+                           [  0,  0, 1]])
+    xp_assert_close(Rotation.from_matrix(mat).as_matrix(), expected, atol=1e-6)
+
+    # Test a mix of normalized and non-normalized matrices
+    mat = xp.stack([mat, xp.eye(3)])
+    expected = xp.stack([expected, xp.eye(3)])
+    xp_assert_close(Rotation.from_matrix(mat).as_matrix(), expected, atol=1e-6)
+
+
+@make_xp_test_case((Rotation, "from_matrix"), (Rotation, "as_matrix"))
+def test_from_matrix_assume_valid(xp):
+    rng = np.random.default_rng(0)
+    dtype = xpx.default_dtype(xp)
+    atol = 1e-12 if dtype == xp.float64 else 1e-6
+    # Test that normal matrices remain unchanged
+    rot = rotation_to_xp(Rotation.from_quat(rng.normal(size=(10, 4))), xp)
+    rot_no_norm = Rotation.from_matrix(rot.as_matrix(), assume_valid=True)
+    assert xp.all(rot.approx_equal(rot_no_norm, atol=atol))
+    # We make no guarantees about matrices that are not orthogonal or do not
+    # have unit norm
+
+
+@make_xp_test_case((Rotation, "from_matrix"), (Rotation, "as_matrix"))
+def test_from_matrix_non_positive_determinant(xp):
+    mat = xp.eye(3)
+    mat = xpx.at(mat)[0, 0].set(0)
+    if is_lazy_array(mat):
+        assert xp.all(xp.isnan(Rotation.from_matrix(mat).as_matrix()))
+    else:
+        with pytest.raises(ValueError, match="Non-positive determinant"):
+            Rotation.from_matrix(mat)
+
+    mat = xpx.at(mat)[0, 0].set(-1)
+    if is_lazy_array(mat):
+        assert xp.all(xp.isnan(Rotation.from_matrix(mat).as_matrix()))
+    else:
+        with pytest.raises(ValueError, match="Non-positive determinant"):
+            Rotation.from_matrix(mat)
+
+
+def test_from_matrix_array_like():
+    rng = np.random.default_rng(123)
+    # Single rotation
+    r_expected = Rotation.random(rng=rng)
+    r = Rotation.from_matrix(r_expected.as_matrix().tolist())
+    assert r_expected.approx_equal(r, atol=1e-12)
+
+    # Multiple rotations
+    r_expected = Rotation.random(3, rng=rng)
+    r = Rotation.from_matrix(r_expected.as_matrix().tolist())
+    assert np.all(r_expected.approx_equal(r, atol=1e-12))
+
+
+@make_xp_test_case((Rotation, "from_matrix"))
+def test_from_matrix_int_dtype(xp):
+    mat = xp.asarray([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
+    r = Rotation.from_matrix(mat)
+    assert r.as_quat().dtype == xp_default_dtype(xp)
+
+
+@make_xp_test_case((Rotation, "from_rotvec"))
+@pytest.mark.parametrize("ndim", list(range(1, 6)))
+def test_from_nd_single_rotvec(xp, ndim: int):
+    atol = 1e-7
+    rotvec = xp.asarray([1, 0, 0])
+    rotvec = xp.reshape(rotvec, (1,) * (ndim - 1) + (3,))
+    expected_quat = xp.asarray([0.4794255, 0, 0, 0.8775826])
+    expected_quat = xp.reshape(expected_quat, (1,) * (ndim - 1) + (4,))
+    result = Rotation.from_rotvec(rotvec)
+    xp_assert_close(result.as_quat(), expected_quat, atol=atol)
+
+
+@make_xp_test_case((Rotation, "from_rotvec"))
+def test_from_generic_rotvec(xp):
+    atol = 1e-7
+    rotvec = xp.asarray([
+            [1, 2, 2],
+            [1, -1, 0.5],
+            [0, 0, 0]])
+    expected_quat = xp.asarray([
+        [0.3324983, 0.6649967, 0.6649967, 0.0707372],
+        [0.4544258, -0.4544258, 0.2272129, 0.7316889],
+        [0, 0, 0, 1]
+        ])
+    xp_assert_close(Rotation.from_rotvec(rotvec).as_quat(), expected_quat, atol=atol)
+
+
+@make_xp_test_case((Rotation, "from_rotvec"))
+def test_from_rotvec_small_angle(xp):
+    rotvec = xp.asarray([
+        [5e-4 / math.sqrt(3), -5e-4 / math.sqrt(3), 5e-4 / math.sqrt(3)],
+        [0.2, 0.3, 0.4],
+        [0, 0, 0]
+        ])
+
+    quat = Rotation.from_rotvec(rotvec).as_quat()
+    # cos(theta/2) ~~ 1 for small theta
+    xp_assert_close(quat[0, 3], xp.asarray(1.0)[()])
+    # sin(theta/2) / theta ~~ 0.5 for small theta
+    xp_assert_close(quat[0, :3], rotvec[0, ...] * 0.5)
+
+    xp_assert_close(quat[1, 3], xp.asarray(0.9639685)[()])
+    xp_assert_close(quat[1, :3],
+            xp.asarray([
+                0.09879603932153465,
+                0.14819405898230198,
+                0.19759207864306931]))
+
+    xp_assert_equal(quat[2, ...], xp.asarray([0.0, 0, 0, 1]))
+
+
+@make_xp_test_case((Rotation, "from_rotvec"), (Rotation, "as_rotvec"))
+def test_from_rotvec_array_like():
+    rng = np.random.default_rng(123)
+    # Single rotation
+    r_expected = Rotation.random(rng=rng)
+    r = Rotation.from_rotvec(r_expected.as_rotvec().tolist())
+    assert r_expected.approx_equal(r, atol=1e-12)
+
+    # Multiple rotations
+    r_expected = Rotation.random(3, rng=rng)
+    r = Rotation.from_rotvec(r_expected.as_rotvec().tolist())
+    assert np.all(r_expected.approx_equal(r, atol=1e-12))
+
+
+@make_xp_test_case((Rotation, "from_rotvec"))
+def test_from_rotvec_int_dtype(xp):
+    rotvec = xp.asarray([1, 0, 0])
+    r = Rotation.from_rotvec(rotvec)
+    assert r.as_quat().dtype == xp_default_dtype(xp)
+
+
+@make_xp_test_case((Rotation, "from_rotvec"))
+def test_degrees_from_rotvec(xp):
+    rotvec1 = xp.asarray([1 / 3 ** (1/3)] * 3)
+    rot1 = Rotation.from_rotvec(rotvec1, degrees=True)
+    quat1 = rot1.as_quat()
+
+    # deg2rad is not implemented in Array API -> / 180 * xp.pi
+    rotvec2 = xp.asarray(rotvec1 / 180 * xp.pi)
+    rot2 = Rotation.from_rotvec(rotvec2)
+    quat2 = rot2.as_quat()
+
+    xp_assert_close(quat1, quat2)
+
+
+@make_xp_test_case((Rotation, "from_rotvec"))
+def test_malformed_1d_from_rotvec(xp):
+    with pytest.raises(ValueError, match='Expected `rot_vec` to have shape'):
+        Rotation.from_rotvec(xp.asarray([1, 2]))
+
+
+@make_xp_test_case((Rotation, "from_rotvec"))
+@pytest.mark.parametrize("ndim", list(range(1, 6)))
+def test_malformed_nd_from_rotvec(xp, ndim: int):
+    shape = (1,) * (ndim - 1) + (2,)
+    with pytest.raises(ValueError, match='Expected `rot_vec` to have shape'):
+        Rotation.from_rotvec(xp.ones(shape))
+
+
+@make_xp_test_case((Rotation, "as_rotvec"))
+def test_as_generic_rotvec(xp):
+    dtype = xpx.default_dtype(xp)
+    atol = 1e-15 if dtype == xp.float64 else 1e-7
+    quat = xp.asarray([
+            [1, 2, -1, 0.5],
+            [1, -1, 1, 0.0003],
+            [0, 0, 0, 1]
+            ])
+    quat /= xp_vector_norm(quat, axis=-1, keepdims=True)
+
+    rotvec = Rotation.from_quat(quat).as_rotvec()
+    angle = xp_vector_norm(rotvec, axis=-1)
+
+    xp_assert_close(quat[:, 3], xp.cos(angle / 2))
+    xp_assert_close(xp.linalg.cross(rotvec, quat[:, :3]), xp.zeros((3, 3)), atol=atol)
+
+
+@make_xp_test_case((Rotation, "as_rotvec"))
+@pytest.mark.parametrize("ndim", list(range(1, 4)))
+def test_as_rotvec_single_nd_input(xp, ndim: int):
+    quat = xp.asarray([1, 2, -3, 2])
+    quat = xp.reshape(quat, (1,) * (ndim - 1) + (4,))
+    expected_rotvec = xp.asarray([0.5772381, 1.1544763, -1.7317144])
+    expected_rotvec = xp.reshape(expected_rotvec, (1,) * (ndim - 1) + (3,))
+    actual_rotvec = Rotation.from_quat(quat).as_rotvec()
+
+    assert_equal(actual_rotvec.shape, expected_rotvec.shape)
+    xp_assert_close(actual_rotvec, expected_rotvec)
+
+
+@make_xp_test_case((Rotation, "from_matrix"), (Rotation, "as_rotvec"))
+def test_as_rotvec_degrees(xp):
+    # x->y, y->z, z->x
+    mat = xp.asarray([[0, 0, 1], [1, 0, 0], [0, 1, 0]])
+    rot = Rotation.from_matrix(mat)
+    rotvec = rot.as_rotvec(degrees=True)
+    angle = xp_vector_norm(rotvec, axis=-1)
+    xp_assert_close(angle, xp.asarray(120.0)[()])
+    xp_assert_close(rotvec[0], rotvec[1])
+    xp_assert_close(rotvec[1], rotvec[2])
+
+
+@make_xp_test_case((Rotation, "from_rotvec"), (Rotation, "as_rotvec"))
+def test_rotvec_calc_pipeline(xp):
+    # Include small angles
+    rotvec = xp.asarray([
+        [0, 0, 0],
+        [1, -1, 2],
+        [-3e-4, 3.5e-4, 7.5e-5]
+        ])
+    xp_assert_close(Rotation.from_rotvec(rotvec).as_rotvec(), rotvec)
+    xp_assert_close(Rotation.from_rotvec(rotvec, degrees=True).as_rotvec(degrees=True),
+                    rotvec)
+
+
+@make_xp_test_case((Rotation, "from_mrp"))
+@pytest.mark.parametrize("ndim", range(1, 4))
+def test_from_mrp_single_nd_input(xp, ndim: int):
+    mrp = xp.asarray([0, 0, 1.0])
+    mrp = xp.reshape(mrp, (1,) * (ndim - 1) + (3,))
+    expected_quat = xp.asarray([0.0, 0, 1, 0])
+    expected_quat = xp.reshape(expected_quat, (1,) * (ndim - 1) + (4,))
+    result = Rotation.from_mrp(mrp)
+    xp_assert_close(result.as_quat(), expected_quat, atol=1e-12)
+    # Regression test for gh-24555
+    assert isinstance(result._quat, type(array_namespace(mrp).empty(0)))
+
+
+def test_from_mrp_array_like():
+    rng = np.random.default_rng(123)
+    # Single rotation
+    r_expected = Rotation.random(rng=rng)
+    r = Rotation.from_mrp(r_expected.as_mrp().tolist())
+    assert r_expected.approx_equal(r, atol=1e-12)
+
+    # Multiple rotations
+    r_expected = Rotation.random(3, rng=rng)
+    r = Rotation.from_mrp(r_expected.as_mrp().tolist())
+    assert np.all(r_expected.approx_equal(r, atol=1e-12))
+
+
+@make_xp_test_case((Rotation, "from_mrp"))
+def test_from_mrp_int_dtype(xp):
+    mrp = xp.asarray([0, 0, 1])
+    r = Rotation.from_mrp(mrp)
+    assert r.as_quat().dtype == xp_default_dtype(xp)
+
+
+@make_xp_test_case((Rotation, "from_mrp"))
+def test_from_generic_mrp(xp):
+    mrp = xp.asarray([
+        [1, 2, 2],
+        [1, -1, 0.5],
+        [0, 0, 0]])
+    expected_quat = xp.asarray([
+        [0.2, 0.4, 0.4, -0.8],
+        [0.61538462, -0.61538462, 0.30769231, -0.38461538],
+        [0, 0, 0, 1]])
+    xp_assert_close(Rotation.from_mrp(mrp).as_quat(), expected_quat)
+
+
+@make_xp_test_case((Rotation, "from_mrp"))
+@pytest.mark.parametrize("ndim", range(1, 4))
+def test_malformed_nd_from_mrp(xp, ndim: int):
+    shape = (1,) * (ndim - 1) + (2,)
+    with pytest.raises(ValueError, match='Expected `mrp` to have shape'):
+        Rotation.from_mrp(xp.ones(shape))
+
+
+@make_xp_test_case((Rotation, "as_mrp"))
+def test_as_generic_mrp(xp):
+    quat = xp.asarray([
+        [1, 2, -1, 0.5],
+        [1, -1, 1, 0.0003],
+        [0, 0, 0, 1]])
+    quat /= xp_vector_norm(quat, axis=1)[:, None]
+
+    expected_mrp = xp.asarray([
+        [0.33333333, 0.66666667, -0.33333333],
+        [0.57725028, -0.57725028, 0.57725028],
+        [0, 0, 0]])
+    xp_assert_close(Rotation.from_quat(quat).as_mrp(), expected_mrp)
+
+
+@make_xp_test_case((Rotation, "from_euler"), (Rotation, "as_mrp"))
+def test_past_180_degree_rotation(xp):
+    # ensure that a > 180 degree rotation is returned as a <180 rotation in MRPs
+    # in this case 270 should be returned as -90
+    expected_mrp = xp.asarray([-math.tan(xp.pi / 2 / 4), 0.0, 0])
+    xp_assert_close(
+        Rotation.from_euler('xyz', xp.asarray([270, 0, 0]), degrees=True).as_mrp(),
+        expected_mrp,
+    )
+
+
+@make_xp_test_case((Rotation, "as_mrp"))
+@pytest.mark.parametrize("ndim", list(range(1, 4)))
+def test_as_mrp_single_nd_input(xp, ndim: int):
+    quat = xp.asarray([1, 2, -3, 2])
+    quat = xp.reshape(quat, (1,) * (ndim - 1) + (4,))
+    expected_mrp = xp.asarray([0.16018862, 0.32037724, -0.48056586])
+    expected_mrp = xp.reshape(expected_mrp, (1,) * (ndim - 1) + (3,))
+    actual_mrp = Rotation.from_quat(quat).as_mrp()
+
+    assert_equal(actual_mrp.shape, expected_mrp.shape)
+    xp_assert_close(actual_mrp, expected_mrp)
+
+
+@make_xp_test_case((Rotation, "from_mrp"), (Rotation, "as_mrp"))
+def test_mrp_calc_pipeline(xp):
+    actual_mrp = xp.asarray([
+        [0, 0, 0],
+        [1, -1, 2],
+        [0.41421356, 0, 0],
+        [0.1, 0.2, 0.1]])
+    expected_mrp = xp.asarray([
+        [0, 0, 0],
+        [-0.16666667, 0.16666667, -0.33333333],
+        [0.41421356, 0, 0],
+        [0.1, 0.2, 0.1]])
+    xp_assert_close(Rotation.from_mrp(actual_mrp).as_mrp(), expected_mrp)
+
+
+@make_xp_test_case((Rotation, "from_euler"))
+def test_from_euler_single_rotation(xp):
+    quat = Rotation.from_euler("z", xp.asarray(90), degrees=True).as_quat()
+    expected_quat = xp.asarray([0.0, 0, 1, 1]) / math.sqrt(2)
+    xp_assert_close(quat, expected_quat)
+
+
+@make_xp_test_case((Rotation, "from_euler"))
+def test_from_euler_input_validation(xp):
+    # Single sequence with multiple angles
+    with pytest.raises(ValueError, match="Expected last dimension of `angles` to"):
+        Rotation.from_euler("X", xp.asarray([0, 90]))
+    # Multiple sequences with single angle
+    with pytest.raises(ValueError, match="Expected last dimension of `angles` to"):
+        Rotation.from_euler("XYZ", xp.asarray([90]))
+
+
+@make_xp_test_case((Rotation, "from_euler"))
+@pytest.mark.parametrize("ndim", list(range(1, 4)))
+def test_from_euler_nd_rotation(xp, ndim: int):
+    angles = xp.reshape(xp.asarray([0, 0, 90]), (1,) * (ndim - 1) + (3,))
+    quat = Rotation.from_euler("xyz", angles, degrees=True).as_quat()
+    expected_quat = xp.asarray([0.0, 0, 1, 1]) / math.sqrt(2)
+    expected_quat = xp.reshape(expected_quat, (1,) * (ndim - 1) + (4,))
+    xp_assert_close(quat, expected_quat)
+
+
+@make_xp_test_case((Rotation, "from_euler"), (Rotation, "as_matrix"))
+def test_single_intrinsic_extrinsic_rotation(xp):
+    extrinsic = Rotation.from_euler('z', xp.asarray(90), degrees=True).as_matrix()
+    intrinsic = Rotation.from_euler('Z', xp.asarray(90), degrees=True).as_matrix()
+    xp_assert_close(extrinsic, intrinsic)
+
+
+@make_xp_test_case((Rotation, "from_euler"))
+def test_from_euler_rotation_order(xp):
+    # Intrinsic rotation is same as extrinsic with order reversed
+    rnd = np.random.RandomState(0)
+    a = xp.asarray(rnd.randint(low=0, high=180, size=(6, 3)))
+    b = xp.flip(a, axis=-1)
+    x = Rotation.from_euler('xyz', a, degrees=True).as_quat()
+    y = Rotation.from_euler('ZYX', b, degrees=True).as_quat()
+    xp_assert_close(x, y)
+
+
+@make_xp_test_case((Rotation, "from_euler"), (Rotation, "as_matrix"))
+def test_from_euler_elementary_extrinsic_rotation(xp):
+    atol = 1e-12
+    # Simple test to check if extrinsic rotations are implemented correctly
+    mat = Rotation.from_euler('zx', xp.asarray([90, 90]), degrees=True).as_matrix()
+    expected_mat = xp.asarray([
+        [0.0, -1, 0],
+        [0, 0, -1],
+        [1, 0, 0]
+    ])
+    xp_assert_close(mat, expected_mat, atol=atol)
+
+
+@make_xp_test_case((Rotation, "from_euler"), (Rotation, "as_matrix"))
+def test_from_euler_intrinsic_rotation_312(xp):
+    atol = 1e-7
+    angles = xp.asarray([
+        [30, 60, 45],
+        [30, 60, 30],
+        [45, 30, 60]
+        ])
+    mat = Rotation.from_euler('ZXY', angles, degrees=True).as_matrix()
+
+    xp_assert_close(mat[0, ...], xp.asarray([
+        [0.3061862, -0.2500000, 0.9185587],
+        [0.8838835, 0.4330127, -0.1767767],
+        [-0.3535534, 0.8660254, 0.3535534]
+    ]), atol=atol)
+
+    xp_assert_close(mat[1, ...], xp.asarray([
+        [0.5334936, -0.2500000, 0.8080127],
+        [0.8080127, 0.4330127, -0.3995191],
+        [-0.2500000, 0.8660254, 0.4330127]
+    ]), atol=atol)
+
+    xp_assert_close(mat[2, ...], xp.asarray([
+        [0.0473672, -0.6123725, 0.7891491],
+        [0.6597396, 0.6123725, 0.4355958],
+        [-0.7500000, 0.5000000, 0.4330127]
+    ]), atol=atol)
+
+
+@make_xp_test_case((Rotation, "from_euler"), (Rotation, "as_matrix"))
+def test_from_euler_intrinsic_rotation_313(xp):
+    angles = xp.asarray([
+        [30, 60, 45],
+        [30, 60, 30],
+        [45, 30, 60]
+        ])
+    mat = Rotation.from_euler('ZXZ', angles, degrees=True).as_matrix()
+
+    xp_assert_close(mat[0, ...], xp.asarray([
+        [0.43559574, -0.78914913, 0.4330127],
+        [0.65973961, -0.04736717, -0.750000],
+        [0.61237244, 0.61237244, 0.500000]
+    ]))
+
+    xp_assert_close(mat[1, ...], xp.asarray([
+        [0.6250000, -0.64951905, 0.4330127],
+        [0.64951905, 0.1250000, -0.750000],
+        [0.4330127, 0.750000, 0.500000]
+    ]))
+
+    xp_assert_close(mat[2, ...], xp.asarray([
+        [-0.1767767, -0.91855865, 0.35355339],
+        [0.88388348, -0.30618622, -0.35355339],
+        [0.4330127, 0.25000000, 0.8660254]
+    ]))
+
+
+@make_xp_test_case((Rotation, "from_euler"), (Rotation, "as_matrix"))
+def test_from_euler_extrinsic_rotation_312(xp):
+    angles = xp.asarray([
+        [30, 60, 45],
+        [30, 60, 30],
+        [45, 30, 60]
+        ])
+    mat = Rotation.from_euler('zxy', angles, degrees=True).as_matrix()
+
+    xp_assert_close(mat[0, ...], xp.asarray([
+        [0.91855865, 0.1767767, 0.35355339],
+        [0.25000000, 0.4330127, -0.8660254],
+        [-0.30618622, 0.88388348, 0.35355339]
+    ]))
+
+    xp_assert_close(mat[1, ...], xp.asarray([
+        [0.96650635, -0.0580127, 0.2500000],
+        [0.25000000, 0.4330127, -0.8660254],
+        [-0.0580127, 0.89951905, 0.4330127]
+    ]))
+
+    xp_assert_close(mat[2, ...], xp.asarray([
+        [0.65973961, -0.04736717, 0.7500000],
+        [0.61237244, 0.61237244, -0.5000000],
+        [-0.43559574, 0.78914913, 0.4330127]
+    ]))
+
+
+@make_xp_test_case((Rotation, "from_euler"), (Rotation, "as_matrix"))
+def test_from_euler_extrinsic_rotation_313(xp):
+    angles = xp.asarray([
+        [30, 60, 45],
+        [30, 60, 30],
+        [45, 30, 60]
+        ])
+    mat = Rotation.from_euler('zxz', angles, degrees=True).as_matrix()
+
+    xp_assert_close(mat[0, ...], xp.asarray([
+        [0.43559574, -0.65973961, 0.61237244],
+        [0.78914913, -0.04736717, -0.61237244],
+        [0.4330127, 0.75000000, 0.500000]
+    ]))
+
+    xp_assert_close(mat[1, ...], xp.asarray([
+        [0.62500000, -0.64951905, 0.4330127],
+        [0.64951905, 0.12500000, -0.750000],
+        [0.4330127, 0.75000000, 0.500000]
+    ]))
+
+    xp_assert_close(mat[2, ...], xp.asarray([
+        [-0.1767767, -0.88388348, 0.4330127],
+        [0.91855865, -0.30618622, -0.250000],
+        [0.35355339, 0.35355339, 0.8660254]
+    ]))
+
+
+def test_from_euler_array_like():
+    rng = np.random.default_rng(123)
+    order = "xyz"
+    # Single rotation
+    r_expected = Rotation.random(rng=rng)
+    r = Rotation.from_euler(order, r_expected.as_euler(order).tolist())
+    assert r_expected.approx_equal(r, atol=1e-12)
+
+    # Multiple rotations
+    r_expected = Rotation.random(3, rng=rng)
+    r = Rotation.from_euler(order, r_expected.as_euler(order).tolist())
+    assert np.all(r_expected.approx_equal(r, atol=1e-12))
+
+
+def test_from_euler_scalar():
+    rng = np.random.default_rng(123)
+    deg = rng.uniform(low=-180, high=180)
+    r_expected = Rotation.from_euler("x", deg, degrees=True)
+    r = Rotation.from_euler("x", float(deg), degrees=True)
+    assert r_expected.approx_equal(r, atol=1e-12)
+
+
+@make_xp_test_case((Rotation, "from_euler"), (Rotation, "as_euler"))
+@pytest.mark.parametrize("seq_tuple", list(permutations("xyz")))
+@pytest.mark.parametrize("intrinsic", (False, True))
+def test_as_euler_asymmetric_axes(xp, seq_tuple, intrinsic):
+    # helper function for mean error tests
+    def test_stats(error, mean_max, rms_max):
+        mean = xp.mean(error, axis=0)
+        std = xp.std(error, axis=0)
+        rms = xp.hypot(mean, std)
+        assert xp.all(xp.abs(mean) < mean_max)
+        assert xp.all(rms < rms_max)
+
+    rnd = np.random.RandomState(0)
+    n = 1000
+    angles = np.empty((n, 3))
+    angles[:, 0] = rnd.uniform(low=-np.pi, high=np.pi, size=(n,))
+    angles[:, 1] = rnd.uniform(low=-np.pi / 2, high=np.pi / 2, size=(n,))
+    angles[:, 2] = rnd.uniform(low=-np.pi, high=np.pi, size=(n,))
+    angles = xp.asarray(angles)
+
+    seq = "".join(seq_tuple)
+    if intrinsic:
+        # Extrinsic rotation (w.r.t. global world) at lower case
+        # intrinsic (WRT the object itself) lower case.
+        seq = seq.upper()
+    rotation = Rotation.from_euler(seq, angles)
+    angles_quat = rotation.as_euler(seq)
+    xp_assert_close(angles, angles_quat, atol=0, rtol=1e-12)
+    test_stats(angles_quat - angles, 1e-15, 1e-14)
+
+
+@make_xp_test_case((Rotation, "from_euler"), (Rotation, "as_euler"))
+@pytest.mark.parametrize("seq_tuple", list(permutations("xyz")))
+@pytest.mark.parametrize("intrinsic", (False, True))
+def test_as_euler_symmetric_axes(xp, seq_tuple, intrinsic):
+    # helper function for mean error tests
+    def test_stats(error, mean_max, rms_max):
+        mean = xp.mean(error, axis=0)
+        std = xp.std(error, axis=0)
+        rms = xp.hypot(mean, std)
+        assert xp.all(xp.abs(mean) < mean_max)
+        assert xp.all(rms < rms_max)
+
+    rnd = np.random.RandomState(0)
+    n = 1000
+    angles = np.empty((n, 3))
+    angles[:, 0] = rnd.uniform(low=-np.pi, high=np.pi, size=(n,))
+    angles[:, 1] = rnd.uniform(low=0, high=np.pi, size=(n,))
+    angles[:, 2] = rnd.uniform(low=-np.pi, high=np.pi, size=(n,))
+    angles = xp.asarray(angles)
+
+    # Rotation of the form A/B/A are rotation around symmetric axes
+    seq = "".join([seq_tuple[0], seq_tuple[1], seq_tuple[0]])
+    if intrinsic:
+        seq = seq.upper()
+    rotation = Rotation.from_euler(seq, angles)
+    angles_quat = rotation.as_euler(seq)
+    xp_assert_close(angles, angles_quat, atol=0, rtol=1.1e-13)
+    test_stats(angles_quat - angles, 1e-16, 1e-14)
+
+
+@contextmanager
+def maybe_warn_gimbal_lock(should_warn, xp):
+    if should_warn:
+        # We can only warn on non-lazy backends because we'd need to condition on
+        # traced booleans
+        with eager_warns(UserWarning, match="Gimbal lock", xp=xp):
+            yield
+
+    else:
+        with warnings.catch_warnings():
+            warnings.simplefilter("error")
+            yield
+
+
+@make_xp_test_case(
+    (Rotation, "from_euler"), (Rotation, "as_matrix"), (Rotation, "as_euler")
+)
+@pytest.mark.parametrize("seq_tuple", list(permutations("xyz")))
+@pytest.mark.parametrize("intrinsic", (False, True))
+@pytest.mark.parametrize("suppress_warnings", (False, True))
+def test_as_euler_degenerate_asymmetric_axes(
+    xp, seq_tuple, intrinsic, suppress_warnings
+):
+    dtype = xpx.default_dtype(xp)
+    atol = 1e-12 if dtype == xp.float64 else 1e-6
+    # Since we cannot check for angle equality, we check for rotation matrix
+    # equality
+    angles = xp.asarray([
+        [45, 90, 35],
+        [35, -90, 20],
+        [35, 90, 25],
+        [25, -90, 15]])
+
+    seq = "".join(seq_tuple)
+    if intrinsic:
+        # Extrinsic rotation (w.r.t. global world) at lower case
+        # Intrinsic (WRT the object itself) upper case.
+        seq = seq.upper()
+    rotation = Rotation.from_euler(seq, angles, degrees=True)
+    mat_expected = rotation.as_matrix()
+
+    with maybe_warn_gimbal_lock(not suppress_warnings, xp):
+        angle_estimates = rotation.as_euler(
+            seq, degrees=True, suppress_warnings=suppress_warnings
+        )
+    mat_estimated = Rotation.from_euler(seq, angle_estimates, degrees=True).as_matrix()
+
+    xp_assert_close(mat_expected, mat_estimated, atol=atol)
+
+
+@make_xp_test_case(
+    (Rotation, "from_euler"), (Rotation, "as_matrix"), (Rotation, "as_euler")
+)
+@pytest.mark.parametrize("seq_tuple", list(permutations("xyz")))
+@pytest.mark.parametrize("intrinsic", (False, True))
+@pytest.mark.parametrize("suppress_warnings", (False, True))
+def test_as_euler_degenerate_symmetric_axes(
+    xp, seq_tuple, intrinsic, suppress_warnings
+):
+    dtype = xpx.default_dtype(xp)
+    atol = 1e-12 if dtype == xp.float64 else 1e-6
+    # Since we cannot check for angle equality, we check for rotation matrix
+    # equality
+    angles = xp.asarray([
+        [15, 0, 60],
+        [35, 0, 75],
+        [60, 180, 35],
+        [15, -180, 25]])
+
+    # Rotation of the form A/B/A are rotation around symmetric axes
+    seq = "".join([seq_tuple[0], seq_tuple[1], seq_tuple[0]])
+    if intrinsic:
+        # Extrinsic rotation (w.r.t. global world) at lower case
+        # Intrinsic (WRT the object itself) upper case.
+        seq = seq.upper()
+    rotation = Rotation.from_euler(seq, angles, degrees=True)
+    mat_expected = rotation.as_matrix()
+
+    with maybe_warn_gimbal_lock(not suppress_warnings, xp):
+        angle_estimates = rotation.as_euler(
+            seq, degrees=True, suppress_warnings=suppress_warnings
+        )
+    mat_estimated = Rotation.from_euler(seq, angle_estimates, degrees=True).as_matrix()
+
+    xp_assert_close(mat_expected, mat_estimated, atol=atol)
+
+
+@make_xp_test_case((Rotation, "from_euler"), (Rotation, "as_euler"))
+@pytest.mark.parametrize("ndim", list(range(1, 4)))
+def test_as_euler_nd_rotation(xp, ndim: int):
+    mat = xp.asarray([
+        [0.0, -1, 0],
+        [1, 0, 0],
+        [0, 0, 1]
+    ])
+    mat = xp.reshape(mat, (1,) * (ndim - 1) + (3, 3))
+    angles = Rotation.from_matrix(mat).as_euler("xyz", degrees=True)
+    expected_angles = xp.asarray([0, 0, 90.0])
+    expected_angles = xp.reshape(expected_angles, (1,) * (ndim - 1) + (3,))
+    xp_assert_close(angles, expected_angles, atol=1e-12)
+
+
+@make_xp_test_case((Rotation, "as_matrix"), (Rotation, "inv"))
+def test_inv(xp):
+    dtype = xpx.default_dtype(xp)
+    atol = 1e-12 if dtype == xp.float64 else 1e-7
+    rnd = np.random.RandomState(0)
+    n = 10
+    # preserve use of old random_state during SPEC 7 transition
+    p = Rotation.random(num=n, random_state=rnd)
+    p = rotation_to_xp(p, xp)
+    p_mat = p.as_matrix()
+    q_mat = p.inv().as_matrix()
+
+    result1 = p_mat @ q_mat
+    result2 = q_mat @ p_mat
+
+    eye3d = xp.empty((n, 3, 3))
+    eye3d = xpx.at(eye3d)[..., :3, :3].set(xp.eye(3))
+
+    xp_assert_close(result1, eye3d, atol=atol)
+    xp_assert_close(result2, eye3d, atol=atol)
+
+    # Batched version
+    batch_shape = (10, 3, 7)
+    atol = 1e-12 if dtype == xp.float64 else 1e-6
+    quat = xp.asarray(rnd.normal(size=batch_shape + (4,)), dtype=dtype)
+    r = Rotation.from_quat(quat)
+    p_mat = r.as_matrix()
+    q_mat = r.inv().as_matrix()
+    result1 = p_mat @ q_mat
+    result2 = q_mat @ p_mat
+    eye_nd = xp.empty(batch_shape + (3, 3))
+    eye_nd = xpx.at(eye_nd)[..., :3, :3].set(xp.eye(3))
+    xp_assert_close(result1, eye_nd, atol=atol)
+    xp_assert_close(result2, eye_nd, atol=atol)
+
+
+@make_xp_test_case((Rotation, "inv"), (Rotation, "as_matrix"))
+def test_inv_single_rotation(xp):
+    dtype = xpx.default_dtype(xp)
+    atol = 1e-12 if dtype == xp.float64 else 1e-7
+    rng = np.random.default_rng(146972845698875399755764481408308808739)
+    p = rotation_to_xp(Rotation.random(rng=rng), xp)
+    q = p.inv()
+
+    p_mat = p.as_matrix()
+    q_mat = q.as_matrix()
+    res1 = xp.matmul(p_mat, q_mat)
+    res2 = xp.matmul(q_mat, p_mat)
+
+    eye = xp.eye(3)
+
+    xp_assert_close(res1, eye, atol=atol)
+    xp_assert_close(res2, eye, atol=atol)
+
+    x = rotation_to_xp(Rotation.random(num=1, rng=rng), xp)
+    y = x.inv()
+
+    x_matrix = x.as_matrix()
+    y_matrix = y.as_matrix()
+    result1 = xp.linalg.matmul(x_matrix, y_matrix)
+    result2 = xp.linalg.matmul(y_matrix, x_matrix)
+
+    eye3d = xp.empty((1, 3, 3))
+    eye3d = xpx.at(eye3d)[..., :3, :3].set(xp.eye(3))
+
+    xp_assert_close(result1, eye3d, atol=atol)
+    xp_assert_close(result2, eye3d, atol=atol)
+
+
+@make_xp_test_case((Rotation, "magnitude"), (Rotation, "inv"))
+def test_identity_magnitude(xp):
+    n = 10
+    r = rotation_to_xp(Rotation.identity(n), xp)
+    expected = xp.zeros(n)
+    xp_assert_close(r.magnitude(), expected)
+    xp_assert_close(r.inv().magnitude(), expected)
+
+
+@make_xp_test_case((Rotation, "magnitude"), (Rotation, "inv"))
+def test_single_identity_magnitude(xp):
+    r = rotation_to_xp(Rotation.identity(), xp)
+    assert r.magnitude() == 0
+    assert r.inv().magnitude() == 0
+
+
+@make_xp_test_case((Rotation, "inv"), (Rotation, "magnitude"))
+def test_identity_invariance(xp):
+    dtype = xpx.default_dtype(xp)
+    atol = 1e-12 if dtype == xp.float64 else 1e-7
+    n = 10
+    p = rotation_to_xp(Rotation.random(n, rng=0), xp)
+    q = rotation_to_xp(Rotation.identity(n), xp)
+    result = p * q
+    xp_assert_close(p.as_quat(), result.as_quat())
+
+    result = result * p.inv()
+    xp_assert_close(result.magnitude(), xp.zeros(n), atol=atol)
+
+
+@make_xp_test_case((Rotation, "inv"), (Rotation, "magnitude"))
+def test_single_identity_invariance(xp):
+    dtype = xpx.default_dtype(xp)
+    atol = 1e-12 if dtype == xp.float64 else 1e-7
+    n = 10
+    p = rotation_to_xp(Rotation.random(n, rng=0), xp)
+    q = rotation_to_xp(Rotation.identity(), xp)
+    result = p * q
+    xp_assert_close(p.as_quat(), result.as_quat())
+
+    result = result * p.inv()
+    xp_assert_close(result.magnitude(), xp.zeros(n), atol=atol)
+
+
+def test_identity_shape():  # Not an xp test, identity is using numpy only for now
+    r = Rotation.identity(shape=())
+    assert r.as_quat().shape == (4,)
+    r = Rotation.identity(shape=5)  # Shape can be int
+    assert r.as_quat().shape == (5, 4)
+    r = Rotation.identity(shape=(2, 3))
+    assert r.as_quat().shape == (2, 3, 4)
+    # Test values
+    r = Rotation.identity(shape=(2, 2, 3))
+    xp_assert_equal(r.as_quat().reshape(-1, 4), np.tile(np.eye(4)[-1], (2 * 2 * 3, 1)))
+    # Errors
+    with pytest.raises(ValueError, match="`shape` must be an int or a tuple of ints"):
+        Rotation.identity(shape=2.5)
+    with pytest.raises(ValueError, match="Only one of `num` or `shape` can be"):
+        Rotation.identity(num=3, shape=(2, 2))
+    with pytest.raises(TypeError, match="takes from 0 to 1 positional arguments"):
+        Rotation.identity(3, 3)
+
+
+@make_xp_test_case((Rotation, "magnitude"))
+@pytest.mark.parametrize("ndim", list(range(1, 4)))
+def test_magnitude(xp, ndim: int):
+    quat_shape = (1,) * (ndim - 1) + (4,)
+    quat = xp.reshape(xp.eye(4), quat_shape + (4,))
+    r = Rotation.from_quat(quat)
+    result = r.magnitude()
+    expected_result = xp.asarray([xp.pi, xp.pi, xp.pi, 0])
+    expected_result = xp.reshape(expected_result, quat_shape)
+    xp_assert_close(result, expected_result)
+
+    r = Rotation.from_quat(-quat)
+    result = r.magnitude()
+    xp_assert_close(result, expected_result)
+
+
+@make_xp_test_case((Rotation, "magnitude"))
+def test_magnitude_single_rotation(xp):
+    r = Rotation.from_quat(xp.eye(4))
+    result1 = r[0].magnitude()
+    xp_assert_close(result1, xp.asarray(xp.pi)[()])
+
+    result2 = r[3].magnitude()
+    xp_assert_close(result2, xp.asarray(0.0)[()])
+
+
+@make_xp_test_case(
+    (Rotation, "inv"), (Rotation, "magnitude"), (Rotation, "approx_equal")
+)
+def test_approx_equal(xp):
+    rng = np.random.default_rng(146972845698875399755764481408308808739)
+    p = Rotation.random(10, rng=rng)
+    q = Rotation.random(10, rng=rng)
+    r_mag = (p * q.inv()).magnitude()
+    p = rotation_to_xp(p, xp)
+    q = rotation_to_xp(q, xp)
+    # ensure we get mix of Trues and Falses
+    atol = xp.asarray(np.median(r_mag))
+    xp_assert_equal(p.approx_equal(q, atol), (xp.asarray(r_mag) < atol))
+
+
+@make_xp_test_case((Rotation, "from_rotvec"), (Rotation, "approx_equal"))
+def test_approx_equal_single_rotation(xp):
+    # also tests passing single argument to approx_equal
+    p = Rotation.from_rotvec(xp.asarray([0, 0, 1e-9]))  # less than default atol of 1e-8
+    q = Rotation.from_quat(xp.eye(4))
+    assert p.approx_equal(q[3])
+    assert not p.approx_equal(q[0])
+    # Regression test for gh-24769: single approx_equal should return a bool
+    assert isinstance(p.approx_equal(q[0]), np.bool_) or not is_numpy(xp)
+
+    # test passing atol and using degrees
+    assert not p.approx_equal(q[3], atol=1e-10)
+    assert not p.approx_equal(q[3], atol=1e-8, degrees=True)
+    with pytest.warns(UserWarning, match="atol must be set"):
+        assert p.approx_equal(q[3], degrees=True)
+
+
+@make_xp_test_case(
+    (Rotation, "inv"), (Rotation, "magnitude"), (Rotation, "approx_equal")
+)
+def test_approx_equal_batched(xp):
+    # Same shapes
+    batch_shape = (2, 10, 3)
+    rng = np.random.default_rng(0)
+    p = Rotation.from_quat(rng.normal(size=batch_shape + (4,)))
+    q = Rotation.from_quat(rng.normal(size=batch_shape + (4,)))
+    r_mag = (p * q.inv()).magnitude()  # Must be computed as numpy array for np.median
+    p = rotation_to_xp(p, xp)
+    q = rotation_to_xp(q, xp)
+    assert r_mag.shape == batch_shape
+    # ensure we get mix of Trues and Falses
+    atol = xp.asarray(np.median(r_mag))
+    xp_assert_equal(p.approx_equal(q, atol), (xp.asarray(r_mag) < atol))
+
+    # Broadcastable shapes of same length
+    p = Rotation.from_quat(rng.normal(size=batch_shape + (4,)))
+    q = Rotation.from_quat(rng.normal(size=(1, 10, 1, 4)))
+    r_mag = (p * q.inv()).magnitude()
+    p = rotation_to_xp(p, xp)
+    q = rotation_to_xp(q, xp)
+    assert r_mag.shape == batch_shape
+    atol = xp.asarray(np.median(r_mag))
+    xp_assert_equal(p.approx_equal(q, atol), (xp.asarray(r_mag) < atol))
+
+    # Broadcastable shapes of different length
+    p = Rotation.from_quat(rng.normal(size=batch_shape + (4,)))
+    q = Rotation.from_quat(rng.normal(size=(1, 3, 4)))
+    r_mag = (p * q.inv()).magnitude()
+    p = rotation_to_xp(p, xp)
+    q = rotation_to_xp(q, xp)
+    assert r_mag.shape == batch_shape
+    atol = xp.asarray(np.median(r_mag))
+    xp_assert_equal(p.approx_equal(q, atol), (xp.asarray(r_mag) < atol))
+
+
+@make_xp_test_case((Rotation, "approx_equal"))
+def test_approx_equal_batched_input_validation(xp):
+    p = Rotation.from_quat(xp.ones((2, 3, 4)))
+    q = Rotation.from_quat(xp.ones((3, 2, 4)))
+    with pytest.raises(ValueError, match="broadcastable shapes"):
+        p.approx_equal(q)
+
+    p = Rotation.from_quat(xp.ones((2, 4)))
+    q = Rotation.from_quat(xp.ones((3, 4)))
+    with pytest.raises(ValueError, match="broadcastable shapes"):
+        p.approx_equal(q)
+
+
+@make_xp_test_case(
+    (Rotation, "from_rotvec"), (Rotation, "mean"), (Rotation, "magnitude")
+)
+@pytest.mark.parametrize("ndim", list(range(1, 4)))
+def test_mean(xp, ndim: int):
+    axes = xp.concat((-xp.eye(3), xp.eye(3)))
+    axes = xp.reshape(axes, (1,) * (ndim - 1) + (6, 3))
+    thetas = xp.linspace(0, xp.pi / 2, 100)
+    desired = xp.asarray(0.0)[()]
+    atol = 1e-6 if xp_default_dtype(xp) is xp.float32 else 1e-10
+    for t in thetas:
+        r_mean = Rotation.from_rotvec(t * axes).mean()
+        assert r_mean.shape == ()
+        xp_assert_close(r_mean.magnitude(), desired, atol=atol)
+
+
+@make_xp_test_case(
+    (Rotation, "from_rotvec"), (Rotation, "mean"), (Rotation, "magnitude")
+)
+@pytest.mark.parametrize("ndim", list(range(1, 5)))
+def test_mean_axis(xp, ndim: int):
+    axes = xp.tile(xp.concat((-xp.eye(3), xp.eye(3))), (3,) * (ndim - 1) + (1, 1))
+    theta = xp.pi / 4
+    r = Rotation.from_rotvec(theta * axes)
+
+    # Test mean over last axis
+    desired = xp.full(axes.shape[:-2], 0.0)
+    if ndim == 1:
+        desired = desired[()]
+    atol = 1e-6 if xp_default_dtype(xp) is xp.float32 else 1e-10
+    xp_assert_close(r.mean(axis=-1).magnitude(), desired, atol=atol)
+
+    # Test tuple axes
+    desired = xp.full(axes.shape[1:-2], 0.0)
+    if ndim < 3:
+        desired = desired[()]
+    xp_assert_close(r.mean(axis=(0, -1)).magnitude(), desired, atol=atol)
+
+    # Empty axis tuple should return Rotation unchanged
+    r_mean = r.mean(axis=())
+    xp_assert_close(r_mean.as_quat(canonical=True), r.as_quat(canonical=True),
+                    atol=atol)
+
+
+@make_xp_test_case((Rotation, "mean"), (Rotation, "magnitude"))
+def test_mean_compare_axis(xp):
+    # Create a random set of rotations and compare the mean over an axis with the
+    # mean without axis of the sliced quaternion
+    atol = 1e-10 if xpx.default_dtype(xp) == xp.float64 else 1e-6
+    rng = np.random.default_rng(0)
+    q = xp.asarray(rng.normal(size=(4, 5, 6, 4)), dtype=xpx.default_dtype(xp))
+    r = Rotation.from_quat(q)
+
+    mean_0 = r.mean(axis=0)
+    for i in range(q.shape[1]):
+        for j in range(q.shape[2]):
+            mean_slice = Rotation.from_quat(q[:, i, j, ...]).mean()
+            xp_assert_close((mean_0[i][j] * mean_slice.inv()).magnitude(),
+                            xp.asarray(0.0)[()], atol=atol)
+    mean_1_2 = r.mean(axis=(1, 2))
+    for i in range(q.shape[0]):
+        mean_slice = Rotation.from_quat(q[i, ...]).mean()
+        xp_assert_close((mean_1_2[i] * mean_slice.inv()).magnitude(),
+                        xp.asarray(0.0)[()], atol=atol)
+
+
+@make_xp_test_case((Rotation, "from_rotvec"), (Rotation, "mean"), (Rotation, "inv"),
+                   (Rotation, "magnitude"))
+@pytest.mark.parametrize("ndim", list(range(1, 4)))
+def test_weighted_mean(xp, ndim: int):
+    # test that doubling a weight is equivalent to including a rotation twice.
+    thetas = xp.linspace(0, xp.pi / 2, 100)
+
+    # Create batched copies of the same setup
+    batch_shape = (ndim,) * (ndim - 1)
+    axes = xp.asarray([[0.0, 0, 0], [1, 0, 0], [1, 0, 0]])
+    weights = xp.asarray([1, 2])
+    axes = xp.tile(axes, batch_shape + (1, 1))
+    weights = xp.tile(weights, batch_shape + (1,))
+
+    expected = xp.asarray(0.0)[()]
+    for t in thetas:
+        rw = Rotation.from_rotvec(t * axes[..., :2, :])
+        mw = rw.mean(weights=weights)
+
+        r = Rotation.from_rotvec(t * axes)
+        m = r.mean()
+        assert m.shape == ()
+        xp_assert_close((m * mw.inv()).magnitude(), expected, atol=1e-6)
+
+
+@make_xp_test_case((Rotation, "mean"))
+def test_mean_input_validation(xp):
+    r = Rotation.from_quat(xp.eye(4))
+    if is_lazy_array(r.as_quat()):
+        m = r.mean(weights=-xp.ones(4))
+        assert xp.all(xp.isnan(m._quat))
+    else:
+        with pytest.raises(ValueError, match="non-negative"):
+            r.mean(weights=-xp.ones(4))
+
+    # Test weight shape mismatch
+    r = Rotation.from_quat(xp.ones((3, 4)))
+    with pytest.raises(ValueError, match="Expected `weights` to"):
+        r.mean(weights=xp.ones((2,)))
+    r = Rotation.from_quat(xp.ones((2, 3, 4)))
+    with pytest.raises(ValueError, match="Expected `weights` to"):
+        r.mean(weights=xp.ones((2, 2)))
+
+    # Test wrong axis
+    with pytest.raises(ValueError, match=r"axis .* is out of bounds"):
+        r.mean(axis=3)
+    with pytest.raises(ValueError, match=r"axis .* is out of bounds"):
+        r.mean(axis=(-1, 2))
+    with pytest.raises(ValueError, match="`axis` must be None, int, or tuple of ints."):
+        r.mean(axis="0")
+    with pytest.raises(ValueError, match=r"axis .* is out of bounds"):
+        r.mean(axis=-12)
+
+
+@make_xp_test_case((Rotation, "reduce"))
+def test_reduction_no_indices(xp):
+    r = Rotation.from_quat(xp.asarray([0.0, 0.0, 0.0, 1.0]))
+    result = r.reduce(return_indices=False)
+    assert isinstance(result, Rotation)
+
+
+@make_xp_test_case((Rotation, "reduce"))
+def test_reduction_none_indices(xp):
+    r = Rotation.from_quat(xp.asarray([0.0, 0.0, 0.0, 1.0]))
+    result = r.reduce(return_indices=True)
+    assert type(result) is tuple
+    assert len(result) == 3
+
+    reduced, left_best, right_best = result
+    assert left_best is None
+    assert right_best is None
+
+
+@make_xp_test_case((Rotation, "reduce"), (Rotation, "inv"), (Rotation, "magnitude"))
+def test_reduction_scalar_calculation(xp):
+    dtype = xpx.default_dtype(xp)
+    atol = 1e-12 if dtype == xp.float64 else 1e-6
+    rng = np.random.default_rng(146972845698875399755764481408308808739)
+    l_np = Rotation.random(5, rng=rng)
+    r_np = Rotation.random(10, rng=rng)
+    p_np = Rotation.random(7, rng=rng)
+    l = rotation_to_xp(l_np, xp)
+    r = rotation_to_xp(r_np, xp)
+    p = rotation_to_xp(p_np, xp)
+    reduced, left_best, right_best = p.reduce(l, r, return_indices=True)
+
+    # Loop implementation of the vectorized calculation in Rotation.reduce
+    scalars = np.zeros((len(l_np), len(p_np), len(r_np)))
+    for i, li in enumerate(l_np):
+        for j, pj in enumerate(p_np):
+            for k, rk in enumerate(r_np):
+                scalars[i, j, k] = np.abs((li * pj * rk).as_quat()[3])
+    scalars = np.reshape(np.moveaxis(scalars, 1, 0), (scalars.shape[1], -1))
+
+    max_ind = np.argmax(np.reshape(scalars, (len(p), -1)), axis=1)
+    left_best_check = xp.asarray(max_ind // len(r))
+    right_best_check = xp.asarray(max_ind % len(r))
+    assert xp.all(left_best == left_best_check)
+    assert xp.all(right_best == right_best_check)
+
+    reduced_check = l[left_best_check] * p * r[right_best_check]
+    mag = (reduced.inv() * reduced_check).magnitude()
+    xp_assert_close(mag, xp.zeros(len(p)), atol=atol)
+
+
+@make_xp_test_case((Rotation, "from_matrix"), (Rotation, "apply"))
+def test_apply_single_rotation_single_point(xp):
+    dtype = xpx.default_dtype(xp)
+    mat = xp.asarray([
+        [0, -1, 0],
+        [1, 0, 0],
+        [0, 0, 1]
+    ])
+    r_1d = Rotation.from_matrix(mat)
+    r_2d = Rotation.from_matrix(xp.expand_dims(mat, axis=0))
+
+    v_1d = xp.asarray([1.0, 2, 3], dtype=dtype)
+    v_2d = xp.expand_dims(v_1d, axis=0)
+    v1d_rotated = xp.asarray([-2.0, 1, 3], dtype=dtype)
+    v2d_rotated = xp.expand_dims(v1d_rotated, axis=0)
+
+    xp_assert_close(r_1d.apply(v_1d), v1d_rotated)
+    xp_assert_close(r_1d.apply(v_2d), v2d_rotated)
+    xp_assert_close(r_2d.apply(v_1d), v2d_rotated)
+    xp_assert_close(r_2d.apply(v_2d), v2d_rotated)
+
+    v1d_inverse = xp.asarray([2.0, -1, 3], dtype=dtype)
+    v2d_inverse = xp.expand_dims(v1d_inverse, axis=0)
+
+    xp_assert_close(r_1d.apply(v_1d, inverse=True), v1d_inverse)
+    xp_assert_close(r_1d.apply(v_2d, inverse=True), v2d_inverse)
+    xp_assert_close(r_2d.apply(v_1d, inverse=True), v2d_inverse)
+    xp_assert_close(r_2d.apply(v_2d, inverse=True), v2d_inverse)
+
+
+@make_xp_test_case((Rotation, "from_matrix"), (Rotation, "apply"))
+@pytest.mark.parametrize("ndim", list(range(1, 4)))
+def test_apply_single_rotation_multiple_points(xp, ndim: int):
+    dtype = xpx.default_dtype(xp)
+    mat = xp.asarray([
+        [0, -1, 0],
+        [1, 0, 0],
+        [0, 0, 1]
+    ])
+    r1 = Rotation.from_matrix(mat)
+    r2 = Rotation.from_matrix(xp.expand_dims(mat, axis=0))
+
+    rng = np.random.default_rng(0)
+    batch_shape = (ndim,) * (ndim - 1)
+    v = xp.asarray(rng.normal(size=batch_shape + (2, 3)), dtype=dtype)
+    v_rotated = xp.stack([-v[..., 1], v[..., 0], v[..., 2]], axis=-1)
+
+    xp_assert_close(r1.apply(v), v_rotated)
+    xp_assert_close(r2.apply(v), v_rotated)
+
+    v_inverse = xp.stack([v[..., 1], -v[..., 0], v[..., 2]], axis=-1)
+
+    xp_assert_close(r1.apply(v, inverse=True), v_inverse)
+    xp_assert_close(r2.apply(v, inverse=True), v_inverse)
+
+
+@make_xp_test_case((Rotation, "from_matrix"), (Rotation, "apply"))
+@pytest.mark.parametrize("ndim", list(range(1, 5)))
+def test_apply_multiple_rotations_single_point(xp, ndim: int):
+    dtype = xpx.default_dtype(xp)
+    mat = np.empty((2, 3, 3))
+    mat[0] = np.array([
+        [0, -1, 0],
+        [1, 0, 0],
+        [0, 0, 1]
+    ])
+    mat[1] = np.array([
+        [1, 0, 0],
+        [0, 0, -1],
+        [0, 1, 0]
+    ])
+    mat = xp.asarray(mat, dtype=dtype)
+    batch_shape = (ndim,) * (ndim - 1)
+    mat = xp.tile(mat, batch_shape + (1, 1, 1))
+    r = Rotation.from_matrix(mat)
+
+    v1 = xp.asarray([1, 2, 3])
+    v2 = xp.expand_dims(v1, axis=0)
+
+    v_rotated = xp.asarray([[-2.0, 1, 3], [1, -3, 2]])
+    v_rotated = xp.tile(v_rotated, batch_shape + (1, 1))
+
+    xp_assert_close(r.apply(v1), v_rotated)
+    xp_assert_close(r.apply(v2), v_rotated)
+
+    v_inverse = xp.asarray([[2.0, -1, 3], [1, 3, -2]])
+    v_inverse = xp.tile(v_inverse, batch_shape + (1, 1))
+
+    xp_assert_close(r.apply(v1, inverse=True), v_inverse)
+    xp_assert_close(r.apply(v2, inverse=True), v_inverse)
+
+
+@make_xp_test_case((Rotation, "from_matrix"), (Rotation, "apply"))
+@pytest.mark.parametrize("ndim", list(range(1, 5)))
+def test_apply_multiple_rotations_multiple_points(xp, ndim: int):
+    dtype = xpx.default_dtype(xp)
+    mat = np.empty((2, 3, 3))
+    mat[0] = np.array([
+        [0, -1, 0],
+        [1, 0, 0],
+        [0, 0, 1]
+    ])
+    mat[1] = np.array([
+        [1, 0, 0],
+        [0, 0, -1],
+        [0, 1, 0]
+    ])
+    mat = xp.asarray(mat, dtype=dtype)
+    batch_shape = (ndim,) * (ndim - 1)
+    mat = xp.tile(mat, batch_shape + (1, 1, 1))
+    r = Rotation.from_matrix(mat)
+
+    v = xp.asarray([[1, 2, 3], [4, 5, 6]], dtype=dtype)
+    v_rotated = xp.asarray([[-2.0, 1, 3], [4, -6, 5]], dtype=dtype)
+    v_rotated = xp.tile(v_rotated, batch_shape + (1, 1))
+    xp_assert_close(r.apply(v), v_rotated)
+
+    v_inverse = xp.asarray([[2.0, -1, 3], [4, 6, -5]], dtype=dtype)
+    v_inverse = xp.tile(v_inverse, batch_shape + (1, 1))
+    xp_assert_close(r.apply(v, inverse=True), v_inverse)
+
+
+@make_xp_test_case((Rotation, "apply"))
+def test_apply_shapes(xp):
+    rng = np.random.default_rng(0)
+    # Broadcast shape: (6, 5, 4, 2) ( + (3,) for vectors, + (4,) for rotations)
+    vector_shapes = [(), (1,), (2,), (1, 2), (5, 1, 2)]
+    rot_shapes = [(), (1,), (2,), (1, 2), (4, 2), (1, 4, 2), (5, 4, 2), (6, 5, 4, 2)]
+
+    for q_shape, v_shape in product(rot_shapes, vector_shapes):
+        v = xp.asarray(rng.normal(size=v_shape + (3,)))
+        q = xp.asarray(rng.normal(size=q_shape + (4,)))
+        r = Rotation.from_quat(q)
+        shape = np.broadcast_shapes(q_shape, v_shape) + (3,)
+        x = r.apply(v)
+        assert x.shape == shape
+        x = r.apply(v, inverse=True)
+        assert x.shape == shape
+
+
+def test_apply_array_like():
+    rng = np.random.default_rng(123)
+    # Single vector
+    r = Rotation.random(rng=rng)
+    t = rng.uniform(-100, 100, size=(3,))
+    v = r.apply(t.tolist())
+    v_expected = r.apply(t)
+    xp_assert_close(v, v_expected, atol=1e-12)
+    # Multiple vectors
+    t = rng.uniform(-100, 100, size=(2, 3))
+    v = r.apply(t.tolist())
+    v_expected = r.apply(t)
+    xp_assert_close(v, v_expected, atol=1e-12)
+
+
+def test_apply_matrix_equivalence():
+    """Test documented equivalence for single rotation:
+    `apply(vectors) == vectors @ as_matrix().T.`"""
+    r = Rotation.from_rotvec([0, 0, 1])
+    # Single vector (3,)
+    v = np.array([1.0, 0.0, 0.0])
+    xp_assert_close(r.apply(v), v @ r.as_matrix().T)
+    # Multiple vectors (P, 3)
+    arr = np.array([[1, 0, 0], [1, 2, 3]], dtype=float)
+    xp_assert_close(r.apply(arr), arr @ r.as_matrix().T)
+    # (3, 3) case: `as_matrix() @ vectors` would not error but give wrong result
+    arr33 = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]], dtype=float)
+    xp_assert_close(r.apply(arr33), arr33 @ r.as_matrix().T)
+    wrong_result = r.as_matrix() @ arr33
+    assert not np.allclose(r.apply(arr33), wrong_result)
+
+
+@make_xp_test_case((Rotation, "apply"))
+def test_apply_input_validation(xp):
+    r = Rotation.from_quat(xp.ones(4))
+    with pytest.raises(ValueError, match="Expected input of shape"):
+        r.apply(xp.ones(2))
+    with pytest.raises(ValueError, match="Expected input of shape"):
+        r.apply(xp.ones((2, 2)))
+    r = Rotation.from_quat(xp.ones((2, 4)))
+    with pytest.raises(ValueError, match="Cannot broadcast"):
+        r.apply(xp.ones((3, 3)))
+    r = Rotation.from_quat(xp.ones((1, 7, 2, 4)))
+    with pytest.raises(ValueError, match="Cannot broadcast"):
+        r.apply(xp.ones((2, 2, 3)))
+
+
+@make_xp_test_case(
+    (Rotation, "from_matrix"), (Rotation, "as_matrix"), (Rotation, "__getitem__")
+)
+@pytest.mark.parametrize("ndim", list(range(1, 4)))
+def test_getitem(xp, ndim: int):
+    rng = np.random.default_rng(0)
+    quat = rng.normal(size=(2, ) + (ndim,) * (ndim - 1) + (4,))
+    mat = xp.asarray(Rotation.from_quat(quat).as_matrix())
+    r = Rotation.from_matrix(mat)
+
+    xp_assert_close(r[0].as_matrix(), mat[0, ...], atol=1e-15)
+    xp_assert_close(r[1].as_matrix(), mat[1, ...], atol=1e-15)
+    xp_assert_close(r[:-1].as_matrix(), xp.expand_dims(mat[0, ...], axis=0), atol=1e-15)
+
+
+@make_xp_test_case((Rotation, "__getitem__"))
+def test_getitem_single(xp):
+    with pytest.raises(TypeError, match='not subscriptable'):
+        Rotation.from_quat(xp.asarray([0, 0, 0, 1]))[0]
+
+
+@make_xp_test_case(
+    (Rotation, "from_matrix"), (Rotation, "__getitem__"), (Rotation, "as_matrix")
+)
+def test_getitem_array_like():
+    mat = np.array([[[0.0, -1, 0],
+                     [1, 0, 0],
+                     [0, 0, 1]],
+                    [[1, 0, 0],
+                     [0, 0, -1],
+                     [0, 1, 0]]])
+    r = Rotation.from_matrix(mat)
+    xp_assert_close(r[[0]].as_matrix(), mat[[0]], atol=1e-15)
+    xp_assert_close(r[[0, 1]].as_matrix(), mat[[0, 1]], atol=1e-15)
+
+
+@make_xp_test_case((Rotation, "__setitem__"))
+def test_setitem_single(xp):
+    r = Rotation.from_quat(xp.asarray([0, 0, 0, 1]))
+    with pytest.raises(TypeError, match='not subscriptable'):
+        r[0] = Rotation.from_quat(xp.asarray([0, 0, 0, 1]))
+
+
+@make_xp_test_case((Rotation, "__setitem__"))
+def test_setitem_slice(xp):
+    rng = np.random.default_rng(146972845698875399755764481408308808739)
+    r1 = rotation_to_xp(Rotation.random(10, rng=rng), xp)
+    r2 = rotation_to_xp(Rotation.random(5, rng=rng), xp)
+    r1[1:6] = r2
+    xp_assert_equal(r1[1:6].as_quat(), r2.as_quat())
+
+    # Multiple dimensions
+    r1 = Rotation.from_quat(xp.asarray(rng.normal(size=(3, 5, 4))))
+    r2 = Rotation.from_quat(xp.asarray(rng.normal(size=(2, 5, 4))))
+    r1[1:3] = r2
+    xp_assert_equal(r1[1:3].as_quat(), r2.as_quat())
+
+
+@make_xp_test_case((Rotation, "__setitem__"))
+def test_setitem_integer(xp):
+    rng = np.random.default_rng(146972845698875399755764481408308808739)
+    r1 = rotation_to_xp(Rotation.random(10, rng=rng), xp)
+    r2 = rotation_to_xp(Rotation.random(rng=rng), xp)
+    r1[1] = r2
+    xp_assert_equal(r1[1].as_quat(), r2.as_quat())
+
+    # Multiple dimensions
+    r1 = Rotation.from_quat(xp.asarray(rng.normal(size=(3, 5, 4))))
+    r2 = Rotation.from_quat(xp.asarray(rng.normal(size=(5, 4))))
+    r1[1] = r2
+    xp_assert_equal(r1[1].as_quat(), r2.as_quat())
+
+
+@make_xp_test_case((Rotation, "__setitem__"))
+def test_setitem_wrong_type(xp):
+    r = rotation_to_xp(Rotation.random(10, rng=0), xp)
+    with pytest.raises(TypeError, match='Rotation object'):
+        r[0] = 1
+
+
+@make_xp_test_case((Rotation, "from_matrix"))
+def test_n_rotations(xp):
+    mat = np.empty((2, 3, 3))
+    mat[0] = np.array([
+        [0, -1, 0],
+        [1, 0, 0],
+        [0, 0, 1]
+    ])
+    mat[1] = np.array([
+        [1, 0, 0],
+        [0, 0, -1],
+        [0, 1, 0]
+    ])
+    mat = xp.asarray(mat)
+    r = Rotation.from_matrix(mat)
+
+    assert_equal(len(r), 2)
+    assert_equal(len(r[:-1]), 1)
+
+
+def test_random_rotation():
+    # No xp testing since random rotations are always using NumPy
+    rng = np.random.default_rng(0)
+    assert_equal(Rotation.random(rng=rng).as_quat().shape, (4,))
+    assert_equal(Rotation.random(None, rng=rng).as_quat().shape, (4,))
+    assert_equal(Rotation.random(1, rng=rng).as_quat().shape, (1, 4))
+    assert_equal(Rotation.random(5, rng=rng).as_quat().shape, (5, 4))
+    # Shape argument
+    assert_equal(Rotation.random(rng=rng, shape=()).as_quat().shape, (4,))
+    assert_equal(Rotation.random(rng=rng, shape=(3,)).as_quat().shape, (3, 4))
+    assert_equal(Rotation.random(rng=rng, shape=(2, 3)).as_quat().shape, (2, 3, 4))
+    # Values should be the same for num=prod(shape)
+    rng1, rng2 = np.random.default_rng(42), np.random.default_rng(42)
+    r_num = Rotation.random(6, rng=rng1)
+    r_shape = Rotation.random(rng=rng2, shape=(2, 3))
+    xp_assert_close(r_num.as_quat(), r_shape.as_quat().reshape(6, 4), atol=1e-12)
+    # Errors
+    with pytest.raises(ValueError, match="Only one of `num` or `shape` can be"):
+        Rotation.random(num=3,rng=rng, shape=(2, 2))
+    with pytest.raises(ValueError, match="`shape` must be an int or a tuple of ints"):
+        Rotation.random(rng=rng, shape=2.5)
+    with pytest.raises(TypeError, match="takes from 0 to 2 positional arguments"):
+        Rotation.random(1, rng, None)  # Shape should be kwarg only
+
+
+@make_xp_test_case((Rotation, "align_vectors"), (Rotation, "as_matrix"))
+def test_align_vectors_no_rotation(xp):
+    dtype = xpx.default_dtype(xp)
+    atol = 1e-12 if dtype == xp.float64 else 1e-5
+    x = xp.asarray([[1, 2, 3], [4, 5, 6]], dtype=dtype)
+    y = xp.asarray(x, copy=True)
+
+    r, rssd = Rotation.align_vectors(x, y)
+    xp_assert_close(r.as_matrix(), xp.eye(3), atol=atol)
+    xp_assert_close(rssd, xp.asarray(0.0)[()], check_shape=False, atol=1e-6)
+
+
+@make_xp_test_case((Rotation, "apply"), (Rotation, "align_vectors"))
+def test_align_vectors_no_noise(xp):
+    dtype = xpx.default_dtype(xp)
+    atol = 1e-7 if dtype == xp.float64 else 2e-3
+    rng = np.random.default_rng(14697284569885399755764481408308808739)
+    c = rotation_to_xp(Rotation.random(rng=rng), xp)
+    b = xp.asarray(rng.normal(size=(5, 3)), dtype=dtype)
+    a = c.apply(b)
+
+    est, rssd = Rotation.align_vectors(a, b)
+    xp_assert_close(c.as_quat(), est.as_quat())
+    xp_assert_close(rssd, xp.asarray(0.0)[()], check_shape=False, atol=atol)
+
+
+@make_xp_test_case((Rotation, "align_vectors"), (Rotation, "apply"))
+def test_align_vectors_improper_rotation(xp):
+    dtype = xpx.default_dtype(xp)
+    atol = 1e-7 if dtype == xp.float64 else 1e-3
+    # Tests correct logic for issue #10444
+    x = xp.asarray([[0.89299824, -0.44372674, 0.0752378],
+                    [0.60221789, -0.47564102, -0.6411702]])
+    y = xp.asarray([[0.02386536, -0.82176463, 0.5693271],
+                    [-0.27654929, -0.95191427, -0.1318321]])
+
+    est, rssd = Rotation.align_vectors(x, y)
+    xp_assert_close(x, est.apply(y), atol=1e-6)
+    xp_assert_close(rssd, xp.asarray(0.0)[()], check_shape=False, atol=atol)
+
+
+@make_xp_test_case((Rotation, "align_vectors"))
+def test_align_vectors_rssd_sensitivity(xp):
+    rssd_expected = xp.asarray(0.141421356237308)[()]
+    sens_expected = xp.asarray([[0.2, 0. , 0.],
+                                [0. , 1.5, 1.],
+                                [0. , 1. , 1.]])
+    atol = 1e-6
+    a = xp.asarray([[0, 1, 0], [0, 1, 1], [0, 1, 1]])
+    b = xp.asarray([[1, 0, 0], [1, 1.1, 0], [1, 0.9, 0]])
+    rot, rssd, sens = Rotation.align_vectors(a, b, return_sensitivity=True)
+    xp_assert_close(rssd, rssd_expected, atol=atol)
+    xp_assert_close(sens, sens_expected, atol=atol)
+
+
+@make_xp_test_case((Rotation, "align_vectors"), (Rotation, "as_matrix"))
+def test_align_vectors_scaled_weights(xp):
+    n = 10
+    a = xp.asarray(Rotation.random(n, rng=0).apply([1, 0, 0]))
+    b = xp.asarray(Rotation.random(n, rng=1).apply([1, 0, 0]))
+    scale = 2
+
+    est1, rssd1, cov1 = Rotation.align_vectors(a, b, xp.ones(n), True)
+    est2, rssd2, cov2 = Rotation.align_vectors(a, b, scale * xp.ones(n), True)
+
+    xp_assert_close(est1.as_matrix(), est2.as_matrix())
+    xp_assert_close(math.sqrt(scale) * rssd1, rssd2, atol=1e-6)
+    xp_assert_close(cov1, cov2)
+
+
+@make_xp_test_case(
+    (Rotation, "apply"), (Rotation, "from_rotvec"), (Rotation, "align_vectors")
+)
+def test_align_vectors_noise(xp):
+    dtype = xpx.default_dtype(xp)
+    rng = np.random.default_rng(146972845698875399755764481408308808739)
+    n_vectors = 100
+    rot = rotation_to_xp(Rotation.random(rng=rng), xp)
+    vectors = xp.asarray(rng.normal(size=(n_vectors, 3)), dtype=dtype)
+    result = rot.apply(vectors)
+
+    # The paper adds noise as independently distributed angular errors
+    sigma = np.deg2rad(1)
+    tolerance = 1.5 * sigma
+    noise = Rotation.from_rotvec(
+        xp.asarray(rng.normal(size=(n_vectors, 3), scale=sigma), dtype=dtype)
+    )
+
+    # Attitude errors must preserve norm. Hence apply individual random
+    # rotations to each vector.
+    noisy_result = noise.apply(result)
+
+    est, rssd, cov = Rotation.align_vectors(noisy_result, vectors,
+                                            return_sensitivity=True)
+
+    # Use rotation compositions to find out closeness
+    error_vector = (rot * est.inv()).as_rotvec()
+    xp_assert_close(error_vector[0], xp.asarray(0.0)[()], atol=tolerance)
+    xp_assert_close(error_vector[1], xp.asarray(0.0)[()], atol=tolerance)
+    xp_assert_close(error_vector[2], xp.asarray(0.0)[()], atol=tolerance)
+
+    # Check error bounds using covariance matrix
+    cov *= xp.asarray(sigma)
+    xp_assert_close(cov[0, 0], xp.asarray(0.0)[()], atol=tolerance)
+    xp_assert_close(cov[1, 1], xp.asarray(0.0)[()], atol=tolerance)
+    xp_assert_close(cov[2, 2], xp.asarray(0.0)[()], atol=tolerance)
+
+    rssd_check = xp.sum((noisy_result - est.apply(vectors)) ** 2) ** 0.5
+    xp_assert_close(rssd, rssd_check, check_shape=False)
+
+
+@make_xp_test_case((Rotation, "align_vectors"))
+def test_align_vectors_invalid_input(xp):
+    with pytest.raises(ValueError, match="Expected input `a` to have shape"):
+        a, b = xp.asarray([1, 2, 3, 4]), xp.asarray([1, 2, 3])
+        Rotation.align_vectors(a, b)
+
+    with pytest.raises(ValueError, match="Expected input `b` to have shape"):
+        a, b = xp.asarray([1, 2, 3]), xp.asarray([1, 2, 3, 4])
+        Rotation.align_vectors(a, b)
+
+    with pytest.raises(ValueError, match="Expected inputs `a` and `b` "
+                                         "to have same shapes"):
+        a, b = xp.asarray([[1, 2, 3], [4, 5, 6]]), xp.asarray([[1, 2, 3]])
+        Rotation.align_vectors(a, b)
+
+    with pytest.raises(ValueError,
+                       match="Expected `weights` to be 1 dimensional"):
+        a, b = xp.asarray([[1, 2, 3]]), xp.asarray([[1, 2, 3]])
+        weights = xp.asarray([[1]])
+        Rotation.align_vectors(a, b, weights)
+
+    with pytest.raises(ValueError,
+                       match="Expected `weights` to have number of values"):
+        a, b = xp.asarray([[1, 2, 3], [4, 5, 6]]), xp.asarray([[1, 2, 3], [4, 5, 6]])
+        weights = xp.asarray([1, 2, 3])
+        Rotation.align_vectors(a, b, weights)
+
+    a, b = xp.asarray([[1, 2, 3]]), xp.asarray([[1, 2, 3]])
+    weights = xp.asarray([-1])
+    if is_lazy_array(weights):
+        r, rssd = Rotation.align_vectors(a, b, weights)
+        assert xp.all(xp.isnan(r.as_quat())), "Quaternion should be nan"
+        assert xp.isnan(rssd), "RSSD should be nan"
+    else:
+        with pytest.raises(ValueError,
+                           match="`weights` may not contain negative values"):
+            Rotation.align_vectors(a, b, weights)
+
+    a, b = xp.asarray([[1, 2, 3], [4, 5, 6]]), xp.asarray([[1, 2, 3], [4, 5, 6]])
+    weights = xp.asarray([xp.inf, xp.inf])
+    if is_lazy_array(weights):
+        r, rssd = Rotation.align_vectors(a, b, weights)
+        assert xp.all(xp.isnan(r.as_quat())), "Quaternion should be nan"
+        assert xp.isnan(rssd), "RSSD should be nan"
+    else:
+        with pytest.raises(ValueError,
+                           match="Only one infinite weight is allowed"):
+            Rotation.align_vectors(a, b, weights)
+
+    a, b = xp.asarray([[0, 0, 0]]), xp.asarray([[1, 2, 3]])
+    if is_lazy_array(a):
+        r, rssd = Rotation.align_vectors(a, b)
+        assert xp.all(xp.isnan(r.as_quat())), "Quaternion should be nan"
+        assert xp.isnan(rssd), "RSSD should be nan"
+    else:
+        with pytest.raises(ValueError,
+                           match="Cannot align zero length primary vectors"):
+            Rotation.align_vectors(a, b)
+
+    a, b = xp.asarray([[1, 2, 3], [4, 5, 6]]), xp.asarray([[1, 2, 3], [4, 5, 6]])
+    weights = xp.asarray([xp.inf, 1])
+    if is_lazy_array(a):
+        r, rssd, sens = Rotation.align_vectors(a, b, weights, return_sensitivity=True)
+        assert xp.all(xp.isnan(sens)), "Sensitivity matrix should be nan"
+    else:
+        with pytest.raises(ValueError,
+                           match="Cannot return sensitivity matrix"):
+            Rotation.align_vectors(a, b, weights, return_sensitivity=True)
+
+    a, b = xp.asarray([[1, 2, 3]]), xp.asarray([[1, 2, 3]])
+    if is_lazy_array(a):
+        r, rssd, sens = Rotation.align_vectors(a, b, return_sensitivity=True)
+        assert xp.all(xp.isnan(sens)), "Sensitivity matrix should be nan"
+    else:
+        with pytest.raises(ValueError,
+                        match="Cannot return sensitivity matrix"):
+                        Rotation.align_vectors(a, b, return_sensitivity=True)
+
+    # No broadcast support for align_vectors
+    a, b = xp.asarray([[[1, 2, 3]]]), xp.asarray([[[1, 2, 3]]])
+    with pytest.raises(ValueError,
+                       match="Expected inputs `a` and `b` to have shape"):
+        Rotation.align_vectors(a, b)
+
+
+@make_xp_test_case(
+    (Rotation, "align_vectors"), (Rotation, "as_matrix"), (Rotation, "apply")
+)
+def test_align_vectors_align_constrain(xp):
+    # Align the primary +X B axis with the primary +Y A axis, and rotate about
+    # it such that the +Y B axis (residual of the [1, 1, 0] secondary b vector)
+    # is aligned with the +Z A axis (residual of the [0, 1, 1] secondary a
+    # vector)
+    dtype = xpx.default_dtype(xp)
+    atol = 1e-12 if dtype == xp.float64 else 1e-6
+    b = xp.asarray([[1, 0, 0], [1, 1, 0]])
+    a = xp.asarray([[0.0, 1, 0], [0, 1, 1]])
+    m_expected = xp.asarray([[0.0, 0, 1],
+                             [1, 0, 0],
+                             [0, 1, 0]])
+    R, rssd = Rotation.align_vectors(a, b, weights=xp.asarray([xp.inf, 1]))
+    xp_assert_close(R.as_matrix(), m_expected, atol=atol)
+    xp_assert_close(R.apply(b), a, atol=atol)  # Pri and sec align exactly
+    xp_assert_close(rssd, xp.asarray(0.0)[()], atol=atol)
+
+    # Do the same but with an inexact secondary rotation
+    b = xp.asarray([[1, 0, 0], [1, 2, 0]])
+    rssd_expected = 1.0
+    R, rssd = Rotation.align_vectors(a, b, weights=xp.asarray([xp.inf, 1]))
+    xp_assert_close(R.as_matrix(), m_expected, atol=atol)
+    xp_assert_close(R.apply(b)[0, ...], a[0, ...], atol=atol)  # Only pri aligns exactly
+    assert xpx.isclose(rssd, rssd_expected, atol=atol, xp=xp)
+    a_expected = xp.asarray([[0.0, 1, 0], [0, 1, 2]])
+    xp_assert_close(R.apply(b), a_expected, atol=atol)
+
+    # Check random vectors
+    b = xp.asarray([[1, 2, 3], [-2, 3, -1]])
+    a = xp.asarray([[-1.0, 3, 2], [1, -1, 2]])
+    rssd_expected = 1.3101595297515016
+    R, rssd = Rotation.align_vectors(a, b, weights=xp.asarray([xp.inf, 1]))
+    xp_assert_close(R.apply(b)[0, ...], a[0, ...], atol=atol)  # Only pri aligns exactly
+    assert xpx.isclose(rssd, rssd_expected, atol=atol, xp=xp)
+
+
+@make_xp_test_case((Rotation, "align_vectors"), (Rotation, "as_matrix"))
+def test_align_vectors_near_inf(xp):
+    # align_vectors should return near the same result for high weights as for
+    # infinite weights. rssd will be different with floating point error on the
+    # exactly aligned vector being multiplied by a large non-infinite weight
+    dtype = xpx.default_dtype(xp)
+    if dtype == xp.float32:
+        pytest.skip("Align vectors near inf is numerically unstable in float32")
+    n = 100
+    mats = []
+    for i in range(6):
+        mats.append(Rotation.random(n, rng=10 + i).as_matrix())
+
+    for i in range(n):
+        # Get random pairs of 3-element vectors
+        a = xp.asarray(np.array([1 * mats[0][i][0], 2 * mats[1][i][0]]), dtype=dtype)
+        b = xp.asarray(np.array([3 * mats[2][i][0], 4 * mats[3][i][0]]), dtype=dtype)
+
+        R, _ = Rotation.align_vectors(a, b, weights=[1e10, 1])
+        R2, _ = Rotation.align_vectors(a, b, weights=[xp.inf, 1])
+        xp_assert_close(R.as_matrix(), R2.as_matrix(), atol=1e-4)
+
+    for i in range(n):
+        # Get random triplets of 3-element vectors
+        a = xp.asarray(np.array([1*mats[0][i][0], 2*mats[1][i][0], 3*mats[2][i][0]]),
+                       dtype=dtype)
+        b = xp.asarray(np.array([4*mats[3][i][0], 5*mats[4][i][0], 6*mats[5][i][0]]),
+                       dtype=dtype)
+
+        R, _ = Rotation.align_vectors(a, b, weights=[1e10, 2, 1])
+        R2, _ = Rotation.align_vectors(a, b, weights=[xp.inf, 2, 1])
+        xp_assert_close(R.as_matrix(), R2.as_matrix(), atol=1e-4)
+
+
+@make_xp_test_case((Rotation, "align_vectors"), (Rotation, "as_matrix"))
+def test_align_vectors_parallel(xp):
+    atol = 1e-12
+    a = xp.asarray([[1.0, 0, 0], [0, 1, 0]])
+    b = xp.asarray([[0.0, 1, 0], [0, 1, 0]])
+    m_expected = xp.asarray([[0.0, 1, 0],
+                             [-1, 0, 0],
+                             [0, 0, 1]])
+    R, _ = Rotation.align_vectors(a, b, weights=[xp.inf, 1])
+    xp_assert_close(R.as_matrix(), m_expected, atol=atol)
+    R, _ = Rotation.align_vectors(a[0, ...], b[0, ...])
+    xp_assert_close(R.as_matrix(), m_expected, atol=atol)
+    xp_assert_close(R.apply(b[0, ...]), a[0, ...], atol=atol)
+
+    b = xp.asarray([[1, 0, 0], [1, 0, 0]])
+    m_expected = xp.asarray([[1.0, 0, 0],
+                             [0, 1, 0],
+                             [0, 0, 1]])
+    R, _ = Rotation.align_vectors(a, b, weights=[xp.inf, 1])
+    xp_assert_close(R.as_matrix(), m_expected, atol=atol)
+    R, _ = Rotation.align_vectors(a[0, ...], b[0, ...])
+    xp_assert_close(R.as_matrix(), m_expected, atol=atol)
+    xp_assert_close(R.apply(b[0, ...]), a[0, ...], atol=atol)
+
+
+@make_xp_test_case(
+    (Rotation, "align_vectors"), (Rotation, "magnitude"), (Rotation, "apply"),
+    (Rotation, "from_rotvec"), (Rotation, "as_rotvec"), (Rotation, "as_matrix")
+)
+def test_align_vectors_antiparallel(xp):
+    dtype = xpx.default_dtype(xp)
+    # Test exact 180 deg rotation
+    atol = 1e-12 if dtype == xp.float64 else 1e-7
+
+    as_to_test = np.array([[[1.0, 0, 0], [0, 1, 0]],
+                           [[0, 1, 0], [1, 0, 0]],
+                           [[0, 0, 1], [0, 1, 0]]])
+
+    bs_to_test = np.array([[-a[0], a[1]] for a in as_to_test])
+    for a, b in zip(as_to_test, bs_to_test):
+        a, b = xp.asarray(a, dtype=dtype), xp.asarray(b, dtype=dtype)
+        R, _ = Rotation.align_vectors(a, b, weights=[xp.inf, 1])
+        xp_assert_close(R.magnitude(), xp.asarray(xp.pi)[()], atol=atol)
+        xp_assert_close(R.apply(b[0, ...]), a[0, ...], atol=atol)
+
+    # Test exact rotations near 180 deg
+    Rs = Rotation.random(100, rng=0)
+    dRs = Rotation.from_rotvec(Rs.as_rotvec()*1e-4)  # scale down to small angle
+    a = [[ 1, 0, 0], [0, 1, 0]]
+    b = [[-1, 0, 0], [0, 1, 0]]
+    as_to_test = []
+    for dR in dRs:
+        as_to_test.append(np.array([dR.apply(a[0]), a[1]]))
+
+    # GPU computations may be less accurate. See e.g.
+    # https://github.com/jax-ml/jax/issues/18934 and
+    # https://docs.pytorch.org/docs/stable/generated/torch.set_float32_matmul_precision.html
+    # We currently have no unified way to check which device is being used. Cupy will
+    # always run on the GPU regardless of SCIPY_DEVICE, hence the explicit check for
+    # cupy. Note that the current implementation lets other frameworks, e.g. numpy, run
+    # on the CPU regardless of SCIPY_DEVICE but with increased GPU tolerances.
+    if xp_device_type(xp.asarray(0)) == "cuda":
+        atol = 1e-7
+
+    for a in as_to_test:
+        a, b = xp.asarray(a), xp.asarray(b)
+        R, _ = Rotation.align_vectors(a, b, weights=[xp.inf, 1])
+        R2, _ = Rotation.align_vectors(a, b, weights=[1e10, 1])
+        xp_assert_close(R.as_matrix(), R2.as_matrix(), atol=atol)
+
+
+@make_xp_test_case((Rotation, "align_vectors"), (Rotation, "apply"))
+def test_align_vectors_primary_only(xp):
+    dtype = xpx.default_dtype(xp)
+    atol = 1e-12 if dtype == xp.float64 else 1e-5
+    mats_a = Rotation.random(100, rng=0).as_matrix()
+    mats_b = Rotation.random(100, rng=1).as_matrix()
+
+    for mat_a, mat_b in zip(mats_a, mats_b):
+        # Get random 3-element unit vectors
+        a = xp.asarray(mat_a[0], dtype=dtype)
+        b = xp.asarray(mat_b[0], dtype=dtype)
+
+        # Compare to align_vectors with primary only
+        R, rssd = Rotation.align_vectors(a, b)
+        xp_assert_close(R.apply(b), a, atol=atol)
+        xp_assert_close(rssd, xp.asarray(0.0)[()], atol=atol)
+
+
+def test_align_vectors_array_like():
+    rng = np.random.default_rng(123)
+    c = Rotation.random(rng=rng)
+    b = rng.normal(size=(5, 3))
+    a = c.apply(b)
+
+    est_expected, rssd_expected = Rotation.align_vectors(a, b)
+    est, rssd = Rotation.align_vectors(a.tolist(), b.tolist())
+    xp_assert_close(est_expected.as_quat(), est.as_quat())
+    xp_assert_close(rssd, rssd_expected)
+
+
+@make_xp_test_case((Rotation, "apply"), (Rotation, "align_vectors"))
+def test_align_vectors_mixed_dtypes(xp):
+    dtype = xpx.default_dtype(xp)
+    rng = np.random.default_rng(123)
+    c = rotation_to_xp(Rotation.random(rng=rng), xp)
+    b = xp.asarray(rng.normal(size=(5, 3)), dtype=dtype)
+    a = xp.asarray(c.apply(b), dtype=xp.float32)  # Intentionally float32
+    # Check that the dtype of the output is the result type of a and b
+    est, _ = Rotation.align_vectors(a, b)
+    xp_assert_close(est.as_quat(), c.as_quat())
+
+
+@make_xp_test_case((Rotation, "__repr__"))
+def test_repr_single_rotation(xp):
+    q = xp.asarray([0, 0, 0, 1])
+    actual = repr(Rotation.from_quat(q))
+    if is_numpy(xp):
+        expected = """\
+Rotation.from_matrix(array([[1., 0., 0.],
+                            [0., 1., 0.],
+                            [0., 0., 1.]]))"""
+        assert actual == expected
+    else:
+        assert actual.startswith("Rotation.from_matrix(")
+
+
+def test_repr_rotation_sequence(xp):
+    q = xp.asarray([[0.0, 1, 0, 1], [0, 0, 1, 1]]) / math.sqrt(2)
+    actual = f"{Rotation.from_quat(q)!r}"
+    if is_numpy(xp):
+        expected = """\
+Rotation.from_matrix(array([[[ 0.,  0.,  1.],
+                             [ 0.,  1.,  0.],
+                             [-1.,  0.,  0.]],
+
+                            [[ 0., -1.,  0.],
+                             [ 1.,  0.,  0.],
+                             [ 0.,  0.,  1.]]]))"""
+        def stripped(s: str) -> str:
+            # don't fail due to leading whitespace differences
+            return "\n".join(map(str.lstrip, s.splitlines()))
+
+        assert stripped(actual) == stripped(expected)
+    else:
+        assert actual.startswith("Rotation.from_matrix(")
+
+
+@make_xp_test_case((Slerp, "__init__"), (Slerp, "__call__"))
+def test_slerp(xp):
+    rnd = np.random.RandomState(0)
+
+    key_rots = Rotation.from_quat(xp.asarray(rnd.uniform(size=(5, 4))))
+    key_quats = key_rots.as_quat()
+
+    key_times = [0, 1, 2, 3, 4]
+    interpolator = Slerp(key_times, key_rots)
+    assert isinstance(interpolator.times, type(xp.asarray(0)))
+
+    times = [0, 0.5, 0.25, 1, 1.5, 2, 2.75, 3, 3.25, 3.60, 4]
+    interp_rots = interpolator(times)
+    interp_quats = interp_rots.as_quat()
+
+    # Dot products are affected by sign of quaternions
+    mask = (interp_quats[:, -1] < 0)[:, None]
+    interp_quats = xp.where(mask, -interp_quats, interp_quats)
+    # Checking for quaternion equality, perform same operation
+    mask = (key_quats[:, -1] < 0)[:, None]
+    key_quats = xp.where(mask, -key_quats, key_quats)
+
+    # Equality at keyframes, including both endpoints
+    xp_assert_close(interp_quats[0, ...], key_quats[0, ...])
+    xp_assert_close(interp_quats[3, ...], key_quats[1, ...])
+    xp_assert_close(interp_quats[5, ...], key_quats[2, ...])
+    xp_assert_close(interp_quats[7, ...], key_quats[3, ...])
+    xp_assert_close(interp_quats[10, ...], key_quats[4, ...])
+
+    # Constant angular velocity between keyframes. Check by equating
+    # cos(theta) between quaternion pairs with equal time difference.
+    cos_theta1 = xp.sum(interp_quats[0, ...] * interp_quats[2, ...])
+    cos_theta2 = xp.sum(interp_quats[2, ...] * interp_quats[1, ...])
+    xp_assert_close(cos_theta1, cos_theta2)
+
+    cos_theta4 = xp.sum(interp_quats[3, ...] * interp_quats[4, ...])
+    cos_theta5 = xp.sum(interp_quats[4, ...] * interp_quats[5, ...])
+    xp_assert_close(cos_theta4, cos_theta5)
+
+    # theta1: 0 -> 0.25, theta3 : 0.5 -> 1
+    # Use double angle formula for double the time difference
+    cos_theta3 = xp.sum(interp_quats[1, ...] * interp_quats[3, ...])
+    xp_assert_close(cos_theta3, 2 * (cos_theta1**2) - 1)
+
+    # Miscellaneous checks
+    assert_equal(len(interp_rots), len(times))
+
+
+@make_xp_test_case((Slerp, "__init__"))
+def test_slerp_rot_is_rotation(xp):
+    with pytest.raises(TypeError, match="must be a `Rotation` instance"):
+        r = xp.asarray([[1,2,3,4],
+                        [0,0,0,1]])
+        t = xp.asarray([0, 1])
+        Slerp(t, r)
+
+
+SLERP_EXCEPTION_MESSAGE = "must be a sequence of at least 2 rotations"
+
+
+@make_xp_test_case((Slerp, "__init__"))
+def test_slerp_single_rot(xp):
+    r = Rotation.from_quat(xp.asarray([[1.0, 2, 3, 4]]))
+    with pytest.raises(ValueError, match=SLERP_EXCEPTION_MESSAGE):
+        Slerp([1], r)
+
+
+@make_xp_test_case((Slerp, "__init__"))
+def test_slerp_rot_len0(xp):
+    r = Rotation.random()
+    r = Rotation.from_quat(xp.asarray(r.as_quat()))
+    with pytest.raises(ValueError, match=SLERP_EXCEPTION_MESSAGE):
+        Slerp([], r)
+
+
+@make_xp_test_case((Slerp, "__init__"))
+def test_slerp_rot_len1(xp):
+    r = Rotation.random(1)
+    r = Rotation.from_quat(xp.asarray(r.as_quat()))
+    with pytest.raises(ValueError, match=SLERP_EXCEPTION_MESSAGE):
+        Slerp([1], r)
+
+
+@make_xp_test_case((Slerp, "__init__"))
+def test_slerp_tensor_rot(xp):
+    r = Rotation.from_quat(xp.ones((2, 2, 4)))
+    with pytest.raises(ValueError, match="Rotations with more than 1 leading"):
+        Slerp([1, 2], r)
+
+
+@make_xp_test_case((Slerp, "__init__"))
+def test_slerp_time_dim_mismatch(xp):
+    with pytest.raises(ValueError,
+                       match="times to be specified in a 1 dimensional array"):
+        rnd = np.random.RandomState(0)
+        r = Rotation.from_quat(xp.asarray(rnd.uniform(size=(2, 4))))
+        t = xp.asarray([[1],
+                        [2]])
+        Slerp(t, r)
+
+
+@make_xp_test_case((Slerp, "__init__"))
+def test_slerp_num_rotations_mismatch(xp):
+    with pytest.raises(ValueError, match="number of rotations to be equal to "
+                                         "number of timestamps"):
+        rnd = np.random.RandomState(0)
+        r = Rotation.from_quat(xp.asarray(rnd.uniform(size=(5, 4))))
+        t = xp.arange(7)
+        Slerp(t, r)
+
+
+@make_xp_test_case((Slerp, "__init__"))
+def test_slerp_equal_times(xp):
+    rnd = np.random.RandomState(0)
+    q = xp.asarray(rnd.uniform(size=(5, 4)))
+    r = Rotation.from_quat(q)
+    t = [0, 1, 2, 2, 4]
+    if is_lazy_array(q):
+        s = Slerp(t, r)
+        assert xp.all(xp.isnan(s.times))
+    else:
+        with pytest.raises(ValueError, match="strictly increasing order"):
+            Slerp(t, r)
+
+
+@make_xp_test_case((Slerp, "__init__"))
+def test_slerp_decreasing_times(xp):
+    rnd = np.random.RandomState(0)
+    q = xp.asarray(rnd.uniform(size=(5, 4)))
+    r = Rotation.from_quat(q)
+    t = [0, 1, 3, 2, 4]
+    if is_lazy_array(q):
+        s = Slerp(t, r)
+        assert xp.all(xp.isnan(s.times))
+    else:
+        with pytest.raises(ValueError, match="strictly increasing order"):
+            Slerp(t, r)
+
+
+@make_xp_test_case((Slerp, "__init__"), (Slerp, "__call__"))
+def test_slerp_call_time_dim_mismatch(xp):
+    rnd = np.random.RandomState(0)
+    r = Rotation.from_quat(xp.asarray(rnd.uniform(size=(5, 4))))
+    t = xp.arange(5)
+    s = Slerp(t, r)
+
+    with pytest.raises(ValueError,
+                       match="`times` must be at most 1-dimensional."):
+        interp_times = xp.asarray([[3.5],
+                                   [4.2]])
+        s(interp_times)
+
+
+@make_xp_test_case((Slerp, "__init__"), (Slerp, "__call__"))
+def test_slerp_call_time_out_of_range(xp):
+    rnd = np.random.RandomState(0)
+    r = Rotation.from_quat(xp.asarray(rnd.uniform(size=(5, 4))))
+    t = xp.arange(5) + 1
+    s = Slerp(t, r)
+
+    times_low = xp.asarray([0, 1, 2])
+    times_high = xp.asarray([1, 2, 6])
+    if is_lazy_array(times_low):
+        q = s(times_low).as_quat()
+        in_range = xp.logical_and(times_low >= xp.min(t), times_low <= xp.max(t))
+        assert xp.all(xp.isnan(q[~in_range, ...]))
+        assert xp.all(~xp.isnan(q[in_range, ...]))
+        q = s(times_high).as_quat()
+        in_range = xp.logical_and(times_high >= xp.min(t), times_high <= xp.max(t))
+        assert xp.all(xp.isnan(q[~in_range, ...]))
+        assert xp.all(~xp.isnan(q[in_range, ...]))
+    else:
+        with pytest.raises(ValueError, match="times must be within the range"):
+            s(times_low)
+        with pytest.raises(ValueError, match="times must be within the range"):
+            s(times_high)
+
+
+@make_xp_test_case(
+    (Slerp, "__init__"), (Slerp, "__call__"), (Rotation, "from_euler"),
+    (Rotation, "inv"), (Rotation, "magnitude")
+)
+def test_slerp_call_scalar_time(xp):
+    dtype = xpx.default_dtype(xp)
+    atol = 1e-16 if dtype == xp.float64 else 1e-7
+    r = Rotation.from_euler('X', xp.asarray([[0], [80]]), degrees=True)
+    s = Slerp([0, 1], r)
+
+    r_interpolated = s(0.25)
+    r_interpolated_expected = Rotation.from_euler('X', xp.asarray(20), degrees=True)
+
+    delta = r_interpolated * r_interpolated_expected.inv()
+
+    xp_assert_close(delta.magnitude(), xp.asarray(0.0)[()], atol=atol)
+
+
+@make_xp_test_case((Rotation, "__mul__"))
+def test_multiplication(xp):
+    r1 = Rotation.from_quat(xp.asarray([0, 0, 0, 1]))
+    r2 = Rotation.from_quat(xp.asarray([0, 0, 0, 1]))
+    r3 = r1 * r2
+    xp_assert_close(r3.as_quat(), xp.asarray([0.0, 0, 0, 1]))
+
+    # Check that multiplication with other types fails
+    with pytest.raises(TypeError, match="unsupported operand type"):
+        r1 * 2
+    # Check that __mul__ returns NotImplemented so that other types can implement
+    # __rmul__. See https://github.com/scipy/scipy/issues/21541
+    assert r1.__mul__(1) is NotImplemented
+
+
+@make_xp_test_case((Rotation, "__mul__"))
+def test_multiplication_nd(xp):
+    # multiple dimensions
+    rng = np.random.default_rng(0)
+    r1 = Rotation.from_quat(xp.asarray(rng.normal(size=(2, 3, 4))))
+    r2 = Rotation.from_quat(xp.asarray(rng.normal(size=(2, 3, 4))))
+    r3 = r1 * r2
+    assert r3.as_quat().shape == (2, 3, 4)
+
+    # same shape len, different dimensions
+    r1 = Rotation.from_quat(xp.asarray(rng.normal(size=(1, 3, 4))))
+    r2 = Rotation.from_quat(xp.asarray(rng.normal(size=(2, 1, 4))))
+    r3 = r1 * r2
+    assert r3.as_quat().shape == (2, 3, 4)
+
+    # different shape len, different dimensions
+    r1 = Rotation.from_quat(xp.asarray(rng.normal(size=(3, 1, 4, 4))))
+    r2 = Rotation.from_quat(xp.asarray(rng.normal(size=(2, 4, 4))))
+    r3 = r1 * r2
+    assert r3.as_quat().shape == (3, 2, 4, 4)
+
+    # transition between 2D and 3D with 2D rotation as first argument. This needs to
+    # choose the xp_backend even though r1's backend is cython
+    r1 = Rotation.from_quat(xp.asarray(rng.normal(size=(2, 4))))
+    r2 = Rotation.from_quat(xp.asarray(rng.normal(size=(2, 2, 4))))
+    r3 = r1 * r2
+    assert r3.as_quat().shape == (2, 2, 4)
+
+
+@make_xp_test_case((Rotation, "__mul__"))
+def test_multiplication_errors(xp):
+    rng = np.random.default_rng(0)
+    r1 = Rotation.from_quat(xp.asarray(rng.normal(size=(2, 4))))
+    r2 = Rotation.from_quat(xp.asarray(rng.normal(size=(1, 4, 4))))
+    with pytest.raises(ValueError, match="Cannot broadcast"):
+        r1 * r2
+
+
+@make_xp_test_case((Rotation, "__mul__"))
+def test_multiplication_stability(xp):
+    qs = rotation_to_xp(Rotation.random(50, rng=0), xp)
+    rs = rotation_to_xp(Rotation.random(1000, rng=1), xp)
+    expected = xp.ones(len(rs))
+    for r in qs:
+        rs = rs * r * rs
+        xp_assert_close(xp_vector_norm(rs.as_quat(), axis=1), expected)
+
+
+@make_xp_test_case(
+    (Rotation, "inv"), (Rotation, "__pow__"), (Rotation, "inv"),
+    (Rotation, "magnitude"), (Rotation, "from_rotvec"), (Rotation, "as_rotvec")
+)
+@pytest.mark.parametrize("ndim", list(range(1, 4)))
+def test_pow(xp, ndim: int):
+    dtype = xpx.default_dtype(xp)
+    atol = 1e-14 if dtype == xp.float64 else 1e-6
+    rng = np.random.default_rng(0)
+    batch_shape = (ndim,) * (ndim - 1)
+    quat = rng.normal(size=batch_shape + (4,))
+    p = Rotation.from_quat(xp.asarray(quat))
+    p_inv = p.inv()
+    # Test the short-cuts and other integers
+    for n in [-5, -2, -1, 0, 1, 2, 5]:
+        # Test accuracy
+        q = p ** n
+        q_identity = xp.asarray([0., 0, 0, 1])
+        # Regression test for gh-24436 
+        assert isinstance(q._quat, type(q_identity))
+        r = Rotation.from_quat(xp.tile(q_identity, batch_shape + (1,)))
+        for _ in range(abs(n)):
+            if n > 0:
+                r = r * p
+            else:
+                r = r * p_inv
+        ang = (q * r.inv()).magnitude()
+        assert xp.all(ang < atol)
+
+        # Test shape preservation
+        r = Rotation.from_quat(xp.tile(q_identity, batch_shape + (1,)))
+        assert (r**n).as_quat().shape == batch_shape + (4,)
+
+    # Large angle fractional
+    for n in [-1.5, -0.5, -0.0, 0.0, 0.5, 1.5]:
+        q = p ** n
+        r = Rotation.from_rotvec(n * p.as_rotvec())
+        xp_assert_close(q.as_quat(), r.as_quat(), atol=atol)
+
+    # Array exponent
+    n = [-5, -2, -1.5, -1, -0.5, -0.0, 0, 0.0, 0.5, 1.0, 1.5, 2]
+    for exponent in n:
+        r = p ** exponent
+        r_array = p ** xp.asarray([exponent])  # Test with 1D array
+        xp_assert_close(r.as_quat(), r_array.as_quat())
+        r_array = p ** xp.asarray(exponent)  # Test with scalar
+        xp_assert_close(r.as_quat(), r_array.as_quat())
+
+    # Small angle
+    rotvec = xp.zeros(batch_shape + (3,))
+    rotvec = xpx.at(rotvec)[..., 0].set(1e-12)
+    p = Rotation.from_rotvec(rotvec)
+    n = 3
+    q = p ** n
+    r = Rotation.from_rotvec(n * p.as_rotvec())
+    xp_assert_close(q.as_quat(), r.as_quat(), atol=atol)
+
+    # Array exponent
+    q = p ** xp.asarray([n])  # Test with 1D array
+    r = Rotation.from_rotvec(n * p.as_rotvec())
+    xp_assert_close(q.as_quat(), r.as_quat(), atol=atol)
+    q = p ** xp.asarray(n)  # Test with scalar
+    r = Rotation.from_rotvec(n * p.as_rotvec())
+    xp_assert_close(q.as_quat(), r.as_quat(), atol=atol)
+
+
+@make_xp_test_case((Rotation, "__pow__"))
+def test_pow_errors(xp):
+    p = rotation_to_xp(Rotation.random(rng=0), xp)
+    with pytest.raises(NotImplementedError, match='modulus not supported'):
+        pow(p, 1, 1)
+    with pytest.raises(ValueError, match="Array exponent must be a scalar"):
+        p ** xp.asarray([1, 2])
+    with pytest.raises(ValueError, match="Array exponent must be a scalar"):
+        p ** xp.asarray([[1], [2]])
+
+
+def test_rotation_within_numpy_array():
+    # TODO: Do we want to support this for all Array API frameworks?
+    single = Rotation.random(rng=0)
+    multiple = Rotation.random(2, rng=1)
+
+    array = np.array(single)
+    assert_equal(array.shape, ())
+
+    array = np.array(multiple)
+    assert_equal(array.shape, (2,))
+    xp_assert_close(array[0].as_matrix(), multiple[0].as_matrix())
+    xp_assert_close(array[1].as_matrix(), multiple[1].as_matrix())
+
+    array = np.array([single])
+    assert_equal(array.shape, (1,))
+    assert_equal(array[0], single)
+
+    array = np.array([multiple])
+    assert_equal(array.shape, (1, 2))
+    xp_assert_close(array[0, 0].as_matrix(), multiple[0].as_matrix())
+    xp_assert_close(array[0, 1].as_matrix(), multiple[1].as_matrix())
+
+    array = np.array([single, multiple], dtype=object)
+    assert_equal(array.shape, (2,))
+    assert_equal(array[0], single)
+    assert_equal(array[1], multiple)
+
+    array = np.array([multiple, multiple, multiple])
+    assert_equal(array.shape, (3, 2))
+
+
+@make_xp_test_case((Rotation, "as_matrix"))
+@pytest.mark.skip_xp_backends("array_api_strict",
+                              reason="array API doesn't support pickling")
+def test_pickling(xp):
+    r = Rotation.from_quat(xp.asarray([0, 0, math.sin(np.pi/4), math.cos(np.pi/4)]))
+    pkl = pickle.dumps(r)
+    unpickled = pickle.loads(pkl)
+    xp_assert_close(r.as_matrix(), unpickled.as_matrix(), atol=1e-15)
+
+
+@make_xp_test_case((Rotation, "as_matrix"))
+@pytest.mark.skip_xp_backends("array_api_strict",
+                              reason="array API doesn't support deepcopy")
+def test_deepcopy(xp):
+    r = Rotation.from_quat(xp.asarray([0, 0, math.sin(np.pi/4), math.cos(np.pi/4)]))
+    r1 = copy.deepcopy(r)
+    xp_assert_close(r.as_matrix(), r1.as_matrix(), atol=1e-15)
+
+
+def test_as_euler_contiguous():
+    # The Array API does not specify contiguous arrays, so we can only check for NumPy
+    r = Rotation.from_quat([0, 0, 0, 1])
+    e1 = r.as_euler('xyz')  # extrinsic euler rotation
+    e2 = r.as_euler('XYZ')  # intrinsic
+    assert e1.flags['C_CONTIGUOUS'] is True
+    assert e2.flags['C_CONTIGUOUS'] is True
+    assert all(i >= 0 for i in e1.strides)
+    assert all(i >= 0 for i in e2.strides)
+
+
+@make_xp_test_case((Rotation, "concatenate"))
+def test_concatenate(xp):
+    rotation = rotation_to_xp(Rotation.random(10, rng=0), xp)
+    sizes = [1, 2, 3, 1, 3]
+    starts = [0] + list(np.cumsum(sizes))
+    split = [rotation[i:i + n] for i, n in zip(starts, sizes)]
+    result = Rotation.concatenate(split)
+    xp_assert_equal(rotation.as_quat(), result.as_quat())
+
+    # Test Rotation input for multiple rotations
+    result = Rotation.concatenate(rotation)
+    xp_assert_equal(rotation.as_quat(), result.as_quat())
+
+    # Test that a copy is returned
+    assert rotation is not result
+
+    # Test Rotation input for single rotations
+    rng = np.random.default_rng(0)
+    quat = xp.asarray(rng.normal(size=(5, 2, 4)))
+    rotation = Rotation.from_quat(quat)
+    r1 = Rotation.from_quat(quat[:3, ...])
+    r2 = Rotation.from_quat(quat[3:, ...])
+    result = Rotation.concatenate([r1, r2])
+    xp_assert_equal(rotation.as_quat(), result.as_quat())
+
+
+@make_xp_test_case((Rotation, "concatenate"))
+def test_concatenate_wrong_type(xp):
+    with pytest.raises(TypeError, match='Rotation objects only'):
+        rot = Rotation(xp.asarray(Rotation.identity().as_quat()))
+        Rotation.concatenate([rot, 1, None])
+
+
+@make_xp_test_case((Rotation, "concatenate"))
+def test_concatenate_wrong_shape(xp):
+    r1 = Rotation.from_quat(xp.ones((5, 2, 4)))
+    r2 = Rotation.from_quat(xp.ones((1, 4)))
+    # Frameworks throw inconsistent error types on concat failures
+    with pytest.raises((ValueError, RuntimeError, TypeError)):
+        Rotation.concatenate([r1, r2])
+
+
+# Regression test for gh-16663
+@make_xp_test_case()
+def test_len_and_bool(xp):
+    rotation_multi_one = Rotation(xp.asarray([[0, 0, 0, 1]]))
+    rotation_multi = Rotation(xp.asarray([[0, 0, 0, 1], [0, 0, 0, 1]]))
+    rotation_single = Rotation(xp.asarray([0, 0, 0, 1]))
+
+    assert len(rotation_multi_one) == 1
+    assert len(rotation_multi) == 2
+    with pytest.raises(TypeError, match="Single rotation has no len()."):
+        len(rotation_single)
+
+    rotation_batched = Rotation.from_quat(xp.ones((3, 2, 4)))
+    assert len(rotation_batched) == 3
+
+    # Rotation should always be truthy. See gh-16663
+    assert rotation_multi_one
+    assert rotation_multi
+    assert rotation_single
+
+
+@make_xp_test_case((Rotation, "from_davenport"))
+def test_from_davenport_single_rotation(xp):
+    axis = xp.asarray([0, 0, 1])
+    quat = Rotation.from_davenport(axis, 'extrinsic', 90,
+                                   degrees=True).as_quat()
+    expected_quat = xp.asarray([0.0, 0, 1, 1]) / math.sqrt(2)
+    xp_assert_close(quat, expected_quat)
+
+
+@make_xp_test_case((Rotation, "from_rotvec"), (Rotation, "from_davenport"))
+def test_from_davenport_one_or_two_axes(xp):
+    ez = xp.asarray([0.0, 0, 1])
+    ey = xp.asarray([0.0, 1, 0])
+
+    # Single rotation, single axis, axes.shape == (3, )
+    rot = Rotation.from_rotvec(ez * xp.pi/4)
+    rot_dav = Rotation.from_davenport(ez, 'e', xp.pi/4)
+    xp_assert_close(rot.as_quat(canonical=True), rot_dav.as_quat(canonical=True))
+
+    # Single rotation, single axis, axes.shape == (1, 3), angles.shape == (1, )
+    # -> Still single rotation
+    axes = xp.reshape(ez, (1, 3))  # Torch can't create tensors from xp.asarray([ez])
+    rot = Rotation.from_rotvec(ez * xp.pi/4)
+    rot_dav = Rotation.from_davenport(axes, 'e', [xp.pi/4])
+    xp_assert_close(rot.as_quat(canonical=True), rot_dav.as_quat(canonical=True))
+
+    # Single rotation, two axes, axes.shape == (2, 3)
+    axes = xp.stack([ez, ey], axis=0)
+    rot = Rotation.from_rotvec(axes * xp.asarray([[xp.pi/4], [xp.pi/6]]))
+    rot = rot[0] * rot[1]
+    axes_dav = xp.stack([ey, ez], axis=0)
+    rot_dav = Rotation.from_davenport(axes_dav, 'e', [xp.pi/6, xp.pi/4])
+    xp_assert_close(rot.as_quat(canonical=True), rot_dav.as_quat(canonical=True))
+
+    # Two rotations, single axis, axes.shape == (3, )
+    axes = xp.stack([ez, ez], axis=0)
+    rot = Rotation.from_rotvec(axes * xp.asarray([[xp.pi/6], [xp.pi/4]]))
+    axes_dav = xp.reshape(ez, (1, 3))
+    rot_dav = Rotation.from_davenport(axes_dav, 'e', [[xp.pi/6], [xp.pi/4]])
+    xp_assert_close(rot.as_quat(canonical=True), rot_dav.as_quat(canonical=True))
+
+
+@make_xp_test_case((Rotation, "from_davenport"))
+@pytest.mark.parametrize("ndim", list(range(1, 4)))
+def test_from_davenport_shapes(xp, ndim: int):
+    # The shape rules for ND rotations are as follows:
+    # axes.shape[-2] must be angles.shape[-1]
+    # Resulting shape is np.broadcast_shapes(axes.shape[:-2], angles.shape[:-1]) + (4,)
+    rng = np.random.default_rng(0)
+    batch_shape = (ndim,) * (ndim - 1)
+    # Create random, orthogonal axes
+    r = Rotation.from_quat(xp.asarray(rng.normal(size=(4,))))
+    axes = r.as_matrix()
+    # axes = (3,)
+    angles = xp.asarray(rng.normal(size=batch_shape + (1,)))
+    rot = Rotation.from_davenport(axes[0, ...], 'e', angles)
+    assert rot.as_quat().shape == batch_shape + (4,)
+    # axes = (1, 3)
+    angles = xp.asarray(rng.normal(size=batch_shape + (1,)))
+    rot = Rotation.from_davenport(axes[0, None, ...], 'e', angles)
+    assert rot.as_quat().shape == batch_shape + (4,)
+    # axes = (2, 3)
+    angles = xp.asarray(rng.normal(size=batch_shape + (2,)))
+    rot = Rotation.from_davenport(axes[:2, ...], 'e', angles)
+    assert rot.as_quat().shape == batch_shape + (4,)
+
+    # axes = (...,3, 3)
+    r = Rotation.from_quat(xp.asarray(rng.normal(size=batch_shape + (4,))))
+    axes = r.as_matrix()
+    angles = xp.asarray(rng.normal(size=batch_shape + (3,)))
+    rot = Rotation.from_davenport(axes, 'e', angles)
+    assert rot.as_quat().shape == batch_shape + (4,)
+
+
+@make_xp_test_case((Rotation, "from_davenport"))
+def test_from_davenport_broadcast(xp):
+    rng = np.random.default_rng(0)
+    # Create random, orthogonal axes
+    r = Rotation.from_quat(xp.asarray(rng.normal(size=(4, 9, 1, 4))))
+    axes = r.as_matrix()
+    angles = xp.asarray(rng.normal(size=(1, 4, 3)))
+    rot = Rotation.from_davenport(axes, 'e', angles)
+    # (4, 9, 1, 3) + (3,) axes, (1, 4, 3) angles -> (4, 9, 4) + (4,) for quaternion
+    assert rot.as_quat().shape == (4, 9, 4, 4)
+
+
+@make_xp_test_case((Rotation, "from_davenport"))
+def test_from_davenport_invalid_input(xp):
+    ez = [0, 0, 1]
+    ey = [0, 1, 0]
+    ezy = [0, 1, 1]
+    # We can only raise in non-lazy frameworks.
+    axes = xp.asarray([ez, ezy])
+    if is_lazy_array(axes):
+        q = Rotation.from_davenport(axes, 'e', [0, 0]).as_quat()
+        assert xp.all(xp.isnan(q))
+    else:
+        with pytest.raises(ValueError, match="must be orthogonal"):
+            Rotation.from_davenport(axes, 'e', [0, 0])
+    axes = xp.asarray([ez, ey, ezy])
+    if is_lazy_array(axes):
+        q = Rotation.from_davenport(axes, 'e', [0, 0, 0]).as_quat()
+        assert xp.all(xp.isnan(q))
+    else:
+        with pytest.raises(ValueError, match="must be orthogonal"):
+            Rotation.from_davenport(axes, 'e', [0, 0, 0])
+    with pytest.raises(ValueError, match="order should be"):
+        Rotation.from_davenport(xp.asarray([ez]), 'xyz', [0])
+    with pytest.raises(ValueError, match="Expected `angles`"):
+        Rotation.from_davenport(xp.asarray([ez, ey, ez]), 'e', [0, 1, 2, 3])
+    with pytest.raises(ValueError, match="Expected `angles`"):  # Too many angles
+        Rotation.from_davenport(xp.asarray(ez), 'e', [0, 1])
+    with pytest.raises(ValueError, match="Expected `angles`"):  # Too few angles
+        Rotation.from_davenport(xp.asarray([ez, ey, ez]), 'e', [0, 1])
+
+
+def test_from_davenport_array_like():
+    rng = np.random.default_rng(123)
+    # Single rotation
+    e1 = np.array([1, 0, 0])
+    e2 = np.array([0, 1, 0])
+    e3 = np.array([0, 0, 1])
+    r_expected = Rotation.random(rng=rng)
+    angles = r_expected.as_davenport([e1, e2, e3], 'e')
+    r = Rotation.from_davenport([e1, e2, e3], 'e', angles.tolist())
+    assert r_expected.approx_equal(r, atol=1e-12)
+
+    # Multiple rotations
+    r_expected = Rotation.random(2, rng=rng)
+    angles = r_expected.as_davenport([e1, e2, e3], 'e')
+    r = Rotation.from_davenport([e1, e2, e3], 'e', angles.tolist())
+    assert np.all(r_expected.approx_equal(r, atol=1e-12))
+
+
+@make_xp_test_case((Rotation, "from_davenport"), (Rotation, "as_davenport"))
+def test_as_davenport(xp):
+    dtype = xpx.default_dtype(xp)
+    rnd = np.random.RandomState(0)
+    n = 100
+    angles = np.empty((n, 3))
+    angles[:, 0] = rnd.uniform(low=-np.pi, high=np.pi, size=(n,))
+    angles_middle = rnd.uniform(low=0, high=np.pi, size=(n,))
+    angles[:, 2] = rnd.uniform(low=-np.pi, high=np.pi, size=(n,))
+    lambdas = rnd.uniform(low=0, high=np.pi, size=(20,))
+
+    e1 = xp.asarray([1.0, 0, 0])
+    e2 = xp.asarray([0.0, 1, 0])
+
+    for lamb in lambdas:
+        e3 = xp.asarray(Rotation.from_rotvec(lamb*e2).apply(e1))
+        ax_lamb = xp.stack([e1, e2, e3], axis=0)
+        angles[:, 1] = angles_middle - lamb
+        for order in ['extrinsic', 'intrinsic']:
+            ax = ax_lamb if order == "intrinsic" else xp.flip(ax_lamb, axis=0)
+            rot = Rotation.from_davenport(ax, order, xp.asarray(angles, dtype=dtype))
+            angles_dav = rot.as_davenport(ax, order)
+            xp_assert_close(angles_dav, xp.asarray(angles, dtype=dtype))
+
+
+@make_xp_test_case((Rotation, "from_davenport"), (Rotation, "as_davenport"))
+def test_as_davenport_nd(xp):
+    rng = np.random.default_rng(0)
+    r = Rotation.from_quat(xp.asarray(rng.normal(size=(4, 9, 1, 4))))
+    axes = r.as_matrix()  # Get orthogonal axes
+    angles = xp.asarray(rng.uniform(low=-np.pi, high=np.pi, size=(4, 9, 1, 3)))
+    angles = xpx.at(angles)[..., 1].set(angles[..., 1] / 2)
+
+    for order in ['extrinsic', 'intrinsic']:
+        if order == "intrinsic":
+            axes = xp.flip(axes, axis=-2)
+        rot = Rotation.from_davenport(axes, order, angles)
+        angles_dav = rot.as_davenport(axes, order)
+        xp_assert_close(angles_dav, angles)
+
+
+@make_xp_test_case(
+    (Rotation, "from_davenport"), (Rotation, "as_davenport"), (Rotation, "as_matrix")
+)
+@pytest.mark.parametrize("suppress_warnings", (False, True))
+def test_as_davenport_degenerate(xp, suppress_warnings):
+    dtype = xpx.default_dtype(xp)
+    atol = 1e-12 if dtype == xp.float64 else 1e-6
+    # Since we cannot check for angle equality, we check for rotation matrix
+    # equality
+    rnd = np.random.RandomState(0)
+    n = 5
+    angles = np.empty((n, 3))
+
+    # symmetric sequences
+    angles[:, 0] = rnd.uniform(low=-np.pi, high=np.pi, size=(n,))
+    angles_middle = [rnd.choice([0, np.pi]) for i in range(n)]
+    angles[:, 2] = rnd.uniform(low=-np.pi, high=np.pi, size=(n,))
+    lambdas = rnd.uniform(low=0, high=np.pi, size=(5,))
+
+    e1 = xp.asarray([1.0, 0, 0])
+    e2 = xp.asarray([0.0, 1, 0])
+
+    for lamb in lambdas:
+        e3 = xp.asarray(Rotation.from_rotvec(lamb*e2).apply(e1))
+        ax_lamb = xp.stack([e1, e2, e3], axis=0)
+        angles[:, 1] = angles_middle - lamb
+        for order in ['extrinsic', 'intrinsic']:
+            ax = ax_lamb if order == 'intrinsic' else xp.flip(ax_lamb, axis=0)
+            rot = Rotation.from_davenport(ax, order, xp.asarray(angles, dtype=dtype))
+            with maybe_warn_gimbal_lock(not suppress_warnings, xp):
+                angles_dav = rot.as_davenport(
+                    ax,
+                    order,
+                    suppress_warnings=suppress_warnings
+                )
+            mat_expected = rot.as_matrix()
+            rot_estimated = Rotation.from_davenport(ax, order, angles_dav)
+            mat_estimated = rot_estimated.as_matrix()
+            xp_assert_close(mat_expected, mat_estimated, atol=atol)
+
+
+@make_xp_test_case((Rotation, "from_euler"), (Rotation, "from_davenport"))
+def test_compare_from_davenport_from_euler(xp):
+    dtype = xpx.default_dtype(xp)
+    rnd = np.random.RandomState(0)
+    n = 100
+    angles = np.empty((n, 3))
+
+    # symmetric sequences
+    rtol = 1e-12 if dtype == xp.float64 else 1e-5
+    angles[:, 0] = rnd.uniform(low=-np.pi, high=np.pi, size=(n,))
+    angles[:, 1] = rnd.uniform(low=0, high=np.pi, size=(n,))
+    angles[:, 2] = rnd.uniform(low=-np.pi, high=np.pi, size=(n,))
+    angles = xp.asarray(angles, dtype=dtype)
+    for order in ['extrinsic', 'intrinsic']:
+        for seq_tuple in permutations('xyz'):
+            seq = ''.join([seq_tuple[0], seq_tuple[1], seq_tuple[0]])
+            ax = xp.asarray([basis_vec(i) for i in seq], dtype=dtype)
+            if order == 'intrinsic':
+                seq = seq.upper()
+            eul = Rotation.from_euler(seq, angles)
+            dav = Rotation.from_davenport(ax, order, angles)
+            xp_assert_close(eul.as_quat(canonical=True), dav.as_quat(canonical=True),
+                            rtol=rtol)
+
+    # asymmetric sequences
+    angles = xpx.at(angles)[:, 1].subtract(np.pi / 2)
+    for order in ['extrinsic', 'intrinsic']:
+        for seq_tuple in permutations('xyz'):
+            seq = ''.join(seq_tuple)
+            ax = xp.asarray([basis_vec(i) for i in seq], dtype=dtype)
+            if order == 'intrinsic':
+                seq = seq.upper()
+            eul = Rotation.from_euler(seq, angles)
+            dav = Rotation.from_davenport(ax, order, angles)
+            xp_assert_close(eul.as_quat(), dav.as_quat(), rtol=rtol)
+
+
+@make_xp_test_case(
+    (Rotation, "from_euler"), (Rotation, "as_euler"), (Rotation, "as_davenport")
+)
+def test_compare_as_davenport_as_euler(xp):
+    rnd = np.random.RandomState(0)
+    n = 100
+    angles = np.empty((n, 3))
+
+    # symmetric sequences
+    angles[:, 0] = rnd.uniform(low=-np.pi, high=np.pi, size=(n,))
+    angles[:, 1] = rnd.uniform(low=0, high=np.pi, size=(n,))
+    angles[:, 2] = rnd.uniform(low=-np.pi, high=np.pi, size=(n,))
+    for order in ['extrinsic', 'intrinsic']:
+        for seq_tuple in permutations('xyz'):
+            seq = ''.join([seq_tuple[0], seq_tuple[1], seq_tuple[0]])
+            ax = [basis_vec(i) for i in seq]
+            if order == 'intrinsic':
+                seq = seq.upper()
+            rot = Rotation.from_euler(seq, xp.asarray(angles))
+            eul = rot.as_euler(seq)
+            dav = rot.as_davenport(xp.asarray(ax), order)
+            xp_assert_close(eul, dav, rtol=1e-12)
+
+    # asymmetric sequences
+    angles[:, 1] -= np.pi / 2
+    for order in ['extrinsic', 'intrinsic']:
+        for seq_tuple in permutations('xyz'):
+            seq = ''.join(seq_tuple)
+            ax = [basis_vec(i) for i in seq]
+            if order == 'intrinsic':
+                seq = seq.upper()
+            rot = Rotation.from_euler(seq, xp.asarray(angles))
+            eul = rot.as_euler(seq)
+            dav = rot.as_davenport(xp.asarray(ax), order)
+            xp_assert_close(eul, dav, rtol=1e-12)
+
+
+@make_xp_test_case(
+    (Rotation, "from_matrix"), (Rotation, "from_euler"), (Rotation, "from_rotvec"),
+    (Rotation, "from_davenport"), (Rotation, "from_mrp")
+)
+def test_zero_rotation_construction(xp):
+    r = Rotation.random(num=0)
+    assert len(r) == 0
+
+    r_ide = Rotation.identity(num=0)
+    assert len(r_ide) == 0
+
+    r_get = Rotation.random(num=3)[[]]
+    assert len(r_get) == 0
+
+    r_quat = Rotation.from_quat(xp.zeros((0, 4)))
+    assert len(r_quat) == 0
+
+    r_matrix = Rotation.from_matrix(xp.zeros((0, 3, 3)))
+    assert len(r_matrix) == 0
+
+    r_euler = Rotation.from_euler("xyz", xp.zeros((0, 3)))
+    assert len(r_euler) == 0
+
+    r_vec = Rotation.from_rotvec(xp.zeros((0, 3)))
+    assert len(r_vec) == 0
+
+    r_dav = Rotation.from_davenport(xp.eye(3), "extrinsic", xp.zeros((0, 3)))
+    assert len(r_dav) == 0
+
+    r_mrp = Rotation.from_mrp(xp.zeros((0, 3)))
+    assert len(r_mrp) == 0
+
+
+@make_xp_test_case(
+    (Rotation, "as_matrix"), (Rotation, "as_euler"), (Rotation, "as_rotvec"),
+    (Rotation, "as_mrp"), (Rotation, "as_davenport")
+)
+def test_zero_rotation_representation(xp):
+    r = Rotation.from_quat(xp.zeros((0, 4)))
+    assert r.as_quat().shape == (0, 4)
+    assert r.as_matrix().shape == (0, 3, 3)
+    assert r.as_euler("xyz").shape == (0, 3)
+    assert r.as_rotvec().shape == (0, 3)
+    assert r.as_mrp().shape == (0, 3)
+    assert r.as_davenport(xp.eye(3), "extrinsic").shape == (0, 3)
+
+
+@make_xp_test_case((Rotation, "apply"))
+def test_zero_rotation_array_rotation(xp):
+    r = Rotation.from_quat(xp.zeros((0, 4)))
+
+    v = xp.asarray([1, 2, 3])
+    v_rotated = r.apply(v)
+    assert v_rotated.shape == (0, 3)
+
+    v0 = xp.zeros((0, 3))
+    v0_rot = r.apply(v0)
+    assert v0_rot.shape == (0, 3)
+
+    v2 = xp.ones((2, 3))
+    with pytest.raises(
+        ValueError, match="Cannot broadcast"):
+        r.apply(v2)
+
+
+@make_xp_test_case((Rotation, "__mul__"))
+def test_zero_rotation_multiplication(xp):
+    r = Rotation.from_quat(xp.zeros((0, 4)))
+
+    r_single = Rotation.from_quat(xp.asarray([0.0, 0, 0, 1]))
+    r_mult_left = r * r_single
+    assert len(r_mult_left) == 0
+
+    r_mult_right = r_single * r
+    assert len(r_mult_right) == 0
+
+    r0 = Rotation.from_quat(xp.zeros((0, 4)))
+    r_mult = r * r0
+    assert len(r_mult) == 0
+
+    r2 = rotation_to_xp(Rotation.random(2), xp)
+    with pytest.raises(ValueError, match="Cannot broadcast"):
+        r0 * r2
+
+    with pytest.raises(ValueError, match="Cannot broadcast"):
+        r2 * r0
+
+
+@make_xp_test_case((Rotation, "concatenate"))
+def test_zero_rotation_concatentation(xp):
+    r = Rotation.from_quat(xp.zeros((0, 4)))
+
+    r0 = Rotation.concatenate([r, r])
+    assert len(r0) == 0
+
+    r1 = Rotation.from_quat(xp.asarray([0.0, 0, 0, 1]))
+    r1 = r.concatenate([r1, r])
+    assert len(r1) == 1
+
+    r3 = rotation_to_xp(Rotation.random(3), xp)
+    r3 = r.concatenate([r3, r])
+    assert len(r3) == 3
+
+    r4 = rotation_to_xp(Rotation.random(4), xp)
+    r4 = r.concatenate([r, r4])
+    r4 = r.concatenate([r, r4])
+    assert len(r4) == 4
+
+
+@make_xp_test_case((Rotation, "__pow__"))
+def test_zero_rotation_power(xp):
+    r = Rotation.from_quat(xp.zeros((0, 4)))
+    for pp in [-1.5, -1, 0, 1, 1.5]:
+        pow0 = r**pp
+        assert len(pow0) == 0
+
+
+@make_xp_test_case((Rotation, "inv"))
+def test_zero_rotation_inverse(xp):
+    r = Rotation.from_quat(xp.zeros((0, 4)))
+    r_inv = r.inv()
+    assert len(r_inv) == 0
+
+
+@make_xp_test_case((Rotation, "magnitude"))
+def test_zero_rotation_magnitude(xp):
+    r = Rotation.from_quat(xp.zeros((0, 4)))
+    magnitude = r.magnitude()
+    assert magnitude.shape == (0,)
+
+
+@make_xp_test_case((Rotation, "mean"))
+def test_zero_rotation_mean(xp):
+    r = Rotation.from_quat(xp.zeros((0, 4)))
+    with pytest.raises(ValueError, match="Mean of an empty rotation set is undefined."):
+        r.mean()
+
+
+@make_xp_test_case((Rotation, "approx_equal"))
+def test_zero_rotation_approx_equal(xp):
+    r = Rotation.from_quat(xp.zeros((0, 4)))
+    r0 = Rotation.from_quat(xp.zeros((0, 4)))
+    assert r.approx_equal(r0).shape == (0,)
+    r1 = Rotation.from_quat(xp.asarray([0.0, 0, 0, 1]))
+    assert r.approx_equal(r1).shape == (0,)
+    r2 = rotation_to_xp(Rotation.random(), xp)
+    assert r2.approx_equal(r).shape == (0,)
+
+    approx_msg = "Expected broadcastable shapes in both rotations"
+    r3 = rotation_to_xp(Rotation.random(2), xp)
+    with pytest.raises(ValueError, match=approx_msg):
+        r.approx_equal(r3)
+
+    with pytest.raises(ValueError, match=approx_msg):
+        r3.approx_equal(r)
+
+
+@pytest.mark.skip_xp_backends("jax.numpy",
+                              reason="JAX out-of-bounds indexing deviates from numpy")
+def test_zero_rotation_get_set(xp):
+    r = Rotation.from_quat(xp.zeros((0, 4)))
+
+    r_get = r[xp.asarray([], dtype=xp.bool)]
+    assert len(r_get) == 0
+
+    r_slice = r[:0]
+    assert len(r_slice) == 0
+
+    with pytest.raises(IndexError):
+        r[xp.asarray([0])]
+
+    with pytest.raises(IndexError):
+        r[xp.asarray([True])]
+
+    with pytest.raises(IndexError):
+        r[0] = Rotation.from_quat(xp.asarray([0, 0, 0, 1]))
+
+
+@make_xp_test_case((Rotation, "__getitem__"))
+def test_boolean_indexes(xp):
+    r = rotation_to_xp(Rotation.random(3), xp)
+
+    r0 = r[xp.asarray([False, False, False])]
+    assert len(r0) == 0
+
+    r1 = r[xp.asarray([False, True, False])]
+    assert len(r1) == 1
+
+    r3 = r[xp.asarray([True, True, True])]
+    assert len(r3) == 3
+
+    # Multiple dimensions
+    r = Rotation.from_quat(xp.ones((3, 2, 4)))
+    r4 = r[xp.asarray([True, False, False])]
+    assert len(r4) == 1
+    assert r4.as_quat().shape == (1, 2, 4)
+
+    with pytest.raises(IndexError):
+        r[xp.asarray([True, True])]
+
+
+@make_xp_test_case((Rotation, "__iter__"))
+def test_rotation_iter(xp):
+    r = rotation_to_xp(Rotation.random(3), xp)
+    for i, r_i in enumerate(r):
+        assert isinstance(r_i, Rotation)
+        xp_assert_equal(r_i.as_quat(), r[i].as_quat())
+        if i > len(r):
+            raise RuntimeError("Iteration exceeded length of rotations")
+
+
+@pytest.mark.parametrize("ndim", list(range(1, 5)))
+def test_rotation_shape(xp, ndim: int):
+    shape = tuple(range(2, 2 + ndim)[:ndim - 1])
+    quat = xp.ones(shape + (4,))
+    r = Rotation.from_quat(quat)
+    assert r.shape == shape, f"Got {r.shape}, expected {shape}"
+
+
+def test_non_writeable():
+    q = np.array([0, 0, 0, 1.0])
+    q.flags.writeable = False
+    Rotation.from_quat(q)  # Regression test against gh-24354, should not raise
+
+
+def test_gh_24751():
+    points = np.array([[0.0, 0.0, 0.0]])
+    points.flags.writeable = False
+    rot = Rotation.from_euler("z", 0.0)
+    rot.apply(points)
+
+
+def test_rotvec_non_writeable():
+    rotvec = np.array([0, 0, 1]) * np.pi / 2
+    rotvec.flags.writeable = False
+    Rotation.from_rotvec(rotvec)
diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/transform/tests/test_rotation_groups.py b/venv/lib/python3.12/site-packages/scipy/spatial/transform/tests/test_rotation_groups.py
new file mode 100644
index 0000000000000000000000000000000000000000..3f8a53b7abfede9b241fed2190e0f1244d76a9ee
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/transform/tests/test_rotation_groups.py
@@ -0,0 +1,169 @@
+import pytest
+
+import numpy as np
+from numpy.testing import assert_array_almost_equal
+from scipy.spatial.transform import Rotation
+from scipy.optimize import linear_sum_assignment
+from scipy.spatial.distance import cdist
+from scipy.constants import golden as phi
+from scipy.spatial import cKDTree
+
+
+TOL = 1E-12
+NS = list(range(1, 13))
+NAMES = ["I", "O", "T"] + [f"C{n}" for n in NS] + [f"D{n}" for n in NS]
+SIZES = [60, 24, 12] + list(NS) + [2 * n for n in NS]
+
+
+def _calculate_rmsd(P, Q):
+    """Calculates the root-mean-square distance between the points of P and Q.
+    The distance is taken as the minimum over all possible matchings. It is
+    zero if P and Q are identical and non-zero if not.
+    """
+    distance_matrix = cdist(P, Q, metric='sqeuclidean')
+    matching = linear_sum_assignment(distance_matrix)
+    return np.sqrt(distance_matrix[matching].sum())
+
+
+def _generate_pyramid(n, axis):
+    thetas = np.linspace(0, 2 * np.pi, n + 1)[:-1]
+    P = np.vstack([np.zeros(n), np.cos(thetas), np.sin(thetas)]).T
+    P = np.concatenate((P, [[1, 0, 0]]))
+    return np.roll(P, axis, axis=1)
+
+
+def _generate_prism(n, axis):
+    thetas = np.linspace(0, 2 * np.pi, n + 1)[:-1]
+    bottom = np.vstack([-np.ones(n), np.cos(thetas), np.sin(thetas)]).T
+    top = np.vstack([+np.ones(n), np.cos(thetas), np.sin(thetas)]).T
+    P = np.concatenate((bottom, top))
+    return np.roll(P, axis, axis=1)
+
+
+def _generate_icosahedron():
+    x = np.array([[0, -1, -phi],
+                  [0, -1, +phi],
+                  [0, +1, -phi],
+                  [0, +1, +phi]])
+    return np.concatenate([np.roll(x, i, axis=1) for i in range(3)])
+
+
+def _generate_octahedron():
+    return np.array([[-1, 0, 0], [+1, 0, 0], [0, -1, 0],
+                     [0, +1, 0], [0, 0, -1], [0, 0, +1]])
+
+
+def _generate_tetrahedron():
+    return np.array([[1, 1, 1], [1, -1, -1], [-1, 1, -1], [-1, -1, 1]])
+
+
+@pytest.mark.parametrize("name", [-1, None, True, np.array(['C3'])])
+def test_group_type(name):
+    with pytest.raises(ValueError,
+                       match="must be a string"):
+        Rotation.create_group(name)
+
+
+@pytest.mark.parametrize("name", ["Q", " ", "CA", "C ", "DA", "D ", "I2", ""])
+def test_group_name(name):
+    with pytest.raises(ValueError,
+                       match="must be one of 'I', 'O', 'T', 'Dn', 'Cn'"):
+        Rotation.create_group(name)
+
+
+@pytest.mark.parametrize("name", ["C0", "D0"])
+def test_group_order_positive(name):
+    with pytest.raises(ValueError,
+                       match="Group order must be positive"):
+        Rotation.create_group(name)
+
+
+@pytest.mark.parametrize("axis", ['A', 'b', 0, 1, 2, 4, False, None])
+def test_axis_valid(axis):
+    with pytest.raises(ValueError,
+                       match="`axis` must be one of"):
+        Rotation.create_group("C1", axis)
+
+
+def test_icosahedral():
+    """The icosahedral group fixes the rotations of an icosahedron. Here we
+    test that the icosahedron is invariant after application of the elements
+    of the rotation group."""
+    P = _generate_icosahedron()
+    for g in Rotation.create_group("I"):
+        g = Rotation.from_quat(g.as_quat())
+        assert _calculate_rmsd(P, g.apply(P)) < TOL
+
+
+def test_octahedral():
+    """Test that the octahedral group correctly fixes the rotations of an
+    octahedron."""
+    P = _generate_octahedron()
+    for g in Rotation.create_group("O"):
+        assert _calculate_rmsd(P, g.apply(P)) < TOL
+
+
+def test_tetrahedral():
+    """Test that the tetrahedral group correctly fixes the rotations of a
+    tetrahedron."""
+    P = _generate_tetrahedron()
+    for g in Rotation.create_group("T"):
+        assert _calculate_rmsd(P, g.apply(P)) < TOL
+
+
+@pytest.mark.parametrize("n", NS)
+@pytest.mark.parametrize("axis", 'XYZ')
+def test_dicyclic(n, axis):
+    """Test that the dicyclic group correctly fixes the rotations of a
+    prism."""
+    P = _generate_prism(n, axis='XYZ'.index(axis))
+    for g in Rotation.create_group(f"D{n}", axis=axis):
+        assert _calculate_rmsd(P, g.apply(P)) < TOL
+
+
+@pytest.mark.parametrize("n", NS)
+@pytest.mark.parametrize("axis", 'XYZ')
+def test_cyclic(n, axis):
+    """Test that the cyclic group correctly fixes the rotations of a
+    pyramid."""
+    P = _generate_pyramid(n, axis='XYZ'.index(axis))
+    for g in Rotation.create_group(f"C{n}", axis=axis):
+        assert _calculate_rmsd(P, g.apply(P)) < TOL
+
+
+@pytest.mark.parametrize("name, size", list(zip(NAMES, SIZES)))
+def test_group_sizes(name, size):
+    assert len(Rotation.create_group(name)) == size
+
+
+@pytest.mark.parametrize("name, size", list(zip(NAMES, SIZES)))
+def test_group_no_duplicates(name, size):
+    g = Rotation.create_group(name)
+    kdtree = cKDTree(g.as_quat())
+    assert len(kdtree.query_pairs(1E-3)) == 0
+
+
+@pytest.mark.parametrize("name, size", list(zip(NAMES, SIZES)))
+def test_group_symmetry(name, size):
+    g = Rotation.create_group(name)
+    q = np.concatenate((-g.as_quat(), g.as_quat()))
+    distance = np.sort(cdist(q, q))
+    deltas = np.max(distance, axis=0) - np.min(distance, axis=0)
+    assert (deltas < TOL).all()
+
+
+@pytest.mark.parametrize("name", NAMES)
+def test_reduction(name):
+    """Test that the elements of the rotation group are correctly
+    mapped onto the identity rotation."""
+    g = Rotation.create_group(name)
+    f = g.reduce(g)
+    assert_array_almost_equal(f.magnitude(), np.zeros(len(g)))
+
+
+@pytest.mark.parametrize("name", NAMES)
+def test_single_reduction(name):
+    g = Rotation.create_group(name)
+    f = g[-1].reduce(g)
+    assert_array_almost_equal(f.magnitude(), 0)
+    assert f.as_quat().shape == (4,)
diff --git a/venv/lib/python3.12/site-packages/scipy/spatial/transform/tests/test_rotation_spline.py b/venv/lib/python3.12/site-packages/scipy/spatial/transform/tests/test_rotation_spline.py
new file mode 100644
index 0000000000000000000000000000000000000000..d268659e06416506243593bc8a4c2e8febf3f98e
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/spatial/transform/tests/test_rotation_spline.py
@@ -0,0 +1,188 @@
+from itertools import product
+import numpy as np
+from numpy.testing import assert_allclose
+import pytest
+from scipy.spatial.transform import Rotation, RotationSpline
+from scipy.spatial.transform._rotation_spline import (
+    _angular_rate_to_rotvec_dot_matrix,
+    _rotvec_dot_to_angular_rate_matrix,
+    _matrix_vector_product_of_stacks,
+    _angular_acceleration_nonlinear_term,
+    _create_block_3_diagonal_matrix)
+
+
+pytestmark = pytest.mark.skip_xp_backends(np_only=True)
+
+
+def test_angular_rate_to_rotvec_conversions():
+    np.random.seed(0)
+    rv = np.random.randn(4, 3)
+    A = _angular_rate_to_rotvec_dot_matrix(rv)
+    A_inv = _rotvec_dot_to_angular_rate_matrix(rv)
+
+    # When the rotation vector is aligned with the angular rate, then
+    # the rotation vector rate and angular rate are the same.
+    assert_allclose(_matrix_vector_product_of_stacks(A, rv), rv)
+    assert_allclose(_matrix_vector_product_of_stacks(A_inv, rv), rv)
+
+    # A and A_inv must be reciprocal to each other.
+    I_stack = np.empty((4, 3, 3))
+    I_stack[:] = np.eye(3)
+    assert_allclose(np.matmul(A, A_inv), I_stack, atol=1e-15)
+
+
+def test_angular_rate_nonlinear_term():
+    # The only simple test is to check that the term is zero when
+    # the rotation vector
+    np.random.seed(0)
+    rv = np.random.rand(4, 3)
+    assert_allclose(_angular_acceleration_nonlinear_term(rv, rv), 0,
+                    atol=1e-19)
+
+
+def test_create_block_3_diagonal_matrix():
+    np.random.seed(0)
+    A = np.empty((4, 3, 3))
+    A[:] = np.arange(1, 5)[:, None, None]
+
+    B = np.empty((4, 3, 3))
+    B[:] = -np.arange(1, 5)[:, None, None]
+    d = 10 * np.arange(10, 15)
+
+    banded = _create_block_3_diagonal_matrix(A, B, d)
+
+    # Convert the banded matrix to the full matrix.
+    k, l = list(zip(*product(np.arange(banded.shape[0]),
+                             np.arange(banded.shape[1]))))
+    k = np.asarray(k)
+    l = np.asarray(l)
+
+    i = k - 5 + l
+    j = l
+    values = banded.ravel()
+    mask = (i >= 0) & (i < 15)
+    i = i[mask]
+    j = j[mask]
+    values = values[mask]
+    full = np.zeros((15, 15))
+    full[i, j] = values
+
+    zero = np.zeros((3, 3))
+    eye = np.eye(3)
+
+    # Create the reference full matrix in the most straightforward manner.
+    ref = np.block([
+        [d[0] * eye, B[0], zero, zero, zero],
+        [A[0], d[1] * eye, B[1], zero, zero],
+        [zero, A[1], d[2] * eye, B[2], zero],
+        [zero, zero, A[2], d[3] * eye, B[3]],
+        [zero, zero, zero, A[3], d[4] * eye],
+    ])
+
+    assert_allclose(full, ref, atol=1e-19)
+
+
+def test_spline_2_rotations():
+    times = [0, 10]
+    rotations = Rotation.from_euler('xyz', [[0, 0, 0], [10, -20, 30]],
+                                    degrees=True)
+    spline = RotationSpline(times, rotations)
+
+    rv = (rotations[0].inv() * rotations[1]).as_rotvec()
+    rate = rv / (times[1] - times[0])
+    times_check = np.array([-1, 5, 12])
+    dt = times_check - times[0]
+    rv_ref = rate * dt[:, None]
+
+    assert_allclose(spline(times_check).as_rotvec(), rv_ref)
+    assert_allclose(spline(times_check, 1), np.resize(rate, (3, 3)))
+    assert_allclose(spline(times_check, 2), 0, atol=1e-16)
+
+
+def test_constant_attitude():
+    times = np.arange(10)
+    rotations = Rotation.from_rotvec(np.ones((10, 3)))
+    spline = RotationSpline(times, rotations)
+
+    times_check = np.linspace(-1, 11)
+    assert_allclose(spline(times_check).as_rotvec(), 1, rtol=1e-15)
+    assert_allclose(spline(times_check, 1), 0, atol=1e-17)
+    assert_allclose(spline(times_check, 2), 0, atol=1e-17)
+
+    assert_allclose(spline(5.5).as_rotvec(), 1, rtol=1e-15)
+    assert_allclose(spline(5.5, 1), 0, atol=1e-17)
+    assert_allclose(spline(5.5, 2), 0, atol=1e-17)
+
+
+def test_spline_properties():
+    times = np.array([0, 5, 15, 27])
+    angles = [[-5, 10, 27], [3, 5, 38], [-12, 10, 25], [-15, 20, 11]]
+
+    rotations = Rotation.from_euler('xyz', angles, degrees=True)
+    spline = RotationSpline(times, rotations)
+
+    assert_allclose(spline(times).as_euler('xyz', degrees=True), angles)
+    assert_allclose(spline(0).as_euler('xyz', degrees=True), angles[0])
+
+    h = 1e-8
+    rv0 = spline(times).as_rotvec()
+    rvm = spline(times - h).as_rotvec()
+    rvp = spline(times + h).as_rotvec()
+    # rtol bumped from 1e-15 to 1.5e-15 in gh18414 for linux 32 bit
+    assert_allclose(rv0, 0.5 * (rvp + rvm), rtol=1.5e-15)
+
+    r0 = spline(times, 1)
+    rm = spline(times - h, 1)
+    rp = spline(times + h, 1)
+    assert_allclose(r0, 0.5 * (rm + rp), rtol=1e-14)
+
+    a0 = spline(times, 2)
+    am = spline(times - h, 2)
+    ap = spline(times + h, 2)
+    assert_allclose(a0, am, rtol=1e-7)
+    assert_allclose(a0, ap, rtol=1e-7)
+
+
+def test_error_handling():
+    with pytest.raises(ValueError):
+        RotationSpline([1.0], Rotation.random())
+
+    r = Rotation.random(10)
+    t = np.arange(10).reshape(5, 2)
+    with pytest.raises(ValueError):
+        RotationSpline(t, r)
+
+    t = np.arange(9)
+    with pytest.raises(ValueError):
+        RotationSpline(t, r)
+
+    t = np.arange(10)
+    t[5] = 0
+    with pytest.raises(ValueError):
+        RotationSpline(t, r)
+
+    t = np.arange(10)
+
+    s = RotationSpline(t, r)
+    with pytest.raises(ValueError):
+        s(10, -1)
+
+    with pytest.raises(ValueError):
+        s(np.arange(10).reshape(5, 2))
+
+    r = Rotation.from_quat(np.array([[[0.0, 0, 0, 1], [1, 0, 0 ,0]]]))
+    t = np.arange(2)
+    with pytest.raises(ValueError):
+        RotationSpline(t, r)  # More than 2 dimensions
+
+
+@pytest.mark.skip_xp_backends("numpy")
+def test_xp_errors(xp):
+    times = xp.asarray([0, 10])
+    r = Rotation.random(2)
+    r = Rotation.from_quat(xp.asarray(r.as_quat()))
+    s = RotationSpline(times, r)
+    t = xp.asarray([0.5, 1.5])
+    # RotationSpline does not have native Array API support, so we check that it
+    # converts any array to NumPy and outputs NumPy arrays.
+    assert isinstance(s(t).as_quat(), np.ndarray)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/__init__.pxd b/venv/lib/python3.12/site-packages/scipy/special/__init__.pxd
new file mode 100644
index 0000000000000000000000000000000000000000..1daa9fb379572aac4bc9b6d74330a18c5c52bf79
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/__init__.pxd
@@ -0,0 +1 @@
+from scipy.special cimport cython_special
diff --git a/venv/lib/python3.12/site-packages/scipy/special/__init__.py b/venv/lib/python3.12/site-packages/scipy/special/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..9bcbfd132896a63ccf689c54ab9c36fae7db695a
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/__init__.py
@@ -0,0 +1,842 @@
+"""
+========================================
+Special functions (:mod:`scipy.special`)
+========================================
+
+.. currentmodule:: scipy.special
+
+.. toctree::
+   :hidden:
+
+   special.cython_special
+
+Almost all of the functions below accept NumPy arrays as input
+arguments as well as single numbers. This means they follow
+broadcasting and automatic array-looping rules. Technically,
+they are `NumPy universal functions
+<https://numpy.org/doc/stable/user/basics.ufuncs.html#ufuncs-basics>`_.
+Functions which do not accept NumPy arrays are marked by a warning
+in the section description.
+
+.. seealso::
+
+   `scipy.special.cython_special` -- Typed Cython versions of special functions
+
+
+Error handling
+==============
+
+Errors are handled by returning NaNs or other appropriate values.
+Some of the special function routines can emit warnings or raise
+exceptions when an error occurs. By default this is disabled, except
+for memory allocation errors, which result in an exception being raised.
+To query and control the current error handling state the following
+functions are provided.
+
+.. autosummary::
+   :toctree: generated/
+
+   geterr                 -- Get the current way of handling special-function errors.
+   seterr                 -- Set how special-function errors are handled.
+   errstate               -- Context manager for special-function error handling.
+   SpecialFunctionWarning -- Warning that can be emitted by special functions.
+   SpecialFunctionError   -- Exception that can be raised by special functions.
+
+Available functions
+===================
+
+Airy functions
+--------------
+
+.. autosummary::
+   :toctree: generated/
+
+   airy     -- Airy functions and their derivatives.
+   airye    -- Exponentially scaled Airy functions and their derivatives.
+   ai_zeros -- Compute `nt` zeros and values of the Airy function Ai and its derivative.
+   bi_zeros -- Compute `nt` zeros and values of the Airy function Bi and its derivative.
+   itairy   -- Integrals of Airy functions
+
+
+Elliptic functions and integrals
+--------------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   ellipj    -- Jacobian elliptic functions.
+   ellipk    -- Complete elliptic integral of the first kind.
+   ellipkm1  -- Complete elliptic integral of the first kind around `m` = 1.
+   ellipkinc -- Incomplete elliptic integral of the first kind.
+   ellipe    -- Complete elliptic integral of the second kind.
+   ellipeinc -- Incomplete elliptic integral of the second kind.
+   elliprc   -- Degenerate symmetric integral RC.
+   elliprd   -- Symmetric elliptic integral of the second kind.
+   elliprf   -- Completely-symmetric elliptic integral of the first kind.
+   elliprg   -- Completely-symmetric elliptic integral of the second kind.
+   elliprj   -- Symmetric elliptic integral of the third kind.
+
+Bessel functions
+----------------
+
+.. autosummary::
+   :toctree: generated/
+
+   jv                -- Bessel function of the first kind of real order and \
+                        complex argument.
+   jve               -- Exponentially scaled Bessel function of order `v`.
+   yn                -- Bessel function of the second kind of integer order and \
+                        real argument.
+   yv                -- Bessel function of the second kind of real order and \
+                        complex argument.
+   yve               -- Exponentially scaled Bessel function of the second kind \
+                        of real order.
+   iv                -- Modified Bessel function of the first kind of real order.
+   ive               -- Exponentially scaled modified Bessel function of the \
+                        first kind.
+   kn                -- Modified Bessel function of the second kind of integer \
+                        order `n`
+   kv                -- Modified Bessel function of the second kind of real order \
+                        `v`
+   kve               -- Exponentially scaled modified Bessel function of the \
+                        second kind.
+   hankel1           -- Hankel function of the first kind.
+   hankel1e          -- Exponentially scaled Hankel function of the first kind.
+   hankel2           -- Hankel function of the second kind.
+   hankel2e          -- Exponentially scaled Hankel function of the second kind.
+   wright_bessel     -- Wright's generalized Bessel function.
+   log_wright_bessel -- Logarithm of Wright's generalized Bessel function.
+
+The following function does not accept NumPy arrays (it is not a
+universal function):
+
+.. autosummary::
+   :toctree: generated/
+
+   lmbda -- Jahnke-Emden Lambda function, Lambdav(x).
+
+Zeros of Bessel functions
+^^^^^^^^^^^^^^^^^^^^^^^^^
+
+The following functions do not accept NumPy arrays (they are not
+universal functions):
+
+.. autosummary::
+   :toctree: generated/
+
+   jnjnp_zeros -- Compute zeros of integer-order Bessel functions Jn and Jn'.
+   jnyn_zeros  -- Compute nt zeros of Bessel functions Jn(x), Jn'(x), Yn(x), and Yn'(x).
+   jn_zeros    -- Compute zeros of integer-order Bessel function Jn(x).
+   jnp_zeros   -- Compute zeros of integer-order Bessel function derivative Jn'(x).
+   yn_zeros    -- Compute zeros of integer-order Bessel function Yn(x).
+   ynp_zeros   -- Compute zeros of integer-order Bessel function derivative Yn'(x).
+   y0_zeros    -- Compute nt zeros of Bessel function Y0(z), and derivative at each zero.
+   y1_zeros    -- Compute nt zeros of Bessel function Y1(z), and derivative at each zero.
+   y1p_zeros   -- Compute nt zeros of Bessel derivative Y1'(z), and value at each zero.
+
+Faster versions of common Bessel functions
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+.. autosummary::
+   :toctree: generated/
+
+   j0  -- Bessel function of the first kind of order 0.
+   j1  -- Bessel function of the first kind of order 1.
+   y0  -- Bessel function of the second kind of order 0.
+   y1  -- Bessel function of the second kind of order 1.
+   i0  -- Modified Bessel function of order 0.
+   i0e -- Exponentially scaled modified Bessel function of order 0.
+   i1  -- Modified Bessel function of order 1.
+   i1e -- Exponentially scaled modified Bessel function of order 1.
+   k0  -- Modified Bessel function of the second kind of order 0, :math:`K_0`.
+   k0e -- Exponentially scaled modified Bessel function K of order 0
+   k1  -- Modified Bessel function of the second kind of order 1, :math:`K_1(x)`.
+   k1e -- Exponentially scaled modified Bessel function K of order 1.
+
+Integrals of Bessel functions
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+.. autosummary::
+   :toctree: generated/
+
+   itj0y0     -- Integrals of Bessel functions of order 0.
+   it2j0y0    -- Integrals related to Bessel functions of order 0.
+   iti0k0     -- Integrals of modified Bessel functions of order 0.
+   it2i0k0    -- Integrals related to modified Bessel functions of order 0.
+   besselpoly -- Weighted integral of a Bessel function.
+
+Derivatives of Bessel functions
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+.. autosummary::
+   :toctree: generated/
+
+   jvp  -- Compute nth derivative of Bessel function Jv(z) with respect to `z`.
+   yvp  -- Compute nth derivative of Bessel function Yv(z) with respect to `z`.
+   ivp  -- Compute nth derivative of modified Bessel function Iv(z) with respect to `z`.
+   kvp  -- Compute nth derivative of real-order modified Bessel function Kv(z)
+   h1vp -- Compute nth derivative of Hankel function H1v(z) with respect to `z`.
+   h2vp -- Compute nth derivative of Hankel function H2v(z) with respect to `z`.
+
+Spherical Bessel functions
+^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+.. autosummary::
+   :toctree: generated/
+
+   spherical_jn -- Spherical Bessel function of the first kind or its derivative.
+   spherical_yn -- Spherical Bessel function of the second kind or its derivative.
+   spherical_in -- Modified spherical Bessel function of the first kind or its derivative.
+   spherical_kn -- Modified spherical Bessel function of the second kind or its derivative.
+
+Riccati-Bessel functions
+^^^^^^^^^^^^^^^^^^^^^^^^
+
+The following functions do not accept NumPy arrays (they are not
+universal functions):
+
+.. autosummary::
+   :toctree: generated/
+
+   riccati_jn -- Compute Riccati-Bessel function of the first kind and its derivative.
+   riccati_yn -- Compute Riccati-Bessel function of the second kind and its derivative.
+
+Struve functions
+----------------
+
+.. autosummary::
+   :toctree: generated/
+
+   struve       -- Struve function.
+   modstruve    -- Modified Struve function.
+   itstruve0    -- Integral of the Struve function of order 0.
+   it2struve0   -- Integral related to the Struve function of order 0.
+   itmodstruve0 -- Integral of the modified Struve function of order 0.
+
+
+Raw statistical functions
+-------------------------
+
+.. seealso:: :mod:`scipy.stats`: Friendly versions of these functions.
+
+Binomial distribution
+^^^^^^^^^^^^^^^^^^^^^
+
+.. autosummary::
+   :toctree: generated/
+
+   bdtr         -- Binomial distribution cumulative distribution function.
+   bdtrc        -- Binomial distribution survival function.
+   bdtri        -- Inverse function to `bdtr` with respect to `p`.
+   bdtrik       -- Inverse function to `bdtr` with respect to `k`.
+   bdtrin       -- Inverse function to `bdtr` with respect to `n`.
+
+Beta distribution
+^^^^^^^^^^^^^^^^^
+
+.. autosummary::
+   :toctree: generated/
+
+   btdtria      -- Inverse of `betainc` with respect to `a`.
+   btdtrib      -- Inverse of `betainc` with respect to `b`.
+
+F distribution
+^^^^^^^^^^^^^^
+
+.. autosummary::
+   :toctree: generated/
+
+   fdtr         -- F cumulative distribution function.
+   fdtrc        -- F survival function.
+   fdtri        -- The `p`-th quantile of the F-distribution.
+   fdtridfd     -- Inverse to `fdtr` vs dfd.
+
+Gamma distribution
+^^^^^^^^^^^^^^^^^^
+
+.. autosummary::
+   :toctree: generated/
+
+   gdtr         -- Gamma distribution cumulative distribution function.
+   gdtrc        -- Gamma distribution survival function.
+   gdtria       -- Inverse of `gdtr` vs a.
+   gdtrib       -- Inverse of `gdtr` vs b.
+   gdtrix       -- Inverse of `gdtr` vs x.
+
+Negative binomial distribution
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+.. autosummary::
+   :toctree: generated/
+
+   nbdtr        -- Negative binomial cumulative distribution function.
+   nbdtrc       -- Negative binomial survival function.
+   nbdtri       -- Inverse of `nbdtr` vs `p`.
+   nbdtrik      -- Inverse of `nbdtr` vs `k`.
+   nbdtrin      -- Inverse of `nbdtr` vs `n`.
+
+Noncentral F distribution
+^^^^^^^^^^^^^^^^^^^^^^^^^
+
+.. autosummary::
+   :toctree: generated/
+
+   ncfdtr       -- Cumulative distribution function of the non-central F distribution.
+   ncfdtridfd   -- Calculate degrees of freedom (denominator) for the noncentral F-distribution.
+   ncfdtridfn   -- Calculate degrees of freedom (numerator) for the noncentral F-distribution.
+   ncfdtri      -- Inverse cumulative distribution function of the non-central F distribution.
+   ncfdtrinc    -- Calculate non-centrality parameter for non-central F distribution.
+
+Noncentral t distribution
+^^^^^^^^^^^^^^^^^^^^^^^^^
+
+.. autosummary::
+   :toctree: generated/
+
+   nctdtr       -- Cumulative distribution function of the non-central `t` distribution.
+   nctdtridf    -- Calculate degrees of freedom for non-central t distribution.
+   nctdtrit     -- Inverse cumulative distribution function of the non-central t distribution.
+   nctdtrinc    -- Calculate non-centrality parameter for non-central t distribution.
+
+Normal distribution
+^^^^^^^^^^^^^^^^^^^
+
+.. autosummary::
+   :toctree: generated/
+
+   nrdtrimn     -- Calculate mean of normal distribution given other params.
+   nrdtrisd     -- Calculate standard deviation of normal distribution given other params.
+   ndtr         -- Normal cumulative distribution function.
+   log_ndtr     -- Logarithm of normal cumulative distribution function.
+   ndtri        -- Inverse of `ndtr` vs x.
+   ndtri_exp    -- Inverse of `log_ndtr` vs x.
+
+Poisson distribution
+^^^^^^^^^^^^^^^^^^^^
+
+.. autosummary::
+   :toctree: generated/
+
+   pdtr         -- Poisson cumulative distribution function.
+   pdtrc        -- Poisson survival function.
+   pdtri        -- Inverse to `pdtr` vs m.
+   pdtrik       -- Inverse to `pdtr` vs k.
+
+Student t distribution
+^^^^^^^^^^^^^^^^^^^^^^
+
+.. autosummary::
+   :toctree: generated/
+
+   stdtr        -- Student t distribution cumulative distribution function.
+   stdtridf     -- Inverse of `stdtr` vs df.
+   stdtrit      -- Inverse of `stdtr` vs `t`.
+
+Chi square distribution
+^^^^^^^^^^^^^^^^^^^^^^^
+
+.. autosummary::
+   :toctree: generated/
+
+   chdtr        -- Chi square cumulative distribution function.
+   chdtrc       -- Chi square survival function.
+   chdtri       -- Inverse to `chdtrc`.
+   chdtriv      -- Inverse to `chdtr` vs `v`.
+
+Non-central chi square distribution
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+.. autosummary::
+   :toctree: generated/
+
+   chndtr       -- Non-central chi square cumulative distribution function.
+   chndtridf    -- Inverse to `chndtr` vs `df`.
+   chndtrinc    -- Inverse to `chndtr` vs `nc`.
+   chndtrix     -- Inverse to `chndtr` vs `x`.
+
+Kolmogorov distribution
+^^^^^^^^^^^^^^^^^^^^^^^
+
+.. autosummary::
+   :toctree: generated/
+
+   smirnov      -- Kolmogorov-Smirnov complementary cumulative distribution function.
+   smirnovi     -- Inverse to `smirnov`.
+   kolmogorov   -- Complementary cumulative distribution function of Kolmogorov distribution.
+   kolmogi      -- Inverse function to `kolmogorov`.
+
+Box-Cox transformation
+^^^^^^^^^^^^^^^^^^^^^^
+
+.. autosummary::
+   :toctree: generated/
+
+   boxcox       -- Compute the Box-Cox transformation.
+   boxcox1p     -- Compute the Box-Cox transformation of 1 + `x`.
+   inv_boxcox   -- Compute the inverse of the Box-Cox transformation.
+   inv_boxcox1p -- Compute the inverse of the Box-Cox transformation.
+
+
+Sigmoidal functions
+^^^^^^^^^^^^^^^^^^^
+
+.. autosummary::
+   :toctree: generated/
+
+   logit        -- Logit ufunc for ndarrays.
+   expit        -- Logistic sigmoid function.
+   log_expit    -- Logarithm of the logistic sigmoid function.
+
+Miscellaneous
+^^^^^^^^^^^^^
+
+.. autosummary::
+   :toctree: generated/
+
+   tklmbda      -- Tukey-Lambda cumulative distribution function.
+   owens_t      -- Owen's T Function.
+
+
+Information Theory functions
+----------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   entr         -- Elementwise function for computing entropy.
+   rel_entr     -- Elementwise function for computing relative entropy.
+   kl_div       -- Elementwise function for computing Kullback-Leibler divergence.
+   huber        -- Huber loss function.
+   pseudo_huber -- Pseudo-Huber loss function.
+
+
+Gamma and related functions
+---------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   gamma        -- Gamma function.
+   gammaln      -- Logarithm of the absolute value of the Gamma function for real inputs.
+   loggamma     -- Principal branch of the logarithm of the Gamma function.
+   gammasgn     -- Sign of the gamma function.
+   gammainc     -- Regularized lower incomplete gamma function.
+   gammaincinv  -- Inverse to `gammainc`.
+   gammaincc    -- Regularized upper incomplete gamma function.
+   gammainccinv -- Inverse to `gammaincc`.
+   beta         -- Beta function.
+   betaln       -- Natural logarithm of absolute value of beta function.
+   betainc      -- Incomplete beta integral.
+   betaincc     -- Complemented incomplete beta integral.
+   betaincinv   -- Inverse function to beta integral.
+   betainccinv  -- Inverse of the complemented incomplete beta integral.
+   psi          -- The digamma function.
+   rgamma       -- Gamma function inverted.
+   polygamma    -- Polygamma function n.
+   multigammaln -- Returns the log of multivariate gamma, also sometimes called the generalized gamma.
+   digamma      -- psi(x[, out]).
+   poch         -- Rising factorial (z)_m.
+
+Error function and Fresnel integrals
+------------------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   erf           -- Returns the error function of complex argument.
+   erfc          -- Complementary error function, ``1 - erf(x)``.
+   erfcx         -- Scaled complementary error function, ``exp(x**2) * erfc(x)``.
+   erfi          -- Imaginary error function, ``-i erf(i z)``.
+   erfinv        -- Inverse function for erf.
+   erfcinv       -- Inverse function for erfc.
+   wofz          -- Faddeeva function.
+   dawsn         -- Dawson's integral.
+   fresnel       -- Fresnel sin and cos integrals.
+   fresnel_zeros -- Compute nt complex zeros of sine and cosine Fresnel integrals S(z) and C(z).
+   modfresnelp   -- Modified Fresnel positive integrals.
+   modfresnelm   -- Modified Fresnel negative integrals.
+   voigt_profile -- Voigt profile.
+
+The following functions do not accept NumPy arrays (they are not
+universal functions):
+
+.. autosummary::
+   :toctree: generated/
+
+   erf_zeros      -- Compute nt complex zeros of error function erf(z).
+   fresnelc_zeros -- Compute nt complex zeros of cosine Fresnel integral C(z).
+   fresnels_zeros -- Compute nt complex zeros of sine Fresnel integral S(z).
+
+Legendre functions
+------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   legendre_p                 -- Legendre polynomials of the first kind.
+   legendre_p_all             -- All Legendre polynomials of the first kind up to a specified order.
+   assoc_legendre_p           -- Associated Legendre polynomials of the first kind.
+   assoc_legendre_p_all       -- All associated Legendre polynomials of the first kind up to a specified order and degree.
+   sph_legendre_p             -- Spherical Legendre polynomials of the first kind.
+   sph_legendre_p_all         -- All spherical Legendre polynomials of the first kind up to a specified order and degree.
+   sph_harm_y                 -- Spherical harmonics.
+   sph_harm_y_all             -- All spherical harmonics up to a specified order and degree.
+
+The following functions are in the process of being deprecated in favor of the above,
+which provide a more flexible and consistent interface.
+
+.. autosummary::
+   :toctree: generated/
+
+   lpmv                       -- Associated Legendre function of integer order and real degree.
+   lqn                        -- Legendre function of the second kind.
+   lqmn                       -- Sequence of associated Legendre functions of the second kind.
+
+Ellipsoidal harmonics
+---------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   ellip_harm   -- Ellipsoidal harmonic functions E^p_n(l).
+   ellip_harm_2 -- Ellipsoidal harmonic functions F^p_n(l).
+   ellip_normal -- Ellipsoidal harmonic normalization constants gamma^p_n.
+
+Orthogonal polynomials
+----------------------
+
+The following functions evaluate values of orthogonal polynomials:
+
+.. autosummary::
+   :toctree: generated/
+
+   assoc_laguerre   -- Compute the generalized (associated) Laguerre polynomial of degree n and order k.
+   eval_legendre    -- Evaluate Legendre polynomial at a point.
+   eval_chebyt      -- Evaluate Chebyshev polynomial of the first kind at a point.
+   eval_chebyu      -- Evaluate Chebyshev polynomial of the second kind at a point.
+   eval_chebyc      -- Evaluate Chebyshev polynomial of the first kind on [-2, 2] at a point.
+   eval_chebys      -- Evaluate Chebyshev polynomial of the second kind on [-2, 2] at a point.
+   eval_jacobi      -- Evaluate Jacobi polynomial at a point.
+   eval_laguerre    -- Evaluate Laguerre polynomial at a point.
+   eval_genlaguerre -- Evaluate generalized Laguerre polynomial at a point.
+   eval_hermite     -- Evaluate physicist's Hermite polynomial at a point.
+   eval_hermitenorm -- Evaluate probabilist's (normalized) Hermite polynomial at a point.
+   eval_gegenbauer  -- Evaluate Gegenbauer polynomial at a point.
+   eval_sh_legendre -- Evaluate shifted Legendre polynomial at a point.
+   eval_sh_chebyt   -- Evaluate shifted Chebyshev polynomial of the first kind at a point.
+   eval_sh_chebyu   -- Evaluate shifted Chebyshev polynomial of the second kind at a point.
+   eval_sh_jacobi   -- Evaluate shifted Jacobi polynomial at a point.
+
+The following functions compute roots and quadrature weights for
+orthogonal polynomials:
+
+.. autosummary::
+   :toctree: generated/
+
+   roots_legendre    -- Gauss-Legendre quadrature.
+   roots_chebyt      -- Gauss-Chebyshev (first kind) quadrature.
+   roots_chebyu      -- Gauss-Chebyshev (second kind) quadrature.
+   roots_chebyc      -- Gauss-Chebyshev (first kind) quadrature.
+   roots_chebys      -- Gauss-Chebyshev (second kind) quadrature.
+   roots_jacobi      -- Gauss-Jacobi quadrature.
+   roots_laguerre    -- Gauss-Laguerre quadrature.
+   roots_genlaguerre -- Gauss-generalized Laguerre quadrature.
+   roots_hermite     -- Gauss-Hermite (physicist's) quadrature.
+   roots_hermitenorm -- Gauss-Hermite (statistician's) quadrature.
+   roots_gegenbauer  -- Gauss-Gegenbauer quadrature.
+   roots_sh_legendre -- Gauss-Legendre (shifted) quadrature.
+   roots_sh_chebyt   -- Gauss-Chebyshev (first kind, shifted) quadrature.
+   roots_sh_chebyu   -- Gauss-Chebyshev (second kind, shifted) quadrature.
+   roots_sh_jacobi   -- Gauss-Jacobi (shifted) quadrature.
+
+The functions below, in turn, return the polynomial coefficients in
+``orthopoly1d`` objects, which function similarly as `numpy.poly1d`.
+The ``orthopoly1d`` class also has an attribute ``weights``, which returns
+the roots, weights, and total weights for the appropriate form of Gaussian
+quadrature. These are returned in an ``n x 3`` array with roots in the first
+column, weights in the second column, and total weights in the final column.
+Note that ``orthopoly1d`` objects are converted to `~numpy.poly1d` when doing
+arithmetic, and lose information of the original orthogonal polynomial.
+
+.. autosummary::
+   :toctree: generated/
+
+   legendre    -- Legendre polynomial.
+   chebyt      -- Chebyshev polynomial of the first kind.
+   chebyu      -- Chebyshev polynomial of the second kind.
+   chebyc      -- Chebyshev polynomial of the first kind on :math:`[-2, 2]`.
+   chebys      -- Chebyshev polynomial of the second kind on :math:`[-2, 2]`.
+   jacobi      -- Jacobi polynomial.
+   laguerre    -- Laguerre polynomial.
+   genlaguerre -- Generalized (associated) Laguerre polynomial.
+   hermite     -- Physicist's Hermite polynomial.
+   hermitenorm -- Normalized (probabilist's) Hermite polynomial.
+   gegenbauer  -- Gegenbauer (ultraspherical) polynomial.
+   sh_legendre -- Shifted Legendre polynomial.
+   sh_chebyt   -- Shifted Chebyshev polynomial of the first kind.
+   sh_chebyu   -- Shifted Chebyshev polynomial of the second kind.
+   sh_jacobi   -- Shifted Jacobi polynomial.
+
+.. warning::
+
+   Computing values of high-order polynomials (around ``order > 20``) using
+   polynomial coefficients is numerically unstable. To evaluate polynomial
+   values, the ``eval_*`` functions should be used instead.
+
+
+Hypergeometric functions
+------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   hyp2f1 -- Gauss hypergeometric function 2F1(a, b; c; z).
+   hyp1f1 -- Confluent hypergeometric function 1F1(a, b; x).
+   hyperu -- Confluent hypergeometric function U(a, b, x) of the second kind.
+   hyp0f1 -- Confluent hypergeometric limit function 0F1.
+
+
+Parabolic cylinder functions
+----------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   pbdv -- Parabolic cylinder function D.
+   pbvv -- Parabolic cylinder function V.
+   pbwa -- Parabolic cylinder function W.
+
+The following functions do not accept NumPy arrays (they are not
+universal functions):
+
+.. autosummary::
+   :toctree: generated/
+
+   pbdv_seq -- Parabolic cylinder functions Dv(x) and derivatives.
+   pbvv_seq -- Parabolic cylinder functions Vv(x) and derivatives.
+   pbdn_seq -- Parabolic cylinder functions Dn(z) and derivatives.
+
+Mathieu and related functions
+-----------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   mathieu_a -- Characteristic value of even Mathieu functions.
+   mathieu_b -- Characteristic value of odd Mathieu functions.
+
+The following functions do not accept NumPy arrays (they are not
+universal functions):
+
+.. autosummary::
+   :toctree: generated/
+
+   mathieu_even_coef -- Fourier coefficients for even Mathieu and modified Mathieu functions.
+   mathieu_odd_coef  -- Fourier coefficients for even Mathieu and modified Mathieu functions.
+
+The following return both function and first derivative:
+
+.. autosummary::
+   :toctree: generated/
+
+   mathieu_cem     -- Even Mathieu function and its derivative.
+   mathieu_sem     -- Odd Mathieu function and its derivative.
+   mathieu_modcem1 -- Even modified Mathieu function of the first kind and its derivative.
+   mathieu_modcem2 -- Even modified Mathieu function of the second kind and its derivative.
+   mathieu_modsem1 -- Odd modified Mathieu function of the first kind and its derivative.
+   mathieu_modsem2 -- Odd modified Mathieu function of the second kind and its derivative.
+
+Spheroidal wave functions
+-------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   pro_ang1   -- Prolate spheroidal angular function of the first kind and its derivative.
+   pro_rad1   -- Prolate spheroidal radial function of the first kind and its derivative.
+   pro_rad2   -- Prolate spheroidal radial function of the second kind and its derivative.
+   obl_ang1   -- Oblate spheroidal angular function of the first kind and its derivative.
+   obl_rad1   -- Oblate spheroidal radial function of the first kind and its derivative.
+   obl_rad2   -- Oblate spheroidal radial function of the second kind and its derivative.
+   pro_cv     -- Characteristic value of prolate spheroidal function.
+   obl_cv     -- Characteristic value of oblate spheroidal function.
+   pro_cv_seq -- Characteristic values for prolate spheroidal wave functions.
+   obl_cv_seq -- Characteristic values for oblate spheroidal wave functions.
+
+The following functions require pre-computed characteristic value:
+
+.. autosummary::
+   :toctree: generated/
+
+   pro_ang1_cv -- Prolate spheroidal angular function pro_ang1 for precomputed characteristic value.
+   pro_rad1_cv -- Prolate spheroidal radial function pro_rad1 for precomputed characteristic value.
+   pro_rad2_cv -- Prolate spheroidal radial function pro_rad2 for precomputed characteristic value.
+   obl_ang1_cv -- Oblate spheroidal angular function obl_ang1 for precomputed characteristic value.
+   obl_rad1_cv -- Oblate spheroidal radial function obl_rad1 for precomputed characteristic value.
+   obl_rad2_cv -- Oblate spheroidal radial function obl_rad2 for precomputed characteristic value.
+
+Kelvin functions
+----------------
+
+.. autosummary::
+   :toctree: generated/
+
+   kelvin       -- Kelvin functions as complex numbers.
+   kelvin_zeros -- Compute nt zeros of all Kelvin functions.
+   ber          -- Kelvin function ber.
+   bei          -- Kelvin function bei
+   berp         -- Derivative of the Kelvin function `ber`.
+   beip         -- Derivative of the Kelvin function `bei`.
+   ker          -- Kelvin function ker.
+   kei          -- Kelvin function ker.
+   kerp         -- Derivative of the Kelvin function ker.
+   keip         -- Derivative of the Kelvin function kei.
+
+The following functions do not accept NumPy arrays (they are not
+universal functions):
+
+.. autosummary::
+   :toctree: generated/
+
+   ber_zeros  -- Compute nt zeros of the Kelvin function ber(x).
+   bei_zeros  -- Compute nt zeros of the Kelvin function bei(x).
+   berp_zeros -- Compute nt zeros of the Kelvin function ber'(x).
+   beip_zeros -- Compute nt zeros of the Kelvin function bei'(x).
+   ker_zeros  -- Compute nt zeros of the Kelvin function ker(x).
+   kei_zeros  -- Compute nt zeros of the Kelvin function kei(x).
+   kerp_zeros -- Compute nt zeros of the Kelvin function ker'(x).
+   keip_zeros -- Compute nt zeros of the Kelvin function kei'(x).
+
+Combinatorics
+-------------
+
+.. autosummary::
+   :toctree: generated/
+
+   comb -- The number of combinations of N things taken k at a time.
+   perm -- Permutations of N things taken k at a time, i.e., k-permutations of N.
+   stirling2 -- Stirling numbers of the second kind.
+
+Lambert W and related functions
+-------------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   lambertw    -- Lambert W function.
+   wrightomega -- Wright Omega function.
+
+Other special functions
+-----------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   agm         -- Arithmetic, Geometric Mean.
+   bernoulli   -- Bernoulli numbers B0..Bn (inclusive).
+   binom       -- Binomial coefficient
+   diric       -- Periodic sinc function, also called the Dirichlet kernel.
+   euler       -- Euler numbers E0..En (inclusive).
+   expn        -- Exponential integral E_n.
+   exp1        -- Exponential integral E_1 of complex argument z.
+   expi        -- Exponential integral Ei.
+   factorial   -- The factorial of a number or array of numbers.
+   factorial2  -- Double factorial.
+   factorialk  -- Multifactorial of n of order k, n(!!...!).
+   shichi      -- Hyperbolic sine and cosine integrals.
+   sici        -- Sine and cosine integrals.
+   softmax     -- Softmax function.
+   log_softmax -- Logarithm of softmax function.
+   spence      -- Spence's function, also known as the dilogarithm.
+   zeta        -- Riemann zeta function.
+   zetac       -- Riemann zeta function minus 1.
+   softplus    -- Softplus function.
+
+Convenience functions
+---------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   cbrt      -- Cube root of `x`.
+   exp10     -- 10**x.
+   exp2      -- 2**x.
+   radian    -- Convert from degrees to radians.
+   cosdg     -- Cosine of the angle `x` given in degrees.
+   sindg     -- Sine of angle given in degrees.
+   tandg     -- Tangent of angle x given in degrees.
+   cotdg     -- Cotangent of the angle `x` given in degrees.
+   log1p     -- Calculates log(1+x) for use when `x` is near zero.
+   expm1     -- ``exp(x) - 1`` for use when `x` is near zero.
+   cosm1     -- ``cos(x) - 1`` for use when `x` is near zero.
+   powm1     -- ``x**y - 1`` for use when `y` is near zero or `x` is near 1.
+   round     -- Round to nearest integer.
+   xlogy     -- Compute ``x*log(y)`` so that the result is 0 if ``x = 0``.
+   xlog1py   -- Compute ``x*log1p(y)`` so that the result is 0 if ``x = 0``.
+   logsumexp -- Compute the log of the sum of exponentials of input elements.
+   exprel    -- Relative error exponential, (exp(x)-1)/x, for use when `x` is near zero.
+   sinc      -- Return the sinc function.
+
+"""  # noqa: E501
+
+
+from ._sf_error import SpecialFunctionWarning, SpecialFunctionError
+
+from . import _ufuncs
+from ._ufuncs import *
+
+from . import _basic
+from ._basic import *
+
+# Replace some function definitions from _ufuncs and _basic
+# to add Array API support
+from ._support_alternative_backends import *
+
+from ._logsumexp import logsumexp, softmax, log_softmax
+
+from . import _multiufuncs
+from ._multiufuncs import *
+
+from . import _orthogonal
+from ._orthogonal import *
+
+from ._ellip_harm import (
+    ellip_harm,
+    ellip_harm_2,
+    ellip_normal
+)
+from ._lambertw import lambertw
+from ._spherical_bessel import (
+    spherical_jn,
+    spherical_yn,
+    spherical_in,
+    spherical_kn
+)
+
+# Deprecated namespaces, to be removed in v2.0.0
+from . import add_newdocs, basic, orthogonal, specfun, sf_error, spfun_stats
+
+# We replace some function definitions from _ufuncs with those from
+# _support_alternative_backends above, but those are all listed in _ufuncs.__all__,
+# so there is no need to consider _support_alternative_backends.__all__ here.
+__all__ = _ufuncs.__all__ + _basic.__all__ + _orthogonal.__all__ + _multiufuncs.__all__
+__all__ += [
+    'SpecialFunctionWarning',
+    'SpecialFunctionError',
+    'logsumexp',
+    'softmax',
+    'log_softmax',
+    'multigammaln',  # pyrefly:ignore[bad-dunder-all]
+    'ellip_harm',
+    'ellip_harm_2',
+    'ellip_normal',
+    'lambertw',
+    'spherical_jn',
+    'spherical_yn',
+    'spherical_in',
+    'spherical_kn',
+]
+
+from scipy._lib._testutils import PytestTester
+test = PytestTester(__name__)
+del PytestTester
diff --git a/venv/lib/python3.12/site-packages/scipy/special/__pycache__/__init__.cpython-312.pyc b/venv/lib/python3.12/site-packages/scipy/special/__pycache__/__init__.cpython-312.pyc
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index 0000000000000000000000000000000000000000..63d2581d620d4c20640f94573f36a25885f6a1a5
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/_add_newdocs.py
@@ -0,0 +1,8913 @@
+# Docstrings for generated ufuncs
+#
+# The syntax is designed to look like the function add_newdoc is being
+# called from numpy.lib, but in this file add_newdoc puts the
+# docstrings in a dictionary. This dictionary is used in
+# _generate_pyx.py to generate the docstrings for the ufuncs in
+# scipy.special at the C level when the ufuncs are created at compile
+# time.
+
+docdict: dict[str, str] = {}
+
+
+def get(name):
+    return docdict.get(name)
+
+
+def add_newdoc(name, doc):
+    docdict[name] = doc
+
+
+add_newdoc("_sf_error_test_function",
+    """
+    Private function; do not use.
+    """)
+
+
+add_newdoc("_cosine_cdf",
+    """
+    _cosine_cdf(x)
+
+    Cumulative distribution function (CDF) of the cosine distribution::
+
+                 {             0,              x < -pi
+        cdf(x) = { (pi + x + sin(x))/(2*pi),   -pi <= x <= pi
+                 {             1,              x > pi
+
+    Parameters
+    ----------
+    x : array_like
+        `x` must contain real numbers.
+
+    Returns
+    -------
+    scalar or ndarray
+        The cosine distribution CDF evaluated at `x`.
+
+    """)
+
+add_newdoc("_cosine_invcdf",
+    """
+    _cosine_invcdf(p)
+
+    Inverse of the cumulative distribution function (CDF) of the cosine
+    distribution.
+
+    The CDF of the cosine distribution is::
+
+        cdf(x) = (pi + x + sin(x))/(2*pi)
+
+    This function computes the inverse of cdf(x).
+
+    Parameters
+    ----------
+    p : array_like
+        `p` must contain real numbers in the interval ``0 <= p <= 1``.
+        `nan` is returned for values of `p` outside the interval [0, 1].
+
+    Returns
+    -------
+    scalar or ndarray
+        The inverse of the cosine distribution CDF evaluated at `p`.
+
+    """)
+
+add_newdoc("_ellip_harm",
+    """
+    Internal function, use `ellip_harm` instead.
+    """)
+
+add_newdoc("_ellip_norm",
+    """
+    Internal function, use `ellip_norm` instead.
+    """)
+
+add_newdoc("wrightomega",
+    r"""
+    wrightomega(z, out=None)
+
+    Wright Omega function.
+
+    Defined as the solution to
+
+    .. math::
+
+        \omega + \log(\omega) = z
+
+    where :math:`\log` is the principal branch of the complex logarithm.
+
+    Parameters
+    ----------
+    z : array_like
+        Points at which to evaluate the Wright Omega function
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    omega : scalar or ndarray
+        Values of the Wright Omega function
+
+    See Also
+    --------
+    lambertw : The Lambert W function
+
+    Notes
+    -----
+    .. versionadded:: 0.19.0
+
+    The function can also be defined as
+
+    .. math::
+
+        \omega(z) = W_{K(z)}(e^z)
+
+    where :math:`K(z) = \lceil (\Im(z) - \pi)/(2\pi) \rceil` is the
+    unwinding number and :math:`W` is the Lambert W function.
+
+    The implementation here is taken from [1]_.
+
+    References
+    ----------
+    .. [1] Lawrence, Corless, and Jeffrey, "Algorithm 917: Complex
+           Double-Precision Evaluation of the Wright :math:`\omega`
+           Function." ACM Transactions on Mathematical Software,
+           2012. :doi:`10.1145/2168773.2168779`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.special import wrightomega, lambertw
+
+    >>> wrightomega([-2, -1, 0, 1, 2])
+    array([0.12002824, 0.27846454, 0.56714329, 1.        , 1.5571456 ])
+
+    Complex input:
+
+    >>> wrightomega(3 + 5j)
+    (1.5804428632097158+3.8213626783287937j)
+
+    Verify that ``wrightomega(z)`` satisfies ``w + log(w) = z``:
+
+    >>> w = -5 + 4j
+    >>> wrightomega(w + np.log(w))
+    (-5+4j)
+
+    Verify the connection to ``lambertw``:
+
+    >>> z = 0.5 + 3j
+    >>> wrightomega(z)
+    (0.0966015889280649+1.4937828458191993j)
+    >>> lambertw(np.exp(z))
+    (0.09660158892806493+1.4937828458191993j)
+
+    >>> z = 0.5 + 4j
+    >>> wrightomega(z)
+    (-0.3362123489037213+2.282986001579032j)
+    >>> lambertw(np.exp(z), k=1)
+    (-0.33621234890372115+2.282986001579032j)
+    """)
+
+
+add_newdoc("agm",
+    """
+    agm(a, b, out=None)
+
+    Compute the arithmetic-geometric mean of `a` and `b`.
+
+    Start with a_0 = a and b_0 = b and iteratively compute::
+
+        a_{n+1} = (a_n + b_n)/2
+        b_{n+1} = sqrt(a_n*b_n)
+
+    a_n and b_n converge to the same limit as n increases; their common
+    limit is agm(a, b).
+
+    Parameters
+    ----------
+    a, b : array_like
+        Real values only. If the values are both negative, the result
+        is negative. If one value is negative and the other is positive,
+        `nan` is returned.
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    scalar or ndarray
+        The arithmetic-geometric mean of `a` and `b`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.special import agm
+    >>> a, b = 24.0, 6.0
+    >>> agm(a, b)
+    13.458171481725614
+
+    Compare that result to the iteration:
+
+    >>> while a != b:
+    ...     a, b = (a + b)/2, np.sqrt(a*b)
+    ...     print("a = %19.16f  b=%19.16f" % (a, b))
+    ...
+    a = 15.0000000000000000  b=12.0000000000000000
+    a = 13.5000000000000000  b=13.4164078649987388
+    a = 13.4582039324993694  b=13.4581390309909850
+    a = 13.4581714817451772  b=13.4581714817060547
+    a = 13.4581714817256159  b=13.4581714817256159
+
+    When array-like arguments are given, broadcasting applies:
+
+    >>> a = np.array([[1.5], [3], [6]])  # a has shape (3, 1).
+    >>> b = np.array([6, 12, 24, 48])    # b has shape (4,).
+    >>> agm(a, b)
+    array([[  3.36454287,   5.42363427,   9.05798751,  15.53650756],
+           [  4.37037309,   6.72908574,  10.84726853,  18.11597502],
+           [  6.        ,   8.74074619,  13.45817148,  21.69453707]])
+    """)
+
+add_newdoc("bdtr",
+    r"""
+    bdtr(k, n, p, out=None)
+
+    Binomial distribution cumulative distribution function.
+
+    Sum of the terms 0 through `floor(k)` of the Binomial probability density.
+
+    .. math::
+        \mathrm{bdtr}(k, n, p) =
+        \sum_{j=0}^{\lfloor k \rfloor} {{n}\choose{j}} p^j (1-p)^{n-j}
+
+    Parameters
+    ----------
+    k : array_like
+        Number of successes (double), rounded down to the nearest integer.
+    n : array_like
+        Number of events (int).
+    p : array_like
+        Probability of success in a single event (float).
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    y : scalar or ndarray
+        Probability of `floor(k)` or fewer successes in `n` independent events with
+        success probabilities of `p`.
+
+    Notes
+    -----
+    The terms are not summed directly; instead the regularized incomplete beta
+    function is employed, according to the formula,
+
+    .. math::
+        \mathrm{bdtr}(k, n, p) =
+        I_{1 - p}(n - \lfloor k \rfloor, \lfloor k \rfloor + 1).
+
+    Wrapper for the Cephes [1]_ routine `bdtr`.
+
+    References
+    ----------
+    .. [1] Cephes Mathematical Functions Library,
+           https://netlib.org/cephes/
+
+    """)
+
+add_newdoc("bdtrc",
+    r"""
+    bdtrc(k, n, p, out=None)
+
+    Binomial distribution survival function.
+
+    Sum of the terms `floor(k) + 1` through `n` of the binomial probability
+    density,
+
+    .. math::
+        \mathrm{bdtrc}(k, n, p) =
+        \sum_{j=\lfloor k \rfloor +1}^n {{n}\choose{j}} p^j (1-p)^{n-j}
+
+    Parameters
+    ----------
+    k : array_like
+        Number of successes (double), rounded down to nearest integer.
+    n : array_like
+        Number of events (int)
+    p : array_like
+        Probability of success in a single event.
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    y : scalar or ndarray
+        Probability of `floor(k) + 1` or more successes in `n` independent
+        events with success probabilities of `p`.
+
+    See Also
+    --------
+    bdtr
+    betainc
+
+    Notes
+    -----
+    The terms are not summed directly; instead the regularized incomplete beta
+    function is employed, according to the formula,
+
+    .. math::
+        \mathrm{bdtrc}(k, n, p) = I_{p}(\lfloor k \rfloor + 1, n - \lfloor k \rfloor).
+
+    Wrapper for the Cephes [1]_ routine `bdtrc`.
+
+    References
+    ----------
+    .. [1] Cephes Mathematical Functions Library,
+           https://netlib.org/cephes/
+
+    """)
+
+add_newdoc("bdtri",
+    r"""
+    bdtri(k, n, y, out=None)
+
+    Inverse function to `bdtr` with respect to `p`.
+
+    Finds the event probability `p` such that the sum of the terms 0 through
+    `k` of the binomial probability density is equal to the given cumulative
+    probability `y`.
+
+    Parameters
+    ----------
+    k : array_like
+        Number of successes (float), rounded down to the nearest integer.
+    n : array_like
+        Number of events (float)
+    y : array_like
+        Cumulative probability (probability of `k` or fewer successes in `n`
+        events).
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    p : scalar or ndarray
+        The event probability such that `bdtr(\lfloor k \rfloor, n, p) = y`.
+
+    See Also
+    --------
+    bdtr
+    betaincinv
+
+    Notes
+    -----
+    The computation is carried out using the inverse beta integral function
+    and the relation,::
+
+        1 - p = betaincinv(n - k, k + 1, y).
+
+    Wrapper for the Cephes [1]_ routine `bdtri`.
+
+    References
+    ----------
+    .. [1] Cephes Mathematical Functions Library,
+           https://netlib.org/cephes/
+    """)
+
+add_newdoc("bdtrik",
+    """
+    bdtrik(y, n, p, out=None)
+
+    Inverse function to `bdtr` with respect to `k`.
+
+    Finds the number of successes `k` such that the sum of the terms 0 through
+    `k` of the Binomial probability density for `n` events with probability
+    `p` is equal to the given cumulative probability `y`.
+
+    Parameters
+    ----------
+    y : array_like
+        Cumulative probability (probability of `k` or fewer successes in `n`
+        events).
+    n : array_like
+        Number of events (float).
+    p : array_like
+        Success probability (float).
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    k : scalar or ndarray
+        The number of successes `k` such that `bdtr(k, n, p) = y`.
+
+    See Also
+    --------
+    bdtr
+
+    Notes
+    -----
+    Formula 26.5.24 of [1]_ (or equivalently [2]_) is used to reduce the binomial
+    distribution to the cumulative incomplete beta distribution.
+
+    Computation of `k` involves a search for a value that produces the desired
+    value of `y`. The search relies on the monotonicity of `y` with `k`.
+
+    Wrapper for the CDFLIB [3]_ Fortran routine `cdfbin`.
+
+    References
+    ----------
+    .. [1] Milton Abramowitz and Irene A. Stegun, eds.
+           Handbook of Mathematical Functions with Formulas,
+           Graphs, and Mathematical Tables. New York: Dover, 1972.
+    .. [2] NIST Digital Library of Mathematical Functions
+           https://dlmf.nist.gov/8.17.5#E5
+    .. [3] Barry Brown, James Lovato, and Kathy Russell,
+           CDFLIB: Library of Fortran Routines for Cumulative Distribution
+           Functions, Inverses, and Other Parameters.
+
+    """)
+
+add_newdoc("bdtrin",
+    r"""
+    bdtrin(k, y, p, out=None)
+
+    Inverse function to `bdtr` with respect to `n`.
+
+    Finds the number of events `n` such that the sum of the terms 0 through
+    `k` of the Binomial probability density for events with probability `p` is
+    equal to the given cumulative probability `y`.
+
+    Parameters
+    ----------
+    k : array_like
+        Number of successes (float).
+    y : array_like
+        Cumulative probability (probability of `k` or fewer successes in `n`
+        events).
+    p : array_like
+        Success probability (float).
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    n : scalar or ndarray
+        The number of events `n` such that `bdtr(k, n, p) = y`.
+
+    See Also
+    --------
+    bdtr
+
+    Notes
+    -----
+    This function uses the `find_minimum_number_of_trials` method of the
+    `binomial_distribution` class of the Boost.Math C++ library [1]_.
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    Examples
+    --------
+    How often do we have to flip a fair coin to have at least a 90% chance
+    of getting 10 heads? `bdtrin` answers this question:
+
+    >>> import scipy.special as sc
+    >>> k = 10  # number of times we want heads
+    >>> p = 0.5  # probability of flipping heads
+    >>> y = 0.9  # cumulative probability
+    >>> result = sc.bdtrin(k, y, p)
+    >>> result
+    15.90442928275109
+
+    To verify, compute the cumulative probability of getting 10 or fewer
+    successes in 16 trials with probability 0.5 using the binomial
+    distribution from `scipy.stats`. Since `bdtrin` returns a non-integer
+    number of trials, we round up to the next integer:
+
+    >>> from scipy.stats import Binomial
+    >>> Binomial(n=16, p=p).cdf(k)
+    0.8949432373046875
+
+    """)
+
+add_newdoc("btdtria",
+    r"""
+    btdtria(p, b, x, out=None)
+
+    Inverse of `betainc` with respect to `a`.
+
+    This is the inverse of the beta cumulative distribution function, `betainc`,
+    considered as a function of `a`, returning the value of `a` for which
+    `betainc(a, b, x) = p`, or
+
+    .. math::
+        p = \int_0^x \frac{\Gamma(a + b)}{\Gamma(a)\Gamma(b)} t^{a-1} (1-t)^{b-1}\,dt
+
+    Parameters
+    ----------
+    p : array_like
+        Cumulative probability, in [0, 1].
+    b : array_like
+        Shape parameter (`b` > 0).
+    x : array_like
+        The quantile, in [0, 1].
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    a : scalar or ndarray
+        The value of the shape parameter `a` such that `betainc(a, b, x) = p`.
+
+    See Also
+    --------
+    betainc : Regularized incomplete beta function
+    betaincinv : Inverse of the regularized incomplete beta function
+    btdtrib : Inverse of the beta cumulative distribution function, with respect to `b`.
+
+    Notes
+    -----
+    This function wraps the ``ibeta_inva`` routine from the
+    Boost Math C++ library [1]_.
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    Examples
+    --------
+    >>> import scipy.special as sc
+
+    This function is the inverse of `betainc` for fixed
+    values of :math:`b` and :math:`x`.
+
+    >>> a, b, x = 1.2, 3.1, 0.2
+    >>> y = sc.betainc(a, b, x)
+    >>> sc.btdtria(y, b, x)
+    1.2
+
+    """)
+
+add_newdoc("btdtrib",
+    r"""
+    btdtria(a, p, x, out=None)
+
+    Inverse of `betainc` with respect to `b`.
+
+    This is the inverse of the beta cumulative distribution function, `betainc`,
+    considered as a function of `b`, returning the value of `b` for which
+    `betainc(a, b, x) = p`, or
+
+    .. math::
+        p = \int_0^x \frac{\Gamma(a + b)}{\Gamma(a)\Gamma(b)} t^{a-1} (1-t)^{b-1}\,dt
+
+    Parameters
+    ----------
+    a : array_like
+        Shape parameter (`a` > 0).
+    p : array_like
+        Cumulative probability, in [0, 1].
+    x : array_like
+        The quantile, in [0, 1].
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    b : scalar or ndarray
+        The value of the shape parameter `b` such that `betainc(a, b, x) = p`.
+
+    See Also
+    --------
+    betainc : Regularized incomplete beta function
+    betaincinv : Inverse of the regularized incomplete beta function with
+                 respect to `x`.
+    btdtria : Inverse of the beta cumulative distribution function, with respect to `a`.
+
+    Notes
+    -----
+    Wrapper for the `ibeta_invb` routine from the Boost Math C++ library [1]_.
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    Examples
+    --------
+    >>> import scipy.special as sc
+    >>> a, b, x = 1.2, 3.1, 0.2
+    >>> y = sc.betainc(a, b, x)
+
+    `btdtrib` is the inverse of `betainc` for fixed values of :math:`a` and
+    :math:`x`:
+
+    >>> sc.btdtrib(a, y, x)
+    3.1
+
+    """)
+
+add_newdoc(
+    "betainc",
+    r"""
+    betainc(a, b, x, out=None)
+
+    Regularized incomplete beta function.
+
+    Computes the regularized incomplete beta function, defined as [1]_:
+
+    .. math::
+
+        I_x(a, b) = \frac{\Gamma(a+b)}{\Gamma(a)\Gamma(b)} \int_0^x
+        t^{a-1}(1-t)^{b-1}dt,
+
+    for :math:`0 \leq x \leq 1`.
+
+    This function is the cumulative distribution function for the beta
+    distribution; its range is [0, 1].
+
+    Parameters
+    ----------
+    a, b : array_like
+           Positive, real-valued parameters.
+    x : array_like
+        Real-valued such that :math:`0 \leq x \leq 1`,
+        the upper limit of integration.
+    out : ndarray, optional
+        Optional output array for the function values.
+
+    Returns
+    -------
+    scalar or ndarray
+        Value of the regularized incomplete beta function.
+
+    See Also
+    --------
+    beta : beta function
+    betaincinv : inverse of the regularized incomplete beta function
+    betaincc : complement of the regularized incomplete beta function
+    scipy.stats.beta : beta distribution
+
+    Notes
+    -----
+    The term *regularized* in the name of this function refers to the
+    scaling of the function by the gamma function terms shown in the
+    formula.  When not qualified as *regularized*, the name *incomplete
+    beta function* often refers to just the integral expression,
+    without the gamma terms.  One can use the function `beta` from
+    `scipy.special` to get this "nonregularized" incomplete beta
+    function by multiplying the result of ``betainc(a, b, x)`` by
+    ``beta(a, b)``.
+
+    ``betainc(a, b, x)`` is treated as a two parameter family of functions
+    of a single variable `x`, rather than as a function of three variables.
+    This impacts only the limiting cases ``a = 0``, ``b = 0``, ``a = inf``,
+    ``b = inf``.
+
+    In general
+
+    .. math::
+
+        \lim_{(a, b) \rightarrow (a_0, b_0)} \mathrm{betainc}(a, b, x)
+
+    is treated as a pointwise limit in ``x``. Thus for example,
+    ``betainc(0, b, 0)`` equals ``0`` for ``b > 0``, although it would be
+    indeterminate when considering the simultaneous limit ``(a, x) -> (0+, 0+)``.
+
+    This function wraps the ``ibeta`` routine from the
+    Boost Math C++ library [2]_.
+
+    References
+    ----------
+    .. [1] NIST Digital Library of Mathematical Functions
+           https://dlmf.nist.gov/8.17
+    .. [2] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    Examples
+    --------
+
+    Let :math:`B(a, b)` be the `beta` function.
+
+    >>> import scipy.special as sc
+
+    The coefficient in terms of `gamma` is equal to
+    :math:`1/B(a, b)`. Also, when :math:`x=1`
+    the integral is equal to :math:`B(a, b)`.
+    Therefore, :math:`I_{x=1}(a, b) = 1` for any :math:`a, b`.
+
+    >>> sc.betainc(0.2, 3.5, 1.0)
+    1.0
+
+    It satisfies
+    :math:`I_x(a, b) = x^a F(a, 1-b, a+1, x)/ (aB(a, b))`,
+    where :math:`F` is the hypergeometric function `hyp2f1`:
+
+    >>> a, b, x = 1.4, 3.1, 0.5
+    >>> x**a * sc.hyp2f1(a, 1 - b, a + 1, x)/(a * sc.beta(a, b))
+    0.8148904036225295
+    >>> sc.betainc(a, b, x)
+    0.8148904036225296
+
+    This functions satisfies the relationship
+    :math:`I_x(a, b) = 1 - I_{1-x}(b, a)`:
+
+    >>> sc.betainc(2.2, 3.1, 0.4)
+    0.49339638807619446
+    >>> 1 - sc.betainc(3.1, 2.2, 1 - 0.4)
+    0.49339638807619446
+
+    """)
+
+
+add_newdoc(
+    "betaincc",
+    r"""
+    betaincc(a, b, x, out=None)
+
+    Complement of the regularized incomplete beta function.
+
+    Computes the complement of the regularized incomplete beta function,
+    defined as [1]_:
+
+    .. math::
+
+        \bar{I}_x(a, b) = 1 - I_x(a, b)
+                        = 1 - \frac{\Gamma(a+b)}{\Gamma(a)\Gamma(b)} \int_0^x
+                                  t^{a-1}(1-t)^{b-1}dt,
+
+    for :math:`0 \leq x \leq 1`.
+
+    Parameters
+    ----------
+    a, b : array_like
+           Positive, real-valued parameters.
+    x : array_like
+        Real-valued such that :math:`0 \leq x \leq 1`,
+        the upper limit of integration.
+    out : ndarray, optional
+        Optional output array for the function values.
+
+    Returns
+    -------
+    scalar or ndarray
+        Value of the complement of the regularized incomplete beta function.
+
+    See Also
+    --------
+    betainc : regularized incomplete beta function
+    betaincinv : inverse of the regularized incomplete beta function
+    betainccinv :
+        inverse of the complement of the regularized incomplete beta function
+    beta : beta function
+    scipy.stats.beta : beta distribution
+
+    Notes
+    -----
+    .. versionadded:: 1.11.0
+
+    Like `betainc`, ``betaincc(a, b, x)`` is treated as a two parameter
+    family of functions of a single variable `x`, rather than as a function of
+    three variables. See the `betainc` docstring for more info on how this
+    impacts limiting cases.
+
+    This function wraps the ``ibetac`` routine from the
+    Boost Math C++ library [2]_.
+
+    References
+    ----------
+    .. [1] NIST Digital Library of Mathematical Functions
+           https://dlmf.nist.gov/8.17
+    .. [2] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    Examples
+    --------
+    >>> from scipy.special import betaincc, betainc
+
+    The naive calculation ``1 - betainc(a, b, x)`` loses precision when
+    the values of ``betainc(a, b, x)`` are close to 1:
+
+    >>> 1 - betainc(0.5, 8, [0.9, 0.99, 0.999])
+    array([2.0574632e-09, 0.0000000e+00, 0.0000000e+00])
+
+    By using ``betaincc``, we get the correct values:
+
+    >>> betaincc(0.5, 8, [0.9, 0.99, 0.999])
+    array([2.05746321e-09, 1.97259354e-17, 1.96467954e-25])
+
+    """)
+
+add_newdoc(
+    "betaincinv",
+    r"""
+    betaincinv(a, b, y, out=None)
+
+    Inverse of the regularized incomplete beta function.
+
+    Computes :math:`x` such that:
+
+    .. math::
+
+        y = I_x(a, b) = \frac{\Gamma(a+b)}{\Gamma(a)\Gamma(b)}
+        \int_0^x t^{a-1}(1-t)^{b-1}dt,
+
+    where :math:`I_x` is the normalized incomplete beta function `betainc`
+    and :math:`\Gamma` is the `gamma` function [1]_.
+
+    Parameters
+    ----------
+    a, b : array_like
+        Positive, real-valued parameters
+    y : array_like
+        Real-valued input
+    out : ndarray, optional
+        Optional output array for function values
+
+    Returns
+    -------
+    scalar or ndarray
+        Value of the inverse of the regularized incomplete beta function
+
+    See Also
+    --------
+    betainc : regularized incomplete beta function
+    gamma : gamma function
+
+    Notes
+    -----
+    This function wraps the ``ibeta_inv`` routine from the
+    Boost Math C++ library [2]_.
+
+    References
+    ----------
+    .. [1] NIST Digital Library of Mathematical Functions
+           https://dlmf.nist.gov/8.17
+    .. [2] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    Examples
+    --------
+    >>> import scipy.special as sc
+
+    This function is the inverse of `betainc` for fixed
+    values of :math:`a` and :math:`b`.
+
+    >>> a, b = 1.2, 3.1
+    >>> y = sc.betainc(a, b, 0.2)
+    >>> sc.betaincinv(a, b, y)
+    0.2
+    >>>
+    >>> a, b = 7.5, 0.4
+    >>> x = sc.betaincinv(a, b, 0.5)
+    >>> sc.betainc(a, b, x)
+    0.5
+
+    """)
+
+
+add_newdoc(
+    "betainccinv",
+    r"""
+    betainccinv(a, b, y, out=None)
+
+    Inverse of the complemented regularized incomplete beta function.
+
+    Computes :math:`x` such that:
+
+    .. math::
+
+        y = 1 - I_x(a, b) = 1 - \frac{\Gamma(a+b)}{\Gamma(a)\Gamma(b)}
+        \int_0^x t^{a-1}(1-t)^{b-1}dt,
+
+    where :math:`I_x` is the normalized incomplete beta function `betainc`
+    and :math:`\Gamma` is the `gamma` function [1]_.
+
+    Parameters
+    ----------
+    a, b : array_like
+        Positive, real-valued parameters
+    y : array_like
+        Real-valued input
+    out : ndarray, optional
+        Optional output array for function values
+
+    Returns
+    -------
+    scalar or ndarray
+        Value of the inverse of the regularized incomplete beta function
+
+    See Also
+    --------
+    betainc : regularized incomplete beta function
+    betaincc : complement of the regularized incomplete beta function
+
+    Notes
+    -----
+    .. versionadded:: 1.11.0
+
+    This function wraps the ``ibetac_inv`` routine from the
+    Boost Math C++ library [2]_.
+
+    References
+    ----------
+    .. [1] NIST Digital Library of Mathematical Functions
+           https://dlmf.nist.gov/8.17
+    .. [2] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    Examples
+    --------
+    >>> from scipy.special import betainccinv, betaincc
+
+    This function is the inverse of `betaincc` for fixed
+    values of :math:`a` and :math:`b`.
+
+    >>> a, b = 1.2, 3.1
+    >>> y = betaincc(a, b, 0.2)
+    >>> betainccinv(a, b, y)
+    0.2
+
+    >>> a, b = 7, 2.5
+    >>> x = betainccinv(a, b, 0.875)
+    >>> betaincc(a, b, x)
+    0.875
+
+    """)
+
+add_newdoc("boxcox",
+    r"""
+    boxcox(x, lmbda, out=None)
+
+    Compute the Box-Cox transformation.
+
+    The Box-Cox transformation is
+
+    .. math::
+
+        y = \begin{cases}
+            (x^\lambda - 1) / \lambda & \text{if } \lambda \neq 0 \\
+            \log(x) & \text{if } \lambda = 0
+        \end{cases}
+
+    Returns ``nan`` if :math:`x < 0`.
+    Returns ``-inf`` if :math:`x = 0` and :math:`\lambda \leq 0`.
+
+    Parameters
+    ----------
+    x : array_like
+        Data to be transformed.
+    lmbda : array_like
+        Power parameter :math:`\lambda` of the Box-Cox transform.
+    out : ndarray, optional
+        Optional output array for the function values.
+
+    Returns
+    -------
+    y : scalar or ndarray
+        Transformed data.
+
+    See Also
+    --------
+    boxcox1p : Box-Cox transformation of ``1 + x``.
+    inv_boxcox : Inverse of the Box-Cox transformation.
+
+    Notes
+    -----
+
+    .. versionadded:: 0.14.0
+
+    Examples
+    --------
+    >>> from scipy.special import boxcox
+    >>> boxcox([1, 4, 10], 2.5)
+    array([   0.        ,   12.4       ,  126.09110641])
+    >>> boxcox(2, [0, 1, 2])
+    array([ 0.69314718,  1.        ,  1.5       ])
+    """)
+
+add_newdoc("boxcox1p",
+    r"""
+    boxcox1p(x, lmbda, out=None)
+
+    Compute the Box-Cox transformation of :math:`1 + x`.
+
+    The Box-Cox transformation computed by `boxcox1p` is
+
+    .. math::
+
+        y = \begin{cases}
+            ((1+x)^\lambda - 1) / \lambda & \text{if } \lambda \neq 0 \\
+            \log(1+x) & \text{if } \lambda = 0
+        \end{cases}
+
+    Returns ``nan`` if :math:`x < -1`.
+    Returns ``-inf`` if :math:`x = -1` and :math:`\lambda \leq 0`.
+
+    Parameters
+    ----------
+    x : array_like
+        Data to be transformed.
+    lmbda : array_like
+        Power parameter :math:`\lambda` of the Box-Cox transform.
+    out : ndarray, optional
+        Optional output array for the function values.
+
+    Returns
+    -------
+    y : scalar or ndarray
+        Transformed data.
+
+    See Also
+    --------
+    boxcox : Box-Cox transformation.
+    inv_boxcox1p : Inverse of the Box-Cox transformation of ``1 + x``.
+
+    Notes
+    -----
+
+    .. versionadded:: 0.14.0
+
+    Examples
+    --------
+    >>> from scipy.special import boxcox1p
+    >>> boxcox1p(1e-4, [0, 0.5, 1])
+    array([  9.99950003e-05,   9.99975001e-05,   1.00000000e-04])
+    >>> boxcox1p([0.01, 0.1], 0.25)
+    array([ 0.00996272,  0.09645476])
+    """)
+
+add_newdoc("inv_boxcox",
+    r"""
+    inv_boxcox(y, lmbda, out=None)
+
+    Compute the inverse of the Box-Cox transformation.
+
+    Find :math:`x` such that
+
+    .. math::
+
+        y = \begin{cases}
+            (x^\lambda - 1) / \lambda & \text{if } \lambda \neq 0 \\
+            \log(x) & \text{if } \lambda = 0
+        \end{cases}
+
+    Parameters
+    ----------
+    y : array_like
+        Transformed data (input to the inverse transform).
+    lmbda : array_like
+        Power parameter :math:`\lambda` of the Box-Cox transform.
+    out : ndarray, optional
+        Optional output array for the function values.
+
+    Returns
+    -------
+    x : scalar or ndarray
+        Original data (inverse Box-Cox transform of `y`).
+
+    See Also
+    --------
+    boxcox : Box-Cox transformation.
+    inv_boxcox1p : Inverse of the Box-Cox transformation of ``1 + x``.
+
+    Notes
+    -----
+
+    .. versionadded:: 0.16.0
+
+    Examples
+    --------
+    >>> from scipy.special import boxcox, inv_boxcox
+    >>> y = boxcox([1, 4, 10], 2.5)
+    >>> inv_boxcox(y, 2.5)
+    array([1., 4., 10.])
+    """)
+
+add_newdoc("inv_boxcox1p",
+    r"""
+    inv_boxcox1p(y, lmbda, out=None)
+
+    Compute the inverse of the Box-Cox transformation of :math:`1 + x`.
+
+    Find :math:`x` such that
+
+    .. math::
+
+        y = \begin{cases}
+            ((1+x)^\lambda - 1) / \lambda & \text{if } \lambda \neq 0 \\
+            \log(1+x) & \text{if } \lambda = 0
+        \end{cases}
+
+    Parameters
+    ----------
+    y : array_like
+        Transformed data (input to the inverse transform).
+    lmbda : array_like
+        Power parameter :math:`\lambda` of the Box-Cox transform.
+    out : ndarray, optional
+        Optional output array for the function values.
+
+    Returns
+    -------
+    x : scalar or ndarray
+        Original data (inverse Box-Cox transform of `y`).
+
+    See Also
+    --------
+    boxcox1p : Box-Cox transformation of ``1 + x``.
+    inv_boxcox : Inverse of the Box-Cox transformation.
+
+    Notes
+    -----
+
+    .. versionadded:: 0.16.0
+
+    Examples
+    --------
+    >>> from scipy.special import boxcox1p, inv_boxcox1p
+    >>> y = boxcox1p([1, 4, 10], 2.5)
+    >>> inv_boxcox1p(y, 2.5)
+    array([1., 4., 10.])
+    """)
+
+add_newdoc("chdtr",
+    r"""
+    chdtr(v, x, out=None)
+
+    Chi square cumulative distribution function.
+
+    Returns the area under the left tail (from 0 to `x`) of the Chi
+    square probability density function with `v` degrees of freedom:
+
+    .. math::
+
+        \frac{1}{2^{v/2} \Gamma(v/2)} \int_0^x t^{v/2 - 1} e^{-t/2} dt
+
+    Here :math:`\Gamma` is the Gamma function; see `gamma`. This
+    integral can be expressed in terms of the regularized lower
+    incomplete gamma function `gammainc` as
+    ``gammainc(v / 2, x / 2)``. [1]_
+
+    Parameters
+    ----------
+    v : array_like
+        Degrees of freedom.
+    x : array_like
+        Upper bound of the integral.
+    out : ndarray, optional
+        Optional output array for the function results.
+
+    Returns
+    -------
+    scalar or ndarray
+        Values of the cumulative distribution function.
+
+    See Also
+    --------
+    chdtrc, chdtri, chdtriv, gammainc
+
+    References
+    ----------
+    .. [1] Chi-Square distribution,
+        https://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import scipy.special as sc
+
+    It can be expressed in terms of the regularized lower incomplete
+    gamma function.
+
+    >>> v = 1
+    >>> x = np.arange(4)
+    >>> sc.chdtr(v, x)
+    array([0.        , 0.68268949, 0.84270079, 0.91673548])
+    >>> sc.gammainc(v / 2, x / 2)
+    array([0.        , 0.68268949, 0.84270079, 0.91673548])
+
+    """)
+
+add_newdoc("chdtrc",
+    r"""
+    chdtrc(v, x, out=None)
+
+    Chi square survival function.
+
+    Returns the area under the right hand tail (from `x` to infinity)
+    of the Chi square probability density function with `v` degrees of
+    freedom:
+
+    .. math::
+
+        \frac{1}{2^{v/2} \Gamma(v/2)} \int_x^\infty t^{v/2 - 1} e^{-t/2} dt
+
+    Here :math:`\Gamma` is the Gamma function; see `gamma`. This
+    integral can be expressed in terms of the regularized upper
+    incomplete gamma function `gammaincc` as
+    ``gammaincc(v / 2, x / 2)``. [1]_
+
+    Parameters
+    ----------
+    v : array_like
+        Degrees of freedom.
+    x : array_like
+        Lower bound of the integral.
+    out : ndarray, optional
+        Optional output array for the function results.
+
+    Returns
+    -------
+    scalar or ndarray
+        Values of the survival function.
+
+    See Also
+    --------
+    chdtr, chdtri, chdtriv, gammaincc
+
+    References
+    ----------
+    .. [1] Chi-Square distribution,
+        https://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import scipy.special as sc
+
+    It can be expressed in terms of the regularized upper incomplete
+    gamma function.
+
+    >>> v = 1
+    >>> x = np.arange(4)
+    >>> sc.chdtrc(v, x)
+    array([1.        , 0.31731051, 0.15729921, 0.08326452])
+    >>> sc.gammaincc(v / 2, x / 2)
+    array([1.        , 0.31731051, 0.15729921, 0.08326452])
+
+    """)
+
+add_newdoc("chdtri",
+    """
+    chdtri(v, p, out=None)
+
+    Inverse to `chdtrc` with respect to `x`.
+
+    Returns `x` such that ``chdtrc(v, x) == p``.
+
+    Parameters
+    ----------
+    v : array_like
+        Degrees of freedom.
+    p : array_like
+        Probability.
+    out : ndarray, optional
+        Optional output array for the function results.
+
+    Returns
+    -------
+    x : scalar or ndarray
+        Value so that the probability a Chi square random variable
+        with `v` degrees of freedom is greater than `x` equals `p`.
+
+    See Also
+    --------
+    chdtrc, chdtr, chdtriv
+
+    References
+    ----------
+    .. [1] Chi-Square distribution,
+        https://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm
+
+    Examples
+    --------
+    >>> import scipy.special as sc
+
+    It inverts `chdtrc`.
+
+    >>> v, p = 1, 0.3
+    >>> sc.chdtrc(v, sc.chdtri(v, p))
+    0.3
+    >>> x = 1
+    >>> sc.chdtri(v, sc.chdtrc(v, x))
+    1.0
+
+    """)
+
+add_newdoc("chdtriv",
+    """
+    chdtriv(p, x, out=None)
+
+    Inverse to `chdtr` with respect to `v`.
+
+    Returns `v` such that ``chdtr(v, x) == p``.
+
+    Parameters
+    ----------
+    p : array_like
+        Probability that the Chi square random variable is less than
+        or equal to `x`.
+    x : array_like
+        Nonnegative input.
+    out : ndarray, optional
+        Optional output array for the function results.
+
+    Returns
+    -------
+    scalar or ndarray
+        Degrees of freedom.
+
+    See Also
+    --------
+    chdtr, chdtrc, chdtri
+
+    Notes
+    -----
+    This function wraps routines from the Boost Math C++ library [1]_.
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+    .. [2] Chi-Square distribution,
+        https://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm
+
+    Examples
+    --------
+    >>> import scipy.special as sc
+
+    It inverts `chdtr`.
+
+    >>> p, x = 0.5, 1
+    >>> sc.chdtr(sc.chdtriv(p, x), x)
+    0.5000000000000003
+    >>> v = 1
+    >>> sc.chdtriv(sc.chdtr(v, x), x)
+    1.0
+
+    """)
+
+add_newdoc("chndtr",
+    r"""
+    chndtr(x, df, nc, out=None)
+
+    Non-central chi-squared cumulative distribution function.
+
+    The cumulative distribution function is given by
+
+    .. math::
+
+        F_{\nu,\lambda}(x)
+        = \sum_{j=0}^{\infty}
+          e^{-\lambda / 2}
+          \frac{(\lambda / 2)^j}{j!}
+          F_{\chi^2_{\nu + 2j}}(x),
+
+    where :math:`\nu > 0` is the degrees of freedom (``df``), :math:`\lambda \geq 0`
+    is the non-centrality parameter (``nc``), and :math:`F_{\chi^2_{\nu + 2j}}` is the
+    CDF of the central chi-squared distribution with :math:`\nu + 2j` degrees of
+    freedom.
+
+    Parameters
+    ----------
+    x : array_like
+        Upper bound of the integral; must satisfy ``x >= 0``.
+    df : array_like
+        Degrees of freedom; must satisfy ``df > 0``.
+    nc : array_like
+        Non-centrality parameter; must satisfy ``nc >= 0``.
+    out : ndarray, optional
+        Optional output array for the function results.
+
+    Returns
+    -------
+    cdf : scalar or ndarray
+        Value of the non-central chi-squared cumulative distribution function.
+
+    See Also
+    --------
+    chndtrix: Noncentral Chi Squared distribution quantile
+    chndtridf: Inverse of `chndtr` with respect to `df`
+    chndtrinc: Inverse of `chndtr` with respect to `nc`
+    scipy.stats.ncx2: Non-central chi-squared distribution
+
+    Notes
+    -----
+    The noncentral chi squared distribution is also available in
+    `scipy.stats.ncx2`. ``scipy.stats.ncx2.cdf`` is equivalent to `chndtr`.
+
+    This function wraps routines from the Boost Math C++ library [1]_.
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import scipy.special as sc
+
+    Compute the noncentral chi squared distribution CDF at one point.
+
+    >>> x = 4.0
+    >>> df = 1.0
+    >>> nc = 5.0
+    >>> sc.chndtr(x, df, nc)
+    0.40667858759710945
+
+    Plot the noncentral chi squared distribution CDF for different parameters.
+
+    >>> import matplotlib.pyplot as plt
+    >>> x = np.linspace(0, 40, 1000)
+    >>> plt.plot(x, sc.chndtr(x, 1, 5), label=r"$df=1,\ nc=5$")
+    >>> plt.plot(x, sc.chndtr(x, 5, 10), label=r"$df=5,\ nc=10$")
+    >>> plt.legend()
+    >>> plt.show()
+
+    """)
+
+add_newdoc("chndtrix",
+    """
+    chndtrix(p, df, nc, out=None)
+
+    Inverse to `chndtr` vs `x`.
+
+    Calculated using a search to find a value for `x` that produces the
+    desired value of `p`.
+
+    Parameters
+    ----------
+    p : array_like
+        Probability; must satisfy ``0 <= p < 1``
+    df : array_like
+        Degrees of freedom; must satisfy ``df > 0``
+    nc : array_like
+        Non-centrality parameter; must satisfy ``nc >= 0``
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    x : scalar or ndarray
+        Value so that the probability a non-central Chi square random variable
+        with `df` degrees of freedom and non-centrality, `nc`, is greater than
+        `x` equals `p`.
+
+    See Also
+    --------
+    chndtr : Noncentral chi-squared distribution CDF
+    chndtridf : inverse of `chndtr` with respect to `cdf`
+    chndtrinc : inverse of `chndtr` with respect to `nc`
+    scipy.stats.ncx2 : Non-central chi-squared distribution
+
+    Notes
+    -----
+    The noncentral chi squared distribution is also available in
+    `scipy.stats.ncx2`. ``scipy.stats.ncx2.ppf`` is equivalent to `chndtrix`.
+
+    This function wraps routines from the Boost Math C++ library [1]_.
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    Examples
+    --------
+    >>> from scipy.special import chndtrix, chndtr
+
+    Compute the noncentral chi squared distribution CDF at one point.
+    >>> x, df, nc = 3, 5, 10
+    >>> p = chndtr(x, df, nc)
+
+    `chndtrix` is the inverse of `chndtr` with respect to `x`:
+
+    >>> chndtrix(p, df, nc)
+    3.0
+
+    """)
+
+add_newdoc("chndtridf",
+    """
+    chndtridf(x, p, nc, out=None)
+
+    Inverse to `chndtr` vs `df`.
+
+    Calculated using a search to find a value for `df` that produces the
+    desired value of `p`.
+
+    Parameters
+    ----------
+    x : array_like
+        Upper bound of the integral; must satisfy ``x >= 0``
+    p : array_like
+        Probability; must satisfy ``0 <= p < 1``
+    nc : array_like
+        Non-centrality parameter; must satisfy ``nc >= 0``
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    df : scalar or ndarray
+        Degrees of freedom
+
+    See Also
+    --------
+    chndtr : Noncentral chi-squared distribution CDF
+    chndtrix : inverse of `chndtr` with respect to `x`
+    chndtrinc : inverse of `chndtr` with respect to `nc`
+    scipy.stats.ncx2 : Non-central chi-squared distribution
+
+    Notes
+    -----
+    The noncentral chi squared distribution is also available in
+    `scipy.stats.ncx2`.
+
+    This function wraps routines from the Boost Math C++ library [1]_.
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    Examples
+    --------
+    >>> from scipy.special import chndtridf, chndtr
+
+    Compute the noncentral chi squared distribution CDF at one point.
+
+    >>> x, df, nc = 3, 5, 10
+    >>> p = chndtr(x, df, nc)
+
+    `chndtridf` is the inverse of `chndtr` with respect to `df`:
+
+    >>> chndtridf(x, p, nc)
+    5.0
+
+    """)
+
+add_newdoc("chndtrinc",
+    """
+    chndtrinc(x, df, p, out=None)
+
+    Inverse of `chndtr` with respect to `nc`.
+
+    Finds the non-centrality parameter `nc` such that
+
+    .. math::
+
+        \\operatorname{chndtr}(x, df, nc) = p.
+
+    Parameters
+    ----------
+    x : array_like
+        Upper bound of the integral; must satisfy ``x >= 0``.
+    df : array_like
+        Degrees of freedom; must satisfy ``df > 0``.
+    p : array_like
+        Probability; must satisfy ``0 <= p < 1``.
+    out : ndarray, optional
+        Optional output array for the function results.
+
+    Returns
+    -------
+    nc : scalar or ndarray
+        Non-centrality parameter.
+
+    See Also
+    --------
+    chndtr : Noncentral chi-squared distribution CDF
+    chndtridf : Inverse of `chndtr` with respect to `df`
+    chndtrinc : Inverse of `chndtr` with respect to `nc`
+    scipy.stats.ncx2 : Non-central chi-squared distribution
+
+    Notes
+    -----
+    The noncentral chi squared distribution is also available in
+    `scipy.stats.ncx2`.
+
+    This function wraps routines from the Boost Math C++ library [1]_.
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    Examples
+    --------
+    >>> from scipy.special import chndtrinc, chndtr
+
+    Compute the noncentral chi squared distribution CDF at one point.
+
+    >>> x, df, nc = 3, 5, 10
+    >>> p = chndtr(x, df, nc)
+
+    `chndtrinc` is the inverse of `chndtr` with respect to `nc`:
+
+    >>> chndtrinc(x, df, p)
+    10.0
+
+    """)
+
+add_newdoc(
+    "elliprc",
+    r"""
+    elliprc(x, y, out=None)
+
+    Degenerate symmetric elliptic integral.
+
+    The function RC is defined as [1]_
+
+    .. math::
+
+        R_{\mathrm{C}}(x, y) =
+           \frac{1}{2} \int_0^{+\infty} (t + x)^{-1/2} (t + y)^{-1} dt
+           = R_{\mathrm{F}}(x, y, y)
+
+    Parameters
+    ----------
+    x, y : array_like
+        Real or complex input parameters. `x` can be any number in the
+        complex plane cut along the negative real axis. `y` must be non-zero.
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    R : scalar or ndarray
+        Value of the integral. If `y` is real and negative, the Cauchy
+        principal value is returned. If both of `x` and `y` are real, the
+        return value is real. Otherwise, the return value is complex.
+
+    See Also
+    --------
+    elliprf : Completely-symmetric elliptic integral of the first kind.
+    elliprd : Symmetric elliptic integral of the second kind.
+    elliprg : Completely-symmetric elliptic integral of the second kind.
+    elliprj : Symmetric elliptic integral of the third kind.
+
+    Notes
+    -----
+    RC is a degenerate case of the symmetric integral RF: ``elliprc(x, y) ==
+    elliprf(x, y, y)``. It is an elementary function rather than an elliptic
+    integral.
+
+    The code implements Carlson's algorithm based on the duplication theorems
+    and series expansion up to the 7th order. [2]_
+
+    .. versionadded:: 1.8.0
+
+    References
+    ----------
+    .. [1] B. C. Carlson, ed., Chapter 19 in "Digital Library of Mathematical
+           Functions," NIST, US Dept. of Commerce.
+           https://dlmf.nist.gov/19.16.E6
+    .. [2] B. C. Carlson, "Numerical computation of real or complex elliptic
+           integrals," Numer. Algorithm, vol. 10, no. 1, pp. 13-26, 1995.
+           :doi:`10.1007/BF02198293`. https://arxiv.org/abs/math/9409227
+
+    Examples
+    --------
+    Basic homogeneity property:
+
+    >>> import numpy as np
+    >>> from scipy.special import elliprc
+
+    >>> x = 1.2 + 3.4j
+    >>> y = 5.
+    >>> scale = 0.3 + 0.4j
+    >>> elliprc(scale*x, scale*y)
+    (0.5484493976710874-0.4169557678995833j)
+
+    >>> elliprc(x, y)/np.sqrt(scale)
+    (0.5484493976710874-0.41695576789958333j)
+
+    When the two arguments coincide, the integral is particularly
+    simple:
+
+    >>> x = 1.2 + 3.4j
+    >>> elliprc(x, x)
+    (0.4299173120614631-0.3041729818745595j)
+
+    >>> 1/np.sqrt(x)
+    (0.4299173120614631-0.30417298187455954j)
+
+    Another simple case: the first argument vanishes:
+
+    >>> y = 1.2 + 3.4j
+    >>> elliprc(0, y)
+    (0.6753125346116815-0.47779380263880866j)
+
+    >>> np.pi/2/np.sqrt(y)
+    (0.6753125346116815-0.4777938026388088j)
+
+    When `x` and `y` are both positive, we can express
+    :math:`R_C(x,y)` in terms of more elementary functions.  For the
+    case :math:`0 \le x < y`,
+
+    >>> x = 3.2
+    >>> y = 6.
+    >>> elliprc(x, y)
+    0.44942991498453444
+
+    >>> np.arctan(np.sqrt((y-x)/x))/np.sqrt(y-x)
+    0.44942991498453433
+
+    And for the case :math:`0 \le y < x`,
+
+    >>> x = 6.
+    >>> y = 3.2
+    >>> elliprc(x,y)
+    0.4989837501576147
+
+    >>> np.log((np.sqrt(x)+np.sqrt(x-y))/np.sqrt(y))/np.sqrt(x-y)
+    0.49898375015761476
+
+    """)
+
+add_newdoc(
+    "elliprd",
+    r"""
+    elliprd(x, y, z, out=None)
+
+    Symmetric elliptic integral of the second kind.
+
+    The function RD is defined as [1]_
+
+    .. math::
+
+        R_{\mathrm{D}}(x, y, z) =
+           \frac{3}{2} \int_0^{+\infty} [(t + x) (t + y)]^{-1/2} (t + z)^{-3/2}
+           dt
+
+    Parameters
+    ----------
+    x, y, z : array_like
+        Real or complex input parameters. `x` or `y` can be any number in the
+        complex plane cut along the negative real axis, but at most one of them
+        can be zero, while `z` must be non-zero.
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    R : scalar or ndarray
+        Value of the integral. If all of `x`, `y`, and `z` are real, the
+        return value is real. Otherwise, the return value is complex.
+
+    See Also
+    --------
+    elliprc : Degenerate symmetric elliptic integral.
+    elliprf : Completely-symmetric elliptic integral of the first kind.
+    elliprg : Completely-symmetric elliptic integral of the second kind.
+    elliprj : Symmetric elliptic integral of the third kind.
+
+    Notes
+    -----
+    RD is a degenerate case of the elliptic integral RJ: ``elliprd(x, y, z) ==
+    elliprj(x, y, z, z)``.
+
+    The code implements Carlson's algorithm based on the duplication theorems
+    and series expansion up to the 7th order. [2]_
+
+    .. versionadded:: 1.8.0
+
+    References
+    ----------
+    .. [1] B. C. Carlson, ed., Chapter 19 in "Digital Library of Mathematical
+           Functions," NIST, US Dept. of Commerce.
+           https://dlmf.nist.gov/19.16.E5
+    .. [2] B. C. Carlson, "Numerical computation of real or complex elliptic
+           integrals," Numer. Algorithm, vol. 10, no. 1, pp. 13-26, 1995.
+           :doi:`10.1007/BF02198293`. https://arxiv.org/abs/math/9409227
+
+    Examples
+    --------
+    Basic homogeneity property:
+
+    >>> import numpy as np
+    >>> from scipy.special import elliprd
+
+    >>> x = 1.2 + 3.4j
+    >>> y = 5.
+    >>> z = 6.
+    >>> scale = 0.3 + 0.4j
+    >>> elliprd(scale*x, scale*y, scale*z)
+    (-0.03703043835680379-0.24500934665683802j)
+
+    >>> elliprd(x, y, z)*np.power(scale, -1.5)
+    (-0.0370304383568038-0.24500934665683805j)
+
+    All three arguments coincide:
+
+    >>> x = 1.2 + 3.4j
+    >>> elliprd(x, x, x)
+    (-0.03986825876151896-0.14051741840449586j)
+
+    >>> np.power(x, -1.5)
+    (-0.03986825876151894-0.14051741840449583j)
+
+    The so-called "second lemniscate constant":
+
+    >>> elliprd(0, 2, 1)/3
+    0.5990701173677961
+
+    >>> from scipy.special import gamma
+    >>> gamma(0.75)**2/np.sqrt(2*np.pi)
+    0.5990701173677959
+
+    """)
+
+add_newdoc(
+    "elliprf",
+    r"""
+    elliprf(x, y, z, out=None)
+
+    Completely-symmetric elliptic integral of the first kind.
+
+    The function RF is defined as [1]_
+
+    .. math::
+
+        R_{\mathrm{F}}(x, y, z) =
+           \frac{1}{2} \int_0^{+\infty} [(t + x) (t + y) (t + z)]^{-1/2} dt
+
+    Parameters
+    ----------
+    x, y, z : array_like
+        Real or complex input parameters. `x`, `y`, or `z` can be any number in
+        the complex plane cut along the negative real axis, but at most one of
+        them can be zero.
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    R : scalar or ndarray
+        Value of the integral. If all of `x`, `y`, and `z` are real, the return
+        value is real. Otherwise, the return value is complex.
+
+    See Also
+    --------
+    elliprc : Degenerate symmetric integral.
+    elliprd : Symmetric elliptic integral of the second kind.
+    elliprg : Completely-symmetric elliptic integral of the second kind.
+    elliprj : Symmetric elliptic integral of the third kind.
+
+    Notes
+    -----
+    The code implements Carlson's algorithm based on the duplication theorems
+    and series expansion up to the 7th order (cf.:
+    https://dlmf.nist.gov/19.36.i) and the AGM algorithm for the complete
+    integral. [2]_
+
+    .. versionadded:: 1.8.0
+
+    References
+    ----------
+    .. [1] B. C. Carlson, ed., Chapter 19 in "Digital Library of Mathematical
+           Functions," NIST, US Dept. of Commerce.
+           https://dlmf.nist.gov/19.16.E1
+    .. [2] B. C. Carlson, "Numerical computation of real or complex elliptic
+           integrals," Numer. Algorithm, vol. 10, no. 1, pp. 13-26, 1995.
+           :doi:`10.1007/BF02198293`. https://arxiv.org/abs/math/9409227
+
+    Examples
+    --------
+    Basic homogeneity property:
+
+    >>> import numpy as np
+    >>> from scipy.special import elliprf
+
+    >>> x = 1.2 + 3.4j
+    >>> y = 5.
+    >>> z = 6.
+    >>> scale = 0.3 + 0.4j
+    >>> elliprf(scale*x, scale*y, scale*z)
+    (0.5328051227278146-0.4008623567957094j)
+
+    >>> elliprf(x, y, z)/np.sqrt(scale)
+    (0.5328051227278147-0.4008623567957095j)
+
+    All three arguments coincide:
+
+    >>> x = 1.2 + 3.4j
+    >>> elliprf(x, x, x)
+    (0.42991731206146316-0.30417298187455954j)
+
+    >>> 1/np.sqrt(x)
+    (0.4299173120614631-0.30417298187455954j)
+
+    The so-called "first lemniscate constant":
+
+    >>> elliprf(0, 1, 2)
+    1.3110287771460598
+
+    >>> from scipy.special import gamma
+    >>> gamma(0.25)**2/(4*np.sqrt(2*np.pi))
+    1.3110287771460598
+
+    """)
+
+add_newdoc(
+    "elliprg",
+    r"""
+    elliprg(x, y, z, out=None)
+
+    Completely-symmetric elliptic integral of the second kind.
+
+    The function RG is defined as [1]_
+
+    .. math::
+
+        R_{\mathrm{G}}(x, y, z) =
+           \frac{1}{4} \int_0^{+\infty} [(t + x) (t + y) (t + z)]^{-1/2}
+           \left(\frac{x}{t + x} + \frac{y}{t + y} + \frac{z}{t + z}\right) t
+           dt
+
+    Parameters
+    ----------
+    x, y, z : array_like
+        Real or complex input parameters. `x`, `y`, or `z` can be any number in
+        the complex plane cut along the negative real axis.
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    R : scalar or ndarray
+        Value of the integral. If all of `x`, `y`, and `z` are real, the return
+        value is real. Otherwise, the return value is complex.
+
+    See Also
+    --------
+    elliprc : Degenerate symmetric integral.
+    elliprd : Symmetric elliptic integral of the second kind.
+    elliprf : Completely-symmetric elliptic integral of the first kind.
+    elliprj : Symmetric elliptic integral of the third kind.
+
+    Notes
+    -----
+    The implementation uses the relation [1]_
+
+    .. math::
+
+        2 R_{\mathrm{G}}(x, y, z) =
+           z R_{\mathrm{F}}(x, y, z) -
+           \frac{1}{3} (x - z) (y - z) R_{\mathrm{D}}(x, y, z) +
+           \sqrt{\frac{x y}{z}}
+
+    and the symmetry of `x`, `y`, `z` when at least one non-zero parameter can
+    be chosen as the pivot. When one of the arguments is close to zero, the AGM
+    method is applied instead. Other special cases are computed following Ref.
+    [2]_
+
+    .. versionadded:: 1.8.0
+
+    References
+    ----------
+    .. [1] B. C. Carlson, "Numerical computation of real or complex elliptic
+           integrals," Numer. Algorithm, vol. 10, no. 1, pp. 13-26, 1995.
+           :doi:`10.1007/BF02198293`. https://arxiv.org/abs/math/9409227
+    .. [2] B. C. Carlson, ed., Chapter 19 in "Digital Library of Mathematical
+           Functions," NIST, US Dept. of Commerce.
+           https://dlmf.nist.gov/19.16.E1
+           https://dlmf.nist.gov/19.20.ii
+
+    Examples
+    --------
+    Basic homogeneity property:
+
+    >>> import numpy as np
+    >>> from scipy.special import elliprg
+
+    >>> x = 1.2 + 3.4j
+    >>> y = 5.
+    >>> z = 6.
+    >>> scale = 0.3 + 0.4j
+    >>> elliprg(scale*x, scale*y, scale*z)
+    (1.195936862005246+0.8470988320464167j)
+
+    >>> elliprg(x, y, z)*np.sqrt(scale)
+    (1.195936862005246+0.8470988320464165j)
+
+    Simplifications:
+
+    >>> elliprg(0, y, y)
+    1.756203682760182
+
+    >>> 0.25*np.pi*np.sqrt(y)
+    1.7562036827601817
+
+    >>> elliprg(0, 0, z)
+    1.224744871391589
+
+    >>> 0.5*np.sqrt(z)
+    1.224744871391589
+
+    The surface area of a triaxial ellipsoid with semiaxes ``a``, ``b``, and
+    ``c`` is given by
+
+    .. math::
+
+        S = 4 \pi a b c R_{\mathrm{G}}(1 / a^2, 1 / b^2, 1 / c^2).
+
+    >>> def ellipsoid_area(a, b, c):
+    ...     r = 4.0 * np.pi * a * b * c
+    ...     return r * elliprg(1.0 / (a * a), 1.0 / (b * b), 1.0 / (c * c))
+    >>> print(ellipsoid_area(1, 3, 5))
+    108.62688289491807
+    """)
+
+add_newdoc(
+    "elliprj",
+    r"""
+    elliprj(x, y, z, p, out=None)
+
+    Symmetric elliptic integral of the third kind.
+
+    The function RJ is defined as [1]_
+
+    .. math::
+
+        R_{\mathrm{J}}(x, y, z, p) =
+           \frac{3}{2} \int_0^{+\infty} [(t + x) (t + y) (t + z)]^{-1/2}
+           (t + p)^{-1} dt
+
+    .. warning::
+        This function should be considered experimental when the inputs are
+        unbalanced.  Check correctness with another independent implementation.
+
+    Parameters
+    ----------
+    x, y, z, p : array_like
+        Real or complex input parameters. `x`, `y`, or `z` are numbers in
+        the complex plane cut along the negative real axis (subject to further
+        constraints, see Notes), and at most one of them can be zero. `p` must
+        be non-zero.
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    R : scalar or ndarray
+        Value of the integral. If all of `x`, `y`, `z`, and `p` are real, the
+        return value is real. Otherwise, the return value is complex.
+
+        If `p` is real and negative, while `x`, `y`, and `z` are real,
+        non-negative, and at most one of them is zero, the Cauchy principal
+        value is returned. [1]_ [2]_
+
+    See Also
+    --------
+    elliprc : Degenerate symmetric integral.
+    elliprd : Symmetric elliptic integral of the second kind.
+    elliprf : Completely-symmetric elliptic integral of the first kind.
+    elliprg : Completely-symmetric elliptic integral of the second kind.
+
+    Notes
+    -----
+    The code implements Carlson's algorithm based on the duplication theorems
+    and series expansion up to the 7th order. [3]_ The algorithm is slightly
+    different from its earlier incarnation as it appears in [1]_, in that the
+    call to `elliprc` (or ``atan``/``atanh``, see [4]_) is no longer needed in
+    the inner loop. Asymptotic approximations are used where arguments differ
+    widely in the order of magnitude. [5]_
+
+    The input values are subject to certain sufficient but not necessary
+    constraints when input arguments are complex. Notably, ``x``, ``y``, and
+    ``z`` must have non-negative real parts, unless two of them are
+    non-negative and complex-conjugates to each other while the other is a real
+    non-negative number. [1]_ If the inputs do not satisfy the sufficient
+    condition described in Ref. [1]_ they are rejected outright with the output
+    set to NaN.
+
+    In the case where one of ``x``, ``y``, and ``z`` is equal to ``p``, the
+    function ``elliprd`` should be preferred because of its less restrictive
+    domain.
+
+    .. versionadded:: 1.8.0
+
+    References
+    ----------
+    .. [1] B. C. Carlson, "Numerical computation of real or complex elliptic
+           integrals," Numer. Algorithm, vol. 10, no. 1, pp. 13-26, 1995.
+           :doi:`10.1007/BF02198293`. https://arxiv.org/abs/math/9409227
+    .. [2] B. C. Carlson, ed., Chapter 19 in "Digital Library of Mathematical
+           Functions," NIST, US Dept. of Commerce.
+           https://dlmf.nist.gov/19.20.iii
+    .. [3] B. C. Carlson, J. FitzSimmons, "Reduction Theorems for Elliptic
+           Integrands with the Square Root of Two Quadratic Factors," J.
+           Comput. Appl. Math., vol. 118, nos. 1-2, pp. 71-85, 2000.
+           :doi:`10.1016/S0377-0427(00)00282-X`.
+    .. [4] F. Johansson, "Numerical Evaluation of Elliptic Functions, Elliptic
+           Integrals and Modular Forms," in J. Blumlein, C. Schneider, P.
+           Paule, eds., "Elliptic Integrals, Elliptic Functions and Modular
+           Forms in Quantum Field Theory," pp. 269-293, 2019 (Cham,
+           Switzerland: Springer Nature Switzerland).
+           :doi:`10.1007/978-3-030-04480-0`. https://arxiv.org/abs/1806.06725
+    .. [5] B. C. Carlson, J. L. Gustafson, "Asymptotic Approximations for
+           Symmetric Elliptic Integrals," SIAM J. Math. Anls., vol. 25, no. 2,
+           pp. 288-303, 1994. :doi:`10.1137/S0036141092228477`.
+           https://arxiv.org/abs/math/9310223
+
+    Examples
+    --------
+    Basic homogeneity property:
+
+    >>> import numpy as np
+    >>> from scipy.special import elliprj
+
+    >>> x = 1.2 + 3.4j
+    >>> y = 5.
+    >>> z = 6.
+    >>> p = 7.
+    >>> scale = 0.3 - 0.4j
+    >>> elliprj(scale*x, scale*y, scale*z, scale*p)
+    (0.10834905565679157+0.19694950747103812j)
+
+    >>> elliprj(x, y, z, p)*np.power(scale, -1.5)
+    (0.10834905565679556+0.19694950747103854j)
+
+    Reduction to simpler elliptic integral:
+
+    >>> elliprj(x, y, z, z)
+    (0.08288462362195129-0.028376809745123258j)
+
+    >>> from scipy.special import elliprd
+    >>> elliprd(x, y, z)
+    (0.08288462362195136-0.028376809745123296j)
+
+    All arguments coincide:
+
+    >>> elliprj(x, x, x, x)
+    (-0.03986825876151896-0.14051741840449586j)
+
+    >>> np.power(x, -1.5)
+    (-0.03986825876151894-0.14051741840449583j)
+
+    """)
+
+add_newdoc("entr",
+    r"""
+    entr(x, out=None)
+
+    Elementwise function for computing entropy.
+
+    .. math:: \text{entr}(x) = \begin{cases} - x \log(x) & x > 0  \\ 0 & x = 0
+              \\ -\infty & \text{otherwise} \end{cases}
+
+    Parameters
+    ----------
+    x : ndarray
+        Input array.
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    res : scalar or ndarray
+        The value of the elementwise entropy function at the given points `x`.
+
+    See Also
+    --------
+    kl_div, rel_entr, scipy.stats.entropy
+
+    Notes
+    -----
+    .. versionadded:: 0.15.0
+
+    This function is concave.
+
+    The origin of this function is in convex programming; see [1]_.
+    Given a probability distribution :math:`p_1, \ldots, p_n`,
+    the definition of entropy in the context of *information theory* is
+
+    .. math::
+
+        \sum_{i = 1}^n \mathrm{entr}(p_i).
+
+    To compute the latter quantity, use `scipy.stats.entropy`.
+
+    References
+    ----------
+    .. [1] Boyd, Stephen and Lieven Vandenberghe. *Convex optimization*.
+           Cambridge University Press, 2004.
+           :doi:`10.1017/CBO9780511804441`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.special import entr
+
+    Calculate the entropy (in nats) of a 3-outcome probability distribution
+
+    >>> p = np.array([0.2, 0.5, 0.3])
+    >>> entr(p)
+    array([0.32188758, 0.34657359, 0.36119184])
+    >>> entr(p).sum()
+    1.0296530140645737
+
+    """)
+
+add_newdoc(
+    "erfinv",
+    """
+    erfinv(y, out=None)
+
+    Inverse of the error function.
+
+    Computes the inverse of the error function.
+
+    In the complex domain, there is no unique complex number w satisfying
+    erf(w)=z. This indicates a true inverse function would be multivalued.
+    When the domain restricts to the real, -1 < x < 1, there is a unique real
+    number satisfying erf(erfinv(x)) = x.
+
+    Parameters
+    ----------
+    y : ndarray
+        Argument at which to evaluate. Domain: [-1, 1]
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    erfinv : scalar or ndarray
+        The inverse of erf of y, element-wise
+
+    See Also
+    --------
+    erf : Error function of a complex argument
+    erfc : Complementary error function, ``1 - erf(x)``
+    erfcinv : Inverse of the complementary error function
+
+    Notes
+    -----
+    This function wraps the ``erf_inv`` routine from the
+    Boost Math C++ library [1]_.
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.special import erfinv, erf
+
+    >>> erfinv(0.5)
+    0.4769362762044699
+
+    >>> y = np.linspace(-1.0, 1.0, num=9)
+    >>> x = erfinv(y)
+    >>> x
+    array([       -inf, -0.81341985, -0.47693628, -0.22531206,  0.        ,
+            0.22531206,  0.47693628,  0.81341985,         inf])
+
+    Verify that ``erf(erfinv(y))`` is ``y``.
+
+    >>> erf(x)
+    array([-1.  , -0.75, -0.5 , -0.25,  0.  ,  0.25,  0.5 ,  0.75,  1.  ])
+
+    Plot the function:
+
+    >>> y = np.linspace(-1, 1, 200)
+    >>> fig, ax = plt.subplots()
+    >>> ax.plot(y, erfinv(y))
+    >>> ax.grid(True)
+    >>> ax.set_xlabel('y')
+    >>> ax.set_title('erfinv(y)')
+    >>> plt.show()
+
+    """)
+
+add_newdoc(
+    "erfcinv",
+    """
+    erfcinv(y, out=None)
+
+    Inverse of the complementary error function.
+
+    Computes the inverse of the complementary error function.
+
+    In the complex domain, there is no unique complex number :math:`w` satisfying
+    :math:`\\operatorname{erfc}(w) = z`. This indicates a true inverse function
+    would be multivalued.
+    When the domain restricts to the real interval :math:`0 < x < 2`, there is
+    a unique real number satisfying
+
+    .. math::
+
+        \\operatorname{erfc}(\\operatorname{erfcinv}(x)) = x
+
+    It is related to the inverse of the error function by
+
+    .. math::
+
+        \\operatorname{erfcinv}(1 - x) = \\operatorname{erfinv}(x)
+
+    Parameters
+    ----------
+    y : ndarray
+        Argument at which to evaluate. Domain: :math:`[0, 2]`
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    erfcinv : scalar or ndarray
+        The inverse of :math:`\\operatorname{erfc}` of :math:`y`, element-wise
+
+    See Also
+    --------
+    erf : Error function
+    erfc : Complementary error function
+    erfinv : Inverse of the error function
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.special import erfcinv
+
+    >>> erfcinv(0.5)
+    0.4769362762044699
+
+    >>> y = np.linspace(0.0, 2.0, num=11)
+    >>> erfcinv(y)
+    array([        inf,  0.9061938 ,  0.59511608,  0.37080716,  0.17914345,
+           -0.        , -0.17914345, -0.37080716, -0.59511608, -0.9061938 ,
+                  -inf])
+
+    Plot the function:
+
+    >>> y = np.linspace(0, 2, 200)
+    >>> fig, ax = plt.subplots()
+    >>> ax.plot(y, erfcinv(y))
+    >>> ax.grid(True)
+    >>> ax.set_xlabel('y')
+    >>> ax.set_title('erfcinv(y)')
+    >>> plt.show()
+
+    """)
+
+add_newdoc("eval_jacobi",
+    r"""
+    eval_jacobi(n, alpha, beta, x, out=None)
+
+    Evaluate Jacobi polynomial at a point.
+
+    The Jacobi polynomials can be defined via the Gauss hypergeometric
+    function :math:`{}_2F_1` as
+
+    .. math::
+
+        P_n^{(\alpha, \beta)}(x) = \frac{(\alpha + 1)_n}{\Gamma(n + 1)}
+          {}_2F_1(-n, 1 + \alpha + \beta + n; \alpha + 1; (1 - x)/2)
+
+    where :math:`(\cdot)_n` is the Pochhammer symbol; see `poch`. When
+    :math:`n` is an integer the result is a polynomial of degree
+    :math:`n`. See 22.5.42 in [AS]_ or [DLMF]_ for details.
+
+    Parameters
+    ----------
+    n : array_like
+        Degree of the polynomial. If not an integer the result is
+        determined via the relation to the Gauss hypergeometric
+        function.
+    alpha : array_like
+        Parameter.
+    beta : array_like
+        Parameter.
+    x : array_like
+        Points at which to evaluate the polynomial.
+    out : ndarray, optional
+        Optional output array for the function values.
+
+    Returns
+    -------
+    P : scalar or ndarray
+        Values of the Jacobi polynomial.
+
+    See Also
+    --------
+    roots_jacobi : roots and quadrature weights of Jacobi polynomials
+    jacobi : Jacobi polynomial object
+    hyp2f1 : Gauss hypergeometric function
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+    .. [DLMF] NIST Digital Library of Mathematical Functions,
+        https://dlmf.nist.gov/18.5.E7
+
+    """)
+
+add_newdoc("eval_sh_jacobi",
+    r"""
+    eval_sh_jacobi(n, p, q, x, out=None)
+
+    Evaluate shifted Jacobi polynomial at a point.
+
+    Defined by
+
+    .. math::
+
+        G_n^{(p, q)}(x)
+          = \binom{2n + p - 1}{n}^{-1} P_n^{(p - q, q - 1)}(2x - 1),
+
+    where :math:`P_n^{(\cdot, \cdot)}` is the n-th Jacobi polynomial.
+    See 22.5.2 in [AS]_ (or equivalently [DLMF]_)  for details.
+
+    Parameters
+    ----------
+    n : int
+        Degree of the polynomial. If not an integer, the result is
+        determined via the relation to `binom` and `eval_jacobi`.
+    p : float
+        Parameter
+    q : float
+        Parameter
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    G : scalar or ndarray
+        Values of the shifted Jacobi polynomial.
+
+    See Also
+    --------
+    roots_sh_jacobi : roots and quadrature weights of shifted Jacobi
+                      polynomials
+    sh_jacobi : shifted Jacobi polynomial object
+    eval_jacobi : evaluate Jacobi polynomials
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+    .. [DLMF] NIST Digital Library of Mathematical Functions,
+        https://dlmf.nist.gov/18.1.E2
+
+    """)
+
+add_newdoc("eval_gegenbauer",
+    r"""
+    eval_gegenbauer(n, alpha, x, out=None)
+
+    Evaluate Gegenbauer (ultraspherical) polynomial at a point.
+
+    The Gegenbauer polynomials can be defined via the Gauss
+    hypergeometric function :math:`{}_2F_1` as
+
+    .. math::
+
+        C_n^{(\alpha)}(x) = \frac{(2\alpha)_n}{\Gamma(n + 1)}
+          {}_2F_1(-n, 2\alpha + n; \alpha + 1/2; (1 - x)/2).
+
+    where :math:`(\cdot)_n` is the Pochhammer symbol; see `poch`. When
+    :math:`n` is an integer the result is a polynomial of degree
+    :math:`n`. See 22.5.46 in [AS]_ (or equivalently [DLMF]_) for details.
+
+    Parameters
+    ----------
+    n : array_like
+        Degree of the polynomial. If not an integer, the result is
+        determined via the relation to the Gauss hypergeometric
+        function.
+    alpha : array_like
+        Parameter.
+    x : array_like
+        Points at which to evaluate the Gegenbauer polynomial.
+    out : ndarray, optional
+        Optional output array for the function values.
+
+    Returns
+    -------
+    C : scalar or ndarray
+        Values of the Gegenbauer polynomial.
+
+    See Also
+    --------
+    roots_gegenbauer : roots and quadrature weights of Gegenbauer
+                       polynomials
+    gegenbauer : Gegenbauer polynomial object
+    hyp2f1 : Gauss hypergeometric function
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+    .. [DLMF] NIST Digital Library of Mathematical Functions,
+        https://dlmf.nist.gov/18.5.E9
+
+    """)
+
+add_newdoc("eval_chebyt",
+    r"""
+    eval_chebyt(n, x, out=None)
+
+    Evaluate Chebyshev polynomial of the first kind at a point.
+
+    The Chebyshev polynomials of the first kind can be defined via the
+    Gauss hypergeometric function :math:`{}_2F_1` as
+
+    .. math::
+
+        T_n(x) = {}_2F_1(n, -n; 1/2; (1 - x)/2).
+
+    When :math:`n` is an integer the result is a polynomial of degree
+    :math:`n`. See 22.5.47 in [AS]_ (or equivalently [DLMF]_) for details.
+
+    Parameters
+    ----------
+    n : array_like
+        Degree of the polynomial. If not an integer, the result is
+        determined via the relation to the Gauss hypergeometric
+        function.
+    x : array_like
+        Points at which to evaluate the Chebyshev polynomial
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    T : scalar or ndarray
+        Values of the Chebyshev polynomial
+
+    See Also
+    --------
+    roots_chebyt : roots and quadrature weights of Chebyshev
+                   polynomials of the first kind
+    chebyu : Chebychev polynomial object
+    eval_chebyu : evaluate Chebyshev polynomials of the second kind
+    hyp2f1 : Gauss hypergeometric function
+    numpy.polynomial.chebyshev.Chebyshev : Chebyshev series
+
+    Notes
+    -----
+    This routine is numerically stable for `x` in ``[-1, 1]`` at least
+    up to order ``10000``.
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+    .. [DLMF] NIST Digital Library of Mathematical Functions,
+        https://dlmf.nist.gov/18.5.E11_2
+
+    """)
+
+add_newdoc("eval_chebyu",
+    r"""
+    eval_chebyu(n, x, out=None)
+
+    Evaluate Chebyshev polynomial of the second kind at a point.
+
+    The Chebyshev polynomials of the second kind can be defined via
+    the Gauss hypergeometric function :math:`{}_2F_1` as
+
+    .. math::
+
+        U_n(x) = (n + 1) {}_2F_1(-n, n + 2; 3/2; (1 - x)/2).
+
+    When :math:`n` is an integer the result is a polynomial of degree
+    :math:`n`. See 22.5.48 in [AS]_ (or equivalently [DLMF]_) for details.
+
+    Parameters
+    ----------
+    n : array_like
+        Degree of the polynomial. If not an integer, the result is
+        determined via the relation to the Gauss hypergeometric
+        function.
+    x : array_like
+        Points at which to evaluate the Chebyshev polynomial
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    U : scalar or ndarray
+        Values of the Chebyshev polynomial
+
+    See Also
+    --------
+    roots_chebyu : roots and quadrature weights of Chebyshev
+                   polynomials of the second kind
+    chebyu : Chebyshev polynomial object
+    eval_chebyt : evaluate Chebyshev polynomials of the first kind
+    hyp2f1 : Gauss hypergeometric function
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+    .. [DLMF] NIST Digital Library of Mathematical Functions,
+        https://dlmf.nist.gov/18.5.E11_4
+
+    """)
+
+add_newdoc("eval_chebys",
+    r"""
+    eval_chebys(n, x, out=None)
+
+    Evaluate Chebyshev polynomial of the second kind on [-2, 2] at a
+    point.
+
+    These polynomials are defined as
+
+    .. math::
+
+        S_n(x) = U_n(x/2)
+
+    where :math:`U_n` is a Chebyshev polynomial of the second kind.
+    See 22.5.13 in [AS]_ (or equivalently [DLMF]_) for details.
+
+    Parameters
+    ----------
+    n : array_like
+        Degree of the polynomial. If not an integer, the result is
+        determined via the relation to `eval_chebyu`.
+    x : array_like
+        Points at which to evaluate the Chebyshev polynomial
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    S : scalar or ndarray
+        Values of the Chebyshev polynomial
+
+    See Also
+    --------
+    roots_chebys : roots and quadrature weights of Chebyshev
+                   polynomials of the second kind on [-2, 2]
+    chebys : Chebyshev polynomial object
+    eval_chebyu : evaluate Chebyshev polynomials of the second kind
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+    .. [DLMF] NIST Digital Library of Mathematical Functions,
+        https://dlmf.nist.gov/18.1.E3
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import scipy.special as sc
+
+    They are a scaled version of the Chebyshev polynomials of the
+    second kind.
+
+    >>> x = np.linspace(-2, 2, 6)
+    >>> sc.eval_chebys(3, x)
+    array([-4.   ,  0.672,  0.736, -0.736, -0.672,  4.   ])
+    >>> sc.eval_chebyu(3, x / 2)
+    array([-4.   ,  0.672,  0.736, -0.736, -0.672,  4.   ])
+
+    """)
+
+add_newdoc("eval_chebyc",
+    r"""
+    eval_chebyc(n, x, out=None)
+
+    Evaluate Chebyshev polynomial of the first kind on [-2, 2] at a
+    point.
+
+    These polynomials are defined as
+
+    .. math::
+
+        C_n(x) = 2 T_n(x/2)
+
+    where :math:`T_n` is a Chebyshev polynomial of the first kind. See
+    22.5.11 in [AS]_ (or equivalently [DLMF]_) for details.
+
+    Parameters
+    ----------
+    n : array_like
+        Degree of the polynomial. If not an integer, the result is
+        determined via the relation to `eval_chebyt`.
+    x : array_like
+        Points at which to evaluate the Chebyshev polynomial
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    C : scalar or ndarray
+        Values of the Chebyshev polynomial
+
+    See Also
+    --------
+    roots_chebyc : roots and quadrature weights of Chebyshev
+                   polynomials of the first kind on [-2, 2]
+    chebyc : Chebyshev polynomial object
+    numpy.polynomial.chebyshev.Chebyshev : Chebyshev series
+    eval_chebyt : evaluate Chebycshev polynomials of the first kind
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+    .. [DLMF] NIST Digital Library of Mathematical Functions,
+        https://dlmf.nist.gov/18.1.E3
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import scipy.special as sc
+
+    They are a scaled version of the Chebyshev polynomials of the
+    first kind.
+
+    >>> x = np.linspace(-2, 2, 6)
+    >>> sc.eval_chebyc(3, x)
+    array([-2.   ,  1.872,  1.136, -1.136, -1.872,  2.   ])
+    >>> 2 * sc.eval_chebyt(3, x / 2)
+    array([-2.   ,  1.872,  1.136, -1.136, -1.872,  2.   ])
+
+    """)
+
+add_newdoc("eval_sh_chebyt",
+    r"""
+    eval_sh_chebyt(n, x, out=None)
+
+    Evaluate shifted Chebyshev polynomial of the first kind at a
+    point.
+
+    These polynomials are defined as
+
+    .. math::
+
+        T_n^*(x) = T_n(2x - 1)
+
+    where :math:`T_n` is a Chebyshev polynomial of the first kind. See
+    22.5.14 in [AS]_ (or equivalently [DLMF]_) for details.
+
+    Parameters
+    ----------
+    n : array_like
+        Degree of the polynomial. If not an integer, the result is
+        determined via the relation to `eval_chebyt`.
+    x : array_like
+        Points at which to evaluate the shifted Chebyshev polynomial
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    T : scalar or ndarray
+        Values of the shifted Chebyshev polynomial
+
+    See Also
+    --------
+    roots_sh_chebyt : roots and quadrature weights of shifted
+                      Chebyshev polynomials of the first kind
+    sh_chebyt : shifted Chebyshev polynomial object
+    eval_chebyt : evaluate Chebyshev polynomials of the first kind
+    numpy.polynomial.chebyshev.Chebyshev : Chebyshev series
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+    .. [DLMF] NIST Digital Library of Mathematical Functions,
+        https://dlmf.nist.gov/18.7.E7
+
+    """)
+
+add_newdoc("eval_sh_chebyu",
+    r"""
+    eval_sh_chebyu(n, x, out=None)
+
+    Evaluate shifted Chebyshev polynomial of the second kind at a
+    point.
+
+    These polynomials are defined as
+
+    .. math::
+
+        U_n^*(x) = U_n(2x - 1)
+
+    where :math:`U_n` is a Chebyshev polynomial of the first kind. See
+    22.5.15 in [AS]_ (or equivalently [DLMF]_) for details.
+
+    Parameters
+    ----------
+    n : array_like
+        Degree of the polynomial. If not an integer, the result is
+        determined via the relation to `eval_chebyu`.
+    x : array_like
+        Points at which to evaluate the shifted Chebyshev polynomial
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    U : scalar or ndarray
+        Values of the shifted Chebyshev polynomial
+
+    See Also
+    --------
+    roots_sh_chebyu : roots and quadrature weights of shifted
+                      Chebychev polynomials of the second kind
+    sh_chebyu : shifted Chebyshev polynomial object
+    eval_chebyu : evaluate Chebyshev polynomials of the second kind
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+    .. [DLMF] NIST Digital Library of Mathematical Functions,
+        https://dlmf.nist.gov/18.7.E8
+
+    """)
+
+add_newdoc("eval_legendre",
+    r"""
+    eval_legendre(n, x, out=None)
+
+    Evaluate Legendre polynomial at a point.
+
+    The Legendre polynomials can be defined via the Gauss
+    hypergeometric function :math:`{}_2F_1` as
+
+    .. math::
+
+        P_n(x) = {}_2F_1(-n, n + 1; 1; (1 - x)/2).
+
+    When :math:`n` is an integer the result is a polynomial of degree
+    :math:`n`. See 22.5.49 in [AS]_ (or equivalently [DLMF]_) for details.
+
+    Parameters
+    ----------
+    n : array_like
+        Degree of the polynomial. If not an integer, the result is
+        determined via the relation to the Gauss hypergeometric
+        function.
+    x : array_like
+        Points at which to evaluate the Legendre polynomial
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    P : scalar or ndarray
+        Values of the Legendre polynomial
+
+    See Also
+    --------
+    roots_legendre : roots and quadrature weights of Legendre
+                     polynomials
+    legendre : Legendre polynomial object
+    hyp2f1 : Gauss hypergeometric function
+    numpy.polynomial.legendre.Legendre : Legendre series
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+    .. [DLMF] NIST Digital Library of Mathematical Functions,
+        https://dlmf.nist.gov/15.9.E7
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.special import eval_legendre
+
+    Evaluate the zero-order Legendre polynomial at x = 0
+
+    >>> eval_legendre(0, 0)
+    1.0
+
+    Evaluate the first-order Legendre polynomial between -1 and 1
+
+    >>> X = np.linspace(-1, 1, 5)  # Domain of Legendre polynomials
+    >>> eval_legendre(1, X)
+    array([-1. , -0.5,  0. ,  0.5,  1. ])
+
+    Evaluate Legendre polynomials of order 0 through 4 at x = 0
+
+    >>> N = range(0, 5)
+    >>> eval_legendre(N, 0)
+    array([ 1.   ,  0.   , -0.5  ,  0.   ,  0.375])
+
+    Plot Legendre polynomials of order 0 through 4
+
+    >>> X = np.linspace(-1, 1)
+
+    >>> import matplotlib.pyplot as plt
+    >>> for n in range(0, 5):
+    ...     y = eval_legendre(n, X)
+    ...     plt.plot(X, y, label=r'$P_{}(x)$'.format(n))
+
+    >>> plt.title("Legendre Polynomials")
+    >>> plt.xlabel("x")
+    >>> plt.ylabel(r'$P_n(x)$')
+    >>> plt.legend(loc='lower right')
+    >>> plt.show()
+
+    """)
+
+add_newdoc("eval_sh_legendre",
+    r"""
+    eval_sh_legendre(n, x, out=None)
+
+    Evaluate shifted Legendre polynomial at a point.
+
+    These polynomials are defined as
+
+    .. math::
+
+        P_n^*(x) = P_n(2x - 1)
+
+    where :math:`P_n` is a Legendre polynomial. See 2.2.11 in [AS]_
+    or [DLMF]_ for details.
+
+    Parameters
+    ----------
+    n : array_like
+        Degree of the polynomial. If not an integer, the value is
+        determined via the relation to `eval_legendre`.
+    x : array_like
+        Points at which to evaluate the shifted Legendre polynomial
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    P : scalar or ndarray
+        Values of the shifted Legendre polynomial
+
+    See Also
+    --------
+    roots_sh_legendre : roots and quadrature weights of shifted
+                        Legendre polynomials
+    sh_legendre : shifted Legendre polynomial object
+    eval_legendre : evaluate Legendre polynomials
+    numpy.polynomial.legendre.Legendre : Legendre series
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+    .. [DLMF] NIST Digital Library of Mathematical Functions,
+        https://dlmf.nist.gov/18.7.E10
+
+    """)
+
+add_newdoc("eval_genlaguerre",
+    r"""
+    eval_genlaguerre(n, alpha, x, out=None)
+
+    Evaluate generalized Laguerre polynomial at a point.
+
+    The generalized Laguerre polynomials can be defined via the
+    confluent hypergeometric function :math:`{}_1F_1` as
+
+    .. math::
+
+        L_n^{(\alpha)}(x) = \binom{n + \alpha}{n}
+          {}_1F_1(-n, \alpha + 1, x).
+
+    When :math:`n` is an integer the result is a polynomial of degree
+    :math:`n`. See 22.5.54 in [AS]_ or [DLMF]_ for details. The Laguerre
+    polynomials are the special case where :math:`\alpha = 0`.
+
+    Parameters
+    ----------
+    n : array_like
+        Degree of the polynomial. If not an integer, the result is
+        determined via the relation to the confluent hypergeometric
+        function.
+    alpha : array_like
+        Parameter; must have ``alpha > -1``
+    x : array_like
+        Points at which to evaluate the generalized Laguerre
+        polynomial
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    L : scalar or ndarray
+        Values of the generalized Laguerre polynomial
+
+    See Also
+    --------
+    roots_genlaguerre : roots and quadrature weights of generalized
+                        Laguerre polynomials
+    genlaguerre : generalized Laguerre polynomial object
+    hyp1f1 : confluent hypergeometric function
+    eval_laguerre : evaluate Laguerre polynomials
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+    .. [DLMF] NIST Digital Library of Mathematical Functions,
+        https://dlmf.nist.gov/18.5.E12
+
+    """)
+
+add_newdoc("eval_laguerre",
+    r"""
+    eval_laguerre(n, x, out=None)
+
+    Evaluate Laguerre polynomial at a point.
+
+    The Laguerre polynomials can be defined via the confluent
+    hypergeometric function :math:`{}_1F_1` as
+
+    .. math::
+
+        L_n(x) = {}_1F_1(-n, 1, x).
+
+    See 22.5.16 and 22.5.54 in [AS]_ (or equivalently [DLMF1]_ and [DLMF2]_)
+    for details. When :math:`n` is an integer the result is a polynomial
+    of degree :math:`n`.
+
+    Parameters
+    ----------
+    n : array_like
+        Degree of the polynomial. If not an integer the result is
+        determined via the relation to the confluent hypergeometric
+        function.
+    x : array_like
+        Points at which to evaluate the Laguerre polynomial
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    L : scalar or ndarray
+        Values of the Laguerre polynomial
+
+    See Also
+    --------
+    roots_laguerre : roots and quadrature weights of Laguerre
+                     polynomials
+    laguerre : Laguerre polynomial object
+    numpy.polynomial.laguerre.Laguerre : Laguerre series
+    eval_genlaguerre : evaluate generalized Laguerre polynomials
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+    .. [DLMF1] NIST Digital Library of Mathematical Functions,
+        https://dlmf.nist.gov/18.1#I1.ix7.p1
+    .. [DLMF2] NIST Digital Library of Mathematical Functions,
+        https://dlmf.nist.gov/18.5.E12
+
+     """)
+
+add_newdoc("eval_hermite",
+    r"""
+    eval_hermite(n, x, out=None)
+
+    Evaluate physicist's Hermite polynomial at a point.
+
+    Defined by
+
+    .. math::
+
+        H_n(x) = (-1)^n e^{x^2} \frac{d^n}{dx^n} e^{-x^2};
+
+    :math:`H_n` is a polynomial of degree :math:`n`. See 22.11.7 in
+    [AS]_ or [DLMF]_ for details.
+
+    Parameters
+    ----------
+    n : array_like
+        Degree of the polynomial
+    x : array_like
+        Points at which to evaluate the Hermite polynomial
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    H : scalar or ndarray
+        Values of the Hermite polynomial
+
+    See Also
+    --------
+    roots_hermite : roots and quadrature weights of physicist's
+                    Hermite polynomials
+    hermite : physicist's Hermite polynomial object
+    numpy.polynomial.hermite.Hermite : Physicist's Hermite series
+    eval_hermitenorm : evaluate Probabilist's Hermite polynomials
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+    .. [DLMF] NIST Digital Library of Mathematical Functions,
+        https://dlmf.nist.gov/18.5.T1
+
+    """)
+
+add_newdoc("eval_hermitenorm",
+    r"""
+    eval_hermitenorm(n, x, out=None)
+
+    Evaluate probabilist's (normalized) Hermite polynomial at a
+    point.
+
+    Defined by
+
+    .. math::
+
+        He_n(x) = (-1)^n e^{x^2/2} \frac{d^n}{dx^n} e^{-x^2/2};
+
+    :math:`He_n` is a polynomial of degree :math:`n`. See 22.11.8 in
+    [AS]_ or [DLMF]_ for details.
+
+    Parameters
+    ----------
+    n : array_like
+        Degree of the polynomial
+    x : array_like
+        Points at which to evaluate the Hermite polynomial
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    He : scalar or ndarray
+        Values of the Hermite polynomial
+
+    See Also
+    --------
+    roots_hermitenorm : roots and quadrature weights of probabilist's
+                        Hermite polynomials
+    hermitenorm : probabilist's Hermite polynomial object
+    numpy.polynomial.hermite_e.HermiteE : Probabilist's Hermite series
+    eval_hermite : evaluate physicist's Hermite polynomials
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+    .. [DLMF] NIST Digital Library of Mathematical Functions,
+        https://dlmf.nist.gov/18.5.T1
+
+    """)
+
+add_newdoc("expn",
+    r"""
+    expn(n, x, out=None)
+
+    Generalized exponential integral En.
+
+    For integer :math:`n \geq 0` and real :math:`x \geq 0` the
+    generalized exponential integral is defined as [DLMF]_
+
+    .. math::
+
+        E_n(x) = x^{n - 1} \int_x^\infty \frac{e^{-t}}{t^n} dt.
+
+    Parameters
+    ----------
+    n : array_like
+        Non-negative integers
+    x : array_like
+        Real argument
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    scalar or ndarray
+        Values of the generalized exponential integral
+
+    See Also
+    --------
+    exp1 : special case of :math:`E_n` for :math:`n = 1`
+    expi : related to :math:`E_n` when :math:`n = 1`
+
+    References
+    ----------
+    .. [DLMF] Digital Library of Mathematical Functions, 8.19.2
+              https://dlmf.nist.gov/8.19#E2
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import scipy.special as sc
+
+    Its domain is nonnegative n and x.
+
+    >>> sc.expn(-1, 1.0), sc.expn(1, -1.0)
+    (nan, nan)
+
+    It has a pole at ``x = 0`` for ``n = 1, 2``; for larger ``n`` it
+    is equal to ``1 / (n - 1)``.
+
+    >>> sc.expn([0, 1, 2, 3, 4], 0)
+    array([       inf,        inf, 1.        , 0.5       , 0.33333333])
+
+    For n equal to 0 it reduces to ``exp(-x) / x``.
+
+    >>> x = np.array([1, 2, 3, 4])
+    >>> sc.expn(0, x)
+    array([0.36787944, 0.06766764, 0.01659569, 0.00457891])
+    >>> np.exp(-x) / x
+    array([0.36787944, 0.06766764, 0.01659569, 0.00457891])
+
+    For n equal to 1 it reduces to `exp1`.
+
+    >>> sc.expn(1, x)
+    array([0.21938393, 0.04890051, 0.01304838, 0.00377935])
+    >>> sc.exp1(x)
+    array([0.21938393, 0.04890051, 0.01304838, 0.00377935])
+
+    """)
+
+add_newdoc("fdtr",
+    r"""
+    fdtr(dfn, dfd, x, out=None)
+
+    F cumulative distribution function.
+
+    Returns the value of the cumulative distribution function of the
+    F-distribution, also known as Snedecor's F-distribution or the
+    Fisher-Snedecor distribution.
+
+    The F-distribution with parameters :math:`d_n` and :math:`d_d` is the
+    distribution of the random variable,
+
+    .. math::
+        X = \frac{U_n/d_n}{U_d/d_d},
+
+    where :math:`U_n` and :math:`U_d` are random variables distributed
+    :math:`\chi^2`, with :math:`d_n` and :math:`d_d` degrees of freedom,
+    respectively.
+
+    Parameters
+    ----------
+    dfn : array_like
+        First parameter (positive float).
+    dfd : array_like
+        Second parameter (positive float).
+    x : array_like
+        Argument (nonnegative float).
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    y : scalar or ndarray
+        The CDF of the F-distribution with parameters `dfn` and `dfd` at `x`.
+
+    See Also
+    --------
+    fdtrc : F distribution survival function
+    fdtri : F distribution inverse cumulative distribution
+    scipy.stats.f : F distribution
+
+    Notes
+    -----
+    The regularized incomplete beta function is used, according to the
+    formula,
+
+    .. math::
+        F(d_n, d_d; x) = I_{xd_n/(d_d + xd_n)}(d_n/2, d_d/2).
+
+    Wrapper for a routine from the Boost Math C++ library [1]_. The
+    F distribution is also available as `scipy.stats.f`. Calling
+    `fdtr` directly can improve performance compared to the ``cdf``
+    method of `scipy.stats.f` (see last example below).
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+
+    Examples
+    --------
+    Calculate the function for ``dfn=1`` and ``dfd=2`` at ``x=1``.
+
+    >>> import numpy as np
+    >>> from scipy.special import fdtr
+    >>> fdtr(1, 2, 1)
+    0.5773502691896258
+
+    Calculate the function at several points by providing a NumPy array for
+    `x`.
+
+    >>> x = np.array([0.5, 2., 3.])
+    >>> fdtr(1, 2, x)
+    array([0.4472136 , 0.70710678, 0.77459667])
+
+    Plot the function for several parameter sets.
+
+    >>> import matplotlib.pyplot as plt
+    >>> dfn_parameters = [1, 5, 10, 50]
+    >>> dfd_parameters = [1, 1, 2, 3]
+    >>> linestyles = ['solid', 'dashed', 'dotted', 'dashdot']
+    >>> parameters_list = list(zip(dfn_parameters, dfd_parameters,
+    ...                            linestyles))
+    >>> x = np.linspace(0, 30, 1000)
+    >>> fig, ax = plt.subplots()
+    >>> for parameter_set in parameters_list:
+    ...     dfn, dfd, style = parameter_set
+    ...     fdtr_vals = fdtr(dfn, dfd, x)
+    ...     ax.plot(x, fdtr_vals, label=rf"$d_n={dfn},\, d_d={dfd}$",
+    ...             ls=style)
+    >>> ax.legend()
+    >>> ax.set_xlabel("$x$")
+    >>> ax.set_title("F distribution cumulative distribution function")
+    >>> plt.show()
+
+    The F distribution is also available as `scipy.stats.f`. Using `fdtr`
+    directly can be much faster than calling the ``cdf`` method of
+    `scipy.stats.f`, especially for small arrays or individual values.
+    To get the same results one must use the following parametrization:
+    ``stats.f(dfn, dfd).cdf(x)=fdtr(dfn, dfd, x)``.
+
+    >>> from scipy.stats import f
+    >>> dfn, dfd = 1, 2
+    >>> x = 1
+    >>> fdtr_res = fdtr(dfn, dfd, x)  # this will often be faster than below
+    >>> f_dist_res = f(dfn, dfd).cdf(x)
+    >>> fdtr_res == f_dist_res  # test that results are equal
+    True
+    """)
+
+add_newdoc("fdtrc",
+    r"""
+    fdtrc(dfn, dfd, x, out=None)
+
+    F survival function.
+
+    Returns the complemented F-distribution function (the integral of the
+    density from `x` to infinity).
+
+    Parameters
+    ----------
+    dfn : array_like
+        First parameter (positive float).
+    dfd : array_like
+        Second parameter (positive float).
+    x : array_like
+        Argument (nonnegative float).
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    y : scalar or ndarray
+        The complemented F-distribution function with parameters `dfn` and
+        `dfd` at `x`.
+
+    See Also
+    --------
+    fdtr : F distribution cumulative distribution function
+    fdtri : F distribution inverse cumulative distribution function
+    scipy.stats.f : F distribution
+
+    Notes
+    -----
+    The regularized incomplete beta function is used, according to the
+    formula,
+
+    .. math::
+        F(d_n, d_d; x) = I_{d_d/(d_d + xd_n)}(d_d/2, d_n/2).
+
+    Wrapper for a routine from the Boost Math C++ library [1]_. The
+    F distribution is also available as `scipy.stats.f`. Calling
+    `fdtrc` directly can improve performance compared to the ``sf``
+    method of `scipy.stats.f` (see last example below).
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    Examples
+    --------
+    Calculate the function for ``dfn=1`` and ``dfd=2`` at ``x=1``.
+
+    >>> import numpy as np
+    >>> from scipy.special import fdtrc
+    >>> fdtrc(1, 2, 1)
+    0.42264973081037427
+
+    Calculate the function at several points by providing a NumPy array for
+    `x`.
+
+    >>> x = np.array([0.5, 2., 3.])
+    >>> fdtrc(1, 2, x)
+    array([0.5527864 , 0.29289322, 0.22540333])
+
+    Plot the function for several parameter sets.
+
+    >>> import matplotlib.pyplot as plt
+    >>> dfn_parameters = [1, 5, 10, 50]
+    >>> dfd_parameters = [1, 1, 2, 3]
+    >>> linestyles = ['solid', 'dashed', 'dotted', 'dashdot']
+    >>> parameters_list = list(zip(dfn_parameters, dfd_parameters,
+    ...                            linestyles))
+    >>> x = np.linspace(0, 30, 1000)
+    >>> fig, ax = plt.subplots()
+    >>> for parameter_set in parameters_list:
+    ...     dfn, dfd, style = parameter_set
+    ...     fdtrc_vals = fdtrc(dfn, dfd, x)
+    ...     ax.plot(x, fdtrc_vals, label=rf"$d_n={dfn},\, d_d={dfd}$",
+    ...             ls=style)
+    >>> ax.legend()
+    >>> ax.set_xlabel("$x$")
+    >>> ax.set_title("F distribution survival function")
+    >>> plt.show()
+
+    The F distribution is also available as `scipy.stats.f`. Using `fdtrc`
+    directly can be much faster than calling the ``sf`` method of
+    `scipy.stats.f`, especially for small arrays or individual values.
+    To get the same results one must use the following parametrization:
+    ``stats.f(dfn, dfd).sf(x)=fdtrc(dfn, dfd, x)``.
+
+    >>> from scipy.stats import f
+    >>> dfn, dfd = 1, 2
+    >>> x = 1
+    >>> fdtrc_res = fdtrc(dfn, dfd, x)  # this will often be faster than below
+    >>> f_dist_res = f(dfn, dfd).sf(x)
+    >>> f_dist_res == fdtrc_res  # test that results are equal
+    True
+    """)
+
+add_newdoc("fdtri",
+    r"""
+    fdtri(dfn, dfd, p, out=None)
+
+    The `p`-th quantile of the F-distribution.
+
+    This function is the inverse of the F-distribution CDF, `fdtr`, returning
+    the `x` such that `fdtr(dfn, dfd, x) = p`.
+
+    Parameters
+    ----------
+    dfn : array_like
+        First parameter (positive float).
+    dfd : array_like
+        Second parameter (positive float).
+    p : array_like
+        Cumulative probability, in [0, 1].
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    x : scalar or ndarray
+        The quantile corresponding to `p`.
+
+    See Also
+    --------
+    fdtr : F distribution cumulative distribution function
+    fdtrc : F distribution survival function
+    scipy.stats.f : F distribution
+
+    Notes
+    -----
+    Wrapper for a routine from the Boost Math C++ library [1]_. The
+    F distribution is also available as `scipy.stats.f`. Calling
+    `fdtri` directly can improve performance compared to the ``ppf``
+    method of `scipy.stats.f` (see last example below).
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    Examples
+    --------
+    `fdtri` represents the inverse of the F distribution CDF which is
+    available as `fdtr`. Here, we calculate the CDF for ``df1=1``, ``df2=2``
+    at ``x=3``. `fdtri` then returns ``3`` given the same values for `df1`,
+    `df2` and the computed CDF value.
+
+    >>> import numpy as np
+    >>> from scipy.special import fdtri, fdtr
+    >>> df1, df2 = 1, 2
+    >>> x = 3
+    >>> cdf_value =  fdtr(df1, df2, x)
+    >>> fdtri(df1, df2, cdf_value)
+    3.000000000000006
+
+    Calculate the function at several points by providing a NumPy array for
+    `x`.
+
+    >>> x = np.array([0.1, 0.4, 0.7])
+    >>> fdtri(1, 2, x)
+    array([0.02020202, 0.38095238, 1.92156863])
+
+    Plot the function for several parameter sets.
+
+    >>> import matplotlib.pyplot as plt
+    >>> dfn_parameters = [50, 10, 1, 50]
+    >>> dfd_parameters = [0.5, 1, 1, 5]
+    >>> linestyles = ['solid', 'dashed', 'dotted', 'dashdot']
+    >>> parameters_list = list(zip(dfn_parameters, dfd_parameters,
+    ...                            linestyles))
+    >>> x = np.linspace(0, 1, 1000)
+    >>> fig, ax = plt.subplots()
+    >>> for parameter_set in parameters_list:
+    ...     dfn, dfd, style = parameter_set
+    ...     fdtri_vals = fdtri(dfn, dfd, x)
+    ...     ax.plot(x, fdtri_vals, label=rf"$d_n={dfn},\, d_d={dfd}$",
+    ...             ls=style)
+    >>> ax.legend()
+    >>> ax.set_xlabel("$x$")
+    >>> title = "F distribution inverse cumulative distribution function"
+    >>> ax.set_title(title)
+    >>> ax.set_ylim(0, 30)
+    >>> plt.show()
+
+    The F distribution is also available as `scipy.stats.f`. Using `fdtri`
+    directly can be much faster than calling the ``ppf`` method of
+    `scipy.stats.f`, especially for small arrays or individual values.
+    To get the same results one must use the following parametrization:
+    ``stats.f(dfn, dfd).ppf(x)=fdtri(dfn, dfd, x)``.
+
+    >>> from scipy.stats import f
+    >>> dfn, dfd = 1, 2
+    >>> x = 0.7
+    >>> fdtri_res = fdtri(dfn, dfd, x)  # this will often be faster than below
+    >>> f_dist_res = f(dfn, dfd).ppf(x)
+    >>> f_dist_res == fdtri_res  # test that results are equal
+    True
+    """)
+
+add_newdoc("fdtridfd",
+    """
+    fdtridfd(dfn, p, x, out=None)
+
+    Inverse to `fdtr` vs dfd.
+
+    Finds the F density argument dfd such that ``fdtr(dfn, dfd, x) == p``.
+
+    Parameters
+    ----------
+    dfn : array_like
+        First parameter (positive float).
+    p : array_like
+        Cumulative probability, in [0, 1].
+    x : array_like
+        Argument (nonnegative float).
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    dfd : scalar or ndarray
+        `dfd` such that ``fdtr(dfn, dfd, x) == p``.
+
+    See Also
+    --------
+    fdtr : F distribution cumulative distribution function
+    fdtrc : F distribution survival function
+    fdtri : F distribution quantile function
+    scipy.stats.f : F distribution
+
+    Examples
+    --------
+    Compute the F distribution cumulative distribution function for one
+    parameter set.
+
+    >>> from scipy.special import fdtridfd, fdtr
+    >>> dfn, dfd, x = 10, 5, 2
+    >>> cdf_value = fdtr(dfn, dfd, x)
+    >>> cdf_value
+    0.7700248806501017
+
+    Verify that `fdtridfd` recovers the original value for `dfd`:
+
+    >>> fdtridfd(dfn, cdf_value, x)
+    5.0
+    """)
+
+'''
+commented out as fdtridfn seems to have bugs and is not in functions.json
+see: https://github.com/scipy/scipy/pull/15622#discussion_r811440983
+
+add_newdoc(
+    "fdtridfn",
+    """
+    fdtridfn(p, dfd, x, out=None)
+
+    Inverse to `fdtr` vs dfn
+
+    finds the F density argument dfn such that ``fdtr(dfn, dfd, x) == p``.
+
+
+    Parameters
+    ----------
+    p : array_like
+        Cumulative probability, in [0, 1].
+    dfd : array_like
+        Second parameter (positive float).
+    x : array_like
+        Argument (nonnegative float).
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    dfn : scalar or ndarray
+        `dfn` such that ``fdtr(dfn, dfd, x) == p``.
+
+    See Also
+    --------
+    fdtr, fdtrc, fdtri, fdtridfd
+
+
+    """)
+'''
+
+add_newdoc("gdtr",
+    r"""
+    gdtr(a, b, x, out=None)
+
+    Gamma distribution cumulative distribution function.
+
+    Returns the integral from zero to `x` of the gamma probability density
+    function,
+
+    .. math::
+
+        F(x) = \int_0^x \frac{a^b}{\Gamma(b)} t^{b-1} e^{-at}\,dt,
+
+    where :math:`\Gamma` is the gamma function.
+
+    Parameters
+    ----------
+    a : array_like
+        The rate parameter of the gamma distribution, sometimes denoted
+        :math:`\beta` (float).  It is also the reciprocal of the scale
+        parameter :math:`\theta`.
+    b : array_like
+        The shape parameter of the gamma distribution, sometimes denoted
+        :math:`\alpha` (float).
+    x : array_like
+        The quantile (upper limit of integration; float).
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    scalar or ndarray
+        The CDF of the gamma distribution with parameters `a` and `b`
+        evaluated at `x`.
+
+    See Also
+    --------
+    gdtrc : 1 - CDF of the gamma distribution.
+    scipy.stats.gamma: Gamma distribution
+
+    Notes
+    -----
+    The evaluation is carried out using the relation to the incomplete gamma
+    integral (regularized gamma function).
+
+    Wrapper for the Cephes [1]_ routine `gdtr`. Calling `gdtr` directly can
+    improve performance compared to the ``cdf`` method of `scipy.stats.gamma`
+    (see last example below).
+
+    References
+    ----------
+    .. [1] Cephes Mathematical Functions Library,
+           https://netlib.org/cephes/
+
+    Examples
+    --------
+    Compute the function for ``a=1``, ``b=2`` at ``x=5``.
+
+    >>> import numpy as np
+    >>> from scipy.special import gdtr
+    >>> import matplotlib.pyplot as plt
+    >>> gdtr(1., 2., 5.)
+    0.9595723180054873
+
+    Compute the function for ``a=1`` and ``b=2`` at several points by
+    providing a NumPy array for `x`.
+
+    >>> xvalues = np.array([1., 2., 3., 4])
+    >>> gdtr(1., 1., xvalues)
+    array([0.63212056, 0.86466472, 0.95021293, 0.98168436])
+
+    `gdtr` can evaluate different parameter sets by providing arrays with
+    broadcasting compatible shapes for `a`, `b` and `x`. Here we compute the
+    function for three different `a` at four positions `x` and ``b=3``,
+    resulting in a 3x4 array.
+
+    >>> a = np.array([[0.5], [1.5], [2.5]])
+    >>> x = np.array([1., 2., 3., 4])
+    >>> a.shape, x.shape
+    ((3, 1), (4,))
+
+    >>> gdtr(a, 3., x)
+    array([[0.01438768, 0.0803014 , 0.19115317, 0.32332358],
+           [0.19115317, 0.57680992, 0.82642193, 0.9380312 ],
+           [0.45618688, 0.87534798, 0.97974328, 0.9972306 ]])
+
+    Plot the function for four different parameter sets.
+
+    >>> a_parameters = [0.3, 1, 2, 6]
+    >>> b_parameters = [2, 10, 15, 20]
+    >>> linestyles = ['solid', 'dashed', 'dotted', 'dashdot']
+    >>> parameters_list = list(zip(a_parameters, b_parameters, linestyles))
+    >>> x = np.linspace(0, 30, 1000)
+    >>> fig, ax = plt.subplots()
+    >>> for parameter_set in parameters_list:
+    ...     a, b, style = parameter_set
+    ...     gdtr_vals = gdtr(a, b, x)
+    ...     ax.plot(x, gdtr_vals, label=fr"$a= {a},\, b={b}$", ls=style)
+    >>> ax.legend()
+    >>> ax.set_xlabel("$x$")
+    >>> ax.set_title("Gamma distribution cumulative distribution function")
+    >>> plt.show()
+
+    The gamma distribution is also available as `scipy.stats.gamma`. Using
+    `gdtr` directly can be much faster than calling the ``cdf`` method of
+    `scipy.stats.gamma`, especially for small arrays or individual values.
+    To get the same results one must use the following parametrization:
+    ``stats.gamma(b, scale=1/a).cdf(x)=gdtr(a, b, x)``.
+
+    >>> from scipy.stats import gamma
+    >>> a = 2.
+    >>> b = 3
+    >>> x = 1.
+    >>> gdtr_result = gdtr(a, b, x)  # this will often be faster than below
+    >>> gamma_dist_result = gamma(b, scale=1/a).cdf(x)
+    >>> gdtr_result == gamma_dist_result  # test that results are equal
+    True
+    """)
+
+add_newdoc("gdtrc",
+    r"""
+    gdtrc(a, b, x, out=None)
+
+    Gamma distribution survival function.
+
+    Integral from `x` to infinity of the gamma probability density function,
+
+    .. math::
+
+        S(x) = \int_x^\infty \frac{a^b}{\Gamma(b)} t^{b-1} e^{-at}\,dt,
+
+    where :math:`\Gamma` is the gamma function.
+
+    Parameters
+    ----------
+    a : array_like
+        The rate parameter of the gamma distribution, sometimes denoted
+        :math:`\beta` (float). It is also the reciprocal of the scale
+        parameter :math:`\theta`.
+    b : array_like
+        The shape parameter of the gamma distribution, sometimes denoted
+        :math:`\alpha` (float).
+    x : array_like
+        The quantile (lower limit of integration; float).
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    scalar or ndarray
+        The survival function of the gamma distribution with parameters `a`
+        and `b` evaluated at `x`.
+
+    See Also
+    --------
+    gdtr: Gamma distribution cumulative distribution function
+    scipy.stats.gamma: Gamma distribution
+    gdtrix
+
+    Notes
+    -----
+    The evaluation is carried out using the relation to the incomplete gamma
+    integral (regularized gamma function).
+
+    Wrapper for the Cephes [1]_ routine `gdtrc`. Calling `gdtrc` directly can
+    improve performance compared to the ``sf`` method of `scipy.stats.gamma`
+    (see last example below).
+
+    References
+    ----------
+    .. [1] Cephes Mathematical Functions Library,
+           https://netlib.org/cephes/
+
+    Examples
+    --------
+    Compute the function for ``a=1`` and ``b=2`` at ``x=5``.
+
+    >>> import numpy as np
+    >>> from scipy.special import gdtrc
+    >>> import matplotlib.pyplot as plt
+    >>> gdtrc(1., 2., 5.)
+    0.04042768199451279
+
+    Compute the function for ``a=1``, ``b=2`` at several points by providing
+    a NumPy array for `x`.
+
+    >>> xvalues = np.array([1., 2., 3., 4])
+    >>> gdtrc(1., 1., xvalues)
+    array([0.36787944, 0.13533528, 0.04978707, 0.01831564])
+
+    `gdtrc` can evaluate different parameter sets by providing arrays with
+    broadcasting compatible shapes for `a`, `b` and `x`. Here we compute the
+    function for three different `a` at four positions `x` and ``b=3``,
+    resulting in a 3x4 array.
+
+    >>> a = np.array([[0.5], [1.5], [2.5]])
+    >>> x = np.array([1., 2., 3., 4])
+    >>> a.shape, x.shape
+    ((3, 1), (4,))
+
+    >>> gdtrc(a, 3., x)
+    array([[0.98561232, 0.9196986 , 0.80884683, 0.67667642],
+           [0.80884683, 0.42319008, 0.17357807, 0.0619688 ],
+           [0.54381312, 0.12465202, 0.02025672, 0.0027694 ]])
+
+    Plot the function for four different parameter sets.
+
+    >>> a_parameters = [0.3, 1, 2, 6]
+    >>> b_parameters = [2, 10, 15, 20]
+    >>> linestyles = ['solid', 'dashed', 'dotted', 'dashdot']
+    >>> parameters_list = list(zip(a_parameters, b_parameters, linestyles))
+    >>> x = np.linspace(0, 30, 1000)
+    >>> fig, ax = plt.subplots()
+    >>> for parameter_set in parameters_list:
+    ...     a, b, style = parameter_set
+    ...     gdtrc_vals = gdtrc(a, b, x)
+    ...     ax.plot(x, gdtrc_vals, label=fr"$a= {a},\, b={b}$", ls=style)
+    >>> ax.legend()
+    >>> ax.set_xlabel("$x$")
+    >>> ax.set_title("Gamma distribution survival function")
+    >>> plt.show()
+
+    The gamma distribution is also available as `scipy.stats.gamma`.
+    Using `gdtrc` directly can be much faster than calling the ``sf`` method
+    of `scipy.stats.gamma`, especially for small arrays or individual
+    values. To get the same results one must use the following parametrization:
+    ``stats.gamma(b, scale=1/a).sf(x)=gdtrc(a, b, x)``.
+
+    >>> from scipy.stats import gamma
+    >>> a = 2
+    >>> b = 3
+    >>> x = 1.
+    >>> gdtrc_result = gdtrc(a, b, x)  # this will often be faster than below
+    >>> gamma_dist_result = gamma(b, scale=1/a).sf(x)
+    >>> gdtrc_result == gamma_dist_result  # test that results are equal
+    True
+    """)
+
+add_newdoc("gdtria",
+    """
+    gdtria(p, b, x, out=None)
+
+    Inverse of `gdtr` vs a.
+
+    Returns the inverse with respect to the parameter `a` of ``p =
+    gdtr(a, b, x)``, the cumulative distribution function of the gamma
+    distribution.
+
+    Parameters
+    ----------
+    p : array_like
+        Probability values.
+    b : array_like
+        `b` parameter values of `gdtr(a, b, x)`. `b` is the "shape" parameter
+        of the gamma distribution.
+    x : array_like
+        Nonnegative real values, from the domain of the gamma distribution.
+    out : ndarray, optional
+        If a fourth argument is given, it must be a numpy.ndarray whose size
+        matches the broadcast result of `a`, `b` and `x`.  `out` is then the
+        array returned by the function.
+
+    Returns
+    -------
+    a : scalar or ndarray
+        Values of the `a` parameter such that ``p = gdtr(a, b, x)`.  ``1/a``
+        is the "scale" parameter of the gamma distribution.
+
+    See Also
+    --------
+    gdtr : CDF of the gamma distribution.
+    gdtrib : Inverse with respect to `b` of `gdtr(a, b, x)`.
+    gdtrix : Inverse with respect to `x` of `gdtr(a, b, x)`.
+    gammaincinv : Inverse of the incomplete regularized gamma function.
+
+    Notes
+    -----
+    `gdtria` is implemented in terms of the incomplete gamma inverse as
+    ``gdtria(p, b, x) = gammaincinv(b, p)/x``.
+
+    Examples
+    --------
+    First evaluate `gdtr`.
+
+    >>> from scipy.special import gdtr, gdtria
+    >>> p = gdtr(1.2, 3.4, 5.6)
+    >>> print(p)
+    0.94378087442
+
+    Verify the inverse.
+
+    >>> gdtria(p, 3.4, 5.6)
+    1.2
+    """)
+
+add_newdoc("gdtrib",
+    """
+    gdtrib(a, p, x, out=None)
+
+    Inverse of `gdtr` vs b.
+
+    Returns the inverse with respect to the parameter `b` of ``p =
+    gdtr(a, b, x)``, the cumulative distribution function of the gamma
+    distribution.
+
+    Parameters
+    ----------
+    a : array_like
+        `a` parameter values of ``gdtr(a, b, x)`. ``1/a`` is the "scale"
+        parameter of the gamma distribution.
+    p : array_like
+        Probability values.
+    x : array_like
+        Nonnegative real values, from the domain of the gamma distribution.
+    out : ndarray, optional
+        If a fourth argument is given, it must be a numpy.ndarray whose size
+        matches the broadcast result of `a`, `b` and `x`.  `out` is then the
+        array returned by the function.
+
+    Returns
+    -------
+    b : scalar or ndarray
+        Values of the `b` parameter such that `p = gdtr(a, b, x)`.  `b` is
+        the "shape" parameter of the gamma distribution.
+
+    See Also
+    --------
+    gdtr : CDF of the gamma distribution.
+    gdtria : Inverse with respect to `a` of `gdtr(a, b, x)`.
+    gdtrix : Inverse with respect to `x` of `gdtr(a, b, x)`.
+
+    Notes
+    -----
+
+    The cumulative distribution function `p` is computed using the Cephes [1]_
+    routines `igam` and `igamc`. Computation of `b` involves a search for a value
+    that produces the desired value of `p` using Chandrupatla's bracketing
+    root finding algorithm [2]_.
+
+    Note that there are some edge cases where `gdtrib` is extended by taking
+    limits where they are uniquely defined. In particular
+    ``x == 0`` with ``p > 0`` and ``p == 0`` with ``x > 0``.
+    For these edge cases, a numerical result will be returned for
+    ``gdtrib(a, p, x)`` even though ``gdtr(a, gdtrib(a, p, x), x)`` is
+    undefined.
+
+    References
+    ----------
+    .. [1] Cephes Mathematical Functions Library,
+           https://netlib.org/cephes/
+    .. [2] Chandrupatla, Tirupathi R.
+           "A new hybrid quadratic/bisection algorithm for finding the zero of a
+           nonlinear function without using derivatives".
+           Advances in Engineering Software, 28(3), 145-149.
+           :doi:`10.1016/s0965-9978(96)00051-8`.
+
+    Examples
+    --------
+    First evaluate `gdtr`.
+
+    >>> from scipy.special import gdtr, gdtrib
+    >>> p = gdtr(1.2, 3.4, 5.6)
+    >>> print(p)
+    0.94378087442
+
+    Verify the inverse.
+
+    >>> gdtrib(1.2, p, 5.6)
+    3.3999999999999995
+    """)
+
+add_newdoc("gdtrix",
+    """
+    gdtrix(a, b, p, out=None)
+
+    Inverse of `gdtr` vs x.
+
+    Returns the inverse with respect to the parameter `x` of ``p =
+    gdtr(a, b, x)``, the cumulative distribution function of the gamma
+    distribution. This is also known as the pth quantile of the
+    distribution.
+
+    Parameters
+    ----------
+    a : array_like
+        `a` parameter values of ``gdtr(a, b, x)``. ``1/a`` is the "scale"
+        parameter of the gamma distribution.
+    b : array_like
+        `b` parameter values of ``gdtr(a, b, x)``. `b` is the "shape" parameter
+        of the gamma distribution.
+    p : array_like
+        Probability values.
+    out : ndarray, optional
+        If a fourth argument is given, it must be a numpy.ndarray whose size
+        matches the broadcast result of `a`, `b` and `x`. `out` is then the
+        array returned by the function.
+
+    Returns
+    -------
+    x : scalar or ndarray
+        Values of the `x` parameter such that `p = gdtr(a, b, x)`.
+
+    See Also
+    --------
+    gdtr : CDF of the gamma distribution.
+    gdtria : Inverse with respect to `a` of ``gdtr(a, b, x)``.
+    gdtrib : Inverse with respect to `b` of ``gdtr(a, b, x)``.
+    gammaincinv : Inverse of the incomplete regularized gamma function.
+
+    Notes
+    -----
+    `gdtrix` is implemented in terms of the incomplete gamma inverse as
+    ``gdtrix(a, b, p) = gammaincinv(b, p)/a``.
+
+    Examples
+    --------
+    First evaluate `gdtr`.
+
+    >>> from scipy.special import gdtr, gdtrix
+    >>> p = gdtr(1.2, 3.4, 5.6)
+    >>> print(p)
+    0.94378087442
+
+    Verify the inverse.
+
+    >>> gdtrix(1.2, 3.4, p)
+    5.6
+    """)
+
+
+
+add_newdoc("huber",
+    r"""
+    huber(delta, r, out=None)
+
+    Huber loss function.
+
+    .. math:: \text{huber}(\delta, r) = \begin{cases} \infty & \delta < 0  \\
+              \frac{1}{2}r^2 & 0 \le \delta, | r | \le \delta \\
+              \delta ( |r| - \frac{1}{2}\delta ) & \text{otherwise} \end{cases}
+
+    Parameters
+    ----------
+    delta : ndarray
+        Input array, indicating the quadratic vs. linear loss changepoint.
+    r : ndarray
+        Input array, possibly representing residuals.
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    scalar or ndarray
+        The computed Huber loss function values.
+
+    See Also
+    --------
+    pseudo_huber : smooth approximation of this function
+
+    Notes
+    -----
+    `huber` is useful as a loss function in robust statistics or machine
+    learning to reduce the influence of outliers as compared to the common
+    squared error loss, residuals with a magnitude higher than `delta` are
+    not squared [1]_.
+
+    Typically, `r` represents residuals, the difference
+    between a model prediction and data. Then, for :math:`|r|\leq\delta`,
+    `huber` resembles the squared error and for :math:`|r|>\delta` the
+    absolute error. This way, the Huber loss often achieves
+    a fast convergence in model fitting for small residuals like the squared
+    error loss function and still reduces the influence of outliers
+    (:math:`|r|>\delta`) like the absolute error loss. As :math:`\delta` is
+    the cutoff between squared and absolute error regimes, it has
+    to be tuned carefully for each problem. `huber` is also
+    convex, making it suitable for gradient based optimization.
+
+    .. versionadded:: 0.15.0
+
+    References
+    ----------
+    .. [1] Peter Huber. "Robust Estimation of a Location Parameter",
+           1964. Annals of Statistics. 53 (1): 73 - 101.
+
+    Examples
+    --------
+    Import all necessary modules.
+
+    >>> import numpy as np
+    >>> from scipy.special import huber
+    >>> import matplotlib.pyplot as plt
+
+    Compute the function for ``delta=1`` at ``r=2``
+
+    >>> huber(1., 2.)
+    1.5
+
+    Compute the function for different `delta` by providing a NumPy array or
+    list for `delta`.
+
+    >>> huber([1., 3., 5.], 4.)
+    array([3.5, 7.5, 8. ])
+
+    Compute the function at different points by providing a NumPy array or
+    list for `r`.
+
+    >>> huber(2., np.array([1., 1.5, 3.]))
+    array([0.5  , 1.125, 4.   ])
+
+    The function can be calculated for different `delta` and `r` by
+    providing arrays for both with compatible shapes for broadcasting.
+
+    >>> r = np.array([1., 2.5, 8., 10.])
+    >>> deltas = np.array([[1.], [5.], [9.]])
+    >>> print(r.shape, deltas.shape)
+    (4,) (3, 1)
+
+    >>> huber(deltas, r)
+    array([[ 0.5  ,  2.   ,  7.5  ,  9.5  ],
+           [ 0.5  ,  3.125, 27.5  , 37.5  ],
+           [ 0.5  ,  3.125, 32.   , 49.5  ]])
+
+    Plot the function for different `delta`.
+
+    >>> x = np.linspace(-4, 4, 500)
+    >>> deltas = [1, 2, 3]
+    >>> linestyles = ["dashed", "dotted", "dashdot"]
+    >>> fig, ax = plt.subplots()
+    >>> combined_plot_parameters = list(zip(deltas, linestyles))
+    >>> for delta, style in combined_plot_parameters:
+    ...     ax.plot(x, huber(delta, x), label=fr"$\delta={delta}$", ls=style)
+    >>> ax.legend(loc="upper center")
+    >>> ax.set_xlabel("$x$")
+    >>> ax.set_title(r"Huber loss function $h_{\delta}(x)$")
+    >>> ax.set_xlim(-4, 4)
+    >>> ax.set_ylim(0, 8)
+    >>> plt.show()
+    """)
+
+add_newdoc("hyp0f1",
+    r"""
+    hyp0f1(v, z, out=None)
+
+    Confluent hypergeometric limit function 0F1.
+
+    Parameters
+    ----------
+    v : array_like
+        Real-valued parameter
+    z : array_like
+        Real- or complex-valued argument
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    scalar or ndarray
+        The confluent hypergeometric limit function
+
+    Notes
+    -----
+    This function is defined as:
+
+    .. math:: _0F_1(v, z) = \sum_{k=0}^{\infty}\frac{z^k}{(v)_k k!}.
+
+    It's also the limit as :math:`q \to \infty` of :math:`_1F_1(q; v; z/q)`,
+    and satisfies the differential equation :math:`f''(z) + vf'(z) =
+    f(z)`. See [1]_ for more information.
+
+    References
+    ----------
+    .. [1] Wolfram MathWorld, "Confluent Hypergeometric Limit Function",
+           https://mathworld.wolfram.com/ConfluentHypergeometricLimitFunction.html
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import scipy.special as sc
+
+    It is one when `z` is zero.
+
+    >>> sc.hyp0f1(1, 0)
+    1.0
+
+    It is the limit of the confluent hypergeometric function as `q`
+    goes to infinity.
+
+    >>> q = np.array([1, 10, 100, 1000])
+    >>> v = 1
+    >>> z = 1
+    >>> sc.hyp1f1(q, v, z / q)
+    array([2.71828183, 2.31481985, 2.28303778, 2.27992985])
+    >>> sc.hyp0f1(v, z)
+    2.2795853023360673
+
+    It is related to Bessel functions.
+
+    >>> n = 1
+    >>> x = np.linspace(0, 1, 5)
+    >>> sc.jv(n, x)
+    array([0.        , 0.12402598, 0.24226846, 0.3492436 , 0.44005059])
+    >>> (0.5 * x)**n / sc.factorial(n) * sc.hyp0f1(n + 1, -0.25 * x**2)
+    array([0.        , 0.12402598, 0.24226846, 0.3492436 , 0.44005059])
+
+    """)
+
+add_newdoc("hyp1f1",
+    r"""
+    hyp1f1(a, b, x, out=None)
+
+    Confluent hypergeometric function 1F1.
+
+    The confluent hypergeometric function is defined by the series
+
+    .. math::
+
+       {}_1F_1(a; b; x) = \sum_{k = 0}^\infty \frac{(a)_k}{(b)_k k!} x^k.
+
+    See [DLMF]_ for more details. Here :math:`(\cdot)_k` is the
+    Pochhammer symbol; see `poch`.
+
+    Parameters
+    ----------
+    a, b : array_like
+        Real parameters
+    x : array_like
+        Real or complex argument
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    scalar or ndarray
+        Values of the confluent hypergeometric function
+
+    See Also
+    --------
+    hyperu : another confluent hypergeometric function
+    hyp0f1 : confluent hypergeometric limit function
+    hyp2f1 : Gaussian hypergeometric function
+
+    Notes
+    -----
+    For real values, this function uses the ``hyp1f1`` routine from the C++ Boost
+    library [2]_, for complex values a C translation of the specfun
+    Fortran library [3]_.
+
+    References
+    ----------
+    .. [DLMF] NIST Digital Library of Mathematical Functions
+              https://dlmf.nist.gov/13.2#E2
+    .. [2] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+    .. [3] S. Zhang and J.M. Jin, "Computation of Special Functions", Wiley 1996.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import scipy.special as sc
+
+    It is one when `x` is zero:
+
+    >>> sc.hyp1f1(0.5, 0.5, 0)
+    1.0
+
+    It is singular when `b` is a nonpositive integer.
+
+    >>> sc.hyp1f1(0.5, -1, 0)
+    inf
+
+    It is a polynomial when `a` is a nonpositive integer.
+
+    >>> a, b, x = -1, 0.5, np.array([1.0, 2.0, 3.0, 4.0])
+    >>> sc.hyp1f1(a, b, x)
+    array([-1., -3., -5., -7.])
+    >>> 1 + (a / b) * x
+    array([-1., -3., -5., -7.])
+
+    It reduces to the exponential function when ``a = b``.
+
+    >>> sc.hyp1f1(2, 2, [1, 2, 3, 4])
+    array([ 2.71828183,  7.3890561 , 20.08553692, 54.59815003])
+    >>> np.exp([1, 2, 3, 4])
+    array([ 2.71828183,  7.3890561 , 20.08553692, 54.59815003])
+
+    """)
+
+add_newdoc("hyperu",
+    r"""
+    hyperu(a, b, x, out=None)
+
+    Confluent hypergeometric function U.
+
+    It is defined as the solution to the equation
+
+    .. math::
+
+       x \frac{d^2w}{dx^2} + (b - x) \frac{dw}{dx} - aw = 0
+
+    which satisfies the property
+
+    .. math::
+
+       U(a, b, x) \sim x^{-a}
+
+    as :math:`x \to \infty`. See [DLMF]_ for more details.
+
+    Parameters
+    ----------
+    a, b : array_like
+        Real-valued parameters
+    x : array_like
+        Real-valued argument
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    scalar or ndarray
+        Values of `U`
+
+    References
+    ----------
+    .. [DLMF] NIST Digital Library of Mathematics Functions
+              https://dlmf.nist.gov/13.2#E6
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import scipy.special as sc
+
+    It has a branch cut along the negative `x` axis.
+
+    >>> x = np.linspace(-0.1, -10, 5)
+    >>> sc.hyperu(1, 1, x)
+    array([nan, nan, nan, nan, nan])
+
+    It approaches zero as `x` goes to infinity.
+
+    >>> x = np.array([1, 10, 100])
+    >>> sc.hyperu(1, 1, x)
+    array([0.59634736, 0.09156333, 0.00990194])
+
+    It satisfies Kummer's transformation.
+
+    >>> a, b, x = 2, 1, 1
+    >>> sc.hyperu(a, b, x)
+    0.1926947246463881
+    >>> x**(1 - b) * sc.hyperu(a - b + 1, 2 - b, x)
+    0.1926947246463881
+
+    """)
+
+add_newdoc("_igam_fac",
+    """
+    Internal function, do not use.
+    """)
+
+add_newdoc("kl_div",
+    r"""
+    kl_div(x, y, out=None)
+
+    Elementwise function for computing Kullback-Leibler divergence.
+
+    .. math::
+
+        \mathrm{kl\_div}(x, y) =
+          \begin{cases}
+            x \log(x / y) - x + y & x > 0, y > 0 \\
+            y & x = 0, y \ge 0 \\
+            \infty & \text{otherwise}
+          \end{cases}
+
+    Parameters
+    ----------
+    x, y : array_like
+        Real arguments
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    scalar or ndarray
+        Values of the Kullback-Liebler divergence.
+
+    See Also
+    --------
+    entr, rel_entr, scipy.stats.entropy
+
+    Notes
+    -----
+    .. versionadded:: 0.15.0
+
+    This function is non-negative and is jointly convex in `x` and `y`.
+
+    The origin of this function is in convex programming; see [1]_ for
+    details. This is why the function contains the extra :math:`-x
+    + y` terms over what might be expected from the Kullback-Leibler
+    divergence. For a version of the function without the extra terms,
+    see `rel_entr`.
+
+    References
+    ----------
+    .. [1] Boyd, Stephen and Lieven Vandenberghe. *Convex optimization*.
+           Cambridge University Press, 2004.
+           :doi:`10.1017/CBO9780511804441`.
+
+    """)
+
+add_newdoc("kn",
+    r"""
+    kn(n, x, out=None)
+
+    Modified Bessel function of the second kind of integer order `n`.
+
+    Returns the modified Bessel function of the second kind for integer order
+    `n` at real `z`.
+
+    These are also sometimes called functions of the third kind, Basset
+    functions, or Macdonald functions.
+
+    Parameters
+    ----------
+    n : array_like of int
+        Order of Bessel functions (floats will truncate with a warning)
+    x : array_like of float
+        Argument at which to evaluate the Bessel functions
+    out : ndarray, optional
+        Optional output array for the function results.
+
+    Returns
+    -------
+    scalar or ndarray
+        Value of the Modified Bessel function of the second kind,
+        :math:`K_n(x)`.
+
+    See Also
+    --------
+    kv : Same function, but accepts real order and complex argument
+    kvp : Derivative of this function
+
+    Notes
+    -----
+    Wrapper for AMOS [1]_ routine `zbesk`.  For a discussion of the
+    algorithm used, see [2]_ and the references therein.
+
+    References
+    ----------
+    .. [1] Donald E. Amos, "AMOS, A Portable Package for Bessel Functions
+           of a Complex Argument and Nonnegative Order",
+           https://netlib.org/amos/
+    .. [2] Donald E. Amos, "Algorithm 644: A portable package for Bessel
+           functions of a complex argument and nonnegative order", ACM
+           TOMS Vol. 12 Issue 3, Sept. 1986, p. 265.
+
+    Examples
+    --------
+    Plot the function of several orders for real input:
+
+    >>> import numpy as np
+    >>> from scipy.special import kn
+    >>> import matplotlib.pyplot as plt
+    >>> x = np.linspace(0, 5, 1000)
+    >>> for N in range(6):
+    ...     plt.plot(x, kn(N, x), label='$K_{}(x)$'.format(N))
+    >>> plt.ylim(0, 10)
+    >>> plt.legend()
+    >>> plt.title(r'Modified Bessel function of the second kind $K_n(x)$')
+    >>> plt.show()
+
+    Calculate for a single value at multiple orders:
+
+    >>> kn([4, 5, 6], 1)
+    array([   44.23241585,   360.9605896 ,  3653.83831186])
+    """)
+
+add_newdoc("kolmogi",
+    """
+    kolmogi(p, out=None)
+
+    Inverse Survival Function of Kolmogorov distribution.
+
+    It is the inverse function to `kolmogorov`.
+    Returns y such that ``kolmogorov(y) == p``.
+
+    Parameters
+    ----------
+    p : float array_like
+        Probability
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    scalar or ndarray
+        The value(s) of kolmogi(p)
+
+    See Also
+    --------
+    kolmogorov : The Survival Function for the distribution
+    scipy.stats.kstwobign : Provides the functionality as a continuous distribution
+    smirnov, smirnovi : Functions for the one-sided distribution
+
+    Notes
+    -----
+    `kolmogorov` is used by `stats.kstest` in the application of the
+    Kolmogorov-Smirnov Goodness of Fit test. For historical reasons this
+    function is exposed in `scpy.special`, but the recommended way to achieve
+    the most accurate CDF/SF/PDF/PPF/ISF computations is to use the
+    `stats.kstwobign` distribution.
+
+    Examples
+    --------
+    >>> from scipy.special import kolmogi
+    >>> kolmogi([0, 0.1, 0.25, 0.5, 0.75, 0.9, 1.0])
+    array([        inf,  1.22384787,  1.01918472,  0.82757356,  0.67644769,
+            0.57117327,  0.        ])
+
+    """)
+
+add_newdoc("kolmogorov",
+    r"""
+    kolmogorov(y, out=None)
+
+    Complementary cumulative distribution (Survival Function) function of
+    Kolmogorov distribution.
+
+    Returns the complementary cumulative distribution function of
+    Kolmogorov's limiting distribution (``D_n*\sqrt(n)`` as n goes to infinity)
+    of a two-sided test for equality between an empirical and a theoretical
+    distribution. It is equal to the (limit as n->infinity of the)
+    probability that ``sqrt(n) * max absolute deviation > y``.
+
+    Parameters
+    ----------
+    y : float array_like
+      Absolute deviation between the Empirical CDF (ECDF) and the target CDF,
+      multiplied by sqrt(n).
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    scalar or ndarray
+        The value(s) of kolmogorov(y)
+
+    See Also
+    --------
+    kolmogi : The Inverse Survival Function for the distribution
+    scipy.stats.kstwobign : Provides the functionality as a continuous distribution
+    smirnov, smirnovi : Functions for the one-sided distribution
+
+    Notes
+    -----
+    `kolmogorov` is used by `stats.kstest` in the application of the
+    Kolmogorov-Smirnov Goodness of Fit test. For historical reasons this
+    function is exposed in `scpy.special`, but the recommended way to achieve
+    the most accurate CDF/SF/PDF/PPF/ISF computations is to use the
+    `stats.kstwobign` distribution.
+
+    Examples
+    --------
+    Show the probability of a gap at least as big as 0, 0.5 and 1.0.
+
+    >>> import numpy as np
+    >>> from scipy.special import kolmogorov
+    >>> from scipy.stats import kstwobign
+    >>> kolmogorov([0, 0.5, 1.0])
+    array([ 1.        ,  0.96394524,  0.26999967])
+
+    Compare a sample of size 1000 drawn from a Laplace(0, 1) distribution against
+    the target distribution, a Normal(0, 1) distribution.
+
+    >>> from scipy.stats import norm, laplace
+    >>> rng = np.random.default_rng()
+    >>> n = 1000
+    >>> lap01 = laplace(0, 1)
+    >>> x = np.sort(lap01.rvs(n, random_state=rng))
+    >>> np.mean(x), np.std(x)
+    (-0.05841730131499543, 1.3968109101997568)
+
+    Construct the Empirical CDF and the K-S statistic Dn.
+
+    >>> target = norm(0,1)  # Normal mean 0, stddev 1
+    >>> cdfs = target.cdf(x)
+    >>> ecdfs = np.arange(n+1, dtype=float)/n
+    >>> gaps = np.column_stack([cdfs - ecdfs[:n], ecdfs[1:] - cdfs])
+    >>> Dn = np.max(gaps)
+    >>> Kn = np.sqrt(n) * Dn
+    >>> print('Dn=%f, sqrt(n)*Dn=%f' % (Dn, Kn))
+    Dn=0.043363, sqrt(n)*Dn=1.371265
+    >>> print(chr(10).join(['For a sample of size n drawn from a N(0, 1) distribution:',
+    ...   ' the approximate Kolmogorov probability that sqrt(n)*Dn>=%f is %f' %
+    ...    (Kn, kolmogorov(Kn)),
+    ...   ' the approximate Kolmogorov probability that sqrt(n)*Dn<=%f is %f' %
+    ...    (Kn, kstwobign.cdf(Kn))]))
+    For a sample of size n drawn from a N(0, 1) distribution:
+     the approximate Kolmogorov probability that sqrt(n)*Dn>=1.371265 is 0.046533
+     the approximate Kolmogorov probability that sqrt(n)*Dn<=1.371265 is 0.953467
+
+    Plot the Empirical CDF against the target N(0, 1) CDF.
+
+    >>> import matplotlib.pyplot as plt
+    >>> plt.step(np.concatenate([[-3], x]), ecdfs, where='post', label='Empirical CDF')
+    >>> x3 = np.linspace(-3, 3, 100)
+    >>> plt.plot(x3, target.cdf(x3), label='CDF for N(0, 1)')
+    >>> plt.ylim([0, 1]); plt.grid(True); plt.legend();
+    >>> # Add vertical lines marking Dn+ and Dn-
+    >>> iminus, iplus = np.argmax(gaps, axis=0)
+    >>> plt.vlines([x[iminus]], ecdfs[iminus], cdfs[iminus],
+    ...            color='r', linestyle='dashed', lw=4)
+    >>> plt.vlines([x[iplus]], cdfs[iplus], ecdfs[iplus+1],
+    ...            color='r', linestyle='dashed', lw=4)
+    >>> plt.show()
+    """)
+
+add_newdoc("_kolmogc",
+    r"""
+    Internal function, do not use.
+    """)
+
+add_newdoc("_kolmogci",
+    r"""
+    Internal function, do not use.
+    """)
+
+add_newdoc("_kolmogp",
+    r"""
+    Internal function, do not use.
+    """)
+
+add_newdoc("_lanczos_sum_expg_scaled",
+    """
+    Internal function, do not use.
+    """)
+
+add_newdoc(
+    "_landau_pdf",
+    """
+    _landau_pdf(x, loc, scale)
+
+    Probability density function of the Landau distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued argument
+    loc : array_like
+        Real-valued distribution location
+    scale : array_like
+        Positive, real-valued distribution scale
+
+    Returns
+    -------
+    scalar or ndarray
+    """)
+
+add_newdoc(
+    "_landau_cdf",
+    """
+    _landau_cdf(x, loc, scale)
+
+    Cumulative distribution function of the Landau distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued argument
+    loc : array_like
+        Real-valued distribution location
+    scale : array_like
+        Positive, real-valued distribution scale
+
+    Returns
+    -------
+    scalar or ndarray
+    """)
+
+add_newdoc(
+    "_landau_sf",
+    """
+    _landau_sf(x, loc, scale)
+
+    Survival function of the Landau distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued argument
+    loc : array_like
+        Real-valued distribution location
+    scale : array_like
+        Positive, real-valued distribution scale
+
+    Returns
+    -------
+    scalar or ndarray
+    """)
+
+add_newdoc(
+    "_landau_ppf",
+    """
+    _landau_ppf(p, loc, scale)
+
+    Percent point function of the Landau distribution.
+
+    Parameters
+    ----------
+    p : array_like
+        Real-valued argument between 0 and 1
+    loc : array_like
+        Real-valued distribution location
+    scale : array_like
+        Positive, real-valued distribution scale
+
+    Returns
+    -------
+    scalar or ndarray
+    """)
+
+add_newdoc(
+    "_landau_isf",
+    """
+    _landau_isf(p, loc, scale)
+
+    Inverse survival function of the Landau distribution.
+
+    Parameters
+    ----------
+    p : array_like
+        Real-valued argument between 0 and 1
+    loc : array_like
+        Real-valued distribution location
+    scale : array_like
+        Positive, real-valued distribution scale
+
+    Returns
+    -------
+    scalar or ndarray
+    """)
+
+add_newdoc("_lgam1p",
+    """
+    Internal function, do not use.
+    """)
+
+add_newdoc("lpmv",
+    r"""
+    lpmv(m, v, x, out=None)
+
+    Associated Legendre function of integer order and real degree.
+
+    Defined as
+
+    .. math::
+
+        P_v^m(x) = (-1)^m (1 - x^2)^{m/2} \frac{d^m}{dx^m} (P_v(x))
+
+    where
+
+    .. math::
+
+        P_v(x) = \sum_{k = 0}^\infty \frac{(-v)_k (v + 1)_k}{(k!)^2}
+                \left(\frac{1 - x}{2}\right)^k
+
+    is the Legendre function of the first kind. Here :math:`(\cdot)_k`
+    is the Pochhammer symbol; see `poch`.
+
+    Parameters
+    ----------
+    m : array_like
+        Order (int or float). If passed a float not equal to an
+        integer the function returns NaN.
+    v : array_like
+        Degree (float).
+    x : array_like
+        Argument (float). Must have ``|x| <= 1``.
+    out : ndarray, optional
+        Optional output array for the function results.
+
+    Returns
+    -------
+    pmv : scalar or ndarray
+        Value of the associated Legendre function.
+
+    Notes
+    -----
+    Note that this implementation includes the Condon-Shortley phase.
+
+    References
+    ----------
+    .. [1] S. Zhang and J.M. Jin, "Computation of Special Functions", Wiley 1996.
+
+    Examples
+    --------
+    Compute a single associated Legendre function value:
+
+    >>> from scipy.special import lpmv
+    >>> lpmv(1, 2.5, 0.3)
+    -0.1292299
+
+    Plot the associated Legendre functions for orders ``m = 1`` and
+    ``m = 2`` and degrees ``v = 0, ..., 5``:
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> nus = np.arange(0, 6)
+    >>> xs = np.linspace(-1+1e-5, 1-1e-5, 101)
+
+    Order 1.
+
+    >>> fig, ax = plt.subplots()
+    >>> ax.plot(xs, lpmv(1, nus, xs[:, np.newaxis]), "-")
+    >>> ax.legend([rf"$\nu={nu}$" for nu in nus])
+    >>> ax.set_xlabel(r"$x$")
+    >>> ax.set_ylabel(r"$P_\nu^1(x)$")
+    >>> plt.show()
+
+    Order 2.
+
+    >>> fig, ax = plt.subplots()
+    >>> ax.plot(xs, lpmv(2, nus, xs[:, np.newaxis]), "-")
+    >>> ax.legend([rf"$\nu={nu}$" for nu in nus])
+    >>> ax.set_xlabel(r"$x$")
+    >>> ax.set_ylabel(r"$P_\nu^2(x)$")
+    >>> plt.show()
+    """)
+
+add_newdoc("nbdtr",
+    r"""
+    nbdtr(k, n, p, out=None)
+
+    Negative binomial cumulative distribution function.
+
+    Returns the sum of the terms 0 through `k` of the negative binomial
+    distribution probability mass function,
+
+    .. math::
+
+        F(k) = \sum_{j=0}^k {{n + j - 1}\choose{j}} p^n (1 - p)^j.
+
+    In a sequence of Bernoulli trials with individual success probabilities
+    `p`, this is the probability that `k` or fewer failures precede the nth
+    success.
+
+    Parameters
+    ----------
+    k : array_like
+        The maximum number of allowed failures (nonnegative int).
+    n : array_like
+        The target number of successes (positive int).
+    p : array_like
+        Probability of success in a single event (float).
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    scalar or ndarray
+        The probability of `k` or fewer failures before `n` successes in a
+        sequence of events with individual success probability `p`.
+
+    See Also
+    --------
+    nbdtrc : Negative binomial survival function
+    nbdtrik : Negative binomial quantile function
+    scipy.stats.nbinom : Negative binomial distribution
+
+    Notes
+    -----
+    If floating point values are passed for `k` or `n`, they will be truncated
+    to integers.
+
+    The terms are not summed directly; instead the regularized incomplete beta
+    function is employed, according to the formula,
+
+    .. math::
+        \mathrm{nbdtr}(k, n, p) = I_{p}(n, k + 1).
+
+    Wrapper for the Cephes [1]_ routine `nbdtr`.
+
+    The negative binomial distribution is also available as
+    `scipy.stats.nbinom`. Using `nbdtr` directly can improve performance
+    compared to the ``cdf`` method of `scipy.stats.nbinom` (see last example).
+
+    References
+    ----------
+    .. [1] Cephes Mathematical Functions Library,
+           https://netlib.org/cephes/
+
+    Examples
+    --------
+    Compute the function for ``k=10`` and ``n=5`` at ``p=0.5``.
+
+    >>> import numpy as np
+    >>> from scipy.special import nbdtr
+    >>> nbdtr(10, 5, 0.5)
+    0.940765380859375
+
+    Compute the function for ``n=10`` and ``p=0.5`` at several points by
+    providing a NumPy array or list for `k`.
+
+    >>> nbdtr([5, 10, 15], 10, 0.5)
+    array([0.15087891, 0.58809853, 0.88523853])
+
+    Plot the function for four different parameter sets.
+
+    >>> import matplotlib.pyplot as plt
+    >>> k = np.arange(130)
+    >>> n_parameters = [20, 20, 20, 80]
+    >>> p_parameters = [0.2, 0.5, 0.8, 0.5]
+    >>> linestyles = ['solid', 'dashed', 'dotted', 'dashdot']
+    >>> parameters_list = list(zip(p_parameters, n_parameters,
+    ...                            linestyles))
+    >>> fig, ax = plt.subplots(figsize=(8, 8))
+    >>> for parameter_set in parameters_list:
+    ...     p, n, style = parameter_set
+    ...     nbdtr_vals = nbdtr(k, n, p)
+    ...     ax.plot(k, nbdtr_vals, label=rf"$n={n},\, p={p}$",
+    ...             ls=style)
+    >>> ax.legend()
+    >>> ax.set_xlabel("$k$")
+    >>> ax.set_title("Negative binomial cumulative distribution function")
+    >>> plt.show()
+
+    The negative binomial distribution is also available as
+    `scipy.stats.nbinom`. Using `nbdtr` directly can be much faster than
+    calling the ``cdf`` method of `scipy.stats.nbinom`, especially for small
+    arrays or individual values. To get the same results one must use the
+    following parametrization: ``nbinom(n, p).cdf(k)=nbdtr(k, n, p)``.
+
+    >>> from scipy.stats import nbinom
+    >>> k, n, p = 5, 3, 0.5
+    >>> nbdtr_res = nbdtr(k, n, p)  # this will often be faster than below
+    >>> stats_res = nbinom(n, p).cdf(k)
+    >>> stats_res, nbdtr_res  # test that results are equal
+    (0.85546875, 0.85546875)
+
+    `nbdtr` can evaluate different parameter sets by providing arrays with
+    shapes compatible for broadcasting for `k`, `n` and `p`. Here we compute
+    the function for three different `k` at four locations `p`, resulting in
+    a 3x4 array.
+
+    >>> k = np.array([[5], [10], [15]])
+    >>> p = np.array([0.3, 0.5, 0.7, 0.9])
+    >>> k.shape, p.shape
+    ((3, 1), (4,))
+
+    >>> nbdtr(k, 5, p)
+    array([[0.15026833, 0.62304687, 0.95265101, 0.9998531 ],
+           [0.48450894, 0.94076538, 0.99932777, 0.99999999],
+           [0.76249222, 0.99409103, 0.99999445, 1.        ]])
+    """)
+
+add_newdoc("nbdtrc",
+    r"""
+    nbdtrc(k, n, p, out=None)
+
+    Negative binomial survival function.
+
+    Returns the sum of the terms `k + 1` to infinity of the negative binomial
+    distribution probability mass function,
+
+    .. math::
+
+        S(k) = \sum_{j=k + 1}^\infty {{n + j - 1}\choose{j}} p^n (1 - p)^j.
+
+    In a sequence of Bernoulli trials with individual success probabilities
+    `p`, this is the probability that more than `k` failures precede the nth
+    success.
+
+    Parameters
+    ----------
+    k : array_like
+        The maximum number of allowed failures (nonnegative int).
+    n : array_like
+        The target number of successes (positive int).
+    p : array_like
+        Probability of success in a single event (float).
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    scalar or ndarray
+        The probability of `k + 1` or more failures before `n` successes in a
+        sequence of events with individual success probability `p`.
+
+    See Also
+    --------
+    nbdtr : Negative binomial cumulative distribution function
+    nbdtrik : Negative binomial percentile function
+    scipy.stats.nbinom : Negative binomial distribution
+
+    Notes
+    -----
+    If floating point values are passed for `k` or `n`, they will be truncated
+    to integers.
+
+    The terms are not summed directly; instead the regularized incomplete beta
+    function is employed, according to the formula,
+
+    .. math::
+        \mathrm{nbdtrc}(k, n, p) = I_{1 - p}(k + 1, n).
+
+    Wrapper for the Cephes [1]_ routine `nbdtrc`.
+
+    The negative binomial distribution is also available as
+    `scipy.stats.nbinom`. Using `nbdtrc` directly can improve performance
+    compared to the ``sf`` method of `scipy.stats.nbinom` (see last example).
+
+    References
+    ----------
+    .. [1] Cephes Mathematical Functions Library,
+           https://netlib.org/cephes/
+
+    Examples
+    --------
+    Compute the function for ``k=10`` and ``n=5`` at ``p=0.5``.
+
+    >>> import numpy as np
+    >>> from scipy.special import nbdtrc
+    >>> nbdtrc(10, 5, 0.5)
+    0.059234619140624986
+
+    Compute the function for ``n=10`` and ``p=0.5`` at several points by
+    providing a NumPy array or list for `k`.
+
+    >>> nbdtrc([5, 10, 15], 10, 0.5)
+    array([0.84912109, 0.41190147, 0.11476147])
+
+    Plot the function for four different parameter sets.
+
+    >>> import matplotlib.pyplot as plt
+    >>> k = np.arange(130)
+    >>> n_parameters = [20, 20, 20, 80]
+    >>> p_parameters = [0.2, 0.5, 0.8, 0.5]
+    >>> linestyles = ['solid', 'dashed', 'dotted', 'dashdot']
+    >>> parameters_list = list(zip(p_parameters, n_parameters,
+    ...                            linestyles))
+    >>> fig, ax = plt.subplots(figsize=(8, 8))
+    >>> for parameter_set in parameters_list:
+    ...     p, n, style = parameter_set
+    ...     nbdtrc_vals = nbdtrc(k, n, p)
+    ...     ax.plot(k, nbdtrc_vals, label=rf"$n={n},\, p={p}$",
+    ...             ls=style)
+    >>> ax.legend()
+    >>> ax.set_xlabel("$k$")
+    >>> ax.set_title("Negative binomial distribution survival function")
+    >>> plt.show()
+
+    The negative binomial distribution is also available as
+    `scipy.stats.nbinom`. Using `nbdtrc` directly can be much faster than
+    calling the ``sf`` method of `scipy.stats.nbinom`, especially for small
+    arrays or individual values. To get the same results one must use the
+    following parametrization: ``nbinom(n, p).sf(k)=nbdtrc(k, n, p)``.
+
+    >>> from scipy.stats import nbinom
+    >>> k, n, p = 3, 5, 0.5
+    >>> nbdtr_res = nbdtrc(k, n, p)  # this will often be faster than below
+    >>> stats_res = nbinom(n, p).sf(k)
+    >>> stats_res, nbdtr_res  # test that results are equal
+    (0.6367187499999999, 0.6367187499999999)
+
+    `nbdtrc` can evaluate different parameter sets by providing arrays with
+    shapes compatible for broadcasting for `k`, `n` and `p`. Here we compute
+    the function for three different `k` at four locations `p`, resulting in
+    a 3x4 array.
+
+    >>> k = np.array([[5], [10], [15]])
+    >>> p = np.array([0.3, 0.5, 0.7, 0.9])
+    >>> k.shape, p.shape
+    ((3, 1), (4,))
+
+    >>> nbdtrc(k, 5, p)
+    array([[8.49731667e-01, 3.76953125e-01, 4.73489874e-02, 1.46902600e-04],
+           [5.15491059e-01, 5.92346191e-02, 6.72234070e-04, 9.29610100e-09],
+           [2.37507779e-01, 5.90896606e-03, 5.55025308e-06, 3.26346760e-13]])
+    """)
+
+add_newdoc(
+    "nbdtri",
+    r"""
+    nbdtri(k, n, y, out=None)
+
+    Returns the inverse with respect to the parameter `p` of
+    ``y = nbdtr(k, n, p)``, the negative binomial cumulative distribution
+    function.
+
+    Parameters
+    ----------
+    k : array_like
+        The maximum number of allowed failures (nonnegative int).
+    n : array_like
+        The target number of successes (positive int).
+    y : array_like
+        The probability of `k` or fewer failures before `n` successes (float).
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    p : scalar or ndarray
+        Probability of success in a single event (float) such that
+        `nbdtr(k, n, p) = y`.
+
+    See Also
+    --------
+    nbdtr : Cumulative distribution function of the negative binomial.
+    nbdtrc : Negative binomial survival function.
+    scipy.stats.nbinom : negative binomial distribution.
+    nbdtrik : Inverse with respect to `k` of `nbdtr(k, n, p)`.
+    nbdtrin : Inverse with respect to `n` of `nbdtr(k, n, p)`.
+    scipy.stats.nbinom : Negative binomial distribution
+
+    Notes
+    -----
+    Wrapper for the Cephes [1]_ routine `nbdtri`.
+
+    The negative binomial distribution is also available as
+    `scipy.stats.nbinom`. Using `nbdtri` directly can improve performance
+    compared to the ``ppf`` method of `scipy.stats.nbinom`.
+
+    References
+    ----------
+    .. [1] Cephes Mathematical Functions Library,
+           https://netlib.org/cephes/
+
+    Examples
+    --------
+    `nbdtri` is the inverse of `nbdtr` with respect to `p`.
+    Up to floating point errors the following holds:
+    ``nbdtri(k, n, nbdtr(k, n, p))=p``.
+
+    >>> import numpy as np
+    >>> from scipy.special import nbdtri, nbdtr
+    >>> k, n, p = 5, 10, 0.2
+    >>> cdf_val = nbdtr(k, n, p)
+    >>> nbdtri(k, n, cdf_val)
+    0.20000000000000004
+
+    Compute the function for ``k=10`` and ``n=5`` at several points by
+    providing a NumPy array or list for `y`.
+
+    >>> y = np.array([0.1, 0.4, 0.8])
+    >>> nbdtri(3, 5, y)
+    array([0.34462319, 0.51653095, 0.69677416])
+
+    Plot the function for three different parameter sets.
+
+    >>> import matplotlib.pyplot as plt
+    >>> n_parameters = [5, 20, 30, 30]
+    >>> k_parameters = [20, 20, 60, 80]
+    >>> linestyles = ['solid', 'dashed', 'dotted', 'dashdot']
+    >>> parameters_list = list(zip(n_parameters, k_parameters, linestyles))
+    >>> cdf_vals = np.linspace(0, 1, 1000)
+    >>> fig, ax = plt.subplots(figsize=(8, 8))
+    >>> for parameter_set in parameters_list:
+    ...     n, k, style = parameter_set
+    ...     nbdtri_vals = nbdtri(k, n, cdf_vals)
+    ...     ax.plot(cdf_vals, nbdtri_vals, label=rf"$k={k},\ n={n}$",
+    ...             ls=style)
+    >>> ax.legend()
+    >>> ax.set_ylabel("$p$")
+    >>> ax.set_xlabel("$CDF$")
+    >>> title = "nbdtri: inverse of negative binomial CDF with respect to $p$"
+    >>> ax.set_title(title)
+    >>> plt.show()
+
+    `nbdtri` can evaluate different parameter sets by providing arrays with
+    shapes compatible for broadcasting for `k`, `n` and `p`. Here we compute
+    the function for three different `k` at four locations `p`, resulting in
+    a 3x4 array.
+
+    >>> k = np.array([[5], [10], [15]])
+    >>> y = np.array([0.3, 0.5, 0.7, 0.9])
+    >>> k.shape, y.shape
+    ((3, 1), (4,))
+
+    >>> nbdtri(k, 5, y)
+    array([[0.37258157, 0.45169416, 0.53249956, 0.64578407],
+           [0.24588501, 0.30451981, 0.36778453, 0.46397088],
+           [0.18362101, 0.22966758, 0.28054743, 0.36066188]])
+    """)
+
+add_newdoc("nbdtrik",
+    r"""
+    nbdtrik(y, n, p, out=None)
+
+    Negative binomial percentile function.
+
+    Returns the inverse with respect to the parameter `k` of
+    ``y = nbdtr(k, n, p)``, the negative binomial cumulative distribution
+    function.
+
+    Parameters
+    ----------
+    y : array_like
+        The probability of `k` or fewer failures before `n` successes (float).
+    n : array_like
+        The target number of successes (positive int).
+    p : array_like
+        Probability of success in a single event (float).
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    k : scalar or ndarray
+        The maximum number of allowed failures such that `nbdtr(k, n, p) = y`.
+
+    See Also
+    --------
+    nbdtr : Cumulative distribution function of the negative binomial.
+    nbdtrc : Survival function of the negative binomial.
+    nbdtri : Inverse with respect to `p` of `nbdtr(k, n, p)`.
+    nbdtrin : Inverse with respect to `n` of `nbdtr(k, n, p)`.
+    scipy.stats.nbinom : Negative binomial distribution
+
+    Notes
+    -----
+    This function wraps routines from the Boost Math C++ library [1]_.
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    Examples
+    --------
+    Compute the negative binomial cumulative distribution function for an
+    exemplary parameter set.
+
+    >>> import numpy as np
+    >>> from scipy.special import nbdtr, nbdtrik
+    >>> k, n, p = 5, 2, 0.5
+    >>> cdf_value = nbdtr(k, n, p)
+    >>> cdf_value
+    0.9375
+
+    Verify that `nbdtrik` recovers the original value for `k`.
+
+    >>> nbdtrik(cdf_value, n, p)
+    5.0
+
+    Plot the function for different parameter sets.
+
+    >>> import matplotlib.pyplot as plt
+    >>> p_parameters = [0.2, 0.5, 0.7, 0.5]
+    >>> n_parameters = [30, 30, 30, 80]
+    >>> linestyles = ['solid', 'dashed', 'dotted', 'dashdot']
+    >>> parameters_list = list(zip(p_parameters, n_parameters, linestyles))
+    >>> cdf_vals = np.linspace(0, 1, 1000)
+    >>> fig, ax = plt.subplots(figsize=(8, 8))
+    >>> for parameter_set in parameters_list:
+    ...     p, n, style = parameter_set
+    ...     nbdtrik_vals = nbdtrik(cdf_vals, n, p)
+    ...     ax.plot(cdf_vals, nbdtrik_vals, label=rf"$n={n},\ p={p}$",
+    ...             ls=style)
+    >>> ax.legend()
+    >>> ax.set_ylabel("$k$")
+    >>> ax.set_xlabel("$CDF$")
+    >>> ax.set_title("Negative binomial percentile function")
+    >>> plt.show()
+
+    The negative binomial distribution is also available as
+    `scipy.stats.nbinom`. The percentile function  method ``ppf``
+    returns the result of `nbdtrik` rounded up to integers:
+
+    >>> from scipy.stats import nbinom
+    >>> q, n, p = 0.6, 5, 0.5
+    >>> nbinom.ppf(q, n, p), nbdtrik(q, n, p)
+    (5.0, 4.800428460273882)
+
+    """)
+
+add_newdoc("nbdtrin",
+    r"""
+    nbdtrin(k, y, p, out=None)
+
+    Inverse of `nbdtr` vs `n`.
+
+    Returns the inverse with respect to the parameter `n` of
+    ``y = nbdtr(k, n, p)``, the negative binomial cumulative distribution
+    function.
+
+    Parameters
+    ----------
+    k : array_like
+        The maximum number of allowed failures (nonnegative int).
+    y : array_like
+        The probability of `k` or fewer failures before `n` successes (float).
+    p : array_like
+        Probability of success in a single event (float).
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    n : scalar or ndarray
+        The number of successes `n` such that `nbdtr(k, n, p) = y`.
+
+    See Also
+    --------
+    nbdtr : Cumulative distribution function of the negative binomial.
+    nbdtri : Inverse with respect to `p` of `nbdtr(k, n, p)`.
+    nbdtrik : Inverse with respect to `k` of `nbdtr(k, n, p)`.
+
+    Notes
+    -----
+    This function wraps routines from the Boost Math C++ library [1]_.
+
+    Formula 26.5.26 of [2]_ or [3]_,
+
+    .. math::
+        \sum_{j=k + 1}^\infty {{n + j - 1}
+        \choose{j}} p^n (1 - p)^j = I_{1 - p}(k + 1, n),
+
+    is used to reduce calculation of the cumulative distribution function to
+    that of a regularized incomplete beta :math:`I`.
+
+    Computation of `n` involves a search for a value that produces the desired
+    value of `y`.  The search relies on the monotonicity of `y` with `n`.
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+    .. [2] Milton Abramowitz and Irene A. Stegun, eds.
+           Handbook of Mathematical Functions with Formulas,
+           Graphs, and Mathematical Tables. New York: Dover, 1972.
+    .. [3] NIST Digital Library of Mathematical Functions
+           https://dlmf.nist.gov/8.17.E24
+
+    Examples
+    --------
+    Compute the negative binomial cumulative distribution function for an
+    exemplary parameter set.
+
+    >>> from scipy.special import nbdtr, nbdtrin
+    >>> k, n, p = 5, 2, 0.5
+    >>> cdf_value = nbdtr(k, n, p)
+    >>> cdf_value
+    0.9375
+
+    Verify that `nbdtrin` recovers the original value for `n` up to floating
+    point accuracy.
+
+    >>> nbdtrin(k, cdf_value, p)
+    2.0
+    """)
+
+add_newdoc("ncfdtr",
+    r"""
+    ncfdtr(dfn, dfd, nc, f, out=None)
+
+    Cumulative distribution function of the non-central F distribution.
+
+    The non-central F describes the distribution of,
+
+    .. math::
+        Z = \frac{X/d_n}{Y/d_d}
+
+    where :math:`X` and :math:`Y` are independently distributed, with
+    :math:`X` distributed non-central :math:`\chi^2` with noncentrality
+    parameter `nc` and :math:`d_n` degrees of freedom, and :math:`Y`
+    distributed :math:`\chi^2` with :math:`d_d` degrees of freedom.
+
+    Parameters
+    ----------
+    dfn : array_like
+        Degrees of freedom of the numerator sum of squares.  Range (0, inf).
+    dfd : array_like
+        Degrees of freedom of the denominator sum of squares.  Range (0, inf).
+    nc : array_like
+        Noncentrality parameter.  Range [0, inf).
+    f : array_like
+        Quantiles, i.e. the upper limit of integration.
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    cdf : scalar or ndarray
+        The calculated CDF.  If all inputs are scalar, the return will be a
+        float.  Otherwise it will be an array.
+
+    See Also
+    --------
+    ncfdtri : Quantile function; inverse of `ncfdtr` with respect to `f`.
+    ncfdtridfd : Inverse of `ncfdtr` with respect to `dfd`.
+    ncfdtridfn : Inverse of `ncfdtr` with respect to `dfn`.
+    ncfdtrinc : Inverse of `ncfdtr` with respect to `nc`.
+    scipy.stats.ncf : Non-central F distribution.
+
+    Notes
+    -----
+    This function calculates the CDF of the non-central f distribution using
+    the Boost Math C++ library [1]_.
+
+    The cumulative distribution function is computed using Formula 26.6.20 of
+    [2]_:
+
+    .. math::
+        F(d_n, d_d, n_c, f) = \sum_{j=0}^\infty e^{-n_c/2}
+        \frac{(n_c/2)^j}{j!} I_{x}(\frac{d_n}{2} + j, \frac{d_d}{2}),
+
+    where :math:`I` is the regularized incomplete beta function, and
+    :math:`x = f d_n/(f d_n + d_d)`.
+
+    Note that argument order of `ncfdtr` is different from that of the
+    similar ``cdf`` method of `scipy.stats.ncf`: `f` is the last
+    parameter of `ncfdtr` but the first parameter of ``scipy.stats.ncf.cdf``.
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+    .. [2] Milton Abramowitz and Irene A. Stegun, eds.
+           Handbook of Mathematical Functions with Formulas,
+           Graphs, and Mathematical Tables. New York: Dover, 1972.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import special
+    >>> from scipy import stats
+    >>> import matplotlib.pyplot as plt
+
+    Plot the CDF of the non-central F distribution, for nc=0.  Compare with the
+    F-distribution from scipy.stats:
+
+    >>> x = np.linspace(-1, 8, num=500)
+    >>> dfn = 3
+    >>> dfd = 2
+    >>> ncf_stats = stats.f.cdf(x, dfn, dfd)
+    >>> ncf_special = special.ncfdtr(dfn, dfd, 0, x)
+
+    >>> fig = plt.figure()
+    >>> ax = fig.add_subplot(111)
+    >>> ax.plot(x, ncf_stats, 'b-', lw=3)
+    >>> ax.plot(x, ncf_special, 'r-')
+    >>> plt.show()
+
+    """)
+
+add_newdoc("ncfdtri",
+    """
+    ncfdtri(dfn, dfd, nc, p, out=None)
+
+    Inverse with respect to `f` of the CDF of the non-central F distribution.
+
+    See `ncfdtr` for more details.
+
+    Parameters
+    ----------
+    dfn : array_like
+        Degrees of freedom of the numerator sum of squares.  Range (0, inf).
+    dfd : array_like
+        Degrees of freedom of the denominator sum of squares.  Range (0, inf).
+    nc : array_like
+        Noncentrality parameter.  Range [0, inf).
+    p : array_like
+        Value of the cumulative distribution function.  Must be in the
+        range [0, 1].
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    f : scalar or ndarray
+        Quantiles, i.e., the upper limit of integration.
+
+    See Also
+    --------
+    ncfdtr : CDF of the non-central F distribution.
+    ncfdtridfd : Inverse of `ncfdtr` with respect to `dfd`.
+    ncfdtridfn : Inverse of `ncfdtr` with respect to `dfn`.
+    ncfdtrinc : Inverse of `ncfdtr` with respect to `nc`.
+    scipy.stats.ncf : Non-central F distribution.
+
+    Notes
+    -----
+    This function calculates the Quantile of the non-central f distribution
+    using the Boost Math C++ library [1]_.
+
+    Note that argument order of `ncfdtri` is different from that of the
+    similar ``ppf`` method of `scipy.stats.ncf`. `p` is the last parameter
+    of `ncfdtri` but the first parameter of ``scipy.stats.ncf.ppf``.
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    Examples
+    --------
+    >>> from scipy.special import ncfdtr, ncfdtri
+
+    Compute the CDF for several values of `f`:
+
+    >>> f = [0.5, 1, 1.5]
+    >>> p = ncfdtr(2, 3, 1.5, f)
+    >>> p
+    array([ 0.20782291,  0.36107392,  0.47345752])
+
+    Compute the inverse.  We recover the values of `f`, as expected:
+
+    >>> ncfdtri(2, 3, 1.5, p)
+    array([ 0.5,  1. ,  1.5])
+
+    """)
+
+add_newdoc("ncfdtridfd",
+    """
+    ncfdtridfd(dfn, p, nc, f, out=None)
+
+    Calculate degrees of freedom (denominator) for the noncentral F-distribution.
+
+    This is the inverse with respect to `dfd` of `ncfdtr`.
+    See `ncfdtr` for more details.
+
+    Parameters
+    ----------
+    dfn : array_like
+        Degrees of freedom of the numerator sum of squares.  Range (0, inf).
+    p : array_like
+        Value of the cumulative distribution function.  Must be in the
+        range [0, 1].
+    nc : array_like
+        Noncentrality parameter.  Should be in range (0, 1e4).
+    f : array_like
+        Quantiles, i.e., the upper limit of integration.
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    dfd : scalar or ndarray
+        Degrees of freedom of the denominator sum of squares.
+
+    See Also
+    --------
+    ncfdtr : CDF of the non-central F distribution.
+    ncfdtri : Quantile function; inverse of `ncfdtr` with respect to `f`.
+    ncfdtridfn : Inverse of `ncfdtr` with respect to `dfn`.
+    ncfdtrinc : Inverse of `ncfdtr` with respect to `nc`.
+
+    Notes
+    -----
+    The value of the cumulative noncentral F distribution is not necessarily
+    monotone in either degrees of freedom. There thus may be two values that
+    provide a given CDF value. This routine assumes monotonicity and will
+    find an arbitrary one of the two values.
+
+    Examples
+    --------
+    >>> from scipy.special import ncfdtr, ncfdtridfd
+
+    Compute the CDF for several values of `dfd`:
+
+    >>> dfd = [1, 2, 3]
+    >>> p = ncfdtr(2, dfd, 0.25, 15)
+    >>> p
+    array([ 0.8097138 ,  0.93020416,  0.96787852])
+
+    Compute the inverse.  We recover the values of `dfd`, as expected:
+
+    >>> ncfdtridfd(2, p, 0.25, 15)
+    array([ 1.,  2.,  3.])
+
+    """)
+
+add_newdoc("ncfdtridfn",
+    """
+    ncfdtridfn(p, dfd, nc, f, out=None)
+
+    Calculate degrees of freedom (numerator) for the noncentral F-distribution.
+
+    This is the inverse with respect to `dfn` of `ncfdtr`.
+    See `ncfdtr` for more details.
+
+    Parameters
+    ----------
+    p : array_like
+        Value of the cumulative distribution function. Must be in the
+        range [0, 1].
+    dfd : array_like
+        Degrees of freedom of the denominator sum of squares. Range (0, inf).
+    nc : array_like
+        Noncentrality parameter.  Should be in range (0, 1e4).
+    f : float
+        Quantiles, i.e., the upper limit of integration.
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    dfn : scalar or ndarray
+        Degrees of freedom of the numerator sum of squares.
+
+    See Also
+    --------
+    ncfdtr : CDF of the non-central F distribution.
+    ncfdtri : Quantile function; inverse of `ncfdtr` with respect to `f`.
+    ncfdtridfd : Inverse of `ncfdtr` with respect to `dfd`.
+    ncfdtrinc : Inverse of `ncfdtr` with respect to `nc`.
+
+    Notes
+    -----
+    The value of the cumulative noncentral F distribution is not necessarily
+    monotone in either degrees of freedom. There thus may be two values that
+    provide a given CDF value. This routine assumes monotonicity and will
+    find an arbitrary one of the two values.
+
+    Examples
+    --------
+    >>> from scipy.special import ncfdtr, ncfdtridfn
+
+    Compute the CDF for several values of `dfn`:
+
+    >>> dfn = [1, 2, 3]
+    >>> p = ncfdtr(dfn, 2, 0.25, 15)
+    >>> p
+    array([ 0.92562363,  0.93020416,  0.93188394])
+
+    Compute the inverse. We recover the values of `dfn`, as expected:
+
+    >>> ncfdtridfn(p, 2, 0.25, 15)
+    array([ 1.,  2.,  3.])
+
+    """)
+
+add_newdoc("ncfdtrinc",
+    """
+    ncfdtrinc(dfn, dfd, p, f, out=None)
+
+    Calculate non-centrality parameter for non-central F distribution.
+
+    This is the inverse with respect to `nc` of `ncfdtr`.
+    See `ncfdtr` for more details.
+
+    Parameters
+    ----------
+    dfn : array_like
+        Degrees of freedom of the numerator sum of squares. Range (0, inf).
+    dfd : array_like
+        Degrees of freedom of the denominator sum of squares. Range (0, inf).
+    p : array_like
+        Value of the cumulative distribution function. Must be in the
+        range [0, 1].
+    f : array_like
+        Quantiles, i.e., the upper limit of integration.
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    nc : scalar or ndarray
+        Noncentrality parameter.
+
+    See Also
+    --------
+    ncfdtr : CDF of the non-central F distribution.
+    ncfdtri : Quantile function; inverse of `ncfdtr` with respect to `f`.
+    ncfdtridfd : Inverse of `ncfdtr` with respect to `dfd`.
+    ncfdtridfn : Inverse of `ncfdtr` with respect to `dfn`.
+
+    Examples
+    --------
+    >>> from scipy.special import ncfdtr, ncfdtrinc
+
+    Compute the CDF for several values of `nc`:
+
+    >>> nc = [0.5, 1.5, 2.0]
+    >>> p = ncfdtr(2, 3, nc, 15)
+    >>> p
+    array([ 0.96309246,  0.94327955,  0.93304098])
+
+    Compute the inverse. We recover the values of `nc`, as expected:
+
+    >>> ncfdtrinc(2, 3, p, 15)
+    array([ 0.5,  1.5,  2. ])
+
+    """)
+
+add_newdoc("nctdtr",
+    """
+    nctdtr(df, nc, t, out=None)
+
+    Cumulative distribution function of the non-central `t` distribution.
+
+    Parameters
+    ----------
+    df : array_like
+        Degrees of freedom of the distribution. Should be in range (0, inf).
+    nc : array_like
+        Noncentrality parameter.
+    t : array_like
+        Quantiles, i.e., the upper limit of integration.
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    cdf : scalar or ndarray
+        The calculated CDF. If all inputs are scalar, the return will be a
+        float. Otherwise, it will be an array.
+
+    See Also
+    --------
+    nctdtrit : Inverse CDF (iCDF) of the non-central t distribution.
+    nctdtridf : Calculate degrees of freedom, given CDF and iCDF values.
+    nctdtrinc : Calculate non-centrality parameter, given CDF iCDF values.
+
+    Notes
+    -----
+    This function calculates the CDF of the non-central t distribution using
+    the Boost Math C++ library [1]_.
+
+    Note that the argument order of `nctdtr` is different from that of the
+    similar ``cdf`` method of `scipy.stats.nct`: `t` is the last
+    parameter of `nctdtr` but the first parameter of ``scipy.stats.nct.cdf``.
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import special
+    >>> from scipy import stats
+    >>> import matplotlib.pyplot as plt
+
+    Plot the CDF of the non-central t distribution, for nc=0. Compare with the
+    t-distribution from scipy.stats:
+
+    >>> x = np.linspace(-5, 5, num=500)
+    >>> df = 3
+    >>> nct_stats = stats.t.cdf(x, df)
+    >>> nct_special = special.nctdtr(df, 0, x)
+
+    >>> fig = plt.figure()
+    >>> ax = fig.add_subplot(111)
+    >>> ax.plot(x, nct_stats, 'b-', lw=3)
+    >>> ax.plot(x, nct_special, 'r-')
+    >>> plt.show()
+
+    """)
+
+add_newdoc("nctdtridf",
+    """
+    nctdtridf(p, nc, t, out=None)
+
+    Calculate degrees of freedom for non-central t distribution.
+
+    See `nctdtr` for more details.
+
+    Parameters
+    ----------
+    p : array_like
+        CDF values, in range (0, 1].
+    nc : array_like
+        Noncentrality parameter. Should be in range (-1e6, 1e6).
+    t : array_like
+        Quantiles, i.e., the upper limit of integration.
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    df : scalar or ndarray
+        The degrees of freedom. If all inputs are scalar, the return will be a
+        float. Otherwise, it will be an array.
+
+    See Also
+    --------
+    nctdtr :  CDF of the non-central `t` distribution.
+    nctdtrit : Inverse CDF (iCDF) of the non-central t distribution.
+    nctdtrinc : Calculate non-centrality parameter, given CDF iCDF values.
+
+    Examples
+    --------
+    >>> from scipy.special import nctdtr, nctdtridf
+
+    Compute the CDF for several values of `df`:
+
+    >>> df = [1, 2, 3]
+    >>> p = nctdtr(df, 0.25, 1)
+    >>> p
+    array([0.67491974, 0.716464  , 0.73349456])
+
+    Compute the inverse. We recover the values of `df`, as expected:
+
+    >>> nctdtridf(p, 0.25, 1)
+    array([1., 2., 3.])
+
+    """)
+
+add_newdoc("nctdtrinc",
+    """
+    nctdtrinc(df, p, t, out=None)
+
+    Calculate non-centrality parameter for non-central t distribution.
+
+    See `nctdtr` for more details.
+
+    Parameters
+    ----------
+    df : array_like
+        Degrees of freedom of the distribution. Should be in range (0, inf).
+    p : array_like
+        CDF values, in range (0, 1].
+    t : array_like
+        Quantiles, i.e., the upper limit of integration.
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    nc : scalar or ndarray
+        Noncentrality parameter
+
+    See Also
+    --------
+    nctdtr :  CDF of the non-central `t` distribution.
+    nctdtrit : Inverse CDF (iCDF) of the non-central t distribution.
+    nctdtridf : Calculate degrees of freedom, given CDF and iCDF values.
+
+    Examples
+    --------
+    >>> from scipy.special import nctdtr, nctdtrinc
+
+    Compute the CDF for several values of `nc`:
+
+    >>> nc = [0.5, 1.5, 2.5]
+    >>> p = nctdtr(3, nc, 1.5)
+    >>> p
+    array([0.77569497, 0.45524533, 0.1668691 ])
+
+    Compute the inverse. We recover the values of `nc`, as expected:
+
+    >>> nctdtrinc(3, p, 1.5)
+    array([0.5, 1.5, 2.5])
+
+    """)
+
+add_newdoc("nctdtrit",
+    """
+    nctdtrit(df, nc, p, out=None)
+
+    Inverse cumulative distribution function of the non-central t distribution.
+
+    See `nctdtr` for more details.
+
+    Parameters
+    ----------
+    df : array_like
+        Degrees of freedom of the distribution. Should be in range (0, inf).
+    nc : array_like
+        Noncentrality parameter.
+    p : array_like
+        CDF values, in range (0, 1].
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    t : scalar or ndarray
+        Quantiles
+
+    See Also
+    --------
+    nctdtr :  CDF of the non-central `t` distribution.
+    nctdtridf : Calculate degrees of freedom, given CDF and iCDF values.
+    nctdtrinc : Calculate non-centrality parameter, given CDF iCDF values.
+
+    Notes
+    -----
+    This function calculates the quantile of the non-central t distribution using
+    the Boost Math C++ library [1]_.
+
+    Note that the argument order of `nctdtrit` is different from that of the
+    similar ``ppf`` method of `scipy.stats.nct`: `t` is the last
+    parameter of `nctdtrit` but the first parameter of ``scipy.stats.nct.ppf``.
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    Examples
+    --------
+    >>> from scipy.special import nctdtr, nctdtrit
+
+    Compute the CDF for several values of `t`:
+
+    >>> t = [0.5, 1, 1.5]
+    >>> p = nctdtr(3, 1, t)
+    >>> p
+    array([0.29811049, 0.46922687, 0.6257559 ])
+
+    Compute the inverse. We recover the values of `t`, as expected:
+
+    >>> nctdtrit(3, 1, p)
+    array([0.5, 1. , 1.5])
+
+    """)
+
+add_newdoc("nrdtrimn",
+    """
+    nrdtrimn(p, std, x, out=None)
+
+    Calculate mean of normal distribution given other params.
+
+    Parameters
+    ----------
+    p : array_like
+        CDF values, in range (0, 1].
+    std : array_like
+        Standard deviation.
+    x : array_like
+        Quantiles, i.e. the upper limit of integration.
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    mn : scalar or ndarray
+        The mean of the normal distribution.
+
+    See Also
+    --------
+    scipy.stats.norm : Normal distribution
+    ndtr : Standard normal cumulative probability distribution
+    ndtri : Inverse of standard normal CDF with respect to quantile
+    nrdtrisd : Inverse of normal distribution CDF with respect to
+               standard deviation
+
+    Examples
+    --------
+    `nrdtrimn` can be used to recover the mean of a normal distribution
+    if we know the CDF value `p` for a given quantile `x` and the
+    standard deviation `std`. First, we calculate
+    the normal distribution CDF for an exemplary parameter set.
+
+    >>> from scipy.stats import norm
+    >>> mean = 3.
+    >>> std = 2.
+    >>> x = 6.
+    >>> p = norm.cdf(x, loc=mean, scale=std)
+    >>> p
+    0.9331927987311419
+
+    Verify that `nrdtrimn` returns the original value for `mean`.
+
+    >>> from scipy.special import nrdtrimn
+    >>> nrdtrimn(p, std, x)
+    3.0000000000000004
+
+    """)
+
+add_newdoc("nrdtrisd",
+    """
+    nrdtrisd(mn, p, x, out=None)
+
+    Calculate standard deviation of normal distribution given other params.
+
+    Parameters
+    ----------
+    mn : scalar or ndarray
+        The mean of the normal distribution.
+    p : array_like
+        CDF values, in range (0, 1].
+    x : array_like
+        Quantiles, i.e. the upper limit of integration.
+
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    std : scalar or ndarray
+        Standard deviation.
+
+    See Also
+    --------
+    scipy.stats.norm : Normal distribution
+    ndtr : Standard normal cumulative probability distribution
+    ndtri : Inverse of standard normal CDF with respect to quantile
+    nrdtrimn : Inverse of normal distribution CDF with respect to
+               mean
+
+    Examples
+    --------
+    `nrdtrisd` can be used to recover the standard deviation of a normal
+    distribution if we know the CDF value `p` for a given quantile `x` and
+    the mean `mn`. First, we calculate the normal distribution CDF for an
+    exemplary parameter set.
+
+    >>> from scipy.stats import norm
+    >>> mean = 3.
+    >>> std = 2.
+    >>> x = 6.
+    >>> p = norm.cdf(x, loc=mean, scale=std)
+    >>> p
+    0.9331927987311419
+
+    Verify that `nrdtrisd` returns the original value for `std`.
+
+    >>> from scipy.special import nrdtrisd
+    >>> nrdtrisd(mean, p, x)
+    2.0000000000000004
+
+    """)
+
+add_newdoc("ndtri",
+    """
+    ndtri(p, out=None)
+
+    Inverse of `ndtr`.
+
+    Returns the quantile `x` such that the cumulative distribution function of the
+    standard normal distribution evaluated at `x` equals `p`, that is, ``ndtr(x) == p``.
+
+    Parameters
+    ----------
+    p : array_like
+        Probability values.
+    out : ndarray, optional
+        Optional output array for the function results.
+
+    Returns
+    -------
+    x : scalar or ndarray
+        Quantile(s) corresponding to the probabilitie(s) in `p`.
+
+    See Also
+    --------
+    ndtr : Standard normal cumulative distribution function
+    ndtri_exp : Inverse of log_ndtr
+
+    Examples
+    --------
+    `ndtri` is the percentile (quantile) function of the standard normal distribution,
+    i.e., the inverse of the cumulative distribution function `ndtr`.
+
+    First, compute a cumulative distribution value:
+
+    >>> import numpy as np
+    >>> from scipy.special import ndtri, ndtr
+    >>> cdf_val = ndtr(2)
+    >>> cdf_val
+    0.9772498680518208
+
+    Verify that `ndtri` yields the original value for `x` up to floating point errors.
+
+    >>> ndtri(cdf_val)
+    2.0000000000000004
+
+    Plot the percentile function over a range of probabilities.
+
+    >>> import matplotlib.pyplot as plt
+    >>> p = np.linspace(1e-3, 1 - 1e-3, 201)
+    >>> fig, ax = plt.subplots()
+    >>> ax.plot(p, ndtri(p))
+    >>> ax.set_title("Standard normal percentile function")
+    >>> plt.show()
+    """)
+
+add_newdoc("pdtr",
+    r"""
+    pdtr(k, m, out=None)
+
+    Poisson cumulative distribution function.
+
+    Defined as the probability that a Poisson-distributed random
+    variable with event rate :math:`m` is less than or equal to
+    :math:`k`. More concretely, this works out to be [1]_
+
+    .. math::
+
+       \exp(-m) \sum_{j = 0}^{\lfloor{k}\rfloor} \frac{m^j}{j!}.
+
+    Parameters
+    ----------
+    k : array_like
+        Number of occurrences (nonnegative, real)
+    m : array_like
+        Shape parameter (nonnegative, real)
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    scalar or ndarray
+        Values of the Poisson cumulative distribution function
+
+    See Also
+    --------
+    pdtrc : Poisson survival function
+    pdtrik : inverse of `pdtr` with respect to `k`
+    pdtri : inverse of `pdtr` with respect to `m`
+
+    References
+    ----------
+    .. [1] https://en.wikipedia.org/wiki/Poisson_distribution
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import scipy.special as sc
+
+    It is a cumulative distribution function, so it converges to 1
+    monotonically as `k` goes to infinity.
+
+    >>> sc.pdtr([1, 10, 100, np.inf], 1)
+    array([0.73575888, 0.99999999, 1.        , 1.        ])
+
+    It is discontinuous at integers and constant between integers.
+
+    >>> sc.pdtr([1, 1.5, 1.9, 2], 1)
+    array([0.73575888, 0.73575888, 0.73575888, 0.9196986 ])
+
+    """)
+
+add_newdoc("pdtrc",
+    """
+    pdtrc(k, m, out=None)
+
+    Poisson survival function.
+
+    Returns the sum of the terms from k+1 to infinity of the Poisson
+    distribution: sum(exp(-m) * m**j / j!, j=k+1..inf) = gammainc(
+    k+1, m). Arguments must both be non-negative doubles.
+
+    Parameters
+    ----------
+    k : array_like
+        Number of occurrences (nonnegative, real)
+    m : array_like
+        Shape parameter (nonnegative, real)
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    scalar or ndarray
+        Values of the Poisson survival function
+
+    See Also
+    --------
+    pdtr : Poisson cumulative distribution function
+    pdtrik : inverse of `pdtr` with respect to `k`
+    pdtri : inverse of `pdtr` with respect to `m`
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import scipy.special as sc
+
+    It is a survival function, so it decreases to 0
+    monotonically as `k` goes to infinity.
+
+    >>> k = np.array([1, 10, 100, np.inf])
+    >>> sc.pdtrc(k, 1)
+    array([2.64241118e-001, 1.00477664e-008, 3.94147589e-161, 0.00000000e+000])
+
+    It can be expressed in terms of the lower incomplete gamma
+    function `gammainc`.
+
+    >>> sc.gammainc(k + 1, 1)
+    array([2.64241118e-001, 1.00477664e-008, 3.94147589e-161, 0.00000000e+000])
+
+    """)
+
+add_newdoc("pdtri",
+    """
+    pdtri(k, y, out=None)
+
+    Inverse of `pdtr` with respect to `m`.
+
+    Returns the Poisson variable `m` such that the sum from 0 to `k` of
+    the Poisson density is equal to the given probability `y`:
+    calculated by ``gammainccinv(k + 1, y)``. `k` must be a nonnegative
+    integer and `y` between 0 and 1.
+
+    Parameters
+    ----------
+    k : array_like
+        Number of occurrences (nonnegative, real).
+    y : array_like
+        Probability.
+    out : ndarray, optional
+        Optional output array for the function results.
+
+    Returns
+    -------
+    scalar or ndarray
+        Values of the shape parameter `m` such that ``pdtr(k, m) = y``.
+
+    See Also
+    --------
+    pdtr : Poisson cumulative distribution function
+    pdtrc : Poisson survival function
+    pdtrik : Inverse of `pdtr` with respect to `k`
+
+    Examples
+    --------
+    >>> import scipy.special as sc
+
+    Compute the CDF for several values of `m`:
+
+    >>> k = 1
+    >>> m = [0.5, 1, 1.5]
+    >>> p = sc.pdtr(k, m)
+    >>> p
+    array([0.90979599, 0.73575888, 0.5578254 ])
+
+    Invert the CDF with respect to the Poisson mean. We recover the values
+    of `m`, as expected:
+
+    >>> sc.pdtri(k, p)
+    array([0.5, 1. , 1.5])
+
+    Verify the relation with `gammainccinv`:
+
+    >>> sc.gammainccinv(k + 1, p)
+    array([0.5, 1. , 1.5])
+
+
+    """)
+
+add_newdoc("pdtrik",
+    """
+    pdtrik(p, m, out=None)
+
+    Inverse of `pdtr` with respect to `k`.
+
+    Parameters
+    ----------
+    p : array_like
+        Probability
+    m : array_like
+        Shape parameter (nonnegative, real)
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    scalar or ndarray
+        The number of occurrences `k` such that ``pdtr(k, m) = p``
+
+    See Also
+    --------
+    pdtr : Poisson cumulative distribution function
+    pdtrc : Poisson survival function
+    pdtri : inverse of `pdtr` with respect to `m`
+
+    Notes
+    -----
+    This function relies on the ``gamma_q_inva`` function from the Boost
+    Math C++ library [1]_.
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    Examples
+    --------
+    >>> import scipy.special as sc
+
+    Compute the CDF for several values of `k`:
+
+    >>> k = [1, 2, 3]
+    >>> p = sc.pdtr(k, 2)
+    >>> p
+    array([0.40600585, 0.67667642, 0.85712346])
+
+    Compute the inverse. We recover the values of `k`, as expected:
+
+    >>> sc.pdtrik(p, 2)
+    array([1., 2., 3.])
+
+    """)
+
+add_newdoc("poch",
+    r"""
+    poch(z, m, out=None)
+
+    Pochhammer symbol.
+
+    The Pochhammer symbol (rising factorial) is defined as
+
+    .. math::
+
+        (z)_m = \frac{\Gamma(z + m)}{\Gamma(z)}
+
+    For positive integer `m` it reads
+
+    .. math::
+
+        (z)_m = z (z + 1) ... (z + m - 1)
+
+    See [DLMF]_ for more details.
+
+    Parameters
+    ----------
+    z, m : array_like
+        Real-valued arguments.
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    scalar or ndarray
+        The value of the function.
+
+    References
+    ----------
+    .. [DLMF] Nist, Digital Library of Mathematical Functions
+        https://dlmf.nist.gov/5.2#iii
+
+    Examples
+    --------
+    >>> import scipy.special as sc
+
+    It is 1 when m is 0.
+
+    >>> sc.poch([1, 2, 3, 4], 0)
+    array([1., 1., 1., 1.])
+
+    For z equal to 1 it reduces to the factorial function.
+
+    >>> sc.poch(1, 5)
+    120.0
+    >>> 1 * 2 * 3 * 4 * 5
+    120
+
+    It can be expressed in terms of the gamma function.
+
+    >>> z, m = 3.7, 2.1
+    >>> sc.poch(z, m)
+    20.529581933776953
+    >>> sc.gamma(z + m) / sc.gamma(z)
+    20.52958193377696
+
+    """)
+
+add_newdoc("powm1", """
+    powm1(x, y, out=None)
+
+    Computes ``x**y - 1``.
+
+    This function is useful when `y` is near 0, or when `x` is near 1.
+
+    The function is implemented for real types only (unlike ``numpy.power``,
+    which accepts complex inputs).
+
+    Parameters
+    ----------
+    x : array_like
+        The base. Must be a real type (i.e. integer or float, not complex).
+    y : array_like
+        The exponent. Must be a real type (i.e. integer or float, not complex).
+
+    Returns
+    -------
+    array_like
+        Result of the calculation
+
+    Notes
+    -----
+    .. versionadded:: 1.10.0
+
+    The underlying code is implemented for single precision and double
+    precision floats only.  Unlike `numpy.power`, integer inputs to
+    `powm1` are converted to floating point, and complex inputs are
+    not accepted.
+
+    Note the following edge cases:
+
+    * ``powm1(x, 0)`` returns 0 for any ``x``, including 0, ``inf``
+      and ``nan``.
+    * ``powm1(1, y)`` returns 0 for any ``y``, including ``nan``
+      and ``inf``.
+
+    This function wraps the ``powm1`` routine from the
+    Boost Math C++ library [1]_.
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.special import powm1
+
+    >>> x = np.array([1.2, 10.0, 0.9999999975])
+    >>> y = np.array([1e-9, 1e-11, 0.1875])
+    >>> powm1(x, y)
+    array([ 1.82321557e-10,  2.30258509e-11, -4.68749998e-10])
+
+    It can be verified that the relative errors in those results
+    are less than 2.5e-16.
+
+    Compare that to the result of ``x**y - 1``, where the
+    relative errors are all larger than 8e-8:
+
+    >>> x**y - 1
+    array([ 1.82321491e-10,  2.30258035e-11, -4.68750039e-10])
+
+    """)
+
+
+add_newdoc("pseudo_huber",
+    r"""
+    pseudo_huber(delta, r, out=None)
+
+    Pseudo-Huber loss function.
+
+    .. math:: \mathrm{pseudo\_huber}(\delta, r) =
+              \delta^2 \left( \sqrt{ 1 + \left( \frac{r}{\delta} \right)^2 } - 1 \right)
+
+    Parameters
+    ----------
+    delta : array_like
+        Input array, indicating the soft quadratic vs. linear loss changepoint.
+    r : array_like
+        Input array, possibly representing residuals.
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    res : scalar or ndarray
+        The computed Pseudo-Huber loss function values.
+
+    See Also
+    --------
+    huber: Similar function which this function approximates
+
+    Notes
+    -----
+    Like `huber`, `pseudo_huber` often serves as a robust loss function
+    in statistics or machine learning to reduce the influence of outliers.
+    Unlike `huber`, `pseudo_huber` is smooth.
+
+    Typically, `r` represents residuals, the difference
+    between a model prediction and data. Then, for :math:`|r|\leq\delta`,
+    `pseudo_huber` resembles the squared error and for :math:`|r|>\delta` the
+    absolute error. This way, the Pseudo-Huber loss often achieves
+    a fast convergence in model fitting for small residuals like the squared
+    error loss function and still reduces the influence of outliers
+    (:math:`|r|>\delta`) like the absolute error loss. As :math:`\delta` is
+    the cutoff between squared and absolute error regimes, it has
+    to be tuned carefully for each problem. `pseudo_huber` is also
+    convex, making it suitable for gradient based optimization. [1]_ [2]_
+
+    .. versionadded:: 0.15.0
+
+    References
+    ----------
+    .. [1] Hartley, Zisserman, "Multiple View Geometry in Computer Vision".
+           2003. Cambridge University Press. p. 619
+    .. [2] Charbonnier et al. "Deterministic edge-preserving regularization
+           in computed imaging". 1997. IEEE Trans. Image Processing.
+           6 (2): 298 - 311.
+
+    Examples
+    --------
+    Import all necessary modules.
+
+    >>> import numpy as np
+    >>> from scipy.special import pseudo_huber, huber
+    >>> import matplotlib.pyplot as plt
+
+    Calculate the function for ``delta=1`` at ``r=2``.
+
+    >>> pseudo_huber(1., 2.)
+    1.2360679774997898
+
+    Calculate the function at ``r=2`` for different `delta` by providing
+    a list or NumPy array for `delta`.
+
+    >>> pseudo_huber([1., 2., 4.], 3.)
+    array([2.16227766, 3.21110255, 4.        ])
+
+    Calculate the function for ``delta=1`` at several points by providing
+    a list or NumPy array for `r`.
+
+    >>> pseudo_huber(2., np.array([1., 1.5, 3., 4.]))
+    array([0.47213595, 1.        , 3.21110255, 4.94427191])
+
+    The function can be calculated for different `delta` and `r` by
+    providing arrays for both with compatible shapes for broadcasting.
+
+    >>> r = np.array([1., 2.5, 8., 10.])
+    >>> deltas = np.array([[1.], [5.], [9.]])
+    >>> print(r.shape, deltas.shape)
+    (4,) (3, 1)
+
+    >>> pseudo_huber(deltas, r)
+    array([[ 0.41421356,  1.6925824 ,  7.06225775,  9.04987562],
+           [ 0.49509757,  2.95084972, 22.16990566, 30.90169944],
+           [ 0.49846624,  3.06693762, 27.37435121, 40.08261642]])
+
+    Plot the function for different `delta`.
+
+    >>> x = np.linspace(-4, 4, 500)
+    >>> deltas = [1, 2, 3]
+    >>> linestyles = ["dashed", "dotted", "dashdot"]
+    >>> fig, ax = plt.subplots()
+    >>> combined_plot_parameters = list(zip(deltas, linestyles))
+    >>> for delta, style in combined_plot_parameters:
+    ...     ax.plot(x, pseudo_huber(delta, x), label=rf"$\delta={delta}$",
+    ...             ls=style)
+    >>> ax.legend(loc="upper center")
+    >>> ax.set_xlabel("$x$")
+    >>> ax.set_title(r"Pseudo-Huber loss function $h_{\delta}(x)$")
+    >>> ax.set_xlim(-4, 4)
+    >>> ax.set_ylim(0, 8)
+    >>> plt.show()
+
+    Finally, illustrate the difference between `huber` and `pseudo_huber` by
+    plotting them and their gradients with respect to `r`. The plot shows
+    that `pseudo_huber` is continuously differentiable while `huber` is not
+    at the points :math:`\pm\delta`.
+
+    >>> def huber_grad(delta, x):
+    ...     grad = np.copy(x)
+    ...     linear_area = np.argwhere(np.abs(x) > delta)
+    ...     grad[linear_area]=delta*np.sign(x[linear_area])
+    ...     return grad
+    >>> def pseudo_huber_grad(delta, x):
+    ...     return x* (1+(x/delta)**2)**(-0.5)
+    >>> x=np.linspace(-3, 3, 500)
+    >>> delta = 1.
+    >>> fig, ax = plt.subplots(figsize=(7, 7))
+    >>> ax.plot(x, huber(delta, x), label="Huber", ls="dashed")
+    >>> ax.plot(x, huber_grad(delta, x), label="Huber Gradient", ls="dashdot")
+    >>> ax.plot(x, pseudo_huber(delta, x), label="Pseudo-Huber", ls="dotted")
+    >>> ax.plot(x, pseudo_huber_grad(delta, x), label="Pseudo-Huber Gradient",
+    ...         ls="solid")
+    >>> ax.legend(loc="upper center")
+    >>> plt.show()
+    """)
+
+add_newdoc("rel_entr",
+    r"""
+    rel_entr(x, y, out=None)
+
+    Elementwise function for computing relative entropy.
+
+    .. math::
+
+        \mathrm{rel\_entr}(x, y) =
+            \begin{cases}
+                x \log(x / y) & x > 0, y > 0 \\
+                0 & x = 0, y \ge 0 \\
+                \infty & \text{otherwise}
+            \end{cases}
+
+    Parameters
+    ----------
+    x, y : array_like
+        Input arrays
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    scalar or ndarray
+        Relative entropy of the inputs
+
+    See Also
+    --------
+    entr, kl_div, scipy.stats.entropy
+
+    Notes
+    -----
+    .. versionadded:: 0.15.0
+
+    This function is jointly convex in x and y.
+
+    The origin of this function is in convex programming; see
+    [1]_. Given two discrete probability distributions :math:`p_1,
+    \ldots, p_n` and :math:`q_1, \ldots, q_n`, the definition of relative
+    entropy in the context of *information theory* is
+
+    .. math::
+
+        \sum_{i = 1}^n \mathrm{rel\_entr}(p_i, q_i).
+
+    To compute the latter quantity, use `scipy.stats.entropy`.
+
+    See [2]_ for details.
+
+    References
+    ----------
+    .. [1] Boyd, Stephen and Lieven Vandenberghe. *Convex optimization*.
+           Cambridge University Press, 2004.
+           :doi:`10.1017/CBO9780511804441`.
+    .. [2] Kullback-Leibler divergence,
+           https://en.wikipedia.org/wiki/Kullback%E2%80%93Leibler_divergence
+
+    """)
+
+add_newdoc("round",
+    """
+    round(x, out=None)
+
+    Round to the nearest integer.
+
+    Returns the nearest integer to `x`.  If `x` ends in 0.5 exactly,
+    the nearest even integer is chosen.
+
+    Parameters
+    ----------
+    x : array_like
+        Real valued input.
+    out : ndarray, optional
+        Optional output array for the function results.
+
+    Returns
+    -------
+    scalar or ndarray
+        The nearest integers to the elements of `x`. The result is of
+        floating type, not integer type.
+
+    Examples
+    --------
+    >>> import scipy.special as sc
+
+    It rounds to even.
+
+    >>> sc.round([0.5, 1.5])
+    array([0., 2.])
+
+    """)
+
+add_newdoc("shichi",
+    r"""
+    shichi(x, out=None)
+
+    Hyperbolic sine and cosine integrals.
+
+    The hyperbolic sine integral is
+
+    .. math::
+
+      \int_0^x \frac{\sinh{t}}{t}dt
+
+    and the hyperbolic cosine integral is
+
+    .. math::
+
+      \gamma + \log(x) + \int_0^x \frac{\cosh{t} - 1}{t} dt
+
+    where :math:`\gamma` is Euler's constant and :math:`\log` is the
+    principal branch of the logarithm [1]_ (see also [2]_).
+
+    Parameters
+    ----------
+    x : array_like
+        Real or complex points at which to compute the hyperbolic sine
+        and cosine integrals.
+    out : tuple of ndarray, optional
+        Optional output arrays for the function results
+
+    Returns
+    -------
+    si : scalar or ndarray
+        Hyperbolic sine integral at ``x``
+    ci : scalar or ndarray
+        Hyperbolic cosine integral at ``x``
+
+    See Also
+    --------
+    sici : Sine and cosine integrals.
+    exp1 : Exponential integral E1.
+    expi : Exponential integral Ei.
+
+    Notes
+    -----
+    For real arguments with ``x < 0``, ``chi`` is the real part of the
+    hyperbolic cosine integral. For such points ``chi(x)`` and ``chi(x
+    + 0j)`` differ by a factor of ``1j*pi``.
+
+    For real arguments the function is computed by calling Cephes'
+    [3]_ *shichi* routine. For complex arguments the algorithm is based
+    on Mpmath's [4]_ *shi* and *chi* routines.
+
+    References
+    ----------
+    .. [1] Milton Abramowitz and Irene A. Stegun, eds.
+           Handbook of Mathematical Functions with Formulas,
+           Graphs, and Mathematical Tables. New York: Dover, 1972.
+           (See Section 5.2.)
+    .. [2] NIST Digital Library of Mathematical Functions
+           https://dlmf.nist.gov/6.2.E15 and https://dlmf.nist.gov/6.2.E16
+    .. [3] Cephes Mathematical Functions Library,
+           https://netlib.org/cephes/
+    .. [4] Fredrik Johansson and others.
+           "mpmath: a Python library for arbitrary-precision floating-point
+           arithmetic" (Version 0.19) https://mpmath.org/
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.special import shichi, sici
+
+    `shichi` accepts real or complex input:
+
+    >>> shichi(0.5)
+    (0.5069967498196671, -0.05277684495649357)
+    >>> shichi(0.5 + 2.5j)
+    ((0.11772029666668238+1.831091777729851j),
+     (0.29912435887648825+1.7395351121166562j))
+
+    The hyperbolic sine and cosine integrals Shi(z) and Chi(z) are
+    related to the sine and cosine integrals Si(z) and Ci(z) by
+
+    * Shi(z) = -i*Si(i*z)
+    * Chi(z) = Ci(-i*z) + i*pi/2
+
+    >>> z = 0.25 + 5j
+    >>> shi, chi = shichi(z)
+    >>> shi, -1j*sici(1j*z)[0]            # Should be the same.
+    ((-0.04834719325101729+1.5469354086921228j),
+     (-0.04834719325101729+1.5469354086921228j))
+    >>> chi, sici(-1j*z)[1] + 1j*np.pi/2  # Should be the same.
+    ((-0.19568708973868087+1.556276312103824j),
+     (-0.19568708973868087+1.556276312103824j))
+
+    Plot the functions evaluated on the real axis:
+
+    >>> xp = np.geomspace(1e-8, 4.0, 250)
+    >>> x = np.concatenate((-xp[::-1], xp))
+    >>> shi, chi = shichi(x)
+
+    >>> fig, ax = plt.subplots()
+    >>> ax.plot(x, shi, label='Shi(x)')
+    >>> ax.plot(x, chi, '--', label='Chi(x)')
+    >>> ax.set_xlabel('x')
+    >>> ax.set_title('Hyperbolic Sine and Cosine Integrals')
+    >>> ax.legend(shadow=True, framealpha=1, loc='lower right')
+    >>> ax.grid(True)
+    >>> plt.show()
+
+    """)
+
+add_newdoc("sici",
+    r"""
+    sici(x, out=None)
+
+    Sine and cosine integrals.
+
+    The sine integral is
+
+    .. math::
+
+      \int_0^x \frac{\sin{t}}{t}dt
+
+    and the cosine integral is
+
+    .. math::
+
+      \gamma + \log(x) + \int_0^x \frac{\cos{t} - 1}{t}dt
+
+    where :math:`\gamma` is Euler's constant and :math:`\log` is the
+    principal branch of the logarithm [1]_ (see also [2]_).
+
+    Parameters
+    ----------
+    x : array_like
+        Real or complex points at which to compute the sine and cosine
+        integrals.
+    out : tuple of ndarray, optional
+        Optional output arrays for the function results
+
+    Returns
+    -------
+    si : scalar or ndarray
+        Sine integral at ``x``
+    ci : scalar or ndarray
+        Cosine integral at ``x``
+
+    See Also
+    --------
+    shichi : Hyperbolic sine and cosine integrals.
+    exp1 : Exponential integral E1.
+    expi : Exponential integral Ei.
+
+    Notes
+    -----
+    For real arguments with ``x < 0``, ``ci`` is the real part of the
+    cosine integral. For such points ``ci(x)`` and ``ci(x + 0j)``
+    differ by a factor of ``1j*pi``.
+
+    For real arguments the function is computed by calling Cephes'
+    [3]_ *sici* routine. For complex arguments the algorithm is based
+    on Mpmath's [4]_ *si* and *ci* routines.
+
+    References
+    ----------
+    .. [1] Milton Abramowitz and Irene A. Stegun, eds.
+           Handbook of Mathematical Functions with Formulas,
+           Graphs, and Mathematical Tables. New York: Dover, 1972.
+           (See Section 5.2.)
+    .. [2] NIST Digital Library of Mathematical Functions
+           https://dlmf.nist.gov/6.2.E9, https://dlmf.nist.gov/6.2.E12,
+           and https://dlmf.nist.gov/6.2.E13
+    .. [3] Cephes Mathematical Functions Library,
+           https://netlib.org/cephes/
+    .. [4] Fredrik Johansson and others.
+           "mpmath: a Python library for arbitrary-precision floating-point
+           arithmetic" (Version 0.19) https://mpmath.org/
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.special import sici, exp1
+
+    `sici` accepts real or complex input:
+
+    >>> sici(2.5)
+    (1.7785201734438267, 0.2858711963653835)
+    >>> sici(2.5 + 3j)
+    ((4.505735874563953+0.06863305018999577j),
+    (0.0793644206906966-2.935510262937543j))
+
+    For z in the right half plane, the sine and cosine integrals are
+    related to the exponential integral E1 (implemented in SciPy as
+    `scipy.special.exp1`) by
+
+    * Si(z) = (E1(i*z) - E1(-i*z))/2i + pi/2
+    * Ci(z) = -(E1(i*z) + E1(-i*z))/2
+
+    See [1]_ (equations 5.2.21 and 5.2.23).
+
+    We can verify these relations:
+
+    >>> z = 2 - 3j
+    >>> sici(z)
+    ((4.54751388956229-1.3991965806460565j),
+    (1.408292501520851+2.9836177420296055j))
+
+    >>> (exp1(1j*z) - exp1(-1j*z))/2j + np.pi/2  # Same as sine integral
+    (4.54751388956229-1.3991965806460565j)
+
+    >>> -(exp1(1j*z) + exp1(-1j*z))/2            # Same as cosine integral
+    (1.408292501520851+2.9836177420296055j)
+
+    Plot the functions evaluated on the real axis; the dotted horizontal
+    lines are at pi/2 and -pi/2:
+
+    >>> x = np.linspace(-16, 16, 150)
+    >>> si, ci = sici(x)
+
+    >>> fig, ax = plt.subplots()
+    >>> ax.plot(x, si, label='Si(x)')
+    >>> ax.plot(x, ci, '--', label='Ci(x)')
+    >>> ax.legend(shadow=True, framealpha=1, loc='upper left')
+    >>> ax.set_xlabel('x')
+    >>> ax.set_title('Sine and Cosine Integrals')
+    >>> ax.axhline(np.pi/2, linestyle=':', alpha=0.5, color='k')
+    >>> ax.axhline(-np.pi/2, linestyle=':', alpha=0.5, color='k')
+    >>> ax.grid(True)
+    >>> plt.show()
+
+    """)
+
+add_newdoc("smirnov",
+    r"""
+    smirnov(n, d, out=None)
+
+    Kolmogorov-Smirnov complementary cumulative distribution function.
+
+    Returns the exact Kolmogorov-Smirnov complementary cumulative
+    distribution function,(aka the Survival Function) of Dn+ (or Dn-)
+    for a one-sided test of equality between an empirical and a
+    theoretical distribution. It is equal to the probability that the
+    maximum difference between a theoretical distribution and an empirical
+    one based on `n` samples is greater than d.
+
+    Parameters
+    ----------
+    n : int
+      Number of samples
+    d : float array_like
+      Deviation between the Empirical CDF (ECDF) and the target CDF.
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    scalar or ndarray
+        The value(s) of smirnov(n, d), Prob(Dn+ >= d) (Also Prob(Dn- >= d))
+
+    See Also
+    --------
+    smirnovi : The Inverse Survival Function for the distribution
+    scipy.stats.ksone : Provides the functionality as a continuous distribution
+    kolmogorov, kolmogi : Functions for the two-sided distribution
+
+    Notes
+    -----
+    `smirnov` is used by `stats.kstest` in the application of the
+    Kolmogorov-Smirnov Goodness of Fit test. For historical reasons this
+    function is exposed in `scpy.special`, but the recommended way to achieve
+    the most accurate CDF/SF/PDF/PPF/ISF computations is to use the
+    `stats.ksone` distribution.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.special import smirnov
+    >>> from scipy.stats import norm
+
+    Show the probability of a gap at least as big as 0, 0.5 and 1.0 for a
+    sample of size 5.
+
+    >>> smirnov(5, [0, 0.5, 1.0])
+    array([ 1.   ,  0.056,  0.   ])
+
+    Compare a sample of size 5 against N(0, 1), the standard normal
+    distribution with mean 0 and standard deviation 1.
+
+    `x` is the sample.
+
+    >>> x = np.array([-1.392, -0.135, 0.114, 0.190, 1.82])
+
+    >>> target = norm(0, 1)
+    >>> cdfs = target.cdf(x)
+    >>> cdfs
+    array([0.0819612 , 0.44630594, 0.5453811 , 0.57534543, 0.9656205 ])
+
+    Construct the empirical CDF and the K-S statistics (Dn+, Dn-, Dn).
+
+    >>> n = len(x)
+    >>> ecdfs = np.arange(n+1, dtype=float)/n
+    >>> cols = np.column_stack([x, ecdfs[1:], cdfs, cdfs - ecdfs[:n],
+    ...                        ecdfs[1:] - cdfs])
+    >>> with np.printoptions(precision=3):
+    ...    print(cols)
+    [[-1.392  0.2    0.082  0.082  0.118]
+     [-0.135  0.4    0.446  0.246 -0.046]
+     [ 0.114  0.6    0.545  0.145  0.055]
+     [ 0.19   0.8    0.575 -0.025  0.225]
+     [ 1.82   1.     0.966  0.166  0.034]]
+    >>> gaps = cols[:, -2:]
+    >>> Dnpm = np.max(gaps, axis=0)
+    >>> print(f'Dn-={Dnpm[0]:f}, Dn+={Dnpm[1]:f}')
+    Dn-=0.246306, Dn+=0.224655
+    >>> probs = smirnov(n, Dnpm)
+    >>> print(f'For a sample of size {n} drawn from N(0, 1):',
+    ...       f' Smirnov n={n}: Prob(Dn- >= {Dnpm[0]:f}) = {probs[0]:.4f}',
+    ...       f' Smirnov n={n}: Prob(Dn+ >= {Dnpm[1]:f}) = {probs[1]:.4f}',
+    ...       sep='\n')
+    For a sample of size 5 drawn from N(0, 1):
+     Smirnov n=5: Prob(Dn- >= 0.246306) = 0.4711
+     Smirnov n=5: Prob(Dn+ >= 0.224655) = 0.5245
+
+    Plot the empirical CDF and the standard normal CDF.
+
+    >>> import matplotlib.pyplot as plt
+    >>> plt.step(np.concatenate(([-2.5], x, [2.5])),
+    ...          np.concatenate((ecdfs, [1])),
+    ...          where='post', label='Empirical CDF')
+    >>> xx = np.linspace(-2.5, 2.5, 100)
+    >>> plt.plot(xx, target.cdf(xx), '--', label='CDF for N(0, 1)')
+
+    Add vertical lines marking Dn+ and Dn-.
+
+    >>> iminus, iplus = np.argmax(gaps, axis=0)
+    >>> plt.vlines([x[iminus]], ecdfs[iminus], cdfs[iminus], color='r',
+    ...            alpha=0.5, lw=4)
+    >>> plt.vlines([x[iplus]], cdfs[iplus], ecdfs[iplus+1], color='m',
+    ...            alpha=0.5, lw=4)
+
+    >>> plt.grid(True)
+    >>> plt.legend(framealpha=1, shadow=True)
+    >>> plt.show()
+    """)
+
+add_newdoc("smirnovi",
+    """
+    smirnovi(n, p, out=None)
+
+    Inverse to `smirnov`.
+
+    Returns `d` such that ``smirnov(n, d) == p``, the critical value
+    corresponding to `p`.
+
+    Parameters
+    ----------
+    n : int
+      Number of samples
+    p : float array_like
+        Probability
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    scalar or ndarray
+        The value(s) of smirnovi(n, p), the critical values.
+
+    See Also
+    --------
+    smirnov : The Survival Function (SF) for the distribution
+    scipy.stats.ksone : Provides the functionality as a continuous distribution
+    kolmogorov, kolmogi : Functions for the two-sided distribution
+    scipy.stats.kstwobign : Two-sided Kolmogorov-Smirnov distribution, large n
+
+    Notes
+    -----
+    `smirnov` is used by `stats.kstest` in the application of the
+    Kolmogorov-Smirnov Goodness of Fit test. For historical reasons this
+    function is exposed in `scpy.special`, but the recommended way to achieve
+    the most accurate CDF/SF/PDF/PPF/ISF computations is to use the
+    `stats.ksone` distribution.
+
+    Examples
+    --------
+    >>> from scipy.special import smirnovi, smirnov
+
+    >>> n = 24
+    >>> deviations = [0.1, 0.2, 0.3]
+
+    Use `smirnov` to compute the complementary CDF of the Smirnov
+    distribution for the given number of samples and deviations.
+
+    >>> p = smirnov(n, deviations)
+    >>> p
+    array([0.58105083, 0.12826832, 0.01032231])
+
+    The inverse function ``smirnovi(n, p)`` returns ``deviations``.
+
+    >>> smirnovi(n, p)
+    array([0.1, 0.2, 0.3])
+
+    """)
+
+add_newdoc("_smirnovc",
+    """
+    _smirnovc(n, d)
+     Internal function, do not use.
+    """)
+
+add_newdoc("_smirnovci",
+    """
+     Internal function, do not use.
+    """)
+
+add_newdoc("_smirnovp",
+    """
+    _smirnovp(n, p)
+     Internal function, do not use.
+    """)
+
+add_newdoc("spence",
+    r"""
+    spence(z, out=None)
+
+    Spence's function, also known as the dilogarithm.
+
+    It is defined to be
+
+    .. math::
+      \int_1^z \frac{\log(t)}{1 - t}dt
+
+    for complex :math:`z`, where the contour of integration is taken
+    to avoid the branch cut of the logarithm. Spence's function is
+    analytic everywhere except the negative real axis where it has a
+    branch cut.
+
+    Parameters
+    ----------
+    z : array_like
+        Points at which to evaluate Spence's function
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    s : scalar or ndarray
+        Computed values of Spence's function
+
+    Notes
+    -----
+    There is a different convention which defines Spence's function by
+    the integral
+
+    .. math::
+      -\int_0^z \frac{\log(1 - t)}{t}dt;
+
+    this is our ``spence(1 - z)``.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.special import spence
+    >>> import matplotlib.pyplot as plt
+
+    The function is defined for complex inputs:
+
+    >>> spence([1-1j, 1.5+2j, 3j, -10-5j])
+    array([-0.20561676+0.91596559j, -0.86766909-1.39560134j,
+           -0.59422064-2.49129918j, -1.14044398+6.80075924j])
+
+    For complex inputs on the branch cut, which is the negative real axis,
+    the function returns the limit for ``z`` with positive imaginary part.
+    For example, in the following, note the sign change of the imaginary
+    part of the output for ``z = -2`` and ``z = -2 - 1e-8j``:
+
+    >>> spence([-2 + 1e-8j, -2, -2 - 1e-8j])
+    array([2.32018041-3.45139229j, 2.32018042-3.4513923j ,
+           2.32018041+3.45139229j])
+
+    The function returns ``nan`` for real inputs on the branch cut:
+
+    >>> spence(-1.5)
+    nan
+
+    Verify some particular values: ``spence(0) = pi**2/6``,
+    ``spence(1) = 0`` and ``spence(2) = -pi**2/12``.
+
+    >>> spence([0, 1, 2])
+    array([ 1.64493407,  0.        , -0.82246703])
+    >>> np.pi**2/6, -np.pi**2/12
+    (1.6449340668482264, -0.8224670334241132)
+
+    Verify the identity::
+
+        spence(z) + spence(1 - z) = pi**2/6 - log(z)*log(1 - z)
+
+    >>> z = 3 + 4j
+    >>> spence(z) + spence(1 - z)
+    (-2.6523186143876067+1.8853470951513935j)
+    >>> np.pi**2/6 - np.log(z)*np.log(1 - z)
+    (-2.652318614387606+1.885347095151394j)
+
+    Plot the function for positive real input.
+
+    >>> fig, ax = plt.subplots()
+    >>> x = np.linspace(0, 6, 400)
+    >>> ax.plot(x, spence(x))
+    >>> ax.grid()
+    >>> ax.set_xlabel('x')
+    >>> ax.set_title('spence(x)')
+    >>> plt.show()
+    """)
+
+add_newdoc(
+    "stdtr",
+    r"""
+    stdtr(df, t, out=None)
+
+    Student t distribution cumulative distribution function.
+
+    Returns the integral:
+
+    .. math::
+        \frac{\Gamma((df+1)/2)}{\sqrt{\pi df} \Gamma(df/2)}
+        \int_{-\infty}^t (1+x^2/df)^{-(df+1)/2}\, dx
+
+    Parameters
+    ----------
+    df : array_like
+        Degrees of freedom
+    t : array_like
+        Upper bound of the integral
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    scalar or ndarray
+        Value of the Student t CDF at t
+
+    See Also
+    --------
+    stdtridf : inverse of stdtr with respect to `df`
+    stdtrit : inverse of stdtr with respect to `t`
+    scipy.stats.t : student t distribution
+
+    Notes
+    -----
+    The student t distribution is also available as `scipy.stats.t`.
+    Calling `stdtr` directly can improve performance compared to the
+    ``cdf`` method of `scipy.stats.t` (see last example below).
+
+    The function is computed using the Boost Math library [1]_, which
+    relies on the incomplete beta function.
+
+    References
+    ----------
+    .. [1] Boost C++ Libraries, https://www.boost.org/
+
+    Examples
+    --------
+    Calculate the function for ``df=3`` at ``t=1``.
+
+    >>> import numpy as np
+    >>> from scipy.special import stdtr
+    >>> import matplotlib.pyplot as plt
+    >>> stdtr(3, 1)
+    0.8044988905221148
+
+    Plot the function for three different degrees of freedom.
+
+    >>> x = np.linspace(-10, 10, 1000)
+    >>> fig, ax = plt.subplots()
+    >>> parameters = [(1, "solid"), (3, "dashed"), (10, "dotted")]
+    >>> for (df, linestyle) in parameters:
+    ...     ax.plot(x, stdtr(df, x), ls=linestyle, label=f"$df={df}$")
+    >>> ax.legend()
+    >>> ax.set_title("Student t distribution cumulative distribution function")
+    >>> plt.show()
+
+    The function can be computed for several degrees of freedom at the same
+    time by providing a NumPy array or list for `df`:
+
+    >>> stdtr([1, 2, 3], 1)
+    array([0.75      , 0.78867513, 0.80449889])
+
+    It is possible to calculate the function at several points for several
+    different degrees of freedom simultaneously by providing arrays for `df`
+    and `t` with shapes compatible for broadcasting. Compute `stdtr` at
+    4 points for 3 degrees of freedom resulting in an array of shape 3x4.
+
+    >>> dfs = np.array([[1], [2], [3]])
+    >>> t = np.array([2, 4, 6, 8])
+    >>> dfs.shape, t.shape
+    ((3, 1), (4,))
+
+    >>> stdtr(dfs, t)
+    array([[0.85241638, 0.92202087, 0.94743154, 0.96041658],
+           [0.90824829, 0.97140452, 0.98666426, 0.99236596],
+           [0.93033702, 0.98599577, 0.99536364, 0.99796171]])
+
+    The t distribution is also available as `scipy.stats.t`. Calling `stdtr`
+    directly can be much faster than calling the ``cdf`` method of
+    `scipy.stats.t`. To get the same results, one must use the following
+    parametrization: ``scipy.stats.t(df).cdf(x) = stdtr(df, x)``.
+
+    >>> from scipy.stats import t
+    >>> df, x = 3, 1
+    >>> stdtr_result = stdtr(df, x)  # this can be faster than below
+    >>> stats_result = t(df).cdf(x)
+    >>> stats_result == stdtr_result  # test that results are equal
+    True
+    """)
+
+add_newdoc("stdtridf",
+    """
+    stdtridf(p, t, out=None)
+
+    Inverse of `stdtr` vs df.
+
+    Returns the argument df such that stdtr(df, t) is equal to `p`.
+
+    Parameters
+    ----------
+    p : array_like
+        Probability
+    t : array_like
+        Upper bound of the integral
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    df : scalar or ndarray
+        Value of `df` such that ``stdtr(df, t) == p``
+
+    See Also
+    --------
+    stdtr : Student t CDF
+    stdtrit : inverse of stdtr with respect to `t`
+    scipy.stats.t : Student t distribution
+
+    Examples
+    --------
+    Compute the student t cumulative distribution function for one
+    parameter set.
+
+    >>> from scipy.special import stdtr, stdtridf
+    >>> df, x = 5, 2
+    >>> cdf_value = stdtr(df, x)
+    >>> cdf_value
+    0.9490302605850709
+
+    Verify that `stdtridf` recovers the original value for `df` given
+    the CDF value and `x`.
+
+    >>> stdtridf(cdf_value, x)
+    5.0
+    """)
+
+add_newdoc("stdtrit",
+    """
+    stdtrit(df, p, out=None)
+
+    The `p`-th quantile of the student t distribution.
+
+    This function is the inverse of the student t distribution cumulative
+    distribution function (CDF), returning `t` such that `stdtr(df, t) = p`.
+
+    Returns the argument `t` such that stdtr(df, t) is equal to `p`.
+
+    Parameters
+    ----------
+    df : array_like
+        Degrees of freedom
+    p : array_like
+        Probability
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    t : scalar or ndarray
+        Value of `t` such that ``stdtr(df, t) == p``
+
+    See Also
+    --------
+    stdtr : Student t CDF
+    stdtridf : inverse of stdtr with respect to `df`
+    scipy.stats.t : Student t distribution
+
+    Notes
+    -----
+    The student t distribution is also available as `scipy.stats.t`. Calling
+    `stdtrit` directly can improve performance compared to the ``ppf``
+    method of `scipy.stats.t` (see last example below).
+
+    The function is computed using the Boost Math library [1]_, which
+    relies on the incomplete beta function.
+
+    References
+    ----------
+    .. [1] Boost C++ Libraries, https://www.boost.org/
+
+    Examples
+    --------
+    `stdtrit` represents the inverse of the student t distribution CDF which
+    is available as `stdtr`. Here, we calculate the CDF for ``df`` at
+    ``x=1``. `stdtrit` then returns ``1`` up to floating point errors
+    given the same value for `df` and the computed CDF value.
+
+    >>> import numpy as np
+    >>> from scipy.special import stdtr, stdtrit
+    >>> import matplotlib.pyplot as plt
+    >>> df = 3
+    >>> x = 1
+    >>> cdf_value = stdtr(df, x)
+    >>> stdtrit(df, cdf_value)
+    0.9999999994418539
+
+    Plot the function for three different degrees of freedom.
+
+    >>> x = np.linspace(0, 1, 1000)
+    >>> parameters = [(1, "solid"), (2, "dashed"), (5, "dotted")]
+    >>> fig, ax = plt.subplots()
+    >>> for (df, linestyle) in parameters:
+    ...     ax.plot(x, stdtrit(df, x), ls=linestyle, label=f"$df={df}$")
+    >>> ax.legend()
+    >>> ax.set_ylim(-10, 10)
+    >>> ax.set_title("Student t distribution quantile function")
+    >>> plt.show()
+
+    The function can be computed for several degrees of freedom at the same
+    time by providing a NumPy array or list for `df`:
+
+    >>> stdtrit([1, 2, 3], 0.7)
+    array([0.72654253, 0.6172134 , 0.58438973])
+
+    It is possible to calculate the function at several points for several
+    different degrees of freedom simultaneously by providing arrays for `df`
+    and `p` with shapes compatible for broadcasting. Compute `stdtrit` at
+    4 points for 3 degrees of freedom resulting in an array of shape 3x4.
+
+    >>> dfs = np.array([[1], [2], [3]])
+    >>> p = np.array([0.2, 0.4, 0.7, 0.8])
+    >>> dfs.shape, p.shape
+    ((3, 1), (4,))
+
+    >>> stdtrit(dfs, p)
+    array([[-1.37638192, -0.3249197 ,  0.72654253,  1.37638192],
+           [-1.06066017, -0.28867513,  0.6172134 ,  1.06066017],
+           [-0.97847231, -0.27667066,  0.58438973,  0.97847231]])
+
+    The t distribution is also available as `scipy.stats.t`. Calling `stdtrit`
+    directly can be much faster than calling the ``ppf`` method of
+    `scipy.stats.t`. To get the same results, one must use the following
+    parametrization: ``scipy.stats.t(df).ppf(x) = stdtrit(df, x)``.
+
+    >>> from scipy.stats import t
+    >>> df, x = 3, 0.5
+    >>> stdtrit_result = stdtrit(df, x)  # this can be faster than below
+    >>> stats_result = t(df).ppf(x)
+    >>> stats_result == stdtrit_result  # test that results are equal
+    True
+    """)
+
+add_newdoc(
+    "tklmbda",
+    r"""
+    tklmbda(x, lmbda, out=None)
+
+    Cumulative distribution function of the Tukey lambda distribution.
+
+    Parameters
+    ----------
+    x, lmbda : array_like
+        Parameters
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    cdf : scalar or ndarray
+        Value of the Tukey lambda CDF
+
+    See Also
+    --------
+    scipy.stats.tukeylambda : Tukey lambda distribution
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.special import tklmbda, expit
+
+    Compute the cumulative distribution function (CDF) of the Tukey lambda
+    distribution at several ``x`` values for `lmbda` = -1.5.
+
+    >>> x = np.linspace(-2, 2, 9)
+    >>> x
+    array([-2. , -1.5, -1. , -0.5,  0. ,  0.5,  1. ,  1.5,  2. ])
+    >>> tklmbda(x, -1.5)
+    array([0.34688734, 0.3786554 , 0.41528805, 0.45629737, 0.5       ,
+           0.54370263, 0.58471195, 0.6213446 , 0.65311266])
+
+    When `lmbda` is 0, the function is the logistic sigmoid function,
+    which is implemented in `scipy.special` as `expit`.
+
+    >>> tklmbda(x, 0)
+    array([0.11920292, 0.18242552, 0.26894142, 0.37754067, 0.5       ,
+           0.62245933, 0.73105858, 0.81757448, 0.88079708])
+    >>> expit(x)
+    array([0.11920292, 0.18242552, 0.26894142, 0.37754067, 0.5       ,
+           0.62245933, 0.73105858, 0.81757448, 0.88079708])
+
+    When `lmbda` is 1, the Tukey lambda distribution is uniform on the
+    interval [-1, 1], so the CDF increases linearly.
+
+    >>> t = np.linspace(-1, 1, 9)
+    >>> tklmbda(t, 1)
+    array([0.   , 0.125, 0.25 , 0.375, 0.5  , 0.625, 0.75 , 0.875, 1.   ])
+
+    In the following, we generate plots for several values of `lmbda`.
+
+    The first figure shows graphs for `lmbda` <= 0.
+
+    >>> styles = ['-', '-.', '--', ':']
+    >>> fig, ax = plt.subplots()
+    >>> x = np.linspace(-12, 12, 500)
+    >>> for k, lmbda in enumerate([-1.0, -0.5, 0.0]):
+    ...     y = tklmbda(x, lmbda)
+    ...     ax.plot(x, y, styles[k], label=rf'$\lambda$ = {lmbda:-4.1f}')
+
+    >>> ax.set_title(r'tklmbda(x, $\lambda$)')
+    >>> ax.set_label('x')
+    >>> ax.legend(framealpha=1, shadow=True)
+    >>> ax.grid(True)
+
+    The second figure shows graphs for `lmbda` > 0.  The dots in the
+    graphs show the bounds of the support of the distribution.
+
+    >>> fig, ax = plt.subplots()
+    >>> x = np.linspace(-4.2, 4.2, 500)
+    >>> lmbdas = [0.25, 0.5, 1.0, 1.5]
+    >>> for k, lmbda in enumerate(lmbdas):
+    ...     y = tklmbda(x, lmbda)
+    ...     ax.plot(x, y, styles[k], label=fr'$\lambda$ = {lmbda}')
+
+    >>> ax.set_prop_cycle(None)
+    >>> for lmbda in lmbdas:
+    ...     ax.plot([-1/lmbda, 1/lmbda], [0, 1], '.', ms=8)
+
+    >>> ax.set_title(r'tklmbda(x, $\lambda$)')
+    >>> ax.set_xlabel('x')
+    >>> ax.legend(framealpha=1, shadow=True)
+    >>> ax.grid(True)
+
+    >>> plt.tight_layout()
+    >>> plt.show()
+
+    The CDF of the Tukey lambda distribution is also implemented as the
+    ``cdf`` method of `scipy.stats.tukeylambda`.  In the following,
+    ``tukeylambda.cdf(x, -0.5)`` and ``tklmbda(x, -0.5)`` compute the
+    same values:
+
+    >>> from scipy.stats import tukeylambda
+    >>> x = np.linspace(-2, 2, 9)
+
+    >>> tukeylambda.cdf(x, -0.5)
+    array([0.21995157, 0.27093858, 0.33541677, 0.41328161, 0.5       ,
+           0.58671839, 0.66458323, 0.72906142, 0.78004843])
+
+    >>> tklmbda(x, -0.5)
+    array([0.21995157, 0.27093858, 0.33541677, 0.41328161, 0.5       ,
+           0.58671839, 0.66458323, 0.72906142, 0.78004843])
+
+    The implementation in ``tukeylambda`` also provides location and scale
+    parameters, and other methods such as ``pdf()`` (the probability
+    density function) and ``ppf()`` (the inverse of the CDF), so for
+    working with the Tukey lambda distribution, ``tukeylambda`` is more
+    generally useful.  The primary advantage of ``tklmbda`` is that it is
+    significantly faster than ``tukeylambda.cdf``.
+    """)
+
+add_newdoc("yn",
+    r"""
+    yn(n, x, out=None)
+
+    Bessel function of the second kind of integer order and real argument.
+
+    Parameters
+    ----------
+    n : array_like
+        Order (integer).
+    x : array_like
+        Argument (float).
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    Y : scalar or ndarray
+        Value of the Bessel function, :math:`Y_n(x)`.
+
+    See Also
+    --------
+    yv : For real order and real or complex argument.
+    y0: faster implementation of this function for order 0
+    y1: faster implementation of this function for order 1
+
+    Notes
+    -----
+    Wrapper for the Cephes [1]_ routine `yn`.
+
+    The function is evaluated by forward recurrence on `n`, starting with
+    values computed by the Cephes routines `y0` and `y1`. If ``n = 0`` or 1,
+    the routine for `y0` or `y1` is called directly.
+
+    References
+    ----------
+    .. [1] Cephes Mathematical Functions Library,
+           https://netlib.org/cephes/
+
+    Examples
+    --------
+    Evaluate the function of order 0 at one point.
+
+    >>> from scipy.special import yn
+    >>> yn(0, 1.)
+    0.08825696421567697
+
+    Evaluate the function at one point for different orders.
+
+    >>> yn(0, 1.), yn(1, 1.), yn(2, 1.)
+    (0.08825696421567697, -0.7812128213002888, -1.6506826068162546)
+
+    The evaluation for different orders can be carried out in one call by
+    providing a list or NumPy array as argument for the `v` parameter:
+
+    >>> yn([0, 1, 2], 1.)
+    array([ 0.08825696, -0.78121282, -1.65068261])
+
+    Evaluate the function at several points for order 0 by providing an
+    array for `z`.
+
+    >>> import numpy as np
+    >>> points = np.array([0.5, 3., 8.])
+    >>> yn(0, points)
+    array([-0.44451873,  0.37685001,  0.22352149])
+
+    If `z` is an array, the order parameter `v` must be broadcastable to
+    the correct shape if different orders shall be computed in one call.
+    To calculate the orders 0 and 1 for a 1D array:
+
+    >>> orders = np.array([[0], [1]])
+    >>> orders.shape
+    (2, 1)
+
+    >>> yn(orders, points)
+    array([[-0.44451873,  0.37685001,  0.22352149],
+           [-1.47147239,  0.32467442, -0.15806046]])
+
+    Plot the functions of order 0 to 3 from 0 to 10.
+
+    >>> import matplotlib.pyplot as plt
+    >>> fig, ax = plt.subplots()
+    >>> x = np.linspace(0., 10., 1000)
+    >>> for i in range(4):
+    ...     ax.plot(x, yn(i, x), label=f'$Y_{i!r}$')
+    >>> ax.set_ylim(-3, 1)
+    >>> ax.legend()
+    >>> plt.show()
+    """)
+
+
+add_newdoc("_struve_asymp_large_z",
+    """
+    _struve_asymp_large_z(v, z, is_h)
+
+    Internal function for testing `struve` & `modstruve`
+
+    Evaluates using asymptotic expansion
+
+    Returns
+    -------
+    v, err
+    """)
+
+add_newdoc("_struve_power_series",
+    """
+    _struve_power_series(v, z, is_h)
+
+    Internal function for testing `struve` & `modstruve`
+
+    Evaluates using power series
+
+    Returns
+    -------
+    v, err
+    """)
+
+add_newdoc("_struve_bessel_series",
+    """
+    _struve_bessel_series(v, z, is_h)
+
+    Internal function for testing `struve` & `modstruve`
+
+    Evaluates using Bessel function series
+
+    Returns
+    -------
+    v, err
+    """)
+
+add_newdoc("_spherical_jn",
+    """
+    Internal function, use `spherical_jn` instead.
+    """)
+
+add_newdoc("_spherical_jn_d",
+    """
+    Internal function, use `spherical_jn` instead.
+    """)
+
+add_newdoc("_spherical_yn",
+    """
+    Internal function, use `spherical_yn` instead.
+    """)
+
+add_newdoc("_spherical_yn_d",
+    """
+    Internal function, use `spherical_yn` instead.
+    """)
+
+add_newdoc("_spherical_in",
+    """
+    Internal function, use `spherical_in` instead.
+    """)
+
+add_newdoc("_spherical_in_d",
+    """
+    Internal function, use `spherical_in` instead.
+    """)
+
+add_newdoc("_spherical_kn",
+    """
+    Internal function, use `spherical_kn` instead.
+    """)
+
+add_newdoc("_spherical_kn_d",
+    """
+    Internal function, use `spherical_kn` instead.
+    """)
+
+add_newdoc("owens_t",
+    """
+    owens_t(h, a, out=None)
+
+    Owen's T Function.
+
+    The function T(h, a) gives the probability of the event
+    (X > h and 0 < Y < a * X) where X and Y are independent
+    standard normal random variables.
+
+    Parameters
+    ----------
+    h : array_like
+        Input value.
+    a : array_like
+        Input value.
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    t: scalar or ndarray
+        Probability of the event (X > h and 0 < Y < a * X),
+        where X and Y are independent standard normal random variables.
+
+    References
+    ----------
+    .. [1] M. Patefield and D. Tandy, "Fast and accurate calculation of
+           Owen's T Function", Statistical Software vol. 5, pp. 1-25, 2000.
+
+    Examples
+    --------
+    >>> from scipy import special
+    >>> a = 3.5
+    >>> h = 0.78
+    >>> special.owens_t(h, a)
+    0.10877216734852274
+    """)
+
+add_newdoc("_factorial",
+    """
+    Internal function, do not use.
+    """)
+
+add_newdoc("ndtri_exp",
+    r"""
+    ndtri_exp(y, out=None)
+
+    Inverse of `log_ndtr` vs x. Allows for greater precision than
+    `ndtri` composed with `numpy.exp` for very small values of y and for
+    y close to 0.
+
+    Parameters
+    ----------
+    y : array_like of float
+        Function argument
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    scalar or ndarray
+        Inverse of the log CDF of the standard normal distribution, evaluated
+        at y.
+
+    See Also
+    --------
+    log_ndtr : log of the standard normal cumulative distribution function
+    ndtr : standard normal cumulative distribution function
+    ndtri : standard normal percentile function
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import scipy.special as sc
+
+    `ndtri_exp` agrees with the naive implementation when the latter does
+    not suffer from underflow.
+
+    >>> sc.ndtri_exp(-1)
+    -0.33747496376420244
+    >>> sc.ndtri(np.exp(-1))
+    -0.33747496376420244
+
+    For extreme values of y, the naive approach fails
+
+    >>> sc.ndtri(np.exp(-800))
+    -inf
+    >>> sc.ndtri(np.exp(-1e-20))
+    inf
+
+    whereas `ndtri_exp` is still able to compute the result to high precision.
+
+    >>> sc.ndtri_exp(-800)
+    -39.88469483825668
+    >>> sc.ndtri_exp(-1e-20)
+    9.262340089798409
+    """)
+
+
+add_newdoc("_stirling2_inexact",
+    r"""
+    Internal function, do not use.
+    """)
+
+add_newdoc(
+    "_beta_pdf",
+    r"""
+    _beta_pdf(x, a, b)
+
+    Probability density function of beta distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued such that :math:`0 \leq x \leq 1`,
+        the upper limit of integration
+    a, b : array_like
+           Positive, real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_beta_ppf",
+    r"""
+    _beta_ppf(x, a, b)
+
+    Percent point function of beta distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued such that :math:`0 \leq x \leq 1`,
+        the upper limit of integration
+    a, b : array_like
+           Positive, real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_invgauss_ppf",
+    """
+    _invgauss_ppf(x, mu)
+
+    Percent point function of inverse gaussian distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Positive real-valued
+    mu : array_like
+        Positive, real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_invgauss_isf",
+    """
+    _invgauss_isf(x, mu, s)
+
+    Inverse survival function of inverse gaussian distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Positive real-valued
+    mu : array_like
+        Positive, real-valued parameters
+    s : array_like
+        Positive, real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_cauchy_ppf",
+    """
+    _cauchy_ppf(p, loc, scale)
+
+    Percent point function (i.e. quantile) of the Cauchy distribution.
+
+    Parameters
+    ----------
+    p : array_like
+        Probabilities
+    loc : array_like
+        Location parameter of the distribution.
+    scale : array_like
+        Scale parameter of the distribution.
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_cauchy_isf",
+    """
+    _cauchy_isf(p, loc, scale)
+
+    Inverse survival function of the Cauchy distribution.
+
+    Parameters
+    ----------
+    p : array_like
+        Probabilities
+    loc : array_like
+        Location parameter of the distribution.
+    scale : array_like
+        Scale parameter of the distribution.
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_ncx2_pdf",
+    """
+    _ncx2_pdf(x, k, l)
+
+    Probability density function of Non-central chi-squared distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Positive real-valued
+    k, l : array_like
+        Positive, real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_ncx2_cdf",
+    """
+    _ncx2_cdf(x, k, l)
+
+    Cumulative density function of Non-central chi-squared distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Positive real-valued
+    k, l : array_like
+        Positive, real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_ncx2_ppf",
+    """
+    _ncx2_ppf(x, k, l)
+
+    Percent point function of Non-central chi-squared distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Positive real-valued
+    k, l : array_like
+        Positive, real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_ncx2_sf",
+    """
+    _ncx2_sf(x, k, l)
+
+    Survival function of Non-central chi-squared distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Positive real-valued
+    k, l : array_like
+        Positive, real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_ncx2_isf",
+    """
+    _ncx2_isf(x, k, l)
+
+    Inverse survival function of Non-central chi-squared distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Positive real-valued
+    k, l : array_like
+        Positive, real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_ncf_pdf",
+    """
+    _ncf_pdf(x, v1, v2, l)
+
+    Probability density function of noncentral F-distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Positive real-valued
+    v1, v2, l : array_like
+        Positive, real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_ncf_cdf",
+    """
+    _ncf_cdf(x, v1, v2, l)
+
+    Cumulative density function of noncentral F-distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Positive real-valued
+    v1, v2, l : array_like
+        Positive, real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_ncf_ppf",
+    """
+    _ncf_ppf(x, v1, v2, l)
+
+    Percent point function of noncentral F-distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Positive real-valued
+    v1, v2, l : array_like
+        Positive, real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_ncf_sf",
+    """
+    _ncf_sf(x, v1, v2, l)
+
+    Survival function of noncentral F-distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Positive real-valued
+    v1, v2, l : array_like
+        Positive, real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_ncf_isf",
+    """
+    _ncf_isf(x, v1, v2, l)
+
+    Inverse survival function of noncentral F-distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Positive real-valued
+    v1, v2, l : array_like
+        Positive, real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_ncf_mean",
+    """
+    _ncf_mean(v1, v2, l)
+
+    Mean of noncentral F-distribution.
+
+    Parameters
+    ----------
+    v1, v2, l : array_like
+        Positive, real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_ncf_variance",
+    """
+    _ncf_variance(v1, v2, l)
+
+    Variance of noncentral F-distribution.
+
+    Parameters
+    ----------
+    v1, v2, l : array_like
+        Positive, real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_ncf_skewness",
+    """
+    _ncf_skewness(v1, v2, l)
+
+    Skewness of noncentral F-distribution.
+
+    Parameters
+    ----------
+    v1, v2, l : array_like
+        Positive, real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_ncf_kurtosis_excess",
+    """
+    _ncf_kurtosis_excess(v1, v2, l)
+
+    Kurtosis excess of noncentral F-distribution.
+
+    Parameters
+    ----------
+    v1, v2, l : array_like
+        Positive, real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_nct_cdf",
+    """
+    _nct_cdf(x, v, l)
+
+    Cumulative density function of noncentral t-distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued
+    v : array_like
+        Positive, real-valued parameters
+    l : array_like
+        Real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_nct_pdf",
+    """
+    _nct_pdf(x, v, l)
+
+    Probability density function of noncentral t-distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued
+    v : array_like
+        Positive, real-valued parameters
+    l : array_like
+        Real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+
+add_newdoc(
+    "_nct_ppf",
+    """
+    _nct_ppf(x, v, l)
+
+    Percent point function of noncentral t-distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued
+    v : array_like
+        Positive, real-valued parameters
+    l : array_like
+        Real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_nct_sf",
+    """
+    _nct_sf(x, v, l)
+
+    Survival function of noncentral t-distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued
+    v : array_like
+        Positive, real-valued parameters
+    l : array_like
+        Real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_nct_isf",
+    """
+    _nct_isf(x, v, l)
+
+    Inverse survival function of noncentral t-distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued
+    v : array_like
+        Positive, real-valued parameters
+    l : array_like
+        Real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_nct_mean",
+    """
+    _nct_mean(v, l)
+
+    Mean of noncentral t-distribution.
+
+    Parameters
+    ----------
+    v : array_like
+        Positive, real-valued parameters
+    l : array_like
+        Real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_nct_variance",
+    """
+    _nct_variance(v, l)
+
+    Variance of noncentral t-distribution.
+
+    Parameters
+    ----------
+    v : array_like
+        Positive, real-valued parameters
+    l : array_like
+        Real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_nct_skewness",
+    """
+    _nct_skewness(v, l)
+
+    Skewness of noncentral t-distribution.
+
+    Parameters
+    ----------
+    v : array_like
+        Positive, real-valued parameters
+    l : array_like
+        Real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_nct_kurtosis_excess",
+    """
+    _nct_kurtosis_excess(v, l)
+
+    Kurtosis excess of noncentral t-distribution.
+
+    Parameters
+    ----------
+    v : array_like
+        Positive, real-valued parameters
+    l : array_like
+        Real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_skewnorm_cdf",
+    """
+    _skewnorm_cdf(x, l, sc, sh)
+
+    Cumulative density function of skewnorm distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued
+    l : array_like
+        Real-valued parameters
+    sc : array_like
+        Positive, Real-valued parameters
+    sh : array_like
+        Real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_skewnorm_ppf",
+    """
+    _skewnorm_ppf(x, l, sc, sh)
+
+    Percent point function of skewnorm distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued
+    l : array_like
+        Real-valued parameters
+    sc : array_like
+        Positive, Real-valued parameters
+    sh : array_like
+        Real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_skewnorm_isf",
+    """
+    _skewnorm_isf(x, l, sc, sh)
+
+    Inverse survival function of skewnorm distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued
+    l : array_like
+        Real-valued parameters
+    sc : array_like
+        Positive, Real-valued parameters
+    sh : array_like
+        Real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_binom_pmf",
+    """
+    _binom_pmf(x, n, p)
+
+    Probability mass function of binomial distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued
+    n : array_like
+        Positive, integer-valued parameter
+    p : array_like
+        Positive, real-valued parameter
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_binom_cdf",
+    """
+    _binom_cdf(x, n, p)
+
+    Cumulative density function of binomial distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued
+    n : array_like
+        Positive, integer-valued parameter
+    p : array_like
+        Positive, real-valued parameter
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_binom_ppf",
+    """
+    _binom_ppf(x, n, p)
+
+    Percent point function of binomial distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued
+    n : array_like
+        Positive, integer-valued parameter
+    p : array_like
+        Positive, real-valued parameter
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_binom_sf",
+    """
+    _binom_sf(x, n, p)
+
+    Survival function of binomial distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued
+    n : array_like
+        Positive, integer-valued parameter
+    p : array_like
+        Positive, real-valued parameter
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_binom_isf",
+    """
+    _binom_isf(x, n, p)
+
+    Inverse survival function of binomial distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued
+    n : array_like
+        Positive, integer-valued parameter
+    p : array_like
+        Positive, real-valued parameter
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_nbinom_pmf",
+    """
+    _nbinom_pmf(x, r, p)
+
+    Probability mass function of negative binomial distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued
+    r : array_like
+        Positive, integer-valued parameter
+    p : array_like
+        Positive, real-valued parameter
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_nbinom_cdf",
+    """
+    _nbinom_cdf(x, r, p)
+
+    Cumulative density function of negative binomial distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued
+    r : array_like
+        Positive, integer-valued parameter
+    p : array_like
+        Positive, real-valued parameter
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_nbinom_ppf",
+    """
+    _nbinom_ppf(x, r, p)
+
+    Percent point function of negative binomial distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued
+    r : array_like
+        Positive, integer-valued parameter
+    p : array_like
+        Positive, real-valued parameter
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_nbinom_sf",
+    """
+    _nbinom_sf(x, r, p)
+
+    Survival function of negative binomial distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued
+    r : array_like
+        Positive, integer-valued parameter
+    p : array_like
+        Positive, real-valued parameter
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_nbinom_isf",
+    """
+    _nbinom_isf(x, r, p)
+
+    Inverse survival function of negative binomial distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued
+    r : array_like
+        Positive, integer-valued parameter
+    p : array_like
+        Positive, real-valued parameter
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_nbinom_mean",
+    """
+    _nbinom_mean(r, p)
+
+    Mean of negative binomial distribution.
+
+    Parameters
+    ----------
+    r : array_like
+        Positive, integer-valued parameter
+    p : array_like
+        Positive, real-valued parameter
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_nbinom_variance",
+    """
+    _nbinom_variance(r, p)
+
+    Variance of negative binomial distribution.
+
+    Parameters
+    ----------
+    r : array_like
+        Positive, integer-valued parameter
+    p : array_like
+        Positive, real-valued parameter
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_nbinom_skewness",
+    """
+    _nbinom_skewness(r, p)
+
+    Skewness of negative binomial distribution.
+
+    Parameters
+    ----------
+    r : array_like
+        Positive, integer-valued parameter
+    p : array_like
+        Positive, real-valued parameter
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_nbinom_kurtosis_excess",
+    """
+    _nbinom_kurtosis_excess(r, p)
+
+    Kurtosis excess of negative binomial distribution.
+
+    Parameters
+    ----------
+    r : array_like
+        Positive, integer-valued parameter
+    p : array_like
+        Positive, real-valued parameter
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_hypergeom_pmf",
+    """
+    _hypergeom_pmf(x, r, N, M)
+
+    Probability mass function of hypergeometric distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued
+    r, N, M : array_like
+        Positive, integer-valued parameter
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_hypergeom_cdf",
+    """
+    _hypergeom_cdf(x, r, N, M)
+
+    Cumulative density function of hypergeometric distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued
+    r, N, M : array_like
+        Positive, integer-valued parameter
+
+    Returns
+    -------
+    scalar or ndarray
+    """)
+
+add_newdoc(
+    "_hypergeom_sf",
+    """
+    _hypergeom_sf(x, r, N, M)
+
+    Survival function of hypergeometric distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued
+    r, N, M : array_like
+        Positive, integer-valued parameter
+
+    Returns
+    -------
+    scalar or ndarray
+    """)
+
+add_newdoc(
+    "_hypergeom_mean",
+    """
+    _hypergeom_mean(r, N, M)
+
+    Mean of hypergeometric distribution.
+
+    Parameters
+    ----------
+    r, N, M : array_like
+        Positive, integer-valued parameter
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_hypergeom_variance",
+    """
+    _hypergeom_variance(r, N, M)
+
+    Variance of hypergeometric distribution.
+
+    Parameters
+    ----------
+    r, N, M : array_like
+        Positive, integer-valued parameter
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_hypergeom_skewness",
+    """
+    _hypergeom_skewness(r, N, M)
+
+    Skewness of hypergeometric distribution.
+
+    Parameters
+    ----------
+    r, N, M : array_like
+        Positive, integer-valued parameter
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/_basic.py b/venv/lib/python3.12/site-packages/scipy/special/_basic.py
new file mode 100644
index 0000000000000000000000000000000000000000..8e017deb4db1eec2562a69f506fcdfed18d3de30
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/_basic.py
@@ -0,0 +1,3504 @@
+#
+# Author:  Travis Oliphant, 2002
+#
+
+import numpy as np
+import math
+import warnings
+from collections import defaultdict
+from heapq import heapify, heappop
+from numpy import (pi, asarray, floor, isscalar, sqrt, where,
+                   sin, place, issubdtype, extract, inexact, nan, zeros, sinc)
+
+from . import _ufuncs
+from ._ufuncs import (mathieu_a, mathieu_b, iv, jv, gamma, rgamma,
+                      psi, hankel1, hankel2, yv, kv, poch, binom,
+                      _stirling2_inexact)
+
+from ._gufuncs import _lqn, _lqmn, _rctj, _rcty
+from ._input_validation import _nonneg_int_or_fail
+from . import _specfun
+from ._comb import _comb_int
+
+
+__all__ = [
+    'ai_zeros',
+    'assoc_laguerre',
+    'bei_zeros',
+    'beip_zeros',
+    'ber_zeros',
+    'bernoulli',
+    'berp_zeros',
+    'bi_zeros',
+    'comb',
+    'digamma',
+    'diric',
+    'erf_zeros',
+    'euler',
+    'factorial',
+    'factorial2',
+    'factorialk',
+    'fresnel_zeros',
+    'fresnelc_zeros',
+    'fresnels_zeros',
+    'h1vp',
+    'h2vp',
+    'ivp',
+    'jn_zeros',
+    'jnjnp_zeros',
+    'jnp_zeros',
+    'jnyn_zeros',
+    'jvp',
+    'kei_zeros',
+    'keip_zeros',
+    'kelvin_zeros',
+    'ker_zeros',
+    'kerp_zeros',
+    'kvp',
+    'lmbda',
+    'lqmn',
+    'lqn',
+    'mathieu_even_coef',
+    'mathieu_odd_coef',
+    'obl_cv_seq',
+    'pbdn_seq',
+    'pbdv_seq',
+    'pbvv_seq',
+    'perm',
+    'polygamma',
+    'pro_cv_seq',
+    'riccati_jn',
+    'riccati_yn',
+    'sinc',
+    'softplus',
+    'stirling2',
+    'y0_zeros',
+    'y1_zeros',
+    'y1p_zeros',
+    'yn_zeros',
+    'ynp_zeros',
+    'yvp',
+    'zeta'
+]
+
+
+# mapping k to last n such that factorialk(n, k) < np.iinfo(np.int64).max
+_FACTORIALK_LIMITS_64BITS = {1: 20, 2: 33, 3: 44, 4: 54, 5: 65,
+                             6: 74, 7: 84, 8: 93, 9: 101}
+# mapping k to last n such that factorialk(n, k) < np.iinfo(np.int32).max
+_FACTORIALK_LIMITS_32BITS = {1: 12, 2: 19, 3: 25, 4: 31, 5: 37,
+                             6: 43, 7: 47, 8: 51, 9: 56}
+
+
+def diric(x, n):
+    """Periodic sinc function, also called the Dirichlet kernel.
+
+    The Dirichlet kernel is defined as::
+
+        diric(x, n) = sin(x * n/2) / (n * sin(x / 2)),
+
+    where `n` is a positive integer.
+
+    Parameters
+    ----------
+    x : array_like
+        Input data
+    n : int
+        Integer defining the periodicity.
+
+    Returns
+    -------
+    diric : ndarray
+        Value of periodic sinc function.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import special
+    >>> import matplotlib.pyplot as plt
+
+    >>> x = np.linspace(-8*np.pi, 8*np.pi, num=201)
+    >>> plt.figure(figsize=(8, 8));
+    >>> for idx, n in enumerate([2, 3, 4, 9]):
+    ...     plt.subplot(2, 2, idx+1)
+    ...     plt.plot(x, special.diric(x, n))
+    ...     plt.title('diric, n={}'.format(n))
+    >>> plt.show()
+
+    The following example demonstrates that `diric` gives the magnitudes
+    (modulo the sign and scaling) of the Fourier coefficients of a
+    rectangular pulse.
+
+    Suppress output of values that are effectively 0:
+
+    >>> np.set_printoptions(suppress=True)
+
+    Create a signal `x` of length `m` with `k` ones:
+
+    >>> m = 8
+    >>> k = 3
+    >>> x = np.zeros(m)
+    >>> x[:k] = 1
+
+    Use the FFT to compute the Fourier transform of `x`, and
+    inspect the magnitudes of the coefficients:
+
+    >>> np.abs(np.fft.fft(x))
+    array([ 3.        ,  2.41421356,  1.        ,  0.41421356,  1.        ,
+            0.41421356,  1.        ,  2.41421356])
+
+    Now find the same values (up to sign) using `diric`. We multiply
+    by `k` to account for the different scaling conventions of
+    `numpy.fft.fft` and `diric`:
+
+    >>> theta = np.linspace(0, 2*np.pi, m, endpoint=False)
+    >>> k * special.diric(theta, k)
+    array([ 3.        ,  2.41421356,  1.        , -0.41421356, -1.        ,
+           -0.41421356,  1.        ,  2.41421356])
+    """
+    x, n = asarray(x), asarray(n)
+    n = asarray(n + (x-x))
+    x = asarray(x + (n-n))
+    if issubdtype(x.dtype, inexact):
+        ytype = x.dtype
+    else:
+        ytype = float
+    y = zeros(x.shape, ytype)
+
+    # empirical minval for 32, 64 or 128 bit float computations
+    # where sin(x/2) < minval, result is fixed at +1 or -1
+    if np.finfo(ytype).eps < 1e-18:
+        minval = 1e-11
+    elif np.finfo(ytype).eps < 1e-15:
+        minval = 1e-7
+    else:
+        minval = 1e-3
+
+    mask1 = (n <= 0) | (n != floor(n))
+    place(y, mask1, nan)
+
+    x = x / 2
+    denom = sin(x)
+    mask2 = (1-mask1) & (abs(denom) < minval)
+    xsub = extract(mask2, x)
+    nsub = extract(mask2, n)
+    zsub = xsub / pi
+    place(y, mask2, pow(-1, np.round(zsub)*(nsub-1)))
+
+    mask = (1-mask1) & (1-mask2)
+    xsub = extract(mask, x)
+    nsub = extract(mask, n)
+    dsub = extract(mask, denom)
+    place(y, mask, sin(nsub*xsub)/(nsub*dsub))
+    return y
+
+
+def jnjnp_zeros(nt):
+    """Compute zeros of integer-order Bessel functions Jn and Jn'.
+
+    Results are arranged in order of the magnitudes of the zeros.
+
+    Parameters
+    ----------
+    nt : int
+        Number (<=1200) of zeros to compute
+
+    Returns
+    -------
+    zo[l-1] : ndarray
+        Value of the lth zero of Jn(x) and Jn'(x). Of length `nt`.
+    n[l-1] : ndarray
+        Order of the Jn(x) or Jn'(x) associated with lth zero. Of length `nt`.
+    m[l-1] : ndarray
+        Serial number of the zeros of Jn(x) or Jn'(x) associated
+        with lth zero. Of length `nt`.
+    t[l-1] : ndarray
+        0 if lth zero in zo is zero of Jn(x), 1 if it is a zero of Jn'(x). Of
+        length `nt`.
+
+    See Also
+    --------
+    jn_zeros, jnp_zeros : to get separated arrays of zeros.
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996, chapter 5.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    """
+    if not isscalar(nt) or (floor(nt) != nt) or (nt > 1200):
+        raise ValueError("Number must be integer <= 1200.")
+    nt = int(nt)
+    n, m, t, zo = _specfun.jdzo(nt)
+    return zo[1:nt+1], n[:nt], m[:nt], t[:nt]
+
+
+def jnyn_zeros(n, nt):
+    """Compute nt zeros of Bessel functions Jn(x), Jn'(x), Yn(x), and Yn'(x).
+
+    Returns 4 arrays of length `nt`, corresponding to the first `nt`
+    zeros of Jn(x), Jn'(x), Yn(x), and Yn'(x), respectively. The zeros
+    are returned in ascending order.
+
+    Parameters
+    ----------
+    n : int
+        Order of the Bessel functions
+    nt : int
+        Number (<=1200) of zeros to compute
+
+    Returns
+    -------
+    Jn : ndarray
+        First `nt` zeros of Jn
+    Jnp : ndarray
+        First `nt` zeros of Jn'
+    Yn : ndarray
+        First `nt` zeros of Yn
+    Ynp : ndarray
+        First `nt` zeros of Yn'
+
+    See Also
+    --------
+    jn_zeros, jnp_zeros, yn_zeros, ynp_zeros
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996, chapter 5.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    Examples
+    --------
+    Compute the first three roots of :math:`J_1`, :math:`J_1'`,
+    :math:`Y_1` and :math:`Y_1'`.
+
+    >>> from scipy.special import jnyn_zeros
+    >>> jn_roots, jnp_roots, yn_roots, ynp_roots = jnyn_zeros(1, 3)
+    >>> jn_roots, yn_roots
+    (array([ 3.83170597,  7.01558667, 10.17346814]),
+     array([2.19714133, 5.42968104, 8.59600587]))
+
+    Plot :math:`J_1`, :math:`J_1'`, :math:`Y_1`, :math:`Y_1'` and their roots.
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.special import jnyn_zeros, jvp, jn, yvp, yn
+    >>> jn_roots, jnp_roots, yn_roots, ynp_roots = jnyn_zeros(1, 3)
+    >>> fig, ax = plt.subplots()
+    >>> xmax= 11
+    >>> x = np.linspace(0, xmax)
+    >>> x[0] += 1e-15
+    >>> ax.plot(x, jn(1, x), label=r"$J_1$", c='r')
+    >>> ax.plot(x, jvp(1, x, 1), label=r"$J_1'$", c='b')
+    >>> ax.plot(x, yn(1, x), label=r"$Y_1$", c='y')
+    >>> ax.plot(x, yvp(1, x, 1), label=r"$Y_1'$", c='c')
+    >>> zeros = np.zeros((3, ))
+    >>> ax.scatter(jn_roots, zeros, s=30, c='r', zorder=5,
+    ...            label=r"$J_1$ roots")
+    >>> ax.scatter(jnp_roots, zeros, s=30, c='b', zorder=5,
+    ...            label=r"$J_1'$ roots")
+    >>> ax.scatter(yn_roots, zeros, s=30, c='y', zorder=5,
+    ...            label=r"$Y_1$ roots")
+    >>> ax.scatter(ynp_roots, zeros, s=30, c='c', zorder=5,
+    ...            label=r"$Y_1'$ roots")
+    >>> ax.hlines(0, 0, xmax, color='k')
+    >>> ax.set_ylim(-0.6, 0.6)
+    >>> ax.set_xlim(0, xmax)
+    >>> ax.legend(ncol=2, bbox_to_anchor=(1., 0.75))
+    >>> plt.tight_layout()
+    >>> plt.show()
+    """
+    if not (isscalar(nt) and isscalar(n)):
+        raise ValueError("Arguments must be scalars.")
+    if (floor(n) != n) or (floor(nt) != nt):
+        raise ValueError("Arguments must be integers.")
+    if (nt <= 0):
+        raise ValueError("nt > 0")
+    return _specfun.jyzo(abs(n), nt)
+
+
+def jn_zeros(n, nt):
+    r"""Compute zeros of integer-order Bessel functions Jn.
+
+    Compute `nt` zeros of the Bessel functions :math:`J_n(x)` on the
+    interval :math:`(0, \infty)`. The zeros are returned in ascending
+    order. Note that this interval excludes the zero at :math:`x = 0`
+    that exists for :math:`n > 0`.
+
+    Parameters
+    ----------
+    n : int
+        Order of Bessel function
+    nt : int
+        Number of zeros to return
+
+    Returns
+    -------
+    ndarray
+        First `nt` zeros of the Bessel function.
+
+    See Also
+    --------
+    jv: Real-order Bessel functions of the first kind
+    jnp_zeros: Zeros of :math:`Jn'`
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996, chapter 5.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    Examples
+    --------
+    Compute the first four positive roots of :math:`J_3`.
+
+    >>> from scipy.special import jn_zeros
+    >>> jn_zeros(3, 4)
+    array([ 6.3801619 ,  9.76102313, 13.01520072, 16.22346616])
+
+    Plot :math:`J_3` and its first four positive roots. Note
+    that the root located at 0 is not returned by `jn_zeros`.
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.special import jn, jn_zeros
+    >>> j3_roots = jn_zeros(3, 4)
+    >>> xmax = 18
+    >>> xmin = -1
+    >>> x = np.linspace(xmin, xmax, 500)
+    >>> fig, ax = plt.subplots()
+    >>> ax.plot(x, jn(3, x), label=r'$J_3$')
+    >>> ax.scatter(j3_roots, np.zeros((4, )), s=30, c='r',
+    ...            label=r"$J_3$_Zeros", zorder=5)
+    >>> ax.scatter(0, 0, s=30, c='k',
+    ...            label=r"Root at 0", zorder=5)
+    >>> ax.hlines(0, 0, xmax, color='k')
+    >>> ax.set_xlim(xmin, xmax)
+    >>> plt.legend()
+    >>> plt.show()
+    """
+    return jnyn_zeros(n, nt)[0]
+
+
+def jnp_zeros(n, nt):
+    r"""Compute zeros of integer-order Bessel function derivatives Jn'.
+
+    Compute `nt` zeros of the functions :math:`J_n'(x)` on the
+    interval :math:`(0, \infty)`. The zeros are returned in ascending
+    order. Note that this interval excludes the zero at :math:`x = 0`
+    that exists for :math:`n > 1`.
+
+    Parameters
+    ----------
+    n : int
+        Order of Bessel function
+    nt : int
+        Number of zeros to return
+
+    Returns
+    -------
+    ndarray
+        First `nt` zeros of the Bessel function.
+
+    See Also
+    --------
+    jvp: Derivatives of integer-order Bessel functions of the first kind
+    jv: Float-order Bessel functions of the first kind
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996, chapter 5.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    Examples
+    --------
+    Compute the first four roots of :math:`J_2'`.
+
+    >>> from scipy.special import jnp_zeros
+    >>> jnp_zeros(2, 4)
+    array([ 3.05423693,  6.70613319,  9.96946782, 13.17037086])
+
+    As `jnp_zeros` yields the roots of :math:`J_n'`, it can be used to
+    compute the locations of the peaks of :math:`J_n`. Plot
+    :math:`J_2`, :math:`J_2'` and the locations of the roots of :math:`J_2'`.
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.special import jn, jnp_zeros, jvp
+    >>> j2_roots = jnp_zeros(2, 4)
+    >>> xmax = 15
+    >>> x = np.linspace(0, xmax, 500)
+    >>> fig, ax = plt.subplots()
+    >>> ax.plot(x, jn(2, x), label=r'$J_2$')
+    >>> ax.plot(x, jvp(2, x, 1), label=r"$J_2'$")
+    >>> ax.hlines(0, 0, xmax, color='k')
+    >>> ax.scatter(j2_roots, np.zeros((4, )), s=30, c='r',
+    ...            label=r"Roots of $J_2'$", zorder=5)
+    >>> ax.set_ylim(-0.4, 0.8)
+    >>> ax.set_xlim(0, xmax)
+    >>> plt.legend()
+    >>> plt.show()
+    """
+    return jnyn_zeros(n, nt)[1]
+
+
+def yn_zeros(n, nt):
+    r"""Compute zeros of integer-order Bessel function Yn(x).
+
+    Compute `nt` zeros of the functions :math:`Y_n(x)` on the interval
+    :math:`(0, \infty)`. The zeros are returned in ascending order.
+
+    Parameters
+    ----------
+    n : int
+        Order of Bessel function
+    nt : int
+        Number of zeros to return
+
+    Returns
+    -------
+    ndarray
+        First `nt` zeros of the Bessel function.
+
+    See Also
+    --------
+    yn: Bessel function of the second kind for integer order
+    yv: Bessel function of the second kind for real order
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996, chapter 5.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    Examples
+    --------
+    Compute the first four roots of :math:`Y_2`.
+
+    >>> from scipy.special import yn_zeros
+    >>> yn_zeros(2, 4)
+    array([ 3.38424177,  6.79380751, 10.02347798, 13.20998671])
+
+    Plot :math:`Y_2` and its first four roots.
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.special import yn, yn_zeros
+    >>> xmin = 2
+    >>> xmax = 15
+    >>> x = np.linspace(xmin, xmax, 500)
+    >>> fig, ax = plt.subplots()
+    >>> ax.hlines(0, xmin, xmax, color='k')
+    >>> ax.plot(x, yn(2, x), label=r'$Y_2$')
+    >>> ax.scatter(yn_zeros(2, 4), np.zeros((4, )), s=30, c='r',
+    ...            label='Roots', zorder=5)
+    >>> ax.set_ylim(-0.4, 0.4)
+    >>> ax.set_xlim(xmin, xmax)
+    >>> plt.legend()
+    >>> plt.show()
+    """
+    return jnyn_zeros(n, nt)[2]
+
+
+def ynp_zeros(n, nt):
+    r"""Compute zeros of integer-order Bessel function derivatives Yn'(x).
+
+    Compute `nt` zeros of the functions :math:`Y_n'(x)` on the
+    interval :math:`(0, \infty)`. The zeros are returned in ascending
+    order.
+
+    Parameters
+    ----------
+    n : int
+        Order of Bessel function
+    nt : int
+        Number of zeros to return
+
+    Returns
+    -------
+    ndarray
+        First `nt` zeros of the Bessel derivative function.
+
+
+    See Also
+    --------
+    yvp
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996, chapter 5.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    Examples
+    --------
+    Compute the first four roots of the first derivative of the
+    Bessel function of second kind for order 0 :math:`Y_0'`.
+
+    >>> from scipy.special import ynp_zeros
+    >>> ynp_zeros(0, 4)
+    array([ 2.19714133,  5.42968104,  8.59600587, 11.74915483])
+
+    Plot :math:`Y_0`, :math:`Y_0'` and confirm visually that the roots of
+    :math:`Y_0'` are located at local extrema of :math:`Y_0`.
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.special import yn, ynp_zeros, yvp
+    >>> zeros = ynp_zeros(0, 4)
+    >>> xmax = 13
+    >>> x = np.linspace(0, xmax, 500)
+    >>> fig, ax = plt.subplots()
+    >>> ax.plot(x, yn(0, x), label=r'$Y_0$')
+    >>> ax.plot(x, yvp(0, x, 1), label=r"$Y_0'$")
+    >>> ax.scatter(zeros, np.zeros((4, )), s=30, c='r',
+    ...            label=r"Roots of $Y_0'$", zorder=5)
+    >>> for root in zeros:
+    ...     y0_extremum =  yn(0, root)
+    ...     lower = min(0, y0_extremum)
+    ...     upper = max(0, y0_extremum)
+    ...     ax.vlines(root, lower, upper, color='r')
+    >>> ax.hlines(0, 0, xmax, color='k')
+    >>> ax.set_ylim(-0.6, 0.6)
+    >>> ax.set_xlim(0, xmax)
+    >>> plt.legend()
+    >>> plt.show()
+    """
+    return jnyn_zeros(n, nt)[3]
+
+
+def y0_zeros(nt, complex=False):
+    """Compute nt zeros of Bessel function Y0(z), and derivative at each zero.
+
+    The derivatives are given by Y0'(z0) = -Y1(z0) at each zero z0.
+
+    Parameters
+    ----------
+    nt : int
+        Number of zeros to return
+    complex : bool, default False
+        Set to False to return only the real zeros; set to True to return only
+        the complex zeros with negative real part and positive imaginary part.
+        Note that the complex conjugates of the latter are also zeros of the
+        function, but are not returned by this routine.
+
+    Returns
+    -------
+    z0n : ndarray
+        Location of nth zero of Y0(z)
+    y0pz0n : ndarray
+        Value of derivative Y0'(z0) for nth zero
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996, chapter 5.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    Examples
+    --------
+    Compute the first 4 real roots and the derivatives at the roots of
+    :math:`Y_0`:
+
+    >>> import numpy as np
+    >>> from scipy.special import y0_zeros
+    >>> zeros, grads = y0_zeros(4)
+    >>> with np.printoptions(precision=5):
+    ...     print(f"Roots: {zeros}")
+    ...     print(f"Gradients: {grads}")
+    Roots: [ 0.89358+0.j  3.95768+0.j  7.08605+0.j 10.22235+0.j]
+    Gradients: [-0.87942+0.j  0.40254+0.j -0.3001 +0.j  0.2497 +0.j]
+
+    Plot the real part of :math:`Y_0` and the first four computed roots.
+
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.special import y0
+    >>> xmin = 0
+    >>> xmax = 11
+    >>> x = np.linspace(xmin, xmax, 500)
+    >>> fig, ax = plt.subplots()
+    >>> ax.hlines(0, xmin, xmax, color='k')
+    >>> ax.plot(x, y0(x), label=r'$Y_0$')
+    >>> zeros, grads = y0_zeros(4)
+    >>> ax.scatter(zeros.real, np.zeros((4, )), s=30, c='r',
+    ...            label=r'$Y_0$_zeros', zorder=5)
+    >>> ax.set_ylim(-0.5, 0.6)
+    >>> ax.set_xlim(xmin, xmax)
+    >>> plt.legend(ncol=2)
+    >>> plt.show()
+
+    Compute the first 4 complex roots and the derivatives at the roots of
+    :math:`Y_0` by setting ``complex=True``:
+
+    >>> y0_zeros(4, True)
+    (array([ -2.40301663+0.53988231j,  -5.5198767 +0.54718001j,
+             -8.6536724 +0.54841207j, -11.79151203+0.54881912j]),
+     array([ 0.10074769-0.88196771j, -0.02924642+0.5871695j ,
+             0.01490806-0.46945875j, -0.00937368+0.40230454j]))
+    """
+    if not isscalar(nt) or (floor(nt) != nt) or (nt <= 0):
+        raise ValueError("Arguments must be scalar positive integer.")
+    kf = 0
+    kc = not complex
+    return _specfun.cyzo(nt, kf, kc)
+
+
+def y1_zeros(nt, complex=False):
+    """Compute nt zeros of Bessel function Y1(z), and derivative at each zero.
+
+    The derivatives are given by Y1'(z1) = Y0(z1) at each zero z1.
+
+    Parameters
+    ----------
+    nt : int
+        Number of zeros to return
+    complex : bool, default False
+        Set to False to return only the real zeros; set to True to return only
+        the complex zeros with negative real part and positive imaginary part.
+        Note that the complex conjugates of the latter are also zeros of the
+        function, but are not returned by this routine.
+
+    Returns
+    -------
+    z1n : ndarray
+        Location of nth zero of Y1(z)
+    y1pz1n : ndarray
+        Value of derivative Y1'(z1) for nth zero
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996, chapter 5.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    Examples
+    --------
+    Compute the first 4 real roots and the derivatives at the roots of
+    :math:`Y_1`:
+
+    >>> import numpy as np
+    >>> from scipy.special import y1_zeros
+    >>> zeros, grads = y1_zeros(4)
+    >>> with np.printoptions(precision=5):
+    ...     print(f"Roots: {zeros}")
+    ...     print(f"Gradients: {grads}")
+    Roots: [ 2.19714+0.j  5.42968+0.j  8.59601+0.j 11.74915+0.j]
+    Gradients: [ 0.52079+0.j -0.34032+0.j  0.27146+0.j -0.23246+0.j]
+
+    Extract the real parts:
+
+    >>> realzeros = zeros.real
+    >>> realzeros
+    array([ 2.19714133,  5.42968104,  8.59600587, 11.74915483])
+
+    Plot :math:`Y_1` and the first four computed roots.
+
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.special import y1
+    >>> xmin = 0
+    >>> xmax = 13
+    >>> x = np.linspace(xmin, xmax, 500)
+    >>> zeros, grads = y1_zeros(4)
+    >>> fig, ax = plt.subplots()
+    >>> ax.hlines(0, xmin, xmax, color='k')
+    >>> ax.plot(x, y1(x), label=r'$Y_1$')
+    >>> ax.scatter(zeros.real, np.zeros((4, )), s=30, c='r',
+    ...            label=r'$Y_1$_zeros', zorder=5)
+    >>> ax.set_ylim(-0.5, 0.5)
+    >>> ax.set_xlim(xmin, xmax)
+    >>> plt.legend()
+    >>> plt.show()
+
+    Compute the first 4 complex roots and the derivatives at the roots of
+    :math:`Y_1` by setting ``complex=True``:
+
+    >>> y1_zeros(4, True)
+    (array([ -0.50274327+0.78624371j,  -3.83353519+0.56235654j,
+             -7.01590368+0.55339305j, -10.17357383+0.55127339j]),
+     array([-0.45952768+1.31710194j,  0.04830191-0.69251288j,
+            -0.02012695+0.51864253j,  0.011614  -0.43203296j]))
+    """
+    if not isscalar(nt) or (floor(nt) != nt) or (nt <= 0):
+        raise ValueError("Arguments must be scalar positive integer.")
+    kf = 1
+    kc = not complex
+    return _specfun.cyzo(nt, kf, kc)
+
+
+def y1p_zeros(nt, complex=False):
+    """Compute nt zeros of Bessel derivative Y1'(z), and value at each zero.
+
+    The values are given by Y1(z1) at each z1 where Y1'(z1)=0.
+
+    Parameters
+    ----------
+    nt : int
+        Number of zeros to return
+    complex : bool, default False
+        Set to False to return only the real zeros; set to True to return only
+        the complex zeros with negative real part and positive imaginary part.
+        Note that the complex conjugates of the latter are also zeros of the
+        function, but are not returned by this routine.
+
+    Returns
+    -------
+    z1pn : ndarray
+        Location of nth zero of Y1'(z)
+    y1z1pn : ndarray
+        Value of derivative Y1(z1) for nth zero
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996, chapter 5.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    Examples
+    --------
+    Compute the first four roots of :math:`Y_1'` and the values of
+    :math:`Y_1` at these roots.
+
+    >>> import numpy as np
+    >>> from scipy.special import y1p_zeros
+    >>> y1grad_roots, y1_values = y1p_zeros(4)
+    >>> with np.printoptions(precision=5):
+    ...     print(f"Y1' Roots: {y1grad_roots.real}")
+    ...     print(f"Y1 values: {y1_values.real}")
+    Y1' Roots: [ 3.68302  6.9415  10.1234  13.28576]
+    Y1 values: [ 0.41673 -0.30317  0.25091 -0.21897]
+
+    `y1p_zeros` can be used to calculate the extremal points of :math:`Y_1`
+    directly. Here we plot :math:`Y_1` and the first four extrema.
+
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.special import y1, yvp
+    >>> y1_roots, y1_values_at_roots = y1p_zeros(4)
+    >>> real_roots = y1_roots.real
+    >>> xmax = 15
+    >>> x = np.linspace(0, xmax, 500)
+    >>> x[0] += 1e-15
+    >>> fig, ax = plt.subplots()
+    >>> ax.plot(x, y1(x), label=r'$Y_1$')
+    >>> ax.plot(x, yvp(1, x, 1), label=r"$Y_1'$")
+    >>> ax.scatter(real_roots, np.zeros((4, )), s=30, c='r',
+    ...            label=r"Roots of $Y_1'$", zorder=5)
+    >>> ax.scatter(real_roots, y1_values_at_roots.real, s=30, c='k',
+    ...            label=r"Extrema of $Y_1$", zorder=5)
+    >>> ax.hlines(0, 0, xmax, color='k')
+    >>> ax.set_ylim(-0.5, 0.5)
+    >>> ax.set_xlim(0, xmax)
+    >>> ax.legend(ncol=2, bbox_to_anchor=(1., 0.75))
+    >>> plt.tight_layout()
+    >>> plt.show()
+    """
+    if not isscalar(nt) or (floor(nt) != nt) or (nt <= 0):
+        raise ValueError("Arguments must be scalar positive integer.")
+    kf = 2
+    kc = not complex
+    return _specfun.cyzo(nt, kf, kc)
+
+
+def _bessel_diff_formula(v, z, n, L, phase):
+    # from AMS55.
+    # L(v, z) = J(v, z), Y(v, z), H1(v, z), H2(v, z), phase = -1
+    # L(v, z) = I(v, z) or exp(v*pi*i)K(v, z), phase = 1
+    # For K, you can pull out the exp((v-k)*pi*i) into the caller
+    v = asarray(v)
+    p = 1.0
+    s = L(v-n, z)
+    for i in range(1, n+1):
+        p = phase * (p * (n-i+1)) / i   # = choose(k, i)
+        s += p*L(v-n + i*2, z)
+    return s / (2.**n)
+
+
+def jvp(v, z, n=1):
+    """Compute derivatives of Bessel functions of the first kind.
+
+    Compute the nth derivative of the Bessel function `Jv` with
+    respect to `z`.
+
+    Parameters
+    ----------
+    v : array_like or float
+        Order of Bessel function
+    z : complex
+        Argument at which to evaluate the derivative; can be real or
+        complex.
+    n : int, default 1
+        Order of derivative. For 0 returns the Bessel function `jv` itself.
+
+    Returns
+    -------
+    scalar or ndarray
+        Values of the derivative of the Bessel function.
+
+    Notes
+    -----
+    The derivative is computed using the relation DLFM 10.6.7 [2]_.
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996, chapter 5.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    .. [2] NIST Digital Library of Mathematical Functions.
+           https://dlmf.nist.gov/10.6.E7
+
+    Examples
+    --------
+
+    Compute the Bessel function of the first kind of order 0 and
+    its first two derivatives at 1.
+
+    >>> from scipy.special import jvp
+    >>> jvp(0, 1, 0), jvp(0, 1, 1), jvp(0, 1, 2)
+    (0.7651976865579666, -0.44005058574493355, -0.3251471008130331)
+
+    Compute the first derivative of the Bessel function of the first
+    kind for several orders at 1 by providing an array for `v`.
+
+    >>> jvp([0, 1, 2], 1, 1)
+    array([-0.44005059,  0.3251471 ,  0.21024362])
+
+    Compute the first derivative of the Bessel function of the first
+    kind of order 0 at several points by providing an array for `z`.
+
+    >>> import numpy as np
+    >>> points = np.array([0., 1.5, 3.])
+    >>> jvp(0, points, 1)
+    array([-0.        , -0.55793651, -0.33905896])
+
+    Plot the Bessel function of the first kind of order 1 and its
+    first three derivatives.
+
+    >>> import matplotlib.pyplot as plt
+    >>> x = np.linspace(-10, 10, 1000)
+    >>> fig, ax = plt.subplots()
+    >>> ax.plot(x, jvp(1, x, 0), label=r"$J_1$")
+    >>> ax.plot(x, jvp(1, x, 1), label=r"$J_1'$")
+    >>> ax.plot(x, jvp(1, x, 2), label=r"$J_1''$")
+    >>> ax.plot(x, jvp(1, x, 3), label=r"$J_1'''$")
+    >>> plt.legend()
+    >>> plt.show()
+    """
+    n = _nonneg_int_or_fail(n, 'n')
+    if n == 0:
+        return jv(v, z)
+    else:
+        return _bessel_diff_formula(v, z, n, jv, -1)
+
+
+def yvp(v, z, n=1):
+    """Compute derivatives of Bessel functions of the second kind.
+
+    Compute the nth derivative of the Bessel function `Yv` with
+    respect to `z`.
+
+    Parameters
+    ----------
+    v : array_like of float
+        Order of Bessel function
+    z : complex
+        Argument at which to evaluate the derivative
+    n : int, default 1
+        Order of derivative. For 0 returns the BEssel function `yv`
+
+    Returns
+    -------
+    scalar or ndarray
+        nth derivative of the Bessel function.
+
+    See Also
+    --------
+    yv : Bessel functions of the second kind
+
+    Notes
+    -----
+    The derivative is computed using the relation DLFM 10.6.7 [2]_.
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996, chapter 5.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    .. [2] NIST Digital Library of Mathematical Functions.
+           https://dlmf.nist.gov/10.6.E7
+
+    Examples
+    --------
+    Compute the Bessel function of the second kind of order 0 and
+    its first two derivatives at 1.
+
+    >>> from scipy.special import yvp
+    >>> yvp(0, 1, 0), yvp(0, 1, 1), yvp(0, 1, 2)
+    (0.088256964215677, 0.7812128213002889, -0.8694697855159659)
+
+    Compute the first derivative of the Bessel function of the second
+    kind for several orders at 1 by providing an array for `v`.
+
+    >>> yvp([0, 1, 2], 1, 1)
+    array([0.78121282, 0.86946979, 2.52015239])
+
+    Compute the first derivative of the Bessel function of the
+    second kind of order 0 at several points by providing an array for `z`.
+
+    >>> import numpy as np
+    >>> points = np.array([0.5, 1.5, 3.])
+    >>> yvp(0, points, 1)
+    array([ 1.47147239,  0.41230863, -0.32467442])
+
+    Plot the Bessel function of the second kind of order 1 and its
+    first three derivatives.
+
+    >>> import matplotlib.pyplot as plt
+    >>> x = np.linspace(0, 5, 1000)
+    >>> x[0] += 1e-15
+    >>> fig, ax = plt.subplots()
+    >>> ax.plot(x, yvp(1, x, 0), label=r"$Y_1$")
+    >>> ax.plot(x, yvp(1, x, 1), label=r"$Y_1'$")
+    >>> ax.plot(x, yvp(1, x, 2), label=r"$Y_1''$")
+    >>> ax.plot(x, yvp(1, x, 3), label=r"$Y_1'''$")
+    >>> ax.set_ylim(-10, 10)
+    >>> plt.legend()
+    >>> plt.show()
+    """
+    n = _nonneg_int_or_fail(n, 'n')
+    if n == 0:
+        return yv(v, z)
+    else:
+        return _bessel_diff_formula(v, z, n, yv, -1)
+
+
+def kvp(v, z, n=1):
+    """Compute derivatives of real-order modified Bessel function Kv(z).
+
+    Kv(z) is the modified Bessel function of the second kind.
+    Derivative is calculated with respect to `z`.
+
+    Parameters
+    ----------
+    v : array_like of float
+        Order of Bessel function
+    z : array_like of complex
+        Argument at which to evaluate the derivative
+    n : int, default 1
+        Order of derivative. For 0 returns the Bessel function `kv` itself.
+
+    Returns
+    -------
+    out : ndarray
+        The results
+
+    See Also
+    --------
+    kv
+
+    Notes
+    -----
+    The derivative is computed using the relation DLFM 10.29.5 [2]_.
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996, chapter 6.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    .. [2] NIST Digital Library of Mathematical Functions.
+           https://dlmf.nist.gov/10.29.E5
+
+    Examples
+    --------
+    Compute the modified bessel function of the second kind of order 0 and
+    its first two derivatives at 1.
+
+    >>> from scipy.special import kvp
+    >>> kvp(0, 1, 0), kvp(0, 1, 1), kvp(0, 1, 2)
+    (0.42102443824070834, -0.6019072301972346, 1.0229316684379428)
+
+    Compute the first derivative of the modified Bessel function of the second
+    kind for several orders at 1 by providing an array for `v`.
+
+    >>> kvp([0, 1, 2], 1, 1)
+    array([-0.60190723, -1.02293167, -3.85158503])
+
+    Compute the first derivative of the modified Bessel function of the
+    second kind of order 0 at several points by providing an array for `z`.
+
+    >>> import numpy as np
+    >>> points = np.array([0.5, 1.5, 3.])
+    >>> kvp(0, points, 1)
+    array([-1.65644112, -0.2773878 , -0.04015643])
+
+    Plot the modified bessel function of the second kind and its
+    first three derivatives.
+
+    >>> import matplotlib.pyplot as plt
+    >>> x = np.linspace(0, 5, 1000)
+    >>> fig, ax = plt.subplots()
+    >>> ax.plot(x, kvp(1, x, 0), label=r"$K_1$")
+    >>> ax.plot(x, kvp(1, x, 1), label=r"$K_1'$")
+    >>> ax.plot(x, kvp(1, x, 2), label=r"$K_1''$")
+    >>> ax.plot(x, kvp(1, x, 3), label=r"$K_1'''$")
+    >>> ax.set_ylim(-2.5, 2.5)
+    >>> plt.legend()
+    >>> plt.show()
+    """
+    n = _nonneg_int_or_fail(n, 'n')
+    if n == 0:
+        return kv(v, z)
+    else:
+        return (-1)**n * _bessel_diff_formula(v, z, n, kv, 1)
+
+
+def ivp(v, z, n=1):
+    """Compute derivatives of modified Bessel functions of the first kind.
+
+    Compute the nth derivative of the modified Bessel function `Iv`
+    with respect to `z`.
+
+    Parameters
+    ----------
+    v : array_like or float
+        Order of Bessel function
+    z : array_like
+        Argument at which to evaluate the derivative; can be real or
+        complex.
+    n : int, default 1
+        Order of derivative. For 0, returns the Bessel function `iv` itself.
+
+    Returns
+    -------
+    scalar or ndarray
+        nth derivative of the modified Bessel function.
+
+    See Also
+    --------
+    iv
+
+    Notes
+    -----
+    The derivative is computed using the relation DLFM 10.29.5 [2]_.
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996, chapter 6.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    .. [2] NIST Digital Library of Mathematical Functions.
+           https://dlmf.nist.gov/10.29.E5
+
+    Examples
+    --------
+    Compute the modified Bessel function of the first kind of order 0 and
+    its first two derivatives at 1.
+
+    >>> from scipy.special import ivp
+    >>> ivp(0, 1, 0), ivp(0, 1, 1), ivp(0, 1, 2)
+    (1.2660658777520084, 0.565159103992485, 0.7009067737595233)
+
+    Compute the first derivative of the modified Bessel function of the first
+    kind for several orders at 1 by providing an array for `v`.
+
+    >>> ivp([0, 1, 2], 1, 1)
+    array([0.5651591 , 0.70090677, 0.29366376])
+
+    Compute the first derivative of the modified Bessel function of the
+    first kind of order 0 at several points by providing an array for `z`.
+
+    >>> import numpy as np
+    >>> points = np.array([0., 1.5, 3.])
+    >>> ivp(0, points, 1)
+    array([0.        , 0.98166643, 3.95337022])
+
+    Plot the modified Bessel function of the first kind of order 1 and its
+    first three derivatives.
+
+    >>> import matplotlib.pyplot as plt
+    >>> x = np.linspace(-5, 5, 1000)
+    >>> fig, ax = plt.subplots()
+    >>> ax.plot(x, ivp(1, x, 0), label=r"$I_1$")
+    >>> ax.plot(x, ivp(1, x, 1), label=r"$I_1'$")
+    >>> ax.plot(x, ivp(1, x, 2), label=r"$I_1''$")
+    >>> ax.plot(x, ivp(1, x, 3), label=r"$I_1'''$")
+    >>> plt.legend()
+    >>> plt.show()
+    """
+    n = _nonneg_int_or_fail(n, 'n')
+    if n == 0:
+        return iv(v, z)
+    else:
+        return _bessel_diff_formula(v, z, n, iv, 1)
+
+
+def h1vp(v, z, n=1):
+    """Compute derivatives of Hankel function H1v(z) with respect to `z`.
+
+    Parameters
+    ----------
+    v : array_like
+        Order of Hankel function
+    z : array_like
+        Argument at which to evaluate the derivative. Can be real or
+        complex.
+    n : int, default 1
+        Order of derivative. For 0 returns the Hankel function `hankel1` itself.
+
+    Returns
+    -------
+    scalar or ndarray
+        Values of the derivative of the Hankel function.
+
+    See Also
+    --------
+    hankel1
+
+    Notes
+    -----
+    The derivative is computed using the relation DLFM 10.6.7 [2]_.
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996, chapter 5.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    .. [2] NIST Digital Library of Mathematical Functions.
+           https://dlmf.nist.gov/10.6.E7
+
+    Examples
+    --------
+    Compute the Hankel function of the first kind of order 0 and
+    its first two derivatives at 1.
+
+    >>> from scipy.special import h1vp
+    >>> h1vp(0, 1, 0), h1vp(0, 1, 1), h1vp(0, 1, 2)
+    ((0.7651976865579664+0.088256964215677j),
+     (-0.44005058574493355+0.7812128213002889j),
+     (-0.3251471008130329-0.8694697855159659j))
+
+    Compute the first derivative of the Hankel function of the first kind
+    for several orders at 1 by providing an array for `v`.
+
+    >>> h1vp([0, 1, 2], 1, 1)
+    array([-0.44005059+0.78121282j,  0.3251471 +0.86946979j,
+           0.21024362+2.52015239j])
+
+    Compute the first derivative of the Hankel function of the first kind
+    of order 0 at several points by providing an array for `z`.
+
+    >>> import numpy as np
+    >>> points = np.array([0.5, 1.5, 3.])
+    >>> h1vp(0, points, 1)
+    array([-0.24226846+1.47147239j, -0.55793651+0.41230863j,
+           -0.33905896-0.32467442j])
+    """
+    n = _nonneg_int_or_fail(n, 'n')
+    if n == 0:
+        return hankel1(v, z)
+    else:
+        return _bessel_diff_formula(v, z, n, hankel1, -1)
+
+
+def h2vp(v, z, n=1):
+    """Compute derivatives of Hankel function H2v(z) with respect to `z`.
+
+    Parameters
+    ----------
+    v : array_like
+        Order of Hankel function
+    z : array_like
+        Argument at which to evaluate the derivative. Can be real or
+        complex.
+    n : int, default 1
+        Order of derivative. For 0 returns the Hankel function `hankel2` itself.
+
+    Returns
+    -------
+    scalar or ndarray
+        Values of the derivative of the Hankel function.
+
+    See Also
+    --------
+    hankel2
+
+    Notes
+    -----
+    The derivative is computed using the relation DLFM 10.6.7 [2]_.
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996, chapter 5.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    .. [2] NIST Digital Library of Mathematical Functions.
+           https://dlmf.nist.gov/10.6.E7
+
+    Examples
+    --------
+    Compute the Hankel function of the second kind of order 0 and
+    its first two derivatives at 1.
+
+    >>> from scipy.special import h2vp
+    >>> h2vp(0, 1, 0), h2vp(0, 1, 1), h2vp(0, 1, 2)
+    ((0.7651976865579664-0.088256964215677j),
+     (-0.44005058574493355-0.7812128213002889j),
+     (-0.3251471008130329+0.8694697855159659j))
+
+    Compute the first derivative of the Hankel function of the second kind
+    for several orders at 1 by providing an array for `v`.
+
+    >>> h2vp([0, 1, 2], 1, 1)
+    array([-0.44005059-0.78121282j,  0.3251471 -0.86946979j,
+           0.21024362-2.52015239j])
+
+    Compute the first derivative of the Hankel function of the second kind
+    of order 0 at several points by providing an array for `z`.
+
+    >>> import numpy as np
+    >>> points = np.array([0.5, 1.5, 3.])
+    >>> h2vp(0, points, 1)
+    array([-0.24226846-1.47147239j, -0.55793651-0.41230863j,
+           -0.33905896+0.32467442j])
+    """
+    n = _nonneg_int_or_fail(n, 'n')
+    if n == 0:
+        return hankel2(v, z)
+    else:
+        return _bessel_diff_formula(v, z, n, hankel2, -1)
+
+
+def riccati_jn(n, x):
+    r"""Compute Riccati-Bessel function of the first kind and its derivative.
+
+    The Riccati-Bessel function of the first kind is defined as :math:`x
+    j_n(x)`, where :math:`j_n` is the spherical Bessel function of the first
+    kind of order :math:`n`.
+
+    This function computes the value and first derivative of the
+    Riccati-Bessel function for all orders up to and including `n`.
+
+    Parameters
+    ----------
+    n : int
+        Maximum order of function to compute
+    x : float
+        Argument at which to evaluate
+
+    Returns
+    -------
+    jn : ndarray
+        Value of j0(x), ..., jn(x)
+    jnp : ndarray
+        First derivative j0'(x), ..., jn'(x)
+
+    Notes
+    -----
+    The computation is carried out via backward recurrence, using the
+    relation DLMF 10.51.1 [2]_.
+
+    Wrapper for a Fortran routine created by Shanjie Zhang and Jianming
+    Jin [1]_.
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+    .. [2] NIST Digital Library of Mathematical Functions.
+           https://dlmf.nist.gov/10.51.E1
+
+    """
+    if not (isscalar(n) and isscalar(x)):
+        raise ValueError("arguments must be scalars.")
+    n = _nonneg_int_or_fail(n, 'n', strict=False)
+    if (n == 0):
+        n1 = 1
+    else:
+        n1 = n
+
+    jn = np.empty((n1 + 1,), dtype=np.float64)
+    jnp = np.empty_like(jn)
+
+    _rctj(x, out=(jn, jnp))
+    return jn[:(n+1)], jnp[:(n+1)]
+
+
+def riccati_yn(n, x):
+    """Compute Riccati-Bessel function of the second kind and its derivative.
+
+    The Riccati-Bessel function of the second kind is defined here as :math:`+x
+    y_n(x)`, where :math:`y_n` is the spherical Bessel function of the second
+    kind of order :math:`n`. *Note that this is in contrast to a common convention
+    that includes a minus sign in the definition.*
+
+    This function computes the value and first derivative of the function for
+    all orders up to and including `n`.
+
+    Parameters
+    ----------
+    n : int
+        Maximum order of function to compute
+    x : float
+        Argument at which to evaluate
+
+    Returns
+    -------
+    yn : ndarray
+        Value of y0(x), ..., yn(x)
+    ynp : ndarray
+        First derivative y0'(x), ..., yn'(x)
+
+    Notes
+    -----
+    The computation is carried out via ascending recurrence, using the
+    relation DLMF 10.51.1 [2]_.
+
+    Wrapper for a Fortran routine created by Shanjie Zhang and Jianming
+    Jin [1]_.
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+    .. [2] NIST Digital Library of Mathematical Functions.
+           https://dlmf.nist.gov/10.51.E1
+
+    """
+    if not (isscalar(n) and isscalar(x)):
+        raise ValueError("arguments must be scalars.")
+    n = _nonneg_int_or_fail(n, 'n', strict=False)
+    if (n == 0):
+        n1 = 1
+    else:
+        n1 = n
+
+    yn = np.empty((n1 + 1,), dtype=np.float64)
+    ynp = np.empty_like(yn)
+    _rcty(x, out=(yn, ynp))
+
+    return yn[:(n+1)], ynp[:(n+1)]
+
+
+def erf_zeros(nt):
+    """Compute the first nt zero in the first quadrant, ordered by absolute value.
+
+    Zeros in the other quadrants can be obtained by using the symmetries
+    erf(-z) = erf(z) and erf(conj(z)) = conj(erf(z)).
+
+
+    Parameters
+    ----------
+    nt : int
+        The number of zeros to compute
+
+    Returns
+    -------
+    The locations of the zeros of erf : ndarray (complex)
+        Complex values at which zeros of erf(z)
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    Examples
+    --------
+    >>> from scipy import special
+    >>> special.erf_zeros(1)
+    array([1.45061616+1.880943j])
+
+    Check that erf is (close to) zero for the value returned by erf_zeros
+
+    >>> special.erf(special.erf_zeros(1))
+    array([4.95159469e-14-1.16407394e-16j])
+
+    """
+    if (floor(nt) != nt) or (nt <= 0) or not isscalar(nt):
+        raise ValueError("Argument must be positive scalar integer.")
+    return _specfun.cerzo(nt)
+
+
+def fresnelc_zeros(nt):
+    """Compute nt complex zeros of cosine Fresnel integral C(z).
+
+    Parameters
+    ----------
+    nt : int
+        Number of zeros to compute
+
+    Returns
+    -------
+    fresnelc_zeros: ndarray
+        Zeros of the cosine Fresnel integral
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    """
+    if (floor(nt) != nt) or (nt <= 0) or not isscalar(nt):
+        raise ValueError("Argument must be positive scalar integer.")
+    return _specfun.fcszo(1, nt)
+
+
+def fresnels_zeros(nt):
+    """Compute nt complex zeros of sine Fresnel integral S(z).
+
+    Parameters
+    ----------
+    nt : int
+        Number of zeros to compute
+
+    Returns
+    -------
+    fresnels_zeros: ndarray
+        Zeros of the sine Fresnel integral
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    """
+    if (floor(nt) != nt) or (nt <= 0) or not isscalar(nt):
+        raise ValueError("Argument must be positive scalar integer.")
+    return _specfun.fcszo(2, nt)
+
+
+def fresnel_zeros(nt):
+    """Compute nt complex zeros of sine and cosine Fresnel integrals S(z) and C(z).
+
+    Parameters
+    ----------
+    nt : int
+        Number of zeros to compute
+
+    Returns
+    -------
+    zeros_sine: ndarray
+        Zeros of the sine Fresnel integral
+    zeros_cosine : ndarray
+        Zeros of the cosine Fresnel integral
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    """
+    if (floor(nt) != nt) or (nt <= 0) or not isscalar(nt):
+        raise ValueError("Argument must be positive scalar integer.")
+    return _specfun.fcszo(2, nt), _specfun.fcszo(1, nt)
+
+
+def assoc_laguerre(x, n, k=0.0):
+    r"""Compute the generalized (associated) Laguerre polynomial of degree :math:`n`
+    and order :math:`k`.
+
+    This function evaluates the generalized Laguerre polynomial
+
+    .. math::
+
+        L^{(k)}_n(x).
+
+    The polynomial is orthogonal over :math:`[0, \infty)` with weight
+    function
+
+    .. math::
+
+        e^{-x}x^k
+
+    for :math:`k > -1`.
+
+    Parameters
+    ----------
+    x : float or ndarray
+        Points where to evaluate the Laguerre polynomial
+    n : int
+        Degree of the Laguerre polynomial
+    k : int
+        Order of the Laguerre polynomial
+
+    Returns
+    -------
+    assoc_laguerre: float or ndarray
+        Associated laguerre polynomial values
+
+    Notes
+    -----
+    `assoc_laguerre` is a simple wrapper around `eval_genlaguerre`, with
+    reversed argument order ``(x, n, k=0.0) --> (n, k, x)``.
+
+    Examples
+    --------
+    Evaluate the associated Laguerre polynomial :math:`L_3^{(2)}` at
+    :math:`x = 1`:
+
+    >>> import numpy as np
+    >>> from scipy.special import assoc_laguerre, eval_genlaguerre
+    >>> np.isclose(assoc_laguerre(1, 3, 2), 7/3)
+    True
+
+    `assoc_laguerre` is equivalent to `eval_genlaguerre` with reversed
+    argument order:
+
+    >>> x = np.linspace(0, 5, 6)
+    >>> np.allclose(assoc_laguerre(x, 3, 2), eval_genlaguerre(3, 2, x))
+    True
+
+    Plot :math:`L_3^{(k)}` for several values of :math:`k`:
+
+    >>> import matplotlib.pyplot as plt
+    >>> x = np.linspace(0, 8, 400)
+    >>> fig, ax = plt.subplots()
+    >>> for k in range(3):
+    ...     ax.plot(x, assoc_laguerre(x, 3, k), label=rf"$k={k}$")
+    >>> ax.set_title(r"Associated Laguerre polynomials $L_3^{(k)}$")
+    >>> ax.set_xlabel("x")
+    >>> ax.legend(loc="best")
+    >>> plt.show()
+
+    """
+    return _ufuncs.eval_genlaguerre(n, k, x)
+
+
+digamma = psi
+
+
+def polygamma(n, x):
+    r"""Polygamma functions.
+
+    Defined as :math:`\psi^{(n)}(x)` where :math:`\psi` is the
+    `digamma` function. See [dlmf]_ for details.
+
+    Parameters
+    ----------
+    n : array_like
+        The order of the derivative of the digamma function; must be
+        integral
+    x : array_like
+        Real valued input
+
+    Returns
+    -------
+    ndarray
+        Function results
+
+    See Also
+    --------
+    digamma
+
+    References
+    ----------
+    .. [dlmf] NIST, Digital Library of Mathematical Functions,
+        https://dlmf.nist.gov/5.15
+
+    Examples
+    --------
+    >>> from scipy import special
+    >>> x = [2, 3, 25.5]
+    >>> special.polygamma(1, x)
+    array([ 0.64493407,  0.39493407,  0.03999467])
+    >>> special.polygamma(0, x) == special.psi(x)
+    array([ True,  True,  True], dtype=bool)
+
+    """
+    n, x = asarray(n), asarray(x)
+    fac2 = (-1.0)**(n+1) * gamma(n+1.0) * zeta(n+1, x)
+    return where(n == 0, psi(x), fac2)
+
+
+def mathieu_even_coef(m, q):
+    r"""Fourier coefficients for even Mathieu and modified Mathieu functions.
+
+    The Fourier series of the even solutions of the Mathieu differential
+    equation are of the form
+
+    .. math:: \mathrm{ce}_{2n}(z, q) = \sum_{k=0}^{\infty} A_{(2n)}^{(2k)} \cos 2kz
+
+    .. math:: \mathrm{ce}_{2n+1}(z, q) =
+              \sum_{k=0}^{\infty} A_{(2n+1)}^{(2k+1)} \cos (2k+1)z
+
+    This function returns the coefficients :math:`A_{(2n)}^{(2k)}` for even
+    input m=2n, and the coefficients :math:`A_{(2n+1)}^{(2k+1)}` for odd input
+    m=2n+1.
+
+    Parameters
+    ----------
+    m : int
+        Order of Mathieu functions.  Must be non-negative.
+    q : float (>=0)
+        Parameter of Mathieu functions.  Must be non-negative.
+
+    Returns
+    -------
+    Ak : ndarray
+        Even or odd Fourier coefficients, corresponding to even or odd m.
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+    .. [2] NIST Digital Library of Mathematical Functions
+           https://dlmf.nist.gov/28.4#i
+
+    """
+    if not (isscalar(m) and isscalar(q)):
+        raise ValueError("m and q must be scalars.")
+    if (q < 0):
+        raise ValueError("q >=0")
+    if (m != floor(m)) or (m < 0):
+        raise ValueError("m must be an integer >=0.")
+
+    if (q <= 1):
+        qm = 7.5 + 56.1*sqrt(q) - 134.7*q + 90.7*sqrt(q)*q
+    else:
+        qm = 17.0 + 3.1*sqrt(q) - .126*q + .0037*sqrt(q)*q
+    km = int(qm + 0.5*m)
+    if km > 251:
+        warnings.warn("Too many predicted coefficients.", RuntimeWarning, stacklevel=2)
+    kd = 1
+    m = int(floor(m))
+    if m % 2:
+        kd = 2
+
+    a = mathieu_a(m, q)
+    fc = _specfun.fcoef(kd, m, q, a)
+    return fc[:km]
+
+
+def mathieu_odd_coef(m, q):
+    r"""Fourier coefficients for odd Mathieu and modified Mathieu functions.
+
+    The Fourier series of the odd solutions of the Mathieu differential
+    equation are of the form
+
+    .. math:: \mathrm{se}_{2n+1}(z, q) =
+              \sum_{k=0}^{\infty} B_{(2n+1)}^{(2k+1)} \sin (2k+1)z
+
+    .. math:: \mathrm{se}_{2n+2}(z, q) =
+              \sum_{k=0}^{\infty} B_{(2n+2)}^{(2k+2)} \sin (2k+2)z
+
+    This function returns the coefficients :math:`B_{(2n+2)}^{(2k+2)}` for even
+    input m=2n+2, and the coefficients :math:`B_{(2n+1)}^{(2k+1)}` for odd
+    input m=2n+1.
+
+    Parameters
+    ----------
+    m : int
+        Order of Mathieu functions.  Must be non-negative.
+    q : float (>=0)
+        Parameter of Mathieu functions.  Must be non-negative.
+
+    Returns
+    -------
+    Bk : ndarray
+        Even or odd Fourier coefficients, corresponding to even or odd m.
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    """
+    if not (isscalar(m) and isscalar(q)):
+        raise ValueError("m and q must be scalars.")
+    if (q < 0):
+        raise ValueError("q >=0")
+    if (m != floor(m)) or (m <= 0):
+        raise ValueError("m must be an integer > 0")
+
+    if (q <= 1):
+        qm = 7.5 + 56.1*sqrt(q) - 134.7*q + 90.7*sqrt(q)*q
+    else:
+        qm = 17.0 + 3.1*sqrt(q) - .126*q + .0037*sqrt(q)*q
+    km = int(qm + 0.5*m)
+    if km > 251:
+        warnings.warn("Too many predicted coefficients.", RuntimeWarning, stacklevel=2)
+    kd = 4
+    m = int(floor(m))
+    if m % 2:
+        kd = 3
+
+    b = mathieu_b(m, q)
+    fc = _specfun.fcoef(kd, m, q, b)
+    return fc[:km]
+
+
+def lqmn(m, n, z):
+    """Sequence of associated Legendre functions of the second kind.
+
+    Computes the associated Legendre function of the second kind of order m and
+    degree n, ``Qmn(z)`` = :math:`Q_n^m(z)`, and its derivative, ``Qmn'(z)``.
+    Returns two arrays of size ``(m+1, n+1)`` containing ``Qmn(z)`` and
+    ``Qmn'(z)`` for all orders from ``0..m`` and degrees from ``0..n``.
+
+    Parameters
+    ----------
+    m : int
+       ``|m| <= n``; the order of the Legendre function.
+    n : int
+       where ``n >= 0``; the degree of the Legendre function.  Often
+       called ``l`` (lower case L) in descriptions of the associated
+       Legendre function
+    z : array_like, complex
+        Input value.
+
+    Returns
+    -------
+    Qmn_z : (m+1, n+1) array
+       Values for all orders 0..m and degrees 0..n
+    Qmn_d_z : (m+1, n+1) array
+       Derivatives for all orders 0..m and degrees 0..n
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    """
+    if not isscalar(m) or (m < 0):
+        raise ValueError("m must be a non-negative integer.")
+    if not isscalar(n) or (n < 0):
+        raise ValueError("n must be a non-negative integer.")
+
+    m, n = int(m), int(n)  # Convert to int to maintain backwards compatibility.
+    # Ensure neither m nor n == 0
+    mm = max(1, m)
+    nn = max(1, n)
+
+    z = np.asarray(z)
+    if (not np.issubdtype(z.dtype, np.inexact)):
+        z = z.astype(np.float64)
+
+    if np.iscomplexobj(z):
+        q = np.empty((mm + 1, nn + 1) + z.shape, dtype=np.complex128)
+    else:
+        q = np.empty((mm + 1, nn + 1) + z.shape, dtype=np.float64)
+    qd = np.empty_like(q)
+    if (z.ndim == 0):
+        _lqmn(z, out=(q, qd))
+    else:
+        # new axes must be last for the ufunc
+        _lqmn(z,
+              out=(np.moveaxis(q, (0, 1), (-2, -1)),
+                   np.moveaxis(qd, (0, 1), (-2, -1))))
+
+    return q[:(m+1), :(n+1)], qd[:(m+1), :(n+1)]
+
+
+def bernoulli(n):
+    """Bernoulli numbers B0..Bn (inclusive).
+
+    Parameters
+    ----------
+    n : int
+        Indicated the number of terms in the Bernoulli series to generate.
+
+    Returns
+    -------
+    ndarray
+        The Bernoulli numbers ``[B(0), B(1), ..., B(n)]``.
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+    .. [2] "Bernoulli number", Wikipedia, https://en.wikipedia.org/wiki/Bernoulli_number
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.special import bernoulli, zeta
+    >>> bernoulli(4)
+    array([ 1.        , -0.5       ,  0.16666667,  0.        , -0.03333333])
+
+    The Wikipedia article ([2]_) points out the relationship between the
+    Bernoulli numbers and the zeta function, ``B_n^+ = -n * zeta(1 - n)``
+    for ``n > 0``:
+
+    >>> n = np.arange(1, 5)
+    >>> -n * zeta(1 - n)
+    array([ 0.5       ,  0.16666667, -0.        , -0.03333333])
+
+    Note that, in the notation used in the wikipedia article,
+    `bernoulli` computes ``B_n^-`` (i.e. it used the convention that
+    ``B_1`` is -1/2).  The relation given above is for ``B_n^+``, so the
+    sign of 0.5 does not match the output of ``bernoulli(4)``.
+
+    """
+    if not isscalar(n) or (n < 0):
+        raise ValueError("n must be a non-negative integer.")
+    n = int(n)
+    if (n < 2):
+        n1 = 2
+    else:
+        n1 = n
+    return _specfun.bernob(int(n1))[:(n+1)]
+
+
+def euler(n):
+    """Euler numbers E(0), E(1), ..., E(n).
+
+    The Euler numbers [1]_ are also known as the secant numbers.
+
+    Because ``euler(n)`` returns floating point values, it does not give
+    exact values for large `n`.  The first inexact value is E(22).
+
+    Parameters
+    ----------
+    n : int
+        The highest index of the Euler number to be returned.
+
+    Returns
+    -------
+    ndarray
+        The Euler numbers [E(0), E(1), ..., E(n)].
+        The odd Euler numbers, which are all zero, are included.
+
+    References
+    ----------
+    .. [1] Sequence A122045, The On-Line Encyclopedia of Integer Sequences,
+           https://oeis.org/A122045
+    .. [2] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.special import euler
+    >>> euler(6)
+    array([  1.,   0.,  -1.,   0.,   5.,   0., -61.])
+
+    >>> euler(13).astype(np.int64)
+    array([      1,       0,      -1,       0,       5,       0,     -61,
+                 0,    1385,       0,  -50521,       0, 2702765,       0])
+
+    >>> euler(22)[-1]  # Exact value of E(22) is -69348874393137901.
+    -69348874393137976.0
+
+    """
+    if not isscalar(n) or (n < 0):
+        raise ValueError("n must be a non-negative integer.")
+    n = int(n)
+    if (n < 2):
+        n1 = 2
+    else:
+        n1 = n
+    return _specfun.eulerb(n1)[:(n+1)]
+
+
+def lqn(n, z):
+    """Legendre functions of the second kind.
+
+    Compute sequence of Legendre functions of the second kind, ``Qn(z)`` and
+    derivatives for all degrees from 0 to `n` (inclusive).
+    Returns two arrays of size ``(n+1,) + z.shape`` containing ``Qn(z)`` and
+    ``Qn'(z)``.
+
+    Parameters
+    ----------
+    n : int
+        Maximum degree of the Legendre functions.
+    z : array_like, complex
+        Real or complex input values.
+
+    Returns
+    -------
+    Qn_z : ndarray, shape (n+1,) + shape(z)
+        Values for all degrees ``0..n``
+    Qn_d_z : ndarray, shape (n+1,) + shape(z)
+        Derivatives for all degrees ``0..n``
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    Examples
+    --------
+    Compute :math:`Q_n(x)` and its derivatives on an interval.
+
+    >>> import numpy as np
+    >>> from scipy.special import lqn
+    >>> import matplotlib.pyplot as plt
+
+    >>> xs = np.linspace(-2, 2, 200)
+    >>> n_max = 3
+    >>> Qn, dQn = lqn(n_max, xs)
+
+    Plot the Legendre functions of the second kind :math:`Q_n(x)`.
+
+    >>> fig, ax = plt.subplots()
+    >>> ax.plot(xs, Qn.T, "-")
+    >>> ax.set_xlabel(r"$x$")
+    >>> ax.set_ylabel(r"$Q_n(x)$")
+    >>> ax.legend([fr"$n={n}$" for n in range(n_max + 1)])
+    >>> plt.show()
+
+    Plot the derivatives :math:`Q_n'(x)`.
+
+    >>> fig, ax = plt.subplots()
+    >>> ax.plot(xs, dQn.T, "-")
+    >>> ax.set_xlabel(r"$x$")
+    >>> ax.set_ylabel(r"$Q_n'(x)$")
+    >>> ax.legend([fr"$n={n}$" for n in range(n_max + 1)])
+    >>> plt.show()
+    """
+    n = _nonneg_int_or_fail(n, 'n', strict=False)
+    if (n < 1):
+        n1 = 1
+    else:
+        n1 = n
+
+    z = np.asarray(z)
+    if (not np.issubdtype(z.dtype, np.inexact)):
+        z = z.astype(float)
+
+    if np.iscomplexobj(z):
+        qn = np.empty((n1 + 1,) + z.shape, dtype=np.complex128)
+    else:
+        qn = np.empty((n1 + 1,) + z.shape, dtype=np.float64)
+    qd = np.empty_like(qn)
+    if (z.ndim == 0):
+        _lqn(z, out=(qn, qd))
+    else:
+          # new axes must be last for the ufunc
+        _lqn(z,
+             out=(np.moveaxis(qn, 0, -1),
+                  np.moveaxis(qd, 0, -1)))
+
+    return qn[:(n+1)], qd[:(n+1)]
+
+
+def ai_zeros(nt):
+    """
+    Compute `nt` zeros and values of the Airy function Ai and its derivative.
+
+    Computes the first `nt` zeros, `a`, of the Airy function Ai(x);
+    first `nt` zeros, `ap`, of the derivative of the Airy function Ai'(x);
+    the corresponding values Ai(a');
+    and the corresponding values Ai'(a).
+
+    Parameters
+    ----------
+    nt : int
+        Number of zeros to compute
+
+    Returns
+    -------
+    a : ndarray
+        First `nt` zeros of Ai(x)
+    ap : ndarray
+        First `nt` zeros of Ai'(x)
+    ai : ndarray
+        Values of Ai(x) evaluated at first `nt` zeros of Ai'(x)
+    aip : ndarray
+        Values of Ai'(x) evaluated at first `nt` zeros of Ai(x)
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    Examples
+    --------
+    >>> from scipy import special
+    >>> a, ap, ai, aip = special.ai_zeros(3)
+    >>> a
+    array([-2.33810741, -4.08794944, -5.52055983])
+    >>> ap
+    array([-1.01879297, -3.24819758, -4.82009921])
+    >>> ai
+    array([ 0.53565666, -0.41901548,  0.38040647])
+    >>> aip
+    array([ 0.70121082, -0.80311137,  0.86520403])
+
+    """
+    kf = 1
+    if not isscalar(nt) or (floor(nt) != nt) or (nt <= 0):
+        raise ValueError("nt must be a positive integer scalar.")
+    return _specfun.airyzo(nt, kf)
+
+
+def bi_zeros(nt):
+    """
+    Compute `nt` zeros and values of the Airy function Bi and its derivative.
+
+    Computes the first `nt` zeros, b, of the Airy function Bi(x);
+    first `nt` zeros, b', of the derivative of the Airy function Bi'(x);
+    the corresponding values Bi(b');
+    and the corresponding values Bi'(b).
+
+    Parameters
+    ----------
+    nt : int
+        Number of zeros to compute
+
+    Returns
+    -------
+    b : ndarray
+        First `nt` zeros of Bi(x)
+    bp : ndarray
+        First `nt` zeros of Bi'(x)
+    bi : ndarray
+        Values of Bi(x) evaluated at first `nt` zeros of Bi'(x)
+    bip : ndarray
+        Values of Bi'(x) evaluated at first `nt` zeros of Bi(x)
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    Examples
+    --------
+    >>> from scipy import special
+    >>> b, bp, bi, bip = special.bi_zeros(3)
+    >>> b
+    array([-1.17371322, -3.2710933 , -4.83073784])
+    >>> bp
+    array([-2.29443968, -4.07315509, -5.51239573])
+    >>> bi
+    array([-0.45494438,  0.39652284, -0.36796916])
+    >>> bip
+    array([ 0.60195789, -0.76031014,  0.83699101])
+
+    """
+    kf = 2
+    if not isscalar(nt) or (floor(nt) != nt) or (nt <= 0):
+        raise ValueError("nt must be a positive integer scalar.")
+    return _specfun.airyzo(nt, kf)
+
+
+def lmbda(v, x):
+    r"""Jahnke-Emden Lambda function, Lambdav(x).
+
+    This function is defined as [2]_,
+
+    .. math:: \Lambda_v(x) = \Gamma(v+1) \frac{J_v(x)}{(x/2)^v},
+
+    where :math:`\Gamma` is the gamma function and :math:`J_v` is the
+    Bessel function of the first kind.
+
+    Parameters
+    ----------
+    v : float
+        Order of the Lambda function
+    x : float
+        Value at which to evaluate the function and derivatives
+
+    Returns
+    -------
+    vl : ndarray
+        Values of Lambda_vi(x), for vi=v-int(v), vi=1+v-int(v), ..., vi=v.
+    dl : ndarray
+        Derivatives Lambda_vi'(x), for vi=v-int(v), vi=1+v-int(v), ..., vi=v.
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+    .. [2] Jahnke, E. and Emde, F. "Tables of Functions with Formulae and
+           Curves" (4th ed.), Dover, 1945
+    """
+    if not (isscalar(v) and isscalar(x)):
+        raise ValueError("arguments must be scalars.")
+    if (v < 0):
+        raise ValueError("argument must be > 0.")
+    n = int(v)
+    v0 = v - n
+    if (n < 1):
+        n1 = 1
+    else:
+        n1 = n
+    v1 = n1 + v0
+    if (v != floor(v)):
+        vm, vl, dl = _specfun.lamv(v1, x)
+    else:
+        vm, vl, dl = _specfun.lamn(v1, x)
+    return vl[:(n+1)], dl[:(n+1)]
+
+
+def pbdv_seq(v, x):
+    """Parabolic cylinder functions Dv(x) and derivatives.
+
+    Parameters
+    ----------
+    v : float
+        Order of the parabolic cylinder function
+    x : float
+        Value at which to evaluate the function and derivatives
+
+    Returns
+    -------
+    dv : ndarray
+        Values of D_vi(x), for vi=v-int(v), vi=1+v-int(v), ..., vi=v.
+    dp : ndarray
+        Derivatives D_vi'(x), for vi=v-int(v), vi=1+v-int(v), ..., vi=v.
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996, chapter 13.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    """
+    if not (isscalar(v) and isscalar(x)):
+        raise ValueError("arguments must be scalars.")
+    n = int(v)
+    v0 = v-n
+    if (n < 1):
+        n1 = 1
+    else:
+        n1 = n
+    v1 = n1 + v0
+    dv, dp, pdf, pdd = _specfun.pbdv(v1, x)
+    return dv[:n1+1], dp[:n1+1]
+
+
+def pbvv_seq(v, x):
+    """Parabolic cylinder functions Vv(x) and derivatives.
+
+    Parameters
+    ----------
+    v : float
+        Order of the parabolic cylinder function
+    x : float
+        Value at which to evaluate the function and derivatives
+
+    Returns
+    -------
+    dv : ndarray
+        Values of V_vi(x), for vi=v-int(v), vi=1+v-int(v), ..., vi=v.
+    dp : ndarray
+        Derivatives V_vi'(x), for vi=v-int(v), vi=1+v-int(v), ..., vi=v.
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996, chapter 13.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    """
+    if not (isscalar(v) and isscalar(x)):
+        raise ValueError("arguments must be scalars.")
+    n = int(v)
+    v0 = v-n
+    if (n <= 1):
+        n1 = 1
+    else:
+        n1 = n
+    v1 = n1 + v0
+    dv, dp, pdf, pdd = _specfun.pbvv(v1, x)
+    return dv[:n1+1], dp[:n1+1]
+
+
+def pbdn_seq(n, z):
+    """Parabolic cylinder functions Dn(z) and derivatives.
+
+    Parameters
+    ----------
+    n : int
+        Order of the parabolic cylinder function
+    z : complex
+        Value at which to evaluate the function and derivatives
+
+    Returns
+    -------
+    dv : ndarray
+        Values of D_i(z), for i=0, ..., i=n.
+    dp : ndarray
+        Derivatives D_i'(z), for i=0, ..., i=n.
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996, chapter 13.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    """
+    if not (isscalar(n) and isscalar(z)):
+        raise ValueError("arguments must be scalars.")
+    if (floor(n) != n):
+        raise ValueError("n must be an integer.")
+    if (abs(n) <= 1):
+        n1 = 1
+    else:
+        n1 = n
+    cpb, cpd = _specfun.cpbdn(n1, z)
+    return cpb[:n1+1], cpd[:n1+1]
+
+
+def ber_zeros(nt):
+    """Compute nt zeros of the Kelvin function ber.
+
+    Parameters
+    ----------
+    nt : int
+        Number of zeros to compute. Must be positive.
+
+    Returns
+    -------
+    ndarray
+        First `nt` zeros of the Kelvin function.
+
+    See Also
+    --------
+    ber
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    """
+    if not isscalar(nt) or (floor(nt) != nt) or (nt <= 0):
+        raise ValueError("nt must be positive integer scalar.")
+    return _specfun.klvnzo(nt, 1)
+
+
+def bei_zeros(nt):
+    """Compute nt zeros of the Kelvin function bei.
+
+    Parameters
+    ----------
+    nt : int
+        Number of zeros to compute. Must be positive.
+
+    Returns
+    -------
+    ndarray
+        First `nt` zeros of the Kelvin function.
+
+    See Also
+    --------
+    bei
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    """
+    if not isscalar(nt) or (floor(nt) != nt) or (nt <= 0):
+        raise ValueError("nt must be positive integer scalar.")
+    return _specfun.klvnzo(nt, 2)
+
+
+def ker_zeros(nt):
+    """Compute nt zeros of the Kelvin function ker.
+
+    Parameters
+    ----------
+    nt : int
+        Number of zeros to compute. Must be positive.
+
+    Returns
+    -------
+    ndarray
+        First `nt` zeros of the Kelvin function.
+
+    See Also
+    --------
+    ker
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    """
+    if not isscalar(nt) or (floor(nt) != nt) or (nt <= 0):
+        raise ValueError("nt must be positive integer scalar.")
+    return _specfun.klvnzo(nt, 3)
+
+
+def kei_zeros(nt):
+    """Compute nt zeros of the Kelvin function kei.
+
+    Parameters
+    ----------
+    nt : int
+        Number of zeros to compute. Must be positive.
+
+    Returns
+    -------
+    ndarray
+        First `nt` zeros of the Kelvin function.
+
+    See Also
+    --------
+    kei
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    """
+    if not isscalar(nt) or (floor(nt) != nt) or (nt <= 0):
+        raise ValueError("nt must be positive integer scalar.")
+    return _specfun.klvnzo(nt, 4)
+
+
+def berp_zeros(nt):
+    """Compute nt zeros of the derivative of the Kelvin function ber.
+
+    Parameters
+    ----------
+    nt : int
+        Number of zeros to compute. Must be positive.
+
+    Returns
+    -------
+    ndarray
+        First `nt` zeros of the derivative of the Kelvin function.
+
+    See Also
+    --------
+    ber, berp
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+
+    Examples
+    --------
+    Compute the first 5 zeros of the derivative of the Kelvin function.
+
+    >>> from scipy.special import berp_zeros
+    >>> berp_zeros(5)
+    array([ 6.03871081, 10.51364251, 14.96844542, 19.41757493, 23.86430432])
+
+    """
+    if not isscalar(nt) or (floor(nt) != nt) or (nt <= 0):
+        raise ValueError("nt must be positive integer scalar.")
+    return _specfun.klvnzo(nt, 5)
+
+
+def beip_zeros(nt):
+    """Compute nt zeros of the derivative of the Kelvin function bei.
+
+    Parameters
+    ----------
+    nt : int
+        Number of zeros to compute. Must be positive.
+
+    Returns
+    -------
+    ndarray
+        First `nt` zeros of the derivative of the Kelvin function.
+
+    See Also
+    --------
+    bei, beip
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    """
+    if not isscalar(nt) or (floor(nt) != nt) or (nt <= 0):
+        raise ValueError("nt must be positive integer scalar.")
+    return _specfun.klvnzo(nt, 6)
+
+
+def kerp_zeros(nt):
+    """Compute nt zeros of the derivative of the Kelvin function ker.
+
+    Parameters
+    ----------
+    nt : int
+        Number of zeros to compute. Must be positive.
+
+    Returns
+    -------
+    ndarray
+        First `nt` zeros of the derivative of the Kelvin function.
+
+    See Also
+    --------
+    ker, kerp
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    """
+    if not isscalar(nt) or (floor(nt) != nt) or (nt <= 0):
+        raise ValueError("nt must be positive integer scalar.")
+    return _specfun.klvnzo(nt, 7)
+
+
+def keip_zeros(nt):
+    """Compute nt zeros of the derivative of the Kelvin function kei.
+
+    Parameters
+    ----------
+    nt : int
+        Number of zeros to compute. Must be positive.
+
+    Returns
+    -------
+    ndarray
+        First `nt` zeros of the derivative of the Kelvin function.
+
+    See Also
+    --------
+    kei, keip
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    """
+    if not isscalar(nt) or (floor(nt) != nt) or (nt <= 0):
+        raise ValueError("nt must be positive integer scalar.")
+    return _specfun.klvnzo(nt, 8)
+
+
+def kelvin_zeros(nt):
+    """Compute `nt` zeros of all Kelvin functions.
+
+    Parameters
+    ----------
+    nt : int
+        Number of zeros to compute for each function.
+
+    Returns
+    -------
+    zeros : tuple of arrays
+        Length-8 tuple of arrays of length `nt`.  The tuple contains the arrays of zeros
+        of ``(ber, bei, ker, kei, ber', bei', ker', kei')``.
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    """
+    if not isscalar(nt) or (floor(nt) != nt) or (nt <= 0):
+        raise ValueError("nt must be positive integer scalar.")
+    return (_specfun.klvnzo(nt, 1),
+            _specfun.klvnzo(nt, 2),
+            _specfun.klvnzo(nt, 3),
+            _specfun.klvnzo(nt, 4),
+            _specfun.klvnzo(nt, 5),
+            _specfun.klvnzo(nt, 6),
+            _specfun.klvnzo(nt, 7),
+            _specfun.klvnzo(nt, 8))
+
+
+def pro_cv_seq(m, n, c):
+    """Characteristic values for prolate spheroidal wave functions.
+
+    Compute a sequence of characteristic values for the prolate
+    spheroidal wave functions for mode `m` and n'=m..n and spheroidal
+    parameter `c`.
+
+    Parameters
+    ----------
+    m, n : int
+        Non-negative mode parameters.
+    c : float
+        Spheroidal parameter.
+
+    Returns
+    -------
+    cv : array of floats
+        Characteristic values.
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    """
+    if not (isscalar(m) and isscalar(n) and isscalar(c)):
+        raise ValueError("Arguments must be scalars.")
+    if (n != floor(n)) or (m != floor(m)):
+        raise ValueError("Modes must be integers.")
+    if (n-m > 199):
+        raise ValueError("Difference between n and m is too large.")
+    maxL = n-m+1
+    return _specfun.segv(m, n, c, 1)[1][:maxL]
+
+
+def obl_cv_seq(m, n, c):
+    """Characteristic values for oblate spheroidal wave functions.
+
+    Compute a sequence of characteristic values for the oblate
+    spheroidal wave functions for mode m and n'=m..n and spheroidal
+    parameter c.
+
+    Parameters
+    ----------
+    m, n : int
+        Non-negative mode parameters.
+    c : float
+        Spheroidal parameter.
+
+    Returns
+    -------
+    cv : array of floats
+        Characteristic values.
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    """
+    if not (isscalar(m) and isscalar(n) and isscalar(c)):
+        raise ValueError("Arguments must be scalars.")
+    if (n != floor(n)) or (m != floor(m)):
+        raise ValueError("Modes must be integers.")
+    if (n-m > 199):
+        raise ValueError("Difference between n and m is too large.")
+    maxL = n-m+1
+    return _specfun.segv(m, n, c, -1)[1][:maxL]
+
+
+def comb(N, k, *, exact=False, repetition=False):
+    """The number of combinations of N things taken k at a time.
+
+    This is often expressed as "N choose k".
+
+    Parameters
+    ----------
+    N : int, ndarray
+        Number of things.
+    k : int, ndarray
+        Number of elements taken.
+    exact : bool, optional
+        For integers, if `exact` is False, then floating point precision is
+        used, otherwise the result is computed exactly.
+    repetition : bool, optional
+        If `repetition` is True, then the number of combinations with
+        repetition is computed.
+
+    Returns
+    -------
+    val : int, float, ndarray
+        The total number of combinations.
+
+    See Also
+    --------
+    binom : Binomial coefficient considered as a function of two real
+            variables.
+
+    Notes
+    -----
+    - Array arguments accepted only for exact=False case.
+    - If N < 0, or k < 0, then 0 is returned.
+    - If k > N and repetition=False, then 0 is returned.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.special import comb
+    >>> k = np.array([3, 4])
+    >>> n = np.array([10, 10])
+    >>> comb(n, k, exact=False)
+    array([ 120.,  210.])
+    >>> comb(10, 3, exact=True)
+    120
+    >>> comb(10, 3, exact=True, repetition=True)
+    220
+
+    """
+    if repetition:
+        # Special case: C(n, 0) with repetition = 1 for n >= 0
+        # Without this check, comb(0, 0, repetition=True) would compute
+        # comb(-1, 0) which incorrectly returns 0
+        if exact:
+            if k == 0 and int(N) == N and N >= 0:
+                return 1
+        else:
+            k, N = asarray(k), asarray(N)
+            cond = (k == 0) & (N >= 0)
+            vals = binom(N + k - 1, k)
+            if isinstance(vals, np.ndarray):
+                vals[cond] = 1.0
+            elif cond:
+                vals = np.float64(1.0)
+            return vals
+        return comb(N + k - 1, k, exact=exact)
+    if exact:
+        if int(N) == N and int(k) == k:
+            # _comb_int casts inputs to integers, which is safe & intended here
+            return _comb_int(N, k)
+        else:
+            raise ValueError("Non-integer `N` and `k` with `exact=True` is not "
+                             "supported.")
+    else:
+        k, N = asarray(k), asarray(N)
+        cond = (k <= N) & (N >= 0) & (k >= 0)
+        vals = binom(N, k)
+        if isinstance(vals, np.ndarray):
+            vals[~cond] = 0
+        elif not cond:
+            vals = np.float64(0)
+        return vals
+
+
+def perm(N, k, exact=False):
+    """Permutations of N things taken k at a time, i.e., k-permutations of N.
+
+    It's also known as "partial permutations".
+
+    Parameters
+    ----------
+    N : int, ndarray
+        Number of things.
+    k : int, ndarray
+        Number of elements taken.
+    exact : bool, optional
+        If ``True``, calculate the answer exactly using long integer arithmetic (`N`
+        and `k` must be scalar integers). If ``False``, a floating point approximation
+        is calculated (more rapidly) using `poch`. Default is ``False``.
+
+    Returns
+    -------
+    val : int, ndarray
+        The number of k-permutations of N.
+
+    Notes
+    -----
+    - Array arguments accepted only for exact=False case.
+    - If k > N, N < 0, or k < 0, then a 0 is returned.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.special import perm
+    >>> k = np.array([3, 4])
+    >>> n = np.array([10, 10])
+    >>> perm(n, k)
+    array([  720.,  5040.])
+    >>> perm(10, 3, exact=True)
+    720
+
+    """
+    if exact:
+        N = np.squeeze(N)[()]  # for backward compatibility (accepted size 1 arrays)
+        k = np.squeeze(k)[()]
+        if not (isscalar(N) and isscalar(k)):
+            raise ValueError("`N` and `k` must be scalar integers with `exact=True`.")
+
+        floor_N, floor_k = int(N), int(k)
+        non_integral = not (floor_N == N and floor_k == k)
+        if non_integral:
+            raise ValueError("Non-integer `N` and `k` with `exact=True` is not "
+                             "supported.")
+
+        if (k > N) or (N < 0) or (k < 0):
+            return 0
+
+        val = 1
+        for i in range(floor_N - floor_k + 1, floor_N + 1):
+            val *= i
+        return val
+    else:
+        k, N = asarray(k), asarray(N)
+        cond = (k <= N) & (N >= 0) & (k >= 0)
+        vals = poch(N - k + 1, k)
+        if isinstance(vals, np.ndarray):
+            vals[~cond] = 0
+        elif not cond:
+            vals = np.float64(0)
+        return vals
+
+
+# https://stackoverflow.com/a/16327037
+def _range_prod(lo, hi, k=1):
+    """
+    Product of a range of numbers spaced k apart (from hi).
+
+    For k=1, this returns the product of
+    lo * (lo+1) * (lo+2) * ... * (hi-2) * (hi-1) * hi
+    = hi! / (lo-1)!
+
+    For k>1, it correspond to taking only every k'th number when
+    counting down from hi - e.g. 18!!!! = _range_prod(1, 18, 4).
+
+    Breaks into smaller products first for speed:
+    _range_prod(2, 9) = ((2*3)*(4*5))*((6*7)*(8*9))
+    """
+    if lo == 1 and k == 1:
+        return math.factorial(hi)
+
+    if lo + k < hi:
+        mid = (hi + lo) // 2
+        if k > 1:
+            # make sure mid is a multiple of k away from hi
+            mid = mid - ((mid - hi) % k)
+        return _range_prod(lo, mid, k) * _range_prod(mid + k, hi, k)
+    elif lo + k == hi:
+        return lo * hi
+    else:
+        return hi
+
+
+def _factorialx_array_exact(n, k=1):
+    """
+    Exact computation of factorial for an array.
+
+    The factorials are computed in incremental fashion, by taking
+    the sorted unique values of n and multiplying the intervening
+    numbers between the different unique values.
+
+    In other words, the factorial for the largest input is only
+    computed once, with each other result computed in the process.
+
+    k > 1 corresponds to the multifactorial.
+    """
+    un = np.unique(n)
+
+    # Convert to object array if np.int64 can't handle size
+    if k in _FACTORIALK_LIMITS_64BITS.keys():
+        if un[-1] > _FACTORIALK_LIMITS_64BITS[k]:
+            # e.g. k=1: 21! > np.iinfo(np.int64).max
+            dt = object
+        elif un[-1] > _FACTORIALK_LIMITS_32BITS[k]:
+            # e.g. k=3: 26!!! > np.iinfo(np.int32).max
+            dt = np.int64
+        else:
+            dt = np.dtype("long")
+    else:
+        # for k >= 10, we always use object
+        dt = object
+
+    out = np.empty_like(n, dtype=dt)
+
+    # Handle invalid/trivial values
+    un = un[un > 1]
+    out[n < 2] = 1
+    out[n < 0] = 0
+
+    # Calculate products of each range of numbers
+    # we can only multiply incrementally if the values are k apart;
+    # therefore we partition `un` into "lanes", i.e. its residues modulo k
+    for lane in range(0, k):
+        ul = un[(un % k) == lane] if k > 1 else un
+        if ul.size:
+            # after np.unique, un resp. ul are sorted, ul[0] is the smallest;
+            # cast to python ints to avoid overflow with np.int-types
+            val = _range_prod(1, int(ul[0]), k=k)
+            out[n == ul[0]] = val
+            for i in range(len(ul) - 1):
+                # by the filtering above, we have ensured that prev & current
+                # are a multiple of k apart
+                prev = ul[i]
+                current = ul[i + 1]
+                # we already multiplied all factors until prev; continue
+                # building the full factorial from the following (`prev + 1`);
+                # use int() for the same reason as above
+                val *= _range_prod(int(prev + 1), int(current), k=k)
+                out[n == current] = val
+
+    return out
+
+
+def _factorialx_array_approx(n, k, extend):
+    """
+    Calculate approximation to multifactorial for array n and integer k.
+
+    Ensure that values aren't calculated unnecessarily.
+    """
+    if extend == "complex":
+        return _factorialx_approx_core(n, k=k, extend=extend)
+
+    # at this point we are guaranteed that extend='zero' and that k>0 is an integer
+    result = zeros(n.shape)
+    # keep nans as nans
+    place(result, np.isnan(n), np.nan)
+    # only compute where n >= 0 (excludes nans), everything else is 0
+    cond = (n >= 0)
+    n_to_compute = extract(cond, n)
+    place(result, cond, _factorialx_approx_core(n_to_compute, k=k, extend=extend))
+    return result
+
+
+def _gamma1p(vals):
+    """
+    returns gamma(n+1), though with NaN at -1 instead of inf, c.f. #21827
+    """
+    res = gamma(vals + 1)
+    # replace infinities at -1 (from gamma function at 0) with nan
+    # gamma only returns inf for real inputs; can ignore complex case
+    if isinstance(res, np.ndarray):
+        if not _is_subdtype(vals.dtype, "c"):
+            res[vals == -1] = np.nan
+    elif np.isinf(res) and vals == -1:
+        res = np.float64("nan")
+    return res
+
+
+def _factorialx_approx_core(n, k, extend):
+    """
+    Core approximation to multifactorial for array n and integer k.
+    """
+    if k == 1:
+        # shortcut for k=1; same for both extensions, because we assume the
+        # handling of extend == 'zero' happens in _factorialx_array_approx
+        result = _gamma1p(n)
+        if isinstance(n, np.ndarray):
+            # gamma does not maintain 0-dim arrays; fix it
+            result = np.array(result)
+        return result
+
+    if extend == "complex":
+        # see https://numpy.org/doc/stable/reference/generated/numpy.power.html
+        p_dtype = complex if (_is_subdtype(type(k), "c") or k < 0) else None
+        with warnings.catch_warnings():
+            # do not warn about 0 * inf, nan / nan etc.; the results are correct
+            warnings.simplefilter("ignore", RuntimeWarning)
+            # don't use `(n-1)/k` in np.power; underflows if 0 is of a uintX type
+            result = np.power(k, n / k, dtype=p_dtype) * _gamma1p(n / k)
+            result *= rgamma(1 / k + 1) / np.power(k, 1 / k, dtype=p_dtype)
+        if isinstance(n, np.ndarray):
+            # ensure we keep array-ness for 0-dim inputs; already n/k above loses it
+            result = np.array(result)
+        return result
+
+    # at this point we are guaranteed that extend='zero' and that k>0 is an integer
+    n_mod_k = n % k
+    # scalar case separately, unified handling would be inefficient for arrays;
+    # don't use isscalar due to numpy/numpy#23574; 0-dim arrays treated below
+    if not isinstance(n, np.ndarray):
+        with warnings.catch_warnings():
+            # large n cause overflow warnings, but infinity is fine
+            warnings.simplefilter("ignore", RuntimeWarning)
+            return (
+                np.power(k, (n - n_mod_k) / k)
+                * gamma(n / k + 1) / gamma(n_mod_k / k + 1)
+                * max(n_mod_k, 1)
+            )
+
+    # factor that's independent of the residue class (see factorialk docstring)
+    with warnings.catch_warnings():
+        # large n cause overflow warnings, but infinity is fine
+        warnings.simplefilter("ignore", RuntimeWarning)
+        result = np.power(k, n / k) * gamma(n / k + 1)
+    # factor dependent on residue r (for `r=0` it's 1, so we skip `r=0`
+    # below and thus also avoid evaluating `max(r, 1)`)
+    def corr(k, r): return np.power(k, -r / k) / gamma(r / k + 1) * r
+    for r in np.unique(n_mod_k):
+        if r == 0:
+            continue
+        # cast to int because uint types break on `-r`
+        result[n_mod_k == r] *= corr(k, int(r))
+    return result
+
+
+def _is_subdtype(dtype, dtypes):
+    """
+    Shorthand for calculating whether dtype is subtype of some dtypes.
+
+    Also allows specifying a list instead of just a single dtype.
+
+    Additionaly, the most important supertypes from
+        https://numpy.org/doc/stable/reference/arrays.scalars.html
+    can optionally be specified using abbreviations as follows:
+        "i": np.integer
+        "f": np.floating
+        "c": np.complexfloating
+        "n": np.number (contains the other three)
+    """
+    dtypes = dtypes if isinstance(dtypes, list) else [dtypes]
+    # map single character abbreviations, if they are in dtypes
+    mapping = {
+        "i": np.integer,
+        "f": np.floating,
+        "c": np.complexfloating,
+        "n": np.number
+    }
+    dtypes = [mapping.get(x, x) for x in dtypes]
+    return any(np.issubdtype(dtype, dt) for dt in dtypes)
+
+
+def _factorialx_wrapper(fname, n, k, exact, extend):
+    """
+    Shared implementation for factorial, factorial2 & factorialk.
+    """
+    if extend not in ("zero", "complex"):
+        raise ValueError(
+            f"argument `extend` must be either 'zero' or 'complex', received: {extend}"
+        )
+    if exact and extend == "complex":
+        raise ValueError("Incompatible options: `exact=True` and `extend='complex'`")
+
+    msg_unsup = (
+        "Unsupported data type for {vname} in {fname}: {dtype}\n"
+    )
+    if fname == "factorial":
+        msg_unsup += (
+            "Permitted data types are integers and floating point numbers, "
+            "as well as complex numbers if `extend='complex' is passed."
+        )
+    else:
+        msg_unsup += (
+            "Permitted data types are integers, as well as floating point "
+            "numbers and complex numbers if `extend='complex' is passed."
+        )
+    msg_exact_not_possible = (
+        "`exact=True` only supports integers, cannot use data type {dtype}"
+    )
+    msg_needs_complex = (
+        "In order to use non-integer arguments, you must opt into this by passing "
+        "`extend='complex'`. Note that this changes the result for all negative "
+        "arguments (which by default return 0)."
+    )
+
+    if fname == "factorial2":
+        msg_needs_complex += (" Additionally, it will rescale the values of the double"
+                              " factorial at even integers by a factor of sqrt(2/pi).")
+    elif fname == "factorialk":
+        msg_needs_complex += (" Additionally, it will perturb the values of the"
+                              " multifactorial at most positive integers `n`.")
+        # check type of k
+        if not _is_subdtype(type(k), ["i", "f", "c"]):
+            raise ValueError(msg_unsup.format(vname="`k`", fname=fname, dtype=type(k)))
+        elif _is_subdtype(type(k), ["f", "c"]) and extend != "complex":
+            raise ValueError(msg_needs_complex)
+        # check value of k
+        if extend == "zero" and k < 1:
+            msg = f"For `extend='zero'`, k must be a positive integer, received: {k}"
+            raise ValueError(msg)
+        elif k == 0:
+            raise ValueError("Parameter k cannot be zero!")
+
+    # factorial allows floats also for extend="zero"
+    types_requiring_complex = "c" if fname == "factorial" else ["f", "c"]
+
+    # don't use isscalar due to numpy/numpy#23574; 0-dim arrays treated below
+    if np.ndim(n) == 0 and not isinstance(n, np.ndarray):
+        # scalar cases
+        if not _is_subdtype(type(n), ["i", "f", "c", type(None)]):
+            raise ValueError(msg_unsup.format(vname="`n`", fname=fname, dtype=type(n)))
+        elif _is_subdtype(type(n), types_requiring_complex) and extend != "complex":
+            raise ValueError(msg_needs_complex)
+        elif n is None or np.isnan(n):
+            complexify = (extend == "complex") and _is_subdtype(type(n), "c")
+            return np.complex128("nan+nanj") if complexify else np.float64("nan")
+        elif extend == "zero" and n < 0:
+            return 0 if exact else np.float64(0)
+        elif n in {0, 1}:
+            return 1 if exact else np.float64(1)
+        elif exact and _is_subdtype(type(n), "i"):
+            # calculate with integers; cast away other int types (like unsigned)
+            return _range_prod(1, int(n), k=k)
+        elif exact:
+            # only relevant for factorial
+            raise ValueError(msg_exact_not_possible.format(dtype=type(n)))
+        # approximation
+        return _factorialx_approx_core(n, k=k, extend=extend)
+
+    # arrays & array-likes
+    n = asarray(n)
+
+    if not _is_subdtype(n.dtype, ["i", "f", "c"]):
+        raise ValueError(msg_unsup.format(vname="`n`", fname=fname, dtype=n.dtype))
+    elif _is_subdtype(n.dtype, types_requiring_complex) and extend != "complex":
+        raise ValueError(msg_needs_complex)
+    elif exact and _is_subdtype(n.dtype, ["f"]):
+        # only relevant for factorial
+        raise ValueError(msg_exact_not_possible.format(dtype=n.dtype))
+
+    if n.size == 0:
+        # return empty arrays unchanged
+        return n
+    elif exact:
+        # calculate with integers
+        return _factorialx_array_exact(n, k=k)
+    # approximation
+    return _factorialx_array_approx(n, k=k, extend=extend)
+
+
+def factorial(n, exact=False, extend="zero"):
+    """
+    The factorial of a number or array of numbers.
+
+    The factorial of non-negative integer `n` is the product of all
+    positive integers less than or equal to `n`::
+
+        n! = n * (n - 1) * (n - 2) * ... * 1
+
+    Parameters
+    ----------
+    n : int or float or complex (or array_like thereof)
+        Input values for ``n!``. Complex values require ``extend='complex'``.
+        By default, the return value for ``n < 0`` is 0.
+    exact : bool, optional
+        If ``exact`` is set to True, calculate the answer exactly using
+        integer arithmetic, otherwise approximate using the gamma function
+        (faster, but yields floats instead of integers).
+        Default is False.
+    extend : str, optional
+        One of ``'zero'`` or ``'complex'``; this determines how values ``n<0``
+        are handled - by default they are 0, but it is possible to opt into the
+        complex extension of the factorial (see below).
+
+    Returns
+    -------
+    nf : int or float or complex or ndarray
+        Factorial of ``n``, as integer, float or complex (depending on ``exact``
+        and ``extend``). Array inputs are returned as arrays.
+
+    Notes
+    -----
+    For arrays with ``exact=True``, the factorial is computed only once, for
+    the largest input, with each other result computed in the process.
+    The output dtype is increased to ``int64`` or ``object`` if necessary.
+
+    With ``exact=False`` the factorial is approximated using the gamma
+    function (which is also the definition of the complex extension):
+
+    .. math:: n! = \\Gamma(n+1)
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.special import factorial
+    >>> arr = np.array([3, 4, 5])
+    >>> factorial(arr, exact=False)
+    array([   6.,   24.,  120.])
+    >>> factorial(arr, exact=True)
+    array([  6,  24, 120])
+    >>> factorial(5, exact=True)
+    120
+
+    """
+    return _factorialx_wrapper("factorial", n, k=1, exact=exact, extend=extend)
+
+
+def factorial2(n, exact=False, extend="zero"):
+    """
+    Double factorial.
+
+    This is the factorial with every second value skipped.  E.g., ``7!! = 7 * 5
+    * 3 * 1``.  It can be approximated numerically as::
+
+      n!! = 2 ** (n / 2) * gamma(n / 2 + 1) * sqrt(2 / pi)  n odd
+          = 2 ** (n / 2) * gamma(n / 2 + 1)                 n even
+          = 2 ** (n / 2) * (n / 2)!                         n even
+
+    The formula for odd ``n`` is the basis for the complex extension.
+
+    Parameters
+    ----------
+    n : int or float or complex (or array_like thereof)
+        Input values for ``n!!``. Non-integer values require ``extend='complex'``.
+        By default, the return value for ``n < 0`` is 0.
+    exact : bool, optional
+        If ``exact`` is set to True, calculate the answer exactly using
+        integer arithmetic, otherwise use above approximation (faster,
+        but yields floats instead of integers).
+        Default is False.
+    extend : str, optional
+        One of ``'zero'`` or ``'complex'``; this determines how values ``n<0``
+        are handled - by default they are 0, but it is possible to opt into the
+        complex extension of the double factorial. This also enables passing
+        complex values to ``n``.
+
+        .. warning::
+
+           Using the ``'complex'`` extension also changes the values of the
+           double factorial for even integers, reducing them by a factor of
+           ``sqrt(2/pi) ~= 0.79``, see [1].
+
+    Returns
+    -------
+    nf : int or float or complex or ndarray
+        Double factorial of ``n``, as integer, float or complex (depending on
+        ``exact`` and ``extend``). Array inputs are returned as arrays.
+
+    References
+    ----------
+    .. [1] Complex extension to double factorial
+            https://en.wikipedia.org/wiki/Double_factorial#Complex_arguments
+
+    Examples
+    --------
+    >>> from scipy.special import factorial2
+    >>> factorial2(7, exact=False)
+    np.float64(105.00000000000001)
+    >>> factorial2(7, exact=True)
+    105
+    """
+    return _factorialx_wrapper("factorial2", n, k=2, exact=exact, extend=extend)
+
+
+def factorialk(n, k, exact=False, extend="zero"):
+    """
+    Multifactorial of n of order k, n(!!...!).
+
+    This is the multifactorial of n skipping k values.  For example,
+
+      factorialk(17, 4) = 17!!!! = 17 * 13 * 9 * 5 * 1
+
+    In particular, for any integer ``n``, we have
+
+      factorialk(n, 1) = factorial(n)
+
+      factorialk(n, 2) = factorial2(n)
+
+    Parameters
+    ----------
+    n : int or float or complex (or array_like thereof)
+        Input values for multifactorial. Non-integer values require
+        ``extend='complex'``. By default, the return value for ``n < 0`` is 0.
+    k : int or float or complex (or array_like thereof)
+        Order of multifactorial. Non-integer values require ``extend='complex'``.
+    exact : bool, optional
+        If ``exact`` is set to True, calculate the answer exactly using
+        integer arithmetic, otherwise use an approximation (faster,
+        but yields floats instead of integers)
+        Default is False.
+    extend : str, optional
+        One of ``'zero'`` or ``'complex'``; this determines how values ``n<0`` are
+        handled - by default they are 0, but it is possible to opt into the complex
+        extension of the multifactorial. This enables passing complex values,
+        not only to ``n`` but also to ``k``.
+
+        .. warning::
+
+           Using the ``'complex'`` extension also changes the values of the
+           multifactorial at integers ``n != 1 (mod k)`` by a factor depending
+           on both ``k`` and ``n % k``, see below or [1].
+
+    Returns
+    -------
+    nf : int or float or complex or ndarray
+        Multifactorial (order ``k``) of ``n``, as integer, float or complex (depending
+        on ``exact`` and ``extend``). Array inputs are returned as arrays.
+
+    Notes
+    -----
+    While less straight-forward than for the double-factorial, it's possible to
+    calculate a general approximation formula of n!(k) by studying ``n`` for a given
+    remainder ``r < k`` (thus ``n = m * k + r``, resp. ``r = n % k``), which can be
+    put together into something valid for all integer values ``n >= 0`` & ``k > 0``::
+
+      n!(k) = k ** ((n - r)/k) * gamma(n/k + 1) / gamma(r/k + 1) * max(r, 1)
+
+    This is the basis of the approximation when ``exact=False``.
+
+    In principle, any fixed choice of ``r`` (ignoring its relation ``r = n%k``
+    to ``n``) would provide a suitable analytic continuation from integer ``n``
+    to complex ``z`` (not only satisfying the functional equation but also
+    being logarithmically convex, c.f. Bohr-Mollerup theorem) -- in fact, the
+    choice of ``r`` above only changes the function by a constant factor. The
+    final constraint that determines the canonical continuation is ``f(1) = 1``,
+    which forces ``r = 1`` (see also [1]).::
+
+      z!(k) = k ** ((z - 1)/k) * gamma(z/k + 1) / gamma(1/k + 1)
+
+    References
+    ----------
+    .. [1] Complex extension to multifactorial
+            https://en.wikipedia.org/wiki/Double_factorial#Alternative_extension_of_the_multifactorial
+
+    Examples
+    --------
+    >>> from scipy.special import factorialk
+    >>> factorialk(5, k=1, exact=True)
+    120
+    >>> factorialk(5, k=3, exact=True)
+    10
+    >>> factorialk([5, 7, 9], k=3, exact=True)
+    array([ 10,  28, 162])
+    >>> factorialk([5, 7, 9], k=3, exact=False)
+    array([ 10.,  28., 162.])
+    """
+    return _factorialx_wrapper("factorialk", n, k=k, exact=exact, extend=extend)
+
+
+def stirling2(N, K, *, exact=False):
+    r"""Generate Stirling number(s) of the second kind.
+
+    Stirling numbers of the second kind count the number of ways to
+    partition a set with N elements into K non-empty subsets.
+
+    The values this function returns are calculated using a dynamic
+    program which avoids redundant computation across the subproblems
+    in the solution. For array-like input, this implementation also
+    avoids redundant computation across the different Stirling number
+    calculations.
+
+    The numbers are sometimes denoted
+
+    .. math::
+
+        {N \brace{K}}
+
+    see [1]_ for details. This is often expressed-verbally-as
+    "N subset K".
+
+    Parameters
+    ----------
+    N : int, ndarray
+        Number of things.
+    K : int, ndarray
+        Number of non-empty subsets taken.
+    exact : bool, optional
+        Uses dynamic programming (DP) with floating point
+        numbers for smaller arrays and uses a second order approximation due to
+        Temme for larger entries  of `N` and `K` that allows trading speed for
+        accuracy. See [2]_ for a description. Temme approximation is used for
+        values ``n>50``. The max error from the DP has max relative error
+        ``4.5*10^-16`` for ``n<=50`` and the max error from the Temme approximation
+        has max relative error ``5*10^-5`` for ``51 <= n < 70`` and
+        ``9*10^-6`` for ``70 <= n < 101``. Note that these max relative errors will
+        decrease further as `n` increases.
+
+    Returns
+    -------
+    val : int, float, ndarray
+        The number of partitions.
+
+    See Also
+    --------
+    comb : The number of combinations of N things taken k at a time.
+
+    Notes
+    -----
+    - If N < 0, or K < 0, then 0 is returned.
+    - If K > N, then 0 is returned.
+
+    The output type will always be `int` or ndarray of `object`.
+    The input must contain either numpy or python integers otherwise a
+    TypeError is raised.
+
+    References
+    ----------
+    .. [1] R. L. Graham, D. E. Knuth and O. Patashnik, "Concrete
+        Mathematics: A Foundation for Computer Science," Addison-Wesley
+        Publishing Company, Boston, 1989. Chapter 6, page 258.
+
+    .. [2] Temme, Nico M. "Asymptotic estimates of Stirling numbers."
+        Studies in Applied Mathematics 89.3 (1993): 233-243.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.special import stirling2
+    >>> k = np.array([3, -1, 3])
+    >>> n = np.array([10, 10, 9])
+    >>> stirling2(n, k)
+    array([9330.0, 0.0, 3025.0])
+
+    """
+    output_is_scalar = np.isscalar(N) and np.isscalar(K)
+    # make a min-heap of unique (n,k) pairs
+    N, K = asarray(N), asarray(K)
+    if not np.issubdtype(N.dtype, np.integer):
+        raise TypeError("Argument `N` must contain only integers")
+    if not np.issubdtype(K.dtype, np.integer):
+        raise TypeError("Argument `K` must contain only integers")
+    if not exact:
+        # NOTE: here we allow np.uint via casting to double types prior to
+        # passing to private ufunc dispatcher. All dispatched functions
+        # take double type for (n,k) arguments and return double.
+        return _stirling2_inexact(N.astype(float), K.astype(float))
+    nk_pairs = list(
+        set([(n.take(0), k.take(0))
+             for n, k in np.nditer([N, K], ['refs_ok'])])
+    )
+    heapify(nk_pairs)
+    # base mapping for small values
+    snsk_vals = defaultdict(int)
+    for pair in [(0, 0), (1, 1), (2, 1), (2, 2)]:
+        snsk_vals[pair] = 1
+    # for each pair in the min-heap, calculate the value, store for later
+    n_old, n_row = 2, [0, 1, 1]
+    while nk_pairs:
+        n, k = heappop(nk_pairs)
+        if n < 2 or k > n or k <= 0:
+            continue
+        elif k == n or k == 1:
+            snsk_vals[(n, k)] = 1
+            continue
+        elif n != n_old:
+            num_iters = n - n_old
+            while num_iters > 0:
+                n_row.append(1)
+                # traverse from back to remove second row
+                for j in range(len(n_row)-2, 1, -1):
+                    n_row[j] = n_row[j]*j + n_row[j-1]
+                num_iters -= 1
+            snsk_vals[(n, k)] = n_row[k]
+        else:
+            snsk_vals[(n, k)] = n_row[k]
+        n_old, n_row = n, n_row
+    out_types = [object, object, object] if exact else [float, float, float]
+    # for each pair in the map, fetch the value, and populate the array
+    it = np.nditer(
+        [N, K, None],
+        ['buffered', 'refs_ok'],
+        [['readonly'], ['readonly'], ['writeonly', 'allocate']],
+        op_dtypes=out_types,
+    )
+    with it:
+        while not it.finished:
+            it[2] = snsk_vals[(int(it[0]), int(it[1]))]
+            it.iternext()
+        output = it.operands[2]
+        # If N and K were both scalars, convert output to scalar.
+        if output_is_scalar:
+            output = output.take(0)
+    return output
+
+
+def zeta(x, q=None, out=None):
+    r"""
+    Riemann or Hurwitz zeta function.
+
+    Parameters
+    ----------
+    x : array_like of float or complex
+        Input data
+    q : array_like of float, optional
+        Input data, must be real.  Defaults to Riemann zeta. When `q` is
+        ``None``, complex inputs `x` are supported. If `q` is not ``None``,
+        then currently only real inputs `x` with ``x >= 1`` are supported,
+        even when ``q = 1.0`` (corresponding to the Riemann zeta function).
+
+    out : ndarray, optional
+        Output array for the computed values.
+
+    Returns
+    -------
+    out : array_like
+        Values of zeta(x).
+
+    See Also
+    --------
+    zetac
+
+    Notes
+    -----
+    The two-argument version is the Hurwitz zeta function
+
+    .. math::
+
+        \zeta(x, q) = \sum_{k=0}^{\infty} \frac{1}{(k + q)^x};
+
+    see [dlmf]_ for details. The Riemann zeta function corresponds to
+    the case when ``q = 1``.
+
+    For complex inputs with ``q = None``, points with
+    ``abs(z.imag) > 1e9`` and ``0 <= abs(z.real) < 2.5`` are currently not
+    supported due to slow convergence causing excessive runtime.
+
+    References
+    ----------
+    .. [dlmf] NIST, Digital Library of Mathematical Functions,
+        https://dlmf.nist.gov/25.11#i
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.special import zeta, polygamma, factorial
+
+    Some specific values:
+
+    >>> zeta(2), np.pi**2/6
+    (1.6449340668482266, 1.6449340668482264)
+
+    >>> zeta(4), np.pi**4/90
+    (1.0823232337111381, 1.082323233711138)
+
+    First nontrivial zero:
+
+    >>> zeta(0.5 + 14.134725141734695j)
+    0 + 0j
+
+    Relation to the `polygamma` function:
+
+    >>> m = 3
+    >>> x = 1.25
+    >>> polygamma(m, x)
+    array(2.782144009188397)
+    >>> (-1)**(m+1) * factorial(m) * zeta(m+1, x)
+    2.7821440091883969
+
+    """
+    if q is None:
+        return _ufuncs._riemann_zeta(x, out)
+    else:
+        return _ufuncs._zeta(x, q, out)
+
+
+def softplus(x, **kwargs):
+    r"""
+    Compute the softplus function element-wise.
+
+    The softplus function is defined as: ``softplus(x) = log(1 + exp(x))``.
+    It is a smooth approximation of the rectifier function (ReLU).
+
+    Parameters
+    ----------
+    x : array_like
+        Input value.
+    **kwargs
+        For other keyword-only arguments, see the
+        `ufunc docs <https://numpy.org/doc/stable/reference/ufuncs.html>`_.
+
+    Returns
+    -------
+    softplus : ndarray
+        Logarithm of ``exp(0) + exp(x)``.
+
+    Examples
+    --------
+    >>> from scipy import special
+
+    >>> special.softplus(0)
+    0.6931471805599453
+
+    >>> special.softplus([-1, 0, 1])
+    array([0.31326169, 0.69314718, 1.31326169])
+    """
+    return np.logaddexp(0, x, **kwargs)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/_comb.cpython-312-x86_64-linux-gnu.so b/venv/lib/python3.12/site-packages/scipy/special/_comb.cpython-312-x86_64-linux-gnu.so
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diff --git a/venv/lib/python3.12/site-packages/scipy/special/_ellip_harm.py b/venv/lib/python3.12/site-packages/scipy/special/_ellip_harm.py
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index 0000000000000000000000000000000000000000..28ebd6cd4402674f4eed8bb9a790f733f3808927
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/_ellip_harm.py
@@ -0,0 +1,214 @@
+import numpy as np
+
+from ._ufuncs import _ellip_harm
+from ._ellip_harm_2 import _ellipsoid, _ellipsoid_norm
+
+
+def ellip_harm(h2, k2, n, p, s, signm=1, signn=1):
+    r"""
+    Ellipsoidal harmonic functions E^p_n(l).
+
+    These are also known as Lamé functions of the first kind, and are
+    solutions to the Lamé equation:
+
+    .. math:: (s^2 - h^2)(s^2 - k^2)E''(s)
+              + s(2s^2 - h^2 - k^2)E'(s) + (a - q s^2)E(s) = 0
+
+    where :math:`q = (n+1)n` and :math:`a` is the eigenvalue (not
+    returned) corresponding to the solutions.
+
+    Parameters
+    ----------
+    h2 : float
+        ``h**2``
+    k2 : float
+        ``k**2``; should be larger than ``h**2``
+    n : int
+        Degree
+    p : int
+        Order, can range between ``[1, 2n+1]``
+    s : float
+        Coordinate
+    signm : {1, -1}, optional
+        Sign of prefactor of functions. Can be +/-1. See Notes.
+    signn : {1, -1}, optional
+        Sign of prefactor of functions. Can be +/-1. See Notes.
+
+    Returns
+    -------
+    E : float
+        the harmonic :math:`E^p_n(s)`
+
+    See Also
+    --------
+    ellip_harm_2, ellip_normal
+
+    Notes
+    -----
+    The geometric interpretation of the ellipsoidal functions is
+    explained in [2]_, [3]_, [4]_. The `signm` and `signn` arguments control the
+    sign of prefactors for functions according to their type::
+
+        K : +1
+        L : signm
+        M : signn
+        N : signm*signn
+
+    .. versionadded:: 0.15.0
+
+    References
+    ----------
+    .. [1] Digital Library of Mathematical Functions 29.12
+       https://dlmf.nist.gov/29.12
+    .. [2] Bardhan and Knepley, "Computational science and
+       re-discovery: open-source implementations of
+       ellipsoidal harmonics for problems in potential theory",
+       Comput. Sci. Disc. 5, 014006 (2012)
+       :doi:`10.1088/1749-4699/5/1/014006`.
+    .. [3] David J.and Dechambre P, "Computation of Ellipsoidal
+       Gravity Field Harmonics for small solar system bodies"
+       pp. 30-36, 2000
+    .. [4] George Dassios, "Ellipsoidal Harmonics: Theory and Applications"
+       pp. 418, 2012
+
+    Examples
+    --------
+    >>> from scipy.special import ellip_harm
+    >>> w = ellip_harm(5,8,1,1,2.5)
+    >>> w
+    2.5
+
+    Check that the functions indeed are solutions to the Lamé equation:
+
+    >>> import numpy as np
+    >>> from scipy.interpolate import UnivariateSpline
+    >>> def eigenvalue(f, df, ddf):
+    ...     r = (((s**2 - h**2) * (s**2 - k**2) * ddf
+    ...           + s * (2*s**2 - h**2 - k**2) * df
+    ...           - n * (n + 1)*s**2*f) / f)
+    ...     return -r.mean(), r.std()
+    >>> s = np.linspace(0.1, 10, 200)
+    >>> k, h, n, p = 8.0, 2.2, 3, 2
+    >>> E = ellip_harm(h**2, k**2, n, p, s)
+    >>> E_spl = UnivariateSpline(s, E)
+    >>> a, a_err = eigenvalue(E_spl(s), E_spl(s,1), E_spl(s,2))
+    >>> a, a_err
+    (583.44366156701483, 6.4580890640310646e-11)
+
+    """  # noqa: E501
+    return _ellip_harm(h2, k2, n, p, s, signm, signn)
+
+
+_ellip_harm_2_vec = np.vectorize(_ellipsoid, otypes='d')
+
+
+def ellip_harm_2(h2, k2, n, p, s):
+    r"""
+    Ellipsoidal harmonic functions F^p_n(l).
+
+    These are also known as Lamé functions of the second kind, and are
+    solutions to the Lamé equation:
+
+    .. math:: (s^2 - h^2)(s^2 - k^2)F''(s)
+              + s(2s^2 - h^2 - k^2)F'(s) + (a - q s^2)F(s) = 0
+
+    where :math:`q = (n+1)n` and :math:`a` is the eigenvalue (not
+    returned) corresponding to the solutions.
+
+    Parameters
+    ----------
+    h2 : float
+        ``h**2``
+    k2 : float
+        ``k**2``; should be larger than ``h**2``
+    n : int
+        Degree.
+    p : int
+        Order, can range between [1,2n+1].
+    s : float
+        Coordinate
+
+    Returns
+    -------
+    F : float
+        The harmonic :math:`F^p_n(s)`
+
+    See Also
+    --------
+    ellip_harm, ellip_normal
+
+    Notes
+    -----
+    Lamé functions of the second kind are related to the functions of the first kind:
+
+    .. math::
+
+       F^p_n(s)=(2n + 1)E^p_n(s)\int_{0}^{1/s}
+       \frac{du}{(E^p_n(1/u))^2\sqrt{(1-u^2k^2)(1-u^2h^2)}}
+
+    .. versionadded:: 0.15.0
+
+    Examples
+    --------
+    >>> from scipy.special import ellip_harm_2
+    >>> w = ellip_harm_2(5,8,2,1,10)
+    >>> w
+    0.00108056853382
+
+    """
+    with np.errstate(all='ignore'):
+        return _ellip_harm_2_vec(h2, k2, n, p, s)
+
+
+def _ellip_normal_vec(h2, k2, n, p):
+    return _ellipsoid_norm(h2, k2, n, p)
+
+
+_ellip_normal_vec = np.vectorize(_ellip_normal_vec, otypes='d')
+
+
+def ellip_normal(h2, k2, n, p):
+    r"""
+    Ellipsoidal harmonic normalization constants gamma^p_n.
+
+    The normalization constant is defined as
+
+    .. math::
+
+       \gamma^p_n=8\int_{0}^{h}dx\int_{h}^{k}dy
+       \frac{(y^2-x^2)(E^p_n(y)E^p_n(x))^2}{\sqrt((k^2-y^2)(y^2-h^2)(h^2-x^2)(k^2-x^2)}
+
+    Parameters
+    ----------
+    h2 : float
+        ``h**2``
+    k2 : float
+        ``k**2``; should be larger than ``h**2``
+    n : int
+        Degree.
+    p : int
+        Order, can range between [1,2n+1].
+
+    Returns
+    -------
+    gamma : float
+        The normalization constant :math:`\gamma^p_n`
+
+    See Also
+    --------
+    ellip_harm, ellip_harm_2
+
+    Notes
+    -----
+    .. versionadded:: 0.15.0
+
+    Examples
+    --------
+    >>> from scipy.special import ellip_normal
+    >>> w = ellip_normal(5,8,3,7)
+    >>> w
+    1723.38796997
+
+    """
+    with np.errstate(all='ignore'):
+        return _ellip_normal_vec(h2, k2, n, p)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/_ellip_harm_2.cpython-312-x86_64-linux-gnu.so b/venv/lib/python3.12/site-packages/scipy/special/_ellip_harm_2.cpython-312-x86_64-linux-gnu.so
new file mode 100644
index 0000000000000000000000000000000000000000..9e563ebe4669b2c03a3e2c008768bfb027208b84
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/_ellip_harm_2.cpython-312-x86_64-linux-gnu.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b4748cee5d175467c3a2c68fca886cf607bd0a58096472dd0beba2f2f4687da0
+size 123528
diff --git a/venv/lib/python3.12/site-packages/scipy/special/_gufuncs.cpython-312-x86_64-linux-gnu.so b/venv/lib/python3.12/site-packages/scipy/special/_gufuncs.cpython-312-x86_64-linux-gnu.so
new file mode 100644
index 0000000000000000000000000000000000000000..14b2bf4422ba814850d48c4ea1fc6c8f85d1197c
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/_gufuncs.cpython-312-x86_64-linux-gnu.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:19efbca6732a4489ac6ae872640b407bc83974a668fa4b7d4b55e3606cab301e
+size 975504
diff --git a/venv/lib/python3.12/site-packages/scipy/special/_input_validation.py b/venv/lib/python3.12/site-packages/scipy/special/_input_validation.py
new file mode 100644
index 0000000000000000000000000000000000000000..e5b7fe36df87617bf91655623ee0076c37a4d08a
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/_input_validation.py
@@ -0,0 +1,17 @@
+import math
+import operator
+
+def _nonneg_int_or_fail(n, var_name, strict=True):
+    try:
+        if strict:
+            # Raises an exception if float
+            n = operator.index(n)
+        elif n == math.floor(n):
+            n = int(n)
+        else:
+            raise ValueError()
+        if n < 0:
+            raise ValueError()
+    except (ValueError, TypeError) as err:
+        raise err.__class__(f"{var_name} must be a non-negative integer") from err
+    return n
diff --git a/venv/lib/python3.12/site-packages/scipy/special/_lambertw.py b/venv/lib/python3.12/site-packages/scipy/special/_lambertw.py
new file mode 100644
index 0000000000000000000000000000000000000000..f758c7c21fdddc0ec1b84727d90c6de7f34a094e
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/_lambertw.py
@@ -0,0 +1,149 @@
+from ._ufuncs import _lambertw
+
+import numpy as np
+
+
+def lambertw(z, k=0, tol=1e-8):
+    r"""
+    lambertw(z, k=0, tol=1e-8)
+
+    Lambert W function.
+
+    The Lambert W function `W(z)` is defined as the inverse function
+    of ``w * exp(w)``. In other words, the value of ``W(z)`` is
+    such that ``z = W(z) * exp(W(z))`` for any complex number
+    ``z``.
+
+    The Lambert W function is a multivalued function with infinitely
+    many branches. Each branch gives a separate solution of the
+    equation ``z = w exp(w)``. Here, the branches are indexed by the
+    integer `k`.
+
+    Parameters
+    ----------
+    z : array_like
+        Input argument.
+    k : int, optional
+        Branch index.
+    tol : float, optional
+        Evaluation tolerance.
+
+    Returns
+    -------
+    w : array
+        `w` will have the same shape as `z`.
+
+    See Also
+    --------
+    wrightomega : the Wright Omega function
+
+    Notes
+    -----
+    All branches are supported by `lambertw`:
+
+    * ``lambertw(z)`` gives the principal solution (branch 0)
+    * ``lambertw(z, k)`` gives the solution on branch `k`
+
+    The Lambert W function has two partially real branches: the
+    principal branch (`k = 0`) is real for real ``z > -1/e``, and the
+    ``k = -1`` branch is real for ``-1/e < z < 0``. All branches except
+    ``k = 0`` have a logarithmic singularity at ``z = 0``.
+
+    **Possible issues**
+
+    The evaluation can become inaccurate very close to the branch point
+    at ``-1/e``. In some corner cases, `lambertw` might currently
+    fail to converge, or can end up on the wrong branch.
+
+    **Algorithm**
+
+    Halley's iteration is used to invert ``w * exp(w)``, using a first-order
+    asymptotic approximation (O(log(w)) or `O(w)`) as the initial estimate.
+
+    The definition, implementation and choice of branches is based on [2]_.
+
+    References
+    ----------
+    .. [1] https://en.wikipedia.org/wiki/Lambert_W_function
+    .. [2] Corless et al, "On the Lambert W function", Adv. Comp. Math. 5
+       (1996) 329-359.
+       https://cs.uwaterloo.ca/research/tr/1993/03/W.pdf
+
+    Examples
+    --------
+    The Lambert W function is the inverse of ``w exp(w)``:
+
+    >>> import numpy as np
+    >>> from scipy.special import lambertw
+    >>> w = lambertw(1)
+    >>> w
+    (0.56714329040978384+0j)
+    >>> w * np.exp(w)
+    (1.0+0j)
+
+    Any branch gives a valid inverse:
+
+    >>> w = lambertw(1, k=3)
+    >>> w
+    (-2.8535817554090377+17.113535539412148j)
+    >>> w*np.exp(w)
+    (1.0000000000000002+1.609823385706477e-15j)
+
+    **Applications to equation-solving**
+
+    The Lambert W function may be used to solve various kinds of
+    equations.  We give two examples here.
+
+    First, the function can be used to solve implicit equations of the
+    form
+
+        :math:`x = a + b e^{c x}`
+
+    for :math:`x`.  We assume :math:`c` is not zero.  After a little
+    algebra, the equation may be written
+
+        :math:`z e^z = -b c e^{a c}`
+
+    where :math:`z = c (a - x)`.  :math:`z` may then be expressed using
+    the Lambert W function
+
+        :math:`z = W(-b c e^{a c})`
+
+    giving
+
+        :math:`x = a - W(-b c e^{a c})/c`
+
+    For example,
+
+    >>> a = 3
+    >>> b = 2
+    >>> c = -0.5
+
+    The solution to :math:`x = a + b e^{c x}` is:
+
+    >>> x = a - lambertw(-b*c*np.exp(a*c))/c
+    >>> x
+    (3.3707498368978794+0j)
+
+    Verify that it solves the equation:
+
+    >>> a + b*np.exp(c*x)
+    (3.37074983689788+0j)
+
+    The Lambert W function may also be used find the value of the infinite
+    power tower :math:`z^{z^{z^{\ldots}}}`:
+
+    >>> def tower(z, n):
+    ...     if n == 0:
+    ...         return z
+    ...     return z ** tower(z, n-1)
+    ...
+    >>> tower(0.5, 100)
+    0.641185744504986
+    >>> -lambertw(-np.log(0.5)) / np.log(0.5)
+    (0.64118574450498589+0j)
+    """
+    # TODO: special expert should inspect this
+    # interception; better place to do it?
+    k = np.asarray(k, dtype=np.dtype("long"))
+    return _lambertw(z, k, tol)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/_logsumexp.py b/venv/lib/python3.12/site-packages/scipy/special/_logsumexp.py
new file mode 100644
index 0000000000000000000000000000000000000000..fdfdcded06e22591ef48117d5ff8af83c339cf74
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/_logsumexp.py
@@ -0,0 +1,420 @@
+import numpy as np
+from scipy._lib._array_api import (
+    array_namespace,
+    xp_capabilities,
+    xp_device,
+    xp_size,
+    xp_promote,
+    xp_float_to_complex,
+)
+from scipy._external import array_api_extra as xpx
+
+__all__ = ["logsumexp", "softmax", "log_softmax"]
+
+
+@xp_capabilities()
+def logsumexp(a, axis=None, b=None, keepdims=False, return_sign=False):
+    """Compute the log of the sum of exponentials of input elements.
+
+    Parameters
+    ----------
+    a : array_like
+        Input array.
+    axis : None or int or tuple of ints, optional
+        Axis or axes over which the sum is taken. By default `axis` is None,
+        and all elements are summed.
+
+        .. versionadded:: 0.11.0
+    b : array-like, optional
+        Scaling factor for exp(`a`) must be of the same shape as `a` or
+        broadcastable to `a`. These values may be negative in order to
+        implement subtraction.
+
+        .. versionadded:: 0.12.0
+    keepdims : bool, optional
+        If this is set to True, the axes which are reduced are left in the
+        result as dimensions with size one. With this option, the result
+        will broadcast correctly against the original array.
+
+        .. versionadded:: 0.15.0
+    return_sign : bool, optional
+        If this is set to True, the result will be a pair containing sign
+        information; if False, results that are negative will be returned
+        as NaN. Default is False (no sign information).
+
+        .. versionadded:: 0.16.0
+
+    Returns
+    -------
+    res : ndarray
+        The result, ``np.log(np.sum(np.exp(a)))`` calculated in a numerically
+        more stable way. If `b` is given then ``np.log(np.sum(b*np.exp(a)))``
+        is returned. If ``return_sign`` is True, ``res`` contains the log of
+        the absolute value of the argument.
+    sgn : ndarray
+        If ``return_sign`` is True, this will be an array of floating-point
+        numbers matching res containing +1, 0, -1 (for real-valued inputs)
+        or a complex phase (for complex inputs). This gives the sign of the
+        argument of the logarithm in ``res``.
+        If ``return_sign`` is False, only one result is returned.
+
+    See Also
+    --------
+    :data:`numpy.logaddexp`
+    :data:`numpy.logaddexp2`
+
+    Notes
+    -----
+    NumPy has a logaddexp function which is very similar to `logsumexp`, but
+    only handles two arguments. `logaddexp.reduce` is similar to this
+    function, but may be less stable.
+
+    The logarithm is a multivalued function: for each :math:`x` there is an
+    infinite number of :math:`z` such that :math:`exp(z) = x`. The convention
+    is to return the :math:`z` whose imaginary part lies in :math:`(-pi, pi]`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.special import logsumexp
+    >>> a = np.arange(10)
+    >>> logsumexp(a)
+    9.4586297444267107
+    >>> np.log(np.sum(np.exp(a)))
+    9.4586297444267107
+
+    With weights
+
+    >>> a = np.arange(10)
+    >>> b = np.arange(10, 0, -1)
+    >>> logsumexp(a, b=b)
+    9.9170178533034665
+    >>> np.log(np.sum(b*np.exp(a)))
+    9.9170178533034647
+
+    Returning a sign flag
+
+    >>> logsumexp([1,2],b=[1,-1],return_sign=True)
+    (1.5413248546129181, -1.0)
+
+    Notice that `logsumexp` does not directly support masked arrays. To use it
+    on a masked array, convert the mask into zero weights:
+
+    >>> a = np.ma.array([np.log(2), 2, np.log(3)],
+    ...                  mask=[False, True, False])
+    >>> b = (~a.mask).astype(int)
+    >>> logsumexp(a.data, b=b), np.log(5)
+    1.6094379124341005, 1.6094379124341005
+
+    """
+    xp = array_namespace(a, b)
+    a, b = xp_promote(a, b, broadcast=True, force_floating=True, xp=xp)
+    a = xpx.atleast_nd(a, ndim=1, xp=xp)
+    b = xpx.atleast_nd(b, ndim=1, xp=xp) if b is not None else b
+    axis = tuple(range(a.ndim)) if axis is None else axis
+
+    if xp_size(a) != 0:
+        with np.errstate(divide='ignore', invalid='ignore', over='ignore'):
+            # Where result is infinite, we use the direct logsumexp calculation to
+            # delegate edge case handling to the behavior of `xp.log` and `xp.exp`,
+            # which should follow the C99 standard for complex values.
+            b_exp_a = xp.exp(a) if b is None else b * xp.exp(a)
+            sum_ = xp.sum(b_exp_a, axis=axis, keepdims=True)
+            sgn_inf = xp.sign(sum_) if return_sign else None
+            sum_ = xp.abs(sum_) if return_sign else sum_
+            out_inf = xp.log(sum_)
+
+        with np.errstate(divide='ignore', invalid='ignore'):  # log of zero is OK
+            out, sgn = _logsumexp(a, b, axis=axis, return_sign=return_sign, xp=xp)
+
+        # Replace infinite results. This probably could be done with an
+        # `apply_where`-like strategy to avoid redundant calculation, but currently
+        # `apply_where` itself is only for elementwise functions.
+        out_finite = xp.isfinite(out)
+        out = xp.where(out_finite, out, out_inf)
+        sgn = xp.where(out_finite, sgn, sgn_inf) if return_sign else sgn
+    else:
+        shape = np.asarray(a.shape)  # NumPy is convenient for shape manipulation
+        shape[axis] = 1
+        out = xp.full(tuple(shape), -xp.inf, dtype=a.dtype, device=xp_device(a))
+        sgn = xp.sign(out)
+
+    if xp.isdtype(out.dtype, 'complex floating'):
+        if return_sign:
+            real = xp.real(sgn)
+            imag = xp_float_to_complex(_wrap_radians(xp.imag(sgn), xp=xp), xp=xp)
+            sgn = real + imag*1j
+        else:
+            real = xp.real(out)
+            imag = xp_float_to_complex(_wrap_radians(xp.imag(out), xp=xp), xp=xp)
+            out = real + imag*1j
+
+    # Deal with shape details - reducing dimensions and convert 0-D to scalar for NumPy
+    out = xp.squeeze(out, axis=axis) if not keepdims else out
+    sgn = xp.squeeze(sgn, axis=axis) if (sgn is not None and not keepdims) else sgn
+    out = out[()] if out.ndim == 0 else out
+    sgn = sgn[()] if (sgn is not None and sgn.ndim == 0) else sgn
+
+    return (out, sgn) if return_sign else out
+
+
+def _wrap_radians(x, *, xp):
+    # Wrap radians to (-pi, pi] interval
+    wrapped = -((-x + xp.pi) % (2 * xp.pi) - xp.pi)
+    # preserve relative precision
+    no_wrap = xp.abs(x) < xp.pi
+    return xp.where(no_wrap, x, wrapped)
+
+
+def _elements_and_indices_with_max_real(a, *, axis=-1, xp):
+    # This is an array-API compatible `max` function that works something
+    # like `np.max` for complex input. The important part is that it finds
+    # the element with maximum real part. When there are multiple complex values
+    # with this real part, it doesn't matter which we choose.
+    # We could use `argmax` on real component, but array API doesn't yet have
+    # `take_along_axis`, and even if it did, we would have problems with axis tuples.
+    # Feel free to rewrite! It's ugly, but it's not the purpose of the PR, and
+    # it gets the job done.
+
+    if xp.isdtype(a.dtype, "complex floating"):
+        # select all elements with max real part.
+        real_a = xp.real(a)
+        max_ = xp.max(real_a, axis=axis, keepdims=True)
+        mask = real_a == max_
+
+        # Of those, choose one arbitrarily. This is a reasonably
+        # simple, array-API compatible way of doing so that doesn't
+        # have a problem with `axis` being a tuple or None.
+        i = xp.reshape(xp.arange(xp_size(a), device=xp_device(a)), a.shape)
+        i = xpx.at(i, ~mask).set(-1)
+        max_i = xp.max(i, axis=axis, keepdims=True)
+        mask = i == max_i
+        a = xp.where(mask, a, 0.)
+        max_ = xp.sum(a, axis=axis, dtype=a.dtype, keepdims=True)
+    else:
+        max_ = xp.max(a, axis=axis, keepdims=True)
+        mask = a == max_
+
+    return max_, mask
+
+
+def _logsumexp(a, b, *, axis, return_sign, xp):
+    # This has been around for about a decade, so let's consider it a feature:
+    # Even if element of `a` is infinite or NaN, it adds nothing to the sum if
+    # the corresponding weight is zero.
+    if b is not None:
+        a = xpx.at(a, b == 0).set(-xp.inf, copy=True)
+
+    # Find element with maximum real part, since this is what affects the magnitude
+    # of the exponential. Possible enhancement: include log of `b` magnitude in `a`.
+    a_max, i_max = _elements_and_indices_with_max_real(a, axis=axis, xp=xp)
+
+    # for precision, these terms are separated out of the main sum.
+    a = xpx.at(a, i_max).set(-xp.inf, copy=True if b is None else None)
+    i_max_dt = xp.astype(i_max, a.dtype)
+    # This is an inefficient way of getting `m` because it is the sum of a sparse
+    # array; however, this is the simplest way I can think of to get the right shape.
+    b_i_max = i_max_dt if b is None else b * i_max_dt
+    m = xp.sum(b_i_max, axis=axis, keepdims=True, dtype=a.dtype)
+
+    # Shift, exponentiate, scale, and sum
+    exp = b * xp.exp(a - a_max) if b is not None else xp.exp(a - a_max)
+    s = xp.sum(exp, axis=axis, keepdims=True, dtype=exp.dtype)
+    s = xp.where(s == 0, s, s/m)
+
+    # Separate sign/magnitude information
+    # Originally, this was only performed if `return_sign=True`.
+    # However, this is also needed if any elements of `m < 0` or `s < -1`.
+    # An improvement would be to perform the calculations only on these entries.
+
+    sgn = xp.sign(s + 1) * xp.sign(m)
+
+    if xp.isdtype(s.dtype, "real floating"):
+        # The log functions need positive arguments
+        s = xp.where(s < -1, -s - 2, s)
+        m = xp.abs(m)
+    else:
+        # `a_max` can have a sign component for complex input
+        sgn = sgn * xp.exp(xp.imag(a_max) * 1.0j)
+
+    # Take log and undo shift
+    out = xp.log1p(s) + xp.log(m) + a_max
+
+    if return_sign:
+        out = xp.real(out)
+    elif xp.isdtype(out.dtype, 'real floating'):
+        out = xpx.at(out)[sgn < 0].set(xp.nan)
+
+    return out, sgn
+
+
+@xp_capabilities()
+def softmax(x, axis=None):
+    r"""Compute the softmax function.
+
+    The softmax function transforms each element of a collection by
+    computing the exponential of each element divided by the sum of the
+    exponentials of all the elements. That is, if `x` is a one-dimensional
+    numpy array::
+
+        softmax(x) = np.exp(x)/sum(np.exp(x))
+
+    Parameters
+    ----------
+    x : array_like
+        Input array.
+    axis : int or tuple of ints, optional
+        Axis to compute values along. Default is None and softmax will be
+        computed over the entire array `x`.
+
+    Returns
+    -------
+    s : ndarray
+        An array the same shape as `x`. The result will sum to 1 along the
+        specified axis.
+
+    Notes
+    -----
+    The formula for the softmax function :math:`\sigma(x)` for a vector
+    :math:`x = \{x_0, x_1, ..., x_{n-1}\}` is
+
+    .. math:: \sigma(x)_j = \frac{e^{x_j}}{\sum_k e^{x_k}}
+
+    The `softmax` function is the gradient of `logsumexp`.
+
+    The implementation uses shifting to avoid overflow. See [1]_ for more
+    details.
+
+    .. versionadded:: 1.2.0
+
+    References
+    ----------
+    .. [1] P. Blanchard, D.J. Higham, N.J. Higham, "Accurately computing the
+       log-sum-exp and softmax functions", IMA Journal of Numerical Analysis,
+       Vol.41(4), :doi:`10.1093/imanum/draa038`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.special import softmax
+    >>> np.set_printoptions(precision=5)
+
+    >>> x = np.array([[1, 0.5, 0.2, 3],
+    ...               [1,  -1,   7, 3],
+    ...               [2,  12,  13, 3]])
+    ...
+
+    Compute the softmax transformation over the entire array.
+
+    >>> m = softmax(x)
+    >>> m
+    array([[  4.48309e-06,   2.71913e-06,   2.01438e-06,   3.31258e-05],
+           [  4.48309e-06,   6.06720e-07,   1.80861e-03,   3.31258e-05],
+           [  1.21863e-05,   2.68421e-01,   7.29644e-01,   3.31258e-05]])
+
+    >>> m.sum()
+    1.0
+
+    Compute the softmax transformation along the first axis (i.e., the
+    columns).
+
+    >>> m = softmax(x, axis=0)
+
+    >>> m
+    array([[  2.11942e-01,   1.01300e-05,   2.75394e-06,   3.33333e-01],
+           [  2.11942e-01,   2.26030e-06,   2.47262e-03,   3.33333e-01],
+           [  5.76117e-01,   9.99988e-01,   9.97525e-01,   3.33333e-01]])
+
+    >>> m.sum(axis=0)
+    array([ 1.,  1.,  1.,  1.])
+
+    Compute the softmax transformation along the second axis (i.e., the rows).
+
+    >>> m = softmax(x, axis=1)
+    >>> m
+    array([[  1.05877e-01,   6.42177e-02,   4.75736e-02,   7.82332e-01],
+           [  2.42746e-03,   3.28521e-04,   9.79307e-01,   1.79366e-02],
+           [  1.22094e-05,   2.68929e-01,   7.31025e-01,   3.31885e-05]])
+
+    >>> m.sum(axis=1)
+    array([ 1.,  1.,  1.])
+
+    """
+    xp = array_namespace(x)
+    x = xp.asarray(x)
+    x_max = xp.max(x, axis=axis, keepdims=True)
+    exp_x_shifted = xp.exp(x - x_max)
+    return exp_x_shifted / xp.sum(exp_x_shifted, axis=axis, keepdims=True)
+
+
+@xp_capabilities()
+def log_softmax(x, axis=None):
+    r"""Compute the logarithm of the softmax function.
+
+    In principle::
+
+        log_softmax(x) = log(softmax(x))
+
+    but using a more accurate implementation.
+
+    Parameters
+    ----------
+    x : array_like
+        Input array.
+    axis : int or tuple of ints, optional
+        Axis to compute values along. Default is None and softmax will be
+        computed over the entire array `x`.
+
+    Returns
+    -------
+    s : ndarray or scalar
+        An array with the same shape as `x`. Exponential of the result will
+        sum to 1 along the specified axis. If `x` is a scalar, a scalar is
+        returned.
+
+    Notes
+    -----
+    `log_softmax` is more accurate than ``np.log(softmax(x))`` with inputs that
+    make `softmax` saturate (see examples below).
+
+    .. versionadded:: 1.5.0
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.special import log_softmax
+    >>> from scipy.special import softmax
+    >>> np.set_printoptions(precision=5)
+
+    >>> x = np.array([1000.0, 1.0])
+
+    >>> y = log_softmax(x)
+    >>> y
+    array([   0., -999.])
+
+    >>> with np.errstate(divide='ignore'):
+    ...   y = np.log(softmax(x))
+    ...
+    >>> y
+    array([  0., -inf])
+
+    """
+    xp = array_namespace(x)
+    x = xp.asarray(x)
+
+    x_max = xp.max(x, axis=axis, keepdims=True)
+
+    if x_max.ndim > 0:
+        x_max = xpx.at(x_max, ~xp.isfinite(x_max)).set(0)
+    elif not xp.isfinite(x_max):
+        x_max = 0
+
+    tmp = x - x_max
+    exp_tmp = xp.exp(tmp)
+
+    # suppress warnings about log of zero
+    with np.errstate(divide='ignore'):
+        s = xp.sum(exp_tmp, axis=axis, keepdims=True)
+        out = xp.log(s)
+
+    return tmp - out
diff --git a/venv/lib/python3.12/site-packages/scipy/special/_mptestutils.py b/venv/lib/python3.12/site-packages/scipy/special/_mptestutils.py
new file mode 100644
index 0000000000000000000000000000000000000000..9e519093dface79e21f16d7063541ad107f5ca96
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/_mptestutils.py
@@ -0,0 +1,453 @@
+import os
+import sys
+import time
+from itertools import zip_longest
+
+import numpy as np
+from numpy.testing import assert_
+import pytest
+
+from scipy.special._testutils import assert_func_equal
+
+try:
+    import mpmath
+except ImportError:
+    pass
+
+
+# ------------------------------------------------------------------------------
+# Machinery for systematic tests with mpmath
+# ------------------------------------------------------------------------------
+
+class Arg:
+    """Generate a set of numbers on the real axis, concentrating on
+    'interesting' regions and covering all orders of magnitude.
+
+    """
+
+    def __init__(self, a=-np.inf, b=np.inf, inclusive_a=True, inclusive_b=True):
+        if a > b:
+            raise ValueError("a should be less than or equal to b")
+        if a == -np.inf:
+            a = -0.5*np.finfo(float).max
+        if b == np.inf:
+            b = 0.5*np.finfo(float).max
+        self.a, self.b = a, b
+
+        self.inclusive_a, self.inclusive_b = inclusive_a, inclusive_b
+
+    def _positive_values(self, a, b, n):
+        if a < 0:
+            raise ValueError("a should be positive")
+
+        # Try to put half of the points into a linspace between a and
+        # 10 the other half in a logspace.
+        if n % 2 == 0:
+            nlogpts = n//2
+            nlinpts = nlogpts
+        else:
+            nlogpts = n//2
+            nlinpts = nlogpts + 1
+
+        if a >= 10:
+            # Outside of linspace range; just return a logspace.
+            pts = np.logspace(np.log10(a), np.log10(b), n)
+        elif a > 0 and b < 10:
+            # Outside of logspace range; just return a linspace
+            pts = np.linspace(a, b, n)
+        elif a > 0:
+            # Linspace between a and 10 and a logspace between 10 and
+            # b.
+            linpts = np.linspace(a, 10, nlinpts, endpoint=False)
+            logpts = np.logspace(1, np.log10(b), nlogpts)
+            pts = np.hstack((linpts, logpts))
+        elif a == 0 and b <= 10:
+            # Linspace between 0 and b and a logspace between 0 and
+            # the smallest positive point of the linspace
+            linpts = np.linspace(0, b, nlinpts)
+            if linpts.size > 1:
+                right = np.log10(linpts[1])
+            else:
+                right = -30
+            logpts = np.logspace(-30, right, nlogpts, endpoint=False)
+            pts = np.hstack((logpts, linpts))
+        else:
+            # Linspace between 0 and 10, logspace between 0 and the
+            # smallest positive point of the linspace, and a logspace
+            # between 10 and b.
+            if nlogpts % 2 == 0:
+                nlogpts1 = nlogpts//2
+                nlogpts2 = nlogpts1
+            else:
+                nlogpts1 = nlogpts//2
+                nlogpts2 = nlogpts1 + 1
+            linpts = np.linspace(0, 10, nlinpts, endpoint=False)
+            if linpts.size > 1:
+                right = np.log10(linpts[1])
+            else:
+                right = -30
+            logpts1 = np.logspace(-30, right, nlogpts1, endpoint=False)
+            logpts2 = np.logspace(1, np.log10(b), nlogpts2)
+            pts = np.hstack((logpts1, linpts, logpts2))
+
+        return np.sort(pts)
+
+    def values(self, n):
+        """Return an array containing n numbers."""
+        a, b = self.a, self.b
+        if a == b:
+            return np.zeros(n)
+
+        if not self.inclusive_a:
+            n += 1
+        if not self.inclusive_b:
+            n += 1
+
+        if n % 2 == 0:
+            n1 = n//2
+            n2 = n1
+        else:
+            n1 = n//2
+            n2 = n1 + 1
+
+        if a >= 0:
+            pospts = self._positive_values(a, b, n)
+            negpts = []
+        elif b <= 0:
+            pospts = []
+            negpts = -self._positive_values(-b, -a, n)
+        else:
+            pospts = self._positive_values(0, b, n1)
+            negpts = -self._positive_values(0, -a, n2 + 1)
+            # Don't want to get zero twice
+            negpts = negpts[1:]
+        pts = np.hstack((negpts[::-1], pospts))
+
+        if not self.inclusive_a:
+            pts = pts[1:]
+        if not self.inclusive_b:
+            pts = pts[:-1]
+        return pts
+
+
+class FixedArg:
+    def __init__(self, values):
+        self._values = np.asarray(values)
+
+    def values(self, n):
+        return self._values
+
+
+class ComplexArg:
+    def __init__(self, a=complex(-np.inf, -np.inf), b=complex(np.inf, np.inf)):
+        self.real = Arg(a.real, b.real)
+        self.imag = Arg(a.imag, b.imag)
+
+    def values(self, n):
+        m = int(np.floor(np.sqrt(n)))
+        x = self.real.values(m)
+        y = self.imag.values(m + 1)
+        return (x[:,None] + 1j*y[None,:]).ravel()
+
+
+class IntArg:
+    def __init__(self, a=-1000, b=1000):
+        self.a = a
+        self.b = b
+
+    def values(self, n):
+        v1 = Arg(self.a, self.b).values(max(1 + n//2, n-5)).astype(int)
+        v2 = np.arange(-5, 5)
+        v = np.unique(np.r_[v1, v2])
+        v = v[(v >= self.a) & (v < self.b)]
+        return v
+
+
+def get_args(argspec, n):
+    if isinstance(argspec, np.ndarray):
+        args = argspec.copy()
+    else:
+        nargs = len(argspec)
+        ms = np.asarray(
+            [1.5 if isinstance(spec, ComplexArg) else 1.0 for spec in argspec]
+        )
+        ms = (n**(ms/sum(ms))).astype(int) + 1
+
+        args = [spec.values(m) for spec, m in zip(argspec, ms)]
+        args = np.array(np.broadcast_arrays(*np.ix_(*args))).reshape(nargs, -1).T
+
+    return args
+
+
+class MpmathData:
+    def __init__(self, scipy_func, mpmath_func, arg_spec, name=None,
+                 dps=None, prec=None, n=None, rtol=1e-7, atol=1e-300,
+                 ignore_inf_sign=False, distinguish_nan_and_inf=True,
+                 nan_ok=True, param_filter=None):
+
+        # mpmath tests are really slow (see gh-6989).  Use a small number of
+        # points by default, increase back to 5000 (old default) if XSLOW is
+        # set
+        if n is None:
+            try:
+                is_xslow = int(os.environ.get('SCIPY_XSLOW', '0'))
+            except ValueError:
+                is_xslow = False
+
+            n = 5000 if is_xslow else 500
+
+        self.scipy_func = scipy_func
+        self.mpmath_func = mpmath_func
+        self.arg_spec = arg_spec
+        self.dps = dps
+        self.prec = prec
+        self.n = n
+        self.rtol = rtol
+        self.atol = atol
+        self.ignore_inf_sign = ignore_inf_sign
+        self.nan_ok = nan_ok
+        if isinstance(self.arg_spec, np.ndarray):
+            self.is_complex = np.issubdtype(self.arg_spec.dtype, np.complexfloating)
+        else:
+            self.is_complex = any(
+                [isinstance(arg, ComplexArg) for arg in self.arg_spec]
+            )
+        self.ignore_inf_sign = ignore_inf_sign
+        self.distinguish_nan_and_inf = distinguish_nan_and_inf
+        if not name or name == '<lambda>':
+            name = getattr(scipy_func, '__name__', None)
+        if not name or name == '<lambda>':
+            name = getattr(mpmath_func, '__name__', None)
+        self.name = name
+        self.param_filter = param_filter
+
+    def check(self):
+        np.random.seed(1234)
+
+        # Generate values for the arguments
+        argarr = get_args(self.arg_spec, self.n)
+
+        # Check
+        old_dps, old_prec = mpmath.mp.dps, mpmath.mp.prec
+        try:
+            if self.dps is not None:
+                dps_list = [self.dps]
+            else:
+                dps_list = [20]
+            if self.prec is not None:
+                mpmath.mp.prec = self.prec
+
+            # Proper casting of mpmath input and output types. Using
+            # native mpmath types as inputs gives improved precision
+            # in some cases.
+            if np.issubdtype(argarr.dtype, np.complexfloating):
+                pytype = mpc2complex
+
+                def mptype(x):
+                    return mpmath.mpc(complex(x))
+            else:
+                def mptype(x):
+                    return mpmath.mpf(float(x))
+
+                def pytype(x):
+                    if abs(x.imag) > 1e-16*(1 + abs(x.real)):
+                        return np.nan
+                    else:
+                        return mpf2float(x.real)
+
+            # Try out different dps until one (or none) works
+            for j, dps in enumerate(dps_list):
+                mpmath.mp.dps = dps
+
+                try:
+                    assert_func_equal(
+                        self.scipy_func,
+                        lambda *a: pytype(self.mpmath_func(*map(mptype, a))),
+                        argarr,
+                        vectorized=False,
+                        rtol=self.rtol,
+                        atol=self.atol,
+                        ignore_inf_sign=self.ignore_inf_sign,
+                        distinguish_nan_and_inf=self.distinguish_nan_and_inf,
+                        nan_ok=self.nan_ok,
+                        param_filter=self.param_filter
+                    )
+                    break
+                except AssertionError:
+                    if j >= len(dps_list)-1:
+                        # reraise the Exception
+                        tp, value, tb = sys.exc_info()
+                        if value.__traceback__ is not tb:
+                            raise value.with_traceback(tb)
+                        raise value
+        finally:
+            mpmath.mp.dps, mpmath.mp.prec = old_dps, old_prec
+
+    def __repr__(self):
+        if self.is_complex:
+            return f"<MpmathData: {self.name} (complex)>"
+        else:
+            return f"<MpmathData: {self.name}>"
+
+
+def assert_mpmath_equal(*a, **kw):
+    d = MpmathData(*a, **kw)
+    d.check()
+
+
+def nonfunctional_tooslow(func):
+    return pytest.mark.skip(
+        reason="    Test not yet functional (too slow), needs more work."
+    )(func)
+
+
+# ------------------------------------------------------------------------------
+# Tools for dealing with mpmath quirks
+# ------------------------------------------------------------------------------
+
+def mpf2float(x):
+    """
+    Convert an mpf to the nearest floating point number. Just using
+    float directly doesn't work because of results like this:
+
+    with mp.workdps(50):
+        float(mpf("0.99999999999999999")) = 0.9999999999999999
+
+    """
+    return float(mpmath.nstr(x, 17, min_fixed=0, max_fixed=0))
+
+
+def mpc2complex(x):
+    return complex(mpf2float(x.real), mpf2float(x.imag))
+
+
+def trace_args(func):
+    def tofloat(x):
+        if isinstance(x, mpmath.mpc):
+            return complex(x)
+        else:
+            return float(x)
+
+    def wrap(*a, **kw):
+        sys.stderr.write(f"{tuple(map(tofloat, a))!r}: ")
+        sys.stderr.flush()
+        try:
+            r = func(*a, **kw)
+            sys.stderr.write(f"-> {r!r}")
+        finally:
+            sys.stderr.write("\n")
+            sys.stderr.flush()
+        return r
+    return wrap
+
+
+try:
+    import signal
+    POSIX = ('setitimer' in dir(signal))
+except ImportError:
+    POSIX = False
+
+
+class TimeoutError(Exception):
+    pass
+
+
+def time_limited(timeout=0.5, return_val=np.nan, use_sigalrm=True):
+    """
+    Decorator for setting a timeout for pure-Python functions.
+
+    If the function does not return within `timeout` seconds, the
+    value `return_val` is returned instead.
+
+    On POSIX this uses SIGALRM by default. On non-POSIX, settrace is
+    used. Do not use this with threads: the SIGALRM implementation
+    does probably not work well. The settrace implementation only
+    traces the current thread.
+
+    The settrace implementation slows down execution speed. Slowdown
+    by a factor around 10 is probably typical.
+    """
+    if POSIX and use_sigalrm:
+        def sigalrm_handler(signum, frame):
+            raise TimeoutError()
+
+        def deco(func):
+            def wrap(*a, **kw):
+                old_handler = signal.signal(signal.SIGALRM, sigalrm_handler)
+                signal.setitimer(signal.ITIMER_REAL, timeout)
+                try:
+                    return func(*a, **kw)
+                except TimeoutError:
+                    return return_val
+                finally:
+                    signal.setitimer(signal.ITIMER_REAL, 0)
+                    signal.signal(signal.SIGALRM, old_handler)
+            return wrap
+    else:
+        def deco(func):
+            def wrap(*a, **kw):
+                start_time = time.time()
+
+                def trace(frame, event, arg):
+                    if time.time() - start_time > timeout:
+                        raise TimeoutError()
+                    return trace
+                sys.settrace(trace)
+                try:
+                    return func(*a, **kw)
+                except TimeoutError:
+                    sys.settrace(None)
+                    return return_val
+                finally:
+                    sys.settrace(None)
+            return wrap
+    return deco
+
+
+def exception_to_nan(func):
+    """Decorate function to return nan if it raises an exception"""
+    def wrap(*a, **kw):
+        try:
+            return func(*a, **kw)
+        except Exception:
+            return np.nan
+    return wrap
+
+
+def inf_to_nan(func):
+    """Decorate function to return nan if it returns inf"""
+    def wrap(*a, **kw):
+        v = func(*a, **kw)
+        if not np.isfinite(v):
+            return np.nan
+        return v
+    return wrap
+
+
+def mp_assert_allclose(res, std, atol=0, rtol=1e-17):
+    """
+    Compare lists of mpmath.mpf's or mpmath.mpc's directly so that it
+    can be done to higher precision than double.
+    """
+    failures = []
+    for k, (resval, stdval) in enumerate(zip_longest(res, std)):
+        if resval is None or stdval is None:
+            raise ValueError('Lengths of inputs res and std are not equal.')
+        if mpmath.fabs(resval - stdval) > atol + rtol*mpmath.fabs(stdval):
+            failures.append((k, resval, stdval))
+
+    nfail = len(failures)
+    if nfail > 0:
+        ndigits = int(abs(np.log10(rtol)))
+        msg = [""]
+        msg.append(f"Bad results ({nfail} out of {k + 1}) for the following points:")
+        for k, resval, stdval in failures:
+            resrep = mpmath.nstr(resval, ndigits, min_fixed=0, max_fixed=0)
+            stdrep = mpmath.nstr(stdval, ndigits, min_fixed=0, max_fixed=0)
+            if stdval == 0:
+                rdiff = "inf"
+            else:
+                rdiff = mpmath.fabs((resval - stdval)/stdval)
+                rdiff = mpmath.nstr(rdiff, 3)
+            msg.append(f"{k}: {resrep} != {stdrep} (rdiff {rdiff})")
+        assert_(False, "\n".join(msg))
diff --git a/venv/lib/python3.12/site-packages/scipy/special/_multiufuncs.py b/venv/lib/python3.12/site-packages/scipy/special/_multiufuncs.py
new file mode 100644
index 0000000000000000000000000000000000000000..f62002ef701f0edffeb8ec348559f1436f80ab08
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/_multiufuncs.py
@@ -0,0 +1,744 @@
+import collections
+import numbers
+import numpy as np
+
+from ._input_validation import _nonneg_int_or_fail
+
+from ._special_ufuncs import (legendre_p, assoc_legendre_p,
+                              sph_legendre_p, sph_harm_y)
+from ._gufuncs import (legendre_p_all, assoc_legendre_p_all,
+                       sph_legendre_p_all, sph_harm_y_all)
+
+__all__ = [
+    "assoc_legendre_p",
+    "assoc_legendre_p_all",
+    "legendre_p",
+    "legendre_p_all",
+    "sph_harm_y",
+    "sph_harm_y_all",
+    "sph_legendre_p",
+    "sph_legendre_p_all",
+]
+
+
+class MultiUFunc:
+    def __init__(self, ufunc_or_ufuncs, name=None, doc=None, *,
+                 force_complex_output=False, **default_kwargs):
+        if not isinstance(ufunc_or_ufuncs, np.ufunc):
+            if isinstance(ufunc_or_ufuncs, collections.abc.Mapping):
+                ufuncs_iter = ufunc_or_ufuncs.values()
+            elif isinstance(ufunc_or_ufuncs, collections.abc.Iterable):
+                ufuncs_iter = ufunc_or_ufuncs
+            else:
+                raise ValueError("ufunc_or_ufuncs should be a ufunc or a"
+                                 " ufunc collection")
+
+            # Perform input validation to ensure all ufuncs in ufuncs are
+            # actually ufuncs and all take the same input types.
+            seen_input_types = set()
+            for ufunc in ufuncs_iter:
+                if not isinstance(ufunc, np.ufunc):
+                    raise ValueError("All ufuncs must have type `numpy.ufunc`."
+                                     f" Received {ufunc_or_ufuncs}")
+                seen_input_types.add(frozenset(x.split("->")[0] for x in ufunc.types))
+            if len(seen_input_types) > 1:
+                raise ValueError("All ufuncs must take the same input types.")
+
+        self.__name__ = name
+        self._ufunc_or_ufuncs = ufunc_or_ufuncs
+        self.__doc = doc
+        self.__force_complex_output = force_complex_output
+        self._default_kwargs = default_kwargs
+        self._resolve_out_shapes = None
+        self._finalize_out = None
+        self._key = None
+        self._ufunc_default_args = lambda *args, **kwargs: ()
+        self._ufunc_default_kwargs = lambda *args, **kwargs: {}
+        self.__text_signature__ = doc.split("\n\n")[0] if doc else None
+
+    @property
+    def __doc__(self):  # pyrefly:ignore[bad-override]
+        return self.__doc
+
+    def _override_key(self, func):
+        """Set `key` method by decorating a function.
+        """
+        self._key = func
+
+    def _override_ufunc_default_args(self, func):
+        self._ufunc_default_args = func
+
+    def _override_ufunc_default_kwargs(self, func):
+        self._ufunc_default_kwargs = func
+
+    def _override_resolve_out_shapes(self, func):
+        """Set `resolve_out_shapes` method by decorating a function."""
+        if func.__doc__ is None:
+            func.__doc__ = \
+                """Resolve to output shapes based on relevant inputs."""
+        func.__name__ = "resolve_out_shapes"
+        self._resolve_out_shapes = func
+
+    def _override_finalize_out(self, func):
+        self._finalize_out = func
+
+    def _resolve_ufunc(self, **kwargs):
+        """Resolve to a ufunc based on keyword arguments."""
+
+        if isinstance(self._ufunc_or_ufuncs, np.ufunc):
+            return self._ufunc_or_ufuncs
+
+        ufunc_key = self._key(**kwargs)
+        return self._ufunc_or_ufuncs[ufunc_key]
+
+    def __call__(self, *args, **kwargs):
+        kwargs = self._default_kwargs | kwargs
+
+        args += self._ufunc_default_args(**kwargs)
+
+        ufunc = self._resolve_ufunc(**kwargs)
+
+        # array arguments to be passed to the ufunc
+        ufunc_args = [np.asarray(arg) for arg in args[-ufunc.nin:]]
+
+        ufunc_kwargs = self._ufunc_default_kwargs(**kwargs)
+
+        if (self._resolve_out_shapes is not None):
+            ufunc_arg_shapes = tuple(np.shape(ufunc_arg) for ufunc_arg in ufunc_args)
+            ufunc_out_shapes = self._resolve_out_shapes(*args[:-ufunc.nin],
+                                                        *ufunc_arg_shapes, ufunc.nout,
+                                                        **kwargs)
+
+            ufunc_arg_dtypes = tuple(ufunc_arg.dtype if hasattr(ufunc_arg, 'dtype')
+                                     else np.dtype(type(ufunc_arg))
+                                     for ufunc_arg in ufunc_args)
+
+            if hasattr(ufunc, 'resolve_dtypes'):
+                ufunc_dtypes = ufunc_arg_dtypes + ufunc.nout * (None,)
+                ufunc_dtypes = ufunc.resolve_dtypes(ufunc_dtypes)
+                ufunc_out_dtypes = ufunc_dtypes[-ufunc.nout:]
+            else:
+                ufunc_out_dtype = np.result_type(*ufunc_arg_dtypes)
+                if (not np.issubdtype(ufunc_out_dtype, np.inexact)):
+                    ufunc_out_dtype = np.float64
+
+                ufunc_out_dtypes = ufunc.nout * (ufunc_out_dtype,)
+
+            if self.__force_complex_output:
+                ufunc_out_dtypes = tuple(np.result_type(1j, ufunc_out_dtype)
+                                         for ufunc_out_dtype in ufunc_out_dtypes)
+
+            out = tuple(np.empty(ufunc_out_shape, dtype=ufunc_out_dtype)
+                        for ufunc_out_shape, ufunc_out_dtype
+                        in zip(ufunc_out_shapes, ufunc_out_dtypes))
+
+            ufunc_kwargs['out'] = out
+
+        out = ufunc(*ufunc_args, **ufunc_kwargs)
+        if (self._finalize_out is not None):
+            out = self._finalize_out(out)
+
+        return out
+
+
+sph_legendre_p = MultiUFunc(
+    sph_legendre_p,
+    "sph_legendre_p",
+    r"""sph_legendre_p(n, m, theta, *, diff_n=0)
+
+    Spherical Legendre polynomial of the first kind.
+
+    Parameters
+    ----------
+    n : array_like of ints
+        Degree of the spherical Legendre polynomial. Must have ``n >= 0``.
+    m : array_like of ints
+        Order of the spherical Legendre polynomial.
+    theta : array_like
+        Input value.
+    diff_n : int, optional
+        A non-negative integer. Compute and return all derivatives up
+        to order `diff_n`. Default is 0.
+
+    Returns
+    -------
+    ndarray or tuple of ndarray
+        Spherical Legendre polynomial with ``diff_n`` derivatives.
+
+    Notes
+    -----
+    The spherical counterpart of an (unnormalized) associated Legendre polynomial has
+    the additional factor
+
+    .. math::
+
+        \sqrt{\frac{(2 n + 1) (n - m)!}{4 \pi (n + m)!}}
+
+    It is the same as the spherical harmonic :math:`Y_{n}^{m}(\theta, \phi)`
+    with :math:`\phi = 0`.
+    """, diff_n=0
+)
+
+
+@sph_legendre_p._override_key
+def _(diff_n):
+    diff_n = _nonneg_int_or_fail(diff_n, "diff_n", strict=False)
+    if not 0 <= diff_n <= 2:
+        raise ValueError(
+            "diff_n is currently only implemented for orders 0, 1, and 2,"
+            f" received: {diff_n}."
+        )
+    return diff_n
+
+
+@sph_legendre_p._override_finalize_out
+def _(out):
+    return np.moveaxis(out, -1, 0)
+
+
+sph_legendre_p_all = MultiUFunc(
+    sph_legendre_p_all,
+    "sph_legendre_p_all",
+    """sph_legendre_p_all(n, m, theta, *, diff_n=0)
+
+    All spherical Legendre polynomials of the first kind up to the
+    specified degree `n`, order `m`, and all derivatives up
+    to order `diff_n`.
+
+    Parameters
+    ----------
+    n : int
+        Degree of the spherical Legendre polynomials. Must have ``n >= 0``.
+    m : int
+        Order of the spherical Legendre polynomials.
+    theta : array_like
+        Input value.
+    diff_n : int, optional
+        A non-negative integer. Compute and return all derivatives up
+        to order `diff_n`. Default is 0.
+
+    Returns
+    -------
+    ndarray
+        Output shape is ``(diff_n + 1, n + 1, 2 * m + 1, ...)``. The entry at
+        ``(i, j, k)`` corresponds to the ``i``-th derivative, degree ``j``, and
+        order ``k`` for all ``0 <= i <= diff_n``, ``0 <= j <= n``, and
+        ``-m <= k <= m``.
+
+    See Also
+    --------
+    sph_legendre_p
+    """, diff_n=0
+)
+
+
+@sph_legendre_p_all._override_key
+def _(diff_n):
+    diff_n = _nonneg_int_or_fail(diff_n, "diff_n", strict=False)
+    if not 0 <= diff_n <= 2:
+        raise ValueError(
+            "diff_n is currently only implemented for orders 0, 1, and 2,"
+            f" received: {diff_n}."
+        )
+    return diff_n
+
+
+@sph_legendre_p_all._override_ufunc_default_kwargs
+def _(diff_n):
+    return {'axes': [()] + [(0, 1, -1)]}
+
+
+@sph_legendre_p_all._override_resolve_out_shapes
+def _(n, m, theta_shape, nout, diff_n):
+    if not isinstance(n, numbers.Integral) or (n < 0):
+        raise ValueError("n must be a non-negative integer.")
+
+    return ((n + 1, 2 * abs(m) + 1) + theta_shape + (diff_n + 1,),)
+
+
+@sph_legendre_p_all._override_finalize_out
+def _(out):
+    return np.moveaxis(out, -1, 0)
+
+
+assoc_legendre_p = MultiUFunc(
+    assoc_legendre_p,
+    "assoc_legendre_p",
+    r"""assoc_legendre_p(n, m, z, *, branch_cut=2, norm=False, diff_n=0)
+
+    Associated Legendre polynomial of the first kind.
+
+    Defined as
+
+    .. math::
+
+        P_n^m(z) = (-1)^m (1 - z^2)^{m/2}
+            \frac{d^m}{dz^m} P_n(z)
+
+    where :math:`P_n` is the Legendre polynomial.
+
+    This definition includes the Condon-Shortley phase :math:`(-1)^m`.
+
+    Parameters
+    ----------
+    n : array_like of ints
+        Degree of the associated Legendre polynomial. Must have ``n >= 0``.
+    m : array_like of ints
+        Order of the associated Legendre polynomial.
+    z : array_like
+        Input value.
+    branch_cut : array_like of ints, optional
+        Selects branch cut. Must be 2 (default) or 3.
+        2: cut on the real axis ``|z| > 1``
+        3: cut on the real axis ``-1 < z < 1``
+    norm : bool, optional
+        If ``True``, compute the normalized associated Legendre polynomial.
+        Default is ``False``.
+    diff_n : int, optional
+        A non-negative integer. Compute and return all derivatives up
+        to order ``diff_n``. Default is 0.
+
+    Returns
+    -------
+    ndarray or tuple of ndarray
+        Associated Legendre polynomial with ``diff_n`` derivatives.
+
+    Notes
+    -----
+    The normalized counterpart of an (unnormalized) associated Legendre
+    polynomial has the additional factor
+
+    .. math::
+
+        \sqrt{\frac{(2 n + 1) (n - m)!}{2 (n + m)!}}
+
+    Examples
+    --------
+    Evaluate :math:`P_2^1(z)` on :math:`[-1, 1]`:
+
+    >>> import numpy as np
+    >>> from scipy.special import assoc_legendre_p
+    >>> z = np.linspace(-1, 1, 11)
+    >>> expected = -3 * z * np.sqrt(1 - z**2)
+    >>> np.allclose(assoc_legendre_p(2, 1, z), expected)
+    True
+
+    Compute the normalized associated Legendre polynomial:
+
+    >>> scale = np.sqrt(5/12)
+    >>> np.allclose(assoc_legendre_p(2, 1, z, norm=True), scale * expected)
+    True
+    """, branch_cut=2, norm=False, diff_n=0
+)
+
+
+@assoc_legendre_p._override_key
+def _(branch_cut, norm, diff_n):
+    diff_n = _nonneg_int_or_fail(diff_n, "diff_n", strict=False)
+    if not 0 <= diff_n <= 2:
+        raise ValueError(
+            "diff_n is currently only implemented for orders 0, 1, and 2,"
+            f" received: {diff_n}."
+        )
+    return norm, diff_n
+
+
+@assoc_legendre_p._override_ufunc_default_args
+def _(branch_cut, norm, diff_n):
+    return branch_cut,
+
+
+@assoc_legendre_p._override_finalize_out
+def _(out):
+    return np.moveaxis(out, -1, 0)
+
+
+assoc_legendre_p_all = MultiUFunc(
+    assoc_legendre_p_all,
+    "assoc_legendre_p_all",
+    """assoc_legendre_p_all(n, m, z, *, branch_cut=2, norm=False, diff_n=0)
+
+    All associated Legendre polynomials of the first kind up to the
+    specified degree `n`, order `m`, and all derivatives up
+    to order `diff_n`.
+
+    Parameters
+    ----------
+    n : int
+        Degree of the associated Legendre polynomials. Must have ``n >= 0``.
+    m : int
+        Order of the associated Legendre polynomials.
+    z : array_like
+        Input value.
+    branch_cut : array_like of ints, optional
+        Selects branch cut. Must be 2 (default) or 3.
+        2: cut on the real axis ``|z| > 1``
+        3: cut on the real axis ``-1 < z < 1``
+    norm : bool, optional
+        If ``True``, compute the normalized associated Legendre polynomials.
+        Default is ``False``.
+    diff_n : int, optional
+        A non-negative integer. Compute and return all derivatives up
+        to order ``diff_n``. Default is 0.
+
+    Returns
+    -------
+    ndarray
+        Output shape is ``(diff_n + 1, n + 1, 2 * m + 1, ...)``. The entry at
+        ``(i, j, k)`` corresponds to the ``i``-th derivative, degree ``j``, and
+        order ``k`` for all ``0 <= i <= diff_n``, ``0 <= j <= n``, and
+        ``-m <= k <= m``.
+
+    See Also
+    --------
+    assoc_legendre_p
+    """, branch_cut=2, norm=False, diff_n=0
+)
+
+
+@assoc_legendre_p_all._override_key
+def _(branch_cut, norm, diff_n):
+    if not ((isinstance(diff_n, numbers.Integral))
+            and diff_n >= 0):
+        raise ValueError(
+            f"diff_n must be a non-negative integer, received: {diff_n}."
+        )
+    if not 0 <= diff_n <= 2:
+        raise ValueError(
+            "diff_n is currently only implemented for orders 0, 1, and 2,"
+            f" received: {diff_n}."
+        )
+    return norm, diff_n
+
+
+@assoc_legendre_p_all._override_ufunc_default_args
+def _(branch_cut, norm, diff_n):
+    return branch_cut,
+
+
+@assoc_legendre_p_all._override_ufunc_default_kwargs
+def _(branch_cut, norm, diff_n):
+    return {'axes': [(), ()] + [(0, 1, -1)]}
+
+
+@assoc_legendre_p_all._override_resolve_out_shapes
+def _(n, m, z_shape, branch_cut_shape, nout, **kwargs):
+    diff_n = kwargs['diff_n']
+
+    if not isinstance(n, numbers.Integral) or (n < 0):
+        raise ValueError("n must be a non-negative integer.")
+    if not isinstance(m, numbers.Integral) or (m < 0):
+        raise ValueError("m must be a non-negative integer.")
+
+    return ((n + 1, 2 * abs(m) + 1) +
+        np.broadcast_shapes(z_shape, branch_cut_shape) + (diff_n + 1,),)
+
+
+@assoc_legendre_p_all._override_finalize_out
+def _(out):
+    return np.moveaxis(out, -1, 0)
+
+
+legendre_p = MultiUFunc(
+    legendre_p,
+    "legendre_p",
+    """legendre_p(n, z, *, diff_n=0)
+
+    Legendre polynomial of the first kind.
+
+    Parameters
+    ----------
+    n : array_like of ints
+        Degree of the Legendre polynomial. Must have ``n >= 0``.
+    z : array_like
+        Input value.
+    diff_n : int, optional
+        A non-negative integer. Compute and return all derivatives up
+        to order ``diff_n``. Default is 0.
+
+    Returns
+    -------
+    p : ndarray or tuple of ndarray
+        Legendre polynomial with ``diff_n`` derivatives.
+
+    See Also
+    --------
+    legendre
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    Examples
+    --------
+    Evaluate the Legendre polynomial :math:`P_3` at :math:`z = 0.5`:
+
+    >>> import numpy as np
+    >>> from scipy.special import legendre_p
+    >>> np.allclose(legendre_p(3, 0.5), -0.4375)
+    True
+
+    Compute the value and first derivative with respect to ``z``:
+
+    >>> p, dp = legendre_p(3, 0.5, diff_n=1)
+    >>> np.allclose([p, dp], [-0.4375, 0.375])
+    True
+    """, diff_n=0
+)
+
+
+@legendre_p._override_key
+def _(diff_n):
+    if (not isinstance(diff_n, numbers.Integral)) or (diff_n < 0):
+        raise ValueError(
+            f"diff_n must be a non-negative integer, received: {diff_n}."
+        )
+    if not 0 <= diff_n <= 2:
+        raise NotImplementedError(
+            "diff_n is currently only implemented for orders 0, 1, and 2,"
+            f" received: {diff_n}."
+        )
+    return diff_n
+
+
+@legendre_p._override_finalize_out
+def _(out):
+    return np.moveaxis(out, -1, 0)
+
+
+legendre_p_all = MultiUFunc(
+    legendre_p_all,
+    "legendre_p_all",
+    """legendre_p_all(n, z, *, diff_n=0)
+
+    All Legendre polynomials of the first kind up to the specified degree
+    `n` and all derivatives up to order `diff_n`.
+
+    Parameters
+    ----------
+    n : int
+        Degree of the Legendre polynomials. Must have ``n >= 0``.
+    z : array_like
+        Input value.
+    diff_n : int, optional
+        A non-negative integer. Compute and return all derivatives up
+        to order ``diff_n``. Default is 0.
+
+    Returns
+    -------
+    ndarray
+        Output shape is ``(diff_n + 1, n + 1, ...)``. The entry at ``(i, j)``
+        corresponds to the ``i``-th derivative and degree ``j`` for all
+        ``0 <= i <= diff_n`` and ``0 <= j <= n``.
+
+    See Also
+    --------
+    legendre_p
+    """, diff_n=0
+)
+
+
+@legendre_p_all._override_key
+def _(diff_n):
+    diff_n = _nonneg_int_or_fail(diff_n, "diff_n", strict=False)
+    if not 0 <= diff_n <= 2:
+        raise ValueError(
+            "diff_n is currently only implemented for orders 0, 1, and 2,"
+            f" received: {diff_n}."
+        )
+    return diff_n
+
+
+@legendre_p_all._override_ufunc_default_kwargs
+def _(diff_n):
+    return {'axes': [(), (0, -1)]}
+
+
+@legendre_p_all._override_resolve_out_shapes
+def _(n, z_shape, nout, diff_n):
+    n = _nonneg_int_or_fail(n, 'n', strict=False)
+
+    return nout * ((n + 1,) + z_shape + (diff_n + 1,),)
+
+
+@legendre_p_all._override_finalize_out
+def _(out):
+    return np.moveaxis(out, -1, 0)
+
+
+sph_harm_y = MultiUFunc(
+    sph_harm_y,
+    "sph_harm_y",
+    r"""sph_harm_y(n, m, theta, phi, *, diff_n=0)
+
+    Spherical harmonics.
+
+    They are defined as
+
+    .. math::
+
+        Y_n^m(\theta,\phi) = \sqrt{\frac{2 n + 1}{4 \pi} \frac{(n - m)!}{(n + m)!}}
+            P_n^m(\cos(\theta)) e^{i m \phi}
+
+    where :math:`P_n^m` are the (unnormalized) associated Legendre polynomials.
+
+    Parameters
+    ----------
+    n : array_like of ints
+        Degree of the harmonic. Must have ``n >= 0``. This is
+        often denoted by ``l`` (lower case L) in descriptions of
+        spherical harmonics.
+    m : array_like of ints
+        Order of the harmonic.
+    theta : array_like
+        Polar (colatitudinal) coordinate; must be in ``[0, pi]``.
+    phi : array_like
+        Azimuthal (longitudinal) coordinate; must be in ``[0, 2*pi]``.
+    diff_n : int, optional
+        A non-negative integer. Compute and return all derivatives up
+        to order `diff_n`. Default is 0.
+
+    Returns
+    -------
+    ndarray or tuple of ndarray
+       Spherical harmonics with `diff_n` derivatives.
+
+    Notes
+    -----
+    There are different conventions for the meanings of the input
+    arguments ``theta`` and ``phi``. In SciPy ``theta`` is the
+    polar angle and ``phi`` is the azimuthal angle. It is common to
+    see the opposite convention, that is, ``theta`` as the azimuthal angle
+    and ``phi`` as the polar angle.
+
+    Note that SciPy's spherical harmonics include the Condon-Shortley
+    phase [2]_ because it is part of `sph_legendre_p`.
+
+    With SciPy's conventions, the first several spherical harmonics
+    are
+
+    .. math::
+
+        Y_0^0(\theta, \phi) &= \frac{1}{2} \sqrt{\frac{1}{\pi}} \\
+        Y_1^{-1}(\theta, \phi) &= \frac{1}{2} \sqrt{\frac{3}{2\pi}}
+                                    e^{-i\phi} \sin(\theta) \\
+        Y_1^0(\theta, \phi) &= \frac{1}{2} \sqrt{\frac{3}{\pi}}
+                                 \cos(\theta) \\
+        Y_1^1(\theta, \phi) &= -\frac{1}{2} \sqrt{\frac{3}{2\pi}}
+                                 e^{i\phi} \sin(\theta).
+
+    References
+    ----------
+    .. [1] Digital Library of Mathematical Functions, 14.30.
+           https://dlmf.nist.gov/14.30
+    .. [2] https://en.wikipedia.org/wiki/Spherical_harmonics#Condon.E2.80.93Shortley_phase
+    """, force_complex_output=True, diff_n=0
+)
+
+
+@sph_harm_y._override_key
+def _(diff_n):
+    diff_n = _nonneg_int_or_fail(diff_n, "diff_n", strict=False)
+    if not 0 <= diff_n <= 2:
+        raise ValueError(
+            "diff_n is currently only implemented for orders 0, 1, and 2,"
+            f" received: {diff_n}."
+        )
+    return diff_n
+
+
+@sph_harm_y._override_finalize_out
+def _(out):
+    if (out.shape[-1] == 1):
+        return out[..., 0, 0]
+
+    if (out.shape[-1] == 2):
+        return out[..., 0, 0], out[..., [1, 0], [0, 1]]
+
+    if (out.shape[-1] == 3):
+        return (out[..., 0, 0], out[..., [1, 0], [0, 1]],
+            out[..., [[2, 1], [1, 0]], [[0, 1], [1, 2]]])
+
+
+sph_harm_y_all = MultiUFunc(
+    sph_harm_y_all,
+    "sph_harm_y_all",
+    """sph_harm_y_all(n, m, theta, phi, *, diff_n=0)
+
+    All spherical harmonics up to the specified degree `n`, order `m`,
+    and all derivatives up to order `diff_n`.
+
+    Parameters
+    ----------
+    n : int
+        Degree of the harmonics. Must have ``n >= 0``. This is
+        often denoted by ``l`` (lower case L) in descriptions of
+        spherical harmonics.
+    m : int
+        Order of the harmonics.
+    theta : array_like
+        Polar (colatitudinal) coordinate; must be in ``[0, pi]``.
+    phi : array_like
+        Azimuthal (longitudinal) coordinate; must be in ``[0, 2*pi]``.
+    diff_n : int, optional
+        A non-negative integer. Compute and return all derivatives up
+        to order `diff_n`. Default is 0.
+
+    Returns
+    -------
+    ndarray or tuple of ndarray
+        Returns a tuple of length ``diff_n + 1`` (if ``diff_n > 0``). The first
+        entry corresponds to the spherical harmonics, the second entry
+        (if ``diff_n >= 1``) to the gradient, and the third entry
+        (if ``diff_n >= 2``)  to the Hessian matrix. Each entry is an array of
+        shape ``(n + 1, 2 * m + 1, ...)``, where the entry at ``(i, j)``
+        corresponds to degree ``i`` and order ``j`` for all ``0 <= i <= n``
+        and ``-m <= j <= m``.
+
+    See Also
+    --------
+    sph_harm_y
+    """, force_complex_output=True, diff_n=0
+)
+
+
+@sph_harm_y_all._override_key
+def _(diff_n):
+    diff_n = _nonneg_int_or_fail(diff_n, "diff_n", strict=False)
+    if not 0 <= diff_n <= 2:
+        raise ValueError(
+            "diff_n is currently only implemented for orders 2,"
+            f" received: {diff_n}."
+        )
+    return diff_n
+
+
+@sph_harm_y_all._override_ufunc_default_kwargs
+def _(diff_n):
+    return {'axes': [(), ()] + [(0, 1, -2, -1)]}
+
+
+@sph_harm_y_all._override_resolve_out_shapes
+def _(n, m, theta_shape, phi_shape, nout, **kwargs):
+    diff_n = kwargs['diff_n']
+
+    if not isinstance(n, numbers.Integral) or (n < 0):
+        raise ValueError("n must be a non-negative integer.")
+
+    return ((n + 1, 2 * abs(m) + 1) + np.broadcast_shapes(theta_shape, phi_shape) +
+        (diff_n + 1, diff_n + 1),)
+
+
+@sph_harm_y_all._override_finalize_out
+def _(out):
+    if (out.shape[-1] == 1):
+        return out[..., 0, 0]
+
+    if (out.shape[-1] == 2):
+        return out[..., 0, 0], out[..., [1, 0], [0, 1]]
+
+    if (out.shape[-1] == 3):
+        return (out[..., 0, 0], out[..., [1, 0], [0, 1]],
+            out[..., [[2, 1], [1, 0]], [[0, 1], [1, 2]]])
diff --git a/venv/lib/python3.12/site-packages/scipy/special/_orthogonal.py b/venv/lib/python3.12/site-packages/scipy/special/_orthogonal.py
new file mode 100644
index 0000000000000000000000000000000000000000..de51d61f6912abd1d28686d2638d1b31527ab836
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/_orthogonal.py
@@ -0,0 +1,2856 @@
+"""
+A collection of functions to find the weights and abscissas for
+Gaussian Quadrature.
+
+These calculations are done by finding the eigenvalues of a
+tridiagonal matrix whose entries are dependent on the coefficients
+in the recursion formula for the orthogonal polynomials with the
+corresponding weighting function over the interval.
+
+Many recursion relations for orthogonal polynomials are given:
+
+.. math::
+
+    a1n f_{n+1} (x) = (a2n + a3n x ) f_n (x) - a4n f_{n-1} (x)
+
+The recursion relation of interest is
+
+.. math::
+
+    P_{n+1} (x) = (x - A_n) P_n (x) - B_n P_{n-1} (x)
+
+where :math:`P` has a different normalization than :math:`f`.
+
+The coefficients can be found as:
+
+.. math::
+
+    A_n = -a2n / a3n
+    \\qquad
+    B_n = ( a4n / a3n \\sqrt{h_n-1 / h_n})^2
+
+where
+
+.. math::
+
+    h_n = \\int_a^b w(x) f_n(x)^2
+
+assume:
+
+.. math::
+
+    P_0 (x) = 1
+    \\qquad
+    P_{-1} (x) == 0
+
+For the mathematical background, see [golub.welsch-1969-mathcomp]_ and
+[abramowitz.stegun-1965]_.
+
+References
+----------
+.. [golub.welsch-1969-mathcomp]
+   Golub, Gene H, and John H Welsch. 1969. Calculation of Gauss
+   Quadrature Rules. *Mathematics of Computation* 23, 221-230+s1--s10.
+
+.. [abramowitz.stegun-1965]
+   Abramowitz, Milton, and Irene A Stegun. (1965) *Handbook of
+   Mathematical Functions: with Formulas, Graphs, and Mathematical
+   Tables*. Gaithersburg, MD: National Bureau of Standards.
+   http://www.math.sfu.ca/~cbm/aands/
+
+.. [townsend.trogdon.olver-2014]
+   Townsend, A. and Trogdon, T. and Olver, S. (2014)
+   *Fast computation of Gauss quadrature nodes and
+   weights on the whole real line*. :arXiv:`1410.5286`.
+
+.. [townsend.trogdon.olver-2015]
+   Townsend, A. and Trogdon, T. and Olver, S. (2015)
+   *Fast computation of Gauss quadrature nodes and
+   weights on the whole real line*.
+   IMA Journal of Numerical Analysis
+   :doi:`10.1093/imanum/drv002`.
+"""
+#
+# Author:  Travis Oliphant 2000
+# Updated Sep. 2003 (fixed bugs --- tested to be accurate)
+
+# SciPy imports.
+import numpy as np
+from numpy import (exp, inf, pi, sqrt, floor, sin, cos, around,
+                   hstack, arccos, arange)
+from scipy.special import airy
+
+# Local imports.
+# There is no .pyi file for _specfun
+from . import _specfun  # type: ignore
+from . import _ufuncs
+_gam = _ufuncs.gamma
+
+_polyfuns = ['legendre', 'chebyt', 'chebyu', 'chebyc', 'chebys',
+             'jacobi', 'laguerre', 'genlaguerre', 'hermite',
+             'hermitenorm', 'gegenbauer', 'sh_legendre', 'sh_chebyt',
+             'sh_chebyu', 'sh_jacobi']
+
+# Correspondence between new and old names of root functions
+_rootfuns_map = {'roots_legendre': 'p_roots',
+                 'roots_chebyt': 't_roots',
+                 'roots_chebyu': 'u_roots',
+                 'roots_chebyc': 'c_roots',
+                 'roots_chebys': 's_roots',
+                 'roots_jacobi': 'j_roots',
+                 'roots_laguerre': 'l_roots',
+                 'roots_genlaguerre': 'la_roots',
+                 'roots_hermite': 'h_roots',
+                 'roots_hermitenorm': 'he_roots',
+                 'roots_gegenbauer': 'cg_roots',
+                 'roots_sh_legendre': 'ps_roots',
+                 'roots_sh_chebyt': 'ts_roots',
+                 'roots_sh_chebyu': 'us_roots',
+                 'roots_sh_jacobi': 'js_roots'}
+
+__all__ = _polyfuns + list(_rootfuns_map.keys())
+
+
+class orthopoly1d(np.poly1d):
+
+    def __init__(self, roots, weights=None, hn=1.0, kn=1.0, wfunc=None,
+                 limits=None, monic=False, eval_func=None):
+        equiv_weights = [weights[k] / wfunc(roots[k]) for
+                         k in range(len(roots))]
+        mu = sqrt(hn)
+        if monic:
+            evf = eval_func
+            if evf:
+                knn = kn
+                def eval_func(x):
+                    return evf(x) / knn
+            mu = mu / abs(kn)
+            kn = 1.0
+
+        # compute coefficients from roots, then scale
+        poly = np.poly1d(roots, r=True)
+        np.poly1d.__init__(self, poly.coeffs * float(kn))
+
+        self.weights = np.array(list(zip(roots, weights, equiv_weights)))
+        self.weight_func = wfunc
+        self.limits = limits
+        self.normcoef = mu
+
+        # Note: eval_func will be discarded on arithmetic
+        self._eval_func = eval_func
+
+    def __call__(self, v):
+        if self._eval_func and not isinstance(v, np.poly1d):
+            return self._eval_func(v)
+        else:
+            return np.poly1d.__call__(self, v)
+
+    def _scale(self, p):
+        if p == 1.0:
+            return
+        self._coeffs *= p
+
+        evf = self._eval_func
+        if evf:
+            self._eval_func = lambda x: evf(x) * p
+        self.normcoef *= p
+
+
+def _gen_roots_and_weights(n, mu0, an_func, bn_func, f, df, symmetrize, mu):
+    """[x,w] = gen_roots_and_weights(n,an_func,sqrt_bn_func,mu)
+
+    Returns the roots (x) of an nth order orthogonal polynomial,
+    and weights (w) to use in appropriate Gaussian quadrature with that
+    orthogonal polynomial.
+
+    The polynomials have the recurrence relation
+          P_n+1(x) = (x - A_n) P_n(x) - B_n P_n-1(x)
+
+    an_func(n)          should return A_n
+    sqrt_bn_func(n)     should return sqrt(B_n)
+    mu ( = h_0 )        is the integral of the weight over the orthogonal
+                        interval
+    """
+    # lazy import to prevent to prevent linalg dependency for whole module (gh-23420)
+    from scipy import linalg
+    k = np.arange(n, dtype='d')
+    c = np.zeros((2, n))
+    c[0,1:] = bn_func(k[1:])
+    c[1,:] = an_func(k)
+    x = linalg.eigvals_banded(c, overwrite_a_band=True)
+
+    # improve roots by one application of Newton's method
+    y = f(n, x)
+    dy = df(n, x)
+    x -= y/dy
+
+    # fm and dy may contain very large/small values, so we
+    # log-normalize them to maintain precision in the product fm*dy
+    fm = f(n-1, x)
+    log_fm = np.log(np.abs(fm))
+    log_dy = np.log(np.abs(dy))
+    fm /= np.exp((log_fm.max() + log_fm.min()) / 2.)
+    dy /= np.exp((log_dy.max() + log_dy.min()) / 2.)
+    w = 1.0 / (fm * dy)
+
+    if symmetrize:
+        w = (w + w[::-1]) / 2
+        x = (x - x[::-1]) / 2
+
+    w *= mu0 / w.sum()
+
+    if mu:
+        return x, w, mu0
+    else:
+        return x, w
+
+# Jacobi Polynomials 1               P^(alpha,beta)_n(x)
+
+
+def roots_jacobi(n, alpha, beta, mu=False):
+    r"""Gauss-Jacobi quadrature.
+
+    Compute the sample points and weights for Gauss-Jacobi
+    quadrature. The sample points are the roots of the nth degree
+    Jacobi polynomial, :math:`P^{\alpha, \beta}_n(x)`. These sample
+    points and weights correctly integrate polynomials of degree
+    :math:`2n - 1` or less over the interval :math:`[-1, 1]` with
+    weight function :math:`w(x) = (1 - x)^{\alpha} (1 +
+    x)^{\beta}`. See 22.2.1 in [AS]_ for details.
+
+    Parameters
+    ----------
+    n : int
+        Quadrature order.
+    alpha : float
+        alpha must be > -1.
+    beta : float
+        beta must be > -1.
+    mu : bool, optional
+        If True, return the sum of the weights in addition to sample points and weights.
+
+    Returns
+    -------
+    x : ndarray
+        Sample points.
+    w : ndarray
+        Weights.
+    mu : float, optional
+        Sum of the weights, only returned if `mu=True`.
+
+    See Also
+    --------
+    scipy.integrate.fixed_quad
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+
+    Examples
+    --------
+    >>> from scipy.special import roots_jacobi
+    >>> x, w = roots_jacobi(3, 0.5, 0.5)
+    >>> x
+    array([-0.70710678,  0.        ,  0.70710678])
+    >>> w
+    array([0.39269908, 0.78539816, 0.39269908])
+
+    >>> x, w, mu = roots_jacobi(3, 0.5, 0.5, mu=True)
+    >>> mu
+    1.5707963267948966  # Sum of weights, equals pi/2 for alpha = beta = 0.5
+    """
+
+    m = int(n)
+    if n < 1 or n != m:
+        raise ValueError("n must be a positive integer.")
+    if alpha <= -1 or beta <= -1:
+        raise ValueError("alpha and beta must be greater than -1.")
+
+    if alpha == 0.0 and beta == 0.0:
+        return roots_legendre(m, mu)
+    if alpha == beta:
+        return roots_gegenbauer(m, alpha+0.5, mu)
+
+    if (alpha + beta) <= 1000:
+        mu0 = 2.0**(alpha+beta+1) * _ufuncs.beta(alpha+1, beta+1)
+    else:
+        # Avoid overflows in pow and beta for very large parameters
+        mu0 = np.exp((alpha + beta + 1) * np.log(2.0)
+                     + _ufuncs.betaln(alpha+1, beta+1))
+    a = alpha
+    b = beta
+    if a + b == 0.0:
+        def an_func(k):
+            return np.where(k == 0, (b - a) / (2 + a + b), 0.0)
+    else:
+        def an_func(k):
+            return np.where(
+                k == 0,
+                (b - a) / (2 + a + b),
+                (b * b - a * a) / ((2.0 * k + a + b) * (2.0 * k + a + b + 2))
+            )
+
+    def bn_func(k):
+        return (
+            2.0 / (2.0 * k + a + b)
+            * np.sqrt((k + a) * (k + b) / (2 * k + a + b + 1))
+            * np.where(k == 1, 1.0, np.sqrt(k * (k + a + b) / (2.0 * k + a + b - 1)))
+        )
+
+    def f(n, x):
+        return _ufuncs.eval_jacobi(n, a, b, x)
+    def df(n, x):
+        return 0.5 * (n + a + b + 1) * _ufuncs.eval_jacobi(n - 1, a + 1, b + 1, x)
+    return _gen_roots_and_weights(m, mu0, an_func, bn_func, f, df, False, mu)
+
+
+def jacobi(n, alpha, beta, monic=False):
+    r"""Jacobi polynomial.
+
+    Defined to be the solution of
+
+    .. math::
+
+        \begin{aligned}
+        (1 - x^2)\frac{d^2}{dx^2} P_n^{(\alpha, \beta)}(x)
+        &+ \left(\beta - \alpha - (\alpha + \beta + 2)x\right)
+        \frac{d}{dx} P_n^{(\alpha, \beta)}(x) \\
+        &+ n(n + \alpha + \beta + 1) P_n^{(\alpha, \beta)}(x) = 0
+        \end{aligned}
+
+    for :math:`\alpha, \beta > -1`; :math:`P_n^{(\alpha, \beta)}` is a
+    polynomial of degree :math:`n`.
+
+    Parameters
+    ----------
+    n : int
+        Degree of the polynomial.
+    alpha : float
+        Parameter, must be greater than -1.
+    beta : float
+        Parameter, must be greater than -1.
+    monic : bool, optional
+        If `True`, scale the leading coefficient to be 1. Default is
+        `False`.
+
+    Returns
+    -------
+    P : orthopoly1d
+        Jacobi polynomial.
+
+    Notes
+    -----
+    For fixed :math:`\alpha, \beta`, the polynomials
+    :math:`P_n^{(\alpha, \beta)}` are orthogonal over :math:`[-1, 1]`
+    with weight function :math:`(1 - x)^\alpha(1 + x)^\beta`.
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+
+    Examples
+    --------
+    The Jacobi polynomials satisfy the recurrence relation:
+
+    .. math::
+        P_n^{(\alpha, \beta-1)}(x) - P_n^{(\alpha-1, \beta)}(x)
+          = P_{n-1}^{(\alpha, \beta)}(x)
+
+    This can be verified, for example, for :math:`\alpha = \beta = 2`
+    and :math:`n = 1` over the interval :math:`[-1, 1]`:
+
+    >>> import numpy as np
+    >>> from scipy.special import jacobi
+    >>> x = np.arange(-1.0, 1.0, 0.01)
+    >>> np.allclose(jacobi(0, 2, 2)(x),
+    ...             jacobi(1, 2, 1)(x) - jacobi(1, 1, 2)(x))
+    True
+
+    Plot of the Jacobi polynomial :math:`P_5^{(\alpha, -0.5)}` for
+    different values of :math:`\alpha`:
+
+    >>> import matplotlib.pyplot as plt
+    >>> x = np.arange(-1.0, 1.0, 0.01)
+    >>> fig, ax = plt.subplots()
+    >>> ax.set_ylim(-2.0, 2.0)
+    >>> ax.set_title(r'Jacobi polynomials $P_5^{(\alpha, -0.5)}$')
+    >>> for alpha in np.arange(0, 4, 1):
+    ...     ax.plot(x, jacobi(5, alpha, -0.5)(x), label=rf'$\alpha={alpha}$')
+    >>> plt.legend(loc='best')
+    >>> plt.show()
+
+    """
+    if n < 0:
+        raise ValueError("n must be nonnegative.")
+
+    def wfunc(x):
+        return (1 - x) ** alpha * (1 + x) ** beta
+    if n == 0:
+        return orthopoly1d([], [], 1.0, 1.0, wfunc, (-1, 1), monic,
+                           eval_func=np.ones_like)
+    x, w, mu = roots_jacobi(n, alpha, beta, mu=True)
+    ab1 = alpha + beta + 1.0
+    hn = 2**ab1 / (2 * n + ab1) * _gam(n + alpha + 1)
+    hn *= _gam(n + beta + 1.0) / _gam(n + 1) / _gam(n + ab1)
+    kn = _gam(2 * n + ab1) / 2.0**n / _gam(n + 1) / _gam(n + ab1)
+    # here kn = coefficient on x^n term
+    p = orthopoly1d(x, w, hn, kn, wfunc, (-1, 1), monic,
+                    lambda x: _ufuncs.eval_jacobi(n, alpha, beta, x))
+    return p
+
+# Jacobi Polynomials shifted         G_n(p,q,x)
+
+
+def roots_sh_jacobi(n, p1, q1, mu=False):
+    """Gauss-Jacobi (shifted) quadrature.
+
+    Compute the sample points and weights for Gauss-Jacobi (shifted)
+    quadrature. The sample points are the roots of the nth degree
+    shifted Jacobi polynomial, :math:`G^{p,q}_n(x)`. These sample
+    points and weights correctly integrate polynomials of degree
+    :math:`2n - 1` or less over the interval :math:`[0, 1]` with
+    weight function :math:`w(x) = (1 - x)^{p-q} x^{q-1}`. See 22.2.2
+    in [AS]_ for details.
+
+    Parameters
+    ----------
+    n : int
+        quadrature order.
+    p1 : float
+        (p1 - q1) must be > -1.
+    q1 : float
+        q1 must be > 0.
+    mu : bool, optional
+        If True, return the sum of the weights, optional.
+
+    Returns
+    -------
+    x : ndarray
+        Sample points
+    w : ndarray
+        Weights
+    mu : float
+        Sum of the weights
+
+    See Also
+    --------
+    scipy.integrate.fixed_quad
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+
+    """
+    if (p1-q1) <= -1 or q1 <= 0:
+        message = "(p - q) must be greater than -1, and q must be greater than 0."
+        raise ValueError(message)
+    x, w, m = roots_jacobi(n, p1-q1, q1-1, True)
+    x = (x + 1) / 2
+    scale = 2.0**p1
+    w /= scale
+    m /= scale
+    if mu:
+        return x, w, m
+    else:
+        return x, w
+
+
+def sh_jacobi(n, p, q, monic=False):
+    r"""Shifted Jacobi polynomial.
+
+    Defined by
+
+    .. math::
+
+        G_n^{(p, q)}(x)
+          = \binom{2n + p - 1}{n}^{-1}P_n^{(p - q, q - 1)}(2x - 1),
+
+    where :math:`P_n^{(\cdot, \cdot)}` is the nth Jacobi polynomial.
+
+    Parameters
+    ----------
+    n : int
+        Degree of the polynomial.
+    p : float
+        Parameter, must have :math:`p > q - 1`.
+    q : float
+        Parameter, must be greater than 0.
+    monic : bool, optional
+        If `True`, scale the leading coefficient to be 1. Default is
+        `False`.
+
+    Returns
+    -------
+    G : orthopoly1d
+        Shifted Jacobi polynomial.
+
+    Notes
+    -----
+    For fixed :math:`p, q`, the polynomials :math:`G_n^{(p, q)}` are
+    orthogonal over :math:`[0, 1]` with weight function :math:`(1 -
+    x)^{p - q}x^{q - 1}`.
+
+    Examples
+    --------
+    Evaluate the shifted Jacobi polynomial :math:`G_3^{(2, 1)}` at
+    :math:`x = 0.5`:
+
+    >>> import numpy as np
+    >>> from scipy.special import binom, jacobi, sh_jacobi
+    >>> np.isclose(sh_jacobi(3, 2, 1)(0.5), -3/280)
+    True
+
+    The polynomial is related to the Jacobi polynomial
+    :math:`P_n^{(p - q, q - 1)}`:
+
+    >>> x = np.linspace(0, 1, 5)
+    >>> n, p, q = 3, 2, 1
+    >>> scale = 1 / binom(2*n + p - 1, n)
+    >>> np.allclose(sh_jacobi(n, p, q)(x),
+    ...             scale * jacobi(n, p - q, q - 1)(2*x - 1))
+    True
+
+    Plot :math:`G_3^{(p, 1)}` for several values of :math:`p`:
+
+    >>> import matplotlib.pyplot as plt
+    >>> x = np.linspace(0, 1, 400)
+    >>> fig, ax = plt.subplots()
+    >>> for p in [1, 2, 3]:
+    ...     ax.plot(x, sh_jacobi(3, p, 1)(x), label=rf"$p={p}$")
+    >>> ax.set_title(r"Shifted Jacobi polynomials $G_3^{(p, 1)}$")
+    >>> ax.set_xlabel("x")
+    >>> ax.legend(loc="best")
+    >>> plt.show()
+
+    """
+    if n < 0:
+        raise ValueError("n must be nonnegative.")
+
+    def wfunc(x):
+        return (1.0 - x) ** (p - q) * x ** (q - 1.0)
+    if n == 0:
+        return orthopoly1d([], [], 1.0, 1.0, wfunc, (-1, 1), monic,
+                           eval_func=np.ones_like)
+    n1 = n
+    x, w = roots_sh_jacobi(n1, p, q)
+    hn = _gam(n + 1) * _gam(n + q) * _gam(n + p) * _gam(n + p - q + 1)
+    hn /= (2 * n + p) * (_gam(2 * n + p)**2)
+    # kn = 1.0 in standard form so monic is redundant. Kept for compatibility.
+    kn = 1.0
+    pp = orthopoly1d(x, w, hn, kn, wfunc=wfunc, limits=(0, 1), monic=monic,
+                     eval_func=lambda x: _ufuncs.eval_sh_jacobi(n, p, q, x))
+    return pp
+
+# Generalized Laguerre               L^(alpha)_n(x)
+
+
+def roots_genlaguerre(n, alpha, mu=False):
+    r"""Gauss-generalized Laguerre quadrature.
+
+    Compute the sample points and weights for Gauss-generalized
+    Laguerre quadrature. The sample points are the roots of the nth
+    degree generalized Laguerre polynomial, :math:`L^{\alpha}_n(x)`.
+    These sample points and weights correctly integrate polynomials of
+    degree :math:`2n - 1` or less over the interval :math:`[0,
+    \infty]` with weight function :math:`w(x) = x^{\alpha}
+    e^{-x}`. See 22.3.9 in [AS]_ for details.
+
+    Parameters
+    ----------
+    n : int
+        quadrature order
+    alpha : float
+        alpha must be > -1
+    mu : bool, optional
+        If True, return the sum of the weights, optional.
+
+    Returns
+    -------
+    x : ndarray
+        Sample points
+    w : ndarray
+        Weights
+    mu : float
+        Sum of the weights
+
+    See Also
+    --------
+    scipy.integrate.fixed_quad
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+
+    """
+    m = int(n)
+    if n < 1 or n != m:
+        raise ValueError("n must be a positive integer.")
+    if alpha < -1:
+        raise ValueError("alpha must be greater than -1.")
+
+    mu0 = _ufuncs.gamma(alpha + 1)
+
+    if m == 1:
+        x = np.array([alpha+1.0], 'd')
+        w = np.array([mu0], 'd')
+        if mu:
+            return x, w, mu0
+        else:
+            return x, w
+
+    def an_func(k):
+        return 2 * k + alpha + 1
+    def bn_func(k):
+        return -np.sqrt(k * (k + alpha))
+    def f(n, x):
+        return _ufuncs.eval_genlaguerre(n, alpha, x)
+    def df(n, x):
+        return (n * _ufuncs.eval_genlaguerre(n, alpha, x)
+                - (n + alpha) * _ufuncs.eval_genlaguerre(n - 1, alpha, x)) / x
+    return _gen_roots_and_weights(m, mu0, an_func, bn_func, f, df, False, mu)
+
+
+def genlaguerre(n, alpha, monic=False):
+    r"""Generalized (associated) Laguerre polynomial.
+
+    Defined to be the solution of
+
+    .. math::
+        x\frac{d^2}{dx^2}L_n^{(\alpha)}(x)
+          + (\alpha + 1 - x)\frac{d}{dx}L_n^{(\alpha)}(x)
+          + nL_n^{(\alpha)}(x) = 0,
+
+    where :math:`\alpha > -1`; :math:`L_n^{(\alpha)}` is a polynomial
+    of degree :math:`n`.
+
+    Parameters
+    ----------
+    n : int
+        Degree of the polynomial.
+    alpha : float
+        Parameter, must be greater than -1.
+    monic : bool, optional
+        If `True`, scale the leading coefficient to be 1. Default is
+        `False`.
+
+    Returns
+    -------
+    L : orthopoly1d
+        Generalized Laguerre polynomial.
+
+    See Also
+    --------
+    laguerre : Laguerre polynomial.
+    hyp1f1 : confluent hypergeometric function
+
+    Notes
+    -----
+    For fixed :math:`\alpha`, the polynomials :math:`L_n^{(\alpha)}`
+    are orthogonal over :math:`[0, \infty)` with weight function
+    :math:`e^{-x}x^\alpha`.
+
+    The Laguerre polynomials are the special case where :math:`\alpha
+    = 0`.
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+
+    Examples
+    --------
+    The generalized Laguerre polynomials are closely related to the confluent
+    hypergeometric function :math:`{}_1F_1`:
+
+        .. math::
+            L_n^{(\alpha)}(x) = \binom{n + \alpha}{n} {}_1F_1(-n, \alpha +1, x)
+
+    This can be verified, for example,  for :math:`n = \alpha = 3` over the
+    interval :math:`[-1, 1]`:
+
+    >>> import numpy as np
+    >>> from scipy.special import binom, genlaguerre, hyp1f1
+    >>> x = np.arange(-1.0, 1.0, 0.01)
+    >>> np.allclose(genlaguerre(3, 3)(x), binom(6, 3) * hyp1f1(-3, 4, x))
+    True
+
+    This is the plot of the generalized Laguerre polynomials
+    :math:`L_3^{(\alpha)}` for some values of :math:`\alpha`:
+
+    >>> import matplotlib.pyplot as plt
+    >>> x = np.arange(-4.0, 12.0, 0.01)
+    >>> fig, ax = plt.subplots()
+    >>> ax.set_ylim(-5.0, 10.0)
+    >>> ax.set_title(r'Generalized Laguerre polynomials $L_3^{(\alpha)}$')
+    >>> for alpha in np.arange(0, 5):
+    ...     ax.plot(x, genlaguerre(3, alpha)(x), label=rf"$L_3^{{({alpha})}}$")
+    >>> plt.legend(loc='best')
+    >>> plt.show()
+
+    """
+    if alpha <= -1:
+        raise ValueError("alpha must be > -1")
+    if n < 0:
+        raise ValueError("n must be nonnegative.")
+
+    if n == 0:
+        n1 = n + 1
+    else:
+        n1 = n
+    x, w = roots_genlaguerre(n1, alpha)
+    def wfunc(x):
+        return exp(-x) * x ** alpha
+    if n == 0:
+        x, w = [], []
+    hn = _gam(n + alpha + 1) / _gam(n + 1)
+    kn = (-1)**n / _gam(n + 1)
+    p = orthopoly1d(x, w, hn, kn, wfunc, (0, inf), monic,
+                    lambda x: _ufuncs.eval_genlaguerre(n, alpha, x))
+    return p
+
+# Laguerre                      L_n(x)
+
+
+def roots_laguerre(n, mu=False):
+    r"""Gauss-Laguerre quadrature.
+
+    Compute the sample points and weights for Gauss-Laguerre
+    quadrature. The sample points are the roots of the nth degree
+    Laguerre polynomial, :math:`L_n(x)`. These sample points and
+    weights correctly integrate polynomials of degree :math:`2n - 1`
+    or less over the interval :math:`[0, \infty]` with weight function
+    :math:`w(x) = e^{-x}`. See 22.2.13 in [AS]_ for details.
+
+    Parameters
+    ----------
+    n : int
+        quadrature order
+    mu : bool, optional
+        If True, return the sum of the weights, optional.
+
+    Returns
+    -------
+    x : ndarray
+        Sample points
+    w : ndarray
+        Weights
+    mu : float
+        Sum of the weights
+
+    See Also
+    --------
+    scipy.integrate.fixed_quad
+    numpy.polynomial.laguerre.laggauss
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+
+    """
+    return roots_genlaguerre(n, 0.0, mu=mu)
+
+
+def laguerre(n, monic=False):
+    r"""Laguerre polynomial.
+
+    Defined to be the solution of
+
+    .. math::
+        x\frac{d^2}{dx^2}L_n(x) + (1 - x)\frac{d}{dx}L_n(x)
+          + nL_n(x) = 0;
+
+    :math:`L_n` is a polynomial of degree :math:`n`.
+
+    Parameters
+    ----------
+    n : int
+        Degree of the polynomial.
+    monic : bool, optional
+        If `True`, scale the leading coefficient to be 1. Default is
+        `False`.
+
+    Returns
+    -------
+    L : orthopoly1d
+        Laguerre Polynomial.
+
+    See Also
+    --------
+    genlaguerre : Generalized (associated) Laguerre polynomial.
+
+    Notes
+    -----
+    The polynomials :math:`L_n` are orthogonal over :math:`[0,
+    \infty)` with weight function :math:`e^{-x}`.
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+
+    Examples
+    --------
+    The Laguerre polynomials :math:`L_n` are the special case
+    :math:`\alpha = 0` of the generalized Laguerre polynomials
+    :math:`L_n^{(\alpha)}`.
+    Let's verify it on the interval :math:`[-1, 1]`:
+
+    >>> import numpy as np
+    >>> from scipy.special import genlaguerre
+    >>> from scipy.special import laguerre
+    >>> x = np.arange(-1.0, 1.0, 0.01)
+    >>> np.allclose(genlaguerre(3, 0)(x), laguerre(3)(x))
+    True
+
+    The polynomials :math:`L_n` also satisfy the recurrence relation:
+
+    .. math::
+        (n + 1)L_{n+1}(x) = (2n +1 -x)L_n(x) - nL_{n-1}(x)
+
+    This can be easily checked on :math:`[0, 1]` for :math:`n = 3`:
+
+    >>> x = np.arange(0.0, 1.0, 0.01)
+    >>> np.allclose(4 * laguerre(4)(x),
+    ...             (7 - x) * laguerre(3)(x) - 3 * laguerre(2)(x))
+    True
+
+    This is the plot of the first few Laguerre polynomials :math:`L_n`:
+
+    >>> import matplotlib.pyplot as plt
+    >>> x = np.arange(-1.0, 5.0, 0.01)
+    >>> fig, ax = plt.subplots()
+    >>> ax.set_ylim(-5.0, 5.0)
+    >>> ax.set_title(r'Laguerre polynomials $L_n$')
+    >>> for n in np.arange(0, 5):
+    ...     ax.plot(x, laguerre(n)(x), label=rf'$L_{n}$')
+    >>> plt.legend(loc='best')
+    >>> plt.show()
+
+    """
+    if n < 0:
+        raise ValueError("n must be nonnegative.")
+
+    if n == 0:
+        n1 = n + 1
+    else:
+        n1 = n
+    x, w = roots_laguerre(n1)
+    if n == 0:
+        x, w = [], []
+    hn = 1.0
+    kn = (-1)**n / _gam(n + 1)
+    p = orthopoly1d(x, w, hn, kn, lambda x: exp(-x), (0, inf), monic,
+                    lambda x: _ufuncs.eval_laguerre(n, x))
+    return p
+
+# Hermite  1                         H_n(x)
+
+
+def roots_hermite(n, mu=False):
+    r"""Gauss-Hermite (physicist's) quadrature.
+
+    Compute the sample points and weights for Gauss-Hermite
+    quadrature. The sample points are the roots of the nth degree
+    Hermite polynomial, :math:`H_n(x)`. These sample points and
+    weights correctly integrate polynomials of degree :math:`2n - 1`
+    or less over the interval :math:`[-\infty, \infty]` with weight
+    function :math:`w(x) = e^{-x^2}`. See 22.2.14 in [AS]_ for
+    details.
+
+    Parameters
+    ----------
+    n : int
+        quadrature order
+    mu : bool, optional
+        If True, return the sum of the weights, optional.
+
+    Returns
+    -------
+    x : ndarray
+        Sample points
+    w : ndarray
+        Weights
+    mu : float
+        Sum of the weights
+
+    See Also
+    --------
+    scipy.integrate.fixed_quad
+    numpy.polynomial.hermite.hermgauss
+    roots_hermitenorm
+
+    Notes
+    -----
+    For small n up to 150 a modified version of the Golub-Welsch
+    algorithm is used. Nodes are computed from the eigenvalue
+    problem and improved by one step of a Newton iteration.
+    The weights are computed from the well-known analytical formula.
+
+    For n larger than 150 an optimal asymptotic algorithm is applied
+    which computes nodes and weights in a numerically stable manner.
+    The algorithm has linear runtime making computation for very
+    large n (several thousand or more) feasible.
+
+    References
+    ----------
+    .. [townsend.trogdon.olver-2014]
+        Townsend, A. and Trogdon, T. and Olver, S. (2014)
+        *Fast computation of Gauss quadrature nodes and
+        weights on the whole real line*. :arXiv:`1410.5286`.
+    .. [townsend.trogdon.olver-2015]
+        Townsend, A. and Trogdon, T. and Olver, S. (2015)
+        *Fast computation of Gauss quadrature nodes and
+        weights on the whole real line*.
+        IMA Journal of Numerical Analysis
+        :doi:`10.1093/imanum/drv002`.
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+
+    """
+    m = int(n)
+    if n < 1 or n != m:
+        raise ValueError("n must be a positive integer.")
+
+    mu0 = np.sqrt(np.pi)
+    if n <= 150:
+        def an_func(k):
+            return 0.0 * k
+        def bn_func(k):
+            return np.sqrt(k / 2.0)
+        f = _ufuncs.eval_hermite
+        def df(n, x):
+            return 2.0 * n * _ufuncs.eval_hermite(n - 1, x)
+        return _gen_roots_and_weights(m, mu0, an_func, bn_func, f, df, True, mu)
+    else:
+        nodes, weights = _roots_hermite_asy(m)
+        if mu:
+            return nodes, weights, mu0
+        else:
+            return nodes, weights
+
+
+def _compute_tauk(n, k, maxit=5):
+    """Helper function for Tricomi initial guesses
+
+    For details, see formula 3.1 in lemma 3.1 in the
+    original paper.
+
+    Parameters
+    ----------
+    n : int
+        Quadrature order
+    k : ndarray of type int
+        Index of roots :math:`\tau_k` to compute
+    maxit : int
+        Number of Newton maxit performed, the default
+        value of 5 is sufficient.
+
+    Returns
+    -------
+    tauk : ndarray
+        Roots of equation 3.1
+
+    See Also
+    --------
+    initial_nodes_a
+    roots_hermite_asy
+    """
+    a = n % 2 - 0.5
+    c = (4.0*floor(n/2.0) - 4.0*k + 3.0)*pi / (4.0*floor(n/2.0) + 2.0*a + 2.0)
+    def f(x):
+        return x - sin(x) - c
+    def df(x):
+        return 1.0 - cos(x)
+    xi = 0.5*pi
+    for i in range(maxit):
+        xi = xi - f(xi)/df(xi)
+    return xi
+
+
+def _initial_nodes_a(n, k):
+    r"""Tricomi initial guesses
+
+    Computes an initial approximation to the square of the `k`-th
+    (positive) root :math:`x_k` of the Hermite polynomial :math:`H_n`
+    of order :math:`n`. The formula is the one from lemma 3.1 in the
+    original paper. The guesses are accurate except in the region
+    near :math:`\sqrt{2n + 1}`.
+
+    Parameters
+    ----------
+    n : int
+        Quadrature order
+    k : ndarray of type int
+        Index of roots to compute
+
+    Returns
+    -------
+    xksq : ndarray
+        Square of the approximate roots
+
+    See Also
+    --------
+    initial_nodes
+    roots_hermite_asy
+    """
+    tauk = _compute_tauk(n, k)
+    sigk = cos(0.5*tauk)**2
+    a = n % 2 - 0.5
+    nu = 4.0*floor(n/2.0) + 2.0*a + 2.0
+    # Initial approximation of Hermite roots (square)
+    xksq = nu*sigk - 1.0/(3.0*nu) * (5.0/(4.0*(1.0-sigk)**2) - 1.0/(1.0-sigk) - 0.25)
+    return xksq
+
+
+def _initial_nodes_b(n, k):
+    r"""Gatteschi initial guesses
+
+    Computes an initial approximation to the square of the kth
+    (positive) root :math:`x_k` of the Hermite polynomial :math:`H_n`
+    of order :math:`n`. The formula is the one from lemma 3.2 in the
+    original paper. The guesses are accurate in the region just
+    below :math:`\sqrt{2n + 1}`.
+
+    Parameters
+    ----------
+    n : int
+        Quadrature order
+    k : ndarray of type int
+        Index of roots to compute
+
+    Returns
+    -------
+    xksq : ndarray
+        Square of the approximate root
+
+    See Also
+    --------
+    initial_nodes
+    roots_hermite_asy
+    """
+    a = n % 2 - 0.5
+    nu = 4.0*floor(n/2.0) + 2.0*a + 2.0
+    # Airy roots by approximation
+    ak = _specfun.airyzo(k.max(), 1)[0][::-1]
+    # Initial approximation of Hermite roots (square)
+    xksq = (nu
+            + 2.0**(2.0/3.0) * ak * nu**(1.0/3.0)
+            + 1.0/5.0 * 2.0**(4.0/3.0) * ak**2 * nu**(-1.0/3.0)
+            + (9.0/140.0 - 12.0/175.0 * ak**3) * nu**(-1.0)
+            + (16.0/1575.0 * ak + 92.0/7875.0 * ak**4) * 2.0**(2.0/3.0) * nu**(-5.0/3.0)
+            - (15152.0/3031875.0 * ak**5 + 1088.0/121275.0 * ak**2)
+              * 2.0**(1.0/3.0) * nu**(-7.0/3.0))
+    return xksq
+
+
+def _initial_nodes(n):
+    """Initial guesses for the Hermite roots
+
+    Computes an initial approximation to the non-negative
+    roots :math:`x_k` of the Hermite polynomial :math:`H_n`
+    of order :math:`n`. The Tricomi and Gatteschi initial
+    guesses are used in the region where they are accurate.
+
+    Parameters
+    ----------
+    n : int
+        Quadrature order
+
+    Returns
+    -------
+    xk : ndarray
+        Approximate roots
+
+    See Also
+    --------
+    roots_hermite_asy
+    """
+    # Turnover point
+    # linear polynomial fit to error of 10, 25, 40, ..., 1000 point rules
+    fit = 0.49082003*n - 4.37859653
+    turnover = around(fit).astype(int)
+    # Compute all approximations
+    ia = arange(1, int(floor(n*0.5)+1))
+    ib = ia[::-1]
+    xasq = _initial_nodes_a(n, ia[:turnover+1])
+    xbsq = _initial_nodes_b(n, ib[turnover+1:])
+    # Combine
+    iv = sqrt(hstack([xasq, xbsq]))
+    # Central node is always zero
+    if n % 2 == 1:
+        iv = hstack([0.0, iv])
+    return iv
+
+
+def _pbcf(n, theta):
+    r"""Asymptotic series expansion of parabolic cylinder function
+
+    The implementation is based on sections 3.2 and 3.3 from the
+    original paper. Compared to the published version this code
+    adds one more term to the asymptotic series. The detailed
+    formulas can be found at [parabolic-asymptotics]_. The evaluation
+    is done in a transformed variable :math:`\theta := \arccos(t)`
+    where :math:`t := x / \mu` and :math:`\mu := \sqrt{2n + 1}`.
+
+    Parameters
+    ----------
+    n : int
+        Quadrature order
+    theta : ndarray
+        Transformed position variable
+
+    Returns
+    -------
+    U : ndarray
+        Value of the parabolic cylinder function :math:`U(a, \theta)`.
+    Ud : ndarray
+        Value of the derivative :math:`U^{\prime}(a, \theta)` of
+        the parabolic cylinder function.
+
+    See Also
+    --------
+    roots_hermite_asy
+
+    References
+    ----------
+    .. [parabolic-asymptotics]
+       https://dlmf.nist.gov/12.10#vii
+    """
+    st = sin(theta)
+    ct = cos(theta)
+    # https://dlmf.nist.gov/12.10#vii
+    mu = 2.0*n + 1.0
+    # https://dlmf.nist.gov/12.10#E23
+    eta = 0.5*theta - 0.5*st*ct
+    # https://dlmf.nist.gov/12.10#E39
+    zeta = -(3.0*eta/2.0) ** (2.0/3.0)
+    # https://dlmf.nist.gov/12.10#E40
+    phi = (-zeta / st**2) ** (0.25)
+    # Coefficients
+    # https://dlmf.nist.gov/12.10#E43
+    a0 = 1.0
+    a1 = 0.10416666666666666667
+    a2 = 0.08355034722222222222
+    a3 = 0.12822657455632716049
+    a4 = 0.29184902646414046425
+    a5 = 0.88162726744375765242
+    b0 = 1.0
+    b1 = -0.14583333333333333333
+    b2 = -0.09874131944444444444
+    b3 = -0.14331205391589506173
+    b4 = -0.31722720267841354810
+    b5 = -0.94242914795712024914
+    # Polynomials
+    # https://dlmf.nist.gov/12.10#E9
+    # https://dlmf.nist.gov/12.10#E10
+    ctp = ct ** arange(16).reshape((-1,1))
+    u0 = 1.0
+    u1 = (1.0*ctp[3,:] - 6.0*ct) / 24.0
+    u2 = (-9.0*ctp[4,:] + 249.0*ctp[2,:] + 145.0) / 1152.0
+    u3 = (-4042.0*ctp[9,:] + 18189.0*ctp[7,:] - 28287.0*ctp[5,:]
+          - 151995.0*ctp[3,:] - 259290.0*ct) / 414720.0
+    u4 = (72756.0*ctp[10,:] - 321339.0*ctp[8,:] - 154982.0*ctp[6,:]
+          + 50938215.0*ctp[4,:] + 122602962.0*ctp[2,:] + 12773113.0) / 39813120.0
+    u5 = (82393456.0*ctp[15,:] - 617950920.0*ctp[13,:] + 1994971575.0*ctp[11,:]
+          - 3630137104.0*ctp[9,:] + 4433574213.0*ctp[7,:] - 37370295816.0*ctp[5,:]
+          - 119582875013.0*ctp[3,:] - 34009066266.0*ct) / 6688604160.0
+    v0 = 1.0
+    v1 = (1.0*ctp[3,:] + 6.0*ct) / 24.0
+    v2 = (15.0*ctp[4,:] - 327.0*ctp[2,:] - 143.0) / 1152.0
+    v3 = (-4042.0*ctp[9,:] + 18189.0*ctp[7,:] - 36387.0*ctp[5,:] 
+          + 238425.0*ctp[3,:] + 259290.0*ct) / 414720.0
+    v4 = (-121260.0*ctp[10,:] + 551733.0*ctp[8,:] - 151958.0*ctp[6,:]
+          - 57484425.0*ctp[4,:] - 132752238.0*ctp[2,:] - 12118727) / 39813120.0
+    v5 = (82393456.0*ctp[15,:] - 617950920.0*ctp[13,:] + 2025529095.0*ctp[11,:]
+          - 3750839308.0*ctp[9,:] + 3832454253.0*ctp[7,:] + 35213253348.0*ctp[5,:]
+          + 130919230435.0*ctp[3,:] + 34009066266*ct) / 6688604160.0
+    # Airy Evaluation (Bi and Bip unused)
+    Ai, Aip, Bi, Bip = airy(mu**(4.0/6.0) * zeta)
+    # Prefactor for U
+    P = 2.0*sqrt(pi) * mu**(1.0/6.0) * phi
+    # Terms for U
+    # https://dlmf.nist.gov/12.10#E42
+    phip = phi ** arange(6, 31, 6).reshape((-1,1))
+    A0 = b0*u0
+    A1 = (b2*u0 + phip[0,:]*b1*u1 + phip[1,:]*b0*u2) / zeta**3
+    A2 = (b4*u0 + phip[0,:]*b3*u1 + phip[1,:]*b2*u2 + phip[2,:]*b1*u3
+          + phip[3,:]*b0*u4) / zeta**6
+    B0 = -(a1*u0 + phip[0,:]*a0*u1) / zeta**2
+    B1 = -(a3*u0 + phip[0,:]*a2*u1 + phip[1,:]*a1*u2 + phip[2,:]*a0*u3) / zeta**5
+    B2 = -(a5*u0 + phip[0,:]*a4*u1 + phip[1,:]*a3*u2 + phip[2,:]*a2*u3
+           + phip[3,:]*a1*u4 + phip[4,:]*a0*u5) / zeta**8
+    # U
+    # https://dlmf.nist.gov/12.10#E35
+    U = P * (Ai * (A0 + A1/mu**2.0 + A2/mu**4.0) +
+             Aip * (B0 + B1/mu**2.0 + B2/mu**4.0) / mu**(8.0/6.0))
+    # Prefactor for derivative of U
+    Pd = sqrt(2.0*pi) * mu**(2.0/6.0) / phi
+    # Terms for derivative of U
+    # https://dlmf.nist.gov/12.10#E46
+    C0 = -(b1*v0 + phip[0,:]*b0*v1) / zeta
+    C1 = -(b3*v0 + phip[0,:]*b2*v1 + phip[1,:]*b1*v2 + phip[2,:]*b0*v3) / zeta**4
+    C2 = -(b5*v0 + phip[0,:]*b4*v1 + phip[1,:]*b3*v2 + phip[2,:]*b2*v3
+           + phip[3,:]*b1*v4 + phip[4,:]*b0*v5) / zeta**7
+    D0 = a0*v0
+    D1 = (a2*v0 + phip[0,:]*a1*v1 + phip[1,:]*a0*v2) / zeta**3
+    D2 = (a4*v0 + phip[0,:]*a3*v1 + phip[1,:]*a2*v2 + phip[2,:]*a1*v3
+          + phip[3,:]*a0*v4) / zeta**6
+    # Derivative of U
+    # https://dlmf.nist.gov/12.10#E36
+    Ud = Pd * (Ai * (C0 + C1/mu**2.0 + C2/mu**4.0) / mu**(4.0/6.0) +
+               Aip * (D0 + D1/mu**2.0 + D2/mu**4.0))
+    return U, Ud
+
+
+def _newton(n, x_initial, maxit=5):
+    """Newton iteration for polishing the asymptotic approximation
+    to the zeros of the Hermite polynomials.
+
+    Parameters
+    ----------
+    n : int
+        Quadrature order
+    x_initial : ndarray
+        Initial guesses for the roots
+    maxit : int
+        Maximal number of Newton iterations.
+        The default 5 is sufficient, usually
+        only one or two steps are needed.
+
+    Returns
+    -------
+    nodes : ndarray
+        Quadrature nodes
+    weights : ndarray
+        Quadrature weights
+
+    See Also
+    --------
+    roots_hermite_asy
+    """
+    # Variable transformation
+    mu = sqrt(2.0*n + 1.0)
+    t = x_initial / mu
+    theta = arccos(t)
+    # Newton iteration
+    for i in range(maxit):
+        u, ud = _pbcf(n, theta)
+        dtheta = u / (sqrt(2.0) * mu * sin(theta) * ud)
+        theta = theta + dtheta
+        if max(abs(dtheta)) < 1e-14:
+            break
+    # Undo variable transformation
+    x = mu * cos(theta)
+    # Central node is always zero
+    if n % 2 == 1:
+        x[0] = 0.0
+    # Compute weights
+    w = exp(-x**2) / (2.0*ud**2)
+    return x, w
+
+
+def _roots_hermite_asy(n):
+    r"""Gauss-Hermite (physicist's) quadrature for large n.
+
+    Computes the sample points and weights for Gauss-Hermite quadrature.
+    The sample points are the roots of the nth degree Hermite polynomial,
+    :math:`H_n(x)`. These sample points and weights correctly integrate
+    polynomials of degree :math:`2n - 1` or less over the interval
+    :math:`[-\infty, \infty]` with weight function :math:`f(x) = e^{-x^2}`.
+
+    This method relies on asymptotic expansions which work best for n > 150.
+    The algorithm has linear runtime making computation for very large n
+    feasible.
+
+    Parameters
+    ----------
+    n : int
+        quadrature order
+
+    Returns
+    -------
+    nodes : ndarray
+        Quadrature nodes
+    weights : ndarray
+        Quadrature weights
+
+    See Also
+    --------
+    roots_hermite
+
+    References
+    ----------
+    .. [townsend.trogdon.olver-2014]
+       Townsend, A. and Trogdon, T. and Olver, S. (2014)
+       *Fast computation of Gauss quadrature nodes and
+       weights on the whole real line*. :arXiv:`1410.5286`.
+
+    .. [townsend.trogdon.olver-2015]
+       Townsend, A. and Trogdon, T. and Olver, S. (2015)
+       *Fast computation of Gauss quadrature nodes and
+       weights on the whole real line*.
+       IMA Journal of Numerical Analysis
+       :doi:`10.1093/imanum/drv002`.
+    """
+    iv = _initial_nodes(n)
+    nodes, weights = _newton(n, iv)
+    # Combine with negative parts
+    if n % 2 == 0:
+        nodes = hstack([-nodes[::-1], nodes])
+        weights = hstack([weights[::-1], weights])
+    else:
+        nodes = hstack([-nodes[-1:0:-1], nodes])
+        weights = hstack([weights[-1:0:-1], weights])
+    # Scale weights
+    weights *= sqrt(pi) / sum(weights)
+    return nodes, weights
+
+
+def hermite(n, monic=False):
+    r"""Physicist's Hermite polynomial.
+
+    Defined by
+
+    .. math::
+
+        H_n(x) = (-1)^ne^{x^2}\frac{d^n}{dx^n}e^{-x^2};
+
+    :math:`H_n` is a polynomial of degree :math:`n`.
+
+    Parameters
+    ----------
+    n : int
+        Degree of the polynomial.
+    monic : bool, optional
+        If `True`, scale the leading coefficient to be 1. Default is
+        `False`.
+
+    Returns
+    -------
+    H : orthopoly1d
+        Physicist's Hermite polynomial.
+
+    Notes
+    -----
+    The polynomials :math:`H_n` are orthogonal over :math:`(-\infty,
+    \infty)` with weight function :math:`e^{-x^2}`.
+
+    Examples
+    --------
+    >>> from scipy import special
+    >>> import matplotlib.pyplot as plt
+    >>> import numpy as np
+
+    >>> p_monic = special.hermite(3, monic=True)
+    >>> p_monic
+    poly1d([ 1. ,  0. , -1.5,  0. ])
+    >>> p_monic(1)
+    -0.49999999999999983
+    >>> x = np.linspace(-3, 3, 400)
+    >>> y = p_monic(x)
+    >>> plt.plot(x, y)
+    >>> plt.title("Monic Hermite polynomial of degree 3")
+    >>> plt.xlabel("x")
+    >>> plt.ylabel("H_3(x)")
+    >>> plt.show()
+
+    """
+    if n < 0:
+        raise ValueError("n must be nonnegative.")
+
+    if n == 0:
+        n1 = n + 1
+    else:
+        n1 = n
+    x, w = roots_hermite(n1)
+    def wfunc(x):
+        return exp(-x * x)
+    if n == 0:
+        x, w = [], []
+    hn = 2**n * _gam(n + 1) * sqrt(pi)
+    kn = 2**n
+    p = orthopoly1d(x, w, hn, kn, wfunc, (-inf, inf), monic,
+                    lambda x: _ufuncs.eval_hermite(n, x))
+    return p
+
+# Hermite  2                         He_n(x)
+
+
+def roots_hermitenorm(n, mu=False):
+    r"""Gauss-Hermite (statistician's) quadrature.
+
+    Compute the sample points and weights for Gauss-Hermite
+    quadrature. The sample points are the roots of the nth degree
+    Hermite polynomial, :math:`He_n(x)`. These sample points and
+    weights correctly integrate polynomials of degree :math:`2n - 1`
+    or less over the interval :math:`[-\infty, \infty]` with weight
+    function :math:`w(x) = e^{-x^2/2}`. See 22.2.15 in [AS]_ for more
+    details.
+
+    Parameters
+    ----------
+    n : int
+        quadrature order.
+    mu : bool, optional
+        If True, return the sum of the weights, optional.
+
+    Returns
+    -------
+    x : ndarray
+        Sample points.
+    w : ndarray
+        Weights.
+    mu : float
+        Sum of the weights.
+
+    See Also
+    --------
+    scipy.integrate.fixed_quad
+    numpy.polynomial.hermite_e.hermegauss
+
+    Notes
+    -----
+    For small n up to 150 a modified version of the Golub-Welsch
+    algorithm is used. Nodes are computed from the eigenvalue
+    problem and improved by one step of a Newton iteration.
+    The weights are computed from the well-known analytical formula.
+
+    For n larger than 150 an optimal asymptotic algorithm is used
+    which computes nodes and weights in a numerical stable manner.
+    The algorithm has linear runtime making computation for very
+    large n (several thousand or more) feasible.
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+
+    """
+    m = int(n)
+    if n < 1 or n != m:
+        raise ValueError("n must be a positive integer.")
+
+    mu0 = np.sqrt(2.0*np.pi)
+    if n <= 150:
+        def an_func(k):
+            return 0.0 * k
+        def bn_func(k):
+            return np.sqrt(k)
+        f = _ufuncs.eval_hermitenorm
+        def df(n, x):
+            return n * _ufuncs.eval_hermitenorm(n - 1, x)
+        return _gen_roots_and_weights(m, mu0, an_func, bn_func, f, df, True, mu)
+    else:
+        nodes, weights = _roots_hermite_asy(m)
+        # Transform
+        nodes *= sqrt(2)
+        weights *= sqrt(2)
+        if mu:
+            return nodes, weights, mu0
+        else:
+            return nodes, weights
+
+
+def hermitenorm(n, monic=False):
+    r"""Probabilist's Hermite polynomial.
+
+    Defined by
+
+    .. math::
+
+        He_n(x) = (-1)^ne^{x^2/2}\frac{d^n}{dx^n}e^{-x^2/2};
+
+    :math:`He_n` is a polynomial of degree :math:`n`.
+
+    Parameters
+    ----------
+    n : int
+        Degree of the polynomial.
+    monic : bool, optional
+        If `True`, scale the leading coefficient to be 1. Default is
+        `False`.
+
+    Returns
+    -------
+    He : orthopoly1d
+        Probabilist's Hermite polynomial.
+
+    Notes
+    -----
+
+    The polynomials :math:`He_n` are orthogonal over :math:`(-\infty,
+    \infty)` with weight function :math:`e^{-x^2/2}`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.special import hermitenorm
+
+    >>> p_monic = hermitenorm(3)
+    >>> p_monic
+    poly1d([ 1.,  0., -3.,  0.])
+
+    Evaluate the probabilist's Hermite polynomial of degree 3 at x = 1:
+
+    >>> p_monic(1)
+    np.float64(-2.0)
+
+    Plot probabilist's Hermite polynomials of degree 0 to 4:
+    
+    >>> x = np.linspace(-3, 3, 100)
+    >>> fig, ax = plt.subplots()
+    >>> for i in range(5):
+    ...     ax.plot(x, hermitenorm(i)(x), label=f"n={i}")
+    >>> plt.title(f"Probabilist's Hermite polynomials $He_n$")
+    >>> plt.xlabel("x")
+    >>> plt.ylabel(rf"$He_n(x)$")
+    >>> plt.legend(loc="best")
+    >>> plt.show()
+
+    """
+    if n < 0:
+        raise ValueError("n must be nonnegative.")
+
+    if n == 0:
+        n1 = n + 1
+    else:
+        n1 = n
+    x, w = roots_hermitenorm(n1)
+    def wfunc(x):
+        return exp(-x * x / 2.0)
+    if n == 0:
+        x, w = [], []
+    hn = sqrt(2 * pi) * _gam(n + 1)
+    kn = 1.0
+    p = orthopoly1d(x, w, hn, kn, wfunc=wfunc, limits=(-inf, inf), monic=monic,
+                    eval_func=lambda x: _ufuncs.eval_hermitenorm(n, x))
+    return p
+
+# The remainder of the polynomials can be derived from the ones above.
+
+# Ultraspherical (Gegenbauer)        C^(alpha)_n(x)
+
+
+def roots_gegenbauer(n, alpha, mu=False):
+    r"""Gauss-Gegenbauer quadrature.
+
+    Compute the sample points and weights for Gauss-Gegenbauer
+    quadrature. The sample points are the roots of the nth degree
+    Gegenbauer polynomial, :math:`C^{\alpha}_n(x)`. These sample
+    points and weights correctly integrate polynomials of degree
+    :math:`2n - 1` or less over the interval :math:`[-1, 1]` with
+    weight function :math:`w(x) = (1 - x^2)^{\alpha - 1/2}`. See
+    22.2.3 in [AS]_ for more details.
+
+    Parameters
+    ----------
+    n : int
+        quadrature order.
+    alpha : float
+        alpha must be > -0.5.
+    mu : bool, optional
+        If True, return the sum of the weights, optional.
+
+    Returns
+    -------
+    x : ndarray
+        Sample points
+    w : ndarray
+        Weights
+    mu : float
+        Sum of the weights
+
+    See Also
+    --------
+    scipy.integrate.fixed_quad
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+
+    """
+    m = int(n)
+    if n < 1 or n != m:
+        raise ValueError("n must be a positive integer.")
+    if alpha < -0.5:
+        raise ValueError("alpha must be greater than -0.5.")
+    elif alpha == 0.0:
+        # C(n,0,x) == 0 uniformly, however, as alpha->0, C(n,alpha,x)->T(n,x)
+        # strictly, we should just error out here, since the roots are not
+        # really defined, but we used to return something useful, so let's
+        # keep doing so.
+        return roots_chebyt(n, mu)
+
+    if alpha <= 170:
+        mu0 = (np.sqrt(np.pi) * _ufuncs.gamma(alpha + 0.5)) \
+              / _ufuncs.gamma(alpha + 1)
+    else:
+        # For large alpha we use a Taylor series expansion around inf,
+        # expressed as a 6th order polynomial of a^-1 and using Horner's
+        # method to minimize computation and maximize precision
+        inv_alpha = 1. / alpha
+        coeffs = np.array([0.000207186, -0.00152206, -0.000640869,
+                           0.00488281, 0.0078125, -0.125, 1.])
+        mu0 = coeffs[0]
+        for term in range(1, len(coeffs)):
+            mu0 = mu0 * inv_alpha + coeffs[term]
+        mu0 = mu0 * np.sqrt(np.pi / alpha)
+    def an_func(k):
+        return 0.0 * k
+    def bn_func(k):
+        return np.sqrt(k * (k + 2 * alpha - 1) / (4 * (k + alpha) * (k + alpha - 1)))
+    def f(n, x):
+        return _ufuncs.eval_gegenbauer(n, alpha, x)
+    def df(n, x):
+        return (
+            -n * x * _ufuncs.eval_gegenbauer(n, alpha, x)
+            + (n + 2 * alpha - 1) * _ufuncs.eval_gegenbauer(n - 1, alpha, x)
+        ) / (1 - x ** 2)
+    return _gen_roots_and_weights(m, mu0, an_func, bn_func, f, df, True, mu)
+
+
+def gegenbauer(n, alpha, monic=False):
+    r"""Gegenbauer (ultraspherical) polynomial.
+
+    Defined to be the solution of the second-order linear ordinary differential equation
+
+    .. math::
+        (1 - x^2)\frac{d^2}{dx^2}C_n^{(\alpha)}(x)
+          - (2\alpha + 1)x\frac{d}{dx}C_n^{(\alpha)}(x)
+          + n(n + 2\alpha)C_n^{(\alpha)}(x) = 0
+
+    for :math:`\alpha > -1/2`; :math:`C_n^{(\alpha)}` is a polynomial
+    of degree :math:`n`.
+
+    Parameters
+    ----------
+    n : int
+        Degree of the polynomial.
+    alpha : float
+        Parameter, must be greater than -0.5.
+    monic : bool, optional
+        If `True`, scale the leading coefficient to be 1. Default is
+        `False`.
+
+    Returns
+    -------
+    C : orthopoly1d
+        Gegenbauer polynomial.
+
+    Notes
+    -----
+    The polynomials :math:`C_n^{(\alpha)}` are orthogonal on
+    :math:`[-1,1]` with respect to the weight function :math:`(1 - x^2)^{(\alpha -
+    1/2)}`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import special
+    >>> import matplotlib.pyplot as plt
+
+    We can initialize a variable ``p`` as a Gegenbauer polynomial using the
+    `gegenbauer` function and evaluate at a point ``x = 1``.
+
+    >>> p = special.gegenbauer(3, 0.5, monic=False)
+    >>> p
+    poly1d([ 2.5,  0. , -1.5,  0. ])
+    >>> p(1)
+    1.0
+
+    To evaluate ``p`` at various points ``x`` in the interval ``(-3, 3)``,
+    simply pass an array ``x`` to ``p`` as follows:
+
+    >>> x = np.linspace(-3, 3, 400)
+    >>> y = p(x)
+
+    We can then visualize ``x, y`` using `matplotlib.pyplot`.
+
+    >>> fig, ax = plt.subplots()
+    >>> ax.plot(x, y)
+    >>> ax.set_title("Gegenbauer (ultraspherical) polynomial of degree 3")
+    >>> ax.set_xlabel("x")
+    >>> ax.set_ylabel(r"$C_3^{(0.5)}(x)$")
+    >>> plt.show()
+
+    """
+    if not np.isfinite(alpha) or alpha <= -0.5 :
+        raise ValueError("`alpha` must be a finite number greater than -1/2")
+    base = jacobi(n, alpha - 0.5, alpha - 0.5, monic=monic)
+    if monic or n == 0:
+        return base
+    #  Abrahmowitz and Stegan 22.5.20
+    factor = (_gam(2*alpha + n) * _gam(alpha + 0.5) /
+              _gam(2*alpha) / _gam(alpha + 0.5 + n))
+    base._scale(factor)
+    base.__dict__['_eval_func'] = lambda x: _ufuncs.eval_gegenbauer(float(n),
+                                                                    alpha, x)
+    return base
+
+# Chebyshev of the first kind: T_n(x) =
+#     n! sqrt(pi) / _gam(n+1./2)* P^(-1/2,-1/2)_n(x)
+# Computed anew.
+
+
+def roots_chebyt(n, mu=False):
+    r"""Gauss-Chebyshev (first kind) quadrature.
+
+    Computes the sample points and weights for Gauss-Chebyshev
+    quadrature. The sample points are the roots of the nth degree
+    Chebyshev polynomial of the first kind, :math:`T_n(x)`. These
+    sample points and weights correctly integrate polynomials of
+    degree :math:`2n - 1` or less over the interval :math:`[-1, 1]`
+    with weight function :math:`w(x) = 1/\sqrt{1 - x^2}`. See 22.2.4
+    in [AS]_ for more details.
+
+    Parameters
+    ----------
+    n : int
+        quadrature order
+    mu : bool, optional
+        If True, return the sum of the weights, optional.
+
+    Returns
+    -------
+    x : ndarray
+        Sample points
+    w : ndarray
+        Weights
+    mu : float
+        Sum of the weights
+
+    See Also
+    --------
+    scipy.integrate.fixed_quad
+    numpy.polynomial.chebyshev.chebgauss
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+
+    """
+    m = int(n)
+    if n < 1 or n != m:
+        raise ValueError('n must be a positive integer.')
+    x = _ufuncs._sinpi(np.arange(-m + 1, m, 2) / (2*m))
+    w = np.full_like(x, pi/m)
+    if mu:
+        return x, w, pi
+    else:
+        return x, w
+
+
+def chebyt(n, monic=False):
+    r"""Chebyshev polynomial of the first kind.
+
+    Defined to be the solution of
+
+    .. math::
+        (1 - x^2)\frac{d^2}{dx^2}T_n(x) - x\frac{d}{dx}T_n(x)
+          + n^2T_n(x) = 0;
+
+    :math:`T_n` is a polynomial of degree :math:`n`.
+
+    Parameters
+    ----------
+    n : int
+        Degree of the polynomial.
+    monic : bool, optional
+        If `True`, scale the leading coefficient to be 1. Default is
+        `False`.
+
+    Returns
+    -------
+    T : orthopoly1d
+        Chebyshev polynomial of the first kind.
+
+    See Also
+    --------
+    chebyu : Chebyshev polynomial of the second kind.
+
+    Notes
+    -----
+    The polynomials :math:`T_n` are orthogonal over :math:`[-1, 1]`
+    with weight function :math:`(1 - x^2)^{-1/2}`.
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+
+    Examples
+    --------
+    Chebyshev polynomials of the first kind of order :math:`n` can
+    be obtained as the determinant of specific :math:`n \times n`
+    matrices. As an example we can check how the points obtained from
+    the determinant of the following :math:`3 \times 3` matrix
+    lay exactly on :math:`T_3`:
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.linalg import det
+    >>> from scipy.special import chebyt
+    >>> x = np.arange(-1.0, 1.0, 0.01)
+    >>> fig, ax = plt.subplots()
+    >>> ax.set_ylim(-2.0, 2.0)
+    >>> ax.set_title(r'Chebyshev polynomial $T_3$')
+    >>> ax.plot(x, chebyt(3)(x), label=rf'$T_3$')
+    >>> for p in np.arange(-1.0, 1.0, 0.1):
+    ...     ax.plot(p,
+    ...             det(np.array([[p, 1, 0], [1, 2*p, 1], [0, 1, 2*p]])),
+    ...             'rx')
+    >>> plt.legend(loc='best')
+    >>> plt.show()
+
+    They are also related to the Jacobi Polynomials
+    :math:`P_n^{(-0.5, -0.5)}` through the relation:
+
+    .. math::
+        P_n^{(-0.5, -0.5)}(x) = \frac{1}{4^n} \binom{2n}{n} T_n(x)
+
+    Let's verify it for :math:`n = 3`:
+
+    >>> from scipy.special import binom
+    >>> from scipy.special import jacobi
+    >>> x = np.arange(-1.0, 1.0, 0.01)
+    >>> np.allclose(jacobi(3, -0.5, -0.5)(x),
+    ...             1/64 * binom(6, 3) * chebyt(3)(x))
+    True
+
+    We can plot the Chebyshev polynomials :math:`T_n` for some values
+    of :math:`n`:
+
+    >>> x = np.arange(-1.5, 1.5, 0.01)
+    >>> fig, ax = plt.subplots()
+    >>> ax.set_ylim(-4.0, 4.0)
+    >>> ax.set_title(r'Chebyshev polynomials $T_n$')
+    >>> for n in np.arange(2,5):
+    ...     ax.plot(x, chebyt(n)(x), label=rf'$T_n={n}$')
+    >>> plt.legend(loc='best')
+    >>> plt.show()
+
+    """
+    if n < 0:
+        raise ValueError("n must be nonnegative.")
+
+    def wfunc(x):
+        return 1.0 / sqrt(1 - x * x)
+    if n == 0:
+        return orthopoly1d([], [], pi, 1.0, wfunc, (-1, 1), monic,
+                           lambda x: _ufuncs.eval_chebyt(n, x))
+    n1 = n
+    x, w, mu = roots_chebyt(n1, mu=True)
+    hn = pi / 2
+    kn = 2**(n - 1)
+    p = orthopoly1d(x, w, hn, kn, wfunc, (-1, 1), monic,
+                    lambda x: _ufuncs.eval_chebyt(n, x))
+    return p
+
+# Chebyshev of the second kind
+#    U_n(x) = (n+1)! sqrt(pi) / (2*_gam(n+3./2)) * P^(1/2,1/2)_n(x)
+
+
+def roots_chebyu(n, mu=False):
+    r"""Gauss-Chebyshev (second kind) quadrature.
+
+    Computes the sample points and weights for Gauss-Chebyshev
+    quadrature. The sample points are the roots of the nth degree
+    Chebyshev polynomial of the second kind, :math:`U_n(x)`. These
+    sample points and weights correctly integrate polynomials of
+    degree :math:`2n - 1` or less over the interval :math:`[-1, 1]`
+    with weight function :math:`w(x) = \sqrt{1 - x^2}`. See 22.2.5 in
+    [AS]_ for details.
+
+    Parameters
+    ----------
+    n : int
+        quadrature order
+    mu : bool, optional
+        If True, return the sum of the weights, optional.
+
+    Returns
+    -------
+    x : ndarray
+        Sample points
+    w : ndarray
+        Weights
+    mu : float
+        Sum of the weights
+
+    See Also
+    --------
+    scipy.integrate.fixed_quad
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+
+    """
+    m = int(n)
+    if n < 1 or n != m:
+        raise ValueError('n must be a positive integer.')
+    t = np.arange(m, 0, -1) * pi / (m + 1)
+    x = np.cos(t)
+    w = pi * np.sin(t)**2 / (m + 1)
+    if mu:
+        return x, w, pi / 2
+    else:
+        return x, w
+
+
+def chebyu(n, monic=False):
+    r"""Chebyshev polynomial of the second kind.
+
+    Defined to be the solution of
+
+    .. math::
+        (1 - x^2)\frac{d^2}{dx^2}U_n(x) - 3x\frac{d}{dx}U_n(x)
+          + n(n + 2)U_n(x) = 0;
+
+    :math:`U_n` is a polynomial of degree :math:`n`.
+
+    Parameters
+    ----------
+    n : int
+        Degree of the polynomial.
+    monic : bool, optional
+        If `True`, scale the leading coefficient to be 1. Default is
+        `False`.
+
+    Returns
+    -------
+    U : orthopoly1d
+        Chebyshev polynomial of the second kind.
+
+    See Also
+    --------
+    chebyt : Chebyshev polynomial of the first kind.
+
+    Notes
+    -----
+    The polynomials :math:`U_n` are orthogonal over :math:`[-1, 1]`
+    with weight function :math:`(1 - x^2)^{1/2}`.
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+
+    Examples
+    --------
+    Chebyshev polynomials of the second kind of order :math:`n` can
+    be obtained as the determinant of specific :math:`n \times n`
+    matrices. As an example we can check how the points obtained from
+    the determinant of the following :math:`3 \times 3` matrix
+    lay exactly on :math:`U_3`:
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.linalg import det
+    >>> from scipy.special import chebyu
+    >>> x = np.arange(-1.0, 1.0, 0.01)
+    >>> fig, ax = plt.subplots()
+    >>> ax.set_ylim(-2.0, 2.0)
+    >>> ax.set_title(r'Chebyshev polynomial $U_3$')
+    >>> ax.plot(x, chebyu(3)(x), label=rf'$U_3$')
+    >>> for p in np.arange(-1.0, 1.0, 0.1):
+    ...     ax.plot(p,
+    ...             det(np.array([[2*p, 1, 0], [1, 2*p, 1], [0, 1, 2*p]])),
+    ...             'rx')
+    >>> plt.legend(loc='best')
+    >>> plt.show()
+
+    They satisfy the recurrence relation:
+
+    .. math::
+        U_{2n-1}(x) = 2 T_n(x)U_{n-1}(x)
+
+    where :math:`T_n` is the Chebyshev polynomial of the first kind.
+    Let's verify it for :math:`n = 2`:
+
+    >>> from scipy.special import chebyt
+    >>> x = np.arange(-1.0, 1.0, 0.01)
+    >>> np.allclose(chebyu(3)(x), 2 * chebyt(2)(x) * chebyu(1)(x))
+    True
+
+    We can plot the Chebyshev polynomials :math:`U_n` for some values
+    of :math:`n`:
+
+    >>> x = np.arange(-1.0, 1.0, 0.01)
+    >>> fig, ax = plt.subplots()
+    >>> ax.set_ylim(-1.5, 1.5)
+    >>> ax.set_title(r'Chebyshev polynomials $U_n$')
+    >>> for n in np.arange(1,5):
+    ...     ax.plot(x, chebyu(n)(x), label=rf'$U_n={n}$')
+    >>> plt.legend(loc='best')
+    >>> plt.show()
+
+    """
+    base = jacobi(n, 0.5, 0.5, monic=monic)
+    if monic:
+        return base
+    factor = sqrt(pi) / 2.0 * _gam(n + 2) / _gam(n + 1.5)
+    base._scale(factor)
+    return base
+
+# Chebyshev of the first kind        C_n(x)
+
+
+def roots_chebyc(n, mu=False):
+    r"""Gauss-Chebyshev (first kind) quadrature.
+
+    Compute the sample points and weights for Gauss-Chebyshev
+    quadrature. The sample points are the roots of the nth degree
+    Chebyshev polynomial of the first kind, :math:`C_n(x)`. These
+    sample points and weights correctly integrate polynomials of
+    degree :math:`2n - 1` or less over the interval :math:`[-2, 2]`
+    with weight function :math:`w(x) = 1 / \sqrt{1 - (x/2)^2}`. See
+    22.2.6 in [AS]_ for more details.
+
+    Parameters
+    ----------
+    n : int
+        quadrature order
+    mu : bool, optional
+        If True, return the sum of the weights, optional.
+
+    Returns
+    -------
+    x : ndarray
+        Sample points
+    w : ndarray
+        Weights
+    mu : float
+        Sum of the weights
+
+    See Also
+    --------
+    scipy.integrate.fixed_quad
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+
+    """
+    x, w, m = roots_chebyt(n, True)
+    x *= 2
+    w *= 2
+    m *= 2
+    if mu:
+        return x, w, m
+    else:
+        return x, w
+
+
+def chebyc(n, monic=False):
+    r"""Chebyshev polynomial of the first kind on :math:`[-2, 2]`.
+
+    Defined as :math:`C_n(x) = 2T_n(x/2)`, where :math:`T_n` is the
+    nth Chebyshev polynomial of the first kind.
+
+    Parameters
+    ----------
+    n : int
+        Degree of the polynomial.
+    monic : bool, optional
+        If `True`, scale the leading coefficient to be 1. Default is
+        `False`.
+
+    Returns
+    -------
+    C : orthopoly1d
+        Chebyshev polynomial of the first kind on :math:`[-2, 2]`.
+
+    See Also
+    --------
+    chebyt : Chebyshev polynomial of the first kind.
+
+    Notes
+    -----
+    The polynomials :math:`C_n(x)` are orthogonal over :math:`[-2, 2]`
+    with weight function :math:`1/\sqrt{1 - (x/2)^2}`.
+
+    References
+    ----------
+    .. [1] Abramowitz and Stegun, "Handbook of Mathematical Functions"
+           Section 22. National Bureau of Standards, 1972.
+
+    Examples
+    --------
+    Evaluate the Chebyshev polynomial :math:`C_3` at :math:`x = 1`:
+
+    >>> import numpy as np
+    >>> from scipy.special import chebyc, chebyt
+    >>> np.isclose(chebyc(3)(1), -2.0)
+    True
+
+    The polynomial :math:`C_n` is a scaled Chebyshev polynomial of the
+    first kind:
+
+    >>> x = np.linspace(-2, 2, 5)
+    >>> np.allclose(chebyc(3)(x), 2 * chebyt(3)(x/2))
+    True
+
+    Plot :math:`C_n` for several values of :math:`n`:
+
+    >>> import matplotlib.pyplot as plt
+    >>> x = np.linspace(-2, 2, 400)
+    >>> fig, ax = plt.subplots()
+    >>> for n in range(4):
+    ...     ax.plot(x, chebyc(n)(x), label=rf"$C_{n}$")
+    >>> ax.set_title(r"Chebyshev polynomials $C_n$")
+    >>> ax.set_xlabel("x")
+    >>> ax.legend(loc="best")
+    >>> plt.show()
+    """
+    if n < 0:
+        raise ValueError("n must be nonnegative.")
+
+    if n == 0:
+        n1 = n + 1
+    else:
+        n1 = n
+    x, w = roots_chebyc(n1)
+    if n == 0:
+        x, w = [], []
+    hn = 4 * pi * ((n == 0) + 1)
+    kn = 1.0
+    p = orthopoly1d(x, w, hn, kn,
+                    wfunc=lambda x: 1.0 / sqrt(1 - x * x / 4.0),
+                    limits=(-2, 2), monic=monic)
+    if not monic:
+        p._scale(2.0 / p(2))
+        p.__dict__['_eval_func'] = lambda x: _ufuncs.eval_chebyc(n, x)
+    return p
+
+# Chebyshev of the second kind       S_n(x)
+
+
+def roots_chebys(n, mu=False):
+    r"""Gauss-Chebyshev (second kind) quadrature.
+
+    Compute the sample points and weights for Gauss-Chebyshev
+    quadrature. The sample points are the roots of the nth degree
+    Chebyshev polynomial of the second kind, :math:`S_n(x)`. These
+    sample points and weights correctly integrate polynomials of
+    degree :math:`2n - 1` or less over the interval :math:`[-2, 2]`
+    with weight function :math:`w(x) = \sqrt{1 - (x/2)^2}`. See 22.2.7
+    in [AS]_ for more details.
+
+    Parameters
+    ----------
+    n : int
+        quadrature order
+    mu : bool, optional
+        If True, return the sum of the weights, optional.
+
+    Returns
+    -------
+    x : ndarray
+        Sample points
+    w : ndarray
+        Weights
+    mu : float
+        Sum of the weights
+
+    See Also
+    --------
+    scipy.integrate.fixed_quad
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+
+    """
+    x, w, m = roots_chebyu(n, True)
+    x *= 2
+    w *= 2
+    m *= 2
+    if mu:
+        return x, w, m
+    else:
+        return x, w
+
+
+def chebys(n, monic=False):
+    r"""Chebyshev polynomial of the second kind on :math:`[-2, 2]`.
+
+    Defined as :math:`S_n(x) = U_n(x/2)` where :math:`U_n` is the
+    nth Chebyshev polynomial of the second kind.
+
+    Parameters
+    ----------
+    n : int
+        Degree of the polynomial.
+    monic : bool, optional
+        If `True`, scale the leading coefficient to be 1. Default is
+        `False`.
+
+    Returns
+    -------
+    S : orthopoly1d
+        Chebyshev polynomial of the second kind on :math:`[-2, 2]`.
+
+    See Also
+    --------
+    chebyu : Chebyshev polynomial of the second kind
+
+    Notes
+    -----
+    The polynomials :math:`S_n(x)` are orthogonal over :math:`[-2, 2]`
+    with weight function :math:`\sqrt{1 - (x/2)^2}`.
+
+    References
+    ----------
+    .. [1] Abramowitz and Stegun, "Handbook of Mathematical Functions"
+           Section 22. National Bureau of Standards, 1972.
+
+    Examples
+    --------
+    Evaluate the Chebyshev polynomial of the second kind :math:`S_3` at :math:`x = 1`:
+
+    >>> import numpy as np
+    >>> from scipy.special import chebys, chebyu
+    >>> np.isclose(chebys(3)(1), -1.0)
+    True
+
+    The polynomial :math:`S_n` is a scaled Chebyshev polynomial of the
+    second kind:
+
+    >>> x = np.linspace(-2, 2, 5)
+    >>> np.allclose(chebys(3)(x), chebyu(3)(x/2))
+    True
+
+    Plot :math:`S_n` for several values of :math:`n`:
+
+    >>> import matplotlib.pyplot as plt
+    >>> x = np.linspace(-2, 2, 400)
+    >>> fig, ax = plt.subplots()
+    >>> for n in range(4):
+    ...     ax.plot(x, chebys(n)(x), label=rf"$S_{n}$")
+    >>> ax.set_title(r"Chebyshev polynomials $S_n$")
+    >>> ax.set_xlabel("x")
+    >>> ax.legend(loc="best")
+    >>> plt.show()
+    """
+    if n < 0:
+        raise ValueError("n must be nonnegative.")
+
+    if n == 0:
+        n1 = n + 1
+    else:
+        n1 = n
+    x, w = roots_chebys(n1)
+    if n == 0:
+        x, w = [], []
+    hn = pi
+    kn = 1.0
+    p = orthopoly1d(x, w, hn, kn,
+                    wfunc=lambda x: sqrt(1 - x * x / 4.0),
+                    limits=(-2, 2), monic=monic)
+    if not monic:
+        factor = (n + 1.0) / p(2)
+        p._scale(factor)
+        p.__dict__['_eval_func'] = lambda x: _ufuncs.eval_chebys(n, x)
+    return p
+
+# Shifted Chebyshev of the first kind     T^*_n(x)
+
+
+def roots_sh_chebyt(n, mu=False):
+    r"""Gauss-Chebyshev (first kind, shifted) quadrature.
+
+    Compute the sample points and weights for Gauss-Chebyshev
+    quadrature. The sample points are the roots of the nth degree
+    shifted Chebyshev polynomial of the first kind, :math:`T_n(x)`.
+    These sample points and weights correctly integrate polynomials of
+    degree :math:`2n - 1` or less over the interval :math:`[0, 1]`
+    with weight function :math:`w(x) = 1/\sqrt{x - x^2}`. See 22.2.8
+    in [AS]_ for more details.
+
+    Parameters
+    ----------
+    n : int
+        quadrature order.
+    mu : bool, optional
+        If True, return the sum of the weights, optional.
+
+    Returns
+    -------
+    x : ndarray
+        Sample points.
+    w : ndarray
+        Weights.
+    mu : float
+        Sum of the weights.
+
+    See Also
+    --------
+    scipy.integrate.fixed_quad
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+
+    """
+    xw = roots_chebyt(n, mu)
+    return ((xw[0] + 1) / 2,) + xw[1:]
+
+
+def sh_chebyt(n, monic=False):
+    r"""Shifted Chebyshev polynomial of the first kind.
+
+    Defined as :math:`T^*_n(x) = T_n(2x - 1)` for :math:`T_n` the nth
+    Chebyshev polynomial of the first kind.
+
+    Parameters
+    ----------
+    n : int
+        Degree of the polynomial.
+    monic : bool, optional
+        If `True`, scale the leading coefficient to be 1. Default is
+        `False`.
+
+    Returns
+    -------
+    T : orthopoly1d
+        Shifted Chebyshev polynomial of the first kind.
+
+    Notes
+    -----
+    The polynomials :math:`T^*_n` are orthogonal over :math:`[0, 1]`
+    with weight function :math:`(x - x^2)^{-1/2}`.
+
+    Examples
+    --------
+    Evaluate the shifted Chebyshev polynomial of the first kind :math:`T^*_3` at
+    :math:`x = 0.75`:
+
+    >>> import numpy as np
+    >>> from scipy.special import chebyt, sh_chebyt
+    >>> np.isclose(sh_chebyt(3)(0.75), -1.0)
+    True
+
+    The polynomial :math:`T^*_n` is the Chebyshev polynomial
+    :math:`T_n` shifted from :math:`[-1, 1]` to :math:`[0, 1]`:
+
+    >>> x = np.linspace(0, 1, 5)
+    >>> np.allclose(sh_chebyt(3)(x), chebyt(3)(2*x - 1))
+    True
+
+    Plot :math:`T^*_n` for several values of :math:`n`:
+
+    >>> import matplotlib.pyplot as plt
+    >>> x = np.linspace(0, 1, 400)
+    >>> fig, ax = plt.subplots()
+    >>> for n in range(4):
+    ...     ax.plot(x, sh_chebyt(n)(x), label=rf"$T^*_{n}$")
+    >>> ax.set_title(r"Shifted Chebyshev polynomials $T^*_n$")
+    >>> ax.set_xlabel("x")
+    >>> ax.legend(loc="best")
+    >>> plt.show()
+
+    """
+    base = sh_jacobi(n, 0.0, 0.5, monic=monic)
+    if monic:
+        return base
+    if n > 0:
+        factor = 4**n / 2.0
+    else:
+        factor = 1.0
+    base._scale(factor)
+    return base
+
+
+# Shifted Chebyshev of the second kind    U^*_n(x)
+def roots_sh_chebyu(n, mu=False):
+    r"""Gauss-Chebyshev (second kind, shifted) quadrature.
+
+    Computes the sample points and weights for Gauss-Chebyshev
+    quadrature. The sample points are the roots of the nth degree
+    shifted Chebyshev polynomial of the second kind, :math:`U_n(x)`.
+    These sample points and weights correctly integrate polynomials of
+    degree :math:`2n - 1` or less over the interval :math:`[0, 1]`
+    with weight function :math:`w(x) = \sqrt{x - x^2}`. See 22.2.9 in
+    [AS]_ for more details.
+
+    Parameters
+    ----------
+    n : int
+        quadrature order
+    mu : bool, optional
+        If True, return the sum of the weights, optional.
+
+    Returns
+    -------
+    x : ndarray
+        Sample points
+    w : ndarray
+        Weights
+    mu : float
+        Sum of the weights
+
+    See Also
+    --------
+    scipy.integrate.fixed_quad
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+
+    """
+    x, w, m = roots_chebyu(n, True)
+    x = (x + 1) / 2
+    m_us = _ufuncs.beta(1.5, 1.5)
+    w *= m_us / m
+    if mu:
+        return x, w, m_us
+    else:
+        return x, w
+
+
+def sh_chebyu(n, monic=False):
+    r"""Shifted Chebyshev polynomial of the second kind.
+
+    Defined as :math:`U^*_n(x) = U_n(2x - 1)` for :math:`U_n` the nth
+    Chebyshev polynomial of the second kind.
+
+    Parameters
+    ----------
+    n : int
+        Degree of the polynomial.
+    monic : bool, optional
+        If `True`, scale the leading coefficient to be 1. Default is
+        `False`.
+
+    Returns
+    -------
+    U : orthopoly1d
+        Shifted Chebyshev polynomial of the second kind.
+
+    Notes
+    -----
+    The polynomials :math:`U^*_n` are orthogonal over :math:`[0, 1]`
+    with weight function :math:`(x - x^2)^{1/2}`.
+
+    Examples
+    --------
+    Evaluate the shifted Chebyshev polynomial of the second kind :math:`U^*_3` at
+    :math:`x = 0.75`:
+
+    >>> import numpy as np
+    >>> from scipy.special import chebyu, sh_chebyu
+    >>> np.isclose(sh_chebyu(3)(0.75), -1.0)
+    True
+
+    The polynomial :math:`U^*_n` is the Chebyshev polynomial
+    :math:`U_n` shifted from :math:`[-1, 1]` to :math:`[0, 1]`:
+
+    >>> x = np.linspace(0, 1, 5)
+    >>> np.allclose(sh_chebyu(3)(x), chebyu(3)(2*x - 1))
+    True
+
+    Plot :math:`U^*_n` for several values of :math:`n`:
+
+    >>> import matplotlib.pyplot as plt
+    >>> x = np.linspace(0, 1, 400)
+    >>> fig, ax = plt.subplots()
+    >>> for n in range(4):
+    ...     ax.plot(x, sh_chebyu(n)(x), label=rf"$U^*_{n}$")
+    >>> ax.set_title(r"Shifted Chebyshev polynomials $U^*_n$")
+    >>> ax.set_xlabel("x")
+    >>> ax.legend(loc="best")
+    >>> plt.show()
+
+    """
+    base = sh_jacobi(n, 2.0, 1.5, monic=monic)
+    if monic:
+        return base
+    factor = 4**n
+    base._scale(factor)
+    return base
+
+# Legendre
+
+
+def roots_legendre(n, mu=False):
+    r"""Gauss-Legendre quadrature.
+
+    Compute the sample points and weights for Gauss-Legendre
+    quadrature [GL]_. The sample points are the roots of the nth degree
+    Legendre polynomial :math:`P_n(x)`. These sample points and
+    weights correctly integrate polynomials of degree :math:`2n - 1`
+    or less over the interval :math:`[-1, 1]` with weight function
+    :math:`w(x) = 1`. See 2.2.10 in [AS]_ for more details.
+
+    Parameters
+    ----------
+    n : int
+        quadrature order.
+    mu : bool, optional
+        If True, return the sum of the weights, optional.
+
+    Returns
+    -------
+    x : ndarray
+        Sample points.
+    w : ndarray
+        Weights.
+    mu : float
+        Sum of the weights.
+
+    See Also
+    --------
+    scipy.integrate.fixed_quad
+    numpy.polynomial.legendre.leggauss
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+    .. [GL] Gauss-Legendre quadrature, Wikipedia,
+        https://en.wikipedia.org/wiki/Gauss%E2%80%93Legendre_quadrature
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.special import roots_legendre, eval_legendre
+    >>> roots, weights = roots_legendre(9)
+
+    ``roots`` holds the roots, and ``weights`` holds the weights for
+    Gauss-Legendre quadrature.
+
+    >>> roots
+    array([-0.96816024, -0.83603111, -0.61337143, -0.32425342,  0.        ,
+            0.32425342,  0.61337143,  0.83603111,  0.96816024])
+    >>> weights
+    array([0.08127439, 0.18064816, 0.2606107 , 0.31234708, 0.33023936,
+           0.31234708, 0.2606107 , 0.18064816, 0.08127439])
+
+    Verify that we have the roots by evaluating the degree 9 Legendre
+    polynomial at ``roots``.  All the values are approximately zero:
+
+    >>> eval_legendre(9, roots)
+    array([-8.88178420e-16, -2.22044605e-16,  1.11022302e-16,  1.11022302e-16,
+            0.00000000e+00, -5.55111512e-17, -1.94289029e-16,  1.38777878e-16,
+           -8.32667268e-17])
+
+    Here we'll show how the above values can be used to estimate the
+    integral from 1 to 2 of f(t) = t + 1/t with Gauss-Legendre
+    quadrature [GL]_.  First define the function and the integration
+    limits.
+
+    >>> def f(t):
+    ...    return t + 1/t
+    ...
+    >>> a = 1
+    >>> b = 2
+
+    We'll use ``integral(f(t), t=a, t=b)`` to denote the definite integral
+    of f from t=a to t=b.  The sample points in ``roots`` are from the
+    interval [-1, 1], so we'll rewrite the integral with the simple change
+    of variable::
+
+        x = 2/(b - a) * t - (a + b)/(b - a)
+
+    with inverse::
+
+        t = (b - a)/2 * x + (a + b)/2
+
+    Then::
+
+        integral(f(t), a, b) =
+            (b - a)/2 * integral(f((b-a)/2*x + (a+b)/2), x=-1, x=1)
+
+    We can approximate the latter integral with the values returned
+    by `roots_legendre`.
+
+    Map the roots computed above from [-1, 1] to [a, b].
+
+    >>> t = (b - a)/2 * roots + (a + b)/2
+
+    Approximate the integral as the weighted sum of the function values.
+
+    >>> (b - a)/2 * f(t).dot(weights)
+    2.1931471805599276
+
+    Compare that to the exact result, which is 3/2 + log(2):
+
+    >>> 1.5 + np.log(2)
+    2.1931471805599454
+
+    """
+    m = int(n)
+    if n < 1 or n != m:
+        raise ValueError("n must be a positive integer.")
+
+    mu0 = 2.0
+    def an_func(k):
+        return 0.0 * k
+    def bn_func(k):
+        return k * np.sqrt(1.0 / (4 * k * k - 1))
+    f = _ufuncs.eval_legendre
+    def df(n, x):
+        return (-n * x * _ufuncs.eval_legendre(n, x)
+                + n * _ufuncs.eval_legendre(n - 1, x)) / (1 - x ** 2)
+    return _gen_roots_and_weights(m, mu0, an_func, bn_func, f, df, True, mu)
+
+
+def legendre(n, monic=False):
+    r"""Legendre polynomial.
+
+    Defined to be the solution of
+
+    .. math::
+        \frac{d}{dx}\left[(1 - x^2)\frac{d}{dx}P_n(x)\right]
+          + n(n + 1)P_n(x) = 0;
+
+    :math:`P_n(x)` is a polynomial of degree :math:`n`.
+
+    Parameters
+    ----------
+    n : int
+        Degree of the polynomial.
+    monic : bool, optional
+        If `True`, scale the leading coefficient to be 1. Default is
+        `False`.
+
+    Returns
+    -------
+    P : orthopoly1d
+        Legendre polynomial.
+
+    Notes
+    -----
+    The polynomials :math:`P_n` are orthogonal over :math:`[-1, 1]`
+    with weight function 1.
+
+    Examples
+    --------
+    Generate the 3rd-order Legendre polynomial 1/2*(5x^3 + 0x^2 - 3x + 0):
+
+    >>> from scipy.special import legendre
+    >>> legendre(3)
+    poly1d([ 2.5,  0. , -1.5,  0. ])
+
+    """
+    if n < 0:
+        raise ValueError("n must be nonnegative.")
+
+    if n == 0:
+        n1 = n + 1
+    else:
+        n1 = n
+    x, w = roots_legendre(n1)
+    if n == 0:
+        x, w = [], []
+    hn = 2.0 / (2 * n + 1)
+    kn = _gam(2 * n + 1) / _gam(n + 1)**2 / 2.0**n
+    p = orthopoly1d(x, w, hn, kn, wfunc=lambda x: 1.0, limits=(-1, 1),
+                    monic=monic,
+                    eval_func=lambda x: _ufuncs.eval_legendre(n, x))
+    return p
+
+# Shifted Legendre              P^*_n(x)
+
+
+def roots_sh_legendre(n, mu=False):
+    r"""Gauss-Legendre (shifted) quadrature.
+
+    Compute the sample points and weights for Gauss-Legendre
+    quadrature. The sample points are the roots of the nth degree
+    shifted Legendre polynomial :math:`P^*_n(x)`. These sample points
+    and weights correctly integrate polynomials of degree :math:`2n -
+    1` or less over the interval :math:`[0, 1]` with weight function
+    :math:`w(x) = 1.0`. See 2.2.11 in [AS]_ for details.
+
+    Parameters
+    ----------
+    n : int
+        quadrature order
+    mu : bool, optional
+        If True, return the sum of the weights, optional.
+
+    Returns
+    -------
+    x : ndarray
+        Sample points
+    w : ndarray
+        Weights
+    mu : float
+        Sum of the weights
+
+    See Also
+    --------
+    scipy.integrate.fixed_quad
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+
+    Examples
+    --------
+
+    Compute nodes and weights for a 7th-order shifted Gauss-Legendre quadrature:
+
+    >>> from scipy.special import roots_sh_legendre, eval_sh_legendre
+    >>> x, w = roots_sh_legendre(7)
+    >>> x
+    array([0.02544604, 0.12923441, 0.29707742, 0.5, 0.70292258, 0.87076559,
+        0.97455396])
+    >>> w
+    array([0.06474248, 0.1398527, 0.19091503, 0.20897959, 0.19091503, 0.1398527,
+        0.06474248])
+
+    Verify that ``x`` are the roots of the degree-7 shifted Legendre polynomial:
+
+    >>> eval_sh_legendre(7, x)
+    array([5.55111512e-16, 1.11022302e-16,  3.33066907e-16,  0.00000000e+00,
+        -2.22044605e-16, -1.11022302e-16, -1.85962357e-15])
+
+    The sum of the weights for shifted Gauss-Legendre quadrature is always 1:
+
+    >>> x, w, mu = roots_sh_legendre(10, mu=True)
+    >>> mu 
+    1.0  # Sum of weights of shifted Gauss-Legendre quadrature is always 1
+
+    """
+    x, w = roots_legendre(n)
+    x = (x + 1) / 2
+    w /= 2
+    if mu:
+        return x, w, 1.0
+    else:
+        return x, w
+
+
+def sh_legendre(n, monic=False):
+    r"""
+    Shifted Legendre polynomial.
+
+    Defined as :math:`P^*_n(x) = P_n(2x - 1)` for :math:`P_n` the nth
+    Legendre polynomial.
+
+    Parameters
+    ----------
+    n : int
+        Degree of the polynomial.
+    monic : bool, optional
+        If `True`, scale the leading coefficient to be 1. Default is
+        `False`.
+
+    Returns
+    -------
+    P : orthopoly1d
+        Shifted Legendre polynomial.
+
+    See Also
+    --------
+    scipy.special.legendre
+    scipy.special.roots_sh_legendre
+
+    Notes
+    -----
+    The polynomials :math:`P^*_n` are orthogonal over :math:`[0, 1]`
+    with weight function 1.
+
+    Examples
+    --------
+    The shifted Legendre polynomials :math:`P_n^*` are related
+    to the non-shifted polynomials :math:`P_n` by
+    :math:`P_n^*(x) = P_n(2x - 1)`. We can verify this on the
+    interval :math:`[0, 1]`:
+
+    >>> import numpy as np
+    >>> from scipy.special import sh_legendre, legendre
+    >>> from scipy.integrate import trapezoid
+    >>> x = np.arange(0.0, 1.0, 0.01)
+    >>> n = 3
+    >>> np.allclose(sh_legendre(n)(x), legendre(n)(2*x - 1))
+    True
+
+    The polynomials :math:`P_n^*` satisfy a recurrence
+    relation obtained by the change of variables
+    :math:`t = 2x - 1` in the standard Legendre recurrence:
+
+    .. math::
+
+        (n+1) P_{n+1}^*(x) = (2n+1)(2x-1)\,P_n^*(x) - n\,P_{n-1}^*(x).
+
+    This can be easily checked on :math:`[0, 1]`
+    for :math:`n = 3`:
+
+    >>> n = 3
+    >>> x = np.linspace(0.0, 1.0, 101)
+    >>> lhs = (n + 1) * sh_legendre(n + 1)(x)
+    >>> rhs = (
+    ...     (2*n + 1) * (2*x - 1) * sh_legendre(n)(x)
+    ...     - n * sh_legendre(n - 1)(x)
+    ... )
+    >>> np.allclose(lhs, rhs)
+    True
+
+    Orthogonality over :math:`[0,1]` with weight 1 can be
+    checked numerically; for example, :math:`P_2^*`
+    is orthogonal to :math:`P_3^*`:
+
+    >>> x = np.linspace(0.0, 1.0, 400)
+    >>> y = sh_legendre(2)(x) * sh_legendre(3)(x)
+    >>> np.isclose(trapezoid(y, x), 0.0, atol=1e-12)
+    True
+    """
+    if n < 0:
+        raise ValueError("n must be nonnegative.")
+
+    def wfunc(x):
+        return 0.0 * x + 1.0
+    if n == 0:
+        return orthopoly1d([], [], 1.0, 1.0, wfunc, (0, 1), monic,
+                           lambda x: _ufuncs.eval_sh_legendre(n, x))
+    x, w = roots_sh_legendre(n)
+    hn = 1.0 / (2 * n + 1.0)
+    kn = _gam(2 * n + 1) / _gam(n + 1)**2
+    p = orthopoly1d(x, w, hn, kn, wfunc, limits=(0, 1), monic=monic,
+                    eval_func=lambda x: _ufuncs.eval_sh_legendre(n, x))
+    return p
+
+
+# Make the old root function names an alias for the new ones
+_modattrs = globals()
+for newfun, oldfun in _rootfuns_map.items():
+    _modattrs[oldfun] = _modattrs[newfun]
+    __all__.append(oldfun)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/_orthogonal.pyi b/venv/lib/python3.12/site-packages/scipy/special/_orthogonal.pyi
new file mode 100644
index 0000000000000000000000000000000000000000..d2f95577650a2c2112c088412a88d1ba6e5ca30a
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/_orthogonal.pyi
@@ -0,0 +1,329 @@
+from typing import (
+    Any,
+    Literal,
+    overload,
+)
+from collections.abc import Callable
+
+import numpy as np
+
+_IntegerType = int | np.integer
+_FloatingType = float | np.floating
+_PointsAndWeights = tuple[np.ndarray, np.ndarray]
+_PointsAndWeightsAndMu = tuple[np.ndarray, np.ndarray, float]
+
+_ArrayLike0D = bool | int | float | complex | str | bytes | np.generic
+
+__all__ = [
+    'legendre',
+    'chebyt',
+    'chebyu',
+    'chebyc',
+    'chebys',
+    'jacobi',
+    'laguerre',
+    'genlaguerre',
+    'hermite',
+    'hermitenorm',
+    'gegenbauer',
+    'sh_legendre',
+    'sh_chebyt',
+    'sh_chebyu',
+    'sh_jacobi',
+    'roots_legendre',
+    'roots_chebyt',
+    'roots_chebyu',
+    'roots_chebyc',
+    'roots_chebys',
+    'roots_jacobi',
+    'roots_laguerre',
+    'roots_genlaguerre',
+    'roots_hermite',
+    'roots_hermitenorm',
+    'roots_gegenbauer',
+    'roots_sh_legendre',
+    'roots_sh_chebyt',
+    'roots_sh_chebyu',
+    'roots_sh_jacobi',
+]
+
+@overload
+def roots_jacobi(
+        n: _IntegerType,
+        alpha: _FloatingType,
+        beta: _FloatingType,
+) -> _PointsAndWeights: ...
+@overload
+def roots_jacobi(
+        n: _IntegerType,
+        alpha: _FloatingType,
+        beta: _FloatingType,
+        mu: Literal[False],
+) -> _PointsAndWeights: ...
+@overload
+def roots_jacobi(
+        n: _IntegerType,
+        alpha: _FloatingType,
+        beta: _FloatingType,
+        mu: Literal[True],
+) -> _PointsAndWeightsAndMu: ...
+
+@overload
+def roots_sh_jacobi(
+        n: _IntegerType,
+        p1: _FloatingType,
+        q1: _FloatingType,
+) -> _PointsAndWeights: ...
+@overload
+def roots_sh_jacobi(
+        n: _IntegerType,
+        p1: _FloatingType,
+        q1: _FloatingType,
+        mu: Literal[False],
+) -> _PointsAndWeights: ...
+@overload
+def roots_sh_jacobi(
+        n: _IntegerType,
+        p1: _FloatingType,
+        q1: _FloatingType,
+        mu: Literal[True],
+) -> _PointsAndWeightsAndMu: ...
+
+@overload
+def roots_genlaguerre(
+        n: _IntegerType,
+        alpha: _FloatingType,
+) -> _PointsAndWeights: ...
+@overload
+def roots_genlaguerre(
+        n: _IntegerType,
+        alpha: _FloatingType,
+        mu: Literal[False],
+) -> _PointsAndWeights: ...
+@overload
+def roots_genlaguerre(
+        n: _IntegerType,
+        alpha: _FloatingType,
+        mu: Literal[True],
+) -> _PointsAndWeightsAndMu: ...
+
+@overload
+def roots_laguerre(n: _IntegerType) -> _PointsAndWeights: ...
+@overload
+def roots_laguerre(
+        n: _IntegerType,
+        mu: Literal[False],
+) -> _PointsAndWeights: ...
+@overload
+def roots_laguerre(
+        n: _IntegerType,
+        mu: Literal[True],
+) -> _PointsAndWeightsAndMu: ...
+
+@overload
+def roots_hermite(n: _IntegerType) -> _PointsAndWeights: ...
+@overload
+def roots_hermite(
+        n: _IntegerType,
+        mu: Literal[False],
+) -> _PointsAndWeights: ...
+@overload
+def roots_hermite(
+        n: _IntegerType,
+        mu: Literal[True],
+) -> _PointsAndWeightsAndMu: ...
+
+@overload
+def roots_hermitenorm(n: _IntegerType) -> _PointsAndWeights: ...
+@overload
+def roots_hermitenorm(
+        n: _IntegerType,
+        mu: Literal[False],
+) -> _PointsAndWeights: ...
+@overload
+def roots_hermitenorm(
+        n: _IntegerType,
+        mu: Literal[True],
+) -> _PointsAndWeightsAndMu: ...
+
+@overload
+def roots_gegenbauer(
+        n: _IntegerType,
+        alpha: _FloatingType,
+) -> _PointsAndWeights: ...
+@overload
+def roots_gegenbauer(
+        n: _IntegerType,
+        alpha: _FloatingType,
+        mu: Literal[False],
+) -> _PointsAndWeights: ...
+@overload
+def roots_gegenbauer(
+        n: _IntegerType,
+        alpha: _FloatingType,
+        mu: Literal[True],
+) -> _PointsAndWeightsAndMu: ...
+
+@overload
+def roots_chebyt(n: _IntegerType) -> _PointsAndWeights: ...
+@overload
+def roots_chebyt(
+        n: _IntegerType,
+        mu: Literal[False],
+) -> _PointsAndWeights: ...
+@overload
+def roots_chebyt(
+        n: _IntegerType,
+        mu: Literal[True],
+) -> _PointsAndWeightsAndMu: ...
+
+@overload
+def roots_chebyu(n: _IntegerType) -> _PointsAndWeights: ...
+@overload
+def roots_chebyu(
+        n: _IntegerType,
+        mu: Literal[False],
+) -> _PointsAndWeights: ...
+@overload
+def roots_chebyu(
+        n: _IntegerType,
+        mu: Literal[True],
+) -> _PointsAndWeightsAndMu: ...
+
+@overload
+def roots_chebyc(n: _IntegerType) -> _PointsAndWeights: ...
+@overload
+def roots_chebyc(
+        n: _IntegerType,
+        mu: Literal[False],
+) -> _PointsAndWeights: ...
+@overload
+def roots_chebyc(
+        n: _IntegerType,
+        mu: Literal[True],
+) -> _PointsAndWeightsAndMu: ...
+
+@overload
+def roots_chebys(n: _IntegerType) -> _PointsAndWeights: ...
+@overload
+def roots_chebys(
+        n: _IntegerType,
+        mu: Literal[False],
+) -> _PointsAndWeights: ...
+@overload
+def roots_chebys(
+        n: _IntegerType,
+        mu: Literal[True],
+) -> _PointsAndWeightsAndMu: ...
+
+@overload
+def roots_sh_chebyt(n: _IntegerType) -> _PointsAndWeights: ...
+@overload
+def roots_sh_chebyt(
+        n: _IntegerType,
+        mu: Literal[False],
+) -> _PointsAndWeights: ...
+@overload
+def roots_sh_chebyt(
+        n: _IntegerType,
+        mu: Literal[True],
+) -> _PointsAndWeightsAndMu: ...
+
+@overload
+def roots_sh_chebyu(n: _IntegerType) -> _PointsAndWeights: ...
+@overload
+def roots_sh_chebyu(
+        n: _IntegerType,
+        mu: Literal[False],
+) -> _PointsAndWeights: ...
+@overload
+def roots_sh_chebyu(
+        n: _IntegerType,
+        mu: Literal[True],
+) -> _PointsAndWeightsAndMu: ...
+
+@overload
+def roots_legendre(n: _IntegerType) -> _PointsAndWeights: ...
+@overload
+def roots_legendre(
+        n: _IntegerType,
+        mu: Literal[False],
+) -> _PointsAndWeights: ...
+@overload
+def roots_legendre(
+        n: _IntegerType,
+        mu: Literal[True],
+) -> _PointsAndWeightsAndMu: ...
+
+@overload
+def roots_sh_legendre(n: _IntegerType) -> _PointsAndWeights: ...
+@overload
+def roots_sh_legendre(
+        n: _IntegerType,
+        mu: Literal[False],
+) -> _PointsAndWeights: ...
+@overload
+def roots_sh_legendre(
+        n: _IntegerType,
+        mu: Literal[True],
+) -> _PointsAndWeightsAndMu: ...
+
+class orthopoly1d(np.poly1d):
+    def __init__(
+            self,
+            roots: np.typing.ArrayLike,
+            weights: np.typing.ArrayLike | None = None,
+            hn: float = ...,
+            kn: float = ...,
+            wfunc: Callable[[float], float] | None = None,
+            limits: tuple[float, float] | None = None,
+            monic: bool = ...,
+            eval_func: np.ufunc | None = None,
+    ) -> None: ...
+    @property
+    def limits(self) -> tuple[float, float]: ...
+    def weight_func(self, x: float) -> float: ...
+    @overload
+    def __call__(self, x: _ArrayLike0D) -> Any: ...
+    @overload
+    def __call__(self, x: np.poly1d) -> np.poly1d: ...  # type: ignore[overload-overlap]
+    @overload
+    def __call__(self, x: np.typing.ArrayLike) -> np.ndarray: ...
+
+def legendre(n: _IntegerType, monic: bool = ...) -> orthopoly1d: ...
+def chebyt(n: _IntegerType, monic: bool = ...) -> orthopoly1d: ...
+def chebyu(n: _IntegerType, monic: bool = ...) -> orthopoly1d: ...
+def chebyc(n: _IntegerType, monic: bool = ...) -> orthopoly1d: ...
+def chebys(n: _IntegerType, monic: bool = ...) -> orthopoly1d: ...
+def jacobi(
+        n: _IntegerType,
+        alpha: _FloatingType,
+        beta: _FloatingType,
+        monic: bool = ...,
+) -> orthopoly1d: ...
+def laguerre(n: _IntegerType, monic: bool = ...) -> orthopoly1d: ...
+def genlaguerre(
+        n: _IntegerType,
+        alpha: _FloatingType,
+        monic: bool = ...,
+) -> orthopoly1d: ...
+def hermite(n: _IntegerType, monic: bool = ...) -> orthopoly1d: ...
+def hermitenorm(n: _IntegerType, monic: bool = ...) -> orthopoly1d: ...
+def gegenbauer(
+        n: _IntegerType,
+        alpha: _FloatingType,
+        monic: bool = ...,
+) -> orthopoly1d: ...
+def sh_legendre(n: _IntegerType, monic: bool = ...) -> orthopoly1d: ...
+def sh_chebyt(n: _IntegerType, monic: bool = ...) -> orthopoly1d: ...
+def sh_chebyu(n: _IntegerType, monic: bool = ...) -> orthopoly1d: ...
+def sh_jacobi(
+        n: _IntegerType,
+        p: _FloatingType,
+        q: _FloatingType,
+        monic: bool = ...,
+) -> orthopoly1d: ...
+
+# These functions are not public, but still need stubs because they
+# get checked in the tests.
+def _roots_hermite_asy(n: _IntegerType) -> _PointsAndWeights: ...
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diff --git a/venv/lib/python3.12/site-packages/scipy/special/_precompute/cosine_cdf.py b/venv/lib/python3.12/site-packages/scipy/special/_precompute/cosine_cdf.py
new file mode 100644
index 0000000000000000000000000000000000000000..662c12bc74b31478c87471fbd1cce8bea285e765
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/_precompute/cosine_cdf.py
@@ -0,0 +1,17 @@
+import mpmath
+
+
+def f(x):
+    return (mpmath.pi + x + mpmath.sin(x)) / (2*mpmath.pi)
+
+
+# Note: 40 digits might be overkill; a few more digits than the default
+# might be sufficient.
+mpmath.mp.dps = 40
+ts = mpmath.taylor(f, -mpmath.pi, 20)
+p, q = mpmath.pade(ts, 9, 10)
+
+p = [float(c) for c in p]
+q = [float(c) for c in q]
+print('p =', p)
+print('q =', q)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/_precompute/expn_asy.py b/venv/lib/python3.12/site-packages/scipy/special/_precompute/expn_asy.py
new file mode 100644
index 0000000000000000000000000000000000000000..3491b8acd588a2cacfc48f0a3a60c6ae88c3e8c5
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/_precompute/expn_asy.py
@@ -0,0 +1,54 @@
+"""Precompute the polynomials for the asymptotic expansion of the
+generalized exponential integral.
+
+Sources
+-------
+[1] NIST, Digital Library of Mathematical Functions,
+    https://dlmf.nist.gov/8.20#ii
+
+"""
+import os
+
+try:
+    import sympy
+    from sympy import Poly
+    x = sympy.symbols('x')
+except ImportError:
+    pass
+
+
+def generate_A(K):
+    A = [Poly(1, x)]
+    for k in range(K):
+        A.append(Poly(1 - 2*k*x, x)*A[k] + Poly(x*(x + 1))*A[k].diff())
+    return A
+
+
+WARNING = """\
+/* This file was automatically generated by _precompute/expn_asy.py.
+ * Do not edit it manually!
+ */
+"""
+
+
+def main():
+    print(__doc__)
+    fn = os.path.join('..', 'cephes', 'expn.h')
+
+    K = 12
+    A = generate_A(K)
+    with open(fn + '.new', 'w') as f:
+        f.write(WARNING)
+        f.write(f"#define nA {len(A)}\n")
+        for k, Ak in enumerate(A):
+            ', '.join([str(x.evalf(18)) for x in Ak.coeffs()])
+            f.write(f"static const double A{k}[] = {{tmp}};\n")
+        ", ".join([f"A{k}" for k in range(K + 1)])
+        f.write("static const double *A[] = {{tmp}};\n")
+        ", ".join([str(Ak.degree()) for Ak in A])
+        f.write("static const int Adegs[] = {{tmp}};\n")
+    os.rename(fn + '.new', fn)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/venv/lib/python3.12/site-packages/scipy/special/_precompute/gammainc_asy.py b/venv/lib/python3.12/site-packages/scipy/special/_precompute/gammainc_asy.py
new file mode 100644
index 0000000000000000000000000000000000000000..98035457c78706ae01c02273ae1ab458b4ca140d
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/_precompute/gammainc_asy.py
@@ -0,0 +1,116 @@
+"""
+Precompute coefficients of Temme's asymptotic expansion for gammainc.
+
+This takes about 8 hours to run on a 2.3 GHz Macbook Pro with 4GB ram.
+
+Sources:
+[1] NIST, "Digital Library of Mathematical Functions",
+    https://dlmf.nist.gov/
+
+"""
+import os
+from scipy.special._precompute.utils import lagrange_inversion
+
+try:
+    import mpmath as mp
+except ImportError:
+    pass
+
+
+def compute_a(n):
+    """a_k from DLMF 5.11.6"""
+    a = [mp.sqrt(2)/2]
+    for k in range(1, n):
+        ak = a[-1]/k
+        for j in range(1, len(a)):
+            ak -= a[j]*a[-j]/(j + 1)
+        ak /= a[0]*(1 + mp.mpf(1)/(k + 1))
+        a.append(ak)
+    return a
+
+
+def compute_g(n):
+    """g_k from DLMF 5.11.3/5.11.5"""
+    a = compute_a(2*n)
+    g = [mp.sqrt(2)*mp.rf(0.5, k)*a[2*k] for k in range(n)]
+    return g
+
+
+def eta(lam):
+    """Function from DLMF 8.12.1 shifted to be centered at 0."""
+    if lam > 0:
+        return mp.sqrt(2*(lam - mp.log(lam + 1)))
+    elif lam < 0:
+        return -mp.sqrt(2*(lam - mp.log(lam + 1)))
+    else:
+        return 0
+
+
+def compute_alpha(n):
+    """alpha_n from DLMF 8.12.13"""
+    coeffs = mp.taylor(eta, 0, n - 1)
+    return lagrange_inversion(coeffs)
+
+
+def compute_d(K, N):
+    """d_{k, n} from DLMF 8.12.12"""
+    M = N + 2*K
+    d0 = [-mp.mpf(1)/3]
+    alpha = compute_alpha(M + 2)
+    for n in range(1, M):
+        d0.append((n + 2)*alpha[n+2])
+    d = [d0]
+    g = compute_g(K)
+    for k in range(1, K):
+        dk = []
+        for n in range(M - 2*k):
+            dk.append((-1)**k*g[k]*d[0][n] + (n + 2)*d[k-1][n+2])
+        d.append(dk)
+    for k in range(K):
+        d[k] = d[k][:N]
+    return d
+
+
+header = \
+r"""/* This file was automatically generated by _precomp/gammainc.py.
+ * Do not edit it manually!
+ */
+
+#ifndef IGAM_H
+#define IGAM_H
+
+#define K {}
+#define N {}
+
+static const double d[K][N] =
+{{"""
+
+footer = \
+r"""
+#endif
+"""
+
+
+def main():
+    print(__doc__)
+    K = 25
+    N = 25
+    with mp.workdps(50):
+        d = compute_d(K, N)
+    fn = os.path.join(os.path.dirname(__file__), '..', 'cephes', 'igam.h')
+    with open(fn + '.new', 'w') as f:
+        f.write(header.format(K, N))
+        for k, row in enumerate(d):
+            row = [mp.nstr(x, 17, min_fixed=0, max_fixed=0) for x in row]
+            f.write('{')
+            f.write(", ".join(row))
+            if k < K - 1:
+                f.write('},\n')
+            else:
+                f.write('}};\n')
+        f.write(footer)
+    os.rename(fn + '.new', fn)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/venv/lib/python3.12/site-packages/scipy/special/_precompute/gammainc_data.py b/venv/lib/python3.12/site-packages/scipy/special/_precompute/gammainc_data.py
new file mode 100644
index 0000000000000000000000000000000000000000..ebbe39f6159fb80c424dbb38eedeba46bd8cccf2
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/_precompute/gammainc_data.py
@@ -0,0 +1,124 @@
+"""Compute gammainc and gammaincc for large arguments and parameters
+and save the values to data files for use in tests. We can't just
+compare to mpmath's gammainc in test_mpmath.TestSystematic because it
+would take too long.
+
+Note that mpmath's gammainc is computed using hypercomb, but since it
+doesn't allow the user to increase the maximum number of terms used in
+the series it doesn't converge for many arguments. To get around this
+we copy the mpmath implementation but use more terms.
+
+This takes about 17 minutes to run on a 2.3 GHz Macbook Pro with 4GB
+ram.
+
+Sources:
+[1] Fredrik Johansson and others. mpmath: a Python library for
+    arbitrary-precision floating-point arithmetic (version 0.19),
+    December 2013. http://mpmath.org/.
+
+"""
+import os
+from time import time
+import numpy as np
+from numpy import pi
+
+from scipy.special._mptestutils import mpf2float
+
+try:
+    import mpmath as mp
+except ImportError:
+    pass
+
+
+def gammainc(a, x, dps=50, maxterms=10**8):
+    """Compute gammainc exactly like mpmath does but allow for more
+    summands in hypercomb. See
+
+    mpmath/functions/expintegrals.py#L134
+
+    in the mpmath GitHub repository.
+
+    """
+    with mp.workdps(dps):
+        z, a, b = mp.mpf(a), mp.mpf(x), mp.mpf(x)
+        G = [z]
+        negb = mp.fneg(b, exact=True)
+
+        def h(z):
+            T1 = [mp.exp(negb), b, z], [1, z, -1], [], G, [1], [1+z], b
+            return (T1,)
+
+        res = mp.hypercomb(h, [z], maxterms=maxterms)
+        return mpf2float(res)
+
+
+def gammaincc(a, x, dps=50, maxterms=10**8):
+    """Compute gammaincc exactly like mpmath does but allow for more
+    terms in hypercomb. See
+
+    mpmath/functions/expintegrals.py#L187
+
+    in the mpmath GitHub repository.
+
+    """
+    with mp.workdps(dps):
+        z, a = a, x
+
+        if mp.isint(z):
+            try:
+                # mpmath has a fast integer path
+                return mpf2float(mp.gammainc(z, a=a, regularized=True))
+            except mp.libmp.NoConvergence:
+                pass
+        nega = mp.fneg(a, exact=True)
+        G = [z]
+        # Use 2F0 series when possible; fall back to lower gamma representation
+        try:
+            def h(z):
+                r = z-1
+                return [([mp.exp(nega), a], [1, r], [], G, [1, -r], [], 1/nega)]
+            return mpf2float(mp.hypercomb(h, [z], force_series=True))
+        except mp.libmp.NoConvergence:
+            def h(z):
+                T1 = [], [1, z-1], [z], G, [], [], 0
+                T2 = [-mp.exp(nega), a, z], [1, z, -1], [], G, [1], [1+z], a
+                return T1, T2
+            return mpf2float(mp.hypercomb(h, [z], maxterms=maxterms))
+
+
+def main():
+    t0 = time()
+    # It would be nice to have data for larger values, but either this
+    # requires prohibitively large precision (dps > 800) or mpmath has
+    # a bug. For example, gammainc(1e20, 1e20, dps=800) returns a
+    # value around 0.03, while the true value should be close to 0.5
+    # (DLMF 8.12.15).
+    print(__doc__)
+    pwd = os.path.dirname(__file__)
+    r = np.logspace(4, 14, 30)
+    ltheta = np.logspace(np.log10(pi/4), np.log10(np.arctan(0.6)), 30)
+    utheta = np.logspace(np.log10(pi/4), np.log10(np.arctan(1.4)), 30)
+
+    regimes = [(gammainc, ltheta), (gammaincc, utheta)]
+    for func, theta in regimes:
+        rg, thetag = np.meshgrid(r, theta)
+        a, x = rg*np.cos(thetag), rg*np.sin(thetag)
+        a, x = a.flatten(), x.flatten()
+        dataset = []
+        for i, (a0, x0) in enumerate(zip(a, x)):
+            if func == gammaincc:
+                # Exploit the fast integer path in gammaincc whenever
+                # possible so that the computation doesn't take too
+                # long
+                a0, x0 = np.floor(a0), np.floor(x0)
+            dataset.append((a0, x0, func(a0, x0)))
+        dataset = np.array(dataset)
+        filename = os.path.join(pwd, '..', 'tests', 'data', 'local',
+                                f'{func.__name__}.txt')
+        np.savetxt(filename, dataset)
+
+    print(f"{(time() - t0)/60} minutes elapsed")
+
+
+if __name__ == "__main__":
+    main()
diff --git a/venv/lib/python3.12/site-packages/scipy/special/_precompute/hyp2f1_data.py b/venv/lib/python3.12/site-packages/scipy/special/_precompute/hyp2f1_data.py
new file mode 100644
index 0000000000000000000000000000000000000000..c4adf14f49184bf75048a28a823909d24e778e04
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/_precompute/hyp2f1_data.py
@@ -0,0 +1,484 @@
+"""This script evaluates scipy's implementation of hyp2f1 against mpmath's.
+
+Author: Albert Steppi
+
+This script is long running and generates a large output file. With default
+arguments, the generated file is roughly 700MB in size and it takes around
+40 minutes using an Intel(R) Core(TM) i5-8250U CPU with n_jobs set to 8
+(full utilization). There are optional arguments which can be used to restrict
+(or enlarge) the computations performed. These are described below.
+The output of this script can be analyzed to identify suitable test cases and
+to find parameter and argument regions where hyp2f1 needs to be improved.
+
+The script has one mandatory positional argument for specifying the path to
+the location where the output file is to be placed, and 4 optional arguments
+--n_jobs, --grid_size, --regions, and --parameter_groups. --n_jobs specifies
+the number of processes to use if running in parallel. The default value is 1.
+The other optional arguments are explained below.
+
+Produces a tab separated values file with 11 columns. The first four columns
+contain the parameters a, b, c and the argument z. The next two contain |z| and
+a region code for which region of the complex plane belongs to. The regions are
+
+    0) z == 1
+    1) |z| < 0.9 and real(z) >= 0
+    2) |z| <= 1 and real(z) < 0
+    3) 0.9 <= |z| <= 1 and |1 - z| < 0.9:
+    4) 0.9 <= |z| <= 1 and |1 - z| >= 0.9 and real(z) >= 0:
+    5) 1 < |z| < 1.1 and |1 - z| >= 0.9 and real(z) >= 0
+    6) |z| > 1 and not in 5)
+
+The --regions optional argument allows the user to specify a list of regions
+to which computation will be restricted.
+
+Parameters a, b, c are taken from a 10 * 10 * 10 grid with values at
+
+    -16, -8, -4, -2, -1, 1, 2, 4, 8, 16
+
+with random perturbations applied.
+
+There are 9 parameter groups handling the following cases.
+
+    1) A, B, C, B - A, C - A, C - B, C - A - B all non-integral.
+    2) B - A integral
+    3) C - A integral
+    4) C - B integral
+    5) C - A - B integral
+    6) A integral
+    7) B integral
+    8) C integral
+    9) Wider range with c - a - b > 0.
+
+The seventh column of the output file is an integer between 1 and 8 specifying
+the parameter group as above.
+
+The --parameter_groups optional argument allows the user to specify a list of
+parameter groups to which computation will be restricted.
+
+The argument z is taken from a grid in the box
+    -box_size <= real(z) <= box_size, -box_size <= imag(z) <= box_size.
+with grid size specified using the optional command line argument --grid_size,
+and box_size specified with the command line argument --box_size.
+The default value of grid_size is 20 and the default value of box_size is 2.0,
+yielding a 20 * 20 grid in the box with corners -2-2j, -2+2j, 2-2j, 2+2j.
+
+The final four columns have the expected value of hyp2f1 for the given
+parameters and argument as calculated with mpmath, the observed value
+calculated with scipy's hyp2f1, the relative error, and the absolute error.
+
+As special cases of hyp2f1 are moved from the original Fortran implementation
+into Cython, this script can be used to ensure that no regressions occur and
+to point out where improvements are needed.
+"""
+
+
+import os
+import csv
+import argparse
+import numpy as np
+from itertools import product
+from multiprocessing import Pool
+
+
+from scipy.special import hyp2f1
+from scipy.special.tests.test_hyp2f1 import mp_hyp2f1
+
+
+def get_region(z):
+    """Assign numbers for regions where hyp2f1 must be handled differently."""
+    if z == 1 + 0j:
+        return 0
+    elif abs(z) < 0.9 and z.real >= 0:
+        return 1
+    elif abs(z) <= 1 and z.real < 0:
+        return 2
+    elif 0.9 <= abs(z) <= 1 and abs(1 - z) < 0.9:
+        return 3
+    elif 0.9 <= abs(z) <= 1 and abs(1 - z) >= 0.9:
+        return 4
+    elif 1 < abs(z) < 1.1 and abs(1 - z) >= 0.9 and z.real >= 0:
+        return 5
+    else:
+        return 6
+
+
+def get_result(a, b, c, z, group):
+    """Get results for given parameter and value combination."""
+    expected, observed = mp_hyp2f1(a, b, c, z), hyp2f1(a, b, c, z)
+    if (
+            np.isnan(observed) and np.isnan(expected) or
+            expected == observed
+    ):
+        relative_error = 0.0
+        absolute_error = 0.0
+    elif np.isnan(observed):
+        # Set error to infinity if result is nan when not expected to be.
+        # Makes results easier to interpret.
+        relative_error = float("inf")
+        absolute_error = float("inf")
+    else:
+        absolute_error = abs(expected - observed)
+        relative_error = absolute_error / abs(expected)
+
+    return (
+        a,
+        b,
+        c,
+        z,
+        abs(z),
+        get_region(z),
+        group,
+        expected,
+        observed,
+        relative_error,
+        absolute_error,
+    )
+
+
+def get_result_no_mp(a, b, c, z, group):
+    """Get results for given parameter and value combination."""
+    expected, observed = complex('nan'), hyp2f1(a, b, c, z)
+    relative_error, absolute_error = float('nan'), float('nan')
+    return (
+        a,
+        b,
+        c,
+        z,
+        abs(z),
+        get_region(z),
+        group,
+        expected,
+        observed,
+        relative_error,
+        absolute_error,
+    )
+
+
+def get_results(params, Z, n_jobs=1, compute_mp=True):
+    """Batch compute results for multiple parameter and argument values.
+
+    Parameters
+    ----------
+    params : iterable
+        iterable of tuples of floats (a, b, c) specifying parameter values
+        a, b, c for hyp2f1
+    Z : iterable of complex
+        Arguments at which to evaluate hyp2f1
+    n_jobs : Optional[int]
+        Number of jobs for parallel execution.
+
+    Returns
+    -------
+    list
+        List of tuples of results values. See return value in source code
+        of `get_result`.
+    """
+    input_ = (
+        (a, b, c, z, group) for (a, b, c, group), z in product(params, Z)
+    )
+
+    with Pool(n_jobs) as pool:
+        rows = pool.starmap(
+            get_result if compute_mp else get_result_no_mp,
+            input_
+        )
+    return rows
+
+
+def _make_hyp2f1_test_case(a, b, c, z, rtol):
+    """Generate string for single test case as used in test_hyp2f1.py."""
+    expected = mp_hyp2f1(a, b, c, z)
+    return (
+        "    pytest.param(\n"
+        "        Hyp2f1TestCase(\n"
+        f"            a={a},\n"
+        f"            b={b},\n"
+        f"            c={c},\n"
+        f"            z={z},\n"
+        f"            expected={expected},\n"
+        f"            rtol={rtol},\n"
+        "        ),\n"
+        "    ),"
+    )
+
+
+def make_hyp2f1_test_cases(rows):
+    """Generate string for a list of test cases for test_hyp2f1.py.
+
+    Parameters
+    ----------
+    rows : list
+        List of lists of the form [a, b, c, z, rtol] where a, b, c, z are
+        parameters and the argument for hyp2f1 and rtol is an expected
+        relative error for the associated test case.
+
+    Returns
+    -------
+    str
+        String for a list of test cases. The output string can be printed
+        or saved to a file and then copied into an argument for
+        `pytest.mark.parameterize` within `scipy.special.tests.test_hyp2f1.py`.
+    """
+    result = "[\n"
+    result += '\n'.join(
+        _make_hyp2f1_test_case(a, b, c, z, rtol)
+        for a, b, c, z, rtol in rows
+    )
+    result += "\n]"
+    return result
+
+
+def main(
+        outpath,
+        n_jobs=1,
+        box_size=2.0,
+        grid_size=20,
+        regions=None,
+        parameter_groups=None,
+        compute_mp=True,
+):
+    outpath = os.path.realpath(os.path.expanduser(outpath))
+
+    random_state = np.random.RandomState(1234)
+    # Parameters a, b, c selected near these values.
+    root_params = np.array(
+        [-16, -8, -4, -2, -1, 1, 2, 4, 8, 16]
+    )
+    # Perturbations to apply to root values.
+    perturbations = 0.1 * random_state.random_sample(
+        size=(3, len(root_params))
+    )
+
+    params = []
+    # Parameter group 1
+    # -----------------
+    # No integer differences. This has been confirmed for the above seed.
+    A = root_params + perturbations[0, :]
+    B = root_params + perturbations[1, :]
+    C = root_params + perturbations[2, :]
+    params.extend(
+        sorted(
+            ((a, b, c, 1) for a, b, c in product(A, B, C)),
+            key=lambda x: max(abs(x[0]), abs(x[1])),
+        )
+    )
+
+    # Parameter group 2
+    # -----------------
+    # B - A an integer
+    A = root_params + 0.5
+    B = root_params + 0.5
+    C = root_params + perturbations[1, :]
+    params.extend(
+        sorted(
+            ((a, b, c, 2) for a, b, c in product(A, B, C)),
+            key=lambda x: max(abs(x[0]), abs(x[1])),
+        )
+    )
+
+    # Parameter group 3
+    # -----------------
+    # C - A an integer
+    A = root_params + 0.5
+    B = root_params + perturbations[1, :]
+    C = root_params + 0.5
+    params.extend(
+        sorted(
+            ((a, b, c, 3) for a, b, c in product(A, B, C)),
+            key=lambda x: max(abs(x[0]), abs(x[1])),
+        )
+    )
+
+    # Parameter group 4
+    # -----------------
+    # C - B an integer
+    A = root_params + perturbations[0, :]
+    B = root_params + 0.5
+    C = root_params + 0.5
+    params.extend(
+        sorted(
+            ((a, b, c, 4) for a, b, c in product(A, B, C)),
+            key=lambda x: max(abs(x[0]), abs(x[1])),
+        )
+    )
+
+    # Parameter group 5
+    # -----------------
+    # C - A - B an integer
+    A = root_params + 0.25
+    B = root_params + 0.25
+    C = root_params + 0.5
+    params.extend(
+        sorted(
+            ((a, b, c, 5) for a, b, c in product(A, B, C)),
+            key=lambda x: max(abs(x[0]), abs(x[1])),
+        )
+    )
+
+    # Parameter group 6
+    # -----------------
+    # A an integer
+    A = root_params
+    B = root_params + perturbations[0, :]
+    C = root_params + perturbations[1, :]
+    params.extend(
+        sorted(
+            ((a, b, c, 6) for a, b, c in product(A, B, C)),
+            key=lambda x: max(abs(x[0]), abs(x[1])),
+        )
+    )
+
+    # Parameter group 7
+    # -----------------
+    # B an integer
+    A = root_params + perturbations[0, :]
+    B = root_params
+    C = root_params + perturbations[1, :]
+    params.extend(
+        sorted(
+            ((a, b, c, 7) for a, b, c in product(A, B, C)),
+            key=lambda x: max(abs(x[0]), abs(x[1])),
+        )
+    )
+
+    # Parameter group 8
+    # -----------------
+    # C an integer
+    A = root_params + perturbations[0, :]
+    B = root_params + perturbations[1, :]
+    C = root_params
+    params.extend(
+        sorted(
+            ((a, b, c, 8) for a, b, c in product(A, B, C)),
+            key=lambda x: max(abs(x[0]), abs(x[1])),
+        )
+    )
+
+    # Parameter group 9
+    # -----------------
+    # Wide range of magnitudes, c - a - b > 0.
+    phi = (1 + np.sqrt(5))/2
+    P = phi**np.arange(16)
+    P = np.hstack([-P, P])
+    group_9_params = sorted(
+        (
+            (a, b, c, 9) for a, b, c in product(P, P, P) if c - a - b > 0
+        ),
+        key=lambda x: max(abs(x[0]), abs(x[1])),
+    )
+
+    if parameter_groups is not None:
+        # Group 9 params only used if specified in arguments.
+        params.extend(group_9_params)
+        params = [
+            (a, b, c, group) for a, b, c, group in params
+            if group in parameter_groups
+        ]
+
+    # grid_size * grid_size grid in box with corners
+    # -2 - 2j, -2 + 2j, 2 - 2j, 2 + 2j
+    X, Y = np.meshgrid(
+        np.linspace(-box_size, box_size, grid_size),
+        np.linspace(-box_size, box_size, grid_size)
+    )
+    Z = X + Y * 1j
+    Z = Z.flatten().tolist()
+    # Add z = 1 + 0j (region 0).
+    Z.append(1 + 0j)
+    if regions is not None:
+        Z = [z for z in Z if get_region(z) in regions]
+
+    # Evaluate scipy and mpmath's hyp2f1 for all parameter combinations
+    # above against all arguments in the grid Z
+    rows = get_results(params, Z, n_jobs=n_jobs, compute_mp=compute_mp)
+
+    with open(outpath, "w", newline="") as f:
+        writer = csv.writer(f, delimiter="\t")
+        writer.writerow(
+            [
+                "a",
+                "b",
+                "c",
+                "z",
+                "|z|",
+                "region",
+                "parameter_group",
+                "expected",  # mpmath's hyp2f1
+                "observed",  # scipy's hyp2f1
+                "relative_error",
+                "absolute_error",
+            ]
+        )
+        for row in rows:
+            writer.writerow(row)
+
+
+if __name__ == "__main__":
+    parser = argparse.ArgumentParser(
+        description="Test scipy's hyp2f1 against mpmath's on a grid in the"
+        " complex plane over a grid of parameter values. Saves output to file"
+        " specified in positional argument \"outpath\"."
+        " Caution: With default arguments, the generated output file is"
+        " roughly 700MB in size. Script may take several hours to finish if"
+        " \"--n_jobs\" is set to 1."
+    )
+    parser.add_argument(
+        "outpath", type=str, help="Path to output tsv file."
+    )
+    parser.add_argument(
+        "--n_jobs",
+        type=int,
+        default=1,
+        help="Number of jobs for multiprocessing.",
+    )
+    parser.add_argument(
+        "--box_size",
+        type=float,
+        default=2.0,
+        help="hyp2f1 is evaluated in box of side_length 2*box_size centered"
+        " at the origin."
+    )
+    parser.add_argument(
+        "--grid_size",
+        type=int,
+        default=20,
+        help="hyp2f1 is evaluated on grid_size * grid_size grid in box of side"
+        " length 2*box_size centered at the origin."
+    )
+    parser.add_argument(
+        "--parameter_groups",
+        type=int,
+        nargs='+',
+        default=None,
+        help="Restrict to supplied parameter groups. See the Docstring for"
+        " this module for more info on parameter groups. Calculate for all"
+        " parameter groups by default."
+    )
+    parser.add_argument(
+        "--regions",
+        type=int,
+        nargs='+',
+        default=None,
+        help="Restrict to argument z only within the supplied regions. See"
+        " the Docstring for this module for more info on regions. Calculate"
+        " for all regions by default."
+    )
+    parser.add_argument(
+        "--no_mp",
+        action='store_true',
+        help="If this flag is set, do not compute results with mpmath. Saves"
+        " time if results have already been computed elsewhere. Fills in"
+        " \"expected\" column with None values."
+    )
+    args = parser.parse_args()
+    compute_mp = not args.no_mp
+    print(args.parameter_groups)
+    main(
+        args.outpath,
+        n_jobs=args.n_jobs,
+        box_size=args.box_size,
+        grid_size=args.grid_size,
+        parameter_groups=args.parameter_groups,
+        regions=args.regions,
+        compute_mp=compute_mp,
+    )
diff --git a/venv/lib/python3.12/site-packages/scipy/special/_precompute/lambertw.py b/venv/lib/python3.12/site-packages/scipy/special/_precompute/lambertw.py
new file mode 100644
index 0000000000000000000000000000000000000000..1fdbf35b2cf85f1f7a6e73579546ed5cfe508fa6
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/_precompute/lambertw.py
@@ -0,0 +1,68 @@
+"""Compute a Pade approximation for the principal branch of the
+Lambert W function around 0 and compare it to various other
+approximations.
+
+"""
+import numpy as np
+
+try:
+    import mpmath
+    import matplotlib.pyplot as plt
+except ImportError:
+    pass
+
+
+def lambertw_pade():
+    derivs = [mpmath.diff(mpmath.lambertw, 0, n=n) for n in range(6)]
+    p, q = mpmath.pade(derivs, 3, 2)
+    return p, q
+
+
+def main():
+    print(__doc__)
+    with mpmath.workdps(50):
+        p, q = lambertw_pade()
+        p, q = p[::-1], q[::-1]
+        print(f"p = {p}")
+        print(f"q = {q}")
+
+    x, y = np.linspace(-1.5, 1.5, 75), np.linspace(-1.5, 1.5, 75)
+    x, y = np.meshgrid(x, y)
+    z = x + 1j*y
+    lambertw_std = []
+    for z0 in z.flatten():
+        lambertw_std.append(complex(mpmath.lambertw(z0)))
+    lambertw_std = np.array(lambertw_std).reshape(x.shape)
+
+    fig, axes = plt.subplots(nrows=3, ncols=1)
+    # Compare Pade approximation to true result
+    p = np.array([float(p0) for p0 in p])
+    q = np.array([float(q0) for q0 in q])
+    pade_approx = np.polyval(p, z)/np.polyval(q, z)
+    pade_err = abs(pade_approx - lambertw_std)
+    axes[0].pcolormesh(x, y, pade_err)
+    # Compare two terms of asymptotic series to true result
+    asy_approx = np.log(z) - np.log(np.log(z))
+    asy_err = abs(asy_approx - lambertw_std)
+    axes[1].pcolormesh(x, y, asy_err)
+    # Compare two terms of the series around the branch point to the
+    # true result
+    p = np.sqrt(2*(np.exp(1)*z + 1))
+    series_approx = -1 + p - p**2/3
+    series_err = abs(series_approx - lambertw_std)
+    im = axes[2].pcolormesh(x, y, series_err)
+
+    fig.colorbar(im, ax=axes.ravel().tolist())
+    plt.show()
+
+    fig, ax = plt.subplots(nrows=1, ncols=1)
+    pade_better = pade_err < asy_err
+    im = ax.pcolormesh(x, y, pade_better)
+    t = np.linspace(-0.3, 0.3)
+    ax.plot(-2.5*abs(t) - 0.2, t, 'r')
+    fig.colorbar(im, ax=ax)
+    plt.show()
+
+
+if __name__ == '__main__':
+    main()
diff --git a/venv/lib/python3.12/site-packages/scipy/special/_precompute/loggamma.py b/venv/lib/python3.12/site-packages/scipy/special/_precompute/loggamma.py
new file mode 100644
index 0000000000000000000000000000000000000000..74051ac7b46c70dc01919a362d05a8bbbe11333a
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/_precompute/loggamma.py
@@ -0,0 +1,43 @@
+"""Precompute series coefficients for log-Gamma."""
+
+try:
+    import mpmath
+except ImportError:
+    pass
+
+
+def stirling_series(N):
+    with mpmath.workdps(100):
+        coeffs = [mpmath.bernoulli(2*n)/(2*n*(2*n - 1))
+                  for n in range(1, N + 1)]
+    return coeffs
+
+
+def taylor_series_at_1(N):
+    coeffs = []
+    with mpmath.workdps(100):
+        coeffs.append(-mpmath.euler)
+        for n in range(2, N + 1):
+            coeffs.append((-1)**n*mpmath.zeta(n)/n)
+    return coeffs
+
+
+def main():
+    print(__doc__)
+    print()
+    stirling_coeffs = [mpmath.nstr(x, 20, min_fixed=0, max_fixed=0)
+                       for x in stirling_series(8)[::-1]]
+    taylor_coeffs = [mpmath.nstr(x, 20, min_fixed=0, max_fixed=0)
+                     for x in taylor_series_at_1(23)[::-1]]
+    print("Stirling series coefficients")
+    print("----------------------------")
+    print("\n".join(stirling_coeffs))
+    print()
+    print("Taylor series coefficients")
+    print("--------------------------")
+    print("\n".join(taylor_coeffs))
+    print()
+
+
+if __name__ == '__main__':
+    main()
diff --git a/venv/lib/python3.12/site-packages/scipy/special/_precompute/struve_convergence.py b/venv/lib/python3.12/site-packages/scipy/special/_precompute/struve_convergence.py
new file mode 100644
index 0000000000000000000000000000000000000000..dbf6009368540dbf603b61f5b72510f0acd1a65b
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/_precompute/struve_convergence.py
@@ -0,0 +1,131 @@
+"""
+Convergence regions of the expansions used in ``struve.c``
+
+Note that for v >> z both functions tend rapidly to 0,
+and for v << -z, they tend to infinity.
+
+The floating-point functions over/underflow in the lower left and right
+corners of the figure.
+
+
+Figure legend
+=============
+
+Red region
+    Power series is close (1e-12) to the mpmath result
+
+Blue region
+    Asymptotic series is close to the mpmath result
+
+Green region
+    Bessel series is close to the mpmath result
+
+Dotted colored lines
+    Boundaries of the regions
+
+Solid colored lines
+    Boundaries estimated by the routine itself. These will be used
+    for determining which of the results to use.
+
+Black dashed line
+    The line z = 0.7*|v| + 12
+
+"""
+import numpy as np
+import matplotlib.pyplot as plt
+
+import mpmath
+
+
+def err_metric(a, b, atol=1e-290):
+    m = abs(a - b) / (atol + abs(b))
+    m[np.isinf(b) & (a == b)] = 0
+    return m
+
+
+def do_plot(is_h=True):
+    from scipy.special._ufuncs import (_struve_power_series,
+                                       _struve_asymp_large_z,
+                                       _struve_bessel_series)
+
+    vs = np.linspace(-1000, 1000, 91)
+    zs = np.sort(np.r_[1e-5, 1.0, np.linspace(0, 700, 91)[1:]])
+
+    rp = _struve_power_series(vs[:,None], zs[None,:], is_h)
+    ra = _struve_asymp_large_z(vs[:,None], zs[None,:], is_h)
+    rb = _struve_bessel_series(vs[:,None], zs[None,:], is_h)
+
+    mpmath.mp.dps = 50
+    if is_h:
+        def sh(v, z):
+            return float(mpmath.struveh(mpmath.mpf(v), mpmath.mpf(z)))
+    else:
+        def sh(v, z):
+            return float(mpmath.struvel(mpmath.mpf(v), mpmath.mpf(z)))
+    ex = np.vectorize(sh, otypes='d')(vs[:,None], zs[None,:])
+
+    err_a = err_metric(ra[0], ex) + 1e-300
+    err_p = err_metric(rp[0], ex) + 1e-300
+    err_b = err_metric(rb[0], ex) + 1e-300
+
+    err_est_a = abs(ra[1]/ra[0])
+    err_est_p = abs(rp[1]/rp[0])
+    err_est_b = abs(rb[1]/rb[0])
+
+    z_cutoff = 0.7*abs(vs) + 12
+
+    levels = [-1000, -12]
+
+    plt.cla()
+
+    plt.hold(1)
+    plt.contourf(vs, zs, np.log10(err_p).T,
+                 levels=levels, colors=['r', 'r'], alpha=0.1)
+    plt.contourf(vs, zs, np.log10(err_a).T,
+                 levels=levels, colors=['b', 'b'], alpha=0.1)
+    plt.contourf(vs, zs, np.log10(err_b).T,
+                 levels=levels, colors=['g', 'g'], alpha=0.1)
+
+    plt.contour(vs, zs, np.log10(err_p).T,
+                levels=levels, colors=['r', 'r'], linestyles=[':', ':'])
+    plt.contour(vs, zs, np.log10(err_a).T,
+                levels=levels, colors=['b', 'b'], linestyles=[':', ':'])
+    plt.contour(vs, zs, np.log10(err_b).T,
+                levels=levels, colors=['g', 'g'], linestyles=[':', ':'])
+
+    lp = plt.contour(vs, zs, np.log10(err_est_p).T,
+                     levels=levels, colors=['r', 'r'], linestyles=['-', '-'])
+    la = plt.contour(vs, zs, np.log10(err_est_a).T,
+                     levels=levels, colors=['b', 'b'], linestyles=['-', '-'])
+    lb = plt.contour(vs, zs, np.log10(err_est_b).T,
+                     levels=levels, colors=['g', 'g'], linestyles=['-', '-'])
+
+    plt.clabel(lp, fmt={-1000: 'P', -12: 'P'})
+    plt.clabel(la, fmt={-1000: 'A', -12: 'A'})
+    plt.clabel(lb, fmt={-1000: 'B', -12: 'B'})
+
+    plt.plot(vs, z_cutoff, 'k--')
+
+    plt.xlim(vs.min(), vs.max())
+    plt.ylim(zs.min(), zs.max())
+
+    plt.xlabel('v')
+    plt.ylabel('z')
+
+
+def main():
+    plt.clf()
+    plt.subplot(121)
+    do_plot(True)
+    plt.title('Struve H')
+
+    plt.subplot(122)
+    do_plot(False)
+    plt.title('Struve L')
+
+    plt.savefig('struve_convergence.png')
+    plt.show()
+
+
+if __name__ == "__main__":
+    main()
diff --git a/venv/lib/python3.12/site-packages/scipy/special/_precompute/utils.py b/venv/lib/python3.12/site-packages/scipy/special/_precompute/utils.py
new file mode 100644
index 0000000000000000000000000000000000000000..55cf4083ed5e5a6628fd3316c02ce1a5ce21a92c
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/_precompute/utils.py
@@ -0,0 +1,38 @@
+try:
+    import mpmath as mp
+except ImportError:
+    pass
+
+try:
+    from sympy.abc import x
+except ImportError:
+    pass
+
+
+def lagrange_inversion(a):
+    """Given a series
+
+    f(x) = a[1]*x + a[2]*x**2 + ... + a[n-1]*x**(n - 1),
+
+    use the Lagrange inversion formula to compute a series
+
+    g(x) = b[1]*x + b[2]*x**2 + ... + b[n-1]*x**(n - 1)
+
+    so that f(g(x)) = g(f(x)) = x mod x**n. We must have a[0] = 0, so
+    necessarily b[0] = 0 too.
+
+    The algorithm is naive and could be improved, but speed isn't an
+    issue here and it's easy to read.
+
+    """
+    n = len(a)
+    f = sum(a[i]*x**i for i in range(n))
+    h = (x/f).series(x, 0, n).removeO()
+    hpower = [h**0]
+    for k in range(n):
+        hpower.append((hpower[-1]*h).expand())
+    b = [mp.mpf(0)]
+    for k in range(1, n):
+        b.append(hpower[k].coeff(x, k - 1)/k)
+    b = [mp.mpf(x) for x in b]
+    return b
diff --git a/venv/lib/python3.12/site-packages/scipy/special/_precompute/wright_bessel.py b/venv/lib/python3.12/site-packages/scipy/special/_precompute/wright_bessel.py
new file mode 100644
index 0000000000000000000000000000000000000000..51d56b1cd5c47c7ef005d21aad9827a1e85ec0d9
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/_precompute/wright_bessel.py
@@ -0,0 +1,342 @@
+"""Precompute coefficients of several series expansions
+of Wright's generalized Bessel function Phi(a, b, x).
+
+See https://dlmf.nist.gov/10.46.E1 with rho=a, beta=b, z=x.
+"""
+from argparse import ArgumentParser, RawTextHelpFormatter
+import numpy as np
+from scipy.integrate import quad
+from scipy.optimize import minimize_scalar, curve_fit
+from time import time
+
+try:
+    import sympy
+    from sympy import EulerGamma, Rational, S, Sum, \
+        factorial, gamma, gammasimp, pi, polygamma, symbols, zeta
+    from sympy.polys.polyfuncs import horner
+except ImportError:
+    pass
+
+
+def series_small_a():
+    """Tylor series expansion of Phi(a, b, x) in a=0 up to order 5.
+    """
+    order = 5
+    a, b, x, k = symbols("a b x k")
+    A = []  # terms with a
+    X = []  # terms with x
+    B = []  # terms with b (polygammas)
+    # Phi(a, b, x) = exp(x)/gamma(b) * sum(A[i] * X[i] * B[i])
+    expression = Sum(x**k/factorial(k)/gamma(a*k+b), (k, 0, S.Infinity))
+    expression = gamma(b)/sympy.exp(x) * expression
+
+    # nth term of taylor series in a=0: a^n/n! * (d^n Phi(a, b, x)/da^n at a=0)
+    for n in range(0, order+1):
+        term = expression.diff(a, n).subs(a, 0).simplify().doit()
+        # set the whole bracket involving polygammas to 1
+        x_part = (term.subs(polygamma(0, b), 1)
+                  .replace(polygamma, lambda *args: 0))
+        # sign convention: x part always positive
+        x_part *= (-1)**n
+
+        A.append(a**n/factorial(n))
+        X.append(horner(x_part))
+        B.append(horner((term/x_part).simplify()))
+
+    s = "Tylor series expansion of Phi(a, b, x) in a=0 up to order 5.\n"
+    s += "Phi(a, b, x) = exp(x)/gamma(b) * sum(A[i] * X[i] * B[i], i=0..5)\n"
+    for name, c in zip(['A', 'X', 'B'], [A, X, B]):
+        for i in range(len(c)):
+            s += f"\n{name}[{i}] = " + str(c[i])
+    return s
+
+
+# expansion of digamma
+def dg_series(z, n):
+    """Symbolic expansion of digamma(z) in z=0 to order n.
+
+    See https://dlmf.nist.gov/5.7.E4 and with https://dlmf.nist.gov/5.5.E2
+    """
+    k = symbols("k")
+    return -1/z - EulerGamma + \
+        sympy.summation((-1)**k * zeta(k) * z**(k-1), (k, 2, n+1))
+
+
+def pg_series(k, z, n):
+    """Symbolic expansion of polygamma(k, z) in z=0 to order n."""
+    return sympy.diff(dg_series(z, n+k), z, k)
+
+
+def series_small_a_small_b():
+    """Tylor series expansion of Phi(a, b, x) in a=0 and b=0 up to order 5.
+
+    Be aware of cancellation of poles in b=0 of digamma(b)/Gamma(b) and
+    polygamma functions.
+
+    digamma(b)/Gamma(b) = -1 - 2*M_EG*b + O(b^2)
+    digamma(b)^2/Gamma(b) = 1/b + 3*M_EG + b*(-5/12*PI^2+7/2*M_EG^2) + O(b^2)
+    polygamma(1, b)/Gamma(b) = 1/b + M_EG + b*(1/12*PI^2 + 1/2*M_EG^2) + O(b^2)
+    and so on.
+    """
+    order = 5
+    a, b, x, k = symbols("a b x k")
+    M_PI, M_EG, M_Z3 = symbols("M_PI M_EG M_Z3")
+    c_subs = {pi: M_PI, EulerGamma: M_EG, zeta(3): M_Z3}
+    A = []  # terms with a
+    X = []  # terms with x
+    B = []  # terms with b (polygammas expanded)
+    C = []  # terms that generate B
+    # Phi(a, b, x) = exp(x) * sum(A[i] * X[i] * B[i])
+    # B[0] = 1
+    # B[k] = sum(C[k] * b**k/k!, k=0..)
+    # Note: C[k] can be obtained from a series expansion of 1/gamma(b).
+    expression = gamma(b)/sympy.exp(x) * \
+        Sum(x**k/factorial(k)/gamma(a*k+b), (k, 0, S.Infinity))
+
+    # nth term of taylor series in a=0: a^n/n! * (d^n Phi(a, b, x)/da^n at a=0)
+    for n in range(0, order+1):
+        term = expression.diff(a, n).subs(a, 0).simplify().doit()
+        # set the whole bracket involving polygammas to 1
+        x_part = (term.subs(polygamma(0, b), 1)
+                  .replace(polygamma, lambda *args: 0))
+        # sign convention: x part always positive
+        x_part *= (-1)**n
+        # expansion of polygamma part with 1/gamma(b)
+        pg_part = term/x_part/gamma(b)
+        if n >= 1:
+            # Note: highest term is digamma^n
+            pg_part = pg_part.replace(polygamma,
+                                      lambda k, x: pg_series(k, x, order+1+n))
+            pg_part = (pg_part.series(b, 0, n=order+1-n)
+                       .removeO()
+                       .subs(polygamma(2, 1), -2*zeta(3))
+                       .simplify()
+                       )
+
+        A.append(a**n/factorial(n))
+        X.append(horner(x_part))
+        B.append(pg_part)
+
+    # Calculate C and put in the k!
+    C = sympy.Poly(B[1].subs(c_subs), b).coeffs()
+    C.reverse()
+    for i in range(len(C)):
+        C[i] = (C[i] * factorial(i)).simplify()
+
+    s = "Tylor series expansion of Phi(a, b, x) in a=0 and b=0 up to order 5."
+    s += "\nPhi(a, b, x) = exp(x) * sum(A[i] * X[i] * B[i], i=0..5)\n"
+    s += "B[0] = 1\n"
+    s += "B[i] = sum(C[k+i-1] * b**k/k!, k=0..)\n"
+    s += "\nM_PI = pi"
+    s += "\nM_EG = EulerGamma"
+    s += "\nM_Z3 = zeta(3)"
+    for name, c in zip(['A', 'X'], [A, X]):
+        for i in range(len(c)):
+            s += f"\n{name}[{i}] = "
+            s += str(c[i])
+    # For C, do also compute the values numerically
+    for i in range(len(C)):
+        s += f"\n# C[{i}] = "
+        s += str(C[i])
+        s += f"\nC[{i}] = "
+        s += str(C[i].subs({M_EG: EulerGamma, M_PI: pi, M_Z3: zeta(3)})
+                 .evalf(17))
+
+    # Does B have the assumed structure?
+    s += "\n\nTest if B[i] does have the assumed structure."
+    s += "\nC[i] are derived from B[1] alone."
+    s += "\nTest B[2] == C[1] + b*C[2] + b^2/2*C[3] + b^3/6*C[4] + .."
+    test = sum([b**k/factorial(k) * C[k+1] for k in range(order-1)])
+    test = (test - B[2].subs(c_subs)).simplify()
+    s += f"\ntest successful = {test==S(0)}"
+    s += "\nTest B[3] == C[2] + b*C[3] + b^2/2*C[4] + .."
+    test = sum([b**k/factorial(k) * C[k+2] for k in range(order-2)])
+    test = (test - B[3].subs(c_subs)).simplify()
+    s += f"\ntest successful = {test==S(0)}"
+    return s
+
+
+def asymptotic_series():
+    """Asymptotic expansion for large x.
+
+    Phi(a, b, x) ~ Z^(1/2-b) * exp((1+a)/a * Z) * sum_k (-1)^k * C_k / Z^k
+    Z = (a*x)^(1/(1+a))
+
+    Wright (1935) lists the coefficients C_0 and C_1 (he calls them a_0 and
+    a_1). With slightly different notation, Paris (2017) lists coefficients
+    c_k up to order k=3.
+    Paris (2017) uses ZP = (1+a)/a * Z  (ZP = Z of Paris) and
+    C_k = C_0 * (-a/(1+a))^k * c_k
+    """
+    order = 8
+
+    class g(sympy.Function):
+        """Helper function g according to Wright (1935)
+
+        g(n, rho, v) = (1 + (rho+2)/3 * v + (rho+2)*(rho+3)/(2*3) * v^2 + ...)
+
+        Note: Wright (1935) uses square root of above definition.
+        """
+        nargs = 3
+
+        @classmethod
+        def eval(cls, n, rho, v):
+            if not n >= 0:
+                raise ValueError("must have n >= 0")
+            elif n == 0:
+                return 1
+            else:
+                return g(n-1, rho, v) \
+                    + gammasimp(gamma(rho+2+n)/gamma(rho+2)) \
+                    / gammasimp(gamma(3+n)/gamma(3))*v**n
+
+    class coef_C(sympy.Function):
+        """Calculate coefficients C_m for integer m.
+
+        C_m is the coefficient of v^(2*m) in the Taylor expansion in v=0 of
+        Gamma(m+1/2)/(2*pi) * (2/(rho+1))^(m+1/2) * (1-v)^(-b)
+            * g(rho, v)^(-m-1/2)
+        """
+        nargs = 3
+
+        @classmethod
+        def eval(cls, m, rho, beta):
+            if not m >= 0:
+                raise ValueError("must have m >= 0")
+
+            v = symbols("v")
+            expression = (1-v)**(-beta) * g(2*m, rho, v)**(-m-Rational(1, 2))
+            res = expression.diff(v, 2*m).subs(v, 0) / factorial(2*m)
+            res = res * (gamma(m + Rational(1, 2)) / (2*pi)
+                         * (2/(rho+1))**(m + Rational(1, 2)))
+            return res
+
+    # in order to have nice ordering/sorting of expressions, we set a = xa.
+    xa, b, xap1 = symbols("xa b xap1")
+    C0 = coef_C(0, xa, b)
+    # a1 = a(1, rho, beta)
+    s = "Asymptotic expansion for large x\n"
+    s += "Phi(a, b, x) = Z**(1/2-b) * exp((1+a)/a * Z) \n"
+    s += "               * sum((-1)**k * C[k]/Z**k, k=0..6)\n\n"
+    s += "Z      = pow(a * x, 1/(1+a))\n"
+    s += "A[k]   = pow(a, k)\n"
+    s += "B[k]   = pow(b, k)\n"
+    s += "Ap1[k] = pow(1+a, k)\n\n"
+    s += "C[0] = 1./sqrt(2. * M_PI * Ap1[1])\n"
+    for i in range(1, order+1):
+        expr = (coef_C(i, xa, b) / (C0/(1+xa)**i)).simplify()
+        factor = [x.denominator() for x in sympy.Poly(expr).coeffs()]
+        factor = sympy.lcm(factor)
+        expr = (expr * factor).simplify().collect(b, sympy.factor)
+        expr = expr.xreplace({xa+1: xap1})
+        s += f"C[{i}] = C[0] / ({factor} * Ap1[{i}])\n"
+        s += f"C[{i}] *= {str(expr)}\n\n"
+    import re
+    re_a = re.compile(r'xa\*\*(\d+)')
+    s = re_a.sub(r'A[\1]', s)
+    re_b = re.compile(r'b\*\*(\d+)')
+    s = re_b.sub(r'B[\1]', s)
+    s = s.replace('xap1', 'Ap1[1]')
+    s = s.replace('xa', 'a')
+    # max integer = 2^31-1 = 2,147,483,647. Solution: Put a point after 10
+    # or more digits.
+    re_digits = re.compile(r'(\d{10,})')
+    s = re_digits.sub(r'\1.', s)
+    return s
+
+
+def optimal_epsilon_integral():
+    """Fit optimal choice of epsilon for integral representation.
+
+    The integrand of
+        int_0^pi P(eps, a, b, x, phi) * dphi
+    can exhibit oscillatory behaviour. It stems from the cosine of P and can be
+    minimized by minimizing the arc length of the argument
+        f(phi) = eps * sin(phi) - x * eps^(-a) * sin(a * phi) + (1 - b) * phi
+    of cos(f(phi)).
+    We minimize the arc length in eps for a grid of values (a, b, x) and fit a
+    parametric function to it.
+    """
+    def fp(eps, a, b, x, phi):
+        """Derivative of f w.r.t. phi."""
+        eps_a = np.power(1. * eps, -a)
+        return eps * np.cos(phi) - a * x * eps_a * np.cos(a * phi) + 1 - b
+
+    def arclength(eps, a, b, x, epsrel=1e-2, limit=100):
+        """Compute Arc length of f.
+
+        Note that the arc length of a function f from t0 to t1 is given by
+            int_t0^t1 sqrt(1 + f'(t)^2) dt
+        """
+        return quad(lambda phi: np.sqrt(1 + fp(eps, a, b, x, phi)**2),
+                    0, np.pi,
+                    epsrel=epsrel, limit=100)[0]
+
+    # grid of minimal arc length values
+    data_a = [1e-3, 0.1, 0.5, 0.9, 1, 2, 4, 5, 6, 8]
+    data_b = [0, 1, 4, 7, 10]
+    data_x = [1, 1.5, 2, 4, 10, 20, 50, 100, 200, 500, 1e3, 5e3, 1e4]
+    data_a, data_b, data_x = np.meshgrid(data_a, data_b, data_x)
+    data_a, data_b, data_x = (data_a.flatten(), data_b.flatten(),
+                              data_x.flatten())
+    best_eps = []
+    for i in range(data_x.size):
+        best_eps.append(
+            minimize_scalar(lambda eps: arclength(eps, data_a[i], data_b[i],
+                                                  data_x[i]),
+                            bounds=(1e-3, 1000),
+                            method='Bounded', options={'xatol': 1e-3}).x
+        )
+    best_eps = np.array(best_eps)
+    # pandas would be nice, but here a dictionary is enough
+    df = {'a': data_a,
+          'b': data_b,
+          'x': data_x,
+          'eps': best_eps,
+          }
+
+    def func(data, A0, A1, A2, A3, A4, A5):
+        """Compute parametric function to fit."""
+        a = data['a']
+        b = data['b']
+        x = data['x']
+        return (A0 * b * np.exp(-0.5 * a)
+                + np.exp(A1 + 1 / (1 + a) * np.log(x) - A2 * np.exp(-A3 * a)
+                         + A4 / (1 + np.exp(A5 * a))))
+
+    func_params = list(curve_fit(func, df, df['eps'], method='trf')[0])
+
+    s = "Fit optimal eps for integrand P via minimal arc length\n"
+    s += "with parametric function:\n"
+    s += "optimal_eps = (A0 * b * exp(-a/2) + exp(A1 + 1 / (1 + a) * log(x)\n"
+    s += "              - A2 * exp(-A3 * a) + A4 / (1 + exp(A5 * a)))\n\n"
+    s += "Fitted parameters A0 to A5 are:\n"
+    s += ', '.join([f'{x:.5g}' for x in func_params])
+    return s
+
+
+def main():
+    t0 = time()
+    parser = ArgumentParser(description=__doc__,
+                            formatter_class=RawTextHelpFormatter)
+    parser.add_argument('action', type=int, choices=[1, 2, 3, 4],
+                        help='chose what expansion to precompute\n'
+                             '1 : Series for small a\n'
+                             '2 : Series for small a and small b\n'
+                             '3 : Asymptotic series for large x\n'
+                             '    This may take some time (>4h).\n'
+                             '4 : Fit optimal eps for integral representation.'
+                        )
+    args = parser.parse_args()
+
+    switch = {1: lambda: print(series_small_a()),
+              2: lambda: print(series_small_a_small_b()),
+              3: lambda: print(asymptotic_series()),
+              4: lambda: print(optimal_epsilon_integral())
+              }
+    switch.get(args.action, lambda: print("Invalid input."))()
+    print(f"\n{(time() - t0)/60:.1f} minutes elapsed.\n")
+
+
+if __name__ == '__main__':
+    main()
diff --git a/venv/lib/python3.12/site-packages/scipy/special/_precompute/wright_bessel_data.py b/venv/lib/python3.12/site-packages/scipy/special/_precompute/wright_bessel_data.py
new file mode 100644
index 0000000000000000000000000000000000000000..1de9b4fe552ca9178c452194ab84af6ca5daac71
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/_precompute/wright_bessel_data.py
@@ -0,0 +1,152 @@
+"""Compute a grid of values for Wright's generalized Bessel function
+and save the values to data files for use in tests. Using mpmath directly in
+tests would take too long.
+
+This takes about 10 minutes to run on a 2.7 GHz i7 Macbook Pro.
+"""
+from functools import lru_cache
+import os
+from time import time
+
+import numpy as np
+from scipy.special._mptestutils import mpf2float
+
+try:
+    import mpmath as mp
+except ImportError:
+    pass
+
+# exp_inf: smallest value x for which exp(x) == inf
+exp_inf = 709.78271289338403
+
+
+# 64 Byte per value
+@lru_cache(maxsize=100_000)
+def rgamma_cached(x, dps):
+    with mp.workdps(dps):
+        return mp.rgamma(x)
+
+
+def mp_wright_bessel(a, b, x, dps=50, maxterms=2000):
+    """Compute Wright's generalized Bessel function as Series with mpmath.
+    """
+    with mp.workdps(dps):
+        a, b, x = mp.mpf(a), mp.mpf(b), mp.mpf(x)
+        res = mp.nsum(lambda k: x**k / mp.fac(k)
+                      * rgamma_cached(a * k + b, dps=dps),
+                      [0, mp.inf],
+                      tol=dps, method='s', steps=[maxterms]
+                      )
+        return mpf2float(res)
+
+
+def main():
+    t0 = time()
+    print(__doc__)
+    pwd = os.path.dirname(__file__)
+    eps = np.finfo(float).eps * 100
+
+    a_range = np.array([eps,
+                        1e-4 * (1 - eps), 1e-4, 1e-4 * (1 + eps),
+                        1e-3 * (1 - eps), 1e-3, 1e-3 * (1 + eps),
+                        0.1, 0.5,
+                        1 * (1 - eps), 1, 1 * (1 + eps),
+                        1.5, 2, 4.999, 5, 10])
+    b_range = np.array([0, eps, 1e-10, 1e-5, 0.1, 1, 2, 10, 20, 100])
+    x_range = np.array([0, eps, 1 - eps, 1, 1 + eps,
+                        1.5,
+                        2 - eps, 2, 2 + eps,
+                        9 - eps, 9, 9 + eps,
+                        10 * (1 - eps), 10, 10 * (1 + eps),
+                        100 * (1 - eps), 100, 100 * (1 + eps),
+                        500, exp_inf, 1e3, 1e5, 1e10, 1e20])
+
+    a_range, b_range, x_range = np.meshgrid(a_range, b_range, x_range,
+                                            indexing='ij')
+    a_range = a_range.flatten()
+    b_range = b_range.flatten()
+    x_range = x_range.flatten()
+
+    # filter out some values, especially too large x
+    bool_filter = ~((a_range < 5e-3) & (x_range >= exp_inf))
+    bool_filter = bool_filter & ~((a_range < 0.2) & (x_range > exp_inf))
+    bool_filter = bool_filter & ~((a_range < 0.5) & (x_range > 1e3))
+    bool_filter = bool_filter & ~((a_range < 0.56) & (x_range > 5e3))
+    bool_filter = bool_filter & ~((a_range < 1) & (x_range > 1e4))
+    bool_filter = bool_filter & ~((a_range < 1.4) & (x_range > 1e5))
+    bool_filter = bool_filter & ~((a_range < 1.8) & (x_range > 1e6))
+    bool_filter = bool_filter & ~((a_range < 2.2) & (x_range > 1e7))
+    bool_filter = bool_filter & ~((a_range < 2.5) & (x_range > 1e8))
+    bool_filter = bool_filter & ~((a_range < 2.9) & (x_range > 1e9))
+    bool_filter = bool_filter & ~((a_range < 3.3) & (x_range > 1e10))
+    bool_filter = bool_filter & ~((a_range < 3.7) & (x_range > 1e11))
+    bool_filter = bool_filter & ~((a_range < 4) & (x_range > 1e12))
+    bool_filter = bool_filter & ~((a_range < 4.4) & (x_range > 1e13))
+    bool_filter = bool_filter & ~((a_range < 4.7) & (x_range > 1e14))
+    bool_filter = bool_filter & ~((a_range < 5.1) & (x_range > 1e15))
+    bool_filter = bool_filter & ~((a_range < 5.4) & (x_range > 1e16))
+    bool_filter = bool_filter & ~((a_range < 5.8) & (x_range > 1e17))
+    bool_filter = bool_filter & ~((a_range < 6.2) & (x_range > 1e18))
+    bool_filter = bool_filter & ~((a_range < 6.2) & (x_range > 1e18))
+    bool_filter = bool_filter & ~((a_range < 6.5) & (x_range > 1e19))
+    bool_filter = bool_filter & ~((a_range < 6.9) & (x_range > 1e20))
+
+    # filter out known values that do not meet the required numerical accuracy
+    # see test test_wright_data_grid_failures
+    failing = np.array([
+        [0.1, 100, 709.7827128933841],
+        [0.5, 10, 709.7827128933841],
+        [0.5, 10, 1000],
+        [0.5, 100, 1000],
+        [1, 20, 100000],
+        [1, 100, 100000],
+        [1.0000000000000222, 20, 100000],
+        [1.0000000000000222, 100, 100000],
+        [1.5, 0, 500],
+        [1.5, 2.220446049250313e-14, 500],
+        [1.5, 1.e-10, 500],
+        [1.5, 1.e-05, 500],
+        [1.5, 0.1, 500],
+        [1.5, 20, 100000],
+        [1.5, 100, 100000],
+        ]).tolist()
+
+    does_fail = np.full_like(a_range, False, dtype=bool)
+    for i in range(x_range.size):
+        if [a_range[i], b_range[i], x_range[i]] in failing:
+            does_fail[i] = True
+
+    # filter and flatten
+    a_range = a_range[bool_filter]
+    b_range = b_range[bool_filter]
+    x_range = x_range[bool_filter]
+    does_fail = does_fail[bool_filter]
+
+    dataset = []
+    print(f"Computing {x_range.size} single points.")
+    print("Tests will fail for the following data points:")
+    for i in range(x_range.size):
+        a = a_range[i]
+        b = b_range[i]
+        x = x_range[i]
+        # take care of difficult corner cases
+        maxterms = 1000
+        if a < 1e-6 and x >= exp_inf/10:
+            maxterms = 2000
+        f = mp_wright_bessel(a, b, x, maxterms=maxterms)
+        if does_fail[i]:
+            print("failing data point a, b, x, value = "
+                  f"[{a}, {b}, {x}, {f}]")
+        else:
+            dataset.append((a, b, x, f))
+    dataset = np.array(dataset)
+
+    filename = os.path.join(pwd, '..', 'tests', 'data', 'local',
+                            'wright_bessel.txt')
+    np.savetxt(filename, dataset)
+
+    print(f"{(time() - t0)/60:.1f} minutes elapsed")
+
+
+if __name__ == "__main__":
+    main()
diff --git a/venv/lib/python3.12/site-packages/scipy/special/_precompute/wrightomega.py b/venv/lib/python3.12/site-packages/scipy/special/_precompute/wrightomega.py
new file mode 100644
index 0000000000000000000000000000000000000000..0bcd0345a9c1b90c45b0e9e3340ab4da4ec5c6d7
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/_precompute/wrightomega.py
@@ -0,0 +1,41 @@
+import numpy as np
+
+try:
+    import mpmath
+except ImportError:
+    pass
+
+
+def mpmath_wrightomega(x):
+    return mpmath.lambertw(mpmath.exp(x), mpmath.mpf('-0.5'))
+
+
+def wrightomega_series_error(x):
+    series = x
+    desired = mpmath_wrightomega(x)
+    return abs(series - desired) / desired
+
+
+def wrightomega_exp_error(x):
+    exponential_approx = mpmath.exp(x)
+    desired = mpmath_wrightomega(x)
+    return abs(exponential_approx - desired) / desired
+
+
+def main():
+    desired_error = 2 * np.finfo(float).eps
+    print('Series Error')
+    for x in [1e5, 1e10, 1e15, 1e20]:
+        with mpmath.workdps(100):
+            error = wrightomega_series_error(x)
+        print(x, error, error < desired_error)
+
+    print('Exp error')
+    for x in [-10, -25, -50, -100, -200, -400, -700, -740]:
+        with mpmath.workdps(100):
+            error = wrightomega_exp_error(x)
+        print(x, error, error < desired_error)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/venv/lib/python3.12/site-packages/scipy/special/_precompute/zetac.py b/venv/lib/python3.12/site-packages/scipy/special/_precompute/zetac.py
new file mode 100644
index 0000000000000000000000000000000000000000..d408b1a2fffb6872287452923fcc9394adc13a7c
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/_precompute/zetac.py
@@ -0,0 +1,27 @@
+"""Compute the Taylor series for zeta(x) - 1 around x = 0."""
+try:
+    import mpmath
+except ImportError:
+    pass
+
+
+def zetac_series(N):
+    coeffs = []
+    with mpmath.workdps(100):
+        coeffs.append(-1.5)
+        for n in range(1, N):
+            coeff = mpmath.diff(mpmath.zeta, 0, n)/mpmath.factorial(n)
+            coeffs.append(coeff)
+    return coeffs
+
+
+def main():
+    print(__doc__)
+    coeffs = zetac_series(10)
+    coeffs = [mpmath.nstr(x, 20, min_fixed=0, max_fixed=0)
+              for x in coeffs]
+    print("\n".join(coeffs[::-1]))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/venv/lib/python3.12/site-packages/scipy/special/_sf_error.py b/venv/lib/python3.12/site-packages/scipy/special/_sf_error.py
new file mode 100644
index 0000000000000000000000000000000000000000..e1edc9800759dfda9e49bde1becc775a64bce958
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/_sf_error.py
@@ -0,0 +1,15 @@
+"""Warnings and Exceptions that can be raised by special functions."""
+import warnings
+
+
+class SpecialFunctionWarning(Warning):
+    """Warning that can be emitted by special functions."""
+    pass
+
+
+warnings.simplefilter("always", category=SpecialFunctionWarning)
+
+
+class SpecialFunctionError(Exception):
+    """Exception that can be raised by special functions."""
+    pass
diff --git a/venv/lib/python3.12/site-packages/scipy/special/_specfun.cpython-312-x86_64-linux-gnu.so b/venv/lib/python3.12/site-packages/scipy/special/_specfun.cpython-312-x86_64-linux-gnu.so
new file mode 100644
index 0000000000000000000000000000000000000000..6dc753a47f1952fe995cf414ce5d795fd12c19c7
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/_specfun.cpython-312-x86_64-linux-gnu.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:2c27f344e2f8d3e97e3b070ee440592ba90324ae4263524ff4e85168388d6924
+size 228336
diff --git a/venv/lib/python3.12/site-packages/scipy/special/_special_ufuncs.cpython-312-x86_64-linux-gnu.so b/venv/lib/python3.12/site-packages/scipy/special/_special_ufuncs.cpython-312-x86_64-linux-gnu.so
new file mode 100644
index 0000000000000000000000000000000000000000..def03c1f1dee7edd728a07429558b89844386033
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/_special_ufuncs.cpython-312-x86_64-linux-gnu.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:5aa5984456082656fa66012b11e4eebff25e1e993cf6d50460a083086f0679d3
+size 1659864
diff --git a/venv/lib/python3.12/site-packages/scipy/special/_spfun_stats.py b/venv/lib/python3.12/site-packages/scipy/special/_spfun_stats.py
new file mode 100644
index 0000000000000000000000000000000000000000..0b54f474ffd5fedeaa5cc44ce363e0761818f216
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/_spfun_stats.py
@@ -0,0 +1,178 @@
+# Last Change: Sat Mar 21 02:00 PM 2009 J
+
+# Copyright (c) 2001, 2002 Enthought, Inc.
+#
+# All rights reserved.
+#
+# Redistribution and use in source and binary forms, with or without
+# modification, are permitted provided that the following conditions are met:
+#
+#   a. Redistributions of source code must retain the above copyright notice,
+#      this list of conditions and the following disclaimer.
+#   b. Redistributions in binary form must reproduce the above copyright
+#      notice, this list of conditions and the following disclaimer in the
+#      documentation and/or other materials provided with the distribution.
+#   c. Neither the name of the Enthought nor the names of its contributors
+#      may be used to endorse or promote products derived from this software
+#      without specific prior written permission.
+#
+#
+# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+# AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+# ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE FOR
+# ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+# DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+# SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+# CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+# LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+# OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH
+# DAMAGE.
+
+"""Some more special functions which may be useful for multivariate statistical
+analysis."""
+
+import numpy as np
+
+import scipy.special._gufuncs as _gufuncs
+from scipy.special import gammaln as loggam
+from scipy.special._ufunc_tools import _with_cache_optimization
+
+
+__all__ = ['multigammaln']
+
+
+def multigammaln(a, d):
+    r"""Returns the log of multivariate gamma, also sometimes called the
+    generalized gamma.
+
+    Parameters
+    ----------
+    a : ndarray
+        The multivariate gamma is computed for each item of `a`.
+    d : int
+        The dimension of the space of integration.
+
+    Returns
+    -------
+    res : ndarray
+        The values of the log multivariate gamma at the given points `a`.
+
+    Notes
+    -----
+    The formal definition of the multivariate gamma of dimension d for a real
+    `a` is
+
+    .. math::
+
+        \Gamma_d(a) = \int_{A>0} e^{-tr(A)} |A|^{a - (d+1)/2} dA
+
+    with the condition :math:`a > (d-1)/2`, and :math:`A > 0` being the set of
+    all the positive definite matrices of dimension `d`.  Note that `a` is a
+    scalar: the integrand only is multivariate, the argument is not (the
+    function is defined over a subset of the real set).
+
+    This can be proven to be equal to the much friendlier equation
+
+    .. math::
+
+        \Gamma_d(a) = \pi^{d(d-1)/4} \prod_{i=1}^{d} \Gamma(a - (i-1)/2).
+
+    References
+    ----------
+    R. J. Muirhead, Aspects of multivariate statistical theory (Wiley Series in
+    probability and mathematical statistics).
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.special import multigammaln, gammaln
+    >>> a = 23.5
+    >>> d = 10
+    >>> multigammaln(a, d)
+    454.1488605074416
+
+    Verify that the result agrees with the logarithm of the equation
+    shown above:
+
+    >>> d*(d-1)/4*np.log(np.pi) + gammaln(a - 0.5*np.arange(0, d)).sum()
+    454.1488605074416
+    """
+    a = np.asarray(a)
+    # Support for 0d arrays is needed for array_api_strict and dask.
+    d = np.asarray(d)[()]
+    if not np.isscalar(d) or (np.floor(d) != d):
+        raise ValueError("d should be a positive integer (dimension)")
+    if np.any(a <= 0.5 * (d - 1)):
+        raise ValueError(f"condition a ({a}) > 0.5 * (d-1) ({0.5 * (d-1)}) not met")
+
+    res = (d * (d-1) * 0.25) * np.log(np.pi)
+    res += np.sum(loggam([(a - (j - 1.)/2) for j in range(1, d+1)]), axis=0)
+    return res
+
+
+_poisson_binom_pmf_doc = (
+    """Returns pmf of Poisson Binomial distribution.
+
+    Parameters
+    ----------
+    k : array
+        Number of successes at which to evaluate pmf.
+
+    p : array
+        Success probabilities of independent Bernoulli trials.
+
+    Notes
+    -----
+    This is equivalent to a gufunc with signature ``()(i)->()``.
+    The last dimension of `p` contains success probabilities and
+    the preceding dimensions are batch dimensions. The batch
+    dimensions are broadcast against ``k``.
+
+    The output will be C contiguous regardless of the contiguity of
+    `k` and `p`.
+
+    """
+)
+
+
+_poisson_binom_pmf = _with_cache_optimization(
+    name="_poisson_binom_pmf",
+    arg_names=["k", "p"],
+    docstring=_poisson_binom_pmf_doc,
+    ufunc=_gufuncs._poisson_binom_pmf,
+    cache_arg_indices=[1],
+)
+
+
+_poisson_binom_cdf_doc = (
+    """Returns cdf of Poisson Binomial distribution.
+
+    Parameters
+    ----------
+    k : array
+        Number of successes at which to evaluate cdf.
+
+    p : array
+        Success probabilities of independent Bernoulli trials.
+
+    Notes
+    -----
+    This is equivalent to a gufunc with signature ``()(i)->()``.
+    The last dimension of `p` contains success probabilities and
+    the preceding dimensions are batch dimensions. The batch
+    dimensions are broadcast against ``k``.
+
+    The output will be C contiguous regardless of the contiguity of
+    `k` and `p`.
+
+    """
+)
+
+_poisson_binom_cdf = _with_cache_optimization(
+    name="_poisson_binom_cdf",
+    arg_names=["k", "p"],
+    docstring=_poisson_binom_cdf_doc,
+    ufunc=_gufuncs._poisson_binom_cdf,
+    cache_arg_indices=[1],
+)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/_spherical_bessel.py b/venv/lib/python3.12/site-packages/scipy/special/_spherical_bessel.py
new file mode 100644
index 0000000000000000000000000000000000000000..56b345b78ad41f8e5c3c0a303b287611f7be9f4c
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/_spherical_bessel.py
@@ -0,0 +1,401 @@
+from functools import wraps
+import scipy._external.array_api_extra as xpx
+import numpy as np
+from ._ufuncs import (_spherical_jn, _spherical_yn, _spherical_in,
+                      _spherical_kn, _spherical_jn_d, _spherical_yn_d,
+                      _spherical_in_d, _spherical_kn_d)
+
+
+def use_reflection(sign_n_even=None, reflection_fun=None):
+    # - If reflection_fun is not specified, reflects negative `z` and multiplies
+    #   output by appropriate sign (indicated by `sign_n_even`).
+    # - If reflection_fun is specified, calls `reflection_fun` instead of `fun`.
+    # See DLMF 10.47(v) https://dlmf.nist.gov/10.47
+    def decorator(fun):
+        def standard_reflection(n, z, derivative):
+            # sign_n_even indicates the sign when the order `n` is even
+            sign = np.where(n % 2 == 0, sign_n_even, -sign_n_even)
+            # By the chain rule, differentiation at `-z` adds a minus sign
+            sign = -sign if derivative else sign
+            # Evaluate at positive z (minus negative z) and adjust the sign
+            return fun(n, -z, derivative) * sign
+
+        @wraps(fun)
+        def wrapper(n, z, derivative=False):
+            z = np.asarray(z)
+
+            if np.issubdtype(z.dtype, np.complexfloating):
+                return fun(n, z, derivative)  # complex dtype just works
+
+            f2 = standard_reflection if reflection_fun is None else reflection_fun
+            return xpx.apply_where(z.real >= 0, (n, z),
+                                   lambda n, z: fun(n, z, derivative),
+                                   lambda n, z: f2(n, z, derivative))[()]
+        return wrapper
+    return decorator
+
+
+@use_reflection(+1)  # See DLMF 10.47(v) https://dlmf.nist.gov/10.47
+def spherical_jn(n, z, derivative=False):
+    r"""Spherical Bessel function of the first kind or its derivative.
+
+    Defined as [1]_,
+
+    .. math:: j_n(z) = \sqrt{\frac{\pi}{2z}} J_{n + 1/2}(z),
+
+    where :math:`J_n` is the Bessel function of the first kind.
+
+    Parameters
+    ----------
+    n : int, array_like
+        Order of the Bessel function (n >= 0).
+    z : complex or float, array_like
+        Argument of the Bessel function.
+    derivative : bool, optional
+        If True, the value of the derivative (rather than the function
+        itself) is returned.
+
+    Returns
+    -------
+    jn : ndarray
+        Value or derivative of spherical Bessel function of the first kind.
+
+    Notes
+    -----
+    For real arguments greater than the order, the function is computed
+    using the ascending recurrence [2]_. For small real or complex
+    arguments, the definitional relation to the cylindrical Bessel function
+    of the first kind is used.
+
+    The derivative is computed using the relations [3]_,
+
+    .. math::
+        j_n'(z) = j_{n-1}(z) - \frac{n + 1}{z} j_n(z).
+
+        j_0'(z) = -j_1(z)
+
+
+    .. versionadded:: 0.18.0
+
+    References
+    ----------
+    .. [1] https://dlmf.nist.gov/10.47.E3
+    .. [2] https://dlmf.nist.gov/10.51.E1
+    .. [3] https://dlmf.nist.gov/10.51.E2
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+
+    Examples
+    --------
+    The spherical Bessel functions of the first kind :math:`j_n` accept
+    both real and complex second argument. They can return a complex type:
+
+    >>> from scipy.special import spherical_jn
+    >>> spherical_jn(0, 3+5j)
+    (-9.878987731663194-8.021894345786002j)
+    >>> type(spherical_jn(0, 3+5j))
+    <class 'numpy.complex128'>
+
+    We can verify the relation for the derivative from the Notes
+    for :math:`n=3` in the interval :math:`[1, 2]`:
+
+    >>> import numpy as np
+    >>> x = np.arange(1.0, 2.0, 0.01)
+    >>> np.allclose(spherical_jn(3, x, True),
+    ...             spherical_jn(2, x) - 4/x * spherical_jn(3, x))
+    True
+
+    The first few :math:`j_n` with real argument:
+
+    >>> import matplotlib.pyplot as plt
+    >>> x = np.arange(0.0, 10.0, 0.01)
+    >>> fig, ax = plt.subplots()
+    >>> ax.set_ylim(-0.5, 1.5)
+    >>> ax.set_title(r'Spherical Bessel functions $j_n$')
+    >>> for n in np.arange(0, 4):
+    ...     ax.plot(x, spherical_jn(n, x), label=rf'$j_{n}$')
+    >>> plt.legend(loc='best')
+    >>> plt.show()
+
+    """
+    n = np.asarray(n, dtype=np.dtype("long"))
+    if derivative:
+        return _spherical_jn_d(n, z)
+    else:
+        return _spherical_jn(n, z)
+
+
+@use_reflection(-1)  # See DLMF 10.47(v) https://dlmf.nist.gov/10.47
+def spherical_yn(n, z, derivative=False):
+    r"""Spherical Bessel function of the second kind or its derivative.
+
+    Defined as [1]_,
+
+    .. math:: y_n(z) = \sqrt{\frac{\pi}{2z}} Y_{n + 1/2}(z),
+
+    where :math:`Y_n` is the Bessel function of the second kind.
+
+    Parameters
+    ----------
+    n : int, array_like
+        Order of the Bessel function (n >= 0).
+    z : complex or float, array_like
+        Argument of the Bessel function.
+    derivative : bool, optional
+        If True, the value of the derivative (rather than the function
+        itself) is returned.
+
+    Returns
+    -------
+    yn : ndarray
+        Value or derivative of spherical Bessel function of the second kind.
+
+    Notes
+    -----
+    For real arguments, the function is computed using the ascending
+    recurrence [2]_.  For complex arguments, the definitional relation to
+    the cylindrical Bessel function of the second kind is used.
+
+    The derivative is computed using the relations [3]_,
+
+    .. math::
+        y_n' = y_{n-1} - \frac{n + 1}{z} y_n.
+
+        y_0' = -y_1
+
+
+    .. versionadded:: 0.18.0
+
+    References
+    ----------
+    .. [1] https://dlmf.nist.gov/10.47.E4
+    .. [2] https://dlmf.nist.gov/10.51.E1
+    .. [3] https://dlmf.nist.gov/10.51.E2
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+
+    Examples
+    --------
+    The spherical Bessel functions of the second kind :math:`y_n` accept
+    both real and complex second argument. They can return a complex type:
+
+    >>> from scipy.special import spherical_yn
+    >>> spherical_yn(0, 3+5j)
+    (8.022343088587197-9.880052589376795j)
+    >>> type(spherical_yn(0, 3+5j))
+    <class 'numpy.complex128'>
+
+    We can verify the relation for the derivative from the Notes
+    for :math:`n=3` in the interval :math:`[1, 2]`:
+
+    >>> import numpy as np
+    >>> x = np.arange(1.0, 2.0, 0.01)
+    >>> np.allclose(spherical_yn(3, x, True),
+    ...             spherical_yn(2, x) - 4/x * spherical_yn(3, x))
+    True
+
+    The first few :math:`y_n` with real argument:
+
+    >>> import matplotlib.pyplot as plt
+    >>> x = np.arange(0.0, 10.0, 0.01)
+    >>> fig, ax = plt.subplots()
+    >>> ax.set_ylim(-2.0, 1.0)
+    >>> ax.set_title(r'Spherical Bessel functions $y_n$')
+    >>> for n in np.arange(0, 4):
+    ...     ax.plot(x, spherical_yn(n, x), label=rf'$y_{n}$')
+    >>> plt.legend(loc='best')
+    >>> plt.show()
+
+    """
+    n = np.asarray(n, dtype=np.dtype("long"))
+    if derivative:
+        return _spherical_yn_d(n, z)
+    else:
+        return _spherical_yn(n, z)
+
+
+@use_reflection(+1)  # See DLMF 10.47(v) https://dlmf.nist.gov/10.47
+def spherical_in(n, z, derivative=False):
+    r"""Modified spherical Bessel function of the first kind or its derivative.
+
+    Defined as [1]_,
+
+    .. math:: i_n(z) = \sqrt{\frac{\pi}{2z}} I_{n + 1/2}(z),
+
+    where :math:`I_n` is the modified Bessel function of the first kind.
+
+    Parameters
+    ----------
+    n : int, array_like
+        Order of the Bessel function (n >= 0).
+    z : complex or float, array_like
+        Argument of the Bessel function.
+    derivative : bool, optional
+        If True, the value of the derivative (rather than the function
+        itself) is returned.
+
+    Returns
+    -------
+    in : ndarray
+        Value or derivative of modified spherical Bessel function of the first kind.
+
+    Notes
+    -----
+    The function is computed using its definitional relation to the
+    modified cylindrical Bessel function of the first kind.
+
+    The derivative is computed using the relations [2]_,
+
+    .. math::
+        i_n' = i_{n-1} - \frac{n + 1}{z} i_n.
+
+        i_1' = i_0
+
+
+    .. versionadded:: 0.18.0
+
+    References
+    ----------
+    .. [1] https://dlmf.nist.gov/10.47.E7
+    .. [2] https://dlmf.nist.gov/10.51.E5
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+
+    Examples
+    --------
+    The modified spherical Bessel functions of the first kind :math:`i_n`
+    accept both real and complex second argument.
+    They can return a complex type:
+
+    >>> from scipy.special import spherical_in
+    >>> spherical_in(0, 3+5j)
+    (-1.1689867793369182-1.2697305267234222j)
+    >>> type(spherical_in(0, 3+5j))
+    <class 'numpy.complex128'>
+
+    We can verify the relation for the derivative from the Notes
+    for :math:`n=3` in the interval :math:`[1, 2]`:
+
+    >>> import numpy as np
+    >>> x = np.arange(1.0, 2.0, 0.01)
+    >>> np.allclose(spherical_in(3, x, True),
+    ...             spherical_in(2, x) - 4/x * spherical_in(3, x))
+    True
+
+    The first few :math:`i_n` with real argument:
+
+    >>> import matplotlib.pyplot as plt
+    >>> x = np.arange(0.0, 6.0, 0.01)
+    >>> fig, ax = plt.subplots()
+    >>> ax.set_ylim(-0.5, 5.0)
+    >>> ax.set_title(r'Modified spherical Bessel functions $i_n$')
+    >>> for n in np.arange(0, 4):
+    ...     ax.plot(x, spherical_in(n, x), label=rf'$i_{n}$')
+    >>> plt.legend(loc='best')
+    >>> plt.show()
+
+    """
+    n = np.asarray(n, dtype=np.dtype("long"))
+    if derivative:
+        return _spherical_in_d(n, z)
+    else:
+        return _spherical_in(n, z)
+
+
+def spherical_kn_reflection(n, z, derivative=False):
+    # More complex than the other cases, and this will likely be re-implemented
+    # in C++ anyway. Would require multiple function evaluations. Probably about
+    # as fast to just resort to complex math, and much simpler.
+    return spherical_kn(n, z + 0j, derivative=derivative).real
+
+
+@use_reflection(reflection_fun=spherical_kn_reflection)
+def spherical_kn(n, z, derivative=False):
+    r"""Modified spherical Bessel function of the second kind or its derivative.
+
+    Defined as [1]_,
+
+    .. math:: k_n(z) = \sqrt{\frac{\pi}{2z}} K_{n + 1/2}(z),
+
+    where :math:`K_n` is the modified Bessel function of the second kind.
+
+    Parameters
+    ----------
+    n : int, array_like
+        Order of the Bessel function (n >= 0).
+    z : complex or float, array_like
+        Argument of the Bessel function.
+    derivative : bool, optional
+        If True, the value of the derivative (rather than the function
+        itself) is returned.
+
+    Returns
+    -------
+    kn : ndarray
+        Value or derivative of modified spherical Bessel function of the second kind.
+
+    Notes
+    -----
+    The function is computed using its definitional relation to the
+    modified cylindrical Bessel function of the second kind.
+
+    The derivative is computed using the relations [2]_,
+
+    .. math::
+        k_n' = -k_{n-1} - \frac{n + 1}{z} k_n.
+
+        k_0' = -k_1
+
+
+    .. versionadded:: 0.18.0
+
+    References
+    ----------
+    .. [1] https://dlmf.nist.gov/10.47.E9
+    .. [2] https://dlmf.nist.gov/10.51.E5
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+
+    Examples
+    --------
+    The modified spherical Bessel functions of the second kind :math:`k_n`
+    accept both real and complex second argument.
+    They can return a complex type:
+
+    >>> from scipy.special import spherical_kn
+    >>> spherical_kn(0, 3+5j)
+    (0.012985785614001561+0.003354691603137546j)
+    >>> type(spherical_kn(0, 3+5j))
+    <class 'numpy.complex128'>
+
+    We can verify the relation for the derivative from the Notes
+    for :math:`n=3` in the interval :math:`[1, 2]`:
+
+    >>> import numpy as np
+    >>> x = np.arange(1.0, 2.0, 0.01)
+    >>> np.allclose(spherical_kn(3, x, True),
+    ...             - 4/x * spherical_kn(3, x) - spherical_kn(2, x))
+    True
+
+    The first few :math:`k_n` with real argument:
+
+    >>> import matplotlib.pyplot as plt
+    >>> x = np.arange(0.0, 4.0, 0.01)
+    >>> fig, ax = plt.subplots()
+    >>> ax.set_ylim(0.0, 5.0)
+    >>> ax.set_title(r'Modified spherical Bessel functions $k_n$')
+    >>> for n in np.arange(0, 4):
+    ...     ax.plot(x, spherical_kn(n, x), label=rf'$k_{n}$')
+    >>> plt.legend(loc='best')
+    >>> plt.show()
+
+    """
+    n = np.asarray(n, dtype=np.dtype("long"))
+    if derivative:
+        return _spherical_kn_d(n, z)
+    else:
+        return _spherical_kn(n, z)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/_support_alternative_backends.py b/venv/lib/python3.12/site-packages/scipy/special/_support_alternative_backends.py
new file mode 100644
index 0000000000000000000000000000000000000000..262b974ee26d3bc1c7f69a9275e7527faff78ffc
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/_support_alternative_backends.py
@@ -0,0 +1,933 @@
+import functools
+import operator
+from collections.abc import Callable, Mapping
+from dataclasses import dataclass
+from types import ModuleType
+
+import numpy as np
+from scipy._lib._array_api import (
+    array_namespace, scipy_namespace_for, is_numpy, is_dask, is_marray, is_jax_array,
+    is_jax, xp_promote, xp_capabilities, SCIPY_ARRAY_API, get_native_namespace_name,
+    is_array_api_obj
+)
+import scipy._external.array_api_extra as xpx
+from . import _basic
+from . import _spfun_stats
+from . import _ufuncs
+
+# mypy: disable-error-code=dict-item
+
+def _special_namespace_for(xp):
+    spx = scipy_namespace_for(xp)
+    return getattr(spx, "special", None)
+
+
+@dataclass
+class _FuncInfo:
+    # NumPy-only function. IT MUST BE ELEMENTWISE.
+    func: Callable
+    # Number of arguments, not counting out=
+    # This is for testing purposes only, due to the fact that
+    # inspect.signature() just returns *args for ufuncs.
+    n_args: int
+    # @xp_capabilities decorator, for the purpose of
+    # documentation and unit testing. Omit to indicate
+    # full support for all backends.
+    xp_capabilities: Callable[[Callable], Callable] | None = None
+    # Generic implementation to fall back on if there is no native dispatch
+    # available. This is a function that accepts (main namespace, scipy namespace)
+    # and returns the final callable, or None if not available.
+    generic_impl: Callable[
+        [ModuleType, ModuleType | None], Callable | None
+    ] | None = None
+    # Handle case where a backend uses an alternative name for a function.
+    # Should map backend names to alternative function names.
+    alt_names_map: dict[str, str] | None = None
+    # Some functions only take integer arrays for some arguments.
+    int_only: tuple[bool, ...] | None = None
+    # For testing purposes, whether tests should only use positive values
+    # for some arguments. If bool and equal to True, restrict to positive
+    # values for all arguments. To restrict only some arguments to positive
+    # values, pass a tuple of bool of the same length as the number of
+    # arguments, the ith entry in the tuple controls positive_only for
+    # the ith argument. To make backend specific choices for positive_only,
+    # pass in a dict mapping backend names to bool or tuple[bool, ...].
+    positive_only: (
+        bool | tuple[bool, ...] | Mapping[str, bool | tuple[bool, ...]]
+    ) = False
+    # Some special functions are not ufuncs and ufunc-specific tests
+    # should not be applied to these.
+    is_ufunc: bool = True
+    # Some non-ufunc special functions take only Python ints for some arguments.
+    # If so, python_int_only should be a tuple of the same length as the number
+    # of arguments,with value True if the corresponding argument needs to be a
+    # Python int.
+    # Can also take a dict mapping backends to such tuples if an argument being
+    # Python int only is backend specific.
+    python_int_only: dict[str, tuple[bool, ...]] | tuple[bool, ...] | None = None
+    # Some functions which seem to be scalar also accept 0d arrays.
+    scalar_or_0d_only: dict[str, tuple[bool, ...]] | tuple[bool, ...] | None = None
+    # Some functions may not work well with very large integer valued arguments.
+    test_large_ints: bool = True
+    # Some non-ufunc special functions don't decay 0d arrays to scalar.
+    produces_0d: bool = False
+    # Whether or not uses native PyTorch or falls back to NumPy/SciPy. This
+    # is needed because in PyTorch, the default dtype affects promotion
+    # rules when mixing integer and floating dtypes, so relying on a
+    # NumPy/SciPy fallback when the default dtype is other than float64 can lead
+    # to float64 output when native PyTorch would have e.g. float32 output. This
+    # must be accounted for in tests. Not putting this in xp_capabilities for now,
+    # but in the future I think it's likely we may want to add a warning to
+    # xp_capabilities when not using native PyTorch on CPU.
+    torch_native: bool = True
+    # Place a backend in this tuple if `func` is available as `xp.func` but not
+    # available in the `scipy.special` namespace for this backend.
+    # One example is `jax.numpy.sinc` being available but not `jax.scipy.special.sinc`.
+    backends_with_func_in_xp: tuple[str, ...] = ()
+
+    @property
+    def name(self):
+        return self.func.__name__
+
+    # These are needed by @lru_cache below
+    def __hash__(self):
+        return hash(self.func)
+
+    def __eq__(self, other):
+        return isinstance(other, _FuncInfo) and self.func == other.func
+
+    @property
+    def wrapper(self):
+        if self.name in globals():
+            # Already initialised. We are likely in a unit test.
+            # Return function potentially overridden by xpx.testing.lazy_xp_function.
+            import scipy.special
+            return getattr(scipy.special, self.name)
+
+        if SCIPY_ARRAY_API:
+            @functools.wraps(self.func)
+            def wrapped(*args, **kwargs):
+                xp = array_namespace(*args)
+                return self._wrapper_for(xp)(*args, **kwargs)
+
+            # Allow pickling the function. Normally this is done by @wraps,
+            # but in this case it doesn't work because self.func is a ufunc.
+            wrapped.__module__ = "scipy.special"
+            wrapped.__qualname__ = self.name
+            func = wrapped
+        else:
+            func = self.func
+
+        capabilities = self.xp_capabilities or xp_capabilities()
+        # In order to retain a naked ufunc when SCIPY_ARRAY_API is
+        # disabled, xp_capabilities must apply its changes in place.
+        cap_func = capabilities(func)
+        assert cap_func is func
+        return func
+
+    @functools.lru_cache(1000)
+    def _wrapper_for(self, xp):
+        if is_numpy(xp):
+            return self.func
+
+        # If a native implementation is available, use that
+        in_xp = get_native_namespace_name(xp) in self.backends_with_func_in_xp
+        namespace = xp if in_xp else _special_namespace_for(xp)
+        f = _get_native_func(
+            xp, namespace, self.name, alt_names_map=self.alt_names_map
+        )
+        if f is not None:
+            return f
+
+        if in_xp:
+            # when namespace is passed to self.generic_impl below, we want to
+            # make sure that it is the special namespace for xp and not xp
+            # itself, so raise if xp was incorrectly placed in
+            # `backends_with_func_in_xp`.
+            raise RuntimeError(
+                f"func {self.func} is not available as {xp.__name__}.{self.func}"
+                f" but {xp.__name__} was passed in ``in_xp``."
+            )
+
+        # If generic Array API implementation is available, use that
+        if self.generic_impl is not None:
+            f = self.generic_impl(xp, namespace)
+            if f is not None:
+                return f
+
+        if is_marray(xp):
+            # Unwrap the array, apply the function on the wrapped namespace,
+            # and then re-wrap it.
+            # IMPORTANT: this only works because all functions in this module
+            # are elementwise. Otherwise, we would not be able to define a
+            # general rule for mask propagation.
+
+            _f = globals()[self.name]  # Allow nested wrapping
+            def f(*args, _f=_f, xp=xp, **kwargs):
+                data_args = [getattr(arg, 'data', arg) for arg in args]
+                out = _f(*data_args, **kwargs)
+                mask = functools.reduce(operator.or_,
+                                        (getattr(arg, 'mask', False) for arg in args))
+                return xp.asarray(out, mask=mask)
+
+            return f
+
+        if is_dask(xp):
+            # Apply the function to each block of the Dask array.
+            # IMPORTANT: map_blocks works only because all functions in this module
+            # are elementwise. It would be a grave mistake to apply this to gufuncs
+            # or any other function with reductions, as they would change their
+            # output depending on chunking!
+
+            _f = globals()[self.name]  # Allow nested wrapping
+            def f(*args, _f=_f, xp=xp, **kwargs):
+                # Hide dtype kwarg from map_blocks
+                return xp.map_blocks(functools.partial(_f, **kwargs), *args)
+
+            return f
+
+        # As a final resort, use the NumPy/SciPy implementation
+        _f = self.func
+
+        if is_jax(xp) and self.is_ufunc:
+            # if this is a ufunc, we can use the resolve_dtypes method to figure
+            # out what the output dtype should be and use lazy_apply to make this
+            # work with the JAX JIT. Since pure_callback used in lazy_apply will
+            # convert all of the inputs to eager JAX arrays, we will also need to
+            # get the input dtypes inferred from resolve_dtypes so that Python
+            # scalar inputs can be cast to the correct dtype under NEP50 weak
+            # promotion rules rather than getting promoted to the default currently
+            # set in JAX. One cannot just use xp_promote for the input dtypes because
+            # some ufuncs have integer only args.
+            def f(*args, _f=_f, xp=xp, **kwargs):
+                dtypes = (arg.dtype if is_jax_array(arg) else type(arg) for arg in args)
+                # result_dtypes needs an arg for the dtype of the optional out param.
+                # Use `None` since `out` is incompatible with JAX's immutability.
+                dtypes = (*dtypes, None)
+                # JAX uses NumPy dtypes so we can just pass these directly to
+                # resolve_dtypes. TODO: generalize to other lazy backends.
+                dtypes = _f.resolve_dtypes(dtypes)
+                out_dtype = dtypes[-1]
+                args = [
+                    xp.asarray(arg, dtype=dtype)
+                    for arg, dtype in zip(args, dtypes[:-1])
+                ]
+                return xpx.lazy_apply(
+                    _f, *args, xp=xp, as_numpy=True, dtype=out_dtype, **kwargs
+                )
+        else:
+            def f(*args, _f=_f, xp=xp, **kwargs):
+                # Check with `is_array_api_obj` to keep Python scalars untouched so that
+                # NEP50 can be followed.
+                args = [
+                    np.asarray(arg) if is_array_api_obj(arg) else arg for arg in args
+                ]
+                out = _f(*args, **kwargs)
+                return xp.asarray(out)
+
+        return f
+
+
+def _get_native_func(xp, namespace, f_name, *, alt_names_map=None):
+    if alt_names_map is None:
+        alt_names_map = {}
+    f_name = alt_names_map.get(get_native_namespace_name(xp), f_name)
+    f = getattr(namespace, f_name, None)
+    if f is None and hasattr(xp, 'special'):
+        # Currently dead branch, in anticipation of 'special' Array API extension
+        # https://github.com/data-apis/array-api/issues/725
+        f = getattr(xp.special, f_name, None)
+    return f
+
+
+def _rel_entr(xp, spsx):
+    def __rel_entr(x, y, *, xp=xp):
+        # https://github.com/data-apis/array-api-extra/issues/160
+        mxp = array_namespace(x._meta, y._meta) if is_dask(xp) else xp
+        x, y = xp_promote(x, y, broadcast=True, force_floating=True, xp=xp)
+        xy_pos = (x > 0) & (y > 0)
+        xy_inf = xp.isinf(x) & xp.isinf(y)
+        res = xpx.apply_where(
+            xy_pos & ~xy_inf,
+            (x, y),
+            # Note: for very large x, this can overflow.
+            lambda x, y: x * (mxp.log(x) - mxp.log(y)),
+            fill_value=xp.inf
+        )
+        res = xpx.at(res)[(x == 0) & (y >= 0)].set(0)
+        res = xpx.at(res)[xp.isnan(x) | xp.isnan(y) | (xy_pos & xy_inf)].set(xp.nan)
+        return res
+
+    return __rel_entr
+
+
+def _xlogy(xp, spsx):
+    def __xlogy(x, y, *, xp=xp):
+        x, y = xp_promote(x, y, force_floating=True, xp=xp)
+        with np.errstate(divide='ignore', invalid='ignore'):
+            temp = x * xp.log(y)
+        return xp.where(x == 0., 0., temp)
+    return __xlogy
+
+
+
+def _chdtr(xp, spsx):
+    # The difference between this and just using `gammainc`
+    # defined by `get_array_special_func` is that if `gammainc`
+    # isn't found, we don't want to use the SciPy version; we'll
+    # return None here and use the SciPy version of `chdtr`.
+    gammainc = _get_native_func(xp, spsx, 'gammainc')
+    if gammainc is None:
+        return None
+
+    def __chdtr(v, x):
+        res = gammainc(v / 2, x / 2)  # this is almost all we need
+        # The rest can be removed when google/jax#20507 is resolved
+        mask = (v == 0) & (x > 0)  # JAX returns NaN
+        res = xp.where(mask, 1., res)
+        mask = xp.isinf(v) & xp.isinf(x)  # JAX returns 1.0
+        return xp.where(mask, xp.nan, res)
+    return __chdtr
+
+
+def _chdtrc(xp, spsx):
+    # The difference between this and just using `gammaincc`
+    # defined by `get_array_special_func` is that if `gammaincc`
+    # isn't found, we don't want to use the SciPy version; we'll
+    # return None here and use the SciPy version of `chdtrc`.
+    gammaincc = _get_native_func(xp, spsx, 'gammaincc')
+    if gammaincc is None:
+        return None
+
+    def __chdtrc(v, x):
+        res = xp.where(x >= 0, gammaincc(v/2, x/2), 1)
+        i_nan = ((x == 0) & (v == 0)) | xp.isnan(x) | xp.isnan(v) | (v < 0)
+        res = xp.where(i_nan, xp.nan, res)
+        return res
+    return __chdtrc
+
+
+def _betaincc(xp, spsx):
+    betainc = _get_native_func(xp, spsx, 'betainc')
+    if betainc is None:
+        return None
+
+    def __betaincc(a, b, x):
+        # not perfect; might want to just rely on SciPy
+        return betainc(b, a, 1-x)
+    return __betaincc
+
+
+def _stdtr(xp, spsx):
+    betainc = _get_native_func(xp, spsx, 'betainc')
+    if betainc is None:
+        return None
+
+    def __stdtr(df, t):
+        x = df / (t ** 2 + df)
+        tail = betainc(df / 2, 0.5, x) / 2
+        return xp.where(t < 0, tail, 1 - tail)
+
+    return __stdtr
+
+
+def _stdtrit(xp, spsx):
+    # Need either native stdtr or native betainc
+    stdtr = _get_native_func(xp, spsx, 'stdtr') or _stdtr(xp, spsx)
+    # If betainc is not defined, the root-finding would be done with `xp`
+    # despite `stdtr` being evaluated with SciPy/NumPy `stdtr`. Save the
+    # conversions: in this case, just evaluate `stdtrit` with SciPy/NumPy.
+    if stdtr is None:
+        return None
+
+    from scipy.optimize.elementwise import bracket_root, find_root
+
+    def __stdtrit(df, p):
+        def fun(t, df, p):  return stdtr(df, t) - p
+        res_bracket = bracket_root(fun, xp.zeros_like(p), args=(df, p))
+        res_root = find_root(fun, res_bracket.bracket, args=(df, p))
+        return res_root.x
+
+    return __stdtrit
+
+
+# Inventory of automatically dispatched functions
+# IMPORTANT: these must all be **elementwise** functions!
+
+# PyTorch doesn't implement `betainc`.
+# On torch CPU we can fall back to NumPy, but on GPU it won't work.
+_needs_betainc = xp_capabilities(cpu_only=True, exceptions=["jax.numpy", "cupy"])
+
+_special_funcs = (
+    _FuncInfo(
+        _ufuncs.bdtr, 3,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=True,
+        ),
+        int_only=(False, True, False), torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.bdtrc, 3,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=True,
+        ),
+        int_only=(False, True, False), torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.bdtri, 3,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=True,
+        ),
+        int_only=(False, True, False), torch_native=False,
+    ),
+    _FuncInfo(_ufuncs.betainc, 3, _needs_betainc, torch_native=False),
+    _FuncInfo(_ufuncs.betaincc, 3, _needs_betainc, generic_impl=_betaincc,
+              torch_native=False),
+    _FuncInfo(
+        _ufuncs.betaincinv, 3,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=True,
+        ),
+        test_large_ints=False, positive_only=True, torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.betaln, 2,
+        xp_capabilities(cpu_only=True, exceptions=["cupy", "jax.numpy"]),
+        # For betaln, nan mismatches can occur at negative integer a or b of
+        # sufficiently large magnitude.
+        positive_only={"jax.numpy": True}, torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.binom, 2,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=True,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.boxcox, 2,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=True,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.boxcox1p, 2,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=True,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.cbrt, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=True,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(_ufuncs.chdtr, 2, generic_impl=_chdtr),
+    _FuncInfo(_ufuncs.chdtrc, 2, generic_impl=_chdtrc,
+              # scipy/scipy#20972
+              positive_only={"cupy": True, "jax.numpy": True, "torch": True}),
+    _FuncInfo(
+        _ufuncs.chdtri, 2,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=True,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.cosdg, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=True,
+        ),
+        test_large_ints=False, torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.cosm1, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=True,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.cotdg, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=True,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.ellipk, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=True,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.ellipkm1, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=True,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(_ufuncs.entr, 1),
+    _FuncInfo(_ufuncs.erf, 1),
+    _FuncInfo(_ufuncs.erfc, 1),
+    _FuncInfo(
+        _ufuncs.erfcx, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy", "torch"],
+            jax_jit=True,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(_ufuncs.erfinv, 1),
+    _FuncInfo(
+        _ufuncs.exp1, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=True,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.exp10, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=True,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.exp2, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=True,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.exprel, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=True,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.expi, 1,
+        xp_capabilities(cpu_only=True, exceptions=["cupy", "jax.numpy"]),
+        torch_native=False,
+    ),
+    _FuncInfo(_ufuncs.expit, 1),
+    _FuncInfo(
+        _ufuncs.expn, 2,
+        xp_capabilities(cpu_only=True, exceptions=["cupy", "jax.numpy"]),
+        # Inconsistent behavior for negative n. expn is not defined here without
+        # taking analytic continuation.
+        positive_only=True,
+        int_only=(True, False), test_large_ints=False,
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.fdtr, 3,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=True,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.fdtrc, 3,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=True,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.fdtri, 3,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=True,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.gamma, 1,
+        xp_capabilities(cpu_only=True, exceptions=["cupy", "jax.numpy"]),
+        torch_native=False,
+    ),
+    _FuncInfo(_ufuncs.gammainc, 2),
+    _FuncInfo(
+        _ufuncs.gammaincc, 2,
+        # google/jax#20699
+        positive_only={"jax.numpy": True},
+    ),
+    _FuncInfo(
+        _ufuncs.gammainccinv, 2,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=True,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.gammaincinv, 2,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=True,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(_ufuncs.gammaln, 1),
+    _FuncInfo(
+        _ufuncs.gammasgn, 1,
+        xp_capabilities(cpu_only=True, exceptions=["cupy", "jax.numpy"]),
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.gdtr, 3,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=True,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.gdtrc, 3,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=True,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.huber, 2,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=True,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.hyp1f1, 3,
+        xp_capabilities(cpu_only=True, exceptions=["jax.numpy"]),
+        positive_only={"jax.numpy": True}, test_large_ints=False,
+        torch_native=False,
+    ),
+    # Comment out when jax>=0.6.1 is available in Conda for CI.
+    # (or add version requirements to xp_capabilities).
+    # _FuncInfo(
+    #     _ufuncs.hyp2f1, 4,
+    #     xp_capabilities(cpu_only=True, exceptions=["jax.numpy"]),
+    #     positive_only={"jax.numpy": True}, test_large_ints=False,
+    #     torch_native=False,
+    # ),
+    _FuncInfo(
+        _ufuncs.inv_boxcox, 2,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=True,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.inv_boxcox1p, 2,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=True,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(_ufuncs.i0, 1),
+    _FuncInfo(_ufuncs.i0e, 1),
+    _FuncInfo(_ufuncs.i1, 1),
+    _FuncInfo(_ufuncs.i1e, 1),
+    _FuncInfo(
+        _ufuncs.j0, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy", "torch"],
+            jax_jit=True,
+        ),
+        alt_names_map={"torch": "bessel_j0"}, test_large_ints=False,
+    ),
+    _FuncInfo(
+        _ufuncs.j1, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy", "torch"],
+            jax_jit=True,
+        ),
+        alt_names_map={"torch": "bessel_j1"}, test_large_ints=False,
+    ),
+    _FuncInfo(
+        _ufuncs.k0, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy", "torch"],
+            jax_jit=True,
+        ),
+        alt_names_map={"torch": "modified_bessel_k0"},
+    ),
+    _FuncInfo(
+        _ufuncs.k0e, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy", "torch"],
+            jax_jit=True,
+        ),
+        alt_names_map={"torch": "scaled_modified_bessel_k0"},
+        test_large_ints=False,
+    ),
+    _FuncInfo(
+        _ufuncs.k1, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy", "torch"],
+            jax_jit=True,
+        ),
+        alt_names_map={"torch": "modified_bessel_k1"},
+    ),
+    _FuncInfo(
+        _ufuncs.k1e, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy", "torch"],
+            jax_jit=True,
+        ),
+        alt_names_map={"torch": "scaled_modified_bessel_k1"},
+        test_large_ints=False),
+    _FuncInfo(
+        _ufuncs.kl_div, 2,
+        xp_capabilities(cpu_only=True, exceptions=["cupy", "jax.numpy"]),
+        torch_native=False,
+    ),
+    _FuncInfo(_ufuncs.log_ndtr, 1),
+    _FuncInfo(
+        _ufuncs.loggamma, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=True,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(_ufuncs.logit, 1),
+    _FuncInfo(
+        _ufuncs.lpmv, 3,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=True,
+        ),
+        torch_native=False,
+        test_large_ints=False,
+    ),
+    _FuncInfo(
+        _spfun_stats.multigammaln, 2,
+        is_ufunc=False,
+        python_int_only={
+            "cupy": (False, True),
+            "jax.numpy": (False, True),
+            "torch": (False, True),
+        },
+        scalar_or_0d_only={
+            "array_api_strict": (False, True),
+            "numpy": (False, True),
+            "dask.array": (False, True),
+            "marray": (False, True),
+        },
+        int_only=(False, True), test_large_ints=False,
+        positive_only=True, torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.nbdtr, 3,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=True,
+        ),
+        int_only=(True, True, False), positive_only=True,
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.nbdtrc, 3,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=True,
+        ),
+        int_only=(True, True, False), positive_only=True,
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.nbdtri, 3,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=True,
+        ),
+        int_only=(True, True, False), positive_only=True,
+        torch_native=False,
+    ),
+    _FuncInfo(_ufuncs.ndtr, 1),
+    _FuncInfo(_ufuncs.ndtri, 1),
+    _FuncInfo(
+        _ufuncs.pdtr, 2,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=True,
+        ),
+        positive_only=True, torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.pdtrc, 2,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=True,
+        ),
+        positive_only=True, torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.pdtri, 2,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=True,
+        ),
+        int_only=(True, False), positive_only=True,
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.poch, 2,
+        xp_capabilities(cpu_only=True, exceptions=["cupy", "jax.numpy"]),
+        test_large_ints=False, torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.pseudo_huber, 2,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=True,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _basic.polygamma, 2, int_only=(True, False), is_ufunc=False,
+              scalar_or_0d_only={"torch": (True, False)}, produces_0d=True,
+              positive_only={"torch": (True, False), "jax.numpy": True},
+              test_large_ints=False,
+    ),
+    _FuncInfo(_ufuncs.psi, 1, alt_names_map={"jax.numpy": "digamma"}),
+    _FuncInfo(
+        _ufuncs.radian, 3,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=True,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(_ufuncs.rel_entr, 2, generic_impl=_rel_entr),
+    _FuncInfo(
+        _ufuncs.rgamma, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=True,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _basic.sinc, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy", "torch"],
+            jax_jit=True,
+        ),
+        is_ufunc=False,
+        backends_with_func_in_xp=("jax.numpy",),
+    ),
+    _FuncInfo(
+        _ufuncs.sindg, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=True,
+        ),
+        test_large_ints=False, torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.spence, 1,
+        xp_capabilities(cpu_only=True, exceptions=["jax.numpy"]),
+        torch_native=False,
+    ),
+    _FuncInfo(_ufuncs.stdtr,  2, _needs_betainc, generic_impl=_stdtr,
+              torch_native=False),
+    _FuncInfo(
+        _ufuncs.stdtrit, 2,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],  # needs betainc
+            skip_backends=[("jax.numpy", "no scipy.optimize support")],
+        ),
+        generic_impl=_stdtrit, torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.tandg, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=True,
+        ),
+        test_large_ints=False, torch_native=False,
+    ),
+    _FuncInfo(_ufuncs.xlog1py, 2),
+    _FuncInfo(_ufuncs.xlogy, 2, generic_impl=_xlogy),
+    _FuncInfo(
+        _ufuncs.y0, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy", "torch"],
+            jax_jit=True,
+        ),
+        alt_names_map={"torch": "bessel_y0"}, test_large_ints=False,
+    ),
+    _FuncInfo(
+        _ufuncs.y1, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy", "torch"],
+            jax_jit=True,
+        ),
+        alt_names_map={"torch": "bessel_y1"}, test_large_ints=False,
+    ),
+    _FuncInfo(
+        _ufuncs.yn, 2,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=True,
+        ),
+        positive_only={"cupy": (True, False)}, int_only=(True, False),
+        test_large_ints=False, torch_native=False,
+    ),
+    _FuncInfo(
+        _basic.zeta, 2, is_ufunc=False,
+        positive_only={"jax.numpy": True, "torch": (True, False)},
+        test_large_ints=False,
+    ),
+    _FuncInfo(
+        _ufuncs.zetac, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=True,
+        ),
+        torch_native=False,
+    ),
+)
+
+# Override ufuncs.
+# When SCIPY_ARRAY_API is disabled, this exclusively updates the docstrings in place
+# and populates the xp_capabilities table, while retaining the original ufuncs.
+globals().update({nfo.func.__name__: nfo.wrapper for nfo in _special_funcs})
+# digamma is an alias for psi. Define here so it also has alternative backend
+# support. Add noqa because the linter gets confused by the sneaky way psi
+# is inserted into globals above.
+digamma = psi  # type:ignore[name-defined]  # noqa: F821
+__all__ = [nfo.func.__name__ for nfo in _special_funcs] + ["digamma"]
diff --git a/venv/lib/python3.12/site-packages/scipy/special/_test_internal.cpython-312-x86_64-linux-gnu.so b/venv/lib/python3.12/site-packages/scipy/special/_test_internal.cpython-312-x86_64-linux-gnu.so
new file mode 100644
index 0000000000000000000000000000000000000000..aa9d4ba427d00583713a5a7b92a13654be00b3e7
Binary files /dev/null and b/venv/lib/python3.12/site-packages/scipy/special/_test_internal.cpython-312-x86_64-linux-gnu.so differ
diff --git a/venv/lib/python3.12/site-packages/scipy/special/_test_internal.pyi b/venv/lib/python3.12/site-packages/scipy/special/_test_internal.pyi
new file mode 100644
index 0000000000000000000000000000000000000000..881b731f8f105c3be38e56fd6dc9e48c6b829553
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/_test_internal.pyi
@@ -0,0 +1,9 @@
+from typing import Literal
+
+import numpy as np
+
+def have_fenv() -> bool: ...
+def random_double(size: int, rng: np.random.RandomState) -> np.ndarray[tuple[int], np.dtype[np.float64]]: ...
+def test_add_round(size: int, mode: Literal["up", "down"], rng: np.random.RandomState) -> None: ...
+def _dd_exp(xhi: float, xlo: float) -> tuple[float, float]: ...
+def _dd_log(xhi: float, xlo: float) -> tuple[float, float]: ...
diff --git a/venv/lib/python3.12/site-packages/scipy/special/_testutils.py b/venv/lib/python3.12/site-packages/scipy/special/_testutils.py
new file mode 100644
index 0000000000000000000000000000000000000000..3ff4130dc3eb504a772f9b0ea2a2c74df714d999
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/_testutils.py
@@ -0,0 +1,321 @@
+import os
+import functools
+import operator
+from scipy._external.packaging_version import version
+
+import numpy as np
+from numpy.testing import assert_
+import pytest
+
+import scipy.special as sc
+
+__all__ = ['with_special_errors', 'assert_func_equal', 'FuncData']
+
+
+#------------------------------------------------------------------------------
+# Check if a module is present to be used in tests
+#------------------------------------------------------------------------------
+
+class MissingModule:
+    def __init__(self, name):
+        self.name = name
+
+
+def check_version(module, min_ver):
+    if type(module) is MissingModule:
+        return pytest.mark.skip(reason=f"{module.name} is not installed")
+    return pytest.mark.skipif(
+        version.parse(module.__version__) < version.Version(min_ver),
+        reason=f"{module.__name__} version >= {min_ver} required"
+    )
+
+
+#------------------------------------------------------------------------------
+# Enable convergence and loss of precision warnings -- turn off one by one
+#------------------------------------------------------------------------------
+
+def with_special_errors(func):
+    """
+    Enable special function errors (such as underflow, overflow,
+    loss of precision, etc.)
+    """
+    @functools.wraps(func)
+    def wrapper(*a, **kw):
+        with sc.errstate(all='raise'):
+            res = func(*a, **kw)
+        return res
+    return wrapper
+
+
+#------------------------------------------------------------------------------
+# Comparing function values at many data points at once, with helpful
+# error reports
+#------------------------------------------------------------------------------
+
+def assert_func_equal(func, results, points, rtol=None, atol=None,
+                      param_filter=None, knownfailure=None,
+                      vectorized=True, dtype=None, nan_ok=False,
+                      ignore_inf_sign=False, distinguish_nan_and_inf=True):
+    if hasattr(points, 'next'):
+        # it's a generator
+        points = list(points)
+
+    points = np.asarray(points)
+    if points.ndim == 1:
+        points = points[:,None]
+    nparams = points.shape[1]
+
+    if hasattr(results, '__name__'):
+        # function
+        data = points
+        result_columns = None
+        result_func = results
+    else:
+        # dataset
+        data = np.c_[points, results]
+        result_columns = list(range(nparams, data.shape[1]))
+        result_func = None
+
+    fdata = FuncData(func, data, list(range(nparams)),
+                     result_columns=result_columns, result_func=result_func,
+                     rtol=rtol, atol=atol, param_filter=param_filter,
+                     knownfailure=knownfailure, nan_ok=nan_ok, vectorized=vectorized,
+                     ignore_inf_sign=ignore_inf_sign,
+                     distinguish_nan_and_inf=distinguish_nan_and_inf)
+    fdata.check()
+
+
+class FuncData:
+    """
+    Data set for checking a special function.
+
+    Parameters
+    ----------
+    func : function
+        Function to test
+    data : numpy array
+        columnar data to use for testing
+    param_columns : int or tuple of ints
+        Columns indices in which the parameters to `func` lie.
+        Can be imaginary integers to indicate that the parameter
+        should be cast to complex.
+    result_columns : int or tuple of ints, optional
+        Column indices for expected results from `func`.
+    result_func : callable, optional
+        Function to call to obtain results.
+    rtol : float, optional
+        Required relative tolerance. Default is 5*eps.
+    atol : float, optional
+        Required absolute tolerance. Default is 5*tiny.
+    param_filter : function, or tuple of functions/Nones, optional
+        Filter functions to exclude some parameter ranges.
+        If omitted, no filtering is done.
+    knownfailure : str, optional
+        Known failure error message to raise when the test is run.
+        If omitted, no exception is raised.
+    nan_ok : bool, optional
+        If nan is always an accepted result.
+    vectorized : bool, optional
+        Whether all functions passed in are vectorized.
+    ignore_inf_sign : bool, optional
+        Whether to ignore signs of infinities.
+        (Doesn't matter for complex-valued functions.)
+    distinguish_nan_and_inf : bool, optional
+        If True, treat numbers which contain nans or infs as
+        equal. Sets ignore_inf_sign to be True.
+
+    """
+
+    def __init__(self, func, data, param_columns, result_columns=None,
+                 result_func=None, rtol=None, atol=None, param_filter=None,
+                 knownfailure=None, dataname=None, nan_ok=False, vectorized=True,
+                 ignore_inf_sign=False, distinguish_nan_and_inf=True):
+        self.func = func
+        self.data = data
+        self.dataname = dataname
+        if not hasattr(param_columns, '__len__'):
+            param_columns = (param_columns,)
+        self.param_columns = tuple(param_columns)
+        if result_columns is not None:
+            if not hasattr(result_columns, '__len__'):
+                result_columns = (result_columns,)
+            self.result_columns = tuple(result_columns)
+            if result_func is not None:
+                message = "Only result_func or result_columns should be provided"
+                raise ValueError(message)
+        elif result_func is not None:
+            self.result_columns = None
+        else:
+            raise ValueError("Either result_func or result_columns should be provided")
+        self.result_func = result_func
+        self.rtol = rtol
+        self.atol = atol
+        if not hasattr(param_filter, '__len__'):
+            param_filter = (param_filter,)
+        self.param_filter = param_filter
+        self.knownfailure = knownfailure
+        self.nan_ok = nan_ok
+        self.vectorized = vectorized
+        self.ignore_inf_sign = ignore_inf_sign
+        self.distinguish_nan_and_inf = distinguish_nan_and_inf
+        if not self.distinguish_nan_and_inf:
+            self.ignore_inf_sign = True
+
+    def get_tolerances(self, dtype):
+        if not np.issubdtype(dtype, np.inexact):
+            dtype = np.dtype(float)
+        info = np.finfo(dtype)
+        rtol, atol = self.rtol, self.atol
+        if rtol is None:
+            rtol = 5*info.eps
+        if atol is None:
+            atol = 5*info.tiny
+        return rtol, atol
+
+    def check(self, data=None, dtype=None, dtypes=None):
+        """Check the special function against the data."""
+        __tracebackhide__ = operator.methodcaller(
+            'errisinstance', AssertionError
+        )
+
+        if self.knownfailure:
+            pytest.xfail(reason=self.knownfailure)
+
+        if data is None:
+            data = self.data
+
+        if dtype is None:
+            dtype = data.dtype
+        else:
+            data = data.astype(dtype)
+
+        rtol, atol = self.get_tolerances(dtype)
+
+        # Apply given filter functions
+        if self.param_filter:
+            param_mask = np.ones((data.shape[0],), np.bool_)
+            for j, filter in zip(self.param_columns, self.param_filter):
+                if filter:
+                    param_mask &= list(filter(data[:,j]))
+            data = data[param_mask]
+
+        # Pick parameters from the correct columns
+        params = []
+        for idx, j in enumerate(self.param_columns):
+            if np.iscomplexobj(j):
+                j = int(j.imag)
+                params.append(data[:,j].astype(complex))
+            elif dtypes and idx < len(dtypes):
+                params.append(data[:, j].astype(dtypes[idx]))
+            else:
+                params.append(data[:,j])
+
+        # Helper for evaluating results
+        def eval_func_at_params(func, skip_mask=None):
+            if self.vectorized:
+                got = func(*params)
+            else:
+                got = []
+                for j in range(len(params[0])):
+                    if skip_mask is not None and skip_mask[j]:
+                        got.append(np.nan)
+                        continue
+                    got.append(func(*tuple([params[i][j] for i in range(len(params))])))
+                got = np.asarray(got)
+            if not isinstance(got, tuple):
+                got = (got,)
+            return got
+
+        # Evaluate function to be tested
+        got = eval_func_at_params(self.func)
+
+        # Grab the correct results
+        if self.result_columns is not None:
+            # Correct results passed in with the data
+            wanted = tuple([data[:,icol] for icol in self.result_columns])
+        else:
+            # Function producing correct results passed in
+            skip_mask = None
+            if self.nan_ok and len(got) == 1:
+                # Don't spend time evaluating what doesn't need to be evaluated
+                skip_mask = np.isnan(got[0])
+            wanted = eval_func_at_params(self.result_func, skip_mask=skip_mask)
+
+        # Check the validity of each output returned
+        assert_(len(got) == len(wanted))
+
+        for output_num, (x, y) in enumerate(zip(got, wanted)):
+            if np.issubdtype(x.dtype, np.complexfloating) or self.ignore_inf_sign:
+                pinf_x = np.isinf(x)
+                pinf_y = np.isinf(y)
+                minf_x = np.isinf(x)
+                minf_y = np.isinf(y)
+            else:
+                pinf_x = np.isposinf(x)
+                pinf_y = np.isposinf(y)
+                minf_x = np.isneginf(x)
+                minf_y = np.isneginf(y)
+            nan_x = np.isnan(x)
+            nan_y = np.isnan(y)
+
+            with np.errstate(all='ignore'):
+                abs_y = np.absolute(y)
+                abs_y[~np.isfinite(abs_y)] = 0
+                diff = np.absolute(x - y)
+                diff[~np.isfinite(diff)] = 0
+
+                rdiff = diff / np.absolute(y)
+                rdiff[~np.isfinite(rdiff)] = 0
+
+            tol_mask = (diff <= atol + rtol*abs_y)
+            pinf_mask = (pinf_x == pinf_y)
+            minf_mask = (minf_x == minf_y)
+
+            nan_mask = (nan_x == nan_y)
+
+            bad_j = ~(tol_mask & pinf_mask & minf_mask & nan_mask)
+
+            point_count = bad_j.size
+            if self.nan_ok:
+                bad_j &= ~nan_x
+                bad_j &= ~nan_y
+                point_count -= (nan_x | nan_y).sum()
+
+            if not self.distinguish_nan_and_inf and not self.nan_ok:
+                # If nan's are okay we've already covered all these cases
+                inf_x = np.isinf(x)
+                inf_y = np.isinf(y)
+                both_nonfinite = (inf_x & nan_y) | (nan_x & inf_y)
+                bad_j &= ~both_nonfinite
+                point_count -= both_nonfinite.sum()
+
+            if np.any(bad_j):
+                # Some bad results: inform what, where, and how bad
+                msg = [""]
+                msg.append(f"Max |adiff|: {diff[bad_j].max():g}")
+                msg.append(f"Max |rdiff|: {rdiff[bad_j].max():g}")
+                msg.append(f"Bad results ({np.sum(bad_j)} out of "
+                           f"{point_count}) for the following points "
+                           f"(in output {output_num}):")
+                for j in np.nonzero(bad_j)[0]:
+                    j = int(j)
+                    def fmt(x):
+                        return f'{np.array2string(x[j], precision=18):30s}'
+                    a = "  ".join(map(fmt, params))
+                    b = "  ".join(map(fmt, got))
+                    c = "  ".join(map(fmt, wanted))
+                    d = fmt(rdiff)
+                    msg.append(f"{a} => {b} != {c}  (rdiff {d})")
+                assert_(False, "\n".join(msg))
+
+    def __repr__(self):
+        """Pretty-printing"""
+        if np.any(list(map(np.iscomplexobj, self.param_columns))):
+            is_complex = " (complex)"
+        else:
+            is_complex = ""
+        if self.dataname:
+            return (f"<Data for {self.func.__name__}{is_complex}: "
+                    f"{os.path.basename(self.dataname)}>")
+        else:
+            return f"<Data for {self.func.__name__}{is_complex}>"
diff --git a/venv/lib/python3.12/site-packages/scipy/special/_ufunc_tools.py b/venv/lib/python3.12/site-packages/scipy/special/_ufunc_tools.py
new file mode 100644
index 0000000000000000000000000000000000000000..d9f97ff78afa4857e18383c7e70c3fbd31da884f
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/_ufunc_tools.py
@@ -0,0 +1,162 @@
+"""Helpers for producing efficient wrappers of ufuncs.
+"""
+
+import re
+import numpy as np
+
+
+def _parse_core_ndims(signature):
+    """Return tuple of num core dims per input from gufunc signature."""
+    input_sig = signature.split('->')[0]
+    groups = re.findall(r"\((.*?)\)", input_sig)
+    return tuple(0 if not g.strip() else g.count(',') + 1 for g in groups)
+
+
+def _with_cache_optimization(
+        *,
+        name,
+        arg_names,
+        docstring,
+        ufunc,
+        cache_arg_indices,
+):
+    """Helper to ensure optimal iteration order for ufuncs that use caching.
+
+    This concerns internal caches which are only live over the course of one
+    call to a ufunc to avoid repeated computations during the course of the
+    loops. See the notes below for more information.
+
+    Parameters
+    ----------
+    name : str
+    arg_names : list[str]
+        The function name and arg names are passed in so that the wrapper
+        can be generated with the create name and argument names, improving
+        documentation and autocomplete.
+    docstring : str
+    ufunc : numpy.ufunc
+    cache_arg_indices : list[int]
+       Arguments to ufunc which are used in the kernel to compute an output
+       which is being cached for reuse when iterating over other arguments.
+
+    Returns
+    -------
+    callable
+        A wrapper for ufunc which transposes the axes of the inputs to ensure
+        iteration precedes in such a way to allow the cache within the ufunc
+        kernel to eliminate redundant computation.
+
+    Notes
+    -----
+    There is a common pattern in ufunc kernels exemplified by the situation
+    where some of the arguments are used to compute coeffients of an expansion
+    that is taken over one or more of the other arguments. A classic example is
+    Mathieu functions, which compute coefficients corresponding to the shape
+    parameter q and order m which in principle could be reused for varying
+    values of the parameter x.
+
+    It had long been the case that the expensive computation of coefficients is
+    repeated unnecessarily across values of x. It is possible to add a cache to
+    the ufunc kernel which stores the expansion coefficients and only updates
+    if the pointers into the q and m arrays advance during the course of the
+    ufunc loops. Such a cache is instantiated each time a ufunc is called and
+    only lives during the course of the loops that are carried out for that
+    particular call.
+
+    Whether such a cache actually helps depends on the order in which iteration
+    occurs. Ideally, one would want q and m to advance most slowly and for the
+    iterations over x for fixed q and m to be pushed to the inner most loops.
+    This helper replaces each input array (and a pre-allocated output array)
+    with a view where the axes which should vary most slowly are transposed to
+    the ends and forces computation in C order. This ensures iteration proceeds
+    in the optimal order.
+
+    Note that because the pre-allocated output array used internally is C
+    contiguous, the output will be C contiguous regardless of contiguity of
+    the inputs.
+
+    """
+
+    # Need to keep track of the number of core dimensions for each input
+    # since core dimensions don't participate in broadcasting.
+    core_ndims = (
+        _parse_core_ndims(ufunc.signature)
+        if ufunc.signature is not None
+        else (0,)*ufunc.nin
+    )
+
+    def _wrapper(*args):
+        args = [np.asarray(arg) for arg in args]
+
+        # Fast path for when the arguments which are used in the cached
+        # computation don't have batches.
+        if all(args[i].ndim == core_ndims[i] for i in cache_arg_indices):
+            return ufunc(*args)
+
+        # To get batch_shapes, need to exclude core dimensions. Again, the core
+        # dimensions won't participate in broadcasting.
+        batch_shapes = [
+            arg.shape[:-core_ndims[i]] if core_ndims[i] > 0 else arg.shape
+            for i, arg in enumerate(args)
+        ]
+        batch_shape = np.broadcast_shapes(*batch_shapes)
+        batch_ndim = len(batch_shape)
+
+        # Broadcast each arg so that the batch shapes all agree, but the
+        # core dimensions may still differ.
+        args_b = [
+            np.broadcast_to(arg, batch_shape + arg.shape[-core_ndims[i]:])
+            if core_ndims[i] > 0 else np.broadcast_to(arg, batch_shape)
+            for i, arg in enumerate(args)
+        ]
+
+        # After broadcasting, determine which axes have stride-length
+        # zero for each of the args participating in the cache. The cached
+        # value will remain the same for iterations across these axes.
+        varying_axes = []
+        constant_axes = []
+
+        for ax in range(batch_ndim):
+            is_constant = all(
+                args_b[i].strides[ax] == 0 for i in cache_arg_indices
+            )
+            if is_constant:
+                constant_axes.append(ax)
+            else:
+                varying_axes.append(ax)
+        sorted_batch_axes = varying_axes + constant_axes
+
+        # Push the non-varying axes to the end so that they will vary most
+        # slowly when iterating in C order.
+        args_t = []
+        for i, arg_b in enumerate(args_b):
+            axes = sorted_batch_axes + list(
+                range(batch_ndim, batch_ndim + core_ndims[i])
+            )
+            args_t.append(np.transpose(arg_b, axes=axes))
+
+        # Premake the output array.
+        input_dtypes = tuple(arg.dtype for arg in args_t) + (None,)*ufunc.nout
+        out_dtype = ufunc.resolve_dtypes(input_dtypes)[-1]
+        out_final = np.empty(batch_shape, dtype=out_dtype, order='C')
+        # a view of the output array with axes sorted as needed.
+        out_t = np.transpose(out_final, axes=sorted_batch_axes)
+
+        # Set out to the above view, but return the C contiguous output.
+        # This avoids having non-contiguous output.
+        ufunc(*args_t, out=out_t, order='C')
+        return out_final
+
+    # Do some metaprogramming with exec so that the arg names and func
+    # name are as expected.
+    arg_str = ", ".join(arg_names)
+    code = (
+        f"""def {name}({arg_str}):
+            return _wrapper({arg_str})
+        """
+        )
+    namespace = {"_wrapper": _wrapper}
+    exec(code, namespace)
+    wrapper = namespace[name]
+    wrapper.__doc__ = docstring
+    return wrapper
diff --git a/venv/lib/python3.12/site-packages/scipy/special/_ufuncs.cpython-312-x86_64-linux-gnu.so b/venv/lib/python3.12/site-packages/scipy/special/_ufuncs.cpython-312-x86_64-linux-gnu.so
new file mode 100644
index 0000000000000000000000000000000000000000..865df35720e065f5fa674ca618dc52a999785ec4
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/_ufuncs.cpython-312-x86_64-linux-gnu.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d68fb91d24c37818f6c2de52b63c8257c29617d62a58d1aabdc51dc9d055d4b5
+size 1496216
diff --git a/venv/lib/python3.12/site-packages/scipy/special/_ufuncs.pyi b/venv/lib/python3.12/site-packages/scipy/special/_ufuncs.pyi
new file mode 100644
index 0000000000000000000000000000000000000000..73e74d31e9ad53644bc66b6896c7f62404562b83
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/_ufuncs.pyi
@@ -0,0 +1,522 @@
+from typing import Any
+
+import numpy as np
+
+__all__ = [
+    'geterr',
+    'seterr',
+    'errstate',
+    'agm',
+    'airy',
+    'airye',
+    'bdtr',
+    'bdtrc',
+    'bdtri',
+    'bdtrik',
+    'bdtrin',
+    'bei',
+    'beip',
+    'ber',
+    'berp',
+    'besselpoly',
+    'beta',
+    'betainc',
+    'betaincc',
+    'betainccinv',
+    'betaincinv',
+    'betaln',
+    'binom',
+    'boxcox',
+    'boxcox1p',
+    'btdtria',
+    'btdtrib',
+    'cbrt',
+    'chdtr',
+    'chdtrc',
+    'chdtri',
+    'chdtriv',
+    'chndtr',
+    'chndtridf',
+    'chndtrinc',
+    'chndtrix',
+    'cosdg',
+    'cosm1',
+    'cotdg',
+    'dawsn',
+    'ellipe',
+    'ellipeinc',
+    'ellipj',
+    'ellipk',
+    'ellipkinc',
+    'ellipkm1',
+    'elliprc',
+    'elliprd',
+    'elliprf',
+    'elliprg',
+    'elliprj',
+    'entr',
+    'erf',
+    'erfc',
+    'erfcinv',
+    'erfcx',
+    'erfi',
+    'erfinv',
+    'eval_chebyc',
+    'eval_chebys',
+    'eval_chebyt',
+    'eval_chebyu',
+    'eval_gegenbauer',
+    'eval_genlaguerre',
+    'eval_hermite',
+    'eval_hermitenorm',
+    'eval_jacobi',
+    'eval_laguerre',
+    'eval_legendre',
+    'eval_sh_chebyt',
+    'eval_sh_chebyu',
+    'eval_sh_jacobi',
+    'eval_sh_legendre',
+    'exp1',
+    'exp10',
+    'exp2',
+    'expi',
+    'expit',
+    'expm1',
+    'expn',
+    'exprel',
+    'fdtr',
+    'fdtrc',
+    'fdtri',
+    'fdtridfd',
+    'fresnel',
+    'gamma',
+    'gammainc',
+    'gammaincc',
+    'gammainccinv',
+    'gammaincinv',
+    'gammaln',
+    'gammasgn',
+    'gdtr',
+    'gdtrc',
+    'gdtria',
+    'gdtrib',
+    'gdtrix',
+    'hankel1',
+    'hankel1e',
+    'hankel2',
+    'hankel2e',
+    'huber',
+    'hyp0f1',
+    'hyp1f1',
+    'hyp2f1',
+    'hyperu',
+    'i0',
+    'i0e',
+    'i1',
+    'i1e',
+    'inv_boxcox',
+    'inv_boxcox1p',
+    'it2i0k0',
+    'it2j0y0',
+    'it2struve0',
+    'itairy',
+    'iti0k0',
+    'itj0y0',
+    'itmodstruve0',
+    'itstruve0',
+    'iv',
+    'ive',
+    'j0',
+    'j1',
+    'jn',
+    'jv',
+    'jve',
+    'k0',
+    'k0e',
+    'k1',
+    'k1e',
+    'kei',
+    'keip',
+    'kelvin',
+    'ker',
+    'kerp',
+    'kl_div',
+    'kn',
+    'kolmogi',
+    'kolmogorov',
+    'kv',
+    'kve',
+    'log1p',
+    'log_expit',
+    'log_ndtr',
+    'log_wright_bessel',
+    'loggamma',
+    'logit',
+    'lpmv',
+    'mathieu_a',
+    'mathieu_b',
+    'mathieu_cem',
+    'mathieu_modcem1',
+    'mathieu_modcem2',
+    'mathieu_modsem1',
+    'mathieu_modsem2',
+    'mathieu_sem',
+    'modfresnelm',
+    'modfresnelp',
+    'modstruve',
+    'nbdtr',
+    'nbdtrc',
+    'nbdtri',
+    'nbdtrik',
+    'nbdtrin',
+    'ncfdtr',
+    'ncfdtri',
+    'ncfdtridfd',
+    'ncfdtridfn',
+    'ncfdtrinc',
+    'nctdtr',
+    'nctdtridf',
+    'nctdtrinc',
+    'nctdtrit',
+    'ndtr',
+    'ndtri',
+    'ndtri_exp',
+    'nrdtrimn',
+    'nrdtrisd',
+    'obl_ang1',
+    'obl_ang1_cv',
+    'obl_cv',
+    'obl_rad1',
+    'obl_rad1_cv',
+    'obl_rad2',
+    'obl_rad2_cv',
+    'owens_t',
+    'pbdv',
+    'pbvv',
+    'pbwa',
+    'pdtr',
+    'pdtrc',
+    'pdtri',
+    'pdtrik',
+    'poch',
+    'powm1',
+    'pro_ang1',
+    'pro_ang1_cv',
+    'pro_cv',
+    'pro_rad1',
+    'pro_rad1_cv',
+    'pro_rad2',
+    'pro_rad2_cv',
+    'pseudo_huber',
+    'psi',
+    'radian',
+    'rel_entr',
+    'rgamma',
+    'round',
+    'shichi',
+    'sici',
+    'sindg',
+    'smirnov',
+    'smirnovi',
+    'spence',
+    'stdtr',
+    'stdtridf',
+    'stdtrit',
+    'struve',
+    'tandg',
+    'tklmbda',
+    'voigt_profile',
+    'wofz',
+    'wright_bessel',
+    'wrightomega',
+    'xlog1py',
+    'xlogy',
+    'y0',
+    'y1',
+    'yn',
+    'yv',
+    'yve',
+    'zetac'
+]
+
+def geterr() -> dict[str, str]: ...
+def seterr(**kwargs: str) -> dict[str, str]: ...
+
+class errstate:
+    def __init__(self, **kargs: str) -> None: ...
+    def __enter__(self) -> None: ...
+    def __exit__(
+        self,
+        exc_type: Any,  # Unused
+        exc_value: Any,  # Unused
+        traceback: Any,  # Unused
+    ) -> None: ...
+
+_cosine_cdf: np.ufunc
+_cosine_invcdf: np.ufunc
+_bivariate_normal_cdf: np.ufunc
+_cospi: np.ufunc
+_ellip_harm: np.ufunc
+_factorial: np.ufunc
+_gen_harmonic: np.ufunc
+_igam_fac: np.ufunc
+_kolmogc: np.ufunc
+_kolmogci: np.ufunc
+_kolmogp: np.ufunc
+_lambertw: np.ufunc
+_lanczos_sum_expg_scaled: np.ufunc
+_lgam1p: np.ufunc
+_log1mexp: np.ufunc
+_log1pmx: np.ufunc
+_normalized_gen_harmonic: np.ufunc
+_riemann_zeta: np.ufunc
+_scaled_exp1: np.ufunc
+_sf_error_test_function: np.ufunc
+_sinpi: np.ufunc
+_smirnovc: np.ufunc
+_smirnovci: np.ufunc
+_smirnovp: np.ufunc
+_spherical_in: np.ufunc
+_spherical_in_d: np.ufunc
+_spherical_jn: np.ufunc
+_spherical_jn_d: np.ufunc
+_spherical_kn: np.ufunc
+_spherical_kn_d: np.ufunc
+_spherical_yn: np.ufunc
+_spherical_yn_d: np.ufunc
+_stirling2_inexact: np.ufunc
+_struve_asymp_large_z: np.ufunc
+_struve_bessel_series: np.ufunc
+_struve_power_series: np.ufunc
+_zeta: np.ufunc
+agm: np.ufunc
+airy: np.ufunc
+airye: np.ufunc
+bdtr: np.ufunc
+bdtrc: np.ufunc
+bdtri: np.ufunc
+bdtrik: np.ufunc
+bdtrin: np.ufunc
+bei: np.ufunc
+beip: np.ufunc
+ber: np.ufunc
+berp: np.ufunc
+besselpoly: np.ufunc
+beta: np.ufunc
+betainc: np.ufunc
+betaincc: np.ufunc
+betainccinv: np.ufunc
+betaincinv: np.ufunc
+betaln: np.ufunc
+binom: np.ufunc
+boxcox1p: np.ufunc
+boxcox: np.ufunc
+btdtria: np.ufunc
+btdtrib: np.ufunc
+cbrt: np.ufunc
+chdtr: np.ufunc
+chdtrc: np.ufunc
+chdtri: np.ufunc
+chdtriv: np.ufunc
+chndtr: np.ufunc
+chndtridf: np.ufunc
+chndtrinc: np.ufunc
+chndtrix: np.ufunc
+cosdg: np.ufunc
+cosm1: np.ufunc
+cotdg: np.ufunc
+dawsn: np.ufunc
+ellipe: np.ufunc
+ellipeinc: np.ufunc
+ellipj: np.ufunc
+ellipk: np.ufunc
+ellipkinc: np.ufunc
+ellipkm1: np.ufunc
+elliprc: np.ufunc
+elliprd: np.ufunc
+elliprf: np.ufunc
+elliprg: np.ufunc
+elliprj: np.ufunc
+entr: np.ufunc
+erf: np.ufunc
+erfc: np.ufunc
+erfcinv: np.ufunc
+erfcx: np.ufunc
+erfi: np.ufunc
+erfinv: np.ufunc
+eval_chebyc: np.ufunc
+eval_chebys: np.ufunc
+eval_chebyt: np.ufunc
+eval_chebyu: np.ufunc
+eval_gegenbauer: np.ufunc
+eval_genlaguerre: np.ufunc
+eval_hermite: np.ufunc
+eval_hermitenorm: np.ufunc
+eval_jacobi: np.ufunc
+eval_laguerre: np.ufunc
+eval_legendre: np.ufunc
+eval_sh_chebyt: np.ufunc
+eval_sh_chebyu: np.ufunc
+eval_sh_jacobi: np.ufunc
+eval_sh_legendre: np.ufunc
+exp10: np.ufunc
+exp1: np.ufunc
+exp2: np.ufunc
+expi: np.ufunc
+expit: np.ufunc
+expm1: np.ufunc
+expn: np.ufunc
+exprel: np.ufunc
+fdtr: np.ufunc
+fdtrc: np.ufunc
+fdtri: np.ufunc
+fdtridfd: np.ufunc
+fresnel: np.ufunc
+gamma: np.ufunc
+gammainc: np.ufunc
+gammaincc: np.ufunc
+gammainccinv: np.ufunc
+gammaincinv: np.ufunc
+gammaln: np.ufunc
+gammasgn: np.ufunc
+gdtr: np.ufunc
+gdtrc: np.ufunc
+gdtria: np.ufunc
+gdtrib: np.ufunc
+gdtrix: np.ufunc
+hankel1: np.ufunc
+hankel1e: np.ufunc
+hankel2: np.ufunc
+hankel2e: np.ufunc
+huber: np.ufunc
+hyp0f1: np.ufunc
+hyp1f1: np.ufunc
+hyp2f1: np.ufunc
+hyperu: np.ufunc
+i0: np.ufunc
+i0e: np.ufunc
+i1: np.ufunc
+i1e: np.ufunc
+inv_boxcox1p: np.ufunc
+inv_boxcox: np.ufunc
+it2i0k0: np.ufunc
+it2j0y0: np.ufunc
+it2struve0: np.ufunc
+itairy: np.ufunc
+iti0k0: np.ufunc
+itj0y0: np.ufunc
+itmodstruve0: np.ufunc
+itstruve0: np.ufunc
+iv: np.ufunc
+ive: np.ufunc
+j0: np.ufunc
+j1: np.ufunc
+jn: np.ufunc
+jv: np.ufunc
+jve: np.ufunc
+k0: np.ufunc
+k0e: np.ufunc
+k1: np.ufunc
+k1e: np.ufunc
+kei: np.ufunc
+keip: np.ufunc
+kelvin: np.ufunc
+ker: np.ufunc
+kerp: np.ufunc
+kl_div: np.ufunc
+kn: np.ufunc
+kolmogi: np.ufunc
+kolmogorov: np.ufunc
+kv: np.ufunc
+kve: np.ufunc
+log1p: np.ufunc
+log_expit: np.ufunc
+log_ndtr: np.ufunc
+log_wright_bessel: np.ufunc
+loggamma: np.ufunc
+logit: np.ufunc
+lpmv: np.ufunc
+mathieu_a: np.ufunc
+mathieu_b: np.ufunc
+mathieu_cem: np.ufunc
+mathieu_modcem1: np.ufunc
+mathieu_modcem2: np.ufunc
+mathieu_modsem1: np.ufunc
+mathieu_modsem2: np.ufunc
+mathieu_sem: np.ufunc
+modfresnelm: np.ufunc
+modfresnelp: np.ufunc
+modstruve: np.ufunc
+nbdtr: np.ufunc
+nbdtrc: np.ufunc
+nbdtri: np.ufunc
+nbdtrik: np.ufunc
+nbdtrin: np.ufunc
+ncfdtr: np.ufunc
+ncfdtri: np.ufunc
+ncfdtridfd: np.ufunc
+ncfdtridfn: np.ufunc
+ncfdtrinc: np.ufunc
+nctdtr: np.ufunc
+nctdtridf: np.ufunc
+nctdtrinc: np.ufunc
+nctdtrit: np.ufunc
+ndtr: np.ufunc
+ndtri: np.ufunc
+ndtri_exp: np.ufunc
+nrdtrimn: np.ufunc
+nrdtrisd: np.ufunc
+obl_ang1: np.ufunc
+obl_ang1_cv: np.ufunc
+obl_cv: np.ufunc
+obl_rad1: np.ufunc
+obl_rad1_cv: np.ufunc
+obl_rad2: np.ufunc
+obl_rad2_cv: np.ufunc
+owens_t: np.ufunc
+pbdv: np.ufunc
+pbvv: np.ufunc
+pbwa: np.ufunc
+pdtr: np.ufunc
+pdtrc: np.ufunc
+pdtri: np.ufunc
+pdtrik: np.ufunc
+poch: np.ufunc
+powm1: np.ufunc
+pro_ang1: np.ufunc
+pro_ang1_cv: np.ufunc
+pro_cv: np.ufunc
+pro_rad1: np.ufunc
+pro_rad1_cv: np.ufunc
+pro_rad2: np.ufunc
+pro_rad2_cv: np.ufunc
+pseudo_huber: np.ufunc
+psi: np.ufunc
+radian: np.ufunc
+rel_entr: np.ufunc
+rgamma: np.ufunc
+round: np.ufunc
+shichi: np.ufunc
+sici: np.ufunc
+sindg: np.ufunc
+smirnov: np.ufunc
+smirnovi: np.ufunc
+spence: np.ufunc
+stdtr: np.ufunc
+stdtridf: np.ufunc
+stdtrit: np.ufunc
+struve: np.ufunc
+tandg: np.ufunc
+tklmbda: np.ufunc
+voigt_profile: np.ufunc
+wofz: np.ufunc
+wright_bessel: np.ufunc
+wrightomega: np.ufunc
+xlog1py: np.ufunc
+xlogy: np.ufunc
+y0: np.ufunc
+y1: np.ufunc
+yn: np.ufunc
+yv: np.ufunc
+yve: np.ufunc
+zetac: np.ufunc
diff --git a/venv/lib/python3.12/site-packages/scipy/special/_ufuncs_cxx.cpython-312-x86_64-linux-gnu.so b/venv/lib/python3.12/site-packages/scipy/special/_ufuncs_cxx.cpython-312-x86_64-linux-gnu.so
new file mode 100644
index 0000000000000000000000000000000000000000..6ccf8f19fa935cebaedbd7d347f273e5dd87a52a
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/_ufuncs_cxx.cpython-312-x86_64-linux-gnu.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:28dd61ac417abb7d4b9917d787d87146ba5ce6df1ce7e42f5a993e7aea66c9d7
+size 2081448
diff --git a/venv/lib/python3.12/site-packages/scipy/special/add_newdocs.py b/venv/lib/python3.12/site-packages/scipy/special/add_newdocs.py
new file mode 100644
index 0000000000000000000000000000000000000000..5549717d35710d71655e42c836625cde9346bcc3
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/add_newdocs.py
@@ -0,0 +1,15 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+__all__: list[str] = []
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="special", module="add_newdocs",
+                                   private_modules=["_add_newdocs"], all=__all__,
+                                   attribute=name)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/basic.py b/venv/lib/python3.12/site-packages/scipy/special/basic.py
new file mode 100644
index 0000000000000000000000000000000000000000..46c179a893c4c9022a7cdd77c8923ff5a012b0eb
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/basic.py
@@ -0,0 +1,84 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.special` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+
+__all__ = [  # noqa: F822
+    'ai_zeros',
+    'assoc_laguerre',
+    'bei_zeros',
+    'beip_zeros',
+    'ber_zeros',
+    'bernoulli',
+    'berp_zeros',
+    'bi_zeros',
+    'comb',
+    'digamma',
+    'diric',
+    'erf_zeros',
+    'euler',
+    'factorial',
+    'factorial2',
+    'factorialk',
+    'fresnel_zeros',
+    'fresnelc_zeros',
+    'fresnels_zeros',
+    'gamma',
+    'h1vp',
+    'h2vp',
+    'hankel1',
+    'hankel2',
+    'iv',
+    'ivp',
+    'jn_zeros',
+    'jnjnp_zeros',
+    'jnp_zeros',
+    'jnyn_zeros',
+    'jv',
+    'jvp',
+    'kei_zeros',
+    'keip_zeros',
+    'kelvin_zeros',
+    'ker_zeros',
+    'kerp_zeros',
+    'kv',
+    'kvp',
+    'lmbda',
+    'lqmn',
+    'lqn',
+    'mathieu_a',
+    'mathieu_b',
+    'mathieu_even_coef',
+    'mathieu_odd_coef',
+    'obl_cv_seq',
+    'pbdn_seq',
+    'pbdv_seq',
+    'pbvv_seq',
+    'perm',
+    'polygamma',
+    'pro_cv_seq',
+    'psi',
+    'riccati_jn',
+    'riccati_yn',
+    'sinc',
+    'y0_zeros',
+    'y1_zeros',
+    'y1p_zeros',
+    'yn_zeros',
+    'ynp_zeros',
+    'yv',
+    'yvp',
+    'zeta'
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="special", module="basic",
+                                   private_modules=["_basic", "_ufuncs"], all=__all__,
+                                   attribute=name)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/cython_special.cpython-312-x86_64-linux-gnu.so b/venv/lib/python3.12/site-packages/scipy/special/cython_special.cpython-312-x86_64-linux-gnu.so
new file mode 100644
index 0000000000000000000000000000000000000000..a8b7feff637c6539cd436288d5276b51d611f424
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/cython_special.cpython-312-x86_64-linux-gnu.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ebd81a54547f57694319ac176a50b7a148e1f41c1dae687a65e2347454b9e699
+size 2446128
diff --git a/venv/lib/python3.12/site-packages/scipy/special/cython_special.pxd b/venv/lib/python3.12/site-packages/scipy/special/cython_special.pxd
new file mode 100644
index 0000000000000000000000000000000000000000..7a6fbae7a279708ab702ef544c7b17250f81f6c1
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/cython_special.pxd
@@ -0,0 +1,258 @@
+
+ctypedef fused number_t:
+    double complex
+    double
+
+cpdef number_t spherical_jn(Py_ssize_t n, number_t z, bint derivative=*) noexcept nogil
+cpdef number_t spherical_yn(Py_ssize_t n, number_t z, bint derivative=*) noexcept nogil
+cpdef number_t spherical_in(Py_ssize_t n, number_t z, bint derivative=*) noexcept nogil
+cpdef number_t spherical_kn(Py_ssize_t n, number_t z, bint derivative=*) noexcept nogil
+
+ctypedef fused Dd_number_t:
+    double complex
+    double
+
+ctypedef fused df_number_t:
+    double
+    float
+
+ctypedef fused dfg_number_t:
+    double
+    float
+    long double
+
+ctypedef fused dlp_number_t:
+    double
+    long
+    Py_ssize_t
+
+cpdef double voigt_profile(double x0, double x1, double x2) noexcept nogil
+cpdef double agm(double x0, double x1) noexcept nogil
+cdef void airy(Dd_number_t x0, Dd_number_t *y0, Dd_number_t *y1, Dd_number_t *y2, Dd_number_t *y3) noexcept nogil
+cdef void airye(Dd_number_t x0, Dd_number_t *y0, Dd_number_t *y1, Dd_number_t *y2, Dd_number_t *y3) noexcept nogil
+cpdef double bdtr(double x0, dlp_number_t x1, double x2) noexcept nogil
+cpdef double bdtrc(double x0, dlp_number_t x1, double x2) noexcept nogil
+cpdef double bdtri(double x0, dlp_number_t x1, double x2) noexcept nogil
+cpdef double bdtrik(double x0, double x1, double x2) noexcept nogil
+cpdef double bdtrin(double x0, double x1, double x2) noexcept nogil
+cpdef double bei(double x0) noexcept nogil
+cpdef double beip(double x0) noexcept nogil
+cpdef double ber(double x0) noexcept nogil
+cpdef double berp(double x0) noexcept nogil
+cpdef double besselpoly(double x0, double x1, double x2) noexcept nogil
+cpdef double beta(double x0, double x1) noexcept nogil
+cpdef df_number_t betainc(df_number_t x0, df_number_t x1, df_number_t x2) noexcept nogil
+cpdef df_number_t betaincc(df_number_t x0, df_number_t x1, df_number_t x2) noexcept nogil
+cpdef df_number_t betaincinv(df_number_t x0, df_number_t x1, df_number_t x2) noexcept nogil
+cpdef df_number_t betainccinv(df_number_t x0, df_number_t x1, df_number_t x2) noexcept nogil
+cpdef double betaln(double x0, double x1) noexcept nogil
+cpdef double binom(double x0, double x1) noexcept nogil
+cpdef double boxcox(double x0, double x1) noexcept nogil
+cpdef double boxcox1p(double x0, double x1) noexcept nogil
+cpdef df_number_t btdtria(df_number_t x0, df_number_t x1, df_number_t x2) noexcept nogil
+cpdef df_number_t btdtrib(df_number_t x0, df_number_t x1, df_number_t x2) noexcept nogil
+cpdef double cbrt(double x0) noexcept nogil
+cpdef double chdtr(double x0, double x1) noexcept nogil
+cpdef double chdtrc(double x0, double x1) noexcept nogil
+cpdef double chdtri(double x0, double x1) noexcept nogil
+cpdef df_number_t chdtriv(df_number_t x0, df_number_t x1) noexcept nogil
+cpdef df_number_t chndtr(df_number_t x0, df_number_t x1, df_number_t x2) noexcept nogil
+cpdef df_number_t chndtridf(df_number_t x0, df_number_t x1, df_number_t x2) noexcept nogil
+cpdef df_number_t chndtrinc(df_number_t x0, df_number_t x1, df_number_t x2) noexcept nogil
+cpdef df_number_t chndtrix(df_number_t x0, df_number_t x1, df_number_t x2) noexcept nogil
+cpdef double cosdg(double x0) noexcept nogil
+cpdef double cosm1(double x0) noexcept nogil
+cpdef double cotdg(double x0) noexcept nogil
+cpdef Dd_number_t dawsn(Dd_number_t x0) noexcept nogil
+cpdef double ellipe(double x0) noexcept nogil
+cpdef double ellipeinc(double x0, double x1) noexcept nogil
+cdef void ellipj(double x0, double x1, double *y0, double *y1, double *y2, double *y3) noexcept nogil
+cpdef double ellipkinc(double x0, double x1) noexcept nogil
+cpdef double ellipkm1(double x0) noexcept nogil
+cpdef double ellipk(double x0) noexcept nogil
+cpdef Dd_number_t elliprc(Dd_number_t x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t elliprd(Dd_number_t x0, Dd_number_t x1, Dd_number_t x2) noexcept nogil
+cpdef Dd_number_t elliprf(Dd_number_t x0, Dd_number_t x1, Dd_number_t x2) noexcept nogil
+cpdef Dd_number_t elliprg(Dd_number_t x0, Dd_number_t x1, Dd_number_t x2) noexcept nogil
+cpdef Dd_number_t elliprj(Dd_number_t x0, Dd_number_t x1, Dd_number_t x2, Dd_number_t x3) noexcept nogil
+cpdef double entr(double x0) noexcept nogil
+cpdef Dd_number_t erf(Dd_number_t x0) noexcept nogil
+cpdef Dd_number_t erfc(Dd_number_t x0) noexcept nogil
+cpdef Dd_number_t erfcx(Dd_number_t x0) noexcept nogil
+cpdef Dd_number_t erfi(Dd_number_t x0) noexcept nogil
+cpdef df_number_t erfinv(df_number_t x0) noexcept nogil
+cpdef double erfcinv(double x0) noexcept nogil
+cpdef Dd_number_t eval_chebyc(dlp_number_t x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t eval_chebys(dlp_number_t x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t eval_chebyt(dlp_number_t x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t eval_chebyu(dlp_number_t x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t eval_gegenbauer(dlp_number_t x0, double x1, Dd_number_t x2) noexcept nogil
+cpdef Dd_number_t eval_genlaguerre(dlp_number_t x0, double x1, Dd_number_t x2) noexcept nogil
+cpdef double eval_hermite(Py_ssize_t x0, double x1) noexcept nogil
+cpdef double eval_hermitenorm(Py_ssize_t x0, double x1) noexcept nogil
+cpdef Dd_number_t eval_jacobi(dlp_number_t x0, double x1, double x2, Dd_number_t x3) noexcept nogil
+cpdef Dd_number_t eval_laguerre(dlp_number_t x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t eval_legendre(dlp_number_t x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t eval_sh_chebyt(dlp_number_t x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t eval_sh_chebyu(dlp_number_t x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t eval_sh_jacobi(dlp_number_t x0, double x1, double x2, Dd_number_t x3) noexcept nogil
+cpdef Dd_number_t eval_sh_legendre(dlp_number_t x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t exp1(Dd_number_t x0) noexcept nogil
+cpdef double exp10(double x0) noexcept nogil
+cpdef double exp2(double x0) noexcept nogil
+cpdef Dd_number_t expi(Dd_number_t x0) noexcept nogil
+cpdef dfg_number_t expit(dfg_number_t x0) noexcept nogil
+cpdef Dd_number_t expm1(Dd_number_t x0) noexcept nogil
+cpdef double expn(dlp_number_t x0, double x1) noexcept nogil
+cpdef double exprel(double x0) noexcept nogil
+cpdef df_number_t fdtr(df_number_t x0, df_number_t x1, df_number_t x2) noexcept nogil
+cpdef df_number_t fdtrc(df_number_t x0, df_number_t x1, df_number_t x2) noexcept nogil
+cpdef df_number_t fdtri(df_number_t x0, df_number_t x1, df_number_t x2) noexcept nogil
+cpdef double fdtridfd(double x0, double x1, double x2) noexcept nogil
+cdef void fresnel(Dd_number_t x0, Dd_number_t *y0, Dd_number_t *y1) noexcept nogil
+cpdef Dd_number_t gamma(Dd_number_t x0) noexcept nogil
+cpdef double gammainc(double x0, double x1) noexcept nogil
+cpdef double gammaincc(double x0, double x1) noexcept nogil
+cpdef double gammainccinv(double x0, double x1) noexcept nogil
+cpdef double gammaincinv(double x0, double x1) noexcept nogil
+cpdef double gammaln(double x0) noexcept nogil
+cpdef double gammasgn(double x0) noexcept nogil
+cpdef double gdtr(double x0, double x1, double x2) noexcept nogil
+cpdef double gdtrc(double x0, double x1, double x2) noexcept nogil
+cpdef double gdtria(double x0, double x1, double x2) noexcept nogil
+cpdef double gdtrib(double x0, double x1, double x2) noexcept nogil
+cpdef double gdtrix(double x0, double x1, double x2) noexcept nogil
+cpdef double complex hankel1(double x0, double complex x1) noexcept nogil
+cpdef double complex hankel1e(double x0, double complex x1) noexcept nogil
+cpdef double complex hankel2(double x0, double complex x1) noexcept nogil
+cpdef double complex hankel2e(double x0, double complex x1) noexcept nogil
+cpdef double huber(double x0, double x1) noexcept nogil
+cpdef Dd_number_t hyp0f1(double x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t hyp1f1(double x0, double x1, Dd_number_t x2) noexcept nogil
+cpdef Dd_number_t hyp2f1(double x0, double x1, double x2, Dd_number_t x3) noexcept nogil
+cpdef double hyperu(double x0, double x1, double x2) noexcept nogil
+cpdef double i0(double x0) noexcept nogil
+cpdef double i0e(double x0) noexcept nogil
+cpdef double i1(double x0) noexcept nogil
+cpdef double i1e(double x0) noexcept nogil
+cpdef double inv_boxcox(double x0, double x1) noexcept nogil
+cpdef double inv_boxcox1p(double x0, double x1) noexcept nogil
+cdef void it2i0k0(double x0, double *y0, double *y1) noexcept nogil
+cdef void it2j0y0(double x0, double *y0, double *y1) noexcept nogil
+cpdef double it2struve0(double x0) noexcept nogil
+cdef void itairy(double x0, double *y0, double *y1, double *y2, double *y3) noexcept nogil
+cdef void iti0k0(double x0, double *y0, double *y1) noexcept nogil
+cdef void itj0y0(double x0, double *y0, double *y1) noexcept nogil
+cpdef double itmodstruve0(double x0) noexcept nogil
+cpdef double itstruve0(double x0) noexcept nogil
+cpdef Dd_number_t iv(double x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t ive(double x0, Dd_number_t x1) noexcept nogil
+cpdef double j0(double x0) noexcept nogil
+cpdef double j1(double x0) noexcept nogil
+cpdef Dd_number_t jv(double x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t jve(double x0, Dd_number_t x1) noexcept nogil
+cpdef double k0(double x0) noexcept nogil
+cpdef double k0e(double x0) noexcept nogil
+cpdef double k1(double x0) noexcept nogil
+cpdef double k1e(double x0) noexcept nogil
+cpdef double kei(double x0) noexcept nogil
+cpdef double keip(double x0) noexcept nogil
+cdef void kelvin(double x0, double complex *y0, double complex *y1, double complex *y2, double complex *y3) noexcept nogil
+cpdef double ker(double x0) noexcept nogil
+cpdef double kerp(double x0) noexcept nogil
+cpdef double kl_div(double x0, double x1) noexcept nogil
+cpdef double kn(dlp_number_t x0, double x1) noexcept nogil
+cpdef double kolmogi(double x0) noexcept nogil
+cpdef double kolmogorov(double x0) noexcept nogil
+cpdef Dd_number_t kv(double x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t kve(double x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t log1p(Dd_number_t x0) noexcept nogil
+cpdef dfg_number_t log_expit(dfg_number_t x0) noexcept nogil
+cpdef Dd_number_t log_ndtr(Dd_number_t x0) noexcept nogil
+cpdef Dd_number_t loggamma(Dd_number_t x0) noexcept nogil
+cpdef dfg_number_t logit(dfg_number_t x0) noexcept nogil
+cpdef double lpmv(double x0, double x1, double x2) noexcept nogil
+cpdef double mathieu_a(double x0, double x1) noexcept nogil
+cpdef double mathieu_b(double x0, double x1) noexcept nogil
+cdef void mathieu_cem(double x0, double x1, double x2, double *y0, double *y1) noexcept nogil
+cdef void mathieu_modcem1(double x0, double x1, double x2, double *y0, double *y1) noexcept nogil
+cdef void mathieu_modcem2(double x0, double x1, double x2, double *y0, double *y1) noexcept nogil
+cdef void mathieu_modsem1(double x0, double x1, double x2, double *y0, double *y1) noexcept nogil
+cdef void mathieu_modsem2(double x0, double x1, double x2, double *y0, double *y1) noexcept nogil
+cdef void mathieu_sem(double x0, double x1, double x2, double *y0, double *y1) noexcept nogil
+cdef void modfresnelm(double x0, double complex *y0, double complex *y1) noexcept nogil
+cdef void modfresnelp(double x0, double complex *y0, double complex *y1) noexcept nogil
+cpdef double modstruve(double x0, double x1) noexcept nogil
+cpdef double nbdtr(dlp_number_t x0, dlp_number_t x1, double x2) noexcept nogil
+cpdef double nbdtrc(dlp_number_t x0, dlp_number_t x1, double x2) noexcept nogil
+cpdef double nbdtri(dlp_number_t x0, dlp_number_t x1, double x2) noexcept nogil
+cpdef double nbdtrik(double x0, double x1, double x2) noexcept nogil
+cpdef double nbdtrin(double x0, double x1, double x2) noexcept nogil
+cpdef df_number_t ncfdtr(df_number_t x0, df_number_t x1, df_number_t x2, df_number_t x3) noexcept nogil
+cpdef df_number_t ncfdtri(df_number_t x0, df_number_t x1, df_number_t x2, df_number_t x3) noexcept nogil
+cpdef double ncfdtridfd(double x0, double x1, double x2, double x3) noexcept nogil
+cpdef double ncfdtridfn(double x0, double x1, double x2, double x3) noexcept nogil
+cpdef double ncfdtrinc(double x0, double x1, double x2, double x3) noexcept nogil
+cpdef df_number_t nctdtr(df_number_t x0, df_number_t x1, df_number_t x2) noexcept nogil
+cpdef double nctdtridf(double x0, double x1, double x2) noexcept nogil
+cpdef double nctdtrinc(double x0, double x1, double x2) noexcept nogil
+cpdef df_number_t nctdtrit(df_number_t x0, df_number_t x1, df_number_t x2) noexcept nogil
+cpdef Dd_number_t ndtr(Dd_number_t x0) noexcept nogil
+cpdef double ndtri(double x0) noexcept nogil
+cpdef double nrdtrimn(double x0, double x1, double x2) noexcept nogil
+cpdef double nrdtrisd(double x0, double x1, double x2) noexcept nogil
+cdef void obl_ang1(double x0, double x1, double x2, double x3, double *y0, double *y1) noexcept nogil
+cdef void obl_ang1_cv(double x0, double x1, double x2, double x3, double x4, double *y0, double *y1) noexcept nogil
+cpdef double obl_cv(double x0, double x1, double x2) noexcept nogil
+cdef void obl_rad1(double x0, double x1, double x2, double x3, double *y0, double *y1) noexcept nogil
+cdef void obl_rad1_cv(double x0, double x1, double x2, double x3, double x4, double *y0, double *y1) noexcept nogil
+cdef void obl_rad2(double x0, double x1, double x2, double x3, double *y0, double *y1) noexcept nogil
+cdef void obl_rad2_cv(double x0, double x1, double x2, double x3, double x4, double *y0, double *y1) noexcept nogil
+cpdef double owens_t(double x0, double x1) noexcept nogil
+cdef void pbdv(double x0, double x1, double *y0, double *y1) noexcept nogil
+cdef void pbvv(double x0, double x1, double *y0, double *y1) noexcept nogil
+cdef void pbwa(double x0, double x1, double *y0, double *y1) noexcept nogil
+cpdef double pdtr(double x0, double x1) noexcept nogil
+cpdef double pdtrc(double x0, double x1) noexcept nogil
+cpdef double pdtri(dlp_number_t x0, double x1) noexcept nogil
+cpdef df_number_t pdtrik(df_number_t x0, df_number_t x1) noexcept nogil
+cpdef double poch(double x0, double x1) noexcept nogil
+cpdef df_number_t powm1(df_number_t x0, df_number_t x1) noexcept nogil
+cdef void pro_ang1(double x0, double x1, double x2, double x3, double *y0, double *y1) noexcept nogil
+cdef void pro_ang1_cv(double x0, double x1, double x2, double x3, double x4, double *y0, double *y1) noexcept nogil
+cpdef double pro_cv(double x0, double x1, double x2) noexcept nogil
+cdef void pro_rad1(double x0, double x1, double x2, double x3, double *y0, double *y1) noexcept nogil
+cdef void pro_rad1_cv(double x0, double x1, double x2, double x3, double x4, double *y0, double *y1) noexcept nogil
+cdef void pro_rad2(double x0, double x1, double x2, double x3, double *y0, double *y1) noexcept nogil
+cdef void pro_rad2_cv(double x0, double x1, double x2, double x3, double x4, double *y0, double *y1) noexcept nogil
+cpdef double pseudo_huber(double x0, double x1) noexcept nogil
+cpdef Dd_number_t psi(Dd_number_t x0) noexcept nogil
+cpdef double radian(double x0, double x1, double x2) noexcept nogil
+cpdef double rel_entr(double x0, double x1) noexcept nogil
+cpdef Dd_number_t rgamma(Dd_number_t x0) noexcept nogil
+cpdef double round(double x0) noexcept nogil
+cdef void shichi(Dd_number_t x0, Dd_number_t *y0, Dd_number_t *y1) noexcept nogil
+cdef void sici(Dd_number_t x0, Dd_number_t *y0, Dd_number_t *y1) noexcept nogil
+cpdef double sindg(double x0) noexcept nogil
+cpdef double smirnov(dlp_number_t x0, double x1) noexcept nogil
+cpdef double smirnovi(dlp_number_t x0, double x1) noexcept nogil
+cpdef Dd_number_t spence(Dd_number_t x0) noexcept nogil
+cpdef df_number_t stdtr(df_number_t x0, df_number_t x1) noexcept nogil
+cpdef double stdtridf(double x0, double x1) noexcept nogil
+cpdef df_number_t stdtrit(df_number_t x0, df_number_t x1) noexcept nogil
+cpdef double struve(double x0, double x1) noexcept nogil
+cpdef double tandg(double x0) noexcept nogil
+cpdef double tklmbda(double x0, double x1) noexcept nogil
+cpdef double complex wofz(double complex x0) noexcept nogil
+cpdef Dd_number_t wrightomega(Dd_number_t x0) noexcept nogil
+cpdef Dd_number_t xlog1py(Dd_number_t x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t xlogy(Dd_number_t x0, Dd_number_t x1) noexcept nogil
+cpdef double y0(double x0) noexcept nogil
+cpdef double y1(double x0) noexcept nogil
+cpdef double yn(dlp_number_t x0, double x1) noexcept nogil
+cpdef Dd_number_t yv(double x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t yve(double x0, Dd_number_t x1) noexcept nogil
+cpdef double zetac(double x0) noexcept nogil
+cpdef double wright_bessel(double x0, double x1, double x2) noexcept nogil
+cpdef double log_wright_bessel(double x0, double x1, double x2) noexcept nogil
+cpdef double ndtri_exp(double x0) noexcept nogil
diff --git a/venv/lib/python3.12/site-packages/scipy/special/cython_special.pyi b/venv/lib/python3.12/site-packages/scipy/special/cython_special.pyi
new file mode 100644
index 0000000000000000000000000000000000000000..024e962b10df8892631eaad20223f7fc8378ea83
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/cython_special.pyi
@@ -0,0 +1,3 @@
+from typing import Any
+
+def __getattr__(name) -> Any: ...
diff --git a/venv/lib/python3.12/site-packages/scipy/special/orthogonal.py b/venv/lib/python3.12/site-packages/scipy/special/orthogonal.py
new file mode 100644
index 0000000000000000000000000000000000000000..0b13a08a96cb683d72a4a00d6962446e1779c88a
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/orthogonal.py
@@ -0,0 +1,45 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.special` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+
+_polyfuns = ['legendre', 'chebyt', 'chebyu', 'chebyc', 'chebys',
+             'jacobi', 'laguerre', 'genlaguerre', 'hermite',
+             'hermitenorm', 'gegenbauer', 'sh_legendre', 'sh_chebyt',
+             'sh_chebyu', 'sh_jacobi']
+
+# Correspondence between new and old names of root functions
+_rootfuns_map = {'roots_legendre': 'p_roots',
+               'roots_chebyt': 't_roots',
+               'roots_chebyu': 'u_roots',
+               'roots_chebyc': 'c_roots',
+               'roots_chebys': 's_roots',
+               'roots_jacobi': 'j_roots',
+               'roots_laguerre': 'l_roots',
+               'roots_genlaguerre': 'la_roots',
+               'roots_hermite': 'h_roots',
+               'roots_hermitenorm': 'he_roots',
+               'roots_gegenbauer': 'cg_roots',
+               'roots_sh_legendre': 'ps_roots',
+               'roots_sh_chebyt': 'ts_roots',
+               'roots_sh_chebyu': 'us_roots',
+               'roots_sh_jacobi': 'js_roots'}
+
+
+__all__ = _polyfuns + list(_rootfuns_map.keys()) + [  # noqa: F822
+    'airy', 'p_roots', 't_roots', 'u_roots', 'c_roots', 's_roots',
+    'j_roots', 'l_roots', 'la_roots', 'h_roots', 'he_roots', 'cg_roots',
+    'ps_roots', 'ts_roots', 'us_roots', 'js_roots'
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="special", module="orthogonal",
+                                   private_modules=["_orthogonal"], all=__all__,
+                                   attribute=name)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/sf_error.py b/venv/lib/python3.12/site-packages/scipy/special/sf_error.py
new file mode 100644
index 0000000000000000000000000000000000000000..00ff73756acd4219a4ba94eb089bce7d4c32266d
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/sf_error.py
@@ -0,0 +1,20 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.special` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+__all__ = [  # noqa: F822
+    'SpecialFunctionWarning',
+    'SpecialFunctionError'
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="special", module="sf_error",
+                                   private_modules=["_sf_error"], all=__all__,
+                                   attribute=name)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/specfun.py b/venv/lib/python3.12/site-packages/scipy/special/specfun.py
new file mode 100644
index 0000000000000000000000000000000000000000..f23284e66f19b55ca1dee380bef02c9a26662ef8
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/specfun.py
@@ -0,0 +1,21 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.special` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+# ruff: noqa: F822
+__all__ = [
+    'lqmn',
+    'pbdv'
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="special", module="specfun",
+                                   private_modules=["_basic", "_specfun"], all=__all__,
+                                   attribute=name)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/spfun_stats.py b/venv/lib/python3.12/site-packages/scipy/special/spfun_stats.py
new file mode 100644
index 0000000000000000000000000000000000000000..a1e58487aaa547483c9f2531ac4efc2ad5e4795c
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/spfun_stats.py
@@ -0,0 +1,17 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.special` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+__all__ = ['multigammaln']  # noqa: F822
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="special", module="spfun_stats",
+                                   private_modules=["_spfun_stats"], all=__all__,
+                                   attribute=name)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/__init__.py b/venv/lib/python3.12/site-packages/scipy/special/tests/__init__.py
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diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/__pycache__/test_basic.cpython-312.pyc b/venv/lib/python3.12/site-packages/scipy/special/tests/__pycache__/test_basic.cpython-312.pyc
new file mode 100644
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--- /dev/null
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diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/_cython_examples/extending.pyx b/venv/lib/python3.12/site-packages/scipy/special/tests/_cython_examples/extending.pyx
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--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/_cython_examples/extending.pyx
@@ -0,0 +1,12 @@
+#!/usr/bin/env python3
+#cython: language_level=3
+#cython: boundscheck=False
+#cython: wraparound=False
+
+from scipy.special.cython_special cimport beta, gamma
+
+cpdef double cy_beta(double a, double b):
+    return beta(a, b)
+
+cpdef double complex cy_gamma(double complex z):
+    return gamma(z)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/_cython_examples/meson.build b/venv/lib/python3.12/site-packages/scipy/special/tests/_cython_examples/meson.build
new file mode 100644
index 0000000000000000000000000000000000000000..a2b2c581ef780758d79796b953abc35008a7a951
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/_cython_examples/meson.build
@@ -0,0 +1,34 @@
+project('random-build-examples', 'c', 'cpp', 'cython')
+
+fs = import('fs')
+
+py3 = import('python').find_installation(pure: false)
+
+cy = meson.get_compiler('cython')
+
+if not cy.version().version_compare('>=3.2.0')
+  error('tests requires Cython >= 3.2.0')
+endif
+
+cython_args = []
+if cy.version().version_compare('>=3.1.0')
+  cython_args += ['-Xfreethreading_compatible=True']
+endif
+
+py3.extension_module(
+  'extending',
+  'extending.pyx',
+  install: false,
+  cython_args: cython_args,
+  c_args: ['-DCYTHON_CCOMPLEX=0'] # see gh-18975 for why we need this
+)
+
+extending_cpp = fs.copyfile('extending.pyx', 'extending_cpp.pyx')
+py3.extension_module(
+  'extending_cpp',
+  extending_cpp,
+  install: false,
+  override_options : ['cython_language=cpp'],
+  cython_args: cython_args,
+  cpp_args: ['-DCYTHON_CCOMPLEX=0']
+)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/cython_abi_signatures.json b/venv/lib/python3.12/site-packages/scipy/special/tests/cython_abi_signatures.json
new file mode 100644
index 0000000000000000000000000000000000000000..6c83a72d0d2760b350833e9b5fd947e3f59aa8fc
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/cython_abi_signatures.json
@@ -0,0 +1,400 @@
+{
+  "scipy.special.cython_special": {
+    "__pyx_fuse_0_0eval_chebyc": "__pyx_t_double_complex (double, __pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0_0eval_chebys": "__pyx_t_double_complex (double, __pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0_0eval_chebyt": "__pyx_t_double_complex (double, __pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0_0eval_chebyu": "__pyx_t_double_complex (double, __pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0_0eval_gegenbauer": "__pyx_t_double_complex (double, double, __pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0_0eval_genlaguerre": "__pyx_t_double_complex (double, double, __pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0_0eval_jacobi": "__pyx_t_double_complex (double, double, double, __pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0_0eval_laguerre": "__pyx_t_double_complex (double, __pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0_0eval_legendre": "__pyx_t_double_complex (double, __pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0_0eval_sh_chebyt": "__pyx_t_double_complex (double, __pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0_0eval_sh_chebyu": "__pyx_t_double_complex (double, __pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0_0eval_sh_jacobi": "__pyx_t_double_complex (double, double, double, __pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0_0eval_sh_legendre": "__pyx_t_double_complex (double, __pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0_1eval_chebyc": "double (double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0_1eval_chebys": "double (double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0_1eval_chebyt": "double (double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0_1eval_chebyu": "double (double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0_1eval_gegenbauer": "double (double, double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0_1eval_genlaguerre": "double (double, double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0_1eval_jacobi": "double (double, double, double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0_1eval_laguerre": "double (double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0_1eval_legendre": "double (double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0_1eval_sh_chebyt": "double (double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0_1eval_sh_chebyu": "double (double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0_1eval_sh_jacobi": "double (double, double, double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0_1eval_sh_legendre": "double (double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0airy": "void (__pyx_t_double_complex, __pyx_t_double_complex *, __pyx_t_double_complex *, __pyx_t_double_complex *, __pyx_t_double_complex *)",
+    "__pyx_fuse_0airye": "void (__pyx_t_double_complex, __pyx_t_double_complex *, __pyx_t_double_complex *, __pyx_t_double_complex *, __pyx_t_double_complex *)",
+    "__pyx_fuse_0bdtr": "double (double, double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0bdtrc": "double (double, double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0bdtri": "double (double, double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0betainc": "double (double, double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0betaincc": "double (double, double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0betainccinv": "double (double, double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0betaincinv": "double (double, double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0btdtria": "double (double, double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0btdtrib": "double (double, double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0chdtriv": "double (double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0chndtr": "double (double, double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0chndtridf": "double (double, double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0chndtrinc": "double (double, double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0chndtrix": "double (double, double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0dawsn": "__pyx_t_double_complex (__pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0elliprc": "__pyx_t_double_complex (__pyx_t_double_complex, __pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0elliprd": "__pyx_t_double_complex (__pyx_t_double_complex, __pyx_t_double_complex, __pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0elliprf": "__pyx_t_double_complex (__pyx_t_double_complex, __pyx_t_double_complex, __pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0elliprg": "__pyx_t_double_complex (__pyx_t_double_complex, __pyx_t_double_complex, __pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0elliprj": "__pyx_t_double_complex (__pyx_t_double_complex, __pyx_t_double_complex, __pyx_t_double_complex, __pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0erf": "__pyx_t_double_complex (__pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0erfc": "__pyx_t_double_complex (__pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0erfcx": "__pyx_t_double_complex (__pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0erfi": "__pyx_t_double_complex (__pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0erfinv": "double (double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0exp1": "__pyx_t_double_complex (__pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0expi": "__pyx_t_double_complex (__pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0expit": "double (double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0expm1": "__pyx_t_double_complex (__pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0expn": "double (double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0fdtr": "double (double, double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0fdtrc": "double (double, double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0fdtri": "double (double, double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0fresnel": "void (__pyx_t_double_complex, __pyx_t_double_complex *, __pyx_t_double_complex *)",
+    "__pyx_fuse_0gamma": "__pyx_t_double_complex (__pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0hyp0f1": "__pyx_t_double_complex (double, __pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0hyp1f1": "__pyx_t_double_complex (double, double, __pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0hyp2f1": "__pyx_t_double_complex (double, double, double, __pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0iv": "__pyx_t_double_complex (double, __pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0ive": "__pyx_t_double_complex (double, __pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0jv": "__pyx_t_double_complex (double, __pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0jve": "__pyx_t_double_complex (double, __pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0kn": "double (double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0kv": "__pyx_t_double_complex (double, __pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0kve": "__pyx_t_double_complex (double, __pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0log1p": "__pyx_t_double_complex (__pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0log_expit": "double (double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0log_ndtr": "__pyx_t_double_complex (__pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0loggamma": "__pyx_t_double_complex (__pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0logit": "double (double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0nbdtr": "double (double, double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0nbdtrc": "double (double, double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0nbdtri": "double (double, double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0ncfdtr": "double (double, double, double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0ncfdtri": "double (double, double, double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0nctdtr": "double (double, double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0nctdtrit": "double (double, double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0ndtr": "__pyx_t_double_complex (__pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0pdtri": "double (double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0pdtrik": "double (double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0powm1": "double (double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0psi": "__pyx_t_double_complex (__pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0rgamma": "__pyx_t_double_complex (__pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0shichi": "void (__pyx_t_double_complex, __pyx_t_double_complex *, __pyx_t_double_complex *)",
+    "__pyx_fuse_0sici": "void (__pyx_t_double_complex, __pyx_t_double_complex *, __pyx_t_double_complex *)",
+    "__pyx_fuse_0smirnov": "double (double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0smirnovi": "double (double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0spence": "__pyx_t_double_complex (__pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0spherical_in": "__pyx_t_double_complex (Py_ssize_t, __pyx_t_double_complex, int __pyx_skip_dispatch, struct __pyx_fuse_0__pyx_opt_args_5scipy_7special_14cython_special_spherical_in *__pyx_optional_args)",
+    "__pyx_fuse_0spherical_jn": "__pyx_t_double_complex (Py_ssize_t, __pyx_t_double_complex, int __pyx_skip_dispatch, struct __pyx_fuse_0__pyx_opt_args_5scipy_7special_14cython_special_spherical_jn *__pyx_optional_args)",
+    "__pyx_fuse_0spherical_kn": "__pyx_t_double_complex (Py_ssize_t, __pyx_t_double_complex, int __pyx_skip_dispatch, struct __pyx_fuse_0__pyx_opt_args_5scipy_7special_14cython_special_spherical_kn *__pyx_optional_args)",
+    "__pyx_fuse_0spherical_yn": "__pyx_t_double_complex (Py_ssize_t, __pyx_t_double_complex, int __pyx_skip_dispatch, struct __pyx_fuse_0__pyx_opt_args_5scipy_7special_14cython_special_spherical_yn *__pyx_optional_args)",
+    "__pyx_fuse_0stdtr": "double (double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0stdtrit": "double (double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0wrightomega": "__pyx_t_double_complex (__pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0xlog1py": "__pyx_t_double_complex (__pyx_t_double_complex, __pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0xlogy": "__pyx_t_double_complex (__pyx_t_double_complex, __pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0yn": "double (double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0yv": "__pyx_t_double_complex (double, __pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_0yve": "__pyx_t_double_complex (double, __pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1_0eval_chebyc": "__pyx_t_double_complex (long, __pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1_0eval_chebys": "__pyx_t_double_complex (long, __pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1_0eval_chebyt": "__pyx_t_double_complex (long, __pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1_0eval_chebyu": "__pyx_t_double_complex (long, __pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1_0eval_gegenbauer": "__pyx_t_double_complex (long, double, __pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1_0eval_genlaguerre": "__pyx_t_double_complex (long, double, __pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1_0eval_jacobi": "__pyx_t_double_complex (long, double, double, __pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1_0eval_laguerre": "__pyx_t_double_complex (long, __pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1_0eval_legendre": "__pyx_t_double_complex (long, __pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1_0eval_sh_chebyt": "__pyx_t_double_complex (long, __pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1_0eval_sh_chebyu": "__pyx_t_double_complex (long, __pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1_0eval_sh_jacobi": "__pyx_t_double_complex (long, double, double, __pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1_0eval_sh_legendre": "__pyx_t_double_complex (long, __pyx_t_double_complex, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1_1eval_chebyc": "double (long, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1_1eval_chebys": "double (long, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1_1eval_chebyt": "double (long, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1_1eval_chebyu": "double (long, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1_1eval_gegenbauer": "double (long, double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1_1eval_genlaguerre": "double (long, double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1_1eval_jacobi": "double (long, double, double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1_1eval_laguerre": "double (long, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1_1eval_legendre": "double (long, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1_1eval_sh_chebyt": "double (long, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1_1eval_sh_chebyu": "double (long, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1_1eval_sh_jacobi": "double (long, double, double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1_1eval_sh_legendre": "double (long, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1airy": "void (double, double *, double *, double *, double *)",
+    "__pyx_fuse_1airye": "void (double, double *, double *, double *, double *)",
+    "__pyx_fuse_1bdtr": "double (double, long, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1bdtrc": "double (double, long, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1bdtri": "double (double, long, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1betainc": "float (float, float, float, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1betaincc": "float (float, float, float, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1betainccinv": "float (float, float, float, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1betaincinv": "float (float, float, float, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1btdtria": "float (float, float, float, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1btdtrib": "float (float, float, float, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1chdtriv": "float (float, float, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1chndtr": "float (float, float, float, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1chndtridf": "float (float, float, float, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1chndtrinc": "float (float, float, float, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1chndtrix": "float (float, float, float, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1dawsn": "double (double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1elliprc": "double (double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1elliprd": "double (double, double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1elliprf": "double (double, double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1elliprg": "double (double, double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1elliprj": "double (double, double, double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1erf": "double (double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1erfc": "double (double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1erfcx": "double (double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1erfi": "double (double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1erfinv": "float (float, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1exp1": "double (double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1expi": "double (double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1expit": "float (float, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1expm1": "double (double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1expn": "double (long, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1fdtr": "float (float, float, float, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1fdtrc": "float (float, float, float, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1fdtri": "float (float, float, float, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1fresnel": "void (double, double *, double *)",
+    "__pyx_fuse_1gamma": "double (double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1hyp0f1": "double (double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1hyp1f1": "double (double, double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1hyp2f1": "double (double, double, double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1iv": "double (double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1ive": "double (double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1jv": "double (double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1jve": "double (double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1kn": "double (long, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1kv": "double (double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1kve": "double (double, double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1log1p": "double (double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1log_expit": "float (float, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1log_ndtr": "double (double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1loggamma": "double (double, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1logit": "float (float, int __pyx_skip_dispatch)",
+    "__pyx_fuse_1nbdtr": "double (long, long, double, int __pyx_skip_dispatch)",
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+  }
+}
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diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/data/boost.npz b/venv/lib/python3.12/site-packages/scipy/special/tests/data/boost.npz
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diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/data/gsl.npz b/venv/lib/python3.12/site-packages/scipy/special/tests/data/gsl.npz
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+size 51433
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diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_basic.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_basic.py
new file mode 100644
index 0000000000000000000000000000000000000000..cfa9587f9c19ce9d37b54e049c6ff9de89b80d3b
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_basic.py
@@ -0,0 +1,4868 @@
+# this program corresponds to special.py
+
+### Means test is not done yet
+# E   Means test is giving error (E)
+# F   Means test is failing (F)
+# EF  Means test is giving error and Failing
+#!   Means test is segfaulting
+# 8   Means test runs forever
+
+###  test_besselpoly
+###  test_modfresnelp
+###  test_modfresnelm
+#    test_pbdv_seq
+###  test_pbvv_seq
+###  test_sph_harm
+
+import functools
+import itertools
+import operator
+import platform
+import sys
+import warnings
+
+import numpy as np
+from numpy import (array, isnan, r_, arange, finfo, pi, sin, cos, tan, exp,
+        log, zeros, sqrt, asarray, inf, nan_to_num, real, arctan, double,
+        array_equal)
+
+import pytest
+from pytest import raises as assert_raises
+from numpy.testing import (assert_equal, assert_array_equal, assert_,
+                           assert_allclose, assert_array_almost_equal_nulp)
+
+from scipy import special
+import scipy.special._ufuncs as cephes
+from scipy.special import ellipe, ellipk, ellipkm1
+from scipy.special import elliprc, elliprd, elliprf, elliprg, elliprj
+from scipy.special import softplus
+from scipy.special import mathieu_odd_coef, mathieu_even_coef, stirling2
+from scipy._lib._array_api import xp_assert_close, xp_assert_equal, SCIPY_ARRAY_API
+
+from scipy.special._basic import (
+    _FACTORIALK_LIMITS_64BITS, _FACTORIALK_LIMITS_32BITS, _is_subdtype
+)
+from scipy.special._testutils import with_special_errors, \
+     assert_func_equal, FuncData
+from scipy.integrate import quad
+
+import math
+
+
+native_int = np.int32 if (
+    sys.platform == 'win32'
+    or platform.architecture()[0] == "32bit"
+) else np.int64
+
+
+class TestCephes:
+    def test_airy(self):
+        cephes.airy(0)
+
+    def test_airye(self):
+        cephes.airye(0)
+
+    def test_binom(self):
+        n = np.array([0.264, 4, 5.2, 17])
+        k = np.array([2, 0.4, 7, 3.3])
+        nk = np.array(np.broadcast_arrays(n[:,None], k[None,:])
+                      ).reshape(2, -1).T
+        rknown = np.array([[-0.097152, 0.9263051596159367, 0.01858423645695389,
+            -0.007581020651518199],[6, 2.0214389119675666, 0, 2.9827344527963846],
+            [10.92, 2.22993515861399, -0.00585728, 10.468891352063146],
+            [136, 3.5252179590758828, 19448, 1024.5526916174495]])
+        assert_func_equal(cephes.binom, rknown.ravel(), nk, rtol=1e-13)
+
+        # Test branches in implementation
+        rng = np.random.RandomState(1234)
+        n = np.r_[np.arange(-7, 30), 1000*rng.rand(30) - 500]
+        k = np.arange(0, 102)
+        nk = np.array(np.broadcast_arrays(n[:,None], k[None,:])
+                      ).reshape(2, -1).T
+
+        assert_func_equal(cephes.binom,
+                          cephes.binom(nk[:,0], nk[:,1] * (1 + 1e-15)),
+                          nk,
+                          atol=1e-10, rtol=1e-10)
+
+    def test_binom_2(self):
+        # Test branches in implementation
+        np.random.seed(1234)
+        n = np.r_[np.logspace(1, 300, 20)]
+        k = np.arange(0, 102)
+        nk = np.array(np.broadcast_arrays(n[:,None], k[None,:])
+                      ).reshape(2, -1).T
+
+        assert_func_equal(cephes.binom,
+                          cephes.binom(nk[:,0], nk[:,1] * (1 + 1e-15)),
+                          nk,
+                          atol=1e-10, rtol=1e-10)
+
+    def test_binom_exact(self):
+        @np.vectorize
+        def binom_int(n, k):
+            n = int(n)
+            k = int(k)
+            num = 1
+            den = 1
+            for i in range(1, k+1):
+                num *= i + n - k
+                den *= i
+            return float(num/den)
+
+        np.random.seed(1234)
+        n = np.arange(1, 15)
+        k = np.arange(0, 15)
+        nk = np.array(np.broadcast_arrays(n[:,None], k[None,:])
+                      ).reshape(2, -1).T
+        nk = nk[nk[:,0] >= nk[:,1]]
+        assert_func_equal(cephes.binom,
+                          binom_int(nk[:,0], nk[:,1]),
+                          nk,
+                          atol=0, rtol=0)
+
+    def test_binom_nooverflow_8346(self):
+        # Test (binom(n, k) doesn't overflow prematurely */
+        dataset = [
+            (1000, 500, 2.70288240945436551e+299),
+            (1002, 501, 1.08007396880791225e+300),
+            (1004, 502, 4.31599279169058121e+300),
+            (1006, 503, 1.72468101616263781e+301),
+            (1008, 504, 6.89188009236419153e+301),
+            (1010, 505, 2.75402257948335448e+302),
+            (1012, 506, 1.10052048531923757e+303),
+            (1014, 507, 4.39774063758732849e+303),
+            (1016, 508, 1.75736486108312519e+304),
+            (1018, 509, 7.02255427788423734e+304),
+            (1020, 510, 2.80626776829962255e+305),
+            (1022, 511, 1.12140876377061240e+306),
+            (1024, 512, 4.48125455209897109e+306),
+            (1026, 513, 1.79075474304149900e+307),
+            (1028, 514, 7.15605105487789676e+307)
+        ]
+        dataset = np.asarray(dataset)
+        FuncData(cephes.binom, dataset, (0, 1), 2, rtol=1e-12).check()
+
+    def test_bdtr(self):
+        assert_equal(cephes.bdtr(1,1,0.5),1.0)
+
+    def test_bdtri(self):
+        assert_equal(cephes.bdtri(1,3,0.5),0.5)
+
+    def test_bdtrc(self):
+        assert_equal(cephes.bdtrc(1,3,0.5),0.5)
+
+    def test_bdtrik(self):
+        cephes.bdtrik(1,3,0.5)
+
+    def test_bei(self):
+        assert_equal(cephes.bei(0),0.0)
+
+    def test_beip(self):
+        assert_equal(cephes.beip(0),0.0)
+
+    def test_ber(self):
+        assert_equal(cephes.ber(0),1.0)
+
+    def test_berp(self):
+        assert_equal(cephes.berp(0),0.0)
+
+    def test_besselpoly(self):
+        assert_equal(cephes.besselpoly(0,0,0),1.0)
+
+    def test_cbrt(self):
+        assert_allclose(cephes.cbrt(1), 1.0, atol=1e-6, rtol=0)
+
+    def test_chdtr(self):
+        assert_equal(cephes.chdtr(1,0),0.0)
+
+    def test_chdtrc(self):
+        assert_equal(cephes.chdtrc(1,0),1.0)
+
+    def test_chdtri(self):
+        assert_equal(cephes.chdtri(1,1),0.0)
+
+    def test_chndtrix(self):
+        assert_equal(cephes.chndtrix(0,1,0),0.0)
+
+    def test_cosdg(self):
+        assert_equal(cephes.cosdg(0),1.0)
+
+    def test_cosm1(self):
+        assert_equal(cephes.cosm1(0),0.0)
+
+    def test_cotdg(self):
+        assert_allclose(cephes.cotdg(45), 1.0, atol=1.5e-7, rtol=0)
+
+    def test_dawsn(self):
+        assert_equal(cephes.dawsn(0),0.0)
+        assert_allclose(cephes.dawsn(1.23), 0.50053727749081767)
+
+    def test_diric(self):
+        # Test behavior near multiples of 2pi.  Regression test for issue
+        # described in gh-4001.
+        n_odd = [1, 5, 25]
+        x = np.array(2*np.pi + 5e-5).astype(np.float32)
+        assert_allclose(special.diric(x, n_odd), 1.0, atol=1.5e-7, rtol=0)
+        x = np.array(2*np.pi + 1e-9).astype(np.float64)
+        assert_allclose(special.diric(x, n_odd), 1.0, atol=1.5e-15, rtol=0)
+        x = np.array(2*np.pi + 1e-15).astype(np.float64)
+        assert_allclose(special.diric(x, n_odd), 1.0, atol=1.5e-15, rtol=0)
+        if hasattr(np, 'float128'):
+            # No float128 available in 32-bit numpy
+            x = np.array(2*np.pi + 1e-12).astype(np.float128)
+            assert_allclose(special.diric(x, n_odd), 1.0, atol=1.5e-19, rtol=0)
+
+        n_even = [2, 4, 24]
+        x = np.array(2*np.pi + 1e-9).astype(np.float64)
+        assert_allclose(special.diric(x, n_even), -1.0, atol=1.5e-15, rtol=0)
+
+        # Test at some values not near a multiple of pi
+        x = np.arange(0.2*np.pi, 1.0*np.pi, 0.2*np.pi)
+        octave_result = [0.872677996249965, 0.539344662916632,
+                         0.127322003750035, -0.206011329583298]
+        assert_allclose(special.diric(x, 3), octave_result, atol=1.5e-15, rtol=0)
+
+    def test_diric_broadcasting(self):
+        x = np.arange(5)
+        n = np.array([1, 3, 7])
+        assert_(special.diric(x[:, np.newaxis], n).shape == (x.size, n.size))
+
+    def test_ellipe(self):
+        assert_equal(cephes.ellipe(1),1.0)
+
+    def test_ellipeinc(self):
+        assert_equal(cephes.ellipeinc(0,1),0.0)
+
+    def test_ellipj(self):
+        cephes.ellipj(0,1)
+
+    def test_ellipk(self):
+        assert_allclose(ellipk(0), pi/2)
+
+    def test_ellipkinc(self):
+        assert_equal(cephes.ellipkinc(0,0),0.0)
+
+    def test_erf(self):
+        assert_equal(cephes.erf(0), 0.0)
+
+    def test_erf_symmetry(self):
+        x = 5.905732037710919
+        assert_equal(cephes.erf(x) + cephes.erf(-x), 0.0)
+
+    def test_erfc(self):
+        assert_equal(cephes.erfc(0), 1.0)
+
+    def test_exp10(self):
+        assert_allclose(cephes.exp10(2), 100.0, atol=1e-6, rtol=0)
+
+    def test_exp2(self):
+        assert_equal(cephes.exp2(2),4.0)
+
+    def test_expm1(self):
+        assert_equal(cephes.expm1(0),0.0)
+        assert_equal(cephes.expm1(np.inf), np.inf)
+        assert_equal(cephes.expm1(-np.inf), -1)
+        assert_equal(cephes.expm1(np.nan), np.nan)
+
+    def test_expm1_complex(self):
+        expm1 = cephes.expm1
+        assert_equal(expm1(0 + 0j), 0 + 0j)
+        assert_equal(expm1(complex(np.inf, 0)), complex(np.inf, 0))
+        assert_equal(expm1(complex(np.inf, 1)), complex(np.inf, np.inf))
+        assert_equal(expm1(complex(np.inf, 2)), complex(-np.inf, np.inf))
+        assert_equal(expm1(complex(np.inf, 4)), complex(-np.inf, -np.inf))
+        assert_equal(expm1(complex(np.inf, 5)), complex(np.inf, -np.inf))
+        assert_equal(expm1(complex(1, np.inf)), complex(np.nan, np.nan))
+        assert_equal(expm1(complex(0, np.inf)), complex(np.nan, np.nan))
+        assert_equal(expm1(complex(np.inf, np.inf)), complex(np.inf, np.nan))
+        assert_equal(expm1(complex(-np.inf, np.inf)), complex(-1, 0))
+        assert_equal(expm1(complex(-np.inf, np.nan)), complex(-1, 0))
+        assert_equal(expm1(complex(np.inf, np.nan)), complex(np.inf, np.nan))
+        assert_equal(expm1(complex(0, np.nan)), complex(np.nan, np.nan))
+        assert_equal(expm1(complex(1, np.nan)), complex(np.nan, np.nan))
+        assert_equal(expm1(complex(np.nan, 1)), complex(np.nan, np.nan))
+        assert_equal(expm1(complex(np.nan, np.nan)), complex(np.nan, np.nan))
+
+    @pytest.mark.xfail(reason='The real part of expm1(z) bad at these points')
+    def test_expm1_complex_hard(self):
+        # The real part of this function is difficult to evaluate when
+        # z.real = -log(cos(z.imag)).
+        y = np.array([0.1, 0.2, 0.3, 5, 11, 20])
+        x = -np.log(np.cos(y))
+        z = x + 1j*y
+
+        # evaluate using mpmath.expm1 with dps=1000
+        expected = np.array([-5.5507901846769623e-17+0.10033467208545054j,
+                              2.4289354732893695e-18+0.20271003550867248j,
+                              4.5235500262585768e-17+0.30933624960962319j,
+                              7.8234305217489006e-17-3.3805150062465863j,
+                             -1.3685191953697676e-16-225.95084645419513j,
+                              8.7175620481291045e-17+2.2371609442247422j])
+        found = cephes.expm1(z)
+        # this passes.
+        assert_array_almost_equal_nulp(found.imag, expected.imag, 3)
+        # this fails.
+        assert_array_almost_equal_nulp(found.real, expected.real, 20)
+
+    def test_fdtr(self):
+        assert_equal(cephes.fdtr(1, 1, 0), 0.0)
+        # Computed using Wolfram Alpha: CDF[FRatioDistribution[1e-6, 5], 10]
+        assert_allclose(cephes.fdtr(1e-6, 5, 10), 0.9999940790193488,
+                        rtol=1e-12)
+
+    def test_fdtrc(self):
+        assert_equal(cephes.fdtrc(1, 1, 0), 1.0)
+        # Computed using Wolfram Alpha:
+        #   1 - CDF[FRatioDistribution[2, 1/10], 1e10]
+        assert_allclose(cephes.fdtrc(2, 0.1, 1e10), 0.27223784621293512,
+                        rtol=1e-12)
+
+    def test_fdtri(self):
+        assert_allclose(cephes.fdtri(1, 1, [0.499, 0.501]),
+                        array([0.9937365, 1.00630298]), rtol=1e-6)
+        # From Wolfram Alpha:
+        #   CDF[FRatioDistribution[1/10, 1], 3] = 0.8756751669632105666874...
+        p = 0.8756751669632105666874
+        assert_allclose(cephes.fdtri(0.1, 1, p), 3, rtol=1e-12)
+
+    def test_gh20835(self):
+        # gh-20835 reported fdtri failing for extreme inputs
+        dfd, dfn, x = 1, 50000, 29.72591544307521
+        assert_allclose(cephes.fdtri(dfd, dfn, cephes.fdtr(dfd, dfn, x)), x, rtol=1e-15)
+
+    def test_fdtri_mysterious_failure(self):
+        assert_allclose(cephes.fdtri(1, 1, 0.5), 1)
+
+    def test_fdtridfd(self):
+        assert_equal(cephes.fdtridfd(1,0,0),5.0)
+
+    def test_fresnel(self):
+        assert_equal(cephes.fresnel(0),(0.0,0.0))
+
+    def test_gamma(self):
+        assert_equal(cephes.gamma(5),24.0)
+
+    def test_gammainccinv(self):
+        assert_equal(cephes.gammainccinv(5,1),0.0)
+
+    def test_gammaln(self):
+        cephes.gammaln(10)
+
+    def test_gammasgn(self):
+        vals = np.array(
+            [-np.inf, -4, -3.5, -2.3, -0.0, 0.0, 1, 4.2, np.inf], np.float64
+        )
+        reference = np.array(
+            [np.nan, np.nan, 1.0, -1.0, -1.0, 1.0, 1.0, 1.0, 1.0], np.float64
+        )
+        assert_array_equal(cephes.gammasgn(vals), reference)
+
+    def test_gdtr(self):
+        assert_equal(cephes.gdtr(1,1,0),0.0)
+
+    def test_gdtr_inf(self):
+        assert_equal(cephes.gdtr(1,1,np.inf),1.0)
+
+    def test_gdtrc(self):
+        assert_equal(cephes.gdtrc(1,1,0),1.0)
+
+    def test_gdtria(self):
+        assert_equal(cephes.gdtria(0,1,1),0.0)
+
+    def test_gdtrib(self):
+        cephes.gdtrib(1,0,1)
+        # assert_equal(cephes.gdtrib(1,0,1),5.0)
+
+    def test_gdtrix(self):
+        cephes.gdtrix(1,1,.1)
+
+    def test_hankel1(self):
+        cephes.hankel1(1,1)
+
+    def test_hankel1e(self):
+        cephes.hankel1e(1,1)
+
+    def test_hankel2(self):
+        cephes.hankel2(1,1)
+
+    def test_hankel2e(self):
+        cephes.hankel2e(1,1)
+
+    def test_hyp1f1(self):
+        assert_allclose(cephes.hyp1f1(1, 1, 1), exp(1.0), atol=1e-6, rtol=0)
+        assert_allclose(cephes.hyp1f1(3, 4, -6), 0.026056422099537251095,
+                        atol=1e-6, rtol=0)
+        cephes.hyp1f1(1,1,1)
+
+    def test_hyp2f1(self):
+        assert_equal(cephes.hyp2f1(1,1,1,0),1.0)
+
+    def test_i0(self):
+        assert_equal(cephes.i0(0),1.0)
+
+    def test_i0e(self):
+        assert_equal(cephes.i0e(0),1.0)
+
+    def test_i1(self):
+        assert_equal(cephes.i1(0),0.0)
+
+    def test_i1e(self):
+        assert_equal(cephes.i1e(0),0.0)
+
+    def test_it2i0k0(self):
+        cephes.it2i0k0(1)
+
+    def test_it2j0y0(self):
+        cephes.it2j0y0(1)
+
+    def test_it2struve0(self):
+        cephes.it2struve0(1)
+
+    def test_itairy(self):
+        cephes.itairy(1)
+
+    def test_iti0k0(self):
+        assert_equal(cephes.iti0k0(0),(0.0,0.0))
+
+    def test_itj0y0(self):
+        assert_equal(cephes.itj0y0(0),(0.0,0.0))
+
+    def test_itmodstruve0(self):
+        assert_equal(cephes.itmodstruve0(0),0.0)
+
+    def test_itstruve0(self):
+        assert_equal(cephes.itstruve0(0),0.0)
+
+    def test_iv(self):
+        assert_equal(cephes.iv(1,0),0.0)
+
+    def test_ive(self):
+        assert_equal(cephes.ive(1,0),0.0)
+
+    def test_j0(self):
+        assert_equal(cephes.j0(0),1.0)
+
+    def test_j1(self):
+        assert_equal(cephes.j1(0),0.0)
+
+    def test_jn(self):
+        assert_equal(cephes.jn(0,0),1.0)
+
+    def test_jv(self):
+        assert_equal(cephes.jv(0,0),1.0)
+
+    def test_jve(self):
+        assert_equal(cephes.jve(0,0),1.0)
+
+    def test_k0(self):
+        cephes.k0(2)
+
+    def test_k0e(self):
+        cephes.k0e(2)
+
+    def test_k1(self):
+        cephes.k1(2)
+
+    def test_k1e(self):
+        cephes.k1e(2)
+
+    def test_kei(self):
+        cephes.kei(2)
+
+    def test_keip(self):
+        assert_equal(cephes.keip(0),0.0)
+
+    def test_ker(self):
+        cephes.ker(2)
+
+    def test_kerp(self):
+        cephes.kerp(2)
+
+    def test_kelvin(self):
+        cephes.kelvin(2)
+
+    def test_kn(self):
+        cephes.kn(1,1)
+
+    def test_kolmogi(self):
+        assert_equal(cephes.kolmogi(1),0.0)
+        assert_(np.isnan(cephes.kolmogi(np.nan)))
+
+    def test_kolmogorov(self):
+        assert_equal(cephes.kolmogorov(0), 1.0)
+
+    def test_kolmogp(self):
+        assert_equal(cephes._kolmogp(0), -0.0)
+
+    def test_kolmogc(self):
+        assert_equal(cephes._kolmogc(0), 0.0)
+
+    def test_kolmogci(self):
+        assert_equal(cephes._kolmogci(0), 0.0)
+        assert_(np.isnan(cephes._kolmogci(np.nan)))
+
+    def test_kv(self):
+        cephes.kv(1,1)
+
+    def test_kve(self):
+        cephes.kve(1,1)
+
+    def test_log1p(self):
+        log1p = cephes.log1p
+        assert_equal(log1p(0), 0.0)
+        assert_equal(log1p(-1), -np.inf)
+        assert_equal(log1p(-2), np.nan)
+        assert_equal(log1p(np.inf), np.inf)
+
+    def test_log1p_complex(self):
+        log1p = cephes.log1p
+        c = complex
+        assert_equal(log1p(0 + 0j), 0 + 0j)
+        assert_equal(log1p(c(-1, 0)), c(-np.inf, 0))
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", "invalid value encountered in multiply", RuntimeWarning)
+            assert_allclose(log1p(c(1, np.inf)), c(np.inf, np.pi/2))
+            assert_equal(log1p(c(1, np.nan)), c(np.nan, np.nan))
+            assert_allclose(log1p(c(-np.inf, 1)), c(np.inf, np.pi))
+            assert_equal(log1p(c(np.inf, 1)), c(np.inf, 0))
+            assert_allclose(log1p(c(-np.inf, np.inf)), c(np.inf, 3*np.pi/4))
+            assert_allclose(log1p(c(np.inf, np.inf)), c(np.inf, np.pi/4))
+            assert_equal(log1p(c(np.inf, np.nan)), c(np.inf, np.nan))
+            assert_equal(log1p(c(-np.inf, np.nan)), c(np.inf, np.nan))
+            assert_equal(log1p(c(np.nan, np.inf)), c(np.inf, np.nan))
+            assert_equal(log1p(c(np.nan, 1)), c(np.nan, np.nan))
+            assert_equal(log1p(c(np.nan, np.nan)), c(np.nan, np.nan))
+
+    def test_lpmv(self):
+        assert_equal(cephes.lpmv(0,0,1),1.0)
+
+    def test_mathieu_a_q0(self):
+        # When q is 0, the exact result is m**2.
+        m = np.array([1, 2, 5])
+        assert_equal(cephes.mathieu_a(m, 0), m**2)
+
+    # Reference values were computed with Wolfram Alpha:
+    #     MathieuCharacteristicA[m, q]
+    @pytest.mark.parametrize(
+        'm, q, ref',
+        [(0, 8, -10.6067292355526479852024),
+         (3, 3/2, 9.19330104768060974047804),
+         (5, 1/4, 25.0013021454698022809572),
+         (8, -10, 64.8008910105046444848962)]
+    )
+    def test_mathieu_a(self, m, q, ref):
+        y = cephes.mathieu_a(m, q)
+        assert_allclose(y, ref, rtol=1e-15)
+
+    def test_mathieu_b_q0(self):
+        # When q is 0, the exact result is m**2.
+        m = np.array([1, 2, 5])
+        assert_equal(cephes.mathieu_b(m, 0), m**2)
+
+    # Reference values were computed with Wolfram Alpha:
+    #     MathieuCharacteristicB[m, q]
+    @pytest.mark.parametrize(
+        'm, q, ref',
+        [(1, 15, -22.5130034974234666335),
+         (5, 3, 25.1870798027185125480),
+         (9, 1/4, 81.00039062627570760760),
+         (10, -3, 100.0454683359769326164)]
+    )
+    def test_mathieu_b(self, m, q, ref):
+        y = cephes.mathieu_b(m, q)
+        assert_allclose(y, ref, rtol=1e-15)
+
+    def test_mathieu_cem(self):
+        assert_equal(cephes.mathieu_cem(1,0,0),(1.0,0.0))
+
+        # Test AMS 20.2.27
+        @np.vectorize
+        def ce_smallq(m, q, z):
+            z *= np.pi/180
+            if m == 0:
+                # + O(q^2)
+                return 2**(-0.5) * (1 - .5*q*cos(2*z))
+            elif m == 1:
+                # + O(q^2)
+                return cos(z) - q/8 * cos(3*z)
+            elif m == 2:
+                # + O(q^2)
+                return cos(2*z) - q*(cos(4*z)/12 - 1/4)
+            else:
+                # + O(q^2)
+                return cos(m*z) - q*(cos((m+2)*z)/(4*(m+1)) - cos((m-2)*z)/(4*(m-1)))
+        m = np.arange(0, 100)
+        q = np.r_[0, np.logspace(-30, -9, 10)]
+        assert_allclose(cephes.mathieu_cem(m[:,None], q[None,:], 0.123)[0],
+                        ce_smallq(m[:,None], q[None,:], 0.123),
+                        rtol=1e-14, atol=0)
+
+    def test_mathieu_sem(self):
+        assert_equal(cephes.mathieu_sem(1,0,0),(0.0,1.0))
+
+        # Test AMS 20.2.27
+        @np.vectorize
+        def se_smallq(m, q, z):
+            z *= np.pi/180
+            if m == 1:
+                # + O(q^2)
+                return sin(z) - q/8 * sin(3*z)
+            elif m == 2:
+                # + O(q^2)
+                return sin(2*z) - q*sin(4*z)/12
+            else:
+                # + O(q^2)
+                return sin(m*z) - q*(sin((m+2)*z)/(4*(m+1)) - sin((m-2)*z)/(4*(m-1)))
+        m = np.arange(1, 100)
+        q = np.r_[0, np.logspace(-30, -9, 10)]
+        assert_allclose(cephes.mathieu_sem(m[:,None], q[None,:], 0.123)[0],
+                        se_smallq(m[:,None], q[None,:], 0.123),
+                        rtol=1e-14, atol=0)
+
+    def test_mathieu_modcem1(self):
+        assert_equal(cephes.mathieu_modcem1(1,0,0),(0.0,0.0))
+
+    def test_mathieu_modcem2(self):
+        cephes.mathieu_modcem2(1,1,1)
+
+        # Test reflection relation AMS 20.6.19
+        m = np.arange(0, 4)[:,None,None]
+        q = np.r_[np.logspace(-2, 2, 10)][None,:,None]
+        z = np.linspace(0, 1, 7)[None,None,:]
+
+        y1 = cephes.mathieu_modcem2(m, q, -z)[0]
+
+        fr = -cephes.mathieu_modcem2(m, q, 0)[0] / cephes.mathieu_modcem1(m, q, 0)[0]
+        y2 = (-cephes.mathieu_modcem2(m, q, z)[0]
+              - 2*fr*cephes.mathieu_modcem1(m, q, z)[0])
+
+        assert_allclose(y1, y2, rtol=1e-10)
+
+    def test_mathieu_modsem1(self):
+        assert_equal(cephes.mathieu_modsem1(1,0,0),(0.0,0.0))
+
+    def test_mathieu_modsem2(self):
+        cephes.mathieu_modsem2(1,1,1)
+
+        # Test reflection relation AMS 20.6.20
+        m = np.arange(1, 4)[:,None,None]
+        q = np.r_[np.logspace(-2, 2, 10)][None,:,None]
+        z = np.linspace(0, 1, 7)[None,None,:]
+
+        y1 = cephes.mathieu_modsem2(m, q, -z)[0]
+        fr = cephes.mathieu_modsem2(m, q, 0)[1] / cephes.mathieu_modsem1(m, q, 0)[1]
+        y2 = (cephes.mathieu_modsem2(m, q, z)[0]
+              - 2*fr*cephes.mathieu_modsem1(m, q, z)[0])
+        assert_allclose(y1, y2, rtol=1e-10)
+
+    def test_mathieu_overflow(self):
+        # Check that these return NaNs instead of causing a SEGV
+        assert_equal(cephes.mathieu_cem(10000, 0, 1.3), (np.nan, np.nan))
+        assert_equal(cephes.mathieu_sem(10000, 0, 1.3), (np.nan, np.nan))
+        assert_equal(cephes.mathieu_cem(10000, 1.5, 1.3), (np.nan, np.nan))
+        assert_equal(cephes.mathieu_sem(10000, 1.5, 1.3), (np.nan, np.nan))
+        assert_equal(cephes.mathieu_modcem1(10000, 1.5, 1.3), (np.nan, np.nan))
+        assert_equal(cephes.mathieu_modsem1(10000, 1.5, 1.3), (np.nan, np.nan))
+        assert_equal(cephes.mathieu_modcem2(10000, 1.5, 1.3), (np.nan, np.nan))
+        assert_equal(cephes.mathieu_modsem2(10000, 1.5, 1.3), (np.nan, np.nan))
+
+    def test_mathieu_ticket_1847(self):
+        # Regression test --- this call had some out-of-bounds access
+        # and could return nan occasionally
+        for k in range(60):
+            v = cephes.mathieu_modsem2(2, 100, -1)
+            # Values from ACM TOMS 804 (derivate by numerical differentiation)
+            assert_allclose(v[0], 0.1431742913063671074347, rtol=1e-10)
+            assert_allclose(v[1], 0.9017807375832909144719, rtol=1e-4)
+
+    def test_modfresnelm(self):
+        cephes.modfresnelm(0)
+
+    def test_modfresnelp(self):
+        cephes.modfresnelp(0)
+
+    def test_modstruve(self):
+        assert_equal(cephes.modstruve(1,0),0.0)
+
+    def test_nbdtr(self):
+        assert_equal(cephes.nbdtr(1,1,1),1.0)
+
+    def test_nbdtrc(self):
+        assert_equal(cephes.nbdtrc(1,1,1),0.0)
+
+    def test_nbdtri(self):
+        assert_equal(cephes.nbdtri(1,1,1),1.0)
+
+    def test_nbdtrik(self):
+        cephes.nbdtrik(1,.4,.5)
+
+    def test_ncfdtr(self):
+        assert_equal(cephes.ncfdtr(1,1,1,0),0.0)
+
+    def test_ncfdtri(self):
+        assert_equal(cephes.ncfdtri(1, 1, 1, 0), 0.0)
+        f = [0.5, 1, 1.5]
+        p = cephes.ncfdtr(2, 3, 1.5, f)
+        assert_allclose(cephes.ncfdtri(2, 3, 1.5, p), f)
+
+    @pytest.mark.xfail(
+        reason=(
+            "ncfdtr uses a Boost math implementation but ncfdtridfd"
+            "inverts the less accurate cdflib implementation of ncfdtr."
+        )
+    )
+    def test_ncfdtridfd(self):
+        dfd = [1, 2, 3]
+        p = cephes.ncfdtr(2, dfd, 0.25, 15)
+        assert_allclose(cephes.ncfdtridfd(2, p, 0.25, 15), dfd)
+
+    @pytest.mark.xfail(
+        reason=(
+            "ncfdtr uses a Boost math implementation but ncfdtridfn"
+            "inverts the less accurate cdflib implementation of ncfdtr."
+        )
+    )
+    def test_ncfdtridfn(self):
+        dfn = [0.1, 1, 2, 3, 1e4]
+        p = cephes.ncfdtr(dfn, 2, 0.25, 15)
+        assert_allclose(cephes.ncfdtridfn(p, 2, 0.25, 15), dfn, rtol=1e-5)
+
+    @pytest.mark.xfail(
+        reason=(
+            "ncfdtr uses a Boost math implementation but ncfdtrinc"
+            "inverts the less accurate cdflib implementation of ncfdtr."
+        )
+    )
+    def test_ncfdtrinc(self):
+        nc = [0.5, 1.5, 2.0]
+        p = cephes.ncfdtr(2, 3, nc, 15)
+        assert_allclose(cephes.ncfdtrinc(2, 3, p, 15), nc)
+
+    def test_nctdtr(self):
+        assert_equal(cephes.nctdtr(1,0,0),0.5)
+        assert_equal(cephes.nctdtr(9, 65536, 45), 0.0)
+
+        assert_allclose(cephes.nctdtr(np.inf, 1., 1.), 0.5, atol=1e-4, rtol=0)
+        assert_(np.isnan(cephes.nctdtr(2., np.inf, 10.)))
+        assert_allclose(cephes.nctdtr(2., 1., np.inf), 1., atol=1e-6, rtol=0)
+
+        assert_(np.isnan(cephes.nctdtr(np.nan, 1., 1.)))
+        assert_(np.isnan(cephes.nctdtr(2., np.nan, 1.)))
+        assert_(np.isnan(cephes.nctdtr(2., 1., np.nan)))
+
+    def test_nctdtridf(self):
+        cephes.nctdtridf(1,0.5,0)
+
+    def test_nctdtrinc(self):
+        cephes.nctdtrinc(1,0,0)
+
+    def test_nctdtrit(self):
+        cephes.nctdtrit(.1,0.2,.5)
+
+    def test_nrdtrimn(self):
+        assert_allclose(cephes.nrdtrimn(0.5, 1, 1), 1.0, atol=1e-6, rtol=0)
+
+    def test_obl_ang1(self):
+        cephes.obl_ang1(1,1,1,0)
+
+    def test_obl_ang1_cv(self):
+        result = cephes.obl_ang1_cv(1,1,1,1,0)
+        assert_allclose(result[0], 1.0, atol=1.5e-7, rtol=0)
+        assert_allclose(result[1], 0.0, atol=1.5e-7, rtol=0)
+
+    def test_obl_cv(self):
+        assert_equal(cephes.obl_cv(1,1,0),2.0)
+
+    def test_obl_rad1(self):
+        cephes.obl_rad1(1,1,1,0)
+
+    def test_obl_rad1_cv(self):
+        cephes.obl_rad1_cv(1,1,1,1,0)
+
+    def test_obl_rad2(self):
+        cephes.obl_rad2(1,1,1,0)
+
+    def test_obl_rad2_cv(self):
+        cephes.obl_rad2_cv(1,1,1,1,0)
+
+    def test_pbdv(self):
+        assert_equal(cephes.pbdv(1,0),(0.0,1.0))
+
+    def test_pbvv(self):
+        cephes.pbvv(1,0)
+
+    def test_pbwa(self):
+        cephes.pbwa(1,0)
+
+    def test_pdtr(self):
+        val = cephes.pdtr(0, 1)
+        assert_allclose(val, np.exp(-1), atol=1.5e-7, rtol=0)
+        # Edge case: m = 0.
+        val = cephes.pdtr([0, 1, 2], 0)
+        assert_array_equal(val, [1, 1, 1])
+
+    def test_pdtrc(self):
+        val = cephes.pdtrc(0, 1)
+        assert_allclose(val, 1 - np.exp(-1), atol=1.5e-7, rtol=0)
+        # Edge case: m = 0.
+        val = cephes.pdtrc([0, 1, 2], 0.0)
+        assert_array_equal(val, [0, 0, 0])
+
+    def test_pdtri(self):
+        with warnings.catch_warnings():
+            msg = "floating point number truncated to an integer"
+            warnings.filterwarnings("ignore", msg, RuntimeWarning)
+            cephes.pdtri(0.5,0.5)
+
+
+    def test_pro_ang1(self):
+        cephes.pro_ang1(1,1,1,0)
+
+    def test_pro_ang1_cv(self):
+        assert_allclose(cephes.pro_ang1_cv(1, 1, 1, 1, 0), array((1.0, 0.0)),
+                        atol=1.5e-7, rtol=0)
+
+    def test_pro_cv(self):
+        assert_equal(cephes.pro_cv(1,1,0),2.0)
+
+    def test_pro_rad1(self):
+        cephes.pro_rad1(1,1,1,0.1)
+
+    def test_pro_rad1_cv(self):
+        cephes.pro_rad1_cv(1,1,1,1,0)
+
+    def test_pro_rad2(self):
+        cephes.pro_rad2(1,1,1,0)
+
+    def test_pro_rad2_cv(self):
+        cephes.pro_rad2_cv(1,1,1,1,0)
+
+    def test_psi(self):
+        cephes.psi(1)
+
+    def test_radian(self):
+        assert_equal(cephes.radian(0,0,0),0)
+
+    def test_rgamma(self):
+        assert_equal(cephes.rgamma(1),1.0)
+
+    def test_round(self):
+        assert_equal(cephes.round(3.4),3.0)
+        assert_equal(cephes.round(-3.4),-3.0)
+        assert_equal(cephes.round(3.6),4.0)
+        assert_equal(cephes.round(-3.6),-4.0)
+        assert_equal(cephes.round(3.5),4.0)
+        assert_equal(cephes.round(-3.5),-4.0)
+
+    def test_shichi(self):
+        cephes.shichi(1)
+
+    def test_sici(self):
+        cephes.sici(1)
+
+        s, c = cephes.sici(np.inf)
+        assert_allclose(s, np.pi * 0.5, atol=1.5e-7, rtol=0)
+        assert_allclose(c, 0, atol=1.5e-7, rtol=0)
+
+        s, c = cephes.sici(-np.inf)
+        assert_allclose(s, -np.pi * 0.5, atol=1.5e-7, rtol=0)
+        assert_(np.isnan(c), "cosine integral(-inf) is not nan")
+
+    def test_sindg(self):
+        assert_equal(cephes.sindg(90),1.0)
+
+    def test_smirnov(self):
+        assert_equal(cephes.smirnov(1,.1),0.9)
+        assert_(np.isnan(cephes.smirnov(1,np.nan)))
+
+    def test_smirnovp(self):
+        assert_equal(cephes._smirnovp(1, .1), -1)
+        assert_equal(cephes._smirnovp(2, 0.75), -2*(0.25)**(2-1))
+        assert_equal(cephes._smirnovp(3, 0.75), -3*(0.25)**(3-1))
+        assert_(np.isnan(cephes._smirnovp(1, np.nan)))
+
+    def test_smirnovc(self):
+        assert_equal(cephes._smirnovc(1,.1),0.1)
+        assert_(np.isnan(cephes._smirnovc(1,np.nan)))
+        x10 = np.linspace(0, 1, 11, endpoint=True)
+        assert_allclose(cephes._smirnovc(3, x10), 1 - cephes.smirnov(3, x10),
+                        atol=1.5e-7, rtol=0)
+        x4 = np.linspace(0, 1, 5, endpoint=True)
+        assert_allclose(cephes._smirnovc(4, x4), 1 - cephes.smirnov(4, x4),
+                        atol=1.5e-7, rtol=0)
+
+    def test_smirnovi(self):
+        assert_allclose(cephes.smirnov(1, cephes.smirnovi(1, 0.4)), 0.4,
+                        atol=1.5e-7, rtol=0)
+        assert_allclose(cephes.smirnov(1, cephes.smirnovi(1, 0.6)), 0.6,
+                        atol=1.5e-7, rtol=0)
+        assert_(np.isnan(cephes.smirnovi(1,np.nan)))
+
+    def test_smirnovci(self):
+        assert_allclose(cephes._smirnovc(1, cephes._smirnovci(1, 0.4)), 0.4,
+                        atol=1.5e-7, rtol=0)
+        assert_allclose(cephes._smirnovc(1, cephes._smirnovci(1, 0.6)), 0.6,
+                        atol=1.5e-7, rtol=0)
+        assert_(np.isnan(cephes._smirnovci(1,np.nan)))
+
+    def test_spence(self):
+        assert_equal(cephes.spence(1),0.0)
+
+    def test_stdtr(self):
+        assert_equal(cephes.stdtr(1,0),0.5)
+        assert_allclose(cephes.stdtr(1, 1), 0.75, atol=1.5e-7, rtol=0)
+        assert_allclose(cephes.stdtr(1, 2), 0.852416382349, atol=1.5e-7, rtol=0)
+
+    def test_stdtridf(self):
+        cephes.stdtridf(0.7,1)
+
+    def test_stdtrit(self):
+        cephes.stdtrit(1,0.7)
+
+    def test_struve(self):
+        assert_equal(cephes.struve(0,0),0.0)
+
+    def test_tandg(self):
+        assert_equal(cephes.tandg(45),1.0)
+
+    def test_tklmbda(self):
+        assert_allclose(cephes.tklmbda(1, 1), 1.0, atol=1.5e-7, rtol=0)
+
+    def test_y0(self):
+        cephes.y0(1)
+
+    def test_y1(self):
+        cephes.y1(1)
+
+    def test_yn(self):
+        cephes.yn(1,1)
+
+    def test_yv(self):
+        cephes.yv(1,1)
+
+    def test_yve(self):
+        cephes.yve(1,1)
+
+    def test_wofz(self):
+        z = [complex(624.2,-0.26123), complex(-0.4,3.), complex(0.6,2.),
+             complex(-1.,1.), complex(-1.,-9.), complex(-1.,9.),
+             complex(-0.0000000234545,1.1234), complex(-3.,5.1),
+             complex(-53,30.1), complex(0.0,0.12345),
+             complex(11,1), complex(-22,-2), complex(9,-28),
+             complex(21,-33), complex(1e5,1e5), complex(1e14,1e14)
+             ]
+        w = [
+            complex(-3.78270245518980507452677445620103199303131110e-7,
+                    0.000903861276433172057331093754199933411710053155),
+            complex(0.1764906227004816847297495349730234591778719532788,
+                    -0.02146550539468457616788719893991501311573031095617),
+            complex(0.2410250715772692146133539023007113781272362309451,
+                    0.06087579663428089745895459735240964093522265589350),
+            complex(0.30474420525691259245713884106959496013413834051768,
+                    -0.20821893820283162728743734725471561394145872072738),
+            complex(7.317131068972378096865595229600561710140617977e34,
+                    8.321873499714402777186848353320412813066170427e34),
+            complex(0.0615698507236323685519612934241429530190806818395,
+                    -0.00676005783716575013073036218018565206070072304635),
+            complex(0.3960793007699874918961319170187598400134746631,
+                    -5.593152259116644920546186222529802777409274656e-9),
+            complex(0.08217199226739447943295069917990417630675021771804,
+                    -0.04701291087643609891018366143118110965272615832184),
+            complex(0.00457246000350281640952328010227885008541748668738,
+                    -0.00804900791411691821818731763401840373998654987934),
+            complex(0.8746342859608052666092782112565360755791467973338452,
+                    0.),
+            complex(0.00468190164965444174367477874864366058339647648741,
+                    0.0510735563901306197993676329845149741675029197050),
+            complex(-0.0023193175200187620902125853834909543869428763219,
+                    -0.025460054739731556004902057663500272721780776336),
+            complex(9.11463368405637174660562096516414499772662584e304,
+                    3.97101807145263333769664875189354358563218932e305),
+            complex(-4.4927207857715598976165541011143706155432296e281,
+                    -2.8019591213423077494444700357168707775769028e281),
+            complex(2.820947917809305132678577516325951485807107151e-6,
+                    2.820947917668257736791638444590253942253354058e-6),
+            complex(2.82094791773878143474039725787438662716372268e-15,
+                    2.82094791773878143474039725773333923127678361e-15)
+        ]
+        assert_func_equal(cephes.wofz, w, z, rtol=1e-13)
+
+
+class TestAiry:
+    def test_airy(self):
+        # This tests the airy function to ensure 8 place accuracy in computation
+
+        x = special.airy(.99)
+        assert_allclose(x, array([0.13689066, -0.16050153, 1.19815925, 0.92046818]),
+                        atol=1.5e-8, rtol=0)
+        x = special.airy(.41)
+        assert_allclose(x, array([0.25238916, -.23480512, 0.80686202, 0.51053919]),
+                        atol=1.5e-8, rtol=0)
+        x = special.airy(-.36)
+        assert_allclose(x, array([0.44508477,-0.23186773,0.44939534,0.48105354]),
+                        atol=1.5e-8, rtol=0)
+
+    def test_airye(self):
+        a = special.airye(0.01)
+        b = special.airy(0.01)
+        b1 = [None]*4
+        for n in range(2):
+            b1[n] = b[n]*exp(2.0/3.0*0.01*sqrt(0.01))
+        for n in range(2,4):
+            b1[n] = b[n]*exp(-abs(real(2.0/3.0*0.01*sqrt(0.01))))
+        assert_allclose(a, b1, atol=1.5e-6, rtol=0)
+
+    def test_bi_zeros(self):
+        bi = special.bi_zeros(2)
+        bia = (array([-1.17371322, -3.2710930]),
+               array([-2.29443968, -4.07315509]),
+               array([-0.45494438, 0.39652284]),
+               array([0.60195789, -0.76031014]))
+        assert_allclose(bi, bia, atol=1.5e-4, rtol=0)
+
+        bi = special.bi_zeros(5)
+        assert_allclose(bi[0], array([-1.173713222709127,
+                                      -3.271093302836352,
+                                      -4.830737841662016,
+                                      -6.169852128310251,
+                                      -7.376762079367764]),
+                        atol=1.5e-11, rtol=0)
+
+        assert_allclose(bi[1], array([-2.294439682614122,
+                                      -4.073155089071828,
+                                      -5.512395729663599,
+                                      -6.781294445990305,
+                                      -7.940178689168587]),
+                        atol=1.5e-10, rtol=0)
+
+        assert_allclose(bi[2], array([-0.454944383639657,
+                                      0.396522836094465,
+                                      -0.367969161486959,
+                                      0.349499116831805,
+                                      -0.336026240133662]),
+                        atol=1.5e-11, rtol=0)
+
+        assert_allclose(bi[3], array([0.601957887976239,
+                                      -0.760310141492801,
+                                      0.836991012619261,
+                                      -0.88947990142654,
+                                      0.929983638568022]),
+                        atol=1.5e-10, rtol=0)
+
+    def test_ai_zeros(self):
+        ai = special.ai_zeros(1)
+        assert_allclose(ai, (array([-2.33810741]),
+                             array([-1.01879297]),
+                             array([0.5357]),
+                             array([0.7012])),
+                        atol=1.5e-4, rtol=0)
+
+    @pytest.mark.fail_slow(5)
+    def test_ai_zeros_big(self):
+        z, zp, ai_zpx, aip_zx = special.ai_zeros(50000)
+        ai_z, aip_z, _, _ = special.airy(z)
+        ai_zp, aip_zp, _, _ = special.airy(zp)
+
+        ai_envelope = 1/abs(z)**(1./4)
+        aip_envelope = abs(zp)**(1./4)
+
+        # Check values
+        assert_allclose(ai_zpx, ai_zp, rtol=1e-10)
+        assert_allclose(aip_zx, aip_z, rtol=1e-10)
+
+        # Check they are zeros
+        assert_allclose(ai_z/ai_envelope, 0, atol=1e-10, rtol=0)
+        assert_allclose(aip_zp/aip_envelope, 0, atol=1e-10, rtol=0)
+
+        # Check first zeros, DLMF 9.9.1
+        assert_allclose(z[:6],
+            [-2.3381074105, -4.0879494441, -5.5205598281,
+             -6.7867080901, -7.9441335871, -9.0226508533], rtol=1e-10)
+        assert_allclose(zp[:6],
+            [-1.0187929716, -3.2481975822, -4.8200992112,
+             -6.1633073556, -7.3721772550, -8.4884867340], rtol=1e-10)
+
+    @pytest.mark.fail_slow(5)
+    def test_bi_zeros_big(self):
+        z, zp, bi_zpx, bip_zx = special.bi_zeros(50000)
+        _, _, bi_z, bip_z = special.airy(z)
+        _, _, bi_zp, bip_zp = special.airy(zp)
+
+        bi_envelope = 1/abs(z)**(1./4)
+        bip_envelope = abs(zp)**(1./4)
+
+        # Check values
+        assert_allclose(bi_zpx, bi_zp, rtol=1e-10)
+        assert_allclose(bip_zx, bip_z, rtol=1e-10)
+
+        # Check they are zeros
+        assert_allclose(bi_z/bi_envelope, 0, atol=1e-10, rtol=0)
+        assert_allclose(bip_zp/bip_envelope, 0, atol=1e-10, rtol=0)
+
+        # Check first zeros, DLMF 9.9.2
+        assert_allclose(z[:6],
+            [-1.1737132227, -3.2710933028, -4.8307378417,
+             -6.1698521283, -7.3767620794, -8.4919488465], rtol=1e-10)
+        assert_allclose(zp[:6],
+            [-2.2944396826, -4.0731550891, -5.5123957297,
+             -6.7812944460, -7.9401786892, -9.0195833588], rtol=1e-10)
+
+
+class TestAssocLaguerre:
+    def test_assoc_laguerre(self):
+        a1 = special.genlaguerre(11,1)
+        a2 = special.assoc_laguerre(.2,11,1)
+        assert_allclose(a2, a1(.2), atol=1.5e-8, rtol=0)
+        a2 = special.assoc_laguerre(1,11,1)
+        assert_allclose(a2, a1(1), atol=1.5e-8, rtol=0)
+
+
+class TestBesselpoly:
+    def test_besselpoly(self):
+        pass
+
+
+class TestKelvin:
+    def test_bei(self):
+        mbei = special.bei(2)
+        # This may not be exact.
+        assert_allclose(mbei, 0.9722916273066613, atol=1.5e-5, rtol=0)
+
+    def test_beip(self):
+        mbeip = special.beip(2)
+        # This may not be exact.
+        assert_allclose(mbeip, 0.91701361338403631, atol=1.5e-5, rtol=0)
+
+    def test_ber(self):
+        mber = special.ber(2)
+        # This may not be exact.
+        assert_allclose(mber, 0.75173418271380821, atol=1.5e-5, rtol=0)
+
+    def test_berp(self):
+        mberp = special.berp(2)
+        # This may not be exact.
+        assert_allclose(mberp, -0.49306712470943909, atol=1.5e-5, rtol=0)
+
+    def test_bei_zeros(self):
+        # Abramowitz & Stegun, Table 9.12
+        bi = special.bei_zeros(5)
+        assert_allclose(bi, array([5.02622,
+                                   9.45541,
+                                   13.89349,
+                                   18.33398,
+                                   22.77544]),
+                        atol=1.5e-4, rtol=0)
+
+    def test_beip_zeros(self):
+        bip = special.beip_zeros(5)
+        assert_allclose(bip, array([3.772673304934953,
+                                    8.280987849760042,
+                                    12.742147523633703,
+                                    17.193431752512542,
+                                    21.641143941167325]),
+                        atol=1.5e-8, rtol=0)
+
+    def test_ber_zeros(self):
+        ber = special.ber_zeros(5)
+        assert_allclose(ber, array([2.84892,
+                                    7.23883,
+                                    11.67396,
+                                    16.11356,
+                                    20.55463]),
+                        atol=1.5e-4, rtol=0)
+
+    def test_berp_zeros(self):
+        brp = special.berp_zeros(5)
+        assert_allclose(brp, array([6.03871,
+                                    10.51364,
+                                    14.96844,
+                                    19.41758,
+                                    23.86430]),
+                        atol=1.5e-4, rtol=0)
+
+    def test_kelvin(self):
+        mkelv = special.kelvin(2)
+        assert_allclose(mkelv, (special.ber(2) + special.bei(2)*1j,
+                                special.ker(2) + special.kei(2)*1j,
+                                special.berp(2) + special.beip(2)*1j,
+                                special.kerp(2) + special.keip(2)*1j),
+                        atol=1.5e-8, rtol=0)
+
+    def test_kei(self):
+        mkei = special.kei(2)
+        assert_allclose(mkei, -0.20240006776470432, atol=1.5e-5, rtol=0)
+
+    def test_keip(self):
+        mkeip = special.keip(2)
+        assert_allclose(mkeip, 0.21980790991960536, atol=1.5e-5, rtol=0)
+
+    def test_ker(self):
+        mker = special.ker(2)
+        assert_allclose(mker, -0.041664513991509472, atol=1.5e-5, rtol=0)
+
+    def test_kerp(self):
+        mkerp = special.kerp(2)
+        assert_allclose(mkerp, -0.10660096588105264, atol=1.5e-5, rtol=0)
+
+    def test_kei_zeros(self):
+        kei = special.kei_zeros(5)
+        assert_allclose(kei, array([3.91467,
+                                    8.34422,
+                                    12.78256,
+                                    17.22314,
+                                    21.66464]),
+                        atol=1.5e-4, rtol=0)
+
+    def test_keip_zeros(self):
+        keip = special.keip_zeros(5)
+        assert_allclose(keip, array([4.93181,
+                                     9.40405,
+                                     13.85827,
+                                     18.30717,
+                                     22.75379]),
+                        atol=1.5e-4, rtol=0)
+
+    # numbers come from 9.9 of A&S pg. 381
+    def test_kelvin_zeros(self):
+        tmp = special.kelvin_zeros(5)
+        berz, beiz, kerz, keiz, berpz, beipz, kerpz, keipz = tmp
+        assert_allclose(berz, array([2.84892,
+                                     7.23883,
+                                     11.67396,
+                                     16.11356,
+                                     20.55463]),
+                        atol=1.5e-4, rtol=0)
+        assert_allclose(beiz, array([5.02622,
+                                     9.45541,
+                                     13.89349,
+                                     18.33398,
+                                     22.77544]),
+                        atol=1.5e-4, rtol=0)
+        assert_allclose(kerz, array([1.71854,
+                                     6.12728,
+                                     10.56294,
+                                     15.00269,
+                                     19.44382]),
+                        atol=1.5e-4, rtol=0)
+        assert_allclose(keiz, array([3.91467,
+                                     8.34422,
+                                     12.78256,
+                                     17.22314,
+                                     21.66464]),
+                        atol=1.5e-4, rtol=0)
+        assert_allclose(berpz, array([6.03871,
+                                      10.51364,
+                                      14.96844,
+                                      19.41758,
+                                      23.86430]),
+                        atol=1.5e-4, rtol=0)
+        assert_allclose(beipz, array([3.77267,
+                # table from 1927 had 3.77320
+                # but this is more accurate
+                                      8.28099,
+                                      12.74215,
+                                      17.19343,
+                                      21.64114]),
+                        atol=1.5e-4, rtol=0)
+        assert_allclose(kerpz, array([2.66584,
+                                      7.17212,
+                                      11.63218,
+                                      16.08312,
+                                      20.53068]),
+                        atol=1.5e-4, rtol=0)
+        assert_allclose(keipz, array([4.93181,
+                                      9.40405,
+                                      13.85827,
+                                      18.30717,
+                                      22.75379]),
+                        atol=1.5e-4, rtol=0)
+
+    def test_ker_zeros(self):
+        ker = special.ker_zeros(5)
+        assert_allclose(ker, array([1.71854,
+                                    6.12728,
+                                    10.56294,
+                                    15.00269,
+                                    19.44381]),
+                        atol=1.5e-4, rtol=0)
+
+    def test_kerp_zeros(self):
+        kerp = special.kerp_zeros(5)
+        assert_allclose(kerp, array([2.66584,
+                                     7.17212,
+                                     11.63218,
+                                     16.08312,
+                                     20.53068]),
+                        atol=1.5e-4, rtol=0)
+
+
+class TestBernoulli:
+    def test_bernoulli(self):
+        brn = special.bernoulli(5)
+        assert_allclose(brn, array([1.0000,
+                                    -0.5000,
+                                    0.1667,
+                                    0.0000,
+                                    -0.0333,
+                                    0.0000]),
+                        atol=1.5e-4, rtol=0)
+
+
+class TestBeta:
+    """
+    Test beta and betaln.
+    """
+
+    def test_beta(self):
+        assert_equal(special.beta(1, 1), 1.0)
+        assert_allclose(special.beta(-100.3, 1e-200), special.gamma(1e-200))
+        assert_allclose(special.beta(0.0342, 171), 24.070498359873497,
+                        rtol=1e-13, atol=0)
+
+        bet = special.beta(2, 4)
+        betg = (special.gamma(2)*special.gamma(4))/special.gamma(6)
+        assert_allclose(bet, betg, rtol=1e-13)
+
+    def test_beta_inf(self):
+        assert_(np.isinf(special.beta(-1, 2)))
+
+    def test_betaln(self):
+        assert_equal(special.betaln(1, 1), 0.0)
+        assert_allclose(special.betaln(-100.3, 1e-200),
+                        special.gammaln(1e-200))
+        assert_allclose(special.betaln(0.0342, 170), 3.1811881124242447,
+                        rtol=1e-14, atol=0)
+
+        betln = special.betaln(2, 4)
+        bet = log(abs(special.beta(2, 4)))
+        assert_allclose(betln, bet, rtol=1e-13)
+
+
+class TestBetaInc:
+    """
+    Tests for betainc, betaincinv, betaincc, betainccinv.
+    """
+
+    def test_a1_b1(self):
+        # betainc(1, 1, x) is x.
+        x = np.array([0, 0.25, 1])
+        assert_equal(special.betainc(1, 1, x), x)
+        assert_equal(special.betaincinv(1, 1, x), x)
+        assert_equal(special.betaincc(1, 1, x), 1 - x)
+        assert_equal(special.betainccinv(1, 1, x), 1 - x)
+
+    # Nontrivial expected values computed with mpmath:
+    #    from mpmath import mp
+    #    mp.dps = 100
+    #    p = mp.betainc(a, b, 0, x, regularized=True)
+    #
+    # or, e.g.,
+    #
+    #    p = 0.25
+    #    a, b = 0.0342, 171
+    #    x = mp.findroot(
+    #        lambda t: mp.betainc(a, b, 0, t, regularized=True) - p,
+    #        (8e-21, 9e-21),
+    #        solver='anderson',
+    #    )
+    #
+    @pytest.mark.parametrize(
+        'a, b, x, p',
+        [(2, 4, 0.3138101704556974, 0.5),
+         (0.0342, 171.0, 1e-10, 0.552699169018070910641),
+         # gh-3761:
+         (0.0342, 171, 8.42313169354797e-21, 0.25),
+         # gh-4244:
+         (0.0002742794749792665, 289206.03125, 1.639984034231756e-56,
+          0.9688708782196045),
+         # gh-12796:
+         (4, 99997, 0.0001947841578892121, 0.999995)])
+    def test_betainc_and_inverses(self, a, b, x, p):
+        p1 = special.betainc(a, b, x)
+        assert_allclose(p1, p, rtol=1e-15)
+        x1 = special.betaincinv(a, b, p)
+        assert_allclose(x1, x, rtol=5e-13)
+        a1 = special.btdtria(p, b, x)
+        assert_allclose(a1, a, rtol=1e-13)
+        b1 = special.btdtrib(a, p, x)
+        assert_allclose(b1, b, rtol=1e-13)
+
+    # Expected values computed with mpmath:
+    #     from mpmath import mp
+    #     mp.dps = 100
+    #     p = mp.betainc(a, b, x, 1, regularized=True)
+    @pytest.mark.parametrize('a, b, x, p',
+                             [(2.5, 3.0, 0.25, 0.833251953125),
+                              (7.5, 13.25, 0.375, 0.43298734645560368593),
+                              (0.125, 7.5, 0.425, 0.0006688257851314237),
+                              (0.125, 18.0, 1e-6, 0.72982359145096327654),
+                              (0.125, 18.0, 0.996, 7.2745875538380150586e-46),
+                              (0.125, 24.0, 0.75, 3.70853404816862016966e-17),
+                              (16.0, 0.75, 0.99999999975,
+                               5.4408759277418629909e-07),
+                              # gh-4677 (numbers from stackoverflow question):
+                              (0.4211959643503401, 16939.046996018118,
+                               0.000815296167195521, 1e-7)])
+    def test_betaincc_betainccinv(self, a, b, x, p):
+        p1 = special.betaincc(a, b, x)
+        assert_allclose(p1, p, rtol=5e-15)
+        x1 = special.betainccinv(a, b, p)
+        assert_allclose(x1, x, rtol=8e-15)
+
+    @pytest.mark.parametrize(
+        'a, b, y, ref',
+        [(14.208308325339239, 14.208308325339239, 7.703145458496392e-307,
+          8.566004561846704e-23),
+         (14.0, 14.5, 1e-280, 2.9343915006642424e-21),
+         (3.5, 15.0, 4e-95, 1.3290751429289227e-28),
+         (10.0, 1.25, 2e-234, 3.982659092143654e-24),
+         (4.0, 99997.0, 5e-88, 3.309800566862242e-27)]
+    )
+    def test_betaincinv_tiny_y(self, a, b, y, ref):
+        # Test with extremely small y values.  This test includes
+        # a regression test for an issue in the boost code;
+        # see https://github.com/boostorg/math/issues/961
+        #
+        # The reference values were computed with mpmath. For example,
+        #
+        #   from mpmath import mp
+        #   mp.dps = 1000
+        #   a = 14.208308325339239
+        #   p = 7.703145458496392e-307
+        #   x = mp.findroot(lambda t: mp.betainc(a, a, 0, t,
+        #                                        regularized=True) - p,
+        #                   x0=8.566e-23)
+        #   print(float(x))
+        #
+        x = special.betaincinv(a, b, y)
+        assert_allclose(x, ref, rtol=1e-14)
+
+    @pytest.mark.parametrize('func', [special.betainc, special.betaincinv,
+                                      special.btdtria, special.btdtrib,
+                                      special.betaincc, special.betainccinv])
+    @pytest.mark.parametrize('args', [(-1.0, 2, 0.5), (1.5, -2.0, 0.5),
+                                      (1.5, 2.0, -0.3), (1.5, 2.0, 1.1)])
+    def test_betainc_domain_errors(self, func, args):
+        with special.errstate(domain='raise'):
+            with pytest.raises(special.SpecialFunctionError, match='domain'):
+                func(*args)
+
+    @pytest.mark.parametrize(
+        "args,expected",
+        [
+            ((0.0, 0.0, 0.0), np.nan),
+            ((0.0, 0.0, 0.5), np.nan),
+            ((0.0, 0.0, 1.0), np.nan),
+            ((np.inf, np.inf, 0.0), np.nan),
+            ((np.inf, np.inf, 0.5), np.nan),
+            ((np.inf, np.inf, 1.0), np.nan),
+            ((0.0, 1.0, 0.0), 0.0),
+            ((0.0, 1.0, 0.5), 1.0),
+            ((0.0, 1.0, 1.0), 1.0),
+            ((1.0, 0.0, 0.0), 0.0),
+            ((1.0, 0.0, 0.5), 0.0),
+            ((1.0, 0.0, 1.0), 1.0),
+            ((0.0, np.inf, 0.0), 0.0),
+            ((0.0, np.inf, 0.5), 1.0),
+            ((0.0, np.inf, 1.0), 1.0),
+            ((np.inf, 0.0, 0.0), 0.0),
+            ((np.inf, 0.0, 0.5), 0.0),
+            ((np.inf, 0.0, 1.0), 1.0),
+            ((1.0, np.inf, 0.0), 0.0),
+            ((1.0, np.inf, 0.5), 1.0),
+            ((1.0, np.inf, 1.0), 1.0),
+            ((np.inf, 1.0, 0.0), 0.0),
+            ((np.inf, 1.0, 0.5), 0.0),
+            ((np.inf, 1.0, 1.0), 1.0),
+        ]
+    )
+    def test_betainc_edge_cases(self, args, expected):
+        observed = special.betainc(*args)
+        assert_equal(observed, expected)
+
+    @pytest.mark.parametrize(
+        "args,expected",
+        [
+            ((0.0, 0.0, 0.0), np.nan),
+            ((0.0, 0.0, 0.5), np.nan),
+            ((0.0, 0.0, 1.0), np.nan),
+            ((np.inf, np.inf, 0.0), np.nan),
+            ((np.inf, np.inf, 0.5), np.nan),
+            ((np.inf, np.inf, 1.0), np.nan),
+            ((0.0, 1.0, 0.0), 1.0),
+            ((0.0, 1.0, 0.5), 0.0),
+            ((0.0, 1.0, 1.0), 0.0),
+            ((1.0, 0.0, 0.0), 1.0),
+            ((1.0, 0.0, 0.5), 1.0),
+            ((1.0, 0.0, 1.0), 0.0),
+            ((0.0, np.inf, 0.0), 1.0),
+            ((0.0, np.inf, 0.5), 0.0),
+            ((0.0, np.inf, 1.0), 0.0),
+            ((np.inf, 0.0, 0.0), 1.0),
+            ((np.inf, 0.0, 0.5), 1.0),
+            ((np.inf, 0.0, 1.0), 0.0),
+            ((1.0, np.inf, 0.0), 1.0),
+            ((1.0, np.inf, 0.5), 0.0),
+            ((1.0, np.inf, 1.0), 0.0),
+            ((np.inf, 1.0, 0.0), 1.0),
+            ((np.inf, 1.0, 0.5), 1.0),
+            ((np.inf, 1.0, 1.0), 0.0),
+        ]
+    )
+    def test_betaincc_edge_cases(self, args, expected):
+        observed = special.betaincc(*args)
+        assert_equal(observed, expected)
+
+    @pytest.mark.parametrize('dtype', [np.float32, np.float64])
+    def test_gh21426(self, dtype):
+        # Test for gh-21426: betaincinv must not return NaN
+        a = np.array([5.], dtype=dtype)
+        x = np.array([0.5], dtype=dtype)
+        result = special.betaincinv(a, a, x)
+        assert_allclose(result, x, rtol=10 * np.finfo(dtype).eps)
+
+    @pytest.mark.parametrize("dtype, rtol",
+                             [(np.float32, 1e-4),
+                              (np.float64, 1e-15)])
+    @pytest.mark.parametrize("a, b, x, reference",
+                             [(1e-20, 1e-21, 0.5, 0.0909090909090909),
+                              (1e-15, 1e-16, 0.5, 0.09090909090909091)])
+    def test_gh22682(self, a, b, x, reference, dtype, rtol):
+        # gh-22682: betainc returned incorrect results for tiny
+        # single precision inputs. test that this is resolved
+        a = np.array(a, dtype=dtype)
+        b = np.array(b, dtype=dtype)
+        x = np.array(x, dtype=dtype)
+        res = special.betainc(a, b, x)
+        assert_allclose(res, reference, rtol=rtol)
+
+
+class TestCombinatorics:
+    def test_comb(self):
+        assert_allclose(special.comb([10, 10], [3, 4]), [120., 210.])
+        assert_allclose(special.comb(10, 3), 120.)
+        assert_equal(special.comb(10, 3, exact=True), 120)
+        assert_equal(special.comb(10, 3, exact=True, repetition=True), 220)
+
+        assert_allclose([special.comb(20, k, exact=True) for k in range(21)],
+                        special.comb(20, list(range(21))), atol=1e-15)
+
+        ii = np.iinfo(int).max + 1
+        assert_equal(special.comb(ii, ii-1, exact=True), ii)
+
+        expected = 100891344545564193334812497256
+        assert special.comb(100, 50, exact=True) == expected
+
+    def test_comb_with_np_int64(self):
+        n = 70
+        k = 30
+        np_n = np.int64(n)
+        np_k = np.int64(k)
+        res_np = special.comb(np_n, np_k, exact=True)
+        res_py = special.comb(n, k, exact=True)
+        assert res_np == res_py
+
+    def test_comb_zeros(self):
+        assert_equal(special.comb(2, 3, exact=True), 0)
+        assert_equal(special.comb(-1, 3, exact=True), 0)
+        assert_equal(special.comb(2, -1, exact=True), 0)
+        assert_equal(special.comb(2, -1, exact=False), 0)
+        assert_allclose(special.comb([2, -1, 2, 10], [3, 3, -1, 3]), [0., 0., 0., 120.])
+
+    def test_comb_exact_non_int_error(self):
+        msg = "`exact=True`"
+        with pytest.raises(ValueError, match=msg):
+            special.comb(3.4, 4, exact=True)
+        with pytest.raises(ValueError, match=msg):
+            special.comb(3, 4.4, exact=True)
+
+    @pytest.mark.parametrize('N', [0, 5, 10])
+    @pytest.mark.parametrize('exact', [True, False])
+    def test_comb_repetition_k_zero(self, N, exact):
+        # Regression test for gh-23867
+        # C(n, 0) should always be 1 for n >= 0, regardless of repetition
+        actual = special.comb(N, 0, exact=exact, repetition=True)
+        assert actual == 1
+        assert type(actual) is int if exact else np.float64
+
+    def test_comb_repetition_k_zero_array(self):
+        # Test array-like input with exact=False for gh-23867
+        N = np.array([0, 5, 10])
+        result = special.comb(N, 0, exact=False, repetition=True)
+        expected = np.array([1.0, 1.0, 1.0])
+        assert_equal(result, expected)
+
+    def test_perm(self):
+        assert_allclose(special.perm([10, 10], [3, 4]), [720., 5040.])
+        assert_allclose(special.perm(10, 3), 720., atol=1.5e-7, rtol=0)
+        assert_equal(special.perm(10, 3, exact=True), 720)
+
+    def test_perm_zeros(self):
+        assert_equal(special.perm(2, 3, exact=True), 0)
+        assert_equal(special.perm(-1, 3, exact=True), 0)
+        assert_equal(special.perm(2, -1, exact=True), 0)
+        assert_equal(special.perm(2, -1, exact=False), 0)
+        assert_allclose(special.perm([2, -1, 2, 10], [3, 3, -1, 3]), [0., 0., 0., 720.])
+
+    def test_perm_iv(self):
+        # currently `exact=True` only support scalars
+        with pytest.raises(ValueError, match="scalar integers"):
+            special.perm([1, 2], [4, 5], exact=True)
+
+        with pytest.raises(ValueError, match="Non-integer"):
+            special.perm(4.6, 6, exact=True)
+        with pytest.raises(ValueError, match="Non-integer"):
+            special.perm(-4.6, 3, exact=True)
+        with pytest.raises(ValueError, match="Non-integer"):
+            special.perm(4, -3.9, exact=True)
+        with pytest.raises(ValueError, match="Non-integer"):
+            special.perm(6.0, 4.6, exact=True)
+
+
+class TestTrigonometric:
+    def test_cbrt(self):
+        cb = special.cbrt(27)
+        cbrl = 27**(1.0/3.0)
+        assert_allclose(cb, cbrl, atol=1.5e-7, rtol=0)
+
+    def test_cbrtmore(self):
+        cb1 = special.cbrt(27.9)
+        cbrl1 = 27.9**(1.0/3.0)
+        assert_allclose(cb1, cbrl1, atol=1.5e-8, rtol=0)
+
+    def test_cosdg(self):
+        cdg = special.cosdg(90)
+        cdgrl = cos(pi/2.0)
+        assert_allclose(cdg, cdgrl, atol=1.5e-8, rtol=0)
+
+    def test_cosdgmore(self):
+        cdgm = special.cosdg(30)
+        cdgmrl = cos(pi/6.0)
+        assert_allclose(cdgm, cdgmrl, atol=1.5e-8, rtol=0)
+
+    def test_cosm1(self):
+        cs = (special.cosm1(0),special.cosm1(.3),special.cosm1(pi/10))
+        csrl = (cos(0)-1,cos(.3)-1,cos(pi/10)-1)
+        assert_allclose(cs, csrl, atol=1.5e-8, rtol=0)
+
+    def test_cotdg(self):
+        ct = special.cotdg(30)
+        ctrl = tan(pi/6.0)**(-1)
+        assert_allclose(ct, ctrl, atol=1.5e-8, rtol=0)
+
+    def test_cotdgmore(self):
+        ct1 = special.cotdg(45)
+        ctrl1 = tan(pi/4.0)**(-1)
+        assert_allclose(ct1, ctrl1, atol=1.5e-8, rtol=0)
+
+    def test_specialpoints(self):
+        assert_allclose(special.cotdg(45), 1.0, atol=1.5e-14, rtol=0)
+        assert_allclose(special.cotdg(-45), -1.0, atol=1.5e-14, rtol=0)
+        assert_allclose(special.cotdg(90), 0.0, atol=1.5e-14, rtol=0)
+        assert_allclose(special.cotdg(-90), 0.0, atol=1.5e-14, rtol=0)
+        assert_allclose(special.cotdg(135), -1.0, atol=1.5e-14, rtol=0)
+        assert_allclose(special.cotdg(-135), 1.0, atol=1.5e-14, rtol=0)
+        assert_allclose(special.cotdg(225), 1.0, atol=1.5e-14, rtol=0)
+        assert_allclose(special.cotdg(-225), -1.0, atol=1.5e-14, rtol=0)
+        assert_allclose(special.cotdg(270), 0.0, atol=1.5e-14, rtol=0)
+        assert_allclose(special.cotdg(-270), 0.0, atol=1.5e-14, rtol=0)
+        assert_allclose(special.cotdg(315), -1.0, atol=1.5e-14, rtol=0)
+        assert_allclose(special.cotdg(-315), 1.0, atol=1.5e-14, rtol=0)
+        assert_allclose(special.cotdg(765), 1.0, atol=1.5e-14, rtol=0)
+
+    def test_sinc(self):
+        # the sinc implementation and more extensive sinc tests are in numpy
+        assert_array_equal(special.sinc([0]), 1)
+        assert_equal(special.sinc(0.0), 1.0)
+
+    def test_sindg(self):
+        sn = special.sindg(90)
+        assert_equal(sn,1.0)
+
+    def test_sindgmore(self):
+        snm = special.sindg(30)
+        snmrl = sin(pi/6.0)
+        assert_allclose(snm, snmrl, atol=1.5e-8, rtol=0)
+        snm1 = special.sindg(45)
+        snmrl1 = sin(pi/4.0)
+        assert_allclose(snm1, snmrl1, atol=1.5e-8, rtol=0)
+
+
+class TestTandg:
+
+    def test_tandg(self):
+        tn = special.tandg(30)
+        tnrl = tan(pi/6.0)
+        assert_allclose(tn, tnrl, atol=1.5e-8, rtol=0)
+
+    def test_tandgmore(self):
+        tnm = special.tandg(45)
+        tnmrl = tan(pi/4.0)
+        assert_allclose(tnm, tnmrl, atol=1.5e-8, rtol=0)
+        tnm1 = special.tandg(60)
+        tnmrl1 = tan(pi/3.0)
+        assert_allclose(tnm1, tnmrl1, atol=1.5e-8, rtol=0)
+
+    def test_specialpoints(self):
+        assert_allclose(special.tandg(0), 0.0, atol=1.5e-14, rtol=0)
+        assert_allclose(special.tandg(45), 1.0, atol=1.5e-14, rtol=0)
+        assert_allclose(special.tandg(-45), -1.0, atol=1.5e-14, rtol=0)
+        assert_allclose(special.tandg(135), -1.0, atol=1.5e-14, rtol=0)
+        assert_allclose(special.tandg(-135), 1.0, atol=1.5e-14, rtol=0)
+        assert_allclose(special.tandg(180), 0.0, atol=1.5e-14, rtol=0)
+        assert_allclose(special.tandg(-180), 0.0, atol=1.5e-14, rtol=0)
+        assert_allclose(special.tandg(225), 1.0, atol=1.5e-14, rtol=0)
+        assert_allclose(special.tandg(-225), -1.0, atol=1.5e-14, rtol=0)
+        assert_allclose(special.tandg(315), -1.0, atol=1.5e-14, rtol=0)
+        assert_allclose(special.tandg(-315), 1.0, atol=1.5e-14, rtol=0)
+
+
+class TestEllip:
+    def test_ellipj_nan(self):
+        """Regression test for #912."""
+        special.ellipj(0.5, np.nan)
+
+    def test_ellipj(self):
+        el = special.ellipj(0.2,0)
+        rel = [sin(0.2),cos(0.2),1.0,0.20]
+        assert_allclose(el, rel, atol=1.5e-13, rtol=0)
+
+    def test_ellipk(self):
+        elk = special.ellipk(.2)
+        assert_allclose(elk, 1.659623598610528, atol=1.5e-11, rtol=0)
+
+        assert_equal(special.ellipkm1(0.0), np.inf)
+        assert_equal(special.ellipkm1(1.0), pi/2)
+        assert_equal(special.ellipkm1(np.inf), 0.0)
+        assert_equal(special.ellipkm1(np.nan), np.nan)
+        assert_equal(special.ellipkm1(-1), np.nan)
+        assert_allclose(special.ellipk(-10), 0.7908718902387385)
+
+    def test_ellipkinc(self):
+        elkinc = special.ellipkinc(pi/2,.2)
+        elk = special.ellipk(0.2)
+        assert_allclose(elkinc, elk, atol=1.5e-15, rtol=0)
+        alpha = 20*pi/180
+        phi = 45*pi/180
+        m = sin(alpha)**2
+        elkinc = special.ellipkinc(phi,m)
+        assert_allclose(elkinc, 0.79398143, atol=1.5e-8, rtol=0)
+        # From pg. 614 of A & S
+
+        assert_equal(special.ellipkinc(pi/2, 0.0), pi/2)
+        assert_equal(special.ellipkinc(pi/2, 1.0), np.inf)
+        assert_equal(special.ellipkinc(pi/2, -np.inf), 0.0)
+        assert_equal(special.ellipkinc(pi/2, np.nan), np.nan)
+        assert_equal(special.ellipkinc(pi/2, 2), np.nan)
+        assert_equal(special.ellipkinc(0, 0.5), 0.0)
+        assert_equal(special.ellipkinc(np.inf, 0.5), np.inf)
+        assert_equal(special.ellipkinc(-np.inf, 0.5), -np.inf)
+        assert_equal(special.ellipkinc(np.inf, np.inf), np.nan)
+        assert_equal(special.ellipkinc(np.inf, -np.inf), np.nan)
+        assert_equal(special.ellipkinc(-np.inf, -np.inf), np.nan)
+        assert_equal(special.ellipkinc(-np.inf, np.inf), np.nan)
+        assert_equal(special.ellipkinc(np.nan, 0.5), np.nan)
+        assert_equal(special.ellipkinc(np.nan, np.nan), np.nan)
+
+        assert_allclose(special.ellipkinc(0.38974112035318718, 1), 0.4, rtol=1e-14)
+        assert_allclose(special.ellipkinc(1.5707, -10), 0.79084284661724946)
+
+    def test_ellipkinc_2(self):
+        # Regression test for gh-3550
+        # ellipkinc(phi, mbad) was NaN and mvals[2:6] were twice the correct value
+        mbad = 0.68359375000000011
+        phi = 0.9272952180016123
+        m = np.nextafter(mbad, 0)
+        mvals = []
+        for j in range(10):
+            mvals.append(m)
+            m = np.nextafter(m, 1)
+        f = special.ellipkinc(phi, mvals)
+        assert_array_almost_equal_nulp(f, np.full_like(f, 1.0259330100195334), 1)
+        # this bug also appears at phi + n * pi for at least small n
+        f1 = special.ellipkinc(phi + pi, mvals)
+        assert_array_almost_equal_nulp(f1, np.full_like(f1, 5.1296650500976675), 2)
+
+    def test_ellipkinc_singular(self):
+        # ellipkinc(phi, 1) has closed form and is finite only for phi in (-pi/2, pi/2)
+        xlog = np.logspace(-300, -17, 25)
+        xlin = np.linspace(1e-17, 0.1, 25)
+        xlin2 = np.linspace(0.1, pi/2, 25, endpoint=False)
+
+        assert_allclose(special.ellipkinc(xlog, 1), np.arcsinh(np.tan(xlog)),
+                        rtol=1e14)
+        assert_allclose(special.ellipkinc(xlin, 1), np.arcsinh(np.tan(xlin)),
+                        rtol=1e14)
+        assert_allclose(special.ellipkinc(xlin2, 1), np.arcsinh(np.tan(xlin2)),
+                        rtol=1e14)
+        assert_equal(special.ellipkinc(np.pi/2, 1), np.inf)
+        assert_allclose(special.ellipkinc(-xlog, 1), np.arcsinh(np.tan(-xlog)),
+                        rtol=1e14)
+        assert_allclose(special.ellipkinc(-xlin, 1), np.arcsinh(np.tan(-xlin)),
+                        rtol=1e14)
+        assert_allclose(special.ellipkinc(-xlin2, 1), np.arcsinh(np.tan(-xlin2)),
+                        rtol=1e14)
+        assert_equal(special.ellipkinc(-np.pi/2, 1), np.inf)
+
+    def test_ellipe(self):
+        ele = special.ellipe(.2)
+        assert_allclose(ele, 1.4890350580958529, atol=1.5e-8, rtol=0)
+
+        assert_equal(special.ellipe(0.0), pi/2)
+        assert_equal(special.ellipe(1.0), 1.0)
+        assert_equal(special.ellipe(-np.inf), np.inf)
+        assert_equal(special.ellipe(np.nan), np.nan)
+        assert_equal(special.ellipe(2), np.nan)
+        assert_allclose(special.ellipe(-10), 3.6391380384177689)
+
+    def test_ellipeinc(self):
+        eleinc = special.ellipeinc(pi/2,.2)
+        ele = special.ellipe(0.2)
+        assert_allclose(eleinc, ele, atol=1.5e-14, rtol=0)
+        # pg 617 of A & S
+        alpha, phi = 52*pi/180,35*pi/180
+        m = sin(alpha)**2
+        eleinc = special.ellipeinc(phi,m)
+        assert_allclose(eleinc, 0.58823065, atol=1.5e-8, rtol=0)
+
+        assert_equal(special.ellipeinc(pi/2, 0.0), pi/2)
+        assert_equal(special.ellipeinc(pi/2, 1.0), 1.0)
+        assert_equal(special.ellipeinc(pi/2, -np.inf), np.inf)
+        assert_equal(special.ellipeinc(pi/2, np.nan), np.nan)
+        assert_equal(special.ellipeinc(pi/2, 2), np.nan)
+        assert_equal(special.ellipeinc(0, 0.5), 0.0)
+        assert_equal(special.ellipeinc(np.inf, 0.5), np.inf)
+        assert_equal(special.ellipeinc(-np.inf, 0.5), -np.inf)
+        assert_equal(special.ellipeinc(np.inf, -np.inf), np.inf)
+        assert_equal(special.ellipeinc(-np.inf, -np.inf), -np.inf)
+        assert_equal(special.ellipeinc(np.inf, np.inf), np.nan)
+        assert_equal(special.ellipeinc(-np.inf, np.inf), np.nan)
+        assert_equal(special.ellipeinc(np.nan, 0.5), np.nan)
+        assert_equal(special.ellipeinc(np.nan, np.nan), np.nan)
+        assert_allclose(special.ellipeinc(1.5707, -10), 3.6388185585822876)
+
+    def test_ellipeinc_2(self):
+        # Regression test for gh-3550
+        # ellipeinc(phi, mbad) was NaN and mvals[2:6] were twice the correct value
+        mbad = 0.68359375000000011
+        phi = 0.9272952180016123
+        m = np.nextafter(mbad, 0)
+        mvals = []
+        for j in range(10):
+            mvals.append(m)
+            m = np.nextafter(m, 1)
+        f = special.ellipeinc(phi, mvals)
+        assert_array_almost_equal_nulp(f, np.full_like(f, 0.84442884574781019), 2)
+        # this bug also appears at phi + n * pi for at least small n
+        f1 = special.ellipeinc(phi + pi, mvals)
+        assert_array_almost_equal_nulp(f1, np.full_like(f1, 3.3471442287390509), 4)
+
+
+class TestEllipCarlson:
+    """Test for Carlson elliptic integrals ellipr[cdfgj].
+    The special values used in these tests can be found in Sec. 3 of Carlson
+    (1994), https://arxiv.org/abs/math/9409227
+    """
+    def test_elliprc(self):
+        assert_allclose(elliprc(1, 1), 1)
+        assert elliprc(1, inf) == 0.0
+        assert isnan(elliprc(1, 0))
+        assert elliprc(1, complex(1, inf)) == 0.0
+        args = array([[0.0, 0.25],
+                      [2.25, 2.0],
+                      [0.0, 1.0j],
+                      [-1.0j, 1.0j],
+                      [0.25, -2.0],
+                      [1.0j, -1.0]])
+        expected_results = array([np.pi,
+                                  np.log(2.0),
+                                  1.1107207345396 * (1.0-1.0j),
+                                  1.2260849569072-0.34471136988768j,
+                                  np.log(2.0) / 3.0,
+                                  0.77778596920447+0.19832484993429j])
+        for i, arr in enumerate(args):
+            assert_allclose(elliprc(*arr), expected_results[i])
+
+    def test_elliprd(self):
+        assert_allclose(elliprd(1, 1, 1), 1)
+        assert_allclose(elliprd(0, 2, 1) / 3.0, 0.59907011736779610371)
+        assert elliprd(1, 1, inf) == 0.0
+        assert np.isinf(elliprd(1, 1, 0))
+        assert np.isinf(elliprd(1, 1, complex(0, 0)))
+        assert np.isinf(elliprd(0, 1, complex(0, 0)))
+        assert isnan(elliprd(1, 1, -np.finfo(np.float64).tiny / 2.0))
+        assert isnan(elliprd(1, 1, complex(-1, 0)))
+        args = array([[0.0, 2.0, 1.0],
+                      [2.0, 3.0, 4.0],
+                      [1.0j, -1.0j, 2.0],
+                      [0.0, 1.0j, -1.0j],
+                      [0.0, -1.0+1.0j, 1.0j],
+                      [-2.0-1.0j, -1.0j, -1.0+1.0j]])
+        expected_results = array([1.7972103521034,
+                                  0.16510527294261,
+                                  0.65933854154220,
+                                  1.2708196271910+2.7811120159521j,
+                                  -1.8577235439239-0.96193450888839j,
+                                  1.8249027393704-1.2218475784827j])
+        for i, arr in enumerate(args):
+            assert_allclose(elliprd(*arr), expected_results[i])
+
+    def test_elliprf(self):
+        assert_allclose(elliprf(1, 1, 1), 1)
+        assert_allclose(elliprf(0, 1, 2), 1.31102877714605990523)
+        assert elliprf(1, inf, 1) == 0.0
+        assert np.isinf(elliprf(0, 1, 0))
+        assert isnan(elliprf(1, 1, -1))
+        assert elliprf(complex(inf), 0, 1) == 0.0
+        assert isnan(elliprf(1, 1, complex(-inf, 1)))
+        args = array([[1.0, 2.0, 0.0],
+                      [1.0j, -1.0j, 0.0],
+                      [0.5, 1.0, 0.0],
+                      [-1.0+1.0j, 1.0j, 0.0],
+                      [2.0, 3.0, 4.0],
+                      [1.0j, -1.0j, 2.0],
+                      [-1.0+1.0j, 1.0j, 1.0-1.0j]])
+        expected_results = array([1.3110287771461,
+                                  1.8540746773014,
+                                  1.8540746773014,
+                                  0.79612586584234-1.2138566698365j,
+                                  0.58408284167715,
+                                  1.0441445654064,
+                                  0.93912050218619-0.53296252018635j])
+        for i, arr in enumerate(args):
+            assert_allclose(elliprf(*arr), expected_results[i])
+
+    def test_elliprg(self):
+        assert_allclose(elliprg(1, 1, 1), 1)
+        assert_allclose(elliprg(0, 0, 1), 0.5)
+        assert_allclose(elliprg(0, 0, 0), 0)
+        assert np.isinf(elliprg(1, inf, 1))
+        assert np.isinf(elliprg(complex(inf), 1, 1))
+        args = array([[0.0, 16.0, 16.0],
+                      [2.0, 3.0, 4.0],
+                      [0.0, 1.0j, -1.0j],
+                      [-1.0+1.0j, 1.0j, 0.0],
+                      [-1.0j, -1.0+1.0j, 1.0j],
+                      [0.0, 0.0796, 4.0]])
+        expected_results = array([np.pi,
+                                  1.7255030280692,
+                                  0.42360654239699,
+                                  0.44660591677018+0.70768352357515j,
+                                  0.36023392184473+0.40348623401722j,
+                                  1.0284758090288])
+        for i, arr in enumerate(args):
+            assert_allclose(elliprg(*arr), expected_results[i])
+
+    def test_elliprj(self):
+        assert_allclose(elliprj(1, 1, 1, 1), 1)
+        assert elliprj(1, 1, inf, 1) == 0.0
+        assert isnan(elliprj(1, 0, 0, 0))
+        assert isnan(elliprj(-1, 1, 1, 1))
+        assert elliprj(1, 1, 1, inf) == 0.0
+        args = array([[0.0, 1.0, 2.0, 3.0],
+                      [2.0, 3.0, 4.0, 5.0],
+                      [2.0, 3.0, 4.0, -1.0+1.0j],
+                      [1.0j, -1.0j, 0.0, 2.0],
+                      [-1.0+1.0j, -1.0-1.0j, 1.0, 2.0],
+                      [1.0j, -1.0j, 0.0, 1.0-1.0j],
+                      [-1.0+1.0j, -1.0-1.0j, 1.0, -3.0+1.0j],
+                      [2.0, 3.0, 4.0, -0.5],    # Cauchy principal value
+                      [2.0, 3.0, 4.0, -5.0]])   # Cauchy principal value
+        expected_results = array([0.77688623778582,
+                                  0.14297579667157,
+                                  0.13613945827771-0.38207561624427j,
+                                  1.6490011662711,
+                                  0.94148358841220,
+                                  1.8260115229009+1.2290661908643j,
+                                  -0.61127970812028-1.0684038390007j,
+                                  0.24723819703052,    # Cauchy principal value
+                                  -0.12711230042964])  # Caucny principal value
+        for i, arr in enumerate(args):
+            assert_allclose(elliprj(*arr), expected_results[i])
+
+    @pytest.mark.xfail(reason="Insufficient accuracy on 32-bit")
+    def test_elliprj_hard(self):
+        assert_allclose(elliprj(6.483625725195452e-08,
+                                1.1649136528196886e-27,
+                                3.6767340167168e+13,
+                                0.493704617023468),
+                        8.63426920644241857617477551054e-6,
+                        rtol=5e-15, atol=1e-20)
+        assert_allclose(elliprj(14.375105857849121,
+                                9.993988969725365e-11,
+                                1.72844262269944e-26,
+                                5.898871222598245e-06),
+                        829774.1424801627252574054378691828,
+                        rtol=5e-15, atol=1e-20)
+
+
+class TestEllipLegendreCarlsonIdentities:
+    """Test identities expressing the Legendre elliptic integrals in terms
+    of Carlson's symmetric integrals.  These identities can be found
+    in the DLMF https://dlmf.nist.gov/19.25#i .
+    """
+
+    def setup_class(self):
+        self.m_n1_1 = np.arange(-1., 1., 0.01)
+        # For double, this is -(2**1024)
+        self.max_neg = finfo(double).min
+        # Lots of very negative numbers
+        self.very_neg_m = -1. * 2.**arange(-1 +
+                                           np.log2(-self.max_neg), 0.,
+                                           -1.)
+        self.ms_up_to_1 = np.concatenate(([self.max_neg],
+                                          self.very_neg_m,
+                                          self.m_n1_1))
+
+    def test_k(self):
+        """Test identity:
+        K(m) = R_F(0, 1-m, 1)
+        """
+        m = self.ms_up_to_1
+        assert_allclose(ellipk(m), elliprf(0., 1.-m, 1.))
+
+    def test_km1(self):
+        """Test identity:
+        K(m) = R_F(0, 1-m, 1)
+        But with the ellipkm1 function
+        """
+        # For double, this is 2**-1022
+        tiny = finfo(double).tiny
+        # All these small powers of 2, up to 2**-1
+        m1 = tiny * 2.**arange(0., -np.log2(tiny))
+        assert_allclose(ellipkm1(m1), elliprf(0., m1, 1.))
+
+    def test_e(self):
+        """Test identity:
+        E(m) = 2*R_G(0, 1-k^2, 1)
+        """
+        m = self.ms_up_to_1
+        assert_allclose(ellipe(m), 2.*elliprg(0., 1.-m, 1.))
+
+
+class TestErf:
+
+    def test_erf(self):
+        er = special.erf(.25)
+        assert_allclose(er, 0.2763263902, atol=1.5e-8, rtol=0)
+
+    def test_erf_zeros(self):
+        erz = special.erf_zeros(5)
+        erzr = array([1.45061616+1.88094300j,
+                     2.24465928+2.61657514j,
+                     2.83974105+3.17562810j,
+                     3.33546074+3.64617438j,
+                     3.76900557+4.06069723j])
+        assert_allclose(erz, erzr, atol=1.5e-4, rtol=0)
+
+    def _check_variant_func(self, func, other_func, rtol, atol=0):
+        rng = np.random.RandomState(1234)
+        n = 10000
+        x = rng.pareto(0.02, n) * (2*rng.randint(0, 2, n) - 1)
+        y = rng.pareto(0.02, n) * (2*rng.randint(0, 2, n) - 1)
+        z = x + 1j*y
+
+        with np.errstate(all='ignore'):
+            w = other_func(z)
+            w_real = other_func(x).real
+
+            mask = np.isfinite(w)
+            w = w[mask]
+            z = z[mask]
+
+            mask = np.isfinite(w_real)
+            w_real = w_real[mask]
+            x = x[mask]
+
+            # test both real and complex variants
+            assert_func_equal(func, w, z, rtol=rtol, atol=atol)
+            assert_func_equal(func, w_real, x, rtol=rtol, atol=atol)
+
+    def test_erfc_consistent(self):
+        self._check_variant_func(
+            cephes.erfc,
+            lambda z: 1 - cephes.erf(z),
+            rtol=1e-12,
+            atol=1e-14  # <- the test function loses precision
+            )
+
+    def test_erfcx_consistent(self):
+        self._check_variant_func(
+            cephes.erfcx,
+            lambda z: np.exp(z*z) * cephes.erfc(z),
+            rtol=1e-12
+            )
+
+    def test_erfi_consistent(self):
+        self._check_variant_func(
+            cephes.erfi,
+            lambda z: -1j * cephes.erf(1j*z),
+            rtol=1e-12
+            )
+
+    def test_dawsn_consistent(self):
+        self._check_variant_func(
+            cephes.dawsn,
+            lambda z: sqrt(pi)/2 * np.exp(-z*z) * cephes.erfi(z),
+            rtol=1e-12
+            )
+
+    def test_erf_nan_inf(self):
+        vals = [np.nan, -np.inf, np.inf]
+        expected = [np.nan, -1, 1]
+        assert_allclose(special.erf(vals), expected, rtol=1e-15)
+
+    def test_erfc_nan_inf(self):
+        vals = [np.nan, -np.inf, np.inf]
+        expected = [np.nan, 2, 0]
+        assert_allclose(special.erfc(vals), expected, rtol=1e-15)
+
+    def test_erfcx_nan_inf(self):
+        vals = [np.nan, -np.inf, np.inf]
+        expected = [np.nan, np.inf, 0]
+        assert_allclose(special.erfcx(vals), expected, rtol=1e-15)
+
+    def test_erfi_nan_inf(self):
+        vals = [np.nan, -np.inf, np.inf]
+        expected = [np.nan, -np.inf, np.inf]
+        assert_allclose(special.erfi(vals), expected, rtol=1e-15)
+
+    def test_dawsn_nan_inf(self):
+        vals = [np.nan, -np.inf, np.inf]
+        expected = [np.nan, -0.0, 0.0]
+        assert_allclose(special.dawsn(vals), expected, rtol=1e-15)
+
+    def test_wofz_nan_inf(self):
+        vals = [np.nan, -np.inf, np.inf]
+        expected = [np.nan + np.nan * 1.j, 0.-0.j, 0.+0.j]
+        assert_allclose(special.wofz(vals), expected, rtol=1e-15)
+
+
+class TestEuler:
+    def test_euler(self):
+        eu0 = special.euler(0)
+        eu1 = special.euler(1)
+        eu2 = special.euler(2)   # just checking segfaults
+        assert_allclose(eu0, [1], rtol=1e-15)
+        assert_allclose(eu1, [1, 0], rtol=1e-15)
+        assert_allclose(eu2, [1, 0, -1], rtol=1e-15)
+        eu24 = special.euler(24)
+        mathworld = [1,1,5,61,1385,50521,2702765,199360981,
+                     19391512145,2404879675441,
+                     370371188237525,69348874393137901,
+                     15514534163557086905]
+        correct = zeros((25,),'d')
+        for k in range(0,13):
+            if (k % 2):
+                correct[2*k] = -float(mathworld[k])
+            else:
+                correct[2*k] = float(mathworld[k])
+        with np.errstate(all='ignore'):
+            err = nan_to_num((eu24-correct)/correct)
+            errmax = max(err)
+        assert_allclose(errmax, 0.0, atol=1.5e-14, rtol=0)
+
+
+class TestExp:
+    def test_exp2(self):
+        ex = special.exp2(2)
+        exrl = 2**2
+        assert_equal(ex,exrl)
+
+    def test_exp2more(self):
+        exm = special.exp2(2.5)
+        exmrl = 2**(2.5)
+        assert_allclose(exm, exmrl, atol=1.5e-8, rtol=0)
+
+    def test_exp10(self):
+        ex = special.exp10(2)
+        exrl = 10**2
+        assert_allclose(ex, exrl, atol=1e-6, rtol=0)
+
+    def test_exp10more(self):
+        exm = special.exp10(2.5)
+        exmrl = 10**(2.5)
+        assert_allclose(exm, exmrl, atol=1.5e-8, rtol=0)
+
+    def test_expm1(self):
+        ex = (special.expm1(2), special.expm1(3), special.expm1(4))
+        exrl = (exp(2) - 1, exp(3) - 1, exp(4) - 1)
+        assert_allclose(ex, exrl, atol=1.5e-8, rtol=0)
+
+    def test_expm1more(self):
+        ex1 = (special.expm1(2), special.expm1(2.1), special.expm1(2.2))
+        exrl1 = (exp(2) - 1, exp(2.1) - 1, exp(2.2) - 1)
+        assert_allclose(ex1, exrl1, atol=1.5e-8, rtol=0)
+
+
+def assert_really_equal(x, y, rtol=None):
+    """
+    Sharper assertion function that is stricter about matching types, not just values
+
+    This is useful/necessary in some cases:
+      * dtypes for arrays that have the same _values_ (e.g. element 1.0 vs 1)
+      * distinguishing complex from real NaN
+      * result types for scalars
+
+    We still want to be able to allow a relative tolerance for the values though.
+    The main logic comparison logic is handled by the xp_assert_* functions.
+    """
+    def assert_func(x, y):
+        xp_assert_equal(x, y) if rtol is None else xp_assert_close(x, y, rtol=rtol)
+
+    def assert_complex_nan(x):
+        assert np.isnan(x.real) and np.isnan(x.imag)
+
+    assert type(x) is type(y), f"types not equal: {type(x)}, {type(y)}"
+
+    # ensure we also compare the values _within_ an array appropriately,
+    # e.g. assert_equal does not distinguish different complex nans in arrays
+    if isinstance(x, np.ndarray):
+        # assert_equal does not compare (all) types, only values
+        assert x.dtype == y.dtype
+        # for empty arrays resp. to ensure shapes match
+        assert_func(x, y)
+        for elem_x, elem_y in zip(x.ravel(), y.ravel()):
+            assert_really_equal(elem_x, elem_y, rtol=rtol)
+    elif np.isnan(x) and np.isnan(y) and _is_subdtype(type(x), "c"):
+        assert_complex_nan(x) and assert_complex_nan(y)
+    # no need to consider complex infinities due to numpy/numpy#25493
+    else:
+        assert_func(x, y)
+
+
+class TestFactorialFunctions:
+    def factorialk_ref(self, n, k, exact, extend):
+        if exact:
+            return special.factorialk(n, k=k, exact=True)
+        # for details / explanation see factorialk-docstring
+        r = np.mod(n, k) if extend == "zero" else 1
+        vals = np.power(k, (n - r)/k) * special.gamma(n/k + 1) * special.rgamma(r/k + 1)
+        # np.maximum is element-wise, which is what we want
+        return vals * np.maximum(r, 1)
+
+    @pytest.mark.parametrize("exact,extend",
+                             [(True, "zero"), (False, "zero"), (False, "complex")])
+    def test_factorialx_scalar_return_type(self, exact, extend):
+        kw = {"exact": exact, "extend": extend}
+        assert np.isscalar(special.factorial(1, **kw))
+        assert np.isscalar(special.factorial2(1, **kw))
+        assert np.isscalar(special.factorialk(1, k=3, **kw))
+
+    @pytest.mark.parametrize("n", [-1, -2, -3])
+    @pytest.mark.parametrize("exact", [True, False])
+    def test_factorialx_negative_extend_zero(self, exact, n):
+        kw = {"exact": exact}
+        assert_equal(special.factorial(n, **kw), 0)
+        assert_equal(special.factorial2(n, **kw), 0)
+        assert_equal(special.factorialk(n, k=3, **kw), 0)
+
+    @pytest.mark.parametrize("exact", [True, False])
+    def test_factorialx_negative_extend_zero_array(self, exact):
+        kw = {"exact": exact}
+        rtol = 1e-15
+        n = [-5, -4, 0, 1]
+        # Consistent output for n < 0
+        expected = np.array([0, 0, 1, 1], dtype=native_int if exact else np.float64)
+        assert_really_equal(special.factorial(n, **kw), expected, rtol=rtol)
+        assert_really_equal(special.factorial2(n, **kw), expected, rtol=rtol)
+        assert_really_equal(special.factorialk(n, k=3, **kw), expected, rtol=rtol)
+
+    @pytest.mark.parametrize("n", [-1.1, -2.2, -3.3])
+    def test_factorialx_negative_extend_complex(self, n):
+        kw = {"extend": "complex"}
+        exp_1 = {-1.1: -10.686287021193184771,
+                 -2.2:   4.8509571405220931958,
+                 -3.3:  -1.4471073942559181166}
+        exp_2 = {-1.1:  1.0725776858167496309,
+                 -2.2: -3.9777171783768419874,
+                 -3.3: -0.99588841846200555977}
+        exp_k = {-1.1:  0.73565345382163025659,
+                 -2.2:  1.1749163167190809498,
+                 -3.3: -2.4780584257450583713}
+        rtol = 3e-15
+        assert_allclose(special.factorial(n, **kw), exp_1[n], rtol=rtol)
+        assert_allclose(special.factorial2(n, **kw), exp_2[n], rtol=rtol)
+        assert_allclose(special.factorialk(n, k=3, **kw), exp_k[n], rtol=rtol)
+        assert_allclose(special.factorial([n], **kw)[0], exp_1[n], rtol=rtol)
+        assert_allclose(special.factorial2([n], **kw)[0], exp_2[n], rtol=rtol)
+        assert_allclose(special.factorialk([n], k=3, **kw)[0], exp_k[n], rtol=rtol)
+
+    @pytest.mark.parametrize("imag", [0, 0j])
+    @pytest.mark.parametrize("n_outer", [-1, -2, -3])
+    def test_factorialx_negative_extend_complex_poles(self, n_outer, imag):
+        kw = {"extend": "complex"}
+        def _check(n):
+            complexify = _is_subdtype(type(n), "c")
+            # like for gamma, we expect complex nans for complex inputs
+            complex_nan = np.complex128("nan+nanj")
+            exp = np.complex128("nan+nanj") if complexify else np.float64("nan")
+            # poles are at negative integers that are multiples of k
+            assert_really_equal(special.factorial(n, **kw), exp)
+            assert_really_equal(special.factorial2(n * 2, **kw), exp)
+            assert_really_equal(special.factorialk(n * 3, k=3, **kw), exp)
+            # also test complex k for factorialk
+            c = 1.5 - 2j
+            assert_really_equal(special.factorialk(n * c, k=c, **kw), complex_nan)
+            # same for array case
+            assert_really_equal(special.factorial([n], **kw)[0], exp)
+            assert_really_equal(special.factorial2([n * 2], **kw)[0], exp)
+            assert_really_equal(special.factorialk([n * 3], k=3, **kw)[0], exp)
+            assert_really_equal(special.factorialk([n * c], k=c, **kw)[0], complex_nan)
+            # more specific tests in test_factorial{,2,k}_complex_reference
+
+        # imag ensures we test both real and complex representations of the poles
+        _check(n_outer + imag)
+        # check for large multiple of period
+        _check(100_000 * n_outer + imag)
+
+    @pytest.mark.parametrize("boxed", [True, False])
+    @pytest.mark.parametrize("extend", ["zero", "complex"])
+    @pytest.mark.parametrize(
+        "n",
+        [
+            np.nan, np.float64("nan"), np.nan + np.nan*1j, np.complex128("nan+nanj"),
+            np.inf, np.inf + 0j, -np.inf, -np.inf + 0j, None, np.datetime64("nat", "s")
+        ],
+        ids=[
+            "NaN", "np.float64('nan')", "NaN+i*NaN", "np.complex128('nan+nanj')",
+            "inf", "inf+0i", "-inf", "-inf+0i", "None", "NaT"
+        ]
+    )
+    @pytest.mark.parametrize(
+        "factorialx",
+        [special.factorial, special.factorial2, special.factorialk]
+    )
+    def test_factorialx_inf_nan(self, factorialx, n, extend, boxed):
+        # NaNs not allowed (by dtype) for exact=True
+        kw = {"exact": False, "extend": extend}
+        if factorialx == special.factorialk:
+            kw["k"] = 3
+
+        # None is allowed for scalars, but would cause object type in array case
+        permissible_types = ["i", "f", "c"] if boxed else ["i", "f", "c", type(None)]
+        # factorial allows floats also for extend="zero"
+        types_need_complex_ext = "c" if factorialx == special.factorial else ["f", "c"]
+
+        if not _is_subdtype(type(n), permissible_types):
+            with pytest.raises(ValueError, match="Unsupported data type.*"):
+                factorialx([n] if boxed else n, **kw)
+        elif _is_subdtype(type(n), types_need_complex_ext) and extend != "complex":
+            with pytest.raises(ValueError, match="In order to use non-integer.*"):
+                factorialx([n] if boxed else n, **kw)
+        else:
+            # account for type and whether extend="complex"
+            complexify = (extend == "complex") and _is_subdtype(type(n), "c")
+            # note that the type of the naïve `np.nan + np.nan * 1j` is `complex`
+            # instead of `numpy.complex128`, which trips up assert_really_equal
+            expected = np.complex128("nan+nanj") if complexify else np.float64("nan")
+            # the only exception are real infinities
+            if _is_subdtype(type(n), "f") and np.isinf(n):
+                # unchanged for positive infinity; negative one depends on extension
+                neg_inf_result = np.float64(0 if (extend == "zero") else "nan")
+                expected = np.float64("inf") if (n > 0) else neg_inf_result
+
+            result = factorialx([n], **kw)[0] if boxed else factorialx(n, **kw)
+            assert_really_equal(result, expected)
+            # also tested in test_factorial{,2,k}_{array,scalar}_corner_cases
+
+    @pytest.mark.parametrize("extend", [0, 1.1, np.nan, "string"])
+    def test_factorialx_raises_extend(self, extend):
+        with pytest.raises(ValueError, match="argument `extend` must be.*"):
+            special.factorial(1, extend=extend)
+        with pytest.raises(ValueError, match="argument `extend` must be.*"):
+            special.factorial2(1, extend=extend)
+        with pytest.raises(ValueError, match="argument `extend` must be.*"):
+            special.factorialk(1, k=3, exact=True, extend=extend)
+
+    @pytest.mark.parametrize("levels", range(1, 5))
+    @pytest.mark.parametrize("exact", [True, False])
+    def test_factorialx_array_shape(self, levels, exact):
+        def _nest_me(x, k=1):
+            """
+            Double x and nest it k times
+
+            For example:
+            >>> _nest_me([3, 4], 2)
+            [[[3, 4], [3, 4]], [[3, 4], [3, 4]]]
+            """
+            if k == 0:
+                return x
+            else:
+                return _nest_me([x, x], k-1)
+
+        def _check(res, nucleus):
+            exp = np.array(_nest_me(nucleus, k=levels), dtype=object)
+            # test that ndarray shape is maintained
+            # need to cast to float due to numpy/numpy#21220
+            assert_allclose(res.astype(np.float64), exp.astype(np.float64))
+
+        n = np.array(_nest_me([5, 25], k=levels))
+        exp_nucleus = {1: [120, math.factorial(25)],
+                       # correctness of factorial{2,k}() is tested elsewhere
+                       2: [15, special.factorial2(25, exact=True)],
+                       3: [10, special.factorialk(25, 3, exact=True)]}
+
+        _check(special.factorial(n, exact=exact), exp_nucleus[1])
+        _check(special.factorial2(n, exact=exact), exp_nucleus[2])
+        _check(special.factorialk(n, 3, exact=exact), exp_nucleus[3])
+
+    @pytest.mark.parametrize("exact", [True, False])
+    @pytest.mark.parametrize("dtype", [
+        None, int, np.int8, np.int16, np.int32, np.int64,
+        np.uint8, np.uint16, np.uint32, np.uint64
+    ])
+    @pytest.mark.parametrize("dim", range(0, 5))
+    def test_factorialx_array_dimension(self, dim, dtype, exact):
+        n = np.array(5, dtype=dtype, ndmin=dim)
+        exp = {1: 120, 2: 15, 3: 10}
+        assert_allclose(special.factorial(n, exact=exact),
+                        np.array(exp[1], ndmin=dim))
+        assert_allclose(special.factorial2(n, exact=exact),
+                        np.array(exp[2], ndmin=dim))
+        assert_allclose(special.factorialk(n, 3, exact=exact),
+                        np.array(exp[3], ndmin=dim))
+
+    @pytest.mark.parametrize("exact", [True, False])
+    @pytest.mark.parametrize("level", range(1, 5))
+    def test_factorialx_array_like(self, level, exact):
+        def _nest_me(x, k=1):
+            if k == 0:
+                return x
+            else:
+                return _nest_me([x], k-1)
+
+        n = _nest_me([5], k=level-1)  # nested list
+        exp_nucleus = {1: 120, 2: 15, 3: 10}
+        assert_func = assert_array_equal if exact else assert_allclose
+        assert_func(special.factorial(n, exact=exact),
+                    np.array(exp_nucleus[1], ndmin=level))
+        assert_func(special.factorial2(n, exact=exact),
+                    np.array(exp_nucleus[2], ndmin=level))
+        assert_func(special.factorialk(n, 3, exact=exact),
+                    np.array(exp_nucleus[3], ndmin=level))
+
+    @pytest.mark.fail_slow(5)
+    @pytest.mark.parametrize("dtype", [np.uint8, np.uint16, np.uint32, np.uint64])
+    @pytest.mark.parametrize("exact,extend",
+                             [(True, "zero"), (False, "zero"), (False, "complex")])
+    def test_factorialx_uint(self, exact, extend, dtype):
+        # ensure that uint types work correctly as inputs
+        kw = {"exact": exact, "extend": extend}
+        assert_func = assert_array_equal if exact else assert_allclose
+        def _check(n):
+            n_ref = n.astype(np.int64) if isinstance(n, np.ndarray) else np.int64(n)
+            assert_func(special.factorial(n, **kw), special.factorial(n_ref, **kw))
+            assert_func(special.factorial2(n, **kw), special.factorial2(n_ref, **kw))
+            assert_func(special.factorialk(n, k=3, **kw),
+                        special.factorialk(n_ref, k=3, **kw))
+        def _check_inf(n):
+            # produce inf of same type/dimension
+            with warnings.catch_warnings():
+                warnings.simplefilter("ignore", RuntimeWarning)
+                shaped_inf = n / 0
+            assert_func(special.factorial(n, **kw), shaped_inf)
+            assert_func(special.factorial2(n, **kw), shaped_inf)
+            assert_func(special.factorialk(n, k=3, **kw), shaped_inf)
+
+        _check(dtype(0))
+        _check(dtype(1))
+        _check(np.array(0, dtype=dtype))
+        _check(np.array([0, 1], dtype=dtype))
+        # test that maximal uint values work as well
+        N = dtype(np.iinfo(dtype).max)
+        # TODO: cannot use N itself yet; factorial uses `gamma(N+1)` resp. `(hi+lo)//2`
+        if dtype == np.uint64:
+            if exact:
+                # avoid attempting huge calculation
+                pass
+            else:
+                # N does not fit into int64 --> cannot use _check
+                _check_inf(dtype(N-1))
+                _check_inf(np.array(N-1, dtype=dtype))
+                _check_inf(np.array([N-1], dtype=dtype))
+        elif dtype in [np.uint8, np.uint16] or not exact:
+            # factorial(65535, exact=True) has 287189 digits and is calculated almost
+            # instantaneously on modern hardware; however, dtypes bigger than uint16
+            # would blow up runtime and memory consumption for exact=True
+            _check(N-1)
+            _check(np.array(N-1, dtype=dtype))
+            _check(np.array([N-2, N-1], dtype=dtype))
+
+    # note that n=170 is the last integer such that factorial(n) fits float64
+    @pytest.mark.parametrize('n', range(30, 180, 10))
+    def test_factorial_accuracy(self, n):
+        # Compare exact=True vs False, i.e. that the accuracy of the
+        # approximation is better than the specified tolerance.
+
+        rtol = 6e-14 if sys.platform == 'win32' else 1e-15
+        # need to cast exact result to float due to numpy/numpy#21220
+        assert_allclose(float(special.factorial(n, exact=True)),
+                        special.factorial(n, exact=False), rtol=rtol)
+        assert_allclose(special.factorial([n], exact=True).astype(float),
+                        special.factorial([n], exact=False), rtol=rtol)
+
+    @pytest.mark.parametrize('n',
+                             list(range(0, 22)) + list(range(30, 180, 10)))
+    def test_factorial_int_reference(self, n):
+        # Compare all with math.factorial
+        correct = math.factorial(n)
+        assert_array_equal(correct, special.factorial(n, exact=True))
+        assert_array_equal(correct, special.factorial([n], exact=True)[0])
+
+        rtol = 8e-14 if sys.platform == 'win32' else 1e-15
+        # need to cast exact result to float due to numpy/numpy#21220
+        correct = float(correct)
+        assert_allclose(correct, special.factorial(n, exact=False), rtol=rtol)
+        assert_allclose(correct, special.factorial([n], exact=False)[0], rtol=rtol)
+
+        # extend="complex" only works for exact=False
+        kw = {"exact": False, "extend": "complex"}
+        assert_allclose(correct, special.factorial(n, **kw), rtol=rtol)
+        assert_allclose(correct, special.factorial([n], **kw)[0], rtol=rtol)
+
+    def test_factorial_float_reference(self):
+        def _check(n, expected):
+            rtol = 8e-14 if sys.platform == 'win32' else 1e-15
+            assert_allclose(special.factorial(n), expected, rtol=rtol)
+            assert_allclose(special.factorial([n])[0], expected, rtol=rtol)
+            # using floats with `exact=True` raises an error for scalars and arrays
+            with pytest.raises(ValueError, match="`exact=True` only supports.*"):
+                special.factorial(n, exact=True)
+            with pytest.raises(ValueError, match="`exact=True` only supports.*"):
+                special.factorial([n], exact=True)
+
+        # Reference values from mpmath for gamma(n+1)
+        _check(0.01, 0.994325851191506032181932988)
+        _check(1.11, 1.051609009483625091514147465)
+        _check(5.55, 314.9503192327208241614959052)
+        _check(11.1, 50983227.84411615655137170553)
+        _check(33.3, 2.493363339642036352229215273e+37)
+        _check(55.5, 9.479934358436729043289162027e+73)
+        _check(77.7, 3.060540559059579022358692625e+114)
+        _check(99.9, 5.885840419492871504575693337e+157)
+        # close to maximum for float64
+        _check(170.6243, 1.79698185749571048960082e+308)
+
+    def test_factorial_complex_reference(self):
+        def _check(n, expected):
+            rtol = 3e-15 if sys.platform == 'win32' else 2e-15
+            kw = {"exact": False, "extend": "complex"}
+            assert_allclose(special.factorial(n, **kw), expected, rtol=rtol)
+            assert_allclose(special.factorial([n], **kw)[0], expected, rtol=rtol)
+
+        # Reference values from mpmath.gamma(n+1)
+        # negative & complex values
+        _check(-0.5, expected=1.7724538509055160276)
+        _check(-0.5 + 0j, expected=1.7724538509055160276 + 0j)
+        _check(2 + 2j, expected=-0.42263728631120216694 + 0.87181425569650686062j)
+        # close to poles
+        _check(-0.9999, expected=9999.422883232725532)
+        _check(-1 + 0.0001j, expected=-0.57721565582674219 - 9999.9999010944009697j)
+
+    @pytest.mark.parametrize("dtype", [np.int64, np.float64,
+                                       np.complex128, object])
+    @pytest.mark.parametrize("extend", ["zero", "complex"])
+    @pytest.mark.parametrize("exact", [True, False])
+    @pytest.mark.parametrize("dim", range(0, 5))
+    # test empty & non-empty arrays, with nans and mixed
+    @pytest.mark.parametrize(
+        "content",
+        [[], [1], [1.1], [np.nan], [np.nan + np.nan * 1j], [np.nan, 1]],
+        ids=["[]", "[1]", "[1.1]", "[NaN]", "[NaN+i*NaN]", "[NaN, 1]"],
+    )
+    def test_factorial_array_corner_cases(self, content, dim, exact, extend, dtype):
+        if dtype is object and SCIPY_ARRAY_API:
+            pytest.skip("object arrays unsupported in array API mode")
+        # get dtype without calling array constructor (that might fail or mutate)
+        if dtype is np.int64 and any(np.isnan(x) or (x != int(x)) for x in content):
+            pytest.skip("impossible combination")
+        if dtype == np.float64 and any(_is_subdtype(type(x), "c") for x in content):
+            pytest.skip("impossible combination")
+
+        kw = {"exact": exact, "extend": extend}
+        # np.array(x, ndim=0) will not be 0-dim. unless x is too
+        content = content if (dim > 0 or len(content) != 1) else content[0]
+        n = np.array(content, ndmin=dim, dtype=dtype)
+
+        result = None
+        if extend == "complex" and exact:
+            with pytest.raises(ValueError, match="Incompatible options:.*"):
+                special.factorial(n, **kw)
+        elif not _is_subdtype(n.dtype, ["i", "f", "c"]):
+            with pytest.raises(ValueError, match="Unsupported data type.*"):
+                special.factorial(n, **kw)
+        elif _is_subdtype(n.dtype, "c") and extend != "complex":
+            with pytest.raises(ValueError, match="In order to use non-integer.*"):
+                special.factorial(n, **kw)
+        elif exact and not _is_subdtype(n.dtype, "i"):
+            with pytest.raises(ValueError, match="`exact=True` only supports.*"):
+                special.factorial(n, **kw)
+        else:
+            result = special.factorial(n, **kw)
+
+        if result is not None:
+            # use scalar case as reference; tested separately in *_scalar_corner_cases
+            ref = [special.factorial(x, **kw) for x in n.ravel()]
+            # unpack length-1 lists so that np.array(x, ndim=0) works correctly
+            ref = ref[0] if len(ref) == 1 else ref
+            # result is empty if and only if n is empty, and has the same dimension
+            # as n; dtype stays the same, except when not empty and not exact:
+            if n.size:
+                cx = (extend == "complex") and _is_subdtype(n.dtype, "c")
+                dtype = np.complex128 if cx else (native_int if exact else np.float64)
+            expected = np.array(ref, ndmin=dim, dtype=dtype)
+            assert_really_equal(result, expected, rtol=1e-15)
+
+    @pytest.mark.parametrize("extend", ["zero", "complex"])
+    @pytest.mark.parametrize("exact", [True, False])
+    @pytest.mark.parametrize("n", [1, 1.1, 2 + 2j, np.nan, np.nan + np.nan*1j, None],
+                             ids=["1", "1.1", "2+2j", "NaN", "NaN+i*NaN", "None"])
+    def test_factorial_scalar_corner_cases(self, n, exact, extend):
+        kw = {"exact": exact, "extend": extend}
+        if extend == "complex" and exact:
+            with pytest.raises(ValueError, match="Incompatible options:.*"):
+                special.factorial(n, **kw)
+        elif not _is_subdtype(type(n), ["i", "f", "c", type(None)]):
+            with pytest.raises(ValueError, match="Unsupported data type.*"):
+                special.factorial(n, **kw)
+        elif _is_subdtype(type(n), "c") and extend != "complex":
+            with pytest.raises(ValueError, match="In order to use non-integer.*"):
+                special.factorial(n, **kw)
+        elif n is None or np.isnan(n):
+            # account for dtype and whether extend="complex"
+            complexify = (extend == "complex") and _is_subdtype(type(n), "c")
+            expected = np.complex128("nan+nanj") if complexify else np.float64("nan")
+            assert_really_equal(special.factorial(n, **kw), expected)
+        elif exact and _is_subdtype(type(n), "f"):
+            with pytest.raises(ValueError, match="`exact=True` only supports.*"):
+                special.factorial(n, **kw)
+        else:
+            assert_equal(special.factorial(n, **kw), special.gamma(n + 1))
+
+    # use odd increment to make sure both odd & even numbers are tested!
+    @pytest.mark.parametrize('n', range(30, 180, 11))
+    def test_factorial2_accuracy(self, n):
+        # Compare exact=True vs False, i.e. that the accuracy of the
+        # approximation is better than the specified tolerance.
+
+        rtol = 2e-14 if sys.platform == 'win32' else 1e-15
+        # need to cast exact result to float due to numpy/numpy#21220
+        assert_allclose(float(special.factorial2(n, exact=True)),
+                        special.factorial2(n, exact=False), rtol=rtol)
+        assert_allclose(special.factorial2([n], exact=True).astype(float),
+                        special.factorial2([n], exact=False), rtol=rtol)
+
+    @pytest.mark.parametrize('n',
+                             list(range(0, 22)) + list(range(30, 180, 11)))
+    def test_factorial2_int_reference(self, n):
+        # Compare all with correct value
+
+        # Cannot use np.product due to overflow
+        correct = functools.reduce(operator.mul, list(range(n, 0, -2)), 1)
+
+        assert_array_equal(correct, special.factorial2(n, exact=True))
+        assert_array_equal(correct, special.factorial2([n], exact=True)[0])
+
+        rtol = 2e-14 if sys.platform == 'win32' else 1e-15
+        # need to cast exact result to float due to numpy/numpy#21220
+        correct = float(correct)
+        assert_allclose(correct, special.factorial2(n, exact=False), rtol=rtol)
+        assert_allclose(correct, special.factorial2([n], exact=False)[0], rtol=rtol)
+
+        # extend="complex" only works for exact=False
+        kw = {"exact": False, "extend": "complex"}
+        # approximation only matches exactly for `n == 1 (mod k)`, see docstring
+        if n % 2 == 1:
+            assert_allclose(correct, special.factorial2(n, **kw), rtol=rtol)
+            assert_allclose(correct, special.factorial2([n], **kw)[0], rtol=rtol)
+
+    def test_factorial2_complex_reference(self):
+        # this tests for both floats and complex
+        def _check(n, expected):
+            rtol = 5e-15
+            kw = {"exact": False, "extend": "complex"}
+            assert_allclose(special.factorial2(n, **kw), expected, rtol=rtol)
+            assert_allclose(special.factorial2([n], **kw)[0], expected, rtol=rtol)
+
+        # Reference values from mpmath for:
+        # mpmath.power(2, n/2) * mpmath.gamma(n/2 + 1) * mpmath.sqrt(2 / mpmath.pi)
+        _check(3, expected=3)
+        _check(4, expected=special.factorial2(4) * math.sqrt(2 / math.pi))
+        _check(20, expected=special.factorial2(20) * math.sqrt(2 / math.pi))
+        # negative & complex values
+        _check(-0.5, expected=0.82217895866245855122)
+        _check(-0.5 + 0j, expected=0.82217895866245855122 + 0j)
+        _check(3 + 3j, expected=-1.0742236630142471526 + 1.4421398439387262897j)
+        # close to poles
+        _check(-1.9999, expected=7978.8918745523440682)
+        _check(-2 + 0.0001j, expected=0.0462499835314308444 - 7978.84559148876374493j)
+
+    @pytest.mark.parametrize("dtype", [np.int64, np.float64,
+                                       np.complex128, object])
+    @pytest.mark.parametrize("extend", ["zero", "complex"])
+    @pytest.mark.parametrize("exact", [True, False])
+    @pytest.mark.parametrize("dim", range(0, 5))
+    # test empty & non-empty arrays, with nans and mixed
+    @pytest.mark.parametrize(
+        "content",
+        [[], [1], [1.1], [np.nan], [np.nan + np.nan * 1j], [np.nan, 1]],
+        ids=["[]", "[1]", "[1.1]", "[NaN]", "[NaN+i*NaN]", "[NaN, 1]"],
+    )
+    def test_factorial2_array_corner_cases(self, content, dim, exact, extend, dtype):
+        # get dtype without calling array constructor (that might fail or mutate)
+        if dtype == np.int64 and any(np.isnan(x) or (x != int(x)) for x in content):
+            pytest.skip("impossible combination")
+        if dtype == np.float64 and any(_is_subdtype(type(x), "c") for x in content):
+            pytest.skip("impossible combination")
+
+        kw = {"exact": exact, "extend": extend}
+        # np.array(x, ndim=0) will not be 0-dim. unless x is too
+        content = content if (dim > 0 or len(content) != 1) else content[0]
+        n = np.array(content, ndmin=dim, dtype=dtype)
+
+        result = None
+        if extend == "complex" and exact:
+            with pytest.raises(ValueError, match="Incompatible options:.*"):
+                special.factorial2(n, **kw)
+        elif not _is_subdtype(n.dtype, ["i", "f", "c"]):
+            with pytest.raises(ValueError, match="Unsupported data type.*"):
+                special.factorial2(n, **kw)
+        elif _is_subdtype(n.dtype, ["f", "c"]) and extend != "complex":
+            with pytest.raises(ValueError, match="In order to use non-integer.*"):
+                special.factorial2(n, **kw)
+        else:
+            result = special.factorial2(n, **kw)
+
+        if result is not None:
+            # use scalar case as reference; tested separately in *_scalar_corner_cases
+            ref = [special.factorial2(x, **kw) for x in n.ravel()]
+            # unpack length-1 lists so that np.array(x, ndim=0) works correctly
+            ref = ref[0] if len(ref) == 1 else ref
+            # result is empty if and only if n is empty, and has the same dimension
+            # as n; dtype stays the same, except when not empty and not exact:
+            if n.size:
+                cx = (extend == "complex") and _is_subdtype(n.dtype, "c")
+                dtype = np.complex128 if cx else (native_int if exact else np.float64)
+            expected = np.array(ref, ndmin=dim, dtype=dtype)
+            assert_really_equal(result, expected, rtol=2e-15)
+
+    @pytest.mark.parametrize("extend", ["zero", "complex"])
+    @pytest.mark.parametrize("exact", [True, False])
+    @pytest.mark.parametrize("n", [1, 1.1, 2 + 2j, np.nan, np.nan + np.nan*1j, None],
+                             ids=["1", "1.1", "2+2j", "NaN", "NaN+i*NaN", "None"])
+    def test_factorial2_scalar_corner_cases(self, n, exact, extend):
+        kw = {"exact": exact, "extend": extend}
+        if extend == "complex" and exact:
+            with pytest.raises(ValueError, match="Incompatible options:.*"):
+                special.factorial2(n, **kw)
+        elif not _is_subdtype(type(n), ["i", "f", "c", type(None)]):
+            with pytest.raises(ValueError, match="Unsupported data type.*"):
+                special.factorial2(n, **kw)
+        elif _is_subdtype(type(n), ["f", "c"]) and extend != "complex":
+            with pytest.raises(ValueError, match="In order to use non-integer.*"):
+                special.factorial2(n, **kw)
+        elif n is None or np.isnan(n):
+            # account for dtype and whether extend="complex"
+            complexify = (extend == "complex") and _is_subdtype(type(n), "c")
+            expected = np.complex128("nan+nanj") if complexify else np.float64("nan")
+            assert_really_equal(special.factorial2(n, **kw), expected)
+        else:
+            expected = self.factorialk_ref(n, k=2, **kw)
+            assert_really_equal(special.factorial2(n, **kw), expected, rtol=1e-15)
+
+    @pytest.mark.parametrize("k", range(1, 5))
+    # note that n=170 is the last integer such that factorial(n) fits float64;
+    # use odd increment to make sure both odd & even numbers are tested
+    @pytest.mark.parametrize('n', range(170, 20, -29))
+    def test_factorialk_accuracy(self, n, k):
+        # Compare exact=True vs False, i.e. that the accuracy of the
+        # approximation is better than the specified tolerance.
+
+        rtol = 6e-14 if sys.platform == 'win32' else 2e-14
+        # need to cast exact result to float due to numpy/numpy#21220
+        assert_allclose(float(special.factorialk(n, k=k, exact=True)),
+                        special.factorialk(n, k=k, exact=False), rtol=rtol)
+        assert_allclose(special.factorialk([n], k=k, exact=True).astype(float),
+                        special.factorialk([n], k=k, exact=False), rtol=rtol)
+
+    @pytest.mark.parametrize('k', list(range(1, 5)) + [10, 20])
+    @pytest.mark.parametrize('n',
+                             list(range(0, 22)) + list(range(22, 100, 11)))
+    def test_factorialk_int_reference(self, n, k):
+        # Compare all with correct value
+
+        # Would be nice to use np.product here, but that's
+        # broken on windows, see numpy/numpy#21219
+        correct = functools.reduce(operator.mul, list(range(n, 0, -k)), 1)
+
+        assert_array_equal(correct, special.factorialk(n, k, exact=True))
+        assert_array_equal(correct, special.factorialk([n], k, exact=True)[0])
+
+        rtol = 3e-14 if sys.platform == 'win32' else 1e-14
+        # need to cast exact result to float due to numpy/numpy#21220
+        correct = float(correct)
+        assert_allclose(correct, special.factorialk(n, k, exact=False), rtol=rtol)
+        assert_allclose(correct, special.factorialk([n], k, exact=False)[0], rtol=rtol)
+
+        # extend="complex" only works for exact=False
+        kw = {"k": k, "exact": False, "extend": "complex"}
+        # approximation only matches exactly for `n == 1 (mod k)`, see docstring
+        if n % k == 1:
+            rtol = 2e-14
+            assert_allclose(correct, special.factorialk(n, **kw), rtol=rtol)
+            assert_allclose(correct, special.factorialk([n], **kw)[0], rtol=rtol)
+
+    def test_factorialk_complex_reference(self):
+        # this tests for both floats and complex
+        def _check(n, k, exp):
+            rtol = 1e-14
+            kw = {"k": k, "exact": False, "extend": "complex"}
+            assert_allclose(special.factorialk(n, **kw), exp, rtol=rtol)
+            assert_allclose(special.factorialk([n], **kw)[0], exp, rtol=rtol)
+
+        # Reference values from mpmath for:
+        # mpmath.power(k, (n-1)/k) * mpmath.gamma(n/k + 1) / mpmath.gamma(1/k + 1)
+        _check(n=4, k=3, exp=special.factorialk(4, k=3, exact=True))
+        _check(n=5, k=3, exp=7.29011132947227083)
+        _check(n=6.5, k=3, exp=19.6805080113566010)
+        # non-integer k
+        _check(n=3, k=2.5, exp=2.58465740293218541)
+        _check(n=11, k=2.5, exp=1963.5)  # ==11*8.5*6*3.5; c.f. n == 1 (mod k)
+        _check(n=-3 + 3j + 1, k=-3 + 3j, exp=-2 + 3j)
+        # complex values
+        _check(n=4 + 4j, k=4, exp=-0.67855904082768043854 + 2.1993925819930311497j)
+        _check(n=4, k=4 - 4j, exp=1.9775338957222718742 + 0.92607172675423901371j)
+        _check(n=4 + 4j, k=4 - 4j, exp=0.1868492880824934475 + 0.87660580316894290247j)
+        # negative values
+        _check(n=-0.5, k=3, exp=0.72981013240713739354)
+        _check(n=-0.5 + 0j, k=3, exp=0.72981013240713739354 + 0j)
+        _check(n=2.9, k=-0.7, exp=0.45396591474966867296 + 0.56925525174685228866j)
+        _check(n=-0.6, k=-0.7, exp=-0.07190820089634757334 - 0.090170031876701730081j)
+        # close to poles
+        _check(n=-2.9999, k=3, exp=7764.7170695908828364)
+        _check(n=-3 + 0.0001j, k=3, exp=0.1349475632879599864 - 7764.5821055158365027j)
+
+    @pytest.mark.parametrize("dtype", [np.int64, np.float64,
+                                       np.complex128, object])
+    @pytest.mark.parametrize("extend", ["zero", "complex"])
+    @pytest.mark.parametrize("exact", [True, False])
+    @pytest.mark.parametrize("dim", range(0, 5))
+    # test empty & non-empty arrays, with nans and mixed
+    @pytest.mark.parametrize(
+        "content",
+        [[], [1], [1.1], [np.nan], [np.nan + np.nan * 1j], [np.nan, 1]],
+        ids=["[]", "[1]", "[1.1]", "[NaN]", "[NaN+i*NaN]", "[NaN, 1]"],
+    )
+    def test_factorialk_array_corner_cases(self, content, dim, exact, extend, dtype):
+        # get dtype without calling array constructor (that might fail or mutate)
+        if dtype == np.int64 and any(np.isnan(x) or (x != int(x)) for x in content):
+            pytest.skip("impossible combination")
+        if dtype == np.float64 and any(_is_subdtype(type(x), "c") for x in content):
+            pytest.skip("impossible combination")
+
+        kw = {"k": 3, "exact": exact, "extend": extend}
+        # np.array(x, ndim=0) will not be 0-dim. unless x is too
+        content = content if (dim > 0 or len(content) != 1) else content[0]
+        n = np.array(content, ndmin=dim, dtype=dtype)
+
+        result = None
+        if extend == "complex" and exact:
+            with pytest.raises(ValueError, match="Incompatible options:.*"):
+                special.factorialk(n, **kw)
+        elif not _is_subdtype(n.dtype, ["i", "f", "c"]):
+            with pytest.raises(ValueError, match="Unsupported data type.*"):
+                special.factorialk(n, **kw)
+        elif _is_subdtype(n.dtype, ["f", "c"]) and extend != "complex":
+            with pytest.raises(ValueError, match="In order to use non-integer.*"):
+                special.factorialk(n, **kw)
+        else:
+            result = special.factorialk(n, **kw)
+
+        if result is not None:
+            # use scalar case as reference; tested separately in *_scalar_corner_cases
+            ref = [special.factorialk(x, **kw) for x in n.ravel()]
+            # unpack length-1 lists so that np.array(x, ndim=0) works correctly
+            ref = ref[0] if len(ref) == 1 else ref
+            # result is empty if and only if n is empty, and has the same dimension
+            # as n; dtype stays the same, except when not empty and not exact:
+            if n.size:
+                cx = (extend == "complex") and _is_subdtype(n.dtype, "c")
+                dtype = np.complex128 if cx else (native_int if exact else np.float64)
+            expected = np.array(ref, ndmin=dim, dtype=dtype)
+            assert_really_equal(result, expected, rtol=2e-15)
+
+    @pytest.mark.parametrize("extend", ["zero", "complex"])
+    @pytest.mark.parametrize("exact", [True, False])
+    @pytest.mark.parametrize("k", range(1, 5))
+    @pytest.mark.parametrize("n", [1, 1.1, 2 + 2j, np.nan, np.nan + np.nan*1j, None],
+                             ids=["1", "1.1", "2+2j", "NaN", "NaN+i*NaN", "None"])
+    def test_factorialk_scalar_corner_cases(self, n, k, exact, extend):
+        kw = {"k": k, "exact": exact, "extend": extend}
+        if extend == "complex" and exact:
+            with pytest.raises(ValueError, match="Incompatible options:.*"):
+                special.factorialk(n, **kw)
+        elif not _is_subdtype(type(n), ["i", "f", "c", type(None)]):
+            with pytest.raises(ValueError, match="Unsupported data type.*"):
+                special.factorialk(n, **kw)
+        elif _is_subdtype(type(n), ["f", "c"]) and extend != "complex":
+            with pytest.raises(ValueError, match="In order to use non-integer.*"):
+                special.factorialk(n, **kw)
+        elif n is None or np.isnan(n):
+            # account for dtype and whether extend="complex"
+            complexify = (extend == "complex") and _is_subdtype(type(n), "c")
+            expected = np.complex128("nan+nanj") if complexify else np.float64("nan")
+            assert_really_equal(special.factorialk(n, **kw), expected)
+        else:
+            expected = self.factorialk_ref(n, **kw)
+            assert_really_equal(special.factorialk(n, **kw), expected, rtol=1e-15)
+
+    @pytest.mark.parametrize("boxed", [True, False])
+    @pytest.mark.parametrize("exact,extend",
+                             [(True, "zero"), (False, "zero"), (False, "complex")])
+    @pytest.mark.parametrize("k", [-1, -1.0, 0, 0.0, 0 + 1j, 1.1, np.nan])
+    def test_factorialk_raises_k_complex(self, k, exact, extend, boxed):
+        n = [1] if boxed else 1
+        kw = {"k": k, "exact": exact, "extend": extend}
+        if extend == "zero":
+            msg = "In order to use non-integer.*"
+            if _is_subdtype(type(k), "i") and (k < 1):
+                msg = "For `extend='zero'`.*"
+            with pytest.raises(ValueError, match=msg):
+                special.factorialk(n, **kw)
+        elif k == 0:
+            with pytest.raises(ValueError, match="Parameter k cannot be zero!"):
+                special.factorialk(n, **kw)
+        else:
+            # no error
+            special.factorialk(n, **kw)
+
+    @pytest.mark.parametrize("boxed", [True, False])
+    @pytest.mark.parametrize("exact,extend",
+                             [(True, "zero"), (False, "zero"), (False, "complex")])
+    # neither integer, float nor complex
+    @pytest.mark.parametrize("k", ["string", np.datetime64("nat", "s")],
+                             ids=["string", "NaT"])
+    def test_factorialk_raises_k_other(self, k, exact, extend, boxed):
+        n = [1] if boxed else 1
+        kw = {"k": k, "exact": exact, "extend": extend}
+        with pytest.raises(ValueError, match="Unsupported data type.*"):
+            special.factorialk(n, **kw)
+
+    @pytest.mark.parametrize("exact,extend",
+                             [(True, "zero"), (False, "zero"), (False, "complex")])
+    @pytest.mark.parametrize("k", range(1, 12))
+    def test_factorialk_dtype(self, k, exact, extend):
+        kw = {"k": k, "exact": exact, "extend": extend}
+        if exact and k in _FACTORIALK_LIMITS_64BITS.keys():
+            n = np.array([_FACTORIALK_LIMITS_32BITS[k]])
+            assert_equal(special.factorialk(n, **kw).dtype, np.long)
+            assert_equal(special.factorialk(n + 1, **kw).dtype, np.int64)
+            # assert maximality of limits for given dtype
+            assert special.factorialk(n + 1, **kw) > np.iinfo(np.int32).max
+
+            n = np.array([_FACTORIALK_LIMITS_64BITS[k]])
+            assert_equal(special.factorialk(n, **kw).dtype, np.int64)
+            assert_equal(special.factorialk(n + 1, **kw).dtype, object)
+            assert special.factorialk(n + 1, **kw) > np.iinfo(np.int64).max
+        else:
+            n = np.array([_FACTORIALK_LIMITS_64BITS.get(k, 1)])
+            # for exact=True and k >= 10, we always return object;
+            # for exact=False it's always float (unless input is complex)
+            dtype = object if exact else np.float64
+            assert_equal(special.factorialk(n, **kw).dtype, dtype)
+
+    def test_factorial_mixed_nan_inputs(self):
+        x = np.array([np.nan, 1, 2, 3, np.nan])
+        expected = np.array([np.nan, 1, 2, 6, np.nan])
+        assert_equal(special.factorial(x, exact=False), expected)
+        with pytest.raises(ValueError, match="`exact=True` only supports.*"):
+            special.factorial(x, exact=True)
+
+
+class TestFresnel:
+    @pytest.mark.parametrize("z, s, c", [
+        # some positive value
+        (.5, 0.064732432859999287, 0.49234422587144644),
+        (.5 + .0j, 0.064732432859999287, 0.49234422587144644),
+        # negative half annulus
+        # https://github.com/scipy/scipy/issues/12309
+        # Reference values can be reproduced with
+        # https://www.wolframalpha.com/input/?i=FresnelS%5B-2.0+%2B+0.1i%5D
+        # https://www.wolframalpha.com/input/?i=FresnelC%5B-2.0+%2B+0.1i%5D
+        (
+            -2.0 + 0.1j,
+            -0.3109538687728942-0.0005870728836383176j,
+            -0.4879956866358554+0.10670801832903172j
+        ),
+        (
+            -0.1 - 1.5j,
+            -0.03918309471866977+0.7197508454568574j,
+            0.09605692502968956-0.43625191013617465j
+        ),
+        # a different algorithm kicks in for "large" values, i.e., |z| >= 4.5,
+        # make sure to test both float and complex values; a different
+        # algorithm is used
+        (6.0, 0.44696076, 0.49953147),
+        (6.0 + 0.0j, 0.44696076, 0.49953147),
+        (6.0j, -0.44696076j, 0.49953147j),
+        (-6.0 + 0.0j, -0.44696076, -0.49953147),
+        (-6.0j, 0.44696076j, -0.49953147j),
+        # inf
+        (np.inf, 0.5, 0.5),
+        (-np.inf, -0.5, -0.5),
+    ])
+    def test_fresnel_values(self, z, s, c):
+        frs = array(special.fresnel(z))
+        assert_allclose(frs, array([s, c]), atol=1.5e-8, rtol=0)
+
+    # values from pg 329  Table 7.11 of A & S
+    #  slightly corrected in 4th decimal place
+    def test_fresnel_zeros(self):
+        szo, czo = special.fresnel_zeros(5)
+        assert_allclose(szo, array([2.0093+0.2885j,
+                                    2.8335+0.2443j,
+                                    3.4675+0.2185j,
+                                    4.0026+0.2009j,
+                                    4.4742+0.1877j]),
+                        atol=1.5e-3, rtol=0)
+        assert_allclose(czo, array([1.7437+0.3057j,
+                                    2.6515+0.2529j,
+                                    3.3204+0.2240j,
+                                    3.8757+0.2047j,
+                                    4.3611+0.1907j]),
+                        atol=1.5e-3, rtol=0)
+        vals1 = special.fresnel(szo)[0]
+        vals2 = special.fresnel(czo)[1]
+        assert_allclose(vals1, 0, atol=1.5e-14, rtol=0)
+        assert_allclose(vals2, 0, atol=1.5e-14, rtol=0)
+
+    def test_fresnelc_zeros(self):
+        szo, czo = special.fresnel_zeros(6)
+        frc = special.fresnelc_zeros(6)
+        assert_allclose(frc, czo, atol=1.5e-12, rtol=0)
+
+    def test_fresnels_zeros(self):
+        szo, czo = special.fresnel_zeros(5)
+        frs = special.fresnels_zeros(5)
+        assert_allclose(frs, szo, atol=1.5e-12, rtol=0)
+
+
+class TestGamma:
+    def test_gamma(self):
+        gam = special.gamma(5)
+        assert_equal(gam,24.0)
+
+    def test_gammaln(self):
+        gamln = special.gammaln(3)
+        lngam = log(special.gamma(3))
+        assert_allclose(gamln, lngam, atol=1.5e-8, rtol=0)
+
+    def test_gammainccinv(self):
+        gccinv = special.gammainccinv(.5,.5)
+        gcinv = special.gammaincinv(.5,.5)
+        assert_allclose(gccinv, gcinv, atol=1.5e-8, rtol=0)
+
+    @with_special_errors
+    def test_gammaincinv(self):
+        y = special.gammaincinv(.4,.4)
+        x = special.gammainc(.4,y)
+        assert_allclose(x, 0.4, atol=1.5e-10, rtol=0)
+        y = special.gammainc(10, 0.05)
+        x = special.gammaincinv(10, 2.5715803516000736e-20)
+        assert_allclose(0.05, x, atol=1.5e-10, rtol=0)
+        assert_allclose(y, 2.5715803516000736e-20, atol=1.5e-10, rtol=0)
+        x = special.gammaincinv(50, 8.20754777388471303050299243573393e-18)
+        assert_allclose(11.0, x, atol=1.5e-10, rtol=0)
+
+    @with_special_errors
+    def test_975(self):
+        # Regression test for ticket #975 -- switch point in algorithm
+        # check that things work OK at the point, immediately next floats
+        # around it, and a bit further away
+        pts = [0.25,
+               np.nextafter(0.25, 0), 0.25 - 1e-12,
+               np.nextafter(0.25, 1), 0.25 + 1e-12]
+        for pt in pts:
+            y = special.gammaincinv(.4, pt)
+            x = special.gammainc(0.4, y)
+            assert_allclose(x, pt, rtol=1e-12)
+
+    def test_rgamma(self):
+        rgam = special.rgamma(8)
+        rlgam = 1/special.gamma(8)
+        assert_allclose(rgam, rlgam, atol=1.5e-8, rtol=0)
+
+    def test_infinity(self):
+        assert_equal(special.rgamma(-1), 0)
+
+    @pytest.mark.parametrize(
+        "x,expected",
+        [
+            # infinities
+            ([-np.inf, np.inf], [np.nan, np.inf]),
+            # negative and positive zero
+            ([-0.0, 0.0], [-np.inf, np.inf]),
+            # small poles
+            (range(-32, 0), np.full(32, np.nan)),
+            # medium sized poles
+            (range(-1024, -32, 99), np.full(11, np.nan)),
+            # large pole
+            ([-4.141512231792294e+16], [np.nan]),
+        ]
+    )
+    def test_poles(self, x, expected):
+        assert_array_equal(special.gamma(x), expected)
+
+
+class TestHankel:
+
+    def test_negv1(self):
+        assert_allclose(special.hankel1(-3, 2), -special.hankel1(3, 2),
+                        atol=1.5e-14, rtol=0)
+
+    def test_hankel1(self):
+        hank1 = special.hankel1(1,.1)
+        hankrl = (special.jv(1,.1) + special.yv(1,.1)*1j)
+        assert_allclose(hank1, hankrl, atol=1.5e-8, rtol=0)
+
+    def test_negv1e(self):
+        assert_allclose(special.hankel1e(-3, 2), -special.hankel1e(3, 2),
+                        atol=1.5e-14, rtol=0)
+
+    def test_hankel1e(self):
+        hank1e = special.hankel1e(1,.1)
+        hankrle = special.hankel1(1,.1)*exp(-.1j)
+        assert_allclose(hank1e, hankrle, atol=1.5e-8, rtol=0)
+
+    def test_negv2(self):
+        assert_allclose(special.hankel2(-3, 2), -special.hankel2(3, 2),
+                        atol=1.5e-14, rtol=0)
+
+    def test_hankel2(self):
+        hank2 = special.hankel2(1,.1)
+        hankrl2 = (special.jv(1,.1) - special.yv(1,.1)*1j)
+        assert_allclose(hank2, hankrl2, atol=1.5e-8, rtol=0)
+
+    def test_neg2e(self):
+        assert_allclose(special.hankel2e(-3, 2), -special.hankel2e(3, 2),
+                        atol=1.5e-14, rtol=0)
+
+    def test_hankl2e(self):
+        hank2e = special.hankel2e(1,.1)
+        hankrl2e = special.hankel2e(1,.1)
+        assert_allclose(hank2e, hankrl2e, atol=1.5e-8, rtol=0)
+
+    def test_hankel2_gh4517(self):
+        # Test edge case reported in https://github.com/scipy/scipy/issues/4517
+        res = special.hankel2(0, 0)
+        assert np.isnan(res.real)
+        assert np.isposinf(res.imag)
+
+
+class TestHyper:
+    def test_h1vp(self):
+        h1 = special.h1vp(1,.1)
+        h1real = (special.jvp(1,.1) + special.yvp(1,.1)*1j)
+        assert_allclose(h1, h1real, atol=1.5e-8, rtol=0)
+
+    def test_h2vp(self):
+        h2 = special.h2vp(1,.1)
+        h2real = (special.jvp(1,.1) - special.yvp(1,.1)*1j)
+        assert_allclose(h2, h2real, atol=1.5e-8, rtol=0)
+
+    def test_hyp0f1(self):
+        # scalar input
+        assert_allclose(special.hyp0f1(2.5, 0.5), 1.21482702689997, rtol=1e-12)
+        assert_allclose(special.hyp0f1(2.5, 0), 1.0, rtol=1e-15)
+
+        # float input, expected values match mpmath
+        x = special.hyp0f1(3.0, [-1.5, -1, 0, 1, 1.5])
+        expected = np.array([0.58493659229143, 0.70566805723127, 1.0,
+                             1.37789689539747, 1.60373685288480])
+        assert_allclose(x, expected, rtol=1e-12)
+
+        # complex input
+        x = special.hyp0f1(3.0, np.array([-1.5, -1, 0, 1, 1.5]) + 0.j)
+        assert_allclose(x, expected.astype(complex), rtol=1e-12)
+
+        # test broadcasting
+        x1 = [0.5, 1.5, 2.5]
+        x2 = [0, 1, 0.5]
+        x = special.hyp0f1(x1, x2)
+        expected = [1.0, 1.8134302039235093, 1.21482702689997]
+        assert_allclose(x, expected, rtol=1e-12)
+        x = special.hyp0f1(np.vstack([x1] * 2), x2)
+        assert_allclose(x, np.vstack([expected] * 2), rtol=1e-12)
+        assert_raises(ValueError, special.hyp0f1,
+                      np.vstack([x1] * 3), [0, 1])
+
+    def test_hyp0f1_gh5764(self):
+        # Just checks the point that failed; there's a more systematic
+        # test in test_mpmath
+        res = special.hyp0f1(0.8, 0.5 + 0.5*1J)
+        # The expected value was generated using mpmath
+        assert_allclose(res, 1.6139719776441115 + 1J*0.80893054061790665,
+                        atol=1.5e-7, rtol=0)
+
+    def test_hyp1f1(self):
+        hyp1 = special.hyp1f1(.1,.1,.3)
+        assert_allclose(hyp1, 1.3498588075760032, atol=1.5e-7, rtol=0)
+
+        # test contributed by Moritz Deger (2008-05-29)
+        # https://github.com/scipy/scipy/issues/1186 (Trac #659)
+
+        # reference data obtained from mathematica [ a, b, x, m(a,b,x)]:
+        # produced with test_hyp1f1.nb
+        ref_data = array([
+            [-8.38132975e+00, -1.28436461e+01, -2.91081397e+01, 1.04178330e+04],
+            [2.91076882e+00, -6.35234333e+00, -1.27083993e+01, 6.68132725e+00],
+            [-1.42938258e+01, 1.80869131e-01, 1.90038728e+01, 1.01385897e+05],
+            [5.84069088e+00, 1.33187908e+01, 2.91290106e+01, 1.59469411e+08],
+            [-2.70433202e+01, -1.16274873e+01, -2.89582384e+01, 1.39900152e+24],
+            [4.26344966e+00, -2.32701773e+01, 1.91635759e+01, 6.13816915e+21],
+            [1.20514340e+01, -3.40260240e+00, 7.26832235e+00, 1.17696112e+13],
+            [2.77372955e+01, -1.99424687e+00, 3.61332246e+00, 3.07419615e+13],
+            [1.50310939e+01, -2.91198675e+01, -1.53581080e+01, -3.79166033e+02],
+            [1.43995827e+01, 9.84311196e+00, 1.93204553e+01, 2.55836264e+10],
+            [-4.08759686e+00, 1.34437025e+01, -1.42072843e+01, 1.70778449e+01],
+            [8.05595738e+00, -1.31019838e+01, 1.52180721e+01, 3.06233294e+21],
+            [1.81815804e+01, -1.42908793e+01, 9.57868793e+00, -2.84771348e+20],
+            [-2.49671396e+01, 1.25082843e+01, -1.71562286e+01, 2.36290426e+07],
+            [2.67277673e+01, 1.70315414e+01, 6.12701450e+00, 7.77917232e+03],
+            [2.49565476e+01, 2.91694684e+01, 6.29622660e+00, 2.35300027e+02],
+            [6.11924542e+00, -1.59943768e+00, 9.57009289e+00, 1.32906326e+11],
+            [-1.47863653e+01, 2.41691301e+01, -1.89981821e+01, 2.73064953e+03],
+            [2.24070483e+01, -2.93647433e+00, 8.19281432e+00, -6.42000372e+17],
+            [8.04042600e-01, 1.82710085e+01, -1.97814534e+01, 5.48372441e-01],
+            [1.39590390e+01, 1.97318686e+01, 2.37606635e+00, 5.51923681e+00],
+            [-4.66640483e+00, -2.00237930e+01, 7.40365095e+00, 4.50310752e+00],
+            [2.76821999e+01, -6.36563968e+00, 1.11533984e+01, -9.28725179e+23],
+            [-2.56764457e+01, 1.24544906e+00, 1.06407572e+01, 1.25922076e+01],
+            [3.20447808e+00, 1.30874383e+01, 2.26098014e+01, 2.03202059e+04],
+            [-1.24809647e+01, 4.15137113e+00, -2.92265700e+01, 2.39621411e+08],
+            [2.14778108e+01, -2.35162960e+00, -1.13758664e+01, 4.46882152e-01],
+            [-9.85469168e+00, -3.28157680e+00, 1.67447548e+01, -1.07342390e+07],
+            [1.08122310e+01, -2.47353236e+01, -1.15622349e+01, -2.91733796e+03],
+            [-2.67933347e+01, -3.39100709e+00, 2.56006986e+01, -5.29275382e+09],
+            [-8.60066776e+00, -8.02200924e+00, 1.07231926e+01, 1.33548320e+06],
+            [-1.01724238e-01, -1.18479709e+01, -2.55407104e+01, 1.55436570e+00],
+            [-3.93356771e+00, 2.11106818e+01, -2.57598485e+01, 2.13467840e+01],
+            [3.74750503e+00, 1.55687633e+01, -2.92841720e+01, 1.43873509e-02],
+            [6.99726781e+00, 2.69855571e+01, -1.63707771e+01, 3.08098673e-02],
+            [-2.31996011e+01, 3.47631054e+00, 9.75119815e-01, 1.79971073e-02],
+            [2.38951044e+01, -2.91460190e+01, -2.50774708e+00, 9.56934814e+00],
+            [1.52730825e+01, 5.77062507e+00, 1.21922003e+01, 1.32345307e+09],
+            [1.74673917e+01, 1.89723426e+01, 4.94903250e+00, 9.90859484e+01],
+            [1.88971241e+01, 2.86255413e+01, 5.52360109e-01, 1.44165360e+00],
+            [1.02002319e+01, -1.66855152e+01, -2.55426235e+01, 6.56481554e+02],
+            [-1.79474153e+01, 1.22210200e+01, -1.84058212e+01, 8.24041812e+05],
+            [-1.36147103e+01, 1.32365492e+00, -7.22375200e+00, 9.92446491e+05],
+            [7.57407832e+00, 2.59738234e+01, -1.34139168e+01, 3.64037761e-02],
+            [2.21110169e+00, 1.28012666e+01, 1.62529102e+01, 1.33433085e+02],
+            [-2.64297569e+01, -1.63176658e+01, -1.11642006e+01, -2.44797251e+13],
+            [-2.46622944e+01, -3.02147372e+00, 8.29159315e+00, -3.21799070e+05],
+            [-1.37215095e+01, -1.96680183e+01, 2.91940118e+01, 3.21457520e+12],
+            [-5.45566105e+00, 2.81292086e+01, 1.72548215e-01, 9.66973000e-01],
+            [-1.55751298e+00, -8.65703373e+00, 2.68622026e+01, -3.17190834e+16],
+            [2.45393609e+01, -2.70571903e+01, 1.96815505e+01, 1.80708004e+37],
+            [5.77482829e+00, 1.53203143e+01, 2.50534322e+01, 1.14304242e+06],
+            [-1.02626819e+01, 2.36887658e+01, -2.32152102e+01, 7.28965646e+02],
+            [-1.30833446e+00, -1.28310210e+01, 1.87275544e+01, -9.33487904e+12],
+            [5.83024676e+00, -1.49279672e+01, 2.44957538e+01, -7.61083070e+27],
+            [-2.03130747e+01, 2.59641715e+01, -2.06174328e+01, 4.54744859e+04],
+            [1.97684551e+01, -2.21410519e+01, -2.26728740e+01, 3.53113026e+06],
+            [2.73673444e+01, 2.64491725e+01, 1.57599882e+01, 1.07385118e+07],
+            [5.73287971e+00, 1.21111904e+01, 1.33080171e+01, 2.63220467e+03],
+            [-2.82751072e+01, 2.08605881e+01, 9.09838900e+00, -6.60957033e-07],
+            [1.87270691e+01, -1.74437016e+01, 1.52413599e+01, 6.59572851e+27],
+            [6.60681457e+00, -2.69449855e+00, 9.78972047e+00, -2.38587870e+12],
+            [1.20895561e+01, -2.51355765e+01, 2.30096101e+01, 7.58739886e+32],
+            [-2.44682278e+01, 2.10673441e+01, -1.36705538e+01, 4.54213550e+04],
+            [-4.50665152e+00, 3.72292059e+00, -4.83403707e+00, 2.68938214e+01],
+            [-7.46540049e+00, -1.08422222e+01, -1.72203805e+01, -2.09402162e+02],
+            [-2.00307551e+01, -7.50604431e+00, -2.78640020e+01, 4.15985444e+19],
+            [1.99890876e+01, 2.20677419e+01, -2.51301778e+01, 1.23840297e-09],
+            [2.03183823e+01, -7.66942559e+00, 2.10340070e+01, 1.46285095e+31],
+            [-2.90315825e+00, -2.55785967e+01, -9.58779316e+00, 2.65714264e-01],
+            [2.73960829e+01, -1.80097203e+01, -2.03070131e+00, 2.52908999e+02],
+            [-2.11708058e+01, -2.70304032e+01, 2.48257944e+01, 3.09027527e+08],
+            [2.21959758e+01, 4.00258675e+00, -1.62853977e+01, -9.16280090e-09],
+            [1.61661840e+01, -2.26845150e+01, 2.17226940e+01, -8.24774394e+33],
+            [-3.35030306e+00, 1.32670581e+00, 9.39711214e+00, -1.47303163e+01],
+            [7.23720726e+00, -2.29763909e+01, 2.34709682e+01, -9.20711735e+29],
+            [2.71013568e+01, 1.61951087e+01, -7.11388906e-01, 2.98750911e-01],
+            [8.40057933e+00, -7.49665220e+00, 2.95587388e+01, 6.59465635e+29],
+            [-1.51603423e+01, 1.94032322e+01, -7.60044357e+00, 1.05186941e+02],
+            [-8.83788031e+00, -2.72018313e+01, 1.88269907e+00, 1.81687019e+00],
+            [-1.87283712e+01, 5.87479570e+00, -1.91210203e+01, 2.52235612e+08],
+            [-5.61338513e-01, 2.69490237e+01, 1.16660111e-01, 9.97567783e-01],
+            [-5.44354025e+00, -1.26721408e+01, -4.66831036e+00, 1.06660735e-01],
+            [-2.18846497e+00, 2.33299566e+01, 9.62564397e+00, 3.03842061e-01],
+            [6.65661299e+00, -2.39048713e+01, 1.04191807e+01, 4.73700451e+13],
+            [-2.57298921e+01, -2.60811296e+01, 2.74398110e+01, -5.32566307e+11],
+            [-1.11431826e+01, -1.59420160e+01, -1.84880553e+01, -1.01514747e+02],
+            [6.50301931e+00, 2.59859051e+01, -2.33270137e+01, 1.22760500e-02],
+            [-1.94987891e+01, -2.62123262e+01, 3.90323225e+00, 1.71658894e+01],
+            [7.26164601e+00, -1.41469402e+01, 2.81499763e+01, -2.50068329e+31],
+            [-1.52424040e+01, 2.99719005e+01, -2.85753678e+01, 1.31906693e+04],
+            [5.24149291e+00, -1.72807223e+01, 2.22129493e+01, 2.50748475e+25],
+            [3.63207230e-01, -9.54120862e-02, -2.83874044e+01, 9.43854939e-01],
+            [-2.11326457e+00, -1.25707023e+01, 1.17172130e+00, 1.20812698e+00],
+            [2.48513582e+00, 1.03652647e+01, -1.84625148e+01, 6.47910997e-02],
+            [2.65395942e+01, 2.74794672e+01, 1.29413428e+01, 2.89306132e+05],
+            [-9.49445460e+00, 1.59930921e+01, -1.49596331e+01, 3.27574841e+02],
+            [-5.89173945e+00, 9.96742426e+00, 2.60318889e+01, -3.15842908e-01],
+            [-1.15387239e+01, -2.21433107e+01, -2.17686413e+01, 1.56724718e-01],
+            [-5.30592244e+00, -2.42752190e+01, 1.29734035e+00, 1.31985534e+00]
+        ])
+
+        for a,b,c,expected in ref_data:
+            result = special.hyp1f1(a,b,c)
+            assert_(abs(expected - result)/expected < 1e-4)
+
+    def test_hyp1f1_gh2957(self):
+        hyp1 = special.hyp1f1(0.5, 1.5, -709.7827128933)
+        hyp2 = special.hyp1f1(0.5, 1.5, -709.7827128934)
+        assert_allclose(hyp1, hyp2, atol=1.5e-12, rtol=0)
+
+    def test_hyp1f1_gh2282(self):
+        hyp = special.hyp1f1(0.5, 1.5, -1000)
+        assert_allclose(hyp, 0.028024956081989643, atol=1.5e-12, rtol=0)
+
+    def test_hyp2f1(self):
+        # a collection of special cases taken from AMS 55
+        values = [
+            [0.5, 1, 1.5, 0.2**2, 0.5/0.2*log((1+0.2)/(1-0.2))],
+            [0.5, 1, 1.5, -0.2**2, 1./0.2*arctan(0.2)],
+            [1, 1, 2, 0.2, -1/0.2*log(1-0.2)],
+            [3, 3.5, 1.5, 0.2**2, 0.5/0.2/(-5)*((1+0.2)**(-5)-(1-0.2)**(-5))],
+            [-3, 3, 0.5, sin(0.2)**2, cos(2*3*0.2)],
+            [3, 4, 8, 1,
+             special.gamma(8) * special.gamma(8-4-3)
+             / special.gamma(8-3) / special.gamma(8-4)],
+            [3, 2, 3-2+1, -1,
+             1./2**3*sqrt(pi) * special.gamma(1+3-2)
+             / special.gamma(1+0.5*3-2) / special.gamma(0.5+0.5*3)],
+            [5, 2, 5-2+1, -1,
+             1./2**5*sqrt(pi) * special.gamma(1+5-2)
+             / special.gamma(1+0.5*5-2) / special.gamma(0.5+0.5*5)],
+            [4, 0.5+4, 1.5-2*4, -1./3,
+             (8./9)**(-2*4)*special.gamma(4./3) * special.gamma(1.5-2*4)
+             / special.gamma(3./2) / special.gamma(4./3-2*4)],
+            # and some others
+            # ticket #424
+            [1.5, -0.5, 1.0, -10.0, 4.1300097765277476484],
+            # negative integer a or b, with c-a-b integer and x > 0.9
+            [-2,3,1,0.95,0.715],
+            [2,-3,1,0.95,-0.007],
+            [-6,3,1,0.95,0.0000810625],
+            [2,-5,1,0.95,-0.000029375],
+            # huge negative integers
+            (10, -900, 10.5, 0.99, 1.91853705796607664803709475658e-24),
+            (10, -900, -10.5, 0.99, 3.54279200040355710199058559155e-18),
+        ]
+        for i, (a, b, c, x, v) in enumerate(values):
+            cv = special.hyp2f1(a, b, c, x)
+            assert_allclose(cv, v, atol=1.5e-8, rtol=0, err_msg=f'test #{i}')
+
+    def test_hyperu(self):
+        val1 = special.hyperu(1,0.1,100)
+        assert_allclose(val1, 0.0098153, atol=1.5e-7, rtol=0)
+        a,b = [0.3,0.6,1.2,-2.7],[1.5,3.2,-0.4,-3.2]
+        a,b = asarray(a), asarray(b)
+        z = 0.5
+        hypu = special.hyperu(a,b,z)
+        hprl = (pi/sin(pi*b))*(special.hyp1f1(a,b,z) /
+                               (special.gamma(1+a-b)*special.gamma(b)) -
+                               z**(1-b)*special.hyp1f1(1+a-b,2-b,z)
+                               / (special.gamma(a)*special.gamma(2-b)))
+        assert_allclose(hypu, hprl, atol=1.5e-12, rtol=0)
+
+    def test_hyperu_gh2287(self):
+        assert_allclose(special.hyperu(1, 1.5, 20.2), 0.048360918656699191,
+                        atol=1.5e-12, rtol=0)
+
+
+class TestBessel:
+    def test_itj0y0(self):
+        it0 = array(special.itj0y0(.2))
+        assert_allclose(it0, array([0.19933433254006822, -0.34570883800412566]),
+                        atol=1.5e-8, rtol=0)
+
+    def test_it2j0y0(self):
+        it2 = array(special.it2j0y0(.2))
+        assert_allclose(it2, array([0.0049937546274601858, -0.43423067011231614]),
+                        atol=1.5e-8, rtol=0)
+
+    def test_negv_iv(self):
+        assert_equal(special.iv(3,2), special.iv(-3,2))
+
+    def test_j0(self):
+        oz = special.j0(.1)
+        ozr = special.jn(0,.1)
+        assert_allclose(oz, ozr, atol=1.5e-8, rtol=0)
+
+    def test_j1(self):
+        o1 = special.j1(.1)
+        o1r = special.jn(1,.1)
+        assert_allclose(o1, o1r, atol=1.5e-8, rtol=0)
+
+    def test_jn(self):
+        jnnr = special.jn(1,.2)
+        assert_allclose(jnnr, 0.099500832639235995, atol=1.5e-8, rtol=0)
+
+    def test_negv_jv(self):
+        assert_allclose(special.jv(-3, 2), -special.jv(3, 2), atol=1.5e-14, rtol=0)
+
+    def test_jv(self):
+        values = [[0, 0.1, 0.99750156206604002],
+                  [2./3, 1e-8, 0.3239028506761532e-5],
+                  [2./3, 1e-10, 0.1503423854873779e-6],
+                  [3.1, 1e-10, 0.1711956265409013e-32],
+                  [2./3, 4.0, -0.2325440850267039],
+                  ]
+        for i, (v, x, y) in enumerate(values):
+            yc = special.jv(v, x)
+            assert_allclose(yc, y, atol=1.5e-8, rtol=0, err_msg=f'test #{i}')
+
+    def test_negv_jve(self):
+        assert_allclose(special.jve(-3, 2), -special.jve(3, 2),
+                        atol=1.5e-14, rtol=0)
+
+    def test_jve(self):
+        jvexp = special.jve(1,.2)
+        assert_allclose(jvexp, 0.099500832639235995, atol=1.5e-8, rtol=0)
+        jvexp1 = special.jve(1,.2+1j)
+        z = .2+1j
+        jvexpr = special.jv(1,z)*exp(-abs(z.imag))
+        assert_allclose(jvexp1, jvexpr, atol=1.5e-8, rtol=0)
+
+    def test_jn_zeros(self):
+        jn0 = special.jn_zeros(0,5)
+        jn1 = special.jn_zeros(1,5)
+        assert_allclose(jn0, array([2.4048255577,
+                                    5.5200781103,
+                                    8.6537279129,
+                                    11.7915344391,
+                                    14.9309177086]),
+                        atol=1.5e-4, rtol=0)
+        assert_allclose(jn1, array([3.83171,
+                                    7.01559,
+                                    10.17347,
+                                    13.32369,
+                                    16.47063]),
+                        atol=1.5e-4, rtol=0)
+
+        jn102 = special.jn_zeros(102,5)
+        assert_allclose(jn102, array([110.89174935992040343,
+                                       117.83464175788308398,
+                                       123.70194191713507279,
+                                       129.02417238949092824,
+                                       134.00114761868422559]), rtol=1e-13)
+
+        jn301 = special.jn_zeros(301,5)
+        assert_allclose(jn301, array([313.59097866698830153,
+                                       323.21549776096288280,
+                                       331.22338738656748796,
+                                       338.39676338872084500,
+                                       345.03284233056064157]), rtol=1e-13)
+
+    def test_jn_zeros_slow(self):
+        jn0 = special.jn_zeros(0, 300)
+        assert_allclose(jn0[260-1], 816.02884495068867280, rtol=1e-13)
+        assert_allclose(jn0[280-1], 878.86068707124422606, rtol=1e-13)
+        assert_allclose(jn0[300-1], 941.69253065317954064, rtol=1e-13)
+
+        jn10 = special.jn_zeros(10, 300)
+        assert_allclose(jn10[260-1], 831.67668514305631151, rtol=1e-13)
+        assert_allclose(jn10[280-1], 894.51275095371316931, rtol=1e-13)
+        assert_allclose(jn10[300-1], 957.34826370866539775, rtol=1e-13)
+
+        jn3010 = special.jn_zeros(3010,5)
+        assert_allclose(jn3010, array([3036.86590780927,
+                                        3057.06598526482,
+                                        3073.66360690272,
+                                        3088.37736494778,
+                                        3101.86438139042]), rtol=1e-8)
+
+    def test_jnjnp_zeros(self):
+        jn = special.jn
+
+        def jnp(n, x):
+            return (jn(n-1,x) - jn(n+1,x))/2
+        for nt in range(1, 30):
+            z, n, m, t = special.jnjnp_zeros(nt)
+            for zz, nn, tt in zip(z, n, t):
+                if tt == 0:
+                    assert_allclose(jn(nn, zz), 0, atol=1e-6)
+                elif tt == 1:
+                    assert_allclose(jnp(nn, zz), 0, atol=1e-6)
+                else:
+                    raise AssertionError(f"Invalid t return for nt={nt}")
+
+    def test_jnp_zeros(self):
+        jnp = special.jnp_zeros(1,5)
+        assert_allclose(jnp, array([1.84118,
+                                    5.33144,
+                                    8.53632,
+                                    11.70600,
+                                    14.86359]),
+                        atol=1.5e-4, rtol=0)
+        jnp = special.jnp_zeros(443,5)
+        assert_allclose(special.jvp(443, jnp), 0, atol=1e-15)
+
+    def test_jnyn_zeros(self):
+        jnz = special.jnyn_zeros(1, 5)
+        assert_allclose(jnz, (array([3.83171,
+                                     7.01559,
+                                     10.17347,
+                                     13.32369,
+                                     16.47063]),
+                              array([1.84118,
+                                     5.33144,
+                                     8.53632,
+                                     11.70600,
+                                     14.86359]),
+                              array([2.19714,
+                                     5.42968,
+                                     8.59601,
+                                     11.74915,
+                                     14.89744]),
+                              array([3.68302,
+                                     6.94150,
+                                     10.12340,
+                                     13.28576,
+                                     16.44006])),
+                        atol=1.5e-5, rtol=0)
+
+    def test_jvp(self):
+        jvprim = special.jvp(2,2)
+        jv0 = (special.jv(1,2)-special.jv(3,2))/2
+        assert_allclose(jvprim, jv0, atol=1.5e-10, rtol=0)
+
+    def test_k0(self):
+        ozk = special.k0(.1)
+        ozkr = special.kv(0,.1)
+        assert_allclose(ozk,ozkr, atol=1.5e-8, rtol=0)
+
+    def test_k0e(self):
+        ozke = special.k0e(.1)
+        ozker = special.kve(0,.1)
+        assert_allclose(ozke, ozker, atol=1.5e-8, rtol=0)
+
+    def test_k1(self):
+        o1k = special.k1(.1)
+        o1kr = special.kv(1,.1)
+        assert_allclose(o1k,o1kr, atol=1.5e-8, rtol=0)
+
+    def test_k1e(self):
+        o1ke = special.k1e(.1)
+        o1ker = special.kve(1,.1)
+        assert_allclose(o1ke, o1ker, atol=1.5e-8, rtol=0)
+
+    def test_jacobi(self):
+        a = 5*np.random.random() - 1
+        b = 5*np.random.random() - 1
+        P0 = special.jacobi(0,a,b)
+        P1 = special.jacobi(1,a,b)
+        P2 = special.jacobi(2,a,b)
+        P3 = special.jacobi(3,a,b)
+
+        assert_allclose(P0.c, [1], atol=1.5e-13, rtol=0)
+        assert_allclose(P1.c, array([a + b + 2, a - b]) / 2.0,
+                        atol=1.5e-13, rtol=0)
+        cp = [(a+b+3)*(a+b+4), 4*(a+b+3)*(a+2), 4*(a+1)*(a+2)]
+        p2c = [cp[0],cp[1]-2*cp[0],cp[2]-cp[1]+cp[0]]
+        assert_allclose(P2.c, array(p2c) / 8.0, atol=1.5e-13, rtol=0)
+        cp = [(a+b+4)*(a+b+5)*(a+b+6),6*(a+b+4)*(a+b+5)*(a+3),
+              12*(a+b+4)*(a+2)*(a+3),8*(a+1)*(a+2)*(a+3)]
+        p3c = [cp[0],cp[1]-3*cp[0],cp[2]-2*cp[1]+3*cp[0],cp[3]-cp[2]+cp[1]-cp[0]]
+        assert_allclose(P3.c, array(p3c) / 48.0, atol=1.5e-13, rtol=0)
+
+    def test_kn(self):
+        kn1 = special.kn(0,.2)
+        assert_allclose(kn1, 1.7527038555281462, atol=1.5e-8, rtol=0)
+
+    def test_negv_kv(self):
+        assert_equal(special.kv(3.0, 2.2), special.kv(-3.0, 2.2))
+
+    def test_kv0(self):
+        kv0 = special.kv(0,.2)
+        assert_allclose(kv0, 1.7527038555281462, atol=1.5e-10, rtol=0)
+
+    def test_kv1(self):
+        kv1 = special.kv(1,0.2)
+        assert_allclose(kv1, 4.775972543220472, atol=1.5e-10, rtol=0)
+
+    def test_kv2(self):
+        kv2 = special.kv(2,0.2)
+        assert_allclose(kv2, 49.51242928773287, atol=1.5e-10, rtol=0)
+
+    def test_kn_largeorder(self):
+        assert_allclose(special.kn(32, 1), 1.7516596664574289e+43)
+
+    def test_kv_largearg(self):
+        assert_equal(special.kv(0, 1e19), 0)
+
+    def test_negv_kve(self):
+        assert_equal(special.kve(3.0, 2.2), special.kve(-3.0, 2.2))
+
+    def test_kve(self):
+        kve1 = special.kve(0,.2)
+        kv1 = special.kv(0,.2)*exp(.2)
+        assert_allclose(kve1, kv1, atol=1.5e-8, rtol=0)
+        z = .2+1j
+        kve2 = special.kve(0,z)
+        kv2 = special.kv(0,z)*exp(z)
+        assert_allclose(kve2, kv2, atol=1.5e-8, rtol=0)
+
+    def test_kvp_v0n1(self):
+        z = 2.2
+        assert_allclose(-special.kv(1, z), special.kvp(0, z, n=1),
+                        atol=1.5e-10, rtol=0)
+
+    def test_kvp_n1(self):
+        v = 3.
+        z = 2.2
+        xc = -special.kv(v+1,z) + v/z*special.kv(v,z)
+        x = special.kvp(v,z, n=1)
+        # this function (kvp) is broken
+        assert_allclose(xc, x, atol=1.5e-10, rtol=0)
+
+    def test_kvp_n2(self):
+        v = 3.
+        z = 2.2
+        xc = (z**2+v**2-v)/z**2 * special.kv(v,z) + special.kv(v+1,z)/z
+        x = special.kvp(v, z, n=2)
+        assert_allclose(xc, x, atol=1.5e-10, rtol=0)
+
+    def test_y0(self):
+        oz = special.y0(.1)
+        ozr = special.yn(0,.1)
+        assert_allclose(oz, ozr, atol=1.5e-8, rtol=0)
+
+    def test_y1(self):
+        o1 = special.y1(.1)
+        o1r = special.yn(1,.1)
+        assert_allclose(o1,o1r, atol=1.5e-8, rtol=0)
+
+    def test_y0_zeros(self):
+        yo,ypo = special.y0_zeros(2)
+        zo,zpo = special.y0_zeros(2,complex=1)
+        all = r_[yo,zo]
+        allval = r_[ypo,zpo]
+        assert_allclose(abs(special.yv(0.0, all)), 0.0, atol=1.5e-11, rtol=0)
+        assert_allclose(abs(special.yv(1, all) - allval), 0.0, atol=1.5e-11, rtol=0)
+
+    def test_y1_zeros(self):
+        y1 = special.y1_zeros(1)
+        assert_allclose(y1, (array([2.19714]), array([0.52079])),
+                        atol=1.5e-5, rtol=0)
+
+    def test_y1p_zeros(self):
+        y1p = special.y1p_zeros(1,complex=1)
+        assert_allclose(y1p, (array([0.5768+0.904j]), array([-0.7635+0.5892j])),
+                        atol=1.5e-3, rtol=0)
+
+    def test_yn_zeros(self):
+        an = special.yn_zeros(4,2)
+        assert_allclose(an, array([5.64515, 9.36162]), atol=1.5e-5, rtol=0)
+        an = special.yn_zeros(443,5)
+        assert_allclose(an, [450.13573091578090314,
+                             463.05692376675001542,
+                             472.80651546418663566,
+                             481.27353184725625838,
+                             488.98055964441374646],
+                        rtol=1e-15,)
+
+    def test_ynp_zeros(self):
+        ao = special.ynp_zeros(0,2)
+        assert_allclose(ao, array([2.19714133, 5.42968104]), atol=1.5e-6, rtol=0)
+        ao = special.ynp_zeros(43,5)
+        assert_allclose(special.yvp(43, ao), 0, atol=1e-15)
+        ao = special.ynp_zeros(443,5)
+        assert_allclose(special.yvp(443, ao), 0, atol=1e-9)
+
+    def test_ynp_zeros_large_order(self):
+        ao = special.ynp_zeros(443,5)
+        assert_allclose(special.yvp(443, ao), 0, atol=1e-14)
+
+    def test_yn(self):
+        yn2n = special.yn(1,.2)
+        assert_allclose(yn2n, -3.3238249881118471, atol=1.5e-8, rtol=0)
+
+    def test_yn_gh_20405(self):
+        # Enforce correct asymptotic behavior for large n.
+        observed = cephes.yn(500, 1)
+        assert observed == -np.inf
+
+    def test_negv_yv(self):
+        assert_allclose(special.yv(-3, 2), -special.yv(3, 2),
+                        atol=1.5e-14, rtol=0)
+
+    def test_yv(self):
+        yv2 = special.yv(1,.2)
+        assert_allclose(yv2, -3.3238249881118471, atol=1.5e-8, rtol=0)
+
+    def test_negv_yve(self):
+        assert_allclose(special.yve(-3, 2), -special.yve(3, 2),
+                        atol=1.5e-14, rtol=0)
+
+    def test_yve(self):
+        yve2 = special.yve(1,.2)
+        assert_allclose(yve2, -3.3238249881118471, atol=1.5e-8, rtol=0)
+        yve2r = special.yv(1,.2+1j)*exp(-1)
+        yve22 = special.yve(1,.2+1j)
+        assert_allclose(yve22, yve2r, atol=1.5e-8, rtol=0)
+
+    def test_yvp(self):
+        yvpr = (special.yv(1,.2) - special.yv(3,.2))/2.0
+        yvp1 = special.yvp(2,.2)
+        assert_allclose(yvp1, yvpr, atol=1.5e-10, rtol=0)
+
+    def _cephes_vs_amos_points(self):
+        """Yield points at which to compare Cephes implementation to AMOS"""
+        # check several points, including large-amplitude ones
+        v = [-120, -100.3, -20., -10., -1., -.5, 0., 1., 12.49, 120., 301]
+        z = [-1300, -11, -10, -1, 1., 10., 200.5, 401., 600.5, 700.6, 1300,
+             10003]
+        yield from itertools.product(v, z)
+
+        # check half-integers; these are problematic points at least
+        # for cephes/iv
+        yield from itertools.product(0.5 + arange(-60, 60), [3.5])
+
+    def check_cephes_vs_amos(self, f1, f2, rtol=1e-11, atol=0, skip=None):
+        for v, z in self._cephes_vs_amos_points():
+            if skip is not None and skip(v, z):
+                continue
+            c1, c2, c3 = f1(v, z), f1(v,z+0j), f2(int(v), z)
+            if np.isinf(c1):
+                assert_(np.abs(c2) >= 1e300, (v, z))
+            elif np.isnan(c1):
+                assert_(c2.imag != 0, (v, z))
+            else:
+                assert_allclose(c1, c2, err_msg=(v, z), rtol=rtol, atol=atol)
+                if v == int(v):
+                    assert_allclose(c3, c2, err_msg=(v, z),
+                                     rtol=rtol, atol=atol)
+
+    @pytest.mark.xfail(platform.machine() == 'ppc64le',
+                       reason="fails on ppc64le")
+    def test_jv_cephes_vs_amos(self):
+        self.check_cephes_vs_amos(special.jv, special.jn, rtol=1e-10, atol=1e-305)
+
+    @pytest.mark.xfail(platform.machine() == 'ppc64le',
+                       reason="fails on ppc64le")
+    def test_yv_cephes_vs_amos(self):
+        self.check_cephes_vs_amos(special.yv, special.yn, rtol=1e-11, atol=1e-305)
+
+    def test_yv_cephes_vs_amos_only_small_orders(self):
+        def skipper(v, z):
+            return abs(v) > 50
+        self.check_cephes_vs_amos(special.yv, special.yn, rtol=1e-11, atol=1e-305,
+                                  skip=skipper)
+
+    def test_iv_cephes_vs_amos(self):
+        with np.errstate(all='ignore'):
+            self.check_cephes_vs_amos(special.iv, special.iv, rtol=5e-9, atol=1e-305)
+
+    @pytest.mark.slow
+    def test_iv_cephes_vs_amos_mass_test(self):
+        N = 1000000
+        np.random.seed(1)
+        v = np.random.pareto(0.5, N) * (-1)**np.random.randint(2, size=N)
+        x = np.random.pareto(0.2, N) * (-1)**np.random.randint(2, size=N)
+
+        imsk = (np.random.randint(8, size=N) == 0)
+        v[imsk] = v[imsk].astype(np.int64)
+
+        with np.errstate(all='ignore'):
+            c1 = special.iv(v, x)
+            c2 = special.iv(v, x+0j)
+
+            # deal with differences in the inf and zero cutoffs
+            c1[abs(c1) > 1e300] = np.inf
+            c2[abs(c2) > 1e300] = np.inf
+            c1[abs(c1) < 1e-300] = 0
+            c2[abs(c2) < 1e-300] = 0
+
+            dc = abs(c1/c2 - 1)
+            dc[np.isnan(dc)] = 0
+
+        k = np.argmax(dc)
+
+        # Most error apparently comes from AMOS and not our implementation;
+        # there are some problems near integer orders there
+        assert_(
+            dc[k] < 2e-7,
+            (v[k], x[k], special.iv(v[k], x[k]), special.iv(v[k], x[k]+0j))
+        )
+
+    def test_kv_cephes_vs_amos(self):
+        self.check_cephes_vs_amos(special.kv, special.kn, rtol=1e-9, atol=1e-305)
+        self.check_cephes_vs_amos(special.kv, special.kv, rtol=1e-9, atol=1e-305)
+
+    def test_ticket_623(self):
+        assert_allclose(special.jv(3, 4), 0.43017147387562193)
+        assert_allclose(special.jv(301, 1300), 0.0183487151115275)
+        assert_allclose(special.jv(301, 1296.0682), -0.0224174325312048)
+
+    def test_ticket_853(self):
+        """Negative-order Bessels"""
+        # cephes
+        assert_allclose(special.jv(-1, 1), -0.4400505857449335)
+        assert_allclose(special.jv(-2, 1), 0.1149034849319005)
+        assert_allclose(special.yv(-1, 1), 0.7812128213002887)
+        assert_allclose(special.yv(-2, 1), -1.650682606816255)
+        assert_allclose(special.iv(-1, 1), 0.5651591039924851)
+        assert_allclose(special.iv(-2, 1), 0.1357476697670383)
+        assert_allclose(special.kv(-1, 1), 0.6019072301972347)
+        assert_allclose(special.kv(-2, 1), 1.624838898635178)
+        assert_allclose(special.jv(-0.5, 1), 0.43109886801837607952)
+        assert_allclose(special.yv(-0.5, 1), 0.6713967071418031)
+        assert_allclose(special.iv(-0.5, 1), 1.231200214592967)
+        assert_allclose(special.kv(-0.5, 1), 0.4610685044478945)
+        # amos
+        assert_allclose(special.jv(-1, 1+0j), -0.4400505857449335)
+        assert_allclose(special.jv(-2, 1+0j), 0.1149034849319005)
+        assert_allclose(special.yv(-1, 1+0j), 0.7812128213002887)
+        assert_allclose(special.yv(-2, 1+0j), -1.650682606816255)
+
+        assert_allclose(special.iv(-1, 1+0j), 0.5651591039924851)
+        assert_allclose(special.iv(-2, 1+0j), 0.1357476697670383)
+        assert_allclose(special.kv(-1, 1+0j), 0.6019072301972347)
+        assert_allclose(special.kv(-2, 1+0j), 1.624838898635178)
+
+        assert_allclose(special.jv(-0.5, 1+0j), 0.43109886801837607952)
+        assert_allclose(special.jv(-0.5, 1+1j), 0.2628946385649065-0.827050182040562j)
+        assert_allclose(special.yv(-0.5, 1+0j), 0.6713967071418031)
+        assert_allclose(special.yv(-0.5, 1+1j), 0.967901282890131+0.0602046062142816j)
+
+        assert_allclose(special.iv(-0.5, 1+0j), 1.231200214592967)
+        assert_allclose(special.iv(-0.5, 1+1j), 0.77070737376928+0.39891821043561j)
+        assert_allclose(special.kv(-0.5, 1+0j), 0.4610685044478945)
+        assert_allclose(special.kv(-0.5, 1+1j), 0.06868578341999-0.38157825981268j)
+
+        assert_allclose(special.jve(-0.5,1+0.3j), special.jv(-0.5, 1+0.3j)*exp(-0.3))
+        assert_allclose(special.yve(-0.5,1+0.3j), special.yv(-0.5, 1+0.3j)*exp(-0.3))
+        assert_allclose(special.ive(-0.5,0.3+1j), special.iv(-0.5, 0.3+1j)*exp(-0.3))
+        assert_allclose(special.kve(-0.5,0.3+1j), special.kv(-0.5, 0.3+1j)*exp(0.3+1j))
+
+        assert_allclose(
+            special.hankel1(-0.5, 1+1j),
+            special.jv(-0.5, 1+1j) + 1j*special.yv(-0.5,1+1j)
+        )
+        assert_allclose(
+            special.hankel2(-0.5, 1+1j),
+            special.jv(-0.5, 1+1j) - 1j*special.yv(-0.5,1+1j)
+        )
+
+    def test_ticket_854(self):
+        """Real-valued Bessel domains"""
+        assert_(isnan(special.jv(0.5, -1)))
+        assert_(isnan(special.iv(0.5, -1)))
+        assert_(isnan(special.yv(0.5, -1)))
+        assert_(isnan(special.yv(1, -1)))
+        assert_(isnan(special.kv(0.5, -1)))
+        assert_(isnan(special.kv(1, -1)))
+        assert_(isnan(special.jve(0.5, -1)))
+        assert_(isnan(special.ive(0.5, -1)))
+        assert_(isnan(special.yve(0.5, -1)))
+        assert_(isnan(special.yve(1, -1)))
+        assert_(isnan(special.kve(0.5, -1)))
+        assert_(isnan(special.kve(1, -1)))
+        assert_(isnan(special.airye(-1)[0:2]).all(), special.airye(-1))
+        assert_(not isnan(special.airye(-1)[2:4]).any(), special.airye(-1))
+
+    def test_gh_7909(self):
+        assert_(special.kv(1.5, 0) == np.inf)
+        assert_(special.kve(1.5, 0) == np.inf)
+
+    def test_ticket_503(self):
+        """Real-valued Bessel I overflow"""
+        assert_allclose(special.iv(1, 700), 1.528500390233901e302)
+        assert_allclose(special.iv(1000, 1120), 1.301564549405821e301)
+
+    def test_iv_hyperg_poles(self):
+        assert_allclose(special.iv(-0.5, 1), 1.231200214592967)
+
+    def iv_series(self, v, z, n=200):
+        k = arange(0, n).astype(double)
+        r = (v+2*k)*log(.5*z) - special.gammaln(k+1) - special.gammaln(v+k+1)
+        r[isnan(r)] = inf
+        r = exp(r)
+        err = abs(r).max() * finfo(double).eps * n + abs(r[-1])*10
+        return r.sum(), err
+
+    def test_i0_series(self):
+        for z in [1., 10., 200.5]:
+            value, err = self.iv_series(0, z)
+            assert_allclose(special.i0(z), value, atol=err, err_msg=z)
+
+    def test_i1_series(self):
+        for z in [1., 10., 200.5]:
+            value, err = self.iv_series(1, z)
+            assert_allclose(special.i1(z), value, atol=err, err_msg=z)
+
+    def test_iv_series(self):
+        for v in [-20., -10., -1., 0., 1., 12.49, 120.]:
+            for z in [1., 10., 200.5, -1+2j]:
+                value, err = self.iv_series(v, z)
+                assert_allclose(special.iv(v, z), value, atol=err, err_msg=(v, z))
+
+    def test_i0(self):
+        values = [[0.0, 1.0],
+                  [1e-10, 1.0],
+                  [0.1, 0.9071009258],
+                  [0.5, 0.6450352706],
+                  [1.0, 0.4657596077],
+                  [2.5, 0.2700464416],
+                  [5.0, 0.1835408126],
+                  [20.0, 0.0897803119],
+                  ]
+        for i, (x, v) in enumerate(values):
+            cv = special.i0(x) * exp(-x)
+            assert_allclose(cv, v, atol=1.5e-8, rtol=0, err_msg=f'test #{i}')
+
+    def test_i0e(self):
+        oize = special.i0e(.1)
+        oizer = special.ive(0, .1)
+        assert_allclose(oize, oizer, atol=1.5e-8, rtol=0)
+
+    def test_i1(self):
+        values = [[0.0, 0.0],
+                  [1e-10, 0.4999999999500000e-10],
+                  [0.1, 0.0452984468],
+                  [0.5, 0.1564208032],
+                  [1.0, 0.2079104154],
+                  [5.0, 0.1639722669],
+                  [20.0, 0.0875062222],
+                  ]
+        for i, (x, v) in enumerate(values):
+            cv = special.i1(x) * exp(-x)
+            assert_allclose(cv, v, atol=1.5e-8, rtol=0, err_msg=f'test #{i}')
+
+    def test_i1e(self):
+        oi1e = special.i1e(.1)
+        oi1er = special.ive(1, .1)
+        assert_allclose(oi1e, oi1er, atol=1.5e-8, rtol=0)
+
+    def test_iti0k0(self):
+        iti0 = array(special.iti0k0(5))
+        assert_allclose(iti0, array([31.848667776169801, 1.5673873907283657]),
+                        atol=1.5e-5, rtol=0)
+
+    def test_it2i0k0(self):
+        it2k = special.it2i0k0(.1)
+        assert_allclose(it2k, array([0.0012503906973464409, 3.3309450354686687]),
+                        atol=1.5e-6, rtol=0)
+
+    def test_iv(self):
+        iv1 = special.iv(0,.1)*exp(-.1)
+        assert_allclose(iv1, 0.90710092578230106, atol=1.5e-10, rtol=0)
+
+    def test_negv_ive(self):
+        assert_equal(special.ive(3,2), special.ive(-3,2))
+
+    def test_ive(self):
+        ive1 = special.ive(0,.1)
+        iv1 = special.iv(0,.1)*exp(-.1)
+        assert_allclose(ive1, iv1, atol=1.5e-10, rtol=0)
+
+    def test_ivp0(self):
+        assert_allclose(special.iv(1, 2), special.ivp(0, 2), atol=1.5e-10, rtol=0)
+
+    def test_ivp(self):
+        y = (special.iv(0,2) + special.iv(2,2))/2
+        x = special.ivp(1,2)
+        assert_allclose(x, y, atol=1.5e-10, rtol=0)
+
+    @pytest.mark.parametrize("x, expected",
+        [(1e15, 6.156638646885021e-09),  # 1/sqrt(eps) < x < 1/eps
+         (1e30, -5.589003016686147e-16)  # x > 1/eps
+        ])
+    def test_gh22705(self, x, expected):
+        # reference values computed with mpmath
+        # from mpmath import mp
+        # mp.dps = 1000
+        # float(mp.besselj(0, mp.mpf('1e15')))
+        assert_allclose(special.j0(x), expected, rtol=5e-15)
+
+
+class TestLaguerre:
+    def test_laguerre(self):
+        lag0 = special.laguerre(0)
+        lag1 = special.laguerre(1)
+        lag2 = special.laguerre(2)
+        lag3 = special.laguerre(3)
+        lag4 = special.laguerre(4)
+        lag5 = special.laguerre(5)
+        assert_allclose(lag0.c, [1], atol=1.5e-13, rtol=0)
+        assert_allclose(lag1.c, [-1, 1], atol=1.5e-13, rtol=0)
+        assert_allclose(lag2.c, array([1, -4,2]) / 2.0, atol=1.5e-13, rtol=0)
+        assert_allclose(lag3.c, array([-1, 9,-18,6])/6.0, atol=1.5e-13, rtol=0)
+        assert_allclose(lag4.c, array([1, -16,72,-96,24])/24.0,
+                        atol=1.5e-13, rtol=0)
+        assert_allclose(lag5.c, array([-1, 25, -200, 600, -600, 120]) / 120.0,
+                        atol=1.5e-13, rtol=0)
+
+    def test_genlaguerre(self):
+        k = 5*np.random.random() - 0.9
+        lag0 = special.genlaguerre(0,k)
+        lag1 = special.genlaguerre(1,k)
+        lag2 = special.genlaguerre(2,k)
+        lag3 = special.genlaguerre(3,k)
+        assert_equal(lag0.c, [1])
+        assert_equal(lag1.c, [-1, k + 1])
+        assert_allclose(lag2.c, array([1, -2 * (k + 2), (k + 1.) * (k + 2.)]) / 2.0,
+                        atol=1.5e-7, rtol=0)
+        expected = array([-1,
+                          3 * (k + 3),
+                          -3 * (k + 2) * (k + 3),
+                          (k + 1) * (k + 2) * (k + 3)]) / 6.0
+        assert_allclose(lag3.c, expected, atol=1.5e-7, rtol=0)
+
+
+class TestLambda:
+    def test_lmbda(self):
+        lam = special.lmbda(1,.1)
+        lamr = (
+            array([special.jn(0,.1), 2*special.jn(1,.1)/.1]),
+            array([special.jvp(0,.1), -2*special.jv(1,.1)/.01 + 2*special.jvp(1,.1)/.1])
+        )
+        assert_allclose(lam, lamr, atol=1.5e-8, rtol=0)
+
+
+class TestLog1p:
+    def test_log1p(self):
+        l1p = (special.log1p(10), special.log1p(11), special.log1p(12))
+        l1prl = (log(11), log(12), log(13))
+        assert_allclose(l1p, l1prl, atol=1.5e-8, rtol=0)
+
+    def test_log1pmore(self):
+        l1pm = (special.log1p(1), special.log1p(1.1), special.log1p(1.2))
+        l1pmrl = (log(2),log(2.1),log(2.2))
+        assert_allclose(l1pm, l1pmrl, atol=1.5e-8, rtol=0)
+
+
+def ce_fourier_coefficient_using_integral(k, n, q):
+    """
+    Compute the Fourier coefficient of the even Mathieu function.
+    The integral definition of a Fourier coefficient is used.
+    This function is used as an alternative implementation of
+    mathieu_even_coef().
+    """
+    period = 180 if n % 2 == 0 else 360
+    # For k = 0, the factor outside the integral is (1/period).
+    # For k = 1, 2, 3, ..., the factor is (2/period).
+    c = (1/period)*quad(lambda t: special.mathieu_cem(n, q, t)[0],
+                        -period/2, period/2,
+                        weight='cos', wvar=2*np.pi*k/period, epsrel=1e-14)[0]
+    if k > 0:
+        c *= 2
+    return c
+
+
+def se_fourier_coefficient_using_integral(k, n, q):
+    """
+    Compute the Fourier coefficient of the odd Mathieu function.
+    The integral definition of a Fourier coefficient is used.
+    This function is used as an alternative implementation of
+    mathieu_odd_coef().
+    """
+    # For k == 0, the result is 0. (The test code won't call this
+    # function with k == 0, but we'll check anyway.)
+    if k == 0:
+        return 0.0
+    period = 180 if n % 2 == 0 else 360
+    c = (2/period)*quad(lambda t: special.mathieu_sem(n, q, t)[0],
+                        -period/2, period/2,
+                        weight='sin', wvar=2*np.pi*k/period, epsrel=1e-14)[0]
+    return c
+
+
+class TestMathieu:
+
+    @pytest.mark.parametrize('n, q', [(4, 3.5), (8, 4.25)])
+    def test_mathieu_even_coef_against_integral_n_even(self, n, q):
+        # Get the nonzero Fourier coefficients.  For the even Mathieu functions
+        # with even n, these are the coefficients of the cosine series. None of
+        # the coefficients are 0 for k = 0, 1, 2, 3, ...
+        A = special.mathieu_even_coef(n, q)
+        # Compare the first four nonzero Fourier coefficients to the coefficients
+        # computed using the integral definition.
+        c = [ce_fourier_coefficient_using_integral(k, n, q) for k in range(4)]
+        assert_allclose(c, A[:len(c)], rtol=1e-10)
+
+    @pytest.mark.parametrize('n, q', [(3, 3.5), (7, 2)])
+    def test_mathieu_even_coef_against_integral_n_odd(self, n, q):
+        # Get the nonzero Fourier coefficients.  For the even Mathieu functions
+        # with odd n, these are the coefficients of the cosine series. Only the
+        # coefficients c[k] for k = 1, 3, 5, 7, ... are nonzero.  These are the
+        # values returned by mathieu_even_coef(n, q).
+        A = special.mathieu_even_coef(n, q)
+        # Compare the first 4 nonzero Fourier coefficients to the coefficients
+        # computed using the integral definition.
+        c = [ce_fourier_coefficient_using_integral(k, n, q) for k in range(1, 9, 2)]
+        assert_allclose(c, A[:len(c)], rtol=1e-10)
+
+    @pytest.mark.parametrize('n, q', [(2, 3.5), (10, 2)])
+    def test_mathieu_odd_coef_against_integral_n_even(self, n, q):
+        # Get the nonzero Fourier coefficients.  For the odd Mathieu functions
+        # with even n, these are the coefficients of the sine series. Only the
+        # coefficients c[k] for k = 1, 2, 3, 4, ... are nonzero.  These are the
+        # values returned by mathieu_odd_coef(n, q).
+        B = special.mathieu_odd_coef(n, q)
+        # Compare the first 4 nonzero Fourier coefficients to the coefficients
+        # computed using the integral definition.
+        c = [se_fourier_coefficient_using_integral(k, n, q) for k in range(1, 5)]
+        assert_allclose(c, B[:len(c)], rtol=1e-10)
+
+    @pytest.mark.parametrize('n, q', [(3, 3.5), (7, 2)])
+    def test_mathieu_odd_coef_against_integral_n_odd(self, n, q):
+        # Get the nonzero Fourier coefficients.  For the odd Mathieu functions
+        # with odd n, these are the coefficients of the sine series. Only the
+        # coefficients c[k] for k = 1, 3, 5, 7, ... are nonzero.  These are the
+        # values returned by mathieu_odd_coef(n, q).
+        B = special.mathieu_odd_coef(n, q)
+        # Compare the first 4 nonzero Fourier coefficients to the coefficients
+        # computed using the integral definition.
+        c = [se_fourier_coefficient_using_integral(k, n, q) for k in range(1, 9, 2)]
+        assert_allclose(c, B[:len(c)], rtol=1e-10)
+
+
+class TestFresnelIntegral:
+
+    def test_modfresnelp(self):
+        pass
+
+    def test_modfresnelm(self):
+        pass
+
+
+class TestOblCvSeq:
+    def test_obl_cv_seq(self):
+        obl = special.obl_cv_seq(0,3,1)
+        assert_allclose(obl, array([-0.348602,
+                                    1.393206,
+                                    5.486800,
+                                    11.492120]),
+                        atol=1.5e-5, rtol=0)
+
+
+class TestParabolicCylinder:
+    def test_pbdn_seq(self):
+        pb = special.pbdn_seq(1, .1)
+        assert_allclose(pb, (array([0.9975,
+                                    0.0998]),
+                             array([-0.0499,
+                                    0.9925])),
+                        atol=1.5e-4, rtol=0)
+
+    def test_pbdv(self):
+        special.pbdv(1,.2)
+        1/2*(.2)*special.pbdv(1,.2)[0] - special.pbdv(0,.2)[0]
+
+    def test_pbdv_seq(self):
+        pbn = special.pbdn_seq(1,.1)
+        pbv = special.pbdv_seq(1,.1)
+        assert_allclose(pbv, (real(pbn[0]), real(pbn[1])), atol=1.5e-4, rtol=0)
+
+    def test_pbdv_points(self):
+        # simple case
+        eta = np.linspace(-10, 10, 5)
+        z = 2**(eta/2)*np.sqrt(np.pi)*special.rgamma(.5-.5*eta)
+        assert_allclose(special.pbdv(eta, 0.)[0], z, rtol=1e-14, atol=1e-14)
+
+        # some points
+        assert_allclose(special.pbdv(10.34, 20.44)[0], 1.3731383034455e-32, rtol=1e-12)
+        assert_allclose(special.pbdv(-9.53, 3.44)[0], 3.166735001119246e-8, rtol=1e-12)
+
+    def test_pbdv_gradient(self):
+        x = np.linspace(-4, 4, 8)[:,None]
+        eta = np.linspace(-10, 10, 5)[None,:]
+
+        p = special.pbdv(eta, x)
+        eps = 1e-7 + 1e-7*abs(x)
+        dp = (special.pbdv(eta, x + eps)[0] - special.pbdv(eta, x - eps)[0]) / eps / 2.
+        assert_allclose(p[1], dp, rtol=1e-6, atol=1e-6)
+
+    def test_pbvv_gradient(self):
+        x = np.linspace(-4, 4, 8)[:,None]
+        eta = np.linspace(-10, 10, 5)[None,:]
+
+        p = special.pbvv(eta, x)
+        eps = 1e-7 + 1e-7*abs(x)
+        dp = (special.pbvv(eta, x + eps)[0] - special.pbvv(eta, x - eps)[0]) / eps / 2.
+        assert_allclose(p[1], dp, rtol=1e-6, atol=1e-6)
+
+    def test_pbvv_seq(self):
+        res1, res2 = special.pbvv_seq(2, 3)
+        assert_allclose(res1, np.array([2.976319645712036,
+                                        1.358840996329579,
+                                        0.5501016716383508]))
+        assert_allclose(res2, np.array([3.105638472238475,
+                                        0.9380581512176672,
+                                        0.533688488872053]))
+
+
+class TestPolygamma:
+    # from Table 6.2 (pg. 271) of A&S
+    def test_polygamma(self):
+        poly2 = special.polygamma(2, 1)
+        poly3 = special.polygamma(3, 1)
+        assert_allclose(poly2, -2.4041138063, atol=1.5e-10, rtol=0)
+        assert_allclose(poly3, 6.4939394023, atol=1.5e-10, rtol=0)
+
+        # Test polygamma(0, x) == psi(x)
+        x = [2, 3, 1.1e14]
+        assert_allclose(special.polygamma(0, x), special.psi(x),
+                        atol=1.5e-7, rtol=0)
+
+        # Test broadcasting
+        n = [0, 1, 2]
+        x = [0.5, 1.5, 2.5]
+        expected = [-1.9635100260214238, 0.93480220054467933,
+                    -0.23620405164172739]
+        assert_allclose(special.polygamma(n, x), expected, atol=1.5e-7, rtol=0)
+        expected = np.vstack([expected]*2)
+        assert_allclose(special.polygamma(n, np.vstack([x]*2)), expected,
+                        atol=1.5e-7, rtol=0)
+        assert_allclose(special.polygamma(np.vstack([n]*2), x), expected,
+                        atol=1.5e-7, rtol=0)
+
+
+class TestProCvSeq:
+    def test_pro_cv_seq(self):
+        prol = special.pro_cv_seq(0, 3, 1)
+        assert_allclose(prol, array([0.319000,
+                                     2.593084,
+                                     6.533471,
+                                     12.514462]),
+                        atol=1.5e-5, rtol=0)
+
+
+class TestPsi:
+    def test_psi(self):
+        ps = special.psi(1)
+        assert_allclose(ps, -0.57721566490153287, atol=1.5e-8, rtol=0)
+
+
+class TestRadian:
+    def test_radian(self):
+        rad = special.radian(90, 0, 0)
+        assert_allclose(rad, pi/2.0, atol=1.5e-5, rtol=0)
+
+    def test_radianmore(self):
+        rad1 = special.radian(90, 1, 60)
+        assert_allclose(rad1, pi/2 + 0.0005816135199345904, atol=1.5e-5, rtol=0)
+
+
+class TestRiccati:
+    def test_riccati_jn(self):
+        N, x = 2, 0.2
+        S = np.empty((N, N))
+        for n in range(N):
+            j = special.spherical_jn(n, x)
+            jp = special.spherical_jn(n, x, derivative=True)
+            S[0,n] = x*j
+            S[1,n] = x*jp + j
+        assert_allclose(S, special.riccati_jn(n, x), atol=1.5e-8, rtol=0)
+
+    def test_riccati_yn(self):
+        N, x = 2, 0.2
+        C = np.empty((N, N))
+        for n in range(N):
+            y = special.spherical_yn(n, x)
+            yp = special.spherical_yn(n, x, derivative=True)
+            C[0,n] = x*y
+            C[1,n] = x*yp + y
+        assert_allclose(C, special.riccati_yn(n, x), atol=1.5e-8, rtol=0)
+
+
+class TestSoftplus:
+    def test_softplus(self):
+        # Test cases for the softplus function. Selected based on Eq.(10) of:
+        # Mächler, M. (2012). log1mexp-note.pdf. Rmpfr: R MPFR - Multiple Precision
+        # Floating-Point Reliable. Retrieved from:
+        # https://cran.r-project.org/web/packages/Rmpfr/vignettes/log1mexp-note.pdf
+        # Reference values computed with `mpmath`
+        import numpy as np
+        rng = np.random.default_rng(3298432985245)
+        n = 3
+        a1 = rng.uniform(-100, -37, size=n)
+        a2 = rng.uniform(-37, 18, size=n)
+        a3 = rng.uniform(18, 33.3, size=n)
+        a4 = rng.uniform(33.33, 100, size=n)
+        a = np.stack([a1, a2, a3, a4])
+
+        # from mpmath import mp
+        # mp.dps = 100
+        # @np.vectorize
+        # def softplus(x):
+        #     return float(mp.log(mp.one + mp.exp(x)))
+        # softplus(a).tolist()
+        ref = [[1.692721323272333e-42, 7.42673911145206e-41, 8.504608846033205e-35],
+               [1.8425343736349797, 9.488245799395577e-15, 7.225195764021444e-08],
+               [31.253760266045106, 27.758244090327832, 29.995959179643634],
+               [73.26040086468937, 76.24944728617226, 37.83955519155184]]
+
+        res = softplus(a)
+        assert_allclose(res, ref, rtol=2e-15)
+
+    def test_softplus_with_kwargs(self):
+        x = np.arange(5) - 2
+        out = np.ones(5)
+        ref = out.copy()
+        where = x > 0
+
+        softplus(x, out=out, where=where)
+        ref[where] = softplus(x[where])
+        assert_allclose(out, ref)
+
+
+class TestRound:
+    def test_round(self):
+        rnd = list(map(int, (special.round(10.1),
+                             special.round(10.4),
+                             special.round(10.5),
+                             special.round(10.6))))
+
+        # Note: According to the documentation, scipy.special.round is
+        # supposed to round to the nearest even number if the fractional
+        # part is exactly 0.5. On some platforms, this does not appear
+        # to work and thus this test may fail. However, this unit test is
+        # correctly written.
+        rndrl = (10,10,10,11)
+        assert_array_equal(rnd,rndrl)
+
+class TestStruve:
+    def _series(self, v, z, n=100):
+        """Compute Struve function & error estimate from its power series."""
+        k = arange(0, n)
+        r = (-1)**k * (.5*z)**(2*k+v+1)/special.gamma(k+1.5)/special.gamma(k+v+1.5)
+        err = abs(r).max() * finfo(double).eps * n
+        return r.sum(), err
+
+    def test_vs_series(self):
+        """Check Struve function versus its power series"""
+        for v in [-20, -10, -7.99, -3.4, -1, 0, 1, 3.4, 12.49, 16]:
+            for z in [1, 10, 19, 21, 30]:
+                value, err = self._series(v, z)
+                assert_allclose(special.struve(v, z), value, rtol=0, atol=err), (v, z)
+
+    def test_some_values(self):
+        assert_allclose(special.struve(-7.99, 21), 0.0467547614113, rtol=1e-7)
+        assert_allclose(special.struve(-8.01, 21), 0.0398716951023, rtol=1e-8)
+        assert_allclose(special.struve(-3.0, 200), 0.0142134427432, rtol=1e-12)
+        assert_allclose(special.struve(-8.0, -41), 0.0192469727846, rtol=1e-11)
+        assert_equal(special.struve(-12, -41), -special.struve(-12, 41))
+        assert_equal(special.struve(+12, -41), -special.struve(+12, 41))
+        assert_equal(special.struve(-11, -41), +special.struve(-11, 41))
+        assert_equal(special.struve(+11, -41), +special.struve(+11, 41))
+
+        assert_(isnan(special.struve(-7.1, -1)))
+        assert_(isnan(special.struve(-10.1, -1)))
+
+    def test_regression_679(self):
+        """Regression test for #679"""
+        assert_allclose(special.struve(-1.0, 20 - 1e-8),
+                        special.struve(-1.0, 20 + 1e-8))
+        assert_allclose(special.struve(-2.0, 20 - 1e-8),
+                        special.struve(-2.0, 20 + 1e-8))
+        assert_allclose(special.struve(-4.3, 20 - 1e-8),
+                        special.struve(-4.3, 20 + 1e-8))
+
+
+def test_chi2_smalldf():
+    assert_allclose(special.chdtr(0.6, 3), 0.957890536704110, atol=1.5e-7, rtol=0)
+
+
+def test_ch2_inf():
+    assert_equal(special.chdtr(0.7,np.inf), 1.0)
+
+
+@pytest.mark.parametrize("x", [-np.inf, -1.0, -0.0, 0.0, np.inf, np.nan])
+def test_chi2_v_nan(x):
+    assert np.isnan(special.chdtr(np.nan, x))
+
+
+@pytest.mark.parametrize("v", [-np.inf, -1.0, -0.0, 0.0, np.inf, np.nan])
+def test_chi2_x_nan(v):
+    assert np.isnan(special.chdtr(v, np.nan))
+
+
+@pytest.mark.parametrize("x", [-np.inf, -1.0, -0.0, 0.0, np.inf, np.nan])
+def test_chi2c_v_nan(x):
+    assert np.isnan(special.chdtrc(np.nan, x))
+
+
+@pytest.mark.parametrize("v", [-np.inf, -1.0, -0.0, 0.0, np.inf, np.nan])
+def test_chi2c_x_nan(v):
+    assert np.isnan(special.chdtrc(v, np.nan))
+
+
+def test_chi2_edgecases_gh20972():
+    # Tests that a variety of edgecases for chi square distribution functions
+    # correctly return NaN when and only when they are supposed to, when
+    # computed through different related ufuncs. See gh-20972.
+    v = np.asarray([-0.01, 0, 0.01, 1, np.inf])[:, np.newaxis]
+    x = np.asarray([-np.inf, -0.01, 0, 0.01, np.inf])
+
+    # Check that `gammainc` is NaN when it should be and finite otherwise
+    ref = special.gammainc(v / 2, x / 2)
+    mask = (x < 0) | (v < 0) | (x == 0) & (v == 0) | np.isinf(v) & np.isinf(x)
+    assert np.all(np.isnan(ref[mask]))
+    assert np.all(np.isfinite(ref[~mask]))
+
+    # Use `gammainc` as a reference for the rest
+    assert_allclose(special.chdtr(v, x), ref)
+    assert_allclose(special.gdtr(1, v / 2, x / 2), ref)
+    assert_allclose(1 - special.gammaincc(v / 2, x / 2), ref)
+    assert_allclose(1 - special.chdtrc(v, x), ref)
+    assert_allclose(1 - special.gdtrc(1, v / 2, x / 2), ref)
+
+
+def test_chi2c_smalldf():
+    assert_allclose(special.chdtrc(0.6, 3), 1 - 0.957890536704110,
+                    atol=1.5e-7, rtol=0)
+
+
+def test_chi2_inv_smalldf():
+    assert_allclose(special.chdtri(0.6, 1 - 0.957890536704110), 3,
+                    atol=1.5e-7, rtol=0)
+
+
+def test_agm_simple():
+    rtol = 1e-13
+
+    # Gauss's constant
+    assert_allclose(1/special.agm(1, np.sqrt(2)), 0.834626841674073186,
+                    rtol=rtol)
+
+    # These values were computed using Wolfram Alpha, with the
+    # function ArithmeticGeometricMean[a, b].
+    agm13 = 1.863616783244897
+    agm15 = 2.604008190530940
+    agm35 = 3.936235503649555
+    assert_allclose(special.agm([[1], [3]], [1, 3, 5]),
+                    [[1, agm13, agm15],
+                     [agm13, 3, agm35]], rtol=rtol)
+
+    # Computed by the iteration formula using mpmath,
+    # with mpmath.mp.prec = 1000:
+    agm12 = 1.4567910310469068
+    assert_allclose(special.agm(1, 2), agm12, rtol=rtol)
+    assert_allclose(special.agm(2, 1), agm12, rtol=rtol)
+    assert_allclose(special.agm(-1, -2), -agm12, rtol=rtol)
+    assert_allclose(special.agm(24, 6), 13.458171481725614, rtol=rtol)
+    assert_allclose(special.agm(13, 123456789.5), 11111458.498599306,
+                    rtol=rtol)
+    assert_allclose(special.agm(1e30, 1), 2.229223055945383e+28, rtol=rtol)
+    assert_allclose(special.agm(1e-22, 1), 0.030182566420169886, rtol=rtol)
+    assert_allclose(special.agm(1e150, 1e180), 2.229223055945383e+178,
+                    rtol=rtol)
+    assert_allclose(special.agm(1e180, 1e-150), 2.0634722510162677e+177,
+                    rtol=rtol)
+    assert_allclose(special.agm(1e-150, 1e-170), 3.3112619670463756e-152,
+                    rtol=rtol)
+    fi = np.finfo(1.0)
+    assert_allclose(special.agm(fi.tiny, fi.max), 1.9892072050015473e+305,
+                    rtol=rtol)
+    assert_allclose(special.agm(0.75*fi.max, fi.max), 1.564904312298045e+308,
+                    rtol=rtol)
+    assert_allclose(special.agm(fi.tiny, 3*fi.tiny), 4.1466849866735005e-308,
+                    rtol=rtol)
+
+    # zero, nan and inf cases.
+    assert_equal(special.agm(0, 0), 0)
+    assert_equal(special.agm(99, 0), 0)
+
+    assert_equal(special.agm(-1, 10), np.nan)
+    assert_equal(special.agm(0, np.inf), np.nan)
+    assert_equal(special.agm(np.inf, 0), np.nan)
+    assert_equal(special.agm(0, -np.inf), np.nan)
+    assert_equal(special.agm(-np.inf, 0), np.nan)
+    assert_equal(special.agm(np.inf, -np.inf), np.nan)
+    assert_equal(special.agm(-np.inf, np.inf), np.nan)
+    assert_equal(special.agm(1, np.nan), np.nan)
+    assert_equal(special.agm(np.nan, -1), np.nan)
+
+    assert_equal(special.agm(1, np.inf), np.inf)
+    assert_equal(special.agm(np.inf, 1), np.inf)
+    assert_equal(special.agm(-1, -np.inf), -np.inf)
+    assert_equal(special.agm(-np.inf, -1), -np.inf)
+
+
+def test_legacy():
+    # Legacy behavior: truncating arguments to integers
+    with warnings.catch_warnings():
+        warnings.filterwarnings(
+            "ignore", "floating point number truncated to an integer", RuntimeWarning)
+        assert_equal(special.expn(1, 0.3), special.expn(1.8, 0.3))
+        assert_equal(special.nbdtrc(1, 2, 0.3), special.nbdtrc(1.8, 2.8, 0.3))
+        assert_equal(special.nbdtr(1, 2, 0.3), special.nbdtr(1.8, 2.8, 0.3))
+        assert_equal(special.nbdtri(1, 2, 0.3), special.nbdtri(1.8, 2.8, 0.3))
+        assert_equal(special.pdtri(1, 0.3), special.pdtri(1.8, 0.3))
+        assert_equal(special.kn(1, 0.3), special.kn(1.8, 0.3))
+        assert_equal(special.yn(1, 0.3), special.yn(1.8, 0.3))
+        assert_equal(special.smirnov(1, 0.3), special.smirnov(1.8, 0.3))
+        assert_equal(special.smirnovi(1, 0.3), special.smirnovi(1.8, 0.3))
+
+
+# This lock can be removed once errstate is made thread-safe (see gh-21956)
+@pytest.fixture
+def errstate_lock():
+    import threading
+    return threading.Lock()
+
+
+@with_special_errors
+def test_error_raising(errstate_lock):
+    with errstate_lock:
+        with special.errstate(all='raise'):
+            assert_raises(special.SpecialFunctionError, special.iv, 1, 1e99j)
+
+
+def test_xlogy():
+    def xfunc(x, y):
+        with np.errstate(invalid='ignore'):
+            if x == 0 and not np.isnan(y):
+                return x
+            else:
+                return x*np.log(y)
+
+    z1 = np.asarray([(0,0), (0, np.nan), (0, np.inf), (1.0, 2.0)], dtype=float)
+    z2 = np.r_[z1, [(0, 1j), (1, 1j)]]
+
+    w1 = np.vectorize(xfunc)(z1[:,0], z1[:,1])
+    assert_func_equal(special.xlogy, w1, z1, rtol=1e-13, atol=1e-13)
+    w2 = np.vectorize(xfunc)(z2[:,0], z2[:,1])
+    assert_func_equal(special.xlogy, w2, z2, rtol=1e-13, atol=1e-13)
+
+
+def test_xlog1py():
+    def xfunc(x, y):
+        with np.errstate(invalid='ignore'):
+            if x == 0 and not np.isnan(y):
+                return x
+            else:
+                return x * np.log1p(y)
+
+    z1 = np.asarray([(0,0), (0, np.nan), (0, np.inf), (1.0, 2.0),
+                     (1, 1e-30)], dtype=float)
+    w1 = np.vectorize(xfunc)(z1[:,0], z1[:,1])
+    assert_func_equal(special.xlog1py, w1, z1, rtol=1e-13, atol=1e-13)
+
+
+def test_entr():
+    def xfunc(x):
+        if x < 0:
+            return -np.inf
+        else:
+            return -special.xlogy(x, x)
+    values = (0, 0.5, 1.0, np.inf)
+    signs = [-1, 1]
+    arr = []
+    for sgn, v in itertools.product(signs, values):
+        arr.append(sgn * v)
+    z = np.array(arr, dtype=float)
+    w = np.vectorize(xfunc, otypes=[np.float64])(z)
+    assert_func_equal(special.entr, w, z, rtol=1e-13, atol=1e-13)
+
+
+def test_kl_div():
+    def xfunc(x, y):
+        if x < 0 or y < 0 or (y == 0 and x != 0):
+            # extension of natural domain to preserve convexity
+            return np.inf
+        elif np.isposinf(x) or np.isposinf(y):
+            # limits within the natural domain
+            return np.inf
+        elif x == 0:
+            return y
+        else:
+            return special.xlogy(x, x/y) - x + y
+    values = (0, 0.5, 1.0)
+    signs = [-1, 1]
+    arr = []
+    for sgna, va, sgnb, vb in itertools.product(signs, values, signs, values):
+        arr.append((sgna*va, sgnb*vb))
+    z = np.array(arr, dtype=float)
+    w = np.vectorize(xfunc, otypes=[np.float64])(z[:,0], z[:,1])
+    assert_func_equal(special.kl_div, w, z, rtol=1e-13, atol=1e-13)
+
+
+def test_rel_entr():
+    def xfunc(x, y):
+        if x > 0 and y > 0:
+            return special.xlogy(x, x/y)
+        elif x == 0 and y >= 0:
+            return 0
+        else:
+            return np.inf
+    values = (0, 0.5, 1.0)
+    signs = [-1, 1]
+    arr = []
+    for sgna, va, sgnb, vb in itertools.product(signs, values, signs, values):
+        arr.append((sgna*va, sgnb*vb))
+    z = np.array(arr, dtype=float)
+    w = np.vectorize(xfunc, otypes=[np.float64])(z[:,0], z[:,1])
+    assert_func_equal(special.rel_entr, w, z, rtol=1e-13, atol=1e-13)
+
+
+def test_rel_entr_gh_20710_near_zero():
+    # Check accuracy of inputs which are very close
+    inputs = np.array([
+        # x, y
+        (0.9456657713430001, 0.9456657713430094),
+        (0.48066098564791515, 0.48066098564794774),
+        (0.786048657854401, 0.7860486578542367),
+    ])
+    # Known values produced using `x * mpmath.log(x / y)` with dps=30
+    expected = [
+        -9.325873406851269e-15,
+        -3.258504577274724e-14,
+        1.6431300764454033e-13,
+    ]
+    x = inputs[:, 0]
+    y = inputs[:, 1]
+    assert_allclose(special.rel_entr(x, y), expected, rtol=1e-13, atol=0)
+
+
+def test_rel_entr_gh_20710_overflow():
+    special.seterr(all='ignore')
+    inputs = np.array([
+        # x, y
+        # Overflow
+        (4, 2.22e-308),
+        # Underflow
+        (1e-200, 1e+200),
+        # Subnormal
+        (2.22e-308, 1e15),
+    ])
+    # Known values produced using `x * mpmath.log(x / y)` with dps=30
+    expected = [
+        2839.139983229607,
+        -9.210340371976183e-198,
+        -1.6493212008074475e-305,
+    ]
+    x = inputs[:, 0]
+    y = inputs[:, 1]
+    assert_allclose(special.rel_entr(x, y), expected, rtol=1e-13, atol=0)
+
+
+def test_huber():
+    assert_equal(special.huber(-1, 1.5), np.inf)
+    assert_allclose(special.huber(2, 1.5), 0.5 * np.square(1.5))
+    assert_allclose(special.huber(2, 2.5), 2 * (2.5 - 0.5 * 2))
+
+    def xfunc(delta, r):
+        if delta < 0:
+            return np.inf
+        elif np.abs(r) < delta:
+            return 0.5 * np.square(r)
+        else:
+            return delta * (np.abs(r) - 0.5 * delta)
+
+    z = np.random.randn(10, 2)
+    w = np.vectorize(xfunc, otypes=[np.float64])(z[:,0], z[:,1])
+    assert_func_equal(special.huber, w, z, rtol=1e-13, atol=1e-13)
+
+
+def test_pseudo_huber():
+    def xfunc(delta, r):
+        if delta < 0:
+            return np.inf
+        elif (not delta) or (not r):
+            return 0
+        else:
+            return delta**2 * (np.sqrt(1 + (r/delta)**2) - 1)
+
+    z = np.array(np.random.randn(10, 2).tolist() + [[0, 0.5], [0.5, 0]])
+    w = np.vectorize(xfunc, otypes=[np.float64])(z[:,0], z[:,1])
+    assert_func_equal(special.pseudo_huber, w, z, rtol=1e-13, atol=1e-13)
+
+
+def test_pseudo_huber_small_r():
+    delta = 1.0
+    r = 1e-18
+    y = special.pseudo_huber(delta, r)
+    # expected computed with mpmath:
+    #     import mpmath
+    #     mpmath.mp.dps = 200
+    #     r = mpmath.mpf(1e-18)
+    #     expected = float(mpmath.sqrt(1 + r**2) - 1)
+    expected = 5.0000000000000005e-37
+    assert_allclose(y, expected, rtol=1e-13)
+
+
+def test_runtime_warning():
+    with pytest.warns(RuntimeWarning,
+                      match=r'Too many predicted coefficients'):
+        mathieu_odd_coef(1000, 1000)
+    with pytest.warns(RuntimeWarning,
+                      match=r'Too many predicted coefficients'):
+        mathieu_even_coef(1000, 1000)
+
+
+class TestStirling2:
+    table = [
+        [1],
+        [0, 1],
+        [0, 1, 1],
+        [0, 1, 3, 1],
+        [0, 1, 7, 6, 1],
+        [0, 1, 15, 25, 10, 1],
+        [0, 1, 31, 90, 65, 15, 1],
+        [0, 1, 63, 301, 350, 140, 21, 1],
+        [0, 1, 127, 966, 1701, 1050, 266, 28, 1],
+        [0, 1, 255, 3025, 7770, 6951, 2646, 462, 36, 1],
+        [0, 1, 511, 9330, 34105, 42525, 22827, 5880, 750, 45, 1],
+    ]
+
+    @pytest.mark.parametrize("is_exact, comp, kwargs", [
+        (True, assert_equal, {}),
+        (False, assert_allclose, {'rtol': 1e-12})
+    ])
+    def test_table_cases(self, is_exact, comp, kwargs):
+        for n in range(1, len(self.table)):
+            k_values = list(range(n+1))
+            row = self.table[n]
+            comp(row, stirling2([n], k_values, exact=is_exact), **kwargs)
+
+    @pytest.mark.parametrize("is_exact, comp, kwargs", [
+        (True, assert_equal, {}),
+        (False, assert_allclose, {'rtol': 1e-12})
+    ])
+    def test_valid_single_integer(self, is_exact, comp, kwargs):
+        comp(stirling2(0, 0, exact=is_exact), self.table[0][0], **kwargs)
+        comp(stirling2(4, 2, exact=is_exact), self.table[4][2], **kwargs)
+        # a single 2-tuple of integers as arguments must return an int and not
+        # an array whereas arrays of single values should return array
+        comp(stirling2(5, 3, exact=is_exact), 25, **kwargs)
+        comp(stirling2([5], [3], exact=is_exact), [25], **kwargs)
+
+    @pytest.mark.parametrize("is_exact, comp, kwargs", [
+        (True, assert_equal, {}),
+        (False, assert_allclose, {'rtol': 1e-12})
+    ])
+    def test_negative_integer(self, is_exact, comp, kwargs):
+        # negative integers for n or k arguments return 0
+        comp(stirling2(-1, -1, exact=is_exact), 0, **kwargs)
+        comp(stirling2(-1, 2, exact=is_exact), 0, **kwargs)
+        comp(stirling2(2, -1, exact=is_exact), 0, **kwargs)
+
+    @pytest.mark.parametrize("is_exact, comp, kwargs", [
+        (True, assert_equal, {}),
+        (False, assert_allclose, {'rtol': 1e-12})
+    ])
+    def test_array_inputs(self, is_exact, comp, kwargs):
+        ans = [self.table[10][3], self.table[10][4]]
+        comp(stirling2(asarray([10, 10]),
+                               asarray([3, 4]),
+                               exact=is_exact),
+                     ans)
+        comp(stirling2([10, 10],
+                               asarray([3, 4]),
+                               exact=is_exact),
+                     ans)
+        comp(stirling2(asarray([10, 10]),
+                               [3, 4],
+                               exact=is_exact),
+                     ans)
+
+    @pytest.mark.parametrize("is_exact, comp, kwargs", [
+        (True, assert_equal, {}),
+        (False, assert_allclose, {'rtol': 1e-13})
+    ])
+    def test_mixed_values(self, is_exact, comp, kwargs):
+        # negative values-of either n or k-should return 0 for the entry
+        ans = [0, 1, 3, 25, 1050, 5880, 9330]
+        n = [-1, 0, 3, 5, 8, 10, 10]
+        k = [-2, 0, 2, 3, 5, 7, 3]
+        comp(stirling2(n, k, exact=is_exact), ans, **kwargs)
+
+    def test_correct_parity(self):
+        """Test parity follows well known identity.
+
+        en.wikipedia.org/wiki/Stirling_numbers_of_the_second_kind#Parity
+        """
+        n, K = 100, np.arange(101)
+        assert_equal(
+            stirling2(n, K, exact=True) % 2,
+            [math.comb(n - (k // 2) - 1, n - k) % 2 for k in K],
+        )
+
+    def test_big_numbers(self):
+        # via mpmath (bigger than 32bit)
+        ans = asarray([48063331393110, 48004081105038305])
+        n = [25, 30]
+        k = [17, 4]
+        assert array_equal(stirling2(n, k, exact=True), ans)
+        # bigger than 64 bit
+        ans = asarray([2801934359500572414253157841233849412,
+                       14245032222277144547280648984426251])
+        n = [42, 43]
+        k = [17, 23]
+        assert array_equal(stirling2(n, k, exact=True), ans)
+
+    @pytest.mark.parametrize("N", [4.5, 3., 4+1j, "12", np.nan])
+    @pytest.mark.parametrize("K", [3.5, 3, "2", None])
+    @pytest.mark.parametrize("is_exact", [True, False])
+    def test_unsupported_input_types(self, N, K, is_exact):
+        # object, float, string, complex are not supported and raise TypeError
+        with pytest.raises(TypeError):
+            stirling2(N, K, exact=is_exact)
+
+    @pytest.mark.parametrize("is_exact", [True, False])
+    def test_numpy_array_int_object_dtype(self, is_exact):
+        # python integers with arbitrary precision are *not* allowed as
+        # object type in numpy arrays are inconsistent from api perspective
+        ans = asarray(self.table[4][1:])
+        n = asarray([4, 4, 4, 4], dtype=object)
+        k = asarray([1, 2, 3, 4], dtype=object)
+        with pytest.raises(TypeError):
+            array_equal(stirling2(n, k, exact=is_exact), ans)
+
+    @pytest.mark.parametrize("is_exact, comp, kwargs", [
+        (True, assert_equal, {}),
+        (False, assert_allclose, {'rtol': 1e-13})
+    ])
+    def test_numpy_array_unsigned_int_dtype(self, is_exact, comp, kwargs):
+        # numpy unsigned integers are allowed as dtype in numpy arrays
+        ans = asarray(self.table[4][1:])
+        n = asarray([4, 4, 4, 4], dtype=np.ulong)
+        k = asarray([1, 2, 3, 4], dtype=np.ulong)
+        comp(stirling2(n, k, exact=False), ans, **kwargs)
+
+    @pytest.mark.parametrize("is_exact, comp, kwargs", [
+        (True, assert_equal, {}),
+        (False, assert_allclose, {'rtol': 1e-13})
+    ])
+    def test_broadcasting_arrays_correctly(self, is_exact, comp, kwargs):
+        # broadcasting is handled by stirling2
+        # test leading 1s are replicated
+        ans = asarray([[1, 15, 25, 10], [1, 7, 6, 1]])  # shape (2,4)
+        n = asarray([[5, 5, 5, 5], [4, 4, 4, 4]])  # shape (2,4)
+        k = asarray([1, 2, 3, 4])  # shape (4,)
+        comp(stirling2(n, k, exact=is_exact), ans, **kwargs)
+        # test that dims both mismatch broadcast correctly (5,1) & (6,)
+        n = asarray([[4], [4], [4], [4], [4]])
+        k = asarray([0, 1, 2, 3, 4, 5])
+        ans = asarray([[0, 1, 7, 6, 1, 0] for _ in range(5)])
+        comp(stirling2(n, k, exact=False), ans, **kwargs)
+
+    def test_temme_rel_max_error(self):
+        # python integers with arbitrary precision are *not* allowed as
+        # object type in numpy arrays are inconsistent from api perspective
+        x = list(range(51, 101, 5))
+        for n in x:
+            k_entries = list(range(1, n+1))
+            denom = stirling2([n], k_entries, exact=True)
+            num = denom - stirling2([n], k_entries, exact=False)
+            assert np.max(np.abs(num / denom)) < 2e-5
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_bdtr.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_bdtr.py
new file mode 100644
index 0000000000000000000000000000000000000000..4d59c1e8c594166a99b213a217b7851c292d9d64
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_bdtr.py
@@ -0,0 +1,114 @@
+import warnings
+
+import numpy as np
+import scipy.special as sc
+import pytest
+from numpy.testing import assert_allclose, assert_array_equal
+
+
+class TestBdtr:
+    def test(self):
+        val = sc.bdtr(0, 1, 0.5)
+        assert_allclose(val, 0.5)
+
+    def test_sum_is_one(self):
+        val = sc.bdtr([0, 1, 2], 2, 0.5)
+        assert_array_equal(val, [0.25, 0.75, 1.0])
+
+    def test_rounding(self):
+        double_val = sc.bdtr([0.1, 1.1, 2.1], 2, 0.5)
+        int_val = sc.bdtr([0, 1, 2], 2, 0.5)
+        assert_array_equal(double_val, int_val)
+
+    @pytest.mark.parametrize('k, n, p', [
+        (np.inf, 2, 0.5),
+        (1.0, np.inf, 0.5),
+        (1.0, 2, np.inf)
+    ])
+    def test_inf(self, k, n, p):
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", DeprecationWarning)
+            val = sc.bdtr(k, n, p)
+        assert np.isnan(val)
+
+    def test_domain(self):
+        val = sc.bdtr(-1.1, 1, 0.5)
+        assert np.isnan(val)
+
+
+class TestBdtrc:
+    def test_value(self):
+        val = sc.bdtrc(0, 1, 0.5)
+        assert_allclose(val, 0.5)
+
+    def test_sum_is_one(self):
+        val = sc.bdtrc([0, 1, 2], 2, 0.5)
+        assert_array_equal(val, [0.75, 0.25, 0.0])
+
+    def test_rounding(self):
+        double_val = sc.bdtrc([0.1, 1.1, 2.1], 2, 0.5)
+        int_val = sc.bdtrc([0, 1, 2], 2, 0.5)
+        assert_array_equal(double_val, int_val)
+
+    @pytest.mark.parametrize('k, n, p', [
+        (np.inf, 2, 0.5),
+        (1.0, np.inf, 0.5),
+        (1.0, 2, np.inf)
+    ])
+    def test_inf(self, k, n, p):
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", DeprecationWarning)
+            val = sc.bdtrc(k, n, p)
+        assert np.isnan(val)
+
+    def test_domain(self):
+        val = sc.bdtrc(-1.1, 1, 0.5)
+        val2 = sc.bdtrc(2.1, 1, 0.5)
+        assert np.isnan(val2)
+        assert_allclose(val, 1.0)
+
+    def test_bdtr_bdtrc_sum_to_one(self):
+        bdtr_vals = sc.bdtr([0, 1, 2], 2, 0.5)
+        bdtrc_vals = sc.bdtrc([0, 1, 2], 2, 0.5)
+        vals = bdtr_vals + bdtrc_vals
+        assert_allclose(vals, [1.0, 1.0, 1.0])
+
+
+class TestBdtri:
+    def test_value(self):
+        val = sc.bdtri(0, 1, 0.5)
+        assert_allclose(val, 0.5)
+
+    def test_sum_is_one(self):
+        val = sc.bdtri([0, 1], 2, 0.5)
+        actual = np.asarray([1 - 1/np.sqrt(2), 1/np.sqrt(2)])
+        assert_allclose(val, actual)
+
+    def test_rounding(self):
+        double_val = sc.bdtri([0.1, 1.1], 2, 0.5)
+        int_val = sc.bdtri([0, 1], 2, 0.5)
+        assert_allclose(double_val, int_val)
+
+    @pytest.mark.parametrize('k, n, p', [
+        (np.inf, 2, 0.5),
+        (1.0, np.inf, 0.5),
+        (1.0, 2, np.inf)
+    ])
+    def test_inf(self, k, n, p):
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", DeprecationWarning)
+            val = sc.bdtri(k, n, p)
+        assert np.isnan(val)
+
+    @pytest.mark.parametrize('k, n, p', [
+        (-1.1, 1, 0.5),
+        (2.1, 1, 0.5)
+    ])
+    def test_domain(self, k, n, p):
+        val = sc.bdtri(k, n, p)
+        assert np.isnan(val)
+
+    def test_bdtr_bdtri_roundtrip(self):
+        bdtr_vals = sc.bdtr([0, 1, 2], 2, 0.5)
+        roundtrip_vals = sc.bdtri([0, 1, 2], 2, bdtr_vals)
+        assert_allclose(roundtrip_vals, [0.5, 0.5, np.nan])
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_boost_ufuncs.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_boost_ufuncs.py
new file mode 100644
index 0000000000000000000000000000000000000000..e782765da6cf26d10317492c8da3e2f8b1b2b07f
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_boost_ufuncs.py
@@ -0,0 +1,83 @@
+import pytest
+import numpy as np
+from numpy.testing import assert_allclose
+import scipy.special._ufuncs as scu
+from scipy.integrate import tanhsinh
+
+
+type_char_to_type_tol = {'f': (np.float32, 32*np.finfo(np.float32).eps),
+                         'd': (np.float64, 32*np.finfo(np.float64).eps)}
+
+
+# Each item in this list is
+#   (func, args, expected_value)
+# All the values can be represented exactly, even with np.float32.
+#
+# This is not an exhaustive test data set of all the functions!
+# It is a spot check of several functions, primarily for
+# checking that the different data types are handled correctly.
+test_data = [
+    (scu._beta_pdf, (0.5, 2, 3), 1.5),
+    (scu._beta_pdf, (0, 1, 5), 5.0),
+    (scu._beta_pdf, (1, 5, 1), 5.0),
+    (scu._beta_ppf, (0.5, 5., 5.), 0.5),  # gh-21303
+    (scu._binom_cdf, (1, 3, 0.5), 0.5),
+    (scu._binom_pmf, (1, 4, 0.5), 0.25),
+    (scu._hypergeom_cdf, (2, 3, 5, 6), 0.5),
+    (scu._nbinom_cdf, (1, 4, 0.25), 0.015625),
+    (scu._ncf_mean, (10, 12, 2.5), 1.5),
+]
+
+
+@pytest.mark.parametrize('func, args, expected', test_data)
+def test_stats_boost_ufunc(func, args, expected):
+    type_sigs = func.types
+    type_chars = [sig.split('->')[-1] for sig in type_sigs]
+    for type_char in type_chars:
+        typ, rtol = type_char_to_type_tol[type_char]
+        args = [typ(arg) for arg in args]
+        # Harmless overflow warnings are a "feature" of some wrappers on some
+        # platforms. This test is about dtype and accuracy, so let's avoid false
+        # test failures cause by these warnings. See gh-17432.
+        with np.errstate(over='ignore'):
+            value = func(*args)
+        assert isinstance(value, typ)
+        assert_allclose(value, expected, rtol=rtol)
+
+
+def test_landau():
+    # Test that Landau distribution ufuncs are wrapped as expected;
+    # accuracy is tested by Boost.
+    x = np.linspace(-3, 10, 10)
+    args = (0, 1)
+    res = tanhsinh(lambda x: scu._landau_pdf(x, *args), -np.inf, x)
+    cdf = scu._landau_cdf(x, *args)
+    assert_allclose(res.integral, cdf)
+    sf = scu._landau_sf(x, *args)
+    assert_allclose(sf, 1-cdf)
+    ppf = scu._landau_ppf(cdf, *args)
+    assert_allclose(ppf, x)
+    isf = scu._landau_isf(sf, *args)
+    assert_allclose(isf, x, rtol=1e-6)
+
+def test_gh22956():
+    _ = scu._ncx2_pdf(30, 1e307, 16)
+
+@pytest.mark.parametrize("func", [scu._binom_cdf, scu._binom_sf])
+@pytest.mark.parametrize("dtype", [np.float32, np.float64])
+def test_extreme_inputs_for_binomial_probabilities(func, dtype):
+    # certain inputs caused C++ exceptions in boost
+    # resulting in Python interpreter crashes
+    k = 3e18
+    n = 10e18
+    p = 0.3
+    func(dtype(k), dtype(n), dtype(p))
+
+@pytest.mark.parametrize("func", [scu._binom_ppf, scu._binom_isf])
+@pytest.mark.parametrize("dtype", [np.float32, np.float64])
+def test_extreme_inputs_for_binomial_quantiles(func, dtype):
+    # certain inputs caused C++ exceptions in boost
+    # resulting in Python interpreter crashes
+    n = 10e18
+    p = 0.5
+    func(dtype(p), dtype(n), dtype(p))
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_boxcox.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_boxcox.py
new file mode 100644
index 0000000000000000000000000000000000000000..703a1fdee635a484fe53f14e98fb3ce08c811447
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_boxcox.py
@@ -0,0 +1,125 @@
+import numpy as np
+from numpy.testing import assert_equal, assert_allclose
+from scipy.special import boxcox, boxcox1p, inv_boxcox, inv_boxcox1p
+import pytest
+
+
+# There are more tests of boxcox and boxcox1p in test_mpmath.py.
+
+def test_boxcox_basic():
+    x = np.array([0.5, 1, 2, 4])
+
+    # lambda = 0  =>  y = log(x)
+    y = boxcox(x, 0)
+    assert_allclose(y, np.log(x), atol=1.5e-7, rtol=0)
+
+    # lambda = 1  =>  y = x - 1
+    y = boxcox(x, 1)
+    assert_allclose(y, x - 1, atol=1.5e-7, rtol=0)
+
+    # lambda = 2  =>  y = 0.5*(x**2 - 1)
+    y = boxcox(x, 2)
+    assert_allclose(y, 0.5*(x**2 - 1), atol=1.5e-7, rtol=0)
+
+    # x = 0 and lambda > 0  =>  y = -1 / lambda
+    lam = np.array([0.5, 1, 2])
+    y = boxcox(0, lam)
+    assert_allclose(y, -1.0 / lam, atol=1.5e-7, rtol=0)
+
+def test_boxcox_underflow():
+    x = 1 + 1e-15
+    lmbda = 1e-306
+    y = boxcox(x, lmbda)
+    assert_allclose(y, np.log(x), rtol=1e-14)
+
+
+def test_boxcox_nonfinite():
+    # x < 0  =>  y = nan
+    x = np.array([-1, -1, -0.5])
+    y = boxcox(x, [0.5, 2.0, -1.5])
+    assert_equal(y, np.array([np.nan, np.nan, np.nan]))
+
+    # x = 0 and lambda <= 0  =>  y = -inf
+    x = 0
+    y = boxcox(x, [-2.5, 0])
+    assert_equal(y, np.array([-np.inf, -np.inf]))
+
+
+def test_boxcox1p_basic():
+    x = np.array([-0.25, -1e-20, 0, 1e-20, 0.25, 1, 3])
+
+    # lambda = 0  =>  y = log(1+x)
+    y = boxcox1p(x, 0)
+    assert_allclose(y, np.log1p(x), atol=1.5e-7, rtol=0)
+
+    # lambda = 1  =>  y = x
+    y = boxcox1p(x, 1)
+    assert_allclose(y, x, atol=1.5e-7, rtol=0)
+
+    # lambda = 2  =>  y = 0.5*((1+x)**2 - 1) = 0.5*x*(2 + x)
+    y = boxcox1p(x, 2)
+    assert_allclose(y, 0.5*x*(2 + x), atol=1.5e-7, rtol=0)
+
+    # x = -1 and lambda > 0  =>  y = -1 / lambda
+    lam = np.array([0.5, 1, 2])
+    y = boxcox1p(-1, lam)
+    assert_allclose(y, -1.0 / lam, atol=1.5e-7, rtol=0)
+
+
+def test_boxcox1p_underflow():
+    x = np.array([1e-15, 1e-306])
+    lmbda = np.array([1e-306, 1e-18])
+    y = boxcox1p(x, lmbda)
+    assert_allclose(y, np.log1p(x), rtol=1e-14)
+
+
+def test_boxcox1p_nonfinite():
+    # x < -1  =>  y = nan
+    x = np.array([-2, -2, -1.5])
+    y = boxcox1p(x, [0.5, 2.0, -1.5])
+    assert_equal(y, np.array([np.nan, np.nan, np.nan]))
+
+    # x = -1 and lambda <= 0  =>  y = -inf
+    x = -1
+    y = boxcox1p(x, [-2.5, 0])
+    assert_equal(y, np.array([-np.inf, -np.inf]))
+
+
+def test_inv_boxcox():
+    x = np.array([0., 1., 2.])
+    lam = np.array([0., 1., 2.])
+    y = boxcox(x, lam)
+    x2 = inv_boxcox(y, lam)
+    assert_allclose(x, x2, atol=1.5e-7, rtol=0)
+
+    x = np.array([0., 1., 2.])
+    lam = np.array([0., 1., 2.])
+    y = boxcox1p(x, lam)
+    x2 = inv_boxcox1p(y, lam)
+    assert_allclose(x, x2, atol=1.5e-7, rtol=0)
+
+
+def test_inv_boxcox1p_underflow():
+    x = 1e-15
+    lam = 1e-306
+    y = inv_boxcox1p(x, lam)
+    assert_allclose(y, x, rtol=1e-14)
+
+
+@pytest.mark.parametrize(
+    "x, lmb",
+    [[100, 155],
+     [0.01, -155]]
+)
+def test_boxcox_premature_overflow(x, lmb):
+    # test boxcox & inv_boxcox
+    y = boxcox(x, lmb)
+    assert np.isfinite(y)
+    x_inv = inv_boxcox(y, lmb)
+    assert_allclose(x, x_inv)
+
+    # test boxcox1p & inv_boxcox1p
+    y1p = boxcox1p(x-1, lmb)
+    assert np.isfinite(y1p)
+    x1p_inv = inv_boxcox1p(y1p, lmb)
+    assert_allclose(x-1, x1p_inv)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_cdflib.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_cdflib.py
new file mode 100644
index 0000000000000000000000000000000000000000..48938605349829a024f1b9bff5b7af96e57cec6a
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_cdflib.py
@@ -0,0 +1,980 @@
+"""
+Test cdflib functions versus mpmath, if available.
+
+The following functions still need tests:
+
+- ncfdtridfn
+- ncfdtridfd
+- ncfdtrinc
+- nctdtridf
+- nctdtrinc
+
+"""
+import itertools
+
+import numpy as np
+from numpy.testing import assert_equal, assert_allclose, assert_array_equal
+import pytest
+
+import scipy.special as sp
+from scipy.special._testutils import (
+    MissingModule, check_version, FuncData)
+from scipy.special._mptestutils import (
+    Arg, IntArg, get_args, mpf2float, assert_mpmath_equal)
+
+try:
+    import mpmath
+except ImportError:
+    mpmath = MissingModule('mpmath')
+
+
+class ProbArg:
+    """Generate a set of probabilities on [0, 1]."""
+
+    def __init__(self):
+        # Include the endpoints for compatibility with Arg et. al.
+        self.a = 0
+        self.b = 1
+
+    def values(self, n):
+        """Return an array containing approximately n numbers."""
+        m = max(1, n//3)
+        v1 = np.logspace(-30, np.log10(0.3), m)
+        v2 = np.linspace(0.3, 0.7, m + 1, endpoint=False)[1:]
+        v3 = 1 - np.logspace(np.log10(0.3), -15, m)
+        v = np.r_[v1, v2, v3]
+        return np.unique(v)
+
+
+class EndpointFilter:
+    def __init__(self, a, b, rtol, atol):
+        self.a = a
+        self.b = b
+        self.rtol = rtol
+        self.atol = atol
+
+    def __call__(self, x):
+        mask1 = np.abs(x - self.a) < self.rtol*np.abs(self.a) + self.atol
+        mask2 = np.abs(x - self.b) < self.rtol*np.abs(self.b) + self.atol
+        return np.where(mask1 | mask2, False, True)
+
+
+class _CDFData:
+    def __init__(self, spfunc, mpfunc, index, argspec, spfunc_first=True,
+                 dps=20, n=5000, rtol=None, atol=None,
+                 endpt_rtol=None, endpt_atol=None):
+        self.spfunc = spfunc
+        self.mpfunc = mpfunc
+        self.index = index
+        self.argspec = argspec
+        self.spfunc_first = spfunc_first
+        self.dps = dps
+        self.n = n
+        self.rtol = rtol
+        self.atol = atol
+
+        if not isinstance(argspec, list):
+            self.endpt_rtol = None
+            self.endpt_atol = None
+        elif endpt_rtol is not None or endpt_atol is not None:
+            if isinstance(endpt_rtol, list):
+                self.endpt_rtol = endpt_rtol
+            else:
+                self.endpt_rtol = [endpt_rtol]*len(self.argspec)
+            if isinstance(endpt_atol, list):
+                self.endpt_atol = endpt_atol
+            else:
+                self.endpt_atol = [endpt_atol]*len(self.argspec)
+        else:
+            self.endpt_rtol = None
+            self.endpt_atol = None
+
+    def idmap(self, *args):
+        if self.spfunc_first:
+            res = self.spfunc(*args)
+            if np.isnan(res):
+                return np.nan
+            args = list(args)
+            args[self.index] = res
+            with mpmath.workdps(self.dps):
+                res = self.mpfunc(*tuple(args))
+                # Imaginary parts are spurious
+                res = mpf2float(res.real)
+        else:
+            with mpmath.workdps(self.dps):
+                res = self.mpfunc(*args)
+                res = mpf2float(res.real)
+            args = list(args)
+            args[self.index] = res
+            res = self.spfunc(*tuple(args))
+        return res
+
+    def get_param_filter(self):
+        if self.endpt_rtol is None and self.endpt_atol is None:
+            return None
+
+        filters = []
+        for rtol, atol, spec in zip(self.endpt_rtol, self.endpt_atol, self.argspec):
+            if rtol is None and atol is None:
+                filters.append(None)
+                continue
+            elif rtol is None:
+                rtol = 0.0
+            elif atol is None:
+                atol = 0.0
+
+            filters.append(EndpointFilter(spec.a, spec.b, rtol, atol))
+        return filters
+
+    def check(self):
+        # Generate values for the arguments
+        args = get_args(self.argspec, self.n)
+        param_filter = self.get_param_filter()
+        param_columns = tuple(range(args.shape[1]))
+        result_columns = args.shape[1]
+        args = np.hstack((args, args[:, self.index].reshape(args.shape[0], 1)))
+        FuncData(self.idmap, args,
+                 param_columns=param_columns, result_columns=result_columns,
+                 rtol=self.rtol, atol=self.atol, vectorized=False,
+                 param_filter=param_filter).check()
+
+
+def _assert_inverts(*a, **kw):
+    d = _CDFData(*a, **kw)
+    d.check()
+
+
+def _binomial_cdf(k, n, p):
+    k, n, p = mpmath.mpf(k), mpmath.mpf(n), mpmath.mpf(p)
+    if k <= 0:
+        return mpmath.mpf(0)
+    elif k >= n:
+        return mpmath.mpf(1)
+
+    onemp = mpmath.fsub(1, p, exact=True)
+    return mpmath.betainc(n - k, k + 1, x2=onemp, regularized=True)
+
+
+def _f_cdf(dfn, dfd, x):
+    if x < 0:
+        return mpmath.mpf(0)
+    dfn, dfd, x = mpmath.mpf(dfn), mpmath.mpf(dfd), mpmath.mpf(x)
+    ub = dfn*x/(dfn*x + dfd)
+    res = mpmath.betainc(dfn/2, dfd/2, x2=ub, regularized=True)
+    return res
+
+
+def _student_t_cdf(df, t, dps=None):
+    if dps is None:
+        dps = mpmath.mp.dps
+    with mpmath.workdps(dps):
+        df, t = mpmath.mpf(df), mpmath.mpf(t)
+        fac = mpmath.hyp2f1(0.5, 0.5*(df + 1), 1.5, -t**2/df)
+        fac *= t*mpmath.gamma(0.5*(df + 1))
+        fac /= mpmath.sqrt(mpmath.pi*df)*mpmath.gamma(0.5*df)
+        return 0.5 + fac
+
+
+def _noncentral_chi_pdf(t, df, nc):
+    res = mpmath.besseli(df/2 - 1, mpmath.sqrt(nc*t))
+    res *= mpmath.exp(-(t + nc)/2)*(t/nc)**(df/4 - 1/2)/2
+    return res
+
+
+def _noncentral_chi_cdf(x, df, nc, dps=None):
+    if dps is None:
+        dps = mpmath.mp.dps
+    x, df, nc = mpmath.mpf(x), mpmath.mpf(df), mpmath.mpf(nc)
+    with mpmath.workdps(dps):
+        res = mpmath.quad(lambda t: _noncentral_chi_pdf(t, df, nc), [0, x])
+        return res
+
+
+def _tukey_lmbda_quantile(p, lmbda):
+    # For lmbda != 0
+    return (p**lmbda - (1 - p)**lmbda)/lmbda
+
+
+@pytest.mark.slow
+@check_version(mpmath, '0.19')
+class TestCDFlib:
+
+    def test_bdtrin(self):
+        _assert_inverts(
+            sp.bdtrin,
+            _binomial_cdf,
+            1, [IntArg(1, 3000), ProbArg(), ProbArg()],
+            rtol=1e-12, endpt_atol=[None, None, 1e-6])
+
+    def test_btdtria(self):
+        _assert_inverts(
+            sp.btdtria,
+            lambda a, b, x: mpmath.betainc(a, b, x2=x, regularized=True),
+            0, [ProbArg(), Arg(0, 3e2, inclusive_a=False),
+                Arg(0, 1, inclusive_a=False, inclusive_b=False)],
+            rtol=1e-12)
+
+    def test_btdtrib(self):
+        # Use small values of a or mpmath doesn't converge
+        _assert_inverts(
+            sp.btdtrib,
+            lambda a, b, x: mpmath.betainc(a, b, x2=x, regularized=True),
+            1,
+            [Arg(0, 1e2, inclusive_a=False), ProbArg(),
+             Arg(0, 1, inclusive_a=False, inclusive_b=False)],
+            rtol=1e-7,
+            endpt_atol=[None, 1e-18, 1e-15])
+
+    @pytest.mark.xfail(run=False)
+    def test_fdtridfd(self):
+        _assert_inverts(
+            sp.fdtridfd,
+            _f_cdf,
+            1,
+            [IntArg(1, 100), ProbArg(), Arg(0, 100, inclusive_a=False)],
+            rtol=1e-7)
+
+    def test_gdtria(self):
+        _assert_inverts(
+            sp.gdtria,
+            lambda a, b, x: mpmath.gammainc(b, b=a*x, regularized=True),
+            0,
+            [ProbArg(), Arg(0, 1e3, inclusive_a=False),
+             Arg(0, 1e4, inclusive_a=False)],
+            rtol=1e-12,
+            endpt_atol=[None, 1e-7, 1e-10])
+
+    def test_gdtrib(self):
+        # Use small values of a and x or mpmath doesn't converge
+        _assert_inverts(
+            sp.gdtrib,
+            lambda a, b, x: mpmath.gammainc(b, b=a*x, regularized=True),
+            1,
+            [Arg(0, 1e2, inclusive_a=False), ProbArg(),
+             Arg(0, 1e3, inclusive_a=False)],
+            rtol=1e-5)
+
+    def test_gdtrix(self):
+        _assert_inverts(
+            sp.gdtrix,
+            lambda a, b, x: mpmath.gammainc(b, b=a*x, regularized=True),
+            2,
+            [Arg(0, 1e3, inclusive_a=False), Arg(0, 1e3, inclusive_a=False),
+             ProbArg()],
+            rtol=1e-7,
+            endpt_atol=[None, 1e-7, 1e-10])
+
+    # Overall nrdtrimn and nrdtrisd are not performing well with infeasible/edge
+    # combinations of sigma and x, hence restricted the domains to still use the
+    # testing machinery, also see gh-20069
+
+    # nrdtrimn signature: p, sd, x
+    # nrdtrisd signature: mn, p, x
+    def test_nrdtrimn(self):
+        _assert_inverts(
+            sp.nrdtrimn,
+            lambda x, y, z: mpmath.ncdf(z, x, y),
+            0,
+            [ProbArg(),  # CDF value p
+             Arg(0.1, np.inf, inclusive_a=False, inclusive_b=False),  # sigma
+             Arg(-1e10, 1e10)],  # x
+            rtol=1e-5)
+
+    def test_nrdtrisd(self):
+        _assert_inverts(
+            sp.nrdtrisd,
+            lambda x, y, z: mpmath.ncdf(z, x, y),
+            1,
+            [Arg(-np.inf, 10, inclusive_a=False, inclusive_b=False),  # mn
+             ProbArg(),  # CDF value p
+             Arg(10, 1e100)],  # x
+            rtol=1e-5)
+
+    def test_stdtr(self):
+        # Ideally the left endpoint for Arg() should be 0.
+        assert_mpmath_equal(
+            sp.stdtr,
+            _student_t_cdf,
+            [IntArg(1, 100), Arg(1e-10, np.inf)], rtol=1e-7)
+
+    @pytest.mark.xfail(run=False)
+    def test_stdtridf(self):
+        _assert_inverts(
+            sp.stdtridf,
+            _student_t_cdf,
+            0, [ProbArg(), Arg()], rtol=1e-7)
+
+    def test_stdtrit(self):
+        _assert_inverts(
+            sp.stdtrit,
+            _student_t_cdf,
+            1, [IntArg(1, 100), ProbArg()], rtol=1e-7,
+            endpt_atol=[None, 1e-10])
+
+    def test_chdtriv(self):
+        _assert_inverts(
+            sp.chdtriv,
+            lambda v, x: mpmath.gammainc(v/2, b=x/2, regularized=True),
+            0, [ProbArg(), IntArg(1, 100)], rtol=1e-4)
+
+
+    @pytest.mark.xfail(run=False)
+    def test_chndtridf(self):
+        # Use a larger atol since mpmath is doing numerical integration
+        _assert_inverts(
+            sp.chndtridf,
+            _noncentral_chi_cdf,
+            1, [Arg(0, 100, inclusive_a=False), ProbArg(),
+                Arg(0, 100, inclusive_a=False)],
+            n=1000, rtol=1e-4, atol=1e-15)
+
+    @pytest.mark.xfail(run=False)
+    def test_chndtrinc(self):
+        # Use a larger atol since mpmath is doing numerical integration
+        _assert_inverts(
+            sp.chndtrinc,
+            _noncentral_chi_cdf,
+            2, [Arg(0, 100, inclusive_a=False), IntArg(1, 100), ProbArg()],
+            n=1000, rtol=1e-4, atol=1e-15)
+
+    def test_chndtrix(self):
+        # Use a larger atol since mpmath is doing numerical integration
+        _assert_inverts(
+            sp.chndtrix,
+            _noncentral_chi_cdf,
+            0, [ProbArg(), IntArg(1, 100), Arg(0, 100, inclusive_a=False)],
+            n=1000, rtol=1e-4, atol=1e-15,
+            endpt_atol=[1e-6, None, None])
+
+    def test_tklmbda_zero_shape(self):
+        # When lmbda = 0 the CDF has a simple closed form
+        one = mpmath.mpf(1)
+        assert_mpmath_equal(
+            lambda x: sp.tklmbda(x, 0),
+            lambda x: one/(mpmath.exp(-x) + one),
+            [Arg()], rtol=1e-7)
+
+    def test_tklmbda_neg_shape(self):
+        _assert_inverts(
+            sp.tklmbda,
+            _tukey_lmbda_quantile,
+            0, [ProbArg(), Arg(-25, 0, inclusive_b=False)],
+            spfunc_first=False, rtol=1e-5,
+            endpt_atol=[1e-9, 1e-5])
+
+    @pytest.mark.xfail(run=False)
+    def test_tklmbda_pos_shape(self):
+        _assert_inverts(
+            sp.tklmbda,
+            _tukey_lmbda_quantile,
+            0, [ProbArg(), Arg(0, 100, inclusive_a=False)],
+            spfunc_first=False, rtol=1e-5)
+
+    # The values of lmdba are chosen so that 1/lmbda is exact.
+    @pytest.mark.parametrize('lmbda', [0.5, 1.0, 8.0])
+    def test_tklmbda_lmbda1(self, lmbda):
+        bound = 1/lmbda
+        assert_equal(sp.tklmbda([-bound, bound], lmbda), [0.0, 1.0])
+
+
+funcs = [
+    ("btdtria", 3),
+    ("btdtrib", 3),
+    ("bdtrik", 3),
+    ("bdtrin", 3),
+    ("chdtriv", 2),
+    ("chndtr", 3),
+    ("chndtrix", 3),
+    ("chndtridf", 3),
+    ("chndtrinc", 3),
+    ("fdtridfd", 3),
+    ("ncfdtr", 4),
+    ("ncfdtri", 4),
+    ("ncfdtridfn", 4),
+    ("ncfdtridfd", 4),
+    ("ncfdtrinc", 4),
+    ("gdtrix", 3),
+    ("gdtrib", 3),
+    ("gdtria", 3),
+    ("nbdtrik", 3),
+    ("nbdtrin", 3),
+    ("nrdtrimn", 3),
+    ("nrdtrisd", 3),
+    ("pdtrik", 2),
+    ("stdtr", 2),
+    ("stdtrit", 2),
+    ("stdtridf", 2),
+    ("nctdtr", 3),
+    ("nctdtrit", 3),
+    ("nctdtridf", 3),
+    ("nctdtrinc", 3),
+    ("tklmbda", 2),
+]
+
+
+@pytest.mark.parametrize('func,numargs', funcs, ids=[x[0] for x in funcs])
+def test_nonfinite(func, numargs):
+
+    rng = np.random.default_rng(1701299355559735)
+    func = getattr(sp, func)
+    args_choices = [(float(x), np.nan, np.inf, -np.inf) for x in rng.random(numargs)]
+
+    for args in itertools.product(*args_choices):
+        res = func(*args)
+
+        if any(np.isnan(x) for x in args):
+            # Nan inputs should result to nan output
+            assert_equal(res, np.nan)
+        else:
+            # All other inputs should return something (but not
+            # raise exceptions or cause hangs)
+            pass
+
+
+def test_chndtrix_gh2158():
+    # test that gh-2158 is resolved; previously this blew up
+    res = sp.chndtrix(0.999999, 2, np.arange(20.)+1e-6)
+
+    # Generated in R
+    # options(digits=16)
+    # ncp <- seq(0, 19) + 1e-6
+    # print(qchisq(0.999999, df = 2, ncp = ncp))
+    res_exp = [27.63103493142305, 35.25728589950540, 39.97396073236288,
+               43.88033702110538, 47.35206403482798, 50.54112500166103,
+               53.52720257322766, 56.35830042867810, 59.06600769498512,
+               61.67243118946381, 64.19376191277179, 66.64228141346548,
+               69.02756927200180, 71.35726934749408, 73.63759723904816,
+               75.87368842650227, 78.06984431185720, 80.22971052389806,
+               82.35640899964173, 84.45263768373256]
+    assert_allclose(res, res_exp)
+
+
+def test_nctdtrinc_gh19896():
+    # test that gh-19896 is resolved.
+    # Compared to SciPy 1.11 results from Fortran code.
+    dfarr = [0.001, 0.98, 9.8, 98, 980, 10000, 98, 9.8, 0.98, 0.001]
+    parr = [0.001, 0.1, 0.3, 0.8, 0.999, 0.001, 0.1, 0.3, 0.8, 0.999]
+    tarr = [0.0015, 0.15, 1.5, 15, 300, 0.0015, 0.15, 1.5, 15, 300]
+    desired = [3.090232306168629, 1.406141304556198, 2.014225177124157,
+               13.727067118283456, 278.9765683871208, 3.090232306168629,
+               1.4312427877936222, 2.014225177124157, 3.712743137978295,
+               -3.086951096691082]
+    actual = sp.nctdtrinc(dfarr, parr, tarr)
+    assert_allclose(actual, desired, rtol=5e-12, atol=0.0)
+
+
+def test_stdtr_stdtrit_neg_inf():
+    # -inf was treated as +inf and values from the normal were returned
+    assert np.all(np.isnan(sp.stdtr(-np.inf, [-np.inf, -1.0, 0.0, 1.0, np.inf])))
+    assert np.all(np.isnan(sp.stdtrit(-np.inf, [0.0, 0.25, 0.5, 0.75, 1.0])))
+
+
+def test_bdtrik_nbdtrik_inf():
+    y = np.array(
+        [np.nan,-np.inf,-10.0, -1.0, 0.0, .00001, .5, 0.9999, 1.0, 10.0, np.inf])
+    y = y[:,None]
+    p = np.atleast_2d(
+        [np.nan, -np.inf, -10.0, -1.0, 0.0, .00001, .5, 1.0, np.inf])
+    assert np.all(np.isnan(sp.bdtrik(y, np.inf, p)))
+    assert np.all(np.isnan(sp.nbdtrik(y, np.inf, p)))
+
+
+@pytest.mark.parametrize(
+    "dfn,dfd,nc,f,expected_cdf",
+    [[100.0, 0.1, 0.1, 100.0, 0.29787396410092676],
+     [100.0, 100.0, 0.01, 0.1, 4.4344737598690424e-26],
+     [100.0, 0.01, 0.1, 0.01, 0.002848616633080384],
+     [10.0, 0.01, 1.0, 0.1, 0.012339557729057956],
+     [100.0, 100.0, 0.01, 0.01, 1.8926477420964936e-72],
+     [1.0, 100.0, 100.0, 0.1, 1.7925940526821304e-22],
+     [1.0, 0.01, 100.0, 10.0, 0.012334711965024968],
+     [1.0, 0.01, 10.0, 0.01, 0.00021944525290299],
+     [10.0, 1.0, 0.1, 100.0, 0.9219345555070705],
+     [0.1, 0.1, 1.0, 1.0, 0.3136335813423239],
+     [100.0, 100.0, 0.1, 10.0, 1.0],
+     [1.0, 0.1, 100.0, 10.0, 0.02926064279680897],
+     [1e-100, 3, 1.5, 1e100, 0.611815287345399]
+    ]
+)
+def test_ncfdtr_ncfdtri(dfn, dfd, nc, f, expected_cdf):
+    # Reference values computed with mpmath with the following script
+    #
+    # import numpy as np
+    #
+    # from mpmath import mp
+    # from scipy.special import ncfdtr
+    #
+    # mp.dps = 100
+    #
+    # def mp_ncfdtr(dfn, dfd, nc, f):
+    #     # Uses formula 26.2.20 from Abramowitz and Stegun.
+    #     dfn, dfd, nc, f = map(mp.mpf, (dfn, dfd, nc, f))
+    #     def term(j):
+    #         result = mp.exp(-nc/2)*(nc/2)**j / mp.factorial(j)
+    #         result *= mp.betainc(
+    #             dfn/2 + j, dfd/2, 0, f*dfn/(f*dfn + dfd), regularized=True
+    #         )
+    #         return result
+    #     result = mp.nsum(term, [0, mp.inf])
+    #     return float(result)
+    #
+    # dfn = np.logspace(-2, 2, 5)
+    # dfd = np.logspace(-2, 2, 5)
+    # nc = np.logspace(-2, 2, 5)
+    # f = np.logspace(-2, 2, 5)
+    #
+    # dfn, dfd, nc, f = np.meshgrid(dfn, dfd, nc, f)
+    # dfn, dfd, nc, f = map(np.ravel, (dfn, dfd, nc, f))
+    #
+    # cases = []
+    # re = []
+    # for x0, x1, x2, x3 in zip(*(dfn, dfd, nc, f)):
+    #     observed = ncfdtr(x0, x1, x2, x3)
+    #     expected = mp_ncfdtr(x0, x1, x2, x3)
+    #     cases.append((x0, x1, x2, x3, expected))
+    #     re.append((abs(expected - observed)/abs(expected)))
+    #
+    # assert np.max(re) < 1e-13
+    #
+    # rng = np.random.default_rng(1234)
+    # sample_idx = rng.choice(len(re), replace=False, size=12)
+    # cases = np.array(cases)[sample_idx].tolist()
+    assert_allclose(sp.ncfdtr(dfn, dfd, nc, f), expected_cdf, rtol=1e-13, atol=0)
+    # testing tails where the CDF reaches 0 or 1 does not make sense for inverses
+    # of a CDF as they are not bijective in these regions
+    if 0 < expected_cdf < 1:
+        assert_allclose(sp.ncfdtri(dfn, dfd, nc, expected_cdf), f, rtol=5e-11)
+
+@pytest.mark.parametrize(
+    "args",
+    [(-1.0, 0.1, 0.1, 0.5),
+     (1, -1.0, 0.1, 0.5),
+     (1, 1, -1.0, 0.5),
+     (1, 1, 1, 100),
+     (1, 1, 1, -1)]
+)
+def test_ncfdtri_domain_error(args):
+    with sp.errstate(domain="raise"):
+        with pytest.raises(sp.SpecialFunctionError, match="domain"):
+            sp.ncfdtri(*args)
+
+class TestNoncentralTFunctions:
+
+    # Reference values computed with mpmath with the following script
+    # Formula from:
+    # Lenth, Russell V (1989). "Algorithm AS 243: Cumulative Distribution Function
+    # of the Non-central t Distribution". Journal of the Royal Statistical Society,
+    # Series C. 38 (1): 185-189
+    #
+    # Warning: may take a long time to run
+    #
+    # from mpmath import mp
+    # mp.dps = 400
+
+    # def nct_cdf(df, nc, x):
+    #     df, nc, x = map(mp.mpf, (df, nc, x))
+        
+    #     def f(df, nc, x):
+    #         phi = mp.ncdf(-nc)
+    #         y = x * x / (x * x + df)
+    #         constant = mp.exp(-nc * nc / 2.)
+    #         def term(j):
+    #             intermediate = constant * (nc *nc / 2.)**j
+    #             p = intermediate/mp.factorial(j)
+    #             q = nc / (mp.sqrt(2.) * mp.gamma(j + 1.5)) * intermediate
+    #             first_beta_term = mp.betainc(j + 0.5, df/2., x2=y,
+    #                                          regularized=True)
+    #             second_beta_term = mp.betainc(j + mp.one, df/2., x2=y,
+    #                                           regularized=True)
+    #             return p * first_beta_term + q * second_beta_term
+
+    #         sum_term = mp.nsum(term, [0, mp.inf])
+    #         f = phi + 0.5 * sum_term
+    #         return f
+
+    #     if x >= 0:
+    #         result = f(df, nc, x)
+    #     else:
+    #         result = mp.one - f(df, -nc, x)
+    #     return float(result)
+
+    @pytest.mark.parametrize("df, nc, x, expected_cdf", [
+        (0.98, -3.8, 0.0015, 0.9999279987514815),
+        (0.98, -3.8, 0.15, 0.9999528361700505),
+        (0.98, -3.8, 1.5, 0.9999908823016942),
+        (0.98, -3.8, 15, 0.9999990264591945),
+        (0.98, 0.38, 0.0015, 0.35241533122693),
+        (0.98, 0.38, 0.15, 0.39749697267146983),
+        (0.98, 0.38, 1.5, 0.716862963488558),
+        (0.98, 0.38, 15, 0.9656246449257494),
+        (0.98, 3.8, 0.0015, 7.26973354942293e-05),
+        (0.98, 3.8, 0.15, 0.00012416481147589105),
+        (0.98, 3.8, 1.5, 0.035388035775454095),
+        (0.98, 3.8, 15, 0.7954826975430583),
+        (0.98, 38, 0.0015, 3.02106943e-316),
+        (0.98, 38, 0.15, 6.069970616996603e-309),
+        (0.98, 38, 1.5, 2.591995360483094e-97),
+        (0.98, 38, 15, 0.011927265886910935),
+        (9.8, -3.8, 0.0015, 0.9999280776192786),
+        (9.8, -3.8, 0.15, 0.9999599410685442),
+        (9.8, -3.8, 1.5, 0.9999997432394788),
+        (9.8, -3.8, 15, 0.9999999999999984),
+        (9.8, 0.38, 0.0015, 0.3525155979107491),
+        (9.8, 0.38, 0.15, 0.40763120140379194),
+        (9.8, 0.38, 1.5, 0.8476794017024651),
+        (9.8, 0.38, 15, 0.9999999297116268),
+        (9.8, 3.8, 0.0015, 7.277620328149153e-05),
+        (9.8, 3.8, 0.15, 0.00013024802220900652),
+        (9.8, 3.8, 1.5, 0.013477432800072933),
+        (9.8, 3.8, 15, 0.999850151230648),
+        (9.8, 38, 0.0015, 3.05066095e-316),
+        (9.8, 38, 0.15, 1.79065514676e-313),
+        (9.8, 38, 1.5, 2.0935940165900746e-249),
+        (9.8, 38, 15, 2.252076291604796e-09),
+        (98, -3.8, 0.0015, 0.9999280875149109),
+        (98, -3.8, 0.15, 0.9999608250170452),
+        (98, -3.8, 1.5, 0.9999999304757682),
+        (98, -3.8, 15, 1.0),
+        (98, 0.38, 0.0015, 0.35252817848596313),
+        (98, 0.38, 0.15, 0.40890253001794846),
+        (98, 0.38, 1.5, 0.8664672830006552),
+        (98, 0.38, 15, 1.0),
+        (98, 3.8, 0.0015, 7.278609891281275e-05),
+        (98, 3.8, 0.15, 0.0001310318674827004),
+        (98, 3.8, 1.5, 0.010990879189991727),
+        (98, 3.8, 15, 0.9999999999999989),
+        (98, 38, 0.0015, 3.05437385e-316),
+        (98, 38, 0.15, 9.1668336166e-314),
+        (98, 38, 1.5, 1.8085884236563926e-288),
+        (98, 38, 15, 2.7740532792035907e-50),
+        (980, -3.8, 0.0015, 0.9999280885188965),
+        (980, -3.8, 0.15, 0.9999609144559273),
+        (980, -3.8, 1.5, 0.9999999410050979),
+        (980, -3.8, 15, 1.0),
+        (980, 0.38, 0.0015, 0.3525294548792812),
+        (980, 0.38, 0.15, 0.4090315324657382),
+        (980, 0.38, 1.5, 0.8684247068517293),
+        (980, 0.38, 15, 1.0),
+        (980, 3.8, 0.0015, 7.278710289828983e-05),
+        (980, 3.8, 0.15, 0.00013111131667906573),
+        (980, 3.8, 1.5, 0.010750678886113882),
+        (980, 3.8, 15, 1.0),
+        (980, 38, 0.0015, 3.0547506e-316),
+        (980, 38, 0.15, 8.6191646313e-314),
+        (980, 38, 15, 5.407535300713606e-105)
+    ])
+    def test_gh19896(self, df, nc, x, expected_cdf):
+        # test that gh-19896 is resolved.
+        # Originally this was a regression test that used the old Fortran results
+        # as a reference. The Fortran results were not accurate, so the reference
+        # values were recomputed with mpmath.
+        nctdtr_result = sp.nctdtr(df, nc, x)
+        assert_allclose(nctdtr_result, expected_cdf, rtol=1e-13, atol=1e-303)
+
+    def test_gh19896_loose_tolerance(self):
+        # edge case with very small CDF value, requires a looser tolerance to pass
+        assert_allclose(sp.nctdtr(980, 38, 1.5), 1.1824454111413493e-291, rtol=1e-8)
+
+    def test_nctdtr_gh8344(self):
+        # test that gh-8344 is resolved.
+        df, nc, x = 3000, 3, 0.1
+        expected = 0.0018657780826323328
+        assert_allclose(sp.nctdtr(df, nc, x), expected, rtol=1e-14)
+
+    @pytest.mark.parametrize(
+        "df, nc, x, expected, rtol",
+        [[3., 5., -2., 1.5645373999149622e-09, 2e-8],
+         [1000., 10., 1., 1.1493552133826623e-19, 1e-13],
+         [1e-5, -6., 2., 0.9999999990135003, 1e-13],
+         [10., 20., 0.15, 6.426530505957303e-88, 1e-13],
+         [1., 1., np.inf, 1.0, 0.0],
+         [1., 1., -np.inf, 0.0, 0.0]
+        ]
+    )
+    def test_nctdtr_accuracy(self, df, nc, x, expected, rtol):
+        assert_allclose(sp.nctdtr(df, nc, x), expected, rtol=rtol)
+
+    @pytest.mark.parametrize("df, nc, x, expected_cdf", [
+        (0.98, 38, 1.5, 2.591995360483094e-97),
+        (3000, 3, 0.1, 0.0018657780826323328),
+        (0.98, -3.8, 15, 0.9999990264591945),
+        (9.8, 38, 15, 2.252076291604796e-09),
+
+    ])
+    def test_nctdtrit(self, df, nc, x, expected_cdf):
+        assert_allclose(sp.nctdtrit(df, nc, expected_cdf), x, rtol=1e-10)
+
+
+class TestNegativeBinomialFunctions:
+
+    @pytest.mark.parametrize("function", [sp.nbdtrin, sp.nbdtrik])
+    @pytest.mark.parametrize("args",
+        [(np.nan, 1, 1), (1, np.nan, 1), (1, 1, np.nan),
+         (np.nan, np.nan, 1), (np.nan, 1, np.nan), (1, np.nan, np.nan),
+         (np.nan, np.nan, np.nan)]
+    )
+    def test_nan_propagation(self, function, args):
+        assert np.isnan(function(*args))
+
+    @pytest.mark.parametrize("args",
+        [(-1, 1, 1), (1, -1, 1), (1, 1, -1), (-1, -1, 1),
+         (-1, 1, -1), (1, -1, -1), (-1, -1, -1),
+         (1, 1.1, 0.9), (1, 0.9, 1.1)]
+    )  
+    def test_domain_error_nbdtrin(self, args):
+        with sp.errstate(domain="raise"):
+            with pytest.raises(sp.SpecialFunctionError, match="domain"):
+                sp.nbdtrin(*args)
+
+    @pytest.mark.parametrize("args",
+        [(-1, 1, 1), (1, -1, 1), (1, 1, -1), (-1, -1, 1),
+         (-1, 1, -1), (1, -1, -1), (-1, -1, -1),
+         (1, 0.9, 1.1)]
+    )  
+    def test_domain_error_nbdtrik(self, args):
+        with sp.errstate(domain="raise"):
+            with pytest.raises(sp.SpecialFunctionError, match="domain"):
+                sp.nbdtrik(*args)
+
+    @pytest.mark.parametrize("k, y, p, n, rtol",
+        [(5, 0.3214569091796875, 0.25, 3, 5e-16),
+         (10, 3.820379007878081e-70, 0.15, 100, 1e-15),
+         (100, 0.975574722927043, 0.15, 10, 1e-14),
+         (2, 3.503253250000002e-73, 0.001, 25, 5e-15),
+         (2, 0.9999993271029954, 0.999, 15, 1e-10),
+         (500, 0.9999999998603178, 0.1, 15, 1e-8),
+         (0, 1.0000000000000006e-10, 0.1, 10, 5e-16)])
+    def test_inverses(self, k, y, p, n, rtol):
+        # The following code was used to generate the values. 
+        # import mpmath
+        # import scipy
+        # mpmath.mp.dps = 1000
+
+        # def neg_binomial_cdf(k, n, p):
+        #     return mpmath.betainc(n, k+1, x1=0, x2=p, regularized=True)
+
+        assert_allclose(sp.nbdtrin(k, y, p), n, rtol)
+        assert_allclose(sp.nbdtrik(y, n, p), k, rtol)
+
+
+class TestNoncentralChiSquaredFunctions:
+
+    def test_chndtr_and_inverses_against_wolfram_alpha(self):
+        # Each row holds (x, nu, lam, expected_value)
+        # These values were computed using Wolfram Alpha with
+        #     CDF[NoncentralChiSquareDistribution[nu, lam], x]
+        values = np.array([
+            [25.00, 20.0, 400, 4.1210655112396197139e-57],
+            [25.00, 8.00, 250, 2.3988026526832425878e-29],
+            [0.001, 8.00, 40., 5.3761806201366039084e-24],
+            [0.010, 8.00, 40., 5.45396231055999457039e-20],
+            [20.00, 2.00, 107, 1.39390743555819597802e-9],
+            [22.50, 2.00, 107, 7.11803307138105870671e-9],
+            [25.00, 2.00, 107, 3.11041244829864897313e-8],
+            [3.000, 2.00, 1.0, 0.62064365321954362734],
+            [350.0, 300., 10., 0.93880128006276407710],
+            [100.0, 13.5, 10., 0.99999999650104210949],
+            [700.0, 20.0, 400, 0.99999999925680650105],
+            [150.0, 13.5, 10., 0.99999999999999983046],
+            [160.0, 13.5, 10., 0.99999999999999999518],  # 1.0
+        ])
+        cdf = sp.chndtr(values[:, 0], values[:, 1], values[:, 2])
+        assert_allclose(cdf, values[:, 3], rtol=1e-13)
+        # the last two values are very close to 1.0, so we do not
+        # test the inverses for them
+        x = sp.chndtrix(values[:, 3], values[:, 1], values[:, 2])
+        assert_allclose(x[:-2], values[:-2, 0], rtol=1e-8)
+        df = sp.chndtridf(values[:, 0], values[:, 3], values[:, 2])
+        assert_allclose(df[:-2], values[:-2, 1], rtol=1e-8)
+        nc = sp.chndtrinc(values[:, 0], values[:, 1], values[:, 3])
+        assert_allclose(nc[:-2], values[:-2, 2], rtol=1e-8)
+
+    # CDF Reference values computed with mpmath with the following script
+    # Formula from:
+    # https://www.boost.org/doc/libs/1_87_0/libs/math/doc/html/math_toolkit/dist_ref/dists/nc_chi_squared_dist.html  # noqa: E501
+    # which cites:
+    # Computing discrete mixtures of continuous distributions: noncentral chisquare,
+    # noncentral t and the distribution of the square of the
+    # sample multiple correlation coefficient",
+    # Denise Benton and K. Krishnamoorthy,
+    # Computational Statistics & Data Analysis, 43, (2003), 249-267
+
+    # Warning: may take a long time to run
+    # from mpmath import mp
+    #
+    # mp.dps = 400
+    # 
+    # def noncentral_chi_squared_cdf(x, df, nc):
+    #    x, df, nc = map(mp.mpf, (x, df, nc))
+    #    def term(i):
+    #        return mp.exp(-nc/2) * (nc/2)**i / mp.factorial(i) * 
+    #               mp.gammainc(df/2 + i, 0, x/2, regularized=True)
+    #    return float(mp.nsum(term, [0, mp.inf]))
+
+    @pytest.mark.parametrize(
+        "x, df, nc, expected_cdf, rtol_cdf, rtol_inv",
+        [(0.1, 200, 50, 1.1311224867205481e-299, 1e-13, 1e-13),
+         (1e-12, 20, 50, 3.737446313006551e-141, 1e-13, 1e-13),
+         (1, 200, 50, 8.09760974833666e-200, 1e-13, 1e-13),
+         (9e4, 1e5, 1e3, 1.6895533704217566e-141, 5e-12, 5e-12),
+         (30, 3, 1.5, 0.9999508759095675, 5e-13, 5e-13),
+         (500, 300, 1.5, 0.9999999999944232, 1e-13, 1e-5),
+         (1400, 30, 1e3, 0.9999999612246238, 1e-13, 1e-9),
+         (400, 50, 200, 0.9999948255072892, 1e-13, 1e-11)]
+    )
+    def test_tails(self, x, df, nc, expected_cdf, rtol_cdf, rtol_inv):
+        chndtr_result = sp.chndtr(x, df, nc)
+        assert_allclose(chndtr_result, expected_cdf, rtol=rtol_cdf)
+        assert_allclose(sp.chndtrix(expected_cdf, df, nc), x, rtol=rtol_inv)
+        assert_allclose(sp.chndtridf(x, expected_cdf, nc), df, rtol=rtol_inv)
+        assert_allclose(sp.chndtrinc(x, df, expected_cdf), nc, rtol=rtol_inv)
+
+        # test round-trip calculation
+        assert_allclose(sp.chndtrix(chndtr_result, df, nc), x, rtol=rtol_inv)
+        assert_allclose(sp.chndtridf(x, chndtr_result, nc), df, rtol=1e-7)
+        assert_allclose(sp.chndtrinc(x, df, chndtr_result), nc, rtol=1e-5)
+
+    @pytest.mark.parametrize("x, df",
+        [(1, 3), (1, 0), (1, np.inf), (np.inf, 1)]
+    )
+    def test_chndtr_with_nc_zero_equals_chdtr(self, x, df):
+        assert_allclose(sp.chndtr(x, df, 0), sp.chdtr(df, x), rtol=1e-15)
+
+    @pytest.mark.parametrize("fun",
+        [sp.chndtr, sp.chndtrix, sp.chndtridf, sp.chndtrinc]
+    )
+    @pytest.mark.parametrize("args",
+        [(-1, 1, 1), (1, -1, 1), (1, 1, -1), (-1, -1, 1),
+         (-1, 1, -1), (1, -1, -1), (-1, -1, -1)]
+    )  
+    def test_domain_error(self, args, fun):
+        with sp.errstate(domain="raise"):
+            with pytest.raises(sp.SpecialFunctionError, match="domain"):
+                fun(*args)
+
+    @pytest.mark.parametrize("fun",
+        [sp.chndtr, sp.chndtrix, sp.chndtridf, sp.chndtrinc]
+    )
+    @pytest.mark.parametrize("args",
+        [(np.nan, 1, 1), (1, np.nan, 1), (1, 1, np.nan),
+         (np.nan, np.nan, 1), (np.nan, 1, np.nan), (1, np.nan, np.nan),
+         (np.nan, np.nan, np.nan)]
+    )
+    def test_nan_propagation(self, fun, args):
+        assert np.isnan(fun(*args))
+
+    @pytest.mark.parametrize(
+        "x, df, nc, expected",
+        [(1, 0, 1, np.nan),
+         (1, 0, np.inf, np.nan),
+         (1, np.inf, 1, np.nan),
+         (1, np.inf, np.inf, 0),
+         (1, 1, np.inf, 0),
+         (np.inf, 0, 1, np.nan),
+         (np.inf, 1, np.inf, np.nan),
+         (np.inf, 1, 1, 1),
+         (np.inf, np.inf, np.inf, np.nan)]
+    )
+    def test_chndtr_edge_cases(self, x, df, nc, expected):
+        assert_allclose(sp.chndtr(x, df, nc), expected, rtol=1e-15)
+
+
+@pytest.mark.parametrize("x", [0.1, 100])
+def test_chdtriv_p_equals_1_returns_0(x):
+    assert sp.chdtriv(1, x) == 0
+
+
+class TestPdtrik:
+    @pytest.mark.parametrize("p, m, expected",
+                             [(0, 0.5, 0),
+                              (0.5, 0, 0)])
+    def test_edge_cases(self, p, m, expected):
+        assert sp.pdtrik(p, m) == expected
+
+    @pytest.mark.parametrize("m", (0.1, 1, 10))
+    def test_p_equals_1_returns_nan(self, m):
+        assert np.isnan(sp.pdtrik(1, m))
+
+    def test_small_probabilities(self):
+        # Edge case: m = 0 or very small.
+        k = sp.pdtrik([[0], [0.25], [0.95]], [0, 1e-20, 1e-6])
+        assert_array_equal(k, np.zeros((3, 3)))
+
+    def test_roundtrip_against_pdtr(self):
+        m = [10, 50, 500]
+        k = 5
+        p = sp.pdtr(k, m)
+        assert_allclose(sp.pdtrik(p, m), k, rtol=1e-15)
+
+    @pytest.mark.parametrize("p, m, k",
+                             [(1.8976107553682285e-40, 100, 2),
+                              (0.48670120172085135, 100, 99),
+                              (8.30383406699052e-69, 1000, 500),
+                              (2.252837804125894e-227, 100_000, 90_000)])
+    def test_accuracy(self, p, m, k):
+        # Reference values for p were computed with mpmath using
+        # mp.gammainc(k+1, a=m, regularized=True)
+        assert_allclose(sp.pdtrik(p, m), k, rtol=1e-15)
+
+@pytest.mark.parametrize("a, b, p, ref", [
+    (0, 0, 0, np.nan),
+    (0, 0, 1, np.nan),
+    (0, np.inf, 0, np.nan),
+    (0, np.inf, 1, np.nan),
+    (np.inf, 0, 0, np.nan),
+    (np.inf, 0, 1, np.nan),
+    (np.inf, np.inf, 0, np.nan),
+    (np.inf, np.inf, 1, np.nan)
+])
+def test_gdtrix_edge_cases(a, b, p, ref):
+    assert_equal(sp.gdtrix(a, b, p), ref)
+
+@pytest.mark.parametrize("p, b, x, ref", [
+    (0, 0, 0, np.nan),
+    (0, 0, np.inf, np.nan),
+    (0, 1, 0, np.nan),
+    (0, 1, np.inf, 0),
+    (np.inf, 0, 0, np.nan),
+    (np.inf, 0, np.inf, np.nan),
+    (np.inf, 1, 0, np.nan),
+    (np.inf, 1, np.inf, np.nan)
+])
+def test_gdtria_edge_cases(p, b, x, ref):
+    assert_equal(sp.gdtria(p, b, x), ref)
+
+@pytest.mark.parametrize("y, n, p, k", [
+    (6.110236824190975e-78, 100, 0.9, 10),
+    (4.0188255421199357e-224, 1000, 0.9, 500),
+    (0.9999998319058928, 1000, 0.5, 580),
+    (0.9999734386011124, 100, 0.9, 99)
+])
+def test_bdtrik(y, n, p, k):
+    # Reference values for y were computed with mpmath using
+    # the _binomial_cdf function from above.
+    assert_allclose(sp.bdtrik(y, n, p), k, rtol=1e-11)
+
+
+@pytest.mark.parametrize("p, std, x, ref", [
+    (0, 0.1, 0, np.nan),
+    (0.1, np.inf, 1, np.inf),
+    (0.1, 1, np.inf, np.inf),
+    (0.1, 1, -np.inf, -np.inf),
+    (0.1, np.inf, np.inf, np.inf),
+    (0.1, 0.1, np.inf, np.inf),
+    (0.1, 1, -np.inf, -np.inf),
+    (0.3, -1, 1, np.nan)
+])
+def test_nrdtrimn_edge_cases(p, std, x, ref):
+    assert_equal(sp.nrdtrimn(p, std, x), ref)
+
+
+@pytest.mark.parametrize("mn, p, x, ref", [
+    (0, 0, 0, np.nan),
+    (0, 1, 0, np.nan),
+    (0, 1, np.inf, np.nan),
+    (0.1, 1, 1, np.nan),
+    (0.1, 0.1, np.inf, -np.inf),
+    (0.1, 0.1, -np.inf, np.inf),
+])
+def test_nrdtrisd_edge_cases(mn, p, x, ref):
+    assert_equal(sp.nrdtrisd(mn, p, x), ref)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_cdft_asymptotic.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_cdft_asymptotic.py
new file mode 100644
index 0000000000000000000000000000000000000000..2f21b197871a230e3170c21969a8edcc8ebbdfc2
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_cdft_asymptotic.py
@@ -0,0 +1,52 @@
+# gh-14777 regression tests
+# Test stdtr and stdtrit with infinite df and large values of df
+
+import numpy as np
+from numpy.testing import assert_allclose, assert_equal
+from scipy.special import stdtr, stdtrit, ndtr, ndtri
+
+
+def test_stdtr_vs_R_large_df():
+    df = [1e10, 1e12, 1e120, np.inf]
+    t = 1.
+    res = stdtr(df, t)
+    # R Code:
+    #   options(digits=20)
+    #   pt(1., c(1e10, 1e12, 1e120, Inf))
+    res_R = [0.84134474605644460343,
+             0.84134474606842180044,
+             0.84134474606854281475,
+             0.84134474606854292578]
+    assert_allclose(res, res_R, rtol=1e-15)
+    # last value should also agree with ndtr
+    assert_equal(res[3], ndtr(1.))
+
+
+def test_stdtrit_vs_R_large_df():
+    df = [1e10, 1e12, 1e120, np.inf]
+    p = 0.1
+    res = stdtrit(df, p)
+    # R Code:
+    #   options(digits=20)
+    #   qt(0.1, c(1e10, 1e12, 1e120, Inf))
+    res_R = [-1.2815515656292593150,
+             -1.2815515655454472466,
+             -1.2815515655446008125,
+             -1.2815515655446008125]
+    assert_allclose(res, res_R, rtol=1e-15, atol=1e-15)
+    # last value should also agree with ndtri
+    # actually the result from stdtrit is closer to R than ndtri,
+    # so we accept a deviation of one ULP
+    epsilon = np.finfo(np.float64).eps
+    assert_allclose(res[3], ndtri(0.1), rtol=epsilon, atol=epsilon)
+
+
+def test_stdtr_stdtri_invalid():
+    # a mix of large and inf df with t/p equal to nan
+    df = [1e10, 1e12, 1e120, np.inf]
+    x = np.nan
+    res1 = stdtr(df, x)
+    res2 = stdtrit(df, x)
+    res_ex = 4*[np.nan]
+    assert_equal(res1, res_ex)
+    assert_equal(res2, res_ex)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_cephes_intp_cast.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_cephes_intp_cast.py
new file mode 100644
index 0000000000000000000000000000000000000000..05f3d1ae5c101ff50c75d1065e5e234063d192e4
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_cephes_intp_cast.py
@@ -0,0 +1,29 @@
+import pytest
+import numpy as np
+from scipy.special._ufuncs import (
+    _smirnovc, _smirnovci, _smirnovp,
+    _struve_asymp_large_z, _struve_bessel_series, _struve_power_series,
+    bdtr, bdtrc, bdtri, expn, kn, nbdtr, nbdtrc, nbdtri, pdtri,
+    smirnov, smirnovi, yn
+)
+
+
+#
+# For each ufunc here, verify that the default integer type, np.intp,
+# can be safely cast to the integer type found in the input type signatures.
+# For this particular set of functions, the code expects to find just one
+# integer type among the input signatures.
+#
+@pytest.mark.parametrize(
+    'ufunc',
+    [_smirnovc, _smirnovci, _smirnovp,
+     _struve_asymp_large_z, _struve_bessel_series, _struve_power_series,
+     bdtr, bdtrc, bdtri, expn, kn, nbdtr, nbdtrc, nbdtri, pdtri,
+     smirnov, smirnovi, yn],
+)
+def test_intp_safe_cast(ufunc):
+    int_chars = {'i', 'l', 'q'}
+    int_input = [set(sig.split('->')[0]) & int_chars for sig in ufunc.types]
+    int_char = ''.join(s.pop() if s else '' for s in int_input)
+    assert len(int_char) == 1, "More integer types in the signatures than expected"
+    assert np.can_cast(np.intp, np.dtype(int_char))
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_cosine_distr.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_cosine_distr.py
new file mode 100644
index 0000000000000000000000000000000000000000..27e3ca2699d0d1d0b58665f125d99c166095696d
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_cosine_distr.py
@@ -0,0 +1,83 @@
+import numpy as np
+from numpy.testing import assert_allclose
+import pytest
+from scipy.special._ufuncs import _cosine_cdf, _cosine_invcdf
+
+
+# These values are (x, p) where p is the expected exact value of
+# _cosine_cdf(x).  These values will be tested for exact agreement.
+_coscdf_exact = [
+    (-4.0, 0.0),
+    (0, 0.5),
+    (np.pi, 1.0),
+    (4.0, 1.0),
+]
+
+@pytest.mark.parametrize("x, expected", _coscdf_exact)
+def test_cosine_cdf_exact(x, expected):
+    assert _cosine_cdf(x) == expected
+
+
+# These values are (x, p), where p is the expected value of
+# _cosine_cdf(x). The expected values were computed with mpmath using
+# 50 digits of precision.  These values will be tested for agreement
+# with the computed values using a very small relative tolerance.
+# The value at -np.pi is not 0, because -np.pi does not equal -π.
+_coscdf_close = [
+    (3.1409, 0.999999999991185),
+    (2.25, 0.9819328173287907),
+    # -1.6 is the threshold below which the Pade approximant is used.
+    (-1.599, 0.08641959838382553),
+    (-1.601, 0.086110582992713),
+    (-2.0, 0.0369709335961611),
+    (-3.0, 7.522387241801384e-05),
+    (-3.1415, 2.109869685443648e-14),
+    (-3.14159, 4.956444476505336e-19),
+    (-np.pi, 4.871934450264861e-50),
+]
+
+@pytest.mark.parametrize("x, expected", _coscdf_close)
+def test_cosine_cdf(x, expected):
+    assert_allclose(_cosine_cdf(x), expected, rtol=5e-15)
+
+
+# These values are (p, x) where x is the expected exact value of
+# _cosine_invcdf(p).  These values will be tested for exact agreement.
+_cosinvcdf_exact = [
+    (0.0, -np.pi),
+    (0.5, 0.0),
+    (1.0, np.pi),
+]
+
+@pytest.mark.parametrize("p, expected", _cosinvcdf_exact)
+def test_cosine_invcdf_exact(p, expected):
+    assert _cosine_invcdf(p) == expected
+
+
+def test_cosine_invcdf_invalid_p():
+    # Check that p values outside of [0, 1] return nan.
+    assert np.isnan(_cosine_invcdf([-0.1, 1.1])).all()
+
+
+# These values are (p, x), where x is the expected value of _cosine_invcdf(p).
+# The expected values were computed with mpmath using 50 digits of precision.
+_cosinvcdf_close = [
+    (1e-50, -np.pi),
+    (1e-14, -3.1415204137058454),
+    (1e-08, -3.1343686589124524),
+    (0.0018001, -2.732563923138336),
+    (0.010, -2.41276589008678),
+    (0.060, -1.7881244975330157),
+    (0.125, -1.3752523669869274),
+    (0.250, -0.831711193579736),
+    (0.400, -0.3167954512395289),
+    (0.419, -0.25586025626919906),
+    (0.421, -0.24947570750445663),
+    (0.750, 0.831711193579736),
+    (0.940, 1.7881244975330153),
+    (0.9999999996, 3.1391220839917167),
+]
+
+@pytest.mark.parametrize("p, expected", _cosinvcdf_close)
+def test_cosine_invcdf(p, expected):
+    assert_allclose(_cosine_invcdf(p), expected, rtol=1e-14)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_cython_abi.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_cython_abi.py
new file mode 100644
index 0000000000000000000000000000000000000000..56b61ca951d511bf2a73c8c87e3cc7028ed91b0e
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_cython_abi.py
@@ -0,0 +1,87 @@
+# ---------------------------------------------------------------------------
+# AUTO-GENERATED - do not edit by hand.
+# Re-generate with:  python tools/generate_cython_abi_tests.py special
+#
+# Generated against SciPy 1.17.0 on 2026-05-08
+# Python 3.14.4
+# ---------------------------------------------------------------------------
+
+"""
+Regression test for the cython_special binary interface.
+
+The __pyx_capi__ dict of each module contains PyCapsule objects whose
+*name* string encodes the C-level function signature that Cython checks
+at import time when another module does ``cimport``.  Any change to
+those strings is a binary incompatibility that breaks every downstream
+package (e.g., scikit-learn, statsmodels) compiled against the previous release,
+without any compile-time warning.
+
+The expected signatures are stored in cython_abi_signatures.json.
+The test fails if:
+  * an existing name disappears, or
+  * an existing name's signature string changes.
+Adding new names is explicitly allowed (it is not a break).
+"""
+
+import ctypes
+import importlib
+import importlib.resources
+import json
+
+import pytest
+import scipy
+
+CYTHON_BLAS_ILP64 = (
+    scipy.show_config(mode='dicts')['Build Dependencies']['blas']['cython blas ilp64']
+)
+
+
+# ---------------------------------------------------------------------------
+# Helper
+# ---------------------------------------------------------------------------
+
+_get_capsule_name = ctypes.pythonapi.PyCapsule_GetName
+_get_capsule_name.restype = ctypes.c_char_p
+_get_capsule_name.argtypes = [ctypes.py_object]
+
+
+def _extract_capi(module):
+    """Return {name: signature} for every entry in module.__pyx_capi__."""
+    result = {}
+    for name, capsule in module.__pyx_capi__.items():
+        raw = _get_capsule_name(capsule)
+        if raw is not None:
+            result[name] = raw.decode('utf-8')
+    return result
+
+
+_sig_file = importlib.resources.files('scipy.special.tests').joinpath(
+    'cython_abi_signatures.json'
+)
+with importlib.resources.as_file(_sig_file) as _f:
+    _EXPECTED = json.loads(_f.read_text())
+
+
+def test_cython_special_abi_stability():
+    """No existing cython_special signature may change or disappear."""
+    expected = _EXPECTED['scipy.special.cython_special']
+    mod = importlib.import_module('scipy.special.cython_special')
+    actual = _extract_capi(mod)
+    errors = []
+    for name, expected_sig in expected.items():
+        if name not in actual:
+            errors.append(
+                f"REMOVED  {name!r} (was {expected_sig!r})"
+            )
+        elif actual[name] != expected_sig:
+            errors.append(
+                f"CHANGED  {name!r}\n"
+                f"  expected: {expected_sig!r}\n"
+                f"  actual:   {actual[name]!r}"
+            )
+    if errors:
+        joined = '\n'.join(errors)
+        pytest.fail(
+            f"scipy.special.cython_special.__pyx_capi__ has {len(errors)} "
+            f"ABI breakage(s):\n{joined}"
+        )
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_cython_special.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_cython_special.py
new file mode 100644
index 0000000000000000000000000000000000000000..a9307767ddaeb43dd8c319ac8197198f935f132a
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_cython_special.py
@@ -0,0 +1,363 @@
+import warnings
+
+from collections.abc import Callable
+
+import pytest
+from itertools import product
+from numpy.testing import assert_allclose
+from scipy import special
+from scipy.special import cython_special
+
+
+bint_points = [True, False]
+int_points = [-10, -1, 1, 10]
+real_points = [-10.0, -1.0, 1.0, 10.0]
+complex_points = [complex(*tup) for tup in product(real_points, repeat=2)]
+
+
+CYTHON_SIGNATURE_MAP = {
+    'b': 'bint',
+    'f': 'float',
+    'd': 'double',
+    'g': 'long double',
+    'F': 'float complex',
+    'D': 'double complex',
+    'G': 'long double complex',
+    'i': 'int',
+    'l': 'long'
+}
+
+
+TEST_POINTS = {
+    'b': bint_points,
+    'f': real_points,
+    'd': real_points,
+    'g': real_points,
+    'F': complex_points,
+    'D': complex_points,
+    'G': complex_points,
+    'i': int_points,
+    'l': int_points,
+}
+
+
+PARAMS: list[tuple[Callable, Callable, tuple[str, ...], str | None]] = [
+    (special.agm, cython_special.agm, ('dd',), None),
+    (special.airy, cython_special._airy_pywrap, ('d', 'D'), None),
+    (special.airye, cython_special._airye_pywrap, ('d', 'D'), None),
+    (special.bdtr, cython_special.bdtr, ('dld', 'ddd'), None),
+    (special.bdtrc, cython_special.bdtrc, ('dld', 'ddd'), None),
+    (special.bdtri, cython_special.bdtri, ('dld', 'ddd'), None),
+    (special.bdtrik, cython_special.bdtrik, ('ddd',), None),
+    (special.bdtrin, cython_special.bdtrin, ('ddd',), None),
+    (special.bei, cython_special.bei, ('d',), None),
+    (special.beip, cython_special.beip, ('d',), None),
+    (special.ber, cython_special.ber, ('d',), None),
+    (special.berp, cython_special.berp, ('d',), None),
+    (special.besselpoly, cython_special.besselpoly, ('ddd',), None),
+    (special.beta, cython_special.beta, ('dd',), None),
+    (special.betainc, cython_special.betainc, ('ddd',), None),
+    (special.betaincc, cython_special.betaincc, ('ddd',), None),
+    (special.betaincinv, cython_special.betaincinv, ('ddd',), None),
+    (special.betainccinv, cython_special.betainccinv, ('ddd',), None),
+    (special.betaln, cython_special.betaln, ('dd',), None),
+    (special.binom, cython_special.binom, ('dd',), None),
+    (special.boxcox, cython_special.boxcox, ('dd',), None),
+    (special.boxcox1p, cython_special.boxcox1p, ('dd',), None),
+    (special.btdtria, cython_special.btdtria, ('ddd',), None),
+    (special.btdtrib, cython_special.btdtrib, ('ddd',), None),
+    (special.cbrt, cython_special.cbrt, ('d',), None),
+    (special.chdtr, cython_special.chdtr, ('dd',), None),
+    (special.chdtrc, cython_special.chdtrc, ('dd',), None),
+    (special.chdtri, cython_special.chdtri, ('dd',), None),
+    (special.chdtriv, cython_special.chdtriv, ('dd',), None),
+    (special.chndtr, cython_special.chndtr, ('ddd',), None),
+    (special.chndtridf, cython_special.chndtridf, ('ddd',), None),
+    (special.chndtrinc, cython_special.chndtrinc, ('ddd',), None),
+    (special.chndtrix, cython_special.chndtrix, ('ddd',), None),
+    (special.cosdg, cython_special.cosdg, ('d',), None),
+    (special.cosm1, cython_special.cosm1, ('d',), None),
+    (special.cotdg, cython_special.cotdg, ('d',), None),
+    (special.dawsn, cython_special.dawsn, ('d', 'D'), None),
+    (special.ellipe, cython_special.ellipe, ('d',), None),
+    (special.ellipeinc, cython_special.ellipeinc, ('dd',), None),
+    (special.ellipj, cython_special._ellipj_pywrap, ('dd',), None),
+    (special.ellipkinc, cython_special.ellipkinc, ('dd',), None),
+    (special.ellipkm1, cython_special.ellipkm1, ('d',), None),
+    (special.ellipk, cython_special.ellipk, ('d',), None),
+    (special.elliprc, cython_special.elliprc, ('dd', 'DD'), None),
+    (special.elliprd, cython_special.elliprd, ('ddd', 'DDD'), None),
+    (special.elliprf, cython_special.elliprf, ('ddd', 'DDD'), None),
+    (special.elliprg, cython_special.elliprg, ('ddd', 'DDD'), None),
+    (special.elliprj, cython_special.elliprj, ('dddd', 'DDDD'), None),
+    (special.entr, cython_special.entr, ('d',), None),
+    (special.erf, cython_special.erf, ('d', 'D'), None),
+    (special.erfc, cython_special.erfc, ('d', 'D'), None),
+    (special.erfcx, cython_special.erfcx, ('d', 'D'), None),
+    (special.erfi, cython_special.erfi, ('d', 'D'), None),
+    (special.erfinv, cython_special.erfinv, ('d',), None),
+    (special.erfcinv, cython_special.erfcinv, ('d',), None),
+    (special.eval_chebyc, cython_special.eval_chebyc, ('dd', 'dD', 'ld'), None),
+    (special.eval_chebys, cython_special.eval_chebys, ('dd', 'dD', 'ld'),
+     'd and l differ for negative int'),
+    (special.eval_chebyt, cython_special.eval_chebyt, ('dd', 'dD', 'ld'),
+     'd and l differ for negative int'),
+    (special.eval_chebyu, cython_special.eval_chebyu, ('dd', 'dD', 'ld'),
+     'd and l differ for negative int'),
+    (special.eval_gegenbauer, cython_special.eval_gegenbauer, ('ddd', 'ddD', 'ldd'),
+     'd and l differ for negative int'),
+    (special.eval_genlaguerre, cython_special.eval_genlaguerre, ('ddd', 'ddD', 'ldd'),
+     'd and l differ for negative int'),
+    (special.eval_hermite, cython_special.eval_hermite, ('ld',), None),
+    (special.eval_hermitenorm, cython_special.eval_hermitenorm, ('ld',), None),
+    (special.eval_jacobi, cython_special.eval_jacobi, ('dddd', 'dddD', 'lddd'),
+     'd and l differ for negative int'),
+    (special.eval_laguerre, cython_special.eval_laguerre, ('dd', 'dD', 'ld'),
+     'd and l differ for negative int'),
+    (special.eval_legendre, cython_special.eval_legendre, ('dd', 'dD', 'ld'), None),
+    (special.eval_sh_chebyt, cython_special.eval_sh_chebyt, ('dd', 'dD', 'ld'), None),
+    (special.eval_sh_chebyu, cython_special.eval_sh_chebyu, ('dd', 'dD', 'ld'),
+     'd and l differ for negative int'),
+    (special.eval_sh_jacobi, cython_special.eval_sh_jacobi, ('dddd', 'dddD', 'lddd'),
+     'd and l differ for negative int'),
+    (special.eval_sh_legendre, cython_special.eval_sh_legendre, ('dd', 'dD', 'ld'),
+     None),
+    (special.exp1, cython_special.exp1, ('d', 'D'), None),
+    (special.exp10, cython_special.exp10, ('d',), None),
+    (special.exp2, cython_special.exp2, ('d',), None),
+    (special.expi, cython_special.expi, ('d', 'D'), None),
+    (special.expit, cython_special.expit, ('f', 'd', 'g'), None),
+    (special.expm1, cython_special.expm1, ('d', 'D'), None),
+    (special.expn, cython_special.expn, ('ld', 'dd'), None),
+    (special.exprel, cython_special.exprel, ('d',), None),
+    (special.fdtr, cython_special.fdtr, ('ddd',), None),
+    (special.fdtrc, cython_special.fdtrc, ('ddd',), None),
+    (special.fdtri, cython_special.fdtri, ('ddd',), None),
+    (special.fdtridfd, cython_special.fdtridfd, ('ddd',), None),
+    (special.fresnel, cython_special._fresnel_pywrap, ('d', 'D'), None),
+    (special.gamma, cython_special.gamma, ('d', 'D'), None),
+    (special.gammainc, cython_special.gammainc, ('dd',), None),
+    (special.gammaincc, cython_special.gammaincc, ('dd',), None),
+    (special.gammainccinv, cython_special.gammainccinv, ('dd',), None),
+    (special.gammaincinv, cython_special.gammaincinv, ('dd',), None),
+    (special.gammaln, cython_special.gammaln, ('d',), None),
+    (special.gammasgn, cython_special.gammasgn, ('d',), None),
+    (special.gdtr, cython_special.gdtr, ('ddd',), None),
+    (special.gdtrc, cython_special.gdtrc, ('ddd',), None),
+    (special.gdtria, cython_special.gdtria, ('ddd',), None),
+    (special.gdtrib, cython_special.gdtrib, ('ddd',), None),
+    (special.gdtrix, cython_special.gdtrix, ('ddd',), None),
+    (special.hankel1, cython_special.hankel1, ('dD',), None),
+    (special.hankel1e, cython_special.hankel1e, ('dD',), None),
+    (special.hankel2, cython_special.hankel2, ('dD',), None),
+    (special.hankel2e, cython_special.hankel2e, ('dD',), None),
+    (special.huber, cython_special.huber, ('dd',), None),
+    (special.hyp0f1, cython_special.hyp0f1, ('dd', 'dD'), None),
+    (special.hyp1f1, cython_special.hyp1f1, ('ddd', 'ddD'), None),
+    (special.hyp2f1, cython_special.hyp2f1, ('dddd', 'dddD'), None),
+    (special.hyperu, cython_special.hyperu, ('ddd',), None),
+    (special.i0, cython_special.i0, ('d',), None),
+    (special.i0e, cython_special.i0e, ('d',), None),
+    (special.i1, cython_special.i1, ('d',), None),
+    (special.i1e, cython_special.i1e, ('d',), None),
+    (special.inv_boxcox, cython_special.inv_boxcox, ('dd',), None),
+    (special.inv_boxcox1p, cython_special.inv_boxcox1p, ('dd',), None),
+    (special.it2i0k0, cython_special._it2i0k0_pywrap, ('d',), None),
+    (special.it2j0y0, cython_special._it2j0y0_pywrap, ('d',), None),
+    (special.it2struve0, cython_special.it2struve0, ('d',), None),
+    (special.itairy, cython_special._itairy_pywrap, ('d',), None),
+    (special.iti0k0, cython_special._iti0k0_pywrap, ('d',), None),
+    (special.itj0y0, cython_special._itj0y0_pywrap, ('d',), None),
+    (special.itmodstruve0, cython_special.itmodstruve0, ('d',), None),
+    (special.itstruve0, cython_special.itstruve0, ('d',), None),
+    (special.iv, cython_special.iv, ('dd', 'dD'), None),
+    (special.ive, cython_special.ive, ('dd', 'dD'), None),
+    (special.j0, cython_special.j0, ('d',), None),
+    (special.j1, cython_special.j1, ('d',), None),
+    (special.jv, cython_special.jv, ('dd', 'dD'), None),
+    (special.jve, cython_special.jve, ('dd', 'dD'), None),
+    (special.k0, cython_special.k0, ('d',), None),
+    (special.k0e, cython_special.k0e, ('d',), None),
+    (special.k1, cython_special.k1, ('d',), None),
+    (special.k1e, cython_special.k1e, ('d',), None),
+    (special.kei, cython_special.kei, ('d',), None),
+    (special.keip, cython_special.keip, ('d',), None),
+    (special.kelvin, cython_special._kelvin_pywrap, ('d',), None),
+    (special.ker, cython_special.ker, ('d',), None),
+    (special.kerp, cython_special.kerp, ('d',), None),
+    (special.kl_div, cython_special.kl_div, ('dd',), None),
+    (special.kn, cython_special.kn, ('ld', 'dd'), None),
+    (special.kolmogi, cython_special.kolmogi, ('d',), None),
+    (special.kolmogorov, cython_special.kolmogorov, ('d',), None),
+    (special.kv, cython_special.kv, ('dd', 'dD'), None),
+    (special.kve, cython_special.kve, ('dd', 'dD'), None),
+    (special.log1p, cython_special.log1p, ('d', 'D'), None),
+    (special.log_expit, cython_special.log_expit, ('f', 'd', 'g'), None),
+    (special.log_ndtr, cython_special.log_ndtr, ('d', 'D'), None),
+    (special.log_wright_bessel, cython_special.log_wright_bessel, ('ddd',), None),
+    (special.ndtri_exp, cython_special.ndtri_exp, ('d',), None),
+    (special.loggamma, cython_special.loggamma, ('D',), None),
+    (special.logit, cython_special.logit, ('f', 'd', 'g'), None),
+    (special.lpmv, cython_special.lpmv, ('ddd',), None),
+    (special.mathieu_a, cython_special.mathieu_a, ('dd',), None),
+    (special.mathieu_b, cython_special.mathieu_b, ('dd',), None),
+    (special.mathieu_cem, cython_special._mathieu_cem_pywrap, ('ddd',), None),
+    (special.mathieu_modcem1, cython_special._mathieu_modcem1_pywrap, ('ddd',), None),
+    (special.mathieu_modcem2, cython_special._mathieu_modcem2_pywrap, ('ddd',), None),
+    (special.mathieu_modsem1, cython_special._mathieu_modsem1_pywrap, ('ddd',), None),
+    (special.mathieu_modsem2, cython_special._mathieu_modsem2_pywrap, ('ddd',), None),
+    (special.mathieu_sem, cython_special._mathieu_sem_pywrap, ('ddd',), None),
+    (special.modfresnelm, cython_special._modfresnelm_pywrap, ('d',), None),
+    (special.modfresnelp, cython_special._modfresnelp_pywrap, ('d',), None),
+    (special.modstruve, cython_special.modstruve, ('dd',), None),
+    (special.nbdtr, cython_special.nbdtr, ('lld', 'ddd'), None),
+    (special.nbdtrc, cython_special.nbdtrc, ('lld', 'ddd'), None),
+    (special.nbdtri, cython_special.nbdtri, ('lld', 'ddd'), None),
+    (special.nbdtrik, cython_special.nbdtrik, ('ddd',), None),
+    (special.nbdtrin, cython_special.nbdtrin, ('ddd',), None),
+    (special.ncfdtr, cython_special.ncfdtr, ('dddd',), None),
+    (special.ncfdtri, cython_special.ncfdtri, ('dddd',), None),
+    (special.ncfdtridfd, cython_special.ncfdtridfd, ('dddd',), None),
+    (special.ncfdtridfn, cython_special.ncfdtridfn, ('dddd',), None),
+    (special.ncfdtrinc, cython_special.ncfdtrinc, ('dddd',), None),
+    (special.nctdtr, cython_special.nctdtr, ('ddd',), None),
+    (special.nctdtridf, cython_special.nctdtridf, ('ddd',), None),
+    (special.nctdtrinc, cython_special.nctdtrinc, ('ddd',), None),
+    (special.nctdtrit, cython_special.nctdtrit, ('ddd',), None),
+    (special.ndtr, cython_special.ndtr, ('d', 'D'), None),
+    (special.ndtri, cython_special.ndtri, ('d',), None),
+    (special.nrdtrimn, cython_special.nrdtrimn, ('ddd',), None),
+    (special.nrdtrisd, cython_special.nrdtrisd, ('ddd',), None),
+    (special.obl_ang1, cython_special._obl_ang1_pywrap, ('dddd',), None),
+    (special.obl_ang1_cv, cython_special._obl_ang1_cv_pywrap, ('ddddd',), None),
+    (special.obl_cv, cython_special.obl_cv, ('ddd',), None),
+    (special.obl_rad1, cython_special._obl_rad1_pywrap, ('dddd',), "see gh-6211"),
+    (special.obl_rad1_cv, cython_special._obl_rad1_cv_pywrap, ('ddddd',),
+     "see gh-6211"),
+    (special.obl_rad2, cython_special._obl_rad2_pywrap, ('dddd',), "see gh-6211"),
+    (special.obl_rad2_cv, cython_special._obl_rad2_cv_pywrap, ('ddddd',),
+     "see gh-6211"),
+    (special.pbdv, cython_special._pbdv_pywrap, ('dd',), None),
+    (special.pbvv, cython_special._pbvv_pywrap, ('dd',), None),
+    (special.pbwa, cython_special._pbwa_pywrap, ('dd',), None),
+    (special.pdtr, cython_special.pdtr, ('dd', 'dd'), None),
+    (special.pdtrc, cython_special.pdtrc, ('dd', 'dd'), None),
+    (special.pdtri, cython_special.pdtri, ('ld', 'dd'), None),
+    (special.pdtrik, cython_special.pdtrik, ('dd',), None),
+    (special.poch, cython_special.poch, ('dd',), None),
+    (special.powm1, cython_special.powm1, ('dd',), None),
+    (special.pro_ang1, cython_special._pro_ang1_pywrap, ('dddd',), None),
+    (special.pro_ang1_cv, cython_special._pro_ang1_cv_pywrap, ('ddddd',), None),
+    (special.pro_cv, cython_special.pro_cv, ('ddd',), None),
+    (special.pro_rad1, cython_special._pro_rad1_pywrap, ('dddd',), "see gh-6211"),
+    (special.pro_rad1_cv, cython_special._pro_rad1_cv_pywrap, ('ddddd',),
+     "see gh-6211"),
+    (special.pro_rad2, cython_special._pro_rad2_pywrap, ('dddd',), "see gh-6211"),
+    (special.pro_rad2_cv, cython_special._pro_rad2_cv_pywrap, ('ddddd',),
+     "see gh-6211"),
+    (special.pseudo_huber, cython_special.pseudo_huber, ('dd',), None),
+    (special.psi, cython_special.psi, ('d', 'D'), None),
+    (special.radian, cython_special.radian, ('ddd',), None),
+    (special.rel_entr, cython_special.rel_entr, ('dd',), None),
+    (special.rgamma, cython_special.rgamma, ('d', 'D'), None),
+    (special.round, cython_special.round, ('d',), None),
+    (special.spherical_jn, cython_special.spherical_jn, ('ld', 'ldb', 'lD', 'lDb'),
+     "Python version supports negative reals; Cython version doesn't - see gh-21629"),
+    (special.spherical_yn, cython_special.spherical_yn, ('ld', 'ldb', 'lD', 'lDb'),
+     "Python version supports negative reals; Cython version doesn't - see gh-21629"),
+    (special.spherical_in, cython_special.spherical_in, ('ld', 'ldb', 'lD', 'lDb'),
+     "Python version supports negative reals; Cython version doesn't - see gh-21629"),
+    (special.spherical_kn, cython_special.spherical_kn, ('ld', 'ldb', 'lD', 'lDb'),
+     "Python version supports negative reals; Cython version doesn't - see gh-21629"),
+    (special.shichi, cython_special._shichi_pywrap, ('d', 'D'), None),
+    (special.sici, cython_special._sici_pywrap, ('d', 'D'), None),
+    (special.sindg, cython_special.sindg, ('d',), None),
+    (special.smirnov, cython_special.smirnov, ('ld', 'dd'), None),
+    (special.smirnovi, cython_special.smirnovi, ('ld', 'dd'), None),
+    (special.spence, cython_special.spence, ('d', 'D'), None),
+    (special.stdtr, cython_special.stdtr, ('dd',), None),
+    (special.stdtridf, cython_special.stdtridf, ('dd',), None),
+    (special.stdtrit, cython_special.stdtrit, ('dd',), None),
+    (special.struve, cython_special.struve, ('dd',), None),
+    (special.tandg, cython_special.tandg, ('d',), None),
+    (special.tklmbda, cython_special.tklmbda, ('dd',), None),
+    (special.voigt_profile, cython_special.voigt_profile, ('ddd',), None),
+    (special.wofz, cython_special.wofz, ('D',), None),
+    (special.wright_bessel, cython_special.wright_bessel, ('ddd',), None),
+    (special.wrightomega, cython_special.wrightomega, ('D',), None),
+    (special.xlog1py, cython_special.xlog1py, ('dd', 'DD'), None),
+    (special.xlogy, cython_special.xlogy, ('dd', 'DD'), None),
+    (special.y0, cython_special.y0, ('d',), None),
+    (special.y1, cython_special.y1, ('d',), None),
+    (special.yn, cython_special.yn, ('ld', 'dd'), None),
+    (special.yv, cython_special.yv, ('dd', 'dD'), None),
+    (special.yve, cython_special.yve, ('dd', 'dD'), None),
+    (special.zetac, cython_special.zetac, ('d',), None),
+    (special.owens_t, cython_special.owens_t, ('dd',), None)
+]
+
+
+IDS = [x[0].__name__ for x in PARAMS]
+
+
+def _generate_test_points(typecodes):
+    axes = tuple(TEST_POINTS[x] for x in typecodes)
+    pts = list(product(*axes))
+    return pts
+
+
+def test_cython_api_completeness():
+    # Check that everything is tested
+    for name in dir(cython_special):
+        func = getattr(cython_special, name)
+        if callable(func) and not name.startswith('_'):
+            for _, cyfun, _, _ in PARAMS:
+                if cyfun is func:
+                    break
+            else:
+                raise RuntimeError(f"{name} missing from tests!")
+
+
+@pytest.mark.fail_slow(20)
+@pytest.mark.parametrize("param", PARAMS, ids=IDS)
+def test_cython_api(param):
+    pyfunc, cyfunc, specializations, knownfailure = param
+    if knownfailure:
+        pytest.xfail(reason=knownfailure)
+
+    # Check which parameters are expected to be fused types
+    max_params = max(len(spec) for spec in specializations)
+    values = [set() for _ in range(max_params)]
+    for typecodes in specializations:
+        for j, v in enumerate(typecodes):
+            values[j].add(v)
+    seen = set()
+    is_fused_code = [False] * len(values)
+    for j, v in enumerate(values):
+        vv = tuple(sorted(v))
+        if vv in seen:
+            continue
+        is_fused_code[j] = (len(v) > 1)
+        seen.add(vv)
+
+    # Check results
+    for typecodes in specializations:
+        # Pick the correct specialized function
+        signature = [CYTHON_SIGNATURE_MAP[code]
+                     for j, code in enumerate(typecodes)
+                     if is_fused_code[j]]
+
+        if signature:
+            cy_spec_func = cyfunc[tuple(signature)]
+        else:
+            signature = None
+            cy_spec_func = cyfunc
+
+        # Test it
+        pts = _generate_test_points(typecodes)
+        for pt in pts:
+            with warnings.catch_warnings():
+                warnings.simplefilter("ignore", DeprecationWarning)
+                pyval = pyfunc(*pt)
+                cyval = cy_spec_func(*pt)
+            assert_allclose(cyval, pyval, err_msg=f"{pt} {typecodes} {signature}")
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_data.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_data.py
new file mode 100644
index 0000000000000000000000000000000000000000..eafcecd6836710726c0248bdaf02542e7efb8223
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_data.py
@@ -0,0 +1,679 @@
+import importlib.resources
+import warnings
+
+import numpy as np
+import pytest
+
+from scipy.special import (
+    lpmv, lqn, lqmn, eval_legendre, eval_hermite,
+    eval_laguerre, eval_genlaguerre, binom, cbrt, expm1, log1p, zeta,
+    jn, jv, jvp, yn, yv, yvp, iv, ivp, kn, kv, kvp,
+    gamma, gammaln, gammainc, gammaincc, gammaincinv, gammainccinv, digamma,
+    beta, betainc, betaincinv, poch,
+    ellipe, ellipeinc, ellipk, ellipkm1, ellipkinc,
+    elliprc, elliprd, elliprf, elliprg, elliprj,
+    erf, erfc, erfinv, erfcinv, exp1, expi, expn,
+    bdtrik, btdtria, btdtrib, chndtr, gdtr, gdtrc, gdtrix, gdtrib,
+    nbdtrik, pdtrik, owens_t,
+    mathieu_a, mathieu_b, mathieu_cem, mathieu_sem, mathieu_modcem1,
+    mathieu_modsem1, mathieu_modcem2, mathieu_modsem2,
+    ellip_harm, ellip_harm_2, spherical_jn, spherical_yn, wright_bessel
+)
+from scipy.integrate import IntegrationWarning
+
+from scipy.special._testutils import FuncData
+
+
+# The npz files are generated, and hence may live in the build dir. We can only
+# access them through `importlib.resources`, not an explicit path from `__file__`
+_datadir = importlib.resources.files('scipy.special.tests.data')
+
+_boost_npz = _datadir.joinpath('boost.npz')
+with importlib.resources.as_file(_boost_npz) as f:
+    DATASETS_BOOST = np.load(f)
+
+_gsl_npz = _datadir.joinpath('gsl.npz')
+with importlib.resources.as_file(_gsl_npz) as f:
+    DATASETS_GSL = np.load(f)
+
+_local_npz = _datadir.joinpath('local.npz')
+with importlib.resources.as_file(_local_npz) as f:
+    DATASETS_LOCAL = np.load(f)
+
+
+def data(func, dataname, *a, **kw):
+    kw.setdefault('dataname', dataname)
+    return FuncData(func, DATASETS_BOOST[dataname], *a, **kw)
+
+
+def data_gsl(func, dataname, *a, **kw):
+    kw.setdefault('dataname', dataname)
+    return FuncData(func, DATASETS_GSL[dataname], *a, **kw)
+
+
+def data_local(func, dataname, *a, **kw):
+    kw.setdefault('dataname', dataname)
+    return FuncData(func, DATASETS_LOCAL[dataname], *a, **kw)
+
+
+def ellipk_(k):
+    return ellipk(k*k)
+
+
+def ellipkinc_(f, k):
+    return ellipkinc(f, k*k)
+
+
+def ellipe_(k):
+    return ellipe(k*k)
+
+
+def ellipeinc_(f, k):
+    return ellipeinc(f, k*k)
+
+
+def zeta_(x):
+    return zeta(x, 1.)
+
+
+def assoc_legendre_p_boost_(nu, mu, x):
+    # the boost test data is for integer orders only
+    return lpmv(mu, nu.astype(int), x)
+
+def legendre_p_via_assoc_(nu, x):
+    return lpmv(0, nu, x)
+
+def lqn_(n, x):
+    return lqn(n.astype('l'), x)[0][-1]
+
+def legendre_q_via_lqmn(n, x):
+    return lqmn(0, n, x)[0][0,-1]
+
+def mathieu_ce_rad(m, q, x):
+    return mathieu_cem(m, q, x*180/np.pi)[0]
+
+
+def mathieu_se_rad(m, q, x):
+    return mathieu_sem(m, q, x*180/np.pi)[0]
+
+
+def mathieu_mc1_scaled(m, q, x):
+    # GSL follows a different normalization.
+    # We follow Abramowitz & Stegun, they apparently something else.
+    return mathieu_modcem1(m, q, x)[0] * np.sqrt(np.pi/2)
+
+
+def mathieu_ms1_scaled(m, q, x):
+    return mathieu_modsem1(m, q, x)[0] * np.sqrt(np.pi/2)
+
+
+def mathieu_mc2_scaled(m, q, x):
+    return mathieu_modcem2(m, q, x)[0] * np.sqrt(np.pi/2)
+
+
+def mathieu_ms2_scaled(m, q, x):
+    return mathieu_modsem2(m, q, x)[0] * np.sqrt(np.pi/2)
+
+def eval_legendre_ld(n, x):
+    return eval_legendre(n.astype('l'), x)
+
+def eval_legendre_dd(n, x):
+    return eval_legendre(n.astype('d'), x)
+
+def eval_hermite_ld(n, x):
+    return eval_hermite(n.astype('l'), x)
+
+def eval_laguerre_ld(n, x):
+    return eval_laguerre(n.astype('l'), x)
+
+def eval_laguerre_dd(n, x):
+    return eval_laguerre(n.astype('d'), x)
+
+def eval_genlaguerre_ldd(n, a, x):
+    return eval_genlaguerre(n.astype('l'), a, x)
+
+def eval_genlaguerre_ddd(n, a, x):
+    return eval_genlaguerre(n.astype('d'), a, x)
+
+def bdtrik_comp(y, n, p):
+    return bdtrik(1-y, n, p)
+
+def btdtria_comp(p, b, x):
+    return btdtria(1-p, b, x)
+
+def btdtrib_comp(a, p, x):
+    return btdtrib(a, 1-p, x)
+
+def gdtr_(p, x):
+    return gdtr(1.0, p, x)
+
+def gdtrc_(p, x):
+    return gdtrc(1.0, p, x)
+
+def gdtrix_(b, p):
+    return gdtrix(1.0, b, p)
+
+def gdtrix_comp(b, p):
+    return gdtrix(1.0, b, 1-p)
+
+def gdtrib_(p, x):
+    return gdtrib(1.0, p, x)
+
+def gdtrib_comp(p, x):
+    return gdtrib(1.0, 1-p, x)
+
+def nbdtrik_comp(y, n, p):
+    return nbdtrik(1-y, n, p)
+
+def pdtrik_comp(p, m):
+    return pdtrik(1-p, m)
+
+def poch_(z, m):
+    return 1.0 / poch(z, m)
+
+def poch_minus(z, m):
+    return 1.0 / poch(z, -m)
+
+def spherical_jn_(n, x):
+    return spherical_jn(n.astype('l'), x)
+
+def spherical_yn_(n, x):
+    return spherical_yn(n.astype('l'), x)
+
+def cexpm1(x, y):
+    z = expm1(x + 1j*y)
+    return z.real, z.imag
+
+def clog1p(x, y):
+    z = log1p(x + 1j*y)
+    return z.real, z.imag
+
+
+BOOST_TESTS = [
+        data(assoc_legendre_p_boost_, 'assoc_legendre_p_ipp-assoc_legendre_p',
+             (0,1,2), 3, rtol=1e-11),
+
+        data(legendre_p_via_assoc_, 'legendre_p_ipp-legendre_p',
+             (0,1), 2, rtol=1e-11),
+        data(legendre_p_via_assoc_, 'legendre_p_large_ipp-legendre_p_large',
+             (0,1), 2, rtol=9.6e-14),
+        data(eval_legendre_ld, 'legendre_p_ipp-legendre_p',
+             (0,1), 2, rtol=6e-14),
+        data(eval_legendre_ld, 'legendre_p_large_ipp-legendre_p_large',
+             (0,1), 2, rtol=2e-13),
+        data(eval_legendre_dd, 'legendre_p_ipp-legendre_p',
+             (0,1), 2, rtol=2e-14),
+        data(eval_legendre_dd, 'legendre_p_large_ipp-legendre_p_large',
+             (0,1), 2, rtol=2e-13),
+
+        data(lqn_, 'legendre_p_ipp-legendre_p',
+             (0,1), 3, rtol=2e-14, vectorized=False),
+        data(lqn_, 'legendre_p_large_ipp-legendre_p_large',
+             (0,1), 3, rtol=2e-12, vectorized=False),
+        data(legendre_q_via_lqmn, 'legendre_p_ipp-legendre_p',
+             (0,1), 3, rtol=2e-14, vectorized=False),
+        data(legendre_q_via_lqmn, 'legendre_p_large_ipp-legendre_p_large',
+             (0,1), 3, rtol=2e-12, vectorized=False),
+
+        data(beta, 'beta_exp_data_ipp-beta_exp_data',
+             (0,1), 2, rtol=1e-13),
+        data(beta, 'beta_exp_data_ipp-beta_exp_data',
+             (0,1), 2, rtol=1e-13),
+        data(beta, 'beta_med_data_ipp-beta_med_data',
+             (0,1), 2, rtol=5e-13),
+
+        data(betainc, 'ibeta_small_data_ipp-ibeta_small_data',
+             (0,1,2), 5, rtol=6e-15),
+        data(betainc, 'ibeta_data_ipp-ibeta_data',
+             (0,1,2), 5, rtol=5e-13),
+        data(betainc, 'ibeta_int_data_ipp-ibeta_int_data',
+             (0,1,2), 5, rtol=2e-14),
+        data(betainc, 'ibeta_large_data_ipp-ibeta_large_data',
+             (0,1,2), 5, rtol=4e-10),
+
+        data(betaincinv, 'ibeta_inv_data_ipp-ibeta_inv_data',
+             (0,1,2), 3, rtol=1e-5),
+
+        data(btdtria, 'ibeta_inva_data_ipp-ibeta_inva_data',
+             (2,0,1), 3, rtol=5e-9),
+        data(btdtria_comp, 'ibeta_inva_data_ipp-ibeta_inva_data',
+             (2,0,1), 4, rtol=5e-9),
+
+        data(btdtrib, 'ibeta_inva_data_ipp-ibeta_inva_data',
+             (0,2,1), 5, rtol=5e-9),
+        data(btdtrib_comp, 'ibeta_inva_data_ipp-ibeta_inva_data',
+             (0,2,1), 6, rtol=5e-9),
+
+        data(binom, 'binomial_data_ipp-binomial_data',
+             (0,1), 2, rtol=1e-13),
+        data(binom, 'binomial_large_data_ipp-binomial_large_data',
+             (0,1), 2, rtol=5e-13),
+
+        data(bdtrik, 'binomial_quantile_ipp-binomial_quantile_data',
+             (2,0,1), 3, rtol=5e-9),
+        data(bdtrik_comp, 'binomial_quantile_ipp-binomial_quantile_data',
+             (2,0,1), 4, rtol=5e-9),
+
+        data(nbdtrik, 'negative_binomial_quantile_ipp-negative_binomial_quantile_data',
+             (2,0,1), 3, rtol=4e-9),
+        data(nbdtrik_comp,
+             'negative_binomial_quantile_ipp-negative_binomial_quantile_data',
+             (2,0,1), 4, rtol=4e-9),
+
+        data(pdtrik, 'poisson_quantile_ipp-poisson_quantile_data',
+             (1,0), 2, rtol=3e-9),
+        data(pdtrik_comp, 'poisson_quantile_ipp-poisson_quantile_data',
+             (1,0), 3, rtol=4e-9),
+
+        data(cbrt, 'cbrt_data_ipp-cbrt_data', 1, 0),
+
+        data(digamma, 'digamma_data_ipp-digamma_data', 0, 1),
+        data(digamma, 'digamma_data_ipp-digamma_data', 0j, 1),
+        data(digamma, 'digamma_neg_data_ipp-digamma_neg_data', 0, 1, rtol=2e-13),
+        data(digamma, 'digamma_neg_data_ipp-digamma_neg_data', 0j, 1, rtol=1e-13),
+        data(digamma, 'digamma_root_data_ipp-digamma_root_data', 0, 1, rtol=1e-15),
+        data(digamma, 'digamma_root_data_ipp-digamma_root_data', 0j, 1, rtol=1e-15),
+        data(digamma, 'digamma_small_data_ipp-digamma_small_data', 0, 1, rtol=1e-15),
+        data(digamma, 'digamma_small_data_ipp-digamma_small_data', 0j, 1, rtol=1e-14),
+
+        data(ellipk_, 'ellint_k_data_ipp-ellint_k_data', 0, 1),
+        data(ellipkinc_, 'ellint_f_data_ipp-ellint_f_data', (0,1), 2, rtol=1e-14),
+        data(ellipe_, 'ellint_e_data_ipp-ellint_e_data', 0, 1),
+        data(ellipeinc_, 'ellint_e2_data_ipp-ellint_e2_data', (0,1), 2, rtol=1e-14),
+
+        data(erf, 'erf_data_ipp-erf_data', 0, 1),
+        data(erf, 'erf_data_ipp-erf_data', 0j, 1, rtol=1e-13),
+        data(erfc, 'erf_data_ipp-erf_data', 0, 2, rtol=6e-15),
+        data(erf, 'erf_large_data_ipp-erf_large_data', 0, 1),
+        data(erf, 'erf_large_data_ipp-erf_large_data', 0j, 1),
+        data(erfc, 'erf_large_data_ipp-erf_large_data', 0, 2, rtol=4e-14),
+        data(erf, 'erf_small_data_ipp-erf_small_data', 0, 1),
+        data(erf, 'erf_small_data_ipp-erf_small_data', 0j, 1, rtol=1e-13),
+        data(erfc, 'erf_small_data_ipp-erf_small_data', 0, 2),
+
+        data(erfinv, 'erf_inv_data_ipp-erf_inv_data', 0, 1),
+        data(erfcinv, 'erfc_inv_data_ipp-erfc_inv_data', 0, 1),
+        data(erfcinv, 'erfc_inv_big_data_ipp-erfc_inv_big_data', 0, 1,
+             param_filter=(lambda s: s > 0)),
+
+        data(exp1, 'expint_1_data_ipp-expint_1_data', 1, 2, rtol=1e-13),
+        data(exp1, 'expint_1_data_ipp-expint_1_data', 1j, 2, rtol=5e-9),
+        data(expi, 'expinti_data_ipp-expinti_data', 0, 1, rtol=1e-13),
+        data(expi, 'expinti_data_double_ipp-expinti_data_double', 0, 1, rtol=1e-13),
+        data(expi, 'expinti_data_long_ipp-expinti_data_long', 0, 1),
+
+        data(expn, 'expint_small_data_ipp-expint_small_data', (0,1), 2),
+        data(expn, 'expint_data_ipp-expint_data', (0,1), 2, rtol=1e-14),
+
+        data(gamma, 'test_gamma_data_ipp-near_0', 0, 1),
+        data(gamma, 'test_gamma_data_ipp-near_1', 0, 1),
+        data(gamma, 'test_gamma_data_ipp-near_2', 0, 1),
+        data(gamma, 'test_gamma_data_ipp-near_m10', 0, 1),
+        data(gamma, 'test_gamma_data_ipp-near_m55', 0, 1, rtol=7e-12),
+        data(gamma, 'test_gamma_data_ipp-factorials', 0, 1, rtol=4e-14),
+        data(gamma, 'test_gamma_data_ipp-near_0', 0j, 1, rtol=2e-9),
+        data(gamma, 'test_gamma_data_ipp-near_1', 0j, 1, rtol=2e-9),
+        data(gamma, 'test_gamma_data_ipp-near_2', 0j, 1, rtol=2e-9),
+        data(gamma, 'test_gamma_data_ipp-near_m10', 0j, 1, rtol=2e-9),
+        data(gamma, 'test_gamma_data_ipp-near_m55', 0j, 1, rtol=2e-9),
+        data(gamma, 'test_gamma_data_ipp-factorials', 0j, 1, rtol=2e-13),
+        data(gammaln, 'test_gamma_data_ipp-near_0', 0, 2, rtol=5e-11),
+        data(gammaln, 'test_gamma_data_ipp-near_1', 0, 2, rtol=5e-11),
+        data(gammaln, 'test_gamma_data_ipp-near_2', 0, 2, rtol=2e-10),
+        data(gammaln, 'test_gamma_data_ipp-near_m10', 0, 2, rtol=5e-11),
+        data(gammaln, 'test_gamma_data_ipp-near_m55', 0, 2, rtol=5e-11),
+        data(gammaln, 'test_gamma_data_ipp-factorials', 0, 2),
+
+        data(gammainc, 'igamma_small_data_ipp-igamma_small_data', (0,1), 5, rtol=5e-15),
+        data(gammainc, 'igamma_med_data_ipp-igamma_med_data', (0,1), 5, rtol=2e-13),
+        data(gammainc, 'igamma_int_data_ipp-igamma_int_data', (0,1), 5, rtol=2e-13),
+        data(gammainc, 'igamma_big_data_ipp-igamma_big_data', (0,1), 5, rtol=1e-12),
+
+        data(gdtr_, 'igamma_small_data_ipp-igamma_small_data', (0,1), 5, rtol=1e-13),
+        data(gdtr_, 'igamma_med_data_ipp-igamma_med_data', (0,1), 5, rtol=2e-13),
+        data(gdtr_, 'igamma_int_data_ipp-igamma_int_data', (0,1), 5, rtol=2e-13),
+        data(gdtr_, 'igamma_big_data_ipp-igamma_big_data', (0,1), 5, rtol=2e-9),
+
+        data(gammaincc, 'igamma_small_data_ipp-igamma_small_data',
+             (0,1), 3, rtol=1e-13),
+        data(gammaincc, 'igamma_med_data_ipp-igamma_med_data',
+             (0,1), 3, rtol=2e-13),
+        data(gammaincc, 'igamma_int_data_ipp-igamma_int_data',
+             (0,1), 3, rtol=4e-14),
+        data(gammaincc, 'igamma_big_data_ipp-igamma_big_data',
+             (0,1), 3, rtol=1e-11),
+
+        data(gdtrc_, 'igamma_small_data_ipp-igamma_small_data', (0,1), 3, rtol=1e-13),
+        data(gdtrc_, 'igamma_med_data_ipp-igamma_med_data', (0,1), 3, rtol=2e-13),
+        data(gdtrc_, 'igamma_int_data_ipp-igamma_int_data', (0,1), 3, rtol=4e-14),
+        data(gdtrc_, 'igamma_big_data_ipp-igamma_big_data', (0,1), 3, rtol=1e-11),
+
+        data(gdtrib_, 'igamma_inva_data_ipp-igamma_inva_data', (1,0), 2, rtol=5e-9),
+        data(gdtrib_comp, 'igamma_inva_data_ipp-igamma_inva_data', (1,0), 3, rtol=5e-9),
+
+        data(poch_, 'tgamma_delta_ratio_data_ipp-tgamma_delta_ratio_data',
+             (0,1), 2, rtol=2e-13),
+        data(poch_, 'tgamma_delta_ratio_int_ipp-tgamma_delta_ratio_int',
+             (0,1), 2,),
+        data(poch_, 'tgamma_delta_ratio_int2_ipp-tgamma_delta_ratio_int2',
+             (0,1), 2,),
+        data(poch_minus, 'tgamma_delta_ratio_data_ipp-tgamma_delta_ratio_data',
+             (0,1), 3, rtol=2e-13),
+        data(poch_minus, 'tgamma_delta_ratio_int_ipp-tgamma_delta_ratio_int',
+             (0,1), 3),
+        data(poch_minus, 'tgamma_delta_ratio_int2_ipp-tgamma_delta_ratio_int2',
+             (0,1), 3),
+
+        data(eval_hermite_ld, 'hermite_ipp-hermite',
+             (0,1), 2, rtol=2e-14),
+
+        data(eval_laguerre_ld, 'laguerre2_ipp-laguerre2',
+             (0,1), 2, rtol=7e-12),
+        data(eval_laguerre_dd, 'laguerre2_ipp-laguerre2',
+             (0,1), 2, knownfailure='hyp2f1 insufficiently accurate.'),
+        data(eval_genlaguerre_ldd, 'laguerre3_ipp-laguerre3',
+             (0,1,2), 3, rtol=2e-13),
+        data(eval_genlaguerre_ddd, 'laguerre3_ipp-laguerre3',
+             (0,1,2), 3, knownfailure='hyp2f1 insufficiently accurate.'),
+
+        data(log1p, 'log1p_expm1_data_ipp-log1p_expm1_data', 0, 1),
+        data(expm1, 'log1p_expm1_data_ipp-log1p_expm1_data', 0, 2),
+
+        data(iv, 'bessel_i_data_ipp-bessel_i_data',
+             (0,1), 2, rtol=1e-12),
+        data(iv, 'bessel_i_data_ipp-bessel_i_data',
+             (0,1j), 2, rtol=2e-10, atol=1e-306),
+        data(iv, 'bessel_i_int_data_ipp-bessel_i_int_data',
+             (0,1), 2, rtol=1e-9),
+        data(iv, 'bessel_i_int_data_ipp-bessel_i_int_data',
+             (0,1j), 2, rtol=2e-10),
+
+        data(ivp, 'bessel_i_prime_int_data_ipp-bessel_i_prime_int_data',
+             (0,1), 2, rtol=1.2e-13),
+        data(ivp, 'bessel_i_prime_int_data_ipp-bessel_i_prime_int_data',
+             (0,1j), 2, rtol=1.2e-13, atol=1e-300),
+
+        data(jn, 'bessel_j_int_data_ipp-bessel_j_int_data', (0,1), 2, rtol=1e-12),
+        data(jn, 'bessel_j_int_data_ipp-bessel_j_int_data', (0,1j), 2, rtol=1e-12),
+        data(jn, 'bessel_j_large_data_ipp-bessel_j_large_data', (0,1), 2, rtol=6e-11),
+        data(jn, 'bessel_j_large_data_ipp-bessel_j_large_data', (0,1j), 2, rtol=6e-11),
+
+        data(jv, 'bessel_j_int_data_ipp-bessel_j_int_data', (0,1), 2, rtol=1e-12),
+        data(jv, 'bessel_j_int_data_ipp-bessel_j_int_data', (0,1j), 2, rtol=1e-12),
+        data(jv, 'bessel_j_data_ipp-bessel_j_data', (0,1), 2, rtol=1e-12),
+        data(jv, 'bessel_j_data_ipp-bessel_j_data', (0,1j), 2, rtol=1e-12),
+
+        data(jvp, 'bessel_j_prime_int_data_ipp-bessel_j_prime_int_data',
+             (0,1), 2, rtol=1e-13),
+        data(jvp, 'bessel_j_prime_int_data_ipp-bessel_j_prime_int_data',
+             (0,1j), 2, rtol=1e-13),
+        data(jvp, 'bessel_j_prime_large_data_ipp-bessel_j_prime_large_data',
+             (0,1), 2, rtol=1e-11),
+        data(jvp, 'bessel_j_prime_large_data_ipp-bessel_j_prime_large_data',
+             (0,1j), 2, rtol=2e-11),
+
+        data(kn, 'bessel_k_int_data_ipp-bessel_k_int_data', (0,1), 2, rtol=1e-12),
+
+        data(kv, 'bessel_k_int_data_ipp-bessel_k_int_data', (0,1), 2, rtol=1e-12),
+        data(kv, 'bessel_k_int_data_ipp-bessel_k_int_data', (0,1j), 2, rtol=1e-12),
+        data(kv, 'bessel_k_data_ipp-bessel_k_data', (0,1), 2, rtol=1e-12),
+        data(kv, 'bessel_k_data_ipp-bessel_k_data', (0,1j), 2, rtol=1e-12),
+
+        data(kvp, 'bessel_k_prime_int_data_ipp-bessel_k_prime_int_data',
+             (0,1), 2, rtol=3e-14),
+        data(kvp, 'bessel_k_prime_int_data_ipp-bessel_k_prime_int_data',
+             (0,1j), 2, rtol=3e-14),
+        data(kvp, 'bessel_k_prime_data_ipp-bessel_k_prime_data', (0,1), 2, rtol=7e-14),
+        data(kvp, 'bessel_k_prime_data_ipp-bessel_k_prime_data', (0,1j), 2, rtol=7e-14),
+
+        data(yn, 'bessel_y01_data_ipp-bessel_y01_data', (0,1), 2, rtol=1e-12),
+        data(yn, 'bessel_yn_data_ipp-bessel_yn_data', (0,1), 2, rtol=1e-12),
+
+        data(yv, 'bessel_yn_data_ipp-bessel_yn_data', (0,1), 2, rtol=1e-12),
+        data(yv, 'bessel_yn_data_ipp-bessel_yn_data', (0,1j), 2, rtol=1e-12),
+        data(yv, 'bessel_yv_data_ipp-bessel_yv_data', (0,1), 2, rtol=1e-10),
+        data(yv, 'bessel_yv_data_ipp-bessel_yv_data', (0,1j), 2, rtol=1e-10),
+
+        data(yvp, 'bessel_yv_prime_data_ipp-bessel_yv_prime_data',
+             (0, 1), 2, rtol=4e-9),
+        data(yvp, 'bessel_yv_prime_data_ipp-bessel_yv_prime_data',
+             (0, 1j), 2, rtol=4e-9),
+
+        data(zeta_, 'zeta_data_ipp-zeta_data', 0, 1,
+             param_filter=(lambda s: s > 1)),
+        data(zeta_, 'zeta_neg_data_ipp-zeta_neg_data', 0, 1,
+             param_filter=(lambda s: s > 1)),
+        data(zeta_, 'zeta_1_up_data_ipp-zeta_1_up_data', 0, 1,
+             param_filter=(lambda s: s > 1)),
+        data(zeta_, 'zeta_1_below_data_ipp-zeta_1_below_data', 0, 1,
+             param_filter=(lambda s: s > 1)),
+
+        data(gammaincinv, 'gamma_inv_small_data_ipp-gamma_inv_small_data',
+             (0,1), 2, rtol=1e-11),
+        data(gammaincinv, 'gamma_inv_data_ipp-gamma_inv_data',
+             (0,1), 2, rtol=1e-14),
+        data(gammaincinv, 'gamma_inv_big_data_ipp-gamma_inv_big_data',
+             (0,1), 2, rtol=1e-11),
+
+        data(gammainccinv, 'gamma_inv_small_data_ipp-gamma_inv_small_data',
+             (0,1), 3, rtol=1e-12),
+        data(gammainccinv, 'gamma_inv_data_ipp-gamma_inv_data',
+             (0,1), 3, rtol=1e-14),
+        data(gammainccinv, 'gamma_inv_big_data_ipp-gamma_inv_big_data',
+             (0,1), 3, rtol=1e-14),
+
+        data(gdtrix_, 'gamma_inv_small_data_ipp-gamma_inv_small_data',
+             (0,1), 2, rtol=3e-13, knownfailure='gdtrix unflow some points'),
+        data(gdtrix_, 'gamma_inv_data_ipp-gamma_inv_data',
+             (0,1), 2, rtol=3e-15),
+        data(gdtrix_, 'gamma_inv_big_data_ipp-gamma_inv_big_data',
+             (0,1), 2),
+        data(gdtrix_comp, 'gamma_inv_small_data_ipp-gamma_inv_small_data',
+             (0,1), 2, knownfailure='gdtrix bad some points'),
+        data(gdtrix_comp, 'gamma_inv_data_ipp-gamma_inv_data',
+             (0,1), 3, rtol=6e-15),
+        data(gdtrix_comp, 'gamma_inv_big_data_ipp-gamma_inv_big_data',
+             (0,1), 3),
+
+        data(chndtr, 'nccs_ipp-nccs',
+             (2,0,1), 3, rtol=3e-5),
+        data(chndtr, 'nccs_big_ipp-nccs_big',
+             (2,0,1), 3, rtol=5e-4, knownfailure='chndtr inaccurate some points'),
+
+        data(spherical_jn_, 'sph_bessel_data_ipp-sph_bessel_data',
+             (0,1), 2, rtol=1e-13),
+        data(spherical_yn_, 'sph_neumann_data_ipp-sph_neumann_data',
+             (0,1), 2, rtol=8e-15),
+
+        data(owens_t, 'owens_t_ipp-owens_t',
+             (0, 1), 2, rtol=5e-14),
+        data(owens_t, 'owens_t_large_data_ipp-owens_t_large_data',
+             (0, 1), 2, rtol=8e-12),
+
+        # -- test data exists in boost but is not used in scipy --
+
+        # ibeta_derivative_data_ipp/ibeta_derivative_data.txt
+        # ibeta_derivative_int_data_ipp/ibeta_derivative_int_data.txt
+        # ibeta_derivative_large_data_ipp/ibeta_derivative_large_data.txt
+        # ibeta_derivative_small_data_ipp/ibeta_derivative_small_data.txt
+
+        # bessel_y01_prime_data_ipp/bessel_y01_prime_data.txt
+        # bessel_yn_prime_data_ipp/bessel_yn_prime_data.txt
+        # sph_bessel_prime_data_ipp/sph_bessel_prime_data.txt
+        # sph_neumann_prime_data_ipp/sph_neumann_prime_data.txt
+
+        # ellint_d2_data_ipp/ellint_d2_data.txt
+        # ellint_d_data_ipp/ellint_d_data.txt
+        # ellint_pi2_data_ipp/ellint_pi2_data.txt
+        # ellint_pi3_data_ipp/ellint_pi3_data.txt
+        # ellint_pi3_large_data_ipp/ellint_pi3_large_data.txt
+        data(elliprc, 'ellint_rc_data_ipp-ellint_rc_data', (0, 1), 2,
+             rtol=5e-16),
+        data(elliprd, 'ellint_rd_data_ipp-ellint_rd_data', (0, 1, 2), 3,
+             rtol=5e-16),
+        data(elliprd, 'ellint_rd_0xy_ipp-ellint_rd_0xy', (0, 1, 2), 3,
+             rtol=5e-16),
+        data(elliprd, 'ellint_rd_0yy_ipp-ellint_rd_0yy', (0, 1, 2), 3,
+             rtol=5e-16),
+        data(elliprd, 'ellint_rd_xxx_ipp-ellint_rd_xxx', (0, 1, 2), 3,
+             rtol=5e-16),
+        # Some of the following rtol for elliprd may be larger than 5e-16 to
+        # work around some hard cases in the Boost test where we get slightly
+        # larger error than the ideal bound when the x (==y) input is close to
+        # zero.
+        # Also the accuracy on 32-bit builds with g++ may suffer from excess
+        # loss of precision; see GCC bugzilla 323
+        # https://gcc.gnu.org/bugzilla/show_bug.cgi?id=323
+        data(elliprd, 'ellint_rd_xxz_ipp-ellint_rd_xxz', (0, 1, 2), 3,
+             rtol=6.5e-16),
+        data(elliprd, 'ellint_rd_xyy_ipp-ellint_rd_xyy', (0, 1, 2), 3,
+             rtol=6e-16),
+        data(elliprf, 'ellint_rf_data_ipp-ellint_rf_data', (0, 1, 2), 3,
+             rtol=5e-16),
+        data(elliprf, 'ellint_rf_xxx_ipp-ellint_rf_xxx', (0, 1, 2), 3,
+             rtol=5e-16),
+        data(elliprf, 'ellint_rf_xyy_ipp-ellint_rf_xyy', (0, 1, 2), 3,
+             rtol=5e-16),
+        data(elliprf, 'ellint_rf_xy0_ipp-ellint_rf_xy0', (0, 1, 2), 3,
+             rtol=5e-16),
+        data(elliprf, 'ellint_rf_0yy_ipp-ellint_rf_0yy', (0, 1, 2), 3,
+             rtol=5e-16),
+        # The accuracy of R_G is primarily limited by R_D that is used
+        # internally. It is generally worse than R_D. Notice that we increased
+        # the rtol for R_G here. The cases with duplicate arguments are
+        # slightly less likely to be unbalanced (at least two arguments are
+        # already balanced) so the error bound is slightly better. Again,
+        # precision with g++ 32-bit is even worse.
+        data(elliprg, 'ellint_rg_ipp-ellint_rg', (0, 1, 2), 3,
+             rtol=8.0e-16),
+        data(elliprg, 'ellint_rg_xxx_ipp-ellint_rg_xxx', (0, 1, 2), 3,
+             rtol=6e-16),
+        data(elliprg, 'ellint_rg_xyy_ipp-ellint_rg_xyy', (0, 1, 2), 3,
+             rtol=7.5e-16),
+        data(elliprg, 'ellint_rg_xy0_ipp-ellint_rg_xy0', (0, 1, 2), 3,
+             rtol=5e-16),
+        data(elliprg, 'ellint_rg_00x_ipp-ellint_rg_00x', (0, 1, 2), 3,
+             rtol=5e-16),
+        data(elliprj, 'ellint_rj_data_ipp-ellint_rj_data', (0, 1, 2, 3), 4,
+             rtol=5e-16, atol=1e-25,
+             param_filter=(lambda s: s <= 5e-26,)),
+        # ellint_rc_data_ipp/ellint_rc_data.txt
+        # ellint_rd_0xy_ipp/ellint_rd_0xy.txt
+        # ellint_rd_0yy_ipp/ellint_rd_0yy.txt
+        # ellint_rd_data_ipp/ellint_rd_data.txt
+        # ellint_rd_xxx_ipp/ellint_rd_xxx.txt
+        # ellint_rd_xxz_ipp/ellint_rd_xxz.txt
+        # ellint_rd_xyy_ipp/ellint_rd_xyy.txt
+        # ellint_rf_0yy_ipp/ellint_rf_0yy.txt
+        # ellint_rf_data_ipp/ellint_rf_data.txt
+        # ellint_rf_xxx_ipp/ellint_rf_xxx.txt
+        # ellint_rf_xy0_ipp/ellint_rf_xy0.txt
+        # ellint_rf_xyy_ipp/ellint_rf_xyy.txt
+        # ellint_rg_00x_ipp/ellint_rg_00x.txt
+        # ellint_rg_ipp/ellint_rg.txt
+        # ellint_rg_xxx_ipp/ellint_rg_xxx.txt
+        # ellint_rg_xy0_ipp/ellint_rg_xy0.txt
+        # ellint_rg_xyy_ipp/ellint_rg_xyy.txt
+        # ellint_rj_data_ipp/ellint_rj_data.txt
+        # ellint_rj_e2_ipp/ellint_rj_e2.txt
+        # ellint_rj_e3_ipp/ellint_rj_e3.txt
+        # ellint_rj_e4_ipp/ellint_rj_e4.txt
+        # ellint_rj_zp_ipp/ellint_rj_zp.txt
+
+        # jacobi_elliptic_ipp/jacobi_elliptic.txt
+        # jacobi_elliptic_small_ipp/jacobi_elliptic_small.txt
+        # jacobi_large_phi_ipp/jacobi_large_phi.txt
+        # jacobi_near_1_ipp/jacobi_near_1.txt
+        # jacobi_zeta_big_phi_ipp/jacobi_zeta_big_phi.txt
+        # jacobi_zeta_data_ipp/jacobi_zeta_data.txt
+
+        # heuman_lambda_data_ipp/heuman_lambda_data.txt
+
+        # hypergeometric_0F2_ipp/hypergeometric_0F2.txt
+        # hypergeometric_1F1_big_ipp/hypergeometric_1F1_big.txt
+        # hypergeometric_1F1_ipp/hypergeometric_1F1.txt
+        # hypergeometric_1F1_small_random_ipp/hypergeometric_1F1_small_random.txt
+        # hypergeometric_1F2_ipp/hypergeometric_1F2.txt
+        # hypergeometric_1f1_large_regularized_ipp/hypergeometric_1f1_large_regularized.txt  # noqa: E501
+        # hypergeometric_1f1_log_large_unsolved_ipp/hypergeometric_1f1_log_large_unsolved.txt  # noqa: E501
+        # hypergeometric_2F0_half_ipp/hypergeometric_2F0_half.txt
+        # hypergeometric_2F0_integer_a2_ipp/hypergeometric_2F0_integer_a2.txt
+        # hypergeometric_2F0_ipp/hypergeometric_2F0.txt
+        # hypergeometric_2F0_large_z_ipp/hypergeometric_2F0_large_z.txt
+        # hypergeometric_2F1_ipp/hypergeometric_2F1.txt
+        # hypergeometric_2F2_ipp/hypergeometric_2F2.txt
+
+        # ncbeta_big_ipp/ncbeta_big.txt
+        # nct_small_delta_ipp/nct_small_delta.txt
+        # nct_asym_ipp/nct_asym.txt
+        # ncbeta_ipp/ncbeta.txt
+
+        # powm1_data_ipp/powm1_big_data.txt
+        # powm1_sqrtp1m1_test_hpp/sqrtp1m1_data.txt
+
+        # sinc_data_ipp/sinc_data.txt
+
+        # test_gamma_data_ipp/gammap1m1_data.txt
+        # tgamma_ratio_data_ipp/tgamma_ratio_data.txt
+
+        # trig_data_ipp/trig_data.txt
+        # trig_data2_ipp/trig_data2.txt
+]
+
+
+@pytest.mark.parametrize('test', BOOST_TESTS, ids=repr)
+def test_boost(test):
+     _test_factory(test)
+
+
+GSL_TESTS = [
+        data_gsl(mathieu_a, 'mathieu_ab', (0, 1), 2, rtol=1e-13, atol=1e-13),
+        data_gsl(mathieu_b, 'mathieu_ab', (0, 1), 3, rtol=1e-13, atol=1e-13),
+
+        # Also the GSL output has limited accuracy...
+        data_gsl(mathieu_ce_rad, 'mathieu_ce_se', (0, 1, 2), 3, rtol=1e-7, atol=1e-13),
+        data_gsl(mathieu_se_rad, 'mathieu_ce_se', (0, 1, 2), 4, rtol=1e-7, atol=1e-13),
+
+        data_gsl(mathieu_mc1_scaled, 'mathieu_mc_ms',
+                 (0, 1, 2), 3, rtol=1e-7, atol=1e-13),
+        data_gsl(mathieu_ms1_scaled, 'mathieu_mc_ms',
+                 (0, 1, 2), 4, rtol=1e-7, atol=1e-13),
+
+        data_gsl(mathieu_mc2_scaled, 'mathieu_mc_ms',
+                 (0, 1, 2), 5, rtol=1e-7, atol=1e-13),
+        data_gsl(mathieu_ms2_scaled, 'mathieu_mc_ms',
+                 (0, 1, 2), 6, rtol=1e-7, atol=1e-13),
+]
+
+
+@pytest.mark.parametrize('test', GSL_TESTS, ids=repr)
+def test_gsl(test):
+    _test_factory(test)
+
+
+LOCAL_TESTS = [
+    data_local(ellipkinc, 'ellipkinc_neg_m', (0, 1), 2),
+    data_local(ellipkm1, 'ellipkm1', 0, 1),
+    data_local(ellipeinc, 'ellipeinc_neg_m', (0, 1), 2),
+    data_local(clog1p, 'log1p_expm1_complex', (0,1), (2,3), rtol=1e-14),
+    data_local(cexpm1, 'log1p_expm1_complex', (0,1), (4,5), rtol=1e-14),
+    data_local(gammainc, 'gammainc', (0, 1), 2, rtol=1e-12),
+    data_local(gammaincc, 'gammaincc', (0, 1), 2, rtol=1e-11),
+    data_local(ellip_harm_2, 'ellip',(0, 1, 2, 3, 4), 6, rtol=1e-10, atol=1e-13),
+    data_local(ellip_harm, 'ellip',(0, 1, 2, 3, 4), 5, rtol=1e-10, atol=1e-13),
+    data_local(wright_bessel, 'wright_bessel', (0, 1, 2), 3, rtol=1e-11),
+]
+
+
+@pytest.mark.parametrize('test', LOCAL_TESTS, ids=repr)
+def test_local(test):
+    _test_factory(test)
+
+
+def _test_factory(test, dtype=np.float64):
+    """Boost test"""
+    with warnings.catch_warnings():
+        msg = "The occurrence of roundoff error is detected"
+        warnings.filterwarnings("ignore", msg, IntegrationWarning)
+        with np.errstate(all='ignore'):
+            test.check(dtype=dtype)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_dd.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_dd.py
new file mode 100644
index 0000000000000000000000000000000000000000..6da2c8ddddd7341cbb777216e9f2f3cce536a51e
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_dd.py
@@ -0,0 +1,42 @@
+# Tests for a few of the "double-double" C++ functions defined in
+# special/cephes/dd_real.h. Prior to gh-20390 which translated these
+# functions from C to C++, there were test cases for _dd_expm1. It
+# was determined that this function is not used anywhere internally
+# in SciPy, so this function was not translated.
+
+
+import pytest
+from numpy.testing import assert_allclose
+from scipy.special._test_internal import _dd_exp, _dd_log
+
+
+# Each tuple in test_data contains:
+#   (dd_func, xhi, xlo, expected_yhi, expected_ylo)
+# The expected values were computed with mpmath, e.g.
+#
+#   import mpmath
+#   mpmath.mp.dps = 100
+#   xhi = 10.0
+#   xlo = 0.0
+#   x = mpmath.mpf(xhi) + mpmath.mpf(xlo)
+#   y = mpmath.log(x)
+#   expected_yhi = float(y)
+#   expected_ylo = float(y - expected_yhi)
+#
+test_data = [
+    (_dd_exp, -0.3333333333333333, -1.850371707708594e-17,
+     0.7165313105737893, -2.0286948382455594e-17),
+    (_dd_exp, 0.0, 0.0, 1.0, 0.0),
+    (_dd_exp, 10.0, 0.0, 22026.465794806718, -1.3780134700517372e-12),
+    (_dd_log, 0.03125, 0.0, -3.4657359027997265, -4.930038229799327e-18),
+    (_dd_log, 10.0, 0.0, 2.302585092994046, -2.1707562233822494e-16),
+]
+
+
+@pytest.mark.parametrize('dd_func, xhi, xlo, expected_yhi, expected_ylo',
+                         test_data)
+def test_dd(dd_func, xhi, xlo, expected_yhi, expected_ylo):
+    yhi, ylo = dd_func(xhi, xlo)
+    assert yhi == expected_yhi, (f"high double ({yhi}) does not equal the "
+                                 f"expected value {expected_yhi}")
+    assert_allclose(ylo, expected_ylo, rtol=5e-15)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_digamma.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_digamma.py
new file mode 100644
index 0000000000000000000000000000000000000000..d7f27dc7b71c1ae928b4bdd8bd987df9ca420bab
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_digamma.py
@@ -0,0 +1,45 @@
+import numpy as np
+from numpy import pi, log, sqrt
+from numpy.testing import assert_, assert_equal
+
+from scipy.special._testutils import FuncData
+import scipy.special as sc
+
+# Euler-Mascheroni constant
+euler = 0.57721566490153286
+
+
+def test_consistency():
+    # Make sure the implementation of digamma for real arguments
+    # agrees with the implementation of digamma for complex arguments.
+
+    # It's all poles after -1e16
+    x = np.r_[-np.logspace(15, -30, 200), np.logspace(-30, 300, 200)]
+    dataset = np.vstack((x + 0j, sc.digamma(x))).T
+    FuncData(sc.digamma, dataset, 0, 1, rtol=5e-14, nan_ok=True).check()
+
+
+def test_special_values():
+    # Test special values from Gauss's digamma theorem. See
+    #
+    # https://en.wikipedia.org/wiki/Digamma_function
+
+    dataset = [
+        (1, -euler),
+        (0.5, -2*log(2) - euler),
+        (1/3, -pi/(2*sqrt(3)) - 3*log(3)/2 - euler),
+        (1/4, -pi/2 - 3*log(2) - euler),
+        (1/6, -pi*sqrt(3)/2 - 2*log(2) - 3*log(3)/2 - euler),
+        (1/8,
+         -pi/2 - 4*log(2) - (pi + log(2 + sqrt(2)) - log(2 - sqrt(2)))/sqrt(2) - euler)
+    ]
+
+    dataset = np.asarray(dataset)
+    FuncData(sc.digamma, dataset, 0, 1, rtol=1e-14).check()
+
+
+def test_nonfinite():
+    pts = [0.0, -0.0, np.inf]
+    std = [-np.inf, np.inf, np.inf]
+    assert_equal(sc.digamma(pts), std)
+    assert_(all(np.isnan(sc.digamma([-np.inf, -1]))))
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_ellip_harm.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_ellip_harm.py
new file mode 100644
index 0000000000000000000000000000000000000000..68526bc31e7a6caedae7de1cb8f033f9b221062a
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_ellip_harm.py
@@ -0,0 +1,288 @@
+#
+# Tests for the Ellipsoidal Harmonic Function,
+# Distributed under the same license as SciPy itself.
+#
+import warnings
+
+import numpy as np
+from numpy.testing import assert_equal, assert_allclose, assert_
+from scipy.special._testutils import assert_func_equal
+from scipy.special import ellip_harm, ellip_harm_2, ellip_normal
+from scipy.integrate import IntegrationWarning
+from numpy import sqrt, pi
+
+
+def test_ellip_potential():
+    def change_coefficient(lambda1, mu, nu, h2, k2):
+        x = sqrt(lambda1**2*mu**2*nu**2/(h2*k2))
+        y = sqrt((lambda1**2 - h2)*(mu**2 - h2)*(h2 - nu**2)/(h2*(k2 - h2)))
+        z = sqrt((lambda1**2 - k2)*(k2 - mu**2)*(k2 - nu**2)/(k2*(k2 - h2)))
+        return x, y, z
+
+    def solid_int_ellip(lambda1, mu, nu, n, p, h2, k2):
+        return (ellip_harm(h2, k2, n, p, lambda1)*ellip_harm(h2, k2, n, p, mu)
+               * ellip_harm(h2, k2, n, p, nu))
+
+    def solid_int_ellip2(lambda1, mu, nu, n, p, h2, k2):
+        return (ellip_harm_2(h2, k2, n, p, lambda1)
+                * ellip_harm(h2, k2, n, p, mu)*ellip_harm(h2, k2, n, p, nu))
+
+    def summation(lambda1, mu1, nu1, lambda2, mu2, nu2, h2, k2):
+        tol = 1e-8
+        sum1 = 0
+        for n in range(20):
+            xsum = 0
+            for p in range(1, 2*n+2):
+                xsum += (4*pi*(solid_int_ellip(lambda2, mu2, nu2, n, p, h2, k2)
+                    * solid_int_ellip2(lambda1, mu1, nu1, n, p, h2, k2)) /
+                    (ellip_normal(h2, k2, n, p)*(2*n + 1)))
+            if abs(xsum) < 0.1*tol*abs(sum1):
+                break
+            sum1 += xsum
+        return sum1, xsum
+
+    def potential(lambda1, mu1, nu1, lambda2, mu2, nu2, h2, k2):
+        x1, y1, z1 = change_coefficient(lambda1, mu1, nu1, h2, k2)
+        x2, y2, z2 = change_coefficient(lambda2, mu2, nu2, h2, k2)
+        res = sqrt((x2 - x1)**2 + (y2 - y1)**2 + (z2 - z1)**2)
+        return 1/res
+
+    pts = [
+        (120, sqrt(19), 2, 41, sqrt(17), 2, 15, 25),
+        (120, sqrt(16), 3.2, 21, sqrt(11), 2.9, 11, 20),
+       ]
+
+    with warnings.catch_warnings():
+        warnings.filterwarnings(
+            "ignore", "The occurrence of roundoff error", IntegrationWarning)
+        warnings.filterwarnings(
+            "ignore", "The maximum number of subdivisions", IntegrationWarning)
+
+        for p in pts:
+            err_msg = repr(p)
+            exact = potential(*p)
+            result, last_term = summation(*p)
+            assert_allclose(exact, result, atol=0, rtol=1e-8, err_msg=err_msg)
+            assert_(abs(result - exact) < 10*abs(last_term), err_msg)
+
+
+def test_ellip_norm():
+
+    def G01(h2, k2):
+        return 4*pi
+
+    def G11(h2, k2):
+        return 4*pi*h2*k2/3
+
+    def G12(h2, k2):
+        return 4*pi*h2*(k2 - h2)/3
+
+    def G13(h2, k2):
+        return 4*pi*k2*(k2 - h2)/3
+
+    def G22(h2, k2):
+        res = (2*(h2**4 + k2**4) - 4*h2*k2*(h2**2 + k2**2) + 6*h2**2*k2**2 +
+        sqrt(h2**2 + k2**2 - h2*k2)*(-2*(h2**3 + k2**3) + 3*h2*k2*(h2 + k2)))
+        return 16*pi/405*res
+
+    def G21(h2, k2):
+        res = (2*(h2**4 + k2**4) - 4*h2*k2*(h2**2 + k2**2) + 6*h2**2*k2**2
+        + sqrt(h2**2 + k2**2 - h2*k2)*(2*(h2**3 + k2**3) - 3*h2*k2*(h2 + k2)))
+        return 16*pi/405*res
+
+    def G23(h2, k2):
+        return 4*pi*h2**2*k2*(k2 - h2)/15
+
+    def G24(h2, k2):
+        return 4*pi*h2*k2**2*(k2 - h2)/15
+
+    def G25(h2, k2):
+        return 4*pi*h2*k2*(k2 - h2)**2/15
+
+    def G32(h2, k2):
+        res = (16*(h2**4 + k2**4) - 36*h2*k2*(h2**2 + k2**2) + 46*h2**2*k2**2
+        + sqrt(4*(h2**2 + k2**2) - 7*h2*k2)*(-8*(h2**3 + k2**3) +
+        11*h2*k2*(h2 + k2)))
+        return 16*pi/13125*k2*h2*res
+
+    def G31(h2, k2):
+        res = (16*(h2**4 + k2**4) - 36*h2*k2*(h2**2 + k2**2) + 46*h2**2*k2**2
+        + sqrt(4*(h2**2 + k2**2) - 7*h2*k2)*(8*(h2**3 + k2**3) -
+        11*h2*k2*(h2 + k2)))
+        return 16*pi/13125*h2*k2*res
+
+    def G34(h2, k2):
+        res = (6*h2**4 + 16*k2**4 - 12*h2**3*k2 - 28*h2*k2**3 + 34*h2**2*k2**2
+        + sqrt(h2**2 + 4*k2**2 - h2*k2)*(-6*h2**3 - 8*k2**3 + 9*h2**2*k2 +
+                                            13*h2*k2**2))
+        return 16*pi/13125*h2*(k2 - h2)*res
+
+    def G33(h2, k2):
+        res = (6*h2**4 + 16*k2**4 - 12*h2**3*k2 - 28*h2*k2**3 + 34*h2**2*k2**2
+        + sqrt(h2**2 + 4*k2**2 - h2*k2)*(6*h2**3 + 8*k2**3 - 9*h2**2*k2 -
+        13*h2*k2**2))
+        return 16*pi/13125*h2*(k2 - h2)*res
+
+    def G36(h2, k2):
+        res = (16*h2**4 + 6*k2**4 - 28*h2**3*k2 - 12*h2*k2**3 + 34*h2**2*k2**2
+        + sqrt(4*h2**2 + k2**2 - h2*k2)*(-8*h2**3 - 6*k2**3 + 13*h2**2*k2 +
+        9*h2*k2**2))
+        return 16*pi/13125*k2*(k2 - h2)*res
+
+    def G35(h2, k2):
+        res = (16*h2**4 + 6*k2**4 - 28*h2**3*k2 - 12*h2*k2**3 + 34*h2**2*k2**2
+        + sqrt(4*h2**2 + k2**2 - h2*k2)*(8*h2**3 + 6*k2**3 - 13*h2**2*k2 -
+        9*h2*k2**2))
+        return 16*pi/13125*k2*(k2 - h2)*res
+
+    def G37(h2, k2):
+        return 4*pi*h2**2*k2**2*(k2 - h2)**2/105
+
+    known_funcs = {(0, 1): G01, (1, 1): G11, (1, 2): G12, (1, 3): G13,
+                   (2, 1): G21, (2, 2): G22, (2, 3): G23, (2, 4): G24,
+                   (2, 5): G25, (3, 1): G31, (3, 2): G32, (3, 3): G33,
+                   (3, 4): G34, (3, 5): G35, (3, 6): G36, (3, 7): G37}
+
+    def _ellip_norm(n, p, h2, k2):
+        func = known_funcs[n, p]
+        return func(h2, k2)
+    _ellip_norm = np.vectorize(_ellip_norm)
+
+    def ellip_normal_known(h2, k2, n, p):
+        return _ellip_norm(n, p, h2, k2)
+
+    # generate both large and small h2 < k2 pairs
+    np.random.seed(1234)
+    h2 = np.random.pareto(0.5, size=1)
+    k2 = h2 * (1 + np.random.pareto(0.5, size=h2.size))
+
+    points = []
+    for n in range(4):
+        for p in range(1, 2*n+2):
+            points.append((h2, k2, np.full(h2.size, n), np.full(h2.size, p)))
+    points = np.array(points)
+    with warnings.catch_warnings():
+        warnings.filterwarnings(
+            "ignore", "The occurrence of roundoff error", IntegrationWarning)
+        assert_func_equal(ellip_normal, ellip_normal_known, points, rtol=1e-12)
+
+
+def test_ellip_harm_2():
+
+    def I1(h2, k2, s):
+        res = (ellip_harm_2(h2, k2, 1, 1, s)/(3 * ellip_harm(h2, k2, 1, 1, s))
+        + ellip_harm_2(h2, k2, 1, 2, s)/(3 * ellip_harm(h2, k2, 1, 2, s)) +
+        ellip_harm_2(h2, k2, 1, 3, s)/(3 * ellip_harm(h2, k2, 1, 3, s)))
+        return res
+
+    with warnings.catch_warnings():
+        warnings.filterwarnings(
+            "ignore", "The occurrence of roundoff error", IntegrationWarning)
+        assert_allclose(I1(5, 8, 10), 1/(10*sqrt((100-5)*(100-8))),
+                        atol=1.5e-7, rtol=0)
+
+        # Values produced by code from arXiv:1204.0267
+        assert_allclose(ellip_harm_2(5, 8, 2, 1, 10), 0.00108056853382,
+                        atol=1.5e-7, rtol=0)
+        assert_allclose(ellip_harm_2(5, 8, 2, 2, 10), 0.00105820513809,
+                        atol=1.5e-7, rtol=0)
+        assert_allclose(ellip_harm_2(5, 8, 2, 3, 10), 0.00106058384743,
+                        atol=1.5e-7, rtol=0)
+        assert_allclose(ellip_harm_2(5, 8, 2, 4, 10), 0.00106774492306,
+                        atol=1.5e-7, rtol=0)
+        assert_allclose(ellip_harm_2(5, 8, 2, 5, 10), 0.00107976356454,
+                        atol=1.5e-7, rtol=0)
+
+
+def test_ellip_harm():
+
+    def E01(h2, k2, s):
+        return 1
+
+    def E11(h2, k2, s):
+        return s
+
+    def E12(h2, k2, s):
+        return sqrt(abs(s*s - h2))
+
+    def E13(h2, k2, s):
+        return sqrt(abs(s*s - k2))
+
+    def E21(h2, k2, s):
+        return s*s - 1/3*((h2 + k2) + sqrt(abs((h2 + k2)*(h2 + k2)-3*h2*k2)))
+
+    def E22(h2, k2, s):
+        return s*s - 1/3*((h2 + k2) - sqrt(abs((h2 + k2)*(h2 + k2)-3*h2*k2)))
+
+    def E23(h2, k2, s):
+        return s * sqrt(abs(s*s - h2))
+
+    def E24(h2, k2, s):
+        return s * sqrt(abs(s*s - k2))
+
+    def E25(h2, k2, s):
+        return sqrt(abs((s*s - h2)*(s*s - k2)))
+
+    def E31(h2, k2, s):
+        return s*s*s - (s/5)*(2*(h2 + k2) + sqrt(4*(h2 + k2)*(h2 + k2) -
+        15*h2*k2))
+
+    def E32(h2, k2, s):
+        return s*s*s - (s/5)*(2*(h2 + k2) - sqrt(4*(h2 + k2)*(h2 + k2) -
+        15*h2*k2))
+
+    def E33(h2, k2, s):
+        return sqrt(abs(s*s - h2))*(s*s - 1/5*((h2 + 2*k2) + sqrt(abs((h2 +
+        2*k2)*(h2 + 2*k2) - 5*h2*k2))))
+
+    def E34(h2, k2, s):
+        return sqrt(abs(s*s - h2))*(s*s - 1/5*((h2 + 2*k2) - sqrt(abs((h2 +
+        2*k2)*(h2 + 2*k2) - 5*h2*k2))))
+
+    def E35(h2, k2, s):
+        return sqrt(abs(s*s - k2))*(s*s - 1/5*((2*h2 + k2) + sqrt(abs((2*h2
+        + k2)*(2*h2 + k2) - 5*h2*k2))))
+
+    def E36(h2, k2, s):
+        return sqrt(abs(s*s - k2))*(s*s - 1/5*((2*h2 + k2) - sqrt(abs((2*h2
+        + k2)*(2*h2 + k2) - 5*h2*k2))))
+
+    def E37(h2, k2, s):
+        return s * sqrt(abs((s*s - h2)*(s*s - k2)))
+
+    assert_equal(ellip_harm(5, 8, 1, 2, 2.5, 1, 1),
+    ellip_harm(5, 8, 1, 2, 2.5))
+
+    known_funcs = {(0, 1): E01, (1, 1): E11, (1, 2): E12, (1, 3): E13,
+                   (2, 1): E21, (2, 2): E22, (2, 3): E23, (2, 4): E24,
+                   (2, 5): E25, (3, 1): E31, (3, 2): E32, (3, 3): E33,
+                   (3, 4): E34, (3, 5): E35, (3, 6): E36, (3, 7): E37}
+
+    point_ref = []
+
+    def ellip_harm_known(h2, k2, n, p, s):
+        for i in range(h2.size):
+            func = known_funcs[(int(n[i]), int(p[i]))]
+            point_ref.append(func(h2[i], k2[i], s[i]))
+        return point_ref
+
+    rng = np.random.RandomState(1234)
+    h2 = rng.pareto(0.5, size=30)
+    k2 = h2*(1 + rng.pareto(0.5, size=h2.size))
+    s = rng.pareto(0.5, size=h2.size)
+    points = []
+    for i in range(h2.size):
+        for n in range(4):
+            for p in range(1, 2*n+2):
+                points.append((h2[i], k2[i], n, p, s[i]))
+    points = np.array(points)
+    assert_func_equal(ellip_harm, ellip_harm_known, points, rtol=1e-12)
+
+
+def test_ellip_harm_invalid_p():
+    # Regression test. This should return nan.
+    n = 4
+    # Make p > 2*n + 1.
+    p = 2*n + 2
+    result = ellip_harm(0.5, 2.0, n, p, 0.2)
+    assert np.isnan(result)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_erfinv.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_erfinv.py
new file mode 100644
index 0000000000000000000000000000000000000000..98739b93fc6ad75a41a7b80107ee696453b12a09
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_erfinv.py
@@ -0,0 +1,89 @@
+import numpy as np
+from numpy.testing import assert_allclose, assert_equal
+import pytest
+
+import scipy.special as sc
+
+
+class TestInverseErrorFunction:
+    def test_compliment(self):
+        # Test erfcinv(1 - x) == erfinv(x)
+        x = np.linspace(-1, 1, 101)
+        assert_allclose(sc.erfcinv(1 - x), sc.erfinv(x), rtol=0, atol=1e-15)
+
+    def test_literal_values(self):
+        # The expected values were calculated with mpmath:
+        #
+        #   import mpmath
+        #   mpmath.mp.dps = 200
+        #   for y in [0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9]:
+        #       x = mpmath.erfinv(y)
+        #       print(x)
+        #
+        y = np.array([0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9])
+        actual = sc.erfinv(y)
+        expected = [
+            0.0,
+            0.08885599049425769,
+            0.1791434546212917,
+            0.2724627147267543,
+            0.37080715859355795,
+            0.4769362762044699,
+            0.5951160814499948,
+            0.7328690779592167,
+            0.9061938024368233,
+            1.1630871536766743,
+        ]
+        assert_allclose(actual, expected, rtol=0, atol=1e-15)
+
+    @pytest.mark.parametrize(
+        'f, x, y',
+        [
+            (sc.erfinv, -1, -np.inf),
+            (sc.erfinv, 0, 0),
+            (sc.erfinv, 1, np.inf),
+            (sc.erfinv, -100, np.nan),
+            (sc.erfinv, 100, np.nan),
+            (sc.erfcinv, 0, np.inf),
+            (sc.erfcinv, 1, -0.0),
+            (sc.erfcinv, 2, -np.inf),
+            (sc.erfcinv, -100, np.nan),
+            (sc.erfcinv, 100, np.nan),
+        ],
+        ids=[
+            'erfinv at lower bound',
+            'erfinv at midpoint',
+            'erfinv at upper bound',
+            'erfinv below lower bound',
+            'erfinv above upper bound',
+            'erfcinv at lower bound',
+            'erfcinv at midpoint',
+            'erfcinv at upper bound',
+            'erfcinv below lower bound',
+            'erfcinv above upper bound',
+        ]
+    )
+    def test_domain_bounds(self, f, x, y):
+        assert_equal(f(x), y)
+
+    def test_erfinv_asympt(self):
+        # regression test for gh-12758: erfinv(x) loses precision at small x
+        # expected values precomputed with mpmath:
+        # >>> mpmath.mp.dps = 100
+        # >>> expected = [float(mpmath.erfinv(t)) for t in x]
+        x = np.array([1e-20, 1e-15, 1e-14, 1e-10, 1e-8, 0.9e-7, 1.1e-7, 1e-6])
+        expected = np.array([8.86226925452758e-21,
+                             8.862269254527581e-16,
+                             8.86226925452758e-15,
+                             8.862269254527581e-11,
+                             8.86226925452758e-09,
+                             7.97604232907484e-08,
+                             9.74849617998037e-08,
+                             8.8622692545299e-07])
+        assert_allclose(sc.erfinv(x), expected,
+                        rtol=1e-15)
+
+        # also test the roundtrip consistency
+        assert_allclose(sc.erf(sc.erfinv(x)),
+                        x,
+                        rtol=5e-15)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_exponential_integrals.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_exponential_integrals.py
new file mode 100644
index 0000000000000000000000000000000000000000..d6081580b338fbf1c1eb39a846047ee0ea684e66
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_exponential_integrals.py
@@ -0,0 +1,123 @@
+import pytest
+
+import numpy as np
+from numpy.testing import assert_allclose
+import scipy.special as sc
+
+
+class TestExp1:
+
+    def test_branch_cut(self):
+        assert np.isnan(sc.exp1(-1))
+        assert sc.exp1(complex(-1, 0)).imag == (
+            -sc.exp1(complex(-1, -0.0)).imag
+        )
+
+        assert_allclose(
+            sc.exp1(complex(-1, 0)),
+            sc.exp1(-1 + 1e-20j),
+            atol=0,
+            rtol=1e-15
+        )
+        assert_allclose(
+            sc.exp1(complex(-1, -0.0)),
+            sc.exp1(-1 - 1e-20j),
+            atol=0,
+            rtol=1e-15
+        )
+
+    def test_834(self):
+        # Regression test for #834
+        a = sc.exp1(-complex(19.9999990))
+        b = sc.exp1(-complex(19.9999991))
+        assert_allclose(a.imag, b.imag, atol=0, rtol=1e-15)
+
+
+class TestScaledExp1:
+
+    @pytest.mark.parametrize('x, expected', [(0, 0), (np.inf, 1)])
+    def test_limits(self, x, expected):
+        y = sc._ufuncs._scaled_exp1(x)
+        assert y == expected
+
+    # The expected values were computed with mpmath, e.g.:
+    #
+    #   from mpmath import mp
+    #   mp.dps = 80
+    #   x = 1e-25
+    #   print(float(x*mp.exp(x)*np.expint(1, x)))
+    #
+    # prints 5.698741165994961e-24
+    #
+    # The method used to compute _scaled_exp1 changes at x=1
+    # and x=1250, so values at those inputs, and values just
+    # above and below them, are included in the test data.
+    @pytest.mark.parametrize('x, expected',
+                             [(1e-25, 5.698741165994961e-24),
+                              (0.1, 0.20146425447084518),
+                              (0.9995, 0.5962509885831002),
+                              (1.0, 0.5963473623231941),
+                              (1.0005, 0.5964436833238044),
+                              (2.5, 0.7588145912149602),
+                              (10.0, 0.9156333393978808),
+                              (100.0, 0.9901942286733019),
+                              (500.0, 0.9980079523802055),
+                              (1000.0, 0.9990019940238807),
+                              (1249.5, 0.9992009578306811),
+                              (1250.0, 0.9992012769377913),
+                              (1250.25, 0.9992014363957858),
+                              (2000.0, 0.9995004992514963),
+                              (1e4, 0.9999000199940024),
+                              (1e10, 0.9999999999),
+                              (1e15, 0.999999999999999),
+                              ])
+    def test_scaled_exp1(self, x, expected):
+        y = sc._ufuncs._scaled_exp1(x)
+        assert_allclose(y, expected, rtol=2e-15)
+
+
+class TestExpi:
+
+    @pytest.mark.parametrize('result', [
+        sc.expi(complex(-1, 0)),
+        sc.expi(complex(-1, -0.0)),
+        sc.expi(-1)
+    ])
+    def test_branch_cut(self, result):
+        desired = -0.21938393439552027368  # Computed using Mpmath
+        assert_allclose(result, desired, atol=0, rtol=1e-14)
+
+    def test_near_branch_cut(self):
+        lim_from_above = sc.expi(-1 + 1e-20j)
+        lim_from_below = sc.expi(-1 - 1e-20j)
+        assert_allclose(
+            lim_from_above.real,
+            lim_from_below.real,
+            atol=0,
+            rtol=1e-15
+        )
+        assert_allclose(
+            lim_from_above.imag,
+            -lim_from_below.imag,
+            atol=0,
+            rtol=1e-15
+        )
+
+    def test_continuity_on_positive_real_axis(self):
+        assert_allclose(
+            sc.expi(complex(1, 0)),
+            sc.expi(complex(1, -0.0)),
+            atol=0,
+            rtol=1e-15
+        )
+    
+    @pytest.mark.parametrize('x, expected', [(0, -np.inf), (np.inf, np.inf)]) 
+    def test_limits(self, x, expected):
+        y = sc.expi(x)
+        assert y == expected
+
+
+class TestExpn:
+
+    def test_out_of_domain(self):
+        assert all(np.isnan([sc.expn(-1, 1.0), sc.expn(1, -1.0)]))
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_extending.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_extending.py
new file mode 100644
index 0000000000000000000000000000000000000000..3ecaf51545e006e37a451a08f356ce0392a3159c
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_extending.py
@@ -0,0 +1,28 @@
+import os
+import platform
+import sysconfig
+
+import pytest
+
+from scipy._lib._testutils import IS_EDITABLE,_test_cython_extension, cython
+from scipy.special import beta, gamma
+
+
+@pytest.mark.fail_slow(40)
+# essential per https://github.com/scipy/scipy/pull/20487#discussion_r1567057247
+@pytest.mark.skipif(IS_EDITABLE,
+                    reason='Editable install cannot find .pxd headers.')
+@pytest.mark.skipif((platform.system() == 'Windows' and
+                     sysconfig.get_config_var('Py_GIL_DISABLED')),
+                    reason='gh-22039')
+@pytest.mark.skipif(platform.machine() in ["wasm32", "wasm64"],
+                    reason="Can't start subprocess")
+@pytest.mark.skipif(cython is None, reason="requires cython")
+def test_cython(tmp_path):
+    srcdir = os.path.dirname(os.path.dirname(__file__))
+    extensions, extensions_cpp = _test_cython_extension(tmp_path, srcdir)
+    # actually test the cython c-extensions
+    assert extensions.cy_beta(0.5, 0.1) == beta(0.5, 0.1)
+    assert extensions.cy_gamma(0.5 + 1.0j) == gamma(0.5 + 1.0j)
+    assert extensions_cpp.cy_beta(0.5, 0.1) == beta(0.5, 0.1)
+    assert extensions_cpp.cy_gamma(0.5 + 1.0j) == gamma(0.5 + 1.0j)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_faddeeva.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_faddeeva.py
new file mode 100644
index 0000000000000000000000000000000000000000..8868f66c47ce0d4bbb21c78435a6c89d44065252
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_faddeeva.py
@@ -0,0 +1,85 @@
+import pytest
+
+import numpy as np
+from numpy.testing import assert_allclose
+import scipy.special as sc
+from scipy.special._testutils import FuncData
+
+
+class TestVoigtProfile:
+
+    @pytest.mark.parametrize('x, sigma, gamma', [
+        (np.nan, 1, 1),
+        (0, np.nan, 1),
+        (0, 1, np.nan),
+        (1, np.nan, 0),
+        (np.nan, 1, 0),
+        (1, 0, np.nan),
+        (np.nan, 0, 1),
+        (np.nan, 0, 0)
+    ])
+    def test_nan(self, x, sigma, gamma):
+        assert np.isnan(sc.voigt_profile(x, sigma, gamma))
+
+    @pytest.mark.parametrize('x, desired', [
+        (-np.inf, 0),
+        (np.inf, 0)
+    ])
+    def test_inf(self, x, desired):
+        assert sc.voigt_profile(x, 1, 1) == desired
+
+    def test_against_mathematica(self):
+        # Results obtained from Mathematica by computing
+        #
+        # PDF[VoigtDistribution[gamma, sigma], x]
+        #
+        points = np.array([
+            [-7.89, 45.06, 6.66, 0.0077921073660388806401],
+            [-0.05, 7.98, 24.13, 0.012068223646769913478],
+            [-13.98, 16.83, 42.37, 0.0062442236362132357833],
+            [-12.66, 0.21, 6.32, 0.010052516161087379402],
+            [11.34, 4.25, 21.96, 0.0113698923627278917805],
+            [-11.56, 20.40, 30.53, 0.0076332760432097464987],
+            [-9.17, 25.61, 8.32, 0.011646345779083005429],
+            [16.59, 18.05, 2.50, 0.013637768837526809181],
+            [9.11, 2.12, 39.33, 0.0076644040807277677585],
+            [-43.33, 0.30, 45.68, 0.0036680463875330150996]
+        ])
+        FuncData(
+            sc.voigt_profile,
+            points,
+            (0, 1, 2),
+            3,
+            atol=0,
+            rtol=1e-15
+        ).check()
+
+    def test_symmetry(self):
+        x = np.linspace(0, 10, 20)
+        assert_allclose(
+            sc.voigt_profile(x, 1, 1),
+            sc.voigt_profile(-x, 1, 1),
+            rtol=1e-15,
+            atol=0
+        )
+
+    @pytest.mark.parametrize('x, sigma, gamma, desired', [
+        (0, 0, 0, np.inf),
+        (1, 0, 0, 0)
+    ])
+    def test_corner_cases(self, x, sigma, gamma, desired):
+        assert sc.voigt_profile(x, sigma, gamma) == desired
+
+    @pytest.mark.parametrize('sigma1, gamma1, sigma2, gamma2', [
+        (0, 1, 1e-16, 1),
+        (1, 0, 1, 1e-16),
+        (0, 0, 1e-16, 1e-16)
+    ])
+    def test_continuity(self, sigma1, gamma1, sigma2, gamma2):
+        x = np.linspace(1, 10, 20)
+        assert_allclose(
+            sc.voigt_profile(x, sigma1, gamma1),
+            sc.voigt_profile(x, sigma2, gamma2),
+            rtol=1e-16,
+            atol=1e-16
+        )
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_gamma.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_gamma.py
new file mode 100644
index 0000000000000000000000000000000000000000..2e3fbd17dddeed73d311566a930f52899e3b9db6
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_gamma.py
@@ -0,0 +1,12 @@
+import numpy as np
+import scipy.special as sc
+
+
+class TestRgamma:
+
+    def test_gh_11315(self):
+        assert sc.rgamma(-35) == 0
+
+    def test_rgamma_zeros(self):
+        x = np.array([0, -10, -100, -1000, -10000])
+        assert np.all(sc.rgamma(x) == 0)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_gammainc.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_gammainc.py
new file mode 100644
index 0000000000000000000000000000000000000000..b5a0ffb65d6deebf77fe82ebee2dca61f2067c59
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_gammainc.py
@@ -0,0 +1,152 @@
+import pytest
+
+import numpy as np
+from numpy.testing import assert_allclose, assert_array_equal
+
+import scipy.special as sc
+from scipy.special._testutils import FuncData
+
+
+INVALID_POINTS = [
+    (1, -1),
+    (0, 0),
+    (-1, 1),
+    (np.nan, 1),
+    (1, np.nan)
+]
+
+
+class TestGammainc:
+
+    @pytest.mark.parametrize('a, x', INVALID_POINTS)
+    def test_domain(self, a, x):
+        assert np.isnan(sc.gammainc(a, x))
+
+    def test_a_eq_0_x_gt_0(self):
+        assert sc.gammainc(0, 1) == 1
+
+    @pytest.mark.parametrize('a, x, desired', [
+        (np.inf, 1, 0),
+        (np.inf, 0, 0),
+        (np.inf, np.inf, np.nan),
+        (1, np.inf, 1)
+    ])
+    def test_infinite_arguments(self, a, x, desired):
+        result = sc.gammainc(a, x)
+        if np.isnan(desired):
+            assert np.isnan(result)
+        else:
+            assert result == desired
+
+    @pytest.mark.parametrize("x", [-np.inf, -1.0, -0.0, 0.0, np.inf, np.nan])
+    def test_a_nan(self, x):
+        assert np.isnan(sc.gammainc(np.nan, x))
+
+    @pytest.mark.parametrize("a", [-np.inf, -1.0, -0.0, 0.0, np.inf, np.nan])
+    def test_x_nan(self, a):
+        assert np.isnan(sc.gammainc(a, np.nan))
+
+    def test_infinite_limits(self):
+        # Test that large arguments converge to the hard-coded limits
+        # at infinity.
+        assert_allclose(
+            sc.gammainc(1000, 100),
+            sc.gammainc(np.inf, 100),
+            atol=1e-200,  # Use `atol` since the function converges to 0.
+            rtol=0
+        )
+        assert sc.gammainc(100, 1000) == sc.gammainc(100, np.inf)
+
+    def test_x_zero(self):
+        a = np.arange(1, 10)
+        assert_array_equal(sc.gammainc(a, 0), 0)
+
+    def test_limit_check(self):
+        result = sc.gammainc(1e-10, 1)
+        limit = sc.gammainc(0, 1)
+        assert np.isclose(result, limit)
+
+    def gammainc_line(self, x):
+        # The line a = x where a simpler asymptotic expansion (analog
+        # of DLMF 8.12.15) is available.
+        c = np.array([-1/3, -1/540, 25/6048, 101/155520,
+                      -3184811/3695155200, -2745493/8151736420])
+        res = 0
+        xfac = 1
+        for ck in c:
+            res -= ck*xfac
+            xfac /= x
+        res /= np.sqrt(2*np.pi*x)
+        res += 0.5
+        return res
+
+    def test_line(self):
+        x = np.logspace(np.log10(25), 300, 500)
+        a = x
+        dataset = np.vstack((a, x, self.gammainc_line(x))).T
+        FuncData(sc.gammainc, dataset, (0, 1), 2, rtol=1e-11).check()
+
+    def test_roundtrip(self):
+        a = np.logspace(-5, 10, 100)
+        x = np.logspace(-5, 10, 100)
+
+        y = sc.gammaincinv(a, sc.gammainc(a, x))
+        assert_allclose(x, y, rtol=1e-10)
+
+
+class TestGammaincc:
+
+    @pytest.mark.parametrize('a, x', INVALID_POINTS)
+    def test_domain(self, a, x):
+        assert np.isnan(sc.gammaincc(a, x))
+
+    def test_a_eq_0_x_gt_0(self):
+        assert sc.gammaincc(0, 1) == 0
+
+    @pytest.mark.parametrize('a, x, desired', [
+        (np.inf, 1, 1),
+        (np.inf, 0, 1),
+        (np.inf, np.inf, np.nan),
+        (1, np.inf, 0)
+    ])
+    def test_infinite_arguments(self, a, x, desired):
+        result = sc.gammaincc(a, x)
+        if np.isnan(desired):
+            assert np.isnan(result)
+        else:
+            assert result == desired
+
+    @pytest.mark.parametrize("x", [-np.inf, -1.0, -0.0, 0.0, np.inf, np.nan])
+    def test_a_nan(self, x):
+        assert np.isnan(sc.gammaincc(np.nan, x))
+
+    @pytest.mark.parametrize("a", [-np.inf, -1.0, -0.0, 0.0, np.inf, np.nan])
+    def test_x_nan(self, a):
+        assert np.isnan(sc.gammaincc(a, np.nan))
+
+    def test_infinite_limits(self):
+        # Test that large arguments converge to the hard-coded limits
+        # at infinity.
+        assert sc.gammaincc(1000, 100) == sc.gammaincc(np.inf, 100)
+        assert_allclose(
+            sc.gammaincc(100, 1000),
+            sc.gammaincc(100, np.inf),
+            atol=1e-200,  # Use `atol` since the function converges to 0.
+            rtol=0
+        )
+
+    def test_limit_check(self):
+        result = sc.gammaincc(1e-10,1)
+        limit = sc.gammaincc(0,1)
+        assert np.isclose(result, limit)
+
+    def test_x_zero(self):
+        a = np.arange(1, 10)
+        assert_array_equal(sc.gammaincc(a, 0), 1)
+
+    def test_roundtrip(self):
+        a = np.logspace(-5, 10, 100)
+        x = np.logspace(-5, 10, 100)
+
+        y = sc.gammainccinv(a, sc.gammaincc(a, x))
+        assert_allclose(x, y, rtol=1e-14)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_gen_harmonic.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_gen_harmonic.py
new file mode 100644
index 0000000000000000000000000000000000000000..0896142d571ae1d3815ab2eb99a775d52b7d9169
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_gen_harmonic.py
@@ -0,0 +1,99 @@
+import numpy as np
+from numpy.testing import assert_allclose, assert_equal
+import pytest
+from scipy.special._ufuncs import _gen_harmonic, _normalized_gen_harmonic
+
+
+#
+# In the following tests, reference values were computed with mpmath.
+#
+
+@pytest.mark.parametrize('typ', [np.int32, np.int64, np.float64])
+@pytest.mark.parametrize(
+    'n, a, ref',
+    [(8, 9.0, 1.0020083884212339),
+     (1000, 2.5, 1.3414661912046497),
+     (10, 1.5, 1.9953364933456017),
+     (10000, 1.25, 4.1951168257387765),
+     (10000,1.00001, 9.787182620770265),
+     (80, 1.000002, 4.965460167788836),
+     (75, 1 + 1e-12, 4.901355630543771),
+     (100, 1 + 1e-14, 5.187377517639515),
+     (100, 1 + 8e-16, 5.187377517639611),
+     (100, 1.0, 5.187377517639621),
+     (7, 1.0, 2.592857142857143),
+     (8000, 1.0, 9.564474984261423),
+     (5, 1 - 1e-12, 2.2833333333347143),
+     (25000, 1 - 1e-12, 10.703866768669737),
+     (1000, 0.995, 7.6058022857089975),
+     (1000, 0.75, 19.055178975831392),
+     (10000, 0.25, 1332.5700547197382),
+     (5, 1e-8, 4.999999952125083),
+     (15, 1e-16, 14.999999999999996),
+     (100, 0.0, 100.0),
+     (4, -1.0, 10.0),
+     (75, -1.5, 19811.38815892374)]
+)
+def test_gen_harmonic(typ, n, a, ref):
+    h = _gen_harmonic(typ(n), a)
+    assert_allclose(h, ref, rtol=5e-15)
+
+
+@pytest.mark.parametrize('typ', [np.int32, np.int64, np.float64])
+@pytest.mark.parametrize(
+    'n, a, ref',
+    [(10, np.inf, 1.0),
+     (1, np.nan, 1.0),
+     (1, -np.inf, 1.0),
+     (3, np.nan, np.nan),
+     (-3, 1.0, np.nan)]
+)
+def test_gen_harmonic_exact_cases(typ, n, a, ref):
+    h = _gen_harmonic(typ(n), a)
+    assert_equal(h, ref)
+
+
+def test_gen_harmonic_n_nan():
+    h = _gen_harmonic(np.nan, 0.75)
+    assert_equal(h, np.nan)
+
+
+@pytest.mark.parametrize('typ', [np.int32, np.int64, np.float64])
+@pytest.mark.parametrize(
+    'j, k, n, a, ref',
+    [(400, 5000, 5000, 10.0, 4.2821759663214485e-25),
+     (400, 5000, 5000, 3.5, 1.11086549102426e-07),
+     (1, 2, 3, 1.5, 0.8755176866163012),
+     (300, 500, 500, 1 + 1e-14, 0.07559343891632035),
+     (1500, 2500, 3000, 1 - 1e-12, 0.05957291246371843),
+     (10, 12, 16, 0.5, 0.13601665344521513),
+     (16, 16, 20, 0.125, 0.04583107002260924),
+     (10, 12, 16, -0.5, 0.22359306724308234),
+     (1, 8000, 10000, -1.5, 0.5724512895513029)]
+)
+def test_normalized_gen_harmonic(typ, j, k, n, a, ref):
+    h = _normalized_gen_harmonic(typ(j), typ(k), typ(n), a)
+    assert_allclose(h, ref, 5e-15)
+
+
+@pytest.mark.parametrize('typ', [np.int32, np.int64, np.float64])
+@pytest.mark.parametrize(
+    'j, k, n, a, ref',
+    [(1, 1, 1, 0.5, 1.0),
+     (1, 1, 1, np.nan, 1.0),
+     (1, 2, 5, np.nan, np.nan),
+     (1, 2, 1, 1.25, np.nan),
+     (1, 2, 3, np.inf, 1.0),
+     (2, 3, 4, np.inf, 0.0),
+     (1, 1, 10, -np.inf, 0.0),
+     (2, 3, 4, -np.inf, np.nan),
+     (3, 6, 8, 0.0, 0.5)]
+)
+def test_normalized_gen_harmonic_exact_cases(typ, j, k, n, a, ref):
+    h = _normalized_gen_harmonic(typ(j), typ(k), typ(n), a)
+    assert_equal(h, ref)
+
+
+def test_normalized_gen_harmonic_input_nan():
+    h = _normalized_gen_harmonic(1.0, np.nan, 10.0, 1.05)
+    assert_equal(h, np.nan)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_hyp2f1.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_hyp2f1.py
new file mode 100644
index 0000000000000000000000000000000000000000..8e51a48f91440583ddaa88ffe09d48e4376055cf
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_hyp2f1.py
@@ -0,0 +1,2566 @@
+"""Tests for hyp2f1 for complex values.
+
+Author: Albert Steppi, with credit to Adam Kullberg (FormerPhycisist) for
+the implementation of mp_hyp2f1 below, which modifies mpmath's hyp2f1 to
+return the same branch as scipy's on the standard branch cut.
+"""
+
+import sys
+import pytest
+import numpy as np
+from typing import NamedTuple
+from numpy.testing import assert_allclose
+
+from scipy.special import hyp2f1
+from scipy.special._testutils import check_version, MissingModule
+
+
+try:
+    import mpmath
+except ImportError:
+    mpmath = MissingModule("mpmath")
+
+
+def mp_hyp2f1(a, b, c, z):
+    """Return mpmath hyp2f1 calculated on same branch as scipy hyp2f1.
+
+    For most values of a,b,c mpmath returns the x - 0j branch of hyp2f1 on the
+    branch cut x=(1,inf) whereas scipy's hyp2f1 calculates the x + 0j branch.
+    Thus, to generate the right comparison values on the branch cut, we
+    evaluate mpmath.hyp2f1 at x + 1e-15*j.
+
+    The exception to this occurs when c-a=-m in which case both mpmath and
+    scipy calculate the x + 0j branch on the branch cut. When this happens
+    mpmath.hyp2f1 will be evaluated at the original z point.
+    """
+    on_branch_cut = z.real > 1.0 and abs(z.imag) < 1.0e-15
+    cond1 = abs(c - a - round(c - a)) < 1.0e-15 and round(c - a) <= 0
+    cond2 = abs(c - b - round(c - b)) < 1.0e-15 and round(c - b) <= 0
+    # Make sure imaginary part is *exactly* zero
+    if on_branch_cut:
+        z = z.real + 0.0j
+    if on_branch_cut and not (cond1 or cond2):
+        z_mpmath = z.real + 1.0e-15j
+    else:
+        z_mpmath = z
+    return complex(mpmath.hyp2f1(a, b, c, z_mpmath))
+
+
+class Hyp2f1TestCase(NamedTuple):
+    a: float
+    b: float
+    c: float
+    z: complex
+    expected: complex
+    rtol: float
+
+
+class TestHyp2f1:
+    """Tests for hyp2f1 for complex values.
+
+    Expected values for test cases were computed using mpmath. See
+    `scipy.special._precompute.hyp2f1_data`. The verbose style of specifying
+    test cases is used for readability and to make it easier to mark individual
+    cases as expected to fail. Expected failures are used to highlight cases
+    where improvements are needed. See
+    `scipy.special._precompute.hyp2f1_data.make_hyp2f1_test_cases` for a
+    function to generate the boilerplate for the test cases.
+
+    Assertions have been added to each test to ensure that the test cases match
+    the situations that are intended. A final test `test_test_hyp2f1` checks
+    that the expected values in the test cases actually match what is computed
+    by mpmath. This test is marked slow even though it isn't particularly slow
+    so that it won't run by default on continuous integration builds.
+    """
+    @pytest.mark.parametrize(
+        "hyp2f1_test_case",
+        [
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=0.5,
+                    b=0.2,
+                    c=-10,
+                    z=0.2 + 0.2j,
+                    expected=np.inf + 0j,
+                    rtol=0
+                )
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=0.5,
+                    b=0.2,
+                    c=-10,
+                    z=0 + 0j,
+                    expected=1 + 0j,
+                    rtol=0
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=0.5,
+                    b=0,
+                    c=-10,
+                    z=0.2 + 0.2j,
+                    expected=1 + 0j,
+                    rtol=0
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=0.5,
+                    b=0,
+                    c=0,
+                    z=0.2 + 0.2j,
+                    expected=1 + 0j,
+                    rtol=0,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=0.5,
+                    b=0.2,
+                    c=0,
+                    z=0.2 + 0.2j,
+                    expected=np.inf + 0j,
+                    rtol=0,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=0.5,
+                    b=0.2,
+                    c=0,
+                    z=0 + 0j,
+                    expected=np.nan + 0j,
+                    rtol=0,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=0.5,
+                    b=-5,
+                    c=-10,
+                    z=0.2 + 0.2j,
+                    expected=(1.0495404166666666+0.05708208333333334j),
+                    rtol=1e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=0.5,
+                    b=-10,
+                    c=-10,
+                    z=0.2 + 0.2j,
+                    expected=(1.092966013125+0.13455014673750001j),
+                    rtol=1e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-10,
+                    b=-20,
+                    c=-10,
+                    z=0.2 + 0.2j,
+                    expected=(-0.07712512000000005+0.12752814080000005j),
+                    rtol=1e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-1,
+                    b=3.2,
+                    c=-1,
+                    z=0.2 + 0.2j,
+                    expected=(1.6400000000000001+0.6400000000000001j),
+                    rtol=1e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-2,
+                    b=1.2,
+                    c=-4,
+                    z=1 + 0j,
+                    expected=1.8200000000000001 + 0j,
+                    rtol=1e-15,
+                ),
+            ),
+        ]
+    )
+    def test_c_non_positive_int(self, hyp2f1_test_case):
+        a, b, c, z, expected, rtol = hyp2f1_test_case
+        assert_allclose(hyp2f1(a, b, c, z), expected, rtol=rtol)
+
+    @pytest.mark.parametrize(
+        "hyp2f1_test_case",
+        [
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=0.5,
+                    b=0.2,
+                    c=1.5,
+                    z=1 + 0j,
+                    expected=1.1496439092239847 + 0j,
+                    rtol=1e-15
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=12.3,
+                    b=8.0,
+                    c=20.31,
+                    z=1 + 0j,
+                    expected=69280986.75273195 + 0j,
+                    rtol=1e-15
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=290.2,
+                    b=321.5,
+                    c=700.1,
+                    z=1 + 0j,
+                    expected=1.3396562400934e117 + 0j,
+                    rtol=1e-12,
+                ),
+            ),
+            # Note that here even mpmath produces different results for
+            # results that should be equivalent.
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=9.2,
+                    b=621.5,
+                    c=700.1,
+                    z=(1+0j),
+                    expected=(952726652.4158565+0j),
+                    rtol=5e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=621.5,
+                    b=9.2,
+                    c=700.1,
+                    z=(1+0j),
+                    expected=(952726652.4160284+0j),
+                    rtol=5e-12,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-101.2,
+                    b=-400.4,
+                    c=-172.1,
+                    z=(1+0j),
+                    expected=(2.2253618341394838e+37+0j),
+                    rtol=1e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-400.4,
+                    b=-101.2,
+                    c=-172.1,
+                    z=(1+0j),
+                    expected=(2.2253618341394838e+37+0j),
+                    rtol=5e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=172.5,
+                    b=-201.3,
+                    c=151.2,
+                    z=(1+0j),
+                    expected=(7.072266653650905e-135+0j),
+                    rtol=5e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-201.3,
+                    b=172.5,
+                    c=151.2,
+                    z=(1+0j),
+                    expected=(7.072266653650905e-135+0j),
+                    rtol=5e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-102.1,
+                    b=-20.3,
+                    c=1.3,
+                    z=1 + 0j,
+                    expected=2.7899070752746906e22 + 0j,
+                    rtol=3e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-202.6,
+                    b=60.3,
+                    c=1.5,
+                    z=1 + 0j,
+                    expected=-1.3113641413099326e-56 + 0j,
+                    rtol=1e-12,
+                ),
+            ),
+        ],
+    )
+    def test_unital_argument(self, hyp2f1_test_case):
+        """Tests for case z = 1, c - a - b > 0.
+
+        Expected answers computed using mpmath.
+        """
+        a, b, c, z, expected, rtol = hyp2f1_test_case
+        assert z == 1 and c - a - b > 0  # Tests the test
+        assert_allclose(hyp2f1(a, b, c, z), expected, rtol=rtol)
+
+    @pytest.mark.parametrize(
+        "hyp2f1_test_case",
+        [
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=0.5,
+                    b=0.2,
+                    c=1.3,
+                    z=-1 + 0j,
+                    expected=0.9428846409614143 + 0j,
+                    rtol=1e-15),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=12.3,
+                    b=8.0,
+                    c=5.300000000000001,
+                    z=-1 + 0j,
+                    expected=-4.845809986595704e-06 + 0j,
+                    rtol=1e-15
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=221.5,
+                    b=90.2,
+                    c=132.3,
+                    z=-1 + 0j,
+                    expected=2.0490488728377282e-42 + 0j,
+                    rtol=1e-7,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-102.1,
+                    b=-20.3,
+                    c=-80.8,
+                    z=-1 + 0j,
+                    expected=45143784.46783885 + 0j,
+                    rtol=1e-7,
+                ),
+                marks=pytest.mark.xfail(
+                    condition=sys.maxsize < 2**32,
+                    reason="Fails on 32 bit.",
+                )
+            ),
+        ],
+    )
+    def test_special_case_z_near_minus_1(self, hyp2f1_test_case):
+        """Tests for case z ~ -1, c ~ 1 + a - b
+
+        Expected answers computed using mpmath.
+        """
+        a, b, c, z, expected, rtol = hyp2f1_test_case
+        assert abs(1 + a - b - c) < 1e-15 and abs(z + 1) < 1e-15
+        assert_allclose(hyp2f1(a, b, c, z), expected, rtol=rtol)
+
+    @pytest.mark.parametrize(
+        "hyp2f1_test_case",
+        [
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-4,
+                    b=2.02764642551431,
+                    c=1.0561196186065624,
+                    z=(0.9473684210526314-0.10526315789473695j),
+                    expected=(0.0031961077109535375-0.0011313924606557173j),
+                    rtol=1e-12,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-8,
+                    b=-7.937789122896016,
+                    c=-15.964218273004214,
+                    z=(2-0.10526315789473695j),
+                    expected=(0.005543763196412503-0.0025948879065698306j),
+                    rtol=5e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-8,
+                    b=8.095813935368371,
+                    c=4.0013768449590685,
+                    z=(0.9473684210526314-0.10526315789473695j),
+                    expected=(-0.0003054674127221263-9.261359291755414e-05j),
+                    rtol=1e-10,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-4,
+                    b=-3.956227226099288,
+                    c=-3.9316537064827854,
+                    z=(1.1578947368421053-0.3157894736842106j),
+                    expected=(-0.0020809502580892937-0.0041877333232365095j),
+                    rtol=5e-12,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=2.02764642551431,
+                    b=-4,
+                    c=2.050308316530781,
+                    z=(0.9473684210526314-0.10526315789473695j),
+                    expected=(0.0011282435590058734+0.0002027062303465851j),
+                    rtol=5e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-7.937789122896016,
+                    b=-8,
+                    c=-15.964218273004214,
+                    z=(1.3684210526315788+0.10526315789473673j),
+                    expected=(-9.134907719238265e-05-0.00040219233987390723j),
+                    rtol=5e-12,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=4.080187217753502,
+                    b=-4,
+                    c=4.0013768449590685,
+                    z=(0.9473684210526314-0.10526315789473695j),
+                    expected=(-0.000519013062087489-0.0005855883076830948j),
+                    rtol=5e-12,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-10000,
+                    b=2.2,
+                    c=93459345.3,
+                    z=(2+2j),
+                    expected=(0.9995292071559088-0.00047047067522659253j),
+                    rtol=1e-12,
+                ),
+            ),
+        ]
+    )
+    def test_a_b_negative_int(self, hyp2f1_test_case):
+        a, b, c, z, expected, rtol = hyp2f1_test_case
+        assert a == int(a) and a < 0 or b == int(b) and b < 0  # Tests the test
+        assert_allclose(hyp2f1(a, b, c, z), expected, rtol=rtol)
+
+    @pytest.mark.parametrize(
+        "hyp2f1_test_case",
+        [
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-0.5,
+                    b=-0.9629749245209605,
+                    c=-15.5,
+                    z=(1.1578947368421053-1.1578947368421053j),
+                    expected=(0.9778506962676361+0.044083801141231616j),
+                    rtol=3e-12,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=8.5,
+                    b=-3.9316537064827854,
+                    c=1.5,
+                    z=(0.9473684210526314-0.10526315789473695j),
+                    expected=(4.0793167523167675-10.11694246310966j),
+                    rtol=6e-12,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=8.5,
+                    b=-0.9629749245209605,
+                    c=2.5,
+                    z=(1.1578947368421053-0.10526315789473695j),
+                    expected=(-2.9692999501916915+0.6394599899845594j),
+                    rtol=1e-11,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-0.5,
+                    b=-0.9629749245209605,
+                    c=-15.5,
+                    z=(1.5789473684210522-1.1578947368421053j),
+                    expected=(0.9493076367106102-0.04316852977183447j),
+                    rtol=1e-11,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-0.9220024191881196,
+                    b=-0.5,
+                    c=-15.5,
+                    z=(0.5263157894736841+0.10526315789473673j),
+                    expected=(0.9844377175631795-0.003120587561483841j),
+                    rtol=1e-10,
+                ),
+            ),
+        ],
+    )
+    def test_a_b_neg_int_after_euler_hypergeometric_transformation(
+        self, hyp2f1_test_case
+    ):
+        a, b, c, z, expected, rtol = hyp2f1_test_case
+        assert (  # Tests the test
+            (abs(c - a - int(c - a)) < 1e-15 and c - a < 0) or
+            (abs(c - b - int(c - b)) < 1e-15 and c - b < 0)
+        )
+        assert_allclose(hyp2f1(a, b, c, z), expected, rtol=rtol)
+
+    @pytest.mark.parametrize(
+        "hyp2f1_test_case",
+        [
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-0.9220024191881196,
+                    b=-0.9629749245209605,
+                    c=-15.963511401609862,
+                    z=(0.10526315789473673-0.3157894736842106j),
+                    expected=(0.9941449585778349+0.01756335047931358j),
+                    rtol=1e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=1.0272592605282642,
+                    b=-0.9629749245209605,
+                    c=-15.963511401609862,
+                    z=(0.5263157894736841+0.5263157894736841j),
+                    expected=(1.0388722293372104-0.09549450380041416j),
+                    rtol=5e-11,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=2.02764642551431,
+                    b=1.0561196186065624,
+                    c=-7.93846038215665,
+                    z=(0.10526315789473673+0.7368421052631575j),
+                    expected=(2.1948378809826434+24.934157235172222j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=2.02764642551431,
+                    b=16.088264119063613,
+                    c=8.031683612216888,
+                    z=(0.3157894736842106-0.736842105263158j),
+                    expected=(-0.4075277891264672-0.06819344579666956j),
+                    rtol=2e-12,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=4.080187217753502,
+                    b=2.050308316530781,
+                    c=8.031683612216888,
+                    z=(0.7368421052631575-0.10526315789473695j),
+                    expected=(2.833535530740603-0.6925373701408158j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=2.02764642551431,
+                    b=2.050308316530781,
+                    c=4.078873014294075,
+                    z=(0.10526315789473673-0.3157894736842106j),
+                    expected=(1.005347176329683-0.3580736009337313j),
+                    rtol=5e-16,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-0.9220024191881196,
+                    b=-0.9629749245209605,
+                    c=-15.963511401609862,
+                    z=(0.3157894736842106-0.5263157894736843j),
+                    expected=(0.9824353641135369+0.029271018868990268j),
+                    rtol=5e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-0.9220024191881196,
+                    b=-0.9629749245209605,
+                    c=-159.63511401609862,
+                    z=(0.3157894736842106-0.5263157894736843j),
+                    expected=(0.9982436200365834+0.002927268199671111j),
+                    rtol=1e-7,
+                ),
+                marks=pytest.mark.xfail(reason="Poor convergence.")
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=2.02764642551431,
+                    b=16.088264119063613,
+                    c=8.031683612216888,
+                    z=(0.5263157894736841-0.5263157894736843j),
+                    expected=(-0.6906825165778091+0.8176575137504892j),
+                    rtol=5e-13,
+                ),
+            ),
+        ]
+    )
+    def test_region1(self, hyp2f1_test_case):
+        """|z| < 0.9 and real(z) >= 0."""
+        a, b, c, z, expected, rtol = hyp2f1_test_case
+        assert abs(z) < 0.9 and z.real >= 0  # Tests the test
+        assert_allclose(hyp2f1(a, b, c, z), expected, rtol=rtol)
+
+    @pytest.mark.parametrize(
+        "hyp2f1_test_case",
+        [
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=2.02764642551431,
+                    b=1.0561196186065624,
+                    c=4.078873014294075,
+                    z=(-0.3157894736842106+0.7368421052631575j),
+                    expected=(0.7751915029081136+0.24068493258607315j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=16.087593263474208,
+                    b=16.088264119063613,
+                    c=2.0397202577726152,
+                    z=(-0.9473684210526316-0.3157894736842106j),
+                    expected=(6.564549348474962e-07+1.6761570598334562e-06j),
+                    rtol=5e-09,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=1.0272592605282642,
+                    b=2.050308316530781,
+                    c=16.056809865262608,
+                    z=(-0.10526315789473695-0.10526315789473695j),
+                    expected=(0.9862043298997204-0.013293151372712681j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=4.080187217753502,
+                    b=8.077282662161238,
+                    c=16.056809865262608,
+                    z=(-0.3157894736842106-0.736842105263158j),
+                    expected=(0.16163826638754716-0.41378530376373734j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=2.02764642551431,
+                    b=2.050308316530781,
+                    c=-0.906685989801748,
+                    z=(-0.5263157894736843+0.3157894736842106j),
+                    expected=(-6.256871535165936+0.13824973858225484j),
+                    rtol=1e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=2.02764642551431,
+                    b=8.077282662161238,
+                    c=-3.9924618758357022,
+                    z=(-0.9473684210526316-0.3157894736842106j),
+                    expected=(75.54672526086316+50.56157041797548j),
+                    rtol=5e-12,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=16.087593263474208,
+                    b=8.077282662161238,
+                    c=-1.9631175993998025,
+                    z=(-0.5263157894736843+0.5263157894736841j),
+                    expected=(282.0602536306534-82.31597306936214j),
+                    rtol=5e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=8.095813935368371,
+                    b=-3.9316537064827854,
+                    c=8.031683612216888,
+                    z=(-0.5263157894736843-0.10526315789473695j),
+                    expected=(5.179603735575851+1.4445374002099813j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=4.080187217753502,
+                    b=-7.949900487447654,
+                    c=1.0651378143226575,
+                    z=(-0.3157894736842106-0.9473684210526316j),
+                    expected=(2317.623517606141-269.51476321010324j),
+                    rtol=5e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=16.087593263474208,
+                    b=-1.92872979730171,
+                    c=2.0397202577726152,
+                    z=(-0.736842105263158-0.3157894736842106j),
+                    expected=(29.179154096175836+22.126690357535043j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=8.095813935368371,
+                    b=-3.9316537064827854,
+                    c=-15.963511401609862,
+                    z=(-0.736842105263158-0.10526315789473695j),
+                    expected=(0.20820247892032057-0.04763956711248794j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=1.0272592605282642,
+                    b=-15.964218273004214,
+                    c=-1.9631175993998025,
+                    z=(-0.3157894736842106-0.5263157894736843j),
+                    expected=(-157471.63920142158+991294.0587828817j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=8.095813935368371,
+                    b=-7.949900487447654,
+                    c=-7.93846038215665,
+                    z=(-0.10526315789473695-0.10526315789473695j),
+                    expected=(0.30765349653210194-0.2979706363594157j),
+                    rtol=1e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-3.956227226099288,
+                    b=1.0561196186065624,
+                    c=8.031683612216888,
+                    z=(-0.9473684210526316-0.10526315789473695j),
+                    expected=(1.6787607400597109+0.10056620134616838j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-7.937789122896016,
+                    b=16.088264119063613,
+                    c=4.078873014294075,
+                    z=(-0.5263157894736843-0.736842105263158j),
+                    expected=(7062.07842506049-12768.77955655703j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-7.937789122896016,
+                    b=16.088264119063613,
+                    c=2.0397202577726152,
+                    z=(-0.3157894736842106+0.7368421052631575j),
+                    expected=(54749.216391029935-23078.144720887536j),
+                    rtol=2e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-3.956227226099288,
+                    b=1.0561196186065624,
+                    c=-0.906685989801748,
+                    z=(-0.10526315789473695-0.10526315789473695j),
+                    expected=(1.21521766411428-4.449385173946672j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-15.980848054962111,
+                    b=4.0013768449590685,
+                    c=-1.9631175993998025,
+                    z=(-0.736842105263158+0.5263157894736841j),
+                    expected=(19234693144.196907+1617913967.7294445j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-1.9214641416286231,
+                    b=1.0561196186065624,
+                    c=-15.963511401609862,
+                    z=(-0.5263157894736843+0.3157894736842106j),
+                    expected=(0.9345201094534371+0.03745712558992195j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-7.937789122896016,
+                    b=-0.9629749245209605,
+                    c=2.0397202577726152,
+                    z=(-0.10526315789473695+0.10526315789473673j),
+                    expected=(0.605732446296829+0.398171533680972j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-1.9214641416286231,
+                    b=-15.964218273004214,
+                    c=2.0397202577726152,
+                    z=(-0.10526315789473695-0.5263157894736843j),
+                    expected=(-9.753761888305416-4.590126012666959j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-3.956227226099288,
+                    b=-1.92872979730171,
+                    c=2.0397202577726152,
+                    z=(-0.10526315789473695+0.3157894736842106j),
+                    expected=(0.45587226291120714+1.0694545265819797j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-0.9220024191881196,
+                    b=-7.949900487447654,
+                    c=-0.906685989801748,
+                    z=(-0.736842105263158+0.3157894736842106j),
+                    expected=(12.334808243233418-76.26089051819054j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-0.9220024191881196,
+                    b=-7.949900487447654,
+                    c=-15.963511401609862,
+                    z=(-0.5263157894736843+0.10526315789473673j),
+                    expected=(1.2396019687632678-0.047507973161146286j),
+                    rtol=1e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-15.980848054962111,
+                    b=-0.9629749245209605,
+                    c=-0.906685989801748,
+                    z=(-0.3157894736842106-0.5263157894736843j),
+                    expected=(97.7889554372208-18.999754543400016j),
+                    rtol=5e-13,
+                ),
+            ),
+        ]
+    )
+    def test_region2(self, hyp2f1_test_case):
+        """|z| < 1 and real(z) < 0."""
+        a, b, c, z, expected, rtol = hyp2f1_test_case
+        assert abs(z) < 1 and z.real < 0  # Tests the test
+        assert_allclose(hyp2f1(a, b, c, z), expected, rtol=rtol)
+
+    @pytest.mark.parametrize(
+        "hyp2f1_test_case",
+        [
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=16.25,
+                    b=-3.75,
+                    c=-3.5,
+                    z=(0.5263157894736841+0.7368421052631575j),
+                    expected=(-1279.4894322256655-2302.914821389276j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-15.75,
+                    b=8.25,
+                    c=-1.5,
+                    z=(0.9473684210526314+0.3157894736842106j),
+                    expected=(-8889.452798586273-11961.162305065242j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=2.25,
+                    b=2.25,
+                    c=-1.5,
+                    z=(0.5263157894736841-0.736842105263158j),
+                    expected=(-236.58971357952055-238.5228224781136j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-0.75,
+                    b=-7.75,
+                    c=-15.5,
+                    z=(0.5263157894736841+0.7368421052631575j),
+                    expected=(0.8116076584352279-0.29360565398246036j),
+                    rtol=5e-16,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=1.25,
+                    b=4.25,
+                    c=-0.5,
+                    z=(0.5263157894736841-0.736842105263158j),
+                    expected=(-28.119407485189985+98.89858821348005j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-0.75,
+                    b=2.25,
+                    c=1.5,
+                    z=(0.5263157894736841+0.7368421052631575j),
+                    expected=(0.5311049067450484-0.9434347326448517j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=8.25,
+                    b=-15.75,
+                    c=-7.5,
+                    z=(0.9473684210526314+0.10526315789473673j),
+                    expected=(1262084.378141873+1775569.6338380123j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-15.75,
+                    b=-7.75,
+                    c=-15.5,
+                    z=(0.5263157894736841-0.736842105263158j),
+                    expected=(-0.009810480794804165+0.3648997569257999j),
+                    rtol=1e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=8.25,
+                    b=2.25,
+                    c=-3.5,
+                    z=(0.5263157894736841-0.736842105263158j),
+                    expected=(585660.8815535795-33646.68398590896j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=4.080187217753502,
+                    b=-3.9316537064827854,
+                    c=-15.963511401609862,
+                    z=(0.9473684210526314-0.10526315789473695j),
+                    expected=(181899621848365.2-173207123998705.7j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-15.75,
+                    b=8.25,
+                    c=-0.5,
+                    z=(0.9473684210526314-0.10526315789473695j),
+                    expected=(0.04271686244952705-0.14087902824639406j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-7.937789122896016,
+                    b=-1.92872979730171,
+                    c=-0.906685989801748,
+                    z=(0.9473684210526314-0.3157894736842106j),
+                    expected=(-449.5119088817207+320.1423128036188j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-3.956227226099288,
+                    b=1.0561196186065624,
+                    c=8.031683612216888,
+                    z=(0.9473684210526314-0.10526315789473695j),
+                    expected=(0.6361479738012501+0.028575620091205088j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=4.25,
+                    b=16.25,
+                    c=16.5,
+                    z=(0.5263157894736841+0.7368421052631575j),
+                    expected=(-0.9038811840552261-1.5356250756164884j),
+                    rtol=1e-8,
+                ),
+                marks=pytest.mark.xfail(
+                    reason="Unhandled parameters."
+                )
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=8.25,
+                    b=-1.75,
+                    c=-1.5,
+                    z=(0.9473684210526314+0.3157894736842106j),
+                    expected=(653.0109150415394-4554.162605155542j),
+                    rtol=1e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-15.75,
+                    b=-3.75,
+                    c=4.5,
+                    z=(0.9473684210526314-0.10526315789473695j),
+                    expected=(118.7009859241035-34.18713648654642j),
+                    rtol=1e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=4.25,
+                    b=-15.75,
+                    c=-3.5,
+                    z=(0.5263157894736841+0.7368421052631575j),
+                    expected=(-540204.4774526551+4970059.109251281j),
+                    rtol=1e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=8.25,
+                    b=-15.75,
+                    c=-0.5,
+                    z=(0.5263157894736841-0.736842105263158j),
+                    expected=(2253490.972258385+3318620.683390017j),
+                    rtol=5e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=16.25,
+                    b=-7.75,
+                    c=-7.5,
+                    z=(0.9473684210526314+0.3157894736842106j),
+                    expected=(-46159826.46716958-17880663.82218242j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-0.9220024191881196,
+                    b=-7.949900487447654,
+                    c=-7.93846038215665,
+                    z=(0.9473684210526314-0.10526315789473695j),
+                    expected=(0.07116833581404514+0.11823358038036977j),
+                    rtol=5e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=16.087593263474208,
+                    b=4.0013768449590685,
+                    c=-7.93846038215665,
+                    z=(0.7368421052631575+0.5263157894736841j),
+                    expected=(4.7724909620664006e+17-6.039064078946702e+16j),
+                    rtol=5e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=1.25,
+                    b=-7.75,
+                    c=1.5,
+                    z=(0.9473684210526314-0.10526315789473695j),
+                    expected=(0.0188022179759303+0.002921737281641378j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=1.0272592605282642,
+                    b=1.0561196186065624,
+                    c=-7.93846038215665,
+                    z=(0.7368421052631575-0.5263157894736843j),
+                    expected=(-9203.462928334846+12390.110518017136j),
+                    rtol=5e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-3.75,
+                    b=-15.75,
+                    c=8.5,
+                    z=(0.7368421052631575+0.5263157894736841j),
+                    expected=(6.468457061368628+24.190040684917374j),
+                    rtol=6e-16,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=2.02764642551431,
+                    b=16.088264119063613,
+                    c=2.0397202577726152,
+                    z=(0.7368421052631575+0.5263157894736841j),
+                    expected=(2408.3451340186543-4275.257316636014j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-3.75,
+                    b=-7.75,
+                    c=8.5,
+                    z=(0.7368421052631575-0.5263157894736843j),
+                    expected=(4.1379984626381345-5.183654781039423j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=8.25,
+                    b=-7.75,
+                    c=-0.5,
+                    z=(0.5263157894736841+0.7368421052631575j),
+                    expected=(-81177.775295738+56079.73286548954j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=4.080187217753502,
+                    b=2.050308316530781,
+                    c=-0.906685989801748,
+                    z=(0.9473684210526314+0.3157894736842106j),
+                    expected=(1192868.5068926765+3624210.8182139914j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-7.937789122896016,
+                    b=-1.92872979730171,
+                    c=8.031683612216888,
+                    z=(0.5263157894736841+0.7368421052631575j),
+                    expected=(1.8286341846195202+1.9295255682312178j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=1.0272592605282642,
+                    b=1.0561196186065624,
+                    c=16.056809865262608,
+                    z=(0.7368421052631575-0.5263157894736843j),
+                    expected=(1.0514645669696452-0.0430834059440128j),
+                    rtol=5e-10,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=16.087593263474208,
+                    b=-15.964218273004214,
+                    c=2.0397202577726152,
+                    z=(0.5263157894736841+0.7368421052631575j),
+                    expected=(541983.236432269+288200.2043029435j),
+                    rtol=5e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=2.25,
+                    b=8.25,
+                    c=1.5,
+                    z=(0.5263157894736841-0.736842105263158j),
+                    expected=(-10.931988086039945+1.9136272843579096j),
+                    rtol=1e-15,
+                ),
+            ),
+        ]
+    )
+    def test_region3(self, hyp2f1_test_case):
+        """0.9 <= |z| <= 1 and |1 - z| < 0.9."""
+        a, b, c, z, expected, rtol = hyp2f1_test_case
+        assert 0.9 <= abs(z) <= 1 and abs(1 - z) < 0.9  # Tests the test
+        assert_allclose(hyp2f1(a, b, c, z), expected, rtol=rtol)
+
+    @pytest.mark.parametrize(
+        "hyp2f1_test_case",
+        [
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=16.25,
+                    b=4.25,
+                    c=2.5,
+                    z=(0.4931034482758623-0.7965517241379311j),
+                    expected=(38.41207903409937-30.510151276075792j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=2.0,
+                    b=16.087593263474208,
+                    c=16.088264119063613,
+                    z=(0.5689655172413794-0.7965517241379311j),
+                    expected=(-0.6667857912761286-1.0206224321443573j),
+                    rtol=1e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=8.0,
+                    b=1.0272592605282642,
+                    c=-7.949900487447654,
+                    z=(0.4931034482758623-0.7965517241379311j),
+                    expected=(1679024.1647997478-2748129.775857212j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=4.080187217753502,
+                    b=16.0,
+                    c=-7.949900487447654,
+                    z=(0.4931034482758623-0.7965517241379311j),
+                    expected=(424747226301.16986-1245539049327.2856j),
+                    rtol=1e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=2.02764642551431,
+                    b=-15.964218273004214,
+                    c=4.0,
+                    z=(0.4931034482758623-0.7965517241379311j),
+                    expected=(-0.0057826199201757595+0.026359861999025885j),
+                    rtol=5e-06,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=2.02764642551431,
+                    b=-0.9629749245209605,
+                    c=2.0397202577726152,
+                    z=(0.5689655172413794-0.7965517241379311j),
+                    expected=(0.4671901063492606+0.7769632229834897j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=2.0,
+                    b=-3.956227226099288,
+                    c=-7.949900487447654,
+                    z=(0.4931034482758623+0.7965517241379312j),
+                    expected=(0.9422283708145973+1.3476905754773343j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=1.0,
+                    b=-15.980848054962111,
+                    c=-15.964218273004214,
+                    z=(0.4931034482758623-0.7965517241379311j),
+                    expected=(0.4168719497319604-0.9770953555235625j),
+                    rtol=5e-10,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-0.5,
+                    b=16.088264119063613,
+                    c=2.5,
+                    z=(0.5689655172413794+0.7965517241379312j),
+                    expected=(1.279096377550619-2.173827694297929j),
+                    rtol=5e-12,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-1.9214641416286231,
+                    b=4.0013768449590685,
+                    c=2.0397202577726152,
+                    z=(0.4931034482758623+0.7965517241379312j),
+                    expected=(-2.071520656161738-0.7846098268395909j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-0.9220024191881196,
+                    b=8.0,
+                    c=-0.9629749245209605,
+                    z=(0.5689655172413794-0.7965517241379311j),
+                    expected=(-7.740015495862889+3.386766435696699j),
+                    rtol=5e-12,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-1.9214641416286231,
+                    b=16.088264119063613,
+                    c=-7.93846038215665,
+                    z=(0.4931034482758623+0.7965517241379312j),
+                    expected=(-6318.553685853241-7133.416085202879j),
+                    rtol=5e-9,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-15.980848054962111,
+                    b=-3.9316537064827854,
+                    c=16.056809865262608,
+                    z=(0.5689655172413794+0.7965517241379312j),
+                    expected=(-0.8854577905547399+8.135089099967278j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-1.9214641416286231,
+                    b=-0.9629749245209605,
+                    c=4.078873014294075,
+                    z=(0.4931034482758623+0.7965517241379312j),
+                    expected=(1.224291301521487+0.36014711766402485j),
+                    rtol=1e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-15.75,
+                    b=-0.75,
+                    c=-1.5,
+                    z=(0.4931034482758623+0.7965517241379312j),
+                    expected=(-1.5765685855028473-3.9399766961046323j),
+                    rtol=1e-3,
+                ),
+                marks=pytest.mark.xfail(
+                    reason="Unhandled parameters."
+                )
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-15.980848054962111,
+                    b=-1.92872979730171,
+                    c=-7.93846038215665,
+                    z=(0.5689655172413794-0.7965517241379311j),
+                    expected=(56.794588688231194+4.556286783533971j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=4.5,
+                    b=4.5,
+                    c=2.050308316530781,
+                    z=(0.5689655172413794+0.7965517241379312j),
+                    expected=(-4.251456563455306+6.737837111569671j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=4.5,
+                    b=8.5,
+                    c=-1.92872979730171,
+                    z=(0.4931034482758623-0.7965517241379311j),
+                    expected=(2177143.9156599627-3313617.2748088865j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=2.5,
+                    b=-1.5,
+                    c=4.0013768449590685,
+                    z=(0.4931034482758623-0.7965517241379311j),
+                    expected=(0.45563554481603946+0.6212000158060831j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=8.5,
+                    b=-7.5,
+                    c=-15.964218273004214,
+                    z=(0.4931034482758623+0.7965517241379312j),
+                    expected=(61.03201617828073-37.185626416756214j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-15.5,
+                    b=16.5,
+                    c=4.0013768449590685,
+                    z=(0.4931034482758623+0.7965517241379312j),
+                    expected=(-33143.425963520735+20790.608514722644j),
+                    rtol=1e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-0.5,
+                    b=4.5,
+                    c=-0.9629749245209605,
+                    z=(0.5689655172413794+0.7965517241379312j),
+                    expected=(30.778600270824423-26.65160354466787j),
+                    rtol=5e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-0.5,
+                    b=-3.5,
+                    c=16.088264119063613,
+                    z=(0.5689655172413794-0.7965517241379311j),
+                    expected=(1.0629792615560487-0.08308454486044772j),
+                    rtol=1e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-3.5,
+                    b=-7.5,
+                    c=-0.9629749245209605,
+                    z=(0.4931034482758623-0.7965517241379311j),
+                    expected=(17431.571802591767+3553.7129767034507j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=2.25,
+                    b=8.25,
+                    c=16.5,
+                    z=(0.11379310344827598+0.9482758620689657j),
+                    expected=(0.4468600750211926+0.7313214934036885j),
+                    rtol=1e-3,
+                ),
+                marks=pytest.mark.xfail(
+                    reason="Unhandled parameters."
+                )
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=8.25,
+                    b=16.25,
+                    c=4.5,
+                    z=(0.3413793103448277+0.8724137931034486j),
+                    expected=(-3.905704438293991+3.693347860329299j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=4.25,
+                    b=4.25,
+                    c=-0.5,
+                    z=(0.11379310344827598-0.9482758620689655j),
+                    expected=(-40.31777941834244-89.89852492432011j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=1.0272592605282642,
+                    b=8.0,
+                    c=-15.964218273004214,
+                    z=(0.11379310344827598-0.9482758620689655j),
+                    expected=(52584.347773055284-109197.86244309516j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=8.095813935368371,
+                    b=-15.964218273004214,
+                    c=16.056809865262608,
+                    z=(0.03793103448275881+0.9482758620689657j),
+                    expected=(-1.187733570412592-1.5147865053584582j),
+                    rtol=5e-10,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=4.080187217753502,
+                    b=-3.9316537064827854,
+                    c=1.0651378143226575,
+                    z=(0.26551724137931054+0.9482758620689657j),
+                    expected=(13.077494677898947+35.071599628224966j),
+                    rtol=5e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=4.080187217753502,
+                    b=-3.5,
+                    c=-3.5,
+                    z=(0.26551724137931054+0.8724137931034486j),
+                    expected=(-0.5359656237994614-0.2344483936591811j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=4.25,
+                    b=-3.75,
+                    c=-1.5,
+                    z=(0.26551724137931054+0.9482758620689657j),
+                    expected=(1204.8114871663133+64.41022826840198j),
+                    rtol=5e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-1.9214641416286231,
+                    b=16.0,
+                    c=4.0013768449590685,
+                    z=(0.03793103448275881-0.9482758620689655j),
+                    expected=(-9.85268872413994+7.011107558429154j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-7.937789122896016,
+                    b=16.0,
+                    c=4.0013768449590685,
+                    z=(0.3413793103448277-0.8724137931034484j),
+                    expected=(528.5522951158454-1412.21630264791j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-15.5,
+                    b=1.0561196186065624,
+                    c=-7.5,
+                    z=(0.4172413793103451+0.8724137931034486j),
+                    expected=(133306.45260685298+256510.7045225382j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-7.937789122896016,
+                    b=8.077282662161238,
+                    c=-15.963511401609862,
+                    z=(0.3413793103448277-0.8724137931034484j),
+                    expected=(-0.998555715276967+2.774198742229889j),
+                    rtol=5e-11,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-7.75,
+                    b=-0.75,
+                    c=1.5,
+                    z=(0.11379310344827598-0.9482758620689655j),
+                    expected=(2.072445019723025-2.9793504811373515j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-15.5,
+                    b=-1.92872979730171,
+                    c=1.5,
+                    z=(0.11379310344827598-0.9482758620689655j),
+                    expected=(-41.87581944176649-32.52980303527139j),
+                    rtol=5e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-3.75,
+                    b=-15.75,
+                    c=-0.5,
+                    z=(0.11379310344827598-0.9482758620689655j),
+                    expected=(-3729.6214864209774-30627.510509112635j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-3.956227226099288,
+                    b=-15.964218273004214,
+                    c=-0.906685989801748,
+                    z=(0.03793103448275881+0.9482758620689657j),
+                    expected=(-131615.07820609974+145596.13384245415j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=1.5,
+                    b=16.5,
+                    c=16.088264119063613,
+                    z=(0.26551724137931054+0.8724137931034486j),
+                    expected=(0.18981844071070744+0.7855036242583742j),
+                    rtol=1e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=16.5,
+                    b=8.5,
+                    c=-3.9316537064827854,
+                    z=(0.11379310344827598-0.9482758620689655j),
+                    expected=(110224529.2376068+128287212.04290268j),
+                    rtol=5e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=2.5,
+                    b=-7.5,
+                    c=4.0013768449590685,
+                    z=(0.3413793103448277-0.8724137931034484j),
+                    expected=(0.2722302180888523-0.21790187837266162j),
+                    rtol=1.2e-12,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=8.5,
+                    b=-7.5,
+                    c=-15.964218273004214,
+                    z=(0.11379310344827598-0.9482758620689655j),
+                    expected=(-2.8252338010989035+2.430661949756161j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-3.5,
+                    b=16.5,
+                    c=4.0013768449590685,
+                    z=(0.03793103448275881+0.9482758620689657j),
+                    expected=(-20.604894257647945+74.5109432558078j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-7.5,
+                    b=8.5,
+                    c=-0.9629749245209605,
+                    z=(0.3413793103448277+0.8724137931034486j),
+                    expected=(-2764422.521269463-3965966.9965808876j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-1.5,
+                    b=-0.5,
+                    c=1.0561196186065624,
+                    z=(0.26551724137931054+0.9482758620689657j),
+                    expected=(1.2262338560994905+0.6545051266925549j),
+                    rtol=1e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-0.5,
+                    b=-15.5,
+                    c=-7.949900487447654,
+                    z=(0.4172413793103451-0.8724137931034484j),
+                    expected=(-2258.1590330318213+8860.193389158803j),
+                    rtol=1.4e-10,
+                ),
+            ),
+        ]
+    )
+    def test_region4(self, hyp2f1_test_case):
+        """0.9 <= |z| <= 1 and |1 - z| >= 1.
+
+        This region is unhandled by of the standard transformations and
+        needs special care.
+        """
+        a, b, c, z, expected, rtol = hyp2f1_test_case
+        assert 0.9 <= abs(z) <= 1 and abs(1 - z) >= 0.9  # Tests the test
+        assert_allclose(hyp2f1(a, b, c, z), expected, rtol=rtol)
+
+    @pytest.mark.parametrize(
+        "hyp2f1_test_case",
+        [
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=4.5,
+                    b=16.088264119063613,
+                    c=8.5,
+                    z=(0.6448275862068968+0.8724137931034486j),
+                    expected=(0.018601324701770394-0.07618420586062377j),
+                    rtol=5e-08,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=8.25,
+                    b=4.25,
+                    c=4.5,
+                    z=(0.6448275862068968-0.8724137931034484j),
+                    expected=(-1.391549471425551-0.118036604903893j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=2.02764642551431,
+                    b=2.050308316530781,
+                    c=-1.9631175993998025,
+                    z=(0.6448275862068968+0.8724137931034486j),
+                    expected=(-2309.178768155151-1932.7247727595172j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=16.087593263474208,
+                    b=1.0,
+                    c=-15.964218273004214,
+                    z=(0.6448275862068968+0.8724137931034486j),
+                    expected=(85592537010.05054-8061416766688.324j),
+                    rtol=2e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=8.095813935368371,
+                    b=-0.5,
+                    c=1.5,
+                    z=(0.6448275862068968+0.8724137931034486j),
+                    expected=(1.2334498208515172-2.1639498536219732j),
+                    rtol=5e-11,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=16.087593263474208,
+                    b=-15.964218273004214,
+                    c=4.0,
+                    z=(0.6448275862068968+0.8724137931034486j),
+                    expected=(102266.35398605966-44976.97828737755j),
+                    rtol=1e-3,
+                ),
+                marks=pytest.mark.xfail(
+                    reason="Unhandled parameters."
+                )
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=4.0,
+                    b=-3.956227226099288,
+                    c=-15.964218273004214,
+                    z=(0.6448275862068968-0.8724137931034484j),
+                    expected=(-2.9590030930007236-4.190770764773225j),
+                    rtol=5e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=4.080187217753502,
+                    b=-15.5,
+                    c=-7.5,
+                    z=(0.5689655172413794-0.8724137931034484j),
+                    expected=(-112554838.92074208+174941462.9202412j),
+                    rtol=5e-05,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-15.980848054962111,
+                    b=2.050308316530781,
+                    c=1.0,
+                    z=(0.6448275862068968-0.8724137931034484j),
+                    expected=(3.7519882374080145+7.360753798667486j),
+                    rtol=5e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-7.937789122896016,
+                    b=2.050308316530781,
+                    c=4.0,
+                    z=(0.6448275862068968-0.8724137931034484j),
+                    expected=(0.000181132943964693+0.07742903103815582j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-7.937789122896016,
+                    b=4.0013768449590685,
+                    c=-1.9631175993998025,
+                    z=(0.5689655172413794+0.8724137931034486j),
+                    expected=(386338.760913596-386166.51762171905j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-15.980848054962111,
+                    b=8.0,
+                    c=-1.92872979730171,
+                    z=(0.6448275862068968+0.8724137931034486j),
+                    expected=(1348667126.3444858-2375132427.158893j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-3.5,
+                    b=-0.9629749245209605,
+                    c=4.5,
+                    z=(0.5689655172413794+0.8724137931034486j),
+                    expected=(1.428353429538678+0.6472718120804372j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-7.937789122896016,
+                    b=-0.9629749245209605,
+                    c=2.0397202577726152,
+                    z=(0.5689655172413794-0.8724137931034484j),
+                    expected=(3.1439267526119643-3.145305240375117j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-1.9214641416286231,
+                    b=-15.964218273004214,
+                    c=-7.93846038215665,
+                    z=(0.6448275862068968-0.8724137931034484j),
+                    expected=(75.27467675681773+144.0946946292215j),
+                    rtol=1e-07,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-3.75,
+                    b=-7.75,
+                    c=-7.5,
+                    z=(0.5689655172413794+0.8724137931034486j),
+                    expected=(-0.3699450626264222+0.8732812475910993j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=1.5,
+                    b=16.5,
+                    c=1.0561196186065624,
+                    z=(0.5689655172413794-0.8724137931034484j),
+                    expected=(5.5361025821300665-2.4709693474656285j),
+                    rtol=5e-09,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=1.5,
+                    b=8.5,
+                    c=-3.9316537064827854,
+                    z=(0.6448275862068968-0.8724137931034484j),
+                    expected=(-782805.6699207705-537192.581278909j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=2.5,
+                    b=-15.5,
+                    c=1.0561196186065624,
+                    z=(0.6448275862068968+0.8724137931034486j),
+                    expected=(12.345113400639693-14.993248992902007j),
+                    rtol=0.0005,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=1.5,
+                    b=-0.5,
+                    c=-15.964218273004214,
+                    z=(0.6448275862068968+0.8724137931034486j),
+                    expected=(23.698109392667842+97.15002033534108j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-7.5,
+                    b=16.5,
+                    c=4.0013768449590685,
+                    z=(0.6448275862068968-0.8724137931034484j),
+                    expected=(1115.2978631811834+915.9212658718577j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-15.5,
+                    b=16.5,
+                    c=-0.9629749245209605,
+                    z=(0.6448275862068968+0.8724137931034486j),
+                    expected=(642077722221.6489+535274495398.21027j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-7.5,
+                    b=-3.5,
+                    c=4.0013768449590685,
+                    z=(0.5689655172413794+0.8724137931034486j),
+                    expected=(-5.689219222945697+16.877463062787143j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-15.5,
+                    b=-1.5,
+                    c=-0.9629749245209605,
+                    z=(0.5689655172413794-0.8724137931034484j),
+                    expected=(-44.32070290703576+1026.9127058617403j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=16.25,
+                    b=2.25,
+                    c=4.5,
+                    z=(0.11379310344827598-1.024137931034483j),
+                    expected=(-0.021965227124574663+0.009908300237809064j),
+                    rtol=1e-3,
+                ),
+                marks=pytest.mark.xfail(
+                    reason="Unhandled parameters."
+                )
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=2.02764642551431,
+                    b=1.5,
+                    c=16.5,
+                    z=(0.26551724137931054+1.024137931034483j),
+                    expected=(1.0046072901244183+0.19945500134119992j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=16.087593263474208,
+                    b=1.0,
+                    c=-3.9316537064827854,
+                    z=(0.3413793103448277+0.9482758620689657j),
+                    expected=(21022.30133421465+49175.98317370489j),
+                    rtol=5e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=4.080187217753502,
+                    b=16.088264119063613,
+                    c=-1.9631175993998025,
+                    z=(0.4172413793103451-0.9482758620689655j),
+                    expected=(-7024239.358547302+2481375.02681063j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=16.25,
+                    b=-15.75,
+                    c=1.5,
+                    z=(0.18965517241379315+1.024137931034483j),
+                    expected=(92371704.94848-403546832.548352j),
+                    rtol=5e-06,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=8.5,
+                    b=-7.949900487447654,
+                    c=8.5,
+                    z=(0.26551724137931054-1.024137931034483j),
+                    expected=(1.9335109845308265+5.986542524829654j),
+                    rtol=5e-10,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=8.095813935368371,
+                    b=-1.92872979730171,
+                    c=-7.93846038215665,
+                    z=(0.4931034482758623+0.8724137931034486j),
+                    expected=(-122.52639696039328-59.72428067512221j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=16.25,
+                    b=-1.75,
+                    c=-1.5,
+                    z=(0.4931034482758623+0.9482758620689657j),
+                    expected=(-90.40642053579428+50.50649180047921j),
+                    rtol=5e-08,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-3.5,
+                    b=8.077282662161238,
+                    c=16.5,
+                    z=(0.4931034482758623+0.9482758620689657j),
+                    expected=(-0.2155745818150323-0.564628986876639j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-0.9220024191881196,
+                    b=1.0561196186065624,
+                    c=8.031683612216888,
+                    z=(0.4172413793103451-0.9482758620689655j),
+                    expected=(0.9503140488280465+0.11574960074292677j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-0.75,
+                    b=2.25,
+                    c=-15.5,
+                    z=(0.4172413793103451+0.9482758620689657j),
+                    expected=(0.9285862488442175+0.8203699266719692j),
+                    rtol=5e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-7.75,
+                    b=4.25,
+                    c=-15.5,
+                    z=(0.3413793103448277-0.9482758620689655j),
+                    expected=(-1.0509834850116921-1.1145522325486075j),
+                    rtol=1.1e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-7.937789122896016,
+                    b=-0.9629749245209605,
+                    c=2.0397202577726152,
+                    z=(0.4931034482758623-0.9482758620689655j),
+                    expected=(2.88119116536769-3.4249933450696806j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-15.5,
+                    b=-15.964218273004214,
+                    c=16.5,
+                    z=(0.18965517241379315+1.024137931034483j),
+                    expected=(199.65868451496038+347.79384207302877j),
+                    rtol=5e-12,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-15.75,
+                    b=-15.75,
+                    c=-3.5,
+                    z=(0.4931034482758623-0.8724137931034484j),
+                    expected=(-208138312553.07013+58631611809.026955j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-7.937789122896016,
+                    b=-15.5,
+                    c=-7.5,
+                    z=(0.3413793103448277+0.9482758620689657j),
+                    expected=(-23032.90519856288-18256.94050457296j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=4.5,
+                    b=1.5,
+                    c=1.0561196186065624,
+                    z=(0.4931034482758623-0.8724137931034484j),
+                    expected=(1.507342459587056+1.2332023580148403j),
+                    rtol=1e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=2.5,
+                    b=4.5,
+                    c=-3.9316537064827854,
+                    z=(0.4172413793103451+0.9482758620689657j),
+                    expected=(7044.766127108853-40210.365567285575j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=1.5,
+                    b=-1.5,
+                    c=1.0561196186065624,
+                    z=(0.03793103448275881+1.024137931034483j),
+                    expected=(0.2725347741628333-2.247314875514784j),
+                    rtol=1e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=4.5,
+                    b=-1.5,
+                    c=-7.949900487447654,
+                    z=(0.26551724137931054+1.024137931034483j),
+                    expected=(-11.250200011017546+12.597393659160472j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-7.5,
+                    b=8.5,
+                    c=16.088264119063613,
+                    z=(0.26551724137931054+1.024137931034483j),
+                    expected=(-0.18515160890991517+0.7959014164484782j),
+                    rtol=2e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-7.5,
+                    b=16.5,
+                    c=-3.9316537064827854,
+                    z=(0.3413793103448277-1.024137931034483j),
+                    expected=(998246378.8556538+1112032928.103645j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-1.5,
+                    b=-3.5,
+                    c=2.050308316530781,
+                    z=(0.03793103448275881+1.024137931034483j),
+                    expected=(0.5527670397711952+2.697662715303637j),
+                    rtol=1.2e-15,       # rtol bumped from 1e-15 in gh18414
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-15.5,
+                    b=-1.5,
+                    c=-0.9629749245209605,
+                    z=(0.4931034482758623-0.8724137931034484j),
+                    expected=(55.396931662136886+968.467463806326j),
+                    rtol=5e-14,
+                ),
+            ),
+        ]
+    )
+    def test_region5(self, hyp2f1_test_case):
+        """1 < |z| < 1.1 and |1 - z| >= 0.9 and real(z) >= 0"""
+        a, b, c, z, expected, rtol = hyp2f1_test_case
+        assert 1 < abs(z) < 1.1 and abs(1 - z) >= 0.9 and z.real >= 0
+        assert_allclose(hyp2f1(a, b, c, z), expected, rtol=rtol)
+
+    @pytest.mark.parametrize(
+        "hyp2f1_test_case",
+        [
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=8.095813935368371,
+                    b=4.0013768449590685,
+                    c=4.078873014294075,
+                    z=(-0.9473684210526316+0.5263157894736841j),
+                    expected=(-0.0018093573941378783+0.003481887377423739j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=16.087593263474208,
+                    b=2.050308316530781,
+                    c=1.0651378143226575,
+                    z=(-0.736842105263158-0.736842105263158j),
+                    expected=(-0.00023401243818780545-1.7983496305603562e-05j),
+                    rtol=1e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=1.0272592605282642,
+                    b=8.077282662161238,
+                    c=4.078873014294075,
+                    z=(-0.5263157894736843-0.9473684210526316j),
+                    expected=(0.22359773002226846-0.24092487123993353j),
+                    rtol=1e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=1.0272592605282642,
+                    b=2.050308316530781,
+                    c=-15.963511401609862,
+                    z=(-0.9473684210526316-0.5263157894736843j),
+                    expected=(1.191573745740011+0.14347394589721466j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=4.080187217753502,
+                    b=4.0013768449590685,
+                    c=-15.963511401609862,
+                    z=(-0.9473684210526316-0.5263157894736843j),
+                    expected=(31.822620756901784-66.09094396747611j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=4.080187217753502,
+                    b=8.077282662161238,
+                    c=-7.93846038215665,
+                    z=(-0.9473684210526316+0.5263157894736841j),
+                    expected=(207.16750179245952+34.80478274924269j),
+                    rtol=5e-12,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=8.095813935368371,
+                    b=-7.949900487447654,
+                    c=8.031683612216888,
+                    z=(-0.736842105263158+0.7368421052631575j),
+                    expected=(-159.62429364277145+9.154224290644898j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=1.0272592605282642,
+                    b=-1.92872979730171,
+                    c=16.056809865262608,
+                    z=(-0.9473684210526316+0.5263157894736841j),
+                    expected=(1.121122351247184-0.07170260470126685j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=16.087593263474208,
+                    b=-0.9629749245209605,
+                    c=16.056809865262608,
+                    z=(-0.9473684210526316+0.5263157894736841j),
+                    expected=(1.9040596681316053-0.4951799449960107j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=1.0272592605282642,
+                    b=-1.92872979730171,
+                    c=-0.906685989801748,
+                    z=(-0.9473684210526316-0.5263157894736843j),
+                    expected=(-14.496623497780739-21.897524523299875j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=4.080187217753502,
+                    b=-3.9316537064827854,
+                    c=-3.9924618758357022,
+                    z=(-0.5263157894736843-0.9473684210526316j),
+                    expected=(36.33473466026878+253.88728442029577j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=1.0272592605282642,
+                    b=-15.964218273004214,
+                    c=-0.906685989801748,
+                    z=(-0.9473684210526316+0.5263157894736841j),
+                    expected=(1505052.5653144997-50820766.81043443j),
+                    rtol=1e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-3.956227226099288,
+                    b=4.0013768449590685,
+                    c=1.0651378143226575,
+                    z=(-0.5263157894736843+0.9473684210526314j),
+                    expected=(-127.79407519260877-28.69899444941112j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-1.9214641416286231,
+                    b=8.077282662161238,
+                    c=16.056809865262608,
+                    z=(-0.9473684210526316-0.5263157894736843j),
+                    expected=(2.0623331933754976+0.741234463565458j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-3.956227226099288,
+                    b=8.077282662161238,
+                    c=2.0397202577726152,
+                    z=(-0.9473684210526316+0.5263157894736841j),
+                    expected=(30.729193458862525-292.5700835046965j),
+                    rtol=1e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-1.9214641416286231,
+                    b=1.0561196186065624,
+                    c=-1.9631175993998025,
+                    z=(-0.5263157894736843-0.9473684210526316j),
+                    expected=(1.1285917906203495-0.735264575450189j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-0.9220024191881196,
+                    b=1.0561196186065624,
+                    c=-3.9924618758357022,
+                    z=(-0.736842105263158+0.7368421052631575j),
+                    expected=(0.6356474446678052-0.02429663008952248j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-1.9214641416286231,
+                    b=16.088264119063613,
+                    c=-7.93846038215665,
+                    z=(-0.736842105263158+0.7368421052631575j),
+                    expected=(0.4718880510273174+0.655083067736377j),
+                    rtol=1e-11,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-7.937789122896016,
+                    b=-3.9316537064827854,
+                    c=16.056809865262608,
+                    z=(-0.9473684210526316+0.5263157894736841j),
+                    expected=(-0.14681550942352714+0.16092206364265146j),
+                    rtol=5e-11,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-0.9220024191881196,
+                    b=-15.964218273004214,
+                    c=1.0651378143226575,
+                    z=(-0.5263157894736843+0.9473684210526314j),
+                    expected=(-6.436835190526225+22.883156700606182j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-0.9220024191881196,
+                    b=-7.949900487447654,
+                    c=4.078873014294075,
+                    z=(-0.9473684210526316-0.5263157894736843j),
+                    expected=(-0.7505682955068583-1.1026583264249945j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-3.956227226099288,
+                    b=-3.9316537064827854,
+                    c=-7.93846038215665,
+                    z=(-0.9473684210526316-0.5263157894736843j),
+                    expected=(3.6247814989198166+2.596041360148318j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-3.956227226099288,
+                    b=-15.964218273004214,
+                    c=-1.9631175993998025,
+                    z=(-0.5263157894736843-0.9473684210526316j),
+                    expected=(-59537.65287927933-669074.4342539902j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-3.956227226099288,
+                    b=-15.964218273004214,
+                    c=-1.9631175993998025,
+                    z=(-0.9473684210526316-0.5263157894736843j),
+                    expected=(-433084.9970266166+431088.393918521j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=1,
+                    b=1,
+                    c=4,
+                    z=(3 + 4j),
+                    expected=(0.49234384000963544+0.6051340616612397j),
+                    rtol=5e-14,
+                ),
+            ),
+        ]
+    )
+    def test_region6(self, hyp2f1_test_case):
+        """|z| > 1 but not in region 5."""
+        a, b, c, z, expected, rtol = hyp2f1_test_case
+        assert (
+            abs(z) > 1 and
+            not (1 < abs(z) < 1.1 and abs(1 - z) >= 0.9 and z.real >= 0)
+        )
+        assert_allclose(hyp2f1(a, b, c, z), expected, rtol=rtol)
+
+
+    @pytest.mark.parametrize(
+        "hyp2f1_test_case",
+        [
+            # Broke when fixing gamma pole behavior in gh-21827
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=1.3,
+                    b=-0.2,
+                    c=0.3,
+                    z=-2.1,
+                    expected=1.8202169687521206,
+                    rtol=5e-15,
+                ),
+            ),
+        ]
+    )
+    def test_miscellaneous(self, hyp2f1_test_case ):
+        a, b, c, z, expected, rtol = hyp2f1_test_case
+        assert_allclose(hyp2f1(a, b, c, z), expected, rtol=rtol)
+
+    @pytest.mark.slow
+    @check_version(mpmath, "1.0.0")
+    def test_test_hyp2f1(self):
+        """Test that expected values match what is computed by mpmath.
+
+        This gathers the parameters for the test cases out of the pytest marks.
+        The parameters are a, b, c, z, expected, rtol, where expected should
+        be the value of hyp2f1(a, b, c, z) computed with mpmath. The test
+        recomputes hyp2f1(a, b, c, z) using mpmath and verifies that expected
+        actually is the correct value. This allows the data for the tests to
+        live within the test code instead of an external datafile, while
+        avoiding having to compute the results with mpmath during the test,
+        except for when slow tests are being run.
+        """
+        test_methods = [
+            test_method for test_method in dir(self)
+            if test_method.startswith('test') and
+            # Filter properties and attributes (futureproofing).
+            callable(getattr(self, test_method)) and
+            # Filter out this test
+            test_method != 'test_test_hyp2f1'
+        ]
+        for test_method in test_methods:
+            params = self._get_test_parameters(getattr(self, test_method))
+            for a, b, c, z, expected, _ in params:
+                assert_allclose(mp_hyp2f1(a, b, c, z), expected, rtol=2.25e-16)
+
+    def _get_test_parameters(self, test_method):
+        """Get pytest.mark parameters for a test in this class."""
+        return [
+            case.values[0] for mark in test_method.pytestmark
+            if mark.name == 'parametrize'
+            for case in mark.args[1]
+        ]
+
+class TestHyp2f1ExtremeInputs:
+
+    @pytest.mark.parametrize("a", [1.0, 2.0, 3.0, -np.inf, np.inf])
+    @pytest.mark.parametrize("b", [3.0, 4.0, 5.0, -np.inf, np.inf])
+    @pytest.mark.parametrize("c", [3.0, 5.0, 6.0, 7.0])
+    @pytest.mark.parametrize("z", [4.0 + 1.0j])
+    def test_inf_a_b(self, a, b, c, z):
+        if np.any(np.isinf(np.asarray([a, b]))):
+            assert(np.isnan(hyp2f1(a, b, c, z)))
+
+    def test_large_a_b(self):
+        assert(np.isnan(hyp2f1(10**7, 1.0, 3.0, 4.0 + 1.0j)))
+        assert(np.isnan(hyp2f1(-10**7, 1.0, 3.0, 4.0 + 1.0j)))
+
+        assert(np.isnan(hyp2f1(1.0, 10**7, 3.0, 4.0 + 1.0j)))
+        assert(np.isnan(hyp2f1(1.0, -10**7, 3.0, 4.0 + 1.0j)))
+
+        # Already correct in main but testing for surety
+        assert(np.isnan(hyp2f1(np.inf, 1.0, 3.0, 4.0)))
+        assert(np.isnan(hyp2f1(1.0, np.inf, 3.0, 4.0)))
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_hypergeometric.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_hypergeometric.py
new file mode 100644
index 0000000000000000000000000000000000000000..1ad092491905ae66c39cd881836054aef3dc6f6e
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_hypergeometric.py
@@ -0,0 +1,234 @@
+import pytest
+import numpy as np
+from numpy.testing import assert_allclose, assert_equal
+import scipy.special as sc
+
+
+class TestHyperu:
+
+    def test_negative_x(self):
+        a, b, x = np.meshgrid(
+            [-1, -0.5, 0, 0.5, 1],
+            [-1, -0.5, 0, 0.5, 1],
+            np.linspace(-100, -1, 10),
+        )
+        assert np.all(np.isnan(sc.hyperu(a, b, x)))
+
+    def test_special_cases(self):
+        assert sc.hyperu(0, 1, 1) == 1.0
+
+    @pytest.mark.parametrize('a', [0.5, 1, np.nan])
+    @pytest.mark.parametrize('b', [1, 2, np.nan])
+    @pytest.mark.parametrize('x', [0.25, 3, np.nan])
+    def test_nan_inputs(self, a, b, x):
+        assert np.isnan(sc.hyperu(a, b, x)) == np.any(np.isnan([a, b, x]))
+
+    @pytest.mark.parametrize(
+        'a,b,x,expected',
+        [(0.21581740448533887, 1.0, 1e-05, 3.6030558839391325),
+         (0.21581740448533887, 1.0, 0.00021544346900318823, 2.8783254988948976),
+         (0.21581740448533887, 1.0, 0.004641588833612777, 2.154928216691109),
+         (0.21581740448533887, 1.0, 0.1, 1.446546638718792),
+         (0.0030949064301273865, 1.0, 1e-05, 1.0356696454116199),
+         (0.0030949064301273865, 1.0, 0.00021544346900318823, 1.0261510362481985),
+         (0.0030949064301273865, 1.0, 0.004641588833612777, 1.0166326903402296),
+         (0.0030949064301273865, 1.0, 0.1, 1.0071174207698674),
+         (0.1509924314279033, 1.0, 1e-05, 2.806173846998948),
+         (0.1509924314279033, 1.0, 0.00021544346900318823, 2.3092158526816124),
+         (0.1509924314279033, 1.0, 0.004641588833612777, 1.812905980588048),
+         (0.1509924314279033, 1.0, 0.1, 1.3239738117634872),
+         (-0.010678995342969011, 1.0, 1e-05, 0.8775194903781114),
+         (-0.010678995342969011, 1.0, 0.00021544346900318823, 0.9101008998540128),
+         (-0.010678995342969011, 1.0, 0.004641588833612777, 0.9426854294058609),
+         (-0.010678995342969011, 1.0, 0.1, 0.9753065150174902),
+         (-0.06556622211831487, 1.0, 1e-05, 0.26435429752668904),
+         (-0.06556622211831487, 1.0, 0.00021544346900318823, 0.4574756033875781),
+         (-0.06556622211831487, 1.0, 0.004641588833612777, 0.6507121093358457),
+         (-0.06556622211831487, 1.0, 0.1, 0.8453129788602187),
+         (-0.21628242470175185, 1.0, 1e-05, -1.2318314201114489),
+         (-0.21628242470175185, 1.0, 0.00021544346900318823, -0.6704694233529538),
+         (-0.21628242470175185, 1.0, 0.004641588833612777, -0.10795098653682857),
+         (-0.21628242470175185, 1.0, 0.1, 0.4687227684115524)]
+    )
+    def test_gh_15650_mp(self, a, b, x, expected):
+        # See https://github.com/scipy/scipy/issues/15650
+        # b == 1, |a| < 0.25, 0 < x < 1
+        #
+        # This purpose of this test is to check the accuracy of results
+        # in the region that was impacted by gh-15650.
+        #
+        # Reference values computed with mpmath using the script:
+        #
+        # import itertools as it
+        # import numpy as np
+        #
+        # from mpmath import mp
+        #
+        # rng = np.random.default_rng(1234)
+        #
+        # cases = []
+        # for a, x in it.product(
+        #         np.random.uniform(-0.25, 0.25, size=6),
+        #         np.logspace(-5, -1, 4),
+        # ):
+        #     with mp.workdps(100):
+        #         cases.append((float(a), 1.0, float(x), float(mp.hyperu(a, 1.0, x))))
+        assert_allclose(sc.hyperu(a, b, x), expected, rtol=1e-13)
+
+    def test_gh_15650_sanity(self):
+        # The purpose of this test is to sanity check hyperu in the region that
+        # was impacted by gh-15650 by making sure there are no excessively large
+        # results, as were reported there.
+        a = np.linspace(-0.5, 0.5, 500)
+        x = np.linspace(1e-6, 1e-1, 500)
+        a, x = np.meshgrid(a, x)
+        results = sc.hyperu(a, 1.0, x)
+        assert np.all(np.abs(results) < 1e3)
+
+
+class TestHyp1f1:
+
+    @pytest.mark.parametrize('a, b, x', [
+        (np.nan, 1, 1),
+        (1, np.nan, 1),
+        (1, 1, np.nan)
+    ])
+    def test_nan_inputs(self, a, b, x):
+        assert np.isnan(sc.hyp1f1(a, b, x))
+
+    def test_poles(self):
+        assert_equal(sc.hyp1f1(1, [0, -1, -2, -3, -4], 0.5), np.inf)
+
+    @pytest.mark.parametrize('a, b, x, result', [
+        (-1, 1, 0.5, 0.5),
+        (1, 1, 0.5, 1.6487212707001281468),
+        (2, 1, 0.5, 2.4730819060501922203),
+        (1, 2, 0.5, 1.2974425414002562937),
+        (-10, 1, 0.5, -0.38937441413785204475)
+    ])
+    def test_special_cases(self, a, b, x, result):
+        # Hit all the special case branches at the beginning of the
+        # function. Desired answers computed using Mpmath.
+        assert_allclose(sc.hyp1f1(a, b, x), result, atol=0, rtol=1e-15)
+
+    @pytest.mark.parametrize('a, b, x, result', [
+        (1, 1, 0.44, 1.5527072185113360455),
+        (-1, 1, 0.44, 0.55999999999999999778),
+        (100, 100, 0.89, 2.4351296512898745592),
+        (-100, 100, 0.89, 0.40739062490768104667),
+        (1.5, 100, 59.99, 3.8073513625965598107),
+        (-1.5, 100, 59.99, 0.25099240047125826943)
+    ])
+    def test_geometric_convergence(self, a, b, x, result):
+        # Test the region where we are relying on the ratio of
+        #
+        # (|a| + 1) * |x| / |b|
+        #
+        # being small. Desired answers computed using Mpmath
+        assert_allclose(sc.hyp1f1(a, b, x), result, atol=0, rtol=1e-15)
+
+    @pytest.mark.parametrize('a, b, x, result', [
+        (-1, 1, 1.5, -0.5),
+        (-10, 1, 1.5, 0.41801777430943080357),
+        (-25, 1, 1.5, 0.25114491646037839809),
+        (-50, 1, 1.5, -0.25683643975194756115),
+        (-80, 1, 1.5, -0.24554329325751503601),
+        (-150, 1, 1.5, -0.173364795515420454496),
+    ])
+    def test_a_negative_integer(self, a, b, x, result):
+        # Desired answers computed using Mpmath.
+        assert_allclose(sc.hyp1f1(a, b, x), result, atol=0, rtol=2e-14)
+
+    @pytest.mark.parametrize('a, b, x, expected', [
+        (0.01, 150, -4, 0.99973683897677527773),        # gh-3492
+        (1, 5, 0.01, 1.0020033381011970966),            # gh-3593
+        (50, 100, 0.01, 1.0050126452421463411),         # gh-3593
+        (1, 0.3, -1e3, -7.011932249442947651455e-04),   # gh-14149
+        (1, 0.3, -1e4, -7.001190321418937164734e-05),   # gh-14149
+        (9, 8.5, -350, -5.224090831922378361082e-20),   # gh-17120
+        (9, 8.5, -355, -4.595407159813368193322e-20),   # gh-17120
+        (75, -123.5, 15, 3.425753920814889017493e+06),
+    ])
+    def test_assorted_cases(self, a, b, x, expected):
+        # Expected values were computed with mpmath.hyp1f1(a, b, x).
+        assert_allclose(sc.hyp1f1(a, b, x), expected, atol=0, rtol=1e-14)
+
+    def test_a_neg_int_and_b_equal_x(self):
+        # This is a case where the Boost wrapper will call hypergeometric_pFq
+        # instead of hypergeometric_1F1.  When we use a version of Boost in
+        # which https://github.com/boostorg/math/issues/833 is fixed, this
+        # test case can probably be moved into test_assorted_cases.
+        # The expected value was computed with mpmath.hyp1f1(a, b, x).
+        a = -10.0
+        b = 2.5
+        x = 2.5
+        expected = 0.0365323664364104338721
+        computed = sc.hyp1f1(a, b, x)
+        assert_allclose(computed, expected, atol=0, rtol=1e-13)
+
+    @pytest.mark.parametrize('a, b, x, desired', [
+        (-1, -2, 2, 2),
+        (-1, -4, 10, 3.5),
+        (-2, -2, 1, 2.5)
+    ])
+    def test_gh_11099(self, a, b, x, desired):
+        # All desired results computed using Mpmath
+        assert sc.hyp1f1(a, b, x) == desired
+
+    @pytest.mark.parametrize('a', [-3, -2])
+    def test_x_zero_a_and_b_neg_ints_and_a_ge_b(self, a):
+        assert sc.hyp1f1(a, -3, 0) == 1
+
+    # In the following tests with complex z, the reference values
+    # were computed with mpmath.hyp1f1(a, b, z), and verified with
+    # Wolfram Alpha Hypergeometric1F1(a, b, z), except for the
+    # case a=0.1, b=1, z=7-24j, where Wolfram Alpha reported
+    # "Standard computation time exceeded".  That reference value
+    # was confirmed in an online Matlab session, with the commands
+    #
+    #  > format long
+    #  > hypergeom(0.1, 1, 7-24i)
+    #  ans =
+    #   -3.712349651834209 + 4.554636556672912i
+    #
+    @pytest.mark.parametrize(
+        'a, b, z, ref',
+        [(-0.25, 0.5, 1+2j, 1.1814553180903435-1.2792130661292984j),
+         (0.25, 0.5, 1+2j, 0.24636797405707597+1.293434354945675j),
+         (25, 1.5, -2j, -516.1771262822523+407.04142751922024j),
+         (12, -1.5, -10+20j, -5098507.422706547-1341962.8043508842j),
+         pytest.param(
+             10, 250, 10-15j, 1.1985998416598884-0.8613474402403436j,
+             marks=pytest.mark.xfail,
+         ),
+         pytest.param(
+             0.1, 1, 7-24j, -3.712349651834209+4.554636556672913j,
+             marks=pytest.mark.xfail,
+         )
+         ],
+    )
+    def test_complex_z(self, a, b, z, ref):
+        h = sc.hyp1f1(a, b, z)
+        assert_allclose(h, ref, rtol=4e-15)
+
+    # The "legacy edge cases" mentioned in the comments in the following
+    # tests refers to the behavior of hyp1f1(a, b, x) when b is a nonpositive
+    # integer.  In some subcases, the behavior of SciPy does not match that
+    # of Boost (1.81+), mpmath and Mathematica (via Wolfram Alpha online).
+    # If the handling of these edges cases is changed to agree with those
+    # libraries, these test will have to be updated.
+
+    @pytest.mark.parametrize('b', [0, -1, -5])
+    def test_legacy_case1(self, b):
+        # Test results of hyp1f1(0, n, x) for n <= 0.
+        # This is a legacy edge case.
+        # Boost (versions greater than 1.80), Mathematica (via Wolfram Alpha
+        # online) and mpmath all return 1 in this case, but SciPy's hyp1f1
+        # returns inf.
+        assert_equal(sc.hyp1f1(0, b, [-1.5, 0, 1.5]), [np.inf, np.inf, np.inf])
+
+    def test_legacy_case2(self):
+        # This is a legacy edge case.
+        # In software such as boost (1.81+), mpmath and Mathematica,
+        # the value is 1.
+        assert sc.hyp1f1(-4, -3, 0) == np.inf
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_iv_ratio.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_iv_ratio.py
new file mode 100644
index 0000000000000000000000000000000000000000..dafc35982c4d4869ead2136e74466f1c44c64556
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_iv_ratio.py
@@ -0,0 +1,249 @@
+# This file contains unit tests for iv_ratio() and related functions.
+
+import pytest
+import numpy as np
+from numpy.testing import assert_equal, assert_allclose
+from scipy.special._ufuncs import (  # type: ignore[attr-defined]
+    _iv_ratio as iv_ratio,
+    _iv_ratio_c as iv_ratio_c,
+)
+
+
+class TestIvRatio:
+
+    @pytest.mark.parametrize('v,x,r', [
+        (0.5, 0.16666666666666666, 0.16514041292462933),
+        (0.5, 0.3333333333333333, 0.32151273753163434),
+        (0.5, 0.5, 0.46211715726000974),
+        (0.5, 0.6666666666666666, 0.5827829453479101),
+        (0.5, 0.8333333333333335, 0.6822617902381698),
+        (1, 0.3380952380952381, 0.1666773049170313),
+        (1, 0.7083333333333333, 0.33366443586989925),
+        (1, 1.1666666666666667, 0.5023355231537423),
+        (1, 1.8666666666666665, 0.674616572252164),
+        (1, 3.560606060606061, 0.844207659503163),
+        (2.34, 0.7975238095238094, 0.16704903081553285),
+        (2.34, 1.7133333333333334, 0.3360215931268845),
+        (2.34, 2.953333333333333, 0.50681909317803),
+        (2.34, 5.0826666666666656, 0.6755252698800679),
+        (2.34, 10.869696969696973, 0.8379351104498762),
+        (56.789, 19.46575238095238, 0.1667020505391409),
+        (56.789, 42.55008333333333, 0.33353809996933026),
+        (56.789, 75.552, 0.5003932381177826),
+        (56.789, 135.76026666666667, 0.6670528221946127),
+        (56.789, 307.8642424242425, 0.8334999441460798),
+    ])
+    def test_against_reference_values(self, v, x, r):
+        """The reference values are computed using mpmath as follows.
+
+        from mpmath import mp
+        mp.dps = 100
+
+        def iv_ratio_mp(v, x):
+            return mp.besseli(v, x) / mp.besseli(v - 1, x)
+
+        def _sample(n, *, v):
+            '''Return n positive real numbers x such that iv_ratio(v, x) are
+            roughly evenly spaced over (0, 1).  The formula is taken from [1].
+
+            [1] Banerjee A., Dhillon, I. S., Ghosh, J., Sra, S. (2005).
+                "Clustering on the Unit Hypersphere using von Mises-Fisher
+                Distributions."  Journal of Machine Learning Research,
+                6(46):1345-1382.
+            '''
+            r = np.arange(1, n+1) / (n+1)
+            return r * (2*v-r*r) / (1-r*r)
+
+        for v in (0.5, 1, 2.34, 56.789):
+            xs = _sample(5, v=v)
+            for x in xs:
+                print(f"({v}, {x}, {float(iv_ratio_mp(v,x))}),")
+        """
+        assert_allclose(iv_ratio(v, x), r, rtol=4e-16, atol=0)
+
+    @pytest.mark.parametrize('v,x,r', [
+        (1, np.inf, 1),
+        (np.inf, 1, 0),
+    ])
+    def test_inf(self, v, x, r):
+        """If exactly one of v or x is inf and the other is within domain,
+        should return 0 or 1 accordingly."""
+        assert_equal(iv_ratio(v, x), r)
+
+    @pytest.mark.parametrize('v', [0.49, -np.inf, np.nan, np.inf])
+    @pytest.mark.parametrize('x', [-np.finfo(float).smallest_normal,
+                                   -np.finfo(float).smallest_subnormal,
+                                   -np.inf, np.nan, np.inf])
+    def test_nan(self, v, x):
+        """If at least one argument is out of domain, or if v = x = inf,
+        the function should return nan."""
+        assert_equal(iv_ratio(v, x), np.nan)
+
+    @pytest.mark.parametrize('v', [0.5, 1, np.finfo(float).max, np.inf])
+    def test_zero_x(self, v):
+        """If x is +/-0.0, return x to ensure iv_ratio is an odd function."""
+        assert_equal(iv_ratio(v, 0.0), 0.0)
+        assert_equal(iv_ratio(v, -0.0), -0.0)
+
+    @pytest.mark.parametrize('v,x', [
+        (1, np.finfo(float).smallest_normal),
+        (1, np.finfo(float).smallest_subnormal),
+        (1, np.finfo(float).smallest_subnormal*2),
+        (1e20, 123),
+        (np.finfo(float).max, 1),
+        (np.finfo(float).max, np.sqrt(np.finfo(float).max)),
+    ])
+    def test_tiny_x(self, v, x):
+        """If x is much less than v, the bounds
+
+                    x                                 x
+        --------------------------- <= R <= -----------------------
+        v-0.5+sqrt(x**2+(v+0.5)**2)         v-1+sqrt(x**2+(v+1)**2)
+
+        collapses to R ~= x/2v.  Test against this asymptotic expression.
+        """
+        assert_equal(iv_ratio(v, x), (0.5*x)/v)
+
+    @pytest.mark.parametrize('v,x', [
+        (1, 1e16),
+        (1e20, 1e40),
+        (np.sqrt(np.finfo(float).max), np.finfo(float).max),
+    ])
+    def test_huge_x(self, v, x):
+        """If x is much greater than v, the bounds
+
+                    x                                 x
+        --------------------------- <= R <= ---------------------------
+        v-0.5+sqrt(x**2+(v+0.5)**2)         v-0.5+sqrt(x**2+(v-0.5)**2)
+
+        collapses to R ~= 1.  Test against this asymptotic expression.
+        """
+        assert_equal(iv_ratio(v, x), 1.0)
+
+    @pytest.mark.parametrize('v,x', [
+        (np.finfo(float).max, np.finfo(float).max),
+        (np.finfo(float).max / 3, np.finfo(float).max),
+        (np.finfo(float).max, np.finfo(float).max / 3),
+    ])
+    def test_huge_v_x(self, v, x):
+        """If both x and v are very large, the bounds
+
+                    x                                 x
+        --------------------------- <= R <= -----------------------
+        v-0.5+sqrt(x**2+(v+0.5)**2)         v-1+sqrt(x**2+(v+1)**2)
+
+        collapses to R ~= x/(v+sqrt(x**2+v**2).  Test against this asymptotic
+        expression, and in particular that no numerical overflow occurs during
+        intermediate calculations.
+        """
+        t = x / v
+        expected = t / (1 + np.hypot(1, t))
+        assert_allclose(iv_ratio(v, x), expected, rtol=4e-16, atol=0)
+
+
+class TestIvRatioC:
+
+    @pytest.mark.parametrize('v,x,r', [
+        (0.5, 0.16666666666666666, 0.8348595870753707),
+        (0.5, 0.3333333333333333, 0.6784872624683657),
+        (0.5, 0.5, 0.5378828427399902),
+        (0.5, 0.6666666666666666, 0.4172170546520899),
+        (0.5, 0.8333333333333335, 0.3177382097618302),
+        (1, 0.3380952380952381, 0.8333226950829686),
+        (1, 0.7083333333333333, 0.6663355641301008),
+        (1, 1.1666666666666667, 0.4976644768462577),
+        (1, 1.8666666666666665, 0.325383427747836),
+        (1, 3.560606060606061, 0.155792340496837),
+        (2.34, 0.7975238095238094, 0.8329509691844672),
+        (2.34, 1.7133333333333334, 0.6639784068731155),
+        (2.34, 2.953333333333333, 0.49318090682197),
+        (2.34, 5.0826666666666656, 0.3244747301199321),
+        (2.34, 10.869696969696973, 0.16206488955012377),
+        (56.789, 19.46575238095238, 0.8332979494608591),
+        (56.789, 42.55008333333333, 0.6664619000306697),
+        (56.789, 75.552, 0.4996067618822174),
+        (56.789, 135.76026666666667, 0.3329471778053873),
+        (56.789, 307.8642424242425, 0.16650005585392025),
+    ])
+    def test_against_reference_values(self, v, x, r):
+        """The reference values are one minus those of TestIvRatio."""
+        assert_allclose(iv_ratio_c(v, x), r, rtol=1e-15, atol=0)
+
+    @pytest.mark.parametrize('v,x,r', [
+        (1, np.inf, 0),
+        (np.inf, 1, 1),
+    ])
+    def test_inf(self, v, x, r):
+        """If exactly one of v or x is inf and the other is within domain,
+        should return 0 or 1 accordingly."""
+        assert_equal(iv_ratio_c(v, x), r)
+
+    @pytest.mark.parametrize('v', [0.49, -np.inf, np.nan, np.inf])
+    @pytest.mark.parametrize('x', [-np.finfo(float).smallest_normal,
+                                   -np.finfo(float).smallest_subnormal,
+                                   -np.inf, np.nan, np.inf])
+    def test_nan(self, v, x):
+        """If at least one argument is out of domain, or if v = x = inf,
+        the function should return nan."""
+        assert_equal(iv_ratio_c(v, x), np.nan)
+
+    @pytest.mark.parametrize('v', [0.5, 1, np.finfo(float).max, np.inf])
+    def test_zero_x(self, v):
+        """If x is +/-0.0, return 1."""
+        assert_equal(iv_ratio_c(v, 0.0), 1.0)
+        assert_equal(iv_ratio_c(v, -0.0), 1.0)
+
+    @pytest.mark.parametrize('v,x', [
+        (1, np.finfo(float).smallest_normal),
+        (1, np.finfo(float).smallest_subnormal),
+        (1, np.finfo(float).smallest_subnormal*2),
+        (1e20, 123),
+        (np.finfo(float).max, 1),
+        (np.finfo(float).max, np.sqrt(np.finfo(float).max)),
+    ])
+    def test_tiny_x(self, v, x):
+        """If x is much less than v, the bounds
+
+                    x                                 x
+        --------------------------- <= R <= -----------------------
+        v-0.5+sqrt(x**2+(v+0.5)**2)         v-1+sqrt(x**2+(v+1)**2)
+
+        collapses to 1-R ~= 1-x/2v.  Test against this asymptotic expression.
+        """
+        assert_equal(iv_ratio_c(v, x), 1.0-(0.5*x)/v)
+
+    @pytest.mark.parametrize('v,x', [
+        (1, 1e16),
+        (1e20, 1e40),
+        (np.sqrt(np.finfo(float).max), np.finfo(float).max),
+    ])
+    def test_huge_x(self, v, x):
+        """If x is much greater than v, the bounds
+
+                    x                                 x
+        --------------------------- <= R <= ---------------------------
+        v-0.5+sqrt(x**2+(v+0.5)**2)         v-0.5+sqrt(x**2+(v-0.5)**2)
+
+        collapses to 1-R ~= (v-0.5)/x.  Test against this asymptotic expression.
+        """
+        assert_allclose(iv_ratio_c(v, x), (v-0.5)/x, rtol=1e-15, atol=0)
+
+    @pytest.mark.parametrize('v,x', [
+        (np.finfo(float).max, np.finfo(float).max),
+        (np.finfo(float).max / 3, np.finfo(float).max),
+        (np.finfo(float).max, np.finfo(float).max / 3),
+    ])
+    def test_huge_v_x(self, v, x):
+        """If both x and v are very large, the bounds
+
+                    x                                 x
+        --------------------------- <= R <= -----------------------
+        v-0.5+sqrt(x**2+(v+0.5)**2)         v-1+sqrt(x**2+(v+1)**2)
+
+        collapses to 1 - R ~= 1 - x/(v+sqrt(x**2+v**2).  Test against this
+        asymptotic expression, and in particular that no numerical overflow
+        occurs during intermediate calculations.
+        """
+        t = x / v
+        expected = 1 - t / (1 + np.hypot(1, t))
+        assert_allclose(iv_ratio_c(v, x), expected, rtol=4e-16, atol=0)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_kolmogorov.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_kolmogorov.py
new file mode 100644
index 0000000000000000000000000000000000000000..ade38115706808809890e1eba3b938562b0af6e6
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_kolmogorov.py
@@ -0,0 +1,491 @@
+import itertools
+
+import numpy as np
+from numpy.testing import assert_
+from scipy.special._testutils import FuncData
+
+from scipy.special import kolmogorov, kolmogi, smirnov, smirnovi
+from scipy.special._ufuncs import (_kolmogc, _kolmogci, _kolmogp,
+                                   _smirnovc, _smirnovci, _smirnovp)
+
+_rtol = 1e-10
+
+class TestSmirnov:
+    def test_nan(self):
+        assert_(np.isnan(smirnov(1, np.nan)))
+
+    def test_basic(self):
+        dataset = [(1, 0.1, 0.9),
+                   (1, 0.875, 0.125),
+                   (2, 0.875, 0.125 * 0.125),
+                   (3, 0.875, 0.125 * 0.125 * 0.125)]
+
+        dataset = np.asarray(dataset)
+        FuncData(
+            smirnov, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+        dataset[:, -1] = 1 - dataset[:, -1]
+        FuncData(
+            _smirnovc, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+
+    def test_x_equals_0(self):
+        dataset = [(n, 0, 1) for n in itertools.chain(range(2, 20), range(1010, 1020))]
+        dataset = np.asarray(dataset)
+        FuncData(
+            smirnov, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+        dataset[:, -1] = 1 - dataset[:, -1]
+        FuncData(
+            _smirnovc, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+
+    def test_x_equals_1(self):
+        dataset = [(n, 1, 0) for n in itertools.chain(range(2, 20), range(1010, 1020))]
+        dataset = np.asarray(dataset)
+        FuncData(
+            smirnov, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+        dataset[:, -1] = 1 - dataset[:, -1]
+        FuncData(
+            _smirnovc, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+
+    def test_x_equals_0point5(self):
+        dataset = [(1, 0.5, 0.5),
+                   (2, 0.5, 0.25),
+                   (3, 0.5, 0.166666666667),
+                   (4, 0.5, 0.09375),
+                   (5, 0.5, 0.056),
+                   (6, 0.5, 0.0327932098765),
+                   (7, 0.5, 0.0191958707681),
+                   (8, 0.5, 0.0112953186035),
+                   (9, 0.5, 0.00661933257355),
+                   (10, 0.5, 0.003888705)]
+
+        dataset = np.asarray(dataset)
+        FuncData(
+            smirnov, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+        dataset[:, -1] = 1 - dataset[:, -1]
+        FuncData(
+            _smirnovc, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+
+    def test_n_equals_1(self):
+        x = np.linspace(0, 1, 101, endpoint=True)
+        dataset = np.column_stack([[1]*len(x), x, 1-x])
+        FuncData(
+            smirnov, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+        dataset[:, -1] = 1 - dataset[:, -1]
+        FuncData(
+            _smirnovc, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+
+    def test_n_equals_2(self):
+        x = np.linspace(0.5, 1, 101, endpoint=True)
+        p = np.power(1-x, 2)
+        n = np.array([2] * len(x))
+        dataset = np.column_stack([n, x, p])
+        FuncData(
+            smirnov, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+        dataset[:, -1] = 1 - dataset[:, -1]
+        FuncData(
+            _smirnovc, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+
+    def test_n_equals_3(self):
+        x = np.linspace(0.7, 1, 31, endpoint=True)
+        p = np.power(1-x, 3)
+        n = np.array([3] * len(x))
+        dataset = np.column_stack([n, x, p])
+        FuncData(
+            smirnov, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+        dataset[:, -1] = 1 - dataset[:, -1]
+        FuncData(
+            _smirnovc, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+
+    def test_n_large(self):
+        # test for large values of n
+        # Probabilities should go down as n goes up
+        x = 0.4
+        pvals = np.array([smirnov(n, x) for n in range(400, 1100, 20)])
+        dfs = np.diff(pvals)
+        assert_(np.all(dfs <= 0), msg=f'Not all diffs negative {dfs}')
+
+
+class TestSmirnovi:
+    def test_nan(self):
+        assert_(np.isnan(smirnovi(1, np.nan)))
+
+    def test_basic(self):
+        dataset = [(1, 0.4, 0.6),
+                   (1, 0.6, 0.4),
+                   (1, 0.99, 0.01),
+                   (1, 0.01, 0.99),
+                   (2, 0.125 * 0.125, 0.875),
+                   (3, 0.125 * 0.125 * 0.125, 0.875),
+                   (10, 1.0 / 16 ** 10, 1 - 1.0 / 16)]
+
+        dataset = np.asarray(dataset)
+        FuncData(
+            smirnovi, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+        dataset[:, 1] = 1 - dataset[:, 1]
+        FuncData(
+            _smirnovci, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+
+    def test_x_equals_0(self):
+        dataset = [(n, 0, 1) for n in itertools.chain(range(2, 20), range(1010, 1020))]
+        dataset = np.asarray(dataset)
+        FuncData(
+            smirnovi, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+        dataset[:, 1] = 1 - dataset[:, 1]
+        FuncData(
+            _smirnovci, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+
+    def test_x_equals_1(self):
+        dataset = [(n, 1, 0) for n in itertools.chain(range(2, 20), range(1010, 1020))]
+        dataset = np.asarray(dataset)
+        FuncData(
+            smirnovi, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+        dataset[:, 1] = 1 - dataset[:, 1]
+        FuncData(
+            _smirnovci, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+
+    def test_n_equals_1(self):
+        pp = np.linspace(0, 1, 101, endpoint=True)
+        # dataset = np.array([(1, p, 1-p) for p in pp])
+        dataset = np.column_stack([[1]*len(pp), pp, 1-pp])
+        FuncData(
+            smirnovi, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+        dataset[:, 1] = 1 - dataset[:, 1]
+        FuncData(
+            _smirnovci, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+
+    def test_n_equals_2(self):
+        x = np.linspace(0.5, 1, 101, endpoint=True)
+        p = np.power(1-x, 2)
+        n = np.array([2] * len(x))
+        dataset = np.column_stack([n, p, x])
+        FuncData(
+            smirnovi, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+        dataset[:, 1] = 1 - dataset[:, 1]
+        FuncData(
+            _smirnovci, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+
+    def test_n_equals_3(self):
+        x = np.linspace(0.7, 1, 31, endpoint=True)
+        p = np.power(1-x, 3)
+        n = np.array([3] * len(x))
+        dataset = np.column_stack([n, p, x])
+        FuncData(
+            smirnovi, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+        dataset[:, 1] = 1 - dataset[:, 1]
+        FuncData(
+            _smirnovci, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+
+    def test_round_trip(self):
+        def _sm_smi(n, p):
+            return smirnov(n, smirnovi(n, p))
+
+        def _smc_smci(n, p):
+            return _smirnovc(n, _smirnovci(n, p))
+
+        dataset = [(1, 0.4, 0.4),
+                   (1, 0.6, 0.6),
+                   (2, 0.875, 0.875),
+                   (3, 0.875, 0.875),
+                   (3, 0.125, 0.125),
+                   (10, 0.999, 0.999),
+                   (10, 0.0001, 0.0001)]
+
+        dataset = np.asarray(dataset)
+        FuncData(
+            _sm_smi, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+        FuncData(
+            _smc_smci, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+
+    def test_x_equals_0point5(self):
+        dataset = [(1, 0.5, 0.5),
+                   (2, 0.5, 0.366025403784),
+                   (2, 0.25, 0.5),
+                   (3, 0.5, 0.297156508177),
+                   (4, 0.5, 0.255520481121),
+                   (5, 0.5, 0.234559536069),
+                   (6, 0.5, 0.21715965898),
+                   (7, 0.5, 0.202722580034),
+                   (8, 0.5, 0.190621765256),
+                   (9, 0.5, 0.180363501362),
+                   (10, 0.5, 0.17157867006)]
+
+        dataset = np.asarray(dataset)
+        FuncData(
+            smirnovi, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+        dataset[:, 1] = 1 - dataset[:, 1]
+        FuncData(
+            _smirnovci, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+
+
+class TestSmirnovp:
+    def test_nan(self):
+        assert_(np.isnan(_smirnovp(1, np.nan)))
+
+    def test_basic(self):
+        # Check derivative at endpoints
+        n1_10 = np.arange(1, 10)
+        dataset0 = np.column_stack([n1_10,
+                                    np.full_like(n1_10, 0),
+                                    np.full_like(n1_10, -1)])
+        FuncData(
+            _smirnovp, dataset0, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+
+        n2_10 = np.arange(2, 10)
+        dataset1 = np.column_stack([n2_10,
+                                    np.full_like(n2_10, 1.0),
+                                    np.full_like(n2_10, 0)])
+        FuncData(
+            _smirnovp, dataset1, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+
+    def test_oneminusoneovern(self):
+        # Check derivative at x=1-1/n
+        n = np.arange(1, 20)
+        x = 1.0/n
+        xm1 = 1-1.0/n
+        pp1 = -n * x**(n-1)
+        pp1 -= (1-np.sign(n-2)**2) * 0.5  # n=2, x=0.5, 1-1/n = 0.5, need to adjust
+        dataset1 = np.column_stack([n, xm1, pp1])
+        FuncData(
+            _smirnovp, dataset1, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+
+    def test_oneovertwon(self):
+        # Check derivative at x=1/2n  (Discontinuous at x=1/n, so check at x=1/2n)
+        n = np.arange(1, 20)
+        x = 1.0/2/n
+        pp = -(n*x+1) * (1+x)**(n-2)
+        dataset0 = np.column_stack([n, x, pp])
+        FuncData(
+            _smirnovp, dataset0, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+
+    def test_oneovern(self):
+        # Check derivative at x=1/n
+        # (Discontinuous at x=1/n, hard to tell if x==1/n, only use n=power of 2)
+        n = 2**np.arange(1, 10)
+        x = 1.0/n
+        pp = -(n*x+1) * (1+x)**(n-2) + 0.5
+        dataset0 = np.column_stack([n, x, pp])
+        FuncData(
+            _smirnovp, dataset0, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+
+    def test_oneovernclose(self):
+        # Check derivative at x=1/n
+        # (Discontinuous at x=1/n, test on either side: x=1/n +/- 2epsilon)
+        n = np.arange(3, 20)
+
+        x = 1.0/n - 2*np.finfo(float).eps
+        pp = -(n*x+1) * (1+x)**(n-2)
+        dataset0 = np.column_stack([n, x, pp])
+        FuncData(
+            _smirnovp, dataset0, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+
+        x = 1.0/n + 2*np.finfo(float).eps
+        pp = -(n*x+1) * (1+x)**(n-2) + 1
+        dataset1 = np.column_stack([n, x, pp])
+        FuncData(
+            _smirnovp, dataset1, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+
+
+class TestKolmogorov:
+    def test_nan(self):
+        assert_(np.isnan(kolmogorov(np.nan)))
+
+    def test_basic(self):
+        dataset = [(0, 1.0),
+                   (0.5, 0.96394524366487511),
+                   (0.8275735551899077, 0.5000000000000000),
+                   (1, 0.26999967167735456),
+                   (2, 0.00067092525577969533)]
+
+        dataset = np.asarray(dataset)
+        FuncData(kolmogorov, dataset, (0,), 1, rtol=_rtol).check()
+
+    def test_linspace(self):
+        x = np.linspace(0, 2.0, 21)
+        dataset = [1.0000000000000000, 1.0000000000000000, 0.9999999999994950,
+                   0.9999906941986655, 0.9971923267772983, 0.9639452436648751,
+                   0.8642827790506042, 0.7112351950296890, 0.5441424115741981,
+                   0.3927307079406543, 0.2699996716773546, 0.1777181926064012,
+                   0.1122496666707249, 0.0680922218447664, 0.0396818795381144,
+                   0.0222179626165251, 0.0119520432391966, 0.0061774306344441,
+                   0.0030676213475797, 0.0014636048371873, 0.0006709252557797]
+
+        dataset_c = [0.0000000000000000, 6.609305242245699e-53, 5.050407338670114e-13,
+                     9.305801334566668e-06, 0.0028076732227017, 0.0360547563351249,
+                     0.1357172209493958, 0.2887648049703110, 0.4558575884258019,
+                     0.6072692920593457, 0.7300003283226455, 0.8222818073935988,
+                     0.8877503333292751, 0.9319077781552336, 0.9603181204618857,
+                     0.9777820373834749, 0.9880479567608034, 0.9938225693655559,
+                     0.9969323786524203, 0.9985363951628127, 0.9993290747442203]
+
+        dataset = np.column_stack([x, dataset])
+        FuncData(kolmogorov, dataset, (0,), 1, rtol=_rtol).check()
+        dataset_c = np.column_stack([x, dataset_c])
+        FuncData(_kolmogc, dataset_c, (0,), 1, rtol=_rtol).check()
+
+    def test_linspacei(self):
+        p = np.linspace(0, 1.0, 21, endpoint=True)
+        dataset = [np.inf, 1.3580986393225507, 1.2238478702170823,
+                   1.1379465424937751, 1.0727491749396481, 1.0191847202536859,
+                   0.9730633753323726, 0.9320695842357622, 0.8947644549851197,
+                   0.8601710725555463, 0.8275735551899077, 0.7964065373291559,
+                   0.7661855555617682, 0.7364542888171910, 0.7067326523068980,
+                   0.6764476915028201, 0.6448126061663567, 0.6105590999244391,
+                   0.5711732651063401, 0.5196103791686224, 0.0000000000000000]
+
+        dataset_c = [0.0000000000000000, 0.5196103791686225, 0.5711732651063401,
+                     0.6105590999244391, 0.6448126061663567, 0.6764476915028201,
+                     0.7067326523068980, 0.7364542888171910, 0.7661855555617682,
+                     0.7964065373291559, 0.8275735551899077, 0.8601710725555463,
+                     0.8947644549851196, 0.9320695842357622, 0.9730633753323727,
+                     1.0191847202536859, 1.0727491749396481, 1.1379465424937754,
+                     1.2238478702170825, 1.3580986393225509, np.inf]
+
+        dataset = np.column_stack([p[1:], dataset[1:]])
+        FuncData(kolmogi, dataset, (0,), 1, rtol=_rtol).check()
+        dataset_c = np.column_stack([p[:-1], dataset_c[:-1]])
+        FuncData(_kolmogci, dataset_c, (0,), 1, rtol=_rtol).check()
+
+    def test_smallx(self):
+        epsilon = 0.1 ** np.arange(1, 14)
+        x = np.array([0.571173265106, 0.441027698518, 0.374219690278, 0.331392659217,
+                      0.300820537459, 0.277539353999, 0.259023494805, 0.243829561254,
+                      0.231063086389, 0.220135543236, 0.210641372041, 0.202290283658,
+                      0.19487060742])
+
+        dataset = np.column_stack([x, 1-epsilon])
+        FuncData(kolmogorov, dataset, (0,), 1, rtol=_rtol).check()
+
+    def test_round_trip(self):
+        def _ki_k(_x):
+            return kolmogi(kolmogorov(_x))
+
+        def _kci_kc(_x):
+            return _kolmogci(_kolmogc(_x))
+
+        x = np.linspace(0.0, 2.0, 21, endpoint=True)
+        # Exclude 0.1, 0.2.  0.2 almost makes succeeds, but 0.1 has no chance.
+        x02 = x[(x == 0) | (x > 0.21)]
+        dataset02 = np.column_stack([x02, x02])
+        FuncData(_ki_k, dataset02, (0,), 1, rtol=_rtol).check()
+
+        dataset = np.column_stack([x, x])
+        FuncData(_kci_kc, dataset, (0,), 1, rtol=_rtol).check()
+
+
+class TestKolmogi:
+    def test_nan(self):
+        assert_(np.isnan(kolmogi(np.nan)))
+
+    def test_basic(self):
+        dataset = [(1.0, 0),
+                   (0.96394524366487511, 0.5),
+                   (0.9, 0.571173265106),
+                   (0.5000000000000000, 0.8275735551899077),
+                   (0.26999967167735456, 1),
+                   (0.00067092525577969533, 2)]
+
+        dataset = np.asarray(dataset)
+        FuncData(kolmogi, dataset, (0,), 1, rtol=_rtol).check()
+
+    def test_smallpcdf(self):
+        epsilon = 0.5 ** np.arange(1, 55, 3)
+        # kolmogi(1-p) == _kolmogci(p) if  1-(1-p) == p, but not necessarily otherwise
+        # Use epsilon s.t. 1-(1-epsilon)) == epsilon,
+        # so can use same x-array for both results
+
+        x = np.array([0.8275735551899077, 0.5345255069097583, 0.4320114038786941,
+                      0.3736868442620478, 0.3345161714909591, 0.3057833329315859,
+                      0.2835052890528936, 0.2655578150208676, 0.2506869966107999,
+                      0.2380971058736669, 0.2272549289962079, 0.2177876361600040,
+                      0.2094254686862041, 0.2019676748836232, 0.1952612948137504,
+                      0.1891874239646641, 0.1836520225050326, 0.1785795904846466])
+
+        dataset = np.column_stack([1-epsilon, x])
+        FuncData(kolmogi, dataset, (0,), 1, rtol=_rtol).check()
+
+        dataset = np.column_stack([epsilon, x])
+        FuncData(_kolmogci, dataset, (0,), 1, rtol=_rtol).check()
+
+    def test_smallpsf(self):
+        epsilon = 0.5 ** np.arange(1, 55, 3)
+        # kolmogi(p) == _kolmogci(1-p) if  1-(1-p) == p, but not necessarily otherwise
+        # Use epsilon s.t. 1-(1-epsilon)) == epsilon,
+        # so can use same x-array for both results
+
+        x = np.array([0.8275735551899077, 1.3163786275161036, 1.6651092133663343,
+                      1.9525136345289607, 2.2027324540033235, 2.4272929437460848,
+                      2.6327688477341593, 2.8233300509220260, 3.0018183401530627,
+                      3.1702735084088891, 3.3302184446307912, 3.4828258153113318,
+                      3.6290214150152051, 3.7695513262825959, 3.9050272690877326,
+                      4.0359582187082550, 4.1627730557884890, 4.2858371743264527])
+
+        dataset = np.column_stack([epsilon, x])
+        FuncData(kolmogi, dataset, (0,), 1, rtol=_rtol).check()
+
+        dataset = np.column_stack([1-epsilon, x])
+        FuncData(_kolmogci, dataset, (0,), 1, rtol=_rtol).check()
+
+    def test_round_trip(self):
+        def _k_ki(_p):
+            return kolmogorov(kolmogi(_p))
+
+        p = np.linspace(0.1, 1.0, 10, endpoint=True)
+        dataset = np.column_stack([p, p])
+        FuncData(_k_ki, dataset, (0,), 1, rtol=_rtol).check()
+
+
+class TestKolmogp:
+    def test_nan(self):
+        assert_(np.isnan(_kolmogp(np.nan)))
+
+    def test_basic(self):
+        dataset = [(0.000000, -0.0),
+                   (0.200000, -1.532420541338916e-10),
+                   (0.400000, -0.1012254419260496),
+                   (0.600000, -1.324123244249925),
+                   (0.800000, -1.627024345636592),
+                   (1.000000, -1.071948558356941),
+                   (1.200000, -0.538512430720529),
+                   (1.400000, -0.2222133182429472),
+                   (1.600000, -0.07649302775520538),
+                   (1.800000, -0.02208687346347873),
+                   (2.000000, -0.005367402045629683)]
+
+        dataset = np.asarray(dataset)
+        FuncData(_kolmogp, dataset, (0,), 1, rtol=_rtol).check()
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_lambertw.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_lambertw.py
new file mode 100644
index 0000000000000000000000000000000000000000..ac26dfb9ff65dbfd94740220a95a16c902b4be3d
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_lambertw.py
@@ -0,0 +1,109 @@
+#
+# Tests for the lambertw function,
+# Adapted from the MPMath tests [1] by Yosef Meller, mellerf@netvision.net.il
+# Distributed under the same license as SciPy itself.
+#
+# [1] mpmath source code, Subversion revision 992
+#     http://code.google.com/p/mpmath/source/browse/trunk/mpmath/tests/test_functions2.py?spec=svn994&r=992
+
+import pytest
+import numpy as np
+from numpy.testing import assert_, assert_equal, assert_allclose
+from scipy.special import lambertw
+from numpy import nan, inf, pi, e, isnan, log, r_, array, complex128
+
+from scipy.special._testutils import FuncData
+
+
+def test_values():
+    assert_(isnan(lambertw(nan)))
+    assert_equal(lambertw(inf,1).real, inf)
+    assert_equal(lambertw(inf,1).imag, 2*pi)
+    assert_equal(lambertw(-inf,1).real, inf)
+    assert_equal(lambertw(-inf,1).imag, 3*pi)
+
+    assert_equal(lambertw(1.), lambertw(1., 0))
+
+    data = [
+        (0,0, 0),
+        (0+0j,0, 0),
+        (inf,0, inf),
+        (0,-1, -inf),
+        (0,1, -inf),
+        (0,3, -inf),
+        (e,0, 1),
+        (1,0, 0.567143290409783873),
+        (-pi/2,0, 1j*pi/2),
+        (-log(2)/2,0, -log(2)),
+        (0.25,0, 0.203888354702240164),
+        (-0.25,0, -0.357402956181388903),
+        (-1./10000,0, -0.000100010001500266719),
+        (-0.25,-1, -2.15329236411034965),
+        (0.25,-1, -3.00899800997004620-4.07652978899159763j),
+        (-0.25,-1, -2.15329236411034965),
+        (0.25,1, -3.00899800997004620+4.07652978899159763j),
+        (-0.25,1, -3.48973228422959210+7.41405453009603664j),
+        (-4,0, 0.67881197132094523+1.91195078174339937j),
+        (-4,1, -0.66743107129800988+7.76827456802783084j),
+        (-4,-1, 0.67881197132094523-1.91195078174339937j),
+        (1000,0, 5.24960285240159623),
+        (1000,1, 4.91492239981054535+5.44652615979447070j),
+        (1000,-1, 4.91492239981054535-5.44652615979447070j),
+        (1000,5, 3.5010625305312892+29.9614548941181328j),
+        (3+4j,0, 1.281561806123775878+0.533095222020971071j),
+        (-0.4+0.4j,0, -0.10396515323290657+0.61899273315171632j),
+        (3+4j,1, -0.11691092896595324+5.61888039871282334j),
+        (3+4j,-1, 0.25856740686699742-3.85211668616143559j),
+        (-0.5,-1, -0.794023632344689368-0.770111750510379110j),
+        (-1./10000,1, -11.82350837248724344+6.80546081842002101j),
+        (-1./10000,-1, -11.6671145325663544),
+        (-1./10000,-2, -11.82350837248724344-6.80546081842002101j),
+        (-1./100000,4, -14.9186890769540539+26.1856750178782046j),
+        (-1./100000,5, -15.0931437726379218666+32.5525721210262290086j),
+        ((2+1j)/10,0, 0.173704503762911669+0.071781336752835511j),
+        ((2+1j)/10,1, -3.21746028349820063+4.56175438896292539j),
+        ((2+1j)/10,-1, -3.03781405002993088-3.53946629633505737j),
+        ((2+1j)/10,4, -4.6878509692773249+23.8313630697683291j),
+        (-(2+1j)/10,0, -0.226933772515757933-0.164986470020154580j),
+        (-(2+1j)/10,1, -2.43569517046110001+0.76974067544756289j),
+        (-(2+1j)/10,-1, -3.54858738151989450-6.91627921869943589j),
+        (-(2+1j)/10,4, -4.5500846928118151+20.6672982215434637j),
+        (pi,0, 1.073658194796149172092178407024821347547745350410314531),
+
+        # Former bug in generated branch,
+        (-0.5+0.002j,0, -0.78917138132659918344 + 0.76743539379990327749j),
+        (-0.5-0.002j,0, -0.78917138132659918344 - 0.76743539379990327749j),
+        (-0.448+0.4j,0, -0.11855133765652382241 + 0.66570534313583423116j),
+        (-0.448-0.4j,0, -0.11855133765652382241 - 0.66570534313583423116j),
+    ]
+    data = array(data, dtype=complex128)
+
+    def w(x, y):
+        return lambertw(x, y.real.astype(int))
+    with np.errstate(all='ignore'):
+        FuncData(w, data, (0,1), 2, rtol=1e-10, atol=1e-13).check()
+
+
+def test_ufunc():
+    assert_allclose(lambertw(r_[0., e, 1.]), r_[0., 1., 0.567143290409783873],
+                    atol=1.5e-7, rtol=0)
+
+
+def test_lambertw_ufunc_loop_selection():
+    # see https://github.com/scipy/scipy/issues/4895
+    dt = np.dtype(np.complex128)
+    assert_equal(lambertw(0, 0, 0).dtype, dt)
+    assert_equal(lambertw([0], 0, 0).dtype, dt)
+    assert_equal(lambertw(0, [0], 0).dtype, dt)
+    assert_equal(lambertw(0, 0, [0]).dtype, dt)
+    assert_equal(lambertw([0], [0], [0]).dtype, dt)
+
+
+@pytest.mark.parametrize('z', [1e-316, -2e-320j, -5e-318+1e-320j])
+def test_lambertw_subnormal_k0(z):
+    # Verify that subnormal inputs are handled correctly on
+    # the branch k=0 (regression test for gh-16291).
+    w = lambertw(z)
+    # For values this small, we can be sure that numerically,
+    # lambertw(z) is z.
+    assert w == z
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_legendre.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_legendre.py
new file mode 100644
index 0000000000000000000000000000000000000000..7625313ef258de23307c6c4a432069f5c4cd0cd1
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_legendre.py
@@ -0,0 +1,1421 @@
+import math
+import warnings
+
+import numpy as np
+
+import pytest
+from numpy.testing import assert_equal, assert_allclose
+
+from scipy import special
+from scipy.special import (legendre_p, legendre_p_all, assoc_legendre_p,
+    assoc_legendre_p_all, sph_legendre_p, sph_legendre_p_all)
+
+
+# Base polynomials come from Abrahmowitz and Stegan
+class TestLegendre:
+    def test_legendre(self):
+        leg0 = special.legendre(0)
+        leg1 = special.legendre(1)
+        leg2 = special.legendre(2)
+        leg3 = special.legendre(3)
+        leg4 = special.legendre(4)
+        leg5 = special.legendre(5)
+        assert_equal(leg0.c, [1])
+        assert_equal(leg1.c, [1,0])
+        assert_allclose(leg2.c, np.array([3, 0, -1])/2.0,
+                        atol=1.5e-13, rtol=0)
+        assert_allclose(leg3.c, np.array([5, 0, -3, 0])/2.0,
+                        atol=1.5e-7, rtol=0)
+        assert_allclose(leg4.c, np.array([35, 0, -30, 0, 3])/8.0,
+                        atol=1.5e-7, rtol=0)
+        assert_allclose(leg5.c, np.array([63, 0, -70, 0, 15, 0])/8.0,
+                        atol=1.5e-7, rtol=0)
+
+class TestLegendreP:
+    @pytest.mark.parametrize("shape", [(10,), (4, 9), (3, 5, 7)])
+    def test_ode(self, shape):
+        rng = np.random.default_rng(1234)
+
+        n = rng.integers(0, 100, shape)
+        x = rng.uniform(-1, 1, shape)
+
+        p, p_jac, p_hess = legendre_p(n, x, diff_n=2)
+
+        assert p.shape == shape
+        assert p_jac.shape == p.shape
+        assert p_hess.shape == p_jac.shape
+
+        err = (1 - x * x) * p_hess - 2 * x * p_jac + n * (n + 1) * p
+        np.testing.assert_allclose(err, 0, atol=1e-10)
+
+    @pytest.mark.parametrize("n_max", [1, 2, 4, 8, 16, 32])
+    @pytest.mark.parametrize("x_shape", [(10,), (4, 9), (3, 5, 7)])
+    def test_all_ode(self, n_max, x_shape):
+        rng = np.random.default_rng(1234)
+
+        x = rng.uniform(-1, 1, x_shape)
+        p, p_jac, p_hess = legendre_p_all(n_max, x, diff_n=2)
+
+        n = np.arange(n_max + 1)
+        n = np.expand_dims(n, axis = tuple(range(1, x.ndim + 1)))
+
+        assert p.shape == (len(n),) + x.shape
+        assert p_jac.shape == p.shape
+        assert p_hess.shape == p_jac.shape
+
+        err = (1 - x * x) * p_hess - 2 * x * p_jac + n * (n + 1) * p
+        np.testing.assert_allclose(err, 0, atol=1e-10)
+
+
+class TestAssocLegendreP:
+    def test_assoc_legendre_gh23101(self):
+        z = np.array([-1, -.5, 0, .5, 1])
+        expected = assoc_legendre_p_1_0(z)
+        result = assoc_legendre_p(1, 0, z)
+        assert_allclose(np.squeeze(result), expected)
+
+        expected = assoc_legendre_p_3_0(z)
+        result = assoc_legendre_p(3, 0, z)
+        assert_allclose(np.squeeze(result), expected)
+
+    @pytest.mark.parametrize("shape", [(10,), (4, 9), (3, 5, 7, 10)])
+    @pytest.mark.parametrize("m_max", [5, 4])
+    @pytest.mark.parametrize("n_max", [7, 10])
+    def test_lpmn(self, shape, n_max, m_max):
+        rng = np.random.default_rng(1234)
+
+        x = rng.uniform(-0.99, 0.99, shape)
+        p_all, p_all_jac, p_all_hess = \
+            assoc_legendre_p_all(n_max, m_max, x, diff_n=2)
+
+        n = np.arange(n_max + 1)
+        n = np.expand_dims(n, axis = tuple(range(1, x.ndim + 2)))
+
+        m = np.concatenate([np.arange(m_max + 1), np.arange(-m_max, 0)])
+        m = np.expand_dims(m, axis = (0,) + tuple(range(2, x.ndim + 2)))
+
+        x = np.expand_dims(x, axis = (0, 1))
+        p, p_jac, p_hess = assoc_legendre_p(n, m, x, diff_n=2)
+
+        np.testing.assert_allclose(p, p_all)
+        np.testing.assert_allclose(p_jac, p_all_jac)
+        np.testing.assert_allclose(p_hess, p_all_hess)
+
+    @pytest.mark.parametrize("shape", [(10,), (4, 9), (3, 5, 7, 10)])
+    @pytest.mark.parametrize("norm", [True, False])
+    def test_ode(self, shape, norm):
+        rng = np.random.default_rng(1234)
+
+        n = rng.integers(0, 10, shape)
+        m = rng.integers(-10, 10, shape)
+        x = rng.uniform(-1, 1, shape)
+
+        p, p_jac, p_hess = assoc_legendre_p(n, m, x, norm=norm, diff_n=2)
+
+        assert p.shape == shape
+        assert p_jac.shape == p.shape
+        assert p_hess.shape == p_jac.shape
+
+        np.testing.assert_allclose((1 - x * x) * p_hess,
+            2 * x * p_jac - (n * (n + 1) - m * m / (1 - x * x)) * p,
+            rtol=1e-05, atol=1e-08)
+
+    @pytest.mark.parametrize("shape", [(10,), (4, 9), (3, 5, 7)])
+    def test_all(self, shape):
+        rng = np.random.default_rng(1234)
+
+        n_max = 20
+        m_max = 20
+
+        x = rng.uniform(-0.99, 0.99, shape)
+
+        p, p_jac, p_hess = assoc_legendre_p_all(n_max, m_max, x, diff_n=2)
+
+        m = np.concatenate([np.arange(m_max + 1), np.arange(-m_max, 0)])
+        n = np.arange(n_max + 1)
+
+        n = np.expand_dims(n, axis = tuple(range(1, x.ndim + 2)))
+        m = np.expand_dims(m, axis = (0,) + tuple(range(2, x.ndim + 2)))
+        np.testing.assert_allclose((1 - x * x) * p_hess,
+            2 * x * p_jac - (n * (n + 1) - m * m / (1 - x * x)) * p,
+            rtol=1e-05, atol=1e-08)
+
+    @pytest.mark.parametrize("shape", [(10,), (4, 9), (3, 5, 7)])
+    @pytest.mark.parametrize("norm", [True, False])
+    def test_specific(self, shape, norm):
+        rng = np.random.default_rng(1234)
+
+        x = rng.uniform(-0.99, 0.99, shape)
+
+        p, p_jac = assoc_legendre_p_all(4, 4, x, norm=norm, diff_n=1)
+
+        np.testing.assert_allclose(p[0, 0],
+            assoc_legendre_p_0_0(x, norm=norm))
+        np.testing.assert_allclose(p[0, 1], 0)
+        np.testing.assert_allclose(p[0, 2], 0)
+        np.testing.assert_allclose(p[0, 3], 0)
+        np.testing.assert_allclose(p[0, 4], 0)
+        np.testing.assert_allclose(p[0, -3], 0)
+        np.testing.assert_allclose(p[0, -2], 0)
+        np.testing.assert_allclose(p[0, -1], 0)
+
+        np.testing.assert_allclose(p[1, 0],
+            assoc_legendre_p_1_0(x, norm=norm))
+        np.testing.assert_allclose(p[1, 1],
+            assoc_legendre_p_1_1(x, norm=norm))
+        np.testing.assert_allclose(p[1, 2], 0)
+        np.testing.assert_allclose(p[1, 3], 0)
+        np.testing.assert_allclose(p[1, 4], 0)
+        np.testing.assert_allclose(p[1, -4], 0)
+        np.testing.assert_allclose(p[1, -3], 0)
+        np.testing.assert_allclose(p[1, -2], 0)
+        np.testing.assert_allclose(p[1, -1],
+            assoc_legendre_p_1_m1(x, norm=norm))
+
+        np.testing.assert_allclose(p[2, 0],
+            assoc_legendre_p_2_0(x, norm=norm))
+        np.testing.assert_allclose(p[2, 1],
+            assoc_legendre_p_2_1(x, norm=norm))
+        np.testing.assert_allclose(p[2, 2],
+            assoc_legendre_p_2_2(x, norm=norm))
+        np.testing.assert_allclose(p[2, 3], 0)
+        np.testing.assert_allclose(p[2, 4], 0)
+        np.testing.assert_allclose(p[2, -4], 0)
+        np.testing.assert_allclose(p[2, -3], 0)
+        np.testing.assert_allclose(p[2, -2],
+            assoc_legendre_p_2_m2(x, norm=norm))
+        np.testing.assert_allclose(p[2, -1],
+            assoc_legendre_p_2_m1(x, norm=norm))
+
+        np.testing.assert_allclose(p[3, 0],
+            assoc_legendre_p_3_0(x, norm=norm))
+        np.testing.assert_allclose(p[3, 1],
+            assoc_legendre_p_3_1(x, norm=norm))
+        np.testing.assert_allclose(p[3, 2],
+            assoc_legendre_p_3_2(x, norm=norm))
+        np.testing.assert_allclose(p[3, 3],
+            assoc_legendre_p_3_3(x, norm=norm))
+        np.testing.assert_allclose(p[3, 4], 0)
+        np.testing.assert_allclose(p[3, -4], 0)
+        np.testing.assert_allclose(p[3, -3],
+            assoc_legendre_p_3_m3(x, norm=norm))
+        np.testing.assert_allclose(p[3, -2],
+            assoc_legendre_p_3_m2(x, norm=norm))
+        np.testing.assert_allclose(p[3, -1],
+            assoc_legendre_p_3_m1(x, norm=norm))
+
+        np.testing.assert_allclose(p[4, 0],
+            assoc_legendre_p_4_0(x, norm=norm))
+        np.testing.assert_allclose(p[4, 1],
+            assoc_legendre_p_4_1(x, norm=norm))
+        np.testing.assert_allclose(p[4, 2],
+            assoc_legendre_p_4_2(x, norm=norm))
+        np.testing.assert_allclose(p[4, 3],
+            assoc_legendre_p_4_3(x, norm=norm))
+        np.testing.assert_allclose(p[4, 4],
+            assoc_legendre_p_4_4(x, norm=norm))
+        np.testing.assert_allclose(p[4, -4],
+            assoc_legendre_p_4_m4(x, norm=norm))
+        np.testing.assert_allclose(p[4, -3],
+            assoc_legendre_p_4_m3(x, norm=norm))
+        np.testing.assert_allclose(p[4, -2],
+            assoc_legendre_p_4_m2(x, norm=norm))
+        np.testing.assert_allclose(p[4, -1],
+            assoc_legendre_p_4_m1(x, norm=norm))
+
+        np.testing.assert_allclose(p_jac[0, 0],
+            assoc_legendre_p_0_0_jac(x, norm=norm))
+        np.testing.assert_allclose(p_jac[0, 1], 0)
+        np.testing.assert_allclose(p_jac[0, 2], 0)
+        np.testing.assert_allclose(p_jac[0, 3], 0)
+        np.testing.assert_allclose(p_jac[0, 4], 0)
+        np.testing.assert_allclose(p_jac[0, -4], 0)
+        np.testing.assert_allclose(p_jac[0, -3], 0)
+        np.testing.assert_allclose(p_jac[0, -2], 0)
+        np.testing.assert_allclose(p_jac[0, -1], 0)
+
+        np.testing.assert_allclose(p_jac[1, 0],
+            assoc_legendre_p_1_0_jac(x, norm=norm))
+        np.testing.assert_allclose(p_jac[1, 1],
+            assoc_legendre_p_1_1_jac(x, norm=norm))
+        np.testing.assert_allclose(p_jac[1, 2], 0)
+        np.testing.assert_allclose(p_jac[1, 3], 0)
+        np.testing.assert_allclose(p_jac[1, 4], 0)
+        np.testing.assert_allclose(p_jac[1, -4], 0)
+        np.testing.assert_allclose(p_jac[1, -3], 0)
+        np.testing.assert_allclose(p_jac[1, -2], 0)
+        np.testing.assert_allclose(p_jac[1, -1],
+            assoc_legendre_p_1_m1_jac(x, norm=norm))
+
+        np.testing.assert_allclose(p_jac[2, 0],
+            assoc_legendre_p_2_0_jac(x, norm=norm))
+        np.testing.assert_allclose(p_jac[2, 1],
+            assoc_legendre_p_2_1_jac(x, norm=norm))
+        np.testing.assert_allclose(p_jac[2, 2],
+            assoc_legendre_p_2_2_jac(x, norm=norm))
+        np.testing.assert_allclose(p_jac[2, 3], 0)
+        np.testing.assert_allclose(p_jac[2, 4], 0)
+        np.testing.assert_allclose(p_jac[2, -4], 0)
+        np.testing.assert_allclose(p_jac[2, -3], 0)
+        np.testing.assert_allclose(p_jac[2, -2],
+            assoc_legendre_p_2_m2_jac(x, norm=norm))
+        np.testing.assert_allclose(p_jac[2, -1],
+            assoc_legendre_p_2_m1_jac(x, norm=norm))
+
+        np.testing.assert_allclose(p_jac[3, 0],
+            assoc_legendre_p_3_0_jac(x, norm=norm))
+        np.testing.assert_allclose(p_jac[3, 1],
+            assoc_legendre_p_3_1_jac(x, norm=norm))
+        np.testing.assert_allclose(p_jac[3, 2],
+            assoc_legendre_p_3_2_jac(x, norm=norm))
+        np.testing.assert_allclose(p_jac[3, 3],
+            assoc_legendre_p_3_3_jac(x, norm=norm))
+        np.testing.assert_allclose(p_jac[3, 4], 0)
+        np.testing.assert_allclose(p_jac[3, -4], 0)
+        np.testing.assert_allclose(p_jac[3, -3],
+            assoc_legendre_p_3_m3_jac(x, norm=norm))
+        np.testing.assert_allclose(p_jac[3, -2],
+            assoc_legendre_p_3_m2_jac(x, norm=norm))
+        np.testing.assert_allclose(p_jac[3, -1],
+            assoc_legendre_p_3_m1_jac(x, norm=norm))
+
+        np.testing.assert_allclose(p_jac[4, 0],
+            assoc_legendre_p_4_0_jac(x, norm=norm))
+        np.testing.assert_allclose(p_jac[4, 1],
+            assoc_legendre_p_4_1_jac(x, norm=norm))
+        np.testing.assert_allclose(p_jac[4, 2],
+            assoc_legendre_p_4_2_jac(x, norm=norm))
+        np.testing.assert_allclose(p_jac[4, 3],
+            assoc_legendre_p_4_3_jac(x, norm=norm))
+        np.testing.assert_allclose(p_jac[4, 4],
+            assoc_legendre_p_4_4_jac(x, norm=norm))
+        np.testing.assert_allclose(p_jac[4, -4],
+            assoc_legendre_p_4_m4_jac(x, norm=norm))
+        np.testing.assert_allclose(p_jac[4, -3],
+            assoc_legendre_p_4_m3_jac(x, norm=norm))
+        np.testing.assert_allclose(p_jac[4, -2],
+            assoc_legendre_p_4_m2_jac(x, norm=norm))
+        np.testing.assert_allclose(p_jac[4, -1],
+            assoc_legendre_p_4_m1_jac(x, norm=norm))
+
+    @pytest.mark.parametrize("m_max", [7])
+    @pytest.mark.parametrize("n_max", [10])
+    @pytest.mark.parametrize("x", [1, -1])
+    def test_all_limits(self, m_max, n_max, x):
+        p, p_jac = assoc_legendre_p_all(n_max, m_max, x, diff_n=1)
+
+        n = np.arange(n_max + 1)
+
+        np.testing.assert_allclose(p_jac[:, 0],
+            pow(x, n + 1) * n * (n + 1) / 2)
+        np.testing.assert_allclose(p_jac[:, 1],
+            np.where(n >= 1, pow(x, n) * np.inf, 0))
+        np.testing.assert_allclose(p_jac[:, 2],
+            np.where(n >= 2, -pow(x, n + 1) * (n + 2) * (n + 1) * n * (n - 1) / 4, 0))
+        np.testing.assert_allclose(p_jac[:, -2],
+            np.where(n >= 2, -pow(x, n + 1) / 4, 0))
+        np.testing.assert_allclose(p_jac[:, -1],
+            np.where(n >= 1, -pow(x, n) * np.inf, 0))
+
+        for m in range(3, m_max + 1):
+            np.testing.assert_allclose(p_jac[:, m], 0)
+            np.testing.assert_allclose(p_jac[:, -m], 0)
+
+    @pytest.mark.parametrize("n", np.arange(0, 20))
+    def test_assoc_legendre_p_norm_m0(self, n):
+        # gh 24099
+        m = 0
+        z = np.linspace(-1, 1, 101)
+        p = assoc_legendre_p(n, m, z, norm=False)
+        p_norm = assoc_legendre_p(n, m, z, norm=True)
+        factor = np.sqrt((2 * n + 1) / 2)
+        np.testing.assert_allclose(p_norm, factor * p)
+
+    @pytest.mark.parametrize("n", np.arange(0, 20))
+    def test_assoc_legendre_p_all_norm_m0(self, n):
+        # gh 24099
+        m = 0
+        z = np.linspace(-1, 1, 101)
+        p_all = assoc_legendre_p_all(n, m, z, norm=False)[0, : n + 1, 0, :]
+        p_norm_all = assoc_legendre_p_all(n, m, z, norm=True)[0, : n + 1, 0, :]
+        factor = np.sqrt((2 * np.arange(n + 1) + 1) / 2)
+        factor = factor[:, np.newaxis]
+        np.testing.assert_allclose(p_norm_all, factor * p_all)
+
+
+class TestMultiAssocLegendreP:
+    @pytest.mark.parametrize("shape", [(1000,), (4, 9), (3, 5, 7)])
+    @pytest.mark.parametrize("branch_cut", [2, 3])
+    @pytest.mark.parametrize("z_min, z_max", [(-10 - 10j, 10 + 10j),
+        (-1, 1), (-10j, 10j)])
+    @pytest.mark.parametrize("norm", [True, False])
+    def test_specific(self, shape, branch_cut, z_min, z_max, norm):
+        rng = np.random.default_rng(1234)
+
+        z = rng.uniform(z_min.real, z_max.real, shape) + \
+            1j * rng.uniform(z_min.imag, z_max.imag, shape)
+
+        p, p_jac = assoc_legendre_p_all(4, 4,
+            z, branch_cut=branch_cut, norm=norm, diff_n=1)
+
+        np.testing.assert_allclose(p[0, 0],
+            assoc_legendre_p_0_0(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p[0, 1], 0)
+        np.testing.assert_allclose(p[0, 2], 0)
+        np.testing.assert_allclose(p[0, 3], 0)
+        np.testing.assert_allclose(p[0, 4], 0)
+        np.testing.assert_allclose(p[0, -4], 0)
+        np.testing.assert_allclose(p[0, -3], 0)
+        np.testing.assert_allclose(p[0, -2], 0)
+        np.testing.assert_allclose(p[0, -1], 0)
+
+        np.testing.assert_allclose(p[1, 0],
+            assoc_legendre_p_1_0(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p[1, 1],
+            assoc_legendre_p_1_1(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p[1, 2], 0)
+        np.testing.assert_allclose(p[1, 3], 0)
+        np.testing.assert_allclose(p[1, 4], 0)
+        np.testing.assert_allclose(p[1, -4], 0)
+        np.testing.assert_allclose(p[1, -3], 0)
+        np.testing.assert_allclose(p[1, -2], 0)
+        np.testing.assert_allclose(p[1, -1],
+            assoc_legendre_p_1_m1(z, branch_cut=branch_cut, norm=norm))
+
+        np.testing.assert_allclose(p[2, 0],
+            assoc_legendre_p_2_0(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p[2, 1],
+            assoc_legendre_p_2_1(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p[2, 2],
+            assoc_legendre_p_2_2(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p[2, 3], 0)
+        np.testing.assert_allclose(p[2, 4], 0)
+        np.testing.assert_allclose(p[2, -4], 0)
+        np.testing.assert_allclose(p[2, -3], 0)
+        np.testing.assert_allclose(p[2, -2],
+            assoc_legendre_p_2_m2(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p[2, -1],
+            assoc_legendre_p_2_m1(z, branch_cut=branch_cut, norm=norm))
+
+        np.testing.assert_allclose(p[3, 0],
+            assoc_legendre_p_3_0(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p[3, 1],
+            assoc_legendre_p_3_1(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p[3, 2],
+            assoc_legendre_p_3_2(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p[3, 3],
+            assoc_legendre_p_3_3(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p[3, 4], 0)
+        np.testing.assert_allclose(p[3, -4], 0)
+        np.testing.assert_allclose(p[3, -3],
+            assoc_legendre_p_3_m3(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p[3, -2],
+            assoc_legendre_p_3_m2(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p[3, -1],
+            assoc_legendre_p_3_m1(z, branch_cut=branch_cut, norm=norm))
+
+        np.testing.assert_allclose(p[4, 0],
+            assoc_legendre_p_4_0(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p[4, 1],
+            assoc_legendre_p_4_1(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p[4, 2],
+            assoc_legendre_p_4_2(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p[4, 3],
+            assoc_legendre_p_4_3(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p[4, 4],
+            assoc_legendre_p_4_4(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p[4, -4],
+            assoc_legendre_p_4_m4(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p[4, -3],
+            assoc_legendre_p_4_m3(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p[4, -2],
+            assoc_legendre_p_4_m2(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p[4, -1],
+            assoc_legendre_p_4_m1(z, branch_cut=branch_cut, norm=norm))
+
+        np.testing.assert_allclose(p_jac[0, 0],
+            assoc_legendre_p_0_0_jac(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p_jac[0, 1], 0)
+        np.testing.assert_allclose(p_jac[0, 2], 0)
+        np.testing.assert_allclose(p_jac[0, 3], 0)
+        np.testing.assert_allclose(p_jac[0, 4], 0)
+        np.testing.assert_allclose(p_jac[0, -4], 0)
+        np.testing.assert_allclose(p_jac[0, -3], 0)
+        np.testing.assert_allclose(p_jac[0, -2], 0)
+        np.testing.assert_allclose(p_jac[0, -1], 0)
+
+        np.testing.assert_allclose(p_jac[1, 0],
+            assoc_legendre_p_1_0_jac(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p_jac[1, 1],
+            assoc_legendre_p_1_1_jac(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p_jac[1, 2], 0)
+        np.testing.assert_allclose(p_jac[1, 3], 0)
+        np.testing.assert_allclose(p_jac[1, 4], 0)
+        np.testing.assert_allclose(p_jac[1, -4], 0)
+        np.testing.assert_allclose(p_jac[1, -3], 0)
+        np.testing.assert_allclose(p_jac[1, -2], 0)
+        np.testing.assert_allclose(p_jac[1, -1],
+            assoc_legendre_p_1_m1_jac(z, branch_cut=branch_cut, norm=norm))
+
+        np.testing.assert_allclose(p_jac[2, 0],
+            assoc_legendre_p_2_0_jac(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p_jac[2, 1],
+            assoc_legendre_p_2_1_jac(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p_jac[2, 2],
+            assoc_legendre_p_2_2_jac(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p_jac[2, 3], 0)
+        np.testing.assert_allclose(p_jac[2, 4], 0)
+        np.testing.assert_allclose(p_jac[2, -4], 0)
+        np.testing.assert_allclose(p_jac[2, -3], 0)
+        np.testing.assert_allclose(p_jac[2, -2],
+            assoc_legendre_p_2_m2_jac(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p_jac[2, -1],
+            assoc_legendre_p_2_m1_jac(z, branch_cut=branch_cut, norm=norm))
+
+        np.testing.assert_allclose(p_jac[3, 0],
+            assoc_legendre_p_3_0_jac(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p_jac[3, 1],
+            assoc_legendre_p_3_1_jac(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p_jac[3, 2],
+            assoc_legendre_p_3_2_jac(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p_jac[3, 3],
+            assoc_legendre_p_3_3_jac(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p_jac[3, 4], 0)
+        np.testing.assert_allclose(p_jac[3, -4], 0)
+        np.testing.assert_allclose(p_jac[3, -3],
+            assoc_legendre_p_3_m3_jac(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p_jac[3, -2],
+            assoc_legendre_p_3_m2_jac(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p_jac[3, -1],
+            assoc_legendre_p_3_m1_jac(z, branch_cut=branch_cut, norm=norm))
+
+        np.testing.assert_allclose(p_jac[4, 0],
+            assoc_legendre_p_4_0_jac(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p_jac[4, 1],
+            assoc_legendre_p_4_1_jac(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p_jac[4, 2],
+            assoc_legendre_p_4_2_jac(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p_jac[4, 3],
+            assoc_legendre_p_4_3_jac(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p_jac[4, 4],
+            assoc_legendre_p_4_4_jac(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p_jac[4, -4],
+            assoc_legendre_p_4_m4_jac(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p_jac[4, -3],
+            assoc_legendre_p_4_m3_jac(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p_jac[4, -2],
+            assoc_legendre_p_4_m2_jac(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p_jac[4, -1],
+            assoc_legendre_p_4_m1_jac(z, branch_cut=branch_cut, norm=norm))
+
+class TestSphLegendreP:
+    @pytest.mark.parametrize("shape", [(10,), (4, 9), (3, 5, 7)])
+    def test_specific(self, shape):
+        rng = np.random.default_rng(1234)
+
+        theta = rng.uniform(-np.pi, np.pi, shape)
+
+        p, p_jac = sph_legendre_p_all(4, 4, theta, diff_n=1)
+
+        np.testing.assert_allclose(p[0, 0],
+            sph_legendre_p_0_0(theta))
+        np.testing.assert_allclose(p[0, 1], 0)
+        np.testing.assert_allclose(p[0, 2], 0)
+        np.testing.assert_allclose(p[0, 3], 0)
+        np.testing.assert_allclose(p[0, 4], 0)
+        np.testing.assert_allclose(p[0, -3], 0)
+        np.testing.assert_allclose(p[0, -2], 0)
+        np.testing.assert_allclose(p[0, -1], 0)
+
+        np.testing.assert_allclose(p[1, 0],
+            sph_legendre_p_1_0(theta))
+        np.testing.assert_allclose(p[1, 1],
+            sph_legendre_p_1_1(theta))
+        np.testing.assert_allclose(p[1, 2], 0)
+        np.testing.assert_allclose(p[1, 3], 0)
+        np.testing.assert_allclose(p[1, 4], 0)
+        np.testing.assert_allclose(p[1, -4], 0)
+        np.testing.assert_allclose(p[1, -3], 0)
+        np.testing.assert_allclose(p[1, -2], 0)
+        np.testing.assert_allclose(p[1, -1],
+            sph_legendre_p_1_m1(theta))
+
+        np.testing.assert_allclose(p[2, 0],
+            sph_legendre_p_2_0(theta))
+        np.testing.assert_allclose(p[2, 1],
+            sph_legendre_p_2_1(theta))
+        np.testing.assert_allclose(p[2, 2],
+            sph_legendre_p_2_2(theta))
+        np.testing.assert_allclose(p[2, 3], 0)
+        np.testing.assert_allclose(p[2, 4], 0)
+        np.testing.assert_allclose(p[2, -4], 0)
+        np.testing.assert_allclose(p[2, -3], 0)
+        np.testing.assert_allclose(p[2, -2],
+            sph_legendre_p_2_m2(theta))
+        np.testing.assert_allclose(p[2, -1],
+            sph_legendre_p_2_m1(theta))
+
+        np.testing.assert_allclose(p[3, 0],
+            sph_legendre_p_3_0(theta))
+        np.testing.assert_allclose(p[3, 1],
+            sph_legendre_p_3_1(theta))
+        np.testing.assert_allclose(p[3, 2],
+            sph_legendre_p_3_2(theta))
+        np.testing.assert_allclose(p[3, 3],
+            sph_legendre_p_3_3(theta))
+        np.testing.assert_allclose(p[3, 4], 0)
+        np.testing.assert_allclose(p[3, -4], 0)
+        np.testing.assert_allclose(p[3, -3],
+            sph_legendre_p_3_m3(theta))
+        np.testing.assert_allclose(p[3, -2],
+            sph_legendre_p_3_m2(theta))
+        np.testing.assert_allclose(p[3, -1],
+            sph_legendre_p_3_m1(theta))
+
+        np.testing.assert_allclose(p[4, 0],
+            sph_legendre_p_4_0(theta))
+        np.testing.assert_allclose(p[4, 1],
+            sph_legendre_p_4_1(theta))
+        np.testing.assert_allclose(p[4, 2],
+            sph_legendre_p_4_2(theta))
+        np.testing.assert_allclose(p[4, 3],
+            sph_legendre_p_4_3(theta))
+        np.testing.assert_allclose(p[4, 4],
+            sph_legendre_p_4_4(theta))
+        np.testing.assert_allclose(p[4, -4],
+            sph_legendre_p_4_m4(theta))
+        np.testing.assert_allclose(p[4, -3],
+            sph_legendre_p_4_m3(theta))
+        np.testing.assert_allclose(p[4, -2],
+            sph_legendre_p_4_m2(theta))
+        np.testing.assert_allclose(p[4, -1],
+            sph_legendre_p_4_m1(theta))
+
+        np.testing.assert_allclose(p_jac[0, 0],
+            sph_legendre_p_0_0_jac(theta))
+        np.testing.assert_allclose(p_jac[0, 1], 0)
+        np.testing.assert_allclose(p_jac[0, 2], 0)
+        np.testing.assert_allclose(p_jac[0, 3], 0)
+        np.testing.assert_allclose(p_jac[0, 4], 0)
+        np.testing.assert_allclose(p_jac[0, -3], 0)
+        np.testing.assert_allclose(p_jac[0, -2], 0)
+        np.testing.assert_allclose(p_jac[0, -1], 0)
+
+        np.testing.assert_allclose(p_jac[1, 0],
+            sph_legendre_p_1_0_jac(theta))
+        np.testing.assert_allclose(p_jac[1, 1],
+            sph_legendre_p_1_1_jac(theta))
+        np.testing.assert_allclose(p_jac[1, 2], 0)
+        np.testing.assert_allclose(p_jac[1, 3], 0)
+        np.testing.assert_allclose(p_jac[1, 4], 0)
+        np.testing.assert_allclose(p_jac[1, -4], 0)
+        np.testing.assert_allclose(p_jac[1, -3], 0)
+        np.testing.assert_allclose(p_jac[1, -2], 0)
+        np.testing.assert_allclose(p_jac[1, -1],
+            sph_legendre_p_1_m1_jac(theta))
+
+        np.testing.assert_allclose(p_jac[2, 0],
+            sph_legendre_p_2_0_jac(theta))
+        np.testing.assert_allclose(p_jac[2, 1],
+            sph_legendre_p_2_1_jac(theta))
+        np.testing.assert_allclose(p_jac[2, 2],
+            sph_legendre_p_2_2_jac(theta))
+        np.testing.assert_allclose(p_jac[2, 3], 0)
+        np.testing.assert_allclose(p_jac[2, 4], 0)
+        np.testing.assert_allclose(p_jac[2, -4], 0)
+        np.testing.assert_allclose(p_jac[2, -3], 0)
+        np.testing.assert_allclose(p_jac[2, -2],
+            sph_legendre_p_2_m2_jac(theta))
+        np.testing.assert_allclose(p_jac[2, -1],
+            sph_legendre_p_2_m1_jac(theta))
+
+        np.testing.assert_allclose(p_jac[3, 0],
+            sph_legendre_p_3_0_jac(theta))
+        np.testing.assert_allclose(p_jac[3, 1],
+            sph_legendre_p_3_1_jac(theta))
+        np.testing.assert_allclose(p_jac[3, 2],
+            sph_legendre_p_3_2_jac(theta))
+        np.testing.assert_allclose(p_jac[3, 3],
+            sph_legendre_p_3_3_jac(theta))
+        np.testing.assert_allclose(p_jac[3, 4], 0)
+        np.testing.assert_allclose(p_jac[3, -4], 0)
+        np.testing.assert_allclose(p_jac[3, -3],
+            sph_legendre_p_3_m3_jac(theta))
+        np.testing.assert_allclose(p_jac[3, -2],
+            sph_legendre_p_3_m2_jac(theta))
+        np.testing.assert_allclose(p_jac[3, -1],
+            sph_legendre_p_3_m1_jac(theta))
+
+        np.testing.assert_allclose(p_jac[4, 0],
+            sph_legendre_p_4_0_jac(theta))
+        np.testing.assert_allclose(p_jac[4, 1],
+            sph_legendre_p_4_1_jac(theta))
+        np.testing.assert_allclose(p_jac[4, 2],
+            sph_legendre_p_4_2_jac(theta))
+        np.testing.assert_allclose(p_jac[4, 3],
+            sph_legendre_p_4_3_jac(theta))
+        np.testing.assert_allclose(p_jac[4, 4],
+            sph_legendre_p_4_4_jac(theta))
+        np.testing.assert_allclose(p_jac[4, -4],
+            sph_legendre_p_4_m4_jac(theta))
+        np.testing.assert_allclose(p_jac[4, -3],
+            sph_legendre_p_4_m3_jac(theta))
+        np.testing.assert_allclose(p_jac[4, -2],
+            sph_legendre_p_4_m2_jac(theta))
+        np.testing.assert_allclose(p_jac[4, -1],
+            sph_legendre_p_4_m1_jac(theta))
+
+    @pytest.mark.parametrize("shape", [(10,), (4, 9), (3, 5, 7, 10)])
+    def test_ode(self, shape):
+        rng = np.random.default_rng(1234)
+
+        n = rng.integers(0, 10, shape)
+        m = rng.integers(-10, 10, shape)
+        theta = rng.uniform(-np.pi, np.pi, shape)
+
+        p, p_jac, p_hess = sph_legendre_p(n, m, theta, diff_n=2)
+
+        assert p.shape == shape
+        assert p_jac.shape == p.shape
+        assert p_hess.shape == p_jac.shape
+
+        np.testing.assert_allclose(np.sin(theta) * p_hess, -np.cos(theta) * p_jac
+            - (n * (n + 1) * np.sin(theta) - m * m / np.sin(theta)) * p,
+            rtol=1e-05, atol=1e-08)
+
+class TestLegendreFunctions:
+    """
+    @pytest.mark.parametrize("m_max", [3])
+    @pytest.mark.parametrize("n_max", [5])
+    @pytest.mark.parametrize("z", [-1])
+    def test_clpmn_all_limits(self, m_max, n_max, z):
+        rng = np.random.default_rng(1234)
+
+        type = 2
+
+        p, p_jac = special.clpmn_all(m_max, n_max, type, z, diff_n=1)
+
+        n = np.arange(n_max + 1)
+
+        np.testing.assert_allclose(p_jac[0], pow(z, n + 1) * n * (n + 1) / 2)
+        np.testing.assert_allclose(p_jac[1], np.where(n >= 1, pow(z, n) * np.inf, 0))
+        np.testing.assert_allclose(p_jac[2], np.where(n >= 2,
+            -pow(z, n + 1) * (n + 2) * (n + 1) * n * (n - 1) / 4, 0))
+        np.testing.assert_allclose(p_jac[-2], np.where(n >= 2, -pow(z, n + 1) / 4, 0))
+        np.testing.assert_allclose(p_jac[-1], np.where(n >= 1, -pow(z, n) * np.inf, 0))
+
+        for m in range(3, m_max + 1):
+            np.testing.assert_allclose(p_jac[m], 0)
+            np.testing.assert_allclose(p_jac[-m], 0)
+    """
+
+    def test_lpmv(self):
+        lp = special.lpmv(0, 2, .5)
+        assert_allclose(lp, -0.125, atol=1.5e-7, rtol=0)
+        lp = special.lpmv(0, 40, .001)
+        assert_allclose(lp, 0.1252678976534484, atol=1.5e-7, rtol=0)
+
+        # XXX: this is outside the domain of the current implementation,
+        #      so ensure it returns a NaN rather than a wrong answer.
+        with np.errstate(all='ignore'):
+            lp = special.lpmv(-1,-1,.001)
+        assert lp != 0 or np.isnan(lp)
+
+    def test_lqmn(self):
+        lqmnf = special.lqmn(0, 2, .5)
+        lqf = special.lqn(2, .5)
+        assert_allclose(lqmnf[0][0], lqf[0], atol=1.5e-4, rtol=0)
+        assert_allclose(lqmnf[1][0], lqf[1], atol=1.5e-4, rtol=0)
+
+    def test_lqmn_gt1(self):
+        """algorithm for real arguments changes at 1.0001
+           test against analytical result for m=2, n=1
+        """
+        x0 = 1.0001
+        delta = 0.00002
+        for x in (x0-delta, x0+delta):
+            lq = special.lqmn(2, 1, x)[0][-1, -1]
+            expected = 2/(x*x-1)
+            assert_allclose(lq, expected, atol=1.5e-7, rtol=0)
+
+    def test_lqmn_shape(self):
+        a, b = special.lqmn(4, 4, 1.1)
+        assert_equal(a.shape, (5, 5))
+        assert_equal(b.shape, (5, 5))
+
+        a, b = special.lqmn(4, 0, 1.1)
+        assert_equal(a.shape, (5, 1))
+        assert_equal(b.shape, (5, 1))
+
+    def test_lqn(self):
+        lqf = special.lqn(2, .5)
+        assert_allclose(lqf, (np.array([0.5493, -0.7253, -0.8187]),
+                              np.array([1.3333, 1.216, -0.8427])),
+                        atol=1.5e-4, rtol=0)
+
+    @pytest.mark.parametrize("function", [special.lqn])
+    @pytest.mark.parametrize("n", [1, 2, 4, 8, 16, 32])
+    @pytest.mark.parametrize("z_complex", [False, True])
+    @pytest.mark.parametrize("z_inexact", [False, True])
+    @pytest.mark.parametrize(
+        "input_shape",
+        [
+            (), (1, ), (2, ), (2, 1), (1, 2), (2, 2), (2, 2, 1), (2, 2, 2)
+        ]
+    )
+    def test_array_inputs_lxn(self, function, n, z_complex, z_inexact, input_shape):
+        """Tests for correct output shapes."""
+        rng = np.random.default_rng(1234)
+        if z_inexact:
+            z = rng.integers(-3, 3, size=input_shape)
+        else:
+            z = rng.uniform(-1, 1, size=input_shape)
+
+        if z_complex:
+            z = 1j * z + 0.5j * z
+
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", category=DeprecationWarning)
+            P_z, P_d_z = function(n, z)
+        assert P_z.shape == (n + 1, ) + input_shape
+        assert P_d_z.shape == (n + 1, ) + input_shape
+
+    @pytest.mark.parametrize("function", [special.lqmn])
+    @pytest.mark.parametrize(
+        "m,n",
+        [(0, 1), (1, 2), (1, 4), (3, 8), (11, 16), (19, 32)]
+    )
+    @pytest.mark.parametrize("z_inexact", [False, True])
+    @pytest.mark.parametrize(
+        "input_shape", [
+            (), (1, ), (2, ), (2, 1), (1, 2), (2, 2), (2, 2, 1)
+        ]
+    )
+    def test_array_inputs_lxmn(self, function, m, n, z_inexact, input_shape):
+        """Tests for correct output shapes and dtypes."""
+        rng = np.random.default_rng(1234)
+        if z_inexact:
+            z = rng.integers(-3, 3, size=input_shape)
+        else:
+            z = rng.uniform(-1, 1, size=input_shape)
+
+        P_z, P_d_z = function(m, n, z)
+        assert P_z.shape == (m + 1, n + 1) + input_shape
+        assert P_d_z.shape == (m + 1, n + 1) + input_shape
+
+    @pytest.mark.parametrize("function", [special.lqmn])
+    @pytest.mark.parametrize(
+        "m,n",
+        [(0, 1), (1, 2), (1, 4), (3, 8), (11, 16), (19, 32)]
+    )
+    @pytest.mark.parametrize(
+        "input_shape", [
+            (), (1, ), (2, ), (2, 1), (1, 2), (2, 2), (2, 2, 1)
+        ]
+    )
+    def test_array_inputs_clxmn(self, function, m, n, input_shape):
+        """Tests for correct output shapes and dtypes."""
+        rng = np.random.default_rng(1234)
+        z = rng.uniform(-1, 1, size=input_shape)
+        z = 1j * z + 0.5j * z
+
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", category=DeprecationWarning)
+            P_z, P_d_z = function(m, n, z)
+
+        assert P_z.shape == (m + 1, n + 1) + input_shape
+        assert P_d_z.shape == (m + 1, n + 1) + input_shape
+
+def assoc_legendre_factor(n, m, norm):
+    if norm:
+        return (math.sqrt((2 * n + 1) *
+            math.factorial(n - m) / (2 * math.factorial(n + m))))
+
+    return 1
+
+def assoc_legendre_p_0_0(z, *, branch_cut=2, norm=False):
+    fac = assoc_legendre_factor(0, 0, norm)
+
+    return np.full_like(z, fac)
+
+def assoc_legendre_p_1_0(z, *, branch_cut=2, norm=False):
+    fac = assoc_legendre_factor(1, 0, norm)
+
+    return fac * z
+
+def assoc_legendre_p_1_1(z, *, branch_cut=2, norm=False):
+    branch_sign = np.where(branch_cut == 3, np.where(np.signbit(np.real(z)), 1, -1), -1)
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(1, 1, norm)
+
+    w = np.sqrt(np.where(branch_cut == 3, z * z - 1, 1 - z * z))
+
+    return branch_cut_sign * branch_sign * fac * w
+
+def assoc_legendre_p_1_m1(z, *, branch_cut=2, norm=False):
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(1, -1, norm)
+
+    return (-branch_cut_sign * fac *
+        assoc_legendre_p_1_1(z, branch_cut=branch_cut) / 2)
+
+def assoc_legendre_p_2_0(z, *, branch_cut=2, norm=False):
+    fac = assoc_legendre_factor(2, 0, norm)
+
+    return fac * (3 * z * z - 1) / 2
+
+def assoc_legendre_p_2_1(z, *, branch_cut=2, norm=False):
+    fac = assoc_legendre_factor(2, 1, norm)
+
+    return (3 * fac * z *
+        assoc_legendre_p_1_1(z, branch_cut=branch_cut))
+
+def assoc_legendre_p_2_2(z, *, branch_cut=2, norm=False):
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(2, 2, norm)
+
+    return 3 * branch_cut_sign * fac * (1 - z * z)
+
+def assoc_legendre_p_2_m2(z, *, branch_cut=2, norm=False):
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(2, -2, norm)
+
+    return branch_cut_sign * fac * (1 - z * z) / 8
+
+def assoc_legendre_p_2_m1(z, *, branch_cut=2, norm=False):
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(2, -1, norm)
+
+    return (-branch_cut_sign * fac * z *
+        assoc_legendre_p_1_1(z, branch_cut=branch_cut) / 2)
+
+def assoc_legendre_p_3_0(z, *, branch_cut=2, norm=False):
+    fac = assoc_legendre_factor(3, 0, norm)
+
+    return fac * (5 * z * z - 3) * z / 2
+
+def assoc_legendre_p_3_1(z, *, branch_cut=2, norm=False):
+    fac = assoc_legendre_factor(3, 1, norm)
+
+    return (3 * fac * (5 * z * z - 1) *
+        assoc_legendre_p_1_1(z, branch_cut=branch_cut) / 2)
+
+def assoc_legendre_p_3_2(z, *, branch_cut=2, norm=False):
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(3, 2, norm)
+
+    return 15 * branch_cut_sign * fac * (1 - z * z) * z
+
+def assoc_legendre_p_3_3(z, *, branch_cut=2, norm=False):
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(3, 3, norm)
+
+    return (15 * branch_cut_sign * fac * (1 - z * z) *
+        assoc_legendre_p_1_1(z, branch_cut=branch_cut))
+
+def assoc_legendre_p_3_m3(z, *, branch_cut=2, norm=False):
+    fac = assoc_legendre_factor(3, -3, norm)
+
+    return (fac * (z * z - 1) *
+        assoc_legendre_p_1_1(z, branch_cut=branch_cut) / 48)
+
+def assoc_legendre_p_3_m2(z, *, branch_cut=2, norm=False):
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(3, -2, norm)
+
+    return branch_cut_sign * fac * (1 - z * z) * z / 8
+
+def assoc_legendre_p_3_m1(z, *, branch_cut=2, norm=False):
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(3, -1, norm)
+
+    return (branch_cut_sign * fac * (1 - 5 * z * z) *
+        assoc_legendre_p_1_1(z, branch_cut=branch_cut) / 8)
+
+def assoc_legendre_p_4_0(z, *, branch_cut=2, norm=False):
+    fac = assoc_legendre_factor(4, 0, norm)
+
+    return fac * ((35 * z * z - 30) * z * z + 3) / 8
+
+def assoc_legendre_p_4_1(z, *, branch_cut=2, norm=False):
+    fac = assoc_legendre_factor(4, 1, norm)
+
+    return (5 * fac * (7 * z * z - 3) * z *
+       assoc_legendre_p_1_1(z, branch_cut=branch_cut) / 2)
+
+def assoc_legendre_p_4_2(z, *, branch_cut=2, norm=False):
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(4, 2, norm)
+
+    return 15 * branch_cut_sign * fac * ((8 - 7 * z * z) * z * z - 1) / 2
+
+def assoc_legendre_p_4_3(z, *, branch_cut=2, norm=False):
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(4, 3, norm)
+
+    return (105 * branch_cut_sign * fac * (1 - z * z) * z *
+        assoc_legendre_p_1_1(z, branch_cut=branch_cut))
+
+def assoc_legendre_p_4_4(z, *, branch_cut=2, norm=False):
+    fac = assoc_legendre_factor(4, 4, norm)
+
+    return 105 * fac * np.square(z * z - 1)
+
+def assoc_legendre_p_4_m4(z, *, branch_cut=2, norm=False):
+    fac = assoc_legendre_factor(4, -4, norm)
+
+    return fac * np.square(z * z - 1) / 384
+
+def assoc_legendre_p_4_m3(z, *, branch_cut=2, norm=False):
+    fac = assoc_legendre_factor(4, -3, norm)
+
+    return (fac * (z * z - 1) * z *
+        assoc_legendre_p_1_1(z, branch_cut=branch_cut) / 48)
+
+def assoc_legendre_p_4_m2(z, *, branch_cut=2, norm=False):
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(4, -2, norm)
+
+    return branch_cut_sign * fac * ((8 - 7 * z * z) * z * z - 1) / 48
+
+def assoc_legendre_p_4_m1(z, *, branch_cut=2, norm=False):
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(4, -1, norm)
+
+    return (branch_cut_sign * fac * (3 - 7 * z * z) * z *
+        assoc_legendre_p_1_1(z, branch_cut=branch_cut) / 8)
+
+def assoc_legendre_p_1_1_jac_div_z(z, branch_cut=2):
+    branch_sign = np.where(branch_cut == 3, np.where(np.signbit(np.real(z)), 1, -1), -1)
+
+    out11_div_z = (-branch_sign /
+        np.sqrt(np.where(branch_cut == 3, z * z - 1, 1 - z * z)))
+
+    return out11_div_z
+
+def assoc_legendre_p_0_0_jac(z, *, branch_cut=2, norm=False):
+    return np.zeros_like(z)
+
+def assoc_legendre_p_1_0_jac(z, *, branch_cut=2, norm=False):
+    fac = assoc_legendre_factor(1, 0, norm)
+
+    return np.full_like(z, fac)
+
+def assoc_legendre_p_1_1_jac(z, *, branch_cut=2, norm=False):
+    fac = assoc_legendre_factor(1, 1, norm)
+
+    return (fac * z *
+        assoc_legendre_p_1_1_jac_div_z(z, branch_cut=branch_cut))
+
+def assoc_legendre_p_1_m1_jac(z, *, branch_cut=2, norm=False):
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(1, -1, norm)
+
+    return (-branch_cut_sign * fac * z *
+        assoc_legendre_p_1_1_jac_div_z(z, branch_cut=branch_cut) / 2)
+
+def assoc_legendre_p_2_0_jac(z, *, branch_cut=2, norm=False):
+    fac = assoc_legendre_factor(2, 0, norm)
+
+    return 3 * fac * z
+
+def assoc_legendre_p_2_1_jac(z, *, branch_cut=2, norm=False):
+    fac = assoc_legendre_factor(2, 1, norm)
+
+    return (3 * fac * (2 * z * z - 1) *
+        assoc_legendre_p_1_1_jac_div_z(z, branch_cut=branch_cut))
+
+def assoc_legendre_p_2_2_jac(z, *, branch_cut=2, norm=False):
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(2, 2, norm)
+
+    return -6 * branch_cut_sign * fac * z
+
+def assoc_legendre_p_2_m1_jac(z, *, branch_cut=2, norm=False):
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(2, -1, norm)
+
+    return (branch_cut_sign * fac * (1 - 2 * z * z) *
+        assoc_legendre_p_1_1_jac_div_z(z, branch_cut=branch_cut) / 2)
+
+def assoc_legendre_p_2_m2_jac(z, *, branch_cut=2, norm=False):
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(2, -2, norm)
+
+    return -branch_cut_sign * fac * z / 4
+
+def assoc_legendre_p_3_0_jac(z, *, branch_cut=2, norm=False):
+    fac = assoc_legendre_factor(3, 0, norm)
+
+    return 3 * fac * (5 * z * z - 1) / 2
+
+def assoc_legendre_p_3_1_jac(z, *, branch_cut=2, norm=False):
+    fac = assoc_legendre_factor(3, 1, norm)
+
+    return (3 * fac * (15 * z * z - 11) * z *
+        assoc_legendre_p_1_1_jac_div_z(z, branch_cut=branch_cut) / 2)
+
+def assoc_legendre_p_3_2_jac(z, *, branch_cut=2, norm=False):
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(3, 2, norm)
+
+    return 15 * branch_cut_sign * fac * (1 - 3 * z * z)
+
+def assoc_legendre_p_3_3_jac(z, *, branch_cut=2, norm=False):
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(3, 3, norm)
+
+    return (45 * branch_cut_sign * fac * (1 - z * z) * z *
+        assoc_legendre_p_1_1_jac_div_z(z, branch_cut=branch_cut))
+
+def assoc_legendre_p_3_m3_jac(z, *, branch_cut=2, norm=False):
+    fac = assoc_legendre_factor(3, -3, norm)
+
+    return (fac * (z * z - 1) * z *
+        assoc_legendre_p_1_1_jac_div_z(z, branch_cut=branch_cut) / 16)
+
+def assoc_legendre_p_3_m2_jac(z, *, branch_cut=2, norm=False):
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(3, -2, norm)
+
+    return branch_cut_sign * fac * (1 - 3 * z * z) / 8
+
+def assoc_legendre_p_3_m1_jac(z, *, branch_cut=2, norm=False):
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(3, -1, norm)
+
+    return (branch_cut_sign * fac * (11 - 15 * z * z) * z *
+        assoc_legendre_p_1_1_jac_div_z(z, branch_cut=branch_cut) / 8)
+
+def assoc_legendre_p_4_0_jac(z, *, branch_cut=2, norm=False):
+    fac = assoc_legendre_factor(4, 0, norm)
+
+    return 5 * fac * (7 * z * z - 3) * z / 2
+
+def assoc_legendre_p_4_1_jac(z, *, branch_cut=2, norm=False):
+    fac = assoc_legendre_factor(4, 1, norm)
+
+    return (5 * fac * ((28 * z * z - 27) * z * z + 3) *
+        assoc_legendre_p_1_1_jac_div_z(z, branch_cut=branch_cut) / 2)
+
+def assoc_legendre_p_4_2_jac(z, *, branch_cut=2, norm=False):
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(4, 2, norm)
+
+    return 30 * branch_cut_sign * fac * (4 - 7 * z * z) * z
+
+def assoc_legendre_p_4_3_jac(z, *, branch_cut=2, norm=False):
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(4, 3, norm)
+
+    return (105 * branch_cut_sign * fac * ((5 - 4 * z * z) * z * z - 1) *
+        assoc_legendre_p_1_1_jac_div_z(z, branch_cut=branch_cut))
+
+def assoc_legendre_p_4_4_jac(z, *, branch_cut=2, norm=False):
+    fac = assoc_legendre_factor(4, 4, norm)
+
+    return 420 * fac * (z * z - 1) * z
+
+def assoc_legendre_p_4_m4_jac(z, *, branch_cut=2, norm=False):
+    fac = assoc_legendre_factor(4, -4, norm)
+
+    return fac * (z * z - 1) * z / 96
+
+def assoc_legendre_p_4_m3_jac(z, *, branch_cut=2, norm=False):
+    fac = assoc_legendre_factor(4, -3, norm)
+
+    return (fac * ((4 * z * z - 5) * z * z + 1) *
+        assoc_legendre_p_1_1_jac_div_z(z, branch_cut=branch_cut) / 48)
+
+def assoc_legendre_p_4_m2_jac(z, *, branch_cut=2, norm=False):
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(4, -2, norm)
+
+    return branch_cut_sign * fac * (4 - 7 * z * z) * z / 12
+
+def assoc_legendre_p_4_m1_jac(z, *, branch_cut=2, norm=False):
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(4, -1, norm)
+
+    return (branch_cut_sign * fac * ((27 - 28 * z * z) * z * z - 3) *
+        assoc_legendre_p_1_1_jac_div_z(z, branch_cut=branch_cut) / 8)
+
+def sph_legendre_factor(n, m):
+    return assoc_legendre_factor(n, m, norm=True) / np.sqrt(2 * np.pi)
+
+def sph_legendre_p_0_0(theta):
+    fac = sph_legendre_factor(0, 0)
+
+    return np.full_like(theta, fac)
+
+def sph_legendre_p_1_0(theta):
+    fac = sph_legendre_factor(1, 0)
+
+    return fac * np.cos(theta)
+
+def sph_legendre_p_1_1(theta):
+    fac = sph_legendre_factor(1, 1)
+
+    return -fac * np.abs(np.sin(theta))
+
+def sph_legendre_p_1_m1(theta):
+    fac = sph_legendre_factor(1, -1)
+
+    return fac * np.abs(np.sin(theta)) / 2
+
+def sph_legendre_p_2_0(theta):
+    fac = sph_legendre_factor(2, 0)
+
+    return fac * (3 * np.square(np.cos(theta)) - 1) / 2
+
+def sph_legendre_p_2_1(theta):
+    fac = sph_legendre_factor(2, 1)
+
+    return -3 * fac * np.abs(np.sin(theta)) * np.cos(theta)
+
+def sph_legendre_p_2_2(theta):
+    fac = sph_legendre_factor(2, 2)
+
+    return 3 * fac * (1 - np.square(np.cos(theta)))
+
+def sph_legendre_p_2_m2(theta):
+    fac = sph_legendre_factor(2, -2)
+
+    return fac * (1 - np.square(np.cos(theta))) / 8
+
+def sph_legendre_p_2_m1(theta):
+    fac = sph_legendre_factor(2, -1)
+
+    return fac * np.cos(theta) * np.abs(np.sin(theta)) / 2
+
+def sph_legendre_p_3_0(theta):
+    fac = sph_legendre_factor(3, 0)
+
+    return (fac * (5 * np.square(np.cos(theta)) - 3) *
+        np.cos(theta) / 2)
+
+def sph_legendre_p_3_1(theta):
+    fac = sph_legendre_factor(3, 1)
+
+    return (-3 * fac * (5 * np.square(np.cos(theta)) - 1) *
+        np.abs(np.sin(theta)) / 2)
+
+def sph_legendre_p_3_2(theta):
+    fac = sph_legendre_factor(3, 2)
+
+    return (-15 * fac * (np.square(np.cos(theta)) - 1) *
+        np.cos(theta))
+
+def sph_legendre_p_3_3(theta):
+    fac = sph_legendre_factor(3, 3)
+
+    return -15 * fac * np.power(np.abs(np.sin(theta)), 3)
+
+def sph_legendre_p_3_m3(theta):
+    fac = sph_legendre_factor(3, -3)
+
+    return fac * np.power(np.abs(np.sin(theta)), 3) / 48
+
+def sph_legendre_p_3_m2(theta):
+    fac = sph_legendre_factor(3, -2)
+
+    return (-fac * (np.square(np.cos(theta)) - 1) *
+        np.cos(theta) / 8)
+
+def sph_legendre_p_3_m1(theta):
+    fac = sph_legendre_factor(3, -1)
+
+    return (fac * (5 * np.square(np.cos(theta)) - 1) *
+        np.abs(np.sin(theta)) / 8)
+
+def sph_legendre_p_4_0(theta):
+    fac = sph_legendre_factor(4, 0)
+
+    return (fac * (35 * np.square(np.square(np.cos(theta))) -
+        30 * np.square(np.cos(theta)) + 3) / 8)
+
+def sph_legendre_p_4_1(theta):
+    fac = sph_legendre_factor(4, 1)
+
+    return (-5 * fac * (7 * np.square(np.cos(theta)) - 3) *
+        np.cos(theta) * np.abs(np.sin(theta)) / 2)
+
+def sph_legendre_p_4_2(theta):
+    fac = sph_legendre_factor(4, 2)
+
+    return (-15 * fac * (7 * np.square(np.cos(theta)) - 1) *
+        (np.square(np.cos(theta)) - 1) / 2)
+
+def sph_legendre_p_4_3(theta):
+    fac = sph_legendre_factor(4, 3)
+
+    return -105 * fac * np.power(np.abs(np.sin(theta)), 3) * np.cos(theta)
+
+def sph_legendre_p_4_4(theta):
+    fac = sph_legendre_factor(4, 4)
+
+    return 105 * fac * np.square(np.square(np.cos(theta)) - 1)
+
+def sph_legendre_p_4_m4(theta):
+    fac = sph_legendre_factor(4, -4)
+
+    return fac * np.square(np.square(np.cos(theta)) - 1) / 384
+
+def sph_legendre_p_4_m3(theta):
+    fac = sph_legendre_factor(4, -3)
+
+    return (fac * np.power(np.abs(np.sin(theta)), 3) *
+        np.cos(theta) / 48)
+
+def sph_legendre_p_4_m2(theta):
+    fac = sph_legendre_factor(4, -2)
+
+    return (-fac * (7 * np.square(np.cos(theta)) - 1) *
+        (np.square(np.cos(theta)) - 1) / 48)
+
+def sph_legendre_p_4_m1(theta):
+    fac = sph_legendre_factor(4, -1)
+
+    return (fac * (7 * np.square(np.cos(theta)) - 3) *
+        np.cos(theta) * np.abs(np.sin(theta)) / 8)
+
+def sph_legendre_p_0_0_jac(theta):
+    return np.zeros_like(theta)
+
+def sph_legendre_p_1_0_jac(theta):
+    fac = sph_legendre_factor(1, 0)
+
+    return -fac * np.sin(theta)
+
+def sph_legendre_p_1_1_jac(theta):
+    fac = sph_legendre_factor(1, 1)
+
+    return -fac * np.cos(theta) * (2 * np.heaviside(np.sin(theta), 1) - 1)
+
+def sph_legendre_p_1_m1_jac(theta):
+    fac = sph_legendre_factor(1, -1)
+
+    return fac * np.cos(theta) * (2 * np.heaviside(np.sin(theta), 1) - 1) / 2
+
+def sph_legendre_p_2_0_jac(theta):
+    fac = sph_legendre_factor(2, 0)
+
+    return -3 * fac * np.cos(theta) * np.sin(theta)
+
+def sph_legendre_p_2_1_jac(theta):
+    fac = sph_legendre_factor(2, 1)
+
+    return (3 * fac * (-np.square(np.cos(theta)) *
+        (2 * np.heaviside(np.sin(theta), 1) - 1) +
+        np.abs(np.sin(theta)) * np.sin(theta)))
+
+def sph_legendre_p_2_2_jac(theta):
+    fac = sph_legendre_factor(2, 2)
+
+    return 6 * fac * np.sin(theta) * np.cos(theta)
+
+def sph_legendre_p_2_m2_jac(theta):
+    fac = sph_legendre_factor(2, -2)
+
+    return fac * np.sin(theta) * np.cos(theta) / 4
+
+def sph_legendre_p_2_m1_jac(theta):
+    fac = sph_legendre_factor(2, -1)
+
+    return (-fac * (-np.square(np.cos(theta)) *
+        (2 * np.heaviside(np.sin(theta), 1) - 1) +
+        np.abs(np.sin(theta)) * np.sin(theta)) / 2)
+
+def sph_legendre_p_3_0_jac(theta):
+    fac = sph_legendre_factor(3, 0)
+
+    return 3 * fac * (1 - 5 * np.square(np.cos(theta))) * np.sin(theta) / 2
+
+def sph_legendre_p_3_1_jac(theta):
+    fac = sph_legendre_factor(3, 1)
+
+    return (3 * fac * (11 - 15 * np.square(np.cos(theta))) * np.cos(theta) *
+        (2 * np.heaviside(np.sin(theta), 1) - 1) / 2)
+
+def sph_legendre_p_3_2_jac(theta):
+    fac = sph_legendre_factor(3, 2)
+
+    return 15 * fac * (3 * np.square(np.cos(theta)) - 1) * np.sin(theta)
+
+def sph_legendre_p_3_3_jac(theta):
+    fac = sph_legendre_factor(3, 3)
+
+    return -45 * fac * np.abs(np.sin(theta)) * np.sin(theta) * np.cos(theta)
+
+def sph_legendre_p_3_m3_jac(theta):
+    fac = sph_legendre_factor(3, -3)
+
+    return fac * np.abs(np.sin(theta)) * np.sin(theta) * np.cos(theta) / 16
+
+def sph_legendre_p_3_m2_jac(theta):
+    fac = sph_legendre_factor(3, -2)
+
+    return fac * (3 * np.square(np.cos(theta)) - 1) * np.sin(theta) / 8
+
+def sph_legendre_p_3_m1_jac(theta):
+    fac = sph_legendre_factor(3, -1)
+
+    return (-fac * (11 - 15 * np.square(np.cos(theta))) *
+        np.cos(theta) *
+        (2 * np.heaviside(np.sin(theta), 1) - 1) / 8)
+
+def sph_legendre_p_4_0_jac(theta):
+    fac = sph_legendre_factor(4, 0)
+
+    return (-5 * fac * (7 * np.square(np.cos(theta)) - 3) *
+        np.sin(theta) * np.cos(theta) / 2)
+
+def sph_legendre_p_4_1_jac(theta):
+    fac = sph_legendre_factor(4, 1)
+
+    return (5 * fac * (-3 + 27 * np.square(np.cos(theta)) -
+        28 * np.square(np.square(np.cos(theta)))) *
+        (2 * np.heaviside(np.sin(theta), 1) - 1) / 2)
+
+def sph_legendre_p_4_2_jac(theta):
+    fac = sph_legendre_factor(4, 2)
+
+    return (30 * fac * (7 * np.square(np.cos(theta)) - 4) *
+        np.sin(theta) * np.cos(theta))
+
+def sph_legendre_p_4_3_jac(theta):
+    fac = sph_legendre_factor(4, 3)
+
+    return (-105 * fac * (4 * np.square(np.cos(theta)) - 1) *
+        np.abs(np.sin(theta)) * np.sin(theta))
+
+def sph_legendre_p_4_4_jac(theta):
+    fac = sph_legendre_factor(4, 4)
+
+    return (-420 * fac * (np.square(np.cos(theta)) - 1) *
+        np.sin(theta) * np.cos(theta))
+
+def sph_legendre_p_4_m4_jac(theta):
+    fac = sph_legendre_factor(4, -4)
+
+    return (-fac * (np.square(np.cos(theta)) - 1) *
+        np.sin(theta) * np.cos(theta) / 96)
+
+def sph_legendre_p_4_m3_jac(theta):
+    fac = sph_legendre_factor(4, -3)
+
+    return (fac * (4 * np.square(np.cos(theta)) - 1) *
+        np.abs(np.sin(theta)) * np.sin(theta) / 48)
+
+def sph_legendre_p_4_m2_jac(theta):
+    fac = sph_legendre_factor(4, -2)
+
+    return (fac * (7 * np.square(np.cos(theta)) - 4) * np.sin(theta) *
+        np.cos(theta) / 12)
+
+def sph_legendre_p_4_m1_jac(theta):
+    fac = sph_legendre_factor(4, -1)
+
+    return (-fac * (-3 + 27 * np.square(np.cos(theta)) -
+        28 * np.square(np.square(np.cos(theta)))) *
+        (2 * np.heaviside(np.sin(theta), 1) - 1) / 8)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_log1mexp.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_log1mexp.py
new file mode 100644
index 0000000000000000000000000000000000000000..ed8b1958eabd973704c32e9be157397c7b3472e3
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_log1mexp.py
@@ -0,0 +1,85 @@
+import numpy as np
+import pytest
+
+from numpy.testing import assert_allclose, assert_equal
+
+from scipy.special._ufuncs import _log1mexp
+
+# # Test cases generated with the script
+#
+# import numpy as np
+
+# from mpmath import mp
+
+
+# def mp_log1mexp(x):
+#     with mp.workdps(324):
+#         return float(mp.log(mp.one - mp.exp(x)))
+
+# X = np.concat([-np.logspace(-1, -300, 20), np.linspace(-745, -1, 20)])
+
+# cases = [(float(x), mp_log1mexp(x)) for x in X]
+
+@pytest.mark.parametrize(
+    "x,expected",
+    [
+        (-0.1, -2.3521684610440907),
+        (-1.8329807108324374e-17, -38.538003135374026),
+        (-3.359818286283788e-33, -74.773421177754),
+        (-6.1584821106602796e-49, -111.00883922013399),
+        (-1.1288378916846929e-64, -147.24425726251397),
+        (-2.0691380811148324e-80, -183.47967530489393),
+        (-3.792690190732269e-96, -219.71509334727392),
+        (-6.951927961775534e-112, -255.95051138965394),
+        (-1.2742749857031425e-127, -292.1859294320339),
+        (-2.3357214690901785e-143, -328.42134747441384),
+        (-4.281332398719571e-159, -364.6567655167938),
+        (-7.847599703514559e-175, -400.8921835591739),
+        (-1.4384498882876776e-190, -437.1276016015538),
+        (-2.6366508987304307e-206, -473.3630196439338),
+        (-4.832930238571653e-222, -509.59843768631384),
+        (-8.858667904100796e-238, -545.8338557286938),
+        (-1.623776739188744e-253, -582.0692737710738),
+        (-2.9763514416312156e-269, -618.3046918134538),
+        (-5.455594781168782e-285, -654.5401098558336),
+        (-1e-300, -690.7755278982137),
+        (-745.0, -5e-324),
+        (-705.8421052631579, -2.8619931451743316e-307),
+        (-666.6842105263158, -2.9021923726875757e-290),
+        (-627.5263157894738, -2.9429562339405562e-273),
+        (-588.3684210526316, -2.9842926597143714e-256),
+        (-549.2105263157895, -3.0262096921839423e-239),
+        (-510.0526315789474, -3.0687154864846747e-222),
+        (-470.89473684210526, -3.1118183122979086e-205),
+        (-431.7368421052632, -3.155526555459449e-188),
+        (-392.5789473684211, -3.1998487195921207e-171),
+        (-353.42105263157896, -3.2447934277596653e-154),
+        (-314.2631578947369, -3.2903694241438367e-137),
+        (-275.1052631578948, -3.3365855757467166e-120),
+        (-235.94736842105266, -3.3834508741152875e-103),
+        (-196.78947368421052, -3.4309744370903894e-86),
+        (-157.63157894736844, -3.4791655105810003e-69),
+        (-118.47368421052636, -3.528033470363468e-52),
+        (-79.31578947368428, -3.577587823905024e-35),
+        (-40.157894736842195, -3.627838212213697e-18),
+        (-1.0, -0.4586751453870819),
+    ]
+)
+def test_log1mexp(x, expected):
+    observed = _log1mexp(x)
+    assert_allclose(observed, expected, rtol=1e-15, atol=1e-300)
+
+
+@pytest.mark.parametrize("x", [1.1, 1e10, np.inf])
+def test_log1mexp_out_of_domain(x):
+    observed = _log1mexp(x)
+    assert np.isnan(observed)
+
+
+@pytest.mark.parametrize(
+    "x,expected",
+    [(-np.inf, -0.0), (0.0, -np.inf), (-0.0, -np.inf), (np.nan, np.nan)]
+)
+def test_log1mexp_extreme(x, expected):
+    observed = _log1mexp(x)
+    assert_equal(expected, observed)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_loggamma.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_loggamma.py
new file mode 100644
index 0000000000000000000000000000000000000000..2fcb5a20037de46df939895d38fbe5fe6b85c9aa
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_loggamma.py
@@ -0,0 +1,70 @@
+import numpy as np
+from numpy.testing import assert_allclose, assert_
+
+from scipy.special._testutils import FuncData
+from scipy.special import gamma, gammaln, loggamma
+
+
+def test_identities1():
+    # test the identity exp(loggamma(z)) = gamma(z)
+    x = np.array([-99.5, -9.5, -0.5, 0.5, 9.5, 99.5])
+    y = x.copy()
+    x, y = np.meshgrid(x, y)
+    z = (x + 1J*y).flatten()
+    dataset = np.vstack((z, gamma(z))).T
+
+    def f(z):
+        return np.exp(loggamma(z))
+
+    FuncData(f, dataset, 0, 1, rtol=1e-14, atol=1e-14).check()
+
+
+def test_identities2():
+    # test the identity loggamma(z + 1) = log(z) + loggamma(z)
+    x = np.array([-99.5, -9.5, -0.5, 0.5, 9.5, 99.5])
+    y = x.copy()
+    x, y = np.meshgrid(x, y)
+    z = (x + 1J*y).flatten()
+    dataset = np.vstack((z, np.log(z) + loggamma(z))).T
+
+    def f(z):
+        return loggamma(z + 1)
+
+    FuncData(f, dataset, 0, 1, rtol=1e-14, atol=1e-14).check()
+
+
+def test_complex_dispatch_realpart():
+    # Test that the real parts of loggamma and gammaln agree on the
+    # real axis.
+    x = np.r_[-np.logspace(10, -10), np.logspace(-10, 10)] + 0.5
+
+    dataset = np.vstack((x, gammaln(x))).T
+
+    def f(z):
+        z = np.array(z, dtype='complex128')
+        return loggamma(z).real
+
+    FuncData(f, dataset, 0, 1, rtol=1e-14, atol=1e-14).check()
+
+
+def test_real_dispatch():
+    x = np.logspace(-10, 10) + 0.5
+    dataset = np.vstack((x, gammaln(x))).T
+
+    FuncData(loggamma, dataset, 0, 1, rtol=1e-14, atol=1e-14).check()
+    assert_(loggamma(0) == np.inf)
+    assert_(np.isnan(loggamma(-1)))
+
+
+def test_gh_6536():
+    z = loggamma(complex(-3.4, +0.0))
+    zbar = loggamma(complex(-3.4, -0.0))
+    assert_allclose(z, zbar.conjugate(), rtol=1e-15, atol=0)
+
+
+def test_branch_cut():
+    # Make sure negative zero is treated correctly
+    x = -np.logspace(300, -30, 100)
+    z = np.asarray([complex(x0, 0.0) for x0 in x])
+    zbar = np.asarray([complex(x0, -0.0) for x0 in x])
+    assert_allclose(z, zbar.conjugate(), rtol=1e-15, atol=0)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_logit.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_logit.py
new file mode 100644
index 0000000000000000000000000000000000000000..ae8dd8851d8932dcbbda68c7f11edbe2daafcf00
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_logit.py
@@ -0,0 +1,161 @@
+import numpy as np
+from numpy.testing import assert_equal, assert_allclose
+from scipy.special import logit, expit, log_expit
+
+
+class TestLogit:
+
+    def check_logit_out(self, a, expected):
+        actual = logit(a)
+        assert_equal(actual.dtype, a.dtype)
+        rtol = 16*np.finfo(a.dtype).eps
+        assert_allclose(actual, expected, rtol=rtol)
+
+    def test_float32(self):
+        a = np.concatenate((np.linspace(0, 1, 10, dtype=np.float32),
+                            [np.float32(0.0001), np.float32(0.49999),
+                             np.float32(0.50001)]))
+        # Expected values computed with mpmath from float32 inputs, e.g.
+        #   from mpmath import mp
+        #   mp.dps = 200
+        #   a = np.float32(1/9)
+        #   print(np.float32(mp.log(a) - mp.log1p(-a)))
+        # prints `-2.0794415`.
+        expected = np.array([-np.inf, -2.0794415, -1.2527629, -6.9314712e-01,
+                             -2.2314353e-01,  2.2314365e-01,  6.9314724e-01,
+                             1.2527630, 2.0794415, np.inf,
+                             -9.2102404, -4.0054321e-05, 4.0054321e-05],
+                            dtype=np.float32)
+        self.check_logit_out(a, expected)
+
+    def test_float64(self):
+        a = np.concatenate((np.linspace(0, 1, 10, dtype=np.float64),
+                            [1e-8, 0.4999999999999, 0.50000000001]))
+        # Expected values computed with mpmath.
+        expected = np.array([-np.inf,
+                             -2.079441541679836,
+                             -1.252762968495368,
+                             -0.6931471805599454,
+                             -0.22314355131420985,
+                             0.22314355131420985,
+                             0.6931471805599452,
+                             1.2527629684953674,
+                             2.0794415416798353,
+                             np.inf,
+                             -18.420680733952366,
+                             -3.999023334699814e-13,
+                             4.000000330961484e-11])
+        self.check_logit_out(a, expected)
+
+    def test_nan(self):
+        expected = np.array([np.nan]*4)
+        with np.errstate(invalid='ignore'):
+            actual = logit(np.array([-3., -2., 2., 3.]))
+
+        assert_equal(expected, actual)
+
+
+class TestExpit:
+    def check_expit_out(self, dtype, expected):
+        a = np.linspace(-4, 4, 10)
+        a = np.array(a, dtype=dtype)
+        actual = expit(a)
+        assert_allclose(actual, expected, atol=1.5e-7, rtol=0)
+        assert_equal(actual.dtype, np.dtype(dtype))
+
+    def test_float32(self):
+        expected = np.array([0.01798621, 0.04265125,
+                            0.09777259, 0.20860852,
+                            0.39068246, 0.60931754,
+                            0.79139149, 0.9022274,
+                            0.95734876, 0.98201376], dtype=np.float32)
+        self.check_expit_out('f4', expected)
+
+    def test_float64(self):
+        expected = np.array([0.01798621, 0.04265125,
+                            0.0977726, 0.20860853,
+                            0.39068246, 0.60931754,
+                            0.79139147, 0.9022274,
+                            0.95734875, 0.98201379])
+        self.check_expit_out('f8', expected)
+
+    def test_large(self):
+        for dtype in (np.float32, np.float64, np.longdouble):
+            for n in (88, 89, 709, 710, 11356, 11357):
+                n = np.array(n, dtype=dtype)
+                assert_allclose(expit(n), 1.0, atol=1e-20)
+                assert_allclose(expit(-n), 0.0, atol=1e-20)
+                assert_equal(expit(n).dtype, dtype)
+                assert_equal(expit(-n).dtype, dtype)
+
+
+class TestLogExpit:
+
+    def test_large_negative(self):
+        x = np.array([-10000.0, -750.0, -500.0, -35.0])
+        y = log_expit(x)
+        assert_equal(y, x)
+
+    def test_large_positive(self):
+        x = np.array([750.0, 1000.0, 10000.0])
+        y = log_expit(x)
+        # y will contain -0.0, and -0.0 is used in the expected value,
+        # but assert_equal does not check the sign of zeros, and I don't
+        # think the sign is an essential part of the test (i.e. it would
+        # probably be OK if log_expit(1000) returned 0.0 instead of -0.0).
+        assert_equal(y, np.array([-0.0, -0.0, -0.0]))
+
+    def test_basic_float64(self):
+        x = np.array([-32, -20, -10, -3, -1, -0.1, -1e-9,
+                      0, 1e-9, 0.1, 1, 10, 100, 500, 710, 725, 735])
+        y = log_expit(x)
+        #
+        # Expected values were computed with mpmath:
+        #
+        #   import mpmath
+        #
+        #   mpmath.mp.dps = 100
+        #
+        #   def mp_log_expit(x):
+        #       return -mpmath.log1p(mpmath.exp(-x))
+        #
+        #   expected = [float(mp_log_expit(t)) for t in x]
+        #
+        expected = [-32.000000000000014, -20.000000002061153,
+                    -10.000045398899218, -3.048587351573742,
+                    -1.3132616875182228, -0.7443966600735709,
+                    -0.6931471810599453, -0.6931471805599453,
+                    -0.6931471800599454, -0.6443966600735709,
+                    -0.3132616875182228, -4.539889921686465e-05,
+                    -3.720075976020836e-44, -7.124576406741286e-218,
+                    -4.47628622567513e-309, -1.36930634e-315,
+                    -6.217e-320]
+
+        # When tested locally, only one value in y was not exactly equal to
+        # expected.  That was for x=1, and the y value differed from the
+        # expected by 1 ULP.  For this test, however, I'll use rtol=1e-15.
+        assert_allclose(y, expected, rtol=1e-15)
+
+    def test_basic_float32(self):
+        x = np.array([-32, -20, -10, -3, -1, -0.1, -1e-9,
+                      0, 1e-9, 0.1, 1, 10, 100], dtype=np.float32)
+        y = log_expit(x)
+        #
+        # Expected values were computed with mpmath:
+        #
+        #   import mpmath
+        #
+        #   mpmath.mp.dps = 100
+        #
+        #   def mp_log_expit(x):
+        #       return -mpmath.log1p(mpmath.exp(-x))
+        #
+        #   expected = [np.float32(mp_log_expit(t)) for t in x]
+        #
+        expected = np.array([-32.0, -20.0, -10.000046, -3.0485873,
+                             -1.3132616, -0.7443967, -0.6931472,
+                             -0.6931472, -0.6931472, -0.64439666,
+                             -0.3132617, -4.5398898e-05, -3.8e-44],
+                            dtype=np.float32)
+
+        assert_allclose(y, expected, rtol=5e-7)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_logsumexp.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_logsumexp.py
new file mode 100644
index 0000000000000000000000000000000000000000..51196a3d5e3ec3376b4311c374d13bec37f37f00
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_logsumexp.py
@@ -0,0 +1,481 @@
+import itertools as it
+import math
+import pytest
+
+import numpy as np
+
+from scipy._lib._array_api import (is_array_api_strict, make_xp_test_case,
+                                   xp_default_dtype, xp_device)
+from scipy._lib._array_api_no_0d import (xp_assert_equal, xp_assert_close,
+                                         xp_assert_less)
+
+from scipy.special import log_softmax, logsumexp, softmax
+from scipy.special._logsumexp import _wrap_radians
+
+
+dtypes = ['float32', 'float64', 'int32', 'int64', 'complex64', 'complex128']
+integral_dtypes = ['int32', 'int64']
+
+
+@pytest.mark.uses_xp_capabilities(False, reason="private")
+def test_wrap_radians(xp):
+    x = xp.asarray([-math.pi-1, -math.pi, -1, -1e-300,
+                    0, 1e-300, 1, math.pi, math.pi+1])
+    ref = xp.asarray([math.pi-1, math.pi, -1, -1e-300,
+                    0, 1e-300, 1, math.pi, -math.pi+1])
+    res = _wrap_radians(x, xp=xp)
+    xp_assert_close(res, ref, atol=0)
+
+
+# numpy warning filters don't work for dask (dask/dask#3245)
+# (also we should not expect the numpy warning filter to work for any Array API
+# library)
+@pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning")
+@pytest.mark.filterwarnings("ignore:divide by zero encountered:RuntimeWarning")
+@pytest.mark.filterwarnings("ignore:overflow encountered:RuntimeWarning")
+@make_xp_test_case(logsumexp)
+class TestLogSumExp:
+    def test_logsumexp(self, xp):
+        # Test with zero-size array
+        a = xp.asarray([])
+        desired = xp.asarray(-xp.inf)
+        xp_assert_equal(logsumexp(a), desired)
+
+        # Test whether logsumexp() function correctly handles large inputs.
+        a = xp.arange(200., dtype=xp.float64)
+        desired = xp.log(xp.sum(xp.exp(a)))
+        xp_assert_close(logsumexp(a), desired)
+
+        # Now test with large numbers
+        b = xp.asarray([1000., 1000.])
+        desired = xp.asarray(1000.0 + math.log(2.0))
+        xp_assert_close(logsumexp(b), desired)
+
+        n = 1000
+        b = xp.full((n,), 10000)
+        desired = xp.asarray(10000.0 + math.log(n))
+        xp_assert_close(logsumexp(b), desired)
+
+        x = xp.asarray([1e-40] * 1000000)
+        logx = xp.log(x)
+        X = xp.stack([x, x])
+        logX = xp.stack([logx, logx])
+        xp_assert_close(xp.exp(logsumexp(logX)), xp.sum(X))
+        xp_assert_close(xp.exp(logsumexp(logX, axis=0)), xp.sum(X, axis=0))
+        xp_assert_close(xp.exp(logsumexp(logX, axis=1)), xp.sum(X, axis=1))
+
+        # Handling special values properly
+        inf = xp.asarray([xp.inf])
+        nan = xp.asarray([xp.nan])
+        xp_assert_equal(logsumexp(inf), inf[0])
+        xp_assert_equal(logsumexp(-inf), -inf[0])
+        xp_assert_equal(logsumexp(nan), nan[0])
+        xp_assert_equal(logsumexp(xp.asarray([-xp.inf, -xp.inf])), -inf[0])
+
+        # Handling an array with different magnitudes on the axes
+        a = xp.asarray([[1e10, 1e-10],
+                        [-1e10, -np.inf]])
+        ref = xp.asarray([1e10, -1e10])
+        xp_assert_close(logsumexp(a, axis=-1), ref)
+
+        # Test keeping dimensions
+        ref = xp.expand_dims(ref, axis=-1)
+        xp_assert_close(logsumexp(a, axis=-1, keepdims=True), ref)
+
+        # Test multiple axes
+        xp_assert_close(logsumexp(a, axis=(-1, -2)), xp.asarray(1e10))
+
+    def test_logsumexp_b(self, xp):
+        a = xp.arange(200., dtype=xp.float64)
+        b = xp.arange(200., 0., -1.)
+        desired = xp.log(xp.sum(b*xp.exp(a)))
+        xp_assert_close(logsumexp(a, b=b), desired)
+
+        a = xp.asarray([1000, 1000])
+        b = xp.asarray([1.2, 1.2])
+        desired = xp.asarray(1000 + math.log(2 * 1.2))
+        xp_assert_close(logsumexp(a, b=b), desired)
+
+        x = xp.asarray([1e-40] * 100000)
+        b = xp.linspace(1, 1000, 100000)
+        logx = xp.log(x)
+        X = xp.stack((x, x))
+        logX = xp.stack((logx, logx))
+        B = xp.stack((b, b))
+        xp_assert_close(xp.exp(logsumexp(logX, b=B)), xp.sum(B * X))
+        xp_assert_close(xp.exp(logsumexp(logX, b=B, axis=0)), xp.sum(B * X, axis=0))
+        xp_assert_close(xp.exp(logsumexp(logX, b=B, axis=1)), xp.sum(B * X, axis=1))
+
+    def test_logsumexp_sign(self, xp):
+        a = xp.asarray([1, 1, 1])
+        b = xp.asarray([1, -1, -1])
+
+        r, s = logsumexp(a, b=b, return_sign=True)
+        xp_assert_close(r, xp.asarray(1.))
+        xp_assert_equal(s, xp.asarray(-1.))
+
+    def test_logsumexp_sign_zero(self, xp):
+        a = xp.asarray([1, 1])
+        b = xp.asarray([1, -1])
+
+        r, s = logsumexp(a, b=b, return_sign=True)
+        assert not xp.isfinite(r)
+        assert not xp.isnan(r)
+        assert r < 0
+        assert s == 0
+
+    def test_logsumexp_sign_shape(self, xp):
+        a = xp.ones((1, 2, 3, 4))
+        b = xp.ones_like(a)
+
+        r, s = logsumexp(a, axis=2, b=b, return_sign=True)
+        assert r.shape == s.shape == (1, 2, 4)
+
+        r, s = logsumexp(a, axis=(1, 3), b=b, return_sign=True)
+        assert r.shape == s.shape == (1,3)
+
+    def test_logsumexp_complex_sign(self, xp):
+        a = xp.asarray([1 + 1j, 2 - 1j, -2 + 3j])
+
+        r, s = logsumexp(a, return_sign=True)
+
+        expected_sumexp = xp.sum(xp.exp(a))
+        # This is the numpy>=2.0 convention for np.sign
+        expected_sign = expected_sumexp / xp.abs(expected_sumexp)
+
+        xp_assert_close(s, expected_sign)
+        xp_assert_close(s * xp.exp(r), expected_sumexp)
+
+    def test_logsumexp_shape(self, xp):
+        a = xp.ones((1, 2, 3, 4))
+        b = xp.ones_like(a)
+
+        r = logsumexp(a, axis=2, b=b)
+        assert r.shape == (1, 2, 4)
+
+        r = logsumexp(a, axis=(1, 3), b=b)
+        assert r.shape == (1, 3)
+
+    def test_logsumexp_b_zero(self, xp):
+        a = xp.asarray([1, 10000])
+        b = xp.asarray([1, 0])
+
+        xp_assert_close(logsumexp(a, b=b), xp.asarray(1.))
+
+    def test_logsumexp_b_shape(self, xp):
+        a = xp.zeros((4, 1, 2, 1))
+        b = xp.ones((3, 1, 5))
+
+        logsumexp(a, b=b)
+
+    @pytest.mark.parametrize('arg', (1, [1, 2, 3]))
+    def test_xp_invalid_input(self, arg):
+        assert logsumexp(arg) == logsumexp(np.asarray(np.atleast_1d(arg)))
+
+    def test_array_like(self):
+        a = [1000, 1000]
+        desired = np.asarray(1000.0 + math.log(2.0))
+        xp_assert_close(logsumexp(a), desired)
+
+    @pytest.mark.parametrize('dtype', dtypes)
+    def test_dtypes_a(self, dtype, xp):
+        dtype = getattr(xp, dtype)
+        a = xp.asarray([1000., 1000.], dtype=dtype)
+        desired_dtype = (xp.asarray(1.).dtype if xp.isdtype(dtype, 'integral')
+                         else dtype)  # true for all libraries tested
+        desired = xp.asarray(1000.0 + math.log(2.0), dtype=desired_dtype)
+        xp_assert_close(logsumexp(a), desired)
+
+    @pytest.mark.parametrize('dtype_a', dtypes)
+    @pytest.mark.parametrize('dtype_b', dtypes)
+    def test_dtypes_ab(self, dtype_a, dtype_b, xp):
+        xp_dtype_a = getattr(xp, dtype_a)
+        xp_dtype_b = getattr(xp, dtype_b)
+        a = xp.asarray([2, 1], dtype=xp_dtype_a)
+        b = xp.asarray([1, -1], dtype=xp_dtype_b)
+        if is_array_api_strict(xp):
+            # special-case for `TypeError: array_api_strict.float32 and
+            # and array_api_strict.int64 cannot be type promoted together`
+            xp_float_dtypes = [dtype for dtype in [xp_dtype_a, xp_dtype_b]
+                               if not xp.isdtype(dtype, 'integral')]
+            if len(xp_float_dtypes) < 2:  # at least one is integral
+                xp_float_dtypes.append(xp.asarray(1.).dtype)
+            desired_dtype = xp.result_type(*xp_float_dtypes)
+        else:
+            desired_dtype = xp.result_type(xp_dtype_a, xp_dtype_b)
+            if xp.isdtype(desired_dtype, 'integral'):
+               desired_dtype = xp_default_dtype(xp)
+        desired = xp.asarray(math.log(math.exp(2) - math.exp(1)), dtype=desired_dtype)
+        xp_assert_close(logsumexp(a, b=b), desired)
+
+    def test_gh18295(self, xp):
+        # gh-18295 noted loss of precision when real part of one element is much
+        # larger than the rest. Check that this is resolved.
+        a = xp.asarray([0.0, -40.0])
+        res = logsumexp(a)
+        ref = xp.logaddexp(a[0], a[1])
+        xp_assert_close(res, ref)
+
+    @pytest.mark.parametrize('dtype', ['complex64', 'complex128'])
+    def test_gh21610(self, xp, dtype):
+        # gh-21610 noted that `logsumexp` could return imaginary components
+        # outside the range (-pi, pi]. Check that this is resolved.
+        # While working on this, I noticed that all other tests passed even
+        # when the imaginary component of the result was zero. This suggested
+        # the need of a stronger test with imaginary dtype.
+        rng = np.random.default_rng(324984329582349862)
+        dtype = getattr(xp, dtype)
+        shape = (10, 100)
+        x = rng.uniform(1, 40, shape) + 1.j * rng.uniform(1, 40, shape)
+        x = xp.asarray(x, dtype=dtype)
+
+        res = logsumexp(x, axis=1)
+        ref = xp.log(xp.sum(xp.exp(x), axis=1))
+        max = xp.full_like(xp.imag(res), xp.pi)
+        xp_assert_less(xp.abs(xp.imag(res)), max)
+        xp_assert_close(res, ref)
+
+        out, sgn = logsumexp(x, return_sign=True, axis=1)
+        ref = xp.sum(xp.exp(x), axis=1)
+        xp_assert_less(xp.abs(xp.imag(sgn)), max)
+        xp_assert_close(out, xp.real(xp.log(ref)))
+        xp_assert_close(sgn, ref/xp.abs(ref))
+
+    def test_gh21709_small_imaginary(self, xp):
+        # Test that `logsumexp` does not lose relative precision of
+        # small imaginary components
+        x = xp.asarray([0, 0.+2.2204460492503132e-17j])
+        res = logsumexp(x)
+        # from mpmath import mp
+        # mp.dps = 100
+        # x, y = mp.mpc(0), mp.mpc('0', '2.2204460492503132e-17')
+        # ref = complex(mp.log(mp.exp(x) + mp.exp(y)))
+        ref = xp.asarray(0.6931471805599453+1.1102230246251566e-17j)
+        xp_assert_close(xp.real(res), xp.real(ref))
+        xp_assert_close(xp.imag(res), xp.imag(ref), atol=0, rtol=1e-15)
+
+
+    @pytest.mark.parametrize('x,y', list(it.product(
+        [
+            -np.inf,
+            np.inf,
+            complex(-np.inf, 0.),
+            complex(-np.inf, -0.),
+            complex(-np.inf, np.inf),
+            complex(-np.inf, -np.inf),
+            complex(np.inf, 0.),
+            complex(np.inf, -0.),
+            complex(np.inf, np.inf),
+            complex(np.inf, -np.inf),
+            # Phase in each quadrant.
+            complex(-np.inf, 0.7533),
+            complex(-np.inf, 2.3562),
+            complex(-np.inf, 3.9270),
+            complex(-np.inf, 5.4978),
+            complex(np.inf, 0.7533),
+            complex(np.inf, 2.3562),
+            complex(np.inf, 3.9270),
+            complex(np.inf, 5.4978),
+        ], repeat=2)
+    ))
+    def test_gh22601_infinite_elements(self, x, y, xp):
+        # Test that `logsumexp` does reasonable things in the presence of
+        # real and complex infinities.
+        res = logsumexp(xp.asarray([x, y]))
+        ref = xp.log(xp.sum(xp.exp(xp.asarray([x, y]))))
+        xp_assert_equal(res, ref)
+
+    def test_no_writeback(self, xp):
+        """Test that logsumexp doesn't accidentally write back to its parameters."""
+        a = xp.asarray([5., 4.])
+        b = xp.asarray([3., 2.])
+        logsumexp(a)
+        logsumexp(a, b=b)
+        xp_assert_equal(a, xp.asarray([5., 4.]))
+        xp_assert_equal(b, xp.asarray([3., 2.]))
+
+    @pytest.mark.parametrize("x_raw", [1.0, 1.0j, []])
+    def test_device(self, x_raw, xp, devices):
+        """Test input device propagation to output."""
+        for d in devices:
+            x = xp.asarray(x_raw, device=d)
+            assert xp_device(logsumexp(x)) == xp_device(x)
+            assert xp_device(logsumexp(x, b=x)) == xp_device(x)
+
+    def test_gh22903(self, xp):
+        # gh-22903 reported that `logsumexp` produced NaN where the weight associated
+        # with the max magnitude element was negative and `return_sign=False`, even if
+        # the net result should be the log of a positive number.
+
+        # result is log of positive number
+        a = xp.asarray([3.06409428, 0.37251854, 3.87471931])
+        b = xp.asarray([1.88190708, 2.84174795, -0.85016884])
+        xp_assert_close(logsumexp(a, b=b), logsumexp(a, b=b, return_sign=True)[0])
+
+        # result is log of negative number
+        b = xp.asarray([1.88190708, 2.84174795, -3.85016884])
+        xp_assert_close(logsumexp(a, b=b), xp.asarray(xp.nan))
+
+    @pytest.mark.parametrize("a, b, sign_ref",
+                             [([np.inf], None, 1.),
+                              ([np.inf], [-1.], -1.)])
+    def test_gh23548(self, xp, a, b, sign_ref):
+        # gh-23548 reported that `logsumexp` with `return_sign=True` returned a sign
+        # of NaN with infinite reals
+        a, b = xp.asarray(a), xp.asarray(b) if b is not None else None
+        val, sign = logsumexp(a, b=b, return_sign=True)
+        assert xp.isinf(val)
+        xp_assert_equal(sign, xp.asarray(sign_ref))
+
+
+@make_xp_test_case(softmax)
+class TestSoftmax:
+    def test_softmax_fixtures(self, xp):
+        xp_assert_close(softmax(xp.asarray([1000., 0., 0., 0.])),
+                        xp.asarray([1., 0., 0., 0.]), rtol=1e-13)
+        xp_assert_close(softmax(xp.asarray([1., 1.])),
+                        xp.asarray([.5, .5]), rtol=1e-13)
+        xp_assert_close(softmax(xp.asarray([0., 1.])),
+                        xp.asarray([1., np.e])/(1 + np.e),
+                        rtol=1e-13)
+
+        # Expected value computed using mpmath (with mpmath.mp.dps = 200) and then
+        # converted to float.
+        x = xp.arange(4, dtype=xp.float64)
+        expected = xp.asarray([0.03205860328008499,
+                               0.08714431874203256,
+                               0.23688281808991013,
+                               0.6439142598879722], dtype=xp.float64)
+
+        xp_assert_close(softmax(x), expected, rtol=1e-13)
+
+        # Translation property.  If all the values are changed by the same amount,
+        # the softmax result does not change.
+        xp_assert_close(softmax(x + 100), expected, rtol=1e-13)
+
+        # When axis=None, softmax operates on the entire array, and preserves
+        # the shape.
+        xp_assert_close(softmax(xp.reshape(x, (2, 2))),
+                        xp.reshape(expected, (2, 2)), rtol=1e-13)
+
+    def test_softmax_multi_axes(self, xp):
+        xp_assert_close(softmax(xp.asarray([[1000., 0.], [1000., 0.]]), axis=0),
+                        xp.asarray([[.5, .5], [.5, .5]]), rtol=1e-13)
+        xp_assert_close(softmax(xp.asarray([[1000., 0.], [1000., 0.]]), axis=1),
+                        xp.asarray([[1., 0.], [1., 0.]]), rtol=1e-13)
+
+        # Expected value computed using mpmath (with mpmath.mp.dps = 200) and then
+        # converted to float.
+        x = xp.asarray([[-25.,   0.,  25.,  50.],
+                        [  1., 325., 749., 750.]])
+        expected = xp.asarray([[2.678636961770877e-33,
+                                1.9287498479371314e-22,
+                                1.3887943864771144e-11,
+                                0.999999999986112],
+                               [0.0,
+                                1.9444526359919372e-185,
+                                0.2689414213699951,
+                                0.7310585786300048]])
+        xp_assert_close(softmax(x, axis=1), expected, rtol=1e-13)
+        xp_assert_close(softmax(x.T, axis=0), expected.T, rtol=1e-13)
+
+        # 3-d input, with a tuple for the axis.
+        x3d = xp.reshape(x, (2, 2, 2))
+        xp_assert_close(softmax(x3d, axis=(1, 2)),
+                        xp.reshape(expected, (2, 2, 2)), rtol=1e-13)
+
+    @pytest.mark.xfail_xp_backends("array_api_strict", reason="int->float promotion")
+    def test_softmax_int_array(self, xp):
+        xp_assert_close(softmax(xp.asarray([1000, 0, 0, 0])),
+                        xp.asarray([1., 0., 0., 0.]), rtol=1e-13)
+
+    def test_softmax_scalar(self):
+        xp_assert_close(softmax(1000), np.asarray(1.), rtol=1e-13)
+
+    def test_softmax_array_like(self):
+        xp_assert_close(softmax([1000, 0, 0, 0]),
+                        np.asarray([1., 0., 0., 0.]), rtol=1e-13)
+
+
+@make_xp_test_case(log_softmax)
+class TestLogSoftmax:
+    def test_log_softmax_basic(self, xp):
+        xp_assert_close(log_softmax(xp.asarray([1000., 1.])),
+                        xp.asarray([0., -999.]), rtol=1e-13)
+
+    @pytest.mark.xfail_xp_backends("array_api_strict", reason="int->float promotion")
+    def test_log_softmax_int_array(self, xp):
+        xp_assert_close(log_softmax(xp.asarray([1000, 1])),
+                        xp.asarray([0., -999.]), rtol=1e-13)
+
+    def test_log_softmax_scalar(self):
+        xp_assert_close(log_softmax(1.0), 0.0, rtol=1e-13)
+
+    def test_log_softmax_array_like(self):
+        xp_assert_close(log_softmax([1000, 1]),
+                        np.asarray([0., -999.]), rtol=1e-13)
+
+    @staticmethod
+    def data_1d(xp):
+        x = xp.arange(4, dtype=xp.float64)
+        # Expected value computed using mpmath (with mpmath.mp.dps = 200)
+        expect = [-3.4401896985611953,
+                  -2.4401896985611953,
+                  -1.4401896985611953,
+                  -0.44018969856119533]
+        return x, xp.asarray(expect, dtype=xp.float64)
+
+    @staticmethod
+    def data_2d(xp):
+        x = xp.reshape(xp.arange(8, dtype=xp.float64), (2, 4))
+
+        # Expected value computed using mpmath (with mpmath.mp.dps = 200)
+        expect = [[-3.4401896985611953,
+                   -2.4401896985611953,
+                   -1.4401896985611953,
+                   -0.44018969856119533],
+                  [-3.4401896985611953,
+                   -2.4401896985611953,
+                   -1.4401896985611953,
+                   -0.44018969856119533]]
+        return x, xp.asarray(expect, dtype=xp.float64)
+
+    @pytest.mark.parametrize("offset", [0, 100])
+    def test_log_softmax_translation(self, offset, xp):
+        # Translation property.  If all the values are changed by the same amount,
+        # the softmax result does not change.
+        x, expect = self.data_1d(xp)
+        x += offset
+        xp_assert_close(log_softmax(x), expect, rtol=1e-13)
+
+    def test_log_softmax_noneaxis(self, xp):
+        # When axis=None, softmax operates on the entire array, and preserves
+        # the shape.
+        x, expect = self.data_1d(xp)
+        x = xp.reshape(x, (2, 2))
+        expect = xp.reshape(expect, (2, 2))
+        xp_assert_close(log_softmax(x), expect, rtol=1e-13)
+
+    @pytest.mark.parametrize('axis_2d, expected_2d', [
+        (0, np.log(0.5) * np.ones((2, 2))),
+        (1, [[0., -999.], [0., -999.]]),
+    ])
+    def test_axes(self, axis_2d, expected_2d, xp):
+        x = xp.asarray([[1000., 1.], [1000., 1.]])
+        xp_assert_close(log_softmax(x, axis=axis_2d),
+                        xp.asarray(expected_2d, dtype=x.dtype), rtol=1e-13)
+
+    def test_log_softmax_2d_axis1(self, xp):
+        x, expect = self.data_2d(xp)
+        xp_assert_close(log_softmax(x, axis=1), expect, rtol=1e-13)
+
+    def test_log_softmax_2d_axis0(self, xp):
+        x, expect = self.data_2d(xp)
+        xp_assert_close(log_softmax(x.T, axis=0), expect.T, rtol=1e-13)
+
+    def test_log_softmax_3d(self, xp):
+        # 3D input, with a tuple for the axis.
+        x, expect = self.data_2d(xp)
+        x = xp.reshape(x, (2, 2, 2))
+        expect = xp.reshape(expect, (2, 2, 2))
+        xp_assert_close(log_softmax(x, axis=(1, 2)), expect, rtol=1e-13)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_mpmath.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_mpmath.py
new file mode 100644
index 0000000000000000000000000000000000000000..8a2c5d9874eb1f80c211a2bfa1bcbf06502ac84b
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_mpmath.py
@@ -0,0 +1,2160 @@
+"""
+Test SciPy functions versus mpmath, if available.
+
+"""
+import numpy as np
+from numpy.testing import assert_, assert_allclose
+from numpy import pi
+import pytest
+import itertools
+
+from scipy._external.packaging_version import version
+
+import scipy.special as sc
+from scipy.special._testutils import (
+    MissingModule, check_version, FuncData,
+    assert_func_equal)
+from scipy.special._mptestutils import (
+    Arg, FixedArg, ComplexArg, IntArg, assert_mpmath_equal,
+    nonfunctional_tooslow, trace_args, time_limited, exception_to_nan,
+    inf_to_nan)
+from scipy.special._ufuncs import (
+    _sinpi, _cospi, _lgam1p, _lanczos_sum_expg_scaled, _log1pmx,
+    _igam_fac)
+
+try:
+    import mpmath
+except ImportError:
+    mpmath = MissingModule('mpmath')
+
+pytestmark = pytest.mark.thread_unsafe(
+    reason=("mpmath gmpy2 backend is not thread-safe, "
+            "see https://github.com/mpmath/mpmath/issues/974"))
+
+# ------------------------------------------------------------------------------
+# expi
+# ------------------------------------------------------------------------------
+
+@check_version(mpmath, '0.10')
+def test_expi_complex():
+    dataset = []
+    for r in np.logspace(-99, 2, 10):
+        for p in np.linspace(0, 2*np.pi, 30):
+            z = r*np.exp(1j*p)
+            dataset.append((z, complex(mpmath.ei(z))))
+    dataset = np.array(dataset, dtype=np.cdouble)
+
+    FuncData(sc.expi, dataset, 0, 1).check()
+
+
+# ------------------------------------------------------------------------------
+# expn
+# ------------------------------------------------------------------------------
+
+@check_version(mpmath, '0.19')
+def test_expn_large_n():
+    # Test the transition to the asymptotic regime of n.
+    dataset = []
+    for n in [50, 51]:
+        for x in np.logspace(0, 4, 200):
+            with mpmath.workdps(100):
+                dataset.append((n, x, float(mpmath.expint(n, x))))
+    dataset = np.asarray(dataset)
+
+    FuncData(sc.expn, dataset, (0, 1), 2, rtol=1e-13).check()
+
+# ------------------------------------------------------------------------------
+# hyp0f1
+# ------------------------------------------------------------------------------
+
+
+@check_version(mpmath, '0.19')
+def test_hyp0f1_gh5764():
+    # Do a small and somewhat systematic test that runs quickly
+    dataset = []
+    axis = [-99.5, -9.5, -0.5, 0.5, 9.5, 99.5]
+    for v in axis:
+        for x in axis:
+            for y in axis:
+                z = x + 1j*y
+                # mpmath computes the answer correctly at dps ~ 17 but
+                # fails for 20 < dps < 120 (uses a different method);
+                # set the dps high enough that this isn't an issue
+                with mpmath.workdps(120):
+                    res = complex(mpmath.hyp0f1(v, z))
+                dataset.append((v, z, res))
+    dataset = np.array(dataset)
+
+    FuncData(lambda v, z: sc.hyp0f1(v.real, z), dataset, (0, 1), 2,
+             rtol=1e-13).check()
+
+
+@check_version(mpmath, '0.19')
+def test_hyp0f1_gh_1609():
+    # this is a regression test for gh-1609
+    vv = np.linspace(150, 180, 21)
+    af = sc.hyp0f1(vv, 0.5)
+    mf = np.array([mpmath.hyp0f1(v, 0.5) for v in vv])
+    assert_allclose(af, mf.astype(float), rtol=1e-12)
+
+
+# ------------------------------------------------------------------------------
+# hyperu
+# ------------------------------------------------------------------------------
+
+@check_version(mpmath, '1.1.0')
+def test_hyperu_around_0():
+    dataset = []
+    # DLMF 13.2.14-15 test points.
+    for n in np.arange(-5, 5):
+        for b in np.linspace(-5, 5, 20):
+            a = -n
+            dataset.append((a, b, 0, float(mpmath.hyperu(a, b, 0))))
+            a = -n + b - 1
+            dataset.append((a, b, 0, float(mpmath.hyperu(a, b, 0))))
+    # DLMF 13.2.16-22 test points.
+    for a in [-10.5, -1.5, -0.5, 0, 0.5, 1, 10]:
+        for b in [-1.0, -0.5, 0, 0.5, 1, 1.5, 2, 2.5]:
+            dataset.append((a, b, 0, float(mpmath.hyperu(a, b, 0))))
+    dataset = np.array(dataset)
+
+    FuncData(sc.hyperu, dataset, (0, 1, 2), 3, rtol=1e-15, atol=5e-13).check()
+
+
+# ------------------------------------------------------------------------------
+# hyp2f1
+# ------------------------------------------------------------------------------
+
+@check_version(mpmath, '1.0.0')
+def test_hyp2f1_strange_points():
+    pts = [
+        (2, -1, -1, 0.7),  # expected: 2.4
+        (2, -2, -2, 0.7),  # expected: 3.87
+    ]
+    pts += list(itertools.product([2, 1, -0.7, -1000], repeat=4))
+    pts = [
+        (a, b, c, x) for a, b, c, x in pts
+        if b == c and round(b) == b and b < 0 and b != -1000
+    ]
+    kw = dict(eliminate=True)
+    dataset = [p + (float(mpmath.hyp2f1(*p, **kw)),) for p in pts]
+    dataset = np.array(dataset, dtype=np.float64)
+
+    FuncData(sc.hyp2f1, dataset, (0,1,2,3), 4, rtol=1e-10).check()
+
+
+@check_version(mpmath, '0.13')
+def test_hyp2f1_real_some_points():
+    pts = [
+        (1, 2, 3, 0),
+        (1./3, 2./3, 5./6, 27./32),
+        (1./4, 1./2, 3./4, 80./81),
+        (2,-2, -3, 3),
+        (2, -3, -2, 3),
+        (2, -1.5, -1.5, 3),
+        (1, 2, 3, 0),
+        (0.7235, -1, -5, 0.3),
+        (0.25, 1./3, 2, 0.999),
+        (0.25, 1./3, 2, -1),
+        (2, 3, 5, 0.99),
+        (3./2, -0.5, 3, 0.99),
+        (2, 2.5, -3.25, 0.999),
+        (-8, 18.016500331508873, 10.805295997850628, 0.90875647507000001),
+        (-10, 900, -10.5, 0.99),
+        (-10, 900, 10.5, 0.99),
+        (-1, 2, 1, 1.0),
+        (-1, 2, 1, -1.0),
+        (-3, 13, 5, 1.0),
+        (-3, 13, 5, -1.0),
+        (0.5, 1 - 270.5, 1.5, 0.999**2),  # from issue 1561
+    ]
+    dataset = [p + (float(mpmath.hyp2f1(*p)),) for p in pts]
+    dataset = np.array(dataset, dtype=np.float64)
+
+    with np.errstate(invalid='ignore'):
+        FuncData(sc.hyp2f1, dataset, (0,1,2,3), 4, rtol=1e-10).check()
+
+
+@check_version(mpmath, '0.14')
+def test_hyp2f1_some_points_2():
+    # Taken from mpmath unit tests -- this point failed for mpmath 0.13 but
+    # was fixed in their SVN since then
+    pts = [
+        (112, (51,10), (-9,10), -0.99999),
+        (10,-900,10.5,0.99),
+        (10,-900,-10.5,0.99),
+    ]
+
+    def fev(x):
+        if isinstance(x, tuple):
+            return float(x[0]) / x[1]
+        else:
+            return x
+
+    dataset = [tuple(map(fev, p)) + (float(mpmath.hyp2f1(*p)),) for p in pts]
+    dataset = np.array(dataset, dtype=np.float64)
+
+    FuncData(sc.hyp2f1, dataset, (0,1,2,3), 4, rtol=1e-10).check()
+
+
+@check_version(mpmath, '0.13')
+def test_hyp2f1_real_some():
+    dataset = []
+    for a in [-10, -5, -1.8, 1.8, 5, 10]:
+        for b in [-2.5, -1, 1, 7.4]:
+            for c in [-9, -1.8, 5, 20.4]:
+                for z in [-10, -1.01, -0.99, 0, 0.6, 0.95, 1.5, 10]:
+                    try:
+                        v = float(mpmath.hyp2f1(a, b, c, z))
+                    except Exception:
+                        continue
+                    dataset.append((a, b, c, z, v))
+    dataset = np.array(dataset, dtype=np.float64)
+
+    with np.errstate(invalid='ignore'):
+        FuncData(sc.hyp2f1, dataset, (0,1,2,3), 4, rtol=1e-9,
+                 ignore_inf_sign=True).check()
+
+
+@check_version(mpmath, '0.12')
+@pytest.mark.slow
+def test_hyp2f1_real_random():
+    npoints = 500
+    dataset = np.zeros((npoints, 5), np.float64)
+
+    np.random.seed(1234)
+    dataset[:, 0] = np.random.pareto(1.5, npoints)
+    dataset[:, 1] = np.random.pareto(1.5, npoints)
+    dataset[:, 2] = np.random.pareto(1.5, npoints)
+    dataset[:, 3] = 2*np.random.rand(npoints) - 1
+
+    dataset[:, 0] *= (-1)**np.random.randint(2, npoints)
+    dataset[:, 1] *= (-1)**np.random.randint(2, npoints)
+    dataset[:, 2] *= (-1)**np.random.randint(2, npoints)
+
+    for ds in dataset:
+        if mpmath.__version__ < '0.14':
+            # mpmath < 0.14 fails for c too much smaller than a, b
+            if abs(ds[:2]).max() > abs(ds[2]):
+                ds[2] = abs(ds[:2]).max()
+        ds[4] = float(mpmath.hyp2f1(*tuple(ds[:4])))
+
+    FuncData(sc.hyp2f1, dataset, (0, 1, 2, 3), 4, rtol=1e-9).check()
+
+
+# ------------------------------------------------------------------------------
+# erf (complex)
+# ------------------------------------------------------------------------------
+
+@pytest.mark.slow()
+@check_version(mpmath, '0.14')
+def test_erf_complex():
+    # need to increase mpmath precision for this test
+    old_dps, old_prec = mpmath.mp.dps, mpmath.mp.prec
+    try:
+        mpmath.mp.dps = 70
+        x1, y1 = np.meshgrid(np.linspace(-10, 1, 31), np.linspace(-10, 1, 11))
+        x2, y2 = np.meshgrid(np.logspace(-80, .8, 31), np.logspace(-80, .8, 11))
+        points = np.r_[x1.ravel(),x2.ravel()] + 1j*np.r_[y1.ravel(), y2.ravel()]
+
+        assert_func_equal(sc.erf, lambda x: complex(mpmath.erf(x)), points,
+                          vectorized=False, rtol=1e-13)
+        assert_func_equal(sc.erfc, lambda x: complex(mpmath.erfc(x)), points,
+                          vectorized=False, rtol=1e-13)
+    finally:
+        mpmath.mp.dps, mpmath.mp.prec = old_dps, old_prec
+
+
+# ------------------------------------------------------------------------------
+# lpmv
+# ------------------------------------------------------------------------------
+
+@check_version(mpmath, '0.15')
+def test_lpmv():
+    pts = []
+    for x in [-0.99, -0.557, 1e-6, 0.132, 1]:
+        pts.extend([
+            (1, 1, x),
+            (1, -1, x),
+            (-1, 1, x),
+            (-1, -2, x),
+            (1, 1.7, x),
+            (1, -1.7, x),
+            (-1, 1.7, x),
+            (-1, -2.7, x),
+            (1, 10, x),
+            (1, 11, x),
+            (3, 8, x),
+            (5, 11, x),
+            (-3, 8, x),
+            (-5, 11, x),
+            (3, -8, x),
+            (5, -11, x),
+            (-3, -8, x),
+            (-5, -11, x),
+            (3, 8.3, x),
+            (5, 11.3, x),
+            (-3, 8.3, x),
+            (-5, 11.3, x),
+            (3, -8.3, x),
+            (5, -11.3, x),
+            (-3, -8.3, x),
+            (-5, -11.3, x),
+        ])
+
+    def mplegenp(nu, mu, x):
+        if mu == int(mu) and x == 1:
+            # mpmath 0.17 gets this wrong
+            if mu == 0:
+                return 1
+            else:
+                return 0
+        return mpmath.legenp(nu, mu, x)
+
+    dataset = [p + (mplegenp(p[1], p[0], p[2]),) for p in pts]
+    dataset = np.array(dataset, dtype=np.float64)
+
+    def evf(mu, nu, x):
+        return sc.lpmv(mu.astype(int), nu, x)
+
+    with np.errstate(invalid='ignore'):
+        FuncData(evf, dataset, (0,1,2), 3, rtol=1e-10, atol=1e-14).check()
+
+
+# ------------------------------------------------------------------------------
+# beta
+# ------------------------------------------------------------------------------
+
+@pytest.mark.slow
+@check_version(mpmath, '0.15')
+def test_beta():
+    np.random.seed(1234)
+
+    b = np.r_[np.logspace(-200, 200, 4),
+              np.logspace(-10, 10, 4),
+              np.logspace(-1, 1, 4),
+              np.arange(-10, 11, 1),
+              np.arange(-10, 11, 1) + 0.5,
+              -1, -2.3, -3, -100.3, -10003.4]
+    a = b
+
+    ab = np.array(np.broadcast_arrays(a[:,None], b[None,:])).reshape(2, -1).T
+
+    old_dps, old_prec = mpmath.mp.dps, mpmath.mp.prec
+    try:
+        mpmath.mp.dps = 400
+
+        assert_func_equal(sc.beta,
+                          lambda a, b: float(mpmath.beta(a, b)),
+                          ab,
+                          vectorized=False,
+                          rtol=1e-10,
+                          ignore_inf_sign=True)
+
+        assert_func_equal(
+            sc.betaln,
+            lambda a, b: float(mpmath.log(abs(mpmath.beta(a, b)))),
+            ab,
+            vectorized=False,
+            rtol=1e-10)
+    finally:
+        mpmath.mp.dps, mpmath.mp.prec = old_dps, old_prec
+
+
+# ------------------------------------------------------------------------------
+# loggamma
+# ------------------------------------------------------------------------------
+
+LOGGAMMA_TAYLOR_RADIUS = 0.2
+
+
+@check_version(mpmath, '0.19')
+def test_loggamma_taylor_transition():
+    # Make sure there isn't a big jump in accuracy when we move from
+    # using the Taylor series to using the recurrence relation.
+
+    r = LOGGAMMA_TAYLOR_RADIUS + np.array([-0.1, -0.01, 0, 0.01, 0.1])
+    theta = np.linspace(0, 2*np.pi, 20)
+    r, theta = np.meshgrid(r, theta)
+    dz = r*np.exp(1j*theta)
+    z = np.r_[1 + dz, 2 + dz].flatten()
+
+    dataset = [(z0, complex(mpmath.loggamma(z0))) for z0 in z]
+    dataset = np.array(dataset)
+
+    FuncData(sc.loggamma, dataset, 0, 1, rtol=5e-14).check()
+
+
+@check_version(mpmath, '0.19')
+def test_loggamma_taylor():
+    # Test around the zeros at z = 1, 2.
+
+    r = np.logspace(-16, np.log10(LOGGAMMA_TAYLOR_RADIUS), 10)
+    theta = np.linspace(0, 2*np.pi, 20)
+    r, theta = np.meshgrid(r, theta)
+    dz = r*np.exp(1j*theta)
+    z = np.r_[1 + dz, 2 + dz].flatten()
+
+    dataset = [(z0, complex(mpmath.loggamma(z0))) for z0 in z]
+    dataset = np.array(dataset)
+
+    FuncData(sc.loggamma, dataset, 0, 1, rtol=5e-14).check()
+
+
+# ------------------------------------------------------------------------------
+# rgamma
+# ------------------------------------------------------------------------------
+
+@check_version(mpmath, '0.19')
+@pytest.mark.slow
+def test_rgamma_zeros():
+    # Test around the zeros at z = 0, -1, -2, ...,  -169. (After -169 we
+    # get values that are out of floating point range even when we're
+    # within 0.1 of the zero.)
+
+    # Can't use too many points here or the test takes forever.
+    dx = np.r_[-np.logspace(-1, -13, 3), 0, np.logspace(-13, -1, 3)]
+    dy = dx.copy()
+    dx, dy = np.meshgrid(dx, dy)
+    dz = dx + 1j*dy
+    zeros = np.arange(0, -170, -1).reshape(1, 1, -1)
+    z = (zeros + np.dstack((dz,)*zeros.size)).flatten()
+    with mpmath.workdps(100):
+        dataset = [(z0, complex(mpmath.rgamma(z0))) for z0 in z]
+
+    dataset = np.array(dataset)
+    FuncData(sc.rgamma, dataset, 0, 1, rtol=1e-12).check()
+
+
+# ------------------------------------------------------------------------------
+# digamma
+# ------------------------------------------------------------------------------
+
+@check_version(mpmath, '0.19')
+@pytest.mark.slow
+def test_digamma_roots():
+    # Test the special-cased roots for digamma.
+    root = mpmath.findroot(mpmath.digamma, 1.5)
+    roots = [float(root)]
+    root = mpmath.findroot(mpmath.digamma, -0.5)
+    roots.append(float(root))
+    roots = np.array(roots)
+
+    # If we test beyond a radius of 0.24 mpmath will take forever.
+    dx = np.r_[-0.24, -np.logspace(-1, -15, 10), 0, np.logspace(-15, -1, 10), 0.24]
+    dy = dx.copy()
+    dx, dy = np.meshgrid(dx, dy)
+    dz = dx + 1j*dy
+    z = (roots + np.dstack((dz,)*roots.size)).flatten()
+    with mpmath.workdps(30):
+        dataset = [(z0, complex(mpmath.digamma(z0))) for z0 in z]
+
+    dataset = np.array(dataset)
+    FuncData(sc.digamma, dataset, 0, 1, rtol=1e-14).check()
+
+
+@check_version(mpmath, '0.19')
+def test_digamma_negreal():
+    # Test digamma around the negative real axis. Don't do this in
+    # TestSystematic because the points need some jiggering so that
+    # mpmath doesn't take forever.
+
+    digamma = exception_to_nan(mpmath.digamma)
+
+    x = -np.logspace(300, -30, 100)
+    y = np.r_[-np.logspace(0, -3, 5), 0, np.logspace(-3, 0, 5)]
+    x, y = np.meshgrid(x, y)
+    z = (x + 1j*y).flatten()
+
+    with mpmath.workdps(40):
+        dataset = [(z0, complex(digamma(z0))) for z0 in z]
+    dataset = np.asarray(dataset)
+
+    FuncData(sc.digamma, dataset, 0, 1, rtol=1e-13).check()
+
+
+@check_version(mpmath, '0.19')
+def test_digamma_boundary():
+    # Check that there isn't a jump in accuracy when we switch from
+    # using the asymptotic series to the reflection formula.
+
+    x = -np.logspace(300, -30, 100)
+    y = np.array([-6.1, -5.9, 5.9, 6.1])
+    x, y = np.meshgrid(x, y)
+    z = (x + 1j*y).flatten()
+
+    with mpmath.workdps(30):
+        dataset = [(z0, complex(mpmath.digamma(z0))) for z0 in z]
+    dataset = np.asarray(dataset)
+
+    FuncData(sc.digamma, dataset, 0, 1, rtol=1e-13).check()
+
+
+# ------------------------------------------------------------------------------
+# gammainc
+# ------------------------------------------------------------------------------
+
+@check_version(mpmath, '0.19')
+@pytest.mark.slow
+def test_gammainc_boundary():
+    # Test the transition to the asymptotic series.
+    small = 20
+    a = np.linspace(0.5*small, 2*small, 50)
+    x = a.copy()
+    a, x = np.meshgrid(a, x)
+    a, x = a.flatten(), x.flatten()
+    with mpmath.workdps(100):
+        dataset = [(a0, x0, float(mpmath.gammainc(a0, b=x0, regularized=True)))
+                   for a0, x0 in zip(a, x)]
+    dataset = np.array(dataset)
+
+    FuncData(sc.gammainc, dataset, (0, 1), 2, rtol=1e-12).check()
+
+
+# ------------------------------------------------------------------------------
+# spence
+# ------------------------------------------------------------------------------
+
+@check_version(mpmath, '0.19')
+@pytest.mark.slow
+def test_spence_circle():
+    # The trickiest region for spence is around the circle |z - 1| = 1,
+    # so test that region carefully.
+
+    def spence(z):
+        return complex(mpmath.polylog(2, 1 - z))
+
+    r = np.linspace(0.5, 1.5)
+    theta = np.linspace(0, 2*pi)
+    z = (1 + np.outer(r, np.exp(1j*theta))).flatten()
+    dataset = np.asarray([(z0, spence(z0)) for z0 in z])
+
+    FuncData(sc.spence, dataset, 0, 1, rtol=1e-14).check()
+
+
+# ------------------------------------------------------------------------------
+# sinpi and cospi
+# ------------------------------------------------------------------------------
+
+@check_version(mpmath, '0.19')
+def test_sinpi_zeros():
+    eps = np.finfo(float).eps
+    dx = np.r_[-np.logspace(0, -13, 3), 0, np.logspace(-13, 0, 3)]
+    dy = dx.copy()
+    dx, dy = np.meshgrid(dx, dy)
+    dz = dx + 1j*dy
+    zeros = np.arange(-100, 100, 1).reshape(1, 1, -1)
+    z = (zeros + np.dstack((dz,)*zeros.size)).flatten()
+    dataset = np.asarray([(z0, complex(mpmath.sinpi(z0)))
+                          for z0 in z])
+    FuncData(_sinpi, dataset, 0, 1, rtol=2*eps).check()
+
+
+@check_version(mpmath, '0.19')
+def test_cospi_zeros():
+    eps = np.finfo(float).eps
+    dx = np.r_[-np.logspace(0, -13, 3), 0, np.logspace(-13, 0, 3)]
+    dy = dx.copy()
+    dx, dy = np.meshgrid(dx, dy)
+    dz = dx + 1j*dy
+    zeros = (np.arange(-100, 100, 1) + 0.5).reshape(1, 1, -1)
+    z = (zeros + np.dstack((dz,)*zeros.size)).flatten()
+    dataset = np.asarray([(z0, complex(mpmath.cospi(z0)))
+                          for z0 in z])
+
+    FuncData(_cospi, dataset, 0, 1, rtol=2*eps).check()
+
+
+# ------------------------------------------------------------------------------
+# ellipj
+# ------------------------------------------------------------------------------
+
+@check_version(mpmath, '0.19')
+def test_dn_quarter_period():
+    def dn(u, m):
+        return sc.ellipj(u, m)[2]
+
+    def mpmath_dn(u, m):
+        return float(mpmath.ellipfun("dn", u=u, m=m))
+
+    m = np.linspace(0, 1, 20)
+    du = np.r_[-np.logspace(-1, -15, 10), 0, np.logspace(-15, -1, 10)]
+    dataset = []
+    for m0 in m:
+        u0 = float(mpmath.ellipk(m0))
+        for du0 in du:
+            p = u0 + du0
+            dataset.append((p, m0, mpmath_dn(p, m0)))
+    dataset = np.asarray(dataset)
+
+    FuncData(dn, dataset, (0, 1), 2, rtol=1e-10).check()
+
+
+# ------------------------------------------------------------------------------
+# Wright Omega
+# ------------------------------------------------------------------------------
+
+def _mpmath_wrightomega(z, dps):
+    with mpmath.workdps(dps):
+        z = mpmath.mpc(z)
+        unwind = mpmath.ceil((z.imag - mpmath.pi)/(2*mpmath.pi))
+        res = mpmath.lambertw(mpmath.exp(z), unwind)
+    return res
+
+
+@pytest.mark.slow
+@check_version(mpmath, '0.19')
+def test_wrightomega_branch():
+    x = -np.logspace(10, 0, 25)
+    picut_above = [np.nextafter(np.pi, np.inf)]
+    picut_below = [np.nextafter(np.pi, -np.inf)]
+    npicut_above = [np.nextafter(-np.pi, np.inf)]
+    npicut_below = [np.nextafter(-np.pi, -np.inf)]
+    for i in range(50):
+        picut_above.append(np.nextafter(picut_above[-1], np.inf))
+        picut_below.append(np.nextafter(picut_below[-1], -np.inf))
+        npicut_above.append(np.nextafter(npicut_above[-1], np.inf))
+        npicut_below.append(np.nextafter(npicut_below[-1], -np.inf))
+    y = np.hstack((picut_above, picut_below, npicut_above, npicut_below))
+    x, y = np.meshgrid(x, y)
+    z = (x + 1j*y).flatten()
+
+    dataset = np.asarray([(z0, complex(_mpmath_wrightomega(z0, 25)))
+                          for z0 in z])
+
+    FuncData(sc.wrightomega, dataset, 0, 1, rtol=1e-8).check()
+
+
+@pytest.mark.slow
+@check_version(mpmath, '0.19')
+def test_wrightomega_region1():
+    # This region gets less coverage in the TestSystematic test
+    x = np.linspace(-2, 1)
+    y = np.linspace(1, 2*np.pi)
+    x, y = np.meshgrid(x, y)
+    z = (x + 1j*y).flatten()
+
+    dataset = np.asarray([(z0, complex(_mpmath_wrightomega(z0, 25)))
+                          for z0 in z])
+
+    FuncData(sc.wrightomega, dataset, 0, 1, rtol=1e-15).check()
+
+
+@pytest.mark.slow
+@check_version(mpmath, '0.19')
+def test_wrightomega_region2():
+    # This region gets less coverage in the TestSystematic test
+    x = np.linspace(-2, 1)
+    y = np.linspace(-2*np.pi, -1)
+    x, y = np.meshgrid(x, y)
+    z = (x + 1j*y).flatten()
+
+    dataset = np.asarray([(z0, complex(_mpmath_wrightomega(z0, 25)))
+                          for z0 in z])
+
+    FuncData(sc.wrightomega, dataset, 0, 1, rtol=1e-15).check()
+
+
+# ------------------------------------------------------------------------------
+# lambertw
+# ------------------------------------------------------------------------------
+
+@pytest.mark.slow
+@check_version(mpmath, '0.19')
+def test_lambertw_smallz():
+    x, y = np.linspace(-1, 1, 25), np.linspace(-1, 1, 25)
+    x, y = np.meshgrid(x, y)
+    z = (x + 1j*y).flatten()
+
+    dataset = np.asarray([(z0, complex(mpmath.lambertw(z0)))
+                          for z0 in z])
+
+    FuncData(sc.lambertw, dataset, 0, 1, rtol=1e-13).check()
+
+
+# ------------------------------------------------------------------------------
+# Systematic tests
+# ------------------------------------------------------------------------------
+
+HYPERKW = dict(maxprec=200, maxterms=200)
+
+
+@pytest.mark.slow
+@check_version(mpmath, '0.17')
+class TestSystematic:
+
+    def test_airyai(self):
+        # oscillating function, limit range
+        assert_mpmath_equal(lambda z: sc.airy(z)[0],
+                            mpmath.airyai,
+                            [Arg(-1e8, 1e8)],
+                            rtol=1e-5)
+        assert_mpmath_equal(lambda z: sc.airy(z)[0],
+                            mpmath.airyai,
+                            [Arg(-1e3, 1e3)])
+
+    def test_airyai_complex(self):
+        assert_mpmath_equal(lambda z: sc.airy(z)[0],
+                            mpmath.airyai,
+                            [ComplexArg()])
+
+    def test_airyai_prime(self):
+        # oscillating function, limit range
+        assert_mpmath_equal(lambda z: sc.airy(z)[1], lambda z:
+                            mpmath.airyai(z, derivative=1),
+                            [Arg(-1e8, 1e8)],
+                            rtol=1e-5)
+        assert_mpmath_equal(lambda z: sc.airy(z)[1], lambda z:
+                            mpmath.airyai(z, derivative=1),
+                            [Arg(-1e3, 1e3)])
+
+    def test_airyai_prime_complex(self):
+        assert_mpmath_equal(lambda z: sc.airy(z)[1], lambda z:
+                            mpmath.airyai(z, derivative=1),
+                            [ComplexArg()])
+
+    def test_airybi(self):
+        # oscillating function, limit range
+        assert_mpmath_equal(lambda z: sc.airy(z)[2], lambda z:
+                            mpmath.airybi(z),
+                            [Arg(-1e8, 1e8)],
+                            rtol=1e-5)
+        assert_mpmath_equal(lambda z: sc.airy(z)[2], lambda z:
+                            mpmath.airybi(z),
+                            [Arg(-1e3, 1e3)])
+
+    def test_airybi_complex(self):
+        assert_mpmath_equal(lambda z: sc.airy(z)[2], lambda z:
+                            mpmath.airybi(z),
+                            [ComplexArg()])
+
+    def test_airybi_prime(self):
+        # oscillating function, limit range
+        assert_mpmath_equal(lambda z: sc.airy(z)[3], lambda z:
+                            mpmath.airybi(z, derivative=1),
+                            [Arg(-1e8, 1e8)],
+                            rtol=1e-5)
+        assert_mpmath_equal(lambda z: sc.airy(z)[3], lambda z:
+                            mpmath.airybi(z, derivative=1),
+                            [Arg(-1e3, 1e3)])
+
+    def test_airybi_prime_complex(self):
+        assert_mpmath_equal(lambda z: sc.airy(z)[3], lambda z:
+                            mpmath.airybi(z, derivative=1),
+                            [ComplexArg()])
+
+    def test_bei(self):
+        assert_mpmath_equal(sc.bei,
+                            exception_to_nan(lambda z: mpmath.bei(0, z, **HYPERKW)),
+                            [Arg(-1e3, 1e3)])
+
+    def test_ber(self):
+        assert_mpmath_equal(sc.ber,
+                            exception_to_nan(lambda z: mpmath.ber(0, z, **HYPERKW)),
+                            [Arg(-1e3, 1e3)])
+
+    def test_bernoulli(self):
+        assert_mpmath_equal(lambda n: sc.bernoulli(int(n))[int(n)],
+                            lambda n: float(mpmath.bernoulli(int(n))),
+                            [IntArg(0, 13000)],
+                            rtol=1e-9, n=13000)
+
+    def test_besseli(self):
+        assert_mpmath_equal(
+            sc.iv,
+            exception_to_nan(lambda v, z: mpmath.besseli(v, z, **HYPERKW)),
+            [Arg(-1e100, 1e100), Arg()],
+            atol=1e-270,
+        )
+
+    def test_besseli_complex(self):
+        assert_mpmath_equal(
+            lambda v, z: sc.iv(v.real, z),
+            exception_to_nan(lambda v, z: mpmath.besseli(v, z, **HYPERKW)),
+            [Arg(-1e100, 1e100), ComplexArg()],
+        )
+
+    def test_besselj(self):
+        assert_mpmath_equal(
+            sc.jv,
+            exception_to_nan(lambda v, z: mpmath.besselj(v, z, **HYPERKW)),
+            [Arg(-1e100, 1e100), Arg(-1e3, 1e3)],
+            ignore_inf_sign=True,
+        )
+
+        # loss of precision at large arguments due to oscillation
+        assert_mpmath_equal(
+            sc.jv,
+            exception_to_nan(lambda v, z: mpmath.besselj(v, z, **HYPERKW)),
+            [Arg(-1e100, 1e100), Arg(-1e8, 1e8)],
+            ignore_inf_sign=True,
+            rtol=1e-5,
+        )
+
+    def test_besselj_complex(self):
+        assert_mpmath_equal(
+            lambda v, z: sc.jv(v.real, z),
+            exception_to_nan(lambda v, z: mpmath.besselj(v, z, **HYPERKW)),
+            [Arg(), ComplexArg()]
+        )
+
+    def test_besselk(self):
+        assert_mpmath_equal(
+            sc.kv,
+            mpmath.besselk,
+            [Arg(-200, 200), Arg(0, np.inf)],
+            nan_ok=False,
+            rtol=1e-12,
+        )
+
+    def test_besselk_int(self):
+        assert_mpmath_equal(
+            sc.kn,
+            mpmath.besselk,
+            [IntArg(-200, 200), Arg(0, np.inf)],
+            nan_ok=False,
+            rtol=1e-12,
+        )
+
+    def test_besselk_complex(self):
+        assert_mpmath_equal(
+            lambda v, z: sc.kv(v.real, z),
+            exception_to_nan(lambda v, z: mpmath.besselk(v, z, **HYPERKW)),
+            [Arg(-1e100, 1e100), ComplexArg()],
+        )
+
+    def test_bessely(self):
+        def mpbessely(v, x):
+            r = float(mpmath.bessely(v, x, **HYPERKW))
+            if abs(r) > 1e305:
+                # overflowing to inf a bit earlier is OK
+                r = np.inf * np.sign(r)
+            if abs(r) == 0 and x == 0:
+                # invalid result from mpmath, point x=0 is a divergence
+                return np.nan
+            return r
+        assert_mpmath_equal(
+            sc.yv,
+            exception_to_nan(mpbessely),
+            [Arg(-1e100, 1e100), Arg(-1e8, 1e8)],
+            n=5000,
+        )
+
+    def test_bessely_complex(self):
+        def mpbessely(v, x):
+            r = complex(mpmath.bessely(v, x, **HYPERKW))
+            if abs(r) > 1e305:
+                # overflowing to inf a bit earlier is OK
+                with np.errstate(invalid='ignore'):
+                    r = np.inf * np.sign(r)
+            return r
+        assert_mpmath_equal(
+            lambda v, z: sc.yv(v.real, z),
+            exception_to_nan(mpbessely),
+            [Arg(), ComplexArg()],
+            n=15000,
+        )
+
+    def test_bessely_int(self):
+        def mpbessely(v, x):
+            r = float(mpmath.bessely(v, x))
+            if abs(r) == 0 and x == 0:
+                # invalid result from mpmath, point x=0 is a divergence
+                return np.nan
+            return r
+        assert_mpmath_equal(
+            lambda v, z: sc.yn(int(v), z),
+            exception_to_nan(mpbessely),
+            [IntArg(-1000, 1000), Arg(-1e8, 1e8)],
+        )
+
+    def test_beta(self):
+        bad_points = []
+
+        def beta(a, b, nonzero=False):
+            if a < -1e12 or b < -1e12:
+                # Function is defined here only at integers, but due
+                # to loss of precision this is numerically
+                # ill-defined. Don't compare values here.
+                return np.nan
+            if (a < 0 or b < 0) and (abs(float(a + b)) % 1) == 0:
+                # close to a zero of the function: mpmath and scipy
+                # will not round here the same, so the test needs to be
+                # run with an absolute tolerance
+                if nonzero:
+                    bad_points.append((float(a), float(b)))
+                    return np.nan
+            return mpmath.beta(a, b)
+
+        assert_mpmath_equal(
+            sc.beta,
+            lambda a, b: beta(a, b, nonzero=True),
+            [Arg(), Arg()],
+            dps=400,
+            ignore_inf_sign=True,
+        )
+
+        assert_mpmath_equal(
+            sc.beta,
+            beta,
+            np.array(bad_points),
+            dps=400,
+            ignore_inf_sign=True,
+            atol=1e-11,
+        )
+
+    def test_betainc(self):
+        assert_mpmath_equal(
+            sc.betainc,
+            time_limited()(
+                exception_to_nan(
+                    lambda a, b, x: mpmath.betainc(a, b, 0, x, regularized=True)
+                )
+            ),
+            [Arg(), Arg(), Arg()],
+        )
+
+    def test_betaincc(self):
+        assert_mpmath_equal(
+            sc.betaincc,
+            time_limited()(
+                exception_to_nan(
+                    lambda a, b, x: mpmath.betainc(a, b, x, 1, regularized=True)
+                )
+            ),
+            [Arg(), Arg(), Arg()],
+            dps=400,
+        )
+
+    def test_binom(self):
+        bad_points = []
+
+        def binomial(n, k, nonzero=False):
+            if abs(k) > 1e8*(abs(n) + 1):
+                # The binomial is rapidly oscillating in this region,
+                # and the function is numerically ill-defined. Don't
+                # compare values here.
+                return np.nan
+            if n < k and abs(float(n-k) - np.round(float(n-k))) < 1e-15:
+                # close to a zero of the function: mpmath and scipy
+                # will not round here the same, so the test needs to be
+                # run with an absolute tolerance
+                if nonzero:
+                    bad_points.append((float(n), float(k)))
+                    return np.nan
+            return mpmath.binomial(n, k)
+
+        assert_mpmath_equal(
+            sc.binom,
+            lambda n, k: binomial(n, k, nonzero=True),
+            [Arg(), Arg()],
+            dps=400,
+        )
+
+        assert_mpmath_equal(
+            sc.binom,
+            binomial,
+            np.array(bad_points),
+            dps=400,
+            atol=1e-14,
+        )
+
+    def test_chebyt_int(self):
+        assert_mpmath_equal(
+            lambda n, x: sc.eval_chebyt(int(n), x),
+            exception_to_nan(lambda n, x: mpmath.chebyt(n, x, **HYPERKW)),
+            [IntArg(), Arg()],
+            dps=50,
+        )
+
+    @pytest.mark.xfail(run=False, reason="some cases in hyp2f1 not fully accurate")
+    def test_chebyt(self):
+        assert_mpmath_equal(
+            sc.eval_chebyt,
+            lambda n, x: time_limited()(
+                exception_to_nan(mpmath.chebyt)
+            )(n, x, **HYPERKW),
+            [Arg(-101, 101), Arg()],
+            n=10000,
+        )
+
+    def test_chebyu_int(self):
+        assert_mpmath_equal(
+            lambda n, x: sc.eval_chebyu(int(n), x),
+            exception_to_nan(lambda n, x: mpmath.chebyu(n, x, **HYPERKW)),
+            [IntArg(), Arg()],
+            dps=50,
+        )
+
+    @pytest.mark.xfail(run=False, reason="some cases in hyp2f1 not fully accurate")
+    def test_chebyu(self):
+        assert_mpmath_equal(
+            sc.eval_chebyu,
+            lambda n, x: time_limited()(
+                exception_to_nan(mpmath.chebyu)
+            )(n, x, **HYPERKW),
+            [Arg(-101, 101), Arg()],
+        )
+
+    def test_chi(self):
+        def chi(x):
+            return sc.shichi(x)[1]
+        assert_mpmath_equal(chi, mpmath.chi, [Arg()])
+        # check asymptotic series cross-over
+        assert_mpmath_equal(chi, mpmath.chi, [FixedArg([88 - 1e-9, 88, 88 + 1e-9])])
+
+    def test_chi_complex(self):
+        def chi(z):
+            return sc.shichi(z)[1]
+        # chi oscillates as Im[z] -> +- inf, so limit range
+        assert_mpmath_equal(
+            chi,
+            mpmath.chi,
+            [ComplexArg(complex(-np.inf, -1e8), complex(np.inf, 1e8))],
+            rtol=1e-12,
+        )
+
+    def test_ci(self):
+        def ci(x):
+            return sc.sici(x)[1]
+        # oscillating function: limit range
+        assert_mpmath_equal(ci, mpmath.ci, [Arg(-1e8, 1e8)])
+
+    def test_ci_complex(self):
+        def ci(z):
+            return sc.sici(z)[1]
+        # ci oscillates as Re[z] -> +- inf, so limit range
+        assert_mpmath_equal(
+            ci,
+            mpmath.ci,
+            [ComplexArg(complex(-1e8, -np.inf), complex(1e8, np.inf))],
+            rtol=1e-8,
+        )
+
+    def test_cospi(self):
+        eps = np.finfo(float).eps
+        assert_mpmath_equal(_cospi, mpmath.cospi, [Arg()], nan_ok=False, rtol=2*eps)
+
+    def test_cospi_complex(self):
+        assert_mpmath_equal(
+            _cospi,
+            mpmath.cospi,
+            [ComplexArg()],
+            nan_ok=False,
+            rtol=1e-13,
+        )
+
+    def test_digamma(self):
+        assert_mpmath_equal(
+            sc.digamma,
+            exception_to_nan(mpmath.digamma),
+            [Arg()],
+            rtol=1e-12,
+            dps=50,
+        )
+
+    def test_digamma_complex(self):
+        # Test on a cut plane because mpmath will hang. See
+        # test_digamma_negreal for tests on the negative real axis.
+        def param_filter(z):
+            return np.where((z.real < 0) & (np.abs(z.imag) < 1.12), False, True)
+
+        assert_mpmath_equal(
+            sc.digamma,
+            exception_to_nan(mpmath.digamma),
+            [ComplexArg()],
+            rtol=1e-13,
+            dps=40,
+            param_filter=param_filter
+        )
+
+    def test_e1(self):
+        assert_mpmath_equal(
+            sc.exp1,
+            mpmath.e1,
+            [Arg()],
+            rtol=1e-14,
+        )
+
+    def test_e1_complex(self):
+        # E_1 oscillates as Im[z] -> +- inf, so limit range
+        assert_mpmath_equal(
+            sc.exp1,
+            mpmath.e1,
+            [ComplexArg(complex(-np.inf, -1e8), complex(np.inf, 1e8))],
+            rtol=1e-11,
+        )
+
+        # Check cross-over region
+        assert_mpmath_equal(
+            sc.exp1,
+            mpmath.e1,
+            (np.linspace(-50, 50, 171)[:, None]
+             + np.r_[0, np.logspace(-3, 2, 61), -np.logspace(-3, 2, 11)]*1j).ravel(),
+            rtol=1e-11,
+        )
+        assert_mpmath_equal(
+            sc.exp1,
+            mpmath.e1,
+            (np.linspace(-50, -35, 10000) + 0j),
+            rtol=1e-11,
+        )
+
+    def test_exprel(self):
+        assert_mpmath_equal(
+            sc.exprel,
+            lambda x: mpmath.expm1(x)/x if x != 0 else mpmath.mpf('1.0'),
+            [Arg(a=-np.log(np.finfo(np.float64).max),
+                 b=np.log(np.finfo(np.float64).max))],
+        )
+        assert_mpmath_equal(
+            sc.exprel,
+            lambda x: mpmath.expm1(x)/x if x != 0 else mpmath.mpf('1.0'),
+            np.array([1e-12, 1e-24, 0, 1e12, 1e24, np.inf]),
+            rtol=1e-11,
+        )
+        assert_(np.isinf(sc.exprel(np.inf)))
+        assert_(sc.exprel(-np.inf) == 0)
+
+    def test_expm1_complex(self):
+        # Oscillates as a function of Im[z], so limit range to avoid loss of precision
+        assert_mpmath_equal(
+            sc.expm1,
+            mpmath.expm1,
+            [ComplexArg(complex(-np.inf, -1e7), complex(np.inf, 1e7))],
+        )
+
+    def test_log1p_complex(self):
+        assert_mpmath_equal(
+            sc.log1p,
+            lambda x: mpmath.log(x+1),
+            [ComplexArg()],
+            dps=60,
+        )
+
+    def test_log1pmx(self):
+        assert_mpmath_equal(
+            _log1pmx,
+            lambda x: mpmath.log(x + 1) - x,
+            [Arg()],
+            dps=60,
+            rtol=1e-14,
+        )
+
+    def test_ei(self):
+        assert_mpmath_equal(sc.expi, mpmath.ei, [Arg()], rtol=1e-11)
+
+    def test_ei_complex(self):
+        # Ei oscillates as Im[z] -> +- inf, so limit range
+        assert_mpmath_equal(
+            sc.expi,
+            mpmath.ei,
+            [ComplexArg(complex(-np.inf, -1e8), complex(np.inf, 1e8))],
+            rtol=1e-9,
+        )
+
+    def test_ellipe(self):
+        assert_mpmath_equal(sc.ellipe, mpmath.ellipe, [Arg(b=1.0)])
+
+    def test_ellipeinc(self):
+        assert_mpmath_equal(sc.ellipeinc, mpmath.ellipe, [Arg(-1e3, 1e3), Arg(b=1.0)])
+
+    def test_ellipeinc_largephi(self):
+        assert_mpmath_equal(sc.ellipeinc, mpmath.ellipe, [Arg(), Arg()])
+
+    def test_ellipf(self):
+        assert_mpmath_equal(sc.ellipkinc, mpmath.ellipf, [Arg(-1e3, 1e3), Arg()])
+
+    def test_ellipf_largephi(self):
+        assert_mpmath_equal(sc.ellipkinc, mpmath.ellipf, [Arg(), Arg()])
+
+    def test_ellipk(self):
+        assert_mpmath_equal(sc.ellipk, mpmath.ellipk, [Arg(b=1.0)])
+        assert_mpmath_equal(
+            sc.ellipkm1,
+            lambda m: mpmath.ellipk(1 - m),
+            [Arg(a=0.0)],
+            dps=400,
+        )
+
+    def test_ellipkinc(self):
+        def ellipkinc(phi, m):
+            return mpmath.ellippi(0, phi, m)
+        assert_mpmath_equal(
+            sc.ellipkinc,
+            ellipkinc,
+            [Arg(-1e3, 1e3), Arg(b=1.0)],
+            ignore_inf_sign=True,
+        )
+
+    def test_ellipkinc_largephi(self):
+        def ellipkinc(phi, m):
+            return mpmath.ellippi(0, phi, m)
+        assert_mpmath_equal(
+            sc.ellipkinc,
+            ellipkinc,
+            [Arg(), Arg(b=1.0)],
+            ignore_inf_sign=True,
+        )
+
+    def test_ellipfun_sn(self):
+        def sn(u, m):
+            # mpmath doesn't get the zero at u = 0--fix that
+            if u == 0:
+                return 0
+            else:
+                return mpmath.ellipfun("sn", u=u, m=m)
+
+        # Oscillating function --- limit range of first argument; the
+        # loss of precision there is an expected numerical feature
+        # rather than an actual bug
+        assert_mpmath_equal(
+            lambda u, m: sc.ellipj(u, m)[0],
+            sn,
+            [Arg(-1e6, 1e6), Arg(a=0, b=1)],
+            rtol=1e-8,
+        )
+
+    def test_ellipfun_cn(self):
+        # see comment in ellipfun_sn
+        assert_mpmath_equal(
+            lambda u, m: sc.ellipj(u, m)[1],
+            lambda u, m: mpmath.ellipfun("cn", u=u, m=m),
+            [Arg(-1e6, 1e6), Arg(a=0, b=1)],
+            rtol=1e-8,
+        )
+
+    def test_ellipfun_dn(self):
+        # see comment in ellipfun_sn
+        assert_mpmath_equal(
+            lambda u, m: sc.ellipj(u, m)[2],
+            lambda u, m: mpmath.ellipfun("dn", u=u, m=m),
+            [Arg(-1e6, 1e6), Arg(a=0, b=1)],
+            rtol=1e-8,
+        )
+
+    def test_erf(self):
+        assert_mpmath_equal(sc.erf, lambda z: mpmath.erf(z), [Arg()])
+
+    def test_erf_complex(self):
+        assert_mpmath_equal(sc.erf, lambda z: mpmath.erf(z), [ComplexArg()], n=200)
+
+    def test_erfc(self):
+        assert_mpmath_equal(
+            sc.erfc,
+            exception_to_nan(lambda z: mpmath.erfc(z)),
+            [Arg()],
+            rtol=1e-13,
+        )
+
+    def test_erfc_complex(self):
+        assert_mpmath_equal(
+            sc.erfc,
+            exception_to_nan(lambda z: mpmath.erfc(z)),
+            [ComplexArg()],
+            n=200,
+        )
+
+    def test_erfi(self):
+        assert_mpmath_equal(sc.erfi, mpmath.erfi, [Arg()], n=200)
+
+    def test_erfi_complex(self):
+        assert_mpmath_equal(sc.erfi, mpmath.erfi, [ComplexArg()], n=200)
+
+    def test_ndtr(self):
+        assert_mpmath_equal(
+            sc.ndtr,
+            exception_to_nan(lambda z: mpmath.ncdf(z)),
+            [Arg()],
+            n=200,
+        )
+
+    def test_ndtr_complex(self):
+        assert_mpmath_equal(
+            sc.ndtr,
+            lambda z: mpmath.erfc(-z/np.sqrt(2.))/2.,
+            [ComplexArg(a=complex(-10000, -10000), b=complex(10000, 10000))],
+            n=400,
+        )
+
+    def test_log_ndtr(self):
+        assert_mpmath_equal(
+            sc.log_ndtr,
+            exception_to_nan(lambda z: mpmath.log(mpmath.ncdf(z))),
+            [Arg()], n=600, dps=300, rtol=1e-13,
+        )
+
+    def test_log_ndtr_complex(self):
+        assert_mpmath_equal(
+            sc.log_ndtr,
+            exception_to_nan(lambda z: mpmath.log(mpmath.erfc(-z/np.sqrt(2.))/2.)),
+            [ComplexArg(a=complex(-10000, -100), b=complex(10000, 100))],
+            n=200, dps=300,
+        )
+
+    def test_eulernum(self):
+        assert_mpmath_equal(
+            lambda n: sc.euler(n)[-1],
+            mpmath.eulernum,
+            [IntArg(1, 10000)],
+            n=10000,
+        )
+
+    def test_expint(self):
+        assert_mpmath_equal(
+            sc.expn,
+            mpmath.expint,
+            [IntArg(0, 200), Arg(0, np.inf)],
+            rtol=1e-13,
+            dps=160,
+        )
+
+    def test_fresnels(self):
+        def fresnels(x):
+            return sc.fresnel(x)[0]
+        assert_mpmath_equal(fresnels, mpmath.fresnels, [Arg()])
+
+    def test_fresnelc(self):
+        def fresnelc(x):
+            return sc.fresnel(x)[1]
+        assert_mpmath_equal(fresnelc, mpmath.fresnelc, [Arg()])
+
+    def test_gamma(self):
+        assert_mpmath_equal(sc.gamma, exception_to_nan(mpmath.gamma), [Arg()])
+
+    def test_gamma_complex(self):
+        assert_mpmath_equal(
+            sc.gamma,
+            exception_to_nan(mpmath.gamma),
+            [ComplexArg()],
+            rtol=5e-13,
+        )
+
+    def test_gammainc(self):
+        # Larger arguments are tested in test_data.py:test_local
+        assert_mpmath_equal(
+            sc.gammainc,
+            lambda z, b: mpmath.gammainc(z, b=b, regularized=True),
+            [Arg(0, 1e4, inclusive_a=False), Arg(0, 1e4)],
+            nan_ok=False,
+            rtol=1e-11,
+        )
+
+    def test_gammaincc(self):
+        # Larger arguments are tested in test_data.py:test_local
+        assert_mpmath_equal(
+            sc.gammaincc,
+            lambda z, a: mpmath.gammainc(z, a=a, regularized=True),
+            [Arg(0, 1e4, inclusive_a=False), Arg(0, 1e4)],
+            nan_ok=False,
+            rtol=1e-11,
+        )
+
+    def test_gammaln(self):
+        # The real part of loggamma is log(|gamma(z)|).
+        def f(z):
+            return mpmath.loggamma(z).real
+
+        assert_mpmath_equal(sc.gammaln, exception_to_nan(f), [Arg()])
+
+    @pytest.mark.xfail(run=False)
+    def test_gegenbauer(self):
+        assert_mpmath_equal(
+            sc.eval_gegenbauer,
+            exception_to_nan(mpmath.gegenbauer),
+            [Arg(-1e3, 1e3), Arg(), Arg()],
+        )
+
+    def test_gegenbauer_int(self):
+        # Redefine functions to deal with numerical + mpmath issues
+        def gegenbauer(n, a, x):
+            # Avoid overflow at large `a` (mpmath would need an even larger
+            # dps to handle this correctly, so just skip this region)
+            if abs(a) > 1e100:
+                return np.nan
+
+            # Deal with n=0, n=1 correctly; mpmath 0.17 doesn't do these
+            # always correctly
+            if n == 0:
+                r = 0.0 if a == 0.0 else 1.0
+            elif n == 1:
+                r = 2*a*x
+            else:
+                r = mpmath.gegenbauer(n, a, x)
+
+            # Mpmath 0.17 gives wrong results (spurious zero) in some cases, so
+            # compute the value by perturbing the result
+            if float(r) == 0 and a < -1 and float(a) == int(float(a)):
+                r = mpmath.gegenbauer(n, a + mpmath.mpf('1e-50'), x)
+                if abs(r) < mpmath.mpf('1e-50'):
+                    r = mpmath.mpf('0.0')
+
+            # Differing overflow thresholds in scipy vs. mpmath
+            if abs(r) > 1e270:
+                return np.inf
+            return r
+
+        def sc_gegenbauer(n, a, x):
+            r = sc.eval_gegenbauer(int(n), a, x)
+            # Differing overflow thresholds in scipy vs. mpmath
+            if abs(r) > 1e270:
+                return np.inf
+            return r
+        assert_mpmath_equal(
+            sc_gegenbauer,
+            exception_to_nan(gegenbauer),
+            [IntArg(0, 100), Arg(-1e9, 1e9), Arg()],
+            dps=100, ignore_inf_sign=True, rtol=1e-6,
+        )
+
+        # Check the small-x expansion
+        assert_mpmath_equal(
+            sc_gegenbauer,
+            exception_to_nan(gegenbauer),
+            [IntArg(0, 100), Arg(), FixedArg(np.logspace(-30, -4, 30))],
+            dps=100, ignore_inf_sign=True,
+        )
+
+    @pytest.mark.xfail(run=False)
+    def test_gegenbauer_complex(self):
+        assert_mpmath_equal(
+            lambda n, a, x: sc.eval_gegenbauer(int(n), a.real, x),
+            exception_to_nan(mpmath.gegenbauer),
+            [IntArg(0, 100), Arg(), ComplexArg()],
+        )
+
+    @nonfunctional_tooslow
+    def test_gegenbauer_complex_general(self):
+        assert_mpmath_equal(
+            lambda n, a, x: sc.eval_gegenbauer(n.real, a.real, x),
+            exception_to_nan(mpmath.gegenbauer),
+            [Arg(-1e3, 1e3), Arg(), ComplexArg()],
+        )
+
+    def test_hankel1(self):
+        assert_mpmath_equal(
+            sc.hankel1,
+            exception_to_nan(lambda v, x: mpmath.hankel1(v, x, **HYPERKW)),
+            [Arg(-1e20, 1e20), Arg()],
+        )
+
+    def test_hankel2(self):
+        assert_mpmath_equal(
+            sc.hankel2,
+            exception_to_nan(lambda v, x: mpmath.hankel2(v, x, **HYPERKW)),
+            [Arg(-1e20, 1e20), Arg()],
+        )
+
+    @pytest.mark.xfail(run=False, reason="issues at intermediately large orders")
+    def test_hermite(self):
+        assert_mpmath_equal(
+            lambda n, x: sc.eval_hermite(int(n), x),
+            exception_to_nan(mpmath.hermite),
+            [IntArg(0, 10000), Arg()],
+        )
+
+    # hurwitz: same as zeta
+
+    def test_hyp0f1(self):
+        # mpmath reports no convergence unless maxterms is large enough
+        KW = dict(maxprec=400, maxterms=1500)
+        # n=500 (non-xslow default) fails for one bad point
+        assert_mpmath_equal(
+            sc.hyp0f1,
+            lambda a, x: mpmath.hyp0f1(a, x, **KW),
+            [Arg(-1e7, 1e7), Arg(0, 1e5)],
+            n=5000,
+        )
+        # NB: The range of the second parameter ("z") is limited from below
+        # because of an overflow in the intermediate calculations. The way
+        # for fix it is to implement an asymptotic expansion for Bessel J
+        # (similar to what is implemented for Bessel I here).
+
+    def test_hyp0f1_complex(self):
+        assert_mpmath_equal(
+            lambda a, z: sc.hyp0f1(a.real, z),
+            exception_to_nan(lambda a, x: mpmath.hyp0f1(a, x, **HYPERKW)),
+            [Arg(-10, 10), ComplexArg(complex(-120, -120), complex(120, 120))],
+        )
+        # NB: The range of the first parameter ("v") are limited by an overflow
+        # in the intermediate calculations. Can be fixed by implementing an
+        # asymptotic expansion for Bessel functions for large order.
+
+    def test_hyp1f1(self):
+        def mpmath_hyp1f1(a, b, x):
+            try:
+                return mpmath.hyp1f1(a, b, x)
+            except ZeroDivisionError:
+                return np.inf
+
+        assert_mpmath_equal(
+            sc.hyp1f1,
+            mpmath_hyp1f1,
+            [Arg(-50, 50), Arg(1, 50, inclusive_a=False), Arg(-50, 50)],
+            n=500,
+            nan_ok=False,
+        )
+
+    @pytest.mark.xfail(run=False)
+    def test_hyp1f1_complex(self):
+        assert_mpmath_equal(
+            inf_to_nan(lambda a, b, x: sc.hyp1f1(a.real, b.real, x)),
+            exception_to_nan(lambda a, b, x: mpmath.hyp1f1(a, b, x, **HYPERKW)),
+            [Arg(-1e3, 1e3), Arg(-1e3, 1e3), ComplexArg()],
+            n=2000,
+        )
+
+    @nonfunctional_tooslow
+    def test_hyp2f1_complex(self):
+        # SciPy's hyp2f1 seems to have performance and accuracy problems
+        assert_mpmath_equal(
+            lambda a, b, c, x: sc.hyp2f1(a.real, b.real, c.real, x),
+            exception_to_nan(lambda a, b, c, x: mpmath.hyp2f1(a, b, c, x, **HYPERKW)),
+            [Arg(-1e2, 1e2), Arg(-1e2, 1e2), Arg(-1e2, 1e2), ComplexArg()],
+            n=10,
+        )
+
+    @pytest.mark.xfail(run=False)
+    def test_hyperu(self):
+        assert_mpmath_equal(
+            sc.hyperu,
+            exception_to_nan(lambda a, b, x: mpmath.hyperu(a, b, x, **HYPERKW)),
+            [Arg(), Arg(), Arg()],
+        )
+
+    @pytest.mark.xfail_on_32bit("mpmath issue gh-342: "
+                                "unsupported operand mpz, long for pow")
+    def test_igam_fac(self):
+        def mp_igam_fac(a, x):
+            return mpmath.power(x, a)*mpmath.exp(-x)/mpmath.gamma(a)
+
+        assert_mpmath_equal(
+            _igam_fac,
+            mp_igam_fac,
+            [Arg(0, 1e14, inclusive_a=False), Arg(0, 1e14)],
+            rtol=1e-10,
+            dps=29,
+        )
+
+    def test_j0(self):
+        # The Bessel function at large arguments is j0(x) ~ cos(x + phi)/sqrt(x)
+        # and at large arguments the phase of the cosine loses precision.
+        #
+        # This is numerically expected behavior, so we compare only up to
+        # 1e8 = 1e15 * 1e-7
+        assert_mpmath_equal(sc.j0, mpmath.j0, [Arg(-1e3, 1e3)])
+        assert_mpmath_equal(sc.j0, mpmath.j0, [Arg(-1e8, 1e8)], rtol=1e-5)
+
+    def test_j1(self):
+        # See comment in test_j0
+        assert_mpmath_equal(sc.j1, mpmath.j1, [Arg(-1e3, 1e3)])
+        assert_mpmath_equal(sc.j1, mpmath.j1, [Arg(-1e8, 1e8)], rtol=1e-5)
+
+    @pytest.mark.xfail(run=False)
+    def test_jacobi(self):
+        assert_mpmath_equal(
+            sc.eval_jacobi,
+            exception_to_nan(lambda a, b, c, x: mpmath.jacobi(a, b, c, x, **HYPERKW)),
+            [Arg(), Arg(), Arg(), Arg()],
+        )
+        assert_mpmath_equal(
+            lambda n, b, c, x: sc.eval_jacobi(int(n), b, c, x),
+            exception_to_nan(lambda a, b, c, x: mpmath.jacobi(a, b, c, x, **HYPERKW)),
+            [IntArg(), Arg(), Arg(), Arg()],
+        )
+
+    def test_jacobi_int(self):
+        # Redefine functions to deal with numerical + mpmath issues
+        def jacobi(n, a, b, x):
+            # Mpmath does not handle n=0 case always correctly
+            if n == 0:
+                return 1.0
+            return mpmath.jacobi(n, a, b, x)
+        assert_mpmath_equal(
+            lambda n, a, b, x: sc.eval_jacobi(int(n), a, b, x),
+            lambda n, a, b, x: exception_to_nan(jacobi)(n, a, b, x, **HYPERKW),
+            [IntArg(), Arg(), Arg(), Arg()],
+            n=4095,
+            dps=50,
+        )
+
+    def test_kei(self):
+        def kei(x):
+            if x == 0:
+                # work around mpmath issue at x=0
+                return -pi/4
+            return exception_to_nan(mpmath.kei)(0, x, **HYPERKW)
+        assert_mpmath_equal(sc.kei, kei, [Arg(-1e30, 1e30)], n=1000)
+
+    def test_ker(self):
+        assert_mpmath_equal(
+            sc.ker,
+            exception_to_nan(lambda x: mpmath.ker(0, x, **HYPERKW)),
+            [Arg(-1e30, 1e30)],
+            n=1000,
+        )
+
+    @nonfunctional_tooslow
+    def test_laguerre(self):
+        assert_mpmath_equal(
+            trace_args(sc.eval_laguerre),
+            lambda n, x: exception_to_nan(mpmath.laguerre)(n, x, **HYPERKW),
+            [Arg(), Arg()],
+        )
+
+    def test_laguerre_int(self):
+        assert_mpmath_equal(
+            lambda n, x: sc.eval_laguerre(int(n), x),
+            lambda n, x: exception_to_nan(mpmath.laguerre)(n, x, **HYPERKW),
+            [IntArg(), Arg()],
+            n=20000,
+        )
+
+    @pytest.mark.xfail_on_32bit("see gh-3551 for bad points")
+    def test_lambertw_real(self):
+        assert_mpmath_equal(
+            lambda x, k: sc.lambertw(x, int(k.real)),
+            lambda x, k: mpmath.lambertw(x, int(k.real)),
+            [ComplexArg(-np.inf, np.inf), IntArg(0, 10)],
+            rtol=1e-13, nan_ok=False,
+        )
+
+    def test_lanczos_sum_expg_scaled(self):
+        maxgamma = 171.624376956302725
+        e = np.exp(1)
+        g = 6.024680040776729583740234375
+
+        def gamma(x):
+            with np.errstate(over='ignore'):
+                fac = ((x + g - 0.5)/e)**(x - 0.5)
+                if fac != np.inf:
+                    res = fac*_lanczos_sum_expg_scaled(x)
+                else:
+                    fac = ((x + g - 0.5)/e)**(0.5*(x - 0.5))
+                    res = fac*_lanczos_sum_expg_scaled(x)
+                    res *= fac
+            return res
+
+        assert_mpmath_equal(
+            gamma,
+            mpmath.gamma,
+            [Arg(0, maxgamma, inclusive_a=False)],
+            rtol=1e-13,
+        )
+
+    @nonfunctional_tooslow
+    def test_legendre(self):
+        assert_mpmath_equal(sc.eval_legendre, mpmath.legendre, [Arg(), Arg()])
+
+    def test_legendre_int(self):
+        assert_mpmath_equal(
+            lambda n, x: sc.eval_legendre(int(n), x),
+            lambda n, x: exception_to_nan(mpmath.legendre)(n, x, **HYPERKW),
+            [IntArg(), Arg()],
+            n=20000,
+        )
+
+        # Check the small-x expansion
+        assert_mpmath_equal(
+            lambda n, x: sc.eval_legendre(int(n), x),
+            lambda n, x: exception_to_nan(mpmath.legendre)(n, x, **HYPERKW),
+            [IntArg(), FixedArg(np.logspace(-30, -4, 20))],
+        )
+
+    @pytest.mark.xfail(run=False, reason="apparently picks wrong function at |z| > 1")
+    def test_legenq(self):
+        def lqnm(n, m, z):
+            return sc.lqmn(m, n, z)[0][-1,-1]
+
+        def legenq(n, m, z):
+            if abs(z) < 1e-15:
+                # mpmath has bad performance here
+                return np.nan
+            return exception_to_nan(mpmath.legenq)(n, m, z, type=2)
+
+        assert_mpmath_equal(
+            lqnm,
+            legenq,
+            [IntArg(0, 100), IntArg(0, 100), Arg()],
+        )
+
+    @nonfunctional_tooslow
+    def test_legenq_complex(self):
+        def lqnm(n, m, z):
+            return sc.lqmn(int(m.real), int(n.real), z)[0][-1,-1]
+
+        def legenq(n, m, z):
+            if abs(z) < 1e-15:
+                # mpmath has bad performance here
+                return np.nan
+            return exception_to_nan(mpmath.legenq)(int(n.real), int(m.real), z, type=2)
+
+        assert_mpmath_equal(
+            lqnm,
+            legenq,
+            [IntArg(0, 100), IntArg(0, 100), ComplexArg()],
+            n=100,
+        )
+
+    def test_lgam1p(self):
+        def param_filter(x):
+            # Filter the poles
+            return np.where((np.floor(x) == x) & (x <= 0), False, True)
+
+        def mp_lgam1p(z):
+            # The real part of loggamma is log(|gamma(z)|)
+            return mpmath.loggamma(1 + z).real
+
+        assert_mpmath_equal(
+            _lgam1p,
+            mp_lgam1p,
+            [Arg()],
+            rtol=1e-13,
+            dps=100,
+            param_filter=param_filter,
+        )
+
+    def test_loggamma(self):
+        def mpmath_loggamma(z):
+            try:
+                res = mpmath.loggamma(z)
+            except ValueError:
+                res = complex(np.nan, np.nan)
+            return res
+
+        assert_mpmath_equal(
+            sc.loggamma,
+            mpmath_loggamma,
+            [ComplexArg()],
+            nan_ok=False,
+            distinguish_nan_and_inf=False,
+            rtol=5e-14,
+        )
+
+    @pytest.mark.xfail(run=False)
+    def test_pcfd(self):
+        def pcfd(v, x):
+            return sc.pbdv(v, x)[0]
+        assert_mpmath_equal(
+            pcfd,
+            exception_to_nan(lambda v, x: mpmath.pcfd(v, x, **HYPERKW)),
+            [Arg(), Arg()],
+        )
+
+    @pytest.mark.xfail(run=False, reason="it's not the same as the mpmath function --- "
+                                         "maybe different definition?")
+    def test_pcfv(self):
+        def pcfv(v, x):
+            return sc.pbvv(v, x)[0]
+        assert_mpmath_equal(
+            pcfv,
+            lambda v, x: time_limited()(exception_to_nan(mpmath.pcfv))(v, x, **HYPERKW),
+            [Arg(), Arg()],
+            n=1000,
+        )
+
+    def test_pcfw(self):
+        def pcfw(a, x):
+            return sc.pbwa(a, x)[0]
+
+        def dpcfw(a, x):
+            return sc.pbwa(a, x)[1]
+
+        def mpmath_dpcfw(a, x):
+            return mpmath.diff(mpmath.pcfw, (a, x), (0, 1))
+
+        # The Zhang and Jin implementation only uses Taylor series and
+        # is thus accurate in only a very small range.
+        assert_mpmath_equal(
+            pcfw,
+            mpmath.pcfw,
+            [Arg(-5, 5), Arg(-5, 5)],
+            rtol=2e-8,
+            n=100,
+        )
+
+        assert_mpmath_equal(
+            dpcfw,
+            mpmath_dpcfw,
+            [Arg(-5, 5), Arg(-5, 5)],
+            rtol=2e-9,
+            n=100,
+        )
+
+    @pytest.mark.xfail(run=False,
+                       reason="issues at large arguments (atol OK, rtol not) "
+                              "and <eps-close to z=0")
+    def test_polygamma(self):
+        assert_mpmath_equal(
+            sc.polygamma,
+            time_limited()(exception_to_nan(mpmath.polygamma)),
+            [IntArg(0, 1000), Arg()],
+        )
+
+    def test_rgamma(self):
+        assert_mpmath_equal(
+            sc.rgamma,
+            mpmath.rgamma,
+            [Arg(-8000, np.inf)],
+            n=5000,
+            nan_ok=False,
+            ignore_inf_sign=True,
+        )
+
+    def test_rgamma_complex(self):
+        assert_mpmath_equal(
+            sc.rgamma,
+            exception_to_nan(mpmath.rgamma),
+            [ComplexArg()],
+            rtol=5e-13,
+        )
+
+    @pytest.mark.xfail(reason=("see gh-3551 for bad points on 32 bit "
+                               "systems and gh-8095 for another bad "
+                               "point"))
+    def test_rf(self):
+        if version.parse(mpmath.__version__) >= version.Version("1.0.0"):
+            # no workarounds needed
+            mppoch = mpmath.rf
+        else:
+            def mppoch(a, m):
+                # deal with cases where the result in double precision
+                # hits exactly a non-positive integer, but the
+                # corresponding extended-precision mpf floats don't
+                if float(a + m) == int(a + m) and float(a + m) <= 0:
+                    a = mpmath.mpf(a)
+                    m = int(a + m) - a
+                return mpmath.rf(a, m)
+
+        assert_mpmath_equal(sc.poch, mppoch, [Arg(), Arg()], dps=400)
+
+    def test_sinpi(self):
+        eps = np.finfo(float).eps
+        assert_mpmath_equal(
+            _sinpi,
+            mpmath.sinpi,
+            [Arg()],
+            nan_ok=False,
+            rtol=2*eps,
+        )
+
+    def test_sinpi_complex(self):
+        assert_mpmath_equal(
+            _sinpi,
+            mpmath.sinpi,
+            [ComplexArg()],
+            nan_ok=False,
+            rtol=2e-14,
+        )
+
+    def test_shi(self):
+        def shi(x):
+            return sc.shichi(x)[0]
+        assert_mpmath_equal(shi, mpmath.shi, [Arg()])
+        # check asymptotic series cross-over
+        assert_mpmath_equal(shi, mpmath.shi, [FixedArg([88 - 1e-9, 88, 88 + 1e-9])])
+
+    def test_shi_complex(self):
+        def shi(z):
+            return sc.shichi(z)[0]
+        # shi oscillates as Im[z] -> +- inf, so limit range
+        assert_mpmath_equal(
+            shi,
+            mpmath.shi,
+            [ComplexArg(complex(-np.inf, -1e8), complex(np.inf, 1e8))],
+            rtol=1e-12,
+        )
+
+    def test_si(self):
+        def si(x):
+            return sc.sici(x)[0]
+        assert_mpmath_equal(si, mpmath.si, [Arg()])
+
+    def test_si_complex(self):
+        def si(z):
+            return sc.sici(z)[0]
+        # si oscillates as Re[z] -> +- inf, so limit range
+        assert_mpmath_equal(
+            si,
+            mpmath.si,
+            [ComplexArg(complex(-1e8, -np.inf), complex(1e8, np.inf))],
+            rtol=1e-12,
+        )
+
+    def test_spence(self):
+        # mpmath uses a different convention for the dilogarithm
+        def dilog(x):
+            return mpmath.polylog(2, 1 - x)
+        # Spence has a branch cut on the negative real axis
+        assert_mpmath_equal(
+            sc.spence,
+            exception_to_nan(dilog),
+            [Arg(0, np.inf)],
+            rtol=1e-14,
+        )
+
+    def test_spence_complex(self):
+        def dilog(z):
+            return mpmath.polylog(2, 1 - z)
+        assert_mpmath_equal(
+            sc.spence,
+            exception_to_nan(dilog),
+            [ComplexArg()],
+            rtol=1e-14,
+        )
+
+    def test_struveh(self):
+        assert_mpmath_equal(
+            sc.struve,
+            exception_to_nan(mpmath.struveh),
+            [Arg(-1e4, 1e4), Arg(0, 1e4)],
+            rtol=5e-10,
+        )
+
+    def test_struvel(self):
+        def mp_struvel(v, z):
+            if v < 0 and z < -v and abs(v) > 1000:
+                # larger DPS needed for correct results
+                old_dps = mpmath.mp.dps
+                try:
+                    mpmath.mp.dps = 500
+                    return mpmath.struvel(v, z)
+                finally:
+                    mpmath.mp.dps = old_dps
+            return mpmath.struvel(v, z)
+
+        assert_mpmath_equal(
+            sc.modstruve,
+            exception_to_nan(mp_struvel),
+            [Arg(-1e4, 1e4), Arg(0, 1e4)],
+            rtol=5e-10,
+            ignore_inf_sign=True,
+        )
+
+    def test_wrightomega_real(self):
+        def mpmath_wrightomega_real(x):
+            return mpmath.lambertw(mpmath.exp(x), mpmath.mpf('-0.5'))
+
+        # For x < -1000 the Wright Omega function is just 0 to double
+        # precision, and for x > 1e21 it is just x to double
+        # precision.
+        assert_mpmath_equal(
+            sc.wrightomega,
+            mpmath_wrightomega_real,
+            [Arg(-1000, 1e21)],
+            rtol=5e-15,
+            atol=0,
+            nan_ok=False,
+        )
+
+    def test_wrightomega(self):
+        assert_mpmath_equal(
+            sc.wrightomega,
+            lambda z: _mpmath_wrightomega(z, 25),
+            [ComplexArg()],
+            rtol=1e-14,
+            nan_ok=False,
+        )
+
+    def test_hurwitz_zeta(self):
+        assert_mpmath_equal(
+            sc.zeta,
+            exception_to_nan(mpmath.zeta),
+            [Arg(a=1, b=1e10, inclusive_a=False), Arg(a=0, inclusive_a=False)],
+        )
+
+    def test_riemann_zeta(self):
+        assert_mpmath_equal(
+            sc.zeta,
+            lambda x: mpmath.zeta(x) if x != 1 else mpmath.inf,
+            [Arg(-100, 100)],
+            nan_ok=False,
+            rtol=5e-13,
+        )
+
+    def test_zetac(self):
+        assert_mpmath_equal(
+            sc.zetac,
+            lambda x: mpmath.zeta(x) - 1 if x != 1 else mpmath.inf,
+            [Arg(-100, 100)],
+            nan_ok=False,
+            dps=45,
+            rtol=5e-13,
+        )
+
+    def test_boxcox(self):
+
+        def mp_boxcox(x, lmbda):
+            x = mpmath.mp.mpf(x)
+            lmbda = mpmath.mp.mpf(lmbda)
+            if lmbda == 0:
+                return mpmath.mp.log(x)
+            else:
+                return mpmath.mp.powm1(x, lmbda) / lmbda
+
+        assert_mpmath_equal(
+            sc.boxcox,
+            exception_to_nan(mp_boxcox),
+            [Arg(a=0, inclusive_a=False), Arg()],
+            n=200,
+            dps=60,
+            rtol=1e-13,
+        )
+
+    def test_boxcox1p(self):
+
+        def mp_boxcox1p(x, lmbda):
+            x = mpmath.mp.mpf(x)
+            lmbda = mpmath.mp.mpf(lmbda)
+            one = mpmath.mp.mpf(1)
+            if lmbda == 0:
+                return mpmath.mp.log(one + x)
+            else:
+                return mpmath.mp.powm1(one + x, lmbda) / lmbda
+
+        assert_mpmath_equal(
+            sc.boxcox1p,
+            exception_to_nan(mp_boxcox1p),
+            [Arg(a=-1, inclusive_a=False), Arg()],
+            n=200,
+            dps=60,
+            rtol=1e-13,
+        )
+
+    def test_spherical_jn(self):
+        def mp_spherical_jn(n, z):
+            arg = mpmath.mpmathify(z)
+            out = (mpmath.besselj(n + mpmath.mpf(1)/2, arg) /
+                   mpmath.sqrt(2*arg/mpmath.pi))
+            if arg.imag == 0:
+                return out.real
+            else:
+                return out
+
+        assert_mpmath_equal(
+            lambda n, z: sc.spherical_jn(int(n), z),
+            exception_to_nan(mp_spherical_jn),
+            [IntArg(0, 200), Arg(-1e8, 1e8)],
+            dps=300,
+            # underflow of `spherical_jn` is a bit premature; see gh-21629
+            param_filter=(None, lambda z: np.abs(z) > 1e-20),
+        )
+
+    def test_spherical_jn_complex(self):
+        def mp_spherical_jn(n, z):
+            arg = mpmath.mpmathify(z)
+            out = (mpmath.besselj(n + mpmath.mpf(1)/2, arg) /
+                   mpmath.sqrt(2*arg/mpmath.pi))
+            if arg.imag == 0:
+                return out.real
+            else:
+                return out
+
+        assert_mpmath_equal(
+            lambda n, z: sc.spherical_jn(int(n.real), z),
+            exception_to_nan(mp_spherical_jn),
+            [IntArg(0, 200), ComplexArg()]
+        )
+
+    def test_spherical_yn(self):
+        def mp_spherical_yn(n, z):
+            arg = mpmath.mpmathify(z)
+            out = (mpmath.bessely(n + mpmath.mpf(1)/2, arg) /
+                   mpmath.sqrt(2*arg/mpmath.pi))
+            if arg.imag == 0:
+                return out.real
+            else:
+                return out
+
+        assert_mpmath_equal(
+            lambda n, z: sc.spherical_yn(int(n), z),
+            exception_to_nan(mp_spherical_yn),
+            [IntArg(0, 200), Arg(-1e10, 1e10)],
+            dps=100,
+        )
+
+    def test_spherical_yn_complex(self):
+        def mp_spherical_yn(n, z):
+            arg = mpmath.mpmathify(z)
+            out = (mpmath.bessely(n + mpmath.mpf(1)/2, arg) /
+                   mpmath.sqrt(2*arg/mpmath.pi))
+            if arg.imag == 0:
+                return out.real
+            else:
+                return out
+
+        assert_mpmath_equal(
+            lambda n, z: sc.spherical_yn(int(n.real), z),
+            exception_to_nan(mp_spherical_yn),
+            [IntArg(0, 200), ComplexArg()],
+        )
+
+    def test_spherical_in(self):
+        def mp_spherical_in(n, z):
+            arg = mpmath.mpmathify(z)
+            out = (mpmath.besseli(n + mpmath.mpf(1)/2, arg) /
+                   mpmath.sqrt(2*arg/mpmath.pi))
+            if arg.imag == 0:
+                return out.real
+            else:
+                return out
+
+        assert_mpmath_equal(
+            lambda n, z: sc.spherical_in(int(n), z),
+            exception_to_nan(mp_spherical_in),
+            [IntArg(0, 200), Arg()],
+            dps=200,
+            atol=10**(-278),
+        )
+
+    def test_spherical_in_complex(self):
+        def mp_spherical_in(n, z):
+            arg = mpmath.mpmathify(z)
+            out = (mpmath.besseli(n + mpmath.mpf(1)/2, arg) /
+                   mpmath.sqrt(2*arg/mpmath.pi))
+            if arg.imag == 0:
+                return out.real
+            else:
+                return out
+
+        assert_mpmath_equal(
+            lambda n, z: sc.spherical_in(int(n.real), z),
+            exception_to_nan(mp_spherical_in),
+            [IntArg(0, 200), ComplexArg()],
+        )
+
+    def test_spherical_kn(self):
+        def mp_spherical_kn(n, z):
+            arg = mpmath.mpmathify(z)
+            out = (mpmath.besselk(n + mpmath.mpf(1)/2, arg) /
+                   mpmath.sqrt(2*arg/mpmath.pi))
+            if mpmath.mpmathify(z).imag == 0:
+                return out.real
+            else:
+                return out
+
+        assert_mpmath_equal(
+            lambda n, z: sc.spherical_kn(int(n), z),
+            exception_to_nan(mp_spherical_kn),
+            [IntArg(0, 150), Arg()],
+            dps=100,
+        )
+
+    @pytest.mark.xfail(run=False,
+                       reason="Accuracy issues near z = -1 inherited from kv.")
+    def test_spherical_kn_complex(self):
+        def mp_spherical_kn(n, z):
+            arg = mpmath.mpmathify(z)
+            out = (mpmath.besselk(n + mpmath.mpf(1)/2, arg) /
+                   mpmath.sqrt(2*arg/mpmath.pi))
+            if arg.imag == 0:
+                return out.real
+            else:
+                return out
+
+        assert_mpmath_equal(
+            lambda n, z: sc.spherical_kn(int(n.real), z),
+            exception_to_nan(mp_spherical_kn),
+            [IntArg(0, 200), ComplexArg()],
+            dps=200,
+        )
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_nan_inputs.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_nan_inputs.py
new file mode 100644
index 0000000000000000000000000000000000000000..76af3032b62484b630713631e23d95110161b759
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_nan_inputs.py
@@ -0,0 +1,72 @@
+"""Test how the ufuncs in special handle nan inputs.
+
+"""
+import warnings
+
+from collections.abc import Callable
+
+import numpy as np
+from numpy.testing import assert_array_equal, assert_
+import pytest
+import scipy.special as sc
+
+
+KNOWNFAILURES: dict[str, Callable] = {}
+
+POSTPROCESSING: dict[str, Callable] = {}
+
+
+def _get_ufuncs():
+    ufuncs = []
+    ufunc_names = []
+    for name in sorted(sc.__dict__):
+        obj = sc.__dict__[name]
+        if not isinstance(obj, np.ufunc):
+            continue
+        msg = KNOWNFAILURES.get(obj)
+        if msg is None:
+            ufuncs.append(obj)
+            ufunc_names.append(name)
+        else:
+            fail = pytest.mark.xfail(run=False, reason=msg)
+            ufuncs.append(pytest.param(obj, marks=fail))
+            ufunc_names.append(name)
+    return ufuncs, ufunc_names
+
+
+UFUNCS, UFUNC_NAMES = _get_ufuncs()
+
+
+@pytest.mark.parametrize("func", UFUNCS, ids=UFUNC_NAMES)
+def test_nan_inputs(func):
+    args = (np.nan,)*func.nin
+    with warnings.catch_warnings():
+        # Ignore warnings about unsafe casts from legacy wrappers
+        warnings.filterwarnings(
+            "ignore",
+            "floating point number truncated to an integer",
+            RuntimeWarning
+        )
+        try:
+            with warnings.catch_warnings():
+                warnings.simplefilter("ignore", DeprecationWarning)
+                res = func(*args)
+        except TypeError:
+            # One of the arguments doesn't take real inputs
+            return
+    if func in POSTPROCESSING:
+        res = POSTPROCESSING[func](*res)
+
+    msg = f"got {res} instead of nan"
+    assert_array_equal(np.isnan(res), True, err_msg=msg)
+
+
+def test_legacy_cast():
+    with warnings.catch_warnings():
+        warnings.filterwarnings(
+            "ignore",
+            "floating point number truncated to an integer",
+            RuntimeWarning
+        )
+        res = sc.bdtrc(np.nan, 1, 0.5)
+        assert_(np.isnan(res))
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_ndtr.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_ndtr.py
new file mode 100644
index 0000000000000000000000000000000000000000..ba9b689b34384585cc65204000febcb99c910d55
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_ndtr.py
@@ -0,0 +1,77 @@
+import numpy as np
+from numpy.testing import assert_equal, assert_allclose
+import scipy.special as sc
+
+
+def test_ndtr():
+    assert_equal(sc.ndtr(0), 0.5)
+    assert_allclose(sc.ndtr(1), 0.8413447460685429)
+
+
+class TestNdtri:
+
+    def test_zero(self):
+        assert sc.ndtri(0.5) == 0.0
+
+    def test_asymptotes(self):
+        assert_equal(sc.ndtri([0.0, 1.0]), [-np.inf, np.inf])
+
+    def test_outside_of_domain(self):
+        assert all(np.isnan(sc.ndtri([-1.5, 1.5])))
+
+
+class TestLogNdtr:
+
+    # The expected values in these tests were computed with mpmath:
+    #
+    #   def log_ndtr_mp(x):
+    #       return mpmath.log(mpmath.ncdf(x))
+    #
+
+    def test_log_ndtr_moderate_le8(self):
+        x = np.array([-0.75, -0.25, 0, 0.5, 1.5, 2.5, 3, 4, 5, 7, 8])
+        expected = np.array([-1.4844482299196562,
+                             -0.9130617648111351,
+                             -0.6931471805599453,
+                             -0.3689464152886564,
+                             -0.06914345561223398,
+                             -0.006229025485860002,
+                             -0.0013508099647481938,
+                             -3.167174337748927e-05,
+                             -2.866516129637636e-07,
+                             -1.279812543886654e-12,
+                             -6.220960574271786e-16])
+        y = sc.log_ndtr(x)
+        assert_allclose(y, expected, rtol=1e-14)
+
+    def test_log_ndtr_values_8_16(self):
+        x = np.array([8.001, 8.06, 8.15, 8.5, 10, 12, 14, 16])
+        expected = [-6.170639424817055e-16,
+                    -3.814722443652823e-16,
+                    -1.819621363526629e-16,
+                    -9.479534822203318e-18,
+                    -7.619853024160525e-24,
+                    -1.776482112077679e-33,
+                    -7.7935368191928e-45,
+                    -6.388754400538087e-58]
+        y = sc.log_ndtr(x)
+        assert_allclose(y, expected, rtol=5e-14)
+
+    def test_log_ndtr_values_16_31(self):
+        x = np.array([16.15, 20.3, 21.4, 26.2, 30.9])
+        expected = [-5.678084565148492e-59,
+                    -6.429244467698346e-92,
+                    -6.680402412553295e-102,
+                    -1.328698078458869e-151,
+                    -5.972288641838264e-210]
+        y = sc.log_ndtr(x)
+        assert_allclose(y, expected, rtol=2e-13)
+
+    def test_log_ndtr_values_gt31(self):
+        x = np.array([31.6, 32.8, 34.9, 37.1])
+        expected = [-1.846036234858162e-219,
+                    -2.9440539964066835e-236,
+                    -3.71721649450857e-267,
+                    -1.4047119663106221e-301]
+        y = sc.log_ndtr(x)
+        assert_allclose(y, expected, rtol=3e-13)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_ndtri_exp.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_ndtri_exp.py
new file mode 100644
index 0000000000000000000000000000000000000000..82a9fbd3bcda117770e00018facda3f56630a6bc
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_ndtri_exp.py
@@ -0,0 +1,94 @@
+import pytest
+import numpy as np
+from numpy.testing import assert_equal, assert_allclose
+from scipy.special import log_ndtr, ndtri_exp
+from scipy.special._testutils import assert_func_equal
+
+
+def log_ndtr_ndtri_exp(y):
+    return log_ndtr(ndtri_exp(y))
+
+
+@pytest.fixture(scope="class")
+def uniform_random_points():
+    random_state = np.random.RandomState(1234)
+    points = random_state.random_sample(1000)
+    return points
+
+
+class TestNdtriExp:
+    """Tests that ndtri_exp is sufficiently close to an inverse of log_ndtr.
+
+    We have separate tests for the five intervals (-inf, -10),
+    [-10, -2), [-2, -0.14542), [-0.14542, -1e-6), and [-1e-6, 0).
+    ndtri_exp(y) is computed in three different ways depending on if y
+    is in (-inf, -2), [-2, log(1 - exp(-2))], or [log(1 - exp(-2), 0).
+    Each of these intervals is given its own test with two additional tests
+    for handling very small values and values very close to zero.
+    """
+
+    @pytest.mark.parametrize(
+        "test_input", [-1e1, -1e2, -1e10, -1e20, -np.finfo(float).max]
+    )
+    def test_very_small_arg(self, test_input, uniform_random_points):
+        scale = test_input
+        points = scale * (0.5 * uniform_random_points + 0.5)
+        assert_func_equal(
+            log_ndtr_ndtri_exp,
+            lambda y: y, points,
+            rtol=1e-14,
+            nan_ok=True
+        )
+
+    @pytest.mark.parametrize(
+        "interval,expected_rtol",
+        [
+            ((-10, -2), 1e-14),
+            ((-2, -0.14542), 1e-12),
+            ((-0.14542, -1e-6), 1e-10),
+            ((-1e-6, 0), 1e-6),
+        ],
+    )
+    def test_in_interval(self, interval, expected_rtol, uniform_random_points):
+        left, right = interval
+        points = (right - left) * uniform_random_points + left
+        assert_func_equal(
+            log_ndtr_ndtri_exp,
+            lambda y: y, points,
+            rtol=expected_rtol,
+            nan_ok=True
+        )
+
+    def test_extreme(self):
+        # bigneg is not quite the largest negative double precision value.
+        # Here's why:
+        # The round-trip calculation
+        #    y = ndtri_exp(bigneg)
+        #    bigneg2 = log_ndtr(y)
+        # where bigneg is a very large negative value, would--with infinite
+        # precision--result in bigneg2 == bigneg.  When bigneg is large enough,
+        # y is effectively equal to -sqrt(2)*sqrt(-bigneg), and log_ndtr(y) is
+        # effectively -(y/sqrt(2))**2.  If we use bigneg = np.finfo(float).min,
+        # then by construction, the theoretical value is the most negative
+        # finite value that can be represented with 64 bit float point.  This
+        # means tiny changes in how the computation proceeds can result in the
+        # return value being -inf.  (E.g. changing the constant representation
+        # of 1/sqrt(2) from 0.7071067811865475--which is the value returned by
+        # 1/np.sqrt(2)--to 0.7071067811865476--which is the most accurate 64
+        # bit floating point representation of 1/sqrt(2)--results in the
+        # round-trip that starts with np.finfo(float).min returning -inf.  So
+        # we'll move the bigneg value a few ULPs towards 0 to avoid this
+        # sensitivity.
+        # Use the reduce method to apply nextafter four times.
+        bigneg = np.nextafter.reduce([np.finfo(float).min, 0, 0, 0, 0])
+        # tinyneg is approx. -2.225e-308.
+        tinyneg = -np.finfo(float).tiny
+        x = np.array([tinyneg, bigneg])
+        result = log_ndtr_ndtri_exp(x)
+        assert_allclose(result, x, rtol=1e-12)
+
+    def test_asymptotes(self):
+        assert_equal(ndtri_exp([-np.inf, 0.0]), [-np.inf, np.inf])
+
+    def test_outside_domain(self):
+        assert np.isnan(ndtri_exp(1.0))
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_orthogonal.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_orthogonal.py
new file mode 100644
index 0000000000000000000000000000000000000000..130d52073b3da0a27fc7a15ca18506ca9094942f
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_orthogonal.py
@@ -0,0 +1,823 @@
+import pytest
+from pytest import raises as assert_raises
+
+import numpy as np
+from numpy import array, sqrt
+from numpy.testing import assert_equal, assert_allclose
+
+from scipy import integrate
+import scipy.special as sc
+from scipy.special import gamma
+import scipy.special._orthogonal as orth
+
+
+class TestCheby:
+    def test_chebyc(self):
+        C0 = orth.chebyc(0)
+        C1 = orth.chebyc(1)
+        with np.errstate(all='ignore'):
+            C2 = orth.chebyc(2)
+            C3 = orth.chebyc(3)
+            C4 = orth.chebyc(4)
+            C5 = orth.chebyc(5)
+
+        assert_allclose(C0.c, [2], atol=1.5e-13, rtol=0)
+        assert_allclose(C1.c, [1, 0], atol=1.5e-13, rtol=0)
+        assert_allclose(C2.c, [1, 0, -2], atol=1.5e-13, rtol=0)
+        assert_allclose(C3.c, [1, 0, -3, 0], atol=1.5e-13, rtol=0)
+        assert_allclose(C4.c, [1, 0, -4, 0, 2], atol=1.5e-13, rtol=0)
+        assert_allclose(C5.c, [1, 0, -5, 0, 5, 0],atol=1.5e-13, rtol=0)
+
+    def test_chebys(self):
+        S0 = orth.chebys(0)
+        S1 = orth.chebys(1)
+        S2 = orth.chebys(2)
+        S3 = orth.chebys(3)
+        S4 = orth.chebys(4)
+        S5 = orth.chebys(5)
+        assert_allclose(S0.c, [1], atol=1.5e-13, rtol=0)
+        assert_allclose(S1.c, [1, 0], atol=1.5e-13, rtol=0)
+        assert_allclose(S2.c, [1, 0, -1], atol=1.5e-13, rtol=0)
+        assert_allclose(S3.c, [1, 0, -2, 0], atol=1.5e-13, rtol=0)
+        assert_allclose(S4.c, [1, 0, -3, 0, 1], atol=1.5e-13, rtol=0)
+        assert_allclose(S5.c, [1, 0, -4, 0, 3, 0], atol=1.5e-13, rtol=0)
+
+    def test_chebyt(self):
+        T0 = orth.chebyt(0)
+        T1 = orth.chebyt(1)
+        T2 = orth.chebyt(2)
+        T3 = orth.chebyt(3)
+        T4 = orth.chebyt(4)
+        T5 = orth.chebyt(5)
+        assert_allclose(T0.c, [1], atol=1.5e-13, rtol=0)
+        assert_allclose(T1.c, [1, 0], atol=1.5e-13, rtol=0)
+        assert_allclose(T2.c, [2, 0, -1], atol=1.5e-13, rtol=0)
+        assert_allclose(T3.c, [4, 0, -3, 0], atol=1.5e-13, rtol=0)
+        assert_allclose(T4.c, [8, 0, -8, 0, 1], atol=1.5e-13, rtol=0)
+        assert_allclose(T5.c, [16, 0, -20, 0, 5, 0], atol=1.5e-13, rtol=0)
+
+    def test_chebyu(self):
+        U0 = orth.chebyu(0)
+        U1 = orth.chebyu(1)
+        U2 = orth.chebyu(2)
+        U3 = orth.chebyu(3)
+        U4 = orth.chebyu(4)
+        U5 = orth.chebyu(5)
+        assert_allclose(U0.c, [1], atol=1.5e-13, rtol=0)
+        assert_allclose(U1.c, [2, 0], atol=1.5e-13, rtol=0)
+        assert_allclose(U2.c, [4, 0, -1], atol=1.5e-13, rtol=0)
+        assert_allclose(U3.c, [8, 0, -4, 0], atol=1.5e-13, rtol=0)
+        assert_allclose(U4.c, [16, 0, -12, 0, 1], atol=1.5e-13, rtol=0)
+        assert_allclose(U5.c, [32, 0, -32, 0, 6, 0], atol=1.5e-13, rtol=0)
+
+
+class TestGegenbauer:
+
+    def test_gegenbauer(self):
+        a = 5*np.random.random() - 0.5
+        if np.any(a == 0):
+            a = -0.2
+        Ca0 = orth.gegenbauer(0,a)
+        Ca1 = orth.gegenbauer(1,a)
+        Ca2 = orth.gegenbauer(2,a)
+        Ca3 = orth.gegenbauer(3,a)
+        Ca4 = orth.gegenbauer(4,a)
+        Ca5 = orth.gegenbauer(5,a)
+
+        assert_allclose(Ca0.c, array([1]), atol=1.5e-13, rtol=0)
+        assert_allclose(Ca1.c, array([2*a, 0]), atol=1.5e-13, rtol=0)
+        assert_allclose(Ca2.c, array([2*a*(a + 1), 0, -a]),
+                        atol=1.5e-13, rtol=0)
+        assert_allclose(Ca3.c, array([4*sc.poch(a, 3), 0,-6*a*(a + 1), 0])/3.0,
+                        atol=1.5e-11, rtol=0)
+        assert_allclose(Ca4.c, array([4*sc.poch(a, 4), 0, -12*sc.poch(a, 3),
+                                      0, 3*a*(a + 1)])/6.0,
+                        atol=1.5e-11, rtol=0)
+        assert_allclose(Ca5.c, array([4*sc.poch(a, 5), 0, -20*sc.poch(a, 4),
+                                      0, 15*sc.poch(a, 3), 0])/15.0,
+                        atol=1.5e-11, rtol=0)
+
+    @pytest.mark.parametrize('a', [0, 1])
+    def test_n_zero_gh8888(self, a):
+        # gh-8888 reported that gegenbauer(0, 0) returns NaN polynomial
+        Cn0 = orth.gegenbauer(0, a)
+        assert_equal(Cn0.c, np.asarray([1.]))
+
+    def test_valid_alpha(self):
+        # Check input validation of `alpha`
+        message = '`alpha` must be a finite number greater...'
+        with pytest.raises(ValueError, match=message):
+            orth.gegenbauer(0, np.nan)
+        with pytest.raises(ValueError, match=message):
+            orth.gegenbauer(1, -0.5)
+        with pytest.raises(ValueError, match=message):
+            orth.gegenbauer(2, -np.inf)
+
+
+class TestHermite:
+    def test_hermite(self):
+        H0 = orth.hermite(0)
+        H1 = orth.hermite(1)
+        H2 = orth.hermite(2)
+        H3 = orth.hermite(3)
+        H4 = orth.hermite(4)
+        H5 = orth.hermite(5)
+        assert_allclose(H0.c, [1], atol=1.5e-13, rtol=0)
+        assert_allclose(H1.c, [2, 0], atol=1.5e-13, rtol=0)
+        assert_allclose(H2.c, [4, 0, -2], atol=1.5e-13, rtol=0)
+        assert_allclose(H3.c, [8, 0, -12, 0], atol=1.5e-13, rtol=0)
+        assert_allclose(H4.c, [16, 0, -48, 0, 12], atol=1.5e-12, rtol=0)
+        assert_allclose(H5.c, [32, 0, -160, 0, 120, 0], atol=1.5e-12, rtol=0)
+
+    def test_hermitenorm(self):
+        # He_n(x) = 2**(-n/2) H_n(x/sqrt(2))
+        psub = np.poly1d([1.0/sqrt(2),0])
+        H0 = orth.hermitenorm(0)
+        H1 = orth.hermitenorm(1)
+        H2 = orth.hermitenorm(2)
+        H3 = orth.hermitenorm(3)
+        H4 = orth.hermitenorm(4)
+        H5 = orth.hermitenorm(5)
+        he0 = orth.hermite(0)(psub)
+        he1 = orth.hermite(1)(psub) / sqrt(2)
+        he2 = orth.hermite(2)(psub) / 2.0
+        he3 = orth.hermite(3)(psub) / (2*sqrt(2))
+        he4 = orth.hermite(4)(psub) / 4.0
+        he5 = orth.hermite(5)(psub) / (4.0*sqrt(2))
+
+        assert_allclose(H0.c, he0.c, atol=1.5e-13, rtol=0)
+        assert_allclose(H1.c, he1.c, atol=1.5e-13, rtol=0)
+        assert_allclose(H2.c, he2.c, atol=1.5e-13, rtol=0)
+        assert_allclose(H3.c, he3.c, atol=1.5e-13, rtol=0)
+        assert_allclose(H4.c, he4.c, atol=1.5e-13, rtol=0)
+        assert_allclose(H5.c, he5.c, atol=1.5e-13, rtol=0)
+
+
+class TestShLegendre:
+    def test_sh_legendre(self):
+        # P*_n(x) = P_n(2x-1)
+        psub = np.poly1d([2,-1])
+        Ps0 = orth.sh_legendre(0)
+        Ps1 = orth.sh_legendre(1)
+        Ps2 = orth.sh_legendre(2)
+        Ps3 = orth.sh_legendre(3)
+        Ps4 = orth.sh_legendre(4)
+        Ps5 = orth.sh_legendre(5)
+        pse0 = orth.legendre(0)(psub)
+        pse1 = orth.legendre(1)(psub)
+        pse2 = orth.legendre(2)(psub)
+        pse3 = orth.legendre(3)(psub)
+        pse4 = orth.legendre(4)(psub)
+        pse5 = orth.legendre(5)(psub)
+        assert_allclose(Ps0.c, pse0.c, atol=1.5e-13, rtol=0)
+        assert_allclose(Ps1.c, pse1.c, atol=1.5e-13, rtol=0)
+        assert_allclose(Ps2.c, pse2.c, atol=1.5e-13, rtol=0)
+        assert_allclose(Ps3.c, pse3.c, atol=1.5e-13, rtol=0)
+        assert_allclose(Ps4.c, pse4.c, atol=1.5e-12, rtol=0)
+        assert_allclose(Ps5.c, pse5.c, atol=1.5e-12, rtol=0)
+
+
+class TestShChebyt:
+    def test_sh_chebyt(self):
+        # T*_n(x) = T_n(2x-1)
+        psub = np.poly1d([2,-1])
+        Ts0 = orth.sh_chebyt(0)
+        Ts1 = orth.sh_chebyt(1)
+        Ts2 = orth.sh_chebyt(2)
+        Ts3 = orth.sh_chebyt(3)
+        Ts4 = orth.sh_chebyt(4)
+        Ts5 = orth.sh_chebyt(5)
+        tse0 = orth.chebyt(0)(psub)
+        tse1 = orth.chebyt(1)(psub)
+        tse2 = orth.chebyt(2)(psub)
+        tse3 = orth.chebyt(3)(psub)
+        tse4 = orth.chebyt(4)(psub)
+        tse5 = orth.chebyt(5)(psub)
+        assert_allclose(Ts0.c, tse0.c, atol=1.5e-13, rtol=0)
+        assert_allclose(Ts1.c, tse1.c, atol=1.5e-13, rtol=0)
+        assert_allclose(Ts2.c, tse2.c, atol=1.5e-13, rtol=0)
+        assert_allclose(Ts3.c, tse3.c, atol=1.5e-13, rtol=0)
+        assert_allclose(Ts4.c, tse4.c, atol=1.5e-12, rtol=0)
+        assert_allclose(Ts5.c, tse5.c, atol=1.5e-12, rtol=0)
+
+
+class TestShChebyu:
+    def test_sh_chebyu(self):
+        # U*_n(x) = U_n(2x-1)
+        psub = np.poly1d([2,-1])
+        Us0 = orth.sh_chebyu(0)
+        Us1 = orth.sh_chebyu(1)
+        Us2 = orth.sh_chebyu(2)
+        Us3 = orth.sh_chebyu(3)
+        Us4 = orth.sh_chebyu(4)
+        Us5 = orth.sh_chebyu(5)
+        use0 = orth.chebyu(0)(psub)
+        use1 = orth.chebyu(1)(psub)
+        use2 = orth.chebyu(2)(psub)
+        use3 = orth.chebyu(3)(psub)
+        use4 = orth.chebyu(4)(psub)
+        use5 = orth.chebyu(5)(psub)
+        assert_allclose(Us0.c, use0.c, atol=1.5e-13, rtol=0)
+        assert_allclose(Us1.c, use1.c, atol=1.5e-13, rtol=0)
+        assert_allclose(Us2.c, use2.c, atol=1.5e-13, rtol=0)
+        assert_allclose(Us3.c, use3.c, atol=1.5e-13, rtol=0)
+        assert_allclose(Us4.c, use4.c, atol=1.5e-12, rtol=0)
+        assert_allclose(Us5.c, use5.c, atol=1.5e-11, rtol=0)
+
+
+class TestShJacobi:
+    def test_sh_jacobi(self):
+        # G^(p,q)_n(x) = n! gamma(n+p)/gamma(2*n+p) * P^(p-q,q-1)_n(2*x-1)
+        def conv(n, p):
+            return gamma(n + 1) * gamma(n + p) / gamma(2 * n + p)
+        psub = np.poly1d([2,-1])
+        q = 4 * np.random.random()
+        p = q-1 + 2*np.random.random()
+        # print("shifted jacobi p,q = ", p, q)
+        G0 = orth.sh_jacobi(0,p,q)
+        G1 = orth.sh_jacobi(1,p,q)
+        G2 = orth.sh_jacobi(2,p,q)
+        G3 = orth.sh_jacobi(3,p,q)
+        G4 = orth.sh_jacobi(4,p,q)
+        G5 = orth.sh_jacobi(5,p,q)
+        ge0 = orth.jacobi(0,p-q,q-1)(psub) * conv(0,p)
+        ge1 = orth.jacobi(1,p-q,q-1)(psub) * conv(1,p)
+        ge2 = orth.jacobi(2,p-q,q-1)(psub) * conv(2,p)
+        ge3 = orth.jacobi(3,p-q,q-1)(psub) * conv(3,p)
+        ge4 = orth.jacobi(4,p-q,q-1)(psub) * conv(4,p)
+        ge5 = orth.jacobi(5,p-q,q-1)(psub) * conv(5,p)
+
+        assert_allclose(G0.c, ge0.c, atol=1.5e-13, rtol=0)
+        assert_allclose(G1.c, ge1.c, atol=1.5e-13, rtol=0)
+        assert_allclose(G2.c, ge2.c, atol=1.5e-13, rtol=0)
+        assert_allclose(G3.c, ge3.c, atol=1.5e-13, rtol=0)
+        assert_allclose(G4.c, ge4.c, atol=1.5e-13, rtol=0)
+        assert_allclose(G5.c, ge5.c, atol=1.5e-13, rtol=0)
+
+
+class TestCall:
+    def test_call(self):
+        poly = []
+        for n in range(5):
+            poly.extend([x.strip() for x in
+                (f"""
+                orth.jacobi({n},0.3,0.9)
+                orth.sh_jacobi({n},0.3,0.9)
+                orth.genlaguerre({n},0.3)
+                orth.laguerre({n})
+                orth.hermite({n})
+                orth.hermitenorm({n})
+                orth.gegenbauer({n},0.3)
+                orth.chebyt({n})
+                orth.chebyu({n})
+                orth.chebyc({n})
+                orth.chebys({n})
+                orth.sh_chebyt({n})
+                orth.sh_chebyu({n})
+                orth.legendre({n})
+                orth.sh_legendre({n})
+                """).split()])
+        with np.errstate(all='ignore'):
+            for pstr in poly:
+                p = eval(pstr)
+                assert_allclose(p(0.315), np.poly1d(p.coef)(0.315),
+                                atol=1.5e-7, rtol=0, err_msg=pstr)
+
+
+class TestGenlaguerre:
+    def test_regression(self):
+        assert_equal(orth.genlaguerre(1, 1, monic=False)(0), 2.)
+        assert_equal(orth.genlaguerre(1, 1, monic=True)(0), -2.)
+        assert_equal(orth.genlaguerre(1, 1, monic=False), np.poly1d([-1, 2]))
+        assert_equal(orth.genlaguerre(1, 1, monic=True), np.poly1d([1, -2]))
+
+
+def verify_gauss_quad(root_func, eval_func, weight_func, a, b, N,
+                      rtol=1e-15, atol=5e-14):
+    # this test is copied from numpy's TestGauss in test_hermite.py
+    x, w, mu = root_func(N, True)
+
+    n = np.arange(N, dtype=np.dtype("long"))
+    v = eval_func(n[:,np.newaxis], x)
+    vv = np.dot(v*w, v.T)
+    vd = 1 / np.sqrt(vv.diagonal())
+    vv = vd[:, np.newaxis] * vv * vd
+    assert_allclose(vv, np.eye(N), rtol, atol)
+
+    # check that the integral of 1 is correct
+    assert_allclose(w.sum(), mu, rtol, atol)
+
+    # compare the results of integrating a function with quad.
+    def f(x):
+        return x ** 3 - 3 * x ** 2 + x - 2
+    resI = integrate.quad(lambda x: f(x)*weight_func(x), a, b)
+    resG = np.vdot(f(x), w)
+    rtol = 1e-6 if 1e-6 < resI[1] else resI[1] * 10
+    assert_allclose(resI[0], resG, rtol=rtol)
+
+def test_roots_jacobi():
+    def rf(a, b):
+        return lambda n, mu: sc.roots_jacobi(n, a, b, mu)
+    def ef(a, b):
+        return lambda n, x: sc.eval_jacobi(n, a, b, x)
+    def wf(a, b):
+        return lambda x: (1 - x) ** a * (1 + x) ** b
+
+    vgq = verify_gauss_quad
+    vgq(rf(-0.5, -0.75), ef(-0.5, -0.75), wf(-0.5, -0.75), -1., 1., 5)
+    vgq(rf(-0.5, -0.75), ef(-0.5, -0.75), wf(-0.5, -0.75), -1., 1.,
+        25, atol=1e-12)
+    vgq(rf(-0.5, -0.75), ef(-0.5, -0.75), wf(-0.5, -0.75), -1., 1.,
+        100, atol=1e-11)
+
+    vgq(rf(0.5, -0.5), ef(0.5, -0.5), wf(0.5, -0.5), -1., 1., 5)
+    vgq(rf(0.5, -0.5), ef(0.5, -0.5), wf(0.5, -0.5), -1., 1., 25, atol=1.5e-13)
+    vgq(rf(0.5, -0.5), ef(0.5, -0.5), wf(0.5, -0.5), -1., 1., 100, atol=2e-12)
+
+    vgq(rf(1, 0.5), ef(1, 0.5), wf(1, 0.5), -1., 1., 5, atol=2e-13)
+    vgq(rf(1, 0.5), ef(1, 0.5), wf(1, 0.5), -1., 1., 25, atol=2e-13)
+    vgq(rf(1, 0.5), ef(1, 0.5), wf(1, 0.5), -1., 1., 100, atol=1e-12)
+
+    vgq(rf(0.9, 2), ef(0.9, 2), wf(0.9, 2), -1., 1., 5)
+    vgq(rf(0.9, 2), ef(0.9, 2), wf(0.9, 2), -1., 1., 25, atol=1e-13)
+    vgq(rf(0.9, 2), ef(0.9, 2), wf(0.9, 2), -1., 1., 100, atol=3e-13)
+
+    vgq(rf(18.24, 27.3), ef(18.24, 27.3), wf(18.24, 27.3), -1., 1., 5)
+    vgq(rf(18.24, 27.3), ef(18.24, 27.3), wf(18.24, 27.3), -1., 1., 25,
+        atol=1.1e-14)
+    vgq(rf(18.24, 27.3), ef(18.24, 27.3), wf(18.24, 27.3), -1., 1.,
+        100, atol=1e-13)
+
+    vgq(rf(47.1, -0.2), ef(47.1, -0.2), wf(47.1, -0.2), -1., 1., 5, atol=1e-13)
+    vgq(rf(47.1, -0.2), ef(47.1, -0.2), wf(47.1, -0.2), -1., 1., 25, atol=2e-13)
+    vgq(rf(47.1, -0.2), ef(47.1, -0.2), wf(47.1, -0.2), -1., 1.,
+        100, atol=1e-11)
+
+    vgq(rf(1., 658.), ef(1., 658.), wf(1., 658.), -1., 1., 5, atol=2e-13)
+    vgq(rf(1., 658.), ef(1., 658.), wf(1., 658.), -1., 1., 25, atol=1e-12)
+    vgq(rf(1., 658.), ef(1., 658.), wf(1., 658.), -1., 1., 100, atol=1e-11)
+    vgq(rf(1., 658.), ef(1., 658.), wf(1., 658.), -1., 1., 250, atol=1e-11)
+
+    vgq(rf(511., 511.), ef(511., 511.), wf(511., 511.), -1., 1., 5,
+        atol=1e-12)
+    vgq(rf(511., 511.), ef(511., 511.), wf(511., 511.), -1., 1., 25,
+        atol=1e-11)
+    vgq(rf(511., 511.), ef(511., 511.), wf(511., 511.), -1., 1., 100,
+        atol=1e-10)
+
+    vgq(rf(511., 512.), ef(511., 512.), wf(511., 512.), -1., 1., 5,
+        atol=1e-12)
+    vgq(rf(511., 512.), ef(511., 512.), wf(511., 512.), -1., 1., 25,
+        atol=1e-11)
+    vgq(rf(511., 512.), ef(511., 512.), wf(511., 512.), -1., 1., 100,
+        atol=1e-10)
+
+    vgq(rf(1000., 500.), ef(1000., 500.), wf(1000., 500.), -1., 1., 5,
+        atol=1e-12)
+    vgq(rf(1000., 500.), ef(1000., 500.), wf(1000., 500.), -1., 1., 25,
+        atol=1e-11)
+    vgq(rf(1000., 500.), ef(1000., 500.), wf(1000., 500.), -1., 1., 100,
+        atol=1e-10)
+
+    vgq(rf(2.25, 68.9), ef(2.25, 68.9), wf(2.25, 68.9), -1., 1., 5)
+    vgq(rf(2.25, 68.9), ef(2.25, 68.9), wf(2.25, 68.9), -1., 1., 25,
+        atol=1e-13)
+    vgq(rf(2.25, 68.9), ef(2.25, 68.9), wf(2.25, 68.9), -1., 1., 100,
+        atol=1e-13)
+
+    # when alpha == beta == 0, P_n^{a,b}(x) == P_n(x)
+    xj, wj = sc.roots_jacobi(6, 0.0, 0.0)
+    xl, wl = sc.roots_legendre(6)
+    assert_allclose(xj, xl, 1e-14, 1e-14)
+    assert_allclose(wj, wl, 1e-14, 1e-14)
+
+    # when alpha == beta != 0, P_n^{a,b}(x) == C_n^{alpha+0.5}(x)
+    xj, wj = sc.roots_jacobi(6, 4.0, 4.0)
+    xc, wc = sc.roots_gegenbauer(6, 4.5)
+    assert_allclose(xj, xc, 1e-14, 1e-14)
+    assert_allclose(wj, wc, 1e-14, 1e-14)
+
+    x, w = sc.roots_jacobi(5, 2, 3, False)
+    y, v, m = sc.roots_jacobi(5, 2, 3, True)
+    assert_allclose(x, y, 1e-14, 1e-14)
+    assert_allclose(w, v, 1e-14, 1e-14)
+
+    muI, muI_err = integrate.quad(wf(2,3), -1, 1)
+    assert_allclose(m, muI, rtol=muI_err)
+
+    assert_raises(ValueError, sc.roots_jacobi, 0, 1, 1)
+    assert_raises(ValueError, sc.roots_jacobi, 3.3, 1, 1)  # type: ignore[call-overload]
+    assert_raises(ValueError, sc.roots_jacobi, 3, -2, 1)
+    assert_raises(ValueError, sc.roots_jacobi, 3, 1, -2)
+    assert_raises(ValueError, sc.roots_jacobi, 3, -2, -2)
+
+def test_roots_sh_jacobi():
+    def rf(a, b):
+        return lambda n, mu: sc.roots_sh_jacobi(n, a, b, mu)
+    def ef(a, b):
+        return lambda n, x: sc.eval_sh_jacobi(n, a, b, x)
+    def wf(a, b):
+        return lambda x: (1.0 - x) ** (a - b) * x ** (b - 1.0)
+
+    vgq = verify_gauss_quad
+    vgq(rf(-0.5, 0.25), ef(-0.5, 0.25), wf(-0.5, 0.25), 0., 1., 5)
+    vgq(rf(-0.5, 0.25), ef(-0.5, 0.25), wf(-0.5, 0.25), 0., 1.,
+        25, atol=1e-12)
+    vgq(rf(-0.5, 0.25), ef(-0.5, 0.25), wf(-0.5, 0.25), 0., 1.,
+        100, atol=1e-11)
+
+    vgq(rf(0.5, 0.5), ef(0.5, 0.5), wf(0.5, 0.5), 0., 1., 5)
+    vgq(rf(0.5, 0.5), ef(0.5, 0.5), wf(0.5, 0.5), 0., 1., 25, atol=1e-13)
+    vgq(rf(0.5, 0.5), ef(0.5, 0.5), wf(0.5, 0.5), 0., 1., 100, atol=1e-12)
+
+    vgq(rf(1, 0.5), ef(1, 0.5), wf(1, 0.5), 0., 1., 5)
+    vgq(rf(1, 0.5), ef(1, 0.5), wf(1, 0.5), 0., 1., 25, atol=1.5e-13)
+    vgq(rf(1, 0.5), ef(1, 0.5), wf(1, 0.5), 0., 1., 100, atol=2e-12)
+
+    vgq(rf(2, 0.9), ef(2, 0.9), wf(2, 0.9), 0., 1., 5)
+    vgq(rf(2, 0.9), ef(2, 0.9), wf(2, 0.9), 0., 1., 25, atol=1e-13)
+    vgq(rf(2, 0.9), ef(2, 0.9), wf(2, 0.9), 0., 1., 100, atol=1e-12)
+
+    vgq(rf(27.3, 18.24), ef(27.3, 18.24), wf(27.3, 18.24), 0., 1., 5)
+    vgq(rf(27.3, 18.24), ef(27.3, 18.24), wf(27.3, 18.24), 0., 1., 25)
+    vgq(rf(27.3, 18.24), ef(27.3, 18.24), wf(27.3, 18.24), 0., 1.,
+        100, atol=1e-13)
+
+    vgq(rf(47.1, 0.2), ef(47.1, 0.2), wf(47.1, 0.2), 0., 1., 5, atol=1e-12)
+    vgq(rf(47.1, 0.2), ef(47.1, 0.2), wf(47.1, 0.2), 0., 1., 25, atol=1e-11)
+    vgq(rf(47.1, 0.2), ef(47.1, 0.2), wf(47.1, 0.2), 0., 1., 100, atol=1e-10)
+
+    vgq(rf(68.9, 2.25), ef(68.9, 2.25), wf(68.9, 2.25), 0., 1., 5, atol=3.5e-14)
+    vgq(rf(68.9, 2.25), ef(68.9, 2.25), wf(68.9, 2.25), 0., 1., 25, atol=2e-13)
+    vgq(rf(68.9, 2.25), ef(68.9, 2.25), wf(68.9, 2.25), 0., 1.,
+        100, atol=1e-12)
+
+    x, w = sc.roots_sh_jacobi(5, 3, 2, False)
+    y, v, m = sc.roots_sh_jacobi(5, 3, 2, True)
+    assert_allclose(x, y, 1e-14, 1e-14)
+    assert_allclose(w, v, 1e-14, 1e-14)
+
+    muI, muI_err = integrate.quad(wf(3,2), 0, 1)
+    assert_allclose(m, muI, rtol=muI_err)
+
+    assert_raises(ValueError, sc.roots_sh_jacobi, 0, 1, 1)
+    assert_raises(ValueError, sc.roots_sh_jacobi, 3.3, 1, 1)  # type: ignore[call-overload]
+    assert_raises(ValueError, sc.roots_sh_jacobi, 3, 1, 2)    # p - q <= -1
+    assert_raises(ValueError, sc.roots_sh_jacobi, 3, 2, -1)   # q <= 0
+    assert_raises(ValueError, sc.roots_sh_jacobi, 3, -2, -1)  # both
+
+def test_roots_hermite():
+    rootf = sc.roots_hermite
+    evalf = sc.eval_hermite
+    weightf = orth.hermite(5).weight_func
+
+    verify_gauss_quad(rootf, evalf, weightf, -np.inf, np.inf, 5)
+    verify_gauss_quad(rootf, evalf, weightf, -np.inf, np.inf, 25, atol=1e-13)
+    verify_gauss_quad(rootf, evalf, weightf, -np.inf, np.inf, 100, atol=1e-12)
+
+    # Golub-Welsch branch
+    x, w = sc.roots_hermite(5, False)
+    y, v, m = sc.roots_hermite(5, True)
+    assert_allclose(x, y, 1e-14, 1e-14)
+    assert_allclose(w, v, 1e-14, 1e-14)
+
+    muI, muI_err = integrate.quad(weightf, -np.inf, np.inf)
+    assert_allclose(m, muI, rtol=muI_err)
+
+    # Asymptotic branch (switch over at n >= 150)
+    x, w = sc.roots_hermite(200, False)
+    y, v, m = sc.roots_hermite(200, True)
+    assert_allclose(x, y, 1e-14, 1e-14)
+    assert_allclose(w, v, 1e-14, 1e-14)
+    assert_allclose(sum(v), m, 1e-14, 1e-14)
+
+    assert_raises(ValueError, sc.roots_hermite, 0)
+    assert_raises(ValueError, sc.roots_hermite, 3.3)  # type: ignore[call-overload]
+
+def test_roots_hermite_asy():
+    # Recursion for Hermite functions
+    def hermite_recursion(n, nodes):
+        H = np.zeros((n, nodes.size))
+        H[0,:] = np.pi**(-0.25) * np.exp(-0.5*nodes**2)
+        if n > 1:
+            H[1,:] = sqrt(2.0) * nodes * H[0,:]
+            for k in range(2, n):
+                H[k,:] = sqrt(2.0/k) * nodes * H[k-1,:] - sqrt((k-1.0)/k) * H[k-2,:]
+        return H
+
+    # This tests only the nodes
+    def test(N, rtol=1e-15, atol=1e-14):
+        x, w = orth._roots_hermite_asy(N)
+        H = hermite_recursion(N+1, x)
+        assert_allclose(H[-1,:], np.zeros(N), rtol, atol)
+        assert_allclose(sum(w), sqrt(np.pi), rtol, atol)
+
+    test(150, atol=1e-12)
+    test(151, atol=1e-12)
+    test(300, atol=1e-12)
+    test(301, atol=1e-12)
+    test(500, atol=1e-12)
+    test(501, atol=1e-12)
+    test(999, atol=1e-12)
+    test(1000, atol=1e-12)
+    test(2000, atol=1e-12)
+    test(5000, atol=1e-12)
+
+def test_roots_hermitenorm():
+    rootf = sc.roots_hermitenorm
+    evalf = sc.eval_hermitenorm
+    weightf = orth.hermitenorm(5).weight_func
+
+    verify_gauss_quad(rootf, evalf, weightf, -np.inf, np.inf, 5)
+    verify_gauss_quad(rootf, evalf, weightf, -np.inf, np.inf, 25, atol=1e-13)
+    verify_gauss_quad(rootf, evalf, weightf, -np.inf, np.inf, 100, atol=1e-12)
+
+    x, w = sc.roots_hermitenorm(5, False)
+    y, v, m = sc.roots_hermitenorm(5, True)
+    assert_allclose(x, y, 1e-14, 1e-14)
+    assert_allclose(w, v, 1e-14, 1e-14)
+
+    muI, muI_err = integrate.quad(weightf, -np.inf, np.inf)
+    assert_allclose(m, muI, rtol=muI_err)
+
+    assert_raises(ValueError, sc.roots_hermitenorm, 0)
+    assert_raises(ValueError, sc.roots_hermitenorm, 3.3)  # type: ignore[call-overload]
+
+def test_roots_gegenbauer():
+    def rootf(a):
+        return lambda n, mu: sc.roots_gegenbauer(n, a, mu)
+    def evalf(a):
+        return lambda n, x: sc.eval_gegenbauer(n, a, x)
+    def weightf(a):
+        return lambda x: (1 - x ** 2) ** (a - 0.5)
+
+    vgq = verify_gauss_quad
+    vgq(rootf(-0.25), evalf(-0.25), weightf(-0.25), -1., 1., 5)
+    vgq(rootf(-0.25), evalf(-0.25), weightf(-0.25), -1., 1., 25, atol=1e-12)
+    vgq(rootf(-0.25), evalf(-0.25), weightf(-0.25), -1., 1., 100, atol=1e-11)
+
+    vgq(rootf(0.1), evalf(0.1), weightf(0.1), -1., 1., 5)
+    vgq(rootf(0.1), evalf(0.1), weightf(0.1), -1., 1., 25, atol=1e-13)
+    vgq(rootf(0.1), evalf(0.1), weightf(0.1), -1., 1., 100, atol=1e-12)
+
+    vgq(rootf(1), evalf(1), weightf(1), -1., 1., 5)
+    vgq(rootf(1), evalf(1), weightf(1), -1., 1., 25, atol=1e-13)
+    vgq(rootf(1), evalf(1), weightf(1), -1., 1., 100, atol=1e-12)
+
+    vgq(rootf(10), evalf(10), weightf(10), -1., 1., 5)
+    vgq(rootf(10), evalf(10), weightf(10), -1., 1., 25, atol=1e-13)
+    vgq(rootf(10), evalf(10), weightf(10), -1., 1., 100, atol=1e-12)
+
+    vgq(rootf(50), evalf(50), weightf(50), -1., 1., 5, atol=1e-13)
+    vgq(rootf(50), evalf(50), weightf(50), -1., 1., 25, atol=1e-12)
+    vgq(rootf(50), evalf(50), weightf(50), -1., 1., 100, atol=1e-11)
+
+    # Alpha=170 is where the approximation used in roots_gegenbauer changes
+    vgq(rootf(170), evalf(170), weightf(170), -1., 1., 5, atol=1e-13)
+    vgq(rootf(170), evalf(170), weightf(170), -1., 1., 25, atol=1e-12)
+    vgq(rootf(170), evalf(170), weightf(170), -1., 1., 100, atol=1e-11)
+    vgq(rootf(170.5), evalf(170.5), weightf(170.5), -1., 1., 5, atol=1.25e-13)
+    vgq(rootf(170.5), evalf(170.5), weightf(170.5), -1., 1., 25, atol=1e-12)
+    vgq(rootf(170.5), evalf(170.5), weightf(170.5), -1., 1., 100, atol=1e-11)
+
+    # Test for failures, e.g. overflows, resulting from large alphas
+    vgq(rootf(238), evalf(238), weightf(238), -1., 1., 5, atol=1e-13)
+    vgq(rootf(238), evalf(238), weightf(238), -1., 1., 25, atol=1e-12)
+    vgq(rootf(238), evalf(238), weightf(238), -1., 1., 100, atol=1e-11)
+    vgq(rootf(512.5), evalf(512.5), weightf(512.5), -1., 1., 5, atol=1e-12)
+    vgq(rootf(512.5), evalf(512.5), weightf(512.5), -1., 1., 25, atol=1e-11)
+    vgq(rootf(512.5), evalf(512.5), weightf(512.5), -1., 1., 100, atol=1e-10)
+
+    # this is a special case that the old code supported.
+    # when alpha = 0, the gegenbauer polynomial is uniformly 0. but it goes
+    # to a scaled down copy of T_n(x) there.
+    vgq(rootf(0), sc.eval_chebyt, weightf(0), -1., 1., 5)
+    vgq(rootf(0), sc.eval_chebyt, weightf(0), -1., 1., 25)
+    vgq(rootf(0), sc.eval_chebyt, weightf(0), -1., 1., 100, atol=1e-12)
+
+    x, w = sc.roots_gegenbauer(5, 2, False)
+    y, v, m = sc.roots_gegenbauer(5, 2, True)
+    assert_allclose(x, y, 1e-14, 1e-14)
+    assert_allclose(w, v, 1e-14, 1e-14)
+
+    muI, muI_err = integrate.quad(weightf(2), -1, 1)
+    assert_allclose(m, muI, rtol=muI_err)
+
+    assert_raises(ValueError, sc.roots_gegenbauer, 0, 2)
+    assert_raises(ValueError, sc.roots_gegenbauer, 3.3, 2)  # type: ignore[call-overload]
+    assert_raises(ValueError, sc.roots_gegenbauer, 3, -.75)
+
+def test_roots_chebyt():
+    weightf = orth.chebyt(5).weight_func
+    verify_gauss_quad(sc.roots_chebyt, sc.eval_chebyt, weightf, -1., 1., 5)
+    verify_gauss_quad(sc.roots_chebyt, sc.eval_chebyt, weightf, -1., 1., 25)
+    verify_gauss_quad(sc.roots_chebyt, sc.eval_chebyt, weightf, -1., 1., 100,
+                      atol=1e-12)
+
+    x, w = sc.roots_chebyt(5, False)
+    y, v, m = sc.roots_chebyt(5, True)
+    assert_allclose(x, y, 1e-14, 1e-14)
+    assert_allclose(w, v, 1e-14, 1e-14)
+
+    muI, muI_err = integrate.quad(weightf, -1, 1)
+    assert_allclose(m, muI, rtol=muI_err)
+
+    assert_raises(ValueError, sc.roots_chebyt, 0)
+    assert_raises(ValueError, sc.roots_chebyt, 3.3)  # type: ignore[call-overload]
+
+def test_chebyt_symmetry():
+    x, w = sc.roots_chebyt(21)
+    pos, neg = x[:10], x[11:]
+    assert_equal(neg, -pos[::-1])
+    assert_equal(x[10], 0)
+
+def test_roots_chebyu():
+    weightf = orth.chebyu(5).weight_func
+    verify_gauss_quad(sc.roots_chebyu, sc.eval_chebyu, weightf, -1., 1., 5)
+    verify_gauss_quad(sc.roots_chebyu, sc.eval_chebyu, weightf, -1., 1., 25)
+    verify_gauss_quad(sc.roots_chebyu, sc.eval_chebyu, weightf, -1., 1., 100)
+
+    x, w = sc.roots_chebyu(5, False)
+    y, v, m = sc.roots_chebyu(5, True)
+    assert_allclose(x, y, 1e-14, 1e-14)
+    assert_allclose(w, v, 1e-14, 1e-14)
+
+    muI, muI_err = integrate.quad(weightf, -1, 1)
+    assert_allclose(m, muI, rtol=muI_err)
+
+    assert_raises(ValueError, sc.roots_chebyu, 0)
+    assert_raises(ValueError, sc.roots_chebyu, 3.3)  # type: ignore[call-overload]
+
+def test_roots_chebyc():
+    weightf = orth.chebyc(5).weight_func
+    verify_gauss_quad(sc.roots_chebyc, sc.eval_chebyc, weightf, -2., 2., 5)
+    verify_gauss_quad(sc.roots_chebyc, sc.eval_chebyc, weightf, -2., 2., 25)
+    verify_gauss_quad(sc.roots_chebyc, sc.eval_chebyc, weightf, -2., 2., 100,
+                      atol=1e-12)
+
+    x, w = sc.roots_chebyc(5, False)
+    y, v, m = sc.roots_chebyc(5, True)
+    assert_allclose(x, y, 1e-14, 1e-14)
+    assert_allclose(w, v, 1e-14, 1e-14)
+
+    muI, muI_err = integrate.quad(weightf, -2, 2)
+    assert_allclose(m, muI, rtol=muI_err)
+
+    assert_raises(ValueError, sc.roots_chebyc, 0)
+    assert_raises(ValueError, sc.roots_chebyc, 3.3)  # type: ignore[call-overload]
+
+def test_roots_chebys():
+    weightf = orth.chebys(5).weight_func
+    verify_gauss_quad(sc.roots_chebys, sc.eval_chebys, weightf, -2., 2., 5)
+    verify_gauss_quad(sc.roots_chebys, sc.eval_chebys, weightf, -2., 2., 25)
+    verify_gauss_quad(sc.roots_chebys, sc.eval_chebys, weightf, -2., 2., 100)
+
+    x, w = sc.roots_chebys(5, False)
+    y, v, m = sc.roots_chebys(5, True)
+    assert_allclose(x, y, 1e-14, 1e-14)
+    assert_allclose(w, v, 1e-14, 1e-14)
+
+    muI, muI_err = integrate.quad(weightf, -2, 2)
+    assert_allclose(m, muI, rtol=muI_err)
+
+    assert_raises(ValueError, sc.roots_chebys, 0)
+    assert_raises(ValueError, sc.roots_chebys, 3.3)  # type: ignore[call-overload]
+
+def test_roots_sh_chebyt():
+    weightf = orth.sh_chebyt(5).weight_func
+    verify_gauss_quad(sc.roots_sh_chebyt, sc.eval_sh_chebyt, weightf, 0., 1., 5)
+    verify_gauss_quad(sc.roots_sh_chebyt, sc.eval_sh_chebyt, weightf, 0., 1., 25)
+    verify_gauss_quad(sc.roots_sh_chebyt, sc.eval_sh_chebyt, weightf, 0., 1.,
+                      100, atol=1e-13)
+
+    x, w = sc.roots_sh_chebyt(5, False)
+    y, v, m = sc.roots_sh_chebyt(5, True)
+    assert_allclose(x, y, 1e-14, 1e-14)
+    assert_allclose(w, v, 1e-14, 1e-14)
+
+    muI, muI_err = integrate.quad(weightf, 0, 1)
+    assert_allclose(m, muI, rtol=muI_err)
+
+    assert_raises(ValueError, sc.roots_sh_chebyt, 0)
+    assert_raises(ValueError, sc.roots_sh_chebyt, 3.3)  # type: ignore[call-overload]
+
+def test_roots_sh_chebyu():
+    weightf = orth.sh_chebyu(5).weight_func
+    verify_gauss_quad(sc.roots_sh_chebyu, sc.eval_sh_chebyu, weightf, 0., 1., 5)
+    verify_gauss_quad(sc.roots_sh_chebyu, sc.eval_sh_chebyu, weightf, 0., 1., 25)
+    verify_gauss_quad(sc.roots_sh_chebyu, sc.eval_sh_chebyu, weightf, 0., 1.,
+                      100, atol=1e-13)
+
+    x, w = sc.roots_sh_chebyu(5, False)
+    y, v, m = sc.roots_sh_chebyu(5, True)
+    assert_allclose(x, y, 1e-14, 1e-14)
+    assert_allclose(w, v, 1e-14, 1e-14)
+
+    muI, muI_err = integrate.quad(weightf, 0, 1)
+    assert_allclose(m, muI, rtol=muI_err)
+
+    assert_raises(ValueError, sc.roots_sh_chebyu, 0)
+    assert_raises(ValueError, sc.roots_sh_chebyu, 3.3)  # type: ignore[call-overload]
+
+def test_roots_legendre():
+    weightf = orth.legendre(5).weight_func
+    verify_gauss_quad(sc.roots_legendre, sc.eval_legendre, weightf, -1., 1., 5)
+    verify_gauss_quad(sc.roots_legendre, sc.eval_legendre, weightf, -1., 1.,
+                      25, atol=1e-13)
+    verify_gauss_quad(sc.roots_legendre, sc.eval_legendre, weightf, -1., 1.,
+                      100, atol=1e-12)
+
+    x, w = sc.roots_legendre(5, False)
+    y, v, m = sc.roots_legendre(5, True)
+    assert_allclose(x, y, 1e-14, 1e-14)
+    assert_allclose(w, v, 1e-14, 1e-14)
+
+    muI, muI_err = integrate.quad(weightf, -1, 1)
+    assert_allclose(m, muI, rtol=muI_err)
+
+    assert_raises(ValueError, sc.roots_legendre, 0)
+    assert_raises(ValueError, sc.roots_legendre, 3.3)  # type: ignore[call-overload]
+
+def test_roots_sh_legendre():
+    weightf = orth.sh_legendre(5).weight_func
+    verify_gauss_quad(sc.roots_sh_legendre, sc.eval_sh_legendre, weightf, 0., 1., 5)
+    verify_gauss_quad(sc.roots_sh_legendre, sc.eval_sh_legendre, weightf, 0., 1.,
+                      25, atol=1e-13)
+    verify_gauss_quad(sc.roots_sh_legendre, sc.eval_sh_legendre, weightf, 0., 1.,
+                      100, atol=1e-12)
+
+    x, w = sc.roots_sh_legendre(5, False)
+    y, v, m = sc.roots_sh_legendre(5, True)
+    assert_allclose(x, y, 1e-14, 1e-14)
+    assert_allclose(w, v, 1e-14, 1e-14)
+
+    muI, muI_err = integrate.quad(weightf, 0, 1)
+    assert_allclose(m, muI, rtol=muI_err)
+
+    assert_raises(ValueError, sc.roots_sh_legendre, 0)
+    assert_raises(ValueError, sc.roots_sh_legendre, 3.3)  # type: ignore[call-overload]
+
+def test_roots_laguerre():
+    weightf = orth.laguerre(5).weight_func
+    verify_gauss_quad(sc.roots_laguerre, sc.eval_laguerre, weightf, 0., np.inf, 5)
+    verify_gauss_quad(sc.roots_laguerre, sc.eval_laguerre, weightf, 0., np.inf,
+                      25, atol=1e-13)
+    verify_gauss_quad(sc.roots_laguerre, sc.eval_laguerre, weightf, 0., np.inf,
+                      100, atol=1e-12)
+
+    x, w = sc.roots_laguerre(5, False)
+    y, v, m = sc.roots_laguerre(5, True)
+    assert_allclose(x, y, 1e-14, 1e-14)
+    assert_allclose(w, v, 1e-14, 1e-14)
+
+    muI, muI_err = integrate.quad(weightf, 0, np.inf)
+    assert_allclose(m, muI, rtol=muI_err)
+
+    assert_raises(ValueError, sc.roots_laguerre, 0)
+    assert_raises(ValueError, sc.roots_laguerre, 3.3)  # type: ignore[call-overload]
+
+def test_roots_genlaguerre():
+    def rootf(a):
+        return lambda n, mu: sc.roots_genlaguerre(n, a, mu)
+    def evalf(a):
+        return lambda n, x: sc.eval_genlaguerre(n, a, x)
+    def weightf(a):
+        return lambda x: x ** a * np.exp(-x)
+
+    vgq = verify_gauss_quad
+    vgq(rootf(-0.5), evalf(-0.5), weightf(-0.5), 0., np.inf, 5)
+    vgq(rootf(-0.5), evalf(-0.5), weightf(-0.5), 0., np.inf, 25, atol=1e-13)
+    vgq(rootf(-0.5), evalf(-0.5), weightf(-0.5), 0., np.inf, 100, atol=1e-12)
+
+    vgq(rootf(0.1), evalf(0.1), weightf(0.1), 0., np.inf, 5)
+    vgq(rootf(0.1), evalf(0.1), weightf(0.1), 0., np.inf, 25, atol=1e-13)
+    vgq(rootf(0.1), evalf(0.1), weightf(0.1), 0., np.inf, 100, atol=1.6e-13)
+
+    vgq(rootf(1), evalf(1), weightf(1), 0., np.inf, 5)
+    vgq(rootf(1), evalf(1), weightf(1), 0., np.inf, 25, atol=1e-13)
+    vgq(rootf(1), evalf(1), weightf(1), 0., np.inf, 100, atol=1.03e-13)
+
+    vgq(rootf(10), evalf(10), weightf(10), 0., np.inf, 5)
+    vgq(rootf(10), evalf(10), weightf(10), 0., np.inf, 25, atol=1e-13)
+    vgq(rootf(10), evalf(10), weightf(10), 0., np.inf, 100, atol=1e-12)
+
+    vgq(rootf(50), evalf(50), weightf(50), 0., np.inf, 5)
+    vgq(rootf(50), evalf(50), weightf(50), 0., np.inf, 25, atol=1e-13)
+    vgq(rootf(50), evalf(50), weightf(50), 0., np.inf, 100, rtol=1e-14, atol=2e-13)
+
+    x, w = sc.roots_genlaguerre(5, 2, False)
+    y, v, m = sc.roots_genlaguerre(5, 2, True)
+    assert_allclose(x, y, 1e-14, 1e-14)
+    assert_allclose(w, v, 1e-14, 1e-14)
+
+    muI, muI_err = integrate.quad(weightf(2.), 0., np.inf)
+    assert_allclose(m, muI, rtol=muI_err)
+
+    assert_raises(ValueError, sc.roots_genlaguerre, 0, 2)
+    assert_raises(ValueError, sc.roots_genlaguerre, 3.3, 2)  # type: ignore[call-overload]
+    assert_raises(ValueError, sc.roots_genlaguerre, 3, -1.1)
+
+
+def test_gh_6721():
+    # Regression test for gh_6721. This should not raise.
+    sc.chebyt(65)(0.2)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_orthogonal_eval.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_orthogonal_eval.py
new file mode 100644
index 0000000000000000000000000000000000000000..c70105aeaed63019acb9c4136cda3079af0b6a3a
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_orthogonal_eval.py
@@ -0,0 +1,383 @@
+import numpy as np
+from numpy.testing import assert_, assert_allclose
+import pytest
+
+from scipy.special import _ufuncs, gammasgn
+import scipy.special._orthogonal as orth
+from scipy.special._testutils import FuncData
+
+
+def test_eval_chebyt():
+    n = np.arange(0, 10000, 7, dtype=np.dtype("long"))
+    x = 2*np.random.rand() - 1
+    v1 = np.cos(n*np.arccos(x))
+    v2 = _ufuncs.eval_chebyt(n, x)
+    assert_(np.allclose(v1, v2, rtol=1e-15))
+
+
+def test_eval_chebyt_gh20129():
+    # https://github.com/scipy/scipy/issues/20129
+    assert _ufuncs.eval_chebyt(7, 2 + 0j) == 5042.0
+
+
+def test_eval_genlaguerre_restriction():
+    # check it returns nan for alpha <= -1
+    assert_(np.isnan(_ufuncs.eval_genlaguerre(0, -1, 0)))
+    assert_(np.isnan(_ufuncs.eval_genlaguerre(0.1, -1, 0)))
+
+
+def test_warnings():
+    # ticket 1334
+    with np.errstate(all='raise'):
+        # these should raise no fp warnings
+        _ufuncs.eval_legendre(1, 0)
+        _ufuncs.eval_laguerre(1, 1)
+        _ufuncs.eval_gegenbauer(1, 1, 0)
+
+
+class TestPolys:
+    """
+    Check that the eval_* functions agree with the constructed polynomials
+
+    """
+
+    def check_poly(self, func, cls, param_ranges=(), x_range=(), nn=10,
+                   nparam=10, nx=10, rtol=1e-8):
+        rng = np.random.RandomState(1234)
+
+        dataset = []
+        for n in np.arange(nn):
+            params = [a + (b-a)*rng.rand(nparam) for a,b in param_ranges]
+            params = np.asarray(params).T
+            if not param_ranges:
+                params = [0]
+            for p in params:
+                if param_ranges:
+                    p = (n,) + tuple(p)
+                else:
+                    p = (n,)
+                x = x_range[0] + (x_range[1] - x_range[0])*rng.rand(nx)
+                x[0] = x_range[0]  # always include domain start point
+                x[1] = x_range[1]  # always include domain end point
+                poly = np.poly1d(cls(*p).coef)
+                z = np.c_[np.tile(p, (nx,1)), x, poly(x)]
+                dataset.append(z)
+
+        dataset = np.concatenate(dataset, axis=0)
+
+        def polyfunc(*p):
+            p = (p[0].astype(np.dtype("long")),) + p[1:]
+            return func(*p)
+
+        with np.errstate(all='raise'):
+            ds = FuncData(polyfunc, dataset, list(range(len(param_ranges)+2)), -1,
+                          rtol=rtol)
+            ds.check()
+
+    def test_jacobi(self):
+        self.check_poly(_ufuncs.eval_jacobi, orth.jacobi,
+                        param_ranges=[(-0.99, 10), (-0.99, 10)],
+                        x_range=[-1, 1], rtol=1e-5)
+
+    def test_sh_jacobi(self):
+        self.check_poly(_ufuncs.eval_sh_jacobi, orth.sh_jacobi,
+                        param_ranges=[(1, 10), (0, 1)], x_range=[0, 1],
+                        rtol=1e-5)
+
+    def test_gegenbauer(self):
+        self.check_poly(_ufuncs.eval_gegenbauer, orth.gegenbauer,
+                        param_ranges=[(-0.499, 10)], x_range=[-1, 1],
+                        rtol=1e-7)
+
+    def test_chebyt(self):
+        self.check_poly(_ufuncs.eval_chebyt, orth.chebyt,
+                        param_ranges=[], x_range=[-1, 1])
+
+    def test_chebyu(self):
+        self.check_poly(_ufuncs.eval_chebyu, orth.chebyu,
+                        param_ranges=[], x_range=[-1, 1])
+
+    def test_chebys(self):
+        self.check_poly(_ufuncs.eval_chebys, orth.chebys,
+                        param_ranges=[], x_range=[-2, 2])
+
+    def test_chebyc(self):
+        self.check_poly(_ufuncs.eval_chebyc, orth.chebyc,
+                        param_ranges=[], x_range=[-2, 2])
+
+    def test_sh_chebyt(self):
+        with np.errstate(all='ignore'):
+            self.check_poly(_ufuncs.eval_sh_chebyt, orth.sh_chebyt,
+                            param_ranges=[], x_range=[0, 1])
+
+    def test_sh_chebyu(self):
+        self.check_poly(_ufuncs.eval_sh_chebyu, orth.sh_chebyu,
+                        param_ranges=[], x_range=[0, 1])
+
+    def test_legendre(self):
+        self.check_poly(_ufuncs.eval_legendre, orth.legendre,
+                        param_ranges=[], x_range=[-1, 1])
+
+    def test_sh_legendre(self):
+        with np.errstate(all='ignore'):
+            self.check_poly(_ufuncs.eval_sh_legendre, orth.sh_legendre,
+                            param_ranges=[], x_range=[0, 1])
+
+    def test_genlaguerre(self):
+        self.check_poly(_ufuncs.eval_genlaguerre, orth.genlaguerre,
+                        param_ranges=[(-0.99, 10)], x_range=[0, 100])
+
+    def test_laguerre(self):
+        self.check_poly(_ufuncs.eval_laguerre, orth.laguerre,
+                        param_ranges=[], x_range=[0, 100])
+
+    def test_hermite(self):
+        self.check_poly(_ufuncs.eval_hermite, orth.hermite,
+                        param_ranges=[], x_range=[-100, 100])
+
+    def test_hermitenorm(self):
+        self.check_poly(_ufuncs.eval_hermitenorm, orth.hermitenorm,
+                        param_ranges=[], x_range=[-100, 100])
+
+
+class TestRecurrence:
+    """
+    Check that the eval_* functions sig='ld->d' and 'dd->d' agree.
+
+    """
+
+    def check_poly(self, func, param_ranges=(), x_range=(), nn=10,
+                   nparam=10, nx=10, rtol=1e-8):
+        rng = np.random.default_rng(1234)
+
+        dataset = []
+        for n in np.arange(nn):
+            params = [a + (b-a)*rng.random(nparam) for a,b in param_ranges]
+            params = np.asarray(params).T
+            if not param_ranges:
+                params = [0]
+            for p in params:
+                if param_ranges:
+                    p = (n,) + tuple(p)
+                else:
+                    p = (n,)
+                x = x_range[0] + (x_range[1] - x_range[0])*rng.random(nx)
+                x[0] = x_range[0]  # always include domain start point
+                x[1] = x_range[1]  # always include domain end point
+                kw = dict(sig=(len(p)+1)*'d'+'->d')
+                z = np.c_[np.tile(p, (nx,1)), x, func(*(p + (x,)), **kw)]
+                dataset.append(z)
+
+        dataset = np.concatenate(dataset, axis=0)
+
+        def polyfunc(*p):
+            p0 = p[0].astype(np.intp)
+            p = (p0,) + p[1:]
+            p0_type_char = p0.dtype.char
+            kw = dict(sig=p0_type_char + (len(p)-1)*'d' + '->d')
+            return func(*p, **kw)
+
+        with np.errstate(all='raise'):
+            ds = FuncData(polyfunc, dataset, list(range(len(param_ranges)+2)), -1,
+                          rtol=rtol)
+            ds.check()
+
+    def test_jacobi(self):
+        self.check_poly(_ufuncs.eval_jacobi,
+                        param_ranges=[(-0.99, 10), (-0.99, 10)],
+                        x_range=[-1, 1])
+
+    def test_sh_jacobi(self):
+        self.check_poly(_ufuncs.eval_sh_jacobi,
+                        param_ranges=[(1, 10), (0, 1)], x_range=[0, 1])
+
+    def test_gegenbauer(self):
+        self.check_poly(_ufuncs.eval_gegenbauer,
+                        param_ranges=[(-0.499, 10)], x_range=[-1, 1])
+
+    def test_chebyt(self):
+        self.check_poly(_ufuncs.eval_chebyt,
+                        param_ranges=[], x_range=[-1, 1])
+
+    def test_chebyu(self):
+        self.check_poly(_ufuncs.eval_chebyu,
+                        param_ranges=[], x_range=[-1, 1])
+
+    def test_chebys(self):
+        self.check_poly(_ufuncs.eval_chebys,
+                        param_ranges=[], x_range=[-2, 2])
+
+    def test_chebyc(self):
+        self.check_poly(_ufuncs.eval_chebyc,
+                        param_ranges=[], x_range=[-2, 2])
+
+    def test_sh_chebyt(self):
+        self.check_poly(_ufuncs.eval_sh_chebyt,
+                        param_ranges=[], x_range=[0, 1])
+
+    def test_sh_chebyu(self):
+        self.check_poly(_ufuncs.eval_sh_chebyu,
+                        param_ranges=[], x_range=[0, 1])
+
+    def test_legendre(self):
+        self.check_poly(_ufuncs.eval_legendre,
+                        param_ranges=[], x_range=[-1, 1])
+
+    def test_sh_legendre(self):
+        self.check_poly(_ufuncs.eval_sh_legendre,
+                        param_ranges=[], x_range=[0, 1])
+
+    def test_genlaguerre(self):
+        self.check_poly(_ufuncs.eval_genlaguerre,
+                        param_ranges=[(-0.99, 10)], x_range=[0, 100])
+
+    def test_laguerre(self):
+        self.check_poly(_ufuncs.eval_laguerre,
+                        param_ranges=[], x_range=[0, 100])
+
+    def test_hermite(self):
+        v = _ufuncs.eval_hermite(70, 1.0)
+        a = -1.457076485701412e60
+        assert_allclose(v, a)
+
+
+def test_hermite_domain():
+    # Regression test for gh-11091.
+    assert np.isnan(_ufuncs.eval_hermite(-1, 1.0))
+    assert np.isnan(_ufuncs.eval_hermitenorm(-1, 1.0))
+
+
+@pytest.mark.parametrize("n", [0, 1, 2])
+@pytest.mark.parametrize("x", [0, 1, np.nan])
+def test_hermite_nan(n, x):
+    # Regression test for gh-11369.
+    assert np.isnan(_ufuncs.eval_hermite(n, x)) == np.any(np.isnan([n, x]))
+    assert np.isnan(_ufuncs.eval_hermitenorm(n, x)) == np.any(np.isnan([n, x]))
+
+
+@pytest.mark.parametrize('n', [0, 1, 2, 3.2])
+@pytest.mark.parametrize('alpha', [1, np.nan])
+@pytest.mark.parametrize('x', [2, np.nan])
+def test_genlaguerre_nan(n, alpha, x):
+    # Regression test for gh-11361.
+    nan_laguerre = np.isnan(_ufuncs.eval_genlaguerre(n, alpha, x))
+    nan_arg = np.any(np.isnan([n, alpha, x]))
+    assert nan_laguerre == nan_arg
+
+
+@pytest.mark.parametrize('n', [0, 1, 2, 3.2])
+@pytest.mark.parametrize('alpha', [0.0, 1, np.nan])
+@pytest.mark.parametrize('x', [1e-6, 2, np.nan])
+def test_gegenbauer_nan(n, alpha, x):
+    # Regression test for gh-11370.
+    nan_gegenbauer = np.isnan(_ufuncs.eval_gegenbauer(n, alpha, x))
+    nan_arg = np.any(np.isnan([n, alpha, x]))
+    assert nan_gegenbauer == nan_arg
+
+@pytest.mark.parametrize("n", np.arange(10))
+@pytest.mark.parametrize("alpha", [-0.45, -0.25, -0.125, 0.0, 0.25, 1.0, 2.0])
+@pytest.mark.parametrize("x", [-np.inf, np.inf])
+def test_gegenbauer_infinity(n, alpha, x):
+    # gh-11713 - check correct handling of x = +inf and x = -inf
+    if alpha == 0.0:
+        expected = 0.0
+    elif n == 0.0:
+        expected = 1.0
+    else:
+        # sign of leading coefficient: 2^n * Gamma(n+alpha) / (n! Gamma(alpha))
+        lead_sign = gammasgn(n + alpha) * gammasgn(alpha)
+        expected = lead_sign * (np.sign(x) ** n) * np.inf
+    assert_allclose(_ufuncs.eval_gegenbauer(int(n), alpha, x), expected, rtol=1e-10)
+    assert_allclose(_ufuncs.eval_gegenbauer(float(n), alpha, x), expected, rtol=1e-10)
+
+@pytest.mark.parametrize(
+    "n, expected",
+    [
+        (0, [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]),
+        (1, [-2.0, -1.8, -1.6, -1.4, -1.2, -1.0, -0.8, -0.6, -0.4, -0.2, 0.0]),
+        (2, [3.0, 2.16, 1.44, 0.84, 0.36, 0.0, -0.24, -0.36, -0.36, -0.24, 0.0]),
+        (3, [-4.0, -1.98, -0.64, 0.14, 0.48, 0.5, 0.32, 0.06, -0.16, -0.22, 0.0]),
+        (
+            4,
+            [5.0, 1.332, -0.288, -0.658, -0.408, 0.0, 0.272, 0.282, 0.072, -0.148, 0.0],
+        ),
+        (
+            5,
+            [
+                -6.0,
+                -0.43308,
+                0.79104,
+                0.36876,
+                -0.21312,
+                -0.375,
+                -0.14208,
+                0.15804,
+                0.19776,
+                -0.04812,
+                0.0,
+            ],
+        ),
+    ],
+)
+def test_jacobi_alpha_minus_one_beta_plus_one(n, expected):
+    # gh-7001 - expected values were computed with mathematica
+    x = np.linspace(-1.0, 1.0, 11)
+    a, b = -1, 1  # alpha, beta
+    assert_allclose(_ufuncs.eval_jacobi(n, a, b, x), expected, rtol=1e-10, atol=1e-14)
+    assert_allclose(
+        _ufuncs.eval_jacobi(float(n), a, b, x), expected, rtol=1e-10, atol=1e-14
+    )
+
+
+@pytest.mark.parametrize(
+    "n, expected",
+    [
+        (0, [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]),
+        (1, [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]),
+        (2, [0.0, -0.09, -0.16, -0.21, -0.24, -0.25, -0.24, -0.21, -0.16, -0.09, 0.0]),
+        (
+            3,
+            [0.0, 0.144, 0.192, 0.168, 0.096, 0.0, -0.096, -0.168, -0.192, -0.144, 0.0],
+        ),
+        (
+            4,
+            [
+                0.0,
+                -0.1485,
+                -0.096,
+                0.0315,
+                0.144,
+                0.1875,
+                0.144,
+                0.0315,
+                -0.096,
+                -0.1485,
+                0.0,
+            ],
+        ),
+        (
+            5,
+            [
+                0.0,
+                0.10656,
+                -0.04608,
+                -0.15792,
+                -0.13056,
+                0.0,
+                0.13056,
+                0.15792,
+                0.04608,
+                -0.10656,
+                0.0,
+            ],
+        ),
+    ],
+)
+def test_jacobi_alpha_minus_one_beta_minus_one(n, expected):
+    # gh-7001 - expected values were computed with mathematica
+    x = np.linspace(-1.0, 1.0, 11)
+    a, b = -1, -1  # alpha, beta
+    assert_allclose(_ufuncs.eval_jacobi(n, a, b, x), expected, rtol=1e-10, atol=1e-14)
+    assert_allclose(
+        _ufuncs.eval_jacobi(float(n), a, b, x), expected, rtol=1e-10, atol=1e-14
+    )
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_owens_t.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_owens_t.py
new file mode 100644
index 0000000000000000000000000000000000000000..8d15aead25302023c5f07d8392c0931995764ced
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_owens_t.py
@@ -0,0 +1,53 @@
+import numpy as np
+from numpy.testing import assert_equal, assert_allclose
+
+import scipy.special as sc
+
+
+def test_symmetries():
+    np.random.seed(1234)
+    a, h = np.random.rand(100), np.random.rand(100)
+    assert_equal(sc.owens_t(h, a), sc.owens_t(-h, a))
+    assert_equal(sc.owens_t(h, a), -sc.owens_t(h, -a))
+
+
+def test_special_cases():
+    assert_equal(sc.owens_t(5, 0), 0)
+    assert_allclose(sc.owens_t(0, 5), 0.5*np.arctan(5)/np.pi,
+                    rtol=5e-14)
+    # Target value is 0.5*Phi(5)*(1 - Phi(5)) for Phi the CDF of the
+    # standard normal distribution
+    assert_allclose(sc.owens_t(5, 1), 1.4332574485503512543e-07,
+                    rtol=5e-14)
+
+
+def test_nans():
+    assert_equal(sc.owens_t(20, np.nan), np.nan)
+    assert_equal(sc.owens_t(np.nan, 20), np.nan)
+    assert_equal(sc.owens_t(np.nan, np.nan), np.nan)
+
+
+def test_infs():
+    h, a = 0, np.inf
+    # T(0, a) = 1/2π * arctan(a)
+    res = 1/(2*np.pi) * np.arctan(a)
+    assert_allclose(sc.owens_t(h, a), res, rtol=5e-14)
+    assert_allclose(sc.owens_t(h, -a), -res, rtol=5e-14)
+
+    h = 1
+    # Refer Owens T function definition in Wikipedia
+    # https://en.wikipedia.org/wiki/Owen%27s_T_function
+    # Value approximated through Numerical Integration
+    # using scipy.integrate.quad
+    # quad(lambda x: 1/(2*pi)*(exp(-0.5*(1*1)*(1+x*x))/(1+x*x)), 0, inf)
+    res = 0.07932762696572854
+    assert_allclose(sc.owens_t(h, np.inf), res, rtol=5e-14)
+    assert_allclose(sc.owens_t(h, -np.inf), -res, rtol=5e-14)
+
+    assert_equal(sc.owens_t(np.inf, 1), 0)
+    assert_equal(sc.owens_t(-np.inf, 1), 0)
+
+    assert_equal(sc.owens_t(np.inf, np.inf), 0)
+    assert_equal(sc.owens_t(-np.inf, np.inf), 0)
+    assert_equal(sc.owens_t(np.inf, -np.inf), -0.0)
+    assert_equal(sc.owens_t(-np.inf, -np.inf), -0.0)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_pcf.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_pcf.py
new file mode 100644
index 0000000000000000000000000000000000000000..a8c42aa688081fb58f79ad2c8ea932d03b33523b
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_pcf.py
@@ -0,0 +1,24 @@
+"""Tests for parabolic cylinder functions.
+
+"""
+import numpy as np
+from numpy.testing import assert_allclose, assert_equal
+import scipy.special as sc
+
+
+def test_pbwa_segfault():
+    # Regression test for https://github.com/scipy/scipy/issues/6208.
+    #
+    # Data generated by mpmath.
+    #
+    w = 1.02276567211316867161
+    wp = -0.48887053372346189882
+    assert_allclose(sc.pbwa(0, 0), (w, wp), rtol=1e-13, atol=0)
+
+
+def test_pbwa_nan():
+    # Check that NaN's are returned outside of the range in which the
+    # implementation is accurate.
+    pts = [(-6, -6), (-6, 6), (6, -6), (6, 6)]
+    for p in pts:
+        assert_equal(sc.pbwa(*p), (np.nan, np.nan))
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_pdtr.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_pdtr.py
new file mode 100644
index 0000000000000000000000000000000000000000..f2159e6bd3acd60f4bdc98fc9ce0f6d44ac76485
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_pdtr.py
@@ -0,0 +1,48 @@
+import numpy as np
+import scipy.special as sc
+from numpy.testing import assert_allclose, assert_array_equal
+
+
+class TestPdtr:
+    def test(self):
+        val = sc.pdtr(0, 1)
+        assert_allclose(val, np.exp(-1), atol=1.5e-7, rtol=0)
+
+    def test_m_zero(self):
+        val = sc.pdtr([0, 1, 2], 0)
+        assert_allclose(val, [1, 1, 1], atol=1.5e-7, rtol=0)
+
+    def test_rounding(self):
+        double_val = sc.pdtr([0.1, 1.1, 2.1], 1.0)
+        int_val = sc.pdtr([0, 1, 2], 1.0)
+        assert_array_equal(double_val, int_val)
+
+    def test_inf(self):
+        val = sc.pdtr(np.inf, 1.0)
+        assert_allclose(val, 1.0, atol=1.5e-7, rtol=0)
+
+    def test_domain(self):
+        val = sc.pdtr(-1.1, 1.0)
+        assert np.isnan(val)
+
+class TestPdtrc:
+    def test_value(self):
+        val = sc.pdtrc(0, 1)
+        assert_allclose(val, 1 - np.exp(-1), atol=1.5e-7, rtol=0)
+
+    def test_m_zero(self):
+        val = sc.pdtrc([0, 1, 2], 0.0)
+        assert_array_equal(val, [0, 0, 0])
+
+    def test_rounding(self):
+        double_val = sc.pdtrc([0.1, 1.1, 2.1], 1.0)
+        int_val = sc.pdtrc([0, 1, 2], 1.0)
+        assert_array_equal(double_val, int_val)
+
+    def test_inf(self):
+        val = sc.pdtrc(np.inf, 1.0)
+        assert_allclose(val, 0.0, atol=1.5e-7, rtol=0)
+
+    def test_domain(self):
+        val = sc.pdtrc(-1.1, 1.0)
+        assert np.isnan(val)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_powm1.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_powm1.py
new file mode 100644
index 0000000000000000000000000000000000000000..3d809963f64ddaedf6b59de80dcd5f7ca8fa18a9
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_powm1.py
@@ -0,0 +1,65 @@
+import pytest
+import numpy as np
+from numpy.testing import assert_allclose
+from scipy.special import powm1
+
+
+# Expected values were computed with mpmath, e.g.
+#
+#   >>> import mpmath
+#   >>> mpmath.np.dps = 200
+#   >>> print(float(mpmath.powm1(2.0, 1e-7))
+#   6.931472045825965e-08
+#
+powm1_test_cases = [
+    (1.25, 0.75, 0.18217701125396976, 1e-15),
+    (2.0, 1e-7, 6.931472045825965e-08, 1e-15),
+    (25.0, 5e-11, 1.6094379125636148e-10, 1e-15),
+    (0.99996, 0.75, -3.0000150002530058e-05, 1e-15),
+    (0.9999999999990905, 20, -1.81898940353014e-11, 1e-15),
+    (-1.25, 751.0, -6.017550852453444e+72, 2e-15)
+]
+
+
+@pytest.mark.parametrize('x, y, expected, rtol', powm1_test_cases)
+def test_powm1(x, y, expected, rtol):
+    p = powm1(x, y)
+    assert_allclose(p, expected, rtol=rtol)
+
+
+@pytest.mark.parametrize('x, y, expected',
+                         [(0.0, 0.0, 0.0),
+                          (0.0, -1.5, np.inf),
+                          (0.0, 1.75, -1.0),
+                          (-1.5, 2.0, 1.25),
+                          (-1.5, 3.0, -4.375),
+                          (np.nan, 0.0, 0.0),
+                          (1.0, np.nan, 0.0),
+                          (1.0, np.inf, 0.0),
+                          (1.0, -np.inf, 0.0),
+                          (np.inf, 7.5, np.inf),
+                          (np.inf, -7.5, -1.0),
+                          (3.25, np.inf, np.inf),
+                          (np.inf, np.inf, np.inf),
+                          (np.inf, -np.inf, -1.0),
+                          (np.inf, 0.0, 0.0),
+                          (-np.inf, 0.0, 0.0),
+                          (-np.inf, 2.0, np.inf),
+                          (-np.inf, 3.0, -np.inf),
+                          (-1.0, float(2**53 - 1), -2.0)])
+def test_powm1_exact_cases(x, y, expected):
+    # Test cases where we have an exact expected value.
+    p = powm1(x, y)
+    assert p == expected
+
+
+@pytest.mark.parametrize('x, y',
+                         [(-1.25, 751.03),
+                          (-1.25, np.inf),
+                          (np.nan, np.nan),
+                          (-np.inf, -np.inf),
+                          (-np.inf, 2.5)])
+def test_powm1_return_nan(x, y):
+    # Test cases where the expected return value is nan.
+    p = powm1(x, y)
+    assert np.isnan(p)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_precompute_expn_asy.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_precompute_expn_asy.py
new file mode 100644
index 0000000000000000000000000000000000000000..7b6c6cba21d5c1d5fdfab879153ba8f125e98d5f
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_precompute_expn_asy.py
@@ -0,0 +1,24 @@
+from numpy.testing import assert_equal
+
+from scipy.special._testutils import check_version, MissingModule
+from scipy.special._precompute.expn_asy import generate_A
+
+try:
+    import sympy
+    from sympy import Poly
+except ImportError:
+    sympy = MissingModule("sympy")
+
+
+@check_version(sympy, "1.0")
+def test_generate_A():
+    # Data from DLMF 8.20.5
+    x = sympy.symbols('x')
+    Astd = [Poly(1, x),
+            Poly(1, x),
+            Poly(1 - 2*x),
+            Poly(1 - 8*x + 6*x**2)]
+    Ares = generate_A(len(Astd))
+
+    for p, q in zip(Astd, Ares):
+        assert_equal(p, q)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_precompute_gammainc.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_precompute_gammainc.py
new file mode 100644
index 0000000000000000000000000000000000000000..86278b065a58bdde3fcde32a2f7ec0d53d17077d
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_precompute_gammainc.py
@@ -0,0 +1,112 @@
+import pytest
+
+from scipy.special._testutils import MissingModule, check_version
+from scipy.special._mptestutils import (
+    Arg, IntArg, mp_assert_allclose, assert_mpmath_equal)
+from scipy.special._precompute.gammainc_asy import (
+    compute_g, compute_alpha, compute_d)
+from scipy.special._precompute.gammainc_data import gammainc, gammaincc
+
+try:
+    import sympy
+except ImportError:
+    sympy = MissingModule('sympy')
+
+try:
+    import mpmath as mp
+except ImportError:
+    mp = MissingModule('mpmath')
+
+
+pytestmark = pytest.mark.thread_unsafe(
+    reason=("mpmath gmpy2 backend is not thread-safe, "
+            "see https://github.com/mpmath/mpmath/issues/974"))
+
+@check_version(mp, '0.19')
+def test_g():
+    # Test data for the g_k. See DLMF 5.11.4.
+    with mp.workdps(30):
+        g = [mp.mpf(1), mp.mpf(1)/12, mp.mpf(1)/288,
+             -mp.mpf(139)/51840, -mp.mpf(571)/2488320,
+             mp.mpf(163879)/209018880, mp.mpf(5246819)/75246796800]
+        mp_assert_allclose(compute_g(7), g)
+
+
+@pytest.mark.slow
+@check_version(mp, '0.19')
+@check_version(sympy, '0.7')
+@pytest.mark.xfail_on_32bit("rtol only 2e-11, see gh-6938")
+def test_alpha():
+    # Test data for the alpha_k. See DLMF 8.12.14.
+    with mp.workdps(30):
+        alpha = [mp.mpf(0), mp.mpf(1), mp.mpf(1)/3, mp.mpf(1)/36,
+                 -mp.mpf(1)/270, mp.mpf(1)/4320, mp.mpf(1)/17010,
+                 -mp.mpf(139)/5443200, mp.mpf(1)/204120]
+        mp_assert_allclose(compute_alpha(9), alpha)
+
+
+@pytest.mark.xslow
+@check_version(mp, '0.19')
+@check_version(sympy, '0.7')
+def test_d():
+    # Compare the d_{k, n} to the results in appendix F of [1].
+    #
+    # Sources
+    # -------
+    # [1] DiDonato and Morris, Computation of the Incomplete Gamma
+    #     Function Ratios and their Inverse, ACM Transactions on
+    #     Mathematical Software, 1986.
+
+    with mp.workdps(50):
+        dataset = [(0, 0, -mp.mpf('0.333333333333333333333333333333')),
+                   (0, 12, mp.mpf('0.102618097842403080425739573227e-7')),
+                   (1, 0, -mp.mpf('0.185185185185185185185185185185e-2')),
+                   (1, 12, mp.mpf('0.119516285997781473243076536700e-7')),
+                   (2, 0, mp.mpf('0.413359788359788359788359788360e-2')),
+                   (2, 12, -mp.mpf('0.140925299108675210532930244154e-7')),
+                   (3, 0, mp.mpf('0.649434156378600823045267489712e-3')),
+                   (3, 12, -mp.mpf('0.191111684859736540606728140873e-7')),
+                   (4, 0, -mp.mpf('0.861888290916711698604702719929e-3')),
+                   (4, 12, mp.mpf('0.288658297427087836297341274604e-7')),
+                   (5, 0, -mp.mpf('0.336798553366358150308767592718e-3')),
+                   (5, 12, mp.mpf('0.482409670378941807563762631739e-7')),
+                   (6, 0, mp.mpf('0.531307936463992223165748542978e-3')),
+                   (6, 12, -mp.mpf('0.882860074633048352505085243179e-7')),
+                   (7, 0, mp.mpf('0.344367606892377671254279625109e-3')),
+                   (7, 12, -mp.mpf('0.175629733590604619378669693914e-6')),
+                   (8, 0, -mp.mpf('0.652623918595309418922034919727e-3')),
+                   (8, 12, mp.mpf('0.377358774161109793380344937299e-6')),
+                   (9, 0, -mp.mpf('0.596761290192746250124390067179e-3')),
+                   (9, 12, mp.mpf('0.870823417786464116761231237189e-6'))]
+        d = compute_d(10, 13)
+        res = [d[k][n] for k, n, std in dataset]
+        std = [x[2] for x in dataset]
+        mp_assert_allclose(res, std)
+
+
+@check_version(mp, '0.19')
+def test_gammainc():
+    # Quick check that the gammainc in
+    # special._precompute.gammainc_data agrees with mpmath's
+    # gammainc.
+    assert_mpmath_equal(gammainc,
+                        lambda a, x: mp.gammainc(a, b=x, regularized=True),
+                        [Arg(0, 100, inclusive_a=False), Arg(0, 100)],
+                        nan_ok=False, rtol=1e-17, n=50, dps=50)
+
+
+@pytest.mark.xslow
+@check_version(mp, '0.19')
+def test_gammaincc():
+    # Check that the gammaincc in special._precompute.gammainc_data
+    # agrees with mpmath's gammainc.
+    assert_mpmath_equal(lambda a, x: gammaincc(a, x, dps=1000),
+                        lambda a, x: mp.gammainc(a, a=x, regularized=True),
+                        [Arg(20, 100), Arg(20, 100)],
+                        nan_ok=False, rtol=1e-17, n=50, dps=1000)
+
+    # Test the fast integer path
+    assert_mpmath_equal(gammaincc,
+                        lambda a, x: mp.gammainc(a, a=x, regularized=True),
+                        [IntArg(1, 100), Arg(0, 100)],
+                        nan_ok=False, rtol=1e-17, n=50, dps=50)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_precompute_utils.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_precompute_utils.py
new file mode 100644
index 0000000000000000000000000000000000000000..89616b92329691ca76039fe11a7e08f7f3db1150
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_precompute_utils.py
@@ -0,0 +1,36 @@
+import pytest
+
+from scipy.special._testutils import MissingModule, check_version
+from scipy.special._mptestutils import mp_assert_allclose
+from scipy.special._precompute.utils import lagrange_inversion
+
+try:
+    import sympy
+except ImportError:
+    sympy = MissingModule('sympy')
+
+try:
+    import mpmath as mp
+except ImportError:
+    mp = MissingModule('mpmath')
+
+
+@pytest.mark.slow
+@check_version(sympy, '0.7')
+@check_version(mp, '0.19')
+class TestInversion:
+    @pytest.mark.xfail_on_32bit("rtol only 2e-9, see gh-6938")
+    def test_log(self):
+        with mp.workdps(30):
+            logcoeffs = mp.taylor(lambda x: mp.log(1 + x), 0, 10)
+            expcoeffs = mp.taylor(lambda x: mp.exp(x) - 1, 0, 10)
+            invlogcoeffs = lagrange_inversion(logcoeffs)
+            mp_assert_allclose(invlogcoeffs, expcoeffs)
+
+    @pytest.mark.xfail_on_32bit("rtol only 1e-15, see gh-6938")
+    def test_sin(self):
+        with mp.workdps(30):
+            sincoeffs = mp.taylor(mp.sin, 0, 10)
+            asincoeffs = mp.taylor(mp.asin, 0, 10)
+            invsincoeffs = lagrange_inversion(sincoeffs)
+            mp_assert_allclose(invsincoeffs, asincoeffs, atol=1e-30)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_round.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_round.py
new file mode 100644
index 0000000000000000000000000000000000000000..ba28b7c1cff95327df0ed69086dd92b93399c3c4
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_round.py
@@ -0,0 +1,18 @@
+import numpy as np
+import pytest
+
+from scipy.special import _test_internal
+
+
+@pytest.mark.fail_slow(20)
+@pytest.mark.skipif(not _test_internal.have_fenv(), reason="no fenv()")
+def test_add_round_up():
+    rng = np.random.RandomState(1234)
+    _test_internal.test_add_round(10**5, 'up', rng)
+
+
+@pytest.mark.fail_slow(20)
+@pytest.mark.skipif(not _test_internal.have_fenv(), reason="no fenv()")
+def test_add_round_down():
+    rng = np.random.RandomState(1234)
+    _test_internal.test_add_round(10**5, 'down', rng)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_sf_error.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_sf_error.py
new file mode 100644
index 0000000000000000000000000000000000000000..337bd0c65ebd712bfda1385072c15a47e8a495c2
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_sf_error.py
@@ -0,0 +1,153 @@
+import sys
+import warnings
+
+import numpy as np
+from numpy.testing import assert_, assert_equal, HAS_REFCOUNT
+import pytest
+from pytest import raises as assert_raises
+
+import scipy.special as sc
+from scipy.special._ufuncs import _sf_error_test_function
+
+_sf_error_code_map = {
+    # skip 'ok'
+    'singular': 1,
+    'underflow': 2,
+    'overflow': 3,
+    'slow': 4,
+    'loss': 5,
+    'no_result': 6,
+    'domain': 7,
+    'arg': 8,
+    'other': 9,
+    'memory': 10,
+}
+
+_sf_error_actions = [
+    'ignore',
+    'warn',
+    'raise'
+]
+
+
+def _check_action(fun, args, action):
+    # TODO: special expert should correct
+    # the coercion at the true location?
+    args = np.asarray(args, dtype=np.dtype("long"))
+    if action == 'warn':
+        with pytest.warns(sc.SpecialFunctionWarning):
+            fun(*args)
+    elif action == 'raise':
+        with assert_raises(sc.SpecialFunctionError):
+            fun(*args)
+    else:
+        # action == 'ignore', make sure there are no warnings/exceptions
+        with warnings.catch_warnings():
+            warnings.simplefilter("error")
+            fun(*args)
+
+
+def test_geterr():
+    err = sc.geterr()
+    for key, value in err.items():
+        assert_(key in _sf_error_code_map)
+        assert_(value in _sf_error_actions)
+
+
+def test_seterr():
+    entry_err = sc.geterr()
+    try:
+        for category, error_code in _sf_error_code_map.items():
+            for action in _sf_error_actions:
+                geterr_olderr = sc.geterr()
+                seterr_olderr = sc.seterr(**{category: action})
+                assert_(geterr_olderr == seterr_olderr)
+                newerr = sc.geterr()
+                assert_(newerr[category] == action)
+                geterr_olderr.pop(category)
+                newerr.pop(category)
+                assert_(geterr_olderr == newerr)
+                _check_action(_sf_error_test_function, (error_code,), action)
+    finally:
+        sc.seterr(**entry_err)
+
+
+@pytest.mark.thread_unsafe(reason="module refcounts are not stable in multiple threads")
+@pytest.mark.skipif(not HAS_REFCOUNT, reason="Python lacks refcounts")
+def test_sf_error_special_refcount():
+    # Regression test for gh-16233.
+    # Check that the reference count of scipy.special is not increased
+    # when a SpecialFunctionError is raised.
+    refcount_before = sys.getrefcount(sc)
+    with sc.errstate(all='raise'):
+        with pytest.raises(sc.SpecialFunctionError, match='domain error'):
+            sc.ndtri(2.0)
+    refcount_after = sys.getrefcount(sc)
+    assert refcount_after == refcount_before
+
+
+def test_errstate_pyx_basic():
+    olderr = sc.geterr()
+    with sc.errstate(singular='raise'):
+        with assert_raises(sc.SpecialFunctionError):
+            sc.loggamma(0)
+    assert_equal(olderr, sc.geterr())
+
+
+def test_errstate_c_basic():
+    olderr = sc.geterr()
+    with sc.errstate(domain='raise'):
+        with assert_raises(sc.SpecialFunctionError):
+            sc.spence(-1)
+    assert_equal(olderr, sc.geterr())
+
+
+def test_errstate_cpp_basic():
+    olderr = sc.geterr()
+    with sc.errstate(underflow='raise'):
+        with assert_raises(sc.SpecialFunctionError):
+            sc.wrightomega(-1000)
+    assert_equal(olderr, sc.geterr())
+
+
+def test_errstate_cpp_scipy_special():
+    olderr = sc.geterr()
+    with sc.errstate(singular='raise'):
+        with assert_raises(sc.SpecialFunctionError):
+            sc.lambertw(0, 1)
+    assert_equal(olderr, sc.geterr())
+
+
+def test_errstate_cpp_alt_ufunc_machinery():
+    olderr = sc.geterr()
+    with sc.errstate(singular='raise'):
+        with assert_raises(sc.SpecialFunctionError):
+            sc.gammaln(0)
+    assert_equal(olderr, sc.geterr())
+
+
+def test_errstate():
+    for category, error_code in _sf_error_code_map.items():
+        for action in _sf_error_actions:
+            olderr = sc.geterr()
+            with sc.errstate(**{category: action}):
+                _check_action(_sf_error_test_function, (error_code,), action)
+            assert_equal(olderr, sc.geterr())
+
+
+def test_errstate_all_but_one():
+    olderr = sc.geterr()
+    with sc.errstate(all='raise', singular='ignore'):
+        sc.gammaln(0)
+        with assert_raises(sc.SpecialFunctionError):
+            sc.spence(-1.0)
+    assert_equal(olderr, sc.geterr())
+
+
+def test_check_overflow_message():
+    # Regression test for a bug where the overflow and underflow
+    # messages were switched.
+    with pytest.raises(sc.SpecialFunctionError, match="overflow"):
+        with sc.errstate(all='raise'):
+            # This should trigger an overflow:
+            sc.yn(3, 1e-105)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_sici.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_sici.py
new file mode 100644
index 0000000000000000000000000000000000000000..d33c1795641ba74f777fcfdcffe80d86463477e3
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_sici.py
@@ -0,0 +1,36 @@
+import numpy as np
+
+import scipy.special as sc
+from scipy.special._testutils import FuncData
+
+
+def test_sici_consistency():
+    # Make sure the implementation of sici for real arguments agrees
+    # with the implementation of sici for complex arguments.
+
+    # On the negative real axis Cephes drops the imaginary part in ci
+    def sici(x):
+        si, ci = sc.sici(x + 0j)
+        return si.real, ci.real
+    
+    x = np.r_[-np.logspace(8, -30, 200), 0, np.logspace(-30, 8, 200)]
+    si, ci = sc.sici(x)
+    dataset = np.column_stack((x, si, ci))
+    FuncData(sici, dataset, 0, (1, 2), rtol=1e-12).check()
+
+
+def test_shichi_consistency():
+    # Make sure the implementation of shichi for real arguments agrees
+    # with the implementation of shichi for complex arguments.
+
+    # On the negative real axis Cephes drops the imaginary part in chi
+    def shichi(x):
+        shi, chi = sc.shichi(x + 0j)
+        return shi.real, chi.real
+
+    # Overflow happens quickly, so limit range
+    x = np.r_[-np.logspace(np.log10(700), -30, 200), 0,
+              np.logspace(-30, np.log10(700), 200)]
+    shi, chi = sc.shichi(x)
+    dataset = np.column_stack((x, shi, chi))
+    FuncData(shichi, dataset, 0, (1, 2), rtol=1e-14).check()
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_specfun.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_specfun.py
new file mode 100644
index 0000000000000000000000000000000000000000..f36fd2915be8c8d14138493c34dfd5733a2a1e6d
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_specfun.py
@@ -0,0 +1,48 @@
+"""
+Various made-up tests to hit different branches of the code in specfun.c
+"""
+
+import numpy as np
+from numpy.testing import assert_allclose
+from scipy import special
+
+
+def test_cva2_cv0_branches():
+    res, resp = special.mathieu_cem([40, 129], [13, 14], [30, 45])
+    assert_allclose(res, np.array([-0.3741211, 0.74441928]))
+    assert_allclose(resp, np.array([-37.02872758, -86.13549877]))
+
+    res, resp = special.mathieu_sem([40, 129], [13, 14], [30, 45])
+    assert_allclose(res, np.array([0.92955551, 0.66771207]))
+    assert_allclose(resp, np.array([-14.91073448, 96.02954185]))
+
+
+def test_chgm_branches():
+    res = special.eval_genlaguerre(-3.2, 3, 2.5)
+    assert_allclose(res, -0.7077721935779854)
+
+
+def test_hygfz_branches():
+    """(z == 1.0) && (c-a-b > 0.0)"""
+    res = special.hyp2f1(1.5, 2.5, 4.5, 1.+0.j)
+    assert_allclose(res, 10.30835089459151+0j)
+    """(cabs(z+1) < eps) && (fabs(c-a+b - 1.0) < eps)"""
+    res = special.hyp2f1(5+5e-16, 2, 2, -1.0 + 5e-16j)
+    assert_allclose(res, 0.031249999999999986+3.9062499999999994e-17j)
+
+
+def test_pro_rad1():
+    # https://github.com/scipy/scipy/issues/21058
+    # Reference values taken from WolframAlpha
+    # SpheroidalS1(1, 1, 30, 1.1)
+    # SpheroidalS1Prime(1, 1, 30, 1.1)
+    res = special.pro_rad1(1, 1, 30, 1.1)
+    assert_allclose(res, (0.009657872296166435, 3.253369651472877), rtol=2e-5)
+
+def test_pro_rad2():
+    # https://github.com/scipy/scipy/issues/21461
+    # Reference values taken from WolframAlpha
+    # SpheroidalS2(0, 0, 3, 1.02)
+    # SpheroidalS2Prime(0, 0, 3, 1.02)
+    res = special.pro_rad2(0, 0, 3, 1.02)
+    assert_allclose(res, (-0.35089596858528077, 13.652764213480872), rtol=10e-10)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_spence.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_spence.py
new file mode 100644
index 0000000000000000000000000000000000000000..fbb26ac281dff81ea71b30318731065fe5a78f94
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_spence.py
@@ -0,0 +1,32 @@
+import numpy as np
+from numpy import sqrt, log, pi
+from scipy.special._testutils import FuncData
+from scipy.special import spence
+
+
+def test_consistency():
+    # Make sure the implementation of spence for real arguments
+    # agrees with the implementation of spence for imaginary arguments.
+
+    x = np.logspace(-30, 300, 200)
+    dataset = np.vstack((x + 0j, spence(x))).T
+    FuncData(spence, dataset, 0, 1, rtol=1e-14).check()
+
+
+def test_special_points():
+    # Check against known values of Spence's function.
+
+    phi = (1 + sqrt(5))/2
+    dataset = [(1, 0),
+               (2, -pi**2/12),
+               (0.5, pi**2/12 - log(2)**2/2),
+               (0, pi**2/6),
+               (-1, pi**2/4 - 1j*pi*log(2)),
+               ((-1 + sqrt(5))/2, pi**2/15 - log(phi)**2),
+               ((3 - sqrt(5))/2, pi**2/10 - log(phi)**2),
+               (phi, -pi**2/15 + log(phi)**2/2),
+               # Corrected from Zagier, "The Dilogarithm Function"
+               ((3 + sqrt(5))/2, -pi**2/10 - log(phi)**2)]
+
+    dataset = np.asarray(dataset)
+    FuncData(spence, dataset, 0, 1, rtol=1e-14).check()
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_spfun_stats.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_spfun_stats.py
new file mode 100644
index 0000000000000000000000000000000000000000..7dd4164bbab3ba88765617148dc7ea488bf81c65
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_spfun_stats.py
@@ -0,0 +1,61 @@
+import numpy as np
+from numpy.testing import (assert_array_equal, assert_array_almost_equal_nulp,
+                           assert_allclose)
+from pytest import raises as assert_raises
+
+from scipy.special import gammaln, multigammaln  # type:ignore[attr-defined]
+
+
+class TestMultiGammaLn:
+
+    def test1(self):
+        # A test of the identity
+        #     Gamma_1(a) = Gamma(a)
+        np.random.seed(1234)
+        a = np.abs(np.random.randn())
+        assert_array_equal(multigammaln(a, 1), gammaln(a))
+
+    def test2(self):
+        # A test of the identity
+        #     Gamma_2(a) = sqrt(pi) * Gamma(a) * Gamma(a - 0.5)
+        a = np.array([2.5, 10.0])
+        result = multigammaln(a, 2)
+        expected = np.log(np.sqrt(np.pi)) + gammaln(a) + gammaln(a - 0.5)
+        assert_allclose(result, expected, atol=1.5e-7, rtol=0)
+
+    def test_bararg(self):
+        assert_raises(ValueError, multigammaln, 0.5, 1.2)
+
+
+def _check_multigammaln_array_result(a, d):
+    # Test that the shape of the array returned by multigammaln
+    # matches the input shape, and that all the values match
+    # the value computed when multigammaln is called with a scalar.
+    result = multigammaln(a, d)
+    assert_array_equal(a.shape, result.shape)
+    a1 = a.ravel()
+    result1 = result.ravel()
+    for i in range(a.size):
+        assert_array_almost_equal_nulp(result1[i], multigammaln(a1[i], d))
+
+
+def test_multigammaln_array_arg():
+    # Check that the array returned by multigammaln has the correct
+    # shape and contains the correct values.  The cases have arrays
+    # with several different shapes.
+    # The cases include a regression test for ticket #1849
+    # (a = np.array([2.0]), an array with a single element).
+    np.random.seed(1234)
+
+    cases = [
+        # a, d
+        (np.abs(np.random.randn(3, 2)) + 5, 5),
+        (np.abs(np.random.randn(1, 2)) + 5, 5),
+        (np.arange(10.0, 18.0).reshape(2, 2, 2), 3),
+        (np.array([2.0]), 3),
+        (np.float64(2.0), 3),
+    ]
+
+    for a, d in cases:
+        _check_multigammaln_array_result(a, d)
+
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_sph_harm.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_sph_harm.py
new file mode 100644
index 0000000000000000000000000000000000000000..117f0938379082125f97d738d27364f7821eaefc
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_sph_harm.py
@@ -0,0 +1,48 @@
+import numpy as np
+import pytest
+
+from numpy.testing import assert_allclose
+import scipy.special as sc
+
+class TestSphHarm:
+    @pytest.mark.slow
+    def test_p(self):
+        m_max = 20
+        n_max = 10
+
+        theta = np.linspace(0, np.pi)
+        phi = np.linspace(0, 2*np.pi)
+        theta, phi = np.meshgrid(theta, phi)
+
+        y, y_jac, y_hess = sc.sph_harm_y_all(n_max, m_max, theta, phi, diff_n=2)
+        p, p_jac, p_hess = sc.sph_legendre_p_all(n_max, m_max, theta, diff_n=2)
+
+        m = np.concatenate([np.arange(m_max + 1), np.arange(-m_max, 0)])
+        m = np.expand_dims(m, axis=(0,)+tuple(range(2,theta.ndim+2)))
+
+        assert_allclose(y, p * np.exp(1j * m * phi))
+
+        assert_allclose(y_jac[..., 0], p_jac * np.exp(1j * m * phi))
+        assert_allclose(y_jac[..., 1], 1j * m * p * np.exp(1j * m * phi))
+
+        assert_allclose(y_hess[..., 0, 0], p_hess * np.exp(1j * m * phi))
+        assert_allclose(y_hess[..., 0, 1], 1j * m * p_jac * np.exp(1j * m * phi))
+        assert_allclose(y_hess[..., 1, 0], y_hess[..., 0, 1])
+        assert_allclose(y_hess[..., 1, 1], -m * m * p * np.exp(1j * m * phi))
+
+    @pytest.mark.parametrize("n_max", [7, 10, 50])
+    @pytest.mark.parametrize("m_max", [1, 4, 5, 9, 14])
+    def test_all(self, n_max, m_max):
+        theta = np.linspace(0, np.pi)
+        phi = np.linspace(0, 2 * np.pi)
+
+        n = np.arange(n_max + 1)
+        n = np.expand_dims(n, axis=tuple(range(1,theta.ndim+2)))
+
+        m = np.concatenate([np.arange(m_max + 1), np.arange(-m_max, 0)])
+        m = np.expand_dims(m, axis=(0,)+tuple(range(2,theta.ndim+2)))
+
+        y_actual = sc.sph_harm_y_all(n_max, m_max, theta, phi)
+        y_desired = sc.sph_harm_y(n, m, theta, phi)
+
+        np.testing.assert_allclose(y_actual, y_desired, rtol=1e-05)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_spherical_bessel.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_spherical_bessel.py
new file mode 100644
index 0000000000000000000000000000000000000000..8444a4c16aa9e3b9ffc204f824a3f136a030f2be
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_spherical_bessel.py
@@ -0,0 +1,407 @@
+#
+# Tests of spherical Bessel functions.
+#
+import warnings
+
+import numpy as np
+from numpy.testing import assert_allclose
+import pytest
+from numpy import sin, cos, sinh, cosh, exp, inf, nan, r_, pi
+
+from scipy.special import spherical_jn, spherical_yn, spherical_in, spherical_kn
+from scipy.integrate import quad
+
+
+class TestSphericalJn:
+    def test_spherical_jn_exact(self):
+        # https://dlmf.nist.gov/10.49.E3
+        # Note: exact expression is numerically stable only for small
+        # n or z >> n.
+        x = np.array([0.12, 1.23, 12.34, 123.45, 1234.5])
+        assert_allclose(spherical_jn(2, x),
+                        (-1/x + 3/x**3)*sin(x) - 3/x**2*cos(x))
+
+    def test_spherical_jn_recurrence_complex(self):
+        # https://dlmf.nist.gov/10.51.E1
+        n = np.array([1, 2, 3, 7, 12])
+        x = 1.1 + 1.5j
+        assert_allclose(spherical_jn(n - 1, x) + spherical_jn(n + 1, x),
+                        (2*n + 1)/x*spherical_jn(n, x))
+
+    def test_spherical_jn_recurrence_real(self):
+        # https://dlmf.nist.gov/10.51.E1
+        n = np.array([1, 2, 3, 7, 12])
+        x = 0.12
+        assert_allclose(spherical_jn(n - 1, x) + spherical_jn(n + 1,x),
+                        (2*n + 1)/x*spherical_jn(n, x))
+
+    def test_spherical_jn_inf_real(self):
+        # https://dlmf.nist.gov/10.52.E3
+        n = 6
+        x = np.array([-inf, inf])
+        assert_allclose(spherical_jn(n, x), np.array([0, 0]))
+
+    def test_spherical_jn_inf_complex(self):
+        # https://dlmf.nist.gov/10.52.E3
+        n = 7
+        x = np.array([-inf + 0j, inf + 0j, inf*(1+1j)])
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", "invalid value encountered in multiply", RuntimeWarning)
+            assert_allclose(spherical_jn(n, x), np.array([0, 0, inf*(1+1j)]))
+
+    def test_spherical_jn_large_arg_1(self):
+        # https://github.com/scipy/scipy/issues/2165
+        # Reference value computed using mpmath, via
+        # besselj(n + mpf(1)/2, z)*sqrt(pi/(2*z))
+        assert_allclose(spherical_jn(2, 3350.507), -0.00029846226538040747)
+
+    def test_spherical_jn_large_arg_2(self):
+        # https://github.com/scipy/scipy/issues/1641
+        # Reference value computed using mpmath, via
+        # besselj(n + mpf(1)/2, z)*sqrt(pi/(2*z))
+        assert_allclose(spherical_jn(2, 10000), 3.0590002633029811e-05)
+
+    def test_spherical_jn_at_zero(self):
+        # https://dlmf.nist.gov/10.52.E1
+        # But note that n = 0 is a special case: j0 = sin(x)/x -> 1
+        n = np.array([0, 1, 2, 5, 10, 100])
+        x = 0
+        assert_allclose(spherical_jn(n, x), np.array([1, 0, 0, 0, 0, 0]))
+
+
+class TestSphericalYn:
+    def test_spherical_yn_exact(self):
+        # https://dlmf.nist.gov/10.49.E5
+        # Note: exact expression is numerically stable only for small
+        # n or z >> n.
+        x = np.array([0.12, 1.23, 12.34, 123.45, 1234.5])
+        assert_allclose(spherical_yn(2, x),
+                        (1/x - 3/x**3)*cos(x) - 3/x**2*sin(x))
+
+    def test_spherical_yn_recurrence_real(self):
+        # https://dlmf.nist.gov/10.51.E1
+        n = np.array([1, 2, 3, 7, 12])
+        x = 0.12
+        assert_allclose(spherical_yn(n - 1, x) + spherical_yn(n + 1,x),
+                        (2*n + 1)/x*spherical_yn(n, x))
+
+    def test_spherical_yn_recurrence_complex(self):
+        # https://dlmf.nist.gov/10.51.E1
+        n = np.array([1, 2, 3, 7, 12])
+        x = 1.1 + 1.5j
+        assert_allclose(spherical_yn(n - 1, x) + spherical_yn(n + 1, x),
+                        (2*n + 1)/x*spherical_yn(n, x))
+
+    def test_spherical_yn_inf_real(self):
+        # https://dlmf.nist.gov/10.52.E3
+        n = 6
+        x = np.array([-inf, inf])
+        assert_allclose(spherical_yn(n, x), np.array([0, 0]))
+
+    def test_spherical_yn_inf_complex(self):
+        # https://dlmf.nist.gov/10.52.E3
+        n = 7
+        x = np.array([-inf + 0j, inf + 0j, inf*(1+1j)])
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", "invalid value encountered in multiply", RuntimeWarning)
+            assert_allclose(spherical_yn(n, x), np.array([0, 0, inf*(1+1j)]))
+
+    def test_spherical_yn_at_zero(self):
+        # https://dlmf.nist.gov/10.52.E2
+        n = np.array([0, 1, 2, 5, 10, 100])
+        x = 0
+        assert_allclose(spherical_yn(n, x), np.full(n.shape, -inf))
+
+    def test_spherical_yn_at_zero_complex(self):
+        # Consistently with numpy:
+        # >>> -np.cos(0)/0
+        # -inf
+        # >>> -np.cos(0+0j)/(0+0j)
+        # (-inf + nan*j)
+        n = np.array([0, 1, 2, 5, 10, 100])
+        x = 0 + 0j
+        assert_allclose(spherical_yn(n, x), np.full(n.shape, nan))
+
+
+class TestSphericalJnYnCrossProduct:
+    def test_spherical_jn_yn_cross_product_1(self):
+        # https://dlmf.nist.gov/10.50.E3
+        n = np.array([1, 5, 8])
+        x = np.array([0.1, 1, 10])
+        left = (spherical_jn(n + 1, x) * spherical_yn(n, x) -
+                spherical_jn(n, x) * spherical_yn(n + 1, x))
+        right = 1/x**2
+        assert_allclose(left, right)
+
+    def test_spherical_jn_yn_cross_product_2(self):
+        # https://dlmf.nist.gov/10.50.E3
+        n = np.array([1, 5, 8])
+        x = np.array([0.1, 1, 10])
+        left = (spherical_jn(n + 2, x) * spherical_yn(n, x) -
+                spherical_jn(n, x) * spherical_yn(n + 2, x))
+        right = (2*n + 3)/x**3
+        assert_allclose(left, right)
+
+
+class TestSphericalIn:
+    def test_spherical_in_exact(self):
+        # https://dlmf.nist.gov/10.49.E9
+        x = np.array([0.12, 1.23, 12.34, 123.45])
+        assert_allclose(spherical_in(2, x),
+                        (1/x + 3/x**3)*sinh(x) - 3/x**2*cosh(x))
+
+    def test_spherical_in_recurrence_real(self):
+        # https://dlmf.nist.gov/10.51.E4
+        n = np.array([1, 2, 3, 7, 12])
+        x = 0.12
+        assert_allclose(spherical_in(n - 1, x) - spherical_in(n + 1,x),
+                        (2*n + 1)/x*spherical_in(n, x))
+
+    def test_spherical_in_recurrence_complex(self):
+        # https://dlmf.nist.gov/10.51.E1
+        n = np.array([1, 2, 3, 7, 12])
+        x = 1.1 + 1.5j
+        assert_allclose(spherical_in(n - 1, x) - spherical_in(n + 1,x),
+                        (2*n + 1)/x*spherical_in(n, x))
+
+    def test_spherical_in_inf_real(self):
+        # https://dlmf.nist.gov/10.52.E3
+        n = 5
+        x = np.array([-inf, inf])
+        assert_allclose(spherical_in(n, x), np.array([-inf, inf]))
+
+    def test_spherical_in_inf_complex(self):
+        # https://dlmf.nist.gov/10.52.E5
+        # Ideally, i1n(n, 1j*inf) = 0 and i1n(n, (1+1j)*inf) = (1+1j)*inf, but
+        # this appears impossible to achieve because C99 regards any complex
+        # value with at least one infinite  part as a complex infinity, so
+        # 1j*inf cannot be distinguished from (1+1j)*inf.  Therefore, nan is
+        # the correct return value.
+        n = 7
+        x = np.array([-inf + 0j, inf + 0j, inf*(1+1j)])
+        assert_allclose(spherical_in(n, x), np.array([-inf, inf, nan]))
+
+    def test_spherical_in_at_zero(self):
+        # https://dlmf.nist.gov/10.52.E1
+        # But note that n = 0 is a special case: i0 = sinh(x)/x -> 1
+        n = np.array([0, 1, 2, 5, 10, 100])
+        x = 0
+        assert_allclose(spherical_in(n, x), np.array([1, 0, 0, 0, 0, 0]))
+
+
+class TestSphericalKn:
+    def test_spherical_kn_exact(self):
+        # https://dlmf.nist.gov/10.49.E13
+        x = np.array([0.12, 1.23, 12.34, 123.45])
+        assert_allclose(spherical_kn(2, x),
+                        pi/2*exp(-x)*(1/x + 3/x**2 + 3/x**3))
+
+    def test_spherical_kn_recurrence_real(self):
+        # https://dlmf.nist.gov/10.51.E4
+        n = np.array([1, 2, 3, 7, 12])
+        x = 0.12
+        assert_allclose(
+            (-1)**(n - 1)*spherical_kn(n - 1, x) - (-1)**(n + 1)*spherical_kn(n + 1,x),
+            (-1)**n*(2*n + 1)/x*spherical_kn(n, x)
+        )
+
+    def test_spherical_kn_recurrence_complex(self):
+        # https://dlmf.nist.gov/10.51.E4
+        n = np.array([1, 2, 3, 7, 12])
+        x = 1.1 + 1.5j
+        assert_allclose(
+            (-1)**(n - 1)*spherical_kn(n - 1, x) - (-1)**(n + 1)*spherical_kn(n + 1,x),
+            (-1)**n*(2*n + 1)/x*spherical_kn(n, x)
+        )
+
+    def test_spherical_kn_inf_real(self):
+        # https://dlmf.nist.gov/10.52.E6
+        n = 5
+        x = np.array([-inf, inf])
+        assert_allclose(spherical_kn(n, x), np.array([-inf, 0]))
+
+    def test_spherical_kn_inf_complex(self):
+        # https://dlmf.nist.gov/10.52.E6
+        # The behavior at complex infinity depends on the sign of the real
+        # part: if Re(z) >= 0, then the limit is 0; if Re(z) < 0, then it's
+        # z*inf.  This distinction cannot be captured, so we return nan.
+        n = 7
+        x = np.array([-inf + 0j, inf + 0j, inf*(1+1j)])
+        assert_allclose(spherical_kn(n, x), np.array([-inf, 0, nan]))
+
+    def test_spherical_kn_at_zero(self):
+        # https://dlmf.nist.gov/10.52.E2
+        n = np.array([0, 1, 2, 5, 10, 100])
+        x = 0
+        assert_allclose(spherical_kn(n, x), np.full(n.shape, inf))
+
+    def test_spherical_kn_at_zero_complex(self):
+        # https://dlmf.nist.gov/10.52.E2
+        n = np.array([0, 1, 2, 5, 10, 100])
+        x = 0 + 0j
+        assert_allclose(spherical_kn(n, x), np.full(n.shape, nan))
+
+
+class SphericalDerivativesTestCase:
+    def fundamental_theorem(self, n, a, b):
+        integral, tolerance = quad(lambda z: self.df(n, z), a, b)
+        assert_allclose(integral,
+                        self.f(n, b) - self.f(n, a),
+                        atol=tolerance)
+
+    @pytest.mark.slow
+    def test_fundamental_theorem_0(self):
+        self.fundamental_theorem(0, 3.0, 15.0)
+
+    @pytest.mark.slow
+    def test_fundamental_theorem_7(self):
+        self.fundamental_theorem(7, 0.5, 1.2)
+
+
+class TestSphericalJnDerivatives(SphericalDerivativesTestCase):
+    def f(self, n, z):
+        return spherical_jn(n, z)
+
+    def df(self, n, z):
+        return spherical_jn(n, z, derivative=True)
+
+    def test_spherical_jn_d_zero(self):
+        n = np.array([0, 1, 2, 3, 7, 15])
+        assert_allclose(spherical_jn(n, 0, derivative=True),
+                        np.array([0, 1/3, 0, 0, 0, 0]))
+
+
+class TestSphericalYnDerivatives(SphericalDerivativesTestCase):
+    def f(self, n, z):
+        return spherical_yn(n, z)
+
+    def df(self, n, z):
+        return spherical_yn(n, z, derivative=True)
+
+
+class TestSphericalInDerivatives(SphericalDerivativesTestCase):
+    def f(self, n, z):
+        return spherical_in(n, z)
+
+    def df(self, n, z):
+        return spherical_in(n, z, derivative=True)
+
+    def test_spherical_in_d_zero(self):
+        n = np.array([0, 1, 2, 3, 7, 15])
+        spherical_in(n, 0, derivative=False)
+        assert_allclose(spherical_in(n, 0, derivative=True),
+                        np.array([0, 1/3, 0, 0, 0, 0]))
+
+
+class TestSphericalKnDerivatives(SphericalDerivativesTestCase):
+    def f(self, n, z):
+        return spherical_kn(n, z)
+
+    def df(self, n, z):
+        return spherical_kn(n, z, derivative=True)
+
+
+class TestSphericalOld:
+    # These are tests from the TestSpherical class of test_basic.py,
+    # rewritten to use spherical_* instead of sph_* but otherwise unchanged.
+
+    def test_sph_in(self):
+        # This test reproduces test_basic.TestSpherical.test_sph_in.
+        i1n = np.empty((2,2))
+        x = 0.2
+
+        i1n[0][0] = spherical_in(0, x)
+        i1n[0][1] = spherical_in(1, x)
+        i1n[1][0] = spherical_in(0, x, derivative=True)
+        i1n[1][1] = spherical_in(1, x, derivative=True)
+
+        inp0 = (i1n[0][1])
+        inp1 = (i1n[0][0] - 2.0/0.2 * i1n[0][1])
+        assert_allclose(i1n[0], np.array([1.0066800127054699381,
+                                          0.066933714568029540839]),
+                        atol=1.5e-12, rtol=0.0)
+        assert_allclose(i1n[1], [inp0, inp1], atol=1.5e-12, rtol=0)
+
+    def test_sph_in_kn_order0(self):
+        x = 1.
+        sph_i0 = np.empty((2,))
+        sph_i0[0] = spherical_in(0, x)
+        sph_i0[1] = spherical_in(0, x, derivative=True)
+        sph_i0_expected = np.array([np.sinh(x)/x,
+                                    np.cosh(x)/x-np.sinh(x)/x**2])
+        assert_allclose(r_[sph_i0], sph_i0_expected, atol=1.5e-7, rtol=0)
+
+        sph_k0 = np.empty((2,))
+        sph_k0[0] = spherical_kn(0, x)
+        sph_k0[1] = spherical_kn(0, x, derivative=True)
+        sph_k0_expected = np.array([0.5*pi*exp(-x)/x,
+                                    -0.5*pi*exp(-x)*(1/x+1/x**2)])
+        assert_allclose(r_[sph_k0], sph_k0_expected, atol=1.5e-7, rtol=0)
+
+    def test_sph_jn(self):
+        s1 = np.empty((2,3))
+        x = 0.2
+
+        s1[0][0] = spherical_jn(0, x)
+        s1[0][1] = spherical_jn(1, x)
+        s1[0][2] = spherical_jn(2, x)
+        s1[1][0] = spherical_jn(0, x, derivative=True)
+        s1[1][1] = spherical_jn(1, x, derivative=True)
+        s1[1][2] = spherical_jn(2, x, derivative=True)
+
+        s10 = -s1[0][1]
+        s11 = s1[0][0]-2.0/0.2*s1[0][1]
+        s12 = s1[0][1]-3.0/0.2*s1[0][2]
+        assert_allclose(s1[0], [0.99334665397530607731,
+                                0.066400380670322230863,
+                                0.0026590560795273856680],
+                        atol=1.5e-12, rtol=0)
+        assert_allclose(s1[1], [s10, s11, s12], atol=1.5e-12, rtol=0)
+
+    def test_sph_kn(self):
+        kn = np.empty((2,3))
+        x = 0.2
+
+        kn[0][0] = spherical_kn(0, x)
+        kn[0][1] = spherical_kn(1, x)
+        kn[0][2] = spherical_kn(2, x)
+        kn[1][0] = spherical_kn(0, x, derivative=True)
+        kn[1][1] = spherical_kn(1, x, derivative=True)
+        kn[1][2] = spherical_kn(2, x, derivative=True)
+
+        kn0 = -kn[0][1]
+        kn1 = -kn[0][0]-2.0/0.2*kn[0][1]
+        kn2 = -kn[0][1]-3.0/0.2*kn[0][2]
+        assert_allclose(kn[0], [6.4302962978445670140,
+                                38.581777787067402086,
+                                585.15696310385559829],
+                        atol=1.5e-12, rtol=0)
+        assert_allclose(kn[1], [kn0, kn1, kn2], atol=1.5e-9, rtol=0)
+
+    def test_sph_yn(self):
+        sy1 = spherical_yn(2, 0.2)
+        sy2 = spherical_yn(0, 0.2)
+        # previous values in the system
+        assert_allclose(sy1, -377.52483, atol=1.5e-5, rtol=0)
+        assert_allclose(sy2, -4.9003329, atol=1.5e-5, rtol=0)
+        sphpy = (spherical_yn(0, 0.2) - 2*spherical_yn(2, 0.2))/3
+        sy3 = spherical_yn(1, 0.2, derivative=True)
+        # compare correct derivative val. (correct =-system val).
+        assert_allclose(sy3, sphpy, atol=1.5e-4, rtol=0)
+
+
+@pytest.mark.parametrize('derivative', [False, True])
+@pytest.mark.parametrize('fun', [spherical_jn, spherical_in,
+                                 spherical_yn, spherical_kn])
+def test_negative_real_gh14582(derivative, fun):
+    # gh-14582 reported that the spherical Bessel functions did not work
+    # with negative real argument `z`. Check that this is resolved.
+    rng = np.random.default_rng(3598435982345987234)
+    size = 25
+    n = rng.integers(0, 10, size=size)
+    z = rng.standard_normal(size=size)
+    res = fun(n, z, derivative=derivative)
+    ref = fun(n, z+0j, derivative=derivative)
+    assert_allclose(res, ref.real)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_support_alternative_backends.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_support_alternative_backends.py
new file mode 100644
index 0000000000000000000000000000000000000000..34d239e4e8f8a619b59ef79f5ce2e4842e5c41a0
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_support_alternative_backends.py
@@ -0,0 +1,404 @@
+from functools import partial
+import pickle
+
+import pytest
+from hypothesis import given, strategies
+import hypothesis.extra.numpy as npst
+from packaging import version
+
+from scipy import special
+from scipy.special._support_alternative_backends import _special_funcs
+from scipy._lib._array_api_no_0d import xp_assert_close
+from scipy._lib._array_api import (is_cupy, is_dask, is_jax, is_torch,
+                                   make_xp_pytest_param, make_xp_test_case,
+                                   get_native_namespace_name)
+from scipy._external.array_api_compat import numpy as np
+import scipy._external.array_api_extra as xpx
+
+
+# Run all tests in this module in the Array API CI, including those without
+# the xp fixture
+pytestmark = pytest.mark.array_api_backends
+
+lazy_xp_modules = [special]
+
+
+def _skip_or_tweak_alternative_backends(xp, nfo, dtypes, int_only):
+    """Skip tests for specific intersections of scipy.special functions 
+    vs. backends vs. dtypes vs. devices.
+    Also suggest bespoke tweaks.
+
+    Returns
+    -------
+    positive_only : list[bool]
+        Whether you should exclusively test positive inputs.
+    dtypes : list[str]
+        dtype strings 'float64', 'int32', 'int64', etc. with integer types
+        mapped to the type of the NumPy default int.
+    """
+    f_name = nfo.name
+    if isinstance(nfo.positive_only, dict):
+        positive_only = nfo.positive_only.get(get_native_namespace_name(xp), False)
+    else:
+        positive_only = nfo.positive_only
+    if isinstance(positive_only, bool):
+        positive_only = [positive_only]*nfo.n_args
+
+    dtypes = [np.intp.__name__ if dtype == "intp" else dtype for dtype in dtypes]
+
+    if f_name in {'betaincinv'} and is_cupy(xp):
+        pytest.xfail("CuPy uses different convention for out of domain input.")
+
+    if not any('int' in dtype for dtype in dtypes):
+        return positive_only, dtypes
+
+    # Integer-specific issues from this point onwards
+
+    if f_name in {'gamma', 'gammasgn'} and is_cupy(xp):
+        # CuPy has not yet updated gamma pole behavior to match
+        # https://github.com/scipy/scipy/pull/21827.
+        positive_only = [True]
+
+    if f_name in {'poch'} and is_jax(xp):
+        # Jax uses a different convention at gamma poles.
+        positive_only = [True, True]
+
+    if f_name == 'multigammaln':
+        pytest.skip("multigammaln raises for out of domain inputs.")
+
+    if ((is_torch(xp) and f_name in {'gammainc', 'gammaincc'})
+        or (is_cupy(xp) and f_name in {'stdtr', 'i0e', 'i1e'})
+        or (is_jax(xp) and f_name in {'stdtr', 'ndtr', 'ndtri', 'log_ndtr', 'hyp1f1',
+                                      'hyp2f1', 'spence', 'kl_div'})
+    ):
+        pytest.skip(f"`{f_name}` does not support integer types")
+
+    # int/float mismatched args support is sketchy
+    if (any('float' in dtype for dtype in dtypes)
+        and ((is_torch(xp) and f_name in ('rel_entr', 'xlogy', 'polygamma',
+                                          'zeta', 'xlog1py'))
+             or (is_jax(xp) and f_name in ('gammainc', 'gammaincc', 'expn',
+                                           'rel_entr', 'xlogy', 'betaln',
+                                           'polygamma', 'zeta', 'poch',
+                                           'xlog1py')))
+    ):
+        pytest.xfail("dtypes do not match")
+
+    if (is_torch(xp) and xpx.default_dtype(xp) == xp.float32):
+        # On PyTorch with float32 default dtype, all ints are promoted
+        # to float32, but when falling back to NumPy/SciPy int64 is promoted
+        # instead to float64. Integer only parameters essentially do not
+        # participate in determination of the result type in PyTorch with
+        # float32 default dtype, but will impact the output dtype as if
+        # they were float64 when falling back to NumPy/SciPy.
+        if not nfo.torch_native:
+            pytest.xfail("dtypes do not match")
+
+    return positive_only, dtypes
+
+
+@pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning:dask")
+@pytest.mark.filterwarnings("ignore:overflow encountered:RuntimeWarning")
+@pytest.mark.parametrize('shapes', [[(0,)]*4, [tuple()]*4, [(10,)]*4,
+                                    [(10,), (11, 1), (12, 1, 1), (13, 1, 1, 1)]])
+@pytest.mark.parametrize('base_dtype', ['float32', 'float64', 'intp'])
+@pytest.mark.parametrize(
+    'func,nfo', [make_xp_pytest_param(i.wrapper, i) for i in _special_funcs])
+def test_support_alternative_backends(xp, func, nfo, base_dtype, shapes):
+    int_only = nfo.int_only
+    if int_only is None:
+        int_only = (False, ) * nfo.n_args
+        dtypes = (base_dtype, ) * nfo.n_args
+    else:
+        dtypes = tuple(
+            'intp' if needs_int else base_dtype for needs_int in int_only
+        )
+
+    positive_only, dtypes = _skip_or_tweak_alternative_backends(
+        xp, nfo, dtypes, int_only
+    )
+
+    dtypes_np = [getattr(np, dtype) for dtype in dtypes]
+    dtypes_xp = [getattr(xp, dtype) for dtype in dtypes]
+
+    shapes = shapes[:nfo.n_args]
+    rng = np.random.default_rng(984254252920492019)
+    args_np = []
+
+    # Handle cases where there's an argument which only takes scalar values.
+    python_int_only = nfo.python_int_only
+    if isinstance(python_int_only, dict):
+        python_int_only = python_int_only.get(get_native_namespace_name(xp))
+    scalar_or_0d_only = nfo.scalar_or_0d_only
+    if isinstance(scalar_or_0d_only, dict):
+        scalar_or_0d_only = scalar_or_0d_only.get(get_native_namespace_name(xp))
+
+    test_large_ints = nfo.test_large_ints
+    if isinstance(nfo.test_large_ints, dict):
+        test_large_ints = test_large_ints.get(get_native_namespace_name(xp), False)
+
+    if python_int_only is None:
+        python_int_only = [False] * nfo.n_args
+    if scalar_or_0d_only is None:
+        scalar_or_0d_only = [False] * nfo.n_args
+
+    no_shape = [
+        cond1 or cond2 for cond1, cond2 in zip(python_int_only, scalar_or_0d_only)
+    ]
+
+    shapes = [shape if not cond else None for shape, cond in zip(shapes, no_shape)]
+
+    for dtype, dtype_np, shape, needs_python_int in zip(
+            dtypes, dtypes_np, shapes, python_int_only
+    ):
+        if 'int' in dtype and test_large_ints:
+            iinfo = np.iinfo(dtype_np)
+            rand = partial(rng.integers, iinfo.min, iinfo.max + 1)
+        elif 'int' in dtype:
+            rand = partial(rng.integers, -20, 21)
+        else:
+            rand = rng.standard_normal
+        val = rand(size=shape, dtype=dtype_np)
+        if needs_python_int:
+            # The logic above for determining shapes guarantees that
+            # shape will be None in the above line when a Python int is required,
+            # so this can safely be converted to an int.
+            val = int(val)
+        args_np.append(val)
+
+    args_np = [
+        np.abs(arg) if cond else arg for arg, cond in zip(args_np, positive_only)
+    ]
+
+    args_xp = [
+        xp.asarray(arg, dtype=dtype_xp) if not needs_python_int
+        else arg
+        for arg, dtype_xp, needs_python_int
+        in zip(args_np, dtypes_xp, python_int_only)
+    ]
+
+    args_np = [
+        np.asarray(arg, dtype=dtype_np) if not needs_python_int
+        else arg
+        for arg, dtype_np, needs_python_int
+        in zip(args_np, dtypes_np, python_int_only)
+    ]
+
+    if is_dask(xp):
+        # We're using map_blocks to dispatch the function to Dask.
+        # This is the correct thing to do IF all tested functions are elementwise;
+        # otherwise the output would change depending on chunking.
+        # Try to trigger bugs related to having multiple chunks.
+        args_xp = [arg.rechunk(5) for arg in args_xp]
+
+    res = nfo.wrapper(*args_xp)  # Also wrapped by lazy_xp_function
+    ref = nfo.func(*args_np)  # Unwrapped ufunc
+    if (
+            is_torch(xp)
+            and xpx.default_dtype(xp) == xp.float32
+            and "float64" not in dtypes
+    ):
+        # int64 promotes like float32 on torch with default dtype = float32
+        # cast reference if needed
+        ref = np.float32(ref)
+    # When dtype_np is integer, the output dtype can be float
+    atol = 0 if ref.dtype.kind in 'iu' else 10 * np.finfo(ref.dtype).eps
+    rtol = None
+    if is_torch(xp) and func.__name__ == 'j1':
+        # If we end up needing more function/backend specific tolerance
+        # adjustments, this should be factored out properly.
+        atol = 1e-7
+        rtol = 1e-5
+    xp_assert_close(
+        res, xp.asarray(ref), rtol=rtol, atol=atol, check_0d=nfo.produces_0d
+    )
+
+
+@pytest.mark.parametrize(
+    'func, nfo',
+    [make_xp_pytest_param(i.wrapper, i) for i in _special_funcs if i.n_args >= 2])
+@pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning:dask")
+def test_support_alternative_backends_mismatched_dtypes(xp, func, nfo):
+    """Test mix-n-match of int and float arguments"""
+    if func.__name__ in {'expn', 'polygamma', 'multigammaln', 'bdtr', 'bdtrc', 'bdtri',
+                         'nbdtr', 'nbdtrc', 'nbdtri', 'pdtri'}:
+        pytest.skip(f"dtypes for {func.__name__} make it a bad fit for this test.")
+    dtypes = ['intp', 'float32', 'float64', 'float64'][:nfo.n_args]
+
+    positive_only, dtypes = _skip_or_tweak_alternative_backends(
+        xp, nfo, dtypes, (False,)*nfo.n_args
+    )
+    dtypes_np = [getattr(np, dtype) for dtype in dtypes]
+    dtypes_xp = [getattr(xp, dtype) for dtype in dtypes]
+
+    rng = np.random.default_rng(984254252920492019)
+    iinfo = np.iinfo(np.intp)
+    if nfo.test_large_ints:
+        randint = partial(rng.integers, iinfo.min, iinfo.max + 1)
+    else:
+        randint = partial(rng.integers, -20, 21)
+    args_np = [
+        randint(size=1, dtype=np.int64),
+        rng.standard_normal(size=1, dtype=np.float32),
+        rng.standard_normal(size=1, dtype=np.float64),
+        rng.standard_normal(size=1, dtype=np.float64),
+    ][:nfo.n_args]
+    args_np = [
+        np.abs(arg) if cond else arg for arg, cond in zip(args_np, positive_only)
+    ]
+
+    args_xp = [xp.asarray(arg, dtype=dtype_xp)
+               for arg, dtype_xp in zip(args_np, dtypes_xp)]
+    args_np = [np.asarray(arg, dtype=dtype_np)
+               for arg, dtype_np in zip(args_np, dtypes_np)]
+
+    res = nfo.wrapper(*args_xp)  # Also wrapped by lazy_xp_function
+    ref = nfo.func(*args_np)  # Unwrapped ufunc
+    if (
+            is_torch(xp)
+            and xpx.default_dtype(xp) == xp.float32
+            and "float64" not in dtypes
+    ):
+        # int64 promotes like float32 on torch with default dtype = float32
+        # cast reference if needed
+        ref = np.float32(ref)
+
+    atol = 10 * np.finfo(ref.dtype).eps
+    xp_assert_close(res, xp.asarray(ref), atol=atol)
+
+
+@pytest.mark.xslow
+@given(data=strategies.data())
+@pytest.mark.fail_slow(5)
+@pytest.mark.parametrize(
+    'func,nfo', [make_xp_pytest_param(nfo.wrapper, nfo) for nfo in _special_funcs])
+@pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning:dask")
+@pytest.mark.filterwarnings("ignore:divide by zero encountered:RuntimeWarning:dask")
+@pytest.mark.filterwarnings("ignore:overflow encountered:RuntimeWarning:dask")
+@pytest.mark.filterwarnings(
+    "ignore:overflow encountered:RuntimeWarning:array_api_strict"
+)
+def test_support_alternative_backends_hypothesis(xp, func, nfo, data):
+    if func.__name__ in {'expn', 'polygamma', 'multigammaln', 'bdtr', 'bdtrc', 'bdtri',
+                         'nbdtr', 'nbdtrc', 'nbdtri', 'pdtri'}:
+        pytest.skip(f"dtypes for {func.__name__} make it a bad fit for this test.")
+    dtype = data.draw(strategies.sampled_from(['float32', 'float64', 'intp']))
+    positive_only, dtypes = _skip_or_tweak_alternative_backends(
+        xp, nfo, [dtype], (False,)*nfo.n_args
+    )
+    dtype_np = getattr(np, dtypes[0])
+    dtype_xp = getattr(xp, dtypes[0])
+
+    elements = {'allow_subnormal': False}
+    # Most failures are due to NaN or infinity; uncomment to suppress them
+    # elements['allow_infinity'] = False
+    # elements['allow_nan'] = False
+    if any(positive_only):
+        elements['min_value'] = 0
+
+    shapes, _ = data.draw(
+        npst.mutually_broadcastable_shapes(num_shapes=nfo.n_args))
+    args_np = [data.draw(npst.arrays(dtype_np, shape, elements=elements))
+               for shape in shapes]
+
+    args_xp = [xp.asarray(arg, dtype=dtype_xp) for arg in args_np]
+    args_np = [np.asarray(arg, dtype=dtype_np) for arg in args_np]
+
+    res = nfo.wrapper(*args_xp)  # Also wrapped by lazy_xp_function
+    ref = nfo.func(*args_np)  # Unwrapped ufunc
+    if (
+            is_torch(xp)
+            and xpx.default_dtype(xp) == xp.float32
+            and dtype != "float64"
+    ):
+        # int64 promotes like float32 on torch with default dtype = float32
+        # cast reference if needed
+        ref = np.float32(ref)
+
+    # When dtype_np is integer, the output dtype can be float
+    atol = 0 if ref.dtype.kind in 'iu' else 10 * np.finfo(ref.dtype).eps
+    xp_assert_close(res, xp.asarray(ref), atol=atol)
+
+
+@pytest.mark.filterwarnings("ignore:numpy.core is deprecated:DeprecationWarning")
+@pytest.mark.parametrize("func", [nfo.wrapper for nfo in _special_funcs])
+def test_pickle(func):
+    roundtrip = pickle.loads(pickle.dumps(func))
+    assert roundtrip is func
+
+
+@pytest.mark.parametrize("func", [nfo.wrapper for nfo in _special_funcs])
+def test_repr(func):
+    assert func.__name__ in repr(func)
+    assert "locals" not in repr(func)
+
+
+@pytest.mark.skipif(
+    version.parse(np.__version__) < version.parse("2.2"),  # type:ignore[attr-defined]
+    reason="Can't update ufunc __doc__ when SciPy is compiled vs. NumPy < 2.2")
+@pytest.mark.parametrize('func', [nfo.wrapper for nfo in _special_funcs])
+def test_doc(func):
+    """xp_capabilities updates the docstring in place. 
+    Make sure it does so exactly once, including when SCIPY_ARRAY_API is not set.
+    """
+    match = "has experimental support for Python Array API"
+    assert func.__doc__.count(match) == 1
+
+
+@pytest.mark.parametrize(
+    'func,n_args,int_only,is_ufunc',
+    [(nfo.wrapper, nfo.n_args, nfo.int_only, nfo.is_ufunc)
+     for nfo in _special_funcs]
+)
+def test_ufunc_kwargs(func, n_args, int_only, is_ufunc):
+    """Test that numpy-specific out= and dtype= keyword arguments
+    of ufuncs still work when SCIPY_ARRAY_API is set.
+    """
+    if not is_ufunc:
+        pytest.skip(f"{func.__name__} is not a ufunc.")
+    if int_only is None:
+        int_only = (False, ) * n_args
+    # out=
+    args = [
+        np.asarray([.1, .2]) if not needs_int
+        else np.asarray([1, 2])
+        for needs_int in int_only
+    ]
+    out = np.empty(2)
+    y = func(*args, out=out)
+    xp_assert_close(y, out)
+
+    # out= with out.dtype != args.dtype
+    out = np.empty(2, dtype=np.float32)
+    y = func(*args, out=out)
+    xp_assert_close(y, out)
+
+    if func.__name__ in {"bdtr", "bdtrc", "bdtri"}:
+        # The below function evaluation will trigger a deprecation warning
+        # with dtype=np.float32. This will go away if the trigger is actually
+        # pulled on the deprecation.
+        return
+
+    # dtype=
+    y = func(*args, dtype=np.float32)
+    assert y.dtype == np.float32
+
+
+@make_xp_test_case(special.chdtr)
+def test_chdtr_gh21311(xp):
+    # the edge case behavior of generic chdtr was not right; see gh-21311
+    # be sure to test at least these cases
+    # should add `np.nan` into the mix when gh-21317 is resolved
+    x = np.asarray([-np.inf, -1., 0., 1., np.inf])
+    v = x.reshape(-1, 1)
+    ref = special.chdtr(v, x)
+    res = special.chdtr(xp.asarray(v), xp.asarray(x))
+    xp_assert_close(res, xp.asarray(ref))
+
+
+@make_xp_test_case(special.fdtrc)
+def test_mixed_arrays_and_python_scalars(xp):
+    # Tests that the delegation infrastructure respects NEP50.
+    res = special.fdtrc(1.1, 2., xp.asarray(1., dtype=xp.float32))
+    ref = xp.asarray(0.4349004, dtype=xp.float32)
+    xp_assert_close(res, ref)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_trig.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_trig.py
new file mode 100644
index 0000000000000000000000000000000000000000..e5f8f79f8d2cac51bf9476f04f13df2bfac587a5
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_trig.py
@@ -0,0 +1,76 @@
+import warnings
+
+import pytest
+import numpy as np
+from numpy.testing import assert_equal, assert_allclose
+
+from scipy.special._ufuncs import _sinpi as sinpi
+from scipy.special._ufuncs import _cospi as cospi
+
+
+def test_integer_real_part():
+    x = np.arange(-100, 101)
+    y = np.hstack((-np.linspace(310, -30, 10), np.linspace(-30, 310, 10)))
+    x, y = np.meshgrid(x, y)
+    z = x + 1j*y
+    # In the following we should be *exactly* right
+    res = sinpi(z)
+    assert_equal(res.real, 0.0)
+    res = cospi(z)
+    assert_equal(res.imag, 0.0)
+
+
+def test_half_integer_real_part():
+    x = np.arange(-100, 101) + 0.5
+    y = np.hstack((-np.linspace(310, -30, 10), np.linspace(-30, 310, 10)))
+    x, y = np.meshgrid(x, y)
+    z = x + 1j*y
+    # In the following we should be *exactly* right
+    res = sinpi(z)
+    assert_equal(res.imag, 0.0)
+    res = cospi(z)
+    assert_equal(res.real, 0.0)
+
+
+@pytest.mark.skip("Temporary skip while gh-19526 is being resolved")
+def test_intermediate_overlow():
+    # Make sure we avoid overflow in situations where cosh/sinh would
+    # overflow but the product with sin/cos would not
+    sinpi_pts = [complex(1 + 1e-14, 227),
+                 complex(1e-35, 250),
+                 complex(1e-301, 445)]
+    # Data generated with mpmath
+    sinpi_std = [complex(-8.113438309924894e+295, -np.inf),
+                 complex(1.9507801934611995e+306, np.inf),
+                 complex(2.205958493464539e+306, np.inf)]
+    with warnings.catch_warnings():
+        warnings.filterwarnings(
+            "ignore", "invalid value encountered in multiply", RuntimeWarning)
+        for p, std in zip(sinpi_pts, sinpi_std):
+            res = sinpi(p)
+            assert_allclose(res.real, std.real)
+            assert_allclose(res.imag, std.imag)
+
+    # Test for cosine, less interesting because cos(0) = 1.
+    p = complex(0.5 + 1e-14, 227)
+    std = complex(-8.113438309924894e+295, -np.inf)
+    with warnings.catch_warnings():
+        warnings.filterwarnings(
+            "ignore", "invalid value encountered in multiply", RuntimeWarning)
+        res = cospi(p)
+        assert_allclose(res.real, std.real)
+        assert_allclose(res.imag, std.imag)
+
+
+def test_zero_sign():
+    y = sinpi(-0.0)
+    assert y == 0.0
+    assert np.signbit(y)
+
+    y = sinpi(0.0)
+    assert y == 0.0
+    assert not np.signbit(y)
+
+    y = cospi(0.5)
+    assert y == 0.0
+    assert not np.signbit(y)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_ufunc_infra.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_ufunc_infra.py
new file mode 100644
index 0000000000000000000000000000000000000000..30b08cde365de9c115935d1100001f8ba1349276
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_ufunc_infra.py
@@ -0,0 +1,34 @@
+import numpy as np
+import pytest
+
+from scipy.special import mathieu_sem
+# from scipy.special._ufuncs import _mathieu_sem
+
+
+@pytest.mark.parametrize("m_shape,q_shape,x_shape,where_shape", [
+    ((5, 1), (1, 1), (1, 10), ()),
+    ((2, 3), (2, 3), (2, 3), ()),
+    ((1, 5), (1, 5), (10, 5), ()),
+    ((5, 1), (1, 1), (1, 10), (1, 10)),
+    ((2, 3), (2, 3), (2, 3), (2, 3)),
+    ((1, 5), (1, 5), (10, 5), (10, 5)),
+    ((5, 1), (1, 1), (1, 10), (5, 1)),
+])
+def test_out(m_shape, q_shape, x_shape, where_shape):
+    rng = np.random.default_rng(1234)
+
+    m = rng.integers(1, 20, m_shape)
+    q = rng.uniform(0, 10, q_shape)
+    x = rng.uniform(0, 90, x_shape)
+
+    if where_shape == ():
+        batch_shape = np.broadcast_shapes(m_shape, q_shape, x_shape)
+        where = True
+    else:
+        where = rng.choice([True, False], size=where_shape)
+        batch_shape = np.broadcast_shapes(m_shape, q_shape, x_shape, where_shape)
+
+    out0 = np.empty(batch_shape)
+    out1 = np.empty(batch_shape)
+    res0, res1 = mathieu_sem(m, q, x, out=(out0, out1), where=where)
+    assert res0 is out0 and res1 is out1
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_ufunc_signatures.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_ufunc_signatures.py
new file mode 100644
index 0000000000000000000000000000000000000000..e4fdb02a855797923a792dfce7747a10f6b407db
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_ufunc_signatures.py
@@ -0,0 +1,119 @@
+"""Test that all ufuncs have float32-preserving signatures.
+
+This was once guaranteed through the code generation script for
+generating ufuncs, `scipy/special/_generate_pyx.py`. Starting with
+gh-20260, SciPy developers have begun moving to generate ufuncs
+through direct use of the NumPy C API (through C++). Existence of
+float32 preserving signatures must now be tested since it is no
+longer guaranteed.
+"""
+
+import numpy as np
+import pytest
+import scipy.special._ufuncs
+import scipy.special._gufuncs
+import scipy.special as special
+
+from numpy.testing import assert_equal
+
+
+# Single precision is not implemented for these ufuncs;
+# floating point inputs must be float64.
+exceptions = ['_gen_harmonic', '_normalized_gen_harmonic']
+
+_ufuncs = []
+for funcname in dir(scipy.special._ufuncs):
+    if funcname not in exceptions:
+        _ufuncs.append(getattr(scipy.special._ufuncs, funcname))
+for funcname in dir(scipy.special._gufuncs):
+    _ufuncs.append(getattr(scipy.special._gufuncs, funcname))
+
+# Not all module members are actually ufuncs
+_ufuncs = [func for func in _ufuncs if isinstance(func, np.ufunc)]
+
+@pytest.mark.parametrize("ufunc", _ufuncs)
+def test_ufunc_signatures(ufunc):
+
+    # From _generate_pyx.py
+    # "Don't add float32 versions of ufuncs with integer arguments, as this
+    # can lead to incorrect dtype selection if the integer arguments are
+    # arrays, but float arguments are scalars.
+    # This may be a NumPy bug, but we need to work around it.
+    # cf. gh-4895, https://github.com/numpy/numpy/issues/5895"
+    types = set(sig for sig in ufunc.types
+                if not ("l" in sig or "i" in sig or "q" in sig or "p" in sig))
+
+    # Generate the full expanded set of signatures which should exist. There
+    # should be matching float and double versions of any existing signature.
+    expanded_types = set()
+    for sig in types:
+        expanded_types.update(
+            [sig.replace("d", "f").replace("D", "F"),
+             sig.replace("f", "d").replace("F", "D")]
+        )
+    assert types == expanded_types
+
+
+def _get_nan_val(typecode):
+    return {
+        "f": np.asarray(np.nan, dtype=np.float32),
+        "d": np.asarray(np.nan, dtype=np.float64),
+        "g": np.asarray(np.nan, dtype=np.longdouble),
+        "F": np.asarray(np.nan + np.nan*1j, dtype=np.complex64),
+        "D": np.asarray(np.nan + np.nan*1j, dtype=np.complex128),
+        "G": np.asarray(np.nan + np.nan*1j, dtype=np.clongdouble),
+    }[typecode]
+
+skips = {
+    # These hit https://github.com/scipy/xsf/issues/94
+    "eval_chebyc",
+    "eval_chebys",
+    "eval_chebyt",
+    "eval_chebyu",
+    "eval_gegenbauer",
+    "eval_genlaguerre",
+    "eval_jacobi",
+    "eval_laguerre",
+    "eval_legendre",
+    "eval_sh_chebyt",
+    "eval_sh_chebyu",
+    "eval_sh_jacobi",
+    "eval_sh_legendre",
+    "hyp1f1",
+    "hyp2f1",
+    # warns if called with noninteger values of some args
+    "bdtr",
+    "bdtrc",
+    "bdtri",
+}
+_multi_arg_public_ufuncs = [
+    ufunc for ufunc in _ufuncs if ufunc.nargs - ufunc.nout > 1
+    and ufunc.__name__ not in skips and ufunc.__name__ in special.__all__
+]
+
+
+@pytest.mark.parametrize("ufunc", _multi_arg_public_ufuncs)
+def test_nep50(ufunc):
+    # Test that functions with multiple arguments respect nep50 promotion rules.
+    rng = np.random.default_rng(1234)
+    # As in test_ufunc_signatures, filter out signatures involving integers.
+    types = set(sig for sig in ufunc.types
+                if not ("l" in sig or "i" in sig or "q" in sig or "p" in sig))
+    for sig in types:
+        input_types, output_types = sig.split("->")
+        # since we only care about dtypes and not values here, just use an appropriately
+        # typed nan for each argument.
+        args = [_get_nan_val(typecode) for typecode in input_types]
+        # swap out a random one of the nans with an appropriately typed numpy scalar.
+        idx = rng.choice(len(args))
+        args[idx] = float("nan") if np.isrealobj(args[idx]) else complex("nan")
+        result = ufunc(*args)
+        result = [result] if len(output_types) == 1 else result
+        result = np.asarray(result)
+        
+        # Test that the output is an appropriately typed nan. This also implicitly
+        # tests that ufuncs propagate nans correctly.
+        assert_equal(
+            result, np.asarray([_get_nan_val(typecode) for typecode in output_types]),
+            strict=True
+        )
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_wright_bessel.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_wright_bessel.py
new file mode 100644
index 0000000000000000000000000000000000000000..ef30163f55c90850fe32ca600eb47547e4fa5e03
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_wright_bessel.py
@@ -0,0 +1,205 @@
+# Reference MPMATH implementation:
+#
+# import mpmath
+# from mpmath import nsum
+#
+# def Wright_Series_MPMATH(a, b, z, dps=50, method='r+s+e', steps=[1000]):
+#    """Compute Wright' generalized Bessel function as Series.
+#
+#    This uses mpmath for arbitrary precision.
+#    """
+#    with mpmath.workdps(dps):
+#        res = nsum(lambda k: z**k/mpmath.fac(k) * mpmath.rgamma(a*k+b),
+#                          [0, mpmath.inf],
+#                          tol=dps, method=method, steps=steps
+#                          )
+#
+#    return res
+
+from itertools import product
+
+import pytest
+import numpy as np
+from numpy.testing import assert_equal, assert_allclose
+
+import scipy.special as sc
+from scipy.special import log_wright_bessel, loggamma, rgamma, wright_bessel
+
+
+@pytest.mark.parametrize('a', [0, 1e-6, 0.1, 0.5, 1, 10])
+@pytest.mark.parametrize('b', [0, 1e-6, 0.1, 0.5, 1, 10])
+def test_wright_bessel_zero(a, b):
+    """Test at x = 0."""
+    assert_equal(wright_bessel(a, b, 0.), rgamma(b))
+    assert_allclose(log_wright_bessel(a, b, 0.), -loggamma(b))
+
+
+@pytest.mark.parametrize('b', [0, 1e-6, 0.1, 0.5, 1, 10])
+@pytest.mark.parametrize('x', [0, 1e-6, 0.1, 0.5, 1])
+def test_wright_bessel_iv(b, x):
+    """Test relation of wright_bessel and modified bessel function iv.
+
+    iv(z) = (1/2*z)**v * Phi(1, v+1; 1/4*z**2).
+    See https://dlmf.nist.gov/10.46.E2
+    """
+    if x != 0:
+        v = b - 1
+        wb = wright_bessel(1, v + 1, x**2 / 4.)
+        # Note: iv(v, x) has precision of less than 1e-12 for some cases
+        # e.g v=1-1e-6 and x=1e-06)
+        assert_allclose(np.power(x / 2., v) * wb,
+                        sc.iv(v, x),
+                        rtol=1e-11, atol=1e-11)
+
+
+@pytest.mark.parametrize('a', [0, 1e-6, 0.1, 0.5, 1, 10])
+@pytest.mark.parametrize('b', [1, 1 + 1e-3, 2, 5, 10])
+@pytest.mark.parametrize('x', [0, 1e-6, 0.1, 0.5, 1, 5, 10, 100])
+def test_wright_functional(a, b, x):
+    """Test functional relation of wright_bessel.
+
+    Phi(a, b-1, z) = a*z*Phi(a, b+a, z) + (b-1)*Phi(a, b, z)
+
+    Note that d/dx Phi(a, b, x) = Phi(a, b-1, x)
+    See Eq. (22) of
+    B. Stankovic, On the Function of E. M. Wright,
+    Publ. de l' Institut Mathematique, Beograd,
+    Nouvelle S`er. 10 (1970), 113-124.
+    """
+    assert_allclose(wright_bessel(a, b - 1, x),
+                    a * x * wright_bessel(a, b + a, x)
+                    + (b - 1) * wright_bessel(a, b, x),
+                    rtol=1e-8, atol=1e-8)
+
+
+# grid of rows [a, b, x, value, accuracy] that do not reach 1e-11 accuracy
+# see output of:
+# cd scipy/scipy/_precompute
+# python wright_bessel_data.py
+grid_a_b_x_value_acc = np.array([
+    [0.1, 100.0, 709.7827128933841, 8.026353022981087e+34, 2e-8],
+    [0.5, 10.0, 709.7827128933841, 2.680788404494657e+48, 9e-8],
+    [0.5, 10.0, 1000.0, 2.005901980702872e+64, 1e-8],
+    [0.5, 100.0, 1000.0, 3.4112367580445246e-117, 6e-8],
+    [1.0, 20.0, 100000.0, 1.7717158630699857e+225, 3e-11],
+    [1.0, 100.0, 100000.0, 1.0269334596230763e+22, np.nan],
+    [1.0000000000000222, 20.0, 100000.0, 1.7717158630001672e+225, 3e-11],
+    [1.0000000000000222, 100.0, 100000.0, 1.0269334595866202e+22, np.nan],
+    [1.5, 0.0, 500.0, 15648961196.432373, 3e-11],
+    [1.5, 2.220446049250313e-14, 500.0, 15648961196.431465, 3e-11],
+    [1.5, 1e-10, 500.0, 15648961192.344728, 3e-11],
+    [1.5, 1e-05, 500.0, 15648552437.334162, 3e-11],
+    [1.5, 0.1, 500.0, 12049870581.10317, 2e-11],
+    [1.5, 20.0, 100000.0, 7.81930438331405e+43, 3e-9],
+    [1.5, 100.0, 100000.0, 9.653370857459075e-130, np.nan],
+    ])
+
+
+@pytest.mark.xfail
+@pytest.mark.parametrize(
+    'a, b, x, phi',
+    grid_a_b_x_value_acc[:, :4].tolist())
+def test_wright_data_grid_failures(a, b, x, phi):
+    """Test cases of test_data that do not reach relative accuracy of 1e-11"""
+    assert_allclose(wright_bessel(a, b, x), phi, rtol=1e-11)
+
+
+@pytest.mark.parametrize(
+    'a, b, x, phi, accuracy',
+    grid_a_b_x_value_acc.tolist())
+def test_wright_data_grid_less_accurate(a, b, x, phi, accuracy):
+    """Test cases of test_data that do not reach relative accuracy of 1e-11
+
+    Here we test for reduced accuracy or even nan.
+    """
+    if np.isnan(accuracy):
+        assert np.isnan(wright_bessel(a, b, x))
+    else:
+        assert_allclose(wright_bessel(a, b, x), phi, rtol=accuracy)
+
+
+@pytest.mark.parametrize(
+    'a, b, x',
+    list(
+        product([0, 0.1, 0.5, 1.5, 5, 10], [1, 2], [1e-3, 1, 1.5, 5, 10])
+    )
+)
+def test_log_wright_bessel_same_as_wright_bessel(a, b, x):
+    """Test that log_wright_bessel equals log of wright_bessel."""
+    assert_allclose(
+        log_wright_bessel(a, b, x),
+        np.log(wright_bessel(a, b, x)),
+        rtol=1e-8,
+    )
+
+
+# Computed with, see also mp_wright_bessel from wright_bessel_data.py:
+#
+# from functools import lru_cache
+# import mpmath as mp
+#
+# @lru_cache(maxsize=1_000_000)
+# def rgamma_cached(x, dps):
+#     with mp.workdps(dps):
+#         return mp.rgamma(x)
+#
+# def mp_log_wright_bessel(a, b, x, dps=100, maxterms=10_000, method="d"):
+#     """Compute log of Wright's generalized Bessel function as Series with mpmath."""
+#     with mp.workdps(dps):
+#         a, b, x = mp.mpf(a), mp.mpf(b), mp.mpf(x)
+#         res = mp.nsum(lambda k: x**k / mp.fac(k)
+#                       * rgamma_cached(a * k + b, dps=dps),
+#                       [0, mp.inf],
+#                       tol=dps, method=method, steps=[maxterms]
+#                       )
+#         return mp.log(res)
+#
+# Sometimes, one needs to set maxterms as high as 1_00_000 to get accurate results for
+# phi.
+# At the end of the day, we can only hope that results are correct for very large x,
+# e.g. by the asymptotic series, as there is no way to produce those in "exact"
+# arithmetic.
+# Note: accuracy = np.nan means log_wright_bessel returns nan.
+@pytest.mark.parametrize(
+    'a, b, x, phi, accuracy',
+    [
+        (0, 0, 0, -np.inf, 1e-11),
+        (0, 0, 1, -np.inf, 1e-11),
+        (0, 1, 1.23, 1.23, 1e-11),
+        (0, 1, 1e50, 1e50, 1e-11),
+        (1e-5, 0, 700, 695.0421608273609, 1e-11),
+        (1e-5, 0, 1e3, 995.40052566540066, 1e-11),
+        (1e-5, 100, 1e3, 640.8197935670078, 1e-11),
+        (1e-3, 0, 1e4, 9987.2229532297262, 1e-11),
+        (1e-3, 0, 1e5, 99641.920687169507, 1e-11),
+        (1e-3, 0, 1e6, 994118.55560054416, 1e-11),  # maxterms=1_000_000
+        (1e-3, 10, 1e5, 99595.47710802537, 1e-11),
+        (1e-3, 50, 1e5, 99401.240922855647, 1e-3),
+        (1e-3, 100, 1e5, 99143.465191656527, np.nan),
+        (0.5, 0, 1e5, 4074.1112442197941, 1e-11),
+        (0.5, 0, 1e7, 87724.552120038896, 1e-11),
+        (0.5, 100, 1e5, 3350.3928746306163, np.nan),
+        (0.5, 100, 1e7, 86696.109975301719, 1e-11),
+        (1, 0, 1e5, 634.06765787997266, 1e-11),
+        (1, 0, 1e8, 20003.339639312035, 1e-11),
+        (1.5, 0, 1e5, 197.01777556071194, 1e-11),
+        (1.5, 0, 1e8, 3108.987414395706, 1e-11),
+        (1.5, 100, 1e8, 2354.8915946283275, np.nan),
+        (5, 0, 1e5, 9.8980480013203547, 1e-11),
+        (5, 0, 1e8, 33.642337258687465, 1e-11),
+        (5, 0, 1e12, 157.53704288117429, 1e-11),
+        (5, 100, 1e5, -359.13419630792148, 1e-11),
+        (5, 100, 1e12, -337.07722086995229, 1e-4),
+        (5, 100, 1e20, 2588.2471229986845, 2e-6),
+        (100, 0, 1e5, -347.62127990460517, 1e-11),
+        (100, 0, 1e20, -313.08250350969449, 1e-11),
+        (100, 100, 1e5, -359.1342053695754, 1e-11),
+        (100, 100, 1e20, -359.1342053695754, 1e-11),
+    ]
+)
+def test_log_wright_bessel(a, b, x, phi, accuracy):
+    """Test for log_wright_bessel, in particular for large x."""
+    if np.isnan(accuracy):
+        assert np.isnan(log_wright_bessel(a, b, x))
+    else:
+        assert_allclose(log_wright_bessel(a, b, x), phi, rtol=accuracy)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_wrightomega.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_wrightomega.py
new file mode 100644
index 0000000000000000000000000000000000000000..c1a93ca007e42fea3a0dec634c51b37f03effa9e
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_wrightomega.py
@@ -0,0 +1,117 @@
+import pytest
+import numpy as np
+from numpy.testing import assert_, assert_equal, assert_allclose
+
+import scipy.special as sc
+from scipy.special._testutils import assert_func_equal
+
+
+def test_wrightomega_nan():
+    pts = [complex(np.nan, 0),
+           complex(0, np.nan),
+           complex(np.nan, np.nan),
+           complex(np.nan, 1),
+           complex(1, np.nan)]
+    for p in pts:
+        res = sc.wrightomega(p)
+        assert_(np.isnan(res.real))
+        assert_(np.isnan(res.imag))
+
+
+def test_wrightomega_inf_branch():
+    pts = [complex(-np.inf, np.pi/4),
+           complex(-np.inf, -np.pi/4),
+           complex(-np.inf, 3*np.pi/4),
+           complex(-np.inf, -3*np.pi/4)]
+    expected_results = [complex(0.0, 0.0),
+                        complex(0.0, -0.0),
+                        complex(-0.0, 0.0),
+                        complex(-0.0, -0.0)]
+    for p, expected in zip(pts, expected_results):
+        res = sc.wrightomega(p)
+        # We can't use assert_equal(res, expected) because in older versions of
+        # numpy, assert_equal doesn't check the sign of the real and imaginary
+        # parts when comparing complex zeros. It does check the sign when the
+        # arguments are *real* scalars.
+        assert_equal(res.real, expected.real)
+        assert_equal(res.imag, expected.imag)
+
+
+def test_wrightomega_inf():
+    pts = [complex(np.inf, 10),
+           complex(-np.inf, 10),
+           complex(10, np.inf),
+           complex(10, -np.inf)]
+    for p in pts:
+        assert_equal(sc.wrightomega(p), p)
+
+
+def test_wrightomega_singular():
+    pts = [complex(-1.0, np.pi),
+           complex(-1.0, -np.pi)]
+    for p in pts:
+        res = sc.wrightomega(p)
+        assert_equal(res, -1.0)
+        assert_(np.signbit(res.imag) == np.bool_(False))
+
+
+@pytest.mark.parametrize('x, desired', [
+    (-np.inf, 0),
+    (np.inf, np.inf),
+])
+def test_wrightomega_real_infinities(x, desired):
+    assert sc.wrightomega(x) == desired
+
+
+def test_wrightomega_real_nan():
+    assert np.isnan(sc.wrightomega(np.nan))
+
+
+def test_wrightomega_real_series_crossover():
+    desired_error = 2 * np.finfo(float).eps
+    crossover = 1e20
+    x_before_crossover = np.nextafter(crossover, -np.inf)
+    x_after_crossover = np.nextafter(crossover, np.inf)
+    # Computed using Mpmath
+    desired_before_crossover = 99999999999999983569.948
+    desired_after_crossover = 100000000000000016337.948
+    assert_allclose(
+        sc.wrightomega(x_before_crossover),
+        desired_before_crossover,
+        atol=0,
+        rtol=desired_error,
+    )
+    assert_allclose(
+        sc.wrightomega(x_after_crossover),
+        desired_after_crossover,
+        atol=0,
+        rtol=desired_error,
+    )
+
+
+def test_wrightomega_exp_approximation_crossover():
+    desired_error = 2 * np.finfo(float).eps
+    crossover = -50
+    x_before_crossover = np.nextafter(crossover, np.inf)
+    x_after_crossover = np.nextafter(crossover, -np.inf)
+    # Computed using Mpmath
+    desired_before_crossover = 1.9287498479639314876e-22
+    desired_after_crossover = 1.9287498479639040784e-22
+    assert_allclose(
+        sc.wrightomega(x_before_crossover),
+        desired_before_crossover,
+        atol=0,
+        rtol=desired_error,
+    )
+    assert_allclose(
+        sc.wrightomega(x_after_crossover),
+        desired_after_crossover,
+        atol=0,
+        rtol=desired_error,
+    )
+
+
+def test_wrightomega_real_versus_complex():
+    x = np.linspace(-500, 500, 1001)
+    results = sc.wrightomega(x + 0j).real
+    assert_func_equal(sc.wrightomega, results, x, atol=0, rtol=1e-14)
diff --git a/venv/lib/python3.12/site-packages/scipy/special/tests/test_zeta.py b/venv/lib/python3.12/site-packages/scipy/special/tests/test_zeta.py
new file mode 100644
index 0000000000000000000000000000000000000000..988f9a716196fb8f65a92a0a2e894038c2474cfa
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/special/tests/test_zeta.py
@@ -0,0 +1,301 @@
+import scipy
+import scipy.special as sc
+import sys
+import numpy as np
+import pytest
+
+from numpy.testing import assert_equal, assert_allclose
+
+
+def test_zeta():
+    assert_allclose(sc.zeta(2,2), np.pi**2/6 - 1, rtol=1e-12)
+
+
+def test_zetac():
+    # Expected values in the following were computed using Wolfram
+    # Alpha's `Zeta[x] - 1`
+    x = [-2.1, 0.8, 0.9999, 9, 50, 75]
+    desired = [
+        -0.9972705002153750,
+        -5.437538415895550,
+        -10000.42279161673,
+        0.002008392826082214,
+        8.881784210930816e-16,
+        2.646977960169853e-23,
+    ]
+    assert_allclose(sc.zetac(x), desired, rtol=1e-12)
+
+
+def test_zetac_special_cases():
+    assert sc.zetac(np.inf) == 0
+    assert np.isnan(sc.zetac(-np.inf))
+    assert sc.zetac(0) == -1.5
+    assert sc.zetac(1.0) == np.inf
+
+    assert_equal(sc.zetac([-2, -50, -100]), -1)
+
+
+def test_riemann_zeta_special_cases():
+    assert np.isnan(sc.zeta(np.nan))
+    assert sc.zeta(np.inf) == 1
+    assert sc.zeta(0) == -0.5
+
+    # Riemann zeta is zero add negative even integers.
+    assert_equal(sc.zeta([-2, -4, -6, -8, -10]), 0)
+
+    assert_allclose(sc.zeta(2), np.pi**2/6, rtol=1e-12)
+    assert_allclose(sc.zeta(4), np.pi**4/90, rtol=1e-12)
+
+
+def test_riemann_zeta_avoid_overflow():
+    s = -260.00000000001
+    desired = -5.6966307844402683127e+297  # Computed with Mpmath
+    assert_allclose(sc.zeta(s), desired, atol=0, rtol=5e-14)
+
+
+@pytest.mark.parametrize(
+    "z, desired, rtol",
+    [
+        ## Test cases taken from mpmath with the script:
+
+        # import numpy as np
+        # import scipy.stats as stats
+
+        # from mpmath import mp
+
+        # # seed = np.random.SeedSequence().entropy
+        # seed = 154689806791763421822480125722191067828
+        # rng = np.random.default_rng(seed)
+        # default_rtol = 1e-13
+
+        # # A small point in each quadrant outside of the critical strip
+        # cases = []
+        # for x_sign, y_sign in [1, 1], [1, -1], [-1, 1], [-1, -1]:
+        #     x = x_sign * rng.uniform(2, 8)
+        #     y = y_sign * rng.uniform(2, 8)
+        #     z = x + y*1j
+        #     reference = complex(mp.zeta(z))
+        #     cases.append((z, reference, default_rtol))
+
+        # # Moderately large imaginary part in each quadrant outside of critical strip
+        # for x_sign, y_sign in [1, 1], [1, -1], [-1, 1], [-1, -1]:
+        #     x = x_sign * rng.uniform(2, 8)
+        #     y = y_sign * rng.uniform(50, 80)
+        #     z = x + y*1j
+        #     reference = complex(mp.zeta(z))
+        #     cases.append((z, reference, default_rtol))
+
+        # # points in critical strip
+        # x = rng.uniform(0.0, 1.0, size=5)
+        # y = np.exp(rng.uniform(0, 5, size=5))
+        # z = x + y*1j
+        # for t in z:
+        #     reference = complex(mp.zeta(t))
+        #     cases.append((complex(t), reference, default_rtol))
+        # z = x - y*1j
+        # for t in z:
+        #     reference = complex(mp.zeta(t))
+        #     cases.append((complex(t), reference, default_rtol))
+
+        # # Near small trivial zeros
+        # x = np.array([-2, -4, -6, -8])
+        # y = np.array([1e-15, -1e-15])
+        # x, y = np.meshgrid(x, y)
+        # x, y = x.ravel(), y.ravel()
+        # z = x + y*1j
+        # for t in z:
+        #     reference = complex(mp.zeta(t))
+        #     cases.append((complex(t), reference, 1e-7))
+
+        # # Some other points near real axis
+        # x = np.array([-0.5, 0, 0.2, 0.75])
+        # y = np.array([1e-15, -1e-15])
+        # x, y = np.meshgrid(x, y)
+        # x, y = x.ravel(), y.ravel()
+        # z = x + y*1j
+        # for t in z:
+        #     reference = complex(mp.zeta(t))
+        #     cases.append((complex(t), reference, 1e-7))
+
+        # # Moderately large real part
+        # x = np.array([49.33915930750887, 50.55805244181687])
+        # y = rng.uniform(20, 100, size=3)
+        # x, y = np.meshgrid(x, y)
+        # x, y = x.ravel(), y.ravel()
+        # z = x + y*1j
+        # for t in z:
+        #     reference = complex(mp.zeta(t))
+        #     cases.append((complex(t), reference, default_rtol))
+
+        # # Very large imaginary part
+        # x = np.array([0.5, 34.812847097948854, 50.55805244181687])
+        # y = np.array([1e6, -1e6])
+        # x, y = np.meshgrid(x, y)
+        # x, y = x.ravel(), y.ravel()
+        # z = x + y*1j
+        # for t in z:
+        #     reference = complex(mp.zeta(t))
+        #     rtol = 1e-7 if t.real == 0.5 else default_rtol
+        #     cases.append((complex(t), reference, rtol))
+        #
+        # # Naive implementation of reflection formula suffers internal overflow
+        # x = -rng.uniform(200, 300, 3)
+        # y = np.array([rng.uniform(10, 30), -rng.uniform(10, 30)])
+        # x, y = np.meshgrid(x, y)
+        # x, y = x.ravel(), y.ravel()
+        # z = x + y*1j
+        # for t in z:
+        #     reference = complex(mp.zeta(t))
+        #     cases.append((complex(t), reference, default_rtol))
+        #
+        # A small point in each quadrant outside of the critical strip
+        ((3.12838509346655+7.111085974836645j),
+         (1.0192654793474945+0.08795174413289127j),
+         1e-13),
+        ((7.06791362314716-7.219497492626728j),
+         (1.0020740683598117-0.006752725913243711j),
+         1e-13),
+        ((-6.806227077655519+2.724411451005281j),
+         (0.06312488213559667-0.061641496333765956j),
+         1e-13),
+        ((-3.0170751511621026-6.3686522550665945j),
+         (-0.10330747857150148-1.214541994832571j),
+         1e-13),
+        # Moderately large imaginary part in each quadrant outside of critical strip
+        ((6.133994402212294+60.03091448000761j),
+         (0.9885701843417336+0.009636925981078128j),
+         1e-13),
+        ((6.17268142822657-64.74883149743795j),
+         (1.0080474225840865+0.012032804974965354j),
+         1e-13),
+        ((-3.462191939791879+76.16258975567534j),
+         (18672.072070850158+2908.5104826247184j),
+         1e-13),
+        ((-6.955735216531752-74.75791554155748j),
+         (-77672258.72276545+71625206.0401107j),
+         1e-13),
+        # Points in critical strip
+        ((0.4088038289823922+1.4596830498094384j),
+         (0.3032837969400845-0.47272237994110344j),
+         1e-13),
+        ((0.9673493951209633+4.918968547259143j),
+         (0.7488756907431944+0.17281553371482428j),
+         1e-13),
+        ((0.8692482679977754+66.6142398421354j),
+         (0.5831942469552066-0.26848904799062334j),
+         1e-13),
+        ((0.42771847720003764+21.783747851715468j),
+         (0.4767032638444329+0.6898148744603123j),
+         1e-13),
+        ((0.20479494678428956+33.17656449538932j),
+         (-0.6983038977487848+0.18060923618150224j),
+         1e-13),
+        ((0.4088038289823922-1.4596830498094384j),
+         (0.3032837969400845+0.47272237994110344j),
+         1e-13),
+        ((0.9673493951209633-4.918968547259143j),
+         (0.7488756907431944-0.17281553371482428j),
+         1e-13),
+        ((0.8692482679977754-66.6142398421354j),
+         (0.5831942469552066+0.26848904799062334j),
+         1e-13),
+        ((0.42771847720003764-21.783747851715468j),
+         (0.4767032638444329-0.6898148744603123j),
+         1e-13),
+        ((0.20479494678428956-33.17656449538932j),
+         (-0.6983038977487848-0.18060923618150224j),
+         1e-13),
+        # Near small trivial zeros
+        ((-2+1e-15j), (3.288175809370978e-32-3.0448457058393275e-17j), 1e-07),
+        ((-4+1e-15j), (-2.868707923051182e-33+7.983811450268625e-18j), 1e-07),
+        ((-6+1e-15j), (-1.7064292323640116e-34-5.8997591435159376e-18j), 1e-07),
+        ((-8+1e-15j), (2.5060859548261706e-33+8.316161985602247e-18j), 1e-07),
+        ((-2-1e-15j), (3.288175809371319e-32+3.0448457058393275e-17j), 1e-07),
+        ((-4-1e-15j), (-2.8687079230520114e-33-7.983811450268625e-18j), 1e-07),
+        ((-6-1e-15j), (-1.70642923235801e-34+5.8997591435159376e-18j), 1e-07),
+        ((-8-1e-15j), (2.5060859548253293e-33-8.316161985602247e-18j), 1e-07),
+        # Some other points near real axis
+        ((-0.5+1e-15j), (-0.20788622497735457-3.608543395999408e-16j), 1e-07),
+        (1e-15j, (-0.5-9.189384239689193e-16j), 1e-07),
+        ((0.2+1e-15j), (-0.7339209248963406-1.4828001150329085e-15j), 1e-07),
+        ((0.75+1e-15j), (-3.4412853869452227-1.5924832114302393e-14j), 1e-13),
+        ((-0.5-1e-15j), (-0.20788622497735457+3.608543395999408e-16j), 1e-07),
+        (-1e-15j, (-0.5+9.189387416062746e-16j), 1e-07),
+        ((0.2-1e-15j), (-0.7339209248963406+1.4828004007675122e-15j), 1e-07),
+        ((0.75-1e-15j), (-3.4412853869452227+1.5924831974403957e-14j), 1e-13),
+        # Moderately large real part
+        ((49.33915930750887+53.213478698903955j),
+         (1.0000000000000009+1.0212452494616078e-15j),
+         1e-13),
+        ((50.55805244181687+53.213478698903955j),
+         (1.0000000000000004+4.387394180390787e-16j),
+         1e-13),
+        ((49.33915930750887+40.6366015728302j),
+         (0.9999999999999986-1.502268709924849e-16j),
+         1e-13),
+        ((50.55805244181687+40.6366015728302j),
+         (0.9999999999999994-6.453929613571651e-17j),
+         1e-13),
+        ((49.33915930750887+85.83555435273925j),
+         (0.9999999999999987-2.7014400611995846e-16j),
+         1e-13),
+        ((50.55805244181687+85.83555435273925j),
+         (0.9999999999999994-1.160571605555322e-16j),
+         1e-13),
+        # Very large imaginary part
+        ((0.5+1e6j), (0.0760890697382271+2.805102101019299j), 1e-07),
+        ((34.812847097948854+1e6j),
+         (1.0000000000102545+3.150848654056419e-11j),
+         1e-13),
+        ((50.55805244181687+1e6j),
+         (1.0000000000000002+5.736517078070873e-16j),
+         1e-13),
+        ((0.5-1e6j), (0.0760890697382271-2.805102101019299j), 1e-07),
+        ((34.812847097948854-1e6j),
+         (1.0000000000102545-3.150848654056419e-11j),
+         1e-13),
+        ((50.55805244181687-1e6j),
+         (1.0000000000000002-5.736517078070873e-16j),
+         1e-13),
+        ((-294.86605461349745+13.992648136816397j), (-np.inf+np.inf*1j), 1e-13),
+        ((-294.86605461349745-16.147667799398363j), (np.inf-np.inf*1j), 1e-13),
+    ]
+)
+def test_riemann_zeta_complex(z, desired, rtol):
+    assert_allclose(sc.zeta(z), desired, rtol=rtol)
+
+
+# Some of the test cases below fail for intel compilers
+cpp_compiler = scipy.__config__.CONFIG["Compilers"]["c++"]["name"]
+gcc_linux = cpp_compiler == "gcc" and sys.platform == "linux"
+clang_macOS = cpp_compiler == "clang" and sys.platform == "darwin"
+
+
+@pytest.mark.skipif(
+    not (gcc_linux or clang_macOS),
+    reason="Underflow may not be avoided on other platforms",
+)
+@pytest.mark.parametrize(
+    "z, desired, rtol",
+    [
+        # Test cases generated as part of same script for
+        # test_riemann_zeta_complex. These cases are split off because
+        # they fail on some platforms.
+        #
+        # Naive implementation of reflection formula suffers internal overflow
+        ((-217.40285743524163+13.992648136816397j),
+         (-6.012818500554211e+249-1.926943776932387e+250j),
+         5e-13,),
+        ((-237.71710702931668+13.992648136816397j),
+         (-8.823803086106129e+281-5.009074181335139e+281j),
+         1e-13,),
+        ((-217.40285743524163-16.147667799398363j),
+         (-5.111612904844256e+251-4.907132127666742e+250j),
+         5e-13,),
+        ((-237.71710702931668-16.147667799398363j),
+         (-1.3256112779883167e+283-2.253002003455494e+283j),
+         5e-13,),
+    ],
+)
+def test_riemann_zeta_complex_avoid_underflow(z, desired, rtol):
+    assert_allclose(sc.zeta(z), desired, rtol=rtol)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/__init__.py b/venv/lib/python3.12/site-packages/scipy/stats/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e67ecbe12091add03d50815fe8307e746af3b85b
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/__init__.py
@@ -0,0 +1,644 @@
+"""
+.. _statsrefmanual:
+
+==========================================
+Statistical functions (:mod:`scipy.stats`)
+==========================================
+
+.. currentmodule:: scipy.stats
+
+This module contains a large number of probability distributions,
+summary and frequency statistics, correlation functions and statistical
+tests, masked statistics, kernel density estimation, quasi-Monte Carlo
+functionality, and more.
+
+Statistics is a very large area, and there are topics that are out of scope
+for SciPy and are covered by other packages. Some of the most important ones
+are:
+
+- `statsmodels <https://www.statsmodels.org/stable/index.html>`__:
+  regression, linear models, time series analysis, extensions to topics
+  also covered by ``scipy.stats``.
+- `Pandas <https://pandas.pydata.org/>`__: tabular data, time series
+  functionality, interfaces to other statistical languages.
+- `PyMC <https://docs.pymc.io/>`__: Bayesian statistical
+  modeling, probabilistic machine learning.
+- `scikit-learn <https://scikit-learn.org/>`__: classification, regression,
+  model selection.
+- `Seaborn <https://seaborn.pydata.org/>`__: statistical data visualization.
+- `rpy2 <https://rpy2.github.io/>`__: Python to R bridge.
+
+
+Probability distributions
+=========================
+
+Each univariate distribution is an instance of a subclass of `rv_continuous`
+(`rv_discrete` for discrete distributions):
+
+.. autosummary::
+   :toctree: generated/
+
+   rv_continuous
+   rv_discrete
+   rv_histogram
+
+Continuous distributions
+------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   alpha             -- Alpha
+   anglit            -- Anglit
+   arcsine           -- Arcsine
+   argus             -- Argus
+   beta              -- Beta
+   betaprime         -- Beta Prime
+   bradford          -- Bradford
+   burr              -- Burr (Type III)
+   burr12            -- Burr (Type XII)
+   cauchy            -- Cauchy
+   chi               -- Chi
+   chi2              -- Chi-squared
+   cosine            -- Cosine
+   crystalball       -- Crystalball
+   dgamma            -- Double Gamma
+   dpareto_lognorm   -- Double Pareto Lognormal
+   dweibull          -- Double Weibull
+   erlang            -- Erlang
+   expon             -- Exponential
+   exponnorm         -- Exponentially Modified Normal
+   exponweib         -- Exponentiated Weibull
+   exponpow          -- Exponential Power
+   f                 -- F (Snecdor F)
+   fatiguelife       -- Fatigue Life (Birnbaum-Saunders)
+   fisk              -- Fisk
+   foldcauchy        -- Folded Cauchy
+   foldnorm          -- Folded Normal
+   genlogistic       -- Generalized Logistic
+   gennorm           -- Generalized normal
+   genpareto         -- Generalized Pareto
+   genexpon          -- Generalized Exponential
+   genextreme        -- Generalized Extreme Value
+   gausshyper        -- Gauss Hypergeometric
+   gamma             -- Gamma
+   gengamma          -- Generalized gamma
+   genhalflogistic   -- Generalized Half Logistic
+   genhyperbolic     -- Generalized Hyperbolic
+   geninvgauss       -- Generalized Inverse Gaussian
+   gibrat            -- Gibrat
+   gompertz          -- Gompertz (Truncated Gumbel)
+   gumbel_r          -- Right Sided Gumbel, Log-Weibull, Fisher-Tippett, Extreme Value Type I
+   gumbel_l          -- Left Sided Gumbel, etc.
+   halfcauchy        -- Half Cauchy
+   halflogistic      -- Half Logistic
+   halfnorm          -- Half Normal
+   halfgennorm       -- Generalized Half Normal
+   hypsecant         -- Hyperbolic Secant
+   invgamma          -- Inverse Gamma
+   invgauss          -- Inverse Gaussian
+   invweibull        -- Inverse Weibull
+   irwinhall         -- Irwin-Hall
+   jf_skew_t         -- Jones and Faddy Skew-T
+   johnsonsb         -- Johnson SB
+   johnsonsu         -- Johnson SU
+   kappa4            -- Kappa 4 parameter
+   kappa3            -- Kappa 3 parameter
+   ksone             -- Distribution of Kolmogorov-Smirnov one-sided test statistic
+   kstwo             -- Distribution of Kolmogorov-Smirnov two-sided test statistic
+   kstwobign         -- Limiting Distribution of scaled Kolmogorov-Smirnov two-sided test statistic.
+   landau            -- Landau
+   laplace           -- Laplace
+   laplace_asymmetric    -- Asymmetric Laplace
+   levy              -- Levy
+   levy_l
+   levy_stable
+   logistic          -- Logistic
+   loggamma          -- Log-Gamma
+   loglaplace        -- Log-Laplace (Log Double Exponential)
+   lognorm           -- Log-Normal
+   loguniform        -- Log-Uniform
+   lomax             -- Lomax (Pareto of the second kind)
+   maxwell           -- Maxwell
+   mielke            -- Mielke's Beta-Kappa
+   moyal             -- Moyal
+   nakagami          -- Nakagami
+   ncx2              -- Non-central chi-squared
+   ncf               -- Non-central F
+   nct               -- Non-central Student's T
+   norm              -- Normal (Gaussian)
+   norminvgauss      -- Normal Inverse Gaussian
+   pareto            -- Pareto
+   pearson3          -- Pearson type III
+   powerlaw          -- Power-function
+   powerlognorm      -- Power log normal
+   powernorm         -- Power normal
+   rdist             -- R-distribution
+   rayleigh          -- Rayleigh
+   rel_breitwigner   -- Relativistic Breit-Wigner
+   rice              -- Rice
+   recipinvgauss     -- Reciprocal Inverse Gaussian
+   semicircular      -- Semicircular
+   skewcauchy        -- Skew Cauchy
+   skewnorm          -- Skew normal
+   studentized_range    -- Studentized Range
+   t                 -- Student's T
+   trapezoid         -- Trapezoidal
+   triang            -- Triangular
+   truncexpon        -- Truncated Exponential
+   truncnorm         -- Truncated Normal
+   truncpareto       -- Truncated Pareto
+   truncweibull_min  -- Truncated minimum Weibull distribution
+   tukeylambda       -- Tukey-Lambda
+   uniform           -- Uniform
+   vonmises          -- Von-Mises (Circular)
+   vonmises_line     -- Von-Mises (Line)
+   wald              -- Wald
+   weibull_min       -- Minimum Weibull (see Frechet)
+   weibull_max       -- Maximum Weibull (see Frechet)
+   wrapcauchy        -- Wrapped Cauchy
+
+The ``fit`` method of the univariate continuous distributions uses
+maximum likelihood estimation to fit the distribution to a data set.
+The ``fit`` method can accept regular data or *censored data*.
+Censored data is represented with instances of the `CensoredData`
+class.
+
+.. autosummary::
+   :toctree: generated/
+
+   CensoredData
+
+
+Multivariate distributions
+--------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   multivariate_normal    -- Multivariate normal distribution
+   matrix_normal          -- Matrix normal distribution
+   dirichlet              -- Dirichlet
+   dirichlet_multinomial  -- Dirichlet multinomial distribution
+   wishart                -- Wishart
+   invwishart             -- Inverse Wishart
+   multinomial            -- Multinomial distribution
+   special_ortho_group    -- SO(N) group
+   ortho_group            -- O(N) group
+   unitary_group          -- U(N) group
+   random_correlation     -- random correlation matrices
+   multivariate_t         -- Multivariate t-distribution
+   multivariate_hypergeom -- Multivariate hypergeometric distribution
+   normal_inverse_gamma   -- Normal-inverse-gamma distribution
+   random_table           -- Distribution of random tables with given marginals
+   uniform_direction      -- Uniform distribution on S(N-1)
+   vonmises_fisher        -- Von Mises-Fisher distribution
+   matrix_t               -- Matrix variate t distribution
+
+`scipy.stats.multivariate_normal` methods accept instances
+of the following class to represent the covariance.
+
+.. autosummary::
+   :toctree: generated/
+
+   Covariance             -- Representation of a covariance matrix
+
+
+Discrete distributions
+----------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   bernoulli                -- Bernoulli
+   betabinom                -- Beta-Binomial
+   betanbinom               -- Beta-Negative Binomial
+   binom                    -- Binomial
+   boltzmann                -- Boltzmann (Truncated Discrete Exponential)
+   dlaplace                 -- Discrete Laplacian
+   geom                     -- Geometric
+   hypergeom                -- Hypergeometric
+   logser                   -- Logarithmic (Log-Series, Series)
+   nbinom                   -- Negative Binomial
+   nchypergeom_fisher       -- Fisher's Noncentral Hypergeometric
+   nchypergeom_wallenius    -- Wallenius's Noncentral Hypergeometric
+   nhypergeom               -- Negative Hypergeometric
+   planck                   -- Planck (Discrete Exponential)
+   poisson                  -- Poisson
+   poisson_binom            -- Poisson Binomial
+   randint                  -- Discrete Uniform
+   skellam                  -- Skellam
+   yulesimon                -- Yule-Simon
+   zipf                     -- Zipf (Zeta)
+   zipfian                  -- Zipfian
+
+
+An overview of statistical functions is given below.  Many of these functions
+have a similar version in `scipy.stats.mstats` which work for masked arrays.
+
+Summary statistics
+==================
+
+.. autosummary::
+   :toctree: generated/
+
+   describe          -- Descriptive statistics
+   gmean             -- Geometric mean
+   hmean             -- Harmonic mean
+   pmean             -- Power mean
+   kurtosis          -- Fisher or Pearson kurtosis
+   mode              -- Modal value
+   moment            -- Central moment
+   lmoment
+   expectile         -- Expectile
+   skew              -- Skewness
+   kstat             --
+   kstatvar          --
+   tmean             -- Truncated arithmetic mean
+   tvar              -- Truncated variance
+   tmin              --
+   tmax              --
+   tstd              --
+   tsem              --
+   variation         -- Coefficient of variation
+   rankdata
+   tiecorrect
+   trim_mean
+   gstd              -- Geometric Standard Deviation
+   iqr
+   sem
+   bayes_mvs
+   mvsdist
+   entropy
+   differential_entropy
+   median_abs_deviation
+
+Frequency statistics
+====================
+
+.. autosummary::
+   :toctree: generated/
+
+   quantile
+   estimated_cdf
+   cumfreq
+   relfreq
+   percentileofscore
+   scoreatpercentile
+
+.. autosummary::
+   :toctree: generated/
+
+   binned_statistic     -- Compute a binned statistic for a set of data.
+   binned_statistic_2d  -- Compute a 2-D binned statistic for a set of data.
+   binned_statistic_dd  -- Compute a d-D binned statistic for a set of data.
+
+.. _hypotests:
+
+Hypothesis Tests and related functions
+======================================
+SciPy has many functions for performing hypothesis tests that return a
+test statistic and a p-value, and several of them return confidence intervals
+and/or other related information.
+
+The headings below are based on common uses of the functions within, but due to
+the wide variety of statistical procedures, any attempt at coarse-grained
+categorization will be imperfect. Also, note that tests within the same heading
+are not interchangeable in general (e.g. many have different distributional
+assumptions).
+
+One Sample Tests / Paired Sample Tests
+--------------------------------------
+One sample tests are typically used to assess whether a single sample was
+drawn from a specified distribution or a distribution with specified properties
+(e.g. zero mean).
+
+.. autosummary::
+   :toctree: generated/
+
+   ttest_1samp
+   binomtest
+   quantile_test
+   skewtest
+   kurtosistest
+   normaltest
+   jarque_bera
+   shapiro
+   anderson
+   cramervonmises
+   ks_1samp
+   goodness_of_fit
+   chisquare
+   power_divergence
+
+Paired sample tests are often used to assess whether two samples were drawn
+from the same distribution; they differ from the independent sample tests below
+in that each observation in one sample is treated as paired with a
+closely-related observation in the other sample (e.g. when environmental
+factors are controlled between observations within a pair but not among pairs).
+They can also be interpreted or used as one-sample tests (e.g. tests on the
+mean or median of *differences* between paired observations).
+
+.. autosummary::
+   :toctree: generated/
+
+   ttest_rel
+   wilcoxon
+
+Association/Correlation Tests
+-----------------------------
+
+These tests are often used to assess whether there is a relationship (e.g.
+linear) between paired observations in multiple samples or among the
+coordinates of multivariate observations.
+
+.. autosummary::
+   :toctree: generated/
+
+   linregress
+   pearsonr
+   spearmanrho
+   pointbiserialr
+   kendalltau
+   chatterjeexi
+   weightedtau
+   somersd
+   siegelslopes
+   theilslopes
+   page_trend_test
+   multiscale_graphcorr
+   spearmanr
+
+These association tests and are to work with samples in the form of contingency
+tables. Supporting functions are available in `scipy.stats.contingency`.
+
+.. autosummary::
+   :toctree: generated/
+
+   chi2_contingency
+   fisher_exact
+   barnard_exact
+   boschloo_exact
+
+Independent Sample Tests
+------------------------
+Independent sample tests are typically used to assess whether multiple samples
+were independently drawn from the same distribution or different distributions
+with a shared property (e.g. equal means).
+
+Some tests are specifically for comparing two samples.
+
+.. autosummary::
+   :toctree: generated/
+
+   ttest_ind_from_stats
+   poisson_means_test
+   ttest_ind
+   mannwhitneyu
+   bws_test
+   ranksums
+   brunnermunzel
+   mood
+   ansari
+   cramervonmises_2samp
+   epps_singleton_2samp
+   ks_2samp
+   kstest
+
+Others are generalized to multiple samples.
+
+.. autosummary::
+   :toctree: generated/
+
+   f_oneway
+   tukey_hsd
+   dunnett
+   kruskal
+   alexandergovern
+   fligner
+   levene
+   bartlett
+   median_test
+   friedmanchisquare
+   anderson_ksamp
+
+Resampling and Monte Carlo Methods
+----------------------------------
+The following functions can reproduce the p-value and confidence interval
+results of most of the functions above, and often produce accurate results in a
+wider variety of conditions. They can also be used to perform hypothesis tests
+and generate confidence intervals for custom statistics. This flexibility comes
+at the cost of greater computational requirements and stochastic results.
+
+.. autosummary::
+   :toctree: generated/
+
+   monte_carlo_test
+   permutation_test
+   bootstrap
+   power
+
+Instances of the following object can be passed into some hypothesis test
+functions to perform a resampling or Monte Carlo version of the hypothesis
+test.
+
+.. autosummary::
+   :toctree: generated/
+
+   MonteCarloMethod
+   PermutationMethod
+   BootstrapMethod
+
+Multiple Hypothesis Testing and Meta-Analysis
+---------------------------------------------
+These functions are for assessing the results of individual tests as a whole.
+Functions for performing specific multiple hypothesis tests (e.g. post hoc
+tests) are listed above.
+
+.. autosummary::
+   :toctree: generated/
+
+   combine_pvalues
+   false_discovery_control
+
+Random Variables
+================
+
+.. autosummary::
+   :toctree: generated/
+
+   make_distribution
+   Normal
+   Logistic
+   Uniform
+   Binomial
+   Mixture
+   order_statistic
+   truncate
+   abs
+   exp
+   log
+
+Other statistical functionality
+===============================
+.. toctree::
+   :maxdepth: 1
+
+   stats.qmc
+   stats.contingency
+   stats.mstats
+   stats.sampling
+
+Transformations
+---------------
+
+.. autosummary::
+   :toctree: generated/
+
+   boxcox
+   boxcox_normmax
+   boxcox_llf
+   yeojohnson
+   yeojohnson_normmax
+   yeojohnson_llf
+   obrientransform
+   sigmaclip
+   trimboth
+   trim1
+   zmap
+   zscore
+   gzscore
+
+Statistical distances
+---------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   wasserstein_distance
+   wasserstein_distance_nd
+   energy_distance
+
+Fitting / Survival Analysis
+---------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   fit
+   ecdf
+   logrank
+
+Directional statistical functions
+---------------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   directional_stats
+   circmean
+   circvar
+   circstd
+
+Sensitivity Analysis
+--------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   sobol_indices
+
+Plot-tests
+----------
+
+.. autosummary::
+   :toctree: generated/
+
+   ppcc_max
+   ppcc_plot
+   probplot
+   boxcox_normplot
+   yeojohnson_normplot
+
+Univariate and multivariate kernel density estimation
+-----------------------------------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   gaussian_kde
+
+Warnings / Errors used in :mod:`scipy.stats`
+--------------------------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   DegenerateDataWarning
+   ConstantInputWarning
+   NearConstantInputWarning
+   FitError
+
+Result classes used in :mod:`scipy.stats`
+-----------------------------------------
+
+.. warning::
+
+    These classes are private, but they are included here because instances
+    of them are returned by other statistical functions. User import and
+    instantiation is not supported.
+
+.. toctree::
+   :maxdepth: 2
+
+   stats._result_classes
+
+"""  # noqa: E501
+
+from ._warnings_errors import (ConstantInputWarning, NearConstantInputWarning,
+                               DegenerateDataWarning, FitError)
+from ._stats_py import *
+from ._variation import variation
+from .distributions import *
+from ._morestats import *
+from ._multicomp import *
+from ._binomtest import binomtest
+from ._binned_statistic import *
+from ._kde import gaussian_kde
+from . import mstats
+from . import qmc
+from ._multivariate import *
+from . import contingency
+from .contingency import chi2_contingency
+from ._censored_data import CensoredData
+from ._resampling import (bootstrap, monte_carlo_test, permutation_test, power,
+                          MonteCarloMethod, PermutationMethod, BootstrapMethod)
+from ._entropy import *
+from ._hypotests import *
+from ._page_trend_test import page_trend_test
+from ._mannwhitneyu import mannwhitneyu
+from ._bws_test import bws_test
+from ._fit import fit, goodness_of_fit
+from ._covariance import Covariance
+from ._sensitivity_analysis import *
+from ._survival import *
+from ._distribution_infrastructure import (
+    make_distribution, Mixture, order_statistic, truncate, exp, log, abs
+)
+from ._new_distributions import Normal, Logistic, Uniform, Binomial
+from ._mgc import multiscale_graphcorr
+from ._correlation import chatterjeexi, spearmanrho, theilslopes, siegelslopes
+from ._quantile import quantile, estimated_cdf
+
+
+# Deprecated namespaces, to be removed in v2.0.0
+from . import (
+    biasedurn, kde, morestats, mstats_basic, mstats_extras, mvn, stats
+)
+
+
+__all__ = [s for s in dir() if not s.startswith("_")]  # Remove dunders.
+
+from scipy._lib._testutils import PytestTester
+test = PytestTester(__name__)
+del PytestTester
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+version https://git-lfs.github.com/spec/v1
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+size 107992
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_axis_nan_policy.py b/venv/lib/python3.12/site-packages/scipy/stats/_axis_nan_policy.py
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--- /dev/null
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+# Many scipy.stats functions support `axis` and `nan_policy` parameters.
+# When the two are combined, it can be tricky to get all the behavior just
+# right. This file contains utility functions useful for scipy.stats functions
+# that support `axis` and `nan_policy`, including a decorator that
+# automatically adds `axis` and `nan_policy` arguments to a function.
+
+import math
+import warnings
+import numpy as np
+from functools import wraps
+from scipy._lib._array_api import xp_ravel
+from scipy._lib._docscrape import FunctionDoc, Parameter
+from scipy._lib._util import _contains_nan, AxisError, _get_nan
+from scipy._lib._array_api import (array_namespace, is_numpy, xp_size, xp_copy,
+                                   xp_promote, is_dask, is_jax, xp_capabilities)
+import scipy._external.array_api_extra as xpx
+
+import inspect
+
+too_small_1d_not_omit = (
+    "One or more sample arguments is too small; all "
+    "returned values will be NaN. "
+    "See documentation for sample size requirements.")
+
+too_small_1d_omit = (
+    "After omitting NaNs, one or more sample arguments "
+    "is too small; all returned values will be NaN. "
+    "See documentation for sample size requirements.")
+
+too_small_nd_not_omit = (
+    "All axis-slices of one or more sample arguments are "
+    "too small; all elements of returned arrays will be NaN. "
+    "See documentation for sample size requirements.")
+
+too_small_nd_omit = (
+    "After omitting NaNs, one or more axis-slices of one "
+    "or more sample arguments is too small; corresponding "
+    "elements of returned arrays will be NaN. "
+    "See documentation for sample size requirements.")
+
+class SmallSampleWarning(RuntimeWarning):
+    pass
+
+
+def _broadcast_arrays(arrays, axis=None, xp=None):
+    """
+    Broadcast shapes of arrays, ignoring incompatibility of specified axes
+    """
+    arrays = tuple(arrays)
+    if not arrays:
+        return arrays
+    xp = array_namespace(*arrays) if xp is None else xp
+    arrays = [xp.asarray(arr) for arr in arrays]
+    shapes = [arr.shape for arr in arrays]
+    new_shapes = _broadcast_shapes(shapes, axis)
+    if axis is None:
+        new_shapes = [new_shapes]*len(arrays)
+    return [xp.broadcast_to(array, new_shape)
+            for array, new_shape in zip(arrays, new_shapes)]
+
+
+def _broadcast_shapes(shapes, axis=None):
+    """
+    Broadcast shapes, ignoring incompatibility of specified axes
+    """
+    if not shapes:
+        return shapes
+
+    # input validation
+    if axis is not None:
+        axis = np.atleast_1d(axis)
+        message = '`axis` must be an integer, a tuple of integers, or `None`.'
+        try:
+            with np.errstate(invalid='ignore'):
+                axis_int = axis.astype(int)
+        except ValueError as e:
+            raise AxisError(message) from e
+        if not np.array_equal(axis_int, axis):
+            raise AxisError(message)
+        axis = axis_int
+
+    # First, ensure all shapes have same number of dimensions by prepending 1s.
+    n_dims = max([len(shape) for shape in shapes])
+    new_shapes = np.ones((len(shapes), n_dims), dtype=int)
+    for row, shape in zip(new_shapes, shapes):
+        row[len(row)-len(shape):] = shape  # can't use negative indices (-0:)
+
+    # Remove the shape elements of the axes to be ignored, but remember them.
+    if axis is not None:
+        axis[axis < 0] = n_dims + axis[axis < 0]
+        axis = np.sort(axis)
+        if axis[-1] >= n_dims or axis[0] < 0:
+            message = (f"`axis` is out of bounds "
+                       f"for array of dimension {n_dims}")
+            raise AxisError(message)
+
+        if len(np.unique(axis)) != len(axis):
+            raise AxisError("`axis` must contain only distinct elements")
+
+        removed_shapes = new_shapes[:, axis]
+        new_shapes = np.delete(new_shapes, axis, axis=1)
+
+    # If arrays are broadcastable, shape elements that are 1 may be replaced
+    # with a corresponding non-1 shape element. Assuming arrays are
+    # broadcastable, that final shape element can be found with:
+    new_shape = np.max(new_shapes, axis=0)
+    # except in case of an empty array:
+    new_shape *= new_shapes.all(axis=0)
+
+    # Among all arrays, there can only be one unique non-1 shape element.
+    # Therefore, if any non-1 shape element does not match what we found
+    # above, the arrays must not be broadcastable after all.
+    if np.any(~((new_shapes == 1) | (new_shapes == new_shape))):
+        raise ValueError("Array shapes are incompatible for broadcasting.")
+
+    if axis is not None:
+        # Add back the shape elements that were ignored
+        new_axis = axis - np.arange(len(axis))
+        new_shapes = [tuple(np.insert(new_shape, new_axis, removed_shape))
+                      for removed_shape in removed_shapes]
+        return new_shapes
+    else:
+        return tuple(new_shape)
+
+
+def _broadcast_array_shapes_remove_axis(arrays, axis=None):
+    """
+    Broadcast shapes of arrays, dropping specified axes
+
+    Given a sequence of arrays `arrays` and an integer or tuple `axis`, find
+    the shape of the broadcast result after consuming/dropping `axis`.
+    In other words, return output shape of a typical hypothesis test on
+    `arrays` vectorized along `axis`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats._axis_nan_policy import _broadcast_array_shapes_remove_axis
+    >>> a = np.zeros((5, 2, 1))
+    >>> b = np.zeros((9, 3))
+    >>> _broadcast_array_shapes_remove_axis((a, b), 1)
+    (5, 3)
+    """
+    # Note that here, `axis=None` means do not consume/drop any axes - _not_
+    # ravel arrays before broadcasting.
+    shapes = [arr.shape for arr in arrays]
+    return _broadcast_shapes_remove_axis(shapes, axis)
+
+
+def _broadcast_shapes_remove_axis(shapes, axis=None):
+    """
+    Broadcast shapes, dropping specified axes
+
+    Same as _broadcast_array_shapes_remove_axis, but given a sequence
+    of array shapes `shapes` instead of the arrays themselves.
+    """
+    shapes = _broadcast_shapes(shapes, axis)
+    shape = shapes[0]
+    if axis is not None:
+        shape = np.delete(shape, axis)
+    return tuple(shape)
+
+
+@xp_capabilities()
+def _broadcast_concatenate(arrays, axis, paired=False, xp=None):
+    """Concatenate arrays along an axis with broadcasting."""
+    xp = array_namespace(*arrays) if xp is None else xp
+    arrays = _broadcast_arrays(arrays, axis if not paired else None, xp=xp)
+    res = xp.concat(arrays, axis=axis)
+    return res
+
+
+def _remove_nans(samples, paired, xp=None):
+    "Remove nans from paired or unpaired 1D samples"
+    # potential optimization: don't copy arrays that don't contain nans
+    xp = array_namespace(*samples)
+    if not paired:
+        return [sample[~xp.isnan(sample)] for sample in samples]
+
+    # for paired samples, we need to remove the whole pair when any part
+    # has a nan
+    nans = xp.isnan(samples[0])
+    for sample in samples[1:]:
+        nans = nans | xp.isnan(sample)
+    not_nans = ~nans
+    return [sample[not_nans] for sample in samples]
+
+
+def _remove_sentinel(samples, paired, sentinel):
+    "Remove sentinel values from paired or unpaired 1D samples"
+    # could consolidate with `_remove_nans`, but it's not quite as simple as
+    # passing `sentinel=np.nan` because `(np.nan == np.nan) is False`
+
+    # potential optimization: don't copy arrays that don't contain sentinel
+    if not paired:
+        return [sample[sample != sentinel] for sample in samples]
+
+    # for paired samples, we need to remove the whole pair when any part
+    # has a nan
+    sentinels = (samples[0] == sentinel)
+    for sample in samples[1:]:
+        sentinels = sentinels | (sample == sentinel)
+    not_sentinels = ~sentinels
+    return [sample[not_sentinels] for sample in samples]
+
+
+def _masked_arrays_2_sentinel_arrays(samples):
+    # masked arrays in `samples` are converted to regular arrays, and values
+    # corresponding with masked elements are replaced with a sentinel value
+
+    # return without modifying arrays if none have a mask
+    has_mask = False
+    for sample in samples:
+        mask = getattr(sample, 'mask', False)
+        has_mask = has_mask or np.any(mask)
+    if not has_mask:
+        return samples, None  # None means there is no sentinel value
+
+    # Choose a sentinel value. We can't use `np.nan`, because sentinel (masked)
+    # values are always omitted, but there are different nan policies.
+    dtype = np.result_type(*samples)
+    dtype = dtype if np.issubdtype(dtype, np.number) else np.float64
+    for i in range(len(samples)):
+        # Things get more complicated if the arrays are of different types.
+        # We could have different sentinel values for each array, but
+        # the purpose of this code is convenience, not efficiency.
+        samples[i] = samples[i].astype(dtype, copy=False)
+
+    inexact = np.issubdtype(dtype, np.inexact)
+    info = np.finfo if inexact else np.iinfo
+    max_possible, min_possible = info(dtype).max, info(dtype).min
+    nextafter = np.nextafter if inexact else (lambda x, _: x - 1)
+
+    sentinel = max_possible
+    # For simplicity, min_possible/np.infs are not candidate sentinel values
+    while sentinel > min_possible:
+        for sample in samples:
+            if np.any(sample == sentinel):  # choose a new sentinel value
+                sentinel = nextafter(sentinel, -np.inf)
+                break
+        else:  # when sentinel value is OK, break the while loop
+            break
+    else:
+        message = ("This function replaces masked elements with sentinel "
+                   "values, but the data contains all distinct values of this "
+                   "data type. Consider promoting the dtype to `np.float64`.")
+        raise ValueError(message)
+
+    # replace masked elements with sentinel value
+    out_samples = []
+    for sample in samples:
+        mask = getattr(sample, 'mask', None)
+        if mask is not None:  # turn all masked arrays into sentinel arrays
+            mask = np.broadcast_to(mask, sample.shape)
+            sample = sample.data.copy() if np.any(mask) else sample.data
+            sample = np.asarray(sample)  # `sample.data` could be a memoryview?
+            sample[mask] = sentinel
+        out_samples.append(sample)
+
+    return out_samples, sentinel
+
+
+def _check_empty_inputs(samples, axis, xp=None):
+    """
+    Check for empty sample; return appropriate output for a vectorized hypotest
+    """
+    xp = array_namespace(*samples) if xp is None else xp
+    # if none of the samples are empty, we need to perform the test
+    if not any(xp_size(sample) == 0 for sample in samples):
+        return None
+    # otherwise, the statistic and p-value will be either empty arrays or
+    # arrays with NaNs. Produce the appropriate array and return it.
+    output_shape = _broadcast_array_shapes_remove_axis(samples, axis)
+    NaN = _get_nan(*samples)
+    output = xp.full(output_shape, xp.nan, dtype=NaN.dtype)
+    return output
+
+
+def _add_reduced_axes(res, reduced_axes, keepdims, xp=np):
+    """
+    Add reduced axes back to all the arrays in the result object
+    if keepdims = True.
+    """
+    return ([xpx.expand_dims(output, axis=reduced_axes)
+             if not isinstance(output, int) else output for output in res]
+            if keepdims else res)
+
+
+# Standard docstring / signature entries for `axis`, `nan_policy`, `keepdims`
+_name = 'axis'
+_desc = (
+    """If an int, the axis of the input along which to compute the statistic.
+The statistic of each axis-slice (e.g. row) of the input will appear in a
+corresponding element of the output.
+If ``None``, the input will be raveled before computing the statistic."""
+    .split('\n'))
+
+
+def _get_axis_params(default_axis=0, _name=_name, _desc=_desc):  # bind NOW
+    _type = f"int or None, default: {default_axis}"
+    _axis_parameter_doc = Parameter(_name, _type, _desc)
+    _axis_parameter = inspect.Parameter(_name,
+                                        inspect.Parameter.KEYWORD_ONLY,
+                                        default=default_axis)
+    return _axis_parameter_doc, _axis_parameter
+
+
+_name = 'nan_policy'
+_type = "{'propagate', 'omit', 'raise'}"
+_desc = (
+    """Defines how to handle input NaNs.
+
+- ``propagate``: if a NaN is present in the axis slice (e.g. row) along
+  which the  statistic is computed, the corresponding entry of the output
+  will be NaN.
+- ``omit``: NaNs will be omitted when performing the calculation.
+  If insufficient data remains in the axis slice along which the
+  statistic is computed, the corresponding entry of the output will be
+  NaN.
+- ``raise``: if a NaN is present, a ``ValueError`` will be raised."""
+    .split('\n'))
+_nan_policy_parameter_doc = Parameter(_name, _type, _desc)
+_nan_policy_parameter = inspect.Parameter(_name,
+                                          inspect.Parameter.KEYWORD_ONLY,
+                                          default='propagate')
+
+_name = 'keepdims'
+_type = "bool, default: False"
+_desc = (
+    """If this is set to True, the axes which are reduced are left
+in the result as dimensions with size one. With this option,
+the result will broadcast correctly against the input array."""
+    .split('\n'))
+_keepdims_parameter_doc = Parameter(_name, _type, _desc)
+_keepdims_parameter = inspect.Parameter(_name,
+                                        inspect.Parameter.KEYWORD_ONLY,
+                                        default=False)
+
+_standard_note_addition = (
+    """\nBeginning in SciPy 1.9, ``np.matrix`` inputs (not recommended for new
+code) are converted to ``np.ndarray`` before the calculation is performed. In
+this case, the output will be a scalar or ``np.ndarray`` of appropriate shape
+rather than a 2D ``np.matrix``. Similarly, while masked elements of masked
+arrays are ignored, the output will be a scalar or ``np.ndarray`` rather than a
+masked array with ``mask=False``.""").split('\n')
+
+
+def _axis_nan_policy_factory(tuple_to_result, default_axis=0,
+                             n_samples=1, paired=False,
+                             result_to_tuple=None, too_small=0,
+                             n_outputs=2, kwd_samples=(), override=None):
+    """Factory for a wrapper that adds axis/nan_policy params to a function.
+
+    Parameters
+    ----------
+    tuple_to_result : callable
+        Callable that returns an object of the type returned by the function
+        being wrapped (e.g. the namedtuple or dataclass returned by a
+        statistical test) provided the separate components (e.g. statistic,
+        pvalue).
+    default_axis : int, default: 0
+        The default value of the axis argument. Standard is 0 except when
+        backwards compatibility demands otherwise (e.g. `None`).
+    n_samples : int or callable, default: 1
+        The number of data samples accepted by the function
+        (e.g. `mannwhitneyu`), a callable that accepts a dictionary of
+        parameters passed into the function and returns the number of data
+        samples (e.g. `wilcoxon`), or `None` to indicate an arbitrary number
+        of samples (e.g. `kruskal`).
+    paired : {False, True}
+        Whether the function being wrapped treats the samples as paired (i.e.
+        corresponding elements of each sample should be considered as different
+        components of the same sample.)
+    result_to_tuple : callable, optional
+        Function that unpacks the results of the function being wrapped into
+        a tuple. This is essentially the inverse of `tuple_to_result`. Default
+        is `None`, which is appropriate for statistical tests that return a
+        statistic, pvalue tuple (rather than, e.g., a non-iterable dataclass).
+    too_small : int or callable, default: 0
+        The largest unacceptably small sample for the function being wrapped.
+        For example, some functions require samples of size two or more or they
+        raise an error. This argument prevents the error from being raised when
+        input is not 1D and instead places a NaN in the corresponding element
+        of the result. If callable, it must accept a list of samples, axis,
+        and a dictionary of keyword arguments passed to the wrapper function as
+        arguments and return a bool indicating whether the samples passed are
+        too small.
+    n_outputs : int or callable, default: 2
+        The number of outputs produced by the function given 1d sample(s). For
+        example, hypothesis tests that return a namedtuple or result object
+        with attributes ``statistic`` and ``pvalue`` use the default
+        ``n_outputs=2``; summary statistics with scalar output use
+        ``n_outputs=1``. Alternatively, may be a callable that accepts a
+        dictionary of arguments passed into the wrapped function and returns
+        the number of outputs corresponding with those arguments.
+    kwd_samples : sequence, default: ()
+        The names of keyword parameters that should be treated as samples. For
+        example, `gmean` accepts as its first argument a sample `a` but
+        also `weights` as a fourth, optional keyword argument. In this case, we
+        use `n_samples=1` and kwd_samples=['weights'].
+    override : dict, default: {'vectorization': False, 'nan_propagation': True}
+        Pass a dictionary with ``'vectorization': True`` to ensure that the
+        decorator overrides the function's behavior for multimensional input.
+        Use ``'nan_propagation': False`` to ensure that the decorator does not
+        override the function's behavior for ``nan_policy='propagate'``.
+    """
+    # Specify which existing behaviors the decorator must override
+    temp = override or {}
+    override = {'vectorization': False,
+                'nan_propagation': True}
+    override.update(temp)
+
+    if result_to_tuple is None:
+        def result_to_tuple(res, _):
+            return res
+
+    if not callable(too_small):
+        def is_too_small(samples, *ts_args, axis=-1, **ts_kwargs):
+            for sample in samples:
+                if sample.shape[axis] <= too_small:
+                    return True
+            return False
+    else:
+        is_too_small = too_small
+
+    def axis_nan_policy_decorator(hypotest_fun_in):
+        @wraps(hypotest_fun_in)
+        def axis_nan_policy_wrapper(*args, _no_deco=False, **kwds):
+
+            if _no_deco:  # for testing, decorator does nothing
+                return hypotest_fun_in(*args, **kwds)
+
+            # For now, skip the decorator entirely if using array API. In the future,
+            # we'll probably want to use it for `keepdims`, `axis` tuples, etc.
+            if len(args) == 0:  # extract sample from `kwds` if there are no `args`
+                used_kwd_samples = list(set(kwds).intersection(set(kwd_samples)))
+                temp = used_kwd_samples[:1]
+            else:
+                temp = args[0]
+
+            if is_dask(array_namespace(temp)):
+                msg = ("Use of `nan_policy` and `keepdims` "
+                       "is incompatible with lazy arrays.")
+                if 'nan_policy' in kwds or 'keepdims' in kwds:
+                    raise NotImplementedError(msg)
+                return hypotest_fun_in(*args, **kwds)
+
+            # We need to be flexible about whether position or keyword
+            # arguments are used, but we need to make sure users don't pass
+            # both for the same parameter. To complicate matters, some
+            # functions accept samples with *args, and some functions already
+            # accept `axis` and `nan_policy` as positional arguments.
+            # The strategy is to make sure that there is no duplication
+            # between `args` and `kwds`, combine the two into `kwds`, then
+            # the samples, `nan_policy`, and `axis` from `kwds`, as they are
+            # dealt with separately.
+
+            # Check for intersection between positional and keyword args
+            params = list(inspect.signature(hypotest_fun_in).parameters)
+            if n_samples is None:
+                # Give unique names to each positional sample argument
+                # Note that *args can't be provided as a keyword argument
+                params = [f"arg{i}" for i in range(len(args))] + params[1:]
+
+            # raise if there are too many positional args
+            maxarg = (np.inf if inspect.getfullargspec(hypotest_fun_in).varargs
+                      else len(inspect.getfullargspec(hypotest_fun_in).args))
+            if len(args) > maxarg:  # let the function raise the right error
+                hypotest_fun_in(*args, **kwds)
+
+            # raise if multiple values passed for same parameter
+            d_args = dict(zip(params, args))
+            intersection = set(d_args) & set(kwds)
+            if intersection:  # let the function raise the right error
+                hypotest_fun_in(*args, **kwds)
+
+            # Consolidate other positional and keyword args into `kwds`
+            kwds.update(d_args)
+
+            # rename avoids UnboundLocalError
+            if callable(n_samples):
+                # Future refactoring idea: no need for callable n_samples.
+                # Just replace `n_samples` and `kwd_samples` with a single
+                # list of the names of all samples, and treat all of them
+                # as `kwd_samples` are treated below.
+                n_samp = n_samples(kwds)
+            else:
+                n_samp = n_samples or len(args)
+
+            # get the number of outputs
+            n_out = n_outputs  # rename to avoid UnboundLocalError
+            if callable(n_out):
+                n_out = n_out(kwds)
+
+            # If necessary, rearrange function signature: accept other samples
+            # as positional args right after the first n_samp args
+            kwd_samp = [name for name in kwd_samples
+                        if kwds.get(name, None) is not None]
+            n_kwd_samp = len(kwd_samp)
+            if not kwd_samp:
+                hypotest_fun_out = hypotest_fun_in
+            else:
+                def hypotest_fun_out(*samples, **kwds):
+                    new_kwds = dict(zip(kwd_samp, samples[n_samp:]))
+                    kwds.update(new_kwds)
+                    return hypotest_fun_in(*samples[:n_samp], **kwds)
+
+            # Extract the things we need here
+            try:  # if something is missing
+                samples = [kwds.pop(param) for param in (params[:n_samp] + kwd_samp)]
+                xp = array_namespace(*samples)
+                samples = xp_promote(*samples, xp=xp)
+                samples = (samples,) if not isinstance(samples, tuple) else samples
+                samples = [xpx.atleast_nd(sample, ndim=1) for sample in samples]
+            except KeyError:  # let the function raise the right error
+                # might need to revisit this if required arg is not a "sample"
+                hypotest_fun_in(*args, **kwds)
+            vectorized = True if 'axis' in params else False
+            vectorized = vectorized and not override['vectorization']
+            axis = kwds.pop('axis', default_axis)
+            nan_policy = kwds.pop('nan_policy', 'propagate')
+            keepdims = kwds.pop("keepdims", False)
+            del args  # avoid the possibility of passing both `args` and `kwds`
+
+            # convert masked arrays to regular arrays with sentinel values
+            sentinel = None
+            if is_numpy(xp):
+                samples, sentinel = _masked_arrays_2_sentinel_arrays(samples)
+
+            # standardize to always work along last axis
+            reduced_axes = axis
+            if axis is None:
+                if samples:
+                    # when axis=None, take the maximum of all dimensions since
+                    # all the dimensions are reduced.
+                    n_dims = max([xp.asarray(sample).ndim for sample in samples])
+                    reduced_axes = tuple(range(n_dims))
+                samples = [xp_ravel(sample) for sample in samples]
+            else:
+                # don't ignore any axes when broadcasting if paired
+                samples = _broadcast_arrays(samples, axis=axis if not paired else None)
+                axis = (axis,) if np.isscalar(axis) else axis
+                n_axes = len(axis)
+                # move all axes in `axis` to the end to be raveled
+                samples = [xp.moveaxis(sample, axis, tuple(range(-len(axis), 0)))
+                           for sample in samples]
+                shapes = [sample.shape for sample in samples]
+                # New shape is unchanged for all axes _not_ in `axis`
+                # At the end, we append the product of the shapes of the axes
+                # in `axis`. Appending -1 doesn't work for zero-size arrays!
+                new_shapes = [shape[:-n_axes] + (math.prod(shape[-n_axes:]),)
+                              for shape in shapes]
+                samples = [xp.reshape(sample, new_shape)
+                           for sample, new_shape in zip(samples, new_shapes)]
+            axis = -1  # work over the last axis
+
+            NaN = _get_nan(*samples) if samples else xp.nan
+
+            # if axis is not needed, just handle nan_policy and return
+            ndims = np.array([sample.ndim for sample in samples])  # NumPy OK for ndims
+            if np.all(ndims <= 1):
+                # Addresses nan_policy == "raise"
+                if nan_policy != 'propagate' or override['nan_propagation']:
+                    contains_nan = [_contains_nan(sample, nan_policy)
+                                    for sample in samples]
+                else:
+                    # Behave as though there are no NaNs (even if there are)
+                    contains_nan = [False] * len(samples)
+
+                # To give JAX most benefits of the `_axis_nan_policy` decorator without
+                # value-dependent branching, the decorator will always treat JAX arrays
+                # as if there are no NaNs. Typically, this means that NaNs will
+                # multidimensional naturally. However, there may be cases in which this
+                # doesn't produce the desired result, so for now, JAX users should
+                # treat all functions as though there is no explicit`nan_policy`.
+                # Future work tracked in gh-14651.
+                any_contains_nan = not is_jax(xp) and any(contains_nan)
+                # Addresses nan_policy == "propagate"
+                if any_contains_nan and (nan_policy == 'propagate'
+                                         and override['nan_propagation']):
+                    res = xp.full(n_out, xp.nan, dtype=NaN.dtype)
+                    res = _add_reduced_axes(res, reduced_axes, keepdims)
+                    return tuple_to_result(*res)
+
+                # Addresses nan_policy == "omit"
+                too_small_msg = too_small_1d_not_omit
+                if any_contains_nan and nan_policy == 'omit':
+                    # consider passing in contains_nan
+                    samples = _remove_nans(samples, paired)
+                    too_small_msg = too_small_1d_omit
+
+                if sentinel:
+                    samples = _remove_sentinel(samples, paired, sentinel)
+
+                if is_too_small(samples, kwds):
+                    warnings.warn(too_small_msg, SmallSampleWarning, stacklevel=2)
+                    res = xp.full(n_out, xp.nan, dtype=NaN.dtype)
+                    res = _add_reduced_axes(res, reduced_axes, keepdims)
+                    return tuple_to_result(*res)
+
+                res = hypotest_fun_out(*samples, **kwds)
+                res = result_to_tuple(res, n_out)
+                res = _add_reduced_axes(res, reduced_axes, keepdims)
+                return tuple_to_result(*res)
+
+            # check for empty input
+            empty_output = _check_empty_inputs(samples, axis, xp=xp)
+            # only return empty output if zero sized input is too small.
+            if (
+                empty_output is not None
+                and (is_too_small(samples, kwds) or xp_size(empty_output) == 0)
+            ):
+                if is_too_small(samples, kwds) and xp_size(empty_output) != 0:
+                    warnings.warn(too_small_nd_not_omit, SmallSampleWarning,
+                                  stacklevel=2)
+                res = [xp_copy(empty_output) for i in range(n_out)]
+                res = _add_reduced_axes(res, reduced_axes, keepdims)
+                return tuple_to_result(*res)
+
+            if not is_numpy(xp) and 'nan_policy' in kwds:
+                msg = ("Use of `nan_policy` is incompatible with multidimensional "
+                       "non-NumPy arrays.")
+                raise NotImplementedError(msg)
+
+            if not is_numpy(xp):
+                res = hypotest_fun_out(*samples, axis=axis, **kwds)
+                res = result_to_tuple(res, n_out)
+                res = _add_reduced_axes(res, reduced_axes, keepdims, xp=xp)
+                return tuple_to_result(*res)
+
+            # otherwise, concatenate all samples along axis, remembering where
+            # each separate sample begins
+            lengths = np.array([sample.shape[axis] for sample in samples])
+            split_indices = np.cumsum(lengths)
+            x = _broadcast_concatenate(samples, axis, paired=paired)
+
+            # Addresses nan_policy == "raise"
+            if nan_policy != 'propagate' or override['nan_propagation']:
+                contains_nan = _contains_nan(x, nan_policy)
+            else:
+                contains_nan = False  # behave like there are no NaNs
+
+            if vectorized and not contains_nan and not sentinel:
+                res = hypotest_fun_out(*samples, axis=axis, **kwds)
+                res = result_to_tuple(res, n_out)
+                res = _add_reduced_axes(res, reduced_axes, keepdims)
+                return tuple_to_result(*res)
+
+            # Addresses nan_policy == "omit"
+            if contains_nan and nan_policy == 'omit':
+                def hypotest_fun(x):
+                    samples = np.split(x, split_indices)[:n_samp+n_kwd_samp]
+                    samples = _remove_nans(samples, paired)
+                    if sentinel:
+                        samples = _remove_sentinel(samples, paired, sentinel)
+                    if is_too_small(samples, kwds):
+                        warnings.warn(too_small_nd_omit, SmallSampleWarning,
+                                      stacklevel=4)
+                        return np.full(n_out, NaN)
+                    return result_to_tuple(hypotest_fun_out(*samples, **kwds), n_out)
+
+            # Addresses nan_policy == "propagate"
+            elif (contains_nan and nan_policy == 'propagate'
+                  and override['nan_propagation']):
+                def hypotest_fun(x):
+                    if np.isnan(x).any():
+                        return np.full(n_out, NaN)
+
+                    samples = np.split(x, split_indices)[:n_samp+n_kwd_samp]
+                    if sentinel:
+                        samples = _remove_sentinel(samples, paired, sentinel)
+                    if is_too_small(samples, kwds):
+                        return np.full(n_out, NaN)
+                    return result_to_tuple(hypotest_fun_out(*samples, **kwds), n_out)
+
+            else:
+                def hypotest_fun(x):
+                    samples = np.split(x, split_indices)[:n_samp+n_kwd_samp]
+                    if sentinel:
+                        samples = _remove_sentinel(samples, paired, sentinel)
+                    if is_too_small(samples, kwds):
+                        return np.full(n_out, NaN)
+                    return result_to_tuple(hypotest_fun_out(*samples, **kwds), n_out)
+
+            x = np.moveaxis(x, axis, 0)
+            res = np.apply_along_axis(hypotest_fun, axis=0, arr=x)
+            res = _add_reduced_axes(res, reduced_axes, keepdims)
+            return tuple_to_result(*res)
+
+        _axis_parameter_doc, _axis_parameter = _get_axis_params(default_axis)
+        doc = FunctionDoc(axis_nan_policy_wrapper)
+        parameter_names = [param.name for param in doc['Parameters']]
+        if 'axis' in parameter_names:
+            doc['Parameters'][parameter_names.index('axis')] = (
+                _axis_parameter_doc)
+        else:
+            doc['Parameters'].append(_axis_parameter_doc)
+        if 'nan_policy' in parameter_names:
+            doc['Parameters'][parameter_names.index('nan_policy')] = (
+                _nan_policy_parameter_doc)
+        else:
+            doc['Parameters'].append(_nan_policy_parameter_doc)
+        if 'keepdims' in parameter_names:
+            doc['Parameters'][parameter_names.index('keepdims')] = (
+                _keepdims_parameter_doc)
+        else:
+            doc['Parameters'].append(_keepdims_parameter_doc)
+        doc['Notes'] += _standard_note_addition
+        doc = str(doc).split("\n", 1)[1].lstrip(" \n")  # remove signature
+        axis_nan_policy_wrapper.__doc__ = str(doc)
+
+        sig = inspect.signature(axis_nan_policy_wrapper)
+        parameters = sig.parameters
+        parameter_list = list(parameters.values())
+        if 'axis' not in parameters:
+            parameter_list.append(_axis_parameter)
+        if 'nan_policy' not in parameters:
+            parameter_list.append(_nan_policy_parameter)
+        if 'keepdims' not in parameters:
+            parameter_list.append(_keepdims_parameter)
+        sig = sig.replace(parameters=parameter_list)
+        axis_nan_policy_wrapper.__signature__ = sig
+
+        return axis_nan_policy_wrapper
+    return axis_nan_policy_decorator
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_biasedurn.cpython-312-x86_64-linux-gnu.so b/venv/lib/python3.12/site-packages/scipy/stats/_biasedurn.cpython-312-x86_64-linux-gnu.so
new file mode 100644
index 0000000000000000000000000000000000000000..ad1fd20250ade99c557428e4f19cb1189c72dc8c
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_biasedurn.cpython-312-x86_64-linux-gnu.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:5de2fd26b29b90c9e3090f1b0b738782f601b92222ba94d9cb6a4b1a898b46c5
+size 239008
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_biasedurn.pxd b/venv/lib/python3.12/site-packages/scipy/stats/_biasedurn.pxd
new file mode 100644
index 0000000000000000000000000000000000000000..92785f08dbec30a4db286fcb85b42d7221e2228e
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_biasedurn.pxd
@@ -0,0 +1,27 @@
+# Declare the class with cdef
+cdef extern from "biasedurn/stocc.h" nogil:
+    cdef cppclass CFishersNCHypergeometric:
+        CFishersNCHypergeometric(int, int, int, double, double) except +
+        int mode()
+        double mean()
+        double variance()
+        double probability(int x)
+        double moments(double * mean, double * var)
+
+    cdef cppclass CWalleniusNCHypergeometric:
+        CWalleniusNCHypergeometric() except +
+        CWalleniusNCHypergeometric(int, int, int, double, double) except +
+        int mode()
+        double mean()
+        double variance()
+        double probability(int x)
+        double moments(double * mean, double * var)
+
+    cdef cppclass StochasticLib3:
+        StochasticLib3(int seed) except +
+        double Random() except +
+        void SetAccuracy(double accur)
+        int FishersNCHyp (int n, int m, int N, double odds) except +
+        int WalleniusNCHyp (int n, int m, int N, double odds) except +
+        double(*next_double)()
+        double(*next_normal)(const double m, const double s)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_binned_statistic.py b/venv/lib/python3.12/site-packages/scipy/stats/_binned_statistic.py
new file mode 100644
index 0000000000000000000000000000000000000000..5a11a1caa4bc48d2e6a0a42793f79635a3e58d36
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_binned_statistic.py
@@ -0,0 +1,806 @@
+import builtins
+from warnings import catch_warnings, simplefilter
+import numpy as np
+from operator import index
+from collections import namedtuple
+
+from scipy._lib._array_api import xp_capabilities
+
+__all__ = ['binned_statistic',
+           'binned_statistic_2d',
+           'binned_statistic_dd']
+
+
+BinnedStatisticResult = namedtuple('BinnedStatisticResult',
+                                   ('statistic', 'bin_edges', 'binnumber'))
+
+
+@xp_capabilities(np_only=True)
+def binned_statistic(x, values, statistic='mean',
+                     bins=10, range=None):
+    """
+    Compute a binned statistic for one or more sets of data.
+
+    This is a generalization of a histogram function.  A histogram divides
+    the space into bins, and returns the count of the number of points in
+    each bin.  This function allows the computation of the sum, mean, median,
+    or other statistic of the values (or set of values) within each bin.
+
+    Parameters
+    ----------
+    x : (N,) array_like
+        A sequence of values to be binned.
+    values : (N,) array_like or list of (N,) array_like
+        The data on which the statistic will be computed.  This must be
+        the same shape as `x`, or a set of sequences - each the same shape as
+        `x`.  If `values` is a set of sequences, the statistic will be computed
+        on each independently.
+    statistic : str or callable, optional
+        The statistic to compute (default is 'mean').
+        The following statistics are available:
+
+        * 'mean' : compute the mean of values for points within each bin.
+          Empty bins will be represented by NaN.
+        * 'std' : compute the standard deviation within each bin. This
+          is implicitly calculated with ddof=0.
+        * 'median' : compute the median of values for points within each
+          bin. Empty bins will be represented by NaN.
+        * 'count' : compute the count of points within each bin.  This is
+          identical to an unweighted histogram.  `values` array is not
+          referenced.
+        * 'sum' : compute the sum of values for points within each bin.
+          This is identical to a weighted histogram.
+        * 'min' : compute the minimum of values for points within each bin.
+          Empty bins will be represented by NaN.
+        * 'max' : compute the maximum of values for point within each bin.
+          Empty bins will be represented by NaN.
+        * function : a user-defined function which takes a 1D array of
+          values, and outputs a single numerical statistic. This function
+          will be called on the values in each bin.  Empty bins will be
+          represented by function([]), or NaN if this returns an error.
+
+    bins : int or sequence of scalars, optional
+        If `bins` is an int, it defines the number of equal-width bins in the
+        given range (10 by default).  If `bins` is a sequence, it defines the
+        bin edges, including the rightmost edge, allowing for non-uniform bin
+        widths.  Values in `x` that are smaller than lowest bin edge are
+        assigned to bin number 0, values beyond the highest bin are assigned to
+        ``bins[-1]``.  If the bin edges are specified, the number of bins will
+        be, (nx = len(bins)-1).
+    range : (float, float) or [(float, float)], optional
+        The lower and upper range of the bins.  If not provided, range
+        is simply ``(x.min(), x.max())``.  Values outside the range are
+        ignored.
+
+    Returns
+    -------
+    statistic : array
+        The values of the selected statistic in each bin.
+    bin_edges : array of dtype float
+        Return the bin edges ``(length(statistic)+1)``.
+    binnumber: 1-D ndarray of ints
+        Indices of the bins (corresponding to `bin_edges`) in which each value
+        of `x` belongs.  Same length as `values`.  A binnumber of `i` means the
+        corresponding value is between (bin_edges[i-1], bin_edges[i]).
+
+    See Also
+    --------
+    numpy.digitize, numpy.histogram, binned_statistic_2d, binned_statistic_dd
+
+    Notes
+    -----
+    All but the last (righthand-most) bin is half-open.  In other words, if
+    `bins` is ``[1, 2, 3, 4]``, then the first bin is ``[1, 2)`` (including 1,
+    but excluding 2) and the second ``[2, 3)``.  The last bin, however, is
+    ``[3, 4]``, which *includes* 4.
+
+    .. versionadded:: 0.11.0
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> import matplotlib.pyplot as plt
+
+    First some basic examples:
+
+    Create two evenly spaced bins in the range of the given sample, and sum the
+    corresponding values in each of those bins:
+
+    >>> values = [1.0, 1.0, 2.0, 1.5, 3.0]
+    >>> stats.binned_statistic([1, 1, 2, 5, 7], values, 'sum', bins=2)
+    BinnedStatisticResult(statistic=array([4. , 4.5]),
+            bin_edges=array([1., 4., 7.]), binnumber=array([1, 1, 1, 2, 2]))
+
+    Multiple arrays of values can also be passed.  The statistic is calculated
+    on each set independently:
+
+    >>> values = [[1.0, 1.0, 2.0, 1.5, 3.0], [2.0, 2.0, 4.0, 3.0, 6.0]]
+    >>> stats.binned_statistic([1, 1, 2, 5, 7], values, 'sum', bins=2)
+    BinnedStatisticResult(statistic=array([[4. , 4.5],
+           [8. , 9. ]]), bin_edges=array([1., 4., 7.]),
+           binnumber=array([1, 1, 1, 2, 2]))
+
+    >>> stats.binned_statistic([1, 2, 1, 2, 4], np.arange(5), statistic='mean',
+    ...                        bins=3)
+    BinnedStatisticResult(statistic=array([1., 2., 4.]),
+            bin_edges=array([1., 2., 3., 4.]),
+            binnumber=array([1, 2, 1, 2, 3]))
+
+    As a second example, we now generate some random data of sailing boat speed
+    as a function of wind speed, and then determine how fast our boat is for
+    certain wind speeds:
+
+    >>> rng = np.random.default_rng()
+    >>> windspeed = 8 * rng.random(500)
+    >>> boatspeed = .3 * windspeed**.5 + .2 * rng.random(500)
+    >>> bin_means, bin_edges, binnumber = stats.binned_statistic(windspeed,
+    ...                 boatspeed, statistic='median', bins=[1,2,3,4,5,6,7])
+    >>> plt.figure()
+    >>> plt.plot(windspeed, boatspeed, 'b.', label='raw data')
+    >>> plt.hlines(bin_means, bin_edges[:-1], bin_edges[1:], colors='g', lw=5,
+    ...            label='binned statistic of data')
+    >>> plt.legend()
+
+    Now we can use ``binnumber`` to select all datapoints with a windspeed
+    below 1:
+
+    >>> low_boatspeed = boatspeed[binnumber == 0]
+
+    As a final example, we will use ``bin_edges`` and ``binnumber`` to make a
+    plot of a distribution that shows the mean and distribution around that
+    mean per bin, on top of a regular histogram and the probability
+    distribution function:
+
+    >>> x = np.linspace(0, 5, num=500)
+    >>> x_pdf = stats.maxwell.pdf(x)
+    >>> samples = stats.maxwell.rvs(size=10000)
+
+    >>> bin_means, bin_edges, binnumber = stats.binned_statistic(x, x_pdf,
+    ...         statistic='mean', bins=25)
+    >>> bin_width = (bin_edges[1] - bin_edges[0])
+    >>> bin_centers = bin_edges[1:] - bin_width/2
+
+    >>> plt.figure()
+    >>> plt.hist(samples, bins=50, density=True, histtype='stepfilled',
+    ...          alpha=0.2, label='histogram of data')
+    >>> plt.plot(x, x_pdf, 'r-', label='analytical pdf')
+    >>> plt.hlines(bin_means, bin_edges[:-1], bin_edges[1:], colors='g', lw=2,
+    ...            label='binned statistic of data')
+    >>> plt.plot((binnumber - 0.5) * bin_width, x_pdf, 'g.', alpha=0.5)
+    >>> plt.legend(fontsize=10)
+    >>> plt.show()
+
+    """
+    try:
+        N = len(bins)
+    except TypeError:
+        N = 1
+
+    if N != 1:
+        bins = [np.asarray(bins, float)]
+
+    if range is not None:
+        if len(range) == 2:
+            range = [range]
+
+    medians, edges, binnumbers = binned_statistic_dd(
+        [x], values, statistic, bins, range)
+
+    return BinnedStatisticResult(medians, edges[0], binnumbers)
+
+
+BinnedStatistic2dResult = namedtuple('BinnedStatistic2dResult',
+                                     ('statistic', 'x_edge', 'y_edge',
+                                      'binnumber'))
+
+
+@xp_capabilities(np_only=True)
+def binned_statistic_2d(x, y, values, statistic='mean',
+                        bins=10, range=None, expand_binnumbers=False):
+    """
+    Compute a bidimensional binned statistic for one or more sets of data.
+
+    This is a generalization of a histogram2d function.  A histogram divides
+    the space into bins, and returns the count of the number of points in
+    each bin.  This function allows the computation of the sum, mean, median,
+    or other statistic of the values (or set of values) within each bin.
+
+    Parameters
+    ----------
+    x : (N,) array_like
+        A sequence of values to be binned along the first dimension.
+    y : (N,) array_like
+        A sequence of values to be binned along the second dimension.
+    values : (N,) array_like or list of (N,) array_like
+        The data on which the statistic will be computed.  This must be
+        the same shape as `x`, or a list of sequences - each with the same
+        shape as `x`.  If `values` is such a list, the statistic will be
+        computed on each independently.
+    statistic : str or callable, optional
+        The statistic to compute (default is 'mean').
+        The following statistics are available:
+
+        * 'mean' : compute the mean of values for points within each bin.
+          Empty bins will be represented by NaN.
+        * 'std' : compute the standard deviation within each bin. This
+          is implicitly calculated with ddof=0.
+        * 'median' : compute the median of values for points within each
+          bin. Empty bins will be represented by NaN.
+        * 'count' : compute the count of points within each bin.  This is
+          identical to an unweighted histogram.  `values` array is not
+          referenced.
+        * 'sum' : compute the sum of values for points within each bin.
+          This is identical to a weighted histogram.
+        * 'min' : compute the minimum of values for points within each bin.
+          Empty bins will be represented by NaN.
+        * 'max' : compute the maximum of values for point within each bin.
+          Empty bins will be represented by NaN.
+        * function : a user-defined function which takes a 1D array of
+          values, and outputs a single numerical statistic. This function
+          will be called on the values in each bin.  Empty bins will be
+          represented by function([]), or NaN if this returns an error.
+
+    bins : int or [int, int] or array_like or [array, array], optional
+        The bin specification:
+
+        * the number of bins for the two dimensions (nx = ny = bins),
+        * the number of bins in each dimension (nx, ny = bins),
+        * the bin edges for the two dimensions (x_edge = y_edge = bins),
+        * the bin edges in each dimension (x_edge, y_edge = bins).
+
+        If the bin edges are specified, the number of bins will be,
+        (nx = len(x_edge)-1, ny = len(y_edge)-1).
+
+    range : (2,2) array_like, optional
+        The leftmost and rightmost edges of the bins along each dimension
+        (if not specified explicitly in the `bins` parameters):
+        [[xmin, xmax], [ymin, ymax]]. All values outside of this range will be
+        considered outliers and not tallied in the histogram.
+    expand_binnumbers : bool, optional
+        'False' (default): the returned `binnumber` is a shape (N,) array of
+        linearized bin indices.
+        'True': the returned `binnumber` is 'unraveled' into a shape (2,N)
+        ndarray, where each row gives the bin numbers in the corresponding
+        dimension.
+        See the `binnumber` returned value, and the `Examples` section.
+
+        .. versionadded:: 0.17.0
+
+    Returns
+    -------
+    statistic : (nx, ny) ndarray
+        The values of the selected statistic in each two-dimensional bin.
+    x_edge : (nx + 1) ndarray
+        The bin edges along the first dimension.
+    y_edge : (ny + 1) ndarray
+        The bin edges along the second dimension.
+    binnumber : (N,) array of ints or (2,N) ndarray of ints
+        This assigns to each element of `sample` an integer that represents the
+        bin in which this observation falls.  The representation depends on the
+        `expand_binnumbers` argument.  See `Notes` for details.
+
+
+    See Also
+    --------
+    numpy.digitize, numpy.histogram2d, binned_statistic, binned_statistic_dd
+
+    Notes
+    -----
+    Binedges:
+    All but the last (righthand-most) bin is half-open.  In other words, if
+    `bins` is ``[1, 2, 3, 4]``, then the first bin is ``[1, 2)`` (including 1,
+    but excluding 2) and the second ``[2, 3)``.  The last bin, however, is
+    ``[3, 4]``, which *includes* 4.
+
+    `binnumber`:
+    This returned argument assigns to each element of `sample` an integer that
+    represents the bin in which it belongs.  The representation depends on the
+    `expand_binnumbers` argument. If 'False' (default): The returned
+    `binnumber` is a shape (N,) array of linearized indices mapping each
+    element of `sample` to its corresponding bin (using row-major ordering).
+    Note that the returned linearized bin indices are used for an array with
+    extra bins on the outer binedges to capture values outside of the defined
+    bin bounds.
+    If 'True': The returned `binnumber` is a shape (2,N) ndarray where
+    each row indicates bin placements for each dimension respectively.  In each
+    dimension, a binnumber of `i` means the corresponding value is between
+    (D_edge[i-1], D_edge[i]), where 'D' is either 'x' or 'y'.
+
+    .. versionadded:: 0.11.0
+
+    Examples
+    --------
+    >>> from scipy import stats
+
+    Calculate the counts with explicit bin-edges:
+
+    >>> x = [0.1, 0.1, 0.1, 0.6]
+    >>> y = [2.1, 2.6, 2.1, 2.1]
+    >>> binx = [0.0, 0.5, 1.0]
+    >>> biny = [2.0, 2.5, 3.0]
+    >>> ret = stats.binned_statistic_2d(x, y, None, 'count', bins=[binx, biny])
+    >>> ret.statistic
+    array([[2., 1.],
+           [1., 0.]])
+
+    The bin in which each sample is placed is given by the `binnumber`
+    returned parameter.  By default, these are the linearized bin indices:
+
+    >>> ret.binnumber
+    array([5, 6, 5, 9])
+
+    The bin indices can also be expanded into separate entries for each
+    dimension using the `expand_binnumbers` parameter:
+
+    >>> ret = stats.binned_statistic_2d(x, y, None, 'count', bins=[binx, biny],
+    ...                                 expand_binnumbers=True)
+    >>> ret.binnumber
+    array([[1, 1, 1, 2],
+           [1, 2, 1, 1]])
+
+    Which shows that the first three elements belong in the xbin 1, and the
+    fourth into xbin 2; and so on for y.
+
+    """
+
+    # This code is based on np.histogram2d
+    try:
+        N = len(bins)
+    except TypeError:
+        N = 1
+
+    if N != 1 and N != 2:
+        xedges = yedges = np.asarray(bins, float)
+        bins = [xedges, yedges]
+
+    medians, edges, binnumbers = binned_statistic_dd(
+        [x, y], values, statistic, bins, range,
+        expand_binnumbers=expand_binnumbers)
+
+    return BinnedStatistic2dResult(medians, edges[0], edges[1], binnumbers)
+
+
+BinnedStatisticddResult = namedtuple('BinnedStatisticddResult',
+                                     ('statistic', 'bin_edges',
+                                      'binnumber'))
+
+
+def _bincount(x, weights):
+    if np.iscomplexobj(weights):
+        a = np.bincount(x, np.real(weights))
+        b = np.bincount(x, np.imag(weights))
+        z = a + b*1j
+
+    else:
+        z = np.bincount(x, weights)
+    return z
+
+
+@xp_capabilities(np_only=True)
+def binned_statistic_dd(sample, values, statistic='mean',
+                        bins=10, range=None, expand_binnumbers=False,
+                        binned_statistic_result=None):
+    """
+    Compute a multidimensional binned statistic for a set of data.
+
+    This is a generalization of a histogramdd function.  A histogram divides
+    the space into bins, and returns the count of the number of points in
+    each bin.  This function allows the computation of the sum, mean, median,
+    or other statistic of the values within each bin.
+
+    Parameters
+    ----------
+    sample : array_like
+        Data to histogram passed as a sequence of N arrays of length D, or
+        as an (N,D) array.
+    values : (N,) array_like or list of (N,) array_like
+        The data on which the statistic will be computed.  This must be
+        the same shape as `sample`, or a list of sequences - each with the
+        same shape as `sample`.  If `values` is such a list, the statistic
+        will be computed on each independently.
+    statistic : str or callable, optional
+        The statistic to compute (default is 'mean').
+        The following statistics are available:
+
+        * 'mean' : compute the mean of values for points within each bin.
+          Empty bins will be represented by NaN.
+        * 'median' : compute the median of values for points within each
+          bin. Empty bins will be represented by NaN.
+        * 'count' : compute the count of points within each bin.  This is
+          identical to an unweighted histogram.  `values` array is not
+          referenced.
+        * 'sum' : compute the sum of values for points within each bin.
+          This is identical to a weighted histogram.
+        * 'std' : compute the standard deviation within each bin. This
+          is implicitly calculated with ddof=0. If the number of values
+          within a given bin is 0 or 1, the computed standard deviation value
+          will be 0 for the bin.
+        * 'min' : compute the minimum of values for points within each bin.
+          Empty bins will be represented by NaN.
+        * 'max' : compute the maximum of values for point within each bin.
+          Empty bins will be represented by NaN.
+        * function : a user-defined function which takes a 1D array of
+          values, and outputs a single numerical statistic. This function
+          will be called on the values in each bin.  Empty bins will be
+          represented by function([]), or NaN if this returns an error.
+
+    bins : sequence or positive int, optional
+        The bin specification must be in one of the following forms:
+
+        * A sequence of arrays describing the bin edges along each dimension.
+        * The number of bins for each dimension (nx, ny, ... = bins).
+        * The number of bins for all dimensions (nx = ny = ... = bins).
+
+    range : sequence, optional
+        A sequence of lower and upper bin edges to be used if the edges are
+        not given explicitly in `bins`. Defaults to the minimum and maximum
+        values along each dimension.
+    expand_binnumbers : bool, optional
+        'False' (default): the returned `binnumber` is a shape (N,) array of
+        linearized bin indices.
+        'True': the returned `binnumber` is 'unraveled' into a shape (D,N)
+        ndarray, where each row gives the bin numbers in the corresponding
+        dimension.
+        See the `binnumber` returned value, and the `Examples` section of
+        `binned_statistic_2d`.
+    binned_statistic_result : binnedStatisticddResult
+        Result of a previous call to the function in order to reuse bin edges
+        and bin numbers with new values and/or a different statistic.
+        To reuse bin numbers, `expand_binnumbers` must have been set to False
+        (the default)
+
+        .. versionadded:: 0.17.0
+
+    Returns
+    -------
+    statistic : ndarray, shape(nx1, nx2, nx3,...)
+        The values of the selected statistic in each two-dimensional bin.
+    bin_edges : list of ndarrays
+        A list of D arrays describing the (nxi + 1) bin edges for each
+        dimension.
+    binnumber : (N,) array of ints or (D,N) ndarray of ints
+        This assigns to each element of `sample` an integer that represents the
+        bin in which this observation falls.  The representation depends on the
+        `expand_binnumbers` argument.  See `Notes` for details.
+
+
+    See Also
+    --------
+    numpy.digitize, numpy.histogramdd, binned_statistic, binned_statistic_2d
+
+    Notes
+    -----
+    Binedges:
+    All but the last (righthand-most) bin is half-open in each dimension.  In
+    other words, if `bins` is ``[1, 2, 3, 4]``, then the first bin is
+    ``[1, 2)`` (including 1, but excluding 2) and the second ``[2, 3)``.  The
+    last bin, however, is ``[3, 4]``, which *includes* 4.
+
+    `binnumber`:
+    This returned argument assigns to each element of `sample` an integer that
+    represents the bin in which it belongs.  The representation depends on the
+    `expand_binnumbers` argument. If 'False' (default): The returned
+    `binnumber` is a shape (N,) array of linearized indices mapping each
+    element of `sample` to its corresponding bin (using row-major ordering).
+    If 'True': The returned `binnumber` is a shape (D,N) ndarray where
+    each row indicates bin placements for each dimension respectively.  In each
+    dimension, a binnumber of `i` means the corresponding value is between
+    (bin_edges[D][i-1], bin_edges[D][i]), for each dimension 'D'.
+
+    .. versionadded:: 0.11.0
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> import matplotlib.pyplot as plt
+    >>> from mpl_toolkits.mplot3d import Axes3D
+
+    Take an array of 600 (x, y) coordinates as an example.
+    `binned_statistic_dd` can handle arrays of higher dimension `D`. But a plot
+    of dimension `D+1` is required.
+
+    >>> mu = np.array([0., 1.])
+    >>> sigma = np.array([[1., -0.5],[-0.5, 1.5]])
+    >>> multinormal = stats.multivariate_normal(mu, sigma)
+    >>> data = multinormal.rvs(size=600, random_state=235412)
+    >>> data.shape
+    (600, 2)
+
+    Create bins and count how many arrays fall in each bin:
+
+    >>> N = 60
+    >>> x = np.linspace(-3, 3, N)
+    >>> y = np.linspace(-3, 4, N)
+    >>> ret = stats.binned_statistic_dd(data, np.arange(600), bins=[x, y],
+    ...                                 statistic='count')
+    >>> bincounts = ret.statistic
+
+    Set the volume and the location of bars:
+
+    >>> dx = x[1] - x[0]
+    >>> dy = y[1] - y[0]
+    >>> x, y = np.meshgrid(x[:-1]+dx/2, y[:-1]+dy/2)
+    >>> z = 0
+
+    >>> bincounts = bincounts.ravel()
+    >>> x = x.ravel()
+    >>> y = y.ravel()
+
+    >>> fig = plt.figure()
+    >>> ax = fig.add_subplot(111, projection='3d')
+    >>> with np.errstate(divide='ignore'):   # silence random axes3d warning
+    ...     ax.bar3d(x, y, z, dx, dy, bincounts)
+
+    Reuse bin numbers and bin edges with new values:
+
+    >>> ret2 = stats.binned_statistic_dd(data, -np.arange(600),
+    ...                                  binned_statistic_result=ret,
+    ...                                  statistic='mean')
+    """
+    known_stats = ['mean', 'median', 'count', 'sum', 'std', 'min', 'max']
+    if not callable(statistic) and statistic not in known_stats:
+        raise ValueError(f'invalid statistic {statistic!r}')
+
+    try:
+        bins = index(bins)
+    except TypeError:
+        # bins is not an integer
+        pass
+    # If bins was an integer-like object, now it is an actual Python int.
+
+    # For context: see gh-23751 and linked issues/PRs
+    if np.isnan(sample).any():
+        message = ("The sample on which `values` is to be binned contains at least one "
+                   "NaN, and the meaning is ambiguous. Consider removing or replacing "
+                   "with numerical outliers.")
+        raise ValueError(message)
+
+    # `Ndim` is the number of dimensions (e.g. `2` for `binned_statistic_2d`)
+    # `Dlen` is the length of elements along each dimension.
+    # This code is based on np.histogramdd
+    try:
+        # `sample` is an ND-array.
+        Dlen, Ndim = sample.shape
+    except (AttributeError, ValueError):
+        # `sample` is a sequence of 1D arrays.
+        sample = np.atleast_2d(sample).T
+        Dlen, Ndim = sample.shape
+
+    # Store initial shape of `values` to preserve it in the output
+    values = np.asarray(values)
+    input_shape = list(values.shape)
+    # Make sure that `values` is 2D to iterate over rows
+    values = np.atleast_2d(values)
+    Vdim, Vlen = values.shape
+
+    # Make sure `values` match `sample`
+    if statistic != 'count' and Vlen != Dlen:
+        raise AttributeError('The number of `values` elements must match the '
+                             'length of each `sample` dimension.')
+
+    try:
+        M = len(bins)
+        if M != Ndim:
+            raise AttributeError('The dimension of bins must be equal '
+                                 'to the dimension of the sample x.')
+    except TypeError:
+        bins = Ndim * [bins]
+
+    if binned_statistic_result is None:
+        nbin, edges, dedges = _bin_edges(sample, bins, range)
+        binnumbers = _bin_numbers(sample, nbin, edges, dedges)
+    else:
+        edges = binned_statistic_result.bin_edges
+        nbin = np.array([len(edges[i]) + 1 for i in builtins.range(Ndim)])
+        # +1 for outlier bins
+        dedges = [np.diff(edges[i]) for i in builtins.range(Ndim)]
+        binnumbers = binned_statistic_result.binnumber
+
+    # Avoid overflow with double precision. Complex `values` -> `complex128`.
+    result_type = np.result_type(values, np.float64)
+    result = np.empty([Vdim, nbin.prod()], dtype=result_type)
+
+    if statistic in {'mean', np.mean}:
+        result.fill(np.nan)
+        flatcount = _bincount(binnumbers, None)
+        a = flatcount.nonzero()
+        for vv in builtins.range(Vdim):
+            flatsum = _bincount(binnumbers, values[vv])
+            result[vv, a] = flatsum[a] / flatcount[a]
+    elif statistic in {'std', np.std}:
+        result.fill(np.nan)
+        flatcount = _bincount(binnumbers, None)
+        a = flatcount.nonzero()
+        for vv in builtins.range(Vdim):
+            flatsum = _bincount(binnumbers, values[vv])
+            delta = values[vv] - flatsum[binnumbers] / flatcount[binnumbers]
+            std = np.sqrt(
+                _bincount(binnumbers, delta*np.conj(delta))[a] / flatcount[a]
+            )
+            result[vv, a] = std
+        result = np.real(result)
+    elif statistic == 'count':
+        result = np.empty([Vdim, nbin.prod()], dtype=np.float64)
+        result.fill(0)
+        flatcount = _bincount(binnumbers, None)
+        a = np.arange(len(flatcount))
+        result[:, a] = flatcount[np.newaxis, :]
+    elif statistic in {'sum', np.sum}:
+        result.fill(0)
+        for vv in builtins.range(Vdim):
+            flatsum = _bincount(binnumbers, values[vv])
+            a = np.arange(len(flatsum))
+            result[vv, a] = flatsum
+    elif statistic in {'median', np.median}:
+        result.fill(np.nan)
+        for vv in builtins.range(Vdim):
+            i = np.lexsort((values[vv], binnumbers))
+            _, j, counts = np.unique(binnumbers[i],
+                                     return_index=True, return_counts=True)
+            mid = j + (counts - 1) / 2
+            mid_a = values[vv, i][np.floor(mid).astype(int)]
+            mid_b = values[vv, i][np.ceil(mid).astype(int)]
+            medians = (mid_a + mid_b) / 2
+            result[vv, binnumbers[i][j]] = medians
+    elif statistic in {'min', np.min}:
+        result.fill(np.nan)
+        for vv in builtins.range(Vdim):
+            i = np.argsort(values[vv])[::-1]  # Reversed so the min is last
+            result[vv, binnumbers[i]] = values[vv, i]
+    elif statistic in {'max', np.max}:
+        result.fill(np.nan)
+        for vv in builtins.range(Vdim):
+            i = np.argsort(values[vv])
+            result[vv, binnumbers[i]] = values[vv, i]
+    elif callable(statistic):
+        with np.errstate(invalid='ignore'), catch_warnings():
+            simplefilter("ignore", RuntimeWarning)
+            try:
+                null = statistic([])
+            except Exception:
+                null = np.nan
+        if np.iscomplexobj(null):
+            result = result.astype(np.complex128)
+        result.fill(null)
+        try:
+            _calc_binned_statistic(
+                Vdim, binnumbers, result, values, statistic
+            )
+        except ValueError:
+            result = result.astype(np.complex128)
+            _calc_binned_statistic(
+                Vdim, binnumbers, result, values, statistic
+            )
+
+    # Shape into a proper matrix
+    result = result.reshape(np.append(Vdim, nbin))
+
+    # Remove outliers (indices 0 and -1 for each bin-dimension).
+    core = tuple([slice(None)] + Ndim * [slice(1, -1)])
+    result = result[core]
+
+    # Unravel binnumbers into an ndarray, each row the bins for each dimension
+    if expand_binnumbers and Ndim > 1:
+        binnumbers = np.asarray(np.unravel_index(binnumbers, nbin))
+
+    if np.any(result.shape[1:] != nbin - 2):
+        raise RuntimeError('Internal Shape Error')
+
+    # Reshape to have output (`result`) match input (`values`) shape
+    result = result.reshape(input_shape[:-1] + list(nbin-2))
+
+    return BinnedStatisticddResult(result, edges, binnumbers)
+
+
+def _calc_binned_statistic(Vdim, bin_numbers, result, values, stat_func):
+    unique_bin_numbers = np.unique(bin_numbers)
+    for vv in builtins.range(Vdim):
+        bin_map = _create_binned_data(bin_numbers, unique_bin_numbers,
+                                      values, vv)
+        for i in unique_bin_numbers:
+            stat = stat_func(np.array(bin_map[i]))
+            if np.iscomplexobj(stat) and not np.iscomplexobj(result):
+                raise ValueError("The statistic function returns complex ")
+            result[vv, i] = stat
+
+
+def _create_binned_data(bin_numbers, unique_bin_numbers, values, vv):
+    """ Create hashmap of bin ids to values in bins
+    key: bin number
+    value: list of binned data
+    """
+    bin_map = dict()
+    for i in unique_bin_numbers:
+        bin_map[i] = []
+    for i in builtins.range(len(bin_numbers)):
+        bin_map[bin_numbers[i]].append(values[vv, i])
+    return bin_map
+
+
+def _bin_edges(sample, bins=None, range=None):
+    """ Create edge arrays
+    """
+    Dlen, Ndim = sample.shape
+
+    nbin = np.empty(Ndim, int)    # Number of bins in each dimension
+    edges = Ndim * [None]         # Bin edges for each dim (will be 2D array)
+    dedges = Ndim * [None]        # Spacing between edges (will be 2D array)
+
+    # Preserve sample floating point precision in bin edges
+    edges_dtype = (sample.dtype if np.issubdtype(sample.dtype, np.floating)
+                   else float)
+
+    # Select range for each dimension
+    # Used only if number of bins is given.
+    if range is None:
+        sample = sample.astype(float, copy=True)
+        sample[np.isinf(sample)] = np.nan
+        smin = np.atleast_1d(np.nanmin(sample, axis=0))
+        smax = np.atleast_1d(np.nanmax(sample, axis=0))
+    else:
+        if len(range) != Ndim:
+            raise ValueError(
+                f"range given for {len(range)} dimensions; {Ndim} required")
+        smin = np.empty(Ndim)
+        smax = np.empty(Ndim)
+        for i in builtins.range(Ndim):
+            if range[i][1] < range[i][0]:
+                raise ValueError(
+                    f"In {f'dimension {i + 1} of ' if Ndim > 1 else ''}range,"
+                    " start must be <= stop")
+            smin[i], smax[i] = range[i]
+
+    # Make sure the bins have a finite width.
+    for i in builtins.range(len(smin)):
+        if smin[i] == smax[i]:
+            smin[i] = smin[i] - .5
+            smax[i] = smax[i] + .5
+
+    # Create edge arrays
+    for i in builtins.range(Ndim):
+        if np.isscalar(bins[i]):
+            nbin[i] = bins[i] + 2  # +2 for outlier bins
+            edges[i] = np.linspace(smin[i], smax[i], nbin[i] - 1,
+                                   dtype=edges_dtype)
+        else:
+            edges[i] = np.asarray(bins[i], edges_dtype)
+            nbin[i] = len(edges[i]) + 1  # +1 for outlier bins
+        dedges[i] = np.diff(edges[i])
+
+    nbin = np.asarray(nbin)
+
+    return nbin, edges, dedges
+
+
+def _bin_numbers(sample, nbin, edges, dedges):
+    """Compute the bin number each sample falls into, in each dimension
+    """
+    Dlen, Ndim = sample.shape
+
+    sampBin = [
+        np.digitize(sample[:, i], edges[i])
+        for i in range(Ndim)
+    ]
+
+    # Using `digitize`, values that fall on an edge are put in the right bin.
+    # For the rightmost bin, we want values equal to the right
+    # edge to be counted in the last bin, and not as an outlier.
+    for i in range(Ndim):
+        # Find the rounding precision
+        dedges_min = dedges[i].min()
+        if dedges_min == 0:
+            raise ValueError('The smallest edge difference is numerically 0.')
+        decimal = int(-np.log10(dedges_min)) + 6
+        # Find which points are on the rightmost edge.
+        on_edge = np.where((sample[:, i] >= edges[i][-1]) &
+                           (np.around(sample[:, i], decimal) ==
+                            np.around(edges[i][-1], decimal)))[0]
+        # Shift these points one bin to the left.
+        sampBin[i][on_edge] -= 1
+
+    # Compute the sample indices in the flattened statistic matrix.
+    binnumbers = np.ravel_multi_index(sampBin, nbin)
+
+    return binnumbers
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_binomtest.py b/venv/lib/python3.12/site-packages/scipy/stats/_binomtest.py
new file mode 100644
index 0000000000000000000000000000000000000000..98251adbb66a025d401d9a66e23c9cd7221cf826
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_binomtest.py
@@ -0,0 +1,410 @@
+import numpy as np
+import scipy._external.array_api_extra as xpx
+from scipy._lib._array_api import xp_capabilities, array_namespace, xp_promote, is_jax
+from scipy.optimize.elementwise import find_root
+from scipy.special import ndtri
+from scipy.special import _ufuncs as scu
+from ._common import ConfidenceInterval
+
+
+class BinomTestResult:
+    """
+    Result of `scipy.stats.binomtest`.
+
+    Attributes
+    ----------
+    k : int
+        The number of successes (copied from `binomtest` input).
+    n : int
+        The number of trials (copied from `binomtest` input).
+    alternative : str
+        Indicates the alternative hypothesis specified in the input
+        to `binomtest`.  It will be one of ``'two-sided'``, ``'greater'``,
+        or ``'less'``.
+    statistic: float
+        The estimate of the proportion of successes.
+    pvalue : float
+        The p-value of the hypothesis test.
+
+    """
+    def __init__(self, k, n, alternative, statistic, pvalue, xp):
+        self.k = k
+        self.n = n
+        self.alternative = alternative
+        self.statistic = statistic
+        self.pvalue = pvalue
+        self._xp = xp
+
+        # add alias for backward compatibility
+        self.proportion_estimate = statistic
+
+    def __repr__(self):
+        s = ("BinomTestResult("
+             f"k={self.k}, "
+             f"n={self.n}, "
+             f"alternative={self.alternative!r}, "
+             f"statistic={self.statistic}, "
+             f"pvalue={self.pvalue})")
+        return s
+
+    def proportion_ci(self, confidence_level=0.95, method='exact'):
+        """
+        Compute the confidence interval for ``statistic``.
+
+        Parameters
+        ----------
+        confidence_level : float, optional
+            Confidence level for the computed confidence interval
+            of the estimated proportion. Default is 0.95.
+        method : {'exact', 'wilson', 'wilsoncc'}, optional
+            Selects the method used to compute the confidence interval
+            for the estimate of the proportion:
+
+            'exact' :
+                Use the Clopper-Pearson exact method [1]_.
+            'wilson' :
+                Wilson's method, without continuity correction ([2]_, [3]_).
+            'wilsoncc' :
+                Wilson's method, with continuity correction ([2]_, [3]_).
+
+            Default is ``'exact'``.
+
+        Returns
+        -------
+        ci : ``ConfidenceInterval`` object
+            The object has attributes ``low`` and ``high`` that hold the
+            lower and upper bounds of the confidence interval.
+
+        References
+        ----------
+        .. [1] C. J. Clopper and E. S. Pearson, The use of confidence or
+               fiducial limits illustrated in the case of the binomial,
+               Biometrika, Vol. 26, No. 4, pp 404-413 (Dec. 1934).
+        .. [2] E. B. Wilson, Probable inference, the law of succession, and
+               statistical inference, J. Amer. Stat. Assoc., 22, pp 209-212
+               (1927).
+        .. [3] Robert G. Newcombe, Two-sided confidence intervals for the
+               single proportion: comparison of seven methods, Statistics
+               in Medicine, 17, pp 857-872 (1998).
+
+        Examples
+        --------
+        >>> from scipy.stats import binomtest
+        >>> result = binomtest(k=7, n=50, p=0.1)
+        >>> result.statistic
+        0.14
+        >>> result.proportion_ci()
+        ConfidenceInterval(low=0.05819170033997342, high=0.26739600249700846)
+        """
+        if method not in ('exact', 'wilson', 'wilsoncc'):
+            raise ValueError(f"method ('{method}') must be one of 'exact', "
+                             "'wilson' or 'wilsoncc'.")
+        if not (0 <= confidence_level <= 1):
+            raise ValueError(f'confidence_level ({confidence_level}) must be in '
+                             'the interval [0, 1].')
+
+        xp = self._xp
+        k, n, confidence_level = xp_promote(self.k, self.n, confidence_level, xp=xp)
+        if method == 'exact':
+            low, high = _binom_exact_conf_int(
+                k, n, confidence_level, self.alternative, xp=xp)
+        else:
+            # method is 'wilson' or 'wilsoncc'
+            correction = method == 'wilsoncc'
+            low, high = _binom_wilson_conf_int(
+                k, n, confidence_level, self.alternative, correction, xp=xp)
+        low = low[()] if low.ndim == 0 else low
+        high = high[()] if high.ndim == 0 else high
+        return ConfidenceInterval(low=low, high=high)
+
+
+def _binom_exact_conf_int(k, n, confidence_level, alternative, *, xp):
+    """
+    Compute the estimate and confidence interval for the binomial test.
+
+    Returns proportion, prop_low, prop_high
+    """
+    init = (xp.zeros_like(k), xp.ones_like(k))
+    args = (k, n)
+    alpha = ((1 - confidence_level) / 2 if alternative == 'two-sided'
+             else 1 - confidence_level)
+
+    # I think using the private methods here is fine, since we will only evaluate with
+    # valid `p`, `k`, and `n` (or all NaNs). One exception is when `k=0` and
+    # `binom._sf(k-1, n, p)`: evaluates to NaN, but that's not a problem because
+    # `plow` has a special case for `k=0` below.
+    plow = (xp.zeros_like(k) if alternative == 'less' else
+            find_root(lambda p, k, n: _SimpleBinomial(n, p).sf(k-1) - alpha,
+                      init, args=args).x)
+    phigh = (xp.ones_like(k) if alternative == 'greater' else
+             find_root(lambda p, k, n: _SimpleBinomial(n, p).cdf(k) - alpha,
+                       init, args=args).x)
+
+    plow = xp.where(k == 0, 0.0, plow)
+    phigh = xp.where(k == n, 1.0, phigh)
+    return plow, phigh
+
+
+def _binom_wilson_conf_int(k, n, confidence_level, alternative, correction, *, xp):
+    # This function assumes that the arguments have already been validated.
+    # In particular, `alternative` must be one of 'two-sided', 'less' or
+    # 'greater'.
+    p = k / n
+    if alternative == 'two-sided':
+        z = ndtri(0.5 + 0.5*confidence_level)
+    else:
+        z = ndtri(confidence_level)
+
+    # For reference, the formulas implemented here are from
+    # Newcombe (1998) (ref. [3] in the proportion_ci docstring).
+    denom = 2*(n + z**2)
+    center = (2*n*p + z**2)/denom
+    q = 1 - p
+
+    if correction:
+        with np.errstate(divide='ignore', invalid='ignore'):
+            dlo = (1 + z*xp.sqrt(z**2 - 2 - 1/n + 4*p*(n*q + 1)))/denom
+            dhi = (1 + z*xp.sqrt(z**2 + 2 - 1/n + 4*p*(n*q - 1)))/denom
+    else:
+        delta = z / denom * xp.sqrt(4*n*p*q + z**2)
+        dlo, dhi = delta, delta
+
+    lo = xp.where((k == 0) | (alternative == 'less'), 0.0, center - dlo)
+    hi = xp.where((k == n) | (alternative == 'greater'), 1.0, center + dhi)
+    return lo, hi
+
+
+@xp_capabilities(skip_backends=[('dask.array', "")], cpu_only=True,
+                 reason="binomial distribution ufuncs only available for NumPy",
+                 extra_note="`alternative='two-sided'` is incompatible with JAX arrays.")
+def binomtest(k, n, p=0.5, alternative='two-sided'):
+    """
+    Perform a test that the probability of success is p.
+
+    The binomial test [1]_ is a test of the null hypothesis that the
+    probability of success in a Bernoulli experiment is `p`.
+
+    Details of the test can be found in many texts on statistics, such
+    as section 24.5 of [2]_.
+
+    The documentation is written as though the function accepts and returns Python
+    scalars, but the function is vectorized to work elementwise with NumPy arrays.
+
+    Parameters
+    ----------
+    k : int
+        The number of successes.
+    n : int
+        The number of trials.
+    p : float, optional
+        The hypothesized probability of success, i.e. the expected
+        proportion of successes.  The value must be in the interval
+        ``0 <= p <= 1``. The default value is ``p = 0.5``.
+    alternative : {'two-sided', 'greater', 'less'}, optional
+        Indicates the alternative hypothesis. The default value is
+        'two-sided'.
+
+    Returns
+    -------
+    result : `~scipy.stats._result_classes.BinomTestResult` instance
+        The return value is an object with the following attributes:
+
+        k : int
+            The number of successes (copied from `binomtest` input).
+        n : int
+            The number of trials (copied from `binomtest` input).
+        alternative : str
+            Indicates the alternative hypothesis specified in the input
+            to `binomtest`.  It will be one of ``'two-sided'``, ``'greater'``,
+            or ``'less'``.
+        statistic : float
+            The estimate of the proportion of successes.
+        pvalue : float
+            The p-value of the hypothesis test.
+
+        The object has the following methods:
+
+        proportion_ci(confidence_level=0.95, method='exact') :
+            Compute the confidence interval for ``statistic``.
+
+    Notes
+    -----
+    .. versionadded:: 1.7.0
+
+    References
+    ----------
+    .. [1] Binomial test, https://en.wikipedia.org/wiki/Binomial_test
+    .. [2] Jerrold H. Zar, Biostatistical Analysis (fifth edition),
+           Prentice Hall, Upper Saddle River, New Jersey USA (2010)
+
+    Examples
+    --------
+    >>> from scipy.stats import binomtest
+
+    A car manufacturer claims that no more than 10% of their cars are unsafe.
+    15 cars are inspected for safety, 3 were found to be unsafe. Test the
+    manufacturer's claim:
+
+    >>> result = binomtest(3, n=15, p=0.1, alternative='greater')
+    >>> result.pvalue
+    0.18406106910639114
+
+    The null hypothesis cannot be rejected at the 5% level of significance
+    because the returned p-value is greater than the critical value of 5%.
+
+    The test statistic is equal to the estimated proportion, which is simply
+    ``3/15``:
+
+    >>> result.statistic
+    0.2
+
+    We can use the `proportion_ci()` method of the result to compute the
+    confidence interval of the estimate:
+
+    >>> result.proportion_ci(confidence_level=0.95)
+    ConfidenceInterval(low=0.05684686759024681, high=1.0)
+
+    """
+    xp = array_namespace(k, n, p)
+    k, n, p = xp_promote(k, n, p, force_floating=True, broadcast=True, xp=xp)
+    k_valid = (k >= 0) & (k <= n) & (k == xp.floor(k))
+    n_valid = (n >= 1) & (n == xp.floor(n))
+    p_valid = (p >= 0) & (p <= 1)
+    valid = k_valid & n_valid & p_valid
+    k = xp.where(valid, k, xp.nan)
+    n = xp.where(valid, n, xp.nan)
+    p = xp.where(valid, p, xp.nan)
+
+    if alternative not in ('two-sided', 'less', 'greater'):
+        raise ValueError(f"alternative ('{alternative}') not recognized; \n"
+                         "must be 'two-sided', 'less' or 'greater'")
+
+    B = _SimpleBinomial(n, p)
+    if alternative == 'less':
+        pval = B.cdf(k)
+    elif alternative == 'greater':
+        pval = B.sf(k - 1)
+    else:
+        if is_jax(xp):
+            message = "`alternative='two-sided'` is incompatible with JAX arrays."
+            raise ValueError(message)
+
+        # alternative is 'two-sided'
+        d = B.pmf(k)
+        rerr = 1 + 1e-7
+
+        def k_lt_pn(d, k, p, n):
+            B = _SimpleBinomial(n, p)
+            ix = _binary_search_for_binom_tst(lambda x1: -B.pmf(x1), -d*rerr,
+                                              xp.ceil(p * n), n, xp=xp)
+            # y is the number of terms between mode and n that are <= d*rerr.
+            # ix gave us the first term where a(ix) <= d*rerr < a(ix-1)
+            # if the first equality doesn't hold, y=n-ix. Otherwise, we
+            # need to include ix as well as the equality holds. Note that
+            # the equality will hold in very very rare situations due to rerr.
+            y = n - ix + xp.asarray(d*rerr == B.pmf(ix), dtype=ix.dtype)
+            pval = B.cdf(k) + B.sf(n - y)
+            return pval
+
+        def k_gte_pn(d, k, p, n):
+            B = _SimpleBinomial(n, p)
+            ix = _binary_search_for_binom_tst(B.pmf, d*rerr,
+                                              xp.zeros_like(n), xp.floor(p * n), xp=xp)
+            # y is the number of terms between 0 and mode that are <= d*rerr.
+            # we need to add a 1 to account for the 0 index.
+            # For comparing this with old behavior, see
+            # tst_binary_srch_for_binom_tst method in test_morestats.
+            y = ix + 1
+            pval = B.cdf(y-1) + B.sf(k-1)
+            return pval
+
+        pval = xpx.apply_where(k < p*n, (d, k, p, n), k_lt_pn,  k_gte_pn)
+        # xp.minimum(1.0, pval) but for data-apis/array-api-compat#271
+        pval = xp.minimum(xp.asarray(1.0, dtype=pval.dtype), pval)
+
+    statistic = xp.where(valid, k/n, xp.nan)
+    pval = xp.where(valid, pval, xp.nan)
+    if statistic.ndim == 0:
+        k, n, statistic, pval = k[()], n[()], statistic[()], pval[()]
+
+    result = BinomTestResult(k=k, n=n, alternative=alternative,
+                             statistic=statistic, pvalue=pval, xp=xp)
+    return result
+
+
+def _binary_search_for_binom_tst(a, d, lo, hi, *, xp):
+    """
+    Conducts an implicit binary search on a function specified by `a`.
+
+    Meant to be used on the binomial PMF for the case of two-sided tests
+    to obtain the value on the other side of the mode where the tail
+    probability should be computed. The values on either side of
+    the mode are always in order, meaning binary search is applicable.
+
+    Parameters
+    ----------
+    a : callable
+      The function over which to perform binary search. Its values
+      for inputs lo and hi should be in ascending order.
+    d : float
+      The value to search.
+    lo : int
+      The lower end of range to search.
+    hi : int
+      The higher end of the range to search.
+
+    Returns
+    -------
+    int
+      The index, i between lo and hi
+      such that a(i)<=d<a(i+1)
+    """
+    d = xp.asarray(d, copy=True)
+    lo = xp.asarray(lo, copy=True)
+    hi = xp.asarray(hi, copy=True)
+    while xp.any(lo < hi):
+        mid = lo + (hi-lo)//2
+        midval = a(mid)
+
+        i_lt = midval < d
+        lo = xpx.at(lo)[i_lt].set(mid[i_lt] + 1)
+
+        i_gt = midval > d
+        hi = xpx.at(hi)[i_gt].set(mid[i_gt] - 1)
+
+        i_eq = (midval == d)
+        mid_i_eq = mid[i_eq]
+        lo = xpx.at(lo)[i_eq].set(mid_i_eq)
+        hi = xpx.at(hi)[i_eq].set(mid_i_eq)
+
+    return xp.where(a(lo) <= d, lo, lo-1)
+
+
+class _SimpleBinomial:
+    # A very simple, array-API compatible binomial distribution for use in
+    # hypothesis tests. May be replaced by new infrastructure Binomial
+    # distribution in due time.
+    def __init__(self, n, p, *, xp=None):
+        xp = array_namespace(n, p) if xp is None else xp
+        self.n = n
+        self.p = p
+        self.xp = xp
+
+    def f(self, x, fun):
+        xp = self.xp
+        return xpx.lazy_apply(fun, x, self.n, self.p, as_numpy=True, xp=xp)
+
+    def cdf(self, x):
+        return self.xp.where(x >= 0, self.f(self.xp.floor(x), scu._binom_cdf), 0.0)
+
+    def sf(self, x):
+        return self.xp.where(x >= 0, self.f(self.xp.floor(x), scu._binom_sf), 1.0)
+
+    def ppf(self, x):
+        return self.f(x, scu._binom_ppf)
+
+    def isf(self, x):
+        return self.f(x, scu._binom_isf)
+
+    def pmf(self, x):
+        return self.f(self.xp.floor(x), scu._binom_pmf)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_bws_test.py b/venv/lib/python3.12/site-packages/scipy/stats/_bws_test.py
new file mode 100644
index 0000000000000000000000000000000000000000..786b5ebe57ada5aa0bda7dc583494004769daf3f
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_bws_test.py
@@ -0,0 +1,204 @@
+import numpy as np
+from functools import partial
+
+from scipy import stats
+from scipy.stats._axis_nan_policy import _broadcast_arrays
+from scipy._external import array_api_extra as xpx
+from scipy._lib._array_api import (xp_capabilities, array_namespace, xp_ravel,
+                                   xp_result_type)
+
+
+def _bws_input_validation(x, y, alternative, axis, method):
+    ''' Input validation and standardization for bws test'''
+    xp = array_namespace(x, y)
+    x, y = xp.asarray(x), xp.asarray(y)
+    x, y = xpx.atleast_nd(x, ndim=1), xpx.atleast_nd(y, ndim=1)
+
+    axis_none = axis is None
+    ndim = max(x.ndim, y.ndim)
+    if axis_none:
+        x = xp_ravel(x, xp=xp)
+        y = xp_ravel(y, xp=xp)
+        axis = 0
+    elif np.iterable(axis) or int(axis) != axis:
+        message = "`axis` must be an integer or None."
+        raise ValueError(message)
+    elif (axis >= ndim) or (axis < -ndim):
+        message = "`axis` is not compatible with the shapes of the inputs."
+        raise ValueError(message)
+    axis = int(axis)
+
+    x, y = _broadcast_arrays((x, y), axis=axis, xp=xp)
+    nx, ny = x.shape[-1], y.shape[-1]
+    if nx < 2 or ny < 2:
+        raise ValueError('`x` and `y` must contain at least two observations each.')
+
+    x, y = xp.moveaxis(x, axis, -1), xp.moveaxis(y, axis, -1)
+    z = stats.rankdata(xp.concat((x, y), axis=-1), axis=-1)
+    z = xp.astype(z, xp_result_type(x, y, force_floating=True, xp=xp))
+    x, y = z[..., :x.shape[-1]], z[..., x.shape[-1]:]
+    x, y = xp.moveaxis(x, -1, axis), xp.moveaxis(y, -1, axis)
+
+    alternatives = {'two-sided', 'less', 'greater'}
+    alternative = alternative.lower()
+    if alternative not in alternatives:
+        raise ValueError(f'`alternative` must be one of {alternatives}.')
+
+    method = stats.PermutationMethod() if method is None else method
+    if not isinstance(method, stats.PermutationMethod):
+        raise ValueError('`method` must be an instance of '
+                         '`scipy.stats.PermutationMethod`')
+
+    return x, y, alternative, axis, method, xp
+
+
+def _bws_statistic(x, y, alternative, axis, xp):
+    '''Compute the BWS test statistic for two independent samples'''
+    # Public function currently does not accept `axis`, but `permutation_test`
+    # uses `axis` to make vectorized call.
+
+    Ri, Hj = xp.sort(x, axis=axis), xp.sort(y, axis=axis)
+    n, m = Ri.shape[axis], Hj.shape[axis]
+    i, j = xp.arange(1, n+1, dtype=Ri.dtype), xp.arange(1, m+1, dtype=Hj.dtype)
+
+    Bx_num = Ri - (m + n)/n * i
+    By_num = Hj - (m + n)/m * j
+
+    if alternative == 'two-sided':
+        Bx_num = xpx.at(Bx_num)[...].multiply(Bx_num)
+        By_num = xpx.at(By_num)[...].multiply(By_num)
+    else:
+        Bx_num = xpx.at(Bx_num)[...].multiply(xp.abs(Bx_num))
+        By_num = xpx.at(By_num)[...].multiply(xp.abs(By_num))
+
+    Bx_den = i/(n+1) * (1 - i/(n+1)) * m*(m+n)/n
+    By_den = j/(m+1) * (1 - j/(m+1)) * n*(m+n)/m
+
+    Bx = 1/n * xp.sum(Bx_num/Bx_den, axis=axis)
+    By = 1/m * xp.sum(By_num/By_den, axis=axis)
+
+    B = (Bx + By) / 2 if alternative == 'two-sided' else (Bx - By) / 2
+
+    return B
+
+
+@xp_capabilities(skip_backends=[('dask.array', 'no rankdata')])
+def bws_test(x, y, *, alternative="two-sided", axis=0, method=None):
+    r'''Perform the Baumgartner-Weiss-Schindler test on two independent samples.
+
+    The Baumgartner-Weiss-Schindler (BWS) test is a nonparametric test of
+    the null hypothesis that the distribution underlying sample `x`
+    is the same as the distribution underlying sample `y`. Unlike
+    the Kolmogorov-Smirnov, Wilcoxon, and Cramer-Von Mises tests,
+    the BWS test weights the integral by the variance of the difference
+    in cumulative distribution functions (CDFs), emphasizing the tails of the
+    distributions, which increases the power of the test in many applications.
+
+    Parameters
+    ----------
+    x, y : array-like
+        Arrays of samples. Shapes must be broadcastable except along `axis`.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis. Default is 'two-sided'.
+        Let *F(u)* and *G(u)* be the cumulative distribution functions of the
+        distributions underlying `x` and `y`, respectively. Then the following
+        alternative hypotheses are available:
+
+        * 'two-sided': the distributions are not equal, i.e. *F(u) ≠ G(u)* for
+          at least one *u*.
+        * 'less': the distribution underlying `x` is stochastically less than
+          the distribution underlying `y`, i.e. *F(u) >= G(u)* for all *u*.
+        * 'greater': the distribution underlying `x` is stochastically greater
+          than the distribution underlying `y`, i.e. *F(u) <= G(u)* for all
+          *u*.
+
+        Under a more restrictive set of assumptions, the alternative hypotheses
+        can be expressed in terms of the locations of the distributions;
+        see [2] section 5.1.
+    axis : int or None, default: 0
+        Axis along which the quantiles are computed.
+        ``None`` ravels both `x` and `y` before performing the calculation.
+    method : PermutationMethod, optional
+        Configures the method used to compute the p-value. The default is
+        the default `PermutationMethod` object.
+
+    Returns
+    -------
+    res : PermutationTestResult
+        An object with attributes:
+
+        statistic : float
+            The observed test statistic of the data.
+        pvalue : float
+            The p-value for the given alternative.
+        null_distribution : ndarray
+            The values of the test statistic generated under the null hypothesis.
+
+    See Also
+    --------
+    scipy.stats.wilcoxon, scipy.stats.mannwhitneyu, scipy.stats.ttest_ind
+
+    Notes
+    -----
+    When ``alternative=='two-sided'``, the statistic is defined by the
+    equations given in [1]_ Section 2. This statistic is not appropriate for
+    one-sided alternatives; in that case, the statistic is the *negative* of
+    that given by the equations in [1]_ Section 2. Consequently, when the
+    distribution of the first sample is stochastically greater than that of the
+    second sample, the statistic will tend to be positive.
+
+    References
+    ----------
+    .. [1] Neuhäuser, M. (2005). Exact Tests Based on the
+           Baumgartner-Weiss-Schindler Statistic: A Survey. Statistical Papers,
+           46(1), 1-29.
+    .. [2] Fay, M. P., & Proschan, M. A. (2010). Wilcoxon-Mann-Whitney or t-test?
+           On assumptions for hypothesis tests and multiple interpretations of
+           decision rules. Statistics surveys, 4, 1.
+
+    Examples
+    --------
+    We follow the example of table 3 in [1]_: Fourteen children were divided
+    randomly into two groups. Their ranks at performing a specific tests are
+    as follows.
+
+    >>> import numpy as np
+    >>> x = [1, 2, 3, 4, 6, 7, 8]
+    >>> y = [5, 9, 10, 11, 12, 13, 14]
+
+    We use the BWS test to assess whether there is a statistically significant
+    difference between the two groups.
+    The null hypothesis is that there is no difference in the distributions of
+    performance between the two groups. We decide that a significance level of
+    1% is required to reject the null hypothesis in favor of the alternative
+    that the distributions are different.
+    Since the number of samples is very small, we can compare the observed test
+    statistic against the *exact* distribution of the test statistic under the
+    null hypothesis.
+
+    >>> from scipy.stats import bws_test
+    >>> res = bws_test(x, y)
+    >>> print(res.statistic)
+    5.132167152575315
+
+    This agrees with :math:`B = 5.132` reported in [1]_. The *p*-value produced
+    by `bws_test` also agrees with :math:`p = 0.0029` reported in [1]_.
+
+    >>> print(res.pvalue)
+    0.002913752913752914
+
+    Because the p-value is below our threshold of 1%, we take this as evidence
+    against the null hypothesis in favor of the alternative that there is a
+    difference in performance between the two groups.
+    '''
+
+    x, y, alternative, axis, method, xp = _bws_input_validation(x, y, alternative,
+                                                                axis, method)
+    bws_statistic = partial(_bws_statistic, alternative=alternative, xp=xp)
+
+    permutation_alternative = 'less' if alternative == 'less' else 'greater'
+    res = stats.permutation_test((x, y), bws_statistic,
+                                 alternative=permutation_alternative, axis=axis,
+                                 **method._asdict())
+
+    return res
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_censored_data.py b/venv/lib/python3.12/site-packages/scipy/stats/_censored_data.py
new file mode 100644
index 0000000000000000000000000000000000000000..14c90aa3edb8c5303642a9b36a3323fe6fbcac2c
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_censored_data.py
@@ -0,0 +1,468 @@
+from types import GenericAlias
+import numpy as np
+
+
+def _validate_1d(a, name, allow_inf=False):
+    if np.ndim(a) != 1:
+        raise ValueError(f'`{name}` must be a one-dimensional sequence.')
+    if np.isnan(a).any():
+        raise ValueError(f'`{name}` must not contain nan.')
+    if not allow_inf and np.isinf(a).any():
+        raise ValueError(f'`{name}` must contain only finite values.')
+
+
+def _validate_interval(interval):
+    interval = np.asarray(interval)
+    if interval.shape == (0,):
+        # The input was a sequence with length 0.
+        interval = interval.reshape((0, 2))
+    if interval.ndim != 2 or interval.shape[-1] != 2:
+        raise ValueError('`interval` must be a two-dimensional array with '
+                         'shape (m, 2), where m is the number of '
+                         'interval-censored values, but got shape '
+                         f'{interval.shape}')
+
+    if np.isnan(interval).any():
+        raise ValueError('`interval` must not contain nan.')
+    if np.isinf(interval).all(axis=1).any():
+        raise ValueError('In each row in `interval`, both values must not'
+                         ' be infinite.')
+    if (interval[:, 0] > interval[:, 1]).any():
+        raise ValueError('In each row of `interval`, the left value must not'
+                         ' exceed the right value.')
+
+    uncensored_mask = interval[:, 0] == interval[:, 1]
+    left_mask = np.isinf(interval[:, 0])
+    right_mask = np.isinf(interval[:, 1])
+    interval_mask = np.isfinite(interval).all(axis=1) & ~uncensored_mask
+
+    uncensored2 = interval[uncensored_mask, 0]
+    left2 = interval[left_mask, 1]
+    right2 = interval[right_mask, 0]
+    interval2 = interval[interval_mask]
+
+    return uncensored2, left2, right2, interval2
+
+
+def _validate_x_censored(x, censored):
+    x = np.asarray(x)
+    if x.ndim != 1:
+        raise ValueError('`x` must be one-dimensional.')
+    censored = np.asarray(censored)
+    if censored.ndim != 1:
+        raise ValueError('`censored` must be one-dimensional.')
+    if (~np.isfinite(x)).any():
+        raise ValueError('`x` must not contain nan or inf.')
+    if censored.size != x.size:
+        raise ValueError('`x` and `censored` must have the same length.')
+    return x, censored.astype(bool)
+
+
+class CensoredData:
+    """
+    Instances of this class represent censored data.
+
+    Instances may be passed to the ``fit`` method of continuous
+    univariate SciPy distributions for maximum likelihood estimation.
+    The *only* method of the univariate continuous distributions that
+    understands `CensoredData` is the ``fit`` method.  An instance of
+    `CensoredData` can not be passed to methods such as ``pdf`` and
+    ``cdf``.
+
+    An observation is said to be *censored* when the precise value is unknown,
+    but it has a known upper and/or lower bound.  The conventional terminology
+    is:
+
+    * left-censored: an observation is below a certain value but it is
+      unknown by how much.
+    * right-censored: an observation is above a certain value but it is
+      unknown by how much.
+    * interval-censored: an observation lies somewhere on an interval between
+      two values.
+
+    Left-, right-, and interval-censored data can be represented by
+    `CensoredData`.
+
+    For convenience, the class methods ``left_censored`` and
+    ``right_censored`` are provided to create a `CensoredData`
+    instance from a single one-dimensional array of measurements
+    and a corresponding boolean array to indicate which measurements
+    are censored.  The class method ``interval_censored`` accepts two
+    one-dimensional arrays that hold the lower and upper bounds of the
+    intervals.
+
+    Parameters
+    ----------
+    uncensored : array_like, 1D
+        Uncensored observations.
+    left : array_like, 1D
+        Left-censored observations.
+    right : array_like, 1D
+        Right-censored observations.
+    interval : array_like, 2D, with shape (m, 2)
+        Interval-censored observations.  Each row ``interval[k, :]``
+        represents the interval for the kth interval-censored observation.
+
+    Notes
+    -----
+    In the input array `interval`, the lower bound of the interval may
+    be ``-inf``, and the upper bound may be ``inf``, but at least one must be
+    finite. When the lower bound is ``-inf``, the row represents a left-
+    censored observation, and when the upper bound is ``inf``, the row
+    represents a right-censored observation.  If the length of an interval
+    is 0 (i.e. ``interval[k, 0] == interval[k, 1]``, the observation is
+    treated as uncensored.  So one can represent all the types of censored
+    and uncensored data in ``interval``, but it is generally more convenient
+    to use `uncensored`, `left` and `right` for uncensored, left-censored and
+    right-censored observations, respectively.
+
+    Examples
+    --------
+    In the most general case, a censored data set may contain values that
+    are left-censored, right-censored, interval-censored, and uncensored.
+    For example, here we create a data set with five observations.  Two
+    are uncensored (values 1 and 1.5), one is a left-censored observation
+    of 0, one is a right-censored observation of 10 and one is
+    interval-censored in the interval [2, 3].
+
+    >>> import numpy as np
+    >>> from scipy.stats import CensoredData
+    >>> data = CensoredData(uncensored=[1, 1.5], left=[0], right=[10],
+    ...                     interval=[[2, 3]])
+    >>> print(data)
+    CensoredData(5 values: 2 not censored, 1 left-censored,
+    1 right-censored, 1 interval-censored)
+
+    Equivalently,
+
+    >>> data = CensoredData(interval=[[1, 1],
+    ...                               [1.5, 1.5],
+    ...                               [-np.inf, 0],
+    ...                               [10, np.inf],
+    ...                               [2, 3]])
+    >>> print(data)
+    CensoredData(5 values: 2 not censored, 1 left-censored,
+    1 right-censored, 1 interval-censored)
+
+    A common case is to have a mix of uncensored observations and censored
+    observations that are all right-censored (or all left-censored). For
+    example, consider an experiment in which six devices are started at
+    various times and left running until they fail.  Assume that time is
+    measured in hours, and the experiment is stopped after 30 hours, even
+    if all the devices have not failed by that time.  We might end up with
+    data such as this::
+
+        Device  Start-time  Fail-time  Time-to-failure
+           1         0         13           13
+           2         2         24           22
+           3         5         22           17
+           4         8         23           15
+           5        10        ***          >20
+           6        12        ***          >18
+
+    Two of the devices had not failed when the experiment was stopped;
+    the observations of the time-to-failure for these two devices are
+    right-censored.  We can represent this data with
+
+    >>> data = CensoredData(uncensored=[13, 22, 17, 15], right=[20, 18])
+    >>> print(data)
+    CensoredData(6 values: 4 not censored, 2 right-censored)
+
+    Alternatively, we can use the method `CensoredData.right_censored` to
+    create a representation of this data.  The time-to-failure observations
+    are put the list ``ttf``.  The ``censored`` list indicates which values
+    in ``ttf`` are censored.
+
+    >>> ttf = [13, 22, 17, 15, 20, 18]
+    >>> censored = [False, False, False, False, True, True]
+
+    Pass these lists to `CensoredData.right_censored` to create an
+    instance of `CensoredData`.
+
+    >>> data = CensoredData.right_censored(ttf, censored)
+    >>> print(data)
+    CensoredData(6 values: 4 not censored, 2 right-censored)
+
+    If the input data is interval censored and already stored in two
+    arrays, one holding the low end of the intervals and another
+    holding the high ends, the class method ``interval_censored`` can
+    be used to create the `CensoredData` instance.
+
+    This example creates an instance with four interval-censored values.
+    The intervals are [10, 11], [0.5, 1], [2, 3], and [12.5, 13.5].
+
+    >>> a = [10, 0.5, 2, 12.5]  # Low ends of the intervals
+    >>> b = [11, 1.0, 3, 13.5]  # High ends of the intervals
+    >>> data = CensoredData.interval_censored(low=a, high=b)
+    >>> print(data)
+    CensoredData(4 values: 0 not censored, 4 interval-censored)
+
+    Finally, we create and censor some data from the `weibull_min`
+    distribution, and then fit `weibull_min` to that data. We'll assume
+    that the location parameter is known to be 0.
+
+    >>> from scipy.stats import weibull_min
+    >>> rng = np.random.default_rng()
+
+    Create the random data set.
+
+    >>> x = weibull_min.rvs(2.5, loc=0, scale=30, size=250, random_state=rng)
+    >>> x[x > 40] = 40  # Right-censor values greater or equal to 40.
+
+    Create the `CensoredData` instance with the `right_censored` method.
+    The censored values are those where the value is 40.
+
+    >>> data = CensoredData.right_censored(x, x == 40)
+    >>> print(data)
+    CensoredData(250 values: 215 not censored, 35 right-censored)
+
+    35 values have been right-censored.
+
+    Fit `weibull_min` to the censored data.  We expect to shape and scale
+    to be approximately 2.5 and 30, respectively.
+
+    >>> weibull_min.fit(data, floc=0)
+    (2.3575922823897315, 0, 30.40650074451254)
+
+    """
+
+    # generic type compatibility with scipy-stubs
+    __class_getitem__: classmethod = classmethod(GenericAlias)
+
+    def __init__(self, uncensored=None, *, left=None, right=None,
+                 interval=None):
+        if uncensored is None:
+            uncensored = []
+        if left is None:
+            left = []
+        if right is None:
+            right = []
+        if interval is None:
+            interval = np.empty((0, 2))
+
+        _validate_1d(uncensored, 'uncensored')
+        _validate_1d(left, 'left')
+        _validate_1d(right, 'right')
+        uncensored2, left2, right2, interval2 = _validate_interval(interval)
+
+        self._uncensored = np.concatenate((uncensored, uncensored2))
+        self._left = np.concatenate((left, left2))
+        self._right = np.concatenate((right, right2))
+        # Note that by construction, the private attribute _interval
+        # will be a 2D array that contains only finite values representing
+        # intervals with nonzero but finite length.
+        self._interval = interval2
+
+    def __repr__(self):
+        uncensored_str = " ".join(np.array_repr(self._uncensored).split())
+        left_str = " ".join(np.array_repr(self._left).split())
+        right_str = " ".join(np.array_repr(self._right).split())
+        interval_str = " ".join(np.array_repr(self._interval).split())
+        return (f"CensoredData(uncensored={uncensored_str}, left={left_str}, "
+                f"right={right_str}, interval={interval_str})")
+
+    def __str__(self):
+        num_nc = len(self._uncensored)
+        num_lc = len(self._left)
+        num_rc = len(self._right)
+        num_ic = len(self._interval)
+        n = num_nc + num_lc + num_rc + num_ic
+        parts = [f'{num_nc} not censored']
+        if num_lc > 0:
+            parts.append(f'{num_lc} left-censored')
+        if num_rc > 0:
+            parts.append(f'{num_rc} right-censored')
+        if num_ic > 0:
+            parts.append(f'{num_ic} interval-censored')
+        return f'CensoredData({n} values: ' + ', '.join(parts) + ')'
+
+    # This is not a complete implementation of the arithmetic operators.
+    # All we need is subtracting a scalar and dividing by a scalar.
+
+    def __sub__(self, other):
+        return CensoredData(uncensored=self._uncensored - other,
+                            left=self._left - other,
+                            right=self._right - other,
+                            interval=self._interval - other)
+
+    def __truediv__(self, other):
+        return CensoredData(uncensored=self._uncensored / other,
+                            left=self._left / other,
+                            right=self._right / other,
+                            interval=self._interval / other)
+
+    def __len__(self):
+        """
+        The number of values (censored and not censored).
+        """
+        return (len(self._uncensored) + len(self._left) + len(self._right)
+                + len(self._interval))
+
+    def num_censored(self):
+        """
+        Number of censored values.
+
+        Returns
+        -------
+        int
+            The number of censored values.
+        """
+        return len(self._left) + len(self._right) + len(self._interval)
+
+    @classmethod
+    def right_censored(cls, x, censored):
+        """
+        Create a `CensoredData` instance of right-censored data.
+
+        Parameters
+        ----------
+        x : array_like
+            `x` is the array of observed data or measurements.
+            `x` must be a one-dimensional sequence of finite numbers.
+        censored : array_like of bool
+            `censored` must be a one-dimensional sequence of boolean
+            values.  If ``censored[k]`` is True, the corresponding value
+            in `x` is right-censored.  That is, the value ``x[k]``
+            is the lower bound of the true (but unknown) value.
+
+        Returns
+        -------
+        data : `CensoredData`
+            An instance of `CensoredData` that represents the
+            collection of uncensored and right-censored values.
+
+        Examples
+        --------
+        >>> from scipy.stats import CensoredData
+
+        Two uncensored values (4 and 10) and two right-censored values
+        (24 and 25).
+
+        >>> data = CensoredData.right_censored([4, 10, 24, 25],
+        ...                                    [False, False, True, True])
+        >>> data
+        CensoredData(uncensored=array([ 4., 10.]),
+        left=array([], dtype=float64), right=array([24., 25.]),
+        interval=array([], shape=(0, 2), dtype=float64))
+        >>> print(data)
+        CensoredData(4 values: 2 not censored, 2 right-censored)
+        """
+        x, censored = _validate_x_censored(x, censored)
+        return cls(uncensored=x[~censored], right=x[censored])
+
+    @classmethod
+    def left_censored(cls, x, censored):
+        """
+        Create a `CensoredData` instance of left-censored data.
+
+        Parameters
+        ----------
+        x : array_like
+            `x` is the array of observed data or measurements.
+            `x` must be a one-dimensional sequence of finite numbers.
+        censored : array_like of bool
+            `censored` must be a one-dimensional sequence of boolean
+            values.  If ``censored[k]`` is True, the corresponding value
+            in `x` is left-censored.  That is, the value ``x[k]``
+            is the upper bound of the true (but unknown) value.
+
+        Returns
+        -------
+        data : `CensoredData`
+            An instance of `CensoredData` that represents the
+            collection of uncensored and left-censored values.
+
+        Examples
+        --------
+        >>> from scipy.stats import CensoredData
+
+        Two uncensored values (0.12 and 0.033) and two left-censored values
+        (both 1e-3).
+
+        >>> data = CensoredData.left_censored([0.12, 0.033, 1e-3, 1e-3],
+        ...                                   [False, False, True, True])
+        >>> data
+        CensoredData(uncensored=array([0.12 , 0.033]),
+        left=array([0.001, 0.001]), right=array([], dtype=float64),
+        interval=array([], shape=(0, 2), dtype=float64))
+        >>> print(data)
+        CensoredData(4 values: 2 not censored, 2 left-censored)
+        """
+        x, censored = _validate_x_censored(x, censored)
+        return cls(uncensored=x[~censored], left=x[censored])
+
+    @classmethod
+    def interval_censored(cls, low, high):
+        """
+        Create a `CensoredData` instance of interval-censored data.
+
+        This method is useful when all the data is interval-censored, and
+        the low and high ends of the intervals are already stored in
+        separate one-dimensional arrays.
+
+        Parameters
+        ----------
+        low : array_like
+            The one-dimensional array containing the low ends of the
+            intervals.
+        high : array_like
+            The one-dimensional array containing the high ends of the
+            intervals.
+
+        Returns
+        -------
+        data : `CensoredData`
+            An instance of `CensoredData` that represents the
+            collection of censored values.
+
+        Examples
+        --------
+        >>> import numpy as np
+        >>> from scipy.stats import CensoredData
+
+        ``a`` and ``b`` are the low and high ends of a collection of
+        interval-censored values.
+
+        >>> a = [0.5, 2.0, 3.0, 5.5]
+        >>> b = [1.0, 2.5, 3.5, 7.0]
+        >>> data = CensoredData.interval_censored(low=a, high=b)
+        >>> print(data)
+        CensoredData(4 values: 0 not censored, 4 interval-censored)
+        """
+        _validate_1d(low, 'low', allow_inf=True)
+        _validate_1d(high, 'high', allow_inf=True)
+        if len(low) != len(high):
+            raise ValueError('`low` and `high` must have the same length.')
+        interval = np.column_stack((low, high))
+        uncensored, left, right, interval = _validate_interval(interval)
+        return cls(uncensored=uncensored, left=left, right=right,
+                   interval=interval)
+
+    def _uncensor(self):
+        """
+        This function is used when a non-censored version of the data
+        is needed to create a rough estimate of the parameters of a
+        distribution via the method of moments or some similar method.
+        The data is "uncensored" by taking the given endpoints as the
+        data for the left- or right-censored data, and the mean for the
+        interval-censored data.
+        """
+        data = np.concatenate((self._uncensored, self._left, self._right,
+                               self._interval.mean(axis=1)))
+        return data
+
+    def _supported(self, a, b):
+        """
+        Return a subset of self containing the values that are in
+        (or overlap with) the interval (a, b).
+        """
+        uncensored = self._uncensored
+        uncensored = uncensored[(a < uncensored) & (uncensored < b)]
+        left = self._left
+        left = left[a < left]
+        right = self._right
+        right = right[right < b]
+        interval = self._interval
+        interval = interval[(a < interval[:, 1]) & (interval[:, 0] < b)]
+        return CensoredData(uncensored, left=left, right=right,
+                            interval=interval)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_common.py b/venv/lib/python3.12/site-packages/scipy/stats/_common.py
new file mode 100644
index 0000000000000000000000000000000000000000..4011d425cc4afea3c7ee8937526b13f1f92b0850
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_common.py
@@ -0,0 +1,5 @@
+from collections import namedtuple
+
+
+ConfidenceInterval = namedtuple("ConfidenceInterval", ["low", "high"])
+ConfidenceInterval. __doc__ = "Class for confidence intervals."
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_constants.py b/venv/lib/python3.12/site-packages/scipy/stats/_constants.py
new file mode 100644
index 0000000000000000000000000000000000000000..b539ce8146ebdbc8e08c66143461b04d742804f2
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_constants.py
@@ -0,0 +1,42 @@
+"""
+Statistics-related constants.
+
+"""
+import numpy as np
+
+
+# The smallest representable positive number such that 1.0 + _EPS != 1.0.
+_EPS = np.finfo(float).eps
+
+# The largest [in magnitude] usable floating value.
+_XMAX = np.finfo(float).max
+
+# The log of the largest usable floating value; useful for knowing
+# when exp(something) will overflow
+_LOGXMAX = np.log(_XMAX)
+
+# The smallest [in magnitude] usable (i.e. not subnormal) double precision
+# floating value.
+_XMIN = np.finfo(float).tiny
+
+# The log of the smallest [in magnitude] usable (i.e not subnormal)
+# double precision floating value.
+_LOGXMIN = np.log(_XMIN)
+
+# -special.psi(1)
+_EULER = 0.577215664901532860606512090082402431042
+
+# special.zeta(3, 1)  Apery's constant
+_ZETA3 = 1.202056903159594285399738161511449990765
+
+# sqrt(pi)
+_SQRT_PI = 1.772453850905516027298167483341145182798
+
+# sqrt(2/pi)
+_SQRT_2_OVER_PI = 0.7978845608028654
+
+# log(pi)
+_LOG_PI = 1.1447298858494002
+
+# log(sqrt(2/pi))
+_LOG_SQRT_2_OVER_PI = -0.22579135264472744
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_continued_fraction.py b/venv/lib/python3.12/site-packages/scipy/stats/_continued_fraction.py
new file mode 100644
index 0000000000000000000000000000000000000000..4966b1c99ed092ba3578aa7ca15b5ba8ea4bc6a9
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_continued_fraction.py
@@ -0,0 +1,387 @@
+import numpy as np
+
+from scipy._lib._array_api import (
+    array_namespace, xp_ravel, xp_copy, xp_promote
+)
+import scipy._lib._elementwise_iterative_method as eim
+from scipy._lib._util import _RichResult
+from scipy import special
+
+# Todo:
+# Avoid special-casing key 'n' in _lib._elementwise_iterative_method::_check_termination
+# Rearrange termination condition to allow absolute and relative tolerances?
+# Interpret/return |f_n - f_{n-1}| as an error estimate?
+# Return gracefully for size=0 arrays
+
+def _logaddexp(x, y, xp=None):
+    # logaddexp that supports complex numbers
+    xp = array_namespace(x, y) if xp is None else xp
+    x, y = xp.broadcast_arrays(x, y)
+    xy = xp.stack((x, y), axis=0)
+    return special.logsumexp(xy, axis=0)
+
+
+def _continued_fraction_iv(a, b, args, tolerances, maxiter, log):
+    # Input validation for `_continued_fraction`
+
+    if not callable(a) or not callable(b):
+        raise ValueError('`a` and `b` must be callable.')
+
+    if not np.iterable(args):
+        args = (args,)
+
+    # Call each callable once to determine namespace and dtypes
+    a0, b0 = a(0, *args), b(0, *args)
+    xp = array_namespace(a0, b0, *args)
+    a0, b0, *args = xp_promote(a0, b0, *args, force_floating=True, broadcast=True,
+                               xp=xp)
+    shape, dtype = a0.shape, a0.dtype
+    a0, b0, *args = (xp_ravel(arg) for arg in (a0, b0) + tuple(args))
+
+    tolerances = {} if tolerances is None else tolerances
+    eps = tolerances.get('eps', None)
+    tiny = tolerances.get('tiny', None)
+
+    # tolerances are floats, not arrays, so it's OK to use NumPy
+    message = ('`eps` and `tiny` must be (or represent the logarithm of) '
+               'finite, positive, real scalars.')
+    tols = np.asarray([eps if eps is not None else 1,
+                       tiny if tiny is not None else 1])
+    not_real = (not np.issubdtype(tols.dtype, np.number)
+                or np.issubdtype(tols.dtype, np.complexfloating))
+    not_positive = np.any(tols <= 0) if not log else False
+    not_finite = not np.all(np.isfinite(tols))
+    not_scalar = tols.shape != (2,)
+    if not_real or not_positive or not_finite or not_scalar:
+        raise ValueError(message)
+
+    maxiter_int = int(maxiter)
+    if maxiter != maxiter_int or maxiter < 0:
+        raise ValueError('`maxiter` must be a non-negative integer.')
+
+    if not isinstance(log, bool):
+        raise ValueError('`log` must be boolean.')
+
+    return a, b, args, eps, tiny, maxiter, log, a0, b0, shape, dtype, xp
+
+
+def _continued_fraction(a, b, *, args=(), tolerances=None, maxiter=100, log=False):
+    r"""Evaluate a generalized continued fraction numerically.
+
+    `_continued_fraction` iteratively evaluates convergents of a continued fraction
+    given coefficients returned by callables `a` and `b`. Iteration terminates when
+    `maxiter` terms have been evaluated or a termination criterion controlled by
+    `tolerances` is satisfied, and the final convergent is returned as the ``f``
+    attribute of the result object.
+
+    This function works elementwise when `args` contains (broadcastable) arrays.
+
+    Parameters
+    ----------
+    a, b: callable
+        Functions that provide the *numerator* and *denominator* coefficients of
+        the continued fraction, respectively.
+
+        The signature of each must be::
+
+            a(n: int, *argsj) -> ndarray
+
+        where ``n`` is the coefficient number and ``argsj`` is a tuple, which may
+        contain an arbitrary number of arrays of any shape. `a` and `b` must be
+        elementwise functions: each scalar element ``a(n, *argsj)[i]`` must equal
+        ``a(n, *[argj[i] for argj in argsj])`` for valid indices ``i``.
+        `a` and `b` must not mutate the arrays in ``argsj``.
+
+        The result shape is the broadcasted shape of ``a(0, *args)`` and
+        ``b(0, *args)``. The dtype used throughout computation is the result dtype
+        of these terms if it is a float, and the default float of the array library
+        otherwise. The numerical value of ``a(0, *args)`` is ignored, and
+        the value of the leading term ``b(0, *args)`` is the so-called "integer"
+        part of the continued fraction (although it need not be integral).
+
+    args : tuple of array_like, optional
+        Additional positional *array* arguments to be passed to `a` and `b`. Arrays
+        must be broadcastable with one another. If the coefficient callables
+        require additional arguments that are not broadcastable with one
+        another, wrap them with callables `a` and `b` such that `a` and `b` accept
+        only ``n`` and broadcastable array arguments.
+    tolerances : dictionary of floats, optional
+        Tolerances and numerical thresholds used by the algorithm. Currently,
+        valid keys of the dictionary are:
+
+        - ``eps`` - the convergence threshold of Lentz' algorithm
+        - ``tiny`` - not strictly a "tolerance", but a very small positive number
+          used to avoid division by zero
+
+        The default `eps` is the precision of the appropriate dtype, and the default
+        `tiny` is the precision squared. [1]_ advises that ``eps`` is "as small as
+        you like", but for most purposes, it should not be set smaller than the default
+        because it may prevent convergence of the algorithm. [1]_ also advises that
+        ``tiny`` should be less than typical values of ``eps * b(n)``, so the default
+        is a good choice unless the :math:`b_n` are very small. See [1]_ for details.
+    maxiter : int, default: 100
+        The maximum number of iterations of the algorithm to perform.
+    log : bool, default: False
+        If True, `a` and `b` return the (natural) logarithm of the terms, `tolerances`
+        contains the logarithm of the tolerances, and the result object reports the
+        logarithm of the convergent.
+
+    Returns
+    -------
+    res : _RichResult
+        An object similar to an instance of `scipy.optimize.OptimizeResult` with the
+        following attributes. The descriptions are written as though the values will
+        be scalars; however, if `f` returns an array, the outputs will be
+        arrays of the same shape.
+
+        success : bool array
+            ``True`` where the algorithm terminated successfully (status ``0``);
+            ``False`` otherwise.
+        status : int array
+            An integer representing the exit status of the algorithm.
+
+            - ``0`` : The algorithm converged to the specified tolerances.
+            - ``-2`` : The maximum number of iterations was reached.
+            - ``-3`` : A non-finite value was encountered.
+
+        f : float array
+            The convergent which satisfied a termination criterion.
+        nit : int array
+            The number of iterations of the algorithm that were performed.
+        nfev : int array
+            The number of terms that were evaluated.
+
+    Notes
+    -----
+    A generalized continued fraction is an expression of the form
+
+    .. math::
+
+        b_0 + \frac{a_1}{b_1 + \frac{a_2}{b_2 + \frac{a_3}{b_3 + \cdots}}}
+
+    Successive "convergents" approximate the infinitely recursive continued fraction
+    with a finite number of terms :math:`a_n` and :math:`b_n`, which are provided
+    by callables `a` and `b`, respectively. This implementation follows the modified
+    Lentz algorithm ([1]_, [2]_) to evaluate successive convergents until a
+    termination condition is satisfied.
+
+    References
+    ----------
+    .. [1] Press, William H., and Saul A. Teukolsky. "Evaluating continued fractions
+           and computing exponential integrals." Computers in Physics 2.5 (1988): 88-89.
+    .. [2] Lentz's algorithm. Wikipedia.
+           https://en.wikipedia.org/wiki/Lentz%27s_algorithm
+    .. [3] Continued fraction. Wikipedia.
+           https://en.wikipedia.org/wiki/Continued_fraction
+    .. [4] Generalized continued fraction. Wikipedia.
+           https://en.wikipedia.org/wiki/Generalized_continued_fraction
+
+    Examples
+    --------
+    The "simple continued fraction" of :math:`\pi` is given in [3]_ as
+
+    .. math::
+
+        3 + \frac{1}{7 + \frac{1}{15 + \frac{1}{1 + \cdots}}}
+
+    where the :math:`b_n` terms follow no obvious pattern:
+
+    >>> b = [3, 7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1]
+
+    and the :math:`a_n` terms are all :math:`1`.
+    In this case, all the terms have been precomputed, so we call `_continued_fraction`
+    with simple callables which simply return the precomputed coefficients:
+
+    >>> import numpy as np
+    >>> from scipy.special._continued_fraction import _continued_fraction
+    >>> res = _continued_fraction(a=lambda n: 1, b=lambda n: b[n], maxiter=len(b) - 1)
+    >>> (res.f - np.pi) / np.pi
+    np.float64(7.067899292141148e-15)
+
+    A generalized continued fraction for :math:`\pi` is given by:
+
+    .. math::
+
+        3 + \frac{1^2}{6 + \frac{3^2}{6 + \frac{5^2}{6 + \cdots}}}
+
+    We define the coefficient callables as:
+
+    >>> def a(n):
+    ...     return (2*n - 1)**2
+    >>>
+    >>> def b(n):
+    ...     if n == 0:
+    ...         return 3
+    ...     else:
+    ...         return 6
+
+    Then the continued fraction can be evaluated as:
+
+    >>> res = _continued_fraction(a, b)
+    >>> res
+         success: False
+          status: -2
+               f: 3.1415924109719846
+             nit: 100
+            nfev: 101
+
+    Note that the requested tolerance was not reached within the (default)
+    maximum number of iterations because it converges very slowly.
+    An expression that converges more rapidly is expressed as the difference
+    between two continued fractions. We will compute both of them in one
+    vectorized call to `_continued_fraction`.
+
+    >>> u, v = 5, 239
+    >>>
+    >>> def a(n, a1, _):
+    ...     # The shape of the output must be the shape of the arguments
+    ...     shape = a1.shape
+    ...     if n == 0:
+    ...         return np.zeros(shape)
+    ...     elif n == 1:
+    ...         return a1
+    ...     else:
+    ...         return np.full(shape, (n-1)**2)
+    >>>
+    >>> def b(n, _, uv):
+    ...     shape = uv.shape
+    ...     if  n == 0:
+    ...         return np.zeros(shape)
+    ...     return np.full(shape, (2*n - 1)*uv)
+    >>>
+    >>> res = _continued_fraction(a, b, args=([16, 4], [u, v]))
+    >>> res
+         success: [ True  True]
+          status: [0 0]
+               f: [ 3.158e+00  1.674e-02]
+             nit: [10  4]
+            nfev: [11  5]
+
+    Note that the second term converged in fewer than half the number of iterations
+    as the first. The approximation of :math:`\pi` is the difference between the two:
+
+    >>> pi = res.f[0] - res.f[1]
+    >>> (pi - np.pi) / np.pi
+    np.float64(2.8271597168564594e-16)
+
+    If it is more efficient to compute the :math:`a_n` and :math:`b_n` terms together,
+    consider instantiating a class with a method that computes both terms and stores
+    the results in an attribute. Separate methods of the class retrieve the
+    coefficients, and these methods are passed to `_continued_fraction` as arguments
+    `a` and `b`. Similarly,if the coefficients can be computed recursively in terms of
+    previous coefficients, use a class to maintain state between callable evaluations.
+
+    """
+
+    res = _continued_fraction_iv(a, b, args, tolerances, maxiter, log)
+    a, b, args, eps, tiny, maxiter, log, a0, b0, shape, dtype, xp = res
+    callback = None  # don't want to test it, but easy to add later
+
+    # The EIM framework was designed for the case in where there would
+    # be only one callable, and all arguments of the callable would be
+    # arrays. We're going a bit beyond that here, since we have two callables,
+    # and the first argument is an integer (the number of the term). Rather
+    # than complicate the framework, we wrap the user-provided callables to
+    # make this problem fit within the existing framework.
+
+    def a(n, *args, a=a):
+        n = int(xp.real(xp_ravel(n))[0])
+        return a(n, *args)
+
+    def b(n, *args, b=b):
+        n = int(xp.real(xp_ravel(n))[0])
+        return b(n, *args)
+
+    def func(n, *args):
+        return xp.stack((a(n, *args), b(n, *args)), axis=-1)
+
+    status = xp.full_like(a0, eim._EINPROGRESS, dtype=xp.int32)  # in progress
+    nit, nfev = 0, 1  # one function evaluation (per function) performed above
+    maxiter = 100 if maxiter is None else maxiter
+
+    # Quotations describing the algorithm are from [1]_
+    # "... as small as you like, say eps"
+    if eps is None:
+        eps = xp.finfo(dtype).eps if not log else np.log(xp.finfo(dtype).eps)
+
+    # "The parameter tiny should be less than typical values of eps |b_n|"
+    if tiny is None:
+        tiny = xp.finfo(dtype).eps**2 if not log else 2*np.log(xp.finfo(dtype).eps)
+
+    # "Set f0 and C0 to the value b0 or to tiny if b0=0. Set D0 = 0.
+    zero = -xp.inf if log else 0
+    fn = xp.where(b0 == zero, tiny, b0)
+    Cnm1 = xp_copy(fn)
+    Dnm1 = xp.full_like(fn, zero)
+
+    CnDn = xp.full_like(fn, xp.inf)
+
+    work = _RichResult(n=0, fn=fn, Cnm1=Cnm1, Dnm1=Dnm1, CnDn=CnDn,
+                       eps=eps, tiny=tiny,
+                       nit=nit, nfev=nfev, status=status)
+    res_work_pairs = [('status', 'status'), ('f', 'fn'),
+                      ('nit', 'nit'), ('nfev', 'nfev')]
+
+    def pre_func_eval(work):
+        work.n = xp.reshape(xp.asarray(work.n + 1), (-1,))
+        return work.n
+
+    def post_func_eval(n, ab, work):
+        an, bn = ab[..., 0], ab[..., 1]
+
+        zero = 0 if not log else -xp.inf
+
+        # "Set D_n = 1/(b_n + a_n D_{n-1}) or 1/tiny, if the denominator vanishes"
+        denominator = (bn + an*work.Dnm1 if not log
+                       else _logaddexp(bn, an + work.Dnm1, xp=xp))
+        denominator[denominator == zero] = tiny
+        Dn = (1/denominator if not log
+              else -denominator)
+
+        # "Set C_n = b_n + a_n / C_{n-1} (or =tiny, if the expression vanishes)"
+        Cn = (bn + an / work.Cnm1 if not log
+              else _logaddexp(bn, an - work.Cnm1, xp=xp))
+        Cn[Cn == zero] = tiny
+
+        # "and set f_n = f_{n-1} C_n D_n"
+        work.CnDn = (Cn * Dn if not log
+                     else Cn + Dn)
+        work.fn = (work.fn * work.CnDn if not log
+                   else work.fn + work.CnDn)
+
+
+        work.Cnm1, work.Dnm1 = Cn, Dn
+
+    def check_termination(work):
+        # Check for all terminal conditions and record statuses.
+        stop = xp.zeros_like(work.CnDn, dtype=xp.bool)
+
+        # "You quit when |D_n C_n - 1| is as small as you like, say eps"
+        pij = xp.full_like(work.CnDn, xp.pi*1j) if log else None
+        residual = (xp.abs(work.CnDn - 1) if not log
+                    else xp.real(_logaddexp(work.CnDn, pij, xp=xp)))
+        i = residual < work.eps
+        work.status[i] = eim._ECONVERGED
+        stop[i] = True
+
+        # If function value is NaN, report failure.
+        i = (~xp.isfinite(work.fn) if not log
+             else ~(xp.isfinite(work.fn) | (work.fn == -xp.inf)))
+        work.status[i] = eim._EVALUEERR
+        stop[i] = True
+
+        return stop
+
+    def post_termination_check(work):
+        pass
+
+    def customize_result(res, shape):
+        # Only needed pre-NEP 50
+        res['f'] = xp.asarray(res['f'], dtype=dtype)
+        res['f'] = res['f'][()] if res['f'].ndim == 0 else res['f']
+        return shape
+
+    return eim._loop(work, callback, shape, maxiter, func, args, dtype,
+                     pre_func_eval, post_func_eval, check_termination,
+                     post_termination_check, customize_result, res_work_pairs,
+                     xp=xp)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_continuous_distns.py b/venv/lib/python3.12/site-packages/scipy/stats/_continuous_distns.py
new file mode 100644
index 0000000000000000000000000000000000000000..98029b3ec326e29bb33ce9832232b89ab31e2641
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_continuous_distns.py
@@ -0,0 +1,12628 @@
+#
+# Author:  Travis Oliphant  2002-2011 with contributions from
+#          SciPy Developers 2004-2011
+#
+import warnings
+from collections.abc import Iterable
+from functools import wraps, cached_property
+import ctypes
+import operator
+
+import numpy as np
+from numpy.polynomial import Polynomial
+from scipy.interpolate import BSpline
+from scipy._lib.doccer import (extend_notes_in_docstring,
+                               replace_notes_in_docstring,
+                               inherit_docstring_from)
+from scipy._lib._ccallback import LowLevelCallable
+from scipy import optimize
+from scipy import integrate
+import scipy.special as sc
+
+import scipy.special._ufuncs as scu
+from scipy._lib._util import _lazyselect
+import scipy._external.array_api_extra as xpx
+from scipy._lib._array_api import xp_promote
+
+from . import _stats
+from ._tukeylambda_stats import (tukeylambda_variance as _tlvar,
+                                 tukeylambda_kurtosis as _tlkurt)
+from ._distn_infrastructure import (_vectorize_rvs_over_shapes,
+    get_distribution_names, _kurtosis, _isintegral,
+    rv_continuous, _skew, _get_fixed_fit_value, _check_shape, _ShapeInfo)
+from ._ksstats import kolmogn, kolmognp, kolmogni
+from ._constants import (_XMIN, _LOGXMIN, _EULER, _ZETA3, _SQRT_PI,
+                         _SQRT_2_OVER_PI, _LOG_PI, _LOG_SQRT_2_OVER_PI)
+from ._censored_data import CensoredData
+from scipy.optimize import root_scalar
+from scipy.stats._warnings_errors import FitError
+import scipy.stats as stats
+
+def _remove_optimizer_parameters(kwds):
+    """
+    Remove the optimizer-related keyword arguments 'loc', 'scale' and
+    'optimizer' from `kwds`.  Then check that `kwds` is empty, and
+    raise `TypeError("Unknown arguments: %s." % kwds)` if it is not.
+
+    This function is used in the fit method of distributions that override
+    the default method and do not use the default optimization code.
+
+    `kwds` is modified in-place.
+    """
+    kwds.pop('loc', None)
+    kwds.pop('scale', None)
+    kwds.pop('optimizer', None)
+    kwds.pop('method', None)
+    if kwds:
+        raise TypeError(f"Unknown arguments: {kwds}.")
+
+
+def _call_super_mom(fun):
+    # If fit method is overridden only for MLE and doesn't specify what to do
+    # if method == 'mm' or with censored data, this decorator calls the generic
+    # implementation.
+    @wraps(fun)
+    def wrapper(self, data, *args, **kwds):
+        method = kwds.get('method', 'mle').lower()
+        censored = isinstance(data, CensoredData)
+        if method == 'mm' or (censored and data.num_censored() > 0):
+            return super(type(self), self).fit(data, *args, **kwds)
+        else:
+            if censored:
+                # data is an instance of CensoredData, but actually holds
+                # no censored values, so replace it with the array of
+                # uncensored values.
+                data = data._uncensored
+            return fun(self, data, *args, **kwds)
+
+    return wrapper
+
+
+def _get_left_bracket(fun, rbrack, lbrack=None):
+    # find left bracket for `root_scalar`. A guess for lbrack may be provided.
+    lbrack = lbrack or rbrack - 1
+    diff = rbrack - lbrack
+
+    # if there is no sign change in `fun` between the brackets, expand
+    # rbrack - lbrack until a sign change occurs
+    def interval_contains_root(lbrack, rbrack):
+        # return true if the signs disagree.
+        return np.sign(fun(lbrack)) != np.sign(fun(rbrack))
+
+    while not interval_contains_root(lbrack, rbrack):
+        diff *= 2
+        lbrack = rbrack - diff
+
+        msg = ("The solver could not find a bracket containing a "
+               "root to an MLE first order condition.")
+        if np.isinf(lbrack):
+            raise FitSolverError(msg)
+
+    return lbrack
+
+
+class ksone_gen(rv_continuous):
+    r"""Kolmogorov-Smirnov one-sided test statistic distribution.
+
+    This is the distribution of the one-sided Kolmogorov-Smirnov (KS)
+    statistics :math:`D_n^+` and :math:`D_n^-`
+    for a finite sample size ``n >= 1`` (the shape parameter).
+
+    %(before_notes)s
+
+    See Also
+    --------
+    kstwobign, kstwo, kstest
+
+    Notes
+    -----
+    :math:`D_n^+` and :math:`D_n^-` are given by
+
+    .. math::
+
+        D_n^+ &= \text{sup}_x (F_n(x) - F(x)),\\
+        D_n^- &= \text{sup}_x (F(x) - F_n(x)),\\
+
+    where :math:`F` is a continuous CDF and :math:`F_n` is an empirical CDF.
+    `ksone` describes the distribution under the null hypothesis of the KS test
+    that the empirical CDF corresponds to :math:`n` i.i.d. random variates
+    with CDF :math:`F`.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] Birnbaum, Z. W. and Tingey, F.H. "One-sided confidence contours
+       for probability distribution functions", The Annals of Mathematical
+       Statistics, 22(4), pp 592-596 (1951).
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import ksone
+    >>> import matplotlib.pyplot as plt
+    >>> fig, ax = plt.subplots(1, 1)
+
+    Display the probability density function (``pdf``):
+
+    >>> n = 1e+03
+    >>> x = np.linspace(ksone.ppf(0.01, n),
+    ...                 ksone.ppf(0.99, n), 100)
+    >>> ax.plot(x, ksone.pdf(x, n),
+    ...         'r-', lw=5, alpha=0.6, label='ksone pdf')
+
+    Alternatively, the distribution object can be called (as a function)
+    to fix the shape, location and scale parameters. This returns a "frozen"
+    RV object holding the given parameters fixed.
+
+    Freeze the distribution and display the frozen ``pdf``:
+
+    >>> rv = ksone(n)
+    >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
+    >>> ax.legend(loc='best', frameon=False)
+    >>> plt.show()
+
+    Check accuracy of ``cdf`` and ``ppf``:
+
+    >>> vals = ksone.ppf([0.001, 0.5, 0.999], n)
+    >>> np.allclose([0.001, 0.5, 0.999], ksone.cdf(vals, n))
+    True
+
+    """
+    def _argcheck(self, n):
+        return (n >= 1) & (n == np.round(n))
+
+    def _shape_info(self):
+        return [_ShapeInfo("n", True, (1, np.inf), (True, False))]
+
+    def _pdf(self, x, n):
+        return -scu._smirnovp(n, x)
+
+    def _cdf(self, x, n):
+        return scu._smirnovc(n, x)
+
+    def _sf(self, x, n):
+        return sc.smirnov(n, x)
+
+    def _ppf(self, q, n):
+        return scu._smirnovci(n, q)
+
+    def _isf(self, q, n):
+        return sc.smirnovi(n, q)
+
+
+ksone = ksone_gen(a=0.0, b=1.0, name='ksone')
+
+
+class kstwo_gen(rv_continuous):
+    r"""Kolmogorov-Smirnov two-sided test statistic distribution.
+
+    This is the distribution of the two-sided Kolmogorov-Smirnov (KS)
+    statistic :math:`D_n` for a finite sample size ``n >= 1``
+    (the shape parameter).
+
+    %(before_notes)s
+
+    See Also
+    --------
+    kstwobign, ksone, kstest
+
+    Notes
+    -----
+    :math:`D_n` is given by
+
+    .. math::
+
+        D_n = \text{sup}_x |F_n(x) - F(x)|
+
+    where :math:`F` is a (continuous) CDF and :math:`F_n` is an empirical CDF.
+    `kstwo` describes the distribution under the null hypothesis of the KS test
+    that the empirical CDF corresponds to :math:`n` i.i.d. random variates
+    with CDF :math:`F`.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] Simard, R., L'Ecuyer, P. "Computing the Two-Sided
+       Kolmogorov-Smirnov Distribution",  Journal of Statistical Software,
+       Vol 39, 11, 1-18 (2011).
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import kstwo
+    >>> import matplotlib.pyplot as plt
+    >>> fig, ax = plt.subplots(1, 1)
+
+    Display the probability density function (``pdf``):
+
+    >>> n = 10
+    >>> x = np.linspace(kstwo.ppf(0.01, n),
+    ...                 kstwo.ppf(0.99, n), 100)
+    >>> ax.plot(x, kstwo.pdf(x, n),
+    ...         'r-', lw=5, alpha=0.6, label='kstwo pdf')
+
+    Alternatively, the distribution object can be called (as a function)
+    to fix the shape, location and scale parameters. This returns a "frozen"
+    RV object holding the given parameters fixed.
+
+    Freeze the distribution and display the frozen ``pdf``:
+
+    >>> rv = kstwo(n)
+    >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
+    >>> ax.legend(loc='best', frameon=False)
+    >>> plt.show()
+
+    Check accuracy of ``cdf`` and ``ppf``:
+
+    >>> vals = kstwo.ppf([0.001, 0.5, 0.999], n)
+    >>> np.allclose([0.001, 0.5, 0.999], kstwo.cdf(vals, n))
+    True
+
+    """
+    def _argcheck(self, n):
+        return (n >= 1) & (n == np.round(n))
+
+    def _shape_info(self):
+        return [_ShapeInfo("n", True, (1, np.inf), (True, False))]
+
+    def _get_support(self, n):
+        return (0.5/(n if not isinstance(n, Iterable) else np.asanyarray(n)),
+                1.0)
+
+    def _pdf(self, x, n):
+        return kolmognp(n, x)
+
+    def _cdf(self, x, n):
+        return kolmogn(n, x)
+
+    def _sf(self, x, n):
+        return kolmogn(n, x, cdf=False)
+
+    def _ppf(self, q, n):
+        return kolmogni(n, q, cdf=True)
+
+    def _isf(self, q, n):
+        return kolmogni(n, q, cdf=False)
+
+
+# Use the pdf, (not the ppf) to compute moments
+kstwo = kstwo_gen(momtype=0, a=0.0, b=1.0, name='kstwo')
+
+
+class kstwobign_gen(rv_continuous):
+    r"""Limiting distribution of scaled Kolmogorov-Smirnov two-sided test statistic.
+
+    This is the asymptotic distribution of the two-sided Kolmogorov-Smirnov
+    statistic :math:`\sqrt{n} D_n` that measures the maximum absolute
+    distance of the theoretical (continuous) CDF from the empirical CDF.
+    (see `kstest`).
+
+    %(before_notes)s
+
+    See Also
+    --------
+    ksone, kstwo, kstest
+
+    Notes
+    -----
+    :math:`\sqrt{n} D_n` is given by
+
+    .. math::
+
+        D_n = \text{sup}_x |F_n(x) - F(x)|
+
+    where :math:`F` is a continuous CDF and :math:`F_n` is an empirical CDF.
+    `kstwobign`  describes the asymptotic distribution (i.e. the limit of
+    :math:`\sqrt{n} D_n`) under the null hypothesis of the KS test that the
+    empirical CDF corresponds to i.i.d. random variates with CDF :math:`F`.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] Feller, W. "On the Kolmogorov-Smirnov Limit Theorems for Empirical
+       Distributions",  Ann. Math. Statist. Vol 19, 177-189 (1948).
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return []
+
+    def _pdf(self, x):
+        return -scu._kolmogp(x)
+
+    def _cdf(self, x):
+        return scu._kolmogc(x)
+
+    def _sf(self, x):
+        return sc.kolmogorov(x)
+
+    def _ppf(self, q):
+        return scu._kolmogci(q)
+
+    def _isf(self, q):
+        return sc.kolmogi(q)
+
+
+kstwobign = kstwobign_gen(a=0.0, name='kstwobign')
+
+
+## Normal distribution
+
+# loc = mu, scale = std
+# Keep these implementations out of the class definition so they can be reused
+# by other distributions.
+_norm_pdf_C = np.sqrt(2*np.pi)
+_norm_pdf_logC = np.log(_norm_pdf_C)
+
+
+def _norm_pdf(x):
+    return np.exp(-x**2/2.0) / _norm_pdf_C
+
+
+def _norm_logpdf(x):
+    return -x**2 / 2.0 - _norm_pdf_logC
+
+
+def _norm_cdf(x):
+    return sc.ndtr(x)
+
+
+def _norm_logcdf(x):
+    return sc.log_ndtr(x)
+
+
+def _norm_ppf(q):
+    return sc.ndtri(q)
+
+
+def _norm_sf(x):
+    return _norm_cdf(-x)
+
+
+def _norm_logsf(x):
+    return _norm_logcdf(-x)
+
+
+def _norm_isf(q):
+    return -_norm_ppf(q)
+
+
+class norm_gen(rv_continuous):
+    r"""A normal continuous random variable.
+
+    The location (``loc``) keyword specifies the mean.
+    The scale (``scale``) keyword specifies the standard deviation.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `norm` is:
+
+    .. math::
+
+        f(x) = \frac{\exp(-x^2/2)}{\sqrt{2\pi}}
+
+    for a real number :math:`x`.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return []
+
+    def _rvs(self, size=None, random_state=None):
+        return random_state.standard_normal(size)
+
+    def _pdf(self, x):
+        # norm.pdf(x) = exp(-x**2/2)/sqrt(2*pi)
+        return _norm_pdf(x)
+
+    def _logpdf(self, x):
+        return _norm_logpdf(x)
+
+    def _cdf(self, x):
+        return _norm_cdf(x)
+
+    def _logcdf(self, x):
+        return _norm_logcdf(x)
+
+    def _sf(self, x):
+        return _norm_sf(x)
+
+    def _logsf(self, x):
+        return _norm_logsf(x)
+
+    def _ppf(self, q):
+        return _norm_ppf(q)
+
+    def _isf(self, q):
+        return _norm_isf(q)
+
+    def _stats(self):
+        return 0.0, 1.0, 0.0, 0.0
+
+    def _entropy(self):
+        return 0.5*(np.log(2*np.pi)+1)
+
+    @_call_super_mom
+    @replace_notes_in_docstring(rv_continuous, notes="""\
+        For the normal distribution, method of moments and maximum likelihood
+        estimation give identical fits, and explicit formulas for the estimates
+        are available.
+        This function uses these explicit formulas for the maximum likelihood
+        estimation of the normal distribution parameters, so the
+        `optimizer` and `method` arguments are ignored.\n\n""")
+    def fit(self, data, **kwds):
+        floc = kwds.pop('floc', None)
+        fscale = kwds.pop('fscale', None)
+
+        _remove_optimizer_parameters(kwds)
+
+        if floc is not None and fscale is not None:
+            # This check is for consistency with `rv_continuous.fit`.
+            # Without this check, this function would just return the
+            # parameters that were given.
+            raise ValueError("All parameters fixed. There is nothing to "
+                             "optimize.")
+
+        data = np.asarray(data)
+
+        if not np.isfinite(data).all():
+            raise ValueError("The data contains non-finite values.")
+
+        if floc is None:
+            loc = data.mean()
+        else:
+            loc = floc
+
+        if fscale is None:
+            scale = np.sqrt(((data - loc)**2).mean())
+        else:
+            scale = fscale
+
+        return loc, scale
+
+    def _munp(self, n):
+        """
+        @returns Moments of standard normal distribution for integer n >= 0
+
+        See eq. 16 of https://arxiv.org/abs/1209.4340v2
+        """
+        if n == 0:
+            return 1.
+        if n % 2 == 0:
+            return sc.factorial2(int(n) - 1)
+        else:
+            return 0.
+
+
+norm = norm_gen(name='norm')
+
+
+class alpha_gen(rv_continuous):
+    r"""An alpha continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `alpha` ([1]_, [2]_) is:
+
+    .. math::
+
+        f(x, a) = \frac{1}{x^2 \Phi(a) \sqrt{2\pi}} *
+                  \exp(-\frac{1}{2} (a-1/x)^2)
+
+    where :math:`\Phi` is the normal CDF, :math:`x > 0`, and :math:`a > 0`.
+
+    `alpha` takes ``a`` as a shape parameter.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] Johnson, Kotz, and Balakrishnan, "Continuous Univariate
+           Distributions, Volume 1", Second Edition, John Wiley and Sons,
+           p. 173 (1994).
+    .. [2] Anthony A. Salvia, "Reliability applications of the Alpha
+           Distribution", IEEE Transactions on Reliability, Vol. R-34,
+           No. 3, pp. 251-252 (1985).
+
+    %(example)s
+
+    """
+    _support_mask = rv_continuous._open_support_mask
+
+    def _shape_info(self):
+        return [_ShapeInfo("a", False, (0, np.inf), (False, False))]
+
+    def _pdf(self, x, a):
+        # alpha.pdf(x, a) = 1/(x**2*Phi(a)*sqrt(2*pi)) * exp(-1/2 * (a-1/x)**2)
+        return 1.0/(x**2)/_norm_cdf(a)*_norm_pdf(a-1.0/x)
+
+    def _logpdf(self, x, a):
+        return -2*np.log(x) + _norm_logpdf(a-1.0/x) - np.log(_norm_cdf(a))
+
+    def _cdf(self, x, a):
+        return _norm_cdf(a-1.0/x) / _norm_cdf(a)
+
+    def _ppf(self, q, a):
+        return 1.0/np.asarray(a - _norm_ppf(q*_norm_cdf(a)))
+
+    def _stats(self, a):
+        return [np.inf]*2 + [np.nan]*2
+
+
+alpha = alpha_gen(a=0.0, name='alpha')
+
+
+class anglit_gen(rv_continuous):
+    r"""An anglit continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `anglit` is:
+
+    .. math::
+
+        f(x) = \sin(2x + \pi/2) = \cos(2x)
+
+    for :math:`-\pi/4 \le x \le \pi/4`.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return []
+
+    def _pdf(self, x):
+        # anglit.pdf(x) = sin(2*x + \pi/2) = cos(2*x)
+        return np.cos(2*x)
+
+    def _cdf(self, x):
+        return np.sin(x+np.pi/4)**2.0
+
+    def _sf(self, x):
+        return np.cos(x + np.pi / 4) ** 2.0
+
+    def _ppf(self, q):
+        return np.arcsin(np.sqrt(q))-np.pi/4
+
+    def _stats(self):
+        return 0.0, np.pi*np.pi/16-0.5, 0.0, -2*(np.pi**4 - 96)/(np.pi*np.pi-8)**2
+
+    def _entropy(self):
+        return 1-np.log(2)
+
+
+anglit = anglit_gen(a=-np.pi/4, b=np.pi/4, name='anglit')
+
+
+class arcsine_gen(rv_continuous):
+    r"""An arcsine continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `arcsine` is:
+
+    .. math::
+
+        f(x) = \frac{1}{\pi \sqrt{x (1-x)}}
+
+    for :math:`0 < x < 1`.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return []
+
+    def _pdf(self, x):
+        # arcsine.pdf(x) = 1/(pi*sqrt(x*(1-x)))
+        with np.errstate(divide='ignore'):
+            return 1.0/np.pi/np.sqrt(x*(1-x))
+
+    def _cdf(self, x):
+        return 2.0/np.pi*np.arcsin(np.sqrt(x))
+
+    def _ppf(self, q):
+        return np.sin(np.pi/2.0*q)**2.0
+
+    def _stats(self):
+        mu = 0.5
+        mu2 = 1.0/8
+        g1 = 0
+        g2 = -3.0/2.0
+        return mu, mu2, g1, g2
+
+    def _entropy(self):
+        return -0.24156447527049044468
+
+
+arcsine = arcsine_gen(a=0.0, b=1.0, name='arcsine')
+
+
+class FitDataError(ValueError):
+    """Raised when input data is inconsistent with fixed parameters."""
+    # This exception is raised by, for example, beta_gen.fit when both floc
+    # and fscale are fixed and there are values in the data not in the open
+    # interval (floc, floc+fscale).
+    def __init__(self, distr, lower, upper):
+        self.args = (
+            "Invalid values in `data`.  Maximum likelihood "
+            f"estimation with {distr!r} requires that {lower!r} < "
+            f"(x - loc)/scale  < {upper!r} for each x in `data`.",
+        )
+
+
+class FitSolverError(FitError):
+    """
+    Raised when a solver fails to converge while fitting a distribution.
+    """
+    # This exception is raised by, for example, beta_gen.fit when
+    # optimize.fsolve returns with ier != 1.
+    def __init__(self, mesg):
+        emsg = "Solver for the MLE equations failed to converge: "
+        emsg += mesg.replace('\n', '')
+        self.args = (emsg,)
+
+
+def _beta_mle_a(a, b, n, s1):
+    # The zeros of this function give the MLE for `a`, with
+    # `b`, `n` and `s1` given.  `s1` is the sum of the logs of
+    # the data. `n` is the number of data points.
+    psiab = sc.psi(a + b)
+    func = s1 - n * (-psiab + sc.psi(a))
+    return func
+
+
+def _beta_mle_ab(theta, n, s1, s2):
+    # Zeros of this function are critical points of
+    # the maximum likelihood function.  Solving this system
+    # for theta (which contains a and b) gives the MLE for a and b
+    # given `n`, `s1` and `s2`.  `s1` is the sum of the logs of the data,
+    # and `s2` is the sum of the logs of 1 - data.  `n` is the number
+    # of data points.
+    a, b = theta
+    psiab = sc.psi(a + b)
+    func = [s1 - n * (-psiab + sc.psi(a)),
+            s2 - n * (-psiab + sc.psi(b))]
+    return func
+
+
+class beta_gen(rv_continuous):
+    r"""A beta continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `beta` is:
+
+    .. math::
+
+        f(x, a, b) = \frac{\Gamma(a+b) x^{a-1} (1-x)^{b-1}}
+                          {\Gamma(a) \Gamma(b)}
+
+    for :math:`0 <= x <= 1`, :math:`a > 0`, :math:`b > 0`, where
+    :math:`\Gamma` is the gamma function (`scipy.special.gamma`).
+
+    `beta` takes :math:`a` and :math:`b` as shape parameters.
+
+    This distribution uses routines from the Boost Math C++ library for
+    the computation of the ``pdf``, ``cdf``, ``ppf``, ``sf`` and ``isf``
+    methods. [1]_
+
+    Maximum likelihood estimates of parameters are only available when the location and
+    scale are fixed. When either of these parameters is free, ``beta.fit`` resorts to
+    numerical optimization, but this problem is unbounded: the location and scale may be
+    chosen to make the minimum and maximum elements of the data coincide with the
+    endpoints of the support, and the shape parameters may be chosen to make the PDF at
+    these points infinite. For best results, pass ``floc`` and ``fscale`` keyword
+    arguments to fix the location and scale, or use `scipy.stats.fit` with
+    ``method='mse'``.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        ia = _ShapeInfo("a", False, (0, np.inf), (False, False))
+        ib = _ShapeInfo("b", False, (0, np.inf), (False, False))
+        return [ia, ib]
+
+    def _rvs(self, a, b, size=None, random_state=None):
+        return random_state.beta(a, b, size)
+
+    def _pdf(self, x, a, b):
+        #                     gamma(a+b) * x**(a-1) * (1-x)**(b-1)
+        # beta.pdf(x, a, b) = ------------------------------------
+        #                              gamma(a)*gamma(b)
+        with np.errstate(over='ignore'):
+            return scu._beta_pdf(x, a, b)
+
+    def _logpdf(self, x, a, b):
+        lPx = sc.xlog1py(b - 1.0, -x) + sc.xlogy(a - 1.0, x)
+        lPx -= sc.betaln(a, b)
+        return lPx
+
+    def _cdf(self, x, a, b):
+        return sc.betainc(a, b, x)
+
+    def _sf(self, x, a, b):
+        return sc.betaincc(a, b, x)
+
+    def _isf(self, x, a, b):
+        return sc.betainccinv(a, b, x)
+
+    def _ppf(self, q, a, b):
+        return scu._beta_ppf(q, a, b)
+
+    def _stats(self, a, b):
+        a_plus_b = a + b
+        _beta_mean = a/a_plus_b
+        _beta_variance = a*b / (a_plus_b**2 * (a_plus_b + 1))
+        _beta_skewness = ((2 * (b - a) * np.sqrt(a_plus_b + 1)) /
+                          ((a_plus_b + 2) * np.sqrt(a * b)))
+        _beta_kurtosis_excess_n = 6 * ((a - b)**2 * (a_plus_b + 1) -
+                                       a * b * (a_plus_b + 2))
+        _beta_kurtosis_excess_d = a * b * (a_plus_b + 2) * (a_plus_b + 3)
+        _beta_kurtosis_excess = _beta_kurtosis_excess_n / _beta_kurtosis_excess_d
+        return (
+            _beta_mean,
+            _beta_variance,
+            _beta_skewness,
+            _beta_kurtosis_excess)
+
+    def _fitstart(self, data):
+        if isinstance(data, CensoredData):
+            data = data._uncensor()
+
+        g1 = _skew(data)
+        g2 = _kurtosis(data)
+
+        def func(x):
+            a, b = x
+            sk = 2*(b-a)*np.sqrt(a + b + 1) / (a + b + 2) / np.sqrt(a*b)
+            ku = a**3 - a**2*(2*b-1) + b**2*(b+1) - 2*a*b*(b+2)
+            ku /= a*b*(a+b+2)*(a+b+3)
+            ku *= 6
+            return [sk-g1, ku-g2]
+        a, b = optimize.fsolve(func, (1.0, 1.0))
+        return super()._fitstart(data, args=(a, b))
+
+    @_call_super_mom
+    @extend_notes_in_docstring(rv_continuous, notes="""\
+        In the special case where `method="MLE"` and
+        both `floc` and `fscale` are given, a
+        `ValueError` is raised if any value `x` in `data` does not satisfy
+        `floc < x < floc + fscale`.\n\n""")
+    def fit(self, data, *args, **kwds):
+        # Override rv_continuous.fit, so we can more efficiently handle the
+        # case where floc and fscale are given.
+
+        floc = kwds.get('floc', None)
+        fscale = kwds.get('fscale', None)
+
+        if floc is None or fscale is None:
+            # do general fit
+            return super().fit(data, *args, **kwds)
+
+        # We already got these from kwds, so just pop them.
+        kwds.pop('floc', None)
+        kwds.pop('fscale', None)
+
+        f0 = _get_fixed_fit_value(kwds, ['f0', 'fa', 'fix_a'])
+        f1 = _get_fixed_fit_value(kwds, ['f1', 'fb', 'fix_b'])
+
+        _remove_optimizer_parameters(kwds)
+
+        if f0 is not None and f1 is not None:
+            # This check is for consistency with `rv_continuous.fit`.
+            raise ValueError("All parameters fixed. There is nothing to "
+                             "optimize.")
+
+        # Special case: loc and scale are constrained, so we are fitting
+        # just the shape parameters.  This can be done much more efficiently
+        # than the method used in `rv_continuous.fit`.  (See the subsection
+        # "Two unknown parameters" in the section "Maximum likelihood" of
+        # the Wikipedia article on the Beta distribution for the formulas.)
+
+        if not np.isfinite(data).all():
+            raise ValueError("The data contains non-finite values.")
+
+        # Normalize the data to the interval [0, 1].
+        data = (np.ravel(data) - floc) / fscale
+        if np.any(data <= 0) or np.any(data >= 1):
+            raise FitDataError("beta", lower=floc, upper=floc + fscale)
+
+        xbar = data.mean()
+
+        if f0 is not None or f1 is not None:
+            # One of the shape parameters is fixed.
+
+            if f0 is not None:
+                # The shape parameter a is fixed, so swap the parameters
+                # and flip the data.  We always solve for `a`.  The result
+                # will be swapped back before returning.
+                b = f0
+                data = 1 - data
+                xbar = 1 - xbar
+            else:
+                b = f1
+
+            # Initial guess for a.  Use the formula for the mean of the beta
+            # distribution, E[x] = a / (a + b), to generate a reasonable
+            # starting point based on the mean of the data and the given
+            # value of b.
+            a = b * xbar / (1 - xbar)
+
+            # Compute the MLE for `a` by solving _beta_mle_a.
+            theta, info, ier, mesg = optimize.fsolve(
+                _beta_mle_a, a,
+                args=(b, len(data), np.log(data).sum()),
+                full_output=True
+            )
+            if ier != 1:
+                raise FitSolverError(mesg=mesg)
+            a = theta[0]
+
+            if f0 is not None:
+                # The shape parameter a was fixed, so swap back the
+                # parameters.
+                a, b = b, a
+
+        else:
+            # Neither of the shape parameters is fixed.
+
+            # s1 and s2 are used in the extra arguments passed to _beta_mle_ab
+            # by optimize.fsolve.
+            s1 = np.log(data).sum()
+            s2 = sc.log1p(-data).sum()
+
+            # Use the "method of moments" to estimate the initial
+            # guess for a and b.
+            fac = xbar * (1 - xbar) / data.var(ddof=0) - 1
+            a = xbar * fac
+            b = (1 - xbar) * fac
+
+            # Compute the MLE for a and b by solving _beta_mle_ab.
+            theta, info, ier, mesg = optimize.fsolve(
+                _beta_mle_ab, [a, b],
+                args=(len(data), s1, s2),
+                full_output=True
+            )
+            if ier != 1:
+                raise FitSolverError(mesg=mesg)
+            a, b = theta
+
+        return a, b, floc, fscale
+
+    def _entropy(self, a, b):
+        def regular(a, b):
+            return (sc.betaln(a, b) - (a - 1) * sc.psi(a) -
+                    (b - 1) * sc.psi(b) + (a + b - 2) * sc.psi(a + b))
+
+        def asymptotic_ab_large(a, b):
+            sum_ab = a + b
+            log_term = 0.5 * (
+                np.log(2*np.pi) + np.log(a) + np.log(b) - 3*np.log(sum_ab) + 1
+            )
+            t1 = 110/sum_ab + 20*sum_ab**-2.0 + sum_ab**-3.0 - 2*sum_ab**-4.0
+            t2 = -50/a - 10*a**-2.0 - a**-3.0 + a**-4.0
+            t3 = -50/b - 10*b**-2.0 - b**-3.0 + b**-4.0
+            return log_term + (t1 + t2 + t3) / 120
+
+        def asymptotic_b_large(a, b):
+            sum_ab = a + b
+            t1 = sc.gammaln(a) - (a - 1) * sc.psi(a)
+            t2 = (
+                - 1/(2*b) + 1/(12*b) - b**-2.0/12 - b**-3.0/120 + b**-4.0/120
+                + b**-5.0/252 - b**-6.0/252 + 1/sum_ab - 1/(12*sum_ab)
+                + sum_ab**-2.0/6 + sum_ab**-3.0/120 - sum_ab**-4.0/60
+                - sum_ab**-5.0/252 + sum_ab**-6.0/126
+            )
+            log_term = sum_ab*np.log1p(a/b) + np.log(b) - 2*np.log(sum_ab)
+            return t1 + t2 + log_term
+
+        def asymptotic_a_large(a, b):
+            return asymptotic_b_large(b, a)
+
+        def threshold_large(v):
+            j = np.floor(np.log10(v))
+            d = np.floor(v / 10 ** j) + 2
+            return xpx.apply_where(v != 1.0, (d, j), lambda d_, j_: d_ * 10**(7 + j_),
+                                   fill_value=1000)
+
+        threshold_a = threshold_large(a)
+        threshold_b = threshold_large(b)
+        return _lazyselect([(a >= 4.96e6) & (b >= 4.96e6),
+                            (a <= 4.9e6) & (b - a >= 1e6) & (b >= threshold_a),
+                            (b <= 4.9e6) & (a - b >= 1e6) & (a >= threshold_b),
+                            (a < 4.9e6) & (b < 4.9e6)
+                           ],
+                           [asymptotic_ab_large, asymptotic_b_large,
+                            asymptotic_a_large, regular],
+                           [a, b]
+        )
+
+
+beta = beta_gen(a=0.0, b=1.0, name='beta')
+
+
+class betaprime_gen(rv_continuous):
+    r"""A beta prime continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `betaprime` is:
+
+    .. math::
+
+        f(x, a, b) = \frac{x^{a-1} (1+x)^{-a-b}}{\beta(a, b)}
+
+    for :math:`x >= 0`, :math:`a > 0`, :math:`b > 0`, where
+    :math:`\beta(a, b)` is the beta function (see `scipy.special.beta`).
+
+    `betaprime` takes ``a`` and ``b`` as shape parameters.
+
+    The distribution is related to the `beta` distribution as follows:
+    If :math:`X` follows a beta distribution with parameters :math:`a, b`,
+    then :math:`Y = X/(1-X)` has a beta prime distribution with
+    parameters :math:`a, b` ([1]_).
+
+    The beta prime distribution is a reparametrized version of the
+    F distribution.  The beta prime distribution with shape parameters
+    ``a`` and ``b`` and ``scale = s`` is equivalent to the F distribution
+    with parameters ``d1 = 2*a``, ``d2 = 2*b`` and ``scale = (a/b)*s``.
+    For example,
+
+    >>> from scipy.stats import betaprime, f
+    >>> x = [1, 2, 5, 10]
+    >>> a = 12
+    >>> b = 5
+    >>> betaprime.pdf(x, a, b, scale=2)
+    array([0.00541179, 0.08331299, 0.14669185, 0.03150079])
+    >>> f.pdf(x, 2*a, 2*b, scale=(a/b)*2)
+    array([0.00541179, 0.08331299, 0.14669185, 0.03150079])
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] Beta prime distribution, Wikipedia,
+           https://en.wikipedia.org/wiki/Beta_prime_distribution
+
+    %(example)s
+
+    """
+    _support_mask = rv_continuous._open_support_mask
+
+    def _shape_info(self):
+        ia = _ShapeInfo("a", False, (0, np.inf), (False, False))
+        ib = _ShapeInfo("b", False, (0, np.inf), (False, False))
+        return [ia, ib]
+
+    def _rvs(self, a, b, size=None, random_state=None):
+        u1 = gamma.rvs(a, size=size, random_state=random_state)
+        u2 = gamma.rvs(b, size=size, random_state=random_state)
+        return u1 / u2
+
+    def _pdf(self, x, a, b):
+        # betaprime.pdf(x, a, b) = x**(a-1) * (1+x)**(-a-b) / beta(a, b)
+        return np.exp(self._logpdf(x, a, b))
+
+    def _logpdf(self, x, a, b):
+        return sc.xlogy(a - 1.0, x) - sc.xlog1py(a + b, x) - sc.betaln(a, b)
+
+    def _cdf(self, x, a, b):
+        # note: f2 is the direct way to compute the cdf if the relationship
+        # to the beta distribution is used.
+        # however, for very large x, x/(1+x) == 1. since the distribution
+        # has very fat tails if b is small, this can cause inaccurate results
+        # use the following relationship of the incomplete beta function:
+        # betainc(x, a, b) = 1 - betainc(1-x, b, a)
+        # see gh-17631
+        return xpx.apply_where(
+            x > 1, (x, a, b),
+            lambda x_, a_, b_: beta._sf(1 / (1 + x_), b_, a_),
+            lambda x_, a_, b_: beta._cdf(x_ / (1 + x_), a_, b_))
+
+    def _sf(self, x, a, b):
+        return xpx.apply_where(
+            x > 1, (x, a, b),
+            lambda x_, a_, b_: beta._cdf(1 / (1 + x_), b_, a_),
+            lambda x_, a_, b_: beta._sf(x_ / (1 + x_), a_, b_))
+
+    def _ppf(self, p, a, b):
+        p, a, b = np.broadcast_arrays(p, a, b)
+        # By default, compute the ppf by solving the following:
+        # p = beta._cdf(x/(1+x), a, b). This implies x = r/(1-r) with
+        # r = beta._ppf(p, a, b). This can cause numerical issues if r is
+        # very close to 1. In that case, invert the alternative expression of
+        # the cdf: p = beta._sf(1/(1+x), b, a).
+        r = stats.beta._ppf(p, a, b)
+        with np.errstate(divide='ignore'):
+            out = r / (1 - r)
+        rnear1 = r > 0.9999
+        if np.isscalar(r):
+            if rnear1:
+                out = 1/stats.beta._isf(p, b, a) - 1
+        else:
+            out[rnear1] = 1/stats.beta._isf(p[rnear1], b[rnear1], a[rnear1]) - 1
+        return out
+
+    def _munp(self, n, a, b):
+        return xpx.apply_where(
+            b > n, (a, b),
+            lambda a, b: np.prod([(a+i-1)/(b-i) for i in range(1, int(n)+1)], axis=0),
+            fill_value=np.inf)
+
+
+betaprime = betaprime_gen(a=0.0, name='betaprime')
+
+
+class bradford_gen(rv_continuous):
+    r"""A Bradford continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `bradford` is:
+
+    .. math::
+
+        f(x, c) = \frac{c}{\log(1+c) (1+cx)}
+
+    for :math:`0 <= x <= 1` and :math:`c > 0`.
+
+    `bradford` takes ``c`` as a shape parameter for :math:`c`.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("c", False, (0, np.inf), (False, False))]
+
+    def _pdf(self, x, c):
+        # bradford.pdf(x, c) = c / (k * (1+c*x))
+        return c / (c*x + 1.0) / sc.log1p(c)
+
+    def _cdf(self, x, c):
+        return sc.log1p(c*x) / sc.log1p(c)
+
+    def _ppf(self, q, c):
+        return sc.expm1(q * sc.log1p(c)) / c
+
+    def _stats(self, c, moments='mv'):
+        k = np.log(1.0+c)
+        mu = (c-k)/(c*k)
+        mu2 = ((c+2.0)*k-2.0*c)/(2*c*k*k)
+        g1 = None
+        g2 = None
+        if 's' in moments:
+            g1 = np.sqrt(2)*(12*c*c-9*c*k*(c+2)+2*k*k*(c*(c+3)+3))
+            g1 /= np.sqrt(c*(c*(k-2)+2*k))*(3*c*(k-2)+6*k)
+        if 'k' in moments:
+            g2 = (c**3*(k-3)*(k*(3*k-16)+24)+12*k*c*c*(k-4)*(k-3) +
+                  6*c*k*k*(3*k-14) + 12*k**3)
+            g2 /= 3*c*(c*(k-2)+2*k)**2
+        return mu, mu2, g1, g2
+
+    def _entropy(self, c):
+        k = np.log(1+c)
+        return k/2.0 - np.log(c/k)
+
+
+bradford = bradford_gen(a=0.0, b=1.0, name='bradford')
+
+
+class burr_gen(rv_continuous):
+    r"""A Burr (Type III) continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    fisk : a special case of either `burr` or `burr12` with ``d=1``
+    burr12 : Burr Type XII distribution
+    mielke : Mielke Beta-Kappa / Dagum distribution
+
+    Notes
+    -----
+    The probability density function for `burr` is:
+
+    .. math::
+
+        f(x; c, d) = c d \frac{x^{-c - 1}}
+                              {{(1 + x^{-c})}^{d + 1}}
+
+    for :math:`x >= 0` and :math:`c, d > 0`.
+
+    `burr` takes ``c`` and ``d`` as shape parameters for :math:`c` and
+    :math:`d`.
+
+    This is the PDF corresponding to the third CDF given in Burr's list;
+    specifically, it is equation (11) in Burr's paper [1]_. The distribution
+    is also commonly referred to as the Dagum distribution [2]_. If the
+    parameter :math:`c < 1` then the mean of the distribution does not
+    exist and if :math:`c < 2` the variance does not exist [2]_.
+    The PDF is finite at the left endpoint :math:`x = 0` if :math:`c * d >= 1`.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] Burr, I. W. "Cumulative frequency functions", Annals of
+       Mathematical Statistics, 13(2), pp 215-232 (1942).
+    .. [2] https://en.wikipedia.org/wiki/Dagum_distribution
+    .. [3] Kleiber, Christian. "A guide to the Dagum distributions."
+       Modeling Income Distributions and Lorenz Curves  pp 97-117 (2008).
+
+    %(example)s
+
+    """
+    # Do not set _support_mask to rv_continuous._open_support_mask
+    # Whether the left-hand endpoint is suitable for pdf evaluation is dependent
+    # on the values of c and d: if c*d >= 1, the pdf is finite, otherwise infinite.
+
+    def _shape_info(self):
+        ic = _ShapeInfo("c", False, (0, np.inf), (False, False))
+        id = _ShapeInfo("d", False, (0, np.inf), (False, False))
+        return [ic, id]
+
+    def _pdf(self, x, c, d):
+        # burr.pdf(x, c, d) = c * d * x**(-c-1) * (1+x**(-c))**(-d-1)
+        output = xpx.apply_where(
+            x == 0, (x, c, d),
+            lambda x_, c_, d_: c_ * d_ * (x_**(c_*d_-1)) / (1 + x_**c_),
+            lambda x_, c_, d_: (c_ * d_ * (x_ ** (-c_ - 1.0)) /
+                                ((1 + x_ ** (-c_)) ** (d_ + 1.0))))
+        return output[()] if output.ndim == 0 else output
+
+    def _logpdf(self, x, c, d):
+        output = xpx.apply_where(
+            x == 0, (x, c, d),
+            lambda x_, c_, d_: (np.log(c_) + np.log(d_) + sc.xlogy(c_*d_ - 1, x_)
+                                - (d_+1) * sc.log1p(x_**(c_))),
+            lambda x_, c_, d_: (np.log(c_) + np.log(d_)
+                                + sc.xlogy(-c_ - 1, x_)
+                                - sc.xlog1py(d_+1, x_**(-c_))))
+        return output[()] if output.ndim == 0 else output
+
+    def _cdf(self, x, c, d):
+        return (1 + x**(-c))**(-d)
+
+    def _logcdf(self, x, c, d):
+        return sc.log1p(x**(-c)) * (-d)
+
+    def _sf(self, x, c, d):
+        return np.exp(self._logsf(x, c, d))
+
+    def _logsf(self, x, c, d):
+        return np.log1p(- (1 + x**(-c))**(-d))
+
+    def _ppf(self, q, c, d):
+        return (q**(-1.0/d) - 1)**(-1.0/c)
+
+    def _isf(self, q, c, d):
+        _q = sc.xlog1py(-1.0 / d, -q)
+        return sc.expm1(_q) ** (-1.0 / c)
+
+    def _stats(self, c, d):
+        nc = np.arange(1, 5).reshape(4,1) / c
+        # ek is the kth raw moment, e1 is the mean e2-e1**2 variance etc.
+        e1, e2, e3, e4 = sc.beta(d + nc, 1. - nc) * d
+        mu = np.where(c > 1.0, e1, np.nan)
+        mu2_if_c = e2 - mu**2
+        mu2 = np.where(c > 2.0, mu2_if_c, np.nan)
+        g1 = xpx.apply_where(
+            c > 3.0, (e1, e2, e3, mu2_if_c),
+            lambda e1, e2, e3, mu2_if_c: ((e3 - 3*e2*e1 + 2*e1**3)
+                                           / np.sqrt((mu2_if_c)**3)),
+            fill_value=np.nan)
+        g2 = xpx.apply_where(
+            c > 4.0, (e1, e2, e3, e4, mu2_if_c),
+            lambda e1, e2, e3, e4, mu2_if_c: (
+                ((e4 - 4*e3*e1 + 6*e2*e1**2 - 3*e1**4) / mu2_if_c**2) - 3),
+            fill_value=np.nan)
+        if np.ndim(c) == 0:
+            return mu.item(), mu2.item(), g1.item(), g2.item()
+        return mu, mu2, g1, g2
+
+    def _munp(self, n, c, d):
+        def __munp(n, c, d):
+            nc = 1. * n / c
+            return d * sc.beta(1.0 - nc, d + nc)
+        n, c, d = np.asarray(n), np.asarray(c), np.asarray(d)
+        return xpx.apply_where((c > n) & (n == n) & (d == d),
+                               (n, c, d), __munp, fill_value=np.nan)
+
+
+burr = burr_gen(a=0.0, name='burr')
+
+
+class burr12_gen(rv_continuous):
+    r"""A Burr (Type XII) continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    fisk : a special case of either `burr` or `burr12` with ``d=1``
+    burr : Burr Type III distribution
+
+    Notes
+    -----
+    The probability density function for `burr12` is:
+
+    .. math::
+
+        f(x; c, d) = c d \frac{x^{c-1}}
+                              {(1 + x^c)^{d + 1}}
+
+    for :math:`x >= 0` and :math:`c, d > 0`.
+
+    `burr12` takes ``c`` and ``d`` as shape parameters for :math:`c`
+    and :math:`d`.
+
+    This is the PDF corresponding to the twelfth CDF given in Burr's list;
+    specifically, it is equation (20) in Burr's paper [1]_.
+
+    %(after_notes)s
+
+    The Burr type 12 distribution is also sometimes referred to as
+    the Singh-Maddala distribution from NIST [2]_.
+
+    References
+    ----------
+    .. [1] Burr, I. W. "Cumulative frequency functions", Annals of
+       Mathematical Statistics, 13(2), pp 215-232 (1942).
+
+    .. [2] https://www.itl.nist.gov/div898/software/dataplot/refman2/auxillar/b12pdf.htm
+
+    .. [3] "Burr distribution",
+       https://en.wikipedia.org/wiki/Burr_distribution
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        ic = _ShapeInfo("c", False, (0, np.inf), (False, False))
+        id = _ShapeInfo("d", False, (0, np.inf), (False, False))
+        return [ic, id]
+
+    def _pdf(self, x, c, d):
+        # burr12.pdf(x, c, d) = c * d * x**(c-1) * (1+x**(c))**(-d-1)
+        return np.exp(self._logpdf(x, c, d))
+
+    def _logpdf(self, x, c, d):
+        return np.log(c) + np.log(d) + sc.xlogy(c - 1, x) + sc.xlog1py(-d-1, x**c)
+
+    def _cdf(self, x, c, d):
+        return -sc.expm1(self._logsf(x, c, d))
+
+    def _logcdf(self, x, c, d):
+        return sc.log1p(-(1 + x**c)**(-d))
+
+    def _sf(self, x, c, d):
+        return np.exp(self._logsf(x, c, d))
+
+    def _logsf(self, x, c, d):
+        return sc.xlog1py(-d, x**c)
+
+    def _ppf(self, q, c, d):
+        # The following is an implementation of
+        #   ((1 - q)**(-1.0/d) - 1)**(1.0/c)
+        # that does a better job handling small values of q.
+        return sc.expm1(-1/d * sc.log1p(-q))**(1/c)
+
+    def _isf(self, p, c, d):
+        return sc.expm1(-1/d * np.log(p))**(1/c)
+
+    def _munp(self, n, c, d):
+        def moment_if_exists(n, c, d):
+            nc = 1. * n / c
+            return d * sc.beta(1.0 + nc, d - nc)
+
+        return xpx.apply_where(c * d > n, (n, c, d), moment_if_exists,
+                               fill_value=np.nan)
+
+
+burr12 = burr12_gen(a=0.0, name='burr12')
+
+
+class fisk_gen(burr_gen):
+    r"""A Fisk continuous random variable.
+
+    The Fisk distribution is also known as the log-logistic distribution.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    burr
+
+    Notes
+    -----
+    The probability density function for `fisk` is:
+
+    .. math::
+
+        f(x, c) = \frac{c x^{c-1}}
+                       {(1 + x^c)^2}
+
+    for :math:`x >= 0` and :math:`c > 0`.
+
+    Please note that the above expression can be transformed into the following
+    one, which is also commonly used:
+
+    .. math::
+
+        f(x, c) = \frac{c x^{-c-1}}
+                       {(1 + x^{-c})^2}
+
+    `fisk` takes ``c`` as a shape parameter for :math:`c`.
+
+    `fisk` is a special case of `burr` or `burr12` with ``d=1``.
+
+    Suppose ``X`` is a logistic random variable with location ``l``
+    and scale ``s``. Then ``Y = exp(X)`` is a Fisk (log-logistic)
+    random variable with ``scale = exp(l)`` and shape ``c = 1/s``.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("c", False, (0, np.inf), (False, False))]
+
+    def _pdf(self, x, c):
+        # fisk.pdf(x, c) = c * x**(-c-1) * (1 + x**(-c))**(-2)
+        return burr._pdf(x, c, 1.0)
+
+    def _cdf(self, x, c):
+        return burr._cdf(x, c, 1.0)
+
+    def _sf(self, x, c):
+        return burr._sf(x, c, 1.0)
+
+    def _logpdf(self, x, c):
+        # fisk.pdf(x, c) = c * x**(-c-1) * (1 + x**(-c))**(-2)
+        return burr._logpdf(x, c, 1.0)
+
+    def _logcdf(self, x, c):
+        return burr._logcdf(x, c, 1.0)
+
+    def _logsf(self, x, c):
+        return burr._logsf(x, c, 1.0)
+
+    def _ppf(self, x, c):
+        return burr._ppf(x, c, 1.0)
+
+    def _isf(self, q, c):
+        return burr._isf(q, c, 1.0)
+
+    def _munp(self, n, c):
+        return burr._munp(n, c, 1.0)
+
+    def _stats(self, c):
+        return burr._stats(c, 1.0)
+
+    def _entropy(self, c):
+        return 2 - np.log(c)
+
+
+fisk = fisk_gen(a=0.0, name='fisk')
+
+
+class cauchy_gen(rv_continuous):
+    r"""A Cauchy continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `cauchy` is
+
+    .. math::
+
+        f(x) = \frac{1}{\pi (1 + x^2)}
+
+    for a real number :math:`x`.
+
+    This distribution uses routines from the Boost Math C++ library for
+    the computation of the ``ppf`` and ``isf`` methods. [1]_
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return []
+
+    def _pdf(self, x):
+        # cauchy.pdf(x) = 1 / (pi * (1 + x**2))
+        with np.errstate(over='ignore'):
+            return 1.0/np.pi/(1.0+x*x)
+
+    def _logpdf(self, x):
+        # The formulas
+        #     log(1/(pi*(1 + x**2))) = -log(pi) - log(1 + x**2)
+        #                            = -log(pi) - log(x**2*(1 + 1/x**2))
+        #                            = -log(pi) - (2log(|x|) + log1p(1/x**2))
+        # are used here.
+        absx = np.abs(x)
+        # In the following apply_where, `f1` provides better precision than `f2`
+        # for small and moderate x, while `f2` avoids the overflow that can
+        # occur with absx**2.
+        return xpx.apply_where(
+            absx < 1, absx,
+            lambda absx: -_LOG_PI - np.log1p(absx**2),
+            lambda absx: (-_LOG_PI - (2*np.log(absx) + np.log1p((1/absx)**2))))
+
+    def _cdf(self, x):
+        return np.arctan2(1, -x)/np.pi
+
+    def _ppf(self, q):
+        return scu._cauchy_ppf(q, 0, 1)
+
+    def _sf(self, x):
+        return np.arctan2(1, x)/np.pi
+
+    def _isf(self, q):
+        return scu._cauchy_isf(q, 0, 1)
+
+    def _stats(self):
+        return np.nan, np.nan, np.nan, np.nan
+
+    def _entropy(self):
+        return np.log(4*np.pi)
+
+    def _fitstart(self, data, args=None):
+        # Initialize ML guesses using quartiles instead of moments.
+        if isinstance(data, CensoredData):
+            data = data._uncensor()
+        p25, p50, p75 = np.percentile(data, [25, 50, 75])
+        return p50, (p75 - p25)/2
+
+
+cauchy = cauchy_gen(name='cauchy')
+
+
+class chi_gen(rv_continuous):
+    r"""A chi continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `chi` is:
+
+    .. math::
+
+        f(x, k) = \frac{1}{2^{k/2-1} \Gamma \left( k/2 \right)}
+                   x^{k-1} \exp \left( -x^2/2 \right)
+
+    for :math:`x >= 0` and :math:`k > 0` (degrees of freedom, denoted ``df``
+    in the implementation). :math:`\Gamma` is the gamma function
+    (`scipy.special.gamma`).
+
+    Special cases of `chi` are:
+
+    - ``chi(1, loc, scale)`` is equivalent to `halfnorm`
+    - ``chi(2, 0, scale)`` is equivalent to `rayleigh`
+    - ``chi(3, 0, scale)`` is equivalent to `maxwell`
+
+    `chi` takes ``df`` as a shape parameter.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("df", False, (0, np.inf), (False, False))]
+
+    def _rvs(self, df, size=None, random_state=None):
+        return np.sqrt(chi2.rvs(df, size=size, random_state=random_state))
+
+    def _pdf(self, x, df):
+        #                   x**(df-1) * exp(-x**2/2)
+        # chi.pdf(x, df) =  -------------------------
+        #                   2**(df/2-1) * gamma(df/2)
+        return np.exp(self._logpdf(x, df))
+
+    def _logpdf(self, x, df):
+        l = np.log(2) - .5*np.log(2)*df - sc.gammaln(.5*df)
+        return l + sc.xlogy(df - 1., x) - .5*x**2
+
+    def _cdf(self, x, df):
+        return sc.gammainc(.5*df, .5*x**2)
+
+    def _sf(self, x, df):
+        return sc.gammaincc(.5*df, .5*x**2)
+
+    def _ppf(self, q, df):
+        return np.sqrt(2*sc.gammaincinv(.5*df, q))
+
+    def _isf(self, q, df):
+        return np.sqrt(2*sc.gammainccinv(.5*df, q))
+
+    def _stats(self, df):
+        # poch(df/2, 1/2) = gamma(df/2 + 1/2) / gamma(df/2)
+        mu = np.sqrt(2) * sc.poch(0.5 * df, 0.5)
+        mu2 = df - mu*mu
+        g1 = (2*mu**3.0 + mu*(1-2*df))/np.asarray(np.power(mu2, 1.5))
+        g2 = 2*df*(1.0-df)-6*mu**4 + 4*mu**2 * (2*df-1)
+        g2 /= np.asarray(mu2**2.0)
+        return mu, mu2, g1, g2
+
+    def _entropy(self, df):
+
+        def regular_formula(df):
+            return (sc.gammaln(.5 * df)
+                    + 0.5 * (df - np.log(2) - (df - 1) * sc.digamma(0.5 * df)))
+
+        def asymptotic_formula(df):
+            return (0.5 + np.log(np.pi)/2 - (df**-1)/6 - (df**-2)/6
+                    - 4/45*(df**-3) + (df**-4)/15)
+
+        return xpx.apply_where(df < 300, df, regular_formula, asymptotic_formula)
+
+
+chi = chi_gen(a=0.0, name='chi')
+
+
+class chi2_gen(rv_continuous):
+    r"""A chi-squared continuous random variable.
+
+    For the noncentral chi-square distribution, see `ncx2`.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    ncx2
+
+    Notes
+    -----
+    The probability density function for `chi2` is:
+
+    .. math::
+
+        f(x, k) = \frac{1}{2^{k/2} \Gamma \left( k/2 \right)}
+                   x^{k/2-1} \exp \left( -x/2 \right)
+
+    for :math:`x > 0`  and :math:`k > 0` (degrees of freedom, denoted ``df``
+    in the implementation).
+
+    `chi2` takes ``df`` as a shape parameter.
+
+    The chi-squared distribution is a special case of the gamma
+    distribution, with gamma parameters ``a = df/2``, ``loc = 0`` and
+    ``scale = 2``.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("df", False, (0, np.inf), (False, False))]
+
+    def _rvs(self, df, size=None, random_state=None):
+        return random_state.chisquare(df, size)
+
+    def _pdf(self, x, df):
+        # chi2.pdf(x, df) = 1 / (2*gamma(df/2)) * (x/2)**(df/2-1) * exp(-x/2)
+        return np.exp(self._logpdf(x, df))
+
+    def _logpdf(self, x, df):
+        return sc.xlogy(df/2.-1, x) - x/2. - sc.gammaln(df/2.) - (np.log(2)*df)/2.
+
+    def _cdf(self, x, df):
+        return sc.chdtr(df, x)
+
+    def _sf(self, x, df):
+        return sc.chdtrc(df, x)
+
+    def _isf(self, p, df):
+        return sc.chdtri(df, p)
+
+    def _ppf(self, p, df):
+        return 2*sc.gammaincinv(df/2, p)
+
+    def _stats(self, df):
+        mu = df
+        mu2 = 2*df
+        g1 = 2*np.sqrt(2.0/df)
+        g2 = 12.0/df
+        return mu, mu2, g1, g2
+
+    def _entropy(self, df):
+        half_df = 0.5 * df
+
+        def regular_formula(half_df):
+            return (half_df + np.log(2) + sc.gammaln(half_df) +
+                    (1 - half_df) * sc.psi(half_df))
+
+        def asymptotic_formula(half_df):
+            # plug in the above formula the following asymptotic
+            # expansions:
+            # ln(gamma(a)) ~ (a - 0.5) * ln(a) - a + 0.5 * ln(2 * pi) +
+            #                 1/(12 * a) - 1/(360 * a**3)
+            # psi(a) ~ ln(a) - 1/(2 * a) - 1/(3 * a**2) + 1/120 * a**4)
+            c = np.log(2) + 0.5*(1 + np.log(2*np.pi))
+            h = 0.5/half_df
+            return (h*(-2/3 + h*(-1/3 + h*(-4/45 + h/7.5))) +
+                    0.5*np.log(half_df) + c)
+
+        return xpx.apply_where(half_df < 125, half_df,
+                               regular_formula, asymptotic_formula)
+
+
+chi2 = chi2_gen(a=0.0, name='chi2')
+
+
+class cosine_gen(rv_continuous):
+    r"""A cosine continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The cosine distribution is an approximation to the normal distribution.
+    The probability density function for `cosine` is:
+
+    .. math::
+
+        f(x) = \frac{1}{2\pi} (1+\cos(x))
+
+    for :math:`-\pi \le x \le \pi`.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return []
+
+    def _pdf(self, x):
+        # cosine.pdf(x) = 1/(2*pi) * (1+cos(x))
+        return 1.0/2/np.pi*(1+np.cos(x))
+
+    def _logpdf(self, x):
+        c = np.cos(x)
+        return xpx.apply_where(c != -1, c,
+                               lambda c: np.log1p(c) - np.log(2*np.pi),
+                               fill_value=-np.inf)
+
+    def _cdf(self, x):
+        return scu._cosine_cdf(x)
+
+    def _sf(self, x):
+        return scu._cosine_cdf(-x)
+
+    def _ppf(self, p):
+        return scu._cosine_invcdf(p)
+
+    def _isf(self, p):
+        return -scu._cosine_invcdf(p)
+
+    def _stats(self):
+        v = (np.pi * np.pi / 3.0) - 2.0
+        k = -6.0 * (np.pi**4 - 90) / (5.0 * (np.pi * np.pi - 6)**2)
+        return 0.0, v, 0.0, k
+
+    def _entropy(self):
+        return np.log(4*np.pi)-1.0
+
+
+cosine = cosine_gen(a=-np.pi, b=np.pi, name='cosine')
+
+
+class dgamma_gen(rv_continuous):
+    r"""A double gamma continuous random variable.
+
+    The double gamma distribution is also known as the reflected gamma
+    distribution [1]_.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `dgamma` is:
+
+    .. math::
+
+        f(x, a) = \frac{1}{2\Gamma(a)} |x|^{a-1} \exp(-|x|)
+
+    for a real number :math:`x` and :math:`a > 0`. :math:`\Gamma` is the
+    gamma function (`scipy.special.gamma`).
+
+    `dgamma` takes ``a`` as a shape parameter for :math:`a`.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] Johnson, Kotz, and Balakrishnan, "Continuous Univariate
+           Distributions, Volume 1", Second Edition, John Wiley and Sons
+           (1994).
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("a", False, (0, np.inf), (False, False))]
+
+    def _rvs(self, a, size=None, random_state=None):
+        u = random_state.uniform(size=size)
+        gm = gamma.rvs(a, size=size, random_state=random_state)
+        return gm * np.where(u >= 0.5, 1, -1)
+
+    def _pdf(self, x, a):
+        # dgamma.pdf(x, a) = 1 / (2*gamma(a)) * abs(x)**(a-1) * exp(-abs(x))
+        ax = abs(x)
+        return 1.0/(2*sc.gamma(a))*ax**(a-1.0) * np.exp(-ax)
+
+    def _logpdf(self, x, a):
+        ax = abs(x)
+        return sc.xlogy(a - 1.0, ax) - ax - np.log(2) - sc.gammaln(a)
+
+    def _cdf(self, x, a):
+        return np.where(x > 0,
+                        0.5 + 0.5*sc.gammainc(a, x),
+                        0.5*sc.gammaincc(a, -x))
+
+    def _sf(self, x, a):
+        return np.where(x > 0,
+                        0.5*sc.gammaincc(a, x),
+                        0.5 + 0.5*sc.gammainc(a, -x))
+
+    def _entropy(self, a):
+        return stats.gamma._entropy(a) - np.log(0.5)
+
+    def _ppf(self, q, a):
+        return np.where(q > 0.5,
+                        sc.gammaincinv(a, 2*q - 1),
+                        -sc.gammainccinv(a, 2*q))
+
+    def _isf(self, q, a):
+        return np.where(q > 0.5,
+                        -sc.gammaincinv(a, 2*q - 1),
+                        sc.gammainccinv(a, 2*q))
+
+    def _stats(self, a):
+        mu2 = a*(a+1.0)
+        return 0.0, mu2, 0.0, (a+2.0)*(a+3.0)/mu2-3.0
+
+
+dgamma = dgamma_gen(name='dgamma')
+
+
+class dpareto_lognorm_gen(rv_continuous):
+    r"""A double Pareto lognormal continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `dpareto_lognorm` is:
+
+    .. math::
+
+        f(x, \mu, \sigma, \alpha, \beta) =
+        \frac{\alpha \beta}{(\alpha + \beta) x}
+        \phi\left( \frac{\log x - \mu}{\sigma} \right)
+        \left( R(y_1) + R(y_2) \right)
+
+    where :math:`R(t) = \frac{1 - \Phi(t)}{\phi(t)}`,
+    :math:`\phi` and :math:`\Phi` are the normal PDF and CDF, respectively,
+    :math:`y_1 = \alpha \sigma - \frac{\log x - \mu}{\sigma}`,
+    and :math:`y_2 = \beta \sigma + \frac{\log x - \mu}{\sigma}`
+    for real numbers :math:`x` and :math:`\mu`, :math:`\sigma > 0`,
+    :math:`\alpha > 0`, and :math:`\beta > 0` [1]_.
+
+    `dpareto_lognorm` takes
+    ``u`` as a shape parameter for :math:`\mu`,
+    ``s`` as a shape parameter for :math:`\sigma`,
+    ``a`` as a shape parameter for :math:`\alpha`, and
+    ``b`` as a shape parameter for :math:`\beta`.
+
+    A random variable :math:`X` distributed according to the PDF above
+    can be represented as :math:`X = U \frac{V_1}{V_2}` where :math:`U`,
+    :math:`V_1`, and :math:`V_2` are independent, :math:`U` is lognormally
+    distributed such that :math:`\log U \sim N(\mu, \sigma^2)`, and
+    :math:`V_1` and :math:`V_2` follow Pareto distributions with parameters
+    :math:`\alpha` and :math:`\beta`, respectively [2]_.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] Hajargasht, Gholamreza, and William E. Griffiths. "Pareto-lognormal
+           distributions: Inequality, poverty, and estimation from grouped income
+           data." Economic Modelling 33 (2013): 593-604.
+    .. [2] Reed, William J., and Murray Jorgensen. "The double Pareto-lognormal
+           distribution - a new parametric model for size distributions."
+           Communications in Statistics - Theory and Methods 33.8 (2004): 1733-1753.
+
+    %(example)s
+
+    """
+    _logphi = norm._logpdf
+    _logPhi = norm._logcdf
+    _logPhic = norm._logsf
+    _phi = norm._pdf
+    _Phi = norm._cdf
+    _Phic = norm._sf
+
+    def _R(self, z):
+        return self._Phic(z) / self._phi(z)
+
+    def _logR(self, z):
+        return self._logPhic(z) - self._logphi(z)
+
+    def _shape_info(self):
+        return [_ShapeInfo("u", False, (-np.inf, np.inf), (False, False)),
+                _ShapeInfo("s", False, (0, np.inf), (False, False)),
+                _ShapeInfo("a", False, (0, np.inf), (False, False)),
+                _ShapeInfo("b", False, (0, np.inf), (False, False))]
+
+    def _argcheck(self, u, s, a, b):
+        return (s > 0) & (a > 0) & (b > 0)
+
+    def _rvs(self, u, s, a, b, size=None, random_state=None):
+        # From [1] after Equation (12): "To generate pseudo-random
+        # deviates from the dPlN distribution, one can exponentiate
+        # pseudo-random deviates from NL generated using (6)."
+        Z = random_state.normal(u, s, size=size)
+        E1 = random_state.standard_exponential(size=size)
+        E2 = random_state.standard_exponential(size=size)
+        return np.exp(Z + E1 / a - E2 / b)
+
+    def _logpdf(self, x, u, s, a, b):
+        with np.errstate(invalid='ignore', divide='ignore'):
+            log_y, m = np.log(x), u  # compare against [1] Eq. 1
+            z = (log_y - m) / s
+            x1 = a * s - z
+            x2 = b * s + z
+            out = np.asarray(np.log(a) + np.log(b) - np.log(a + b) - log_y)
+            out += self._logphi(z)
+            out += np.logaddexp(self._logR(x1), self._logR(x2))
+        out[(x == 0) | np.isinf(x)] = -np.inf
+        return out[()]
+
+    def _logcdf(self, x, u, s, a, b):
+        with np.errstate(invalid='ignore', divide='ignore'):
+            log_y, m = np.log(x), u  # compare against [1] Eq. 2
+            z = (log_y - m) / s
+            x1 = a * s - z
+            x2 = b * s + z
+            t1 = self._logPhi(z)
+            t2 = self._logphi(z)
+            t3 = (np.log(b) + self._logR(x1))
+            t4 = (np.log(a) + self._logR(x2))
+            t1, t2, t3, t4, one = np.broadcast_arrays(t1, t2, t3, t4, 1)
+            # t3 can be smaller than t4, so we have to consider log of negative number
+            # This would be much simpler, but `return_sign` is available, so use it?
+            # t5 =  sc.logsumexp([t3, t4 + np.pi*1j])
+            t5, sign =  sc.logsumexp([t3, t4], b=[one, -one], axis=0, return_sign=True)
+            temp = [t1, t2 + t5 - np.log(a + b)]
+            out = np.asarray(sc.logsumexp(temp, b=[one, -one*sign], axis=0))
+        out[x == 0] = -np.inf
+        return out[()]
+
+    def _logsf(self, x, u, s, a, b):
+        return scu._log1mexp(self._logcdf(x, u, s, a, b))
+
+    # Infrastructure doesn't seem to do this, so...
+
+    def _pdf(self, x, u, s, a, b):
+        return np.exp(self._logpdf(x, u, s, a, b))
+
+    def _cdf(self, x, u, s, a, b):
+        return np.exp(self._logcdf(x, u, s, a, b))
+
+    def _sf(self, x, u, s, a, b):
+        return np.exp(self._logsf(x, u, s, a, b))
+
+    def _munp(self, n, u, s, a, b):
+        m, k = u, float(n)  # compare against [1] Eq. 6
+        out = (a * b) / ((a - k) * (b + k)) * np.exp(k * m + k ** 2 * s ** 2 / 2)
+        out = np.asarray(out)
+        out[a <= k] = np.nan
+        return out
+
+
+dpareto_lognorm = dpareto_lognorm_gen(a=0, name='dpareto_lognorm')
+
+
+class dweibull_gen(rv_continuous):
+    r"""A double Weibull continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `dweibull` is given by
+
+    .. math::
+
+        f(x, c) = c / 2 |x|^{c-1} \exp(-|x|^c)
+
+    for a real number :math:`x` and :math:`c > 0`.
+
+    `dweibull` takes ``c`` as a shape parameter for :math:`c`.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("c", False, (0, np.inf), (False, False))]
+
+    def _rvs(self, c, size=None, random_state=None):
+        u = random_state.uniform(size=size)
+        w = weibull_min.rvs(c, size=size, random_state=random_state)
+        return w * (np.where(u >= 0.5, 1, -1))
+
+    def _pdf(self, x, c):
+        # dweibull.pdf(x, c) = c / 2 * abs(x)**(c-1) * exp(-abs(x)**c)
+        ax = abs(x)
+        Px = c / 2.0 * ax**(c-1.0) * np.exp(-ax**c)
+        return Px
+
+    def _logpdf(self, x, c):
+        ax = abs(x)
+        return np.log(c) - np.log(2.0) + sc.xlogy(c - 1.0, ax) - ax**c
+
+    def _cdf(self, x, c):
+        Cx1 = 0.5 * np.exp(-abs(x)**c)
+        return np.where(x > 0, 1 - Cx1, Cx1)
+
+    def _ppf(self, q, c):
+        fac = 2. * np.where(q <= 0.5, q, 1. - q)
+        fac = np.power(-np.log(fac), 1.0 / c)
+        return np.where(q > 0.5, fac, -fac)
+
+    def _sf(self, x, c):
+        half_weibull_min_sf = 0.5 * stats.weibull_min._sf(np.abs(x), c)
+        return np.where(x > 0, half_weibull_min_sf, 1 - half_weibull_min_sf)
+
+    def _isf(self, q, c):
+        double_q = 2. * np.where(q <= 0.5, q, 1. - q)
+        weibull_min_isf = stats.weibull_min._isf(double_q, c)
+        return np.where(q > 0.5, -weibull_min_isf, weibull_min_isf)
+
+    def _munp(self, n, c):
+        return (1 - (n % 2)) * sc.gamma(1.0 + 1.0 * n / c)
+
+    # since we know that all odd moments are zeros, return them at once.
+    # returning Nones from _stats makes the public stats call _munp
+    # so overall we're saving one or two gamma function evaluations here.
+    def _stats(self, c):
+        return 0, None, 0, None
+
+    def _entropy(self, c):
+        h = stats.weibull_min._entropy(c) - np.log(0.5)
+        return h
+
+
+dweibull = dweibull_gen(name='dweibull')
+
+
+class expon_gen(rv_continuous):
+    r"""An exponential continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `expon` is:
+
+    .. math::
+
+        f(x) = \exp(-x)
+
+    for :math:`x \ge 0`.
+
+    %(after_notes)s
+
+    A common parameterization for `expon` is in terms of the rate parameter
+    ``lambda``, such that ``pdf = lambda * exp(-lambda * x)``. This
+    parameterization corresponds to using ``scale = 1 / lambda``.
+
+    The exponential distribution is a special case of the gamma
+    distributions, with gamma shape parameter ``a = 1``.
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return []
+
+    def _rvs(self, size=None, random_state=None):
+        return random_state.standard_exponential(size)
+
+    def _pdf(self, x):
+        # expon.pdf(x) = exp(-x)
+        return np.exp(-x)
+
+    def _logpdf(self, x):
+        return -x
+
+    def _cdf(self, x):
+        return -sc.expm1(-x)
+
+    def _ppf(self, q):
+        return -sc.log1p(-q)
+
+    def _sf(self, x):
+        return np.exp(-x)
+
+    def _logsf(self, x):
+        return -x
+
+    def _isf(self, q):
+        return -np.log(q)
+
+    def _stats(self):
+        return 1.0, 1.0, 2.0, 6.0
+
+    def _entropy(self):
+        return 1.0
+
+    @_call_super_mom
+    @replace_notes_in_docstring(rv_continuous, notes="""\
+        When `method='MLE'`,
+        this function uses explicit formulas for the maximum likelihood
+        estimation of the exponential distribution parameters, so the
+        `optimizer`, `loc` and `scale` keyword arguments are
+        ignored.\n\n""")
+    def fit(self, data, *args, **kwds):
+        if len(args) > 0:
+            raise TypeError("Too many arguments.")
+
+        floc = kwds.pop('floc', None)
+        fscale = kwds.pop('fscale', None)
+
+        _remove_optimizer_parameters(kwds)
+
+        if floc is not None and fscale is not None:
+            # This check is for consistency with `rv_continuous.fit`.
+            raise ValueError("All parameters fixed. There is nothing to "
+                             "optimize.")
+
+        data = np.asarray(data)
+
+        if not np.isfinite(data).all():
+            raise ValueError("The data contains non-finite values.")
+
+        data_min = data.min()
+
+        if floc is None:
+            # ML estimate of the location is the minimum of the data.
+            loc = data_min
+        else:
+            loc = floc
+            if data_min < loc:
+                # There are values that are less than the specified loc.
+                raise FitDataError("expon", lower=floc, upper=np.inf)
+
+        if fscale is None:
+            # ML estimate of the scale is the shifted mean.
+            scale = data.mean() - loc
+        else:
+            scale = fscale
+
+        # We expect the return values to be floating point, so ensure it
+        # by explicitly converting to float.
+        return float(loc), float(scale)
+
+
+expon = expon_gen(a=0.0, name='expon')
+
+
+class exponnorm_gen(rv_continuous):
+    r"""An exponentially modified Normal continuous random variable.
+
+    Also known as the exponentially modified Gaussian distribution [1]_.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `exponnorm` is:
+
+    .. math::
+
+        f(x, K) = \frac{1}{2K} \exp\left(\frac{1}{2 K^2} - x / K \right)
+                  \text{erfc}\left(-\frac{x - 1/K}{\sqrt{2}}\right)
+
+    where :math:`x` is a real number and :math:`K > 0`.
+
+    It can be thought of as the sum of a standard normal random variable
+    and an independent exponentially distributed random variable with rate
+    ``1/K``.
+
+    %(after_notes)s
+
+    An alternative parameterization of this distribution (for example, in
+    the Wikipedia article [1]_) involves three parameters, :math:`\mu`,
+    :math:`\lambda` and :math:`\sigma`.
+
+    In the present parameterization this corresponds to having ``loc`` and
+    ``scale`` equal to :math:`\mu` and :math:`\sigma`, respectively, and
+    shape parameter :math:`K = 1/(\sigma\lambda)`.
+
+    .. versionadded:: 0.16.0
+
+    References
+    ----------
+    .. [1] Exponentially modified Gaussian distribution, Wikipedia,
+           https://en.wikipedia.org/wiki/Exponentially_modified_Gaussian_distribution
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("K", False, (0, np.inf), (False, False))]
+
+    def _rvs(self, K, size=None, random_state=None):
+        expval = random_state.standard_exponential(size) * K
+        gval = random_state.standard_normal(size)
+        return expval + gval
+
+    def _pdf(self, x, K):
+        return np.exp(self._logpdf(x, K))
+
+    def _logpdf(self, x, K):
+        u = (-x + 1.0 / K) / np.sqrt(2)
+        def logpdf_erfcx(x, K, u):
+            erfcx_term = np.log(sc.erfcx(u))
+            return -np.log(2) - 0.5 * (x ** 2) - np.log(K) + erfcx_term
+        def logpdf_default(x, K, u):
+            invK = 1.0 / K
+            exparg = invK * (-x + 0.5 * invK)
+            return exparg + _norm_logcdf(x - invK) - np.log(K)
+        use_erfcx = np.logical_and(u >= 0, K < 1)
+        return xpx.apply_where(
+            use_erfcx, (x, K, u), logpdf_erfcx, logpdf_default)
+
+    def _cdf(self, x, K):
+        u = (-x + 1.0 / K) / np.sqrt(2)
+        def cdf_erfcx(x, K, u):
+            return _norm_cdf(x) - 0.5 * np.exp(-0.5 * x ** 2) * sc.erfcx(u)
+        def cdf_default(x, K, u):
+            invK = 1.0 / K
+            expval = invK * (0.5 * invK - x)
+            logprod = expval + _norm_logcdf(x - invK)
+            return _norm_cdf(x) - np.exp(logprod)
+        use_erfcx = np.logical_and(u >= 0, K < 1)
+        return xpx.apply_where(
+            use_erfcx, (x, K, u), cdf_erfcx, cdf_default)
+
+    def _sf(self, x, K):
+        u = (-x + 1.0 / K) / np.sqrt(2)
+        def sf_erfcx(x, K, u):
+            return _norm_cdf(-x) + 0.5 * np.exp(-0.5 * x ** 2) * sc.erfcx(u)
+        def sf_default(x, K, u):
+            invK = 1.0 / K
+            expval = invK * (0.5 * invK - x)
+            logprod = expval + _norm_logcdf(x - invK)
+            return _norm_cdf(-x) + np.exp(logprod)
+        use_erfcx = np.logical_and(u >= 0, K < 1)
+        return xpx.apply_where(
+            use_erfcx, (x, K, u), sf_erfcx, sf_default)
+
+    def _stats(self, K):
+        K2 = K * K
+        opK2 = 1.0 + K2
+        skw = 2 * K**3 * opK2**(-1.5)
+        krt = 6.0 * K2 * K2 * opK2**(-2)
+        return K, opK2, skw, krt
+
+exponnorm = exponnorm_gen(name='exponnorm')
+
+
+def _pow1pm1(x, y):
+    """
+    Compute (1 + x)**y - 1.
+
+    Uses expm1 and xlog1py to avoid loss of precision when
+    (1 + x)**y is close to 1.
+
+    Note that the inverse of this function with respect to x is
+    ``_pow1pm1(x, 1/y)``.  That is, if
+
+        t = _pow1pm1(x, y)
+
+    then
+
+        x = _pow1pm1(t, 1/y)
+    """
+    return np.expm1(sc.xlog1py(y, x))
+
+
+class exponweib_gen(rv_continuous):
+    r"""An exponentiated Weibull continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    weibull_min, numpy.random.Generator.weibull
+
+    Notes
+    -----
+    The probability density function for `exponweib` is:
+
+    .. math::
+
+        f(x, a, c) = a c [1-\exp(-x^c)]^{a-1} \exp(-x^c) x^{c-1}
+
+    and its cumulative distribution function is:
+
+    .. math::
+
+        F(x, a, c) = [1-\exp(-x^c)]^a
+
+    for :math:`x > 0`, :math:`a > 0`, :math:`c > 0`.
+
+    `exponweib` takes :math:`a` and :math:`c` as shape parameters:
+
+    * :math:`a` is the exponentiation parameter,
+      with the special case :math:`a=1` corresponding to the
+      (non-exponentiated) Weibull distribution `weibull_min`.
+    * :math:`c` is the shape parameter of the non-exponentiated Weibull law.
+
+    %(after_notes)s
+
+    References
+    ----------
+    https://en.wikipedia.org/wiki/Exponentiated_Weibull_distribution
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        ia = _ShapeInfo("a", False, (0, np.inf), (False, False))
+        ic = _ShapeInfo("c", False, (0, np.inf), (False, False))
+        return [ia, ic]
+
+    def _pdf(self, x, a, c):
+        # exponweib.pdf(x, a, c) =
+        #     a * c * (1-exp(-x**c))**(a-1) * exp(-x**c)*x**(c-1)
+        return np.exp(self._logpdf(x, a, c))
+
+    def _logpdf(self, x, a, c):
+        negxc = -x**c
+        exm1c = -sc.expm1(negxc)
+        logp = (np.log(a) + np.log(c) + sc.xlogy(a - 1.0, exm1c) +
+                negxc + sc.xlogy(c - 1.0, x))
+        return logp
+
+    def _cdf(self, x, a, c):
+        exm1c = -sc.expm1(-x**c)
+        return exm1c**a
+
+    def _ppf(self, q, a, c):
+        return (-sc.log1p(-q**(1.0/a)))**np.asarray(1.0/c)
+
+    def _sf(self, x, a, c):
+        return -_pow1pm1(-np.exp(-x**c), a)
+
+    def _isf(self, p, a, c):
+        return (-np.log(-_pow1pm1(-p, 1/a)))**(1/c)
+
+
+exponweib = exponweib_gen(a=0.0, name='exponweib')
+
+
+class exponpow_gen(rv_continuous):
+    r"""An exponential power continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `exponpow` is:
+
+    .. math::
+
+        f(x, b) = b x^{b-1} \exp(1 + x^b - \exp(x^b))
+
+    for :math:`x \ge 0`, :math:`b > 0`.  Note that this is a different
+    distribution from the exponential power distribution that is also known
+    under the names "generalized normal" or "generalized Gaussian".
+
+    `exponpow` takes ``b`` as a shape parameter for :math:`b`.
+
+    %(after_notes)s
+
+    References
+    ----------
+    http://www.math.wm.edu/~leemis/chart/UDR/PDFs/Exponentialpower.pdf
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("b", False, (0, np.inf), (False, False))]
+
+    def _pdf(self, x, b):
+        # exponpow.pdf(x, b) = b * x**(b-1) * exp(1 + x**b - exp(x**b))
+        return np.exp(self._logpdf(x, b))
+
+    def _logpdf(self, x, b):
+        xb = x**b
+        f = 1 + np.log(b) + sc.xlogy(b - 1.0, x) + xb - np.exp(xb)
+        return f
+
+    def _cdf(self, x, b):
+        return -sc.expm1(-sc.expm1(x**b))
+
+    def _sf(self, x, b):
+        return np.exp(-sc.expm1(x**b))
+
+    def _isf(self, x, b):
+        return (sc.log1p(-np.log(x)))**(1./b)
+
+    def _ppf(self, q, b):
+        return pow(sc.log1p(-sc.log1p(-q)), 1.0/b)
+
+
+exponpow = exponpow_gen(a=0.0, name='exponpow')
+
+
+class fatiguelife_gen(rv_continuous):
+    r"""A fatigue-life (Birnbaum-Saunders) continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `fatiguelife` is:
+
+    .. math::
+
+        f(x, c) = \frac{x+1}{2c\sqrt{2\pi x^3}} \exp(-\frac{(x-1)^2}{2x c^2})
+
+    for :math:`x >= 0` and :math:`c > 0`.
+
+    `fatiguelife` takes ``c`` as a shape parameter for :math:`c`.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] "Birnbaum-Saunders distribution",
+           https://en.wikipedia.org/wiki/Birnbaum-Saunders_distribution
+
+    %(example)s
+
+    """
+    _support_mask = rv_continuous._open_support_mask
+
+    def _shape_info(self):
+        return [_ShapeInfo("c", False, (0, np.inf), (False, False))]
+
+    def _rvs(self, c, size=None, random_state=None):
+        z = random_state.standard_normal(size)
+        x = 0.5*c*z
+        x2 = x*x
+        t = 1.0 + 2*x2 + 2*x*np.sqrt(1 + x2)
+        return t
+
+    def _pdf(self, x, c):
+        # fatiguelife.pdf(x, c) =
+        #     (x+1) / (2*c*sqrt(2*pi*x**3)) * exp(-(x-1)**2/(2*x*c**2))
+        return np.exp(self._logpdf(x, c))
+
+    def _logpdf(self, x, c):
+        return (np.log(x+1) - (x-1)**2 / (2.0*x*c**2) - np.log(2*c) -
+                0.5*(np.log(2*np.pi) + 3*np.log(x)))
+
+    def _cdf(self, x, c):
+        return _norm_cdf(1.0 / c * (np.sqrt(x) - 1.0/np.sqrt(x)))
+
+    def _ppf(self, q, c):
+        tmp = c * _norm_ppf(q)
+        return 0.25 * (tmp + np.sqrt(tmp**2 + 4))**2
+
+    def _sf(self, x, c):
+        return _norm_sf(1.0 / c * (np.sqrt(x) - 1.0/np.sqrt(x)))
+
+    def _isf(self, q, c):
+        tmp = -c * _norm_ppf(q)
+        return 0.25 * (tmp + np.sqrt(tmp**2 + 4))**2
+
+    def _stats(self, c):
+        # NB: the formula for kurtosis in wikipedia seems to have an error:
+        # it's 40, not 41. At least it disagrees with the one from Wolfram
+        # Alpha.  And the latter one, below, passes the tests, while the wiki
+        # one doesn't So far I didn't have the guts to actually check the
+        # coefficients from the expressions for the raw moments.
+        c2 = c*c
+        mu = c2 / 2.0 + 1.0
+        den = 5.0 * c2 + 4.0
+        mu2 = c2*den / 4.0
+        g1 = 4 * c * (11*c2 + 6.0) / np.power(den, 1.5)
+        g2 = 6 * c2 * (93*c2 + 40.0) / den**2.0
+        return mu, mu2, g1, g2
+
+
+fatiguelife = fatiguelife_gen(a=0.0, name='fatiguelife')
+
+
+class foldcauchy_gen(rv_continuous):
+    r"""A folded Cauchy continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `foldcauchy` is:
+
+    .. math::
+
+        f(x, c) = \frac{1}{\pi (1+(x-c)^2)} + \frac{1}{\pi (1+(x+c)^2)}
+
+    for :math:`x \ge 0` and :math:`c \ge 0`.
+
+    `foldcauchy` takes ``c`` as a shape parameter for :math:`c`.
+
+    %(example)s
+
+    """
+    def _argcheck(self, c):
+        return c >= 0
+
+    def _shape_info(self):
+        return [_ShapeInfo("c", False, (0, np.inf), (True, False))]
+
+    def _rvs(self, c, size=None, random_state=None):
+        return abs(cauchy.rvs(loc=c, size=size,
+                              random_state=random_state))
+
+    def _pdf(self, x, c):
+        # foldcauchy.pdf(x, c) = 1/(pi*(1+(x-c)**2)) + 1/(pi*(1+(x+c)**2))
+        return 1.0/np.pi*(1.0/(1+(x-c)**2) + 1.0/(1+(x+c)**2))
+
+    def _cdf(self, x, c):
+        return 1.0/np.pi*(np.arctan(x-c) + np.arctan(x+c))
+
+    def _sf(self, x, c):
+        # 1 - CDF(x, c) = 1 - (atan(x - c) + atan(x + c))/pi
+        #               = ((pi/2 - atan(x - c)) + (pi/2 - atan(x + c)))/pi
+        #               = (acot(x - c) + acot(x + c))/pi
+        #               = (atan2(1, x - c) + atan2(1, x + c))/pi
+        return (np.arctan2(1, x - c) + np.arctan2(1, x + c))/np.pi
+
+    def _stats(self, c):
+        return np.inf, np.inf, np.nan, np.nan
+
+
+foldcauchy = foldcauchy_gen(a=0.0, name='foldcauchy')
+
+
+class f_gen(rv_continuous):
+    r"""An F continuous random variable.
+
+    For the noncentral F distribution, see `ncf`.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    ncf
+
+    Notes
+    -----
+    The F distribution with :math:`df_1 > 0` and :math:`df_2 > 0` degrees of freedom is
+    the distribution of the ratio of two independent chi-squared distributions with
+    :math:`df_1` and :math:`df_2` degrees of freedom, after rescaling by
+    :math:`df_2 / df_1`.
+
+    The probability density function for `f` is:
+
+    .. math::
+
+        f(x, df_1, df_2) = \frac{df_2^{df_2/2} df_1^{df_1/2} x^{df_1 / 2-1}}
+                                {(df_2+df_1 x)^{(df_1+df_2)/2}
+                                 B(df_1/2, df_2/2)}
+
+    for :math:`x > 0`.
+
+    `f` accepts shape parameters ``dfn`` and ``dfd`` for :math:`df_1`, the degrees of
+    freedom of the chi-squared distribution in the numerator, and :math:`df_2`, the
+    degrees of freedom of the chi-squared distribution in the denominator, respectively.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        idfn = _ShapeInfo("dfn", False, (0, np.inf), (False, False))
+        idfd = _ShapeInfo("dfd", False, (0, np.inf), (False, False))
+        return [idfn, idfd]
+
+    def _rvs(self, dfn, dfd, size=None, random_state=None):
+        return random_state.f(dfn, dfd, size)
+
+    def _pdf(self, x, dfn, dfd):
+        #                      df2**(df2/2) * df1**(df1/2) * x**(df1/2-1)
+        # F.pdf(x, df1, df2) = --------------------------------------------
+        #                      (df2+df1*x)**((df1+df2)/2) * B(df1/2, df2/2)
+        return np.exp(self._logpdf(x, dfn, dfd))
+
+    def _logpdf(self, x, dfn, dfd):
+        n = 1.0 * dfn
+        m = 1.0 * dfd
+        lPx = (m/2 * np.log(m) + n/2 * np.log(n) + sc.xlogy(n/2 - 1, x)
+               - (((n+m)/2) * np.log(m + n*x) + sc.betaln(n/2, m/2)))
+        return lPx
+
+    def _cdf(self, x, dfn, dfd):
+        return sc.fdtr(dfn, dfd, x)
+
+    def _sf(self, x, dfn, dfd):
+        return sc.fdtrc(dfn, dfd, x)
+
+    def _ppf(self, q, dfn, dfd):
+        return sc.fdtri(dfn, dfd, q)
+
+    def _stats(self, dfn, dfd):
+        v1, v2 = 1. * dfn, 1. * dfd
+        v2_2, v2_4, v2_6, v2_8 = v2 - 2., v2 - 4., v2 - 6., v2 - 8.
+
+        mu = xpx.apply_where(
+            v2 > 2, (v2, v2_2),
+            lambda v2, v2_2: v2 / v2_2,
+            fill_value=np.inf)
+
+        mu2 = xpx.apply_where(
+            v2 > 4, (v1, v2, v2_2, v2_4),
+            lambda v1, v2, v2_2, v2_4:
+            2 * v2 * v2 * (v1 + v2_2) / (v1 * v2_2**2 * v2_4),
+            fill_value=np.inf)
+
+        g1 = xpx.apply_where(
+            v2 > 6, (v1, v2_2, v2_4, v2_6),
+            lambda v1, v2_2, v2_4, v2_6:
+            (2 * v1 + v2_2) / v2_6 * np.sqrt(v2_4 / (v1 * (v1 + v2_2))),
+            fill_value=np.nan)
+        g1 *= np.sqrt(8.)
+
+        g2 = xpx.apply_where(
+            v2 > 8, (g1, v2_6, v2_8),
+            lambda g1, v2_6, v2_8: (8 + g1 * g1 * v2_6) / v2_8,
+            fill_value=np.nan)
+        g2 *= 3. / 2.
+
+        return mu, mu2, g1, g2
+
+    def _entropy(self, dfn, dfd):
+        # the formula found in literature is incorrect. This one yields the
+        # same result as numerical integration using the generic entropy
+        # definition. This is also tested in tests/test_conntinous_basic
+        half_dfn = 0.5 * dfn
+        half_dfd = 0.5 * dfd
+        half_sum = 0.5 * (dfn + dfd)
+
+        return (np.log(dfd) - np.log(dfn) + sc.betaln(half_dfn, half_dfd) +
+                (1 - half_dfn) * sc.psi(half_dfn) - (1 + half_dfd) *
+                sc.psi(half_dfd) + half_sum * sc.psi(half_sum))
+
+
+f = f_gen(a=0.0, name='f')
+
+
+## Folded Normal
+##   abs(Z) where (Z is normal with mu=L and std=S so that c=abs(L)/S)
+##
+##  note: regress docs have scale parameter correct, but first parameter
+##    he gives is a shape parameter A = c * scale
+
+##  Half-normal is folded normal with shape-parameter c=0.
+
+class foldnorm_gen(rv_continuous):
+    r"""A folded normal continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `foldnorm` is:
+
+    .. math::
+
+        f(x, c) = \sqrt{2/\pi} cosh(c x) \exp(-\frac{x^2+c^2}{2})
+
+    for :math:`x \ge 0` and :math:`c \ge 0`.
+
+    `foldnorm` takes ``c`` as a shape parameter for :math:`c`.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _argcheck(self, c):
+        return c >= 0
+
+    def _shape_info(self):
+        return [_ShapeInfo("c", False, (0, np.inf), (True, False))]
+
+    def _rvs(self, c, size=None, random_state=None):
+        return abs(random_state.standard_normal(size) + c)
+
+    def _pdf(self, x, c):
+        # foldnormal.pdf(x, c) = sqrt(2/pi) * cosh(c*x) * exp(-(x**2+c**2)/2)
+        return _norm_pdf(x + c) + _norm_pdf(x-c)
+
+    def _cdf(self, x, c):
+        sqrt_two = np.sqrt(2)
+        return 0.5 * (sc.erf((x - c)/sqrt_two) + sc.erf((x + c)/sqrt_two))
+
+    def _sf(self, x, c):
+        return _norm_sf(x - c) + _norm_sf(x + c)
+
+    def _stats(self, c):
+        # Regina C. Elandt, Technometrics 3, 551 (1961)
+        # https://www.jstor.org/stable/1266561
+        #
+        c2 = c*c
+        expfac = np.exp(-0.5*c2) / np.sqrt(2.*np.pi)
+
+        mu = 2.*expfac + c * sc.erf(c/np.sqrt(2))
+        mu2 = c2 + 1 - mu*mu
+
+        g1 = 2. * (mu*mu*mu - c2*mu - expfac)
+        g1 /= np.power(mu2, 1.5)
+
+        g2 = c2 * (c2 + 6.) + 3 + 8.*expfac*mu
+        g2 += (2. * (c2 - 3.) - 3. * mu**2) * mu**2
+        g2 = g2 / mu2**2.0 - 3.
+
+        return mu, mu2, g1, g2
+
+
+foldnorm = foldnorm_gen(a=0.0, name='foldnorm')
+
+
+class weibull_min_gen(rv_continuous):
+    r"""Weibull minimum continuous random variable.
+
+    The Weibull Minimum Extreme Value distribution, from extreme value theory
+    (Fisher-Gnedenko theorem), is also often simply called the Weibull
+    distribution. It arises as the limiting distribution of the rescaled
+    minimum of iid random variables.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    weibull_max, numpy.random.Generator.weibull, exponweib
+
+    Notes
+    -----
+    The probability density function for `weibull_min` is:
+
+    .. math::
+
+        f(x, c) = c x^{c-1} \exp(-x^c)
+
+    for :math:`x > 0`, :math:`c > 0`.
+
+    `weibull_min` takes ``c`` as a shape parameter for :math:`c`.
+    (named :math:`k` in Wikipedia article and :math:`a` in
+    ``numpy.random.weibull``).  Special shape values are :math:`c=1` and
+    :math:`c=2` where Weibull distribution reduces to the `expon` and
+    `rayleigh` distributions respectively.
+
+    Suppose ``X`` is an exponentially distributed random variable with
+    scale ``s``. Then ``Y = X**k`` is `weibull_min` distributed with shape
+    ``c = 1/k`` and scale ``s**k``.
+
+    %(after_notes)s
+
+    References
+    ----------
+    https://en.wikipedia.org/wiki/Weibull_distribution
+
+    https://en.wikipedia.org/wiki/Fisher-Tippett-Gnedenko_theorem
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("c", False, (0, np.inf), (False, False))]
+
+    def _pdf(self, x, c):
+        # weibull_min.pdf(x, c) = c * x**(c-1) * exp(-x**c)
+        return c*pow(x, c-1)*np.exp(-pow(x, c))
+
+    def _logpdf(self, x, c):
+        return np.log(c) + sc.xlogy(c - 1, x) - pow(x, c)
+
+    def _cdf(self, x, c):
+        return -sc.expm1(-pow(x, c))
+
+    def _ppf(self, q, c):
+        return pow(-sc.log1p(-q), 1.0/c)
+
+    def _sf(self, x, c):
+        return np.exp(self._logsf(x, c))
+
+    def _logsf(self, x, c):
+        return -pow(x, c)
+
+    def _isf(self, q, c):
+        return (-np.log(q))**(1/c)
+
+    def _munp(self, n, c):
+        return sc.gamma(1.0+n*1.0/c)
+
+    def _entropy(self, c):
+        return -_EULER / c - np.log(c) + _EULER + 1
+
+    @extend_notes_in_docstring(rv_continuous, notes="""\
+        If ``method='mm'``, parameters fixed by the user are respected, and the
+        remaining parameters are used to match distribution and sample moments
+        where possible. For example, if the user fixes the location with
+        ``floc``, the parameters will only match the distribution skewness and
+        variance to the sample skewness and variance; no attempt will be made
+        to match the means or minimize a norm of the errors.
+        \n\n""")
+    def fit(self, data, *args, **kwds):
+
+        if isinstance(data, CensoredData):
+            if data.num_censored() == 0:
+                data = data._uncensor()
+            else:
+                return super().fit(data, *args, **kwds)
+
+        if kwds.pop('superfit', False):
+            return super().fit(data, *args, **kwds)
+
+        # this extracts fixed shape, location, and scale however they
+        # are specified, and also leaves them in `kwds`
+        data, fc, floc, fscale = _check_fit_input_parameters(self, data,
+                                                             args, kwds)
+        method = kwds.get("method", "mle").lower()
+
+        # See https://en.wikipedia.org/wiki/Weibull_distribution#Moments for
+        # moment formulas.
+        def skew(c):
+            gamma1 = sc.gamma(1+1/c)
+            gamma2 = sc.gamma(1+2/c)
+            gamma3 = sc.gamma(1+3/c)
+            num = 2 * gamma1**3 - 3*gamma1*gamma2 + gamma3
+            den = (gamma2 - gamma1**2)**(3/2)
+            return num/den
+
+        # For c in [1e2, 3e4], population skewness appears to approach
+        # asymptote near -1.139, but past c > 3e4, skewness begins to vary
+        # wildly, and MoM won't provide a good guess. Get out early.
+        s = stats.skew(data)
+        max_c = 1e4
+        s_min = skew(max_c)
+        if s < s_min and method != "mm" and fc is None and not args:
+            return super().fit(data, *args, **kwds)
+
+        # If method is method of moments, we don't need the user's guesses.
+        # Otherwise, extract the guesses from args and kwds.
+        if method == "mm":
+            c, loc, scale = None, None, None
+        else:
+            c = args[0] if len(args) else None
+            loc = kwds.pop('loc', None)
+            scale = kwds.pop('scale', None)
+
+        if fc is None and c is None:  # not fixed and no guess: use MoM
+            # Solve for c that matches sample distribution skewness to sample
+            # skewness.
+            # we start having numerical issues with `weibull_min` with
+            # parameters outside this range - and not just in this method.
+            # We could probably improve the situation by doing everything
+            # in the log space, but that is for another time.
+            c = root_scalar(lambda c: skew(c) - s, bracket=[0.02, max_c],
+                            method='bisect').root
+        elif fc is not None:  # fixed: use it
+            c = fc
+
+        if fscale is None and scale is None:
+            v = np.var(data)
+            scale = np.sqrt(v / (sc.gamma(1+2/c) - sc.gamma(1+1/c)**2))
+        elif fscale is not None:
+            scale = fscale
+
+        if floc is None and loc is None:
+            m = np.mean(data)
+            loc = m - scale*sc.gamma(1 + 1/c)
+        elif floc is not None:
+            loc = floc
+
+        if method == 'mm':
+            return c, loc, scale
+        else:
+            # At this point, parameter "guesses" may equal the fixed parameters
+            # in kwds. No harm in passing them as guesses, too.
+            return super().fit(data, c, loc=loc, scale=scale, **kwds)
+
+
+weibull_min = weibull_min_gen(a=0.0, name='weibull_min')
+
+
+class truncweibull_min_gen(rv_continuous):
+    r"""A doubly truncated Weibull minimum continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    weibull_min, truncexpon
+
+    Notes
+    -----
+    The probability density function for `truncweibull_min` is:
+
+    .. math::
+
+        f(x, a, b, c) = \frac{c x^{c-1} \exp(-x^c)}{\exp(-a^c) - \exp(-b^c)}
+
+    for :math:`a < x <= b`, :math:`0 \le a < b` and :math:`c > 0`.
+
+    `truncweibull_min` takes :math:`a`, :math:`b`, and :math:`c` as shape
+    parameters.
+
+    Notice that the truncation values, :math:`a` and :math:`b`, are defined in
+    standardized form:
+
+    .. math::
+
+        a = (u_l - loc)/scale
+        b = (u_r - loc)/scale
+
+    where :math:`u_l` and :math:`u_r` are the specific left and right
+    truncation values, respectively. In other words, the support of the
+    distribution becomes :math:`(a*scale + loc) < x <= (b*scale + loc)` when
+    :math:`loc` and/or :math:`scale` are provided.
+
+    %(after_notes)s
+
+    References
+    ----------
+
+    .. [1] Rinne, H. "The Weibull Distribution: A Handbook". CRC Press (2009).
+
+    %(example)s
+
+    """
+    def _argcheck(self, c, a, b):
+        return (a >= 0.) & (b > a) & (c > 0.)
+
+    def _shape_info(self):
+        ic = _ShapeInfo("c", False, (0, np.inf), (False, False))
+        ia = _ShapeInfo("a", False, (0, np.inf), (True, False))
+        ib = _ShapeInfo("b", False, (0, np.inf), (False, False))
+        return [ic, ia, ib]
+
+    def _fitstart(self, data):
+        # Arbitrary, but default a=b=c=1 is not valid
+        return super()._fitstart(data, args=(1, 0, 1))
+
+    def _get_support(self, c, a, b):
+        return a, b
+
+    def _pdf(self, x, c, a, b):
+        denum = (np.exp(-pow(a, c)) - np.exp(-pow(b, c)))
+        return (c * pow(x, c-1) * np.exp(-pow(x, c))) / denum
+
+    def _logpdf(self, x, c, a, b):
+        logdenum = np.log(np.exp(-pow(a, c)) - np.exp(-pow(b, c)))
+        return np.log(c) + sc.xlogy(c - 1, x) - pow(x, c) - logdenum
+
+    def _cdf(self, x, c, a, b):
+        num = (np.exp(-pow(a, c)) - np.exp(-pow(x, c)))
+        denum = (np.exp(-pow(a, c)) - np.exp(-pow(b, c)))
+        return num / denum
+
+    def _logcdf(self, x, c, a, b):
+        lognum = np.log(np.exp(-pow(a, c)) - np.exp(-pow(x, c)))
+        logdenum = np.log(np.exp(-pow(a, c)) - np.exp(-pow(b, c)))
+        return lognum - logdenum
+
+    def _sf(self, x, c, a, b):
+        num = (np.exp(-pow(x, c)) - np.exp(-pow(b, c)))
+        denum = (np.exp(-pow(a, c)) - np.exp(-pow(b, c)))
+        return num / denum
+
+    def _logsf(self, x, c, a, b):
+        lognum = np.log(np.exp(-pow(x, c)) - np.exp(-pow(b, c)))
+        logdenum = np.log(np.exp(-pow(a, c)) - np.exp(-pow(b, c)))
+        return lognum - logdenum
+
+    def _isf(self, q, c, a, b):
+        return pow(
+            -np.log((1 - q) * np.exp(-pow(b, c)) + q * np.exp(-pow(a, c))), 1/c
+            )
+
+    def _ppf(self, q, c, a, b):
+        return pow(
+            -np.log((1 - q) * np.exp(-pow(a, c)) + q * np.exp(-pow(b, c))), 1/c
+            )
+
+    def _munp(self, n, c, a, b):
+        gamma_fun = sc.gamma(n/c + 1.) * (
+            sc.gammainc(n/c + 1., pow(b, c)) - sc.gammainc(n/c + 1., pow(a, c))
+            )
+        denum = (np.exp(-pow(a, c)) - np.exp(-pow(b, c)))
+        return gamma_fun / denum
+
+
+truncweibull_min = truncweibull_min_gen(name='truncweibull_min')
+truncweibull_min._support = ('a', 'b')
+
+
+class weibull_max_gen(rv_continuous):
+    r"""Weibull maximum continuous random variable.
+
+    The Weibull Maximum Extreme Value distribution, from extreme value theory
+    (Fisher-Gnedenko theorem), is the limiting distribution of rescaled
+    maximum of iid random variables. This is the distribution of -X
+    if X is from the `weibull_min` function.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    weibull_min
+
+    Notes
+    -----
+    The probability density function for `weibull_max` is:
+
+    .. math::
+
+        f(x, c) = c (-x)^{c-1} \exp(-(-x)^c)
+
+    for :math:`x < 0`, :math:`c > 0`.
+
+    `weibull_max` takes ``c`` as a shape parameter for :math:`c`.
+
+    %(after_notes)s
+
+    References
+    ----------
+    https://en.wikipedia.org/wiki/Weibull_distribution
+
+    https://en.wikipedia.org/wiki/Fisher-Tippett-Gnedenko_theorem
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("c", False, (0, np.inf), (False, False))]
+
+    def _pdf(self, x, c):
+        # weibull_max.pdf(x, c) = c * (-x)**(c-1) * exp(-(-x)**c)
+        return c*pow(-x, c-1)*np.exp(-pow(-x, c))
+
+    def _logpdf(self, x, c):
+        return np.log(c) + sc.xlogy(c-1, -x) - pow(-x, c)
+
+    def _cdf(self, x, c):
+        return np.exp(-pow(-x, c))
+
+    def _logcdf(self, x, c):
+        return -pow(-x, c)
+
+    def _sf(self, x, c):
+        return -sc.expm1(-pow(-x, c))
+
+    def _ppf(self, q, c):
+        return -pow(-np.log(q), 1.0/c)
+
+    def _munp(self, n, c):
+        val = sc.gamma(1.0+n*1.0/c)
+        if int(n) % 2:
+            sgn = -1
+        else:
+            sgn = 1
+        return sgn * val
+
+    def _entropy(self, c):
+        return -_EULER / c - np.log(c) + _EULER + 1
+
+
+weibull_max = weibull_max_gen(b=0.0, name='weibull_max')
+
+
+class genlogistic_gen(rv_continuous):
+    r"""A generalized logistic continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `genlogistic` is:
+
+    .. math::
+
+        f(x, c) = c \frac{\exp(-x)}
+                         {(1 + \exp(-x))^{c+1}}
+
+    for real :math:`x` and :math:`c > 0`. In literature, different
+    generalizations of the logistic distribution can be found. This is the type 1
+    generalized logistic distribution according to [1]_. It is also referred to
+    as the skew-logistic distribution [2]_.
+
+    `genlogistic` takes ``c`` as a shape parameter for :math:`c`.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] Johnson et al. "Continuous Univariate Distributions", Volume 2,
+           Wiley. 1995.
+    .. [2] "Generalized Logistic Distribution", Wikipedia,
+           https://en.wikipedia.org/wiki/Generalized_logistic_distribution
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("c", False, (0, np.inf), (False, False))]
+
+    def _pdf(self, x, c):
+        # genlogistic.pdf(x, c) = c * exp(-x) / (1 + exp(-x))**(c+1)
+        return np.exp(self._logpdf(x, c))
+
+    def _logpdf(self, x, c):
+        # Two mathematically equivalent expressions for log(pdf(x, c)):
+        #     log(pdf(x, c)) = log(c) - x - (c + 1)*log(1 + exp(-x))
+        #                    = log(c) + c*x - (c + 1)*log(1 + exp(x))
+        mult = -(c - 1) * (x < 0) - 1
+        absx = np.abs(x)
+        return np.log(c) + mult*absx - (c+1) * sc.log1p(np.exp(-absx))
+
+    def _cdf(self, x, c):
+        Cx = (1+np.exp(-x))**(-c)
+        return Cx
+
+    def _logcdf(self, x, c):
+        return -c * np.log1p(np.exp(-x))
+
+    def _ppf(self, q, c):
+        return -np.log(sc.powm1(q, -1.0/c))
+
+    def _sf(self, x, c):
+        return -sc.expm1(self._logcdf(x, c))
+
+    def _isf(self, q, c):
+        return self._ppf(1 - q, c)
+
+    def _stats(self, c):
+        mu = _EULER + sc.psi(c)
+        mu2 = np.pi*np.pi/6.0 + sc.zeta(2, c)
+        g1 = -2*sc.zeta(3, c) + 2*_ZETA3
+        g1 /= np.power(mu2, 1.5)
+        g2 = np.pi**4/15.0 + 6*sc.zeta(4, c)
+        g2 /= mu2**2.0
+        return mu, mu2, g1, g2
+
+    def _entropy(self, c):
+        return xpx.apply_where(
+            c < 8e6, c,
+            lambda c: -np.log(c) + sc.psi(c + 1) + _EULER + 1,
+            # asymptotic expansion: psi(c) ~ log(c) - 1 / (2 * c)
+            # a = -log(c) + psi(c + 1)
+            #   = -log(c) + psi(c) + 1 / c
+            #   ~ -log(c) + log(c) - 1 / (2 * c) + 1 / c
+            #   = 1 / (2 * c)
+            lambda c: 1 / (2 * c) + _EULER + 1)
+
+
+genlogistic = genlogistic_gen(name='genlogistic')
+
+
+class genpareto_gen(rv_continuous):
+    r"""A generalized Pareto continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `genpareto` is:
+
+    .. math::
+
+        f(x, c) = (1 + c x)^{-1 - 1/c}
+
+    defined for :math:`x \ge 0` if :math:`c \ge 0`, and for
+    :math:`0 \le x \le -1/c` if :math:`c < 0`.
+
+    `genpareto` takes ``c`` as a shape parameter for :math:`c`.
+
+    For :math:`c=0`, `genpareto` reduces to the exponential
+    distribution, `expon`:
+
+    .. math::
+
+        f(x, 0) = \exp(-x)
+
+    For :math:`c=-1`, `genpareto` is uniform on ``[0, 1]``:
+
+    .. math::
+
+        f(x, -1) = 1
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _argcheck(self, c):
+        return np.isfinite(c)
+
+    def _shape_info(self):
+        return [_ShapeInfo("c", False, (-np.inf, np.inf), (False, False))]
+
+    def _get_support(self, c):
+        c = np.asarray(c)
+        a = np.broadcast_arrays(self.a, c)[0].copy()
+        b = xpx.apply_where(c < 0, c, lambda c: -1. / c,
+                            fill_value=np.inf)
+        return a, b
+
+    def _pdf(self, x, c):
+        # genpareto.pdf(x, c) = (1 + c * x)**(-1 - 1/c)
+        return np.exp(self._logpdf(x, c))
+
+    def _logpdf(self, x, c):
+        return xpx.apply_where((x == x) & (c != 0), (x, c),
+                               lambda x, c: -sc.xlog1py(c + 1., c*x) / c,
+                               fill_value=-x)
+
+    def _cdf(self, x, c):
+        return -sc.inv_boxcox1p(-x, -c)
+
+    def _sf(self, x, c):
+        return sc.inv_boxcox(-x, -c)
+
+    def _logsf(self, x, c):
+        return xpx.apply_where((x == x) & (c != 0), (x, c),
+                               lambda x, c: -sc.log1p(c*x) / c,
+                               fill_value=-x)
+
+    def _ppf(self, q, c):
+        return -sc.boxcox1p(-q, -c)
+
+    def _isf(self, q, c):
+        return -sc.boxcox(q, -c)
+
+    def _stats(self, c, moments='mv'):
+        m, v, s, k = None, None, None, None
+
+        if 'm' in moments:
+            m = xpx.apply_where(c < 1, c,
+                                lambda xi: 1 / (1 - xi),
+                                fill_value=np.inf)
+
+        if 'v' in moments:
+            v = xpx.apply_where(c < 1/2, c,
+                                lambda xi: 1 / (1 - xi)**2 / (1 - 2 * xi),
+                                fill_value=np.nan)
+
+        if 's' in moments:
+            s = xpx.apply_where(
+                c < 1/3, c,
+                lambda xi: 2 * (1 + xi) * np.sqrt(1 - 2*xi) / (1 - 3*xi),
+                fill_value=np.nan)
+
+        if 'k' in moments:
+            k = xpx.apply_where(
+                c < 1/4, c,
+                lambda xi: 3 * (1 - 2*xi) * (2*xi**2 + xi + 3)
+                           / (1 - 3*xi) / (1 - 4*xi) - 3,
+                fill_value=np.nan)
+
+        return m, v, s, k
+
+    def _munp(self, n, c):
+        def __munp(c):
+            val = 0.0
+            k = np.arange(0, n + 1)
+            for ki, cnk in zip(k, sc.comb(n, k)):
+                val = val + cnk * (-1) ** ki / (1.0 - c * ki)
+            return np.where(c * n < 1, val * (-1.0 / c) ** n, np.inf)
+
+        return xpx.apply_where(c != 0, c, __munp, fill_value=sc.gamma(n + 1))
+
+    def _entropy(self, c):
+        return 1. + c
+
+
+genpareto = genpareto_gen(a=0.0, name='genpareto')
+
+
+class genexpon_gen(rv_continuous):
+    r"""A generalized exponential continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `genexpon` is:
+
+    .. math::
+
+        f(x, a, b, c) = (a + b (1 - \exp(-c x)))
+                        \exp(-a x - b x + \frac{b}{c}  (1-\exp(-c x)))
+
+    for :math:`x \ge 0`, :math:`a, b, c > 0`.
+
+    `genexpon` takes :math:`a`, :math:`b` and :math:`c` as shape parameters.
+
+    %(after_notes)s
+
+    References
+    ----------
+    H.K. Ryu, "An Extension of Marshall and Olkin's Bivariate Exponential
+    Distribution", Journal of the American Statistical Association, 1993.
+
+    N. Balakrishnan, Asit P. Basu (editors), *The Exponential Distribution:
+    Theory, Methods and Applications*, Gordon and Breach, 1995.
+    ISBN 10: 2884491929
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        ia = _ShapeInfo("a", False, (0, np.inf), (False, False))
+        ib = _ShapeInfo("b", False, (0, np.inf), (False, False))
+        ic = _ShapeInfo("c", False, (0, np.inf), (False, False))
+        return [ia, ib, ic]
+
+    def _pdf(self, x, a, b, c):
+        # genexpon.pdf(x, a, b, c) = (a + b * (1 - exp(-c*x))) * \
+        #                            exp(-a*x - b*x + b/c * (1-exp(-c*x)))
+        return (a + b*(-sc.expm1(-c*x)))*np.exp((-a-b)*x +
+                                                b*(-sc.expm1(-c*x))/c)
+
+    def _logpdf(self, x, a, b, c):
+        return np.log(a+b*(-sc.expm1(-c*x))) + (-a-b)*x+b*(-sc.expm1(-c*x))/c
+
+    def _cdf(self, x, a, b, c):
+        return -sc.expm1((-a-b)*x + b*(-sc.expm1(-c*x))/c)
+
+    def _ppf(self, p, a, b, c):
+        s = a + b
+        t = (b - c*np.log1p(-p))/s
+        return (t + sc.lambertw(-b/s * np.exp(-t)).real)/c
+
+    def _sf(self, x, a, b, c):
+        return np.exp((-a-b)*x + b*(-sc.expm1(-c*x))/c)
+
+    def _isf(self, p, a, b, c):
+        s = a + b
+        t = (b - c*np.log(p))/s
+        return (t + sc.lambertw(-b/s * np.exp(-t)).real)/c
+
+
+genexpon = genexpon_gen(a=0.0, name='genexpon')
+
+
+class genextreme_gen(rv_continuous):
+    r"""A generalized extreme value continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    gumbel_r
+
+    Notes
+    -----
+    For :math:`c=0`, `genextreme` is equal to `gumbel_r` with
+    probability density function
+
+    .. math::
+
+        f(x) = \exp(-\exp(-x)) \exp(-x),
+
+    where :math:`-\infty < x < \infty`.
+
+    For :math:`c \ne 0`, the probability density function for `genextreme` is:
+
+    .. math::
+
+        f(x, c) = \exp(-(1-c x)^{1/c}) (1-c x)^{1/c-1},
+
+    where :math:`-\infty < x \le 1/c` if :math:`c > 0` and
+    :math:`1/c \le x < \infty` if :math:`c < 0`.
+
+    Note that several sources and software packages use the opposite
+    convention for the sign of the shape parameter :math:`c`.
+
+    `genextreme` takes ``c`` as a shape parameter for :math:`c`.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _argcheck(self, c):
+        return np.isfinite(c)
+
+    def _shape_info(self):
+        return [_ShapeInfo("c", False, (-np.inf, np.inf), (False, False))]
+
+    def _get_support(self, c):
+        c = np.asarray(c)
+        _b = np.where(c > 0, 1.0 / np.maximum(c, _XMIN), np.inf)
+        _a = np.where(c < 0, 1.0 / np.minimum(c, -_XMIN), -np.inf)
+        return _a, _b
+
+    def _loglogcdf(self, x, c):
+        # Returns log(-log(cdf(x, c)))
+        return xpx.apply_where(
+            (x == x) & (c != 0), (x, c),
+            lambda x, c: sc.log1p(-c*x)/c,
+            fill_value=-x)
+
+    def _pdf(self, x, c):
+        # genextreme.pdf(x, c) =
+        #     exp(-exp(-x))*exp(-x),                    for c==0
+        #     exp(-(1-c*x)**(1/c))*(1-c*x)**(1/c-1),    for x \le 1/c, c > 0
+        return np.exp(self._logpdf(x, c))
+
+    def _logpdf(self, x, c):
+        # Suppress warnings 0 * inf
+        cx = xpx.apply_where((x == x) & (c != 0), (c, x),
+                             operator.mul, fill_value=0.0)
+        logex2 = sc.log1p(-cx)
+        logpex2 = self._loglogcdf(x, c)
+        pex2 = np.exp(logpex2)
+        # Handle special cases
+        np.putmask(logpex2, (c == 0) & (x == -np.inf), 0.0)
+        logpdf = xpx.apply_where(
+            ~((cx == 1) | (cx == -np.inf)),
+            (pex2, logpex2, logex2),
+            lambda pex2, lpex2, lex2: -pex2 + lpex2 - lex2,
+            fill_value=-np.inf)
+        np.putmask(logpdf, (c == 1) & (x == 1), 0.0)
+        return logpdf
+
+    def _logcdf(self, x, c):
+        return -np.exp(self._loglogcdf(x, c))
+
+    def _cdf(self, x, c):
+        return np.exp(self._logcdf(x, c))
+
+    def _sf(self, x, c):
+        return -sc.expm1(self._logcdf(x, c))
+
+    def _ppf(self, q, c):
+        x = -np.log(-np.log(q))
+        return xpx.apply_where(
+            (x == x) & (c != 0), (x, c),
+            lambda x, c: -sc.expm1(-c * x) / c,
+            fill_value=x)
+
+    def _isf(self, q, c):
+        x = -np.log(-sc.log1p(-q))
+        return xpx.apply_where(
+            (x == x) & (c != 0), (x, c),
+            lambda x, c: -sc.expm1(-c * x) / c,
+            fill_value=x)
+
+    def _stats(self, c):
+        def g(n):
+            return sc.gamma(n * c + 1)
+        g1 = g(1)
+        g2 = g(2)
+        g3 = g(3)
+        g4 = g(4)
+        g2mg12 = np.where(abs(c) < 1e-7, (c*np.pi)**2.0/6.0, g2-g1**2.0)
+        def gam2k_f(c):
+            return sc.expm1(sc.gammaln(2.0*c+1.0)-2*sc.gammaln(c + 1.0))/c**2.0
+        gam2k = xpx.apply_where(abs(c) >= 1e-7, c, gam2k_f, fill_value=np.pi**2.0/6.0)
+        eps = 1e-14
+        def gamk_f(c):
+            return sc.expm1(sc.gammaln(c + 1))/c
+        gamk = xpx.apply_where(abs(c) >= eps, c, gamk_f, fill_value=-_EULER)
+
+        # mean
+        m = np.where(c < -1.0, np.nan, -gamk)
+
+        # variance
+        v = np.where(c < -0.5, np.nan, g1**2.0*gam2k)
+
+        # skewness
+        def sk1_eval(c, *args):
+            def sk1_eval_f(c, g1, g2, g3, g2mg12):
+                return np.sign(c)*(-g3 + (g2 + 2*g2mg12)*g1)/g2mg12**1.5
+            return xpx.apply_where(c >= -1./3, (c, *args),
+                                   sk1_eval_f, fill_value=np.nan)
+
+        sk_fill = 12*np.sqrt(6)*_ZETA3/np.pi**3
+        args = (g1, g2, g3, g2mg12)
+        sk = xpx.apply_where(abs(c) > eps**0.29, (c, *args),
+                             sk1_eval, fill_value=sk_fill)
+
+        # kurtosis
+        def ku1_eval(c, *args):
+            def ku1_eval_f(g1, g2, g3, g4, g2mg12):
+                return (g4 + (-4*g3 + 3*(g2 + g2mg12)*g1)*g1)/g2mg12**2 - 3
+            return xpx.apply_where(c >= -1./4, args, ku1_eval_f, fill_value=np.nan)
+
+        args = (g1, g2, g3, g4, g2mg12)
+        ku = xpx.apply_where(abs(c) > eps**0.23, (c, *args),
+                             ku1_eval, fill_value=12.0/5.0)
+
+        return m, v, sk, ku
+
+    def _fitstart(self, data):
+        if isinstance(data, CensoredData):
+            data = data._uncensor()
+        # This is better than the default shape of (1,).
+        g = _skew(data)
+        if g < 0:
+            a = 0.5
+        else:
+            a = -0.5
+        return super()._fitstart(data, args=(a,))
+
+    def _munp(self, n, c):
+        k = np.arange(0, n+1)
+        k = np.reshape(k, (-1,) + (1,)*c.ndim)
+        vals = 1.0/c**n * np.sum(
+            sc.comb(n, k) * (-1)**k * sc.gamma(c*k + 1),
+            axis=0)
+        return np.where(c*n > -1, vals, np.inf)
+
+    def _entropy(self, c):
+        return _EULER*(1 - c) + 1
+
+
+genextreme = genextreme_gen(name='genextreme')
+
+
+def _digammainv(y):
+    """Inverse of the digamma function (real positive arguments only).
+
+    This function is used in the `fit` method of `gamma_gen`.
+    The function uses either optimize.fsolve or optimize.newton
+    to solve `sc.digamma(x) - y = 0`.  There is probably room for
+    improvement, but currently it works over a wide range of y:
+
+    >>> import numpy as np
+    >>> rng = np.random.default_rng()
+    >>> y = 64*rng.standard_normal(1000000)
+    >>> y.min(), y.max()
+    (-311.43592651416662, 351.77388222276869)
+    >>> x = [_digammainv(t) for t in y]
+    >>> np.abs(sc.digamma(x) - y).max()
+    1.1368683772161603e-13
+
+    """
+    _em = 0.5772156649015328606065120
+
+    def func(x):
+        return sc.digamma(x) - y
+
+    if y > -0.125:
+        x0 = np.exp(y) + 0.5
+        if y < 10:
+            # Some experimentation shows that newton reliably converges
+            # must faster than fsolve in this y range.  For larger y,
+            # newton sometimes fails to converge.
+            value = optimize.newton(func, x0, tol=1e-10)
+            return value
+    elif y > -3:
+        x0 = np.exp(y/2.332) + 0.08661
+    else:
+        x0 = 1.0 / (-y - _em)
+
+    value, info, ier, mesg = optimize.fsolve(func, x0, xtol=1e-11,
+                                             full_output=True)
+    if ier != 1:
+        raise RuntimeError(f"_digammainv: fsolve failed, y = {y!r}")
+
+    return value[0]
+
+
+## Gamma (Use MATLAB and MATHEMATICA (b=theta=scale, a=alpha=shape) definition)
+
+## gamma(a, loc, scale)  with a an integer is the Erlang distribution
+## gamma(1, loc, scale)  is the Exponential distribution
+## gamma(df/2, 0, 2) is the chi2 distribution with df degrees of freedom.
+
+class gamma_gen(rv_continuous):
+    r"""A gamma continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    erlang, expon
+
+    Notes
+    -----
+    The probability density function for `gamma` is:
+
+    .. math::
+
+        f(x, a) = \frac{x^{a-1} e^{-x}}{\Gamma(a)}
+
+    for :math:`x \ge 0`, :math:`a > 0`. Here :math:`\Gamma(a)` refers to the
+    gamma function.
+
+    `gamma` takes ``a`` as a shape parameter for :math:`a`.
+
+    When :math:`a` is an integer, `gamma` reduces to the Erlang
+    distribution, and when :math:`a=1` to the exponential distribution.
+
+    Gamma distributions are sometimes parameterized with two variables,
+    with a probability density function of:
+
+    .. math::
+
+        f(x, \alpha, \beta) =
+        \frac{\beta^\alpha x^{\alpha - 1} e^{-\beta x }}{\Gamma(\alpha)}
+
+    Note that this parameterization is equivalent to the above, with
+    ``scale = 1 / beta``.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("a", False, (0, np.inf), (False, False))]
+
+    def _rvs(self, a, size=None, random_state=None):
+        return random_state.standard_gamma(a, size)
+
+    def _pdf(self, x, a):
+        # gamma.pdf(x, a) = x**(a-1) * exp(-x) / gamma(a)
+        return np.exp(self._logpdf(x, a))
+
+    def _logpdf(self, x, a):
+        return sc.xlogy(a-1.0, x) - x - sc.gammaln(a)
+
+    def _cdf(self, x, a):
+        return sc.gammainc(a, x)
+
+    def _sf(self, x, a):
+        return sc.gammaincc(a, x)
+
+    def _ppf(self, q, a):
+        return sc.gammaincinv(a, q)
+
+    def _isf(self, q, a):
+        return sc.gammainccinv(a, q)
+
+    def _stats(self, a):
+        return a, a, 2.0/np.sqrt(a), 6.0/a
+
+    def _munp(self, n, a):
+        return sc.poch(a, n)
+
+    def _entropy(self, a):
+
+        def regular_formula(a):
+            return sc.psi(a) * (1-a) + a + sc.gammaln(a)
+
+        def asymptotic_formula(a):
+            # plug in above formula the expansions:
+            # psi(a) ~ ln(a) - 1/2a - 1/12a^2 + 1/120a^4
+            # gammaln(a) ~ a * ln(a) - a - 1/2 * ln(a) + 1/2 ln(2 * pi) +
+            #              1/12a - 1/360a^3
+            return (0.5 * (1. + np.log(2*np.pi) + np.log(a)) - 1/(3 * a)
+                    - (a**-2.)/12 - (a**-3.)/90 + (a**-4.)/120)
+
+        return xpx.apply_where(a < 250, a, regular_formula, asymptotic_formula)
+
+    def _fitstart(self, data):
+        # The skewness of the gamma distribution is `2 / np.sqrt(a)`.
+        # We invert that to estimate the shape `a` using the skewness
+        # of the data.  The formula is regularized with 1e-8 in the
+        # denominator to allow for degenerate data where the skewness
+        # is close to 0.
+        if isinstance(data, CensoredData):
+            data = data._uncensor()
+        sk = _skew(data)
+        a = 4 / (1e-8 + sk**2)
+        return super()._fitstart(data, args=(a,))
+
+    @extend_notes_in_docstring(rv_continuous, notes="""\
+        When the location is fixed by using the argument `floc`
+        and `method='MLE'`, this
+        function uses explicit formulas or solves a simpler numerical
+        problem than the full ML optimization problem.  So in that case,
+        the `optimizer`, `loc` and `scale` arguments are ignored.
+        \n\n""")
+    def fit(self, data, *args, **kwds):
+        floc = kwds.get('floc', None)
+        method = kwds.get('method', 'mle')
+
+        if (isinstance(data, CensoredData) or
+                floc is None and method.lower() != 'mm'):
+            # loc is not fixed or we're not doing standard MLE.
+            # Use the default fit method.
+            return super().fit(data, *args, **kwds)
+
+        # We already have this value, so just pop it from kwds.
+        kwds.pop('floc', None)
+
+        f0 = _get_fixed_fit_value(kwds, ['f0', 'fa', 'fix_a'])
+        fscale = kwds.pop('fscale', None)
+
+        _remove_optimizer_parameters(kwds)
+
+        if f0 is not None and floc is not None and fscale is not None:
+            # This check is for consistency with `rv_continuous.fit`.
+            # Without this check, this function would just return the
+            # parameters that were given.
+            raise ValueError("All parameters fixed. There is nothing to "
+                             "optimize.")
+
+        # Fixed location is handled by shifting the data.
+        data = np.asarray(data)
+
+        if not np.isfinite(data).all():
+            raise ValueError("The data contains non-finite values.")
+
+        # Use explicit formulas for mm (gh-19884)
+        if method.lower() == 'mm':
+            m1 = np.mean(data)
+            m2 = np.var(data)
+            m3 = np.mean((data - m1) ** 3)
+            a, loc, scale = f0, floc, fscale
+            # Three unknowns
+            if a is None and loc is None and scale is None:
+                scale = m3 / (2 * m2)
+            # Two unknowns
+            if loc is None and scale is None:
+                scale = np.sqrt(m2 / a)
+            if a is None and scale is None:
+                scale = m2 / (m1 - loc)
+            if a is None and loc is None:
+                a = m2 / (scale ** 2)
+            # One unknown
+            if a is None:
+                a = (m1 - loc) / scale
+            if loc is None:
+                loc = m1 - a * scale
+            if scale is None:
+                scale = (m1 - loc) / a
+            return a, loc, scale
+
+        # Special case: loc is fixed.
+
+        # NB: data == loc is ok if a >= 1; the below check is more strict.
+        if np.any(data <= floc):
+            raise FitDataError("gamma", lower=floc, upper=np.inf)
+
+        if floc != 0:
+            # Don't do the subtraction in-place, because `data` might be a
+            # view of the input array.
+            data = data - floc
+        xbar = data.mean()
+
+        # Three cases to handle:
+        # * shape and scale both free
+        # * shape fixed, scale free
+        # * shape free, scale fixed
+
+        if fscale is None:
+            # scale is free
+            if f0 is not None:
+                # shape is fixed
+                a = f0
+            else:
+                # shape and scale are both free.
+                # The MLE for the shape parameter `a` is the solution to:
+                # np.log(a) - sc.digamma(a) - np.log(xbar) +
+                #                             np.log(data).mean() = 0
+                s = np.log(xbar) - np.log(data).mean()
+                aest = (3-s + np.sqrt((s-3)**2 + 24*s)) / (12*s)
+                xa = aest*(1-0.4)
+                xb = aest*(1+0.4)
+                a = optimize.brentq(lambda a: np.log(a) - sc.digamma(a) - s,
+                                    xa, xb, disp=0)
+
+            # The MLE for the scale parameter is just the data mean
+            # divided by the shape parameter.
+            scale = xbar / a
+        else:
+            # scale is fixed, shape is free
+            # The MLE for the shape parameter `a` is the solution to:
+            # sc.digamma(a) - np.log(data).mean() + np.log(fscale) = 0
+            c = np.log(data).mean() - np.log(fscale)
+            a = _digammainv(c)
+            scale = fscale
+
+        return a, floc, scale
+
+
+gamma = gamma_gen(a=0.0, name='gamma')
+
+
+class erlang_gen(gamma_gen):
+    """An Erlang continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    gamma
+
+    Notes
+    -----
+    The Erlang distribution is a special case of the Gamma distribution, with
+    the shape parameter `a` an integer.  Note that this restriction is not
+    enforced by `erlang`. It will, however, generate a warning the first time
+    a non-integer value is used for the shape parameter.
+
+    Refer to `gamma` for examples.
+
+    """
+
+    def _argcheck(self, a):
+        allint = np.all(np.floor(a) == a)
+        if not allint:
+            # An Erlang distribution shouldn't really have a non-integer
+            # shape parameter, so warn the user.
+            message = ('The shape parameter of the erlang distribution '
+                       f'has been given a non-integer value {a!r}.')
+            warnings.warn(message, RuntimeWarning, stacklevel=3)
+        return a > 0
+
+    def _shape_info(self):
+        return [_ShapeInfo("a", True, (1, np.inf), (True, False))]
+
+    def _fitstart(self, data):
+        # Override gamma_gen_fitstart so that an integer initial value is
+        # used.  (Also regularize the division, to avoid issues when
+        # _skew(data) is 0 or close to 0.)
+        if isinstance(data, CensoredData):
+            data = data._uncensor()
+        a = int(4.0 / (1e-8 + _skew(data)**2))
+        return super(gamma_gen, self)._fitstart(data, args=(a,))
+
+    # Trivial override of the fit method, so we can monkey-patch its
+    # docstring.
+    @extend_notes_in_docstring(rv_continuous, notes="""\
+        The Erlang distribution is generally defined to have integer values
+        for the shape parameter.  This is not enforced by the `erlang` class.
+        When fitting the distribution, it will generally return a non-integer
+        value for the shape parameter.  By using the keyword argument
+        `f0=<integer>`, the fit method can be constrained to fit the data to
+        a specific integer shape parameter.""")
+    def fit(self, data, *args, **kwds):
+        return super().fit(data, *args, **kwds)
+
+
+erlang = erlang_gen(a=0.0, name='erlang')
+
+
+class gengamma_gen(rv_continuous):
+    r"""A generalized gamma continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    gamma, halfgennorm, invgamma, weibull_min
+
+    Notes
+    -----
+    The probability density function for `gengamma` is ([1]_, [2]_):
+
+    .. math::
+
+        f(x, a, c) = \frac{|c| x^{c a-1} \exp(-x^c)}{\Gamma(a)}
+
+    for :math:`x \ge 0`, :math:`a > 0`, and :math:`c \ne 0`.
+    :math:`\Gamma` is the gamma function (`scipy.special.gamma`).
+
+    `gengamma` takes :math:`a` and :math:`c` as shape parameters.
+
+    The SciPy distribution `halfgennorm` is a special case of
+    `gengamma`: ``halfgennorm(beta) = gengamma(a=1/beta, c=beta)``.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] E.W. Stacy, "A Generalization of the Gamma Distribution",
+           Annals of Mathematical Statistics, Vol 33(3), pp. 1187--1192.
+    .. [2] "Generalized gamma distribution", Wikipedia,
+           https://en.wikipedia.org/wiki/Generalized_gamma_distribution
+
+    %(example)s
+
+    """
+    def _argcheck(self, a, c):
+        return (a > 0) & (c != 0)
+
+    def _shape_info(self):
+        ia = _ShapeInfo("a", False, (0, np.inf), (False, False))
+        ic = _ShapeInfo("c", False, (-np.inf, np.inf), (False, False))
+        return [ia, ic]
+
+    def _pdf(self, x, a, c):
+        return np.exp(self._logpdf(x, a, c))
+
+    def _logpdf(self, x, a, c):
+        return xpx.apply_where(
+            (x != 0) | (c > 0), (x, c, a),
+            lambda x, c, a: (np.log(abs(c)) + sc.xlogy(c*a - 1, x)
+                             - x**c - sc.gammaln(a)),
+            fill_value=-np.inf)
+
+    def _cdf(self, x, a, c):
+        xc = x**c
+        val1 = sc.gammainc(a, xc)
+        val2 = sc.gammaincc(a, xc)
+        return np.where(c > 0, val1, val2)
+
+    def _rvs(self, a, c, size=None, random_state=None):
+        r = random_state.standard_gamma(a, size=size)
+        return r**(1./c)
+
+    def _sf(self, x, a, c):
+        xc = x**c
+        val1 = sc.gammainc(a, xc)
+        val2 = sc.gammaincc(a, xc)
+        return np.where(c > 0, val2, val1)
+
+    def _ppf(self, q, a, c):
+        val1 = sc.gammaincinv(a, q)
+        val2 = sc.gammainccinv(a, q)
+        return np.where(c > 0, val1, val2)**(1.0/c)
+
+    def _isf(self, q, a, c):
+        val1 = sc.gammaincinv(a, q)
+        val2 = sc.gammainccinv(a, q)
+        return np.where(c > 0, val2, val1)**(1.0/c)
+
+    def _munp(self, n, a, c):
+        # Pochhammer symbol: sc.pocha,n) = gamma(a+n)/gamma(a)
+        return sc.poch(a, n*1.0/c)
+
+    def _entropy(self, a, c):
+        def regular(a, c):
+            val = sc.psi(a)
+            A = a * (1 - val) + val / c
+            B = sc.gammaln(a) - np.log(abs(c))
+            h = A + B
+            return h
+
+        def asymptotic(a, c):
+            # using asymptotic expansions for gammaln and psi (see gh-18093)
+            return (norm._entropy() - np.log(a)/2
+                    - np.log(np.abs(c)) + (a**-1.)/6 - (a**-3.)/90
+                    + (np.log(a) - (a**-1.)/2 - (a**-2.)/12 + (a**-4.)/120)/c)
+
+        return xpx.apply_where(a >= 200, (a, c), asymptotic, regular)
+
+
+gengamma = gengamma_gen(a=0.0, name='gengamma')
+
+
+class genhalflogistic_gen(rv_continuous):
+    r"""A generalized half-logistic continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `genhalflogistic` is:
+
+    .. math::
+
+        f(x, c) = \frac{2 (1 - c x)^{1/(c-1)}}{[1 + (1 - c x)^{1/c}]^2}
+
+    for :math:`0 \le x \le 1/c`, and :math:`c > 0`.
+
+    `genhalflogistic` takes ``c`` as a shape parameter for :math:`c`.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("c", False, (0, np.inf), (False, False))]
+
+    def _get_support(self, c):
+        return self.a, 1.0/c
+
+    def _pdf(self, x, c):
+        # genhalflogistic.pdf(x, c) =
+        #    2 * (1-c*x)**(1/c-1) / (1+(1-c*x)**(1/c))**2
+        limit = 1.0/c
+        tmp = np.asarray(1-c*x)
+        tmp0 = tmp**(limit-1)
+        tmp2 = tmp0*tmp
+        return 2*tmp0 / (1+tmp2)**2
+
+    def _cdf(self, x, c):
+        limit = 1.0/c
+        tmp = np.asarray(1-c*x)
+        tmp2 = tmp**(limit)
+        return (1.0-tmp2) / (1+tmp2)
+
+    def _ppf(self, q, c):
+        return 1.0/c*(1-((1.0-q)/(1.0+q))**c)
+
+    def _entropy(self, c):
+        return 2 - (2*c+1)*np.log(2)
+
+
+genhalflogistic = genhalflogistic_gen(a=0.0, name='genhalflogistic')
+
+
+class genhyperbolic_gen(rv_continuous):
+    r"""A generalized hyperbolic continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    t, norminvgauss, geninvgauss, laplace, cauchy
+
+    Notes
+    -----
+    The probability density function for `genhyperbolic` is:
+
+    .. math::
+
+        f(x, p, a, b) =
+            \frac{(a^2 - b^2)^{p/2}}
+            {\sqrt{2\pi}a^{p-1/2}
+            K_p\Big(\sqrt{a^2 - b^2}\Big)}
+            e^{bx} \times \frac{K_{p - 1/2}
+            (a \sqrt{1 + x^2})}
+            {(\sqrt{1 + x^2})^{1/2 - p}}
+
+    for :math:`x, p \in ( - \infty; \infty)`,
+    :math:`|b| < a` if :math:`p \ge 0`,
+    :math:`|b| \le a` if :math:`p < 0`.
+    :math:`K_{p}(.)` denotes the modified Bessel function of the second
+    kind and order :math:`p` (`scipy.special.kv`)
+
+    `genhyperbolic` takes ``p`` as a tail parameter,
+    ``a`` as a shape parameter,
+    ``b`` as a skewness parameter.
+
+    %(after_notes)s
+
+    The original parameterization of the Generalized Hyperbolic Distribution
+    is found in [1]_ as follows
+
+    .. math::
+
+        f(x, \lambda, \alpha, \beta, \delta, \mu) =
+           \frac{(\gamma/\delta)^\lambda}{\sqrt{2\pi}K_\lambda(\delta \gamma)}
+           e^{\beta (x - \mu)} \times \frac{K_{\lambda - 1/2}
+           (\alpha \sqrt{\delta^2 + (x - \mu)^2})}
+           {(\sqrt{\delta^2 + (x - \mu)^2} / \alpha)^{1/2 - \lambda}}
+
+    for :math:`x \in ( - \infty; \infty)`,
+    :math:`\gamma := \sqrt{\alpha^2 - \beta^2}`,
+    :math:`\lambda, \mu \in ( - \infty; \infty)`,
+    :math:`\delta \ge 0, |\beta| < \alpha` if :math:`\lambda \ge 0`,
+    :math:`\delta > 0, |\beta| \le \alpha` if :math:`\lambda < 0`.
+
+    The location-scale-based parameterization implemented in
+    SciPy is based on [2]_, where :math:`a = \alpha\delta`,
+    :math:`b = \beta\delta`, :math:`p = \lambda`,
+    :math:`scale=\delta` and :math:`loc=\mu`
+
+    Moments are implemented based on [3]_ and [4]_.
+
+    For the distributions that are a special case such as Student's t,
+    it is not recommended to rely on the implementation of genhyperbolic.
+    To avoid potential numerical problems and for performance reasons,
+    the methods of the specific distributions should be used.
+
+    References
+    ----------
+    .. [1] O. Barndorff-Nielsen, "Hyperbolic Distributions and Distributions
+       on Hyperbolae", Scandinavian Journal of Statistics, Vol. 5(3),
+       pp. 151-157, 1978. https://www.jstor.org/stable/4615705
+
+    .. [2] Eberlein E., Prause K. (2002) The Generalized Hyperbolic Model:
+        Financial Derivatives and Risk Measures. In: Geman H., Madan D.,
+        Pliska S.R., Vorst T. (eds) Mathematical Finance - Bachelier
+        Congress 2000. Springer Finance. Springer, Berlin, Heidelberg.
+        :doi:`10.1007/978-3-662-12429-1_12`
+
+    .. [3] Scott, David J, Würtz, Diethelm, Dong, Christine and Tran,
+       Thanh Tam, (2009), Moments of the generalized hyperbolic
+       distribution, MPRA Paper, University Library of Munich, Germany,
+       https://EconPapers.repec.org/RePEc:pra:mprapa:19081.
+
+    .. [4] E. Eberlein and E. A. von Hammerstein. Generalized hyperbolic
+       and inverse Gaussian distributions: Limiting cases and approximation
+       of processes. FDM Preprint 80, April 2003. University of Freiburg.
+       https://freidok.uni-freiburg.de/fedora/objects/freidok:7974/datastreams/FILE1/content
+
+    %(example)s
+
+    """
+
+    def _argcheck(self, p, a, b):
+        return (np.logical_and(np.abs(b) < a, p >= 0)
+                | np.logical_and(np.abs(b) <= a, p < 0))
+
+    def _shape_info(self):
+        ip = _ShapeInfo("p", False, (-np.inf, np.inf), (False, False))
+        ia = _ShapeInfo("a", False, (0, np.inf), (True, False))
+        ib = _ShapeInfo("b", False, (-np.inf, np.inf), (False, False))
+        return [ip, ia, ib]
+
+    def _fitstart(self, data):
+        # Arbitrary, but the default p = a = b = 1 is not valid; the
+        # distribution requires |b| < a if p >= 0.
+        return super()._fitstart(data, args=(1, 1, 0.5))
+
+    def _logpdf(self, x, p, a, b):
+        # kve instead of kv works better for large values of p
+        # and smaller values of sqrt(a^2  - b^2)
+        @np.vectorize
+        def _logpdf_single(x, p, a, b):
+            return _stats.genhyperbolic_logpdf(x, p, a, b)
+
+        return _logpdf_single(x, p, a, b)
+
+    def _pdf(self, x, p, a, b):
+        # kve instead of kv works better for large values of p
+        # and smaller values of sqrt(a^2  - b^2)
+        @np.vectorize
+        def _pdf_single(x, p, a, b):
+            return _stats.genhyperbolic_pdf(x, p, a, b)
+
+        return _pdf_single(x, p, a, b)
+
+    # np.vectorize isn't currently designed to be used as a decorator,
+    # so use a lambda instead.  This allows us to decorate the function
+    # with `np.vectorize` and still provide the `otypes` parameter.
+    @lambda func: np.vectorize(func, otypes=[np.float64])
+    @staticmethod
+    def _integrate_pdf(x0, x1, p, a, b):
+        """
+        Integrate the pdf of the genhyberbolic distribution from x0 to x1.
+        This is a private function used by _cdf() and _sf() only; either x0
+        will be -inf or x1 will be inf.
+        """
+        user_data = np.array([p, a, b], float).ctypes.data_as(ctypes.c_void_p)
+        llc = LowLevelCallable.from_cython(_stats, '_genhyperbolic_pdf',
+                                           user_data)
+        d = np.sqrt((a + b)*(a - b))
+        mean = b/d * sc.kv(p + 1, d) / sc.kv(p, d)
+        epsrel = 1e-10
+        epsabs = 0
+        if x0 < mean < x1:
+            # If the interval includes the mean, integrate over the two
+            # intervals [x0, mean] and [mean, x1] and add. If we try to do
+            # the integral in one call of quad and the non-infinite endpoint
+            # is far in the tail, quad might return an incorrect result
+            # because it does not "see" the peak of the PDF.
+            intgrl = (integrate.quad(llc, x0, mean,
+                                     epsrel=epsrel, epsabs=epsabs)[0]
+                      + integrate.quad(llc, mean, x1,
+                                       epsrel=epsrel, epsabs=epsabs)[0])
+        else:
+            intgrl = integrate.quad(llc, x0, x1,
+                                    epsrel=epsrel, epsabs=epsabs)[0]
+        if np.isnan(intgrl):
+            msg = ("Infinite values encountered in scipy.special.kve. "
+                   "Values replaced by NaN to avoid incorrect results.")
+            warnings.warn(msg, RuntimeWarning, stacklevel=3)
+        return max(0.0, min(1.0, intgrl))
+
+    def _cdf(self, x, p, a, b):
+        return self._integrate_pdf(-np.inf, x, p, a, b)
+
+    def _sf(self, x, p, a, b):
+        return self._integrate_pdf(x, np.inf, p, a, b)
+
+    def _rvs(self, p, a, b, size=None, random_state=None):
+        # note: X = b * V + sqrt(V) * X  has a
+        # generalized hyperbolic distribution
+        # if X is standard normal and V is
+        # geninvgauss(p = p, b = t2, loc = loc, scale = t3)
+        t1 = np.float_power(a, 2) - np.float_power(b, 2)
+        # b in the GIG
+        t2 = np.float_power(t1, 0.5)
+        # scale in the GIG
+        t3 = np.float_power(t1, - 0.5)
+        gig = geninvgauss.rvs(
+            p=p,
+            b=t2,
+            scale=t3,
+            size=size,
+            random_state=random_state
+            )
+        normst = norm.rvs(size=size, random_state=random_state)
+
+        return b * gig + np.sqrt(gig) * normst
+
+    def _stats(self, p, a, b):
+        # https://mpra.ub.uni-muenchen.de/19081/1/MPRA_paper_19081.pdf
+        # https://freidok.uni-freiburg.de/fedora/objects/freidok:7974/datastreams/FILE1/content
+        # standardized moments
+        p, a, b = np.broadcast_arrays(p, a, b)
+        t1 = np.float_power(a, 2) - np.float_power(b, 2)
+        t1 = np.float_power(t1, 0.5)
+        t2 = np.float_power(1, 2) * np.float_power(t1, - 1)
+        integers = np.linspace(0, 4, 5)
+        # make integers perpendicular to existing dimensions
+        integers = integers.reshape(integers.shape + (1,) * p.ndim)
+        b0, b1, b2, b3, b4 = sc.kv(p + integers, t1)
+        r1, r2, r3, r4 = (b / b0 for b in (b1, b2, b3, b4))
+
+        m = b * t2 * r1
+        v = (
+            t2 * r1 + np.float_power(b, 2) * np.float_power(t2, 2) *
+            (r2 - np.float_power(r1, 2))
+        )
+        m3e = (
+            np.float_power(b, 3) * np.float_power(t2, 3) *
+            (r3 - 3 * b2 * b1 * np.float_power(b0, -2) +
+             2 * np.float_power(r1, 3)) +
+            3 * b * np.float_power(t2, 2) *
+            (r2 - np.float_power(r1, 2))
+        )
+        s = m3e * np.float_power(v, - 3 / 2)
+        m4e = (
+            np.float_power(b, 4) * np.float_power(t2, 4) *
+            (r4 - 4 * b3 * b1 * np.float_power(b0, - 2) +
+             6 * b2 * np.float_power(b1, 2) * np.float_power(b0, - 3) -
+             3 * np.float_power(r1, 4)) +
+            np.float_power(b, 2) * np.float_power(t2, 3) *
+            (6 * r3 - 12 * b2 * b1 * np.float_power(b0, - 2) +
+             6 * np.float_power(r1, 3)) +
+            3 * np.float_power(t2, 2) * r2
+        )
+        k = m4e * np.float_power(v, -2) - 3
+
+        return m, v, s, k
+
+
+genhyperbolic = genhyperbolic_gen(name='genhyperbolic')
+
+
+class gompertz_gen(rv_continuous):
+    r"""A Gompertz (or truncated Gumbel) continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `gompertz` is:
+
+    .. math::
+
+        f(x, c) = c \exp(x) \exp(-c (e^x-1))
+
+    for :math:`x \ge 0`, :math:`c > 0`.
+
+    `gompertz` takes ``c`` as a shape parameter for :math:`c`.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("c", False, (0, np.inf), (False, False))]
+
+    def _pdf(self, x, c):
+        # gompertz.pdf(x, c) = c * exp(x) * exp(-c*(exp(x)-1))
+        return np.exp(self._logpdf(x, c))
+
+    def _logpdf(self, x, c):
+        return np.log(c) + x - c * sc.expm1(x)
+
+    def _cdf(self, x, c):
+        return -sc.expm1(-c * sc.expm1(x))
+
+    def _ppf(self, q, c):
+        return sc.log1p(-1.0 / c * sc.log1p(-q))
+
+    def _sf(self, x, c):
+        return np.exp(-c * sc.expm1(x))
+
+    def _isf(self, p, c):
+        return sc.log1p(-np.log(p)/c)
+
+    def _entropy(self, c):
+        return 1.0 - np.log(c) - sc._ufuncs._scaled_exp1(c)/c
+
+
+gompertz = gompertz_gen(a=0.0, name='gompertz')
+
+
+def _average_with_log_weights(x, logweights):
+    x = np.asarray(x)
+    logweights = np.asarray(logweights)
+    maxlogw = logweights.max()
+    weights = np.exp(logweights - maxlogw)
+    return np.average(x, weights=weights)
+
+
+class gumbel_r_gen(rv_continuous):
+    r"""A right-skewed Gumbel continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    gumbel_l, gompertz, genextreme
+
+    Notes
+    -----
+    The probability density function for `gumbel_r` is:
+
+    .. math::
+
+        f(x) = \exp(-(x + e^{-x}))
+
+    for real :math:`x`.
+
+    The Gumbel distribution is sometimes referred to as a type I Fisher-Tippett
+    distribution.  It is also related to the extreme value distribution,
+    log-Weibull and Gompertz distributions.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return []
+
+    def _pdf(self, x):
+        # gumbel_r.pdf(x) = exp(-(x + exp(-x)))
+        return np.exp(self._logpdf(x))
+
+    def _logpdf(self, x):
+        return -x - np.exp(-x)
+
+    def _cdf(self, x):
+        return np.exp(-np.exp(-x))
+
+    def _logcdf(self, x):
+        return -np.exp(-x)
+
+    def _ppf(self, q):
+        return -np.log(-np.log(q))
+
+    def _sf(self, x):
+        return -sc.expm1(-np.exp(-x))
+
+    def _isf(self, p):
+        return -np.log(-np.log1p(-p))
+
+    def _stats(self):
+        return _EULER, np.pi*np.pi/6.0, 12*np.sqrt(6)/np.pi**3 * _ZETA3, 12.0/5
+
+    def _entropy(self):
+        # https://en.wikipedia.org/wiki/Gumbel_distribution
+        return _EULER + 1.
+
+    @_call_super_mom
+    @inherit_docstring_from(rv_continuous)
+    def fit(self, data, *args, **kwds):
+        data, floc, fscale = _check_fit_input_parameters(self, data,
+                                                         args, kwds)
+
+        # By the method of maximum likelihood, the estimators of the
+        # location and scale are the roots of the equations defined in
+        # `func` and the value of the expression for `loc` that follows.
+        # The first `func` is a first order derivative of the log-likelihood
+        # equation and the second is from Source: Statistical Distributions,
+        # 3rd Edition. Evans, Hastings, and Peacock (2000), Page 101.
+
+        def get_loc_from_scale(scale):
+            return -scale * (sc.logsumexp(-data / scale) - np.log(len(data)))
+
+        if fscale is not None:
+            # if the scale is fixed, the location can be analytically
+            # determined.
+            scale = fscale
+            loc = get_loc_from_scale(scale)
+        else:
+            # A different function is solved depending on whether the location
+            # is fixed.
+            if floc is not None:
+                loc = floc
+
+                # equation to use if the location is fixed.
+                # note that one cannot use the equation in Evans, Hastings,
+                # and Peacock (2000) (since it assumes that the derivative
+                # w.r.t. the log-likelihood is zero). however, it is easy to
+                # derive the MLE condition directly if loc is fixed
+                def func(scale):
+                    term1 = (loc - data) * np.exp((loc - data) / scale) + data
+                    term2 = len(data) * (loc + scale)
+                    return term1.sum() - term2
+            else:
+
+                # equation to use if both location and scale are free
+                def func(scale):
+                    sdata = -data / scale
+                    wavg = _average_with_log_weights(data, logweights=sdata)
+                    return data.mean() - wavg - scale
+
+            # set brackets for `root_scalar` to use when optimizing over the
+            # scale such that a root is likely between them. Use user supplied
+            # guess or default 1.
+            brack_start = kwds.get('scale', 1)
+            lbrack, rbrack = brack_start / 2, brack_start * 2
+
+            # if a root is not between the brackets, iteratively expand them
+            # until they include a sign change, checking after each bracket is
+            # modified.
+            def interval_contains_root(lbrack, rbrack):
+                # return true if the signs disagree.
+                return (np.sign(func(lbrack)) !=
+                        np.sign(func(rbrack)))
+            while (not interval_contains_root(lbrack, rbrack)
+                   and (lbrack > 0 or rbrack < np.inf)):
+                lbrack /= 2
+                rbrack *= 2
+
+            res = optimize.root_scalar(func, bracket=(lbrack, rbrack),
+                                       rtol=1e-14, xtol=1e-14)
+            scale = res.root
+            loc = floc if floc is not None else get_loc_from_scale(scale)
+        return loc, scale
+
+
+gumbel_r = gumbel_r_gen(name='gumbel_r')
+
+
+class gumbel_l_gen(rv_continuous):
+    r"""A left-skewed Gumbel continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    gumbel_r, gompertz, genextreme
+
+    Notes
+    -----
+    The probability density function for `gumbel_l` is:
+
+    .. math::
+
+        f(x) = \exp(x - e^x)
+
+    for real :math:`x`.
+
+    The Gumbel distribution is sometimes referred to as a type I Fisher-Tippett
+    distribution.  It is also related to the extreme value distribution,
+    log-Weibull and Gompertz distributions.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+
+    def _shape_info(self):
+        return []
+
+    def _pdf(self, x):
+        # gumbel_l.pdf(x) = exp(x - exp(x))
+        return np.exp(self._logpdf(x))
+
+    def _logpdf(self, x):
+        return x - np.exp(x)
+
+    def _cdf(self, x):
+        return -sc.expm1(-np.exp(x))
+
+    def _ppf(self, q):
+        return np.log(-sc.log1p(-q))
+
+    def _logsf(self, x):
+        return -np.exp(x)
+
+    def _sf(self, x):
+        return np.exp(-np.exp(x))
+
+    def _isf(self, x):
+        return np.log(-np.log(x))
+
+    def _stats(self):
+        return -_EULER, np.pi*np.pi/6.0, \
+               -12*np.sqrt(6)/np.pi**3 * _ZETA3, 12.0/5
+
+    def _entropy(self):
+        return _EULER + 1.
+
+    @_call_super_mom
+    @inherit_docstring_from(rv_continuous)
+    def fit(self, data, *args, **kwds):
+        # The fit method of `gumbel_r` can be used for this distribution with
+        # small modifications. The process to do this is
+        # 1. pass the sign negated data into `gumbel_r.fit`
+        #    - if the location is fixed, it should also be negated.
+        # 2. negate the sign of the resulting location, leaving the scale
+        #    unmodified.
+        # `gumbel_r.fit` holds necessary input checks.
+
+        if kwds.get('floc') is not None:
+            kwds['floc'] = -kwds['floc']
+        loc_r, scale_r, = gumbel_r.fit(-np.asarray(data), *args, **kwds)
+        return -loc_r, scale_r
+
+
+gumbel_l = gumbel_l_gen(name='gumbel_l')
+
+
+class halfcauchy_gen(rv_continuous):
+    r"""A Half-Cauchy continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `halfcauchy` is:
+
+    .. math::
+
+        f(x) = \frac{2}{\pi (1 + x^2)}
+
+    for :math:`x \ge 0`.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return []
+
+    def _pdf(self, x):
+        # halfcauchy.pdf(x) = 2 / (pi * (1 + x**2))
+        return 2.0/np.pi/(1.0+x*x)
+
+    def _logpdf(self, x):
+        return np.log(2.0/np.pi) - sc.log1p(x*x)
+
+    def _cdf(self, x):
+        return 2.0/np.pi*np.arctan(x)
+
+    def _ppf(self, q):
+        return np.tan(np.pi/2*q)
+
+    def _sf(self, x):
+        return 2.0/np.pi * np.arctan2(1, x)
+
+    def _isf(self, p):
+        return 1.0/np.tan(np.pi*p/2)
+
+    def _stats(self):
+        return np.inf, np.inf, np.nan, np.nan
+
+    def _entropy(self):
+        return np.log(2*np.pi)
+
+    @_call_super_mom
+    @inherit_docstring_from(rv_continuous)
+    def fit(self, data, *args, **kwds):
+        if kwds.pop('superfit', False):
+            return super().fit(data, *args, **kwds)
+
+        data, floc, fscale = _check_fit_input_parameters(self, data,
+                                                         args, kwds)
+
+        # location is independent from the scale
+        data_min = np.min(data)
+        if floc is not None:
+            if data_min < floc:
+                # There are values that are less than the specified loc.
+                raise FitDataError("halfcauchy", lower=floc, upper=np.inf)
+            loc = floc
+        else:
+            # if not provided, location MLE is the minimal data point
+            loc = data_min
+
+        # find scale
+        def find_scale(loc, data):
+            shifted_data = data - loc
+            n = data.size
+            shifted_data_squared = np.square(shifted_data)
+
+            def fun_to_solve(scale):
+                denominator = scale**2 + shifted_data_squared
+                return 2 * np.sum(shifted_data_squared/denominator) - n
+
+            small = np.finfo(1.0).tiny**0.5  # avoid underflow
+            res = root_scalar(fun_to_solve, bracket=(small, np.max(shifted_data)))
+            return res.root
+
+        if fscale is not None:
+            scale = fscale
+        else:
+            scale = find_scale(loc, data)
+
+        return loc, scale
+
+
+halfcauchy = halfcauchy_gen(a=0.0, name='halfcauchy')
+
+
+class halflogistic_gen(rv_continuous):
+    r"""A half-logistic continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `halflogistic` is:
+
+    .. math::
+
+        f(x) = \frac{ 2 e^{-x} }{ (1+e^{-x})^2 }
+             = \frac{1}{2} \text{sech}(x/2)^2
+
+    for :math:`x \ge 0`.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] Asgharzadeh et al (2011). "Comparisons of Methods of Estimation for the
+           Half-Logistic Distribution". Selcuk J. Appl. Math. 93-108.
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return []
+
+    def _pdf(self, x):
+        # halflogistic.pdf(x) = 2 * exp(-x) / (1+exp(-x))**2
+        #                     = 1/2 * sech(x/2)**2
+        return np.exp(self._logpdf(x))
+
+    def _logpdf(self, x):
+        return np.log(2) - x - 2. * sc.log1p(np.exp(-x))
+
+    def _cdf(self, x):
+        return np.tanh(x/2.0)
+
+    def _ppf(self, q):
+        return 2*np.arctanh(q)
+
+    def _sf(self, x):
+        return 2 * sc.expit(-x)
+
+    def _isf(self, q):
+        return xpx.apply_where(q < 0.5, q,
+                               lambda q: -sc.logit(0.5 * q),
+                               lambda q: 2*np.arctanh(1 - q))
+
+    def _munp(self, n):
+        if n == 0:
+            return 1  # otherwise returns NaN
+        if n == 1:
+            return 2*np.log(2)
+        if n == 2:
+            return np.pi*np.pi/3.0
+        if n == 3:
+            return 9*_ZETA3
+        if n == 4:
+            return 7*np.pi**4 / 15.0
+        return 2*(1-pow(2.0, 1-n))*sc.gamma(n+1)*sc.zeta(n, 1)
+
+    def _entropy(self):
+        return 2-np.log(2)
+
+    @_call_super_mom
+    @inherit_docstring_from(rv_continuous)
+    def fit(self, data, *args, **kwds):
+        if kwds.pop('superfit', False):
+            return super().fit(data, *args, **kwds)
+
+        data, floc, fscale = _check_fit_input_parameters(self, data,
+                                                         args, kwds)
+
+        def find_scale(data, loc):
+            # scale is solution to a fix point problem ([1] 2.6)
+            # use approximate MLE as starting point ([1] 3.1)
+            n_observations = data.shape[0]
+            sorted_data = np.sort(data, axis=0)
+            p = np.arange(1, n_observations + 1)/(n_observations + 1)
+            q = 1 - p
+            pp1 = 1 + p
+            alpha = p - 0.5 * q * pp1 * np.log(pp1 / q)
+            beta = 0.5 * q * pp1
+            sorted_data = sorted_data - loc
+            B = 2 * np.sum(alpha[1:] * sorted_data[1:])
+            C = 2 * np.sum(beta[1:] * sorted_data[1:]**2)
+            # starting guess
+            scale = ((B + np.sqrt(B**2 + 8 * n_observations * C))
+                    /(4 * n_observations))
+
+            # relative tolerance of fix point iterator
+            rtol = 1e-8
+            relative_residual = 1
+            shifted_mean = sorted_data.mean()  # y_mean - y_min
+
+            # find fix point by repeated application of eq. (2.6)
+            # simplify as
+            # exp(-x) / (1 + exp(-x)) = 1 / (1 + exp(x))
+            #                         = expit(-x))
+            while relative_residual > rtol:
+                sum_term = sorted_data * sc.expit(-sorted_data/scale)
+                scale_new = shifted_mean - 2/n_observations * sum_term.sum()
+                relative_residual = abs((scale - scale_new)/scale)
+                scale = scale_new
+            return scale
+
+        # location is independent from the scale
+        data_min = np.min(data)
+        if floc is not None:
+            if data_min < floc:
+                # There are values that are less than the specified loc.
+                raise FitDataError("halflogistic", lower=floc, upper=np.inf)
+            loc = floc
+        else:
+            # if not provided, location MLE is the minimal data point
+            loc = data_min
+
+        # scale depends on location
+        scale = fscale if fscale is not None else find_scale(data, loc)
+
+        return loc, scale
+
+
+halflogistic = halflogistic_gen(a=0.0, name='halflogistic')
+
+
+class halfnorm_gen(rv_continuous):
+    r"""A half-normal continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `halfnorm` is:
+
+    .. math::
+
+        f(x) = \sqrt{2/\pi} \exp(-x^2 / 2)
+
+    for :math:`x >= 0`.
+
+    `halfnorm` is a special case of `chi` with ``df=1``.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return []
+
+    def _rvs(self, size=None, random_state=None):
+        return abs(random_state.standard_normal(size=size))
+
+    def _pdf(self, x):
+        # halfnorm.pdf(x) = sqrt(2/pi) * exp(-x**2/2)
+        return np.sqrt(2.0/np.pi)*np.exp(-x*x/2.0)
+
+    def _logpdf(self, x):
+        return 0.5 * np.log(2.0/np.pi) - x*x/2.0
+
+    def _cdf(self, x):
+        return sc.erf(x / np.sqrt(2))
+
+    def _ppf(self, q):
+        return _norm_ppf((1+q)/2.0)
+
+    def _sf(self, x):
+        return 2 * _norm_sf(x)
+
+    def _isf(self, p):
+        return _norm_isf(p/2)
+
+    def _stats(self):
+        return (np.sqrt(2.0/np.pi),
+                1-2.0/np.pi,
+                np.sqrt(2)*(4-np.pi)/(np.pi-2)**1.5,
+                8*(np.pi-3)/(np.pi-2)**2)
+
+    def _entropy(self):
+        return 0.5*np.log(np.pi/2.0)+0.5
+
+    @_call_super_mom
+    @inherit_docstring_from(rv_continuous)
+    def fit(self, data, *args, **kwds):
+        if kwds.pop('superfit', False):
+            return super().fit(data, *args, **kwds)
+
+        data, floc, fscale = _check_fit_input_parameters(self, data,
+                                                         args, kwds)
+
+        data_min = np.min(data)
+
+        if floc is not None:
+            if data_min < floc:
+                # There are values that are less than the specified loc.
+                raise FitDataError("halfnorm", lower=floc, upper=np.inf)
+            loc = floc
+        else:
+            loc = data_min
+
+        if fscale is not None:
+            scale = fscale
+        else:
+            scale = stats.moment(data, order=2, center=loc)**0.5
+
+        return loc, scale
+
+
+halfnorm = halfnorm_gen(a=0.0, name='halfnorm')
+
+
+class hypsecant_gen(rv_continuous):
+    r"""A hyperbolic secant continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `hypsecant` is:
+
+    .. math::
+
+        f(x) = \frac{1}{\pi} \text{sech}(x)
+
+    for a real number :math:`x`.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return []
+
+    def _pdf(self, x):
+        # hypsecant.pdf(x) = 1/pi * sech(x)
+        return 1.0/(np.pi*np.cosh(x))
+
+    def _cdf(self, x):
+        return 2.0/np.pi*np.arctan(np.exp(x))
+
+    def _ppf(self, q):
+        return np.log(np.tan(np.pi*q/2.0))
+
+    def _sf(self, x):
+        return 2.0/np.pi*np.arctan(np.exp(-x))
+
+    def _isf(self, q):
+        return -np.log(np.tan(np.pi*q/2.0))
+
+    def _stats(self):
+        return 0, np.pi*np.pi/4, 0, 2
+
+    def _entropy(self):
+        return np.log(2*np.pi)
+
+
+hypsecant = hypsecant_gen(name='hypsecant')
+
+
+class gausshyper_gen(rv_continuous):
+    r"""A Gauss hypergeometric continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `gausshyper` is:
+
+    .. math::
+
+        f(x, a, b, c, z) = C x^{a-1} (1-x)^{b-1} (1+zx)^{-c}
+
+    for :math:`0 \le x \le 1`, :math:`a,b > 0`, :math:`c` a real number,
+    :math:`z > -1`, and :math:`C = \frac{1}{B(a, b) F[2, 1](c, a; a+b; -z)}`.
+    :math:`F[2, 1]` is the Gauss hypergeometric function
+    `scipy.special.hyp2f1`.
+
+    `gausshyper` takes :math:`a`, :math:`b`, :math:`c` and :math:`z` as shape
+    parameters.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] Armero, C., and M. J. Bayarri. "Prior Assessments for Prediction in
+           Queues." *Journal of the Royal Statistical Society*. Series D (The
+           Statistician) 43, no. 1 (1994): 139-53. :doi:`10.2307/2348939`.
+
+    %(example)s
+
+    """
+
+    def _argcheck(self, a, b, c, z):
+        # z > -1 per gh-10134
+        return (a > 0) & (b > 0) & (c == c) & (z > -1)
+
+    def _shape_info(self):
+        ia = _ShapeInfo("a", False, (0, np.inf), (False, False))
+        ib = _ShapeInfo("b", False, (0, np.inf), (False, False))
+        ic = _ShapeInfo("c", False, (-np.inf, np.inf), (False, False))
+        iz = _ShapeInfo("z", False, (-1, np.inf), (False, False))
+        return [ia, ib, ic, iz]
+
+    def _pdf(self, x, a, b, c, z):
+        normalization_constant = sc.beta(a, b) * sc.hyp2f1(c, a, a + b, -z)
+        return (1./normalization_constant * x**(a - 1.) * (1. - x)**(b - 1.0)
+                / (1.0 + z*x)**c)
+
+    def _munp(self, n, a, b, c, z):
+        fac = sc.beta(n+a, b) / sc.beta(a, b)
+        num = sc.hyp2f1(c, a+n, a+b+n, -z)
+        den = sc.hyp2f1(c, a, a+b, -z)
+        return fac*num / den
+
+
+gausshyper = gausshyper_gen(a=0.0, b=1.0, name='gausshyper')
+
+
+class invgamma_gen(rv_continuous):
+    r"""An inverted gamma continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `invgamma` is:
+
+    .. math::
+
+        f(x, a) = \frac{x^{-a-1}}{\Gamma(a)} \exp(-\frac{1}{x})
+
+    for :math:`x >= 0`, :math:`a > 0`. :math:`\Gamma` is the gamma function
+    (`scipy.special.gamma`).
+
+    `invgamma` takes ``a`` as a shape parameter for :math:`a`.
+
+    `invgamma` is a special case of `gengamma` with ``c=-1``, and it is a
+    different parameterization of the scaled inverse chi-squared distribution.
+    Specifically, if the scaled inverse chi-squared distribution is
+    parameterized with degrees of freedom :math:`\nu` and scaling parameter
+    :math:`\tau^2`, then it can be modeled using `invgamma` with
+    ``a=`` :math:`\nu/2` and ``scale=`` :math:`\nu \tau^2/2`.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    _support_mask = rv_continuous._open_support_mask
+
+    def _shape_info(self):
+        return [_ShapeInfo("a", False, (0, np.inf), (False, False))]
+
+    def _pdf(self, x, a):
+        # invgamma.pdf(x, a) = x**(-a-1) / gamma(a) * exp(-1/x)
+        return np.exp(self._logpdf(x, a))
+
+    def _logpdf(self, x, a):
+        return -(a+1) * np.log(x) - sc.gammaln(a) - 1.0/x
+
+    def _cdf(self, x, a):
+        return sc.gammaincc(a, 1.0 / x)
+
+    def _ppf(self, q, a):
+        return 1.0 / sc.gammainccinv(a, q)
+
+    def _sf(self, x, a):
+        return sc.gammainc(a, 1.0 / x)
+
+    def _isf(self, q, a):
+        return 1.0 / sc.gammaincinv(a, q)
+
+    def _stats(self, a, moments='mvsk'):
+        m1 = xpx.apply_where(a > 1, a,
+                             lambda x: 1. / (x - 1.),
+                             fill_value=np.inf)
+        m2 = xpx.apply_where(a > 2, a,
+                             lambda x: 1. / (x - 1.)**2 / (x - 2.),
+                             fill_value=np.inf)
+
+        g1, g2 = None, None
+        if 's' in moments:
+            g1 = xpx.apply_where(a > 3, a,
+                                 lambda x: 4. * np.sqrt(x - 2.) / (x - 3.),
+                                 fill_value=np.nan)
+        if 'k' in moments:
+            g2 = xpx.apply_where(a > 4, a,
+                                 lambda x: 6. * (5. * x - 11.) / (x - 3.) / (x - 4.),
+                                 fill_value=np.nan)
+
+        return m1, m2, g1, g2
+
+    def _entropy(self, a):
+        def regular(a):
+            h = a - (a + 1.0) * sc.psi(a) + sc.gammaln(a)
+            return h
+
+        def asymptotic(a):
+            # gammaln(a) ~ a * ln(a) - a - 0.5 * ln(a) + 0.5 * ln(2 * pi)
+            # psi(a) ~ ln(a) - 1 / (2 * a)
+            h = ((1 - 3*np.log(a) + np.log(2) + np.log(np.pi))/2
+                 + 2/3*a**-1. + a**-2./12 - a**-3./90 - a**-4./120)
+            return h
+
+        h = xpx.apply_where(a >= 200, a, asymptotic, regular)
+        return h
+
+
+invgamma = invgamma_gen(a=0.0, name='invgamma')
+
+
+class invgauss_gen(rv_continuous):
+    r"""An inverse Gaussian continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `invgauss` is:
+
+    .. math::
+
+        f(x; \mu) = \frac{1}{\sqrt{2 \pi x^3}}
+                    \exp\left(-\frac{(x-\mu)^2}{2 \mu^2 x}\right)
+
+    for :math:`x \ge 0` and :math:`\mu > 0`.
+
+    `invgauss` takes ``mu`` as a shape parameter for :math:`\mu`.
+
+    %(after_notes)s
+
+    A common shape-scale parameterization of the inverse Gaussian distribution
+    has density
+
+    .. math::
+
+        f(x; \nu, \lambda) = \sqrt{\frac{\lambda}{2 \pi x^3}}
+                    \exp\left( -\frac{\lambda(x-\nu)^2}{2 \nu^2 x}\right)
+
+    Using ``nu`` for :math:`\nu` and ``lam`` for :math:`\lambda`, this
+    parameterization is equivalent to the one above with ``mu = nu/lam``,
+    ``loc = 0``, and ``scale = lam``.
+
+    This distribution uses routines from the Boost Math C++ library for
+    the computation of the ``ppf`` and ``isf`` methods. [1]_
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    %(example)s
+
+    """
+    _support_mask = rv_continuous._open_support_mask
+
+    def _shape_info(self):
+        return [_ShapeInfo("mu", False, (0, np.inf), (False, False))]
+
+    def _rvs(self, mu, size=None, random_state=None):
+        return random_state.wald(mu, 1.0, size=size)
+
+    def _pdf(self, x, mu):
+        # invgauss.pdf(x, mu) =
+        #                  1 / sqrt(2*pi*x**3) * exp(-(x-mu)**2/(2*x*mu**2))
+        return 1.0/np.sqrt(2*np.pi*x**3.0)*np.exp(-1.0/(2*x)*(x/mu - 1)**2)
+
+    def _logpdf(self, x, mu):
+        return -0.5*np.log(2*np.pi) - 1.5*np.log(x) - (x/mu - 1)**2/(2*x)
+
+    # approach adapted from equations in
+    # https://journal.r-project.org/archive/2016-1/giner-smyth.pdf,
+    # not R code. see gh-13616
+
+    def _logcdf(self, x, mu):
+        fac = 1 / np.sqrt(x)
+        a = _norm_logcdf(fac * (x/mu - 1))
+        b = 2 / mu + _norm_logcdf(-fac * (x/mu + 1))
+        return a + np.log1p(np.exp(b - a))
+
+    def _logsf(self, x, mu):
+        fac = 1 / np.sqrt(x)
+        a = _norm_logsf(fac * (x/mu - 1))
+        b = 2 / mu + _norm_logcdf(-fac * (x/mu + 1))
+        return a + np.log1p(-np.exp(b - a))
+
+    def _sf(self, x, mu):
+        return np.exp(self._logsf(x, mu))
+
+    def _cdf(self, x, mu):
+        return np.exp(self._logcdf(x, mu))
+
+    def _ppf(self, x, mu):
+        with np.errstate(divide='ignore', over='ignore', invalid='ignore'):
+            x, mu = np.broadcast_arrays(x, mu)
+            ppf = np.asarray(scu._invgauss_ppf(x, mu, 1))
+            i_wt = x > 0.5  # "wrong tail" - sometimes too inaccurate
+            ppf[i_wt] = scu._invgauss_isf(1-x[i_wt], mu[i_wt], 1)
+            i_nan = np.isnan(ppf)
+            ppf[i_nan] = super()._ppf(x[i_nan], mu[i_nan])
+        return ppf
+
+    def _isf(self, x, mu):
+        with np.errstate(divide='ignore', over='ignore', invalid='ignore'):
+            x, mu = np.broadcast_arrays(x, mu)
+            isf = scu._invgauss_isf(x, mu, 1)
+            i_wt = x > 0.5  # "wrong tail" - sometimes too inaccurate
+            isf[i_wt] = scu._invgauss_ppf(1-x[i_wt], mu[i_wt], 1)
+            i_nan = np.isnan(isf)
+            isf[i_nan] = super()._isf(x[i_nan], mu[i_nan])
+        return isf
+
+    def _stats(self, mu):
+        return mu, mu**3.0, 3*np.sqrt(mu), 15*mu
+
+    @inherit_docstring_from(rv_continuous)
+    def fit(self, data, *args, **kwds):
+        method = kwds.get('method', 'mle')
+
+        if (isinstance(data, CensoredData) or isinstance(self, wald_gen)
+                or method.lower() == 'mm'):
+            return super().fit(data, *args, **kwds)
+
+        data, fshape_s, floc, fscale = _check_fit_input_parameters(self, data,
+                                                                   args, kwds)
+        '''
+        Source: Statistical Distributions, 3rd Edition. Evans, Hastings,
+        and Peacock (2000), Page 121. Their shape parameter is equivalent to
+        SciPy's with the conversion `fshape_s = fshape / scale`.
+
+        MLE formulas are not used in 3 conditions:
+
+        - `loc` is not fixed
+        - `mu` is fixed
+
+        These cases fall back on the superclass fit method.
+
+        - `loc` is fixed but translation results in negative data raises
+          a `FitDataError`.
+        '''
+        if floc is None or fshape_s is not None:
+            return super().fit(data, *args, **kwds)
+        elif np.any(data - floc < 0):
+            raise FitDataError("invgauss", lower=0, upper=np.inf)
+        else:
+            data = data - floc
+            fshape_n = np.mean(data)
+            if fscale is None:
+                fscale = len(data) / (np.sum(data ** -1 - fshape_n ** -1))
+            fshape_s = fshape_n / fscale
+        return fshape_s, floc, fscale
+
+    def _entropy(self, mu):
+        """
+        Ref.: https://moser-isi.ethz.ch/docs/papers/smos-2012-10.pdf (eq. 9)
+        """
+        # a = log(2*pi*e*mu**3)
+        #   = 1 + log(2*pi) + 3 * log(mu)
+        a = 1. + np.log(2 * np.pi) + 3 * np.log(mu)
+        # b = exp(2/mu) * exp1(2/mu)
+        #   = _scaled_exp1(2/mu) / (2/mu)
+        r = 2/mu
+        b = sc._ufuncs._scaled_exp1(r)/r
+        return 0.5 * a - 1.5 * b
+
+
+invgauss = invgauss_gen(a=0.0, name='invgauss')
+
+
+class geninvgauss_gen(rv_continuous):
+    r"""A Generalized Inverse Gaussian continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `geninvgauss` is:
+
+    .. math::
+
+        f(x, p, b) = x^{p-1} \exp(-b (x + 1/x) / 2) / (2 K_p(b))
+
+    where ``x > 0``, `p` is a real number and ``b > 0``\([1]_).
+    :math:`K_p` is the modified Bessel function of second kind of order `p`
+    (`scipy.special.kv`).
+
+    %(after_notes)s
+
+    The inverse Gaussian distribution `stats.invgauss(mu)` is a special case of
+    `geninvgauss` with ``p = -1/2``, ``b = 1 / mu`` and ``scale = mu``.
+
+    Generating random variates is challenging for this distribution. The
+    implementation is based on [2]_.
+
+    References
+    ----------
+    .. [1] O. Barndorff-Nielsen, P. Blaesild, C. Halgreen, "First hitting time
+       models for the generalized inverse gaussian distribution",
+       Stochastic Processes and their Applications 7, pp. 49--54, 1978.
+
+    .. [2] W. Hoermann and J. Leydold, "Generating generalized inverse Gaussian
+       random variates", Statistics and Computing, 24(4), p. 547--557, 2014.
+
+    %(example)s
+
+    """
+    def _argcheck(self, p, b):
+        return (p == p) & (b > 0)
+
+    def _shape_info(self):
+        ip = _ShapeInfo("p", False, (-np.inf, np.inf), (False, False))
+        ib = _ShapeInfo("b", False, (0, np.inf), (False, False))
+        return [ip, ib]
+
+    def _logpdf(self, x, p, b):
+        # kve instead of kv works better for large values of b
+        # warn if kve produces infinite values and replace by nan
+        # otherwise c = -inf and the results are often incorrect
+        def logpdf_single(x, p, b):
+            return _stats.geninvgauss_logpdf(x, p, b)
+
+        logpdf_single = np.vectorize(logpdf_single, otypes=[np.float64])
+
+        z = logpdf_single(x, p, b)
+        if np.isnan(z).any():
+            msg = ("Infinite values encountered in scipy.special.kve(p, b). "
+                   "Values replaced by NaN to avoid incorrect results.")
+            warnings.warn(msg, RuntimeWarning, stacklevel=3)
+        return z
+
+    def _pdf(self, x, p, b):
+        # relying on logpdf avoids overflow of x**(p-1) for large x and p
+        return np.exp(self._logpdf(x, p, b))
+
+    def _cdf(self, x, p, b):
+        _a, _b = self._get_support(p, b)
+
+        def _cdf_single(x, p, b):
+            user_data = np.array([p, b], float).ctypes.data_as(ctypes.c_void_p)
+            llc = LowLevelCallable.from_cython(_stats, '_geninvgauss_pdf',
+                                               user_data)
+
+            return integrate.quad(llc, _a, x)[0]
+
+        _cdf_single = np.vectorize(_cdf_single, otypes=[np.float64])
+
+        return _cdf_single(x, p, b)
+
+    def _logquasipdf(self, x, p, b):
+        # log of the quasi-density (w/o normalizing constant) used in _rvs
+        return xpx.apply_where(x > 0, (x, p, b),
+                               lambda x, p, b: (p - 1)*np.log(x) - b*(x + 1/x)/2,
+                               fill_value=-np.inf)
+
+    def _rvs(self, p, b, size=None, random_state=None):
+        # if p and b are scalar, use _rvs_scalar, otherwise need to create
+        # output by iterating over parameters
+        if np.isscalar(p) and np.isscalar(b):
+            out = self._rvs_scalar(p, b, size, random_state)
+        elif p.size == 1 and b.size == 1:
+            out = self._rvs_scalar(p.item(), b.item(), size, random_state)
+        else:
+            # When this method is called, size will be a (possibly empty)
+            # tuple of integers.  It will not be None; if `size=None` is passed
+            # to `rvs()`, size will be the empty tuple ().
+
+            p, b = np.broadcast_arrays(p, b)
+            # p and b now have the same shape.
+
+            # `shp` is the shape of the blocks of random variates that are
+            # generated for each combination of parameters associated with
+            # broadcasting p and b.
+            # bc is a tuple the same length as size.  The values
+            # in bc are bools.  If bc[j] is True, it means that
+            # entire axis is filled in for a given combination of the
+            # broadcast arguments.
+            shp, bc = _check_shape(p.shape, size)
+
+            # `numsamples` is the total number of variates to be generated
+            # for each combination of the input arguments.
+            numsamples = int(np.prod(shp))
+
+            # `out` is the array to be returned.  It is filled in the
+            # loop below.
+            out = np.empty(size)
+
+            it = np.nditer([p, b],
+                           flags=['multi_index'],
+                           op_flags=[['readonly'], ['readonly']])
+            while not it.finished:
+                # Convert the iterator's multi_index into an index into the
+                # `out` array where the call to _rvs_scalar() will be stored.
+                # Where bc is True, we use a full slice; otherwise we use the
+                # index value from it.multi_index.  len(it.multi_index) might
+                # be less than len(bc), and in that case we want to align these
+                # two sequences to the right, so the loop variable j runs from
+                # -len(size) to 0.  This doesn't cause an IndexError, as
+                # bc[j] will be True in those cases where it.multi_index[j]
+                # would cause an IndexError.
+                idx = tuple((it.multi_index[j] if not bc[j] else slice(None))
+                            for j in range(-len(size), 0))
+                out[idx] = self._rvs_scalar(it[0], it[1], numsamples,
+                                            random_state).reshape(shp)
+                it.iternext()
+
+        if size == ():
+            out = out.item()
+        return out
+
+    def _rvs_scalar(self, p, b, numsamples, random_state):
+        # following [2], the quasi-pdf is used instead of the pdf for the
+        # generation of rvs
+        invert_res = False
+        if not numsamples:
+            numsamples = 1
+        if p < 0:
+            # note: if X is geninvgauss(p, b), then 1/X is geninvgauss(-p, b)
+            p = -p
+            invert_res = True
+        m = self._mode(p, b)
+
+        # determine method to be used following [2]
+        ratio_unif = True
+        if p >= 1 or b > 1:
+            # ratio of uniforms with mode shift below
+            mode_shift = True
+        elif b >= min(0.5, 2 * np.sqrt(1 - p) / 3):
+            # ratio of uniforms without mode shift below
+            mode_shift = False
+        else:
+            # new algorithm in [2]
+            ratio_unif = False
+
+        # prepare sampling of rvs
+        size1d = tuple(np.atleast_1d(numsamples))
+        N = np.prod(size1d)  # number of rvs needed, reshape upon return
+        x = np.zeros(N)
+        simulated = 0
+
+        if ratio_unif:
+            # use ratio of uniforms method
+            if mode_shift:
+                a2 = -2 * (p + 1) / b - m
+                a1 = 2 * m * (p - 1) / b - 1
+                # find roots of x**3 + a2*x**2 + a1*x + m (Cardano's formula)
+                p1 = a1 - a2**2 / 3
+                q1 = 2 * a2**3 / 27 - a2 * a1 / 3 + m
+                phi = np.arccos(-q1 * np.sqrt(-27 / p1**3) / 2)
+                s1 = -np.sqrt(-4 * p1 / 3)
+                root1 = s1 * np.cos(phi / 3 + np.pi / 3) - a2 / 3
+                root2 = -s1 * np.cos(phi / 3) - a2 / 3
+                # root3 = s1 * np.cos(phi / 3 - np.pi / 3) - a2 / 3
+
+                # if g is the quasipdf, rescale: g(x) / g(m) which we can write
+                # as exp(log(g(x)) - log(g(m))). This is important
+                # since for large values of p and b, g cannot be evaluated.
+                # denote the rescaled quasipdf by h
+                lm = self._logquasipdf(m, p, b)
+                d1 = self._logquasipdf(root1, p, b) - lm
+                d2 = self._logquasipdf(root2, p, b) - lm
+                # compute the bounding rectangle w.r.t. h. Note that
+                # np.exp(0.5*d1) = np.sqrt(g(root1)/g(m)) = np.sqrt(h(root1))
+                vmin = (root1 - m) * np.exp(0.5 * d1)
+                vmax = (root2 - m) * np.exp(0.5 * d2)
+                umax = 1  # umax = sqrt(h(m)) = 1
+
+                def logqpdf(x):
+                    return self._logquasipdf(x, p, b) - lm
+
+                c = m
+            else:
+                # ratio of uniforms without mode shift
+                # compute np.sqrt(quasipdf(m))
+                umax = np.exp(0.5*self._logquasipdf(m, p, b))
+                xplus = ((1 + p) + np.sqrt((1 + p)**2 + b**2))/b
+                vmin = 0
+                # compute xplus * np.sqrt(quasipdf(xplus))
+                vmax = xplus * np.exp(0.5 * self._logquasipdf(xplus, p, b))
+                c = 0
+
+                def logqpdf(x):
+                    return self._logquasipdf(x, p, b)
+
+            if vmin >= vmax:
+                raise ValueError("vmin must be smaller than vmax.")
+            if umax <= 0:
+                raise ValueError("umax must be positive.")
+
+            i = 1
+            while simulated < N:
+                k = N - simulated
+                # simulate uniform rvs on [0, umax] and [vmin, vmax]
+                u = umax * random_state.uniform(size=k)
+                v = random_state.uniform(size=k)
+                v = vmin + (vmax - vmin) * v
+                rvs = v / u + c
+                # rewrite acceptance condition u**2 <= pdf(rvs) by taking logs
+                accept = (2*np.log(u) <= logqpdf(rvs))
+                num_accept = np.sum(accept)
+                if num_accept > 0:
+                    x[simulated:(simulated + num_accept)] = rvs[accept]
+                    simulated += num_accept
+
+                if (simulated == 0) and (i*N >= 50000):
+                    msg = ("Not a single random variate could be generated "
+                           f"in {i*N} attempts. Sampling does not appear to "
+                           "work for the provided parameters.")
+                    raise RuntimeError(msg)
+                i += 1
+        else:
+            # use new algorithm in [2]
+            x0 = b / (1 - p)
+            xs = np.max((x0, 2 / b))
+            k1 = np.exp(self._logquasipdf(m, p, b))
+            A1 = k1 * x0
+            if x0 < 2 / b:
+                k2 = np.exp(-b)
+                if p > 0:
+                    A2 = k2 * ((2 / b)**p - x0**p) / p
+                else:
+                    A2 = k2 * np.log(2 / b**2)
+            else:
+                k2, A2 = 0, 0
+            k3 = xs**(p - 1)
+            A3 = 2 * k3 * np.exp(-xs * b / 2) / b
+            A = A1 + A2 + A3
+
+            # [2]: rejection constant is < 2.73; so expected runtime is finite
+            while simulated < N:
+                k = N - simulated
+                h, rvs = np.zeros(k), np.zeros(k)
+                # simulate uniform rvs on [x1, x2] and [0, y2]
+                u = random_state.uniform(size=k)
+                v = A * random_state.uniform(size=k)
+                cond1 = v <= A1
+                cond2 = np.logical_not(cond1) & (v <= A1 + A2)
+                cond3 = np.logical_not(cond1 | cond2)
+                # subdomain (0, x0)
+                rvs[cond1] = x0 * v[cond1] / A1
+                h[cond1] = k1
+                # subdomain (x0, 2 / b)
+                if p > 0:
+                    rvs[cond2] = (x0**p + (v[cond2] - A1) * p / k2)**(1 / p)
+                else:
+                    rvs[cond2] = b * np.exp((v[cond2] - A1) * np.exp(b))
+                h[cond2] = k2 * rvs[cond2]**(p - 1)
+                # subdomain (xs, infinity)
+                z = np.exp(-xs * b / 2) - b * (v[cond3] - A1 - A2) / (2 * k3)
+                rvs[cond3] = -2 / b * np.log(z)
+                h[cond3] = k3 * np.exp(-rvs[cond3] * b / 2)
+                # apply rejection method
+                accept = (np.log(u * h) <= self._logquasipdf(rvs, p, b))
+                num_accept = sum(accept)
+                if num_accept > 0:
+                    x[simulated:(simulated + num_accept)] = rvs[accept]
+                    simulated += num_accept
+
+        rvs = np.reshape(x, size1d)
+        if invert_res:
+            rvs = 1 / rvs
+        return rvs
+
+    def _mode(self, p, b):
+        # distinguish cases to avoid catastrophic cancellation (see [2])
+        if p < 1:
+            return b / (np.sqrt((p - 1)**2 + b**2) + 1 - p)
+        else:
+            return (np.sqrt((1 - p)**2 + b**2) - (1 - p)) / b
+
+    def _munp(self, n, p, b):
+        num = sc.kve(p + n, b)
+        denom = sc.kve(p, b)
+        inf_vals = np.isinf(num) | np.isinf(denom)
+        if inf_vals.any():
+            msg = ("Infinite values encountered in the moment calculation "
+                   "involving scipy.special.kve. Values replaced by NaN to "
+                   "avoid incorrect results.")
+            warnings.warn(msg, RuntimeWarning, stacklevel=3)
+            m = np.full_like(num, np.nan, dtype=np.float64)
+            m[~inf_vals] = num[~inf_vals] / denom[~inf_vals]
+        else:
+            m = num / denom
+        return m
+
+
+geninvgauss = geninvgauss_gen(a=0.0, name="geninvgauss")
+
+
+@np.vectorize(otypes=[np.float64])
+def _norminvgauss_quadrature(x, y, a, b):
+    # gh-23196 reported that the norminvgauss CDF would drop to zero in the far right
+    # tail. The SF had a similar problem, dropping to zero at the far left.
+    # This fixes the bug by using 1 - SF to compute the CDF in the right tail and
+    # 1 - CDF to compute the SF in the left tail. The mean is guaranteed to be beyond
+    # the median, so there is no loss of precision due to subtractive cancellation.
+    mean = b / np.sqrt((a + b) * (a - b))
+    if np.isneginf(x) and y > abs(mean):
+        return 1 - integrate.quad(norminvgauss._pdf, y, np.inf, args=(a, b))[0]
+    if np.isposinf(y) and x < -abs(mean):
+        return 1 - integrate.quad(norminvgauss._pdf, -np.inf, x, args=(a, b))[0]
+    else:
+        res = integrate.quad(norminvgauss._pdf, x, y, args=(a, b))[0]
+    return np.clip(res, 0, 1)
+
+
+class norminvgauss_gen(rv_continuous):
+    r"""A Normal Inverse Gaussian continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `norminvgauss` is:
+
+    .. math::
+
+        f(x, a, b) = \frac{a \, K_1(a \sqrt{1 + x^2})}{\pi \sqrt{1 + x^2}} \,
+                     \exp(\sqrt{a^2 - b^2} + b x)
+
+    where :math:`x` is a real number, the parameter :math:`a` is the tail
+    heaviness and :math:`b` is the asymmetry parameter satisfying
+    :math:`a > 0` and :math:`|b| <= a`.
+    :math:`K_1` is the modified Bessel function of second kind
+    (`scipy.special.k1`).
+
+    %(after_notes)s
+
+    A normal inverse Gaussian random variable `Y` with parameters `a` and `b`
+    can be expressed as a normal mean-variance mixture:
+    ``Y = b * V + sqrt(V) * X`` where `X` is ``norm(0,1)`` and `V` is
+    ``invgauss(mu=1/sqrt(a**2 - b**2))``. This representation is used
+    to generate random variates.
+
+    Another common parametrization of the distribution (see Equation 2.1 in
+    [2]_) is given by the following expression of the pdf:
+
+    .. math::
+
+        g(x, \alpha, \beta, \delta, \mu) =
+        \frac{\alpha\delta K_1\left(\alpha\sqrt{\delta^2 + (x - \mu)^2}\right)}
+        {\pi \sqrt{\delta^2 + (x - \mu)^2}} \,
+        e^{\delta \sqrt{\alpha^2 - \beta^2} + \beta (x - \mu)}
+
+    In SciPy, this corresponds to
+    :math:`a=\alpha \delta, b=\beta \delta, \text{loc}=\mu, \text{scale}=\delta`.
+
+    References
+    ----------
+    .. [1] O. Barndorff-Nielsen, "Hyperbolic Distributions and Distributions on
+           Hyperbolae", Scandinavian Journal of Statistics, Vol. 5(3),
+           pp. 151-157, 1978.
+
+    .. [2] O. Barndorff-Nielsen, "Normal Inverse Gaussian Distributions and
+           Stochastic Volatility Modelling", Scandinavian Journal of
+           Statistics, Vol. 24, pp. 1-13, 1997.
+
+    %(example)s
+
+    """
+    _support_mask = rv_continuous._open_support_mask
+
+    def _argcheck(self, a, b):
+        return (a > 0) & (np.absolute(b) < a)
+
+    def _shape_info(self):
+        ia = _ShapeInfo("a", False, (0, np.inf), (False, False))
+        ib = _ShapeInfo("b", False, (-np.inf, np.inf), (False, False))
+        return [ia, ib]
+
+    def _fitstart(self, data):
+        # Arbitrary, but the default a = b = 1 is not valid; the distribution
+        # requires |b| < a.
+        return super()._fitstart(data, args=(1, 0.5))
+
+    def _pdf(self, x, a, b):
+        gamma = np.sqrt((a + b) * (a - b))
+        fac1 = a / np.pi
+        sq = np.hypot(1, x)  # reduce overflows
+        return fac1 * sc.k1e(a * sq) * np.exp(b*x - a*sq + gamma) / sq
+
+    def _cdf(self, x, a, b):
+        return _norminvgauss_quadrature(-np.inf, x, a, b)
+
+    def _sf(self, x, a, b):
+        return _norminvgauss_quadrature(x, np.inf, a, b)
+
+    def _isf(self, q, a, b):
+        def _isf_scalar(q, a, b):
+
+            def eq(x, a, b, q):
+                # Solve eq(x, a, b, q) = 0 to obtain isf(x, a, b) = q.
+                return self._sf(x, a, b) - q
+
+            # Find a bracketing interval for the root.
+            # Start at the mean, and grow the length of the interval
+            # by 2 each iteration until there is a sign change in eq.
+            xm = self.mean(a, b)
+            em = eq(xm, a, b, q)
+            if em == 0:
+                # Unlikely, but might as well check.
+                return xm
+            if em > 0:
+                delta = 1
+                left = xm
+                right = xm + delta
+                while eq(right, a, b, q) > 0:
+                    delta = 2*delta
+                    right = xm + delta
+            else:
+                # em < 0
+                delta = 1
+                right = xm
+                left = xm - delta
+                while eq(left, a, b, q) < 0:
+                    delta = 2*delta
+                    left = xm - delta
+            result = optimize.brentq(eq, left, right, args=(a, b, q),
+                                     xtol=self.xtol)
+            return result
+
+        if np.isscalar(q):
+            return _isf_scalar(q, a, b)
+        else:
+            result = []
+            for (q0, a0, b0) in zip(q, a, b):
+                result.append(_isf_scalar(q0, a0, b0))
+            return np.array(result)
+
+    def _rvs(self, a, b, size=None, random_state=None):
+        # note: X = b * V + sqrt(V) * X is norminvgaus(a,b) if X is standard
+        # normal and V is invgauss(mu=1/sqrt(a**2 - b**2))
+        gamma = np.sqrt((a + b) * (a - b))
+        ig = invgauss.rvs(mu=1/gamma, size=size, random_state=random_state)
+        return b * ig + np.sqrt(ig) * norm.rvs(size=size,
+                                               random_state=random_state)
+
+    def _stats(self, a, b):
+        gamma = np.sqrt((a + b) * (a - b))
+        mean = b / gamma
+        variance = a**2 / gamma**3
+        skewness = 3.0 * b / (a * np.sqrt(gamma))
+        kurtosis = 3.0 * (1 + 4 * b**2 / a**2) / gamma
+        return mean, variance, skewness, kurtosis
+
+
+norminvgauss = norminvgauss_gen(name="norminvgauss")
+
+
+class invweibull_gen(rv_continuous):
+    """An inverted Weibull continuous random variable.
+
+    This distribution is also known as the Fréchet distribution or the
+    type II extreme value distribution.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `invweibull` is:
+
+    .. math::
+
+        f(x, c) = c x^{-c-1} \\exp(-x^{-c})
+
+    for :math:`x > 0`, :math:`c > 0`.
+
+    `invweibull` takes ``c`` as a shape parameter for :math:`c`.
+
+    %(after_notes)s
+
+    References
+    ----------
+    F.R.S. de Gusmao, E.M.M Ortega and G.M. Cordeiro, "The generalized inverse
+    Weibull distribution", Stat. Papers, vol. 52, pp. 591-619, 2011.
+
+    %(example)s
+
+    """
+    _support_mask = rv_continuous._open_support_mask
+
+    def _shape_info(self):
+        return [_ShapeInfo("c", False, (0, np.inf), (False, False))]
+
+    def _pdf(self, x, c):
+        # invweibull.pdf(x, c) = c * x**(-c-1) * exp(-x**(-c))
+        xc1 = np.power(x, -c - 1.0)
+        xc2 = np.power(x, -c)
+        xc2 = np.exp(-xc2)
+        return c * xc1 * xc2
+
+    def _cdf(self, x, c):
+        xc1 = np.power(x, -c)
+        return np.exp(-xc1)
+
+    def _sf(self, x, c):
+        return -np.expm1(-x**-c)
+
+    def _ppf(self, q, c):
+        return np.power(-np.log(q), -1.0/c)
+
+    def _isf(self, p, c):
+        return (-np.log1p(-p))**(-1/c)
+
+    def _munp(self, n, c):
+        return sc.gamma(1 - n / c)
+
+    def _entropy(self, c):
+        return 1+_EULER + _EULER / c - np.log(c)
+
+    def _fitstart(self, data, args=None):
+        # invweibull requires c > 1 for the first moment to exist, so use 2.0
+        args = (2.0,) if args is None else args
+        return super()._fitstart(data, args=args)
+
+
+invweibull = invweibull_gen(a=0, name='invweibull')
+
+
+class jf_skew_t_gen(rv_continuous):
+    r"""Jones and Faddy skew-t distribution.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `jf_skew_t` is:
+
+    .. math::
+
+        f(x; a, b) = C_{a,b}^{-1}
+                    \left(1+\frac{x}{\left(a+b+x^2\right)^{1/2}}\right)^{a+1/2}
+                    \left(1-\frac{x}{\left(a+b+x^2\right)^{1/2}}\right)^{b+1/2}
+
+    for real numbers :math:`a>0` and :math:`b>0`, where
+    :math:`C_{a,b} = 2^{a+b-1}B(a,b)(a+b)^{1/2}`, and :math:`B` denotes the
+    beta function (`scipy.special.beta`).
+
+    When :math:`a<b`, the distribution is negatively skewed, and when
+    :math:`a>b`, the distribution is positively skewed. If :math:`a=b`, then
+    we recover the `t` distribution with :math:`2a` degrees of freedom.
+
+    `jf_skew_t` takes :math:`a` and :math:`b` as shape parameters.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] M.C. Jones and M.J. Faddy. "A skew extension of the t distribution,
+           with applications" *Journal of the Royal Statistical Society*.
+           Series B (Statistical Methodology) 65, no. 1 (2003): 159-174.
+           :doi:`10.1111/1467-9868.00378`
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        ia = _ShapeInfo("a", False, (0, np.inf), (False, False))
+        ib = _ShapeInfo("b", False, (0, np.inf), (False, False))
+        return [ia, ib]
+
+    def _pdf(self, x, a, b):
+        c = 2 ** (a + b - 1) * sc.beta(a, b) * np.sqrt(a + b)
+        d1 = (1 + x / np.sqrt(a + b + x ** 2)) ** (a + 0.5)
+        d2 = (1 - x / np.sqrt(a + b + x ** 2)) ** (b + 0.5)
+        return d1 * d2 / c
+
+    def _rvs(self, a, b, size=None, random_state=None):
+        d1 = random_state.beta(a, b, size)
+        d2 = (2 * d1 - 1) * np.sqrt(a + b)
+        d3 = 2 * np.sqrt(d1 * (1 - d1))
+        return d2 / d3
+
+    def _cdf(self, x, a, b):
+        y = (1 + x / np.sqrt(a + b + x ** 2)) * 0.5
+        return sc.betainc(a, b, y)
+
+    def _sf(self, x, a, b):
+        y = (1 + x / np.sqrt(a + b + x ** 2)) * 0.5
+        return sc.betaincc(a, b, y)
+
+    def _ppf(self, q, a, b):
+        d1 = beta.ppf(q, a, b)
+        d2 = (2 * d1 - 1) * np.sqrt(a + b)
+        d3 = 2 * np.sqrt(d1 * (1 - d1))
+        return d2 / d3
+
+    def _munp(self, n, a, b):
+        """Returns the n-th moment(s) where all the following hold:
+
+        - n >= 0
+        - a > n / 2
+        - b > n / 2
+
+        The result is np.nan in all other cases.
+        """
+        def nth_moment(n_k, a_k, b_k):
+            """Computes E[T^(n_k)] where T is skew-t distributed with
+            parameters a_k and b_k.
+            """
+            num = (a_k + b_k) ** (0.5 * n_k)
+            denom = 2 ** n_k * sc.beta(a_k, b_k)
+
+            indices = np.arange(n_k + 1)
+            sgn = np.where(indices % 2 > 0, -1, 1)
+            d = sc.beta(a_k + 0.5 * n_k - indices, b_k - 0.5 * n_k + indices)
+            sum_terms = sc.comb(n_k, indices) * sgn * d
+
+            return num / denom * sum_terms.sum()
+
+        nth_moment_valid = (a > 0.5 * n) & (b > 0.5 * n) & (n >= 0)
+        return xpx.apply_where(
+            nth_moment_valid,
+            (n, a, b),
+            np.vectorize(nth_moment, otypes=[np.float64]),
+            fill_value=np.nan,
+        )
+
+
+jf_skew_t = jf_skew_t_gen(name='jf_skew_t')
+
+
+class johnsonsb_gen(rv_continuous):
+    r"""A Johnson SB continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    johnsonsu
+
+    Notes
+    -----
+    The probability density function for `johnsonsb` is:
+
+    .. math::
+
+        f(x, a, b) = \frac{b}{x(1-x)}  \phi(a + b \log \frac{x}{1-x} )
+
+    where :math:`x`, :math:`a`, and :math:`b` are real scalars; :math:`b > 0`
+    and :math:`x \in [0,1]`.  :math:`\phi` is the pdf of the normal
+    distribution.
+
+    `johnsonsb` takes :math:`a` and :math:`b` as shape parameters.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    _support_mask = rv_continuous._open_support_mask
+
+    def _argcheck(self, a, b):
+        return (b > 0) & (a == a)
+
+    def _shape_info(self):
+        ia = _ShapeInfo("a", False, (-np.inf, np.inf), (False, False))
+        ib = _ShapeInfo("b", False, (0, np.inf), (False, False))
+        return [ia, ib]
+
+    def _pdf(self, x, a, b):
+        # johnsonsb.pdf(x, a, b) = b / (x*(1-x)) * phi(a + b * log(x/(1-x)))
+        trm = _norm_pdf(a + b*sc.logit(x))
+        return b*1.0/(x*(1-x))*trm
+
+    def _cdf(self, x, a, b):
+        return _norm_cdf(a + b*sc.logit(x))
+
+    def _ppf(self, q, a, b):
+        return sc.expit(1.0 / b * (_norm_ppf(q) - a))
+
+    def _sf(self, x, a, b):
+        return _norm_sf(a + b*sc.logit(x))
+
+    def _isf(self, q, a, b):
+        return sc.expit(1.0 / b * (_norm_isf(q) - a))
+
+
+johnsonsb = johnsonsb_gen(a=0.0, b=1.0, name='johnsonsb')
+
+
+class johnsonsu_gen(rv_continuous):
+    r"""A Johnson SU continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    johnsonsb
+
+    Notes
+    -----
+    The probability density function for `johnsonsu` is:
+
+    .. math::
+
+        f(x, a, b) = \frac{b}{\sqrt{x^2 + 1}}
+                     \phi(a + b \log(x + \sqrt{x^2 + 1}))
+
+    where :math:`x`, :math:`a`, and :math:`b` are real scalars; :math:`b > 0`.
+    :math:`\phi` is the pdf of the normal distribution.
+
+    `johnsonsu` takes :math:`a` and :math:`b` as shape parameters.
+
+    The first four central moments are calculated according to the formulas
+    in [1]_.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] Taylor Enterprises. "Johnson Family of Distributions".
+       https://variation.com/wp-content/distribution_analyzer_help/hs126.htm
+
+    %(example)s
+
+    """
+    def _argcheck(self, a, b):
+        return (b > 0) & (a == a)
+
+    def _shape_info(self):
+        ia = _ShapeInfo("a", False, (-np.inf, np.inf), (False, False))
+        ib = _ShapeInfo("b", False, (0, np.inf), (False, False))
+        return [ia, ib]
+
+    def _pdf(self, x, a, b):
+        # johnsonsu.pdf(x, a, b) = b / sqrt(x**2 + 1) *
+        #                          phi(a + b * log(x + sqrt(x**2 + 1)))
+        x2 = x*x
+        trm = _norm_pdf(a + b * np.arcsinh(x))
+        return b*1.0/np.sqrt(x2+1.0)*trm
+
+    def _cdf(self, x, a, b):
+        return _norm_cdf(a + b * np.arcsinh(x))
+
+    def _ppf(self, q, a, b):
+        return np.sinh((_norm_ppf(q) - a) / b)
+
+    def _sf(self, x, a, b):
+        return _norm_sf(a + b * np.arcsinh(x))
+
+    def _isf(self, x, a, b):
+        return np.sinh((_norm_isf(x) - a) / b)
+
+    def _stats(self, a, b, moments='mv'):
+        # Naive implementation of first and second moment to address gh-18071.
+        # https://variation.com/wp-content/distribution_analyzer_help/hs126.htm
+        # Numerical improvements left to future enhancements.
+        mu, mu2, g1, g2 = None, None, None, None
+
+        bn2 = b**-2.
+        expbn2 = np.exp(bn2)
+        a_b = a / b
+
+        if 'm' in moments:
+            mu = -expbn2**0.5 * np.sinh(a_b)
+        if 'v' in moments:
+            mu2 = 0.5*sc.expm1(bn2)*(expbn2*np.cosh(2*a_b) + 1)
+        if 's' in moments:
+            t1 = expbn2**.5 * sc.expm1(bn2)**0.5
+            t2 = 3*np.sinh(a_b)
+            t3 = expbn2 * (expbn2 + 2) * np.sinh(3*a_b)
+            denom = np.sqrt(2) * (1 + expbn2 * np.cosh(2*a_b))**(3/2)
+            g1 = -t1 * (t2 + t3) / denom
+        if 'k' in moments:
+            t1 = 3 + 6*expbn2
+            t2 = 4*expbn2**2 * (expbn2 + 2) * np.cosh(2*a_b)
+            t3 = expbn2**2 * np.cosh(4*a_b)
+            t4 = -3 + 3*expbn2**2 + 2*expbn2**3 + expbn2**4
+            denom = 2*(1 + expbn2*np.cosh(2*a_b))**2
+            g2 = (t1 + t2 + t3*t4) / denom - 3
+        return mu, mu2, g1, g2
+
+
+johnsonsu = johnsonsu_gen(name='johnsonsu')
+
+
+class landau_gen(rv_continuous):
+    r"""A Landau continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    :ref:`landau_energy_loss` : Extended example in a particle physics context.
+
+    Notes
+    -----
+    The probability density function for `landau` ([1]_, [2]_) is:
+
+    .. math::
+
+        f(x) = \frac{1}{\pi}\int_0^\infty \exp(-t \log t - xt)\sin(\pi t) dt
+
+    for a real number :math:`x`.
+
+    %(after_notes)s
+
+    Often (e.g. [2]_), the Landau distribution is parameterized in terms of a
+    location parameter :math:`\mu` and scale parameter :math:`c`, the latter of
+    which *also* introduces a location shift. If ``mu`` and ``c`` are used to
+    represent these parameters, this corresponds with SciPy's parameterization
+    with ``loc = mu + 2*c / np.pi * np.log(c)`` and ``scale = c``.
+
+    This distribution uses routines from the Boost Math C++ library for
+    the computation of the ``pdf``, ``cdf``, ``ppf``, ``sf`` and ``isf``
+    methods. [1]_
+
+    References
+    ----------
+    .. [1] Landau, L. (1944). "On the energy loss of fast particles by
+           ionization". J. Phys. (USSR). 8: 201.
+    .. [2] "Landau Distribution", Wikipedia,
+           https://en.wikipedia.org/wiki/Landau_distribution
+    .. [3] Chambers, J. M., Mallows, C. L., & Stuck, B. (1976).
+           "A method for simulating stable random variables."
+           Journal of the American Statistical Association, 71(354), 340-344.
+    .. [4] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+    .. [5] Yoshimura, T. "Numerical Evaluation and High Precision Approximation
+           Formula for Landau Distribution".
+           :doi:`10.36227/techrxiv.171822215.53612870/v2`
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return []
+
+    def _entropy(self):
+        # Computed with mpmath - see gh-19145
+        return 2.37263644000448182
+
+    def _pdf(self, x):
+        return scu._landau_pdf(x, 0, 1)
+
+    def _cdf(self, x):
+        return scu._landau_cdf(x, 0, 1)
+
+    def _sf(self, x):
+        return scu._landau_sf(x, 0, 1)
+
+    def _ppf(self, p):
+        return scu._landau_ppf(p, 0, 1)
+
+    def _isf(self, p):
+        return scu._landau_isf(p, 0, 1)
+
+    def _stats(self):
+        return np.nan, np.nan, np.nan, np.nan
+
+    def _munp(self, n):
+        return np.nan if n > 0 else 1
+
+    def _fitstart(self, data, args=None):
+        # Initialize ML guesses using quartiles instead of moments.
+        if isinstance(data, CensoredData):
+            data = data._uncensor()
+        p25, p50, p75 = np.percentile(data, [25, 50, 75])
+        return p50, (p75 - p25)/2
+
+    def _rvs(self, size=None, random_state=None):
+        # Method from https://www.jstor.org/stable/2285309 Eq. 2.4
+        pi_2 = np.pi / 2
+        U = random_state.uniform(-np.pi / 2, np.pi / 2, size=size)
+        W = random_state.standard_exponential(size=size)
+        S = 2 / np.pi * ((pi_2 + U) * np.tan(U)
+                         - np.log((pi_2 * W * np.cos(U)) / (pi_2 + U)))
+        return S
+
+
+landau = landau_gen(name='landau')
+
+
+class laplace_gen(rv_continuous):
+    r"""A Laplace continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `laplace` is
+
+    .. math::
+
+        f(x) = \frac{1}{2} \exp(-|x|)
+
+    for a real number :math:`x`.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return []
+
+    def _rvs(self, size=None, random_state=None):
+        return random_state.laplace(0, 1, size=size)
+
+    def _pdf(self, x):
+        # laplace.pdf(x) = 1/2 * exp(-abs(x))
+        return 0.5*np.exp(-abs(x))
+
+    def _cdf(self, x):
+        with np.errstate(over='ignore'):
+            return np.where(x > 0, 1.0 - 0.5*np.exp(-x), 0.5*np.exp(x))
+
+    def _sf(self, x):
+        # By symmetry...
+        return self._cdf(-x)
+
+    def _ppf(self, q):
+        return np.where(q > 0.5, -np.log(2*(1-q)), np.log(2*q))
+
+    def _isf(self, q):
+        # By symmetry...
+        return -self._ppf(q)
+
+    def _stats(self):
+        return 0, 2, 0, 3
+
+    def _entropy(self):
+        return np.log(2)+1
+
+    @_call_super_mom
+    @replace_notes_in_docstring(rv_continuous, notes="""\
+        This function uses explicit formulas for the maximum likelihood
+        estimation of the Laplace distribution parameters, so the keyword
+        arguments `loc`, `scale`, and `optimizer` are ignored.\n\n""")
+    def fit(self, data, *args, **kwds):
+        data, floc, fscale = _check_fit_input_parameters(self, data,
+                                                         args, kwds)
+
+        # Source: Statistical Distributions, 3rd Edition. Evans, Hastings,
+        # and Peacock (2000), Page 124
+
+        if floc is None:
+            floc = np.median(data)
+
+        if fscale is None:
+            fscale = (np.sum(np.abs(data - floc))) / len(data)
+
+        return floc, fscale
+
+
+laplace = laplace_gen(name='laplace')
+
+
+class laplace_asymmetric_gen(rv_continuous):
+    r"""An asymmetric Laplace continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    laplace : Laplace distribution
+
+    Notes
+    -----
+    The probability density function for `laplace_asymmetric` is
+
+    .. math::
+
+       f(x, \kappa) &= \frac{1}{\kappa+\kappa^{-1}}\exp(-x\kappa),\quad x\ge0\\
+                    &= \frac{1}{\kappa+\kappa^{-1}}\exp(x/\kappa),\quad x<0\\
+
+    for :math:`-\infty < x < \infty`, :math:`\kappa > 0`.
+
+    `laplace_asymmetric` takes ``kappa`` as a shape parameter for
+    :math:`\kappa`. For :math:`\kappa = 1`, it is identical to a
+    Laplace distribution.
+
+    %(after_notes)s
+
+    Note that the scale parameter of some references is the reciprocal of
+    SciPy's ``scale``. For example, :math:`\lambda = 1/2` in the
+    parameterization of [1]_ is equivalent to ``scale = 2`` with
+    `laplace_asymmetric`.
+
+    References
+    ----------
+    .. [1] "Asymmetric Laplace distribution", Wikipedia
+            https://en.wikipedia.org/wiki/Asymmetric_Laplace_distribution
+
+    .. [2] Kozubowski TJ and Podgórski K. A Multivariate and
+           Asymmetric Generalization of Laplace Distribution,
+           Computational Statistics 15, 531--540 (2000).
+           :doi:`10.1007/PL00022717`
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("kappa", False, (0, np.inf), (False, False))]
+
+    def _pdf(self, x, kappa):
+        return np.exp(self._logpdf(x, kappa))
+
+    def _logpdf(self, x, kappa):
+        kapinv = 1/kappa
+        lPx = x * np.where(x >= 0, -kappa, kapinv)
+        lPx -= np.log(kappa+kapinv)
+        return lPx
+
+    def _cdf(self, x, kappa):
+        kapinv = 1/kappa
+        kappkapinv = kappa+kapinv
+        return np.where(x >= 0,
+                        1 - np.exp(-x*kappa)*(kapinv/kappkapinv),
+                        np.exp(x*kapinv)*(kappa/kappkapinv))
+
+    def _sf(self, x, kappa):
+        kapinv = 1/kappa
+        kappkapinv = kappa+kapinv
+        return np.where(x >= 0,
+                        np.exp(-x*kappa)*(kapinv/kappkapinv),
+                        1 - np.exp(x*kapinv)*(kappa/kappkapinv))
+
+    def _ppf(self, q, kappa):
+        kapinv = 1/kappa
+        kappkapinv = kappa+kapinv
+        return np.where(q >= kappa/kappkapinv,
+                        -np.log((1 - q)*kappkapinv*kappa)*kapinv,
+                        np.log(q*kappkapinv/kappa)*kappa)
+
+    def _isf(self, q, kappa):
+        kapinv = 1/kappa
+        kappkapinv = kappa+kapinv
+        return np.where(q <= kapinv/kappkapinv,
+                        -np.log(q*kappkapinv*kappa)*kapinv,
+                        np.log((1 - q)*kappkapinv/kappa)*kappa)
+
+    def _stats(self, kappa):
+        kapinv = 1/kappa
+        mn = kapinv - kappa
+        var = kapinv*kapinv + kappa*kappa
+        g1 = 2.0*(1-np.power(kappa, 6))/np.power(1+np.power(kappa, 4), 1.5)
+        g2 = 6.0*(1+np.power(kappa, 8))/np.power(1+np.power(kappa, 4), 2)
+        return mn, var, g1, g2
+
+    def _entropy(self, kappa):
+        return 1 + np.log(kappa+1/kappa)
+
+
+laplace_asymmetric = laplace_asymmetric_gen(name='laplace_asymmetric')
+
+
+def _check_fit_input_parameters(dist, data, args, kwds):
+    if not isinstance(data, CensoredData):
+        data = np.asarray(data)
+
+    floc = kwds.get('floc', None)
+    fscale = kwds.get('fscale', None)
+
+    num_shapes = len(dist.shapes.split(",")) if dist.shapes else 0
+    fshape_keys = []
+    fshapes = []
+
+    # user has many options for fixing the shape, so here we standardize it
+    # into 'f' + the number of the shape.
+    # Adapted from `_reduce_func` in `_distn_infrastructure.py`:
+    if dist.shapes:
+        shapes = dist.shapes.replace(',', ' ').split()
+        for j, s in enumerate(shapes):
+            key = 'f' + str(j)
+            names = [key, 'f' + s, 'fix_' + s]
+            val = _get_fixed_fit_value(kwds, names)
+            fshape_keys.append(key)
+            fshapes.append(val)
+            if val is not None:
+                kwds[key] = val
+
+    # determine if there are any unknown arguments in kwds
+    known_keys = {'loc', 'scale', 'optimizer', 'method',
+                  'floc', 'fscale', *fshape_keys}
+    unknown_keys = set(kwds).difference(known_keys)
+    if unknown_keys:
+        raise TypeError(f"Unknown keyword arguments: {unknown_keys}.")
+
+    if len(args) > num_shapes:
+        raise TypeError("Too many positional arguments.")
+
+    if None not in {floc, fscale, *fshapes}:
+        # This check is for consistency with `rv_continuous.fit`.
+        # Without this check, this function would just return the
+        # parameters that were given.
+        raise RuntimeError("All parameters fixed. There is nothing to "
+                           "optimize.")
+
+    uncensored = data._uncensor() if isinstance(data, CensoredData) else data
+    if not np.isfinite(uncensored).all():
+        raise ValueError("The data contains non-finite values.")
+
+    return (data, *fshapes, floc, fscale)
+
+
+class levy_gen(rv_continuous):
+    r"""A Levy continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    levy_stable, levy_l
+
+    Notes
+    -----
+    The probability density function for `levy` is:
+
+    .. math::
+
+        f(x) = \frac{1}{\sqrt{2\pi x^3}} \exp\left(-\frac{1}{2x}\right)
+
+    for :math:`x > 0`.
+
+    This is the same as the Levy-stable distribution with :math:`a=1/2` and
+    :math:`b=1`.
+
+    %(after_notes)s
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import levy
+    >>> import matplotlib.pyplot as plt
+    >>> fig, ax = plt.subplots(1, 1)
+
+    Calculate the first four moments:
+
+    >>> mean, var, skew, kurt = levy.stats(moments='mvsk')
+
+    Display the probability density function (``pdf``):
+
+    >>> # `levy` is very heavy-tailed.
+    >>> # To show a nice plot, let's cut off the upper 40 percent.
+    >>> a, b = levy.ppf(0), levy.ppf(0.6)
+    >>> x = np.linspace(a, b, 100)
+    >>> ax.plot(x, levy.pdf(x),
+    ...        'r-', lw=5, alpha=0.6, label='levy pdf')
+
+    Alternatively, the distribution object can be called (as a function)
+    to fix the shape, location and scale parameters. This returns a "frozen"
+    RV object holding the given parameters fixed.
+
+    Freeze the distribution and display the frozen ``pdf``:
+
+    >>> rv = levy()
+    >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
+
+    Check accuracy of ``cdf`` and ``ppf``:
+
+    >>> vals = levy.ppf([0.001, 0.5, 0.999])
+    >>> np.allclose([0.001, 0.5, 0.999], levy.cdf(vals))
+    True
+
+    Generate random numbers:
+
+    >>> r = levy.rvs(size=1000)
+
+    And compare the histogram:
+
+    >>> # manual binning to ignore the tail
+    >>> bins = np.concatenate((np.linspace(a, b, 20), [np.max(r)]))
+    >>> ax.hist(r, bins=bins, density=True, histtype='stepfilled', alpha=0.2)
+    >>> ax.set_xlim([x[0], x[-1]])
+    >>> ax.legend(loc='best', frameon=False)
+    >>> plt.show()
+
+    """
+    _support_mask = rv_continuous._open_support_mask
+
+    def _shape_info(self):
+        return []
+
+    def _pdf(self, x):
+        # levy.pdf(x) = 1 / (x * sqrt(2*pi*x)) * exp(-1/(2*x))
+        return 1 / np.sqrt(2*np.pi*x) / x * np.exp(-1/(2*x))
+
+    def _cdf(self, x):
+        # Equivalent to 2*norm.sf(np.sqrt(1/x))
+        return sc.erfc(np.sqrt(0.5 / x))
+
+    def _sf(self, x):
+        return sc.erf(np.sqrt(0.5 / x))
+
+    def _ppf(self, q):
+        # Equivalent to 1.0/(norm.isf(q/2)**2) or 0.5/(erfcinv(q)**2)
+        val = _norm_isf(q/2)
+        return 1.0 / (val * val)
+
+    def _isf(self, p):
+        return 1/(2*sc.erfinv(p)**2)
+
+    def _stats(self):
+        return np.inf, np.inf, np.nan, np.nan
+
+
+levy = levy_gen(a=0.0, name="levy")
+
+
+class levy_l_gen(rv_continuous):
+    r"""A left-skewed Levy continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    levy, levy_stable
+
+    Notes
+    -----
+    The probability density function for `levy_l` is:
+
+    .. math::
+        f(x) = \frac{1}{|x| \sqrt{2\pi |x|}} \exp{ \left(-\frac{1}{2|x|} \right)}
+
+    for :math:`x < 0`.
+
+    This is the same as the Levy-stable distribution with :math:`a=1/2` and
+    :math:`b=-1`.
+
+    %(after_notes)s
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import levy_l
+    >>> import matplotlib.pyplot as plt
+    >>> fig, ax = plt.subplots(1, 1)
+
+    Calculate the first four moments:
+
+    >>> mean, var, skew, kurt = levy_l.stats(moments='mvsk')
+
+    Display the probability density function (``pdf``):
+
+    >>> # `levy_l` is very heavy-tailed.
+    >>> # To show a nice plot, let's cut off the lower 40 percent.
+    >>> a, b = levy_l.ppf(0.4), levy_l.ppf(1)
+    >>> x = np.linspace(a, b, 100)
+    >>> ax.plot(x, levy_l.pdf(x),
+    ...        'r-', lw=5, alpha=0.6, label='levy_l pdf')
+
+    Alternatively, the distribution object can be called (as a function)
+    to fix the shape, location and scale parameters. This returns a "frozen"
+    RV object holding the given parameters fixed.
+
+    Freeze the distribution and display the frozen ``pdf``:
+
+    >>> rv = levy_l()
+    >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
+
+    Check accuracy of ``cdf`` and ``ppf``:
+
+    >>> vals = levy_l.ppf([0.001, 0.5, 0.999])
+    >>> np.allclose([0.001, 0.5, 0.999], levy_l.cdf(vals))
+    True
+
+    Generate random numbers:
+
+    >>> r = levy_l.rvs(size=1000)
+
+    And compare the histogram:
+
+    >>> # manual binning to ignore the tail
+    >>> bins = np.concatenate(([np.min(r)], np.linspace(a, b, 20)))
+    >>> ax.hist(r, bins=bins, density=True, histtype='stepfilled', alpha=0.2)
+    >>> ax.set_xlim([x[0], x[-1]])
+    >>> ax.legend(loc='best', frameon=False)
+    >>> plt.show()
+
+    """
+    _support_mask = rv_continuous._open_support_mask
+
+    def _shape_info(self):
+        return []
+
+    def _pdf(self, x):
+        # levy_l.pdf(x) = 1 / (abs(x) * sqrt(2*pi*abs(x))) * exp(-1/(2*abs(x)))
+        ax = abs(x)
+        return 1/np.sqrt(2*np.pi*ax)/ax*np.exp(-1/(2*ax))
+
+    def _cdf(self, x):
+        ax = abs(x)
+        return 2 * _norm_cdf(1 / np.sqrt(ax)) - 1
+
+    def _sf(self, x):
+        ax = abs(x)
+        return 2 * _norm_sf(1 / np.sqrt(ax))
+
+    def _ppf(self, q):
+        val = _norm_ppf((q + 1.0) / 2)
+        return -1.0 / (val * val)
+
+    def _isf(self, p):
+        return -1/_norm_isf(p/2)**2
+
+    def _stats(self):
+        return np.inf, np.inf, np.nan, np.nan
+
+
+levy_l = levy_l_gen(b=0.0, name="levy_l")
+
+
+class logistic_gen(rv_continuous):
+    r"""A logistic (or Sech-squared) continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `logistic` is:
+
+    .. math::
+
+        f(x) = \frac{\exp(-x)}
+                    {(1+\exp(-x))^2}
+
+    `logistic` is a special case of `genlogistic` with ``c=1``.
+
+    Remark that the survival function (``logistic.sf``) is equal to the
+    Fermi-Dirac distribution describing fermionic statistics.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return []
+
+    def _rvs(self, size=None, random_state=None):
+        return random_state.logistic(size=size)
+
+    def _pdf(self, x):
+        # logistic.pdf(x) = exp(-x) / (1+exp(-x))**2
+        return np.exp(self._logpdf(x))
+
+    def _logpdf(self, x):
+        y = -np.abs(x)
+        return y - 2. * sc.log1p(np.exp(y))
+
+    def _cdf(self, x):
+        return sc.expit(x)
+
+    def _logcdf(self, x):
+        return sc.log_expit(x)
+
+    def _ppf(self, q):
+        return sc.logit(q)
+
+    def _sf(self, x):
+        return sc.expit(-x)
+
+    def _logsf(self, x):
+        return sc.log_expit(-x)
+
+    def _isf(self, q):
+        return -sc.logit(q)
+
+    def _stats(self):
+        return 0, np.pi*np.pi/3.0, 0, 6.0/5.0
+
+    def _entropy(self):
+        # https://en.wikipedia.org/wiki/Logistic_distribution
+        return 2.0
+
+    @_call_super_mom
+    @inherit_docstring_from(rv_continuous)
+    def fit(self, data, *args, **kwds):
+        if kwds.pop('superfit', False):
+            return super().fit(data, *args, **kwds)
+
+        data, floc, fscale = _check_fit_input_parameters(self, data,
+                                                         args, kwds)
+        n = len(data)
+
+        # rv_continuous provided guesses
+        loc, scale = self._fitstart(data)
+        # these are trumped by user-provided guesses
+        loc, scale = kwds.get('loc', loc), kwds.get('scale', scale)
+
+        # the maximum likelihood estimators `a` and `b` of the location and
+        # scale parameters are roots of the two equations described in `func`.
+        # Source: Statistical Distributions, 3rd Edition. Evans, Hastings, and
+        # Peacock (2000), Page 130
+
+        def dl_dloc(loc, scale=fscale):
+            c = (data - loc) / scale
+            return np.sum(sc.expit(c)) - n/2
+
+        def dl_dscale(scale, loc=floc):
+            c = (data - loc) / scale
+            return np.sum(c*np.tanh(c/2)) - n
+
+        def func(params):
+            loc, scale = params
+            return dl_dloc(loc, scale), dl_dscale(scale, loc)
+
+        if fscale is not None and floc is None:
+            res = optimize.root(dl_dloc, (loc,))
+            loc = res.x[0]
+            scale = fscale
+        elif floc is not None and fscale is None:
+            res = optimize.root(dl_dscale, (scale,))
+            scale = res.x[0]
+            loc = floc
+        else:
+            res = optimize.root(func, (loc, scale))
+            loc, scale = res.x
+
+        # Note: gh-18176 reported data for which the reported MLE had
+        # `scale < 0`. To fix the bug, we return abs(scale). This is OK because
+        # `dl_dscale` and `dl_dloc` are even and odd functions of `scale`,
+        # respectively, so if `-scale` is a solution, so is `scale`.
+        scale = abs(scale)
+        return ((loc, scale) if res.success
+                else super().fit(data, *args, **kwds))
+
+
+logistic = logistic_gen(name='logistic')
+
+
+class loggamma_gen(rv_continuous):
+    r"""A log gamma continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `loggamma` is:
+
+    .. math::
+
+        f(x, c) = \frac{\exp(c x - \exp(x))}
+                       {\Gamma(c)}
+
+    for all :math:`x, c > 0`. Here, :math:`\Gamma` is the
+    gamma function (`scipy.special.gamma`).
+
+    `loggamma` takes ``c`` as a shape parameter for :math:`c`.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+
+    def _shape_info(self):
+        return [_ShapeInfo("c", False, (0, np.inf), (False, False))]
+
+    def _rvs(self, c, size=None, random_state=None):
+        # Use the property of the gamma distribution Gamma(c)
+        #    Gamma(c) ~ Gamma(c + 1)*U**(1/c),
+        # where U is uniform on [0, 1]. (See, e.g.,
+        # G. Marsaglia and W.W. Tsang, "A simple method for generating gamma
+        # variables", https://doi.org/10.1145/358407.358414)
+        # So
+        #    log(Gamma(c)) ~ log(Gamma(c + 1)) + log(U)/c
+        # Generating a sample with this formulation is a bit slower
+        # than the more obvious log(Gamma(c)), but it avoids loss
+        # of precision when c << 1.
+        return (np.log(random_state.gamma(c + 1, size=size))
+                + np.log(random_state.uniform(size=size))/c)
+
+    def _pdf(self, x, c):
+        # loggamma.pdf(x, c) = exp(c*x-exp(x)) / gamma(c)
+        return np.exp(c*x-np.exp(x)-sc.gammaln(c))
+
+    def _logpdf(self, x, c):
+        return c*x - np.exp(x) - sc.gammaln(c)
+
+    def _cdf(self, x, c):
+        # This function is gammainc(c, exp(x)), where gammainc(c, z) is
+        # the regularized incomplete gamma function.
+        # The first term in a series expansion of gamminc(c, z) is
+        # z**c/Gamma(c+1); see 6.5.29 of Abramowitz & Stegun (and refer
+        # back to 6.5.1, 6.5.2 and 6.5.4 for the relevant notation).
+        # This can also be found in the wikipedia article
+        # https://en.wikipedia.org/wiki/Incomplete_gamma_function.
+        # Here we use that formula when x is sufficiently negative that
+        # exp(x) will result in subnormal numbers and lose precision.
+        # We evaluate the log of the expression first to allow the possible
+        # cancellation of the terms in the division, and then exponentiate.
+        # That is,
+        #     exp(x)**c/Gamma(c+1) = exp(log(exp(x)**c/Gamma(c+1)))
+        #                          = exp(c*x - gammaln(c+1))
+        return xpx.apply_where(
+            x < _LOGXMIN, (x, c),
+            lambda x, c: np.exp(c*x - sc.gammaln(c+1)),
+            lambda x, c: sc.gammainc(c, np.exp(x)))
+
+    def _ppf(self, q, c):
+        # The expression used when g < _XMIN inverts the one term expansion
+        # given in the comments of _cdf().
+        g = sc.gammaincinv(c, q)
+        return xpx.apply_where(
+            g < _XMIN, (g, q, c),
+            lambda g, q, c: (np.log(q) + sc.gammaln(c+1))/c,
+            lambda g, q, c: np.log(g))
+
+    def _sf(self, x, c):
+        # See the comments for _cdf() for how x < _LOGXMIN is handled.
+        return xpx.apply_where(
+            x < _LOGXMIN, (x, c),
+            lambda x, c: -np.expm1(c*x - sc.gammaln(c+1)),
+            lambda x, c: sc.gammaincc(c, np.exp(x)))
+
+    def _isf(self, q, c):
+        # The expression used when g < _XMIN inverts the complement of
+        # the one term expansion given in the comments of _cdf().
+        g = sc.gammainccinv(c, q)
+        return xpx.apply_where(
+            g < _XMIN, (g, q, c),
+            lambda g, q, c: (np.log1p(-q) + sc.gammaln(c+1))/c,
+            lambda g, q, c: np.log(g))
+
+    def _stats(self, c):
+        # See, for example, "A Statistical Study of Log-Gamma Distribution", by
+        # Ping Shing Chan (thesis, McMaster University, 1993).
+        mean = sc.digamma(c)
+        var = sc.polygamma(1, c)
+        skewness = sc.polygamma(2, c) / np.power(var, 1.5)
+        excess_kurtosis = sc.polygamma(3, c) / (var*var)
+        return mean, var, skewness, excess_kurtosis
+
+    def _entropy(self, c):
+        def regular(c):
+            h = sc.gammaln(c) - c * sc.digamma(c) + c
+            return h
+
+        def asymptotic(c):
+            # using asymptotic expansions for gammaln and psi (see gh-18093)
+            term = -0.5*np.log(c) + c**-1./6 - c**-3./90 + c**-5./210
+            h = norm._entropy() + term
+            return h
+
+        return xpx.apply_where(c >= 45, c, asymptotic, regular)
+
+
+loggamma = loggamma_gen(name='loggamma')
+
+
+class loglaplace_gen(rv_continuous):
+    r"""A log-Laplace continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `loglaplace` is:
+
+    .. math::
+
+        f(x, c) = \begin{cases}\frac{c}{2} x^{ c-1}  &\text{for } 0 < x < 1\\
+                               \frac{c}{2} x^{-c-1}  &\text{for } x \ge 1
+                  \end{cases}
+
+    for :math:`c > 0`.
+
+    `loglaplace` takes ``c`` as a shape parameter for :math:`c`.
+
+    %(after_notes)s
+
+    Suppose a random variable ``X`` follows the Laplace distribution with
+    location ``a`` and scale ``b``.  Then ``Y = exp(X)`` follows the
+    log-Laplace distribution with ``c = 1 / b`` and ``scale = exp(a)``.
+
+    References
+    ----------
+    T.J. Kozubowski and K. Podgorski, "A log-Laplace growth rate model",
+    The Mathematical Scientist, vol. 28, pp. 49-60, 2003.
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("c", False, (0, np.inf), (False, False))]
+
+    def _pdf(self, x, c):
+        # loglaplace.pdf(x, c) = c / 2 * x**(c-1),   for 0 < x < 1
+        #                      = c / 2 * x**(-c-1),  for x >= 1
+        cd2 = c/2.0
+        c = np.where(x < 1, c, -c)
+        return cd2*x**(c-1)
+
+    def _cdf(self, x, c):
+        return np.where(x < 1, 0.5*x**c, 1-0.5*x**(-c))
+
+    def _sf(self, x, c):
+        return np.where(x < 1, 1 - 0.5*x**c, 0.5*x**(-c))
+
+    def _ppf(self, q, c):
+        return np.where(q < 0.5, (2.0*q)**(1.0/c), (2*(1.0-q))**(-1.0/c))
+
+    def _isf(self, q, c):
+        return np.where(q > 0.5, (2.0*(1.0 - q))**(1.0/c), (2*q)**(-1.0/c))
+
+    def _munp(self, n, c):
+        with np.errstate(divide='ignore'):
+            c2, n2 = c**2, n**2
+            return np.where(n2 < c2, c2 / (c2 - n2), np.inf)
+
+    def _entropy(self, c):
+        return np.log(2.0/c) + 1.0
+
+    @_call_super_mom
+    @inherit_docstring_from(rv_continuous)
+    def fit(self, data, *args, **kwds):
+        data, fc, floc, fscale = _check_fit_input_parameters(self, data,
+                                                             args, kwds)
+
+        # Specialize MLE only when location is known.
+        if floc is None:
+            return super(type(self), self).fit(data, *args, **kwds)
+
+        # Raise an error if any observation has zero likelihood.
+        if np.any(data <= floc):
+            raise FitDataError("loglaplace", lower=floc, upper=np.inf)
+
+        # Remove location from data.
+        if floc != 0:
+            data = data - floc
+
+        # When location is zero, the log-Laplace distribution is related to
+        # the Laplace distribution in that if X ~ Laplace(loc=a, scale=b),
+        # then Y = exp(X) ~ LogLaplace(c=1/b, loc=0, scale=exp(a)).  It can
+        # be shown that the MLE for Y is the same as the MLE for X = ln(Y).
+        # Therefore, we reuse the formulas from laplace.fit() and transform
+        # the result back into log-laplace's parameter space.
+        a, b = laplace.fit(np.log(data),
+                           floc=np.log(fscale) if fscale is not None else None,
+                           fscale=1/fc if fc is not None else None,
+                           method='mle')
+        loc = floc
+        scale = np.exp(a) if fscale is None else fscale
+        c = 1 / b if fc is None else fc
+        return c, loc, scale
+
+loglaplace = loglaplace_gen(a=0.0, name='loglaplace')
+
+
+def _lognorm_logpdf(x, s):
+    return xpx.apply_where(
+        x != 0, (x, s),
+        lambda x, s: (-np.log(x)**2 / (2 * s**2)
+                      - np.log(s * x * np.sqrt(2 * np.pi))),
+        fill_value=-np.inf)
+
+
+class lognorm_gen(rv_continuous):
+    r"""A lognormal continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `lognorm` is:
+
+    .. math::
+
+        f(x, s) = \frac{1}{s x \sqrt{2\pi}}
+                  \exp\left(-\frac{\log^2(x)}{2s^2}\right)
+
+    for :math:`x > 0`, :math:`s > 0`.
+
+    `lognorm` takes ``s`` as a shape parameter for :math:`s`.
+
+    %(after_notes)s
+
+    Suppose a normally distributed random variable ``X`` has  mean ``mu`` and
+    standard deviation ``sigma``. Then ``Y = exp(X)`` is lognormally
+    distributed with ``s = sigma`` and ``scale = exp(mu)``.
+
+    %(example)s
+
+    The logarithm of a log-normally distributed random variable is
+    normally distributed:
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy import stats
+    >>> fig, ax = plt.subplots(1, 1)
+    >>> mu, sigma = 2, 0.5
+    >>> X = stats.norm(loc=mu, scale=sigma)
+    >>> Y = stats.lognorm(s=sigma, scale=np.exp(mu))
+    >>> x = np.linspace(*X.interval(0.999))
+    >>> y = Y.rvs(size=10000)
+    >>> ax.plot(x, X.pdf(x), label='X (pdf)')
+    >>> ax.hist(np.log(y), density=True, bins=x, label='log(Y) (histogram)')
+    >>> ax.legend()
+    >>> plt.show()
+
+    """
+    _support_mask = rv_continuous._open_support_mask
+
+    def _shape_info(self):
+        return [_ShapeInfo("s", False, (0, np.inf), (False, False))]
+
+    def _rvs(self, s, size=None, random_state=None):
+        return np.exp(s * random_state.standard_normal(size))
+
+    def _pdf(self, x, s):
+        # lognorm.pdf(x, s) = 1 / (s*x*sqrt(2*pi)) * exp(-1/2*(log(x)/s)**2)
+        return np.exp(self._logpdf(x, s))
+
+    def _logpdf(self, x, s):
+        return _lognorm_logpdf(x, s)
+
+    def _cdf(self, x, s):
+        return _norm_cdf(np.log(x) / s)
+
+    def _logcdf(self, x, s):
+        return _norm_logcdf(np.log(x) / s)
+
+    def _ppf(self, q, s):
+        return np.exp(s * _norm_ppf(q))
+
+    def _sf(self, x, s):
+        return _norm_sf(np.log(x) / s)
+
+    def _logsf(self, x, s):
+        return _norm_logsf(np.log(x) / s)
+
+    def _isf(self, q, s):
+        return np.exp(s * _norm_isf(q))
+
+    def _stats(self, s):
+        p = np.exp(s*s)
+        mu = np.sqrt(p)
+        mu2 = p*(p-1)
+        g1 = np.sqrt(p-1)*(2+p)
+        g2 = np.polyval([1, 2, 3, 0, -6.0], p)
+        return mu, mu2, g1, g2
+
+    def _entropy(self, s):
+        return 0.5 * (1 + np.log(2*np.pi) + 2 * np.log(s))
+
+    @_call_super_mom
+    @extend_notes_in_docstring(rv_continuous, notes="""\
+        When `method='MLE'` and
+        the location parameter is fixed by using the `floc` argument,
+        this function uses explicit formulas for the maximum likelihood
+        estimation of the log-normal shape and scale parameters, so the
+        `optimizer`, `loc` and `scale` keyword arguments are ignored.
+        If the location is free, a likelihood maximum is found by
+        setting its partial derivative w.r.t. location to 0, and
+        solving by substituting the analytical expressions of shape
+        and scale (or provided parameters).
+        See, e.g., equation 3.1 in
+        A. Clifford Cohen & Betty Jones Whitten (1980)
+        Estimation in the Three-Parameter Lognormal Distribution,
+        Journal of the American Statistical Association, 75:370, 399-404
+        https://doi.org/10.2307/2287466
+        \n\n""")
+    def fit(self, data, *args, **kwds):
+        if kwds.pop('superfit', False):
+            return super().fit(data, *args, **kwds)
+
+        parameters = _check_fit_input_parameters(self, data, args, kwds)
+        data, fshape, floc, fscale = parameters
+        data_min = np.min(data)
+
+        def get_shape_scale(loc):
+            # Calculate maximum likelihood scale and shape with analytical
+            # formulas unless provided by the user
+            if fshape is None or fscale is None:
+                lndata = np.log(data - loc)
+            scale = fscale or np.exp(lndata.mean())
+            shape = fshape or np.sqrt(np.mean((lndata - np.log(scale))**2))
+            return shape, scale
+
+        def dL_dLoc(loc):
+            # Derivative of (positive) LL w.r.t. loc
+            shape, scale = get_shape_scale(loc)
+            shifted = data - loc
+            return np.sum((1 + np.log(shifted/scale)/shape**2)/shifted)
+
+        def ll(loc):
+            # (Positive) log-likelihood
+            shape, scale = get_shape_scale(loc)
+            return -self.nnlf((shape, loc, scale), data)
+
+        if floc is None:
+            # The location must be less than the minimum of the data.
+            # Back off a bit to avoid numerical issues.
+            spacing = np.spacing(data_min)
+            rbrack = data_min - spacing
+
+            # Find the right end of the bracket by successive doubling of the
+            # distance to data_min. We're interested in a maximum LL, so the
+            # slope dL_dLoc_rbrack should be negative at the right end.
+            # optimization for later: share shape, scale
+            dL_dLoc_rbrack = dL_dLoc(rbrack)
+            ll_rbrack = ll(rbrack)
+            delta = 2 * spacing  # 2 * (data_min - rbrack)
+            while dL_dLoc_rbrack >= -1e-6:
+                rbrack = data_min - delta
+                dL_dLoc_rbrack = dL_dLoc(rbrack)
+                delta *= 2
+
+            if not np.isfinite(rbrack) or not np.isfinite(dL_dLoc_rbrack):
+                # If we never find a negative slope, either we missed it or the
+                # slope is always positive. It's usually the latter,
+                # which means
+                # loc = data_min - spacing
+                # But sometimes when shape and/or scale are fixed there are
+                # other issues, so be cautious.
+                return super().fit(data, *args, **kwds)
+
+            # Now find the left end of the bracket. Guess is `rbrack-1`
+            # unless that is too small of a difference to resolve. Double
+            # the size of the interval until the left end is found.
+            lbrack = np.minimum(np.nextafter(rbrack, -np.inf), rbrack-1)
+            dL_dLoc_lbrack = dL_dLoc(lbrack)
+            delta = 2 * (rbrack - lbrack)
+            while (np.isfinite(lbrack) and np.isfinite(dL_dLoc_lbrack)
+                   and np.sign(dL_dLoc_lbrack) == np.sign(dL_dLoc_rbrack)):
+                lbrack = rbrack - delta
+                dL_dLoc_lbrack = dL_dLoc(lbrack)
+                delta *= 2
+
+            # I don't recall observing this, but just in case...
+            if not np.isfinite(lbrack) or not np.isfinite(dL_dLoc_lbrack):
+                return super().fit(data, *args, **kwds)
+
+            # If we have a valid bracket, find the root
+            res = root_scalar(dL_dLoc, bracket=(lbrack, rbrack))
+            if not res.converged:
+                return super().fit(data, *args, **kwds)
+
+            # If the slope was positive near the minimum of the data,
+            # the maximum LL could be there instead of at the root. Compare
+            # the LL of the two points to decide.
+            ll_root = ll(res.root)
+            loc = res.root if ll_root > ll_rbrack else data_min-spacing
+
+        else:
+            if floc >= data_min:
+                raise FitDataError("lognorm", lower=0., upper=np.inf)
+            loc = floc
+
+        shape, scale = get_shape_scale(loc)
+        if not (self._argcheck(shape) and scale > 0):
+            return super().fit(data, *args, **kwds)
+        return shape, loc, scale
+
+
+lognorm = lognorm_gen(a=0.0, name='lognorm')
+
+
+class gibrat_gen(rv_continuous):
+    r"""A Gibrat continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `gibrat` is:
+
+    .. math::
+
+        f(x) = \frac{1}{x \sqrt{2\pi}} \exp(-\frac{1}{2} (\log(x))^2)
+
+    for :math:`x >= 0`.
+
+    `gibrat` is a special case of `lognorm` with ``s=1``.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    _support_mask = rv_continuous._open_support_mask
+
+    def _shape_info(self):
+        return []
+
+    def _rvs(self, size=None, random_state=None):
+        return np.exp(random_state.standard_normal(size))
+
+    def _pdf(self, x):
+        # gibrat.pdf(x) = 1/(x*sqrt(2*pi)) * exp(-1/2*(log(x))**2)
+        return np.exp(self._logpdf(x))
+
+    def _logpdf(self, x):
+        return _lognorm_logpdf(x, 1.0)
+
+    def _cdf(self, x):
+        return _norm_cdf(np.log(x))
+
+    def _ppf(self, q):
+        return np.exp(_norm_ppf(q))
+
+    def _sf(self, x):
+        return _norm_sf(np.log(x))
+
+    def _isf(self, p):
+        return np.exp(_norm_isf(p))
+
+    def _stats(self):
+        p = np.e
+        mu = np.sqrt(p)
+        mu2 = p * (p - 1)
+        g1 = np.sqrt(p - 1) * (2 + p)
+        g2 = np.polyval([1, 2, 3, 0, -6.0], p)
+        return mu, mu2, g1, g2
+
+    def _entropy(self):
+        return 0.5 * np.log(2 * np.pi) + 0.5
+
+
+gibrat = gibrat_gen(a=0.0, name='gibrat')
+
+
+class maxwell_gen(rv_continuous):
+    r"""A Maxwell continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    A special case of a `chi` distribution,  with ``df=3``, ``loc=0.0``,
+    and given ``scale = a``, where ``a`` is the parameter used in the
+    Mathworld description [1]_.
+
+    The probability density function for `maxwell` is:
+
+    .. math::
+
+        f(x) = \sqrt{2/\pi}x^2 \exp(-x^2/2)
+
+    for :math:`x >= 0`.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] http://mathworld.wolfram.com/MaxwellDistribution.html
+
+    %(example)s
+    """
+    def _shape_info(self):
+        return []
+
+    def _rvs(self, size=None, random_state=None):
+        return chi.rvs(3.0, size=size, random_state=random_state)
+
+    def _pdf(self, x):
+        # maxwell.pdf(x) = sqrt(2/pi)x**2 * exp(-x**2/2)
+        return _SQRT_2_OVER_PI*x*x*np.exp(-x*x/2.0)
+
+    def _logpdf(self, x):
+        # Allow x=0 without 'divide by zero' warnings
+        with np.errstate(divide='ignore'):
+            return _LOG_SQRT_2_OVER_PI + 2*np.log(x) - 0.5*x*x
+
+    def _cdf(self, x):
+        return sc.gammainc(1.5, x*x/2.0)
+
+    def _ppf(self, q):
+        return np.sqrt(2*sc.gammaincinv(1.5, q))
+
+    def _sf(self, x):
+        return sc.gammaincc(1.5, x*x/2.0)
+
+    def _isf(self, q):
+        return np.sqrt(2*sc.gammainccinv(1.5, q))
+
+    def _stats(self):
+        val = 3*np.pi-8
+        return (2*np.sqrt(2.0/np.pi),
+                3-8/np.pi,
+                np.sqrt(2)*(32-10*np.pi)/val**1.5,
+                (-12*np.pi*np.pi + 160*np.pi - 384) / val**2.0)
+
+    def _entropy(self):
+        return _EULER + 0.5*np.log(2*np.pi)-0.5
+
+
+maxwell = maxwell_gen(a=0.0, name='maxwell')
+
+
+class mielke_gen(rv_continuous):
+    r"""A Mielke Beta-Kappa / Dagum continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `mielke` is:
+
+    .. math::
+
+        f(x, k, s) = \frac{k x^{k-1}}{(1+x^s)^{1+k/s}}
+
+    for :math:`x > 0` and :math:`k, s > 0`. The distribution is sometimes
+    called Dagum distribution ([2]_). It was already defined in [3]_, called
+    a Burr Type III distribution (`burr` with parameters ``c=s`` and
+    ``d=k/s``).
+
+    `mielke` takes ``k`` and ``s`` as shape parameters.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] Mielke, P.W., 1973 "Another Family of Distributions for Describing
+           and Analyzing Precipitation Data." J. Appl. Meteor., 12, 275-280
+    .. [2] Dagum, C., 1977 "A new model for personal income distribution."
+           Economie Appliquee, 33, 327-367.
+    .. [3] Burr, I. W. "Cumulative frequency functions", Annals of
+           Mathematical Statistics, 13(2), pp 215-232 (1942).
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        ik = _ShapeInfo("k", False, (0, np.inf), (False, False))
+        i_s = _ShapeInfo("s", False, (0, np.inf), (False, False))
+        return [ik, i_s]
+
+    def _pdf(self, x, k, s):
+        return k*x**(k-1.0) / (1.0+x**s)**(1.0+k*1.0/s)
+
+    def _logpdf(self, x, k, s):
+        # Allow x=0 without 'divide by zero' warnings.
+        with np.errstate(divide='ignore'):
+            return np.log(k) + np.log(x)*(k - 1) - np.log1p(x**s)*(1 + k/s)
+
+    def _cdf(self, x, k, s):
+        return x**k / (1.0+x**s)**(k*1.0/s)
+
+    def _ppf(self, q, k, s):
+        qsk = pow(q, s*1.0/k)
+        return pow(qsk/(1.0-qsk), 1.0/s)
+
+    def _munp(self, n, k, s):
+        def nth_moment(n, k, s):
+            # n-th moment is defined for -k < n < s
+            return sc.gamma((k+n)/s)*sc.gamma(1-n/s)/sc.gamma(k/s)
+
+        return xpx.apply_where(n < s, (n, k, s), nth_moment, fill_value=np.inf)
+
+
+mielke = mielke_gen(a=0.0, name='mielke')
+
+
+class kappa4_gen(rv_continuous):
+    r"""Kappa 4 parameter distribution.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for kappa4 is:
+
+    .. math::
+
+        f(x, h, k) = (1 - k x)^{1/k - 1} (1 - h (1 - k x)^{1/k})^{1/h-1}
+
+    if :math:`h` and :math:`k` are not equal to 0.
+
+    If :math:`h` or :math:`k` are zero then the pdf can be simplified:
+
+    :math:`h = 0` and :math:`k \neq 0`::
+
+        kappa4.pdf(x, h, k) = (1.0 - k*x)**(1.0/k - 1.0)*
+                              exp(-(1.0 - k*x)**(1.0/k))
+
+    :math:`h \neq 0` and :math:`k = 0`::
+
+        kappa4.pdf(x, h, k) = exp(-x)*(1.0 - h*exp(-x))**(1.0/h - 1.0)
+
+    :math:`h = 0` and :math:`k = 0`::
+
+        kappa4.pdf(x, h, k) = exp(-x)*exp(-exp(-x))
+
+    kappa4 takes :math:`h` and :math:`k` as shape parameters.
+
+    The kappa4 distribution returns other distributions when certain
+    :math:`h` and :math:`k` values are used.
+
+    +------+-------------+----------------+------------------+
+    | h    | k=0.0       | k=1.0          | -inf<=k<=inf     |
+    +======+=============+================+==================+
+    | -1.0 | Logistic    |                | Generalized      |
+    |      |             |                | Logistic(1)      |
+    |      |             |                |                  |
+    |      | logistic(x) |                |                  |
+    +------+-------------+----------------+------------------+
+    |  0.0 | Gumbel      | Reverse        | Generalized      |
+    |      |             | Exponential(2) | Extreme Value    |
+    |      |             |                |                  |
+    |      | gumbel_r(x) |                | genextreme(x, k) |
+    +------+-------------+----------------+------------------+
+    |  1.0 | Exponential | Uniform        | Generalized      |
+    |      |             |                | Pareto           |
+    |      |             |                |                  |
+    |      | expon(x)    | uniform(x)     | genpareto(x, -k) |
+    +------+-------------+----------------+------------------+
+
+    (1) There are at least five generalized logistic distributions.
+        Four are described here:
+        https://en.wikipedia.org/wiki/Generalized_logistic_distribution
+        The "fifth" one is the one kappa4 should match which currently
+        isn't implemented in scipy:
+        https://en.wikipedia.org/wiki/Talk:Generalized_logistic_distribution
+        https://www.mathwave.com/help/easyfit/html/analyses/distributions/gen_logistic.html
+    (2) This distribution is currently not in scipy.
+
+    References
+    ----------
+    J.C. Finney, "Optimization of a Skewed Logistic Distribution With Respect
+    to the Kolmogorov-Smirnov Test", A Dissertation Submitted to the Graduate
+    Faculty of the Louisiana State University and Agricultural and Mechanical
+    College, (August, 2004),
+    https://digitalcommons.lsu.edu/gradschool_dissertations/3672
+
+    J.R.M. Hosking, "The four-parameter kappa distribution". IBM J. Res.
+    Develop. 38 (3), 25 1-258 (1994).
+
+    B. Kumphon, A. Kaew-Man, P. Seenoi, "A Rainfall Distribution for the Lampao
+    Site in the Chi River Basin, Thailand", Journal of Water Resource and
+    Protection, vol. 4, 866-869, (2012).
+    :doi:`10.4236/jwarp.2012.410101`
+
+    C. Winchester, "On Estimation of the Four-Parameter Kappa Distribution", A
+    Thesis Submitted to Dalhousie University, Halifax, Nova Scotia, (March
+    2000).
+    http://www.nlc-bnc.ca/obj/s4/f2/dsk2/ftp01/MQ57336.pdf
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _argcheck(self, h, k):
+        shape = np.broadcast_arrays(h, k)[0].shape
+        return np.full(shape, fill_value=True)
+
+    def _shape_info(self):
+        ih = _ShapeInfo("h", False, (-np.inf, np.inf), (False, False))
+        ik = _ShapeInfo("k", False, (-np.inf, np.inf), (False, False))
+        return [ih, ik]
+
+    def _get_support(self, h, k):
+        condlist = [np.logical_and(h > 0, k > 0),
+                    np.logical_and(h > 0, k == 0),
+                    np.logical_and(h > 0, k < 0),
+                    np.logical_and(h <= 0, k > 0),
+                    np.logical_and(h <= 0, k == 0),
+                    np.logical_and(h <= 0, k < 0)]
+
+        def f0(h, k):
+            return (1.0 - np.float_power(h, -k))/k
+
+        def f1(h, k):
+            return np.log(h)
+
+        def f3(h, k):
+            a = np.empty(np.shape(h))
+            a[:] = -np.inf
+            return a
+
+        def f5(h, k):
+            return 1.0/k
+
+        _a = _lazyselect(condlist,
+                         [f0, f1, f0, f3, f3, f5],
+                         [h, k],
+                         default=np.nan)
+
+        def f0(h, k):
+            return 1.0/k
+
+        def f1(h, k):
+            a = np.empty(np.shape(h))
+            a[:] = np.inf
+            return a
+
+        _b = _lazyselect(condlist,
+                         [f0, f1, f1, f0, f1, f1],
+                         [h, k],
+                         default=np.nan)
+        return _a, _b
+
+    def _pdf(self, x, h, k):
+        # kappa4.pdf(x, h, k) = (1.0 - k*x)**(1.0/k - 1.0)*
+        #                       (1.0 - h*(1.0 - k*x)**(1.0/k))**(1.0/h-1)
+        return np.exp(self._logpdf(x, h, k))
+
+    def _logpdf(self, x, h, k):
+        condlist = [np.logical_and(h != 0, k != 0),
+                    np.logical_and(h == 0, k != 0),
+                    np.logical_and(h != 0, k == 0),
+                    np.logical_and(h == 0, k == 0)]
+
+        def f0(x, h, k):
+            '''pdf = (1.0 - k*x)**(1.0/k - 1.0)*(
+                      1.0 - h*(1.0 - k*x)**(1.0/k))**(1.0/h-1.0)
+               logpdf = ...
+            '''
+            return (sc.xlog1py(1.0/k - 1.0, -k*x) +
+                    sc.xlog1py(1.0/h - 1.0, -h*(1.0 - k*x)**(1.0/k)))
+
+        def f1(x, h, k):
+            '''pdf = (1.0 - k*x)**(1.0/k - 1.0)*np.exp(-(
+                      1.0 - k*x)**(1.0/k))
+               logpdf = ...
+            '''
+            return sc.xlog1py(1.0/k - 1.0, -k*x) - (1.0 - k*x)**(1.0/k)
+
+        def f2(x, h, k):
+            '''pdf = np.exp(-x)*(1.0 - h*np.exp(-x))**(1.0/h - 1.0)
+               logpdf = ...
+            '''
+            return -x + sc.xlog1py(1.0/h - 1.0, -h*np.exp(-x))
+
+        def f3(x, h, k):
+            '''pdf = np.exp(-x-np.exp(-x))
+               logpdf = ...
+            '''
+            return -x - np.exp(-x)
+
+        return _lazyselect(condlist,
+                           [f0, f1, f2, f3],
+                           [x, h, k],
+                           default=np.nan)
+
+    def _cdf(self, x, h, k):
+        return np.exp(self._logcdf(x, h, k))
+
+    def _logcdf(self, x, h, k):
+        condlist = [np.logical_and(h != 0, k != 0),
+                    np.logical_and(h == 0, k != 0),
+                    np.logical_and(h != 0, k == 0),
+                    np.logical_and(h == 0, k == 0)]
+
+        def f0(x, h, k):
+            '''cdf = (1.0 - h*(1.0 - k*x)**(1.0/k))**(1.0/h)
+               logcdf = ...
+            '''
+            return (1.0/h)*sc.log1p(-h*(1.0 - k*x)**(1.0/k))
+
+        def f1(x, h, k):
+            '''cdf = np.exp(-(1.0 - k*x)**(1.0/k))
+               logcdf = ...
+            '''
+            return -(1.0 - k*x)**(1.0/k)
+
+        def f2(x, h, k):
+            '''cdf = (1.0 - h*np.exp(-x))**(1.0/h)
+               logcdf = ...
+            '''
+            return (1.0/h)*sc.log1p(-h*np.exp(-x))
+
+        def f3(x, h, k):
+            '''cdf = np.exp(-np.exp(-x))
+               logcdf = ...
+            '''
+            return -np.exp(-x)
+
+        return _lazyselect(condlist,
+                           [f0, f1, f2, f3],
+                           [x, h, k],
+                           default=np.nan)
+
+    def _ppf(self, q, h, k):
+        condlist = [np.logical_and(h != 0, k != 0),
+                    np.logical_and(h == 0, k != 0),
+                    np.logical_and(h != 0, k == 0),
+                    np.logical_and(h == 0, k == 0)]
+
+        def f0(q, h, k):
+            return 1.0/k*(1.0 - ((1.0 - (q**h))/h)**k)
+
+        def f1(q, h, k):
+            return 1.0/k*(1.0 - (-np.log(q))**k)
+
+        def f2(q, h, k):
+            '''ppf = -np.log((1.0 - (q**h))/h)
+            '''
+            return -sc.log1p(-(q**h)) + np.log(h)
+
+        def f3(q, h, k):
+            return -np.log(-np.log(q))
+
+        return _lazyselect(condlist,
+                           [f0, f1, f2, f3],
+                           [q, h, k],
+                           default=np.nan)
+
+    def _get_stats_info(self, h, k):
+        condlist = [
+            np.logical_and(h < 0, k >= 0),
+            k < 0,
+        ]
+
+        def f0(h, k):
+            return (-1.0/h*k).astype(int)
+
+        def f1(h, k):
+            return (-1.0/k).astype(int)
+
+        return _lazyselect(condlist, [f0, f1], [h, k], default=5)
+
+    def _stats(self, h, k):
+        maxr = self._get_stats_info(h, k)
+        outputs = [None if np.any(r < maxr) else np.nan for r in range(1, 5)]
+        return outputs[:]
+
+    def _mom1_sc(self, m, *args):
+        maxr = self._get_stats_info(args[0], args[1])
+        if m >= maxr:
+            return np.nan
+        return integrate.quad(self._mom_integ1, 0, 1, args=(m,)+args)[0]
+
+
+kappa4 = kappa4_gen(name='kappa4')
+
+
+class kappa3_gen(rv_continuous):
+    r"""Kappa 3 parameter distribution.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `kappa3` is:
+
+    .. math::
+
+        f(x, a) = a (a + x^a)^{-(a + 1)/a}
+
+    for :math:`x > 0` and :math:`a > 0`.
+
+    `kappa3` takes ``a`` as a shape parameter for :math:`a`.
+
+    References
+    ----------
+    P.W. Mielke and E.S. Johnson, "Three-Parameter Kappa Distribution Maximum
+    Likelihood and Likelihood Ratio Tests", Methods in Weather Research,
+    701-707, (September, 1973),
+    :doi:`10.1175/1520-0493(1973)101<0701:TKDMLE>2.3.CO;2`
+
+    B. Kumphon, "Maximum Entropy and Maximum Likelihood Estimation for the
+    Three-Parameter Kappa Distribution", Open Journal of Statistics, vol 2,
+    415-419 (2012), :doi:`10.4236/ojs.2012.24050`
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("a", False, (0, np.inf), (False, False))]
+
+    def _pdf(self, x, a):
+        # kappa3.pdf(x, a) = a*(a + x**a)**(-(a + 1)/a),     for x > 0
+        return a*(a + x**a)**(-1.0/a-1)
+
+    def _cdf(self, x, a):
+        return x*(a + x**a)**(-1.0/a)
+
+    def _sf(self, x, a):
+        x, a = np.broadcast_arrays(x, a)  # some code paths pass scalars
+        sf = super()._sf(x, a)
+
+        # When the SF is small, another formulation is typically more accurate.
+        # However, it blows up for large `a`, so use it only if it also returns
+        # a small value of the SF.
+        cutoff = 0.01
+        i = sf < cutoff
+        sf2 = -sc.expm1(sc.xlog1py(-1.0 / a[i], a[i] * x[i]**-a[i]))
+        i2 = sf2 > cutoff
+        sf2[i2] = sf[i][i2]  # replace bad values with original values
+
+        sf[i] = sf2
+        return sf
+
+    def _ppf(self, q, a):
+        return (a/(q**-a - 1.0))**(1.0/a)
+
+    def _isf(self, q, a):
+        lg = sc.xlog1py(-a, -q)
+        denom = sc.expm1(lg)
+        return (a / denom)**(1.0 / a)
+
+    def _stats(self, a):
+        outputs = [None if np.any(i < a) else np.nan for i in range(1, 5)]
+        return outputs[:]
+
+    def _mom1_sc(self, m, *args):
+        if np.any(m >= args[0]):
+            return np.nan
+        return integrate.quad(self._mom_integ1, 0, 1, args=(m,)+args)[0]
+
+
+kappa3 = kappa3_gen(a=0.0, name='kappa3')
+
+
+class moyal_gen(rv_continuous):
+    r"""A Moyal continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `moyal` is:
+
+    .. math::
+
+        f(x) = \exp(-(x + \exp(-x))/2) / \sqrt{2\pi}
+
+    for a real number :math:`x`.
+
+    %(after_notes)s
+
+    This distribution has utility in high-energy physics and radiation
+    detection. It describes the energy loss of a charged relativistic
+    particle due to ionization of the medium [1]_. It also provides an
+    approximation for the Landau distribution. For an in depth description
+    see [2]_. For additional description, see [3]_.
+
+    References
+    ----------
+    .. [1] J.E. Moyal, "XXX. Theory of ionization fluctuations",
+           The London, Edinburgh, and Dublin Philosophical Magazine
+           and Journal of Science, vol 46, 263-280, (1955).
+           :doi:`10.1080/14786440308521076` (gated)
+    .. [2] G. Cordeiro et al., "The beta Moyal: A useful skew distribution",
+           International Journal of Research and Reviews in Applied Sciences,
+           vol 10, 171-192, (2012).
+           https://www.arpapress.com/files/volumes/vol10issue2/ijrras_10_2_02.pdf
+    .. [3] C. Walck, "Handbook on Statistical Distributions for
+           Experimentalists; International Report SUF-PFY/96-01", Chapter 26,
+           University of Stockholm: Stockholm, Sweden, (2007).
+           http://www.stat.rice.edu/~dobelman/textfiles/DistributionsHandbook.pdf
+
+    .. versionadded:: 1.1.0
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return []
+
+    def _rvs(self, size=None, random_state=None):
+        u1 = gamma.rvs(a=0.5, scale=2, size=size,
+                       random_state=random_state)
+        return -np.log(u1)
+
+    def _pdf(self, x):
+        return np.exp(-0.5 * (x + np.exp(-x))) / np.sqrt(2*np.pi)
+
+    def _cdf(self, x):
+        return sc.erfc(np.exp(-0.5 * x) / np.sqrt(2))
+
+    def _sf(self, x):
+        return sc.erf(np.exp(-0.5 * x) / np.sqrt(2))
+
+    def _ppf(self, x):
+        return -np.log(2 * sc.erfcinv(x)**2)
+
+    def _stats(self):
+        mu = np.log(2) + np.euler_gamma
+        mu2 = np.pi**2 / 2
+        g1 = 28 * np.sqrt(2) * sc.zeta(3) / np.pi**3
+        g2 = 4.
+        return mu, mu2, g1, g2
+
+    def _munp(self, n):
+        if n == 1.0:
+            return np.log(2) + np.euler_gamma
+        elif n == 2.0:
+            return np.pi**2 / 2 + (np.log(2) + np.euler_gamma)**2
+        elif n == 3.0:
+            tmp1 = 1.5 * np.pi**2 * (np.log(2)+np.euler_gamma)
+            tmp2 = (np.log(2)+np.euler_gamma)**3
+            tmp3 = 14 * sc.zeta(3)
+            return tmp1 + tmp2 + tmp3
+        elif n == 4.0:
+            tmp1 = 4 * 14 * sc.zeta(3) * (np.log(2) + np.euler_gamma)
+            tmp2 = 3 * np.pi**2 * (np.log(2) + np.euler_gamma)**2
+            tmp3 = (np.log(2) + np.euler_gamma)**4
+            tmp4 = 7 * np.pi**4 / 4
+            return tmp1 + tmp2 + tmp3 + tmp4
+        else:
+            # return generic for higher moments
+            # return rv_continuous._mom1_sc(self, n, b)
+            return self._mom1_sc(n)
+
+
+moyal = moyal_gen(name="moyal")
+
+
+class nakagami_gen(rv_continuous):
+    r"""A Nakagami continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `nakagami` is:
+
+    .. math::
+
+        f(x, \nu) = \frac{2 \nu^\nu}{\Gamma(\nu)} x^{2\nu-1} \exp(-\nu x^2)
+
+    for :math:`x >= 0`, :math:`\nu > 0`. The distribution was introduced in
+    [2]_, see also [1]_ for further information.
+
+    `nakagami` takes ``nu`` as a shape parameter for :math:`\nu`.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] "Nakagami distribution", Wikipedia
+           https://en.wikipedia.org/wiki/Nakagami_distribution
+    .. [2] M. Nakagami, "The m-distribution - A general formula of intensity
+           distribution of rapid fading", Statistical methods in radio wave
+           propagation, Pergamon Press, 1960, 3-36.
+           :doi:`10.1016/B978-0-08-009306-2.50005-4`
+
+    %(example)s
+
+    """
+    def _argcheck(self, nu):
+        return nu > 0
+
+    def _shape_info(self):
+        return [_ShapeInfo("nu", False, (0, np.inf), (False, False))]
+
+    def _pdf(self, x, nu):
+        return np.exp(self._logpdf(x, nu))
+
+    def _logpdf(self, x, nu):
+        # nakagami.pdf(x, nu) = 2 * nu**nu / gamma(nu) *
+        #                       x**(2*nu-1) * exp(-nu*x**2)
+        return (np.log(2) + sc.xlogy(nu, nu) - sc.gammaln(nu) +
+                sc.xlogy(2*nu - 1, x) - nu*x**2)
+
+    def _cdf(self, x, nu):
+        return sc.gammainc(nu, nu*x*x)
+
+    def _ppf(self, q, nu):
+        return np.sqrt(1.0/nu*sc.gammaincinv(nu, q))
+
+    def _sf(self, x, nu):
+        return sc.gammaincc(nu, nu*x*x)
+
+    def _isf(self, p, nu):
+        return np.sqrt(1/nu * sc.gammainccinv(nu, p))
+
+    def _stats(self, nu):
+        mu = sc.poch(nu, 0.5)/np.sqrt(nu)
+        mu2 = 1.0-mu*mu
+        g1 = mu * (1 - 4*nu*mu2) / 2.0 / nu / np.power(mu2, 1.5)
+        g2 = -6*mu**4*nu + (8*nu-2)*mu**2-2*nu + 1
+        g2 /= nu*mu2**2.0
+        return mu, mu2, g1, g2
+
+    def _entropy(self, nu):
+        shape = np.shape(nu)
+        # because somehow this isn't taken care of by the infrastructure...
+        nu = np.atleast_1d(nu)
+        A = sc.gammaln(nu)
+        B = nu - (nu - 0.5) * sc.digamma(nu)
+        C = -0.5 * np.log(nu) - np.log(2)
+        h = A + B + C
+        # This is the asymptotic sum of A and B (see gh-17868)
+        norm_entropy = stats.norm._entropy()
+        # Above, this is lost to rounding error for large nu, so use the
+        # asymptotic sum when the approximation becomes accurate
+        i = nu > 5e4  # roundoff error ~ approximation error
+        # -1 / (12 * nu) is the O(1/nu) term; see gh-17929
+        h[i] = C[i] + norm_entropy - 1/(12*nu[i])
+        return h.reshape(shape)[()]
+
+    def _rvs(self, nu, size=None, random_state=None):
+        # this relationship can be found in [1] or by a direct calculation
+        return np.sqrt(random_state.standard_gamma(nu, size=size) / nu)
+
+    def _fitstart(self, data, args=None):
+        if isinstance(data, CensoredData):
+            data = data._uncensor()
+        if args is None:
+            args = (1.0,) * self.numargs
+        # Analytical justified estimates
+        # see: https://docs.scipy.org/doc/scipy/reference/tutorial/stats/continuous_nakagami.html
+        loc = np.min(data)
+        scale = np.sqrt(np.sum((data - loc)**2) / len(data))
+        return args + (loc, scale)
+
+
+nakagami = nakagami_gen(a=0.0, name="nakagami")
+
+
+# The function name ncx2 is an abbreviation for noncentral chi squared.
+def _ncx2_log_pdf(x, df, nc):
+    # We use (xs**2 + ns**2)/2 = (xs - ns)**2/2  + xs*ns, and include the
+    # factor of exp(-xs*ns) into the ive function to improve numerical
+    # stability at large values of xs. See also `rice.pdf`.
+    df2 = df/2.0 - 1.0
+    xs, ns = np.sqrt(x), np.sqrt(nc)
+    res = sc.xlogy(df2/2.0, x/nc) - 0.5*(xs - ns)**2
+    corr = sc.ive(df2, xs*ns) / 2.0
+    # Return res + np.log(corr) avoiding np.log(0)
+    return xpx.apply_where(
+        corr > 0,
+        (res, corr),
+        lambda r, c: r + np.log(c),
+        fill_value=-np.inf)
+
+
+class ncx2_gen(rv_continuous):
+    r"""A non-central chi-squared continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `ncx2` is:
+
+    .. math::
+
+        f(x, k, \lambda) = \frac{1}{2} \exp(-(\lambda+x)/2)
+            (x/\lambda)^{(k-2)/4}  I_{(k-2)/2}(\sqrt{\lambda x})
+
+    for :math:`x >= 0`, :math:`k > 0` and :math:`\lambda \ge 0`.
+    :math:`k` specifies the degrees of freedom (denoted ``df`` in the
+    implementation) and :math:`\lambda` is the non-centrality parameter
+    (denoted ``nc`` in the implementation). :math:`I_\nu` denotes the
+    modified Bessel function of first order of degree :math:`\nu`
+    (`scipy.special.iv`).
+
+    `ncx2` takes ``df`` and ``nc`` as shape parameters.
+
+    This distribution uses routines from the Boost Math C++ library for
+    the computation of the ``pdf``, ``cdf``, ``ppf``, ``sf`` and ``isf``
+    methods. [1]_
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    %(example)s
+
+    """
+    def _argcheck(self, df, nc):
+        return (df > 0) & np.isfinite(df) & (nc >= 0)
+
+    def _shape_info(self):
+        idf = _ShapeInfo("df", False, (0, np.inf), (False, False))
+        inc = _ShapeInfo("nc", False, (0, np.inf), (True, False))
+        return [idf, inc]
+
+    def _rvs(self, df, nc, size=None, random_state=None):
+        return random_state.noncentral_chisquare(df, nc, size)
+
+    def _logpdf(self, x, df, nc):
+        return xpx.apply_where(nc != 0, (x, df, nc), _ncx2_log_pdf,
+                               lambda x, df, _: chi2._logpdf(x, df))
+
+    def _pdf(self, x, df, nc):
+        with np.errstate(over='ignore'):  # see gh-17432
+            return xpx.apply_where(nc != 0, (x, df, nc), scu._ncx2_pdf,
+                                   lambda x, df, _: chi2._pdf(x, df))
+
+    def _cdf(self, x, df, nc):
+        with np.errstate(over='ignore'):  # see gh-17432
+            return xpx.apply_where(nc != 0, (x, df, nc), sc.chndtr,
+                                   lambda x, df, _: chi2._cdf(x, df))
+
+    def _ppf(self, q, df, nc):
+        with np.errstate(over='ignore'):  # see gh-17432
+            return xpx.apply_where(nc != 0, (q, df, nc), sc.chndtrix,
+                                   lambda x, df, _: chi2._ppf(x, df))
+
+    def _sf(self, x, df, nc):
+        with np.errstate(over='ignore'):  # see gh-17432
+            return xpx.apply_where(nc != 0, (x, df, nc), scu._ncx2_sf,
+                                   lambda x, df, _: chi2._sf(x, df))
+
+    def _isf(self, x, df, nc):
+        with np.errstate(over='ignore'):  # see gh-17432
+            return xpx.apply_where(nc != 0, (x, df, nc), scu._ncx2_isf,
+                                   lambda x, df, _: chi2._isf(x, df))
+
+    def _stats(self, df, nc):
+        _ncx2_mean = df + nc
+        def k_plus_cl(k, l, c):
+            return k + c*l
+        _ncx2_variance =  2.0 * k_plus_cl(df, nc, 2.0)
+        _ncx2_skewness = (np.sqrt(8.0) * k_plus_cl(df, nc, 3) /
+                          np.sqrt(k_plus_cl(df, nc, 2.0)**3))
+        _ncx2_kurtosis_excess = (12.0 * k_plus_cl(df, nc, 4.0) /
+                                 k_plus_cl(df, nc, 2.0)**2)
+        return (
+            _ncx2_mean,
+            _ncx2_variance,
+            _ncx2_skewness,
+            _ncx2_kurtosis_excess,
+        )
+
+
+ncx2 = ncx2_gen(a=0.0, name='ncx2')
+
+
+class ncf_gen(rv_continuous):
+    r"""A non-central F distribution continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    scipy.stats.f : Fisher distribution
+
+    Notes
+    -----
+    The probability density function for `ncf` is:
+
+    .. math::
+
+        f(x, n_1, n_2, \lambda) =
+            \exp\left(\frac{\lambda}{2} +
+                      \lambda n_1 \frac{x}{2(n_1 x + n_2)}
+                \right)
+            n_1^{n_1/2} n_2^{n_2/2} x^{n_1/2 - 1} \\
+            (n_2 + n_1 x)^{-(n_1 + n_2)/2}
+            \gamma(n_1/2) \gamma(1 + n_2/2) \\
+            \frac{L^{\frac{n_1}{2}-1}_{n_2/2}
+                \left(-\lambda n_1 \frac{x}{2(n_1 x + n_2)}\right)}
+            {B(n_1/2, n_2/2)
+                \gamma\left(\frac{n_1 + n_2}{2}\right)}
+
+    for :math:`n_1, n_2 > 0`, :math:`\lambda \ge 0`.  Here :math:`n_1` is the
+    degrees of freedom in the numerator, :math:`n_2` the degrees of freedom in
+    the denominator, :math:`\lambda` the non-centrality parameter,
+    :math:`\gamma` is the logarithm of the Gamma function, :math:`L_n^k` is a
+    generalized Laguerre polynomial and :math:`B` is the beta function.
+
+    `ncf` takes ``dfn``, ``dfd`` and ``nc`` as shape parameters. If ``nc=0``,
+    the distribution becomes equivalent to the Fisher distribution.
+
+    This distribution uses routines from the Boost Math C++ library for
+    the computation of the ``pdf``, ``cdf``, ``ppf``, ``stats``, ``sf`` and
+    ``isf`` methods. [1]_
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    %(example)s
+
+    """
+    def _argcheck(self, dfn, dfd, nc):
+        return (dfn > 0) & (dfd > 0) & (nc >= 0)
+
+    def _shape_info(self):
+        idf1 = _ShapeInfo("dfn", False, (0, np.inf), (False, False))
+        idf2 = _ShapeInfo("dfd", False, (0, np.inf), (False, False))
+        inc = _ShapeInfo("nc", False, (0, np.inf), (True, False))
+        return [idf1, idf2, inc]
+
+    def _rvs(self, dfn, dfd, nc, size=None, random_state=None):
+        return random_state.noncentral_f(dfn, dfd, nc, size)
+
+    def _pdf(self, x, dfn, dfd, nc):
+        return scu._ncf_pdf(x, dfn, dfd, nc)
+
+    def _cdf(self, x, dfn, dfd, nc):
+        return sc.ncfdtr(dfn, dfd, nc, x)
+
+    def _ppf(self, q, dfn, dfd, nc):
+        with np.errstate(over='ignore'):  # see gh-17432
+            return sc.ncfdtri(dfn, dfd, nc, q)
+
+    def _sf(self, x, dfn, dfd, nc):
+        return scu._ncf_sf(x, dfn, dfd, nc)
+
+    def _isf(self, x, dfn, dfd, nc):
+        with np.errstate(over='ignore'):  # see gh-17432
+            return scu._ncf_isf(x, dfn, dfd, nc)
+
+    # # Produces bogus values as written - maybe it's close, though?
+    # def _munp(self, n, dfn, dfd, nc):
+    #     val = (dfn * 1.0/dfd)**n
+    #     term = sc.gammaln(n+0.5*dfn) + sc.gammaln(0.5*dfd-n) - sc.gammaln(dfd*0.5)
+    #     val *= np.exp(-nc / 2.0+term)
+    #     val *= sc.hyp1f1(n+0.5*dfn, 0.5*dfn, 0.5*nc)
+    #     return val
+
+    def _stats(self, dfn, dfd, nc, moments='mv'):
+        mu = scu._ncf_mean(dfn, dfd, nc)
+        mu2 = scu._ncf_variance(dfn, dfd, nc)
+        g1 = scu._ncf_skewness(dfn, dfd, nc) if 's' in moments else None
+        g2 = scu._ncf_kurtosis_excess(  # isn't really excess kurtosis!
+            dfn, dfd, nc) - 3 if 'k' in moments else None
+        # Mathematica: Kurtosis[NoncentralFRatioDistribution[27, 27, 0.415784417992261]]
+        return mu, mu2, g1, g2
+
+
+ncf = ncf_gen(a=0.0, name='ncf')
+
+
+class t_gen(rv_continuous):
+    r"""A Student's t continuous random variable.
+
+    For the noncentral t distribution, see `nct`.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    nct
+
+    Notes
+    -----
+    The probability density function for `t` is:
+
+    .. math::
+
+        f(x, \nu) = \frac{\Gamma((\nu+1)/2)}
+                        {\sqrt{\pi \nu} \Gamma(\nu/2)}
+                    (1+x^2/\nu)^{-(\nu+1)/2}
+
+    where :math:`x` is a real number and the degrees of freedom parameter
+    :math:`\nu` (denoted ``df`` in the implementation) satisfies
+    :math:`\nu > 0`. :math:`\Gamma` is the gamma function
+    (`scipy.special.gamma`).
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("df", False, (0, np.inf), (False, False))]
+
+    def _rvs(self, df, size=None, random_state=None):
+        return random_state.standard_t(df, size=size)
+
+    def _pdf(self, x, df):
+        return xpx.apply_where(
+            df == np.inf, (x, df),
+            lambda x, df: norm._pdf(x),
+            lambda x, df: np.exp(self._logpdf(x, df)))
+
+    def _logpdf(self, x, df):
+
+        def t_logpdf(x, df):
+            return (np.log(sc.poch(0.5 * df, 0.5))
+                    - 0.5 * (np.log(df) + np.log(np.pi))
+                    - (df + 1)/2*np.log1p(x * x/df))
+
+        def norm_logpdf(x, df):
+            return norm._logpdf(x)
+
+        return xpx.apply_where(df == np.inf, (x, df), norm_logpdf, t_logpdf)
+
+    def _cdf(self, x, df):
+        return sc.stdtr(df, x)
+
+    def _sf(self, x, df):
+        return sc.stdtr(df, -x)
+
+    def _ppf(self, q, df):
+        return sc.stdtrit(df, q)
+
+    def _isf(self, q, df):
+        return -sc.stdtrit(df, q)
+
+    def _stats(self, df):
+        # infinite df -> normal distribution (0.0, 1.0, 0.0, 0.0)
+        infinite_df = np.isposinf(df)
+
+        mu = np.where(df > 1, 0.0, np.inf)
+
+        condlist = ((df > 1) & (df <= 2),
+                    (df > 2) & np.isfinite(df),
+                    infinite_df)
+        choicelist = (lambda df: np.broadcast_to(np.inf, df.shape),
+                      lambda df: df / (df-2.0),
+                      lambda df: np.broadcast_to(1, df.shape))
+        mu2 = _lazyselect(condlist, choicelist, (df,), np.nan)
+
+        g1 = np.where(df > 3, 0.0, np.nan)
+
+        condlist = ((df > 2) & (df <= 4),
+                    (df > 4) & np.isfinite(df),
+                    infinite_df)
+        choicelist = (lambda df: np.broadcast_to(np.inf, df.shape),
+                      lambda df: 6.0 / (df-4.0),
+                      lambda df: np.broadcast_to(0, df.shape))
+        g2 = _lazyselect(condlist, choicelist, (df,), np.nan)
+
+        return mu, mu2, g1, g2
+
+    def _entropy(self, df):
+
+        def regular(df):
+            half = df/2
+            half1 = (df + 1)/2
+            return (half1*(sc.digamma(half1) - sc.digamma(half))
+                    + np.log(np.sqrt(df)*sc.beta(half, 0.5)))
+
+        def asymptotic(df):
+            # Formula from Wolfram Alpha:
+            # "asymptotic expansion (d+1)/2 * (digamma((d+1)/2) - digamma(d/2))
+            #  + log(sqrt(d) * beta(d/2, 1/2))"
+            h = (norm._entropy() + 1/df + (df**-2.)/4 - (df**-3.)/6
+                 - (df**-4.)/8 + 3/10*(df**-5.) + (df**-6.)/4)
+            return h
+
+        return xpx.apply_where(df >= 100, df, asymptotic, regular)
+
+
+t = t_gen(name='t')
+
+
+class nct_gen(rv_continuous):
+    r"""A non-central Student's t continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    If :math:`Y` is a standard normal random variable and :math:`V` is
+    an independent chi-square random variable (`chi2`) with :math:`k` degrees
+    of freedom, then
+
+    .. math::
+
+        X = \frac{Y + c}{\sqrt{V/k}}
+
+    has a non-central Student's t distribution on the real line.
+    The degrees of freedom parameter :math:`k` (denoted ``df`` in the
+    implementation) satisfies :math:`k > 0` and the noncentrality parameter
+    :math:`c` (denoted ``nc`` in the implementation) is a real number.
+
+    This distribution uses routines from the Boost Math C++ library for
+    the computation of the ``pdf``, ``cdf``, ``ppf``, ``sf`` and ``isf``
+    methods. [1]_
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    %(example)s
+
+    """
+    def _argcheck(self, df, nc):
+        return (df > 0) & (nc == nc)
+
+    def _shape_info(self):
+        idf = _ShapeInfo("df", False, (0, np.inf), (False, False))
+        inc = _ShapeInfo("nc", False, (-np.inf, np.inf), (False, False))
+        return [idf, inc]
+
+    def _rvs(self, df, nc, size=None, random_state=None):
+        n = norm.rvs(loc=nc, size=size, random_state=random_state)
+        c2 = chi2.rvs(df, size=size, random_state=random_state)
+        return n * np.sqrt(df) / np.sqrt(c2)
+
+    def _pdf(self, x, df, nc):
+        return scu._nct_pdf(x, df, nc)
+
+    def _cdf(self, x, df, nc):
+        return sc.nctdtr(df, nc, x)
+
+    def _ppf(self, q, df, nc):
+        return sc.nctdtrit(df, nc, q)
+
+    def _sf(self, x, df, nc):
+        with np.errstate(over='ignore'):  # see gh-17432
+            return np.clip(scu._nct_sf(x, df, nc), 0, 1)
+
+    def _isf(self, x, df, nc):
+        with np.errstate(over='ignore'):  # see gh-17432
+            return scu._nct_isf(x, df, nc)
+
+    def _stats(self, df, nc, moments='mv'):
+        mu = scu._nct_mean(df, nc)
+        mu2 = scu._nct_variance(df, nc)
+        g1 = scu._nct_skewness(df, nc) if 's' in moments else None
+        g2 = scu._nct_kurtosis_excess(df, nc) if 'k' in moments else None
+        return mu, mu2, g1, g2
+
+
+nct = nct_gen(name="nct")
+
+
+class pareto_gen(rv_continuous):
+    r"""A Pareto continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `pareto` is:
+
+    .. math::
+
+        f(x, b) = \frac{b}{x^{b+1}}
+
+    for :math:`x \ge 1`, :math:`b > 0`.
+
+    `pareto` takes ``b`` as a shape parameter for :math:`b`.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("b", False, (0, np.inf), (False, False))]
+
+    def _pdf(self, x, b):
+        # pareto.pdf(x, b) = b / x**(b+1)
+        return b * x**(-b-1)
+
+    def _cdf(self, x, b):
+        return 1 - x**(-b)
+
+    def _ppf(self, q, b):
+        return pow(1-q, -1.0/b)
+
+    def _sf(self, x, b):
+        return x**(-b)
+
+    def _isf(self, q, b):
+        return np.power(q, -1.0 / b)
+
+    def _stats(self, b, moments='mv'):
+        mu, mu2, g1, g2 = None, None, None, None
+        if 'm' in moments:
+            mask = b > 1
+            bt = np.extract(mask, b)
+            mu = np.full(np.shape(b), fill_value=np.inf)
+            np.place(mu, mask, bt / (bt-1.0))
+        if 'v' in moments:
+            mask = b > 2
+            bt = np.extract(mask, b)
+            mu2 = np.full(np.shape(b), fill_value=np.inf)
+            np.place(mu2, mask, bt / (bt-2.0) / (bt-1.0)**2)
+        if 's' in moments:
+            mask = b > 3
+            bt = np.extract(mask, b)
+            g1 = np.full(np.shape(b), fill_value=np.nan)
+            vals = 2 * (bt + 1.0) * np.sqrt(bt - 2.0) / ((bt - 3.0) * np.sqrt(bt))
+            np.place(g1, mask, vals)
+        if 'k' in moments:
+            mask = b > 4
+            bt = np.extract(mask, b)
+            g2 = np.full(np.shape(b), fill_value=np.nan)
+            vals = (6.0*np.polyval([1.0, 1.0, -6, -2], bt) /
+                    np.polyval([1.0, -7.0, 12.0, 0.0], bt))
+            np.place(g2, mask, vals)
+        return mu, mu2, g1, g2
+
+    def _entropy(self, b):
+        return 1 + 1.0/b - np.log(b)
+
+    @_call_super_mom
+    @inherit_docstring_from(rv_continuous)
+    def fit(self, data, *args, **kwds):
+        parameters = _check_fit_input_parameters(self, data, args, kwds)
+        data, fshape, floc, fscale = parameters
+
+        # ensure that any fixed parameters don't violate constraints of the
+        # distribution before continuing.
+        if floc is not None and np.min(data) - floc < (fscale or 0):
+            raise FitDataError("pareto", lower=1, upper=np.inf)
+
+        ndata = data.shape[0]
+
+        def get_shape(scale, location):
+            # The first-order necessary condition on `shape` can be solved in
+            # closed form
+            return ndata / np.sum(np.log((data - location) / scale))
+
+        if floc is fscale is None:
+            # The support of the distribution is `(x - loc)/scale > 0`.
+            # The method of Lagrange multipliers turns this constraint
+            # into an equation that can be solved numerically.
+            # See gh-12545 for details.
+
+            def dL_dScale(shape, scale):
+                # The partial derivative of the log-likelihood function w.r.t.
+                # the scale.
+                return ndata * shape / scale
+
+            def dL_dLocation(shape, location):
+                # The partial derivative of the log-likelihood function w.r.t.
+                # the location.
+                return (shape + 1) * np.sum(1 / (data - location))
+
+            def fun_to_solve(scale):
+                # optimize the scale by setting the partial derivatives
+                # w.r.t. location and scale equal and solving.
+                location = np.min(data) - scale
+                shape = fshape or get_shape(scale, location)
+                return dL_dLocation(shape, location) - dL_dScale(shape, scale)
+
+            def interval_contains_root(lbrack, rbrack):
+                # return true if the signs disagree.
+                return (np.sign(fun_to_solve(lbrack)) !=
+                        np.sign(fun_to_solve(rbrack)))
+
+            # set brackets for `root_scalar` to use when optimizing over the
+            # scale such that a root is likely between them. Use user supplied
+            # guess or default 1.
+            brack_start = float(kwds.get('scale', 1))
+            lbrack, rbrack = brack_start / 2, brack_start * 2
+            # if a root is not between the brackets, iteratively expand them
+            # until they include a sign change, checking after each bracket is
+            # modified.
+            while (not interval_contains_root(lbrack, rbrack)
+                   and (lbrack > 0 or rbrack < np.inf)):
+                lbrack /= 2
+                rbrack *= 2
+            res = root_scalar(fun_to_solve, bracket=[lbrack, rbrack])
+            if res.converged:
+                scale = res.root
+                loc = np.min(data) - scale
+                shape = fshape or get_shape(scale, loc)
+
+                # The Pareto distribution requires that its parameters satisfy
+                # the condition `fscale + floc <= min(data)`. However, to
+                # avoid numerical issues, we require that `fscale + floc`
+                # is strictly less than `min(data)`. If this condition
+                # is not satisfied, reduce the scale with `np.nextafter` to
+                # ensure that data does not fall outside of the support.
+                if not (scale + loc) < np.min(data):
+                    scale = np.min(data) - loc
+                    scale = np.nextafter(scale, 0)
+                return shape, loc, scale
+            else:
+                return super().fit(data, **kwds)
+        elif floc is None:
+            loc = np.min(data) - fscale
+        else:
+            loc = floc
+        # Source: Evans, Hastings, and Peacock (2000), Statistical
+        # Distributions, 3rd. Ed., John Wiley and Sons. Page 149.
+        scale = fscale or np.min(data) - loc
+        shape = fshape or get_shape(scale, loc)
+        return shape, loc, scale
+
+
+pareto = pareto_gen(a=1.0, name="pareto")
+
+
+class lomax_gen(rv_continuous):
+    r"""A Lomax (Pareto of the second kind) continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `lomax` is:
+
+    .. math::
+
+        f(x, c) = \frac{c}{(1+x)^{c+1}}
+
+    for :math:`x \ge 0`, :math:`c > 0`.
+
+    `lomax` takes ``c`` as a shape parameter for :math:`c`.
+
+    `lomax` is a special case of `pareto` with ``loc=-1.0``.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("c", False, (0, np.inf), (False, False))]
+
+    def _pdf(self, x, c):
+        # lomax.pdf(x, c) = c / (1+x)**(c+1)
+        return c*1.0/(1.0+x)**(c+1.0)
+
+    def _logpdf(self, x, c):
+        return np.log(c) - (c+1)*sc.log1p(x)
+
+    def _cdf(self, x, c):
+        return -sc.expm1(-c*sc.log1p(x))
+
+    def _sf(self, x, c):
+        return np.exp(-c*sc.log1p(x))
+
+    def _logsf(self, x, c):
+        return -c*sc.log1p(x)
+
+    def _ppf(self, q, c):
+        return sc.expm1(-sc.log1p(-q)/c)
+
+    def _isf(self, q, c):
+        return q**(-1.0 / c) - 1
+
+    def _stats(self, c):
+        mu, mu2, g1, g2 = pareto.stats(c, loc=-1.0, moments='mvsk')
+        return mu, mu2, g1, g2
+
+    def _entropy(self, c):
+        return 1+1.0/c-np.log(c)
+
+
+lomax = lomax_gen(a=0.0, name="lomax")
+
+
+class pearson3_gen(rv_continuous):
+    r"""
+    A pearson type III continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `pearson3` is:
+
+    .. math::
+
+        f(x, \kappa) = \frac{|\beta|}{\Gamma(\alpha)}
+                       (\beta (x - \zeta))^{\alpha - 1}
+                       \exp(-\beta (x - \zeta))
+
+    where:
+
+    .. math::
+
+            \beta = \frac{2}{\kappa}
+
+            \alpha = \beta^2 = \frac{4}{\kappa^2}
+
+            \zeta = -\frac{\alpha}{\beta} = -\beta
+
+    :math:`\Gamma` is the gamma function (`scipy.special.gamma`).
+    Pass the skew :math:`\kappa` into `pearson3` as the shape parameter
+    ``skew``.
+
+    %(after_notes)s
+
+    References
+    ----------
+    R.W. Vogel and D.E. McMartin, "Probability Plot Goodness-of-Fit and
+    Skewness Estimation Procedures for the Pearson Type 3 Distribution", Water
+    Resources Research, Vol.27, 3149-3158 (1991).
+
+    L.R. Salvosa, "Tables of Pearson's Type III Function", Ann. Math. Statist.,
+    Vol.1, 191-198 (1930).
+
+    "Using Modern Computing Tools to Fit the Pearson Type III Distribution to
+    Aviation Loads Data", Office of Aviation Research (2003).
+
+    %(example)s
+    """
+    def _preprocess(self, x, skew):
+        # The real 'loc' and 'scale' are handled in the calling pdf(...). The
+        # local variables 'loc' and 'scale' within pearson3._pdf are set to
+        # the defaults just to keep them as part of the equations for
+        # documentation.
+        loc = 0.0
+        scale = 1.0
+
+        # If skew is small, return _norm_pdf. The divide between pearson3
+        # and norm was found by brute force and is approximately a skew of
+        # 0.000016.  No one, I hope, would actually use a skew value even
+        # close to this small.
+        norm2pearson_transition = 0.000016
+
+        ans, x, skew = np.broadcast_arrays(1.0, x, skew)
+        ans = ans.copy()
+
+        # mask is True where skew is small enough to use the normal approx.
+        mask = np.absolute(skew) < norm2pearson_transition
+        invmask = ~mask
+
+        beta = 2.0 / (skew[invmask] * scale)
+        alpha = (scale * beta)**2
+        zeta = loc - alpha / beta
+
+        transx = beta * (x[invmask] - zeta)
+        return ans, x, transx, mask, invmask, beta, alpha, zeta
+
+    def _argcheck(self, skew):
+        # The _argcheck function in rv_continuous only allows positive
+        # arguments.  The skew argument for pearson3 can be zero (which I want
+        # to handle inside pearson3._pdf) or negative.  So just return True
+        # for all skew args.
+        return np.isfinite(skew)
+
+    def _shape_info(self):
+        return [_ShapeInfo("skew", False, (-np.inf, np.inf), (False, False))]
+
+    def _stats(self, skew):
+        m = 0.0
+        v = 1.0
+        s = skew
+        k = 1.5*skew**2
+        return m, v, s, k
+
+    def _pdf(self, x, skew):
+        # pearson3.pdf(x, skew) = abs(beta) / gamma(alpha) *
+        #     (beta * (x - zeta))**(alpha - 1) * exp(-beta*(x - zeta))
+        # Do the calculation in _logpdf since helps to limit
+        # overflow/underflow problems
+        ans = np.exp(self._logpdf(x, skew))
+        if ans.ndim == 0:
+            if np.isnan(ans):
+                return 0.0
+            return ans
+        ans[np.isnan(ans)] = 0.0
+        return ans
+
+    def _logpdf(self, x, skew):
+        #   PEARSON3 logpdf                           GAMMA logpdf
+        #   np.log(abs(beta))
+        # + (alpha - 1)*np.log(beta*(x - zeta))          + (a - 1)*np.log(x)
+        # - beta*(x - zeta)                           - x
+        # - sc.gammalnalpha)                              - sc.gammalna)
+        ans, x, transx, mask, invmask, beta, alpha, _ = (
+            self._preprocess(x, skew))
+
+        ans[mask] = np.log(_norm_pdf(x[mask]))
+        # use logpdf instead of _logpdf to fix issue mentioned in gh-12640
+        # (_logpdf does not return correct result for alpha = 1)
+        ans[invmask] = np.log(abs(beta)) + gamma.logpdf(transx, alpha)
+        return ans
+
+    def _cdf(self, x, skew):
+        ans, x, transx, mask, invmask, _, alpha, _ = (
+            self._preprocess(x, skew))
+
+        ans[mask] = _norm_cdf(x[mask])
+
+        skew = np.broadcast_to(skew, invmask.shape)
+        invmask1a = np.logical_and(invmask, skew > 0)
+        invmask1b = skew[invmask] > 0
+        # use cdf instead of _cdf to fix issue mentioned in gh-12640
+        # (_cdf produces NaNs for inputs outside support)
+        ans[invmask1a] = gamma.cdf(transx[invmask1b], alpha[invmask1b])
+
+        # The gamma._cdf approach wasn't working with negative skew.
+        # Note that multiplying the skew by -1 reflects about x=0.
+        # So instead of evaluating the CDF with negative skew at x,
+        # evaluate the SF with positive skew at -x.
+        invmask2a = np.logical_and(invmask, skew < 0)
+        invmask2b = skew[invmask] < 0
+        # gamma._sf produces NaNs when transx < 0, so use gamma.sf
+        ans[invmask2a] = gamma.sf(transx[invmask2b], alpha[invmask2b])
+
+        return ans
+
+    def _sf(self, x, skew):
+        ans, x, transx, mask, invmask, _, alpha, _ = (
+            self._preprocess(x, skew))
+
+        ans[mask] = _norm_sf(x[mask])
+
+        skew = np.broadcast_to(skew, invmask.shape)
+        invmask1a = np.logical_and(invmask, skew > 0)
+        invmask1b = skew[invmask] > 0
+        ans[invmask1a] = gamma.sf(transx[invmask1b], alpha[invmask1b])
+
+        invmask2a = np.logical_and(invmask, skew < 0)
+        invmask2b = skew[invmask] < 0
+        ans[invmask2a] = gamma.cdf(transx[invmask2b], alpha[invmask2b])
+
+        return ans
+
+    def _rvs(self, skew, size=None, random_state=None):
+        skew = np.broadcast_to(skew, size)
+        ans, _, _, mask, invmask, beta, alpha, zeta = (
+            self._preprocess([0], skew))
+
+        nsmall = mask.sum()
+        nbig = mask.size - nsmall
+        ans[mask] = random_state.standard_normal(nsmall)
+        ans[invmask] = random_state.standard_gamma(alpha, nbig)/beta + zeta
+
+        if size == ():
+            ans = ans[0]
+        return ans
+
+    def _ppf(self, q, skew):
+        ans, q, _, mask, invmask, beta, alpha, zeta = (
+            self._preprocess(q, skew))
+        ans[mask] = _norm_ppf(q[mask])
+        q = q[invmask]
+        q[beta < 0] = 1 - q[beta < 0]  # for negative skew; see gh-17050
+        ans[invmask] = sc.gammaincinv(alpha, q)/beta + zeta
+        return ans
+
+    @_call_super_mom
+    @extend_notes_in_docstring(rv_continuous, notes="""\
+        Note that method of moments (`method='MM'`) is not
+        available for this distribution.\n\n""")
+    def fit(self, data, *args, **kwds):
+        if kwds.get("method", None) == 'MM':
+            raise NotImplementedError("Fit `method='MM'` is not available for "
+                                      "the Pearson3 distribution. Please try "
+                                      "the default `method='MLE'`.")
+        else:
+            return super(type(self), self).fit(data, *args, **kwds)
+
+
+pearson3 = pearson3_gen(name="pearson3")
+
+
+class powerlaw_gen(rv_continuous):
+    r"""A power-function continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    pareto
+
+    Notes
+    -----
+    The probability density function for `powerlaw` is:
+
+    .. math::
+
+        f(x, a) = a x^{a-1}
+
+    for :math:`0 \le x \le 1`, :math:`a > 0`.
+
+    `powerlaw` takes ``a`` as a shape parameter for :math:`a`.
+
+    %(after_notes)s
+
+    For example, the support of `powerlaw` can be adjusted from the default
+    interval ``[0, 1]`` to the interval ``[c, c+d]`` by setting ``loc=c`` and
+    ``scale=d``. For a power-law distribution with infinite support, see
+    `pareto`. For a power-law distribution described by PDF:
+
+    .. math::
+
+        f(x; a, l, h) = \frac{a}{h^a - l^2} x^{a-1}
+
+    with :math:`a \neq 0` and :math:`0 < l < x < h`, see `truncpareto`.
+
+    `powerlaw` is a special case of `beta` with ``b=1``.
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("a", False, (0, np.inf), (False, False))]
+
+    def _pdf(self, x, a):
+        # powerlaw.pdf(x, a) = a * x**(a-1)
+        return a*x**(a-1.0)
+
+    def _logpdf(self, x, a):
+        return np.log(a) + sc.xlogy(a - 1, x)
+
+    def _cdf(self, x, a):
+        return x**(a*1.0)
+
+    def _logcdf(self, x, a):
+        return a*np.log(x)
+
+    def _ppf(self, q, a):
+        return pow(q, 1.0/a)
+
+    def _sf(self, p, a):
+        return -sc.powm1(p, a)
+
+    def _munp(self, n, a):
+        # The following expression is correct for all real n (provided a > 0).
+        return a / (a + n)
+
+    def _stats(self, a):
+        return (a / (a + 1.0),
+                a / (a + 2.0) / (a + 1.0) ** 2,
+                -2.0 * ((a - 1.0) / (a + 3.0)) * np.sqrt((a + 2.0) / a),
+                6 * np.polyval([1, -1, -6, 2], a) / (a * (a + 3.0) * (a + 4)))
+
+    def _entropy(self, a):
+        return 1 - 1.0/a - np.log(a)
+
+    def _support_mask(self, x, a):
+        return (super()._support_mask(x, a)
+                & ((x != 0) | (a >= 1)))
+
+    @_call_super_mom
+    @extend_notes_in_docstring(rv_continuous, notes="""\
+        Notes specifically for ``powerlaw.fit``: If the location is a free
+        parameter and the value returned for the shape parameter is less than
+        one, the true maximum likelihood approaches infinity. This causes
+        numerical difficulties, and the resulting estimates are approximate.
+        \n\n""")
+    def fit(self, data, *args, **kwds):
+        # Summary of the strategy:
+        #
+        # 1) If the scale and location are fixed, return the shape according
+        #    to a formula.
+        #
+        # 2) If the scale is fixed, there are two possibilities for the other
+        #    parameters - one corresponding with shape less than one, and
+        #    another with shape greater than one. Calculate both, and return
+        #    whichever has the better log-likelihood.
+        #
+        # At this point, the scale is known to be free.
+        #
+        # 3) If the location is fixed, return the scale and shape according to
+        #    formulas (or, if the shape is fixed, the fixed shape).
+        #
+        # At this point, the location and scale are both free. There are
+        # separate equations depending on whether the shape is less than one or
+        # greater than one.
+        #
+        # 4a) If the shape is less than one, there are formulas for shape,
+        #     location, and scale.
+        # 4b) If the shape is greater than one, there are formulas for shape
+        #     and scale, but there is a condition for location to be solved
+        #     numerically.
+        #
+        # If the shape is fixed and less than one, we use 4a.
+        # If the shape is fixed and greater than one, we use 4b.
+        # If the shape is also free, we calculate fits using both 4a and 4b
+        # and choose the one that results a better log-likelihood.
+        #
+        # In many cases, the use of `np.nextafter` is used to avoid numerical
+        # issues.
+        if kwds.pop('superfit', False):
+            return super().fit(data, *args, **kwds)
+
+        if len(np.unique(data)) == 1:
+            return super().fit(data, *args, **kwds)
+
+        data, fshape, floc, fscale = _check_fit_input_parameters(self, data,
+                                                                 args, kwds)
+        penalized_nllf_args = [data, (self._fitstart(data),)]
+        penalized_nllf = self._reduce_func(penalized_nllf_args, {})[1]
+
+        # ensure that any fixed parameters don't violate constraints of the
+        # distribution before continuing. The support of the distribution
+        # is `0 < (x - loc)/scale < 1`.
+        if floc is not None:
+            if not data.min() > floc:
+                raise FitDataError('powerlaw', 0, 1)
+            if fscale is not None and not data.max() <= floc + fscale:
+                raise FitDataError('powerlaw', 0, 1)
+
+        if fscale is not None:
+            if fscale <= 0:
+                raise ValueError("Negative or zero `fscale` is outside the "
+                                 "range allowed by the distribution.")
+            if fscale <= np.ptp(data):
+                msg = "`fscale` must be greater than the range of data."
+                raise ValueError(msg)
+
+        def get_shape(data, loc, scale):
+            # The first-order necessary condition on `shape` can be solved in
+            # closed form. It can be used no matter the assumption of the
+            # value of the shape.
+            N = len(data)
+            return - N / (np.sum(np.log(data - loc)) - N*np.log(scale))
+
+        def get_scale(data, loc):
+            # analytical solution for `scale` based on the location.
+            # It can be used no matter the assumption of the value of the
+            # shape.
+            return data.max() - loc
+
+        # 1) The location and scale are both fixed. Analytically determine the
+        # shape.
+        if fscale is not None and floc is not None:
+            return get_shape(data, floc, fscale), floc, fscale
+
+        # 2) The scale is fixed. There are two possibilities for the other
+        # parameters. Choose the option with better log-likelihood.
+        if fscale is not None:
+            # using `data.min()` as the optimal location
+            loc_lt1 = np.nextafter(data.min(), -np.inf)
+            shape_lt1 = fshape or get_shape(data, loc_lt1, fscale)
+            ll_lt1 = penalized_nllf((shape_lt1, loc_lt1, fscale), data)
+
+            # using `data.max() - scale` as the optimal location
+            loc_gt1 = np.nextafter(data.max() - fscale, np.inf)
+            shape_gt1 = fshape or get_shape(data, loc_gt1, fscale)
+            ll_gt1 = penalized_nllf((shape_gt1, loc_gt1, fscale), data)
+
+            if ll_lt1 < ll_gt1:
+                return shape_lt1, loc_lt1, fscale
+            else:
+                return shape_gt1, loc_gt1, fscale
+
+        # 3) The location is fixed. Return the analytical scale and the
+        # analytical (or fixed) shape.
+        if floc is not None:
+            scale = get_scale(data, floc)
+            shape = fshape or get_shape(data, floc, scale)
+            return shape, floc, scale
+
+        # 4) Location and scale are both free
+        # 4a) Use formulas that assume `shape <= 1`.
+
+        def fit_loc_scale_w_shape_lt_1():
+            loc = np.nextafter(data.min(), -np.inf)
+            if np.abs(loc) < np.finfo(loc.dtype).tiny:
+                loc = np.sign(loc) * np.finfo(loc.dtype).tiny
+            scale = np.nextafter(get_scale(data, loc), np.inf)
+            shape = fshape or get_shape(data, loc, scale)
+            return shape, loc, scale
+
+        # 4b) Fit under the assumption that `shape > 1`. The support
+        # of the distribution is `(x - loc)/scale <= 1`. The method of Lagrange
+        # multipliers turns this constraint into the condition that
+        # dL_dScale - dL_dLocation must be zero, which is solved numerically.
+        # (Alternatively, substitute the constraint into the objective
+        # function before deriving the likelihood equation for location.)
+
+        def dL_dScale(data, shape, scale):
+            # The partial derivative of the log-likelihood function w.r.t.
+            # the scale.
+            return -data.shape[0] * shape / scale
+
+        def dL_dLocation(data, shape, loc):
+            # The partial derivative of the log-likelihood function w.r.t.
+            # the location.
+            return (shape - 1) * np.sum(1 / (loc - data))  # -1/(data-loc)
+
+        def dL_dLocation_star(loc):
+            # The derivative of the log-likelihood function w.r.t.
+            # the location, given optimal shape and scale
+            scale = np.nextafter(get_scale(data, loc), -np.inf)
+            shape = fshape or get_shape(data, loc, scale)
+            return dL_dLocation(data, shape, loc)
+
+        def fun_to_solve(loc):
+            # optimize the location by setting the partial derivatives
+            # w.r.t. location and scale equal and solving.
+            scale = np.nextafter(get_scale(data, loc), -np.inf)
+            shape = fshape or get_shape(data, loc, scale)
+            return (dL_dScale(data, shape, scale)
+                    - dL_dLocation(data, shape, loc))
+
+        def fit_loc_scale_w_shape_gt_1():
+            # set brackets for `root_scalar` to use when optimizing over the
+            # location such that a root is likely between them.
+            rbrack = np.nextafter(data.min(), -np.inf)
+
+            # if the sign of `dL_dLocation_star` is positive at rbrack,
+            # we're not going to find the root we're looking for
+            delta = (data.min() - rbrack)
+            while dL_dLocation_star(rbrack) > 0:
+                rbrack = data.min() - delta
+                delta *= 2
+
+            def interval_contains_root(lbrack, rbrack):
+                # Check if the interval (lbrack, rbrack) contains the root.
+                return (np.sign(fun_to_solve(lbrack))
+                        != np.sign(fun_to_solve(rbrack)))
+
+            lbrack = rbrack - 1
+
+            # if the sign doesn't change between the brackets, move the left
+            # bracket until it does. (The right bracket remains fixed at the
+            # maximum permissible value.)
+            i = 1.0
+            while (not interval_contains_root(lbrack, rbrack)
+                   and lbrack != -np.inf):
+                lbrack = (data.min() - i)
+                i *= 2
+
+            root = optimize.root_scalar(fun_to_solve, bracket=(lbrack, rbrack))
+
+            loc = np.nextafter(root.root, -np.inf)
+            scale = np.nextafter(get_scale(data, loc), np.inf)
+            shape = fshape or get_shape(data, loc, scale)
+            return shape, loc, scale
+
+        # Shape is fixed - choose 4a or 4b accordingly.
+        if fshape is not None and fshape <= 1:
+            return fit_loc_scale_w_shape_lt_1()
+        elif fshape is not None and fshape > 1:
+            return fit_loc_scale_w_shape_gt_1()
+
+        # Shape is free
+        fit_shape_lt1 = fit_loc_scale_w_shape_lt_1()
+        ll_lt1 = self.nnlf(fit_shape_lt1, data)
+
+        fit_shape_gt1 = fit_loc_scale_w_shape_gt_1()
+        ll_gt1 = self.nnlf(fit_shape_gt1, data)
+
+        if ll_lt1 <= ll_gt1 and fit_shape_lt1[0] <= 1:
+            return fit_shape_lt1
+        elif ll_lt1 > ll_gt1 and fit_shape_gt1[0] > 1:
+            return fit_shape_gt1
+        else:
+            return super().fit(data, *args, **kwds)
+
+
+powerlaw = powerlaw_gen(a=0.0, b=1.0, name="powerlaw")
+
+
+class powerlognorm_gen(rv_continuous):
+    r"""A power log-normal continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `powerlognorm` is:
+
+    .. math::
+
+        f(x, c, s) = \frac{c}{x s} \phi(\log(x)/s)
+                     (\Phi(-\log(x)/s))^{c-1}
+
+    where :math:`\phi` is the normal pdf, and :math:`\Phi` is the normal cdf,
+    and :math:`x > 0`, :math:`s, c > 0`.
+
+    `powerlognorm` takes :math:`c` and :math:`s` as shape parameters.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    _support_mask = rv_continuous._open_support_mask
+
+    def _shape_info(self):
+        ic = _ShapeInfo("c", False, (0, np.inf), (False, False))
+        i_s = _ShapeInfo("s", False, (0, np.inf), (False, False))
+        return [ic, i_s]
+
+    def _pdf(self, x, c, s):
+        return np.exp(self._logpdf(x, c, s))
+
+    def _logpdf(self, x, c, s):
+        return (np.log(c) - np.log(x) - np.log(s) +
+                _norm_logpdf(np.log(x) / s) +
+                _norm_logcdf(-np.log(x) / s) * (c - 1.))
+
+    def _cdf(self, x, c, s):
+        return -sc.expm1(self._logsf(x, c, s))
+
+    def _ppf(self, q, c, s):
+        return self._isf(1 - q, c, s)
+
+    def _sf(self, x, c, s):
+        return np.exp(self._logsf(x, c, s))
+
+    def _logsf(self, x, c, s):
+        return _norm_logcdf(-np.log(x) / s) * c
+
+    def _isf(self, q, c, s):
+        return np.exp(-_norm_ppf(q**(1/c)) * s)
+
+
+powerlognorm = powerlognorm_gen(a=0.0, name="powerlognorm")
+
+
+class powernorm_gen(rv_continuous):
+    r"""A power normal continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `powernorm` is:
+
+    .. math::
+
+        f(x, c) = c \phi(x) (\Phi(-x))^{c-1}
+
+    where :math:`\phi` is the normal pdf, :math:`\Phi` is the normal cdf,
+    :math:`x` is any real, and :math:`c > 0` [1]_.
+
+    `powernorm` takes ``c`` as a shape parameter for :math:`c`.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] NIST Engineering Statistics Handbook, Section 1.3.6.6.13,
+           https://www.itl.nist.gov/div898/handbook//eda/section3/eda366d.htm
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("c", False, (0, np.inf), (False, False))]
+
+    def _pdf(self, x, c):
+        # powernorm.pdf(x, c) = c * phi(x) * (Phi(-x))**(c-1)
+        return c*_norm_pdf(x) * (_norm_cdf(-x)**(c-1.0))
+
+    def _logpdf(self, x, c):
+        return np.log(c) + _norm_logpdf(x) + (c-1)*_norm_logcdf(-x)
+
+    def _cdf(self, x, c):
+        return -sc.expm1(self._logsf(x, c))
+
+    def _ppf(self, q, c):
+        return -_norm_ppf(pow(1.0 - q, 1.0 / c))
+
+    def _sf(self, x, c):
+        return np.exp(self._logsf(x, c))
+
+    def _logsf(self, x, c):
+        return c * _norm_logcdf(-x)
+
+    def _isf(self, q, c):
+        return -_norm_ppf(np.exp(np.log(q) / c))
+
+
+powernorm = powernorm_gen(name='powernorm')
+
+
+class rdist_gen(rv_continuous):
+    r"""An R-distributed (symmetric beta) continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `rdist` is:
+
+    .. math::
+
+        f(x, c) = \frac{(1-x^2)^{c/2-1}}{B(1/2, c/2)}
+
+    for :math:`-1 \le x \le 1`, :math:`c > 0`. `rdist` is also called the
+    symmetric beta distribution: if B has a `beta` distribution with
+    parameters (c/2, c/2), then X = 2*B - 1 follows a R-distribution with
+    parameter c.
+
+    `rdist` takes ``c`` as a shape parameter for :math:`c`.
+
+    This distribution includes the following distribution kernels as
+    special cases::
+
+        c = 2:  uniform
+        c = 3:  `semicircular`
+        c = 4:  Epanechnikov (parabolic)
+        c = 6:  quartic (biweight)
+        c = 8:  triweight
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("c", False, (0, np.inf), (False, False))]
+
+    # use relation to the beta distribution for pdf, cdf, etc
+    def _pdf(self, x, c):
+        return np.exp(self._logpdf(x, c))
+
+    def _logpdf(self, x, c):
+        return -np.log(2) + beta._logpdf((x + 1)/2, c/2, c/2)
+
+    def _cdf(self, x, c):
+        return beta._cdf((x + 1)/2, c/2, c/2)
+
+    def _sf(self, x, c):
+        return beta._sf((x + 1)/2, c/2, c/2)
+
+    def _ppf(self, q, c):
+        return 2*beta._ppf(q, c/2, c/2) - 1
+
+    def _rvs(self, c, size=None, random_state=None):
+        return 2 * random_state.beta(c/2, c/2, size) - 1
+
+    def _munp(self, n, c):
+        numerator = (1 - (n % 2)) * sc.beta((n + 1.0) / 2, c / 2.0)
+        return numerator / sc.beta(1. / 2, c / 2.)
+
+
+rdist = rdist_gen(a=-1.0, b=1.0, name="rdist")
+
+
+class rayleigh_gen(rv_continuous):
+    r"""A Rayleigh continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `rayleigh` is:
+
+    .. math::
+
+        f(x) = x \exp(-x^2/2)
+
+    for :math:`x \ge 0`.
+
+    `rayleigh` is a special case of `chi` with ``df=2``.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    _support_mask = rv_continuous._open_support_mask
+
+    def _shape_info(self):
+        return []
+
+    def _rvs(self, size=None, random_state=None):
+        return chi.rvs(2, size=size, random_state=random_state)
+
+    def _pdf(self, r):
+        # rayleigh.pdf(r) = r * exp(-r**2/2)
+        return np.exp(self._logpdf(r))
+
+    def _logpdf(self, r):
+        return np.log(r) - 0.5 * r * r
+
+    def _cdf(self, r):
+        return -sc.expm1(-0.5 * r**2)
+
+    def _ppf(self, q):
+        return np.sqrt(-2 * sc.log1p(-q))
+
+    def _sf(self, r):
+        return np.exp(self._logsf(r))
+
+    def _logsf(self, r):
+        return -0.5 * r * r
+
+    def _isf(self, q):
+        return np.sqrt(-2 * np.log(q))
+
+    def _stats(self):
+        val = 4 - np.pi
+        return (np.sqrt(np.pi/2),
+                val/2,
+                2*(np.pi-3)*np.sqrt(np.pi)/val**1.5,
+                6*np.pi/val-16/val**2)
+
+    def _entropy(self):
+        return _EULER/2.0 + 1 - 0.5*np.log(2)
+
+    @_call_super_mom
+    @extend_notes_in_docstring(rv_continuous, notes="""\
+        Notes specifically for ``rayleigh.fit``: If the location is fixed with
+        the `floc` parameter, this method uses an analytical formula to find
+        the scale.  Otherwise, this function uses a numerical root finder on
+        the first order conditions of the log-likelihood function to find the
+        MLE.  Only the (optional) `loc` parameter is used as the initial guess
+        for the root finder; the `scale` parameter and any other parameters
+        for the optimizer are ignored.\n\n""")
+    def fit(self, data, *args, **kwds):
+        if kwds.pop('superfit', False):
+            return super().fit(data, *args, **kwds)
+        data, floc, fscale = _check_fit_input_parameters(self, data,
+                                                         args, kwds)
+
+        def scale_mle(loc):
+            # Source: Statistical Distributions, 3rd Edition. Evans, Hastings,
+            # and Peacock (2000), Page 175
+            return (np.sum((data - loc) ** 2) / (2 * len(data))) ** .5
+
+        def loc_mle(loc):
+            # This implicit equation for `loc` is used when
+            # both `loc` and `scale` are free.
+            xm = data - loc
+            s1 = xm.sum()
+            s2 = (xm**2).sum()
+            s3 = (1/xm).sum()
+            return s1 - s2/(2*len(data))*s3
+
+        def loc_mle_scale_fixed(loc, scale=fscale):
+            # This implicit equation for `loc` is used when
+            # `scale` is fixed but `loc` is not.
+            xm = data - loc
+            return xm.sum() - scale**2 * (1/xm).sum()
+
+        if floc is not None:
+            # `loc` is fixed, analytically determine `scale`.
+            if np.any(data - floc <= 0):
+                raise FitDataError("rayleigh", lower=1, upper=np.inf)
+            else:
+                return floc, scale_mle(floc)
+
+        # Account for user provided guess of `loc`.
+        loc0 = kwds.get('loc')
+        if loc0 is None:
+            # Use _fitstart to estimate loc; ignore the returned scale.
+            loc0 = self._fitstart(data)[0]
+
+        fun = loc_mle if fscale is None else loc_mle_scale_fixed
+        rbrack = np.nextafter(np.min(data), -np.inf)
+        lbrack = _get_left_bracket(fun, rbrack)
+        res = optimize.root_scalar(fun, bracket=(lbrack, rbrack))
+        if not res.converged:
+            raise FitSolverError(res.flag)
+        loc = res.root
+        scale = fscale or scale_mle(loc)
+        return loc, scale
+
+
+rayleigh = rayleigh_gen(a=0.0, name="rayleigh")
+
+
+class reciprocal_gen(rv_continuous):
+    r"""A loguniform or reciprocal continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for this class is:
+
+    .. math::
+
+        f(x, a, b) = \frac{1}{x \log(b/a)}
+
+    for :math:`a \le x \le b`, :math:`b > a > 0`. This class takes
+    :math:`a` and :math:`b` as shape parameters.
+
+    %(after_notes)s
+
+    %(example)s
+
+    This doesn't show the equal probability of ``0.01``, ``0.1`` and
+    ``1``. This is best when the x-axis is log-scaled:
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> fig, ax = plt.subplots(1, 1)
+    >>> ax.hist(np.log10(r))
+    >>> ax.set_ylabel("Frequency")
+    >>> ax.set_xlabel("Value of random variable")
+    >>> ax.xaxis.set_major_locator(plt.FixedLocator([-2, -1, 0]))
+    >>> ticks = ["$10^{{ {} }}$".format(i) for i in [-2, -1, 0]]
+    >>> ax.set_xticklabels(ticks)  # doctest: +SKIP
+    >>> plt.show()
+
+    This random variable will be log-uniform regardless of the base chosen for
+    ``a`` and ``b``. Let's specify with base ``2`` instead:
+
+    >>> rvs = %(name)s(2**-2, 2**0).rvs(size=1000)
+
+    Values of ``1/4``, ``1/2`` and ``1`` are equally likely with this random
+    variable.  Here's the histogram:
+
+    >>> fig, ax = plt.subplots(1, 1)
+    >>> ax.hist(np.log2(rvs))
+    >>> ax.set_ylabel("Frequency")
+    >>> ax.set_xlabel("Value of random variable")
+    >>> ax.xaxis.set_major_locator(plt.FixedLocator([-2, -1, 0]))
+    >>> ticks = ["$2^{{ {} }}$".format(i) for i in [-2, -1, 0]]
+    >>> ax.set_xticklabels(ticks)  # doctest: +SKIP
+    >>> plt.show()
+
+    """
+    def _argcheck(self, a, b):
+        return (a > 0) & (b > a)
+
+    def _shape_info(self):
+        ia = _ShapeInfo("a", False, (0, np.inf), (False, False))
+        ib = _ShapeInfo("b", False, (0, np.inf), (False, False))
+        return [ia, ib]
+
+    def _fitstart(self, data):
+        if isinstance(data, CensoredData):
+            data = data._uncensor()
+        # Reasonable, since support is [a, b]
+        return super()._fitstart(data, args=(np.min(data), np.max(data)))
+
+    def _get_support(self, a, b):
+        return a, b
+
+    def _pdf(self, x, a, b):
+        # reciprocal.pdf(x, a, b) = 1 / (x*(log(b) - log(a)))
+        return np.exp(self._logpdf(x, a, b))
+
+    def _logpdf(self, x, a, b):
+        return -np.log(x) - np.log(np.log(b) - np.log(a))
+
+    def _cdf(self, x, a, b):
+        return (np.log(x)-np.log(a)) / (np.log(b) - np.log(a))
+
+    def _ppf(self, q, a, b):
+        return np.exp(np.log(a) + q*(np.log(b) - np.log(a)))
+
+    def _munp(self, n, a, b):
+        if n == 0:
+            return 1.0
+        t1 = 1 / (np.log(b) - np.log(a)) / n
+        t2 = np.real(np.exp(_log_diff(n * np.log(b), n*np.log(a))))
+        return t1 * t2
+
+    def _entropy(self, a, b):
+        return 0.5*(np.log(a) + np.log(b)) + np.log(np.log(b) - np.log(a))
+
+    fit_note = """\
+        `loguniform`/`reciprocal` is over-parameterized. `fit` automatically
+         fixes `scale` to 1 unless `fscale` is provided by the user.\n\n"""
+
+    @extend_notes_in_docstring(rv_continuous, notes=fit_note)
+    def fit(self, data, *args, **kwds):
+        fscale = kwds.pop('fscale', 1)
+        return super().fit(data, *args, fscale=fscale, **kwds)
+
+    # Details related to the decision of not defining
+    # the survival function for this distribution can be
+    # found in the PR: https://github.com/scipy/scipy/pull/18614
+
+
+loguniform = reciprocal_gen(name="loguniform")
+reciprocal = reciprocal_gen(name="reciprocal")
+loguniform._support = ('a', 'b')
+reciprocal._support = ('a', 'b')
+
+
+class rice_gen(rv_continuous):
+    r"""A Rice continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `rice` is:
+
+    .. math::
+
+        f(x, b) = x \exp(- \frac{x^2 + b^2}{2}) I_0(x b)
+
+    for :math:`x >= 0`, :math:`b > 0`. :math:`I_0` is the modified Bessel
+    function of order zero (`scipy.special.i0`).
+
+    `rice` takes ``b`` as a shape parameter for :math:`b`.
+
+    %(after_notes)s
+
+    The Rice distribution describes the length, :math:`r`, of a 2-D vector with
+    components :math:`(U+u, V+v)`, where :math:`U, V` are constant, :math:`u,
+    v` are independent Gaussian random variables with standard deviation
+    :math:`s`.  Let :math:`R = \sqrt{U^2 + V^2}`. Then the pdf of :math:`r` is
+    ``rice.pdf(x, R/s, scale=s)``.
+
+    %(example)s
+
+    """
+    def _argcheck(self, b):
+        return b >= 0
+
+    def _shape_info(self):
+        return [_ShapeInfo("b", False, (0, np.inf), (True, False))]
+
+    def _rvs(self, b, size=None, random_state=None):
+        # https://en.wikipedia.org/wiki/Rice_distribution
+        t = b/np.sqrt(2) + random_state.standard_normal(size=(2,) + size)
+        return np.sqrt((t*t).sum(axis=0))
+
+    def _cdf(self, x, b):
+        return sc.chndtr(np.square(x), 2, np.square(b))
+
+    def _ppf(self, q, b):
+        return np.sqrt(sc.chndtrix(q, 2, np.square(b)))
+
+    def _pdf(self, x, b):
+        # rice.pdf(x, b) = x * exp(-(x**2+b**2)/2) * I[0](x*b)
+        #
+        # We use (x**2 + b**2)/2 = ((x-b)**2)/2 + xb.
+        # The factor of np.exp(-xb) is then included in the i0e function
+        # in place of the modified Bessel function, i0, improving
+        # numerical stability for large values of xb.
+        return x * np.exp(-(x-b)*(x-b)/2.0) * sc.i0e(x*b)
+
+    def _munp(self, n, b):
+        nd2 = n/2.0
+        n1 = 1 + nd2
+        b2 = b*b/2.0
+        return (2.0**(nd2) * np.exp(-b2) * sc.gamma(n1) *
+                sc.hyp1f1(n1, 1, b2))
+
+
+rice = rice_gen(a=0.0, name="rice")
+
+class irwinhall_gen(rv_continuous):
+    r"""An Irwin-Hall (Uniform Sum) continuous random variable.
+
+    An `Irwin-Hall <https://en.wikipedia.org/wiki/Irwin-Hall_distribution/>`_
+    continuous random variable is the sum of :math:`n` independent
+    standard uniform random variables [1]_ [2]_.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    Applications include `Rao's Spacing Test
+    <https://jammalam.faculty.pstat.ucsb.edu/html/favorite/test.htm>`_,
+    a more powerful alternative to the Rayleigh test
+    when the data are not unimodal, and radar [3]_.
+
+    Conveniently, the pdf and cdf are the :math:`n`-fold convolution of
+    the ones for the standard uniform distribution, which is also the
+    definition of the cardinal B-splines of degree :math:`n-1`
+    having knots evenly spaced from :math:`1` to :math:`n` [4]_ [5]_.
+
+    The Bates distribution, which represents the *mean* of statistically
+    independent, uniformly distributed random variables, is simply the
+    Irwin-Hall distribution scaled by :math:`1/n`. For example, the frozen
+    distribution ``bates = irwinhall(10, scale=1/10)`` represents the
+    distribution of the mean of 10 uniformly distributed random variables.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] P. Hall, "The distribution of means for samples of size N drawn
+            from a population in which the variate takes values between 0 and 1,
+            all such values being equally probable",
+            Biometrika, Volume 19, Issue 3-4, December 1927, Pages 240-244,
+            :doi:`10.1093/biomet/19.3-4.240`.
+    .. [2] J. O. Irwin, "On the frequency distribution of the means of samples
+            from a population having any law of frequency with finite moments,
+            with special reference to Pearson's Type II,
+            Biometrika, Volume 19, Issue 3-4, December 1927, Pages 225-239,
+            :doi:`0.1093/biomet/19.3-4.225`.
+    .. [3] K. Buchanan, T. Adeyemi, C. Flores-Molina, S. Wheeland and D. Overturf,
+            "Sidelobe behavior and bandwidth characteristics
+            of distributed antenna arrays,"
+            2018 United States National Committee of
+            URSI National Radio Science Meeting (USNC-URSI NRSM),
+            Boulder, CO, USA, 2018, pp. 1-2.
+            https://www.usnc-ursi-archive.org/nrsm/2018/papers/B15-9.pdf.
+    .. [4] Amos Ron, "Lecture 1: Cardinal B-splines and convolution operators", p. 1
+            https://pages.cs.wisc.edu/~deboor/887/lec1new.pdf.
+    .. [5] Trefethen, N. (2012, July). B-splines and convolution. Chebfun.
+            Retrieved April 30, 2024, from http://www.chebfun.org/examples/approx/BSplineConv.html.
+
+    %(example)s
+    """  # noqa: E501
+
+    @replace_notes_in_docstring(rv_continuous, notes="""\
+        Raises a ``NotImplementedError`` for the Irwin-Hall distribution because
+        the generic `fit` implementation is unreliable and no custom implementation
+        is available. Consider using `scipy.stats.fit`.\n\n""")
+    def fit(self, data, *args, **kwds):
+        fit_notes = ("The generic `fit` implementation is unreliable for this "
+                     "distribution, and no custom implementation is available. "
+                     "Consider using `scipy.stats.fit`.")
+        raise NotImplementedError(fit_notes)
+
+    def _argcheck(self, n):
+        return (n > 0) & _isintegral(n) & np.isrealobj(n)
+
+    def _get_support(self, n):
+        return 0, n
+
+    def _shape_info(self):
+        return [_ShapeInfo("n", True, (1, np.inf), (True, False))]
+
+    def _munp(self, order, n):
+        # see https://link.springer.com/content/pdf/10.1007/s10959-020-01050-9.pdf
+        # page 640, with m=n, j=n+order
+        def vmunp(order, n):
+            n = np.asarray(n, dtype=np.int64)
+            return (sc.stirling2(n+order, n, exact=True)
+                    / sc.comb(n+order, n, exact=True))
+
+        # exact rationals, but we convert to float anyway
+        return np.vectorize(vmunp, otypes=[np.float64])(order, n)
+
+    @staticmethod
+    def _cardbspl(n):
+        t = np.arange(n+1)
+        return BSpline.basis_element(t)
+
+    def _pdf(self, x, n):
+        def vpdf(x, n):
+            return self._cardbspl(n)(x)
+        return np.vectorize(vpdf, otypes=[np.float64])(x, n)
+
+    def _cdf(self, x, n):
+        def vcdf(x, n):
+            return self._cardbspl(n).antiderivative()(x)
+        return np.vectorize(vcdf, otypes=[np.float64])(x, n)
+
+    def _sf(self, x, n):
+        def vsf(x, n):
+            return self._cardbspl(n).antiderivative()(n-x)
+        return np.vectorize(vsf, otypes=[np.float64])(x, n)
+
+    def _rvs(self, n, size=None, random_state=None, *args):
+        @_vectorize_rvs_over_shapes
+        def _rvs1(n, size=None, random_state=None):
+            n = np.floor(n).astype(int)
+            usize = (n,) if size is None else (n, *size)
+            return random_state.uniform(size=usize).sum(axis=0)
+        return _rvs1(n, size=size, random_state=random_state)
+
+    def _stats(self, n):
+        # mgf = ((exp(t) - 1)/t)**n
+        # m'th derivative follows from the generalized Leibniz rule
+        # Moments follow directly from the definition as the sum of n iid unif(0,1)
+        # and the summation rules for moments of a sum of iid random variables
+        # E(IH((n))) = n*E(U(0,1)) = n/2
+        # Var(IH((n))) = n*Var(U(0,1)) = n/12
+        # Skew(IH((n))) = Skew(U(0,1))/sqrt(n) = 0
+        # Kurt(IH((n))) = Kurt(U(0,1))/n = -6/(5*n) -- Fisher's excess kurtosis
+        # See e.g. https://en.wikipedia.org/wiki/Irwin%E2%80%93Hall_distribution
+
+        return n/2, n/12, 0, -6/(5*n)
+
+
+irwinhall = irwinhall_gen(name="irwinhall")
+irwinhall._support = (0.0, 'n')
+
+
+class recipinvgauss_gen(rv_continuous):
+    r"""A reciprocal inverse Gaussian continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `recipinvgauss` is:
+
+    .. math::
+
+        f(x, \mu) = \frac{1}{\sqrt{2\pi x}}
+                    \exp\left(\frac{-(1-\mu x)^2}{2\mu^2x}\right)
+
+    for :math:`x \ge 0`.
+
+    `recipinvgauss` takes ``mu`` as a shape parameter for :math:`\mu`.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("mu", False, (0, np.inf), (False, False))]
+
+    def _pdf(self, x, mu):
+        # recipinvgauss.pdf(x, mu) =
+        #                     1/sqrt(2*pi*x) * exp(-(1-mu*x)**2/(2*x*mu**2))
+        return np.exp(self._logpdf(x, mu))
+
+    def _logpdf(self, x, mu):
+        return xpx.apply_where(
+            x > 0, (x, mu),
+            lambda x, mu: (-(1 - mu*x)**2.0 / (2*x*mu**2.0)
+                           - 0.5*np.log(2*np.pi*x)),
+            fill_value=-np.inf)
+
+    def _cdf(self, x, mu):
+        trm1 = 1.0/mu - x
+        trm2 = 1.0/mu + x
+        isqx = 1.0/np.sqrt(x)
+        return _norm_cdf(-isqx*trm1) - np.exp(2.0/mu)*_norm_cdf(-isqx*trm2)
+
+    def _sf(self, x, mu):
+        trm1 = 1.0/mu - x
+        trm2 = 1.0/mu + x
+        isqx = 1.0/np.sqrt(x)
+        return _norm_cdf(isqx*trm1) + np.exp(2.0/mu)*_norm_cdf(-isqx*trm2)
+
+    def _rvs(self, mu, size=None, random_state=None):
+        return 1.0/random_state.wald(mu, 1.0, size=size)
+
+
+recipinvgauss = recipinvgauss_gen(a=0.0, name='recipinvgauss')
+
+
+class semicircular_gen(rv_continuous):
+    r"""A semicircular continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    rdist
+
+    Notes
+    -----
+    The probability density function for `semicircular` is:
+
+    .. math::
+
+        f(x) = \frac{2}{\pi} \sqrt{1-x^2}
+
+    for :math:`-1 \le x \le 1`.
+
+    The distribution is a special case of `rdist` with ``c = 3``.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] "Wigner semicircle distribution",
+           https://en.wikipedia.org/wiki/Wigner_semicircle_distribution
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return []
+
+    def _pdf(self, x):
+        return 2.0/np.pi*np.sqrt(1-x*x)
+
+    def _logpdf(self, x):
+        return np.log(2/np.pi) + 0.5*sc.log1p(-x*x)
+
+    def _cdf(self, x):
+        return 0.5+1.0/np.pi*(x*np.sqrt(1-x*x) + np.arcsin(x))
+
+    def _ppf(self, q):
+        return rdist._ppf(q, 3)
+
+    def _rvs(self, size=None, random_state=None):
+        # generate values uniformly distributed on the area under the pdf
+        # (semi-circle) by randomly generating the radius and angle
+        r = np.sqrt(random_state.uniform(size=size))
+        a = np.cos(np.pi * random_state.uniform(size=size))
+        return r * a
+
+    def _stats(self):
+        return 0, 0.25, 0, -1.0
+
+    def _entropy(self):
+        return 0.64472988584940017414
+
+
+semicircular = semicircular_gen(a=-1.0, b=1.0, name="semicircular")
+
+
+class skewcauchy_gen(rv_continuous):
+    r"""A skewed Cauchy random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    cauchy : Cauchy distribution
+
+    Notes
+    -----
+
+    The probability density function for `skewcauchy` is:
+
+    .. math::
+
+        f(x) = \frac{1}{\pi \left(\frac{x^2}{\left(a\, \text{sign}(x) + 1
+                                                   \right)^2} + 1 \right)}
+
+    for a real number :math:`x` and skewness parameter :math:`-1 < a < 1`.
+
+    When :math:`a=0`, the distribution reduces to the usual Cauchy
+    distribution.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] "Skewed generalized *t* distribution", Wikipedia
+       https://en.wikipedia.org/wiki/Skewed_generalized_t_distribution#Skewed_Cauchy_distribution
+
+    %(example)s
+
+    """
+    def _argcheck(self, a):
+        return np.abs(a) < 1
+
+    def _shape_info(self):
+        return [_ShapeInfo("a", False, (-1.0, 1.0), (False, False))]
+
+    def _pdf(self, x, a):
+        return 1 / (np.pi * (x**2 / (a * np.sign(x) + 1)**2 + 1))
+
+    def _cdf(self, x, a):
+        return np.where(x <= 0,
+                        (1 - a) / 2 + (1 - a) / np.pi * np.arctan(x / (1 - a)),
+                        (1 - a) / 2 + (1 + a) / np.pi * np.arctan(x / (1 + a)))
+
+    def _ppf(self, x, a):
+        i = x < self._cdf(0, a)
+        return np.where(i,
+                        np.tan(np.pi / (1 - a) * (x - (1 - a) / 2)) * (1 - a),
+                        np.tan(np.pi / (1 + a) * (x - (1 - a) / 2)) * (1 + a))
+
+    def _stats(self, a, moments='mvsk'):
+        return np.nan, np.nan, np.nan, np.nan
+
+    def _fitstart(self, data):
+        # Use 0 as the initial guess of the skewness shape parameter.
+        # For the location and scale, estimate using the median and
+        # quartiles.
+        if isinstance(data, CensoredData):
+            data = data._uncensor()
+        p25, p50, p75 = np.percentile(data, [25, 50, 75])
+        return 0.0, p50, (p75 - p25)/2
+
+
+skewcauchy = skewcauchy_gen(name='skewcauchy')
+
+
+class skewnorm_gen(rv_continuous):
+    r"""A skew-normal random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The pdf is::
+
+        skewnorm.pdf(x, a) = 2 * norm.pdf(x) * norm.cdf(a*x)
+
+    `skewnorm` takes a real number :math:`a` as a skewness parameter
+    When ``a = 0`` the distribution is identical to a normal distribution
+    (`norm`). `rvs` implements the method of [1]_.
+
+    This distribution uses routines from the Boost Math C++ library for
+    the computation of ``cdf``, ``ppf`` and ``isf`` methods. [2]_
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] A. Azzalini and A. Capitanio (1999). Statistical applications of
+        the multivariate skew-normal distribution. J. Roy. Statist. Soc.,
+        B 61, 579-602. :arxiv:`0911.2093`
+    .. [2] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    %(example)s
+
+    """
+    def _argcheck(self, a):
+        return np.isfinite(a)
+
+    def _shape_info(self):
+        return [_ShapeInfo("a", False, (-np.inf, np.inf), (False, False))]
+
+    def _pdf(self, x, a):
+        return xpx.apply_where(
+            a == 0, (x, a),
+            lambda x, a: _norm_pdf(x),
+            lambda x, a: 2.*_norm_pdf(x)*_norm_cdf(a*x))
+
+    def _logpdf(self, x, a):
+        return xpx.apply_where(
+            a == 0, (x, a),
+            lambda x, a: _norm_logpdf(x),
+            lambda x, a: np.log(2)+_norm_logpdf(x)+_norm_logcdf(a*x))
+
+    def _cdf(self, x, a):
+        a = np.atleast_1d(a)
+        cdf = scu._skewnorm_cdf(x, 0.0, 1.0, a)
+        # for some reason, a isn't broadcasted if some of x are invalid
+        a = np.broadcast_to(a, cdf.shape)
+        # Boost is not accurate in left tail when a > 0
+        i_small_cdf = (cdf < 1e-6) & (a > 0)
+        cdf[i_small_cdf] = super()._cdf(x[i_small_cdf], a[i_small_cdf])
+        return np.clip(cdf, 0, 1)
+
+    def _ppf(self, x, a):
+        return scu._skewnorm_ppf(x, 0.0, 1.0, a)
+
+    def _sf(self, x, a):
+        # Boost's SF is implemented this way. Use whatever customizations
+        # we made in the _cdf.
+        return self._cdf(-x, -a)
+
+    def _isf(self, x, a):
+        return scu._skewnorm_isf(x, 0.0, 1.0, a)
+
+    def _rvs(self, a, size=None, random_state=None):
+        u0 = random_state.normal(size=size)
+        v = random_state.normal(size=size)
+        d = a/np.sqrt(1 + a**2)
+        u1 = d*u0 + v*np.sqrt(1 - d**2)
+        return np.where(u0 >= 0, u1, -u1)
+
+    def _stats(self, a, moments='mvsk'):
+        output = [None, None, None, None]
+        const = np.sqrt(2/np.pi) * a/np.sqrt(1 + a**2)
+
+        if 'm' in moments:
+            output[0] = const
+        if 'v' in moments:
+            output[1] = 1 - const**2
+        if 's' in moments:
+            output[2] = ((4 - np.pi)/2) * (const/np.sqrt(1 - const**2))**3
+        if 'k' in moments:
+            output[3] = (2*(np.pi - 3)) * (const**4/(1 - const**2)**2)
+
+        return output
+
+    # For odd order, the each noncentral moment of the skew-normal distribution
+    # with location 0 and scale 1 can be expressed as a polynomial in delta,
+    # where delta = a/sqrt(1 + a**2) and `a` is the skew-normal shape
+    # parameter.  The dictionary _skewnorm_odd_moments defines those
+    # polynomials for orders up to 19.  The dict is implemented as a cached
+    # property to reduce the impact of the creation of the dict on import time.
+    @cached_property
+    def _skewnorm_odd_moments(self):
+        skewnorm_odd_moments = {
+            1: Polynomial([1]),
+            3: Polynomial([3, -1]),
+            5: Polynomial([15, -10, 3]),
+            7: Polynomial([105, -105, 63, -15]),
+            9: Polynomial([945, -1260, 1134, -540, 105]),
+            11: Polynomial([10395, -17325, 20790, -14850, 5775, -945]),
+            13: Polynomial([135135, -270270, 405405, -386100, 225225, -73710,
+                            10395]),
+            15: Polynomial([2027025, -4729725, 8513505, -10135125, 7882875,
+                            -3869775, 1091475, -135135]),
+            17: Polynomial([34459425, -91891800, 192972780, -275675400,
+                            268017750, -175429800, 74220300, -18378360,
+                            2027025]),
+            19: Polynomial([654729075, -1964187225, 4714049340, -7856748900,
+                            9166207050, -7499623950, 4230557100, -1571349780,
+                            346621275, -34459425]),
+        }
+        return skewnorm_odd_moments
+
+    def _munp(self, order, a):
+        if order % 2:
+            if order > 19:
+                raise NotImplementedError("skewnorm noncentral moments not "
+                                          "implemented for odd orders greater "
+                                          "than 19.")
+            # Use the precomputed polynomials that were derived from the
+            # moment generating function.
+            delta = a/np.sqrt(1 + a**2)
+            return (delta * self._skewnorm_odd_moments[order](delta**2)
+                    * _SQRT_2_OVER_PI)
+        else:
+            # For even order, the moment is just (order-1)!!, where !! is the
+            # notation for the double factorial; for an odd integer m, m!! is
+            # m*(m-2)*...*3*1.
+            # We could use special.factorial2, but we know the argument is odd,
+            # so avoid the overhead of that function and compute the result
+            # directly here.
+            return sc.gamma((order + 1)/2) * 2**(order/2) / _SQRT_PI
+
+    @extend_notes_in_docstring(rv_continuous, notes="""\
+        If ``method='mm'``, parameters fixed by the user are respected, and the
+        remaining parameters are used to match distribution and sample moments
+        where possible. For example, if the user fixes the location with
+        ``floc``, the parameters will only match the distribution skewness and
+        variance to the sample skewness and variance; no attempt will be made
+        to match the means or minimize a norm of the errors.
+        Note that the maximum possible skewness magnitude of a
+        `scipy.stats.skewnorm` distribution is approximately 0.9952717; if the
+        magnitude of the data's sample skewness exceeds this, the returned
+        shape parameter ``a`` will be infinite.
+        \n\n""")
+    def fit(self, data, *args, **kwds):
+        if kwds.pop("superfit", False):
+            return super().fit(data, *args, **kwds)
+        if isinstance(data, CensoredData):
+            if data.num_censored() == 0:
+                data = data._uncensor()
+            else:
+                return super().fit(data, *args, **kwds)
+
+        # this extracts fixed shape, location, and scale however they
+        # are specified, and also leaves them in `kwds`
+        data, fa, floc, fscale = _check_fit_input_parameters(self, data,
+                                                             args, kwds)
+        method = kwds.get("method", "mle").lower()
+
+        # See https://en.wikipedia.org/wiki/Skew_normal_distribution for
+        # moment formulas.
+        def skew_d(d):  # skewness in terms of delta
+            return (4-np.pi)/2 * ((d * np.sqrt(2 / np.pi))**3
+                                  / (1 - 2*d**2 / np.pi)**(3/2))
+
+        def d_skew(skew):  # delta in terms of skewness
+            s_23 = np.abs(skew)**(2/3)
+            return np.sign(skew) * np.sqrt(
+                np.pi/2 * s_23 / (s_23 + ((4 - np.pi)/2)**(2/3))
+            )
+
+        # If method is method of moments, we don't need the user's guesses.
+        # Otherwise, extract the guesses from args and kwds.
+        if method == "mm":
+            a, loc, scale = None, None, None
+        else:
+            a = args[0] if len(args) else None
+            loc = kwds.pop('loc', None)
+            scale = kwds.pop('scale', None)
+
+        if fa is None and a is None:  # not fixed and no guess: use MoM
+            # Solve for a that matches sample distribution skewness to sample
+            # skewness.
+            s = stats.skew(data)
+            if method == 'mle':
+                # For MLE initial conditions, clip skewness to a large but
+                # reasonable value in case the data skewness is out-of-range.
+                s = np.clip(s, -0.99, 0.99)
+            else:
+                s_max = skew_d(1)
+                s = np.clip(s, -s_max, s_max)
+            d = d_skew(s)
+            with np.errstate(divide='ignore'):
+                a = np.sqrt(np.divide(d**2, (1-d**2)))*np.sign(s)
+        else:
+            a = fa if fa is not None else a
+            d = a / np.sqrt(1 + a**2)
+
+        if fscale is None and scale is None:
+            v = np.var(data)
+            scale = np.sqrt(v / (1 - 2*d**2/np.pi))
+        elif fscale is not None:
+            scale = fscale
+
+        if floc is None and loc is None:
+            m = np.mean(data)
+            loc = m - scale*d*np.sqrt(2/np.pi)
+        elif floc is not None:
+            loc = floc
+
+        if method == 'mm':
+            return a, loc, scale
+        else:
+            # At this point, parameter "guesses" may equal the fixed parameters
+            # in kwds. No harm in passing them as guesses, too.
+            return super().fit(data, a, loc=loc, scale=scale, **kwds)
+
+
+skewnorm = skewnorm_gen(name='skewnorm')
+
+
+class trapezoid_gen(rv_continuous):
+    r"""
+    A trapezoidal continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The trapezoidal distribution can be represented with an up-sloping line
+    from ``loc`` to ``(loc + c*scale)``, then constant to ``(loc + d*scale)``
+    and then downsloping from ``(loc + d*scale)`` to ``(loc+scale)``.  This
+    defines the trapezoid base from ``loc`` to ``(loc+scale)`` and the flat
+    top from ``c`` to ``d`` proportional to the position along the base
+    with ``0 <= c <= d <= 1``.  When ``c=d``, this is equivalent to `triang`
+    with the same values for `loc`, `scale` and `c`.
+    The method of [1]_ is used for computing moments.
+
+    `trapezoid` takes :math:`c` and :math:`d` as shape parameters.
+
+    %(after_notes)s
+
+    The standard form is in the range [0, 1] with c the mode.
+    The location parameter shifts the start to `loc`.
+    The scale parameter changes the width from 1 to `scale`.
+
+    References
+    ----------
+    .. [1] Kacker, R.N. and Lawrence, J.F. (2007). Trapezoidal and triangular
+       distributions for Type B evaluation of standard uncertainty.
+       Metrologia 44, 117-127. :doi:`10.1088/0026-1394/44/2/003`
+
+    %(example)s
+    """
+    def _argcheck(self, c, d):
+        return (c >= 0) & (c <= 1) & (d >= 0) & (d <= 1) & (d >= c)
+
+    def _shape_info(self):
+        ic = _ShapeInfo("c", False, (0, 1.0), (True, True))
+        id = _ShapeInfo("d", False, (0, 1.0), (True, True))
+        return [ic, id]
+
+    def _pdf(self, x, c, d):
+        u = 2 / (d-c+1)
+
+        return _lazyselect([x < c,
+                            (c <= x) & (x <= d),
+                            x > d],
+                           [lambda x, c, d, u: u * x / c,
+                            lambda x, c, d, u: u,
+                            lambda x, c, d, u: u * (1-x) / (1-d)],
+                           (x, c, d, u))
+
+    def _cdf(self, x, c, d):
+        return _lazyselect([x < c,
+                            (c <= x) & (x <= d),
+                            x > d],
+                           [lambda x, c, d: x**2 / c / (d-c+1),
+                            lambda x, c, d: (c + 2 * (x-c)) / (d-c+1),
+                            lambda x, c, d: 1-((1-x) ** 2
+                                               / (d-c+1) / (1-d))],
+                           (x, c, d))
+
+    def _ppf(self, q, c, d):
+        qc, qd = self._cdf(c, c, d), self._cdf(d, c, d)
+        condlist = [q < qc, q <= qd, q > qd]
+        choicelist = [np.sqrt(q * c * (1 + d - c)),
+                      0.5 * q * (1 + d - c) + 0.5 * c,
+                      1 - np.sqrt((1 - q) * (d - c + 1) * (1 - d))]
+        return np.select(condlist, choicelist)
+
+    def _munp(self, n, c, d):
+        # Using the parameterization from Kacker, 2007, with
+        # a=bottom left, c=top left, d=top right, b=bottom right, then
+        #     E[X^n] = h/(n+1)/(n+2) [(b^{n+2}-d^{n+2})/(b-d)
+        #                             - ((c^{n+2} - a^{n+2})/(c-a)]
+        # with h = 2/((b-a) - (d-c)). The corresponding parameterization
+        # in scipy, has a'=loc, c'=loc+c*scale, d'=loc+d*scale, b'=loc+scale,
+        # which for standard form reduces to a'=0, b'=1, c'=c, d'=d.
+        # Substituting into E[X^n] gives the bd' term as (1 - d^{n+2})/(1 - d)
+        # and the ac' term as c^{n-1} for the standard form. The bd' term has
+        # numerical difficulties near d=1, so replace (1 - d^{n+2})/(1-d)
+        # with expm1((n+2)*log(d))/(d-1).
+        # Testing with n=18 for c=(1e-30,1-eps) shows that this is stable.
+        # We still require an explicit test for d=1 to prevent divide by zero,
+        # and now a test for d=0 to prevent log(0).
+        ab_term = c**(n+1)
+        dc_term = _lazyselect(
+            [d == 0.0, (0.0 < d) & (d < 1.0), d == 1.0],
+            [lambda d: 1.0,
+             lambda d: np.expm1((n+2) * np.log(d)) / (d-1.0),
+             lambda d: n+2],
+            [d])
+        val = 2.0 / (1.0+d-c) * (dc_term - ab_term) / ((n+1) * (n+2))
+        return val
+
+    def _entropy(self, c, d):
+        # Using the parameterization from Wikipedia (van Dorp, 2003)
+        # with a=bottom left, c=top left, d=top right, b=bottom right
+        # gives a'=loc, b'=loc+c*scale, c'=loc+d*scale, d'=loc+scale,
+        # which for loc=0, scale=1 is a'=0, b'=c, c'=d, d'=1.
+        # Substituting into the entropy formula from Wikipedia gives
+        # the following result.
+        return 0.5 * (1.0-d+c) / (1.0+d-c) + np.log(0.5 * (1.0+d-c))
+
+    def _fitstart(self, data, args=None):
+        # Arbitrary, but c=d=1 fails due to being on edge of bounds
+        if args is None:
+            args = (0.33, 0.66)
+        return super()._fitstart(data, args=args)
+
+
+trapezoid = trapezoid_gen(a=0.0, b=1.0, name="trapezoid")
+
+
+class triang_gen(rv_continuous):
+    r"""A triangular continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The triangular distribution can be represented with an up-sloping line from
+    ``loc`` to ``(loc + c*scale)`` and then downsloping for ``(loc + c*scale)``
+    to ``(loc + scale)``.
+
+    `triang` takes ``c`` as a shape parameter for :math:`0 \le c \le 1`.
+
+    %(after_notes)s
+
+    The standard form is in the range [0, 1] with c the mode.
+    The location parameter shifts the start to `loc`.
+    The scale parameter changes the width from 1 to `scale`.
+
+    %(example)s
+
+    """
+    def _rvs(self, c, size=None, random_state=None):
+        return random_state.triangular(0, c, 1, size)
+
+    def _argcheck(self, c):
+        return (c >= 0) & (c <= 1)
+
+    def _shape_info(self):
+        return [_ShapeInfo("c", False, (0, 1.0), (True, True))]
+
+    def _pdf(self, x, c):
+        # 0: edge case where c=0
+        # 1: generalised case for x < c, don't use x <= c, as it doesn't cope
+        #    with c = 0.
+        # 2: generalised case for x >= c, but doesn't cope with c = 1
+        # 3: edge case where c=1
+        r = _lazyselect([c == 0,
+                         x < c,
+                         (x >= c) & (c != 1),
+                         c == 1],
+                        [lambda x, c: 2 - 2 * x,
+                         lambda x, c: 2 * x / c,
+                         lambda x, c: 2 * (1 - x) / (1 - c),
+                         lambda x, c: 2 * x],
+                        (x, c))
+        return r
+
+    def _cdf(self, x, c):
+        r = _lazyselect([c == 0,
+                         x < c,
+                         (x >= c) & (c != 1),
+                         c == 1],
+                        [lambda x, c: 2*x - x*x,
+                         lambda x, c: x * x / c,
+                         lambda x, c: (x*x - 2*x + c) / (c-1),
+                         lambda x, c: x * x],
+                        (x, c))
+        return r
+
+    def _ppf(self, q, c):
+        return np.where(q < c, np.sqrt(c * q), 1-np.sqrt((1-c) * (1-q)))
+
+    def _stats(self, c):
+        return ((c+1.0)/3.0,
+                (1.0-c+c*c)/18,
+                np.sqrt(2)*(2*c-1)*(c+1)*(c-2) / (5*np.power((1.0-c+c*c), 1.5)),
+                -3.0/5.0)
+
+    def _entropy(self, c):
+        return 0.5-np.log(2)
+
+
+triang = triang_gen(a=0.0, b=1.0, name="triang")
+
+
+class truncexpon_gen(rv_continuous):
+    r"""A truncated exponential continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `truncexpon` is:
+
+    .. math::
+
+        f(x, b) = \frac{\exp(-x)}{1 - \exp(-b)}
+
+    for :math:`0 <= x <= b`.
+
+    `truncexpon` takes ``b`` as a shape parameter for :math:`b`.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("b", False, (0, np.inf), (False, False))]
+
+    def _get_support(self, b):
+        return self.a, b
+
+    def _pdf(self, x, b):
+        # truncexpon.pdf(x, b) = exp(-x) / (1-exp(-b))
+        return np.exp(-x)/(-sc.expm1(-b))
+
+    def _logpdf(self, x, b):
+        return -x - np.log(-sc.expm1(-b))
+
+    def _cdf(self, x, b):
+        return sc.expm1(-x)/sc.expm1(-b)
+
+    def _ppf(self, q, b):
+        return -sc.log1p(q*sc.expm1(-b))
+
+    def _sf(self, x, b):
+        return (np.exp(-b) - np.exp(-x))/sc.expm1(-b)
+
+    def _isf(self, q, b):
+        return -np.log(np.exp(-b) - q * sc.expm1(-b))
+
+    def _munp(self, n, b):
+        # wrong answer with formula, same as in continuous.pdf
+        # return sc.gamman+1)-sc.gammainc1+n, b)
+        if n == 1:
+            return (1-(b+1)*np.exp(-b))/(-sc.expm1(-b))
+        elif n == 2:
+            return 2*(1-0.5*(b*b+2*b+2)*np.exp(-b))/(-sc.expm1(-b))
+        else:
+            # return generic for higher moments
+            return super()._munp(n, b)
+
+    def _entropy(self, b):
+        eB = np.exp(b)
+        return np.log(eB-1)+(1+eB*(b-1.0))/(1.0-eB)
+
+
+truncexpon = truncexpon_gen(a=0.0, name='truncexpon')
+truncexpon._support = (0.0, 'b')
+
+
+# logsumexp trick for log(p + q) with only log(p) and log(q)
+def _log_sum(log_p, log_q):
+    return sc.logsumexp([log_p, log_q], axis=0)
+
+
+# same as above, but using -exp(x) = exp(x + πi)
+def _log_diff(log_p, log_q):
+    return sc.logsumexp([log_p, log_q+np.pi*1j], axis=0)
+
+
+def _log_gauss_mass(a, b):
+    """Log of Gaussian probability mass within an interval"""
+    a, b = np.broadcast_arrays(a, b)
+
+    # Calculations in right tail are inaccurate, so we'll exploit the
+    # symmetry and work only in the left tail
+    case_left = b <= 0
+    case_right = a > 0
+    case_central = ~(case_left | case_right)
+
+    def mass_case_left(a, b):
+        return _log_diff(_norm_logcdf(b), _norm_logcdf(a))
+
+    def mass_case_right(a, b):
+        return mass_case_left(-b, -a)
+
+    def mass_case_central(a, b):
+        # Previously, this was implemented as:
+        # left_mass = mass_case_left(a, 0)
+        # right_mass = mass_case_right(0, b)
+        # return _log_sum(left_mass, right_mass)
+        # Catastrophic cancellation occurs as np.exp(log_mass) approaches 1.
+        # Correct for this with an alternative formulation.
+        # We're not concerned with underflow here: if only one term
+        # underflows, it was insignificant; if both terms underflow,
+        # the result can't accurately be represented in logspace anyway
+        # because sc.log1p(x) ~ x for small x.
+        return sc.log1p(-_norm_cdf(a) - _norm_cdf(-b))
+
+    # _lazyselect not working; don't care to debug it
+    out = np.full_like(a, fill_value=np.nan, dtype=np.complex128)
+    if a[case_left].size:
+        out[case_left] = mass_case_left(a[case_left], b[case_left])
+    if a[case_right].size:
+        out[case_right] = mass_case_right(a[case_right], b[case_right])
+    if a[case_central].size:
+        out[case_central] = mass_case_central(a[case_central], b[case_central])
+    return np.real(out)  # discard ~0j
+
+
+class truncnorm_gen(rv_continuous):
+    r"""A truncated normal continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    This distribution is the normal distribution centered on ``loc`` (default
+    0), with standard deviation ``scale`` (default 1), and truncated at ``a``
+    and ``b`` *standard deviations* from ``loc``. For arbitrary ``loc`` and
+    ``scale``, ``a`` and ``b`` are *not* the abscissae at which the shifted
+    and scaled distribution is truncated.
+
+    .. note::
+        If ``a_trunc`` and ``b_trunc`` are the abscissae at which we wish
+        to truncate the distribution (as opposed to the number of standard
+        deviations from ``loc``), then we can calculate the distribution
+        parameters ``a`` and ``b`` as follows::
+
+            a, b = (a_trunc - loc) / scale, (b_trunc - loc) / scale
+
+        This is a common point of confusion. For additional clarification,
+        please see the example below.
+
+    %(example)s
+
+    In the examples above, ``loc=0`` and ``scale=1``, so the plot is truncated
+    at ``a`` on the left and ``b`` on the right. However, suppose we were to
+    produce the same histogram with ``loc = 1`` and ``scale=0.5``.
+
+    >>> loc, scale = 1, 0.5
+    >>> rv = truncnorm(a, b, loc=loc, scale=scale)
+    >>> x = np.linspace(truncnorm.ppf(0.01, a, b),
+    ...                 truncnorm.ppf(0.99, a, b), 100)
+    >>> r = rv.rvs(size=1000)
+
+    >>> fig, ax = plt.subplots(1, 1)
+    >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
+    >>> ax.hist(r, density=True, bins='auto', histtype='stepfilled', alpha=0.2)
+    >>> ax.set_xlim(a, b)
+    >>> ax.legend(loc='best', frameon=False)
+    >>> plt.show()
+
+    Note that the distribution is no longer appears to be truncated at
+    abscissae ``a`` and ``b``. That is because the *standard* normal
+    distribution is first truncated at ``a`` and ``b``, *then* the resulting
+    distribution is scaled by ``scale`` and shifted by ``loc``. If we instead
+    want the shifted and scaled distribution to be truncated at ``a`` and
+    ``b``, we need to transform these values before passing them as the
+    distribution parameters.
+
+    >>> a_transformed, b_transformed = (a - loc) / scale, (b - loc) / scale
+    >>> rv = truncnorm(a_transformed, b_transformed, loc=loc, scale=scale)
+    >>> x = np.linspace(truncnorm.ppf(0.01, a, b),
+    ...                 truncnorm.ppf(0.99, a, b), 100)
+    >>> r = rv.rvs(size=10000)
+
+    >>> fig, ax = plt.subplots(1, 1)
+    >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
+    >>> ax.hist(r, density=True, bins='auto', histtype='stepfilled', alpha=0.2)
+    >>> ax.set_xlim(a-0.1, b+0.1)
+    >>> ax.legend(loc='best', frameon=False)
+    >>> plt.show()
+    """
+
+    def _argcheck(self, a, b):
+        return a < b
+
+    def _shape_info(self):
+        ia = _ShapeInfo("a", False, (-np.inf, np.inf), (True, False))
+        ib = _ShapeInfo("b", False, (-np.inf, np.inf), (False, True))
+        return [ia, ib]
+
+    def _fitstart(self, data):
+        # Reasonable, since support is [a, b]
+        if isinstance(data, CensoredData):
+            data = data._uncensor()
+        return super()._fitstart(data, args=(np.min(data), np.max(data)))
+
+    def _get_support(self, a, b):
+        return a, b
+
+    def _pdf(self, x, a, b):
+        return np.exp(self._logpdf(x, a, b))
+
+    def _logpdf(self, x, a, b):
+        return _norm_logpdf(x) - _log_gauss_mass(a, b)
+
+    def _cdf(self, x, a, b):
+        return np.exp(self._logcdf(x, a, b))
+
+    def _logcdf(self, x, a, b):
+        x, a, b = np.broadcast_arrays(x, a, b)
+        logcdf = np.asarray(_log_gauss_mass(a, x) - _log_gauss_mass(a, b))
+        i = logcdf > -0.1  # avoid catastrophic cancellation
+        if np.any(i):
+            logcdf[i] = np.log1p(-np.exp(self._logsf(x[i], a[i], b[i])))
+        return logcdf
+
+    def _sf(self, x, a, b):
+        return np.exp(self._logsf(x, a, b))
+
+    def _logsf(self, x, a, b):
+        x, a, b = np.broadcast_arrays(x, a, b)
+        logsf = np.asarray(_log_gauss_mass(x, b) - _log_gauss_mass(a, b))
+        i = logsf > -0.1  # avoid catastrophic cancellation
+        if np.any(i):
+            logsf[i] = np.log1p(-np.exp(self._logcdf(x[i], a[i], b[i])))
+        return logsf
+
+    def _entropy(self, a, b):
+        A = _norm_cdf(a)
+        B = _norm_cdf(b)
+        Z = B - A
+        C = np.log(np.sqrt(2 * np.pi * np.e) * Z)
+        D = (a * _norm_pdf(a) - b * _norm_pdf(b)) / (2 * Z)
+        h = C + D
+        return h
+
+    def _ppf(self, q, a, b):
+        q, a, b = np.broadcast_arrays(q, a, b)
+
+        case_left = a < 0
+        case_right = ~case_left
+
+        def ppf_left(q, a, b):
+            log_Phi_x = _log_sum(_norm_logcdf(a),
+                                 np.log(q) + _log_gauss_mass(a, b))
+            return sc.ndtri_exp(log_Phi_x)
+
+        def ppf_right(q, a, b):
+            log_Phi_x = _log_sum(_norm_logcdf(-b),
+                                 np.log1p(-q) + _log_gauss_mass(a, b))
+            return -sc.ndtri_exp(log_Phi_x)
+
+        out = np.empty_like(q)
+
+        q_left = q[case_left]
+        q_right = q[case_right]
+
+        if q_left.size:
+            out[case_left] = ppf_left(q_left, a[case_left], b[case_left])
+        if q_right.size:
+            out[case_right] = ppf_right(q_right, a[case_right], b[case_right])
+
+        return out
+
+    def _isf(self, q, a, b):
+        # Mostly copy-paste of _ppf, but I think this is simpler than combining
+        q, a, b = np.broadcast_arrays(q, a, b)
+
+        case_left = b < 0
+        case_right = ~case_left
+
+        def isf_left(q, a, b):
+            log_Phi_x = _log_diff(_norm_logcdf(b),
+                                  np.log(q) + _log_gauss_mass(a, b))
+            return sc.ndtri_exp(np.real(log_Phi_x))
+
+        def isf_right(q, a, b):
+            log_Phi_x = _log_diff(_norm_logcdf(-a),
+                                  np.log1p(-q) + _log_gauss_mass(a, b))
+            return -sc.ndtri_exp(np.real(log_Phi_x))
+
+        out = np.empty_like(q)
+
+        q_left = q[case_left]
+        q_right = q[case_right]
+
+        if q_left.size:
+            out[case_left] = isf_left(q_left, a[case_left], b[case_left])
+        if q_right.size:
+            out[case_right] = isf_right(q_right, a[case_right], b[case_right])
+
+        return out
+
+    def _munp(self, n, a, b):
+        def n_th_moment(n, a, b):
+            """
+            Returns n-th moment. Defined only if n >= 0.
+            Function cannot broadcast due to the loop over n
+            """
+            ab = np.asarray([a, b])
+            pA, pB = self._pdf(ab, a, b)
+            probs = np.asarray([pA, -pB])
+            cond = probs != 0
+            moments = [0, 1]
+            for k in range(1, n+1):
+                # a or b might be infinite, and the corresponding pdf value
+                # is 0 in that case, but nan is returned for the
+                # multiplication.  However, as b->infinity,  pdf(b)*b**k -> 0.
+                # So it is safe to use xpx.apply_where to avoid the nan.
+                vals = xpx.apply_where(cond, (probs, ab),
+                                       lambda x, y: x * y**(k-1),
+                                       fill_value=0)
+                mk = np.sum(vals) + (k-1) * moments[-2]
+                moments.append(mk)
+            return moments[-1]
+
+        return xpx.apply_where((n >= 0) & (a == a) & (b == b), (n, a, b),
+                               np.vectorize(n_th_moment, otypes=[np.float64]),
+                               fill_value=np.nan)
+
+    def _stats(self, a, b, moments='mv'):
+        pA, pB = self.pdf(np.array([a, b]), a, b)
+
+        def _truncnorm_stats_scalar(a, b, pA, pB):
+            ab = np.asarray([a, b])
+            m1 = pA - pB
+            mu = m1
+            # use xpx.apply_where to avoid nan (See detailed comment in _munp)
+            probs = np.asarray([pA, -pB])
+            cond = probs != 0
+            vals = xpx.apply_where(cond, (probs, ab), lambda x, y: x*y,
+                                   fill_value=0)
+            m2 = 1 + np.sum(vals)
+            vals = xpx.apply_where(cond, (probs, ab - mu), lambda x, y: x*y,
+                                   fill_value=0)
+            # mu2 = m2 - mu**2, but not as numerically stable as:
+            # mu2 = (a-mu)*pA - (b-mu)*pB + 1
+            mu2 = 1 + np.sum(vals)
+            vals = xpx.apply_where(cond, (probs, ab), lambda x, y: x*y**2,
+                                   fill_value=0)
+            m3 = 2*m1 + np.sum(vals)
+            vals = xpx.apply_where(cond, (probs, ab), lambda x, y: x*y**3,
+                                   fill_value=0)
+            m4 = 3*m2 + np.sum(vals)
+
+            mu3 = m3 + m1 * (-3*m2 + 2*m1**2)
+            g1 = mu3 / np.power(mu2, 1.5)
+            mu4 = m4 + m1*(-4*m3 + 3*m1*(2*m2 - m1**2))
+            g2 = mu4 / mu2**2 - 3
+            return mu, mu2, g1, g2
+
+        _truncnorm_stats = np.vectorize(_truncnorm_stats_scalar)
+        return _truncnorm_stats(a, b, pA, pB)
+
+
+truncnorm = truncnorm_gen(name='truncnorm', momtype=1)
+truncnorm._support = ('a', 'b')
+
+
+class truncpareto_gen(rv_continuous):
+    r"""An upper truncated Pareto continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    pareto : Pareto distribution
+
+    Notes
+    -----
+    The probability density function for `truncpareto` is:
+
+    .. math::
+
+        f(x, b, c) = \frac{b}{1 - c^{-b}} \frac{1}{x^{b+1}}
+
+    for :math:`b \neq 0`, :math:`c > 1` and :math:`1 \le x \le c`.
+
+    `truncpareto` takes `b` and `c` as shape parameters for :math:`b` and
+    :math:`c`.
+
+    Notice that the upper truncation value :math:`c` is defined in
+    standardized form so that random values of an unscaled, unshifted variable
+    are within the range ``[1, c]``.
+    If ``u_r`` is the upper bound to a scaled and/or shifted variable,
+    then ``c = (u_r - loc) / scale``. In other words, the support of the
+    distribution becomes ``(scale + loc) <= x <= (c*scale + loc)`` when
+    `scale` and/or `loc` are provided.
+
+    The ``fit`` method assumes that :math:`b` is positive; it does not produce
+    good results when the data is more consistent with negative :math:`b`.
+
+    `truncpareto` can also be used to model a general power law distribution
+    with PDF:
+
+    .. math::
+
+        f(x; a, l, h) = \frac{a}{h^a - l^a} x^{a-1}
+
+    for :math:`a \neq 0` and :math:`0 < l < x < h`. Suppose :math:`a`,
+    :math:`l`, and :math:`h` are represented in code as ``a``, ``l``, and
+    ``h``, respectively. In this case, use `truncpareto` with parameters
+    ``b = -a``, ``c = h / l``, ``scale = l``, and ``loc = 0``.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] Burroughs, S. M., and Tebbens S. F.
+        "Upper-truncated power laws in natural systems."
+        Pure and Applied Geophysics 158.4 (2001): 741-757.
+
+    %(example)s
+
+    """
+
+    def _shape_info(self):
+        ib = _ShapeInfo("b", False, (-np.inf, np.inf), (False, False))
+        ic = _ShapeInfo("c", False, (1.0, np.inf), (False, False))
+        return [ib, ic]
+
+    def _argcheck(self, b, c):
+        return (b != 0.) & (c > 1.)
+
+    def _get_support(self, b, c):
+        return self.a, c
+
+    def _pdf(self, x, b, c):
+        # here and below, avoid int to negative int power
+        x, b, c = xp_promote(x, b, c, force_floating=True, xp=np)
+        return b * x**-(b+1) / (1 - 1/c**b)
+
+    def _logpdf(self, x, b, c):
+        x, b, c = xp_promote(x, b, c, force_floating=True, xp=np)
+        return xpx.apply_where(b > 0, (x, b, c), self._logpdf_pos_b, super()._logpdf)
+
+    def _logpdf_pos_b(self, x, b, c):
+        return np.log(b) - np.log(-np.expm1(-b*np.log(c))) - (b+1)*np.log(x)
+
+    def _cdf(self, x, b, c):
+        x, b, c = xp_promote(x, b, c, force_floating=True, xp=np)
+        return (1 - x**-b) / (1 - 1/c**b)
+
+    def _logcdf(self, x, b, c):
+        x, b, c = xp_promote(x, b, c, force_floating=True, xp=np)
+        return xpx.apply_where(b > 0, (x, b, c), self._logcdf_pos_b, super()._logcdf)
+
+    def _logcdf_pos_b(self, x, b, c):
+        return np.log1p(-x**-b) - np.log1p(-1/c**b)
+
+    def _ppf(self, q, b, c):
+        q, b, c = xp_promote(q, b, c, force_floating=True, xp=np)
+        return pow(1 - (1 - 1/c**b)*q, -1/b)
+
+    def _sf(self, x, b, c):
+        x, b, c = xp_promote(x, b, c, force_floating=True, xp=np)
+        return (x**-b - 1/c**b) / (1 - 1/c**b)
+
+    def _logsf(self, x, b, c):
+        x, b, c = xp_promote(x, b, c, force_floating=True, xp=np)
+        return xpx.apply_where(b > 0, (x, b, c), self._logsf_pos_b, super()._logsf)
+
+    def _logsf_pos_b(self, x, b, c):
+        return np.log(x**-b - 1/c**b) - np.log1p(-1/c**b)
+
+    def _isf(self, q, b, c):
+        q, b, c = xp_promote(q, b, c, force_floating=True, xp=np)
+        return pow(1/c**b + (1 - 1/c**b)*q, -1/b)
+
+    def _entropy(self, b, c):
+        return -(np.log(b/(1 - 1/c**b))
+                 + (b+1)*(np.log(c)/(c**b - 1) - 1/b))
+
+    def _munp(self, n, b, c):
+        n, b, c = xp_promote(n, b, c, force_floating=True, xp=np)
+        if (n == b).all():
+            return b*np.log(c) / (1 - 1/c**b)
+        else:
+            return b / (b-n) * (c**b - c**n) / (c**b - 1)
+
+    def _fitstart(self, data):
+        if isinstance(data, CensoredData):
+            data = data._uncensor()
+        b, loc, scale = pareto.fit(data)
+        c = (max(data) - loc)/scale
+        return b, c, loc, scale
+
+    @_call_super_mom
+    @inherit_docstring_from(rv_continuous)
+    def fit(self, data, *args, **kwds):
+        if kwds.pop("superfit", False):
+            return super().fit(data, *args, **kwds)
+
+        def log_mean(x):
+            return np.mean(np.log(x))
+
+        def harm_mean(x):
+            return 1/np.mean(1/x)
+
+        def get_b(c, loc, scale):
+            u = (data-loc)/scale
+            harm_m = harm_mean(u)
+            log_m = log_mean(u)
+            quot = (harm_m-1)/log_m
+            return (1 - (quot-1) / (quot - (1 - 1/c)*harm_m/np.log(c)))/log_m
+
+        def get_c(loc, scale):
+            return (mx - loc)/scale
+
+        def get_loc(fc, fscale):
+            if fscale:  # (fscale and fc) or (fscale and not fc)
+                loc = mn - fscale
+                return loc
+            if fc:
+                loc = (fc*mn - mx)/(fc - 1)
+                return loc
+
+        def get_scale(loc):
+            return mn - loc
+
+        # Functions used for optimisation; partial derivatives of
+        # the Lagrangian, set to equal 0.
+
+        def dL_dLoc(loc, b_=None):
+            # Partial derivative wrt location.
+            # Optimised upon when no parameters, or only b, are fixed.
+            scale = get_scale(loc)
+            c = get_c(loc, scale)
+            b = get_b(c, loc, scale) if b_ is None else b_
+            harm_m = harm_mean((data - loc)/scale)
+            return 1 - (1 + (c - 1)/(c**(b+1) - c)) * (1 - 1/(b+1)) * harm_m
+
+        def dL_dB(b, logc, logm):
+            # Partial derivative wrt b.
+            # Optimised upon whenever at least one parameter but b is fixed,
+            # and b is free.
+            return b - np.log1p(b*logc / (1 - b*logm)) / logc
+
+        def fallback(data, *args, **kwargs):
+            # Should any issue arise, default to the general fit method.
+            return super(truncpareto_gen, self).fit(data, *args, **kwargs)
+
+        parameters = _check_fit_input_parameters(self, data, args, kwds)
+        data, fb, fc, floc, fscale = parameters
+        mn, mx = data.min(), data.max()
+        mn_inf = np.nextafter(mn, -np.inf)
+
+        if (fb is not None
+                and fc is not None
+                and floc is not None
+                and fscale is not None):
+            raise ValueError("All parameters fixed."
+                             "There is nothing to optimize.")
+        elif fc is None and floc is None and fscale is None:
+            if fb is None:
+                def cond_b(loc):
+                    # b is positive only if this function is positive
+                    scale = get_scale(loc)
+                    c = get_c(loc, scale)
+                    harm_m = harm_mean((data - loc)/scale)
+                    return (1 + 1/(c-1)) * np.log(c) / harm_m - 1
+
+                # This gives an upper bound on loc allowing for a positive b.
+                # Iteratively look for a bracket for root_scalar.
+                mn_inf = np.nextafter(mn, -np.inf)
+                rbrack = mn_inf
+                i = 0
+                lbrack = rbrack - 1
+                while ((lbrack > -np.inf)
+                       and (cond_b(lbrack)*cond_b(rbrack) >= 0)):
+                    i += 1
+                    lbrack = rbrack - np.power(2., i)
+                if not lbrack > -np.inf:
+                    return fallback(data, *args, **kwds)
+                res = root_scalar(cond_b, bracket=(lbrack, rbrack))
+                if not res.converged:
+                    return fallback(data, *args, **kwds)
+
+                # Determine the MLE for loc.
+                # Iteratively look for a bracket for root_scalar.
+                rbrack = res.root - 1e-3  # grad_loc is numerically ill-behaved
+                lbrack = rbrack - 1
+                i = 0
+                while ((lbrack > -np.inf)
+                       and (dL_dLoc(lbrack)*dL_dLoc(rbrack) >= 0)):
+                    i += 1
+                    lbrack = rbrack - np.power(2., i)
+                if not lbrack > -np.inf:
+                    return fallback(data, *args, **kwds)
+                res = root_scalar(dL_dLoc, bracket=(lbrack, rbrack))
+                if not res.converged:
+                    return fallback(data, *args, **kwds)
+                loc = res.root
+                scale = get_scale(loc)
+                c = get_c(loc, scale)
+                b = get_b(c, loc, scale)
+
+                std_data = (data - loc)/scale
+                # The expression of b relies on b being bounded above.
+                up_bound_b = min(1/log_mean(std_data),
+                                 1/(harm_mean(std_data)-1))
+                if not (b < up_bound_b):
+                    return fallback(data, *args, **kwds)
+            else:
+                # We know b is positive (or a FitError will be triggered)
+                # so we let loc get close to min(data).
+                rbrack = mn_inf
+                lbrack = mn_inf - 1
+                i = 0
+                # Iteratively look for a bracket for root_scalar.
+                while (lbrack > -np.inf
+                       and (dL_dLoc(lbrack, fb)
+                            * dL_dLoc(rbrack, fb) >= 0)):
+                    i += 1
+                    lbrack = rbrack - 2**i
+                if not lbrack > -np.inf:
+                    return fallback(data, *args, **kwds)
+                res = root_scalar(dL_dLoc, (fb,),
+                                  bracket=(lbrack, rbrack))
+                if not res.converged:
+                    return fallback(data, *args, **kwds)
+                loc = res.root
+                scale = get_scale(loc)
+                c = get_c(loc, scale)
+                b = fb
+        else:
+            # At least one of the parameters determining the support is fixed;
+            # the others then have analytical expressions from the constraints.
+            # The completely determined case (fixed c, loc and scale)
+            # has to be checked for not overflowing the support.
+            # If not fixed, b has to be determined numerically.
+            loc = floc if floc is not None else get_loc(fc, fscale)
+            scale = fscale or get_scale(loc)
+            c = fc or get_c(loc, scale)
+
+            # Unscaled, translated values should be positive when the location
+            # is fixed. If it is not the case, we end up with negative `scale`
+            # and `c`, which would trigger a FitError before exiting the
+            # method.
+            if floc is not None and data.min() - floc < 0:
+                raise FitDataError("truncpareto", lower=1, upper=c)
+
+            # Standardised values should be within the distribution support
+            # when all parameters controlling it are fixed. If it not the case,
+            # `fc` is overridden by `c` determined from `floc` and `fscale` when
+            # raising the exception.
+            if fc and (floc is not None) and fscale:
+                if data.max() > fc*fscale + floc:
+                    raise FitDataError("truncpareto", lower=1,
+                                       upper=get_c(loc, scale))
+
+            # The other constraints should be automatically satisfied
+            # from the analytical expressions of the parameters.
+            # If fc or fscale are respectively less than one or less than 0,
+            # a FitError is triggered before exiting the method.
+
+            if fb is None:
+                std_data = (data - loc)/scale
+                logm = log_mean(std_data)
+                logc = np.log(c)
+                # Condition for a positive root to exist.
+                if not (2*logm < logc):
+                    return fallback(data, *args, **kwds)
+
+                lbrack = 1/logm + 1/(logm - logc)
+                rbrack = np.nextafter(1/logm, 0)
+                try:
+                    res = root_scalar(dL_dB, (logc, logm),
+                                      bracket=(lbrack, rbrack))
+                    # we should then never get there
+                    if not res.converged:
+                        return fallback(data, *args, **kwds)
+                    b = res.root
+                except ValueError:
+                    b = rbrack
+            else:
+                b = fb
+
+        # The distribution requires that `scale+loc <= data <= c*scale+loc`.
+        # To avoid numerical issues, some tuning may be necessary.
+        # We adjust `scale` to satisfy the lower bound, and we adjust
+        # `c` to satisfy the upper bound.
+        if not (scale+loc) < mn:
+            if fscale:
+                loc = np.nextafter(loc, -np.inf)
+            else:
+                scale = get_scale(loc)
+                scale = np.nextafter(scale, 0)
+        if not (c*scale+loc) > mx:
+            c = get_c(loc, scale)
+            c = np.nextafter(c, np.inf)
+
+        if not (np.all(self._argcheck(b, c)) and (scale > 0)):
+            return fallback(data, *args, **kwds)
+
+        params_override = b, c, loc, scale
+        if floc is None and fscale is None:
+            # Based on testing in gh-16782, the following methods are only
+            # reliable if either `floc` or `fscale` are provided. They are
+            # fast, though, so might as well see if they are better than the
+            # generic method.
+            params_super = fallback(data, *args, **kwds)
+            nllf_override = self.nnlf(params_override, data)
+            nllf_super = self.nnlf(params_super, data)
+            if nllf_super < nllf_override:
+                return params_super
+
+        return params_override
+
+
+truncpareto = truncpareto_gen(a=1.0, name='truncpareto')
+truncpareto._support = (1.0, 'c')
+
+
+class tukeylambda_gen(rv_continuous):
+    r"""A Tukey-Lamdba continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    A flexible distribution, able to represent and interpolate between the
+    following distributions:
+
+    - Cauchy                (:math:`lambda = -1`)
+    - logistic              (:math:`lambda = 0`)
+    - approx Normal         (:math:`lambda = 0.14`)
+    - uniform from -1 to 1  (:math:`lambda = 1`)
+
+    `tukeylambda` takes a real number :math:`lambda` (denoted ``lam``
+    in the implementation) as a shape parameter.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    _support_mask = rv_continuous._open_support_mask
+
+    def _argcheck(self, lam):
+        return np.isfinite(lam)
+
+    def _shape_info(self):
+        return [_ShapeInfo("lam", False, (-np.inf, np.inf), (False, False))]
+
+    def _get_support(self, lam):
+        b = xpx.apply_where(lam > 0, lam,
+                            lambda lam: 1/lam,
+                            fill_value=np.inf)
+        return -b, b
+
+    def _pdf(self, x, lam):
+        Fx = np.asarray(sc.tklmbda(x, lam))
+        Px = Fx**(lam-1.0) + (np.asarray(1-Fx))**(lam-1.0)
+        with np.errstate(divide='ignore'):
+            Px = 1.0/np.asarray(Px)
+            return np.where((lam <= 0) | (abs(x) < 1.0/np.asarray(lam)), Px, 0.0)
+
+    def _cdf(self, x, lam):
+        return sc.tklmbda(x, lam)
+
+    def _ppf(self, q, lam):
+        return sc.boxcox(q, lam) - sc.boxcox1p(-q, lam)
+
+    def _stats(self, lam):
+        return 0, _tlvar(lam), 0, _tlkurt(lam)
+
+    def _entropy(self, lam):
+        @np.vectorize
+        def entropy_1d(lam):
+            def integ(p):
+                return np.log(pow(p, lam - 1) + pow(1 - p, lam - 1))
+            return integrate.quad(integ, 0, 1)[0]
+        return entropy_1d(lam)
+
+
+tukeylambda = tukeylambda_gen(name='tukeylambda')
+
+
+class FitUniformFixedScaleDataError(FitDataError):
+    def __init__(self, ptp, fscale):
+        self.args = (
+            "Invalid values in `data`.  Maximum likelihood estimation with "
+            "the uniform distribution and fixed scale requires that "
+            f"np.ptp(data) <= fscale, but np.ptp(data) = {ptp} and "
+            f"fscale = {fscale}."
+        )
+
+
+class uniform_gen(rv_continuous):
+    r"""A uniform continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `uniform` is:
+
+    .. math::
+
+        f(x) = \begin{cases}
+                 1  & \text{for } 0 \le x \le 1 \\
+                 0  & \text{otherwise}
+               \end{cases}
+
+    In the standard form, the distribution is uniform on ``[0, 1]``. Using
+    the parameters ``loc`` and ``scale``, one obtains the uniform distribution
+    on ``[loc, loc + scale]``.
+
+    References
+    ----------
+    .. [1] "Continuous uniform distribution", Wikipedia,
+           https://en.wikipedia.org/wiki/Continuous_uniform_distribution
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return []
+
+    def _rvs(self, size=None, random_state=None):
+        return random_state.uniform(0.0, 1.0, size)
+
+    def _pdf(self, x):
+        return 1.0*(x == x)
+
+    def _cdf(self, x):
+        return x
+
+    def _ppf(self, q):
+        return q
+
+    def _stats(self):
+        return 0.5, 1.0/12, 0, -1.2
+
+    def _entropy(self):
+        return 0.0
+
+    @_call_super_mom
+    def fit(self, data, *args, **kwds):
+        """
+        Maximum likelihood estimate for the location and scale parameters.
+
+        `uniform.fit` uses only the following parameters.  Because exact
+        formulas are used, the parameters related to optimization that are
+        available in the `fit` method of other distributions are ignored
+        here.  The only positional argument accepted is `data`.
+
+        Parameters
+        ----------
+        data : array_like
+            Data to use in calculating the maximum likelihood estimate.
+        floc : float, optional
+            Hold the location parameter fixed to the specified value.
+        fscale : float, optional
+            Hold the scale parameter fixed to the specified value.
+
+        Returns
+        -------
+        loc, scale : float
+            Maximum likelihood estimates for the location and scale.
+
+        Notes
+        -----
+        An error is raised if `floc` is given and any values in `data` are
+        less than `floc`, or if `fscale` is given and `fscale` is less
+        than ``data.max() - data.min()``.  An error is also raised if both
+        `floc` and `fscale` are given.
+
+        Examples
+        --------
+        >>> import numpy as np
+        >>> from scipy.stats import uniform
+
+        We'll fit the uniform distribution to `x`:
+
+        >>> x = np.array([2, 2.5, 3.1, 9.5, 13.0])
+
+        For a uniform distribution MLE, the location is the minimum of the
+        data, and the scale is the maximum minus the minimum.
+
+        >>> loc, scale = uniform.fit(x)
+        >>> loc
+        2.0
+        >>> scale
+        11.0
+
+        If we know the data comes from a uniform distribution where the support
+        starts at 0, we can use ``floc=0``:
+
+        >>> loc, scale = uniform.fit(x, floc=0)
+        >>> loc
+        0.0
+        >>> scale
+        13.0
+
+        Alternatively, if we know the length of the support is 12, we can use
+        ``fscale=12``:
+
+        >>> loc, scale = uniform.fit(x, fscale=12)
+        >>> loc
+        1.5
+        >>> scale
+        12.0
+
+        In that last example, the support interval is [1.5, 13.5].  This
+        solution is not unique.  For example, the distribution with ``loc=2``
+        and ``scale=12`` has the same likelihood as the one above.  When
+        `fscale` is given and it is larger than ``data.max() - data.min()``,
+        the parameters returned by the `fit` method center the support over
+        the interval ``[data.min(), data.max()]``.
+
+        """
+        if len(args) > 0:
+            raise TypeError("Too many arguments.")
+
+        floc = kwds.pop('floc', None)
+        fscale = kwds.pop('fscale', None)
+
+        _remove_optimizer_parameters(kwds)
+
+        if floc is not None and fscale is not None:
+            # This check is for consistency with `rv_continuous.fit`.
+            raise ValueError("All parameters fixed. There is nothing to "
+                             "optimize.")
+
+        data = np.asarray(data)
+
+        if not np.isfinite(data).all():
+            raise ValueError("The data contains non-finite values.")
+
+        # MLE for the uniform distribution
+        # --------------------------------
+        # The PDF is
+        #
+        #     f(x, loc, scale) = {1/scale  for loc <= x <= loc + scale
+        #                        {0        otherwise}
+        #
+        # The likelihood function is
+        #     L(x, loc, scale) = (1/scale)**n
+        # where n is len(x), assuming loc <= x <= loc + scale for all x.
+        # The log-likelihood is
+        #     l(x, loc, scale) = -n*log(scale)
+        # The log-likelihood is maximized by making scale as small as possible,
+        # while keeping loc <= x <= loc + scale.   So if neither loc nor scale
+        # are fixed, the log-likelihood is maximized by choosing
+        #     loc = x.min()
+        #     scale = np.ptp(x)
+        # If loc is fixed, it must be less than or equal to x.min(), and then
+        # the scale is
+        #     scale = x.max() - loc
+        # If scale is fixed, it must not be less than np.ptp(x).  If scale is
+        # greater than np.ptp(x), the solution is not unique.  Note that the
+        # likelihood does not depend on loc, except for the requirement that
+        # loc <= x <= loc + scale.  All choices of loc for which
+        #     x.max() - scale <= loc <= x.min()
+        # have the same log-likelihood.  In this case, we choose loc such that
+        # the support is centered over the interval [data.min(), data.max()]:
+        #     loc = x.min() = 0.5*(scale - np.ptp(x))
+
+        if fscale is None:
+            # scale is not fixed.
+            if floc is None:
+                # loc is not fixed, scale is not fixed.
+                loc = data.min()
+                scale = np.ptp(data)
+            else:
+                # loc is fixed, scale is not fixed.
+                loc = floc
+                scale = data.max() - loc
+                if data.min() < loc:
+                    raise FitDataError("uniform", lower=loc, upper=loc + scale)
+        else:
+            # loc is not fixed, scale is fixed.
+            ptp = np.ptp(data)
+            if ptp > fscale:
+                raise FitUniformFixedScaleDataError(ptp=ptp, fscale=fscale)
+            # If ptp < fscale, the ML estimate is not unique; see the comments
+            # above.  We choose the distribution for which the support is
+            # centered over the interval [data.min(), data.max()].
+            loc = data.min() - 0.5*(fscale - ptp)
+            scale = fscale
+
+        # We expect the return values to be floating point, so ensure it
+        # by explicitly converting to float.
+        return float(loc), float(scale)
+
+
+uniform = uniform_gen(a=0.0, b=1.0, name='uniform')
+
+
+class vonmises_gen(rv_continuous):
+    r"""A Von Mises continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    scipy.stats.vonmises_fisher : Von-Mises Fisher distribution on a
+                                  hypersphere
+
+    Notes
+    -----
+    The probability density function for `vonmises` and `vonmises_line` is:
+
+    .. math::
+
+        f(x, \kappa) = \frac{ \exp(\kappa \cos(x)) }{ 2 \pi I_0(\kappa) }
+
+    for :math:`-\pi \le x \le \pi`, :math:`\kappa \ge 0`. :math:`I_0` is the
+    modified Bessel function of order zero (`scipy.special.i0`).
+
+    `vonmises` is a circular distribution which does not restrict the
+    distribution to a fixed interval. Currently, there is no circular
+    distribution framework in SciPy. The ``cdf`` is implemented such that
+    ``cdf(x + 2*np.pi) == cdf(x) + 1``.
+
+    `vonmises_line` is the same distribution, defined on :math:`[-\pi, \pi]`
+    on the real line. This is a regular (i.e. non-circular) distribution.
+
+    Note about distribution parameters: `vonmises` and `vonmises_line` take
+    ``kappa`` as a shape parameter (concentration) and ``loc`` as the location
+    (circular mean). A ``scale`` parameter is accepted but does not have any
+    effect.
+
+    References
+    ----------
+    .. [1] Mardia, K. V. and Jupp, P. E. *Directional Statistics*.
+           John Wiley & Sons, 1999, p. 36.
+    .. [2] "von Mises distribution", Wikipedia,
+           https://en.wikipedia.org/wiki/Von_Mises_distribution
+
+    Examples
+    --------
+    Import the necessary modules.
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.stats import vonmises
+
+    Define distribution parameters.
+
+    >>> loc = 0.5 * np.pi  # circular mean
+    >>> kappa = 1  # concentration
+
+    Compute the probability density at ``x=0`` via the ``pdf`` method.
+
+    >>> vonmises.pdf(0, loc=loc, kappa=kappa)
+    0.12570826359722018
+
+    Verify that the percentile function ``ppf`` inverts the cumulative
+    distribution function ``cdf`` up to floating point accuracy.
+
+    >>> x = 1
+    >>> cdf_value = vonmises.cdf(x, loc=loc, kappa=kappa)
+    >>> ppf_value = vonmises.ppf(cdf_value, loc=loc, kappa=kappa)
+    >>> x, cdf_value, ppf_value
+    (1, 0.31489339900904967, 1.0000000000000004)
+
+    Draw 1000 random variates by calling the ``rvs`` method.
+
+    >>> sample_size = 1000
+    >>> sample = vonmises(loc=loc, kappa=kappa).rvs(sample_size)
+
+    Plot the von Mises density on a Cartesian and polar grid to emphasize
+    that it is a circular distribution.
+
+    >>> fig = plt.figure(figsize=(12, 6))
+    >>> left = plt.subplot(121)
+    >>> right = plt.subplot(122, projection='polar')
+    >>> x = np.linspace(-np.pi, np.pi, 500)
+    >>> vonmises_pdf = vonmises.pdf(x, loc=loc, kappa=kappa)
+    >>> ticks = [0, 0.15, 0.3]
+
+    The left image contains the Cartesian plot.
+
+    >>> left.plot(x, vonmises_pdf)
+    >>> left.set_yticks(ticks)
+    >>> number_of_bins = int(np.sqrt(sample_size))
+    >>> left.hist(sample, density=True, bins=number_of_bins)
+    >>> left.set_title("Cartesian plot")
+    >>> left.set_xlim(-np.pi, np.pi)
+    >>> left.grid(True)
+
+    The right image contains the polar plot.
+
+    >>> right.plot(x, vonmises_pdf, label="PDF")
+    >>> right.set_yticks(ticks)
+    >>> right.hist(sample, density=True, bins=number_of_bins,
+    ...            label="Histogram")
+    >>> right.set_title("Polar plot")
+    >>> right.legend(bbox_to_anchor=(0.15, 1.06))
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("kappa", False, (0, np.inf), (True, False))]
+
+    def _argcheck(self, kappa):
+        return kappa >= 0
+
+    def _rvs(self, kappa, size=None, random_state=None):
+        return random_state.vonmises(0.0, kappa, size=size)
+
+    @inherit_docstring_from(rv_continuous)
+    def rvs(self, *args, **kwds):
+        rvs = super().rvs(*args, **kwds)
+        return np.mod(rvs + np.pi, 2*np.pi) - np.pi
+
+    def _pdf(self, x, kappa):
+        # vonmises.pdf(x, kappa) = exp(kappa * cos(x)) / (2*pi*I[0](kappa))
+        #                        = exp(kappa * (cos(x) - 1)) /
+        #                          (2*pi*exp(-kappa)*I[0](kappa))
+        #                        = exp(kappa * cosm1(x)) / (2*pi*i0e(kappa))
+        return np.exp(kappa*sc.cosm1(x)) / (2*np.pi*sc.i0e(kappa))
+
+    def _logpdf(self, x, kappa):
+        # vonmises.pdf(x, kappa) = exp(kappa * cosm1(x)) / (2*pi*i0e(kappa))
+        return kappa * sc.cosm1(x) - np.log(2*np.pi) - np.log(sc.i0e(kappa))
+
+    def _cdf(self, x, kappa):
+        return _stats.von_mises_cdf(kappa, x)
+
+    def _stats_skip(self, kappa):
+        return 0, None, 0, None
+
+    def _entropy(self, kappa):
+        # vonmises.entropy(kappa) = -kappa * I[1](kappa) / I[0](kappa) +
+        #                           log(2 * np.pi * I[0](kappa))
+        #                         = -kappa * I[1](kappa) * exp(-kappa) /
+        #                           (I[0](kappa) * exp(-kappa)) +
+        #                           log(2 * np.pi *
+        #                           I[0](kappa) * exp(-kappa) / exp(-kappa))
+        #                         = -kappa * sc.i1e(kappa) / sc.i0e(kappa) +
+        #                           log(2 * np.pi * i0e(kappa)) + kappa
+        return (-kappa * sc.i1e(kappa) / sc.i0e(kappa) +
+                np.log(2 * np.pi * sc.i0e(kappa)) + kappa)
+
+    @extend_notes_in_docstring(rv_continuous, notes="""\
+        The default limits of integration are endpoints of the interval
+        of width ``2*pi`` centered at `loc` (e.g. ``[-pi, pi]`` when
+        ``loc=0``).\n\n""")
+    def expect(self, func=None, args=(), loc=0, scale=1, lb=None, ub=None,
+               conditional=False, **kwds):
+        _a, _b = -np.pi, np.pi
+
+        if lb is None:
+            lb = loc + _a
+        if ub is None:
+            ub = loc + _b
+
+        return super().expect(func, args, loc,
+                              scale, lb, ub, conditional, **kwds)
+
+    @_call_super_mom
+    @extend_notes_in_docstring(rv_continuous, notes="""\
+        Fit data is assumed to represent angles and will be wrapped onto the
+        unit circle. `f0` and `fscale` are ignored; the returned shape is
+        always the maximum likelihood estimate and the scale is always
+        1. Initial guesses are ignored.\n\n""")
+    def fit(self, data, *args, **kwds):
+        if kwds.pop('superfit', False):
+            return super().fit(data, *args, **kwds)
+
+        data, fshape, floc, fscale = _check_fit_input_parameters(self, data,
+                                                                 args, kwds)
+        if self.a == -np.pi:
+            # vonmises line case, here the default fit method will be used
+            return super().fit(data, *args, **kwds)
+
+        # wrap data to interval [0, 2*pi]
+        data = np.mod(data, 2 * np.pi)
+
+        def find_mu(data):
+            return stats.circmean(data)
+
+        def find_kappa(data, loc):
+            # Usually, sources list the following as the equation to solve for
+            # the MLE of the shape parameter:
+            # r = I[1](kappa)/I[0](kappa), where r = mean resultant length
+            # This is valid when the location is the MLE of location.
+            # More generally, when the location may be fixed at an arbitrary
+            # value, r should be defined as follows:
+            r = np.sum(np.cos(loc - data))/len(data)
+            # See gh-18128 for more information.
+
+            # The function r[0](kappa) := I[1](kappa)/I[0](kappa) is monotonic
+            # increasing from r[0](0) = 0 to r[0](+inf) = 1.  The partial
+            # derivative of the log likelihood function with respect to kappa
+            # is monotonic decreasing in kappa.
+            if r == 1:
+                # All observations are (almost) equal to the mean.  Return
+                # some large kappa such that r[0](kappa) = 1.0 numerically.
+                return 1e16
+            elif r > 0:
+                def solve_for_kappa(kappa):
+                    return sc.i1e(kappa)/sc.i0e(kappa) - r
+
+                # The bounds of the root of r[0](kappa) = r are derived from
+                # selected bounds of r[0](x) given in [1, Eq. 11 & 16].  See
+                # gh-20102 for details.
+                #
+                # [1] Amos, D. E. (1973).  Computation of Modified Bessel
+                #     Functions and Their Ratios.  Mathematics of Computation,
+                #     28(125): 239-251.
+                lower_bound = r/(1-r)/(1+r)
+                upper_bound = 2*lower_bound
+
+                # The bounds are violated numerically for certain values of r,
+                # where solve_for_kappa evaluated at the bounds have the same
+                # sign.  This indicates numerical imprecision of i1e()/i0e().
+                # Return the violated bound in this case as it's more accurate.
+                if solve_for_kappa(lower_bound) >= 0:
+                    return lower_bound
+                elif solve_for_kappa(upper_bound) <= 0:
+                    return upper_bound
+                else:
+                    root_res = root_scalar(solve_for_kappa, method="brentq",
+                                           bracket=(lower_bound, upper_bound))
+                    return root_res.root
+            else:
+                # if the provided floc is very far from the circular mean,
+                # the mean resultant length r can become negative.
+                # In that case, the equation
+                # I[1](kappa)/I[0](kappa) = r does not have a solution.
+                # The maximum likelihood kappa is then 0 which practically
+                # results in the uniform distribution on the circle. As
+                # vonmises is defined for kappa > 0, return instead the
+                # smallest floating point value.
+                # See gh-18190 for more information
+                return np.finfo(float).tiny
+
+        # location likelihood equation has a solution independent of kappa
+        loc = floc if floc is not None else find_mu(data)
+        # shape likelihood equation depends on location
+        shape = fshape if fshape is not None else find_kappa(data, loc)
+
+        loc = np.mod(loc + np.pi, 2 * np.pi) - np.pi  # ensure in [-pi, pi]
+        return shape, loc, 1  # scale is not handled
+
+
+vonmises = vonmises_gen(name='vonmises')
+vonmises_line = vonmises_gen(a=-np.pi, b=np.pi, name='vonmises_line')
+
+
+class wald_gen(invgauss_gen):
+    r"""A Wald continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `wald` is:
+
+    .. math::
+
+        f(x) = \frac{1}{\sqrt{2\pi x^3}} \exp(- \frac{ (x-1)^2 }{ 2x })
+
+    for :math:`x >= 0`.
+
+    `wald` is a special case of `invgauss` with ``mu=1``.
+
+    %(after_notes)s
+
+    %(example)s
+    """
+    _support_mask = rv_continuous._open_support_mask
+
+    def _shape_info(self):
+        return []
+
+    def _rvs(self, size=None, random_state=None):
+        return random_state.wald(1.0, 1.0, size=size)
+
+    def _pdf(self, x):
+        # wald.pdf(x) = 1/sqrt(2*pi*x**3) * exp(-(x-1)**2/(2*x))
+        return invgauss._pdf(x, 1.0)
+
+    def _cdf(self, x):
+        return invgauss._cdf(x, 1.0)
+
+    def _sf(self, x):
+        return invgauss._sf(x, 1.0)
+
+    def _ppf(self, x):
+        return invgauss._ppf(x, 1.0)
+
+    def _isf(self, x):
+        return invgauss._isf(x, 1.0)
+
+    def _logpdf(self, x):
+        return invgauss._logpdf(x, 1.0)
+
+    def _logcdf(self, x):
+        return invgauss._logcdf(x, 1.0)
+
+    def _logsf(self, x):
+        return invgauss._logsf(x, 1.0)
+
+    def _stats(self):
+        return 1.0, 1.0, 3.0, 15.0
+
+    def _entropy(self):
+        return invgauss._entropy(1.0)
+
+
+wald = wald_gen(a=0.0, name="wald")
+
+
+class wrapcauchy_gen(rv_continuous):
+    r"""A wrapped Cauchy continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `wrapcauchy` is:
+
+    .. math::
+
+        f(x, c) = \frac{1-c^2}{2\pi (1+c^2 - 2c \cos(x))}
+
+    for :math:`0 \le x \le 2\pi`, :math:`0 < c < 1`.
+
+    `wrapcauchy` takes ``c`` as a shape parameter for :math:`c`.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _argcheck(self, c):
+        return (c > 0) & (c < 1)
+
+    def _shape_info(self):
+        return [_ShapeInfo("c", False, (0, 1), (False, False))]
+
+    def _pdf(self, x, c):
+        # wrapcauchy.pdf(x, c) = (1-c**2) / (2*pi*(1+c**2-2*c*cos(x)))
+        return (1.0-c*c)/(2*np.pi*(1+c*c-2*c*np.cos(x)))
+
+    def _cdf(self, x, c):
+
+        def f1(x, cr):
+            # CDF for 0 <= x < pi
+            return 1/np.pi * np.arctan(cr*np.tan(x/2))
+
+        def f2(x, cr):
+            # CDF for pi <= x <= 2*pi
+            return 1 - 1/np.pi * np.arctan(cr*np.tan((2*np.pi - x)/2))
+
+        cr = (1 + c)/(1 - c)
+        return xpx.apply_where(x < np.pi, (x, cr), f1, f2)
+
+    def _ppf(self, q, c):
+        val = (1.0-c)/(1.0+c)
+        rcq = 2*np.arctan(val*np.tan(np.pi*q))
+        rcmq = 2*np.pi-2*np.arctan(val*np.tan(np.pi*(1-q)))
+        return np.where(q < 1.0/2, rcq, rcmq)
+
+    def _entropy(self, c):
+        return np.log(2*np.pi*(1-c*c))
+
+    def _fitstart(self, data):
+        # Use 0.5 as the initial guess of the shape parameter.
+        # For the location and scale, use the minimum and
+        # peak-to-peak/(2*pi), respectively.
+        if isinstance(data, CensoredData):
+            data = data._uncensor()
+        return 0.5, np.min(data), np.ptp(data)/(2*np.pi)
+
+    @inherit_docstring_from(rv_continuous)
+    def rvs(self, *args, **kwds):
+        rvs = super().rvs(*args, **kwds)
+        return np.mod(rvs, 2*np.pi)
+
+wrapcauchy = wrapcauchy_gen(a=0.0, b=2*np.pi, name='wrapcauchy')
+
+
+class gennorm_gen(rv_continuous):
+    r"""A (symmetric) generalized normal continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    laplace : Laplace distribution
+    norm : normal distribution
+
+    Notes
+    -----
+    The (symmetric) generalized normal distribution is also known as the
+    Subbotin distribution, exponential power distribution, and generalized
+    error distribution [1]_.
+
+    The probability density function for `gennorm` is [1]_:
+
+    .. math::
+
+        f(x, \beta) = \frac{\beta}{2 \Gamma(1/\beta)} \exp(-|x|^\beta),
+
+    where :math:`x` is a real number, :math:`\beta > 0` and
+    :math:`\Gamma` is the gamma function (`scipy.special.gamma`).
+
+    `gennorm` takes ``beta`` as a shape parameter for :math:`\beta`.
+    For :math:`\beta = 1`, it is identical to a Laplace distribution.
+    For :math:`\beta = 2`, it is identical to a normal distribution
+    (with ``scale=1/sqrt(2)``).
+
+    References
+    ----------
+
+    .. [1] "Generalized normal distribution, Version 1",
+           https://en.wikipedia.org/wiki/Generalized_normal_distribution#Version_1
+
+    .. [2] Nardon, Martina, and Paolo Pianca. "Simulation techniques for
+           generalized Gaussian densities." Journal of Statistical
+           Computation and Simulation 79.11 (2009): 1317-1329
+
+    .. [3] Wicklin, Rick. "Simulate data from a generalized Gaussian
+           distribution" in The DO Loop blog, September 21, 2016,
+           https://blogs.sas.com/content/iml/2016/09/21/simulate-generalized-gaussian-sas.html
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("beta", False, (0, np.inf), (False, False))]
+
+    def _pdf(self, x, beta):
+        return np.exp(self._logpdf(x, beta))
+
+    def _logpdf(self, x, beta):
+        return np.log(0.5*beta) - sc.gammaln(1.0/beta) - abs(x)**beta
+
+    def _cdf(self, x, beta):
+        c = 0.5 * np.sign(x)
+        # evaluating (.5 + c) first prevents numerical cancellation
+        return (0.5 + c) - c * sc.gammaincc(1.0/beta, abs(x)**beta)
+
+    def _ppf(self, x, beta):
+        c = np.sign(x - 0.5)
+        # evaluating (1. + c) first prevents numerical cancellation
+        return c * sc.gammainccinv(1.0/beta, (1.0 + c) - 2.0*c*x)**(1.0/beta)
+
+    def _sf(self, x, beta):
+        return self._cdf(-x, beta)
+
+    def _isf(self, x, beta):
+        return -self._ppf(x, beta)
+
+    def _munp(self, n, beta):
+        if n == 0:
+            return 1.
+        if n % 2 == 0:
+            c1, cn = sc.gammaln([1.0/beta, (n + 1.0)/beta])
+            return np.exp(cn - c1)
+        else:
+            return 0.
+
+    def _stats(self, beta):
+        c1, c3, c5 = sc.gammaln([1.0/beta, 3.0/beta, 5.0/beta])
+        return 0., np.exp(c3 - c1), 0., np.exp(c5 + c1 - 2.0*c3) - 3.
+
+    def _entropy(self, beta):
+        return 1. / beta - np.log(.5 * beta) + sc.gammaln(1. / beta)
+
+    def _rvs(self, beta, size=None, random_state=None):
+        # see [2]_ for the algorithm
+        # see [3]_ for reference implementation in SAS
+        z = random_state.gamma(1/beta, size=size)
+        y = z ** (1/beta)
+        # convert y to array to ensure masking support
+        y = np.asarray(y)
+        mask = random_state.random(size=y.shape) < 0.5
+        y[mask] = -y[mask]
+        return y
+
+
+gennorm = gennorm_gen(name='gennorm')
+
+
+class halfgennorm_gen(rv_continuous):
+    r"""The upper half of a generalized normal continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    gengamma : generalized gamma distribution
+    gennorm : generalized normal distribution
+    expon : exponential distribution
+    halfnorm : half normal distribution
+
+    Notes
+    -----
+    The probability density function for `halfgennorm` is:
+
+    .. math::
+
+        f(x, \beta) = \frac{\beta}{\Gamma(1/\beta)} \exp(-|x|^\beta)
+
+    for :math:`x, \beta > 0`. :math:`\Gamma` is the gamma function
+    (`scipy.special.gamma`).
+
+    `halfgennorm` takes ``beta`` as a shape parameter for :math:`\beta`.
+    For :math:`\beta = 1`, it is identical to an exponential distribution.
+    For :math:`\beta = 2`, it is identical to a half normal distribution
+    (with ``scale=1/sqrt(2)``).
+
+    `halfgennorm` is the upper half of a generalized normal continuous
+    random variable [1]_.
+
+    `halfgennorm` is a special case of the generalized gamma distribution [2]_,
+    which is implemented in SciPy as `gengamma`:
+    ``halfgennorm(beta) = gengamma(a=1/beta, c=beta)``.
+
+    References
+    ----------
+
+    .. [1] "Generalized normal distribution, Version 1",  Wikipedia,
+           https://en.wikipedia.org/wiki/Generalized_normal_distribution#Version_1
+    .. [2] "Generalized gamma distribution", Wikipedia,
+           https://en.wikipedia.org/wiki/Generalized_gamma_distribution
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("beta", False, (0, np.inf), (False, False))]
+
+    def _pdf(self, x, beta):
+        #                                 beta
+        # halfgennorm.pdf(x, beta) =  -------------  exp(-|x|**beta)
+        #                             gamma(1/beta)
+        return np.exp(self._logpdf(x, beta))
+
+    def _logpdf(self, x, beta):
+        return np.log(beta) - sc.gammaln(1.0/beta) - x**beta
+
+    def _cdf(self, x, beta):
+        return sc.gammainc(1.0/beta, x**beta)
+
+    def _ppf(self, x, beta):
+        return sc.gammaincinv(1.0/beta, x)**(1.0/beta)
+
+    def _sf(self, x, beta):
+        return sc.gammaincc(1.0/beta, x**beta)
+
+    def _isf(self, x, beta):
+        return sc.gammainccinv(1.0/beta, x)**(1.0/beta)
+
+    def _munp(self, n, beta):
+        return sc.poch(1/beta, n/beta)
+
+    def _entropy(self, beta):
+        return 1.0/beta - np.log(beta) + sc.gammaln(1.0/beta)
+
+
+halfgennorm = halfgennorm_gen(a=0, name='halfgennorm')
+
+
+class crystalball_gen(rv_continuous):
+    r"""
+    Crystalball distribution.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `crystalball` is:
+
+    .. math::
+
+        f(x, \beta, m) =  \begin{cases}
+                            N \exp(-x^2 / 2),  &\text{for } x > -\beta\\
+                            N A (B - x)^{-m}  &\text{for } x \le -\beta
+                          \end{cases}
+
+    where :math:`A = (m / |\beta|)^m  \exp(-\beta^2 / 2)`,
+    :math:`B = m/|\beta| - |\beta|` and :math:`N` is a normalisation constant.
+
+    `crystalball` takes :math:`\beta > 0` and :math:`m > 1` as shape
+    parameters.  :math:`\beta` defines the point where the pdf changes
+    from a power-law to a Gaussian distribution.  :math:`m` is the power
+    of the power-law tail.
+
+    %(after_notes)s
+
+    .. versionadded:: 0.19.0
+
+    References
+    ----------
+    .. [1] "Crystal Ball Function",
+           https://en.wikipedia.org/wiki/Crystal_Ball_function
+
+    %(example)s
+    """
+    def _argcheck(self, beta, m):
+        """
+        Shape parameter bounds are m > 1 and beta > 0.
+        """
+        return (m > 1) & (beta > 0)
+
+    def _shape_info(self):
+        ibeta = _ShapeInfo("beta", False, (0, np.inf), (False, False))
+        im = _ShapeInfo("m", False, (1, np.inf), (False, False))
+        return [ibeta, im]
+
+    def _fitstart(self, data):
+        # Arbitrary, but the default m=1 is not valid
+        return super()._fitstart(data, args=(1, 1.5))
+
+    def _pdf(self, x, beta, m):
+        """
+        Return PDF of the crystalball function.
+
+                                            --
+                                           | exp(-x**2 / 2),  for x > -beta
+        crystalball.pdf(x, beta, m) =  N * |
+                                           | A * (B - x)**(-m), for x <= -beta
+                                            --
+        """
+        N = 1.0 / (m/beta / (m-1) * np.exp(-beta**2 / 2.0) +
+                   _norm_pdf_C * _norm_cdf(beta))
+
+        def rhs(x, beta, m):
+            return np.exp(-x**2 / 2)
+
+        def lhs(x, beta, m):
+            return ((m/beta)**m * np.exp(-beta**2 / 2.0) *
+                    (m/beta - beta - x)**(-m))
+
+        return N * xpx.apply_where(x > -beta, (x, beta, m), rhs, lhs)
+
+    def _logpdf(self, x, beta, m):
+        """
+        Return the log of the PDF of the crystalball function.
+        """
+        N = 1.0 / (m/beta / (m-1) * np.exp(-beta**2 / 2.0) +
+                   _norm_pdf_C * _norm_cdf(beta))
+
+        def rhs(x, beta, m):
+            return -x**2/2
+
+        def lhs(x, beta, m):
+            return m*np.log(m/beta) - beta**2/2 - m*np.log(m/beta - beta - x)
+
+        return np.log(N) + xpx.apply_where(x > -beta, (x, beta, m), rhs, lhs)
+
+    def _cdf(self, x, beta, m):
+        """
+        Return CDF of the crystalball function
+        """
+        N = 1.0 / (m/beta / (m-1) * np.exp(-beta**2 / 2.0) +
+                   _norm_pdf_C * _norm_cdf(beta))
+
+        def rhs(x, beta, m):
+            return ((m/beta) * np.exp(-beta**2 / 2.0) / (m-1) +
+                    _norm_pdf_C * (_norm_cdf(x) - _norm_cdf(-beta)))
+
+        def lhs(x, beta, m):
+            return ((m/beta)**m * np.exp(-beta**2 / 2.0) *
+                    (m/beta - beta - x)**(-m+1) / (m-1))
+
+        return N * xpx.apply_where(x > -beta, (x, beta, m), rhs, lhs)
+
+    def _sf(self, x, beta, m):
+        """
+        Survival function of the crystalball distribution.
+        """
+
+        def rhs(x, beta, m):
+            # M is the same as 1/N used elsewhere.
+            M = m/beta/(m - 1)*np.exp(-beta**2/2) + _norm_pdf_C*_norm_cdf(beta)
+            return _norm_pdf_C*_norm_sf(x)/M
+
+        def lhs(x, beta, m):
+            # Default behavior is OK in the left tail of the SF.
+            return 1 - self._cdf(x, beta, m)
+
+        return xpx.apply_where(x > -beta, (x, beta, m), rhs, lhs)
+
+    def _ppf(self, p, beta, m):
+        N = 1.0 / (m/beta / (m-1) * np.exp(-beta**2 / 2.0) +
+                   _norm_pdf_C * _norm_cdf(beta))
+        pbeta = N * (m/beta) * np.exp(-beta**2/2) / (m - 1)
+
+        def ppf_less(p, beta, m):
+            eb2 = np.exp(-beta**2/2)
+            C = (m/beta) * eb2 / (m-1)
+            N = 1/(C + _norm_pdf_C * _norm_cdf(beta))
+            return (m/beta - beta -
+                    ((m - 1)*(m/beta)**(-m)/eb2*p/N)**(1/(1-m)))
+
+        def ppf_greater(p, beta, m):
+            eb2 = np.exp(-beta**2/2)
+            C = (m/beta) * eb2 / (m-1)
+            N = 1/(C + _norm_pdf_C * _norm_cdf(beta))
+            return _norm_ppf(_norm_cdf(-beta) + (1/_norm_pdf_C)*(p/N - C))
+
+        return xpx.apply_where(p < pbeta, (p, beta, m), ppf_less, ppf_greater)
+
+    def _munp(self, n, beta, m):
+        """
+        Returns the n-th non-central moment of the crystalball function.
+        """
+        N = 1.0 / (m/beta / (m-1) * np.exp(-beta**2 / 2.0) +
+                   _norm_pdf_C * _norm_cdf(beta))
+
+        def n_th_moment(n, beta, m):
+            """
+            Returns n-th moment. Defined only if n+1 < m
+            Function cannot broadcast due to the loop over n
+            """
+            A = (m/beta)**m * np.exp(-beta**2 / 2.0)
+            B = m/beta - beta
+            rhs = (2**((n-1)/2.0) * sc.gamma((n+1)/2) *
+                   (1.0 + (-1)**n * sc.gammainc((n+1)/2, beta**2 / 2)))
+            lhs = np.zeros(rhs.shape)
+            for k in range(int(n) + 1):
+                lhs += (sc.binom(n, k) * B**(n-k) * (-1)**k / (m - k - 1) *
+                        (m/beta)**(-m + k + 1))
+            return A * lhs + rhs
+
+        return N * xpx.apply_where(n + 1 < m, (n, beta, m),
+                                   np.vectorize(n_th_moment, otypes=[np.float64]),
+                                   fill_value=np.inf)
+
+
+crystalball = crystalball_gen(name='crystalball', longname="A Crystalball Function")
+
+
+def _argus_phi(chi):
+    """
+    Utility function for the argus distribution used in the pdf, sf and
+    moment calculation.
+    Note that for all x > 0:
+    gammainc(1.5, x**2/2) = 2 * (_norm_cdf(x) - x * _norm_pdf(x) - 0.5).
+    This can be verified directly by noting that the cdf of Gamma(1.5) can
+    be written as erf(sqrt(x)) - 2*sqrt(x)*exp(-x)/sqrt(Pi).
+    We use gammainc instead of the usual definition because it is more precise
+    for small chi.
+    """
+    return sc.gammainc(1.5, chi**2/2) / 2
+
+
+class argus_gen(rv_continuous):
+    r"""
+    Argus distribution.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `argus` is:
+
+    .. math::
+
+        f(x, \chi) = \frac{\chi^3}{\sqrt{2\pi} \Psi(\chi)} x \sqrt{1-x^2}
+                     \exp(-\chi^2 (1 - x^2)/2)
+
+    for :math:`0 < x < 1` and :math:`\chi > 0`, where
+
+    .. math::
+
+        \Psi(\chi) = \Phi(\chi) - \chi \phi(\chi) - 1/2
+
+    with :math:`\Phi` and :math:`\phi` being the CDF and PDF of a standard
+    normal distribution, respectively.
+
+    `argus` takes :math:`\chi` as shape a parameter. Details about sampling
+    from the ARGUS distribution can be found in [2]_.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] "ARGUS distribution",
+           https://en.wikipedia.org/wiki/ARGUS_distribution
+    .. [2] Christoph Baumgarten "Random variate generation by fast numerical
+           inversion in the varying parameter case." Research in Statistics,
+           vol. 1, 2023. :doi:`10.1080/27684520.2023.2279060`
+
+    .. versionadded:: 0.19.0
+
+    %(example)s
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("chi", False, (0, np.inf), (False, False))]
+
+    def _logpdf(self, x, chi):
+        # for x = 0 or 1, logpdf returns -np.inf
+        with np.errstate(divide='ignore'):
+            y = 1.0 - x*x
+            A = 3*np.log(chi) - _norm_pdf_logC - np.log(_argus_phi(chi))
+            return A + np.log(x) + 0.5*np.log1p(-x*x) - chi**2 * y / 2
+
+    def _pdf(self, x, chi):
+        return np.exp(self._logpdf(x, chi))
+
+    def _cdf(self, x, chi):
+        return 1.0 - self._sf(x, chi)
+
+    def _sf(self, x, chi):
+        return _argus_phi(chi * np.sqrt((1 - x)*(1 + x))) / _argus_phi(chi)
+
+    def _rvs(self, chi, size=None, random_state=None):
+        chi = np.asarray(chi)
+        if chi.size == 1:
+            out = self._rvs_scalar(chi, numsamples=size,
+                                   random_state=random_state)
+        else:
+            shp, bc = _check_shape(chi.shape, size)
+            numsamples = int(np.prod(shp))
+            out = np.empty(size)
+            it = np.nditer([chi],
+                           flags=['multi_index'],
+                           op_flags=[['readonly']])
+            while not it.finished:
+                idx = tuple((it.multi_index[j] if not bc[j] else slice(None))
+                            for j in range(-len(size), 0))
+                r = self._rvs_scalar(it[0], numsamples=numsamples,
+                                     random_state=random_state)
+                out[idx] = r.reshape(shp)
+                it.iternext()
+
+        if size == ():
+            out = out[()]
+        return out
+
+    def _rvs_scalar(self, chi, numsamples=None, random_state=None):
+        # if chi <= 1.8:
+        # use rejection method, see Devroye:
+        # Non-Uniform Random Variate Generation, 1986, section II.3.2.
+        # write: PDF f(x) = c * g(x) * h(x), where
+        # h is [0,1]-valued and g is a density
+        # we use two ways to write f
+        #
+        # Case 1:
+        # write g(x) = 3*x*sqrt(1-x**2), h(x) = exp(-chi**2 (1-x**2) / 2)
+        # If X has a distribution with density g its ppf G_inv is given by:
+        # G_inv(u) = np.sqrt(1 - u**(2/3))
+        #
+        # Case 2:
+        # g(x) = chi**2 * x * exp(-chi**2 * (1-x**2)/2) / (1 - exp(-chi**2 /2))
+        # h(x) = sqrt(1 - x**2), 0 <= x <= 1
+        # one can show that
+        # G_inv(u) = np.sqrt(2*np.log(u*(np.exp(chi**2/2)-1)+1))/chi
+        #          = np.sqrt(1 + 2*np.log(np.exp(-chi**2/2)*(1-u)+u)/chi**2)
+        # the latter expression is used for precision with small chi
+        #
+        # In both cases, the inverse cdf of g can be written analytically, and
+        # we can apply the rejection method:
+        #
+        # REPEAT
+        #    Generate U uniformly distributed on [0, 1]
+        #    Generate X with density g (e.g. via inverse transform sampling:
+        #    X = G_inv(V) with V uniformly distributed on [0, 1])
+        # UNTIL X <= h(X)
+        # RETURN X
+        #
+        # We use case 1 for chi <= 0.5 as it maintains precision for small chi
+        # and case 2 for 0.5 < chi <= 1.8 due to its speed for moderate chi.
+        #
+        # if chi > 1.8:
+        # use relation to the Gamma distribution: if X is ARGUS with parameter
+        # chi), then Y = chi**2 * (1 - X**2) / 2 has density proportional to
+        # sqrt(u) * exp(-u) on [0, chi**2 / 2], i.e. a Gamma(3/2) distribution
+        # conditioned on [0, chi**2 / 2]). Therefore, to sample X from the
+        # ARGUS distribution, we sample Y from the gamma distribution, keeping
+        # only samples on [0, chi**2 / 2], and apply the inverse
+        # transformation X = (1 - 2*Y/chi**2)**(1/2). Since we only
+        # look at chi > 1.8, gamma(1.5).cdf(chi**2/2) is large enough such
+        # Y falls in the interval [0, chi**2 / 2] with a high probability:
+        # stats.gamma(1.5).cdf(1.8**2/2) = 0.644...
+        #
+        # The points to switch between the different methods are determined
+        # by a comparison of the runtime of the different methods. However,
+        # the runtime is platform-dependent. The implemented values should
+        # ensure a good overall performance and are supported by an analysis
+        # of the rejection constants of different methods.
+
+        size1d = tuple(np.atleast_1d(numsamples))
+        N = int(np.prod(size1d))
+        x = np.zeros(N)
+        simulated = 0
+        chi2 = chi * chi
+        if chi <= 0.5:
+            d = -chi2 / 2
+            while simulated < N:
+                k = N - simulated
+                u = random_state.uniform(size=k)
+                v = random_state.uniform(size=k)
+                z = v**(2/3)
+                # acceptance condition: u <= h(G_inv(v)). This simplifies to
+                accept = (np.log(u) <= d * z)
+                num_accept = np.sum(accept)
+                if num_accept > 0:
+                    # we still need to transform z=v**(2/3) to X = G_inv(v)
+                    rvs = np.sqrt(1 - z[accept])
+                    x[simulated:(simulated + num_accept)] = rvs
+                    simulated += num_accept
+        elif chi <= 1.8:
+            echi = np.exp(-chi2 / 2)
+            while simulated < N:
+                k = N - simulated
+                u = random_state.uniform(size=k)
+                v = random_state.uniform(size=k)
+                z = 2 * np.log(echi * (1 - v) + v) / chi2
+                # as in case one, simplify u <= h(G_inv(v)) and then transform
+                # z to the target distribution X = G_inv(v)
+                accept = (u**2 + z <= 0)
+                num_accept = np.sum(accept)
+                if num_accept > 0:
+                    rvs = np.sqrt(1 + z[accept])
+                    x[simulated:(simulated + num_accept)] = rvs
+                    simulated += num_accept
+        else:
+            # conditional Gamma for chi > 1.8
+            while simulated < N:
+                k = N - simulated
+                g = random_state.standard_gamma(1.5, size=k)
+                accept = (g <= chi2 / 2)
+                num_accept = np.sum(accept)
+                if num_accept > 0:
+                    x[simulated:(simulated + num_accept)] = g[accept]
+                    simulated += num_accept
+            x = np.sqrt(1 - 2 * x / chi2)
+
+        return np.reshape(x, size1d)
+
+    def _stats(self, chi):
+        # need to ensure that dtype is float
+        # otherwise the mask below does not work for integers
+        chi = np.asarray(chi, dtype=float)
+        phi = _argus_phi(chi)
+        m = np.sqrt(np.pi/8) * chi * sc.ive(1, chi**2/4) / phi
+        # compute second moment, use Taylor expansion for small chi (<= 0.1)
+        mu2 = np.empty_like(chi)
+        mask = chi > 0.1
+        c = chi[mask]
+        mu2[mask] = 1 - 3 / c**2 + c * _norm_pdf(c) / phi[mask]
+        c = chi[~mask]
+        coef = [-358/65690625, 0, -94/1010625, 0, 2/2625, 0, 6/175, 0, 0.4]
+        mu2[~mask] = np.polyval(coef, c)
+        return m, mu2 - m**2, None, None
+
+
+argus = argus_gen(name='argus', longname="An Argus Function", a=0.0, b=1.0)
+
+
+class rv_histogram(rv_continuous):
+    """
+    Generates a distribution given by a histogram.
+    This is useful to generate a template distribution from a binned
+    datasample.
+
+    As a subclass of the `rv_continuous` class, `rv_histogram` inherits from it
+    a collection of generic methods (see `rv_continuous` for the full list),
+    and implements them based on the properties of the provided binned
+    datasample.
+
+    Parameters
+    ----------
+    histogram : tuple of array_like
+        Tuple containing two array_like objects.
+        The first containing the content of n bins,
+        the second containing the (n+1) bin boundaries.
+        In particular, the return value of `numpy.histogram` is accepted.
+
+    density : bool, optional
+        If False, assumes the histogram is proportional to counts per bin;
+        otherwise, assumes it is proportional to a density.
+        For constant bin widths, these are equivalent, but the distinction
+        is important when bin widths vary (see Notes).
+        If None (default), sets ``density=True`` for backwards compatibility,
+        but warns if the bin widths are variable. Set `density` explicitly
+        to silence the warning.
+
+        .. versionadded:: 1.10.0
+
+    Notes
+    -----
+    When a histogram has unequal bin widths, there is a distinction between
+    histograms that are proportional to counts per bin and histograms that are
+    proportional to probability density over a bin. If `numpy.histogram` is
+    called with its default ``density=False``, the resulting histogram is the
+    number of counts per bin, so ``density=False`` should be passed to
+    `rv_histogram`. If `numpy.histogram` is called with ``density=True``, the
+    resulting histogram is in terms of probability density, so ``density=True``
+    should be passed to `rv_histogram`. To avoid warnings, always pass
+    ``density`` explicitly when the input histogram has unequal bin widths.
+
+    There are no additional shape parameters except for the loc and scale.
+    The pdf is defined as a stepwise function from the provided histogram.
+    The cdf is a linear interpolation of the pdf.
+
+    .. versionadded:: 0.19.0
+
+    Examples
+    --------
+
+    Create a scipy.stats distribution from a numpy histogram
+
+    >>> import scipy.stats
+    >>> import numpy as np
+    >>> data = scipy.stats.norm.rvs(size=100000, loc=0, scale=1.5,
+    ...                             random_state=123)
+    >>> hist = np.histogram(data, bins=100)
+    >>> hist_dist = scipy.stats.rv_histogram(hist, density=False)
+
+    Behaves like an ordinary scipy rv_continuous distribution
+
+    >>> hist_dist.pdf(1.0)
+    0.20538577847618705
+    >>> hist_dist.cdf(2.0)
+    0.90818568543056499
+
+    PDF is zero above (below) the highest (lowest) bin of the histogram,
+    defined by the max (min) of the original dataset
+
+    >>> hist_dist.pdf(np.max(data))
+    0.0
+    >>> hist_dist.cdf(np.max(data))
+    1.0
+    >>> hist_dist.pdf(np.min(data))
+    7.7591907244498314e-05
+    >>> hist_dist.cdf(np.min(data))
+    0.0
+
+    PDF and CDF follow the histogram
+
+    >>> import matplotlib.pyplot as plt
+    >>> X = np.linspace(-5.0, 5.0, 100)
+    >>> fig, ax = plt.subplots()
+    >>> ax.set_title("PDF from Template")
+    >>> ax.hist(data, density=True, bins=100)
+    >>> ax.plot(X, hist_dist.pdf(X), label='PDF')
+    >>> ax.plot(X, hist_dist.cdf(X), label='CDF')
+    >>> ax.legend()
+    >>> fig.show()
+
+    """
+    _support_mask = rv_continuous._support_mask
+
+    def __init__(self, histogram, *args, density=None, **kwargs):
+        """
+        Create a new distribution using the given histogram
+
+        Parameters
+        ----------
+        histogram : tuple of array_like
+            Tuple containing two array_like objects.
+            The first containing the content of n bins,
+            the second containing the (n+1) bin boundaries.
+            In particular, the return value of np.histogram is accepted.
+        density : bool, optional
+            If False, assumes the histogram is proportional to counts per bin;
+            otherwise, assumes it is proportional to a density.
+            For constant bin widths, these are equivalent.
+            If None (default), sets ``density=True`` for backward
+            compatibility, but warns if the bin widths are variable. Set
+            `density` explicitly to silence the warning.
+        """
+        self._histogram = histogram
+        self._density = density
+        if len(histogram) != 2:
+            raise ValueError("Expected length 2 for parameter histogram")
+        self._hpdf = np.asarray(histogram[0])
+        self._hbins = np.asarray(histogram[1])
+        if len(self._hpdf) + 1 != len(self._hbins):
+            raise ValueError("Number of elements in histogram content "
+                             "and histogram boundaries do not match, "
+                             "expected n and n+1.")
+        self._hbin_widths = self._hbins[1:] - self._hbins[:-1]
+        bins_vary = not np.allclose(self._hbin_widths, self._hbin_widths[0])
+        if density is None and bins_vary:
+            message = ("Bin widths are not constant. Assuming `density=True`."
+                       "Specify `density` explicitly to silence this warning.")
+            warnings.warn(message, RuntimeWarning, stacklevel=2)
+            density = True
+        elif not density:
+            self._hpdf = self._hpdf / self._hbin_widths
+
+        self._hpdf = self._hpdf / float(np.sum(self._hpdf * self._hbin_widths))
+        self._hcdf = np.cumsum(self._hpdf * self._hbin_widths)
+        self._hpdf = np.hstack([0.0, self._hpdf, 0.0])
+        self._hcdf = np.hstack([0.0, self._hcdf])
+        # Set support
+        kwargs['a'] = self.a = self._hbins[0]
+        kwargs['b'] = self.b = self._hbins[-1]
+        super().__init__(*args, **kwargs)
+
+    def _pdf(self, x):
+        """
+        PDF of the histogram
+        """
+        return self._hpdf[np.searchsorted(self._hbins, x, side='right')]
+
+    def _cdf(self, x):
+        """
+        CDF calculated from the histogram
+        """
+        return np.interp(x, self._hbins, self._hcdf)
+
+    def _ppf(self, x):
+        """
+        Percentile function calculated from the histogram
+        """
+        return np.interp(x, self._hcdf, self._hbins)
+
+    def _munp(self, n):
+        """Compute the n-th non-central moment."""
+        integrals = (self._hbins[1:]**(n+1) - self._hbins[:-1]**(n+1)) / (n+1)
+        return np.sum(self._hpdf[1:-1] * integrals)
+
+    def _entropy(self):
+        """Compute entropy of distribution"""
+        hpdf = self._hpdf[1:-1]
+        res = xpx.apply_where(hpdf > 0.0, hpdf, np.log, fill_value=0.0)
+        return -np.sum(hpdf * res * self._hbin_widths)
+
+    def _updated_ctor_param(self):
+        """
+        Set the histogram as additional constructor argument
+        """
+        dct = super()._updated_ctor_param()
+        dct['histogram'] = self._histogram
+        dct['density'] = self._density
+        return dct
+
+
+class studentized_range_gen(rv_continuous):
+    r"""A studentized range continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    t: Student's t distribution
+
+    Notes
+    -----
+    The probability density function for `studentized_range` is:
+
+    .. math::
+
+         f(x; k, \nu) = \frac{k(k-1)\nu^{\nu/2}}{\Gamma(\nu/2)
+                        2^{\nu/2-1}} \int_{0}^{\infty} \int_{-\infty}^{\infty}
+                        s^{\nu} e^{-\nu s^2/2} \phi(z) \phi(sx + z)
+                        [\Phi(sx + z) - \Phi(z)]^{k-2} \,dz \,ds
+
+    for :math:`x ≥ 0`, :math:`k > 1`, and :math:`\nu > 0`.
+
+    `studentized_range` takes ``k`` for :math:`k` and ``df`` for :math:`\nu`
+    as shape parameters.
+
+    When :math:`\nu` exceeds 100,000, an asymptotic approximation (infinite
+    degrees of freedom) is used to compute the cumulative distribution
+    function [4]_ and probability distribution function.
+
+    %(after_notes)s
+
+    References
+    ----------
+
+    .. [1] "Studentized range distribution",
+           https://en.wikipedia.org/wiki/Studentized_range_distribution
+    .. [2] Batista, Ben Dêivide, et al. "Externally Studentized Normal Midrange
+           Distribution." Ciência e Agrotecnologia, vol. 41, no. 4, 2017, pp.
+           378-389., :doi:`10.1590/1413-70542017414047716`.
+    .. [3] Harter, H. Leon. "Tables of Range and Studentized Range." The Annals
+           of Mathematical Statistics, vol. 31, no. 4, 1960, pp. 1122-1147.
+           JSTOR, www.jstor.org/stable/2237810. Accessed 18 Feb. 2021.
+    .. [4] Lund, R. E., and J. R. Lund. "Algorithm AS 190: Probabilities and
+           Upper Quantiles for the Studentized Range." Journal of the Royal
+           Statistical Society. Series C (Applied Statistics), vol. 32, no. 2,
+           1983, pp. 204-210. JSTOR, www.jstor.org/stable/2347300. Accessed 18
+           Feb. 2021.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import studentized_range
+    >>> import matplotlib.pyplot as plt
+    >>> fig, ax = plt.subplots(1, 1)
+
+    Display the probability density function (``pdf``):
+
+    >>> k, df = 3, 10
+    >>> x = np.linspace(studentized_range.ppf(0.01, k, df),
+    ...                 studentized_range.ppf(0.99, k, df), 100)
+    >>> ax.plot(x, studentized_range.pdf(x, k, df),
+    ...         'r-', lw=5, alpha=0.6, label='studentized_range pdf')
+
+    Alternatively, the distribution object can be called (as a function)
+    to fix the shape, location and scale parameters. This returns a "frozen"
+    RV object holding the given parameters fixed.
+
+    Freeze the distribution and display the frozen ``pdf``:
+
+    >>> rv = studentized_range(k, df)
+    >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
+
+    Check accuracy of ``cdf`` and ``ppf``:
+
+    >>> vals = studentized_range.ppf([0.001, 0.5, 0.999], k, df)
+    >>> np.allclose([0.001, 0.5, 0.999], studentized_range.cdf(vals, k, df))
+    True
+
+    Rather than using (``studentized_range.rvs``) to generate random variates,
+    which is very slow for this distribution, we can approximate the inverse
+    CDF using an interpolator, and then perform inverse transform sampling
+    with this approximate inverse CDF.
+
+    This distribution has an infinite but thin right tail, so we focus our
+    attention on the leftmost 99.9 percent.
+
+    >>> a, b = studentized_range.ppf([0, .999], k, df)
+    >>> a, b
+    0, 7.41058083802274
+
+    >>> from scipy.interpolate import interp1d
+    >>> rng = np.random.default_rng()
+    >>> xs = np.linspace(a, b, 50)
+    >>> cdf = studentized_range.cdf(xs, k, df)
+    # Create an interpolant of the inverse CDF
+    >>> ppf = interp1d(cdf, xs, fill_value='extrapolate')
+    # Perform inverse transform sampling using the interpolant
+    >>> r = ppf(rng.uniform(size=1000))
+
+    And compare the histogram:
+
+    >>> ax.hist(r, density=True, histtype='stepfilled', alpha=0.2)
+    >>> ax.legend(loc='best', frameon=False)
+    >>> plt.show()
+
+    """
+
+    def _argcheck(self, k, df):
+        return (k > 1) & (df > 0)
+
+    def _shape_info(self):
+        ik = _ShapeInfo("k", False, (1, np.inf), (False, False))
+        idf = _ShapeInfo("df", False, (0, np.inf), (False, False))
+        return [ik, idf]
+
+    def _fitstart(self, data):
+        # Default is k=1, but that is not a valid value of the parameter.
+        return super()._fitstart(data, args=(2, 1))
+
+    def _munp(self, K, k, df):
+        cython_symbol = '_studentized_range_moment'
+        _a, _b = self._get_support()
+        # all three of these are used to create a numpy array so they must
+        # be the same shape.
+
+        def _single_moment(K, k, df):
+            log_const = _stats._studentized_range_pdf_logconst(k, df)
+            arg = [K, k, df, log_const]
+            usr_data = np.array(arg, float).ctypes.data_as(ctypes.c_void_p)
+
+            llc = LowLevelCallable.from_cython(_stats, cython_symbol, usr_data)
+
+            ranges = [(-np.inf, np.inf), (0, np.inf), (_a, _b)]
+            opts = dict(epsabs=1e-11, epsrel=1e-12)
+
+            return integrate.nquad(llc, ranges=ranges, opts=opts)[0]
+
+        ufunc = np.frompyfunc(_single_moment, 3, 1)
+        return np.asarray(ufunc(K, k, df), dtype=np.float64)[()]
+
+    def _pdf(self, x, k, df):
+
+        def _single_pdf(q, k, df):
+            # The infinite form of the PDF is derived from the infinite
+            # CDF.
+            if df < 100000:
+                cython_symbol = '_studentized_range_pdf'
+                log_const = _stats._studentized_range_pdf_logconst(k, df)
+                arg = [q, k, df, log_const]
+                usr_data = np.array(arg, float).ctypes.data_as(ctypes.c_void_p)
+                ranges = [(-np.inf, np.inf), (0, np.inf)]
+
+            else:
+                cython_symbol = '_studentized_range_pdf_asymptotic'
+                arg = [q, k]
+                usr_data = np.array(arg, float).ctypes.data_as(ctypes.c_void_p)
+                ranges = [(-np.inf, np.inf)]
+
+            llc = LowLevelCallable.from_cython(_stats, cython_symbol, usr_data)
+            opts = dict(epsabs=1e-11, epsrel=1e-12)
+            return integrate.nquad(llc, ranges=ranges, opts=opts)[0]
+
+        ufunc = np.frompyfunc(_single_pdf, 3, 1)
+        return np.asarray(ufunc(x, k, df), dtype=np.float64)[()]
+
+    def _cdf(self, x, k, df):
+
+        def _single_cdf(q, k, df):
+            # "When the degrees of freedom V are infinite the probability
+            # integral takes [on a] simpler form," and a single asymptotic
+            # integral is evaluated rather than the standard double integral.
+            # (Lund, Lund, page 205)
+            if df < 100000:
+                cython_symbol = '_studentized_range_cdf'
+                log_const = _stats._studentized_range_cdf_logconst(k, df)
+                arg = [q, k, df, log_const]
+                usr_data = np.array(arg, float).ctypes.data_as(ctypes.c_void_p)
+                ranges = [(-np.inf, np.inf), (0, np.inf)]
+
+            else:
+                cython_symbol = '_studentized_range_cdf_asymptotic'
+                arg = [q, k]
+                usr_data = np.array(arg, float).ctypes.data_as(ctypes.c_void_p)
+                ranges = [(-np.inf, np.inf)]
+
+            llc = LowLevelCallable.from_cython(_stats, cython_symbol, usr_data)
+            opts = dict(epsabs=1e-11, epsrel=1e-12)
+            return integrate.nquad(llc, ranges=ranges, opts=opts)[0]
+
+        ufunc = np.frompyfunc(_single_cdf, 3, 1)
+
+        # clip p-values to ensure they are in [0, 1].
+        return np.clip(np.asarray(ufunc(x, k, df), dtype=np.float64)[()], 0, 1)
+
+
+studentized_range = studentized_range_gen(name='studentized_range', a=0,
+                                          b=np.inf)
+
+
+class rel_breitwigner_gen(rv_continuous):
+    r"""A relativistic Breit-Wigner random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    cauchy: Cauchy distribution, also known as the Breit-Wigner distribution.
+
+    Notes
+    -----
+
+    The probability density function for `rel_breitwigner` is
+
+    .. math::
+
+        f(x, \rho) = \frac{k}{(x^2 - \rho^2)^2 + \rho^2}
+
+    where
+
+    .. math::
+        k = \frac{2\sqrt{2}\rho^2\sqrt{\rho^2 + 1}}
+            {\pi\sqrt{\rho^2 + \rho\sqrt{\rho^2 + 1}}}
+
+    The relativistic Breit-Wigner distribution is used in high energy physics
+    to model resonances [1]_. It gives the uncertainty in the invariant mass,
+    :math:`M` [2]_, of a resonance with characteristic mass :math:`M_0` and
+    decay-width :math:`\Gamma`, where :math:`M`, :math:`M_0` and :math:`\Gamma`
+    are expressed in natural units. In SciPy's parametrization, the shape
+    parameter :math:`\rho` is equal to :math:`M_0/\Gamma` and takes values in
+    :math:`(0, \infty)`.
+
+    Equivalently, the relativistic Breit-Wigner distribution is said to give
+    the uncertainty in the center-of-mass energy :math:`E_{\text{cm}}`. In
+    natural units, the speed of light :math:`c` is equal to 1 and the invariant
+    mass :math:`M` is equal to the rest energy :math:`Mc^2`. In the
+    center-of-mass frame, the rest energy is equal to the total energy [3]_.
+
+    %(after_notes)s
+
+    :math:`\rho = M/\Gamma` and :math:`\Gamma` is the scale parameter. For
+    example, if one seeks to model the :math:`Z^0` boson with :math:`M_0
+    \approx 91.1876 \text{ GeV}` and :math:`\Gamma \approx 2.4952\text{ GeV}`
+    [4]_ one can set ``rho=91.1876/2.4952`` and ``scale=2.4952``.
+
+    To ensure a physically meaningful result when using the `fit` method, one
+    should set ``floc=0`` to fix the location parameter to 0.
+
+    References
+    ----------
+    .. [1] Relativistic Breit-Wigner distribution, Wikipedia,
+           https://en.wikipedia.org/wiki/Relativistic_Breit-Wigner_distribution
+    .. [2] Invariant mass, Wikipedia,
+           https://en.wikipedia.org/wiki/Invariant_mass
+    .. [3] Center-of-momentum frame, Wikipedia,
+           https://en.wikipedia.org/wiki/Center-of-momentum_frame
+    .. [4] M. Tanabashi et al. (Particle Data Group) Phys. Rev. D 98, 030001 -
+           Published 17 August 2018
+
+    %(example)s
+
+    """
+    def _argcheck(self, rho):
+        return rho > 0
+
+    def _shape_info(self):
+        return [_ShapeInfo("rho", False, (0, np.inf), (False, False))]
+
+    def _pdf(self, x, rho):
+        # C = k / rho**2
+        C = np.sqrt(
+            2 * (1 + 1/rho**2) / (1 + np.sqrt(1 + 1/rho**2))
+        ) * 2 / np.pi
+        with np.errstate(over='ignore'):
+            return C / (((x - rho)*(x + rho)/rho)**2 + 1)
+
+    def _cdf(self, x, rho):
+        # C = k / (2 * rho**2) / np.sqrt(1 + 1/rho**2)
+        C = np.sqrt(2/(1 + np.sqrt(1 + 1/rho**2)))/np.pi
+        result = (
+            np.sqrt(-1 + 1j/rho)
+            * np.arctan(x/np.sqrt(-rho*(rho + 1j)))
+        )
+        result = C * 2 * np.imag(result)
+        # Sometimes above formula produces values greater than 1.
+        return np.clip(result, None, 1)
+
+    def _munp(self, n, rho):
+        if n == 0:
+            return 1.
+        if n == 1:
+            # C = k / (2 * rho)
+            C = np.sqrt(
+                2 * (1 + 1/rho**2) / (1 + np.sqrt(1 + 1/rho**2))
+            ) / np.pi * rho
+            return C * (np.pi/2 + np.arctan(rho))
+        if n == 2:
+            # C = pi * k / (4 * rho)
+            C = np.sqrt(
+                (1 + 1/rho**2) / (2 * (1 + np.sqrt(1 + 1/rho**2)))
+            ) * rho
+            result = (1 - rho * 1j) / np.sqrt(-1 - 1j/rho)
+            return 2 * C * np.real(result)
+        else:
+            return np.inf
+
+    def _stats(self, rho):
+        # Returning None from stats makes public stats use _munp.
+        # nan values will be omitted from public stats. Skew and
+        # kurtosis are actually infinite.
+        return None, None, np.nan, np.nan
+
+    @inherit_docstring_from(rv_continuous)
+    def fit(self, data, *args, **kwds):
+        # Override rv_continuous.fit to better handle case where floc is set.
+        data, _, floc, fscale = _check_fit_input_parameters(
+            self, data, args, kwds
+        )
+
+        censored = isinstance(data, CensoredData)
+        if censored:
+            if data.num_censored() == 0:
+                # There are no censored values in data, so replace the
+                # CensoredData instance with a regular array.
+                data = data._uncensored
+                censored = False
+
+        if floc is None or censored:
+            return super().fit(data, *args, **kwds)
+
+        if fscale is None:
+            # The interquartile range approximates the scale parameter gamma.
+            # The median approximates rho * gamma.
+            p25, p50, p75 = np.quantile(data - floc, [0.25, 0.5, 0.75])
+            scale_0 = p75 - p25
+            rho_0 = p50 / scale_0
+            if not args:
+                args = [rho_0]
+            if "scale" not in kwds:
+                kwds["scale"] = scale_0
+        else:
+            M_0 = np.median(data - floc)
+            rho_0 = M_0 / fscale
+            if not args:
+                args = [rho_0]
+        return super().fit(data, *args, **kwds)
+
+
+rel_breitwigner = rel_breitwigner_gen(a=0.0, name="rel_breitwigner")
+
+
+# Collect names of classes and objects in this module.
+pairs = list(globals().copy().items())
+_distn_names, _distn_gen_names = get_distribution_names(pairs, rv_continuous)
+
+__all__ = _distn_names + _distn_gen_names + ['rv_histogram']
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_correlation.py b/venv/lib/python3.12/site-packages/scipy/stats/_correlation.py
new file mode 100644
index 0000000000000000000000000000000000000000..5c72e5eac9300911c8b6281eceb9ca91d3b03a4c
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_correlation.py
@@ -0,0 +1,731 @@
+import numpy as np
+import math
+from scipy import stats, special
+from scipy._external import array_api_extra as xpx
+from scipy._lib._array_api import (xp_capabilities, array_namespace, xp_promote,
+                                   is_numpy, _share_masks, _count_nonmasked, is_marray)
+from scipy.stats._stats_py import (_SimpleNormal, SignificanceResult, _get_pvalue,
+                                   _rankdata)
+from scipy.stats._axis_nan_policy import _axis_nan_policy_factory
+from scipy.stats._stats_mstats_common import (TheilslopesResult, _n_samples_optional_x,
+                                              SiegelslopesResult)
+
+
+__all__ = ['chatterjeexi', 'spearmanrho', 'theilslopes', 'siegelslopes']
+
+
+def _xi_statistic(x, y, y_continuous, xp):
+    # Compute xi correlation statistic
+
+    # `axis=-1` is guaranteed by _axis_nan_policy decorator
+    n = x.shape[-1]
+
+    # "Rearrange the data as (X(1), Y(1)), . . . ,(X(n), Y(n))
+    # such that X(1) ≤ ··· ≤ X(n)"
+    j = xp.argsort(x, axis=-1)
+    j, y = xp.broadcast_arrays(j, y)
+    y = xp.take_along_axis(y, j, axis=-1)
+
+    # "Let ri be the rank of Y(i), that is, the number of j such that Y(j) ≤ Y(i)"
+    r = stats.rankdata(y, method='max', axis=-1)
+    # " additionally define li to be the number of j such that Y(j) ≥ Y(i)"
+    # Could probably compute this from r, but that can be an enhancement
+    l = stats.rankdata(-y, method='max', axis=-1)
+
+    num = xp.sum(xp.abs(xp.diff(r, axis=-1)), axis=-1)
+    if y_continuous:  # [1] Eq. 1.1
+        statistic = 1 - 3 * num / (n ** 2 - 1)
+    else:  # [1] Eq. 1.2
+        den = 2 * xp.sum((n - l) * l, axis=-1)
+        statistic = 1 - n * num / den
+
+    return statistic, r, l
+
+
+def _xi_std(r, l, y_continuous, xp):
+    # Compute asymptotic standard deviation of xi under null hypothesis of independence
+
+    # `axis=-1` is guaranteed by _axis_nan_policy decorator
+    n = r.shape[-1]
+
+    # "Suppose that X and Y are independent and Y is continuous. Then
+    # √n·ξn(X, Y) → N(0, 2/5) in distribution as n → ∞"
+    if y_continuous:  # [1] Theorem 2.1
+        return xp.asarray(math.sqrt(2 / 5) / math.sqrt(n), dtype=r.dtype)
+
+    # "Suppose that X and Y are independent. Then √n·ξn(X, Y)
+    # converges to N(0, τ²) in distribution as n → ∞
+    # [1] Eq. 2.2 and surrounding math
+    i = xp.arange(1, n + 1, dtype=r.dtype)
+    u = xp.sort(r, axis=-1)
+    v = xp.cumulative_sum(u, axis=-1)
+    an = 1 / n**4 * xp.sum((2*n - 2*i + 1) * u**2, axis=-1)
+    bn = 1 / n**5 * xp.sum((v + (n - i)*u)**2, axis=-1)
+    cn = 1 / n**3 * xp.sum((2*n - 2*i + 1) * u, axis=-1)
+    dn = 1 / n**3 * xp.sum((l * (n - l)), axis=-1)
+    tau2 = (an - 2*bn + cn**2) / dn**2
+
+    return xp.sqrt(tau2) / math.sqrt(n)
+
+
+def _chatterjeexi_iv(y_continuous, method):
+    # Input validation for `chatterjeexi`
+    # x, y, `axis` input validation taken care of by decorator
+
+    if y_continuous not in {True, False}:
+        raise ValueError('`y_continuous` must be boolean.')
+
+    if not isinstance(method, stats.PermutationMethod):
+        method = method.lower()
+        message = "`method` must be 'asymptotic' or a `PermutationMethod` instance."
+        if method != 'asymptotic':
+            raise ValueError(message)
+
+    return y_continuous, method
+
+
+def _unpack(res, _):
+    return res.statistic, res.pvalue
+
+
+@xp_capabilities(skip_backends=[('dask.array', 'no take_along_axis')])
+@_axis_nan_policy_factory(SignificanceResult, paired=True, n_samples=2,
+                          result_to_tuple=_unpack, n_outputs=2, too_small=1)
+def chatterjeexi(x, y, *, axis=0, y_continuous=False, method='asymptotic'):
+    r"""Compute the xi correlation and perform a test of independence.
+
+    The xi correlation coefficient is a measure of association between two
+    variables; the value tends to be close to zero when the variables are
+    independent and close to 1 when there is a strong association. Unlike
+    other correlation coefficients, the xi correlation is effective even
+    when the association is not monotonic.
+
+    Parameters
+    ----------
+    x, y : array-like
+        The samples: corresponding observations of the independent and
+        dependent variable. The (N-d) arrays must be broadcastable.
+    axis : int, default: 0
+        Axis along which to perform the test.
+    y_continuous : bool, default: False
+        Whether `y` is assumed to be drawn from a continuous distribution.
+        If `y` is drawn from a continuous distribution, results are valid
+        whether this is assumed or not, but enabling this assumption will
+        result in faster computation and typically produce similar results.
+    method : 'asymptotic' or `PermutationMethod` instance, optional
+        Selects the method used to calculate the *p*-value.
+        Default is 'asymptotic'. The following options are available.
+
+        * ``'asymptotic'``: compares the standardized test statistic
+          against the normal distribution.
+        * `PermutationMethod` instance. In this case, the p-value
+          is computed using `permutation_test` with the provided
+          configuration options and other appropriate settings.
+
+    Returns
+    -------
+    res : SignificanceResult
+        An object containing attributes:
+
+        statistic : float
+            The xi correlation statistic.
+        pvalue : float
+            The associated *p*-value: the probability of a statistic at least as
+            high as the observed value under the null hypothesis of independence.
+
+    See Also
+    --------
+    scipy.stats.pearsonr, scipy.stats.spearmanr, scipy.stats.kendalltau
+
+    Notes
+    -----
+    There is currently no special handling of ties in `x`; they are broken arbitrarily
+    by the implementation. [1]_ recommends: "if there are ties among the Xi's, then
+    choose an increasing rearrangement as above by breaking ties uniformly at random."
+    This is easily accomplished by adding a small amount of random noise to `x`; see
+    examples.
+
+    [1]_ notes that the statistic is not symmetric in `x` and `y` *by design*:
+    "...we may want to understand if :math:`Y` is a function :math:`X`, and not just
+    if one of the variables is a function of the other." See [1]_ Remark 1.
+
+    References
+    ----------
+    .. [1] Chatterjee, Sourav. "A new coefficient of correlation." Journal of
+           the American Statistical Association 116.536 (2021): 2009-2022.
+           :doi:`10.1080/01621459.2020.1758115`.
+
+    Examples
+    --------
+    Generate perfectly correlated data, and observe that the xi correlation is
+    nearly 1.0.
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> rng = np.random.default_rng(348932549825235)
+    >>> x = rng.uniform(0, 10, size=100)
+    >>> y = np.sin(x)
+    >>> res = stats.chatterjeexi(x, y)
+    >>> res.statistic
+    np.float64(0.9012901290129013)
+
+    The probability of observing such a high value of the statistic under the
+    null hypothesis of independence is very low.
+
+    >>> res.pvalue
+    np.float64(2.2206974648177804e-46)
+
+    As noise is introduced, the correlation coefficient decreases.
+
+    >>> noise = rng.normal(scale=[[0.1], [0.5], [1]], size=(3, 100))
+    >>> res = stats.chatterjeexi(x, y + noise, axis=-1)
+    >>> res.statistic
+    array([0.79507951, 0.41824182, 0.16651665])
+
+    Because the distribution of `y` is continuous, it is valid to pass
+    ``y_continuous=True``. The statistic is identical, and the p-value
+    (not shown) is only slightly different.
+
+    >>> stats.chatterjeexi(x, y + noise, y_continuous=True, axis=-1).statistic
+    array([0.79507951, 0.41824182, 0.16651665])
+
+    Consider a case in which there are ties in `x`.
+
+    >>> x = rng.integers(10, size=1000)
+    >>> y = rng.integers(10, size=1000)
+
+    [1]_ recommends breaking the ties uniformly at random.
+
+    >>> d = rng.uniform(1e-5, size=x.size)
+    >>> res = stats.chatterjeexi(x + d, y)
+    >>> res.statistic
+    -0.029919991638798438
+
+    Since this gives a randomized estimate of the statistic, [1]_ also suggests
+    considering the average over all possibilities of breaking ties. This is
+    computationally infeasible when there are many ties, but a randomized estimate of
+    *this* quantity can be obtained by considering many random possibilities of breaking
+    ties.
+
+    >>> d = rng.uniform(1e-5, size=(9999, x.size))
+    >>> res = stats.chatterjeexi(x + d, y, axis=1)
+    >>> np.mean(res.statistic)
+    0.001186895213756626
+
+    """
+    xp = array_namespace(x, y)
+
+    # x, y, `axis` input validation taken care of by decorator
+    # In fact, `axis` is guaranteed to be -1
+    y_continuous, method = _chatterjeexi_iv(y_continuous, method)
+    x, y = xp_promote(x, y, force_floating=True, xp=xp)
+
+    # A highly negative statistic is possible, e.g.
+    # x = np.arange(100.), y = (x % 2 == 0)
+    # Unclear whether we should expose `alternative`, though.
+    alternative = 'greater'
+
+    if method == 'asymptotic':
+        xi, r, l = _xi_statistic(x, y, y_continuous, xp=xp)
+        std = _xi_std(r, l, y_continuous, xp=xp)
+        norm = _SimpleNormal()
+        pvalue = _get_pvalue(xi / std, norm, alternative=alternative, xp=xp)
+    elif isinstance(method, stats.PermutationMethod):
+        res = stats.permutation_test(
+            # Could be faster if we just permuted the ranks; for now, keep it simple.
+            data=(y,),
+            statistic=lambda y, axis: _xi_statistic(x, y, y_continuous, xp=xp)[0],
+            alternative=alternative, permutation_type='pairings', **method._asdict(),
+            axis=-1)  # `axis=-1` is guaranteed by _axis_nan_policy decorator
+
+        xi, pvalue = res.statistic, res.pvalue
+
+    xi = xi[()] if xi.ndim == 0 else xi
+    pvalue = pvalue[()] if pvalue.ndim == 0 else pvalue
+    return SignificanceResult(xi, pvalue)
+
+
+@xp_capabilities(cpu_only=True, exceptions=['jax.numpy'], marray=True,
+    skip_backends=[('dask.array', 'not supported by rankdata (take_along_axis)')],
+    extra_note='Only the default `method` is compatible with MArray input.'
+)
+@_axis_nan_policy_factory(SignificanceResult, paired=True, n_samples=2,
+                          result_to_tuple=_unpack, n_outputs=2, too_small=1)
+def spearmanrho(x, y, /, *, alternative='two-sided', method=None, axis=0):
+    r"""Calculate a Spearman rho correlation coefficient with associated p-value.
+
+    The Spearman rank-order correlation coefficient is a nonparametric measure
+    of the monotonicity of the relationship between two datasets.
+    Like other correlation coefficients, it varies between -1 and +1 with 0
+    implying no correlation. Coefficients of -1 or +1 are associated with an exact
+    monotonic relationship.  Positive correlations indicate that as `x` increases,
+    so does `y`; negative correlations indicate that as `x` increases, `y` decreases.
+    The p-value is the probability of an uncorrelated system producing datasets
+    with a Spearman correlation at least as extreme as the one computed from the
+    observed dataset.
+
+    Parameters
+    ----------
+    x, y : array-like
+        The samples: corresponding observations of the independent and
+        dependent variable. The (N-d) arrays must be broadcastable.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis. Default is 'two-sided'.
+        The following options are available:
+
+        * 'two-sided': the correlation is nonzero
+        * 'less': the correlation is negative (less than zero)
+        * 'greater':  the correlation is positive (greater than zero)
+
+    method : ResamplingMethod, optional
+        Defines the method used to compute the p-value. If `method` is an
+        instance of `PermutationMethod`/`MonteCarloMethod`, the p-value is
+        computed using
+        `scipy.stats.permutation_test`/`scipy.stats.monte_carlo_test` with the
+        provided configuration options and other appropriate settings.
+        Otherwise, the p-value is computed using an asymptotic approximation of
+        the null distribution.
+    axis : int or None, optional
+        If axis=0 (default), then each column represents a variable, with
+        observations in the rows. If axis=1, the relationship is transposed:
+        each row represents a variable, while the columns contain observations.
+        If axis=None, then both arrays will be raveled.
+        Like other `scipy.stats` functions, `axis` is interpreted after the
+        arrays are broadcasted.
+
+    Returns
+    -------
+    res : SignificanceResult
+        An object containing attributes:
+
+        statistic : floating point array or NumPy scalar
+            Spearman correlation coefficient
+        pvalue : floating point array NumPy scalar
+            The p-value - the probabilitiy of realizing such an extreme statistic
+            value under the null hypothesis that two samples have no ordinal
+            correlation. See `alternative` above for alternative hypotheses.
+
+    Warns
+    -----
+    `~scipy.stats.ConstantInputWarning`
+        Raised if an input is a constant array.  The correlation coefficient
+        is not defined in this case, so ``np.nan`` is returned.
+
+    Notes
+    -----
+    `spearmanrho` was created to make improvements to SciPy's implementation of
+    the Spearman correlation test without making backward-incompatible changes
+    to `spearmanr`. Advantages of `spearmanrho` over `spearmanr` include:
+
+    - `spearmanrho` follows standard array broadcasting rules.
+    - `spearmanrho` is compatible with some non-NumPy arrays.
+    - `spearmanrho` can compute exact p-values, even in the presence of ties,
+      when an appropriate instance of `PermutationMethod` is provided via the
+      `method` argument.
+
+    References
+    ----------
+    .. [1] Zwillinger, D. and Kokoska, S. (2000). CRC Standard
+       Probability and Statistics Tables and Formulae. Chapman & Hall: New
+       York. 2000.
+       Section  14.7
+    .. [2] Kendall, M. G. and Stuart, A. (1973).
+       The Advanced Theory of Statistics, Volume 2: Inference and Relationship.
+       Griffin. 1973.
+       Section 31.18
+
+    Examples
+    --------
+    Univariate samples, approximate p-value.
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> x = [1, 2, 3, 4, 5]
+    >>> y = [5, 6, 7, 8, 7]
+    >>> res = stats.spearmanrho(x, y)
+    >>> res.statistic
+    np.float64(0.8207826816681233)
+    >>> res.pvalue
+    np.float64(0.08858700531354405)
+
+    Univariate samples, exact p-value.
+
+    >>> res = stats.spearmanrho(x, y, method=stats.PermutationMethod())
+    >>> res.statistic
+    np.float64(0.8207826816681233)
+    >>> res.pvalue
+    np.float64(0.13333333333333333)
+
+    Batch of univariate samples, one vectorized call.
+
+    >>> rng = np.random.default_rng(98145152315484)
+    >>> x2 = rng.standard_normal((2, 100))
+    >>> y2 = rng.standard_normal((2, 100))
+    >>> res = stats.spearmanrho(x2, y2, axis=-1)
+    >>> res.statistic
+    array([ 0.16585659, -0.12151215])
+    >>> res.pvalue
+    array([0.0991155 , 0.22846869])
+
+    Bivariate samples using standard broadcasting rules.
+
+    >>> res = stats.spearmanrho(x2[np.newaxis, :], x2[:, np.newaxis], axis=-1)
+    >>> res.statistic
+    array([[ 1.        , -0.14670267],
+           [-0.14670267,  1.        ]])
+    >>> res.pvalue
+    array([[0.        , 0.14526128],
+           [0.14526128, 0.        ]])
+
+    """
+    xp = array_namespace(x, y)
+    x, y = _share_masks(x, y, xp=xp)
+    rx = stats.rankdata(x, axis=axis)
+    ry = stats.rankdata(y, axis=axis)
+    res = stats.pearsonr(rx, ry, method=method, alternative=alternative, axis=axis)
+    return SignificanceResult(res.statistic, res.pvalue)
+
+
+@xp_capabilities(skip_backends=[("dask.array", "no take_along_axis"),
+                                ("jax.numpy", "non-concrete boolean indexing")],
+                 marray=True)
+@_axis_nan_policy_factory(TheilslopesResult, default_axis=None, n_outputs=4,
+                          n_samples=_n_samples_optional_x,
+                          result_to_tuple=lambda x, _: tuple(x), paired=True,
+                          too_small=1)
+def theilslopes(y, x=None, alpha=0.95, method='separate', *, axis=None):
+    r"""
+    Computes the Theil-Sen estimator for a set of points (x, y).
+
+    `theilslopes` implements a method for robust linear regression.  It
+    computes the slope as the median of all slopes between paired values.
+
+    Parameters
+    ----------
+    y : array_like
+        Dependent variable.
+    x : array_like or None, optional
+        Independent variable. If None, use ``arange(len(y))`` instead.
+    alpha : float, optional
+        Confidence degree between 0 and 1. Default is 95% confidence.
+        Note that `alpha` is symmetric around 0.5, i.e. both 0.1 and 0.9 are
+        interpreted as "find the 90% confidence interval".
+    method : {'joint', 'separate'}, optional
+        Method to be used for computing estimate for intercept.
+        Following methods are supported,
+
+        * 'joint': Uses ``np.median(y - slope * x)`` as intercept.
+        * 'separate': Uses ``np.median(y) - slope * np.median(x)``
+                      as intercept.
+
+        The default is 'separate'.
+
+        .. versionadded:: 1.8.0
+
+    axis : int or tuple of ints, default: None
+        If an int or tuple of ints, the axis or axes of the input along which
+        to compute the statistic. The statistic of each axis-slice (e.g. row)
+        of the input will appear in a corresponding element of the output.
+        If ``None``, the input will be raveled before computing the statistic.
+
+    Returns
+    -------
+    result : ``TheilslopesResult`` instance
+        The return value is an object with the following attributes:
+
+        slope : float
+            Theil slope.
+        intercept : float
+            Intercept of the Theil line.
+        low_slope : float
+            Lower bound of the confidence interval on `slope`.
+        high_slope : float
+            Upper bound of the confidence interval on `slope`.
+
+    See Also
+    --------
+    siegelslopes : a similar technique using repeated medians
+
+    Notes
+    -----
+    The implementation of `theilslopes` follows [1]_. The intercept is
+    not defined in [1]_, and here it is defined as ``median(y) -
+    slope*median(x)``, which is given in [3]_. Other definitions of
+    the intercept exist in the literature such as  ``median(y - slope*x)``
+    in [4]_. The approach to compute the intercept can be determined by the
+    parameter ``method``. A confidence interval for the intercept is not
+    given as this question is not addressed in [1]_.
+
+    For compatibility with older versions of SciPy, the return value acts
+    like a ``namedtuple`` of length 4, with fields ``slope``, ``intercept``,
+    ``low_slope``, and ``high_slope``, so one can continue to write::
+
+        slope, intercept, low_slope, high_slope = theilslopes(y, x)
+
+    References
+    ----------
+    .. [1] P.K. Sen, "Estimates of the regression coefficient based on
+           Kendall's tau", J. Am. Stat. Assoc., Vol. 63, pp. 1379-1389, 1968.
+    .. [2] H. Theil, "A rank-invariant method of linear and polynomial
+           regression analysis I, II and III",  Nederl. Akad. Wetensch., Proc.
+           53:, pp. 386-392, pp. 521-525, pp. 1397-1412, 1950.
+    .. [3] W.L. Conover, "Practical nonparametric statistics", 2nd ed.,
+           John Wiley and Sons, New York, pp. 493.
+    .. [4] https://en.wikipedia.org/wiki/Theil%E2%80%93Sen_estimator
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> import matplotlib.pyplot as plt
+
+    >>> x = np.linspace(-5, 5, num=150)
+    >>> y = x + np.random.normal(size=x.size)
+    >>> y[11:15] += 10  # add outliers
+    >>> y[-5:] -= 7
+
+    Compute the slope, intercept and 90% confidence interval.  For comparison,
+    also compute the least-squares fit with `linregress`:
+
+    >>> res = stats.theilslopes(y, x, 0.90, method='separate')
+    >>> lsq_res = stats.linregress(x, y)
+
+    Plot the results. The Theil-Sen regression line is shown in red, with the
+    dashed red lines illustrating the confidence interval of the slope (note
+    that the dashed red lines are not the confidence interval of the regression
+    as the confidence interval of the intercept is not included). The green
+    line shows the least-squares fit for comparison.
+
+    >>> fig = plt.figure()
+    >>> ax = fig.add_subplot(111)
+    >>> ax.plot(x, y, 'b.')
+    >>> ax.plot(x, res[1] + res[0] * x, 'r-')
+    >>> ax.plot(x, res[1] + res[2] * x, 'r--')
+    >>> ax.plot(x, res[1] + res[3] * x, 'r--')
+    >>> ax.plot(x, lsq_res[1] + lsq_res[0] * x, 'g-')
+    >>> plt.show()
+
+    """
+    return _robust_slopes(y, x=x, alpha=alpha, method=method, pfun='theilslopes')
+
+
+@xp_capabilities(skip_backends=[("dask.array", "no take_along_axis"),
+                                ("jax.numpy", "quantile needs lazy nan_policy")],
+                 marray=True)
+@_axis_nan_policy_factory(SiegelslopesResult, default_axis=None, n_outputs=2,
+                          n_samples=_n_samples_optional_x,
+                          result_to_tuple=lambda x, _: tuple(x), paired=True,
+                          too_small=1)
+def siegelslopes(y, x=None, method='hierarchical', *, axis=None):
+    r"""
+    Computes the Siegel estimator for a set of points (x, y).
+
+    `siegelslopes` implements a method for robust linear regression
+    using repeated medians (see [1]_) to fit a line to the points (x, y).
+    The method is robust to outliers with an asymptotic breakdown point
+    of 50%.
+
+    Parameters
+    ----------
+    y : array_like
+        Dependent variable.
+    x : array_like or None, optional
+        Independent variable. If None, use ``arange(len(y))`` instead.
+    method : {'hierarchical', 'separate'}
+        If 'hierarchical', estimate the intercept using the estimated
+        slope ``slope`` (default option).
+        If 'separate', estimate the intercept independent of the estimated
+        slope. See Notes for details.
+    axis : int or tuple of ints, default: None
+        If an int or tuple of ints, the axis or axes of the input along which
+        to compute the statistic. The statistic of each axis-slice (e.g. row)
+        of the input will appear in a corresponding element of the output.
+        If ``None``, the input will be raveled before computing the statistic.
+
+    Returns
+    -------
+    result : ``SiegelslopesResult`` instance
+        The return value is an object with the following attributes:
+
+        slope : float
+            Estimate of the slope of the regression line.
+        intercept : float
+            Estimate of the intercept of the regression line.
+
+    See Also
+    --------
+    theilslopes : a similar technique without repeated medians
+
+    Notes
+    -----
+    With ``n = len(y)``, compute ``m_j`` as the median of
+    the slopes of the lines from the point ``(x[j], y[j])`` to all other ``n-1`` points.
+    ``slope`` is then the median of all slopes ``m_j``.
+    Two ways are given to estimate the intercept in [1]_ which can be chosen
+    via the parameter ``method``.
+    The hierarchical approach uses the estimated slope ``slope``
+    and computes ``intercept`` as the median of ``y - slope*x``.
+    The other approach estimates the intercept separately as follows: for
+    each point ``(x[j], y[j])``, compute the intercepts of all the ``n-1``
+    lines through the remaining points and take the median ``i_j``.
+    ``intercept`` is the median of the ``i_j``.
+
+    The implementation computes `n` times the median of a vector of size `n`
+    which can be slow for large vectors. There are more efficient algorithms
+    (see [2]_) which are not implemented here.
+
+    For compatibility with older versions of SciPy, the return value acts
+    like a ``namedtuple`` of length 2, with fields ``slope`` and
+    ``intercept``, so one can continue to write::
+
+        slope, intercept = siegelslopes(y, x)
+
+    References
+    ----------
+    .. [1] A. Siegel, "Robust Regression Using Repeated Medians",
+           Biometrika, Vol. 69, pp. 242-244, 1982.
+
+    .. [2] A. Stein and M. Werman, "Finding the repeated median regression
+           line", Proceedings of the Third Annual ACM-SIAM Symposium on
+           Discrete Algorithms, pp. 409-413, 1992.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> import matplotlib.pyplot as plt
+
+    >>> x = np.linspace(-5, 5, num=150)
+    >>> y = x + np.random.normal(size=x.size)
+    >>> y[11:15] += 10  # add outliers
+    >>> y[-5:] -= 7
+
+    Compute the slope and intercept.  For comparison, also compute the
+    least-squares fit with `linregress`:
+
+    >>> res = stats.siegelslopes(y, x)
+    >>> lsq_res = stats.linregress(x, y)
+
+    Plot the results. The Siegel regression line is shown in red. The green
+    line shows the least-squares fit for comparison.
+
+    >>> fig = plt.figure()
+    >>> ax = fig.add_subplot(111)
+    >>> ax.plot(x, y, 'b.')
+    >>> ax.plot(x, res[1] + res[0] * x, 'r-')
+    >>> ax.plot(x, lsq_res[1] + lsq_res[0] * x, 'g-')
+    >>> plt.show()
+
+    """
+    return _robust_slopes(y, x=x, method=method, pfun='siegelslopes')
+
+
+def _robust_slopes(y, *, x, alpha=None, method, pfun):
+    other_method = 'joint' if pfun == 'theilslopes' else 'hierarchical'
+    if method not in {other_method, 'separate'}:
+        raise ValueError(f"method must be either '{other_method}' or 'separate'. "
+                         f"'{method}' is invalid.")
+
+    xp = array_namespace(y, x)
+    y, x = xp_promote(y, x, force_floating=True, xp=xp)
+    x = xp.arange(y.shape[-1], dtype=y.dtype) if x is None else x
+    y, x = xp.broadcast_arrays(y, x)
+    x, y = _share_masks(x, y, xp=xp)
+
+    if x.shape[-1] < 2 or y.shape[-1] < 2:  # only needed by test_axis_nan_policy
+        raise ValueError("`x` and `y` must have length at least 2.")
+
+    # Compute sorted slopes only when deltax > 0
+    deltax = x[..., :, xp.newaxis] - x[..., xp.newaxis, :]
+    deltay = y[..., :, xp.newaxis] - y[..., xp.newaxis, :]
+
+    if pfun == 'theilslopes':
+        i = xp.astype(xp.triu(xp.ones(deltax.shape[-2:]), k=1), xp.bool)
+        if is_numpy(xp):
+            deltax, deltay = deltax[..., i], deltay[..., i]
+        else:
+            # With array API, mask must be sole index, so we need to broadcast it.
+            # Indexing ravels the array, so we need to reshape the results.
+            i = xp.broadcast_to(i, deltax.shape)
+            deltax, deltay = deltax[i], deltay[i]
+            deltax = xp.reshape(deltax, (*i.shape[:-2], -1))
+            deltay = xp.reshape(deltay, (*i.shape[:-2], -1))
+
+    # Use `.data` to avoid indexing with masked indices. If masked elements of deltax=0,
+    # they can safely be set to xp.nan, too - they're masked, after all.
+    deltax0 = (deltax.data == 0) if is_marray(xp) else (deltax == 0)
+    deltax = xpx.at(deltax)[deltax0].set(xp.nan)
+    slopes = deltay / deltax
+
+    if is_marray(xp):
+        def nanmedian(x, axis):  # use mask to ignore NaNs
+            x_nans_masked = xp.asarray(x.data, mask=x.mask | x._xp.isnan(x.data))
+            return stats.quantile(x_nans_masked, 0.5, axis=axis)
+    else:
+        def nanmedian(x, axis):  # use nan_policy to ignore NaNs
+            return stats.quantile(x, 0.5, axis=axis, nan_policy='omit')
+
+    def median(x, axis): return stats.quantile(x, 0.5, axis=axis)
+
+    # `theilslopes` is median of all slopes. Indexing with `i` above has already raveled
+    # all the slopes, so we only need to take the median along the last axis.
+    # `siegelslope` is a median of medians: we take the median of slopes from point i
+    # to all other points, then the median of those medians.
+    # The slope is NaN wherever the two points are the same, and those don't contribute,
+    # hence the first median omits NaNs. NaNs in the input are propagated by the
+    # `_axis_nan_policy` decorator.
+    medslope = (median(nanmedian(slopes, axis=-1), axis=-1) if pfun == 'siegelslopes'
+                else nanmedian(slopes, axis=-1))
+
+    if method in {'joint', 'hierarchical'}:
+        medinter = median(y - medslope[..., np.newaxis] * x, axis=-1)
+    elif pfun == 'theilslopes':
+        medinter = median(y, axis=-1) - medslope * median(x, axis=-1)
+    else:
+        # Calculate pairwise intercepts given each point (row i) and the slope to each
+        # other point (column j). Then calculate the median of (row) medians.
+        intercepts = y[..., :, xp.newaxis] - slopes*x[..., :, xp.newaxis]
+        medinter = median(nanmedian(intercepts, axis=-1), axis=-1)
+
+    if pfun == 'siegelslopes':
+        return SiegelslopesResult(slope=medslope[()], intercept=medinter[()])
+
+    # Now compute confidence intervals
+    if alpha > 0.5:
+        alpha = 1. - alpha
+
+    z = float(special.ndtri(alpha / 2.))
+    # This implements (2.6) from Sen (1968)
+    # we don't actually need ranks, so an enhancement could be to have
+    # `rankdata` return only the third output. In the meantime, use the
+    # least expensive `method`.
+    _, _, nxreps = _rankdata(x, method='min', return_ties=True)
+    _, _, nyreps = _rankdata(y, method='min', return_ties=True)
+    nt = xp.count_nonzero(xp.isfinite(slopes), axis=-1, keepdims=True)  # N in Sen 1968
+    nt = xp.asarray(nt, dtype=y.dtype)
+    ny = _count_nonmasked(y, keepdims=True, axis=-1)                    # n in Sen 1968
+    # Equation 2.6 in Sen (1968):
+    sigsq = 1/18. * (
+        ny * (ny-1) * (2*ny+5)
+        - xp.sum(nxreps * (nxreps-1) * (2*nxreps + 5), axis=-1, keepdims=True)
+        - xp.sum(nyreps * (nyreps-1) * (2*nyreps + 5), axis=-1, keepdims=True))
+    # Find the confidence interval indices in `slopes`
+    sigma = xp.sqrt(xp.maximum(sigsq, xp.zeros_like(sigsq)))
+    Ru = xp.minimum(xp.astype(xp.round((nt - z*sigma)/2.), xp.int64),
+                    xp.astype(nt, xp.int64)-1)
+    Rl = xp.maximum(xp.astype(xp.round((nt + z*sigma)/2.), xp.int64) - 1,
+                    xp.asarray(0, dtype=xp.int64))
+    R = xp.concat((xpx.atleast_nd(Rl, ndim=1), xpx.atleast_nd(Ru, ndim=1)), axis=-1)
+    slopes = xp.sort(slopes, axis=-1)
+    delta = xp.take_along_axis(slopes, R, axis=-1)
+    i_nan = xp.broadcast_to(sigsq < 0, delta.shape)
+    delta = xpx.at(delta)[i_nan].set(xp.nan)
+
+    slope = medslope[()] if medslope.ndim == 0 else medslope
+    intercept = medinter[()] if medinter.ndim == 0 else medinter
+    low_slope = delta[..., 0]
+    high_slope = delta[..., 1]
+    low_slope = low_slope[()] if low_slope.ndim == 0 else low_slope
+    high_slope = high_slope[()] if high_slope.ndim == 0 else high_slope
+    return TheilslopesResult(slope=slope, intercept=intercept,
+                             low_slope=low_slope, high_slope=high_slope)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_covariance.py b/venv/lib/python3.12/site-packages/scipy/stats/_covariance.py
new file mode 100644
index 0000000000000000000000000000000000000000..f2133b9f3278d19fbb94fd6b8ba74876078dc6dd
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_covariance.py
@@ -0,0 +1,672 @@
+from functools import cached_property
+from types import GenericAlias
+
+import numpy as np
+from scipy import linalg
+from scipy.stats import _multivariate
+
+
+__all__ = ["Covariance"]
+
+
+class Covariance:
+    """
+    Representation of a covariance matrix.
+
+    Calculations involving covariance matrices (e.g. data whitening,
+    multivariate normal function evaluation) are often performed more
+    efficiently using a decomposition of the covariance matrix instead of the
+    covariance matrix itself. This class allows the user to construct an
+    object representing a covariance matrix using any of several
+    decompositions and perform calculations using a common interface.
+
+    .. note::
+
+        The `Covariance` class cannot be instantiated directly. Instead, use
+        one of the factory methods (e.g. `Covariance.from_diagonal`).
+
+    Examples
+    --------
+    The `Covariance` class is used by calling one of its
+    factory methods to create a `Covariance` object, then pass that
+    representation of the `Covariance` matrix as a shape parameter of a
+    multivariate distribution.
+
+    For instance, the multivariate normal distribution can accept an array
+    representing a covariance matrix:
+
+    >>> from scipy import stats
+    >>> import numpy as np
+    >>> d = [1, 2, 3]
+    >>> A = np.diag(d)  # a diagonal covariance matrix
+    >>> x = [4, -2, 5]  # a point of interest
+    >>> dist = stats.multivariate_normal(mean=[0, 0, 0], cov=A)
+    >>> dist.pdf(x)
+    4.9595685102808205e-08
+
+    but the calculations are performed in a very generic way that does not
+    take advantage of any special properties of the covariance matrix. Because
+    our covariance matrix is diagonal, we can use ``Covariance.from_diagonal``
+    to create an object representing the covariance matrix, and
+    `multivariate_normal` can use this to compute the probability density
+    function more efficiently.
+
+    >>> cov = stats.Covariance.from_diagonal(d)
+    >>> dist = stats.multivariate_normal(mean=[0, 0, 0], cov=cov)
+    >>> dist.pdf(x)
+    4.9595685102808205e-08
+
+    """
+
+    # generic type compatibility with scipy-stubs
+    __class_getitem__: classmethod = classmethod(GenericAlias)
+
+    def __init__(self):
+        message = ("The `Covariance` class cannot be instantiated directly. "
+                   "Please use one of the factory methods "
+                   "(e.g. `Covariance.from_diagonal`).")
+        raise NotImplementedError(message)
+
+    @staticmethod
+    def from_diagonal(diagonal):
+        r"""
+        Return a representation of a covariance matrix from its diagonal.
+
+        Parameters
+        ----------
+        diagonal : array_like
+            The diagonal elements of a diagonal matrix.
+
+        Returns
+        -------
+        Covariance
+            A `Covariance` object representing `diagonal`.
+
+        Notes
+        -----
+        Let the diagonal elements of a diagonal covariance matrix :math:`D` be
+        stored in the vector :math:`d`.
+
+        When all elements of :math:`d` are strictly positive, whitening of a
+        data point :math:`x` is performed by computing
+        :math:`x \cdot d^{-1/2}`, where the inverse square root can be taken
+        element-wise.
+        :math:`\log\det{D}` is calculated as :math:`-2 \sum(\log{d})`,
+        where the :math:`\log` operation is performed element-wise.
+
+        This `Covariance` class supports singular covariance matrices. When
+        computing ``_log_pdet``, non-positive elements of :math:`d` are
+        ignored. Whitening is not well defined when the point to be whitened
+        does not lie in the span of the columns of the covariance matrix. The
+        convention taken here is to treat the inverse square root of
+        non-positive elements of :math:`d` as zeros.
+
+        Examples
+        --------
+        Prepare a symmetric positive definite covariance matrix ``A`` and a
+        data point ``x``.
+
+        >>> import numpy as np
+        >>> from scipy import stats
+        >>> rng = np.random.default_rng()
+        >>> n = 5
+        >>> A = np.diag(rng.random(n))
+        >>> x = rng.random(size=n)
+
+        Extract the diagonal from ``A`` and create the `Covariance` object.
+
+        >>> d = np.diag(A)
+        >>> cov = stats.Covariance.from_diagonal(d)
+
+        Compare the functionality of the `Covariance` object against a
+        reference implementations.
+
+        >>> res = cov.whiten(x)
+        >>> ref = np.diag(d**-0.5) @ x
+        >>> np.allclose(res, ref)
+        True
+        >>> res = cov.log_pdet
+        >>> ref = np.linalg.slogdet(A)[-1]
+        >>> np.allclose(res, ref)
+        True
+
+        """
+        return CovViaDiagonal(diagonal)
+
+    @staticmethod
+    def from_precision(precision, covariance=None):
+        r"""
+        Return a representation of a covariance from its precision matrix.
+
+        Parameters
+        ----------
+        precision : array_like
+            The precision matrix; that is, the inverse of a square, symmetric,
+            positive definite covariance matrix.
+        covariance : array_like, optional
+            The square, symmetric, positive definite covariance matrix. If not
+            provided, this may need to be calculated (e.g. to evaluate the
+            cumulative distribution function of
+            `scipy.stats.multivariate_normal`) by inverting `precision`.
+
+        Returns
+        -------
+        Covariance
+            A `Covariance` object representing the covariance matrix
+            corresponding to `precision`.
+
+        Notes
+        -----
+        Let the covariance matrix be :math:`A`, its precision matrix be
+        :math:`P = A^{-1}`, and :math:`L` be the lower Cholesky factor such
+        that :math:`L L^T = P`.
+        Whitening of a data point :math:`x` is performed by computing
+        :math:`x^T L`. :math:`\log\det{A}` is calculated as
+        :math:`-2tr(\log{L})`, where the :math:`\log` operation is performed
+        element-wise.
+
+        This `Covariance` class does not support singular covariance matrices
+        because the precision matrix does not exist for a singular covariance
+        matrix.
+
+        Examples
+        --------
+        Prepare a symmetric positive definite precision matrix ``P`` and a
+        data point ``x``. (If the precision matrix is not already available,
+        consider the other factory methods of the `Covariance` class.)
+
+        >>> import numpy as np
+        >>> from scipy import stats
+        >>> rng = np.random.default_rng()
+        >>> n = 5
+        >>> P = rng.random(size=(n, n))
+        >>> P = P @ P.T  # a precision matrix must be positive definite
+        >>> x = rng.random(size=n)
+
+        Create the `Covariance` object.
+
+        >>> cov = stats.Covariance.from_precision(P)
+
+        Compare the functionality of the `Covariance` object against
+        reference implementations.
+
+        >>> res = cov.whiten(x)
+        >>> ref = x @ np.linalg.cholesky(P)
+        >>> np.allclose(res, ref)
+        True
+        >>> res = cov.log_pdet
+        >>> ref = -np.linalg.slogdet(P)[-1]
+        >>> np.allclose(res, ref)
+        True
+
+        """
+        return CovViaPrecision(precision, covariance)
+
+    @staticmethod
+    def from_cholesky(cholesky):
+        r"""
+        Representation of a covariance provided via the (lower) Cholesky factor.
+
+        Parameters
+        ----------
+        cholesky : array_like
+            The lower triangular Cholesky factor of the covariance matrix.
+
+        Returns
+        -------
+        Covariance
+            A `Covariance` object representing the covariance matrix
+            corresponding to `cholesky`.
+
+        Notes
+        -----
+        Let the covariance matrix be :math:`A` and :math:`L` be the lower
+        Cholesky factor such that :math:`L L^T = A`.
+        Whitening of a data point :math:`x` is performed by computing
+        :math:`L^{-1} x`. :math:`\log\det{A}` is calculated as
+        :math:`2tr(\log{L})`, where the :math:`\log` operation is performed
+        element-wise.
+
+        This `Covariance` class does not support singular covariance matrices
+        because the Cholesky decomposition does not exist for a singular
+        covariance matrix.
+
+        Examples
+        --------
+        Prepare a symmetric positive definite covariance matrix ``A`` and a
+        data point ``x``.
+
+        >>> import numpy as np
+        >>> from scipy import stats
+        >>> rng = np.random.default_rng()
+        >>> n = 5
+        >>> A = rng.random(size=(n, n))
+        >>> A = A @ A.T  # make the covariance symmetric positive definite
+        >>> x = rng.random(size=n)
+
+        Perform the Cholesky decomposition of ``A`` and create the
+        `Covariance` object.
+
+        >>> L = np.linalg.cholesky(A)
+        >>> cov = stats.Covariance.from_cholesky(L)
+
+        Compare the functionality of the `Covariance` object against
+        reference implementation.
+
+        >>> from scipy.linalg import solve_triangular
+        >>> res = cov.whiten(x)
+        >>> ref = solve_triangular(L, x, lower=True)
+        >>> np.allclose(res, ref)
+        True
+        >>> res = cov.log_pdet
+        >>> ref = np.linalg.slogdet(A)[-1]
+        >>> np.allclose(res, ref)
+        True
+
+        """
+        return CovViaCholesky(cholesky)
+
+    @staticmethod
+    def from_eigendecomposition(eigendecomposition):
+        r"""
+        Representation of a covariance provided via eigendecomposition.
+
+        Parameters
+        ----------
+        eigendecomposition : sequence
+            A sequence (nominally a tuple) containing the eigenvalue and
+            eigenvector arrays as computed by `scipy.linalg.eigh` or
+            `numpy.linalg.eigh`.
+
+        Returns
+        -------
+        Covariance
+            A `Covariance` object representing the covariance matrix
+            corresponding to `eigendecomposition`.
+
+        Notes
+        -----
+        Let the covariance matrix be :math:`A`, let :math:`V` be matrix of
+        eigenvectors, and let :math:`W` be the diagonal matrix of eigenvalues
+        such that `V W V^T = A`.
+
+        When all of the eigenvalues are strictly positive, whitening of a
+        data point :math:`x` is performed by computing
+        :math:`x^T (V W^{-1/2})`, where the inverse square root can be taken
+        element-wise.
+        :math:`\log\det{A}` is calculated as  :math:`tr(\log{W})`,
+        where the :math:`\log` operation is performed element-wise.
+
+        This `Covariance` class supports singular covariance matrices. When
+        computing ``_log_pdet``, non-positive eigenvalues are ignored.
+        Whitening is not well defined when the point to be whitened
+        does not lie in the span of the columns of the covariance matrix. The
+        convention taken here is to treat the inverse square root of
+        non-positive eigenvalues as zeros.
+
+        Examples
+        --------
+        Prepare a symmetric positive definite covariance matrix ``A`` and a
+        data point ``x``.
+
+        >>> import numpy as np
+        >>> from scipy import stats
+        >>> rng = np.random.default_rng()
+        >>> n = 5
+        >>> A = rng.random(size=(n, n))
+        >>> A = A @ A.T  # make the covariance symmetric positive definite
+        >>> x = rng.random(size=n)
+
+        Perform the eigendecomposition of ``A`` and create the `Covariance`
+        object.
+
+        >>> w, v = np.linalg.eigh(A)
+        >>> cov = stats.Covariance.from_eigendecomposition((w, v))
+
+        Compare the functionality of the `Covariance` object against
+        reference implementations.
+
+        >>> res = cov.whiten(x)
+        >>> ref = x @ (v @ np.diag(w**-0.5))
+        >>> np.allclose(res, ref)
+        True
+        >>> res = cov.log_pdet
+        >>> ref = np.linalg.slogdet(A)[-1]
+        >>> np.allclose(res, ref)
+        True
+
+        """
+        return CovViaEigendecomposition(eigendecomposition)
+
+    def whiten(self, x):
+        """
+        Perform a whitening transformation on data.
+
+        "Whitening" ("white" as in "white noise", in which each frequency has
+        equal magnitude) transforms a set of random variables into a new set of
+        random variables with unit-diagonal covariance. When a whitening
+        transform is applied to a sample of points distributed according to
+        a multivariate normal distribution with zero mean, the covariance of
+        the transformed sample is approximately the identity matrix.
+
+        Parameters
+        ----------
+        x : array_like
+            An array of points. The last dimension must correspond with the
+            dimensionality of the space, i.e., the number of columns in the
+            covariance matrix.
+
+        Returns
+        -------
+        x_ : array_like
+            The transformed array of points.
+
+        References
+        ----------
+        .. [1] "Whitening Transformation". Wikipedia.
+               https://en.wikipedia.org/wiki/Whitening_transformation
+        .. [2] Novak, Lukas, and Miroslav Vorechovsky. "Generalization of
+               coloring linear transformation". Transactions of VSB 18.2
+               (2018): 31-35. :doi:`10.31490/tces-2018-0013`
+
+        Examples
+        --------
+        >>> import numpy as np
+        >>> from scipy import stats
+        >>> rng = np.random.default_rng()
+        >>> n = 3
+        >>> A = rng.random(size=(n, n))
+        >>> cov_array = A @ A.T  # make matrix symmetric positive definite
+        >>> precision = np.linalg.inv(cov_array)
+        >>> cov_object = stats.Covariance.from_precision(precision)
+        >>> x = rng.multivariate_normal(np.zeros(n), cov_array, size=(10000))
+        >>> x_ = cov_object.whiten(x)
+        >>> np.cov(x_, rowvar=False)  # near-identity covariance
+        array([[0.97862122, 0.00893147, 0.02430451],
+               [0.00893147, 0.96719062, 0.02201312],
+               [0.02430451, 0.02201312, 0.99206881]])
+
+        """
+        return self._whiten(np.asarray(x))
+
+    def colorize(self, x):
+        """
+        Perform a colorizing transformation on data.
+
+        "Colorizing" ("color" as in "colored noise", in which different
+        frequencies may have different magnitudes) transforms a set of
+        uncorrelated random variables into a new set of random variables with
+        the desired covariance. When a coloring transform is applied to a
+        sample of points distributed according to a multivariate normal
+        distribution with identity covariance and zero mean, the covariance of
+        the transformed sample is approximately the covariance matrix used
+        in the coloring transform.
+
+        Parameters
+        ----------
+        x : array_like
+            An array of points. The last dimension must correspond with the
+            dimensionality of the space, i.e., the number of columns in the
+            covariance matrix.
+
+        Returns
+        -------
+        x_ : array_like
+            The transformed array of points.
+
+        References
+        ----------
+        .. [1] "Whitening Transformation". Wikipedia.
+               https://en.wikipedia.org/wiki/Whitening_transformation
+        .. [2] Novak, Lukas, and Miroslav Vorechovsky. "Generalization of
+               coloring linear transformation". Transactions of VSB 18.2
+               (2018): 31-35. :doi:`10.31490/tces-2018-0013`
+
+        Examples
+        --------
+        >>> import numpy as np
+        >>> from scipy import stats
+        >>> rng = np.random.default_rng(1638083107694713882823079058616272161)
+        >>> n = 3
+        >>> A = rng.random(size=(n, n))
+        >>> cov_array = A @ A.T  # make matrix symmetric positive definite
+        >>> cholesky = np.linalg.cholesky(cov_array)
+        >>> cov_object = stats.Covariance.from_cholesky(cholesky)
+        >>> x = rng.multivariate_normal(np.zeros(n), np.eye(n), size=(10000))
+        >>> x_ = cov_object.colorize(x)
+        >>> cov_data = np.cov(x_, rowvar=False)
+        >>> np.allclose(cov_data, cov_array, rtol=3e-2)
+        True
+        """
+        return self._colorize(np.asarray(x))
+
+    @property
+    def log_pdet(self):
+        """
+        Log of the pseudo-determinant of the covariance matrix
+        """
+        return np.array(self._log_pdet, dtype=float)[()]
+
+    @property
+    def rank(self):
+        """
+        Rank of the covariance matrix
+        """
+        return np.array(self._rank, dtype=int)[()]
+
+    @property
+    def covariance(self):
+        """
+        Explicit representation of the covariance matrix
+        """
+        return self._covariance
+
+    @property
+    def shape(self):
+        """
+        Shape of the covariance array
+        """
+        return self._shape
+
+    def _validate_matrix(self, A, name):
+        A = np.atleast_2d(A)
+        m, n = A.shape[-2:]
+        if m != n or A.ndim != 2 or not (np.issubdtype(A.dtype, np.integer) or
+                                         np.issubdtype(A.dtype, np.floating)):
+            message = (f"The input `{name}` must be a square, "
+                       "two-dimensional array of real numbers.")
+            raise ValueError(message)
+        return A
+
+    def _validate_vector(self, A, name):
+        A = np.atleast_1d(A)
+        if A.ndim != 1 or not (np.issubdtype(A.dtype, np.integer) or
+                               np.issubdtype(A.dtype, np.floating)):
+            message = (f"The input `{name}` must be a one-dimensional array "
+                       "of real numbers.")
+            raise ValueError(message)
+        return A
+
+
+class CovViaPrecision(Covariance):
+
+    __class_getitem__ = None  # type:ignore[assignment]
+
+    def __init__(self, precision, covariance=None):
+        precision = self._validate_matrix(precision, 'precision')
+        if covariance is not None:
+            covariance = self._validate_matrix(covariance, 'covariance')
+            message = "`precision.shape` must equal `covariance.shape`."
+            if precision.shape != covariance.shape:
+                raise ValueError(message)
+
+        self._chol_P = np.linalg.cholesky(precision)
+        self._log_pdet = -2*np.log(np.diag(self._chol_P)).sum(axis=-1)
+        self._rank = precision.shape[-1]  # must be full rank if invertible
+        self._precision = precision
+        self._cov_matrix = covariance
+        self._shape = precision.shape
+        self._allow_singular = False
+
+    def _whiten(self, x):
+        return x @ self._chol_P
+
+    @cached_property
+    def _covariance(self):
+        n = self._shape[-1]
+        return (linalg.cho_solve((self._chol_P, True), np.eye(n))
+                if self._cov_matrix is None else self._cov_matrix)
+
+    def _colorize(self, x):
+        m = x.T.shape[0]
+        res = linalg.solve_triangular(self._chol_P.T, x.T.reshape(m, -1), lower=False)
+        return res.reshape(x.T.shape).T
+
+
+def _dot_diag(x, d):
+    # If d were a full diagonal matrix, x @ d would always do what we want.
+    # Special treatment is needed for n-dimensional `d` in which each row
+    # includes only the diagonal elements of a covariance matrix.
+    return x * d if x.ndim < 2 else x * np.expand_dims(d, -2)
+
+
+class CovViaDiagonal(Covariance):
+
+    def __init__(self, diagonal):
+        diagonal = self._validate_vector(diagonal, 'diagonal')
+
+        i_zero = diagonal <= 0
+        positive_diagonal = np.array(diagonal, dtype=np.float64)
+
+        positive_diagonal[i_zero] = 1  # ones don't affect determinant
+        self._log_pdet = np.sum(np.log(positive_diagonal), axis=-1)
+
+        psuedo_reciprocals = 1 / np.sqrt(positive_diagonal)
+        psuedo_reciprocals[i_zero] = 0
+
+        self._sqrt_diagonal = np.sqrt(diagonal)
+        self._LP = psuedo_reciprocals
+        self._rank = positive_diagonal.shape[-1] - i_zero.sum(axis=-1)
+        self._covariance = np.apply_along_axis(np.diag, -1, diagonal)
+        self._i_zero = i_zero
+        self._shape = self._covariance.shape
+        self._allow_singular = True
+
+    def _whiten(self, x):
+        return _dot_diag(x, self._LP)
+
+    def _colorize(self, x):
+        return _dot_diag(x, self._sqrt_diagonal)
+
+    def _support_mask(self, x):
+        """
+        Check whether x lies in the support of the distribution.
+        """
+        return ~np.any(_dot_diag(x, self._i_zero), axis=-1)
+
+
+class CovViaCholesky(Covariance):
+
+    __class_getitem__ = None  # type:ignore[assignment]
+
+    def __init__(self, cholesky):
+        L = self._validate_matrix(cholesky, 'cholesky')
+
+        self._factor = L
+        self._log_pdet = 2*np.log(np.diag(self._factor)).sum(axis=-1)
+        self._rank = L.shape[-1]  # must be full rank for cholesky
+        self._shape = L.shape
+        self._allow_singular = False
+
+    @cached_property
+    def _covariance(self):
+        return self._factor @ self._factor.T
+
+    def _whiten(self, x):
+        m = x.T.shape[0]
+        res = linalg.solve_triangular(self._factor, x.T.reshape(m, -1), lower=True)
+        return res.reshape(x.T.shape).T
+
+    def _colorize(self, x):
+        return x @ self._factor.T
+
+
+class CovViaEigendecomposition(Covariance):
+
+    __class_getitem__ = None  # type:ignore[assignment]
+
+    def __init__(self, eigendecomposition):
+        eigenvalues, eigenvectors = eigendecomposition
+        eigenvalues = self._validate_vector(eigenvalues, 'eigenvalues')
+        eigenvectors = self._validate_matrix(eigenvectors, 'eigenvectors')
+        message = ("The shapes of `eigenvalues` and `eigenvectors` "
+                   "must be compatible.")
+        try:
+            eigenvalues = np.expand_dims(eigenvalues, -2)
+            eigenvectors, eigenvalues = np.broadcast_arrays(eigenvectors,
+                                                            eigenvalues)
+            eigenvalues = eigenvalues[..., 0, :]
+        except ValueError:
+            raise ValueError(message)
+
+        i_zero = eigenvalues <= 0
+        positive_eigenvalues = np.array(eigenvalues, dtype=np.float64)
+
+        positive_eigenvalues[i_zero] = 1  # ones don't affect determinant
+        self._log_pdet = np.sum(np.log(positive_eigenvalues), axis=-1)
+
+        psuedo_reciprocals = 1 / np.sqrt(positive_eigenvalues)
+        psuedo_reciprocals[i_zero] = 0
+
+        self._LP = eigenvectors * psuedo_reciprocals
+        self._LA = eigenvectors * np.sqrt(eigenvalues)
+        self._rank = positive_eigenvalues.shape[-1] - i_zero.sum(axis=-1)
+        self._w = eigenvalues
+        self._v = eigenvectors
+        self._shape = eigenvectors.shape
+        self._null_basis = eigenvectors * i_zero
+        # This is only used for `_support_mask`, not to decide whether
+        # the covariance is singular or not.
+        self._eps = _multivariate._eigvalsh_to_eps(eigenvalues) * 10**3
+        self._allow_singular = True
+
+    def _whiten(self, x):
+        return x @ self._LP
+
+    def _colorize(self, x):
+        return x @ self._LA.T
+
+    @cached_property
+    def _covariance(self):
+        return (self._v * self._w) @ self._v.T
+
+    def _support_mask(self, x):
+        """
+        Check whether x lies in the support of the distribution.
+        """
+        residual = np.linalg.norm(x @ self._null_basis, axis=-1)
+        in_support = residual < self._eps
+        return in_support
+
+
+class CovViaPSD(Covariance):
+    """
+    Representation of a covariance provided via an instance of _PSD
+    """
+
+    __class_getitem__ = None  # type:ignore[assignment]
+
+    def __init__(self, psd):
+        self._LP = psd.U
+        self._log_pdet = psd.log_pdet
+        self._rank = psd.rank
+        self._covariance = psd._M
+        self._shape = psd._M.shape
+        self._psd = psd
+        self._allow_singular = False  # by default
+
+    def _whiten(self, x):
+        return x @ self._LP
+
+    def _support_mask(self, x):
+        return self._psd._support_mask(x)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_crosstab.py b/venv/lib/python3.12/site-packages/scipy/stats/_crosstab.py
new file mode 100644
index 0000000000000000000000000000000000000000..dd016a11627968c5fa8361c439c9c55a60a592c2
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_crosstab.py
@@ -0,0 +1,198 @@
+import numpy as np
+from scipy.sparse import coo_array
+from scipy._lib._bunch import _make_tuple_bunch
+
+
+CrosstabResult = _make_tuple_bunch(
+    "CrosstabResult", ["elements", "count"]
+)
+
+
+def crosstab(*args, levels=None, sparse=False):
+    """
+    Return table of counts for each possible unique combination in ``*args``.
+
+    When ``len(args) > 1``, the array computed by this function is
+    often referred to as a *contingency table* [1]_.
+
+    The arguments must be sequences with the same length.  The second return
+    value, `count`, is an integer array with ``len(args)`` dimensions.  If
+    `levels` is None, the shape of `count` is ``(n0, n1, ...)``, where ``nk``
+    is the number of unique elements in ``args[k]``.
+
+    Parameters
+    ----------
+    *args : sequences
+        A sequence of sequences whose unique aligned elements are to be
+        counted.  The sequences in args must all be the same length.
+    levels : sequence, optional
+        If `levels` is given, it must be a sequence that is the same length as
+        `args`.  Each element in `levels` is either a sequence or None.  If it
+        is a sequence, it gives the values in the corresponding sequence in
+        `args` that are to be counted.  If any value in the sequences in `args`
+        does not occur in the corresponding sequence in `levels`, that value
+        is ignored and not counted in the returned array `count`.  The default
+        value of `levels` for ``args[i]`` is ``np.unique(args[i])``
+    sparse : bool, optional
+        If True, return a sparse array.  The array will be an instance of
+        the `scipy.sparse.coo_array` class.
+        Default is False.
+
+    Returns
+    -------
+    res : CrosstabResult
+        An object containing the following attributes:
+
+        elements : tuple of numpy.ndarrays.
+            Tuple of length ``len(args)`` containing the arrays of elements
+            that are counted in `count`.  These can be interpreted as the
+            labels of the corresponding dimensions of `count`. If `levels` was
+            given, then if ``levels[i]`` is not None, ``elements[i]`` will
+            hold the values given in ``levels[i]``.
+        count : numpy.ndarray or scipy.sparse.coo_array
+            Counts of the unique elements in ``zip(*args)``, stored in an
+            array. Also known as a *contingency table* when ``len(args) > 1``.
+
+    See Also
+    --------
+    numpy.unique
+
+    Notes
+    -----
+    .. versionadded:: 1.7.0
+
+    References
+    ----------
+    .. [1] "Contingency table", http://en.wikipedia.org/wiki/Contingency_table
+
+    Examples
+    --------
+    >>> from scipy.stats.contingency import crosstab
+
+    Given the lists `a` and `x`, create a contingency table that counts the
+    frequencies of the corresponding pairs.
+
+    >>> a = ['A', 'B', 'A', 'A', 'B', 'B', 'A', 'A', 'B', 'B']
+    >>> x = ['X', 'X', 'X', 'Y', 'Z', 'Z', 'Y', 'Y', 'Z', 'Z']
+    >>> res = crosstab(a, x)
+    >>> avals, xvals = res.elements
+    >>> avals
+    array(['A', 'B'], dtype='<U1')
+    >>> xvals
+    array(['X', 'Y', 'Z'], dtype='<U1')
+    >>> res.count
+    array([[2, 3, 0],
+           [1, 0, 4]])
+
+    So ``('A', 'X')`` occurs twice, ``('A', 'Y')`` occurs three times, etc.
+
+    Higher dimensional contingency tables can be created.
+
+    >>> p = [0, 0, 0, 0, 1, 1, 1, 0, 0, 1]
+    >>> res = crosstab(a, x, p)
+    >>> res.count
+    array([[[2, 0],
+            [2, 1],
+            [0, 0]],
+           [[1, 0],
+            [0, 0],
+            [1, 3]]])
+    >>> res.count.shape
+    (2, 3, 2)
+
+    The values to be counted can be set by using the `levels` argument.
+    It allows the elements of interest in each input sequence to be
+    given explicitly instead finding the unique elements of the sequence.
+
+    For example, suppose one of the arguments is an array containing the
+    answers to a survey question, with integer values 1 to 4.  Even if the
+    value 1 does not occur in the data, we want an entry for it in the table.
+
+    >>> q1 = [2, 3, 3, 2, 4, 4, 2, 3, 4, 4, 4, 3, 3, 3, 4]  # 1 does not occur.
+    >>> q2 = [4, 4, 2, 2, 2, 4, 1, 1, 2, 2, 4, 2, 2, 2, 4]  # 3 does not occur.
+    >>> options = [1, 2, 3, 4]
+    >>> res = crosstab(q1, q2, levels=(options, options))
+    >>> res.count
+    array([[0, 0, 0, 0],
+           [1, 1, 0, 1],
+           [1, 4, 0, 1],
+           [0, 3, 0, 3]])
+
+    If `levels` is given, but an element of `levels` is None, the unique values
+    of the corresponding argument are used. For example,
+
+    >>> res = crosstab(q1, q2, levels=(None, options))
+    >>> res.elements
+    [array([2, 3, 4]), [1, 2, 3, 4]]
+    >>> res.count
+    array([[1, 1, 0, 1],
+           [1, 4, 0, 1],
+           [0, 3, 0, 3]])
+
+    If we want to ignore the pairs where 4 occurs in ``q2``, we can
+    give just the values [1, 2] to `levels`, and the 4 will be ignored:
+
+    >>> res = crosstab(q1, q2, levels=(None, [1, 2]))
+    >>> res.elements
+    [array([2, 3, 4]), [1, 2]]
+    >>> res.count
+    array([[1, 1],
+           [1, 4],
+           [0, 3]])
+
+    Finally, let's repeat the first example, but return a sparse array:
+
+    >>> res = crosstab(a, x, sparse=True)
+    >>> res.count
+    <COOrdinate sparse array of dtype 'int64'
+        with 4 stored elements and shape (2, 3)>
+    >>> res.count.toarray()
+    array([[2, 3, 0],
+           [1, 0, 4]])
+
+    """
+    nargs = len(args)
+    if nargs == 0:
+        raise TypeError("At least one input sequence is required.")
+
+    len0 = len(args[0])
+    if not all(len(a) == len0 for a in args[1:]):
+        raise ValueError("All input sequences must have the same length.")
+
+    if levels is None:
+        # Call np.unique with return_inverse=True on each argument.
+        actual_levels, indices = zip(*[np.unique(a, return_inverse=True)
+                                       for a in args])
+    else:
+        # `levels` is not None...
+        if len(levels) != nargs:
+            raise ValueError('len(levels) must equal the number of input '
+                             'sequences')
+
+        args = [np.asarray(arg) for arg in args]
+        mask = np.zeros((nargs, len0), dtype=np.bool_)
+        inv = np.zeros((nargs, len0), dtype=np.intp)
+        actual_levels = []
+        for k, (levels_list, arg) in enumerate(zip(levels, args)):
+            if levels_list is None:
+                levels_list, inv[k, :] = np.unique(arg, return_inverse=True)
+                mask[k, :] = True
+            else:
+                q = arg == np.asarray(levels_list).reshape(-1, 1)
+                mask[k, :] = np.any(q, axis=0)
+                qnz = q.T.nonzero()
+                inv[k, qnz[0]] = qnz[1]
+            actual_levels.append(levels_list)
+
+        mask_all = mask.all(axis=0)
+        indices = tuple(inv[:, mask_all])
+
+    if sparse:
+        count = coo_array((np.ones(len(indices[0]), dtype=int), indices))
+        count.sum_duplicates()
+    else:
+        shape = [len(u) for u in actual_levels]
+        count = np.zeros(shape, dtype=int)
+        np.add.at(count, indices, 1)
+
+    return CrosstabResult(actual_levels, count)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_discrete_distns.py b/venv/lib/python3.12/site-packages/scipy/stats/_discrete_distns.py
new file mode 100644
index 0000000000000000000000000000000000000000..07b02cf7283c33fa1e9d133d7500dc99bff6df27
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_discrete_distns.py
@@ -0,0 +1,2105 @@
+#
+# Author:  Travis Oliphant  2002-2011 with contributions from
+#          SciPy Developers 2004-2011
+#
+from functools import partial
+from types import MethodType
+
+from scipy import special
+from scipy.special import entr, logsumexp, betaln, gammaln as gamln
+import scipy.special._ufuncs as scu
+from scipy.special._spfun_stats import _poisson_binom_pmf, _poisson_binom_cdf
+from scipy._lib._util import rng_integers
+import scipy._external.array_api_extra as xpx
+from scipy.interpolate import interp1d
+
+from numpy import floor, ceil, log, exp, sqrt, log1p, expm1, tanh, cosh, sinh
+
+import numpy as np
+
+from ._distn_infrastructure import (rv_discrete, get_distribution_names,
+                                    _vectorize_rvs_over_shapes,
+                                    _ShapeInfo, _isintegral,
+                                    rv_discrete_frozen)
+from ._biasedurn import (_PyFishersNCHypergeometric,
+                         _PyWalleniusNCHypergeometric,
+                         _PyStochasticLib3)
+
+
+class binom_gen(rv_discrete):
+    r"""
+    A binomial discrete random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    hypergeom, nbinom, nhypergeom
+
+    Notes
+    -----
+    The probability mass function for `binom` is:
+
+    .. math::
+
+       f(k) = \binom{n}{k} p^k (1-p)^{n-k}
+
+    for :math:`k \in \{0, 1, \dots, n\}`, :math:`0 \leq p \leq 1`
+
+    `binom` takes :math:`n` and :math:`p` as shape parameters,
+    where :math:`p` is the probability of a single success
+    and :math:`1-p` is the probability of a single failure.
+
+    This distribution uses routines from the Boost Math C++ library for
+    the computation of the ``pmf``, ``cdf``, ``sf``, ``ppf`` and ``isf``
+    methods. [1]_
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    %(example)s
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("n", True, (0, np.inf), (True, False)),
+                _ShapeInfo("p", False, (0, 1), (True, True))]
+
+    def _rvs(self, n, p, size=None, random_state=None):
+        if not np.all(n == np.floor(n)):
+            raise ValueError("`n` must be integral.")
+        return random_state.binomial(np.asarray(n, dtype=int), p, size)
+
+    def _argcheck(self, n, p):
+        return (n >= 0) & _isintegral(n) & (p >= 0) & (p <= 1)
+
+    def _get_support(self, n, p):
+        return self.a, n
+
+    def _logpmf(self, x, n, p):
+        k = floor(x)
+        combiln = (gamln(n+1) - (gamln(k+1) + gamln(n-k+1)))
+        return combiln + special.xlogy(k, p) + special.xlog1py(n-k, -p)
+
+    def _pmf(self, x, n, p):
+        # binom.pmf(k) = choose(n, k) * p**k * (1-p)**(n-k)
+        return scu._binom_pmf(x, n, p)
+
+    def _cdf(self, x, n, p):
+        k = floor(x)
+        return scu._binom_cdf(k, n, p)
+
+    def _sf(self, x, n, p):
+        k = floor(x)
+        return scu._binom_sf(k, n, p)
+
+    def _isf(self, x, n, p):
+        return scu._binom_isf(x, n, p)
+
+    def _ppf(self, q, n, p):
+        return scu._binom_ppf(q, n, p)
+
+    def _stats(self, n, p, moments='mv'):
+        mu = n * p
+        var = mu - n * np.square(p)
+        g1, g2 = None, None
+        if 's' in moments:
+            pq = p - np.square(p)
+            npq_sqrt = np.sqrt(n * pq)
+            t1 = np.reciprocal(npq_sqrt)
+            t2 = (2.0 * p) / npq_sqrt
+            g1 = t1 - t2
+        if 'k' in moments:
+            pq = p - np.square(p)
+            npq = n * pq
+            t1 = np.reciprocal(npq)
+            t2 = 6.0/n
+            g2 = t1 - t2
+        return mu, var, g1, g2
+
+
+binom = binom_gen(name='binom')
+
+
+class bernoulli_gen(binom_gen):
+    r"""A Bernoulli discrete random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability mass function for `bernoulli` is:
+
+    .. math::
+
+       f(k) = \begin{cases}1-p  &\text{if } k = 0\\
+                           p    &\text{if } k = 1\end{cases}
+
+    for :math:`k` in :math:`\{0, 1\}`, :math:`0 \leq p \leq 1`
+
+    `bernoulli` takes :math:`p` as shape parameter,
+    where :math:`p` is the probability of a single success
+    and :math:`1-p` is the probability of a single failure.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("p", False, (0, 1), (True, True))]
+
+    def _rvs(self, p, size=None, random_state=None):
+        return binom_gen._rvs(self, 1, p, size=size, random_state=random_state)
+
+    def _argcheck(self, p):
+        return (p >= 0) & (p <= 1)
+
+    def _get_support(self, p):
+        # Overrides binom_gen._get_support!x
+        return self.a, self.b
+
+    def _logpmf(self, x, p):
+        return binom._logpmf(x, 1, p)
+
+    def _pmf(self, x, p):
+        # bernoulli.pmf(k) = 1-p  if k = 0
+        #                  = p    if k = 1
+        return binom._pmf(x, 1, p)
+
+    def _cdf(self, x, p):
+        return binom._cdf(x, 1, p)
+
+    def _sf(self, x, p):
+        return binom._sf(x, 1, p)
+
+    def _isf(self, x, p):
+        return binom._isf(x, 1, p)
+
+    def _ppf(self, q, p):
+        return binom._ppf(q, 1, p)
+
+    def _stats(self, p):
+        return binom._stats(1, p)
+
+    def _entropy(self, p):
+        return entr(p) + entr(1-p)
+
+
+bernoulli = bernoulli_gen(b=1, name='bernoulli')
+
+
+class betabinom_gen(rv_discrete):
+    r"""
+    A beta-binomial discrete random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    beta, binom
+
+    Notes
+    -----
+    The beta-binomial distribution is a binomial distribution with a
+    probability of success `p` that follows a beta distribution.
+
+    The probability mass function for `betabinom` is:
+
+    .. math::
+
+       f(k) = \binom{n}{k} \frac{B(k + a, n - k + b)}{B(a, b)}
+
+    for :math:`k \in \{0, 1, \dots, n\}`, :math:`n \geq 0`, :math:`a > 0`,
+    :math:`b > 0`, where :math:`B(a, b)` is the beta function.
+
+    `betabinom` takes :math:`n`, :math:`a`, and :math:`b` as shape parameters.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] https://en.wikipedia.org/wiki/Beta-binomial_distribution
+
+    .. versionadded:: 1.4.0
+
+    %(example)s
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("n", True, (0, np.inf), (True, False)),
+                _ShapeInfo("a", False, (0, np.inf), (False, False)),
+                _ShapeInfo("b", False, (0, np.inf), (False, False))]
+
+    def _rvs(self, n, a, b, size=None, random_state=None):
+        p = random_state.beta(a, b, size)
+        if not np.all(n == np.floor(n)):
+            raise ValueError("`n` must be integral.")
+        return random_state.binomial(np.asarray(n, dtype=int), p, size)
+
+    def _get_support(self, n, a, b):
+        return 0, n
+
+    def _argcheck(self, n, a, b):
+        return (n >= 0) & _isintegral(n) & (a > 0) & (b > 0)
+
+    def _logpmf(self, x, n, a, b):
+        k = floor(x)
+        combiln = -log(n + 1) - betaln(n - k + 1, k + 1)
+        return combiln + betaln(k + a, n - k + b) - betaln(a, b)
+
+    def _pmf(self, x, n, a, b):
+        return exp(self._logpmf(x, n, a, b))
+
+    def _stats(self, n, a, b, moments='mv'):
+        e_p = a / (a + b)
+        e_q = 1 - e_p
+        mu = n * e_p
+        var = n * (a + b + n) * e_p * e_q / (a + b + 1)
+        g1, g2 = None, None
+        if 's' in moments:
+            g1 = 1.0 / sqrt(var)
+            g1 *= (a + b + 2 * n) * (b - a)
+            g1 /= (a + b + 2) * (a + b)
+        if 'k' in moments:
+            g2 = (a + b).astype(e_p.dtype)
+            g2 *= (a + b - 1 + 6 * n)
+            g2 += 3 * a * b * (n - 2)
+            g2 += 6 * n ** 2
+            g2 -= 3 * e_p * b * n * (6 - n)
+            g2 -= 18 * e_p * e_q * n ** 2
+            g2 *= (a + b) ** 2 * (1 + a + b)
+            g2 /= (n * a * b * (a + b + 2) * (a + b + 3) * (a + b + n))
+            g2 -= 3
+        return mu, var, g1, g2
+
+
+betabinom = betabinom_gen(name='betabinom')
+
+
+class nbinom_gen(rv_discrete):
+    r"""
+    A negative binomial discrete random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    hypergeom, binom, nhypergeom
+
+    Notes
+    -----
+    Negative binomial distribution describes a sequence of i.i.d. Bernoulli
+    trials, repeated until a predefined, non-random number of successes occurs.
+
+    The probability mass function of the number of failures for `nbinom` is:
+
+    .. math::
+
+       f(k) = \binom{k+n-1}{n-1} p^n (1-p)^k
+
+    for :math:`k \ge 0`, :math:`0 < p \leq 1`
+
+    `nbinom` takes :math:`n` and :math:`p` as shape parameters where :math:`n`
+    is the number of successes, :math:`p` is the probability of a single
+    success, and :math:`1-p` is the probability of a single failure.
+
+    Another common parameterization of the negative binomial distribution is
+    in terms of the mean number of failures :math:`\mu` to achieve :math:`n`
+    successes. The mean :math:`\mu` is related to the probability of success
+    as
+
+    .. math::
+
+       p = \frac{n}{n + \mu}
+
+    The number of successes :math:`n` may also be specified in terms of a
+    "dispersion", "heterogeneity", or "aggregation" parameter :math:`\alpha`,
+    which relates the mean :math:`\mu` to the variance :math:`\sigma^2`,
+    e.g. :math:`\sigma^2 = \mu + \alpha \mu^2`. Regardless of the convention
+    used for :math:`\alpha`,
+
+    .. math::
+
+       p &= \frac{\mu}{\sigma^2} \\
+       n &= \frac{\mu^2}{\sigma^2 - \mu}
+
+    This distribution uses routines from the Boost Math C++ library for
+    the computation of the ``pmf``, ``cdf``, ``sf``, ``ppf``, ``isf``
+    and ``stats`` methods. [1]_
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    %(example)s
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("n", True, (0, np.inf), (True, False)),
+                _ShapeInfo("p", False, (0, 1), (True, True))]
+
+    def _rvs(self, n, p, size=None, random_state=None):
+        return random_state.negative_binomial(n, p, size)
+
+    def _argcheck(self, n, p):
+        return (n > 0) & (p > 0) & (p <= 1)
+
+    def _pmf(self, x, n, p):
+        # nbinom.pmf(k) = choose(k+n-1, n-1) * p**n * (1-p)**k
+        return scu._nbinom_pmf(x, n, p)
+
+    def _logpmf(self, x, n, p):
+        coeff = gamln(n+x) - gamln(x+1) - gamln(n)
+        return coeff + n*log(p) + special.xlog1py(x, -p)
+
+    def _cdf(self, x, n, p):
+        k = floor(x)
+        return scu._nbinom_cdf(k, n, p)
+
+    def _logcdf(self, x, n, p):
+        k = floor(x)
+        k, n, p = np.broadcast_arrays(k, n, p)
+        cdf = self._cdf(k, n, p)
+        cond = cdf > 0.5
+        def f1(k, n, p):
+            return np.log1p(-special.betainc(k + 1, n, 1 - p))
+
+        # do calc in place
+        logcdf = cdf
+        with np.errstate(divide='ignore'):
+            logcdf[cond] = f1(k[cond], n[cond], p[cond])
+            logcdf[~cond] = np.log(cdf[~cond])
+        return logcdf
+
+    def _sf(self, x, n, p):
+        k = floor(x)
+        return scu._nbinom_sf(k, n, p)
+
+    def _isf(self, x, n, p):
+        with np.errstate(over='ignore'):  # see gh-17432
+            return scu._nbinom_isf(x, n, p)
+
+    def _ppf(self, q, n, p):
+        with np.errstate(over='ignore'):  # see gh-17432
+            return scu._nbinom_ppf(q, n, p)
+
+    def _stats(self, n, p):
+        return (
+            scu._nbinom_mean(n, p),
+            scu._nbinom_variance(n, p),
+            scu._nbinom_skewness(n, p),
+            scu._nbinom_kurtosis_excess(n, p),
+        )
+
+
+nbinom = nbinom_gen(name='nbinom')
+
+
+class betanbinom_gen(rv_discrete):
+    r"""
+    A beta-negative-binomial discrete random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    betabinom : Beta binomial distribution
+
+    Notes
+    -----
+    The beta-negative-binomial distribution is a negative binomial
+    distribution with a probability of success `p` that follows a
+    beta distribution.
+
+    The probability mass function for `betanbinom` is:
+
+    .. math::
+
+       f(k) = \binom{n + k - 1}{k} \frac{B(a + n, b + k)}{B(a, b)}
+
+    for :math:`k \ge 0`, :math:`n \geq 0`, :math:`a > 0`,
+    :math:`b > 0`, where :math:`B(a, b)` is the beta function.
+
+    `betanbinom` takes :math:`n`, :math:`a`, and :math:`b` as shape parameters.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] https://en.wikipedia.org/wiki/Beta_negative_binomial_distribution
+
+    .. versionadded:: 1.12.0
+
+    %(example)s
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("n", True, (0, np.inf), (True, False)),
+                _ShapeInfo("a", False, (0, np.inf), (False, False)),
+                _ShapeInfo("b", False, (0, np.inf), (False, False))]
+
+    def _rvs(self, n, a, b, size=None, random_state=None):
+        p = random_state.beta(a, b, size)
+        return random_state.negative_binomial(n, p, size)
+
+    def _argcheck(self, n, a, b):
+        return (n >= 0) & _isintegral(n) & (a > 0) & (b > 0)
+
+    def _logpmf(self, x, n, a, b):
+        k = floor(x)
+        combiln = -np.log(n + k) - betaln(n, k + 1)
+        return combiln + betaln(a + n, b + k) - betaln(a, b)
+
+    def _pmf(self, x, n, a, b):
+        return exp(self._logpmf(x, n, a, b))
+
+    def _stats(self, n, a, b, moments='mv'):
+        # reference: Wolfram Alpha input
+        # BetaNegativeBinomialDistribution[a, b, n]
+        def mean(n, a, b):
+            return n * b / (a - 1.)
+        mu = xpx.apply_where(a > 1, (n, a, b), mean, fill_value=np.inf)
+        def var(n, a, b):
+            return (n * b * (n + a - 1.) * (a + b - 1.)
+                    / ((a - 2.) * (a - 1.)**2.))
+        var = xpx.apply_where(a > 2, (n, a, b), var, fill_value=np.inf)
+        g1, g2 = None, None
+        def skew(n, a, b):
+            return ((2 * n + a - 1.) * (2 * b + a - 1.)
+                    / (a - 3.) / sqrt(n * b * (n + a - 1.) * (b + a - 1.)
+                    / (a - 2.)))
+        if 's' in moments:
+            g1 = xpx.apply_where(a > 3, (n, a, b), skew, fill_value=np.inf)
+        def kurtosis(n, a, b):
+            term = (a - 2.)
+            term_2 = ((a - 1.)**2. * (a**2. + a * (6 * b - 1.)
+                      + 6. * (b - 1.) * b)
+                      + 3. * n**2. * ((a + 5.) * b**2. + (a + 5.)
+                      * (a - 1.) * b + 2. * (a - 1.)**2)
+                      + 3 * (a - 1.) * n
+                      * ((a + 5.) * b**2. + (a + 5.) * (a - 1.) * b
+                      + 2. * (a - 1.)**2.))
+            denominator = ((a - 4.) * (a - 3.) * b * n
+                           * (a + b - 1.) * (a + n - 1.))
+            # Wolfram Alpha uses Pearson kurtosis, so we subtract 3 to get
+            # scipy's Fisher kurtosis
+            return term * term_2 / denominator - 3.
+        if 'k' in moments:
+            g2 = xpx.apply_where(a > 4, (n, a, b), kurtosis, fill_value=np.inf)
+        return mu, var, g1, g2
+
+
+betanbinom = betanbinom_gen(name='betanbinom')
+
+
+class geom_gen(rv_discrete):
+    r"""A geometric discrete random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    planck
+
+    Notes
+    -----
+    The probability mass function for `geom` is:
+
+    .. math::
+
+        f(k) = (1-p)^{k-1} p
+
+    for :math:`k \ge 1`, :math:`0 < p \leq 1`
+
+    `geom` takes :math:`p` as shape parameter,
+    where :math:`p` is the probability of a single success
+    and :math:`1-p` is the probability of a single failure.
+
+    Note that when drawing random samples, the probability of observations that exceed
+    ``np.iinfo(np.int64).max`` increases rapidly as $p$ decreases below $10^{-17}$. For
+    $p < 10^{-20}$, almost all observations would exceed the maximum ``int64``; however,
+    the output dtype is always ``int64``, so these values are clipped to the maximum.
+
+    %(after_notes)s
+
+    %(example)s
+    """
+
+    def _shape_info(self):
+        return [_ShapeInfo("p", False, (0, 1), (True, True))]
+
+    def _rvs(self, p, size=None, random_state=None):
+        res = random_state.geometric(p, size=size)
+        # RandomState.geometric can wrap around to negative values; make behavior
+        # consistent with Generator.geometric by replacing with maximum integer.
+        max_int = np.iinfo(res.dtype).max
+        return np.where(res < 0, max_int, res)
+
+    def _argcheck(self, p):
+        return (p <= 1) & (p > 0)
+
+    def _pmf(self, k, p):
+        return np.power(1-p, k-1) * p
+
+    def _logpmf(self, k, p):
+        return special.xlog1py(k - 1, -p) + log(p)
+
+    def _cdf(self, x, p):
+        k = floor(x)
+        return -expm1(log1p(-p)*k)
+
+    def _sf(self, x, p):
+        return np.exp(self._logsf(x, p))
+
+    def _logsf(self, x, p):
+        k = floor(x)
+        return k*log1p(-p)
+
+    def _ppf(self, q, p):
+        vals = ceil(log1p(-q) / log1p(-p))
+        temp = self._cdf(vals-1, p)
+        return np.where((temp >= q) & (vals > 0), vals-1, vals)
+
+    def _stats(self, p):
+        mu = 1.0/p
+        qr = 1.0-p
+        var = qr / p / p
+        g1 = (2.0-p) / sqrt(qr)
+        g2 = np.polyval([1, -6, 6], p)/(1.0-p)
+        return mu, var, g1, g2
+
+    def _entropy(self, p):
+        return -np.log(p) - np.log1p(-p) * (1.0-p) / p
+
+
+geom = geom_gen(a=1, name='geom', longname="A geometric")
+
+
+class hypergeom_gen(rv_discrete):
+    r"""A hypergeometric discrete random variable.
+
+    The hypergeometric distribution models drawing objects from a bin.
+    `M` is the total number of objects, `n` is total number of Type I objects.
+    The random variate represents the number of Type I objects in `N` drawn
+    without replacement from the total population.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    nhypergeom, binom, nbinom
+
+    Notes
+    -----
+    The symbols used to denote the shape parameters (`M`, `n`, and `N`) are not
+    universally accepted.  See the Examples for a clarification of the
+    definitions used here.
+
+    The probability mass function is defined as,
+
+    .. math:: p(k, M, n, N) = \frac{\binom{n}{k} \binom{M - n}{N - k}}
+                                   {\binom{M}{N}}
+
+    for :math:`k \in [\max(0, N - M + n), \min(n, N)]`, where the binomial
+    coefficients are defined as,
+
+    .. math:: \binom{n}{k} \equiv \frac{n!}{k! (n - k)!}.
+
+    This distribution uses routines from the Boost Math C++ library for
+    the computation of the ``pmf``, ``cdf``, ``sf`` and ``stats`` methods. [1]_
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import hypergeom
+    >>> import matplotlib.pyplot as plt
+
+    Suppose we have a collection of 20 animals, of which 7 are dogs.  Then if
+    we want to know the probability of finding a given number of dogs if we
+    choose at random 12 of the 20 animals, we can initialize a frozen
+    distribution and plot the probability mass function:
+
+    >>> [M, n, N] = [20, 7, 12]
+    >>> rv = hypergeom(M, n, N)
+    >>> x = np.arange(0, n+1)
+    >>> pmf_dogs = rv.pmf(x)
+
+    >>> fig = plt.figure()
+    >>> ax = fig.add_subplot(111)
+    >>> ax.plot(x, pmf_dogs, 'bo')
+    >>> ax.vlines(x, 0, pmf_dogs, lw=2)
+    >>> ax.set_xlabel('# of dogs in our group of chosen animals')
+    >>> ax.set_ylabel('hypergeom PMF')
+    >>> plt.show()
+
+    Instead of using a frozen distribution we can also use `hypergeom`
+    methods directly.  To for example obtain the cumulative distribution
+    function, use:
+
+    >>> prb = hypergeom.cdf(x, M, n, N)
+
+    And to generate random numbers:
+
+    >>> R = hypergeom.rvs(M, n, N, size=10)
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("M", True, (0, np.inf), (True, False)),
+                _ShapeInfo("n", True, (0, np.inf), (True, False)),
+                _ShapeInfo("N", True, (0, np.inf), (True, False))]
+
+    def _rvs(self, M, n, N, size=None, random_state=None):
+        return random_state.hypergeometric(n, M-n, N, size=size)
+
+    def _get_support(self, M, n, N):
+        return np.maximum(N-(M-n), 0), np.minimum(n, N)
+
+    def _argcheck(self, M, n, N):
+        cond = (M > 0) & (n >= 0) & (N >= 0)
+        cond &= (n <= M) & (N <= M)
+        cond &= _isintegral(M) & _isintegral(n) & _isintegral(N)
+        return cond
+
+    def _logpmf(self, k, M, n, N):
+        tot, good = M, n
+        bad = tot - good
+        result = (betaln(good+1, 1) + betaln(bad+1, 1) + betaln(tot-N+1, N+1) -
+                  betaln(k+1, good-k+1) - betaln(N-k+1, bad-N+k+1) -
+                  betaln(tot+1, 1))
+        return result
+
+    def _pmf(self, k, M, n, N):
+        return scu._hypergeom_pmf(k, n, N, M)
+
+    def _cdf(self, k, M, n, N):
+        return scu._hypergeom_cdf(k, n, N, M)
+
+    def _stats(self, M, n, N):
+        M, n, N = 1. * M, 1. * n, 1. * N
+        m = M - n
+
+        # Boost kurtosis_excess doesn't return the same as the value
+        # computed here.
+        g2 = M * (M + 1) - 6. * N * (M - N) - 6. * n * m
+        g2 *= (M - 1) * M * M
+        g2 += 6. * n * N * (M - N) * m * (5. * M - 6)
+        g2 /= n * N * (M - N) * m * (M - 2.) * (M - 3.)
+        return (
+            scu._hypergeom_mean(n, N, M),
+            scu._hypergeom_variance(n, N, M),
+            scu._hypergeom_skewness(n, N, M),
+            g2,
+        )
+
+    def _entropy(self, M, n, N):
+        k = np.r_[N - (M - n):min(n, N) + 1]
+        vals = self.pmf(k, M, n, N)
+        return np.sum(entr(vals), axis=0)
+
+    def _sf(self, k, M, n, N):
+        return scu._hypergeom_sf(k, n, N, M)
+
+    def _logsf(self, k, M, n, N):
+        res = []
+        for quant, tot, good, draw in zip(*np.broadcast_arrays(k, M, n, N)):
+            if (quant + 0.5) * (tot + 0.5) < (good - 0.5) * (draw - 0.5):
+                # Less terms to sum if we calculate log(1-cdf)
+                res.append(log1p(-exp(self.logcdf(quant, tot, good, draw))))
+            else:
+                # Integration over probability mass function using logsumexp
+                k2 = np.arange(quant + 1, draw + 1)
+                res.append(logsumexp(self._logpmf(k2, tot, good, draw)))
+        return np.asarray(res)
+
+    def _logcdf(self, k, M, n, N):
+        res = []
+        for quant, tot, good, draw in zip(*np.broadcast_arrays(k, M, n, N)):
+            if (quant + 0.5) * (tot + 0.5) > (good - 0.5) * (draw - 0.5):
+                # Less terms to sum if we calculate log(1-sf)
+                res.append(log1p(-exp(self.logsf(quant, tot, good, draw))))
+            else:
+                # Integration over probability mass function using logsumexp
+                k2 = np.arange(0, quant + 1)
+                res.append(logsumexp(self._logpmf(k2, tot, good, draw)))
+        return np.asarray(res)
+
+
+hypergeom = hypergeom_gen(name='hypergeom')
+
+
+class nhypergeom_gen(rv_discrete):
+    r"""A negative hypergeometric discrete random variable.
+
+    Consider a box containing :math:`M` balls:, :math:`n` red and
+    :math:`M-n` blue. We randomly sample balls from the box, one
+    at a time and *without* replacement, until we have picked :math:`r`
+    blue balls. `nhypergeom` is the distribution of the number of
+    red balls :math:`k` we have picked.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    hypergeom, binom, nbinom
+
+    Notes
+    -----
+    The symbols used to denote the shape parameters (`M`, `n`, and `r`) are not
+    universally accepted. See the Examples for a clarification of the
+    definitions used here.
+
+    The probability mass function is defined as,
+
+    .. math:: f(k; M, n, r) = \frac{{{k+r-1}\choose{k}}{{M-r-k}\choose{n-k}}}
+                                   {{M \choose n}}
+
+    for :math:`k \in [0, n]`, :math:`n \in [0, M]`, :math:`r \in [0, M-n]`,
+    and the binomial coefficient is:
+
+    .. math:: \binom{n}{k} \equiv \frac{n!}{k! (n - k)!}.
+
+    It is equivalent to observing :math:`k` successes in :math:`k+r-1`
+    samples with :math:`k+r`'th sample being a failure. The former
+    can be modelled as a hypergeometric distribution. The probability
+    of the latter is simply the number of failures remaining
+    :math:`M-n-(r-1)` divided by the size of the remaining population
+    :math:`M-(k+r-1)`. This relationship can be shown as:
+
+    .. math:: NHG(k;M,n,r) = HG(k;M,n,k+r-1)\frac{(M-n-(r-1))}{(M-(k+r-1))}
+
+    where :math:`NHG` is probability mass function (PMF) of the
+    negative hypergeometric distribution and :math:`HG` is the
+    PMF of the hypergeometric distribution.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] Negative Hypergeometric Distribution on Wikipedia
+           https://en.wikipedia.org/wiki/Negative_hypergeometric_distribution
+
+    .. [2] Negative Hypergeometric Distribution from
+           http://www.math.wm.edu/~leemis/chart/UDR/PDFs/Negativehypergeometric.pdf
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import nhypergeom
+    >>> import matplotlib.pyplot as plt
+
+    Suppose we have a collection of 20 animals, of which 7 are dogs.
+    Then if we want to know the probability of finding a given number
+    of dogs (successes) in a sample with exactly 12 animals that
+    aren't dogs (failures), we can initialize a frozen distribution
+    and plot the probability mass function:
+
+    >>> M, n, r = [20, 7, 12]
+    >>> rv = nhypergeom(M, n, r)
+    >>> x = np.arange(0, n+2)
+    >>> pmf_dogs = rv.pmf(x)
+
+    >>> fig = plt.figure()
+    >>> ax = fig.add_subplot(111)
+    >>> ax.plot(x, pmf_dogs, 'bo')
+    >>> ax.vlines(x, 0, pmf_dogs, lw=2)
+    >>> ax.set_xlabel('# of dogs in our group with given 12 failures')
+    >>> ax.set_ylabel('nhypergeom PMF')
+    >>> plt.show()
+
+    Instead of using a frozen distribution we can also use `nhypergeom`
+    methods directly.  To for example obtain the probability mass
+    function, use:
+
+    >>> prb = nhypergeom.pmf(x, M, n, r)
+
+    And to generate random numbers:
+
+    >>> R = nhypergeom.rvs(M, n, r, size=10)
+
+    To verify the relationship between `hypergeom` and `nhypergeom`, use:
+
+    >>> from scipy.stats import hypergeom, nhypergeom
+    >>> M, n, r = 45, 13, 8
+    >>> k = 6
+    >>> nhypergeom.pmf(k, M, n, r)
+    0.06180776620271643
+    >>> hypergeom.pmf(k, M, n, k+r-1) * (M - n - (r-1)) / (M - (k+r-1))
+    0.06180776620271644
+    """
+
+    def _shape_info(self):
+        return [_ShapeInfo("M", True, (0, np.inf), (True, False)),
+                _ShapeInfo("n", True, (0, np.inf), (True, False)),
+                _ShapeInfo("r", True, (0, np.inf), (True, False))]
+
+    def _get_support(self, M, n, r):
+        return 0, n
+
+    def _argcheck(self, M, n, r):
+        cond = (n >= 0) & (n <= M) & (r >= 0) & (r <= M-n)
+        cond &= _isintegral(M) & _isintegral(n) & _isintegral(r)
+        return cond
+
+    def _rvs(self, M, n, r, size=None, random_state=None):
+
+        @_vectorize_rvs_over_shapes
+        def _rvs1(M, n, r, size, random_state):
+            # invert cdf by calculating all values in support, scalar M, n, r
+            a, b = self.support(M, n, r)
+            ks = np.arange(a, b+1)
+            cdf = self.cdf(ks, M, n, r)
+            ppf = interp1d(cdf, ks, kind='next', fill_value='extrapolate')
+            rvs = ppf(random_state.uniform(size=size)).astype(int)
+            if size is None:
+                return rvs.item()
+            return rvs
+
+        return _rvs1(M, n, r, size=size, random_state=random_state)
+
+    def _logpmf(self, k, M, n, r):
+        return xpx.apply_where(
+            (r != 0) | (k != 0), (k, M, n, r),
+            lambda k, M, n, r:
+                (-betaln(k+1, r) + betaln(k+r, 1)
+                 - betaln(n-k+1, M-r-n+1) + betaln(M-r-k+1, 1)
+                 + betaln(n+1, M-n+1) - betaln(M+1, 1)),
+            fill_value=0.0)
+
+    def _pmf(self, k, M, n, r):
+        # same as the following but numerically more precise
+        # return comb(k+r-1, k) * comb(M-r-k, n-k) / comb(M, n)
+        return exp(self._logpmf(k, M, n, r))
+
+    def _stats(self, M, n, r):
+        # Promote the datatype to at least float
+        # mu = rn / (M-n+1)
+        M, n, r = 1.*M, 1.*n, 1.*r
+        mu = r*n / (M-n+1)
+
+        var = r*(M+1)*n / ((M-n+1)*(M-n+2)) * (1 - r / (M-n+1))
+
+        # The skew and kurtosis are mathematically
+        # intractable so return `None`. See [2]_.
+        g1, g2 = None, None
+        return mu, var, g1, g2
+
+
+nhypergeom = nhypergeom_gen(name='nhypergeom')
+
+
+# FIXME: Fails _cdfvec
+class logser_gen(rv_discrete):
+    r"""A Logarithmic (Log-Series, Series) discrete random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability mass function for `logser` is:
+
+    .. math::
+
+        f(k) = - \frac{p^k}{k \log(1-p)}
+
+    for :math:`k \ge 1`, :math:`0 < p < 1`
+
+    `logser` takes :math:`p` as shape parameter,
+    where :math:`p` is the probability of a single success
+    and :math:`1-p` is the probability of a single failure.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+
+    def _shape_info(self):
+        return [_ShapeInfo("p", False, (0, 1), (True, True))]
+
+    def _rvs(self, p, size=None, random_state=None):
+        # looks wrong for p>0.5, too few k=1
+        # trying to use generic is worse, no k=1 at all
+        return random_state.logseries(p, size=size)
+
+    def _argcheck(self, p):
+        return (p > 0) & (p < 1)
+
+    def _pmf(self, k, p):
+        # logser.pmf(k) = - p**k / (k*log(1-p))
+        return -np.power(p, k) * 1.0 / k / special.log1p(-p)
+
+    def _sf(self, k, p):
+        tiny = 1e-100
+        # Ideally, this is the unregularized beta function with `b=0`. We don't have
+        # an unregularized beta function (yet, although we could get it from Boost),
+        # and neither technically support `b=0` - despite the function being accurate
+        # for `b` super close to zero. See https://github.com/scipy/scipy/issues/3890.
+        return -special.betainc(k+1, tiny, p) * special.beta(k+1, tiny) / np.log1p(-p)
+
+    def _stats(self, p):
+        r = special.log1p(-p)
+        mu = p / (p - 1.0) / r
+        mu2p = -p / r / (p - 1.0)**2
+        var = mu2p - mu*mu
+        mu3p = -p / r * (1.0+p) / (1.0 - p)**3
+        mu3 = mu3p - 3*mu*mu2p + 2*mu**3
+        g1 = mu3 / np.power(var, 1.5)
+
+        mu4p = -p / r * (
+            1.0 / (p-1)**2 - 6*p / (p - 1)**3 + 6*p*p / (p-1)**4)
+        mu4 = mu4p - 4*mu3p*mu + 6*mu2p*mu*mu - 3*mu**4
+        g2 = mu4 / var**2 - 3.0
+        return mu, var, g1, g2
+
+
+logser = logser_gen(a=1, name='logser', longname='A logarithmic')
+
+
+class poisson_gen(rv_discrete):
+    r"""A Poisson discrete random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability mass function for `poisson` is:
+
+    .. math::
+
+        f(k) = \exp(-\mu) \frac{\mu^k}{k!}
+
+    for :math:`k \ge 0`.
+
+    `poisson` takes :math:`\mu \geq 0` as shape parameter.
+    When :math:`\mu = 0`, the ``pmf`` method
+    returns ``1.0`` at quantile :math:`k = 0`.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+
+    def _shape_info(self):
+        return [_ShapeInfo("mu", False, (0, np.inf), (True, False))]
+
+    # Override rv_discrete._argcheck to allow mu=0.
+    def _argcheck(self, mu):
+        return mu >= 0
+
+    def _rvs(self, mu, size=None, random_state=None):
+        return random_state.poisson(mu, size)
+
+    def _logpmf(self, k, mu):
+        Pk = special.xlogy(k, mu) - gamln(k + 1) - mu
+        return Pk
+
+    def _pmf(self, k, mu):
+        # poisson.pmf(k) = exp(-mu) * mu**k / k!
+        return exp(self._logpmf(k, mu))
+
+    def _cdf(self, x, mu):
+        k = floor(x)
+        return special.pdtr(k, mu)
+
+    def _sf(self, x, mu):
+        k = floor(x)
+        return special.pdtrc(k, mu)
+
+    def _ppf(self, q, mu):
+        vals = ceil(special.pdtrik(q, mu))
+        vals1 = np.maximum(vals - 1, 0)
+        temp = special.pdtr(vals1, mu)
+        return np.where(temp >= q, vals1, vals)
+
+    def _stats(self, mu):
+        var = mu
+        tmp = np.asarray(mu)
+        mu_nonzero = tmp > 0
+        g1 = xpx.apply_where(mu_nonzero, tmp, lambda x: sqrt(1.0/x), fill_value=np.inf)
+        g2 = xpx.apply_where(mu_nonzero, tmp, lambda x: 1.0/x, fill_value=np.inf)
+        return mu, var, g1, g2
+
+
+poisson = poisson_gen(name="poisson", longname='A Poisson')
+
+
+class planck_gen(rv_discrete):
+    r"""A Planck discrete exponential random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    geom
+
+    Notes
+    -----
+    The probability mass function for `planck` is:
+
+    .. math::
+
+        f(k) = (1-\exp(-\lambda)) \exp(-\lambda k)
+
+    for :math:`k \ge 0` and :math:`\lambda > 0`.
+
+    `planck` takes :math:`\lambda` as shape parameter. The Planck distribution
+    can be written as a geometric distribution (`geom`) with
+    :math:`p = 1 - \exp(-\lambda)` shifted by ``loc = -1``.
+
+    %(after_notes)s
+
+    %(example)s
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("lambda_", False, (0, np.inf), (False, False))]
+
+    def _argcheck(self, lambda_):
+        return lambda_ > 0
+
+    def _pmf(self, k, lambda_):
+        return -expm1(-lambda_)*exp(-lambda_*k)
+
+    def _cdf(self, x, lambda_):
+        k = floor(x)
+        return -expm1(-lambda_*(k+1))
+
+    def _sf(self, x, lambda_):
+        return exp(self._logsf(x, lambda_))
+
+    def _logsf(self, x, lambda_):
+        k = floor(x)
+        return -lambda_*(k+1)
+
+    def _ppf(self, q, lambda_):
+        vals = ceil(-1.0/lambda_ * log1p(-q)-1)
+        vals1 = (vals-1).clip(*(self._get_support(lambda_)))
+        temp = self._cdf(vals1, lambda_)
+        return np.where(temp >= q, vals1, vals)
+
+    def _rvs(self, lambda_, size=None, random_state=None):
+        # use relation to geometric distribution for sampling
+        p = -expm1(-lambda_)
+        return random_state.geometric(p, size=size) - 1.0
+
+    def _stats(self, lambda_):
+        mu = 1/expm1(lambda_)
+        var = exp(-lambda_)/(expm1(-lambda_))**2
+        g1 = 2*cosh(lambda_/2.0)
+        g2 = 4+2*cosh(lambda_)
+        return mu, var, g1, g2
+
+    def _entropy(self, lambda_):
+        C = -expm1(-lambda_)
+        return lambda_*exp(-lambda_)/C - log(C)
+
+
+planck = planck_gen(a=0, name='planck', longname='A discrete exponential ')
+
+
+class boltzmann_gen(rv_discrete):
+    r"""A Boltzmann (Truncated Discrete Exponential) random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability mass function for `boltzmann` is:
+
+    .. math::
+
+        f(k) = (1-\exp(-\lambda)) \exp(-\lambda k) / (1-\exp(-\lambda N))
+
+    for :math:`k = 0,..., N-1`.
+
+    `boltzmann` takes :math:`\lambda > 0` and :math:`N > 0` as shape parameters.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("lambda_", False, (0, np.inf), (False, False)),
+                _ShapeInfo("N", True, (0, np.inf), (False, False))]
+
+    def _argcheck(self, lambda_, N):
+        return (lambda_ > 0) & (N > 0) & _isintegral(N)
+
+    def _get_support(self, lambda_, N):
+        return self.a, N - 1
+
+    def _pmf(self, k, lambda_, N):
+        # boltzmann.pmf(k) =
+        #               (1-exp(-lambda_)*exp(-lambda_*k)/(1-exp(-lambda_*N))
+        fact = (1-exp(-lambda_))/(1-exp(-lambda_*N))
+        return fact*exp(-lambda_*k)
+
+    def _cdf(self, x, lambda_, N):
+        k = floor(x)
+        return (1-exp(-lambda_*(k+1)))/(1-exp(-lambda_*N))
+
+    def _ppf(self, q, lambda_, N):
+        qnew = q*(1-exp(-lambda_*N))
+        vals = ceil(-1.0/lambda_ * log(1-qnew)-1)
+        vals1 = (vals-1).clip(0.0, np.inf)
+        temp = self._cdf(vals1, lambda_, N)
+        return np.where(temp >= q, vals1, vals)
+
+    def _stats(self, lambda_, N):
+        z = exp(-lambda_)
+        zN = exp(-lambda_*N)
+        mu = z/(1.0-z)-N*zN/(1-zN)
+        var = z/(1.0-z)**2 - N*N*zN/(1-zN)**2
+        trm = (1-zN)/(1-z)
+        trm2 = (z*trm**2 - N*N*zN)
+        g1 = z*(1+z)*trm**3 - N**3*zN*(1+zN)
+        g1 = g1 / trm2**(1.5)
+        g2 = z*(1+4*z+z*z)*trm**4 - N**4 * zN*(1+4*zN+zN*zN)
+        g2 = g2 / trm2 / trm2
+        return mu, var, g1, g2
+
+
+boltzmann = boltzmann_gen(name='boltzmann', a=0,
+                          longname='A truncated discrete exponential ')
+
+
+class randint_gen(rv_discrete):
+    r"""A uniform discrete random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability mass function for `randint` is:
+
+    .. math::
+
+        f(k) = \frac{1}{\texttt{high} - \texttt{low}}
+
+    for :math:`k \in \{\texttt{low}, \dots, \texttt{high} - 1\}`.
+
+    `randint` takes :math:`\texttt{low}` and :math:`\texttt{high}` as shape
+    parameters.
+
+    %(after_notes)s
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import randint
+    >>> import matplotlib.pyplot as plt
+    >>> fig, ax = plt.subplots(1, 1)
+
+    Calculate the first four moments:
+
+    >>> low, high = 7, 31
+    >>> mean, var, skew, kurt = randint.stats(low, high, moments='mvsk')
+
+    Display the probability mass function (``pmf``):
+
+    >>> x = np.arange(low - 5, high + 5)
+    >>> ax.plot(x, randint.pmf(x, low, high), 'bo', ms=8, label='randint pmf')
+    >>> ax.vlines(x, 0, randint.pmf(x, low, high), colors='b', lw=5, alpha=0.5)
+
+    Alternatively, the distribution object can be called (as a function) to
+    fix the shape and location. This returns a "frozen" RV object holding the
+    given parameters fixed.
+
+    Freeze the distribution and display the frozen ``pmf``:
+
+    >>> rv = randint(low, high)
+    >>> ax.vlines(x, 0, rv.pmf(x), colors='k', linestyles='-',
+    ...           lw=1, label='frozen pmf')
+    >>> ax.legend(loc='lower center')
+    >>> plt.show()
+
+    Check the relationship between the cumulative distribution function
+    (``cdf``) and its inverse, the percent point function (``ppf``):
+
+    >>> q = np.arange(low, high)
+    >>> p = randint.cdf(q, low, high)
+    >>> np.allclose(q, randint.ppf(p, low, high))
+    True
+
+    Generate random numbers:
+
+    >>> r = randint.rvs(low, high, size=1000)
+
+    """
+
+    def _shape_info(self):
+        return [_ShapeInfo("low", True, (-np.inf, np.inf), (False, False)),
+                _ShapeInfo("high", True, (-np.inf, np.inf), (False, False))]
+
+    def _argcheck(self, low, high):
+        return (high > low) & _isintegral(low) & _isintegral(high)
+
+    def _get_support(self, low, high):
+        return low, high-1
+
+    def _pmf(self, k, low, high):
+        # randint.pmf(k) = 1./(high - low)
+        p = np.ones_like(k) / (np.asarray(high, dtype=np.int64) - low)
+        return np.where((k >= low) & (k < high), p, 0.)
+
+    def _cdf(self, x, low, high):
+        k = floor(x)
+        return (k - low + 1.) / (high - low)
+
+    def _ppf(self, q, low, high):
+        vals = ceil(q * (high - low) + low) - 1
+        vals1 = (vals - 1).clip(low, high)
+        temp = self._cdf(vals1, low, high)
+        return np.where(temp >= q, vals1, vals)
+
+    def _stats(self, low, high):
+        m2, m1 = np.asarray(high), np.asarray(low)
+        mu = (m2 + m1 - 1.0) / 2
+        d = m2 - m1
+        var = (d*d - 1) / 12.0
+        g1 = 0.0
+        g2 = -6.0/5.0 * (d*d + 1.0) / (d*d - 1.0)
+        return mu, var, g1, g2
+
+    def _rvs(self, low, high, size=None, random_state=None):
+        """An array of *size* random integers >= ``low`` and < ``high``."""
+        if np.asarray(low).size == 1 and np.asarray(high).size == 1:
+            # no need to vectorize in that case
+            return rng_integers(random_state, low, high, size=size)
+
+        if size is not None:
+            # NumPy's RandomState.randint() doesn't broadcast its arguments.
+            # Use `broadcast_to()` to extend the shapes of low and high
+            # up to size.  Then we can use the numpy.vectorize'd
+            # randint without needing to pass it a `size` argument.
+            low = np.broadcast_to(low, size)
+            high = np.broadcast_to(high, size)
+        randint = np.vectorize(partial(rng_integers, random_state),
+                               otypes=[np.dtype(int)])
+        return randint(low, high)
+
+    def _entropy(self, low, high):
+        return log(high - low)
+
+
+randint = randint_gen(name='randint', longname='A discrete uniform '
+                      '(random integer)')
+
+
+# FIXME: problems sampling.
+class zipf_gen(rv_discrete):
+    r"""A Zipf (Zeta) discrete random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    zipfian
+
+    Notes
+    -----
+    The probability mass function for `zipf` is:
+
+    .. math::
+
+        f(k, a) = \frac{1}{\zeta(a) k^a}
+
+    for :math:`k \ge 1`, :math:`a > 1`.
+
+    `zipf` takes :math:`a > 1` as shape parameter. :math:`\zeta` is the
+    Riemann zeta function (`scipy.special.zeta`)
+
+    The Zipf distribution is also known as the zeta distribution, which is
+    a special case of the Zipfian distribution (`zipfian`).
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] "Zeta Distribution", Wikipedia,
+           https://en.wikipedia.org/wiki/Zeta_distribution
+
+    %(example)s
+
+    Confirm that `zipf` is the large `n` limit of `zipfian`.
+
+    >>> import numpy as np
+    >>> from scipy.stats import zipf, zipfian
+    >>> k = np.arange(11)
+    >>> np.allclose(zipf.pmf(k, a), zipfian.pmf(k, a, n=10000000))
+    True
+
+    """
+
+    def _shape_info(self):
+        return [_ShapeInfo("a", False, (1, np.inf), (False, False))]
+
+    def _rvs(self, a, size=None, random_state=None):
+        return random_state.zipf(a, size=size)
+
+    def _argcheck(self, a):
+        return a > 1
+
+    def _pmf(self, k, a):
+        k = k.astype(np.float64)
+        # zipf.pmf(k, a) = 1/(zeta(a) * k**a)
+        Pk = 1.0 / special.zeta(a, 1) * k**-a
+        return Pk
+
+    def _munp(self, n, a):
+        return xpx.apply_where(
+            a > n + 1, (a, n),
+            lambda a, n: special.zeta(a - n, 1) / special.zeta(a, 1),
+            fill_value=np.inf)
+
+
+zipf = zipf_gen(a=1, name='zipf', longname='A Zipf')
+
+
+class zipfian_gen(rv_discrete):
+    r"""A Zipfian discrete random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    zipf
+
+    Notes
+    -----
+    The probability mass function for `zipfian` is:
+
+    .. math::
+
+        f(k, a, n) = \frac{1}{H_{n,a} k^a}
+
+    for :math:`k \in \{1, 2, \dots, n-1, n\}`, :math:`a \ge 0`,
+    :math:`n \in \{1, 2, 3, \dots\}`.
+
+    `zipfian` takes :math:`a` and :math:`n` as shape parameters.
+    :math:`H_{n,a}` is the :math:`n`:sup:`th` generalized harmonic
+    number of order :math:`a`.
+
+    The SciPy implementation of this distribution requires :math:`1 \le n \le 2^{53}`.
+    For larger values of :math:`n`, the `zipfian` methods (`pmf`, `cdf`, `mean`, etc.)
+    will return `nan`.
+
+    When :math:`a > 1`, the Zipfian distribution reduces to the Zipf (zeta)
+    distribution as :math:`n \rightarrow \infty`.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] "Zipf's Law", Wikipedia, https://en.wikipedia.org/wiki/Zipf's_law
+    .. [2] Larry Leemis, "Zipf Distribution", Univariate Distribution
+           Relationships. http://www.math.wm.edu/~leemis/chart/UDR/PDFs/Zipf.pdf
+
+    %(example)s
+
+    Confirm that `zipfian` reduces to `zipf` for large `n`, ``a > 1``.
+
+    >>> import numpy as np
+    >>> from scipy.stats import zipf, zipfian
+    >>> k = np.arange(11)
+    >>> np.allclose(zipfian.pmf(k, a=3.5, n=10000000), zipf.pmf(k, a=3.5))
+    True
+
+    """
+
+    def _shape_info(self):
+        return [_ShapeInfo("a", False, (0, np.inf), (True, False)),
+                _ShapeInfo("n", True, (0, np.inf), (False, False))]
+
+    def _argcheck(self, a, n):
+        # The upper bound on n is for practical numerical reasons.  The numerical
+        # methods for computing the PMF, CDF and SF involve sums over range(1, n+1)
+        # when a <= 1, so there is no way they can be computed for extremely large
+        # n--even 2**53 is ridiculously large for those calculations.  The bound is
+        # also required to ensure that the loops compute the sums correctly when
+        # the inputs are double precision instead of integers.
+        #
+        # n may be an integer or a float, but the value must be an integer in the
+        # range 1 <= n <= 2**53.  The expression below clips n to the accepted range
+        # before attempting to cast to integer to avoid warnings generated by an
+        # input such as n=1e100.  The extra `np.asarray()` wrapper avoids the error
+        # that arises with an input such as `n=2**100`.
+        # upper limit changed in gh-24119 because of overflow on windows, linux32 bit
+        return ((a >= 0) &
+                (n == np.asarray(np.clip(n, 1, 2**31 - 1)).astype(dtype=np.int64)))
+
+    def _get_support(self, a, n):
+        return 1, np.floor(n)
+
+    def _pmf(self, k, a, n):
+        k = np.floor(k)
+        n = np.floor(n)
+        return scu._normalized_gen_harmonic(k, k, n, a)
+
+    def _cdf(self, k, a, n):
+        k = np.floor(k)
+        n = np.floor(n)
+        return scu._normalized_gen_harmonic(1, k, n, a)
+
+    def _sf(self, k, a, n):
+        k = np.floor(k)
+        n = np.floor(n)
+        return scu._normalized_gen_harmonic(k + 1, n, n, a)
+
+    def _stats(self, a, n):
+        n = np.floor(n)
+        # see http://www.math.wm.edu/~leemis/chart/UDR/PDFs/Zipf.pdf
+        Hna = scu._gen_harmonic(n, a)
+        Hna1 = scu._gen_harmonic(n, a-1)
+        Hna2 = scu._gen_harmonic(n, a-2)
+        Hna3 = scu._gen_harmonic(n, a-3)
+        Hna4 = scu._gen_harmonic(n, a-4)
+        mu1 = Hna1/Hna
+        mu2n = (Hna2*Hna - Hna1**2)
+        mu2d = Hna**2
+        mu2 = mu2n / mu2d
+        g1 = (Hna3/Hna - 3*Hna1*Hna2/Hna**2 + 2*Hna1**3/Hna**3)/mu2**(3/2)
+        g2 = (Hna**3*Hna4 - 4*Hna**2*Hna1*Hna3 + 6*Hna*Hna1**2*Hna2
+              - 3*Hna1**4) / mu2n**2
+        g2 -= 3
+        return mu1, mu2, g1, g2
+
+
+zipfian = zipfian_gen(a=1, name='zipfian', longname='A Zipfian')
+
+
+class dlaplace_gen(rv_discrete):
+    r"""A  Laplacian discrete random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability mass function for `dlaplace` is:
+
+    .. math::
+
+        f(k) = \tanh(a/2) \exp(-a |k|)
+
+    for integers :math:`k` and :math:`a > 0`.
+
+    `dlaplace` takes :math:`a` as shape parameter.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+
+    def _shape_info(self):
+        return [_ShapeInfo("a", False, (0, np.inf), (False, False))]
+
+    def _pmf(self, k, a):
+        # dlaplace.pmf(k) = tanh(a/2) * exp(-a*abs(k))
+        return tanh(a/2.0) * exp(-a * abs(k))
+
+    def _cdf(self, x, a):
+        k = floor(x)
+
+        def f1(k, a):
+            return 1.0 - exp(-a * k) / (exp(a) + 1)
+
+        def f2(k, a):
+            return exp(a * (k + 1)) / (exp(a) + 1)
+
+        return xpx.apply_where(k >= 0, (k, a), f1, f2)
+
+    def _ppf(self, q, a):
+        const = 1 + exp(a)
+        vals = ceil(np.where(q < 1.0 / (1 + exp(-a)),
+                             log(q*const) / a - 1,
+                             -log((1-q) * const) / a))
+        vals1 = vals - 1
+        return np.where(self._cdf(vals1, a) >= q, vals1, vals)
+
+    def _stats(self, a):
+        ea = exp(a)
+        mu2 = 2.*ea/(ea-1.)**2
+        mu4 = 2.*ea*(ea**2+10.*ea+1.) / (ea-1.)**4
+        return 0., mu2, 0., mu4/mu2**2 - 3.
+
+    def _entropy(self, a):
+        return a / sinh(a) - log(tanh(a/2.0))
+
+    def _rvs(self, a, size=None, random_state=None):
+        # The discrete Laplace is equivalent to the two-sided geometric
+        # distribution with PMF:
+        #   f(k) = (1 - alpha)/(1 + alpha) * alpha^abs(k)
+        #   Reference:
+        #     https://www.sciencedirect.com/science/
+        #     article/abs/pii/S0378375804003519
+        # Furthermore, the two-sided geometric distribution is
+        # equivalent to the difference between two iid geometric
+        # distributions.
+        #   Reference (page 179):
+        #     https://pdfs.semanticscholar.org/61b3/
+        #     b99f466815808fd0d03f5d2791eea8b541a1.pdf
+        # Thus, we can leverage the following:
+        #   1) alpha = e^-a
+        #   2) probability_of_success = 1 - alpha (Bernoulli trial)
+        probOfSuccess = -np.expm1(-np.asarray(a))
+        x = random_state.geometric(probOfSuccess, size=size)
+        y = random_state.geometric(probOfSuccess, size=size)
+        return x - y
+
+
+dlaplace = dlaplace_gen(a=-np.inf,
+                        name='dlaplace', longname='A discrete Laplacian')
+
+
+class poisson_binom_gen(rv_discrete):
+    r"""A Poisson Binomial discrete random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    binom
+
+    Notes
+    -----
+    The probability mass function for `poisson_binom` is:
+
+    .. math::
+
+     f(k; p_1, p_2, ..., p_n) = \sum_{A \in F_k} \prod_{i \in A} p_i \prod_{j \in A^C} 1 - p_j
+
+    where :math:`k \in \{0, 1, \dots, n-1, n\}`, :math:`F_k` is the set of all
+    subsets of :math:`k` integers that can be selected :math:`\{0, 1, \dots, n-1, n\}`,
+    and :math:`A^C` is the complement of a set :math:`A`.
+
+    `poisson_binom` accepts a single array argument ``p`` for shape parameters
+    :math:`0 ≤ p_i ≤ 1`, where the last axis corresponds with the index :math:`i` and
+    any others are for batch dimensions. Broadcasting behaves according to the usual
+    rules except that the last axis of ``p`` is ignored. Instances of this class do
+    not support serialization/unserialization.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] "Poisson binomial distribution", Wikipedia,
+           https://en.wikipedia.org/wiki/Poisson_binomial_distribution
+    .. [2] Biscarri, William, Sihai Dave Zhao, and Robert J. Brunner. "A simple and
+           fast method for computing the Poisson binomial distribution function".
+           Computational Statistics & Data Analysis 122 (2018) 92-100.
+           :doi:`10.1016/j.csda.2018.01.007`
+
+    %(example)s
+
+    """  # noqa: E501
+
+    _parse_args_rvs: MethodType
+    _parse_args_stats: MethodType
+    _parse_args: MethodType
+
+    def _shape_info(self):
+        # message = 'Fitting is not implemented for this distribution."
+        # raise NotImplementedError(message)
+        return []
+
+    def _argcheck(self, *args):
+        p = np.stack(args, axis=0)
+        conds = (0 <= p) & (p <= 1)
+        return np.all(conds, axis=0)
+
+    def _rvs(self, *args, size=None, random_state=None):
+        # convenient to work along the last axis here to avoid interference with `size`
+        p = np.stack(args, axis=-1)
+        # Size passed by the user is the *shape of the returned array*, so it won't
+        # contain the length of the last axis of p.
+        size = (p.shape if size is None else
+                (size, 1) if np.isscalar(size) else tuple(size) + (1,))
+        size = np.broadcast_shapes(p.shape, size)
+        return bernoulli._rvs(p, size=size, random_state=random_state).sum(axis=-1)
+
+    def _get_support(self, *args):
+        return 0, len(args)
+
+    def _pmf(self, k, *args):
+        k = np.atleast_1d(k).astype(np.int64)
+        k, *args = np.broadcast_arrays(k, *args)
+        p = np.stack(args, dtype=np.float64, axis=-1)
+        return _poisson_binom_pmf(k, p)
+
+    def _cdf(self, k, *args):
+        k = np.atleast_1d(k).astype(np.int64)
+        k, *args = np.broadcast_arrays(k, *args)
+        p = np.stack(args, dtype=np.float64, axis=-1)
+        return _poisson_binom_cdf(k, p)
+
+    def _stats(self, *args, **kwds):
+        p = np.stack(args, axis=0)
+        mean = np.sum(p, axis=0)
+        var = np.sum(p * (1-p), axis=0)
+        return (mean, var, None, None)
+
+    def __call__(self, *args, **kwds):
+        return poisson_binomial_frozen(self, *args, **kwds)
+
+
+poisson_binom = poisson_binom_gen(name='poisson_binom', longname='A Poisson binomial',
+                                  shapes='p')
+
+# The _parse_args methods don't work with vector-valued shape parameters, so we rewrite
+# them. Note that `p` is accepted as an array with the index `i` of `p_i` corresponding
+# with the last axis; we return it as a tuple (p_1, p_2, ..., p_n) so that it looks
+# like `n` scalar (or arrays of scalar-valued) shape parameters to the infrastructure.
+
+def _parse_args_rvs(self, p, loc=0, size=None):
+    return tuple(np.moveaxis(p, -1, 0)), loc, 1.0, size
+
+def _parse_args_stats(self, p, loc=0, moments='mv'):
+    return tuple(np.moveaxis(p, -1, 0)), loc, 1.0, moments
+
+def _parse_args(self, p, loc=0):
+    return tuple(np.moveaxis(p, -1, 0)), loc, 1.0
+
+# The infrastructure manually binds these methods to the instance, so
+# we can only override them by manually binding them, too.
+_pb_obj, _pb_cls = poisson_binom, poisson_binom_gen  # shorter names (for PEP8)
+poisson_binom._parse_args_rvs = _parse_args_rvs.__get__(_pb_obj, _pb_cls)
+poisson_binom._parse_args_stats = _parse_args_stats.__get__(_pb_obj, _pb_cls)
+poisson_binom._parse_args = _parse_args.__get__(_pb_obj, _pb_cls)
+
+class poisson_binomial_frozen(rv_discrete_frozen):
+    # copied from rv_frozen; we just need to bind the `_parse_args` methods
+    def __init__(self, dist, *args, **kwds):                        # verbatim
+        self.args = args                                            # verbatim
+        self.kwds = kwds                                            # verbatim
+
+        # create a new instance                                     # verbatim
+        self.dist = dist.__class__(**dist._updated_ctor_param())    # verbatim
+
+        # Here is the only modification
+        self.dist._parse_args_rvs = _parse_args_rvs.__get__(_pb_obj, _pb_cls)
+        self.dist._parse_args_stats = _parse_args_stats.__get__(_pb_obj, _pb_cls)
+        self.dist._parse_args = _parse_args.__get__(_pb_obj, _pb_cls)
+
+        shapes, _, _ = self.dist._parse_args(*args, **kwds)         # verbatim
+        self.a, self.b = self.dist._get_support(*shapes)            # verbatim
+
+    def expect(self, func=None, lb=None, ub=None, conditional=False, **kwds):
+        a, loc, scale = self.dist._parse_args(*self.args, **self.kwds)
+        # Here's the modification: we pass all args (including `loc`) into the `args`
+        # parameter of `expect` so the shape only goes through `_parse_args` once.
+        return self.dist.expect(func, self.args, loc, lb, ub, conditional, **kwds)
+
+
+class skellam_gen(rv_discrete):
+    r"""A  Skellam discrete random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    Probability distribution of the difference of two correlated or
+    uncorrelated Poisson random variables.
+
+    Let :math:`k_1` and :math:`k_2` be two Poisson-distributed r.v. with
+    expected values :math:`\lambda_1` and :math:`\lambda_2`. Then,
+    :math:`k_1 - k_2` follows a Skellam distribution with parameters
+    :math:`\mu_1 = \lambda_1 - \rho \sqrt{\lambda_1 \lambda_2}` and
+    :math:`\mu_2 = \lambda_2 - \rho \sqrt{\lambda_1 \lambda_2}`, where
+    :math:`\rho` is the correlation coefficient between :math:`k_1` and
+    :math:`k_2`. If the two Poisson-distributed r.v. are independent then
+    :math:`\rho = 0`.
+
+    Parameters :math:`\mu_1` and :math:`\mu_2` must be strictly positive.
+
+    `skellam` takes :math:`\mu_1` and :math:`\mu_2` as shape parameters.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] Skellam, J. G. "The Frequency Distribution of the Difference
+           Between Two Poisson Variates Belonging to Different Populations."
+           *Journal of the Royal Statistical Society* 109, no. 3 (1946): 296-296.
+           :doi:`10.2307/2981372`
+    .. [2] "Skellam distribution", Wikipedia,
+           https://en.wikipedia.org/wiki/Skellam_distribution
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("mu1", False, (0, np.inf), (False, False)),
+                _ShapeInfo("mu2", False, (0, np.inf), (False, False))]
+
+    def _rvs(self, mu1, mu2, size=None, random_state=None):
+        n = size
+        return (random_state.poisson(mu1, n) -
+                random_state.poisson(mu2, n))
+
+    def _pmf(self, x, mu1, mu2):
+        with np.errstate(over='ignore'):  # see gh-17432
+            px = np.where(x < 0,
+                          scu._ncx2_pdf(2*mu2, 2*(1-x), 2*mu1)*2,
+                          scu._ncx2_pdf(2*mu1, 2*(1+x), 2*mu2)*2)
+            # ncx2.pdf() returns nan's for extremely low probabilities
+        return px
+
+    def _cdf(self, x, mu1, mu2):
+        x = floor(x)
+        with np.errstate(over='ignore'):  # see gh-17432
+            px = np.where(x < 0,
+                          special.chndtr(2*mu2, -2*x, 2*mu1),
+                          scu._ncx2_sf(2*mu1, 2*(x+1), 2*mu2))
+        return px
+
+    def _stats(self, mu1, mu2):
+        mean = mu1 - mu2
+        var = mu1 + mu2
+        g1 = mean / sqrt((var)**3)
+        g2 = 1 / var
+        return mean, var, g1, g2
+
+
+skellam = skellam_gen(a=-np.inf, name="skellam", longname='A Skellam')
+
+
+class yulesimon_gen(rv_discrete):
+    r"""A Yule-Simon discrete random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+
+    The probability mass function for the `yulesimon` is:
+
+    .. math::
+
+        f(k) =  \alpha B(k, \alpha+1)
+
+    for :math:`k=1,2,3,...`, where :math:`\alpha>0`.
+    Here :math:`B` refers to the `scipy.special.beta` function.
+
+    The sampling of random variates is based on pg 553, Section 6.3 of [1]_.
+    Our notation maps to the referenced logic via :math:`\alpha=a-1`.
+
+    For details see the wikipedia entry [2]_.
+
+    References
+    ----------
+    .. [1] Devroye, Luc. "Non-uniform Random Variate Generation",
+         (1986) Springer, New York.
+
+    .. [2] https://en.wikipedia.org/wiki/Yule-Simon_distribution
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("alpha", False, (0, np.inf), (False, False))]
+
+    def _rvs(self, alpha, size=None, random_state=None):
+        E1 = random_state.standard_exponential(size)
+        E2 = random_state.standard_exponential(size)
+        ans = ceil(-E1 / log1p(-exp(-E2 / alpha)))
+        return ans
+
+    def _pmf(self, x, alpha):
+        return alpha * special.beta(x, alpha + 1)
+
+    def _argcheck(self, alpha):
+        return (alpha > 0)
+
+    def _logpmf(self, x, alpha):
+        return log(alpha) + special.betaln(x, alpha + 1)
+
+    def _cdf(self, x, alpha):
+        return 1 - x * special.beta(x, alpha + 1)
+
+    def _sf(self, x, alpha):
+        return x * special.beta(x, alpha + 1)
+
+    def _logsf(self, x, alpha):
+        return log(x) + special.betaln(x, alpha + 1)
+
+    def _stats(self, alpha):
+        mu = np.where(alpha <= 1, np.inf, alpha / (alpha - 1))
+        mu2 = np.where(alpha > 2,
+                       alpha**2 / ((alpha - 2.0) * (alpha - 1)**2),
+                       np.inf)
+        mu2 = np.where(alpha <= 1, np.nan, mu2)
+        g1 = np.where(alpha > 3,
+                      sqrt(alpha - 2) * (alpha + 1)**2 / (alpha * (alpha - 3)),
+                      np.inf)
+        g1 = np.where(alpha <= 2, np.nan, g1)
+        g2 = np.where(alpha > 4,
+                      alpha + 3 + ((11 * alpha**3 - 49 * alpha - 22) /
+                                   (alpha * (alpha - 4) * (alpha - 3))),
+                      np.inf)
+        g2 = np.where(alpha <= 2, np.nan, g2)
+        return mu, mu2, g1, g2
+
+
+yulesimon = yulesimon_gen(name='yulesimon', a=1)
+
+
+class _nchypergeom_gen(rv_discrete):
+    r"""A noncentral hypergeometric discrete random variable.
+
+    For subclassing by nchypergeom_fisher_gen and nchypergeom_wallenius_gen.
+
+    """
+
+    rvs_name = None
+    dist = None
+
+    def _shape_info(self):
+        return [_ShapeInfo("M", True, (0, np.inf), (True, False)),
+                _ShapeInfo("n", True, (0, np.inf), (True, False)),
+                _ShapeInfo("N", True, (0, np.inf), (True, False)),
+                _ShapeInfo("odds", False, (0, np.inf), (False, False))]
+
+    def _get_support(self, M, n, N, odds):
+        N, m1, n = M, n, N  # follow Wikipedia notation
+        m2 = N - m1
+        x_min = np.maximum(0, n - m2)
+        x_max = np.minimum(n, m1)
+        return x_min, x_max
+
+    def _argcheck(self, M, n, N, odds):
+        M, n = np.asarray(M), np.asarray(n),
+        N, odds = np.asarray(N), np.asarray(odds)
+        cond1 = (~np.isnan(M)) & (M.astype(int) == M) & (M >= 0)
+        cond2 = (~np.isnan(n)) & (n.astype(int) == n) & (n >= 0)
+        cond3 = (~np.isnan(N)) & (N.astype(int) == N) & (N >= 0)
+        cond4 = odds > 0
+        cond5 = N <= M
+        cond6 = n <= M
+        return cond1 & cond2 & cond3 & cond4 & cond5 & cond6
+
+    def _rvs(self, M, n, N, odds, size=None, random_state=None):
+
+        @_vectorize_rvs_over_shapes
+        def _rvs1(M, n, N, odds, size, random_state):
+            if np.isnan(M) | np.isnan(n) | np.isnan(N):
+                return np.full(size, np.nan)
+            length = np.prod(size)
+            urn = _PyStochasticLib3()
+            rv_gen = getattr(urn, self.rvs_name)
+            rvs = rv_gen(N, n, M, odds, length, random_state)
+            rvs = rvs.reshape(size)
+            return rvs
+
+        return _rvs1(M, n, N, odds, size=size, random_state=random_state)
+
+    def _pmf(self, x, M, n, N, odds):
+
+        x, M, n, N, odds = np.broadcast_arrays(x, M, n, N, odds)
+        if x.size == 0:  # np.vectorize doesn't work with zero size input
+            return np.empty_like(x)
+
+        @np.vectorize
+        def _pmf1(x, M, n, N, odds):
+            if np.isnan(x) | np.isnan(M) | np.isnan(n) | np.isnan(N):
+                return np.nan
+            urn = self.dist(N, n, M, odds, 1e-12)
+            return urn.probability(x)
+
+        return _pmf1(x, M, n, N, odds)
+
+    def _stats(self, M, n, N, odds, moments='mv'):
+
+        @np.vectorize
+        def _moments1(M, n, N, odds):
+            if np.isnan(M) | np.isnan(n) | np.isnan(N):
+                return np.nan, np.nan
+            urn = self.dist(N, n, M, odds, 1e-12)
+            return urn.moments()
+
+        m, v = (_moments1(M, n, N, odds) if ("m" in moments or "v" in moments)
+                else (None, None))
+        s, k = None, None
+        return m, v, s, k
+
+
+class nchypergeom_fisher_gen(_nchypergeom_gen):
+    r"""A Fisher's noncentral hypergeometric discrete random variable.
+
+    Fisher's noncentral hypergeometric distribution models drawing objects of
+    two types from a bin. `M` is the total number of objects, `n` is the
+    number of Type I objects, and `odds` is the odds ratio: the odds of
+    selecting a Type I object rather than a Type II object when there is only
+    one object of each type.
+    The random variate represents the number of Type I objects drawn if we
+    take a handful of objects from the bin at once and find out afterwards
+    that we took `N` objects.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    nchypergeom_wallenius, hypergeom, nhypergeom
+
+    Notes
+    -----
+    Let mathematical symbols :math:`N`, :math:`n`, and :math:`M` correspond
+    with parameters `N`, `n`, and `M` (respectively) as defined above.
+
+    The probability mass function is defined as
+
+    .. math::
+
+        p(x; M, n, N, \omega) =
+        \frac{\binom{n}{x}\binom{M - n}{N-x}\omega^x}{P_0},
+
+    for
+    :math:`x \in [x_l, x_u]`,
+    :math:`M \in {\mathbb N}`,
+    :math:`n \in [0, M]`,
+    :math:`N \in [0, M]`,
+    :math:`\omega > 0`,
+    where
+    :math:`x_l = \max(0, N - (M - n))`,
+    :math:`x_u = \min(N, n)`,
+
+    .. math::
+
+        P_0 = \sum_{y=x_l}^{x_u} \binom{n}{y}\binom{M - n}{N-y}\omega^y,
+
+    and the binomial coefficients are defined as
+
+    .. math:: \binom{n}{k} \equiv \frac{n!}{k! (n - k)!}.
+
+    `nchypergeom_fisher` uses the BiasedUrn package by Agner Fog with
+    permission for it to be distributed under SciPy's license.
+
+    The symbols used to denote the shape parameters (`N`, `n`, and `M`) are not
+    universally accepted; they are chosen for consistency with `hypergeom`.
+
+    Note that Fisher's noncentral hypergeometric distribution is distinct
+    from Wallenius' noncentral hypergeometric distribution, which models
+    drawing a pre-determined `N` objects from a bin one by one.
+    When the odds ratio is unity, however, both distributions reduce to the
+    ordinary hypergeometric distribution.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] Agner Fog, "Biased Urn Theory".
+           https://cran.r-project.org/web/packages/BiasedUrn/vignettes/UrnTheory.pdf
+
+    .. [2] "Fisher's noncentral hypergeometric distribution", Wikipedia,
+           https://en.wikipedia.org/wiki/Fisher's_noncentral_hypergeometric_distribution
+
+    %(example)s
+
+    """
+
+    rvs_name = "rvs_fisher"
+    dist = _PyFishersNCHypergeometric
+
+
+nchypergeom_fisher = nchypergeom_fisher_gen(
+    name='nchypergeom_fisher',
+    longname="A Fisher's noncentral hypergeometric")
+
+
+class nchypergeom_wallenius_gen(_nchypergeom_gen):
+    r"""A Wallenius' noncentral hypergeometric discrete random variable.
+
+    Wallenius' noncentral hypergeometric distribution models drawing objects of
+    two types from a bin. `M` is the total number of objects, `n` is the
+    number of Type I objects, and `odds` is the odds ratio: the odds of
+    selecting a Type I object rather than a Type II object when there is only
+    one object of each type.
+    The random variate represents the number of Type I objects drawn if we
+    draw a pre-determined `N` objects from a bin one by one.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    nchypergeom_fisher, hypergeom, nhypergeom
+
+    Notes
+    -----
+    Let mathematical symbols :math:`N`, :math:`n`, and :math:`M` correspond
+    with parameters `N`, `n`, and `M` (respectively) as defined above.
+
+    The probability mass function is defined as
+
+    .. math::
+
+        p(x; N, n, M) = \binom{n}{x} \binom{M - n}{N-x}
+        \int_0^1 \left(1-t^{\omega/D}\right)^x\left(1-t^{1/D}\right)^{N-x} dt
+
+    for
+    :math:`x \in [x_l, x_u]`,
+    :math:`M \in {\mathbb N}`,
+    :math:`n \in [0, M]`,
+    :math:`N \in [0, M]`,
+    :math:`\omega > 0`,
+    where
+    :math:`x_l = \max(0, N - (M - n))`,
+    :math:`x_u = \min(N, n)`,
+
+    .. math::
+
+        D = \omega(n - x) + ((M - n)-(N-x)),
+
+    and the binomial coefficients are defined as
+
+    .. math:: \binom{n}{k} \equiv \frac{n!}{k! (n - k)!}.
+
+    `nchypergeom_wallenius` uses the BiasedUrn package by Agner Fog with
+    permission for it to be distributed under SciPy's license.
+
+    The symbols used to denote the shape parameters (`N`, `n`, and `M`) are not
+    universally accepted; they are chosen for consistency with `hypergeom`.
+
+    Note that Wallenius' noncentral hypergeometric distribution is distinct
+    from Fisher's noncentral hypergeometric distribution, which models
+    take a handful of objects from the bin at once, finding out afterwards
+    that `N` objects were taken.
+    When the odds ratio is unity, however, both distributions reduce to the
+    ordinary hypergeometric distribution.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] Agner Fog, "Biased Urn Theory".
+           https://cran.r-project.org/web/packages/BiasedUrn/vignettes/UrnTheory.pdf
+
+    .. [2] "Wallenius' noncentral hypergeometric distribution", Wikipedia,
+           https://en.wikipedia.org/wiki/Wallenius'_noncentral_hypergeometric_distribution
+
+    %(example)s
+
+    """
+
+    rvs_name = "rvs_wallenius"
+    dist = _PyWalleniusNCHypergeometric
+
+
+nchypergeom_wallenius = nchypergeom_wallenius_gen(
+    name='nchypergeom_wallenius',
+    longname="A Wallenius' noncentral hypergeometric")
+
+
+# Collect names of classes and objects in this module.
+pairs = list(globals().copy().items())
+_distn_names, _distn_gen_names = get_distribution_names(pairs, rv_discrete)
+
+__all__ = _distn_names + _distn_gen_names
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_distn_infrastructure.py b/venv/lib/python3.12/site-packages/scipy/stats/_distn_infrastructure.py
new file mode 100644
index 0000000000000000000000000000000000000000..457b9ddb511d4dcba37e375a77c1a8a1dedd6554
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_distn_infrastructure.py
@@ -0,0 +1,4274 @@
+#
+# Author:  Travis Oliphant  2002-2011 with contributions from
+#          SciPy Developers 2004-2011
+#
+from scipy._lib._util import getfullargspec_no_self as _getfullargspec
+
+import sys
+import keyword
+import re
+import types
+import warnings
+from itertools import zip_longest
+
+from scipy._lib import doccer
+from scipy._lib._docscrape import FunctionDoc
+from ._distr_params import distcont, distdiscrete
+from scipy._lib._util import check_random_state
+import scipy._external.array_api_extra as xpx
+
+from scipy.special import comb, entr
+
+
+# for root finding for continuous distribution ppf, and maximum likelihood
+# estimation
+from scipy import optimize
+
+# for functions of continuous distributions (e.g. moments, entropy, cdf)
+from scipy import integrate
+
+# to approximate the pdf of a continuous distribution given its cdf
+from scipy.stats._finite_differences import _derivative
+
+# for scipy.stats.entropy. Attempts to import just that function or file
+# have cause import problems
+from scipy import stats
+
+from numpy import (arange, putmask, ones, shape, ndarray, zeros, floor,
+                   logical_and, log, sqrt, place, argmax, vectorize, asarray,
+                   nan, inf, isinf, empty)
+
+import numpy as np
+from ._constants import _XMAX, _LOGXMAX
+from ._censored_data import CensoredData
+from scipy.stats._warnings_errors import FitError
+
+# These are the docstring parts used for substitution in specific
+# distribution docstrings
+
+docheaders = {'methods': """\nMethods\n-------\n""",
+              'notes': """\nNotes\n-----\n""",
+              'examples': """\nExamples\n--------\n"""}
+
+_doc_rvs = """\
+rvs(%(shapes)s, loc=0, scale=1, size=1, random_state=None)
+    Random variates.
+"""
+_doc_pdf = """\
+pdf(x, %(shapes)s, loc=0, scale=1)
+    Probability density function.
+"""
+_doc_logpdf = """\
+logpdf(x, %(shapes)s, loc=0, scale=1)
+    Log of the probability density function.
+"""
+_doc_pmf = """\
+pmf(k, %(shapes)s, loc=0, scale=1)
+    Probability mass function.
+"""
+_doc_logpmf = """\
+logpmf(k, %(shapes)s, loc=0, scale=1)
+    Log of the probability mass function.
+"""
+_doc_cdf = """\
+cdf(x, %(shapes)s, loc=0, scale=1)
+    Cumulative distribution function.
+"""
+_doc_logcdf = """\
+logcdf(x, %(shapes)s, loc=0, scale=1)
+    Log of the cumulative distribution function.
+"""
+_doc_sf = """\
+sf(x, %(shapes)s, loc=0, scale=1)
+    Survival function  (also defined as ``1 - cdf``, but `sf` is sometimes more accurate).
+"""  # noqa: E501
+_doc_logsf = """\
+logsf(x, %(shapes)s, loc=0, scale=1)
+    Log of the survival function.
+"""
+_doc_ppf = """\
+ppf(q, %(shapes)s, loc=0, scale=1)
+    Percent point function (inverse of ``cdf`` --- percentiles).
+"""
+_doc_isf = """\
+isf(q, %(shapes)s, loc=0, scale=1)
+    Inverse survival function (inverse of ``sf``).
+"""
+_doc_moment = """\
+moment(order, %(shapes)s, loc=0, scale=1)
+    Non-central moment of the specified order.
+"""
+_doc_stats = """\
+stats(%(shapes)s, loc=0, scale=1, moments='mv')
+    Mean('m'), variance('v'), skew('s'), and/or kurtosis('k').
+"""
+_doc_entropy = """\
+entropy(%(shapes)s, loc=0, scale=1)
+    (Differential) entropy of the RV.
+"""
+_doc_fit = """\
+fit(data)
+    Parameter estimates for generic data.
+    See `scipy.stats.rv_continuous.fit <https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_continuous.fit.html#scipy.stats.rv_continuous.fit>`__ for detailed documentation of the
+    keyword arguments.
+"""  # noqa: E501
+_doc_expect = """\
+expect(func, args=(%(shapes_)s), loc=0, scale=1, lb=None, ub=None, conditional=False, **kwds)
+    Expected value of a function (of one argument) with respect to the distribution.
+"""  # noqa: E501
+_doc_expect_discrete = """\
+expect(func, args=(%(shapes_)s), loc=0, lb=None, ub=None, conditional=False)
+    Expected value of a function (of one argument) with respect to the distribution.
+"""
+_doc_median = """\
+median(%(shapes)s, loc=0, scale=1)
+    Median of the distribution.
+"""
+_doc_mean = """\
+mean(%(shapes)s, loc=0, scale=1)
+    Mean of the distribution.
+"""
+_doc_var = """\
+var(%(shapes)s, loc=0, scale=1)
+    Variance of the distribution.
+"""
+_doc_std = """\
+std(%(shapes)s, loc=0, scale=1)
+    Standard deviation of the distribution.
+"""
+_doc_interval = """\
+interval(confidence, %(shapes)s, loc=0, scale=1)
+    Confidence interval with equal areas around the median.
+"""
+_doc_allmethods = ''.join([docheaders['methods'], _doc_rvs, _doc_pdf,
+                           _doc_logpdf, _doc_cdf, _doc_logcdf, _doc_sf,
+                           _doc_logsf, _doc_ppf, _doc_isf, _doc_moment,
+                           _doc_stats, _doc_entropy, _doc_fit,
+                           _doc_expect, _doc_median,
+                           _doc_mean, _doc_var, _doc_std, _doc_interval])
+
+_doc_default_longsummary = """\
+As an instance of the `rv_continuous` class, `%(name)s` object inherits from it
+a collection of generic methods (see below for the full list),
+and completes them with details specific for this particular distribution.
+"""
+
+_doc_default_frozen_note = """
+Alternatively, the object may be called (as a function) to fix the shape,
+location, and scale parameters returning a "frozen" continuous RV object:
+
+rv = %(name)s(%(shapes)s, loc=0, scale=1)
+    - Frozen RV object with the same methods but holding the given shape,
+      location, and scale fixed.
+"""
+_doc_default_example = """\
+Examples
+--------
+>>> import numpy as np
+>>> from scipy.stats import %(name)s
+>>> import matplotlib.pyplot as plt
+>>> fig, ax = plt.subplots(1, 1)
+
+Get the support:
+
+%(set_vals_stmt)s
+>>> lb, ub = %(name)s.support(%(shapes)s)
+
+Calculate the first four moments:
+
+>>> mean, var, skew, kurt = %(name)s.stats(%(shapes)s, moments='mvsk')
+
+Display the probability density function (``pdf``):
+
+>>> x = np.linspace(%(name)s.ppf(0.01, %(shapes)s),
+...                 %(name)s.ppf(0.99, %(shapes)s), 100)
+>>> ax.plot(x, %(name)s.pdf(x, %(shapes)s),
+...        'r-', lw=5, alpha=0.6, label='%(name)s pdf')
+
+Alternatively, the distribution object can be called (as a function)
+to fix the shape, location and scale parameters. This returns a "frozen"
+RV object holding the given parameters fixed.
+
+Freeze the distribution and display the frozen ``pdf``:
+
+>>> rv = %(name)s(%(shapes)s)
+>>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
+
+Check accuracy of ``cdf`` and ``ppf``:
+
+>>> vals = %(name)s.ppf([0.001, 0.5, 0.999], %(shapes)s)
+>>> np.allclose([0.001, 0.5, 0.999], %(name)s.cdf(vals, %(shapes)s))
+True
+
+Generate random numbers:
+
+>>> r = %(name)s.rvs(%(shapes)s, size=1000)
+
+And compare the histogram:
+
+>>> ax.hist(r, density=True, bins='auto', histtype='stepfilled', alpha=0.2)
+>>> ax.set_xlim([x[0], x[-1]])
+>>> ax.legend(loc='best', frameon=False)
+>>> plt.show()
+
+"""
+
+_doc_default_locscale = """\
+The probability density above is defined in the "standardized" form. To shift
+and/or scale the distribution use the ``loc`` and ``scale`` parameters.
+Specifically, ``%(name)s.pdf(x, %(shapes)s, loc, scale)`` is identically
+equivalent to ``%(name)s.pdf(y, %(shapes)s) / scale`` with
+``y = (x - loc) / scale``. Note that shifting the location of a distribution
+does not make it a "noncentral" distribution; noncentral generalizations of
+some distributions are available in separate classes.
+"""
+
+_doc_default = ''.join([_doc_default_longsummary,
+                        _doc_allmethods,
+                        '\n',
+                        _doc_default_example])
+
+_doc_default_before_notes = ''.join([_doc_default_longsummary,
+                                     _doc_allmethods])
+
+docdict = {
+    'rvs': _doc_rvs,
+    'pdf': _doc_pdf,
+    'logpdf': _doc_logpdf,
+    'cdf': _doc_cdf,
+    'logcdf': _doc_logcdf,
+    'sf': _doc_sf,
+    'logsf': _doc_logsf,
+    'ppf': _doc_ppf,
+    'isf': _doc_isf,
+    'stats': _doc_stats,
+    'entropy': _doc_entropy,
+    'fit': _doc_fit,
+    'moment': _doc_moment,
+    'expect': _doc_expect,
+    'interval': _doc_interval,
+    'mean': _doc_mean,
+    'std': _doc_std,
+    'var': _doc_var,
+    'median': _doc_median,
+    'allmethods': _doc_allmethods,
+    'longsummary': _doc_default_longsummary,
+    'frozennote': _doc_default_frozen_note,
+    'example': _doc_default_example,
+    'default': _doc_default,
+    'before_notes': _doc_default_before_notes,
+    'after_notes': _doc_default_locscale
+}
+
+# Reuse common content between continuous and discrete docs, change some
+# minor bits.
+docdict_discrete = docdict.copy()
+
+docdict_discrete['pmf'] = _doc_pmf
+docdict_discrete['logpmf'] = _doc_logpmf
+docdict_discrete['expect'] = _doc_expect_discrete
+_doc_disc_methods = ['rvs', 'pmf', 'logpmf', 'cdf', 'logcdf', 'sf', 'logsf',
+                     'ppf', 'isf', 'stats', 'entropy', 'expect', 'median',
+                     'mean', 'var', 'std', 'interval']
+for obj in _doc_disc_methods:
+    docdict_discrete[obj] = docdict_discrete[obj].replace(', scale=1', '')
+
+_doc_disc_methods_err_varname = ['cdf', 'logcdf', 'sf', 'logsf']
+for obj in _doc_disc_methods_err_varname:
+    docdict_discrete[obj] = docdict_discrete[obj].replace('(x, ', '(k, ')
+
+docdict_discrete.pop('pdf')
+docdict_discrete.pop('logpdf')
+
+_doc_allmethods = ''.join([docdict_discrete[obj] for obj in _doc_disc_methods])
+docdict_discrete['allmethods'] = docheaders['methods'] + _doc_allmethods
+
+docdict_discrete['longsummary'] = _doc_default_longsummary.replace(
+    'rv_continuous', 'rv_discrete')
+
+_doc_default_frozen_note = """
+Alternatively, the object may be called (as a function) to fix the shape and
+location parameters returning a "frozen" discrete RV object:
+
+rv = %(name)s(%(shapes)s, loc=0)
+    - Frozen RV object with the same methods but holding the given shape and
+      location fixed.
+"""
+docdict_discrete['frozennote'] = _doc_default_frozen_note
+
+_doc_default_discrete_example = """\
+Examples
+--------
+>>> import numpy as np
+>>> from scipy.stats import %(name)s
+>>> import matplotlib.pyplot as plt
+>>> fig, ax = plt.subplots(1, 1)
+
+Get the support:
+
+%(set_vals_stmt)s
+>>> lb, ub = %(name)s.support(%(shapes)s)
+
+Calculate the first four moments:
+
+>>> mean, var, skew, kurt = %(name)s.stats(%(shapes)s, moments='mvsk')
+
+Display the probability mass function (``pmf``):
+
+>>> x = np.arange(%(name)s.ppf(0.01, %(shapes)s),
+...               %(name)s.ppf(0.99, %(shapes)s))
+>>> ax.plot(x, %(name)s.pmf(x, %(shapes)s), 'bo', ms=8, label='%(name)s pmf')
+>>> ax.vlines(x, 0, %(name)s.pmf(x, %(shapes)s), colors='b', lw=5, alpha=0.5)
+
+Alternatively, the distribution object can be called (as a function)
+to fix the shape and location. This returns a "frozen" RV object holding
+the given parameters fixed.
+
+Freeze the distribution and display the frozen ``pmf``:
+
+>>> rv = %(name)s(%(shapes)s)
+>>> ax.vlines(x, 0, rv.pmf(x), colors='k', linestyles='-', lw=1,
+...         label='frozen pmf')
+>>> ax.legend(loc='best', frameon=False)
+>>> plt.show()
+
+Check accuracy of ``cdf`` and ``ppf``:
+
+>>> prob = %(name)s.cdf(x, %(shapes)s)
+>>> np.allclose(x, %(name)s.ppf(prob, %(shapes)s))
+True
+
+Generate random numbers:
+
+>>> r = %(name)s.rvs(%(shapes)s, size=1000)
+"""
+
+
+_doc_default_discrete_locscale = """\
+The probability mass function above is defined in the "standardized" form.
+To shift distribution use the ``loc`` parameter.
+Specifically, ``%(name)s.pmf(k, %(shapes)s, loc)`` is identically
+equivalent to ``%(name)s.pmf(k - loc, %(shapes)s)``.
+"""
+
+docdict_discrete['example'] = _doc_default_discrete_example
+docdict_discrete['after_notes'] = _doc_default_discrete_locscale
+
+_doc_default_before_notes = ''.join([docdict_discrete['longsummary'],
+                                     docdict_discrete['allmethods']])
+docdict_discrete['before_notes'] = _doc_default_before_notes
+
+_doc_default_disc = ''.join([docdict_discrete['longsummary'],
+                             docdict_discrete['allmethods'],
+                             docdict_discrete['frozennote'],
+                             docdict_discrete['example']])
+docdict_discrete['default'] = _doc_default_disc
+
+# clean up all the separate docstring elements, we do not need them anymore
+for obj in [s for s in dir() if s.startswith('_doc_')]:
+    exec('del ' + obj)
+del obj
+
+
+def _moment(data, n, mu=None):
+    if mu is None:
+        mu = data.mean()
+    return ((data - mu)**n).mean()
+
+
+def _moment_from_stats(n, mu, mu2, g1, g2, moment_func, args):
+    if (n == 0):
+        return 1.0
+    elif (n == 1):
+        if mu is None:
+            val = moment_func(1, *args)
+        else:
+            val = mu
+    elif (n == 2):
+        if mu2 is None or mu is None:
+            val = moment_func(2, *args)
+        else:
+            val = mu2 + mu*mu
+    elif (n == 3):
+        if g1 is None or mu2 is None or mu is None:
+            val = moment_func(3, *args)
+        else:
+            mu3 = g1 * np.power(mu2, 1.5)  # 3rd central moment
+            val = mu3+3*mu*mu2+mu*mu*mu  # 3rd non-central moment
+    elif (n == 4):
+        if g1 is None or g2 is None or mu2 is None or mu is None:
+            val = moment_func(4, *args)
+        else:
+            mu4 = (g2+3.0)*(mu2**2.0)  # 4th central moment
+            mu3 = g1*np.power(mu2, 1.5)  # 3rd central moment
+            val = mu4+4*mu*mu3+6*mu*mu*mu2+mu*mu*mu*mu
+    else:
+        val = moment_func(n, *args)
+
+    return val
+
+
+def _skew(data):
+    """
+    skew is third central moment / variance**(1.5)
+    """
+    data = np.ravel(data)
+    mu = data.mean()
+    m2 = ((data - mu)**2).mean()
+    m3 = ((data - mu)**3).mean()
+    return m3 / np.power(m2, 1.5)
+
+
+def _kurtosis(data):
+    """Fisher's excess kurtosis is fourth central moment / variance**2 - 3."""
+    data = np.ravel(data)
+    mu = data.mean()
+    m2 = ((data - mu)**2).mean()
+    m4 = ((data - mu)**4).mean()
+    return m4 / m2**2 - 3
+
+def _vectorize_rvs_over_shapes(_rvs1):
+    """Decorator that vectorizes _rvs method to work on ndarray shapes"""
+    # _rvs1 must be a _function_ that accepts _scalar_ args as positional
+    # arguments, `size` and `random_state` as keyword arguments.
+    # _rvs1 must return a random variate array with shape `size`. If `size` is
+    # None, _rvs1 must return a scalar.
+    # When applied to _rvs1, this decorator broadcasts ndarray args
+    # and loops over them, calling _rvs1 for each set of scalar args.
+    # For usage example, see _nchypergeom_gen
+    def _rvs(*args, size, random_state):
+        _rvs1_size, _rvs1_indices = _check_shape(args[0].shape, size)
+
+        size = np.array(size)
+        _rvs1_size = np.array(_rvs1_size)
+        _rvs1_indices = np.array(_rvs1_indices)
+
+        if np.all(_rvs1_indices):  # all args are scalars
+            return _rvs1(*args, size, random_state)
+
+        out = np.empty(size)
+
+        # out.shape can mix dimensions associated with arg_shape and _rvs1_size
+        # Sort them to arg_shape + _rvs1_size for easy indexing of dimensions
+        # corresponding with the different sets of scalar args
+        j0 = np.arange(out.ndim)
+        j1 = np.hstack((j0[~_rvs1_indices], j0[_rvs1_indices]))
+        out = np.moveaxis(out, j1, j0)
+
+        for i in np.ndindex(*size[~_rvs1_indices]):
+            # arg can be squeezed because singleton dimensions will be
+            # associated with _rvs1_size, not arg_shape per _check_shape
+            out[i] = _rvs1(*[np.squeeze(arg)[i] for arg in args],
+                           _rvs1_size, random_state)
+
+        return np.moveaxis(out, j0, j1)  # move axes back before returning
+    return _rvs
+
+
+def _fit_determine_optimizer(optimizer):
+    if not callable(optimizer) and isinstance(optimizer, str):
+        if not optimizer.startswith('fmin_'):
+            optimizer = "fmin_"+optimizer
+        if optimizer == 'fmin_':
+            optimizer = 'fmin'
+        try:
+            optimizer = getattr(optimize, optimizer)
+        except AttributeError as e:
+            raise ValueError(f"{optimizer} is not a valid optimizer") from e
+    return optimizer
+
+def _isintegral(x):
+    return x == np.round(x)
+
+def _sum_finite(x):
+    """
+    For a 1D array x, return a tuple containing the sum of the
+    finite values of x and the number of nonfinite values.
+
+    This is a utility function used when evaluating the negative
+    loglikelihood for a distribution and an array of samples.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats._distn_infrastructure import _sum_finite
+    >>> tot, nbad = _sum_finite(np.array([-2, -np.inf, 5, 1]))
+    >>> tot
+    4.0
+    >>> nbad
+    1
+    """
+    finite_x = np.isfinite(x)
+    bad_count = finite_x.size - np.count_nonzero(finite_x)
+    return np.sum(x[finite_x]), bad_count
+
+
+# Frozen RV class
+class rv_frozen:
+
+    # generic type compatibility with scipy-stubs
+    __class_getitem__: classmethod = classmethod(types.GenericAlias)
+
+    def __init__(self, dist, *args, **kwds):
+        self.args = args
+        self.kwds = kwds
+
+        # create a new instance
+        self.dist = dist.__class__(**dist._updated_ctor_param())
+
+        shapes, _, _ = self.dist._parse_args(*args, **kwds)
+        self.a, self.b = self.dist._get_support(*shapes)
+
+    @property
+    def random_state(self):
+        return self.dist._random_state
+
+    @random_state.setter
+    def random_state(self, seed):
+        self.dist._random_state = check_random_state(seed)
+
+    def cdf(self, x):
+        return self.dist.cdf(x, *self.args, **self.kwds)
+
+    def logcdf(self, x):
+        return self.dist.logcdf(x, *self.args, **self.kwds)
+
+    def ppf(self, q):
+        return self.dist.ppf(q, *self.args, **self.kwds)
+
+    def isf(self, q):
+        return self.dist.isf(q, *self.args, **self.kwds)
+
+    def rvs(self, size=None, random_state=None):
+        kwds = self.kwds.copy()
+        kwds.update({'size': size, 'random_state': random_state})
+        return self.dist.rvs(*self.args, **kwds)
+
+    def sf(self, x):
+        return self.dist.sf(x, *self.args, **self.kwds)
+
+    def logsf(self, x):
+        return self.dist.logsf(x, *self.args, **self.kwds)
+
+    def stats(self, moments='mv'):
+        kwds = self.kwds.copy()
+        kwds.update({'moments': moments})
+        return self.dist.stats(*self.args, **kwds)
+
+    def median(self):
+        return self.dist.median(*self.args, **self.kwds)
+
+    def mean(self):
+        return self.dist.mean(*self.args, **self.kwds)
+
+    def var(self):
+        return self.dist.var(*self.args, **self.kwds)
+
+    def std(self):
+        return self.dist.std(*self.args, **self.kwds)
+
+    def moment(self, order=None):
+        return self.dist.moment(order, *self.args, **self.kwds)
+
+    def entropy(self):
+        return self.dist.entropy(*self.args, **self.kwds)
+
+    def interval(self, confidence=None):
+        return self.dist.interval(confidence, *self.args, **self.kwds)
+
+    def expect(self, func=None, lb=None, ub=None, conditional=False, **kwds):
+        # expect method only accepts shape parameters as positional args
+        # hence convert self.args, self.kwds, also loc/scale
+        # See the .expect method docstrings for the meaning of
+        # other parameters.
+        a, loc, scale = self.dist._parse_args(*self.args, **self.kwds)
+        if isinstance(self.dist, rv_discrete):
+            return self.dist.expect(func, a, loc, lb, ub, conditional, **kwds)
+        else:
+            return self.dist.expect(func, a, loc, scale, lb, ub,
+                                    conditional, **kwds)
+
+    def support(self):
+        return self.dist.support(*self.args, **self.kwds)
+
+
+class rv_discrete_frozen(rv_frozen):
+
+    def pmf(self, k):
+        return self.dist.pmf(k, *self.args, **self.kwds)
+
+    def logpmf(self, k):  # No error
+        return self.dist.logpmf(k, *self.args, **self.kwds)
+
+
+class rv_continuous_frozen(rv_frozen):
+
+    def pdf(self, x):
+        return self.dist.pdf(x, *self.args, **self.kwds)
+
+    def logpdf(self, x):
+        return self.dist.logpdf(x, *self.args, **self.kwds)
+
+
+def argsreduce(cond, *args):
+    """Clean arguments to:
+
+    1. Ensure all arguments are iterable (arrays of dimension at least one
+    2. If cond != True and size > 1, ravel(args[i]) where ravel(condition) is
+       True, in 1D.
+
+    Return list of processed arguments.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats._distn_infrastructure import argsreduce
+    >>> rng = np.random.default_rng()
+    >>> A = rng.random((4, 5))
+    >>> B = 2
+    >>> C = rng.random((1, 5))
+    >>> cond = np.ones(A.shape)
+    >>> [A1, B1, C1] = argsreduce(cond, A, B, C)
+    >>> A1.shape
+    (4, 5)
+    >>> B1.shape
+    (1,)
+    >>> C1.shape
+    (1, 5)
+    >>> cond[2,:] = 0
+    >>> [A1, B1, C1] = argsreduce(cond, A, B, C)
+    >>> A1.shape
+    (15,)
+    >>> B1.shape
+    (1,)
+    >>> C1.shape
+    (15,)
+
+    """
+    # some distributions assume arguments are iterable.
+    newargs = np.atleast_1d(*args)
+
+    # np.atleast_1d returns an array if only one argument, or a list of arrays
+    # if more than one argument.
+    if not isinstance(newargs, (list | tuple)):
+        newargs = (newargs,)
+
+    if np.all(cond):
+        # broadcast arrays with cond
+        *newargs, cond = np.broadcast_arrays(*newargs, cond)
+        return [arg.ravel() for arg in newargs]
+
+    s = cond.shape
+    # np.extract returns flattened arrays, which are not broadcastable together
+    # unless they are either the same size or size == 1.
+    return [(arg if np.size(arg) == 1
+            else np.extract(cond, np.broadcast_to(arg, s)))
+            for arg in newargs]
+
+
+parse_arg_template = """
+def _parse_args(self, %(shape_arg_str)s %(locscale_in)s):
+    return (%(shape_arg_str)s), %(locscale_out)s
+
+def _parse_args_rvs(self, %(shape_arg_str)s %(locscale_in)s, size=None):
+    return self._argcheck_rvs(%(shape_arg_str)s %(locscale_out)s, size=size)
+
+def _parse_args_stats(self, %(shape_arg_str)s %(locscale_in)s, moments='mv'):
+    return (%(shape_arg_str)s), %(locscale_out)s, moments
+"""
+
+
+class rv_generic:
+    """Class which encapsulates common functionality between rv_discrete
+    and rv_continuous.
+
+    """
+
+    def __init__(self, seed=None):
+        super().__init__()
+
+        # figure out if _stats signature has 'moments' keyword
+        sig = _getfullargspec(self._stats)
+        self._stats_has_moments = ((sig.varkw is not None) or
+                                   ('moments' in sig.args) or
+                                   ('moments' in sig.kwonlyargs))
+        self._random_state = check_random_state(seed)
+
+    @property
+    def random_state(self):
+        """Get or set the generator object for generating random variates.
+
+        If `random_state` is None (or `np.random`), the
+        `numpy.random.RandomState` singleton is used.
+        If `random_state` is an int, a new ``RandomState`` instance is used,
+        seeded with `random_state`.
+        If `random_state` is already a ``Generator`` or ``RandomState``
+        instance, that instance is used.
+
+        """
+        return self._random_state
+
+    @random_state.setter
+    def random_state(self, seed):
+        self._random_state = check_random_state(seed)
+
+    def __setstate__(self, state):
+        try:
+            self.__dict__.update(state)
+            # attaches the dynamically created methods on each instance.
+            # if a subclass overrides rv_generic.__setstate__, or implements
+            # it's own _attach_methods, then it must make sure that
+            # _attach_argparser_methods is called.
+            self._attach_methods()
+        except ValueError:
+            # reconstitute an old pickle scipy<1.6, that contains
+            # (_ctor_param, random_state) as state
+            self._ctor_param = state[0]
+            self._random_state = state[1]
+            self.__init__()
+
+    def _attach_methods(self):
+        """Attaches dynamically created methods to the rv_* instance.
+
+        This method must be overridden by subclasses, and must itself call
+         _attach_argparser_methods. This method is called in __init__ in
+         subclasses, and in __setstate__
+        """
+        raise NotImplementedError
+
+    def _attach_argparser_methods(self):
+        """
+        Generates the argument-parsing functions dynamically and attaches
+        them to the instance.
+
+        Should be called from `_attach_methods`, typically in __init__ and
+        during unpickling (__setstate__)
+        """
+        ns = {}
+        exec(self._parse_arg_template, ns)
+        # NB: attach to the instance, not class
+        for name in ['_parse_args', '_parse_args_stats', '_parse_args_rvs']:
+            setattr(self, name, types.MethodType(ns[name], self))
+
+    def _construct_argparser(
+            self, meths_to_inspect, locscale_in, locscale_out):
+        """Construct the parser string for the shape arguments.
+
+        This method should be called in __init__ of a class for each
+        distribution. It creates the `_parse_arg_template` attribute that is
+        then used by `_attach_argparser_methods` to dynamically create and
+        attach the `_parse_args`, `_parse_args_stats`, `_parse_args_rvs`
+        methods to the instance.
+
+        If self.shapes is a non-empty string, interprets it as a
+        comma-separated list of shape parameters.
+
+        Otherwise inspects the call signatures of `meths_to_inspect`
+        and constructs the argument-parsing functions from these.
+        In this case also sets `shapes` and `numargs`.
+        """
+
+        if self.shapes:
+            # sanitize the user-supplied shapes
+            if not isinstance(self.shapes, str):
+                raise TypeError('shapes must be a string.')
+
+            shapes = self.shapes.replace(',', ' ').split()
+
+            for field in shapes:
+                if keyword.iskeyword(field):
+                    raise SyntaxError('keywords cannot be used as shapes.')
+                if not re.match('^[_a-zA-Z][_a-zA-Z0-9]*$', field):
+                    raise SyntaxError(
+                        'shapes must be valid python identifiers')
+        else:
+            # find out the call signatures (_pdf, _cdf etc), deduce shape
+            # arguments. Generic methods only have 'self, x', any further args
+            # are shapes.
+            shapes_list = []
+            for meth in meths_to_inspect:
+                shapes_args = _getfullargspec(meth)  # NB does not contain self
+                args = shapes_args.args[1:]       # peel off 'x', too
+
+                if args:
+                    shapes_list.append(args)
+
+                    # *args or **kwargs are not allowed w/automatic shapes
+                    if shapes_args.varargs is not None:
+                        raise TypeError(
+                            '*args are not allowed w/out explicit shapes')
+                    if shapes_args.varkw is not None:
+                        raise TypeError(
+                            '**kwds are not allowed w/out explicit shapes')
+                    if shapes_args.kwonlyargs:
+                        raise TypeError(
+                            'kwonly args are not allowed w/out explicit shapes')
+                    if shapes_args.defaults is not None:
+                        raise TypeError('defaults are not allowed for shapes')
+
+            if shapes_list:
+                shapes = shapes_list[0]
+
+                # make sure the signatures are consistent
+                for item in shapes_list:
+                    if item != shapes:
+                        raise TypeError('Shape arguments are inconsistent.')
+            else:
+                shapes = []
+
+        # have the arguments, construct the method from template
+        shapes_str = ', '.join(shapes) + ', ' if shapes else ''  # NB: not None
+        dct = dict(shape_arg_str=shapes_str,
+                   locscale_in=locscale_in,
+                   locscale_out=locscale_out,
+                   )
+
+        # this string is used by _attach_argparser_methods
+        self._parse_arg_template = parse_arg_template % dct
+
+        self.shapes = ', '.join(shapes) if shapes else None
+        if not hasattr(self, 'numargs'):
+            # allows more general subclassing with *args
+            self.numargs = len(shapes)
+
+    def _construct_doc(self, docdict, shapes_vals=None):
+        """Construct the instance docstring with string substitutions."""
+        if sys.flags.optimize > 1:
+            # if run with -OO, docstrings are stripped
+            # see https://docs.python.org/3/using/cmdline.html#cmdoption-OO
+            return
+        tempdict = docdict.copy()
+        tempdict['name'] = self.name or 'distname'
+        tempdict['shapes'] = self.shapes or ''
+
+        if shapes_vals is None:
+            shapes_vals = ()
+        try:
+            vals = ', '.join(f'{val:.3g}' for val in shapes_vals)
+        except TypeError:
+            vals = ', '.join(f'{val}' for val in shapes_vals)
+        tempdict['vals'] = vals
+
+        tempdict['shapes_'] = self.shapes or ''
+        if self.shapes and self.numargs == 1:
+            tempdict['shapes_'] += ','
+
+        if self.shapes:
+            tempdict['set_vals_stmt'] = f'>>> {self.shapes} = {vals}'
+        else:
+            tempdict['set_vals_stmt'] = ''
+
+        if self.shapes is None:
+            # remove shapes from call parameters if there are none
+            for item in ['default', 'before_notes']:
+                tempdict[item] = tempdict[item].replace(
+                    "\n%(shapes)s : array_like\n    shape parameters", "")
+        for i in range(2):
+            if self.shapes is None:
+                # necessary because we use %(shapes)s in two forms (w w/o ", ")
+                self.__doc__ = self.__doc__.replace("%(shapes)s, ", "")
+            try:
+                self.__doc__ = doccer.docformat(self.__doc__, tempdict)
+            except TypeError as e:
+                raise Exception("Unable to construct docstring for "
+                                f"distribution \"{self.name}\": {repr(e)}") from e
+
+        # correct for empty shapes
+        self.__doc__ = self.__doc__.replace('(, ', '(').replace(', )', ')')
+
+    def _construct_default_doc(self, longname=None,
+                               docdict=None, discrete='continuous'):
+        """Construct instance docstring from the default template."""
+        if sys.flags.optimize > 1:
+            # if run with -OO, docstrings are stripped
+            # see https://docs.python.org/3/using/cmdline.html#cmdoption-OO
+            return
+        if longname is None:
+            longname = 'A'
+        self.__doc__ = ''.join([f'{longname} {discrete} random variable.',
+                                '\n\n%(before_notes)s\n', docheaders['notes'],
+                                '\n%(example)s'])
+        self._construct_doc(docdict)
+
+    def freeze(self, *args, **kwds):
+        """Freeze the distribution for the given arguments.
+
+        Parameters
+        ----------
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution.  Should include all
+            the non-optional arguments, may include ``loc`` and ``scale``.
+
+        Returns
+        -------
+        rv_frozen : rv_frozen instance
+            The frozen distribution.
+
+        """
+        if isinstance(self, rv_continuous):
+            return rv_continuous_frozen(self, *args, **kwds)
+        else:
+            return rv_discrete_frozen(self, *args, **kwds)
+
+    def __call__(self, *args, **kwds):
+        return self.freeze(*args, **kwds)
+    __call__.__doc__ = freeze.__doc__
+
+    # The actual calculation functions (no basic checking need be done)
+    # If these are defined, the others won't be looked at.
+    # Otherwise, the other set can be defined.
+    def _stats(self, *args, **kwds):
+        return None, None, None, None
+
+    # Noncentral moments (also known as the moment about the origin).
+    # Expressed in LaTeX, munp would be $\mu'_{n}$, i.e. "mu-sub-n-prime".
+    # The primed mu is a widely used notation for the noncentral moment.
+    def _munp(self, n, *args):
+        # Silence floating point warnings from integration.
+        with np.errstate(all='ignore'):
+            vals = self.generic_moment(n, *args)
+        return vals
+
+    def _argcheck_rvs(self, *args, **kwargs):
+        # Handle broadcasting and size validation of the rvs method.
+        # Subclasses should not have to override this method.
+        # The rule is that if `size` is not None, then `size` gives the
+        # shape of the result (integer values of `size` are treated as
+        # tuples with length 1; i.e. `size=3` is the same as `size=(3,)`.)
+        #
+        # `args` is expected to contain the shape parameters (if any), the
+        # location and the scale in a flat tuple (e.g. if there are two
+        # shape parameters `a` and `b`, `args` will be `(a, b, loc, scale)`).
+        # The only keyword argument expected is 'size'.
+        size = kwargs.get('size', None)
+        all_bcast = np.broadcast_arrays(*args)
+
+        def squeeze_left(a):
+            while a.ndim > 0 and a.shape[0] == 1:
+                a = a[0]
+            return a
+
+        # Eliminate trivial leading dimensions.  In the convention
+        # used by numpy's random variate generators, trivial leading
+        # dimensions are effectively ignored.  In other words, when `size`
+        # is given, trivial leading dimensions of the broadcast parameters
+        # in excess of the number of dimensions  in size are ignored, e.g.
+        #   >>> np.random.normal([[1, 3, 5]], [[[[0.01]]]], size=3)
+        #   array([ 1.00104267,  3.00422496,  4.99799278])
+        # If `size` is not given, the exact broadcast shape is preserved:
+        #   >>> np.random.normal([[1, 3, 5]], [[[[0.01]]]])
+        #   array([[[[ 1.00862899,  3.00061431,  4.99867122]]]])
+        #
+        all_bcast = [squeeze_left(a) for a in all_bcast]
+        bcast_shape = all_bcast[0].shape
+        bcast_ndim = all_bcast[0].ndim
+
+        if size is None:
+            size_ = bcast_shape
+        else:
+            size_ = tuple(np.atleast_1d(size))
+
+        # Check compatibility of size_ with the broadcast shape of all
+        # the parameters.  This check is intended to be consistent with
+        # how the numpy random variate generators (e.g. np.random.normal,
+        # np.random.beta) handle their arguments.   The rule is that, if size
+        # is given, it determines the shape of the output.  Broadcasting
+        # can't change the output size.
+
+        # This is the standard broadcasting convention of extending the
+        # shape with fewer dimensions with enough dimensions of length 1
+        # so that the two shapes have the same number of dimensions.
+        ndiff = bcast_ndim - len(size_)
+        if ndiff < 0:
+            bcast_shape = (1,)*(-ndiff) + bcast_shape
+        elif ndiff > 0:
+            size_ = (1,)*ndiff + size_
+
+        # This compatibility test is not standard.  In "regular" broadcasting,
+        # two shapes are compatible if for each dimension, the lengths are the
+        # same or one of the lengths is 1.  Here, the length of a dimension in
+        # size_ must not be less than the corresponding length in bcast_shape.
+        ok = all([bcdim == 1 or bcdim == szdim
+                  for (bcdim, szdim) in zip(bcast_shape, size_)])
+        if not ok:
+            raise ValueError("size does not match the broadcast shape of "
+                             f"the parameters. {size}, {size_}, {bcast_shape}")
+
+        param_bcast = all_bcast[:-2]
+        loc_bcast = all_bcast[-2]
+        scale_bcast = all_bcast[-1]
+
+        return param_bcast, loc_bcast, scale_bcast, size_
+
+    # These are the methods you must define (standard form functions)
+    # NB: generic _pdf, _logpdf, _cdf are different for
+    # rv_continuous and rv_discrete hence are defined in there
+    def _argcheck(self, *args):
+        """Default check for correct values on args and keywords.
+
+        Returns condition array of 1's where arguments are correct and
+         0's where they are not.
+
+        """
+        cond = 1
+        for arg in args:
+            cond = logical_and(cond, (asarray(arg) > 0))
+        return cond
+
+    def _get_support(self, *args, **kwargs):
+        """Return the support of the (unscaled, unshifted) distribution.
+
+        *Must* be overridden by distributions which have support dependent
+        upon the shape parameters of the distribution.  Any such override
+        *must not* set or change any of the class members, as these members
+        are shared amongst all instances of the distribution.
+
+        Parameters
+        ----------
+        arg1, arg2, ... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information).
+
+        Returns
+        -------
+        a, b : numeric (float, or int or +/-np.inf)
+            end-points of the distribution's support for the specified
+            shape parameters.
+        """
+        return self.a, self.b
+
+    def _support_mask(self, x, *args):
+        a, b = self._get_support(*args)
+        with np.errstate(invalid='ignore'):
+            return (a <= x) & (x <= b)
+
+    def _open_support_mask(self, x, *args):
+        a, b = self._get_support(*args)
+        with np.errstate(invalid='ignore'):
+            return (a < x) & (x < b)
+
+    def _rvs(self, *args, size=None, random_state=None):
+        # This method must handle size being a tuple, and it must
+        # properly broadcast *args and size.  size might be
+        # an empty tuple, which means a scalar random variate is to be
+        # generated.
+
+        # Use basic inverse cdf algorithm for RV generation as default.
+        U = random_state.uniform(size=size)
+        Y = self._ppf(U, *args)
+        return Y
+
+    def _logcdf(self, x, *args):
+        with np.errstate(divide='ignore'):
+            return log(self._cdf(x, *args))
+
+    def _sf(self, x, *args):
+        return 1.0-self._cdf(x, *args)
+
+    def _logsf(self, x, *args):
+        with np.errstate(divide='ignore'):
+            return log(self._sf(x, *args))
+
+    def _ppf(self, q, *args):
+        return self._ppfvec(q, *args)
+
+    def _isf(self, q, *args):
+        return self._ppf(1.0-q, *args)  # use correct _ppf for subclasses
+
+    # These are actually called, and should not be overwritten if you
+    # want to keep error checking.
+    def rvs(self, *args, **kwds):
+        """Random variates of given type.
+
+        Parameters
+        ----------
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information).
+        loc : array_like, optional
+            Location parameter (default=0).
+        scale : array_like, optional
+            Scale parameter (default=1).
+        size : int or tuple of ints, optional
+            Defining number of random variates (default is 1).
+        random_state : {None, int, `numpy.random.Generator`,
+                        `numpy.random.RandomState`}, optional
+
+            If `random_state` is None (or `np.random`), the
+            `numpy.random.RandomState` singleton is used.
+            If `random_state` is an int, a new ``RandomState`` instance is
+            used, seeded with `random_state`.
+            If `random_state` is already a ``Generator`` or ``RandomState``
+            instance, that instance is used.
+
+        Returns
+        -------
+        rvs : ndarray or scalar
+            Random variates of given `size`.
+
+        """
+        discrete = kwds.pop('discrete', None)
+        rndm = kwds.pop('random_state', None)
+        args, loc, scale, size = self._parse_args_rvs(*args, **kwds)
+        cond = logical_and(self._argcheck(*args), (scale >= 0))
+        if not np.all(cond):
+            message = ("Domain error in arguments. The `scale` parameter must "
+                       "be positive for all distributions, and many "
+                       "distributions have restrictions on shape parameters. "
+                       f"Please see the `scipy.stats.{self.name}` "
+                       "documentation for details.")
+            raise ValueError(message)
+
+        if np.all(scale == 0):
+            return loc*ones(size, 'd')
+
+        # extra gymnastics needed for a custom random_state
+        if rndm is not None:
+            random_state_saved = self._random_state
+            random_state = check_random_state(rndm)
+        else:
+            random_state = self._random_state
+
+        vals = self._rvs(*args, size=size, random_state=random_state)
+
+        vals = vals * scale + loc
+
+        # do not forget to restore the _random_state
+        if rndm is not None:
+            self._random_state = random_state_saved
+
+        # Cast to int if discrete
+        if discrete and not isinstance(self, rv_sample):
+            if size == ():
+                vals = int(vals)
+            else:
+                vals = vals.astype(np.int64)
+
+        return vals
+
+    def stats(self, *args, **kwds):
+        """Some statistics of the given RV.
+
+        Parameters
+        ----------
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information)
+        loc : array_like, optional
+            location parameter (default=0)
+        scale : array_like, optional
+            scale parameter (default=1)
+        moments : str, optional
+            composed of letters ['mvsk'] defining which moments to compute:
+            'm' = mean,
+            'v' = variance,
+            's' = (Fisher's) skew,
+            'k' = (Fisher's) kurtosis.
+            (default is 'mv')
+
+        Returns
+        -------
+        stats : sequence
+            of requested moments.
+
+        """
+        args, loc, scale, moments = self._parse_args_stats(*args, **kwds)
+        # scale = 1 by construction for discrete RVs
+        loc, scale = map(asarray, (loc, scale))
+        args = tuple(map(asarray, args))
+        cond = self._argcheck(*args) & (scale > 0) & (loc == loc)
+        output = []
+        default = np.full(shape(cond), fill_value=self.badvalue)
+
+        # Use only entries that are valid in calculation
+        if np.any(cond):
+            goodargs = argsreduce(cond, *(args+(scale, loc)))
+            scale, loc, goodargs = goodargs[-2], goodargs[-1], goodargs[:-2]
+
+            if self._stats_has_moments:
+                mu, mu2, g1, g2 = self._stats(*goodargs,
+                                              **{'moments': moments})
+            else:
+                mu, mu2, g1, g2 = self._stats(*goodargs)
+
+            if 'm' in moments:
+                if mu is None:
+                    mu = self._munp(1, *goodargs)
+                out0 = default.copy()
+                place(out0, cond, mu * scale + loc)
+                output.append(out0)
+
+            if 'v' in moments:
+                if mu2 is None:
+                    mu2p = self._munp(2, *goodargs)
+                    if mu is None:
+                        mu = self._munp(1, *goodargs)
+                    # if mean is inf then var is also inf
+                    with np.errstate(invalid='ignore'):
+                        mu2 = np.where(~np.isinf(mu), mu2p - mu**2, np.inf)
+                out0 = default.copy()
+                place(out0, cond, mu2 * scale * scale)
+                output.append(out0)
+
+            if 's' in moments:
+                if g1 is None:
+                    mu3p = self._munp(3, *goodargs)
+                    if mu is None:
+                        mu = self._munp(1, *goodargs)
+                    if mu2 is None:
+                        mu2p = self._munp(2, *goodargs)
+                        with np.errstate(invalid='ignore'):
+                            mu2 = mu2p - mu * mu
+                    with np.errstate(invalid='ignore'):
+                        mu3 = (-mu*mu - 3*mu2)*mu + mu3p
+                        g1 = mu3 / np.power(mu2, 1.5)
+                out0 = default.copy()
+                place(out0, cond, g1)
+                output.append(out0)
+
+            if 'k' in moments:
+                if g2 is None:
+                    mu4p = self._munp(4, *goodargs)
+                    if mu is None:
+                        mu = self._munp(1, *goodargs)
+                    if mu2 is None:
+                        mu2p = self._munp(2, *goodargs)
+                        with np.errstate(invalid='ignore'):
+                            mu2 = mu2p - mu * mu
+                    if g1 is None:
+                        mu3 = None
+                    else:
+                        # (mu2**1.5) breaks down for nan and inf
+                        mu3 = g1 * np.power(mu2, 1.5)
+                    if mu3 is None:
+                        mu3p = self._munp(3, *goodargs)
+                        with np.errstate(invalid='ignore'):
+                            mu3 = (-mu * mu - 3 * mu2) * mu + mu3p
+                    with np.errstate(invalid='ignore'):
+                        mu4 = ((-mu**2 - 6*mu2) * mu - 4*mu3)*mu + mu4p
+                        g2 = mu4 / mu2**2.0 - 3.0
+                out0 = default.copy()
+                place(out0, cond, g2)
+                output.append(out0)
+        else:  # no valid args
+            output = [default.copy() for _ in moments]
+
+        output = [out[()] for out in output]
+        if len(output) == 1:
+            return output[0]
+        else:
+            return tuple(output)
+
+    def entropy(self, *args, **kwds):
+        """Differential entropy of the RV.
+
+        Parameters
+        ----------
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information).
+        loc : array_like, optional
+            Location parameter (default=0).
+        scale : array_like, optional
+            Scale parameter (default=1).
+
+        Notes
+        -----
+        Entropy is defined base `e`:
+
+        >>> import numpy as np
+        >>> from scipy.stats._distn_infrastructure import rv_discrete
+        >>> drv = rv_discrete(values=((0, 1), (0.5, 0.5)))
+        >>> np.allclose(drv.entropy(), np.log(2.0))
+        True
+
+        """
+        args, loc, scale = self._parse_args(*args, **kwds)
+        # NB: for discrete distributions scale=1 by construction in _parse_args
+        loc, scale = map(asarray, (loc, scale))
+        args = tuple(map(asarray, args))
+        cond0 = self._argcheck(*args) & (scale > 0) & (loc == loc)
+        output = zeros(shape(cond0), 'd')
+        place(output, (1-cond0), self.badvalue)
+        goodargs = argsreduce(cond0, scale, *args)
+        goodscale = goodargs[0]
+        goodargs = goodargs[1:]
+        place(output, cond0, self.vecentropy(*goodargs) + log(goodscale))
+        return output[()]
+
+    def moment(self, order, *args, **kwds):
+        """non-central moment of distribution of specified order.
+
+        Parameters
+        ----------
+        order : int, order >= 1
+            Order of moment.
+        arg1, arg2, arg3,... : float
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information).
+        loc : array_like, optional
+            location parameter (default=0)
+        scale : array_like, optional
+            scale parameter (default=1)
+
+        """
+        n = order
+        shapes, loc, scale = self._parse_args(*args, **kwds)
+        args = np.broadcast_arrays(*(*shapes, loc, scale))
+        *shapes, loc, scale = args
+
+        i0 = np.logical_and(self._argcheck(*shapes), scale > 0)
+        i1 = np.logical_and(i0, loc == 0)
+        i2 = np.logical_and(i0, loc != 0)
+
+        args = argsreduce(i0, *shapes, loc, scale)
+        *shapes, loc, scale = args
+
+        if (floor(n) != n):
+            raise ValueError("Moment must be an integer.")
+        if (n < 0):
+            raise ValueError("Moment must be positive.")
+        mu, mu2, g1, g2 = None, None, None, None
+        if (n > 0) and (n < 5):
+            if self._stats_has_moments:
+                mdict = {'moments': {1: 'm', 2: 'v', 3: 'vs', 4: 'mvsk'}[n]}
+            else:
+                mdict = {}
+            mu, mu2, g1, g2 = self._stats(*shapes, **mdict)
+        val = np.empty(loc.shape)  # val needs to be indexed by loc
+        val[...] = _moment_from_stats(n, mu, mu2, g1, g2, self._munp, shapes)
+
+        # Convert to transformed  X = L + S*Y
+        # E[X^n] = E[(L+S*Y)^n] = L^n sum(comb(n, k)*(S/L)^k E[Y^k], k=0...n)
+        result = zeros(i0.shape)
+        place(result, ~i0, self.badvalue)
+
+        if i1.any():
+            res1 = scale[loc == 0]**n * val[loc == 0]
+            place(result, i1, res1)
+
+        if i2.any():
+            mom = [mu, mu2, g1, g2]
+            arrs = [i for i in mom if i is not None]
+            idx = [i for i in range(4) if mom[i] is not None]
+            if any(idx):
+                arrs = argsreduce(loc != 0, *arrs)
+                j = 0
+                for i in idx:
+                    mom[i] = arrs[j]
+                    j += 1
+            mu, mu2, g1, g2 = mom
+            args = argsreduce(loc != 0, *shapes, loc, scale, val)
+            *shapes, loc, scale, val = args
+
+            res2 = zeros(loc.shape, dtype='d')
+            fac = scale / loc
+            for k in range(n):
+                valk = _moment_from_stats(k, mu, mu2, g1, g2, self._munp,
+                                          shapes)
+                res2 += comb(n, k, exact=True)*fac**k * valk
+            res2 += fac**n * val
+            res2 *= loc**n
+            place(result, i2, res2)
+
+        return result[()]
+
+    def median(self, *args, **kwds):
+        """Median of the distribution.
+
+        Parameters
+        ----------
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information)
+        loc : array_like, optional
+            Location parameter, Default is 0.
+        scale : array_like, optional
+            Scale parameter, Default is 1.
+
+        Returns
+        -------
+        median : float
+            The median of the distribution.
+
+        See Also
+        --------
+        rv_discrete.ppf
+            Inverse of the CDF
+
+        """
+        return self.ppf(0.5, *args, **kwds)
+
+    def mean(self, *args, **kwds):
+        """Mean of the distribution.
+
+        Parameters
+        ----------
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information)
+        loc : array_like, optional
+            location parameter (default=0)
+        scale : array_like, optional
+            scale parameter (default=1)
+
+        Returns
+        -------
+        mean : float
+            the mean of the distribution
+
+        """
+        kwds['moments'] = 'm'
+        res = self.stats(*args, **kwds)
+        if isinstance(res, ndarray) and res.ndim == 0:
+            return res[()]
+        return res
+
+    def var(self, *args, **kwds):
+        """Variance of the distribution.
+
+        Parameters
+        ----------
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information)
+        loc : array_like, optional
+            location parameter (default=0)
+        scale : array_like, optional
+            scale parameter (default=1)
+
+        Returns
+        -------
+        var : float
+            the variance of the distribution
+
+        """
+        kwds['moments'] = 'v'
+        res = self.stats(*args, **kwds)
+        if isinstance(res, ndarray) and res.ndim == 0:
+            return res[()]
+        return res
+
+    def std(self, *args, **kwds):
+        """Standard deviation of the distribution.
+
+        Parameters
+        ----------
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information)
+        loc : array_like, optional
+            location parameter (default=0)
+        scale : array_like, optional
+            scale parameter (default=1)
+
+        Returns
+        -------
+        std : float
+            standard deviation of the distribution
+
+        """
+        kwds['moments'] = 'v'
+        res = sqrt(self.stats(*args, **kwds))
+        return res
+
+    def interval(self, confidence, *args, **kwds):
+        """Confidence interval with equal areas around the median.
+
+        Parameters
+        ----------
+        confidence : array_like of float
+            Probability that an rv will be drawn from the returned range.
+            Each value should be in the range [0, 1].
+        arg1, arg2, ... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information).
+        loc : array_like, optional
+            location parameter, Default is 0.
+        scale : array_like, optional
+            scale parameter, Default is 1.
+
+        Returns
+        -------
+        a, b : ndarray of float
+            end-points of range that contain ``100 * alpha %`` of the rv's
+            possible values.
+
+        Notes
+        -----
+        This is implemented as ``ppf([p_tail, 1-p_tail])``, where
+        ``ppf`` is the inverse cumulative distribution function and
+        ``p_tail = (1-confidence)/2``. Suppose ``[c, d]`` is the support of a
+        discrete distribution; then ``ppf([0, 1]) == (c-1, d)``. Therefore,
+        when ``confidence=1`` and the distribution is discrete, the left end
+        of the interval will be beyond the support of the distribution.
+        For discrete distributions, the interval will limit the probability
+        in each tail to be less than or equal to ``p_tail`` (usually
+        strictly less).
+
+        """
+        alpha = confidence
+
+        alpha = asarray(alpha)
+        if np.any((alpha > 1) | (alpha < 0)):
+            raise ValueError("alpha must be between 0 and 1 inclusive")
+        q1 = (1.0-alpha)/2
+        q2 = (1.0+alpha)/2
+        a = self.ppf(q1, *args, **kwds)
+        b = self.ppf(q2, *args, **kwds)
+        return a, b
+
+    def support(self, *args, **kwargs):
+        """Support of the distribution.
+
+        Parameters
+        ----------
+        arg1, arg2, ... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information).
+        loc : array_like, optional
+            location parameter, Default is 0.
+        scale : array_like, optional
+            scale parameter, Default is 1.
+
+        Returns
+        -------
+        a, b : array_like
+            end-points of the distribution's support.
+
+        """
+        args, loc, scale = self._parse_args(*args, **kwargs)
+        arrs = np.broadcast_arrays(*args, loc, scale)
+        args, loc, scale = arrs[:-2], arrs[-2], arrs[-1]
+        cond = self._argcheck(*args) & (scale > 0)
+        _a, _b = self._get_support(*args)
+        if cond.all():
+            return _a * scale + loc, _b * scale + loc
+        elif cond.ndim == 0:
+            return self.badvalue, self.badvalue
+        # promote bounds to at least float to fill in the badvalue
+        _a, _b = np.asarray(_a).astype('d'), np.asarray(_b).astype('d')
+        out_a, out_b = _a * scale + loc, _b * scale + loc
+        place(out_a, 1-cond, self.badvalue)
+        place(out_b, 1-cond, self.badvalue)
+        return out_a, out_b
+
+    def nnlf(self, theta, x):
+        """Negative loglikelihood function.
+        Notes
+        -----
+        This is ``-sum(log pdf(x, theta), axis=0)`` where `theta` are the
+        parameters (including loc and scale).
+        """
+        loc, scale, args = self._unpack_loc_scale(theta)
+        if not self._argcheck(*args) or scale <= 0:
+            return inf
+        x = (asarray(x)-loc) / scale
+        n_log_scale = len(x) * log(scale)
+        if np.any(~self._support_mask(x, *args)):
+            return inf
+        return self._nnlf(x, *args) + n_log_scale
+
+    def _nnlf(self, x, *args):
+        return -np.sum(self._logpxf(x, *args), axis=0)
+
+    def _nlff_and_penalty(self, x, args, log_fitfun):
+        # negative log fit function
+        cond0 = ~self._support_mask(x, *args)
+        n_bad = np.count_nonzero(cond0, axis=0)
+        if n_bad > 0:
+            x = argsreduce(~cond0, x)[0]
+        logff = log_fitfun(x, *args)
+        finite_logff = np.isfinite(logff)
+        n_bad += np.sum(~finite_logff, axis=0)
+        if n_bad > 0:
+            penalty = n_bad * log(_XMAX) * 100
+            return -np.sum(logff[finite_logff], axis=0) + penalty
+        return -np.sum(logff, axis=0)
+
+    def _penalized_nnlf(self, theta, x):
+        """Penalized negative loglikelihood function.
+        i.e., - sum (log pdf(x, theta), axis=0) + penalty
+        where theta are the parameters (including loc and scale)
+        """
+        loc, scale, args = self._unpack_loc_scale(theta)
+        if not self._argcheck(*args) or scale <= 0:
+            return inf
+        x = asarray((x-loc) / scale)
+        n_log_scale = len(x) * log(scale)
+        return self._nlff_and_penalty(x, args, self._logpxf) + n_log_scale
+
+    def _penalized_nlpsf(self, theta, x):
+        """Penalized negative log product spacing function.
+        i.e., - sum (log (diff (cdf (x, theta))), axis=0) + penalty
+        where theta are the parameters (including loc and scale)
+        Follows reference [1] of scipy.stats.fit
+        """
+        loc, scale, args = self._unpack_loc_scale(theta)
+        if not self._argcheck(*args) or scale <= 0:
+            return inf
+        x = (np.sort(x) - loc)/scale
+
+        def log_psf(x, *args):
+            x, lj = np.unique(x, return_counts=True)  # fast for sorted x
+            cdf_data = self._cdf(x, *args) if x.size else []
+            if not (x.size and 1 - cdf_data[-1] <= 0):
+                cdf = np.concatenate(([0], cdf_data, [1]))
+                lj = np.concatenate((lj, [1]))
+            else:
+                cdf = np.concatenate(([0], cdf_data))
+            # here we could use logcdf w/ logsumexp trick to take differences,
+            # but in the context of the method, it seems unlikely to matter
+            return lj * np.log(np.diff(cdf) / lj)
+
+        return self._nlff_and_penalty(x, args, log_psf)
+
+
+class _ShapeInfo:
+    def __init__(self, name, integrality=False, domain=(-np.inf, np.inf),
+                 inclusive=(True, True)):
+        self.name = name
+        self.integrality = integrality
+        self.endpoints = domain
+        self.inclusive = inclusive
+
+        domain = list(domain)
+        if np.isfinite(domain[0]) and not inclusive[0]:
+            domain[0] = np.nextafter(domain[0], np.inf)
+        if np.isfinite(domain[1]) and not inclusive[1]:
+            domain[1] = np.nextafter(domain[1], -np.inf)
+        self.domain = domain
+
+
+def _get_fixed_fit_value(kwds, names):
+    """
+    Given names such as ``['f0', 'fa', 'fix_a']``, check that there is
+    at most one non-None value in `kwds` associated with those names.
+    Return that value, or None if none of the names occur in `kwds`.
+    As a side effect, all occurrences of those names in `kwds` are
+    removed.
+    """
+    vals = [(name, kwds.pop(name)) for name in names if name in kwds]
+    if len(vals) > 1:
+        repeated = [name for name, val in vals]
+        raise ValueError("fit method got multiple keyword arguments to "
+                         "specify the same fixed parameter: " +
+                         ', '.join(repeated))
+    return vals[0][1] if vals else None
+
+
+#  continuous random variables: implement maybe later
+#
+#  hf  --- Hazard Function (PDF / SF)
+#  chf  --- Cumulative hazard function (-log(SF))
+#  psf --- Probability sparsity function (reciprocal of the pdf) in
+#                units of percent-point-function (as a function of q).
+#                Also, the derivative of the percent-point function.
+
+
+class rv_continuous(rv_generic):
+    """A generic continuous random variable class meant for subclassing.
+
+    `rv_continuous` is a base class to construct specific distribution classes
+    and instances for continuous random variables. It cannot be used
+    directly as a distribution.
+
+    Parameters
+    ----------
+    momtype : int, optional
+        The type of generic moment calculation to use: 0 for pdf, 1 (default)
+        for ppf.
+    a : float, optional
+        Lower bound of the support of the distribution, default is minus
+        infinity.
+    b : float, optional
+        Upper bound of the support of the distribution, default is plus
+        infinity.
+    xtol : float, optional
+        The tolerance for fixed point calculation for generic ppf.
+    badvalue : float, optional
+        The value in a result arrays that indicates a value that for which
+        some argument restriction is violated, default is np.nan.
+    name : str, optional
+        The name of the instance. This string is used to construct the default
+        example for distributions.
+    longname : str, optional
+        This string is used as part of the first line of the docstring returned
+        when a subclass has no docstring of its own. Note: `longname` exists
+        for backwards compatibility, do not use for new subclasses.
+    shapes : str, optional
+        The shape of the distribution. For example ``"m, n"`` for a
+        distribution that takes two integers as the two shape arguments for all
+        its methods. If not provided, shape parameters will be inferred from
+        the signature of the private methods, ``_pdf`` and ``_cdf`` of the
+        instance.
+    seed : {None, int, `numpy.random.Generator`, `numpy.random.RandomState`}, optional
+        If `seed` is None (or `np.random`), the `numpy.random.RandomState`
+        singleton is used.
+        If `seed` is an int, a new ``RandomState`` instance is used,
+        seeded with `seed`.
+        If `seed` is already a ``Generator`` or ``RandomState`` instance then
+        that instance is used.
+
+    Attributes
+    ----------
+    a, b : float, optional
+        Lower/upper bound of the support of the unshifted/unscaled distribution.
+        This value is unaffected by the `loc` and `scale` parameters.
+        To calculate the support of the shifted/scaled distribution,
+        use the `support` method.
+
+    Methods
+    -------
+    rvs
+    pdf
+    logpdf
+    cdf
+    logcdf
+    sf
+    logsf
+    ppf
+    isf
+    moment
+    stats
+    entropy
+    expect
+    median
+    mean
+    std
+    var
+    interval
+    __call__
+    fit
+    fit_loc_scale
+    nnlf
+    support
+
+    Notes
+    -----
+    Public methods of an instance of a distribution class (e.g., ``pdf``,
+    ``cdf``) check their arguments and pass valid arguments to private,
+    computational methods (``_pdf``, ``_cdf``). For ``pdf(x)``, ``x`` is valid
+    if it is within the support of the distribution.
+    Whether a shape parameter is valid is decided by an ``_argcheck`` method
+    (which defaults to checking that its arguments are strictly positive.)
+
+    **Subclassing**
+
+    New random variables can be defined by subclassing the `rv_continuous` class
+    and re-defining at least the ``_pdf`` or the ``_cdf`` method (normalized
+    to location 0 and scale 1).
+
+    If positive argument checking is not correct for your RV
+    then you will also need to re-define the ``_argcheck`` method.
+
+    For most of the scipy.stats distributions, the support interval doesn't
+    depend on the shape parameters. ``x`` being in the support interval is
+    equivalent to ``self.a <= x <= self.b``.  If either of the endpoints of
+    the support do depend on the shape parameters, then
+    i) the distribution must implement the ``_get_support`` method; and
+    ii) those dependent endpoints must be omitted from the distribution's
+    call to the ``rv_continuous`` initializer.
+
+    Correct, but potentially slow defaults exist for the remaining
+    methods but for speed and/or accuracy you can over-ride::
+
+      _logpdf, _cdf, _logcdf, _ppf, _rvs, _isf, _sf, _logsf
+
+    The default method ``_rvs`` relies on the inverse of the cdf, ``_ppf``,
+    applied to a uniform random variate. In order to generate random variates
+    efficiently, either the default ``_ppf`` needs to be overwritten (e.g.
+    if the inverse cdf can expressed in an explicit form) or a sampling
+    method needs to be implemented in a custom ``_rvs`` method.
+
+    If possible, you should override ``_isf``, ``_sf`` or ``_logsf``.
+    The main reason would be to improve numerical accuracy: for example,
+    the survival function ``_sf`` is computed as ``1 - _cdf`` which can
+    result in loss of precision if ``_cdf(x)`` is close to one.
+
+    **Methods that can be overwritten by subclasses**
+    ::
+
+      _rvs
+      _pdf
+      _cdf
+      _sf
+      _ppf
+      _isf
+      _stats
+      _munp
+      _entropy
+      _argcheck
+      _get_support
+
+    There are additional (internal and private) generic methods that can
+    be useful for cross-checking and for debugging, but might work in all
+    cases when directly called.
+
+    A note on ``shapes``: subclasses need not specify them explicitly. In this
+    case, `shapes` will be automatically deduced from the signatures of the
+    overridden methods (`pdf`, `cdf` etc).
+    If, for some reason, you prefer to avoid relying on introspection, you can
+    specify ``shapes`` explicitly as an argument to the instance constructor.
+
+
+    **Frozen Distributions**
+
+    Normally, you must provide shape parameters (and, optionally, location and
+    scale parameters to each call of a method of a distribution.
+
+    Alternatively, the object may be called (as a function) to fix the shape,
+    location, and scale parameters returning a "frozen" continuous RV object:
+
+    rv = generic(<shape(s)>, loc=0, scale=1)
+        `rv_frozen` object with the same methods but holding the given shape,
+        location, and scale fixed
+
+    **Statistics**
+
+    Statistics are computed using numerical integration by default.
+    For speed you can redefine this using ``_stats``:
+
+    - take shape parameters and return mu, mu2, g1, g2
+    - If you can't compute one of these, return it as None
+    - Can also be defined with a keyword argument ``moments``, which is a
+      string composed of "m", "v", "s", and/or "k".
+      Only the components appearing in string should be computed and
+      returned in the order "m", "v", "s", or "k"  with missing values
+      returned as None.
+
+    Alternatively, you can override ``_munp``, which takes ``n`` and shape
+    parameters and returns the n-th non-central moment of the distribution.
+
+    **Deepcopying / Pickling**
+
+    If a distribution or frozen distribution is deepcopied (pickled/unpickled,
+    etc.), any underlying random number generator is deepcopied with it. An
+    implication is that if a distribution relies on the singleton RandomState
+    before copying, it will rely on a copy of that random state after copying,
+    and ``np.random.seed`` will no longer control the state.
+
+    Examples
+    --------
+    To create a new Gaussian distribution, we would do the following:
+
+    >>> from scipy.stats import rv_continuous
+    >>> class gaussian_gen(rv_continuous):
+    ...     "Gaussian distribution"
+    ...     def _pdf(self, x):
+    ...         return np.exp(-x**2 / 2.) / np.sqrt(2.0 * np.pi)
+    >>> gaussian = gaussian_gen(name='gaussian')
+
+    ``scipy.stats`` distributions are *instances*, so here we subclass
+    `rv_continuous` and create an instance. With this, we now have
+    a fully functional distribution with all relevant methods automagically
+    generated by the framework.
+
+    Note that above we defined a standard normal distribution, with zero mean
+    and unit variance. Shifting and scaling of the distribution can be done
+    by using ``loc`` and ``scale`` parameters: ``gaussian.pdf(x, loc, scale)``
+    essentially computes ``y = (x - loc) / scale`` and
+    ``gaussian._pdf(y) / scale``.
+
+    """
+
+    _support: tuple[float | str, float | str]  # not required
+
+    def __init__(self, momtype=1, a=None, b=None, xtol=1e-14,
+                 badvalue=None, name=None, longname=None,
+                 shapes=None, seed=None):
+
+        super().__init__(seed)
+
+        # save the ctor parameters, cf generic freeze
+        self._ctor_param = dict(
+            momtype=momtype, a=a, b=b, xtol=xtol,
+            badvalue=badvalue, name=name, longname=longname,
+            shapes=shapes, seed=seed)
+
+        if badvalue is None:
+            badvalue = nan
+        if name is None:
+            name = 'Distribution'
+        self.badvalue = badvalue
+        self.name = name
+        self.a = a
+        self.b = b
+        if a is None:
+            self.a = -inf
+        if b is None:
+            self.b = inf
+        self.xtol = xtol
+        self.moment_type = momtype
+        self.shapes = shapes
+
+        self._construct_argparser(meths_to_inspect=[self._pdf, self._cdf],
+                                  locscale_in='loc=0, scale=1',
+                                  locscale_out='loc, scale')
+        self._attach_methods()
+
+        if longname is None:
+            if name[0] in ['aeiouAEIOU']:
+                hstr = "An "
+            else:
+                hstr = "A "
+            longname = hstr + name
+
+        if sys.flags.optimize < 2:
+            # Skip adding docstrings if interpreter is run with -OO
+            if self.__doc__ is None:
+                self._construct_default_doc(longname=longname,
+                                            docdict=docdict,
+                                            discrete='continuous')
+            else:
+                dct = dict(distcont)
+                self._construct_doc(docdict, dct.get(self.name))
+
+    def __getstate__(self):
+        dct = self.__dict__.copy()
+
+        # these methods will be remade in __setstate__
+        # _random_state attribute is taken care of by rv_generic
+        attrs = ["_parse_args", "_parse_args_stats", "_parse_args_rvs",
+                 "_cdfvec", "_ppfvec", "vecentropy", "generic_moment"]
+        [dct.pop(attr, None) for attr in attrs]
+        return dct
+
+    def _attach_methods(self):
+        """
+        Attaches dynamically created methods to the rv_continuous instance.
+        """
+        # _attach_methods is responsible for calling _attach_argparser_methods
+        self._attach_argparser_methods()
+
+        # nin correction
+        self._ppfvec = vectorize(self._ppf_single, otypes='d')
+        self._ppfvec.nin = self.numargs + 1
+        self.vecentropy = vectorize(self._entropy, otypes='d')
+        self._cdfvec = vectorize(self._cdf_single, otypes='d')
+        self._cdfvec.nin = self.numargs + 1
+
+        if self.moment_type == 0:
+            self.generic_moment = vectorize(self._mom0_sc, otypes='d')
+        else:
+            self.generic_moment = vectorize(self._mom1_sc, otypes='d')
+        # Because of the *args argument of _mom0_sc, vectorize cannot count the
+        # number of arguments correctly.
+        self.generic_moment.nin = self.numargs + 1
+
+    def _updated_ctor_param(self):
+        """Return the current version of _ctor_param, possibly updated by user.
+
+        Used by freezing.
+        Keep this in sync with the signature of __init__.
+        """
+        dct = self._ctor_param.copy()
+        dct['a'] = self.a
+        dct['b'] = self.b
+        dct['xtol'] = self.xtol
+        dct['badvalue'] = self.badvalue
+        dct['name'] = self.name
+        dct['shapes'] = self.shapes
+        return dct
+
+    def _ppf_to_solve(self, x, q, *args):
+        return self.cdf(*(x, )+args)-q
+
+    def _ppf_single(self, q, *args):
+        factor = 10.
+        left, right = self._get_support(*args)
+
+        if np.isinf(left):
+            left = min(-factor, right)
+            while self._ppf_to_solve(left, q, *args) > 0.:
+                left, right = left * factor, left
+            # left is now such that cdf(left) <= q
+            # if right has changed, then cdf(right) > q
+
+        if np.isinf(right):
+            right = max(factor, left)
+            while self._ppf_to_solve(right, q, *args) < 0.:
+                left, right = right, right * factor
+            # right is now such that cdf(right) >= q
+
+        return optimize.brentq(self._ppf_to_solve,
+                               left, right, args=(q,)+args, xtol=self.xtol)
+
+    # moment from definition
+    def _mom_integ0(self, x, m, *args):
+        return x**m * self.pdf(x, *args)
+
+    def _mom0_sc(self, m, *args):
+        _a, _b = self._get_support(*args)
+        return integrate.quad(self._mom_integ0, _a, _b,
+                              args=(m,)+args)[0]
+
+    # moment calculated using ppf
+    def _mom_integ1(self, q, m, *args):
+        return (self.ppf(q, *args))**m
+
+    def _mom1_sc(self, m, *args):
+        return integrate.quad(self._mom_integ1, 0, 1, args=(m,)+args)[0]
+
+    def _pdf(self, x, *args):
+        return _derivative(self._cdf, x, dx=1e-5, args=args, order=5)
+
+    # Could also define any of these
+    def _logpdf(self, x, *args):
+        p = self._pdf(x, *args)
+        with np.errstate(divide='ignore'):
+            return log(p)
+
+    def _logpxf(self, x, *args):
+        # continuous distributions have PDF, discrete have PMF, but sometimes
+        # the distinction doesn't matter. This lets us use `_logpxf` for both
+        # discrete and continuous distributions.
+        return self._logpdf(x, *args)
+
+    def _cdf_single(self, x, *args):
+        _a, _b = self._get_support(*args)
+        return integrate.quad(self._pdf, _a, x, args=args)[0]
+
+    def _cdf(self, x, *args):
+        return self._cdfvec(x, *args)
+
+    def _logcdf(self, x, *args):
+        median = self._ppf(0.5, *args)
+        with np.errstate(divide='ignore'):
+            return xpx.apply_where(
+                x < median, (x,) + args,
+                lambda x, *args: np.log(self._cdf(x, *args)),
+                lambda x, *args: np.log1p(-self._sf(x, *args)))
+
+    def _logsf(self, x, *args):
+        median = self._ppf(0.5, *args)
+        with np.errstate(divide='ignore'):
+            return xpx.apply_where(
+                x > median, (x,) + args,
+                lambda x, *args: np.log(self._sf(x, *args)),
+                lambda x, *args: np.log1p(-self._cdf(x, *args)))
+
+    # generic _argcheck, _sf, _ppf, _isf, _rvs are defined
+    # in rv_generic
+
+    def pdf(self, x, *args, **kwds):
+        """Probability density function at x of the given RV.
+
+        Parameters
+        ----------
+        x : array_like
+            quantiles
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information)
+        loc : array_like, optional
+            location parameter (default=0)
+        scale : array_like, optional
+            scale parameter (default=1)
+
+        Returns
+        -------
+        pdf : ndarray
+            Probability density function evaluated at x
+
+        """
+        args, loc, scale = self._parse_args(*args, **kwds)
+        x, loc, scale = map(asarray, (x, loc, scale))
+        args = tuple(map(asarray, args))
+        dtyp = np.promote_types(x.dtype, np.float64)
+        x = np.asarray((x - loc)/scale, dtype=dtyp)
+        cond0 = self._argcheck(*args) & (scale > 0)
+        cond1 = self._support_mask(x, *args) & (scale > 0)
+        cond = cond0 & cond1
+        output = zeros(shape(cond), dtyp)
+        putmask(output, (1-cond0)+np.isnan(x), self.badvalue)
+        if np.any(cond):
+            goodargs = argsreduce(cond, *((x,)+args+(scale,)))
+            scale, goodargs = goodargs[-1], goodargs[:-1]
+            place(output, cond, self._pdf(*goodargs) / scale)
+        if output.ndim == 0:
+            return output[()]
+        return output
+
+    def logpdf(self, x, *args, **kwds):
+        """Log of the probability density function at x of the given RV.
+
+        This uses a more numerically accurate calculation if available.
+
+        Parameters
+        ----------
+        x : array_like
+            quantiles
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information)
+        loc : array_like, optional
+            location parameter (default=0)
+        scale : array_like, optional
+            scale parameter (default=1)
+
+        Returns
+        -------
+        logpdf : array_like
+            Log of the probability density function evaluated at x
+
+        """
+        args, loc, scale = self._parse_args(*args, **kwds)
+        x, loc, scale = map(asarray, (x, loc, scale))
+        args = tuple(map(asarray, args))
+        dtyp = np.promote_types(x.dtype, np.float64)
+        x = np.asarray((x - loc)/scale, dtype=dtyp)
+        cond0 = self._argcheck(*args) & (scale > 0)
+        cond1 = self._support_mask(x, *args) & (scale > 0)
+        cond = cond0 & cond1
+        output = empty(shape(cond), dtyp)
+        output.fill(-inf)
+        putmask(output, (1-cond0)+np.isnan(x), self.badvalue)
+        if np.any(cond):
+            goodargs = argsreduce(cond, *((x,)+args+(scale,)))
+            scale, goodargs = goodargs[-1], goodargs[:-1]
+            place(output, cond, self._logpdf(*goodargs) - log(scale))
+        if output.ndim == 0:
+            return output[()]
+        return output
+
+    def cdf(self, x, *args, **kwds):
+        """
+        Cumulative distribution function of the given RV.
+
+        Parameters
+        ----------
+        x : array_like
+            quantiles
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information)
+        loc : array_like, optional
+            location parameter (default=0)
+        scale : array_like, optional
+            scale parameter (default=1)
+
+        Returns
+        -------
+        cdf : ndarray
+            Cumulative distribution function evaluated at `x`
+
+        """
+        args, loc, scale = self._parse_args(*args, **kwds)
+        x, loc, scale = map(asarray, (x, loc, scale))
+        args = tuple(map(asarray, args))
+        _a, _b = self._get_support(*args)
+        dtyp = np.promote_types(x.dtype, np.float64)
+        x = np.asarray((x - loc)/scale, dtype=dtyp)
+        cond0 = self._argcheck(*args) & (scale > 0)
+        cond1 = self._open_support_mask(x, *args) & (scale > 0)
+        cond2 = (x >= np.asarray(_b)) & cond0
+        cond = cond0 & cond1
+        output = zeros(shape(cond), dtyp)
+        place(output, (1-cond0)+np.isnan(x), self.badvalue)
+        place(output, cond2, 1.0)
+        if np.any(cond):  # call only if at least 1 entry
+            goodargs = argsreduce(cond, *((x,)+args))
+            place(output, cond, self._cdf(*goodargs))
+        if output.ndim == 0:
+            return output[()]
+        return output
+
+    def logcdf(self, x, *args, **kwds):
+        """Log of the cumulative distribution function at x of the given RV.
+
+        Parameters
+        ----------
+        x : array_like
+            quantiles
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information)
+        loc : array_like, optional
+            location parameter (default=0)
+        scale : array_like, optional
+            scale parameter (default=1)
+
+        Returns
+        -------
+        logcdf : array_like
+            Log of the cumulative distribution function evaluated at x
+
+        """
+        args, loc, scale = self._parse_args(*args, **kwds)
+        x, loc, scale = map(asarray, (x, loc, scale))
+        args = tuple(map(asarray, args))
+        _a, _b = self._get_support(*args)
+        dtyp = np.promote_types(x.dtype, np.float64)
+        x = np.asarray((x - loc)/scale, dtype=dtyp)
+        cond0 = self._argcheck(*args) & (scale > 0)
+        cond1 = self._open_support_mask(x, *args) & (scale > 0)
+        cond2 = (x >= _b) & cond0
+        cond = cond0 & cond1
+        output = empty(shape(cond), dtyp)
+        output.fill(-inf)
+        place(output, (1-cond0)*(cond1 == cond1)+np.isnan(x), self.badvalue)
+        place(output, cond2, 0.0)
+        if np.any(cond):  # call only if at least 1 entry
+            goodargs = argsreduce(cond, *((x,)+args))
+            place(output, cond, self._logcdf(*goodargs))
+        if output.ndim == 0:
+            return output[()]
+        return output
+
+    def sf(self, x, *args, **kwds):
+        """Survival function (1 - `cdf`) at x of the given RV.
+
+        Parameters
+        ----------
+        x : array_like
+            quantiles
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information)
+        loc : array_like, optional
+            location parameter (default=0)
+        scale : array_like, optional
+            scale parameter (default=1)
+
+        Returns
+        -------
+        sf : array_like
+            Survival function evaluated at x
+
+        """
+        args, loc, scale = self._parse_args(*args, **kwds)
+        x, loc, scale = map(asarray, (x, loc, scale))
+        args = tuple(map(asarray, args))
+        _a, _b = self._get_support(*args)
+        dtyp = np.promote_types(x.dtype, np.float64)
+        x = np.asarray((x - loc)/scale, dtype=dtyp)
+        cond0 = self._argcheck(*args) & (scale > 0)
+        cond1 = self._open_support_mask(x, *args) & (scale > 0)
+        cond2 = cond0 & (x <= _a)
+        cond = cond0 & cond1
+        output = zeros(shape(cond), dtyp)
+        place(output, (1-cond0)+np.isnan(x), self.badvalue)
+        place(output, cond2, 1.0)
+        if np.any(cond):
+            goodargs = argsreduce(cond, *((x,)+args))
+            place(output, cond, self._sf(*goodargs))
+        if output.ndim == 0:
+            return output[()]
+        return output
+
+    def logsf(self, x, *args, **kwds):
+        """Log of the survival function of the given RV.
+
+        Returns the log of the "survival function," defined as (1 - `cdf`),
+        evaluated at `x`.
+
+        Parameters
+        ----------
+        x : array_like
+            quantiles
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information)
+        loc : array_like, optional
+            location parameter (default=0)
+        scale : array_like, optional
+            scale parameter (default=1)
+
+        Returns
+        -------
+        logsf : ndarray
+            Log of the survival function evaluated at `x`.
+
+        """
+        args, loc, scale = self._parse_args(*args, **kwds)
+        x, loc, scale = map(asarray, (x, loc, scale))
+        args = tuple(map(asarray, args))
+        _a, _b = self._get_support(*args)
+        dtyp = np.promote_types(x.dtype, np.float64)
+        x = np.asarray((x - loc)/scale, dtype=dtyp)
+        cond0 = self._argcheck(*args) & (scale > 0)
+        cond1 = self._open_support_mask(x, *args) & (scale > 0)
+        cond2 = cond0 & (x <= _a)
+        cond = cond0 & cond1
+        output = empty(shape(cond), dtyp)
+        output.fill(-inf)
+        place(output, (1-cond0)+np.isnan(x), self.badvalue)
+        place(output, cond2, 0.0)
+        if np.any(cond):
+            goodargs = argsreduce(cond, *((x,)+args))
+            place(output, cond, self._logsf(*goodargs))
+        if output.ndim == 0:
+            return output[()]
+        return output
+
+    def ppf(self, q, *args, **kwds):
+        """Percent point function (inverse of `cdf`) at q of the given RV.
+
+        Parameters
+        ----------
+        q : array_like
+            lower tail probability
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information)
+        loc : array_like, optional
+            location parameter (default=0)
+        scale : array_like, optional
+            scale parameter (default=1)
+
+        Returns
+        -------
+        x : array_like
+            quantile corresponding to the lower tail probability q.
+
+        """
+        args, loc, scale = self._parse_args(*args, **kwds)
+        q, loc, scale = map(asarray, (q, loc, scale))
+        args = tuple(map(asarray, args))
+        _a, _b = self._get_support(*args)
+        cond0 = self._argcheck(*args) & (scale > 0) & (loc == loc)
+        cond1 = (0 < q) & (q < 1)
+        cond2 = cond0 & (q == 0)
+        cond3 = cond0 & (q == 1)
+        cond = cond0 & cond1
+        output = np.full(shape(cond), fill_value=self.badvalue)
+
+        lower_bound = _a * scale + loc
+        upper_bound = _b * scale + loc
+        place(output, cond2, argsreduce(cond2, lower_bound)[0])
+        place(output, cond3, argsreduce(cond3, upper_bound)[0])
+
+        if np.any(cond):  # call only if at least 1 entry
+            goodargs = argsreduce(cond, *((q,)+args+(scale, loc)))
+            scale, loc, goodargs = goodargs[-2], goodargs[-1], goodargs[:-2]
+            place(output, cond, self._ppf(*goodargs) * scale + loc)
+        if output.ndim == 0:
+            return output[()]
+        return output
+
+    def isf(self, q, *args, **kwds):
+        """Inverse survival function (inverse of `sf`) at q of the given RV.
+
+        Parameters
+        ----------
+        q : array_like
+            upper tail probability
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information)
+        loc : array_like, optional
+            location parameter (default=0)
+        scale : array_like, optional
+            scale parameter (default=1)
+
+        Returns
+        -------
+        x : ndarray or scalar
+            Quantile corresponding to the upper tail probability q.
+
+        """
+        args, loc, scale = self._parse_args(*args, **kwds)
+        q, loc, scale = map(asarray, (q, loc, scale))
+        args = tuple(map(asarray, args))
+        _a, _b = self._get_support(*args)
+        cond0 = self._argcheck(*args) & (scale > 0) & (loc == loc)
+        cond1 = (0 < q) & (q < 1)
+        cond2 = cond0 & (q == 1)
+        cond3 = cond0 & (q == 0)
+        cond = cond0 & cond1
+        output = np.full(shape(cond), fill_value=self.badvalue)
+
+        lower_bound = _a * scale + loc
+        upper_bound = _b * scale + loc
+        place(output, cond2, argsreduce(cond2, lower_bound)[0])
+        place(output, cond3, argsreduce(cond3, upper_bound)[0])
+
+        if np.any(cond):
+            goodargs = argsreduce(cond, *((q,)+args+(scale, loc)))
+            scale, loc, goodargs = goodargs[-2], goodargs[-1], goodargs[:-2]
+            place(output, cond, self._isf(*goodargs) * scale + loc)
+        if output.ndim == 0:
+            return output[()]
+        return output
+
+    def _unpack_loc_scale(self, theta):
+        try:
+            loc = theta[-2]
+            scale = theta[-1]
+            args = tuple(theta[:-2])
+        except IndexError as e:
+            raise ValueError("Not enough input arguments.") from e
+        return loc, scale, args
+
+    def _nnlf_and_penalty(self, x, args):
+        """
+        Compute the penalized negative log-likelihood for the
+        "standardized" data (i.e. already shifted by loc and
+        scaled by scale) for the shape parameters in `args`.
+
+        `x` can be a 1D numpy array or a CensoredData instance.
+        """
+        if isinstance(x, CensoredData):
+            # Filter out the data that is not in the support.
+            xs = x._supported(*self._get_support(*args))
+            n_bad = len(x) - len(xs)
+            i1, i2 = xs._interval.T
+            terms = [
+                # logpdf of the noncensored data.
+                self._logpdf(xs._uncensored, *args),
+                # logcdf of the left-censored data.
+                self._logcdf(xs._left, *args),
+                # logsf of the right-censored data.
+                self._logsf(xs._right, *args),
+                # log of probability of the interval-censored data.
+                np.log(self._delta_cdf(i1, i2, *args)),
+            ]
+        else:
+            cond0 = ~self._support_mask(x, *args)
+            n_bad = np.count_nonzero(cond0)
+            if n_bad > 0:
+                x = argsreduce(~cond0, x)[0]
+            terms = [self._logpdf(x, *args)]
+
+        totals, bad_counts = zip(*[_sum_finite(term) for term in terms])
+        total = sum(totals)
+        n_bad += sum(bad_counts)
+
+        return -total + n_bad * _LOGXMAX * 100
+
+    def _penalized_nnlf(self, theta, x):
+        """Penalized negative loglikelihood function.
+
+        i.e., - sum (log pdf(x, theta), axis=0) + penalty
+        where theta are the parameters (including loc and scale)
+        """
+        loc, scale, args = self._unpack_loc_scale(theta)
+        if not self._argcheck(*args) or scale <= 0:
+            return inf
+        if isinstance(x, CensoredData):
+            x = (x - loc) / scale
+            n_log_scale = (len(x) - x.num_censored()) * log(scale)
+        else:
+            x = (x - loc) / scale
+            n_log_scale = len(x) * log(scale)
+
+        return self._nnlf_and_penalty(x, args) + n_log_scale
+
+    def _fitstart(self, data, args=None):
+        """Starting point for fit (shape arguments + loc + scale)."""
+        if args is None:
+            args = (1.0,)*self.numargs
+        loc, scale = self._fit_loc_scale_support(data, *args)
+        return args + (loc, scale)
+
+    def _reduce_func(self, args, kwds, data=None):
+        """
+        Return the (possibly reduced) function to optimize in order to find MLE
+        estimates for the .fit method.
+        """
+        # Convert fixed shape parameters to the standard numeric form: e.g. for
+        # stats.beta, shapes='a, b'. To fix `a`, the caller can give a value
+        # for `f0`, `fa` or 'fix_a'.  The following converts the latter two
+        # into the first (numeric) form.
+        shapes = []
+        if self.shapes:
+            shapes = self.shapes.replace(',', ' ').split()
+            for j, s in enumerate(shapes):
+                key = 'f' + str(j)
+                names = [key, 'f' + s, 'fix_' + s]
+                val = _get_fixed_fit_value(kwds, names)
+                if val is not None:
+                    kwds[key] = val
+
+        args = list(args)
+        Nargs = len(args)
+        fixedn = []
+        names = [f'f{n}' for n in range(Nargs - 2)] + ['floc', 'fscale']
+        x0 = []
+        for n, key in enumerate(names):
+            if key in kwds:
+                fixedn.append(n)
+                args[n] = kwds.pop(key)
+            else:
+                x0.append(args[n])
+
+        methods = {"mle", "mm"}
+        method = kwds.pop('method', "mle").lower()
+        if method == "mm":
+            n_params = len(shapes) + 2 - len(fixedn)
+            exponents = (np.arange(1, n_params+1))[:, np.newaxis]
+            data_moments = np.sum(data[None, :]**exponents/len(data), axis=1)
+
+            def objective(theta, x):
+                return self._moment_error(theta, x, data_moments)
+
+        elif method == "mle":
+            objective = self._penalized_nnlf
+        else:
+            raise ValueError(f"Method '{method}' not available; "
+                             f"must be one of {methods}")
+
+        if len(fixedn) == 0:
+            func = objective
+            restore = None
+        else:
+            if len(fixedn) == Nargs:
+                raise ValueError(
+                    "All parameters fixed. There is nothing to optimize.")
+
+            def restore(args, theta):
+                # Replace with theta for all numbers not in fixedn
+                # This allows the non-fixed values to vary, but
+                #  we still call self.nnlf with all parameters.
+                i = 0
+                for n in range(Nargs):
+                    if n not in fixedn:
+                        args[n] = theta[i]
+                        i += 1
+                return args
+
+            def func(theta, x):
+                newtheta = restore(args[:], theta)
+                return objective(newtheta, x)
+
+        return x0, func, restore, args
+
+    def _moment_error(self, theta, x, data_moments):
+        loc, scale, args = self._unpack_loc_scale(theta)
+        if not self._argcheck(*args) or scale <= 0:
+            return inf
+
+        dist_moments = np.array([self.moment(i+1, *args, loc=loc, scale=scale)
+                                 for i in range(len(data_moments))])
+        if np.any(np.isnan(dist_moments)):
+            raise ValueError("Method of moments encountered a non-finite "
+                             "distribution moment and cannot continue. "
+                             "Consider trying method='MLE'.")
+
+        return (((data_moments - dist_moments) /
+                 np.maximum(np.abs(data_moments), 1e-8))**2).sum()
+
+    def fit(self, data, *args, **kwds):
+        r"""
+        Return estimates of shape (if applicable), location, and scale
+        parameters from data. The default estimation method is Maximum
+        Likelihood Estimation (MLE), but Method of Moments (MM)
+        is also available.
+
+        Starting estimates for the fit are given by input arguments;
+        for any arguments not provided with starting estimates,
+        ``self._fitstart(data)`` is called to generate such.
+
+        One can hold some parameters fixed to specific values by passing in
+        keyword arguments ``f0``, ``f1``, ..., ``fn`` (for shape parameters)
+        and ``floc`` and ``fscale`` (for location and scale parameters,
+        respectively).
+
+        Parameters
+        ----------
+        data : array_like or `CensoredData` instance
+            Data to use in estimating the distribution parameters.
+        arg1, arg2, arg3,... : floats, optional
+            Starting value(s) for any shape-characterizing arguments (those not
+            provided will be determined by a call to ``_fitstart(data)``).
+            No default value.
+        **kwds : floats, optional
+            - `loc`: initial guess of the distribution's location parameter.
+            - `scale`: initial guess of the distribution's scale parameter.
+
+            Special keyword arguments are recognized as holding certain
+            parameters fixed:
+
+            - f0, ..., fn : hold respective shape parameters fixed.
+              Alternatively, shape parameters to fix can be specified by name.
+              For example, if ``self.shapes == "a, b"``, ``fa`` and ``fix_a``
+              are equivalent to ``f0``, and ``fb`` and ``fix_b`` are
+              equivalent to ``f1``.
+
+            - floc : hold location parameter fixed to specified value.
+
+            - fscale : hold scale parameter fixed to specified value.
+
+            - optimizer : The optimizer to use.  The optimizer must take
+              ``func`` and starting position as the first two arguments,
+              plus ``args`` (for extra arguments to pass to the
+              function to be optimized) and ``disp``.
+              The ``fit`` method calls the optimizer with ``disp=0`` to suppress output.
+              The optimizer must return the estimated parameters.
+
+            - method : The method to use. The default is "MLE" (Maximum
+              Likelihood Estimate); "MM" (Method of Moments)
+              is also available.
+
+        Raises
+        ------
+        TypeError, ValueError
+            If an input is invalid
+        `~scipy.stats.FitError`
+            If fitting fails or the fit produced would be invalid
+
+        Returns
+        -------
+        parameter_tuple : tuple of floats
+            Estimates for any shape parameters (if applicable), followed by
+            those for location and scale. For most random variables, shape
+            statistics will be returned, but there are exceptions (e.g.
+            ``norm``).
+
+        Notes
+        -----
+        With ``method="MLE"`` (default), the fit is computed by minimizing
+        the negative log-likelihood function. A large, finite penalty
+        (rather than infinite negative log-likelihood) is applied for
+        observations beyond the support of the distribution.
+
+        With ``method="MM"``, the fit is computed by minimizing the L2 norm
+        of the relative errors between the first *k* raw (about zero) data
+        moments and the corresponding distribution moments, where *k* is the
+        number of non-fixed parameters.
+        More precisely, the objective function is::
+
+            (((data_moments - dist_moments)
+              / np.maximum(np.abs(data_moments), 1e-8))**2).sum()
+
+        where the constant ``1e-8`` avoids division by zero in case of
+        vanishing data moments. Typically, this error norm can be reduced to
+        zero.
+        Note that the standard method of moments can produce parameters for
+        which some data are outside the support of the fitted distribution;
+        this implementation does nothing to prevent this.
+
+        For either method,
+        the returned answer is not guaranteed to be globally optimal; it
+        may only be locally optimal, or the optimization may fail altogether.
+        If the data contain any of ``np.nan``, ``np.inf``, or ``-np.inf``,
+        the `fit` method will raise a ``RuntimeError``.
+
+        When passing a ``CensoredData`` instance to ``data``, the log-likelihood
+        function is defined as:
+
+        .. math::
+
+            l(\pmb{\theta}; k) & = \sum
+                                    \log(f(k_u; \pmb{\theta}))
+                                + \sum
+                                    \log(F(k_l; \pmb{\theta})) \\
+                                & + \sum
+                                    \log(1 - F(k_r; \pmb{\theta})) \\
+                                & + \sum
+                                    \log(F(k_{\text{high}, i}; \pmb{\theta})
+                                    - F(k_{\text{low}, i}; \pmb{\theta}))
+
+        where :math:`f` and :math:`F` are the pdf and cdf, respectively, of the
+        function being fitted, :math:`\pmb{\theta}` is the parameter vector,
+        :math:`u` are the indices of uncensored observations,
+        :math:`l` are the indices of left-censored observations,
+        :math:`r` are the indices of right-censored observations,
+        subscripts "low"/"high" denote endpoints of interval-censored observations, and
+        :math:`i` are the indices of interval-censored observations.
+
+        Examples
+        --------
+
+        Generate some data to fit: draw random variates from the `beta`
+        distribution
+
+        >>> import numpy as np
+        >>> from scipy.stats import beta
+        >>> a, b = 1., 2.
+        >>> rng = np.random.default_rng(172786373191770012695001057628748821561)
+        >>> x = beta.rvs(a, b, size=1000, random_state=rng)
+
+        Now we can fit all four parameters (``a``, ``b``, ``loc`` and
+        ``scale``):
+
+        >>> a1, b1, loc1, scale1 = beta.fit(x)
+        >>> a1, b1, loc1, scale1
+        (1.0198945204435628, 1.9484708982737828, 4.372241314917588e-05, 0.9979078845964814)
+
+        The fit can be done also using a custom optimizer:
+
+        >>> from scipy.optimize import minimize
+        >>> def custom_optimizer(func, x0, args=(), disp=0):
+        ...     res = minimize(func, x0, args, method="slsqp", options={"disp": disp})
+        ...     if res.success:
+        ...         return res.x
+        ...     raise RuntimeError('optimization routine failed')
+        >>> a1, b1, loc1, scale1 = beta.fit(x, method="MLE", optimizer=custom_optimizer)
+        >>> a1, b1, loc1, scale1
+        (1.0198821087258905, 1.948484145914738, 4.3705304486881485e-05, 0.9979104663953395)
+
+        We can also use some prior knowledge about the dataset: let's keep
+        ``loc`` and ``scale`` fixed:
+
+        >>> a1, b1, loc1, scale1 = beta.fit(x, floc=0, fscale=1)
+        >>> loc1, scale1
+        (0, 1)
+
+        We can also keep shape parameters fixed by using ``f``-keywords. To
+        keep the zero-th shape parameter ``a`` equal 1, use ``f0=1`` or,
+        equivalently, ``fa=1``:
+
+        >>> a1, b1, loc1, scale1 = beta.fit(x, fa=1, floc=0, fscale=1)
+        >>> a1
+        1
+
+        Not all distributions return estimates for the shape parameters.
+        ``norm`` for example just returns estimates for location and scale:
+
+        >>> from scipy.stats import norm
+        >>> x = norm.rvs(a, b, size=1000, random_state=123)
+        >>> loc1, scale1 = norm.fit(x)
+        >>> loc1, scale1
+        (0.92087172783841631, 2.0015750750324668)
+        """ # noqa: E501
+        method = kwds.get('method', "mle").lower()
+
+        censored = isinstance(data, CensoredData)
+        if censored:
+            if method != 'mle':
+                raise ValueError('For censored data, the method must'
+                                 ' be "MLE".')
+            if data.num_censored() == 0:
+                # There are no censored values in data, so replace the
+                # CensoredData instance with a regular array.
+                data = data._uncensored
+                censored = False
+
+        Narg = len(args)
+        if Narg > self.numargs:
+            raise TypeError("Too many input arguments.")
+
+        # Check the finiteness of data only if data is not an instance of
+        # CensoredData.  The arrays in a CensoredData instance have already
+        # been validated.
+        if not censored:
+            # Note: `ravel()` is called for backwards compatibility.
+            data = np.asarray(data).ravel()
+            if not np.isfinite(data).all():
+                raise ValueError("The data contains non-finite values.")
+
+        start = [None]*2
+        if (Narg < self.numargs) or not ('loc' in kwds and
+                                         'scale' in kwds):
+            # get distribution specific starting locations
+            start = self._fitstart(data)
+            args += start[Narg:-2]
+        loc = kwds.pop('loc', start[-2])
+        scale = kwds.pop('scale', start[-1])
+        args += (loc, scale)
+        x0, func, restore, args = self._reduce_func(args, kwds, data=data)
+        optimizer = kwds.pop('optimizer', optimize.fmin)
+        # convert string to function in scipy.optimize
+        optimizer = _fit_determine_optimizer(optimizer)
+        # by now kwds must be empty, since everybody took what they needed
+        if kwds:
+            raise TypeError(f"Unknown arguments: {kwds}.")
+
+        # In some cases, method of moments can be done with fsolve/root
+        # instead of an optimizer, but sometimes no solution exists,
+        # especially when the user fixes parameters. Minimizing the sum
+        # of squares of the error generalizes to these cases.
+        vals = optimizer(func, x0, args=(data,), disp=0)
+        obj = func(vals, data)
+
+        if restore is not None:
+            vals = restore(args, vals)
+        vals = tuple(vals)
+
+        loc, scale, shapes = self._unpack_loc_scale(vals)
+        if not (np.all(self._argcheck(*shapes)) and scale > 0):
+            raise FitError("Optimization converged to parameters that are "
+                           "outside the range allowed by the distribution.")
+
+        if method == 'mm':
+            if not np.isfinite(obj):
+                raise FitError("Optimization failed: either a data moment "
+                               "or fitted distribution moment is "
+                               "non-finite.")
+
+        return vals
+
+    def _fit_loc_scale_support(self, data, *args):
+        """Estimate loc and scale parameters from data accounting for support.
+
+        Parameters
+        ----------
+        data : array_like
+            Data to fit.
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information).
+
+        Returns
+        -------
+        Lhat : float
+            Estimated location parameter for the data.
+        Shat : float
+            Estimated scale parameter for the data.
+
+        """
+        if isinstance(data, CensoredData):
+            # For this estimate, "uncensor" the data by taking the
+            # given endpoints as the data for the left- or right-censored
+            # data, and the mean for the interval-censored data.
+            data = data._uncensor()
+        else:
+            data = np.asarray(data)
+
+        # Estimate location and scale according to the method of moments.
+        loc_hat, scale_hat = self.fit_loc_scale(data, *args)
+
+        # Compute the support according to the shape parameters.
+        self._argcheck(*args)
+        _a, _b = self._get_support(*args)
+        a, b = _a, _b
+        support_width = b - a
+
+        # If the support is empty then return the moment-based estimates.
+        if support_width <= 0:
+            return loc_hat, scale_hat
+
+        # Compute the proposed support according to the loc and scale
+        # estimates.
+        a_hat = loc_hat + a * scale_hat
+        b_hat = loc_hat + b * scale_hat
+
+        # Use the moment-based estimates if they are compatible with the data.
+        data_a = np.min(data)
+        data_b = np.max(data)
+        if a_hat < data_a and data_b < b_hat:
+            return loc_hat, scale_hat
+
+        # Otherwise find other estimates that are compatible with the data.
+        data_width = data_b - data_a
+        rel_margin = 0.1
+        margin = data_width * rel_margin
+
+        # For a finite interval, both the location and scale
+        # should have interesting values.
+        if support_width < np.inf:
+            loc_hat = (data_a - a) - margin
+            scale_hat = (data_width + 2 * margin) / support_width
+            return loc_hat, scale_hat
+
+        # For a one-sided interval, use only an interesting location parameter.
+        if a > -np.inf:
+            return (data_a - a) - margin, 1
+        elif b < np.inf:
+            return (data_b - b) + margin, 1
+        else:
+            raise RuntimeError
+
+    def fit_loc_scale(self, data, *args):
+        """
+        Estimate loc and scale parameters from data using 1st and 2nd moments.
+
+        Parameters
+        ----------
+        data : array_like
+            Data to fit.
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information).
+
+        Returns
+        -------
+        Lhat : float
+            Estimated location parameter for the data.
+        Shat : float
+            Estimated scale parameter for the data.
+
+        """
+        mu, mu2 = self.stats(*args, **{'moments': 'mv'})
+        tmp = asarray(data)
+        muhat = tmp.mean()
+        mu2hat = tmp.var()
+        Shat = sqrt(mu2hat / mu2)
+        with np.errstate(invalid='ignore'):
+            Lhat = muhat - Shat*mu
+        if not np.isfinite(Lhat):
+            Lhat = 0
+        if not (np.isfinite(Shat) and (0 < Shat)):
+            Shat = 1
+        return Lhat, Shat
+
+    def _entropy(self, *args):
+        def integ(x):
+            val = self._pdf(x, *args)
+            return entr(val)
+
+        # upper limit is often inf, so suppress warnings when integrating
+        _a, _b = self._get_support(*args)
+        with np.errstate(over='ignore'):
+            h = integrate.quad(integ, _a, _b)[0]
+
+        if not np.isnan(h):
+            return h
+        else:
+            # try with different limits if integration problems
+            low, upp = self.ppf([1e-10, 1. - 1e-10], *args)
+            if np.isinf(_b):
+                upper = upp
+            else:
+                upper = _b
+            if np.isinf(_a):
+                lower = low
+            else:
+                lower = _a
+            return integrate.quad(integ, lower, upper)[0]
+
+    def expect(self, func=None, args=(), loc=0, scale=1, lb=None, ub=None,
+               conditional=False, **kwds):
+        """Calculate expected value of a function with respect to the
+        distribution by numerical integration.
+
+        The expected value of a function ``f(x)`` with respect to a
+        distribution ``dist`` is defined as::
+
+                    ub
+            E[f(x)] = Integral(f(x) * dist.pdf(x)),
+                    lb
+
+        where ``ub`` and ``lb`` are arguments and ``x`` has the ``dist.pdf(x)``
+        distribution. If the bounds ``lb`` and ``ub`` correspond to the
+        support of the distribution, e.g. ``[-inf, inf]`` in the default
+        case, then the integral is the unrestricted expectation of ``f(x)``.
+        Also, the function ``f(x)`` may be defined such that ``f(x)`` is ``0``
+        outside a finite interval in which case the expectation is
+        calculated within the finite range ``[lb, ub]``.
+
+        Parameters
+        ----------
+        func : callable, optional
+            Function for which integral is calculated. Takes only one argument.
+            The default is the identity mapping f(x) = x.
+        args : tuple, optional
+            Shape parameters of the distribution.
+        loc : float, optional
+            Location parameter (default=0).
+        scale : float, optional
+            Scale parameter (default=1).
+        lb, ub : scalar, optional
+            Lower and upper bound for integration. Default is set to the
+            support of the distribution.
+        conditional : bool, optional
+            If True, the integral is corrected by the conditional probability
+            of the integration interval.  The return value is the expectation
+            of the function, conditional on being in the given interval.
+            Default is False.
+
+        Additional keyword arguments are passed to the integration routine.
+
+        Returns
+        -------
+        expect : float
+            The calculated expected value.
+
+        Notes
+        -----
+        The integration behavior of this function is inherited from
+        `scipy.integrate.quad`. Neither this function nor
+        `scipy.integrate.quad` can verify whether the integral exists or is
+        finite. For example ``cauchy(0).mean()`` returns ``np.nan`` and
+        ``cauchy(0).expect()`` returns ``0.0``.
+
+        Likewise, the accuracy of results is not verified by the function.
+        `scipy.integrate.quad` is typically reliable for integrals that are
+        numerically favorable, but it is not guaranteed to converge
+        to a correct value for all possible intervals and integrands. This
+        function is provided for convenience; for critical applications,
+        check results against other integration methods.
+
+        The function is not vectorized.
+
+        Examples
+        --------
+
+        To understand the effect of the bounds of integration consider
+
+        >>> from scipy.stats import expon
+        >>> expon(1).expect(lambda x: 1, lb=0.0, ub=2.0)
+        0.6321205588285578
+
+        This is close to
+
+        >>> expon(1).cdf(2.0) - expon(1).cdf(0.0)
+        0.6321205588285577
+
+        If ``conditional=True``
+
+        >>> expon(1).expect(lambda x: 1, lb=0.0, ub=2.0, conditional=True)
+        1.0000000000000002
+
+        The slight deviation from 1 is due to numerical integration.
+
+        The integrand can be treated as a complex-valued function
+        by passing ``complex_func=True`` to `scipy.integrate.quad` .
+
+        >>> import numpy as np
+        >>> from scipy.stats import vonmises
+        >>> res = vonmises(loc=2, kappa=1).expect(lambda x: np.exp(1j*x),
+        ...                                       complex_func=True)
+        >>> res
+        (-0.18576377217422957+0.40590124735052263j)
+
+        >>> np.angle(res)  # location of the (circular) distribution
+        2.0
+
+        """
+        lockwds = {'loc': loc,
+                   'scale': scale}
+        self._argcheck(*args)
+        _a, _b = self._get_support(*args)
+        if func is None:
+            def fun(x, *args):
+                return x * self.pdf(x, *args, **lockwds)
+        else:
+            def fun(x, *args):
+                return func(x) * self.pdf(x, *args, **lockwds)
+        if lb is None:
+            lb = loc + _a * scale
+        if ub is None:
+            ub = loc + _b * scale
+
+        cdf_bounds = self.cdf([lb, ub], *args, **lockwds)
+        invfac = cdf_bounds[1] - cdf_bounds[0]
+
+        kwds['args'] = args
+
+        # split interval to help integrator w/ infinite support; see gh-8928
+        alpha = 0.05  # split body from tails at probability mass `alpha`
+        inner_bounds = np.array([alpha, 1-alpha])
+        cdf_inner_bounds = cdf_bounds[0] + invfac * inner_bounds
+        c, d = loc + self._ppf(cdf_inner_bounds, *args) * scale
+
+        # Do not silence warnings from integration.
+        lbc = integrate.quad(fun, lb, c, **kwds)[0]
+        cd = integrate.quad(fun, c, d, **kwds)[0]
+        dub = integrate.quad(fun, d, ub, **kwds)[0]
+        vals = (lbc + cd + dub)
+
+        if conditional:
+            vals /= invfac
+        return np.array(vals)[()]  # make it a numpy scalar like other methods
+
+    def _param_info(self):
+        shape_info = self._shape_info()
+        loc_info = _ShapeInfo("loc", False, (-np.inf, np.inf), (False, False))
+        scale_info = _ShapeInfo("scale", False, (0, np.inf), (False, False))
+        param_info = shape_info + [loc_info, scale_info]
+        return param_info
+
+    # For now, _delta_cdf is a private method.
+    def _delta_cdf(self, x1, x2, *args, loc=0, scale=1):
+        """
+        Compute CDF(x2) - CDF(x1).
+
+        Where x1 is greater than the median, compute SF(x1) - SF(x2),
+        otherwise compute CDF(x2) - CDF(x1).
+
+        This function is only useful if `dist.sf(x, ...)` has an implementation
+        that is numerically more accurate than `1 - dist.cdf(x, ...)`.
+        """
+        cdf1 = self.cdf(x1, *args, loc=loc, scale=scale)
+        # Possible optimizations (needs investigation-these might not be
+        # better):
+        # * Use xpx.apply_where instead of np.where
+        # * Instead of cdf1 > 0.5, compare x1 to the median.
+        result = np.where(cdf1 > 0.5,
+                          (self.sf(x1, *args, loc=loc, scale=scale)
+                           - self.sf(x2, *args, loc=loc, scale=scale)),
+                          self.cdf(x2, *args, loc=loc, scale=scale) - cdf1)
+        if result.ndim == 0:
+            result = result[()]
+        return result
+
+
+# Helpers for the discrete distributions
+def _drv2_moment(self, n, *args):
+    """Non-central moment of discrete distribution."""
+    def fun(x):
+        return np.power(x, n) * self._pmf(x, *args)
+
+    _a, _b = self._get_support(*args)
+    return _expect(fun, _a, _b, self._ppf(0.5, *args), self.inc)
+
+
+def _drv2_ppfsingle(self, q, *args):  # Use basic bisection algorithm
+    _a, _b = self._get_support(*args)
+    b = _b
+    a = _a
+
+    step = 10
+    if isinf(b):            # Be sure ending point is > q
+        b = float(max(100*q, 10))
+        while 1:
+            if b >= _b:
+                qb = 1.0
+                break
+            qb = self._cdf(b, *args)
+            if (qb < q):
+                b += step
+                step *= 2
+            else:
+                break
+    else:
+        qb = 1.0
+
+    step = 10
+    if isinf(a):    # be sure starting point < q
+        a = float(min(-100*q, -10))
+        while 1:
+            if a <= _a:
+                qb = 0.0
+                break
+            qa = self._cdf(a, *args)
+            if (qa > q):
+                a -= step
+                step *= 2
+            else:
+                break
+    else:
+        qa = self._cdf(a, *args)
+
+    if np.isinf(a) or np.isinf(b):
+        message = "Arguments that bracket the requested quantile could not be found."
+        raise RuntimeError(message)
+
+    # maximum number of bisections within the normal float64s
+    # maxiter = int(np.log2(finfo.max) - np.log2(finfo.smallest_normal))
+    maxiter = 2046
+    for i in range(maxiter):
+        if (qa == q):
+            return a
+        if (qb == q):
+            return b
+        if b <= a+1:
+            if qa > q:
+                return a
+            else:
+                return b
+        c = int((a+b)/2.0)
+        qc = self._cdf(c, *args)
+        if (qc < q):
+            if a != c:
+                a = c
+            else:
+                raise RuntimeError('updating stopped, endless loop')
+            qa = qc
+        elif (qc > q):
+            if b != c:
+                b = c
+            else:
+                raise RuntimeError('updating stopped, endless loop')
+            qb = qc
+        else:
+            return c
+
+
+# Must over-ride one of _pmf or _cdf or pass in
+#  x_k, p(x_k) lists in initialization
+
+
+class rv_discrete(rv_generic):
+    """A generic discrete random variable class meant for subclassing.
+
+    `rv_discrete` is a base class to construct specific distribution classes
+    and instances for discrete random variables. It can also be used
+    to construct an arbitrary distribution defined by a list of support
+    points and corresponding probabilities.
+
+    Parameters
+    ----------
+    a : float, optional
+        Lower bound of the support of the distribution, default: 0
+    b : float, optional
+        Upper bound of the support of the distribution, default: plus infinity
+    moment_tol : float, optional
+        The tolerance for the generic calculation of moments.
+    values : tuple of two array_like, optional
+        ``(xk, pk)`` where ``xk`` are integers and ``pk`` are the non-zero
+        probabilities between 0 and 1 with ``sum(pk) = 1``. ``xk``
+        and ``pk`` must have the same shape, and ``xk`` must be unique.
+    inc : int, optional
+        Increment for the support of the distribution.
+        Default is 1. (other values have not been tested)
+    badvalue : float, optional
+        The value in a result arrays that indicates a value that for which
+        some argument restriction is violated, default is np.nan.
+    name : str, optional
+        The name of the instance. This string is used to construct the default
+        example for distributions.
+    longname : str, optional
+        This string is used as part of the first line of the docstring returned
+        when a subclass has no docstring of its own. Note: `longname` exists
+        for backwards compatibility, do not use for new subclasses.
+    shapes : str, optional
+        The shape of the distribution. For example "m, n" for a distribution
+        that takes two integers as the two shape arguments for all its methods
+        If not provided, shape parameters will be inferred from
+        the signatures of the private methods, ``_pmf`` and ``_cdf`` of
+        the instance.
+    seed : {None, int, `numpy.random.Generator`, `numpy.random.RandomState`}, optional
+        If `seed` is None (or `np.random`), the `numpy.random.RandomState`
+        singleton is used.
+        If `seed` is an int, a new ``RandomState`` instance is used,
+        seeded with `seed`.
+        If `seed` is already a ``Generator`` or ``RandomState`` instance then
+        that instance is used.
+
+    Attributes
+    ----------
+    a, b : float, optional
+        Lower/upper bound of the support of the unshifted/unscaled distribution.
+        This value is unaffected by the `loc` and `scale` parameters.
+        To calculate the support of the shifted/scaled distribution,
+        use the `support` method.
+
+    Methods
+    -------
+    rvs
+    pmf
+    logpmf
+    cdf
+    logcdf
+    sf
+    logsf
+    ppf
+    isf
+    moment
+    stats
+    entropy
+    expect
+    median
+    mean
+    std
+    var
+    interval
+    __call__
+    support
+
+    Notes
+    -----
+    This class is similar to `rv_continuous`. Whether a shape parameter is
+    valid is decided by an ``_argcheck`` method (which defaults to checking
+    that its arguments are strictly positive.)
+    The main differences are as follows.
+
+    - The support of the distribution is a set of integers.
+    - Instead of the probability density function, ``pdf`` (and the
+      corresponding private ``_pdf``), this class defines the
+      *probability mass function*, `pmf` (and the corresponding
+      private ``_pmf``.)
+    - There is no ``scale`` parameter.
+    - The default implementations of methods (e.g. ``_cdf``) are not designed
+      for distributions with support that is unbounded below (i.e.
+      ``a=-np.inf``), so they must be overridden.
+
+    To create a new discrete distribution, we would do the following:
+
+    >>> from scipy.stats import rv_discrete
+    >>> class poisson_gen(rv_discrete):
+    ...     "Poisson distribution"
+    ...     def _pmf(self, k, mu):
+    ...         return exp(-mu) * mu**k / factorial(k)
+
+    and create an instance::
+
+    >>> poisson = poisson_gen(name="poisson")
+
+    Note that above we defined the Poisson distribution in the standard form.
+    Shifting the distribution can be done by providing the ``loc`` parameter
+    to the methods of the instance. For example, ``poisson.pmf(x, mu, loc)``
+    delegates the work to ``poisson._pmf(x-loc, mu)``.
+
+    **Discrete distributions from a list of probabilities**
+
+    Alternatively, you can construct an arbitrary discrete rv defined
+    on a finite set of values ``xk`` with ``Prob{X=xk} = pk`` by using the
+    ``values`` keyword argument to the `rv_discrete` constructor.
+
+    **Deepcopying / Pickling**
+
+    If a distribution or frozen distribution is deepcopied (pickled/unpickled,
+    etc.), any underlying random number generator is deepcopied with it. An
+    implication is that if a distribution relies on the singleton RandomState
+    before copying, it will rely on a copy of that random state after copying,
+    and ``np.random.seed`` will no longer control the state.
+
+    Examples
+    --------
+    Custom made discrete distribution:
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> xk = np.arange(7)
+    >>> pk = (0.1, 0.2, 0.3, 0.1, 0.1, 0.0, 0.2)
+    >>> custm = stats.rv_discrete(name='custm', values=(xk, pk))
+    >>>
+    >>> import matplotlib.pyplot as plt
+    >>> fig, ax = plt.subplots(1, 1)
+    >>> ax.plot(xk, custm.pmf(xk), 'ro', ms=12, mec='r')
+    >>> ax.vlines(xk, 0, custm.pmf(xk), colors='r', lw=4)
+    >>> plt.show()
+
+    Random number generation:
+
+    >>> R = custm.rvs(size=100)
+
+    """
+    def __new__(cls, a=0, b=inf, name=None, badvalue=None,
+                moment_tol=1e-8, values=None, inc=1, longname=None,
+                shapes=None, seed=None):
+
+        if values is not None:
+            # dispatch to a subclass
+            return super().__new__(rv_sample)
+        else:
+            # business as usual
+            return super().__new__(cls)
+
+    def __init__(self, a=0, b=inf, name=None, badvalue=None,
+                 moment_tol=1e-8, values=None, inc=1, longname=None,
+                 shapes=None, seed=None):
+
+        super().__init__(seed)
+
+        # cf generic freeze
+        self._ctor_param = dict(
+            a=a, b=b, name=name, badvalue=badvalue,
+            moment_tol=moment_tol, values=values, inc=inc,
+            longname=longname, shapes=shapes, seed=seed)
+
+        if badvalue is None:
+            badvalue = nan
+        self.badvalue = badvalue
+        self.a = a
+        self.b = b
+        self.moment_tol = moment_tol
+        self.inc = inc
+        self.shapes = shapes
+
+        if values is not None:
+            raise ValueError("rv_discrete.__init__(..., values != None, ...)")
+
+        self._construct_argparser(meths_to_inspect=[self._pmf, self._cdf],
+                                  locscale_in='loc=0',
+                                  # scale=1 for discrete RVs
+                                  locscale_out='loc, 1')
+        self._attach_methods()
+        self._construct_docstrings(name, longname)
+
+    def __getstate__(self):
+        dct = self.__dict__.copy()
+        # these methods will be remade in __setstate__
+        attrs = ["_parse_args", "_parse_args_stats", "_parse_args_rvs",
+                 "_cdfvec", "_ppfvec", "generic_moment"]
+        [dct.pop(attr, None) for attr in attrs]
+        return dct
+
+    def _attach_methods(self):
+        """Attaches dynamically created methods to the rv_discrete instance."""
+        self._cdfvec = vectorize(self._cdf_single, otypes='d')
+        self.vecentropy = vectorize(self._entropy)
+
+        # _attach_methods is responsible for calling _attach_argparser_methods
+        self._attach_argparser_methods()
+
+        # nin correction needs to be after we know numargs
+        # correct nin for generic moment vectorization
+        _vec_generic_moment = vectorize(_drv2_moment, otypes='d')
+        _vec_generic_moment.nin = self.numargs + 2
+        self.generic_moment = types.MethodType(_vec_generic_moment, self)
+
+        # correct nin for ppf vectorization
+        _vppf = vectorize(_drv2_ppfsingle, otypes='d')
+        _vppf.nin = self.numargs + 2
+        self._ppfvec = types.MethodType(_vppf, self)
+
+        # now that self.numargs is defined, we can adjust nin
+        self._cdfvec.nin = self.numargs + 1
+
+    def _construct_docstrings(self, name, longname):
+        if name is None:
+            name = 'Distribution'
+        self.name = name
+
+        # generate docstring for subclass instances
+        if longname is None:
+            if name[0] in ['aeiouAEIOU']:
+                hstr = "An "
+            else:
+                hstr = "A "
+            longname = hstr + name
+
+        if sys.flags.optimize < 2:
+            # Skip adding docstrings if interpreter is run with -OO
+            if self.__doc__ is None:
+                self._construct_default_doc(longname=longname,
+                                            docdict=docdict_discrete,
+                                            discrete='discrete')
+            else:
+                dct = dict(distdiscrete)
+                self._construct_doc(docdict_discrete, dct.get(self.name))
+
+            # discrete RV do not have the scale parameter, remove it
+            self.__doc__ = self.__doc__.replace(
+                '\n    scale : array_like, '
+                'optional\n        scale parameter (default=1)', '')
+
+    def _updated_ctor_param(self):
+        """Return the current version of _ctor_param, possibly updated by user.
+
+        Used by freezing.
+        Keep this in sync with the signature of __init__.
+        """
+        dct = self._ctor_param.copy()
+        dct['a'] = self.a
+        dct['b'] = self.b
+        dct['badvalue'] = self.badvalue
+        dct['moment_tol'] = self.moment_tol
+        dct['inc'] = self.inc
+        dct['name'] = self.name
+        dct['shapes'] = self.shapes
+        return dct
+
+    def _nonzero(self, k, *args):
+        return floor(k) == k
+
+    def _pmf(self, k, *args):
+        return self._cdf(k, *args) - self._cdf(k-1, *args)
+
+    def _logpmf(self, k, *args):
+        with np.errstate(divide='ignore'):
+            return log(self._pmf(k, *args))
+
+    def _logpxf(self, k, *args):
+        # continuous distributions have PDF, discrete have PMF, but sometimes
+        # the distinction doesn't matter. This lets us use `_logpxf` for both
+        # discrete and continuous distributions.
+        return self._logpmf(k, *args)
+
+    def _unpack_loc_scale(self, theta):
+        try:
+            loc = theta[-1]
+            scale = 1
+            args = tuple(theta[:-1])
+        except IndexError as e:
+            raise ValueError("Not enough input arguments.") from e
+        return loc, scale, args
+
+    def _cdf_single(self, k, *args):
+        _a, _b = self._get_support(*args)
+        m = arange(int(_a), k+1)
+        return np.sum(self._pmf(m, *args), axis=0)
+
+    def _cdf(self, x, *args):
+        k = floor(x).astype(np.float64)
+        return self._cdfvec(k, *args)
+
+    # generic _logcdf, _sf, _logsf, _ppf, _isf, _rvs defined in rv_generic
+
+    def rvs(self, *args, **kwargs):
+        """Random variates of given type.
+
+        Parameters
+        ----------
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information).
+        loc : array_like, optional
+            Location parameter (default=0).
+        size : int or tuple of ints, optional
+            Defining number of random variates (Default is 1). Note that `size`
+            has to be given as keyword, not as positional argument.
+        random_state : {None, int, `numpy.random.Generator`,
+                        `numpy.random.RandomState`}, optional
+
+            If `random_state` is None (or `np.random`), the
+            `numpy.random.RandomState` singleton is used.
+            If `random_state` is an int, a new ``RandomState`` instance is
+            used, seeded with `random_state`.
+            If `random_state` is already a ``Generator`` or ``RandomState``
+            instance, that instance is used.
+
+        Returns
+        -------
+        rvs : ndarray or scalar
+            Random variates of given `size`.
+
+        """
+        kwargs['discrete'] = True
+        return super().rvs(*args, **kwargs)
+
+    def pmf(self, k, *args, **kwds):
+        """Probability mass function at k of the given RV.
+
+        Parameters
+        ----------
+        k : array_like
+            Quantiles.
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information)
+        loc : array_like, optional
+            Location parameter (default=0).
+
+        Returns
+        -------
+        pmf : array_like
+            Probability mass function evaluated at k
+
+        """
+        args, loc, _ = self._parse_args(*args, **kwds)
+        k, loc = map(asarray, (k, loc))
+        args = tuple(map(asarray, args))
+        _a, _b = self._get_support(*args)
+        k = asarray(k-loc)
+        cond0 = self._argcheck(*args)
+        cond1 = (k >= _a) & (k <= _b)
+        if not isinstance(self, rv_sample):
+            cond1 = cond1 & self._nonzero(k, *args)
+        cond = cond0 & cond1
+        output = zeros(shape(cond), 'd')
+        place(output, (1-cond0) + np.isnan(k), self.badvalue)
+        if np.any(cond):
+            goodargs = argsreduce(cond, *((k,)+args))
+            place(output, cond, np.clip(self._pmf(*goodargs), 0, 1))
+        if output.ndim == 0:
+            return output[()]
+        return output
+
+    def logpmf(self, k, *args, **kwds):
+        """Log of the probability mass function at k of the given RV.
+
+        Parameters
+        ----------
+        k : array_like
+            Quantiles.
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information).
+        loc : array_like, optional
+            Location parameter. Default is 0.
+
+        Returns
+        -------
+        logpmf : array_like
+            Log of the probability mass function evaluated at k.
+
+        """
+        args, loc, _ = self._parse_args(*args, **kwds)
+        k, loc = map(asarray, (k, loc))
+        args = tuple(map(asarray, args))
+        _a, _b = self._get_support(*args)
+        k = asarray(k-loc)
+        cond0 = self._argcheck(*args)
+        cond1 = (k >= _a) & (k <= _b)
+        if not isinstance(self, rv_sample):
+            cond1 = cond1 & self._nonzero(k, *args)
+        cond = cond0 & cond1
+        output = empty(shape(cond), 'd')
+        output.fill(-inf)
+        place(output, (1-cond0) + np.isnan(k), self.badvalue)
+        if np.any(cond):
+            goodargs = argsreduce(cond, *((k,)+args))
+            place(output, cond, self._logpmf(*goodargs))
+        if output.ndim == 0:
+            return output[()]
+        return output
+
+    def cdf(self, k, *args, **kwds):
+        """Cumulative distribution function of the given RV.
+
+        Parameters
+        ----------
+        k : array_like, int
+            Quantiles.
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information).
+        loc : array_like, optional
+            Location parameter (default=0).
+
+        Returns
+        -------
+        cdf : ndarray
+            Cumulative distribution function evaluated at `k`.
+
+        """
+        args, loc, _ = self._parse_args(*args, **kwds)
+        k, loc = map(asarray, (k, loc))
+        args = tuple(map(asarray, args))
+        _a, _b = self._get_support(*args)
+        k = asarray(k-loc)
+        cond0 = self._argcheck(*args)
+        cond1 = (k >= _a) & (k < _b)
+        cond2 = (k >= _b)
+        cond3 = np.isneginf(k)
+        cond = cond0 & cond1 & np.isfinite(k)
+
+        output = zeros(shape(cond), 'd')
+        place(output, cond2*(cond0 == cond0), 1.0)
+        place(output, cond3*(cond0 == cond0), 0.0)
+        place(output, (1-cond0) + np.isnan(k), self.badvalue)
+
+        if np.any(cond):
+            goodargs = argsreduce(cond, *((k,)+args))
+            place(output, cond, np.clip(self._cdf(*goodargs), 0, 1))
+        if output.ndim == 0:
+            return output[()]
+        return output
+
+    def logcdf(self, k, *args, **kwds):
+        """Log of the cumulative distribution function at k of the given RV.
+
+        Parameters
+        ----------
+        k : array_like, int
+            Quantiles.
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information).
+        loc : array_like, optional
+            Location parameter (default=0).
+
+        Returns
+        -------
+        logcdf : array_like
+            Log of the cumulative distribution function evaluated at k.
+
+        """
+        args, loc, _ = self._parse_args(*args, **kwds)
+        k, loc = map(asarray, (k, loc))
+        args = tuple(map(asarray, args))
+        _a, _b = self._get_support(*args)
+        k = asarray(k-loc)
+        cond0 = self._argcheck(*args)
+        cond1 = (k >= _a) & (k < _b)
+        cond2 = (k >= _b)
+        cond = cond0 & cond1
+        output = empty(shape(cond), 'd')
+        output.fill(-inf)
+        place(output, (1-cond0) + np.isnan(k), self.badvalue)
+        place(output, cond2*(cond0 == cond0), 0.0)
+
+        if np.any(cond):
+            goodargs = argsreduce(cond, *((k,)+args))
+            place(output, cond, self._logcdf(*goodargs))
+        if output.ndim == 0:
+            return output[()]
+        return output
+
+    def sf(self, k, *args, **kwds):
+        """Survival function (1 - `cdf`) at k of the given RV.
+
+        Parameters
+        ----------
+        k : array_like
+            Quantiles.
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information).
+        loc : array_like, optional
+            Location parameter (default=0).
+
+        Returns
+        -------
+        sf : array_like
+            Survival function evaluated at k.
+
+        """
+        args, loc, _ = self._parse_args(*args, **kwds)
+        k, loc = map(asarray, (k, loc))
+        args = tuple(map(asarray, args))
+        _a, _b = self._get_support(*args)
+        k = asarray(k-loc)
+        cond0 = self._argcheck(*args)
+        cond1 = (k >= _a) & (k < _b)
+        cond2 = ((k < _a) | np.isneginf(k)) & cond0
+        cond = cond0 & cond1 & np.isfinite(k)
+        output = zeros(shape(cond), 'd')
+        place(output, (1-cond0) + np.isnan(k), self.badvalue)
+        place(output, cond2, 1.0)
+        if np.any(cond):
+            goodargs = argsreduce(cond, *((k,)+args))
+            place(output, cond, np.clip(self._sf(*goodargs), 0, 1))
+        if output.ndim == 0:
+            return output[()]
+        return output
+
+    def logsf(self, k, *args, **kwds):
+        """Log of the survival function of the given RV.
+
+        Returns the log of the "survival function," defined as 1 - `cdf`,
+        evaluated at `k`.
+
+        Parameters
+        ----------
+        k : array_like
+            Quantiles.
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information).
+        loc : array_like, optional
+            Location parameter (default=0).
+
+        Returns
+        -------
+        logsf : ndarray
+            Log of the survival function evaluated at `k`.
+
+        """
+        args, loc, _ = self._parse_args(*args, **kwds)
+        k, loc = map(asarray, (k, loc))
+        args = tuple(map(asarray, args))
+        _a, _b = self._get_support(*args)
+        k = asarray(k-loc)
+        cond0 = self._argcheck(*args)
+        cond1 = (k >= _a) & (k < _b)
+        cond2 = (k < _a) & cond0
+        cond = cond0 & cond1
+        output = empty(shape(cond), 'd')
+        output.fill(-inf)
+        place(output, (1-cond0) + np.isnan(k), self.badvalue)
+        place(output, cond2, 0.0)
+        if np.any(cond):
+            goodargs = argsreduce(cond, *((k,)+args))
+            place(output, cond, self._logsf(*goodargs))
+        if output.ndim == 0:
+            return output[()]
+        return output
+
+    def ppf(self, q, *args, **kwds):
+        """Percent point function (inverse of `cdf`) at q of the given RV.
+
+        Parameters
+        ----------
+        q : array_like
+            Lower tail probability.
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information).
+        loc : array_like, optional
+            Location parameter (default=0).
+
+        Returns
+        -------
+        k : array_like
+            Quantile corresponding to the lower tail probability, q.
+
+        Notes
+        -----
+        For discrete distributions, the `cdf` is not strictly invertible. By convention,
+        this method returns the minimum value `k` for which the `cdf` at `k` is at
+        least `q`. There is one exception:  the `ppf` of ``0`` is ``a-1``,
+        where ``a`` is the left endpoint of the support.
+
+        """
+        args, loc, _ = self._parse_args(*args, **kwds)
+        q, loc = map(asarray, (q, loc))
+        args = tuple(map(asarray, args))
+        _a, _b = self._get_support(*args)
+        cond0 = self._argcheck(*args) & (loc == loc)
+        cond1 = (q > 0) & (q < 1)
+        cond2 = (q == 0) & cond0
+        cond3 = (q == 1) & cond0
+        cond = cond0 & cond1
+        output = np.full(shape(cond), fill_value=self.badvalue, dtype='d')
+        # output type 'd' to handle nin and inf
+
+        place(output, cond2, argsreduce(cond2, _a-1 + loc)[0])
+        place(output, cond3, argsreduce(cond3, _b + loc)[0])
+        if np.any(cond):
+            goodargs = argsreduce(cond, *((q,)+args+(loc,)))
+            loc, goodargs = goodargs[-1], goodargs[:-1]
+            place(output, cond, self._ppf(*goodargs) + loc)
+
+        if output.ndim == 0:
+            return output[()]
+        return output
+
+    def isf(self, q, *args, **kwds):
+        """Inverse survival function (inverse of `sf`) at q of the given RV.
+
+        Parameters
+        ----------
+        q : array_like
+            Upper tail probability.
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information).
+        loc : array_like, optional
+            Location parameter (default=0).
+
+        Returns
+        -------
+        k : ndarray or scalar
+            Quantile corresponding to the upper tail probability, q.
+
+        Notes
+        -----
+        For discrete distributions, the `sf` is not strictly invertible. By convention,
+        this method returns the minimum value `k` for which the `sf` at `k` is
+        no greater than `q`. There is one exception: the `isf` of ``1`` is ``a-1``,
+        where ``a`` is the left endpoint of the support.
+
+        """
+        args, loc, _ = self._parse_args(*args, **kwds)
+        q, loc = map(asarray, (q, loc))
+        args = tuple(map(asarray, args))
+        _a, _b = self._get_support(*args)
+        cond0 = self._argcheck(*args) & (loc == loc)
+        cond1 = (q > 0) & (q < 1)
+        cond2 = (q == 1) & cond0
+        cond3 = (q == 0) & cond0
+        cond = cond0 & cond1
+
+        # same problem as with ppf; copied from ppf and changed
+        output = np.full(shape(cond), fill_value=self.badvalue, dtype='d')
+        # output type 'd' to handle nin and inf
+        lower_bound = _a - 1 + loc
+        upper_bound = _b + loc
+        place(output, cond2, argsreduce(cond2, lower_bound)[0])
+        place(output, cond3, argsreduce(cond3, upper_bound)[0])
+
+        # call place only if at least 1 valid argument
+        if np.any(cond):
+            goodargs = argsreduce(cond, *((q,)+args+(loc,)))
+            loc, goodargs = goodargs[-1], goodargs[:-1]
+            # PB same as ticket 766
+            place(output, cond, self._isf(*goodargs) + loc)
+
+        if output.ndim == 0:
+            return output[()]
+        return output
+
+    def _entropy(self, *args):
+        if hasattr(self, 'pk'):
+            return stats.entropy(self.pk)
+        else:
+            _a, _b = self._get_support(*args)
+            return _expect(lambda x: entr(self._pmf(x, *args)),
+                           _a, _b, self._ppf(0.5, *args), self.inc)
+
+    def expect(self, func=None, args=(), loc=0, lb=None, ub=None,
+               conditional=False, maxcount=1000, tolerance=1e-10, chunksize=32):
+        """
+        Calculate expected value of a function with respect to the distribution
+        for discrete distribution by numerical summation.
+
+        Parameters
+        ----------
+        func : callable, optional
+            Function for which the expectation value is calculated.
+            Takes only one argument.
+            The default is the identity mapping f(k) = k.
+        args : tuple, optional
+            Shape parameters of the distribution.
+        loc : float, optional
+            Location parameter.
+            Default is 0.
+        lb, ub : int, optional
+            Lower and upper bound for the summation, default is set to the
+            support of the distribution, inclusive (``lb <= k <= ub``).
+        conditional : bool, optional
+            If true then the expectation is corrected by the conditional
+            probability of the summation interval. The return value is the
+            expectation of the function, `func`, conditional on being in
+            the given interval (k such that ``lb <= k <= ub``).
+            Default is False.
+        maxcount : int, optional
+            Maximal number of terms to evaluate (to avoid an endless loop for
+            an infinite sum). Default is 1000.
+        tolerance : float, optional
+            Absolute tolerance for the summation. Default is 1e-10.
+        chunksize : int, optional
+            Iterate over the support of a distributions in chunks of this size.
+            Default is 32.
+
+        Returns
+        -------
+        expect : float
+            Expected value.
+
+        Notes
+        -----
+        For heavy-tailed distributions, the expected value may or
+        may not exist,
+        depending on the function, `func`. If it does exist, but the
+        sum converges
+        slowly, the accuracy of the result may be rather low. For instance, for
+        ``zipf(4)``, accuracy for mean, variance in example is only 1e-5.
+        increasing `maxcount` and/or `chunksize` may improve the result,
+        but may also make zipf very slow.
+
+        The function is not vectorized.
+
+        """
+        # Although `args` is just the shape parameters, `poisson_binom` needs this
+        # to split the vector-valued shape into a tuple of separate shapes
+        args, _, _ = self._parse_args(*args)
+
+        if func is None:
+            def fun(x):
+                # loc and args from outer scope
+                return (x+loc)*self._pmf(x, *args)
+        else:
+            def fun(x):
+                # loc and args from outer scope
+                return func(x+loc)*self._pmf(x, *args)
+        # used pmf because _pmf does not check support in randint and there
+        # might be problems(?) with correct self.a, self.b at this stage maybe
+        # not anymore, seems to work now with _pmf
+
+        _a, _b = self._get_support(*args)
+        if lb is None:
+            lb = _a
+        else:
+            lb = lb - loc   # convert bound for standardized distribution
+        if ub is None:
+            ub = _b
+        else:
+            ub = ub - loc   # convert bound for standardized distribution
+        if conditional:
+            invfac = self.sf(lb-1, *args) - self.sf(ub, *args)
+        else:
+            invfac = 1.0
+
+        if isinstance(self, rv_sample):
+            res = self._expect(fun, lb, ub)
+            return res / invfac
+
+        # iterate over the support, starting from the median
+        x0 = self._ppf(0.5, *args)
+        res = _expect(fun, lb, ub, x0, self.inc, maxcount, tolerance, chunksize)
+        return res / invfac
+
+    def _param_info(self):
+        shape_info = self._shape_info()
+        loc_info = _ShapeInfo("loc", True, (-np.inf, np.inf), (False, False))
+        param_info = shape_info + [loc_info]
+        return param_info
+
+    # these methods are identical to those of `rv_generic` except that
+    # they don't accept the `scale` parameter. They need their own copy
+    # of the methods so we can adjust the documentation.
+
+    def entropy(self, *args, **kwargs):
+        return super().entropy(*args, **kwargs)
+
+    def interval(self, confidence, *args, **kwargs):
+        return super().interval(confidence, *args, **kwargs)
+
+    def mean(self, *args, **kwargs):
+        return super().mean(*args, **kwargs)
+
+    def median(self, *args, **kwargs):
+        return super().median(*args, **kwargs)
+
+    def moment(self, order, *args, **kwargs):
+        return super().moment(order, *args, **kwargs)
+
+    def stats(self, *args, **kwargs):
+        return super().stats(*args, **kwargs)
+
+    def std(self, *args, **kwargs):
+        return super().std(*args, **kwargs)
+
+    def support(self, *args, **kwargs):
+        return super().support(*args, **kwargs)
+
+    def var(self, *args, **kwargs):
+        return super().var(*args, **kwargs)
+
+
+_remove_scale_methods = ['entropy', 'interval', 'mean', 'median',
+                         'moment', 'stats', 'std', 'support', 'var']
+for method_name in _remove_scale_methods:
+    # remove `scale` parameter from method documentation
+    method = getattr(rv_discrete, method_name)
+    doc = FunctionDoc(method)
+    doc['Parameters'] = [p for p in doc['Parameters'] if p.name != 'scale']
+    doc = str(doc).split("\n", 1)[1].lstrip(" \n")  # remove signature
+    method.__doc__ = doc
+del method_name, method, doc  # pyrefly:ignore[unbound-name]
+
+
+def _expect(fun, lb, ub, x0, inc, maxcount=1000, tolerance=1e-10,
+            chunksize=32):
+    """Helper for computing the expectation value of `fun`."""
+    # short-circuit if the support size is small enough
+    if (ub - lb) <= chunksize:
+        supp = np.arange(lb, ub+1, inc)
+        vals = fun(supp)
+        return np.sum(vals)
+
+    # otherwise, iterate starting from x0
+    if x0 < lb:
+        x0 = lb
+    if x0 > ub:
+        x0 = ub
+
+    count, tot = 0, 0.
+    # iterate over [x0, ub] inclusive
+    for x in _iter_chunked(x0, ub+1, chunksize=chunksize, inc=inc):
+        count += x.size
+        delta = np.sum(fun(x))
+        tot += delta
+        if abs(delta) < tolerance * x.size:
+            break
+        if count > maxcount:
+            warnings.warn('expect(): sum did not converge',
+                          RuntimeWarning, stacklevel=3)
+            return tot
+
+    # iterate over [lb, x0)
+    for x in _iter_chunked(x0-1, lb-1, chunksize=chunksize, inc=-inc):
+        count += x.size
+        delta = np.sum(fun(x))
+        tot += delta
+        if abs(delta) < tolerance * x.size:
+            break
+        if count > maxcount:
+            warnings.warn('expect(): sum did not converge',
+                          RuntimeWarning, stacklevel=3)
+            break
+
+    return tot
+
+
+def _iter_chunked(x0, x1, chunksize=4, inc=1):
+    """Iterate from x0 to x1 in chunks of chunksize and steps inc.
+
+    x0 must be finite, x1 need not be. In the latter case, the iterator is
+    infinite.
+    Handles both x0 < x1 and x0 > x1. In the latter case, iterates downwards
+    (make sure to set inc < 0.)
+
+    >>> from scipy.stats._distn_infrastructure import _iter_chunked
+    >>> [x for x in _iter_chunked(2, 5, inc=2)]
+    [array([2, 4])]
+    >>> [x for x in _iter_chunked(2, 11, inc=2)]
+    [array([2, 4, 6, 8]), array([10])]
+    >>> [x for x in _iter_chunked(2, -5, inc=-2)]
+    [array([ 2,  0, -2, -4])]
+    >>> [x for x in _iter_chunked(2, -9, inc=-2)]
+    [array([ 2,  0, -2, -4]), array([-6, -8])]
+
+    """
+    if inc == 0:
+        raise ValueError('Cannot increment by zero.')
+    if chunksize <= 0:
+        raise ValueError(f'Chunk size must be positive; got {chunksize}.')
+
+    s = 1 if inc > 0 else -1
+    stepsize = abs(chunksize * inc)
+
+    x = np.copy(x0)
+    while (x - x1) * inc < 0:
+        delta = min(stepsize, abs(x - x1))
+        step = delta * s
+        supp = np.arange(x, x + step, inc)
+        x += step
+        yield supp
+
+
+class rv_sample(rv_discrete):
+    """A 'sample' discrete distribution defined by the support and values.
+
+    The ctor ignores most of the arguments, only needs the `values` argument.
+    """
+
+    def __init__(self, a=0, b=inf, name=None, badvalue=None,
+                 moment_tol=1e-8, values=None, inc=1, longname=None,
+                 shapes=None, seed=None):
+
+        super(rv_discrete, self).__init__(seed)
+
+        if values is None:
+            raise ValueError("rv_sample.__init__(..., values=None,...)")
+
+        # cf generic freeze
+        self._ctor_param = dict(
+            a=a, b=b, name=name, badvalue=badvalue,
+            moment_tol=moment_tol, values=values, inc=inc,
+            longname=longname, shapes=shapes, seed=seed)
+
+        if badvalue is None:
+            badvalue = nan
+        self.badvalue = badvalue
+        self.moment_tol = moment_tol
+        self.inc = inc
+        self.shapes = shapes
+        self.vecentropy = self._entropy
+
+        xk, pk = values
+
+        if np.shape(xk) != np.shape(pk):
+            raise ValueError("xk and pk must have the same shape.")
+        if np.less(pk, 0.0).any():
+            raise ValueError("All elements of pk must be non-negative.")
+        if not np.allclose(np.sum(pk), 1):
+            raise ValueError("The sum of provided pk is not 1.")
+        if not len(set(np.ravel(xk))) == np.size(xk):
+            raise ValueError("xk may not contain duplicate values.")
+
+        indx = np.argsort(np.ravel(xk))
+        self.xk = np.take(np.ravel(xk), indx, 0)
+        self.pk = np.take(np.ravel(pk), indx, 0)
+        self.a = self.xk[0]
+        self.b = self.xk[-1]
+
+        self.qvals = np.cumsum(self.pk, axis=0)
+
+        self.shapes = ' '   # bypass inspection
+
+        self._construct_argparser(meths_to_inspect=[self._pmf],
+                                  locscale_in='loc=0',
+                                  # scale=1 for discrete RVs
+                                  locscale_out='loc, 1')
+
+        self._attach_methods()
+
+        self._construct_docstrings(name, longname)
+
+    def __getstate__(self):
+        dct = self.__dict__.copy()
+
+        # these methods will be remade in rv_generic.__setstate__,
+        # which calls rv_generic._attach_methods
+        attrs = ["_parse_args", "_parse_args_stats", "_parse_args_rvs"]
+        [dct.pop(attr, None) for attr in attrs]
+
+        return dct
+
+    def _attach_methods(self):
+        """Attaches dynamically created argparser methods."""
+        self._attach_argparser_methods()
+
+    def _get_support(self, *args):
+        """Return the support of the (unscaled, unshifted) distribution.
+
+        Parameters
+        ----------
+        arg1, arg2, ... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information).
+
+        Returns
+        -------
+        a, b : numeric (float, or int or +/-np.inf)
+            end-points of the distribution's support.
+        """
+        return self.a, self.b
+
+    def _pmf(self, x):
+        return np.select([x == k for k in self.xk],
+                         [np.broadcast_arrays(p, x)[0] for p in self.pk], 0)
+
+    def _cdf(self, x):
+        xx, xxk = np.broadcast_arrays(x[:, None], self.xk)
+        indx = np.argmax(xxk > xx, axis=-1) - 1
+        return self.qvals[indx]
+
+    def _ppf(self, q):
+        qq, sqq = np.broadcast_arrays(q[..., None], self.qvals)
+        indx = argmax(sqq >= qq, axis=-1)
+        return self.xk[indx]
+
+    def _rvs(self, size=None, random_state=None):
+        # Need to define it explicitly, otherwise .rvs() with size=None
+        # fails due to explicit broadcasting in _ppf
+        U = random_state.uniform(size=size)
+        if size is None:
+            U = np.array(U, ndmin=1)
+            Y = self._ppf(U)[0]
+        else:
+            Y = self._ppf(U)
+        return Y
+
+    def _entropy(self):
+        return stats.entropy(self.pk)
+
+    def generic_moment(self, n):
+        n = asarray(n)
+        return np.sum(self.xk**n[np.newaxis, ...] * self.pk, axis=0)
+
+    def _expect(self, fun, lb, ub, *args, **kwds):
+        # ignore all args, just do a brute force summation
+        supp = self.xk[(lb <= self.xk) & (self.xk <= ub)]
+        vals = fun(supp)
+        return np.sum(vals)
+
+
+def _check_shape(argshape, size):
+    """
+    This is a utility function used by `_rvs()` in the class geninvgauss_gen.
+    It compares the tuple argshape to the tuple size.
+
+    Parameters
+    ----------
+    argshape : tuple of integers
+        Shape of the arguments.
+    size : tuple of integers or integer
+        Size argument of rvs().
+
+    Returns
+    -------
+    The function returns two tuples, scalar_shape and bc.
+
+    scalar_shape : tuple
+        Shape to which the 1-d array of random variates returned by
+        _rvs_scalar() is converted when it is copied into the
+        output array of _rvs().
+
+    bc : tuple of booleans
+        bc is a tuple the same length as size. bc[j] is True if the data
+        associated with that index is generated in one call of _rvs_scalar().
+
+    """
+    scalar_shape = []
+    bc = []
+    for argdim, sizedim in zip_longest(argshape[::-1], size[::-1],
+                                       fillvalue=1):
+        if sizedim > argdim or (argdim == sizedim == 1):
+            scalar_shape.append(sizedim)
+            bc.append(True)
+        else:
+            bc.append(False)
+    return tuple(scalar_shape[::-1]), tuple(bc[::-1])
+
+
+def get_distribution_names(namespace_pairs, rv_base_class):
+    """Collect names of statistical distributions and their generators.
+
+    Parameters
+    ----------
+    namespace_pairs : sequence
+        A snapshot of (name, value) pairs in the namespace of a module.
+    rv_base_class : class
+        The base class of random variable generator classes in a module.
+
+    Returns
+    -------
+    distn_names : list of strings
+        Names of the statistical distributions.
+    distn_gen_names : list of strings
+        Names of the generators of the statistical distributions.
+        Note that these are not simply the names of the statistical
+        distributions, with a _gen suffix added.
+
+    """
+    distn_names = []
+    distn_gen_names = []
+    for name, value in namespace_pairs:
+        if name.startswith('_'):
+            continue
+        if name.endswith('_gen') and issubclass(value, rv_base_class):
+            distn_gen_names.append(name)
+        if isinstance(value, rv_base_class):
+            distn_names.append(name)
+    return distn_names, distn_gen_names
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_distr_params.py b/venv/lib/python3.12/site-packages/scipy/stats/_distr_params.py
new file mode 100644
index 0000000000000000000000000000000000000000..3234bae358fffd18b70a008a00110c6f3e348530
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_distr_params.py
@@ -0,0 +1,300 @@
+"""
+Sane parameters for stats.distributions.
+"""
+import numpy as np
+
+distcont = [
+    ['alpha', (3.5704770516650459,)],
+    ['anglit', ()],
+    ['arcsine', ()],
+    ['argus', (1.0,)],
+    ['beta', (2.3098496451481823, 0.62687954300963677)],
+    ['betaprime', (5, 6)],
+    ['bradford', (0.29891359763170633,)],
+    ['burr', (10.5, 4.3)],
+    ['burr12', (10, 4)],
+    ['cauchy', ()],
+    ['chi', (78,)],
+    ['chi2', (55,)],
+    ['cosine', ()],
+    ['crystalball', (2.0, 3.0)],
+    ['dgamma', (1.1023326088288166,)],
+    ['dpareto_lognorm', (3, 1.2, 1.5, 2)],
+    ['dweibull', (2.0685080649914673,)],
+    ['erlang', (10,)],
+    ['expon', ()],
+    ['exponnorm', (1.5,)],
+    ['exponpow', (2.697119160358469,)],
+    ['exponweib', (2.8923945291034436, 1.9505288745913174)],
+    ['f', (29, 18)],
+    ['fatiguelife', (29,)],   # correction numargs = 1
+    ['fisk', (3.0857548622253179,)],
+    ['foldcauchy', (4.7164673455831894,)],
+    ['foldnorm', (1.9521253373555869,)],
+    ['gamma', (1.9932305483800778,)],
+    ['gausshyper', (13.763771604130699, 3.1189636648681431,
+                    2.5145980350183019, 5.1811649903971615)],  # veryslow
+    ['genexpon', (9.1325976465418908, 16.231956600590632, 3.2819552690843983)],
+    ['genextreme', (-0.1,)],
+    ['gengamma', (4.4162385429431925, 3.1193091679242761)],
+    ['gengamma', (4.4162385429431925, -3.1193091679242761)],
+    ['genhalflogistic', (0.77274727809929322,)],
+    ['genhyperbolic', (0.5, 1.5, -0.5,)],
+    ['geninvgauss', (2.3, 1.5)],
+    ['genlogistic', (0.41192440799679475,)],
+    ['gennorm', (1.2988442399460265,)],
+    ['halfgennorm', (0.6748054997000371,)],
+    ['genpareto', (0.1,)],   # use case with finite moments
+    ['gibrat', ()],
+    ['gompertz', (0.94743713075105251,)],
+    ['gumbel_l', ()],
+    ['gumbel_r', ()],
+    ['halfcauchy', ()],
+    ['halflogistic', ()],
+    ['halfnorm', ()],
+    ['hypsecant', ()],
+    ['invgamma', (4.0668996136993067,)],
+    ['invgauss', (0.14546264555347513,)],
+    ['invweibull', (10.58,)],
+    ['irwinhall', (10,)],
+    ['jf_skew_t', (8, 4)],
+    ['johnsonsb', (4.3172675099141058, 3.1837781130785063)],
+    ['johnsonsu', (2.554395574161155, 2.2482281679651965)],
+    ['kappa4', (0.0, 0.0)],
+    ['kappa4', (-0.1, 0.1)],
+    ['kappa4', (0.0, 0.1)],
+    ['kappa4', (0.1, 0.0)],
+    ['kappa3', (1.0,)],
+    ['ksone', (1000,)],  # replace 22 by 100 to avoid failing range, ticket 956
+    ['kstwo', (10,)],
+    ['kstwobign', ()],
+    ['landau', ()],
+    ['laplace', ()],
+    ['laplace_asymmetric', (2,)],
+    ['levy', ()],
+    ['levy_l', ()],
+    ['levy_stable', (1.8, -0.5)],
+    ['loggamma', (0.41411931826052117,)],
+    ['logistic', ()],
+    ['loglaplace', (3.2505926592051435,)],
+    ['lognorm', (0.95368226960575331,)],
+    ['loguniform', (0.01, 1.25)],
+    ['lomax', (1.8771398388773268,)],
+    ['maxwell', ()],
+    ['mielke', (10.4, 4.6)],
+    ['moyal', ()],
+    ['nakagami', (4.9673794866666237,)],
+    ['ncf', (27, 27, 0.41578441799226107)],
+    ['nct', (14, 0.24045031331198066)],
+    ['ncx2', (21, 1.0560465975116415)],
+    ['norm', ()],
+    ['norminvgauss', (1.25, 0.5)],
+    ['pareto', (2.621716532144454,)],
+    ['pearson3', (0.1,)],
+    ['pearson3', (-2,)],
+    ['powerlaw', (1.6591133289905851,)],
+    ['powerlaw', (0.6591133289905851,)],
+    ['powerlognorm', (2.1413923530064087, 0.44639540782048337)],
+    ['powernorm', (4.4453652254590779,)],
+    ['rayleigh', ()],
+    ['rdist', (1.6,)],
+    ['recipinvgauss', (0.63004267809369119,)],
+    ['reciprocal', (0.01, 1.25)],
+    ['rel_breitwigner', (36.545206797050334, )],
+    ['rice', (0.7749725210111873,)],
+    ['semicircular', ()],
+    ['skewcauchy', (0.5,)],
+    ['skewnorm', (4.0,)],
+    ['studentized_range', (3.0, 10.0)],
+    ['t', (2.7433514990818093,)],
+    ['trapezoid', (0.2, 0.8)],
+    ['triang', (0.15785029824528218,)],
+    ['truncexpon', (4.6907725456810478,)],
+    ['truncnorm', (-1.0978730080013919, 2.7306754109031979)],
+    ['truncnorm', (0.1, 2.)],
+    ['truncpareto', (1.8, 5.3)],
+    ['truncpareto', (2, 5)],
+    ['truncpareto', (-2, 5)],
+    ['truncweibull_min', (2.5, 0.25, 1.75)],
+    ['tukeylambda', (3.1321477856738267,)],
+    ['uniform', ()],
+    ['vonmises', (3.9939042581071398,)],
+    ['vonmises_line', (3.9939042581071398,)],
+    ['wald', ()],
+    ['weibull_max', (2.8687961709100187,)],
+    ['weibull_min', (1.7866166930421596,)],
+    ['wrapcauchy', (0.031071279018614728,)]
+]
+
+
+distdiscrete = [
+    ['bernoulli',(0.3,)],
+    ['betabinom', (5, 2.3, 0.63)],
+    ['betanbinom', (5, 9.3, 1)],
+    ['binom', (5, 0.4)],
+    ['boltzmann',(1.4, 19)],
+    ['dlaplace', (0.8,)],  # 0.5
+    ['geom', (0.5,)],
+    ['hypergeom',(30, 12, 6)],
+    ['hypergeom',(21,3,12)],  # numpy.random (3,18,12) numpy ticket:921
+    ['hypergeom',(21,18,11)],  # numpy.random (18,3,11) numpy ticket:921
+    ['nchypergeom_fisher', (140, 80, 60, 0.5)],
+    ['nchypergeom_wallenius', (140, 80, 60, 0.5)],
+    ['logser', (0.6,)],  # re-enabled, numpy ticket:921
+    ['nbinom', (0.4, 0.4)],  # from tickets: 583
+    ['nbinom', (5, 0.5)],
+    ['planck', (0.51,)],   # 4.1
+    ['poisson', (0.6,)],
+    ['poisson_binom', ([0.1, 0.6, 0.7, 0.8],)],
+    ['randint', (7, 31)],
+    ['skellam', (15, 8)],
+    ['zipf', (6.6,)],
+    ['zipfian', (0.75, 15)],
+    ['zipfian', (1.25, 10)],
+    ['yulesimon', (11.0,)],
+    ['nhypergeom', (20, 7, 1)]
+]
+
+
+invdistdiscrete = [
+    # In each of the following, at least one shape parameter is invalid
+    ['hypergeom', (3, 3, 4)],
+    ['nhypergeom', (5, 2, 8)],
+    ['nchypergeom_fisher', (3, 3, 4, 1)],
+    ['nchypergeom_wallenius', (3, 3, 4, 1)],
+    ['bernoulli', (1.5, )],
+    ['binom', (10, 1.5)],
+    ['betabinom', (10, -0.4, -0.5)],
+    ['betanbinom', (10, -0.4, -0.5)],
+    ['boltzmann', (-1, 4)],
+    ['dlaplace', (-0.5, )],
+    ['geom', (1.5, )],
+    ['logser', (1.5, )],
+    ['nbinom', (10, 1.5)],
+    ['planck', (-0.5, )],
+    ['poisson', (-0.5, )],
+    ['poisson_binom', ([-1, 2, 0.5],)],
+    ['randint', (5, 2)],
+    ['skellam', (-5, -2)],
+    ['zipf', (-2, )],
+    ['yulesimon', (-2, )],
+    ['zipfian', (-0.75, 15)]
+]
+
+
+invdistcont = [
+    # In each of the following, at least one shape parameter is invalid
+    ['alpha', (-1, )],
+    ['anglit', ()],
+    ['arcsine', ()],
+    ['argus', (-1, )],
+    ['beta', (-2, 2)],
+    ['betaprime', (-2, 2)],
+    ['bradford', (-1, )],
+    ['burr', (-1, 1)],
+    ['burr12', (-1, 1)],
+    ['cauchy', ()],
+    ['chi', (-1, )],
+    ['chi2', (-1, )],
+    ['cosine', ()],
+    ['crystalball', (-1, 2)],
+    ['dgamma', (-1, )],
+    ['dpareto_lognorm', (3, -1.2, 1.5, 2)],
+    ['dweibull', (-1, )],
+    ['erlang', (-1, )],
+    ['expon', ()],
+    ['exponnorm', (-1, )],
+    ['exponweib', (1, -1)],
+    ['exponpow', (-1, )],
+    ['f', (10, -10)],
+    ['fatiguelife', (-1, )],
+    ['fisk', (-1, )],
+    ['foldcauchy', (-1, )],
+    ['foldnorm', (-1, )],
+    ['genlogistic', (-1, )],
+    ['gennorm', (-1, )],
+    ['genpareto', (np.inf, )],
+    ['genexpon', (1, 2, -3)],
+    ['genextreme', (np.inf, )],
+    ['genhyperbolic', (0.5, -0.5, -1.5,)],
+    ['gausshyper', (1, 2, 3, -4)],
+    ['gamma', (-1, )],
+    ['gengamma', (-1, 0)],
+    ['genhalflogistic', (-1, )],
+    ['geninvgauss', (1, 0)],
+    ['gibrat', ()],
+    ['gompertz', (-1, )],
+    ['gumbel_r', ()],
+    ['gumbel_l', ()],
+    ['halfcauchy', ()],
+    ['halflogistic', ()],
+    ['halfnorm', ()],
+    ['halfgennorm', (-1, )],
+    ['hypsecant', ()],
+    ['invgamma', (-1, )],
+    ['invgauss', (-1, )],
+    ['invweibull', (-1, )],
+    ['irwinhall', (-1,)],
+    ['irwinhall', (0,)],
+    ['irwinhall', (2.5,)],
+    ['jf_skew_t', (-1, 0)],
+    ['johnsonsb', (1, -2)],
+    ['johnsonsu', (1, -2)],
+    ['kappa4', (np.nan, 0)],
+    ['kappa3', (-1, )],
+    ['ksone', (-1, )],
+    ['kstwo', (-1, )],
+    ['kstwobign', ()],
+    ['landau', ()],
+    ['laplace', ()],
+    ['laplace_asymmetric', (-1, )],
+    ['levy', ()],
+    ['levy_l', ()],
+    ['levy_stable', (-1, 1)],
+    ['logistic', ()],
+    ['loggamma', (-1, )],
+    ['loglaplace', (-1, )],
+    ['lognorm', (-1, )],
+    ['loguniform', (10, 5)],
+    ['lomax', (-1, )],
+    ['maxwell', ()],
+    ['mielke', (1, -2)],
+    ['moyal', ()],
+    ['nakagami', (-1, )],
+    ['ncx2', (-1, 2)],
+    ['ncf', (10, 20, -1)],
+    ['nct', (-1, 2)],
+    ['norm', ()],
+    ['norminvgauss', (5, -10)],
+    ['pareto', (-1, )],
+    ['pearson3', (np.nan, )],
+    ['powerlaw', (-1, )],
+    ['powerlognorm', (1, -2)],
+    ['powernorm', (-1, )],
+    ['rdist', (-1, )],
+    ['rayleigh', ()],
+    ['rice', (-1, )],
+    ['recipinvgauss', (-1, )],
+    ['semicircular', ()],
+    ['skewnorm', (np.inf, )],
+    ['studentized_range', (-1, 1)],
+    ['rel_breitwigner', (-2, )],
+    ['t', (-1, )],
+    ['trapezoid', (0, 2)],
+    ['triang', (2, )],
+    ['truncexpon', (-1, )],
+    ['truncnorm', (10, 5)],
+    ['truncpareto', (-1, -5)],
+    ['truncpareto', (1.8, .5)],
+    ['truncweibull_min', (-2.5, 0.25, 1.75)],
+    ['tukeylambda', (np.nan, )],
+    ['uniform', ()],
+    ['vonmises', (-1, )],
+    ['vonmises_line', (-1, )],
+    ['wald', ()],
+    ['weibull_min', (-1, )],
+    ['weibull_max', (-1, )],
+    ['wrapcauchy', (2, )],
+    ['reciprocal', (15, 10)],
+    ['skewcauchy', (2, )]
+]
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_distribution_infrastructure.py b/venv/lib/python3.12/site-packages/scipy/stats/_distribution_infrastructure.py
new file mode 100644
index 0000000000000000000000000000000000000000..ab05372648e813dc962c4ddcd3fc5171dcab07c0
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_distribution_infrastructure.py
@@ -0,0 +1,5764 @@
+import functools
+from abc import ABC, abstractmethod
+from functools import cached_property
+from types import GenericAlias
+import inspect
+import math
+
+import numpy as np
+from numpy import inf
+
+from scipy._lib._array_api import xp_capabilities, xp_promote
+from scipy._lib._util import _rng_spawn
+from scipy._lib._docscrape import ClassDoc, NumpyDocString
+from scipy._external import array_api_extra as xpx
+from scipy import special, stats
+from scipy.special._ufuncs import _log1mexp
+from scipy.integrate import tanhsinh as _tanhsinh, nsum
+from scipy.optimize import elementwise
+from scipy.stats._probability_distribution import _ProbabilityDistribution
+from scipy.stats import qmc
+
+# in case we need to distinguish between None and not specified
+# Typically this is used to determine whether the tolerance has been set by the
+# user and make a decision about which method to use to evaluate a distribution
+# function. Sometimes, the logic does not consider the value of the tolerance,
+# only whether this has been defined or not. This is not intended to be the
+# best possible logic; the intent is to establish the structure, which can
+# be refined in follow-up work.
+# See https://github.com/scipy/scipy/pull/21050#discussion_r1714195433.
+_null = object()
+def _isnull(x):
+    return type(x) is object or x is None
+
+__all__ = ['make_distribution', 'Mixture', 'order_statistic',
+           'truncate', 'abs', 'exp', 'log']
+
+# Could add other policies for broadcasting and edge/out-of-bounds case handling
+# For instance, when edge case handling is known not to be needed, it's much
+# faster to turn it off, but it might still be nice to have array conversion
+# and shaping done so the user doesn't need to be so careful.
+_SKIP_ALL = "skip_all"
+# Other cache policies would be useful, too.
+_NO_CACHE = "no_cache"
+
+# TODO:
+#  Test sample dtypes
+#  Add dtype kwarg (especially for distributions with no parameters)
+#  Rewrite `test_continuous` without Hypothesis, more modular tests that are easier to
+#    run individually.
+#  Add distribution-specific tests - just enough to confirm that distribution is the
+#    one it is supposed to be; maybe check finite vs undefined vs infinite moments.
+#  `_tanhsinh` special case when there are no abscissae between the limits
+#     example: cdf of uniform betweeen 1.0 and np.nextafter(1.0, np.inf)
+#  implement symmetric distribution (take advantage of symmetry)
+#  implement composite distribution (for using different implementations depending on
+#    shape parameters - e.g. t distribution with df = np.inf delegates to normal)
+#  Add array API support
+#  Investigate use `median` information throughout, e.g. to improve integration of
+#    CDF or to provide initial bracket for ICDF. (Only if `_median_formula` is 
+#    provided.)
+#  Document user tips for faster execution:
+#  - pass NumPy arrays
+#  - pass inputs of floating point type (not integers)
+#  - prefer NumPy scalars or 0d arrays over other size 1 arrays
+#  - pass no invalid parameters and disable invalid parameter checks (validation_policy)
+#  - provide a Generator if you're going to do sampling
+#  Add options for drawing parameters: log-spacing
+#  Accuracy benchmark suite. Ideally, when all code is array API compatible and mparray
+#    provides an array-API compatible arbitrary precision array, we can just compare
+#    results when using NumPy backend against mparray backend.
+#  Should caches be attributes so we can more easily ensure that they are not
+#    modified when caching is turned off?
+#  Make ShiftedScaledDistribution more efficient - only process underlying
+#    distribution parameters as necessary.
+#  Reconsider `all_inclusive` - see comment in `contains` method of `_interval`
+# `validation_policy` needs testing
+# `tol` does not offer very fine-grained control; consider improving
+# report accuracy estimates? How?
+# reconsider distribution mutability
+
+# Originally, I planned to filter out invalid distribution parameters;
+# distribution implementation functions would always work with "compressed",
+# 1D arrays containing only valid distribution parameters. There are two
+# problems with this:
+# - This essentially requires copying all arrays, even if there is only a
+#   single invalid parameter combination. This is expensive. Then, to output
+#   the original size data to the user, we need to "decompress" the arrays
+#   and fill in the NaNs, so more copying. Unless we branch the code when
+#   there are no invalid data, these copies happen even in the normal case,
+#   where there are no invalid parameter combinations. We should not incur
+#   all this overhead in the normal case.
+# - For methods that accept arguments other than distribution parameters, the
+#   user will pass in arrays that are broadcastable with the original arrays,
+#   not the compressed arrays. This means that this same sort of invalid
+#   value detection needs to be repeated every time one of these methods is
+#   called.
+# The much simpler solution is to keep the data uncompressed but to replace
+# the invalid parameters and arguments with NaNs (and only if some are
+# invalid). With this approach, the copying happens only if/when it is
+# needed. Most functions involved in stats distribution calculations don't
+# mind NaNs; they just return NaN. The behavior "If x_i is NaN, the result
+# is NaN" is explicit in the array API. So this should be fine.
+#
+# Currently, I am still leaving the parameters and function arguments
+# in their broadcasted shapes rather than, say, raveling. The intent
+# is to avoid back and forth reshaping. If authors of distributions have
+# trouble dealing with N-D arrays, we can reconsider this.
+#
+# Another important decision is that the *private* methods must accept
+# the distribution parameters as inputs rather than relying on these
+# cached properties directly (although the public methods typically pass
+# the cached values to the private methods). This is because the elementwise
+# algorithms for quadrature, differentiation, root-finding, and minimization
+# prefer that the input functions are strictly elementwise in the sense
+# that the value output for a given input element does not depend on the
+# shape of the input or that element's location within the input array.
+# When the computation has converged for an element, it is removed from
+# the computation entirely. As a result, the shape of the arrays passed to
+# the function will almost never be broadcastable with the shape of the
+# cached parameter arrays.
+#
+# I've sprinkled in some optimizations for scalars and same-shape/type arrays
+# throughout. The biggest time sinks before were:
+# - broadcast_arrays
+# - result_dtype
+# - is_subdtype
+# It is much faster to check whether these are necessary than to do them.
+
+
+class _Domain(ABC):
+    r""" Representation of the applicable domain of a parameter or variable.
+
+    A `_Domain` object is responsible for storing information about the
+    domain of a parameter or variable, determining whether a value is within
+    the domain (`contains`), and providing a text/mathematical representation
+    of itself (`__str__`). Because the domain of a parameter/variable can have
+    a complicated relationship with other parameters and variables of a
+    distribution, `_Domain` itself does not try to represent all possibilities;
+    in fact, it has no implementation and is meant for subclassing.
+
+    Attributes
+    ----------
+    symbols : dict
+        A map from special numerical values to symbols for use in `__str__`
+
+    Methods
+    -------
+    contains(x)
+        Determine whether the argument is contained within the domain (True)
+        or not (False). Used for input validation.
+    get_numerical_endpoints()
+        Gets the numerical values of the domain endpoints, which may have been
+        defined symbolically or through a callable.
+    __str__()
+        Returns a text representation of the domain (e.g. ``[0, b)``).
+        Used for generating documentation.
+
+    """
+    symbols = {np.inf: r"\infty", -np.inf: r"-\infty", np.pi: r"\pi", -np.pi: r"-\pi"}
+
+    # generic type compatibility with scipy-stubs
+    __class_getitem__: classmethod = classmethod(GenericAlias)
+
+    @abstractmethod
+    def contains(self, x):
+        raise NotImplementedError()
+
+    @abstractmethod
+    def draw(self, n):
+        raise NotImplementedError()
+
+    @abstractmethod
+    def get_numerical_endpoints(self, x):
+        raise NotImplementedError()
+
+    @abstractmethod
+    def __str__(self):
+        raise NotImplementedError()
+
+
+class _Interval(_Domain):
+    r""" Representation of an interval defined by two endpoints.
+
+    Each endpoint may be a finite scalar, positive or negative infinity, or
+    be given by a single parameter. The domain may include the endpoints or
+    not.
+
+    This class still does not provide an implementation of the __str__ method,
+    so it is meant for subclassing (e.g. a subclass for domains on the real
+    line).
+
+    Attributes
+    ----------
+    symbols : dict
+        Inherited. A map from special values to symbols for use in `__str__`.
+    endpoints : 2-tuple of float(s) and/or str(s) and/or callable(s).
+        A tuple with two values. Each may be either a float (the numerical
+        value of the endpoints of the domain), a string (the name of the
+        parameters that will define the endpoint), or a callable taking the
+        parameters used to define the endpoints of the domain as keyword only
+        arguments and returning a numerical value for the endpoint.
+    inclusive : 2-tuple of bools
+        A tuple with two boolean values; each indicates whether the
+        corresponding endpoint is included within the domain or not.
+
+    Methods
+    -------
+    define_parameters(*parameters)
+        Records any parameters used to define the endpoints of the domain
+    get_numerical_endpoints(parameter_values)
+        Gets the numerical values of the domain endpoints, which may have been
+        defined symbolically or through a callable.
+    contains(item, parameter_values)
+        Determines whether the argument is contained within the domain
+    draw(size, rng, proportions, parameter_values)
+        Draws random values based on the domain.
+
+    """
+    def __init__(self, endpoints=(-inf, inf), inclusive=(False, False)):
+        self.symbols = super().symbols.copy()
+        a, b = endpoints
+        self.endpoints = np.asarray(a)[()], np.asarray(b)[()]
+        self.inclusive = inclusive
+
+    def define_parameters(self, *parameters):
+        r""" Records any parameters used to define the endpoints of the domain.
+
+        Adds the keyword name of each parameter and its text representation
+        to the  `symbols` attribute as key:value pairs.
+        For instance, a parameter may be passed into to a distribution's
+        initializer using the keyword `log_a`, and the corresponding
+        string representation may be '\log(a)'. To form the text
+        representation of the domain for use in documentation, the
+        _Domain object needs to map from the keyword name used in the code
+        to the string representation.
+
+        Returns None, but updates the `symbols` attribute.
+
+        Parameters
+        ----------
+        *parameters : _Parameter objects
+            Parameters that may define the endpoints of the domain.
+
+        """
+        new_symbols = {param.name: param.symbol for param in parameters}
+        self.symbols.update(new_symbols)
+
+    def get_numerical_endpoints(self, parameter_values):
+        r""" Get the numerical values of the domain endpoints.
+
+        Domain endpoints may be defined symbolically or through a callable.
+        This returns numerical values of the endpoints given numerical values for
+        any variables.
+
+        Parameters
+        ----------
+        parameter_values : dict
+            A dictionary that maps between string variable names and numerical
+            values of parameters, which may define the endpoints.
+
+        Returns
+        -------
+        a, b : ndarray
+            Numerical values of the endpoints
+
+        """
+        a, b = self.endpoints
+        # If `a` (`b`) is a string - the name of the parameter that defines
+        # the endpoint of the domain - then corresponding numerical values
+        # will be found in the `parameter_values` dictionary.
+        # If a callable, it will be executed with `parameter_values` passed as
+        # keyword arguments, and it will return the numerical values.
+        # Otherwise, it is itself the array of numerical values of the endpoint.
+        try:
+            if callable(a):
+                a = a(**parameter_values)
+            else:
+                a = np.asarray(parameter_values.get(a, a))
+            if callable(b):
+                b = b(**parameter_values)
+            else:
+                b = np.asarray(parameter_values.get(b, b))
+        except TypeError as e:
+            message = ("The endpoints of the distribution are defined by "
+                       "parameters, but their values were not provided. When "
+                       f"using a private method of {self.__class__}, pass "
+                       "all required distribution parameters as keyword "
+                       "arguments.")
+            raise TypeError(message) from e
+        # Floating point types are used for even integer parameters.
+        # Convert to float here to ensure consistency throughout framework.
+        a, b = xp_promote(a, b, force_floating=True, xp=np)
+        return a, b
+
+    def contains(self, item, parameter_values=None):
+        r"""Determine whether the argument is contained within the domain.
+
+        Parameters
+        ----------
+        item : ndarray
+            The argument
+        parameter_values : dict
+            A dictionary that maps between string variable names and numerical
+            values of parameters, which may define the endpoints.
+
+        Returns
+        -------
+        out : bool
+            True if `item` is within the domain; False otherwise.
+
+        """
+        parameter_values = parameter_values or {}
+        # if self.all_inclusive:
+        #     # Returning a 0d value here makes things much faster.
+        #     # I'm not sure if it's safe, though. If it causes a bug someday,
+        #     # I guess it wasn't.
+        #     # Even if there is no bug because of the shape, it is incorrect for
+        #     # `contains` to return True when there are invalid (e.g. NaN)
+        #     # parameters.
+        #     return np.asarray(True)
+
+        a, b = self.get_numerical_endpoints(parameter_values)
+        left_inclusive, right_inclusive = self.inclusive
+
+        in_left = item >= a if left_inclusive else item > a
+        in_right = item <= b if right_inclusive else item < b
+        return in_left & in_right
+
+    def draw(self, n, type_, min, max, squeezed_base_shape, rng=None):
+        r""" Draw random values from the domain.
+
+        Parameters
+        ----------
+        n : int
+            The number of values to be drawn from the domain.
+        type_ : str
+            A string indicating whether the values are
+
+            - strictly within the domain ('in'),
+            - at one of the two endpoints ('on'),
+            - strictly outside the domain ('out'), or
+            - NaN ('nan').
+        min, max : ndarray
+            The endpoints of the domain.
+        squeezed_based_shape : tuple of ints
+            See _RealParameter.draw.
+        rng : np.Generator
+            The Generator used for drawing random values.
+
+        """
+        rng = np.random.default_rng(rng)
+
+        def ints(*args, **kwargs): return rng.integers(*args, **kwargs, endpoint=True)
+        uniform = rng.uniform if isinstance(self, _RealInterval) else ints
+
+        # get copies of min and max with no nans so that uniform doesn't fail
+        min_nn, max_nn = min.copy(), max.copy()
+        i = np.isnan(min_nn) | np.isnan(max_nn)
+        min_nn[i] = 0
+        max_nn[i] = 1
+
+        shape = (n,) + squeezed_base_shape
+
+        if type_ == 'in':
+            z = uniform(min_nn, max_nn, size=shape)
+
+        elif type_ == 'on':
+            z_on_shape = shape
+            z = np.ones(z_on_shape)
+            i = rng.random(size=n) < 0.5
+            z[i] = min
+            z[~i] = max
+
+        elif type_ == 'out':
+            z = min_nn - uniform(1, 5, size=shape)   # 1, 5 is arbitary; we just want
+            zr = max_nn + uniform(1, 5, size=shape)  # some numbers outside domain
+            i = rng.random(size=n) < 0.5
+            z[i] = zr[i]
+
+        elif type_ == 'nan':
+            z = np.full(shape, np.nan)
+
+        return z
+
+
+class _RealInterval(_Interval):
+    r""" Represents a simply-connected subset of the real line; i.e., an interval
+
+    Completes the implementation of the `_Interval` class for intervals
+    on the real line.
+
+    Methods
+    -------
+    define_parameters(*parameters)
+        (Inherited) Records any parameters used to define the endpoints of the
+        domain.
+    get_numerical_endpoints(parameter_values)
+        (Inherited) Gets the numerical values of the domain endpoints, which
+        may have been defined symbolically.
+    contains(item, parameter_values)
+        (Inherited) Determines whether the argument is contained within the
+        domain
+    __str__()
+        Returns a string representation of the domain, e.g. "[a, b)".
+    """
+
+    def __str__(self):
+        a, b = self.endpoints
+        a, b = self._get_endpoint_str(a, "f1"), self._get_endpoint_str(b, "f2")
+        left_inclusive, right_inclusive = self.inclusive
+        left = "[" if left_inclusive else "("
+        right = "]" if right_inclusive else ")"
+
+        return f"{left}{a}, {b}{right}"
+
+    def _get_endpoint_str(self, endpoint, funcname):
+        if callable(endpoint):
+            if endpoint.__doc__ is not None:
+                return endpoint.__doc__
+            params = inspect.signature(endpoint).parameters.values()
+            params = [
+                p.name for p in params if p.kind == inspect.Parameter.KEYWORD_ONLY
+            ]
+            return f"{funcname}({','.join(params)})"
+        return self.symbols.get(endpoint, f"{endpoint}")
+
+
+class _IntegerInterval(_Interval):
+    r""" Represents an interval of integers
+
+    Completes the implementation of the `_Interval` class for simple
+    domains on the integers.
+
+    Methods
+    -------
+    define_parameters(*parameters)
+        (Inherited) Records any parameters used to define the endpoints of the
+        domain.
+    get_numerical_endpoints(parameter_values)
+        (Inherited) Gets the numerical values of the domain endpoints, which
+        may have been defined symbolically.
+    contains(item, parameter_values)
+        (Overridden) Determines whether the argument is contained within the
+        domain
+    draw(n, type_, min, max, squeezed_base_shape, rng=None)
+        (Inherited) Draws random values based on the domain.
+    __str__()
+        Returns a string representation of the domain, e.g. "{a, a+1, ..., b-1, b}".
+
+    """
+    def contains(self, item, parameter_values=None):
+        super_contains = super().contains(item, parameter_values)
+        integral = (item == np.round(item))
+        return super_contains & integral
+
+    def __str__(self):
+        a, b = self.endpoints
+        a = self.symbols.get(a, a)
+        b = self.symbols.get(b, b)
+
+        a_str, b_str = isinstance(a, str), isinstance(b, str)
+        a_inf = a == r"-\infty" if a_str else np.isinf(a)
+        b_inf = b == r"\infty" if b_str else np.isinf(b)
+
+        # This doesn't work well for cases where ``a`` is floating point
+        # number large enough that ``nextafter(a, inf) > a + 1``, and
+        # similarly for ``b`` and nextafter(b, -inf). There may not be any
+        # distributions fit for SciPy where we would actually need to handle these
+        # cases though.
+        ap1 = f"{a} + 1" if a_str else f"{a + 1}"
+        bm1 = f"{b} - 1" if b_str else f"{b - 1}"
+
+        if not a_str and not b_str:
+            gap = b - a
+            if gap == 3:
+                return f"\\{{{a}, {ap1}, {bm1}, {b}\\}}"
+            if gap == 2:
+                return f"\\{{{a}, {ap1}, {b}\\}}"
+            if gap == 1:
+                return f"\\{{{a}, {b}\\}}"
+            if gap == 0:
+                return f"\\{{{a}\\}}"
+
+        if not a_inf and b_inf:
+            ap2 = f"{a} + 2" if a_str else f"{a + 2}"
+            return f"\\{{{a}, {ap1}, {ap2}, ...\\}}"
+        if a_inf and not b_inf:
+            bm2 = f"{b} - 2" if b_str else f"{b - 2}"
+            return f"\\{{{b}, {bm1}, {bm2}, ...\\}}"
+        if a_inf and b_inf:
+            return "\\{..., -2, -1, 0, 1, 2, ...\\}"
+
+        return f"\\{{{a}, {ap1}, ..., {bm1}, {b}\\}}"
+
+
+class _Parameter(ABC):
+    r""" Representation of a distribution parameter or variable.
+
+    A `_Parameter` object is responsible for storing information about a
+    parameter or variable, providing input validation/standardization of
+    values passed for that parameter, providing a text/mathematical
+    representation of the parameter for the documentation (`__str__`), and
+    drawing random values of itself for testing and benchmarking. It does
+    not provide a complete implementation of this functionality and is meant
+    for subclassing.
+
+    Attributes
+    ----------
+    name : str
+        The keyword used to pass numerical values of the parameter into the
+        initializer of the distribution
+    symbol : str
+        The text representation of the variable in the documentation. May
+        include LaTeX.
+    domain : _Domain
+        The domain of the parameter for which the distribution is valid.
+    typical : 2-tuple of floats or strings (consider making a _Domain)
+        Defines the endpoints of a typical range of values of the parameter.
+        Used for sampling.
+
+    Methods
+    -------
+    __str__():
+        Returns a string description of the variable for use in documentation,
+        including the keyword used to represent it in code, the symbol used to
+        represent it mathemtatically, and a description of the valid domain.
+    draw(size, *, rng, domain, proportions)
+        Draws random values of the parameter. Proportions of values within
+        the valid domain, on the endpoints of the domain, outside the domain,
+        and having value NaN are specified by `proportions`.
+    validate(x):
+        Validates and standardizes the argument for use as numerical values
+        of the parameter.
+
+   """
+
+    # generic type compatibility with scipy-stubs
+    __class_getitem__: classmethod = classmethod(GenericAlias)
+
+    def __init__(self, name, *, domain, symbol=None, typical=None):
+        self.name = name
+        self.symbol = symbol or name
+        self.domain = domain
+        if typical is not None and not isinstance(typical, _Domain):
+            typical = domain.__class__(typical)
+        self.typical = typical or domain
+
+    def __str__(self):
+        r""" String representation of the parameter for use in documentation."""
+        return f"`{self.name}` for :math:`{self.symbol} \\in {str(self.domain)}`"
+
+    def draw(self, size=None, *, rng=None, region='domain', proportions=None,
+             parameter_values=None):
+        r""" Draw random values of the parameter for use in testing.
+
+        Parameters
+        ----------
+        size : tuple of ints
+            The shape of the array of valid values to be drawn.
+        rng : np.Generator
+            The Generator used for drawing random values.
+        region : str
+            The region of the `_Parameter` from which to draw. Default is
+            "domain" (the *full* domain); alternative is "typical". An
+            enhancement would give a way to interpolate between the two.
+        proportions : tuple of numbers
+            A tuple of four non-negative numbers that indicate the expected
+            relative proportion of elements that:
+
+            - are strictly within the domain,
+            - are at one of the two endpoints,
+            - are strictly outside the domain, and
+            - are NaN,
+
+            respectively. Default is (1, 0, 0, 0). The number of elements in
+            each category is drawn from the multinomial distribution with
+            `np.prod(size)` as the number of trials and `proportions` as the
+            event probabilities. The values in `proportions` are automatically
+            normalized to sum to 1.
+        parameter_values : dict
+            Map between the names of parameters (that define the endpoints of
+            `typical`) and numerical values (arrays).
+
+        """
+        parameter_values = parameter_values or {}
+        domain = self.domain
+        proportions = (1, 0, 0, 0) if proportions is None else proportions
+
+        pvals = proportions / np.sum(proportions)
+
+        a, b = domain.get_numerical_endpoints(parameter_values)
+        a, b = np.broadcast_arrays(a, b)
+
+        base_shape = a.shape
+        extended_shape = np.broadcast_shapes(size, base_shape)
+        n_extended = np.prod(extended_shape)
+        n_base = np.prod(base_shape)
+        n = int(n_extended / n_base) if n_extended else 0
+
+        rng = np.random.default_rng(rng)
+        n_in, n_on, n_out, n_nan = rng.multinomial(n, pvals)
+
+        # `min` and `max` can have singleton dimensions that correspond with
+        # non-singleton dimensions in `size`. We need to be careful to avoid
+        # shuffling results (e.g. a value that was generated for the domain
+        # [min[i], max[i]] ends up at index j). To avoid this:
+        # - Squeeze the singleton dimensions out of `min`/`max`. Squeezing is
+        #   often not the right thing to do, but here is equivalent to moving
+        #   all the dimensions that are singleton in `min`/`max` (which may be
+        #   non-singleton in the result) to the left. This is what we want.
+        # - Now all the non-singleton dimensions of the result are on the left.
+        #   Ravel them to a single dimension of length `n`, which is now along
+        #   the 0th axis.
+        # - Reshape the 0th axis back to the required dimensions, and move
+        #   these axes back to their original places.
+        base_shape_padded = ((1,)*(len(extended_shape) - len(base_shape))
+                             + base_shape)
+        base_singletons = np.where(np.asarray(base_shape_padded)==1)[0]
+        new_base_singletons = tuple(range(len(base_singletons)))
+        # Base singleton dimensions are going to get expanded to these lengths
+        shape_expansion = np.asarray(extended_shape)[base_singletons]
+
+        # assert(np.prod(shape_expansion) == n)  # check understanding
+        # min = np.reshape(min, base_shape_padded)
+        # max = np.reshape(max, base_shape_padded)
+        # min = np.moveaxis(min, base_singletons, new_base_singletons)
+        # max = np.moveaxis(max, base_singletons, new_base_singletons)
+        # squeezed_base_shape = max.shape[len(base_singletons):]
+        # assert np.all(min.reshape(squeezed_base_shape) == min.squeeze())
+        # assert np.all(max.reshape(squeezed_base_shape) == max.squeeze())
+
+        # min = np.maximum(a, _fiinfo(a).min/10) if np.any(np.isinf(a)) else a
+        # max = np.minimum(b, _fiinfo(b).max/10) if np.any(np.isinf(b)) else b
+        min = np.asarray(a.squeeze())
+        max = np.asarray(b.squeeze())
+        squeezed_base_shape = max.shape
+
+        if region == 'typical':
+            typical = self.typical
+            a, b = typical.get_numerical_endpoints(parameter_values)
+            a, b = np.broadcast_arrays(a, b)
+            min_here = np.asarray(a.squeeze())
+            max_here = np.asarray(b.squeeze())
+            z_in = typical.draw(n_in, 'in', min_here, max_here, squeezed_base_shape,
+                                rng=rng)
+        else:
+            z_in = domain.draw(n_in, 'in', min, max, squeezed_base_shape, rng=rng)
+        z_on = domain.draw(n_on, 'on', min, max, squeezed_base_shape, rng=rng)
+        z_out = domain.draw(n_out, 'out', min, max, squeezed_base_shape, rng=rng)
+        z_nan= domain.draw(n_nan, 'nan', min, max, squeezed_base_shape, rng=rng)
+
+        z = np.concatenate((z_in, z_on, z_out, z_nan), axis=0)
+        z = rng.permuted(z, axis=0)
+
+        z = np.reshape(z, tuple(shape_expansion) + squeezed_base_shape)
+        z = np.moveaxis(z, new_base_singletons, base_singletons)
+        return z
+
+    @abstractmethod
+    def validate(self, arr):
+        raise NotImplementedError()
+
+
+class _RealParameter(_Parameter):
+    r""" Represents a real-valued parameter.
+
+    Implements the remaining methods of _Parameter for real parameters.
+    All attributes are inherited.
+
+    """
+    def validate(self, arr, parameter_values):
+        r""" Input validation/standardization of numerical values of a parameter.
+
+        Checks whether elements of the argument `arr` are reals, ensuring that
+        the dtype reflects this. Also produces a logical array that indicates
+        which elements meet the requirements.
+
+        Parameters
+        ----------
+        arr : ndarray
+            The argument array to be validated and standardized.
+        parameter_values : dict
+            Map of parameter names to parameter value arrays.
+
+        Returns
+        -------
+        arr : ndarray
+            The argument array that has been validated and standardized
+            (converted to an appropriate dtype, if necessary).
+        dtype : NumPy dtype
+            The appropriate floating point dtype of the parameter.
+        valid : bool ndarray
+            Logical array indicating which elements are valid (True) and
+            which are not (False). The arrays of all distribution parameters
+            will be broadcasted, and elements for which any parameter value
+            does not meet the requirements will be replaced with NaN.
+
+        """
+        arr = np.asarray(arr)
+
+        valid_dtype = None
+        # minor optimization - fast track the most common types to avoid
+        # overhead of np.issubdtype. Checking for `in {...}` doesn't work : /
+        if arr.dtype == np.float64 or arr.dtype == np.float32:
+            pass
+        elif arr.dtype == np.int32 or arr.dtype == np.int64:
+            arr = np.asarray(arr, dtype=np.float64)
+        elif np.issubdtype(arr.dtype, np.floating):
+            pass
+        elif np.issubdtype(arr.dtype, np.integer):
+            arr = np.asarray(arr, dtype=np.float64)
+        else:
+            message = f"Parameter `{self.name}` must be of real dtype."
+            raise TypeError(message)
+
+        valid = self.domain.contains(arr, parameter_values)
+        valid = valid & valid_dtype if valid_dtype is not None else valid
+
+        return arr[()], arr.dtype, valid
+
+
+class _Parameterization:
+    r""" Represents a parameterization of a distribution.
+
+    Distributions can have multiple parameterizations. A `_Parameterization`
+    object is responsible for recording the parameters used by the
+    parameterization, checking whether keyword arguments passed to the
+    distribution match the parameterization, and performing input validation
+    of the numerical values of these parameters.
+
+    Attributes
+    ----------
+    parameters : dict
+        String names (of keyword arguments) and the corresponding _Parameters.
+
+    Methods
+    -------
+    __len__()
+        Returns the number of parameters in the parameterization.
+    __str__()
+        Returns a string representation of the parameterization.
+    copy
+        Returns a copy of the parameterization. This is needed for transformed
+        distributions that add parameters to the parameterization.
+    matches(parameters)
+        Checks whether the keyword arguments match the parameterization.
+    validation(parameter_values)
+        Input validation / standardization of parameterization. Validates the
+        numerical values of all parameters.
+    draw(sizes, rng, proportions)
+        Draw random values of all parameters of the parameterization for use
+        in testing.
+    """
+    def __init__(self, *parameters):
+        self.parameters = {param.name: param for param in parameters}
+
+    def __len__(self):
+        return len(self.parameters)
+
+    def copy(self):
+        return _Parameterization(*self.parameters.values())
+
+    def matches(self, parameters):
+        r""" Checks whether the keyword arguments match the parameterization.
+
+        Parameters
+        ----------
+        parameters : set
+            Set of names of parameters passed into the distribution as keyword
+            arguments.
+
+        Returns
+        -------
+        out : bool
+            True if the keyword arguments names match the names of the
+            parameters of this parameterization.
+        """
+        return parameters == set(self.parameters.keys())
+
+    def validation(self, parameter_values):
+        r""" Input validation / standardization of parameterization.
+
+        Parameters
+        ----------
+        parameter_values : dict
+            The keyword arguments passed as parameter values to the
+            distribution.
+
+        Returns
+        -------
+        all_valid : ndarray
+            Logical array indicating the elements of the broadcasted arrays
+            for which all parameter values are valid.
+        dtype : dtype
+            The common dtype of the parameter arrays. This will determine
+            the dtype of the output of distribution methods.
+        """
+        all_valid = True
+        dtypes = set()  # avoid np.result_type if there's only one type
+        for name, arr in parameter_values.items():
+            parameter = self.parameters[name]
+            arr, dtype, valid = parameter.validate(arr, parameter_values)
+            dtypes.add(dtype)
+            all_valid = all_valid & valid
+            parameter_values[name] = arr
+        dtype = arr.dtype if len(dtypes)==1 else np.result_type(*list(dtypes))
+
+        return all_valid, dtype
+
+    def __str__(self):
+        r"""Returns a string representation of the parameterization."""
+        messages = [str(param) for name, param in self.parameters.items()]
+        return ", ".join(messages)
+
+    def draw(self, sizes=None, rng=None, proportions=None, region='domain'):
+        r"""Draw random values of all parameters for use in testing.
+
+        Parameters
+        ----------
+        sizes : iterable of shape tuples
+            The size of the array to be generated for each parameter in the
+            parameterization. Note that the order of sizes is arbitary; the
+            size of the array generated for a specific parameter is not
+            controlled individually as written.
+        rng : NumPy Generator
+            The generator used to draw random values.
+        proportions : tuple
+            A tuple of four non-negative numbers that indicate the expected
+            relative proportion of elements that are within the parameter's
+            domain, are on the boundary of the parameter's domain, are outside
+            the parameter's domain, and have value NaN. For more information,
+            see the `draw` method of the _Parameter subclasses.
+        domain : str
+            The domain of the `_Parameter` from which to draw. Default is
+            "domain" (the *full* domain); alternative is "typical".
+
+        Returns
+        -------
+        parameter_values : dict (string: array)
+            A dictionary of parameter name/value pairs.
+        """
+        # ENH: be smart about the order. The domains of some parameters
+        # depend on others. If the relationshp is simple (e.g. a < b < c),
+        # we can draw values in order a, b, c.
+        parameter_values = {}
+
+        if sizes is None or not len(sizes) or not np.iterable(sizes[0]):
+            sizes = [sizes]*len(self.parameters)
+
+        for size, param in zip(sizes, self.parameters.values()):
+            parameter_values[param.name] = param.draw(
+                size, rng=rng, proportions=proportions,
+                parameter_values=parameter_values,
+                region=region
+            )
+
+        return parameter_values
+
+
+def _set_invalid_nan(f):
+    # Wrapper for input / output validation and standardization of distribution
+    # functions that accept either the quantile or percentile as an argument:
+    # logpdf, pdf
+    # logpmf, pmf
+    # logcdf, cdf
+    # logccdf, ccdf
+    # ilogcdf, icdf
+    # ilogccdf, iccdf
+    # Arguments that are outside the required range are replaced by NaN before
+    # passing them into the underlying function. The corresponding outputs
+    # are replaced by the appropriate value before being returned to the user.
+    # For example, when the argument of `cdf` exceeds the right end of the
+    # distribution's support, the wrapper replaces the argument with NaN,
+    # ignores the output of the underlying function, and returns 1.0. It also
+    # ensures that output is of the appropriate shape and dtype.
+
+    endpoints = {'icdf': (0, 1), 'iccdf': (0, 1),
+                 'ilogcdf': (-np.inf, 0), 'ilogccdf': (-np.inf, 0)}
+    replacements = {'logpdf': (-inf, -inf), 'pdf': (0, 0),
+                    'logpmf': (-inf, -inf), 'pmf': (0, 0),
+                    '_logcdf1': (-inf, 0), '_logccdf1': (0, -inf),
+                    '_cdf1': (0, 1), '_ccdf1': (1, 0)}
+    replace_strict = {'pdf', 'logpdf', 'pmf', 'logpmf'}
+    replace_exact = {'icdf', 'iccdf', 'ilogcdf', 'ilogccdf'}
+    clip = {'_cdf1', '_ccdf1'}
+    clip_log = {'_logcdf1', '_logccdf1'}
+    # relevant to discrete distributions only
+    replace_non_integral = {'pmf', 'logpmf', 'pdf', 'logpdf'}
+
+    @functools.wraps(f)
+    def filtered(self, x, *args, **kwargs):
+        if self.validation_policy == _SKIP_ALL:
+            return f(self, x, *args, **kwargs)
+
+        method_name = f.__name__
+        x = np.asarray(x)
+        dtype = self._dtype
+        shape = self._shape
+        discrete = isinstance(self, DiscreteDistribution)
+        keep_low_endpoint = discrete and method_name in {'_cdf1', '_logcdf1',
+                                                         '_ccdf1', '_logccdf1'}
+
+        # Ensure that argument is at least as precise as distribution
+        # parameters, which are already at least floats. This will avoid issues
+        # with raising integers to negative integer powers and failure to replace
+        # invalid integers with NaNs.
+        if x.dtype != dtype:
+            dtype = np.result_type(x.dtype, dtype)
+            x = np.asarray(x, dtype=dtype)
+
+        # Broadcasting is slow. Do it only if necessary.
+        if not x.shape == shape:
+            try:
+                shape = np.broadcast_shapes(x.shape, shape)
+                x = np.broadcast_to(x, shape)
+                # Should we broadcast the distribution parameters to this shape, too?
+            except ValueError as e:
+                message = (
+                    f"The argument provided to `{self.__class__.__name__}"
+                    f".{method_name}` cannot be be broadcast to the same "
+                    "shape as the distribution parameters.")
+                raise ValueError(message) from e
+
+        low, high = endpoints.get(method_name, self.support())
+
+        # Check for arguments outside of domain. They'll be replaced with NaNs,
+        # and the result will be set to the appropriate value.
+        left_inc, right_inc = self._variable.domain.inclusive
+        mask_low = (x < low if (method_name in replace_strict and left_inc)
+                    or keep_low_endpoint else x <= low)
+        mask_high = (x > high if (method_name in replace_strict and right_inc)
+                     else x >= high)
+        mask_invalid = (mask_low | mask_high)
+        any_invalid = (mask_invalid if mask_invalid.shape == ()
+                       else np.any(mask_invalid))
+
+        # Check for arguments at domain endpoints, whether they
+        # are part of the domain or not.
+        any_endpoint = False
+        if method_name in replace_exact:
+            mask_low_endpoint = (x == low)
+            mask_high_endpoint = (x == high)
+            mask_endpoint = (mask_low_endpoint | mask_high_endpoint)
+            any_endpoint = (mask_endpoint if mask_endpoint.shape == ()
+                            else np.any(mask_endpoint))
+
+        # Check for non-integral arguments to PMF method
+        # or PDF of a discrete distribution.
+        any_non_integral = False
+        if discrete and method_name in replace_non_integral:
+            mask_non_integral = (x != np.floor(x))
+            any_non_integral = (mask_non_integral if mask_non_integral.shape == ()
+                                else np.any(mask_non_integral))
+
+        # Set out-of-domain arguments to NaN. The result will be set to the
+        # appropriate value later.
+        if any_invalid:
+            x = np.array(x, dtype=dtype, copy=True)
+            x[mask_invalid] = np.nan
+
+        res = np.asarray(f(self, x, *args, **kwargs))
+
+        # Ensure that the result is the correct dtype and shape,
+        # copying (only once) if necessary.
+        res_needs_copy = False
+        if res.dtype != dtype:
+            dtype = np.result_type(dtype, self._dtype)
+            res_needs_copy = True
+
+        if res.shape != shape:  # faster to check first
+            res = np.broadcast_to(res, self._shape)
+            res_needs_copy = (res_needs_copy or any_invalid
+                              or any_endpoint or any_non_integral)
+
+        if res_needs_copy:
+            res = np.array(res, dtype=dtype, copy=True)
+
+        # For non-integral arguments to PMF (and PDF of discrete distribution)
+        # replace with zero.
+        if any_non_integral:
+            zero = -np.inf if method_name in {'logpmf', 'logpdf'} else 0
+            res[mask_non_integral & ~np.isnan(res)] = zero
+
+        # For arguments outside the function domain, replace results
+        if any_invalid:
+            replace_low, replace_high = (
+                replacements.get(method_name, (np.nan, np.nan)))
+            res[mask_low] = replace_low
+            res[mask_high] = replace_high
+
+        # For arguments at the endpoints of the domain, replace results
+        if any_endpoint:
+            a, b = self.support()
+            if a.shape != shape:
+                a = np.array(np.broadcast_to(a, shape), copy=True)
+                b = np.array(np.broadcast_to(b, shape), copy=True)
+
+            replace_low_endpoint = (
+                b[mask_low_endpoint] if method_name.endswith('ccdf')
+                else a[mask_low_endpoint])
+            replace_high_endpoint = (
+                a[mask_high_endpoint] if method_name.endswith('ccdf')
+                else b[mask_high_endpoint])
+
+            if not keep_low_endpoint:
+                res[mask_low_endpoint] = replace_low_endpoint
+            res[mask_high_endpoint] = replace_high_endpoint
+
+        # Clip probabilities to [0, 1]
+        if method_name in clip:
+            res = np.clip(res, 0., 1.)
+        elif method_name in clip_log:
+            res = res.real  # exp(res) > 0
+            res = np.clip(res, None, 0.)  # exp(res) < 1
+
+        return res[()]
+
+    return filtered
+
+
+def _set_invalid_nan_property(f):
+    # Wrapper for input / output validation and standardization of distribution
+    # functions that represent properties of the distribution itself:
+    # logentropy, entropy
+    # median, mode
+    # moment
+    # It ensures that the output is of the correct shape and dtype and that
+    # there are NaNs wherever the distribution parameters were invalid.
+
+    @functools.wraps(f)
+    def filtered(self, *args, **kwargs):
+        if self.validation_policy == _SKIP_ALL:
+            return f(self, *args, **kwargs)
+
+        res = f(self, *args, **kwargs)
+        if res is None:
+            # message could be more appropriate
+            raise NotImplementedError(self._not_implemented)
+
+        res = np.asarray(res)
+        needs_copy = False
+        dtype = res.dtype
+
+        if dtype != self._dtype:  # this won't work for logmoments (complex)
+            dtype = np.result_type(dtype, self._dtype)
+            needs_copy = True
+
+        if res.shape != self._shape:  # faster to check first
+            res = np.broadcast_to(res, self._shape)
+            needs_copy = needs_copy or self._any_invalid
+
+        if needs_copy:
+            res = res.astype(dtype=dtype, copy=True)
+
+        if self._any_invalid:
+            # may be redundant when quadrature is used, but not necessarily
+            # when formulas are used.
+            res[self._invalid] = np.nan
+
+        return res[()]
+
+    return filtered
+
+
+def _dispatch(f):
+    # For each public method (instance function) of a distribution (e.g. ccdf),
+    # there may be several ways ("method"s) that it can be computed (e.g. a
+    # formula, as the complement of the CDF, or via numerical integration).
+    # Each "method" is implemented by a different private method (instance
+    # function).
+    # This wrapper calls the appropriate private method based on the public
+    # method and any specified `method` keyword option.
+    # - If `method` is specified as a string (by the user), the appropriate
+    #   private method is called.
+    # - If `method` is None:
+    #   - The appropriate private method for the public method is looked up
+    #     in a cache.
+    #   - If the cache does not have an entry for the public method, the
+    #     appropriate "dispatch " function is called to determine which method
+    #     is most appropriate given the available private methods and
+    #     settings (e.g. tolerance).
+
+    @functools.wraps(f)
+    def wrapped(self, *args, method=None, **kwargs):
+        func_name = f.__name__
+        method = method or self._method_cache.get(func_name, None)
+        if callable(method):
+            pass
+        elif method is not None:
+            method = 'logexp' if method == 'log/exp' else method
+            method_name = func_name.replace('dispatch', method)
+            method = getattr(self, method_name)
+        else:
+            method = f(self, *args, method=method, **kwargs)
+            if func_name != '_sample_dispatch' and self.cache_policy != _NO_CACHE:
+                self._method_cache[func_name] = method
+
+        try:
+            return method(*args, **kwargs)
+        except KeyError as e:
+            raise NotImplementedError(self._not_implemented) from e
+
+    return wrapped
+
+
+def _cdf2_input_validation(f):
+    # Wrapper that does the job of `_set_invalid_nan` when `cdf` or `logcdf`
+    # is called with two quantile arguments.
+    # Let's keep it simple; no special cases for speed right now.
+    # The strategy is a bit different than for 1-arg `cdf` (and other methods
+    # covered by `_set_invalid_nan`). For 1-arg `cdf`, elements of `x` that
+    # are outside (or at the edge of) the support get replaced by `nan`,
+    # and then the results get replaced by the appropriate value (0 or 1).
+    # We *could* do something similar, dispatching to `_cdf1` in these
+    # cases. That would be a bit more robust, but it would also be quite
+    # a bit more complex, since we'd have to do different things when
+    # `x` and `y` are both out of bounds, when just `x` is out of bounds,
+    # when just `y` is out of bounds, and when both are out of bounds.
+    # I'm not going to do that right now. Instead, simply replace values
+    # outside the support by those at the edge of the support. Here, we also
+    # omit some of the optimizations that make `_set_invalid_nan` faster for
+    # simple arguments (e.g. float64 scalars).
+
+    @functools.wraps(f)
+    def wrapped(self, x, y, *args, **kwargs):
+        func_name = f.__name__
+
+        low, high = self.support()
+        x, y, low, high = np.broadcast_arrays(x, y, low, high)
+        dtype = np.result_type(x.dtype, y.dtype, self._dtype)
+        # yes, copy to avoid modifying input arrays
+        x, y = x.astype(dtype, copy=True), y.astype(dtype, copy=True)
+
+        # Swap arguments to ensure that x < y, and replace
+        # out-of domain arguments with domain endpoints. We'll
+        # transform the result later.
+        i_swap = y < x
+        x[i_swap], y[i_swap] = y[i_swap], x[i_swap]
+        i = x < low
+        x[i] = low[i]
+        i = y < low
+        y[i] = low[i]
+        i = x > high
+        x[i] = high[i]
+        i = y > high
+        y[i] = high[i]
+
+        res = f(self, x, y, *args, **kwargs)
+
+        # Clipping probability to [0, 1]
+        if func_name in {'_cdf2', '_ccdf2'}:
+            res = np.clip(res, 0., 1.)
+        else:
+            res = np.clip(res, None, 0.)  # exp(res) < 1
+
+        # Transform the result to account for swapped argument order
+        res = np.asarray(res)
+        if func_name == '_cdf2':
+            res[i_swap] *= -1.
+        elif func_name == '_ccdf2':
+            res[i_swap] *= -1
+            res[i_swap] += 2.
+        elif func_name == '_logcdf2':
+            res = np.asarray(res + 0j) if np.any(i_swap) else res
+            res[i_swap] = res[i_swap] + np.pi*1j
+        else:
+            # res[i_swap] is always positive and less than 1, so it's
+            # safe to ensure that the result is real
+            res[i_swap] = _logexpxmexpy(np.log(2), res[i_swap]).real
+        return res[()]
+
+    return wrapped
+
+
+def _fiinfo(x):
+    if np.issubdtype(x.dtype, np.inexact):
+        return np.finfo(x.dtype)
+    else:
+        return np.iinfo(x)
+
+
+def _logexpxmexpy(x, y):
+    """ Compute the log of the difference of the exponentials of two arguments.
+
+    Avoids over/underflow, but does not prevent loss of precision otherwise.
+    """
+    return xpx.apply_where(x != y, (x, y),
+                           lambda x, y: special.logsumexp([x, y+np.pi*1j], axis=0),
+                           fill_value=-np.inf)
+
+
+def _guess_bracket(xmin, xmax):
+    a = np.full_like(xmin, -1.0)
+    b = np.ones_like(xmax)
+
+    i = np.isfinite(xmin) & np.isfinite(xmax)
+    a[i] = xmin[i]
+    b[i] = xmax[i]
+
+    i = np.isfinite(xmin) & ~np.isfinite(xmax)
+    a[i] = xmin[i]
+    b[i] = xmin[i] + 1
+
+    i = np.isfinite(xmax) & ~np.isfinite(xmin)
+    a[i] = xmax[i] - 1
+    b[i] = xmax[i]
+
+    return a, b
+
+
+def _log_real_standardize(x):
+    """Standardizes the (complex) logarithm of a real number.
+
+    The logarithm of a real number may be represented by a complex number with
+    imaginary part that is a multiple of pi*1j. Even multiples correspond with
+    a positive real and odd multiples correspond with a negative real.
+
+    Given a logarithm of a real number `x`, this function returns an equivalent
+    representation in a standard form: the log of a positive real has imaginary
+    part `0` and the log of a negative real has imaginary part `pi`.
+
+    """
+    shape = x.shape
+    x = np.atleast_1d(x)
+    real = np.real(x).astype(x.dtype)
+    complex = np.imag(x)
+    y = real
+    negative = np.exp(complex*1j) < 0.5
+    y[negative] = y[negative] + np.pi * 1j
+    return y.reshape(shape)[()]
+
+
+def _combine_docs(dist_family, *, include_examples=True):
+    fields = set(NumpyDocString.sections)
+    fields.remove('index')
+    if not include_examples:
+        fields.remove('Examples')
+
+    doc = ClassDoc(dist_family)
+    superdoc = ClassDoc(UnivariateDistribution)
+    for field in fields:
+        if field in {"Methods", "Attributes"}:
+            doc[field] = superdoc[field]
+        elif field in {"Summary"}:
+            pass
+        elif field == "Extended Summary":
+            doc[field].append(_generate_domain_support(dist_family))
+        elif field == 'Examples':
+            doc[field] = [_generate_example(dist_family)]
+        else:
+            doc[field] += superdoc[field]
+    return str(doc)
+
+
+def _generate_domain_support(dist_family):
+    n_parameterizations = len(dist_family._parameterizations)
+
+    domain = f"\nfor :math:`x \\in {dist_family._variable.domain}`.\n"
+
+    if n_parameterizations == 0:
+        support = """
+        This class accepts no distribution parameters.
+        """
+    elif n_parameterizations == 1:
+        support = f"""
+        This class accepts one parameterization:
+        {str(dist_family._parameterizations[0])}.
+        """
+    else:
+        number = {2: 'two', 3: 'three', 4: 'four', 5: 'five'}[
+            n_parameterizations]
+        parameterizations = [f"- {str(p)}" for p in
+                             dist_family._parameterizations]
+        parameterizations = "\n".join(parameterizations)
+        support = f"""
+        This class accepts {number} parameterizations:
+
+        {parameterizations}
+        """
+    support = "\n".join([line.lstrip() for line in support.split("\n")][1:])
+    return domain + support
+
+
+def _generate_example(dist_family):
+    n_parameters = dist_family._num_parameters(0)
+    shapes = [()] * n_parameters
+    rng = np.random.default_rng(615681484984984)
+    i = 0
+    dist = dist_family._draw(shapes, rng=rng, i_parameterization=i)
+
+    rng = np.random.default_rng(2354873452)
+    name = dist_family.__name__
+    if n_parameters:
+        parameter_names = list(dist._parameterizations[i].parameters)
+        parameter_values = [round(getattr(dist, name), 2) for name in
+                            parameter_names]
+        name_values = [f"{name}={value}" for name, value in
+                       zip(parameter_names, parameter_values)]
+        instantiation = f"{name}({', '.join(name_values)})"
+        attributes = ", ".join([f"X.{param}" for param in dist._parameters])
+        X = dist_family(**dict(zip(parameter_names, parameter_values)))
+    else:
+        instantiation = f"{name}()"
+        X = dist
+
+    p = 0.32
+    x = round(X.icdf(p), 2)
+    y = round(X.icdf(2 * p), 2)  # noqa: F841
+
+    example = f"""
+    To use the distribution class, it must be instantiated using keyword
+    parameters corresponding with one of the accepted parameterizations.
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy import stats
+    >>> from scipy.stats import {name}
+    >>> X = {instantiation}
+
+    For convenience, the ``plot`` method can be used to visualize the density
+    and other functions of the distribution.
+
+    >>> X.plot()
+    >>> plt.show()
+
+    The support of the underlying distribution is available using the ``support``
+    method.
+
+    >>> X.support()
+    {X.support()}
+    """
+
+    if n_parameters:
+        example += f"""
+        The numerical values of parameters associated with all parameterizations
+        are available as attributes.
+
+        >>> {attributes}
+        {tuple(X._parameters.values())}
+        """
+
+    example += f"""
+    To evaluate the probability density/mass function of the underlying distribution
+    at argument ``x={x}``:
+
+    >>> x = {x}
+    >>> X.pdf(x), X.pmf(x)
+    {X.pdf(x), X.pmf(x)}
+
+    The cumulative distribution function, its complement, and the logarithm
+    of these functions are evaluated similarly.
+
+    >>> np.allclose(np.exp(X.logccdf(x)), 1 - X.cdf(x))
+    True
+    """
+
+    # When two-arg CDF is implemented for DiscreteDistribution, consider removing
+    # the special-casing here.
+    if issubclass(dist_family, ContinuousDistribution):
+        example_continuous = f"""
+    The inverse of these functions with respect to the argument ``x`` is also
+    available.
+
+    >>> logp = np.log(1 - X.ccdf(x))
+    >>> np.allclose(X.ilogcdf(logp), x)
+    True
+
+    Note that distribution functions and their logarithms also have two-argument
+    versions for working with the probability mass between two arguments. The
+    result tends to be more accurate than the naive implementation because it avoids
+    subtractive cancellation.
+
+    >>> y = {y}
+    >>> np.allclose(X.ccdf(x, y), 1 - (X.cdf(y) - X.cdf(x)))
+    True
+        """
+        example += example_continuous
+
+    example += f"""
+    There are methods for computing measures of central tendency,
+    dispersion, higher moments, and entropy.
+
+    >>> X.mean(), X.median(), X.mode()
+    {X.mean(), X.median(), X.mode()}
+
+    >>> X.variance(), X.standard_deviation()
+    {X.variance(), X.standard_deviation()}
+
+    >>> X.skewness(), X.kurtosis()
+    {X.skewness(), X.kurtosis()}
+
+    >>> np.allclose(X.moment(order=6, kind='standardized'),
+    ...             X.moment(order=6, kind='central') / X.variance()**3)
+    True
+    """
+
+    # When logentropy is implemented for DiscreteDistribution, remove special-casing
+    if issubclass(dist_family, ContinuousDistribution):
+        example += """
+    >>> np.allclose(np.exp(X.logentropy()), X.entropy())
+    True
+        """
+    else:
+        example += f"""
+        >>> X.entropy()
+        {X.entropy()}
+        """
+
+    example += f"""
+    Pseudo-random samples can be drawn from
+    the underlying distribution using ``sample``.
+
+    >>> X.sample(shape=(4,))
+    {repr(X.sample(shape=(4,)))}  # may vary
+    """
+    # remove the indentation due to use of block quote within function;
+    # eliminate blank first line
+    example = "\n".join([line.lstrip() for line in example.split("\n")][1:])
+    return example
+
+
+class UnivariateDistribution(_ProbabilityDistribution):
+    r""" Class that represents a continuous statistical distribution.
+
+    Parameters
+    ----------
+    tol : positive float, optional
+        The desired relative tolerance of calculations. Left unspecified,
+        calculations may be faster; when provided, calculations may be
+        more likely to meet the desired accuracy.
+    validation_policy : {None, "skip_all"}
+        Specifies the level of input validation to perform. Left unspecified,
+        input validation is performed to ensure appropriate behavior in edge
+        case (e.g. parameters out of domain, argument outside of distribution
+        support, etc.) and improve consistency of output dtype, shape, etc.
+        Pass ``'skip_all'`` to avoid the computational overhead of these
+        checks when rough edges are acceptable.
+    cache_policy : {None, "no_cache"}
+        Specifies the extent to which intermediate results are cached. Left
+        unspecified, intermediate results of some calculations (e.g. distribution
+        support, moments, etc.) are cached to improve performance of future
+        calculations. Pass ``'no_cache'`` to reduce memory reserved by the class
+        instance.
+
+    Attributes
+    ----------
+    All parameters are available as attributes.
+
+    Methods
+    -------
+    support
+
+    plot
+
+    sample
+
+    moment
+    lmoment
+
+    mean
+    median
+    mode
+
+    variance
+    standard_deviation
+
+    skewness
+    kurtosis
+
+    pdf
+    logpdf
+
+    cdf
+    icdf
+    ccdf
+    iccdf
+
+    logcdf
+    ilogcdf
+    logccdf
+    ilogccdf
+
+    entropy
+    logentropy
+
+    See Also
+    --------
+    :ref:`rv_infrastructure` : Tutorial
+
+    Notes
+    -----
+    The following abbreviations are used throughout the documentation.
+
+    - PDF: probability density function
+    - CDF: cumulative distribution function
+    - CCDF: complementary CDF
+    - entropy: differential entropy
+    - log-*F*: logarithm of *F* (e.g. log-CDF)
+    - inverse *F*: inverse function of *F* (e.g. inverse CDF)
+
+    The API documentation is written to describe the API, not to serve as
+    a statistical reference. Effort is made to be correct at the level
+    required to use the functionality, not to be mathematically rigorous.
+    For example, continuity and differentiability may be implicitly assumed.
+    For precise mathematical definitions, consult your preferred mathematical
+    text.
+
+    """
+    __array_priority__ = 1
+    _parameterizations = []  # type: ignore[var-annotated]
+
+    ### Initialization
+
+    def __init__(self, *, tol=_null, validation_policy=None, cache_policy=None,
+                 **parameters):
+        self.tol = tol
+        self.validation_policy = validation_policy
+        self.cache_policy = cache_policy
+        self._not_implemented = (
+            f"`{self.__class__.__name__}` does not provide an accurate "
+            "implementation of the required method. Consider leaving "
+            "`method` and `tol` unspecified to use another implementation."
+        )
+        self._original_parameters = {}
+        # We may want to override the `__init__` method with parameters so
+        # IDEs can suggest parameter names. If there are multiple parameterizations,
+        # we'll need the default values of parameters to be None; this will
+        # filter out the parameters that were not actually specified by the user.
+        parameters = {key: val for key, val in
+                      sorted(parameters.items()) if val is not None}
+        self._update_parameters(**parameters)
+
+    def _update_parameters(self, *, validation_policy=None, **params):
+        r""" Update the numerical values of distribution parameters.
+
+        Parameters
+        ----------
+        validation_policy : {None, "skip_all"}
+            Specifies the level of input validation to perform. Left unspecified,
+            input validation is performed to ensure appropriate behavior in edge
+            case (e.g. parameters out of domain, argument outside of distribution
+            support, etc.) and improve consistency of output dtype, shape, etc.
+            Pass ``'skip_all'`` to avoid the computational overhead of these
+            checks when rough edges are acceptable.
+
+        **params : array_like
+            Desired numerical values of the distribution parameters. Any or all
+            of the parameters initially used to instantiate the distribution
+            may be modified. Parameters used in alternative parameterizations
+            are not accepted.
+        """
+
+        parameters = original_parameters = self._original_parameters.copy()
+        parameters.update(**params)
+        parameterization = None
+        self._invalid = np.asarray(False)
+        self._any_invalid = False
+        self._shape = tuple()
+        self._ndim = 0
+        self._size = 1
+        self._dtype = np.float64
+
+        if (validation_policy or self.validation_policy) == _SKIP_ALL:
+            parameters = self._process_parameters(**parameters)
+        elif not len(self._parameterizations):
+            if parameters:
+                message = (f"The `{self.__class__.__name__}` distribution "
+                           "family does not accept parameters, but parameters "
+                           f"`{set(parameters)}` were provided.")
+                raise ValueError(message)
+        else:
+            # This is default behavior, which re-runs all parameter validations
+            # even when only a single parameter is modified. For many
+            # distributions, the domain of a parameter doesn't depend on other
+            # parameters, so parameters could safely be modified without
+            # re-validating all other parameters. To handle these cases more
+            # efficiently, we could allow the developer to override this
+            # behavior.
+
+            # Currently the user can only update the original parameterization.
+            # Even though that parameterization is already known,
+            # `_identify_parameterization` is called to produce a nice error
+            # message if the user passes other values. To be a little more
+            # efficient, we could detect whether the values passed are
+            # consistent with the original parameterization rather than finding
+            # it from scratch. However, we might want other parameterizations
+            # to be accepted, which would require other changes, so I didn't
+            # optimize this.
+
+            parameterization = self._identify_parameterization(parameters)
+            parameters, shape, size, ndim = self._broadcast(parameters)
+            parameters, invalid, any_invalid, dtype = (
+                self._validate(parameterization, parameters))
+            parameters = self._process_parameters(**parameters)
+
+            self._invalid = invalid
+            self._any_invalid = any_invalid
+            self._shape = shape
+            self._size = size
+            self._ndim = ndim
+            self._dtype = dtype
+
+        self.reset_cache()
+        self._parameters = parameters
+        self._parameterization = parameterization
+        self._original_parameters = original_parameters
+        for name in self._parameters.keys():
+            # Make parameters properties of the class; return values from the instance
+            if hasattr(self.__class__, name):
+                continue
+            setattr(self.__class__, name, property(lambda self_, name_=name:
+                                                   self_._parameters[name_].copy()[()]))
+
+    def reset_cache(self):
+        r""" Clear all cached values.
+
+        To improve the speed of some calculations, the distribution's support
+        and moments are cached.
+
+        This function is called automatically whenever the distribution
+        parameters are updated.
+
+        """
+        # We could offer finer control over what is cleared.
+        # For simplicity, these will still exist even if cache_policy is
+        # NO_CACHE; they just won't be populated. This allows caching to be
+        # turned on and off easily.
+        self._moment_raw_cache = {}
+        self._moment_central_cache = {}
+        self._moment_standardized_cache = {}
+        self._lmoment_cache = {}
+        self._support_cache = None
+        self._method_cache = {}
+        self._constant_cache = None
+
+    def _identify_parameterization(self, parameters):
+        # Determine whether a `parameters` dictionary matches is consistent
+        # with one of the parameterizations of the distribution. If so,
+        # return that parameterization object; if not, raise an error.
+        #
+        # I've come back to this a few times wanting to avoid this explicit
+        # loop. I've considered several possibilities, but they've all been a
+        # little unusual. For example, we could override `_eq_` so we can
+        # use _parameterizations.index() to retrieve the parameterization,
+        # or the user could put the parameterizations in a dictionary so we
+        # could look them up with a key (e.g. frozenset of parameter names).
+        # I haven't been sure enough of these approaches to implement them.
+        parameter_names_set = set(parameters)
+
+        for parameterization in self._parameterizations:
+            if parameterization.matches(parameter_names_set):
+                break
+        else:
+            if not parameter_names_set:
+                message = (f"The `{self.__class__.__name__}` distribution "
+                           "family requires parameters, but none were "
+                           "provided.")
+            else:
+                parameter_names = self._get_parameter_str(parameters)
+                message = (f"The provided parameters `{parameter_names}` "
+                           "do not match a supported parameterization of the "
+                           f"`{self.__class__.__name__}` distribution family.")
+            raise ValueError(message)
+
+        return parameterization
+
+    def _broadcast(self, parameters):
+        # Broadcast the distribution parameters to the same shape. If the
+        # arrays are not broadcastable, raise a meaningful error.
+        #
+        # We always make sure that the parameters *are* the same shape
+        # and not just broadcastable. Users can access parameters as
+        # attributes, and I think they should see the arrays as the same shape.
+        # More importantly, arrays should be the same shape before logical
+        # indexing operations, which are needed in infrastructure code when
+        # there are invalid parameters, and may be needed in
+        # distribution-specific code. We don't want developers to need to
+        # broadcast in implementation functions.
+
+        # It's much faster to check whether broadcasting is necessary than to
+        # broadcast when it's not necessary.
+        parameter_vals = [np.asarray(parameter)
+                          for parameter in parameters.values()]
+        parameter_shapes = set(parameter.shape for parameter in parameter_vals)
+        if len(parameter_shapes) == 1:
+            return (parameters, parameter_vals[0].shape,
+                    parameter_vals[0].size, parameter_vals[0].ndim)
+
+        try:
+            parameter_vals = np.broadcast_arrays(*parameter_vals)
+        except ValueError as e:
+            parameter_names = self._get_parameter_str(parameters)
+            message = (f"The parameters `{parameter_names}` provided to the "
+                       f"`{self.__class__.__name__}` distribution family "
+                       "cannot be broadcast to the same shape.")
+            raise ValueError(message) from e
+        return (dict(zip(parameters.keys(), parameter_vals)),
+                parameter_vals[0].shape,
+                parameter_vals[0].size,
+                parameter_vals[0].ndim)
+
+    def _validate(self, parameterization, parameters):
+        # Broadcasts distribution parameter arrays and converts them to a
+        # consistent dtype. Replaces invalid parameters with `np.nan`.
+        # Returns the validated parameters, a boolean mask indicated *which*
+        # elements are invalid, a boolean scalar indicating whether *any*
+        # are invalid (to skip special treatments if none are invalid), and
+        # the common dtype.
+        valid, dtype = parameterization.validation(parameters)
+        invalid = ~valid
+        any_invalid = invalid if invalid.shape == () else np.any(invalid)
+        # If necessary, make the arrays contiguous and replace invalid with NaN
+        if any_invalid:
+            for parameter_name in parameters:
+                parameters[parameter_name] = np.copy(
+                    parameters[parameter_name])
+                parameters[parameter_name][invalid] = np.nan
+
+        return parameters, invalid, any_invalid, dtype
+
+    def _process_parameters(self, **params):
+        r""" Process and cache distribution parameters for reuse.
+
+        This is intended to be overridden by subclasses. It allows distribution
+        authors to pre-process parameters for re-use. For instance, when a user
+        parameterizes a LogUniform distribution with `a` and `b`, it makes
+        sense to calculate `log(a)` and `log(b)` because these values will be
+        used in almost all distribution methods. The dictionary returned by
+        this method is passed to all private methods that calculate functions
+        of the distribution.
+        """
+        return params
+
+    def _get_parameter_str(self, parameters):
+        # Get a string representation of the parameters like "{a, b, c}".
+        return f"{{{', '.join(parameters.keys())}}}"
+
+    def _copy_parameterization(self):
+        self._parameterizations = self._parameterizations.copy()
+        for i in range(len(self._parameterizations)):
+            self._parameterizations[i] = self._parameterizations[i].copy()
+
+    ### Attributes
+
+    @property
+    def tol(self):
+        r"""positive float:
+        The desired relative tolerance of calculations. Left unspecified,
+        calculations may be faster; when provided, calculations may be
+        more likely to meet the desired accuracy.
+        """
+        return self._tol
+
+    @tol.setter
+    def tol(self, tol):
+        if _isnull(tol):
+            self._tol = tol
+            return
+
+        tol = np.asarray(tol)
+        if (tol.shape != () or not tol > 0 or  # catches NaNs
+                not np.issubdtype(tol.dtype, np.floating)):
+            message = (f"Attribute `tol` of `{self.__class__.__name__}` must "
+                       "be a positive float, if specified.")
+            raise ValueError(message)
+        self._tol = tol[()]
+
+    @property
+    def cache_policy(self):
+        r"""{None, "no_cache"}:
+        Specifies the extent to which intermediate results are cached. Left
+        unspecified, intermediate results of some calculations (e.g. distribution
+        support, moments, etc.) are cached to improve performance of future
+        calculations. Pass ``'no_cache'`` to reduce memory reserved by the class
+        instance.
+        """
+        return self._cache_policy
+
+    @cache_policy.setter
+    def cache_policy(self, cache_policy):
+        cache_policy = str(cache_policy).lower() if cache_policy is not None else None
+        cache_policies = {None, 'no_cache'}
+        if cache_policy not in cache_policies:
+            message = (f"Attribute `cache_policy` of `{self.__class__.__name__}` "
+                       f"must be one of {cache_policies}, if specified.")
+            raise ValueError(message)
+        self._cache_policy = cache_policy
+
+    @property
+    def validation_policy(self):
+        r"""{None, "skip_all"}:
+        Specifies the level of input validation to perform. Left unspecified,
+        input validation is performed to ensure appropriate behavior in edge
+        case (e.g. parameters out of domain, argument outside of distribution
+        support, etc.) and improve consistency of output dtype, shape, etc.
+        Use ``'skip_all'`` to avoid the computational overhead of these
+        checks when rough edges are acceptable.
+        """
+        return self._validation_policy
+
+    @validation_policy.setter
+    def validation_policy(self, validation_policy):
+        validation_policy = (str(validation_policy).lower()
+                             if validation_policy is not None else None)
+        iv_policies = {None, 'skip_all'}
+        if validation_policy not in iv_policies:
+            message = (f"Attribute `validation_policy` of `{self.__class__.__name__}` "
+                       f"must be one of {iv_policies}, if specified.")
+            raise ValueError(message)
+        self._validation_policy = validation_policy
+
+    ### Other magic methods
+
+    def __repr__(self):
+        r""" Returns a string representation of the distribution.
+
+        Includes the name of the distribution family, the names of the
+        parameters and the `repr` of each of their values.
+
+
+        """
+        class_name = self.__class__.__name__
+        parameters = list(self._original_parameters.items())
+        info = []
+        with np.printoptions(threshold=10):
+            str_parameters = [f"{symbol}={repr(value)}" for symbol, value in parameters]
+        str_parameters = f"{', '.join(str_parameters)}"
+        info.append(str_parameters)
+        return f"{class_name}({', '.join(info)})"
+
+    def __str__(self):
+        class_name = self.__class__.__name__
+        parameters = list(self._original_parameters.items())
+        info = []
+        with np.printoptions(threshold=10):
+            str_parameters = [f"{symbol}={str(value)}" for symbol, value in parameters]
+        str_parameters = f"{', '.join(str_parameters)}"
+        info.append(str_parameters)
+        return f"{class_name}({', '.join(info)})"
+
+    def __add__(self, loc):
+        return ShiftedScaledDistribution(self, loc=loc)
+
+    def __sub__(self, loc):
+        return ShiftedScaledDistribution(self, loc=-loc)
+
+    def __mul__(self, scale):
+        return ShiftedScaledDistribution(self, scale=scale)
+
+    def __truediv__(self, scale):
+        return ShiftedScaledDistribution(self, scale=1/scale)
+
+    def __pow__(self, other):
+        if not np.isscalar(other) or other <= 0 or other != int(other):
+            message = ("Raising a random variable to the power of an argument is only "
+                       "implemented when the argument is a positive integer.")
+            raise NotImplementedError(message)
+
+        # Fill in repr_pattern with the repr of self before taking abs.
+        # Avoids having unnecessary abs in the repr.
+        with np.printoptions(threshold=10):
+            repr_pattern = f"({repr(self)})**{repr(other)}"
+            str_pattern = f"({str(self)})**{str(other)}"
+        X = abs(self) if other % 2 == 0 else self
+
+        funcs = dict(g=lambda u: u**other, repr_pattern=repr_pattern,
+                     str_pattern=str_pattern,
+                     h=lambda u: np.sign(u) * np.abs(u)**(1 / other),
+                     dh=lambda u: 1/other * np.abs(u)**(1/other - 1))
+
+        return MonotonicTransformedDistribution(X, **funcs, increasing=True)
+
+    def __radd__(self, other):
+        return self.__add__(other)
+
+    def __rsub__(self, other):
+        return self.__neg__().__add__(other)
+
+    def __rmul__(self, other):
+        return self.__mul__(other)
+
+    def __rtruediv__(self, other):
+        a, b = self.support()
+        with np.printoptions(threshold=10):
+            funcs = dict(g=lambda u: 1 / u,
+                         repr_pattern=f"{repr(other)}/({repr(self)})",
+                         str_pattern=f"{str(other)}/({str(self)})",
+                         h=lambda u: 1 / u, dh=lambda u: 1 / u ** 2)
+        if np.all(a >= 0) or np.all(b <= 0):
+            out = MonotonicTransformedDistribution(self, **funcs, increasing=False)
+        else:
+            message = ("Division by a random variable is only implemented "
+                       "when the support is either non-negative or non-positive.")
+            raise NotImplementedError(message)
+        if np.all(other == 1):
+            return out
+        else:
+            return out * other
+
+    def __rpow__(self, other):
+        with np.printoptions(threshold=10):
+            funcs = dict(g=lambda u: other**u,
+                         h=lambda u: np.log(u) / np.log(other),
+                         dh=lambda u: 1 / np.abs(u * np.log(other)),
+                         repr_pattern=f"{repr(other)}**({repr(self)})",
+                         str_pattern=f"{str(other)}**({str(self)})",)
+
+        if not np.isscalar(other) or other <= 0 or other == 1:
+            message = ("Raising an argument to the power of a random variable is only "
+                       "implemented when the argument is a positive scalar other than "
+                       "1.")
+            raise NotImplementedError(message)
+
+        if other > 1:
+            return MonotonicTransformedDistribution(self, **funcs, increasing=True)
+        else:
+            return MonotonicTransformedDistribution(self, **funcs, increasing=False)
+
+    def __neg__(self):
+        return self * -1
+
+    def __abs__(self):
+        return FoldedDistribution(self)
+
+    ### Utilities
+
+    ## Input validation
+
+    def _validate_order(self, order, fname='moment', min_order=0):
+        # Yet another integer validating function. Unlike others in SciPy, it
+        # Is quite flexible about what is allowed as an integer, and it
+        # raises a distribution-specific error message to facilitate
+        # identification of the source of the error.
+        if self.validation_policy == _SKIP_ALL:
+            return order
+
+        order = np.asarray(order, dtype=self._dtype)[()]
+        message = (f"Argument `order` of `{self.__class__.__name__}.{fname}` "
+                   f"must be a finite integer greater than or equal to {min_order}.")
+        try:
+            order_int = round(order.item())
+            # If this fails for any reason (e.g. it's an array, it's infinite)
+            # it's not a valid `order`.
+        except Exception as e:
+            raise ValueError(message) from e
+
+        if order_int < min_order or order_int != order:
+            raise ValueError(message)
+
+        return order
+
+    def _validate_kind(self, kind, kinds):
+        message = (f"Argument `kind` of `{self.__class__.__name__}.moment` "
+                   f"must be one of {set(kinds)}.")
+        kind = kind.lower()
+        if kind not in kinds:
+            raise ValueError(message)
+        return kind
+
+    def _preserve_type(self, x):
+        x = np.asarray(x)
+        if x.dtype != self._dtype:
+            x = x.astype(self._dtype)
+        return x[()]
+
+    ## Testing
+
+    @classmethod
+    def _draw(cls, sizes=None, rng=None, i_parameterization=None,
+              proportions=None):
+        r""" Draw a specific (fully-defined) distribution from the family.
+
+        See _Parameterization.draw for documentation details.
+        """
+        rng = np.random.default_rng(rng)
+        if len(cls._parameterizations) == 0:
+            return cls()
+        if i_parameterization is None:
+            n = cls._num_parameterizations()
+            i_parameterization = rng.integers(0, max(0, n - 1), endpoint=True)
+
+        parameterization = cls._parameterizations[i_parameterization]
+        parameters = parameterization.draw(sizes, rng, proportions=proportions,
+                                           region='typical')
+        return cls(**parameters)
+
+    @classmethod
+    def _num_parameterizations(cls):
+        # Returns the number of parameterizations accepted by the family.
+        return len(cls._parameterizations)
+
+    @classmethod
+    def _num_parameters(cls, i_parameterization=0):
+        # Returns the number of parameters used in the specified
+        # parameterization.
+        return (0 if not cls._num_parameterizations()
+                else len(cls._parameterizations[i_parameterization]))
+
+    ## Algorithms
+
+    def _quadrature(self, integrand, limits=None, args=(), params=None, log=False):
+        # Performs numerical integration/summation between limits or over support.
+        a, b = self._support(**params) if limits is None else limits
+        rtol = None if _isnull(self.tol) else self.tol
+
+        # For now, we ignore the status, but I want to return the error estimate
+        if isinstance(self, ContinuousDistribution):
+            return _tanhsinh(integrand, a, b, args=args, kwargs=params,
+                             log=log, rtol=rtol).integral
+        else:
+            res = nsum(integrand, a, b, args=args, kwargs=params,
+                       log=log, tolerances=dict(rtol=rtol)).sum
+
+            # b > a -> sum is zero... unless the parameters are nan.
+            # (Resolving gh-22321 should fix this in nsum.)
+            cond = np.isnan(params.popitem()[1]) if params else np.True_
+            return np.where(cond, np.nan, res)[()]
+
+    def _solve_bounded(self, f, p, *, bounds=None, params=None, xatol=None):
+        # Finds the argument of a function that produces the desired output.
+        xmin, xmax = self._support(**params) if bounds is None else bounds
+
+        def f2(x, _p, **kwargs):  # named `_p` to avoid conflict with shape `p`
+            return f(x, **kwargs) - _p
+
+        xl0, xr0 = _guess_bracket(xmin, xmax)
+
+        res = elementwise.bracket_root(f2, xl0=xl0, xr0=xr0, xmin=xmin, xmax=xmax,
+                                       args=(p,), kwargs=params)
+        # For now, we ignore the status, but I want to use the bracket width
+        # as an error estimate.
+
+        xrtol = None if _isnull(self.tol) else self.tol
+        xatol = None if xatol is None else xatol
+        tolerances = dict(xrtol=xrtol, xatol=xatol, fatol=0, frtol=0)
+        return elementwise.find_root(f2, res.bracket, args=(p,),
+                                     kwargs=params, tolerances=tolerances)
+
+    ## Other
+
+    def _overrides(self, method_name):
+        # Determines whether a class overrides a specified method.
+        # Returns True if the method implementation exists and is the same as
+        # that of the `ContinuousDistribution` class; otherwise returns False.
+
+        # Sometimes we use `_overrides` to check whether a certain method is overridden
+        # and if so, call it. This begs the questions of why we don't do the more
+        # obvious thing: restructure so that if the private method is overridden,
+        # Python will call it instead of the inherited version automatically. The short
+        # answer is that there are multiple ways a use might wish to evaluate a method,
+        # and simply overriding the method with a formula is not always the best option.
+        # For more complete discussion of the considerations, see:
+        # https://github.com/scipy/scipy/pull/21050#discussion_r1707798901
+        method = getattr(self.__class__, method_name, None)
+        super_method = getattr(UnivariateDistribution, method_name, None)
+        return method is not super_method
+
+    ### Distribution properties
+    # The following "distribution properties" are exposed via a public method
+    # that accepts only options (not distribution parameters or quantile/
+    # percentile argument).
+    # support
+    # logentropy, entropy,
+    # median, mode, mean,
+    # variance, standard_deviation
+    # skewness, kurtosis
+    # Common options are:
+    # method - a string that indicates which method should be used to compute
+    #          the quantity (e.g. a formula or numerical integration).
+    # Input/output validation is provided by the `_set_invalid_nan_property`
+    # decorator. These are the methods meant to be called by users.
+    #
+    # Each public method calls a private "dispatch" method that
+    # determines which "method" (strategy for calculating the desired quantity)
+    # to use by default and, via the `@_dispatch` decorator, calls the
+    # method and computes the result.
+    # Dispatch methods always accept:
+    # method - as passed from the public method
+    # params - a dictionary of distribution shape parameters passed by
+    #          the public method.
+    # Dispatch methods accept `params` rather than relying on the state of the
+    # object because iterative algorithms like `tanhsinh` and `find_root`
+    # need their callable to follow a strict elementwise protocol: each element
+    # of the output is determined solely by the values of the inputs at the
+    # corresponding location. The public methods do not satisfy this protocol
+    # because they do not accept the parameters as arguments, producing an
+    # output that generally has a different shape than that of the input. Also,
+    # by calling "dispatch" methods rather than the public methods, the
+    # iterative algorithms avoid the overhead of input validation.
+    #
+    # Each dispatch method can designate the responsibility of computing
+    # the required value to any of several "implementation" methods. These
+    # methods accept only `**params`, the parameter dictionary passed from
+    # the public method via the dispatch method. We separate the implementation
+    # methods from the dispatch methods for the sake of simplicity (via
+    # compartmentalization) and to allow subclasses to override certain
+    # implementation methods (typically only the "formula" methods). The names
+    # of implementation methods are combinations of the public method name and
+    # the name of the "method" (strategy for calculating the desired quantity)
+    # string. (In fact, the name of the implementation method is calculated
+    # from these two strings in the `_dispatch` decorator.) Common method
+    # strings are:
+    # formula - distribution-specific analytical expressions to be implemented
+    #           by subclasses.
+    # log/exp - Compute the log of a number and then exponentiate it or vice
+    #           versa.
+    # quadrature - Compute the value via numerical integration.
+    #
+    # The default method (strategy) is determined based on what implementation
+    # methods are available and the error tolerance of the user. Typically,
+    # a formula is always used if available. We fall back to "log/exp" if a
+    # formula for the logarithm or exponential of the quantity is available,
+    # and we use quadrature otherwise.
+
+    def support(self):
+        # If this were a `cached_property`, we couldn't update the value
+        # when the distribution parameters change.
+        # Caching is important, though, because calls to _support take a few
+        # microseconds even when `a` and `b` are already the same shape.
+        if self._support_cache is not None:
+            return self._support_cache
+
+        a, b = self._support(**self._parameters)
+        if a.shape != self._shape:
+            a = np.broadcast_to(a, self._shape)
+        if b.shape != self._shape:
+            b = np.broadcast_to(b, self._shape)
+
+        if self._any_invalid:
+            a, b = np.asarray(a).copy(), np.asarray(b).copy()
+            a[self._invalid], b[self._invalid] = np.nan, np.nan
+            a, b = a[()], b[()]
+
+        support = (a, b)
+
+        if self.cache_policy != _NO_CACHE:
+            self._support_cache = support
+
+        return support
+
+    def _support(self, **params):
+        # Computes the support given distribution parameters
+        a, b = self._variable.domain.get_numerical_endpoints(params)
+        if len(params):
+            # the parameters should all be of the same dtype and shape at this point
+            vals = list(params.values())
+            shape = vals[0].shape
+            a = np.broadcast_to(a, shape) if a.shape != shape else a
+            b = np.broadcast_to(b, shape) if b.shape != shape else b
+        return self._preserve_type(a), self._preserve_type(b)
+
+    @_set_invalid_nan_property
+    def logentropy(self, *, method=None):
+        return self._logentropy_dispatch(method=method, **self._parameters) + 0j
+
+    @_dispatch
+    def _logentropy_dispatch(self, method=None, **params):
+        if self._overrides('_logentropy_formula'):
+            method = self._logentropy_formula
+        elif self._overrides('_entropy_formula'):
+            method = self._logentropy_logexp_safe
+        else:
+            method = self._logentropy_quadrature
+        return method
+
+    def _logentropy_formula(self, **params):
+        raise NotImplementedError(self._not_implemented)
+
+    def _logentropy_logexp(self, **params):
+        res = np.log(self._entropy_dispatch(**params)+0j)
+        return _log_real_standardize(res)
+
+    def _logentropy_logexp_safe(self, **params):
+        out = self._logentropy_logexp(**params)
+        mask = np.isinf(out.real)
+        if np.any(mask):
+            params_mask = {key:val[mask] for key, val in params.items()}
+            out = np.asarray(out)
+            out[mask] = self._logentropy_quadrature(**params_mask)
+        return out[()]
+
+    def _logentropy_quadrature(self, **params):
+        def logintegrand(x, **params):
+            logpxf = self._logpxf_dispatch(x, **params)
+            return logpxf + np.log(0j+logpxf)
+        res = self._quadrature(logintegrand, params=params, log=True)
+        return _log_real_standardize(res + np.pi*1j)
+
+    @_set_invalid_nan_property
+    def entropy(self, *, method=None):
+        return self._entropy_dispatch(method=method, **self._parameters)
+
+    @_dispatch
+    def _entropy_dispatch(self, method=None, **params):
+        if self._overrides('_entropy_formula'):
+            method = self._entropy_formula
+        elif self._overrides('_logentropy_formula'):
+            method = self._entropy_logexp
+        else:
+            method = self._entropy_quadrature
+        return method
+
+    def _entropy_formula(self, **params):
+        raise NotImplementedError(self._not_implemented)
+
+    def _entropy_logexp(self, **params):
+        return np.real(np.exp(self._logentropy_dispatch(**params)))
+
+    def _entropy_quadrature(self, **params):
+        def integrand(x, **params):
+            pxf = self._pxf_dispatch(x, **params)
+            logpxf = self._logpxf_dispatch(x, **params)
+            temp = np.asarray(pxf)
+            i = (pxf != 0)  # 0 * inf -> nan; should be 0
+            temp[i] = -pxf[i]*logpxf[i]
+            return temp
+        return self._quadrature(integrand, params=params)
+
+    @_set_invalid_nan_property
+    def median(self, *, method=None):
+        return self._median_dispatch(method=method, **self._parameters)
+
+    @_dispatch
+    def _median_dispatch(self, method=None, **params):
+        if self._overrides('_median_formula'):
+            method = self._median_formula
+        else:
+            method = self._median_icdf
+        return method
+
+    def _median_formula(self, **params):
+        raise NotImplementedError(self._not_implemented)
+
+    def _median_icdf(self, **params):
+        return self._icdf_dispatch(np.asarray(0.5, dtype=self._dtype), **params)
+
+    @_set_invalid_nan_property
+    def mode(self, *, method=None):
+        return self._mode_dispatch(method=method, **self._parameters)
+
+    @_dispatch
+    def _mode_dispatch(self, method=None, **params):
+        # We could add a method that looks for a critical point with
+        # differentiation and the root finder
+        if self._overrides('_mode_formula'):
+            method = self._mode_formula
+        else:
+            method = self._mode_optimization
+        return method
+
+    def _mode_formula(self, **params):
+        raise NotImplementedError(self._not_implemented)
+
+    def _mode_optimization(self, xatol=None, **params):
+        a, b = self._support(**params)
+        m = self._median_dispatch(**params)
+
+        def f(x, **params):
+            return -self._pxf_dispatch(x, **params)
+
+        res_b = elementwise.bracket_minimum(f, m, xmin=a, xmax=b, kwargs=params)
+        res = elementwise.find_minimum(f, res_b.bracket, kwargs=params,
+                                       tolerances=dict(xatol=xatol))
+        mode = np.asarray(res.x)
+
+        # bracket_minimum fails with status == -1 if the mode is at a boundary.
+        # We have to consider this as a special case; there's no way to include
+        # this logic in find_minimum; it has to treat the bracket as invalid.
+        mode_at_boundary = res.status == -1
+        fl, fm, fr = res_b.f_bracket
+        mode_at_left = mode_at_boundary & (fl <= fm)
+        mode_at_right = mode_at_boundary & (fr < fm)
+        mode[mode_at_left] = a[mode_at_left]
+        mode[mode_at_right] = b[mode_at_right]
+        return mode[()]
+
+    def mean(self, *, method=None):
+        return self.moment(1, kind='raw', method=method)
+
+    def variance(self, *, method=None):
+        return self.moment(2, kind='central', method=method)
+
+    def standard_deviation(self, *, method=None):
+        return np.sqrt(self.variance(method=method))
+
+    def skewness(self, *, method=None):
+        return self.moment(3, kind='standardized', method=method)
+
+    def kurtosis(self, *, method=None, convention='non-excess'):
+        conventions = {'non-excess', 'excess'}
+        message = (f'Parameter `convention` of `{self.__class__.__name__}.kurtosis` '
+                   f"must be one of {conventions}.")
+        convention = convention.lower()
+        if convention not in conventions:
+            raise ValueError(message)
+        k = self.moment(4, kind='standardized', method=method)
+        return k - 3 if convention == 'excess' else k
+
+    ### Distribution functions
+    # The following functions related to the distribution PDF and CDF are
+    # exposed via a public method that accepts one positional argument - the
+    # quantile - and keyword options (but not distribution parameters).
+    # logpdf, pdf
+    # logcdf, cdf
+    # logccdf, ccdf
+    # The `logcdf` and `cdf` functions can also be called with two positional
+    # arguments - lower and upper quantiles - and they return the probability
+    # mass (integral of the PDF) between them. The 2-arg versions of `logccdf`
+    # and `ccdf` return the complement of this quantity.
+    # All the (1-arg) cumulative distribution functions have inverse
+    # functions, which accept one positional argument - the percentile.
+    # ilogcdf, icdf
+    # ilogccdf, iccdf
+    # Common keyword options include:
+    # method - a string that indicates which method should be used to compute
+    #          the quantity (e.g. a formula or numerical integration).
+    # Tolerance options should be added.
+    # Input/output validation is provided by the `_set_invalid_nan`
+    # decorator. These are the methods meant to be called by users.
+    #
+    # Each public method calls a private "dispatch" method that
+    # determines which "method" (strategy for calculating the desired quantity)
+    # to use by default and, via the `@_dispatch` decorator, calls the
+    # method and computes the result.
+    # Each dispatch method can designate the responsibility of computing
+    # the required value to any of several "implementation" methods. These
+    # methods accept only `**params`, the parameter dictionary passed from
+    # the public method via the dispatch method.
+    # See the note corresponding with the "Distribution Parameters" for more
+    # information.
+
+    ## Probability Density/Mass Functions
+
+    @_set_invalid_nan
+    def logpdf(self, x, /, *, method=None):
+        return self._logpdf_dispatch(x, method=method, **self._parameters)
+
+    @_dispatch
+    def _logpdf_dispatch(self, x, *, method=None, **params):
+        if self._overrides('_logpdf_formula'):
+            method = self._logpdf_formula
+        elif _isnull(self.tol):  # ensure that developers override _logpdf
+            method = self._logpdf_logexp
+        return method
+
+    def _logpdf_formula(self, x, **params):
+        raise NotImplementedError(self._not_implemented)
+
+    def _logpdf_logexp(self, x, **params):
+        return np.log(self._pdf_dispatch(x, **params))
+
+    @_set_invalid_nan
+    def pdf(self, x, /, *, method=None):
+        return self._pdf_dispatch(x, method=method, **self._parameters)
+
+    @_dispatch
+    def _pdf_dispatch(self, x, *, method=None, **params):
+        if self._overrides('_pdf_formula'):
+            method = self._pdf_formula
+        else:
+            method = self._pdf_logexp
+        return method
+
+    def _pdf_formula(self, x, **params):
+        raise NotImplementedError(self._not_implemented)
+
+    def _pdf_logexp(self, x, **params):
+        return np.exp(self._logpdf_dispatch(x, **params))
+
+    @_set_invalid_nan
+    def logpmf(self, x, /, *, method=None):
+        return self._logpmf_dispatch(x, method=method, **self._parameters)
+
+    @_dispatch
+    def _logpmf_dispatch(self, x, *, method=None, **params):
+        if self._overrides('_logpmf_formula'):
+            method = self._logpmf_formula
+        elif _isnull(self.tol):  # ensure that developers override _logpmf
+            method = self._logpmf_logexp
+        return method
+
+    def _logpmf_formula(self, x, **params):
+        raise NotImplementedError(self._not_implemented)
+
+    def _logpmf_logexp(self, x, **params):
+        with np.errstate(divide='ignore'):
+            return np.log(self._pmf_dispatch(x, **params))
+
+    @_set_invalid_nan
+    def pmf(self, x, /, *, method=None):
+        return self._pmf_dispatch(x, method=method, **self._parameters)
+
+    @_dispatch
+    def _pmf_dispatch(self, x, *, method=None, **params):
+        if self._overrides('_pmf_formula'):
+            method = self._pmf_formula
+        else:
+            method = self._pmf_logexp
+        return method
+
+    def _pmf_formula(self, x, **params):
+        raise NotImplementedError(self._not_implemented)
+
+    def _pmf_logexp(self, x, **params):
+        return np.exp(self._logpmf_dispatch(x, **params))
+
+    ## Cumulative Distribution Functions
+
+    def logcdf(self, x, y=None, /, *, method=None):
+        if y is None:
+            return self._logcdf1(x, method=method)
+        else:
+            return self._logcdf2(x, y, method=method)
+
+    @_cdf2_input_validation
+    def _logcdf2(self, x, y, *, method):
+        out = self._logcdf2_dispatch(x, y, method=method, **self._parameters)
+        return (out + 0j) if not np.issubdtype(out.dtype, np.complexfloating) else out
+
+    @_dispatch
+    def _logcdf2_dispatch(self, x, y, *, method=None, **params):
+        if self._overrides('_logcdf2_formula'):
+            method = self._logcdf2_formula
+        elif (self._overrides('_logcdf_formula')
+              or self._overrides('_logccdf_formula')):
+            method = self._logcdf2_subtraction
+        elif (self._overrides('_cdf_formula')
+              or self._overrides('_ccdf_formula')):
+            method = self._logcdf2_logexp_safe
+        else:
+            method = self._logcdf2_quadrature
+        return method
+
+    def _logcdf2_formula(self, x, y, **params):
+        raise NotImplementedError(self._not_implemented)
+
+    def _logcdf2_subtraction(self, x, y, **params):
+        flip_sign = x > y  # some results will be negative
+        x, y = np.minimum(x, y), np.maximum(x, y)
+        logcdf_x = self._logcdf_dispatch(x, **params)
+        logcdf_y = self._logcdf_dispatch(y, **params)
+        logccdf_x = self._logccdf_dispatch(x, **params)
+        logccdf_y = self._logccdf_dispatch(y, **params)
+        case_left = (logcdf_x < -1) & (logcdf_y < -1)
+        case_right = (logccdf_x < -1) & (logccdf_y < -1)
+        case_central = ~(case_left | case_right)
+        log_mass = _logexpxmexpy(logcdf_y, logcdf_x)
+        log_mass[case_right] = _logexpxmexpy(logccdf_x, logccdf_y)[case_right]
+        log_tail = np.logaddexp(logcdf_x, logccdf_y)[case_central]
+        log_mass[case_central] = _log1mexp(log_tail)
+        log_mass[flip_sign] += np.pi * 1j
+        return log_mass[()] if np.any(flip_sign) else log_mass.real[()]
+
+    def _logcdf2_logexp(self, x, y, **params):
+        expres = self._cdf2_dispatch(x, y, **params)
+        expres = expres + 0j if np.any(x > y) else expres
+        return np.log(expres)
+
+    def _logcdf2_logexp_safe(self, x, y, **params):
+        out = self._logcdf2_logexp(x, y, **params)
+        mask = np.isinf(out.real)
+        if np.any(mask):
+            params_mask = {key: np.broadcast_to(val, mask.shape)[mask]
+                           for key, val in params.items()}
+            out = np.asarray(out)
+            out[mask] = self._logcdf2_quadrature(x[mask], y[mask], **params_mask)
+        return out[()]
+
+    def _logcdf2_quadrature(self, x, y, **params):
+        logres = self._quadrature(self._logpxf_dispatch, limits=(x, y),
+                                  log=True, params=params)
+        return logres
+
+    @_set_invalid_nan
+    def _logcdf1(self, x, *, method=None):
+        return self._logcdf_dispatch(x, method=method, **self._parameters)
+
+    @_dispatch
+    def _logcdf_dispatch(self, x, *, method=None, **params):
+        if self._overrides('_logcdf_formula'):
+            method = self._logcdf_formula
+        elif self._overrides('_logccdf_formula'):
+            method = self._logcdf_complement
+        elif self._overrides('_cdf_formula'):
+            method = self._logcdf_logexp_safe
+        else:
+            method = self._logcdf_quadrature
+        return method
+
+    def _logcdf_formula(self, x, **params):
+        raise NotImplementedError(self._not_implemented)
+
+    def _logcdf_complement(self, x, **params):
+        return _log1mexp(self._logccdf_dispatch(x, **params))
+
+    def _logcdf_logexp(self, x, **params):
+        return np.log(self._cdf_dispatch(x, **params))
+
+    def _logcdf_logexp_safe(self, x, **params):
+        out = self._logcdf_logexp(x, **params)
+        mask = np.isinf(out)
+        if np.any(mask):
+            params_mask = {key:np.broadcast_to(val, mask.shape)[mask]
+                           for key, val in params.items()}
+            out = np.asarray(out)
+            out[mask] = self._logcdf_quadrature(x[mask], **params_mask)
+        return out[()]
+
+    def _logcdf_quadrature(self, x, **params):
+        a, _ = self._support(**params)
+        return self._quadrature(self._logpxf_dispatch, limits=(a, x),
+                                params=params, log=True)
+
+    def cdf(self, x, y=None, /, *, method=None):
+        if y is None:
+            return self._cdf1(x, method=method)
+        else:
+            return self._cdf2(x, y, method=method)
+
+    @_cdf2_input_validation
+    def _cdf2(self, x, y, *, method):
+        return self._cdf2_dispatch(x, y, method=method, **self._parameters)
+
+    @_dispatch
+    def _cdf2_dispatch(self, x, y, *, method=None, **params):
+        if self._overrides('_cdf2_formula'):
+            method = self._cdf2_formula
+        elif (self._overrides('_logcdf_formula')
+              or self._overrides('_logccdf_formula')):
+            method = self._cdf2_logexp
+        elif self._overrides('_cdf_formula') or self._overrides('_ccdf_formula'):
+            method = self._cdf2_subtraction_safe
+        else:
+            method = self._cdf2_quadrature
+        return method
+
+    def _cdf2_formula(self, x, y, **params):
+        raise NotImplementedError(self._not_implemented)
+
+    def _cdf2_logexp(self, x, y, **params):
+        return np.real(np.exp(self._logcdf2_dispatch(x, y, **params)))
+
+    def _cdf2_subtraction(self, x, y, **params):
+        # Improvements:
+        # Lazy evaluation of cdf/ccdf only where needed
+        # Stack x and y to reduce function calls?
+        cdf_x = self._cdf_dispatch(x, **params)
+        cdf_y = self._cdf_dispatch(y, **params)
+        ccdf_x = self._ccdf_dispatch(x, **params)
+        ccdf_y = self._ccdf_dispatch(y, **params)
+        i = (ccdf_x < 0.5) & (ccdf_y < 0.5)
+        return np.where(i, ccdf_x-ccdf_y, cdf_y-cdf_x)
+
+    def _cdf2_subtraction_safe(self, x, y, **params):
+        cdf_x = self._cdf_dispatch(x, **params)
+        cdf_y = self._cdf_dispatch(y, **params)
+        ccdf_x = self._ccdf_dispatch(x, **params)
+        ccdf_y = self._ccdf_dispatch(y, **params)
+        i = (ccdf_x < 0.5) & (ccdf_y < 0.5)
+        out = np.where(i, ccdf_x-ccdf_y, cdf_y-cdf_x)
+
+        eps = np.finfo(self._dtype).eps
+        tol = self.tol if not _isnull(self.tol) else np.sqrt(eps)
+
+        cdf_max = np.maximum(cdf_x, cdf_y)
+        ccdf_max = np.maximum(ccdf_x, ccdf_y)
+        spacing = np.spacing(np.where(i, ccdf_max, cdf_max))
+        mask = np.abs(tol * out) < spacing
+
+        if np.any(mask):
+            params_mask = {key: np.broadcast_to(val, mask.shape)[mask]
+                           for key, val in params.items()}
+            out = np.asarray(out)
+            out[mask] = self._cdf2_quadrature(x[mask], y[mask], **params_mask)
+        return out[()]
+
+    def _cdf2_quadrature(self, x, y, **params):
+        return self._quadrature(self._pxf_dispatch, limits=(x, y), params=params)
+
+    @_set_invalid_nan
+    def _cdf1(self, x, *, method):
+        return self._cdf_dispatch(x, method=method, **self._parameters)
+
+    @_dispatch
+    def _cdf_dispatch(self, x, *, method=None, **params):
+        if self._overrides('_cdf_formula'):
+            method = self._cdf_formula
+        elif self._overrides('_logcdf_formula'):
+            method = self._cdf_logexp
+        elif self._overrides('_ccdf_formula'):
+            method = self._cdf_complement_safe
+        else:
+            method = self._cdf_quadrature
+        return method
+
+    def _cdf_formula(self, x, **params):
+        raise NotImplementedError(self._not_implemented)
+
+    def _cdf_logexp(self, x, **params):
+        return np.exp(self._logcdf_dispatch(x, **params))
+
+    def _cdf_complement(self, x, **params):
+        return 1 - self._ccdf_dispatch(x, **params)
+
+    def _cdf_complement_safe(self, x, **params):
+        ccdf = self._ccdf_dispatch(x, **params)
+        out = 1 - ccdf
+        eps = np.finfo(self._dtype).eps
+        tol = self.tol if not _isnull(self.tol) else np.sqrt(eps)
+        mask = tol * out < np.spacing(ccdf)
+        if np.any(mask):
+            params_mask = {key: np.broadcast_to(val, mask.shape)[mask]
+                           for key, val in params.items()}
+            out = np.asarray(out)
+            out[mask] = self._cdf_quadrature(x[mask], **params_mask)
+        return out[()]
+
+    def _cdf_quadrature(self, x, **params):
+        a, _ = self._support(**params)
+        return self._quadrature(self._pxf_dispatch, limits=(a, x),
+                                params=params)
+
+    def logccdf(self, x, y=None, /, *, method=None):
+        if y is None:
+            return self._logccdf1(x, method=method)
+        else:
+            return self._logccdf2(x, y, method=method)
+
+    @_cdf2_input_validation
+    def _logccdf2(self, x, y, *, method):
+        return self._logccdf2_dispatch(x, y, method=method, **self._parameters)
+
+    @_dispatch
+    def _logccdf2_dispatch(self, x, y, *, method=None, **params):
+        # if _logccdf2_formula exists, we could use the complement
+        # if _ccdf2_formula exists, we could use log/exp
+        if self._overrides('_logccdf2_formula'):
+            method = self._logccdf2_formula
+        else:
+            method = self._logccdf2_addition
+        return method
+
+    def _logccdf2_formula(self, x, y, **params):
+        raise NotImplementedError(self._not_implemented)
+
+    def _logccdf2_addition(self, x, y, **params):
+        logcdf_x = self._logcdf_dispatch(x, **params)
+        logccdf_y = self._logccdf_dispatch(y, **params)
+        return special.logsumexp([logcdf_x, logccdf_y], axis=0)
+
+    @_set_invalid_nan
+    def _logccdf1(self, x, *, method=None):
+        return self._logccdf_dispatch(x, method=method, **self._parameters)
+
+    @_dispatch
+    def _logccdf_dispatch(self, x, method=None, **params):
+        if self._overrides('_logccdf_formula'):
+            method = self._logccdf_formula
+        elif self._overrides('_logcdf_formula'):
+            method = self._logccdf_complement
+        elif self._overrides('_ccdf_formula'):
+            method = self._logccdf_logexp_safe
+        else:
+            method = self._logccdf_quadrature
+        return method
+
+    def _logccdf_formula(self, x, **params):
+        raise NotImplementedError(self._not_implemented)
+
+    def _logccdf_complement(self, x, **params):
+        return _log1mexp(self._logcdf_dispatch(x, **params))
+
+    def _logccdf_logexp(self, x, **params):
+        return np.log(self._ccdf_dispatch(x, **params))
+
+    def _logccdf_logexp_safe(self, x, **params):
+        out = self._logccdf_logexp(x, **params)
+        mask = np.isinf(out)
+        if np.any(mask):
+            params_mask = {key: np.broadcast_to(val, mask.shape)[mask]
+                           for key, val in params.items()}
+            out = np.asarray(out)
+            out[mask] = self._logccdf_quadrature(x[mask], **params_mask)
+        return out[()]
+
+    def _logccdf_quadrature(self, x, **params):
+        _, b = self._support(**params)
+        return self._quadrature(self._logpxf_dispatch, limits=(x, b),
+                                params=params, log=True)
+
+    def ccdf(self, x, y=None, /, *, method=None):
+        if y is None:
+            return self._ccdf1(x, method=method)
+        else:
+            return self._ccdf2(x, y, method=method)
+
+    @_cdf2_input_validation
+    def _ccdf2(self, x, y, *, method):
+        return self._ccdf2_dispatch(x, y, method=method, **self._parameters)
+
+    @_dispatch
+    def _ccdf2_dispatch(self, x, y, *, method=None, **params):
+        if self._overrides('_ccdf2_formula'):
+            method = self._ccdf2_formula
+        else:
+            method = self._ccdf2_addition
+        return method
+
+    def _ccdf2_formula(self, x, y, **params):
+        raise NotImplementedError(self._not_implemented)
+
+    def _ccdf2_addition(self, x, y, **params):
+        cdf_x = self._cdf_dispatch(x, **params)
+        ccdf_y = self._ccdf_dispatch(y, **params)
+        # even if x > y, cdf(x, y) + ccdf(x,y) sums to 1
+        return cdf_x + ccdf_y
+
+    @_set_invalid_nan
+    def _ccdf1(self, x, *, method):
+        return self._ccdf_dispatch(x, method=method, **self._parameters)
+
+    @_dispatch
+    def _ccdf_dispatch(self, x, method=None, **params):
+        if self._overrides('_ccdf_formula'):
+            method = self._ccdf_formula
+        elif self._overrides('_logccdf_formula'):
+            method = self._ccdf_logexp
+        elif self._overrides('_cdf_formula'):
+            method = self._ccdf_complement_safe
+        else:
+            method = self._ccdf_quadrature
+        return method
+
+    def _ccdf_formula(self, x, **params):
+        raise NotImplementedError(self._not_implemented)
+
+    def _ccdf_logexp(self, x, **params):
+        return np.exp(self._logccdf_dispatch(x, **params))
+
+    def _ccdf_complement(self, x, **params):
+        return 1 - self._cdf_dispatch(x, **params)
+
+    def _ccdf_complement_safe(self, x, **params):
+        cdf = self._cdf_dispatch(x, **params)
+        out = 1 - cdf
+        eps = np.finfo(self._dtype).eps
+        tol = self.tol if not _isnull(self.tol) else np.sqrt(eps)
+        mask = tol * out < np.spacing(cdf)
+        if np.any(mask):
+            params_mask = {key: np.broadcast_to(val, mask.shape)[mask]
+                           for key, val in params.items()}
+            out = np.asarray(out)
+            out[mask] = self._ccdf_quadrature(x[mask], **params_mask)
+        return out[()]
+
+    def _ccdf_quadrature(self, x, **params):
+        _, b = self._support(**params)
+        return self._quadrature(self._pxf_dispatch, limits=(x, b),
+                                params=params)
+
+    ## Inverse cumulative distribution functions
+
+    @_set_invalid_nan
+    def ilogcdf(self, logp, /, *, method=None):
+        return self._ilogcdf_dispatch(logp, method=method, **self._parameters)
+
+    @_dispatch
+    def _ilogcdf_dispatch(self, x, method=None, **params):
+        if self._overrides('_ilogcdf_formula'):
+            method = self._ilogcdf_formula
+        elif self._overrides('_ilogccdf_formula'):
+            method = self._ilogcdf_complement
+        else:
+            method = self._ilogcdf_inversion
+        return method
+
+    def _ilogcdf_formula(self, x, **params):
+        raise NotImplementedError(self._not_implemented)
+
+    def _ilogcdf_complement(self, x, **params):
+        return self._ilogccdf_dispatch(_log1mexp(x), **params)
+
+    def _ilogcdf_inversion(self, x, **params):
+        return self._solve_bounded_continuous(self._logcdf_dispatch, x, params=params)
+
+    @_set_invalid_nan
+    def icdf(self, p, /, *, method=None):
+        return self._icdf_dispatch(p, method=method, **self._parameters)
+
+    @_dispatch
+    def _icdf_dispatch(self, x, method=None, **params):
+        if self._overrides('_icdf_formula'):
+            method = self._icdf_formula
+        elif self._overrides('_iccdf_formula'):
+            method = self._icdf_complement_safe
+        else:
+            method = self._icdf_inversion
+        return method
+
+    def _icdf_formula(self, x, **params):
+        raise NotImplementedError(self._not_implemented)
+
+    def _icdf_complement(self, x, **params):
+        return self._iccdf_dispatch(1 - x, **params)
+
+    def _icdf_complement_safe(self, x, **params):
+        out = self._icdf_complement(x, **params)
+        eps = np.finfo(self._dtype).eps
+        tol = self.tol if not _isnull(self.tol) else np.sqrt(eps)
+        mask = tol * x < np.spacing(1 - x)
+        if np.any(mask):
+            params_mask = {key: np.broadcast_to(val, mask.shape)[mask]
+                           for key, val in params.items()}
+            out = np.asarray(out)
+            out[mask] = self._icdf_inversion(x[mask], **params_mask)
+        return out[()]
+
+    def _icdf_inversion(self, x, **params):
+        return self._solve_bounded_continuous(self._cdf_dispatch, x, params=params)
+
+    @_set_invalid_nan
+    def ilogccdf(self, logp, /, *, method=None):
+        return self._ilogccdf_dispatch(logp, method=method, **self._parameters)
+
+    @_dispatch
+    def _ilogccdf_dispatch(self, x, method=None, **params):
+        if self._overrides('_ilogccdf_formula'):
+            method = self._ilogccdf_formula
+        elif self._overrides('_ilogcdf_formula'):
+            method = self._ilogccdf_complement
+        else:
+            method = self._ilogccdf_inversion
+        return method
+
+    def _ilogccdf_formula(self, x, **params):
+        raise NotImplementedError(self._not_implemented)
+
+    def _ilogccdf_complement(self, x, **params):
+        return self._ilogcdf_dispatch(_log1mexp(x), **params)
+
+    def _ilogccdf_inversion(self, x, **params):
+        return self._solve_bounded_continuous(self._logccdf_dispatch, x, params=params)
+
+    @_set_invalid_nan
+    def iccdf(self, p, /, *, method=None):
+        return self._iccdf_dispatch(p, method=method, **self._parameters)
+
+    @_dispatch
+    def _iccdf_dispatch(self, x, method=None, **params):
+        if self._overrides('_iccdf_formula'):
+            method = self._iccdf_formula
+        elif self._overrides('_icdf_formula'):
+            method = self._iccdf_complement_safe
+        else:
+            method = self._iccdf_inversion
+        return method
+
+    def _iccdf_formula(self, x, **params):
+        raise NotImplementedError(self._not_implemented)
+
+    def _iccdf_complement(self, x, **params):
+        return self._icdf_dispatch(1 - x, **params)
+
+    def _iccdf_complement_safe(self, x, **params):
+        out = self._iccdf_complement(x, **params)
+        eps = np.finfo(self._dtype).eps
+        tol = self.tol if not _isnull(self.tol) else np.sqrt(eps)
+        mask = tol * x < np.spacing(1 - x)
+        if np.any(mask):
+            params_mask = {key: np.broadcast_to(val, mask.shape)[mask]
+                           for key, val in params.items()}
+            out = np.asarray(out)
+            out[mask] = self._iccdf_inversion(x[mask], **params_mask)
+        return out[()]
+
+    def _iccdf_inversion(self, x, **params):
+        return self._solve_bounded_continuous(self._ccdf_dispatch, x, params=params)
+
+    ### Sampling Functions
+    # The following functions for drawing samples from the distribution are
+    # exposed via a public method that accepts one positional argument - the
+    # shape of the sample - and keyword options (but not distribution
+    # parameters).
+    # sample
+    # ~~qmc_sample~~ built into sample now
+    #
+    # Common keyword options include:
+    # method - a string that indicates which method should be used to compute
+    #          the quantity (e.g. a formula or numerical integration).
+    # rng - the NumPy Generator/SciPy QMCEngine object to used for drawing numbers.
+    #
+    # Input/output validation is included in each function, since there is
+    # little code to be shared.
+    # These are the methods meant to be called by users.
+    #
+    # Each public method calls a private "dispatch" method that
+    # determines which "method" (strategy for calculating the desired quantity)
+    # to use by default and, via the `@_dispatch` decorator, calls the
+    # method and computes the result.
+    # Each dispatch method can designate the responsibility of sampling to any
+    # of several "implementation" methods. These methods accept only
+    # `**params`, the parameter dictionary passed from the public method via
+    # the "dispatch" method.
+    # See the note corresponding with the "Distribution Parameters" for more
+    # information.
+
+    def sample(self, shape=(), *, method=None, rng=None):
+        # needs output validation to ensure that developer returns correct
+        # dtype and shape
+        sample_shape = (shape,) if not np.iterable(shape) else tuple(shape)
+        full_shape = sample_shape + self._shape
+        rng = np.random.default_rng(rng) if not isinstance(rng, qmc.QMCEngine) else rng
+        res = self._sample_dispatch(full_shape, method=method, rng=rng,
+                                    **self._parameters)
+
+        return res.astype(self._dtype, copy=False)
+
+    @_dispatch
+    def _sample_dispatch(self, full_shape, *, method, rng, **params):
+        # make sure that tests catch if sample is 0d array
+        if self._overrides('_sample_formula') and not isinstance(rng, qmc.QMCEngine):
+            method = self._sample_formula
+        else:
+            method = self._sample_inverse_transform
+        return method
+
+    def _sample_formula(self, full_shape, *, rng, **params):
+        raise NotImplementedError(self._not_implemented)
+
+    def _sample_inverse_transform(self, full_shape, *, rng, **params):
+        if isinstance(rng, qmc.QMCEngine):
+            uniform = self._qmc_uniform(full_shape, qrng=rng, **params)
+        else:
+            uniform = rng.random(size=full_shape, dtype=self._dtype)
+        return self._icdf_dispatch(uniform, **params)
+
+    def _qmc_uniform(self, full_shape, *, qrng, **params):
+        # Generate QMC uniform sample(s) on unit interval with specified shape;
+        # if `sample_shape != ()`, then each slice along axis 0 is independent.
+
+        sample_shape = full_shape[:len(full_shape)-len(self._shape)]
+        # Determine the number of independent sequences and the length of each.
+        n_low_discrepancy = sample_shape[0] if sample_shape else 1
+        n_independent = math.prod(full_shape[1:] if sample_shape else full_shape)
+
+        # For each independent sequence, we'll need a new QRNG of the appropriate class
+        # with its own RNG. (If scramble=False, we don't really need all the separate
+        # rngs, but I'm not going to add a special code path right now.)
+        rngs = _rng_spawn(qrng.rng, n_independent)
+        qrng_class = qrng.__class__
+        kwargs = dict(d=1, scramble=qrng.scramble, optimization=qrng._optimization)
+        if isinstance(qrng, qmc.Sobol):
+            kwargs['bits'] = qrng.bits
+
+        # Draw uniform low-discrepancy sequences scrambled with each RNG
+        uniforms = []
+        for rng in rngs:
+            qrng = qrng_class(seed=rng, **kwargs)
+            uniform = qrng.random(n_low_discrepancy)
+            uniform = uniform.reshape(n_low_discrepancy if sample_shape else ())[()]
+            uniforms.append(uniform)
+
+        # Reorder the axes and ensure that the shape is correct
+        uniform = np.moveaxis(np.stack(uniforms), -1, 0) if uniforms else np.asarray([])
+        return uniform.reshape(full_shape)
+
+    ### Moments
+    # The `moment` method accepts two positional arguments - the order and kind
+    # (raw, central, or standard) of the moment - and a keyword option:
+    # method - a string that indicates which method should be used to compute
+    #          the quantity (e.g. a formula or numerical integration).
+    # Like the distribution properties, input/output validation is provided by
+    # the `_set_invalid_nan_property` decorator.
+    #
+    # Unlike most public methods above, `moment` dispatches to one of three
+    # private methods - one for each 'kind'. Like most *public* methods above,
+    # each of these private methods calls a private "dispatch" method that
+    # determines which "method" (strategy for calculating the desired quantity)
+    # to use. Also, each dispatch method can designate the responsibility
+    # computing the moment to one of several "implementation" methods.
+    # Unlike the dispatch methods above, however, the `@_dispatch` decorator
+    # is not used, and both logic and method calls are included in the function
+    # itself.
+    # Instead of determining which method will be used based solely on the
+    # implementation methods available and calling only the corresponding
+    # implementation method, *all* the implementation methods are called
+    # in sequence until one returns the desired information. When an
+    # implementation methods cannot provide the requested information, it
+    # returns the object None (which is distinct from arrays with NaNs or infs,
+    # which are valid values of moments).
+    # The reason for this approach is that although formulae for the first
+    # few moments of a distribution may be found, general formulae that work
+    # for all orders are not always easy to find. This approach allows the
+    # developer to write "formula" implementation functions that return the
+    # desired moment when it is available and None otherwise.
+    #
+    # Note that the first implementation method called is a cache. This is
+    # important because lower-order moments are often needed to compute
+    # higher moments from formulae, so we eliminate redundant calculations
+    # when moments of several orders are needed.
+
+    @cached_property
+    def _moment_methods(self):
+        return {'cache', 'formula', 'transform',
+                'normalize', 'general', 'quadrature'}
+
+    @cached_property
+    def _lmoment_methods(self):
+        return {'cache', 'formula', 'general', 'order_statistics', 'quadrature_icdf'}
+
+    @property
+    def _zero(self):
+        return self._constants()[0]
+
+    @property
+    def _one(self):
+        return self._constants()[1]
+
+    def _constants(self):
+        if self._constant_cache is not None:
+            return self._constant_cache
+
+        constants = self._preserve_type([0, 1])
+
+        if self.cache_policy != _NO_CACHE:
+            self._constant_cache = constants
+
+        return constants
+
+    @_set_invalid_nan_property
+    def moment(self, order=1, kind='raw', *, method=None):
+        kinds = {'raw': self._moment_raw,
+                 'central': self._moment_central,
+                 'standardized': self._moment_standardized}
+        order = self._validate_order(order)
+        kind = self._validate_kind(kind, kinds)
+        moment_kind = kinds[kind]
+        return moment_kind(order, method=method)
+
+    def _moment_raw(self, order=1, *, method=None):
+        """Raw distribution moment about the origin."""
+        # Consider exposing the point about which moments are taken as an
+        # option. This is easy to support, since `_moment_transform_center`
+        # does all the work.
+        methods = self._moment_methods if method is None else {method}
+        return self._moment_raw_dispatch(order, methods=methods, **self._parameters)
+
+    def _moment_raw_dispatch(self, order, *, methods, **params):
+        moment = None
+
+        if 'cache' in methods:
+            moment = self._moment_raw_cache.get(order, None)
+
+        if moment is None and 'formula' in methods:
+            moment = self._moment_raw_formula(order, **params)
+
+        if moment is None and 'transform' in methods and order > 1:
+            moment = self._moment_raw_transform(order, **params)
+
+        if moment is None and 'general' in methods:
+            moment = self._moment_raw_general(order, **params)
+
+        if moment is None and 'quadrature' in methods:
+            moment = self._moment_from_pxf(order, center=self._zero, **params)
+
+        if moment is None and 'quadrature_icdf' in methods:
+            moment = self._moment_integrate_icdf(order, center=self._zero, **params)
+
+        if moment is not None and self.cache_policy != _NO_CACHE:
+            self._moment_raw_cache[order] = moment
+
+        return moment
+
+    def _moment_raw_formula(self, order, **params):
+        return None
+
+    def _moment_raw_transform(self, order, **params):
+        central_moments = []
+        for i in range(int(order) + 1):
+            methods = {'cache', 'formula', 'normalize', 'general'}
+            moment_i = self._moment_central_dispatch(order=i, methods=methods, **params)
+            if moment_i is None:
+                return None
+            central_moments.append(moment_i)
+
+        # Doesn't make sense to get the mean by "transform", since that's
+        # how we got here. Questionable whether 'quadrature' should be here.
+        mean_methods = {'cache', 'formula', 'quadrature'}
+        mean = self._moment_raw_dispatch(self._one, methods=mean_methods, **params)
+        if mean is None:
+            return None
+
+        moment = self._moment_transform_center(order, central_moments, mean, self._zero)
+        return moment
+
+    def _moment_raw_general(self, order, **params):
+        # This is the only general formula for a raw moment of a probability
+        # distribution
+        return self._one if order == 0 else None
+
+    def _moment_central(self, order=1, *, method=None):
+        """Distribution moment about the mean."""
+        methods = self._moment_methods if method is None else {method}
+        return self._moment_central_dispatch(order, methods=methods, **self._parameters)
+
+    def _moment_central_dispatch(self, order, *, methods, **params):
+        moment = None
+
+        if 'cache' in methods:
+            moment = self._moment_central_cache.get(order, None)
+
+        if moment is None and 'formula' in methods:
+            moment = self._moment_central_formula(order, **params)
+
+        if moment is None and 'transform' in methods:
+            moment = self._moment_central_transform(order, **params)
+
+        if moment is None and 'normalize' in methods and order > 2:
+            moment = self._moment_central_normalize(order, **params)
+
+        if moment is None and 'general' in methods:
+            moment = self._moment_central_general(order, **params)
+
+        if moment is None and 'quadrature' in methods:
+            mean = self._moment_raw_dispatch(self._one, **params,
+                                             methods=self._moment_methods)
+            moment = self._moment_from_pxf(order, center=mean, **params)
+
+        if moment is None and 'quadrature_icdf' in methods:
+            mean = self._moment_raw_dispatch(self._one, **params,
+                                             methods=self._moment_methods)
+            moment = self._moment_integrate_icdf(order, center=mean, **params)
+
+        if moment is not None and self.cache_policy != _NO_CACHE:
+            self._moment_central_cache[order] = moment
+
+        return moment
+
+    def _moment_central_formula(self, order, **params):
+        return None
+
+    def _moment_central_transform(self, order, **params):
+
+        raw_moments = []
+        for i in range(int(order) + 1):
+            methods = {'cache', 'formula', 'general'}
+            moment_i = self._moment_raw_dispatch(order=i, methods=methods, **params)
+            if moment_i is None:
+                return None
+            raw_moments.append(moment_i)
+
+        mean_methods = self._moment_methods
+        mean = self._moment_raw_dispatch(self._one, methods=mean_methods, **params)
+
+        moment = self._moment_transform_center(order, raw_moments, self._zero, mean)
+        return moment
+
+    def _moment_central_normalize(self, order, **params):
+        methods = {'cache', 'formula', 'general'}
+        standard_moment = self._moment_standardized_dispatch(order, **params,
+                                                             methods=methods)
+        if standard_moment is None:
+            return None
+        var = self._moment_central_dispatch(2, methods=self._moment_methods, **params)
+        return standard_moment*var**(order/2)
+
+    def _moment_central_general(self, order, **params):
+        general_central_moments = {0: self._one, 1: self._zero}
+        return general_central_moments.get(order, None)
+
+    def _moment_standardized(self, order=1, *, method=None):
+        """Standardized distribution moment."""
+        methods = self._moment_methods if method is None else {method}
+        return self._moment_standardized_dispatch(order, methods=methods,
+                                                  **self._parameters)
+
+    def _moment_standardized_dispatch(self, order, *, methods, **params):
+        moment = None
+
+        if 'cache' in methods:
+            moment = self._moment_standardized_cache.get(order, None)
+
+        if moment is None and 'formula' in methods:
+            moment = self._moment_standardized_formula(order, **params)
+
+        if moment is None and 'normalize' in methods:
+            moment = self._moment_standardized_normalize(order, False, **params)
+
+        if moment is None and 'general' in methods:
+            moment = self._moment_standardized_general(order, **params)
+
+        if moment is None and 'normalize' in methods:
+            moment = self._moment_standardized_normalize(order, True, **params)
+
+        if moment is not None and self.cache_policy != _NO_CACHE:
+            self._moment_standardized_cache[order] = moment
+
+        return moment
+
+    def _moment_standardized_formula(self, order, **params):
+        return None
+
+    def _moment_standardized_normalize(self, order, use_quadrature, **params):
+        methods = ({'quadrature'} if use_quadrature
+                   else {'cache', 'formula', 'transform'})
+        central_moment = self._moment_central_dispatch(order, **params,
+                                                       methods=methods)
+        if central_moment is None:
+            return None
+        var = self._moment_central_dispatch(2, methods=self._moment_methods,
+                                            **params)
+        return central_moment/var**(order/2)
+
+    def _moment_standardized_general(self, order, **params):
+        general_standard_moments = {0: self._one, 1: self._zero, 2: self._one}
+        return general_standard_moments.get(order, None)
+
+    def _moment_from_pxf(self, order, center, **params):
+        def integrand(x, order, center, **params):
+            pxf = self._pxf_dispatch(x, **params)
+            return pxf*(x-center)**order
+        return self._quadrature(integrand, args=(order, center), params=params)
+
+    def _moment_integrate_icdf(self, order, center, **params):
+        def integrand(x, order, center, **params):
+            x = self._icdf_dispatch(x, **params)
+            return (x-center)**order
+        return self._quadrature(integrand, limits=(0., 1.),
+                                args=(order, center), params=params)
+
+    def _moment_transform_center(self, order, moment_as, a, b):
+        a, b, *moment_as = np.broadcast_arrays(a, b, *moment_as)
+        n = order
+        i = np.arange(n+1).reshape([-1]+[1]*a.ndim)  # orthogonal to other axes
+        i = self._preserve_type(i)
+        n_choose_i = special.binom(n, i)
+        with np.errstate(invalid='ignore'):  # can happen with infinite moment
+            moment_b = np.sum(n_choose_i*moment_as*(a-b)**(n-i), axis=0)
+        return moment_b
+
+    ### L-Moments
+
+    @_set_invalid_nan_property
+    def lmoment(self, order=1, *, standardize=True, method=None):
+        order = self._validate_order(order, fname='lmoment', min_order=1)
+        return self._lmoment(order, standardize=standardize, method=method)
+
+    def _lmoment(self, order, *, standardize, method):
+        methods = self._lmoment_methods if method is None else {method}
+
+        lmoment = self._lmoment_dispatch(order, methods=methods, **self._parameters)
+        if lmoment is None:
+            return None
+
+        if standardize and order >= 3 and lmoment is not None:
+            lscale = self._lmoment_dispatch(2, methods=methods, **self._parameters)
+            if lscale is None:
+                return None
+            lmoment = lmoment / lscale
+
+        return lmoment
+
+    def _lmoment_dispatch(self, order, *, methods, **params):
+        lmoment = None
+
+        if 'cache' in methods:
+            lmoment = self._lmoment_cache.get(order, None)
+
+        if lmoment is None and 'formula' in methods:
+            lmoment = self._lmoment_formula(order, **params)
+
+        if lmoment is None and 'general' in methods:
+            lmoment = self._lmoment_general(order, **params)
+
+        if lmoment is None and 'quadrature_icdf' in methods and (
+                self._overrides('_icdf_formula') or self._overrides('_iccdf_formula')):
+            lmoment = self._lmoment_integrate_icdf(order, **params)
+
+        if lmoment is None and 'order_statistics' in methods:
+            lmoment = self._lmoment_from_order_statistics(order, **params)
+
+        if lmoment is None and 'quadrature_icdf' in methods:
+            lmoment = self._lmoment_integrate_icdf(order, **params)
+
+        if lmoment is not None and self.cache_policy != _NO_CACHE:
+            self._lmoment_cache[order] = lmoment
+
+        return lmoment
+
+    def _lmoment_formula(self, order, **params):
+        return None
+
+    def _lmoment_general(self, order, **params):
+        return self.mean() if order == 1 else None
+
+    def _lmoment_from_order_statistics(self, order, **params):
+        k = np.arange(order)
+        k = xpx.atleast_nd(k, ndim=self._ndim + 1).T
+        E = order_statistic(self, r=order-k, n=order).mean()
+        bc = special.binom(order-1, k)
+        return np.sum((-1)**k * bc * E, axis=0) / order
+
+    def _lmoment_integrate_icdf(self, order, **params):
+        def integrand(p, **params):
+            x = self._icdf_dispatch(p, **params)
+            P = special.eval_sh_legendre(order - 1, p)
+            return x * P
+        return self._quadrature(integrand, limits=(0., 1.), params=params)
+
+    ### Convenience
+
+    def plot(self, x='x', y=None, *, t=None, ax=None):
+        r"""Plot a function of the distribution.
+
+        Convenience function for quick visualization of the distribution
+        underlying the random variable.
+
+        Parameters
+        ----------
+        x, y : str, optional
+            String indicating the quantities to be used as the abscissa and
+            ordinate (horizontal and vertical coordinates), respectively.
+            Defaults are ``'x'`` (the domain of the random variable) and either
+            ``'pdf'`` (the probability density function) (continuous) or
+            ``'pdf'`` (the probability density function) (discrete).
+            Valid values are:
+            'x', 'pdf', 'pmf', 'cdf', 'ccdf', 'icdf', 'iccdf', 'logpdf', 'logpmf',
+            'logcdf', 'logccdf', 'ilogcdf', 'ilogccdf'.
+        t : 3-tuple of (str, float, float), optional
+            Tuple indicating the limits within which the quantities are plotted.
+            The default is ``('cdf', 0.0005, 0.9995)`` if the domain is infinite,
+            indicating that the central 99.9% of the distribution is to be shown;
+            otherwise, endpoints of the support are used where they are finite.
+            Valid values are:
+            'x', 'cdf', 'ccdf', 'icdf', 'iccdf', 'logcdf', 'logccdf',
+            'ilogcdf', 'ilogccdf'.
+        ax : `matplotlib.axes`, optional
+            Axes on which to generate the plot. If not provided, use the
+            current axes.
+
+        Returns
+        -------
+        ax : `matplotlib.axes`
+            Axes on which the plot was generated.
+            The plot can be customized by manipulating this object.
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> import numpy as np
+        >>> import matplotlib.pyplot as plt
+        >>> from scipy import stats
+        >>> X = stats.Normal(mu=1., sigma=2.)
+
+        Plot the PDF over the central 99.9% of the distribution.
+        Compare against a histogram of a random sample.
+
+        >>> ax = X.plot()
+        >>> sample = X.sample(10000)
+        >>> ax.hist(sample, density=True, bins=50, alpha=0.5)
+        >>> plt.show()
+
+        Plot ``logpdf(x)`` as a function of ``x`` in the left tail,
+        where the log of the CDF is between -10 and ``np.log(0.5)``.
+
+        >>> X.plot('x', 'logpdf', t=('logcdf', -10, np.log(0.5)))
+        >>> plt.show()
+
+        Plot the PDF of the normal distribution as a function of the
+        CDF for various values of the scale parameter.
+
+        >>> X = stats.Normal(mu=0., sigma=[0.5, 1., 2])
+        >>> X.plot('cdf', 'pdf')
+        >>> plt.show()
+
+        """
+
+        # Strategy: given t limits, get quantile limits. Form grid of
+        # quantiles, compute requested x and y at quantiles, and plot.
+        # Currently, the grid of quantiles is always linearly spaced.
+        # Instead of always computing linearly-spaced quantiles, it
+        # would be better to choose:
+        # a) quantiles or probabilities
+        # b) linearly or logarithmically spaced
+        # based on the specified `t`.
+        # TODO:
+        # - smart spacing of points
+        # - when the parameters of the distribution are an array,
+        #   use the full range of abscissae for all curves
+
+        discrete = isinstance(self, DiscreteDistribution)
+        t_is_quantile = {'x', 'icdf', 'iccdf', 'ilogcdf', 'ilogccdf'}
+        t_is_probability = {'cdf', 'ccdf', 'logcdf', 'logccdf'}
+        valid_t = t_is_quantile.union(t_is_probability)
+        valid_xy =  valid_t.union({'pdf', 'logpdf', 'pmf', 'logpmf'})
+        y_default = 'pmf' if discrete else 'pdf'
+        y = y_default if y is None else y
+
+        ndim = self._ndim
+        x_name, y_name = x, y
+        t_name = 'cdf' if t is None else t[0]
+
+        a, b = self.support()
+        tliml_default = 0 if np.all(np.isfinite(a)) else 0.0005
+        tliml = tliml_default if t is None else t[1]
+        tlimr_default = 1 if np.all(np.isfinite(b)) else 0.9995
+        tlimr = tlimr_default if t is None else t[2]
+        tlim = np.asarray([tliml, tlimr])
+        tlim = tlim[:, np.newaxis] if ndim else tlim
+
+        # pdf/logpdf are not valid for `t` because we can't easily invert them
+        message = (f'Argument `t` of `{self.__class__.__name__}.plot` "'
+                   f'must be one of {valid_t}')
+        if t_name not in valid_t:
+            raise ValueError(message)
+
+        message = (f'Argument `x` of `{self.__class__.__name__}.plot` "'
+                   f'must be one of {valid_xy}')
+        if x_name not in valid_xy:
+            raise ValueError(message)
+
+        message = (f'Argument `y` of `{self.__class__.__name__}.plot` "'
+                   f'must be one of {valid_xy}')
+        if y_name not in valid_xy:
+            raise ValueError(message)
+
+        # This could just be a warning
+        message = (f'`{self.__class__.__name__}.plot` was called on a random '
+                   'variable with at least one invalid shape parameters. When '
+                   'a parameter is invalid, no plot can be shown.')
+        if self._any_invalid:
+            raise ValueError(message)
+
+        # We could automatically ravel, but do we want to? For now, raise.
+        message = ("To use `plot`, distribution parameters must be "
+                   "scalars or arrays with one or fewer dimensions.")
+        if ndim > 1:
+            raise ValueError(message)
+
+        try:
+            import matplotlib.pyplot as plt  # noqa: F401, E402
+        except ModuleNotFoundError as exc:
+            message = ("`matplotlib` must be installed to use "
+                       f"`{self.__class__.__name__}.plot`.")
+            raise ModuleNotFoundError(message) from exc
+        ax = plt.gca() if ax is None else ax
+
+        # get quantile limits given t limits
+        qlim = tlim if t_name in t_is_quantile else getattr(self, 'i'+t_name)(tlim)
+
+        message = (f"`{self.__class__.__name__}.plot` received invalid input for `t`: "
+                   f"calling {'i'+t_name}({tlim}) produced {qlim}.")
+        if not np.all(np.isfinite(qlim)):
+            raise ValueError(message)
+
+        # form quantile grid
+        if discrete and x_name in t_is_quantile:
+            # should probably aggregate for large ranges
+            q = np.arange(np.min(qlim[0]), np.max(qlim[1]) + 1)
+            q = q[:, np.newaxis] if ndim else q
+        else:
+            grid = np.linspace(0, 1, 300)
+            grid = grid[:, np.newaxis] if ndim else grid
+            q = qlim[0] + (qlim[1] - qlim[0]) * grid
+            q = np.round(q) if discrete else q
+
+        # compute requested x and y at quantile grid
+        x = q if x_name in t_is_quantile else getattr(self, x_name)(q)
+        y = q if y_name in t_is_quantile else getattr(self, y_name)(q)
+
+        # make plot
+        x, y = np.broadcast_arrays(x.T, np.atleast_2d(y.T))
+        for xi, yi in zip(x, y):  # plot is vectorized, but bar/step don't seem to be
+            if discrete and x_name in t_is_quantile and y_name == 'pmf':
+                # should this just be a step plot, too?
+                ax.bar(xi, yi, alpha=np.sqrt(1/y.shape[0]))  # alpha heuristic
+            elif discrete and x_name in t_is_quantile:
+                values = yi
+                edges = np.concatenate((xi, [xi[-1]+1]))
+                ax.stairs(values, edges, baseline=None)
+            else:
+                ax.plot(xi, yi)
+        ax.set_xlabel(f"${x_name}$")
+        ax.set_ylabel(f"${y_name}$")
+        ax.set_title(str(self))
+
+        # only need a legend if distribution has parameters
+        if len(self._parameters):
+            label = []
+            parameters = self._parameterization.parameters
+            param_names = list(parameters)
+            param_arrays = [np.atleast_1d(self._parameters[pname])
+                            for pname in param_names]
+            for param_vals in zip(*param_arrays):
+                assignments = [f"${parameters[name].symbol}$ = {val:.4g}"
+                               for name, val in zip(param_names, param_vals)]
+                label.append(", ".join(assignments))
+            ax.legend(label)
+
+        return ax
+
+
+    ### Fitting
+    # All methods above treat the distribution parameters as fixed, and the
+    # variable argument may be a quantile or probability. The fitting functions
+    # are fundamentally different because the quantiles (often observations)
+    # are considered to be fixed, and the distribution parameters are the
+    # variables. In a sense, they are like an inverse of the sampling
+    # functions.
+    #
+    # At first glance, it would seem ideal for `fit` to be a classmethod,
+    # called like `LogUniform.fit(sample=sample)`.
+    # I tried this. I insisted on it for a while. But if `fit` is a
+    # classmethod, it cannot call instance methods. If we want to support MLE,
+    # MPS, MoM, MoLM, then we end up with most of the distribution functions
+    # above needing to be classmethods, too. All state information, such as
+    # tolerances and the underlying distribution of `ShiftedScaledDistribution`
+    # and `OrderStatisticDistribution`, would need to be passed into all
+    # methods. And I'm not really sure how we would call `fit` as a
+    # classmethod of a transformed distribution - maybe
+    # ShiftedScaledDistribution.fit would accept the class of the
+    # shifted/scaled distribution as an argument?
+    #
+    # In any case, it was a conscious decision for the infrastructure to
+    # treat the parameters as "fixed" and the quantile/percentile arguments
+    # as "variable". There are a lot of advantages to this structure, and I
+    # don't think the fact that a few methods reverse the fixed and variable
+    # quantities should make us question that choice. It can still accommodate
+    # these methods reasonably efficiently.
+
+
+class ContinuousDistribution(UnivariateDistribution):
+    def _overrides(self, method_name):
+        if method_name in {'_logpmf_formula', '_pmf_formula'}:
+            return True
+        return super()._overrides(method_name)
+
+    def _pmf_formula(self, x, **params):
+        return np.zeros_like(x)
+
+    def _logpmf_formula(self, x, **params):
+        return np.full_like(x, -np.inf)
+
+    def _pxf_dispatch(self, x, *, method=None, **params):
+        return self._pdf_dispatch(x, method=method, **params)
+
+    def _logpxf_dispatch(self, x, *, method=None, **params):
+        return self._logpdf_dispatch(x, method=method, **params)
+
+    def _solve_bounded_continuous(self, func, p, params, xatol=None):
+        return self._solve_bounded(func, p, params=params, xatol=xatol).x
+
+
+class DiscreteDistribution(UnivariateDistribution):
+    def _overrides(self, method_name):
+        if method_name in {'_logpdf_formula', '_pdf_formula'}:
+            return True
+        return super()._overrides(method_name)
+
+    def _logpdf_formula(self, x, **params):
+        if params:
+            p = next(iter(params.values()))
+            nan_result = np.isnan(x) | np.isnan(p)
+        else:
+            nan_result = np.isnan(x)
+        return np.where(nan_result, np.nan, np.inf)
+
+    def _pdf_formula(self, x, **params):
+        if params:
+            p = next(iter(params.values()))
+            nan_result = np.isnan(x) | np.isnan(p)
+        else:
+            nan_result = np.isnan(x)
+        return np.where(nan_result, np.nan, np.inf)
+
+    def _pxf_dispatch(self, x, *, method=None, **params):
+        return self._pmf_dispatch(x, method=method, **params)
+
+    def _logpxf_dispatch(self, x, *, method=None, **params):
+        return self._logpmf_dispatch(x, method=method, **params)
+
+    def _cdf_quadrature(self, x, **params):
+        return super()._cdf_quadrature(np.floor(x), **params)
+
+    def _logcdf_quadrature(self, x, **params):
+        return super()._logcdf_quadrature(np.floor(x), **params)
+
+    def _ccdf_quadrature(self, x, **params):
+        return super()._ccdf_quadrature(np.floor(x + 1), **params)
+
+    def _logccdf_quadrature(self, x, **params):
+        return super()._logccdf_quadrature(np.floor(x + 1), **params)
+
+    def _cdf2(self, x, y, *, method):
+        raise NotImplementedError(
+            "Two argument cdf functions are currently only supported for "
+            "continuous distributions.")
+
+    def _ccdf2(self, x, y, *, method):
+        raise NotImplementedError(
+            "Two argument cdf functions are currently only supported for "
+            "continuous distributions.")
+
+    def _logcdf2(self, x, y, *, method):
+        raise NotImplementedError(
+            "Two argument cdf functions are currently only supported for "
+            "continuous distributions.")
+
+    def _logccdf2(self, x, y, *, method):
+        raise NotImplementedError(
+            "Two argument cdf functions are currently only supported for "
+            "continuous distributions.")
+
+    def _lmoment(self, order, *, standardize, method):
+        raise NotImplementedError(
+            "L-moments are currently available only "
+            "for continuous distributions.")
+
+    def _solve_bounded_discrete(self, func, p, params, comp):
+        # We're trying to solve one of these two problems:
+        # a) find the smallest integer x* within the support s.t. F(x*) >= p
+        # b) find the smallest integer x* within the support s.t. G(x*) = 1 - F(x*) <= p
+        # Our approach is to solve a continuous version of the problem that narrows the
+        # solution down to an integer x s.t. either x* = x or x* = x + 1. At the end,
+        # we'll choose between them.
+
+        # First, solve func(x) == p where func is a continuous, monotone interpolant
+        # of either the monotone increasing F or monotone decreasing G.
+        res = self._solve_bounded(func, p, params=params, xatol=0.9)
+        # Here, `_solve_bounded` can terminate for one of three reasons:
+        # 1. `func(res.x) == p` (`fatol = 0` is satisfied),
+        # 2. `res.xl` and `res.xr` bracket the root and `|res.xr - res.xl| <= xatol`, or
+        # 3. There is no solution within the support.
+        # There are several possible strategies for using `res.xl`, `res.x`, and/or
+        # `res.xr` to find a solution to the original, discrete problem. Here is ours.
+
+        # Consider case 2a. Because F is an increasing function, we know
+        # that F(xr) >= p (and F(xl) <= p), so F(floor(xr) + 1) >= p.
+        # F(floor(xr)) *may* be >= p, but we can't know until we evaluate it.
+        # F(floor(xr) - 1) < p (strictly) because floor(xr) - 1 < xl and F decreases
+        # monotonically as the argument decreases. So we choose x = floor(xr), and
+        # later we'll choose between x* = x and x* = x + 1.
+        x = np.asarray(np.floor(res.bracket[-1]))
+        # This is also suitable for case 2b. Because G is a *decreasing* function, we
+        # know that G(xr) <= p (and G(xl) >= p), so G(floor(xr) + 1) <= p.
+        # G(floor(xr)) *may* be <= p, but we can't know until we evaluate it.
+        # G(floor(xr) - 1) > p (strictly) because floor(xr) - 1 < xl and G increases
+        # as the argument decreases. So we would still want to choose x = floor(xr), and
+        # later we'll choose between x* = x and x* = x + 1.
+
+        # Now we consider case 1a/b. In this case, `res.x` solved the equation
+        # *exactly*, so the algorithm may have terminated before the bracket is tight
+        # enough to rely on `res.xr`. If `res.x` happens to be integral, `res.x` is
+        # the solution to the discrete problem, and floor(res.x) == res.x, so
+        # floor(res.x) is the solution to the discrete problem. If not:
+        # a) F(floor(res.x)) < p (strictly) and F(floor(res.x) + 1) > p (strictly). So
+        #    floor(res.x) + 1 is the solution to the discrete problem.
+        # b) G(floor(res.x)) > p (strictly) and G(floor(res.x) + 1) < p (strictly). So
+        #    floor(res.x) + 1 is again the solution to the discrete problem.
+        # Either way, we can choose x = res.x, and at the end we'll choose between
+        # x* = x and x* = x + 1.
+        mask = res.f_x == 0
+        x[mask] = np.floor(res.x[mask])
+
+        # For case 3, let xmin be the left endpoint of the support, and note that in
+        # general, F(xmin) > 0 and G(xmin) < 1. Therefore it is possible that:
+        # a) F(x) > p for all x in the support (e.g. because p ~ 0)
+        # a) G(x) < p for all x in the support (e.g. because p ~ 1)
+        # In these cases, `_solve_bounded` would fail to find a root of the continuous
+        # equation above, but the solution to the original, discrete problem is the left
+        # endpoint of the support.
+        # This case is handled before we get to this function; otherwise,
+        # `_solve_bounded` may spin its wheels for a long time in vain.
+
+        # Now, we choose between x* = x and x* = x + 1: if func(x) satisfies the
+        # comparison `comp` (>= for cdf, <= for ccdf), the solution is x* = x;
+        # otherwise the solution must be x* = x + 1.
+        f = func(x, **params)
+        x = np.where(comp(f, p), x, x + 1.0)
+        x[np.isnan(f)] = np.nan  # needed? why would func(x) be NaN within support?
+
+        return x
+
+    def _base_discrete_inversion(self, p, func, comp, /, **params):
+        # For discrete distributions, icdf(p) is defined as the minimum integer x*
+        # within the support such that F(x*) >= p; iccdf(p) is the minimum integer x*
+        # within the support such that G(x*) <= p.
+
+        # Identify where the solution is xmin.
+        # (See rationale in `_solve_bounded_discrete`.)
+        xmin, xmax = self._support(**params)
+        p, xmin, _ = np.broadcast_arrays(p, xmin, xmax)
+        mask = comp(func(xmin, **params), p)
+
+        # Use `apply_where` to perform the inversion only when necessary.
+        def f1(p, *args):
+            return self._solve_bounded_discrete(
+                func, p, params=dict(zip(params.keys(), args)), comp=comp)
+
+        x = xpx.apply_where(~mask, (p, *params.values()), f1, fill_value=xmin)
+
+        # x above may be a finite value even when p is NaN, so the returned value
+        # should be NaN. We need to handle this as a special case.
+        x[np.isnan(p)] = np.nan
+        return x[()]
+
+    def _icdf_inversion(self, x, **params):
+        return self._base_discrete_inversion(x, self._cdf_dispatch,
+                                             np.greater_equal, **params)
+
+    def _ilogcdf_inversion(self, x, **params):
+        return self._base_discrete_inversion(x, self._logcdf_dispatch,
+                                             np.greater_equal, **params)
+
+    def _iccdf_inversion(self, x, **params):
+        return self._base_discrete_inversion(x, self._ccdf_dispatch,
+                                             np.less_equal, **params)
+
+    def _ilogccdf_inversion(self, x, **params):
+        return self._base_discrete_inversion(x, self._logccdf_dispatch,
+                                             np.less_equal, **params)
+
+    def _mode_optimization(self, **params):
+        # If `x` is the true mode of a unimodal continuous function, we can find
+        # the mode among integers by rounding in each direction and checking
+        # which is better. If the difference between `x` and the nearest integer
+        # is less than `xatol`, the computed value of `x` may end up on the wrong
+        # side of the nearest integer. Setting `xatol=0.5` guarantees that at most
+        # three integers need to be checked, the two nearest integers, ``floor(x)``
+        # and ``round(x)`` and the nearest integer other than these.
+        x = super()._mode_optimization(xatol=0.5, **params)
+        low, high = self.support()
+        xl, xr = np.floor(x), np.ceil(x)
+        nearest = np.round(x)
+        # Clip to stay within support. There will be redundant calculation
+        # when clipping since `xo` will be one of `xl` or `xr`, but let's
+        # keep the implementation simple for now.
+        xo = np.clip(nearest + np.copysign(1, nearest - x), low, high)
+        x = np.stack([xl, xo, xr])
+        idx = np.argmax(self._pmf_dispatch(x, **params), axis=0)
+        return np.choose(idx, [xl, xo, xr])
+
+    def _logentropy_quadrature(self, **params):
+        def logintegrand(x, **params):
+            logpmf = self._logpmf_dispatch(x, **params)
+            # Entropy summand is -pmf*log(pmf), so log-entropy summand is
+            # logpmf + log(logpmf) + pi*j. But pmf is always between 0 and 1,
+            # so logpmf is always negative, and so log(logpmf) = log(-logpmf) + pi*j.
+            # The two imaginary components "cancel" each other out (which we would
+            # expect because each term of the entropy summand is positive).
+            return np.where(np.isfinite(logpmf), logpmf + np.log(-logpmf), -np.inf)
+        return self._quadrature(logintegrand, params=params, log=True)
+
+
+# Special case the names of some new-style distributions in `make_distribution`
+_distribution_names = {
+    # Continuous
+    'argus': 'ARGUS',
+    'betaprime': 'BetaPrime',
+    'chi2': 'ChiSquared',
+    'crystalball': 'CrystalBall',
+    'dgamma': 'DoubleGamma',
+    'dweibull': 'DoubleWeibull',
+    'expon': 'Exponential',
+    'exponnorm': 'ExponentiallyModifiedNormal',
+    'exponweib': 'ExponentialWeibull',
+    'exponpow': 'ExponentialPower',
+    'fatiguelife': 'FatigueLife',
+    'foldcauchy': 'FoldedCauchy',
+    'foldnorm': 'FoldedNormal',
+    'genlogistic': 'GeneralizedLogistic',
+    'gennorm': 'GeneralizedNormal',
+    'genpareto': 'GeneralizedPareto',
+    'genexpon': 'GeneralizedExponential',
+    'genextreme': 'GeneralizedExtremeValue',
+    'gausshyper': 'GaussHypergeometric',
+    'gengamma': 'GeneralizedGamma',
+    'genhalflogistic': 'GeneralizedHalfLogistic',
+    'geninvgauss': 'GeneralizedInverseGaussian',
+    'gumbel_r': 'Gumbel',
+    'gumbel_l': 'ReflectedGumbel',
+    'halfcauchy': 'HalfCauchy',
+    'halflogistic': 'HalfLogistic',
+    'halfnorm': 'HalfNormal',
+    'halfgennorm': 'HalfGeneralizedNormal',
+    'hypsecant': 'HyperbolicSecant',
+    'invgamma': 'InverseGammma',
+    'invgauss': 'InverseGaussian',
+    'invweibull': 'InverseWeibull',
+    'irwinhall': 'IrwinHall',
+    'jf_skew_t': 'JonesFaddySkewT',
+    'johnsonsb': 'JohnsonSB',
+    'johnsonsu': 'JohnsonSU',
+    'ksone': 'KSOneSided',
+    'kstwo': 'KSTwoSided',
+    'kstwobign': 'KSTwoSidedAsymptotic',
+    'laplace_asymmetric': 'LaplaceAsymmetric',
+    'levy_l': 'LevyLeft',
+    'levy_stable': 'LevyStable',
+    'loggamma': 'ExpGamma',  # really the Exponential Gamma Distribution
+    'loglaplace': 'LogLaplace',
+    'lognorm': 'LogNormal',
+    'loguniform': 'LogUniform',
+    'ncx2': 'NoncentralChiSquared',
+    'nct': 'NoncentralT',
+    'norm': 'Normal',
+    'norminvgauss': 'NormalInverseGaussian',
+    'powerlaw': 'PowerLaw',
+    'powernorm': 'PowerNormal',
+    'rdist': 'R',
+    'rel_breitwigner': 'RelativisticBreitWigner',
+    'recipinvgauss': 'ReciprocalInverseGaussian',
+    'reciprocal': 'LogUniform',
+    'semicircular': 'SemiCircular',
+    'skewcauchy': 'SkewCauchy',
+    'skewnorm': 'SkewNormal',
+    'studentized_range': 'StudentizedRange',
+    't': 'StudentT',
+    'trapezoid': 'Trapezoidal',
+    'triang': 'Triangular',
+    'truncexpon': 'TruncatedExponential',
+    'truncnorm': 'TruncatedNormal',
+    'truncpareto': 'TruncatedPareto',
+    'truncweibull_min': 'TruncatedWeibull',
+    'tukeylambda': 'TukeyLambda',
+    'vonmises_line': 'VonMisesLine',
+    'weibull_min': 'Weibull',
+    'weibull_max': 'ReflectedWeibull',
+    'wrapcauchy': 'WrappedCauchyLine',
+    # Discrete
+    'betabinom': 'BetaBinomial',
+    'betanbinom': 'BetaNegativeBinomial',
+    'dlaplace': 'LaplaceDiscrete',
+    'geom': 'Geometric',
+    'hypergeom': 'Hypergeometric',
+    'logser': 'LogarithmicSeries',
+    'nbinom': 'NegativeBinomial',
+    'nchypergeom_fisher': 'NoncentralHypergeometricFisher',
+    'nchypergeom_wallenius': 'NoncentralHypergeometricWallenius',
+    'nhypergeom': 'NegativeHypergeometric',
+    'poisson_binom': 'PoissonBinomial',
+    'randint': 'UniformDiscrete',
+    'yulesimon': 'YuleSimon',
+    'zipf': 'Zeta',
+}
+
+
+@xp_capabilities(np_only=True)
+def make_distribution(dist):
+    """Generate a `UnivariateDistribution` class from a compatible object.
+
+    The argument may be an instance of `rv_continuous` or an instance of
+    another class that satisfies the interface described below.
+
+    The returned value is a `ContinuousDistribution` subclass if the input is an
+    instance of `rv_continuous` or a `DiscreteDistribution` subclass if the input
+    is an instance of `rv_discrete`. Like any subclass of `UnivariateDistribution`,
+    it must be instantiated (i.e. by passing all shape parameters as keyword
+    arguments) before use. Once instantiated, the resulting object will have the
+    same interface as any other instance of `UnivariateDistribution`; e.g.,
+    `scipy.stats.Normal`, `scipy.stats.Binomial`.
+
+    .. note::
+
+        `make_distribution` does not work perfectly with all instances of
+        `rv_continuous`. Known failures include `levy_stable`, `vonmises`,
+        `hypergeom`, 'nchypergeom_fisher', 'nchypergeom_wallenius', and
+        `poisson_binom`. Some methods of some distributions will not support
+        array shape parameters.
+
+    Parameters
+    ----------
+    dist : `rv_continuous`
+        Instance of `rv_continuous`, `rv_discrete`, or an instance of any class with
+        the following attributes:
+
+        __make_distribution_version__ : str
+            A string containing the version number of SciPy in which this interface
+            is defined. The preferred interface may change in future SciPy versions,
+            in which case support for an old interface version may be deprecated
+            and eventually removed.
+        parameters : dict or tuple
+            If a dictionary, each key is the name of a parameter,
+            and the corresponding value is either a dictionary or tuple.
+            If the value is a dictionary, it may have the following items, with default
+            values used for entries which aren't present.
+
+            endpoints : tuple, default: (-inf, inf)
+                A tuple defining the lower and upper endpoints of the domain of the
+                parameter; allowable values are floats, the name (string) of another
+                parameter, or a callable taking parameters as keyword only
+                arguments and returning the numerical value of an endpoint for
+                given parameter values.
+
+            inclusive : tuple of bool, default: (False, False)
+                A tuple specifying whether the endpoints are included within the domain
+                of the parameter.
+
+            typical : tuple, default: ``endpoints``
+                Defining endpoints of a typical range of values of a parameter. Can be
+                used for sampling parameter values for testing. Behaves like the
+                ``endpoints`` tuple above, and should define a subinterval of the
+                domain given by ``endpoints``.
+
+            A tuple value ``(a, b)`` associated to a key in the ``parameters``
+            dictionary is equivalent to ``{endpoints: (a, b)}``.
+
+            Custom distributions with multiple parameterizations can be defined by
+            having the ``parameters`` attribute be a tuple of dictionaries with
+            the structure described above. In this case, ``dist``\'s class must also
+            define a method ``process_parameters`` to map between the different
+            parameterizations. It must take all parameters from all parameterizations
+            as optional keyword arguments and return a dictionary mapping parameters to
+            values, filling in values from other parameterizations using values from
+            the supplied parameterization. See example.
+
+        support : dict or tuple
+            A dictionary describing the support of the distribution or a tuple
+            describing the endpoints of the support. This behaves identically to
+            the values of the parameters dict described above.
+
+        The class **must** also define a ``pdf`` method and **may** define methods
+        ``logentropy``, ``entropy``, ``median``, ``mode``, ``logpdf``,
+        ``logcdf``, ``cdf``, ``logccdf``, ``ccdf``,
+        ``ilogcdf``, ``icdf``, ``ilogccdf``, ``iccdf``,
+        ``moment``, ``lmoment``, and ``sample``.
+        If defined, these methods must accept the parameters of the distribution as
+        keyword arguments and also accept any positional-only arguments accepted by
+        the corresponding method of `ContinuousDistribution`.
+        When multiple parameterizations are defined, these methods must accept
+        all parameters from all parameterizations. The ``moment`` method
+        must accept the ``order`` and ``kind`` arguments by position or keyword, but
+        may return ``None`` if a formula is not available for the arguments; in this
+        case, the infrastructure will fall back to a default implementation.
+        The ``lmoment`` method must accept the ``order`` argument by position or
+        keyword and return the specified L-moment (not the L-moment ratio), but may
+        return ``None`` if a formula is not available for the arguments. The
+        ``sample`` method must accept ``shape`` by position or keyword, but contrary
+        to the public method of the same name, the argument it receives will be the
+        *full* shape of the output array - that is, the shape passed to the public
+        method prepended to the broadcasted shape of random variable parameters.
+
+    Returns
+    -------
+    CustomDistribution : `UnivariateDistribution`
+        A subclass of `UnivariateDistribution` corresponding with `dist`. The
+        initializer requires all shape parameters to be passed as keyword arguments
+        (using the same names as the instance of `rv_continuous`/`rv_discrete`).
+
+    Notes
+    -----
+    The documentation of `UnivariateDistribution` is not rendered. See below for
+    an example of how to instantiate the class (i.e. pass all shape parameters of
+    `dist` to the initializer as keyword arguments). Documentation of all methods
+    is identical to that of `scipy.stats.Normal`. Use ``help`` on the returned
+    class or its methods for more information.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy import stats
+    >>> from scipy import special
+
+    Create a `ContinuousDistribution` from `scipy.stats.loguniform`.
+
+    >>> LogUniform = stats.make_distribution(stats.loguniform)
+    >>> X = LogUniform(a=1.0, b=3.0)
+    >>> np.isclose((X + 0.25).median(), stats.loguniform.ppf(0.5, 1, 3, loc=0.25))
+    np.True_
+    >>> X.plot()
+    >>> sample = X.sample(10000, rng=np.random.default_rng())
+    >>> plt.hist(sample, density=True, bins=30)
+    >>> plt.legend(('pdf', 'histogram'))
+    >>> plt.show()
+
+    Create a custom distribution.
+
+    >>> class MyLogUniform:
+    ...     @property
+    ...     def __make_distribution_version__(self):
+    ...         return "1.16.0"
+    ...
+    ...     @property
+    ...     def parameters(self):
+    ...         return {'a': {'endpoints': (0, np.inf),
+    ...                       'inclusive': (False, False)},
+    ...                 'b': {'endpoints': ('a', np.inf),
+    ...                       'inclusive': (False, False)}}
+    ...
+    ...     @property
+    ...     def support(self):
+    ...         return {'endpoints': ('a', 'b'), 'inclusive': (True, True)}
+    ...
+    ...     def pdf(self, x, a, b):
+    ...         return 1 / (x * (np.log(b)- np.log(a)))
+    >>>
+    >>> MyLogUniform = stats.make_distribution(MyLogUniform())
+    >>> Y = MyLogUniform(a=1.0, b=3.0)
+    >>> np.isclose(Y.cdf(2.), X.cdf(2.))
+    np.True_
+
+    Create a custom distribution with variable support.
+
+    >>> class MyUniformCube:
+    ...     @property
+    ...     def __make_distribution_version__(self):
+    ...         return "1.16.0"
+    ...
+    ...     @property
+    ...     def parameters(self):
+    ...         return {"a": (-np.inf, np.inf),
+    ...                 "b": {'endpoints':('a', np.inf), 'inclusive':(True, False)}}
+    ...
+    ...     @property
+    ...     def support(self):
+    ...         def left(*, a, b):
+    ...             return a**3
+    ...
+    ...         def right(*, a, b):
+    ...             return b**3
+    ...         return (left, right)
+    ...
+    ...     def pdf(self, x, *, a, b):
+    ...         return 1 / (3*(b - a)*np.cbrt(x)**2)
+    ...
+    ...     def cdf(self, x, *, a, b):
+    ...         return (np.cbrt(x) - a) / (b - a)
+    >>>
+    >>> MyUniformCube = stats.make_distribution(MyUniformCube())
+    >>> X = MyUniformCube(a=-2, b=2)
+    >>> Y = stats.Uniform(a=-2, b=2)**3
+    >>> X.support()
+    (-8.0, 8.0)
+    >>> np.isclose(X.cdf(2.1), Y.cdf(2.1))
+    np.True_
+
+    Create a custom distribution with multiple parameterizations. Here we create a
+    custom version of the beta distribution that has an alternative parameterization
+    in terms of the mean ``mu`` and a dispersion parameter ``nu``.
+
+    >>> class MyBeta:
+    ...     @property
+    ...     def __make_distribution_version__(self):
+    ...         return "1.16.0"
+    ...
+    ...     @property
+    ...     def parameters(self):
+    ...         return ({"a": (0, np.inf), "b": (0, np.inf)},
+    ...                 {"mu": (0, 1), "nu": (0, np.inf)})
+    ...
+    ...     def process_parameters(self, a=None, b=None, mu=None, nu=None):
+    ...         if a is not None and b is not None:
+    ...             nu = a + b
+    ...             mu = a / nu
+    ...         else:
+    ...             a = mu * nu
+    ...             b = nu - a
+    ...         return dict(a=a, b=b, mu=mu, nu=nu)
+    ...
+    ...     @property
+    ...     def support(self):
+    ...         return {'endpoints': (0, 1)}
+    ...
+    ...     def pdf(self, x, a, b, mu, nu):
+    ...         return special._ufuncs._beta_pdf(x, a, b)
+    ...
+    ...     def cdf(self, x, a, b, mu, nu):
+    ...         return special.betainc(a, b, x)
+    >>>
+    >>> MyBeta = stats.make_distribution(MyBeta())
+    >>> X = MyBeta(a=2.0, b=2.0)
+    >>> Y = MyBeta(mu=0.5, nu=4.0)
+    >>> np.isclose(X.pdf(0.3), Y.pdf(0.3))
+    np.True_
+
+    """
+    if dist in {stats.levy_stable, stats.vonmises, stats.hypergeom,
+                stats.nchypergeom_fisher, stats.nchypergeom_wallenius,
+                stats.poisson_binom}:
+        raise NotImplementedError(f"`{dist.name}` is not supported.")
+
+    if isinstance(dist, stats.rv_continuous | stats.rv_discrete):
+        return _make_distribution_rv_generic(dist)
+    elif getattr(dist, "__make_distribution_version__", "0.0.0") >= "1.16.0":
+        return _make_distribution_custom(dist)
+    else:
+        message = ("The argument must be an instance of `rv_continuous`, "
+                   "`rv_discrete`, or an instance of a class with attribute "
+                   "`__make_distribution_version__ >= 1.16`.")
+        raise ValueError(message)
+
+def _make_distribution_rv_generic(dist):
+    parameters = []
+    names = []
+    support = getattr(dist, '_support', (dist.a, dist.b))
+    for shape_info in dist._shape_info():
+        domain = _RealInterval(endpoints=shape_info.endpoints,
+                               inclusive=shape_info.inclusive)
+        param = _RealParameter(shape_info.name, domain=domain)
+        parameters.append(param)
+        names.append(shape_info.name)
+
+    repr_str = _distribution_names.get(dist.name, dist.name.capitalize())
+    if isinstance(dist, stats.rv_continuous):
+        old_class, new_class = stats.rv_continuous, ContinuousDistribution
+    else:
+        old_class, new_class = stats.rv_discrete, DiscreteDistribution
+
+    def _overrides(method_name):
+        return (getattr(dist.__class__, method_name, None)
+                is not getattr(old_class, method_name, None))
+
+    if _overrides("_get_support"):
+        def left(**parameter_values):
+            a, _ = dist._get_support(**parameter_values)
+            return np.asarray(a)[()]
+
+        def right(**parameter_values):
+            _, b = dist._get_support(**parameter_values)
+            return np.asarray(b)[()]
+
+        endpoints = (left, right)
+    else:
+        endpoints = support
+
+    _x_support = _RealInterval(endpoints=endpoints, inclusive=(True, True))
+    _x_param = _RealParameter('x', domain=_x_support, typical=(-1, 1))
+
+    class CustomDistribution(new_class):
+        _parameterizations = ([_Parameterization(*parameters)] if parameters
+                              else [])
+        _variable = _x_param
+
+        __class_getitem__ = None
+
+        def __repr__(self):
+            s = super().__repr__()
+            return s.replace('CustomDistribution', repr_str)
+
+        def __str__(self):
+            s = super().__str__()
+            return s.replace('CustomDistribution', repr_str)
+
+    def _sample_formula(self, full_shape=(), *, rng=None, **kwargs):
+        return dist._rvs(size=full_shape, random_state=rng, **kwargs)
+
+    def _moment_raw_formula(self, order, **kwargs):
+        return dist._munp(int(order), **kwargs)
+
+    def _moment_raw_formula_1(self, order, **kwargs):
+        if order != 1:
+            return None
+        return dist._stats(**kwargs)[0]
+
+    def _moment_central_formula(self, order, **kwargs):
+        if order != 2:
+            return None
+        return dist._stats(**kwargs)[1]
+
+    def _moment_standard_formula(self, order, **kwargs):
+        if order == 3:
+            if dist._stats_has_moments:
+                kwargs['moments'] = 's'
+            return dist._stats(**kwargs)[int(order - 1)]
+        elif order == 4:
+            if dist._stats_has_moments:
+                kwargs['moments'] = 'k'
+            k = dist._stats(**kwargs)[int(order - 1)]
+            return k if k is None else k + 3
+        else:
+            return None
+
+    methods = {'_logpdf': '_logpdf_formula',
+               '_pdf': '_pdf_formula',
+               '_logpmf': '_logpmf_formula',
+               '_pmf': '_pmf_formula',
+               '_logcdf': '_logcdf_formula',
+               '_cdf': '_cdf_formula',
+               '_logsf': '_logccdf_formula',
+               '_sf': '_ccdf_formula',
+               '_ppf': '_icdf_formula',
+               '_isf': '_iccdf_formula',
+               '_entropy': '_entropy_formula',
+               '_median': '_median_formula'}
+
+    # These are not desirable overrides for the new infrastructure
+    skip_override = {'norminvgauss': {'_sf', '_isf'}}
+
+    for old_method, new_method in methods.items():
+        if dist.name in skip_override and old_method in skip_override[dist.name]:
+            continue
+        # If method of old distribution overrides generic implementation...
+        method = getattr(dist.__class__, old_method, None)
+        super_method = getattr(old_class, old_method, None)
+        if method is not super_method:
+            # Make it an attribute of the new object with the new name
+            setattr(CustomDistribution, new_method, getattr(dist, old_method))
+
+    if _overrides('_munp'):
+        CustomDistribution._moment_raw_formula = _moment_raw_formula
+
+    if _overrides('_rvs'):
+        CustomDistribution._sample_formula = _sample_formula
+
+    if _overrides('_stats'):
+        CustomDistribution._moment_standardized_formula = _moment_standard_formula
+        if not _overrides('_munp'):
+            CustomDistribution._moment_raw_formula = _moment_raw_formula_1
+            CustomDistribution._moment_central_formula = _moment_central_formula
+
+    support_etc = _combine_docs(CustomDistribution, include_examples=False).lstrip()
+    docs = [
+        f"This class represents `scipy.stats.{dist.name}` as a subclass of "
+        f"`{new_class}`.",
+        f"The `repr`/`str` of class instances is `{repr_str}`.",
+        f"The PDF of the distribution is defined {support_etc}"
+    ]
+    CustomDistribution.__doc__ = ("\n".join(docs))
+
+    return CustomDistribution
+
+
+def _get_domain_info(info):
+    domain_info = {"endpoints": info} if isinstance(info, tuple) else info
+    typical = domain_info.pop("typical", None)
+    return domain_info, typical
+
+
+def _make_distribution_custom(dist):
+    dist_parameters = (
+        dist.parameters if isinstance(dist.parameters, tuple) else (dist.parameters, )
+    )
+    parameterizations = []
+    for parameterization in dist_parameters:
+        # The attribute name ``parameters`` appears reasonable from a user facing
+        # perspective, but there is a little tension here with the internal. It's
+        # important to keep in mind that the ``parameters`` attribute in a
+        # user-created custom distribution specifies ``_parameterizations`` within
+        # the infrastructure.
+        parameters = []
+
+        for name, info in parameterization.items():
+            domain_info, typical = _get_domain_info(info)
+            domain = _RealInterval(**domain_info)
+            param = _RealParameter(name, domain=domain, typical=typical)
+            parameters.append(param)
+
+        if parameters:
+            parameterizations.append(_Parameterization(*parameters))
+
+    domain_info, typical = _get_domain_info(dist.support)
+    _x_support = _RealInterval(**domain_info)
+    _x_param = _RealParameter('x', domain=_x_support, typical=typical)
+    repr_str = dist.__class__.__name__
+
+    class CustomDistribution(ContinuousDistribution):
+        _parameterizations = parameterizations
+        _variable = _x_param
+
+        def __repr__(self):
+            s = super().__repr__()
+            return s.replace('CustomDistribution', repr_str)
+
+        def __str__(self):
+            s = super().__str__()
+            return s.replace('CustomDistribution', repr_str)
+
+    methods = {'sample', 'logentropy', 'entropy',
+               'median', 'mode', 'logpdf', 'pdf',
+               'logcdf2', 'logcdf', 'cdf2', 'cdf',
+               'logccdf2', 'logccdf', 'ccdf2', 'ccdf',
+               'ilogcdf', 'icdf', 'ilogccdf', 'iccdf',
+               'lmoment'}
+
+    for method in methods:
+        if hasattr(dist, method):
+            # Make it an attribute of the new object with the new name
+            new_method = f"_{method}_formula"
+            setattr(CustomDistribution, new_method, getattr(dist, method))
+
+    if hasattr(dist, 'moment'):
+        def _moment_raw_formula(self, order, **kwargs):
+            return dist.moment(order, kind='raw', **kwargs)
+
+        def _moment_central_formula(self, order, **kwargs):
+            return dist.moment(order, kind='central', **kwargs)
+
+        def _moment_standardized_formula(self, order, **kwargs):
+            return dist.moment(order, kind='standardized', **kwargs)
+
+        CustomDistribution._moment_raw_formula = _moment_raw_formula
+        CustomDistribution._moment_central_formula = _moment_central_formula
+        CustomDistribution._moment_standardized_formula = _moment_standardized_formula
+
+    if hasattr(dist, 'process_parameters'):
+        setattr(
+            CustomDistribution,
+            "_process_parameters",
+            getattr(dist, "process_parameters")
+        )
+
+    support_etc = _combine_docs(CustomDistribution, include_examples=False).lstrip()
+    docs = [
+        f"This class represents `{repr_str}` as a subclass of "
+        "`ContinuousDistribution`.",
+        f"The PDF of the distribution is defined {support_etc}"
+    ]
+    CustomDistribution.__doc__ = ("\n".join(docs))
+
+    return CustomDistribution
+
+
+# The purpose of making ShiftedScaledDistribution a separate class is for
+# a) simplicity of the ContinuousDistribution class and
+# b) avoiding the requirement that every distribution accept loc/scale.
+# The simplicity of ContinuousDistribution is important, because there are
+# several other distribution transformations to be supported; e.g., truncation,
+# wrapping, folding, and doubling. We wouldn't want to cram all of this
+# into the `ContinuousDistribution` class. Also, the order of the composition
+# matters (e.g. truncate then shift/scale or vice versa). It's easier to
+# accommodate different orders if the transformation is built up from
+# components rather than all built into `ContinuousDistribution`.
+
+def _shift_scale_distribution_function_2arg(func):
+    def wrapped(self, x, y, *args, loc, scale, sign, **kwargs):
+        item = func.__name__
+
+        f = getattr(self._dist, item)
+
+        # Obviously it's possible to get away with half of the work here.
+        # Let's focus on correct results first and optimize later.
+        xt = self._transform(x, loc, scale)
+        yt = self._transform(y, loc, scale)
+        fxy = f(xt, yt, *args, **kwargs)
+        fyx = f(yt, xt, *args, **kwargs)
+        return np.real_if_close(np.where(sign, fxy, fyx))[()]
+
+    return wrapped
+
+def _shift_scale_distribution_function(func):
+    # c is for complementary
+    citem = {'_logcdf_dispatch': '_logccdf_dispatch',
+             '_cdf_dispatch': '_ccdf_dispatch',
+             '_logccdf_dispatch': '_logcdf_dispatch',
+             '_ccdf_dispatch': '_cdf_dispatch'}
+    def wrapped(self, x, *args, loc, scale, sign, **kwargs):
+        item = func.__name__
+
+        f = getattr(self._dist, item)
+        cf = getattr(self._dist, citem[item])
+
+        # Obviously it's possible to get away with half of the work here.
+        # Let's focus on correct results first and optimize later.
+        xt = self._transform(x, loc, scale)
+        fx = f(xt, *args, **kwargs)
+        cfx = cf(xt, *args, **kwargs)
+        return np.where(sign, fx, cfx)[()]
+
+    return wrapped
+
+def _shift_scale_inverse_function(func):
+    citem = {'_ilogcdf_dispatch': '_ilogccdf_dispatch',
+             '_icdf_dispatch': '_iccdf_dispatch',
+             '_ilogccdf_dispatch': '_ilogcdf_dispatch',
+             '_iccdf_dispatch': '_icdf_dispatch'}
+    def wrapped(self, p, *args, loc, scale, sign, **kwargs):
+        item = func.__name__
+
+        f = getattr(self._dist, item)
+        cf = getattr(self._dist, citem[item])
+
+        # Obviously it's possible to get away with half of the work here.
+        # Let's focus on correct results first and optimize later.
+        fx =  self._itransform(f(p, *args, **kwargs), loc, scale)
+        cfx = self._itransform(cf(p, *args, **kwargs), loc, scale)
+        return np.where(sign, fx, cfx)[()]
+
+    return wrapped
+
+
+class TransformedDistribution(ContinuousDistribution):
+    def __init__(self, X, /, *args, **kwargs):
+        if not isinstance(X, ContinuousDistribution):
+            message = "Transformations are currently only supported for continuous RVs."
+            raise NotImplementedError(message)
+        self._copy_parameterization()
+        self._variable = X._variable
+        self._dist = X
+        if X._parameterization:
+            # Add standard distribution parameters to our parameterization
+            dist_parameters = X._parameterization.parameters
+            set_params = set(dist_parameters)
+            if not self._parameterizations:
+                self._parameterizations.append(_Parameterization())
+            for parameterization in self._parameterizations:
+                if set_params.intersection(parameterization.parameters):
+                    message = (f"One or more of the parameters of {X} has "
+                               "the same name as a parameter of "
+                               f"{self.__class__.__name__}. Name collisions "
+                               "create ambiguities and are not supported.")
+                    raise ValueError(message)
+                parameterization.parameters.update(dist_parameters)
+        super().__init__(*args, **kwargs)
+
+    def _overrides(self, method_name):
+        return (self._dist._overrides(method_name)
+                or super()._overrides(method_name))
+
+    def reset_cache(self):
+        super().reset_cache()
+
+    def _update_parameters(self, *, validation_policy=None, **params):
+        # maybe broadcast everything before processing?
+        parameters = {}
+        # There may be some issues with _original_parameters
+        # We only want to update with _dist._original_parameters during
+        # initialization. Afterward that, we want to start with
+        # self._original_parameters.
+        parameters.update(self._dist._original_parameters)
+        parameters.update(params)
+        super()._update_parameters(validation_policy=validation_policy, **parameters)
+
+    def _process_parameters(self, **params):
+        return self._dist._process_parameters(**params)
+
+    def __repr__(self):
+        raise NotImplementedError()
+
+    def __str__(self):
+        raise NotImplementedError()
+
+
+class TruncatedDistribution(TransformedDistribution):
+    """Truncated distribution."""
+    # TODO:
+    # - consider avoiding catastropic cancellation by using appropriate tail
+    # - if the mode of `_dist` is within the support, it's still the mode
+    # - rejection sampling might be more efficient than inverse transform
+
+    _lb_domain = _RealInterval(endpoints=(-inf, 'ub'), inclusive=(True, False))
+    _lb_param = _RealParameter('lb', symbol=r'b_l',
+                                domain=_lb_domain, typical=(0.1, 0.2))
+
+    _ub_domain = _RealInterval(endpoints=('lb', inf), inclusive=(False, True))
+    _ub_param = _RealParameter('ub', symbol=r'b_u',
+                                  domain=_ub_domain, typical=(0.8, 0.9))
+
+    _parameterizations = [_Parameterization(_lb_param, _ub_param),
+                          _Parameterization(_lb_param),
+                          _Parameterization(_ub_param)]
+
+    def __init__(self, X, /, *args, lb=-np.inf, ub=np.inf, **kwargs):
+        return super().__init__(X, *args, lb=lb, ub=ub, **kwargs)
+
+    def _process_parameters(self, lb=None, ub=None, **params):
+        lb = lb if lb is not None else np.full_like(lb, -np.inf)[()]
+        ub = ub if ub is not None else np.full_like(ub, np.inf)[()]
+        parameters = self._dist._process_parameters(**params)
+        a, b = self._support(lb=lb, ub=ub, **parameters)
+        logmass = self._dist._logcdf2_dispatch(a, b, **parameters)
+        parameters.update(dict(lb=lb, ub=ub, _a=a, _b=b, logmass=logmass))
+        return parameters
+
+    def _support(self, lb, ub, **params):
+        a, b = self._dist._support(**params)
+        return np.maximum(a, lb), np.minimum(b, ub)
+
+    def _overrides(self, method_name):
+        return False
+
+    def _logpdf_dispatch(self, x, *args, lb, ub, _a, _b, logmass, **params):
+        logpdf = self._dist._logpdf_dispatch(x, *args, **params)
+        return logpdf - logmass
+
+    def _logcdf_dispatch(self, x, *args, lb, ub, _a, _b, logmass, **params):
+        logcdf = self._dist._logcdf2_dispatch(_a, x, *args, **params)
+        # of course, if this result is small we could compute with the other tail
+        return logcdf - logmass
+
+    def _logccdf_dispatch(self, x, *args, lb, ub, _a, _b, logmass, **params):
+        logccdf = self._dist._logcdf2_dispatch(x, _b, *args, **params)
+        return logccdf - logmass
+
+    def _logcdf2_dispatch(self, x, y, *args, lb, ub, _a, _b, logmass, **params):
+        logcdf2 = self._dist._logcdf2_dispatch(x, y, *args, **params)
+        return logcdf2 - logmass
+
+    def _ilogcdf_dispatch(self, logp, *args, lb, ub, _a, _b, logmass, **params):
+        log_Fa = self._dist._logcdf_dispatch(_a, *args, **params)
+        logp_adjusted = np.logaddexp(log_Fa, logp + logmass)
+        return self._dist._ilogcdf_dispatch(logp_adjusted, *args, **params)
+
+    def _ilogccdf_dispatch(self, logp, *args, lb, ub, _a, _b, logmass, **params):
+        log_cFb = self._dist._logccdf_dispatch(_b, *args, **params)
+        logp_adjusted = np.logaddexp(log_cFb, logp + logmass)
+        return self._dist._ilogccdf_dispatch(logp_adjusted, *args, **params)
+
+    def _icdf_dispatch(self, p, *args, lb, ub, _a, _b, logmass, **params):
+        Fa = self._dist._cdf_dispatch(_a, *args, **params)
+        p_adjusted = Fa + p*np.exp(logmass)
+        return self._dist._icdf_dispatch(p_adjusted, *args, **params)
+
+    def _iccdf_dispatch(self, p, *args, lb, ub, _a, _b, logmass, **params):
+        cFb = self._dist._ccdf_dispatch(_b, *args, **params)
+        p_adjusted = cFb + p*np.exp(logmass)
+        return self._dist._iccdf_dispatch(p_adjusted, *args, **params)
+
+    def __repr__(self):
+        with np.printoptions(threshold=10):
+            return (f"truncate({repr(self._dist)}, "
+                    f"lb={repr(self.lb)}, ub={repr(self.ub)})")
+
+    def __str__(self):
+        with np.printoptions(threshold=10):
+            return (f"truncate({str(self._dist)}, "
+                    f"lb={str(self.lb)}, ub={str(self.ub)})")
+
+
+@xp_capabilities(np_only=True)
+def truncate(X, lb=-np.inf, ub=np.inf):
+    """Truncate the support of a random variable.
+
+    Given a random variable `X`, `truncate` returns a random variable with
+    support truncated to the interval between `lb` and `ub`. The underlying
+    probability density function is normalized accordingly.
+
+    Parameters
+    ----------
+    X : `ContinuousDistribution`
+        The random variable to be truncated.
+    lb, ub : float array-like
+        The lower and upper truncation points, respectively. Must be
+        broadcastable with one another and the shape of `X`.
+
+    Returns
+    -------
+    X : `ContinuousDistribution`
+        The truncated random variable.
+
+    References
+    ----------
+    .. [1] "Truncated Distribution". *Wikipedia*.
+           https://en.wikipedia.org/wiki/Truncated_distribution
+
+    Examples
+    --------
+    Compare against `scipy.stats.truncnorm`, which truncates a standard normal,
+    *then* shifts and scales it.
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy import stats
+    >>> loc, scale, lb, ub = 1, 2, -2, 2
+    >>> X = stats.truncnorm(lb, ub, loc, scale)
+    >>> Y = scale * stats.truncate(stats.Normal(), lb, ub) + loc
+    >>> x = np.linspace(-3, 5, 300)
+    >>> plt.plot(x, X.pdf(x), '-', label='X')
+    >>> plt.plot(x, Y.pdf(x), '--', label='Y')
+    >>> plt.xlabel('x')
+    >>> plt.ylabel('PDF')
+    >>> plt.title('Truncated, then Shifted/Scaled Normal')
+    >>> plt.legend()
+    >>> plt.show()
+
+    However, suppose we wish to shift and scale a normal random variable,
+    then truncate its support to given values. This is straightforward with
+    `truncate`.
+
+    >>> Z = stats.truncate(scale * stats.Normal() + loc, lb, ub)
+    >>> Z.plot()
+    >>> plt.show()
+
+    Furthermore, `truncate` can be applied to any random variable:
+
+    >>> Rayleigh = stats.make_distribution(stats.rayleigh)
+    >>> W = stats.truncate(Rayleigh(), lb=0.5, ub=3)
+    >>> W.plot()
+    >>> plt.show()
+
+    """
+    return TruncatedDistribution(X, lb=lb, ub=ub)
+
+
+class ShiftedScaledDistribution(TransformedDistribution):
+    """Distribution with a standard shift/scale transformation."""
+    # Unclear whether infinite loc/scale will work reasonably in all cases
+    _loc_domain = _RealInterval(endpoints=(-inf, inf), inclusive=(True, True))
+    _loc_param = _RealParameter('loc', symbol=r'\mu',
+                                domain=_loc_domain, typical=(1, 2))
+
+    _scale_domain = _RealInterval(endpoints=(-inf, inf), inclusive=(True, True))
+    _scale_param = _RealParameter('scale', symbol=r'\sigma',
+                                  domain=_scale_domain, typical=(0.1, 10))
+
+    _parameterizations = [_Parameterization(_loc_param, _scale_param),
+                          _Parameterization(_loc_param),
+                          _Parameterization(_scale_param)]
+
+    def _process_parameters(self, loc=None, scale=None, **params):
+        loc = loc if loc is not None else np.zeros_like(scale)[()]
+        scale = scale if scale is not None else np.ones_like(loc)[()]
+        sign = scale > 0
+        parameters = self._dist._process_parameters(**params)
+        parameters.update(dict(loc=loc, scale=scale, sign=sign))
+        return parameters
+
+    def _transform(self, x, loc, scale, **kwargs):
+        return (x - loc)/scale
+
+    def _itransform(self, x, loc, scale, **kwargs):
+        return x * scale + loc
+
+    def _support(self, loc, scale, sign, **params):
+        # Add shortcut for infinite support?
+        a, b = self._dist._support(**params)
+        a, b = self._itransform(a, loc, scale), self._itransform(b, loc, scale)
+        return np.where(sign, a, b)[()], np.where(sign, b, a)[()]
+
+    def __repr__(self):
+        with np.printoptions(threshold=10):
+            result =  f"{repr(self.scale)}*{repr(self._dist)}"
+            if not self.loc.ndim and self.loc < 0:
+                result += f" - {repr(-self.loc)}"
+            elif (np.any(self.loc != 0)
+                  or not np.can_cast(self.loc.dtype, self.scale.dtype)):
+                # We don't want to hide a zero array loc if it can cause
+                # a type promotion.
+                result += f" + {repr(self.loc)}"
+        return result
+
+    def __str__(self):
+        with np.printoptions(threshold=10):
+            result =  f"{str(self.scale)}*{str(self._dist)}"
+            if not self.loc.ndim and self.loc < 0:
+                result += f" - {str(-self.loc)}"
+            elif (np.any(self.loc != 0)
+                  or not np.can_cast(self.loc.dtype, self.scale.dtype)):
+                # We don't want to hide a zero array loc if it can cause
+                # a type promotion.
+                result += f" + {str(self.loc)}"
+        return result
+
+    # Here, we override all the `_dispatch` methods rather than the public
+    # methods or _formula methods. Why not the public methods?
+    # If we were to override the public methods, then other
+    # TransformedDistribution classes (which could transform a
+    # ShiftedScaledDistribution) would need to call the public methods of
+    # ShiftedScaledDistribution, which would run the input validation again.
+    # Why not the _formula methods? For distributions that rely on the
+    # default implementation of methods (e.g. `quadrature`, `inversion`),
+    # the implementation would "see" the location and scale like other
+    # distribution parameters, so they could affect the accuracy of the
+    # calculations. I think it is cleaner if `loc` and `scale` do not affect
+    # the underlying calculations at all.
+
+    def _entropy_dispatch(self, *args, loc, scale, sign, **params):
+        return (self._dist._entropy_dispatch(*args, **params)
+                + np.log(np.abs(scale)))
+
+    def _logentropy_dispatch(self, *args, loc, scale, sign, **params):
+        lH0 = self._dist._logentropy_dispatch(*args, **params)
+        lls = np.log(np.log(np.abs(scale))+0j)
+        return special.logsumexp(np.broadcast_arrays(lH0, lls), axis=0)
+
+    def _median_dispatch(self, *, method, loc, scale, sign, **params):
+        raw = self._dist._median_dispatch(method=method, **params)
+        return self._itransform(raw, loc, scale)
+
+    def _mode_dispatch(self, *, method, loc, scale, sign, **params):
+        raw = self._dist._mode_dispatch(method=method, **params)
+        return self._itransform(raw, loc, scale)
+
+    def _logpdf_dispatch(self, x, *args, loc, scale, sign, **params):
+        x = self._transform(x, loc, scale)
+        logpdf = self._dist._logpdf_dispatch(x, *args, **params)
+        return logpdf - np.log(np.abs(scale))
+
+    def _pdf_dispatch(self, x, *args, loc, scale, sign, **params):
+        x = self._transform(x, loc, scale)
+        pdf = self._dist._pdf_dispatch(x, *args, **params)
+        return pdf / np.abs(scale)
+
+    def _logpmf_dispatch(self, x, *args, loc, scale, sign, **params):
+        x = self._transform(x, loc, scale)
+        logpmf = self._dist._logpmf_dispatch(x, *args, **params)
+        return logpmf - np.log(np.abs(scale))
+
+    def _pmf_dispatch(self, x, *args, loc, scale, sign, **params):
+        x = self._transform(x, loc, scale)
+        pmf = self._dist._pmf_dispatch(x, *args, **params)
+        return pmf / np.abs(scale)
+
+    def _logpxf_dispatch(self, x, *args, loc, scale, sign, **params):
+        x = self._transform(x, loc, scale)
+        logpxf = self._dist._logpxf_dispatch(x, *args, **params)
+        return logpxf - np.log(np.abs(scale))
+
+    def _pxf_dispatch(self, x, *args, loc, scale, sign, **params):
+        x = self._transform(x, loc, scale)
+        pxf = self._dist._pxf_dispatch(x, *args, **params)
+        return pxf / np.abs(scale)
+
+    @_shift_scale_distribution_function
+    def _logcdf_dispatch(self, x, *, method=None, **params):
+        pass
+
+    @_shift_scale_distribution_function
+    def _cdf_dispatch(self, x, *, method=None, **params):
+        pass
+
+    @_shift_scale_distribution_function
+    def _logccdf_dispatch(self, x, *, method=None, **params):
+        pass
+
+    @_shift_scale_distribution_function
+    def _ccdf_dispatch(self, x, *, method=None, **params):
+        pass
+
+    @_shift_scale_distribution_function_2arg
+    def _logcdf2_dispatch(self, x, y, *, method=None, **params):
+        pass
+
+    @_shift_scale_distribution_function_2arg
+    def _cdf2_dispatch(self, x, y, *, method=None, **params):
+        pass
+
+    @_shift_scale_distribution_function_2arg
+    def _logccdf2_dispatch(self, x, y, *, method=None, **params):
+        pass
+
+    @_shift_scale_distribution_function_2arg
+    def _ccdf2_dispatch(self, x, y, *, method=None, **params):
+        pass
+
+    @_shift_scale_inverse_function
+    def _ilogcdf_dispatch(self, x, *, method=None, **params):
+        pass
+
+    @_shift_scale_inverse_function
+    def _icdf_dispatch(self, x, *, method=None, **params):
+        pass
+
+    @_shift_scale_inverse_function
+    def _ilogccdf_dispatch(self, x, *, method=None, **params):
+        pass
+
+    @_shift_scale_inverse_function
+    def _iccdf_dispatch(self, x, *, method=None, **params):
+        pass
+
+    def _moment_standardized_dispatch(self, order, *, loc, scale, sign, methods,
+                                      **params):
+        res = (self._dist._moment_standardized_dispatch(
+            order, methods=methods, **params))
+        return None if res is None else res * np.sign(scale)**order
+
+    def _moment_central_dispatch(self, order, *, loc, scale, sign, methods,
+                                 **params):
+        res = (self._dist._moment_central_dispatch(
+            order, methods=methods, **params))
+        return None if res is None else res * scale**order
+
+    def _moment_raw_dispatch(self, order, *, loc, scale, sign, methods,
+                             **params):
+        raw_moments = []
+        methods_highest_order = methods
+        for i in range(int(order) + 1):
+            methods = (self._moment_methods if i < order
+                       else methods_highest_order)
+            raw = self._dist._moment_raw_dispatch(i, methods=methods, **params)
+            if raw is None:
+                return None
+            moment_i = raw * scale**i
+            raw_moments.append(moment_i)
+
+        return self._moment_transform_center(
+            order, raw_moments, loc, self._zero)
+
+    def _lmoment_dispatch(self, order, *, loc, scale, sign, methods, **params):
+        res = self._dist._lmoment_dispatch(order, methods=methods, **params)
+        if res is None:  # if a specific method is requested but not available
+            return None
+        res = res * np.abs(scale) * np.sign(scale)**order
+        return res + loc if order == 1 else res
+
+    def _sample_dispatch(self, full_shape, *,
+                         rng, loc, scale, sign, method, **params):
+        rvs = self._dist._sample_dispatch(full_shape, method=method, rng=rng, **params)
+        return self._itransform(rvs, loc=loc, scale=scale, sign=sign, **params)
+
+    def __add__(self, loc):
+        return ShiftedScaledDistribution(self._dist, loc=self.loc + loc,
+                                         scale=self.scale)
+
+    def __sub__(self, loc):
+        return ShiftedScaledDistribution(self._dist, loc=self.loc - loc,
+                                         scale=self.scale)
+
+    def __mul__(self, scale):
+        return ShiftedScaledDistribution(self._dist,
+                                         loc=self.loc * scale,
+                                         scale=self.scale * scale)
+
+    def __truediv__(self, scale):
+        return ShiftedScaledDistribution(self._dist,
+                                         loc=self.loc / scale,
+                                         scale=self.scale / scale)
+
+
+class OrderStatisticDistribution(TransformedDistribution):
+    r"""Probability distribution of an order statistic.
+
+    An instance of this class represents a random variable that follows the
+    distribution of the :math:`r^{\text{th}}` order statistic of a
+    sample of :math:`n` observations of a random variable :math:`X`.
+
+    Parameters
+    ----------
+    dist : `ContinuousDistribution`
+        The random variable :math:`X`.
+    n : array_like
+        The (positive integer) sample size :math:`n`.
+    r : array_like
+        The (positive integer) rank of the order statistic :math:`r`,
+        satisfying :math:`1 \leq r \leq n`.
+
+
+    Notes
+    -----
+    If we make :math:`n` observations of a continuous random variable
+    :math:`X` and sort them in increasing order
+    :math:`X_{(1)}, \dots, X_{(r)}, \dots, X_{(n)}`, then :math:`X_{(r)}`
+    is known as the :math:`r^{\text{th}}` order statistic.
+
+    If the PDF, CDF, and CCDF of :math:`X` are denoted by :math:`f`,
+    :math:`F`, and :math:`G = 1 - F`, respectively, then the PDF of
+    :math:`X_{(r)}` is given by:
+
+    .. math::
+
+        f_r(x) = \frac{n!}{(r-1)! (n-r)!} f(x) F(x)^{r-1} G(x)^{n - r}
+
+    The CDF and other methods of the distribution of :math:`X_{(r)}`
+    are calculated using the fact that :math:`X = F^{-1}(U)`, where :math:`U` is a
+    standard uniform random variable, together with the fact that the order statistics
+    of i.i.d. uniform random variables follow a beta distribution
+    :math:`B(r, n - r + 1)`.
+
+    References
+    ----------
+    .. [1] Order statistic. *Wikipedia*. https://en.wikipedia.org/wiki/Order_statistic
+
+    Examples
+    --------
+    Suppose we are interested in order statistics of samples of size five drawn
+    from the standard normal distribution. Plot the PDF of the fourth
+    order statistic and compare with a normalized histogram from simulation.
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy import stats
+    >>> from scipy.stats._distribution_infrastructure import OrderStatisticDistribution
+    >>>
+    >>> X = stats.Normal()
+    >>> data = X.sample(shape=(10000, 5))
+    >>> sorted_data = np.sort(data, axis=1)
+    >>> Y = OrderStatisticDistribution(X, r=4, n=5)
+    >>>
+    >>> ax = plt.gca()
+    >>> Y.plot(ax=ax)
+    >>> ax.hist(sorted_data[:, 3], density=True, bins=30)
+    >>> plt.show()
+
+    """
+
+    _r_domain = _IntegerInterval(endpoints=(1, 'n'), inclusive=(True, True))
+    _r_param = _RealParameter('r', domain=_r_domain, typical=(1, 2))
+
+    _n_domain = _IntegerInterval(endpoints=(1, np.inf), inclusive=(True, True))
+    _n_param = _RealParameter('n', domain=_n_domain, typical=(1, 4))
+
+    _r_domain.define_parameters(_n_param)
+
+    _parameterizations = [_Parameterization(_r_param, _n_param)]
+
+    def __init__(self, dist, /, *args, r, n, **kwargs):
+        super().__init__(dist, *args, r=r, n=n, **kwargs)
+
+    def _support(self, *args, r, n, **kwargs):
+        return self._dist._support(*args, **kwargs)
+
+    def _process_parameters(self, r=None, n=None, **params):
+        parameters = self._dist._process_parameters(**params)
+        parameters.update(dict(r=r, n=n))
+        return parameters
+
+    def _overrides(self, method_name):
+        return method_name in {'_logpdf_formula', '_pdf_formula',
+                               '_cdf_formula', '_ccdf_formula',
+                               '_icdf_formula', '_iccdf_formula'}
+
+    def _logpdf_formula(self, x, r, n, **kwargs):
+        log_factor = special.betaln(r, n - r + 1)
+        log_fX = self._dist._logpdf_dispatch(x, **kwargs)
+        # log-methods sometimes use complex dtype with 0 imaginary component,
+        # but `_tanhsinh` doesn't accept complex limits of integration; take `real`.
+        log_FX = self._dist._logcdf_dispatch(x.real, **kwargs)
+        log_cFX = self._dist._logccdf_dispatch(x.real, **kwargs)
+        # This can be problematic when (r - 1)|(n-r) = 0 and `log_FX`|log_cFX = -inf
+        # The PDF in these cases is 0^0, so these should be replaced with log(1)=0
+        # return log_fX + (r-1)*log_FX + (n-r)*log_cFX - log_factor
+        rm1_log_FX = np.where((r - 1 == 0) & np.isneginf(log_FX), 0, (r-1)*log_FX)
+        nmr_log_cFX = np.where((n - r == 0) & np.isneginf(log_cFX), 0, (n-r)*log_cFX)
+        return log_fX + rm1_log_FX + nmr_log_cFX - log_factor
+
+    def _pdf_formula(self, x, r, n, **kwargs):
+        # 1 / factor = factorial(n) / (factorial(r-1) * factorial(n-r))
+        factor = special.beta(r, n - r + 1)
+        fX = self._dist._pdf_dispatch(x, **kwargs)
+        FX = self._dist._cdf_dispatch(x, **kwargs)
+        cFX = self._dist._ccdf_dispatch(x, **kwargs)
+        return fX * FX**(r-1) * cFX**(n-r) / factor
+
+    def _cdf_formula(self, x, r, n, **kwargs):
+        x_ = self._dist._cdf_dispatch(x, **kwargs)
+        return special.betainc(r, n-r+1, x_)
+
+    def _ccdf_formula(self, x, r, n, **kwargs):
+        x_ = self._dist._cdf_dispatch(x, **kwargs)
+        return special.betaincc(r, n-r+1, x_)
+
+    def _icdf_formula(self, p, r, n, **kwargs):
+        p_ = special.betaincinv(r, n-r+1, p)
+        return self._dist._icdf_dispatch(p_, **kwargs)
+
+    def _iccdf_formula(self, p, r, n, **kwargs):
+        p_ = special.betainccinv(r, n-r+1, p)
+        return self._dist._icdf_dispatch(p_, **kwargs)
+
+    def __repr__(self):
+        with np.printoptions(threshold=10):
+            return (f"order_statistic({repr(self._dist)}, r={repr(self.r)}, "
+                    f"n={repr(self.n)})")
+
+    def __str__(self):
+        with np.printoptions(threshold=10):
+            return (f"order_statistic({str(self._dist)}, r={str(self.r)}, "
+                    f"n={str(self.n)})")
+
+
+@xp_capabilities(np_only=True)
+def order_statistic(X, /, *, r, n):
+    r"""Probability distribution of an order statistic.
+
+    Returns a random variable that follows the distribution of the
+    :math:`r^{\text{th}}` order statistic of a sample of :math:`n`
+    observations of a random variable :math:`X`.
+
+    Parameters
+    ----------
+    X : `ContinuousDistribution`
+        The random variable :math:`X`.
+    r : array_like
+        The (positive integer) rank of the order statistic :math:`r`,
+        satisfying ``1 <= r <= n``.
+    n : array_like
+        The (positive integer) sample size :math:`n`.
+
+    Returns
+    -------
+    Y : `ContinuousDistribution`
+        A random variable that follows the distribution of the prescribed
+        order statistic.
+
+    Notes
+    -----
+    If we make :math:`n` observations of a continuous random variable
+    :math:`X` and sort them in increasing order
+    :math:`X_{(1)}, \dots, X_{(r)}, \dots, X_{(n)}`, then :math:`X_{(r)}`
+    is known as the :math:`r^{\text{th}}` order statistic.
+
+    If the PDF, CDF, and CCDF of :math:`X` are denoted by :math:`f`,
+    :math:`F`, and :math:`G = 1 - F`, respectively, then the PDF of
+    :math:`X_{(r)}` is given by:
+
+    .. math::
+
+        f_r(x) = \frac{n!}{(r-1)! (n-r)!} f(x) F(x)^{r-1} G(x)^{n - r}
+
+    The CDF and other methods of the distribution of :math:`X_{(r)}`
+    are calculated using the fact that :math:`X = F^{-1}(U)`, where :math:`U` is a
+    standard uniform random variable, together with the fact that the order statistics
+    of i.i.d. uniform random variables follow a beta distribution
+    :math:`B(r, n - r + 1)`.
+
+    References
+    ----------
+    .. [1] Order statistic. *Wikipedia*. https://en.wikipedia.org/wiki/Order_statistic
+
+    Examples
+    --------
+    Suppose we are interested in order statistics of samples of size five drawn
+    from the standard normal distribution. Plot the PDF of each
+    order statistic and compare with a normalized histogram from simulation.
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy import stats
+    >>>
+    >>> X = stats.Normal()
+    >>> data = X.sample(shape=(10000, 5))
+    >>> sorted_data = np.sort(data, axis=1)
+    >>> Y = stats.order_statistic(X, r=[1, 2, 3, 4, 5], n=5)
+    >>>
+    >>> ax = plt.gca()
+    >>> colors = plt.rcParams['axes.prop_cycle'].by_key()['color']
+    >>> for i in range(5):
+    ...     y = sorted_data[:, i]
+    ...     ax.hist(y, density=True, bins=30, alpha=0.1, color=colors[i])
+    >>> Y.plot(ax=ax)
+    >>> plt.show()
+
+    """
+    r, n = np.asarray(r), np.asarray(n)
+    if np.any((r != np.floor(r)) | (r < 0)) or np.any((n != np.floor(n)) | (n < 0)):
+        message = "`r` and `n` must contain only positive integers."
+        raise ValueError(message)
+    return OrderStatisticDistribution(X, r=r, n=n)
+
+
+class Mixture(_ProbabilityDistribution):
+    r"""Representation of a mixture distribution.
+
+    A mixture distribution is the distribution of a random variable
+    defined in the following way: first, a random variable is selected
+    from `components` according to the probabilities given by `weights`, then
+    the selected random variable is realized.
+
+    Parameters
+    ----------
+    components : sequence of `ContinuousDistribution`
+        The underlying instances of `ContinuousDistribution`.
+        All must have scalar shape parameters (if any); e.g., the `pdf` evaluated
+        at a scalar argument must return a scalar.
+    weights : sequence of floats, optional
+        The corresponding probabilities of selecting each random variable.
+        Must be non-negative and sum to one. The default behavior is to weight
+        all components equally.
+
+    Attributes
+    ----------
+    components : sequence of `ContinuousDistribution`
+        The underlying instances of `ContinuousDistribution`.
+    weights : ndarray
+        The corresponding probabilities of selecting each random variable.
+
+    Methods
+    -------
+    support
+
+    sample
+
+    moment
+
+    mean
+    median
+    mode
+
+    variance
+    standard_deviation
+
+    skewness
+    kurtosis
+
+    pdf
+    logpdf
+
+    cdf
+    icdf
+    ccdf
+    iccdf
+
+    logcdf
+    ilogcdf
+    logccdf
+    ilogccdf
+
+    entropy
+
+    Notes
+    -----
+    The following abbreviations are used throughout the documentation.
+
+    - PDF: probability density function
+    - CDF: cumulative distribution function
+    - CCDF: complementary CDF
+    - entropy: differential entropy
+    - log-*F*: logarithm of *F* (e.g. log-CDF)
+    - inverse *F*: inverse function of *F* (e.g. inverse CDF)
+
+    References
+    ----------
+    .. [1] Mixture distribution, *Wikipedia*,
+           https://en.wikipedia.org/wiki/Mixture_distribution
+
+
+    Examples
+    --------
+    A mixture of normal distributions:
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> import matplotlib.pyplot as plt
+    >>> X1 = stats.Normal(mu=-2, sigma=1)
+    >>> X2 = stats.Normal(mu=2, sigma=1)
+    >>> mixture = stats.Mixture([X1, X2], weights=[0.4, 0.6])
+    >>> print(f'mean: {mixture.mean():.2f}, '
+    ...       f'median: {mixture.median():.2f}, '
+    ...       f'mode: {mixture.mode():.2f}')
+    mean: 0.40, median: 1.04, mode: 2.00
+    >>> x = np.linspace(-10, 10, 300)
+    >>> plt.plot(x, mixture.pdf(x))
+    >>> plt.title('PDF of normal distribution mixture')
+    >>> plt.show()
+
+    """
+    # Todo:
+    # Add support for array shapes, weights
+
+    def _input_validation(self, components, weights):
+        if len(components) == 0:
+            message = ("`components` must contain at least one random variable.")
+            raise ValueError(message)
+
+        for var in components:
+            # will generalize to other kinds of distributions when there
+            # *are* other kinds of distributions
+            if not isinstance(var, ContinuousDistribution):
+                message = ("Each element of `components` must be an instance of "
+                           "`ContinuousDistribution`.")
+                raise ValueError(message)
+            if not var._shape == ():
+                message = "All elements of `components` must have scalar shapes."
+                raise ValueError(message)
+
+        if weights is None:
+            return components, weights
+
+        weights = np.asarray(weights)
+        if weights.shape != (len(components),):
+            message = "`components` and `weights` must have the same length."
+            raise ValueError(message)
+
+        if not np.issubdtype(weights.dtype, np.inexact):
+            message = "`weights` must have floating point dtype."
+            raise ValueError(message)
+
+        if not np.isclose(np.sum(weights), 1.0):
+            message = "`weights` must sum to 1.0."
+            raise ValueError(message)
+
+        if not np.all(weights >= 0):
+            message = "All `weights` must be non-negative."
+            raise ValueError(message)
+
+        return components, weights
+
+    def __init__(self, components, *, weights=None):
+        components, weights = self._input_validation(components, weights)
+        n = len(components)
+        dtype = np.result_type(*(var._dtype for var in components))
+        self._shape = np.broadcast_shapes(*(var._shape for var in components))
+        self._dtype, self._components = dtype, components
+        self._weights = np.full(n, 1/n, dtype=dtype) if weights is None else weights
+        self.validation_policy = None
+
+    @property
+    def components(self):
+        return list(self._components)
+
+    @property
+    def weights(self):
+        return self._weights.copy()
+
+    def _full(self, val, *args):
+        args = [np.asarray(arg) for arg in args]
+        dtype = np.result_type(self._dtype, *(arg.dtype for arg in args))
+        shape = np.broadcast_shapes(self._shape, *(arg.shape for arg in args))
+        return np.full(shape, val, dtype=dtype)
+
+    def _sum(self, fun, *args):
+        out = self._full(0, *args)
+        for var, weight in zip(self._components, self._weights):
+            out += getattr(var, fun)(*args) * weight
+        return out[()]
+
+    def _logsum(self, fun, *args):
+        out = self._full(-np.inf, *args)
+        for var, log_weight in zip(self._components, np.log(self._weights)):
+            np.logaddexp(out, getattr(var, fun)(*args) + log_weight, out=out)
+        return out[()]
+
+    def support(self):
+        a = self._full(np.inf)
+        b = self._full(-np.inf)
+        for var in self._components:
+            a = np.minimum(a, var.support()[0])
+            b = np.maximum(b, var.support()[1])
+        return a, b
+
+    def _raise_if_method(self, method):
+        if method is not None:
+            raise NotImplementedError("`method` not implemented for this distribution.")
+
+    def logentropy(self, *, method=None):
+        self._raise_if_method(method)
+        def log_integrand(x):
+            # `x` passed by `_tanhsinh` will be of complex dtype because
+            # `log_integrand` returns complex values, but the imaginary
+            # component is always zero. Extract the real part because
+            # `logpdf` uses `logaddexp`, which fails for complex input.
+            return self.logpdf(x.real) + np.log(self.logpdf(x.real) + 0j)
+
+        res = _tanhsinh(log_integrand, *self.support(), log=True).integral
+        return _log_real_standardize(res + np.pi*1j)
+
+    def entropy(self, *, method=None):
+        self._raise_if_method(method)
+        return _tanhsinh(lambda x: -self.pdf(x) * self.logpdf(x),
+                         *self.support()).integral
+
+    def mode(self, *, method=None):
+        self._raise_if_method(method)
+        a, b = self.support()
+        def f(x): return -self.pdf(x)
+        res = elementwise.bracket_minimum(f, 1., xmin=a, xmax=b)
+        res = elementwise.find_minimum(f, res.bracket)
+        return res.x
+
+    def median(self, *, method=None):
+        self._raise_if_method(method)
+        return self.icdf(0.5)
+
+    def mean(self, *, method=None):
+        self._raise_if_method(method)
+        return self._sum('mean')
+
+    def variance(self, *, method=None):
+        self._raise_if_method(method)
+        return self._moment_central(2)
+
+    def standard_deviation(self, *, method=None):
+        self._raise_if_method(method)
+        return self.variance()**0.5
+
+    def skewness(self, *, method=None):
+        self._raise_if_method(method)
+        return self._moment_standardized(3)
+
+    def kurtosis(self, *, method=None):
+        self._raise_if_method(method)
+        return self._moment_standardized(4)
+
+    def moment(self, order=1, kind='raw', *, method=None):
+        self._raise_if_method(method)
+        kinds = {'raw': self._moment_raw,
+                 'central': self._moment_central,
+                 'standardized': self._moment_standardized}
+        order = ContinuousDistribution._validate_order(self, order)
+        kind = ContinuousDistribution._validate_kind(self, kind, kinds)
+        moment_kind = kinds[kind]
+        return moment_kind(order)
+
+    def _moment_raw(self, order):
+        out = self._full(0)
+        for var, weight in zip(self._components, self._weights):
+            out += var.moment(order, kind='raw') * weight
+        return out[()]
+
+    def _moment_central(self, order):
+        order = int(order)
+        out = self._full(0)
+        for var, weight in zip(self._components, self._weights):
+            moment_as = [var.moment(order, kind='central')
+                         for order in range(order + 1)]
+            a, b = var.mean(), self.mean()
+            moment = var._moment_transform_center(order, moment_as, a, b)
+            out += moment * weight
+        return out[()]
+
+    def lmoment(self, order=1, *, standardize=True, method=None):
+        message = "L-moments are not currently available for mixture distributions."
+        raise NotImplementedError(message)
+
+    def _moment_standardized(self, order):
+        return self._moment_central(order) / self.standard_deviation()**order
+
+    def pdf(self, x, /, *, method=None):
+        self._raise_if_method(method)
+        return self._sum('pdf', x)
+
+    def logpdf(self, x, /, *, method=None):
+        self._raise_if_method(method)
+        return self._logsum('logpdf', x)
+
+    def pmf(self, x, /, *, method=None):
+        self._raise_if_method(method)
+        return self._sum('pmf', x)
+
+    def logpmf(self, x, /, *, method=None):
+        self._raise_if_method(method)
+        return self._logsum('logpmf', x)
+
+    def cdf(self, x, y=None, /, *, method=None):
+        self._raise_if_method(method)
+        args = (x,) if y is None else (x, y)
+        return self._sum('cdf', *args)
+
+    def logcdf(self, x, y=None, /, *, method=None):
+        self._raise_if_method(method)
+        args = (x,) if y is None else (x, y)
+        return self._logsum('logcdf', *args)
+
+    def ccdf(self, x, y=None, /, *, method=None):
+        self._raise_if_method(method)
+        args = (x,) if y is None else (x, y)
+        return self._sum('ccdf', *args)
+
+    def logccdf(self, x, y=None, /, *, method=None):
+        self._raise_if_method(method)
+        args = (x,) if y is None else (x, y)
+        return self._logsum('logccdf', *args)
+
+    def _invert(self, fun, p):
+        xmin, xmax = self.support()
+        fun = getattr(self, fun)
+        f = lambda x, p: fun(x) - p  # noqa: E731 is silly
+        xl0, xr0 = _guess_bracket(xmin, xmax)
+        res = elementwise.bracket_root(f, xl0=xl0, xr0=xr0,
+                                       xmin=xmin, xmax=xmax, args=(p,))
+        return elementwise.find_root(f, res.bracket, args=(p,)).x
+
+    def icdf(self, p, /, *, method=None):
+        self._raise_if_method(method)
+        return self._invert('cdf', p)
+
+    def iccdf(self, p, /, *, method=None):
+        self._raise_if_method(method)
+        return self._invert('ccdf', p)
+
+    def ilogcdf(self, p, /, *, method=None):
+        self._raise_if_method(method)
+        return self._invert('logcdf', p)
+
+    def ilogccdf(self, p, /, *, method=None):
+        self._raise_if_method(method)
+        return self._invert('logccdf', p)
+
+    def sample(self, shape=(), *, rng=None, method=None):
+        self._raise_if_method(method)
+        rng = np.random.default_rng(rng)
+        size = np.prod(np.atleast_1d(shape))
+        ns = rng.multinomial(size, self._weights)
+        x = [var.sample(shape=n, rng=rng) for n, var in zip(ns, self._components)]
+        x = np.reshape(rng.permuted(np.concatenate(x)), shape)
+        return x[()]
+
+    def __repr__(self):
+        result = "Mixture(\n"
+        result += "    [\n"
+        with np.printoptions(threshold=10):
+            for component in self.components:
+                result += f"        {repr(component)},\n"
+            result += "    ],\n"
+            result += f"    weights={repr(self.weights)},\n"
+        result += ")"
+        return result
+
+    def __str__(self):
+        result = "Mixture(\n"
+        result += "    [\n"
+        with np.printoptions(threshold=10):
+            for component in self.components:
+                result += f"        {str(component)},\n"
+            result += "    ],\n"
+            result += f"    weights={str(self.weights)},\n"
+        result += ")"
+        return result
+
+
+class MonotonicTransformedDistribution(TransformedDistribution):
+    r"""Distribution underlying a strictly monotonic function of a random variable
+
+    Given a random variable :math:`X`; a strictly monotonic function
+    :math:`g(u)`, its inverse :math:`h(u) = g^{-1}(u)`, and the derivative magnitude
+    :math: `|h'(u)| = \left| \frac{dh(u)}{du} \right|`, define the distribution
+    underlying the random variable :math:`Y = g(X)`.
+
+    Parameters
+    ----------
+    X : `ContinuousDistribution`
+        The random variable :math:`X`.
+    g, h, dh : callable
+        Elementwise functions representing the mathematical functions
+        :math:`g(u)`, :math:`h(u)`, and :math:`|h'(u)|`
+    logdh : callable, optional
+        Elementwise function representing :math:`\log(h'(u))`.
+        The default is ``lambda u: np.log(dh(u))``, but providing
+        a custom implementation may avoid over/underflow.
+    increasing : bool, optional
+        Whether the function is strictly increasing (True, default)
+        or strictly decreasing (False).
+    repr_pattern : str, optional
+        A string pattern for determining the __repr__. The __repr__
+        for X will be substituted into the position where `***` appears.
+        For example:
+            ``"exp(***)"`` for the repr of an exponentially transformed
+            distribution
+        The default is ``f"{g.__name__}(***)"``.
+    str_pattern : str, optional
+        A string pattern for determining `__str__`. The `__str__`
+        for X will be substituted into the position where `***` appears.
+        For example:
+            ``"exp(***)"`` for the repr of an exponentially transformed
+            distribution
+        The default is the value `repr_pattern` takes.
+    """
+
+    def __init__(self, X, /, *args, g, h, dh, logdh=None,
+                 increasing=True, repr_pattern=None,
+                 str_pattern=None, **kwargs):
+        super().__init__(X, *args, **kwargs)
+        self._g = g
+        self._h = h
+        self._dh = dh
+        self._logdh = (logdh if logdh is not None
+                       else lambda u: np.log(dh(u)))
+        if increasing:
+            self._xdf = self._dist._cdf_dispatch
+            self._cxdf = self._dist._ccdf_dispatch
+            self._ixdf = self._dist._icdf_dispatch
+            self._icxdf = self._dist._iccdf_dispatch
+            self._logxdf = self._dist._logcdf_dispatch
+            self._logcxdf = self._dist._logccdf_dispatch
+            self._ilogxdf = self._dist._ilogcdf_dispatch
+            self._ilogcxdf = self._dist._ilogccdf_dispatch
+        else:
+            self._xdf = self._dist._ccdf_dispatch
+            self._cxdf = self._dist._cdf_dispatch
+            self._ixdf = self._dist._iccdf_dispatch
+            self._icxdf = self._dist._icdf_dispatch
+            self._logxdf = self._dist._logccdf_dispatch
+            self._logcxdf = self._dist._logcdf_dispatch
+            self._ilogxdf = self._dist._ilogccdf_dispatch
+            self._ilogcxdf = self._dist._ilogcdf_dispatch
+        self._increasing = increasing
+        self._repr_pattern = repr_pattern or f"{g.__name__}(***)"
+        self._str_pattern = str_pattern or self._repr_pattern
+
+    def __repr__(self):
+        with np.printoptions(threshold=10):
+            return self._repr_pattern.replace("***", repr(self._dist))
+
+    def __str__(self):
+        with np.printoptions(threshold=10):
+            return self._str_pattern.replace("***", str(self._dist))
+
+    def _overrides(self, method_name):
+        # Do not use the generic overrides of TransformedDistribution
+        return False
+
+    def _support(self, **params):
+        a, b = self._dist._support(**params)
+        # For reciprocal transformation, we want this zero to become -inf
+        b = np.where(b==0, np.asarray("-0", dtype=b.dtype), b)
+        with np.errstate(divide='ignore'):
+            if self._increasing:
+                return self._g(a), self._g(b)
+            else:
+                return self._g(b), self._g(a)
+
+    def _logpdf_dispatch(self, x, *args, **params):
+        return self._dist._logpdf_dispatch(self._h(x), *args, **params) + self._logdh(x)
+
+    def _pdf_dispatch(self, x, *args, **params):
+        return self._dist._pdf_dispatch(self._h(x), *args, **params) * self._dh(x)
+
+    def _logcdf_dispatch(self, x, *args, **params):
+        return self._logxdf(self._h(x), *args, **params)
+
+    def _cdf_dispatch(self, x, *args, **params):
+        return self._xdf(self._h(x), *args, **params)
+
+    def _logccdf_dispatch(self, x, *args, **params):
+        return self._logcxdf(self._h(x), *args, **params)
+
+    def _ccdf_dispatch(self, x, *args, **params):
+        return self._cxdf(self._h(x), *args, **params)
+
+    def _ilogcdf_dispatch(self, p, *args, **params):
+        return self._g(self._ilogxdf(p, *args, **params))
+
+    def _icdf_dispatch(self, p, *args, **params):
+        return self._g(self._ixdf(p, *args, **params))
+
+    def _ilogccdf_dispatch(self, p, *args, **params):
+        return self._g(self._ilogcxdf(p, *args, **params))
+
+    def _iccdf_dispatch(self, p, *args, **params):
+        return self._g(self._icxdf(p, *args, **params))
+
+    def _sample_dispatch(self, full_shape, *, method, rng, **params):
+        rvs = self._dist._sample_dispatch(full_shape, method=method, rng=rng, **params)
+        return self._g(rvs)
+
+
+class FoldedDistribution(TransformedDistribution):
+    r"""Distribution underlying the absolute value of a random variable
+
+    Given a random variable :math:`X`; define the distribution
+    underlying the random variable :math:`Y = |X|`.
+
+    Parameters
+    ----------
+    X : `ContinuousDistribution`
+        The random variable :math:`X`.
+
+    Returns
+    -------
+    Y : `ContinuousDistribution`
+        The random variable :math:`Y = |X|`
+
+    """
+    # Many enhancements are possible if distribution is symmetric. Start
+    # with the general case; enhance later.
+
+    def __init__(self, X, /, *args, **kwargs):
+        super().__init__(X, *args, **kwargs)
+        # I think we need to allow `_support` to define whether the endpoints
+        # are inclusive or not. In the meantime, it's best to ensure that the lower
+        # endpoint (typically 0 for folded distribution) is inclusive so PDF evaluates
+        # correctly at that point.
+        self._variable.domain.inclusive = (True, self._variable.domain.inclusive[1])
+
+    def _overrides(self, method_name):
+        # Do not use the generic overrides of TransformedDistribution
+        return False
+
+    def _support(self, **params):
+        a, b = self._dist._support(**params)
+        a_, b_ = np.abs(a), np.abs(b)
+        a_, b_ = np.minimum(a_, b_), np.maximum(a_, b_)
+        i = (a < 0) & (b > 0)
+        a_ = np.asarray(a_)
+        a_[i] = 0
+        return a_[()], b_[()]
+
+    def _logpdf_dispatch(self, x, *args, method=None, **params):
+        x = np.abs(x)
+        right = self._dist._logpdf_dispatch(x, *args, method=method, **params)
+        left = self._dist._logpdf_dispatch(-x, *args, method=method, **params)
+        left = np.asarray(left)
+        right = np.asarray(right)
+        a, b = self._dist._support(**params)
+        left[-x < a] = -np.inf
+        right[x > b] = -np.inf
+        logpdfs = np.stack([left, right])
+        return special.logsumexp(logpdfs, axis=0)
+
+    def _pdf_dispatch(self, x, *args, method=None, **params):
+        x = np.abs(x)
+        right = self._dist._pdf_dispatch(x, *args, method=method, **params)
+        left = self._dist._pdf_dispatch(-x, *args, method=method, **params)
+        left = np.asarray(left)
+        right = np.asarray(right)
+        a, b = self._dist._support(**params)
+        left[-x < a] = 0
+        right[x > b] = 0
+        return left + right
+
+    def _logcdf_dispatch(self, x, *args, method=None, **params):
+        x = np.abs(x)
+        a, b = self._dist._support(**params)
+        xl = np.maximum(-x, a)
+        xr = np.minimum(x, b)
+        return self._dist._logcdf2_dispatch(xl, xr, *args, method=method, **params).real
+
+    def _cdf_dispatch(self, x, *args, method=None, **params):
+        x = np.abs(x)
+        a, b = self._dist._support(**params)
+        xl = np.maximum(-x, a)
+        xr = np.minimum(x, b)
+        return self._dist._cdf2_dispatch(xl, xr, *args, **params)
+
+    def _logccdf_dispatch(self, x, *args, method=None, **params):
+        x = np.abs(x)
+        a, b = self._dist._support(**params)
+        xl = np.maximum(-x, a)
+        xr = np.minimum(x, b)
+        return self._dist._logccdf2_dispatch(xl, xr, *args, method=method,
+                                             **params).real
+
+    def _ccdf_dispatch(self, x, *args, method=None, **params):
+        x = np.abs(x)
+        a, b = self._dist._support(**params)
+        xl = np.maximum(-x, a)
+        xr = np.minimum(x, b)
+        return self._dist._ccdf2_dispatch(xl, xr, *args, method=method, **params)
+
+    def _sample_dispatch(self, full_shape, *, method, rng, **params):
+        rvs = self._dist._sample_dispatch(full_shape, method=method, rng=rng, **params)
+        return np.abs(rvs)
+
+    def __repr__(self):
+        with np.printoptions(threshold=10):
+            return f"abs({repr(self._dist)})"
+
+    def __str__(self):
+        with np.printoptions(threshold=10):
+            return f"abs({str(self._dist)})"
+
+
+@xp_capabilities(np_only=True)
+def abs(X, /):
+    r"""Absolute value of a random variable.
+
+    Parameters
+    ----------
+    X : `ContinuousDistribution`
+        The random variable :math:`X`.
+
+    Returns
+    -------
+    Y : `ContinuousDistribution`
+        A random variable :math:`Y = |X|`.
+
+    Examples
+    --------
+    Suppose we have a normally distributed random variable :math:`X`:
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> X = stats.Normal()
+
+    We wish to have a random variable :math:`Y` distributed according to
+    the folded normal distribution; that is, a random variable :math:`|X|`.
+
+    >>> Y = stats.abs(X)
+
+    The PDF of the distribution in the left half plane is "folded" over to
+    the right half plane. Because the normal PDF is symmetric, the resulting
+    PDF is zero for negative arguments and doubled for positive arguments.
+
+    >>> import matplotlib.pyplot as plt
+    >>> x = np.linspace(0, 5, 300)
+    >>> ax = plt.gca()
+    >>> Y.plot(x='x', y='pdf', t=('x', -1, 5), ax=ax)
+    >>> plt.plot(x, 2 * X.pdf(x), '--')
+    >>> plt.legend(('PDF of `Y`', 'Doubled PDF of `X`'))
+    >>> plt.show()
+
+    """
+    return FoldedDistribution(X)
+
+
+@xp_capabilities(np_only=True)
+def exp(X, /):
+    r"""Natural exponential of a random variable.
+
+    Parameters
+    ----------
+    X : `ContinuousDistribution`
+        The random variable :math:`X`.
+
+    Returns
+    -------
+    Y : `ContinuousDistribution`
+        A random variable :math:`Y = \exp(X)`.
+
+    Examples
+    --------
+    Suppose we have a normally distributed random variable :math:`X`:
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> X = stats.Normal()
+
+    We wish to have a lognormally distributed random variable :math:`Y`,
+    a random variable whose natural logarithm is :math:`X`.
+    If :math:`X` is to be the natural logarithm of :math:`Y`, then we
+    must take :math:`Y` to be the natural exponential of :math:`X`.
+
+    >>> Y = stats.exp(X)
+
+    To demonstrate that ``X`` represents the logarithm of ``Y``,
+    we plot a normalized histogram of the logarithm of observations of
+    ``Y`` against the PDF underlying ``X``.
+
+    >>> import matplotlib.pyplot as plt
+    >>> rng = np.random.default_rng(435383595582522)
+    >>> y = Y.sample(shape=10000, rng=rng)
+    >>> ax = plt.gca()
+    >>> ax.hist(np.log(y), bins=50, density=True)
+    >>> X.plot(ax=ax)
+    >>> plt.legend(('PDF of `X`', 'histogram of `log(y)`'))
+    >>> plt.show()
+
+    """
+    return MonotonicTransformedDistribution(X, g=np.exp, h=np.log, dh=lambda u: 1 / u,
+                                            logdh=lambda u: -np.log(u))
+
+
+@xp_capabilities(np_only=True)
+def log(X, /):
+    r"""Natural logarithm of a non-negative random variable.
+
+    Parameters
+    ----------
+    X : `ContinuousDistribution`
+        The random variable :math:`X` with positive support.
+
+    Returns
+    -------
+    Y : `ContinuousDistribution`
+        A random variable :math:`Y = \log(X)`.
+
+    Examples
+    --------
+    Suppose we have a gamma distributed random variable :math:`X`:
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> Gamma = stats.make_distribution(stats.gamma)
+    >>> X = Gamma(a=1.0)
+
+    We wish to have an exp-gamma distributed random variable :math:`Y`,
+    a random variable whose natural exponential is :math:`X`.
+    If :math:`X` is to be the natural exponential of :math:`Y`, then we
+    must take :math:`Y` to be the natural logarithm of :math:`X`.
+
+    >>> Y = stats.log(X)
+
+    To demonstrate that ``X`` represents the exponential of ``Y``,
+    we plot a normalized histogram of the exponential of observations of
+    ``Y`` against the PDF underlying ``X``.
+
+    >>> import matplotlib.pyplot as plt
+    >>> rng = np.random.default_rng(435383595582522)
+    >>> y = Y.sample(shape=10000, rng=rng)
+    >>> ax = plt.gca()
+    >>> ax.hist(np.exp(y), bins=50, density=True)
+    >>> X.plot(ax=ax)
+    >>> plt.legend(('PDF of `X`', 'histogram of `exp(y)`'))
+    >>> plt.show()
+
+    """
+    if np.any(X.support()[0] < 0):
+        message = ("The logarithm of a random variable is only implemented when the "
+                   "support is non-negative.")
+        raise NotImplementedError(message)
+    return MonotonicTransformedDistribution(X, g=np.log, h=np.exp, dh=np.exp,
+                                            logdh=lambda u: u)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_entropy.py b/venv/lib/python3.12/site-packages/scipy/stats/_entropy.py
new file mode 100644
index 0000000000000000000000000000000000000000..ab5a874cf4aeaa0bb12e63292cd3f5122658f509
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_entropy.py
@@ -0,0 +1,431 @@
+"""
+Created on Fri Apr  2 09:06:05 2021
+
+@author: matth
+"""
+
+import math
+import numpy as np
+from scipy import special
+from ._axis_nan_policy import _axis_nan_policy_factory
+from scipy._lib._array_api import (array_namespace, xp_promote, xp_device,
+                                   _masked_apply, _share_masks, xp_capabilities)
+
+__all__ = ['entropy', 'differential_entropy']
+
+
+@xp_capabilities(marray=True)
+@_axis_nan_policy_factory(
+    lambda x: x,
+    n_samples=lambda kwgs: (
+        2 if ("qk" in kwgs and kwgs["qk"] is not None)
+        else 1
+    ),
+    n_outputs=1, result_to_tuple=lambda x, _: (x,), paired=True,
+    too_small=-1  # entropy doesn't have too small inputs
+)
+def entropy(pk: np.typing.ArrayLike,
+            qk: np.typing.ArrayLike | None = None,
+            base: float | None = None,
+            axis: int = 0
+            ) -> np.number | np.ndarray:
+    """
+    Calculate the Shannon entropy/relative entropy of given distribution(s).
+
+    If only probabilities `pk` are given, the Shannon entropy is calculated as
+    ``H = -sum(pk * log(pk))``.
+
+    If `qk` is not None, then compute the relative entropy
+    ``D = sum(pk * log(pk / qk))``. This quantity is also known
+    as the Kullback-Leibler divergence.
+
+    This routine will normalize `pk` and `qk` if they don't sum to 1.
+
+    Parameters
+    ----------
+    pk : array_like
+        Defines the (discrete) distribution. Along each axis-slice of ``pk``,
+        element ``i`` is the  (possibly unnormalized) probability of event
+        ``i``.
+    qk : array_like, optional
+        Sequence against which the relative entropy is computed. Should be in
+        the same format as `pk`.
+    base : float, optional
+        The logarithmic base to use, defaults to ``e`` (natural logarithm).
+    axis : int, optional
+        The axis along which the entropy is calculated. Default is 0.
+
+    Returns
+    -------
+    S : {float, array_like}
+        The calculated entropy.
+
+    Notes
+    -----
+    Informally, the Shannon entropy quantifies the expected uncertainty
+    inherent in the possible outcomes of a discrete random variable.
+    For example,
+    if messages consisting of sequences of symbols from a set are to be
+    encoded and transmitted over a noiseless channel, then the Shannon entropy
+    ``H(pk)`` gives a tight lower bound for the average number of units of
+    information needed per symbol if the symbols occur with frequencies
+    governed by the discrete distribution `pk` [1]_. The choice of base
+    determines the choice of units; e.g., ``e`` for nats, ``2`` for bits, etc.
+
+    The relative entropy, ``D(pk|qk)``, quantifies the increase in the average
+    number of units of information needed per symbol if the encoding is
+    optimized for the probability distribution `qk` instead of the true
+    distribution `pk`. Informally, the relative entropy quantifies the expected
+    excess in surprise experienced if one believes the true distribution is
+    `qk` when it is actually `pk`.
+
+    A related quantity, the cross entropy ``CE(pk, qk)``, satisfies the
+    equation ``CE(pk, qk) = H(pk) + D(pk|qk)`` and can also be calculated with
+    the formula ``CE = -sum(pk * log(qk))``. It gives the average
+    number of units of information needed per symbol if an encoding is
+    optimized for the probability distribution `qk` when the true distribution
+    is `pk`. It is not computed directly by `entropy`, but it can be computed
+    using two calls to the function (see Examples).
+
+    See [2]_ for more information.
+
+    References
+    ----------
+    .. [1] Shannon, C.E. (1948), A Mathematical Theory of Communication.
+           Bell System Technical Journal, 27: 379-423.
+           :doi:`10.1002/j.1538-7305.1948.tb01338.x`.
+    .. [2] Thomas M. Cover and Joy A. Thomas. 2006. Elements of Information
+           Theory (Wiley Series in Telecommunications and Signal Processing).
+           Wiley-Interscience, USA.
+
+
+    Examples
+    --------
+    The outcome of a fair coin is the most uncertain:
+
+    >>> import numpy as np
+    >>> from scipy.stats import entropy
+    >>> base = 2  # work in units of bits
+    >>> pk = np.array([1/2, 1/2])  # fair coin
+    >>> H = entropy(pk, base=base)
+    >>> H
+    1.0
+    >>> H == -np.sum(pk * np.log(pk)) / np.log(base)
+    True
+
+    The outcome of a biased coin is less uncertain:
+
+    >>> qk = np.array([9/10, 1/10])  # biased coin
+    >>> entropy(qk, base=base)
+    0.46899559358928117
+
+    The relative entropy between the fair coin and biased coin is calculated
+    as:
+
+    >>> D = entropy(pk, qk, base=base)
+    >>> D
+    0.7369655941662062
+    >>> np.isclose(D, np.sum(pk * np.log(pk/qk)) / np.log(base), rtol=4e-16, atol=0)
+    True
+
+    The cross entropy can be calculated as the sum of the entropy and
+    relative entropy`:
+
+    >>> CE = entropy(pk, base=base) + entropy(pk, qk, base=base)
+    >>> CE
+    1.736965594166206
+    >>> CE == -np.sum(pk * np.log(qk)) / np.log(base)
+    True
+
+    """
+    if base is not None and base <= 0:
+        raise ValueError("`base` must be a positive number or `None`.")
+
+    xp = array_namespace(pk, qk)
+    pk, qk = xp_promote(pk, qk, broadcast=True, xp=xp)
+
+    with np.errstate(invalid='ignore'):
+        if qk is not None:
+            pk, qk = _share_masks(pk, qk, xp=xp)
+            qk = qk / xp.sum(qk, axis=axis, keepdims=True)
+        pk = pk / xp.sum(pk, axis=axis, keepdims=True)
+
+    if qk is None:
+        vec = special.entr(pk)
+    else:
+        vec = _masked_apply(special.rel_entr, args=(pk, qk), xp=xp)
+
+    S = xp.sum(vec, axis=axis)
+    if base is not None:
+        S /= math.log(base)
+    return S
+
+
+def _differential_entropy_is_too_small(samples, kwargs, axis=-1):
+    values = samples[0]
+    n = values.shape[axis]
+    window_length = kwargs.get("window_length")
+    if window_length is None:
+        window_length = math.floor(math.sqrt(n) + 0.5)
+    if not 2 <= 2 * window_length < n:
+        return True
+    return False
+
+
+@xp_capabilities()
+@_axis_nan_policy_factory(
+    lambda x: x, n_outputs=1, result_to_tuple=lambda x, _: (x,),
+    too_small=_differential_entropy_is_too_small
+)
+def differential_entropy(
+    values: np.typing.ArrayLike,
+    *,
+    window_length: int | None = None,
+    base: float | None = None,
+    axis: int = 0,
+    method: str = "auto",
+) -> np.number | np.ndarray:
+    r"""Given a sample of a distribution, estimate the differential entropy.
+
+    Several estimation methods are available using the `method` parameter. By
+    default, a method is selected based the size of the sample.
+
+    Parameters
+    ----------
+    values : sequence
+        Sample from a continuous distribution.
+    window_length : int, optional
+        Window length for computing Vasicek estimate. Must be an integer
+        between 1 and half of the sample size. If ``None`` (the default), it
+        uses the heuristic value
+
+        .. math::
+            \left \lfloor \sqrt{n} + 0.5 \right \rfloor
+
+        where :math:`n` is the sample size. This heuristic was originally
+        proposed in [2]_ and has become common in the literature.
+    base : float, optional
+        The logarithmic base to use, defaults to ``e`` (natural logarithm).
+    axis : int, optional
+        The axis along which the differential entropy is calculated.
+        Default is 0.
+    method : {'vasicek', 'van es', 'ebrahimi', 'correa', 'auto'}, optional
+        The method used to estimate the differential entropy from the sample.
+        Default is ``'auto'``.  See Notes for more information.
+
+    Returns
+    -------
+    entropy : float
+        The calculated differential entropy.
+
+    Notes
+    -----
+    This function will converge to the true differential entropy in the limit
+
+    .. math::
+        n \to \infty, \quad m \to \infty, \quad \frac{m}{n} \to 0
+
+    The optimal choice of ``window_length`` for a given sample size depends on
+    the (unknown) distribution. Typically, the smoother the density of the
+    distribution, the larger the optimal value of ``window_length`` [1]_.
+
+    The following options are available for the `method` parameter.
+
+    * ``'vasicek'`` uses the estimator presented in [1]_. This is
+      one of the first and most influential estimators of differential entropy.
+    * ``'van es'`` uses the bias-corrected estimator presented in [3]_, which
+      is not only consistent but, under some conditions, asymptotically normal.
+    * ``'ebrahimi'`` uses an estimator presented in [4]_, which was shown
+      in simulation to have smaller bias and mean squared error than
+      the Vasicek estimator.
+    * ``'correa'`` uses the estimator presented in [5]_ based on local linear
+      regression. In a simulation study, it had consistently smaller mean
+      square error than the Vasiceck estimator, but it is more expensive to
+      compute.
+    * ``'auto'`` selects the method automatically (default). Currently,
+      this selects ``'van es'`` for very small samples (<10), ``'ebrahimi'``
+      for moderate sample sizes (11-1000), and ``'vasicek'`` for larger
+      samples, but this behavior is subject to change in future versions.
+
+    All estimators are implemented as described in [6]_.
+
+    References
+    ----------
+    .. [1] Vasicek, O. (1976). A test for normality based on sample entropy.
+           Journal of the Royal Statistical Society:
+           Series B (Methodological), 38(1), 54-59.
+    .. [2] Crzcgorzewski, P., & Wirczorkowski, R. (1999). Entropy-based
+           goodness-of-fit test for exponentiality. Communications in
+           Statistics-Theory and Methods, 28(5), 1183-1202.
+    .. [3] Van Es, B. (1992). Estimating functionals related to a density by a
+           class of statistics based on spacings. Scandinavian Journal of
+           Statistics, 61-72.
+    .. [4] Ebrahimi, N., Pflughoeft, K., & Soofi, E. S. (1994). Two measures
+           of sample entropy. Statistics & Probability Letters, 20(3), 225-234.
+    .. [5] Correa, J. C. (1995). A new estimator of entropy. Communications
+           in Statistics-Theory and Methods, 24(10), 2439-2449.
+    .. [6] Noughabi, H. A. (2015). Entropy Estimation Using Numerical Methods.
+           Annals of Data Science, 2(2), 231-241.
+           https://link.springer.com/article/10.1007/s40745-015-0045-9
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import differential_entropy, norm
+
+    Entropy of a standard normal distribution:
+
+    >>> rng = np.random.default_rng()
+    >>> values = rng.standard_normal(100)
+    >>> differential_entropy(values)
+    1.3407817436640392
+
+    Compare with the true entropy:
+
+    >>> float(norm.entropy())
+    1.4189385332046727
+
+    For several sample sizes between 5 and 1000, compare the accuracy of
+    the ``'vasicek'``, ``'van es'``, and ``'ebrahimi'`` methods. Specifically,
+    compare the root mean squared error (over 1000 trials) between the estimate
+    and the true differential entropy of the distribution.
+
+    >>> from scipy import stats
+    >>> import matplotlib.pyplot as plt
+    >>>
+    >>>
+    >>> def rmse(res, expected):
+    ...     '''Root mean squared error'''
+    ...     return np.sqrt(np.mean((res - expected)**2))
+    >>>
+    >>>
+    >>> a, b = np.log10(5), np.log10(1000)
+    >>> ns = np.round(np.logspace(a, b, 10)).astype(int)
+    >>> reps = 1000  # number of repetitions for each sample size
+    >>> expected = stats.expon.entropy()
+    >>>
+    >>> method_errors = {'vasicek': [], 'van es': [], 'ebrahimi': []}
+    >>> for method in method_errors:
+    ...     for n in ns:
+    ...        rvs = stats.expon.rvs(size=(reps, n), random_state=rng)
+    ...        res = stats.differential_entropy(rvs, method=method, axis=-1)
+    ...        error = rmse(res, expected)
+    ...        method_errors[method].append(error)
+    >>>
+    >>> for method, errors in method_errors.items():
+    ...     plt.loglog(ns, errors, label=method)
+    >>>
+    >>> plt.legend()
+    >>> plt.xlabel('sample size')
+    >>> plt.ylabel('RMSE (1000 trials)')
+    >>> plt.title('Entropy Estimator Error (Exponential Distribution)')
+
+    """
+    xp = array_namespace(values)
+    values = xp_promote(values, force_floating=True, xp=xp)
+    values = xp.moveaxis(values, axis, -1)
+    n = values.shape[-1]  # type: ignore[union-attr]
+
+    if window_length is None:
+        window_length = math.floor(math.sqrt(n) + 0.5)
+
+    if not 2 <= 2 * window_length < n:
+        raise ValueError(
+            f"Window length ({window_length}) must be positive and less "
+            f"than half the sample size ({n}).",
+        )
+
+    if base is not None and base <= 0:
+        raise ValueError("`base` must be a positive number or `None`.")
+
+    sorted_data = xp.sort(values, axis=-1)
+
+    methods = {"vasicek": _vasicek_entropy,
+               "van es": _van_es_entropy,
+               "correa": _correa_entropy,
+               "ebrahimi": _ebrahimi_entropy,
+               "auto": _vasicek_entropy}
+    method = method.lower()
+    if method not in methods:
+        message = f"`method` must be one of {set(methods)}"
+        raise ValueError(message)
+
+    if method == "auto":
+        if n <= 10:
+            method = 'van es'
+        elif n <= 1000:
+            method = 'ebrahimi'
+        else:
+            method = 'vasicek'
+
+    res = methods[method](sorted_data, window_length, xp=xp)
+
+    if base is not None:
+        res /= math.log(base)
+
+    # avoid dtype changes due to data-apis/array-api-compat#152
+    # can be removed when data-apis/array-api-compat#152 is resolved
+    return xp.astype(res, values.dtype)  # type: ignore[union-attr]
+
+
+def _pad_along_last_axis(X, m, *, xp):
+    """Pad the data for computing the rolling window difference."""
+    # scales a  bit better than method in _vasicek_like_entropy
+    shape = X.shape[:-1] + (m,)
+    Xl = xp.broadcast_to(X[..., :1], shape)  # :1 vs 0 to maintain shape
+    Xr = xp.broadcast_to(X[..., -1:], shape)
+    return xp.concat((Xl, X, Xr), axis=-1)
+
+
+def _vasicek_entropy(X, m, *, xp):
+    """Compute the Vasicek estimator as described in [6] Eq. 1.3."""
+    n = X.shape[-1]
+    X = _pad_along_last_axis(X, m, xp=xp)
+    differences = X[..., 2 * m:] - X[..., : -2 * m:]
+    logs = xp.log(n/(2*m) * differences)
+    return xp.mean(logs, axis=-1)
+
+
+def _van_es_entropy(X, m, *, xp):
+    """Compute the van Es estimator as described in [6]."""
+    # No equation number, but referred to as HVE_mn.
+    # Typo: there should be a log within the summation.
+    n = X.shape[-1]
+    difference = X[..., m:] - X[..., :-m]
+    term1 = 1/(n-m) * xp.sum(xp.log((n+1)/m * difference), axis=-1)
+    k = xp.arange(m, n+1, dtype=term1.dtype, device=xp_device(X))
+    return term1 + xp.sum(1/k) + math.log(m) - math.log(n+1)
+
+
+def _ebrahimi_entropy(X, m, *, xp):
+    """Compute the Ebrahimi estimator as described in [6]."""
+    # No equation number, but referred to as HE_mn
+    n = X.shape[-1]
+    X = _pad_along_last_axis(X, m, xp=xp)
+
+    differences = X[..., 2 * m:] - X[..., : -2 * m:]
+
+    i = xp.arange(1, n+1, dtype=X.dtype, device=xp_device(X))
+    ci = xp.where(i <= m, 1 + (i - 1)/m, 2.)
+    ci = xp.where(i >= n - m + 1, 1 + (n - i)/m, ci)
+
+    logs = xp.log(n * differences / (ci * m))
+    return xp.mean(logs, axis=-1)
+
+
+def _correa_entropy(X, m, *, xp):
+    """Compute the Correa estimator as described in [6]."""
+    # No equation number, but referred to as HC_mn
+    n = X.shape[-1]
+    X = _pad_along_last_axis(X, m, xp=xp)
+
+    i = xp.arange(1, n+1, device=xp_device(X))
+    dj = xp.arange(-m, m+1, device=xp_device(X))[:, None]
+    j = i + dj
+    j0 = j + m - 1  # 0-indexed version of j
+
+    Xibar = xp.mean(X[..., j0], axis=-2, keepdims=True)
+    difference = X[..., j0] - Xibar
+    num = xp.sum(difference*dj, axis=-2)  # dj is d-i
+    den = n*xp.sum(difference**2, axis=-2)
+    return -xp.mean(xp.log(num/den), axis=-1)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_finite_differences.py b/venv/lib/python3.12/site-packages/scipy/stats/_finite_differences.py
new file mode 100644
index 0000000000000000000000000000000000000000..6ec91654c4e95f73f32edc5aa357a4e3f80fff1f
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_finite_differences.py
@@ -0,0 +1,145 @@
+from numpy import arange, newaxis, hstack, prod, array
+from scipy import linalg
+
+
+def _central_diff_weights(Np, ndiv=1):
+    """
+    Return weights for an Np-point central derivative.
+
+    Assumes equally-spaced function points.
+
+    If weights are in the vector w, then
+    derivative is w[0] * f(x-ho*dx) + ... + w[-1] * f(x+h0*dx)
+
+    Parameters
+    ----------
+    Np : int
+        Number of points for the central derivative.
+    ndiv : int, optional
+        Number of divisions. Default is 1.
+
+    Returns
+    -------
+    w : ndarray
+        Weights for an Np-point central derivative. Its size is `Np`.
+
+    Notes
+    -----
+    Can be inaccurate for a large number of points.
+
+    Examples
+    --------
+    We can calculate a derivative value of a function.
+
+    >>> def f(x):
+    ...     return 2 * x**2 + 3
+    >>> x = 3.0 # derivative point
+    >>> h = 0.1 # differential step
+    >>> Np = 3 # point number for central derivative
+    >>> weights = _central_diff_weights(Np) # weights for first derivative
+    >>> vals = [f(x + (i - Np/2) * h) for i in range(Np)]
+    >>> sum(w * v for (w, v) in zip(weights, vals))/h
+    11.79999999999998
+
+    This value is close to the analytical solution:
+    f'(x) = 4x, so f'(3) = 12
+
+    References
+    ----------
+    .. [1] https://en.wikipedia.org/wiki/Finite_difference
+
+    """
+    if Np < ndiv + 1:
+        raise ValueError(
+            "Number of points must be at least the derivative order + 1."
+        )
+    if Np % 2 == 0:
+        raise ValueError("The number of points must be odd.")
+
+    ho = Np >> 1
+    x = arange(-ho, ho + 1.0)
+    x = x[:, newaxis]
+    X = x**0.0
+    for k in range(1, Np):
+        X = hstack([X, x**k])
+    w = prod(arange(1, ndiv + 1), axis=0) * linalg.inv(X)[ndiv]
+    return w
+
+
+def _derivative(func, x0, dx=1.0, n=1, args=(), order=3):
+    """
+    Find the nth derivative of a function at a point.
+
+    Given a function, use a central difference formula with spacing `dx` to
+    compute the nth derivative at `x0`.
+
+    Parameters
+    ----------
+    func : function
+        Input function.
+    x0 : float
+        The point at which the nth derivative is found.
+    dx : float, optional
+        Spacing.
+    n : int, optional
+        Order of the derivative. Default is 1.
+    args : tuple, optional
+        Arguments
+    order : int, optional
+        Number of points to use, must be odd.
+
+    Notes
+    -----
+    Decreasing the step size too small can result in round-off error.
+
+    Examples
+    --------
+    >>> def f(x):
+    ...     return x**3 + x**2
+    >>> _derivative(f, 1.0, dx=1e-6)
+    4.9999999999217337
+
+    """
+    if order < n + 1:
+        raise ValueError(
+            "'order' (the number of points used to compute the derivative), "
+            "must be at least the derivative order 'n' + 1."
+        )
+    if order % 2 == 0:
+        raise ValueError(
+            "'order' (the number of points used to compute the derivative) "
+            "must be odd."
+        )
+    # pre-computed for n=1 and 2 and low-order for speed.
+    if n == 1:
+        if order == 3:
+            weights = array([-1, 0, 1]) / 2.0
+        elif order == 5:
+            weights = array([1, -8, 0, 8, -1]) / 12.0
+        elif order == 7:
+            weights = array([-1, 9, -45, 0, 45, -9, 1]) / 60.0
+        elif order == 9:
+            weights = array([3, -32, 168, -672, 0, 672, -168, 32, -3]) / 840.0
+        else:
+            weights = _central_diff_weights(order, 1)
+    elif n == 2:
+        if order == 3:
+            weights = array([1, -2.0, 1])
+        elif order == 5:
+            weights = array([-1, 16, -30, 16, -1]) / 12.0
+        elif order == 7:
+            weights = array([2, -27, 270, -490, 270, -27, 2]) / 180.0
+        elif order == 9:
+            weights = (
+                array([-9, 128, -1008, 8064, -14350, 8064, -1008, 128, -9])
+                / 5040.0
+            )
+        else:
+            weights = _central_diff_weights(order, 2)
+    else:
+        weights = _central_diff_weights(order, n)
+    val = 0.0
+    ho = order >> 1
+    for k in range(order):
+        val += weights[k] * func(x0 + (k - ho) * dx, *args)
+    return val / prod((dx,) * n, axis=0)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_fit.py b/venv/lib/python3.12/site-packages/scipy/stats/_fit.py
new file mode 100644
index 0000000000000000000000000000000000000000..a73e410753dcfc9992e31f9395bbe72e45077749
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_fit.py
@@ -0,0 +1,1349 @@
+import warnings
+from collections import namedtuple
+import numpy as np
+from scipy import optimize, stats
+from scipy._lib._array_api import xp_capabilities
+from scipy._lib._util import check_random_state, _transition_to_rng
+
+
+def _combine_bounds(name, user_bounds, shape_domain, integral):
+    """Intersection of user-defined bounds and distribution PDF/PMF domain"""
+
+    user_bounds = np.atleast_1d(user_bounds)
+
+    if user_bounds[0] > user_bounds[1]:
+        message = (f"There are no values for `{name}` on the interval "
+                   f"{list(user_bounds)}.")
+        raise ValueError(message)
+
+    bounds = (max(user_bounds[0], shape_domain[0]),
+              min(user_bounds[1], shape_domain[1]))
+
+    if integral and (np.ceil(bounds[0]) > np.floor(bounds[1])):
+        message = (f"There are no integer values for `{name}` on the interval "
+                   f"defined by the user-provided bounds and the domain "
+                   "of the distribution.")
+        raise ValueError(message)
+    elif not integral and (bounds[0] > bounds[1]):
+        message = (f"There are no values for `{name}` on the interval "
+                   f"defined by the user-provided bounds and the domain "
+                   "of the distribution.")
+        raise ValueError(message)
+
+    if not np.all(np.isfinite(bounds)):
+        message = (f"The intersection of user-provided bounds for `{name}` "
+                   f"and the domain of the distribution is not finite. Please "
+                   f"provide finite bounds for shape `{name}` in `bounds`.")
+        raise ValueError(message)
+
+    return bounds
+
+
+class FitResult:
+    r"""Result of fitting a discrete or continuous distribution to data
+
+    Attributes
+    ----------
+    params : namedtuple
+        A namedtuple containing the maximum likelihood estimates of the
+        shape parameters, location, and (if applicable) scale of the
+        distribution.
+    success : bool or None
+        Whether the optimizer considered the optimization to terminate
+        successfully or not.
+    message : str or None
+        Any status message provided by the optimizer.
+
+    """
+
+    def __init__(self, dist, data, discrete, res):
+        self._dist = dist
+        self._data = data
+        self.discrete = discrete
+        self.pxf = getattr(dist, "pmf", None) or getattr(dist, "pdf", None)
+
+        shape_names = [] if dist.shapes is None else dist.shapes.split(", ")
+        if not discrete:
+            FitParams = namedtuple('FitParams', shape_names + ['loc', 'scale'])
+        else:
+            FitParams = namedtuple('FitParams', shape_names + ['loc'])
+
+        self.params = FitParams(*res.x)
+
+        # Optimizer can report success even when nllf is infinite
+        if res.success and not np.isfinite(self.nllf()):
+            res.success = False
+            res.message = ("Optimization converged to parameter values that "
+                           "are inconsistent with the data.")
+        self.success = getattr(res, "success", None)
+        self.message = getattr(res, "message", None)
+
+    def __repr__(self):
+        keys = ["params", "success", "message"]
+        m = max(map(len, keys)) + 1
+        return '\n'.join([key.rjust(m) + ': ' + repr(getattr(self, key))
+                          for key in keys if getattr(self, key) is not None])
+
+    def nllf(self, params=None, data=None):
+        """Negative log-likelihood function
+
+        Evaluates the negative of the log-likelihood function of the provided
+        data at the provided parameters.
+
+        Parameters
+        ----------
+        params : tuple, optional
+            The shape parameters, location, and (if applicable) scale of the
+            distribution as a single tuple. Default is the maximum likelihood
+            estimates (``self.params``).
+        data : array_like, optional
+            The data for which the log-likelihood function is to be evaluated.
+            Default is the data to which the distribution was fit.
+
+        Returns
+        -------
+        nllf : float
+            The negative of the log-likelihood function.
+
+        """
+        params = params if params is not None else self.params
+        data = data if data is not None else self._data
+        return self._dist.nnlf(theta=params, x=data)
+
+    def plot(self, ax=None, *, plot_type="hist"):
+        """Visually compare the data against the fitted distribution.
+
+        Available only if `matplotlib` is installed.
+
+        Parameters
+        ----------
+        ax : `matplotlib.axes.Axes`
+            Axes object to draw the plot onto, otherwise uses the current Axes.
+        plot_type : {"hist", "qq", "pp", "cdf"}
+            Type of plot to draw. Options include:
+
+            - "hist": Superposes the PDF/PMF of the fitted distribution
+              over a normalized histogram of the data.
+            - "qq": Scatter plot of theoretical quantiles against the
+              empirical quantiles. Specifically, the x-coordinates are the
+              values of the fitted distribution PPF evaluated at the
+              percentiles ``(np.arange(1, n) - 0.5)/n``, where ``n`` is the
+              number of data points, and the y-coordinates are the sorted
+              data points.
+            - "pp": Scatter plot of theoretical percentiles against the
+              observed percentiles. Specifically, the x-coordinates are the
+              percentiles ``(np.arange(1, n) - 0.5)/n``, where ``n`` is
+              the number of data points, and the y-coordinates are the values
+              of the fitted distribution CDF evaluated at the sorted
+              data points.
+            - "cdf": Superposes the CDF of the fitted distribution over the
+              empirical CDF. Specifically, the x-coordinates of the empirical
+              CDF are the sorted data points, and the y-coordinates are the
+              percentiles ``(np.arange(1, n) - 0.5)/n``, where ``n`` is
+              the number of data points.
+
+        Returns
+        -------
+        ax : `matplotlib.axes.Axes`
+            The matplotlib Axes object on which the plot was drawn.
+
+        Examples
+        --------
+        >>> import numpy as np
+        >>> from scipy import stats
+        >>> import matplotlib.pyplot as plt  # matplotlib must be installed
+        >>> rng = np.random.default_rng()
+        >>> data = stats.nbinom(5, 0.5).rvs(size=1000, random_state=rng)
+        >>> bounds = [(0, 30), (0, 1)]
+        >>> res = stats.fit(stats.nbinom, data, bounds)
+        >>> ax = res.plot()  # save matplotlib Axes object
+
+        The `matplotlib.axes.Axes` object can be used to customize the plot.
+        See `matplotlib.axes.Axes` documentation for details.
+
+        >>> ax.set_xlabel('number of trials')  # customize axis label
+        >>> ax.get_children()[0].set_linewidth(5)  # customize line widths
+        >>> ax.legend()
+        >>> plt.show()
+        """
+        try:
+            import matplotlib  # noqa: F401
+        except ModuleNotFoundError as exc:
+            message = "matplotlib must be installed to use method `plot`."
+            raise ModuleNotFoundError(message) from exc
+
+        plots = {'histogram': self._hist_plot, 'qq': self._qq_plot,
+                 'pp': self._pp_plot, 'cdf': self._cdf_plot,
+                 'hist': self._hist_plot}
+        if plot_type.lower() not in plots:
+            message = f"`plot_type` must be one of {set(plots.keys())}"
+            raise ValueError(message)
+        plot = plots[plot_type.lower()]
+
+        if ax is None:
+            import matplotlib.pyplot as plt
+            ax = plt.gca()
+
+        fit_params = np.atleast_1d(self.params)
+
+        return plot(ax=ax, fit_params=fit_params)
+
+    def _hist_plot(self, ax, fit_params):
+        from matplotlib.ticker import MaxNLocator
+
+        support = self._dist.support(*fit_params)
+        lb = support[0] if np.isfinite(support[0]) else min(self._data)
+        ub = support[1] if np.isfinite(support[1]) else max(self._data)
+        pxf = "PMF" if self.discrete else "PDF"
+
+        if self.discrete:
+            x = np.arange(lb, ub + 2)
+            y = self.pxf(x, *fit_params)
+            ax.vlines(x[:-1], 0, y[:-1], label='Fitted Distribution PMF',
+                      color='C0')
+            options = dict(density=True, bins=x, align='left', color='C1')
+            ax.xaxis.set_major_locator(MaxNLocator(integer=True))
+            ax.set_xlabel('k')
+            ax.set_ylabel('PMF')
+        else:
+            x = np.linspace(lb, ub, 200)
+            y = self.pxf(x, *fit_params)
+            ax.plot(x, y, '--', label='Fitted Distribution PDF', color='C0')
+            options = dict(density=True, bins=50, align='mid', color='C1')
+            ax.set_xlabel('x')
+            ax.set_ylabel('PDF')
+
+        if len(self._data) > 50 or self.discrete:
+            ax.hist(self._data, label="Histogram of Data", **options)
+        else:
+            ax.plot(self._data, np.zeros_like(self._data), "*",
+                    label='Data', color='C1')
+
+        ax.set_title(rf"Fitted $\tt {self._dist.name}$ {pxf} and Histogram")
+        ax.legend(*ax.get_legend_handles_labels())
+        return ax
+
+    def _qp_plot(self, ax, fit_params, qq):
+        data = np.sort(self._data)
+        ps = self._plotting_positions(len(self._data))
+
+        if qq:
+            qp = "Quantiles"
+            plot_type = 'Q-Q'
+            x = self._dist.ppf(ps, *fit_params)
+            y = data
+        else:
+            qp = "Percentiles"
+            plot_type = 'P-P'
+            x = ps
+            y = self._dist.cdf(data, *fit_params)
+
+        ax.plot(x, y, '.', label=f'Fitted Distribution {plot_type}',
+                color='C0', zorder=1)
+        xlim = ax.get_xlim()
+        ylim = ax.get_ylim()
+        lim = [min(xlim[0], ylim[0]), max(xlim[1], ylim[1])]
+        if not qq:
+            lim = max(lim[0], 0), min(lim[1], 1)
+
+        if self.discrete and qq:
+            q_min, q_max = int(lim[0]), int(lim[1]+1)
+            q_ideal = np.arange(q_min, q_max)
+            # q_ideal = np.unique(self._dist.ppf(ps, *fit_params))
+            ax.plot(q_ideal, q_ideal, 'o', label='Reference', color='k',
+                    alpha=0.25, markerfacecolor='none', clip_on=True)
+        elif self.discrete and not qq:
+            # The intent of this is to match the plot that would be produced
+            # if x were continuous on [0, 1] and y were cdf(ppf(x)).
+            # It can be approximated by letting x = np.linspace(0, 1, 1000),
+            # but this might not look great when zooming in. The vertical
+            # portions are included to indicate where the transition occurs
+            # where the data completely obscures the horizontal portions.
+            p_min, p_max = lim
+            a, b = self._dist.support(*fit_params)
+            p_min = max(p_min, 0 if np.isfinite(a) else 1e-3)
+            p_max = min(p_max, 1 if np.isfinite(b) else 1-1e-3)
+            q_min, q_max = self._dist.ppf([p_min, p_max], *fit_params)
+            qs = np.arange(q_min-1, q_max+1)
+            ps = self._dist.cdf(qs, *fit_params)
+            ax.step(ps, ps, '-', label='Reference', color='k', alpha=0.25,
+                    clip_on=True)
+        else:
+            ax.plot(lim, lim, '-', label='Reference', color='k', alpha=0.25,
+                    clip_on=True)
+
+        ax.set_xlim(lim)
+        ax.set_ylim(lim)
+        ax.set_xlabel(rf"Fitted $\tt {self._dist.name}$ Theoretical {qp}")
+        ax.set_ylabel(f"Data {qp}")
+        ax.set_title(rf"Fitted $\tt {self._dist.name}$ {plot_type} Plot")
+        ax.legend(*ax.get_legend_handles_labels())
+        ax.set_aspect('equal')
+        return ax
+
+    def _qq_plot(self, **kwargs):
+        return self._qp_plot(qq=True, **kwargs)
+
+    def _pp_plot(self, **kwargs):
+        return self._qp_plot(qq=False, **kwargs)
+
+    def _plotting_positions(self, n, a=.5):
+        # See https://en.wikipedia.org/wiki/Q%E2%80%93Q_plot#Plotting_positions
+        k = np.arange(1, n+1)
+        return (k-a) / (n + 1 - 2*a)
+
+    def _cdf_plot(self, ax, fit_params):
+        data = np.sort(self._data)
+        ecdf = self._plotting_positions(len(self._data))
+        ls = '--' if len(np.unique(data)) < 30 else '.'
+        xlabel = 'k' if self.discrete else 'x'
+        ax.step(data, ecdf, ls, label='Empirical CDF', color='C1', zorder=0)
+
+        xlim = ax.get_xlim()
+        q = np.linspace(*xlim, 300)
+        tcdf = self._dist.cdf(q, *fit_params)
+
+        ax.plot(q, tcdf, label='Fitted Distribution CDF', color='C0', zorder=1)
+        ax.set_xlim(xlim)
+        ax.set_ylim(0, 1)
+        ax.set_xlabel(xlabel)
+        ax.set_ylabel("CDF")
+        ax.set_title(rf"Fitted $\tt {self._dist.name}$ and Empirical CDF")
+        handles, labels = ax.get_legend_handles_labels()
+        ax.legend(handles[::-1], labels[::-1])
+        return ax
+
+
+@xp_capabilities(out_of_scope=True)
+def fit(dist, data, bounds=None, *, guess=None, method='mle',
+        optimizer=optimize.differential_evolution):
+    r"""Fit a discrete or continuous distribution to data.
+
+    Given a distribution, data, and bounds on the parameters of the
+    distribution, return maximum likelihood estimates of the parameters.
+
+    Parameters
+    ----------
+    dist : `scipy.stats.rv_continuous` or `scipy.stats.rv_discrete`
+        The object representing the distribution to be fit to the data.
+    data : 1D array_like
+        The data to which the distribution is to be fit. If the data contain
+        any of ``np.nan``, ``np.inf``, or -``np.inf``, the fit method will
+        raise a ``ValueError``.
+    bounds : dict or sequence of tuples, optional
+        If a dictionary, each key is the name of a parameter of the
+        distribution, and the corresponding value is a tuple containing the
+        lower and upper bound on that parameter.  If the distribution is
+        defined only for a finite range of values of that parameter, no entry
+        for that parameter is required; e.g., some distributions have
+        parameters which must be on the interval [0, 1]. Bounds for parameters
+        location (``loc``) and scale (``scale``) are optional; by default,
+        they are fixed to 0 and 1, respectively.
+
+        If a sequence, element *i* is a tuple containing the lower and upper
+        bound on the *i*\ th parameter of the distribution. In this case,
+        bounds for *all* distribution shape parameters must be provided.
+        Optionally, bounds for location and scale may follow the
+        distribution shape parameters.
+
+        If a shape is to be held fixed (e.g. if it is known), the
+        lower and upper bounds may be equal. If a user-provided lower or upper
+        bound is beyond a bound of the domain for which the distribution is
+        defined, the bound of the distribution's domain will replace the
+        user-provided value. Similarly, parameters which must be integral
+        will be constrained to integral values within the user-provided bounds.
+    guess : dict or array_like, optional
+        If a dictionary, each key is the name of a parameter of the
+        distribution, and the corresponding value is a guess for the value
+        of the parameter.
+
+        If a sequence, element *i* is a guess for the *i*\ th parameter of the
+        distribution. In this case, guesses for *all* distribution shape
+        parameters must be provided.
+
+        If `guess` is not provided, guesses for the decision variables will
+        not be passed to the optimizer. If `guess` is provided, guesses for
+        any missing parameters will be set at the mean of the lower and
+        upper bounds. Guesses for parameters which must be integral will be
+        rounded to integral values, and guesses that lie outside the
+        intersection of the user-provided bounds and the domain of the
+        distribution will be clipped.
+    method : {'mle', 'mse'}
+        With ``method="mle"`` (default), the fit is computed by minimizing
+        the negative log-likelihood function. A large, finite penalty
+        (rather than infinite negative log-likelihood) is applied for
+        observations beyond the support of the distribution.
+        With ``method="mse"``, the fit is computed by minimizing
+        the negative log-product spacing function. The same penalty is applied
+        for observations beyond the support. We follow the approach of [1]_,
+        which is generalized for samples with repeated observations.
+    optimizer : callable, optional
+        `optimizer` is a callable that accepts the following positional
+        argument.
+
+        fun : callable
+            The objective function to be optimized. `fun` accepts one argument
+            ``x``, candidate shape parameters of the distribution, and returns
+            the objective function value given ``x``, `dist`, and the provided
+            `data`.
+            The job of `optimizer` is to find values of the decision variables
+            that minimizes `fun`.
+
+        `optimizer` must also accept the following keyword argument.
+
+        bounds : sequence of tuples
+            The bounds on values of the decision variables; each element will
+            be a tuple containing the lower and upper bound on a decision
+            variable.
+
+        If `guess` is provided, `optimizer` must also accept the following
+        keyword argument.
+
+        x0 : array_like
+            The guesses for each decision variable.
+
+        If the distribution has any shape parameters that must be integral or
+        if the distribution is discrete and the location parameter is not
+        fixed, `optimizer` must also accept the following keyword argument.
+
+        integrality : array_like of bools
+            For each decision variable, True if the decision variable
+            must be constrained to integer values and False if the decision
+            variable is continuous.
+
+        `optimizer` must return an object, such as an instance of
+        `scipy.optimize.OptimizeResult`, which holds the optimal values of
+        the decision variables in an attribute ``x``. If attributes
+        ``fun``, ``status``, or ``message`` are provided, they will be
+        included in the result object returned by `fit`.
+
+    Returns
+    -------
+    result : `~scipy.stats._result_classes.FitResult`
+        An object with the following fields.
+
+        params : namedtuple
+            A namedtuple containing the maximum likelihood estimates of the
+            shape parameters, location, and (if applicable) scale of the
+            distribution.
+        success : bool or None
+            Whether the optimizer considered the optimization to terminate
+            successfully or not.
+        message : str or None
+            Any status message provided by the optimizer.
+
+        The object has the following method:
+
+        nllf(params=None, data=None)
+            By default, the negative log-likelihood function at the fitted
+            `params` for the given `data`. Accepts a tuple containing
+            alternative shapes, location, and scale of the distribution and
+            an array of alternative data.
+
+        plot(ax=None)
+            Superposes the PDF/PMF of the fitted distribution over a normalized
+            histogram of the data.
+
+    See Also
+    --------
+    rv_continuous,  rv_discrete
+
+    Notes
+    -----
+    Optimization is more likely to converge to the maximum likelihood estimate
+    when the user provides tight bounds containing the maximum likelihood
+    estimate. For example, when fitting a binomial distribution to data, the
+    number of experiments underlying each sample may be known, in which case
+    the corresponding shape parameter ``n`` can be fixed.
+
+    References
+    ----------
+    .. [1] Shao, Yongzhao, and Marjorie G. Hahn. "Maximum product of spacings
+           method: a unified formulation with illustration of strong
+           consistency." Illinois Journal of Mathematics 43.3 (1999): 489-499.
+
+    Examples
+    --------
+    Suppose we wish to fit a distribution to the following data.
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> rng = np.random.default_rng()
+    >>> dist = stats.nbinom
+    >>> shapes = (5, 0.5)
+    >>> data = dist.rvs(*shapes, size=1000, random_state=rng)
+
+    Suppose we do not know how the data were generated, but we suspect that
+    it follows a negative binomial distribution with parameters *n* and *p*\.
+    (See `scipy.stats.nbinom`.) We believe that the parameter *n* was fewer
+    than 30, and we know that the parameter *p* must lie on the interval
+    [0, 1]. We record this information in a variable `bounds` and pass
+    this information to `fit`.
+
+    >>> bounds = [(0, 30), (0, 1)]
+    >>> res = stats.fit(dist, data, bounds)
+
+    `fit` searches within the user-specified `bounds` for the
+    values that best match the data (in the sense of maximum likelihood
+    estimation). In this case, it found shape values similar to those
+    from which the data were actually generated.
+
+    >>> res.params
+    FitParams(n=5.0, p=0.5028157644634368, loc=0.0)  # may vary
+
+    We can visualize the results by superposing the probability mass function
+    of the distribution (with the shapes fit to the data) over a normalized
+    histogram of the data.
+
+    >>> import matplotlib.pyplot as plt  # matplotlib must be installed to plot
+    >>> res.plot()
+    >>> plt.show()
+
+    Note that the estimate for *n* was exactly integral; this is because
+    the domain of the `nbinom` PMF includes only integral *n*, and the `nbinom`
+    object "knows" that. `nbinom` also knows that the shape *p* must be a
+    value between 0 and 1. In such a case - when the domain of the distribution
+    with respect to a parameter is finite - we are not required to specify
+    bounds for the parameter.
+
+    >>> bounds = {'n': (0, 30)}  # omit parameter p using a `dict`
+    >>> res2 = stats.fit(dist, data, bounds)
+    >>> res2.params
+    FitParams(n=5.0, p=0.5016492009232932, loc=0.0)  # may vary
+
+    If we wish to force the distribution to be fit with *n* fixed at 6, we can
+    set both the lower and upper bounds on *n* to 6. Note, however, that the
+    value of the objective function being optimized is typically worse (higher)
+    in this case.
+
+    >>> bounds = {'n': (6, 6)}  # fix parameter `n`
+    >>> res3 = stats.fit(dist, data, bounds)
+    >>> res3.params
+    FitParams(n=6.0, p=0.5486556076755706, loc=0.0)  # may vary
+    >>> res3.nllf() > res.nllf()
+    True  # may vary
+
+    Note that the numerical results of the previous examples are typical, but
+    they may vary because the default optimizer used by `fit`,
+    `scipy.optimize.differential_evolution`, is stochastic. However, we can
+    customize the settings used by the optimizer to ensure reproducibility -
+    or even use a different optimizer entirely - using the `optimizer`
+    parameter.
+
+    >>> from scipy.optimize import differential_evolution
+    >>> rng = np.random.default_rng(767585560716548)
+    >>> def optimizer(fun, bounds, *, integrality):
+    ...     return differential_evolution(fun, bounds, strategy='best2bin',
+    ...                                   rng=rng, integrality=integrality)
+    >>> bounds = [(0, 30), (0, 1)]
+    >>> res4 = stats.fit(dist, data, bounds, optimizer=optimizer)
+    >>> res4.params
+    FitParams(n=5.0, p=0.5015183149259951, loc=0.0)
+
+    """
+    # --- Input Validation / Standardization --- #
+    user_bounds = bounds
+    user_guess = guess
+
+    # distribution input validation and information collection
+    if hasattr(dist, "pdf"):  # can't use isinstance for types
+        default_bounds = {'loc': (0, 0), 'scale': (1, 1)}
+        discrete = False
+    elif hasattr(dist, "pmf"):
+        default_bounds = {'loc': (0, 0)}
+        discrete = True
+    else:
+        message = ("`dist` must be an instance of `rv_continuous` "
+                   "or `rv_discrete.`")
+        raise ValueError(message)
+
+    try:
+        param_info = dist._param_info()
+    except AttributeError as e:
+        message = (f"Distribution `{dist.name}` is not yet supported by "
+                   "`scipy.stats.fit` because shape information has "
+                   "not been defined.")
+        raise ValueError(message) from e
+
+    # data input validation
+    data = np.asarray(data)
+    if data.ndim != 1:
+        message = "`data` must be exactly one-dimensional."
+        raise ValueError(message)
+    if not (np.issubdtype(data.dtype, np.number)
+            and np.all(np.isfinite(data))):
+        message = "All elements of `data` must be finite numbers."
+        raise ValueError(message)
+
+    # bounds input validation and information collection
+    n_params = len(param_info)
+    n_shapes = n_params - (1 if discrete else 2)
+    param_list = [param.name for param in param_info]
+    param_names = ", ".join(param_list)
+    shape_names = ", ".join(param_list[:n_shapes])
+
+    if user_bounds is None:
+        user_bounds = {}
+
+    if isinstance(user_bounds, dict):
+        default_bounds.update(user_bounds)
+        user_bounds = default_bounds
+        user_bounds_array = np.empty((n_params, 2))
+        for i in range(n_params):
+            param_name = param_info[i].name
+            user_bound = user_bounds.pop(param_name, None)
+            if user_bound is None:
+                user_bound = param_info[i].domain
+            user_bounds_array[i] = user_bound
+        if user_bounds:
+            message = ("Bounds provided for the following unrecognized "
+                       f"parameters will be ignored: {set(user_bounds)}")
+            warnings.warn(message, RuntimeWarning, stacklevel=2)
+
+    else:
+        try:
+            user_bounds = np.asarray(user_bounds, dtype=float)
+            if user_bounds.size == 0:
+                user_bounds = np.empty((0, 2))
+        except ValueError as e:
+            message = ("Each element of a `bounds` sequence must be a tuple "
+                       "containing two elements: the lower and upper bound of "
+                       "a distribution parameter.")
+            raise ValueError(message) from e
+        if (user_bounds.ndim != 2 or user_bounds.shape[1] != 2):
+            message = ("Each element of `bounds` must be a tuple specifying "
+                       "the lower and upper bounds of a shape parameter")
+            raise ValueError(message)
+        if user_bounds.shape[0] < n_shapes:
+            message = (f"A `bounds` sequence must contain at least {n_shapes} "
+                       "elements: tuples specifying the lower and upper "
+                       f"bounds of all shape parameters {shape_names}.")
+            raise ValueError(message)
+        if user_bounds.shape[0] > n_params:
+            message = ("A `bounds` sequence may not contain more than "
+                       f"{n_params} elements: tuples specifying the lower and "
+                       "upper bounds of distribution parameters "
+                       f"{param_names}.")
+            raise ValueError(message)
+
+        user_bounds_array = np.empty((n_params, 2))
+        user_bounds_array[n_shapes:] = list(default_bounds.values())
+        user_bounds_array[:len(user_bounds)] = user_bounds
+
+    user_bounds = user_bounds_array
+    validated_bounds = []
+    for i in range(n_params):
+        name = param_info[i].name
+        user_bound = user_bounds_array[i]
+        param_domain = param_info[i].domain
+        integral = param_info[i].integrality
+        combined = _combine_bounds(name, user_bound, param_domain, integral)
+        validated_bounds.append(combined)
+
+    bounds = np.asarray(validated_bounds)
+    integrality = [param.integrality for param in param_info]
+
+    # guess input validation
+
+    if user_guess is None:
+        guess_array = None
+    elif isinstance(user_guess, dict):
+        default_guess = {param.name: np.mean(bound)
+                         for param, bound in zip(param_info, bounds)}
+        unrecognized = set(user_guess) - set(default_guess)
+        if unrecognized:
+            message = ("Guesses provided for the following unrecognized "
+                       f"parameters will be ignored: {unrecognized}")
+            warnings.warn(message, RuntimeWarning, stacklevel=2)
+        default_guess.update(user_guess)
+
+        message = ("Each element of `guess` must be a scalar "
+                   "guess for a distribution parameter.")
+        try:
+            guess_array = np.asarray([default_guess[param.name]
+                                      for param in param_info], dtype=float)
+        except ValueError as e:
+            raise ValueError(message) from e
+
+    else:
+        message = ("Each element of `guess` must be a scalar "
+                   "guess for a distribution parameter.")
+        try:
+            user_guess = np.asarray(user_guess, dtype=float)
+        except ValueError as e:
+            raise ValueError(message) from e
+        if user_guess.ndim != 1:
+            raise ValueError(message)
+        if user_guess.shape[0] < n_shapes:
+            message = (f"A `guess` sequence must contain at least {n_shapes} "
+                       "elements: scalar guesses for the distribution shape "
+                       f"parameters {shape_names}.")
+            raise ValueError(message)
+        if user_guess.shape[0] > n_params:
+            message = ("A `guess` sequence may not contain more than "
+                       f"{n_params} elements: scalar guesses for the "
+                       f"distribution parameters {param_names}.")
+            raise ValueError(message)
+
+        guess_array = np.mean(bounds, axis=1)
+        guess_array[:len(user_guess)] = user_guess
+
+    if guess_array is not None:
+        guess_rounded = guess_array.copy()
+
+        guess_rounded[integrality] = np.round(guess_rounded[integrality])
+        rounded = np.where(guess_rounded != guess_array)[0]
+        for i in rounded:
+            message = (f"Guess for parameter `{param_info[i].name}` "
+                       f"rounded from {guess_array[i]} to {guess_rounded[i]}.")
+            warnings.warn(message, RuntimeWarning, stacklevel=2)
+
+        guess_clipped = np.clip(guess_rounded, bounds[:, 0], bounds[:, 1])
+        clipped = np.where(guess_clipped != guess_rounded)[0]
+        for i in clipped:
+            message = (f"Guess for parameter `{param_info[i].name}` "
+                       f"clipped from {guess_rounded[i]} to "
+                       f"{guess_clipped[i]}.")
+            warnings.warn(message, RuntimeWarning, stacklevel=2)
+
+        guess = guess_clipped
+    else:
+        guess = None
+
+    # --- Fitting --- #
+    def nllf(free_params, data=data):  # bind data NOW
+        with np.errstate(invalid='ignore', divide='ignore'):
+            return dist._penalized_nnlf(free_params, data)
+
+    def nlpsf(free_params, data=data):  # bind data NOW
+        with np.errstate(invalid='ignore', divide='ignore'):
+            return dist._penalized_nlpsf(free_params, data)
+
+    methods = {'mle': nllf, 'mse': nlpsf}
+    objective = methods[method.lower()]
+
+    with np.errstate(invalid='ignore', divide='ignore'):
+        kwds = {}
+        if bounds is not None:
+            kwds['bounds'] = bounds
+        if np.any(integrality):
+            kwds['integrality'] = integrality
+        if guess is not None:
+            kwds['x0'] = guess
+        res = optimizer(objective, **kwds)
+
+    return FitResult(dist, data, discrete, res)
+
+
+GoodnessOfFitResult = namedtuple('GoodnessOfFitResult',
+                                 ('fit_result', 'statistic', 'pvalue',
+                                  'null_distribution'))
+
+
+@xp_capabilities(out_of_scope=True)
+@_transition_to_rng('random_state')
+def goodness_of_fit(dist, data, *, known_params=None, fit_params=None,
+                    guessed_params=None, statistic='ad', n_mc_samples=9999,
+                    rng=None):
+    r"""
+    Perform a goodness of fit test comparing data to a distribution family.
+
+    Given a distribution family and data, perform a test of the null hypothesis
+    that the data were drawn from a distribution in that family. Any known
+    parameters of the distribution may be specified. Remaining parameters of
+    the distribution will be fit to the data, and the p-value of the test
+    is computed accordingly. Several statistics for comparing the distribution
+    to data are available.
+
+    Parameters
+    ----------
+    dist : `scipy.stats.rv_continuous`
+        The object representing the distribution family under the null
+        hypothesis.
+    data : 1D array_like
+        Finite, uncensored data to be tested.
+    known_params : dict, optional
+        A dictionary containing name-value pairs of known distribution
+        parameters. Monte Carlo samples are randomly drawn from the
+        null-hypothesized distribution with these values of the parameters.
+        Before the statistic is evaluated for the observed `data` and each
+        Monte Carlo sample, only remaining unknown parameters of the
+        null-hypothesized distribution family are fit to the samples; the
+        known parameters are held fixed. If all parameters of the distribution
+        family are known, then the step of fitting the distribution family to
+        each sample is omitted.
+    fit_params : dict, optional
+        A dictionary containing name-value pairs of distribution parameters
+        that have already been fit to the data, e.g. using `scipy.stats.fit`
+        or the ``fit`` method of `dist`. Monte Carlo samples are drawn from the
+        null-hypothesized distribution with these specified values of the
+        parameter. However, these and all other unknown parameters of the
+        null-hypothesized distribution family are always fit to the sample,
+        whether that is the observed `data` or a Monte Carlo sample, before
+        the statistic is evaluated.
+    guessed_params : dict, optional
+        A dictionary containing name-value pairs of distribution parameters
+        which have been guessed. These parameters are always considered as
+        free parameters and are fit both to the provided `data` as well as
+        to the Monte Carlo samples drawn from the null-hypothesized
+        distribution. The purpose of these `guessed_params` is to be used as
+        initial values for the numerical fitting procedure.
+    statistic : {"ad", "ks", "cvm", "filliben"} or callable, optional
+        The statistic used to compare data to a distribution after fitting
+        unknown parameters of the distribution family to the data. The
+        Anderson-Darling ("ad") [1]_, Kolmogorov-Smirnov ("ks") [1]_,
+        Cramer-von Mises ("cvm") [1]_, and Filliben ("filliben") [7]_
+        statistics are available.  Alternatively, a callable with signature
+        ``(dist, data, axis)`` may be supplied to compute the statistic. Here
+        ``dist`` is a frozen distribution object (potentially with array
+        parameters), ``data`` is an array of Monte Carlo samples (of
+        compatible shape), and ``axis`` is the axis of ``data`` along which
+        the statistic must be computed.
+    n_mc_samples : int, default: 9999
+        The number of Monte Carlo samples drawn from the null hypothesized
+        distribution to form the null distribution of the statistic. The
+        sample size of each is the same as the given `data`.
+    rng : `numpy.random.Generator`, optional
+        Pseudorandom number generator state. When `rng` is None, a new
+        `numpy.random.Generator` is created using entropy from the
+        operating system. Types other than `numpy.random.Generator` are
+        passed to `numpy.random.default_rng` to instantiate a ``Generator``.
+
+    Returns
+    -------
+    res : GoodnessOfFitResult
+        An object with the following attributes.
+
+        fit_result : `~scipy.stats._result_classes.FitResult`
+            An object representing the fit of the provided `dist` to `data`.
+            This  object includes the values of distribution family parameters
+            that fully define the null-hypothesized distribution, that is,
+            the distribution from which Monte Carlo samples are drawn.
+        statistic : float
+            The value of the statistic comparing provided `data` to the
+            null-hypothesized distribution.
+        pvalue : float
+            The proportion of elements in the null distribution with
+            statistic values at least as extreme as the statistic value of the
+            provided `data`.
+        null_distribution : ndarray
+            The value of the statistic for each Monte Carlo sample
+            drawn from the null-hypothesized distribution.
+
+    Notes
+    -----
+    This is a generalized Monte Carlo goodness-of-fit procedure, special cases
+    of which correspond with various Anderson-Darling tests, Lilliefors' test,
+    etc. The test is described in [2]_, [3]_, and [4]_ as a parametric
+    bootstrap test. This is a Monte Carlo test in which parameters that
+    specify the distribution from which samples are drawn have been estimated
+    from the data. We describe the test using "Monte Carlo" rather than
+    "parametric bootstrap" throughout to avoid confusion with the more familiar
+    nonparametric bootstrap, and describe how the test is performed below.
+
+    *Traditional goodness of fit tests*
+
+    Traditionally, critical values corresponding with a fixed set of
+    significance levels are pre-calculated using Monte Carlo methods. Users
+    perform the test by calculating the value of the test statistic only for
+    their observed `data` and comparing this value to tabulated critical
+    values. This practice is not very flexible, as tables are not available for
+    all distributions and combinations of known and unknown parameter values.
+    Also, results can be inaccurate when critical values are interpolated from
+    limited tabulated data to correspond with the user's sample size and
+    fitted parameter values. To overcome these shortcomings, this function
+    allows the user to perform the Monte Carlo trials adapted to their
+    particular data.
+
+    *Algorithmic overview*
+
+    In brief, this routine executes the following steps:
+
+      1. Fit unknown parameters to the given `data`, thereby forming the
+         "null-hypothesized" distribution, and compute the statistic of
+         this pair of data and distribution.
+      2. Draw random samples from this null-hypothesized distribution.
+      3. Fit the unknown parameters to each random sample.
+      4. Calculate the statistic between each sample and the distribution that
+         has been fit to the sample.
+      5. Compare the value of the statistic corresponding with `data` from (1)
+         against the values of the statistic corresponding with the random
+         samples from (4). The p-value is the proportion of samples with a
+         statistic value greater than or equal to the statistic of the observed
+         data.
+
+    In more detail, the steps are as follows.
+
+    First, any unknown parameters of the distribution family specified by
+    `dist` are fit to the provided `data` using maximum likelihood estimation.
+    (One exception is the normal distribution with unknown location and scale:
+    we use the bias-corrected standard deviation ``np.std(data, ddof=1)`` for
+    the scale as recommended in [1]_.)
+    These values of the parameters specify a particular member of the
+    distribution family referred to as the "null-hypothesized distribution",
+    that is, the distribution from which the data were sampled under the null
+    hypothesis. The `statistic`, which compares data to a distribution, is
+    computed between `data` and the null-hypothesized distribution.
+
+    Next, many (specifically `n_mc_samples`) new samples, each containing the
+    same number of observations as `data`, are drawn from the
+    null-hypothesized distribution. All unknown parameters of the distribution
+    family `dist` are fit to *each resample*, and the `statistic` is computed
+    between each sample and its corresponding fitted distribution. These
+    values of the statistic form the Monte Carlo null distribution (not to be
+    confused with the "null-hypothesized distribution" above).
+
+    The p-value of the test is the proportion of statistic values in the Monte
+    Carlo null distribution that are at least as extreme as the statistic value
+    of the provided `data`. More precisely, the p-value is given by
+
+    .. math::
+
+        p = \frac{b + 1}
+                 {m + 1}
+
+    where :math:`b` is the number of statistic values in the Monte Carlo null
+    distribution that are greater than or equal to the statistic value
+    calculated for `data`, and :math:`m` is the number of elements in the
+    Monte Carlo null distribution (`n_mc_samples`). The addition of :math:`1`
+    to the numerator and denominator can be thought of as including the
+    value of the statistic corresponding with `data` in the null distribution,
+    but a more formal explanation is given in [5]_.
+
+    *Limitations*
+
+    The test can be very slow for some distribution families because unknown
+    parameters of the distribution family must be fit to each of the Monte
+    Carlo samples, and for most distributions in SciPy, distribution fitting
+    performed via numerical optimization.
+
+    *Anti-Pattern*
+
+    For this reason, it may be tempting
+    to treat parameters of the distribution pre-fit to `data` (by the user)
+    as though they were `known_params`, as specification of all parameters of
+    the distribution precludes the need to fit the distribution to each Monte
+    Carlo sample. (This is essentially how the original Kilmogorov-Smirnov
+    test is performed.) Although such a test can provide evidence against the
+    null hypothesis, the test is conservative in the sense that small p-values
+    will tend to (greatly) *overestimate* the probability of making a type I
+    error (that is, rejecting the null hypothesis although it is true), and the
+    power of the test is low (that is, it is less likely to reject the null
+    hypothesis even when the null hypothesis is false).
+    This is because the Monte Carlo samples are less likely to agree with the
+    null-hypothesized distribution as well as `data`. This tends to increase
+    the values of the statistic recorded in the null distribution, so that a
+    larger number of them exceed the value of statistic for `data`, thereby
+    inflating the p-value.
+
+    References
+    ----------
+    .. [1] M. A. Stephens (1974). "EDF Statistics for Goodness of Fit and
+           Some Comparisons." Journal of the American Statistical Association,
+           Vol. 69, pp. 730-737.
+    .. [2] W. Stute, W. G. Manteiga, and M. P. Quindimil (1993).
+           "Bootstrap based goodness-of-fit-tests." Metrika 40.1: 243-256.
+    .. [3] C. Genest, & B Rémillard. (2008). "Validity of the parametric
+           bootstrap for goodness-of-fit testing in semiparametric models."
+           Annales de l'IHP Probabilités et statistiques. Vol. 44. No. 6.
+    .. [4] I. Kojadinovic and J. Yan (2012). "Goodness-of-fit testing based on
+           a weighted bootstrap: A fast large-sample alternative to the
+           parametric bootstrap." Canadian Journal of Statistics 40.3: 480-500.
+    .. [5] B. Phipson and G. K. Smyth (2010). "Permutation P-values Should
+           Never Be Zero: Calculating Exact P-values When Permutations Are
+           Randomly Drawn." Statistical Applications in Genetics and Molecular
+           Biology 9.1.
+    .. [6] H. W. Lilliefors (1967). "On the Kolmogorov-Smirnov test for
+           normality with mean and variance unknown." Journal of the American
+           statistical Association 62.318: 399-402.
+    .. [7] Filliben, James J. "The probability plot correlation coefficient
+           test for normality." Technometrics 17.1 (1975): 111-117.
+
+    Examples
+    --------
+    A well-known test of the null hypothesis that data were drawn from a
+    given distribution is the Kolmogorov-Smirnov (KS) test, available in SciPy
+    as `scipy.stats.ks_1samp`. Suppose we wish to test whether the following
+    data:
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> rng = np.random.default_rng(1638083107694713882823079058616272161)
+    >>> x = stats.uniform.rvs(size=75, random_state=rng)
+
+    were sampled from a normal distribution. To perform a KS test, the
+    empirical distribution function of the observed data will be compared
+    against the (theoretical) cumulative distribution function of a normal
+    distribution. Of course, to do this, the normal distribution under the null
+    hypothesis must be fully specified. This is commonly done by first fitting
+    the ``loc`` and ``scale`` parameters of the distribution to the observed
+    data, then performing the test.
+
+    >>> loc, scale = np.mean(x), np.std(x, ddof=1)
+    >>> cdf = stats.norm(loc, scale).cdf
+    >>> stats.ks_1samp(x, cdf)
+    KstestResult(statistic=0.1119257570456813,
+                 pvalue=0.2827756409939257,
+                 statistic_location=0.7751845155861765,
+                 statistic_sign=-1)
+
+    An advantage of the KS-test is that the p-value - the probability of
+    obtaining a value of the test statistic under the null hypothesis as
+    extreme as the value obtained from the observed data - can be calculated
+    exactly and efficiently. `goodness_of_fit` can only approximate these
+    results.
+
+    >>> known_params = {'loc': loc, 'scale': scale}
+    >>> res = stats.goodness_of_fit(stats.norm, x, known_params=known_params,
+    ...                             statistic='ks', rng=rng)
+    >>> res.statistic, res.pvalue
+    (0.1119257570456813, 0.2788)
+
+    The statistic matches exactly, but the p-value is estimated by forming
+    a "Monte Carlo null distribution", that is, by explicitly drawing random
+    samples from `scipy.stats.norm` with the provided parameters and
+    calculating the stastic for each. The fraction of these statistic values
+    at least as extreme as ``res.statistic`` approximates the exact p-value
+    calculated by `scipy.stats.ks_1samp`.
+
+    However, in many cases, we would prefer to test only that the data were
+    sampled from one of *any* member of the normal distribution family, not
+    specifically from the normal distribution with the location and scale
+    fitted to the observed sample. In this case, Lilliefors [6]_ argued that
+    the KS test is far too conservative (that is, the p-value overstates
+    the actual probability of rejecting a true null hypothesis) and thus lacks
+    power - the ability to reject the null hypothesis when the null hypothesis
+    is actually false.
+    Indeed, our p-value above is approximately 0.28, which is far too large
+    to reject the null hypothesis at any common significance level.
+
+    Consider why this might be. Note that in the KS test above, the statistic
+    always compares data against the CDF of a normal distribution fitted to the
+    *observed data*. This tends to reduce the value of the statistic for the
+    observed data, but it is "unfair" when computing the statistic for other
+    samples, such as those we randomly draw to form the Monte Carlo null
+    distribution. It is easy to correct for this: whenever we compute the KS
+    statistic of a sample, we use the CDF of a normal distribution fitted
+    to *that sample*. The null distribution in this case has not been
+    calculated exactly and is tyically approximated using Monte Carlo methods
+    as described above. This is where `goodness_of_fit` excels.
+
+    >>> res = stats.goodness_of_fit(stats.norm, x, statistic='ks', rng=rng)
+    >>> res.statistic, res.pvalue
+    (0.1119257570456813, 0.0196)
+
+    Indeed, this p-value is much smaller, and small enough to (correctly)
+    reject the null hypothesis at common significance levels, including 5% and
+    2.5%.
+
+    However, the KS statistic is not very sensitive to all deviations from
+    normality. The original advantage of the KS statistic was the ability
+    to compute the null distribution theoretically, but a more sensitive
+    statistic - resulting in a higher test power - can be used now that we can
+    approximate the null distribution
+    computationally. The Anderson-Darling statistic [1]_ tends to be more
+    sensitive, and critical values of this statistic have been tabulated
+    for various significance levels and sample sizes using Monte Carlo methods.
+
+    >>> res = stats.anderson(x, 'norm', method='interpolate')
+    >>> print(res.statistic)
+    1.2139573337497467
+    >>> print(res.pvalue)
+    0.01
+
+    Here, the observed value of the statistic exceeds the critical value
+    corresponding with a 1% significance level. This tells us that the p-value
+    of the observed data is 1% or less, but what is it? `goodness_of_fit` can
+    estimate it directly.
+
+    >>> res = stats.goodness_of_fit(stats.norm, x, statistic='ad', rng=rng)
+    >>> res.statistic, res.pvalue
+    (1.2139573337497467, 0.0034)
+
+    A further advantage is that use of `goodness_of_fit` is not limited to
+    a particular set of distributions or conditions on which parameters
+    are known versus which must be estimated from data. Instead,
+    `goodness_of_fit` can estimate p-values relatively quickly for any
+    distribution with a sufficiently fast and reliable ``fit`` method. For
+    instance, here we perform a goodness of fit test using the Cramer-von Mises
+    statistic against the Rayleigh distribution with known location and unknown
+    scale.
+
+    >>> rng = np.random.default_rng()
+    >>> x = stats.chi(df=2.2, loc=0, scale=2).rvs(size=1000, random_state=rng)
+    >>> res = stats.goodness_of_fit(stats.rayleigh, x, statistic='cvm',
+    ...                             known_params={'loc': 0}, rng=rng)
+
+    This executes fairly quickly, but to check the reliability of the ``fit``
+    method, we should inspect the fit result.
+
+    >>> res.fit_result  # location is as specified, and scale is reasonable
+      params: FitParams(loc=0.0, scale=2.1026719844231243)
+     success: True
+     message: 'The fit was performed successfully.'
+    >>> import matplotlib.pyplot as plt  # matplotlib must be installed to plot
+    >>> res.fit_result.plot()
+    >>> plt.show()
+
+    If the distribution is not fit to the observed data as well as possible,
+    the test may not control the type I error rate, that is, the chance of
+    rejecting the null hypothesis even when it is true.
+
+    We should also look for extreme outliers in the null distribution that
+    may be caused by unreliable fitting. These do not necessarily invalidate
+    the result, but they tend to reduce the test's power.
+
+    >>> _, ax = plt.subplots()
+    >>> ax.hist(np.log10(res.null_distribution))
+    >>> ax.set_xlabel("log10 of CVM statistic under the null hypothesis")
+    >>> ax.set_ylabel("Frequency")
+    >>> ax.set_title("Histogram of the Monte Carlo null distribution")
+    >>> plt.show()
+
+    This plot seems reassuring.
+
+    If ``fit`` method is working reliably, and if the distribution of the test
+    statistic is not particularly sensitive to the values of the fitted
+    parameters, then the p-value provided by `goodness_of_fit` is expected to
+    be a good approximation.
+
+    >>> res.statistic, res.pvalue
+    (0.2231991510248692, 0.0525)
+
+    """
+    args = _gof_iv(dist, data, known_params, fit_params, guessed_params,
+                   statistic, n_mc_samples, rng)
+    (dist, data, fixed_nhd_params, fixed_rfd_params, guessed_nhd_params,
+     guessed_rfd_params, statistic, n_mc_samples_int, rng) = args
+
+    # Fit null hypothesis distribution to data
+    nhd_fit_fun = _get_fit_fun(dist, data, guessed_nhd_params,
+                               fixed_nhd_params)
+    nhd_vals = nhd_fit_fun(data)
+    nhd_dist = dist(*nhd_vals)
+
+    def rvs(size):
+        return nhd_dist.rvs(size=size, random_state=rng)
+
+    # Define statistic
+    fit_fun = _get_fit_fun(dist, data, guessed_rfd_params, fixed_rfd_params)
+    if callable(statistic):
+        compare_fun = statistic
+    else:
+        compare_fun = _compare_dict[statistic]
+    alternative = getattr(compare_fun, 'alternative', 'greater')
+
+    def statistic_fun(data, axis):
+        # Make things simple by always working along the last axis.
+        data = np.moveaxis(data, axis, -1)
+        rfd_vals = fit_fun(data)
+        rfd_dist = dist(*rfd_vals)
+        return compare_fun(rfd_dist, data, axis=-1)
+
+    res = stats.monte_carlo_test(data, rvs, statistic_fun, vectorized=True,
+                                 n_resamples=n_mc_samples, axis=-1,
+                                 alternative=alternative)
+    opt_res = optimize.OptimizeResult()
+    opt_res.success = True
+    opt_res.message = "The fit was performed successfully."
+    opt_res.x = nhd_vals
+    # Only continuous distributions for now, hence discrete=False
+    # There's no fundamental limitation; it's just that we're not using
+    # stats.fit, discrete distributions don't have `fit` method, and
+    # we haven't written any vectorized fit functions for a discrete
+    # distribution yet.
+    return GoodnessOfFitResult(FitResult(dist, data, False, opt_res),
+                               res.statistic, res.pvalue,
+                               res.null_distribution)
+
+
+def _get_fit_fun(dist, data, guessed_params, fixed_params):
+
+    shape_names = [] if dist.shapes is None else dist.shapes.split(", ")
+    param_names = shape_names + ['loc', 'scale']
+    fparam_names = ['f'+name for name in param_names]
+    all_fixed = not set(fparam_names).difference(fixed_params)
+    guessed_shapes = [guessed_params.pop(x, None)
+                      for x in shape_names if x in guessed_params]
+
+    if all_fixed:
+        def fit_fun(data):
+            return [fixed_params[name] for name in fparam_names]
+    # Define statistic, including fitting distribution to data
+    elif dist in _fit_funs:
+        def fit_fun(data):
+            params = _fit_funs[dist](data, **fixed_params)
+            params = np.asarray(np.broadcast_arrays(*params))
+            if params.ndim > 1:
+                params = params[..., np.newaxis]
+            return params
+    else:
+        def fit_fun_1d(data):
+            return dist.fit(data, *guessed_shapes, **guessed_params,
+                            **fixed_params)
+
+        def fit_fun(data):
+            params = np.apply_along_axis(fit_fun_1d, axis=-1, arr=data)
+            if params.ndim > 1:
+                params = params.T[..., np.newaxis]
+            return params
+
+    return fit_fun
+
+
+# Vectorized fitting functions. These are to accept ND `data` in which each
+# row (slice along last axis) is a sample to fit and scalar fixed parameters.
+# They return a tuple of shape parameter arrays, each of shape data.shape[:-1].
+def _fit_norm(data, floc=None, fscale=None):
+    loc = floc
+    scale = fscale
+    if loc is None and scale is None:
+        loc = np.mean(data, axis=-1)
+        scale = np.std(data, ddof=1, axis=-1)
+    elif loc is None:
+        loc = np.mean(data, axis=-1)
+    elif scale is None:
+        scale = np.sqrt(((data - loc)**2).mean(axis=-1))
+    return loc, scale
+
+
+_fit_funs = {stats.norm: _fit_norm}  # type: ignore[attr-defined]
+
+
+# Vectorized goodness of fit statistic functions. These accept a frozen
+# distribution object and `data` in which each row (slice along last axis) is
+# a sample.
+
+
+def _anderson_darling(dist, data, axis):
+    x = np.sort(data, axis=-1)
+    n = data.shape[-1]
+    i = np.arange(1, n+1)
+    Si = (2*i - 1)/n * (dist.logcdf(x) + dist.logsf(x[..., ::-1]))
+    S = np.sum(Si, axis=-1)
+    return -n - S
+
+
+def _compute_dplus(cdfvals):  # adapted from _stats_py before gh-17062
+    n = cdfvals.shape[-1]
+    return (np.arange(1.0, n + 1) / n - cdfvals).max(axis=-1)
+
+
+def _compute_dminus(cdfvals):
+    n = cdfvals.shape[-1]
+    return (cdfvals - np.arange(0.0, n)/n).max(axis=-1)
+
+
+def _kolmogorov_smirnov(dist, data, axis=-1):
+    x = np.sort(data, axis=axis)
+    cdfvals = dist.cdf(x)
+    cdfvals = np.moveaxis(cdfvals, axis, -1)
+    Dplus = _compute_dplus(cdfvals)  # always works along last axis
+    Dminus = _compute_dminus(cdfvals)
+    return np.maximum(Dplus, Dminus)
+
+
+def _corr(X, M):
+    # Correlation coefficient r, simplified and vectorized as we need it.
+    # See [7] Equation (2). Lemma 1/2 are only for distributions symmetric
+    # about 0.
+    Xm = X.mean(axis=-1, keepdims=True)
+    Mm = M.mean(axis=-1, keepdims=True)
+    num = np.sum((X - Xm) * (M - Mm), axis=-1)
+    den = np.sqrt(np.sum((X - Xm)**2, axis=-1) * np.sum((M - Mm)**2, axis=-1))
+    return num/den
+
+
+def _filliben(dist, data, axis):
+    # [7] Section 8 # 1
+    X = np.sort(data, axis=-1)
+
+    # [7] Section 8 # 2
+    n = data.shape[-1]
+    k = np.arange(1, n+1)
+    # Filliben used an approximation for the uniform distribution order
+    # statistic medians.
+    # m = (k - .3175)/(n + 0.365)
+    # m[-1] = 0.5**(1/n)
+    # m[0] = 1 - m[-1]
+    # We can just as easily use the (theoretically) exact values. See e.g.
+    # https://en.wikipedia.org/wiki/Order_statistic
+    # "Order statistics sampled from a uniform distribution"
+    m = stats.beta(k, n + 1 - k).median()
+
+    # [7] Section 8 # 3
+    M = dist.ppf(m)
+
+    # [7] Section 8 # 4
+    return _corr(X, M)
+_filliben.alternative = 'less'  # type: ignore[attr-defined]
+
+
+def _cramer_von_mises(dist, data, axis):
+    x = np.sort(data, axis=-1)
+    n = data.shape[-1]
+    cdfvals = dist.cdf(x)
+    u = (2*np.arange(1, n+1) - 1)/(2*n)
+    w = 1 / (12*n) + np.sum((u - cdfvals)**2, axis=-1)
+    return w
+
+
+_compare_dict = {"ad": _anderson_darling, "ks": _kolmogorov_smirnov,
+                 "cvm": _cramer_von_mises, "filliben": _filliben}
+
+
+def _gof_iv(dist, data, known_params, fit_params, guessed_params, statistic,
+            n_mc_samples, rng):
+
+    if not isinstance(dist, stats.rv_continuous):
+        message = ("`dist` must be a (non-frozen) instance of "
+                   "`stats.rv_continuous`.")
+        raise TypeError(message)
+
+    data = np.asarray(data, dtype=float)
+    if not data.ndim == 1:
+        message = "`data` must be a one-dimensional array of numbers."
+        raise ValueError(message)
+
+    # Leave validation of these key/value pairs to the `fit` method,
+    # but collect these into dictionaries that will be used
+    known_params = known_params or dict()
+    fit_params = fit_params or dict()
+    guessed_params = guessed_params or dict()
+
+    known_params_f = {("f"+key): val for key, val in known_params.items()}
+    fit_params_f = {("f"+key): val for key, val in fit_params.items()}
+
+    # These are the values of parameters of the null distribution family
+    # with which resamples are drawn
+    fixed_nhd_params = known_params_f.copy()
+    fixed_nhd_params.update(fit_params_f)
+
+    # These are fixed when fitting the distribution family to resamples
+    fixed_rfd_params = known_params_f.copy()
+
+    # These are used as guesses when fitting the distribution family to
+    # the original data
+    guessed_nhd_params = guessed_params.copy()
+
+    # These are used as guesses when fitting the distribution family to
+    # resamples
+    guessed_rfd_params = fit_params.copy()
+    guessed_rfd_params.update(guessed_params)
+
+    if not callable(statistic):
+        statistic = statistic.lower()
+        statistics = {'ad', 'ks', 'cvm', 'filliben'}
+        if statistic not in statistics:
+            message = f"`statistic` must be one of {statistics}."
+            raise ValueError(message)
+
+    n_mc_samples_int = int(n_mc_samples)
+    if n_mc_samples_int != n_mc_samples:
+        message = "`n_mc_samples` must be an integer."
+        raise TypeError(message)
+
+    rng = check_random_state(rng)
+
+    return (dist, data, fixed_nhd_params, fixed_rfd_params, guessed_nhd_params,
+            guessed_rfd_params, statistic, n_mc_samples_int, rng)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_hypotests.py b/venv/lib/python3.12/site-packages/scipy/stats/_hypotests.py
new file mode 100644
index 0000000000000000000000000000000000000000..b905654a99a08b2a856923279aa3a112363cb6cf
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_hypotests.py
@@ -0,0 +1,2201 @@
+from collections import namedtuple
+from dataclasses import dataclass
+import math
+import numpy as np
+import warnings
+from itertools import combinations
+import scipy.stats
+from scipy.optimize import shgo
+from . import distributions
+from ._common import ConfidenceInterval
+from ._continuous_distns import norm
+from scipy._lib._array_api import (xp_capabilities, array_namespace, xp_size,
+                                   xp_promote, xp_result_type, xp_copy, is_numpy,
+                                   is_lazy_array, _count_nonmasked, is_marray,
+                                   _masked_apply)
+import scipy._external.array_api_extra as xpx
+from scipy.special import gamma, kv, gammaln
+from scipy.fft import ifft
+from ._stats_pythran import _a_ij_Aij_Dij2
+from ._stats_pythran import (
+    _concordant_pairs as _P, _discordant_pairs as _Q
+)
+from ._axis_nan_policy import _axis_nan_policy_factory
+from scipy.stats import _stats_py
+
+__all__ = ['epps_singleton_2samp', 'cramervonmises', 'somersd',
+           'barnard_exact', 'boschloo_exact', 'cramervonmises_2samp',
+           'tukey_hsd', 'poisson_means_test']
+
+Epps_Singleton_2sampResult = namedtuple('Epps_Singleton_2sampResult',
+                                        ('statistic', 'pvalue'))
+
+
+@xp_capabilities(skip_backends=[("dask.array", "lazy -> no _axis_nan_policy")])
+@_axis_nan_policy_factory(Epps_Singleton_2sampResult, n_samples=2, too_small=4)
+def epps_singleton_2samp(x, y, t=(0.4, 0.8), *, axis=0):
+    """Compute the Epps-Singleton (ES) test statistic.
+
+    Test the null hypothesis that two samples have the same underlying
+    probability distribution.
+
+    Parameters
+    ----------
+    x, y : array-like
+        The two samples of observations to be tested. Input must not have more
+        than one dimension. Samples can have different lengths, but both
+        must have at least five observations.
+    t : array-like, optional
+        The points (t1, ..., tn) where the empirical characteristic function is
+        to be evaluated. It should be positive distinct numbers. The default
+        value (0.4, 0.8) is proposed in [1]_. Input must not have more than
+        one dimension.
+    axis : int or tuple of ints, default: 0
+        If an int or tuple of ints, the axis or axes of the input along which
+        to compute the statistic. The statistic of each axis-slice (e.g. row)
+        of the input will appear in a corresponding element of the output.
+        If ``None``, the input will be raveled before computing the statistic.
+
+    Returns
+    -------
+    statistic : float
+        The test statistic.
+    pvalue : float
+        The associated p-value based on the asymptotic chi2-distribution.
+
+    See Also
+    --------
+    ks_2samp, anderson_ksamp
+
+    Notes
+    -----
+    Testing whether two samples are generated by the same underlying
+    distribution is a classical question in statistics. A widely used test is
+    the Kolmogorov-Smirnov (KS) test which relies on the empirical
+    distribution function. Epps and Singleton introduce a test based on the
+    empirical characteristic function in [1]_.
+
+    One advantage of the ES test compared to the KS test is that is does
+    not assume a continuous distribution. In [1]_, the authors conclude
+    that the test also has a higher power than the KS test in many
+    examples. They recommend the use of the ES test for discrete samples as
+    well as continuous samples with at least 25 observations each, whereas
+    `anderson_ksamp` is recommended for smaller sample sizes in the
+    continuous case.
+
+    The p-value is computed from the asymptotic distribution of the test
+    statistic which follows a `chi2` distribution. If the sample size of both
+    `x` and `y` is below 25, the small sample correction proposed in [1]_ is
+    applied to the test statistic.
+
+    The default values of `t` are determined in [1]_ by considering
+    various distributions and finding good values that lead to a high power
+    of the test in general. Table III in [1]_ gives the optimal values for
+    the distributions tested in that study. The values of `t` are scaled by
+    the semi-interquartile range in the implementation, see [1]_.
+
+    References
+    ----------
+    .. [1] T. W. Epps and K. J. Singleton, "An omnibus test for the two-sample
+       problem using the empirical characteristic function", Journal of
+       Statistical Computation and Simulation 26, p. 177--203, 1986.
+
+    .. [2] S. J. Goerg and J. Kaiser, "Nonparametric testing of distributions
+       - the Epps-Singleton two-sample test using the empirical characteristic
+       function", The Stata Journal 9(3), p. 454--465, 2009.
+
+    Examples
+    --------
+    Generate random samples ``x`` and ``y``.
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> rng = np.random.default_rng(66326777)
+    >>> x = rng.normal(0, 1, size=100)
+    >>> y = rng.normal(5, 3, size=100)
+
+    Test the null hypothesis that ``x`` and ``y`` are sampled from the same
+    distribution.
+
+    >>> res = stats.epps_singleton_2samp(x, y)
+    >>> res.statistic
+    np.float64(316.6441136688085)
+    >>> res.pvalue
+    np.float64(2.778946959815902e-67)
+    
+    The large value of the statistic and small p-value may be taken as evidence that
+    ``x`` and ``y`` were not sampled from the same distribution. 
+    """
+    xp = array_namespace(x, y)
+    # x and y are converted to arrays by the decorator
+    # and `axis` is guaranteed to be -1.
+    x, y = xp_promote(x, y, force_floating=True, xp=xp)
+    t = xp.asarray(t, dtype=x.dtype)
+    # check if x and y are valid inputs
+    nx, ny = x.shape[-1], y.shape[-1]
+    if (nx < 5) or (ny < 5):  # only used by test_axis_nan_policy
+        raise ValueError('x and y should have at least 5 elements, but len(x) '
+                         f'= {nx} and len(y) = {ny}.')
+    n = nx + ny
+
+    # check if t is valid
+    if t.ndim > 1:
+        raise ValueError(f't must be 1d, but t.ndim equals {t.ndim}.')
+    if is_lazy_array(t):
+        t = xpx.at(t)[t <= 0].set(xp.nan)
+    elif xp.any(t <= 0):
+        raise ValueError('t must contain positive elements only.')
+
+    # Previously, non-finite input caused an error in linalg functions.
+    # To prevent an issue in one slice from halting the calculation, replace non-finite
+    # values with a harmless one, and replace results with NaN at the end.
+    i_x = ~xp.isfinite(x)
+    i_y = ~xp.isfinite(y)
+    # Ideally we would avoid copying all data here; see
+    # discussion in data-apis/array-api-extra#506.
+    x = xp.where(i_x, 1., x)
+    y = xp.where(i_y, 1., y)
+    invalid_result = xp.any(i_x, axis=-1) | xp.any(i_y, axis=-1)
+
+    # rescale t with semi-iqr as proposed in [1]; import iqr here to avoid
+    # circular import
+    from scipy.stats import iqr
+    sigma = iqr(xp.concat((x, y), axis=-1), axis=-1, keepdims=True) / 2
+    ts = xp.reshape(t, (-1,) + (1,)*x.ndim) / sigma
+
+    # covariance estimation of ES test
+    gx = xp.concat((xp.cos(ts*x), xp.sin(ts*x)), axis=0)
+    gy = xp.concat((xp.cos(ts*y), xp.sin(ts*y)), axis=0)
+    gx, gy = xp.moveaxis(gx, 0, -2), xp.moveaxis(gy, 0, -2)
+    cov_x = xpx.cov(gx) * (nx-1)/nx  # the test uses biased cov-estimate
+    cov_y = xpx.cov(gy) * (ny-1)/ny
+    cov_x, cov_y = xp.astype(cov_x, x.dtype), xp.astype(cov_y, y.dtype)
+    est_cov = (n/nx)*cov_x + (n/ny)*cov_y
+    est_cov_inv = xp.linalg.pinv(est_cov)
+    r = xp.asarray(xp.linalg.matrix_rank(est_cov_inv), dtype=est_cov_inv.dtype)
+    if not is_lazy_array(r) and xp.any(r < 2*xp_size(t)):
+        warnings.warn('Estimated covariance matrix does not have full rank. '
+                      'This indicates a bad choice of the input t and the '
+                      'test might not be consistent.', # see p. 183 in [1]_
+                      stacklevel=2)
+
+    # compute test statistic w distributed asympt. as chisquare with df=r
+    g_diff = xp.mean(gx, axis=-1, keepdims=True) - xp.mean(gy, axis=-1, keepdims=True)
+    w = n*xp.matmul(xp.matrix_transpose(g_diff), xp.matmul(est_cov_inv, g_diff))
+    w = w[..., 0, 0]
+
+    # apply small-sample correction
+    if (max(nx, ny) < 25):
+        corr = 1.0/(1.0 + n**(-0.45) + 10.1*(nx**(-1.7) + ny**(-1.7)))
+        w *= corr
+
+    chi2 = _stats_py._SimpleChi2(r)
+    p = _stats_py._get_pvalue(w, chi2, alternative='greater', symmetric=False, xp=xp)
+
+    w = xpx.at(w)[invalid_result].set(xp.nan)
+    p = xpx.at(p)[invalid_result].set(xp.nan)
+    w = w[()] if w.ndim == 0 else w
+    p = p[()] if p.ndim == 0 else p
+    return Epps_Singleton_2sampResult(w, p)
+
+
+@xp_capabilities(np_only=True)
+def poisson_means_test(k1, n1, k2, n2, *, diff=0, alternative='two-sided'):
+    r"""
+    Performs the Poisson means test, AKA the "E-test".
+
+    This is a test of the null hypothesis that the difference between means of
+    two Poisson distributions is `diff`. The samples are provided as the
+    number of events `k1` and `k2` observed within measurement intervals
+    (e.g. of time, space, number of observations) of sizes `n1` and `n2`.
+
+    Parameters
+    ----------
+    k1 : int
+        Number of events observed from distribution 1.
+    n1 : float
+        Size of sample from distribution 1.
+    k2 : int
+        Number of events observed from distribution 2.
+    n2 : float
+        Size of sample from distribution 2.
+    diff : float, default=0
+        The hypothesized difference in means between the distributions
+        underlying the samples.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis.
+        The following options are available (default is 'two-sided'):
+
+        * 'two-sided': the difference between distribution means is not
+          equal to `diff`
+        * 'less': the difference between distribution means is less than
+          `diff`
+        * 'greater': the difference between distribution means is greater
+          than `diff`
+
+    Returns
+    -------
+    statistic : float
+        The test statistic (see [1]_ equation 3.3).
+    pvalue : float
+        The probability of achieving such an extreme value of the test
+        statistic under the null hypothesis.
+
+    Notes
+    -----
+
+    Let:
+
+    .. math:: X_1 \sim \mbox{Poisson}(\mathtt{n1}\lambda_1)
+
+    be a random variable independent of
+
+    .. math:: X_2  \sim \mbox{Poisson}(\mathtt{n2}\lambda_2)
+
+    and let ``k1`` and ``k2`` be the observed values of :math:`X_1`
+    and :math:`X_2`, respectively. Then `poisson_means_test` uses the number
+    of observed events ``k1`` and ``k2`` from samples of size ``n1`` and
+    ``n2``, respectively, to test the null hypothesis that
+
+    .. math::
+       H_0: \lambda_1 - \lambda_2 = \mathtt{diff}
+
+    A benefit of the E-test is that it has good power for small sample sizes,
+    which can reduce sampling costs [1]_. It has been evaluated and determined
+    to be more powerful than the comparable C-test, sometimes referred to as
+    the Poisson exact test.
+
+    References
+    ----------
+    .. [1]  Krishnamoorthy, K., & Thomson, J. (2004). A more powerful test for
+       comparing two Poisson means. Journal of Statistical Planning and
+       Inference, 119(1), 23-35.
+
+    .. [2]  Przyborowski, J., & Wilenski, H. (1940). Homogeneity of results in
+       testing samples from Poisson series: With an application to testing
+       clover seed for dodder. Biometrika, 31(3/4), 313-323.
+
+    Examples
+    --------
+
+    Suppose that a gardener wishes to test the number of dodder (weed) seeds
+    in a sack of clover seeds that they buy from a seed company. It has
+    previously been established that the number of dodder seeds in clover
+    follows the Poisson distribution.
+
+    A 100 gram sample is drawn from the sack before being shipped to the
+    gardener. The sample is analyzed, and it is found to contain no dodder
+    seeds; that is, `k1` is 0. However, upon arrival, the gardener draws
+    another 100 gram sample from the sack. This time, three dodder seeds are
+    found in the sample; that is, `k2` is 3. The gardener would like to
+    know if the difference is significant and not due to chance. The
+    null hypothesis is that the difference between the two samples is merely
+    due to chance, or that :math:`\lambda_1 - \lambda_2 = \mathtt{diff}`
+    where :math:`\mathtt{diff} = 0`. The alternative hypothesis is that the
+    difference is not due to chance, or :math:`\lambda_1 - \lambda_2 \ne 0`.
+    The gardener selects a significance level of 5% to reject the null
+    hypothesis in favor of the alternative [2]_.
+
+    >>> import scipy.stats as stats
+    >>> res = stats.poisson_means_test(0, 100, 3, 100)
+    >>> res.statistic, res.pvalue
+    (-1.7320508075688772, 0.08837900929018157)
+
+    The p-value is .088, indicating a near 9% chance of observing a value of
+    the test statistic under the null hypothesis. This exceeds 5%, so the
+    gardener does not reject the null hypothesis as the difference cannot be
+    regarded as significant at this level.
+    """
+
+    _poisson_means_test_iv(k1, n1, k2, n2, diff, alternative)
+
+    # "for a given k_1 and k_2, an estimate of \lambda_2 is given by" [1] (3.4)
+    lmbd_hat2 = ((k1 + k2) / (n1 + n2) - diff * n1 / (n1 + n2))
+
+    # "\hat{\lambda_{2k}} may be less than or equal to zero ... and in this
+    # case the null hypothesis cannot be rejected ... [and] it is not necessary
+    # to compute the p-value". [1] page 26 below eq. (3.6).
+    if lmbd_hat2 <= 0:
+        return _stats_py.SignificanceResult(0, 1)
+
+    # The unbiased variance estimate [1] (3.2)
+    var = k1 / (n1 ** 2) + k2 / (n2 ** 2)
+
+    # The _observed_ pivot statistic from the input. It follows the
+    # unnumbered equation following equation (3.3) This is used later in
+    # comparison with the computed pivot statistics in an indicator function.
+    t_k1k2 = (k1 / n1 - k2 / n2 - diff) / np.sqrt(var)
+
+    # Equation (3.5) of [1] is lengthy, so it is broken into several parts,
+    # beginning here. Note that the probability mass function of poisson is
+    # exp^(-\mu)*\mu^k/k!, so and this is called with shape \mu, here noted
+    # here as nlmbd_hat*. The strategy for evaluating the double summation in
+    # (3.5) is to create two arrays of the values of the two products inside
+    # the summation and then broadcast them together into a matrix, and then
+    # sum across the entire matrix.
+
+    # Compute constants (as seen in the first and second separated products in
+    # (3.5).). (This is the shape (\mu) parameter of the poisson distribution.)
+    nlmbd_hat1 = n1 * (lmbd_hat2 + diff)
+    nlmbd_hat2 = n2 * lmbd_hat2
+
+    # Determine summation bounds for tail ends of distribution rather than
+    # summing to infinity. `x1*` is for the outer sum and `x2*` is the inner
+    # sum.
+    x1_lb, x1_ub = distributions.poisson.ppf([1e-10, 1 - 1e-16], nlmbd_hat1)
+    x2_lb, x2_ub = distributions.poisson.ppf([1e-10, 1 - 1e-16], nlmbd_hat2)
+
+    # Construct arrays to function as the x_1 and x_2 counters on the summation
+    # in (3.5). `x1` is in columns and `x2` is in rows to allow for
+    # broadcasting.
+    x1 = np.arange(x1_lb, x1_ub + 1)
+    x2 = np.arange(x2_lb, x2_ub + 1)[:, None]
+
+    # These are the two products in equation (3.5) with `prob_x1` being the
+    # first (left side) and `prob_x2` being the second (right side). (To
+    # make as clear as possible: the 1st contains a "+ d" term, the 2nd does
+    # not.)
+    prob_x1 = distributions.poisson.pmf(x1, nlmbd_hat1)
+    prob_x2 = distributions.poisson.pmf(x2, nlmbd_hat2)
+
+    # compute constants for use in the "pivot statistic" per the
+    # unnumbered equation following (3.3).
+    lmbd_x1 = x1 / n1
+    lmbd_x2 = x2 / n2
+    lmbds_diff = lmbd_x1 - lmbd_x2 - diff
+    var_x1x2 = lmbd_x1 / n1 + lmbd_x2 / n2
+
+    # This is the 'pivot statistic' for use in the indicator of the summation
+    # (left side of "I[.]").
+    with np.errstate(invalid='ignore', divide='ignore'):
+        t_x1x2 = lmbds_diff / np.sqrt(var_x1x2)
+
+    # `[indicator]` implements the "I[.] ... the indicator function" per
+    # the paragraph following equation (3.5).
+    if alternative == 'two-sided':
+        indicator = np.abs(t_x1x2) >= np.abs(t_k1k2)
+    elif alternative == 'less':
+        indicator = t_x1x2 <= t_k1k2
+    else:
+        indicator = t_x1x2 >= t_k1k2
+
+    # Multiply all combinations of the products together, exclude terms
+    # based on the `indicator` and then sum. (3.5)
+    pvalue = np.sum((prob_x1 * prob_x2)[indicator])
+    return _stats_py.SignificanceResult(t_k1k2, pvalue)
+
+
+def _poisson_means_test_iv(k1, n1, k2, n2, diff, alternative):
+    # """check for valid types and values of input to `poisson_mean_test`."""
+    if k1 != int(k1) or k2 != int(k2):
+        raise TypeError('`k1` and `k2` must be integers.')
+
+    count_err = '`k1` and `k2` must be greater than or equal to 0.'
+    if k1 < 0 or k2 < 0:
+        raise ValueError(count_err)
+
+    if n1 <= 0 or n2 <= 0:
+        raise ValueError('`n1` and `n2` must be greater than 0.')
+
+    if diff < 0:
+        raise ValueError('diff must be greater than or equal to 0.')
+
+    alternatives = {'two-sided', 'less', 'greater'}
+    if alternative.lower() not in alternatives:
+        raise ValueError(f"Alternative must be one of '{alternatives}'.")
+
+
+class CramerVonMisesResult:
+    def __init__(self, statistic, pvalue):
+        self.statistic = statistic
+        self.pvalue = pvalue
+
+    def __repr__(self):
+        return (f"{self.__class__.__name__}(statistic={self.statistic}, "
+                f"pvalue={self.pvalue})")
+
+
+def _psi1_mod(x, *, xp=None):
+    """
+    psi1 is defined in equation 1.10 in Csörgő, S. and Faraway, J. (1996).
+    This implements a modified version by excluding the term V(x) / 12
+    (here: _cdf_cvm_inf(x) / 12) to avoid evaluating _cdf_cvm_inf(x)
+    twice in _cdf_cvm.
+
+    Implementation based on MAPLE code of Julian Faraway and R code of the
+    function pCvM in the package goftest (v1.1.1), permission granted
+    by Adrian Baddeley. Main difference in the implementation: the code
+    here keeps adding terms of the series until the terms are small enough.
+    """
+    xp = array_namespace(x) if xp is None else xp
+
+    def _ed2(y):
+        z = y**2 / 4
+        z_ = np.asarray(z)
+        b = xp.asarray(kv(1/4, z_) + kv(3/4, z_))
+        return xp.exp(-z) * (y/2)**(3/2) * b / math.sqrt(np.pi)
+
+    def _ed3(y):
+        z = y**2 / 4
+        z_ = np.asarray(z)
+        c = xp.exp(-z) / math.sqrt(np.pi)
+        kv_terms = xp.asarray(2*kv(1/4, z_)
+                              + 3*kv(3/4, z_) - kv(5/4, z_))
+        return c * (y/2)**(5/2) * kv_terms
+
+    def _Ak(k, x):
+        m = 2*k + 1
+        sx = 2 * xp.sqrt(x)
+        y1 = x**(3/4)
+        y2 = x**(5/4)
+
+        gamma_kp1_2 = float(gamma(k + 1 / 2))
+        gamma_kp3_2 = float(gamma(k + 3 / 2))
+
+        e1 = m * gamma_kp1_2 * _ed2((4 * k + 3)/sx) / (9 * y1)
+        e2 = gamma_kp1_2 * _ed3((4 * k + 1) / sx) / (72 * y2)
+        e3 = 2 * (m + 2) * gamma_kp3_2 * _ed3((4 * k + 5) / sx) / (12 * y2)
+        e4 = 7 * m * gamma_kp1_2 * _ed2((4 * k + 1) / sx) / (144 * y1)
+        e5 = 7 * m * gamma_kp1_2 * _ed2((4 * k + 5) / sx) / (144 * y1)
+
+        return e1 + e2 + e3 + e4 + e5
+
+    x = xp.asarray(x)
+    tot = xp.zeros_like(x)
+    cond = xp.ones_like(x, dtype=xp.bool)
+    k = 0
+    while xp.any(cond):
+        gamma_kp1 = float(gamma(k + 1))
+        z = -_Ak(k, x[cond]) / (xp.pi * gamma_kp1)
+        tot = xpx.at(tot)[cond].set(tot[cond] + z)
+        # For float32 arithmetic, the tolerance may need to be adjusted or the
+        # algorithm may prove to be unsuitable.
+        cond = xpx.at(cond)[xp_copy(cond)].set(xp.abs(z) >= 1e-7)
+        k += 1
+
+    return tot
+
+
+def _cdf_cvm_inf(x, *, xp=None):
+    """
+    Calculate the cdf of the Cramér-von Mises statistic (infinite sample size).
+
+    See equation 1.2 in Csörgő, S. and Faraway, J. (1996).
+
+    Implementation based on MAPLE code of Julian Faraway and R code of the
+    function pCvM in the package goftest (v1.1.1), permission granted
+    by Adrian Baddeley. Main difference in the implementation: the code
+    here keeps adding terms of the series until the terms are small enough.
+
+    The function is not expected to be accurate for large values of x, say
+    x > 4, when the cdf is very close to 1.
+    """
+    xp = array_namespace(x) if xp is None else xp
+    x = xp.asarray(x)
+
+    def term(x, k):
+        # this expression can be found in [2], second line of (1.3)
+        u = math.exp(gammaln(k + 0.5) - gammaln(k+1)) / (xp.pi**1.5 * xp.sqrt(x))
+        y = 4*k + 1
+        q = y**2 / (16*x)
+        b = xp.asarray(kv(0.25, np.asarray(q)), dtype=u.dtype)  # not automatic?
+        return u * math.sqrt(y) * xp.exp(-q) * b
+
+    tot = xp.zeros_like(x, dtype=x.dtype)
+    cond = xp.ones_like(x, dtype=xp.bool)
+    k = 0
+    while xp.any(cond):
+        z = term(x[cond], k)
+        # tot[cond] = tot[cond] + z
+        tot = xpx.at(tot)[cond].add(z)
+        # cond[cond] = np.abs(z) >= 1e-7
+        cond = xpx.at(cond)[xp_copy(cond)].set(xp.abs(z) >= 1e-7)  # torch needs copy
+        k += 1
+
+    return tot
+
+
+def _cdf_cvm(x, n=None, *, xp=None):
+    """
+    Calculate the cdf of the Cramér-von Mises statistic for a finite sample
+    size n. If N is None, use the asymptotic cdf (n=inf).
+
+    See equation 1.8 in Csörgő, S. and Faraway, J. (1996) for finite samples,
+    1.2 for the asymptotic cdf.
+
+    The function is not expected to be accurate for large values of x, say
+    x > 2, when the cdf is very close to 1 and it might return values > 1
+    in that case, e.g. _cdf_cvm(2.0, 12) = 1.0000027556716846. Moreover, it
+    is not accurate for small values of n, especially close to the bounds of
+    the distribution's domain, [1/(12*n), n/3], where the value jumps to 0
+    and 1, respectively. These are limitations of the approximation by Csörgő
+    and Faraway (1996) implemented in this function.
+    """
+    xp = array_namespace(x) if xp is None else xp
+    x = xp.asarray(x)
+
+    if n is None:
+        y = _cdf_cvm_inf(x, xp=xp)
+    else:
+        # support of the test statistic is [12/n, n/3], see 1.1 in [2]
+        y = xp.zeros_like(x, dtype=x.dtype)
+        sup = (1./(12*n) < x) & (x < n/3.)
+        # note: _psi1_mod does not include the term _cdf_cvm_inf(x) / 12
+        # therefore, we need to add it here
+        y = xpx.at(y)[sup].set(_cdf_cvm_inf(x[sup], xp=xp) * (1 + 1./(12*n))
+                               + _psi1_mod(x[sup], xp=xp) / n)
+        y = xpx.at(y)[x >= n/3].set(1.)
+
+    return y[()] if y.ndim == 0 else y
+
+
+def _cvm_result_to_tuple(res, _):
+    return res.statistic, res.pvalue
+
+
+@xp_capabilities(cpu_only=True,  # needs special function `kv`
+                 skip_backends=[('dask.array', 'typical dask issues')],
+                 jax_jit=False,  # array boolean indices must be concrete
+                 marray=True)
+@_axis_nan_policy_factory(CramerVonMisesResult, n_samples=1, too_small=1,
+                          result_to_tuple=_cvm_result_to_tuple)
+def cramervonmises(rvs, cdf, args=(), *, axis=0):
+    r"""Perform the one-sample Cramér-von Mises test for goodness of fit.
+
+    This performs a test of the goodness of fit of a cumulative distribution
+    function (cdf) :math:`F` compared to the empirical distribution function
+    :math:`F_n` of observed random variates :math:`X_1, ..., X_n` that are
+    assumed to be independent and identically distributed ([1]_).
+    The null hypothesis is that the :math:`X_i` have cumulative distribution
+    :math:`F`.
+
+    The test statistic :math:`T` is defined as in [1]_, where :math:`\omega^2`
+    is the Cramér-von Mises criterion and :math:`x_i` are the observed values.
+
+    .. math::
+        T = n\omega^2 =
+        \frac{1}{12n} + \sum_{i=1}^n \left[ \frac{2i-1}{2n} - F(x_i) \right]^2
+
+    Parameters
+    ----------
+    rvs : array_like
+        A 1-D array of observed values of the random variables :math:`X_i`.
+        The sample must contain at least two observations.
+    cdf : str or callable
+        The cumulative distribution function :math:`F` to test the
+        observations against. If a string, it should be the name of a
+        distribution in `scipy.stats`. If a callable, that callable is used
+        to calculate the cdf: ``cdf(x, *args) -> float``.
+    args : tuple, optional
+        Distribution parameters. These are assumed to be known; see Notes.
+    axis : int or tuple of ints, default: 0
+        If an int or tuple of ints, the axis or axes of the input along which
+        to compute the statistic. The statistic of each axis-slice (e.g. row)
+        of the input will appear in a corresponding element of the output.
+        If ``None``, the input will be raveled before computing the statistic.
+
+    Returns
+    -------
+    res : object with attributes
+        statistic : float
+            Cramér-von Mises statistic :math:`T`.
+        pvalue : float
+            The p-value.
+
+    See Also
+    --------
+    kstest, cramervonmises_2samp
+
+    Notes
+    -----
+    .. versionadded:: 1.6.0
+
+    The p-value relies on the approximation given by equation 1.8 in [2]_.
+    It is important to keep in mind that the p-value is only accurate if
+    one tests a simple hypothesis, i.e. the parameters of the reference
+    distribution are known. If the parameters are estimated from the data
+    (composite hypothesis), the computed p-value is not reliable.
+
+    References
+    ----------
+    .. [1] Cramér-von Mises criterion, Wikipedia,
+           https://en.wikipedia.org/wiki/Cram%C3%A9r%E2%80%93von_Mises_criterion
+    .. [2] Csörgő, S. and Faraway, J. (1996). The Exact and Asymptotic
+           Distribution of Cramér-von Mises Statistics. Journal of the
+           Royal Statistical Society, pp. 221-234.
+
+    Examples
+    --------
+
+    Suppose we wish to test whether data generated by ``scipy.stats.norm.rvs``
+    were, in fact, drawn from the standard normal distribution. We choose a
+    significance level of ``alpha=0.05``.
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> rng = np.random.default_rng(165417232101553420507139617764912913465)
+    >>> x = stats.norm.rvs(size=500, random_state=rng)
+    >>> res = stats.cramervonmises(x, 'norm')
+    >>> res.statistic, res.pvalue
+    (0.1072085112565724, 0.5508482238203407)
+
+    The p-value exceeds our chosen significance level, so we do not
+    reject the null hypothesis that the observed sample is drawn from the
+    standard normal distribution.
+
+    Now suppose we wish to check whether the same samples shifted by 2.1 is
+    consistent with being drawn from a normal distribution with a mean of 2.
+
+    >>> y = x + 2.1
+    >>> res = stats.cramervonmises(y, 'norm', args=(2,))
+    >>> res.statistic, res.pvalue
+    (0.8364446265294695, 0.00596286797008283)
+
+    Here we have used the `args` keyword to specify the mean (``loc``)
+    of the normal distribution to test the data against. This is equivalent
+    to the following, in which we create a frozen normal distribution with
+    mean 2.1, then pass its ``cdf`` method as an argument.
+
+    >>> frozen_dist = stats.norm(loc=2)
+    >>> res = stats.cramervonmises(y, frozen_dist.cdf)
+    >>> res.statistic, res.pvalue
+    (0.8364446265294695, 0.00596286797008283)
+
+    In either case, we would reject the null hypothesis that the observed
+    sample is drawn from a normal distribution with a mean of 2 (and default
+    variance of 1) because the p-value is less than our chosen
+    significance level.
+
+    """
+    # `_axis_nan_policy` decorator ensures `axis=-1`
+    xp = array_namespace(rvs)
+
+    if isinstance(cdf, str) and is_numpy(xp):
+        cdf = getattr(distributions, cdf).cdf
+    elif isinstance(cdf, str):
+        message = "`cdf` must be a callable if `rvs` is a non-NumPy array."
+        raise ValueError(message)
+
+    n_length = rvs.shape[-1]
+    if n_length <= 1:  # only needed for `test_axis_nan_policy.py`; not user-facing
+        raise ValueError('The sample must contain at least two observations.')
+
+    rvs = xp_promote(rvs, force_floating=True, xp=xp)
+    vals = xp.sort(rvs, axis=-1)
+    cdfvals = _masked_apply(cdf, args=(vals, *args), xp=xp)
+    n_count = xp.asarray(_count_nonmasked(rvs, axis=-1, xp=xp), dtype=rvs.dtype)
+
+    u = (2*xp.arange(1, n_length+1, dtype=rvs.dtype) - 1)/(2*n_count[..., xp.newaxis])
+    w = 1/(12*n_count) + xp.sum((u - cdfvals)**2, axis=-1)
+
+    # avoid small negative values that can occur due to the approximation
+    p = xp.clip(1. - _masked_apply(_cdf_cvm, args=(w, n_count), xp=xp), 0., None)
+
+    return CramerVonMisesResult(statistic=w, pvalue=p)
+
+
+def _get_wilcoxon_distr(n):
+    """
+    Distribution of probability of the Wilcoxon ranksum statistic r_plus (sum
+    of ranks of positive differences).
+    Returns an array with the probabilities of all the possible ranks
+    r = 0, ..., n*(n+1)/2
+    """
+    c = np.ones(1, dtype=np.float64)
+    for k in range(1, n + 1):
+        prev_c = c
+        c = np.zeros(k * (k + 1) // 2 + 1, dtype=np.float64)
+        m = len(prev_c)
+        c[:m] = prev_c * 0.5
+        c[-m:] += prev_c * 0.5
+    return c
+
+
+def _get_wilcoxon_distr2(n):
+    """
+    Distribution of probability of the Wilcoxon ranksum statistic r_plus (sum
+    of ranks of positive differences).
+    Returns an array with the probabilities of all the possible ranks
+    r = 0, ..., n*(n+1)/2
+    This is a slower reference function
+    References
+    ----------
+    .. [1] 1. Harris T, Hardin JW. Exact Wilcoxon Signed-Rank and Wilcoxon
+        Mann-Whitney Ranksum Tests. The Stata Journal. 2013;13(2):337-343.
+    """
+    ai = np.arange(1, n+1)[:, None]
+    t = n*(n+1)/2
+    q = 2*t
+    j = np.arange(q)
+    theta = 2*np.pi/q*j
+    phi_sp = np.prod(np.cos(theta*ai), axis=0)
+    phi_s = np.exp(1j*theta*t) * phi_sp
+    p = np.real(ifft(phi_s))
+    res = np.zeros(int(t)+1)
+    res[:-1:] = p[::2]
+    res[0] /= 2
+    res[-1] = res[0]
+    return res
+
+
+def _tau_b(A):
+    """Calculate Kendall's tau-b and p-value from contingency table."""
+    # See [2] 2.2 and 4.2
+
+    # contingency table must be truly 2D
+    if A.shape[0] == 1 or A.shape[1] == 1:
+        return np.nan, np.nan
+
+    NA = A.sum()
+    PA = _P(A)
+    QA = _Q(A)
+    Sri2 = (A.sum(axis=1)**2).sum()
+    Scj2 = (A.sum(axis=0)**2).sum()
+    denominator = (NA**2 - Sri2)*(NA**2 - Scj2)
+
+    tau = (PA-QA)/(denominator)**0.5
+
+    numerator = 4*(_a_ij_Aij_Dij2(A) - (PA - QA)**2 / NA)
+    s02_tau_b = numerator/denominator
+    if s02_tau_b == 0:  # Avoid divide by zero
+        return tau, 0
+    Z = tau/s02_tau_b**0.5
+    p = 2*norm.sf(abs(Z))  # 2-sided p-value
+
+    return tau, p
+
+
+def _somers_d(A, alternative='two-sided'):
+    """Calculate Somers' D and p-value from contingency table."""
+    # See [3] page 1740
+
+    # contingency table must be truly 2D
+    if A.shape[0] <= 1 or A.shape[1] <= 1:
+        return np.nan, np.nan
+
+    NA = A.sum()
+    NA2 = NA**2
+    PA = _P(A)
+    QA = _Q(A)
+    Sri2 = (A.sum(axis=1)**2).sum()
+
+    d = (PA - QA)/(NA2 - Sri2)
+
+    S = _a_ij_Aij_Dij2(A) - (PA-QA)**2/NA
+
+    with np.errstate(divide='ignore'):
+        Z = (PA - QA)/(4*(S))**0.5
+
+    norm = _stats_py._SimpleNormal()
+    p = _stats_py._get_pvalue(Z, norm, alternative, xp=np)
+
+    return d, p
+
+
+@dataclass
+class SomersDResult:
+    statistic: float
+    pvalue: float
+    table: np.ndarray
+
+
+@xp_capabilities(np_only=True)
+def somersd(x, y=None, alternative='two-sided'):
+    r"""Calculates Somers' D, an asymmetric measure of ordinal association.
+
+    Like Kendall's :math:`\tau`, Somers' :math:`D` is a measure of the
+    correspondence between two rankings. Both statistics consider the
+    difference between the number of concordant and discordant pairs in two
+    rankings :math:`X` and :math:`Y`, and both are normalized such that values
+    close  to 1 indicate strong agreement and values close to -1 indicate
+    strong disagreement. They differ in how they are normalized. To show the
+    relationship, Somers' :math:`D` can be defined in terms of Kendall's
+    :math:`\tau_a`:
+
+    .. math::
+        D(Y|X) = \frac{\tau_a(X, Y)}{\tau_a(X, X)}
+
+    Suppose the first ranking :math:`X` has :math:`r` distinct ranks and the
+    second ranking :math:`Y` has :math:`s` distinct ranks. These two lists of
+    :math:`n` rankings can also be viewed as an :math:`r \times s` contingency
+    table in which element :math:`i, j` is the number of rank pairs with rank
+    :math:`i` in ranking :math:`X` and rank :math:`j` in ranking :math:`Y`.
+    Accordingly, `somersd` also allows the input data to be supplied as a
+    single, 2D contingency table instead of as two separate, 1D rankings.
+
+    Note that the definition of Somers' :math:`D` is asymmetric: in general,
+    :math:`D(Y|X) \neq D(X|Y)`. ``somersd(x, y)`` calculates Somers'
+    :math:`D(Y|X)`: the "row" variable :math:`X` is treated as an independent
+    variable, and the "column" variable :math:`Y` is dependent. For Somers'
+    :math:`D(X|Y)`, swap the input lists or transpose the input table.
+
+    Parameters
+    ----------
+    x : array_like
+        1D array of rankings, treated as the (row) independent variable.
+        Alternatively, a 2D contingency table.
+    y : array_like, optional
+        If `x` is a 1D array of rankings, `y` is a 1D array of rankings of the
+        same length, treated as the (column) dependent variable.
+        If `x` is 2D, `y` is ignored.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis. Default is 'two-sided'.
+        The following options are available:
+
+        * 'two-sided': the rank correlation is nonzero
+        * 'less': the rank correlation is negative (less than zero)
+        * 'greater':  the rank correlation is positive (greater than zero)
+
+    Returns
+    -------
+    res : SomersDResult
+        A `SomersDResult` object with the following fields:
+
+        statistic : float
+           The Somers' :math:`D` statistic.
+        pvalue : float
+           The p-value for a hypothesis test whose null
+           hypothesis is an absence of association, :math:`D=0`.
+           See notes for more information.
+        table : 2D array
+           The contingency table formed from rankings `x` and `y` (or the
+           provided contingency table, if `x` is a 2D array)
+
+    See Also
+    --------
+    kendalltau : Calculates Kendall's tau, another correlation measure.
+    weightedtau : Computes a weighted version of Kendall's tau.
+    spearmanr : Calculates a Spearman rank-order correlation coefficient.
+    pearsonr : Calculates a Pearson correlation coefficient.
+
+    Notes
+    -----
+    This function follows the contingency table approach of [2]_ and
+    [3]_. *p*-values are computed based on an asymptotic approximation of
+    the test statistic distribution under the null hypothesis :math:`D=0`.
+
+    Theoretically, hypothesis tests based on Kendall's :math:`tau` and Somers'
+    :math:`D` should be identical.
+    However, the *p*-values returned by `kendalltau` are based
+    on the null hypothesis of *independence* between :math:`X` and :math:`Y`
+    (i.e. the population from which pairs in :math:`X` and :math:`Y` are
+    sampled contains equal numbers of all possible pairs), which is more
+    specific than the null hypothesis :math:`D=0` used here. If the null
+    hypothesis of independence is desired, it is acceptable to use the
+    *p*-value returned by `kendalltau` with the statistic returned by
+    `somersd` and vice versa. For more information, see [2]_.
+
+    Contingency tables are formatted according to the convention used by
+    SAS and R: the first ranking supplied (``x``) is the "row" variable, and
+    the second ranking supplied (``y``) is the "column" variable. This is
+    opposite the convention of Somers' original paper [1]_.
+
+    References
+    ----------
+    .. [1] Robert H. Somers, "A New Asymmetric Measure of Association for
+           Ordinal Variables", *American Sociological Review*, Vol. 27, No. 6,
+           pp. 799--811, 1962.
+
+    .. [2] Morton B. Brown and Jacqueline K. Benedetti, "Sampling Behavior of
+           Tests for Correlation in Two-Way Contingency Tables", *Journal of
+           the American Statistical Association* Vol. 72, No. 358, pp.
+           309--315, 1977.
+
+    .. [3] SAS Institute, Inc., "The FREQ Procedure (Book Excerpt)",
+           *SAS/STAT 9.2 User's Guide, Second Edition*, SAS Publishing, 2009.
+
+    .. [4] Laerd Statistics, "Somers' d using SPSS Statistics", *SPSS
+           Statistics Tutorials and Statistical Guides*,
+           https://statistics.laerd.com/spss-tutorials/somers-d-using-spss-statistics.php,
+           Accessed July 31, 2020.
+
+    Examples
+    --------
+    We calculate Somers' D for the example given in [4]_, in which a hotel
+    chain owner seeks to determine the association between hotel room
+    cleanliness and customer satisfaction. The independent variable, hotel
+    room cleanliness, is ranked on an ordinal scale: "below average (1)",
+    "average (2)", or "above average (3)". The dependent variable, customer
+    satisfaction, is ranked on a second scale: "very dissatisfied (1)",
+    "moderately dissatisfied (2)", "neither dissatisfied nor satisfied (3)",
+    "moderately satisfied (4)", or "very satisfied (5)". 189 customers
+    respond to the survey, and the results are cast into a contingency table
+    with the hotel room cleanliness as the "row" variable and customer
+    satisfaction as the "column" variable.
+
+    +-----+-----+-----+-----+-----+-----+
+    |     | (1) | (2) | (3) | (4) | (5) |
+    +=====+=====+=====+=====+=====+=====+
+    | (1) | 27  | 25  | 14  | 7   | 0   |
+    +-----+-----+-----+-----+-----+-----+
+    | (2) | 7   | 14  | 18  | 35  | 12  |
+    +-----+-----+-----+-----+-----+-----+
+    | (3) | 1   | 3   | 2   | 7   | 17  |
+    +-----+-----+-----+-----+-----+-----+
+
+    For example, 27 customers assigned their room a cleanliness ranking of
+    "below average (1)" and a corresponding satisfaction of "very
+    dissatisfied (1)". We perform the analysis as follows.
+
+    >>> from scipy.stats import somersd
+    >>> table = [[27, 25, 14, 7, 0], [7, 14, 18, 35, 12], [1, 3, 2, 7, 17]]
+    >>> res = somersd(table)
+    >>> res.statistic
+    0.6032766111513396
+    >>> res.pvalue
+    1.0007091191074533e-27
+
+    The value of the Somers' D statistic is approximately 0.6, indicating
+    a positive correlation between room cleanliness and customer satisfaction
+    in the sample.
+    The *p*-value is very small, indicating a very small probability of
+    observing such an extreme value of the statistic under the null
+    hypothesis that the statistic of the entire population (from which
+    our sample of 189 customers is drawn) is zero. This supports the
+    alternative hypothesis that the true value of Somers' D for the population
+    is nonzero.
+
+    """
+    x, y = np.array(x), np.array(y)
+    if x.ndim == 1:
+        if x.size != y.size:
+            raise ValueError("Rankings must be of equal length.")
+        table = scipy.stats.contingency.crosstab(x, y)[1]
+    elif x.ndim == 2:
+        if np.any(x < 0):
+            raise ValueError("All elements of the contingency table must be "
+                             "non-negative.")
+        if np.any(x != x.astype(int)):
+            raise ValueError("All elements of the contingency table must be "
+                             "integer.")
+        if x.nonzero()[0].size < 2:
+            raise ValueError("At least two elements of the contingency table "
+                             "must be nonzero.")
+        table = x
+    else:
+        raise ValueError("x must be either a 1D or 2D array")
+    # The table type is converted to a float to avoid an integer overflow
+    d, p = _somers_d(table.astype(float), alternative)
+
+    # add alias for consistency with other correlation functions
+    res = SomersDResult(d, p, table)
+    res.correlation = d
+    return res
+
+
+# This could be combined with `_all_partitions` in `_resampling.py`
+def _all_partitions(nx, ny):
+    """
+    Partition a set of indices into two fixed-length sets in all possible ways
+
+    Partition a set of indices 0 ... nx + ny - 1 into two sets of length nx and
+    ny in all possible ways (ignoring order of elements).
+    """
+    z = np.arange(nx+ny)
+    for c in combinations(z, nx):
+        x = np.array(c)
+        mask = np.ones(nx+ny, bool)
+        mask[x] = False
+        y = z[mask]
+        yield x, y
+
+
+def _compute_log_combinations(n):
+    """Compute all log combination of C(n, k)."""
+    gammaln_arr = gammaln(np.arange(n + 1) + 1)
+    return gammaln(n + 1) - gammaln_arr - gammaln_arr[::-1]
+
+
+@dataclass
+class BarnardExactResult:
+    statistic: float
+    pvalue: float
+
+
+@xp_capabilities(np_only=True)
+def barnard_exact(table, alternative="two-sided", pooled=True, n=32):
+    r"""Perform a Barnard exact test on a 2x2 contingency table.
+
+    Parameters
+    ----------
+    table : array_like of ints
+        A 2x2 contingency table.  Elements should be non-negative integers.
+
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the null and alternative hypotheses. Default is 'two-sided'.
+        Please see explanations in the Notes section below.
+
+    pooled : bool, optional
+        Whether to compute score statistic with pooled variance (as in
+        Student's t-test, for example) or unpooled variance (as in Welch's
+        t-test). Default is ``True``.
+
+    n : int, optional
+        Number of sampling points used in the construction of the sampling
+        method. Note that this argument will automatically be converted to
+        the next higher power of 2 since `scipy.stats.qmc.Sobol` is used to
+        select sample points. Default is 32. Must be positive. In most cases,
+        32 points is enough to reach good precision. More points comes at
+        performance cost.
+
+    Returns
+    -------
+    ber : BarnardExactResult
+        A result object with the following attributes.
+
+        statistic : float
+            The Wald statistic with pooled or unpooled variance, depending
+            on the user choice of `pooled`.
+
+        pvalue : float
+            P-value, the probability of obtaining a distribution at least as
+            extreme as the one that was actually observed, assuming that the
+            null hypothesis is true.
+
+    See Also
+    --------
+    chi2_contingency : Chi-square test of independence of variables in a
+        contingency table.
+    fisher_exact : Fisher exact test on a 2x2 contingency table.
+    boschloo_exact : Boschloo's exact test on a 2x2 contingency table,
+        which is a uniformly more powerful alternative to Fisher's exact test.
+
+    Notes
+    -----
+    Barnard's test is an exact test used in the analysis of contingency
+    tables. It examines the association of two categorical variables, and
+    is a more powerful alternative than Fisher's exact test
+    for 2x2 contingency tables.
+
+    Let's define :math:`X_0` a 2x2 matrix representing the observed sample,
+    where each column stores the binomial experiment, as in the example
+    below. Let's also define :math:`p_1, p_2` the theoretical binomial
+    probabilities for  :math:`x_{11}` and :math:`x_{12}`. When using
+    Barnard exact test, we can assert three different null hypotheses :
+
+    - :math:`H_0 : p_1 \geq p_2` versus :math:`H_1 : p_1 < p_2`,
+      with `alternative` = "less"
+
+    - :math:`H_0 : p_1 \leq p_2` versus :math:`H_1 : p_1 > p_2`,
+      with `alternative` = "greater"
+
+    - :math:`H_0 : p_1 = p_2` versus :math:`H_1 : p_1 \neq p_2`,
+      with `alternative` = "two-sided" (default one)
+
+    In order to compute Barnard's exact test, we are using the Wald
+    statistic [3]_ with pooled or unpooled variance.
+    Under the default assumption that both variances are equal
+    (``pooled = True``), the statistic is computed as:
+
+    .. math::
+
+        T(X) = \frac{
+            \hat{p}_1 - \hat{p}_2
+        }{
+            \sqrt{
+                \hat{p}(1 - \hat{p})
+                (\frac{1}{c_1} +
+                \frac{1}{c_2})
+            }
+        }
+
+    with :math:`\hat{p}_1, \hat{p}_2` and :math:`\hat{p}` the estimator of
+    :math:`p_1, p_2` and :math:`p`, the latter being the combined probability,
+    given the assumption that :math:`p_1 = p_2`.
+
+    If this assumption is invalid (``pooled = False``), the statistic is:
+
+    .. math::
+
+        T(X) = \frac{
+            \hat{p}_1 - \hat{p}_2
+        }{
+            \sqrt{
+                \frac{\hat{p}_1 (1 - \hat{p}_1)}{c_1} +
+                \frac{\hat{p}_2 (1 - \hat{p}_2)}{c_2}
+            }
+        }
+
+    The p-value is then computed as:
+
+    .. math::
+
+        \sum
+            \binom{c_1}{x_{11}}
+            \binom{c_2}{x_{12}}
+            \pi^{x_{11} + x_{12}}
+            (1 - \pi)^{t - x_{11} - x_{12}}
+
+    where the sum is over all  2x2 contingency tables :math:`X` such that:
+
+    * :math:`T(X) \leq T(X_0)` when `alternative` = "less",
+    * :math:`T(X) \geq T(X_0)` when `alternative` = "greater", or
+    * :math:`T(X) \geq |T(X_0)|` when `alternative` = "two-sided".
+
+    Above, :math:`c_1, c_2` are the sum of the columns 1 and 2,
+    and :math:`t` the total (sum of the 4 sample's element).
+
+    The returned p-value is the maximum p-value taken over the nuisance
+    parameter :math:`\pi`, where :math:`0 \leq \pi \leq 1`.
+
+    This function's complexity is :math:`O(n c_1 c_2)`, where `n` is the
+    number of sample points.
+
+    References
+    ----------
+    .. [1] Barnard, G. A. "Significance Tests for 2x2 Tables". *Biometrika*.
+           34.1/2 (1947): 123-138. :doi:`10.2307/2332517`.
+
+    .. [2] Mehta, Cyrus R., and Pralay Senchaudhuri. "Conditional versus
+           unconditional exact tests for comparing two binomials."
+           *Cytel Software Corporation* 675 (2003): 1-5.
+
+    .. [3] "Wald Test". *Wikipedia*. https://en.wikipedia.org/wiki/Wald_test
+
+    Examples
+    --------
+    An example use of Barnard's test is presented in [2]_.
+
+        Consider the following example of a vaccine efficacy study
+        (Chan, 1998). In a randomized clinical trial of 30 subjects, 15 were
+        inoculated with a recombinant DNA influenza vaccine and the 15 were
+        inoculated with a placebo. Twelve of the 15 subjects in the placebo
+        group (80%) eventually became infected with influenza whereas for the
+        vaccine group, only 7 of the 15 subjects (47%) became infected. The
+        data are tabulated as a 2 x 2 table::
+
+                Vaccine  Placebo
+            Yes     7        12
+            No      8        3
+
+    When working with statistical hypothesis testing, we usually use a
+    threshold probability or significance level upon which we decide
+    to reject the null hypothesis :math:`H_0`. Suppose we choose the common
+    significance level of 5%.
+
+    Our alternative hypothesis is that the vaccine will lower the chance of
+    becoming infected with the virus; that is, the probability :math:`p_1` of
+    catching the virus with the vaccine will be *less than* the probability
+    :math:`p_2` of catching the virus without the vaccine.  Therefore, we call
+    `barnard_exact` with the ``alternative="less"`` option:
+
+    >>> import scipy.stats as stats
+    >>> res = stats.barnard_exact([[7, 12], [8, 3]], alternative="less")
+    >>> res.statistic
+    -1.894
+    >>> res.pvalue
+    0.03407
+
+    Under the null hypothesis that the vaccine will not lower the chance of
+    becoming infected, the probability of obtaining test results at least as
+    extreme as the observed data is approximately 3.4%. Since this p-value is
+    less than our chosen significance level, we have evidence to reject
+    :math:`H_0` in favor of the alternative.
+
+    Suppose we had used Fisher's exact test instead:
+
+    >>> _, pvalue = stats.fisher_exact([[7, 12], [8, 3]], alternative="less")
+    >>> pvalue
+    0.0640
+
+    With the same threshold significance of 5%, we would not have been able
+    to reject the null hypothesis in favor of the alternative. As stated in
+    [2]_, Barnard's test is uniformly more powerful than Fisher's exact test
+    because Barnard's test does not condition on any margin. Fisher's test
+    should only be used when both sets of marginals are fixed.
+
+    """
+    if n <= 0:
+        raise ValueError(
+            "Number of points `n` must be strictly positive, "
+            f"found {n!r}"
+        )
+
+    table = np.asarray(table, dtype=np.int64)
+
+    if not table.shape == (2, 2):
+        raise ValueError("The input `table` must be of shape (2, 2).")
+
+    if np.any(table < 0):
+        raise ValueError("All values in `table` must be nonnegative.")
+
+    if 0 in table.sum(axis=0):
+        # If both values in column are zero, the p-value is 1 and
+        # the score's statistic is NaN.
+        return BarnardExactResult(np.nan, 1.0)
+
+    total_col_1, total_col_2 = table.sum(axis=0)
+
+    x1 = np.arange(total_col_1 + 1, dtype=np.int64).reshape(-1, 1)
+    x2 = np.arange(total_col_2 + 1, dtype=np.int64).reshape(1, -1)
+
+    # We need to calculate the wald statistics for each combination of x1 and
+    # x2.
+    p1, p2 = x1 / total_col_1, x2 / total_col_2
+
+    if pooled:
+        p = (x1 + x2) / (total_col_1 + total_col_2)
+        variances = p * (1 - p) * (1 / total_col_1 + 1 / total_col_2)
+    else:
+        variances = p1 * (1 - p1) / total_col_1 + p2 * (1 - p2) / total_col_2
+
+    # To avoid warning when dividing by 0
+    with np.errstate(divide="ignore", invalid="ignore"):
+        wald_statistic = np.divide((p1 - p2), np.sqrt(variances))
+
+    wald_statistic[p1 == p2] = 0  # Removing NaN values
+
+    wald_stat_obs = wald_statistic[table[0, 0], table[0, 1]]
+
+    if alternative == "two-sided":
+        index_arr = np.abs(wald_statistic) >= abs(wald_stat_obs)
+    elif alternative == "less":
+        index_arr = wald_statistic <= wald_stat_obs
+    elif alternative == "greater":
+        index_arr = wald_statistic >= wald_stat_obs
+    else:
+        msg = (
+            "`alternative` should be one of {'two-sided', 'less', 'greater'},"
+            f" found {alternative!r}"
+        )
+        raise ValueError(msg)
+
+    x1_sum_x2 = x1 + x2
+
+    x1_log_comb = _compute_log_combinations(total_col_1)
+    x2_log_comb = _compute_log_combinations(total_col_2)
+    x1_sum_x2_log_comb = x1_log_comb[x1] + x2_log_comb[x2]
+
+    result = shgo(
+        _get_binomial_log_p_value_with_nuisance_param,
+        args=(x1_sum_x2, x1_sum_x2_log_comb, index_arr),
+        bounds=((0, 1),),
+        n=n,
+        sampling_method="sobol",
+    )
+
+    # result.fun is the negative log pvalue and therefore needs to be
+    # changed before return
+    p_value = np.clip(np.exp(-result.fun), a_min=0, a_max=1)
+    return BarnardExactResult(wald_stat_obs, p_value)
+
+
+@dataclass
+class BoschlooExactResult:
+    statistic: float
+    pvalue: float
+
+
+@xp_capabilities(np_only=True)
+def boschloo_exact(table, alternative="two-sided", n=32):
+    r"""Perform Boschloo's exact test on a 2x2 contingency table.
+
+    Parameters
+    ----------
+    table : array_like of ints
+        A 2x2 contingency table.  Elements should be non-negative integers.
+
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the null and alternative hypotheses. Default is 'two-sided'.
+        Please see explanations in the Notes section below.
+
+    n : int, optional
+        Number of sampling points used in the construction of the sampling
+        method. Note that this argument will automatically be converted to
+        the next higher power of 2 since `scipy.stats.qmc.Sobol` is used to
+        select sample points. Default is 32. Must be positive. In most cases,
+        32 points is enough to reach good precision. More points comes at
+        performance cost.
+
+    Returns
+    -------
+    ber : BoschlooExactResult
+        A result object with the following attributes.
+
+        statistic : float
+            The statistic used in Boschloo's test; that is, the p-value
+            from Fisher's exact test.
+
+        pvalue : float
+            P-value, the probability of obtaining a distribution at least as
+            extreme as the one that was actually observed, assuming that the
+            null hypothesis is true.
+
+    See Also
+    --------
+    chi2_contingency : Chi-square test of independence of variables in a
+        contingency table.
+    fisher_exact : Fisher exact test on a 2x2 contingency table.
+    barnard_exact : Barnard's exact test, which is a more powerful alternative
+        than Fisher's exact test for 2x2 contingency tables.
+
+    Notes
+    -----
+    Boschloo's test is an exact test used in the analysis of contingency
+    tables. It examines the association of two categorical variables, and
+    is a uniformly more powerful alternative to Fisher's exact test
+    for 2x2 contingency tables.
+
+    Boschloo's exact test uses the p-value of Fisher's exact test as a
+    statistic, and Boschloo's p-value is the probability under the null
+    hypothesis of observing such an extreme value of this statistic.
+
+    Let's define :math:`X_0` a 2x2 matrix representing the observed sample,
+    where each column stores the binomial experiment, as in the example
+    below. Let's also define :math:`p_1, p_2` the theoretical binomial
+    probabilities for  :math:`x_{11}` and :math:`x_{12}`. When using
+    Boschloo exact test, we can assert three different alternative hypotheses:
+
+    - :math:`H_0 : p_1=p_2` versus :math:`H_1 : p_1 < p_2`,
+      with `alternative` = "less"
+
+    - :math:`H_0 : p_1=p_2` versus :math:`H_1 : p_1 > p_2`,
+      with `alternative` = "greater"
+
+    - :math:`H_0 : p_1=p_2` versus :math:`H_1 : p_1 \neq p_2`,
+      with `alternative` = "two-sided" (default)
+
+    There are multiple conventions for computing a two-sided p-value when the
+    null distribution is asymmetric. Here, we apply the convention that the
+    p-value of a two-sided test is twice the minimum of the p-values of the
+    one-sided tests (clipped to 1.0). Note that `fisher_exact` follows a
+    different convention, so for a given `table`, the statistic reported by
+    `boschloo_exact` may differ from the p-value reported by `fisher_exact`
+    when ``alternative='two-sided'``.
+
+    .. versionadded:: 1.7.0
+
+    References
+    ----------
+    .. [1] R.D. Boschloo. "Raised conditional level of significance for the
+       2 x 2-table when testing the equality of two probabilities",
+       Statistica Neerlandica, 24(1), 1970
+
+    .. [2] "Boschloo's test", Wikipedia,
+       https://en.wikipedia.org/wiki/Boschloo%27s_test
+
+    .. [3] Lise M. Saari et al. "Employee attitudes and job satisfaction",
+       Human Resource Management, 43(4), 395-407, 2004,
+       :doi:`10.1002/hrm.20032`.
+
+    Examples
+    --------
+    In the following example, we consider the article "Employee
+    attitudes and job satisfaction" [3]_
+    which reports the results of a survey from 63 scientists and 117 college
+    professors. Of the 63 scientists, 31 said they were very satisfied with
+    their jobs, whereas 74 of the college professors were very satisfied
+    with their work. Is this significant evidence that college
+    professors are happier with their work than scientists?
+    The following table summarizes the data mentioned above::
+
+                         college professors   scientists
+        Very Satisfied   74                     31
+        Dissatisfied     43                     32
+
+    When working with statistical hypothesis testing, we usually use a
+    threshold probability or significance level upon which we decide
+    to reject the null hypothesis :math:`H_0`. Suppose we choose the common
+    significance level of 5%.
+
+    Our alternative hypothesis is that college professors are truly more
+    satisfied with their work than scientists. Therefore, we expect
+    :math:`p_1` the proportion of very satisfied college professors to be
+    greater than :math:`p_2`, the proportion of very satisfied scientists.
+    We thus call `boschloo_exact` with the ``alternative="greater"`` option:
+
+    >>> import scipy.stats as stats
+    >>> res = stats.boschloo_exact([[74, 31], [43, 32]], alternative="greater")
+    >>> res.statistic
+    0.0483
+    >>> res.pvalue
+    0.0355
+
+    Under the null hypothesis that scientists are happier in their work than
+    college professors, the probability of obtaining test
+    results at least as extreme as the observed data is approximately 3.55%.
+    Since this p-value is less than our chosen significance level, we have
+    evidence to reject :math:`H_0` in favor of the alternative hypothesis.
+
+    """
+    hypergeom = distributions.hypergeom
+
+    if n <= 0:
+        raise ValueError(
+            "Number of points `n` must be strictly positive,"
+            f" found {n!r}"
+        )
+
+    table = np.asarray(table, dtype=np.int64)
+
+    if not table.shape == (2, 2):
+        raise ValueError("The input `table` must be of shape (2, 2).")
+
+    if np.any(table < 0):
+        raise ValueError("All values in `table` must be nonnegative.")
+
+    if 0 in table.sum(axis=0):
+        # If both values in column are zero, the p-value is 1 and
+        # the score's statistic is NaN.
+        return BoschlooExactResult(np.nan, np.nan)
+
+    total_col_1, total_col_2 = table.sum(axis=0)
+    total = total_col_1 + total_col_2
+    x1 = np.arange(total_col_1 + 1, dtype=np.int64).reshape(1, -1)
+    x2 = np.arange(total_col_2 + 1, dtype=np.int64).reshape(-1, 1)
+    x1_sum_x2 = x1 + x2
+
+    if alternative == 'less':
+        pvalues = hypergeom.cdf(x1, total, x1_sum_x2, total_col_1).T
+    elif alternative == 'greater':
+        # Same formula as the 'less' case, but with the second column.
+        pvalues = hypergeom.cdf(x2, total, x1_sum_x2, total_col_2).T
+    elif alternative == 'two-sided':
+        boschloo_less = boschloo_exact(table, alternative="less", n=n)
+        boschloo_greater = boschloo_exact(table, alternative="greater", n=n)
+
+        res = (
+            boschloo_less if boschloo_less.pvalue < boschloo_greater.pvalue
+            else boschloo_greater
+        )
+
+        # Two-sided p-value is defined as twice the minimum of the one-sided
+        # p-values
+        pvalue = np.clip(2 * res.pvalue, a_min=0, a_max=1)
+        return BoschlooExactResult(res.statistic, pvalue)
+    else:
+        msg = (
+            f"`alternative` should be one of {'two-sided', 'less', 'greater'},"
+            f" found {alternative!r}"
+        )
+        raise ValueError(msg)
+
+    fisher_stat = pvalues[table[0, 0], table[0, 1]]
+
+    # fisher_stat * (1+1e-13) guards us from small numerical error. It is
+    # equivalent to np.isclose with relative tol of 1e-13 and absolute tol of 0
+    # For more throughout explanations, see gh-14178
+    index_arr = pvalues <= fisher_stat * (1+1e-13)
+
+    x1, x2, x1_sum_x2 = x1.T, x2.T, x1_sum_x2.T
+    x1_log_comb = _compute_log_combinations(total_col_1)
+    x2_log_comb = _compute_log_combinations(total_col_2)
+    x1_sum_x2_log_comb = x1_log_comb[x1] + x2_log_comb[x2]
+
+    result = shgo(
+        _get_binomial_log_p_value_with_nuisance_param,
+        args=(x1_sum_x2, x1_sum_x2_log_comb, index_arr),
+        bounds=((0, 1),),
+        n=n,
+        sampling_method="sobol",
+    )
+
+    # result.fun is the negative log pvalue and therefore needs to be
+    # changed before return
+    p_value = np.clip(np.exp(-result.fun), a_min=0, a_max=1)
+    return BoschlooExactResult(fisher_stat, p_value)
+
+
+def _get_binomial_log_p_value_with_nuisance_param(
+    nuisance_param, x1_sum_x2, x1_sum_x2_log_comb, index_arr
+):
+    r"""
+    Compute the log pvalue in respect of a nuisance parameter considering
+    a 2x2 sample space.
+
+    Parameters
+    ----------
+    nuisance_param : float
+        nuisance parameter used in the computation of the maximisation of
+        the p-value. Must be between 0 and 1
+
+    x1_sum_x2 : ndarray
+        Sum of x1 and x2 inside barnard_exact
+
+    x1_sum_x2_log_comb : ndarray
+        sum of the log combination of x1 and x2
+
+    index_arr : ndarray of boolean
+
+    Returns
+    -------
+    p_value : float
+        Return the maximum p-value considering every nuisance parameter
+        between 0 and 1
+
+    Notes
+    -----
+
+    Both Barnard's test and Boschloo's test iterate over a nuisance parameter
+    :math:`\pi \in [0, 1]` to find the maximum p-value. To search this
+    maxima, this function return the negative log pvalue with respect to the
+    nuisance parameter passed in params. This negative log p-value is then
+    used in `shgo` to find the minimum negative pvalue which is our maximum
+    pvalue.
+
+    Also, to compute the different combination used in the
+    p-values' computation formula, this function uses `gammaln` which is
+    more tolerant for large value than `scipy.special.comb`. `gammaln` gives
+    a log combination. For the little precision loss, performances are
+    improved a lot.
+    """
+    t1, t2 = x1_sum_x2.shape
+    n = t1 + t2 - 2
+    with np.errstate(divide="ignore", invalid="ignore"):
+        log_nuisance = np.log(
+            nuisance_param,
+            out=np.zeros_like(nuisance_param),
+            where=nuisance_param >= 0,
+        )
+        log_1_minus_nuisance = np.log(
+            1 - nuisance_param,
+            out=np.zeros_like(nuisance_param),
+            where=1 - nuisance_param >= 0,
+        )
+
+        nuisance_power_x1_x2 = log_nuisance * x1_sum_x2
+        nuisance_power_x1_x2[(x1_sum_x2 == 0)[:, :]] = 0
+
+        nuisance_power_n_minus_x1_x2 = log_1_minus_nuisance * (n - x1_sum_x2)
+        nuisance_power_n_minus_x1_x2[(x1_sum_x2 == n)[:, :]] = 0
+
+        tmp_log_values_arr = (
+            x1_sum_x2_log_comb
+            + nuisance_power_x1_x2
+            + nuisance_power_n_minus_x1_x2
+        )
+
+    tmp_values_from_index = tmp_log_values_arr[index_arr]
+
+    # To avoid dividing by zero in log function and getting inf value,
+    # values are centered according to the max
+    max_value = tmp_values_from_index.max()
+
+    # To have better result's precision, the log pvalue is taken here.
+    # Indeed, pvalue is included inside [0, 1] interval. Passing the
+    # pvalue to log makes the interval a lot bigger ([-inf, 0]), and thus
+    # help us to achieve better precision
+    with np.errstate(divide="ignore", invalid="ignore"):
+        log_probs = np.exp(tmp_values_from_index - max_value).sum()
+        log_pvalue = max_value + np.log(
+            log_probs,
+            out=np.full_like(log_probs, -np.inf),
+            where=log_probs > 0,
+        )
+
+    # Since shgo find the minima, minus log pvalue is returned
+    return -log_pvalue
+
+
+@np.vectorize(otypes=[np.float64])
+def _pval_cvm_2samp_exact(s, m, n):
+    """
+    Compute the exact p-value of the Cramer-von Mises two-sample test
+    for a given value s of the test statistic.
+    m and n are the sizes of the samples.
+
+    [1] Y. Xiao, A. Gordon, and A. Yakovlev, "A C++ Program for
+        the Cramér-Von Mises Two-Sample Test", J. Stat. Soft.,
+        vol. 17, no. 8, pp. 1-15, Dec. 2006.
+    [2] T. W. Anderson "On the Distribution of the Two-Sample Cramer-von Mises
+        Criterion," The Annals of Mathematical Statistics, Ann. Math. Statist.
+        33(3), 1148-1159, (September, 1962)
+    """
+
+    # [1, p. 3]
+    m, n = int(m), int(n)
+    lcm = np.lcm(m, n)
+    # [1, p. 4], below eq. 3
+    a = lcm // m
+    b = lcm // n
+    # Combine Eq. 9 in [2] with Eq. 2 in [1] and solve for $\zeta$
+    # Hint: `s` is $U$ in [2], and $T_2$ in [1] is $T$ in [2]
+    mn = m * n
+    zeta = lcm ** 2 * (m + n) * (6 * s - mn * (4 * mn - 1)) // (6 * mn ** 2)
+
+    # bound maximum value that may appear in `gs` (remember both rows!)
+    zeta_bound = lcm**2 * (m + n)  # bound elements in row 1
+    combinations = math.comb(m + n, m)  # sum of row 2
+    max_gs = max(zeta_bound, combinations)
+    dtype = np.min_scalar_type(max_gs)
+
+    # the frequency table of $g_{u, v}^+$ defined in [1, p. 6]
+    gs = ([np.array([[0], [1]], dtype=dtype)]
+          + [np.empty((2, 0), dtype=dtype) for _ in range(m)])
+    for u in range(n + 1):
+        next_gs = []
+        tmp = np.empty((2, 0), dtype=dtype)
+        for v, g in enumerate(gs):
+            # Calculate g recursively with eq. 11 in [1]. Even though it
+            # doesn't look like it, this also does 12/13 (all of Algorithm 1).
+            vi, i0, i1 = np.intersect1d(tmp[0], g[0], return_indices=True)
+            tmp = np.concatenate([
+                np.stack([vi, tmp[1, i0] + g[1, i1]]),
+                np.delete(tmp, i0, 1),
+                np.delete(g, i1, 1)
+            ], 1)
+            res = (a * v - b * u) ** 2
+            tmp[0] += res.astype(dtype)
+            next_gs.append(tmp)
+        gs = next_gs
+    value, freq = gs[m]
+    return np.float64(np.sum(freq[value >= zeta]) / combinations)
+
+
+def _pval_cvm_2samp_asymptotic(t, N, nx, ny, k, *, xp):
+    # compute expected value and variance of T (eq. 11 and 14 in [2])
+    nx, ny = xp.asarray(nx, dtype=t.dtype), xp.asarray(ny, dtype=t.dtype)
+    et = (1 + 1 / N) / 6
+    vt = (N + 1) * (4 * k * N - 3 * (nx ** 2 + ny ** 2) - 2 * k)
+    vt = vt / (45 * N ** 2 * 4 * k)
+
+    # computed the normalized statistic (eq. 15 in [2])
+    tn = 1 / 6 + (t - et) / xp.sqrt(45 * vt)
+
+    # approximate distribution of tn with limiting distribution
+    # of the one-sample test statistic
+    # if tn < 0.003, the _cdf_cvm_inf(tn) < 1.28*1e-18, return 1.0 directly
+    p = xpx.apply_where(tn >= 0.003,
+                        (tn,),
+                        lambda tn: xp.clip(1. - _cdf_cvm_inf(tn, xp=xp), 0.),
+                        fill_value = 1.)
+    return p
+
+
+@xp_capabilities(skip_backends=[('dask.array', 'needs rankdata')],
+                 cpu_only=True, jax_jit=False,  # due to p-value calculation
+                 marray=True,
+                 extra_note="Only `method='exact'` is compatible with MArray input.")
+@_axis_nan_policy_factory(CramerVonMisesResult, n_samples=2, too_small=1,
+                          result_to_tuple=_cvm_result_to_tuple)
+def cramervonmises_2samp(x, y, method='auto', *, axis=0):
+    r"""Perform the two-sample Cramér-von Mises test for goodness of fit.
+
+    This is the two-sample version of the Cramér-von Mises test ([1]_):
+    for two independent samples :math:`X_1, ..., X_n` and
+    :math:`Y_1, ..., Y_m`, the null hypothesis is that the samples
+    come from the same (unspecified) continuous distribution.
+
+    The test statistic :math:`T` is defined as in [1]_:
+
+    .. math::
+        T = \frac{nm}{n+m}\omega^2 =
+        \frac{U}{n m (n+m)} - \frac{4 m n - 1}{6(m+n)}
+
+    where :math:`U` is defined as below, and :math:`\omega^2` is the Cramér-von
+    Mises criterion. The function :math:`r(\cdot)` here denotes the rank of the
+    observed values :math:`x_i` and :math:`y_j` within the pooled sample of size
+    :math:`n + m`, with ties assigned mid-rank values:
+
+    .. math::
+        U = n \sum_{i=1}^n (r(x_i)-i)^2 + m \sum_{j=1}^m (r(y_j)-j)^2
+
+    Parameters
+    ----------
+    x : array_like
+        A 1-D array of observed values of the random variables :math:`X_i`.
+        Must contain at least two observations.
+    y : array_like
+        A 1-D array of observed values of the random variables :math:`Y_i`.
+        Must contain at least two observations.
+    method : {'auto', 'asymptotic', 'exact'}, optional
+        The method used to compute the p-value, see Notes for details.
+        The default is 'auto'.
+    axis : int or tuple of ints, default: 0
+        If an int or tuple of ints, the axis or axes of the input along which
+        to compute the statistic. The statistic of each axis-slice (e.g. row)
+        of the input will appear in a corresponding element of the output.
+        If ``None``, the input will be raveled before computing the statistic.
+
+    Returns
+    -------
+    res : object with attributes
+        statistic : float
+            Cramér-von Mises statistic :math:`T`.
+        pvalue : float
+            The p-value.
+
+    See Also
+    --------
+    cramervonmises, anderson_ksamp, epps_singleton_2samp, ks_2samp
+
+    Notes
+    -----
+    .. versionadded:: 1.7.0
+
+    The statistic is computed according to equation 9 in [2]_. The
+    calculation of the p-value depends on the keyword `method`:
+
+    - ``asymptotic``: The p-value is approximated by using the limiting
+      distribution of the test statistic.
+    - ``exact``: The exact p-value is computed by enumerating all
+      possible combinations of the test statistic, see [2]_.
+
+    If ``method='auto'``, the exact approach is used
+    if both samples contain equal to or less than 20 observations,
+    otherwise the asymptotic distribution is used.
+
+    If the underlying distribution is not continuous, the p-value is likely to
+    be conservative (Section 6.2 in [3]_). When ranking the data to compute
+    the test statistic, midranks are used if there are ties.
+
+    References
+    ----------
+    .. [1] https://en.wikipedia.org/wiki/Cramer-von_Mises_criterion
+    .. [2] Anderson, T.W. (1962). On the distribution of the two-sample
+           Cramer-von-Mises criterion. The Annals of Mathematical
+           Statistics, pp. 1148-1159.
+    .. [3] Conover, W.J., Practical Nonparametric Statistics, 1971.
+
+    Examples
+    --------
+
+    Suppose we wish to test whether two samples generated by
+    ``scipy.stats.norm.rvs`` have the same distribution. We choose a
+    significance level of alpha=0.05.
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> rng = np.random.default_rng()
+    >>> x = stats.norm.rvs(size=100, random_state=rng)
+    >>> y = stats.norm.rvs(size=70, random_state=rng)
+    >>> res = stats.cramervonmises_2samp(x, y)
+    >>> res.statistic, res.pvalue
+    (0.29376470588235293, 0.1412873014573014)
+
+    The p-value exceeds our chosen significance level, so we do not
+    reject the null hypothesis that the observed samples are drawn from the
+    same distribution.
+
+    For small sample sizes, one can compute the exact p-values:
+
+    >>> x = stats.norm.rvs(size=7, random_state=rng)
+    >>> y = stats.t.rvs(df=2, size=6, random_state=rng)
+    >>> res = stats.cramervonmises_2samp(x, y, method='exact')
+    >>> res.statistic, res.pvalue
+    (0.197802197802198, 0.31643356643356646)
+
+    The p-value based on the asymptotic distribution is a good approximation
+    even though the sample size is small.
+
+    >>> res = stats.cramervonmises_2samp(x, y, method='asymptotic')
+    >>> res.statistic, res.pvalue
+    (0.197802197802198, 0.2966041181527128)
+
+    Independent of the method, one would not reject the null hypothesis at the
+    chosen significance level in this example.
+
+    """
+    xp = array_namespace(x, y)
+    length_x = x.shape[-1]
+    length_y = y.shape[-1]
+    count_x = _count_nonmasked(x, axis=-1, xp=xp)
+    count_y = _count_nonmasked(y, axis=-1, xp=xp)
+
+    if length_x <= 1 or length_y <= 1:  # only needed for `test_axis_nan_policy`
+        raise ValueError('x and y must contain at least two observations.')
+    if method not in ['auto', 'exact', 'asymptotic']:
+        raise ValueError('method must be either auto, exact or asymptotic.')
+
+    if is_marray(xp) and method in {'auto', 'asymptotic'}:
+        message = "Only `method='exact'` is compatible with MArray."
+        raise ValueError(message)
+
+    if method == 'auto':
+        if max(count_x, count_y) > 20:
+            method = 'asymptotic'
+        else:
+            method = 'exact'
+
+    # axis=-1 is guaranteed by _axis_nan_policy decorator
+    xa = xp.sort(x, axis=-1)
+    ya = xp.sort(y, axis=-1)
+
+    # get ranks of x and y in the pooled sample
+    z = xp.concat([xa, ya], axis=-1)
+    # in case of ties, use midrank (see [1])
+    r = scipy.stats.rankdata(z, method='average', axis=-1)
+    dtype = xp_result_type(x, y, force_floating=True, xp=xp)
+    rx = r[..., :length_x]
+    ry = r[..., length_x:]
+
+    # compute U (eq. 10 in [2])
+    u = (count_x * xp.sum((rx - xp.arange(1, length_x+1, dtype=dtype))**2, axis=-1)
+         + count_y * xp.sum((ry - xp.arange(1, length_y+1, dtype=dtype))**2, axis=-1))
+
+    # compute T (eq. 9 in [2])
+    k, N = count_x*count_y, count_x + count_y
+    t = u / (k*N) - (4*k - 1)/(6*N)
+
+    if method == 'exact':
+        if is_marray(xp):
+            u, count_x, count_y = u.data, count_x.data, count_y.data
+        p = _pval_cvm_2samp_exact(np.asarray(u), count_x, count_y)
+        p = xp.asarray(p, dtype=dtype)
+    else:
+        p = _pval_cvm_2samp_asymptotic(t, N, count_x, count_y, k, xp=xp)
+
+    t = t[()] if t.ndim == 0 else t
+    p = p[()] if p.ndim == 0 else p
+    return CramerVonMisesResult(statistic=t, pvalue=p)
+
+
+class TukeyHSDResult:
+    """Result of `scipy.stats.tukey_hsd`.
+
+    Attributes
+    ----------
+    statistic : float ndarray
+        The computed statistic of the test for each comparison. The element
+        at index ``(i, j)`` is the statistic for the comparison between groups
+        ``i`` and ``j``.
+    pvalue : float ndarray
+        The associated p-value from the studentized range distribution. The
+        element at index ``(i, j)`` is the p-value for the comparison
+        between groups ``i`` and ``j``.
+
+    Notes
+    -----
+    The string representation of this object displays the most recently
+    calculated confidence interval, and if none have been previously
+    calculated, it will evaluate ``confidence_interval()``.
+
+    References
+    ----------
+    .. [1] NIST/SEMATECH e-Handbook of Statistical Methods, "7.4.7.1. Tukey's
+           Method."
+           https://www.itl.nist.gov/div898/handbook/prc/section4/prc471.htm,
+           28 November 2020.
+    .. [2] P. A. Games and J. F. Howell, "Pairwise Multiple Comparison Procedures
+           with Unequal N's and/or Variances: A Monte Carlo Study," Journal of
+           Educational Statistics, vol. 1, no. 2, pp. 113-125, Jun. 1976,
+           :doi:`10.3102/10769986001002113`.
+    """
+
+    def __init__(self, statistic, pvalue, _ntreatments, _df, _stand_err):
+        self.statistic = statistic
+        self.pvalue = pvalue
+        self._ntreatments = _ntreatments
+        self._df = _df
+        self._stand_err = _stand_err
+        self._ci = None
+        self._ci_cl = None
+
+    def __str__(self):
+        # Note: `__str__` prints the confidence intervals from the most
+        # recent call to `confidence_interval`. If it has not been called,
+        # it will be called with the default CL of .95.
+        if self._ci is None:
+            self.confidence_interval(confidence_level=.95)
+        s = ("Pairwise Group Comparisons"
+             f" ({self._ci_cl*100:.1f}% Confidence Interval)\n")
+        s += "Comparison  Statistic  p-value  Lower CI  Upper CI\n"
+        for i, j in np.ndindex(self.pvalue.shape):
+            if i != j:
+                s += (f" ({i} - {j}) {self.statistic[i, j]:>10.3f}"
+                      f"{self.pvalue[i, j]:>10.3f}"
+                      f"{self._ci.low[i, j]:>10.3f}"
+                      f"{self._ci.high[i, j]:>10.3f}\n")
+        return s
+
+    def confidence_interval(self, confidence_level=.95):
+        """Compute the confidence interval for the specified confidence level.
+
+        Parameters
+        ----------
+        confidence_level : float, optional
+            Confidence level for the computed confidence interval
+            of the estimated proportion. Default is .95.
+
+        Returns
+        -------
+        ci : ``ConfidenceInterval`` object
+            The object has attributes ``low`` and ``high`` that hold the
+            lower and upper bounds of the confidence intervals for each
+            comparison. The high and low values are accessible for each
+            comparison at index ``(i, j)`` between groups ``i`` and ``j``.
+
+        References
+        ----------
+        .. [1] NIST/SEMATECH e-Handbook of Statistical Methods, "7.4.7.1.
+               Tukey's Method."
+               https://www.itl.nist.gov/div898/handbook/prc/section4/prc471.htm,
+               28 November 2020.
+        .. [2] P. A. Games and J. F. Howell, "Pairwise Multiple Comparison Procedures
+               with Unequal N's and/or Variances: A Monte Carlo Study," Journal of
+               Educational Statistics, vol. 1, no. 2, pp. 113-125, Jun. 1976,
+               :doi:`10.3102/10769986001002113`.
+
+        Examples
+        --------
+        >>> from scipy.stats import tukey_hsd
+        >>> group0 = [24.5, 23.5, 26.4, 27.1, 29.9]
+        >>> group1 = [28.4, 34.2, 29.5, 32.2, 30.1]
+        >>> group2 = [26.1, 28.3, 24.3, 26.2, 27.8]
+        >>> result = tukey_hsd(group0, group1, group2)
+        >>> ci = result.confidence_interval()
+        >>> ci.low
+        array([[-3.649159, -8.249159, -3.909159],
+               [ 0.950841, -3.649159,  0.690841],
+               [-3.389159, -7.989159, -3.649159]])
+        >>> ci.high
+        array([[ 3.649159, -0.950841,  3.389159],
+               [ 8.249159,  3.649159,  7.989159],
+               [ 3.909159, -0.690841,  3.649159]])
+        """
+        # check to see if the supplied confidence level matches that of the
+        # previously computed CI.
+        if (self._ci is not None and self._ci_cl is not None and
+                confidence_level == self._ci_cl):
+            return self._ci
+
+        if not 0 < confidence_level < 1:
+            raise ValueError("Confidence level must be between 0 and 1.")
+        # determine the critical value of the studentized range using the
+        # appropriate confidence level, number of treatments, and degrees
+        # of freedom. See [1] "Confidence limits for Tukey's method" / [2] p.117
+        # "H0 was rejected if...". Note that in the cases of unequal sample sizes,
+        # there will be a criterion for each group comparison.
+        params = (confidence_level, self._ntreatments, self._df)
+        srd = distributions.studentized_range.ppf(*params)
+        # also called maximum critical value, the confidence_radius is the
+        # studentized range critical value * the square root of mean square
+        # error over the sample size.
+        confidence_radius = srd * self._stand_err
+        # the confidence levels are determined by the
+        # `mean_differences` +- `confidence_radius`
+        upper_conf = self.statistic + confidence_radius
+        lower_conf = self.statistic - confidence_radius
+        self._ci = ConfidenceInterval(low=lower_conf, high=upper_conf)
+        self._ci_cl = confidence_level
+        return self._ci
+
+
+def _tukey_hsd_iv(args, equal_var):
+    if (len(args)) < 2:
+        raise ValueError("There must be more than 1 treatment.")
+    if not isinstance(equal_var, bool):
+        raise TypeError("Expected a boolean value for 'equal_var'")
+    args = [np.asarray(arg) for arg in args]
+    for arg in args:
+        if arg.ndim != 1:
+            raise ValueError("Input samples must be one-dimensional.")
+        if arg.size <= 1:
+            raise ValueError("Input sample size must be greater than one.")
+        if np.isinf(arg).any():
+            raise ValueError("Input samples must be finite.")
+    return args
+
+
+@xp_capabilities(np_only=True)
+def tukey_hsd(*samples, equal_var=True):
+    """Perform Tukey's HSD test for equality of means over multiple treatments.
+
+    Tukey's honestly significant difference (HSD) test performs pairwise
+    comparison of means for a set of samples. Whereas ANOVA (e.g. `f_oneway`)
+    assesses whether the true means underlying each sample are identical,
+    Tukey's HSD is a post hoc test used to compare the mean of each sample
+    to the mean of each other sample.
+
+    The null hypothesis is that the distributions underlying the samples all
+    have the same mean. The test statistic, which is computed for every
+    possible pairing of samples, is simply the difference between the sample
+    means. For each pair, the p-value is the probability under the null
+    hypothesis (and other assumptions; see notes) of observing such an extreme
+    value of the statistic, considering that many pairwise comparisons are
+    being performed. Confidence intervals for the difference between each pair
+    of means are also available.
+
+    Parameters
+    ----------
+    *samples : array_like
+        The sample measurements for each group. There must be at least
+        two arguments.
+    equal_var : bool, optional
+        If True (default) and equal sample size, perform Tukey-HSD test [6].
+        If True and unequal sample size, perform Tukey-Kramer test [4]_.
+        If False, perform Games-Howell test [7]_, which does not assume equal variances.
+
+    Returns
+    -------
+    result : `~scipy.stats._result_classes.TukeyHSDResult` instance
+        The return value is an object with the following attributes:
+
+        statistic : float ndarray
+            The computed statistic of the test for each comparison. The element
+            at index ``(i, j)`` is the statistic for the comparison between
+            groups ``i`` and ``j``.
+        pvalue : float ndarray
+            The computed p-value of the test for each comparison. The element
+            at index ``(i, j)`` is the p-value for the comparison between
+            groups ``i`` and ``j``.
+
+        The object has the following methods:
+
+        confidence_interval(confidence_level=0.95):
+            Compute the confidence interval for the specified confidence level.
+
+    See Also
+    --------
+    dunnett : performs comparison of means against a control group.
+
+    Notes
+    -----
+    The use of this test relies on several assumptions.
+
+    1. The observations are independent within and among groups.
+    2. The observations within each group are normally distributed.
+    3. The distributions from which the samples are drawn have the same finite
+       variance.
+
+    The original formulation of the test was for samples of equal size drawn from
+    populations assumed to have equal variances [6]_. In case of unequal sample sizes,
+    the test uses the Tukey-Kramer method [4]_. When equal variances are not assumed
+    (``equal_var=False``), the test uses the Games-Howell method [7]_.
+
+    References
+    ----------
+    .. [1] NIST/SEMATECH e-Handbook of Statistical Methods, "7.4.7.1. Tukey's
+           Method."
+           https://www.itl.nist.gov/div898/handbook/prc/section4/prc471.htm,
+           28 November 2020.
+    .. [2] Abdi, Herve & Williams, Lynne. (2021). "Tukey's Honestly Significant
+           Difference (HSD) Test."
+           https://personal.utdallas.edu/~herve/abdi-HSD2010-pretty.pdf
+    .. [3] "One-Way ANOVA Using SAS PROC ANOVA & PROC GLM." SAS
+           Tutorials, 2007.
+           https://www.stattutorials.com/SAS/TUTORIAL-PROC-GLM.htm
+    .. [4] Kramer, Clyde Young. "Extension of Multiple Range Tests to Group
+           Means with Unequal Numbers of Replications." Biometrics, vol. 12,
+           no. 3, 1956, pp. 307-310. https://www.jstor.org/stable/3001469
+    .. [5] NIST/SEMATECH e-Handbook of Statistical Methods, "7.4.3.3.
+           The ANOVA table and tests of hypotheses about means"
+           https://www.itl.nist.gov/div898/handbook/prc/section4/prc433.htm,
+           2 June 2021.
+    .. [6] Tukey, John W. "Comparing Individual Means in the Analysis of
+           Variance." Biometrics, vol. 5, no. 2, 1949, pp. 99-114.
+           https://www.jstor.org/stable/3001913
+    .. [7] P. A. Games and J. F. Howell, "Pairwise Multiple Comparison Procedures
+           with Unequal N's and/or Variances: A Monte Carlo Study," Journal of
+           Educational Statistics, vol. 1, no. 2, pp. 113-125, Jun. 1976.
+           :doi:`10.3102/10769986001002113`.
+
+
+    Examples
+    --------
+    Here are some data comparing the time to relief of three brands of
+    headache medicine, reported in minutes. Data adapted from [3]_.
+
+    >>> import numpy as np
+    >>> from scipy.stats import tukey_hsd
+    >>> group0 = [24.5, 23.5, 26.4, 27.1, 29.9]
+    >>> group1 = [28.4, 34.2, 29.5, 32.2, 30.1]
+    >>> group2 = [26.1, 28.3, 24.3, 26.2, 27.8]
+
+    We would like to see if the means between any of the groups are
+    significantly different. First, visually examine a box and whisker plot.
+
+    >>> import matplotlib.pyplot as plt
+    >>> fig, ax = plt.subplots(1, 1)
+    >>> ax.boxplot([group0, group1, group2])
+    >>> ax.set_xticklabels(["group0", "group1", "group2"]) # doctest: +SKIP
+    >>> ax.set_ylabel("mean") # doctest: +SKIP
+    >>> plt.show()
+
+    From the box and whisker plot, we can see overlap in the interquartile
+    ranges group 1 to group 2 and group 3, but we can apply the ``tukey_hsd``
+    test to determine if the difference between means is significant. We
+    set a significance level of .05 to reject the null hypothesis.
+
+    >>> res = tukey_hsd(group0, group1, group2)
+    >>> print(res)
+    Pairwise Group Comparisons (95.0% Confidence Interval)
+    Comparison  Statistic  p-value  Lower CI  Upper CI
+     (0 - 1)     -4.600     0.014    -8.249    -0.951
+     (0 - 2)     -0.260     0.980    -3.909     3.389
+     (1 - 0)      4.600     0.014     0.951     8.249
+     (1 - 2)      4.340     0.020     0.691     7.989
+     (2 - 0)      0.260     0.980    -3.389     3.909
+     (2 - 1)     -4.340     0.020    -7.989    -0.691
+
+    The null hypothesis is that each group has the same mean. The p-value for
+    comparisons between ``group0`` and ``group1`` as well as ``group1`` and
+    ``group2`` do not exceed .05, so we reject the null hypothesis that they
+    have the same means. The p-value of the comparison between ``group0``
+    and ``group2`` exceeds .05, so we accept the null hypothesis that there
+    is not a significant difference between their means.
+
+    We can also compute the confidence interval associated with our chosen
+    confidence level.
+
+    >>> group0 = [24.5, 23.5, 26.4, 27.1, 29.9]
+    >>> group1 = [28.4, 34.2, 29.5, 32.2, 30.1]
+    >>> group2 = [26.1, 28.3, 24.3, 26.2, 27.8]
+    >>> result = tukey_hsd(group0, group1, group2)
+    >>> conf = res.confidence_interval(confidence_level=.99)
+    >>> for ((i, j), l) in np.ndenumerate(conf.low):
+    ...     # filter out self comparisons
+    ...     if i != j:
+    ...         h = conf.high[i,j]
+    ...         print(f"({i} - {j}) {l:>6.3f} {h:>6.3f}")
+    (0 - 1) -9.480  0.280
+    (0 - 2) -5.140  4.620
+    (1 - 0) -0.280  9.480
+    (1 - 2) -0.540  9.220
+    (2 - 0) -4.620  5.140
+    (2 - 1) -9.220  0.540
+    """
+    args = _tukey_hsd_iv(samples, equal_var)
+    ntreatments = len(args)
+    means = np.asarray([np.mean(arg) for arg in args])
+    nsamples_treatments = np.asarray([a.size for a in args])
+    nobs = np.sum(nsamples_treatments)
+    vars_ = np.asarray([np.var(arg, ddof=1) for arg in args])
+
+    if equal_var:
+        # determine mean square error [5]. Note that this is sometimes called
+        # mean square error within.
+        mse = (np.sum(vars_ * (nsamples_treatments - 1)) / (nobs - ntreatments))
+
+        # The calculation of the standard error differs when treatments differ in
+        # size. See ("Unequal sample sizes")[1].
+        if np.unique(nsamples_treatments).size == 1:
+            # all input groups are the same length, so only one value needs to be
+            # calculated [1].
+            normalize = 2 / nsamples_treatments[0]
+        else:
+            # to compare groups of differing sizes, we must compute a variance
+            # value for each individual comparison. Use broadcasting to get the
+            # resulting matrix. [3], verified against [4] (page 308).
+            normalize = 1 / nsamples_treatments + 1 / nsamples_treatments[None].T
+
+        # the standard error is used in the computation of the tukey criterion and
+        # finding the p-values.
+        stand_err = np.sqrt(normalize * mse / 2)
+        df = nobs - ntreatments
+    else:
+        # `stand_err` is the denominator of the Behrens-Fisher statistic ($v$)
+        # with a factor of $\sqrt{2}$. Compare [7] p.116 "t-solution rejects H0 if...",
+        # [7] p. 117 "H0 was rejected", and definition of `t_stat` below.
+        sj2_nj = vars_ / nsamples_treatments
+        si2_ni = sj2_nj[:, np.newaxis]
+        stand_err = np.sqrt(si2_ni + sj2_nj) / 2**0.5
+
+        # `df` is the Welch degree of freedom $\nu$.
+        # See [7] p. 116 "and the degrees of freedom, $\nu$, are given by...".
+        njm1 = nsamples_treatments - 1
+        nim1 = njm1[:, np.newaxis]
+        df = (si2_ni + sj2_nj)**2 / (si2_ni**2 / nim1 + sj2_nj**2 / njm1)
+
+    # the mean difference is the test statistic.
+    mean_differences = means[None].T - means
+
+    # Calculate the t-statistic to use within the survival function of the
+    # studentized range to get the p-value.
+    t_stat = np.abs(mean_differences) / stand_err
+
+    params = t_stat, ntreatments, df
+    pvalues = distributions.studentized_range.sf(*params)
+
+    return TukeyHSDResult(mean_differences, pvalues, ntreatments,
+                          df, stand_err)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_kde.py b/venv/lib/python3.12/site-packages/scipy/stats/_kde.py
new file mode 100644
index 0000000000000000000000000000000000000000..a1be45bfa59f7816235886763761dc3a2107c9cd
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_kde.py
@@ -0,0 +1,765 @@
+#-------------------------------------------------------------------------------
+#
+#  Define classes for (uni/multi)-variate kernel density estimation.
+#
+#  Currently, only Gaussian kernels are implemented.
+#
+#  Written by: Robert Kern
+#
+#  Date: 2004-08-09
+#
+#  Modified: 2005-02-10 by Robert Kern.
+#              Contributed to SciPy
+#            2005-10-07 by Robert Kern.
+#              Some fixes to match the new scipy_core
+#
+#  Copyright 2004-2005 by Enthought, Inc.
+#
+#-------------------------------------------------------------------------------
+
+from types import GenericAlias
+
+# SciPy imports.
+from scipy import linalg, special
+from scipy._lib._util import check_random_state
+
+from numpy import (asarray, atleast_2d, reshape, zeros, newaxis, exp, pi,
+                   sqrt, ravel, power, atleast_1d, squeeze, sum, transpose,
+                   ones, cov)
+import numpy as np
+
+# Local imports.
+from ._stats import gaussian_kernel_estimate, gaussian_kernel_estimate_log
+from ._multivariate import multivariate_normal
+
+__all__ = ['gaussian_kde']
+
+
+class gaussian_kde:
+    """Representation of a kernel-density estimate using Gaussian kernels.
+
+    Kernel density estimation is a way to estimate the probability density
+    function (PDF) of a random variable in a non-parametric way.
+    `gaussian_kde` works for both uni-variate and multi-variate data.   It
+    includes automatic bandwidth determination.  The estimation works best for
+    a unimodal distribution; bimodal or multi-modal distributions tend to be
+    oversmoothed.
+
+    Parameters
+    ----------
+    dataset : array_like
+        Datapoints to estimate from. In case of univariate data this is a 1-D
+        array, otherwise a 2-D array with shape (# of dims, # of data).
+    bw_method : str, scalar or callable, optional
+        The method used to calculate the bandwidth factor.  This can be
+        'scott', 'silverman', a scalar constant or a callable.  If a scalar,
+        this will be used directly as `factor`.  If a callable, it should
+        take a `gaussian_kde` instance as only parameter and return a scalar.
+        If None (default), 'scott' is used.  See Notes for more details.
+    weights : array_like, optional
+        weights of datapoints. This must be the same shape as dataset.
+        If None (default), the samples are assumed to be equally weighted
+
+    Attributes
+    ----------
+    dataset : ndarray
+        The dataset with which `gaussian_kde` was initialized.
+    d : int
+        Number of dimensions.
+    n : int
+        Number of datapoints.
+    neff : int
+        Effective number of datapoints.
+
+        .. versionadded:: 1.2.0
+    factor : float
+        The bandwidth factor obtained from `covariance_factor`.
+    covariance : ndarray
+        The kernel covariance matrix; this is the data covariance matrix
+        multiplied by the square of the bandwidth factor, e.g.
+        ``np.cov(dataset) * factor**2``.
+    inv_cov : ndarray
+        The inverse of `covariance`.
+
+    Methods
+    -------
+    evaluate
+    __call__
+    integrate_gaussian
+    integrate_box_1d
+    integrate_box
+    integrate_kde
+    pdf
+    logpdf
+    resample
+    set_bandwidth
+    covariance_factor
+    marginal
+
+    Notes
+    -----
+    Bandwidth selection strongly influences the estimate obtained from the KDE
+    (much more so than the actual shape of the kernel).  Bandwidth selection
+    can be done by a "rule of thumb", by cross-validation, by "plug-in
+    methods" or by other means; see [3]_, [4]_ for reviews.  `gaussian_kde`
+    uses a rule of thumb, the default is Scott's Rule.
+
+    Scott's Rule [1]_, implemented as `scotts_factor`, is::
+
+        n**(-1./(d+4)),
+
+    with ``n`` the number of data points and ``d`` the number of dimensions.
+    In the case of unequally weighted points, `scotts_factor` becomes::
+
+        neff**(-1./(d+4)),
+
+    with ``neff`` the effective number of datapoints.
+    Silverman's suggestion for *multivariate* data [2]_, implemented as
+    `silverman_factor`, is::
+
+        (n * (d + 2) / 4.)**(-1. / (d + 4)).
+
+    or in the case of unequally weighted points::
+
+        (neff * (d + 2) / 4.)**(-1. / (d + 4)).
+
+    Note that this is not the same as "Silverman's rule of thumb" [6]_, which
+    may be more robust in the univariate case; see documentation of the
+    ``set_bandwidth`` method for implementing a custom bandwidth rule.
+
+    Good general descriptions of kernel density estimation can be found in [1]_
+    and [2]_, the mathematics for this multi-dimensional implementation can be
+    found in [1]_.
+
+    With a set of weighted samples, the effective number of datapoints ``neff``
+    is defined by::
+
+        neff = sum(weights)^2 / sum(weights^2)
+
+    as detailed in [5]_.
+
+    `gaussian_kde` does not currently support data that lies in a
+    lower-dimensional subspace of the space in which it is expressed. For such
+    data, consider performing principal component analysis / dimensionality
+    reduction and using `gaussian_kde` with the transformed data.
+
+    References
+    ----------
+    .. [1] D.W. Scott, "Multivariate Density Estimation: Theory, Practice, and
+           Visualization", John Wiley & Sons, New York, Chicester, 1992.
+    .. [2] B.W. Silverman, "Density Estimation for Statistics and Data
+           Analysis", Vol. 26, Monographs on Statistics and Applied Probability,
+           Chapman and Hall, London, 1986.
+    .. [3] B.A. Turlach, "Bandwidth Selection in Kernel Density Estimation: A
+           Review", CORE and Institut de Statistique, Vol. 19, pp. 1-33, 1993.
+    .. [4] D.M. Bashtannyk and R.J. Hyndman, "Bandwidth selection for kernel
+           conditional density estimation", Computational Statistics & Data
+           Analysis, Vol. 36, pp. 279-298, 2001.
+    .. [5] Gray P. G., 1969, Journal of the Royal Statistical Society.
+           Series A (General), 132, 272
+    .. [6] Kernel density estimation. *Wikipedia.*
+           https://en.wikipedia.org/wiki/Kernel_density_estimation
+
+    Examples
+    --------
+    Generate some random two-dimensional data:
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> def measure(n):
+    ...     "Measurement model, return two coupled measurements."
+    ...     m1 = np.random.normal(size=n)
+    ...     m2 = np.random.normal(scale=0.5, size=n)
+    ...     return m1+m2, m1-m2
+
+    >>> m1, m2 = measure(2000)
+    >>> xmin = m1.min()
+    >>> xmax = m1.max()
+    >>> ymin = m2.min()
+    >>> ymax = m2.max()
+
+    Perform a kernel density estimate on the data:
+
+    >>> X, Y = np.mgrid[xmin:xmax:100j, ymin:ymax:100j]
+    >>> positions = np.vstack([X.ravel(), Y.ravel()])
+    >>> values = np.vstack([m1, m2])
+    >>> kernel = stats.gaussian_kde(values)
+    >>> Z = np.reshape(kernel(positions).T, X.shape)
+
+    Plot the results:
+
+    >>> import matplotlib.pyplot as plt
+    >>> fig, ax = plt.subplots()
+    >>> ax.imshow(np.rot90(Z), cmap=plt.cm.gist_earth_r,
+    ...           extent=[xmin, xmax, ymin, ymax])
+    >>> ax.plot(m1, m2, 'k.', markersize=2)
+    >>> ax.set_xlim([xmin, xmax])
+    >>> ax.set_ylim([ymin, ymax])
+    >>> plt.show()
+
+    Compare against manual KDE at a point:
+
+    >>> point = [1, 2]
+    >>> mean = values.T
+    >>> cov = kernel.factor**2 * np.cov(values)
+    >>> X = stats.multivariate_normal(cov=cov)
+    >>> res = kernel.pdf(point)
+    >>> ref = X.pdf(point - mean).sum() / len(mean)
+    >>> np.allclose(res, ref)
+    True
+    """
+
+    # generic type compatibility with scipy-stubs
+    __class_getitem__: classmethod = classmethod(GenericAlias)
+
+    def __init__(self, dataset, bw_method=None, weights=None):
+        self.dataset = atleast_2d(asarray(dataset))
+        if not self.dataset.size > 1:
+            raise ValueError("`dataset` input should have multiple elements.")
+
+        self.d, self.n = self.dataset.shape
+
+        if weights is not None:
+            self._weights = atleast_1d(weights).astype(float)
+            self._weights /= sum(self._weights)
+            if self.weights.ndim != 1:
+                raise ValueError("`weights` input should be one-dimensional.")
+            if len(self._weights) != self.n:
+                raise ValueError("`weights` input should be of length n")
+            self._neff = 1/np.vecdot(self._weights, self._weights)
+
+        # This can be converted to a warning once gh-10205 is resolved
+        if self.d > self.n:
+            msg = ("Number of dimensions is greater than number of samples. "
+                   "This results in a singular data covariance matrix, which "
+                   "cannot be treated using the algorithms implemented in "
+                   "`gaussian_kde`. Note that `gaussian_kde` interprets each "
+                   "*column* of `dataset` to be a point; consider transposing "
+                   "the input to `dataset`.")
+            raise ValueError(msg)
+
+        try:
+            self.set_bandwidth(bw_method=bw_method)
+        except linalg.LinAlgError as e:
+            msg = ("The data appears to lie in a lower-dimensional subspace "
+                   "of the space in which it is expressed. This has resulted "
+                   "in a singular data covariance matrix, which cannot be "
+                   "treated using the algorithms implemented in "
+                   "`gaussian_kde`. Consider performing principal component "
+                   "analysis / dimensionality reduction and using "
+                   "`gaussian_kde` with the transformed data.")
+            raise linalg.LinAlgError(msg) from e
+
+    def evaluate(self, points):
+        """Evaluate the estimated pdf on a set of points.
+
+        Parameters
+        ----------
+        points : (# of dimensions, # of points)-array
+            Alternatively, a (# of dimensions,) vector can be passed in and
+            treated as a single point.
+
+        Returns
+        -------
+        values : (# of points,)-array
+            The values at each point.
+
+        Raises
+        ------
+        ValueError : if the dimensionality of the input points is different than
+                     the dimensionality of the KDE.
+
+        """
+        points = atleast_2d(asarray(points))
+
+        d, m = points.shape
+        if d != self.d:
+            if d == 1 and m == self.d:
+                # points was passed in as a row vector
+                points = reshape(points, (self.d, 1))
+                m = 1
+            else:
+                msg = (f"points have dimension {d}, "
+                       f"dataset has dimension {self.d}")
+                raise ValueError(msg)
+
+        output_dtype, spec = _get_output_dtype(self.covariance, points)
+        result = gaussian_kernel_estimate[spec](
+            self.dataset.T, self.weights[:, None],
+            points.T, self.cho_cov, output_dtype)
+
+        return result[:, 0]
+
+    __call__ = evaluate
+
+    def integrate_gaussian(self, mean, cov):
+        """
+        Multiply estimated density by a multivariate Gaussian and integrate
+        over the whole space.
+
+        Parameters
+        ----------
+        mean : aray_like
+            A 1-D array, specifying the mean of the Gaussian.
+        cov : array_like
+            A 2-D array, specifying the covariance matrix of the Gaussian.
+
+        Returns
+        -------
+        result : scalar
+            The value of the integral.
+
+        Raises
+        ------
+        ValueError
+            If the mean or covariance of the input Gaussian differs from
+            the KDE's dimensionality.
+
+        """
+        mean = atleast_1d(squeeze(mean))
+        cov = atleast_2d(cov)
+
+        if mean.shape != (self.d,):
+            raise ValueError(f"mean does not have dimension {self.d}")
+        if cov.shape != (self.d, self.d):
+            raise ValueError(f"covariance does not have dimension {self.d}")
+
+        # make mean a column vector
+        mean = mean[:, newaxis]
+
+        sum_cov = self.covariance + cov
+
+        # This will raise LinAlgError if the new cov matrix is not s.p.d
+        # cho_factor returns (ndarray, bool) where bool is a flag for whether
+        # or not ndarray is upper or lower triangular
+        sum_cov_chol = linalg.cho_factor(sum_cov)
+
+        diff = self.dataset - mean
+        tdiff = linalg.cho_solve(sum_cov_chol, diff)
+
+        sqrt_det = np.prod(np.diagonal(sum_cov_chol[0]))
+        norm_const = power(2 * pi, sum_cov.shape[0] / 2.0) * sqrt_det
+
+        energies = np.vecdot(diff, tdiff, axis=0) / 2.0
+        result = np.vecdot(exp(-energies), self.weights, axis=0) / norm_const
+
+        return result
+
+    def integrate_box_1d(self, low, high):
+        """
+        Computes the integral of a 1D pdf between two bounds.
+
+        Parameters
+        ----------
+        low : scalar
+            Lower bound of integration.
+        high : scalar
+            Upper bound of integration.
+
+        Returns
+        -------
+        value : scalar
+            The result of the integral.
+
+        Raises
+        ------
+        ValueError
+            If the KDE is over more than one dimension.
+
+        """
+        if self.d != 1:
+            raise ValueError("integrate_box_1d() only handles 1D pdfs")
+
+        stdev = ravel(sqrt(self.covariance))[0]
+
+        normalized_low = ravel((low - self.dataset) / stdev)
+        normalized_high = ravel((high - self.dataset) / stdev)
+
+        delta = special.ndtr(normalized_high) - special.ndtr(normalized_low)
+        value = np.vecdot(self.weights, delta)
+        return value
+
+    def integrate_box(self, low_bounds, high_bounds, maxpts=None, *, rng=None):
+        """Computes the integral of a pdf over a rectangular interval.
+
+        Parameters
+        ----------
+        low_bounds : array_like
+            A 1-D array containing the lower bounds of integration.
+        high_bounds : array_like
+            A 1-D array containing the upper bounds of integration.
+        maxpts : int, optional
+            The maximum number of points to use for integration.
+        rng : `numpy.random.Generator`, optional
+            Pseudorandom number generator state. When `rng` is None, a new
+            generator is created using entropy from the operating system. Types
+            other than `numpy.random.Generator` are passed to
+            `numpy.random.default_rng` to instantiate a ``Generator``.
+
+        Returns
+        -------
+        value : scalar
+            The result of the integral.
+
+        """
+        low, high = low_bounds - self.dataset.T, high_bounds - self.dataset.T
+        values = multivariate_normal.cdf(
+            high, lower_limit=low, cov=self.covariance, maxpts=maxpts,
+            rng=rng
+        )
+        return np.vecdot(values, self.weights, axis=-1)
+
+    def integrate_kde(self, other):
+        """
+        Computes the integral of the product of this  kernel density estimate
+        with another.
+
+        Parameters
+        ----------
+        other : gaussian_kde instance
+            The other kde.
+
+        Returns
+        -------
+        value : scalar
+            The result of the integral.
+
+        Raises
+        ------
+        ValueError
+            If the KDEs have different dimensionality.
+
+        """
+        if other.d != self.d:
+            raise ValueError("KDEs are not the same dimensionality")
+
+        # we want to iterate over the smallest number of points
+        if other.n < self.n:
+            small = other
+            large = self
+        else:
+            small = self
+            large = other
+
+        sum_cov = small.covariance + large.covariance
+        sum_cov_chol = linalg.cho_factor(sum_cov)
+        result = 0.0
+        for i in range(small.n):
+            mean = small.dataset[:, i, newaxis]
+            diff = large.dataset - mean
+            tdiff = linalg.cho_solve(sum_cov_chol, diff)
+
+            energies = np.vecdot(diff, tdiff, axis=0) / 2.0
+            result += np.vecdot(exp(-energies), large.weights, axis=0)*small.weights[i]
+
+        sqrt_det = np.prod(np.diagonal(sum_cov_chol[0]))
+        norm_const = power(2 * pi, sum_cov.shape[0] / 2.0) * sqrt_det
+
+        result /= norm_const
+
+        return result
+
+    def resample(self, size=None, seed=None):
+        """Randomly sample a dataset from the estimated pdf.
+
+        Parameters
+        ----------
+        size : int, optional
+            The number of samples to draw.  If not provided, then the size is
+            the same as the effective number of samples in the underlying
+            dataset.
+        seed : {None, int, `numpy.random.Generator`, `numpy.random.RandomState`}, optional
+            If `seed` is None (or `np.random`), the `numpy.random.RandomState`
+            singleton is used.
+            If `seed` is an int, a new ``RandomState`` instance is used,
+            seeded with `seed`.
+            If `seed` is already a ``Generator`` or ``RandomState`` instance then
+            that instance is used.
+
+        Returns
+        -------
+        resample : (self.d, `size`) ndarray
+            The sampled dataset.
+
+        """ # numpy/numpydoc#87  # noqa: E501
+        if size is None:
+            size = int(self.neff)
+
+        random_state = check_random_state(seed)
+        norm = transpose(random_state.multivariate_normal(
+            zeros((self.d,), float), self.covariance, size=size
+        ))
+        indices = random_state.choice(self.n, size=size, p=self.weights)
+        means = self.dataset[:, indices]
+
+        return means + norm
+
+    def scotts_factor(self):
+        """Compute Scott's factor.
+
+        Returns
+        -------
+        s : float
+            Scott's factor.
+        """
+        return power(self.neff, -1./(self.d+4))
+
+    def silverman_factor(self):
+        """Compute the Silverman factor.
+
+        Returns
+        -------
+        s : float
+            The silverman factor.
+        """
+        return power(self.neff*(self.d+2.0)/4.0, -1./(self.d+4))
+
+    #  Default method to calculate bandwidth, can be overwritten by subclass
+    covariance_factor = scotts_factor
+    covariance_factor.__doc__ = """Computes the bandwidth factor `factor`.
+        The default is `scotts_factor`.  A subclass can overwrite this
+        method to provide a different method, or set it through a call to
+        `set_bandwidth`.
+
+        Returns
+        -------
+        factor : float
+            The bandwidth factor.
+        """
+
+    def set_bandwidth(self, bw_method=None):
+        """Compute the bandwidth factor with given method.
+
+        The new bandwidth calculated after a call to `set_bandwidth` is used
+        for subsequent evaluations of the estimated density.
+
+        Parameters
+        ----------
+        bw_method : str, scalar or callable, optional
+            The method used to calculate the bandwidth factor.  This can be
+            'scott', 'silverman', a scalar constant or a callable.  If a
+            scalar, this will be used directly as `factor`.  If a callable,
+            it should take a `gaussian_kde` instance as only parameter and
+            return a scalar.  If None (default), nothing happens; the current
+            `covariance_factor` method is kept.
+
+        Notes
+        -----
+        .. versionadded:: 0.11
+
+        Examples
+        --------
+        >>> import numpy as np
+        >>> import scipy.stats as stats
+        >>> x1 = np.array([-7, -5, 1, 4, 5.])
+        >>> kde = stats.gaussian_kde(x1)
+        >>> xs = np.linspace(-10, 10, num=50)
+        >>> y1 = kde(xs)
+        >>> kde.set_bandwidth(bw_method='silverman')
+        >>> y2 = kde(xs)
+        >>> kde.set_bandwidth(bw_method=kde.factor / 3.)
+        >>> y3 = kde(xs)
+
+        >>> import matplotlib.pyplot as plt
+        >>> fig, ax = plt.subplots()
+        >>> ax.plot(x1, np.full(x1.shape, 1 / (4. * x1.size)), 'bo',
+        ...         label='Data points (rescaled)')
+        >>> ax.plot(xs, y1, label='Scott (default)')
+        >>> ax.plot(xs, y2, label='Silverman')
+        >>> ax.plot(xs, y3, label='Const (1/3 * Silverman)')
+        >>> ax.legend()
+        >>> plt.show()
+
+        """
+        if bw_method is None:
+            pass
+        elif bw_method == 'scott':
+            self.covariance_factor = self.scotts_factor
+        elif bw_method == 'silverman':
+            self.covariance_factor = self.silverman_factor
+        elif np.isscalar(bw_method) and not isinstance(bw_method, str):
+            self._bw_method = 'use constant'
+            self.covariance_factor = lambda: bw_method
+        elif callable(bw_method):
+            self._bw_method = bw_method
+            self.covariance_factor = lambda: self._bw_method(self)
+        else:
+            msg = "`bw_method` should be 'scott', 'silverman', a scalar " \
+                  "or a callable."
+            raise ValueError(msg)
+
+        self._compute_covariance()
+
+    def _compute_covariance(self):
+        """Computes the covariance matrix for each Gaussian kernel using
+        covariance_factor().
+        """
+        self.factor = self.covariance_factor()
+        # Cache covariance and Cholesky decomp of covariance
+        if not hasattr(self, '_data_cho_cov'):
+            self._data_covariance = atleast_2d(cov(self.dataset, rowvar=1,
+                                               bias=False,
+                                               aweights=self.weights))
+            self._data_cho_cov = linalg.cholesky(self._data_covariance,
+                                                 lower=True)
+
+        self.covariance = self._data_covariance * self.factor**2
+        self.cho_cov = (self._data_cho_cov * self.factor).astype(np.float64)
+        self.log_det = 2*np.log(np.diag(self.cho_cov
+                                        * np.sqrt(2*pi))).sum()
+
+    @property
+    def inv_cov(self):
+        # Re-compute from scratch each time because I'm not sure how this is
+        # used in the wild. (Perhaps users change the `dataset`, since it's
+        # not a private attribute?) `_compute_covariance` used to recalculate
+        # all these, so we'll recalculate everything now that this is a
+        # a property.
+        self.factor = self.covariance_factor()
+        self._data_covariance = atleast_2d(cov(self.dataset, rowvar=1,
+                                           bias=False, aweights=self.weights))
+        return linalg.inv(self._data_covariance) / self.factor**2
+
+    def pdf(self, x):
+        """
+        Evaluate the estimated pdf on a provided set of points.
+
+        Parameters
+        ----------
+        x : array_like
+            Points at which to evaluate the pdf.
+
+        Returns
+        -------
+        pdf : ndarray
+            The pdf evaluated at `x`.
+
+        Notes
+        -----
+        This is an alias for `gaussian_kde.evaluate`.  See the ``evaluate``
+        docstring for more details.
+
+        """
+        return self.evaluate(x)
+
+    def logpdf(self, x):
+        """
+        Evaluate the log of the estimated pdf on a provided set of points.
+
+        Parameters
+        ----------
+        x : array_like
+            Points at which to evaluate the log-pdf.
+
+        Returns
+        -------
+        logpdf : ndarray
+            The log-pdf evaluated at `x`.
+        """
+        points = atleast_2d(x)
+
+        d, m = points.shape
+        if d != self.d:
+            if d == 1 and m == self.d:
+                # points was passed in as a row vector
+                points = reshape(points, (self.d, 1))
+                m = 1
+            else:
+                msg = (f"points have dimension {d}, "
+                       f"dataset has dimension {self.d}")
+                raise ValueError(msg)
+
+        output_dtype, spec = _get_output_dtype(self.covariance, points)
+        result = gaussian_kernel_estimate_log[spec](
+            self.dataset.T, self.weights[:, None],
+            points.T, self.cho_cov, output_dtype)
+
+        return result[:, 0]
+
+    def marginal(self, dimensions):
+        """Return a marginal KDE distribution.
+
+        Parameters
+        ----------
+        dimensions : int or 1-d array_like
+            The dimensions of the multivariate distribution corresponding
+            with the marginal variables, that is, the indices of the dimensions
+            that are being retained. The other dimensions are marginalized out.
+
+        Returns
+        -------
+        marginal_kde : gaussian_kde
+            An object representing the marginal distribution.
+
+        Notes
+        -----
+        .. versionadded:: 1.10.0
+
+        """
+
+        dims = np.atleast_1d(dimensions)
+
+        if not np.issubdtype(dims.dtype, np.integer):
+            msg = ("Elements of `dimensions` must be integers - the indices "
+                   "of the marginal variables being retained.")
+            raise ValueError(msg)
+
+        n = len(self.dataset)  # number of dimensions
+        original_dims = dims.copy()
+
+        dims[dims < 0] = n + dims[dims < 0]
+
+        if len(np.unique(dims)) != len(dims):
+            msg = ("All elements of `dimensions` must be unique.")
+            raise ValueError(msg)
+
+        i_invalid = (dims < 0) | (dims >= n)
+        if np.any(i_invalid):
+            msg = (f"Dimensions {original_dims[i_invalid]} are invalid "
+                   f"for a distribution in {n} dimensions.")
+            raise ValueError(msg)
+
+        dataset = self.dataset[dims]
+        weights = self.weights
+
+        return gaussian_kde(dataset, bw_method=self.covariance_factor(),
+                            weights=weights)
+
+    @property
+    def weights(self):
+        try:
+            return self._weights
+        except AttributeError:
+            self._weights = ones(self.n)/self.n
+            return self._weights
+
+    @property
+    def neff(self):
+        try:
+            return self._neff
+        except AttributeError:
+            self._neff = 1/np.vecdot(self.weights, self.weights)
+            return self._neff
+
+
+def _get_output_dtype(covariance, points):
+    """
+    Calculates the output dtype and the "spec" (=C type name).
+
+    This was necessary in order to deal with the fused types in the Cython
+    routine `gaussian_kernel_estimate`. See gh-10824 for details.
+    """
+    output_dtype = np.common_type(covariance, points)
+    itemsize = np.dtype(output_dtype).itemsize
+    if itemsize == 4:
+        spec = 'float'
+    elif itemsize == 8:
+        spec = 'double'
+    elif itemsize in (12, 16):
+        spec = 'long double'
+    else:
+        raise ValueError(
+                f"{output_dtype} has unexpected item size: {itemsize}"
+            )
+
+    return output_dtype, spec
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_ksstats.py b/venv/lib/python3.12/site-packages/scipy/stats/_ksstats.py
new file mode 100644
index 0000000000000000000000000000000000000000..f6884bb834bbb060fdec5ed49869517e5b7c941b
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_ksstats.py
@@ -0,0 +1,600 @@
+# Compute the two-sided one-sample Kolmogorov-Smirnov Prob(Dn <= d) where:
+#    D_n = sup_x{|F_n(x) - F(x)|},
+#    F_n(x) is the empirical CDF for a sample of size n {x_i: i=1,...,n},
+#    F(x) is the CDF of a probability distribution.
+#
+# Exact methods:
+# Prob(D_n >= d) can be computed via a matrix algorithm of Durbin[1]
+#   or a recursion algorithm due to Pomeranz[2].
+# Marsaglia, Tsang & Wang[3] gave a computation-efficient way to perform
+#   the Durbin algorithm.
+#   D_n >= d <==>  D_n+ >= d or D_n- >= d (the one-sided K-S statistics), hence
+#   Prob(D_n >= d) = 2*Prob(D_n+ >= d) - Prob(D_n+ >= d and D_n- >= d).
+#   For d > 0.5, the latter intersection probability is 0.
+#
+# Approximate methods:
+# For d close to 0.5, ignoring that intersection term may still give a
+#   reasonable approximation.
+# Li-Chien[4] and Korolyuk[5] gave an asymptotic formula extending
+# Kolmogorov's initial asymptotic, suitable for large d. (See
+#   scipy.special.kolmogorov for that asymptotic)
+# Pelz-Good[6] used the functional equation for Jacobi theta functions to
+#   transform the Li-Chien/Korolyuk formula produce a computational formula
+#   suitable for small d.
+#
+# Simard and L'Ecuyer[7] provided an algorithm to decide when to use each of
+#   the above approaches and it is that which is used here.
+#
+# Other approaches:
+# Carvalho[8] optimizes Durbin's matrix algorithm for large values of d.
+# Moscovich and Nadler[9] use FFTs to compute the convolutions.
+
+# References:
+# [1] Durbin J (1968).
+#     "The Probability that the Sample Distribution Function Lies Between Two
+#     Parallel Straight Lines."
+#     Annals of Mathematical Statistics, 39, 398-411.
+# [2] Pomeranz J (1974).
+#     "Exact Cumulative Distribution of the Kolmogorov-Smirnov Statistic for
+#     Small Samples (Algorithm 487)."
+#     Communications of the ACM, 17(12), 703-704.
+# [3] Marsaglia G, Tsang WW, Wang J (2003).
+#     "Evaluating Kolmogorov's Distribution."
+#     Journal of Statistical Software, 8(18), 1-4.
+# [4] LI-CHIEN, C. (1956).
+#     "On the exact distribution of the statistics of A. N. Kolmogorov and
+#     their asymptotic expansion."
+#     Acta Matematica Sinica, 6, 55-81.
+# [5] KOROLYUK, V. S. (1960).
+#     "Asymptotic analysis of the distribution of the maximum deviation in
+#     the Bernoulli scheme."
+#     Theor. Probability Appl., 4, 339-366.
+# [6] Pelz W, Good IJ (1976).
+#     "Approximating the Lower Tail-areas of the Kolmogorov-Smirnov One-sample
+#     Statistic."
+#     Journal of the Royal Statistical Society, Series B, 38(2), 152-156.
+#  [7] Simard, R., L'Ecuyer, P. (2011)
+# 	  "Computing the Two-Sided Kolmogorov-Smirnov Distribution",
+# 	  Journal of Statistical Software, Vol 39, 11, 1-18.
+#  [8] Carvalho, Luis (2015)
+#     "An Improved Evaluation of Kolmogorov's Distribution"
+#     Journal of Statistical Software, Code Snippets; Vol 65(3), 1-8.
+#  [9] Amit Moscovich, Boaz Nadler (2017)
+#     "Fast calculation of boundary crossing probabilities for Poisson
+#     processes",
+#     Statistics & Probability Letters, Vol 123, 177-182.
+
+
+import numpy as np
+import scipy.special
+import scipy.special._ufuncs as scu
+from scipy.stats._finite_differences import _derivative
+
+_E128 = 128
+_EP128 = np.ldexp(np.longdouble(1), _E128)
+_EM128 = np.ldexp(np.longdouble(1), -_E128)
+
+_SQRT2PI = np.sqrt(2 * np.pi)
+_LOG_2PI = np.log(2 * np.pi)
+_MIN_LOG = -708
+_SQRT3 = np.sqrt(3)
+_PI_SQUARED = np.pi ** 2
+_PI_FOUR = np.pi ** 4
+_PI_SIX = np.pi ** 6
+
+# [Lifted from _loggamma.pxd.] If B_m are the Bernoulli numbers,
+# then Stirling coeffs are B_{2j}/(2j)/(2j-1) for j=8,...1.
+_STIRLING_COEFFS = [-2.955065359477124183e-2, 6.4102564102564102564e-3,
+                    -1.9175269175269175269e-3, 8.4175084175084175084e-4,
+                    -5.952380952380952381e-4, 7.9365079365079365079e-4,
+                    -2.7777777777777777778e-3, 8.3333333333333333333e-2]
+
+
+def _log_nfactorial_div_n_pow_n(n):
+    # Computes n! / n**n
+    #    = (n-1)! / n**(n-1)
+    # Uses Stirling's approximation, but removes n*log(n) up-front to
+    # avoid subtractive cancellation.
+    #    = log(n)/2 - n + log(sqrt(2pi)) + sum B_{2j}/(2j)/(2j-1)/n**(2j-1)
+    rn = 1.0/n
+    return np.log(n)/2 - n + _LOG_2PI/2 + rn * np.polyval(_STIRLING_COEFFS, rn/n)
+
+
+def _clip_prob(p):
+    """clips a probability to range 0<=p<=1."""
+    return np.clip(p, 0.0, 1.0)
+
+
+def _select_and_clip_prob(cdfprob, sfprob, cdf=True):
+    """Selects either the CDF or SF, and then clips to range 0<=p<=1."""
+    p = np.where(cdf, cdfprob, sfprob)
+    return _clip_prob(p)
+
+
+def _kolmogn_DMTW(n, d, cdf=True):
+    r"""Computes the Kolmogorov CDF:  Pr(D_n <= d) using the MTW approach to
+    the Durbin matrix algorithm.
+
+    Durbin (1968); Marsaglia, Tsang, Wang (2003). [1], [3].
+    """
+    # Write d = (k-h)/n, where k is positive integer and 0 <= h < 1
+    # Generate initial matrix H of size m*m where m=(2k-1)
+    # Compute k-th row of (n!/n^n) * H^n, scaling intermediate results.
+    # Requires memory O(m^2) and computation O(m^2 log(n)).
+    # Most suitable for small m.
+
+    if d >= 1.0:
+        return _select_and_clip_prob(1.0, 0.0, cdf)
+    nd = n * d
+    if nd <= 0.5:
+        return _select_and_clip_prob(0.0, 1.0, cdf)
+    k = int(np.ceil(nd))
+    h = k - nd
+    m = 2 * k - 1
+
+    H = np.zeros([m, m])
+
+    # Initialize: v is first column (and last row) of H
+    #  v[j] = (1-h^(j+1)/(j+1)!  (except for v[-1])
+    #  w[j] = 1/(j)!
+    # q = k-th row of H (actually i!/n^i*H^i)
+    intm = np.arange(1, m + 1)
+    v = 1.0 - h ** intm
+    w = np.empty(m)
+    fac = 1.0
+    for j in intm:
+        w[j - 1] = fac
+        fac /= j  # This might underflow.  Isn't a problem.
+        v[j - 1] *= fac
+    tt = max(2 * h - 1.0, 0)**m - 2*h**m
+    v[-1] = (1.0 + tt) * fac
+
+    for i in range(1, m):
+        H[i - 1:, i] = w[:m - i + 1]
+    H[:, 0] = v
+    H[-1, :] = np.flip(v, axis=0)
+
+    Hpwr = np.eye(np.shape(H)[0])  # Holds intermediate powers of H
+    nn = n
+    expnt = 0  # Scaling of Hpwr
+    Hexpnt = 0  # Scaling of H
+    while nn > 0:
+        if nn % 2:
+            Hpwr = np.matmul(Hpwr, H)
+            expnt += Hexpnt
+        H = np.matmul(H, H)
+        Hexpnt *= 2
+        # Scale as needed.
+        if np.abs(H[k - 1, k - 1]) > _EP128:
+            H /= _EP128
+            Hexpnt += _E128
+        nn = nn // 2
+
+    p = Hpwr[k - 1, k - 1]
+
+    # Multiply by n!/n^n
+    for i in range(1, n + 1):
+        p = i * p / n
+        if np.abs(p) < _EM128:
+            p *= _EP128
+            expnt -= _E128
+
+    # unscale
+    if expnt != 0:
+        p = np.ldexp(p, expnt)
+
+    return _select_and_clip_prob(p, 1.0-p, cdf)
+
+
+def _pomeranz_compute_j1j2(i, n, ll, ceilf, roundf):
+    """Compute the endpoints of the interval for row i."""
+    if i == 0:
+        j1, j2 = -ll - ceilf - 1, ll + ceilf - 1
+    else:
+        # i + 1 = 2*ip1div2 + ip1mod2
+        ip1div2, ip1mod2 = divmod(i + 1, 2)
+        if ip1mod2 == 0:  # i is odd
+            if ip1div2 == n + 1:
+                j1, j2 = n - ll - ceilf - 1, n + ll + ceilf - 1
+            else:
+                j1, j2 = ip1div2 - 1 - ll - roundf - 1, ip1div2 + ll - 1 + ceilf - 1
+        else:
+            j1, j2 = ip1div2 - 1 - ll - 1, ip1div2 + ll + roundf - 1
+
+    return max(j1 + 2, 0), min(j2, n)
+
+
+def _kolmogn_Pomeranz(n, x, cdf=True):
+    r"""Computes Pr(D_n <= d) using the Pomeranz recursion algorithm.
+
+    Pomeranz (1974) [2]
+    """
+
+    # V is n*(2n+2) matrix.
+    # Each row is convolution of the previous row and probabilities from a
+    #  Poisson distribution.
+    # Desired CDF probability is n! V[n-1, 2n+1]  (final entry in final row).
+    # Only two rows are needed at any given stage:
+    #  - Call them V0 and V1.
+    #  - Swap each iteration
+    # Only a few (contiguous) entries in each row can be non-zero.
+    #  - Keep track of start and end (j1 and j2 below)
+    #  - V0s and V1s track the start in the two rows
+    # Scale intermediate results as needed.
+    # Only a few different Poisson distributions can occur
+    t = n * x
+    ll = int(np.floor(t))
+    f = 1.0 * (t - ll)  # fractional part of t
+    g = min(f, 1.0 - f)
+    ceilf = (1 if f > 0 else 0)
+    roundf = (1 if f > 0.5 else 0)
+    npwrs = 2 * (ll + 1)    # Maximum number of powers needed in convolutions
+    gpower = np.empty(npwrs)  # gpower = (g/n)^m/m!
+    twogpower = np.empty(npwrs)  # twogpower = (2g/n)^m/m!
+    onem2gpower = np.empty(npwrs)  # onem2gpower = ((1-2g)/n)^m/m!
+    # gpower etc are *almost* Poisson probs, just missing normalizing factor.
+
+    gpower[0] = 1.0
+    twogpower[0] = 1.0
+    onem2gpower[0] = 1.0
+    expnt = 0
+    g_over_n, two_g_over_n, one_minus_two_g_over_n = g/n, 2*g/n, (1 - 2*g)/n
+    for m in range(1, npwrs):
+        gpower[m] = gpower[m - 1] * g_over_n / m
+        twogpower[m] = twogpower[m - 1] * two_g_over_n / m
+        onem2gpower[m] = onem2gpower[m - 1] * one_minus_two_g_over_n / m
+
+    V0 = np.zeros([npwrs])
+    V1 = np.zeros([npwrs])
+    V1[0] = 1  # first row
+    V0s, V1s = 0, 0  # start indices of the two rows
+
+    j1, j2 = _pomeranz_compute_j1j2(0, n, ll, ceilf, roundf)
+    for i in range(1, 2 * n + 2):
+        # Preserve j1, V1, V1s, V0s from last iteration
+        k1 = j1
+        V0, V1 = V1, V0
+        V0s, V1s = V1s, V0s
+        V1.fill(0.0)
+        j1, j2 = _pomeranz_compute_j1j2(i, n, ll, ceilf, roundf)
+        if i == 1 or i == 2 * n + 1:
+            pwrs = gpower
+        else:
+            pwrs = (twogpower if i % 2 else onem2gpower)
+        ln2 = j2 - k1 + 1
+        if ln2 > 0:
+            conv = np.convolve(V0[k1 - V0s:k1 - V0s + ln2], pwrs[:ln2])
+            conv_start = j1 - k1  # First index to use from conv
+            conv_len = j2 - j1 + 1  # Number of entries to use from conv
+            V1[:conv_len] = conv[conv_start:conv_start + conv_len]
+            # Scale to avoid underflow.
+            if 0 < np.max(V1) < _EM128:
+                V1 *= _EP128
+                expnt -= _E128
+            V1s = V0s + j1 - k1
+
+    # multiply by n!
+    ans = V1[n - V1s]
+    for m in range(1, n + 1):
+        if np.abs(ans) > _EP128:
+            ans *= _EM128
+            expnt += _E128
+        ans *= m
+
+    # Undo any intermediate scaling
+    if expnt != 0:
+        ans = np.ldexp(ans, expnt)
+    ans = _select_and_clip_prob(ans, 1.0 - ans, cdf)
+    return ans
+
+
+def _kolmogn_PelzGood(n, x, cdf=True):
+    """Computes the Pelz-Good approximation to Prob(Dn <= x) with 0<=x<=1.
+
+    Start with Li-Chien, Korolyuk approximation:
+        Prob(Dn <= x) ~ K0(z) + K1(z)/sqrt(n) + K2(z)/n + K3(z)/n**1.5
+    where z = x*sqrt(n).
+    Transform each K_(z) using Jacobi theta functions into a form suitable
+    for small z.
+    Pelz-Good (1976). [6]
+    """
+    if x <= 0.0:
+        return _select_and_clip_prob(0.0, 1.0, cdf=cdf)
+    if x >= 1.0:
+        return _select_and_clip_prob(1.0, 0.0, cdf=cdf)
+
+    z = np.sqrt(n) * x
+    zsquared, zthree, zfour, zsix = z**2, z**3, z**4, z**6
+
+    qlog = -_PI_SQUARED / 8 / zsquared
+    if qlog < _MIN_LOG:  # z ~ 0.041743441416853426
+        return _select_and_clip_prob(0.0, 1.0, cdf=cdf)
+
+    q = np.exp(qlog)
+
+    # Coefficients of terms in the sums for K1, K2 and K3
+    k1a = -zsquared
+    k1b = _PI_SQUARED / 4
+
+    k2a = 6 * zsix + 2 * zfour
+    k2b = (2 * zfour - 5 * zsquared) * _PI_SQUARED / 4
+    k2c = _PI_FOUR * (1 - 2 * zsquared) / 16
+
+    k3d = _PI_SIX * (5 - 30 * zsquared) / 64
+    k3c = _PI_FOUR * (-60 * zsquared + 212 * zfour) / 16
+    k3b = _PI_SQUARED * (135 * zfour - 96 * zsix) / 4
+    k3a = -30 * zsix - 90 * z**8
+
+    K0to3 = np.zeros(4)
+    # Use a Horner scheme to evaluate sum c_i q^(i^2)
+    # Reduces to a sum over odd integers.
+    maxk = int(np.ceil(16 * z / np.pi))
+    for k in range(maxk, 0, -1):
+        m = 2 * k - 1
+        msquared, mfour, msix = m**2, m**4, m**6
+        qpower = np.power(q, 8 * k)
+        coeffs = np.array([1.0,
+                           k1a + k1b*msquared,
+                           k2a + k2b*msquared + k2c*mfour,
+                           k3a + k3b*msquared + k3c*mfour + k3d*msix])
+        K0to3 *= qpower
+        K0to3 += coeffs
+    K0to3 *= q
+    K0to3 *= _SQRT2PI
+    # z**10 > 0 as z > 0.04
+    K0to3 /= np.array([z, 6 * zfour, 72 * z**7, 6480 * z**10])
+
+    # Now do the other sum over the other terms, all integers k
+    # K_2:  (pi^2 k^2) q^(k^2),
+    # K_3:  (3pi^2 k^2 z^2 - pi^4 k^4)*q^(k^2)
+    # Don't expect much subtractive cancellation so use direct calculation
+    q = np.exp(-_PI_SQUARED / 2 / zsquared)
+    ks = np.arange(maxk, 0, -1)
+    ksquared = ks ** 2
+    sqrt3z = _SQRT3 * z
+    kspi = np.pi * ks
+    qpwers = q ** ksquared
+    k2extra = np.sum(ksquared * qpwers)
+    k2extra *= _PI_SQUARED * _SQRT2PI/(-36 * zthree)
+    K0to3[2] += k2extra
+    k3extra = np.sum((sqrt3z + kspi) * (sqrt3z - kspi) * ksquared * qpwers)
+    k3extra *= _PI_SQUARED * _SQRT2PI/(216 * zsix)
+    K0to3[3] += k3extra
+    powers_of_n = np.power(n * 1.0, np.arange(len(K0to3)) / 2.0)
+    K0to3 /= powers_of_n
+
+    if not cdf:
+        K0to3 *= -1
+        K0to3[0] += 1
+
+    Ksum = sum(K0to3)
+    return Ksum
+
+
+def _kolmogn(n, x, cdf=True):
+    """Computes the CDF(or SF) for the two-sided Kolmogorov-Smirnov statistic.
+
+    x must be of type float, n of type integer.
+
+    Simard & L'Ecuyer (2011) [7].
+    """
+    if np.isnan(n):
+        return n  # Keep the same type of nan
+    if int(n) != n or n <= 0:
+        return np.nan
+    if x >= 1.0:
+        return _select_and_clip_prob(1.0, 0.0, cdf=cdf)
+    if x <= 0.0:
+        return _select_and_clip_prob(0.0, 1.0, cdf=cdf)
+    t = n * x
+    if t <= 1.0:  # Ruben-Gambino: 1/2n <= x <= 1/n
+        if t <= 0.5:
+            return _select_and_clip_prob(0.0, 1.0, cdf=cdf)
+        if n <= 140:
+            prob = np.prod(np.arange(1, n+1) * (1.0/n) * (2*t - 1))
+        else:
+            prob = np.exp(_log_nfactorial_div_n_pow_n(n) + n * np.log(2*t-1))
+        return _select_and_clip_prob(prob, 1.0 - prob, cdf=cdf)
+    if t >= n - 1:  # Ruben-Gambino
+        prob = 2 * (1.0 - x)**n
+        return _select_and_clip_prob(1 - prob, prob, cdf=cdf)
+    if x >= 0.5:  # Exact: 2 * smirnov
+        prob = 2 * scipy.special.smirnov(n, x)
+        return _select_and_clip_prob(1.0 - prob, prob, cdf=cdf)
+
+    nxsquared = t * x
+    if n <= 140:
+        if nxsquared <= 0.754693:
+            prob = _kolmogn_DMTW(n, x, cdf=True)
+            return _select_and_clip_prob(prob, 1.0 - prob, cdf=cdf)
+        if nxsquared <= 4:
+            prob = _kolmogn_Pomeranz(n, x, cdf=True)
+            return _select_and_clip_prob(prob, 1.0 - prob, cdf=cdf)
+        # Now use Miller approximation of 2*smirnov
+        prob = 2 * scipy.special.smirnov(n, x)
+        return _select_and_clip_prob(1.0 - prob, prob, cdf=cdf)
+
+    # Split CDF and SF as they have different cutoffs on nxsquared.
+    if not cdf:
+        if nxsquared >= 370.0:
+            return 0.0
+        if nxsquared >= 2.2:
+            prob = 2 * scipy.special.smirnov(n, x)
+            return _clip_prob(prob)
+        # Fall through and compute the SF as 1.0-CDF
+    if nxsquared >= 18.0:
+        cdfprob = 1.0
+    elif n <= 100000 and n * x**1.5 <= 1.4:
+        cdfprob = _kolmogn_DMTW(n, x, cdf=True)
+    else:
+        cdfprob = _kolmogn_PelzGood(n, x, cdf=True)
+    return _select_and_clip_prob(cdfprob, 1.0 - cdfprob, cdf=cdf)
+
+
+def _kolmogn_p(n, x):
+    """Computes the PDF for the two-sided Kolmogorov-Smirnov statistic.
+
+    x must be of type float, n of type integer.
+    """
+    if np.isnan(n):
+        return n  # Keep the same type of nan
+    if int(n) != n or n <= 0:
+        return np.nan
+    if x >= 1.0 or x <= 0:
+        return 0
+    t = n * x
+    if t <= 1.0:
+        # Ruben-Gambino: n!/n^n * (2t-1)^n -> 2 n!/n^n * n^2 * (2t-1)^(n-1)
+        if t <= 0.5:
+            return 0.0
+        if n <= 140:
+            prd = np.prod(np.arange(1, n) * (1.0 / n) * (2 * t - 1))
+        else:
+            prd = np.exp(_log_nfactorial_div_n_pow_n(n) + (n-1) * np.log(2 * t - 1))
+        return prd * 2 * n**2
+    if t >= n - 1:
+        # Ruben-Gambino : 1-2(1-x)**n -> 2n*(1-x)**(n-1)
+        return 2 * (1.0 - x) ** (n-1) * n
+    if x >= 0.5:
+        return 2 * scipy.stats.ksone.pdf(x, n)
+
+    # Just take a small delta.
+    # Ideally x +/- delta would stay within [i/n, (i+1)/n] for some integer a.
+    # as the CDF is a piecewise degree n polynomial.
+    # It has knots at 1/n, 2/n, ... (n-1)/n
+    # and is not a C-infinity function at the knots
+    delta = x / 2.0**16
+    delta = min(delta, x - 1.0/n)
+    delta = min(delta, 0.5 - x)
+
+    def _kk(_x):
+        return kolmogn(n, _x)
+
+    return _derivative(_kk, x, dx=delta, order=5)
+
+
+def _kolmogni(n, p, q):
+    """Computes the PPF/ISF of kolmogn.
+
+    n of type integer, n>= 1
+    p is the CDF, q the SF, p+q=1
+    """
+    if np.isnan(n):
+        return n  # Keep the same type of nan
+    if int(n) != n or n <= 0:
+        return np.nan
+    if p <= 0:
+        return 1.0/n
+    if q <= 0:
+        return 1.0
+    delta = np.exp((np.log(p) - scipy.special.loggamma(n+1))/n)
+    if delta <= 1.0/n:
+        return (delta + 1.0 / n) / 2
+    x = -np.expm1(np.log(q/2.0)/n)
+    if x >= 1 - 1.0/n:
+        return x
+    x1 = scu._kolmogci(p)/np.sqrt(n)
+    x1 = min(x1, 1.0 - 1.0/n)
+
+    def _f(x):
+        return _kolmogn(n, x) - p
+
+    return scipy.optimize.brentq(_f, 1.0/n, x1, xtol=1e-14)
+
+
+def kolmogn(n, x, cdf=True):
+    """Computes the CDF for the two-sided Kolmogorov-Smirnov distribution.
+
+    The two-sided Kolmogorov-Smirnov distribution has as its CDF Pr(D_n <= x),
+    for a sample of size n drawn from a distribution with CDF F(t), where
+    :math:`D_n &= sup_t |F_n(t) - F(t)|`, and
+    :math:`F_n(t)` is the Empirical Cumulative Distribution Function of the sample.
+
+    Parameters
+    ----------
+    n : int, array_like
+        the number of samples
+    x : float, array_like
+        The K-S statistic, float between 0 and 1
+    cdf : bool, optional
+        whether to compute the CDF(default=true) or the SF.
+
+    Returns
+    -------
+    cdf : ndarray
+        CDF (or SF it cdf is False) at the specified locations.
+
+    The return value has shape the result of numpy broadcasting n and x.
+    """
+    it = np.nditer([n, x, cdf, None], flags=['zerosize_ok'],
+                   op_dtypes=[None, np.float64, np.bool_, np.float64])
+    for _n, _x, _cdf, z in it:
+        if np.isnan(_n):
+            z[...] = _n
+            continue
+        if int(_n) != _n:
+            raise ValueError(f'n is not integral: {_n}')
+        z[...] = _kolmogn(int(_n), _x, cdf=_cdf)
+    result = it.operands[-1]
+    return result
+
+
+def kolmognp(n, x):
+    """Computes the PDF for the two-sided Kolmogorov-Smirnov distribution.
+
+    Parameters
+    ----------
+    n : int, array_like
+        the number of samples
+    x : float, array_like
+        The K-S statistic, float between 0 and 1
+
+    Returns
+    -------
+    pdf : ndarray
+        The PDF at the specified locations
+
+    The return value has shape the result of numpy broadcasting n and x.
+    """
+    it = np.nditer([n, x, None])
+    for _n, _x, z in it:
+        if np.isnan(_n):
+            z[...] = _n
+            continue
+        if int(_n) != _n:
+            raise ValueError(f'n is not integral: {_n}')
+        z[...] = _kolmogn_p(int(_n), _x)
+    result = it.operands[-1]
+    return result
+
+
+def kolmogni(n, q, cdf=True):
+    """Computes the PPF(or ISF) for the two-sided Kolmogorov-Smirnov distribution.
+
+    Parameters
+    ----------
+    n : int, array_like
+        the number of samples
+    q : float, array_like
+        Probabilities, float between 0 and 1
+    cdf : bool, optional
+        whether to compute the PPF(default=true) or the ISF.
+
+    Returns
+    -------
+    ppf : ndarray
+        PPF (or ISF if cdf is False) at the specified locations
+
+    The return value has shape the result of numpy broadcasting n and x.
+    """
+    it = np.nditer([n, q, cdf, None])
+    for _n, _q, _cdf, z in it:
+        if np.isnan(_n):
+            z[...] = _n
+            continue
+        if int(_n) != _n:
+            raise ValueError(f'n is not integral: {_n}')
+        _pcdf, _psf = (_q, 1-_q) if _cdf else (1-_q, _q)
+        z[...] = _kolmogni(int(_n), _pcdf, _psf)
+    result = it.operands[-1]
+    return result
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_levy_stable/__init__.py b/venv/lib/python3.12/site-packages/scipy/stats/_levy_stable/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..127c2464cebd4c168e5f01f0c88cfcdd1c9da8ad
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_levy_stable/__init__.py
@@ -0,0 +1,1247 @@
+#
+
+import warnings
+from functools import partial
+
+import numpy as np
+
+from scipy import optimize
+from scipy import integrate
+from scipy.integrate._quadrature import _builtincoeffs
+from scipy import interpolate
+from scipy.interpolate import RectBivariateSpline
+import scipy._external.array_api_extra as xpx
+import scipy.special as sc
+from .._distn_infrastructure import rv_continuous, _ShapeInfo, rv_continuous_frozen
+from .._continuous_distns import uniform, expon, _norm_pdf, _norm_cdf
+from .levyst import Nolan
+from scipy._lib.doccer import inherit_docstring_from
+
+
+__all__ = ["levy_stable", "levy_stable_gen", "pdf_from_cf_with_fft"]
+
+# Stable distributions are known for various parameterisations
+# some being advantageous for numerical considerations and others
+# useful due to their location/scale awareness.
+#
+# Here we follow [NO] convention (see the references in the docstring
+# for levy_stable_gen below).
+#
+# S0 / Z0 / x0 (aka Zoleterav's M)
+# S1 / Z1 / x1
+#
+# Where S* denotes parameterisation, Z* denotes standardized
+# version where gamma = 1, delta = 0 and x* denotes variable.
+#
+# Scipy's original Stable was a random variate generator. It
+# uses S1 and unfortunately is not a location/scale aware.
+
+
+# default numerical integration tolerance
+# used for epsrel in piecewise and both epsrel and epsabs in dni
+# (epsabs needed in dni since weighted quad requires epsabs > 0)
+_QUAD_EPS = 1.2e-14
+
+
+def _Phi_Z0(alpha, t):
+    return (
+        -np.tan(np.pi * alpha / 2) * (np.abs(t) ** (1 - alpha) - 1)
+        if alpha != 1
+        else -2.0 * np.log(np.abs(t)) / np.pi
+    )
+
+
+def _Phi_Z1(alpha, t):
+    return (
+        np.tan(np.pi * alpha / 2)
+        if alpha != 1
+        else -2.0 * np.log(np.abs(t)) / np.pi
+    )
+
+
+def _cf(Phi, t, alpha, beta):
+    """Characteristic function."""
+    return np.exp(
+        -(np.abs(t) ** alpha) * (1 - 1j * beta * np.sign(t) * Phi(alpha, t))
+    )
+
+
+_cf_Z0 = partial(_cf, _Phi_Z0)
+_cf_Z1 = partial(_cf, _Phi_Z1)
+
+
+def _pdf_single_value_cf_integrate(Phi, x, alpha, beta, **kwds):
+    """To improve DNI accuracy convert characteristic function in to real
+    valued integral using Euler's formula, then exploit cosine symmetry to
+    change limits to [0, inf). Finally use cosine addition formula to split
+    into two parts that can be handled by weighted quad pack.
+    """
+    quad_eps = kwds.get("quad_eps", _QUAD_EPS)
+
+    def integrand1(t):
+        if t == 0:
+            return 0
+        return np.exp(-(t ** alpha)) * (
+            np.cos(beta * (t ** alpha) * Phi(alpha, t))
+        )
+
+    def integrand2(t):
+        if t == 0:
+            return 0
+        return np.exp(-(t ** alpha)) * (
+            np.sin(beta * (t ** alpha) * Phi(alpha, t))
+        )
+
+    with np.errstate(invalid="ignore"):
+        int1, *ret1 = integrate.quad(
+            integrand1,
+            0,
+            np.inf,
+            weight="cos",
+            wvar=x,
+            limit=1000,
+            epsabs=quad_eps,
+            epsrel=quad_eps,
+            full_output=1,
+        )
+
+        int2, *ret2 = integrate.quad(
+            integrand2,
+            0,
+            np.inf,
+            weight="sin",
+            wvar=x,
+            limit=1000,
+            epsabs=quad_eps,
+            epsrel=quad_eps,
+            full_output=1,
+        )
+
+    return (int1 + int2) / np.pi
+
+
+_pdf_single_value_cf_integrate_Z0 = partial(
+    _pdf_single_value_cf_integrate, _Phi_Z0
+)
+_pdf_single_value_cf_integrate_Z1 = partial(
+    _pdf_single_value_cf_integrate, _Phi_Z1
+)
+
+
+def _nolan_round_x_near_zeta(x0, alpha, zeta, x_tol_near_zeta):
+    """Round x close to zeta for Nolan's method in [NO]."""
+    #   "8. When |x0-beta*tan(pi*alpha/2)| is small, the
+    #   computations of the density and cumulative have numerical problems.
+    #   The program works around this by setting
+    #   z = beta*tan(pi*alpha/2) when
+    #   |z-beta*tan(pi*alpha/2)| < tol(5)*alpha**(1/alpha).
+    #   (The bound on the right is ad hoc, to get reasonable behavior
+    #   when alpha is small)."
+    # where tol(5) = 0.5e-2 by default.
+    #
+    # We seem to have partially addressed this through re-expression of
+    # g(theta) here, but it still needs to be used in some extreme cases.
+    # Perhaps tol(5) = 0.5e-2 could be reduced for our implementation.
+    if np.abs(x0 - zeta) < x_tol_near_zeta * alpha ** (1 / alpha):
+        x0 = zeta
+    return x0
+
+
+def _nolan_round_difficult_input(
+    x0, alpha, beta, zeta, x_tol_near_zeta, alpha_tol_near_one
+):
+    """Round difficult input values for Nolan's method in [NO]."""
+
+    # following Nolan's STABLE,
+    #   "1. When 0 < |alpha-1| < 0.005, the program has numerical problems
+    #   evaluating the pdf and cdf.  The current version of the program sets
+    #   alpha=1 in these cases. This approximation is not bad in the S0
+    #   parameterization."
+    if np.abs(alpha - 1) < alpha_tol_near_one:
+        alpha = 1.0
+
+    #   "2. When alpha=1 and |beta| < 0.005, the program has numerical
+    #   problems.  The current version sets beta=0."
+    # We seem to have addressed this through re-expression of g(theta) here
+
+    x0 = _nolan_round_x_near_zeta(x0, alpha, zeta, x_tol_near_zeta)
+    return x0, alpha, beta
+
+
+def _pdf_single_value_piecewise_Z1(x, alpha, beta, **kwds):
+    # convert from Nolan's S_1 (aka S) to S_0 (aka Zolaterev M)
+    # parameterization
+
+    zeta = -beta * np.tan(np.pi * alpha / 2.0)
+    x0 = x + zeta if alpha != 1 else x
+
+    return _pdf_single_value_piecewise_Z0(x0, alpha, beta, **kwds)
+
+
+def _pdf_single_value_piecewise_Z0(x0, alpha, beta, **kwds):
+
+    quad_eps = kwds.get("quad_eps", _QUAD_EPS)
+    x_tol_near_zeta = kwds.get("piecewise_x_tol_near_zeta", 0.005)
+    alpha_tol_near_one = kwds.get("piecewise_alpha_tol_near_one", 0.005)
+
+    zeta = -beta * np.tan(np.pi * alpha / 2.0)
+    x0, alpha, beta = _nolan_round_difficult_input(
+        x0, alpha, beta, zeta, x_tol_near_zeta, alpha_tol_near_one
+    )
+
+    # some other known distribution pdfs / analytical cases
+    # TODO: add more where possible with test coverage,
+    # eg https://en.wikipedia.org/wiki/Stable_distribution#Other_analytic_cases
+    if alpha == 2.0:
+        # normal
+        return _norm_pdf(x0 / np.sqrt(2)) / np.sqrt(2)
+    elif alpha == 0.5 and beta == 1.0:
+        # levy
+        # since S(1/2, 1, gamma, delta; <x>) ==
+        # S(1/2, 1, gamma, gamma + delta; <x0>).
+        _x = x0 + 1
+        if _x <= 0:
+            return 0
+
+        return 1 / np.sqrt(2 * np.pi * _x) / _x * np.exp(-1 / (2 * _x))
+    elif alpha == 0.5 and beta == 0.0 and x0 != 0:
+        # analytical solution [HO]
+        S, C = sc.fresnel([1 / np.sqrt(2 * np.pi * np.abs(x0))])
+        arg = 1 / (4 * np.abs(x0))
+        return (
+            np.sin(arg) * (0.5 - S[0]) + np.cos(arg) * (0.5 - C[0])
+        ) / np.sqrt(2 * np.pi * np.abs(x0) ** 3)
+    elif alpha == 1.0 and beta == 0.0:
+        # cauchy
+        return 1 / (1 + x0 ** 2) / np.pi
+
+    return _pdf_single_value_piecewise_post_rounding_Z0(
+        x0, alpha, beta, quad_eps, x_tol_near_zeta
+    )
+
+
+def _pdf_single_value_piecewise_post_rounding_Z0(x0, alpha, beta, quad_eps,
+                                                 x_tol_near_zeta):
+    """Calculate pdf using Nolan's methods as detailed in [NO]."""
+
+    _nolan = Nolan(alpha, beta, x0)
+    zeta = _nolan.zeta
+    xi = _nolan.xi
+    c2 = _nolan.c2
+    g = _nolan.g
+
+    # round x0 to zeta again if needed. zeta was recomputed and may have
+    # changed due to floating point differences.
+    # See https://github.com/scipy/scipy/pull/18133
+    x0 = _nolan_round_x_near_zeta(x0, alpha, zeta, x_tol_near_zeta)
+    # handle Nolan's initial case logic
+    if x0 == zeta:
+        return (
+            sc.gamma(1 + 1 / alpha)
+            * np.cos(xi)
+            / np.pi
+            / ((1 + zeta ** 2) ** (1 / alpha / 2))
+        )
+    elif x0 < zeta:
+        return _pdf_single_value_piecewise_post_rounding_Z0(
+            -x0, alpha, -beta, quad_eps, x_tol_near_zeta
+        )
+
+    # following Nolan, we may now assume
+    #   x0 > zeta when alpha != 1
+    #   beta != 0 when alpha == 1
+
+    # spare calculating integral on null set
+    # use isclose as macos has fp differences
+    if np.isclose(-xi, np.pi / 2, rtol=1e-014, atol=1e-014):
+        return 0.0
+
+    def integrand(theta):
+        # limit any numerical issues leading to g_1 < 0 near theta limits
+        g_1 = g(theta)
+        if not np.isfinite(g_1) or g_1 < 0:
+            g_1 = 0
+        return g_1 * np.exp(-g_1)
+
+    with np.errstate(all="ignore"):
+        peak = optimize.bisect(
+            lambda t: g(t) - 1, -xi, np.pi / 2, xtol=quad_eps
+        )
+
+        # this integrand can be very peaked, so we need to force
+        # QUADPACK to evaluate the function inside its support
+        #
+
+        # lastly, we add additional samples at
+        #   ~exp(-100), ~exp(-10), ~exp(-5), ~exp(-1)
+        # to improve QUADPACK's detection of rapidly descending tail behavior
+        # (this choice is fairly ad hoc)
+        tail_points = [
+            optimize.bisect(lambda t: g(t) - exp_height, -xi, np.pi / 2)
+            for exp_height in [100, 10, 5]
+            # exp_height = 1 is handled by peak
+        ]
+        # Symmetry is used to ensure x > zeta as above. Integration 
+        # becomes numerically unstable so let `quad` handle 
+        # integration points
+        if beta != -1:
+            intg_points = [0, peak] + tail_points
+        else:
+            intg_points = None
+
+        intg, *ret = integrate.quad(
+            integrand,
+            -xi,
+            np.pi / 2,
+            points=intg_points,
+            limit=100,
+            epsrel=quad_eps,
+            epsabs=0,
+            full_output=1,
+        )
+
+    return c2 * intg
+
+
+def _cdf_single_value_piecewise_Z1(x, alpha, beta, **kwds):
+    # convert from Nolan's S_1 (aka S) to S_0 (aka Zolaterev M)
+    # parameterization
+
+    zeta = -beta * np.tan(np.pi * alpha / 2.0)
+    x0 = x + zeta if alpha != 1 else x
+
+    return _cdf_single_value_piecewise_Z0(x0, alpha, beta, **kwds)
+
+
+def _cdf_single_value_piecewise_Z0(x0, alpha, beta, **kwds):
+
+    quad_eps = kwds.get("quad_eps", _QUAD_EPS)
+    x_tol_near_zeta = kwds.get("piecewise_x_tol_near_zeta", 0.005)
+    alpha_tol_near_one = kwds.get("piecewise_alpha_tol_near_one", 0.005)
+
+    zeta = -beta * np.tan(np.pi * alpha / 2.0)
+    x0, alpha, beta = _nolan_round_difficult_input(
+        x0, alpha, beta, zeta, x_tol_near_zeta, alpha_tol_near_one
+    )
+
+    # some other known distribution cdfs / analytical cases
+    # TODO: add more where possible with test coverage,
+    # eg https://en.wikipedia.org/wiki/Stable_distribution#Other_analytic_cases
+    if alpha == 2.0:
+        # normal
+        return _norm_cdf(x0 / np.sqrt(2))
+    elif alpha == 0.5 and beta == 1.0:
+        # levy
+        # since S(1/2, 1, gamma, delta; <x>) ==
+        # S(1/2, 1, gamma, gamma + delta; <x0>).
+        _x = x0 + 1
+        if _x <= 0:
+            return 0
+
+        return sc.erfc(np.sqrt(0.5 / _x))
+    elif alpha == 1.0 and beta == 0.0:
+        # cauchy
+        return 0.5 + np.arctan(x0) / np.pi
+
+    return _cdf_single_value_piecewise_post_rounding_Z0(
+        x0, alpha, beta, quad_eps, x_tol_near_zeta
+    )
+
+
+def _cdf_single_value_piecewise_post_rounding_Z0(x0, alpha, beta, quad_eps,
+                                                 x_tol_near_zeta):
+    """Calculate cdf using Nolan's methods as detailed in [NO]."""
+    _nolan = Nolan(alpha, beta, x0)
+    zeta = _nolan.zeta
+    xi = _nolan.xi
+    c1 = _nolan.c1
+    # c2 = _nolan.c2
+    c3 = _nolan.c3
+    g = _nolan.g
+    # round x0 to zeta again if needed. zeta was recomputed and may have
+    # changed due to floating point differences.
+    # See https://github.com/scipy/scipy/pull/18133
+    x0 = _nolan_round_x_near_zeta(x0, alpha, zeta, x_tol_near_zeta)
+    # handle Nolan's initial case logic
+    if (alpha == 1 and beta < 0) or x0 < zeta:
+        # NOTE: Nolan's paper has a typo here!
+        # He states F(x) = 1 - F(x, alpha, -beta), but this is clearly
+        # incorrect since F(-infty) would be 1.0 in this case
+        # Indeed, the alpha != 1, x0 < zeta case is correct here.
+        return 1 - _cdf_single_value_piecewise_post_rounding_Z0(
+            -x0, alpha, -beta, quad_eps, x_tol_near_zeta
+        )
+    elif x0 == zeta:
+        return 0.5 - xi / np.pi
+
+    # following Nolan, we may now assume
+    #   x0 > zeta when alpha != 1
+    #   beta > 0 when alpha == 1
+
+    # spare calculating integral on null set
+    # use isclose as macos has fp differences
+    if np.isclose(-xi, np.pi / 2, rtol=1e-014, atol=1e-014):
+        return c1
+
+    def integrand(theta):
+        g_1 = g(theta)
+        return np.exp(-g_1)
+
+    with np.errstate(all="ignore"):
+        # shrink supports where required
+        left_support = -xi
+        right_support = np.pi / 2
+        if alpha > 1:
+            # integrand(t) monotonic 0 to 1
+            if integrand(-xi) != 0.0:
+                res = optimize.minimize(
+                    integrand,
+                    (-xi,),
+                    method="L-BFGS-B",
+                    bounds=[(-xi, np.pi / 2)],
+                )
+                left_support = res.x[0]
+        else:
+            # integrand(t) monotonic 1 to 0
+            if integrand(np.pi / 2) != 0.0:
+                res = optimize.minimize(
+                    integrand,
+                    (np.pi / 2,),
+                    method="L-BFGS-B",
+                    bounds=[(-xi, np.pi / 2)],
+                )
+                right_support = res.x[0]
+
+        intg, *ret = integrate.quad(
+            integrand,
+            left_support,
+            right_support,
+            points=[left_support, right_support],
+            limit=100,
+            epsrel=quad_eps,
+            epsabs=0,
+            full_output=1,
+        )
+
+    return c1 + c3 * intg
+
+
+def _rvs_Z1(alpha, beta, size=None, random_state=None):
+    """Simulate random variables using Nolan's methods as detailed in [NO].
+    """
+
+    def alpha1func(alpha, beta, TH, aTH, bTH, cosTH, tanTH, W):
+        return (
+            2
+            / np.pi
+            * (
+                (np.pi / 2 + bTH) * tanTH
+                - beta * np.log((np.pi / 2 * W * cosTH) / (np.pi / 2 + bTH))
+            )
+        )
+
+    def beta0func(alpha, beta, TH, aTH, bTH, cosTH, tanTH, W):
+        return (
+            W
+            / (cosTH / np.tan(aTH) + np.sin(TH))
+            * ((np.cos(aTH) + np.sin(aTH) * tanTH) / W) ** (1.0 / alpha)
+        )
+
+    def otherwise(alpha, beta, TH, aTH, bTH, cosTH, tanTH, W):
+        # alpha is not 1 and beta is not 0
+        val0 = beta * np.tan(np.pi * alpha / 2)
+        th0 = np.arctan(val0) / alpha
+        val3 = W / (cosTH / np.tan(alpha * (th0 + TH)) + np.sin(TH))
+        res3 = val3 * (
+            (
+                np.cos(aTH)
+                + np.sin(aTH) * tanTH
+                - val0 * (np.sin(aTH) - np.cos(aTH) * tanTH)
+            )
+            / W
+        ) ** (1.0 / alpha)
+        return res3
+
+    def alphanot1func(alpha, beta, TH, aTH, bTH, cosTH, tanTH, W):
+        return xpx.apply_where(
+            beta == 0, (alpha, beta, TH, aTH, bTH, cosTH, tanTH, W),
+            beta0func, otherwise)
+
+    alpha = np.broadcast_to(alpha, size)
+    beta = np.broadcast_to(beta, size)
+    TH = uniform.rvs(
+        loc=-np.pi / 2.0, scale=np.pi, size=size, random_state=random_state
+    )
+    W = expon.rvs(size=size, random_state=random_state)
+    aTH = alpha * TH
+    bTH = beta * TH
+    cosTH = np.cos(TH)
+    tanTH = np.tan(TH)
+    return xpx.apply_where(
+        alpha == 1, (alpha, beta, TH, aTH, bTH, cosTH, tanTH, W),
+        alpha1func, alphanot1func)
+
+
+def _fitstart_S0(data):
+    alpha, beta, delta1, gamma = _fitstart_S1(data)
+
+    # Formulas for mapping parameters in S1 parameterization to
+    # those in S0 parameterization can be found in [NO]. Note that
+    # only delta changes.
+    if alpha != 1:
+        delta0 = delta1 + beta * gamma * np.tan(np.pi * alpha / 2.0)
+    else:
+        delta0 = delta1 + 2 * beta * gamma * np.log(gamma) / np.pi
+
+    return alpha, beta, delta0, gamma
+
+
+def _fitstart_S1(data):
+    # We follow McCullock 1986 method - Simple Consistent Estimators
+    # of Stable Distribution Parameters
+
+    # fmt: off
+    # Table III and IV
+    nu_alpha_range = [2.439, 2.5, 2.6, 2.7, 2.8, 3, 3.2, 3.5, 4,
+                      5, 6, 8, 10, 15, 25]
+    nu_beta_range = [0, 0.1, 0.2, 0.3, 0.5, 0.7, 1]
+
+    # table III - alpha = psi_1(nu_alpha, nu_beta)
+    alpha_table = np.array([
+        [2.000, 2.000, 2.000, 2.000, 2.000, 2.000, 2.000],
+        [1.916, 1.924, 1.924, 1.924, 1.924, 1.924, 1.924],
+        [1.808, 1.813, 1.829, 1.829, 1.829, 1.829, 1.829],
+        [1.729, 1.730, 1.737, 1.745, 1.745, 1.745, 1.745],
+        [1.664, 1.663, 1.663, 1.668, 1.676, 1.676, 1.676],
+        [1.563, 1.560, 1.553, 1.548, 1.547, 1.547, 1.547],
+        [1.484, 1.480, 1.471, 1.460, 1.448, 1.438, 1.438],
+        [1.391, 1.386, 1.378, 1.364, 1.337, 1.318, 1.318],
+        [1.279, 1.273, 1.266, 1.250, 1.210, 1.184, 1.150],
+        [1.128, 1.121, 1.114, 1.101, 1.067, 1.027, 0.973],
+        [1.029, 1.021, 1.014, 1.004, 0.974, 0.935, 0.874],
+        [0.896, 0.892, 0.884, 0.883, 0.855, 0.823, 0.769],
+        [0.818, 0.812, 0.806, 0.801, 0.780, 0.756, 0.691],
+        [0.698, 0.695, 0.692, 0.689, 0.676, 0.656, 0.597],
+        [0.593, 0.590, 0.588, 0.586, 0.579, 0.563, 0.513]]).T
+    # transpose because interpolation with `RectBivariateSpline` is with
+    # `nu_beta` as `x` and `nu_alpha` as `y`
+
+    # table IV - beta = psi_2(nu_alpha, nu_beta)
+    beta_table = np.array([
+        [0, 2.160, 1.000, 1.000, 1.000, 1.000, 1.000],
+        [0, 1.592, 3.390, 1.000, 1.000, 1.000, 1.000],
+        [0, 0.759, 1.800, 1.000, 1.000, 1.000, 1.000],
+        [0, 0.482, 1.048, 1.694, 1.000, 1.000, 1.000],
+        [0, 0.360, 0.760, 1.232, 2.229, 1.000, 1.000],
+        [0, 0.253, 0.518, 0.823, 1.575, 1.000, 1.000],
+        [0, 0.203, 0.410, 0.632, 1.244, 1.906, 1.000],
+        [0, 0.165, 0.332, 0.499, 0.943, 1.560, 1.000],
+        [0, 0.136, 0.271, 0.404, 0.689, 1.230, 2.195],
+        [0, 0.109, 0.216, 0.323, 0.539, 0.827, 1.917],
+        [0, 0.096, 0.190, 0.284, 0.472, 0.693, 1.759],
+        [0, 0.082, 0.163, 0.243, 0.412, 0.601, 1.596],
+        [0, 0.074, 0.147, 0.220, 0.377, 0.546, 1.482],
+        [0, 0.064, 0.128, 0.191, 0.330, 0.478, 1.362],
+        [0, 0.056, 0.112, 0.167, 0.285, 0.428, 1.274]]).T
+
+    # Table V and VII
+    # These are ordered with decreasing `alpha_range`; so we will need to
+    # reverse them as required by RectBivariateSpline.
+    alpha_range = [2, 1.9, 1.8, 1.7, 1.6, 1.5, 1.4, 1.3, 1.2, 1.1,
+                   1, 0.9, 0.8, 0.7, 0.6, 0.5][::-1]
+    beta_range = [0, 0.25, 0.5, 0.75, 1]
+
+    # Table V - nu_c = psi_3(alpha, beta)
+    nu_c_table = np.array([
+        [1.908, 1.908, 1.908, 1.908, 1.908],
+        [1.914, 1.915, 1.916, 1.918, 1.921],
+        [1.921, 1.922, 1.927, 1.936, 1.947],
+        [1.927, 1.930, 1.943, 1.961, 1.987],
+        [1.933, 1.940, 1.962, 1.997, 2.043],
+        [1.939, 1.952, 1.988, 2.045, 2.116],
+        [1.946, 1.967, 2.022, 2.106, 2.211],
+        [1.955, 1.984, 2.067, 2.188, 2.333],
+        [1.965, 2.007, 2.125, 2.294, 2.491],
+        [1.980, 2.040, 2.205, 2.435, 2.696],
+        [2.000, 2.085, 2.311, 2.624, 2.973],
+        [2.040, 2.149, 2.461, 2.886, 3.356],
+        [2.098, 2.244, 2.676, 3.265, 3.912],
+        [2.189, 2.392, 3.004, 3.844, 4.775],
+        [2.337, 2.634, 3.542, 4.808, 6.247],
+        [2.588, 3.073, 4.534, 6.636, 9.144]])[::-1].T
+    # transpose because interpolation with `RectBivariateSpline` is with
+    # `beta` as `x` and `alpha` as `y`
+
+    # Table VII - nu_zeta = psi_5(alpha, beta)
+    nu_zeta_table = np.array([
+        [0, 0.000, 0.000, 0.000, 0.000],
+        [0, -0.017, -0.032, -0.049, -0.064],
+        [0, -0.030, -0.061, -0.092, -0.123],
+        [0, -0.043, -0.088, -0.132, -0.179],
+        [0, -0.056, -0.111, -0.170, -0.232],
+        [0, -0.066, -0.134, -0.206, -0.283],
+        [0, -0.075, -0.154, -0.241, -0.335],
+        [0, -0.084, -0.173, -0.276, -0.390],
+        [0, -0.090, -0.192, -0.310, -0.447],
+        [0, -0.095, -0.208, -0.346, -0.508],
+        [0, -0.098, -0.223, -0.380, -0.576],
+        [0, -0.099, -0.237, -0.424, -0.652],
+        [0, -0.096, -0.250, -0.469, -0.742],
+        [0, -0.089, -0.262, -0.520, -0.853],
+        [0, -0.078, -0.272, -0.581, -0.997],
+        [0, -0.061, -0.279, -0.659, -1.198]])[::-1].T
+    # fmt: on
+
+    psi_1 = RectBivariateSpline(nu_beta_range, nu_alpha_range,
+                                alpha_table, kx=1, ky=1, s=0)
+
+    def psi_1_1(nu_beta, nu_alpha):
+        return psi_1(nu_beta, nu_alpha) \
+            if nu_beta > 0 else psi_1(-nu_beta, nu_alpha)
+
+    psi_2 = RectBivariateSpline(nu_beta_range, nu_alpha_range,
+                                beta_table, kx=1, ky=1, s=0)
+
+    def psi_2_1(nu_beta, nu_alpha):
+        return psi_2(nu_beta, nu_alpha) \
+            if nu_beta > 0 else -psi_2(-nu_beta, nu_alpha)
+
+    phi_3 = RectBivariateSpline(beta_range, alpha_range, nu_c_table,
+                                kx=1, ky=1, s=0)
+
+    def phi_3_1(beta, alpha):
+        return phi_3(beta, alpha) if beta > 0 else phi_3(-beta, alpha)
+
+    phi_5 = RectBivariateSpline(beta_range, alpha_range, nu_zeta_table,
+                                kx=1, ky=1, s=0)
+
+    def phi_5_1(beta, alpha):
+        return phi_5(beta, alpha) if beta > 0 else -phi_5(-beta, alpha)
+
+    # quantiles
+    p05 = np.percentile(data, 5)
+    p50 = np.percentile(data, 50)
+    p95 = np.percentile(data, 95)
+    p25 = np.percentile(data, 25)
+    p75 = np.percentile(data, 75)
+
+    nu_alpha = (p95 - p05) / (p75 - p25)
+    nu_beta = (p95 + p05 - 2 * p50) / (p95 - p05)
+
+    if nu_alpha >= 2.439:
+        eps = np.finfo(float).eps
+        alpha = np.clip(psi_1_1(nu_beta, nu_alpha)[0, 0], eps, 2.)
+        beta = np.clip(psi_2_1(nu_beta, nu_alpha)[0, 0], -1.0, 1.0)
+    else:
+        alpha = 2.0
+        beta = np.sign(nu_beta)
+    c = (p75 - p25) / phi_3_1(beta, alpha)[0, 0]
+    zeta = p50 + c * phi_5_1(beta, alpha)[0, 0]
+    delta = zeta-beta*c*np.tan(np.pi*alpha/2.) if alpha != 1. else zeta
+
+    return (alpha, beta, delta, c)
+
+
+class levy_stable_gen(rv_continuous):
+    r"""A Levy-stable continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    levy, levy_l, cauchy, norm
+
+    Notes
+    -----
+    The distribution for `levy_stable` has characteristic function:
+
+    .. math::
+
+        \varphi(t, \alpha, \beta, c, \mu) =
+        e^{it\mu -|ct|^{\alpha}(1-i\beta\operatorname{sign}(t)\Phi)}
+
+    where
+
+    - :math:`\alpha` is the stability parameter (:math:`0 < \alpha \le 2`),
+    - :math:`\beta` is the skewness parameter (:math:`-1 \le \beta \le 1`),
+    - :math:`c` is the scale parameter (:math:`c > 0`),
+    - :math:`\mu` is the location parameter (:math:`-\infty < \mu < \infty`).
+
+    Two parameterizations of :math:`\Phi` are supported.
+
+    The :math:`S_1` parameterization (default):
+
+    .. math::
+
+        \Phi = \begin{cases}
+                \tan \left({\frac {\pi \alpha }{2}}\right)&\alpha \neq 1\\
+                -{\frac {2}{\pi }}\log |t|&\alpha =1
+                \end{cases}
+
+    The :math:`S_0` parameterization:
+
+    .. math::
+
+        \Phi = \begin{cases}
+                -\tan \left({\frac {\pi \alpha }{2}}\right)(|ct|^{1-\alpha}-1)
+                &\alpha \neq 1\\
+                -{\frac {2}{\pi }}\log |ct|&\alpha =1
+                \end{cases}
+
+
+    The probability density function for `levy_stable` is:
+
+    .. math::
+
+        f(x) = \frac{1}{2\pi}\int_{-\infty}^\infty \varphi(t)e^{-ixt}\,dt
+
+    where :math:`-\infty < x < \infty`. This integral does not have a known
+    closed form.
+
+    `levy_stable` generalizes several distributions.  Where possible, they
+    should be used instead.  Specifically, when the shape parameters
+    assume the values in the table below, the corresponding equivalent
+    distribution should be used.
+
+    =========  ========  ===========
+    ``alpha``  ``beta``   Equivalent
+    =========  ========  ===========
+     1/2       -1        `levy_l`
+     1/2       1         `levy`
+     1         0         `cauchy`
+     2         any       `norm` (with ``scale=sqrt(2)``)
+    =========  ========  ===========
+
+    Evaluation of the pdf uses Nolan's piecewise integration approach with the
+    Zolotarev :math:`M` parameterization by default. There is also the option
+    to use direct numerical integration of the standard parameterization of the
+    characteristic function or to evaluate by taking the FFT of the
+    characteristic function.
+
+    The default method can changed by setting the class variable
+    ``levy_stable.pdf_default_method`` to one of 'piecewise' for Nolan's
+    approach, 'dni' for direct numerical integration, or 'fft-simpson' for the
+    FFT based approach. For the sake of backwards compatibility, the methods
+    'best' and 'zolotarev' are equivalent to 'piecewise' and the method
+    'quadrature' is equivalent to 'dni'.
+
+    The parameterization can be changed  by setting the class variable
+    ``levy_stable.parameterization`` to either 'S0' or 'S1'.
+    The default is 'S1'.
+
+    To improve performance of piecewise and direct numerical integration one
+    can specify ``levy_stable.quad_eps`` (defaults to 1.2e-14). This is used
+    as both the absolute and relative quadrature tolerance for direct numerical
+    integration and as the relative quadrature tolerance for the piecewise
+    method. One can also specify ``levy_stable.piecewise_x_tol_near_zeta``
+    (defaults to 0.005) for how close x is to zeta before it is considered the
+    same as x [NO]. The exact check is
+    ``abs(x0 - zeta) < piecewise_x_tol_near_zeta*alpha**(1/alpha)``. One can
+    also specify ``levy_stable.piecewise_alpha_tol_near_one`` (defaults to
+    0.005) for how close alpha is to 1 before being considered equal to 1.
+
+    To increase accuracy of FFT calculation one can specify
+    ``levy_stable.pdf_fft_grid_spacing`` (defaults to 0.001) and
+    ``pdf_fft_n_points_two_power`` (defaults to None which means a value is
+    calculated that sufficiently covers the input range).
+
+    Further control over FFT calculation is available by setting
+    ``pdf_fft_interpolation_degree`` (defaults to 3) for spline order and
+    ``pdf_fft_interpolation_level`` for determining the number of points to use
+    in the Newton-Cotes formula when approximating the characteristic function
+    (considered experimental).
+
+    Evaluation of the cdf uses Nolan's piecewise integration approach with the
+    Zolatarev :math:`S_0` parameterization by default. There is also the option
+    to evaluate through integration of an interpolated spline of the pdf
+    calculated by means of the FFT method. The settings affecting FFT
+    calculation are the same as for pdf calculation. The default cdf method can
+    be changed by setting ``levy_stable.cdf_default_method`` to either
+    'piecewise' or 'fft-simpson'.  For cdf calculations the Zolatarev method is
+    superior in accuracy, so FFT is disabled by default.
+
+    Fitting estimate uses quantile estimation method in [MC]. MLE estimation of
+    parameters in fit method uses this quantile estimate initially. Note that
+    MLE doesn't always converge if using FFT for pdf calculations; this will be
+    the case if alpha <= 1 where the FFT approach doesn't give good
+    approximations.
+
+    Any non-missing value for the attribute
+    ``levy_stable.pdf_fft_min_points_threshold`` will set
+    ``levy_stable.pdf_default_method`` to 'fft-simpson' if a valid
+    default method is not otherwise set.
+
+
+
+    .. warning::
+
+        For pdf calculations FFT calculation is considered experimental.
+
+        For cdf calculations FFT calculation is considered experimental. Use
+        Zolatarev's method instead (default).
+
+    The probability density above is defined in the "standardized" form. To
+    shift and/or scale the distribution use the ``loc`` and ``scale``
+    parameters.
+    Generally ``%(name)s.pdf(x, %(shapes)s, loc, scale)`` is identically
+    equivalent to ``%(name)s.pdf(y, %(shapes)s) / scale`` with
+    ``y = (x - loc) / scale``, except in the ``S1`` parameterization if
+    ``alpha == 1``.  In that case ``%(name)s.pdf(x, %(shapes)s, loc, scale)``
+    is identically equivalent to ``%(name)s.pdf(y, %(shapes)s) / scale`` with
+    ``y = (x - loc - 2 * beta * scale * np.log(scale) / np.pi) / scale``.
+    See [NO2]_ Definition 1.8 for more information.
+    Note that shifting the location of a distribution
+    does not make it a "noncentral" distribution.
+
+    References
+    ----------
+    .. [MC] McCulloch, J., 1986. Simple consistent estimators of stable
+        distribution parameters. Communications in Statistics - Simulation and
+        Computation 15, 11091136.
+    .. [WZ] Wang, Li and Zhang, Ji-Hong, 2008. Simpson's rule based FFT method
+        to compute densities of stable distribution.
+    .. [NO] Nolan, J., 1997. Numerical Calculation of Stable Densities and
+        distributions Functions.
+    .. [NO2] Nolan, J., 2018. Stable Distributions: Models for Heavy Tailed
+        Data.
+    .. [HO] Hopcraft, K. I., Jakeman, E., Tanner, R. M. J., 1999. Lévy random
+        walks with fluctuating step number and multiscale behavior.
+
+    %(example)s
+
+    """
+    # Configurable options as class variables
+    # (accessible from self by attribute lookup).
+    parameterization = "S1"
+    pdf_default_method = "piecewise"
+    cdf_default_method = "piecewise"
+    quad_eps = _QUAD_EPS
+    piecewise_x_tol_near_zeta = 0.005
+    piecewise_alpha_tol_near_one = 0.005
+    pdf_fft_min_points_threshold = None
+    pdf_fft_grid_spacing = 0.001
+    pdf_fft_n_points_two_power = None
+    pdf_fft_interpolation_level = 3
+    pdf_fft_interpolation_degree = 3
+
+    def __call__(self, *args, **params):
+        dist = levy_stable_frozen(self, *args, **params)
+        dist.parameterization = self.parameterization
+        return dist
+
+    def _argcheck(self, alpha, beta):
+        return (alpha > 0) & (alpha <= 2) & (beta <= 1) & (beta >= -1)
+
+    def _shape_info(self):
+        ialpha = _ShapeInfo("alpha", False, (0, 2), (False, True))
+        ibeta = _ShapeInfo("beta", False, (-1, 1), (True, True))
+        return [ialpha, ibeta]
+
+    def _parameterization(self):
+        allowed = ("S0", "S1")
+        pz = self.parameterization
+        if pz not in allowed:
+            raise RuntimeError(
+                f"Parameterization '{pz}' in supported list: {allowed}"
+            )
+        return pz
+
+    @inherit_docstring_from(rv_continuous)
+    def rvs(self, *args, **kwds):
+        X1 = super().rvs(*args, **kwds)
+
+        kwds.pop("discrete", None)
+        kwds.pop("random_state", None)
+        (alpha, beta), delta, gamma, size = self._parse_args_rvs(*args, **kwds)
+
+        # shift location for this parameterisation (S1)
+        X1 = np.where(
+            alpha == 1.0, X1 + 2 * beta * gamma * np.log(gamma) / np.pi, X1
+        )
+
+        if self._parameterization() == "S0":
+            return np.where(
+                alpha == 1.0,
+                X1 - (beta * 2 * gamma * np.log(gamma) / np.pi),
+                X1 - gamma * beta * np.tan(np.pi * alpha / 2.0),
+            )
+        elif self._parameterization() == "S1":
+            return X1
+
+    def _rvs(self, alpha, beta, size=None, random_state=None):
+        return _rvs_Z1(alpha, beta, size, random_state)
+
+    @inherit_docstring_from(rv_continuous)
+    def pdf(self, x, *args, **kwds):
+        # override base class version to correct
+        # location for S1 parameterization
+        if self._parameterization() == "S0":
+            return super().pdf(x, *args, **kwds)
+        elif self._parameterization() == "S1":
+            (alpha, beta), delta, gamma = self._parse_args(*args, **kwds)
+            if np.all(np.reshape(alpha, (1, -1))[0, :] != 1):
+                return super().pdf(x, *args, **kwds)
+            else:
+                # correct location for this parameterisation
+                x = np.reshape(x, (1, -1))[0, :]
+                x, alpha, beta = np.broadcast_arrays(x, alpha, beta)
+
+                data_in = np.dstack((x, alpha, beta))[0]
+                data_out = np.empty(shape=(len(data_in), 1))
+                # group data in unique arrays of alpha, beta pairs
+                uniq_param_pairs = np.unique(data_in[:, 1:], axis=0)
+                for pair in uniq_param_pairs:
+                    _alpha, _beta = pair
+                    _delta = (
+                        delta + 2 * _beta * gamma * np.log(gamma) / np.pi
+                        if _alpha == 1.0
+                        else delta
+                    )
+                    data_mask = np.all(data_in[:, 1:] == pair, axis=-1)
+                    _x = data_in[data_mask, 0]
+                    data_out[data_mask] = (
+                        super()
+                        .pdf(_x, _alpha, _beta, loc=_delta, scale=gamma)
+                        .reshape(len(_x), 1)
+                    )
+                output = data_out.T[0]
+                if output.shape == (1,):
+                    return output[0]
+                return output
+
+    def _pdf(self, x, alpha, beta):
+        if self._parameterization() == "S0":
+            _pdf_single_value_piecewise = _pdf_single_value_piecewise_Z0
+            _pdf_single_value_cf_integrate = _pdf_single_value_cf_integrate_Z0
+            _cf = _cf_Z0
+        elif self._parameterization() == "S1":
+            _pdf_single_value_piecewise = _pdf_single_value_piecewise_Z1
+            _pdf_single_value_cf_integrate = _pdf_single_value_cf_integrate_Z1
+            _cf = _cf_Z1
+
+        x = np.asarray(x).reshape(1, -1)[0, :]
+
+        x, alpha, beta = np.broadcast_arrays(x, alpha, beta)
+
+        data_in = np.dstack((x, alpha, beta))[0]
+        data_out = np.empty(shape=(len(data_in), 1))
+
+        pdf_default_method_name = self.pdf_default_method
+        if pdf_default_method_name in ("piecewise", "best", "zolotarev"):
+            pdf_single_value_method = _pdf_single_value_piecewise
+        elif pdf_default_method_name in ("dni", "quadrature"):
+            pdf_single_value_method = _pdf_single_value_cf_integrate
+        elif (
+            pdf_default_method_name == "fft-simpson"
+            or self.pdf_fft_min_points_threshold is not None
+        ):
+            pdf_single_value_method = None
+
+        pdf_single_value_kwds = {
+            "quad_eps": self.quad_eps,
+            "piecewise_x_tol_near_zeta": self.piecewise_x_tol_near_zeta,
+            "piecewise_alpha_tol_near_one": self.piecewise_alpha_tol_near_one,
+        }
+
+        fft_grid_spacing = self.pdf_fft_grid_spacing
+        fft_n_points_two_power = self.pdf_fft_n_points_two_power
+        fft_interpolation_level = self.pdf_fft_interpolation_level
+        fft_interpolation_degree = self.pdf_fft_interpolation_degree
+
+        # group data in unique arrays of alpha, beta pairs
+        uniq_param_pairs = np.unique(data_in[:, 1:], axis=0)
+        for pair in uniq_param_pairs:
+            data_mask = np.all(data_in[:, 1:] == pair, axis=-1)
+            data_subset = data_in[data_mask]
+            if pdf_single_value_method is not None:
+                data_out[data_mask] = np.array(
+                    [
+                        pdf_single_value_method(
+                            _x, _alpha, _beta, **pdf_single_value_kwds
+                        )
+                        for _x, _alpha, _beta in data_subset
+                    ]
+                ).reshape(len(data_subset), 1)
+            else:
+                warnings.warn(
+                    "Density calculations experimental for FFT method."
+                    + " Use combination of piecewise and dni methods instead.",
+                    RuntimeWarning, stacklevel=3,
+                )
+                _alpha, _beta = pair
+                _x = data_subset[:, (0,)]
+
+                if _alpha < 1.0:
+                    raise RuntimeError(
+                        "FFT method does not work well for alpha less than 1."
+                    )
+
+                # need enough points to "cover" _x for interpolation
+                if fft_grid_spacing is None and fft_n_points_two_power is None:
+                    raise ValueError(
+                        "One of fft_grid_spacing or fft_n_points_two_power "
+                        + "needs to be set."
+                    )
+                max_abs_x = np.max(np.abs(_x))
+                h = (
+                    2 ** (3 - fft_n_points_two_power) * max_abs_x
+                    if fft_grid_spacing is None
+                    else fft_grid_spacing
+                )
+                q = (
+                    np.ceil(np.log(2 * max_abs_x / h) / np.log(2)) + 2
+                    if fft_n_points_two_power is None
+                    else int(fft_n_points_two_power)
+                )
+
+                # for some parameters, the range of x can be quite
+                # large, let's choose an arbitrary cut off (8GB) to save on
+                # computer memory.
+                MAX_Q = 30
+                if q > MAX_Q:
+                    raise RuntimeError(
+                        "fft_n_points_two_power has a maximum "
+                        + f"value of {MAX_Q}"
+                    )
+
+                density_x, density = pdf_from_cf_with_fft(
+                    lambda t: _cf(t, _alpha, _beta),
+                    h=h,
+                    q=q,
+                    level=fft_interpolation_level,
+                )
+                f = interpolate.InterpolatedUnivariateSpline(
+                    density_x, np.real(density), k=fft_interpolation_degree
+                )  # patch FFT to use cubic
+                data_out[data_mask] = f(_x)
+
+        return data_out.T[0]
+
+    @inherit_docstring_from(rv_continuous)
+    def cdf(self, x, *args, **kwds):
+        # override base class version to correct
+        # location for S1 parameterization
+        # NOTE: this is near identical to pdf() above
+        if self._parameterization() == "S0":
+            return super().cdf(x, *args, **kwds)
+        elif self._parameterization() == "S1":
+            (alpha, beta), delta, gamma = self._parse_args(*args, **kwds)
+            if np.all(np.reshape(alpha, (1, -1))[0, :] != 1):
+                return super().cdf(x, *args, **kwds)
+            else:
+                # correct location for this parameterisation
+                x = np.reshape(x, (1, -1))[0, :]
+                x, alpha, beta = np.broadcast_arrays(x, alpha, beta)
+
+                data_in = np.dstack((x, alpha, beta))[0]
+                data_out = np.empty(shape=(len(data_in), 1))
+                # group data in unique arrays of alpha, beta pairs
+                uniq_param_pairs = np.unique(data_in[:, 1:], axis=0)
+                for pair in uniq_param_pairs:
+                    _alpha, _beta = pair
+                    _delta = (
+                        delta + 2 * _beta * gamma * np.log(gamma) / np.pi
+                        if _alpha == 1.0
+                        else delta
+                    )
+                    data_mask = np.all(data_in[:, 1:] == pair, axis=-1)
+                    _x = data_in[data_mask, 0]
+                    data_out[data_mask] = (
+                        super()
+                        .cdf(_x, _alpha, _beta, loc=_delta, scale=gamma)
+                        .reshape(len(_x), 1)
+                    )
+                output = data_out.T[0]
+                if output.shape == (1,):
+                    return output[0]
+                return output
+
+    def _cdf(self, x, alpha, beta):
+        if self._parameterization() == "S0":
+            _cdf_single_value_piecewise = _cdf_single_value_piecewise_Z0
+            _cf = _cf_Z0
+        elif self._parameterization() == "S1":
+            _cdf_single_value_piecewise = _cdf_single_value_piecewise_Z1
+            _cf = _cf_Z1
+
+        x = np.asarray(x).reshape(1, -1)[0, :]
+
+        x, alpha, beta = np.broadcast_arrays(x, alpha, beta)
+
+        data_in = np.dstack((x, alpha, beta))[0]
+        data_out = np.empty(shape=(len(data_in), 1))
+
+        cdf_default_method_name = self.cdf_default_method
+        if cdf_default_method_name == "piecewise":
+            cdf_single_value_method = _cdf_single_value_piecewise
+        elif cdf_default_method_name == "fft-simpson":
+            cdf_single_value_method = None
+
+        cdf_single_value_kwds = {
+            "quad_eps": self.quad_eps,
+            "piecewise_x_tol_near_zeta": self.piecewise_x_tol_near_zeta,
+            "piecewise_alpha_tol_near_one": self.piecewise_alpha_tol_near_one,
+        }
+
+        fft_grid_spacing = self.pdf_fft_grid_spacing
+        fft_n_points_two_power = self.pdf_fft_n_points_two_power
+        fft_interpolation_level = self.pdf_fft_interpolation_level
+        fft_interpolation_degree = self.pdf_fft_interpolation_degree
+
+        # group data in unique arrays of alpha, beta pairs
+        uniq_param_pairs = np.unique(data_in[:, 1:], axis=0)
+        for pair in uniq_param_pairs:
+            data_mask = np.all(data_in[:, 1:] == pair, axis=-1)
+            data_subset = data_in[data_mask]
+            if cdf_single_value_method is not None:
+                data_out[data_mask] = np.array(
+                    [
+                        cdf_single_value_method(
+                            _x, _alpha, _beta, **cdf_single_value_kwds
+                        )
+                        for _x, _alpha, _beta in data_subset
+                    ]
+                ).reshape(len(data_subset), 1)
+            else:
+                warnings.warn(
+                    "Cumulative density calculations experimental for FFT"
+                    + " method. Use piecewise method instead.",
+                    RuntimeWarning, stacklevel=3,
+                )
+                _alpha, _beta = pair
+                _x = data_subset[:, (0,)]
+
+                # need enough points to "cover" _x for interpolation
+                if fft_grid_spacing is None and fft_n_points_two_power is None:
+                    raise ValueError(
+                        "One of fft_grid_spacing or fft_n_points_two_power "
+                        + "needs to be set."
+                    )
+                max_abs_x = np.max(np.abs(_x))
+                h = (
+                    2 ** (3 - fft_n_points_two_power) * max_abs_x
+                    if fft_grid_spacing is None
+                    else fft_grid_spacing
+                )
+                q = (
+                    np.ceil(np.log(2 * max_abs_x / h) / np.log(2)) + 2
+                    if fft_n_points_two_power is None
+                    else int(fft_n_points_two_power)
+                )
+
+                density_x, density = pdf_from_cf_with_fft(
+                    lambda t: _cf(t, _alpha, _beta),
+                    h=h,
+                    q=q,
+                    level=fft_interpolation_level,
+                )
+                f = interpolate.InterpolatedUnivariateSpline(
+                    density_x, np.real(density), k=fft_interpolation_degree
+                )
+                data_out[data_mask] = np.array(
+                    [f.integral(self.a, float(x_1.squeeze())) for x_1 in _x]
+                ).reshape(data_out[data_mask].shape)
+
+        return data_out.T[0]
+
+    def _fitstart(self, data):
+        if self._parameterization() == "S0":
+            _fitstart = _fitstart_S0
+        elif self._parameterization() == "S1":
+            _fitstart = _fitstart_S1
+        return _fitstart(data)
+
+    def _stats(self, alpha, beta):
+        mu = 0 if alpha > 1 else np.nan
+        mu2 = 2 if alpha == 2 else np.inf
+        g1 = 0.0 if alpha == 2.0 else np.nan
+        g2 = 0.0 if alpha == 2.0 else np.nan
+        return mu, mu2, g1, g2
+
+
+# cotes numbers - see sequence from http://oeis.org/A100642
+Cotes_table = np.array(
+    [[], [1]] + [v[2] for v in _builtincoeffs.values()], dtype=object
+)
+Cotes = np.array(
+    [
+        np.pad(r, (0, len(Cotes_table) - 1 - len(r)), mode='constant')
+        for r in Cotes_table
+    ]
+)
+
+
+def pdf_from_cf_with_fft(cf, h=0.01, q=9, level=3):
+    """Calculates pdf from characteristic function.
+
+    Uses fast Fourier transform with Newton-Cotes integration following [WZ].
+    Defaults to using Simpson's method (3-point Newton-Cotes integration).
+
+    Parameters
+    ----------
+    cf : callable
+        Single argument function from float -> complex expressing a
+        characteristic function for some distribution.
+    h : Optional[float]
+        Step size for Newton-Cotes integration. Default: 0.01
+    q : Optional[int]
+        Use 2**q steps when performing Newton-Cotes integration.
+        The infinite integral in the inverse Fourier transform will then
+        be restricted to the interval [-2**q * h / 2, 2**q * h / 2]. Setting
+        the number of steps equal to a power of 2 allows the fft to be
+        calculated in O(n*log(n)) time rather than O(n**2).
+        Default: 9
+    level : Optional[int]
+        Calculate integral using n-point Newton-Cotes integration for
+        n = level. The 3-point Newton-Cotes formula corresponds to Simpson's
+        rule. Default: 3
+
+    Returns
+    -------
+    x_l : ndarray
+        Array of points x at which pdf is estimated. 2**q equally spaced
+        points from -pi/h up to but not including pi/h.
+    density : ndarray
+        Estimated values of pdf corresponding to cf at points in x_l.
+
+    References
+    ----------
+    .. [WZ] Wang, Li and Zhang, Ji-Hong, 2008. Simpson's rule based FFT method
+        to compute densities of stable distribution.
+    """
+    n = level
+    N = 2**q
+    steps = np.arange(0, N)
+    L = N * h / 2
+    x_l = np.pi * (steps - N / 2) / L
+    if level > 1:
+        indices = np.arange(n).reshape(n, 1)
+        s1 = np.sum(
+            (-1) ** steps * Cotes[n, indices] * np.fft.fft(
+                (-1)**steps * cf(-L + h * steps + h * indices / (n - 1))
+            ) * np.exp(
+                1j * np.pi * indices / (n - 1)
+                - 2 * 1j * np.pi * indices * steps /
+                (N * (n - 1))
+            ),
+            axis=0
+        )
+    else:
+        s1 = (-1) ** steps * Cotes[n, 0] * np.fft.fft(
+            (-1) ** steps * cf(-L + h * steps)
+        )
+    density = h * s1 / (2 * np.pi * np.sum(Cotes[n]))
+    return (x_l, density)
+
+
+levy_stable = levy_stable_gen(name="levy_stable")
+
+
+class levy_stable_frozen(rv_continuous_frozen):
+    @property
+    def parameterization(self):
+        return self.dist.parameterization
+
+    @parameterization.setter
+    def parameterization(self, value):
+        self.dist.parameterization = value
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@@ -0,0 +1,537 @@
+import threading
+import numpy as np
+
+from scipy._lib._array_api import (array_namespace, xp_capabilities, xp_size,
+                                   xp_promote, is_lazy_array, is_jax, is_marray,
+                                   _count_nonmasked)
+from scipy._lib._bunch import _make_tuple_bunch
+import scipy._external.array_api_extra as xpx
+from scipy import special
+from scipy import stats
+from scipy.stats._stats_py import _rankdata, _get_pvalue, _SimpleNormal
+from scipy.stats._morestats import wilcoxon_result_unpacker, wilcoxon_outputs
+from scipy.stats._wilcoxon import _correction_sign
+from ._axis_nan_policy import _axis_nan_policy_factory
+
+class _MWU:
+    '''Distribution of MWU statistic under the null hypothesis'''
+
+    def __init__(self, n1, n2):
+        self._reset(n1, n2)
+
+    def set_shapes(self, n1, n2):
+        n1, n2 = min(n1, n2), max(n1, n2)
+        if (n1, n2) == (self.n1, self.n2):
+            return
+
+        self.n1 = n1
+        self.n2 = n2
+        self.s_array = np.zeros(0, dtype=int)
+        self.configurations = np.zeros(0, dtype=np.uint64)
+
+    def reset(self):
+        self._reset(self.n1, self.n2)
+
+    def _reset(self, n1, n2):
+        self.n1 = None
+        self.n2 = None
+        self.set_shapes(n1, n2)
+
+    def pmf(self, k):
+
+        # In practice, `pmf` is never called with k > m*n/2.
+        # If it were, we'd exploit symmetry here:
+        # k = np.array(k, copy=True)
+        # k2 = m*n - k
+        # i = k2 < k
+        # k[i] = k2[i]
+
+        pmfs = self.build_u_freqs_array(np.max(k))
+        return pmfs[k]
+
+    def cdf(self, k):
+        '''Cumulative distribution function'''
+
+        # In practice, `cdf` is never called with k > m*n/2.
+        # If it were, we'd exploit symmetry here rather than in `sf`
+        pmfs = self.build_u_freqs_array(np.max(k))
+        cdfs = np.cumsum(pmfs)
+        return cdfs[k]
+
+    def sf(self, k):
+        '''Survival function'''
+        # Note that both CDF and SF include the PMF at k. The p-value is
+        # calculated from the SF and should include the mass at k, so this
+        # is desirable
+
+        # Use the fact that the distribution is symmetric and sum from the left
+        kc = np.asarray(self.n1*self.n2 - k)  # complement of k
+        i = k < kc
+        if np.any(i):
+            kc[i] = k[i]
+            cdfs = np.asarray(self.cdf(kc))
+            cdfs[i] = 1. - cdfs[i] + self.pmf(kc[i])
+        else:
+            cdfs = np.asarray(self.cdf(kc))
+        return cdfs[()]
+
+    # build_sigma_array and build_u_freqs_array adapted from code
+    # by @toobaz with permission. Thanks to @andreasloe for the suggestion.
+    # See https://github.com/scipy/scipy/pull/4933#issuecomment-1898082691
+    def build_sigma_array(self, a):
+        n1, n2 = self.n1, self.n2
+        if a + 1 <= self.s_array.size:
+            return self.s_array[1:a+1]
+
+        s_array = np.zeros(a + 1, dtype=int)
+
+        for d in np.arange(1, n1 + 1):
+            # All multiples of d, except 0:
+            indices = np.arange(d, a + 1, d)
+            # \epsilon_d = 1:
+            s_array[indices] += d
+
+        for d in np.arange(n2 + 1, n2 + n1 + 1):
+            # All multiples of d, except 0:
+            indices = np.arange(d, a + 1, d)
+            # \epsilon_d = -1:
+            s_array[indices] -= d
+
+        # We don't need 0:
+        self.s_array = s_array
+        return s_array[1:]
+
+    def build_u_freqs_array(self, maxu):
+        """
+        Build all the array of frequencies for u from 0 to maxu.
+        Assumptions:
+          n1 <= n2
+          maxu <= n1 * n2 / 2
+        """
+        n1, n2 = self.n1, self.n2
+        total = special.binom(n1 + n2, n1)
+
+        if maxu + 1 <= self.configurations.size:
+            return self.configurations[:maxu + 1] / total
+
+        s_array = self.build_sigma_array(maxu)
+
+        # Start working with ints, for maximum precision and efficiency:
+        configurations = np.zeros(maxu + 1, dtype=np.uint64)
+        configurations_is_uint = True
+        uint_max = np.iinfo(np.uint64).max
+        # How many ways to have U=0? 1
+        configurations[0] = 1
+
+        for u in np.arange(1, maxu + 1):
+            coeffs = s_array[u - 1::-1]
+            new_val = np.dot(configurations[:u], coeffs) / u
+            if new_val > uint_max and configurations_is_uint:
+                # OK, we got into numbers too big for uint64.
+                # So now we start working with floats.
+                # By doing this since the beginning, we would have lost precision.
+                # (And working on python long ints would be unbearably slow)
+                configurations = configurations.astype(float)
+                configurations_is_uint = False
+            configurations[u] = new_val
+
+        self.configurations = configurations
+        return configurations / total
+
+
+# Maintain state for faster repeat calls to `mannwhitneyu`.
+# _MWU() is calculated once per thread and stored as an attribute on
+# this thread-local variable inside mannwhitneyu().
+_mwu_state = threading.local()
+
+
+def _get_mwu_z(U, n1, n2, t, continuity=True, *, alternative, xp):
+    '''Standardized MWU statistic'''
+    # Follows mannwhitneyu [2]
+    mu = n1 * n2 / 2
+    n = n1 + n2
+
+    # Tie correction according to [2], "Normal approximation and tie correction"
+    # "A more computationally-efficient form..."
+    tie_term = xp.sum(t**3 - t, axis=-1)
+    s = xp.sqrt(n1*n2/12 * ((n + 1) - tie_term/(n*(n-1))))
+
+    numerator = U - mu
+
+    # Continuity correction.
+    # Sign is chosen to always increase the p-value to account for the rest of the
+    # probability mass _at_ q = U.
+    if continuity:
+        sign = _correction_sign(numerator, alternative, xp=xp)
+        numerator -= 0.5 * sign
+
+    # no problem evaluating the norm SF at an infinity
+    with np.errstate(divide='ignore', invalid='ignore'):
+        z = numerator / s
+    return z
+
+
+def _mwu_input_validation(x, y, use_continuity, alternative, axis, method):
+    ''' Input validation and standardization for mannwhitneyu '''
+    xp = array_namespace(x, y)
+
+    if not is_lazy_array(x) and (xp.any(xp.isnan(x)) or xp.any(xp.isnan(y))):
+        raise ValueError('`x` and `y` must not contain NaNs.')
+    if xp_size(x) == 0 or xp_size(y) == 0:
+        raise ValueError('`x` and `y` must be of nonzero size.')
+    x, y = xp_promote(x, y, force_floating=True, xp=xp)
+
+    bools = {True, False}
+    if use_continuity not in bools:
+        raise ValueError(f'`use_continuity` must be one of {bools}.')
+
+    alternatives = {"two-sided", "less", "greater"}
+    alternative = alternative.lower()
+    if alternative not in alternatives:
+        raise ValueError(f'`alternative` must be one of {alternatives}.')
+
+    axis_int = int(axis)
+    if axis != axis_int:
+        raise ValueError('`axis` must be an integer.')
+
+    if not isinstance(method, stats.PermutationMethod):
+        methods = {"asymptotic", "exact", "auto"}
+        method = method.lower()
+        if method not in methods:
+            raise ValueError(f'`method` must be one of {methods}.')
+
+    if is_marray(xp) and method != "asymptotic":
+        message = "Only `method='asymptotic'` is compatible with MArrays."
+        raise ValueError(message)
+
+    output_z = True if method == 'asymptotic' else False
+
+    return x, y, use_continuity, alternative, axis_int, method, output_z, xp
+
+
+def _mwu_choose_method(n1, n2, ties):
+    """Choose method 'asymptotic' or 'exact' depending on input size, ties"""
+
+    # if both inputs are large, asymptotic is OK
+    if n1 > 8 and n2 > 8:
+        return "asymptotic"
+
+    # if there are any ties, asymptotic is preferred
+    if ties:
+        return "asymptotic"
+
+    return "exact"
+
+
+MannwhitneyuResult = _make_tuple_bunch('MannwhitneyuResult', ['statistic', 'pvalue'])
+
+
+def mwu_result_object(statistic, pvalue, zstatistic=None):
+    res = MannwhitneyuResult(statistic, pvalue)
+    if zstatistic is not None:
+        res.zstatistic = zstatistic
+    return res
+
+
+@xp_capabilities(
+    cpu_only=True,  # exact calculation only implemented in NumPy
+    skip_backends=[('dask.array', 'needs rankdata')],
+    jax_jit=False,  # the exact null distribution is NumPy-only
+    marray=True,
+    extra_note=("Only ``method='asymptotic'`` is compatible with MArray input."
+                "``method='auto'`` is incompatible with JAX arrays."))
+@_axis_nan_policy_factory(mwu_result_object, n_samples=2,
+                          result_to_tuple=wilcoxon_result_unpacker,
+                          n_outputs=wilcoxon_outputs)
+def mannwhitneyu(x, y, use_continuity=True, alternative="two-sided",
+                 axis=0, method="auto"):
+    r'''Perform the Mann-Whitney U rank test on two independent samples.
+
+    The Mann-Whitney U test is a nonparametric test of the null hypothesis
+    that the distribution underlying sample `x` is the same as the
+    distribution underlying sample `y`. It is often used as a test of
+    difference in location between distributions.
+
+    Parameters
+    ----------
+    x, y : array-like
+        N-d arrays of samples. The arrays must be broadcastable except along
+        the dimension given by `axis`.
+    use_continuity : bool, optional
+            Whether a continuity correction (1/2) should be applied.
+            Default is True when `method` is ``'asymptotic'``; has no effect
+            otherwise.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis. Default is 'two-sided'.
+        Let *SX(u)* and *SY(u)* be the survival functions of the
+        distributions underlying `x` and `y`, respectively. Then the following
+        alternative hypotheses are available:
+
+        * 'two-sided': the distributions are not equal, i.e. *SX(u) ≠ SY(u)* for
+          at least one *u*.
+        * 'less': the distribution underlying `x` is stochastically less
+          than the distribution underlying `y`, i.e. *SX(u) < SY(u)* for all *u*.
+        * 'greater': the distribution underlying `x` is stochastically greater
+          than the distribution underlying `y`, i.e. *SX(u) > SY(u)* for all *u*.
+
+        Under a more restrictive set of assumptions, the alternative hypotheses
+        can be expressed in terms of the locations of the distributions;
+        see [5]_ section 5.1.
+    axis : int, optional
+        Axis along which to perform the test. Default is 0.
+    method : {'auto', 'asymptotic', 'exact'} or `PermutationMethod` instance, optional
+        Selects the method used to calculate the *p*-value.
+        Default is 'auto'. The following options are available.
+
+        * ``'asymptotic'``: compares the standardized test statistic
+          against the normal distribution, correcting for ties.
+        * ``'exact'``: computes the exact *p*-value by comparing the observed
+          :math:`U` statistic against the exact distribution of the :math:`U`
+          statistic under the null hypothesis. No correction is made for ties.
+        * ``'auto'``: chooses ``'exact'`` when the size of one of the samples
+          is less than or equal to 8 and there are no ties;
+          chooses ``'asymptotic'`` otherwise.
+        * `PermutationMethod` instance. In this case, the p-value
+          is computed using `permutation_test` with the provided
+          configuration options and other appropriate settings.
+
+    Returns
+    -------
+    res : MannwhitneyuResult
+        An object containing attributes:
+
+        statistic : float
+            The Mann-Whitney U statistic corresponding with sample `x`. See
+            Notes for the test statistic corresponding with sample `y`.
+        pvalue : float
+            The associated *p*-value for the chosen `alternative`.
+        zstatistic : array_like
+            When ``method = 'approx'``, this is the normalized z-statistic::
+
+                z = (U - mn - d) / se
+
+            where ``U`` is `statistic` as defined above, ``mn`` is the mean of the
+            distribution under the null hypothesis, ``d`` is a continuity
+            correction, and ``se`` is the standard error.
+            When ``method != 'asymptotic'``, this attribute is not available.
+
+    Notes
+    -----
+    If ``U1`` is the statistic corresponding with sample `x`, then the
+    statistic corresponding with sample `y` is
+    ``U2 = x.shape[axis] * y.shape[axis] - U1``.
+
+    The p-value and standardized z-statistic produced by the Mann-Whitney U test is
+    identical to that produced by a Wilcoxon *rank sum* test, but different raw
+    statistics are associated with the tests. Specifically, the rank sum statistic
+    corresponding with the first sample is
+    ``R1 = U1 + x.shape[axis] * (x.shape[axis] + 1) / 2``.
+
+    `mannwhitneyu` is for independent samples. For related / paired samples,
+    consider `scipy.stats.wilcoxon`.
+
+    `method` ``'exact'`` is recommended when there are no ties and when either
+    sample size is less than 8 [1]_. The implementation follows the algorithm
+    reported in [3]_.
+    Note that the exact method is *not* corrected for ties, but
+    `mannwhitneyu` will not raise errors or warnings if there are ties in the
+    data. If there are ties and either samples is small (fewer than ~10
+    observations), consider passing an instance of `PermutationMethod`
+    as the `method` to perform a permutation test.
+
+    The Mann-Whitney U test is a non-parametric version of the t-test for
+    independent samples. When the means of samples from the populations
+    are normally distributed, consider `scipy.stats.ttest_ind`.
+
+    See Also
+    --------
+    scipy.stats.wilcoxon, scipy.stats.ttest_ind
+
+    References
+    ----------
+    .. [1] H.B. Mann and D.R. Whitney, "On a test of whether one of two random
+           variables is stochastically larger than the other", The Annals of
+           Mathematical Statistics, Vol. 18, pp. 50-60, 1947.
+    .. [2] Mann-Whitney U Test, Wikipedia,
+           http://en.wikipedia.org/wiki/Mann-Whitney_U_test
+    .. [3] Andreas Löffler,
+           "Über eine Partition der nat. Zahlen und ihr Anwendung beim U-Test",
+           Wiss. Z. Univ. Halle, XXXII'83 pp. 87-89.
+    .. [4] Rosie Shier, "Statistics: 2.3 The Mann-Whitney U Test", Mathematics
+           Learning Support Centre, 2004.
+    .. [5] Michael P. Fay and Michael A. Proschan. "Wilcoxon-Mann-Whitney
+           or t-test? On assumptions for hypothesis tests and multiple \
+           interpretations of decision rules." Statistics surveys, Vol. 4, pp.
+           1-39, 2010. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2857732/
+    .. [6] MathWorks. "ranksum - Wilcoxon rank sum test - MATLAB".
+           https://www.mathworks.com/help/stats/ranksum.html.
+
+    Examples
+    --------
+    We follow the example from [4]_: nine randomly sampled young adults were
+    diagnosed with type II diabetes at the ages below.
+
+    >>> males = [19, 22, 16, 29, 24]
+    >>> females = [20, 11, 17, 12]
+
+    We use the Mann-Whitney U test to assess whether there is a statistically
+    significant difference in the diagnosis age of males and females.
+    The null hypothesis is that the distribution of male diagnosis ages is
+    the same as the distribution of female diagnosis ages. We decide
+    that a confidence level of 95% is required to reject the null hypothesis
+    in favor of the alternative that the distributions are different.
+    Since the number of samples is very small and there are no ties in the
+    data, we can compare the observed test statistic against the *exact*
+    distribution of the test statistic under the null hypothesis.
+
+    >>> from scipy.stats import mannwhitneyu
+    >>> U1, p = mannwhitneyu(males, females, method="exact")
+    >>> print(U1)
+    17.0
+
+    `mannwhitneyu` always reports the statistic associated with the first
+    sample, which, in this case, is males. This agrees with :math:`U_M = 17`
+    reported in [4]_. The statistic associated with the second statistic
+    can be calculated:
+
+    >>> nx, ny = len(males), len(females)
+    >>> U2 = nx*ny - U1
+    >>> print(U2)
+    3.0
+
+    This agrees with :math:`U_F = 3` reported in [4]_. The two-sided
+    *p*-value can be calculated from either statistic, and the value produced
+    by `mannwhitneyu` agrees with :math:`p = 0.11` reported in [4]_.
+
+    >>> print(p)
+    0.1111111111111111
+
+    The exact distribution of the test statistic is asymptotically normal, so
+    the example continues by comparing the exact *p*-value against the
+    *p*-value produced using the normal approximation.
+
+    >>> _, pnorm = mannwhitneyu(males, females, method="asymptotic")
+    >>> print(pnorm)
+    0.11134688653314041
+
+    Here `mannwhitneyu`'s reported *p*-value appears to conflict with the
+    value :math:`p = 0.09` given in [4]_. The reason is that [4]_
+    does not apply the continuity correction performed by `mannwhitneyu`;
+    `mannwhitneyu` reduces the distance between the test statistic and the
+    mean :math:`\mu = n_x n_y / 2` by 0.5 to correct for the fact that the
+    discrete statistic is being compared against a continuous distribution.
+    Here, the :math:`U` statistic used is less than the mean, so we reduce
+    the distance by adding 0.5 in the numerator.
+
+    >>> import numpy as np
+    >>> from scipy.stats import norm
+    >>> U = min(U1, U2)
+    >>> N = nx + ny
+    >>> z = (U - nx*ny/2 + 0.5) / np.sqrt(nx*ny * (N + 1)/ 12)
+    >>> p = 2 * norm.cdf(z)  # use CDF to get p-value from smaller statistic
+    >>> print(p)
+    0.11134688653314041
+
+    If desired, we can disable the continuity correction to get a result
+    that agrees with that reported in [4]_.
+
+    >>> _, pnorm = mannwhitneyu(males, females, use_continuity=False,
+    ...                         method="asymptotic")
+    >>> print(pnorm)
+    0.0864107329737
+
+    Regardless of whether we perform an exact or asymptotic test, the
+    probability of the test statistic being as extreme or more extreme by
+    chance exceeds 5%, so we do not consider the results statistically
+    significant.
+
+    Suppose that, before seeing the data, we had hypothesized that females
+    would tend to be diagnosed at a younger age than males.
+    In that case, it would be natural to provide the female ages as the
+    first input, and we would have performed a one-sided test using
+    ``alternative = 'less'``: females are diagnosed at an age that is
+    stochastically less than that of males.
+
+    >>> res = mannwhitneyu(females, males, alternative="less", method="exact")
+    >>> print(res)
+    MannwhitneyuResult(statistic=3.0, pvalue=0.05555555555555555)
+
+    Again, the probability of getting a sufficiently low value of the
+    test statistic by chance under the null hypothesis is greater than 5%,
+    so we do not reject the null hypothesis in favor of our alternative.
+
+    If it is reasonable to assume that the means of samples from the
+    populations are normally distributed, we could have used a t-test to
+    perform the analysis.
+
+    >>> from scipy.stats import ttest_ind
+    >>> res = ttest_ind(females, males, alternative="less")
+    >>> print(res)
+    TtestResult(statistic=-2.239334696520584,
+                pvalue=0.030068441095757924,
+                df=7.0)
+
+    Under this assumption, the *p*-value would be low enough to reject the
+    null hypothesis in favor of the alternative.
+
+    '''
+
+    x, y, use_continuity, alternative, axis_int, method, output_z, xp = (
+        _mwu_input_validation(x, y, use_continuity, alternative, axis, method))
+
+    # axis=-1 and arrays broadcasted due to _axis_nan_policy decorator
+    xy = xp.concat((x, y), axis=-1)
+
+    n1 = _count_nonmasked(x, axis=-1, xp=xp)
+    n2 = _count_nonmasked(y, axis=-1, xp=xp)
+
+    # Follows [2]
+    ranks, _, t = _rankdata(xy, 'average', return_ties=True)  # method 2, step 1
+    ranks = xp.astype(ranks, x.dtype, copy=False)
+    t = xp.astype(t, x.dtype, copy=False)
+    R1 = xp.sum(ranks[..., :x.shape[-1]], axis=-1)         # method 2, step 2
+    U1 = R1 - n1*(n1+1)/2                                  # method 2, step 3
+    U2 = n1 * n2 - U1                                      # as U1 + U2 = n1 * n2
+
+    if alternative == "greater":
+        U, f = U1, 1  # U is the statistic to use for exact p-value, f is a factor
+    elif alternative == "less":
+        U, f = U2, 1  # Due to symmetry, it uses SF of U2 rather than CDF of U1
+    else:
+        U, f = xp.maximum(U1, U2), 2  # and will multiply SF by two for two-sided test
+
+    if method == "auto":
+        if is_jax(xp):
+            message = "`method='auto'` is incompatible with JAX arrays."
+            raise ValueError(message)
+        method = _mwu_choose_method(n1, n2, xp.any(t > 1))
+
+    if method == "exact":
+        if not hasattr(_mwu_state, 's'):
+            _mwu_state.s = _MWU(0, 0)
+        _mwu_state.s.set_shapes(n1, n2)
+        p = xpx.lazy_apply(_mwu_state.s.sf, xp.astype(U, xp.int64),
+                           as_numpy=True, dtype=xp.float64)
+        p = xp.astype(p, x.dtype, copy=False) * f
+    elif method == "asymptotic":
+        z = _get_mwu_z(U1, n1, n2, t, continuity=use_continuity,
+                       alternative=alternative, xp=xp)
+        p = _get_pvalue(z, _SimpleNormal(), alternative, xp=xp)
+    else:  # `PermutationMethod` instance (already validated)
+        def statistic(x, y, axis):
+            return mannwhitneyu(x, y, use_continuity=use_continuity,
+                                alternative=alternative, axis=axis,
+                                method="asymptotic").statistic
+
+        res = stats.permutation_test((x, y), statistic, axis=axis,
+                                     **method._asdict(), alternative=alternative)
+        p = res.pvalue
+
+    # Ensure that test statistic is not greater than 1
+    # This could happen for exact test when U = m*n/2
+    p = xp.clip(p, 0., 1.)
+
+    res = MannwhitneyuResult(U1, p)
+    if output_z:
+        res.zstatistic = z[()] if z.ndim == 0 else z
+    return res
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_mgc.py b/venv/lib/python3.12/site-packages/scipy/stats/_mgc.py
new file mode 100644
index 0000000000000000000000000000000000000000..f2ecbe9747acdcb4731a2755c88352896be10d0a
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_mgc.py
@@ -0,0 +1,552 @@
+import warnings
+import numpy as np
+
+from scipy._lib._array_api import xp_capabilities
+from scipy._lib._util import check_random_state, MapWrapper, rng_integers, _contains_nan
+from scipy._lib._bunch import _make_tuple_bunch
+from scipy.spatial.distance import cdist
+from scipy.ndimage import _measurements
+
+from ._stats import _local_correlations  # type: ignore[import-not-found]
+from . import distributions
+
+__all__ = ['multiscale_graphcorr']
+
+# FROM MGCPY: https://github.com/neurodata/mgcpy
+
+
+class _ParallelP:
+    """Helper function to calculate parallel p-value."""
+
+    def __init__(self, x, y, random_states):
+        self.x = x
+        self.y = y
+        self.random_states = random_states
+
+    def __call__(self, index):
+        order = self.random_states[index].permutation(self.y.shape[0])
+        permy = self.y[order][:, order]
+
+        # calculate permuted stats, store in null distribution
+        perm_stat = _mgc_stat(self.x, permy)[0]
+
+        return perm_stat
+
+
+def _perm_test(x, y, stat, reps=1000, workers=-1, random_state=None):
+    r"""Helper function that calculates the p-value. See below for uses.
+
+    Parameters
+    ----------
+    x, y : ndarray
+        `x` and `y` have shapes ``(n, p)`` and ``(n, q)``.
+    stat : float
+        The sample test statistic.
+    reps : int, optional
+        The number of replications used to estimate the null when using the
+        permutation test. The default is 1000 replications.
+    workers : int or map-like callable, optional
+        If `workers` is an int the population is subdivided into `workers`
+        sections and evaluated in parallel (uses
+        `multiprocessing.Pool <multiprocessing>`). Supply `-1` to use all cores
+        available to the Process. Alternatively supply a map-like callable,
+        such as `multiprocessing.Pool.map` for evaluating the population in
+        parallel. This evaluation is carried out as `workers(func, iterable)`.
+        Requires that `func` be pickleable.
+    random_state : {None, int, `numpy.random.Generator`,
+                    `numpy.random.RandomState`}, optional
+
+        If `seed` is None (or `np.random`), the `numpy.random.RandomState`
+        singleton is used.
+        If `seed` is an int, a new ``RandomState`` instance is used,
+        seeded with `seed`.
+        If `seed` is already a ``Generator`` or ``RandomState`` instance then
+        that instance is used.
+
+    Returns
+    -------
+    pvalue : float
+        The sample test p-value.
+    null_dist : list
+        The approximated null distribution.
+
+    """
+    # generate seeds for each rep (change to new parallel random number
+    # capabilities in numpy >= 1.17+)
+    random_state = check_random_state(random_state)
+    random_states = [np.random.RandomState(rng_integers(random_state, 1 << 32,
+                     size=4, dtype=np.uint32)) for _ in range(reps)]
+
+    # parallelizes with specified workers over number of reps and set seeds
+    parallelp = _ParallelP(x=x, y=y, random_states=random_states)
+    with MapWrapper(workers) as mapwrapper:
+        null_dist = np.array(list(mapwrapper(parallelp, range(reps))))
+
+    # calculate p-value and significant permutation map through list
+    pvalue = (1 + (null_dist >= stat).sum()) / (1 + reps)
+
+    return pvalue, null_dist
+
+
+def _euclidean_dist(x):
+    return cdist(x, x)
+
+
+MGCResult = _make_tuple_bunch('MGCResult',
+                              ['statistic', 'pvalue', 'mgc_dict'], [])
+
+
+@xp_capabilities(np_only=True)
+def multiscale_graphcorr(x, y, compute_distance=_euclidean_dist, reps=1000,
+                         workers=1, is_twosamp=False, random_state=None):
+    r"""Computes the Multiscale Graph Correlation (MGC) test statistic.
+
+    Specifically, for each point, MGC finds the :math:`k`-nearest neighbors for
+    one property (e.g. cloud density), and the :math:`l`-nearest neighbors for
+    the other property (e.g. grass wetness) [1]_. This pair :math:`(k, l)` is
+    called the "scale". A priori, however, it is not know which scales will be
+    most informative. So, MGC computes all distance pairs, and then efficiently
+    computes the distance correlations for all scales. The local correlations
+    illustrate which scales are relatively informative about the relationship.
+    The key, therefore, to successfully discover and decipher relationships
+    between disparate data modalities is to adaptively determine which scales
+    are the most informative, and the geometric implication for the most
+    informative scales. Doing so not only provides an estimate of whether the
+    modalities are related, but also provides insight into how the
+    determination was made. This is especially important in high-dimensional
+    data, where simple visualizations do not reveal relationships to the
+    unaided human eye. Characterizations of this implementation in particular
+    have been derived from and benchmarked within in [2]_.
+
+    Parameters
+    ----------
+    x, y : ndarray
+        If ``x`` and ``y`` have shapes ``(n, p)`` and ``(n, q)`` where `n` is
+        the number of samples and `p` and `q` are the number of dimensions,
+        then the MGC independence test will be run.  Alternatively, ``x`` and
+        ``y`` can have shapes ``(n, n)`` if they are distance or similarity
+        matrices, and ``compute_distance`` must be sent to ``None``. If ``x``
+        and ``y`` have shapes ``(n, p)`` and ``(m, p)``, an unpaired
+        two-sample MGC test will be run.
+    compute_distance : callable, optional
+        A function that computes the distance or similarity among the samples
+        within each data matrix. Set to ``None`` if ``x`` and ``y`` are
+        already distance matrices. The default uses the euclidean norm metric.
+        If you are calling a custom function, either create the distance
+        matrix before-hand or create a function of the form
+        ``compute_distance(x)`` where `x` is the data matrix for which
+        pairwise distances are calculated.
+    reps : int, optional
+        The number of replications used to estimate the null when using the
+        permutation test. The default is ``1000``.
+    workers : int or map-like callable, optional
+        If ``workers`` is an int the population is subdivided into ``workers``
+        sections and evaluated in parallel (uses ``multiprocessing.Pool
+        <multiprocessing>``). Supply ``-1`` to use all cores available to the
+        Process. Alternatively supply a map-like callable, such as
+        ``multiprocessing.Pool.map`` for evaluating the p-value in parallel.
+        This evaluation is carried out as ``workers(func, iterable)``.
+        Requires that `func` be pickleable. The default is ``1``.
+    is_twosamp : bool, optional
+        If `True`, a two sample test will be run. If ``x`` and ``y`` have
+        shapes ``(n, p)`` and ``(m, p)``, this optional will be overridden and
+        set to ``True``. Set to ``True`` if ``x`` and ``y`` both have shapes
+        ``(n, p)`` and a two sample test is desired. The default is ``False``.
+        Note that this will not run if inputs are distance matrices.
+    random_state : {None, int, `numpy.random.Generator`,
+                    `numpy.random.RandomState`}, optional
+
+        If `seed` is None (or `np.random`), the `numpy.random.RandomState`
+        singleton is used.
+        If `seed` is an int, a new ``RandomState`` instance is used,
+        seeded with `seed`.
+        If `seed` is already a ``Generator`` or ``RandomState`` instance then
+        that instance is used.
+
+    Returns
+    -------
+    res : MGCResult
+        An object containing attributes:
+
+        statistic : float
+            The sample MGC test statistic within ``[-1, 1]``.
+        pvalue : float
+            The p-value obtained via permutation.
+        mgc_dict : dict
+            Contains additional useful results:
+
+            - mgc_map : ndarray
+                A 2D representation of the latent geometry of the
+                relationship.
+            - opt_scale : (int, int)
+                The estimated optimal scale as a ``(x, y)`` pair.
+            - null_dist : list
+                The null distribution derived from the permuted matrices.
+
+    See Also
+    --------
+    pearsonr : Pearson correlation coefficient and p-value for testing
+               non-correlation.
+    kendalltau : Calculates Kendall's tau.
+    spearmanr : Calculates a Spearman rank-order correlation coefficient.
+
+    Notes
+    -----
+    A description of the process of MGC and applications on neuroscience data
+    can be found in [1]_. It is performed using the following steps:
+
+    #. Two distance matrices :math:`D^X` and :math:`D^Y` are computed and
+       modified to be mean zero columnwise. This results in two
+       :math:`n \times n` distance matrices :math:`A` and :math:`B` (the
+       centering and unbiased modification) [3]_.
+
+    #. For all values :math:`k` and :math:`l` from :math:`1, ..., n`,
+
+       * The :math:`k`-nearest neighbor and :math:`l`-nearest neighbor graphs
+         are calculated for each property. Here, :math:`G_k (i, j)` indicates
+         the :math:`k`-smallest values of the :math:`i`-th row of :math:`A`
+         and :math:`H_l (i, j)` indicates the :math:`l` smallested values of
+         the :math:`i`-th row of :math:`B`
+
+       * Let :math:`\circ` denotes the entry-wise matrix product, then local
+         correlations are summed and normalized using the following statistic:
+
+    .. math::
+
+        c^{kl} = \frac{\sum_{ij} A G_k B H_l}
+                      {\sqrt{\sum_{ij} A^2 G_k \times \sum_{ij} B^2 H_l}}
+
+    #. The MGC test statistic is the smoothed optimal local correlation of
+       :math:`\{ c^{kl} \}`. Denote the smoothing operation as :math:`R(\cdot)`
+       (which essentially set all isolated large correlations) as 0 and
+       connected large correlations the same as before, see [3]_.) MGC is,
+
+    .. math::
+
+        MGC_n (x, y) = \max_{(k, l)} R \left(c^{kl} \left( x_n, y_n \right)
+                                                    \right)
+
+    The test statistic returns a value between :math:`(-1, 1)` since it is
+    normalized.
+
+    The p-value returned is calculated using a permutation test. This process
+    is completed by first randomly permuting :math:`y` to estimate the null
+    distribution and then calculating the probability of observing a test
+    statistic, under the null, at least as extreme as the observed test
+    statistic.
+
+    MGC requires at least 5 samples to run with reliable results. It can also
+    handle high-dimensional data sets.
+    In addition, by manipulating the input data matrices, the two-sample
+    testing problem can be reduced to the independence testing problem [4]_.
+    Given sample data :math:`U` and :math:`V` of sizes :math:`p \times n`
+    :math:`p \times m`, data matrix :math:`X` and :math:`Y` can be created as
+    follows:
+
+    .. math::
+
+        X = [U | V] \in \mathcal{R}^{p \times (n + m)}
+        Y = [0_{1 \times n} | 1_{1 \times m}] \in \mathcal{R}^{(n + m)}
+
+    Then, the MGC statistic can be calculated as normal. This methodology can
+    be extended to similar tests such as distance correlation [4]_.
+
+    .. versionadded:: 1.4.0
+
+    References
+    ----------
+    .. [1] Vogelstein, J. T., Bridgeford, E. W., Wang, Q., Priebe, C. E.,
+           Maggioni, M., & Shen, C. (2019). Discovering and deciphering
+           relationships across disparate data modalities. ELife.
+    .. [2] Panda, S., Palaniappan, S., Xiong, J., Swaminathan, A.,
+           Ramachandran, S., Bridgeford, E. W., ... Vogelstein, J. T. (2019).
+           mgcpy: A Comprehensive High Dimensional Independence Testing Python
+           Package. :arXiv:`1907.02088`
+    .. [3] Shen, C., Priebe, C.E., & Vogelstein, J. T. (2019). From distance
+           correlation to multiscale graph correlation. Journal of the American
+           Statistical Association.
+    .. [4] Shen, C. & Vogelstein, J. T. (2018). The Exact Equivalence of
+           Distance and Kernel Methods for Hypothesis Testing.
+           :arXiv:`1806.05514`
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import multiscale_graphcorr
+    >>> x = np.arange(100)
+    >>> y = x
+    >>> res = multiscale_graphcorr(x, y)
+    >>> res.statistic, res.pvalue
+    (1.0, 0.001)
+
+    To run an unpaired two-sample test,
+
+    >>> x = np.arange(100)
+    >>> y = np.arange(79)
+    >>> res = multiscale_graphcorr(x, y)
+    >>> res.statistic, res.pvalue  # doctest: +SKIP
+    (0.033258146255703246, 0.023)
+
+    or, if shape of the inputs are the same,
+
+    >>> x = np.arange(100)
+    >>> y = x
+    >>> res = multiscale_graphcorr(x, y, is_twosamp=True)
+    >>> res.statistic, res.pvalue  # doctest: +SKIP
+    (-0.008021809890200488, 1.0)
+
+    """
+    if not isinstance(x, np.ndarray) or not isinstance(y, np.ndarray):
+        raise ValueError("x and y must be ndarrays")
+
+    # convert arrays of type (n,) to (n, 1)
+    if x.ndim == 1:
+        x = x[:, np.newaxis]
+    elif x.ndim != 2:
+        raise ValueError(f"Expected a 2-D array `x`, found shape {x.shape}")
+    if y.ndim == 1:
+        y = y[:, np.newaxis]
+    elif y.ndim != 2:
+        raise ValueError(f"Expected a 2-D array `y`, found shape {y.shape}")
+
+    nx, px = x.shape
+    ny, py = y.shape
+
+    # check for NaNs
+    _contains_nan(x, nan_policy='raise')
+    _contains_nan(y, nan_policy='raise')
+
+    # check for positive or negative infinity and raise error
+    if np.sum(np.isinf(x)) > 0 or np.sum(np.isinf(y)) > 0:
+        raise ValueError("Inputs contain infinities")
+
+    if nx != ny:
+        if px == py:
+            # reshape x and y for two sample testing
+            is_twosamp = True
+        else:
+            raise ValueError("Shape mismatch, x and y must have shape [n, p] "
+                             "and [n, q] or have shape [n, p] and [m, p].")
+
+    if nx < 5 or ny < 5:
+        raise ValueError("MGC requires at least 5 samples to give reasonable "
+                         "results.")
+
+    # convert x and y to float
+    x = x.astype(np.float64)
+    y = y.astype(np.float64)
+
+    # check if compute_distance_matrix if a callable()
+    if not callable(compute_distance) and compute_distance is not None:
+        raise ValueError("Compute_distance must be a function.")
+
+    # check if number of reps exists, integer, or > 0 (if under 1000 raises
+    # warning)
+    if not isinstance(reps, int) or reps < 0:
+        raise ValueError("Number of reps must be an integer greater than 0.")
+    elif reps < 1000:
+        msg = ("The number of replications is low (under 1000), and p-value "
+               "calculations may be unreliable. Use the p-value result, with "
+               "caution!")
+        warnings.warn(msg, RuntimeWarning, stacklevel=2)
+
+    if is_twosamp:
+        if compute_distance is None:
+            raise ValueError("Cannot run if inputs are distance matrices")
+        x, y = _two_sample_transform(x, y)
+
+    if compute_distance is not None:
+        # compute distance matrices for x and y
+        x = compute_distance(x)
+        y = compute_distance(y)
+
+    # calculate MGC stat
+    stat, stat_dict = _mgc_stat(x, y)
+    stat_mgc_map = stat_dict["stat_mgc_map"]
+    opt_scale = stat_dict["opt_scale"]
+
+    # calculate permutation MGC p-value
+    pvalue, null_dist = _perm_test(x, y, stat, reps=reps, workers=workers,
+                                   random_state=random_state)
+
+    # save all stats (other than stat/p-value) in dictionary
+    mgc_dict = {"mgc_map": stat_mgc_map,
+                "opt_scale": opt_scale,
+                "null_dist": null_dist}
+
+    # create result object with alias for backward compatibility
+    res = MGCResult(stat, pvalue, mgc_dict)
+    res.stat = stat
+    return res
+
+
+def _mgc_stat(distx, disty):
+    r"""Helper function that calculates the MGC stat. See above for use.
+
+    Parameters
+    ----------
+    distx, disty : ndarray
+        `distx` and `disty` have shapes ``(n, p)`` and ``(n, q)`` or
+        ``(n, n)`` and ``(n, n)``
+        if distance matrices.
+
+    Returns
+    -------
+    stat : float
+        The sample MGC test statistic within ``[-1, 1]``.
+    stat_dict : dict
+        Contains additional useful additional returns containing the following
+        keys:
+
+        - stat_mgc_map : ndarray
+            MGC-map of the statistics.
+        - opt_scale : (float, float)
+            The estimated optimal scale as a ``(x, y)`` pair.
+
+    """
+    # calculate MGC map and optimal scale
+    stat_mgc_map = _local_correlations(distx, disty, global_corr='mgc')
+
+    m, n = stat_mgc_map.shape
+    if m == 1 or n == 1:
+        # the global scale at is the statistic calculated at maximal nearest
+        # neighbors. There is not enough local scale to search over, so
+        # default to global scale
+        stat = stat_mgc_map[m - 1][n - 1]
+        opt_scale = m * n
+    else:
+        samp_size = len(distx) - 1
+
+        # threshold to find connected region of significant local correlations
+        sig_connect = _threshold_mgc_map(stat_mgc_map, samp_size)
+
+        # maximum within the significant region
+        stat, opt_scale = _smooth_mgc_map(sig_connect, stat_mgc_map)
+
+    stat_dict = {"stat_mgc_map": stat_mgc_map,
+                 "opt_scale": opt_scale}
+
+    return stat, stat_dict
+
+
+def _threshold_mgc_map(stat_mgc_map, samp_size):
+    r"""
+    Finds a connected region of significance in the MGC-map by thresholding.
+
+    Parameters
+    ----------
+    stat_mgc_map : ndarray
+        All local correlations within ``[-1,1]``.
+    samp_size : int
+        The sample size of original data.
+
+    Returns
+    -------
+    sig_connect : ndarray
+        A binary matrix with 1's indicating the significant region.
+
+    """
+    m, n = stat_mgc_map.shape
+
+    # 0.02 is simply an empirical threshold, this can be set to 0.01 or 0.05
+    # with varying levels of performance. Threshold is based on a beta
+    # approximation.
+    per_sig = 1 - (0.02 / samp_size)  # Percentile to consider as significant
+    threshold = samp_size * (samp_size - 3)/4 - 1/2  # Beta approximation
+    threshold = distributions.beta.ppf(per_sig, threshold, threshold) * 2 - 1
+
+    # the global scale at is the statistic calculated at maximal nearest
+    # neighbors. Threshold is the maximum on the global and local scales
+    threshold = max(threshold, stat_mgc_map[m - 1][n - 1])
+
+    # find the largest connected component of significant correlations
+    sig_connect = stat_mgc_map > threshold
+    if np.sum(sig_connect) > 0:
+        sig_connect, _ = _measurements.label(sig_connect)
+        _, label_counts = np.unique(sig_connect, return_counts=True)
+
+        # skip the first element in label_counts, as it is count(zeros)
+        max_label = np.argmax(label_counts[1:]) + 1
+        sig_connect = sig_connect == max_label
+    else:
+        sig_connect = np.array([[False]])
+
+    return sig_connect
+
+
+def _smooth_mgc_map(sig_connect, stat_mgc_map):
+    """Finds the smoothed maximal within the significant region R.
+
+    If area of R is too small it returns the last local correlation. Otherwise,
+    returns the maximum within significant_connected_region.
+
+    Parameters
+    ----------
+    sig_connect : ndarray
+        A binary matrix with 1's indicating the significant region.
+    stat_mgc_map : ndarray
+        All local correlations within ``[-1, 1]``.
+
+    Returns
+    -------
+    stat : float
+        The sample MGC statistic within ``[-1, 1]``.
+    opt_scale: (float, float)
+        The estimated optimal scale as an ``(x, y)`` pair.
+
+    """
+    m, n = stat_mgc_map.shape
+
+    # the global scale at is the statistic calculated at maximal nearest
+    # neighbors. By default, statistic and optimal scale are global.
+    stat = stat_mgc_map[m - 1][n - 1]
+    opt_scale = [m, n]
+
+    if np.linalg.norm(sig_connect) != 0:
+        # proceed only when the connected region's area is sufficiently large
+        # 0.02 is simply an empirical threshold, this can be set to 0.01 or 0.05
+        # with varying levels of performance
+        if np.sum(sig_connect) >= np.ceil(0.02 * max(m, n)) * min(m, n):
+            max_corr = max(stat_mgc_map[sig_connect])
+
+            # find all scales within significant_connected_region that maximize
+            # the local correlation
+            max_corr_index = np.where((stat_mgc_map >= max_corr) & sig_connect)
+
+            if max_corr >= stat:
+                stat = max_corr
+
+                k, l = max_corr_index
+                one_d_indices = k * n + l  # 2D to 1D indexing
+                k = np.max(one_d_indices) // n
+                l = np.max(one_d_indices) % n
+                opt_scale = [k+1, l+1]  # adding 1s to match R indexing
+
+    return stat, opt_scale
+
+
+def _two_sample_transform(u, v):
+    """Helper function that concatenates x and y for two sample MGC stat.
+
+    See above for use.
+
+    Parameters
+    ----------
+    u, v : ndarray
+        `u` and `v` have shapes ``(n, p)`` and ``(m, p)``.
+
+    Returns
+    -------
+    x : ndarray
+        Concatenate `u` and `v` along the ``axis = 0``. `x` thus has shape
+        ``(2n, p)``.
+    y : ndarray
+        Label matrix for `x` where 0 refers to samples that comes from `u` and
+        1 refers to samples that come from `v`. `y` thus has shape ``(2n, 1)``.
+
+    """
+    nx = u.shape[0]
+    ny = v.shape[0]
+    x = np.concatenate([u, v], axis=0)
+    y = np.concatenate([np.zeros(nx), np.ones(ny)], axis=0).reshape(-1, 1)
+    return x, y
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_morestats.py b/venv/lib/python3.12/site-packages/scipy/stats/_morestats.py
new file mode 100644
index 0000000000000000000000000000000000000000..3ead2e29323cd51229e4e5bb018d8bf52bd87fb6
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_morestats.py
@@ -0,0 +1,5086 @@
+import itertools
+import math
+import warnings
+import threading
+from collections import namedtuple
+
+import numpy as np
+from numpy import (isscalar, log, around, arange, sort, amin, amax, sqrt, array,
+                   pi, exp, ravel, count_nonzero)
+
+from scipy import optimize, special, interpolate, stats
+from scipy._lib._bunch import _make_tuple_bunch
+from scipy._lib._util import _rename_parameter, _contains_nan, _get_nan
+from scipy._lib.deprecation import _NoValue
+import scipy._external.array_api_extra as xpx
+
+from scipy._lib._array_api import (
+    array_namespace,
+    is_marray,
+    xp_capabilities,
+    is_numpy,
+    is_jax,
+    is_dask,
+    xp_size,
+    xp_vector_norm,
+    xp_promote,
+    xp_result_type,
+    xp_device,
+    xp_ravel,
+    _count_nonmasked,
+    is_lazy_array,
+)
+
+from ._ansari_swilk_statistics import gscale
+from . import _stats_py, _wilcoxon
+from ._fit import FitResult
+from ._stats_py import (_get_pvalue, SignificanceResult,  # noqa:F401
+                        _SimpleNormal, _SimpleChi2, _SimpleF, _demean)
+from .contingency import chi2_contingency
+from . import distributions
+from ._distn_infrastructure import rv_generic
+from ._axis_nan_policy import _axis_nan_policy_factory, _broadcast_arrays
+
+
+__all__ = ['mvsdist',
+           'bayes_mvs', 'kstat', 'kstatvar', 'probplot', 'ppcc_max', 'ppcc_plot',
+           'boxcox_llf', 'boxcox', 'boxcox_normmax', 'boxcox_normplot',
+           'shapiro', 'anderson', 'ansari', 'bartlett', 'levene',
+           'fligner', 'mood', 'wilcoxon', 'median_test',
+           'circmean', 'circvar', 'circstd', 'anderson_ksamp',
+           'yeojohnson_llf', 'yeojohnson', 'yeojohnson_normmax',
+           'yeojohnson_normplot', 'directional_stats',
+           'false_discovery_control'
+           ]
+
+
+Mean = namedtuple('Mean', ('statistic', 'minmax'))
+Variance = namedtuple('Variance', ('statistic', 'minmax'))
+Std_dev = namedtuple('Std_dev', ('statistic', 'minmax'))
+
+
+@xp_capabilities(np_only=True)
+def bayes_mvs(data, alpha=0.90):
+    r"""
+    Bayesian confidence intervals for the mean, var, and std.
+
+    Parameters
+    ----------
+    data : array_like
+        Input data, if multi-dimensional it is flattened to 1-D by `bayes_mvs`.
+        Requires 2 or more data points.
+    alpha : float, optional
+        Probability that the returned confidence interval contains
+        the true parameter.
+
+    Returns
+    -------
+    mean_cntr, var_cntr, std_cntr : tuple
+        The three results are for the mean, variance and standard deviation,
+        respectively.  Each result is a tuple of the form::
+
+            (center, (lower, upper))
+
+        with ``center`` the mean of the conditional pdf of the value given the
+        data, and ``(lower, upper)`` a confidence interval, centered on the
+        median, containing the estimate to a probability ``alpha``.
+
+    See Also
+    --------
+    mvsdist
+
+    Notes
+    -----
+    Each tuple of mean, variance, and standard deviation estimates represent
+    the (center, (lower, upper)) with center the mean of the conditional pdf
+    of the value given the data and (lower, upper) is a confidence interval
+    centered on the median, containing the estimate to a probability
+    ``alpha``.
+
+    Converts data to 1-D and assumes all data has the same mean and variance.
+    Uses Jeffrey's prior for variance and std.
+
+    Equivalent to ``tuple((x.mean(), x.interval(alpha)) for x in mvsdist(dat))``
+
+    References
+    ----------
+    T.E. Oliphant, "A Bayesian perspective on estimating mean, variance, and
+    standard-deviation from data", https://scholarsarchive.byu.edu/facpub/278,
+    2006.
+
+    Examples
+    --------
+    First a basic example to demonstrate the outputs:
+
+    >>> from scipy import stats
+    >>> data = [6, 9, 12, 7, 8, 8, 13]
+    >>> mean, var, std = stats.bayes_mvs(data)
+    >>> mean
+    Mean(statistic=9.0, minmax=(7.103650222612533, 10.896349777387467))
+    >>> var
+    Variance(statistic=10.0, minmax=(3.176724206, 24.45910382))
+    >>> std
+    Std_dev(statistic=2.9724954732045084,
+            minmax=(1.7823367265645143, 4.945614605014631))
+
+    Now we generate some normally distributed random data, and get estimates of
+    mean and standard deviation with 95% confidence intervals for those
+    estimates:
+
+    >>> n_samples = 100000
+    >>> data = stats.norm.rvs(size=n_samples)
+    >>> res_mean, res_var, res_std = stats.bayes_mvs(data, alpha=0.95)
+
+    >>> import matplotlib.pyplot as plt
+    >>> fig = plt.figure()
+    >>> ax = fig.add_subplot(111)
+    >>> ax.hist(data, bins=100, density=True, label='Histogram of data')
+    >>> ax.vlines(res_mean.statistic, 0, 0.5, colors='r', label='Estimated mean')
+    >>> ax.axvspan(res_mean.minmax[0],res_mean.minmax[1], facecolor='r',
+    ...            alpha=0.2, label=r'Estimated mean (95% limits)')
+    >>> ax.vlines(res_std.statistic, 0, 0.5, colors='g', label='Estimated scale')
+    >>> ax.axvspan(res_std.minmax[0],res_std.minmax[1], facecolor='g', alpha=0.2,
+    ...            label=r'Estimated scale (95% limits)')
+
+    >>> ax.legend(fontsize=10)
+    >>> ax.set_xlim([-4, 4])
+    >>> ax.set_ylim([0, 0.5])
+    >>> plt.show()
+
+    """
+    m, v, s = mvsdist(data)
+    if alpha >= 1 or alpha <= 0:
+        raise ValueError(f"0 < alpha < 1 is required, but {alpha=} was given.")
+
+    m_res = Mean(m.mean(), m.interval(alpha))
+    v_res = Variance(v.mean(), v.interval(alpha))
+    s_res = Std_dev(s.mean(), s.interval(alpha))
+
+    return m_res, v_res, s_res
+
+
+@xp_capabilities(np_only=True)
+def mvsdist(data):
+    """
+    'Frozen' distributions for mean, variance, and standard deviation of data.
+
+    Parameters
+    ----------
+    data : array_like
+        Input array. Converted to 1-D using ravel.
+        Requires 2 or more data-points.
+
+    Returns
+    -------
+    mdist : "frozen" distribution object
+        Distribution object representing the mean of the data.
+    vdist : "frozen" distribution object
+        Distribution object representing the variance of the data.
+    sdist : "frozen" distribution object
+        Distribution object representing the standard deviation of the data.
+
+    See Also
+    --------
+    bayes_mvs
+
+    Notes
+    -----
+    The return values from ``bayes_mvs(data)`` is equivalent to
+    ``tuple((x.mean(), x.interval(0.90)) for x in mvsdist(data))``.
+
+    In other words, calling ``<dist>.mean()`` and ``<dist>.interval(0.90)``
+    on the three distribution objects returned from this function will give
+    the same results that are returned from `bayes_mvs`.
+
+    References
+    ----------
+    T.E. Oliphant, "A Bayesian perspective on estimating mean, variance, and
+    standard-deviation from data", https://scholarsarchive.byu.edu/facpub/278,
+    2006.
+
+    Examples
+    --------
+    >>> from scipy import stats
+    >>> data = [6, 9, 12, 7, 8, 8, 13]
+    >>> mean, var, std = stats.mvsdist(data)
+
+    We now have frozen distribution objects "mean", "var" and "std" that we can
+    examine:
+
+    >>> mean.mean()
+    9.0
+    >>> mean.interval(0.95)
+    (6.6120585482655692, 11.387941451734431)
+    >>> mean.std()
+    1.1952286093343936
+
+    """
+    x = ravel(data)
+    n = len(x)
+    if n < 2:
+        raise ValueError("Need at least 2 data-points.")
+    xbar = x.mean()
+    C = x.var()
+    if n > 1000:  # gaussian approximations for large n
+        mdist = distributions.norm(loc=xbar, scale=math.sqrt(C / n))
+        sdist = distributions.norm(loc=math.sqrt(C), scale=math.sqrt(C / (2. * n)))
+        vdist = distributions.norm(loc=C, scale=math.sqrt(2.0 / n) * C)
+    else:
+        nm1 = n - 1
+        fac = n * C / 2.
+        val = nm1 / 2.
+        mdist = distributions.t(nm1, loc=xbar, scale=math.sqrt(C / nm1))
+        sdist = distributions.gengamma(val, -2, scale=math.sqrt(fac))
+        vdist = distributions.invgamma(val, scale=fac)
+    return mdist, vdist, sdist
+
+
+@xp_capabilities(marray=True)
+@_axis_nan_policy_factory(
+    lambda x: x, result_to_tuple=lambda x, _: (x,), n_outputs=1, default_axis=None
+)
+def kstat(data, n=2, *, axis=None):
+    r"""
+    Return the `n` th k-statistic ( ``1<=n<=4`` so far).
+
+    The `n` th k-statistic ``k_n`` is the unique symmetric unbiased estimator of the
+    `n` th cumulant :math:`\kappa_n` [1]_ [2]_.
+
+    Parameters
+    ----------
+    data : array_like
+        Input array.
+    n : int, {1, 2, 3, 4}, optional
+        Default is equal to 2.
+    axis : int or None, default: None
+        If an int, the axis of the input along which to compute the statistic.
+        The statistic of each axis-slice (e.g. row) of the input will appear
+        in a corresponding element of the output. If ``None``, the input will
+        be raveled before computing the statistic.
+
+    Returns
+    -------
+    kstat : float
+        The `n` th k-statistic.
+
+    See Also
+    --------
+    kstatvar : Returns an unbiased estimator of the variance of the k-statistic
+    moment : Returns the n-th central moment about the mean for a sample.
+
+    Notes
+    -----
+    For a sample size :math:`n`, the first few k-statistics are given by
+
+    .. math::
+
+        k_1 &= \frac{S_1}{n}, \\
+        k_2 &= \frac{nS_2 - S_1^2}{n(n-1)}, \\
+        k_3 &= \frac{2S_1^3 - 3nS_1S_2 + n^2S_3}{n(n-1)(n-2)}, \\
+        k_4 &= \frac{-6S_1^4 + 12nS_1^2S_2 - 3n(n-1)S_2^2 - 4n(n+1)S_1S_3
+        + n^2(n+1)S_4}{n (n-1)(n-2)(n-3)},
+
+    where
+
+    .. math::
+
+        S_r \equiv \sum_{i=1}^n X_i^r,
+
+    and :math:`X_i` is the :math:`i` th data point.
+
+    References
+    ----------
+    .. [1] http://mathworld.wolfram.com/k-Statistic.html
+
+    .. [2] http://mathworld.wolfram.com/Cumulant.html
+
+    Examples
+    --------
+    >>> from scipy import stats
+    >>> from numpy.random import default_rng
+    >>> rng = default_rng()
+
+    As sample size increases, `n`-th moment and `n`-th k-statistic converge to the
+    same number (although they aren't identical). In the case of the normal
+    distribution, they converge to zero.
+
+    >>> for i in range(2,8):
+    ...     x = rng.normal(size=10**i)
+    ...     m, k = stats.moment(x, 3), stats.kstat(x, 3)
+    ...     print(f"{i=}: {m=:.3g}, {k=:.3g}, {(m-k)=:.3g}")
+    i=2: m=-0.631, k=-0.651, (m-k)=0.0194  # random
+    i=3: m=0.0282, k=0.0283, (m-k)=-8.49e-05
+    i=4: m=-0.0454, k=-0.0454, (m-k)=1.36e-05
+    i=6: m=7.53e-05, k=7.53e-05, (m-k)=-2.26e-09
+    i=7: m=0.00166, k=0.00166, (m-k)=-4.99e-09
+    i=8: m=-2.88e-06 k=-2.88e-06, (m-k)=8.63e-13
+    """
+    xp = array_namespace(data)
+    data = xp.asarray(data)
+    if n > 4 or n < 1:
+        raise ValueError("k-statistics only supported for 1<=n<=4")
+    n = int(n)
+    if axis is None:
+        data = xp.reshape(data, (-1,))
+        axis = 0
+
+    N = _count_nonmasked(data, axis, xp=xp)
+
+    S = [None] + [xp.sum(data**k, axis=axis) for k in range(1, n + 1)]
+    if n == 1:
+        return S[1] * 1.0/N
+    elif n == 2:
+        return (N*S[2] - S[1]**2.0) / (N*(N - 1.0))
+    elif n == 3:
+        return (2*S[1]**3 - 3*N*S[1]*S[2] + N*N*S[3]) / (N*(N - 1.0)*(N - 2.0))
+    elif n == 4:
+        return ((-6*S[1]**4 + 12*N*S[1]**2 * S[2] - 3*N*(N-1.0)*S[2]**2 -
+                 4*N*(N+1)*S[1]*S[3] + N*N*(N+1)*S[4]) /
+                (N*(N-1.0)*(N-2.0)*(N-3.0)))
+    else:
+        raise ValueError("Should not be here.")
+
+
+@xp_capabilities(marray=True)
+@_axis_nan_policy_factory(
+    lambda x: x, result_to_tuple=lambda x, _: (x,), n_outputs=1, default_axis=None
+)
+def kstatvar(data, n=2, *, axis=None):
+    r"""Return an unbiased estimator of the variance of the k-statistic.
+
+    See `kstat` and [1]_ for more details about the k-statistic.
+
+    Parameters
+    ----------
+    data : array_like
+        Input array.
+    n : int, {1, 2}, optional
+        Default is equal to 2.
+    axis : int or None, default: None
+        If an int, the axis of the input along which to compute the statistic.
+        The statistic of each axis-slice (e.g. row) of the input will appear
+        in a corresponding element of the output. If ``None``, the input will
+        be raveled before computing the statistic.
+
+    Returns
+    -------
+    kstatvar : float
+        The `n` th k-statistic variance.
+
+    See Also
+    --------
+    kstat : Returns the n-th k-statistic.
+    moment : Returns the n-th central moment about the mean for a sample.
+
+    Notes
+    -----
+    Unbiased estimators of the variances of the first two k-statistics are given by
+
+    .. math::
+
+        \mathrm{var}(k_1) &= \frac{k_2}{n}, \\
+        \mathrm{var}(k_2) &= \frac{2k_2^2n + (n-1)k_4}{n(n + 1)}.
+
+    References
+    ----------
+    .. [1] http://mathworld.wolfram.com/k-Statistic.html
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> rng = np.random.default_rng(92366746)
+
+    As the sample size increases, the estimated variance of the k-statistic converges
+    to zero.
+
+    >>> for n in np.astype(np.logspace(1, 6, 6), int):
+    ...     x = rng.normal(size=n)
+    ...     kvar = stats.kstatvar(x, 1)
+    ...     print(f"{n=:<8}: {kvar=:.3g}")
+    n=10      : kvar=0.0954
+    n=100     : kvar=0.00974
+    n=1000    : kvar=0.000962
+    n=10000   : kvar=0.0001
+    n=100000  : kvar=9.94e-06
+    n=1000000 : kvar=9.99e-07
+    """  # noqa: E501
+    xp = array_namespace(data)
+    data = xp.asarray(data)
+    if axis is None:
+        data = xp.reshape(data, (-1,))
+        axis = 0
+    N = _count_nonmasked(data, axis, xp=xp)
+
+    if n == 1:
+        return kstat(data, n=2, axis=axis, _no_deco=True) * 1.0/N
+    elif n == 2:
+        k2 = kstat(data, n=2, axis=axis, _no_deco=True)
+        k4 = kstat(data, n=4, axis=axis, _no_deco=True)
+        return (2*N*k2**2 + (N-1)*k4) / (N*(N+1))
+    else:
+        raise ValueError("Only n=1 or n=2 supported.")
+
+
+def _calc_uniform_order_statistic_medians(n):
+    """Approximations of uniform order statistic medians.
+
+    Parameters
+    ----------
+    n : int
+        Sample size.
+
+    Returns
+    -------
+    v : 1d float array
+        Approximations of the order statistic medians.
+
+    References
+    ----------
+    .. [1] James J. Filliben, "The Probability Plot Correlation Coefficient
+           Test for Normality", Technometrics, Vol. 17, pp. 111-117, 1975.
+
+    Examples
+    --------
+    Order statistics of the uniform distribution on the unit interval
+    are marginally distributed according to beta distributions.
+    The expectations of these order statistic are evenly spaced across
+    the interval, but the distributions are skewed in a way that
+    pushes the medians slightly towards the endpoints of the unit interval:
+
+    >>> import numpy as np
+    >>> n = 4
+    >>> k = np.arange(1, n+1)
+    >>> from scipy.stats import beta
+    >>> a = k
+    >>> b = n-k+1
+    >>> beta.mean(a, b)
+    array([0.2, 0.4, 0.6, 0.8])
+    >>> beta.median(a, b)
+    array([0.15910358, 0.38572757, 0.61427243, 0.84089642])
+
+    The Filliben approximation uses the exact medians of the smallest
+    and greatest order statistics, and the remaining medians are approximated
+    by points spread evenly across a sub-interval of the unit interval:
+
+    >>> from scipy.stats._morestats import _calc_uniform_order_statistic_medians
+    >>> _calc_uniform_order_statistic_medians(n)
+    array([0.15910358, 0.38545246, 0.61454754, 0.84089642])
+
+    This plot shows the skewed distributions of the order statistics
+    of a sample of size four from a uniform distribution on the unit interval:
+
+    >>> import matplotlib.pyplot as plt
+    >>> x = np.linspace(0.0, 1.0, num=50, endpoint=True)
+    >>> pdfs = [beta.pdf(x, a[i], b[i]) for i in range(n)]
+    >>> plt.figure()
+    >>> plt.plot(x, pdfs[0], x, pdfs[1], x, pdfs[2], x, pdfs[3])
+
+    """
+    v = np.empty(n, dtype=np.float64)
+    v[-1] = 0.5**(1.0 / n)
+    v[0] = 1 - v[-1]
+    i = np.arange(2, n)
+    v[1:-1] = (i - 0.3175) / (n + 0.365)
+    return v
+
+
+def _parse_dist_kw(dist, enforce_subclass=True):
+    """Parse `dist` keyword.
+
+    Parameters
+    ----------
+    dist : str or stats.distributions instance.
+        Several functions take `dist` as a keyword, hence this utility
+        function.
+    enforce_subclass : bool, optional
+        If True (default), `dist` needs to be a
+        `_distn_infrastructure.rv_generic` instance.
+        It can sometimes be useful to set this keyword to False, if a function
+        wants to accept objects that just look somewhat like such an instance
+        (for example, they have a ``ppf`` method).
+
+    """
+    if isinstance(dist, rv_generic):
+        pass
+    elif isinstance(dist, str):
+        try:
+            dist = getattr(distributions, dist)
+        except AttributeError as e:
+            raise ValueError(f"{dist} is not a valid distribution name") from e
+    elif enforce_subclass:
+        msg = ("`dist` should be a stats.distributions instance or a string "
+               "with the name of such a distribution.")
+        raise ValueError(msg)
+
+    return dist
+
+
+def _add_axis_labels_title(plot, xlabel, ylabel, title):
+    """Helper function to add axes labels and a title to stats plots."""
+    try:
+        if hasattr(plot, 'set_title'):
+            # Matplotlib Axes instance or something that looks like it
+            plot.set_title(title)
+            plot.set_xlabel(xlabel)
+            plot.set_ylabel(ylabel)
+        else:
+            # matplotlib.pyplot module
+            plot.title(title)
+            plot.xlabel(xlabel)
+            plot.ylabel(ylabel)
+    except Exception:
+        # Not an MPL object or something that looks (enough) like it.
+        # Don't crash on adding labels or title
+        pass
+
+
+@xp_capabilities(np_only=True)
+def probplot(x, sparams=(), dist='norm', fit=True, plot=None, rvalue=False):
+    """
+    Calculate quantiles for a probability plot, and optionally show the plot.
+
+    Generates a probability plot of sample data against the quantiles of a
+    specified theoretical distribution (the normal distribution by default).
+    `probplot` optionally calculates a best-fit line for the data and plots the
+    results using Matplotlib or a given plot function.
+
+    Parameters
+    ----------
+    x : array_like
+        Sample/response data from which `probplot` creates the plot.
+    sparams : tuple, optional
+        Distribution-specific shape parameters (shape parameters plus location
+        and scale).
+    dist : str or stats.distributions instance, optional
+        Distribution or distribution function name. The default is 'norm' for a
+        normal probability plot.  Objects that look enough like a
+        stats.distributions instance (i.e. they have a ``ppf`` method) are also
+        accepted.
+    fit : bool, optional
+        Fit a least-squares regression (best-fit) line to the sample data if
+        True (default).
+    plot : object, optional
+        If given, plots the quantiles.
+        If given and `fit` is True, also plots the least squares fit.
+        `plot` is an object that has to have methods "plot" and "text".
+        The `matplotlib.pyplot` module or a Matplotlib Axes object can be used,
+        or a custom object with the same methods.
+        Default is None, which means that no plot is created.
+    rvalue : bool, optional
+        If `plot` is provided and `fit` is True, setting `rvalue` to True
+        includes the coefficient of determination on the plot.
+        Default is False.
+
+    Returns
+    -------
+    (osm, osr) : tuple of ndarrays
+        Tuple of theoretical quantiles (osm, or order statistic medians) and
+        ordered responses (osr).  `osr` is simply sorted input `x`.
+        For details on how `osm` is calculated see the Notes section.
+    (slope, intercept, r) : tuple of floats, optional
+        Tuple  containing the result of the least-squares fit, if that is
+        performed by `probplot`. `r` is the square root of the coefficient of
+        determination.  If ``fit=False`` and ``plot=None``, this tuple is not
+        returned.
+
+    Notes
+    -----
+    Even if `plot` is given, the figure is not shown or saved by `probplot`;
+    ``plt.show()`` or ``plt.savefig('figname.png')`` should be used after
+    calling `probplot`.
+
+    `probplot` generates a probability plot, which should not be confused with
+    a Q-Q or a P-P plot.  Statsmodels has more extensive functionality of this
+    type, see ``statsmodels.api.ProbPlot``.
+
+    The formula used for the theoretical quantiles (horizontal axis of the
+    probability plot) is Filliben's estimate::
+
+        quantiles = dist.ppf(val), for
+
+                0.5**(1/n),                  for i = n
+          val = (i - 0.3175) / (n + 0.365),  for i = 2, ..., n-1
+                1 - 0.5**(1/n),              for i = 1
+
+    where ``i`` indicates the i-th ordered value and ``n`` is the total number
+    of values.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> import matplotlib.pyplot as plt
+    >>> nsample = 100
+    >>> rng = np.random.default_rng()
+
+    A t distribution with small degrees of freedom:
+
+    >>> ax1 = plt.subplot(221)
+    >>> x = stats.t.rvs(3, size=nsample, random_state=rng)
+    >>> res = stats.probplot(x, plot=plt)
+
+    A t distribution with larger degrees of freedom:
+
+    >>> ax2 = plt.subplot(222)
+    >>> x = stats.t.rvs(25, size=nsample, random_state=rng)
+    >>> res = stats.probplot(x, plot=plt)
+
+    A mixture of two normal distributions with broadcasting:
+
+    >>> ax3 = plt.subplot(223)
+    >>> x = stats.norm.rvs(loc=[0,5], scale=[1,1.5],
+    ...                    size=(nsample//2,2), random_state=rng).ravel()
+    >>> res = stats.probplot(x, plot=plt)
+
+    A standard normal distribution:
+
+    >>> ax4 = plt.subplot(224)
+    >>> x = stats.norm.rvs(loc=0, scale=1, size=nsample, random_state=rng)
+    >>> res = stats.probplot(x, plot=plt)
+
+    Produce a new figure with a loggamma distribution, using the ``dist`` and
+    ``sparams`` keywords:
+
+    >>> fig = plt.figure()
+    >>> ax = fig.add_subplot(111)
+    >>> x = stats.loggamma.rvs(c=2.5, size=500, random_state=rng)
+    >>> res = stats.probplot(x, dist=stats.loggamma, sparams=(2.5,), plot=ax)
+    >>> ax.set_title("Probplot for loggamma dist with shape parameter 2.5")
+
+    Show the results with Matplotlib:
+
+    >>> plt.show()
+
+    """
+    x = np.asarray(x)
+    if x.size == 0:
+        if fit:
+            return (x, x), (np.nan, np.nan, 0.0)
+        else:
+            return x, x
+
+    osm_uniform = _calc_uniform_order_statistic_medians(len(x))
+    dist = _parse_dist_kw(dist, enforce_subclass=False)
+    if sparams is None:
+        sparams = ()
+    if isscalar(sparams):
+        sparams = (sparams,)
+    if not isinstance(sparams, tuple):
+        sparams = tuple(sparams)
+
+    osm = dist.ppf(osm_uniform, *sparams)
+    osr = sort(x)
+    if fit:
+        # perform a linear least squares fit.
+        slope, intercept, r, prob, _ = _stats_py.linregress(osm, osr)
+
+    if plot is not None:
+        plot.plot(osm, osr, 'bo')
+        if fit:
+            plot.plot(osm, slope*osm + intercept, 'r-')
+        _add_axis_labels_title(plot, xlabel='Theoretical quantiles',
+                               ylabel='Ordered Values',
+                               title='Probability Plot')
+
+        # Add R^2 value to the plot as text
+        if fit and rvalue:
+            xmin = amin(osm)
+            xmax = amax(osm)
+            ymin = amin(x)
+            ymax = amax(x)
+            posx = xmin + 0.70 * (xmax - xmin)
+            posy = ymin + 0.01 * (ymax - ymin)
+            plot.text(posx, posy, f"$R^2={r ** 2:1.4f}$")
+
+    if fit:
+        return (osm, osr), (slope, intercept, r)
+    else:
+        return osm, osr
+
+
+@xp_capabilities(np_only=True)
+def ppcc_max(x, brack=(0.0, 1.0), dist='tukeylambda'):
+    """Calculate the shape parameter that maximizes the PPCC.
+
+    The probability plot correlation coefficient (PPCC) plot can be used
+    to determine the optimal shape parameter for a one-parameter family
+    of distributions. ``ppcc_max`` returns the shape parameter that would
+    maximize the probability plot correlation coefficient for the given
+    data to a one-parameter family of distributions.
+
+    Parameters
+    ----------
+    x : array_like
+        Input array.
+    brack : tuple, optional
+        Triple (a,b,c) where (a<b<c). If bracket consists of two numbers (a, c)
+        then they are assumed to be a starting interval for a downhill bracket
+        search (see `scipy.optimize.brent`).
+    dist : str or stats.distributions instance, optional
+        Distribution or distribution function name.  Objects that look enough
+        like a stats.distributions instance (i.e. they have a ``ppf`` method)
+        are also accepted.  The default is ``'tukeylambda'``.
+
+    Returns
+    -------
+    shape_value : float
+        The shape parameter at which the probability plot correlation
+        coefficient reaches its max value.
+
+    See Also
+    --------
+    ppcc_plot, probplot, boxcox
+
+    Notes
+    -----
+    The brack keyword serves as a starting point which is useful in corner
+    cases. One can use a plot to obtain a rough visual estimate of the location
+    for the maximum to start the search near it.
+
+    References
+    ----------
+    .. [1] J.J. Filliben, "The Probability Plot Correlation Coefficient Test
+           for Normality", Technometrics, Vol. 17, pp. 111-117, 1975.
+    .. [2] Engineering Statistics Handbook, NIST/SEMATEC,
+           https://www.itl.nist.gov/div898/handbook/eda/section3/ppccplot.htm
+
+    Examples
+    --------
+    First we generate some random data from a Weibull distribution
+    with shape parameter 2.5:
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> import matplotlib.pyplot as plt
+    >>> rng = np.random.default_rng()
+    >>> c = 2.5
+    >>> x = stats.weibull_min.rvs(c, scale=4, size=2000, random_state=rng)
+
+    Generate the PPCC plot for this data with the Weibull distribution.
+
+    >>> fig, ax = plt.subplots(figsize=(8, 6))
+    >>> res = stats.ppcc_plot(x, c/2, 2*c, dist='weibull_min', plot=ax)
+
+    We calculate the value where the shape should reach its maximum and a
+    red line is drawn there. The line should coincide with the highest
+    point in the PPCC graph.
+
+    >>> cmax = stats.ppcc_max(x, brack=(c/2, 2*c), dist='weibull_min')
+    >>> ax.axvline(cmax, color='r')
+    >>> plt.show()
+
+    """
+    dist = _parse_dist_kw(dist)
+    osm_uniform = _calc_uniform_order_statistic_medians(len(x))
+    osr = sort(x)
+
+    # this function computes the x-axis values of the probability plot
+    #  and computes a linear regression (including the correlation)
+    #  and returns 1-r so that a minimization function maximizes the
+    #  correlation
+    def tempfunc(shape, mi, yvals, func):
+        xvals = func(mi, shape)
+        r, prob = _stats_py.pearsonr(xvals, yvals)
+        return 1 - r
+
+    return optimize.brent(tempfunc, brack=brack,
+                          args=(osm_uniform, osr, dist.ppf))
+
+
+@xp_capabilities(np_only=True)
+def ppcc_plot(x, a, b, dist='tukeylambda', plot=None, N=80):
+    """Calculate and optionally plot probability plot correlation coefficient.
+
+    The probability plot correlation coefficient (PPCC) plot can be used to
+    determine the optimal shape parameter for a one-parameter family of
+    distributions.  It cannot be used for distributions without shape
+    parameters
+    (like the normal distribution) or with multiple shape parameters.
+
+    By default a Tukey-Lambda distribution (`stats.tukeylambda`) is used. A
+    Tukey-Lambda PPCC plot interpolates from long-tailed to short-tailed
+    distributions via an approximately normal one, and is therefore
+    particularly useful in practice.
+
+    Parameters
+    ----------
+    x : array_like
+        Input array.
+    a, b : scalar
+        Lower and upper bounds of the shape parameter to use.
+    dist : str or stats.distributions instance, optional
+        Distribution or distribution function name.  Objects that look enough
+        like a stats.distributions instance (i.e. they have a ``ppf`` method)
+        are also accepted.  The default is ``'tukeylambda'``.
+    plot : object, optional
+        If given, plots PPCC against the shape parameter.
+        `plot` is an object that has to have methods "plot" and "text".
+        The `matplotlib.pyplot` module or a Matplotlib Axes object can be used,
+        or a custom object with the same methods.
+        Default is None, which means that no plot is created.
+    N : int, optional
+        Number of points on the horizontal axis (equally distributed from
+        `a` to `b`).
+
+    Returns
+    -------
+    svals : ndarray
+        The shape values for which `ppcc` was calculated.
+    ppcc : ndarray
+        The calculated probability plot correlation coefficient values.
+
+    See Also
+    --------
+    ppcc_max, probplot, boxcox_normplot, tukeylambda
+
+    References
+    ----------
+    J.J. Filliben, "The Probability Plot Correlation Coefficient Test for
+    Normality", Technometrics, Vol. 17, pp. 111-117, 1975.
+
+    Examples
+    --------
+    First we generate some random data from a Weibull distribution
+    with shape parameter 2.5, and plot the histogram of the data:
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> import matplotlib.pyplot as plt
+    >>> rng = np.random.default_rng()
+    >>> c = 2.5
+    >>> x = stats.weibull_min.rvs(c, scale=4, size=2000, random_state=rng)
+
+    Take a look at the histogram of the data.
+
+    >>> fig1, ax = plt.subplots(figsize=(9, 4))
+    >>> ax.hist(x, bins=50)
+    >>> ax.set_title('Histogram of x')
+    >>> plt.show()
+
+    Now we explore this data with a PPCC plot as well as the related
+    probability plot and Box-Cox normplot.  A red line is drawn where we
+    expect the PPCC value to be maximal (at the shape parameter ``c``
+    used above):
+
+    >>> fig2 = plt.figure(figsize=(12, 4))
+    >>> ax1 = fig2.add_subplot(1, 3, 1)
+    >>> ax2 = fig2.add_subplot(1, 3, 2)
+    >>> ax3 = fig2.add_subplot(1, 3, 3)
+    >>> res = stats.probplot(x, plot=ax1)
+    >>> res = stats.boxcox_normplot(x, -4, 4, plot=ax2)
+    >>> res = stats.ppcc_plot(x, c/2, 2*c, dist='weibull_min', plot=ax3)
+    >>> ax3.axvline(c, color='r')
+    >>> plt.show()
+
+    """
+    if b <= a:
+        raise ValueError("`b` has to be larger than `a`.")
+
+    svals = np.linspace(a, b, num=N)
+    ppcc = np.empty_like(svals)
+    for k, sval in enumerate(svals):
+        _, r2 = probplot(x, sval, dist=dist, fit=True)
+        ppcc[k] = r2[-1]
+
+    if plot is not None:
+        plot.plot(svals, ppcc, 'x')
+        _add_axis_labels_title(plot, xlabel='Shape Values',
+                               ylabel='Prob Plot Corr. Coef.',
+                               title=f'({dist}) PPCC Plot')
+
+    return svals, ppcc
+
+
+def _log_mean(logx, axis):
+    # compute log of mean of x from log(x)
+    return (
+        special.logsumexp(logx, axis=axis, keepdims=True)
+        - math.log(logx.shape[axis])
+    )
+
+
+def _log_var(logx, xp, axis):
+    # compute log of variance of x from log(x)
+    logmean = xp.broadcast_to(_log_mean(logx, axis=axis), logx.shape)
+    ones = xp.ones_like(logx)
+    logxmu, _ = special.logsumexp(xp.stack((logx, logmean), axis=0), axis=0,
+                                  b=xp.stack((ones, -ones), axis=0), return_sign=True)
+    return special.logsumexp(2 * logxmu, axis=axis) - math.log(logx.shape[axis])
+
+
+@xp_capabilities()
+def boxcox_llf(lmb, data, *, axis=0, keepdims=False, nan_policy='propagate'):
+    r"""The boxcox log-likelihood function.
+
+    Parameters
+    ----------
+    lmb : scalar
+        Parameter for Box-Cox transformation.  See `boxcox` for details.
+    data : array_like
+        Data to calculate Box-Cox log-likelihood for.  If `data` is
+        multi-dimensional, the log-likelihood is calculated along the first
+        axis.
+    axis : int, default: 0
+        If an int, the axis of the input along which to compute the statistic.
+        The statistic of each axis-slice (e.g. row) of the input will appear in a
+        corresponding element of the output.
+        If ``None``, the input will be raveled before computing the statistic.
+    keepdims : bool, default: False
+        If this is set to True, the axes which are reduced are left
+        in the result as dimensions with size one. With this option,
+        the result will broadcast correctly against the input array.
+    nan_policy : {'propagate', 'omit', 'raise'}
+        Defines how to handle input NaNs.
+
+        - ``propagate``: if a NaN is present in the axis slice (e.g. row) along
+          which the  statistic is computed, the corresponding entry of the output
+          will be NaN.
+        - ``omit``: NaNs will be omitted when performing the calculation.
+          If insufficient data remains in the axis slice along which the
+          statistic is computed, the corresponding entry of the output will be
+          NaN.
+        - ``raise``: if a NaN is present, a ``ValueError`` will be raised.
+
+    Returns
+    -------
+    llf : float or ndarray
+        Box-Cox log-likelihood of `data` given `lmb`.  A float for 1-D `data`,
+        an array otherwise.
+
+    See Also
+    --------
+    boxcox, probplot, boxcox_normplot, boxcox_normmax
+
+    Notes
+    -----
+    The Box-Cox log-likelihood function :math:`l` is defined here as
+
+    .. math::
+
+        l = (\lambda - 1) \sum_i^N \log(x_i) -
+              \frac{N}{2} \log\left(\sum_i^N (y_i - \bar{y})^2 / N\right),
+
+    where :math:`N` is the number of data points ``data`` and :math:`y` is the Box-Cox
+    transformed input data.
+    This corresponds to the *profile log-likelihood* of the original data :math:`x`
+    with some constant terms dropped.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> import matplotlib.pyplot as plt
+    >>> from mpl_toolkits.axes_grid1.inset_locator import inset_axes
+
+    Generate some random variates and calculate Box-Cox log-likelihood values
+    for them for a range of ``lmbda`` values:
+
+    >>> rng = np.random.default_rng()
+    >>> x = stats.loggamma.rvs(5, loc=10, size=1000, random_state=rng)
+    >>> lmbdas = np.linspace(-2, 10)
+    >>> llf = np.zeros(lmbdas.shape, dtype=float)
+    >>> for ii, lmbda in enumerate(lmbdas):
+    ...     llf[ii] = stats.boxcox_llf(lmbda, x)
+
+    Also find the optimal lmbda value with `boxcox`:
+
+    >>> x_most_normal, lmbda_optimal = stats.boxcox(x)
+
+    Plot the log-likelihood as function of lmbda.  Add the optimal lmbda as a
+    horizontal line to check that that's really the optimum:
+
+    >>> fig = plt.figure()
+    >>> ax = fig.add_subplot(111)
+    >>> ax.plot(lmbdas, llf, 'b.-')
+    >>> ax.axhline(stats.boxcox_llf(lmbda_optimal, x), color='r')
+    >>> ax.set_xlabel('lmbda parameter')
+    >>> ax.set_ylabel('Box-Cox log-likelihood')
+
+    Now add some probability plots to show that where the log-likelihood is
+    maximized the data transformed with `boxcox` looks closest to normal:
+
+    >>> locs = [3, 10, 4]  # 'lower left', 'center', 'lower right'
+    >>> for lmbda, loc in zip([-1, lmbda_optimal, 9], locs):
+    ...     xt = stats.boxcox(x, lmbda=lmbda)
+    ...     (osm, osr), (slope, intercept, r_sq) = stats.probplot(xt)
+    ...     ax_inset = inset_axes(ax, width="20%", height="20%", loc=loc)
+    ...     ax_inset.plot(osm, osr, 'c.', osm, slope*osm + intercept, 'k-')
+    ...     ax_inset.set_xticklabels([])
+    ...     ax_inset.set_yticklabels([])
+    ...     ax_inset.set_title(r'$\lambda=%1.2f$' % lmbda)
+
+    >>> plt.show()
+
+    """
+    # _axis_nan_policy decorator does not currently support these for lazy arrays.
+    # We want to run tests with lazy backends, so don't pass the arguments explicitly
+    # unless necessary.
+    kwargs = {}
+    if keepdims is not False:
+        kwargs['keepdims'] = keepdims
+    if nan_policy != 'propagate':
+        kwargs['nan_policy'] = nan_policy
+    return _boxcox_llf(data, lmb=lmb, axis=axis, **kwargs)
+
+
+@_axis_nan_policy_factory(lambda x: x, n_outputs=1, default_axis=0,
+                          result_to_tuple=lambda x, _: (x,))
+def _boxcox_llf(data, axis=0, *, lmb):
+    xp = array_namespace(data)
+    dtype = xp_result_type(lmb, data, force_floating=True, xp=xp)
+    data = xp.asarray(data, dtype=dtype)
+    N = data.shape[axis]
+    if N == 0:
+        return _get_nan(data, xp=xp)
+
+    logdata = xp.log(data)
+
+    # Compute the variance of the transformed data.
+    if lmb == 0:
+        logvar = xp.log(xp.var(logdata, axis=axis))
+    else:
+        # Transform without the constant offset 1/lmb.  The offset does
+        # not affect the variance, and the subtraction of the offset can
+        # lead to loss of precision.
+        # Division by lmb can be factored out to enhance numerical stability.
+        logx = lmb * logdata
+        logvar = _log_var(logx, xp, axis) - 2 * math.log(abs(lmb))
+
+    res = (lmb - 1) * xp.sum(logdata, axis=axis) - N/2 * logvar
+    res = xp.astype(res, data.dtype, copy=False)  # compensate for NumPy <2.0
+    res = res[()] if res.ndim == 0 else res
+    return res
+
+
+def _boxcox_conf_interval(x, lmax, alpha):
+    # Need to find the lambda for which
+    #  f(x,lmbda) >= f(x,lmax) - 0.5*chi^2_alpha;1
+    fac = 0.5 * distributions.chi2.ppf(1 - alpha, 1)
+    target = boxcox_llf(lmax, x) - fac
+
+    def rootfunc(lmbda, data, target):
+        return boxcox_llf(lmbda, data) - target
+
+    # Find positive endpoint of interval in which answer is to be found
+    newlm = lmax + 0.5
+    N = 0
+    while (rootfunc(newlm, x, target) > 0.0) and (N < 500):
+        newlm += 0.1
+        N += 1
+
+    if N == 500:
+        raise RuntimeError("Could not find endpoint.")
+
+    lmplus = optimize.brentq(rootfunc, lmax, newlm, args=(x, target))
+
+    # Now find negative interval in the same way
+    newlm = lmax - 0.5
+    N = 0
+    while (rootfunc(newlm, x, target) > 0.0) and (N < 500):
+        newlm -= 0.1
+        N += 1
+
+    if N == 500:
+        raise RuntimeError("Could not find endpoint.")
+
+    lmminus = optimize.brentq(rootfunc, newlm, lmax, args=(x, target))
+    return lmminus, lmplus
+
+
+@xp_capabilities(np_only=True)
+def boxcox(x, lmbda=None, alpha=None, optimizer=None, *, nan_policy='propagate'):
+    r"""Return a dataset transformed by a Box-Cox power transformation.
+
+    Parameters
+    ----------
+    x : ndarray
+        Input array to be transformed.
+
+        If `lmbda` is not None, this is an alias of
+        `scipy.special.boxcox`.
+        Returns nan if ``x < 0``; returns -inf if ``x == 0 and lmbda < 0``.
+
+        If `lmbda` is None, array must be positive, 1-dimensional, and
+        non-constant.
+
+    lmbda : scalar, optional
+        If `lmbda` is None (default), find the value of `lmbda` that maximizes
+        the log-likelihood function and return it as the second output
+        argument.
+
+        If `lmbda` is not None, do the transformation for that value.
+
+    alpha : float, optional
+        If `lmbda` is None and `alpha` is not None (default), return the
+        ``100 * (1-alpha)%`` confidence  interval for `lmbda` as the third
+        output argument. Must be between 0.0 and 1.0.
+
+        If `lmbda` is not None, `alpha` is ignored.
+    optimizer : callable, optional
+        If `lmbda` is None, `optimizer` is the scalar optimizer used to find
+        the value of `lmbda` that minimizes the negative log-likelihood
+        function. `optimizer` is a callable that accepts one argument:
+
+        fun : callable
+            The objective function, which evaluates the negative
+            log-likelihood function at a provided value of `lmbda`
+
+        and returns an object, such as an instance of
+        `scipy.optimize.OptimizeResult`, which holds the optimal value of
+        `lmbda` in an attribute `x`.
+
+        See the example in `boxcox_normmax` or the documentation of
+        `scipy.optimize.minimize_scalar` for more information.
+
+        If `lmbda` is not None, `optimizer` is ignored.
+    nan_policy : {'propagate', 'omit', 'raise'}
+        Defines how to handle NaNs in `x`.
+
+        - ``propagate``: if a NaN is present, all outputs will contain NaNs.
+        - ``omit``: NaNs will be omitted when calculating the optimal `maxlog` and
+          confidence interval; NaNs in `x` will remain NaNs in the transformed data.
+        - ``raise``: if a NaN is present, a ``ValueError`` will be raised.
+
+    Returns
+    -------
+    boxcox : ndarray
+        Box-Cox power transformed array.
+    maxlog : float, optional
+        If the `lmbda` parameter is None, the second returned argument is
+        the `lmbda` that maximizes the log-likelihood function.
+    (min_ci, max_ci) : tuple of float, optional
+        If `lmbda` parameter is None and `alpha` is not None, this returned
+        tuple of floats represents the minimum and maximum confidence limits
+        given `alpha`.
+
+    See Also
+    --------
+    probplot, boxcox_normplot, boxcox_normmax, boxcox_llf
+
+    Notes
+    -----
+    The Box-Cox transform is given by:
+
+    .. math::
+
+        y =
+        \begin{cases}
+          \frac{x^\lambda - 1}{\lambda}, &\text{for } \lambda \neq 0 \\
+          \log(x),                       &\text{for } \lambda = 0
+        \end{cases}
+
+    `boxcox` requires the input data to be positive.  Sometimes a Box-Cox
+    transformation provides a shift parameter to achieve this; `boxcox` does
+    not.  Such a shift parameter is equivalent to adding a positive constant to
+    `x` before calling `boxcox`.
+
+    The confidence limits returned when `alpha` is provided give the interval
+    where:
+
+    .. math::
+
+        l(\hat{\lambda}) - l(\lambda) < \frac{1}{2}\chi^2(1 - \alpha, 1),
+
+    with :math:`l` the log-likelihood function and :math:`\chi^2` the chi-squared
+    function.
+
+    References
+    ----------
+    G.E.P. Box and D.R. Cox, "An Analysis of Transformations", Journal of the
+    Royal Statistical Society B, 26, 211-252 (1964).
+
+    Examples
+    --------
+    >>> from scipy import stats
+    >>> import matplotlib.pyplot as plt
+
+    We generate some random variates from a non-normal distribution and make a
+    probability plot for it, to show it is non-normal in the tails:
+
+    >>> fig = plt.figure()
+    >>> ax1 = fig.add_subplot(211)
+    >>> x = stats.loggamma.rvs(5, size=500) + 5
+    >>> prob = stats.probplot(x, dist=stats.norm, plot=ax1)
+    >>> ax1.set_xlabel('')
+    >>> ax1.set_title('Probplot against normal distribution')
+
+    We now use `boxcox` to transform the data so it's closest to normal:
+
+    >>> ax2 = fig.add_subplot(212)
+    >>> xt, _ = stats.boxcox(x)
+    >>> prob = stats.probplot(xt, dist=stats.norm, plot=ax2)
+    >>> ax2.set_title('Probplot after Box-Cox transformation')
+
+    >>> plt.show()
+
+    """
+    x = np.asarray(x)
+
+    if lmbda is not None:  # single transformation
+        _contains_nan(x, nan_policy, xp_omit_okay=True)  # handle nan_policy='raise'
+        return special.boxcox(x, lmbda)
+
+    if x.ndim != 1:
+        raise ValueError("Data must be 1-dimensional.")
+
+    if x.size == 0:
+        return x
+
+    if np.all(x == x[0]):
+        raise ValueError("Data must not be constant.")
+
+    if np.any(x <= 0):
+        raise ValueError("Data must be positive.")
+
+    # If lmbda=None, find the lmbda that maximizes the log-likelihood function.
+    lmax = boxcox_normmax(x, method='mle', optimizer=optimizer, nan_policy=nan_policy)
+    y = special.boxcox(x, lmax)
+
+    if alpha is None:
+        return y, lmax
+    else:
+        # Find confidence interval
+        interval = ((lmax, lmax) if np.isnan(lmax) else
+                    _boxcox_conf_interval(x[~np.isnan(x)], lmax, alpha))
+        return y, lmax, interval
+
+
+def _boxcox_inv_lmbda(x, y):
+    # compute lmbda given x and y for Box-Cox transformation
+    num = special.lambertw(-(x ** (-1 / y)) * np.log(x) / y, k=-1)
+    return np.real(-num / np.log(x) - 1 / y)
+
+
+class _BigFloat:
+    def __repr__(self):
+        return "BIG_FLOAT"
+
+
+_BigFloat_singleton = _BigFloat()
+
+
+@xp_capabilities(np_only=True)
+def boxcox_normmax(
+    x, brack=None, method='pearsonr', optimizer=None, *, ymax=_BigFloat_singleton,
+    nan_policy='propagate'
+):
+    """Compute optimal Box-Cox transform parameter for input data.
+
+    Parameters
+    ----------
+    x : array_like
+        Input array. All entries must be positive, finite, real numbers.
+    brack : 2-tuple, optional, default (-2.0, 2.0)
+         The starting interval for a downhill bracket search for the default
+         `optimize.brent` solver. Note that this is in most cases not
+         critical; the final result is allowed to be outside this bracket.
+         If `optimizer` is passed, `brack` must be None.
+    method : str, optional
+        The method to determine the optimal transform parameter (`boxcox`
+        ``lmbda`` parameter). Options are:
+
+        'pearsonr'  (default)
+            Maximizes the Pearson correlation coefficient between
+            ``y = boxcox(x)`` and the expected values for ``y`` if `x` would be
+            normally-distributed.
+
+        'mle'
+            Maximizes the log-likelihood `boxcox_llf`.  This is the method used
+            in `boxcox`.
+
+        'all'
+            Use all optimization methods available, and return all results.
+            Useful to compare different methods.
+    optimizer : callable, optional
+        `optimizer` is a callable that accepts one argument:
+
+        fun : callable
+            The objective function to be minimized. `fun` accepts one argument,
+            the Box-Cox transform parameter `lmbda`, and returns the value of
+            the function (e.g., the negative log-likelihood) at the provided
+            argument. The job of `optimizer` is to find the value of `lmbda`
+            that *minimizes* `fun`.
+
+        and returns an object, such as an instance of
+        `scipy.optimize.OptimizeResult`, which holds the optimal value of
+        `lmbda` in an attribute `x`.
+
+        See the example below or the documentation of
+        `scipy.optimize.minimize_scalar` for more information.
+    ymax : float, optional
+        The unconstrained optimal transform parameter may cause Box-Cox
+        transformed data to have extreme magnitude or even overflow.
+        This parameter constrains MLE optimization such that the magnitude
+        of the transformed `x` does not exceed `ymax`. The default is
+        the maximum value of the input dtype. If set to infinity,
+        `boxcox_normmax` returns the unconstrained optimal lambda.
+        Ignored when ``method='pearsonr'``.
+    nan_policy : {'propagate', 'omit', 'raise'}
+        Defines how to handle input NaNs.
+
+        - ``propagate``: if a NaN is present in the input, the output will be NaN.
+        - ``omit``: NaNs will be omitted when performing the calculation.
+        - ``raise``: if a NaN is present, a ``ValueError`` will be raised.
+
+    Returns
+    -------
+    maxlog : float or ndarray
+        The optimal transform parameter found.  An array instead of a scalar
+        for ``method='all'``.
+
+    See Also
+    --------
+    boxcox, boxcox_llf, boxcox_normplot, scipy.optimize.minimize_scalar
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> import matplotlib.pyplot as plt
+
+    We can generate some data and determine the optimal ``lmbda`` in various
+    ways:
+
+    >>> rng = np.random.default_rng()
+    >>> x = stats.loggamma.rvs(5, size=30, random_state=rng) + 5
+    >>> y, lmax_mle = stats.boxcox(x)
+    >>> lmax_pearsonr = stats.boxcox_normmax(x)
+
+    >>> lmax_mle
+    2.217563431465757
+    >>> lmax_pearsonr
+    2.238318660200961
+    >>> stats.boxcox_normmax(x, method='all')
+    array([2.23831866, 2.21756343])
+
+    >>> fig = plt.figure()
+    >>> ax = fig.add_subplot(111)
+    >>> prob = stats.boxcox_normplot(x, -10, 10, plot=ax)
+    >>> ax.axvline(lmax_mle, color='r')
+    >>> ax.axvline(lmax_pearsonr, color='g', ls='--')
+
+    >>> plt.show()
+
+    Alternatively, we can define our own `optimizer` function. Suppose we
+    are only interested in values of `lmbda` on the interval [6, 7], we
+    want to use `scipy.optimize.minimize_scalar` with ``method='bounded'``,
+    and we want to use tighter tolerances when optimizing the log-likelihood
+    function. To do this, we define a function that accepts positional argument
+    `fun` and uses `scipy.optimize.minimize_scalar` to minimize `fun` subject
+    to the provided bounds and tolerances:
+
+    >>> from scipy import optimize
+    >>> options = {'xatol': 1e-12}  # absolute tolerance on `x`
+    >>> def optimizer(fun):
+    ...     return optimize.minimize_scalar(fun, bounds=(6, 7),
+    ...                                     method="bounded", options=options)
+    >>> stats.boxcox_normmax(x, optimizer=optimizer)
+    6.000000000
+    """
+    x = np.asarray(x)
+
+    contains_nan = _contains_nan(x, nan_policy, xp_omit_okay=True)
+    if contains_nan:
+        if nan_policy == 'propagate':
+            NaN = _get_nan(x, xp=np)[()]
+            return np.asarray([NaN, NaN]) if method == 'all' else NaN
+        x = x[~np.isnan(x)]  # `nan_policy='omit
+
+    if not np.all(np.isfinite(x) & (x >= 0)):
+        message = ("The `x` argument of `boxcox_normmax` must contain "
+                   "only positive, finite, real numbers.")
+        raise ValueError(message)
+
+    end_msg = "exceed specified `ymax`."
+    if ymax is _BigFloat_singleton:
+        dtype = x.dtype if np.issubdtype(x.dtype, np.floating) else np.float64
+        # 10000 is a safety factor because `special.boxcox` overflows prematurely.
+        ymax = np.finfo(dtype).max / 10000
+        end_msg = f"overflow in {dtype}."
+    elif ymax <= 0:
+        raise ValueError("`ymax` must be strictly positive")
+
+    # If optimizer is not given, define default 'brent' optimizer.
+    if optimizer is None:
+
+        # Set default value for `brack`.
+        if brack is None:
+            brack = (-2.0, 2.0)
+
+        def _optimizer(func, args):
+            return optimize.brent(func, args=args, brack=brack)
+
+    # Otherwise check optimizer.
+    else:
+        if not callable(optimizer):
+            raise ValueError("`optimizer` must be a callable")
+
+        if brack is not None:
+            raise ValueError("`brack` must be None if `optimizer` is given")
+
+        # `optimizer` is expected to return a `OptimizeResult` object, we here
+        # get the solution to the optimization problem.
+        def _optimizer(func, args):
+            def func_wrapped(x):
+                return func(x, *args)
+            return getattr(optimizer(func_wrapped), 'x', None)
+
+    def _pearsonr(x):
+        osm_uniform = _calc_uniform_order_statistic_medians(len(x))
+        xvals = distributions.norm.ppf(osm_uniform)
+
+        def _eval_pearsonr(lmbda, xvals, samps):
+            # This function computes the x-axis values of the probability plot
+            # and computes a linear regression (including the correlation) and
+            # returns ``1 - r`` so that a minimization function maximizes the
+            # correlation.
+            y = boxcox(samps, lmbda)
+            yvals = np.sort(y)
+            r, prob = _stats_py.pearsonr(xvals, yvals)
+            return 1 - r
+
+        return _optimizer(_eval_pearsonr, args=(xvals, x))
+
+    def _mle(x):
+        def _eval_mle(lmb, data):
+            # function to minimize
+            return -boxcox_llf(lmb, data)
+
+        return _optimizer(_eval_mle, args=(x,))
+
+    def _all(x):
+        maxlog = np.empty(2, dtype=float)
+        maxlog[0] = _pearsonr(x)
+        maxlog[1] = _mle(x)
+        return maxlog
+
+    methods = {'pearsonr': _pearsonr,
+               'mle': _mle,
+               'all': _all}
+    if method not in methods.keys():
+        raise ValueError(f"Method {method} not recognized.")
+
+    optimfunc = methods[method]
+
+    res = optimfunc(x)
+
+    if res is None:
+        message = ("The `optimizer` argument of `boxcox_normmax` must return "
+                   "an object containing the optimal `lmbda` in attribute `x`.")
+        raise ValueError(message)
+    elif not np.isinf(ymax):  # adjust the final lambda
+        # x > 1, boxcox(x) > 0; x < 1, boxcox(x) < 0
+        xmax, xmin = np.max(x), np.min(x)
+        if xmin >= 1:
+            x_treme = xmax
+        elif xmax <= 1:
+            x_treme = xmin
+        else:  # xmin < 1 < xmax
+            indicator = special.boxcox(xmax, res) > abs(special.boxcox(xmin, res))
+            if isinstance(res, np.ndarray):
+                indicator = indicator[1]  # select corresponds with 'mle'
+            x_treme = xmax if indicator else xmin
+
+        mask = abs(special.boxcox(x_treme, res)) > ymax
+        if np.any(mask):
+            message = (
+                f"The optimal lambda is {res}, but the returned lambda is the "
+                f"constrained optimum to ensure that the maximum or the minimum "
+                f"of the transformed data does not " + end_msg
+            )
+            warnings.warn(message, stacklevel=2)
+
+            # Return the constrained lambda to ensure the transformation
+            # does not cause overflow or exceed specified `ymax`
+            constrained_res = _boxcox_inv_lmbda(x_treme, ymax * np.sign(x_treme - 1))
+
+            if isinstance(res, np.ndarray):
+                res[mask] = constrained_res
+            else:
+                res = constrained_res
+    return res
+
+
+def _normplot(method, x, la, lb, plot=None, N=80):
+    """Compute parameters for a Box-Cox or Yeo-Johnson normality plot,
+    optionally show it.
+
+    See `boxcox_normplot` or `yeojohnson_normplot` for details.
+    """
+
+    if method == 'boxcox':
+        title = 'Box-Cox Normality Plot'
+        transform_func = boxcox
+    else:
+        title = 'Yeo-Johnson Normality Plot'
+        transform_func = yeojohnson
+
+    x = np.asarray(x)
+    if x.size == 0:
+        return x
+
+    if lb <= la:
+        raise ValueError("`lb` has to be larger than `la`.")
+
+    if method == 'boxcox' and np.any(x <= 0):
+        raise ValueError("Data must be positive.")
+
+    lmbdas = np.linspace(la, lb, num=N)
+    ppcc = lmbdas * 0.0
+    for i, val in enumerate(lmbdas):
+        # Determine for each lmbda the square root of correlation coefficient
+        # of transformed x
+        z = transform_func(x, lmbda=val)
+        _, (_, _, r) = probplot(z, dist='norm', fit=True)
+        ppcc[i] = r
+
+    if plot is not None:
+        plot.plot(lmbdas, ppcc, 'x')
+        _add_axis_labels_title(plot, xlabel='$\\lambda$',
+                               ylabel='Prob Plot Corr. Coef.',
+                               title=title)
+
+    return lmbdas, ppcc
+
+
+@xp_capabilities(np_only=True)
+def boxcox_normplot(x, la, lb, plot=None, N=80):
+    """Compute parameters for a Box-Cox normality plot, optionally show it.
+
+    A Box-Cox normality plot shows graphically what the best transformation
+    parameter is to use in `boxcox` to obtain a distribution that is close
+    to normal.
+
+    Parameters
+    ----------
+    x : array_like
+        Input array.
+    la, lb : scalar
+        The lower and upper bounds for the ``lmbda`` values to pass to `boxcox`
+        for Box-Cox transformations.  These are also the limits of the
+        horizontal axis of the plot if that is generated.
+    plot : object, optional
+        If given, plots the quantiles and least squares fit.
+        `plot` is an object that has to have methods "plot" and "text".
+        The `matplotlib.pyplot` module or a Matplotlib Axes object can be used,
+        or a custom object with the same methods.
+        Default is None, which means that no plot is created.
+    N : int, optional
+        Number of points on the horizontal axis (equally distributed from
+        `la` to `lb`).
+
+    Returns
+    -------
+    lmbdas : ndarray
+        The ``lmbda`` values for which a Box-Cox transform was done.
+    ppcc : ndarray
+        Probability Plot Correlation Coefficient, as obtained from `probplot`
+        when fitting the Box-Cox transformed input `x` against a normal
+        distribution.
+
+    See Also
+    --------
+    probplot, boxcox, boxcox_normmax, boxcox_llf, ppcc_max
+
+    Notes
+    -----
+    Even if `plot` is given, the figure is not shown or saved by
+    `boxcox_normplot`; ``plt.show()`` or ``plt.savefig('figname.png')``
+    should be used after calling `probplot`.
+
+    Examples
+    --------
+    >>> from scipy import stats
+    >>> import matplotlib.pyplot as plt
+
+    Generate some non-normally distributed data, and create a Box-Cox plot:
+
+    >>> x = stats.loggamma.rvs(5, size=500) + 5
+    >>> fig = plt.figure()
+    >>> ax = fig.add_subplot(111)
+    >>> prob = stats.boxcox_normplot(x, -20, 20, plot=ax)
+
+    Determine and plot the optimal ``lmbda`` to transform ``x`` and plot it in
+    the same plot:
+
+    >>> _, maxlog = stats.boxcox(x)
+    >>> ax.axvline(maxlog, color='r')
+
+    >>> plt.show()
+
+    """
+    return _normplot('boxcox', x, la, lb, plot, N)
+
+
+@xp_capabilities(np_only=True)
+def yeojohnson(x, lmbda=None, *, nan_policy='propagate'):
+    r"""Return a dataset transformed by a Yeo-Johnson power transformation.
+
+    Parameters
+    ----------
+    x : ndarray
+        Input array.  Should be 1-dimensional.
+    lmbda : float, optional
+        If ``lmbda`` is ``None``, find the lambda that maximizes the
+        log-likelihood function and return it as the second output argument.
+        Otherwise the transformation is done for the given value.
+    nan_policy : {'propagate', 'omit', 'raise'}
+        Defines how to handle NaNs in `x`.
+
+        - ``propagate``: if a NaN is present, all outputs will contain NaNs.
+        - ``omit``: NaNs will be omitted when calculating the optimal `maxlog`;
+           NaNs in `x` will remain NaNs in the transformed data.
+        - ``raise``: if a NaN is present, a ``ValueError`` will be raised.
+
+    Returns
+    -------
+    yeojohnson: ndarray
+        Yeo-Johnson power transformed array.
+    maxlog : float, optional
+        If the `lmbda` parameter is None, the second returned argument is
+        the lambda that maximizes the log-likelihood function.
+
+    See Also
+    --------
+    probplot, yeojohnson_normplot, yeojohnson_normmax, yeojohnson_llf, boxcox
+
+    Notes
+    -----
+    The Yeo-Johnson transform is given by:
+
+    .. math::
+
+        y =
+        \begin{cases}
+        \frac{(x + 1)^\lambda - 1}{\lambda},
+        &\text{for } x \geq 0, \lambda \neq 0
+        \\
+        \log(x + 1),
+        &\text{for } x \geq 0, \lambda = 0
+        \\
+        -\frac{(-x + 1)^{2 - \lambda} - 1}{2 - \lambda},
+        &\text{for } x < 0, \lambda \neq 2
+        \\
+        -\log(-x + 1),
+        &\text{for } x < 0, \lambda = 2
+        \end{cases}
+
+    Unlike `boxcox`, `yeojohnson` does not require the input data to be
+    positive.
+
+    .. versionadded:: 1.2.0
+
+
+    References
+    ----------
+    I. Yeo and R.A. Johnson, "A New Family of Power Transformations to
+    Improve Normality or Symmetry", Biometrika 87.4 (2000):
+
+
+    Examples
+    --------
+    >>> from scipy import stats
+    >>> import matplotlib.pyplot as plt
+
+    We generate some random variates from a non-normal distribution and make a
+    probability plot for it, to show it is non-normal in the tails:
+
+    >>> fig = plt.figure()
+    >>> ax1 = fig.add_subplot(211)
+    >>> x = stats.loggamma.rvs(5, size=500) + 5
+    >>> prob = stats.probplot(x, dist=stats.norm, plot=ax1)
+    >>> ax1.set_xlabel('')
+    >>> ax1.set_title('Probplot against normal distribution')
+
+    We now use `yeojohnson` to transform the data so it's closest to normal:
+
+    >>> ax2 = fig.add_subplot(212)
+    >>> xt, lmbda = stats.yeojohnson(x)
+    >>> prob = stats.probplot(xt, dist=stats.norm, plot=ax2)
+    >>> ax2.set_title('Probplot after Yeo-Johnson transformation')
+
+    >>> plt.show()
+
+    """
+    x = np.asarray(x)
+    if x.size == 0:
+        return x
+
+    if np.issubdtype(x.dtype, np.complexfloating):
+        raise ValueError('Yeo-Johnson transformation is not defined for '
+                         'complex numbers.')
+
+    if np.issubdtype(x.dtype, np.integer):
+        x = x.astype(np.float64, copy=False)
+
+    if lmbda is not None:
+        _contains_nan(x, nan_policy, xp_omit_okay=True)  # handle nan_policy='raise'
+        return _yeojohnson_transform(x, lmbda)
+
+    # if lmbda=None, find the lmbda that maximizes the log-likelihood function.
+    lmax = yeojohnson_normmax(x, nan_policy=nan_policy)
+    y = _yeojohnson_transform(x, lmax)
+
+    return y, lmax
+
+
+def _yeojohnson_transform(x, lmbda, xp=None):
+    """Returns `x` transformed by the Yeo-Johnson power transform with given
+    parameter `lmbda`.
+    """
+    xp = array_namespace(x) if xp is None else xp
+    dtype = xp_result_type(x, lmbda, force_floating=True, xp=xp)
+    eps = xp.finfo(dtype).eps
+    out = xp.zeros_like(x, dtype=dtype)
+    pos = x >= 0  # binary mask
+
+    if is_jax(xp):
+        return xp.select(
+            [(abs(lmbda) < eps) & pos, (abs(lmbda - 2) < eps) & ~pos, pos],
+            [xp.log1p(x), -xp.log1p(-x), xp.expm1(lmbda * xp.log1p(x)) / lmbda],
+            -xp.expm1((2 - lmbda) * xp.log1p(-x)) / (2 - lmbda),
+        )
+
+    # when x >= 0
+    if abs(lmbda) < eps:
+        out = xpx.at(out)[pos].set(xp.log1p(x[pos]))
+    else:  # lmbda != 0
+        # more stable version of: ((x + 1) ** lmbda - 1) / lmbda
+        out = xpx.at(out)[pos].set(xp.expm1(lmbda * xp.log1p(x[pos])) / lmbda)
+
+    # when x < 0
+    if abs(lmbda - 2) > eps:
+        out = xpx.at(out)[~pos].set(
+            -xp.expm1((2 - lmbda) * xp.log1p(-x[~pos])) / (2 - lmbda))
+    else:  # lmbda == 2
+        out = xpx.at(out)[~pos].set(-xp.log1p(-x[~pos]))
+
+    return out
+
+
+@xp_capabilities(skip_backends=[("dask.array", "Dask can't broadcast nan shapes")])
+def yeojohnson_llf(lmb, data, *, axis=0, nan_policy='propagate', keepdims=False):
+    r"""The Yeo-Johnson log-likelihood function.
+
+    Parameters
+    ----------
+    lmb : scalar
+        Parameter for Yeo-Johnson transformation. See `yeojohnson` for
+        details.
+    data : array_like
+        Data to calculate Yeo-Johnson log-likelihood for.
+    axis : int, default: 0
+        If an int, the axis of the input along which to compute the statistic.
+        The statistic of each axis-slice (e.g. row) of the input will appear in a
+        corresponding element of the output.
+        If ``None``, the input will be raveled before computing the statistic.
+    nan_policy : {'propagate', 'omit', 'raise'
+        Defines how to handle input NaNs.
+
+        - ``propagate``: if a NaN is present in the axis slice (e.g. row) along
+          which the  statistic is computed, the corresponding entry of the output
+          will be NaN.
+        - ``omit``: NaNs will be omitted when performing the calculation.
+          If insufficient data remains in the axis slice along which the
+          statistic is computed, the corresponding entry of the output will be
+          NaN.
+        - ``raise``: if a NaN is present, a ``ValueError`` will be raised.
+
+    keepdims : bool, default: False
+        If this is set to True, the axes which are reduced are left
+        in the result as dimensions with size one. With this option,
+        the result will broadcast correctly against the input array.
+
+    Returns
+    -------
+    llf : float
+        Yeo-Johnson log-likelihood of `data` given `lmb`.
+
+    See Also
+    --------
+    yeojohnson, probplot, yeojohnson_normplot, yeojohnson_normmax
+
+    Notes
+    -----
+    The Yeo-Johnson log-likelihood function :math:`l` is defined here as
+
+    .. math::
+
+        l = -\frac{N}{2} \log(\hat{\sigma}^2) + (\lambda - 1)
+              \sum_i^N \text{sign}(x_i) \log(|x_i| + 1)
+
+    where :math:`N` is the number of data points :math:`x` = ``data`` and
+    :math:`\hat{\sigma}^2` is the estimated variance of the Yeo-Johnson transformed
+    input data :math:`x`.
+    This corresponds to the *profile log-likelihood* of the original data :math:`x`
+    with some constant terms dropped.
+
+    .. versionadded:: 1.2.0
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> import matplotlib.pyplot as plt
+    >>> from mpl_toolkits.axes_grid1.inset_locator import inset_axes
+
+    Generate some random variates and calculate Yeo-Johnson log-likelihood
+    values for them for a range of ``lmbda`` values:
+
+    >>> x = stats.loggamma.rvs(5, loc=10, size=1000)
+    >>> lmbdas = np.linspace(-2, 10)
+    >>> llf = np.zeros(lmbdas.shape, dtype=float)
+    >>> for ii, lmbda in enumerate(lmbdas):
+    ...     llf[ii] = stats.yeojohnson_llf(lmbda, x)
+
+    Also find the optimal lmbda value with `yeojohnson`:
+
+    >>> x_most_normal, lmbda_optimal = stats.yeojohnson(x)
+
+    Plot the log-likelihood as function of lmbda.  Add the optimal lmbda as a
+    horizontal line to check that that's really the optimum:
+
+    >>> fig = plt.figure()
+    >>> ax = fig.add_subplot(111)
+    >>> ax.plot(lmbdas, llf, 'b.-')
+    >>> ax.axhline(stats.yeojohnson_llf(lmbda_optimal, x), color='r')
+    >>> ax.set_xlabel('lmbda parameter')
+    >>> ax.set_ylabel('Yeo-Johnson log-likelihood')
+
+    Now add some probability plots to show that where the log-likelihood is
+    maximized the data transformed with `yeojohnson` looks closest to normal:
+
+    >>> locs = [3, 10, 4]  # 'lower left', 'center', 'lower right'
+    >>> for lmbda, loc in zip([-1, lmbda_optimal, 9], locs):
+    ...     xt = stats.yeojohnson(x, lmbda=lmbda)
+    ...     (osm, osr), (slope, intercept, r_sq) = stats.probplot(xt)
+    ...     ax_inset = inset_axes(ax, width="20%", height="20%", loc=loc)
+    ...     ax_inset.plot(osm, osr, 'c.', osm, slope*osm + intercept, 'k-')
+    ...     ax_inset.set_xticklabels([])
+    ...     ax_inset.set_yticklabels([])
+    ...     ax_inset.set_title(r'$\lambda=%1.2f$' % lmbda)
+
+    >>> plt.show()
+
+    """
+    # _axis_nan_policy decorator does not currently support these for lazy arrays.
+    # We want to run tests with lazy backends, so don't pass the arguments explicitly
+    # unless necessary.
+    kwargs = {}
+    if keepdims is not False:
+        kwargs['keepdims'] = keepdims
+    if nan_policy != 'propagate':
+        kwargs['nan_policy'] = nan_policy
+    res = _yeojohnson_llf(data, lmb=lmb, axis=axis, **kwargs)
+    return res[()] if res.ndim == 0 else res
+
+
+@_axis_nan_policy_factory(lambda x: x, n_outputs=1, default_axis=0,
+                          result_to_tuple=lambda x, _: (x,))
+def _yeojohnson_llf(data, *, lmb, axis=0):
+    xp = array_namespace(data)
+    dtype = xp_result_type(lmb, data, force_floating=True, xp=xp)
+    data = xp.asarray(data, dtype=dtype)
+
+    n = data.shape[axis]
+    if n == 0:
+        return _get_nan(data, xp=xp)
+    eps = xp.finfo(dtype).eps
+    # Special case all-positive/negative data to avoid overflow and precision loss
+    pos = data >= 0  # binary mask
+
+    # There exists numerical instability when abs(lmb) or abs(lmb - 2) is very small
+    if not is_lazy_array(pos) and xp.all(pos):
+        if abs(lmb) < eps:
+            logvar = xp.log(xp.var(xp.log1p(data), axis=axis))
+        else:
+            logvar = _log_var(lmb * xp.log1p(data), xp, axis) - 2 * math.log(abs(lmb))
+
+    elif not is_lazy_array(pos) and xp.all(~pos):
+        if abs(lmb - 2) < eps:
+            logvar = xp.log(xp.var(xp.log1p(-data), axis=axis))
+        else:
+            logvar = _log_var((2 - lmb) * xp.log1p(-data), xp, axis) - 2 * math.log(
+                abs(2 - lmb)
+            )
+
+    # overflow/precision loss not reported for mixed data; calculate `logvar` directly
+    else:  # mixed positive and negative data
+        y = _yeojohnson_transform(data, lmb, xp=xp)
+        sigma = xp.var(y, axis=axis)
+
+        # Suppress RuntimeWarning raised by np.log when the variance is too low
+        finite_variance = sigma >= xp.finfo(sigma.dtype).smallest_normal
+        logvar = xpx.apply_where(finite_variance, (sigma,), xp.log, fill_value=-xp.inf)
+
+    loglike = (-n / 2 * logvar
+               + (lmb - 1) * xp.sum(xp.sign(data) * xp.log1p(xp.abs(data)), axis=axis))
+
+    return loglike
+
+
+@xp_capabilities(np_only=True)
+def yeojohnson_normmax(x, brack=None, *, nan_policy='propagate'):
+    """Compute optimal Yeo-Johnson transform parameter.
+
+    Compute optimal Yeo-Johnson transform parameter for input data, using
+    maximum likelihood estimation.
+
+    Parameters
+    ----------
+    x : array_like
+        Input array.
+    brack : 2-tuple, optional
+        The starting interval for a downhill bracket search with
+        `optimize.brent`. Note that this is in most cases not critical; the
+        final result is allowed to be outside this bracket. If None,
+        `optimize.fminbound` is used with bounds that avoid overflow.
+    nan_policy : {'propagate', 'omit', 'raise'}
+        Defines how to handle input NaNs.
+
+        - ``propagate``: if a NaN is present in the input, the output will be NaN.
+        - ``omit``: NaNs will be omitted when performing the calculation.
+        - ``raise``: if a NaN is present, a ``ValueError`` will be raised.
+
+    Returns
+    -------
+    maxlog : float
+        The optimal transform parameter found.
+
+    See Also
+    --------
+    yeojohnson, yeojohnson_llf, yeojohnson_normplot
+
+    Notes
+    -----
+    .. versionadded:: 1.2.0
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> import matplotlib.pyplot as plt
+
+    Generate some data and determine optimal ``lmbda``
+
+    >>> rng = np.random.default_rng()
+    >>> x = stats.loggamma.rvs(5, size=30, random_state=rng) + 5
+    >>> lmax = stats.yeojohnson_normmax(x)
+
+    >>> fig = plt.figure()
+    >>> ax = fig.add_subplot(111)
+    >>> prob = stats.yeojohnson_normplot(x, -10, 10, plot=ax)
+    >>> ax.axvline(lmax, color='r')
+
+    >>> plt.show()
+
+    """
+    def _neg_llf(lmbda, data):
+        llf = np.asarray(yeojohnson_llf(lmbda, data))
+        # reject likelihoods that are inf which are likely due to small
+        # variance in the transformed space
+        llf[np.isinf(llf)] = -np.inf
+        return -llf
+
+    with np.errstate(invalid='ignore'):
+        x = np.asarray(x)
+
+        contains_nan = _contains_nan(x, nan_policy, xp_omit_okay=True)
+        if contains_nan:
+            if nan_policy == 'propagate':
+                return _get_nan(x, xp=np)[()]
+            x = x[~np.isnan(x)]  # `nan_policy='omit
+
+        if not np.all(np.isfinite(x)):
+            raise ValueError('Yeo-Johnson input must be finite.')
+        if np.all(x == 0):
+            return 1.0
+        if brack is not None:
+            return optimize.brent(_neg_llf, brack=brack, args=(x,))
+
+        dtype = x.dtype if np.issubdtype(x.dtype, np.floating) else np.float64
+        # Allow values up to 20 times the maximum observed value to be safely
+        # transformed without over- or underflow.
+        log1p_max_x = np.log1p(20 * np.max(np.abs(x)))
+        # Use half of floating point's exponent range to allow safe computation
+        # of the variance of the transformed data.
+        log_eps = np.log(np.finfo(dtype).eps)
+        log_tiny_float = (np.log(np.finfo(dtype).tiny) - log_eps) / 2
+        log_max_float = (np.log(np.finfo(dtype).max) + log_eps) / 2
+        # Compute the bounds by approximating the inverse of the Yeo-Johnson
+        # transform on the smallest and largest floating point exponents, given
+        # the largest data we expect to observe. See [1] for further details.
+        # [1] https://github.com/scipy/scipy/pull/18852#issuecomment-1630286174
+        lb = log_tiny_float / log1p_max_x
+        ub = log_max_float / log1p_max_x
+        # Convert the bounds if all or some of the data is negative.
+        if np.all(x < 0):
+            lb, ub = 2 - ub, 2 - lb
+        elif np.any(x < 0):
+            lb, ub = max(2 - ub, lb), min(2 - lb, ub)
+        # Match `optimize.brent`'s tolerance.
+        tol_brent = 1.48e-08
+        return optimize.fminbound(_neg_llf, lb, ub, args=(x,), xtol=tol_brent)
+
+
+@xp_capabilities(np_only=True)
+def yeojohnson_normplot(x, la, lb, plot=None, N=80):
+    """Compute parameters for a Yeo-Johnson normality plot, optionally show it.
+
+    A Yeo-Johnson normality plot shows graphically what the best
+    transformation parameter is to use in `yeojohnson` to obtain a
+    distribution that is close to normal.
+
+    Parameters
+    ----------
+    x : array_like
+        Input array.
+    la, lb : scalar
+        The lower and upper bounds for the ``lmbda`` values to pass to
+        `yeojohnson` for Yeo-Johnson transformations. These are also the
+        limits of the horizontal axis of the plot if that is generated.
+    plot : object, optional
+        If given, plots the quantiles and least squares fit.
+        `plot` is an object that has to have methods "plot" and "text".
+        The `matplotlib.pyplot` module or a Matplotlib Axes object can be used,
+        or a custom object with the same methods.
+        Default is None, which means that no plot is created.
+    N : int, optional
+        Number of points on the horizontal axis (equally distributed from
+        `la` to `lb`).
+
+    Returns
+    -------
+    lmbdas : ndarray
+        The ``lmbda`` values for which a Yeo-Johnson transform was done.
+    ppcc : ndarray
+        Probability Plot Correlation Coefficient, as obtained from `probplot`
+        when fitting the Box-Cox transformed input `x` against a normal
+        distribution.
+
+    See Also
+    --------
+    probplot, yeojohnson, yeojohnson_normmax, yeojohnson_llf, ppcc_max
+
+    Notes
+    -----
+    Even if `plot` is given, the figure is not shown or saved by
+    `boxcox_normplot`; ``plt.show()`` or ``plt.savefig('figname.png')``
+    should be used after calling `probplot`.
+
+    .. versionadded:: 1.2.0
+
+    Examples
+    --------
+    >>> from scipy import stats
+    >>> import matplotlib.pyplot as plt
+
+    Generate some non-normally distributed data, and create a Yeo-Johnson plot:
+
+    >>> x = stats.loggamma.rvs(5, size=500) + 5
+    >>> fig = plt.figure()
+    >>> ax = fig.add_subplot(111)
+    >>> prob = stats.yeojohnson_normplot(x, -20, 20, plot=ax)
+
+    Determine and plot the optimal ``lmbda`` to transform ``x`` and plot it in
+    the same plot:
+
+    >>> _, maxlog = stats.yeojohnson(x)
+    >>> ax.axvline(maxlog, color='r')
+
+    >>> plt.show()
+
+    """
+    return _normplot('yeojohnson', x, la, lb, plot, N)
+
+
+ShapiroResult = namedtuple('ShapiroResult', ('statistic', 'pvalue'))
+
+
+@xp_capabilities()
+@_axis_nan_policy_factory(ShapiroResult, n_samples=1, too_small=2, default_axis=None)
+def shapiro(x, *, axis=None):
+    r"""Perform the Shapiro-Wilk test for normality.
+
+    The Shapiro-Wilk test tests the null hypothesis that the
+    data was drawn from a normal distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Array of sample data. Must contain at least three observations.
+    axis : int or tuple of ints, default: 0
+        If an int or tuple of ints, the axis or axes of the input along which
+        to compute the statistic. The statistic of each axis-slice (e.g. row)
+        of the input will appear in a corresponding element of the output.
+        If ``None``, the input will be raveled before computing the statistic.
+
+    Returns
+    -------
+    statistic : float
+        The test statistic.
+    p-value : float
+        The p-value for the hypothesis test.
+
+    See Also
+    --------
+    anderson : The Anderson-Darling test for normality
+    kstest : The Kolmogorov-Smirnov test for goodness of fit.
+    :ref:`hypothesis_shapiro` : Extended example
+
+    Notes
+    -----
+    The algorithm used is described in [4]_, but censoring parameters as
+    described are not implemented. For N > 5000 the W test statistic is
+    accurate, but the p-value may not be.
+
+    References
+    ----------
+    .. [1] https://www.itl.nist.gov/div898/handbook/prc/section2/prc213.htm
+           :doi:`10.18434/M32189`
+    .. [2] Shapiro, S. S. & Wilk, M.B, "An analysis of variance test for
+           normality (complete samples)", Biometrika, 1965, Vol. 52,
+           pp. 591-611, :doi:`10.2307/2333709`
+    .. [3] Razali, N. M. & Wah, Y. B., "Power comparisons of Shapiro-Wilk,
+           Kolmogorov-Smirnov, Lilliefors and Anderson-Darling tests", Journal
+           of Statistical Modeling and Analytics, 2011, Vol. 2, pp. 21-33.
+    .. [4] Royston, P. "A toolkit for testing for non-normality in complete and
+           censored samples." Journal of the Royal Statistical Society: Series D
+           (The Statistician) 42.1 (1993): 37-43.
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> rng = np.random.default_rng()
+    >>> x = stats.norm.rvs(loc=5, scale=3, size=100, random_state=rng)
+    >>> shapiro_test = stats.shapiro(x)
+    >>> shapiro_test
+    ShapiroResult(statistic=0.9813305735588074, pvalue=0.16855233907699585)
+    >>> shapiro_test.statistic
+    0.9813305735588074
+    >>> shapiro_test.pvalue
+    0.16855233907699585
+
+    For a more detailed example, see :ref:`hypothesis_shapiro`.
+    """
+    # `x` is an array and axis=-1 due to _axis_nan_policy decorator
+    xp = array_namespace(x)
+
+    N = x.shape[-1]
+    if N < 3:
+        raise ValueError("Data must be at least length 3.")
+
+    y = xp.sort(x, axis=-1)
+    y -= x[..., N//2:N//2+1]  # subtract the median (or a nearby value); see gh-15777
+
+    y = xp_promote(y, force_floating=True, xp=xp)
+    w, pw = _swilk(y, xp=xp)
+    if N > 5000:
+        warnings.warn("scipy.stats.shapiro: For N > 5000, computed p-value "
+                      f"may not be accurate. Current N is {N}.",
+                      stacklevel=2)
+
+    # `w` and `pw` are always Python floats, which are double precision.
+    # We want to ensure that they are NumPy floats, so until dtypes are
+    # respected, we can explicitly convert each to float64 (faster than
+    # `np.array([w, pw])`).
+    return ShapiroResult(w[()], pw[()])
+
+
+def _swilk_w(y, a, *, xp):
+    # calculate Shapiro-Wilk statistic given sorted sample and weights
+    # Follows [4] Section 2.1
+    num = xp.vecdot(a, y, axis=-1) ** 2
+    y_ = _demean(y, mean=xp.mean(y, axis=-1, keepdims=True), axis=-1, xp=xp)
+    den = xp.vecdot(y_, y_, axis=-1)
+    return num / den
+
+
+def _swilk(y, *, xp):
+    # calculate Shapiro-Wilk statistic and p-value from sorted sample
+    n = y.shape[-1]
+
+    if n == 3:
+        # [2] Table 5 gives the first four digits
+        c = math.sqrt(2) / 2
+        a = xp.asarray([-c, 0, c])
+        # [2] Corollary 4; discussed in https://github.com/scipy/scipy/issues/18322
+        W = xp.clip(_swilk_w(y, a, xp=xp), 0.75, 1.)
+        pvalue = xp.clip(1. - 6/np.pi * xp.acos(xp.sqrt(W)), 0., 1.)
+        return W, pvalue
+
+    # Follows [4] section 2.2
+    # could calculate half the coefficients and get the rest by antisymmetry
+    i = xp.arange(1, n + 1, dtype=y.dtype)
+    m = special.ndtri((i - 3 / 8) / (n + 1 / 4))
+    u = n**(-0.5)
+    mTm = xp.vecdot(m, m)
+    c = mTm**(-0.5) * m
+    mnm1, mn = m[..., -2], m[..., -1]
+    cnm1, cn = c[..., -2], c[..., -1]
+    an = (cn + 0.221157*u - 0.147981*u**2
+          - 2.071190*u**3 + 4.434685*u**4 - 2.706056*u**5)
+    anm1 = (cnm1 + 0.042981*u - 0.293762*u**2
+            - 1.752461*u**3 + 5.682633*u**4 - 3.582633*u**5)
+    phi = ((mTm - 2*mn**2) / (1 - 2*an**2) if n <= 5
+           else (mTm - 2*mn**2 - 2*mnm1**2) / (1 - 2*an**2 - 2*anm1**2))
+    a = phi**(-0.5) * m
+    if n > 5:
+        a = xpx.at(a)[..., -2].set(anm1)
+        a = xpx.at(a)[..., 1].set(-anm1)
+    a = xpx.at(a)[..., -1].set(an)
+    a = xpx.at(a)[..., -0].set(-an)
+    W = _swilk_w(y, a, xp=xp)
+
+    # Follows [4] Table 1
+    if n <= 11:
+        u = n
+        gamma = -2.273 + 0.459*u
+        mu = 0.5440 - 0.39978*u + 0.025054*u**2 - 0.0006714*u**3
+        sigma = math.exp(1.3822 - 0.77857*u + 0.062767*u**2 - 0.0020322*u**3)
+        gW = -xp.log(gamma - xp.log(1 - W))
+    else:
+        u = math.log(n)
+        mu = -1.5861 - 0.31082*u - 0.083751*u**2 + 0.0038915*u**3
+        sigma = math.exp(-0.4803 - 0.082676*u + 0.0030302*u**2)
+        gW = xp.log(1 - W)
+
+    z = (gW - mu) / sigma
+    pvalue = special.ndtr(-z)
+    return W, pvalue
+
+
+# Values from [8]
+_Avals_norm = array([0.561, 0.631, 0.752, 0.873, 1.035])
+_Avals_expon = array([0.916, 1.062, 1.321, 1.591, 1.959])
+# From Stephens, M A, "Goodness of Fit for the Extreme Value Distribution",
+#             Biometrika, Vol. 64, Issue 3, Dec. 1977, pp 583-588.
+_Avals_gumbel = array([0.474, 0.637, 0.757, 0.877, 1.038])
+# From Stephens, M A, "Tests of Fit for the Logistic Distribution Based
+#             on the Empirical Distribution Function.", Biometrika,
+#             Vol. 66, Issue 3, Dec. 1979, pp 591-595.
+_Avals_logistic = array([0.426, 0.563, 0.660, 0.769, 0.906, 1.010])
+# From Richard A. Lockhart and Michael A. Stephens "Estimation and Tests of
+#             Fit for the Three-Parameter Weibull Distribution"
+#             Journal of the Royal Statistical Society.Series B(Methodological)
+#             Vol. 56, No. 3 (1994), pp. 491-500, table 1. Keys are c*100
+_Avals_weibull = [[0.292, 0.395, 0.467, 0.522, 0.617, 0.711, 0.836, 0.931],
+                  [0.295, 0.399, 0.471, 0.527, 0.623, 0.719, 0.845, 0.941],
+                  [0.298, 0.403, 0.476, 0.534, 0.631, 0.728, 0.856, 0.954],
+                  [0.301, 0.408, 0.483, 0.541, 0.640, 0.738, 0.869, 0.969],
+                  [0.305, 0.414, 0.490, 0.549, 0.650, 0.751, 0.885, 0.986],
+                  [0.309, 0.421, 0.498, 0.559, 0.662, 0.765, 0.902, 1.007],
+                  [0.314, 0.429, 0.508, 0.570, 0.676, 0.782, 0.923, 1.030],
+                  [0.320, 0.438, 0.519, 0.583, 0.692, 0.802, 0.947, 1.057],
+                  [0.327, 0.448, 0.532, 0.598, 0.711, 0.824, 0.974, 1.089],
+                  [0.334, 0.469, 0.547, 0.615, 0.732, 0.850, 1.006, 1.125],
+                  [0.342, 0.472, 0.563, 0.636, 0.757, 0.879, 1.043, 1.167]]
+_Avals_weibull = np.array(_Avals_weibull)
+_cvals_weibull = np.linspace(0, 0.5, 11)
+_get_As_weibull = interpolate.interp1d(_cvals_weibull, _Avals_weibull.T,
+                                       kind='linear', bounds_error=False,
+                                       fill_value=_Avals_weibull[-1])
+
+
+def _weibull_fit_check(params, x):
+    # Refine the fit returned by `weibull_min.fit` to ensure that the first
+    # order necessary conditions are satisfied. If not, raise an error.
+    # Here, use `m` for the shape parameter to be consistent with [7]
+    # and avoid confusion with `c` as defined in [7].
+    n = len(x)
+    m, u, s = params
+
+    def dnllf_dm(m, u):
+        # Partial w.r.t. shape w/ optimal scale. See [7] Equation 5.
+        xu = x-u
+        return (1/m - (xu**m*np.log(xu)).sum()/(xu**m).sum()
+                + np.log(xu).sum()/n)
+
+    def dnllf_du(m, u):
+        # Partial w.r.t. loc w/ optimal scale. See [7] Equation 6.
+        xu = x-u
+        return (m-1)/m*(xu**-1).sum() - n*(xu**(m-1)).sum()/(xu**m).sum()
+
+    def get_scale(m, u):
+        # Partial w.r.t. scale solved in terms of shape and location.
+        # See [7] Equation 7.
+        return ((x-u)**m/n).sum()**(1/m)
+
+    def dnllf(params):
+        # Partial derivatives of the NLLF w.r.t. parameters, i.e.
+        # first order necessary conditions for MLE fit.
+        return [dnllf_dm(*params), dnllf_du(*params)]
+
+    suggestion = ("Maximum likelihood estimation is known to be challenging "
+                  "for the three-parameter Weibull distribution. Consider "
+                  "performing a custom goodness-of-fit test using "
+                  "`scipy.stats.monte_carlo_test`.")
+
+    if np.allclose(u, np.min(x)) or m < 1:
+        # The critical values provided by [7] don't seem to control the
+        # Type I error rate in this case. Error out.
+        message = ("Maximum likelihood estimation has converged to "
+                   "a solution in which the location is equal to the minimum "
+                   "of the data, the shape parameter is less than 2, or both. "
+                   "The table of critical values in [7] does not "
+                   "include this case. " + suggestion)
+        raise ValueError(message)
+
+    try:
+        # Refine the MLE / verify that first-order necessary conditions are
+        # satisfied. If so, the critical values provided in [7] seem reliable.
+        with np.errstate(over='raise', invalid='raise'):
+            res = optimize.root(dnllf, params[:-1])
+
+        message = ("Solution of MLE first-order conditions failed: "
+                   f"{res.message}. `anderson` cannot continue. " + suggestion)
+        if not res.success:
+            raise ValueError(message)
+
+    except (FloatingPointError, ValueError) as e:
+        message = ("An error occurred while fitting the Weibull distribution "
+                   "to the data, so `anderson` cannot continue. " + suggestion)
+        raise ValueError(message) from e
+
+    m, u = res.x
+    s = get_scale(m, u)
+    return m, u, s
+
+
+AndersonResult = _make_tuple_bunch('AndersonResult',
+                                   ['statistic', 'critical_values',
+                                    'significance_level'], ['fit_result'])
+
+
+_anderson_warning_message = (
+"""As of SciPy 1.17, users must choose a p-value calculation method by providing the
+`method` parameter. `method='interpolate'` interpolates the p-value from pre-calculated
+tables; `method` may also be an instance of `MonteCarloMethod` to approximate the
+p-value via Monte Carlo simulation. When `method` is specified, the result object will
+include a `pvalue` attribute and not attributes `critical_value`, `significance_level`,
+or `fit_result`. Beginning in 1.19.0, these other attributes will no longer be
+available, and a p-value will always be computed according to one of the available
+`method` options.""".replace('\n', ' '))
+
+
+@xp_capabilities(np_only=True)
+def anderson(x, dist='norm', *, method=None):
+    """Anderson-Darling test for data coming from a particular distribution.
+
+    The Anderson-Darling test tests the null hypothesis that a sample is
+    drawn from a population that follows a particular distribution.
+    For the Anderson-Darling test, the critical values depend on
+    which distribution is being tested against.  This function works
+    for normal, exponential, logistic, weibull_min, or Gumbel (Extreme Value
+    Type I) distributions.
+
+    Parameters
+    ----------
+    x : array_like
+        Array of sample data.
+    dist : {'norm', 'expon', 'logistic', 'gumbel', 'gumbel_l', 'gumbel_r', 'extreme1', 'weibull_min'}, optional
+        The type of distribution to test against.  The default is 'norm'.
+        The names 'extreme1', 'gumbel_l' and 'gumbel' are synonyms for the
+        same distribution.
+    method : str or instance of `MonteCarloMethod`
+        Defines the method used to compute the p-value.
+        If `method` is ``"interpolated"``, the p-value is interpolated from
+        pre-calculated tables.
+        If `method` is an instance of `MonteCarloMethod`, the p-value is computed using
+        `scipy.stats.monte_carlo_test` with the provided configuration options and other
+        appropriate settings.
+
+        .. versionadded:: 1.17.0
+            If `method` is not specified, `anderson` will emit a ``FutureWarning``
+            specifying that the user must opt into a p-value calculation method.
+            When `method` is specified, the object returned will include a ``pvalue``
+            attribute, but no ``critical_value``, ``significance_level``, or
+            ``fit_result`` attributes. Beginning in 1.19.0, these other attributes will
+            no longer be available, and a p-value will always be computed according to
+            one of the available `method` options.
+
+    Returns
+    -------
+    result : AndersonResult
+        If `method` is provided, this is an object with the following attributes:
+
+        statistic : float
+            The Anderson-Darling test statistic.
+        pvalue: float
+            The p-value corresponding with the test statistic, calculated according to
+            the specified `method`.
+
+        If `method` is unspecified, this is an object with the following attributes:
+
+        statistic : float
+            The Anderson-Darling test statistic.
+        critical_values : list
+            The critical values for this distribution.
+        significance_level : list
+            The significance levels for the corresponding critical values
+            in percents.  The function returns critical values for a
+            differing set of significance levels depending on the
+            distribution that is being tested against.
+        fit_result : `~scipy.stats._result_classes.FitResult`
+            An object containing the results of fitting the distribution to
+            the data.
+
+        .. deprecated:: 1.17.0
+            The tuple-unpacking behavior of the return object and attributes
+            ``critical_values``, ``significance_level``, and ``fit_result`` are
+            deprecated. Beginning in SciPy 1.19.0, these features will no longer be
+            available, and the object returned will have attributes ``statistic`` and
+            ``pvalue``.
+
+    See Also
+    --------
+    kstest : The Kolmogorov-Smirnov test for goodness-of-fit.
+
+    Notes
+    -----
+    Critical values provided when `method` is unspecified are for the following
+    significance levels:
+
+    normal/exponential
+        15%, 10%, 5%, 2.5%, 1%
+    logistic
+        25%, 10%, 5%, 2.5%, 1%, 0.5%
+    gumbel_l / gumbel_r
+        25%, 10%, 5%, 2.5%, 1%
+    weibull_min
+        50%, 25%, 15%, 10%, 5%, 2.5%, 1%, 0.5%
+
+    If the returned statistic is larger than these critical values then
+    for the corresponding significance level, the null hypothesis that
+    the data come from the chosen distribution can be rejected.
+    The returned statistic is referred to as 'A2' in the references.
+
+    For `weibull_min`, maximum likelihood estimation is known to be
+    challenging. If the test returns successfully, then the first order
+    conditions for a maximum likelihood estimate have been verified and
+    the critical values correspond relatively well to the significance levels,
+    provided that the sample is sufficiently large (>10 observations [7]).
+    However, for some data - especially data with no left tail - `anderson`
+    is likely to result in an error message. In this case, consider
+    performing a custom goodness of fit test using
+    `scipy.stats.monte_carlo_test`.
+
+    References
+    ----------
+    .. [1] https://www.itl.nist.gov/div898/handbook/prc/section2/prc213.htm
+    .. [2] Stephens, M. A. (1974). EDF Statistics for Goodness of Fit and
+           Some Comparisons, Journal of the American Statistical Association,
+           Vol. 69, pp. 730-737.
+    .. [3] Stephens, M. A. (1976). Asymptotic Results for Goodness-of-Fit
+           Statistics with Unknown Parameters, Annals of Statistics, Vol. 4,
+           pp. 357-369.
+    .. [4] Stephens, M. A. (1977). Goodness of Fit for the Extreme Value
+           Distribution, Biometrika, Vol. 64, pp. 583-588.
+    .. [5] Stephens, M. A. (1977). Goodness of Fit with Special Reference
+           to Tests for Exponentiality , Technical Report No. 262,
+           Department of Statistics, Stanford University, Stanford, CA.
+    .. [6] Stephens, M. A. (1979). Tests of Fit for the Logistic Distribution
+           Based on the Empirical Distribution Function, Biometrika, Vol. 66,
+           pp. 591-595.
+    .. [7] Richard A. Lockhart and Michael A. Stephens "Estimation and Tests of
+           Fit for the Three-Parameter Weibull Distribution"
+           Journal of the Royal Statistical Society.Series B(Methodological)
+           Vol. 56, No. 3 (1994), pp. 491-500, Table 0.
+    .. [8] D'Agostino, Ralph B. (1986). "Tests for the Normal Distribution".
+           In: Goodness-of-Fit Techniques. Ed. by Ralph B. D'Agostino and
+           Michael A. Stephens. New York: Marcel Dekker, pp. 122-141. ISBN:
+           0-8247-7487-6.
+
+    Examples
+    --------
+    Test the null hypothesis that a random sample was drawn from a normal
+    distribution (with unspecified mean and standard deviation).
+
+    >>> import numpy as np
+    >>> from scipy.stats import anderson
+    >>> rng = np.random.default_rng(9781234521)
+    >>> data = rng.random(size=35)
+    >>> res = anderson(data, dist='norm', method='interpolate')
+    >>> res.statistic
+    np.float64(0.9887620209957291)
+    >>> res.pvalue
+    np.float64(0.012111200538380142)
+
+    The p-value is approximately 0.012,, so the null hypothesis may be rejected
+    at a significance level of 2.5%, but not at a significance level of 1%.
+
+    """ # numpy/numpydoc#87  # noqa: E501
+    dist = dist.lower()
+    if dist in {'extreme1', 'gumbel'}:
+        dist = 'gumbel_l'
+    dists = {'norm', 'expon', 'gumbel_l',
+             'gumbel_r', 'logistic', 'weibull_min'}
+
+    if dist not in dists:
+        raise ValueError(f"Invalid distribution; dist must be in {dists}.")
+    y = sort(x)
+    xbar = np.mean(x, axis=0)
+    N = len(y)
+    if dist == 'norm':
+        s = np.std(x, ddof=1, axis=0)
+        w = (y - xbar) / s
+        fit_params = xbar, s
+        logcdf = distributions.norm.logcdf(w)
+        logsf = distributions.norm.logsf(w)
+        sig = array([15, 10, 5, 2.5, 1])
+        critical = around(_Avals_norm / (1.0 + 0.75/N + 2.25/N/N), 3)
+    elif dist == 'expon':
+        w = y / xbar
+        fit_params = 0, xbar
+        logcdf = distributions.expon.logcdf(w)
+        logsf = distributions.expon.logsf(w)
+        sig = array([15, 10, 5, 2.5, 1])
+        critical = around(_Avals_expon / (1.0 + 0.6/N), 3)
+    elif dist == 'logistic':
+        def rootfunc(ab, xj, N):
+            a, b = ab
+            tmp = (xj - a) / b
+            tmp2 = exp(tmp)
+            val = [np.sum(1.0/(1+tmp2), axis=0) - 0.5*N,
+                   np.sum(tmp*(1.0-tmp2)/(1+tmp2), axis=0) + N]
+            return array(val)
+
+        sol0 = array([xbar, np.std(x, ddof=1, axis=0)])
+        sol = optimize.fsolve(rootfunc, sol0, args=(x, N), xtol=1e-5)
+        w = (y - sol[0]) / sol[1]
+        fit_params = sol
+        logcdf = distributions.logistic.logcdf(w)
+        logsf = distributions.logistic.logsf(w)
+        sig = array([25, 10, 5, 2.5, 1, 0.5])
+        critical = around(_Avals_logistic / (1.0 + 0.25/N), 3)
+    elif dist == 'gumbel_r':
+        xbar, s = distributions.gumbel_r.fit(x)
+        w = (y - xbar) / s
+        fit_params = xbar, s
+        logcdf = distributions.gumbel_r.logcdf(w)
+        logsf = distributions.gumbel_r.logsf(w)
+        sig = array([25, 10, 5, 2.5, 1])
+        critical = around(_Avals_gumbel / (1.0 + 0.2/sqrt(N)), 3)
+    elif dist == 'gumbel_l':
+        xbar, s = distributions.gumbel_l.fit(x)
+        w = (y - xbar) / s
+        fit_params = xbar, s
+        logcdf = distributions.gumbel_l.logcdf(w)
+        logsf = distributions.gumbel_l.logsf(w)
+        sig = array([25, 10, 5, 2.5, 1])
+        critical = around(_Avals_gumbel / (1.0 + 0.2/sqrt(N)), 3)
+    elif dist == 'weibull_min':
+        message = ("Critical values of the test statistic are given for the "
+                   "asymptotic distribution. These may not be accurate for "
+                   "samples with fewer than 10 observations. Consider using "
+                   "`scipy.stats.monte_carlo_test`.")
+        if N < 10:
+            warnings.warn(message, stacklevel=2)
+        # [7] writes our 'c' as 'm', and they write `c = 1/m`. Use their names.
+        m, loc, scale = distributions.weibull_min.fit(y)
+        m, loc, scale = _weibull_fit_check((m, loc, scale), y)
+        fit_params = m, loc, scale
+        logcdf = stats.weibull_min(*fit_params).logcdf(y)
+        logsf = stats.weibull_min(*fit_params).logsf(y)
+        c = 1 / m  # m and c are as used in [7]
+        sig = array([0.5, 0.75, 0.85, 0.9, 0.95, 0.975, 0.99, 0.995])
+        critical = _get_As_weibull(c)
+        # Goodness-of-fit tests should only be used to provide evidence
+        # _against_ the null hypothesis. Be conservative and round up.
+        critical = np.round(critical + 0.0005, decimals=3)
+
+    i = arange(1, N + 1)
+    A2 = -N - np.sum((2*i - 1.0) / N * (logcdf + logsf[::-1]), axis=0)
+
+    # FitResult initializer expects an optimize result, so let's work with it
+    message = '`anderson` successfully fit the distribution to the data.'
+    res = optimize.OptimizeResult(success=True, message=message)
+    res.x = np.array(fit_params)
+    fit_result = FitResult(getattr(distributions, dist), y,
+                           discrete=False, res=res)
+
+    if method is None:
+        warnings.warn(_anderson_warning_message, FutureWarning, stacklevel=2)
+        return AndersonResult(A2, critical, sig, fit_result=fit_result)
+
+    if method == 'interpolate':
+        sig = 1 - sig if dist == 'weibull_min' else sig / 100
+        pvalue = np.interp(A2, critical, sig)
+    elif isinstance(method, stats.MonteCarloMethod):
+        pvalue = _anderson_simulate_pvalue(x, dist, method)
+    else:
+        message = ("`method` must be either 'interpolate' or "
+                   "an instance of `MonteCarloMethod`.")
+        raise ValueError(message)
+    return SignificanceResult(statistic=A2, pvalue=pvalue)
+
+
+def _anderson_simulate_pvalue(x, dist, method):
+    message = ("The `___` attribute of a `MonteCarloMethod` object passed as the "
+               "`method` parameter of `scipy.stats.anderson` is ignored.")
+
+    method = method._asdict()
+    if method.pop('rvs', False):
+        warnings.warn(message.replace('___', 'rvs'), UserWarning, stacklevel=3)
+    if method.pop('batch', False):
+        warnings.warn(message.replace('___', 'batch'), UserWarning, stacklevel=3)
+    method['n_mc_samples'] = method.pop('n_resamples')
+
+    kwargs= {'known_params': {'loc': 0}} if dist == 'expon' else {}
+    dist = getattr(stats, dist)
+    res = stats.goodness_of_fit(dist, x, statistic='ad', **kwargs, **method)
+    return res.pvalue
+
+
+def _anderson_ksamp_continuous(samples, Z, Zstar, k, n, N):
+    """Compute A2akN equation 3 of Scholz & Stephens.
+
+    Parameters
+    ----------
+    samples : sequence of 1-D array_like
+        Array of sample arrays.
+    Z : array_like
+        Sorted array of all observations.
+    Zstar : array_like
+        Sorted array of unique observations. Unused.
+    k : int
+        Number of samples.
+    n : array_like
+        Number of observations in each sample.
+    N : int
+        Total number of observations.
+
+    Returns
+    -------
+    A2KN : float
+        The A2KN statistics of Scholz and Stephens 1987.
+
+    """
+    A2kN = 0.
+
+    j = np.arange(1, N)
+    for i in arange(0, k):
+        s = np.sort(samples[i])
+        Mij = s.searchsorted(Z[:-1], side='right')
+        inner = (N*Mij - j*n[i])**2 / (j * (N - j))
+        A2kN += inner.sum() / n[i]
+    return A2kN / N
+
+
+def _anderson_ksamp_midrank(samples, Z, Zstar, k, n, N):
+    """Compute A2akN equation 7 of Scholz and Stephens.
+
+    Parameters
+    ----------
+    samples : sequence of 1-D array_like
+        Array of sample arrays.
+    Z : array_like
+        Sorted array of all observations.
+    Zstar : array_like
+        Sorted array of unique observations.
+    k : int
+        Number of samples.
+    n : array_like
+        Number of observations in each sample.
+    N : int
+        Total number of observations.
+
+    Returns
+    -------
+    A2aKN : float
+        The A2aKN statistics of Scholz and Stephens 1987.
+
+    """
+    A2akN = 0.
+    Z_ssorted_left = Z.searchsorted(Zstar, 'left')
+    if N == Zstar.size:
+        lj = 1.
+    else:
+        lj = Z.searchsorted(Zstar, 'right') - Z_ssorted_left
+    Bj = Z_ssorted_left + lj / 2.
+    for i in arange(0, k):
+        s = np.sort(samples[i])
+        s_ssorted_right = s.searchsorted(Zstar, side='right')
+        Mij = s_ssorted_right.astype(float)
+        fij = s_ssorted_right - s.searchsorted(Zstar, 'left')
+        Mij -= fij / 2.
+        inner = lj / float(N) * (N*Mij - Bj*n[i])**2 / (Bj*(N - Bj) - N*lj/4.)
+        A2akN += inner.sum() / n[i]
+    A2akN *= (N - 1.) / N
+    return A2akN
+
+
+def _anderson_ksamp_right(samples, Z, Zstar, k, n, N):
+    """Compute A2akN equation 6 of Scholz & Stephens.
+
+    Parameters
+    ----------
+    samples : sequence of 1-D array_like
+        Array of sample arrays.
+    Z : array_like
+        Sorted array of all observations.
+    Zstar : array_like
+        Sorted array of unique observations.
+    k : int
+        Number of samples.
+    n : array_like
+        Number of observations in each sample.
+    N : int
+        Total number of observations.
+
+    Returns
+    -------
+    A2KN : float
+        The A2KN statistics of Scholz and Stephens 1987.
+
+    """
+    A2kN = 0.
+    lj = Z.searchsorted(Zstar[:-1], 'right') - Z.searchsorted(Zstar[:-1],
+                                                              'left')
+    Bj = lj.cumsum()
+    for i in arange(0, k):
+        s = np.sort(samples[i])
+        Mij = s.searchsorted(Zstar[:-1], side='right')
+        inner = lj / float(N) * (N * Mij - Bj * n[i])**2 / (Bj * (N - Bj))
+        A2kN += inner.sum() / n[i]
+    return A2kN
+
+
+Anderson_ksampResult = _make_tuple_bunch(
+    'Anderson_ksampResult',
+    ['statistic', 'critical_values', 'pvalue'], []
+)
+
+
+@xp_capabilities(np_only=True)
+def anderson_ksamp(samples, midrank=_NoValue, *, variant=_NoValue, method=None):
+    """The Anderson-Darling test for k-samples.
+
+    The k-sample Anderson-Darling test is a modification of the
+    one-sample Anderson-Darling test. It tests the null hypothesis
+    that k-samples are drawn from the same population without having
+    to specify the distribution function of that population. The
+    critical values depend on the number of samples.
+
+    Parameters
+    ----------
+    samples : sequence of 1-D array_like
+        Array of sample data in arrays.
+    midrank : bool, optional
+        Variant of Anderson-Darling test which is computed. Default
+        (True) is the midrank test applicable to continuous and
+        discrete populations. If False, the right side empirical
+        distribution is used.
+
+        .. deprecated:: 1.17.0
+            Use parameter `variant` instead.
+    variant : {'midrank', 'right', 'continuous'}
+        Variant of Anderson-Darling test to be computed. ``'midrank'`` is applicable
+        to both continuous and discrete populations. ``'discrete'`` and ``'continuous'``
+        perform alternative versions of the test for discrete  and continuous
+        populations, respectively.
+        When `variant` is specified, the return object will not be unpackable as a
+        tuple, and only attributes ``statistic`` and ``pvalue`` will be present.
+    method : PermutationMethod, optional
+        Defines the method used to compute the p-value. If `method` is an
+        instance of `PermutationMethod`, the p-value is computed using
+        `scipy.stats.permutation_test` with the provided configuration options
+        and other appropriate settings. Otherwise, the p-value is interpolated
+        from tabulated values.
+
+    Returns
+    -------
+    res : Anderson_ksampResult
+        An object containing attributes:
+
+        statistic : float
+            Normalized k-sample Anderson-Darling test statistic.
+        critical_values : array
+            The critical values for significance levels 25%, 10%, 5%, 2.5%, 1%,
+            0.5%, 0.1%.
+
+            .. deprecated:: 1.17.0
+                 Present only when `variant` is unspecified.
+
+        pvalue : float
+            The approximate p-value of the test. If `method` is not
+            provided, the value is floored / capped at 0.1% / 25%.
+
+    Raises
+    ------
+    ValueError
+        If fewer than 2 samples are provided, a sample is empty, or no
+        distinct observations are in the samples.
+
+    See Also
+    --------
+    ks_2samp : 2 sample Kolmogorov-Smirnov test
+    anderson : 1 sample Anderson-Darling test
+
+    Notes
+    -----
+    [1]_ defines three versions of the k-sample Anderson-Darling test:
+    one for continuous distributions and two for discrete
+    distributions, in which ties between samples may occur. The
+    default of this routine is to compute the version based on the
+    midrank empirical distribution function. This test is applicable
+    to continuous and discrete data. If `variant` is set to ``'discrete'``, the
+    right side empirical distribution is used for a test for discrete
+    data; if `variant` is ``'continuous'``, the same test statistic and p-value are
+    computed for data with no ties, but with less computation. According to [1]_,
+    the two discrete test statistics differ only slightly if a few collisions due
+    to round-off errors occur in the test not adjusted for ties between samples.
+
+    The critical values corresponding to the significance levels from 0.01
+    to 0.25 are taken from [1]_. p-values are floored / capped
+    at 0.1% / 25%. Since the range of critical values might be extended in
+    future releases, it is recommended not to test ``p == 0.25``, but rather
+    ``p >= 0.25`` (analogously for the lower bound).
+
+    .. versionadded:: 0.14.0
+
+    References
+    ----------
+    .. [1] Scholz, F. W and Stephens, M. A. (1987), K-Sample
+           Anderson-Darling Tests, Journal of the American Statistical
+           Association, Vol. 82, pp. 918-924.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> rng = np.random.default_rng(44925884305279435)
+    >>> res = stats.anderson_ksamp([rng.normal(size=50), rng.normal(loc=0.5, size=30)],
+    ...                            variant='midrank')
+    >>> res.statistic, res.pvalue
+    (3.4444310693448936, 0.013106682406720973)
+
+    The null hypothesis that the two random samples come from the same
+    distribution can be rejected at the 5% level because the returned
+    p-value is less than 0.05, but not at the 1% level.
+
+    >>> samples = [rng.normal(size=50), rng.normal(size=30),
+    ...            rng.normal(size=20)]
+    >>> res = stats.anderson_ksamp(samples, variant='continuous')
+    >>> res.statistic, res.pvalue
+    (-0.6309662273193832, 0.25)
+
+    As we might expect, the null hypothesis cannot be rejected here for three samples
+    from an identical distribution. The reported p-value (25%) has been capped at the
+    maximum value for which pre-computed p-values are available.
+
+    In such cases where the p-value is capped or when sample sizes are
+    small, a permutation test may be more accurate.
+
+    >>> method = stats.PermutationMethod(n_resamples=9999, random_state=rng)
+    >>> res = stats.anderson_ksamp(samples, variant='continuous', method=method)
+    >>> res.pvalue
+    0.699
+
+    """
+    k = len(samples)
+    if (k < 2):
+        raise ValueError("anderson_ksamp needs at least two samples")
+
+    samples = list(map(np.asarray, samples))
+    Z = np.sort(np.hstack(samples))
+    N = Z.size
+    Zstar = np.unique(Z)
+    if Zstar.size < 2:
+        raise ValueError("anderson_ksamp needs more than one distinct "
+                         "observation")
+
+    n = np.array([sample.size for sample in samples])
+    if np.any(n == 0):
+        raise ValueError("anderson_ksamp encountered sample without "
+                         "observations")
+
+    if variant == _NoValue or midrank != _NoValue:
+        message = ("Parameter `variant` has been introduced to replace `midrank`; "
+                   "`midrank` will be removed in SciPy 1.19.0. Specify `variant` to "
+                   "silence this warning. Note that the returned object will no longer "
+                   "be unpackable as a tuple, and `critical_values` will be omitted.")
+        warnings.warn(message, category=UserWarning, stacklevel=2)
+
+    return_critical_values = False
+    if variant == _NoValue:
+        return_critical_values = True
+        variant = 'midrank' if midrank else 'right'
+
+    if variant == 'midrank':
+        A2kN_fun = _anderson_ksamp_midrank
+    elif variant == 'right':
+        A2kN_fun = _anderson_ksamp_right
+    elif variant == 'continuous':
+        A2kN_fun = _anderson_ksamp_continuous
+    else:
+        message = "`variant` must be one of 'midrank', 'right', or 'continuous'."
+        raise ValueError(message)
+
+    A2kN = A2kN_fun(samples, Z, Zstar, k, n, N)
+
+    def statistic(*samples):
+        return A2kN_fun(samples, Z, Zstar, k, n, N)
+
+    if method is not None:
+        res = stats.permutation_test(samples, statistic, **method._asdict(),
+                                     alternative='greater')
+
+    H = (1. / n).sum()
+    hs_cs = (1. / arange(N - 1, 1, -1)).cumsum()
+    h = hs_cs[-1] + 1
+    g = (hs_cs / arange(2, N)).sum()
+
+    a = (4*g - 6) * (k - 1) + (10 - 6*g)*H
+    b = (2*g - 4)*k**2 + 8*h*k + (2*g - 14*h - 4)*H - 8*h + 4*g - 6
+    c = (6*h + 2*g - 2)*k**2 + (4*h - 4*g + 6)*k + (2*h - 6)*H + 4*h
+    d = (2*h + 6)*k**2 - 4*h*k
+    sigmasq = (a*N**3 + b*N**2 + c*N + d) / ((N - 1.) * (N - 2.) * (N - 3.))
+    m = k - 1
+    A2 = (A2kN - m) / math.sqrt(sigmasq)
+
+    # The b_i values are the interpolation coefficients from Table 2
+    # of Scholz and Stephens 1987
+    b0 = np.array([0.675, 1.281, 1.645, 1.96, 2.326, 2.573, 3.085])
+    b1 = np.array([-0.245, 0.25, 0.678, 1.149, 1.822, 2.364, 3.615])
+    b2 = np.array([-0.105, -0.305, -0.362, -0.391, -0.396, -0.345, -0.154])
+    critical = b0 + b1 / math.sqrt(m) + b2 / m
+
+    sig = np.array([0.25, 0.1, 0.05, 0.025, 0.01, 0.005, 0.001])
+
+    if A2 < critical.min() and method is None:
+        p = sig.max()
+        msg = (f"p-value capped: true value larger than {p}. Consider "
+               "specifying `method` "
+               "(e.g. `method=stats.PermutationMethod()`.)")
+        warnings.warn(msg, stacklevel=2)
+    elif A2 > critical.max() and method is None:
+        p = sig.min()
+        msg = (f"p-value floored: true value smaller than {p}. Consider "
+               "specifying `method` "
+               "(e.g. `method=stats.PermutationMethod()`.)")
+        warnings.warn(msg, stacklevel=2)
+    elif method is None:
+        # interpolation of probit of significance level
+        pf = np.polyfit(critical, log(sig), 2)
+        p = math.exp(np.polyval(pf, A2))
+    else:
+        p = res.pvalue if method is not None else p
+
+    if return_critical_values:
+        # create result object with alias for backward compatibility
+        res = Anderson_ksampResult(A2, critical, p)
+        res.significance_level = p
+    else:
+        res = SignificanceResult(statistic=A2, pvalue=p)
+
+    return res
+
+
+
+AnsariResult = namedtuple('AnsariResult', ('statistic', 'pvalue'))
+
+
+class _ABW:
+    """Distribution of Ansari-Bradley W-statistic under the null hypothesis."""
+    # TODO: calculate exact distribution considering ties
+    # We could avoid summing over more than half the frequencies,
+    # but initially it doesn't seem worth the extra complexity
+
+    def __init__(self):
+        """Minimal initializer."""
+        self.m = None
+        self.n = None
+        self.astart = None
+        self.total = None
+        self.freqs = None
+
+    def _recalc(self, n, m):
+        """When necessary, recalculate exact distribution."""
+        if n != self.n or m != self.m:
+            self.n, self.m = n, m
+            # distribution is NOT symmetric when m + n is odd
+            # n is len(x), m is len(y), and ratio of scales is defined x/y
+            astart, a1, _ = gscale(n, m)
+            self.astart = astart  # minimum value of statistic
+            # Exact distribution of test statistic under null hypothesis
+            # expressed as frequencies/counts/integers to maintain precision.
+            # Stored as floats to avoid overflow of sums.
+            self.freqs = a1.astype(np.float64)
+            self.total = self.freqs.sum()  # could calculate from m and n
+            # probability mass is self.freqs / self.total;
+
+    def pmf(self, k, n, m):
+        """Probability mass function."""
+        self._recalc(n, m)
+        # The convention here is that PMF at k = 12.5 is the same as at k = 12,
+        # -> use `floor` in case of ties.
+        ind = np.floor(k - self.astart).astype(int)
+        return self.freqs[ind] / self.total
+
+    def cdf(self, k, n, m):
+        """Cumulative distribution function."""
+        self._recalc(n, m)
+        # Null distribution derived without considering ties is
+        # approximate. Round down to avoid Type I error.
+        ind = np.ceil(k - self.astart).astype(int)
+        return self.freqs[:ind+1].sum() / self.total
+
+    def sf(self, k, n, m):
+        """Survival function."""
+        self._recalc(n, m)
+        # Null distribution derived without considering ties is
+        # approximate. Round down to avoid Type I error.
+        ind = np.floor(k - self.astart).astype(int)
+        return self.freqs[ind:].sum() / self.total
+
+
+# Maintain state for faster repeat calls to ansari w/ method='exact'
+# _ABW() is calculated once per thread and stored as an attribute on
+# this thread-local variable inside ansari().
+_abw_state = threading.local()
+
+
+@xp_capabilities(cpu_only=True, skip_backends=[('dask.array', 'no rankdata')])
+@_axis_nan_policy_factory(AnsariResult, n_samples=2)
+def ansari(x, y, alternative='two-sided', *, axis=0, method='auto'):
+    """Perform the Ansari-Bradley test for equal scale parameters.
+
+    The Ansari-Bradley test ([1]_, [2]_) is a non-parametric test
+    for the equality of the scale parameter of the distributions
+    from which two samples were drawn. The null hypothesis states that
+    the ratio of the scale of the distribution underlying `x` to the scale
+    of the distribution underlying `y` is 1.
+
+    Parameters
+    ----------
+    x, y : array_like
+        Arrays of sample data.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis. Default is 'two-sided'.
+        The following options are available:
+
+        * 'two-sided': the ratio of scales is not equal to 1.
+        * 'less': the ratio of scales is less than 1.
+        * 'greater': the ratio of scales is greater than 1.
+
+        .. versionadded:: 1.7.0
+    axis : int or tuple of ints, default: 0
+        If an int or tuple of ints, the axis or axes of the input along which
+        to compute the statistic. The statistic of each axis-slice (e.g. row)
+        of the input will appear in a corresponding element of the output.
+        If ``None``, the input will be raveled before computing the statistic.
+    method : {'auto', 'asymptotic', 'exact'} or `PermutationMethod` instance, optional
+        Selects the method used to calculate the *p*-value.
+        Default is 'auto'. The following options are available.
+
+        * ``'asymptotic'``: compares the standardized test statistic
+          against the normal distribution, correcting for ties.
+        * ``'exact'``: computes the exact *p*-value by comparing the observed
+          statistic against the exact distribution of the statistic under the
+          null hypothesis. No correction is made for ties.
+        * ``'auto'``: chooses ``'exact'`` when the size of both
+          samples is less than or equal to 55 and there are no ties;
+          chooses ``'asymptotic'`` otherwise.
+        * `PermutationMethod` instance. In this case, the p-value
+          is computed using `permutation_test` with the provided
+          configuration options and other appropriate settings.
+
+    Returns
+    -------
+    statistic : float
+        The Ansari-Bradley test statistic.
+    pvalue : float
+        The p-value of the hypothesis test.
+
+    See Also
+    --------
+    fligner : A non-parametric test for the equality of k variances
+    mood : A non-parametric test for the equality of two scale parameters
+
+    Notes
+    -----
+    The p-value given is exact when the sample sizes are both less than
+    55 and there are no ties, otherwise a normal approximation for the
+    p-value is used.
+
+    References
+    ----------
+    .. [1] Ansari, A. R. and Bradley, R. A. (1960) Rank-sum tests for
+           dispersions, Annals of Mathematical Statistics, 31, 1174-1189.
+    .. [2] Sprent, Peter and N.C. Smeeton.  Applied nonparametric
+           statistical methods.  3rd ed. Chapman and Hall/CRC. 2001.
+           Section 5.8.2.
+    .. [3] Nathaniel E. Helwig "Nonparametric Dispersion and Equality
+           Tests" at http://users.stat.umn.edu/~helwig/notes/npde-Notes.pdf
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import ansari
+    >>> rng = np.random.default_rng()
+
+    For these examples, we'll create three random data sets.  The first
+    two, with sizes 35 and 25, are drawn from a normal distribution with
+    mean 0 and standard deviation 2.  The third data set has size 25 and
+    is drawn from a normal distribution with standard deviation 1.25.
+
+    >>> x1 = rng.normal(loc=0, scale=2, size=35)
+    >>> x2 = rng.normal(loc=0, scale=2, size=25)
+    >>> x3 = rng.normal(loc=0, scale=1.25, size=25)
+
+    First we apply `ansari` to `x1` and `x2`.  These samples are drawn
+    from the same distribution, so we expect the Ansari-Bradley test
+    should not lead us to conclude that the scales of the distributions
+    are different.
+
+    >>> ansari(x1, x2)
+    AnsariResult(statistic=541.0, pvalue=0.9762532927399098)
+
+    With a p-value close to 1, we cannot conclude that there is a
+    significant difference in the scales (as expected).
+
+    Now apply the test to `x1` and `x3`:
+
+    >>> ansari(x1, x3)
+    AnsariResult(statistic=425.0, pvalue=0.0003087020407974518)
+
+    The probability of observing such an extreme value of the statistic
+    under the null hypothesis of equal scales is only 0.03087%. We take this
+    as evidence against the null hypothesis in favor of the alternative:
+    the scales of the distributions from which the samples were drawn
+    are not equal.
+
+    We can use the `alternative` parameter to perform a one-tailed test.
+    In the above example, the scale of `x1` is greater than `x3` and so
+    the ratio of scales of `x1` and `x3` is greater than 1. This means
+    that the p-value when ``alternative='greater'`` should be near 0 and
+    hence we should be able to reject the null hypothesis:
+
+    >>> ansari(x1, x3, alternative='greater')
+    AnsariResult(statistic=425.0, pvalue=0.0001543510203987259)
+
+    As we can see, the p-value is indeed quite low. Use of
+    ``alternative='less'`` should thus yield a large p-value:
+
+    >>> ansari(x1, x3, alternative='less')
+    AnsariResult(statistic=425.0, pvalue=0.9998643258449039)
+
+    """
+    xp = array_namespace(x, y)
+    dtype = xp_result_type(x, y, force_floating=True, xp=xp)
+
+    if alternative not in {'two-sided', 'greater', 'less'}:
+        raise ValueError("'alternative' must be 'two-sided',"
+                         " 'greater', or 'less'.")
+    methods = {'auto', 'asymptotic', 'exact'}
+    if str(method) not in methods and not isinstance(method, stats.PermutationMethod):
+        message = (f"`method` must be one of {methods} or "
+                   "an instance of `PermutationMethod`.")
+        raise ValueError(message)
+    if is_lazy_array(x) and method == 'auto':
+        message = ("`method` must be 'exact', 'asymptotic', or an instance of "
+                   "`PermutationMethod` when used with lazy arrays.")
+        raise ValueError(message)
+
+    if not hasattr(_abw_state, 'a'):
+        _abw_state.a = _ABW()
+
+    # _axis_nan_policy decorator guarantees that axis=-1
+    n = x.shape[-1]
+    m = y.shape[-1]
+    if m < 1:  # needed by test_axis_nan_policy; not user-facing
+        raise ValueError("Not enough other observations.")
+    if n < 1:
+        raise ValueError("Not enough test observations.")
+
+    N = m + n
+    xy = xp.concat([x, y], axis=-1)  # combine
+    rank, _, t = _stats_py._rankdata(xy, method='average', return_ties=True)
+    symrank = xp.minimum(rank, N - rank + 1)
+    AB = xp.sum(symrank[..., :n], axis=-1)
+    repeats = xp.any(t > 1)  # in theory we could branch for each slice separately
+
+    if method == "auto":
+        method = 'exact' if ((m < 55) and (n < 55) and not repeats) else 'asymptotic'
+
+    if method == 'exact':
+        # np.vectorize converts to NumPy here, and we convert back to the result
+        # type before returning
+        cdf = np.vectorize(_abw_state.a.cdf, otypes=[np.float64])
+        sf = np.vectorize(_abw_state.a.sf, otypes=[np.float64])
+        def get_ansari_pvalue(AB):
+            if alternative == 'two-sided':
+                pval = 2.0 * np.minimum(cdf(AB, n, m), sf(AB, n, m))
+            elif alternative == 'greater':
+                # AB statistic is _smaller_ when ratio of scales is larger,
+                # so this is the opposite of the usual calculation
+                pval = cdf(AB, n, m)
+            else:
+                pval = sf(AB, n, m)
+            return pval
+
+        pval = xpx.lazy_apply(get_ansari_pvalue, AB, shape=AB.shape)
+        pval = xp.clip(xp.asarray(pval, dtype=dtype), max=1.0)
+        AB = AB[()] if AB.ndim == 0 else AB
+        pval = pval[()] if pval.ndim == 0 else pval
+        return AnsariResult(AB, pval)
+
+    elif isinstance(method, stats.PermutationMethod):
+        def statistic(x, y, axis):
+            return ansari(x, y, axis=axis, method="asymptotic").statistic
+        alternative = dict(less='greater', greater='less').get(alternative, 'two-sided')
+        res = stats.permutation_test((x, y), statistic, axis=axis,
+                                     **method._asdict(), alternative=alternative)
+        return AnsariResult(AB, res.pvalue)
+
+    mnAB = (n * (N + 1.0) ** 2 / 4.0 / N) if N % 2 else (n * (N + 2.0) / 4.0)
+
+    if is_lazy_array(repeats) or repeats:   # adjust variance estimates
+        # compute np.sum(tj * rj**2,axis=0)
+        fac = xp.sum(symrank**2, axis=-1)
+        if N % 2:  # N odd
+            varAB = m * n * (16*N*fac - (N+1)**4) / (16.0 * N**2 * (N-1))
+        else:  # N even
+            varAB = m * n * (16*fac - N*(N+2)**2) / (16.0 * N * (N-1))
+    else:
+        # otherwise compute normal approximation
+        if N % 2:  # N odd
+            varAB = n * m * (N + 1.0) * (3 + N ** 2) / (48.0 * N ** 2)
+        else:
+            varAB = m * n * (N + 2) * (N - 2.0) / 48 / (N - 1.0)
+        varAB = xp.asarray(varAB, dtype=dtype)
+
+    # Small values of AB indicate larger dispersion for the x sample.
+    # Large values of AB indicate larger dispersion for the y sample.
+    # This is opposite to the way we define the ratio of scales. see [1]_.
+    z = (mnAB - AB) / xp.sqrt(varAB)
+    pvalue = _get_pvalue(z, _SimpleNormal(), alternative, xp=xp)
+    AB = AB[()] if AB.ndim == 0 else AB
+    pvalue = pvalue[()] if pvalue.ndim == 0 else pvalue
+    return AnsariResult(AB, pvalue)
+
+
+BartlettResult = namedtuple('BartlettResult', ('statistic', 'pvalue'))
+
+@xp_capabilities(marray=True)
+@_axis_nan_policy_factory(BartlettResult, n_samples=None)
+def bartlett(*samples, axis=0):
+    r"""Perform Bartlett's test for equal variances.
+
+    Bartlett's test tests the null hypothesis that all input samples
+    are from populations with equal variances.  For samples
+    from significantly non-normal populations, Levene's test
+    `levene` is more robust.
+
+    Parameters
+    ----------
+    *samples : array_like
+        arrays of sample data.  Only 1d arrays are accepted, they may have
+        different lengths.
+
+    Returns
+    -------
+    statistic : float
+        The test statistic.
+    pvalue : float
+        The p-value of the test.
+
+    See Also
+    --------
+    fligner : A non-parametric test for the equality of k variances
+    levene : A robust parametric test for equality of k variances
+    :ref:`hypothesis_bartlett` : Extended example
+
+    Notes
+    -----
+    Conover et al. (1981) examine many of the existing parametric and
+    nonparametric tests by extensive simulations and they conclude that the
+    tests proposed by Fligner and Killeen (1976) and Levene (1960) appear to be
+    superior in terms of robustness of departures from normality and power
+    ([3]_).
+
+    References
+    ----------
+    .. [1]  https://www.itl.nist.gov/div898/handbook/eda/section3/eda357.htm
+    .. [2]  Snedecor, George W. and Cochran, William G. (1989), Statistical
+              Methods, Eighth Edition, Iowa State University Press.
+    .. [3] Park, C. and Lindsay, B. G. (1999). Robust Scale Estimation and
+           Hypothesis Testing based on Quadratic Inference Function. Technical
+           Report #99-03, Center for Likelihood Studies, Pennsylvania State
+           University.
+    .. [4] Bartlett, M. S. (1937). Properties of Sufficiency and Statistical
+           Tests. Proceedings of the Royal Society of London. Series A,
+           Mathematical and Physical Sciences, Vol. 160, No.901, pp. 268-282.
+
+    Examples
+    --------
+
+    Test whether the lists `a`, `b` and `c` come from populations
+    with equal variances.
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> a = [8.88, 9.12, 9.04, 8.98, 9.00, 9.08, 9.01, 8.85, 9.06, 8.99]
+    >>> b = [8.88, 8.95, 9.29, 9.44, 9.15, 9.58, 8.36, 9.18, 8.67, 9.05]
+    >>> c = [8.95, 9.12, 8.95, 8.85, 9.03, 8.84, 9.07, 8.98, 8.86, 8.98]
+    >>> stat, p = stats.bartlett(a, b, c)
+    >>> p
+    1.1254782518834628e-05
+
+    The very small p-value suggests that the populations do not have equal
+    variances.
+
+    This is not surprising, given that the sample variance of `b` is much
+    larger than that of `a` and `c`:
+
+    >>> [np.var(x, ddof=1) for x in [a, b, c]]
+    [0.007054444444444413, 0.13073888888888888, 0.008890000000000002]
+
+    For a more detailed example, see :ref:`hypothesis_bartlett`.
+    """
+    xp = array_namespace(*samples)
+
+    k = len(samples)
+    if k < 2:
+        raise ValueError("Must enter at least two input sample vectors.")
+
+    if axis is None:
+        samples = [xp_ravel(sample) for sample in samples]
+    else:
+        samples = _broadcast_arrays(samples, axis=axis, xp=xp)
+        samples = [xp.moveaxis(sample, axis, -1) for sample in samples]
+
+    Ni = [xp.asarray(_count_nonmasked(sample, axis=-1, xp=xp),
+                     dtype=sample.dtype, device=xp_device(sample))
+          for sample in samples]
+    Ni = [xp.broadcast_to(N, samples[0].shape[:-1]) for N in Ni]
+    ssq = [xp.var(sample, correction=1, axis=-1) for sample in samples]
+    Ni = [arr[xp.newaxis, ...] for arr in Ni]
+    ssq = [arr[xp.newaxis, ...] for arr in ssq]
+    Ni = xp.concat(Ni, axis=0)
+    Ni = xpx.at(Ni)[Ni == 0].set(xp.nan)
+    ssq = xp.concat(ssq, axis=0)
+    dtype = Ni.dtype
+    Ntot = xp.sum(Ni, axis=0)
+    spsq = xp.sum((Ni - 1)*ssq, axis=0, dtype=dtype) / (Ntot - k)
+    numer = ((Ntot - k) * xp.log(spsq)
+             - xp.sum((Ni - 1)*xp.log(ssq), axis=0, dtype=dtype))
+    denom = (1 + 1/(3*(k - 1))
+             * ((xp.sum(1/(Ni - 1), axis=0)) - 1/(Ntot - k)))
+    T = numer / denom
+
+    chi2 = _SimpleChi2(xp.asarray(k-1, dtype=dtype, device=xp_device(T)))
+    pvalue = _get_pvalue(T, chi2, alternative='greater', symmetric=False, xp=xp)
+
+    T = xp.clip(T, min=0., max=xp.inf)
+    T = T[()] if T.ndim == 0 else T
+    pvalue = pvalue[()] if pvalue.ndim == 0 else pvalue
+
+    return BartlettResult(T, pvalue)
+
+
+LeveneResult = namedtuple('LeveneResult', ('statistic', 'pvalue'))
+
+
+@xp_capabilities(cpu_only=True, exceptions=['cupy'], marray=True)
+@_axis_nan_policy_factory(LeveneResult, n_samples=None)
+def levene(*samples, center='median', proportiontocut=0.05, axis=0):
+    r"""Perform Levene test for equal variances.
+
+    The Levene test tests the null hypothesis that all input samples
+    are from populations with equal variances.  Levene's test is an
+    alternative to Bartlett's test `bartlett` in the case where
+    there are significant deviations from normality.
+
+    Parameters
+    ----------
+    *samples : array_like
+        The sample data, possibly with different lengths.
+    center : {'mean', 'median', 'trimmed'}, optional
+        Which statistics to use to center data points within each sample.  Default
+        is 'median'.
+    proportiontocut : float, optional
+        When `center` is 'trimmed', this gives the proportion of data points
+        to cut from each end. (See `scipy.stats.trim_mean`.)
+        Default is 0.05.
+    axis : int or tuple of ints, default: 0
+        If an int or tuple of ints, the axis or axes of the input along which
+        to compute the statistic. The statistic of each axis-slice (e.g. row)
+        of the input will appear in a corresponding element of the output.
+        If ``None``, the input will be raveled before computing the statistic.
+
+    Returns
+    -------
+    statistic : float
+        The test statistic.
+    pvalue : float
+        The p-value for the test.
+
+    See Also
+    --------
+    fligner : A non-parametric test for the equality of k variances
+    bartlett : A parametric test for equality of k variances in normal samples
+    :ref:`hypothesis_levene` : Extended example
+
+    Notes
+    -----
+    Three variations of Levene's test are possible.  The possibilities
+    and their recommended usages are:
+
+    * 'median' : Recommended for skewed (non-normal) distributions>
+    * 'mean' : Recommended for symmetric, moderate-tailed distributions.
+    * 'trimmed' : Recommended for heavy-tailed distributions.
+
+    The test version using the mean was proposed in the original article
+    of Levene ([2]_) while the median and trimmed mean have been studied by
+    Brown and Forsythe ([3]_), sometimes also referred to as Brown-Forsythe
+    test.
+
+    References
+    ----------
+    .. [1] https://www.itl.nist.gov/div898/handbook/eda/section3/eda35a.htm
+    .. [2] Levene, H. (1960). In Contributions to Probability and Statistics:
+           Essays in Honor of Harold Hotelling, I. Olkin et al. eds.,
+           Stanford University Press, pp. 278-292.
+    .. [3] Brown, M. B. and Forsythe, A. B. (1974), Journal of the American
+           Statistical Association, 69, 364-367
+
+    Examples
+    --------
+
+    Test whether the lists `a`, `b` and `c` come from populations
+    with equal variances.
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> a = [8.88, 9.12, 9.04, 8.98, 9.00, 9.08, 9.01, 8.85, 9.06, 8.99]
+    >>> b = [8.88, 8.95, 9.29, 9.44, 9.15, 9.58, 8.36, 9.18, 8.67, 9.05]
+    >>> c = [8.95, 9.12, 8.95, 8.85, 9.03, 8.84, 9.07, 8.98, 8.86, 8.98]
+    >>> stat, p = stats.levene(a, b, c)
+    >>> p
+    0.002431505967249681
+
+    The small p-value suggests that the populations do not have equal
+    variances.
+
+    This is not surprising, given that the sample variance of `b` is much
+    larger than that of `a` and `c`:
+
+    >>> [np.var(x, ddof=1) for x in [a, b, c]]
+    [0.007054444444444413, 0.13073888888888888, 0.008890000000000002]
+
+    For a more detailed example, see :ref:`hypothesis_levene`.
+    """
+    xp = array_namespace(*samples)
+
+    if center not in ['mean', 'median', 'trimmed']:
+        raise ValueError("center must be 'mean', 'median' or 'trimmed'.")
+
+    k = len(samples)
+    if k < 2:
+        raise ValueError("Must provide at least two samples.")
+
+    if center == 'median':
+
+        def func(x):
+            return (xp.median(x, axis=-1, keepdims=True)
+                    if (is_numpy(xp) or is_dask(xp))
+                    else stats.quantile(x, 0.5, axis=-1, keepdims=True))
+
+    elif center == 'mean':
+
+        def func(x):
+            return xp.mean(x, axis=-1, keepdims=True)
+
+    else:  # center == 'trimmed'
+
+        def func(x):
+            # keepdims=True doesn't currently work for Dask
+            return _stats_py.trim_mean(x, proportiontocut, axis=-1)[..., xp.newaxis]
+
+    Nis = [_count_nonmasked(sample, axis=-1, keepdims=True, xp=xp)
+           for sample in samples]
+    Ycis = [func(sample) for sample in samples]
+    Ntot = sum(Nis)
+
+    # compute Zij's
+    Zijs = [xp.abs(sample - Yc) for sample, Yc in zip(samples, Ycis)]
+
+    # compute Zbari
+    Zbaris = [xp.mean(Zij, axis=-1, keepdims=True) for Zij in Zijs]
+    Zbar = sum(Ni*Zbari for Ni, Zbari in zip(Nis, Zbaris)) / Ntot
+
+    # compute numerator and denominator
+    dfd = (Ntot - k)
+    numer = dfd * sum(Ni * (Zbari - Zbar)**2
+                      for Ni, Zbari in zip(Nis, Zbaris))
+    dfn = (k - 1.0)
+    denom = dfn * sum(xp.sum((Zij - Zbari)**2, axis=-1, keepdims=True)
+                      for Zij, Zbari in zip(Zijs, Zbaris))
+
+    W = numer / denom
+    W = xp.squeeze(W, axis=-1)
+    dfd = xp.squeeze(dfd, axis=-1) if is_marray(xp) else dfd
+    dfn, dfd = xp.asarray(dfn, dtype=W.dtype), xp.asarray(dfd, dtype=W.dtype)
+    pval = _get_pvalue(W, _SimpleF(dfn, dfd), 'greater', xp=xp)
+    W = W[()] if W.ndim == 0 else W
+    pval = pval[()] if pval.ndim == 0 else pval
+    return LeveneResult(W, pval)
+
+
+FlignerResult = namedtuple('FlignerResult', ('statistic', 'pvalue'))
+
+
+@xp_capabilities(skip_backends=[('dask.array', 'no rankdata')],
+                 marray=True)
+@_axis_nan_policy_factory(FlignerResult, n_samples=None)
+def fligner(*samples, center='median', proportiontocut=0.05, axis=0):
+    r"""Perform Fligner-Killeen test for equality of variance.
+
+    Fligner's test tests the null hypothesis that all input samples
+    are from populations with equal variances.  Fligner-Killeen's test is
+    distribution free when populations are identical [2]_.
+
+    Parameters
+    ----------
+    *samples : array_like
+        Arrays of sample data.  Need not be the same length.
+    center : {'mean', 'median', 'trimmed'}, optional
+        Which statistics to use to center data points within each sample. Default
+        is 'median'.
+    proportiontocut : float, optional
+        When `center` is 'trimmed', this gives the proportion of data points
+        to cut from each end. (See `scipy.stats.trim_mean`.)
+        Default is 0.05.
+    axis : int or tuple of ints, default: 0
+        If an int or tuple of ints, the axis or axes of the input along which
+        to compute the statistic. The statistic of each axis-slice (e.g. row)
+        of the input will appear in a corresponding element of the output.
+        If ``None``, the input will be raveled before computing the statistic.
+
+    Returns
+    -------
+    statistic : float
+        The test statistic.
+    pvalue : float
+        The p-value for the hypothesis test.
+
+    See Also
+    --------
+    bartlett : A parametric test for equality of k variances in normal samples
+    levene : A robust parametric test for equality of k variances
+    :ref:`hypothesis_fligner` : Extended example
+
+    Notes
+    -----
+    As with Levene's test there are three variants of Fligner's test that
+    differ by the measure of central tendency used in the test.  See `levene`
+    for more information.
+
+    Conover et al. (1981) examine many of the existing parametric and
+    nonparametric tests by extensive simulations and they conclude that the
+    tests proposed by Fligner and Killeen (1976) and Levene (1960) appear to be
+    superior in terms of robustness of departures from normality and power
+    [3]_.
+
+    References
+    ----------
+    .. [1] Qu, A., Lindsay, B. G., and Li, B. (2000). Improving generalized
+           estimating equations using quadratic inference functions.
+           Biometrika, 87(4), 823-836.
+           :doi:`10.1093/biomet/87.4.823`
+    .. [2] Fligner, M.A. and Killeen, T.J. (1976). Distribution-free two-sample
+           tests for scale. Journal of the American Statistical Association.
+           71(353), 210-213.
+    .. [3] Conover, W. J., Johnson, M. E. and Johnson M. M. (1981). A
+           comparative study of tests for homogeneity of variances, with
+           applications to the outer continental shelf bidding data.
+           Technometrics, 23(4), 351-361.
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> from scipy import stats
+
+    Test whether the lists `a`, `b` and `c` come from populations
+    with equal variances.
+
+    >>> a = [8.88, 9.12, 9.04, 8.98, 9.00, 9.08, 9.01, 8.85, 9.06, 8.99]
+    >>> b = [8.88, 8.95, 9.29, 9.44, 9.15, 9.58, 8.36, 9.18, 8.67, 9.05]
+    >>> c = [8.95, 9.12, 8.95, 8.85, 9.03, 8.84, 9.07, 8.98, 8.86, 8.98]
+    >>> stat, p = stats.fligner(a, b, c)
+    >>> p
+    0.00450826080004775
+
+    The small p-value suggests that the populations do not have equal
+    variances.
+
+    This is not surprising, given that the sample variance of `b` is much
+    larger than that of `a` and `c`:
+
+    >>> [np.var(x, ddof=1) for x in [a, b, c]]
+    [0.007054444444444413, 0.13073888888888888, 0.008890000000000002]
+
+    For a more detailed example, see :ref:`hypothesis_fligner`.
+    """
+    xp = array_namespace(*samples)
+
+    if center not in ['mean', 'median', 'trimmed']:
+        raise ValueError("center must be 'mean', 'median' or 'trimmed'.")
+
+    k = len(samples)
+    if k < 2:
+        raise ValueError("Must provide at least two samples.")
+
+    samples = xp_promote(*samples, force_floating=True, xp=xp)
+    dtype = samples[0].dtype
+
+    # Handle empty input
+    for sample in samples:
+        if sample.size == 0:
+            NaN = _get_nan(*samples, xp=xp)
+            return FlignerResult(NaN, NaN)
+
+    if center == 'median':
+
+        def func(x):
+            return (xp.median(x, axis=-1, keepdims=True)
+                    if (is_numpy(xp) or is_dask(xp))
+                    else stats.quantile(x, 0.5, axis=-1, keepdims=True))
+
+    elif center == 'mean':
+
+        def func(x):
+            return xp.mean(x, axis=-1, keepdims=True)
+
+    else:  # center == 'trimmed'
+
+        def func(x):
+            # keepdims=True doesn't currently work for lazy arrays
+            return _stats_py.trim_mean(x, proportiontocut, axis=-1)[..., xp.newaxis]
+
+    lengths = [sample.shape[-1] for sample in samples]
+    ni = [_count_nonmasked(sample, axis=-1, keepdims=True, xp=xp)
+          for sample in samples]
+    N = sum(ni)
+    ni = [xp.squeeze(ni_, axis=-1) for ni_ in ni] if is_marray(xp) else ni
+
+    # Implementation follows [3] pg 355 F-K.
+    Xibar = [func(sample) for sample in samples]
+    Xij_Xibar = [xp.abs(sample - Xibar_) for sample, Xibar_ in zip(samples, Xibar)]
+    Xij_Xibar = xp.concat(Xij_Xibar, axis=-1)
+    ranks = stats.rankdata(Xij_Xibar, method='average', axis=-1)
+    a_Ni = special.ndtri(ranks / (2*(N + 1.0)) + 0.5)
+
+    # [3] Equation 2.1
+    splits = list(itertools.accumulate(lengths, initial=0))
+    Ai = [a_Ni[..., i:j] for i, j in zip(splits[:-1], splits[1:])]
+    Aibar = [xp.mean(Ai_, axis=-1) for Ai_ in Ai]
+    abar = xp.mean(a_Ni, axis=-1)
+    V2 = xp.var(a_Ni, axis=-1, correction=1)
+    statistic = sum(ni_ * (Aibar_ - abar)**2 for ni_, Aibar_ in zip(ni, Aibar)) / V2
+
+    chi2 = _SimpleChi2(xp.asarray(k-1, dtype=dtype))
+    pval = _get_pvalue(statistic, chi2, alternative='greater', symmetric=False, xp=xp)
+    return FlignerResult(statistic, pval)
+
+
+def _mood_statistic_with_ties(x, y, t, m, n, N, xp):
+    # First equation of "Mood's Squared Rank Test", Mielke pg 313
+    E_0_T = m * (N * N - 1) / 12
+
+    # m, n, N, t, and S are defined in the second paragraph of Mielke pg 312
+    # The only difference is that our `t` has zeros interspersed with the relevant
+    # numbers to keep the array rectangular, but these terms add nothing to the sum.
+    S = xp.cumulative_sum(t, include_initial=True, axis=-1)
+    S_i, S_i_m1 = S[..., 1:], S[..., :-1]
+    # Second equation of "Mood's Squared Rank Test", Mielke pg 313
+    varM = (m * n * (N + 1.0) * (N**2 - 4) / 180
+            - m * n / (180 * N * (N - 1))
+            * xp.sum(t * (t ** 2 - 1) * (t ** 2 - 4 + (15 * (N - S_i - S_i_m1) ** 2)),
+                     axis=-1))
+
+    # There is a formula for Phi (`phi` in code) in terms of t, S, and Psi(I) at the
+    # bottom of Mielke pg 312. Psi(I) = [I - (N+1)/2]^2 is defined (with a mistake in
+    # the location of the ^2) at the beginning of "Mood's Squared Rank Test" (pg 313).
+    # To vectorize this calculation, let c = (N + 1) / 2, so Psi(I) = I^2 - 2*c*I + c^2.
+    # We sum each of these three parts of Psi separately using formulas for sums from a
+    # to b (inclusive) of terms I^2, I, and 1 where I takes on successive integers.
+    def sum_I2(a, b=None):
+        return (a * (a + 1) * (2 * a + 1) / 6 if b is None
+                else sum_I2(b) - sum_I2(a) + a**2)
+
+    def sum_I(a, b=None):
+        return (a * (a + 1) / 2 if b is None
+                else sum_I(b) - sum_I(a) + a)
+
+    def sum_1(a, b):
+        return (b - a) + 1
+
+    with np.errstate(invalid='ignore', divide='ignore'):
+        sum_I2 = sum_I2(S_i_m1 + 1, S_i)
+        sum_I = sum_I(S_i_m1 + 1, S_i)
+        sum_1 = sum_1(S_i_m1 + 1, S_i)
+        c = (N + 1) / 2
+        phi = (sum_I2 - 2*c*sum_I + sum_1*c**2) / t
+
+    phi = xpx.at(phi)[t == 0].set(0.)  # where t = 0 we get NaNs; eliminate them
+
+    # Mielke pg 312 defines `a` as the count of elements in sample `x` for each of the
+    # unique values in the combined sample. The tricky thing is getting these to line
+    # up with the locations of nonzero elements in `t`/`phi`.
+    x = xp.sort(x, axis=-1)
+    xy = xp.concat((x, y), axis=-1)
+    i = xp.argsort(xy, stable=True, axis=-1)
+    _, _, a = _stats_py._rankdata(x, method='average', return_ties=True)
+
+    zeros = xp.zeros(a.shape[:-1] + (n,), dtype=a.dtype)
+    a = xp.concat((a, zeros), axis=-1)
+    a = xp.take_along_axis(a, i, axis=-1)
+
+    # Mielke pg 312 defines test statistic `T` as the inner product `a` and `phi`
+    T = xp.vecdot(a, phi, axis=-1)
+
+    return (T - E_0_T) / xp.sqrt(varM)
+
+
+def _mood_statistic_no_ties(r, m, n, N, xp):
+    rx = r[..., :m]
+    M = xp.sum((rx - (N + 1.0) / 2) ** 2, axis=-1)
+    E_0_T = m * (N * N - 1.0) / 12
+    varM = m * n * (N + 1.0) * (N + 2) * (N - 2) / 180
+    return (M - E_0_T) / math.sqrt(varM)
+
+
+def _mood_too_small(samples, kwargs, axis=-1):
+    x, y = samples
+    m = x.shape[axis]
+    n = y.shape[axis]
+    N = m + n
+    return N < 3
+
+
+@xp_capabilities(skip_backends=[('dask.array', 'no rankdata')])
+@_axis_nan_policy_factory(SignificanceResult, n_samples=2, too_small=_mood_too_small)
+def mood(x, y, axis=0, alternative="two-sided"):
+    """Perform Mood's test for equal scale parameters.
+
+    Mood's two-sample test for scale parameters is a non-parametric
+    test for the null hypothesis that two samples are drawn from the
+    same distribution with the same scale parameter.
+
+    Parameters
+    ----------
+    x, y : array_like
+        Arrays of sample data. There must be at least three observations
+        total.
+    axis : int, optional
+        The axis along which the samples are tested.  `x` and `y` can be of
+        different length along `axis`.
+        If `axis` is None, `x` and `y` are flattened and the test is done on
+        all values in the flattened arrays.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis. Default is 'two-sided'.
+        The following options are available:
+
+        * 'two-sided': the scales of the distributions underlying `x` and `y`
+          are different.
+        * 'less': the scale of the distribution underlying `x` is less than
+          the scale of the distribution underlying `y`.
+        * 'greater': the scale of the distribution underlying `x` is greater
+          than the scale of the distribution underlying `y`.
+
+        .. versionadded:: 1.7.0
+
+    Returns
+    -------
+    res : SignificanceResult
+        An object containing attributes:
+
+        statistic : scalar or ndarray
+            The z-score for the hypothesis test.  For 1-D inputs a scalar is
+            returned.
+        pvalue : scalar ndarray
+            The p-value for the hypothesis test.
+
+    See Also
+    --------
+    fligner : A non-parametric test for the equality of k variances
+    ansari : A non-parametric test for the equality of 2 variances
+    bartlett : A parametric test for equality of k variances in normal samples
+    levene : A parametric test for equality of k variances
+
+    Notes
+    -----
+    The data are assumed to be drawn from probability distributions ``f(x)``
+    and ``f(x/s) / s`` respectively, for some probability density function f.
+    The null hypothesis is that ``s == 1``.
+
+    For multi-dimensional arrays, if the inputs are of shapes
+    ``(n0, n1, n2, n3)``  and ``(n0, m1, n2, n3)``, then if ``axis=1``, the
+    resulting z and p values will have shape ``(n0, n2, n3)``.  Note that
+    ``n1`` and ``m1`` don't have to be equal, but the other dimensions do.
+
+    References
+    ----------
+    [1] Mielke, Paul W. "Note on Some Squared Rank Tests with Existing Ties."
+        Technometrics, vol. 9, no. 2, 1967, pp. 312-14. JSTOR,
+        :doi:`10.2307/1266427`. Accessed 18 May 2022.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> rng = np.random.default_rng()
+    >>> x2 = rng.standard_normal((2, 45, 6, 7))
+    >>> x1 = rng.standard_normal((2, 30, 6, 7))
+    >>> res = stats.mood(x1, x2, axis=1)
+    >>> res.pvalue.shape
+    (2, 6, 7)
+
+    Find the number of points where the difference in scale is not significant:
+
+    >>> (res.pvalue > 0.1).sum()
+    78
+
+    Perform the test with different scales:
+
+    >>> x1 = rng.standard_normal((2, 30))
+    >>> x2 = rng.standard_normal((2, 35)) * 10.0
+    >>> stats.mood(x1, x2, axis=1)
+    SignificanceResult(statistic=array([-5.76174136, -6.12650783]),
+                       pvalue=array([8.32505043e-09, 8.98287869e-10]))
+
+    """
+    xp = array_namespace(x, y)
+    x, y = xp_promote(x, y, force_floating=True, xp=xp)
+
+    # _axis_nan_policy decorator ensures axis=-1
+    xy = xp.concat((x, y), axis=-1)
+
+    m = x.shape[-1]
+    n = y.shape[-1]
+    N = m + n
+
+    if m == 0 or n == 0 or N < 3:  # only needed for test_axis_nan_policy
+        NaN = _get_nan(x, y, xp=xp)
+        return SignificanceResult(NaN, NaN)
+
+    # determine if any of the samples contain ties
+    # `a` represents ties within `x`; `t` represents ties within `xy`
+    r, _, t = _stats_py._rankdata(xy, method='average', return_ties=True)
+
+    if is_lazy_array(t) or xp.any(t > 1):
+        z = _mood_statistic_with_ties(x, y, t, m, n, N, xp=xp)
+    else:
+        z = _mood_statistic_no_ties(r, m, n, N, xp=xp)
+
+    pval = _get_pvalue(z, _SimpleNormal(), alternative, xp=xp)
+
+    z = z[()] if z.ndim == 0 else z
+    pval = pval[()] if pval.ndim == 0 else pval
+    return SignificanceResult(z, pval)
+
+
+WilcoxonResult = _make_tuple_bunch('WilcoxonResult', ['statistic', 'pvalue'])
+
+
+def wilcoxon_result_unpacker(res, _):
+    if hasattr(res, 'zstatistic'):
+        return res.statistic, res.pvalue, res.zstatistic
+    else:
+        return res.statistic, res.pvalue
+
+
+def wilcoxon_result_object(statistic, pvalue, zstatistic=None):
+    res = WilcoxonResult(statistic, pvalue)
+    if zstatistic is not None:
+        res.zstatistic = zstatistic
+    return res
+
+
+def wilcoxon_outputs(kwds):
+    method = kwds.get('method', 'auto')
+    if method == 'asymptotic':
+        return 3
+    return 2
+
+
+@xp_capabilities(skip_backends=[("dask.array", "no rankdata")],
+                 cpu_only=True,  # null distribution is CPU only
+                 marray=True,
+                 extra_note=("Only ``method='asymptotic'``/``zero_method='zsplit'`` is "
+                             "compatible with MArray input. "
+                             "``method='auto'`` is incompatible with JAX arrays."))
+@_rename_parameter("mode", "method")
+@_axis_nan_policy_factory(
+    wilcoxon_result_object, paired=True,
+    n_samples=lambda kwds: 2 if kwds.get('y', None) is not None else 1,
+    result_to_tuple=wilcoxon_result_unpacker, n_outputs=wilcoxon_outputs,
+)
+def wilcoxon(x, y=None, zero_method="wilcox", correction=False,
+             alternative="two-sided", method='auto', *, axis=0):
+    """Calculate the Wilcoxon signed-rank test.
+
+    The Wilcoxon signed-rank test tests the null hypothesis that two
+    related paired samples come from the same distribution. In particular,
+    it tests whether the distribution of the differences ``x - y`` is symmetric
+    about zero. It is a non-parametric version of the paired T-test.
+
+    Parameters
+    ----------
+    x : array_like
+        Either the first set of measurements (in which case ``y`` is the second
+        set of measurements), or the differences between two sets of
+        measurements (in which case ``y`` is not to be specified.)  Must be
+        one-dimensional.
+    y : array_like, optional
+        Either the second set of measurements (if ``x`` is the first set of
+        measurements), or not specified (if ``x`` is the differences between
+        two sets of measurements.)  Must be one-dimensional.
+
+        .. warning::
+            When `y` is provided, `wilcoxon` calculates the test statistic
+            based on the ranks of the absolute values of ``d = x - y``.
+            Roundoff error in the subtraction can result in elements of ``d``
+            being assigned different ranks even when they would be tied with
+            exact arithmetic. Rather than passing `x` and `y` separately,
+            consider computing the difference ``x - y``, rounding as needed to
+            ensure that only truly unique elements are numerically distinct,
+            and passing the result as `x`, leaving `y` at the default (None).
+
+    zero_method : {"wilcox", "pratt", "zsplit"}, optional
+        There are different conventions for handling pairs of observations
+        with equal values ("zero-differences", or "zeros").
+
+        * "wilcox": Discards all zero-differences (default); see [4]_.
+        * "pratt": Includes zero-differences in the ranking process,
+          but drops the ranks of the zeros (more conservative); see [3]_.
+          In this case, the normal approximation is adjusted as in [5]_.
+        * "zsplit": Includes zero-differences in the ranking process and
+          splits the zero rank between positive and negative ones.
+
+    correction : bool, optional
+        If True, apply continuity correction by adjusting the Wilcoxon rank
+        statistic by 0.5 towards the mean value when computing the
+        z-statistic if a normal approximation is used.  Default is False.
+    alternative : {"two-sided", "greater", "less"}, optional
+        Defines the alternative hypothesis. Default is 'two-sided'.
+        In the following, let ``d`` represent the difference between the paired
+        samples: ``d = x - y`` if both ``x`` and ``y`` are provided, or
+        ``d = x`` otherwise.
+
+        * 'two-sided': the distribution underlying ``d`` is not symmetric
+          about zero.
+        * 'less': the distribution underlying ``d`` is stochastically less
+          than a distribution symmetric about zero.
+        * 'greater': the distribution underlying ``d`` is stochastically
+          greater than a distribution symmetric about zero.
+
+    method : {"auto", "exact", "asymptotic"} or `PermutationMethod` instance, optional
+        Method to calculate the p-value, see Notes. Default is "auto".
+
+    axis : int or None, default: 0
+        If an int, the axis of the input along which to compute the statistic.
+        The statistic of each axis-slice (e.g. row) of the input will appear
+        in a corresponding element of the output. If ``None``, the input will
+        be raveled before computing the statistic.
+
+    Returns
+    -------
+    result : WilcoxonResult
+        An object with the following attributes.
+
+        statistic : array_like
+            If `alternative` is "two-sided", the sum of the ranks of the
+            differences above or below zero, whichever is smaller.
+            Otherwise the sum of the ranks of the differences above zero.
+        pvalue : array_like
+            The p-value for the test depending on `alternative` and `method`.
+        zstatistic : array_like
+            When ``method = 'asymptotic'``, this is the normalized z-statistic::
+
+                z = (T - mn - d) / se
+
+            where ``T`` is `statistic` as defined above, ``mn`` is the mean of the
+            distribution under the null hypothesis, ``d`` is a continuity
+            correction, and ``se`` is the standard error.
+            When ``method != 'asymptotic'``, this attribute is not available.
+
+    See Also
+    --------
+    kruskal, mannwhitneyu
+
+    Notes
+    -----
+    In the following, let ``d`` represent the difference between the paired
+    samples: ``d = x - y`` if both ``x`` and ``y`` are provided, or ``d = x``
+    otherwise. Assume that all elements of ``d`` are independent and
+    identically distributed observations, and all are distinct and nonzero.
+
+    - When ``len(d)`` is sufficiently large, the null distribution of the
+      normalized test statistic (`zstatistic` above) is approximately normal,
+      and ``method = 'asymptotic'`` can be used to compute the p-value.
+    - When ``len(d)`` is small, the normal approximation may not be accurate,
+      and ``method='exact'`` is preferred (at the cost of additional
+      execution time).
+    - The default, ``method='auto'``, selects between the two:
+      ``method='exact'`` is used when ``len(d) <= 50``, and
+      ``method='asymptotic'`` is used otherwise.
+
+    The presence of "ties" (i.e. not all elements of ``d`` are unique) or
+    "zeros" (i.e. elements of ``d`` are zero) changes the null distribution
+    of the test statistic, and ``method='exact'`` no longer calculates
+    the exact p-value. If ``method='asymptotic'``, the z-statistic is adjusted
+    for more accurate comparison against the standard normal, but still,
+    for finite sample sizes, the standard normal is only an approximation of
+    the true null distribution of the z-statistic. For such situations, the
+    `method` parameter also accepts instances of `PermutationMethod`. In this
+    case, the p-value is computed using `permutation_test` with the provided
+    configuration options and other appropriate settings.
+
+    The presence of ties and zeros affects the resolution of ``method='auto'``
+    accordingly: exhasutive permutations are performed when ``len(d) <= 13``,
+    and the asymptotic method is used otherwise. Note that they asymptotic
+    method may not be very accurate even for ``len(d) > 14``; the threshold
+    was chosen as a compromise between execution time and accuracy under the
+    constraint that the results must be deterministic. Consider providing an
+    instance of `PermutationMethod` method manually, choosing the
+    ``n_resamples`` parameter to balance time constraints and accuracy
+    requirements.
+
+    Please also note that in the edge case that all elements of ``d`` are zero,
+    the p-value relying on the normal approximaton cannot be computed (NaN)
+    if ``zero_method='wilcox'`` or ``zero_method='pratt'``.
+
+    References
+    ----------
+    .. [1] https://en.wikipedia.org/wiki/Wilcoxon_signed-rank_test
+    .. [2] Conover, W.J., Practical Nonparametric Statistics, 1971.
+    .. [3] Pratt, J.W., Remarks on Zeros and Ties in the Wilcoxon Signed
+       Rank Procedures, Journal of the American Statistical Association,
+       Vol. 54, 1959, pp. 655-667. :doi:`10.1080/01621459.1959.10501526`
+    .. [4] Wilcoxon, F., Individual Comparisons by Ranking Methods,
+       Biometrics Bulletin, Vol. 1, 1945, pp. 80-83. :doi:`10.2307/3001968`
+    .. [5] Cureton, E.E., The Normal Approximation to the Signed-Rank
+       Sampling Distribution When Zero Differences are Present,
+       Journal of the American Statistical Association, Vol. 62, 1967,
+       pp. 1068-1069. :doi:`10.1080/01621459.1967.10500917`
+
+    Examples
+    --------
+    In [4]_, the differences in height between cross- and self-fertilized
+    corn plants is given as follows:
+
+    >>> d = [6, 8, 14, 16, 23, 24, 28, 29, 41, -48, 49, 56, 60, -67, 75]
+
+    Cross-fertilized plants appear to be higher. To test the null
+    hypothesis that there is no height difference, we can apply the
+    two-sided test:
+
+    >>> from scipy.stats import wilcoxon
+    >>> res = wilcoxon(d)
+    >>> res.statistic, res.pvalue
+    (24.0, 0.041259765625)
+
+    Hence, we would reject the null hypothesis at a confidence level of 5%,
+    concluding that there is a difference in height between the groups.
+    To confirm that the median of the differences can be assumed to be
+    positive, we use:
+
+    >>> res = wilcoxon(d, alternative='greater')
+    >>> res.statistic, res.pvalue
+    (96.0, 0.0206298828125)
+
+    This shows that the null hypothesis that the median is negative can be
+    rejected at a confidence level of 5% in favor of the alternative that
+    the median is greater than zero. The p-values above are exact. Using the
+    normal approximation gives very similar values:
+
+    >>> res = wilcoxon(d, method='asymptotic')
+    >>> res.statistic, res.pvalue
+    (24.0, 0.04088813291185591)
+
+    Note that the statistic changed to 96 in the one-sided case (the sum
+    of ranks of positive differences) whereas it is 24 in the two-sided
+    case (the minimum of sum of ranks above and below zero).
+
+    In the example above, the differences in height between paired plants are
+    provided to `wilcoxon` directly. Alternatively, `wilcoxon` accepts two
+    samples of equal length, calculates the differences between paired
+    elements, then performs the test. Consider the samples ``x`` and ``y``:
+
+    >>> import numpy as np
+    >>> x = np.array([0.5, 0.825, 0.375, 0.5])
+    >>> y = np.array([0.525, 0.775, 0.325, 0.55])
+    >>> res = wilcoxon(x, y, alternative='greater')
+    >>> res
+    WilcoxonResult(statistic=5.0, pvalue=0.5625)
+
+    Note that had we calculated the differences by hand, the test would have
+    produced different results:
+
+    >>> d = [-0.025, 0.05, 0.05, -0.05]
+    >>> ref = wilcoxon(d, alternative='greater')
+    >>> ref
+    WilcoxonResult(statistic=6.0, pvalue=0.5)
+
+    The substantial difference is due to roundoff error in the results of
+    ``x-y``:
+
+    >>> d - (x-y)
+    array([2.08166817e-17, 6.93889390e-17, 1.38777878e-17, 4.16333634e-17])
+
+    Even though we expected all the elements of ``(x-y)[1:]`` to have the same
+    magnitude ``0.05``, they have slightly different magnitudes in practice,
+    and therefore are assigned different ranks in the test. Before performing
+    the test, consider calculating ``d`` and adjusting it as necessary to
+    ensure that theoretically identically values are not numerically distinct.
+    For example:
+
+    >>> d2 = np.around(x - y, decimals=3)
+    >>> wilcoxon(d2, alternative='greater')
+    WilcoxonResult(statistic=6.0, pvalue=0.5)
+
+    """
+    # replace approx by asymptotic to ensure backwards compatability
+    if method == "approx":
+        method = "asymptotic"
+    return _wilcoxon._wilcoxon_nd(x, y, zero_method, correction, alternative,
+                                  method, axis)
+
+
+MedianTestResult = _make_tuple_bunch(
+    'MedianTestResult',
+    ['statistic', 'pvalue', 'median', 'table'], []
+)
+
+
+@xp_capabilities(np_only=True)
+def median_test(*samples, ties='below', correction=True, lambda_=1,
+                nan_policy='propagate'):
+    """Perform a Mood's median test.
+
+    Test that two or more samples come from populations with the same median.
+
+    Let ``n = len(samples)`` be the number of samples.  The "grand median" of
+    all the data is computed, and a contingency table is formed by
+    classifying the values in each sample as being above or below the grand
+    median.  The contingency table, along with `correction` and `lambda_`,
+    are passed to `scipy.stats.chi2_contingency` to compute the test statistic
+    and p-value.
+
+    Parameters
+    ----------
+    *samples : array_like
+        The set of samples.  There must be at least two samples.
+        Each sample must be a one-dimensional sequence containing at least
+        one value.  The samples are not required to have the same length.
+    ties : str, optional
+        Determines how values equal to the grand median are classified in
+        the contingency table.  The string must be one of::
+
+            "below":
+                Values equal to the grand median are counted as "below".
+            "above":
+                Values equal to the grand median are counted as "above".
+            "ignore":
+                Values equal to the grand median are not counted.
+
+        The default is "below".
+    correction : bool, optional
+        If True, *and* there are just two samples, apply Yates' correction
+        for continuity when computing the test statistic associated with
+        the contingency table.  Default is True.
+    lambda_ : float or str, optional
+        By default, the statistic computed in this test is Pearson's
+        chi-squared statistic.  `lambda_` allows a statistic from the
+        Cressie-Read power divergence family to be used instead.  See
+        `power_divergence` for details.
+        Default is 1 (Pearson's chi-squared statistic).
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains nan. 'propagate' returns nan,
+        'raise' throws an error, 'omit' performs the calculations ignoring nan
+        values. Default is 'propagate'.
+
+    Returns
+    -------
+    res : MedianTestResult
+        An object containing attributes:
+
+        statistic : float
+            The test statistic.  The statistic that is returned is determined
+            by `lambda_`.  The default is Pearson's chi-squared statistic.
+        pvalue : float
+            The p-value of the test.
+        median : float
+            The grand median.
+        table : ndarray
+            The contingency table.  The shape of the table is (2, n), where
+            n is the number of samples.  The first row holds the counts of the
+            values above the grand median, and the second row holds the counts
+            of the values below the grand median.  The table allows further
+            analysis with, for example, `scipy.stats.chi2_contingency`, or with
+            `scipy.stats.fisher_exact` if there are two samples, without having
+            to recompute the table.  If ``nan_policy`` is "propagate" and there
+            are nans in the input, the return value for ``table`` is ``None``.
+
+    See Also
+    --------
+    kruskal : Compute the Kruskal-Wallis H-test for independent samples.
+    mannwhitneyu : Computes the Mann-Whitney rank test on samples x and y.
+
+    Notes
+    -----
+    .. versionadded:: 0.15.0
+
+    References
+    ----------
+    .. [1] Mood, A. M., Introduction to the Theory of Statistics. McGraw-Hill
+        (1950), pp. 394-399.
+    .. [2] Zar, J. H., Biostatistical Analysis, 5th ed. Prentice Hall (2010).
+        See Sections 8.12 and 10.15.
+
+    Examples
+    --------
+    A biologist runs an experiment in which there are three groups of plants.
+    Group 1 has 16 plants, group 2 has 15 plants, and group 3 has 17 plants.
+    Each plant produces a number of seeds.  The seed counts for each group
+    are::
+
+        Group 1: 10 14 14 18 20 22 24 25 31 31 32 39 43 43 48 49
+        Group 2: 28 30 31 33 34 35 36 40 44 55 57 61 91 92 99
+        Group 3:  0  3  9 22 23 25 25 33 34 34 40 45 46 48 62 67 84
+
+    The following code applies Mood's median test to these samples.
+
+    >>> g1 = [10, 14, 14, 18, 20, 22, 24, 25, 31, 31, 32, 39, 43, 43, 48, 49]
+    >>> g2 = [28, 30, 31, 33, 34, 35, 36, 40, 44, 55, 57, 61, 91, 92, 99]
+    >>> g3 = [0, 3, 9, 22, 23, 25, 25, 33, 34, 34, 40, 45, 46, 48, 62, 67, 84]
+    >>> from scipy.stats import median_test
+    >>> res = median_test(g1, g2, g3)
+
+    The median is
+
+    >>> res.median
+    34.0
+
+    and the contingency table is
+
+    >>> res.table
+    array([[ 5, 10,  7],
+           [11,  5, 10]])
+
+    `p` is too large to conclude that the medians are not the same:
+
+    >>> res.pvalue
+    0.12609082774093244
+
+    The "G-test" can be performed by passing ``lambda_="log-likelihood"`` to
+    `median_test`.
+
+    >>> res = median_test(g1, g2, g3, lambda_="log-likelihood")
+    >>> res.pvalue
+    0.12224779737117837
+
+    The median occurs several times in the data, so we'll get a different
+    result if, for example, ``ties="above"`` is used:
+
+    >>> res = median_test(g1, g2, g3, ties="above")
+    >>> res.pvalue
+    0.063873276069553273
+
+    >>> res.table
+    array([[ 5, 11,  9],
+           [11,  4,  8]])
+
+    This example demonstrates that if the data set is not large and there
+    are values equal to the median, the p-value can be sensitive to the
+    choice of `ties`.
+
+    """
+    if len(samples) < 2:
+        raise ValueError('median_test requires two or more samples.')
+
+    ties_options = ['below', 'above', 'ignore']
+    if ties not in ties_options:
+        raise ValueError(f"invalid 'ties' option '{ties}'; 'ties' must be one "
+                         f"of: {str(ties_options)[1:-1]}")
+
+    data = [np.asarray(sample) for sample in samples]
+
+    # Validate the sizes and shapes of the arguments.
+    for k, d in enumerate(data):
+        if d.size == 0:
+            raise ValueError(f"Sample {k + 1} is empty. All samples must "
+                             f"contain at least one value.")
+        if d.ndim != 1:
+            raise ValueError(f"Sample {k + 1} has {d.ndim} dimensions. "
+                             f"All samples must be one-dimensional sequences.")
+
+    cdata = np.concatenate(data)
+    contains_nan = _contains_nan(cdata, nan_policy)
+    if nan_policy == 'propagate' and contains_nan:
+        return MedianTestResult(np.nan, np.nan, np.nan, None)
+
+    if contains_nan:
+        grand_median = np.median(cdata[~np.isnan(cdata)])
+    else:
+        grand_median = np.median(cdata)
+    # When the minimum version of numpy supported by scipy is 1.9.0,
+    # the above if/else statement can be replaced by the single line:
+    #     grand_median = np.nanmedian(cdata)
+
+    # Create the contingency table.
+    table = np.zeros((2, len(data)), dtype=np.int64)
+    for k, sample in enumerate(data):
+        sample = sample[~np.isnan(sample)]
+
+        nabove = count_nonzero(sample > grand_median)
+        nbelow = count_nonzero(sample < grand_median)
+        nequal = sample.size - (nabove + nbelow)
+        table[0, k] += nabove
+        table[1, k] += nbelow
+        if ties == "below":
+            table[1, k] += nequal
+        elif ties == "above":
+            table[0, k] += nequal
+
+    # Check that no row or column of the table is all zero.
+    # Such a table can not be given to chi2_contingency, because it would have
+    # a zero in the table of expected frequencies.
+    rowsums = table.sum(axis=1)
+    if rowsums[0] == 0:
+        raise ValueError(f"All values are below the grand median ({grand_median}).")
+    if rowsums[1] == 0:
+        raise ValueError(f"All values are above the grand median ({grand_median}).")
+    if ties == "ignore":
+        # We already checked that each sample has at least one value, but it
+        # is possible that all those values equal the grand median.  If `ties`
+        # is "ignore", that would result in a column of zeros in `table`.  We
+        # check for that case here.
+        zero_cols = np.nonzero((table == 0).all(axis=0))[0]
+        if len(zero_cols) > 0:
+            raise ValueError(
+                f"All values in sample {zero_cols[0] + 1} are equal to the grand "
+                f"median ({grand_median!r}), so they are ignored, resulting in an "
+                f"empty sample."
+            )
+
+    stat, p, dof, expected = chi2_contingency(table, lambda_=lambda_,
+                                              correction=correction)
+    return MedianTestResult(stat, p, grand_median, table)
+
+
+def _circfuncs_common(samples, period, xp=None):
+    xp = array_namespace(samples) if xp is None else xp
+
+    samples = xp_promote(samples, force_floating=True, xp=xp)
+
+    # Recast samples as radians that range between 0 and 2 pi and calculate
+    # the sine and cosine
+    scaled_samples = samples * ((2.0 * pi) / period)
+    sin_samp = xp.sin(scaled_samples)
+    cos_samp = xp.cos(scaled_samples)
+
+    return samples, sin_samp, cos_samp
+
+
+@xp_capabilities(marray=True)
+@_axis_nan_policy_factory(
+    lambda x: x, n_outputs=1, default_axis=None,
+    result_to_tuple=lambda x, _: (x,)
+)
+def circmean(samples, high=2*pi, low=0, axis=None, nan_policy='propagate'):
+    r"""Compute the circular mean of a sample of angle observations.
+
+    Given :math:`n` angle observations :math:`x_1, \cdots, x_n` measured in
+    radians, their *circular mean* is defined by ([1]_, Eq. 2.2.4)
+
+    .. math::
+
+       \mathrm{Arg} \left( \frac{1}{n} \sum_{k=1}^n e^{i x_k} \right)
+
+    where :math:`i` is the imaginary unit and :math:`\mathop{\mathrm{Arg}} z`
+    gives the principal value of the argument of complex number :math:`z`,
+    restricted to the range :math:`[0,2\pi]` by default.  :math:`z` in the
+    above expression is known as the `mean resultant vector`.
+
+    Parameters
+    ----------
+    samples : array_like
+        Input array of angle observations.  The value of a full angle is
+        equal to ``(high - low)``.
+    high : float, optional
+        Upper boundary of the principal value of an angle.  Default is ``2*pi``.
+    low : float, optional
+        Lower boundary of the principal value of an angle.  Default is ``0``.
+
+    Returns
+    -------
+    circmean : float
+        Circular mean, restricted to the range ``[low, high]``.
+
+        If the mean resultant vector is zero, an input-dependent,
+        implementation-defined number between ``[low, high]`` is returned.
+        If the input array is empty, ``np.nan`` is returned.
+
+    See Also
+    --------
+    circstd : Circular standard deviation.
+    circvar : Circular variance.
+
+    References
+    ----------
+    .. [1] Mardia, K. V. and Jupp, P. E. *Directional Statistics*.
+           John Wiley & Sons, 1999.
+
+    Examples
+    --------
+    For readability, all angles are printed out in degrees.
+
+    >>> import numpy as np
+    >>> from scipy.stats import circmean
+    >>> import matplotlib.pyplot as plt
+    >>> angles = np.deg2rad(np.array([20, 30, 330]))
+    >>> circmean = circmean(angles)
+    >>> np.rad2deg(circmean)
+    7.294976657784009
+
+    >>> mean = angles.mean()
+    >>> np.rad2deg(mean)
+    126.66666666666666
+
+    Plot and compare the circular mean against the arithmetic mean.
+
+    >>> plt.plot(np.cos(np.linspace(0, 2*np.pi, 500)),
+    ...          np.sin(np.linspace(0, 2*np.pi, 500)),
+    ...          c='k')
+    >>> plt.scatter(np.cos(angles), np.sin(angles), c='k')
+    >>> plt.scatter(np.cos(circmean), np.sin(circmean), c='b',
+    ...             label='circmean')
+    >>> plt.scatter(np.cos(mean), np.sin(mean), c='r', label='mean')
+    >>> plt.legend()
+    >>> plt.axis('equal')
+    >>> plt.show()
+
+    """
+    xp = array_namespace(samples)
+    # Needed for non-NumPy arrays to get appropriate NaN result
+    # Apparently atan2(0, 0) is 0, even though it is mathematically undefined
+    if xp_size(samples) == 0:
+        return xp.mean(samples, axis=axis)
+    period = high - low
+    samples, sin_samp, cos_samp = _circfuncs_common(samples, period, xp=xp)
+    sin_sum = xp.sum(sin_samp, axis=axis)
+    cos_sum = xp.sum(cos_samp, axis=axis)
+    res = xp.atan2(sin_sum, cos_sum)
+
+    res = res[()] if res.ndim == 0 else res
+    return (res * (period / (2.0 * pi)) - low) % period + low
+
+
+@xp_capabilities(marray=True)
+@_axis_nan_policy_factory(
+    lambda x: x, n_outputs=1, default_axis=None,
+    result_to_tuple=lambda x, _: (x,)
+)
+def circvar(samples, high=2*pi, low=0, axis=None, nan_policy='propagate'):
+    r"""Compute the circular variance of a sample of angle observations.
+
+    Given :math:`n` angle observations :math:`x_1, \cdots, x_n` measured in
+    radians, their *circular variance* is defined by ([2]_, Eq. 2.3.3)
+
+    .. math::
+
+       1 - \left| \frac{1}{n} \sum_{k=1}^n e^{i x_k} \right|
+
+    where :math:`i` is the imaginary unit and :math:`|z|` gives the length
+    of the complex number :math:`z`.  :math:`|z|` in the above expression
+    is known as the `mean resultant length`.
+
+    Parameters
+    ----------
+    samples : array_like
+        Input array of angle observations.  The value of a full angle is
+        equal to ``(high - low)``.
+    high : float, optional
+        Upper boundary of the principal value of an angle.  Default is ``2*pi``.
+    low : float, optional
+        Lower boundary of the principal value of an angle.  Default is ``0``.
+
+    Returns
+    -------
+    circvar : float
+        Circular variance.  The returned value is in the range ``[0, 1]``,
+        where ``0`` indicates no variance and ``1`` indicates large variance.
+
+        If the input array is empty, ``np.nan`` is returned.
+
+    See Also
+    --------
+    circmean : Circular mean.
+    circstd : Circular standard deviation.
+
+    Notes
+    -----
+    In the limit of small angles, the circular variance is close to
+    half the 'linear' variance if measured in radians.
+
+    References
+    ----------
+    .. [1] Fisher, N.I. *Statistical analysis of circular data*. Cambridge
+           University Press, 1993.
+    .. [2] Mardia, K. V. and Jupp, P. E. *Directional Statistics*.
+           John Wiley & Sons, 1999.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import circvar
+    >>> import matplotlib.pyplot as plt
+    >>> samples_1 = np.array([0.072, -0.158, 0.077, 0.108, 0.286,
+    ...                       0.133, -0.473, -0.001, -0.348, 0.131])
+    >>> samples_2 = np.array([0.111, -0.879, 0.078, 0.733, 0.421,
+    ...                       0.104, -0.136, -0.867,  0.012,  0.105])
+    >>> circvar_1 = circvar(samples_1)
+    >>> circvar_2 = circvar(samples_2)
+
+    Plot the samples.
+
+    >>> fig, (left, right) = plt.subplots(ncols=2)
+    >>> for image in (left, right):
+    ...     image.plot(np.cos(np.linspace(0, 2*np.pi, 500)),
+    ...                np.sin(np.linspace(0, 2*np.pi, 500)),
+    ...                c='k')
+    ...     image.axis('equal')
+    ...     image.axis('off')
+    >>> left.scatter(np.cos(samples_1), np.sin(samples_1), c='k', s=15)
+    >>> left.set_title(f"circular variance: {np.round(circvar_1, 2)!r}")
+    >>> right.scatter(np.cos(samples_2), np.sin(samples_2), c='k', s=15)
+    >>> right.set_title(f"circular variance: {np.round(circvar_2, 2)!r}")
+    >>> plt.show()
+
+    """
+    xp = array_namespace(samples)
+    period = high - low
+    samples, sin_samp, cos_samp = _circfuncs_common(samples, period, xp=xp)
+    sin_mean = xp.mean(sin_samp, axis=axis)
+    cos_mean = xp.mean(cos_samp, axis=axis)
+    hypotenuse = (sin_mean**2. + cos_mean**2.)**0.5
+    # hypotenuse can go slightly above 1 due to rounding errors
+    R = xp.clip(hypotenuse, max=1.)
+
+    res = 1. - R
+    return res
+
+
+@xp_capabilities(marray=True)
+@_axis_nan_policy_factory(
+    lambda x: x, n_outputs=1, default_axis=None,
+    result_to_tuple=lambda x, _: (x,)
+)
+def circstd(samples, high=2*pi, low=0, axis=None, nan_policy='propagate', *,
+            normalize=False):
+    r"""
+    Compute the circular standard deviation of a sample of angle observations.
+
+    Given :math:`n` angle observations :math:`x_1, \cdots, x_n` measured in
+    radians, their `circular standard deviation` is defined by
+    ([2]_, Eq. 2.3.11)
+
+    .. math::
+
+       \sqrt{ -2 \log \left| \frac{1}{n} \sum_{k=1}^n e^{i x_k} \right| }
+
+    where :math:`i` is the imaginary unit and :math:`|z|` gives the length
+    of the complex number :math:`z`.  :math:`|z|` in the above expression
+    is known as the `mean resultant length`.
+
+    Parameters
+    ----------
+    samples : array_like
+        Input array of angle observations.  The value of a full angle is
+        equal to ``(high - low)``.
+    high : float, optional
+        Upper boundary of the principal value of an angle.  Default is ``2*pi``.
+    low : float, optional
+        Lower boundary of the principal value of an angle.  Default is ``0``.
+    axis : int or None, default: None
+        If an int, the axis of the input along which to compute the statistic.
+        The statistic of each axis-slice (e.g. row) of the input will appear in a
+        corresponding element of the output.
+        If ``None``, the input will be raveled before computing the statistic.
+    nan_policy : {'propagate', 'omit', 'raise'}
+        Defines how to handle input NaNs.
+
+        - ``propagate``: if a NaN is present in the axis slice (e.g. row) along
+        which the  statistic is computed, the corresponding entry of the output
+        will be NaN.
+        - ``omit``: NaNs will be omitted when performing the calculation.
+        If insufficient data remains in the axis slice along which the
+        statistic is computed, the corresponding entry of the output will be
+        NaN.
+        - ``raise``: if a NaN is present, a ``ValueError`` will be raised.
+
+    normalize : bool, optional
+        If ``False`` (the default), the return value is computed from the
+        above formula with the input scaled by ``(2*pi)/(high-low)`` and
+        the output scaled (back) by ``(high-low)/(2*pi)``.  If ``True``,
+        the output is not scaled and is returned directly.
+
+    Returns
+    -------
+    circstd : float
+        Circular standard deviation, optionally normalized.
+
+        If the input array is empty, ``np.nan`` is returned.
+
+    See Also
+    --------
+    circmean : Circular mean.
+    circvar : Circular variance.
+
+    Notes
+    -----
+    In the limit of small angles, the circular standard deviation is close
+    to the 'linear' standard deviation if ``normalize`` is ``False``.
+
+    References
+    ----------
+    .. [1] Mardia, K. V. (1972). 2. In *Statistics of Directional Data*
+       (pp. 18-24). Academic Press. :doi:`10.1016/C2013-0-07425-7`.
+    .. [2] Mardia, K. V. and Jupp, P. E. *Directional Statistics*.
+           John Wiley & Sons, 1999.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import circstd
+    >>> import matplotlib.pyplot as plt
+    >>> samples_1 = np.array([0.072, -0.158, 0.077, 0.108, 0.286,
+    ...                       0.133, -0.473, -0.001, -0.348, 0.131])
+    >>> samples_2 = np.array([0.111, -0.879, 0.078, 0.733, 0.421,
+    ...                       0.104, -0.136, -0.867,  0.012,  0.105])
+    >>> circstd_1 = circstd(samples_1)
+    >>> circstd_2 = circstd(samples_2)
+
+    Plot the samples.
+
+    >>> fig, (left, right) = plt.subplots(ncols=2)
+    >>> for image in (left, right):
+    ...     image.plot(np.cos(np.linspace(0, 2*np.pi, 500)),
+    ...                np.sin(np.linspace(0, 2*np.pi, 500)),
+    ...                c='k')
+    ...     image.axis('equal')
+    ...     image.axis('off')
+    >>> left.scatter(np.cos(samples_1), np.sin(samples_1), c='k', s=15)
+    >>> left.set_title(f"circular std: {np.round(circstd_1, 2)!r}")
+    >>> right.plot(np.cos(np.linspace(0, 2*np.pi, 500)),
+    ...            np.sin(np.linspace(0, 2*np.pi, 500)),
+    ...            c='k')
+    >>> right.scatter(np.cos(samples_2), np.sin(samples_2), c='k', s=15)
+    >>> right.set_title(f"circular std: {np.round(circstd_2, 2)!r}")
+    >>> plt.show()
+
+    """
+    xp = array_namespace(samples)
+    period = high - low
+    samples, sin_samp, cos_samp = _circfuncs_common(samples, period, xp=xp)
+    sin_mean = xp.mean(sin_samp, axis=axis)  # [1] (2.2.3)
+    cos_mean = xp.mean(cos_samp, axis=axis)  # [1] (2.2.3)
+    hypotenuse = (sin_mean**2. + cos_mean**2.)**0.5
+    # hypotenuse can go slightly above 1 due to rounding errors
+    R = xp.clip(hypotenuse, max=1.)  # [1] (2.2.4)
+
+    res = (-2*xp.log(R))**0.5+0.0  # torch.pow returns -0.0 if R==1
+    if not normalize:
+        res *= (high-low)/(2.*pi)  # [1] (2.3.14) w/ (2.3.7)
+    return res
+
+
+class DirectionalStats:
+    def __init__(self, mean_direction, mean_resultant_length):
+        self.mean_direction = mean_direction
+        self.mean_resultant_length = mean_resultant_length
+
+    def __repr__(self):
+        return (f"DirectionalStats(mean_direction={self.mean_direction},"
+                f" mean_resultant_length={self.mean_resultant_length})")
+
+
+@xp_capabilities(marray=True)
+def directional_stats(samples, *, axis=0, normalize=True):
+    """
+    Computes sample statistics for directional data.
+
+    Computes the directional mean (also called the mean direction vector) and
+    mean resultant length of a sample of vectors.
+
+    The directional mean is a measure of "preferred direction" of vector data.
+    It is analogous to the sample mean, but it is for use when the length of
+    the data is irrelevant (e.g. unit vectors).
+
+    The mean resultant length is a value between 0 and 1 used to quantify the
+    dispersion of directional data: the smaller the mean resultant length, the
+    greater the dispersion. Several definitions of directional variance
+    involving the mean resultant length are given in [1]_ and [2]_.
+
+    Parameters
+    ----------
+    samples : array_like
+        Input array. Must be at least two-dimensional, and the last axis of the
+        input must correspond with the dimensionality of the vector space.
+        When the input is exactly two dimensional, this means that each row
+        of the data is a vector observation.
+    axis : int, default: 0
+        Axis along which the directional mean is computed.
+    normalize : bool, default: True
+        If True, normalize the input to ensure that each observation is a
+        unit vector. It the observations are already unit vectors, consider
+        setting this to False to avoid unnecessary computation.
+
+    Returns
+    -------
+    res : DirectionalStats
+        An object containing attributes:
+
+        mean_direction : ndarray
+            Directional mean.
+        mean_resultant_length : ndarray
+            The mean resultant length [1]_.
+
+    See Also
+    --------
+    circmean: circular mean; i.e. directional mean for 2D *angles*
+    circvar: circular variance; i.e. directional variance for 2D *angles*
+
+    Notes
+    -----
+    This uses a definition of directional mean from [1]_.
+    Assuming the observations are unit vectors, the calculation is as follows.
+
+    .. code-block:: python
+
+        mean = samples.mean(axis=0)
+        mean_resultant_length = np.linalg.norm(mean)
+        mean_direction = mean / mean_resultant_length
+
+    This definition is appropriate for *directional* data (i.e. vector data
+    for which the magnitude of each observation is irrelevant) but not
+    for *axial* data (i.e. vector data for which the magnitude and *sign* of
+    each observation is irrelevant).
+
+    Several definitions of directional variance involving the mean resultant
+    length ``R`` have been proposed, including ``1 - R`` [1]_, ``1 - R**2``
+    [2]_, and ``2 * (1 - R)`` [2]_. Rather than choosing one, this function
+    returns ``R`` as attribute `mean_resultant_length` so the user can compute
+    their preferred measure of dispersion.
+
+    References
+    ----------
+    .. [1] Mardia, Jupp. (2000). *Directional Statistics*
+       (p. 163). Wiley.
+
+    .. [2] https://en.wikipedia.org/wiki/Directional_statistics
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import directional_stats
+    >>> data = np.array([[3, 4],    # first observation, 2D vector space
+    ...                  [6, -8]])  # second observation
+    >>> dirstats = directional_stats(data)
+    >>> dirstats.mean_direction
+    array([1., 0.])
+
+    In contrast, the regular sample mean of the vectors would be influenced
+    by the magnitude of each observation. Furthermore, the result would not be
+    a unit vector.
+
+    >>> data.mean(axis=0)
+    array([4.5, -2.])
+
+    An exemplary use case for `directional_stats` is to find a *meaningful*
+    center for a set of observations on a sphere, e.g. geographical locations.
+
+    >>> data = np.array([[0.8660254, 0.5, 0.],
+    ...                  [0.8660254, -0.5, 0.]])
+    >>> dirstats = directional_stats(data)
+    >>> dirstats.mean_direction
+    array([1., 0., 0.])
+
+    The regular sample mean on the other hand yields a result which does not
+    lie on the surface of the sphere.
+
+    >>> data.mean(axis=0)
+    array([0.8660254, 0., 0.])
+
+    The function also returns the mean resultant length, which
+    can be used to calculate a directional variance. For example, using the
+    definition ``Var(z) = 1 - R`` from [2]_ where ``R`` is the
+    mean resultant length, we can calculate the directional variance of the
+    vectors in the above example as:
+
+    >>> 1 - dirstats.mean_resultant_length
+    0.13397459716167093
+    """
+    xp = array_namespace(samples)
+    samples = xp.asarray(samples)
+
+    if samples.ndim < 2:
+        raise ValueError("samples must at least be two-dimensional. "
+                         f"Instead samples has shape: {tuple(samples.shape)}")
+    samples = xp.moveaxis(samples, axis, 0)
+
+    if is_marray(xp):
+        _xp = array_namespace(samples.mask)
+        mask = _xp.any(samples.mask, axis=-1, keepdims=True)
+        samples = xp.asarray(samples.data, mask=mask)
+
+    if normalize:
+        vectornorms = xp_vector_norm(samples, axis=-1, keepdims=True, xp=xp)
+        samples = samples/vectornorms
+    mean = xp.mean(samples, axis=0)
+    mean_resultant_length = xp_vector_norm(mean, axis=-1, keepdims=True, xp=xp)
+    mean_direction = mean / mean_resultant_length
+    mrl = xp.squeeze(mean_resultant_length, axis=-1)
+    mean_resultant_length = mrl[()] if mrl.ndim == 0 else mrl
+    return DirectionalStats(mean_direction, mean_resultant_length)
+
+
+@xp_capabilities(skip_backends=[('dask.array', "no take_along_axis")])
+def false_discovery_control(ps, *, axis=0, method='bh'):
+    """Adjust p-values to control the false discovery rate.
+
+    The false discovery rate (FDR) is the expected proportion of rejected null
+    hypotheses that are actually true.
+    If the null hypothesis is rejected when the *adjusted* p-value falls below
+    a specified level, the false discovery rate is controlled at that level.
+
+    Parameters
+    ----------
+    ps : 1D array_like
+        The p-values to adjust. Elements must be real numbers between 0 and 1.
+    axis : int
+        The axis along which to perform the adjustment. The adjustment is
+        performed independently along each axis-slice. If `axis` is None, `ps`
+        is raveled before performing the adjustment.
+    method : {'bh', 'by'}
+        The false discovery rate control procedure to apply: ``'bh'`` is for
+        Benjamini-Hochberg [1]_ (Eq. 1), ``'by'`` is for Benjaminini-Yekutieli
+        [2]_ (Theorem 1.3). The latter is more conservative, but it is
+        guaranteed to control the FDR even when the p-values are not from
+        independent tests.
+
+    Returns
+    -------
+    ps_adusted : array_like
+        The adjusted p-values. If the null hypothesis is rejected where these
+        fall below a specified level, the false discovery rate is controlled
+        at that level.
+
+    See Also
+    --------
+    combine_pvalues
+    statsmodels.stats.multitest.multipletests
+
+    Notes
+    -----
+    In multiple hypothesis testing, false discovery control procedures tend to
+    offer higher power than familywise error rate control procedures (e.g.
+    Bonferroni correction [1]_).
+
+    If the p-values correspond with independent tests (or tests with
+    "positive regression dependencies" [2]_), rejecting null hypotheses
+    corresponding with Benjamini-Hochberg-adjusted p-values below :math:`q`
+    controls the false discovery rate at a level less than or equal to
+    :math:`q m_0 / m`, where :math:`m_0` is the number of true null hypotheses
+    and :math:`m` is the total number of null hypotheses tested. The same is
+    true even for dependent tests when the p-values are adjusted accorded to
+    the more conservative Benjaminini-Yekutieli procedure.
+
+    The adjusted p-values produced by this function are comparable to those
+    produced by the R function ``p.adjust`` and the statsmodels function
+    `statsmodels.stats.multitest.multipletests`. Please consider the latter
+    for more advanced methods of multiple comparison correction.
+
+    References
+    ----------
+    .. [1] Benjamini, Yoav, and Yosef Hochberg. "Controlling the false
+           discovery rate: a practical and powerful approach to multiple
+           testing." Journal of the Royal statistical society: series B
+           (Methodological) 57.1 (1995): 289-300.
+
+    .. [2] Benjamini, Yoav, and Daniel Yekutieli. "The control of the false
+           discovery rate in multiple testing under dependency." Annals of
+           statistics (2001): 1165-1188.
+
+    .. [3] TileStats. FDR - Benjamini-Hochberg explained - Youtube.
+           https://www.youtube.com/watch?v=rZKa4tW2NKs.
+
+    .. [4] Neuhaus, Karl-Ludwig, et al. "Improved thrombolysis in acute
+           myocardial infarction with front-loaded administration of alteplase:
+           results of the rt-PA-APSAC patency study (TAPS)." Journal of the
+           American College of Cardiology 19.5 (1992): 885-891.
+
+    Examples
+    --------
+    We follow the example from [1]_.
+
+        Thrombolysis with recombinant tissue-type plasminogen activator (rt-PA)
+        and anisoylated plasminogen streptokinase activator (APSAC) in
+        myocardial infarction has been proved to reduce mortality. [4]_
+        investigated the effects of a new front-loaded administration of rt-PA
+        versus those obtained with a standard regimen of APSAC, in a randomized
+        multicentre trial in 421 patients with acute myocardial infarction.
+
+    There were four families of hypotheses tested in the study, the last of
+    which was "cardiac and other events after the start of thrombolitic
+    treatment". FDR control may be desired in this family of hypotheses
+    because it would not be appropriate to conclude that the front-loaded
+    treatment is better if it is merely equivalent to the previous treatment.
+
+    The p-values corresponding with the 15 hypotheses in this family were
+
+    >>> ps = [0.0001, 0.0004, 0.0019, 0.0095, 0.0201, 0.0278, 0.0298, 0.0344,
+    ...       0.0459, 0.3240, 0.4262, 0.5719, 0.6528, 0.7590, 1.000]
+
+    If the chosen significance level is 0.05, we may be tempted to reject the
+    null hypotheses for the tests corresponding with the first nine p-values,
+    as the first nine p-values fall below the chosen significance level.
+    However, this would ignore the problem of "multiplicity": if we fail to
+    correct for the fact that multiple comparisons are being performed, we
+    are more likely to incorrectly reject true null hypotheses.
+
+    One approach to the multiplicity problem is to control the family-wise
+    error rate (FWER), that is, the rate at which the null hypothesis is
+    rejected when it is actually true. A common procedure of this kind is the
+    Bonferroni correction [1]_.  We begin by multiplying the p-values by the
+    number of hypotheses tested.
+
+    >>> import numpy as np
+    >>> np.array(ps) * len(ps)
+    array([1.5000e-03, 6.0000e-03, 2.8500e-02, 1.4250e-01, 3.0150e-01,
+           4.1700e-01, 4.4700e-01, 5.1600e-01, 6.8850e-01, 4.8600e+00,
+           6.3930e+00, 8.5785e+00, 9.7920e+00, 1.1385e+01, 1.5000e+01])
+
+    To control the FWER at 5%, we reject only the hypotheses corresponding
+    with adjusted p-values less than 0.05. In this case, only the hypotheses
+    corresponding with the first three p-values can be rejected. According to
+    [1]_, these three hypotheses concerned "allergic reaction" and "two
+    different aspects of bleeding."
+
+    An alternative approach is to control the false discovery rate: the
+    expected fraction of rejected null hypotheses that are actually true. The
+    advantage of this approach is that it typically affords greater power: an
+    increased rate of rejecting the null hypothesis when it is indeed false. To
+    control the false discovery rate at 5%, we apply the Benjamini-Hochberg
+    p-value adjustment.
+
+    >>> from scipy import stats
+    >>> stats.false_discovery_control(ps)
+    array([0.0015    , 0.003     , 0.0095    , 0.035625  , 0.0603    ,
+           0.06385714, 0.06385714, 0.0645    , 0.0765    , 0.486     ,
+           0.58118182, 0.714875  , 0.75323077, 0.81321429, 1.        ])
+
+    Now, the first *four* adjusted p-values fall below 0.05, so we would reject
+    the null hypotheses corresponding with these *four* p-values. Rejection
+    of the fourth null hypothesis was particularly important to the original
+    study as it led to the conclusion that the new treatment had a
+    "substantially lower in-hospital mortality rate."
+
+    For simplicity of exposition, the p-values in the example above were given in
+    sorted order, but this is not required; `false_discovery_control` returns
+    adjusted p-values in order corresponding with the input `ps`.
+
+    >>> stats.false_discovery_control([0.5, 0.6, 0.1, 0.001])
+    array([0.6  , 0.6  , 0.2  , 0.004])
+
+    """
+    xp = array_namespace(ps)
+
+    # Input Validation and Special Cases
+    ps = xp.asarray(ps)
+
+    if not xp.isdtype(ps.dtype, ("integral", "real floating")):
+        raise ValueError("`ps` must contain only real numbers.")
+
+    if is_lazy_array(ps):
+        ps = xp.where((ps < 0.) | (ps > 1.), xp.nan, ps)
+    else:
+        if not xp.all(ps == xp.clip(ps, 0., 1.)):
+            raise ValueError("All values in `ps` must lie between 0. and 1.")
+
+    methods = {'bh', 'by'}
+    if method.lower() not in methods:
+        raise ValueError(f"Unrecognized `method` '{method}'."
+                         f"Method must be one of {methods}.")
+    method = method.lower()
+
+    if axis is None:
+        axis = 0
+        ps = xp_ravel(ps)
+
+    axis = np.asarray(axis)[()]  # use of NumPy for input validation is OK
+    if not np.issubdtype(axis.dtype, np.integer) or axis.size != 1:
+        raise ValueError("`axis` must be an integer or `None`")
+    axis = int(axis)
+
+    if xp_size(ps) <= 1 or ps.shape[axis] <= 1:
+        return ps[()] if ps.ndim == 0 else ps
+
+    ps = xp.moveaxis(ps, axis, -1)
+    m = ps.shape[-1]
+
+    # Main Algorithm
+    # Equivalent to the ideas of [1] and [2], except that this adjusts the
+    # p-values as described in [3]. The results are similar to those produced
+    # by R's p.adjust.
+
+    # "Let [ps] be the ordered observed p-values..."
+    order = xp.argsort(ps, axis=-1)
+    ps = xp.take_along_axis(ps, order, axis=-1)  # this copies ps
+
+    # Equation 1 of [1] rearranged to reject when p is less than specified q
+    i = xp.arange(1, m+1, dtype=ps.dtype, device=xp_device(ps))
+    # ps *= m / i
+    ps = xpx.at(ps)[...].multiply(m / i)
+
+    # Theorem 1.3 of [2]
+    if method == 'by':
+        # ps *= np.sum(1 / i)
+        ps = xpx.at(ps)[...].multiply(xp.sum(1 / i))
+
+    # accounts for rejecting all null hypotheses i for i < k, where k is
+    # defined in Eq. 1 of either [1] or [2]. See [3]. Starting with the index j
+    # of the second to last element, we replace element j with element j+1 if
+    # the latter is smaller.
+    if is_numpy(xp):
+        np.minimum.accumulate(ps[..., ::-1], out=ps[..., ::-1], axis=-1)
+    else:
+        n = ps.shape[-1]
+        for j in range(n-2, -1, -1):
+            # ps[..., j] = xp.minimum(ps[..., j], ps[..., j+1])
+            ps = xpx.at(ps)[..., j].set(xp.minimum(ps[..., j], ps[..., j+1]))
+
+    # Restore original order of axes and data
+    ps = _reorder_along_axis(ps, order, axis=-1, xp=xp)
+    ps = xp.moveaxis(ps, -1, axis)
+
+    return xp.clip(ps, 0., 1.)
+
+
+def _reorder_along_axis(x, i, *, axis, xp):
+    if is_jax(xp):
+        return xp.put_along_axis(x, i, values=x, axis=axis, inplace=False)
+    if hasattr(xp, 'put_along_axis'):
+        xp.put_along_axis(x, i, values=x.copy(), axis=axis)
+        return x
+    else:
+        return xp.take_along_axis(x, xp.argsort(i, axis=-1), axis=-1)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_mstats_basic.py b/venv/lib/python3.12/site-packages/scipy/stats/_mstats_basic.py
new file mode 100644
index 0000000000000000000000000000000000000000..96517b32ae2a8865403d2a02ac9a64fbd3ea5805
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_mstats_basic.py
@@ -0,0 +1,3833 @@
+"""
+An extension of scipy.stats._stats_py to support masked arrays
+
+"""
+# Original author (2007): Pierre GF Gerard-Marchant
+
+
+__all__ = ['argstoarray',
+           'count_tied_groups',
+           'describe',
+           'f_oneway', 'find_repeats','friedmanchisquare',
+           'kendalltau','kendalltau_seasonal','kruskal','kruskalwallis',
+           'ks_twosamp', 'ks_2samp', 'kurtosis', 'kurtosistest',
+           'ks_1samp', 'kstest',
+           'linregress',
+           'mannwhitneyu', 'meppf','mode','moment','mquantiles','msign',
+           'normaltest',
+           'obrientransform',
+           'pearsonr','plotting_positions','pointbiserialr',
+           'rankdata',
+           'scoreatpercentile','sem',
+           'sen_seasonal_slopes','skew','skewtest','spearmanr',
+           'siegelslopes', 'theilslopes',
+           'tmax','tmean','tmin','trim','trimboth',
+           'trimtail','trima','trimr','trimmed_mean','trimmed_std',
+           'trimmed_stde','trimmed_var','tsem','ttest_1samp','ttest_onesamp',
+           'ttest_ind','ttest_rel','tvar',
+           'variation',
+           'winsorize',
+           'brunnermunzel',
+           ]
+
+import numpy as np
+from numpy import ndarray
+import numpy.ma as ma
+from numpy.ma import masked, nomask
+import math
+
+import itertools
+import warnings
+from collections import namedtuple
+
+from . import distributions
+from scipy._lib._util import _rename_parameter, _contains_nan, _dedent_for_py313
+from scipy._lib._bunch import _make_tuple_bunch
+import scipy.special as special
+import scipy.stats._stats_py
+import scipy.stats._stats_py as _stats_py
+from scipy.stats._stats_pythran import siegelslopes as siegelslopes_pythran
+from ._stats_mstats_common import _find_repeats, TheilslopesResult, SiegelslopesResult
+
+
+def _chk_asarray(a, axis):
+    # Always returns a masked array, raveled for axis=None
+    a = ma.asanyarray(a)
+    if axis is None:
+        a = ma.ravel(a)
+        outaxis = 0
+    else:
+        outaxis = axis
+    return a, outaxis
+
+
+def _chk2_asarray(a, b, axis):
+    a = ma.asanyarray(a)
+    b = ma.asanyarray(b)
+    if axis is None:
+        a = ma.ravel(a)
+        b = ma.ravel(b)
+        outaxis = 0
+    else:
+        outaxis = axis
+    return a, b, outaxis
+
+
+def _chk_size(a, b):
+    a = ma.asanyarray(a)
+    b = ma.asanyarray(b)
+    (na, nb) = (a.size, b.size)
+    if na != nb:
+        raise ValueError("The size of the input array should match!"
+                         f" ({na} <> {nb})")
+    return (a, b, na)
+
+
+def _ttest_finish(df, t, alternative):
+    """Common code between all 3 t-test functions."""
+    # We use ``stdtr`` directly here to preserve masked arrays
+
+    if alternative == 'less':
+        pval = special._ufuncs.stdtr(df, t)
+    elif alternative == 'greater':
+        pval = special._ufuncs.stdtr(df, -t)
+    elif alternative == 'two-sided':
+        pval = special._ufuncs.stdtr(df, -np.abs(t))*2
+    else:
+        raise ValueError("alternative must be "
+                         "'less', 'greater' or 'two-sided'")
+
+    if t.ndim == 0:
+        t = t[()]
+    if pval.ndim == 0:
+        pval = pval[()]
+
+    return t, pval
+
+
+def argstoarray(*args):
+    """
+    Constructs a 2D array from a group of sequences.
+
+    Sequences are filled with missing values to match the length of the longest
+    sequence.
+
+    Parameters
+    ----------
+    *args : sequences
+        Group of sequences.
+
+    Returns
+    -------
+    argstoarray : MaskedArray
+        A ( `m` x `n` ) masked array, where `m` is the number of arguments and
+        `n` the length of the longest argument.
+
+    Notes
+    -----
+    `numpy.ma.vstack` has identical behavior, but is called with a sequence
+    of sequences.
+
+    Examples
+    --------
+    A 2D masked array constructed from a group of sequences is returned.
+
+    >>> from scipy.stats.mstats import argstoarray
+    >>> argstoarray([1, 2, 3], [4, 5, 6])
+    masked_array(
+     data=[[1.0, 2.0, 3.0],
+           [4.0, 5.0, 6.0]],
+     mask=[[False, False, False],
+           [False, False, False]],
+     fill_value=1e+20)
+
+    The returned masked array filled with missing values when the lengths of
+    sequences are different.
+
+    >>> argstoarray([1, 3], [4, 5, 6])
+    masked_array(
+     data=[[1.0, 3.0, --],
+           [4.0, 5.0, 6.0]],
+     mask=[[False, False,  True],
+           [False, False, False]],
+     fill_value=1e+20)
+
+    """
+    if len(args) == 1 and not isinstance(args[0], ndarray):
+        output = ma.asarray(args[0])
+        if output.ndim != 2:
+            raise ValueError("The input should be 2D")
+    else:
+        n = len(args)
+        m = max([len(k) for k in args])
+        output = ma.array(np.empty((n,m), dtype=float), mask=True)
+        for (k,v) in enumerate(args):
+            output[k,:len(v)] = v
+
+    output[np.logical_not(np.isfinite(output._data))] = masked
+    return output
+
+
+def find_repeats(arr):
+    """Find repeats in arr and return a tuple (repeats, repeat_count).
+
+    The input is cast to float64. Masked values are discarded.
+
+    Parameters
+    ----------
+    arr : sequence
+        Input array. The array is flattened if it is not 1D.
+
+    Returns
+    -------
+    repeats : ndarray
+        Array of repeated values.
+    counts : ndarray
+        Array of counts.
+
+    Examples
+    --------
+    >>> from scipy.stats import mstats
+    >>> mstats.find_repeats([2, 1, 2, 3, 2, 2, 5])
+    (array([2.]), array([4]))
+
+    In the above example, 2 repeats 4 times.
+
+    >>> mstats.find_repeats([[10, 20, 1, 2], [5, 5, 4, 4]])
+    (array([4., 5.]), array([2, 2]))
+
+    In the above example, both 4 and 5 repeat 2 times.
+
+    """
+    # Make sure we get a copy. ma.compressed promises a "new array", but can
+    # actually return a reference.
+    compr = np.asarray(ma.compressed(arr), dtype=np.float64)
+    need_copy = np.may_share_memory(compr, arr)
+    if need_copy:
+        compr = compr.copy()
+    return _find_repeats(compr)
+
+
+def count_tied_groups(x, use_missing=False):
+    """
+    Counts the number of tied values.
+
+    Parameters
+    ----------
+    x : sequence
+        Sequence of data on which to counts the ties
+    use_missing : bool, optional
+        Whether to consider missing values as tied.
+
+    Returns
+    -------
+    count_tied_groups : dict
+        Returns a dictionary (nb of ties: nb of groups).
+
+    Examples
+    --------
+    >>> from scipy.stats import mstats
+    >>> import numpy as np
+    >>> z = [0, 0, 0, 2, 2, 2, 3, 3, 4, 5, 6]
+    >>> mstats.count_tied_groups(z)
+    {2: 1, 3: 2}
+
+    In the above example, the ties were 0 (3x), 2 (3x) and 3 (2x).
+
+    >>> z = np.ma.array([0, 0, 1, 2, 2, 2, 3, 3, 4, 5, 6])
+    >>> mstats.count_tied_groups(z)
+    {2: 2, 3: 1}
+    >>> z[[1,-1]] = np.ma.masked
+    >>> mstats.count_tied_groups(z, use_missing=True)
+    {2: 2, 3: 1}
+
+    """
+    nmasked = ma.getmask(x).sum()
+    # We need the copy as find_repeats will overwrite the initial data
+    data = ma.compressed(x).copy()
+    (ties, counts) = find_repeats(data)
+    nties = {}
+    if len(ties):
+        nties = dict(zip(np.unique(counts), itertools.repeat(1)))
+        nties.update(dict(zip(*find_repeats(counts))))
+
+    if nmasked and use_missing:
+        try:
+            nties[nmasked] += 1
+        except KeyError:
+            nties[nmasked] = 1
+
+    return nties
+
+
+def rankdata(data, axis=None, use_missing=False):
+    """Returns the rank (also known as order statistics) of each data point
+    along the given axis.
+
+    If some values are tied, their rank is averaged.
+    If some values are masked, their rank is set to 0 if use_missing is False,
+    or set to the average rank of the unmasked values if use_missing is True.
+
+    Parameters
+    ----------
+    data : sequence
+        Input data. The data is transformed to a masked array
+    axis : {None,int}, optional
+        Axis along which to perform the ranking.
+        If None, the array is first flattened. An exception is raised if
+        the axis is specified for arrays with a dimension larger than 2
+    use_missing : bool, optional
+        Whether the masked values have a rank of 0 (False) or equal to the
+        average rank of the unmasked values (True).
+
+    """  # numpydoc ignore=RT01
+    def _rank1d(data, use_missing=False):
+        n = data.count()
+        rk = np.empty(data.size, dtype=float)
+        idx = data.argsort()
+        rk[idx[:n]] = np.arange(1,n+1)
+
+        if use_missing:
+            rk[idx[n:]] = (n+1)/2.
+        else:
+            rk[idx[n:]] = 0
+
+        repeats = find_repeats(data.copy())
+        for r in repeats[0]:
+            condition = (data == r).filled(False)
+            rk[condition] = rk[condition].mean()
+        return rk
+
+    data = ma.array(data, copy=False)
+    if axis is None:
+        if data.ndim > 1:
+            return _rank1d(data.ravel(), use_missing).reshape(data.shape)
+        else:
+            return _rank1d(data, use_missing)
+    else:
+        return ma.apply_along_axis(_rank1d,axis,data,use_missing).view(ndarray)
+
+
+ModeResult = namedtuple('ModeResult', ('mode', 'count'))
+
+
+def mode(a, axis=0):
+    """
+    Returns an array of the modal (most common) value in the passed array.
+
+    Parameters
+    ----------
+    a : array_like
+        n-dimensional array of which to find mode(s).
+    axis : int or None, optional
+        Axis along which to operate. Default is 0. If None, compute over
+        the whole array `a`.
+
+    Returns
+    -------
+    mode : ndarray
+        Array of modal values.
+    count : ndarray
+        Array of counts for each mode.
+
+    Notes
+    -----
+    For more details, see `scipy.stats.mode`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> from scipy.stats import mstats
+    >>> m_arr = np.ma.array([1, 1, 0, 0, 0, 0], mask=[0, 0, 1, 1, 1, 0])
+    >>> mstats.mode(m_arr)  # note that most zeros are masked
+    ModeResult(mode=array([1.]), count=array([2.]))
+
+    """
+    return _mode(a, axis=axis, keepdims=True)
+
+
+def _mode(a, axis=0, keepdims=True):
+    # Don't want to expose `keepdims` from the public `mstats.mode`
+    a, axis = _chk_asarray(a, axis)
+
+    def _mode1D(a):
+        (rep,cnt) = find_repeats(a)
+        if not cnt.ndim:
+            return (0, 0)
+        elif cnt.size:
+            return (rep[cnt.argmax()], cnt.max())
+        else:
+            return (a.min(), 1)
+
+    if axis is None:
+        output = _mode1D(ma.ravel(a))
+        output = (ma.array(output[0]), ma.array(output[1]))
+    else:
+        output = ma.apply_along_axis(_mode1D, axis, a)
+        if keepdims is None or keepdims:
+            newshape = list(a.shape)
+            newshape[axis] = 1
+            slices = [slice(None)] * output.ndim
+            slices[axis] = 0
+            modes = output[tuple(slices)].reshape(newshape)
+            slices[axis] = 1
+            counts = output[tuple(slices)].reshape(newshape)
+            output = (modes, counts)
+        else:
+            output = np.moveaxis(output, axis, 0)
+
+    return ModeResult(*output)
+
+
+def _betai(a, b, x):
+    x = np.asanyarray(x)
+    x = ma.where(x < 1.0, x, 1.0)  # if x > 1 then return 1.0
+    return special.betainc(a, b, x)
+
+
+def msign(x):
+    """Returns the sign of x, or 0 if x is masked."""  # numpydoc ignore=RT01
+    return ma.filled(np.sign(x), 0)
+
+
+def pearsonr(x, y):
+    r"""
+    Pearson correlation coefficient and p-value for testing non-correlation.
+
+    The Pearson correlation coefficient [1]_ measures the linear relationship
+    between two datasets.  The calculation of the p-value relies on the
+    assumption that each dataset is normally distributed.  (See Kowalski [3]_
+    for a discussion of the effects of non-normality of the input on the
+    distribution of the correlation coefficient.)  Like other correlation
+    coefficients, this one varies between -1 and +1 with 0 implying no
+    correlation. Correlations of -1 or +1 imply an exact linear relationship.
+
+    Parameters
+    ----------
+    x : (N,) array_like
+        Input array.
+    y : (N,) array_like
+        Input array.
+
+    Returns
+    -------
+    r : float
+        Pearson's correlation coefficient.
+    p-value : float
+        Two-tailed p-value.
+
+    Warns
+    -----
+    `~scipy.stats.ConstantInputWarning`
+        Raised if an input is a constant array.  The correlation coefficient
+        is not defined in this case, so ``np.nan`` is returned.
+
+    `~scipy.stats.NearConstantInputWarning`
+        Raised if an input is "nearly" constant.  The array ``x`` is considered
+        nearly constant if ``norm(x - mean(x)) < 1e-13 * abs(mean(x))``.
+        Numerical errors in the calculation ``x - mean(x)`` in this case might
+        result in an inaccurate calculation of r.
+
+    See Also
+    --------
+    spearmanr : Spearman rank-order correlation coefficient.
+    kendalltau : Kendall's tau, a correlation measure for ordinal data.
+
+    Notes
+    -----
+    The correlation coefficient is calculated as follows:
+
+    .. math::
+
+        r = \frac{\sum (x - m_x) (y - m_y)}
+                 {\sqrt{\sum (x - m_x)^2 \sum (y - m_y)^2}}
+
+    where :math:`m_x` is the mean of the vector x and :math:`m_y` is
+    the mean of the vector y.
+
+    Under the assumption that x and y are drawn from
+    independent normal distributions (so the population correlation coefficient
+    is 0), the probability density function of the sample correlation
+    coefficient r is ([1]_, [2]_):
+
+    .. math::
+
+        f(r) = \frac{{(1-r^2)}^{n/2-2}}{\mathrm{B}(\frac{1}{2},\frac{n}{2}-1)}
+
+    where n is the number of samples, and B is the beta function.  This
+    is sometimes referred to as the exact distribution of r.  This is
+    the distribution that is used in `pearsonr` to compute the p-value.
+    The distribution is a beta distribution on the interval [-1, 1],
+    with equal shape parameters a = b = n/2 - 1.  In terms of SciPy's
+    implementation of the beta distribution, the distribution of r is::
+
+        dist = scipy.stats.beta(n/2 - 1, n/2 - 1, loc=-1, scale=2)
+
+    The p-value returned by `pearsonr` is a two-sided p-value. The p-value
+    roughly indicates the probability of an uncorrelated system
+    producing datasets that have a Pearson correlation at least as extreme
+    as the one computed from these datasets. More precisely, for a
+    given sample with correlation coefficient r, the p-value is
+    the probability that abs(r') of a random sample x' and y' drawn from
+    the population with zero correlation would be greater than or equal
+    to abs(r). In terms of the object ``dist`` shown above, the p-value
+    for a given r and length n can be computed as::
+
+        p = 2*dist.cdf(-abs(r))
+
+    When n is 2, the above continuous distribution is not well-defined.
+    One can interpret the limit of the beta distribution as the shape
+    parameters a and b approach a = b = 0 as a discrete distribution with
+    equal probability masses at r = 1 and r = -1.  More directly, one
+    can observe that, given the data x = [x1, x2] and y = [y1, y2], and
+    assuming x1 != x2 and y1 != y2, the only possible values for r are 1
+    and -1.  Because abs(r') for any sample x' and y' with length 2 will
+    be 1, the two-sided p-value for a sample of length 2 is always 1.
+
+    References
+    ----------
+    .. [1] "Pearson correlation coefficient", Wikipedia,
+           https://en.wikipedia.org/wiki/Pearson_correlation_coefficient
+    .. [2] Student, "Probable error of a correlation coefficient",
+           Biometrika, Volume 6, Issue 2-3, 1 September 1908, pp. 302-310.
+    .. [3] C. J. Kowalski, "On the Effects of Non-Normality on the Distribution
+           of the Sample Product-Moment Correlation Coefficient"
+           Journal of the Royal Statistical Society. Series C (Applied
+           Statistics), Vol. 21, No. 1 (1972), pp. 1-12.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> from scipy.stats import mstats
+    >>> mstats.pearsonr([1, 2, 3, 4, 5], [10, 9, 2.5, 6, 4])
+    (-0.7426106572325057, 0.1505558088534455)
+
+    There is a linear dependence between x and y if y = a + b*x + e, where
+    a,b are constants and e is a random error term, assumed to be independent
+    of x. For simplicity, assume that x is standard normal, a=0, b=1 and let
+    e follow a normal distribution with mean zero and standard deviation s>0.
+
+    >>> s = 0.5
+    >>> x = stats.norm.rvs(size=500)
+    >>> e = stats.norm.rvs(scale=s, size=500)
+    >>> y = x + e
+    >>> mstats.pearsonr(x, y)
+    (0.9029601878969703, 8.428978827629898e-185) # may vary
+
+    This should be close to the exact value given by
+
+    >>> 1/np.sqrt(1 + s**2)
+    0.8944271909999159
+
+    For s=0.5, we observe a high level of correlation. In general, a large
+    variance of the noise reduces the correlation, while the correlation
+    approaches one as the variance of the error goes to zero.
+
+    It is important to keep in mind that no correlation does not imply
+    independence unless (x, y) is jointly normal. Correlation can even be zero
+    when there is a very simple dependence structure: if X follows a
+    standard normal distribution, let y = abs(x). Note that the correlation
+    between x and y is zero. Indeed, since the expectation of x is zero,
+    cov(x, y) = E[x*y]. By definition, this equals E[x*abs(x)] which is zero
+    by symmetry. The following lines of code illustrate this observation:
+
+    >>> y = np.abs(x)
+    >>> mstats.pearsonr(x, y)
+    (-0.016172891856853524, 0.7182823678751942) # may vary
+
+    A non-zero correlation coefficient can be misleading. For example, if X has
+    a standard normal distribution, define y = x if x < 0 and y = 0 otherwise.
+    A simple calculation shows that corr(x, y) = sqrt(2/Pi) = 0.797...,
+    implying a high level of correlation:
+
+    >>> y = np.where(x < 0, x, 0)
+    >>> mstats.pearsonr(x, y)
+    (0.8537091583771509, 3.183461621422181e-143) # may vary
+
+    This is unintuitive since there is no dependence of x and y if x is larger
+    than zero which happens in about half of the cases if we sample x and y.
+    """
+    (x, y, n) = _chk_size(x, y)
+    (x, y) = (x.ravel(), y.ravel())
+    # Get the common mask and the total nb of unmasked elements
+    m = ma.mask_or(ma.getmask(x), ma.getmask(y))
+    n -= m.sum()
+    df = n-2
+    if df < 0:
+        return (masked, masked)
+
+    return scipy.stats._stats_py.pearsonr(
+                ma.masked_array(x, mask=m).compressed(),
+                ma.masked_array(y, mask=m).compressed())
+
+
+def spearmanr(x, y=None, use_ties=True, axis=None, nan_policy='propagate',
+              alternative='two-sided'):
+    """
+    Calculates a Spearman rank-order correlation coefficient and the p-value
+    to test for non-correlation.
+
+    The Spearman correlation is a nonparametric measure of the linear
+    relationship between two datasets. Unlike the Pearson correlation, the
+    Spearman correlation does not assume that both datasets are normally
+    distributed. Like other correlation coefficients, this one varies
+    between -1 and +1 with 0 implying no correlation. Correlations of -1 or
+    +1 imply a monotonic relationship. Positive correlations imply that
+    as `x` increases, so does `y`. Negative correlations imply that as `x`
+    increases, `y` decreases.
+
+    Missing values are discarded pair-wise: if a value is missing in `x`, the
+    corresponding value in `y` is masked.
+
+    The p-value roughly indicates the probability of an uncorrelated system
+    producing datasets that have a Spearman correlation at least as extreme
+    as the one computed from these datasets. The p-values are not entirely
+    reliable but are probably reasonable for datasets larger than 500 or so.
+
+    Parameters
+    ----------
+    x, y : 1D or 2D array_like, y is optional
+        One or two 1-D or 2-D arrays containing multiple variables and
+        observations. When these are 1-D, each represents a vector of
+        observations of a single variable. For the behavior in the 2-D case,
+        see under ``axis``, below.
+    use_ties : bool, optional
+        DO NOT USE.  Does not do anything, keyword is only left in place for
+        backwards compatibility reasons.
+    axis : int or None, optional
+        If axis=0 (default), then each column represents a variable, with
+        observations in the rows. If axis=1, the relationship is transposed:
+        each row represents a variable, while the columns contain observations.
+        If axis=None, then both arrays will be raveled.
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains nan. 'propagate' returns nan,
+        'raise' throws an error, 'omit' performs the calculations ignoring nan
+        values. Default is 'propagate'.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis. Default is 'two-sided'.
+        The following options are available:
+
+        * 'two-sided': the correlation is nonzero
+        * 'less': the correlation is negative (less than zero)
+        * 'greater':  the correlation is positive (greater than zero)
+
+        .. versionadded:: 1.7.0
+
+    Returns
+    -------
+    res : SignificanceResult
+        An object containing attributes:
+
+        statistic : float or ndarray (2-D square)
+            Spearman correlation matrix or correlation coefficient (if only 2
+            variables are given as parameters). Correlation matrix is square
+            with length equal to total number of variables (columns or rows) in
+            ``a`` and ``b`` combined.
+        pvalue : float
+            The p-value for a hypothesis test whose null hypothesis
+            is that two sets of data are linearly uncorrelated. See
+            `alternative` above for alternative hypotheses. `pvalue` has the
+            same shape as `statistic`.
+
+    References
+    ----------
+    [CRCProbStat2000] section 14.7
+
+    """
+    if not use_ties:
+        raise ValueError("`use_ties=False` is not supported in SciPy >= 1.2.0")
+
+    # Always returns a masked array, raveled if axis=None
+    x, axisout = _chk_asarray(x, axis)
+    if y is not None:
+        # Deal only with 2-D `x` case.
+        y, _ = _chk_asarray(y, axis)
+        if axisout == 0:
+            x = ma.column_stack((x, y))
+        else:
+            x = ma.vstack((x, y))
+
+    if axisout == 1:
+        # To simplify the code that follow (always use `n_obs, n_vars` shape)
+        x = x.T
+
+    if nan_policy == 'omit':
+        x = ma.masked_invalid(x)
+
+    def _spearmanr_2cols(x):
+        # Mask the same observations for all variables, and then drop those
+        # observations (can't leave them masked, rankdata is weird).
+        x = ma.mask_rowcols(x, axis=0)
+        x = x[~x.mask.any(axis=1), :]
+
+        # If either column is entirely NaN or Inf
+        if not np.any(x.data):
+            res = scipy.stats._stats_py.SignificanceResult(np.nan, np.nan)
+            res.correlation = np.nan
+            return res
+
+        m = ma.getmask(x)
+        n_obs = x.shape[0]
+        dof = n_obs - 2 - int(m.sum(axis=0)[0])
+        if dof < 0:
+            raise ValueError("The input must have at least 3 entries!")
+
+        # Gets the ranks and rank differences
+        x_ranked = rankdata(x, axis=0)
+        rs = ma.corrcoef(x_ranked, rowvar=False).data
+
+        # rs can have elements equal to 1, so avoid zero division warnings
+        with np.errstate(divide='ignore'):
+            # clip the small negative values possibly caused by rounding
+            # errors before taking the square root
+            t = rs * np.sqrt((dof / ((rs+1.0) * (1.0-rs))).clip(0))
+
+        t, prob = _ttest_finish(dof, t, alternative)
+
+        # For backwards compatibility, return scalars when comparing 2 columns
+        if rs.shape == (2, 2):
+            res = scipy.stats._stats_py.SignificanceResult(rs[1, 0],
+                                                           prob[1, 0])
+            res.correlation = rs[1, 0]
+            return res
+        else:
+            res = scipy.stats._stats_py.SignificanceResult(rs, prob)
+            res.correlation = rs
+            return res
+
+    # Need to do this per pair of variables, otherwise the dropped observations
+    # in a third column mess up the result for a pair.
+    n_vars = x.shape[1]
+    if n_vars == 2:
+        return _spearmanr_2cols(x)
+    else:
+        rs = np.ones((n_vars, n_vars), dtype=float)
+        prob = np.zeros((n_vars, n_vars), dtype=float)
+        for var1 in range(n_vars - 1):
+            for var2 in range(var1+1, n_vars):
+                result = _spearmanr_2cols(x[:, [var1, var2]])
+                rs[var1, var2] = result.correlation
+                rs[var2, var1] = result.correlation
+                prob[var1, var2] = result.pvalue
+                prob[var2, var1] = result.pvalue
+
+        res = scipy.stats._stats_py.SignificanceResult(rs, prob)
+        res.correlation = rs
+        return res
+
+
+def _kendall_p_exact(n, c, alternative='two-sided'):
+
+    # Use the fact that distribution is symmetric: always calculate a CDF in
+    # the left tail.
+    # This will be the one-sided p-value if `c` is on the side of
+    # the null distribution predicted by the alternative hypothesis.
+    # The two-sided p-value will be twice this value.
+    # If `c` is on the other side of the null distribution, we'll need to
+    # take the complement and add back the probability mass at `c`.
+    in_right_tail = (c >= (n*(n-1))//2 - c)
+    alternative_greater = (alternative == 'greater')
+    c = int(min(c, (n*(n-1))//2 - c))
+
+    # Exact p-value, see Maurice G. Kendall, "Rank Correlation Methods"
+    # (4th Edition), Charles Griffin & Co., 1970.
+    if n <= 0:
+        raise ValueError(f'n ({n}) must be positive')
+    elif c < 0 or 4*c > n*(n-1):
+        raise ValueError(f'c ({c}) must satisfy 0 <= 4c <= n(n-1) = {n*(n-1)}.')
+    elif n == 1:
+        prob = 1.0
+        p_mass_at_c = 1
+    elif n == 2:
+        prob = 1.0
+        p_mass_at_c = 0.5
+    elif c == 0:
+        prob = 2.0/math.factorial(n) if n < 171 else 0.0
+        p_mass_at_c = prob/2
+    elif c == 1:
+        prob = 2.0/math.factorial(n-1) if n < 172 else 0.0
+        p_mass_at_c = (n-1)/math.factorial(n)
+    elif 4*c == n*(n-1) and alternative == 'two-sided':
+        # I'm sure there's a simple formula for p_mass_at_c in this
+        # case, but I don't know it. Use generic formula for one-sided p-value.
+        prob = 1.0
+    elif n < 171:
+        new = np.zeros(c+1)
+        new[0:2] = 1.0
+        for j in range(3,n+1):
+            new = np.cumsum(new)
+            if j <= c:
+                new[j:] -= new[:c+1-j]
+        prob = 2.0*np.sum(new)/math.factorial(n)
+        p_mass_at_c = new[-1]/math.factorial(n)
+    else:
+        new = np.zeros(c+1)
+        new[0:2] = 1.0
+        for j in range(3, n+1):
+            new = np.cumsum(new)/j
+            if j <= c:
+                new[j:] -= new[:c+1-j]
+        prob = np.sum(new)
+        p_mass_at_c = new[-1]/2
+
+    if alternative != 'two-sided':
+        # if the alternative hypothesis and alternative agree,
+        # one-sided p-value is half the two-sided p-value
+        if in_right_tail == alternative_greater:
+            prob /= 2
+        else:
+            prob = 1 - prob/2 + p_mass_at_c
+
+    prob = np.clip(prob, 0, 1)
+
+    return prob
+
+
+def kendalltau(x, y, use_ties=True, use_missing=False, method='auto',
+               alternative='two-sided'):
+    """
+    Computes Kendall's rank correlation tau on two variables *x* and *y*.
+
+    Parameters
+    ----------
+    x : sequence
+        First data list (for example, time).
+    y : sequence
+        Second data list.
+    use_ties : {True, False}, optional
+        Whether ties correction should be performed.
+    use_missing : {False, True}, optional
+        Whether missing data should be allocated a rank of 0 (False) or the
+        average rank (True)
+    method : {'auto', 'asymptotic', 'exact'}, optional
+        Defines which method is used to calculate the p-value [1]_.
+        'asymptotic' uses a normal approximation valid for large samples.
+        'exact' computes the exact p-value, but can only be used if no ties
+        are present. As the sample size increases, the 'exact' computation
+        time may grow and the result may lose some precision.
+        'auto' is the default and selects the appropriate
+        method based on a trade-off between speed and accuracy.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis. Default is 'two-sided'.
+        The following options are available:
+
+        * 'two-sided': the rank correlation is nonzero
+        * 'less': the rank correlation is negative (less than zero)
+        * 'greater':  the rank correlation is positive (greater than zero)
+
+    Returns
+    -------
+    res : SignificanceResult
+        An object containing attributes:
+
+        statistic : float
+           The tau statistic.
+        pvalue : float
+           The p-value for a hypothesis test whose null hypothesis is
+           an absence of association, tau = 0.
+
+    References
+    ----------
+    .. [1] Maurice G. Kendall, "Rank Correlation Methods" (4th Edition),
+           Charles Griffin & Co., 1970.
+
+    """
+    (x, y, n) = _chk_size(x, y)
+    (x, y) = (x.flatten(), y.flatten())
+    m = ma.mask_or(ma.getmask(x), ma.getmask(y))
+    if m is not nomask:
+        x = ma.array(x, mask=m, copy=True)
+        y = ma.array(y, mask=m, copy=True)
+        # need int() here, otherwise numpy defaults to 32 bit
+        # integer on all Windows architectures, causing overflow.
+        # int() will keep it infinite precision.
+        n -= int(m.sum())
+
+    if n < 2:
+        res = scipy.stats._stats_py.SignificanceResult(np.nan, np.nan)
+        res.correlation = np.nan
+        return res
+
+    rx = ma.masked_equal(rankdata(x, use_missing=use_missing), 0)
+    ry = ma.masked_equal(rankdata(y, use_missing=use_missing), 0)
+    idx = rx.argsort()
+    (rx, ry) = (rx[idx], ry[idx])
+    C = np.sum([((ry[i+1:] > ry[i]) * (rx[i+1:] > rx[i])).filled(0).sum()
+                for i in range(len(ry)-1)], dtype=float)
+    D = np.sum([((ry[i+1:] < ry[i])*(rx[i+1:] > rx[i])).filled(0).sum()
+                for i in range(len(ry)-1)], dtype=float)
+    xties = count_tied_groups(x)
+    yties = count_tied_groups(y)
+    if use_ties:
+        corr_x = np.sum([v*k*(k-1) for (k,v) in xties.items()], dtype=float)
+        corr_y = np.sum([v*k*(k-1) for (k,v) in yties.items()], dtype=float)
+        denom = ma.sqrt((n*(n-1)-corr_x)/2. * (n*(n-1)-corr_y)/2.)
+    else:
+        denom = n*(n-1)/2.
+    tau = (C-D) / denom
+
+    if method == 'exact' and (xties or yties):
+        raise ValueError("Ties found, exact method cannot be used.")
+
+    if method == 'auto':
+        if (not xties and not yties) and (n <= 33 or min(C, n*(n-1)/2.0-C) <= 1):
+            method = 'exact'
+        else:
+            method = 'asymptotic'
+
+    if not xties and not yties and method == 'exact':
+        prob = _kendall_p_exact(n, C, alternative)
+
+    elif method == 'asymptotic':
+        var_s = n*(n-1)*(2*n+5)
+        if use_ties:
+            var_s -= np.sum([v*k*(k-1)*(2*k+5)*1. for (k,v) in xties.items()])
+            var_s -= np.sum([v*k*(k-1)*(2*k+5)*1. for (k,v) in yties.items()])
+            v1 = (np.sum([v*k*(k-1) for (k, v) in xties.items()], dtype=float) *
+                  np.sum([v*k*(k-1) for (k, v) in yties.items()], dtype=float))
+            v1 /= 2.*n*(n-1)
+            if n > 2:
+                v2 = np.sum([v*k*(k-1)*(k-2) for (k,v) in xties.items()],
+                            dtype=float) * \
+                     np.sum([v*k*(k-1)*(k-2) for (k,v) in yties.items()],
+                            dtype=float)
+                v2 /= 9.*n*(n-1)*(n-2)
+            else:
+                v2 = 0
+        else:
+            v1 = v2 = 0
+
+        var_s /= 18.
+        var_s += (v1 + v2)
+        z = (C-D)/np.sqrt(var_s)
+        prob = scipy.stats._stats_py._get_pvalue(z, distributions.norm, alternative)
+    else:
+        raise ValueError("Unknown method "+str(method)+" specified, please "
+                         "use auto, exact or asymptotic.")
+
+    res = scipy.stats._stats_py.SignificanceResult(tau[()], prob[()])
+    res.correlation = tau
+    return res
+
+
+def kendalltau_seasonal(x):
+    """
+    Computes a multivariate Kendall's rank correlation tau, for seasonal data.
+
+    Parameters
+    ----------
+    x : 2-D ndarray
+        Array of seasonal data, with seasons in columns.
+
+    """  # numpydoc ignore=RT01
+    x = ma.array(x, subok=True, copy=False, ndmin=2)
+    (n,m) = x.shape
+    n_p = x.count(0)
+
+    S_szn = sum(msign(x[i:]-x[i]).sum(0) for i in range(n))
+    S_tot = S_szn.sum()
+
+    n_tot = x.count()
+    ties = count_tied_groups(x.compressed())
+    corr_ties = sum(v*k*(k-1) for (k,v) in ties.items())
+    denom_tot = ma.sqrt(1.*n_tot*(n_tot-1)*(n_tot*(n_tot-1)-corr_ties))/2.
+
+    R = rankdata(x, axis=0, use_missing=True)
+    K = ma.empty((m,m), dtype=int)
+    covmat = ma.empty((m,m), dtype=float)
+    denom_szn = ma.empty(m, dtype=float)
+    for j in range(m):
+        ties_j = count_tied_groups(x[:,j].compressed())
+        corr_j = sum(v*k*(k-1) for (k,v) in ties_j.items())
+        cmb = n_p[j]*(n_p[j]-1)
+        for k in range(j,m,1):
+            K[j,k] = sum(msign((x[i:,j]-x[i,j])*(x[i:,k]-x[i,k])).sum()
+                         for i in range(n))
+            covmat[j,k] = (K[j,k] + 4*(R[:,j]*R[:,k]).sum() -
+                           n*(n_p[j]+1)*(n_p[k]+1))/3.
+            K[k,j] = K[j,k]
+            covmat[k,j] = covmat[j,k]
+
+        denom_szn[j] = ma.sqrt(cmb*(cmb-corr_j)) / 2.
+
+    var_szn = covmat.diagonal()
+
+    z_szn = msign(S_szn) * (abs(S_szn)-1) / ma.sqrt(var_szn)
+    z_tot_ind = msign(S_tot) * (abs(S_tot)-1) / ma.sqrt(var_szn.sum())
+    z_tot_dep = msign(S_tot) * (abs(S_tot)-1) / ma.sqrt(covmat.sum())
+
+    prob_szn = special.erfc(abs(z_szn.data)/np.sqrt(2))
+    prob_tot_ind = special.erfc(abs(z_tot_ind)/np.sqrt(2))
+    prob_tot_dep = special.erfc(abs(z_tot_dep)/np.sqrt(2))
+
+    chi2_tot = (z_szn*z_szn).sum()
+    chi2_trd = m * z_szn.mean()**2
+    output = {'seasonal tau': S_szn/denom_szn,
+              'global tau': S_tot/denom_tot,
+              'global tau (alt)': S_tot/denom_szn.sum(),
+              'seasonal p-value': prob_szn,
+              'global p-value (indep)': prob_tot_ind,
+              'global p-value (dep)': prob_tot_dep,
+              'chi2 total': chi2_tot,
+              'chi2 trend': chi2_trd,
+              }
+    return output
+
+
+PointbiserialrResult = namedtuple('PointbiserialrResult', ('correlation',
+                                                           'pvalue'))
+
+
+def pointbiserialr(x, y):
+    """Calculates a point biserial correlation coefficient and its p-value.
+
+    Parameters
+    ----------
+    x : array_like of bools
+        Input array.
+    y : array_like
+        Input array.
+
+    Returns
+    -------
+    correlation : float
+        R value
+    pvalue : float
+        2-tailed p-value
+
+    Notes
+    -----
+    Missing values are considered pair-wise: if a value is missing in x,
+    the corresponding value in y is masked.
+
+    For more details on `pointbiserialr`, see `scipy.stats.pointbiserialr`.
+
+    """
+    x = ma.fix_invalid(x, copy=True).astype(bool)
+    y = ma.fix_invalid(y, copy=True).astype(float)
+    # Get rid of the missing data
+    m = ma.mask_or(ma.getmask(x), ma.getmask(y))
+    if m is not nomask:
+        unmask = np.logical_not(m)
+        x = x[unmask]
+        y = y[unmask]
+
+    n = len(x)
+    # phat is the fraction of x values that are True
+    phat = x.sum() / float(n)
+    y0 = y[~x]  # y-values where x is False
+    y1 = y[x]  # y-values where x is True
+    y0m = y0.mean()
+    y1m = y1.mean()
+
+    rpb = (y1m - y0m)*np.sqrt(phat * (1-phat)) / y.std()
+
+    df = n-2
+    t = rpb*ma.sqrt(df/(1.0-rpb**2))
+    prob = _betai(0.5*df, 0.5, df/(df+t*t))
+
+    return PointbiserialrResult(rpb, prob)
+
+
+def linregress(x, y=None):
+    r"""
+    Calculate a linear least-squares regression for two sets of measurements.
+
+    Parameters
+    ----------
+    x, y : array_like
+        Two sets of measurements.  Both arrays should have the same length N.  If
+        only `x` is given (and ``y=None``), then it must be a two-dimensional
+        array where one dimension has length 2.  The two sets of measurements
+        are then found by splitting the array along the length-2 dimension. In
+        the case where ``y=None`` and `x` is a 2xN array, ``linregress(x)`` is
+        equivalent to ``linregress(x[0], x[1])``.
+
+    Returns
+    -------
+    result : ``LinregressResult`` instance
+        The return value is an object with the following attributes:
+
+        slope : float
+            Slope of the regression line.
+        intercept : float
+            Intercept of the regression line.
+        rvalue : float
+            The Pearson correlation coefficient. The square of ``rvalue``
+            is equal to the coefficient of determination.
+        pvalue : float
+            The p-value for a hypothesis test whose null hypothesis is
+            that the slope is zero, using Wald Test with t-distribution of
+            the test statistic. See `alternative` above for alternative
+            hypotheses.
+        stderr : float
+            Standard error of the estimated slope (gradient), under the
+            assumption of residual normality.
+        intercept_stderr : float
+            Standard error of the estimated intercept, under the assumption
+            of residual normality.
+
+    See Also
+    --------
+    scipy.optimize.curve_fit :
+        Use non-linear least squares to fit a function to data.
+    scipy.optimize.leastsq :
+        Minimize the sum of squares of a set of equations.
+
+    Notes
+    -----
+    Missing values are considered pair-wise: if a value is missing in `x`,
+    the corresponding value in `y` is masked.
+
+    For compatibility with older versions of SciPy, the return value acts
+    like a ``namedtuple`` of length 5, with fields ``slope``, ``intercept``,
+    ``rvalue``, ``pvalue`` and ``stderr``, so one can continue to write::
+
+        slope, intercept, r, p, se = linregress(x, y)
+
+    With that style, however, the standard error of the intercept is not
+    available.  To have access to all the computed values, including the
+    standard error of the intercept, use the return value as an object
+    with attributes, e.g.::
+
+        result = linregress(x, y)
+        print(result.intercept, result.intercept_stderr)
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy import stats
+    >>> rng = np.random.default_rng()
+
+    Generate some data:
+
+    >>> x = rng.random(10)
+    >>> y = 1.6*x + rng.random(10)
+
+    Perform the linear regression:
+
+    >>> res = stats.mstats.linregress(x, y)
+
+    Coefficient of determination (R-squared):
+
+    >>> print(f"R-squared: {res.rvalue**2:.6f}")
+    R-squared: 0.717533
+
+    Plot the data along with the fitted line:
+
+    >>> plt.plot(x, y, 'o', label='original data')
+    >>> plt.plot(x, res.intercept + res.slope*x, 'r', label='fitted line')
+    >>> plt.legend()
+    >>> plt.show()
+
+    Calculate 95% confidence interval on slope and intercept:
+
+    >>> # Two-sided inverse Students t-distribution
+    >>> # p - probability, df - degrees of freedom
+    >>> from scipy.stats import t
+    >>> tinv = lambda p, df: abs(t.ppf(p/2, df))
+
+    >>> ts = tinv(0.05, len(x)-2)
+    >>> print(f"slope (95%): {res.slope:.6f} +/- {ts*res.stderr:.6f}")
+    slope (95%): 1.453392 +/- 0.743465
+    >>> print(f"intercept (95%): {res.intercept:.6f}"
+    ...       f" +/- {ts*res.intercept_stderr:.6f}")
+    intercept (95%): 0.616950 +/- 0.544475
+
+    """
+    if y is None:
+        x = ma.array(x)
+        if x.shape[0] == 2:
+            x, y = x
+        elif x.shape[1] == 2:
+            x, y = x.T
+        else:
+            raise ValueError("If only `x` is given as input, "
+                             "it has to be of shape (2, N) or (N, 2), "
+                             f"provided shape was {x.shape}")
+    else:
+        x = ma.array(x)
+        y = ma.array(y)
+
+    x = x.flatten()
+    y = y.flatten()
+
+    if np.amax(x) == np.amin(x) and len(x) > 1:
+        raise ValueError("Cannot calculate a linear regression "
+                         "if all x values are identical")
+
+    m = ma.mask_or(ma.getmask(x), ma.getmask(y), shrink=False)
+    if m is not nomask:
+        x = ma.array(x, mask=m)
+        y = ma.array(y, mask=m)
+        if np.any(~m):
+            result = _stats_py.linregress(x.data[~m], y.data[~m])
+        else:
+            # All data is masked
+            result = _stats_py.LinregressResult(slope=None, intercept=None,
+                                                rvalue=None, pvalue=None,
+                                                stderr=None,
+                                                intercept_stderr=None)
+    else:
+        result = _stats_py.linregress(x.data, y.data)
+
+    return result
+
+
+def _theilslopes(y, x=None, alpha=0.95, method='separate'):
+    r"""
+    Computes the Theil-Sen estimator for a set of points (x, y).
+
+    `theilslopes` implements a method for robust linear regression.  It
+    computes the slope as the median of all slopes between paired values.
+
+    Parameters
+    ----------
+    y : array_like
+        Dependent variable.
+    x : array_like or None, optional
+        Independent variable. If None, use ``arange(len(y))`` instead.
+    alpha : float, optional
+        Confidence degree between 0 and 1. Default is 95% confidence.
+        Note that `alpha` is symmetric around 0.5, i.e. both 0.1 and 0.9 are
+        interpreted as "find the 90% confidence interval".
+    method : {'joint', 'separate'}, optional
+        Method to be used for computing estimate for intercept.
+        Following methods are supported,
+
+        * 'joint': Uses np.median(y - slope * x) as intercept.
+        * 'separate': Uses np.median(y) - slope * np.median(x)
+                      as intercept.
+
+        The default is 'separate'.
+
+        .. versionadded:: 1.8.0
+
+    Returns
+    -------
+    result : ``TheilslopesResult`` instance
+        The return value is an object with the following attributes:
+
+        slope : float
+            Theil slope.
+        intercept : float
+            Intercept of the Theil line.
+        low_slope : float
+            Lower bound of the confidence interval on `slope`.
+        high_slope : float
+            Upper bound of the confidence interval on `slope`.
+
+    See Also
+    --------
+    siegelslopes : a similar technique using repeated medians
+
+    Notes
+    -----
+    The implementation of `theilslopes` follows [1]_. The intercept is
+    not defined in [1]_, and here it is defined as ``median(y) -
+    slope*median(x)``, which is given in [3]_. Other definitions of
+    the intercept exist in the literature such as  ``median(y - slope*x)``
+    in [4]_. The approach to compute the intercept can be determined by the
+    parameter ``method``. A confidence interval for the intercept is not
+    given as this question is not addressed in [1]_.
+
+    For compatibility with older versions of SciPy, the return value acts
+    like a ``namedtuple`` of length 4, with fields ``slope``, ``intercept``,
+    ``low_slope``, and ``high_slope``, so one can continue to write::
+
+        slope, intercept, low_slope, high_slope = theilslopes(y, x)
+
+    References
+    ----------
+    .. [1] P.K. Sen, "Estimates of the regression coefficient based on
+           Kendall's tau", J. Am. Stat. Assoc., Vol. 63, pp. 1379-1389, 1968.
+    .. [2] H. Theil, "A rank-invariant method of linear and polynomial
+           regression analysis I, II and III",  Nederl. Akad. Wetensch., Proc.
+           53:, pp. 386-392, pp. 521-525, pp. 1397-1412, 1950.
+    .. [3] W.L. Conover, "Practical nonparametric statistics", 2nd ed.,
+           John Wiley and Sons, New York, pp. 493.
+    .. [4] https://en.wikipedia.org/wiki/Theil%E2%80%93Sen_estimator
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> import matplotlib.pyplot as plt
+
+    >>> x = np.linspace(-5, 5, num=150)
+    >>> y = x + np.random.normal(size=x.size)
+    >>> y[11:15] += 10  # add outliers
+    >>> y[-5:] -= 7
+
+    Compute the slope, intercept and 90% confidence interval.  For comparison,
+    also compute the least-squares fit with `linregress`:
+
+    >>> res = stats.theilslopes(y, x, 0.90, method='separate')
+    >>> lsq_res = stats.linregress(x, y)
+
+    Plot the results. The Theil-Sen regression line is shown in red, with the
+    dashed red lines illustrating the confidence interval of the slope (note
+    that the dashed red lines are not the confidence interval of the regression
+    as the confidence interval of the intercept is not included). The green
+    line shows the least-squares fit for comparison.
+
+    >>> fig = plt.figure()
+    >>> ax = fig.add_subplot(111)
+    >>> ax.plot(x, y, 'b.')
+    >>> ax.plot(x, res[1] + res[0] * x, 'r-')
+    >>> ax.plot(x, res[1] + res[2] * x, 'r--')
+    >>> ax.plot(x, res[1] + res[3] * x, 'r--')
+    >>> ax.plot(x, lsq_res[1] + lsq_res[0] * x, 'g-')
+    >>> plt.show()
+
+    """
+    if method not in ['joint', 'separate']:
+        raise ValueError("method must be either 'joint' or 'separate'."
+                         f"'{method}' is invalid.")
+    # We copy both x and y so we can use _find_repeats.
+    y = np.array(y, dtype=float, copy=True).ravel()
+    if x is None:
+        x = np.arange(len(y), dtype=float)
+    else:
+        x = np.array(x, dtype=float, copy=True).ravel()
+        if len(x) != len(y):
+            raise ValueError("Array shapes are incompatible for broadcasting.")
+    if len(x) < 2:
+        raise ValueError("`x` and `y` must have length at least 2.")
+
+    # Compute sorted slopes only when deltax > 0
+    deltax = x[:, np.newaxis] - x
+    deltay = y[:, np.newaxis] - y
+    slopes = deltay[deltax > 0] / deltax[deltax > 0]
+    if not slopes.size:
+        msg = "All `x` coordinates are identical."
+        warnings.warn(msg, RuntimeWarning, stacklevel=2)
+    slopes.sort()
+    medslope = np.median(slopes)
+    if method == 'joint':
+        medinter = np.median(y - medslope * x)
+    else:
+        medinter = np.median(y) - medslope * np.median(x)
+    # Now compute confidence intervals
+    if alpha > 0.5:
+        alpha = 1. - alpha
+
+    z = distributions.norm.ppf(alpha / 2.)
+    # This implements (2.6) from Sen (1968)
+    _, nxreps = _find_repeats(x)
+    _, nyreps = _find_repeats(y)
+    nt = len(slopes)       # N in Sen (1968)
+    ny = len(y)            # n in Sen (1968)
+    # Equation 2.6 in Sen (1968):
+    sigsq = 1/18. * (ny * (ny-1) * (2*ny+5) -
+                     sum(k * (k-1) * (2*k + 5) for k in nxreps) -
+                     sum(k * (k-1) * (2*k + 5) for k in nyreps))
+    # Find the confidence interval indices in `slopes`
+    try:
+        sigma = np.sqrt(sigsq)
+        Ru = min(int(np.round((nt - z*sigma)/2.)), len(slopes)-1)
+        Rl = max(int(np.round((nt + z*sigma)/2.)) - 1, 0)
+        delta = slopes[[Rl, Ru]]
+    except (ValueError, IndexError):
+        delta = (np.nan, np.nan)
+
+    return TheilslopesResult(slope=medslope, intercept=medinter,
+                             low_slope=delta[0], high_slope=delta[1])
+
+
+def theilslopes(y, x=None, alpha=0.95, method='separate'):
+    r"""
+    Computes the Theil-Sen estimator for a set of points (x, y).
+
+    `theilslopes` implements a method for robust linear regression.  It
+    computes the slope as the median of all slopes between paired values.
+
+    Parameters
+    ----------
+    y : array_like
+        Dependent variable.
+    x : array_like or None, optional
+        Independent variable. If None, use ``arange(len(y))`` instead.
+    alpha : float, optional
+        Confidence degree between 0 and 1. Default is 95% confidence.
+        Note that `alpha` is symmetric around 0.5, i.e. both 0.1 and 0.9 are
+        interpreted as "find the 90% confidence interval".
+    method : {'joint', 'separate'}, optional
+        Method to be used for computing estimate for intercept.
+        Following methods are supported,
+
+        * 'joint': Uses np.median(y - slope * x) as intercept.
+        * 'separate': Uses np.median(y) - slope * np.median(x)
+                      as intercept.
+
+        The default is 'separate'.
+
+        .. versionadded:: 1.8.0
+
+    Returns
+    -------
+    result : ``TheilslopesResult`` instance
+        The return value is an object with the following attributes:
+
+        slope : float
+            Theil slope.
+        intercept : float
+            Intercept of the Theil line.
+        low_slope : float
+            Lower bound of the confidence interval on `slope`.
+        high_slope : float
+            Upper bound of the confidence interval on `slope`.
+
+    See Also
+    --------
+    siegelslopes : a similar technique using repeated medians
+
+
+    Notes
+    -----
+    For more details on `theilslopes`, see `scipy.stats.theilslopes`.
+
+    """
+    y = ma.asarray(y).flatten()
+    if x is None:
+        x = ma.arange(len(y), dtype=float)
+    else:
+        x = ma.asarray(x).flatten()
+        if len(x) != len(y):
+            raise ValueError(f"Incompatible lengths ! ({len(y)}<>{len(x)})")
+
+    m = ma.mask_or(ma.getmask(x), ma.getmask(y))
+    y._mask = x._mask = m
+    # Disregard any masked elements of x or y
+    y = y.compressed()
+    x = x.compressed().astype(float)
+    # We now have unmasked arrays so can use `scipy.stats.theilslopes`
+    return _theilslopes(y, x, alpha=alpha, method=method)
+
+
+def _siegelslopes(y, x=None, method="hierarchical"):
+    if method not in ['hierarchical', 'separate']:
+        raise ValueError("method can only be 'hierarchical' or 'separate'")
+    y = np.asarray(y).ravel()
+    if x is None:
+        x = np.arange(len(y), dtype=float)
+    else:
+        x = np.asarray(x, dtype=float).ravel()
+        if len(x) != len(y):
+            raise ValueError("Array shapes are incompatible for broadcasting.")
+    if len(x) < 2:
+        raise ValueError("`x` and `y` must have length at least 2.")
+
+    dtype = np.result_type(x, y, np.float32)  # use at least float32
+    y, x = y.astype(dtype), x.astype(dtype)
+    medslope, medinter = siegelslopes_pythran(y, x, method)
+    medslope, medinter = np.asarray(medslope)[()], np.asarray(medinter)[()]
+    return SiegelslopesResult(slope=medslope, intercept=medinter)
+
+
+def siegelslopes(y, x=None, method="hierarchical"):
+    r"""
+    Computes the Siegel estimator for a set of points (x, y).
+
+    `siegelslopes` implements a method for robust linear regression
+    using repeated medians to fit a line to the points (x, y).
+    The method is robust to outliers with an asymptotic breakdown point
+    of 50%.
+
+    Parameters
+    ----------
+    y : array_like
+        Dependent variable.
+    x : array_like or None, optional
+        Independent variable. If None, use ``arange(len(y))`` instead.
+    method : {'hierarchical', 'separate'}
+        If 'hierarchical', estimate the intercept using the estimated
+        slope ``slope`` (default option).
+        If 'separate', estimate the intercept independent of the estimated
+        slope. See Notes for details.
+
+    Returns
+    -------
+    result : ``SiegelslopesResult`` instance
+        The return value is an object with the following attributes:
+
+        slope : float
+            Estimate of the slope of the regression line.
+        intercept : float
+            Estimate of the intercept of the regression line.
+
+    See Also
+    --------
+    theilslopes : a similar technique without repeated medians
+
+    Notes
+    -----
+    For more details on `siegelslopes`, see `scipy.stats.siegelslopes`.
+
+    """
+    y = ma.asarray(y).ravel()
+    if x is None:
+        x = ma.arange(len(y), dtype=float)
+    else:
+        x = ma.asarray(x).ravel()
+        if len(x) != len(y):
+            raise ValueError(f"Incompatible lengths ! ({len(y)}<>{len(x)})")
+
+    m = ma.mask_or(ma.getmask(x), ma.getmask(y))
+    y._mask = x._mask = m
+    # Disregard any masked elements of x or y
+    y = y.compressed()
+    x = x.compressed().astype(float)
+    # We now have unmasked arrays so can use `scipy.stats.siegelslopes`
+    return _siegelslopes(y, x, method=method)
+
+
+SenSeasonalSlopesResult = _make_tuple_bunch('SenSeasonalSlopesResult',
+                                            ['intra_slope', 'inter_slope'])
+
+
+def sen_seasonal_slopes(x):
+    r"""
+    Computes seasonal Theil-Sen and Kendall slope estimators.
+
+    The seasonal generalization of Sen's slope computes the slopes between all
+    pairs of values within a "season" (column) of a 2D array. It returns an
+    array containing the median of these "within-season" slopes for each
+    season (the Theil-Sen slope estimator of each season), and it returns the
+    median of the within-season slopes across all seasons (the seasonal Kendall
+    slope estimator).
+
+    Parameters
+    ----------
+    x : 2D array_like
+        Each column of `x` contains measurements of the dependent variable
+        within a season. The independent variable (usually time) of each season
+        is assumed to be ``np.arange(x.shape[0])``.
+
+    Returns
+    -------
+    result : ``SenSeasonalSlopesResult`` instance
+        The return value is an object with the following attributes:
+
+        intra_slope : ndarray
+            For each season, the Theil-Sen slope estimator: the median of
+            within-season slopes.
+        inter_slope : float
+            The seasonal Kendall slope estimator: the median of within-season
+            slopes *across all* seasons.
+
+    See Also
+    --------
+    theilslopes : the analogous function for non-seasonal data
+    scipy.stats.theilslopes : non-seasonal slopes for non-masked arrays
+
+    Notes
+    -----
+    The slopes :math:`d_{ijk}` within season :math:`i` are:
+
+    .. math::
+
+        d_{ijk} = \frac{x_{ij} - x_{ik}}
+                            {j - k}
+
+    for pairs of distinct integer indices :math:`j, k` of :math:`x`.
+
+    Element :math:`i` of the returned `intra_slope` array is the median of the
+    :math:`d_{ijk}` over all :math:`j < k`; this is the Theil-Sen slope
+    estimator of season :math:`i`. The returned `inter_slope` value, better
+    known as the seasonal Kendall slope estimator, is the median of the
+    :math:`d_{ijk}` over all :math:`i, j, k`.
+
+    References
+    ----------
+    .. [1] Hirsch, Robert M., James R. Slack, and Richard A. Smith.
+           "Techniques of trend analysis for monthly water quality data."
+           *Water Resources Research* 18.1 (1982): 107-121.
+
+    Examples
+    --------
+    Suppose we have 100 observations of a dependent variable for each of four
+    seasons:
+
+    >>> import numpy as np
+    >>> rng = np.random.default_rng()
+    >>> x = rng.random(size=(100, 4))
+
+    We compute the seasonal slopes as:
+
+    >>> from scipy import stats
+    >>> intra_slope, inter_slope = stats.mstats.sen_seasonal_slopes(x)
+
+    If we define a function to compute all slopes between observations within
+    a season:
+
+    >>> def dijk(yi):
+    ...     n = len(yi)
+    ...     x = np.arange(n)
+    ...     dy = yi - yi[:, np.newaxis]
+    ...     dx = x - x[:, np.newaxis]
+    ...     # we only want unique pairs of distinct indices
+    ...     mask = np.triu(np.ones((n, n), dtype=bool), k=1)
+    ...     return dy[mask]/dx[mask]
+
+    then element ``i`` of ``intra_slope`` is the median of ``dijk[x[:, i]]``:
+
+    >>> i = 2
+    >>> np.allclose(np.median(dijk(x[:, i])), intra_slope[i])
+    True
+
+    and ``inter_slope`` is the median of the values returned by ``dijk`` for
+    all seasons:
+
+    >>> all_slopes = np.concatenate([dijk(x[:, i]) for i in range(x.shape[1])])
+    >>> np.allclose(np.median(all_slopes), inter_slope)
+    True
+
+    Because the data are randomly generated, we would expect the median slopes
+    to be nearly zero both within and across all seasons, and indeed they are:
+
+    >>> intra_slope.data
+    array([ 0.00124504, -0.00277761, -0.00221245, -0.00036338])
+    >>> inter_slope
+    -0.0010511779872922058
+
+    """
+    x = ma.array(x, subok=True, copy=False, ndmin=2)
+    (n,_) = x.shape
+    # Get list of slopes per season
+    szn_slopes = ma.vstack([(x[i+1:]-x[i])/np.arange(1,n-i)[:,None]
+                            for i in range(n)])
+    szn_medslopes = ma.median(szn_slopes, axis=0)
+    medslope = ma.median(szn_slopes, axis=None)
+    return SenSeasonalSlopesResult(szn_medslopes, medslope)
+
+
+Ttest_1sampResult = namedtuple('Ttest_1sampResult', ('statistic', 'pvalue'))
+
+
+def ttest_1samp(a, popmean, axis=0, alternative='two-sided'):
+    """
+    Calculates the T-test for the mean of ONE group of scores.
+
+    Parameters
+    ----------
+    a : array_like
+        sample observation
+    popmean : float or array_like
+        expected value in null hypothesis, if array_like than it must have the
+        same shape as `a` excluding the axis dimension
+    axis : int or None, optional
+        Axis along which to compute test. If None, compute over the whole
+        array `a`.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis.
+        The following options are available (default is 'two-sided'):
+
+        * 'two-sided': the mean of the underlying distribution of the sample
+          is different than the given population mean (`popmean`)
+        * 'less': the mean of the underlying distribution of the sample is
+          less than the given population mean (`popmean`)
+        * 'greater': the mean of the underlying distribution of the sample is
+          greater than the given population mean (`popmean`)
+
+        .. versionadded:: 1.7.0
+
+    Returns
+    -------
+    statistic : float or array
+        t-statistic
+    pvalue : float or array
+        The p-value
+
+    Notes
+    -----
+    For more details on `ttest_1samp`, see `scipy.stats.ttest_1samp`.
+
+    """
+    a, axis = _chk_asarray(a, axis)
+    if a.size == 0:
+        return (np.nan, np.nan)
+
+    x = a.mean(axis=axis)
+    v = a.var(axis=axis, ddof=1)
+    n = a.count(axis=axis)
+    # force df to be an array for masked division not to throw a warning
+    df = ma.asanyarray(n - 1.0)
+    svar = ((n - 1.0) * v) / df
+    with np.errstate(divide='ignore', invalid='ignore'):
+        t = (x - popmean) / ma.sqrt(svar / n)
+
+    t, prob = _ttest_finish(df, t, alternative)
+    return Ttest_1sampResult(t, prob)
+
+
+ttest_onesamp = ttest_1samp
+
+
+Ttest_indResult = namedtuple('Ttest_indResult', ('statistic', 'pvalue'))
+
+
+def ttest_ind(a, b, axis=0, equal_var=True, alternative='two-sided'):
+    """
+    Calculates the T-test for the means of TWO INDEPENDENT samples of scores.
+
+    Parameters
+    ----------
+    a, b : array_like
+        The arrays must have the same shape, except in the dimension
+        corresponding to `axis` (the first, by default).
+    axis : int or None, optional
+        Axis along which to compute test. If None, compute over the whole
+        arrays, `a`, and `b`.
+    equal_var : bool, optional
+        If True, perform a standard independent 2 sample test that assumes equal
+        population variances.
+        If False, perform Welch's t-test, which does not assume equal population
+        variance.
+
+        .. versionadded:: 0.17.0
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis.
+        The following options are available (default is 'two-sided'):
+
+        * 'two-sided': the means of the distributions underlying the samples
+          are unequal.
+        * 'less': the mean of the distribution underlying the first sample
+          is less than the mean of the distribution underlying the second
+          sample.
+        * 'greater': the mean of the distribution underlying the first
+          sample is greater than the mean of the distribution underlying
+          the second sample.
+
+        .. versionadded:: 1.7.0
+
+    Returns
+    -------
+    statistic : float or array
+        The calculated t-statistic.
+    pvalue : float or array
+        The p-value.
+
+    Notes
+    -----
+    For more details on `ttest_ind`, see `scipy.stats.ttest_ind`.
+
+    """
+    a, b, axis = _chk2_asarray(a, b, axis)
+
+    if a.size == 0 or b.size == 0:
+        return Ttest_indResult(np.nan, np.nan)
+
+    (x1, x2) = (a.mean(axis), b.mean(axis))
+    (v1, v2) = (a.var(axis=axis, ddof=1), b.var(axis=axis, ddof=1))
+    (n1, n2) = (a.count(axis), b.count(axis))
+
+    if equal_var:
+        # force df to be an array for masked division not to throw a warning
+        df = ma.asanyarray(n1 + n2 - 2.0)
+        svar = ((n1-1)*v1+(n2-1)*v2) / df
+        denom = ma.sqrt(svar*(1.0/n1 + 1.0/n2))  # n-D computation here!
+    else:
+        vn1 = v1/n1
+        vn2 = v2/n2
+        with np.errstate(divide='ignore', invalid='ignore'):
+            df = (vn1 + vn2)**2 / (vn1**2 / (n1 - 1) + vn2**2 / (n2 - 1))
+
+        # If df is undefined, variances are zero.
+        # It doesn't matter what df is as long as it is not NaN.
+        df = np.where(np.isnan(df), 1, df)
+        denom = ma.sqrt(vn1 + vn2)
+
+    with np.errstate(divide='ignore', invalid='ignore'):
+        t = (x1-x2) / denom
+
+    t, prob = _ttest_finish(df, t, alternative)
+    return Ttest_indResult(t, prob)
+
+
+Ttest_relResult = namedtuple('Ttest_relResult', ('statistic', 'pvalue'))
+
+
+def ttest_rel(a, b, axis=0, alternative='two-sided'):
+    """
+    Calculates the T-test on TWO RELATED samples of scores, a and b.
+
+    Parameters
+    ----------
+    a, b : array_like
+        The arrays must have the same shape.
+    axis : int or None, optional
+        Axis along which to compute test. If None, compute over the whole
+        arrays, `a`, and `b`.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis.
+        The following options are available (default is 'two-sided'):
+
+        * 'two-sided': the means of the distributions underlying the samples
+          are unequal.
+        * 'less': the mean of the distribution underlying the first sample
+          is less than the mean of the distribution underlying the second
+          sample.
+        * 'greater': the mean of the distribution underlying the first
+          sample is greater than the mean of the distribution underlying
+          the second sample.
+
+        .. versionadded:: 1.7.0
+
+    Returns
+    -------
+    statistic : float or array
+        t-statistic
+    pvalue : float or array
+        two-tailed p-value
+
+    Notes
+    -----
+    For more details on `ttest_rel`, see `scipy.stats.ttest_rel`.
+
+    """
+    a, b, axis = _chk2_asarray(a, b, axis)
+    if len(a) != len(b):
+        raise ValueError('unequal length arrays')
+
+    if a.size == 0 or b.size == 0:
+        return Ttest_relResult(np.nan, np.nan)
+
+    n = a.count(axis)
+    df = ma.asanyarray(n-1.0)
+    d = (a-b).astype('d')
+    dm = d.mean(axis)
+    v = d.var(axis=axis, ddof=1)
+    denom = ma.sqrt(v / n)
+    with np.errstate(divide='ignore', invalid='ignore'):
+        t = dm / denom
+
+    t, prob = _ttest_finish(df, t, alternative)
+    return Ttest_relResult(t, prob)
+
+
+MannwhitneyuResult = namedtuple('MannwhitneyuResult', ('statistic',
+                                                       'pvalue'))
+
+
+def mannwhitneyu(x,y, use_continuity=True):
+    """
+    Computes the Mann-Whitney statistic
+
+    Missing values in `x` and/or `y` are discarded.
+
+    Parameters
+    ----------
+    x : sequence
+        Input
+    y : sequence
+        Input
+    use_continuity : {True, False}, optional
+        Whether a continuity correction (1/2.) should be taken into account.
+
+    Returns
+    -------
+    statistic : float
+        The minimum of the Mann-Whitney statistics
+    pvalue : float
+        Approximate two-sided p-value assuming a normal distribution.
+
+    """
+    x = ma.asarray(x).compressed().view(ndarray)
+    y = ma.asarray(y).compressed().view(ndarray)
+    ranks = rankdata(np.concatenate([x,y]))
+    (nx, ny) = (len(x), len(y))
+    nt = nx + ny
+    U = ranks[:nx].sum() - nx*(nx+1)/2.
+    U = max(U, nx*ny - U)
+    u = nx*ny - U
+
+    mu = (nx*ny)/2.
+    sigsq = (nt**3 - nt)/12.
+    ties = count_tied_groups(ranks)
+    sigsq -= sum(v*(k**3-k) for (k,v) in ties.items())/12.
+    sigsq *= nx*ny/float(nt*(nt-1))
+
+    if use_continuity:
+        z = (U - 1/2. - mu) / ma.sqrt(sigsq)
+    else:
+        z = (U - mu) / ma.sqrt(sigsq)
+
+    prob = special.erfc(abs(z)/np.sqrt(2))
+    return MannwhitneyuResult(u, prob)
+
+
+KruskalResult = namedtuple('KruskalResult', ('statistic', 'pvalue'))
+
+
+def kruskal(*samples):
+    """
+    Compute the Kruskal-Wallis H-test for independent samples
+
+    Parameters
+    ----------
+    *samples : array_like
+       Two or more arrays with the sample measurements can be given as
+       arguments.
+
+    Returns
+    -------
+    statistic : float
+       The Kruskal-Wallis H statistic, corrected for ties
+    pvalue : float
+       The p-value for the test using the assumption that H has a chi
+       square distribution
+
+    Notes
+    -----
+    For more details on `kruskal`, see `scipy.stats.kruskal`.
+
+    Examples
+    --------
+    >>> from scipy.stats.mstats import kruskal
+
+    Random samples from three different brands of batteries were tested
+    to see how long the charge lasted. Results were as follows:
+
+    >>> a = [6.3, 5.4, 5.7, 5.2, 5.0]
+    >>> b = [6.9, 7.0, 6.1, 7.9]
+    >>> c = [7.2, 6.9, 6.1, 6.5]
+
+    Test the hypothesis that the distribution functions for all of the brands'
+    durations are identical. Use 5% level of significance.
+
+    >>> kruskal(a, b, c)
+    KruskalResult(statistic=7.113812154696133, pvalue=0.028526948491942164)
+
+    The null hypothesis is rejected at the 5% level of significance
+    because the returned p-value is less than the critical value of 5%.
+
+    """
+    output = argstoarray(*samples)
+    ranks = ma.masked_equal(rankdata(output, use_missing=False), 0)
+    sumrk = ranks.sum(-1)
+    ngrp = ranks.count(-1)
+    ntot = ranks.count()
+    H = 12./(ntot*(ntot+1)) * (sumrk**2/ngrp).sum() - 3*(ntot+1)
+    # Tie correction
+    ties = count_tied_groups(ranks)
+    T = 1. - sum(v*(k**3-k) for (k,v) in ties.items())/float(ntot**3-ntot)
+    if T == 0:
+        raise ValueError('All numbers are identical in kruskal')
+
+    H /= T
+    df = len(output) - 1
+    prob = distributions.chi2.sf(H, df)
+    return KruskalResult(H, prob)
+
+
+kruskalwallis = kruskal
+
+
+@_rename_parameter("mode", "method")
+def ks_1samp(x, cdf, args=(), alternative="two-sided", method='auto'):
+    """
+    Computes the Kolmogorov-Smirnov test on one sample of masked values.
+
+    Missing values in `x` are discarded.
+
+    Parameters
+    ----------
+    x : array_like
+        a 1-D array of observations of random variables.
+    cdf : str or callable
+        If a string, it should be the name of a distribution in `scipy.stats`.
+        If a callable, that callable is used to calculate the cdf.
+    args : tuple, sequence, optional
+        Distribution parameters, used if `cdf` is a string.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Indicates the alternative hypothesis.  Default is 'two-sided'.
+    method : {'auto', 'exact', 'asymp'}, optional
+        Defines the method used for calculating the p-value.
+        The following options are available (default is 'auto'):
+
+        * 'auto' : use 'exact' for small size arrays, 'asymp' for large
+        * 'exact' : use approximation to exact distribution of test statistic
+        * 'asymp' : use asymptotic distribution of test statistic
+
+    Returns
+    -------
+    d : float
+        Value of the Kolmogorov Smirnov test
+    p : float
+        Corresponding p-value.
+
+    """
+    alternative = {'t': 'two-sided', 'g': 'greater', 'l': 'less'}.get(
+       alternative.lower()[0], alternative)
+    return scipy.stats._stats_py.ks_1samp(
+        x, cdf, args=args, alternative=alternative, method=method)
+
+
+@_rename_parameter("mode", "method")
+def ks_2samp(data1, data2, alternative="two-sided", method='auto'):
+    """
+    Computes the Kolmogorov-Smirnov test on two samples.
+
+    Missing values in `x` and/or `y` are discarded.
+
+    Parameters
+    ----------
+    data1 : array_like
+        First data set
+    data2 : array_like
+        Second data set
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Indicates the alternative hypothesis.  Default is 'two-sided'.
+    method : {'auto', 'exact', 'asymp'}, optional
+        Defines the method used for calculating the p-value.
+        The following options are available (default is 'auto'):
+
+        * 'auto' : use 'exact' for small size arrays, 'asymp' for large
+        * 'exact' : use approximation to exact distribution of test statistic
+        * 'asymp' : use asymptotic distribution of test statistic
+
+    Returns
+    -------
+    d : float
+        Value of the Kolmogorov Smirnov test
+    p : float
+        Corresponding p-value.
+
+    """
+    # Ideally this would be accomplished by
+    # ks_2samp = scipy.stats._stats_py.ks_2samp
+    # but the circular dependencies between _mstats_basic and stats prevent that.
+    alternative = {'t': 'two-sided', 'g': 'greater', 'l': 'less'}.get(
+       alternative.lower()[0], alternative)
+    return scipy.stats._stats_py.ks_2samp(data1, data2,
+                                          alternative=alternative,
+                                          method=method)
+
+
+ks_twosamp = ks_2samp
+
+
+@_rename_parameter("mode", "method")
+def kstest(data1, data2, args=(), alternative='two-sided', method='auto'):
+    """
+    Performs the Kolmogorov-Smirnov test for goodness of fit.
+
+    Parameters
+    ----------
+    data1 : array_like
+    data2 : str, callable or array_like
+    args : tuple, sequence, optional
+        Distribution parameters, used if `data1` or `data2` are strings.
+    alternative : str, as documented in stats.kstest
+    method : str, as documented in stats.kstest
+
+    Returns
+    -------
+    tuple of (K-S statistic, probability)
+
+    """  # numpydoc ignore=RT03
+    return scipy.stats._stats_py.kstest(data1, data2, args,
+                                        alternative=alternative, method=method)
+
+
+def trima(a, limits=None, inclusive=(True,True)):
+    """
+    Trims an array by masking the data outside some given limits.
+
+    Returns a masked version of the input array.
+
+    Parameters
+    ----------
+    a : array_like
+        Input array.
+    limits : {None, tuple}, optional
+        Tuple of (lower limit, upper limit) in absolute values.
+        Values of the input array lower (greater) than the lower (upper) limit
+        will be masked.  A limit is None indicates an open interval.
+    inclusive : (bool, bool) tuple, optional
+        Tuple of (lower flag, upper flag), indicating whether values exactly
+        equal to the lower (upper) limit are allowed.
+
+    Examples
+    --------
+    >>> from scipy.stats.mstats import trima
+    >>> import numpy as np
+
+    >>> a = np.arange(10)
+
+    The interval is left-closed and right-open, i.e., `[2, 8)`.
+    Trim the array by keeping only values in the interval.
+
+    >>> trima(a, limits=(2, 8), inclusive=(True, False))
+    masked_array(data=[--, --, 2, 3, 4, 5, 6, 7, --, --],
+                 mask=[ True,  True, False, False, False, False, False, False,
+                        True,  True],
+           fill_value=999999)
+
+    """  # numpydoc ignore=RT01
+    a = ma.asarray(a)
+    a.unshare_mask()
+    if (limits is None) or (limits == (None, None)):
+        return a
+
+    (lower_lim, upper_lim) = limits
+    (lower_in, upper_in) = inclusive
+    condition = False
+    if lower_lim is not None:
+        if lower_in:
+            condition |= (a < lower_lim)
+        else:
+            condition |= (a <= lower_lim)
+
+    if upper_lim is not None:
+        if upper_in:
+            condition |= (a > upper_lim)
+        else:
+            condition |= (a >= upper_lim)
+
+    a[condition.filled(True)] = masked
+    return a
+
+
+def trimr(a, limits=None, inclusive=(True, True), axis=None):
+    """
+    Trims an array by masking some proportion of the data on each end.
+    Returns a masked version of the input array.
+
+    Parameters
+    ----------
+    a : sequence
+        Input array.
+    limits : {None, tuple}, optional
+        Tuple of the percentages to cut on each side of the array, with respect
+        to the number of unmasked data, as floats between 0. and 1.
+        Noting n the number of unmasked data before trimming, the
+        (n*limits[0])th smallest data and the (n*limits[1])th largest data are
+        masked, and the total number of unmasked data after trimming is
+        n*(1.-sum(limits)).  The value of one limit can be set to None to
+        indicate an open interval.
+    inclusive : {(True,True) tuple}, optional
+        Tuple of flags indicating whether the number of data being masked on
+        the left (right) end should be truncated (True) or rounded (False) to
+        integers.
+    axis : {None,int}, optional
+        Axis along which to trim. If None, the whole array is trimmed, but its
+        shape is maintained.
+
+    """  # numpydoc ignore=RT01
+    def _trimr1D(a, low_limit, up_limit, low_inclusive, up_inclusive):
+        n = a.count()
+        idx = a.argsort()
+        if low_limit:
+            if low_inclusive:
+                lowidx = int(low_limit*n)
+            else:
+                lowidx = int(np.round(low_limit*n))
+            a[idx[:lowidx]] = masked
+        if up_limit is not None:
+            if up_inclusive:
+                upidx = n - int(n*up_limit)
+            else:
+                upidx = n - int(np.round(n*up_limit))
+            a[idx[upidx:]] = masked
+        return a
+
+    a = ma.asarray(a)
+    a.unshare_mask()
+    if limits is None:
+        return a
+
+    # Check the limits
+    (lolim, uplim) = limits
+    errmsg = "The proportion to cut from the %s should be between 0. and 1."
+    if lolim is not None:
+        if lolim > 1. or lolim < 0:
+            raise ValueError(errmsg % 'beginning' + f"(got {lolim})")
+    if uplim is not None:
+        if uplim > 1. or uplim < 0:
+            raise ValueError(errmsg % 'end' + f"(got {uplim})")
+
+    (loinc, upinc) = inclusive
+
+    if axis is None:
+        shp = a.shape
+        return _trimr1D(a.ravel(),lolim,uplim,loinc,upinc).reshape(shp)
+    else:
+        return ma.apply_along_axis(_trimr1D, axis, a, lolim,uplim,loinc,upinc)
+
+
+trimdoc = _dedent_for_py313("""
+    Parameters
+    ----------
+    a : sequence
+        Input array
+    limits : {None, tuple}, optional
+        If `relative` is False, tuple (lower limit, upper limit) in absolute values.
+        Values of the input array lower (greater) than the lower (upper) limit are
+        masked.
+
+        If `relative` is True, tuple (lower percentage, upper percentage) to cut
+        on each side of the  array, with respect to the number of unmasked data.
+
+        Noting n the number of unmasked data before trimming, the (n*limits[0])th
+        smallest data and the (n*limits[1])th largest data are masked, and the
+        total number of unmasked data after trimming is n*(1.-sum(limits))
+        In each case, the value of one limit can be set to None to indicate an
+        open interval.
+
+        If limits is None, no trimming is performed
+    inclusive : {(bool, bool) tuple}, optional
+        If `relative` is False, tuple indicating whether values exactly equal
+        to the absolute limits are allowed.
+        If `relative` is True, tuple indicating whether the number of data
+        being masked on each side should be rounded (True) or truncated
+        (False).
+    relative : bool, optional
+        Whether to consider the limits as absolute values (False) or proportions
+        to cut (True).
+    axis : int, optional
+        Axis along which to trim.""")
+
+
+def trim(a, limits=None, inclusive=(True,True), relative=False, axis=None):
+    """
+    Trims an array by masking the data outside some given limits.
+
+    Returns a masked version of the input array.
+
+    %s
+
+    Examples
+    --------
+    >>> from scipy.stats.mstats import trim
+    >>> z = [ 1, 2, 3, 4, 5, 6, 7, 8, 9,10]
+    >>> print(trim(z,(3,8)))
+    [-- -- 3 4 5 6 7 8 -- --]
+    >>> print(trim(z,(0.1,0.2),relative=True))
+    [-- 2 3 4 5 6 7 8 -- --]
+
+    """  # numpydoc ignore=RT01
+    if relative:
+        return trimr(a, limits=limits, inclusive=inclusive, axis=axis)
+    else:
+        return trima(a, limits=limits, inclusive=inclusive)
+
+
+if trim.__doc__:
+    trim.__doc__ = trim.__doc__ % trimdoc
+
+
+def trimboth(data, proportiontocut=0.2, inclusive=(True,True), axis=None):
+    """
+    Trims the smallest and largest data values.
+
+    Trims the `data` by masking the ``int(proportiontocut * n)`` smallest and
+    ``int(proportiontocut * n)`` largest values of data along the given axis,
+    where n is the number of unmasked values before trimming.
+
+    Parameters
+    ----------
+    data : ndarray
+        Data to trim.
+    proportiontocut : float, optional
+        Percentage of trimming (as a float between 0 and 1).
+        If n is the number of unmasked values before trimming, the number of
+        values after trimming is ``(1 - 2*proportiontocut) * n``.
+        Default is 0.2.
+    inclusive : {(bool, bool) tuple}, optional
+        Tuple indicating whether the number of data being masked on each side
+        should be rounded (True) or truncated (False).
+    axis : int, optional
+        Axis along which to perform the trimming.
+        If None, the input array is first flattened.
+
+    """  # numpydoc ignore=RT01
+    return trimr(data, limits=(proportiontocut,proportiontocut),
+                 inclusive=inclusive, axis=axis)
+
+
+def trimtail(data, proportiontocut=0.2, tail='left', inclusive=(True,True),
+             axis=None):
+    """
+    Trims the data by masking values from one tail.
+
+    Parameters
+    ----------
+    data : array_like
+        Data to trim.
+    proportiontocut : float, optional
+        Percentage of trimming. If n is the number of unmasked values
+        before trimming, the number of values after trimming is
+        ``(1 - proportiontocut) * n``.  Default is 0.2.
+    tail : {'left','right'}, optional
+        If 'left' the `proportiontocut` lowest values will be masked.
+        If 'right' the `proportiontocut` highest values will be masked.
+        Default is 'left'.
+    inclusive : {(bool, bool) tuple}, optional
+        Tuple indicating whether the number of data being masked on each side
+        should be rounded (True) or truncated (False).  Default is
+        (True, True).
+    axis : int, optional
+        Axis along which to perform the trimming.
+        If None, the input array is first flattened.  Default is None.
+
+    Returns
+    -------
+    trimtail : ndarray
+        Returned array of same shape as `data` with masked tail values.
+
+    """
+    tail = str(tail).lower()[0]
+    if tail == 'l':
+        limits = (proportiontocut,None)
+    elif tail == 'r':
+        limits = (None, proportiontocut)
+    else:
+        raise TypeError("The tail argument should be in ('left','right')")
+
+    return trimr(data, limits=limits, axis=axis, inclusive=inclusive)
+
+
+trim1 = trimtail
+
+
+def trimmed_mean(a, limits=(0.1,0.1), inclusive=(1,1), relative=True,
+                 axis=None):
+    """Returns the trimmed mean of the data along the given axis.
+
+    %s
+
+    """  # numpydoc ignore=RT01
+    if (not isinstance(limits,tuple)) and isinstance(limits,float):
+        limits = (limits, limits)
+    if relative:
+        return trimr(a,limits=limits,inclusive=inclusive,axis=axis).mean(axis=axis)
+    else:
+        return trima(a,limits=limits,inclusive=inclusive).mean(axis=axis)
+
+
+if trimmed_mean.__doc__:
+    trimmed_mean.__doc__ = trimmed_mean.__doc__ % trimdoc
+
+
+def trimmed_var(a, limits=(0.1,0.1), inclusive=(1,1), relative=True,
+                axis=None, ddof=0):
+    """Returns the trimmed variance of the data along the given axis.
+
+    %s
+    ddof : {0,integer}, optional
+        Means Delta Degrees of Freedom. The denominator used during computations
+        is (n-ddof). DDOF=0 corresponds to a biased estimate, DDOF=1 to an un-
+        biased estimate of the variance.
+
+    """  # numpydoc ignore=RT01
+    if (not isinstance(limits,tuple)) and isinstance(limits,float):
+        limits = (limits, limits)
+    if relative:
+        out = trimr(a,limits=limits, inclusive=inclusive,axis=axis)
+    else:
+        out = trima(a,limits=limits,inclusive=inclusive)
+
+    return out.var(axis=axis, ddof=ddof)
+
+
+if trimmed_var.__doc__:
+    trimmed_var.__doc__ = trimmed_var.__doc__ % trimdoc
+
+
+def trimmed_std(a, limits=(0.1,0.1), inclusive=(1,1), relative=True,
+                axis=None, ddof=0):
+    """Returns the trimmed standard deviation of the data along the given axis.
+
+    %s
+    ddof : {0,integer}, optional
+        Means Delta Degrees of Freedom. The denominator used during computations
+        is (n-ddof). DDOF=0 corresponds to a biased estimate, DDOF=1 to an un-
+        biased estimate of the variance.
+
+    """  # numpydoc ignore=RT01
+    if (not isinstance(limits,tuple)) and isinstance(limits,float):
+        limits = (limits, limits)
+    if relative:
+        out = trimr(a,limits=limits,inclusive=inclusive,axis=axis)
+    else:
+        out = trima(a,limits=limits,inclusive=inclusive)
+    return out.std(axis=axis,ddof=ddof)
+
+
+if trimmed_std.__doc__:
+    trimmed_std.__doc__ = trimmed_std.__doc__ % trimdoc
+
+
+def trimmed_stde(a, limits=(0.1,0.1), inclusive=(1,1), axis=None):
+    """
+    Returns the standard error of the trimmed mean along the given axis.
+
+    Parameters
+    ----------
+    a : sequence
+        Input array
+    limits : {(0.1,0.1), tuple of float}, optional
+        tuple (lower percentage, upper percentage) to cut  on each side of the
+        array, with respect to the number of unmasked data.
+
+        If n is the number of unmasked data before trimming, the values
+        smaller than ``n * limits[0]`` and the values larger than
+        ``n * `limits[1]`` are masked, and the total number of unmasked
+        data after trimming is ``n * (1.-sum(limits))``.  In each case,
+        the value of one limit can be set to None to indicate an open interval.
+        If `limits` is None, no trimming is performed.
+    inclusive : {(bool, bool) tuple} optional
+        Tuple indicating whether the number of data being masked on each side
+        should be rounded (True) or truncated (False).
+    axis : int, optional
+        Axis along which to trim.
+
+    Returns
+    -------
+    trimmed_stde : scalar or ndarray
+
+    """  # numpydoc ignore=RT03
+    def _trimmed_stde_1D(a, low_limit, up_limit, low_inclusive, up_inclusive):
+        "Returns the standard error of the trimmed mean for a 1D input data."
+        n = a.count()
+        idx = a.argsort()
+        if low_limit:
+            if low_inclusive:
+                lowidx = int(low_limit*n)
+            else:
+                lowidx = np.round(low_limit*n)
+            a[idx[:lowidx]] = masked
+        if up_limit is not None:
+            if up_inclusive:
+                upidx = n - int(n*up_limit)
+            else:
+                upidx = n - np.round(n*up_limit)
+            a[idx[upidx:]] = masked
+        a[idx[:lowidx]] = a[idx[lowidx]]
+        a[idx[upidx:]] = a[idx[upidx-1]]
+        winstd = a.std(ddof=1)
+        return winstd / ((1-low_limit-up_limit)*np.sqrt(len(a)))
+
+    a = ma.array(a, copy=True, subok=True)
+    a.unshare_mask()
+    if limits is None:
+        return a.std(axis=axis,ddof=1)/ma.sqrt(a.count(axis))
+    if (not isinstance(limits,tuple)) and isinstance(limits,float):
+        limits = (limits, limits)
+
+    # Check the limits
+    (lolim, uplim) = limits
+    errmsg = "The proportion to cut from the %s should be between 0. and 1."
+    if lolim is not None:
+        if lolim > 1. or lolim < 0:
+            raise ValueError(errmsg % 'beginning' + f"(got {lolim})")
+    if uplim is not None:
+        if uplim > 1. or uplim < 0:
+            raise ValueError(errmsg % 'end' + f"(got {uplim})")
+
+    (loinc, upinc) = inclusive
+    if (axis is None):
+        return _trimmed_stde_1D(a.ravel(),lolim,uplim,loinc,upinc)
+    else:
+        if a.ndim > 2:
+            raise ValueError(f"Array 'a' must be at most two dimensional, "
+                             f"but got a.ndim = {a.ndim}")
+        return ma.apply_along_axis(_trimmed_stde_1D, axis, a,
+                                   lolim,uplim,loinc,upinc)
+
+
+def _mask_to_limits(a, limits, inclusive):
+    """Mask an array for values outside of given limits.
+
+    This is primarily a utility function.
+
+    Parameters
+    ----------
+    a : array
+    limits : (float or None, float or None)
+    A tuple consisting of the (lower limit, upper limit).  Values in the
+    input array less than the lower limit or greater than the upper limit
+    will be masked out. None implies no limit.
+    inclusive : (bool, bool)
+    A tuple consisting of the (lower flag, upper flag).  These flags
+    determine whether values exactly equal to lower or upper are allowed.
+
+    Returns
+    -------
+    A MaskedArray.
+
+    Raises
+    ------
+    A ValueError if there are no values within the given limits.
+    """
+    lower_limit, upper_limit = limits
+    lower_include, upper_include = inclusive
+    am = ma.MaskedArray(a)
+    if lower_limit is not None:
+        if lower_include:
+            am = ma.masked_less(am, lower_limit)
+        else:
+            am = ma.masked_less_equal(am, lower_limit)
+
+    if upper_limit is not None:
+        if upper_include:
+            am = ma.masked_greater(am, upper_limit)
+        else:
+            am = ma.masked_greater_equal(am, upper_limit)
+
+    if am.count() == 0:
+        raise ValueError("No array values within given limits")
+
+    return am
+
+
+def tmean(a, limits=None, inclusive=(True, True), axis=None):
+    """
+    Compute the trimmed mean.
+
+    Parameters
+    ----------
+    a : array_like
+        Array of values.
+    limits : None or (lower limit, upper limit), optional
+        Values in the input array less than the lower limit or greater than the
+        upper limit will be ignored.  When limits is None (default), then all
+        values are used.  Either of the limit values in the tuple can also be
+        None representing a half-open interval.
+    inclusive : (bool, bool), optional
+        A tuple consisting of the (lower flag, upper flag).  These flags
+        determine whether values exactly equal to the lower or upper limits
+        are included.  The default value is (True, True).
+    axis : int or None, optional
+        Axis along which to operate. If None, compute over the
+        whole array. Default is None.
+
+    Returns
+    -------
+    tmean : float
+
+    Notes
+    -----
+    For more details on `tmean`, see `scipy.stats.tmean`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import mstats
+    >>> a = np.array([[6, 8, 3, 0],
+    ...               [3, 9, 1, 2],
+    ...               [8, 7, 8, 2],
+    ...               [5, 6, 0, 2],
+    ...               [4, 5, 5, 2]])
+    ...
+    ...
+    >>> mstats.tmean(a, (2,5))
+    3.3
+    >>> mstats.tmean(a, (2,5), axis=0)
+    masked_array(data=[4.0, 5.0, 4.0, 2.0],
+                 mask=[False, False, False, False],
+           fill_value=1e+20)
+
+    """  # numpydoc ignore=RT03
+    return trima(a, limits=limits, inclusive=inclusive).mean(axis=axis)
+
+
+def tvar(a, limits=None, inclusive=(True, True), axis=0, ddof=1):
+    """
+    Compute the trimmed variance
+
+    This function computes the sample variance of an array of values,
+    while ignoring values which are outside of given `limits`.
+
+    Parameters
+    ----------
+    a : array_like
+        Array of values.
+    limits : None or (lower limit, upper limit), optional
+        Values in the input array less than the lower limit or greater than the
+        upper limit will be ignored. When limits is None, then all values are
+        used. Either of the limit values in the tuple can also be None
+        representing a half-open interval.  The default value is None.
+    inclusive : (bool, bool), optional
+        A tuple consisting of the (lower flag, upper flag).  These flags
+        determine whether values exactly equal to the lower or upper limits
+        are included.  The default value is (True, True).
+    axis : int or None, optional
+        Axis along which to operate. If None, compute over the
+        whole array. Default is zero.
+    ddof : int, optional
+        Delta degrees of freedom. Default is 1.
+
+    Returns
+    -------
+    tvar : float
+        Trimmed variance.
+
+    Notes
+    -----
+    For more details on `tvar`, see `scipy.stats.tvar`.
+
+    """
+    a = a.astype(float).ravel()
+    if limits is None:
+        n = (~a.mask).sum()  # todo: better way to do that?
+        return np.ma.var(a) * n/(n-1.)
+    am = _mask_to_limits(a, limits=limits, inclusive=inclusive)
+
+    return np.ma.var(am, axis=axis, ddof=ddof)
+
+
+def tmin(a, lowerlimit=None, axis=0, inclusive=True):
+    """
+    Compute the trimmed minimum
+
+    Parameters
+    ----------
+    a : array_like
+        array of values
+    lowerlimit : None or float, optional
+        Values in the input array less than the given limit will be ignored.
+        When lowerlimit is None, then all values are used. The default value
+        is None.
+    axis : int or None, optional
+        Axis along which to operate. Default is 0. If None, compute over the
+        whole array `a`.
+    inclusive : {True, False}, optional
+        This flag determines whether values exactly equal to the lower limit
+        are included.  The default value is True.
+
+    Returns
+    -------
+    tmin : float, int or ndarray
+
+    Notes
+    -----
+    For more details on `tmin`, see `scipy.stats.tmin`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import mstats
+    >>> a = np.array([[6, 8, 3, 0],
+    ...               [3, 2, 1, 2],
+    ...               [8, 1, 8, 2],
+    ...               [5, 3, 0, 2],
+    ...               [4, 7, 5, 2]])
+    ...
+    >>> mstats.tmin(a, 5)
+    masked_array(data=[5, 7, 5, --],
+                 mask=[False, False, False,  True],
+           fill_value=999999)
+
+    """  # numpydoc ignore=RT03
+    a, axis = _chk_asarray(a, axis)
+    am = trima(a, (lowerlimit, None), (inclusive, False))
+    return ma.minimum.reduce(am, axis)
+
+
+def tmax(a, upperlimit=None, axis=0, inclusive=True):
+    """
+    Compute the trimmed maximum
+
+    This function computes the maximum value of an array along a given axis,
+    while ignoring values larger than a specified upper limit.
+
+    Parameters
+    ----------
+    a : array_like
+        array of values
+    upperlimit : None or float, optional
+        Values in the input array greater than the given limit will be ignored.
+        When upperlimit is None, then all values are used. The default value
+        is None.
+    axis : int or None, optional
+        Axis along which to operate. Default is 0. If None, compute over the
+        whole array `a`.
+    inclusive : {True, False}, optional
+        This flag determines whether values exactly equal to the upper limit
+        are included.  The default value is True.
+
+    Returns
+    -------
+    tmax : float, int or ndarray
+
+    Notes
+    -----
+    For more details on `tmax`, see `scipy.stats.tmax`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import mstats
+    >>> a = np.array([[6, 8, 3, 0],
+    ...               [3, 9, 1, 2],
+    ...               [8, 7, 8, 2],
+    ...               [5, 6, 0, 2],
+    ...               [4, 5, 5, 2]])
+    ...
+    ...
+    >>> mstats.tmax(a, 4)
+    masked_array(data=[4, --, 3, 2],
+                 mask=[False,  True, False, False],
+           fill_value=999999)
+
+    """  # numpydoc ignore=RT03
+    a, axis = _chk_asarray(a, axis)
+    am = trima(a, (None, upperlimit), (False, inclusive))
+    return ma.maximum.reduce(am, axis)
+
+
+def tsem(a, limits=None, inclusive=(True, True), axis=0, ddof=1):
+    """
+    Compute the trimmed standard error of the mean.
+
+    This function finds the standard error of the mean for given
+    values, ignoring values outside the given `limits`.
+
+    Parameters
+    ----------
+    a : array_like
+        array of values
+    limits : None or (lower limit, upper limit), optional
+        Values in the input array less than the lower limit or greater than the
+        upper limit will be ignored. When limits is None, then all values are
+        used. Either of the limit values in the tuple can also be None
+        representing a half-open interval.  The default value is None.
+    inclusive : (bool, bool), optional
+        A tuple consisting of the (lower flag, upper flag).  These flags
+        determine whether values exactly equal to the lower or upper limits
+        are included.  The default value is (True, True).
+    axis : int or None, optional
+        Axis along which to operate. If None, compute over the
+        whole array. Default is zero.
+    ddof : int, optional
+        Delta degrees of freedom. Default is 1.
+
+    Returns
+    -------
+    tsem : float
+
+    Notes
+    -----
+    For more details on `tsem`, see `scipy.stats.tsem`.
+
+    """  # numpydoc ignore=RT03
+    a = ma.asarray(a).ravel()
+    if limits is None:
+        n = float(a.count())
+        return a.std(axis=axis, ddof=ddof)/ma.sqrt(n)
+
+    am = trima(a.ravel(), limits, inclusive)
+    sd = np.sqrt(am.var(axis=axis, ddof=ddof))
+    return sd / np.sqrt(am.count())
+
+
+def winsorize(a, limits=None, inclusive=(True, True), inplace=False,
+              axis=None, nan_policy='propagate'):
+    """Returns a Winsorized version of the input array.
+
+    The (limits[0])th lowest values are set to the (limits[0])th percentile,
+    and the (limits[1])th highest values are set to the (1 - limits[1])th
+    percentile.
+    Masked values are skipped.
+
+
+    Parameters
+    ----------
+    a : sequence
+        Input array.
+    limits : {None, tuple of float}, optional
+        Tuple of the percentages to cut on each side of the array, with respect
+        to the number of unmasked data, as floats between 0. and 1.
+        Noting n the number of unmasked data before trimming, the
+        (n*limits[0])th smallest data and the (n*limits[1])th largest data are
+        masked, and the total number of unmasked data after trimming
+        is n*(1.-sum(limits)) The value of one limit can be set to None to
+        indicate an open interval.
+    inclusive : {(True, True) tuple}, optional
+        Tuple indicating whether the number of data being masked on each side
+        should be truncated (True) or rounded (False).
+    inplace : {False, True}, optional
+        Whether to winsorize in place (True) or to use a copy (False)
+    axis : {None, int}, optional
+        Axis along which to trim. If None, the whole array is trimmed, but its
+        shape is maintained.
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains nan.
+        The following options are available (default is 'propagate'):
+
+        * 'propagate': allows nan values and may overwrite or propagate them
+        * 'raise': throws an error
+        * 'omit': performs the calculations ignoring nan values
+
+    Notes
+    -----
+    This function is applied to reduce the effect of possibly spurious outliers
+    by limiting the extreme values.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats.mstats import winsorize
+
+    A shuffled array contains integers from 1 to 10.
+
+    >>> a = np.array([10, 4, 9, 8, 5, 3, 7, 2, 1, 6])
+
+    The 10% of the lowest value (i.e., ``1``) and the 20% of the highest
+    values (i.e., ``9`` and ``10``) are replaced.
+
+    >>> winsorize(a, limits=[0.1, 0.2])
+    masked_array(data=[8, 4, 8, 8, 5, 3, 7, 2, 2, 6],
+                 mask=False,
+           fill_value=999999)
+
+    """  # numpydoc ignore=RT01
+    def _winsorize1D(a, low_limit, up_limit, low_include, up_include,
+                     contains_nan, nan_policy):
+        n = a.count()
+        idx = a.argsort()
+        if contains_nan:
+            nan_count = np.count_nonzero(np.isnan(a))
+        if low_limit:
+            if low_include:
+                lowidx = int(low_limit * n)
+            else:
+                lowidx = np.round(low_limit * n).astype(int)
+            if contains_nan and nan_policy == 'omit':
+                lowidx = min(lowidx, n-nan_count-1)
+            a[idx[:lowidx]] = a[idx[lowidx]]
+        if up_limit is not None:
+            if up_include:
+                upidx = n - int(n * up_limit)
+            else:
+                upidx = n - np.round(n * up_limit).astype(int)
+            if contains_nan and nan_policy == 'omit':
+                a[idx[upidx:-nan_count]] = a[idx[upidx - 1]]
+            else:
+                a[idx[upidx:]] = a[idx[upidx - 1]]
+        return a
+
+    contains_nan = _contains_nan(a, nan_policy)
+    # We are going to modify a: better make a copy
+    a = ma.array(a, copy=np.logical_not(inplace))
+
+    if limits is None:
+        return a
+    if (not isinstance(limits, tuple)) and isinstance(limits, float):
+        limits = (limits, limits)
+
+    # Check the limits
+    (lolim, uplim) = limits
+    errmsg = "The proportion to cut from the %s should be between 0. and 1."
+    if lolim is not None:
+        if lolim > 1. or lolim < 0:
+            raise ValueError(errmsg % 'beginning' + f"(got {lolim})")
+    if uplim is not None:
+        if uplim > 1. or uplim < 0:
+            raise ValueError(errmsg % 'end' + f"(got {uplim})")
+
+    (loinc, upinc) = inclusive
+
+    if axis is None:
+        shp = a.shape
+        return _winsorize1D(a.ravel(), lolim, uplim, loinc, upinc,
+                            contains_nan, nan_policy).reshape(shp)
+    else:
+        return ma.apply_along_axis(_winsorize1D, axis, a, lolim, uplim, loinc,
+                                   upinc, contains_nan, nan_policy)
+
+
+def moment(a, moment=1, axis=0):
+    """
+    Calculates the nth moment about the mean for a sample.
+
+    Parameters
+    ----------
+    a : array_like
+       data
+    moment : int, optional
+       order of central moment that is returned
+    axis : int or None, optional
+       Axis along which the central moment is computed. Default is 0.
+       If None, compute over the whole array `a`.
+
+    Returns
+    -------
+    n-th central moment : ndarray or float
+       The appropriate moment along the given axis or over all values if axis
+       is None. The denominator for the moment calculation is the number of
+       observations, no degrees of freedom correction is done.
+
+    Notes
+    -----
+    For more details about `moment`, see `scipy.stats.moment`.
+
+    """
+    a, axis = _chk_asarray(a, axis)
+    if a.size == 0:
+        moment_shape = list(a.shape)
+        del moment_shape[axis]
+        dtype = a.dtype.type if a.dtype.kind in 'fc' else np.float64
+        # empty array, return nan(s) with shape matching `moment`
+        out_shape = (moment_shape if np.isscalar(moment)
+                     else [len(moment)] + moment_shape)
+        if len(out_shape) == 0:
+            return dtype(np.nan)
+        else:
+            return ma.array(np.full(out_shape, np.nan, dtype=dtype))
+
+    # for array_like moment input, return a value for each.
+    if not np.isscalar(moment):
+        mean = a.mean(axis, keepdims=True)
+        mmnt = [_moment(a, i, axis, mean=mean) for i in moment]
+        return ma.array(mmnt)
+    else:
+        return _moment(a, moment, axis)
+
+
+# Moment with optional pre-computed mean, equal to a.mean(axis, keepdims=True)
+def _moment(a, moment, axis, *, mean=None):
+    if np.abs(moment - np.round(moment)) > 0:
+        raise ValueError("All moment parameters must be integers")
+
+    if moment == 0 or moment == 1:
+        # By definition the zeroth moment about the mean is 1, and the first
+        # moment is 0.
+        shape = list(a.shape)
+        del shape[axis]
+        dtype = a.dtype.type if a.dtype.kind in 'fc' else np.float64
+
+        if len(shape) == 0:
+            return dtype(1.0 if moment == 0 else 0.0)
+        else:
+            return (ma.ones(shape, dtype=dtype) if moment == 0
+                    else ma.zeros(shape, dtype=dtype))
+    else:
+        # Exponentiation by squares: form exponent sequence
+        n_list = [moment]
+        current_n = moment
+        while current_n > 2:
+            if current_n % 2:
+                current_n = (current_n-1)/2
+            else:
+                current_n /= 2
+            n_list.append(current_n)
+
+        # Starting point for exponentiation by squares
+        mean = a.mean(axis, keepdims=True) if mean is None else mean
+        a_zero_mean = a - mean
+        if n_list[-1] == 1:
+            s = a_zero_mean.copy()
+        else:
+            s = a_zero_mean**2
+
+        # Perform multiplications
+        for n in n_list[-2::-1]:
+            s = s**2
+            if n % 2:
+                s *= a_zero_mean
+        return s.mean(axis)
+
+
+def variation(a, axis=0, ddof=0):
+    """
+    Compute the coefficient of variation.
+
+    The coefficient of variation is the standard deviation divided by the
+    mean.  This function is equivalent to::
+
+        np.std(x, axis=axis, ddof=ddof) / np.mean(x)
+
+    The default for ``ddof`` is 0, but many definitions of the coefficient
+    of variation use the square root of the unbiased sample variance
+    for the sample standard deviation, which corresponds to ``ddof=1``.
+
+    Parameters
+    ----------
+    a : array_like
+        Input array.
+    axis : int or None, optional
+        Axis along which to calculate the coefficient of variation. Default
+        is 0. If None, compute over the whole array `a`.
+    ddof : int, optional
+        Delta degrees of freedom.  Default is 0.
+
+    Returns
+    -------
+    variation : ndarray
+        The calculated variation along the requested axis.
+
+    Notes
+    -----
+    For more details about `variation`, see `scipy.stats.variation`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats.mstats import variation
+    >>> a = np.array([2,8,4])
+    >>> variation(a)
+    0.5345224838248487
+    >>> b = np.array([2,8,3,4])
+    >>> c = np.ma.masked_array(b, mask=[0,0,1,0])
+    >>> variation(c)
+    0.5345224838248487
+
+    In the example above, it can be seen that this works the same as
+    `scipy.stats.variation` except 'stats.mstats.variation' ignores masked
+    array elements.
+
+    """
+    a, axis = _chk_asarray(a, axis)
+    return a.std(axis, ddof=ddof)/a.mean(axis)
+
+
+def skew(a, axis=0, bias=True):
+    """
+    Computes the skewness of a data set.
+
+    Parameters
+    ----------
+    a : ndarray
+        data
+    axis : int or None, optional
+        Axis along which skewness is calculated. Default is 0.
+        If None, compute over the whole array `a`.
+    bias : bool, optional
+        If False, then the calculations are corrected for statistical bias.
+
+    Returns
+    -------
+    skewness : ndarray
+        The skewness of values along an axis, returning 0 where all values are
+        equal.
+
+    Notes
+    -----
+    For more details about `skew`, see `scipy.stats.skew`.
+
+    """
+    a, axis = _chk_asarray(a,axis)
+    mean = a.mean(axis, keepdims=True)
+    m2 = _moment(a, 2, axis, mean=mean)
+    m3 = _moment(a, 3, axis, mean=mean)
+    zero = (m2 <= (np.finfo(m2.dtype).resolution * mean.squeeze(axis))**2)
+    with np.errstate(all='ignore'):
+        vals = ma.where(zero, 0, m3 / m2**1.5)
+
+    if not bias and zero is not ma.masked and m2 is not ma.masked:
+        n = a.count(axis)
+        can_correct = ~zero & (n > 2)
+        if can_correct.any():
+            n = np.extract(can_correct, n)
+            m2 = np.extract(can_correct, m2)
+            m3 = np.extract(can_correct, m3)
+            nval = ma.sqrt((n-1.0)*n)/(n-2.0)*m3/m2**1.5
+            np.place(vals, can_correct, nval)
+    return vals
+
+
+def kurtosis(a, axis=0, fisher=True, bias=True):
+    """
+    Computes the kurtosis (Fisher or Pearson) of a dataset.
+
+    Kurtosis is the fourth central moment divided by the square of the
+    variance. If Fisher's definition is used, then 3.0 is subtracted from
+    the result to give 0.0 for a normal distribution.
+
+    If bias is False then the kurtosis is calculated using k statistics to
+    eliminate bias coming from biased moment estimators
+
+    Use `kurtosistest` to see if result is close enough to normal.
+
+    Parameters
+    ----------
+    a : array
+        data for which the kurtosis is calculated
+    axis : int or None, optional
+        Axis along which the kurtosis is calculated. Default is 0.
+        If None, compute over the whole array `a`.
+    fisher : bool, optional
+        If True, Fisher's definition is used (normal ==> 0.0). If False,
+        Pearson's definition is used (normal ==> 3.0).
+    bias : bool, optional
+        If False, then the calculations are corrected for statistical bias.
+
+    Returns
+    -------
+    kurtosis : array
+        The kurtosis of values along an axis. If all values are equal,
+        return -3 for Fisher's definition and 0 for Pearson's definition.
+
+    Notes
+    -----
+    For more details about `kurtosis`, see `scipy.stats.kurtosis`.
+
+    """
+    a, axis = _chk_asarray(a, axis)
+    mean = a.mean(axis, keepdims=True)
+    m2 = _moment(a, 2, axis, mean=mean)
+    m4 = _moment(a, 4, axis, mean=mean)
+    zero = (m2 <= (np.finfo(m2.dtype).resolution * mean.squeeze(axis))**2)
+    with np.errstate(all='ignore'):
+        vals = ma.where(zero, 0, m4 / m2**2.0)
+
+    if not bias and zero is not ma.masked and m2 is not ma.masked:
+        n = a.count(axis)
+        can_correct = ~zero & (n > 3)
+        if can_correct.any():
+            n = np.extract(can_correct, n)
+            m2 = np.extract(can_correct, m2)
+            m4 = np.extract(can_correct, m4)
+            nval = 1.0/(n-2)/(n-3)*((n*n-1.0)*m4/m2**2.0-3*(n-1)**2.0)
+            np.place(vals, can_correct, nval+3.0)
+    if fisher:
+        return vals - 3
+    else:
+        return vals
+
+
+DescribeResult = namedtuple('DescribeResult', ('nobs', 'minmax', 'mean',
+                                               'variance', 'skewness',
+                                               'kurtosis'))
+
+
+def describe(a, axis=0, ddof=0, bias=True):
+    """
+    Computes several descriptive statistics of the passed array.
+
+    Parameters
+    ----------
+    a : array_like
+        Data array
+    axis : int or None, optional
+        Axis along which to calculate statistics. Default 0. If None,
+        compute over the whole array `a`.
+    ddof : int, optional
+        degree of freedom (default 0); note that default ddof is different
+        from the same routine in stats.describe
+    bias : bool, optional
+        If False, then the skewness and kurtosis calculations are corrected for
+        statistical bias.
+
+    Returns
+    -------
+    nobs : int
+        (size of the data (discarding missing values)
+
+    minmax : (int, int)
+        min, max
+
+    mean : float
+        arithmetic mean
+
+    variance : float
+        unbiased variance
+
+    skewness : float
+        biased skewness
+
+    kurtosis : float
+        biased kurtosis
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats.mstats import describe
+    >>> ma = np.ma.array(range(6), mask=[0, 0, 0, 1, 1, 1])
+    >>> describe(ma)
+    DescribeResult(nobs=np.int64(3), minmax=(masked_array(data=0,
+                 mask=False,
+           fill_value=999999), masked_array(data=2,
+                 mask=False,
+           fill_value=999999)), mean=np.float64(1.0),
+           variance=np.float64(0.6666666666666666),
+           skewness=masked_array(data=0., mask=False, fill_value=1e+20),
+            kurtosis=np.float64(-1.5))
+
+    """
+    a, axis = _chk_asarray(a, axis)
+    n = a.count(axis)
+    mm = (ma.minimum.reduce(a, axis=axis), ma.maximum.reduce(a, axis=axis))
+    m = a.mean(axis)
+    v = a.var(axis, ddof=ddof)
+    sk = skew(a, axis, bias=bias)
+    kurt = kurtosis(a, axis, bias=bias)
+
+    return DescribeResult(n, mm, m, v, sk, kurt)
+
+
+def stde_median(data, axis=None):
+    """Returns the McKean-Schrader estimate of the standard error of the sample
+    median along the given axis. masked values are discarded.
+
+    Parameters
+    ----------
+    data : ndarray
+        Data to trim.
+    axis : {None,int}, optional
+        Axis along which to perform the trimming.
+        If None, the input array is first flattened.
+
+    """
+    def _stdemed_1D(data):
+        data = np.sort(data.compressed())
+        n = len(data)
+        z = 2.5758293035489004
+        k = int(np.round((n+1)/2. - z * np.sqrt(n/4.),0))
+        return ((data[n-k] - data[k-1])/(2.*z))
+
+    data = ma.array(data, copy=False, subok=True)
+    if (axis is None):
+        return _stdemed_1D(data)
+    else:
+        if data.ndim > 2:
+            raise ValueError(f"Array 'data' must be at most two dimensional, "
+                             f"but got data.ndim = {data.ndim}")
+        return ma.apply_along_axis(_stdemed_1D, axis, data)
+
+
+SkewtestResult = namedtuple('SkewtestResult', ('statistic', 'pvalue'))
+
+
+def skewtest(a, axis=0, alternative='two-sided'):
+    """
+    Tests whether the skew is different from the normal distribution.
+
+    Parameters
+    ----------
+    a : array_like
+        The data to be tested
+    axis : int or None, optional
+       Axis along which statistics are calculated. Default is 0.
+       If None, compute over the whole array `a`.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis. Default is 'two-sided'.
+        The following options are available:
+
+        * 'two-sided': the skewness of the distribution underlying the sample
+          is different from that of the normal distribution (i.e. 0)
+        * 'less': the skewness of the distribution underlying the sample
+          is less than that of the normal distribution
+        * 'greater': the skewness of the distribution underlying the sample
+          is greater than that of the normal distribution
+
+        .. versionadded:: 1.7.0
+
+    Returns
+    -------
+    statistic : array_like
+        The computed z-score for this test.
+    pvalue : array_like
+        A p-value for the hypothesis test
+
+    Notes
+    -----
+    For more details about `skewtest`, see `scipy.stats.skewtest`.
+
+    """
+    a, axis = _chk_asarray(a, axis)
+    if axis is None:
+        a = a.ravel()
+        axis = 0
+    b2 = skew(a,axis)
+    n = a.count(axis)
+    if np.min(n) < 8:
+        raise ValueError(f"skewtest is not valid with less than 8 samples; "
+                         f"{np.min(n)} samples were given.")
+
+    y = b2 * ma.sqrt(((n+1)*(n+3)) / (6.0*(n-2)))
+    beta2 = (3.0*(n*n+27*n-70)*(n+1)*(n+3)) / ((n-2.0)*(n+5)*(n+7)*(n+9))
+    W2 = -1 + ma.sqrt(2*(beta2-1))
+    delta = 1/ma.sqrt(0.5*ma.log(W2))
+    alpha = ma.sqrt(2.0/(W2-1))
+    y = ma.where(y == 0, 1, y)
+    Z = delta*ma.log(y/alpha + ma.sqrt((y/alpha)**2+1))
+    pvalue = scipy.stats._stats_py._get_pvalue(Z, distributions.norm, alternative)
+
+    return SkewtestResult(Z[()], pvalue[()])
+
+
+KurtosistestResult = namedtuple('KurtosistestResult', ('statistic', 'pvalue'))
+
+
+def kurtosistest(a, axis=0, alternative='two-sided'):
+    """
+    Tests whether a dataset has normal kurtosis
+
+    Parameters
+    ----------
+    a : array_like
+        array of the sample data
+    axis : int or None, optional
+       Axis along which to compute test. Default is 0. If None,
+       compute over the whole array `a`.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis.
+        The following options are available (default is 'two-sided'):
+
+        * 'two-sided': the kurtosis of the distribution underlying the sample
+          is different from that of the normal distribution
+        * 'less': the kurtosis of the distribution underlying the sample
+          is less than that of the normal distribution
+        * 'greater': the kurtosis of the distribution underlying the sample
+          is greater than that of the normal distribution
+
+        .. versionadded:: 1.7.0
+
+    Returns
+    -------
+    statistic : array_like
+        The computed z-score for this test.
+    pvalue : array_like
+        The p-value for the hypothesis test
+
+    Notes
+    -----
+    For more details about `kurtosistest`, see `scipy.stats.kurtosistest`.
+
+    """
+    a, axis = _chk_asarray(a, axis)
+    n = a.count(axis=axis)
+    if np.min(n) < 5:
+        raise ValueError(f"kurtosistest requires at least 5 observations; "
+                         f"{np.min(n)} observations were given.")
+    if np.min(n) < 20:
+        warnings.warn(f"kurtosistest only valid for n>=20 ... continuing "
+                      f"anyway, n={np.min(n)}", stacklevel=2)
+
+    b2 = kurtosis(a, axis, fisher=False)
+    E = 3.0*(n-1) / (n+1)
+    varb2 = 24.0*n*(n-2.)*(n-3) / ((n+1)*(n+1.)*(n+3)*(n+5))
+    x = (b2-E)/ma.sqrt(varb2)
+    sqrtbeta1 = 6.0*(n*n-5*n+2)/((n+7)*(n+9)) * np.sqrt((6.0*(n+3)*(n+5)) /
+                                                        (n*(n-2)*(n-3)))
+    A = 6.0 + 8.0/sqrtbeta1 * (2.0/sqrtbeta1 + np.sqrt(1+4.0/(sqrtbeta1**2)))
+    term1 = 1 - 2./(9.0*A)
+    denom = 1 + x*ma.sqrt(2/(A-4.0))
+    if np.ma.isMaskedArray(denom):
+        # For multi-dimensional array input
+        denom[denom == 0.0] = masked
+    elif denom == 0.0:
+        denom = masked
+
+    term2 = np.ma.where(denom > 0, ma.power((1-2.0/A)/denom, 1/3.0),
+                        -ma.power(-(1-2.0/A)/denom, 1/3.0))
+    Z = (term1 - term2) / np.sqrt(2/(9.0*A))
+    pvalue = scipy.stats._stats_py._get_pvalue(Z, distributions.norm, alternative)
+
+    return KurtosistestResult(Z[()], pvalue[()])
+
+
+NormaltestResult = namedtuple('NormaltestResult', ('statistic', 'pvalue'))
+
+
+def normaltest(a, axis=0):
+    """
+    Tests whether a sample differs from a normal distribution.
+
+    Parameters
+    ----------
+    a : array_like
+        The array containing the data to be tested.
+    axis : int or None, optional
+        Axis along which to compute test. Default is 0. If None,
+        compute over the whole array `a`.
+
+    Returns
+    -------
+    statistic : float or array
+        ``s^2 + k^2``, where ``s`` is the z-score returned by `skewtest` and
+        ``k`` is the z-score returned by `kurtosistest`.
+    pvalue : float or array
+         A 2-sided chi squared probability for the hypothesis test.
+
+    Notes
+    -----
+    For more details about `normaltest`, see `scipy.stats.normaltest`.
+
+    """
+    a, axis = _chk_asarray(a, axis)
+    s, _ = skewtest(a, axis)
+    k, _ = kurtosistest(a, axis)
+    k2 = s*s + k*k
+
+    return NormaltestResult(k2, distributions.chi2.sf(k2, 2))
+
+
+def mquantiles(a, prob=(.25, .5, .75), alphap=.4, betap=.4, axis=None,
+               limit=()):
+    """
+    Computes empirical quantiles for a data array.
+
+    Samples quantile are defined by ``Q(p) = (1-gamma)*x[j] + gamma*x[j+1]``,
+    where ``x[j]`` is the j-th order statistic, and gamma is a function of
+    ``j = floor(n*p + m)``, ``m = alphap + p*(1 - alphap - betap)`` and
+    ``g = n*p + m - j``.
+
+    Reinterpreting the above equations to compare to **R** lead to the
+    equation: ``p(k) = (k - alphap)/(n + 1 - alphap - betap)``
+
+    Typical values of (alphap,betap) are:
+
+    - (0,1)    : ``p(k) = k/n`` : linear interpolation of cdf
+      (**R** type 4)
+    - (.5,.5)  : ``p(k) = (k - 1/2.)/n`` : piecewise linear function
+      (**R** type 5)
+    - (0,0)    : ``p(k) = k/(n+1)`` :
+      (**R** type 6)
+    - (1,1)    : ``p(k) = (k-1)/(n-1)``: p(k) = mode[F(x[k])].
+      (**R** type 7, **R** default)
+    - (1/3,1/3): ``p(k) = (k-1/3)/(n+1/3)``: Then p(k) ~ median[F(x[k])].
+      The resulting quantile estimates are approximately median-unbiased
+      regardless of the distribution of x.
+      (**R** type 8)
+    - (3/8,3/8): ``p(k) = (k-3/8)/(n+1/4)``: Blom.
+      The resulting quantile estimates are approximately unbiased
+      if x is normally distributed
+      (**R** type 9)
+    - (.4,.4)  : approximately quantile unbiased (Cunnane)
+    - (.35,.35): APL, used with PWM
+
+    Parameters
+    ----------
+    a : array_like
+        Input data, as a sequence or array of dimension at most 2.
+    prob : array_like, optional
+        List of quantiles to compute.
+    alphap : float, optional
+        Plotting positions parameter, default is 0.4.
+    betap : float, optional
+        Plotting positions parameter, default is 0.4.
+    axis : int, optional
+        Axis along which to perform the trimming.
+        If None (default), the input array is first flattened.
+    limit : tuple, optional
+        Tuple of (lower, upper) values.
+        Values of `a` outside this open interval are ignored.
+
+    Returns
+    -------
+    mquantiles : MaskedArray
+        An array containing the calculated quantiles.
+
+    Notes
+    -----
+    This formulation is very similar to **R** except the calculation of
+    ``m`` from ``alphap`` and ``betap``, where in **R** ``m`` is defined
+    with each type.
+
+    References
+    ----------
+    .. [1] *R* statistical software: https://www.r-project.org/
+    .. [2] *R* ``quantile`` function:
+            http://stat.ethz.ch/R-manual/R-devel/library/stats/html/quantile.html
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats.mstats import mquantiles
+    >>> a = np.array([6., 47., 49., 15., 42., 41., 7., 39., 43., 40., 36.])
+    >>> mquantiles(a)
+    array([ 19.2,  40. ,  42.8])
+
+    Using a 2D array, specifying axis and limit.
+
+    >>> data = np.array([[   6.,    7.,    1.],
+    ...                  [  47.,   15.,    2.],
+    ...                  [  49.,   36.,    3.],
+    ...                  [  15.,   39.,    4.],
+    ...                  [  42.,   40., -999.],
+    ...                  [  41.,   41., -999.],
+    ...                  [   7., -999., -999.],
+    ...                  [  39., -999., -999.],
+    ...                  [  43., -999., -999.],
+    ...                  [  40., -999., -999.],
+    ...                  [  36., -999., -999.]])
+    >>> print(mquantiles(data, axis=0, limit=(0, 50)))
+    [[19.2  14.6   1.45]
+     [40.   37.5   2.5 ]
+     [42.8  40.05  3.55]]
+
+    >>> data[:, 2] = -999.
+    >>> print(mquantiles(data, axis=0, limit=(0, 50)))
+    [[19.200000000000003 14.6 --]
+     [40.0 37.5 --]
+     [42.800000000000004 40.05 --]]
+
+    """
+    def _quantiles1D(data,m,p):
+        x = np.sort(data.compressed())
+        n = len(x)
+        if n == 0:
+            return ma.array(np.empty(len(p), dtype=float), mask=True)
+        elif n == 1:
+            return ma.array(np.resize(x, p.shape), mask=nomask)
+        aleph = (n*p + m)
+        k = np.floor(aleph.clip(1, n-1)).astype(int)
+        gamma = (aleph-k).clip(0,1)
+        return (1.-gamma)*x[(k-1).tolist()] + gamma*x[k.tolist()]
+
+    data = ma.array(a, copy=False)
+    if data.ndim > 2:
+        raise TypeError("Array should be 2D at most !")
+
+    if limit:
+        condition = (limit[0] < data) & (data < limit[1])
+        data[~condition.filled(True)] = masked
+
+    p = np.atleast_1d(np.asarray(prob))
+    m = alphap + p*(1.-alphap-betap)
+    # Computes quantiles along axis (or globally)
+    if (axis is None):
+        return _quantiles1D(data, m, p)
+
+    return ma.apply_along_axis(_quantiles1D, axis, data, m, p)
+
+
+def scoreatpercentile(data, per, limit=(), alphap=.4, betap=.4):
+    """Calculate the score at the given 'per' percentile of the
+    sequence a.  For example, the score at per=50 is the median.
+
+    This function is a shortcut to mquantile
+
+    """  # numpydoc ignore=RT01
+    if (per < 0) or (per > 100.):
+        raise ValueError(f"The percentile should be between 0. and 100. ! (got {per})")
+
+    return mquantiles(data, prob=[per/100.], alphap=alphap, betap=betap,
+                      limit=limit, axis=0).squeeze()
+
+
+def plotting_positions(data, alpha=0.4, beta=0.4):
+    """
+    Returns plotting positions (or empirical percentile points) for the data.
+
+    Plotting positions are defined as ``(i-alpha)/(n+1-alpha-beta)``, where:
+
+    - i is the rank order statistics
+    - n is the number of unmasked values along the given axis
+    - `alpha` and `beta` are two parameters.
+
+    Typical values for `alpha` and `beta` are:
+
+    - (0,1)    : ``p(k) = k/n``, linear interpolation of cdf (R, type 4)
+    - (.5,.5)  : ``p(k) = (k-1/2.)/n``, piecewise linear function
+      (R, type 5)
+    - (0,0)    : ``p(k) = k/(n+1)``, Weibull (R type 6)
+    - (1,1)    : ``p(k) = (k-1)/(n-1)``, in this case,
+      ``p(k) = mode[F(x[k])]``. That's R default (R type 7)
+    - (1/3,1/3): ``p(k) = (k-1/3)/(n+1/3)``, then
+      ``p(k) ~ median[F(x[k])]``.
+      The resulting quantile estimates are approximately median-unbiased
+      regardless of the distribution of x. (R type 8)
+    - (3/8,3/8): ``p(k) = (k-3/8)/(n+1/4)``, Blom.
+      The resulting quantile estimates are approximately unbiased
+      if x is normally distributed (R type 9)
+    - (.4,.4)  : approximately quantile unbiased (Cunnane)
+    - (.35,.35): APL, used with PWM
+    - (.3175, .3175): used in scipy.stats.probplot
+
+    Parameters
+    ----------
+    data : array_like
+        Input data, as a sequence or array of dimension at most 2.
+    alpha : float, optional
+        Plotting positions parameter. Default is 0.4.
+    beta : float, optional
+        Plotting positions parameter. Default is 0.4.
+
+    Returns
+    -------
+    positions : MaskedArray
+        The calculated plotting positions.
+
+    """
+    data = ma.array(data, copy=False).reshape(1,-1)
+    n = data.count()
+    plpos = np.empty(data.size, dtype=float)
+    plpos[n:] = 0
+    plpos[data.argsort(axis=None)[:n]] = ((np.arange(1, n+1) - alpha) /
+                                          (n + 1.0 - alpha - beta))
+    return ma.array(plpos, mask=data._mask)
+
+
+meppf = plotting_positions
+
+
+def obrientransform(*args):
+    """
+    Computes a transform on input data (any number of columns).  Used to
+    test for homogeneity of variance prior to running one-way stats.  Each
+    array in ``*args`` is one level of a factor.  If an `f_oneway()` run on
+    the transformed data and found significant, variances are unequal.   From
+    Maxwell and Delaney, p.112.
+
+    Returns: transformed data for use in an ANOVA
+    """  # numpydoc ignore=RT01
+    data = argstoarray(*args).T
+    v = data.var(axis=0,ddof=1)
+    m = data.mean(0)
+    n = data.count(0).astype(float)
+    # result = ((N-1.5)*N*(a-m)**2 - 0.5*v*(n-1))/((n-1)*(n-2))
+    data -= m
+    data **= 2
+    data *= (n-1.5)*n
+    data -= 0.5*v*(n-1)
+    data /= (n-1.)*(n-2.)
+    if not ma.allclose(v,data.mean(0)):
+        raise ValueError("Lack of convergence in obrientransform.")
+
+    return data
+
+
+def sem(a, axis=0, ddof=1):
+    """
+    Calculates the standard error of the mean of the input array.
+
+    Also sometimes called standard error of measurement.
+
+    Parameters
+    ----------
+    a : array_like
+        An array containing the values for which the standard error is
+        returned.
+    axis : int or None, optional
+        If axis is None, ravel `a` first. If axis is an integer, this will be
+        the axis over which to operate. Defaults to 0.
+    ddof : int, optional
+        Delta degrees-of-freedom. How many degrees of freedom to adjust
+        for bias in limited samples relative to the population estimate
+        of variance. Defaults to 1.
+
+    Returns
+    -------
+    s : ndarray or float
+        The standard error of the mean in the sample(s), along the input axis.
+
+    Notes
+    -----
+    The default value for `ddof` changed in scipy 0.15.0 to be consistent with
+    `scipy.stats.sem` as well as with the most common definition used (like in
+    the R documentation).
+
+    Examples
+    --------
+    Find standard error along the first axis:
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> a = np.arange(20).reshape(5,4)
+    >>> print(stats.mstats.sem(a))
+    [2.8284271247461903 2.8284271247461903 2.8284271247461903
+     2.8284271247461903]
+
+    Find standard error across the whole array, using n degrees of freedom:
+
+    >>> print(stats.mstats.sem(a, axis=None, ddof=0))
+    1.2893796958227628
+
+    """
+    a, axis = _chk_asarray(a, axis)
+    n = a.count(axis=axis)
+    s = a.std(axis=axis, ddof=ddof) / ma.sqrt(n)
+    return s
+
+
+F_onewayResult = namedtuple('F_onewayResult', ('statistic', 'pvalue'))
+
+
+def f_oneway(*args):
+    """
+    Performs a 1-way ANOVA, returning an F-value and probability given
+    any number of groups.  From Heiman, pp.394-7.
+
+    Usage: ``f_oneway(*args)``, where ``*args`` is 2 or more arrays,
+    one per treatment group.
+
+    Returns
+    -------
+    statistic : float
+        The computed F-value of the test.
+    pvalue : float
+        The associated p-value from the F-distribution.
+
+    """
+    # Construct a single array of arguments: each row is a group
+    data = argstoarray(*args)
+    ngroups = len(data)
+    ntot = data.count()
+    sstot = (data**2).sum() - (data.sum())**2/float(ntot)
+    ssbg = (data.count(-1) * (data.mean(-1)-data.mean())**2).sum()
+    sswg = sstot-ssbg
+    dfbg = ngroups-1
+    dfwg = ntot - ngroups
+    msb = ssbg/float(dfbg)
+    msw = sswg/float(dfwg)
+    f = msb/msw
+    prob = special.fdtrc(dfbg, dfwg, f)  # equivalent to stats.f.sf
+
+    return F_onewayResult(f, prob)
+
+
+FriedmanchisquareResult = namedtuple('FriedmanchisquareResult',
+                                     ('statistic', 'pvalue'))
+
+
+def friedmanchisquare(*args):
+    """Friedman Chi-Square is a non-parametric, one-way within-subjects ANOVA.
+    This function calculates the Friedman Chi-square test for repeated measures
+    and returns the result, along with the associated probability value.
+
+    Each input is considered a given group. Ideally, the number of treatments
+    among each group should be equal. If this is not the case, only the first
+    n treatments are taken into account, where n is the number of treatments
+    of the smallest group.
+    If a group has some missing values, the corresponding treatments are masked
+    in the other groups.
+    The test statistic is corrected for ties.
+
+    Masked values in one group are propagated to the other groups.
+
+    Returns
+    -------
+    statistic : float
+        the test statistic.
+    pvalue : float
+        the associated p-value.
+
+    """
+    data = argstoarray(*args).astype(float)
+    k = len(data)
+    if k < 3:
+        raise ValueError(f"Less than 3 groups ({k}): the Friedman test "
+                         f"is NOT appropriate.")
+
+    ranked = ma.masked_values(rankdata(data, axis=0), 0)
+    if ranked._mask is not nomask:
+        ranked = ma.mask_cols(ranked)
+        ranked = ranked.compressed().reshape(k,-1).view(ndarray)
+    else:
+        ranked = ranked._data
+    (k,n) = ranked.shape
+    # Ties correction
+    repeats = [find_repeats(row) for row in ranked.T]
+    ties = np.array([y for x, y in repeats if x.size > 0])
+    tie_correction = 1 - (ties**3-ties).sum()/float(n*(k**3-k))
+
+    ssbg = np.sum((ranked.sum(-1) - n*(k+1)/2.)**2)
+    chisq = ssbg * 12./(n*k*(k+1)) * 1./tie_correction
+
+    return FriedmanchisquareResult(chisq,
+                                   distributions.chi2.sf(chisq, k-1))
+
+
+BrunnerMunzelResult = namedtuple('BrunnerMunzelResult', ('statistic', 'pvalue'))
+
+
+def brunnermunzel(x, y, alternative="two-sided", distribution="t"):
+    """
+    Compute the Brunner-Munzel test on samples x and y.
+
+    Any missing values in `x` and/or `y` are discarded.
+
+    The Brunner-Munzel test is a nonparametric test of the null hypothesis that
+    when values are taken one by one from each group, the probabilities of
+    getting large values in both groups are equal.
+    Unlike the Wilcoxon-Mann-Whitney's U test, this does not require the
+    assumption of equivariance of two groups. Note that this does not assume
+    the distributions are same. This test works on two independent samples,
+    which may have different sizes.
+
+    Parameters
+    ----------
+    x, y : array_like
+        Array of samples, should be one-dimensional.
+    alternative : 'less', 'two-sided', or 'greater', optional
+        Whether to get the p-value for the one-sided hypothesis ('less'
+        or 'greater') or for the two-sided hypothesis ('two-sided').
+        Defaults value is 'two-sided' .
+    distribution : 't' or 'normal', optional
+        Whether to get the p-value by t-distribution or by standard normal
+        distribution.
+        Defaults value is 't' .
+
+    Returns
+    -------
+    statistic : float
+        The Brunner-Munzer W statistic.
+    pvalue : float
+        p-value assuming a t distribution. One-sided or
+        two-sided, depending on the choice of `alternative` and `distribution`.
+
+    See Also
+    --------
+    mannwhitneyu : Mann-Whitney rank test on two samples.
+
+    Notes
+    -----
+    For more details on `brunnermunzel`, see `scipy.stats.brunnermunzel`.
+
+    Examples
+    --------
+    >>> from scipy.stats.mstats import brunnermunzel
+    >>> import numpy as np
+    >>> x1 = [1, 2, np.nan, np.nan, 1, 1, 1, 1, 1, 1, 2, 4, 1, 1]
+    >>> x2 = [3, 3, 4, 3, 1, 2, 3, 1, 1, 5, 4]
+    >>> brunnermunzel(x1, x2)
+    BrunnerMunzelResult(statistic=1.4723186918922935, pvalue=0.15479415300426624)  # may vary
+
+    """  # noqa: E501
+    x = ma.asarray(x).compressed().view(ndarray)
+    y = ma.asarray(y).compressed().view(ndarray)
+    nx = len(x)
+    ny = len(y)
+    if nx == 0 or ny == 0:
+        return BrunnerMunzelResult(np.nan, np.nan)
+    rankc = rankdata(np.concatenate((x,y)))
+    rankcx = rankc[0:nx]
+    rankcy = rankc[nx:nx+ny]
+    rankcx_mean = np.mean(rankcx)
+    rankcy_mean = np.mean(rankcy)
+    rankx = rankdata(x)
+    ranky = rankdata(y)
+    rankx_mean = np.mean(rankx)
+    ranky_mean = np.mean(ranky)
+
+    Sx = np.sum(np.power(rankcx - rankx - rankcx_mean + rankx_mean, 2.0))
+    Sx /= nx - 1
+    Sy = np.sum(np.power(rankcy - ranky - rankcy_mean + ranky_mean, 2.0))
+    Sy /= ny - 1
+
+    wbfn = nx * ny * (rankcy_mean - rankcx_mean)
+    wbfn /= (nx + ny) * np.sqrt(nx * Sx + ny * Sy)
+
+    if distribution == "t":
+        df_numer = np.power(nx * Sx + ny * Sy, 2.0)
+        df_denom = np.power(nx * Sx, 2.0) / (nx - 1)
+        df_denom += np.power(ny * Sy, 2.0) / (ny - 1)
+        df = df_numer / df_denom
+        p = distributions.t.cdf(wbfn, df)
+    elif distribution == "normal":
+        p = distributions.norm.cdf(wbfn)
+    else:
+        raise ValueError(
+            "distribution should be 't' or 'normal'")
+
+    if alternative == "greater":
+        pass
+    elif alternative == "less":
+        p = 1 - p
+    elif alternative == "two-sided":
+        p = 2 * np.min([p, 1-p])
+    else:
+        raise ValueError(
+            "alternative should be 'less', 'greater' or 'two-sided'")
+
+    return BrunnerMunzelResult(wbfn, p)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_mstats_extras.py b/venv/lib/python3.12/site-packages/scipy/stats/_mstats_extras.py
new file mode 100644
index 0000000000000000000000000000000000000000..d7b5484fb930edadb0538576e0cb736c82957e7a
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_mstats_extras.py
@@ -0,0 +1,520 @@
+"""
+Additional statistics functions with support for masked arrays.
+
+"""
+
+# Original author (2007): Pierre GF Gerard-Marchant
+
+
+__all__ = ['compare_medians_ms',
+           'hdquantiles', 'hdmedian', 'hdquantiles_sd',
+           'idealfourths',
+           'median_cihs','mjci','mquantiles_cimj',
+           'rsh',
+           'trimmed_mean_ci',]
+
+
+import numpy as np
+from numpy import float64, ndarray
+
+import numpy.ma as ma
+from numpy.ma import MaskedArray
+
+from . import _mstats_basic as mstats
+
+from scipy.stats.distributions import norm, beta, t, binom
+
+
+def hdquantiles(data, prob=(.25, .5, .75), axis=None, var=False,):
+    """
+    Computes quantile estimates with the Harrell-Davis method.
+
+    The quantile estimates are calculated as a weighted linear combination
+    of order statistics.
+
+    Parameters
+    ----------
+    data : array_like
+        Data array.
+    prob : sequence, optional
+        Sequence of probabilities at which to compute the quantiles.
+    axis : int or None, optional
+        Axis along which to compute the quantiles. If None, use a flattened
+        array.
+    var : bool, optional
+        Whether to return the variance of the estimate.
+
+    Returns
+    -------
+    hdquantiles : MaskedArray
+        A (p,) array of quantiles (if `var` is False), or a (2,p) array of
+        quantiles and variances (if `var` is True), where ``p`` is the
+        number of quantiles.
+
+    See Also
+    --------
+    hdquantiles_sd
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats.mstats import hdquantiles
+    >>>
+    >>> # Sample data
+    >>> data = np.array([1.2, 2.5, 3.7, 4.0, 5.1, 6.3, 7.0, 8.2, 9.4])
+    >>>
+    >>> # Probabilities at which to compute quantiles
+    >>> probabilities = [0.25, 0.5, 0.75]
+    >>>
+    >>> # Compute Harrell-Davis quantile estimates
+    >>> quantile_estimates = hdquantiles(data, prob=probabilities)
+    >>>
+    >>> # Display the quantile estimates
+    >>> for i, quantile in enumerate(probabilities):
+    ...     print(f"{int(quantile * 100)}th percentile: {quantile_estimates[i]}")
+    25th percentile: 3.1505820231763066 # may vary
+    50th percentile: 5.194344084883956
+    75th percentile: 7.430626414674935
+
+    """
+    def _hd_1D(data,prob,var):
+        "Computes the HD quantiles for a 1D array. Returns nan for invalid data."
+        xsorted = np.squeeze(np.sort(data.compressed().view(ndarray)))
+        # Don't use length here, in case we have a numpy scalar
+        n = xsorted.size
+
+        hd = np.empty((2,len(prob)), float64)
+        if n < 2:
+            hd.flat = np.nan
+            if var:
+                return hd
+            return hd[0]
+
+        v = np.arange(n+1) / float(n)
+        betacdf = beta.cdf
+        for (i,p) in enumerate(prob):
+            _w = betacdf(v, (n+1)*p, (n+1)*(1-p))
+            w = _w[1:] - _w[:-1]
+            hd_mean = np.dot(w, xsorted)
+            hd[0,i] = hd_mean
+            #
+            hd[1,i] = np.dot(w, (xsorted-hd_mean)**2)
+            #
+        hd[0, prob == 0] = xsorted[0]
+        hd[0, prob == 1] = xsorted[-1]
+        if var:
+            hd[1, prob == 0] = hd[1, prob == 1] = np.nan
+            return hd
+        return hd[0]
+    # Initialization & checks
+    data = ma.array(data, copy=False, dtype=float64)
+    p = np.atleast_1d(np.asarray(prob))
+    # Computes quantiles along axis (or globally)
+    if (axis is None) or (data.ndim == 1):
+        result = _hd_1D(data, p, var)
+    else:
+        if data.ndim > 2:
+            raise ValueError(f"Array 'data' must be at most two dimensional, "
+                             f"but got data.ndim = {data.ndim}")
+        result = ma.apply_along_axis(_hd_1D, axis, data, p, var)
+
+    return ma.fix_invalid(result, copy=False)
+
+
+def hdmedian(data, axis=-1, var=False):
+    """
+    Returns the Harrell-Davis estimate of the median along the given axis.
+
+    Parameters
+    ----------
+    data : ndarray
+        Data array.
+    axis : int, optional
+        Axis along which to compute the quantiles. If None, use a flattened
+        array.
+    var : bool, optional
+        Whether to return the variance of the estimate.
+
+    Returns
+    -------
+    hdmedian : MaskedArray
+        The median values.  If ``var=True``, the variance is returned inside
+        the masked array.  E.g. for a 1-D array the shape change from (1,) to
+        (2,).
+
+    """
+    result = hdquantiles(data,[0.5], axis=axis, var=var)
+    return result.squeeze()
+
+
+def hdquantiles_sd(data, prob=(.25, .5, .75), axis=None):
+    """
+    The standard error of the Harrell-Davis quantile estimates by jackknife.
+
+    Parameters
+    ----------
+    data : array_like
+        Data array.
+    prob : sequence, optional
+        Sequence of quantiles to compute.
+    axis : int, optional
+        Axis along which to compute the quantiles. If None, use a flattened
+        array.
+
+    Returns
+    -------
+    hdquantiles_sd : MaskedArray
+        Standard error of the Harrell-Davis quantile estimates.
+
+    See Also
+    --------
+    hdquantiles
+
+    """
+    def _hdsd_1D(data, prob):
+        "Computes the std error for 1D arrays."
+        xsorted = np.sort(data.compressed())
+        n = len(xsorted)
+
+        hdsd = np.empty(len(prob), float64)
+        if n < 2:
+            hdsd.flat = np.nan
+
+        vv = np.arange(n) / float(n-1)
+        betacdf = beta.cdf
+
+        for (i,p) in enumerate(prob):
+            _w = betacdf(vv, n*p, n*(1-p))
+            w = _w[1:] - _w[:-1]
+            # cumulative sum of weights and data points if
+            # ith point is left out for jackknife
+            mx_ = np.zeros_like(xsorted)
+            mx_[1:] = np.cumsum(w * xsorted[:-1])
+            # similar but from the right
+            mx_[:-1] += np.cumsum(w[::-1] * xsorted[:0:-1])[::-1]
+            hdsd[i] = np.sqrt(mx_.var() * (n - 1))
+        return hdsd
+
+    # Initialization & checks
+    data = ma.array(data, copy=False, dtype=float64)
+    p = np.atleast_1d(np.asarray(prob))
+    # Computes quantiles along axis (or globally)
+    if (axis is None):
+        result = _hdsd_1D(data, p)
+    else:
+        if data.ndim > 2:
+            raise ValueError(f"Array 'data' must be at most two dimensional, "
+                             f"but got data.ndim = {data.ndim}")
+        result = ma.apply_along_axis(_hdsd_1D, axis, data, p)
+
+    return ma.fix_invalid(result, copy=False).ravel()
+
+
+def trimmed_mean_ci(data, limits=(0.2,0.2), inclusive=(True,True),
+                    alpha=0.05, axis=None):
+    """
+    Selected confidence interval of the trimmed mean along the given axis.
+
+    Parameters
+    ----------
+    data : array_like
+        Input data.
+    limits : {None, tuple}, optional
+        None or a two item tuple.
+        Tuple of the percentages to cut on each side of the array, with respect
+        to the number of unmasked data, as floats between 0. and 1. If ``n``
+        is the number of unmasked data before trimming, then
+        (``n * limits[0]``)th smallest data and (``n * limits[1]``)th
+        largest data are masked.  The total number of unmasked data after
+        trimming is ``n * (1. - sum(limits))``.
+        The value of one limit can be set to None to indicate an open interval.
+
+        Defaults to (0.2, 0.2).
+    inclusive : (2,) tuple of boolean, optional
+        If relative==False, tuple indicating whether values exactly equal to
+        the absolute limits are allowed.
+        If relative==True, tuple indicating whether the number of data being
+        masked on each side should be rounded (True) or truncated (False).
+
+        Defaults to (True, True).
+    alpha : float, optional
+        Confidence level of the intervals.
+
+        Defaults to 0.05.
+    axis : int, optional
+        Axis along which to cut. If None, uses a flattened version of `data`.
+
+        Defaults to None.
+
+    Returns
+    -------
+    trimmed_mean_ci : (2,) ndarray
+        The lower and upper confidence intervals of the trimmed data.
+
+    """
+    data = ma.array(data, copy=False)
+    trimmed = mstats.trimr(data, limits=limits, inclusive=inclusive, axis=axis)
+    tmean = trimmed.mean(axis)
+    tstde = mstats.trimmed_stde(data,limits=limits,inclusive=inclusive,axis=axis)
+    df = trimmed.count(axis) - 1
+    tppf = t.ppf(1-alpha/2.,df)
+    return np.array((tmean - tppf*tstde, tmean+tppf*tstde))
+
+
+def mjci(data, prob=(0.25, 0.5, 0.75), axis=None):
+    """
+    Returns the Maritz-Jarrett estimators of the standard error of selected
+    experimental quantiles of the data.
+
+    Parameters
+    ----------
+    data : ndarray
+        Data array.
+    prob : sequence, optional
+        Sequence of quantiles to compute.
+    axis : int or None, optional
+        Axis along which to compute the quantiles. If None, use a flattened
+        array.
+
+    """  # numpydoc ignore=RT01
+    def _mjci_1D(data, p):
+        data = np.sort(data.compressed())
+        n = data.size
+        prob = (np.array(p) * n + 0.5).astype(int)
+        betacdf = beta.cdf
+
+        mj = np.empty(len(prob), float64)
+        x = np.arange(1,n+1, dtype=float64) / n
+        y = x - 1./n
+        for (i,m) in enumerate(prob):
+            W = betacdf(x,m-1,n-m) - betacdf(y,m-1,n-m)
+            C1 = np.dot(W,data)
+            C2 = np.dot(W,data**2)
+            mj[i] = np.sqrt(C2 - C1**2)
+        return mj
+
+    data = ma.array(data, copy=False)
+    if data.ndim > 2:
+        raise ValueError(f"Array 'data' must be at most two dimensional, "
+                         f"but got data.ndim = {data.ndim}")
+
+    p = np.atleast_1d(np.asarray(prob))
+    # Computes quantiles along axis (or globally)
+    if (axis is None):
+        return _mjci_1D(data, p)
+    else:
+        return ma.apply_along_axis(_mjci_1D, axis, data, p)
+
+
+def mquantiles_cimj(data, prob=(0.25, 0.50, 0.75), alpha=0.05, axis=None):
+    """
+    Computes the alpha confidence interval for the selected quantiles of the
+    data, with Maritz-Jarrett estimators.
+
+    Parameters
+    ----------
+    data : ndarray
+        Data array.
+    prob : sequence, optional
+        Sequence of quantiles to compute.
+    alpha : float, optional
+        Confidence level of the intervals.
+    axis : int or None, optional
+        Axis along which to compute the quantiles.
+        If None, use a flattened array.
+
+    Returns
+    -------
+    ci_lower : ndarray
+        The lower boundaries of the confidence interval.  Of the same length as
+        `prob`.
+    ci_upper : ndarray
+        The upper boundaries of the confidence interval.  Of the same length as
+        `prob`.
+
+    """
+    alpha = min(alpha, 1 - alpha)
+    z = norm.ppf(1 - alpha/2.)
+    xq = mstats.mquantiles(data, prob, alphap=0, betap=0, axis=axis)
+    smj = mjci(data, prob, axis=axis)
+    return (xq - z * smj, xq + z * smj)
+
+
+def median_cihs(data, alpha=0.05, axis=None):
+    """
+    Computes the alpha-level confidence interval for the median of the data.
+
+    Uses the Hettmasperger-Sheather method.
+
+    Parameters
+    ----------
+    data : array_like
+        Input data. Masked values are discarded. The input should be 1D only,
+        or `axis` should be set to None.
+    alpha : float, optional
+        Confidence level of the intervals.
+    axis : int or None, optional
+        Axis along which to compute the quantiles. If None, use a flattened
+        array.
+
+    Returns
+    -------
+    median_cihs
+        Alpha level confidence interval.
+
+    """
+    def _cihs_1D(data, alpha):
+        data = np.sort(data.compressed())
+        n = len(data)
+        alpha = min(alpha, 1-alpha)
+        k = int(binom._ppf(alpha/2., n, 0.5))
+        gk = binom.cdf(n-k,n,0.5) - binom.cdf(k-1,n,0.5)
+        if gk < 1-alpha:
+            k -= 1
+            gk = binom.cdf(n-k,n,0.5) - binom.cdf(k-1,n,0.5)
+        gkk = binom.cdf(n-k-1,n,0.5) - binom.cdf(k,n,0.5)
+        I = (gk - 1 + alpha)/(gk - gkk)
+        lambd = (n-k) * I / float(k + (n-2*k)*I)
+        lims = (lambd*data[k] + (1-lambd)*data[k-1],
+                lambd*data[n-k-1] + (1-lambd)*data[n-k])
+        return lims
+    data = ma.array(data, copy=False)
+    # Computes quantiles along axis (or globally)
+    if (axis is None):
+        result = _cihs_1D(data, alpha)
+    else:
+        if data.ndim > 2:
+            raise ValueError(f"Array 'data' must be at most two dimensional, "
+                             f"but got data.ndim = {data.ndim}")
+        result = ma.apply_along_axis(_cihs_1D, axis, data, alpha)
+
+    return result
+
+
+def compare_medians_ms(group_1, group_2, axis=None):
+    """
+    Compares the medians from two independent groups along the given axis.
+
+    The comparison is performed using the McKean-Schrader estimate of the
+    standard error of the medians.
+
+    Parameters
+    ----------
+    group_1 : array_like
+        First dataset.  Has to be of size >=7.
+    group_2 : array_like
+        Second dataset.  Has to be of size >=7.
+    axis : int, optional
+        Axis along which the medians are estimated. If None, the arrays are
+        flattened.  If `axis` is not None, then `group_1` and `group_2`
+        should have the same shape.
+
+    Returns
+    -------
+    compare_medians_ms : {float, ndarray}
+        If `axis` is None, then returns a float, otherwise returns a 1-D
+        ndarray of floats with a length equal to the length of `group_1`
+        along `axis`.
+
+    References
+    ----------
+    .. [1] McKean, Joseph W., and Ronald M. Schrader. "A comparison of methods
+       for studentizing the sample median." Communications in
+       Statistics-Simulation and Computation 13.6 (1984): 751-773.
+
+    Examples
+    --------
+
+    >>> from scipy import stats
+    >>> a = [1, 2, 3, 4, 5, 6, 7]
+    >>> b = [8, 9, 10, 11, 12, 13, 14]
+    >>> stats.mstats.compare_medians_ms(a, b, axis=None)
+    1.0693225866553746e-05
+
+    The function is vectorized to compute along a given axis.
+
+    >>> import numpy as np
+    >>> rng = np.random.default_rng()
+    >>> x = rng.random(size=(3, 7))
+    >>> y = rng.random(size=(3, 8))
+    >>> stats.mstats.compare_medians_ms(x, y, axis=1)
+    array([0.36908985, 0.36092538, 0.2765313 ])
+    """
+    (med_1, med_2) = (ma.median(group_1,axis=axis), ma.median(group_2,axis=axis))
+    (std_1, std_2) = (mstats.stde_median(group_1, axis=axis),
+                      mstats.stde_median(group_2, axis=axis))
+    W = np.abs(med_1 - med_2) / ma.sqrt(std_1**2 + std_2**2)
+    return 1 - norm.cdf(W)
+
+
+def idealfourths(data, axis=None):
+    """
+    Returns an estimate of the lower and upper quartiles.
+
+    Uses the ideal fourths algorithm.
+
+    Parameters
+    ----------
+    data : array_like
+        Input array.
+    axis : int, optional
+        Axis along which the quartiles are estimated. If None, the arrays are
+        flattened.
+
+    Returns
+    -------
+    idealfourths : {list of floats, masked array}
+        Returns the two internal values that divide `data` into four parts
+        using the ideal fourths algorithm either along the flattened array
+        (if `axis` is None) or along `axis` of `data`.
+
+    """
+    def _idf(data):
+        x = data.compressed()
+        n = len(x)
+        if n < 3:
+            return [np.nan,np.nan]
+        (j,h) = divmod(n/4. + 5/12.,1)
+        j = int(j)
+        qlo = (1-h)*x[j-1] + h*x[j]
+        k = n - j
+        qup = (1-h)*x[k] + h*x[k-1]
+        return [qlo, qup]
+    data = ma.sort(data, axis=axis).view(MaskedArray)
+    if (axis is None):
+        return _idf(data)
+    else:
+        return ma.apply_along_axis(_idf, axis, data)
+
+
+def rsh(data, points=None):
+    """
+    Evaluates Rosenblatt's shifted histogram estimators for each data point.
+
+    Rosenblatt's estimator is a centered finite-difference approximation to the
+    derivative of the empirical cumulative distribution function.
+
+    Parameters
+    ----------
+    data : sequence
+        Input data, should be 1-D. Masked values are ignored.
+    points : sequence or None, optional
+        Sequence of points where to evaluate Rosenblatt shifted histogram.
+        If None, use the data.
+
+    """  # numpydoc ignore=RT01
+    data = ma.array(data, copy=False)
+    if points is None:
+        points = data
+    else:
+        points = np.atleast_1d(np.asarray(points))
+
+    if data.ndim != 1:
+        raise AttributeError("The input array should be 1D only !")
+
+    n = data.count()
+    r = idealfourths(data, axis=None)
+    h = 1.2 * (r[-1]-r[0]) / n**(1./5)
+    nhi = (data[:,None] <= points[None,:] + h).sum(0)
+    nlo = (data[:,None] < points[None,:] - h).sum(0)
+    return (nhi-nlo) / (2.*n*h)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_multicomp.py b/venv/lib/python3.12/site-packages/scipy/stats/_multicomp.py
new file mode 100644
index 0000000000000000000000000000000000000000..f7251be0912025e81afee9169e781e9b16ff5ce7
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_multicomp.py
@@ -0,0 +1,457 @@
+import warnings
+from collections.abc import Sequence
+from dataclasses import dataclass, field
+from typing import TYPE_CHECKING, Literal
+
+import numpy as np
+
+from scipy import stats
+from scipy.optimize import minimize_scalar
+from scipy.stats._common import ConfidenceInterval
+from scipy.stats._qmc import check_random_state
+from scipy.stats._stats_py import _var
+from scipy._lib._array_api import xp_capabilities
+from scipy._lib._util import _transition_to_rng, DecimalNumber, SeedType
+
+
+if TYPE_CHECKING:
+    import numpy.typing as npt
+
+
+__all__ = [
+    'dunnett'
+]
+
+
+@dataclass
+class DunnettResult:
+    """Result object returned by `scipy.stats.dunnett`.
+
+    Attributes
+    ----------
+    statistic : float ndarray
+        The computed statistic of the test for each comparison. The element
+        at index ``i`` is the statistic for the comparison between
+        groups ``i`` and the control.
+    pvalue : float ndarray
+        The computed p-value of the test for each comparison. The element
+        at index ``i`` is the p-value for the comparison between
+        group ``i`` and the control.
+    """
+    statistic: np.ndarray
+    pvalue: np.ndarray
+    _alternative: Literal['two-sided', 'less', 'greater'] = field(repr=False)
+    _rho: np.ndarray = field(repr=False)
+    _df: int = field(repr=False)
+    _std: float = field(repr=False)
+    _mean_samples: np.ndarray = field(repr=False)
+    _mean_control: np.ndarray = field(repr=False)
+    _n_samples: np.ndarray = field(repr=False)
+    _n_control: int = field(repr=False)
+    _rng: SeedType = field(repr=False)
+    _ci: ConfidenceInterval | None = field(default=None, repr=False)
+    _ci_cl: DecimalNumber | None = field(default=None, repr=False)
+
+    @classmethod
+    def __class_getitem__(cls, arg, /):
+        # generic type compatibility with scipy-stubs
+        from types import GenericAlias
+        return GenericAlias(cls, arg)
+
+    def __str__(self):
+        # Note: `__str__` prints the confidence intervals from the most
+        # recent call to `confidence_interval`. If it has not been called,
+        # it will be called with the default CL of .95.
+        if self._ci is None:
+            self.confidence_interval(confidence_level=.95)
+        s = (
+            "Dunnett's test"
+            f" ({self._ci_cl*100:.1f}% Confidence Interval)\n"
+            "Comparison               Statistic  p-value  Lower CI  Upper CI\n"
+        )
+        for i in range(self.pvalue.size):
+            s += (f" (Sample {i} - Control) {self.statistic[i]:>10.3f}"
+                  f"{self.pvalue[i]:>10.3f}"
+                  f"{self._ci.low[i]:>10.3f}"
+                  f"{self._ci.high[i]:>10.3f}\n")
+
+        return s
+
+    def _allowance(
+        self, confidence_level: DecimalNumber = 0.95, tol: DecimalNumber = 1e-3
+    ) -> float:
+        """Allowance.
+
+        It is the quantity to add/subtract from the observed difference
+        between the means of observed groups and the mean of the control
+        group. The result gives confidence limits.
+
+        Parameters
+        ----------
+        confidence_level : float, optional
+            Confidence level for the computed confidence interval.
+            Default is .95.
+        tol : float, optional
+            A tolerance for numerical optimization: the allowance will produce
+            a confidence within ``10*tol*(1 - confidence_level)`` of the
+            specified level, or a warning will be emitted. Tight tolerances
+            may be impractical due to noisy evaluation of the objective.
+            Default is 1e-3.
+
+        Returns
+        -------
+        allowance : float
+            Allowance around the mean.
+        """
+        alpha = 1 - confidence_level
+
+        def pvalue_from_stat(statistic):
+            statistic = np.array(statistic)
+            sf = _pvalue_dunnett(
+                rho=self._rho, df=self._df,
+                statistic=statistic, alternative=self._alternative,
+                rng=self._rng
+            )
+            return abs(sf - alpha)/alpha
+
+        # Evaluation of `pvalue_from_stat` is noisy due to the use of RQMC to
+        # evaluate `multivariate_t.cdf`. `minimize_scalar` is not designed
+        # to tolerate a noisy objective function and may fail to find the
+        # minimum accurately. We mitigate this possibility with the validation
+        # step below, but implementation of a noise-tolerant root finder or
+        # minimizer would be a welcome enhancement. See gh-18150.
+        res = minimize_scalar(pvalue_from_stat, method='brent', tol=tol)
+        critical_value = res.x
+
+        # validation
+        # tol*10 because tol=1e-3 means we tolerate a 1% change at most
+        if res.success is False or res.fun >= tol*10:
+            warnings.warn(
+                "Computation of the confidence interval did not converge to "
+                "the desired level. The confidence level corresponding with "
+                f"the returned interval is approximately {alpha*(1+res.fun)}.",
+                stacklevel=3
+            )
+
+        # From [1] p. 1101 between (1) and (3)
+        allowance = critical_value*self._std*np.sqrt(
+            1/self._n_samples + 1/self._n_control
+        )
+        return abs(allowance)
+
+    def confidence_interval(
+        self, confidence_level: DecimalNumber = 0.95
+    ) -> ConfidenceInterval:
+        """Compute the confidence interval for the specified confidence level.
+
+        Parameters
+        ----------
+        confidence_level : float, optional
+            Confidence level for the computed confidence interval.
+            Default is .95.
+
+        Returns
+        -------
+        ci : ``ConfidenceInterval`` object
+            The object has attributes ``low`` and ``high`` that hold the
+            lower and upper bounds of the confidence intervals for each
+            comparison. The high and low values are accessible for each
+            comparison at index ``i`` for each group ``i``.
+
+        """
+        # check to see if the supplied confidence level matches that of the
+        # previously computed CI.
+        if (self._ci is not None) and (confidence_level == self._ci_cl):
+            return self._ci
+
+        if not (0 < confidence_level < 1):
+            raise ValueError("Confidence level must be between 0 and 1.")
+
+        allowance = self._allowance(confidence_level=confidence_level)
+        diff_means = self._mean_samples - self._mean_control
+
+        low = diff_means-allowance
+        high = diff_means+allowance
+
+        if self._alternative == 'greater':
+            high = [np.inf] * len(diff_means)
+        elif self._alternative == 'less':
+            low = [-np.inf] * len(diff_means)
+
+        self._ci_cl = confidence_level
+        self._ci = ConfidenceInterval(
+            low=low,
+            high=high
+        )
+        return self._ci
+
+
+@xp_capabilities(np_only=True)
+@_transition_to_rng('random_state', replace_doc=False)
+def dunnett(
+    *samples: "npt.ArrayLike",  # noqa: D417
+    control: "npt.ArrayLike",
+    alternative: Literal['two-sided', 'less', 'greater'] = "two-sided",
+    rng: SeedType = None
+) -> DunnettResult:
+    """Dunnett's test: multiple comparisons of means against a control group.
+
+    This is an implementation of Dunnett's original, single-step test as
+    described in [1]_.
+
+    Parameters
+    ----------
+    *samples : 1D array_like
+        The sample measurements for each experimental group.
+    control : 1D array_like
+        The sample measurements for the control group.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis.
+
+        The null hypothesis is that the means of the distributions underlying
+        the samples and control are equal. The following alternative
+        hypotheses are available (default is 'two-sided'):
+
+        * 'two-sided': the means of the distributions underlying the samples
+          and control are unequal.
+        * 'less': the means of the distributions underlying the samples
+          are less than the mean of the distribution underlying the control.
+        * 'greater': the means of the distributions underlying the
+          samples are greater than the mean of the distribution underlying
+          the control.
+    rng : `numpy.random.Generator`, optional
+        Pseudorandom number generator state. When `rng` is None, a new
+        `numpy.random.Generator` is created using entropy from the
+        operating system. Types other than `numpy.random.Generator` are
+        passed to `numpy.random.default_rng` to instantiate a ``Generator``.
+
+        .. versionchanged:: 1.15.0
+
+            As part of the `SPEC-007 <https://scientific-python.org/specs/spec-0007/>`_
+            transition from use of `numpy.random.RandomState` to
+            `numpy.random.Generator`, this keyword was changed from `random_state` to
+            `rng`. For an interim period, both keywords will continue to work, although
+            only one may be specified at a time. After the interim period, function
+            calls using the `random_state` keyword will emit warnings. Following a
+            deprecation period, the `random_state` keyword will be removed.
+
+    Returns
+    -------
+    res : `~scipy.stats._result_classes.DunnettResult`
+        An object containing attributes:
+
+        statistic : float ndarray
+            The computed statistic of the test for each comparison. The element
+            at index ``i`` is the statistic for the comparison between
+            groups ``i`` and the control.
+        pvalue : float ndarray
+            The computed p-value of the test for each comparison. The element
+            at index ``i`` is the p-value for the comparison between
+            group ``i`` and the control.
+
+        And the following method:
+
+        confidence_interval(confidence_level=0.95) :
+            Compute the difference in means of the groups
+            with the control +- the allowance.
+
+    See Also
+    --------
+    tukey_hsd : performs pairwise comparison of means.
+    :ref:`hypothesis_dunnett` : Extended example
+
+    Notes
+    -----
+    Like the independent-sample t-test, Dunnett's test [1]_ is used to make
+    inferences about the means of distributions from which samples were drawn.
+    However, when multiple t-tests are performed at a fixed significance level,
+    the "family-wise error rate" - the probability of incorrectly rejecting the
+    null hypothesis in at least one test - will exceed the significance level.
+    Dunnett's test is designed to perform multiple comparisons while
+    controlling the family-wise error rate.
+
+    Dunnett's test compares the means of multiple experimental groups
+    against a single control group. Tukey's Honestly Significant Difference Test
+    is another multiple-comparison test that controls the family-wise error
+    rate, but `tukey_hsd` performs *all* pairwise comparisons between groups.
+    When pairwise comparisons between experimental groups are not needed,
+    Dunnett's test is preferable due to its higher power.
+
+    The use of this test relies on several assumptions.
+
+    1. The observations are independent within and among groups.
+    2. The observations within each group are normally distributed.
+    3. The distributions from which the samples are drawn have the same finite
+       variance.
+
+    References
+    ----------
+    .. [1] Dunnett, Charles W. (1955) "A Multiple Comparison Procedure for
+           Comparing Several Treatments with a Control." Journal of the American
+           Statistical Association, 50:272, 1096-1121,
+           :doi:`10.1080/01621459.1955.10501294`
+    .. [2] Thomson, M. L., & Short, M. D. (1969). Mucociliary function in
+           health, chronic obstructive airway disease, and asbestosis. Journal
+           of applied physiology, 26(5), 535-539.
+           :doi:`10.1152/jappl.1969.26.5.535`
+
+    Examples
+    --------
+    We'll use data from [2]_, Table 1. The null hypothesis is that the means of
+    the distributions underlying the samples and control are equal.
+
+    First, we test that the means of the distributions underlying the samples
+    and control are unequal (``alternative='two-sided'``, the default).
+
+    >>> import numpy as np
+    >>> from scipy.stats import dunnett
+    >>> samples = [[3.8, 2.7, 4.0, 2.4], [2.8, 3.4, 3.7, 2.2, 2.0]]
+    >>> control = [2.9, 3.0, 2.5, 2.6, 3.2]
+    >>> res = dunnett(*samples, control=control)
+    >>> res.statistic
+    array([ 0.90874545, -0.05007117])
+    >>> res.pvalue
+    array([0.58325114, 0.99819341])
+
+    Now, we test that the means of the distributions underlying the samples are
+    greater than the mean of the distribution underlying the control.
+
+    >>> res = dunnett(*samples, control=control, alternative='greater')
+    >>> res.statistic
+    array([ 0.90874545, -0.05007117])
+    >>> res.pvalue
+    array([0.30230596, 0.69115597])
+
+    For a more detailed example, see :ref:`hypothesis_dunnett`.
+    """
+    samples_, control_, rng = _iv_dunnett(
+        samples=samples, control=control,
+        alternative=alternative, rng=rng
+    )
+
+    rho, df, n_group, n_samples, n_control = _params_dunnett(
+        samples=samples_, control=control_
+    )
+
+    statistic, std, mean_control, mean_samples = _statistic_dunnett(
+        samples_, control_, df, n_samples, n_control
+    )
+
+    pvalue = _pvalue_dunnett(
+        rho=rho, df=df, statistic=statistic, alternative=alternative, rng=rng
+    )
+
+    return DunnettResult(
+        statistic=statistic, pvalue=pvalue,
+        _alternative=alternative,
+        _rho=rho, _df=df, _std=std,
+        _mean_samples=mean_samples,
+        _mean_control=mean_control,
+        _n_samples=n_samples,
+        _n_control=n_control,
+        _rng=rng
+    )
+
+
+def _iv_dunnett(
+    samples: Sequence["npt.ArrayLike"],
+    control: "npt.ArrayLike",
+    alternative: Literal['two-sided', 'less', 'greater'],
+    rng: SeedType
+) -> tuple[list[np.ndarray], np.ndarray, SeedType]:
+    """Input validation for Dunnett's test."""
+    rng = check_random_state(rng)
+
+    if alternative not in {'two-sided', 'less', 'greater'}:
+        raise ValueError(
+            "alternative must be 'less', 'greater' or 'two-sided'"
+        )
+
+    ndim_msg = "Control and samples groups must be 1D arrays"
+    n_obs_msg = "Control and samples groups must have at least 1 observation"
+
+    control = np.asarray(control)
+    samples_ = [np.asarray(sample) for sample in samples]
+
+    # samples checks
+    samples_control: list[np.ndarray] = samples_ + [control]
+    for sample in samples_control:
+        if sample.ndim > 1:
+            raise ValueError(ndim_msg)
+
+        if sample.size < 1:
+            raise ValueError(n_obs_msg)
+
+    return samples_, control, rng
+
+
+def _params_dunnett(
+    samples: list[np.ndarray], control: np.ndarray
+) -> tuple[np.ndarray, int, int, np.ndarray, int]:
+    """Specific parameters for Dunnett's test.
+
+    Degree of freedom is the number of observations minus the number of groups
+    including the control.
+    """
+    n_samples = np.array([sample.size for sample in samples])
+
+    # From [1] p. 1100 d.f. = (sum N)-(p+1)
+    n_sample = n_samples.sum()
+    n_control = control.size
+    n = n_sample + n_control
+    n_groups = len(samples)
+    df = n - n_groups - 1
+
+    # From [1] p. 1103 rho_ij = 1/sqrt((N0/Ni+1)(N0/Nj+1))
+    rho = n_control/n_samples + 1
+    rho = 1/np.sqrt(rho[:, None] * rho[None, :])
+    np.fill_diagonal(rho, 1)
+
+    return rho, df, n_groups, n_samples, n_control
+
+
+def _statistic_dunnett(
+    samples: list[np.ndarray], control: np.ndarray, df: int,
+    n_samples: np.ndarray, n_control: int
+) -> tuple[np.ndarray, float, np.ndarray, np.ndarray]:
+    """Statistic of Dunnett's test.
+
+    Computation based on the original single-step test from [1].
+    """
+    mean_control = np.mean(control)
+    mean_samples = np.array([np.mean(sample) for sample in samples])
+    all_samples = [control] + samples
+    all_means = np.concatenate([[mean_control], mean_samples])
+
+    # Variance estimate s^2 from [1] Eq. 1
+    s2 = np.sum([_var(sample, mean=mean)*sample.size
+                 for sample, mean in zip(all_samples, all_means)]) / df
+    std = np.sqrt(s2)
+
+    # z score inferred from [1] unlabeled equation after Eq. 1
+    z = (mean_samples - mean_control) / np.sqrt(1/n_samples + 1/n_control)
+
+    return z / std, std, mean_control, mean_samples
+
+
+def _pvalue_dunnett(
+    rho: np.ndarray, df: int, statistic: np.ndarray,
+    alternative: Literal['two-sided', 'less', 'greater'],
+    rng: SeedType = None
+) -> np.ndarray:
+    """pvalue from the multivariate t-distribution.
+
+    Critical values come from the multivariate student-t distribution.
+    """
+    statistic = statistic.reshape(-1, 1)
+
+    mvt = stats.multivariate_t(shape=rho, df=df, seed=rng)
+    if alternative == "two-sided":
+        statistic = abs(statistic)
+        pvalue = 1 - mvt.cdf(statistic, lower_limit=-statistic)
+    elif alternative == "greater":
+        pvalue = 1 - mvt.cdf(statistic, lower_limit=-np.inf)
+    else:
+        pvalue = 1 - mvt.cdf(np.inf, lower_limit=statistic)
+
+    return np.atleast_1d(pvalue)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_multivariate.py b/venv/lib/python3.12/site-packages/scipy/stats/_multivariate.py
new file mode 100644
index 0000000000000000000000000000000000000000..51e5c8dc8f5272381d17e8edc33662a635628bba
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_multivariate.py
@@ -0,0 +1,8054 @@
+#
+# Author: Joris Vankerschaver 2013
+#
+import math
+import threading
+import types
+import numpy as np
+import scipy.linalg
+from scipy._lib import doccer
+from scipy.special import (gammaln, psi, multigammaln, xlogy, entr, betaln,
+                           ive, loggamma)
+from scipy import special
+import scipy._external.array_api_extra as xpx
+from scipy._lib._util import check_random_state
+from scipy.linalg.blas import get_blas_funcs
+from ._continuous_distns import norm, invgamma
+from ._discrete_distns import binom
+from . import _covariance, _rcont
+from ._qmvnt import _qmvt, _qmvn, _qauto
+from ._morestats import directional_stats
+from scipy.optimize import root_scalar
+
+__all__ = ['multivariate_normal',
+           'matrix_normal',
+           'dirichlet',
+           'dirichlet_multinomial',
+           'wishart',
+           'invwishart',
+           'multinomial',
+           'special_ortho_group',
+           'ortho_group',
+           'random_correlation',
+           'unitary_group',
+           'multivariate_t',
+           'multivariate_hypergeom',
+           'random_table',
+           'uniform_direction',
+           'vonmises_fisher',
+           'normal_inverse_gamma',
+           'matrix_t']
+
+_LOG_2PI = np.log(2 * np.pi)
+_LOG_2 = np.log(2)
+_LOG_PI = np.log(np.pi)
+MVN_LOCK = threading.Lock()
+
+
+_doc_random_state = """\
+seed : {None, int, np.random.RandomState, np.random.Generator}, optional
+    Used for drawing random variates.
+    If `seed` is `None`, the `~np.random.RandomState` singleton is used.
+    If `seed` is an int, a new ``RandomState`` instance is used, seeded
+    with seed.
+    If `seed` is already a ``RandomState`` or ``Generator`` instance,
+    then that object is used.
+    Default is `None`.
+"""
+
+
+def _squeeze_output(out):
+    """
+    Remove single-dimensional entries from array and convert to scalar,
+    if necessary.
+    """
+    out = out.squeeze()
+    if out.ndim == 0:
+        out = out[()]
+    return out
+
+
+def _eigvalsh_to_eps(spectrum, cond=None, rcond=None):
+    """Determine which eigenvalues are "small" given the spectrum.
+
+    This is for compatibility across various linear algebra functions
+    that should agree about whether or not a Hermitian matrix is numerically
+    singular and what is its numerical matrix rank.
+    This is designed to be compatible with scipy.linalg.pinvh.
+
+    Parameters
+    ----------
+    spectrum : 1d ndarray
+        Array of eigenvalues of a Hermitian matrix.
+    cond, rcond : float, optional
+        Cutoff for small eigenvalues.
+        Singular values smaller than rcond * largest_eigenvalue are
+        considered zero.
+        If None or -1, suitable machine precision is used.
+
+    Returns
+    -------
+    eps : float
+        Magnitude cutoff for numerical negligibility.
+
+    """
+    if rcond is not None:
+        cond = rcond
+    if cond in [None, -1]:
+        t = spectrum.dtype.char.lower()
+        factor = {'f': 1E3, 'd': 1E6}
+        cond = factor[t] * np.finfo(t).eps
+    eps = cond * np.max(abs(spectrum))
+    return eps
+
+
+def _pinv_1d(v, eps=1e-5):
+    """A helper function for computing the pseudoinverse.
+
+    Parameters
+    ----------
+    v : iterable of numbers
+        This may be thought of as a vector of eigenvalues or singular values.
+    eps : float
+        Values with magnitude no greater than eps are considered negligible.
+
+    Returns
+    -------
+    v_pinv : 1d float ndarray
+        A vector of pseudo-inverted numbers.
+
+    """
+    return np.array([0 if abs(x) <= eps else 1/x for x in v], dtype=float)
+
+
+def _validate_marginal_input(dimensions, multivariate_dims):
+    """Determine if input dimensions can be marginalized.
+
+    Parameters
+    ----------
+    dimensions : float, ndarray
+        Input dimensions to be marginalized
+    multivariate_dims : int
+        Number of dimensions of multivariate distribution.
+
+    Returns
+    -------
+    dims : ndarray
+        Array of indices to marginalize
+    """
+    dims = np.copy(dimensions)
+    dims = np.atleast_1d(dims)
+
+    if len(dims) == 0:
+        msg = "Cannot marginalize all dimensions."
+        raise ValueError(msg)
+
+    if not np.issubdtype(dims.dtype, np.integer):
+        msg = ("Elements of `dimensions` must be integers - the indices "
+               "of the marginal variables being retained.")
+        raise ValueError(msg)
+
+    original_dims = np.copy(dims)
+
+    dims[dims < 0] += multivariate_dims
+
+    if len(np.unique(dims)) != len(dims):
+        msg = "All elements of `dimensions` must be unique."
+        raise ValueError(msg)
+
+    i_invalid = (dims < 0) | (dims >= multivariate_dims)
+    if np.any(i_invalid):
+        msg = (f"Dimensions {original_dims[i_invalid]} are invalid "
+               f"for a distribution in {multivariate_dims} dimensions.")
+        raise ValueError(msg)
+
+    return dims
+
+
+class _PSD:
+    """
+    Compute coordinated functions of a symmetric positive semidefinite matrix.
+
+    This class addresses two issues.  Firstly it allows the pseudoinverse,
+    the logarithm of the pseudo-determinant, and the rank of the matrix
+    to be computed using one call to eigh instead of three.
+    Secondly it allows these functions to be computed in a way
+    that gives mutually compatible results.
+    All of the functions are computed with a common understanding as to
+    which of the eigenvalues are to be considered negligibly small.
+    The functions are designed to coordinate with scipy.linalg.pinvh()
+    but not necessarily with np.linalg.det() or with np.linalg.matrix_rank().
+
+    Parameters
+    ----------
+    M : array_like
+        Symmetric positive semidefinite matrix (2-D).
+    cond, rcond : float, optional
+        Cutoff for small eigenvalues.
+        Singular values smaller than rcond * largest_eigenvalue are
+        considered zero.
+        If None or -1, suitable machine precision is used.
+    lower : bool, optional
+        Whether the pertinent array data is taken from the lower
+        or upper triangle of M. (Default: lower)
+    check_finite : bool, optional
+        Whether to check that the input matrices contain only finite
+        numbers. Disabling may give a performance gain, but may result
+        in problems (crashes, non-termination) if the inputs do contain
+        infinities or NaNs.
+    allow_singular : bool, optional
+        Whether to allow a singular matrix.  (Default: True)
+
+    Notes
+    -----
+    The arguments are similar to those of scipy.linalg.pinvh().
+
+    """
+
+    def __init__(self, M, cond=None, rcond=None, lower=True,
+                 check_finite=True, allow_singular=True):
+        self._M = np.asarray(M)
+
+        # Compute the symmetric eigendecomposition.
+        # Note that eigh takes care of array conversion, chkfinite,
+        # and assertion that the matrix is square.
+        s, u = scipy.linalg.eigh(M, lower=lower, check_finite=check_finite)
+
+        eps = _eigvalsh_to_eps(s, cond, rcond)
+        if np.min(s) < -eps:
+            msg = "The input matrix must be symmetric positive semidefinite."
+            raise ValueError(msg)
+        d = s[s > eps]
+        if len(d) < len(s) and not allow_singular:
+            msg = ("When `allow_singular is False`, the input matrix must be "
+                   "symmetric positive definite.")
+            raise np.linalg.LinAlgError(msg)
+        s_pinv = _pinv_1d(s, eps)
+        U = np.multiply(u, np.sqrt(s_pinv))
+
+        # Save the eigenvector basis, and tolerance for testing support
+        self.eps = 1e3*eps
+        self.V = u[:, s <= eps]
+
+        # Initialize the eagerly precomputed attributes.
+        self.rank = len(d)
+        self.U = U
+        self.log_pdet = np.sum(np.log(d))
+
+        # Initialize attributes to be lazily computed.
+        self._pinv = None
+
+    def _support_mask(self, x):
+        """
+        Check whether x lies in the support of the distribution.
+        """
+        residual = np.linalg.norm(x @ self.V, axis=-1)
+        in_support = residual < self.eps
+        return in_support
+
+    @property
+    def pinv(self):
+        if self._pinv is None:
+            self._pinv = np.dot(self.U, self.U.T)
+        return self._pinv
+
+
+class multi_rv_generic:
+    """
+    Class which encapsulates common functionality between all multivariate
+    distributions.
+    """
+
+    def __init__(self, seed=None):
+        super().__init__()
+        self._random_state = check_random_state(seed)
+
+    @property
+    def random_state(self):
+        """ Get or set the Generator object for generating random variates.
+
+        If `seed` is None (or `np.random`), the `numpy.random.RandomState`
+        singleton is used.
+        If `seed` is an int, a new ``RandomState`` instance is used,
+        seeded with `seed`.
+        If `seed` is already a ``Generator`` or ``RandomState`` instance then
+        that instance is used.
+
+        """
+        return self._random_state
+
+    @random_state.setter
+    def random_state(self, seed):
+        self._random_state = check_random_state(seed)
+
+    def _get_random_state(self, random_state):
+        if random_state is not None:
+            return check_random_state(random_state)
+        else:
+            return self._random_state
+
+
+class multi_rv_frozen:
+    """
+    Class which encapsulates common functionality between all frozen
+    multivariate distributions.
+    """
+
+    # generic type compatibility with scipy-stubs
+    __class_getitem__: classmethod = classmethod(types.GenericAlias)
+
+    @property
+    def random_state(self):
+        return self._dist._random_state
+
+    @random_state.setter
+    def random_state(self, seed):
+        self._dist._random_state = check_random_state(seed)
+
+
+_mvn_doc_default_callparams = """\
+mean : array_like, default: ``[0]``
+    Mean of the distribution.
+cov : array_like or `Covariance`, default: ``[1]``
+    Symmetric positive (semi)definite covariance matrix of the distribution.
+allow_singular : bool, default: ``False``
+    Whether to allow a singular covariance matrix. This is ignored if `cov` is
+    a `Covariance` object.
+"""
+
+_mvn_doc_callparams_note = """\
+Setting the parameter `mean` to `None` is equivalent to having `mean`
+be the zero-vector. The parameter `cov` can be a scalar, in which case
+the covariance matrix is the identity times that value, a vector of
+diagonal entries for the covariance matrix, a two-dimensional array_like,
+or a `Covariance` object.
+"""
+
+_mvn_doc_frozen_callparams = ""
+
+_mvn_doc_frozen_callparams_note = """\
+See class definition for a detailed description of parameters."""
+
+mvn_docdict_params = {
+    '_mvn_doc_default_callparams': _mvn_doc_default_callparams,
+    '_mvn_doc_callparams_note': _mvn_doc_callparams_note,
+    '_doc_random_state': _doc_random_state
+}
+
+mvn_docdict_noparams = {
+    '_mvn_doc_default_callparams': _mvn_doc_frozen_callparams,
+    '_mvn_doc_callparams_note': _mvn_doc_frozen_callparams_note,
+    '_doc_random_state': _doc_random_state
+}
+
+
+class multivariate_normal_gen(multi_rv_generic):
+    r"""
+    A multivariate normal random variable.
+
+    The `mean` keyword specifies the mean. The `cov` keyword specifies the
+    covariance matrix.
+
+    Parameters
+    ----------
+    %(_mvn_doc_default_callparams)s
+    %(_doc_random_state)s
+
+    Methods
+    -------
+    pdf(x, mean=None, cov=1, allow_singular=False)
+        Probability density function.
+    logpdf(x, mean=None, cov=1, allow_singular=False)
+        Log of the probability density function.
+    cdf(x, mean=None, cov=1, allow_singular=False, maxpts=1000000*dim, abseps=1e-5, releps=1e-5, lower_limit=None)
+        Cumulative distribution function.
+    logcdf(x, mean=None, cov=1, allow_singular=False, maxpts=1000000*dim, abseps=1e-5, releps=1e-5)
+        Log of the cumulative distribution function.
+    rvs(mean=None, cov=1, size=1, random_state=None)
+        Draw random samples from a multivariate normal distribution.
+    entropy(mean=None, cov=1)
+        Compute the differential entropy of the multivariate normal.
+    marginal(dimensions, mean=None, cov=1, allow_singular=False)
+        Return a marginal multivariate normal distribution.
+    fit(x, fix_mean=None, fix_cov=None)
+        Fit a multivariate normal distribution to data.
+
+    Notes
+    -----
+    %(_mvn_doc_callparams_note)s
+
+    The covariance matrix `cov` may be an instance of a subclass of
+    `Covariance`, e.g. `scipy.stats.CovViaPrecision`. If so, `allow_singular`
+    is ignored.
+
+    Otherwise, `cov` must be a symmetric positive semidefinite
+    matrix when `allow_singular` is True; it must be (strictly) positive
+    definite when `allow_singular` is False.
+    Symmetry is not checked; only the lower triangular portion is used.
+    The determinant and inverse of `cov` are computed
+    as the pseudo-determinant and pseudo-inverse, respectively, so
+    that `cov` does not need to have full rank.
+
+    The probability density function for `multivariate_normal` is
+
+    .. math::
+
+        f(x) = \frac{1}{\sqrt{(2 \pi)^k \det \Sigma}}
+               \exp\left( -\frac{1}{2} (x - \mu)^T \Sigma^{-1} (x - \mu) \right),
+
+    where :math:`\mu` is the mean, :math:`\Sigma` the covariance matrix,
+    :math:`k` the rank of :math:`\Sigma`. In case of singular :math:`\Sigma`,
+    SciPy extends this definition according to [1]_.
+
+    .. versionadded:: 0.14.0
+
+    References
+    ----------
+    .. [1] Multivariate Normal Distribution - Degenerate Case, Wikipedia,
+           https://en.wikipedia.org/wiki/Multivariate_normal_distribution#Degenerate_case
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.stats import multivariate_normal
+
+    >>> x = np.linspace(0, 5, 10, endpoint=False)
+    >>> y = multivariate_normal.pdf(x, mean=2.5, cov=0.5); y
+    array([ 0.00108914,  0.01033349,  0.05946514,  0.20755375,  0.43939129,
+            0.56418958,  0.43939129,  0.20755375,  0.05946514,  0.01033349])
+    >>> fig1 = plt.figure()
+    >>> ax = fig1.add_subplot(111)
+    >>> ax.plot(x, y)
+    >>> plt.show()
+
+    Alternatively, the object may be called (as a function) to fix the mean
+    and covariance parameters, returning a "frozen" multivariate normal
+    random variable:
+
+    >>> rv = multivariate_normal(mean=None, cov=1, allow_singular=False)
+    >>> # Frozen object with the same methods but holding the given
+    >>> # mean and covariance fixed.
+
+    The input quantiles can be any shape of array, as long as the last
+    axis labels the components.  This allows us for instance to
+    display the frozen pdf for a non-isotropic random variable in 2D as
+    follows:
+
+    >>> x, y = np.mgrid[-1:1:.01, -1:1:.01]
+    >>> pos = np.dstack((x, y))
+    >>> rv = multivariate_normal([0.5, -0.2], [[2.0, 0.3], [0.3, 0.5]])
+    >>> fig2 = plt.figure()
+    >>> ax2 = fig2.add_subplot(111)
+    >>> ax2.contourf(x, y, rv.pdf(pos))
+    """  # noqa: E501
+
+    def __init__(self, seed=None):
+        super().__init__(seed)
+        self.__doc__ = doccer.docformat(self.__doc__, mvn_docdict_params)
+
+    def __call__(self, mean=None, cov=1, allow_singular=False, seed=None, **kwds):
+        """Create a frozen multivariate normal distribution.
+
+        See `multivariate_normal_frozen` for more information.
+        """
+        return multivariate_normal_frozen(mean, cov,
+                                          allow_singular=allow_singular,
+                                          seed=seed, **kwds)
+
+    def _process_parameters(self, mean, cov, allow_singular=True):
+        """
+        Infer dimensionality from mean or covariance matrix, ensure that
+        mean and covariance are full vector resp. matrix.
+        """
+        if isinstance(cov, _covariance.Covariance):
+            return self._process_parameters_Covariance(mean, cov)
+        else:
+            # Before `Covariance` classes were introduced,
+            # `multivariate_normal` accepted plain arrays as `cov` and used the
+            # following input validation. To avoid disturbing the behavior of
+            # `multivariate_normal` when plain arrays are used, we use the
+            # original input validation here.
+            dim, mean, cov = self._process_parameters_psd(None, mean, cov)
+            # After input validation, some methods then processed the arrays
+            # with a `_PSD` object and used that to perform computation.
+            # To avoid branching statements in each method depending on whether
+            # `cov` is an array or `Covariance` object, we always process the
+            # array with `_PSD`, and then use wrapper that satisfies the
+            # `Covariance` interface, `CovViaPSD`.
+            psd = _PSD(cov, allow_singular=allow_singular)
+            cov_object = _covariance.CovViaPSD(psd)
+            return dim, mean, cov_object
+
+    def _process_parameters_Covariance(self, mean, cov):
+        dim = cov.shape[-1]
+        mean = np.array([0.]) if mean is None else mean
+        message = (f"`cov` represents a covariance matrix in {dim} dimensions,"
+                   f"and so `mean` must be broadcastable to shape {(dim,)}")
+        try:
+            mean = np.broadcast_to(mean, dim)
+        except ValueError as e:
+            raise ValueError(message) from e
+        return dim, mean, cov
+
+    def _process_parameters_psd(self, dim, mean, cov):
+        # Try to infer dimensionality
+        if dim is None:
+            if mean is None:
+                if cov is None:
+                    dim = 1
+                else:
+                    cov = np.asarray(cov, dtype=float)
+                    if cov.ndim < 2:
+                        dim = 1
+                    else:
+                        dim = cov.shape[0]
+            else:
+                mean = np.asarray(mean, dtype=float)
+                dim = mean.size
+        else:
+            if not np.isscalar(dim):
+                raise ValueError("Dimension of random variable must be "
+                                 "a scalar.")
+
+        # Check input sizes and return full arrays for mean and cov if
+        # necessary
+        if mean is None:
+            mean = np.zeros(dim)
+        mean = np.asarray(mean, dtype=float)
+
+        if cov is None:
+            cov = 1.0
+        cov = np.asarray(cov, dtype=float)
+
+        if dim == 1:
+            mean = mean.reshape(1)
+            cov = cov.reshape(1, 1)
+
+        if mean.ndim != 1 or mean.shape[0] != dim:
+            raise ValueError(f"Array 'mean' must be a vector of length {dim}.")
+        if cov.ndim == 0:
+            cov = cov * np.eye(dim)
+        elif cov.ndim == 1:
+            cov = np.diag(cov)
+        elif cov.ndim == 2 and cov.shape != (dim, dim):
+            rows, cols = cov.shape
+            if rows != cols:
+                msg = ("Array 'cov' must be square if it is two dimensional,"
+                       f" but cov.shape = {str(cov.shape)}.")
+            else:
+                msg = (f"Dimension mismatch: array 'cov' is of shape {cov.shape}, "
+                       f"but 'mean' is a vector of length {len(mean)}.")
+            raise ValueError(msg)
+        elif cov.ndim > 2:
+            raise ValueError(f"Array 'cov' must be at most two-dimensional, "
+                             f"but cov.ndim = {cov.ndim}")
+
+        return dim, mean, cov
+
+    def _process_quantiles(self, x, dim):
+        """
+        Adjust quantiles array so that last axis labels the components of
+        each data point.
+        """
+        x = np.asarray(x, dtype=float)
+
+        if x.ndim == 0:
+            x = x[np.newaxis]
+        elif x.ndim == 1:
+            if dim == 1:
+                x = x[:, np.newaxis]
+            else:
+                x = x[np.newaxis, :]
+
+        return x
+
+    def _logpdf(self, x, mean, cov_object):
+        """Log of the multivariate normal probability density function.
+
+        Parameters
+        ----------
+        x : ndarray
+            Points at which to evaluate the log of the probability
+            density function
+        mean : ndarray
+            Mean of the distribution
+        cov_object : Covariance
+            An object representing the Covariance matrix
+
+        Notes
+        -----
+        As this function does no argument checking, it should not be
+        called directly; use 'logpdf' instead.
+
+        """
+        log_det_cov, rank = cov_object.log_pdet, cov_object.rank
+        dev = x - mean
+        if dev.ndim > 1:
+            log_det_cov = log_det_cov[..., np.newaxis]
+            rank = rank[..., np.newaxis]
+        maha = np.sum(np.square(cov_object.whiten(dev)), axis=-1)
+        return -0.5 * (rank * _LOG_2PI + log_det_cov + maha)
+
+    def logpdf(self, x, mean=None, cov=1, allow_singular=False):
+        """Log of the multivariate normal probability density function.
+
+        Parameters
+        ----------
+        x : array_like
+            Quantiles, with the last axis of `x` denoting the components.
+        %(_mvn_doc_default_callparams)s
+
+        Returns
+        -------
+        pdf : ndarray or scalar
+            Log of the probability density function evaluated at `x`
+
+        Notes
+        -----
+        %(_mvn_doc_callparams_note)s
+
+        """
+        params = self._process_parameters(mean, cov, allow_singular)
+        dim, mean, cov_object = params
+        x = self._process_quantiles(x, dim)
+        out = self._logpdf(x, mean, cov_object)
+        if np.any(cov_object.rank < dim):
+            out_of_bounds = ~cov_object._support_mask(x-mean)
+            out[out_of_bounds] = -np.inf
+        return _squeeze_output(out)
+
+    def pdf(self, x, mean=None, cov=1, allow_singular=False):
+        """Multivariate normal probability density function.
+
+        Parameters
+        ----------
+        x : array_like
+            Quantiles, with the last axis of `x` denoting the components.
+        %(_mvn_doc_default_callparams)s
+
+        Returns
+        -------
+        pdf : ndarray or scalar
+            Probability density function evaluated at `x`
+
+        Notes
+        -----
+        %(_mvn_doc_callparams_note)s
+
+        """
+        params = self._process_parameters(mean, cov, allow_singular)
+        dim, mean, cov_object = params
+        x = self._process_quantiles(x, dim)
+        out = np.exp(self._logpdf(x, mean, cov_object))
+        if np.any(cov_object.rank < dim):
+            out_of_bounds = ~cov_object._support_mask(x-mean)
+            out[out_of_bounds] = 0.0
+        return _squeeze_output(out)
+
+    def _cdf(self, x, mean, cov, maxpts, abseps, releps, lower_limit, rng):
+        """Multivariate normal cumulative distribution function.
+
+        Parameters
+        ----------
+        x : ndarray
+            Points at which to evaluate the cumulative distribution function.
+        mean : ndarray
+            Mean of the distribution
+        cov : array_like
+            Covariance matrix of the distribution
+        maxpts : int
+            The maximum number of points to use for integration
+        abseps : float
+            Absolute error tolerance
+        releps : float
+            Relative error tolerance
+        lower_limit : array_like, optional
+            Lower limit of integration of the cumulative distribution function.
+            Default is negative infinity. Must be broadcastable with `x`.
+        rng : Generator
+            an instance of ``np.random.Generator``, which is used internally
+            for QMC integration.
+
+        Notes
+        -----
+        As this function does no argument checking, it should not be
+        called directly; use 'cdf' instead.
+
+
+        .. versionadded:: 1.0.0
+
+        """
+        lower = (np.full(mean.shape, -np.inf)
+                 if lower_limit is None else lower_limit)
+        # In 2d, _mvn.mvnun accepts input in which `lower` bound elements
+        # are greater than `x`. Not so in other dimensions. Fix this by
+        # ensuring that lower bounds are indeed lower when passed, then
+        # set signs of resulting CDF manually.
+        b, a = np.broadcast_arrays(x, lower)
+        b, a = b - mean, a - mean  # _qmvn only accepts zero mean
+        i_swap = b < a
+        signs = (-1)**(i_swap.sum(axis=-1))  # odd # of swaps -> negative
+        a, b = a.copy(), b.copy()
+        a[i_swap], b[i_swap] = b[i_swap], a[i_swap]
+        n = x.shape[-1]
+        limits = np.concatenate((a, b), axis=-1)
+
+        # qmvn expects 1-d arguments, so process points sequentially
+        # XXX: if cov.ndim == 2 and limits.ndim == 1, can avoid apply_along_axis
+        def func1d(limits):
+            # res0 = _qmvn(maxpts, cov, limits[:n], limits[n:], rng)[0]
+            res = _qauto(_qmvn, cov, limits[:n], limits[n:],
+                         rng, error=abseps, limit=maxpts, n_batches=10)
+            return np.squeeze(res[0])
+
+        out = np.apply_along_axis(func1d, -1, limits) * signs
+        return _squeeze_output(out)
+
+    def logcdf(self, x, mean=None, cov=1, allow_singular=False, maxpts=None,
+               abseps=1e-5, releps=1e-5, *, lower_limit=None, rng=None):
+        """Log of the multivariate normal cumulative distribution function.
+
+        Parameters
+        ----------
+        x : array_like
+            Quantiles, with the last axis of `x` denoting the components.
+        %(_mvn_doc_default_callparams)s
+        maxpts : int, optional
+            The maximum number of points to use for integration
+            (default ``1000000*dim``)
+        abseps : float, optional
+            Absolute error tolerance (default 1e-5)
+        releps : float, optional
+            Relative error tolerance (default 1e-5)
+        lower_limit : array_like, optional
+            Lower limit of integration of the cumulative distribution function.
+            Default is negative infinity. Must be broadcastable with `x`.
+        rng : Generator, optional
+            an instance of ``np.random.Generator``, which is used internally
+            for QMC integration.
+
+        Returns
+        -------
+        cdf : ndarray or scalar
+            Log of the cumulative distribution function evaluated at `x`
+
+        Notes
+        -----
+        %(_mvn_doc_callparams_note)s
+
+        .. versionadded:: 1.0.0
+
+        """
+        params = self._process_parameters(mean, cov, allow_singular)
+        dim, mean, cov_object = params
+        cov = cov_object.covariance
+        x = self._process_quantiles(x, dim)
+        if not maxpts:
+            maxpts = 1000000 * dim
+
+        rng = self._get_random_state(rng)
+        cdf = self._cdf(x, mean, cov, maxpts, abseps, releps, lower_limit, rng)
+        # the log of a negative real is complex, and cdf can be negative
+        # if lower limit is greater than upper limit
+        cdf = cdf + 0j if np.any(cdf < 0) else cdf
+        out = np.log(cdf)
+        return out
+
+    def cdf(self, x, mean=None, cov=1, allow_singular=False, maxpts=None,
+            abseps=1e-5, releps=1e-5, *, lower_limit=None, rng=None):
+        """Multivariate normal cumulative distribution function.
+
+        Parameters
+        ----------
+        x : array_like
+            Quantiles, with the last axis of `x` denoting the components.
+        %(_mvn_doc_default_callparams)s
+        maxpts : int, optional
+            The maximum number of points to use for integration
+            (default ``1000000*dim``)
+        abseps : float, optional
+            Absolute error tolerance (default 1e-5)
+        releps : float, optional
+            Relative error tolerance (default 1e-5)
+        lower_limit : array_like, optional
+            Lower limit of integration of the cumulative distribution function.
+            Default is negative infinity. Must be broadcastable with `x`.
+        rng : Generator, optional
+            an instance of ``np.random.Generator``, which is used internally
+            for QMC integration.
+
+        Returns
+        -------
+        cdf : ndarray or scalar
+            Cumulative distribution function evaluated at `x`
+
+        Notes
+        -----
+        %(_mvn_doc_callparams_note)s
+
+        .. versionadded:: 1.0.0
+
+        """
+        params = self._process_parameters(mean, cov, allow_singular)
+        dim, mean, cov_object = params
+        cov = cov_object.covariance
+        x = self._process_quantiles(x, dim)
+        if not maxpts:
+            maxpts = 1000000 * dim
+        rng = self._get_random_state(rng)
+        out = self._cdf(x, mean, cov, maxpts, abseps, releps, lower_limit, rng)
+        return out
+
+    def rvs(self, mean=None, cov=1, size=1, random_state=None):
+        """Draw random samples from a multivariate normal distribution.
+
+        Parameters
+        ----------
+        %(_mvn_doc_default_callparams)s
+        size : int, optional
+            Number of samples to draw (default 1).
+        %(_doc_random_state)s
+
+        Returns
+        -------
+        rvs : ndarray or scalar
+            Random variates of size (`size`, `N`), where `N` is the
+            dimension of the random variable.
+
+        Notes
+        -----
+        %(_mvn_doc_callparams_note)s
+
+        """
+        dim, mean, cov_object = self._process_parameters(mean, cov)
+        random_state = self._get_random_state(random_state)
+
+        if isinstance(cov_object, _covariance.CovViaPSD):
+            cov = cov_object.covariance
+            out = random_state.multivariate_normal(mean, cov, size)
+            out = _squeeze_output(out)
+        else:
+            size = size or tuple()
+            if not np.iterable(size):
+                size = (size,)
+            shape = tuple(size) + (cov_object.shape[-1],)
+            x = random_state.normal(size=shape)
+            out = mean + cov_object.colorize(x)
+        return out
+
+    def entropy(self, mean=None, cov=1):
+        """Compute the differential entropy of the multivariate normal.
+
+        Parameters
+        ----------
+        %(_mvn_doc_default_callparams)s
+
+        Returns
+        -------
+        h : scalar
+            Entropy of the multivariate normal distribution
+
+        Notes
+        -----
+        %(_mvn_doc_callparams_note)s
+
+        """
+        dim, mean, cov_object = self._process_parameters(mean, cov)
+        return 0.5 * (cov_object.rank * (_LOG_2PI + 1) + cov_object.log_pdet)
+
+    def fit(self, x, fix_mean=None, fix_cov=None):
+        """Fit a multivariate normal distribution to data.
+
+        Parameters
+        ----------
+        x : ndarray (m, n)
+            Data the distribution is fitted to. Must have two axes.
+            The first axis of length `m` represents the number of vectors
+            the distribution is fitted to. The second axis of length `n`
+            determines the dimensionality of the fitted distribution.
+        fix_mean : ndarray(n, )
+            Fixed mean vector. Must have length `n`.
+        fix_cov: ndarray (n, n)
+            Fixed covariance matrix. Must have shape ``(n, n)``.
+
+        Returns
+        -------
+        mean : ndarray (n, )
+            Maximum likelihood estimate of the mean vector
+        cov : ndarray (n, n)
+            Maximum likelihood estimate of the covariance matrix
+
+        """
+        # input validation for data to be fitted
+        x = np.asarray(x)
+        if x.ndim != 2:
+            raise ValueError("`x` must be two-dimensional.")
+
+        n_vectors, dim = x.shape
+
+        # parameter estimation
+        # reference: https://home.ttic.edu/~shubhendu/Slides/Estimation.pdf
+        if fix_mean is not None:
+            # input validation for `fix_mean`
+            fix_mean = np.atleast_1d(fix_mean)
+            if fix_mean.shape != (dim, ):
+                msg = ("`fix_mean` must be a one-dimensional array the same "
+                       "length as the dimensionality of the vectors `x`.")
+                raise ValueError(msg)
+            mean = fix_mean
+        else:
+            mean = x.mean(axis=0)
+
+        if fix_cov is not None:
+            # input validation for `fix_cov`
+            fix_cov = np.atleast_2d(fix_cov)
+            # validate shape
+            if fix_cov.shape != (dim, dim):
+                msg = ("`fix_cov` must be a two-dimensional square array "
+                       "of same side length as the dimensionality of the "
+                       "vectors `x`.")
+                raise ValueError(msg)
+            # validate positive semidefiniteness
+            # a trimmed down copy from _PSD
+            s, u = scipy.linalg.eigh(fix_cov, lower=True, check_finite=True)
+            eps = _eigvalsh_to_eps(s)
+            if np.min(s) < -eps:
+                msg = "`fix_cov` must be symmetric positive semidefinite."
+                raise ValueError(msg)
+            cov = fix_cov
+        else:
+            centered_data = x - mean
+            cov = centered_data.T @ centered_data / n_vectors
+        return mean, cov
+
+    def marginal(self, dimensions, mean=None, cov=1, allow_singular=False):
+        """Return a marginal multivariate normal distribution.
+
+        Parameters
+        ----------
+        dimensions : int or 1-d array_like
+            The dimensions of the multivariate distribution corresponding
+            with the marginal variables, that is, the indices of the dimensions
+            that are being retained. The other dimensions are marginalized out.
+        %(_mvn_doc_default_callparams)s
+
+        Returns
+        -------
+        marginal_multivariate_normal : multivariate_normal_frozen
+            An object representing the marginal distribution.
+
+        Notes
+        -----
+        %(_mvn_doc_callparams_note)s
+        """
+        params = self._process_parameters(mean, cov, allow_singular)
+        n, mean, cov_object = params
+        dims = _validate_marginal_input(dimensions, n)
+
+        mean = mean[dims]
+        cov = cov_object.covariance[np.ix_(dims, dims)]
+
+        return multivariate_normal_frozen(mean, cov, allow_singular)
+
+multivariate_normal = multivariate_normal_gen()
+
+
+class multivariate_normal_frozen(multi_rv_frozen):
+    __class_getitem__ = None  # pyrefly:ignore[bad-assignment]
+
+    def __init__(self, mean=None, cov=1, allow_singular=False, seed=None,
+                 maxpts=None, abseps=1e-5, releps=1e-5):
+        """Create a frozen multivariate normal distribution.
+
+        Parameters
+        ----------
+        mean : array_like, default: ``[0]``
+            Mean of the distribution.
+        cov : array_like, default: ``[1]``
+            Symmetric positive (semi)definite covariance matrix of the
+            distribution.
+        allow_singular : bool, default: ``False``
+            Whether to allow a singular covariance matrix.
+        seed : {None, int, `numpy.random.Generator`, `numpy.random.RandomState`}, optional
+            If `seed` is None (or `np.random`), the `numpy.random.RandomState`
+            singleton is used.
+            If `seed` is an int, a new ``RandomState`` instance is used,
+            seeded with `seed`.
+            If `seed` is already a ``Generator`` or ``RandomState`` instance
+            then that instance is used.
+        maxpts : int, optional
+            The maximum number of points to use for integration of the
+            cumulative distribution function (default ``1000000*dim``)
+        abseps : float, optional
+            Absolute error tolerance for the cumulative distribution function
+            (default 1e-5)
+        releps : float, optional
+            Relative error tolerance for the cumulative distribution function
+            (default 1e-5)
+
+        Examples
+        --------
+        When called with the default parameters, this will create a 1D random
+        variable with mean 0 and covariance 1:
+
+        >>> from scipy.stats import multivariate_normal
+        >>> r = multivariate_normal()
+        >>> r.mean
+        array([ 0.])
+        >>> r.cov
+        array([[1.]])
+
+        """ # numpy/numpydoc#87  # noqa: E501
+        self._dist = multivariate_normal_gen(seed)
+        self.dim, self.mean, self.cov_object = (
+            self._dist._process_parameters(mean, cov, allow_singular))
+        self.allow_singular = allow_singular or self.cov_object._allow_singular
+        if not maxpts:
+            maxpts = 1000000 * self.dim
+        self.maxpts = maxpts
+        self.abseps = abseps
+        self.releps = releps
+
+    @property
+    def cov(self):
+        return self.cov_object.covariance
+
+    def logpdf(self, x):
+        x = self._dist._process_quantiles(x, self.dim)
+        out = self._dist._logpdf(x, self.mean, self.cov_object)
+        if np.any(self.cov_object.rank < self.dim):
+            out_of_bounds = ~self.cov_object._support_mask(x-self.mean)
+            out[out_of_bounds] = -np.inf
+        return _squeeze_output(out)
+
+    def pdf(self, x):
+        return np.exp(self.logpdf(x))
+
+    def logcdf(self, x, *, lower_limit=None, rng=None):
+        cdf = self.cdf(x, lower_limit=lower_limit, rng=rng)
+        # the log of a negative real is complex, and cdf can be negative
+        # if lower limit is greater than upper limit
+        cdf = cdf + 0j if np.any(cdf < 0) else cdf
+        out = np.log(cdf)
+        return out
+
+    def cdf(self, x, *, lower_limit=None, rng=None):
+        x = self._dist._process_quantiles(x, self.dim)
+        rng = self._dist._get_random_state(rng)
+        out = self._dist._cdf(x, self.mean, self.cov_object.covariance,
+                              self.maxpts, self.abseps, self.releps,
+                              lower_limit, rng)
+        return _squeeze_output(out)
+
+    def rvs(self, size=1, random_state=None):
+        return self._dist.rvs(self.mean, self.cov_object, size, random_state)
+
+    def entropy(self):
+        """Computes the differential entropy of the multivariate normal.
+
+        Returns
+        -------
+        h : scalar
+            Entropy of the multivariate normal distribution
+
+        """
+        log_pdet = self.cov_object.log_pdet
+        rank = self.cov_object.rank
+        return 0.5 * (rank * (_LOG_2PI + 1) + log_pdet)
+
+    def marginal(self, dimensions):
+        return self._dist.marginal(dimensions, self.mean,
+                                   self.cov_object, self.allow_singular)
+
+# Set frozen generator docstrings from corresponding docstrings in
+# multivariate_normal_gen and fill in default strings in class docstrings
+for name in ['logpdf', 'pdf', 'logcdf', 'cdf', 'rvs']:
+    method = multivariate_normal_gen.__dict__[name]
+    method_frozen = multivariate_normal_frozen.__dict__[name]
+    method_frozen.__doc__ = doccer.docformat(method.__doc__,
+                                             mvn_docdict_noparams)
+    method.__doc__ = doccer.docformat(method.__doc__, mvn_docdict_params)
+
+_matnorm_doc_default_callparams = """\
+mean : array_like, optional
+    Mean of the distribution (default: `None`)
+rowcov : array_like, optional
+    Among-row covariance matrix of the distribution (default: ``1``)
+colcov : array_like, optional
+    Among-column covariance matrix of the distribution (default: ``1``)
+"""
+
+_matnorm_doc_callparams_note = """\
+If `mean` is set to `None` then a matrix of zeros is used for the mean.
+The dimensions of this matrix are inferred from the shape of `rowcov` and
+`colcov`, if these are provided, or set to ``1`` if ambiguous.
+
+`rowcov` and `colcov` can be two-dimensional array_likes specifying the
+covariance matrices directly. Alternatively, a one-dimensional array will
+be be interpreted as the entries of a diagonal matrix, and a scalar or
+zero-dimensional array will be interpreted as this value times the
+identity matrix.
+"""
+
+_matnorm_doc_frozen_callparams = ""
+
+_matnorm_doc_frozen_callparams_note = """\
+See class definition for a detailed description of parameters."""
+
+matnorm_docdict_params = {
+    '_matnorm_doc_default_callparams': _matnorm_doc_default_callparams,
+    '_matnorm_doc_callparams_note': _matnorm_doc_callparams_note,
+    '_doc_random_state': _doc_random_state
+}
+
+matnorm_docdict_noparams = {
+    '_matnorm_doc_default_callparams': _matnorm_doc_frozen_callparams,
+    '_matnorm_doc_callparams_note': _matnorm_doc_frozen_callparams_note,
+    '_doc_random_state': _doc_random_state
+}
+
+
+class matrix_normal_gen(multi_rv_generic):
+    r"""
+    A matrix normal random variable.
+
+    The `mean` keyword specifies the mean. The `rowcov` keyword specifies the
+    among-row covariance matrix. The 'colcov' keyword specifies the
+    among-column covariance matrix.
+
+    Parameters
+    ----------
+    %(_matnorm_doc_default_callparams)s
+    %(_doc_random_state)s
+
+    Methods
+    -------
+    pdf(X, mean=None, rowcov=1, colcov=1)
+        Probability density function.
+    logpdf(X, mean=None, rowcov=1, colcov=1)
+        Log of the probability density function.
+    rvs(mean=None, rowcov=1, colcov=1, size=1, random_state=None)
+        Draw random samples.
+    entropy(rowcol=1, colcov=1)
+        Differential entropy.
+
+    Notes
+    -----
+    %(_matnorm_doc_callparams_note)s
+
+    The covariance matrices specified by `rowcov` and `colcov` must be
+    (symmetric) positive definite. If the samples in `X` are
+    :math:`m \times n`, then `rowcov` must be :math:`m \times m` and
+    `colcov` must be :math:`n \times n`. `mean` must be the same shape as `X`.
+
+    The probability density function for `matrix_normal` is
+
+    .. math::
+
+        f(X) = (2 \pi)^{-\frac{mn}{2}}|U|^{-\frac{n}{2}} |V|^{-\frac{m}{2}}
+               \exp\left( -\frac{1}{2} \mathrm{Tr}\left[ U^{-1} (X-M) V^{-1}
+               (X-M)^T \right] \right),
+
+    where :math:`M` is the mean, :math:`U` the among-row covariance matrix,
+    :math:`V` the among-column covariance matrix.
+
+    The `allow_singular` behaviour of the `multivariate_normal`
+    distribution is not currently supported. Covariance matrices must be
+    full rank.
+
+    The `matrix_normal` distribution is closely related to the
+    `multivariate_normal` distribution. Specifically, :math:`\mathrm{Vec}(X)`
+    (the vector formed by concatenating the columns  of :math:`X`) has a
+    multivariate normal distribution with mean :math:`\mathrm{Vec}(M)`
+    and covariance :math:`V \otimes U` (where :math:`\otimes` is the Kronecker
+    product). Sampling and pdf evaluation are
+    :math:`\mathcal{O}(m^3 + n^3 + m^2 n + m n^2)` for the matrix normal, but
+    :math:`\mathcal{O}(m^3 n^3)` for the equivalent multivariate normal,
+    making this equivalent form algorithmically inefficient.
+
+    .. versionadded:: 0.17.0
+
+    References
+    ----------
+    .. [1] "Matrix normal distribution", Wikipedia,
+           https://en.wikipedia.org/wiki/Matrix_normal_distribution
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> from scipy.stats import matrix_normal
+
+    >>> M = np.arange(6).reshape(3,2); M
+    array([[0, 1],
+           [2, 3],
+           [4, 5]])
+    >>> U = np.diag([1,2,3]); U
+    array([[1, 0, 0],
+           [0, 2, 0],
+           [0, 0, 3]])
+    >>> V = 0.3*np.identity(2); V
+    array([[ 0.3,  0. ],
+           [ 0. ,  0.3]])
+    >>> X = M + 0.1; X
+    array([[ 0.1,  1.1],
+           [ 2.1,  3.1],
+           [ 4.1,  5.1]])
+    >>> matrix_normal.pdf(X, mean=M, rowcov=U, colcov=V)
+    0.023410202050005054
+
+    >>> # Equivalent multivariate normal
+    >>> from scipy.stats import multivariate_normal
+    >>> vectorised_X = X.T.flatten()
+    >>> equiv_mean = M.T.flatten()
+    >>> equiv_cov = np.kron(V,U)
+    >>> multivariate_normal.pdf(vectorised_X, mean=equiv_mean, cov=equiv_cov)
+    0.023410202050005054
+
+    Alternatively, the object may be called (as a function) to fix the mean
+    and covariance parameters, returning a "frozen" matrix normal
+    random variable:
+
+    >>> rv = matrix_normal(mean=None, rowcov=1, colcov=1)
+    >>> # Frozen object with the same methods but holding the given
+    >>> # mean and covariance fixed.
+    """
+
+    def __init__(self, seed=None):
+        super().__init__(seed)
+        self.__doc__ = doccer.docformat(self.__doc__, matnorm_docdict_params)
+
+    def __call__(self, mean=None, rowcov=1, colcov=1, seed=None):
+        """Create a frozen matrix normal distribution.
+
+        See `matrix_normal_frozen` for more information.
+
+        """
+        return matrix_normal_frozen(mean, rowcov, colcov, seed=seed)
+
+    def _process_parameters(self, mean, rowcov, colcov):
+        """
+        Infer dimensionality from mean or covariance matrices. Handle
+        defaults. Ensure compatible dimensions.
+        """
+
+        # Process mean
+        if mean is not None:
+            mean = np.asarray(mean, dtype=float)
+            meanshape = mean.shape
+            if len(meanshape) != 2:
+                raise ValueError("Array `mean` must be two dimensional.")
+            if np.any(meanshape == 0):
+                raise ValueError("Array `mean` has invalid shape.")
+
+        # Process among-row covariance
+        rowcov = np.asarray(rowcov, dtype=float)
+        if rowcov.ndim == 0:
+            if mean is not None:
+                rowcov = rowcov * np.identity(meanshape[0])
+            else:
+                rowcov = rowcov * np.identity(1)
+        elif rowcov.ndim == 1:
+            rowcov = np.diag(rowcov)
+        rowshape = rowcov.shape
+        if len(rowshape) != 2:
+            raise ValueError("`rowcov` must be a scalar or a 2D array.")
+        if rowshape[0] != rowshape[1]:
+            raise ValueError("Array `rowcov` must be square.")
+        if rowshape[0] == 0:
+            raise ValueError("Array `rowcov` has invalid shape.")
+        numrows = rowshape[0]
+
+        # Process among-column covariance
+        colcov = np.asarray(colcov, dtype=float)
+        if colcov.ndim == 0:
+            if mean is not None:
+                colcov = colcov * np.identity(meanshape[1])
+            else:
+                colcov = colcov * np.identity(1)
+        elif colcov.ndim == 1:
+            colcov = np.diag(colcov)
+        colshape = colcov.shape
+        if len(colshape) != 2:
+            raise ValueError("`colcov` must be a scalar or a 2D array.")
+        if colshape[0] != colshape[1]:
+            raise ValueError("Array `colcov` must be square.")
+        if colshape[0] == 0:
+            raise ValueError("Array `colcov` has invalid shape.")
+        numcols = colshape[0]
+
+        # Ensure mean and covariances compatible
+        if mean is not None:
+            if meanshape[0] != numrows:
+                raise ValueError("Arrays `mean` and `rowcov` must have the "
+                                 "same number of rows.")
+            if meanshape[1] != numcols:
+                raise ValueError("Arrays `mean` and `colcov` must have the "
+                                 "same number of columns.")
+        else:
+            mean = np.zeros((numrows, numcols))
+
+        dims = (numrows, numcols)
+
+        return dims, mean, rowcov, colcov
+
+    def _process_quantiles(self, X, dims):
+        """
+        Adjust quantiles array so that last two axes labels the components of
+        each data point.
+        """
+        X = np.asarray(X, dtype=float)
+        if X.ndim == 2:
+            X = X[np.newaxis, :]
+        if X.shape[-2:] != dims:
+            raise ValueError("The shape of array `X` is not compatible "
+                             "with the distribution parameters.")
+        return X
+
+    def _logpdf(self, dims, X, mean, row_prec_rt, log_det_rowcov,
+                col_prec_rt, log_det_colcov):
+        """Log of the matrix normal probability density function.
+
+        Parameters
+        ----------
+        dims : tuple
+            Dimensions of the matrix variates
+        X : ndarray
+            Points at which to evaluate the log of the probability
+            density function
+        mean : ndarray
+            Mean of the distribution
+        row_prec_rt : ndarray
+            A decomposition such that np.dot(row_prec_rt, row_prec_rt.T)
+            is the inverse of the among-row covariance matrix
+        log_det_rowcov : float
+            Logarithm of the determinant of the among-row covariance matrix
+        col_prec_rt : ndarray
+            A decomposition such that np.dot(col_prec_rt, col_prec_rt.T)
+            is the inverse of the among-column covariance matrix
+        log_det_colcov : float
+            Logarithm of the determinant of the among-column covariance matrix
+
+        Notes
+        -----
+        As this function does no argument checking, it should not be
+        called directly; use 'logpdf' instead.
+
+        """
+        numrows, numcols = dims
+        roll_dev = np.moveaxis(X-mean, -1, 0)
+        scale_dev = np.tensordot(col_prec_rt.T,
+                                 np.dot(roll_dev, row_prec_rt), 1)
+        maha = np.sum(np.sum(np.square(scale_dev), axis=-1), axis=0)
+        return -0.5 * (numrows*numcols*_LOG_2PI + numcols*log_det_rowcov
+                       + numrows*log_det_colcov + maha)
+
+    def logpdf(self, X, mean=None, rowcov=1, colcov=1):
+        """Log of the matrix normal probability density function.
+
+        Parameters
+        ----------
+        X : array_like
+            Quantiles, with the last two axes of `X` denoting the components.
+        %(_matnorm_doc_default_callparams)s
+
+        Returns
+        -------
+        logpdf : ndarray
+            Log of the probability density function evaluated at `X`
+
+        Notes
+        -----
+        %(_matnorm_doc_callparams_note)s
+
+        """
+        dims, mean, rowcov, colcov = self._process_parameters(mean, rowcov,
+                                                              colcov)
+        X = self._process_quantiles(X, dims)
+        rowpsd = _PSD(rowcov, allow_singular=False)
+        colpsd = _PSD(colcov, allow_singular=False)
+        out = self._logpdf(dims, X, mean, rowpsd.U, rowpsd.log_pdet, colpsd.U,
+                           colpsd.log_pdet)
+        return _squeeze_output(out)
+
+    def pdf(self, X, mean=None, rowcov=1, colcov=1):
+        """Matrix normal probability density function.
+
+        Parameters
+        ----------
+        X : array_like
+            Quantiles, with the last two axes of `X` denoting the components.
+        %(_matnorm_doc_default_callparams)s
+
+        Returns
+        -------
+        pdf : ndarray
+            Probability density function evaluated at `X`
+
+        Notes
+        -----
+        %(_matnorm_doc_callparams_note)s
+
+        """
+        return np.exp(self.logpdf(X, mean, rowcov, colcov))
+
+    def rvs(self, mean=None, rowcov=1, colcov=1, size=1, random_state=None):
+        """Draw random samples from a matrix normal distribution.
+
+        Parameters
+        ----------
+        %(_matnorm_doc_default_callparams)s
+        size : int, optional
+            Number of samples to draw (default 1).
+        %(_doc_random_state)s
+
+        Returns
+        -------
+        rvs : ndarray or scalar
+            Random variates of size (`size`, `dims`), where `dims` is the
+            dimension of the random matrices.
+
+        Notes
+        -----
+        %(_matnorm_doc_callparams_note)s
+
+        """
+        size = int(size)
+        dims, mean, rowcov, colcov = self._process_parameters(mean, rowcov,
+                                                              colcov)
+        rowchol = scipy.linalg.cholesky(rowcov, lower=True)
+        colchol = scipy.linalg.cholesky(colcov, lower=True)
+        random_state = self._get_random_state(random_state)
+        # We aren't generating standard normal variates with size=(size,
+        # dims[0], dims[1]) directly to ensure random variates remain backwards
+        # compatible. See https://github.com/scipy/scipy/pull/12312 for more
+        # details.
+        std_norm = random_state.standard_normal(
+            size=(dims[1], size, dims[0])
+        ).transpose(1, 2, 0)
+        out = mean + np.einsum('jp,ipq,kq->ijk',
+                               rowchol, std_norm, colchol,
+                               optimize=True)
+        if size == 1:
+            out = out.reshape(mean.shape)
+        return out
+
+    def entropy(self, rowcov=1, colcov=1):
+        """Log of the matrix normal probability density function.
+
+        Parameters
+        ----------
+        rowcov : array_like, optional
+            Among-row covariance matrix of the distribution (default: ``1``)
+        colcov : array_like, optional
+            Among-column covariance matrix of the distribution (default: ``1``)
+
+        Returns
+        -------
+        entropy : float
+            Entropy of the distribution
+
+        Notes
+        -----
+        %(_matnorm_doc_callparams_note)s
+
+        """
+        dummy_mean = np.zeros((rowcov.shape[0], colcov.shape[0]))
+        dims, _, rowcov, colcov = self._process_parameters(dummy_mean,
+                                                           rowcov,
+                                                           colcov)
+        rowpsd = _PSD(rowcov, allow_singular=False)
+        colpsd = _PSD(colcov, allow_singular=False)
+
+        return self._entropy(dims, rowpsd.log_pdet, colpsd.log_pdet)
+
+    def _entropy(self, dims, row_cov_logdet, col_cov_logdet):
+        n, p = dims
+        return (0.5 * n * p * (1 + _LOG_2PI) + 0.5 * p * row_cov_logdet +
+                0.5 * n * col_cov_logdet)
+
+
+matrix_normal = matrix_normal_gen()
+
+
+class matrix_normal_frozen(multi_rv_frozen):
+    """
+    Create a frozen matrix normal distribution.
+
+    Parameters
+    ----------
+    %(_matnorm_doc_default_callparams)s
+    seed : {None, int, `numpy.random.Generator`, `numpy.random.RandomState`}, optional
+        If `seed` is `None` the `~np.random.RandomState` singleton is used.
+        If `seed` is an int, a new ``RandomState`` instance is used, seeded
+        with seed.
+        If `seed` is already a ``RandomState`` or ``Generator`` instance,
+        then that object is used.
+        Default is `None`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import matrix_normal
+
+    >>> distn = matrix_normal(mean=np.zeros((3,3)))
+    >>> X = distn.rvs(); X
+    array([[-0.02976962,  0.93339138, -0.09663178],
+           [ 0.67405524,  0.28250467, -0.93308929],
+           [-0.31144782,  0.74535536,  1.30412916]])
+    >>> distn.pdf(X)
+    2.5160642368346784e-05
+    >>> distn.logpdf(X)
+    -10.590229595124615
+    """
+    __class_getitem__ = None  # pyrefly:ignore[bad-assignment]
+
+    def __init__(self, mean=None, rowcov=1, colcov=1, seed=None):
+        self._dist = matrix_normal_gen(seed)
+        self.dims, self.mean, self.rowcov, self.colcov = \
+            self._dist._process_parameters(mean, rowcov, colcov)
+        self.rowpsd = _PSD(self.rowcov, allow_singular=False)
+        self.colpsd = _PSD(self.colcov, allow_singular=False)
+
+    def logpdf(self, X):
+        X = self._dist._process_quantiles(X, self.dims)
+        out = self._dist._logpdf(self.dims, X, self.mean, self.rowpsd.U,
+                                 self.rowpsd.log_pdet, self.colpsd.U,
+                                 self.colpsd.log_pdet)
+        return _squeeze_output(out)
+
+    def pdf(self, X):
+        return np.exp(self.logpdf(X))
+
+    def rvs(self, size=1, random_state=None):
+        return self._dist.rvs(self.mean, self.rowcov, self.colcov, size,
+                              random_state)
+
+    def entropy(self):
+        return self._dist._entropy(self.dims, self.rowpsd.log_pdet,
+                                   self.colpsd.log_pdet)
+
+# Set frozen generator docstrings from corresponding docstrings in
+# matrix_normal_gen and fill in default strings in class docstrings
+for name in ['logpdf', 'pdf', 'rvs', 'entropy']:
+    method = matrix_normal_gen.__dict__[name]
+    method_frozen = matrix_normal_frozen.__dict__[name]
+    method_frozen.__doc__ = doccer.docformat(method.__doc__,
+                                             matnorm_docdict_noparams)
+    method.__doc__ = doccer.docformat(method.__doc__, matnorm_docdict_params)
+
+
+_matt_doc_default_callparams = """\
+mean : array_like, optional
+    Mean of the distribution (default: `None`)
+row_spread : array_like, optional
+    Row-wise 2nd order raw central moment matrix (default: ``1``)
+col_spread : array_like, optional
+    Column-wise 2nd order raw central moment matrix (default: ``1``)
+df : scalar, optional
+    Degrees of freedom (default: ``1``)
+"""
+
+_matt_doc_callparams_note = """\
+If `mean` is set to `None` then a matrix of zeros is used for the mean.
+The dimensions of this matrix are inferred from the shape of `row_spread` and
+`col_spread`, if these are provided, or set to ``1`` if ambiguous.
+
+`row_spread` and `col_spread` can be two-dimensional array_likes specifying the
+spread matrices directly. Alternatively, a one-dimensional array will
+be be interpreted as the entries of a diagonal matrix, and a scalar or
+zero-dimensional array will be interpreted as this value times the
+identity matrix.
+"""
+
+_matt_doc_frozen_callparams = ""
+
+_matt_doc_frozen_callparams_note = """\
+See class definition for a detailed description of parameters."""
+
+matrix_t_docdict_params = {
+    "_matt_doc_default_callparams": _matt_doc_default_callparams,
+    "_matt_doc_callparams_note": _matt_doc_callparams_note,
+    "_doc_random_state": _doc_random_state,
+}
+
+matrix_t_docdict_noparams = {
+    "_matt_doc_default_callparams": _matt_doc_frozen_callparams,
+    "_matt_doc_callparams_note": _matt_doc_frozen_callparams_note,
+    "_doc_random_state": _doc_random_state,
+}
+
+
+class matrix_t_gen(multi_rv_generic):
+    r"""
+    A matrix t-random variable.
+
+    The `mean` keyword specifies the mean.
+    The `row_spread` keyword specifies the row-wise spread matrix.
+    The `col_spread` keyword specifies the column-wise spread matrix.
+
+    Parameters
+    ----------
+    %(_matt_doc_default_callparams)s
+    %(_doc_random_state)s
+
+    Methods
+    -------
+    pdf(x, mean=None, row_spread=None, col_spread=None)
+        Probability density function.
+    logpdf(x, mean=None, row_spread=None, col_spread=None)
+        Log of the probability density function.
+    rvs(mean=None, row_spread=1, col_spread=1, df=1, size=1, random_state=None)
+        Draw random samples.
+
+    Notes
+    -----
+    %(_matt_doc_callparams_note)s
+
+    The spread matrices specified by `row_spread` and `col_spread` must be
+    (symmetric) positive definite. If the samples in `X` have shape `(m,n)`
+    then `row_spread` must have shape `(m,m)` and `col_spread` must have shape `(n,n)`.
+    Spread matrices must be full rank.
+
+    The probability density function for `matrix_t` is
+
+    .. math::
+
+        f(X \vert \mathrm{M}, \Sigma, \Omega, \mathrm{df}) =
+        \frac{
+            \Gamma_n \left(
+                \frac{\mathrm{df} + m + n - 1}{2}
+            \right)
+            \left(
+            \det \left(
+                I_n + (X - \mathrm{M})^T \Sigma^{-1} (X - \mathrm{M}) \Omega^{-1}
+            \right)
+        \right)^{ -\frac{\mathrm{df} + m + n - 1}{2} }
+        }{
+            \Gamma_n \left(
+                \frac{\mathrm{df} + n - 1}{2}
+            \right)
+            \pi^{mn / 2}
+            \left( \det \Sigma \right)^{n/2}
+            \left( \det \Omega \right)^{m/2}
+        }
+
+    or, alternatively,
+
+    .. math::
+
+        f(X \vert \mathrm{M}, \Sigma, \Omega, \mathrm{df}) =
+        \frac{
+            \Gamma_m \left(
+                \frac{\mathrm{df} + m + n - 1}{2}
+            \right)
+            \left(
+                \det \left(
+                    I_m + \Sigma^{-1} (X - \mathrm{M}) \Omega^{-1} (X - \mathrm{M})^T
+                    \right)
+            \right)^{ -\frac{\mathrm{df} + m + n - 1}{2} }
+        }{
+            \Gamma_m \left(
+                \frac{\mathrm{df} + n - 1}{2}
+            \right)
+            \pi^{mn / 2}
+            \left( \det \Sigma \right)^{n/2}
+            \left( \det \Omega \right)^{m/2}
+        }
+
+    where :math:`\mathrm{M}` is the mean,
+    :math:`\Sigma` is the row-wise spread matrix,
+    :math:`\Omega` is the column-wise matrix,
+    :math:`\mathrm{df}` is the degrees of freedom,
+    and :math:`\Gamma_n` is the multivariate gamma function.
+
+    These equivalent formulations come from the identity
+
+    .. math::
+
+        \det\left( I_m + A B \right) = \det\left( I_n + B A \right)
+
+    for :math:`m \times n` arrays :math:`A` and :math:`B^T`
+    and the fact that
+    :math:`\gamma_n(\mathrm{df} + m) / \gamma_n(\mathrm{df})`
+    is equal to
+    :math:`\gamma_m(\mathrm{df} + n) / \gamma_m(\mathrm{df})`,
+    where
+
+    .. math::
+
+        \gamma_m(\mathrm{df}) = 2^{m(m-1)/2}
+        \Gamma_m\left( (\mathrm{df} + m - 1) / 2 \right)
+
+    denotes a normalized multivariate gamma function.
+
+    When :math:`\mathrm{df} = 1` this distribution is known as the matrix
+    variate Cauchy.
+
+    .. versionadded:: 1.17.0
+
+    References
+    ----------
+    .. [1] Gupta, A.K., & Nagar, D.K. (2000). Matrix Variate Distributions (1st ed.).
+           Chapman and Hall/CRC.
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> from scipy.stats import matrix_t
+    >>> M = np.arange(6).reshape(3,2)
+    >>> M
+    array([[0, 1],
+           [2, 3],
+           [4, 5]])
+    >>> Sigma = np.diag([1,2,3])
+    >>> Sigma
+    array([[1, 0, 0],
+           [0, 2, 0],
+           [0, 0, 3]])
+    >>> Omega = 0.3*np.identity(2)
+    >>> Omega
+    array([[ 0.3,  0. ],
+           [ 0. ,  0.3]])
+    >>> X = M + 0.1
+    >>> X
+    array([[ 0.1,  1.1],
+           [ 2.1,  3.1],
+           [ 4.1,  5.1]])
+    >>> df = 3
+    >>> matrix_t.pdf(X, mean=M, row_spread=Sigma, col_spread=Omega, df=df)
+    0.9972880280135796
+
+    Alternatively, the object may be called (as a function) to fix the mean
+    and spread parameters, returning a "frozen" matrix t
+    random variable:
+
+    >>> rv = matrix_t(mean=None, row_spread=1, col_spread=1, df=1)
+    >>> # Frozen object with the same methods but holding the given
+    >>> # mean and spreads and degrees of freedom fixed.
+    """
+
+    def __init__(self, seed=None):
+        super().__init__(seed)
+        self.__doc__ = scipy._lib.doccer.docformat(
+            self.__doc__, matrix_t_docdict_params
+        )
+
+    def __call__(self, mean=None, row_spread=1, col_spread=1, df=None, seed=None):
+        """Create a frozen matrix t distribution.
+
+        See `matrix_t_frozen` for more information.
+        """
+        return matrix_t_frozen(mean, row_spread, col_spread, df, seed)
+
+    def _process_parameters(self, mean, row_spread, col_spread, df):
+        """
+        Infer dimensionality from mean or covariance matrices.
+        Handle defaults. Ensure conformality.
+
+        Parameters
+        ----------
+        mean : ndarray, shape (m,n)
+            Mean of the distribution
+        row_spread : ndarray, shape (m,m)
+            Row-wise spread matrix
+        col_spread : ndarray, shape (n,n)
+            Column-wise spread matrix
+        df : float
+            Degrees of freedom
+        """
+
+        # Process mean
+        if mean is not None:
+            mean = np.asarray(mean, dtype=float)
+            meanshape = mean.shape
+            if 0 in meanshape:
+                raise ValueError("Array `mean` has invalid shape.")
+            if len(meanshape) != 2:
+                raise ValueError("Array `mean` must be 2D.")
+
+        # Process row-wise spread
+        row_spread = np.asarray(row_spread, dtype=float)
+        if row_spread.ndim == 0:
+            if mean is not None:
+                row_spread = row_spread * np.identity(meanshape[0])
+            else:
+                row_spread = row_spread * np.identity(1)
+        elif row_spread.ndim == 1:
+            row_spread = np.diag(row_spread)
+        rowshape = row_spread.shape
+        if 0 in rowshape:
+            raise ValueError("Array `row_spread` has invalid shape.")
+        if len(rowshape) != 2:
+            raise ValueError("Array `row_spread` must be a scalar or a 2D array.")
+        if rowshape[0] != rowshape[1]:
+            raise ValueError("Array `row_spread` must be square.")
+        numrows = rowshape[0]
+
+        # Process column-wise spread
+        col_spread = np.asarray(col_spread, dtype=float)
+        if col_spread.ndim == 0:
+            if mean is not None:
+                col_spread = col_spread * np.identity(meanshape[1])
+            else:
+                col_spread = col_spread * np.identity(1)
+        elif col_spread.ndim == 1:
+            col_spread = np.diag(col_spread)
+        colshape = col_spread.shape
+        if 0 in colshape:
+            raise ValueError("Array `col_spread` has invalid shape.")
+        if len(colshape) != 2:
+            raise ValueError("Array `col_spread` must be a scalar or a 2D array.")
+        if colshape[0] != colshape[1]:
+            raise ValueError("Array `col_spread` must be square.")
+        numcols = colshape[0]
+
+        # Ensure mean and spreads are conformal
+        if mean is not None:
+            if meanshape[0] != numrows:
+                raise ValueError(
+                    "Arrays `mean` and `row_spread` must have the same number of rows."
+                )
+            if meanshape[1] != numcols:
+                raise ValueError(
+                    "Arrays `mean` and `col_spread` must have the same number "
+                    "of columns."
+                )
+        else:
+            mean = np.zeros((numrows, numcols))
+
+        dims = (numrows, numcols)
+
+        if df is None:
+            df = 1  # default to matrix variate Cauchy
+        elif not np.isscalar(df):
+            raise ValueError("Degrees of freedom must be a scalar.")
+        elif df <= 0:
+            raise ValueError("Degrees of freedom must be positive.")
+
+        return dims, mean, row_spread, col_spread, df
+
+    def _process_quantiles(self, X, dims):
+        """
+        Adjust quantiles array so that last two axes labels the component of
+        each data point.
+        """
+        X = np.asarray(X, dtype=float)
+        if X.ndim == 2:
+            X = X[np.newaxis, :]
+        if X.shape[-2:] != dims:
+            raise ValueError(
+                "The shape of array `X` is not conformal with "
+                "the distribution parameters."
+            )
+        return X
+
+    def _logpdf(
+        self,
+        dims,
+        X,
+        mean,
+        df,
+        invrow_spread,
+        invcol_spread,
+        logdetrow_spread,
+        logdetcol_spread,
+    ):
+        """
+        Log of the matrix t probability density function.
+
+        Parameters
+        ----------
+        dims : tuple
+            Dimensions of the matrix variates
+        X : ndarray, shape (m,n) (equal to `dims`)
+            Points at which to evaluate the log of the probability density function
+        mean : ndarray, shape (m,n)
+            Mean of the distribution
+        df : float
+            Degrees-of-freedom parameter
+        invrow_spread : ndarray, shape (m,m)
+            Inverse of the row-wise spread matrix
+        invcol_spread : ndarray, shape (n,n)
+            Inverse of the column-wise spread matrix
+        logdetrow_spread : float
+            Log-determinant of the row-wise spread matrix
+        detcol_spread : float
+            Log-determinant of the column-wise spread matrix
+
+        Notes
+        -----
+        As this function does no argument checking, it should not be
+        called directly; use `logpdf` instead.
+        """
+        m, n = dims
+        X_shape = X.shape
+        if X.ndim > 3:
+            X = X.reshape(-1, m, n)
+        X_centered = X - mean[np.newaxis, ...]
+        det_arg = np.identity(n) + np.einsum(
+            "nij,njk,nkl,nlp->nip",
+            X_centered.transpose(0, 2, 1),
+            invrow_spread[np.newaxis, ...],
+            X_centered,
+            invcol_spread[np.newaxis, ...],
+            optimize=True,
+        )
+        _, logdet = np.linalg.slogdet(det_arg)
+        log_d_mn = -((df + m + n - 1) / 2) * logdet
+        log_f_mn = (
+            scipy.special.multigammaln((df + m + n - 1) / 2, n)
+            - scipy.special.multigammaln((df + n - 1) / 2, n)
+            - (m * n / 2) * _LOG_PI
+            - (n / 2) * logdetrow_spread
+            - (m / 2) * logdetcol_spread
+        )
+        retval = log_d_mn + log_f_mn
+        if len(X_shape) > 3:
+            retval = retval.reshape(X_shape[:-2])
+        return retval
+
+    def logpdf(self, X, mean=None, row_spread=1, col_spread=1, df=1):
+        """Log of the matrix normal probability density function.
+
+        Parameters
+        ----------
+        X : array_like
+            Quantiles, with the last two axes of `X` denoting the components.
+        %(_matt_doc_default_callparams)s
+
+        Returns
+        -------
+        logpdf : ndarray
+            Log of the probability density function evaluated at `X`
+
+        Notes
+        -----
+        %(_matt_doc_callparams_note)s
+
+        Examples
+        -------
+
+        >>> import numpy as np
+        >>> from scipy.stats import matrix_t
+        >>> M = np.arange(6).reshape(3,2); M
+        array([[0, 1],
+            [2, 3],
+            [4, 5]])
+        >>> Sigma = np.diag([1,2,3]); Sigma
+        array([[1, 0, 0],
+            [0, 2, 0],
+            [0, 0, 3]])
+        >>> Omega = 0.3*np.identity(2); Omega
+        array([[ 0.3,  0. ],
+            [ 0. ,  0.3]])
+        >>> X = M + 0.1; X
+        array([[ 0.1,  1.1],
+            [ 2.1,  3.1],
+            [ 4.1,  5.1]])
+        >>> df = 3; df
+        3
+        >>> matrix_t.logpdf(X, mean=M, row_spread=Sigma, col_spread=Omega, df=df)
+        -0.002715656044664061
+        """
+        dims, mean, row_spread, col_spread, df = self._process_parameters(
+            mean, row_spread, col_spread, df
+        )
+        X = self._process_quantiles(X, dims)
+        rowpsd = _PSD(row_spread, allow_singular=False)
+        colpsd = _PSD(col_spread, allow_singular=False)
+        invrow_spread = rowpsd.pinv
+        invcol_spread = colpsd.pinv
+        logdetrow_spread = rowpsd.log_pdet
+        logdetcol_spread = colpsd.log_pdet
+        out = self._logpdf(
+            dims,
+            X,
+            mean,
+            df,
+            invrow_spread,
+            invcol_spread,
+            logdetrow_spread,
+            logdetcol_spread,
+        )
+        return _squeeze_output(out)
+
+    def pdf(self, X, mean=None, row_spread=1, col_spread=1, df=1):
+        """Matrix t probability density function.
+
+        Parameters
+        ----------
+        X : array_like
+            Quantiles, with the last two axes of `X` denoting the components.
+        %(_matt_doc_default_callparams)s
+
+        Returns
+        -------
+        pdf : ndarray
+            Probability density function evaluated at `X`
+
+        Notes
+        -----
+        %(_matt_doc_callparams_note)s
+
+        Examples
+        --------
+
+        >>> import numpy as np
+        >>> from scipy.stats import matrix_t
+        >>> M = np.arange(6).reshape(3,2); M
+        array([[0, 1],
+            [2, 3],
+            [4, 5]])
+        >>> Sigma = np.diag([1,2,3]); Sigma
+        array([[1, 0, 0],
+            [0, 2, 0],
+            [0, 0, 3]])
+        >>> Omega = 0.3*np.identity(2); Omega
+        array([[ 0.3,  0. ],
+            [ 0. ,  0.3]])
+        >>> X = M + 0.1; X
+        array([[ 0.1,  1.1],
+            [ 2.1,  3.1],
+            [ 4.1,  5.1]])
+        >>> df = 3; df
+        3
+        >>> matrix_t.logpdf(X, mean=M, row_spread=Sigma, col_spread=Omega, df=df)
+        0.9972880280135796
+        """
+        return np.exp(self.logpdf(X, mean, row_spread, col_spread, df))
+
+    def rvs(
+        self, mean=None, row_spread=1, col_spread=1, df=1, size=1, random_state=None
+    ) -> np.ndarray:
+        """Draw random samples from a matrix t distribution.
+
+        Parameters
+        ----------
+        %(_matt_doc_default_callparams)s
+        size : int, optional
+            Number of samples to draw (default 1).
+        %(_doc_random_state)s
+
+        Returns
+        -------
+        rvs : ndarray or scalar
+            Random variates of size (`size`, `dims`), where `dims` is the
+            dimension of the random matrices.
+
+        Notes
+        -----
+        %(_matt_doc_callparams_note)s
+
+        This method takes advantage of the two equivalent expressions of the
+        probability density function. It samples a Cholesky factor of a
+        random variate of the appropriate inverse Wishart distribution using
+        the smaller of the row/column dimensions.
+        """
+        size = int(size)
+        dims, mean, row_spread, col_spread, df = self._process_parameters(
+            mean, row_spread, col_spread, df
+        )
+        random_state = self._get_random_state(random_state)
+        # see scipy.stats.matrix_normal.rvs
+        std_norm = random_state.standard_normal(
+            size=(dims[1], size, dims[0])
+        ).transpose(1, 2, 0)
+        if dims[0] <= dims[1]:
+            rowchol = _cholesky_invwishart_rvs(df, row_spread, size, random_state)
+            colchol = scipy.linalg.cholesky(col_spread, lower=True)[np.newaxis, ...]
+        else:
+            rowchol = scipy.linalg.cholesky(row_spread, lower=True)[np.newaxis, ...]
+            colchol = _cholesky_invwishart_rvs(df, col_spread, size, random_state)
+        t_raw = np.einsum("ijp,ipq,ikq->ijk", rowchol, std_norm, colchol, optimize=True)
+        t_centered = mean[np.newaxis, ...] + t_raw
+        if size == 1:
+            t_centered = t_centered.reshape(mean.shape)
+        return t_centered
+
+
+matrix_t = matrix_t_gen()
+
+
+class matrix_t_frozen:
+    def __init__(self, mean, row_spread, col_spread, df, seed=None):
+        self._dist = matrix_t_gen(seed)
+        self.dims, self.mean, self.row_spread, self.col_spread, self.df = (
+            self._dist._process_parameters(mean, row_spread, col_spread, df)
+        )
+        self._random_state = np.random.RandomState(seed)
+        self.rowpsd = _PSD(self.row_spread, allow_singular=False)
+        self.colpsd = _PSD(self.col_spread, allow_singular=False)
+
+    def logpdf(self, X):
+        X = self._dist._process_quantiles(X, self.dims)
+        rowpsd = _PSD(self.row_spread, allow_singular=False)
+        colpsd = _PSD(self.col_spread, allow_singular=False)
+        invrow_spread = rowpsd.pinv
+        invcol_spread = colpsd.pinv
+        logdetrow_spread = rowpsd.log_pdet
+        logdetcol_spread = colpsd.log_pdet
+        out = self._dist._logpdf(
+            self.dims,
+            X,
+            self.mean,
+            self.df,
+            invrow_spread,
+            invcol_spread,
+            logdetrow_spread,
+            logdetcol_spread,
+        )
+        return _squeeze_output(out)
+
+    def pdf(self, X):
+        return np.exp(self.logpdf(X))
+
+    def rvs(self, size=1, random_state=None):
+        return self._dist.rvs(
+            self.mean, self.row_spread, self.col_spread, self.df, size, random_state
+        )
+
+
+# Set frozen generator docstrings from corresponding docstrings in
+# matrix_t_gen and fill in default strings in class docstrings
+for name in ["logpdf", "pdf", "rvs"]:
+    method = matrix_t_gen.__dict__[name]
+    method_frozen = matrix_t_frozen.__dict__[name]
+    method_frozen.__doc__ = scipy._lib.doccer.docformat(
+        method.__doc__, matrix_t_docdict_noparams
+    )
+    method.__doc__ = scipy._lib.doccer.docformat(
+        method.__doc__, matrix_t_docdict_params
+    )
+
+
+
+def _cholesky_invwishart_rvs(
+    df: float, scale: np.ndarray, size: int, random_state: np.random.Generator
+) -> np.ndarray:
+    r"""Samples the lower Cholesky factor of a matrix following an inverse
+    Wishart distribution.
+
+    Notes
+    -----
+    Intended to be used *as a step in the process* for computing random variates
+    of a matrix t distribution :math:`\mathcal{T}_{m,n}` by appealing to its
+    alternative form as a matrix mixture
+    .. math::
+        \mathcal{T}_{m,n}( \mathrm{df}, \mathrm{M}, \Sigma, \Omega )
+        = \mathcal{N}_{m,n}(
+            \mathrm{M},
+            \mathcal{W}^{-1}_m(\mathrm{df} + m - 1, \Sigma),
+            \Omega
+            )
+        = \mathcal{N}_{m,n}(
+            \mathrm{M},
+            \Sigma,
+            \mathcal{W}^{-1}_n(\mathrm{df} - n + 1, \Omega)
+            )
+    where :math:`\mathcal{N}_{m,n}` is a matrix normal distribution
+    and :math:`\mathcal{W}^{-1}_d` is an inverse Wishart distribution.
+    Accordingly, the degrees of freedom adjustment
+    :math:`\mathrm{df} \to \mathrm{df} + d - 1`
+    occurrs in the scope of this function.
+    """
+    df_iw = df + scale.shape[0] - 1
+    iw_samples = scipy.stats.invwishart.rvs(df_iw, scale, size, random_state)
+    if size == 1:
+        iw_samples = iw_samples[np.newaxis, ...]
+    chol_samples = np.empty_like(iw_samples)
+    for idx in range(size):
+        chol_samples[idx] = scipy.linalg.cholesky(
+            iw_samples[idx], lower=True, check_finite=False
+        ).reshape(iw_samples.shape[1:])
+    return chol_samples.reshape((size, *scale.shape))
+
+
+_dirichlet_doc_default_callparams = """\
+alpha : array_like
+    The concentration parameters. The number of entries determines the
+    dimensionality of the distribution.
+"""
+_dirichlet_doc_frozen_callparams = ""
+
+_dirichlet_doc_frozen_callparams_note = """\
+See class definition for a detailed description of parameters."""
+
+dirichlet_docdict_params = {
+    '_dirichlet_doc_default_callparams': _dirichlet_doc_default_callparams,
+    '_doc_random_state': _doc_random_state
+}
+
+dirichlet_docdict_noparams = {
+    '_dirichlet_doc_default_callparams': _dirichlet_doc_frozen_callparams,
+    '_doc_random_state': _doc_random_state
+}
+
+
+def _dirichlet_check_parameters(alpha):
+    alpha = np.asarray(alpha)
+    if np.min(alpha) <= 0:
+        raise ValueError("All parameters must be greater than 0")
+    elif alpha.ndim != 1:
+        raise ValueError("Parameter vector 'a' must be one dimensional, "
+                         f"but a.shape = {alpha.shape}.")
+    return alpha
+
+
+def _dirichlet_check_input(alpha, x):
+    x = np.asarray(x)
+
+    if x.shape[0] + 1 != alpha.shape[0] and x.shape[0] != alpha.shape[0]:
+        raise ValueError("Vector 'x' must have either the same number "
+                         "of entries as, or one entry fewer than, "
+                         f"parameter vector 'a', but alpha.shape = {alpha.shape} "
+                         f"and x.shape = {x.shape}.")
+
+    if x.shape[0] != alpha.shape[0]:
+        xk = np.array([1 - np.sum(x, 0)])
+        if xk.ndim == 1:
+            x = np.append(x, xk)
+        elif xk.ndim == 2:
+            x = np.vstack((x, xk))
+        else:
+            raise ValueError("The input must be one dimensional or a two "
+                             "dimensional matrix containing the entries.")
+
+    if np.min(x) < 0:
+        raise ValueError("Each entry in 'x' must be greater than or equal "
+                         "to zero.")
+
+    if np.max(x) > 1:
+        raise ValueError("Each entry in 'x' must be smaller or equal one.")
+
+    # Check x_i > 0 or alpha_i > 1
+    xeq0 = (x == 0)
+    alphalt1 = (alpha < 1)
+    if x.shape != alpha.shape:
+        alphalt1 = np.repeat(alphalt1, x.shape[-1], axis=-1).reshape(x.shape)
+    chk = np.logical_and(xeq0, alphalt1)
+
+    if np.sum(chk):
+        raise ValueError("Each entry in 'x' must be greater than zero if its "
+                         "alpha is less than one.")
+
+    if (np.abs(np.sum(x, 0) - 1.0) > 10e-10).any():
+        raise ValueError("The input vector 'x' must lie within the normal "
+                         f"simplex. but np.sum(x, 0) = {np.sum(x, 0)}.")
+
+    return x
+
+
+def _lnB(alpha):
+    r"""Internal helper function to compute the log of the useful quotient.
+
+    .. math::
+
+        B(\alpha) = \frac{\prod_{i=1}{K}\Gamma(\alpha_i)}
+                         {\Gamma\left(\sum_{i=1}^{K} \alpha_i \right)}
+
+    Parameters
+    ----------
+    %(_dirichlet_doc_default_callparams)s
+
+    Returns
+    -------
+    B : scalar
+        Helper quotient, internal use only
+
+    """
+    return np.sum(gammaln(alpha)) - gammaln(np.sum(alpha))
+
+
+class dirichlet_gen(multi_rv_generic):
+    r"""
+    A Dirichlet random variable.
+
+    The ``alpha`` keyword specifies the concentration parameters of the
+    distribution.
+
+    .. versionadded:: 0.15.0
+
+    Parameters
+    ----------
+    %(_dirichlet_doc_default_callparams)s
+    %(_doc_random_state)s
+
+    Methods
+    -------
+    pdf(x, alpha)
+        Probability density function.
+    logpdf(x, alpha)
+        Log of the probability density function.
+    rvs(alpha, size=1, random_state=None)
+        Draw random samples from a Dirichlet distribution.
+    mean(alpha)
+        The mean of the Dirichlet distribution
+    var(alpha)
+        The variance of the Dirichlet distribution
+    cov(alpha)
+        The covariance of the Dirichlet distribution
+    entropy(alpha)
+        Compute the differential entropy of the Dirichlet distribution.
+
+    Notes
+    -----
+    Each :math:`\alpha` entry must be positive. The distribution has only
+    support on the simplex defined by
+
+    .. math::
+        \sum_{i=1}^{K} x_i = 1
+
+    where :math:`0 < x_i < 1`.
+
+    If the quantiles don't lie within the simplex, a ValueError is raised.
+
+    The probability density function for `dirichlet` is
+
+    .. math::
+
+        f(x) = \frac{1}{\mathrm{B}(\boldsymbol\alpha)} \prod_{i=1}^K x_i^{\alpha_i - 1}
+
+    where
+
+    .. math::
+
+        \mathrm{B}(\boldsymbol\alpha) = \frac{\prod_{i=1}^K \Gamma(\alpha_i)}
+                                     {\Gamma\bigl(\sum_{i=1}^K \alpha_i\bigr)}
+
+    and :math:`\boldsymbol\alpha=(\alpha_1,\ldots,\alpha_K)`, the
+    concentration parameters and :math:`K` is the dimension of the space
+    where :math:`x` takes values.
+
+    Note that the `dirichlet` interface is somewhat inconsistent.
+    The array returned by the rvs function is transposed
+    with respect to the format expected by the pdf and logpdf.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import dirichlet
+
+    Generate a dirichlet random variable
+
+    >>> quantiles = np.array([0.2, 0.2, 0.6])  # specify quantiles
+    >>> alpha = np.array([0.4, 5, 15])  # specify concentration parameters
+    >>> dirichlet.pdf(quantiles, alpha)
+    0.2843831684937255
+
+    The same PDF but following a log scale
+
+    >>> dirichlet.logpdf(quantiles, alpha)
+    -1.2574327653159187
+
+    Once we specify the dirichlet distribution
+    we can then calculate quantities of interest
+
+    >>> dirichlet.mean(alpha)  # get the mean of the distribution
+    array([0.01960784, 0.24509804, 0.73529412])
+    >>> dirichlet.var(alpha) # get variance
+    array([0.00089829, 0.00864603, 0.00909517])
+    >>> dirichlet.entropy(alpha)  # calculate the differential entropy
+    -4.3280162474082715
+
+    We can also return random samples from the distribution
+
+    >>> dirichlet.rvs(alpha, size=1, random_state=1)
+    array([[0.00766178, 0.24670518, 0.74563305]])
+    >>> dirichlet.rvs(alpha, size=2, random_state=2)
+    array([[0.01639427, 0.1292273 , 0.85437844],
+           [0.00156917, 0.19033695, 0.80809388]])
+
+    Alternatively, the object may be called (as a function) to fix
+    concentration parameters, returning a "frozen" Dirichlet
+    random variable:
+
+    >>> rv = dirichlet(alpha)
+    >>> # Frozen object with the same methods but holding the given
+    >>> # concentration parameters fixed.
+    """
+
+    def __init__(self, seed=None):
+        super().__init__(seed)
+        self.__doc__ = doccer.docformat(self.__doc__, dirichlet_docdict_params)
+
+    def __call__(self, alpha, seed=None):
+        return dirichlet_frozen(alpha, seed=seed)
+
+    def _logpdf(self, x, alpha):
+        """Log of the Dirichlet probability density function.
+
+        Parameters
+        ----------
+        x : ndarray
+            Points at which to evaluate the log of the probability
+            density function
+        %(_dirichlet_doc_default_callparams)s
+
+        Notes
+        -----
+        As this function does no argument checking, it should not be
+        called directly; use 'logpdf' instead.
+
+        """
+        lnB = _lnB(alpha)
+        return - lnB + np.sum((xlogy(alpha - 1, x.T)).T, 0)
+
+    def logpdf(self, x, alpha):
+        """Log of the Dirichlet probability density function.
+
+        Parameters
+        ----------
+        x : array_like
+            Quantiles, with the last axis of `x` denoting the components.
+        %(_dirichlet_doc_default_callparams)s
+
+        Returns
+        -------
+        pdf : ndarray or scalar
+            Log of the probability density function evaluated at `x`.
+
+        """
+        alpha = _dirichlet_check_parameters(alpha)
+        x = _dirichlet_check_input(alpha, x)
+
+        out = self._logpdf(x, alpha)
+        return _squeeze_output(out)
+
+    def pdf(self, x, alpha):
+        """The Dirichlet probability density function.
+
+        Parameters
+        ----------
+        x : array_like
+            Quantiles, with the last axis of `x` denoting the components.
+        %(_dirichlet_doc_default_callparams)s
+
+        Returns
+        -------
+        pdf : ndarray or scalar
+            The probability density function evaluated at `x`.
+
+        """
+        alpha = _dirichlet_check_parameters(alpha)
+        x = _dirichlet_check_input(alpha, x)
+
+        out = np.exp(self._logpdf(x, alpha))
+        return _squeeze_output(out)
+
+    def mean(self, alpha):
+        """Mean of the Dirichlet distribution.
+
+        Parameters
+        ----------
+        %(_dirichlet_doc_default_callparams)s
+
+        Returns
+        -------
+        mu : ndarray or scalar
+            Mean of the Dirichlet distribution.
+
+        """
+        alpha = _dirichlet_check_parameters(alpha)
+
+        out = alpha / (np.sum(alpha))
+        return _squeeze_output(out)
+
+    def var(self, alpha):
+        """Variance of the Dirichlet distribution.
+
+        Parameters
+        ----------
+        %(_dirichlet_doc_default_callparams)s
+
+        Returns
+        -------
+        v : ndarray or scalar
+            Variance of the Dirichlet distribution.
+
+        """
+
+        alpha = _dirichlet_check_parameters(alpha)
+
+        alpha0 = np.sum(alpha)
+        out = (alpha * (alpha0 - alpha)) / ((alpha0 * alpha0) * (alpha0 + 1))
+        return _squeeze_output(out)
+
+    def cov(self, alpha):
+        """Covariance matrix of the Dirichlet distribution.
+
+        Parameters
+        ----------
+        %(_dirichlet_doc_default_callparams)s
+
+        Returns
+        -------
+        cov : ndarray
+            The covariance matrix of the distribution.
+        """
+
+        alpha = _dirichlet_check_parameters(alpha)
+        alpha0 = np.sum(alpha)
+        a = alpha / alpha0
+
+        cov = (np.diag(a) - np.outer(a, a)) / (alpha0 + 1)
+        return _squeeze_output(cov)
+
+    def entropy(self, alpha):
+        """
+        Differential entropy of the Dirichlet distribution.
+
+        Parameters
+        ----------
+        %(_dirichlet_doc_default_callparams)s
+
+        Returns
+        -------
+        h : scalar
+            Entropy of the Dirichlet distribution
+
+        """
+
+        alpha = _dirichlet_check_parameters(alpha)
+
+        alpha0 = np.sum(alpha)
+        lnB = _lnB(alpha)
+        K = alpha.shape[0]
+
+        out = lnB + (alpha0 - K) * scipy.special.psi(alpha0) - np.sum(
+            (alpha - 1) * scipy.special.psi(alpha))
+        return _squeeze_output(out)
+
+    def rvs(self, alpha, size=1, random_state=None):
+        """
+        Draw random samples from a Dirichlet distribution.
+
+        Parameters
+        ----------
+        %(_dirichlet_doc_default_callparams)s
+        size : int, optional
+            Number of samples to draw (default 1).
+        %(_doc_random_state)s
+
+        Returns
+        -------
+        rvs : ndarray or scalar
+            Random variates of size (`size`, `N`), where `N` is the
+            dimension of the random variable.
+
+        """
+        alpha = _dirichlet_check_parameters(alpha)
+        random_state = self._get_random_state(random_state)
+        return random_state.dirichlet(alpha, size=size)
+
+
+dirichlet = dirichlet_gen()
+
+
+class dirichlet_frozen(multi_rv_frozen):
+    __class_getitem__ = None  # pyrefly:ignore[bad-assignment]
+
+    def __init__(self, alpha, seed=None):
+        self.alpha = _dirichlet_check_parameters(alpha)
+        self._dist = dirichlet_gen(seed)
+
+    def logpdf(self, x):
+        return self._dist.logpdf(x, self.alpha)
+
+    def pdf(self, x):
+        return self._dist.pdf(x, self.alpha)
+
+    def mean(self):
+        return self._dist.mean(self.alpha)
+
+    def var(self):
+        return self._dist.var(self.alpha)
+
+    def cov(self):
+        return self._dist.cov(self.alpha)
+
+    def entropy(self):
+        return self._dist.entropy(self.alpha)
+
+    def rvs(self, size=1, random_state=None):
+        return self._dist.rvs(self.alpha, size, random_state)
+
+
+# Set frozen generator docstrings from corresponding docstrings in
+# multivariate_normal_gen and fill in default strings in class docstrings
+for name in ['logpdf', 'pdf', 'rvs', 'mean', 'var', 'cov', 'entropy']:
+    method = dirichlet_gen.__dict__[name]
+    method_frozen = dirichlet_frozen.__dict__[name]
+    method_frozen.__doc__ = doccer.docformat(
+        method.__doc__, dirichlet_docdict_noparams)
+    method.__doc__ = doccer.docformat(method.__doc__, dirichlet_docdict_params)
+
+
+_wishart_doc_default_callparams = """\
+df : int
+    Degrees of freedom, must be greater than or equal to dimension of the
+    scale matrix
+scale : array_like
+    Symmetric positive definite scale matrix of the distribution
+"""
+
+_wishart_doc_callparams_note = ""
+
+_wishart_doc_frozen_callparams = ""
+
+_wishart_doc_frozen_callparams_note = """\
+See class definition for a detailed description of parameters."""
+
+wishart_docdict_params = {
+    '_doc_default_callparams': _wishart_doc_default_callparams,
+    '_doc_callparams_note': _wishart_doc_callparams_note,
+    '_doc_random_state': _doc_random_state
+}
+
+wishart_docdict_noparams = {
+    '_doc_default_callparams': _wishart_doc_frozen_callparams,
+    '_doc_callparams_note': _wishart_doc_frozen_callparams_note,
+    '_doc_random_state': _doc_random_state
+}
+
+
+class wishart_gen(multi_rv_generic):
+    r"""
+    A Wishart random variable.
+
+    The `df` keyword specifies the degrees of freedom. The `scale` keyword
+    specifies the scale matrix, which must be symmetric and positive definite.
+    In this context, the scale matrix is often interpreted in terms of a
+    multivariate normal precision matrix (the inverse of the covariance
+    matrix). These arguments must satisfy the relationship
+    ``df > scale.ndim - 1``, but see notes on using the `rvs` method with
+    ``df < scale.ndim``.
+
+    Parameters
+    ----------
+    %(_doc_default_callparams)s
+    %(_doc_random_state)s
+
+    Methods
+    -------
+    pdf(x, df, scale)
+        Probability density function.
+    logpdf(x, df, scale)
+        Log of the probability density function.
+    rvs(df, scale, size=1, random_state=None)
+        Draw random samples from a Wishart distribution.
+    entropy()
+        Compute the differential entropy of the Wishart distribution.
+
+    Raises
+    ------
+    scipy.linalg.LinAlgError
+        If the scale matrix `scale` is not positive definite.
+
+    See Also
+    --------
+    invwishart, chi2
+
+    Notes
+    -----
+    %(_doc_callparams_note)s
+
+    The scale matrix `scale` must be a symmetric positive definite
+    matrix. Singular matrices, including the symmetric positive semi-definite
+    case, are not supported. Symmetry is not checked; only the lower triangular
+    portion is used.
+
+    The Wishart distribution is often denoted
+
+    .. math::
+
+        W_p(\nu, \Sigma)
+
+    where :math:`\nu` is the degrees of freedom and :math:`\Sigma` is the
+    :math:`p \times p` scale matrix.
+
+    The probability density function for `wishart` has support over positive
+    definite matrices :math:`S`; if :math:`S \sim W_p(\nu, \Sigma)`, then
+    its PDF is given by:
+
+    .. math::
+
+        f(S) = \frac{|S|^{\frac{\nu - p - 1}{2}}}{2^{ \frac{\nu p}{2} }
+               |\Sigma|^\frac{\nu}{2} \Gamma_p \left ( \frac{\nu}{2} \right )}
+               \exp\left( -tr(\Sigma^{-1} S) / 2 \right)
+
+    If :math:`S \sim W_p(\nu, \Sigma)` (Wishart) then
+    :math:`S^{-1} \sim W_p^{-1}(\nu, \Sigma^{-1})` (inverse Wishart).
+
+    If the scale matrix is 1-dimensional and equal to one, then the Wishart
+    distribution :math:`W_1(\nu, 1)` collapses to the :math:`\chi^2(\nu)`
+    distribution.
+
+    The algorithm [2]_ implemented by the `rvs` method may
+    produce numerically singular matrices with :math:`p - 1 < \nu < p`; the
+    user may wish to check for this condition and generate replacement samples
+    as necessary.
+
+
+    .. versionadded:: 0.16.0
+
+    References
+    ----------
+    .. [1] M.L. Eaton, "Multivariate Statistics: A Vector Space Approach",
+           Wiley, 1983.
+    .. [2] W.B. Smith and R.R. Hocking, "Algorithm AS 53: Wishart Variate
+           Generator", Applied Statistics, vol. 21, pp. 341-345, 1972.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.stats import wishart, chi2
+    >>> x = np.linspace(1e-5, 8, 100)
+    >>> w = wishart.pdf(x, df=3, scale=1); w[:5]
+    array([ 0.00126156,  0.10892176,  0.14793434,  0.17400548,  0.1929669 ])
+    >>> c = chi2.pdf(x, 3); c[:5]
+    array([ 0.00126156,  0.10892176,  0.14793434,  0.17400548,  0.1929669 ])
+    >>> plt.plot(x, w)
+    >>> plt.show()
+
+    The input quantiles can be any shape of array, as long as the last
+    axis labels the components.
+
+    Alternatively, the object may be called (as a function) to fix the degrees
+    of freedom and scale parameters, returning a "frozen" Wishart random
+    variable:
+
+    >>> rv = wishart(df=1, scale=1)
+    >>> # Frozen object with the same methods but holding the given
+    >>> # degrees of freedom and scale fixed.
+    """
+
+    def __init__(self, seed=None):
+        super().__init__(seed)
+        self.__doc__ = doccer.docformat(self.__doc__, wishart_docdict_params)
+
+    def __call__(self, df=None, scale=None, seed=None):
+        """Create a frozen Wishart distribution.
+
+        See `wishart_frozen` for more information.
+        """
+        return wishart_frozen(df, scale, seed)
+
+    def _process_parameters(self, df, scale):
+        if scale is None:
+            scale = 1.0
+        scale = np.asarray(scale, dtype=float)
+
+        if scale.ndim == 0:
+            scale = scale[np.newaxis, np.newaxis]
+        elif scale.ndim == 1:
+            scale = np.diag(scale)
+        elif scale.ndim == 2 and not scale.shape[0] == scale.shape[1]:
+            raise ValueError("Array 'scale' must be square if it is two dimensional,"
+                             f" but scale.scale = {str(scale.shape)}.")
+        elif scale.ndim > 2:
+            raise ValueError(f"Array 'scale' must be at most two-dimensional, "
+                             f"but scale.ndim = {scale.ndim}")
+
+        dim = scale.shape[0]
+
+        if df is None:
+            df = dim
+        elif not np.isscalar(df):
+            raise ValueError("Degrees of freedom must be a scalar.")
+        elif df <= dim - 1:
+            raise ValueError("Degrees of freedom must be greater than the "
+                             "dimension of scale matrix minus 1.")
+
+        return dim, df, scale
+
+    def _process_quantiles(self, x, dim):
+        """
+        Adjust quantiles array so that last axis labels the components of
+        each data point.
+        """
+        x = np.asarray(x, dtype=float)
+
+        if x.ndim == 0:
+            x = x * np.eye(dim)[:, :, np.newaxis]
+        if x.ndim == 1:
+            if dim == 1:
+                x = x[np.newaxis, np.newaxis, :]
+            else:
+                x = np.diag(x)[:, :, np.newaxis]
+        elif x.ndim == 2:
+            if not x.shape[0] == x.shape[1]:
+                raise ValueError(
+                    "Quantiles must be square if they are two dimensional,"
+                    f" but x.shape = {str(x.shape)}.")
+            x = x[:, :, np.newaxis]
+        elif x.ndim == 3:
+            if not x.shape[0] == x.shape[1]:
+                raise ValueError(
+                    "Quantiles must be square in the first two dimensions "
+                    f"if they are three dimensional, but x.shape = {str(x.shape)}.")
+        elif x.ndim > 3:
+            raise ValueError(f"Quantiles must be at most two-dimensional with an "
+                             f"additional dimension for multiple components, "
+                             f"but x.ndim = {x.ndim}")
+
+        # Now we have 3-dim array; should have shape [dim, dim, *]
+        if not x.shape[0:2] == (dim, dim):
+            raise ValueError('Quantiles have incompatible dimensions: should'
+                             f' be {(dim, dim)}, got {x.shape[0:2]}.')
+
+        return x
+
+    def _process_size(self, size):
+        size = np.asarray(size)
+
+        if size.ndim == 0:
+            size = size[np.newaxis]
+        elif size.ndim > 1:
+            raise ValueError('Size must be an integer or tuple of integers;'
+                 ' thus must have dimension <= 1.'
+                 f' Got size.ndim = {str(tuple(size))}')
+        n = size.prod()
+        shape = tuple(size)
+
+        return n, shape
+
+    def _logpdf(self, x, dim, df, scale, log_det_scale, C):
+        """Log of the Wishart probability density function.
+
+        Parameters
+        ----------
+        x : ndarray
+            Points at which to evaluate the log of the probability
+            density function
+        dim : int
+            Dimension of the scale matrix
+        df : int
+            Degrees of freedom
+        scale : ndarray
+            Scale matrix
+        log_det_scale : float
+            Logarithm of the determinant of the scale matrix
+        C : ndarray
+            Cholesky factorization of the scale matrix, lower triangular.
+
+        Notes
+        -----
+        As this function does no argument checking, it should not be
+        called directly; use 'logpdf' instead.
+
+        """
+        # log determinant of x
+        # Note: x has components along the last axis, so that x.T has
+        # components alone the 0-th axis. Then since det(A) = det(A'), this
+        # gives us a 1-dim vector of determinants
+
+        # Retrieve tr(scale^{-1} x)
+        log_det_x = np.empty(x.shape[-1])
+        scale_inv_x = np.empty(x.shape)
+        tr_scale_inv_x = np.empty(x.shape[-1])
+        for i in range(x.shape[-1]):
+            _, log_det_x[i] = self._cholesky_logdet(x[:, :, i])
+            scale_inv_x[:, :, i] = scipy.linalg.cho_solve((C, True), x[:, :, i])
+            tr_scale_inv_x[i] = scale_inv_x[:, :, i].trace()
+
+        # Log PDF
+        out = ((0.5 * (df - dim - 1) * log_det_x - 0.5 * tr_scale_inv_x) -
+               (0.5 * df * dim * _LOG_2 + 0.5 * df * log_det_scale +
+                multigammaln(0.5*df, dim)))
+
+        return out
+
+    def logpdf(self, x, df, scale):
+        """Log of the Wishart probability density function.
+
+        Parameters
+        ----------
+        x : array_like
+            Quantiles, with the last axis of `x` denoting the components.
+            Each quantile must be a symmetric positive definite matrix.
+        %(_doc_default_callparams)s
+
+        Returns
+        -------
+        pdf : ndarray
+            Log of the probability density function evaluated at `x`
+
+        Notes
+        -----
+        %(_doc_callparams_note)s
+
+        """
+        dim, df, scale = self._process_parameters(df, scale)
+        x = self._process_quantiles(x, dim)
+
+        # Cholesky decomposition of scale, get log(det(scale))
+        C, log_det_scale = self._cholesky_logdet(scale)
+
+        out = self._logpdf(x, dim, df, scale, log_det_scale, C)
+        return _squeeze_output(out)
+
+    def pdf(self, x, df, scale):
+        """Wishart probability density function.
+
+        Parameters
+        ----------
+        x : array_like
+            Quantiles, with the last axis of `x` denoting the components.
+            Each quantile must be a symmetric positive definite matrix.
+        %(_doc_default_callparams)s
+
+        Returns
+        -------
+        pdf : ndarray
+            Probability density function evaluated at `x`
+
+        Notes
+        -----
+        %(_doc_callparams_note)s
+
+        """
+        return np.exp(self.logpdf(x, df, scale))
+
+    def _mean(self, dim, df, scale):
+        """Mean of the Wishart distribution.
+
+        Parameters
+        ----------
+        dim : int
+            Dimension of the scale matrix
+        %(_doc_default_callparams)s
+
+        Notes
+        -----
+        As this function does no argument checking, it should not be
+        called directly; use 'mean' instead.
+
+        """
+        return df * scale
+
+    def mean(self, df, scale):
+        """Mean of the Wishart distribution.
+
+        Parameters
+        ----------
+        %(_doc_default_callparams)s
+
+        Returns
+        -------
+        mean : float
+            The mean of the distribution
+        """
+        dim, df, scale = self._process_parameters(df, scale)
+        out = self._mean(dim, df, scale)
+        return _squeeze_output(out)
+
+    def _mode(self, dim, df, scale):
+        """Mode of the Wishart distribution.
+
+        Parameters
+        ----------
+        dim : int
+            Dimension of the scale matrix
+        %(_doc_default_callparams)s
+
+        Notes
+        -----
+        As this function does no argument checking, it should not be
+        called directly; use 'mode' instead.
+
+        """
+        if df >= dim + 1:
+            out = (df-dim-1) * scale
+        else:
+            out = None
+        return out
+
+    def mode(self, df, scale):
+        """Mode of the Wishart distribution
+
+        Only valid if the degrees of freedom are greater than the dimension of
+        the scale matrix.
+
+        Parameters
+        ----------
+        %(_doc_default_callparams)s
+
+        Returns
+        -------
+        mode : float or None
+            The Mode of the distribution
+        """
+        dim, df, scale = self._process_parameters(df, scale)
+        out = self._mode(dim, df, scale)
+        return _squeeze_output(out) if out is not None else out
+
+    def _var(self, dim, df, scale):
+        """Variance of the Wishart distribution.
+
+        Parameters
+        ----------
+        dim : int
+            Dimension of the scale matrix
+        %(_doc_default_callparams)s
+
+        Notes
+        -----
+        As this function does no argument checking, it should not be
+        called directly; use 'var' instead.
+
+        """
+        var = scale**2
+        diag = scale.diagonal()  # 1 x dim array
+        var += np.outer(diag, diag)
+        var *= df
+        return var
+
+    def var(self, df, scale):
+        """Variance of the Wishart distribution.
+
+        Parameters
+        ----------
+        %(_doc_default_callparams)s
+
+        Returns
+        -------
+        var : float
+            The variance of the distribution
+        """
+        dim, df, scale = self._process_parameters(df, scale)
+        out = self._var(dim, df, scale)
+        return _squeeze_output(out)
+
+    def _standard_rvs(self, n, shape, dim, df, random_state):
+        """
+        Parameters
+        ----------
+        n : int
+            Number of variates to generate
+        shape : iterable
+            Shape of the variates to generate
+        dim : int
+            Dimension of the scale matrix
+        df : int
+            Degrees of freedom
+        random_state : {None, int, `numpy.random.Generator`,
+                        `numpy.random.RandomState`}, optional
+
+            If `seed` is None (or `np.random`), the `numpy.random.RandomState`
+            singleton is used.
+            If `seed` is an int, a new ``RandomState`` instance is used,
+            seeded with `seed`.
+            If `seed` is already a ``Generator`` or ``RandomState`` instance
+            then that instance is used.
+
+        Notes
+        -----
+        As this function does no argument checking, it should not be
+        called directly; use 'rvs' instead.
+
+        """
+        # Random normal variates for off-diagonal elements
+        n_tril = dim * (dim-1) // 2
+        covariances = random_state.normal(
+            size=n*n_tril).reshape(shape+(n_tril,))
+
+        # Random chi-square variates for diagonal elements
+        variances = (np.r_[[random_state.chisquare(df-(i+1)+1, size=n)**0.5
+                            for i in range(dim)]].reshape((dim,) +
+                                                          shape[::-1]).T)
+
+        # Create the A matri(ces) - lower triangular
+        A = np.zeros(shape + (dim, dim))
+
+        # Input the covariances
+        size_idx = tuple([slice(None, None, None)]*len(shape))
+        tril_idx = np.tril_indices(dim, k=-1)
+        A[size_idx + tril_idx] = covariances
+
+        # Input the variances
+        diag_idx = np.diag_indices(dim)
+        A[size_idx + diag_idx] = variances
+
+        return A
+
+    def _rvs(self, n, shape, dim, df, C, random_state):
+        """Draw random samples from a Wishart distribution.
+
+        Parameters
+        ----------
+        n : int
+            Number of variates to generate
+        shape : iterable
+            Shape of the variates to generate
+        dim : int
+            Dimension of the scale matrix
+        df : int
+            Degrees of freedom
+        C : ndarray
+            Cholesky factorization of the scale matrix, lower triangular.
+        %(_doc_random_state)s
+
+        Notes
+        -----
+        As this function does no argument checking, it should not be
+        called directly; use 'rvs' instead.
+
+        """
+        random_state = self._get_random_state(random_state)
+        # Calculate the matrices A, which are actually lower triangular
+        # Cholesky factorizations of a matrix B such that B ~ W(df, I)
+        A = self._standard_rvs(n, shape, dim, df, random_state)
+
+        # Calculate SA = C A A' C', where SA ~ W(df, scale)
+        # Note: this is the product of a (lower) (lower) (lower)' (lower)'
+        #       or, denoting B = AA', it is C B C' where C is the lower
+        #       triangular Cholesky factorization of the scale matrix.
+        #       this appears to conflict with the instructions in [1]_, which
+        #       suggest that it should be D' B D where D is the lower
+        #       triangular factorization of the scale matrix. However, it is
+        #       meant to refer to the Bartlett (1933) representation of a
+        #       Wishart random variate as L A A' L' where L is lower triangular
+        #       so it appears that understanding D' to be upper triangular
+        #       is either a typo in or misreading of [1]_.
+        for index in np.ndindex(shape):
+            CA = np.dot(C, A[index])
+            A[index] = np.dot(CA, CA.T)
+
+        return A
+
+    def rvs(self, df, scale, size=1, random_state=None):
+        """Draw random samples from a Wishart distribution.
+
+        Parameters
+        ----------
+        %(_doc_default_callparams)s
+        size : int or iterable of integers, optional
+            Number of samples to draw (default 1).
+        %(_doc_random_state)s
+
+        Returns
+        -------
+        rvs : ndarray
+            Random variates of shape (`size`) + (``dim``, ``dim``), where
+            ``dim`` is the dimension of the scale matrix.
+
+        Notes
+        -----
+        %(_doc_callparams_note)s
+
+        """
+        n, shape = self._process_size(size)
+        dim, df, scale = self._process_parameters(df, scale)
+
+        # Cholesky decomposition of scale
+        C = scipy.linalg.cholesky(scale, lower=True)
+
+        out = self._rvs(n, shape, dim, df, C, random_state)
+
+        return _squeeze_output(out)
+
+    def _entropy(self, dim, df, log_det_scale):
+        """Compute the differential entropy of the Wishart.
+
+        Parameters
+        ----------
+        dim : int
+            Dimension of the scale matrix
+        df : int
+            Degrees of freedom
+        log_det_scale : float
+            Logarithm of the determinant of the scale matrix
+
+        Notes
+        -----
+        As this function does no argument checking, it should not be
+        called directly; use 'entropy' instead.
+
+        """
+        return (
+            0.5 * (dim+1) * log_det_scale +
+            0.5 * dim * (dim+1) * _LOG_2 +
+            multigammaln(0.5*df, dim) -
+            0.5 * (df - dim - 1) * np.sum(
+                [psi(0.5*(df + 1 - (i+1))) for i in range(dim)]
+            ) +
+            0.5 * df * dim
+        )
+
+    def entropy(self, df, scale):
+        """Compute the differential entropy of the Wishart.
+
+        Parameters
+        ----------
+        %(_doc_default_callparams)s
+
+        Returns
+        -------
+        h : scalar
+            Entropy of the Wishart distribution
+
+        Notes
+        -----
+        %(_doc_callparams_note)s
+
+        """
+        dim, df, scale = self._process_parameters(df, scale)
+        _, log_det_scale = self._cholesky_logdet(scale)
+        return self._entropy(dim, df, log_det_scale)
+
+    def _cholesky_logdet(self, scale):
+        """Compute Cholesky decomposition and determine (log(det(scale)).
+
+        Parameters
+        ----------
+        scale : ndarray
+            Scale matrix.
+
+        Returns
+        -------
+        c_decomp : ndarray
+            The Cholesky decomposition of `scale`.
+        logdet : scalar
+            The log of the determinant of `scale`.
+
+        Notes
+        -----
+        This computation of ``logdet`` is equivalent to
+        ``np.linalg.slogdet(scale)``.  It is ~2x faster though.
+
+        """
+        c_decomp = scipy.linalg.cholesky(scale, lower=True)
+        logdet = 2 * np.sum(np.log(c_decomp.diagonal()))
+        return c_decomp, logdet
+
+
+wishart = wishart_gen()
+
+
+class wishart_frozen(multi_rv_frozen):
+    """Create a frozen Wishart distribution.
+
+    Parameters
+    ----------
+    df : array_like
+        Degrees of freedom of the distribution
+    scale : array_like
+        Scale matrix of the distribution
+    seed : {None, int, `numpy.random.Generator`, `numpy.random.RandomState`}, optional
+        If `seed` is None (or `np.random`), the `numpy.random.RandomState`
+        singleton is used.
+        If `seed` is an int, a new ``RandomState`` instance is used,
+        seeded with `seed`.
+        If `seed` is already a ``Generator`` or ``RandomState`` instance then
+        that instance is used.
+
+    """
+    __class_getitem__ = None  # pyrefly:ignore[bad-assignment]
+
+    def __init__(self, df, scale, seed=None):
+        self._dist = wishart_gen(seed)
+        self.dim, self.df, self.scale = self._dist._process_parameters(
+            df, scale)
+        self.C, self.log_det_scale = self._dist._cholesky_logdet(self.scale)
+
+    def logpdf(self, x):
+        x = self._dist._process_quantiles(x, self.dim)
+
+        out = self._dist._logpdf(x, self.dim, self.df, self.scale,
+                                 self.log_det_scale, self.C)
+        return _squeeze_output(out)
+
+    def pdf(self, x):
+        return np.exp(self.logpdf(x))
+
+    def mean(self):
+        out = self._dist._mean(self.dim, self.df, self.scale)
+        return _squeeze_output(out)
+
+    def mode(self):
+        out = self._dist._mode(self.dim, self.df, self.scale)
+        return _squeeze_output(out) if out is not None else out
+
+    def var(self):
+        out = self._dist._var(self.dim, self.df, self.scale)
+        return _squeeze_output(out)
+
+    def rvs(self, size=1, random_state=None):
+        n, shape = self._dist._process_size(size)
+        out = self._dist._rvs(n, shape, self.dim, self.df,
+                              self.C, random_state)
+        return _squeeze_output(out)
+
+    def entropy(self):
+        return self._dist._entropy(self.dim, self.df, self.log_det_scale)
+
+
+# Set frozen generator docstrings from corresponding docstrings in
+# Wishart and fill in default strings in class docstrings
+for name in ['logpdf', 'pdf', 'mean', 'mode', 'var', 'rvs', 'entropy']:
+    method = wishart_gen.__dict__[name]
+    method_frozen = wishart_frozen.__dict__[name]
+    method_frozen.__doc__ = doccer.docformat(
+        method.__doc__, wishart_docdict_noparams)
+    method.__doc__ = doccer.docformat(method.__doc__, wishart_docdict_params)
+
+
+class invwishart_gen(wishart_gen):
+    r"""
+    An inverse Wishart random variable.
+
+    The `df` keyword specifies the degrees of freedom. The `scale` keyword
+    specifies the scale matrix, which must be symmetric and positive definite.
+    In this context, the scale matrix is often interpreted in terms of a
+    multivariate normal covariance matrix.
+
+    Parameters
+    ----------
+    %(_doc_default_callparams)s
+    %(_doc_random_state)s
+
+    Methods
+    -------
+    pdf(x, df, scale)
+        Probability density function.
+    logpdf(x, df, scale)
+        Log of the probability density function.
+    rvs(df, scale, size=1, random_state=None)
+        Draw random samples from an inverse Wishart distribution.
+    entropy(df, scale)
+        Differential entropy of the distribution.
+
+    Raises
+    ------
+    scipy.linalg.LinAlgError
+        If the scale matrix `scale` is not positive definite.
+
+    See Also
+    --------
+    wishart
+
+    Notes
+    -----
+    %(_doc_callparams_note)s
+
+    The scale matrix `scale` must be a symmetric positive definite
+    matrix. Singular matrices, including the symmetric positive semi-definite
+    case, are not supported. Symmetry is not checked; only the lower triangular
+    portion is used.
+
+    The inverse Wishart distribution is often denoted
+
+    .. math::
+
+        W_p^{-1}(\nu, \Psi)
+
+    where :math:`\nu` is the degrees of freedom and :math:`\Psi` is the
+    :math:`p \times p` scale matrix.
+
+    The probability density function for `invwishart` has support over positive
+    definite matrices :math:`S`; if :math:`S \sim W^{-1}_p(\nu, \Sigma)`,
+    then its PDF is given by:
+
+    .. math::
+
+        f(S) = \frac{|\Sigma|^\frac{\nu}{2}}{2^{ \frac{\nu p}{2} }
+               |S|^{\frac{\nu + p + 1}{2}} \Gamma_p \left(\frac{\nu}{2} \right)}
+               \exp\left( -tr(\Sigma S^{-1}) / 2 \right)
+
+    If :math:`S \sim W_p^{-1}(\nu, \Psi)` (inverse Wishart) then
+    :math:`S^{-1} \sim W_p(\nu, \Psi^{-1})` (Wishart).
+
+    If the scale matrix is 1-dimensional and equal to one, then the inverse
+    Wishart distribution :math:`W_1(\nu, 1)` collapses to the
+    inverse Gamma distribution with parameters shape = :math:`\frac{\nu}{2}`
+    and scale = :math:`\frac{1}{2}`.
+
+    Instead of inverting a randomly generated Wishart matrix as described in [2],
+    here the algorithm in [4] is used to directly generate a random inverse-Wishart
+    matrix without inversion.
+
+    .. versionadded:: 0.16.0
+
+    References
+    ----------
+    .. [1] M.L. Eaton, "Multivariate Statistics: A Vector Space Approach",
+           Wiley, 1983.
+    .. [2] M.C. Jones, "Generating Inverse Wishart Matrices", Communications
+           in Statistics - Simulation and Computation, vol. 14.2, pp.511-514,
+           1985.
+    .. [3] Gupta, M. and Srivastava, S. "Parametric Bayesian Estimation of
+           Differential Entropy and Relative Entropy". Entropy 12, 818 - 843.
+           2010.
+    .. [4] S.D. Axen, "Efficiently generating inverse-Wishart matrices and
+           their Cholesky factors", :arXiv:`2310.15884v1`. 2023.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.stats import invwishart, invgamma
+    >>> x = np.linspace(0.01, 1, 100)
+    >>> iw = invwishart.pdf(x, df=6, scale=1)
+    >>> iw[:3]
+    array([  1.20546865e-15,   5.42497807e-06,   4.45813929e-03])
+    >>> ig = invgamma.pdf(x, 6/2., scale=1./2)
+    >>> ig[:3]
+    array([  1.20546865e-15,   5.42497807e-06,   4.45813929e-03])
+    >>> plt.plot(x, iw)
+    >>> plt.show()
+
+    The input quantiles can be any shape of array, as long as the last
+    axis labels the components.
+
+    Alternatively, the object may be called (as a function) to fix the degrees
+    of freedom and scale parameters, returning a "frozen" inverse Wishart
+    random variable:
+
+    >>> rv = invwishart(df=1, scale=1)
+    >>> # Frozen object with the same methods but holding the given
+    >>> # degrees of freedom and scale fixed.
+    """
+
+    def __init__(self, seed=None):
+        super().__init__(seed)
+        self.__doc__ = doccer.docformat(self.__doc__, wishart_docdict_params)
+
+    def __call__(self, df=None, scale=None, seed=None):
+        """Create a frozen inverse Wishart distribution.
+
+        See `invwishart_frozen` for more information.
+
+        """
+        return invwishart_frozen(df, scale, seed)
+
+    def _logpdf(self, x, dim, df, log_det_scale, C):
+        """Log of the inverse Wishart probability density function.
+
+        Parameters
+        ----------
+        x : ndarray
+            Points at which to evaluate the log of the probability
+            density function.
+        dim : int
+            Dimension of the scale matrix
+        df : int
+            Degrees of freedom
+        log_det_scale : float
+            Logarithm of the determinant of the scale matrix
+        C : ndarray
+            Cholesky factorization of the scale matrix, lower triangular.
+
+        Notes
+        -----
+        As this function does no argument checking, it should not be
+        called directly; use 'logpdf' instead.
+
+        """
+        # Retrieve tr(scale x^{-1})
+        log_det_x = np.empty(x.shape[-1])
+        tr_scale_x_inv = np.empty(x.shape[-1])
+        trsm = get_blas_funcs(('trsm'), (x,))
+        if dim > 1:
+            for i in range(x.shape[-1]):
+                Cx, log_det_x[i] = self._cholesky_logdet(x[:, :, i])
+                A = trsm(1., Cx, C, side=0, lower=True)
+                tr_scale_x_inv[i] = np.linalg.norm(A)**2
+        else:
+            log_det_x[:] = np.log(x[0, 0])
+            tr_scale_x_inv[:] = C[0, 0]**2 / x[0, 0]
+
+        # Log PDF
+        out = ((0.5 * df * log_det_scale - 0.5 * tr_scale_x_inv) -
+               (0.5 * df * dim * _LOG_2 + 0.5 * (df + dim + 1) * log_det_x) -
+               multigammaln(0.5*df, dim))
+
+        return out
+
+    def logpdf(self, x, df, scale):
+        """Log of the inverse Wishart probability density function.
+
+        Parameters
+        ----------
+        x : array_like
+            Quantiles, with the last axis of `x` denoting the components.
+            Each quantile must be a symmetric positive definite matrix.
+        %(_doc_default_callparams)s
+
+        Returns
+        -------
+        pdf : ndarray
+            Log of the probability density function evaluated at `x`
+
+        Notes
+        -----
+        %(_doc_callparams_note)s
+
+        """
+        dim, df, scale = self._process_parameters(df, scale)
+        x = self._process_quantiles(x, dim)
+        C, log_det_scale = self._cholesky_logdet(scale)
+        out = self._logpdf(x, dim, df, log_det_scale, C)
+        return _squeeze_output(out)
+
+    def pdf(self, x, df, scale):
+        """Inverse Wishart probability density function.
+
+        Parameters
+        ----------
+        x : array_like
+            Quantiles, with the last axis of `x` denoting the components.
+            Each quantile must be a symmetric positive definite matrix.
+        %(_doc_default_callparams)s
+
+        Returns
+        -------
+        pdf : ndarray
+            Probability density function evaluated at `x`
+
+        Notes
+        -----
+        %(_doc_callparams_note)s
+
+        """
+        return np.exp(self.logpdf(x, df, scale))
+
+    def _mean(self, dim, df, scale):
+        """Mean of the inverse Wishart distribution.
+
+        Parameters
+        ----------
+        dim : int
+            Dimension of the scale matrix
+        %(_doc_default_callparams)s
+
+        Notes
+        -----
+        As this function does no argument checking, it should not be
+        called directly; use 'mean' instead.
+
+        """
+        if df > dim + 1:
+            out = scale / (df - dim - 1)
+        else:
+            out = None
+        return out
+
+    def mean(self, df, scale):
+        """Mean of the inverse Wishart distribution.
+
+        Only valid if the degrees of freedom are greater than the dimension of
+        the scale matrix plus one.
+
+        Parameters
+        ----------
+        %(_doc_default_callparams)s
+
+        Returns
+        -------
+        mean : float or None
+            The mean of the distribution
+
+        """
+        dim, df, scale = self._process_parameters(df, scale)
+        out = self._mean(dim, df, scale)
+        return _squeeze_output(out) if out is not None else out
+
+    def _mode(self, dim, df, scale):
+        """Mode of the inverse Wishart distribution.
+
+        Parameters
+        ----------
+        dim : int
+            Dimension of the scale matrix
+        %(_doc_default_callparams)s
+
+        Notes
+        -----
+        As this function does no argument checking, it should not be
+        called directly; use 'mode' instead.
+
+        """
+        return scale / (df + dim + 1)
+
+    def mode(self, df, scale):
+        """Mode of the inverse Wishart distribution.
+
+        Parameters
+        ----------
+        %(_doc_default_callparams)s
+
+        Returns
+        -------
+        mode : float
+            The Mode of the distribution
+
+        """
+        dim, df, scale = self._process_parameters(df, scale)
+        out = self._mode(dim, df, scale)
+        return _squeeze_output(out)
+
+    def _var(self, dim, df, scale):
+        """Variance of the inverse Wishart distribution.
+
+        Parameters
+        ----------
+        dim : int
+            Dimension of the scale matrix
+        %(_doc_default_callparams)s
+
+        Notes
+        -----
+        As this function does no argument checking, it should not be
+        called directly; use 'var' instead.
+
+        """
+        if df > dim + 3:
+            var = (df - dim + 1) * scale**2
+            diag = scale.diagonal()  # 1 x dim array
+            var += (df - dim - 1) * np.outer(diag, diag)
+            var /= (df - dim) * (df - dim - 1)**2 * (df - dim - 3)
+        else:
+            var = None
+        return var
+
+    def var(self, df, scale):
+        """Variance of the inverse Wishart distribution.
+
+        Only valid if the degrees of freedom are greater than the dimension of
+        the scale matrix plus three.
+
+        Parameters
+        ----------
+        %(_doc_default_callparams)s
+
+        Returns
+        -------
+        var : float
+            The variance of the distribution
+        """
+        dim, df, scale = self._process_parameters(df, scale)
+        out = self._var(dim, df, scale)
+        return _squeeze_output(out) if out is not None else out
+
+    def _inv_standard_rvs(self, n, shape, dim, df, random_state):
+        """
+        Parameters
+        ----------
+        n : int
+            Number of variates to generate
+        shape : iterable
+            Shape of the variates to generate
+        dim : int
+            Dimension of the scale matrix
+        df : int
+            Degrees of freedom
+        random_state : {None, int, `numpy.random.Generator`,
+                        `numpy.random.RandomState`}, optional
+
+            If `seed` is None (or `np.random`), the `numpy.random.RandomState`
+            singleton is used.
+            If `seed` is an int, a new ``RandomState`` instance is used,
+            seeded with `seed`.
+            If `seed` is already a ``Generator`` or ``RandomState`` instance
+            then that instance is used.
+
+        Returns
+        -------
+        A : ndarray
+            Random variates of shape (`shape`) + (``dim``, ``dim``).
+            Each slice `A[..., :, :]` is lower-triangular, and its
+            inverse is the lower Cholesky factor of a draw from
+            `invwishart(df, np.eye(dim))`.
+
+        Notes
+        -----
+        As this function does no argument checking, it should not be
+        called directly; use 'rvs' instead.
+
+        """
+        A = np.zeros(shape + (dim, dim))
+
+        # Random normal variates for off-diagonal elements
+        tri_rows, tri_cols = np.tril_indices(dim, k=-1)
+        n_tril = dim * (dim-1) // 2
+        A[..., tri_rows, tri_cols] = random_state.normal(
+            size=(*shape, n_tril),
+        )
+
+        # Random chi variates for diagonal elements
+        rows = np.arange(dim)
+        chi_dfs = (df - dim + 1) + rows
+        A[..., rows, rows] = random_state.chisquare(
+            df=chi_dfs, size=(*shape, dim),
+        )**0.5
+
+        return A
+
+    def _rvs(self, n, shape, dim, df, C, random_state):
+        """Draw random samples from an inverse Wishart distribution.
+
+        Parameters
+        ----------
+        n : int
+            Number of variates to generate
+        shape : iterable
+            Shape of the variates to generate
+        dim : int
+            Dimension of the scale matrix
+        df : int
+            Degrees of freedom
+        C : ndarray
+            Cholesky factorization of the scale matrix, lower triangular.
+        %(_doc_random_state)s
+
+        Notes
+        -----
+        As this function does no argument checking, it should not be
+        called directly; use 'rvs' instead.
+
+        """
+        random_state = self._get_random_state(random_state)
+        # Get random draws A such that inv(A) ~ iW(df, I)
+        A = self._inv_standard_rvs(n, shape, dim, df, random_state)
+
+        # Calculate SA = (CA)'^{-1} (CA)^{-1} ~ iW(df, scale)
+        trsm = get_blas_funcs(('trsm'), (A,))
+        trmm = get_blas_funcs(('trmm'), (A,))
+
+        for index in np.ndindex(A.shape[:-2]):
+            if dim > 1:
+                # Calculate CA
+                # Get CA = C A^{-1} via triangular solver
+                CA = trsm(1., A[index], C, side=1, lower=True)
+                # get SA
+                A[index] = trmm(1., CA, CA, side=1, lower=True, trans_a=True)
+            else:
+                A[index][0, 0] = (C[0, 0] / A[index][0, 0])**2
+
+        return A
+
+    def rvs(self, df, scale, size=1, random_state=None):
+        """Draw random samples from an inverse Wishart distribution.
+
+        Parameters
+        ----------
+        %(_doc_default_callparams)s
+        size : int or iterable of integers, optional
+            Number of samples to draw (default 1).
+        %(_doc_random_state)s
+
+        Returns
+        -------
+        rvs : ndarray
+            Random variates of shape (`size`) + (``dim``, ``dim``), where
+            ``dim`` is the dimension of the scale matrix.
+
+        Notes
+        -----
+        %(_doc_callparams_note)s
+
+        """
+        n, shape = self._process_size(size)
+        dim, df, scale = self._process_parameters(df, scale)
+
+        # Cholesky decomposition of scale
+        C = scipy.linalg.cholesky(scale, lower=True)
+
+        out = self._rvs(n, shape, dim, df, C, random_state)
+
+        return _squeeze_output(out)
+
+    def _entropy(self, dim, df, log_det_scale):
+        # reference: eq. (17) from ref. 3
+        psi_eval_points = [0.5 * (df - dim + i) for i in range(1, dim + 1)]
+        psi_eval_points = np.asarray(psi_eval_points)
+        return multigammaln(0.5 * df, dim) + 0.5 * dim * df + \
+            0.5 * (dim + 1) * (log_det_scale - _LOG_2) - \
+            0.5 * (df + dim + 1) * \
+            psi(psi_eval_points, out=psi_eval_points).sum()
+
+    def entropy(self, df, scale):
+        dim, df, scale = self._process_parameters(df, scale)
+        _, log_det_scale = self._cholesky_logdet(scale)
+        return self._entropy(dim, df, log_det_scale)
+
+
+invwishart = invwishart_gen()
+
+
+class invwishart_frozen(multi_rv_frozen):
+    __class_getitem__ = None  # pyrefly:ignore[bad-assignment]
+
+    def __init__(self, df, scale, seed=None):
+        """Create a frozen inverse Wishart distribution.
+
+        Parameters
+        ----------
+        df : array_like
+            Degrees of freedom of the distribution
+        scale : array_like
+            Scale matrix of the distribution
+        seed : {None, int, `numpy.random.Generator`}, optional
+            If `seed` is None the `numpy.random.Generator` singleton is used.
+            If `seed` is an int, a new ``Generator`` instance is used,
+            seeded with `seed`.
+            If `seed` is already a ``Generator`` instance then that instance is
+            used.
+
+        """
+        self._dist = invwishart_gen(seed)
+        self.dim, self.df, self.scale = self._dist._process_parameters(
+            df, scale
+        )
+
+        # Get the determinant via Cholesky factorization
+        self.C = scipy.linalg.cholesky(self.scale, lower=True)
+        self.log_det_scale = 2 * np.sum(np.log(self.C.diagonal()))
+
+    def logpdf(self, x):
+        x = self._dist._process_quantiles(x, self.dim)
+        out = self._dist._logpdf(x, self.dim, self.df,
+                                 self.log_det_scale, self.C)
+        return _squeeze_output(out)
+
+    def pdf(self, x):
+        return np.exp(self.logpdf(x))
+
+    def mean(self):
+        out = self._dist._mean(self.dim, self.df, self.scale)
+        return _squeeze_output(out) if out is not None else out
+
+    def mode(self):
+        out = self._dist._mode(self.dim, self.df, self.scale)
+        return _squeeze_output(out)
+
+    def var(self):
+        out = self._dist._var(self.dim, self.df, self.scale)
+        return _squeeze_output(out) if out is not None else out
+
+    def rvs(self, size=1, random_state=None):
+        n, shape = self._dist._process_size(size)
+
+        out = self._dist._rvs(n, shape, self.dim, self.df,
+                              self.C, random_state)
+
+        return _squeeze_output(out)
+
+    def entropy(self):
+        return self._dist._entropy(self.dim, self.df, self.log_det_scale)
+
+
+# Set frozen generator docstrings from corresponding docstrings in
+# inverse Wishart and fill in default strings in class docstrings
+for name in ['logpdf', 'pdf', 'mean', 'mode', 'var', 'rvs']:
+    method = invwishart_gen.__dict__[name]
+    method_frozen = wishart_frozen.__dict__[name]
+    method_frozen.__doc__ = doccer.docformat(
+        method.__doc__, wishart_docdict_noparams)
+    method.__doc__ = doccer.docformat(method.__doc__, wishart_docdict_params)
+
+_multinomial_doc_default_callparams = """\
+n : int
+    Number of trials
+p : array_like
+    Probability of a trial falling into each category; should sum to 1
+"""
+
+_multinomial_doc_callparams_note = """\
+`n` should be a nonnegative integer. Each element of `p` should be in the
+interval :math:`[0,1]` and the elements should sum to 1. If they do not sum to
+1, the last element of the `p` array is not used and is replaced with the
+remaining probability left over from the earlier elements.
+"""
+
+_multinomial_doc_frozen_callparams = ""
+
+_multinomial_doc_frozen_callparams_note = """\
+See class definition for a detailed description of parameters."""
+
+multinomial_docdict_params = {
+    '_doc_default_callparams': _multinomial_doc_default_callparams,
+    '_doc_callparams_note': _multinomial_doc_callparams_note,
+    '_doc_random_state': _doc_random_state
+}
+
+multinomial_docdict_noparams = {
+    '_doc_default_callparams': _multinomial_doc_frozen_callparams,
+    '_doc_callparams_note': _multinomial_doc_frozen_callparams_note,
+    '_doc_random_state': _doc_random_state
+}
+
+
+class multinomial_gen(multi_rv_generic):
+    r"""
+    A multinomial random variable.
+
+    Parameters
+    ----------
+    %(_doc_default_callparams)s
+    %(_doc_random_state)s
+
+    Methods
+    -------
+    pmf(x, n, p)
+        Probability mass function.
+    logpmf(x, n, p)
+        Log of the probability mass function.
+    rvs(n, p, size=1, random_state=None)
+        Draw random samples from a multinomial distribution.
+    entropy(n, p)
+        Compute the entropy of the multinomial distribution.
+    cov(n, p)
+        Compute the covariance matrix of the multinomial distribution.
+
+    See Also
+    --------
+    scipy.stats.binom : The binomial distribution.
+    numpy.random.Generator.multinomial : Sampling from the multinomial distribution.
+    scipy.stats.multivariate_hypergeom :
+        The multivariate hypergeometric distribution.
+
+    Notes
+    -----
+    %(_doc_callparams_note)s
+
+    The probability mass function for `multinomial` is
+
+    .. math::
+
+        f(x) = \frac{n!}{x_1! \cdots x_k!} p_1^{x_1} \cdots p_k^{x_k},
+
+    supported on :math:`x=(x_1, \ldots, x_k)` where each :math:`x_i` is a
+    nonnegative integer and their sum is :math:`n`.
+
+    .. versionadded:: 0.19.0
+
+    Examples
+    --------
+
+    >>> from scipy.stats import multinomial
+    >>> rv = multinomial(8, [0.3, 0.2, 0.5])
+    >>> rv.pmf([1, 3, 4])
+    0.042000000000000072
+
+    The multinomial distribution for :math:`k=2` is identical to the
+    corresponding binomial distribution (tiny numerical differences
+    notwithstanding):
+
+    >>> from scipy.stats import binom
+    >>> multinomial.pmf([3, 4], n=7, p=[0.4, 0.6])
+    0.29030399999999973
+    >>> binom.pmf(3, 7, 0.4)
+    0.29030400000000012
+
+    The functions ``pmf``, ``logpmf``, ``entropy``, and ``cov`` support
+    broadcasting, under the convention that the vector parameters (``x`` and
+    ``p``) are interpreted as if each row along the last axis is a single
+    object. For instance:
+
+    >>> multinomial.pmf([[3, 4], [3, 5]], n=[7, 8], p=[.3, .7])
+    array([0.2268945,  0.25412184])
+
+    Here, ``x.shape == (2, 2)``, ``n.shape == (2,)``, and ``p.shape == (2,)``,
+    but following the rules mentioned above they behave as if the rows
+    ``[3, 4]`` and ``[3, 5]`` in ``x`` and ``[.3, .7]`` in ``p`` were a single
+    object, and as if we had ``x.shape = (2,)``, ``n.shape = (2,)``, and
+    ``p.shape = ()``. To obtain the individual elements without broadcasting,
+    we would do this:
+
+    >>> multinomial.pmf([3, 4], n=7, p=[.3, .7])
+    0.2268945
+    >>> multinomial.pmf([3, 5], 8, p=[.3, .7])
+    0.25412184
+
+    This broadcasting also works for ``cov``, where the output objects are
+    square matrices of size ``p.shape[-1]``. For example:
+
+    >>> multinomial.cov([4, 5], [[.3, .7], [.4, .6]])
+    array([[[ 0.84, -0.84],
+            [-0.84,  0.84]],
+           [[ 1.2 , -1.2 ],
+            [-1.2 ,  1.2 ]]])
+
+    In this example, ``n.shape == (2,)`` and ``p.shape == (2, 2)``, and
+    following the rules above, these broadcast as if ``p.shape == (2,)``.
+    Thus the result should also be of shape ``(2,)``, but since each output is
+    a :math:`2 \times 2` matrix, the result in fact has shape ``(2, 2, 2)``,
+    where ``result[0]`` is equal to ``multinomial.cov(n=4, p=[.3, .7])`` and
+    ``result[1]`` is equal to ``multinomial.cov(n=5, p=[.4, .6])``.
+
+    Alternatively, the object may be called (as a function) to fix the `n` and
+    `p` parameters, returning a "frozen" multinomial random variable:
+
+    >>> rv = multinomial(n=7, p=[.3, .7])
+    >>> # Frozen object with the same methods but holding the given
+    >>> # degrees of freedom and scale fixed.
+    """
+
+    def __init__(self, seed=None):
+        super().__init__(seed)
+        self.__doc__ = \
+            doccer.docformat(self.__doc__, multinomial_docdict_params)
+
+    def __call__(self, n, p, seed=None):
+        """Create a frozen multinomial distribution.
+
+        See `multinomial_frozen` for more information.
+        """
+        return multinomial_frozen(n, p, seed)
+
+    def _process_parameters(self, n, p):
+        """Returns: n_, p_, npcond.
+
+        n_ and p_ are arrays of the correct shape; npcond is a boolean array
+        flagging values out of the domain.
+        """
+        eps = np.finfo(np.result_type(np.asarray(p), np.float32)).eps * 10
+        p = np.array(p, dtype=np.float64, copy=True)
+
+        # true for bad p
+        pcond = np.abs(1 - p.sum(axis=-1)) > eps
+        pcond |= np.any(p < 0, axis=-1)
+        pcond |= np.any(p > 1, axis=-1)
+
+        n = np.array(n, dtype=int, copy=True)
+
+        # true for bad n
+        ncond = n < 0
+
+        return n, p, ncond | pcond
+
+    def _process_quantiles(self, x, n, p):
+        """Returns: x_, xcond.
+
+        x_ is an int array; xcond is a boolean array flagging values out of the
+        domain.
+        """
+        xx = np.asarray(x, dtype=int)
+
+        if xx.ndim == 0:
+            raise ValueError("x must be an array.")
+
+        if xx.size != 0 and not xx.shape[-1] == p.shape[-1]:
+            raise ValueError(f"Size of each quantile should be size of p: "
+                             f"received {xx.shape[-1]}, but expected "
+                             f"{p.shape[-1]}.")
+
+        # true for x out of the domain
+        cond = np.any(xx != x, axis=-1)
+        cond |= np.any(xx < 0, axis=-1)
+        cond = cond | (np.sum(xx, axis=-1) != n)
+
+        return xx, cond
+
+    def _checkresult(self, result, cond, bad_value):
+        result = np.asarray(result)
+
+        if cond.ndim != 0:
+            result[cond] = bad_value
+        elif cond:
+            if result.ndim == 0:
+                return bad_value
+            result[...] = bad_value
+        return result
+
+    def _logpmf(self, x, n, p):
+        return gammaln(n+1) + np.sum(xlogy(x, p) - gammaln(x+1), axis=-1)
+
+    def logpmf(self, x, n, p):
+        """Log of the Multinomial probability mass function.
+
+        Parameters
+        ----------
+        x : array_like
+            Quantiles, with the last axis of `x` denoting the components.
+        %(_doc_default_callparams)s
+
+        Returns
+        -------
+        logpmf : ndarray or scalar
+            Log of the probability mass function evaluated at `x`
+
+        Notes
+        -----
+        %(_doc_callparams_note)s
+        """
+        n, p, npcond = self._process_parameters(n, p)
+        x, xcond = self._process_quantiles(x, n, p)
+
+        result = self._logpmf(x, n, p)
+
+        # replace values for which x was out of the domain; broadcast
+        # xcond to the right shape
+        xcond_ = xcond | np.zeros(npcond.shape, dtype=np.bool_)
+        result = self._checkresult(result, xcond_, -np.inf)
+
+        # replace values bad for n or p; broadcast npcond to the right shape
+        npcond_ = npcond | np.zeros(xcond.shape, dtype=np.bool_)
+        return self._checkresult(result, npcond_, np.nan)
+
+    def pmf(self, x, n, p):
+        """Multinomial probability mass function.
+
+        Parameters
+        ----------
+        x : array_like
+            Quantiles, with the last axis of `x` denoting the components.
+        %(_doc_default_callparams)s
+
+        Returns
+        -------
+        pmf : ndarray or scalar
+            Probability density function evaluated at `x`
+
+        Notes
+        -----
+        %(_doc_callparams_note)s
+        """
+        return np.exp(self.logpmf(x, n, p))
+
+    def mean(self, n, p):
+        """Mean of the Multinomial distribution.
+
+        Parameters
+        ----------
+        %(_doc_default_callparams)s
+
+        Returns
+        -------
+        mean : float
+            The mean of the distribution
+        """
+        n, p, npcond = self._process_parameters(n, p)
+        result = n[..., np.newaxis]*p
+        return self._checkresult(result, npcond, np.nan)
+
+    def cov(self, n, p):
+        """Covariance matrix of the multinomial distribution.
+
+        Parameters
+        ----------
+        %(_doc_default_callparams)s
+
+        Returns
+        -------
+        cov : ndarray
+            The covariance matrix of the distribution
+        """
+        n, p, npcond = self._process_parameters(n, p)
+
+        nn = n[..., np.newaxis, np.newaxis]
+        result = nn * np.einsum('...j,...k->...jk', -p, p)
+
+        # change the diagonal
+        for i in range(p.shape[-1]):
+            result[..., i, i] += n*p[..., i]
+
+        return self._checkresult(result, npcond, np.nan)
+
+    def entropy(self, n, p):
+        r"""Compute the entropy of the multinomial distribution.
+
+        The entropy is computed using this expression:
+
+        .. math::
+
+            f(x) = - \log n! - n\sum_{i=1}^k p_i \log p_i +
+            \sum_{i=1}^k \sum_{x=0}^n \binom n x p_i^x(1-p_i)^{n-x} \log x!
+
+        Parameters
+        ----------
+        %(_doc_default_callparams)s
+
+        Returns
+        -------
+        h : scalar
+            Entropy of the Multinomial distribution
+
+        Notes
+        -----
+        %(_doc_callparams_note)s
+        """
+        n, p, npcond = self._process_parameters(n, p)
+
+        x = np.r_[1:np.max(n)+1]
+
+        term1 = n*np.sum(entr(p), axis=-1)
+        term1 -= gammaln(n+1)
+
+        n = n[..., np.newaxis]
+        new_axes_needed = max(p.ndim, n.ndim) - x.ndim + 1
+        new_shape = x.shape + (1,)*new_axes_needed
+        x = x.reshape(new_shape)
+
+        term2 = np.sum(binom.pmf(x, n, p)*gammaln(x+1),
+                       axis=(-1, -1-new_axes_needed))
+
+        return self._checkresult(term1 + term2, npcond, np.nan)
+
+    def rvs(self, n, p, size=None, random_state=None):
+        """Draw random samples from a Multinomial distribution.
+
+        Parameters
+        ----------
+        %(_doc_default_callparams)s
+        size : int or iterable of integers, optional
+            Number of samples to draw (default 1).
+        %(_doc_random_state)s
+
+        Returns
+        -------
+        rvs : ndarray or scalar
+            Random variates of shape (`size`, `len(p)`)
+
+        Notes
+        -----
+        %(_doc_callparams_note)s
+        """
+        n, p, npcond = self._process_parameters(n, p)
+        if np.any(npcond):
+            message = ("`multinomial.rvs` requires `n > 0`, `(p > 0).all()`, and"
+                       "`p.sum() == 1`.")
+            raise ValueError(message)
+        random_state = self._get_random_state(random_state)
+        return random_state.multinomial(n, p, size)
+
+
+multinomial = multinomial_gen()
+
+
+class multinomial_frozen(multi_rv_frozen):
+    r"""Create a frozen Multinomial distribution.
+
+    Parameters
+    ----------
+    n : int
+        number of trials
+    p: array_like
+        probability of a trial falling into each category; should sum to 1
+    seed : {None, int, `numpy.random.Generator`, `numpy.random.RandomState`}, optional
+        If `seed` is None (or `np.random`), the `numpy.random.RandomState`
+        singleton is used.
+        If `seed` is an int, a new ``RandomState`` instance is used,
+        seeded with `seed`.
+        If `seed` is already a ``Generator`` or ``RandomState`` instance then
+        that instance is used.
+    """
+    def __init__(self, n, p, seed=None):
+        self._dist = multinomial_gen(seed)
+        self.n, self.p, self.npcond = self._dist._process_parameters(n, p)
+
+        # monkey patch self._dist
+        def _process_parameters(n, p):
+            return self.n, self.p, self.npcond
+
+        self._dist._process_parameters = _process_parameters
+
+    def logpmf(self, x):
+        return self._dist.logpmf(x, self.n, self.p)
+
+    def pmf(self, x):
+        return self._dist.pmf(x, self.n, self.p)
+
+    def mean(self):
+        return self._dist.mean(self.n, self.p)
+
+    def cov(self):
+        return self._dist.cov(self.n, self.p)
+
+    def entropy(self):
+        return self._dist.entropy(self.n, self.p)
+
+    def rvs(self, size=1, random_state=None):
+        return self._dist.rvs(self.n, self.p, size, random_state)
+
+
+# Set frozen generator docstrings from corresponding docstrings in
+# multinomial and fill in default strings in class docstrings
+for name in ['logpmf', 'pmf', 'mean', 'cov', 'rvs']:
+    method = multinomial_gen.__dict__[name]
+    method_frozen = multinomial_frozen.__dict__[name]
+    method_frozen.__doc__ = doccer.docformat(
+        method.__doc__, multinomial_docdict_noparams)
+    method.__doc__ = doccer.docformat(method.__doc__,
+                                      multinomial_docdict_params)
+
+
+class special_ortho_group_gen(multi_rv_generic):
+    r"""
+    A Special Orthogonal matrix (SO(N)) random variable.
+
+    Return a random rotation matrix, drawn from the Haar distribution
+    (the only uniform distribution on SO(N)) with a determinant of +1.
+
+    The `dim` keyword specifies the dimension N.
+
+    Parameters
+    ----------
+    dim : scalar
+        Dimension of matrices
+    seed : {None, int, np.random.RandomState, np.random.Generator}, optional
+        Used for drawing random variates.
+        If `seed` is `None`, the `~np.random.RandomState` singleton is used.
+        If `seed` is an int, a new ``RandomState`` instance is used, seeded
+        with seed.
+        If `seed` is already a ``RandomState`` or ``Generator`` instance,
+        then that object is used.
+        Default is `None`.
+
+    Methods
+    -------
+    rvs(dim=None, size=1, random_state=None)
+        Draw random samples from SO(N).
+
+    See Also
+    --------
+    ortho_group, scipy.spatial.transform.Rotation.random
+
+    Notes
+    -----
+    The ``rvs`` method returns a random rotation matrix drawn from the Haar
+    distribution, the only uniform distribution on SO(N). The algorithm generates
+    a Haar-distributed orthogonal matrix in O(N) using the ``rvs`` method of
+    `ortho_group`, then adjusts the matrix to ensure that the determinant is +1.
+
+    For a random rotation in three dimensions, see
+    `scipy.spatial.transform.Rotation.random`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import special_ortho_group
+    >>> x = special_ortho_group.rvs(3)
+
+    >>> np.dot(x, x.T)
+    array([[  1.00000000e+00,   1.13231364e-17,  -2.86852790e-16],
+           [  1.13231364e-17,   1.00000000e+00,  -1.46845020e-16],
+           [ -2.86852790e-16,  -1.46845020e-16,   1.00000000e+00]])
+
+    >>> import scipy.linalg
+    >>> scipy.linalg.det(x)
+    1.0
+
+    This generates one random matrix from SO(3). It is orthogonal and
+    has a determinant of 1.
+
+    Alternatively, the object may be called (as a function) to fix the `dim`
+    parameter, returning a "frozen" special_ortho_group random variable:
+
+    >>> rv = special_ortho_group(5)
+    >>> # Frozen object with the same methods but holding the
+    >>> # dimension parameter fixed.
+    """
+
+    def __init__(self, seed=None):
+        super().__init__(seed)
+        self.__doc__ = doccer.docformat(self.__doc__)
+
+    def __call__(self, dim=None, seed=None):
+        """Create a frozen SO(N) distribution.
+
+        See `special_ortho_group_frozen` for more information.
+        """
+        return special_ortho_group_frozen(dim, seed=seed)
+
+    def _process_parameters(self, dim):
+        """Dimension N must be specified; it cannot be inferred."""
+        if dim is None or not np.isscalar(dim) or dim < 0 or dim != int(dim):
+            raise ValueError("""Dimension of rotation must be specified,
+                                and must be a scalar nonnegative integer.""")
+
+        return dim
+
+    def rvs(self, dim, size=1, random_state=None):
+        """Draw random samples from SO(N).
+
+        Parameters
+        ----------
+        dim : int
+            Dimension of rotation space (N).
+        size : int, optional
+            Number of samples to draw (default 1).
+
+        Returns
+        -------
+        rvs : ndarray or scalar
+            Random size N-dimensional matrices, dimension (size, dim, dim)
+
+        """
+        random_state = self._get_random_state(random_state)
+
+        q = ortho_group.rvs(dim, size, random_state)
+        dets = np.linalg.det(q)
+        if dim:
+            q[..., 0, :] /= dets[..., np.newaxis]
+        return q
+
+special_ortho_group = special_ortho_group_gen()
+
+
+class special_ortho_group_frozen(multi_rv_frozen):
+    __class_getitem__ = None  # pyrefly:ignore[bad-assignment]
+
+    def __init__(self, dim=None, seed=None):
+        """Create a frozen SO(N) distribution.
+
+        Parameters
+        ----------
+        dim : scalar
+            Dimension of matrices
+        seed : {None, int, `numpy.random.Generator`, `numpy.random.RandomState`}, optional
+            If `seed` is None (or `np.random`), the `numpy.random.RandomState`
+            singleton is used.
+            If `seed` is an int, a new ``RandomState`` instance is used,
+            seeded with `seed`.
+            If `seed` is already a ``Generator`` or ``RandomState`` instance
+            then that instance is used.
+
+        Examples
+        --------
+        >>> from scipy.stats import special_ortho_group
+        >>> g = special_ortho_group(5)
+        >>> x = g.rvs()
+
+        """ # numpy/numpydoc#87  # noqa: E501
+        self._dist = special_ortho_group_gen(seed)
+        self.dim = self._dist._process_parameters(dim)
+
+    def rvs(self, size=1, random_state=None):
+        return self._dist.rvs(self.dim, size, random_state)
+
+
+class ortho_group_gen(multi_rv_generic):
+    r"""
+    An Orthogonal matrix (O(N)) random variable.
+
+    Return a random orthogonal matrix, drawn from the O(N) Haar
+    distribution (the only uniform distribution on O(N)).
+
+    The `dim` keyword specifies the dimension N.
+
+    Parameters
+    ----------
+    dim : scalar
+        Dimension of matrices
+    seed : {None, int, np.random.RandomState, np.random.Generator}, optional
+        Used for drawing random variates.
+        If `seed` is `None`, the `~np.random.RandomState` singleton is used.
+        If `seed` is an int, a new ``RandomState`` instance is used, seeded
+        with seed.
+        If `seed` is already a ``RandomState`` or ``Generator`` instance,
+        then that object is used.
+        Default is `None`.
+
+    Methods
+    -------
+    rvs(dim=None, size=1, random_state=None)
+        Draw random samples from O(N).
+
+    See Also
+    --------
+    special_ortho_group
+
+    Notes
+    -----
+    This class is closely related to `special_ortho_group`.
+
+    Some care is taken to avoid numerical error, as per the paper by Mezzadri.
+
+    References
+    ----------
+    .. [1] F. Mezzadri, "How to generate random matrices from the classical
+           compact groups", :arXiv:`math-ph/0609050v2`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import ortho_group
+    >>> x = ortho_group.rvs(3)
+
+    >>> np.dot(x, x.T)
+    array([[  1.00000000e+00,   1.13231364e-17,  -2.86852790e-16],
+           [  1.13231364e-17,   1.00000000e+00,  -1.46845020e-16],
+           [ -2.86852790e-16,  -1.46845020e-16,   1.00000000e+00]])
+
+    >>> import scipy.linalg
+    >>> np.fabs(scipy.linalg.det(x))
+    1.0
+
+    This generates one random matrix from O(3). It is orthogonal and
+    has a determinant of +1 or -1.
+
+    Alternatively, the object may be called (as a function) to fix the `dim`
+    parameter, returning a "frozen" ortho_group random variable:
+
+    >>> rv = ortho_group(5)
+    >>> # Frozen object with the same methods but holding the
+    >>> # dimension parameter fixed.
+    """
+
+    def __init__(self, seed=None):
+        super().__init__(seed)
+        self.__doc__ = doccer.docformat(self.__doc__)
+
+    def __call__(self, dim=None, seed=None):
+        """Create a frozen O(N) distribution.
+
+        See `ortho_group_frozen` for more information.
+        """
+        return ortho_group_frozen(dim, seed=seed)
+
+    def _process_parameters(self, dim):
+        """Dimension N must be specified; it cannot be inferred."""
+        if dim is None or not np.isscalar(dim) or dim < 0 or dim != int(dim):
+            raise ValueError("Dimension of rotation must be specified,"
+                             "and must be a scalar nonnegative integer.")
+
+        return dim
+
+    def rvs(self, dim, size=1, random_state=None):
+        """Draw random samples from O(N).
+
+        Parameters
+        ----------
+        dim : int
+            Dimension of rotation space (N).
+        size : int, optional
+            Number of samples to draw (default 1).
+
+        Returns
+        -------
+        rvs : ndarray or scalar
+            Random size N-dimensional matrices, dimension (size, dim, dim)
+
+        """
+        random_state = self._get_random_state(random_state)
+
+        size = int(size)
+
+        dim = self._process_parameters(dim)
+
+        size = (size,) if size > 1 else ()
+        z = random_state.normal(size=size + (dim, dim))
+        q, r = np.linalg.qr(z)
+        # The last two dimensions are the rows and columns of R matrices.
+        # Extract the diagonals. Note that this eliminates a dimension.
+        d = r.diagonal(offset=0, axis1=-2, axis2=-1)
+        # Add back a dimension for proper broadcasting: we're dividing
+        # each row of each R matrix by the diagonal of the R matrix.
+        q *= (d/abs(d))[..., np.newaxis, :]  # to broadcast properly
+        return q
+
+
+ortho_group = ortho_group_gen()
+
+
+class ortho_group_frozen(multi_rv_frozen):
+    __class_getitem__ = None  # pyrefly:ignore[bad-assignment]
+
+    def __init__(self, dim=None, seed=None):
+        """Create a frozen O(N) distribution.
+
+        Parameters
+        ----------
+        dim : scalar
+            Dimension of matrices
+        seed : {None, int, `numpy.random.Generator`, `numpy.random.RandomState`}, optional
+            If `seed` is None (or `np.random`), the `numpy.random.RandomState`
+            singleton is used.
+            If `seed` is an int, a new ``RandomState`` instance is used,
+            seeded with `seed`.
+            If `seed` is already a ``Generator`` or ``RandomState`` instance
+            then that instance is used.
+
+        Examples
+        --------
+        >>> from scipy.stats import ortho_group
+        >>> g = ortho_group(5)
+        >>> x = g.rvs()
+
+        """ # numpy/numpydoc#87  # noqa: E501
+        self._dist = ortho_group_gen(seed)
+        self.dim = self._dist._process_parameters(dim)
+
+    def rvs(self, size=1, random_state=None):
+        return self._dist.rvs(self.dim, size, random_state)
+
+
+class random_correlation_gen(multi_rv_generic):
+    r"""
+    A random correlation matrix.
+
+    Return a random correlation matrix, given a vector of eigenvalues.
+    The returned matrix is symmetric positive semidefinite with unit diagonal.
+
+    The `eigs` keyword specifies the eigenvalues of the correlation matrix,
+    and implies the dimension.
+
+    Parameters
+    ----------
+    eigs : 1d ndarray
+        Eigenvalues of correlation matrix. All eigenvalues need to be non-negative and
+        need to sum to the number of eigenvalues.
+    seed : {None, int, `numpy.random.Generator`, `numpy.random.RandomState`}, optional
+        If `seed` is None (or `np.random`), the `numpy.random.RandomState`
+        singleton is used.
+        If `seed` is an int, a new ``RandomState`` instance is used,
+        seeded with `seed`.
+        If `seed` is already a ``Generator`` or ``RandomState`` instance
+        then that instance is used.
+    tol : float, optional
+        Tolerance for input parameter checks
+    diag_tol : float, optional
+        Tolerance for deviation of the diagonal of the resulting
+        matrix. Default: 1e-7
+
+    Methods
+    -------
+    rvs(eigs=None, random_state=None)
+        Draw random correlation matrices, all with eigenvalues eigs.
+
+    Returns
+    -------
+    rvs : ndarray or scalar
+        Random size N-dimensional matrices, dimension (size, dim, dim),
+        each having eigenvalues eigs.
+
+    Raises
+    ------
+    RuntimeError
+        Floating point error prevented generating a valid correlation
+        matrix.
+
+    Notes
+    -----
+
+    Generates a random correlation matrix following a numerically stable
+    algorithm spelled out by Davies & Higham. This algorithm uses a single O(N)
+    similarity transformation to construct a symmetric positive semi-definite
+    matrix, and applies a series of Givens rotations to scale it to have ones
+    on the diagonal.
+
+    References
+    ----------
+
+    .. [1] Davies, Philip I; Higham, Nicholas J; "Numerically stable generation
+           of correlation matrices and their factors", BIT 2000, Vol. 40,
+           No. 4, pp. 640 651
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import random_correlation
+    >>> rng = np.random.default_rng()
+    >>> x = random_correlation.rvs((.5, .8, 1.2, 1.5), random_state=rng)
+    >>> x
+    array([[ 1.        , -0.02423399,  0.03130519,  0.4946965 ],
+           [-0.02423399,  1.        ,  0.20334736,  0.04039817],
+           [ 0.03130519,  0.20334736,  1.        ,  0.02694275],
+           [ 0.4946965 ,  0.04039817,  0.02694275,  1.        ]])
+    >>> import scipy.linalg
+    >>> e, v = scipy.linalg.eigh(x)
+    >>> e
+    array([ 0.5,  0.8,  1.2,  1.5])
+    """
+
+    def __init__(self, seed=None):
+        super().__init__(seed)
+        self.__doc__ = doccer.docformat(self.__doc__)
+
+    def __call__(self, eigs, seed=None, tol=1e-13, diag_tol=1e-7):
+        """Create a frozen random correlation matrix.
+
+        See `random_correlation_frozen` for more information.
+        """
+        return random_correlation_frozen(eigs, seed=seed, tol=tol,
+                                         diag_tol=diag_tol)
+
+    def _process_parameters(self, eigs, tol):
+        eigs = np.asarray(eigs, dtype=float)
+        dim = eigs.size
+
+        if eigs.ndim != 1 or eigs.shape[0] != dim or dim <= 1:
+            raise ValueError("Array 'eigs' must be a vector of length "
+                             "greater than 1.")
+
+        if np.fabs(np.sum(eigs) - dim) > tol:
+            raise ValueError("Sum of eigenvalues must equal dimensionality.")
+
+        for x in eigs:
+            if x < -tol:
+                raise ValueError("All eigenvalues must be non-negative.")
+
+        return dim, eigs
+
+    def _givens_to_1(self, aii, ajj, aij):
+        """Computes a 2x2 Givens matrix to put 1's on the diagonal.
+
+        The input matrix is a 2x2 symmetric matrix M = [ aii aij ; aij ajj ].
+
+        The output matrix g is a 2x2 anti-symmetric matrix of the form
+        [ c s ; -s c ];  the elements c and s are returned.
+
+        Applying the output matrix to the input matrix (as b=g.T M g)
+        results in a matrix with bii=1, provided tr(M) - det(M) >= 1
+        and floating point issues do not occur. Otherwise, some other
+        valid rotation is returned. When tr(M)==2, also bjj=1.
+
+        """
+        aiid = aii - 1.
+        ajjd = ajj - 1.
+
+        if ajjd == 0:
+            # ajj==1, so swap aii and ajj to avoid division by zero
+            return 0., 1.
+
+        dd = math.sqrt(max(aij**2 - aiid*ajjd, 0))
+
+        # The choice of t should be chosen to avoid cancellation [1]
+        t = (aij + math.copysign(dd, aij)) / ajjd
+        c = 1. / math.sqrt(1. + t*t)
+        if c == 0:
+            # Underflow
+            s = 1.0
+        else:
+            s = c*t
+        return c, s
+
+    def _to_corr(self, m):
+        """
+        Given a psd matrix m, rotate to put one's on the diagonal, turning it
+        into a correlation matrix.  This also requires the trace equal the
+        dimensionality. Note: modifies input matrix
+        """
+        # Check requirements for in-place Givens
+        if not (m.flags.c_contiguous and m.dtype == np.float64 and
+                m.shape[0] == m.shape[1]):
+            raise ValueError()
+
+        drot = get_blas_funcs('rot', dtype=np.float64, ilp64='preferred')
+
+        d = m.shape[0]
+        for i in range(d-1):
+            if m[i, i] == 1:
+                continue
+            elif m[i, i] > 1:
+                for j in range(i+1, d):
+                    if m[j, j] < 1:
+                        break
+            else:
+                for j in range(i+1, d):
+                    if m[j, j] > 1:
+                        break
+
+            c, s = self._givens_to_1(m[i, i], m[j, j], m[i, j])
+
+            # Use BLAS to apply Givens rotations in-place. Equivalent to:
+            # g = np.eye(d)
+            # g[i, i] = g[j,j] = c
+            # g[j, i] = -s; g[i, j] = s
+            # m = np.dot(g.T, np.dot(m, g))
+            mv = m.ravel()
+            drot(mv, mv, c, -s, n=d,
+                 offx=i*d, incx=1, offy=j*d, incy=1,
+                 overwrite_x=True, overwrite_y=True)
+            drot(mv, mv, c, -s, n=d,
+                 offx=i, incx=d, offy=j, incy=d,
+                 overwrite_x=True, overwrite_y=True)
+
+        return m
+
+    def rvs(self, eigs, random_state=None, tol=1e-13, diag_tol=1e-7):
+        """Draw random correlation matrices.
+
+        Parameters
+        ----------
+        eigs : 1d ndarray
+            Eigenvalues of correlation matrix
+        tol : float, optional
+            Tolerance for input parameter checks
+        diag_tol : float, optional
+            Tolerance for deviation of the diagonal of the resulting
+            matrix. Default: 1e-7
+
+        Raises
+        ------
+        RuntimeError
+            Floating point error prevented generating a valid correlation
+            matrix.
+
+        Returns
+        -------
+        rvs : ndarray or scalar
+            Random size N-dimensional matrices, dimension (size, dim, dim),
+            each having eigenvalues eigs.
+
+        """
+        dim, eigs = self._process_parameters(eigs, tol=tol)
+
+        random_state = self._get_random_state(random_state)
+
+        m = ortho_group.rvs(dim, random_state=random_state)
+        m = np.dot(np.dot(m, np.diag(eigs)), m.T)  # Set the trace of m
+        m = self._to_corr(m)  # Carefully rotate to unit diagonal
+
+        # Check diagonal
+        if abs(m.diagonal() - 1).max() > diag_tol:
+            raise RuntimeError("Failed to generate a valid correlation matrix")
+
+        return m
+
+
+random_correlation = random_correlation_gen()
+
+
+class random_correlation_frozen(multi_rv_frozen):
+    __class_getitem__ = None  # pyrefly:ignore[bad-assignment]
+
+    def __init__(self, eigs, seed=None, tol=1e-13, diag_tol=1e-7):
+        """Create a frozen random correlation matrix distribution.
+
+        Parameters
+        ----------
+        eigs : 1d ndarray
+            Eigenvalues of correlation matrix
+        seed : {None, int, `numpy.random.Generator`, `numpy.random.RandomState`}, optional
+            If `seed` is None (or `np.random`), the `numpy.random.RandomState`
+            singleton is used.
+            If `seed` is an int, a new ``RandomState`` instance is used,
+            seeded with `seed`.
+            If `seed` is already a ``Generator`` or ``RandomState`` instance
+            then that instance is used.
+        tol : float, optional
+            Tolerance for input parameter checks
+        diag_tol : float, optional
+            Tolerance for deviation of the diagonal of the resulting
+            matrix. Default: 1e-7
+
+        Raises
+        ------
+        RuntimeError
+            Floating point error prevented generating a valid correlation
+            matrix.
+
+        Returns
+        -------
+        rvs : ndarray or scalar
+            Random size N-dimensional matrices, dimension (size, dim, dim),
+            each having eigenvalues eigs.
+        """ # numpy/numpydoc#87  # noqa: E501
+
+        self._dist = random_correlation_gen(seed)
+        self.tol = tol
+        self.diag_tol = diag_tol
+        _, self.eigs = self._dist._process_parameters(eigs, tol=self.tol)
+
+    def rvs(self, random_state=None):
+        return self._dist.rvs(self.eigs, random_state=random_state,
+                              tol=self.tol, diag_tol=self.diag_tol)
+
+
+class unitary_group_gen(multi_rv_generic):
+    r"""
+    A matrix-valued U(N) random variable.
+
+    Return a random unitary matrix.
+
+    The `dim` keyword specifies the dimension N.
+
+    Parameters
+    ----------
+    dim : scalar
+        Dimension of matrices.
+    seed : {None, int, np.random.RandomState, np.random.Generator}, optional
+        Used for drawing random variates.
+        If `seed` is `None`, the `~np.random.RandomState` singleton is used.
+        If `seed` is an int, a new ``RandomState`` instance is used, seeded
+        with seed.
+        If `seed` is already a ``RandomState`` or ``Generator`` instance,
+        then that object is used.
+        Default is `None`.
+
+    Methods
+    -------
+    rvs(dim=None, size=1, random_state=None)
+        Draw random samples from U(N).
+
+    See Also
+    --------
+    ortho_group
+
+    Notes
+    -----
+    This class is similar to `ortho_group`.
+
+    References
+    ----------
+    .. [1] F. Mezzadri, "How to generate random matrices from the classical
+           compact groups", :arXiv:`math-ph/0609050v2`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import unitary_group
+    >>> x = unitary_group.rvs(3)
+
+    >>> np.dot(x, x.conj().T)
+    array([[  1.00000000e+00,   1.13231364e-17,  -2.86852790e-16],
+           [  1.13231364e-17,   1.00000000e+00,  -1.46845020e-16],
+           [ -2.86852790e-16,  -1.46845020e-16,   1.00000000e+00]])  # may vary
+
+    This generates one random matrix from U(3). The dot product confirms that
+    it is unitary up to machine precision.
+
+    Alternatively, the object may be called (as a function) to fix the `dim`
+    parameter, return a "frozen" unitary_group random variable:
+
+    >>> rv = unitary_group(5)
+    """
+
+    def __init__(self, seed=None):
+        super().__init__(seed)
+        self.__doc__ = doccer.docformat(self.__doc__)
+
+    def __call__(self, dim=None, seed=None):
+        """Create a frozen (U(N)) n-dimensional unitary matrix distribution.
+
+        See `unitary_group_frozen` for more information.
+        """
+        return unitary_group_frozen(dim, seed=seed)
+
+    def _process_parameters(self, dim):
+        """Dimension N must be specified; it cannot be inferred."""
+        if dim is None or not np.isscalar(dim) or dim < 0 or dim != int(dim):
+            raise ValueError("Dimension of rotation must be specified,"
+                             "and must be a scalar nonnegative integer.")
+
+        return dim
+
+    def rvs(self, dim, size=1, random_state=None):
+        """Draw random samples from U(N).
+
+        Parameters
+        ----------
+        dim : int
+            Dimension of space (N).
+        size : int, optional
+            Number of samples to draw (default 1).
+
+        Returns
+        -------
+        rvs : ndarray or scalar
+            Random size N-dimensional matrices, dimension (size, dim, dim)
+
+        """
+        random_state = self._get_random_state(random_state)
+
+        size = int(size)
+
+        dim = self._process_parameters(dim)
+
+        size = (size,) if size > 1 else ()
+        z = 1/math.sqrt(2)*(random_state.normal(size=size + (dim, dim)) +
+                            1j*random_state.normal(size=size + (dim, dim)))
+        q, r = np.linalg.qr(z)
+        # The last two dimensions are the rows and columns of R matrices.
+        # Extract the diagonals. Note that this eliminates a dimension.
+        d = r.diagonal(offset=0, axis1=-2, axis2=-1)
+        # Add back a dimension for proper broadcasting: we're dividing
+        # each row of each R matrix by the diagonal of the R matrix.
+        q *= (d/abs(d))[..., np.newaxis, :]  # to broadcast properly
+        return q
+
+
+unitary_group = unitary_group_gen()
+
+
+class unitary_group_frozen(multi_rv_frozen):
+    __class_getitem__ = None  # pyrefly:ignore[bad-assignment]
+
+    def __init__(self, dim=None, seed=None):
+        """Create a frozen (U(N)) n-dimensional unitary matrix distribution.
+
+        Parameters
+        ----------
+        dim : scalar
+            Dimension of matrices
+        seed : {None, int, `numpy.random.Generator`, `numpy.random.RandomState`}, optional
+            If `seed` is None (or `np.random`), the `numpy.random.RandomState`
+            singleton is used.
+            If `seed` is an int, a new ``RandomState`` instance is used,
+            seeded with `seed`.
+            If `seed` is already a ``Generator`` or ``RandomState`` instance
+            then that instance is used.
+
+        Examples
+        --------
+        >>> from scipy.stats import unitary_group
+        >>> x = unitary_group(3)
+        >>> x.rvs()
+
+        """ # numpy/numpydoc#87  # noqa: E501
+        self._dist = unitary_group_gen(seed)
+        self.dim = self._dist._process_parameters(dim)
+
+    def rvs(self, size=1, random_state=None):
+        return self._dist.rvs(self.dim, size, random_state)
+
+
+_mvt_doc_default_callparams = """\
+loc : array_like, optional
+    Location of the distribution. (default ``0``)
+shape : array_like, optional
+    Positive semidefinite matrix of the distribution. (default ``1``)
+df : float, optional
+    Degrees of freedom of the distribution; must be greater than zero.
+    If ``np.inf`` then results are multivariate normal. The default is ``1``.
+allow_singular : bool, optional
+    Whether to allow a singular matrix. (default ``False``)
+"""
+
+_mvt_doc_callparams_note = """\
+Setting the parameter `loc` to ``None`` is equivalent to having `loc`
+be the zero-vector. The parameter `shape` can be a scalar, in which case
+the shape matrix is the identity times that value, a vector of
+diagonal entries for the shape matrix, or a two-dimensional array_like.
+"""
+
+_mvt_doc_frozen_callparams_note = """\
+See class definition for a detailed description of parameters."""
+
+mvt_docdict_params = {
+    '_mvt_doc_default_callparams': _mvt_doc_default_callparams,
+    '_mvt_doc_callparams_note': _mvt_doc_callparams_note,
+    '_doc_random_state': _doc_random_state
+}
+
+mvt_docdict_noparams = {
+    '_mvt_doc_default_callparams': "",
+    '_mvt_doc_callparams_note': _mvt_doc_frozen_callparams_note,
+    '_doc_random_state': _doc_random_state
+}
+
+
+class multivariate_t_gen(multi_rv_generic):
+    r"""
+    A multivariate t-distributed random variable.
+
+    The `loc` parameter specifies the location. The `shape` parameter specifies
+    the positive semidefinite shape matrix. The `df` parameter specifies the
+    degrees of freedom.
+
+    In addition to calling the methods below, the object itself may be called
+    as a function to fix the location, shape matrix, and degrees of freedom
+    parameters, returning a "frozen" multivariate t-distribution random.
+
+    Parameters
+    ----------
+    %(_mvt_doc_default_callparams)s
+    %(_doc_random_state)s
+
+    Methods
+    -------
+    pdf(x, loc=None, shape=1, df=1, allow_singular=False)
+        Probability density function.
+    logpdf(x, loc=None, shape=1, df=1, allow_singular=False)
+        Log of the probability density function.
+    cdf(x, loc=None, shape=1, df=1, allow_singular=False, *,
+        maxpts=None, lower_limit=None, random_state=None)
+        Cumulative distribution function.
+    rvs(loc=None, shape=1, df=1, size=1, random_state=None)
+        Draw random samples from a multivariate t-distribution.
+    entropy(loc=None, shape=1, df=1)
+        Differential entropy of a multivariate t-distribution.
+    marginal(dimensions, loc=None, shape=1, df=1, allow_singular=False)
+        Return a marginal multivariate t-distribution.
+
+    Notes
+    -----
+    %(_mvt_doc_callparams_note)s
+    The matrix `shape` must be a (symmetric) positive semidefinite matrix. The
+    determinant and inverse of `shape` are computed as the pseudo-determinant
+    and pseudo-inverse, respectively, so that `shape` does not need to have
+    full rank.
+
+    The probability density function for `multivariate_t` is
+
+    .. math::
+
+        f(x) = \frac{\Gamma((\nu + p)/2)}{\Gamma(\nu/2)\nu^{p/2}\pi^{p/2}|\Sigma|^{1/2}}
+               \left[1 + \frac{1}{\nu} (\mathbf{x} - \boldsymbol{\mu})^{\top}
+               \boldsymbol{\Sigma}^{-1}
+               (\mathbf{x} - \boldsymbol{\mu}) \right]^{-(\nu + p)/2},
+
+    where :math:`p` is the dimension of :math:`\mathbf{x}`,
+    :math:`\boldsymbol{\mu}` is the :math:`p`-dimensional location,
+    :math:`\boldsymbol{\Sigma}` the :math:`p \times p`-dimensional shape
+    matrix, and :math:`\nu` is the degrees of freedom.
+
+    .. versionadded:: 1.6.0
+
+    References
+    ----------
+    .. [1] Arellano-Valle et al. "Shannon Entropy and Mutual Information for
+           Multivariate Skew-Elliptical Distributions". Scandinavian Journal
+           of Statistics. Vol. 40, issue 1.
+
+    Examples
+    --------
+    The object may be called (as a function) to fix the `loc`, `shape`,
+    `df`, and `allow_singular` parameters, returning a "frozen"
+    multivariate_t random variable:
+
+    >>> import numpy as np
+    >>> from scipy.stats import multivariate_t
+    >>> rv = multivariate_t([1.0, -0.5], [[2.1, 0.3], [0.3, 1.5]], df=2)
+    >>> # Frozen object with the same methods but holding the given location,
+    >>> # scale, and degrees of freedom fixed.
+
+    Create a contour plot of the PDF.
+
+    >>> import matplotlib.pyplot as plt
+    >>> x, y = np.mgrid[-1:3:.01, -2:1.5:.01]
+    >>> pos = np.dstack((x, y))
+    >>> fig, ax = plt.subplots(1, 1)
+    >>> ax.set_aspect('equal')
+    >>> plt.contourf(x, y, rv.pdf(pos))
+    """
+
+    def __init__(self, seed=None):
+        """Initialize a multivariate t-distributed random variable.
+
+        Parameters
+        ----------
+        seed : Random state.
+
+        """
+        super().__init__(seed)
+        self.__doc__ = doccer.docformat(self.__doc__, mvt_docdict_params)
+        self._random_state = check_random_state(seed)
+
+    def __call__(self, loc=None, shape=1, df=1, allow_singular=False,
+                 seed=None):
+        """Create a frozen multivariate t-distribution.
+
+        See `multivariate_t_frozen` for parameters.
+        """
+        if df == np.inf:
+            return multivariate_normal_frozen(mean=loc, cov=shape,
+                                              allow_singular=allow_singular,
+                                              seed=seed)
+        return multivariate_t_frozen(loc=loc, shape=shape, df=df,
+                                     allow_singular=allow_singular, seed=seed)
+
+    def pdf(self, x, loc=None, shape=1, df=1, allow_singular=False):
+        """Multivariate t-distribution probability density function.
+
+        Parameters
+        ----------
+        x : array_like
+            Points at which to evaluate the probability density function.
+        %(_mvt_doc_default_callparams)s
+
+        Returns
+        -------
+        pdf : Probability density function evaluated at `x`.
+
+        Examples
+        --------
+        >>> from scipy.stats import multivariate_t
+        >>> x = [0.4, 5]
+        >>> loc = [0, 1]
+        >>> shape = [[1, 0.1], [0.1, 1]]
+        >>> df = 7
+        >>> multivariate_t.pdf(x, loc, shape, df)
+        0.00075713
+
+        """
+        dim, loc, shape, df = self._process_parameters(loc, shape, df)
+        x = self._process_quantiles(x, dim)
+        shape_info = _PSD(shape, allow_singular=allow_singular)
+        logpdf = self._logpdf(x, loc, shape_info.U, shape_info.log_pdet, df,
+                              dim, shape_info.rank)
+        return np.exp(logpdf)
+
+    def logpdf(self, x, loc=None, shape=1, df=1):
+        """Log of the multivariate t-distribution probability density function.
+
+        Parameters
+        ----------
+        x : array_like
+            Points at which to evaluate the log of the probability density
+            function.
+        %(_mvt_doc_default_callparams)s
+
+        Returns
+        -------
+        logpdf : Log of the probability density function evaluated at `x`.
+
+        Examples
+        --------
+        >>> from scipy.stats import multivariate_t
+        >>> x = [0.4, 5]
+        >>> loc = [0, 1]
+        >>> shape = [[1, 0.1], [0.1, 1]]
+        >>> df = 7
+        >>> multivariate_t.logpdf(x, loc, shape, df)
+        -7.1859802
+
+        See Also
+        --------
+        pdf : Probability density function.
+
+        """
+        dim, loc, shape, df = self._process_parameters(loc, shape, df)
+        x = self._process_quantiles(x, dim)
+        shape_info = _PSD(shape)
+        cov_object = _covariance.CovViaPSD(shape_info)
+
+        return self._logpdf(x, loc, shape_info.U, shape_info.log_pdet, df, dim,
+                            shape_info.rank, cov_object)
+
+    def _logpdf(self, x, loc, prec_U, log_pdet, df, dim, rank, cov_object=None):
+        """Utility method `pdf`, `logpdf` for parameters.
+
+        Parameters
+        ----------
+        x : ndarray
+            Points at which to evaluate the log of the probability density
+            function.
+        loc : ndarray
+            Location of the distribution.
+        prec_U : ndarray
+            A decomposition such that `np.dot(prec_U, prec_U.T)` is the inverse
+            of the shape matrix.
+        log_pdet : float
+            Logarithm of the determinant of the shape matrix.
+        df : float
+            Degrees of freedom of the distribution.
+        dim : int
+            Dimension of the quantiles x.
+        rank : int
+            Rank of the shape matrix.
+
+        Notes
+        -----
+        As this function does no argument checking, it should not be called
+        directly; use 'logpdf' instead.
+
+        """
+        if df == np.inf:
+            return multivariate_normal._logpdf(x, loc, cov_object)
+
+        dev = x - loc
+        maha = np.square(np.dot(dev, prec_U)).sum(axis=-1)
+
+        t = 0.5 * (df + dim)
+        A = gammaln(t)
+        B = gammaln(0.5 * df)
+        C = dim/2. * np.log(df * np.pi)
+        D = 0.5 * log_pdet
+        E = -t * np.log(1 + (1./df) * maha)
+
+        return _squeeze_output(A - B - C - D + E)
+
+    def _cdf(self, x, loc, shape, df, dim, maxpts=None, lower_limit=None,
+             random_state=None):
+
+        # All of this -  random state validation, maxpts, apply_along_axis,
+        # etc. needs to go in this private method unless we want
+        # frozen distribution's `cdf` method to duplicate it or call `cdf`,
+        # which would require re-processing parameters
+        if random_state is not None:
+            rng = check_random_state(random_state)
+        else:
+            rng = self._random_state
+
+        if not maxpts:
+            maxpts = 1000 * dim
+
+        x = self._process_quantiles(x, dim)
+        lower_limit = (np.full(loc.shape, -np.inf)
+                       if lower_limit is None else lower_limit)
+
+        # remove the mean
+        x, lower_limit = x - loc, lower_limit - loc
+
+        b, a = np.broadcast_arrays(x, lower_limit)
+        i_swap = b < a
+        signs = (-1)**(i_swap.sum(axis=-1))  # odd # of swaps -> negative
+        a, b = a.copy(), b.copy()
+        a[i_swap], b[i_swap] = b[i_swap], a[i_swap]
+        n = x.shape[-1]
+        limits = np.concatenate((a, b), axis=-1)
+
+        def func1d(limits):
+            a, b = limits[:n], limits[n:]
+            return _qmvt(maxpts, df, shape, a, b, rng)[0]
+
+        res = np.apply_along_axis(func1d, -1, limits) * signs
+        # Fixing the output shape for existing distributions is a separate
+        # issue. For now, let's keep this consistent with pdf.
+        return _squeeze_output(res)
+
+    def cdf(self, x, loc=None, shape=1, df=1, allow_singular=False, *,
+            maxpts=None, lower_limit=None, random_state=None):
+        """Multivariate t-distribution cumulative distribution function.
+
+        Parameters
+        ----------
+        x : array_like
+            Points at which to evaluate the cumulative distribution function.
+        %(_mvt_doc_default_callparams)s
+        maxpts : int, optional
+            Maximum number of points to use for integration. The default is
+            1000 times the number of dimensions.
+        lower_limit : array_like, optional
+            Lower limit of integration of the cumulative distribution function.
+            Default is negative infinity. Must be broadcastable with `x`.
+        %(_doc_random_state)s
+
+        Returns
+        -------
+        cdf : ndarray or scalar
+            Cumulative distribution function evaluated at `x`.
+
+        Examples
+        --------
+        >>> from scipy.stats import multivariate_t
+        >>> x = [0.4, 5]
+        >>> loc = [0, 1]
+        >>> shape = [[1, 0.1], [0.1, 1]]
+        >>> df = 7
+        >>> multivariate_t.cdf(x, loc, shape, df)
+        0.64798491
+
+        """
+        dim, loc, shape, df = self._process_parameters(loc, shape, df)
+        shape = _PSD(shape, allow_singular=allow_singular)._M
+
+        return self._cdf(x, loc, shape, df, dim, maxpts,
+                         lower_limit, random_state)
+
+    def _entropy(self, dim, df=1, shape=1):
+        if df == np.inf:
+            return multivariate_normal(None, cov=shape).entropy()
+
+        shape_info = _PSD(shape)
+        shape_term = 0.5 * shape_info.log_pdet
+
+        def regular(dim, df):
+            halfsum = 0.5 * (dim + df)
+            half_df = 0.5 * df
+            return (
+                -gammaln(halfsum) + gammaln(half_df)
+                + 0.5 * dim * np.log(df * np.pi) + halfsum
+                * (psi(halfsum) - psi(half_df))
+                + shape_term
+            )
+
+        def asymptotic(dim, df):
+            # Formula from Wolfram Alpha:
+            # "asymptotic expansion -gammaln((m+d)/2) + gammaln(d/2) + (m*log(d*pi))/2
+            #  + ((m+d)/2) * (digamma((m+d)/2) - digamma(d/2))"
+            return (
+                dim * norm._entropy() + dim / df
+                - dim * (dim - 2) * df**-2.0 / 4
+                + dim**2 * (dim - 2) * df**-3.0 / 6
+                + dim * (-3 * dim**3 + 8 * dim**2 - 8) * df**-4.0 / 24
+                + dim**2 * (3 * dim**3 - 10 * dim**2 + 16) * df**-5.0 / 30
+                + shape_term
+            )[()]
+
+        # preserves ~12 digits accuracy up to at least `dim=1e5`. See gh-18465.
+        threshold = dim * 100 * 4 / (np.log(dim) + 1)
+        return xpx.apply_where(df >= threshold, (dim, df), asymptotic, regular)
+
+    def entropy(self, loc=None, shape=1, df=1):
+        """Calculate the differential entropy of a multivariate
+        t-distribution.
+
+        Parameters
+        ----------
+        %(_mvt_doc_default_callparams)s
+
+        Returns
+        -------
+        h : float
+            Differential entropy
+
+        """
+        dim, loc, shape, df = self._process_parameters(None, shape, df)
+        return self._entropy(dim, df, shape)
+
+    def rvs(self, loc=None, shape=1, df=1, size=1, random_state=None):
+        """Draw random samples from a multivariate t-distribution.
+
+        Parameters
+        ----------
+        %(_mvt_doc_default_callparams)s
+        size : int, optional
+            Number of samples to draw (default 1).
+        %(_doc_random_state)s
+
+        Returns
+        -------
+        rvs : ndarray or scalar
+            Random variates of size (`size`, `P`), where `P` is the
+            dimension of the random variable.
+
+        Examples
+        --------
+        >>> from scipy.stats import multivariate_t
+        >>> x = [0.4, 5]
+        >>> loc = [0, 1]
+        >>> shape = [[1, 0.1], [0.1, 1]]
+        >>> df = 7
+        >>> multivariate_t.rvs(loc, shape, df)
+        array([[0.93477495, 3.00408716]])
+
+        """
+        # For implementation details, see equation (3):
+        #
+        #    Hofert, "On Sampling from the Multivariatet Distribution", 2013
+        #     http://rjournal.github.io/archive/2013-2/hofert.pdf
+        #
+        dim, loc, shape, df = self._process_parameters(loc, shape, df)
+        if random_state is not None:
+            rng = check_random_state(random_state)
+        else:
+            rng = self._random_state
+
+        if np.isinf(df):
+            x = np.ones(size)
+        else:
+            x = rng.chisquare(df, size=size) / df
+
+        z = rng.multivariate_normal(np.zeros(dim), shape, size=size)
+        samples = loc + z / np.sqrt(x)[..., None]
+        return _squeeze_output(samples)
+
+    def _process_quantiles(self, x, dim):
+        """
+        Adjust quantiles array so that last axis labels the components of
+        each data point.
+        """
+        x = np.asarray(x, dtype=float)
+        if x.ndim == 0:
+            x = x[np.newaxis]
+        elif x.ndim == 1:
+            if dim == 1:
+                x = x[:, np.newaxis]
+            else:
+                x = x[np.newaxis, :]
+        return x
+
+    def _process_parameters(self, loc, shape, df):
+        """
+        Infer dimensionality from location array and shape matrix, handle
+        defaults, and ensure compatible dimensions.
+        """
+        if loc is None and shape is None:
+            loc = np.asarray(0, dtype=float)
+            shape = np.asarray(1, dtype=float)
+            dim = 1
+        elif loc is None:
+            shape = np.asarray(shape, dtype=float)
+            if shape.ndim < 2:
+                dim = 1
+            else:
+                dim = shape.shape[0]
+            loc = np.zeros(dim)
+        elif shape is None:
+            loc = np.asarray(loc, dtype=float)
+            dim = loc.size
+            shape = np.eye(dim)
+        else:
+            shape = np.asarray(shape, dtype=float)
+            loc = np.asarray(loc, dtype=float)
+            dim = loc.size
+
+        if dim == 1:
+            loc = loc.reshape(1)
+            shape = shape.reshape(1, 1)
+
+        if loc.ndim != 1 or loc.shape[0] != dim:
+            raise ValueError(f"Array 'loc' must be a vector of length {dim}.")
+        if shape.ndim == 0:
+            shape = shape * np.eye(dim)
+        elif shape.ndim == 1:
+            shape = np.diag(shape)
+        elif shape.ndim == 2 and shape.shape != (dim, dim):
+            rows, cols = shape.shape
+            if rows != cols:
+                msg = ("Array 'cov' must be square if it is two dimensional,"
+                       f" but cov.shape = {str(shape.shape)}.")
+            else:
+                msg = ("Dimension mismatch: array 'cov' is of shape %s,"
+                       " but 'loc' is a vector of length %d.")
+                msg = msg % (str(shape.shape), len(loc))
+            raise ValueError(msg)
+        elif shape.ndim > 2:
+            raise ValueError(f"Array 'cov' must be at most two-dimensional, "
+                             f"but cov.ndim = {shape.ndim}")
+
+        # Process degrees of freedom.
+        if df is None:
+            df = 1
+        elif df <= 0:
+            raise ValueError("'df' must be greater than zero.")
+        elif np.isnan(df):
+            raise ValueError("'df' is 'nan' but must be greater than zero or 'np.inf'.")
+
+        return dim, loc, shape, df
+
+    def marginal(self, dimensions, loc=None, shape=1, df=1, allow_singular=False):
+        """Return a marginal multivariate t-distribution.
+
+        Parameters
+        ----------
+        dimensions : int or 1-d array_like
+            The dimensions of the multivariate t corresponding
+            with the marginal variables, that is, the indices of the dimensions
+            that are being retained. The other dimensions are marginalized out.
+        %(_mvt_doc_default_callparams)s
+
+        Returns
+        -------
+        marginal_multivariate_t : multivariate_t_frozen
+            An object representing the marginal t-distribution.
+
+        Notes
+        -----
+        %(_mvt_doc_frozen_callparams_note)s
+        """
+        params = self._process_parameters(loc, shape, df)
+        n, loc, shape, df = params
+        dims = _validate_marginal_input(dimensions, n)
+
+        loc = loc[dims]
+        shape = shape[np.ix_(dims, dims)]
+
+        return multivariate_t_frozen(loc, shape, df, allow_singular)
+
+
+class multivariate_t_frozen(multi_rv_frozen):
+    __class_getitem__ = None  # pyrefly:ignore[bad-assignment]
+
+    def __init__(self, loc=None, shape=1, df=1, allow_singular=False,
+                 seed=None):
+        """Create a frozen multivariate t distribution.
+
+        Parameters
+        ----------
+        %(_mvt_doc_default_callparams)s
+
+        Examples
+        --------
+        >>> import numpy as np
+        >>> from scipy.stats import multivariate_t
+        >>> loc = np.zeros(3)
+        >>> shape = np.eye(3)
+        >>> df = 10
+        >>> dist = multivariate_t(loc, shape, df)
+        >>> dist.rvs()
+        array([[ 0.81412036, -1.53612361,  0.42199647]])
+        >>> dist.pdf([1, 1, 1])
+        array([0.01237803])
+
+        """
+        self._dist = multivariate_t_gen(seed)
+        dim, loc, shape, df = self._dist._process_parameters(loc, shape, df)
+        self.dim, self.loc, self.shape, self.df = dim, loc, shape, df
+        self.shape_info = _PSD(shape, allow_singular=allow_singular)
+        self.allow_singular = allow_singular
+
+    def logpdf(self, x):
+        x = self._dist._process_quantiles(x, self.dim)
+        U = self.shape_info.U
+        log_pdet = self.shape_info.log_pdet
+        return self._dist._logpdf(x, self.loc, U, log_pdet, self.df, self.dim,
+                                  self.shape_info.rank)
+
+    def cdf(self, x, *, maxpts=None, lower_limit=None, random_state=None):
+        x = self._dist._process_quantiles(x, self.dim)
+        return self._dist._cdf(x, self.loc, self.shape, self.df, self.dim,
+                               maxpts, lower_limit, random_state)
+
+    def pdf(self, x):
+        return np.exp(self.logpdf(x))
+
+    def rvs(self, size=1, random_state=None):
+        return self._dist.rvs(loc=self.loc,
+                              shape=self.shape,
+                              df=self.df,
+                              size=size,
+                              random_state=random_state)
+
+    def entropy(self):
+        return self._dist._entropy(self.dim, self.df, self.shape)
+
+    def marginal(self, dimensions):
+        return self._dist.marginal(dimensions, self.loc,
+                                   self.shape, self.df, self.allow_singular)
+
+multivariate_t = multivariate_t_gen()
+
+
+# Set frozen generator docstrings from corresponding docstrings in
+# multivariate_t_gen and fill in default strings in class docstrings
+for name in ['logpdf', 'pdf', 'rvs', 'cdf', 'entropy']:
+    method = multivariate_t_gen.__dict__[name]
+    method_frozen = multivariate_t_frozen.__dict__[name]
+    method_frozen.__doc__ = doccer.docformat(method.__doc__,
+                                             mvt_docdict_noparams)
+    method.__doc__ = doccer.docformat(method.__doc__, mvt_docdict_params)
+
+
+_mhg_doc_default_callparams = """\
+m : array_like
+    The number of each type of object in the population.
+    That is, :math:`m[i]` is the number of objects of
+    type :math:`i`.
+n : array_like
+    The number of samples taken from the population.
+"""
+
+_mhg_doc_callparams_note = """\
+`m` must be an array of positive integers. If the quantile
+:math:`i` contains values out of the range :math:`[0, m_i]`
+where :math:`m_i` is the number of objects of type :math:`i`
+in the population or if the parameters are inconsistent with one
+another (e.g. ``x.sum() != n``), methods return the appropriate
+value (e.g. ``0`` for ``pmf``). If `m` or `n` contain negative
+values, the result will contain ``nan`` there.
+"""
+
+_mhg_doc_frozen_callparams = ""
+
+_mhg_doc_frozen_callparams_note = """\
+See class definition for a detailed description of parameters."""
+
+mhg_docdict_params = {
+    '_doc_default_callparams': _mhg_doc_default_callparams,
+    '_doc_callparams_note': _mhg_doc_callparams_note,
+    '_doc_random_state': _doc_random_state
+}
+
+mhg_docdict_noparams = {
+    '_doc_default_callparams': _mhg_doc_frozen_callparams,
+    '_doc_callparams_note': _mhg_doc_frozen_callparams_note,
+    '_doc_random_state': _doc_random_state
+}
+
+
+class multivariate_hypergeom_gen(multi_rv_generic):
+    r"""
+    A multivariate hypergeometric random variable.
+
+    Parameters
+    ----------
+    %(_doc_default_callparams)s
+    %(_doc_random_state)s
+
+    Methods
+    -------
+    pmf(x, m, n)
+        Probability mass function.
+    logpmf(x, m, n)
+        Log of the probability mass function.
+    rvs(m, n, size=1, random_state=None)
+        Draw random samples from a multivariate hypergeometric
+        distribution.
+    mean(m, n)
+        Mean of the multivariate hypergeometric distribution.
+    var(m, n)
+        Variance of the multivariate hypergeometric distribution.
+    cov(m, n)
+        Compute the covariance matrix of the multivariate
+        hypergeometric distribution.
+
+    See Also
+    --------
+    scipy.stats.hypergeom : The hypergeometric distribution.
+    scipy.stats.multinomial : The multinomial distribution.
+
+    Notes
+    -----
+    %(_doc_callparams_note)s
+
+    The probability mass function for `multivariate_hypergeom` is
+
+    .. math::
+
+        P(X_1 = x_1, X_2 = x_2, \ldots, X_k = x_k) = \frac{\binom{m_1}{x_1}
+        \binom{m_2}{x_2} \cdots \binom{m_k}{x_k}}{\binom{M}{n}}, \\ \quad
+        (x_1, x_2, \ldots, x_k) \in \mathbb{N}^k \text{ with }
+        \sum_{i=1}^k x_i = n
+
+    where :math:`m_i` are the number of objects of type :math:`i`, :math:`M`
+    is the total number of objects in the population (sum of all the
+    :math:`m_i`), and :math:`n` is the size of the sample to be taken
+    from the population.
+
+    .. versionadded:: 1.6.0
+
+    References
+    ----------
+    .. [1] The Multivariate Hypergeometric Distribution,
+           http://www.randomservices.org/random/urn/MultiHypergeometric.html
+    .. [2] Thomas J. Sargent and John Stachurski, 2020,
+           Multivariate Hypergeometric Distribution
+           https://python.quantecon.org/multi_hyper.html
+
+    Examples
+    --------
+    To evaluate the probability mass function of the multivariate
+    hypergeometric distribution, with a dichotomous population of size
+    :math:`10` and :math:`20`, at a sample of size :math:`12` with
+    :math:`8` objects of the first type and :math:`4` objects of the
+    second type, use:
+
+    >>> from scipy.stats import multivariate_hypergeom
+    >>> multivariate_hypergeom.pmf(x=[8, 4], m=[10, 20], n=12)
+    0.0025207176631464523
+
+    The `multivariate_hypergeom` distribution is identical to the
+    corresponding `hypergeom` distribution (tiny numerical differences
+    notwithstanding) when only two types (good and bad) of objects
+    are present in the population as in the example above. Consider
+    another example for a comparison with the hypergeometric distribution:
+
+    >>> from scipy.stats import hypergeom
+    >>> multivariate_hypergeom.pmf(x=[3, 1], m=[10, 5], n=4)
+    0.4395604395604395
+    >>> hypergeom.pmf(k=3, M=15, n=4, N=10)
+    0.43956043956044005
+
+    The functions ``pmf``, ``logpmf``, ``mean``, ``var``, ``cov``, and ``rvs``
+    support broadcasting, under the convention that the vector parameters
+    (``x``, ``m``, and ``n``) are interpreted as if each row along the last
+    axis is a single object. For instance, we can combine the previous two
+    calls to `multivariate_hypergeom` as
+
+    >>> multivariate_hypergeom.pmf(x=[[8, 4], [3, 1]], m=[[10, 20], [10, 5]],
+    ...                            n=[12, 4])
+    array([0.00252072, 0.43956044])
+
+    This broadcasting also works for ``cov``, where the output objects are
+    square matrices of size ``m.shape[-1]``. For example:
+
+    >>> multivariate_hypergeom.cov(m=[[7, 9], [10, 15]], n=[8, 12])
+    array([[[ 1.05, -1.05],
+            [-1.05,  1.05]],
+           [[ 1.56, -1.56],
+            [-1.56,  1.56]]])
+
+    That is, ``result[0]`` is equal to
+    ``multivariate_hypergeom.cov(m=[7, 9], n=8)`` and ``result[1]`` is equal
+    to ``multivariate_hypergeom.cov(m=[10, 15], n=12)``.
+
+    Alternatively, the object may be called (as a function) to fix the `m`
+    and `n` parameters, returning a "frozen" multivariate hypergeometric
+    random variable.
+
+    >>> rv = multivariate_hypergeom(m=[10, 20], n=12)
+    >>> rv.pmf(x=[8, 4])
+    0.0025207176631464523
+    """
+    def __init__(self, seed=None):
+        super().__init__(seed)
+        self.__doc__ = doccer.docformat(self.__doc__, mhg_docdict_params)
+
+    def __call__(self, m, n, seed=None):
+        """Create a frozen multivariate_hypergeom distribution.
+
+        See `multivariate_hypergeom_frozen` for more information.
+        """
+        return multivariate_hypergeom_frozen(m, n, seed=seed)
+
+    def _process_parameters(self, m, n):
+        m = np.asarray(m)
+        n = np.asarray(n)
+        if m.size == 0:
+            m = m.astype(int)
+        if n.size == 0:
+            n = n.astype(int)
+        if not np.issubdtype(m.dtype, np.integer):
+            raise TypeError("'m' must an array of integers.")
+        if not np.issubdtype(n.dtype, np.integer):
+            raise TypeError("'n' must an array of integers.")
+        if m.ndim == 0:
+            raise ValueError("'m' must be an array with"
+                             " at least one dimension.")
+
+        # check for empty arrays
+        if m.size != 0:
+            n = n[..., np.newaxis]
+
+        m, n = np.broadcast_arrays(m, n)
+
+        # check for empty arrays
+        if m.size != 0:
+            n = n[..., 0]
+
+        mcond = m < 0
+
+        M = m.sum(axis=-1)
+
+        ncond = (n < 0) | (n > M)
+        return M, m, n, mcond, ncond, np.any(mcond, axis=-1) | ncond
+
+    def _process_quantiles(self, x, M, m, n):
+        x = np.asarray(x)
+        if not np.issubdtype(x.dtype, np.integer):
+            raise TypeError("'x' must an array of integers.")
+        if x.ndim == 0:
+            raise ValueError("'x' must be an array with"
+                             " at least one dimension.")
+        if not x.shape[-1] == m.shape[-1]:
+            raise ValueError(f"Size of each quantile must be size of 'm': "
+                             f"received {x.shape[-1]}, "
+                             f"but expected {m.shape[-1]}.")
+
+        # check for empty arrays
+        if m.size != 0:
+            n = n[..., np.newaxis]
+            M = M[..., np.newaxis]
+
+        x, m, n, M = np.broadcast_arrays(x, m, n, M)
+
+        # check for empty arrays
+        if m.size != 0:
+            n, M = n[..., 0], M[..., 0]
+
+        xcond = (x < 0) | (x > m)
+        return (x, M, m, n, xcond,
+                np.any(xcond, axis=-1) | (x.sum(axis=-1) != n))
+
+    def _checkresult(self, result, cond, bad_value):
+        result = np.asarray(result)
+        if cond.ndim != 0:
+            result[cond] = bad_value
+        elif cond:
+            return bad_value
+        if result.ndim == 0:
+            return result[()]
+        return result
+
+    def _logpmf(self, x, M, m, n, mxcond, ncond):
+        # This equation of the pmf comes from the relation,
+        # n combine r = beta(n+1, 1) / beta(r+1, n-r+1)
+        num = np.zeros_like(m, dtype=np.float64)
+        den = np.zeros_like(n, dtype=np.float64)
+        m, x = m[~mxcond], x[~mxcond]
+        M, n = M[~ncond], n[~ncond]
+        num[~mxcond] = (betaln(m+1, 1) - betaln(x+1, m-x+1))
+        den[~ncond] = (betaln(M+1, 1) - betaln(n+1, M-n+1))
+        num[mxcond] = np.nan
+        den[ncond] = np.nan
+        num = num.sum(axis=-1)
+        return num - den
+
+    def logpmf(self, x, m, n):
+        """Log of the multivariate hypergeometric probability mass function.
+
+        Parameters
+        ----------
+        x : array_like
+            Quantiles, with the last axis of `x` denoting the components.
+        %(_doc_default_callparams)s
+
+        Returns
+        -------
+        logpmf : ndarray or scalar
+            Log of the probability mass function evaluated at `x`
+
+        Notes
+        -----
+        %(_doc_callparams_note)s
+        """
+        M, m, n, mcond, ncond, mncond = self._process_parameters(m, n)
+        (x, M, m, n, xcond,
+         xcond_reduced) = self._process_quantiles(x, M, m, n)
+        mxcond = mcond | xcond
+        ncond = ncond | np.zeros(n.shape, dtype=np.bool_)
+
+        result = self._logpmf(x, M, m, n, mxcond, ncond)
+
+        # replace values for which x was out of the domain; broadcast
+        # xcond to the right shape
+        xcond_ = xcond_reduced | np.zeros(mncond.shape, dtype=np.bool_)
+        result = self._checkresult(result, xcond_, -np.inf)
+
+        # replace values bad for n or m; broadcast
+        # mncond to the right shape
+        mncond_ = mncond | np.zeros(xcond_reduced.shape, dtype=np.bool_)
+        return self._checkresult(result, mncond_, np.nan)
+
+    def pmf(self, x, m, n):
+        """Multivariate hypergeometric probability mass function.
+
+        Parameters
+        ----------
+        x : array_like
+            Quantiles, with the last axis of `x` denoting the components.
+        %(_doc_default_callparams)s
+
+        Returns
+        -------
+        pmf : ndarray or scalar
+            Probability density function evaluated at `x`
+
+        Notes
+        -----
+        %(_doc_callparams_note)s
+        """
+        out = np.exp(self.logpmf(x, m, n))
+        return out
+
+    def mean(self, m, n):
+        """Mean of the multivariate hypergeometric distribution.
+
+        Parameters
+        ----------
+        %(_doc_default_callparams)s
+
+        Returns
+        -------
+        mean : array_like or scalar
+            The mean of the distribution
+        """
+        M, m, n, _, _, mncond = self._process_parameters(m, n)
+        # check for empty arrays
+        if m.size != 0:
+            M, n = M[..., np.newaxis], n[..., np.newaxis]
+        cond = (M == 0)
+        M = np.ma.masked_array(M, mask=cond)
+        mu = n*(m/M)
+        if m.size != 0:
+            mncond = (mncond[..., np.newaxis] |
+                      np.zeros(mu.shape, dtype=np.bool_))
+        return self._checkresult(mu, mncond, np.nan)
+
+    def var(self, m, n):
+        """Variance of the multivariate hypergeometric distribution.
+
+        Parameters
+        ----------
+        %(_doc_default_callparams)s
+
+        Returns
+        -------
+        array_like
+            The variances of the components of the distribution.  This is
+            the diagonal of the covariance matrix of the distribution
+        """
+        M, m, n, _, _, mncond = self._process_parameters(m, n)
+        # check for empty arrays
+        if m.size != 0:
+            M, n = M[..., np.newaxis], n[..., np.newaxis]
+        cond = (M == 0) & (M-1 == 0)
+        M = np.ma.masked_array(M, mask=cond)
+        output = n * m/M * (M-m)/M * (M-n)/(M-1)
+        if m.size != 0:
+            mncond = (mncond[..., np.newaxis] |
+                      np.zeros(output.shape, dtype=np.bool_))
+        return self._checkresult(output, mncond, np.nan)
+
+    def cov(self, m, n):
+        """Covariance matrix of the multivariate hypergeometric distribution.
+
+        Parameters
+        ----------
+        %(_doc_default_callparams)s
+
+        Returns
+        -------
+        cov : array_like
+            The covariance matrix of the distribution
+        """
+        # see [1]_ for the formula and [2]_ for implementation
+        # cov( x_i,x_j ) = -n * (M-n)/(M-1) * (K_i*K_j) / (M**2)
+        M, m, n, _, _, mncond = self._process_parameters(m, n)
+        # check for empty arrays
+        if m.size != 0:
+            M = M[..., np.newaxis, np.newaxis]
+            n = n[..., np.newaxis, np.newaxis]
+        cond = (M == 0) & (M-1 == 0)
+        M = np.ma.masked_array(M, mask=cond)
+        output = (-n * (M-n)/(M-1) *
+                  np.einsum("...i,...j->...ij", m, m) / (M**2))
+        # check for empty arrays
+        if m.size != 0:
+            M, n = M[..., 0, 0], n[..., 0, 0]
+            cond = cond[..., 0, 0]
+        dim = m.shape[-1]
+        # diagonal entries need to be computed differently
+        for i in range(dim):
+            output[..., i, i] = (n * (M-n) * m[..., i]*(M-m[..., i]))
+            output[..., i, i] = output[..., i, i] / (M-1)
+            output[..., i, i] = output[..., i, i] / (M**2)
+        if m.size != 0:
+            mncond = (mncond[..., np.newaxis, np.newaxis] |
+                      np.zeros(output.shape, dtype=np.bool_))
+        return self._checkresult(output, mncond, np.nan)
+
+    def rvs(self, m, n, size=None, random_state=None):
+        """Draw random samples from a multivariate hypergeometric distribution.
+
+        Parameters
+        ----------
+        %(_doc_default_callparams)s
+        size : int or iterable of integers, optional
+            Number of samples to draw. Default is ``None``, in which case a
+            single variate is returned as an array with shape ``m.shape``.
+        %(_doc_random_state)s
+
+        Returns
+        -------
+        rvs : array_like
+            Random variates of shape ``size`` or ``m.shape``
+            (if ``size=None``).
+
+        Notes
+        -----
+        %(_doc_callparams_note)s
+
+        Also note that NumPy's `multivariate_hypergeometric` sampler is not
+        used as it doesn't support broadcasting.
+        """
+        M, m, n, _, _, _ = self._process_parameters(m, n)
+
+        random_state = self._get_random_state(random_state)
+
+        if size is not None and isinstance(size, int):
+            size = (size, )
+
+        if size is None:
+            rvs = np.empty(m.shape, dtype=m.dtype)
+        else:
+            rvs = np.empty(size + (m.shape[-1], ), dtype=m.dtype)
+        rem = M
+
+        # This sampler has been taken from numpy gh-13794
+        # https://github.com/numpy/numpy/pull/13794
+        for c in range(m.shape[-1] - 1):
+            rem = rem - m[..., c]
+            n0mask = n == 0
+            rvs[..., c] = (~n0mask *
+                           random_state.hypergeometric(m[..., c],
+                                                       rem + n0mask,
+                                                       n + n0mask,
+                                                       size=size))
+            n = n - rvs[..., c]
+        rvs[..., m.shape[-1] - 1] = n
+
+        return rvs
+
+
+multivariate_hypergeom = multivariate_hypergeom_gen()
+
+
+class multivariate_hypergeom_frozen(multi_rv_frozen):
+    def __init__(self, m, n, seed=None):
+        self._dist = multivariate_hypergeom_gen(seed)
+        (self.M, self.m, self.n,
+         self.mcond, self.ncond,
+         self.mncond) = self._dist._process_parameters(m, n)
+
+        # monkey patch self._dist
+        def _process_parameters(m, n):
+            return (self.M, self.m, self.n,
+                    self.mcond, self.ncond,
+                    self.mncond)
+        self._dist._process_parameters = _process_parameters
+
+    def logpmf(self, x):
+        return self._dist.logpmf(x, self.m, self.n)
+
+    def pmf(self, x):
+        return self._dist.pmf(x, self.m, self.n)
+
+    def mean(self):
+        return self._dist.mean(self.m, self.n)
+
+    def var(self):
+        return self._dist.var(self.m, self.n)
+
+    def cov(self):
+        return self._dist.cov(self.m, self.n)
+
+    def rvs(self, size=1, random_state=None):
+        return self._dist.rvs(self.m, self.n,
+                              size=size,
+                              random_state=random_state)
+
+
+# Set frozen generator docstrings from corresponding docstrings in
+# multivariate_hypergeom and fill in default strings in class docstrings
+for name in ['logpmf', 'pmf', 'mean', 'var', 'cov', 'rvs']:
+    method = multivariate_hypergeom_gen.__dict__[name]
+    method_frozen = multivariate_hypergeom_frozen.__dict__[name]
+    method_frozen.__doc__ = doccer.docformat(
+        method.__doc__, mhg_docdict_noparams)
+    method.__doc__ = doccer.docformat(method.__doc__,
+                                      mhg_docdict_params)
+
+
+class random_table_gen(multi_rv_generic):
+    r"""
+    Contingency tables from independent samples with fixed marginal sums.
+
+    This is the distribution of random tables with given row and column vector
+    sums. This distribution represents the set of random tables under the null
+    hypothesis that rows and columns are independent. It is used in hypothesis
+    tests of independence.
+
+    Because of assumed independence, the expected frequency of each table
+    element can be computed from the row and column sums, so that the
+    distribution is completely determined by these two vectors.
+
+    Parameters
+    ----------
+    %(_doc_row_col)s
+    %(_doc_random_state)s
+
+    Methods
+    -------
+    logpmf(x)
+        Log-probability of table `x` to occur in the distribution.
+    pmf(x)
+        Probability of table `x` to occur in the distribution.
+    mean(row, col)
+        Mean table.
+    rvs(row, col, size=None, method=None, random_state=None)
+        Draw random tables with given row and column vector sums.
+
+    Notes
+    -----
+    %(_doc_row_col_note)s
+
+    Random elements from the distribution are generated either with Boyett's
+    [1]_ or Patefield's algorithm [2]_. Boyett's algorithm has
+    O(N) time and space complexity, where N is the total sum of entries in the
+    table. Patefield's algorithm has O(K x log(N)) time complexity, where K is
+    the number of cells in the table and requires only a small constant work
+    space. By default, the `rvs` method selects the fastest algorithm based on
+    the input, but you can specify the algorithm with the keyword `method`.
+    Allowed values are "boyett" and "patefield".
+
+    .. versionadded:: 1.10.0
+
+    References
+    ----------
+    .. [1] J. Boyett, AS 144 Appl. Statist. 28 (1979) 329-332
+    .. [2] W.M. Patefield, AS 159 Appl. Statist. 30 (1981) 91-97
+
+    Examples
+    --------
+    >>> from scipy.stats import random_table
+
+    >>> row = [1, 5]
+    >>> col = [2, 3, 1]
+    >>> random_table.mean(row, col)
+    array([[0.33333333, 0.5       , 0.16666667],
+           [1.66666667, 2.5       , 0.83333333]])
+
+    Alternatively, the object may be called (as a function) to fix the row
+    and column vector sums, returning a "frozen" distribution.
+
+    >>> dist = random_table(row, col)
+    >>> dist.rvs(random_state=123)
+    array([[1, 0, 0],
+           [1, 3, 1]])
+    """
+
+    def __init__(self, seed=None):
+        super().__init__(seed)
+
+    def __call__(self, row, col, *, seed=None):
+        """Create a frozen distribution of tables with given marginals.
+
+        See `random_table_frozen` for more information.
+        """
+        return random_table_frozen(row, col, seed=seed)
+
+    def logpmf(self, x, row, col):
+        """Log-probability of table to occur in the distribution.
+
+        Parameters
+        ----------
+        %(_doc_x)s
+        %(_doc_row_col)s
+
+        Returns
+        -------
+        logpmf : ndarray or scalar
+            Log of the probability mass function evaluated at `x`.
+
+        Notes
+        -----
+        %(_doc_row_col_note)s
+
+        If row and column marginals of `x` do not match `row` and `col`,
+        negative infinity is returned.
+
+        Examples
+        --------
+        >>> from scipy.stats import random_table
+        >>> import numpy as np
+
+        >>> x = [[1, 5, 1], [2, 3, 1]]
+        >>> row = np.sum(x, axis=1)
+        >>> col = np.sum(x, axis=0)
+        >>> random_table.logpmf(x, row, col)
+        -1.6306401200847027
+
+        Alternatively, the object may be called (as a function) to fix the row
+        and column vector sums, returning a "frozen" distribution.
+
+        >>> d = random_table(row, col)
+        >>> d.logpmf(x)
+        -1.6306401200847027
+        """
+        r, c, n = self._process_parameters(row, col)
+        x = np.asarray(x)
+
+        if x.ndim < 2:
+            raise ValueError("`x` must be at least two-dimensional")
+
+        dtype_is_int = np.issubdtype(x.dtype, np.integer)
+        with np.errstate(invalid='ignore'):
+            if not dtype_is_int and not np.all(x.astype(int) == x):
+                raise ValueError("`x` must contain only integral values")
+
+        # x does not contain NaN if we arrive here
+        if np.any(x < 0):
+            raise ValueError("`x` must contain only non-negative values")
+
+        r2 = np.sum(x, axis=-1)
+        c2 = np.sum(x, axis=-2)
+
+        if r2.shape[-1] != len(r):
+            raise ValueError("shape of `x` must agree with `row`")
+
+        if c2.shape[-1] != len(c):
+            raise ValueError("shape of `x` must agree with `col`")
+
+        res = np.empty(x.shape[:-2])
+
+        mask = np.all(r2 == r, axis=-1) & np.all(c2 == c, axis=-1)
+
+        def lnfac(x):
+            return gammaln(x + 1)
+
+        res[mask] = (np.sum(lnfac(r), axis=-1) + np.sum(lnfac(c), axis=-1)
+                     - lnfac(n) - np.sum(lnfac(x[mask]), axis=(-1, -2)))
+        res[~mask] = -np.inf
+
+        return res[()]
+
+    def pmf(self, x, row, col):
+        """Probability of table to occur in the distribution.
+
+        Parameters
+        ----------
+        %(_doc_x)s
+        %(_doc_row_col)s
+
+        Returns
+        -------
+        pmf : ndarray or scalar
+            Probability mass function evaluated at `x`.
+
+        Notes
+        -----
+        %(_doc_row_col_note)s
+
+        If row and column marginals of `x` do not match `row` and `col`,
+        zero is returned.
+
+        Examples
+        --------
+        >>> from scipy.stats import random_table
+        >>> import numpy as np
+
+        >>> x = [[1, 5, 1], [2, 3, 1]]
+        >>> row = np.sum(x, axis=1)
+        >>> col = np.sum(x, axis=0)
+        >>> random_table.pmf(x, row, col)
+        0.19580419580419592
+
+        Alternatively, the object may be called (as a function) to fix the row
+        and column vector sums, returning a "frozen" distribution.
+
+        >>> d = random_table(row, col)
+        >>> d.pmf(x)
+        0.19580419580419592
+        """
+        return np.exp(self.logpmf(x, row, col))
+
+    def mean(self, row, col):
+        """Mean of distribution of conditional tables.
+        %(_doc_mean_params)s
+
+        Returns
+        -------
+        mean: ndarray
+            Mean of the distribution.
+
+        Notes
+        -----
+        %(_doc_row_col_note)s
+
+        Examples
+        --------
+        >>> from scipy.stats import random_table
+
+        >>> row = [1, 5]
+        >>> col = [2, 3, 1]
+        >>> random_table.mean(row, col)
+        array([[0.33333333, 0.5       , 0.16666667],
+               [1.66666667, 2.5       , 0.83333333]])
+
+        Alternatively, the object may be called (as a function) to fix the row
+        and column vector sums, returning a "frozen" distribution.
+
+        >>> d = random_table(row, col)
+        >>> d.mean()
+        array([[0.33333333, 0.5       , 0.16666667],
+               [1.66666667, 2.5       , 0.83333333]])
+        """
+        r, c, n = self._process_parameters(row, col)
+        return np.outer(r, c) / n
+
+    def rvs(self, row, col, *, size=None, method=None, random_state=None):
+        """Draw random tables with fixed column and row marginals.
+
+        Parameters
+        ----------
+        %(_doc_row_col)s
+        size : int, optional
+            Number of samples to draw (default 1).
+        method : str, optional
+            Which method to use, "boyett" or "patefield". If None (default),
+            selects the fastest method for this input.
+        %(_doc_random_state)s
+
+        Returns
+        -------
+        rvs : ndarray
+            Random 2D tables of shape (`size`, `len(row)`, `len(col)`).
+
+        Notes
+        -----
+        %(_doc_row_col_note)s
+
+        Examples
+        --------
+        >>> from scipy.stats import random_table
+
+        >>> row = [1, 5]
+        >>> col = [2, 3, 1]
+        >>> random_table.rvs(row, col, random_state=123)
+        array([[1., 0., 0.],
+               [1., 3., 1.]])
+
+        Alternatively, the object may be called (as a function) to fix the row
+        and column vector sums, returning a "frozen" distribution.
+
+        >>> d = random_table(row, col)
+        >>> d.rvs(random_state=123)
+        array([[1., 0., 0.],
+               [1., 3., 1.]])
+        """
+        r, c, n = self._process_parameters(row, col)
+        size, shape = self._process_size_shape(size, r, c)
+
+        random_state = self._get_random_state(random_state)
+        meth = self._process_rvs_method(method, r, c, n)
+
+        return meth(r, c, n, size, random_state).reshape(shape)
+
+    @staticmethod
+    def _process_parameters(row, col):
+        """
+        Check that row and column vectors are one-dimensional, that they do
+        not contain negative or non-integer entries, and that the sums over
+        both vectors are equal.
+        """
+        r = np.array(row, dtype=np.int64, copy=True)
+        c = np.array(col, dtype=np.int64, copy=True)
+
+        if np.ndim(r) != 1:
+            raise ValueError("`row` must be one-dimensional")
+        if np.ndim(c) != 1:
+            raise ValueError("`col` must be one-dimensional")
+
+        if np.any(r < 0):
+            raise ValueError("each element of `row` must be non-negative")
+        if np.any(c < 0):
+            raise ValueError("each element of `col` must be non-negative")
+
+        n = np.sum(r)
+        if n != np.sum(c):
+            raise ValueError("sums over `row` and `col` must be equal")
+
+        if not np.all(r == np.asarray(row)):
+            raise ValueError("each element of `row` must be an integer")
+        if not np.all(c == np.asarray(col)):
+            raise ValueError("each element of `col` must be an integer")
+
+        return r, c, n
+
+    @staticmethod
+    def _process_size_shape(size, r, c):
+        """
+        Compute the number of samples to be drawn and the shape of the output
+        """
+        shape = (len(r), len(c))
+
+        if size is None:
+            return 1, shape
+
+        size = np.atleast_1d(size)
+        if not np.issubdtype(size.dtype, np.integer) or np.any(size < 0):
+            raise ValueError("`size` must be a non-negative integer or `None`")
+
+        return np.prod(size), tuple(size) + shape
+
+    @classmethod
+    def _process_rvs_method(cls, method, r, c, n):
+        known_methods = {
+            None: cls._rvs_select(r, c, n),
+            "boyett": cls._rvs_boyett,
+            "patefield": cls._rvs_patefield,
+        }
+        try:
+            return known_methods[method]
+        except KeyError:
+            raise ValueError(f"'{method}' not recognized, "
+                             f"must be one of {set(known_methods)}")
+
+    @classmethod
+    def _rvs_select(cls, r, c, n):
+        fac = 1.0  # benchmarks show that this value is about 1
+        k = len(r) * len(c)  # number of cells
+        # n + 1 guards against failure if n == 0
+        if n > fac * np.log(n + 1) * k:
+            return cls._rvs_patefield
+        return cls._rvs_boyett
+
+    @staticmethod
+    def _rvs_boyett(row, col, ntot, size, random_state):
+        return _rcont.rvs_rcont1(row, col, ntot, size, random_state)
+
+    @staticmethod
+    def _rvs_patefield(row, col, ntot, size, random_state):
+        return _rcont.rvs_rcont2(row, col, ntot, size, random_state)
+
+
+random_table = random_table_gen()
+
+
+class random_table_frozen(multi_rv_frozen):
+    __class_getitem__ = None  # pyrefly:ignore[bad-assignment]
+
+    def __init__(self, row, col, *, seed=None):
+        self._dist = random_table_gen(seed)
+        self._params = self._dist._process_parameters(row, col)
+
+        # monkey patch self._dist
+        def _process_parameters(r, c):
+            return self._params
+        self._dist._process_parameters = _process_parameters
+
+    def logpmf(self, x):
+        return self._dist.logpmf(x, None, None)
+
+    def pmf(self, x):
+        return self._dist.pmf(x, None, None)
+
+    def mean(self):
+        return self._dist.mean(None, None)
+
+    def rvs(self, size=None, method=None, random_state=None):
+        # optimisations are possible here
+        return self._dist.rvs(None, None, size=size, method=method,
+                              random_state=random_state)
+
+
+_ctab_doc_row_col = """\
+row : array_like
+    Sum of table entries in each row.
+col : array_like
+    Sum of table entries in each column."""
+
+_ctab_doc_x = """\
+x : array-like
+   Two-dimensional table of non-negative integers, or a
+   multi-dimensional array with the last two dimensions
+   corresponding with the tables."""
+
+_ctab_doc_row_col_note = """\
+The row and column vectors must be one-dimensional, not empty,
+and each sum up to the same value. They cannot contain negative
+or noninteger entries."""
+
+_ctab_doc_mean_params = f"""
+Parameters
+----------
+{_ctab_doc_row_col}"""
+
+_ctab_doc_row_col_note_frozen = """\
+See class definition for a detailed description of parameters."""
+
+_ctab_docdict = {
+    "_doc_random_state": _doc_random_state,
+    "_doc_row_col": _ctab_doc_row_col,
+    "_doc_x": _ctab_doc_x,
+    "_doc_mean_params": _ctab_doc_mean_params,
+    "_doc_row_col_note": _ctab_doc_row_col_note,
+}
+
+_ctab_docdict_frozen = _ctab_docdict.copy()
+_ctab_docdict_frozen.update({
+    "_doc_row_col": "",
+    "_doc_mean_params": "",
+    "_doc_row_col_note": _ctab_doc_row_col_note_frozen,
+})
+
+
+def _docfill(obj, docdict, template=None):
+    obj.__doc__ = doccer.docformat(template or obj.__doc__, docdict)
+
+
+# Set frozen generator docstrings from corresponding docstrings in
+# random_table and fill in default strings in class docstrings
+_docfill(random_table_gen, _ctab_docdict)
+for name in ['logpmf', 'pmf', 'mean', 'rvs']:
+    method = random_table_gen.__dict__[name]
+    method_frozen = random_table_frozen.__dict__[name]
+    _docfill(method_frozen, _ctab_docdict_frozen, method.__doc__)
+    _docfill(method, _ctab_docdict)
+
+
+class uniform_direction_gen(multi_rv_generic):
+    r"""
+    A vector-valued uniform direction.
+
+    Return a random direction (unit vector). The `dim` keyword specifies
+    the dimensionality of the space.
+
+    Parameters
+    ----------
+    dim : scalar
+        Dimension of directions.
+    seed : {None, int, `numpy.random.Generator`,
+            `numpy.random.RandomState`}, optional
+
+        Used for drawing random variates.
+        If `seed` is `None`, the `~np.random.RandomState` singleton is used.
+        If `seed` is an int, a new ``RandomState`` instance is used, seeded
+        with seed.
+        If `seed` is already a ``RandomState`` or ``Generator`` instance,
+        then that object is used.
+        Default is `None`.
+
+    Methods
+    -------
+    rvs(dim=None, size=1, random_state=None)
+        Draw random directions.
+
+    Notes
+    -----
+    This distribution generates unit vectors uniformly distributed on
+    the surface of a hypersphere. These can be interpreted as random
+    directions.
+    For example, if `dim` is 3, 3D vectors from the surface of :math:`S^2`
+    will be sampled.
+
+    References
+    ----------
+    .. [1] Marsaglia, G. (1972). "Choosing a Point from the Surface of a
+           Sphere". Annals of Mathematical Statistics. 43 (2): 645-646.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import uniform_direction
+    >>> x = uniform_direction.rvs(3)
+    >>> np.linalg.norm(x)
+    1.
+
+    This generates one random direction, a vector on the surface of
+    :math:`S^2`.
+
+    Alternatively, the object may be called (as a function) to return a frozen
+    distribution with fixed `dim` parameter. Here,
+    we create a `uniform_direction` with ``dim=3`` and draw 5 observations.
+    The samples are then arranged in an array of shape 5x3.
+
+    >>> rng = np.random.default_rng()
+    >>> uniform_sphere_dist = uniform_direction(3)
+    >>> unit_vectors = uniform_sphere_dist.rvs(5, random_state=rng)
+    >>> unit_vectors
+    array([[ 0.56688642, -0.1332634 , -0.81294566],
+           [-0.427126  , -0.74779278,  0.50830044],
+           [ 0.3793989 ,  0.92346629,  0.05715323],
+           [ 0.36428383, -0.92449076, -0.11231259],
+           [-0.27733285,  0.94410968, -0.17816678]])
+    """
+
+    def __init__(self, seed=None):
+        super().__init__(seed)
+        self.__doc__ = doccer.docformat(self.__doc__)
+
+    def __call__(self, dim=None, seed=None):
+        """Create a frozen n-dimensional uniform direction distribution.
+
+        See `uniform_direction` for more information.
+        """
+        return uniform_direction_frozen(dim, seed=seed)
+
+    def _process_parameters(self, dim):
+        """Dimension N must be specified; it cannot be inferred."""
+        if dim is None or not np.isscalar(dim) or dim < 1 or dim != int(dim):
+            raise ValueError("Dimension of vector must be specified, "
+                             "and must be an integer greater than 0.")
+
+        return int(dim)
+
+    def rvs(self, dim, size=None, random_state=None):
+        """Draw random samples from S(N-1).
+
+        Parameters
+        ----------
+        dim : int
+            Dimension of space (N).
+        size : int or tuple of ints, optional
+            Given a shape of, for example, (m,n,k), m*n*k samples are
+            generated, and packed in an m-by-n-by-k arrangement.
+            Because each sample is N-dimensional, the output shape
+            is (m,n,k,N). If no shape is specified, a single (N-D)
+            sample is returned.
+        random_state : {None, int, `numpy.random.Generator`,
+                        `numpy.random.RandomState`}, optional
+
+            Pseudorandom number generator state used to generate resamples.
+
+            If `random_state` is ``None`` (or `np.random`), the
+            `numpy.random.RandomState` singleton is used.
+            If `random_state` is an int, a new ``RandomState`` instance is
+            used, seeded with `random_state`.
+            If `random_state` is already a ``Generator`` or ``RandomState``
+            instance then that instance is used.
+
+        Returns
+        -------
+        rvs : ndarray
+            Random direction vectors
+
+        """
+        random_state = self._get_random_state(random_state)
+        if size is None:
+            size = np.array([], dtype=int)
+        size = np.atleast_1d(size)
+
+        dim = self._process_parameters(dim)
+
+        samples = _sample_uniform_direction(dim, size, random_state)
+        return samples
+
+
+uniform_direction = uniform_direction_gen()
+
+
+class uniform_direction_frozen(multi_rv_frozen):
+    def __init__(self, dim=None, seed=None):
+        """Create a frozen n-dimensional uniform direction distribution.
+
+        Parameters
+        ----------
+        dim : int
+            Dimension of matrices
+        seed : {None, int, `numpy.random.Generator`,
+                `numpy.random.RandomState`}, optional
+
+            If `seed` is None (or `np.random`), the `numpy.random.RandomState`
+            singleton is used.
+            If `seed` is an int, a new ``RandomState`` instance is used,
+            seeded with `seed`.
+            If `seed` is already a ``Generator`` or ``RandomState`` instance
+            then that instance is used.
+
+        Examples
+        --------
+        >>> from scipy.stats import uniform_direction
+        >>> x = uniform_direction(3)
+        >>> x.rvs()
+
+        """
+        self._dist = uniform_direction_gen(seed)
+        self.dim = self._dist._process_parameters(dim)
+
+    def rvs(self, size=None, random_state=None):
+        return self._dist.rvs(self.dim, size, random_state)
+
+
+def _sample_uniform_direction(dim, size, random_state):
+    """
+    Private method to generate uniform directions
+    Reference: Marsaglia, G. (1972). "Choosing a Point from the Surface of a
+               Sphere". Annals of Mathematical Statistics. 43 (2): 645-646.
+    """
+    samples_shape = np.append(size, dim)
+    samples = random_state.standard_normal(samples_shape)
+    samples /= np.linalg.norm(samples, axis=-1, keepdims=True)
+    return samples
+
+
+_dirichlet_mn_doc_default_callparams = """\
+alpha : array_like
+    The concentration parameters. The number of entries along the last axis
+    determines the dimensionality of the distribution. Each entry must be
+    strictly positive.
+n : int or array_like
+    The number of trials. Each element must be a non-negative integer.
+"""
+
+_dirichlet_mn_doc_frozen_callparams = ""
+
+_dirichlet_mn_doc_frozen_callparams_note = """\
+See class definition for a detailed description of parameters."""
+
+dirichlet_mn_docdict_params = {
+    '_dirichlet_mn_doc_default_callparams': _dirichlet_mn_doc_default_callparams,
+    '_doc_random_state': _doc_random_state
+}
+
+dirichlet_mn_docdict_noparams = {
+    '_dirichlet_mn_doc_default_callparams': _dirichlet_mn_doc_frozen_callparams,
+    '_doc_random_state': _doc_random_state
+}
+
+
+def _dirichlet_multinomial_check_parameters(alpha, n, x=None):
+
+    alpha = np.asarray(alpha)
+    n = np.asarray(n)
+
+    if x is not None:
+        # Ensure that `x` and `alpha` are arrays. If the shapes are
+        # incompatible, NumPy will raise an appropriate error.
+        try:
+            x, alpha = np.broadcast_arrays(x, alpha)
+        except ValueError as e:
+            msg = "`x` and `alpha` must be broadcastable."
+            raise ValueError(msg) from e
+
+        x_int = np.floor(x)
+        if np.any(x < 0) or np.any(x != x_int):
+            raise ValueError("`x` must contain only non-negative integers.")
+        x = x_int
+
+    if np.any(alpha <= 0):
+        raise ValueError("`alpha` must contain only positive values.")
+
+    n_int = np.floor(n)
+    if np.any(n < 0) or np.any(n != n_int):
+        raise ValueError("`n` must be a non-negative integer.")
+    n = n_int
+
+    sum_alpha = np.sum(alpha, axis=-1)
+    sum_alpha, n = np.broadcast_arrays(sum_alpha, n)
+
+    return (alpha, sum_alpha, n) if x is None else (alpha, sum_alpha, n, x)
+
+
+class dirichlet_multinomial_gen(multi_rv_generic):
+    r"""
+    A Dirichlet multinomial random variable.
+
+    The Dirichlet multinomial distribution is a compound probability
+    distribution: it is the multinomial distribution with number of trials
+    `n` and class probabilities ``p`` randomly sampled from a Dirichlet
+    distribution with concentration parameters ``alpha``.
+
+    Parameters
+    ----------
+    %(_dirichlet_mn_doc_default_callparams)s
+    %(_doc_random_state)s
+
+    Methods
+    -------
+    logpmf(x, alpha, n):
+        Log of the probability mass function.
+    pmf(x, alpha, n):
+        Probability mass function.
+    mean(alpha, n):
+        Mean of the Dirichlet multinomial distribution.
+    var(alpha, n):
+        Variance of the Dirichlet multinomial distribution.
+    cov(alpha, n):
+        The covariance of the Dirichlet multinomial distribution.
+
+    See Also
+    --------
+    scipy.stats.dirichlet : The dirichlet distribution.
+    scipy.stats.multinomial : The multinomial distribution.
+
+    References
+    ----------
+    .. [1] Dirichlet-multinomial distribution, Wikipedia,
+           https://www.wikipedia.org/wiki/Dirichlet-multinomial_distribution
+
+    Examples
+    --------
+    >>> from scipy.stats import dirichlet_multinomial
+
+    Get the PMF
+
+    >>> n = 6  # number of trials
+    >>> alpha = [3, 4, 5]  # concentration parameters
+    >>> x = [1, 2, 3]  # counts
+    >>> dirichlet_multinomial.pmf(x, alpha, n)
+    0.08484162895927604
+
+    If the sum of category counts does not equal the number of trials,
+    the probability mass is zero.
+
+    >>> dirichlet_multinomial.pmf(x, alpha, n=7)
+    0.0
+
+    Get the log of the PMF
+
+    >>> dirichlet_multinomial.logpmf(x, alpha, n)
+    -2.4669689491013327
+
+    Get the mean
+
+    >>> dirichlet_multinomial.mean(alpha, n)
+    array([1.5, 2. , 2.5])
+
+    Get the variance
+
+    >>> dirichlet_multinomial.var(alpha, n)
+    array([1.55769231, 1.84615385, 2.01923077])
+
+    Get the covariance
+
+    >>> dirichlet_multinomial.cov(alpha, n)
+    array([[ 1.55769231, -0.69230769, -0.86538462],
+           [-0.69230769,  1.84615385, -1.15384615],
+           [-0.86538462, -1.15384615,  2.01923077]])
+
+    Alternatively, the object may be called (as a function) to fix the
+    `alpha` and `n` parameters, returning a "frozen" Dirichlet multinomial
+    random variable.
+
+    >>> dm = dirichlet_multinomial(alpha, n)
+    >>> dm.pmf(x)
+    0.08484162895927579
+
+    All methods are fully vectorized. Each element of `x` and `alpha` is
+    a vector (along the last axis), each element of `n` is an
+    integer (scalar), and the result is computed element-wise.
+
+    >>> x = [[1, 2, 3], [4, 5, 6]]
+    >>> alpha = [[1, 2, 3], [4, 5, 6]]
+    >>> n = [6, 15]
+    >>> dirichlet_multinomial.pmf(x, alpha, n)
+    array([0.06493506, 0.02626937])
+
+    >>> dirichlet_multinomial.cov(alpha, n).shape  # both covariance matrices
+    (2, 3, 3)
+
+    Broadcasting according to standard NumPy conventions is supported. Here,
+    we have four sets of concentration parameters (each a two element vector)
+    for each of three numbers of trials (each a scalar).
+
+    >>> alpha = [[3, 4], [4, 5], [5, 6], [6, 7]]
+    >>> n = [[6], [7], [8]]
+    >>> dirichlet_multinomial.mean(alpha, n).shape
+    (3, 4, 2)
+    """
+    def __init__(self, seed=None):
+        super().__init__(seed)
+        self.__doc__ = doccer.docformat(self.__doc__,
+                                        dirichlet_mn_docdict_params)
+
+    def __call__(self, alpha, n, seed=None):
+        return dirichlet_multinomial_frozen(alpha, n, seed=seed)
+
+    def logpmf(self, x, alpha, n):
+        """The log of the probability mass function.
+
+        Parameters
+        ----------
+        x: ndarray
+            Category counts (non-negative integers). Must be broadcastable
+            with shape parameter ``alpha``. If multidimensional, the last axis
+            must correspond with the categories.
+        %(_dirichlet_mn_doc_default_callparams)s
+
+        Returns
+        -------
+        out: ndarray or scalar
+            Log of the probability mass function.
+
+        """
+
+        a, Sa, n, x = _dirichlet_multinomial_check_parameters(alpha, n, x)
+
+        out = np.asarray(loggamma(Sa) + loggamma(n + 1) - loggamma(n + Sa))
+        out += (loggamma(x + a) - (loggamma(a) + loggamma(x + 1))).sum(axis=-1)
+        np.place(out, n != x.sum(axis=-1), -np.inf)
+        return out[()]
+
+    def pmf(self, x, alpha, n):
+        """Probability mass function for a Dirichlet multinomial distribution.
+
+        Parameters
+        ----------
+        x: ndarray
+            Category counts (non-negative integers). Must be broadcastable
+            with shape parameter ``alpha``. If multidimensional, the last axis
+            must correspond with the categories.
+        %(_dirichlet_mn_doc_default_callparams)s
+
+        Returns
+        -------
+        out: ndarray or scalar
+            Probability mass function.
+
+        """
+        return np.exp(self.logpmf(x, alpha, n))
+
+    def mean(self, alpha, n):
+        """Mean of a Dirichlet multinomial distribution.
+
+        Parameters
+        ----------
+        %(_dirichlet_mn_doc_default_callparams)s
+
+        Returns
+        -------
+        out: ndarray
+            Mean of a Dirichlet multinomial distribution.
+
+        """
+        a, Sa, n = _dirichlet_multinomial_check_parameters(alpha, n)
+        n, Sa = n[..., np.newaxis], Sa[..., np.newaxis]
+        return n * a / Sa
+
+    def var(self, alpha, n):
+        """The variance of the Dirichlet multinomial distribution.
+
+        Parameters
+        ----------
+        %(_dirichlet_mn_doc_default_callparams)s
+
+        Returns
+        -------
+        out: array_like
+            The variances of the components of the distribution. This is
+            the diagonal of the covariance matrix of the distribution.
+
+        """
+        a, Sa, n = _dirichlet_multinomial_check_parameters(alpha, n)
+        n, Sa = n[..., np.newaxis], Sa[..., np.newaxis]
+        return n * a / Sa * (1 - a/Sa) * (n + Sa) / (1 + Sa)
+
+    def cov(self, alpha, n):
+        """Covariance matrix of a Dirichlet multinomial distribution.
+
+        Parameters
+        ----------
+        %(_dirichlet_mn_doc_default_callparams)s
+
+        Returns
+        -------
+        out : array_like
+            The covariance matrix of the distribution.
+
+        """
+        a, Sa, n = _dirichlet_multinomial_check_parameters(alpha, n)
+        var = dirichlet_multinomial.var(a, n)
+
+        n, Sa = n[..., np.newaxis, np.newaxis], Sa[..., np.newaxis, np.newaxis]
+        aiaj = a[..., :, np.newaxis] * a[..., np.newaxis, :]
+        cov = -n * aiaj / Sa ** 2 * (n + Sa) / (1 + Sa)
+
+        ii = np.arange(cov.shape[-1])
+        cov[..., ii, ii] = var
+        return cov
+
+
+dirichlet_multinomial = dirichlet_multinomial_gen()
+
+
+class dirichlet_multinomial_frozen(multi_rv_frozen):
+    def __init__(self, alpha, n, seed=None):
+        alpha, Sa, n = _dirichlet_multinomial_check_parameters(alpha, n)
+        self.alpha = alpha
+        self.n = n
+        self._dist = dirichlet_multinomial_gen(seed)
+
+    def logpmf(self, x):
+        return self._dist.logpmf(x, self.alpha, self.n)
+
+    def pmf(self, x):
+        return self._dist.pmf(x, self.alpha, self.n)
+
+    def mean(self):
+        return self._dist.mean(self.alpha, self.n)
+
+    def var(self):
+        return self._dist.var(self.alpha, self.n)
+
+    def cov(self):
+        return self._dist.cov(self.alpha, self.n)
+
+
+# Set frozen generator docstrings from corresponding docstrings in
+# dirichlet_multinomial and fill in default strings in class docstrings.
+for name in ['logpmf', 'pmf', 'mean', 'var', 'cov']:
+    method = dirichlet_multinomial_gen.__dict__[name]
+    method_frozen = dirichlet_multinomial_frozen.__dict__[name]
+    method_frozen.__doc__ = doccer.docformat(
+        method.__doc__, dirichlet_mn_docdict_noparams)
+    method.__doc__ = doccer.docformat(method.__doc__,
+                                      dirichlet_mn_docdict_params)
+
+
+class vonmises_fisher_gen(multi_rv_generic):
+    r"""
+    A von Mises-Fisher variable.
+
+    The `mu` keyword specifies the mean direction vector. The `kappa` keyword
+    specifies the concentration parameter.
+
+    Parameters
+    ----------
+    mu : array_like
+        Mean direction of the distribution. Must be a one-dimensional unit
+        vector of norm 1.
+    kappa : float
+        Concentration parameter. Must be positive.
+    seed : {None, int, np.random.RandomState, np.random.Generator}, optional
+        Used for drawing random variates.
+        If `seed` is `None`, the `~np.random.RandomState` singleton is used.
+        If `seed` is an int, a new ``RandomState`` instance is used, seeded
+        with seed.
+        If `seed` is already a ``RandomState`` or ``Generator`` instance,
+        then that object is used.
+        Default is `None`.
+
+    Methods
+    -------
+    pdf(x, mu=None, kappa=1)
+        Probability density function.
+    logpdf(x, mu=None, kappa=1)
+        Log of the probability density function.
+    rvs(mu=None, kappa=1, size=1, random_state=None)
+        Draw random samples from a von Mises-Fisher distribution.
+    entropy(mu=None, kappa=1)
+        Compute the differential entropy of the von Mises-Fisher distribution.
+    fit(data)
+        Fit a von Mises-Fisher distribution to data.
+
+    See Also
+    --------
+    scipy.stats.vonmises : Von-Mises Fisher distribution in 2D on a circle
+    uniform_direction : uniform distribution on the surface of a hypersphere
+
+    Notes
+    -----
+    The von Mises-Fisher distribution is a directional distribution on the
+    surface of the unit hypersphere. The probability density
+    function of a unit vector :math:`\mathbf{x}` is
+
+    .. math::
+
+        f(\mathbf{x}) = \frac{\kappa^{d/2-1}}{(2\pi)^{d/2}I_{d/2-1}(\kappa)}
+               \exp\left(\kappa \mathbf{\mu}^T\mathbf{x}\right),
+
+    where :math:`\mathbf{\mu}` is the mean direction, :math:`\kappa` the
+    concentration parameter, :math:`d` the dimension and :math:`I` the
+    modified Bessel function of the first kind. As :math:`\mu` represents
+    a direction, it must be a unit vector or in other words, a point
+    on the hypersphere: :math:`\mathbf{\mu}\in S^{d-1}`. :math:`\kappa` is a
+    concentration parameter, which means that it must be positive
+    (:math:`\kappa>0`) and that the distribution becomes more narrow with
+    increasing :math:`\kappa`. In that sense, the reciprocal value
+    :math:`1/\kappa` resembles the variance parameter of the normal
+    distribution.
+
+    The von Mises-Fisher distribution often serves as an analogue of the
+    normal distribution on the sphere. Intuitively, for unit vectors, a
+    useful distance measure is given by the angle :math:`\alpha` between
+    them. This is exactly what the scalar product
+    :math:`\mathbf{\mu}^T\mathbf{x}=\cos(\alpha)` in the
+    von Mises-Fisher probability density function describes: the angle
+    between the mean direction :math:`\mathbf{\mu}` and the vector
+    :math:`\mathbf{x}`. The larger the angle between them, the smaller the
+    probability to observe :math:`\mathbf{x}` for this particular mean
+    direction :math:`\mathbf{\mu}`.
+
+    In dimensions 2 and 3, specialized algorithms are used for fast sampling
+    [2]_, [3]_. For dimensions of 4 or higher the rejection sampling algorithm
+    described in [4]_ is utilized. This implementation is partially based on
+    the geomstats package [5]_, [6]_.
+
+    .. versionadded:: 1.11
+
+    References
+    ----------
+    .. [1] Von Mises-Fisher distribution, Wikipedia,
+           https://en.wikipedia.org/wiki/Von_Mises%E2%80%93Fisher_distribution
+    .. [2] Mardia, K., and Jupp, P. Directional statistics. Wiley, 2000.
+    .. [3] J. Wenzel. Numerically stable sampling of the von Mises Fisher
+           distribution on S2.
+           https://www.mitsuba-renderer.org/~wenzel/files/vmf.pdf
+    .. [4] Wood, A. Simulation of the von mises fisher distribution.
+           Communications in statistics-simulation and computation 23,
+           1 (1994), 157-164. :doi:`10.1080/03610919408813161`.
+    .. [5] geomstats, Github. MIT License. Accessed: 06.01.2023.
+           https://github.com/geomstats/geomstats
+    .. [6] Miolane, N. et al. Geomstats:  A Python Package for Riemannian
+           Geometry in Machine Learning. Journal of Machine Learning Research
+           21 (2020). http://jmlr.org/papers/v21/19-027.html
+
+    Examples
+    --------
+    **Visualization of the probability density**
+
+    Plot the probability density in three dimensions for increasing
+    concentration parameter. The density is calculated by the ``pdf``
+    method.
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.stats import vonmises_fisher
+    >>> from matplotlib.colors import Normalize
+    >>> n_grid = 100
+    >>> u = np.linspace(0, np.pi, n_grid)
+    >>> v = np.linspace(0, 2 * np.pi, n_grid)
+    >>> u_grid, v_grid = np.meshgrid(u, v)
+    >>> vertices = np.stack([np.cos(v_grid) * np.sin(u_grid),
+    ...                      np.sin(v_grid) * np.sin(u_grid),
+    ...                      np.cos(u_grid)],
+    ...                     axis=2)
+    >>> x = np.outer(np.cos(v), np.sin(u))
+    >>> y = np.outer(np.sin(v), np.sin(u))
+    >>> z = np.outer(np.ones_like(u), np.cos(u))
+    >>> def plot_vmf_density(ax, x, y, z, vertices, mu, kappa):
+    ...     vmf = vonmises_fisher(mu, kappa)
+    ...     pdf_values = vmf.pdf(vertices)
+    ...     pdfnorm = Normalize(vmin=pdf_values.min(), vmax=pdf_values.max())
+    ...     ax.plot_surface(x, y, z, rstride=1, cstride=1,
+    ...                     facecolors=plt.cm.viridis(pdfnorm(pdf_values)),
+    ...                     linewidth=0)
+    ...     ax.set_aspect('equal')
+    ...     ax.view_init(azim=-130, elev=0)
+    ...     ax.axis('off')
+    ...     ax.set_title(rf"$\kappa={kappa}$")
+    >>> fig, axes = plt.subplots(nrows=1, ncols=3, figsize=(9, 4),
+    ...                          subplot_kw={"projection": "3d"})
+    >>> left, middle, right = axes
+    >>> mu = np.array([-np.sqrt(0.5), -np.sqrt(0.5), 0])
+    >>> plot_vmf_density(left, x, y, z, vertices, mu, 5)
+    >>> plot_vmf_density(middle, x, y, z, vertices, mu, 20)
+    >>> plot_vmf_density(right, x, y, z, vertices, mu, 100)
+    >>> plt.subplots_adjust(top=1, bottom=0.0, left=0.0, right=1.0, wspace=0.)
+    >>> plt.show()
+
+    As we increase the concentration parameter, the points are getting more
+    clustered together around the mean direction.
+
+    **Sampling**
+
+    Draw 5 samples from the distribution using the ``rvs`` method resulting
+    in a 5x3 array.
+
+    >>> rng = np.random.default_rng()
+    >>> mu = np.array([0, 0, 1])
+    >>> samples = vonmises_fisher(mu, 20).rvs(5, random_state=rng)
+    >>> samples
+    array([[ 0.3884594 , -0.32482588,  0.86231516],
+           [ 0.00611366, -0.09878289,  0.99509023],
+           [-0.04154772, -0.01637135,  0.99900239],
+           [-0.14613735,  0.12553507,  0.98126695],
+           [-0.04429884, -0.23474054,  0.97104814]])
+
+    These samples are unit vectors on the sphere :math:`S^2`. To verify,
+    let us calculate their euclidean norms:
+
+    >>> np.linalg.norm(samples, axis=1)
+    array([1., 1., 1., 1., 1.])
+
+    Plot 20 observations drawn from the von Mises-Fisher distribution for
+    increasing concentration parameter :math:`\kappa`. The red dot highlights
+    the mean direction :math:`\mu`.
+
+    >>> def plot_vmf_samples(ax, x, y, z, mu, kappa):
+    ...     vmf = vonmises_fisher(mu, kappa)
+    ...     samples = vmf.rvs(20)
+    ...     ax.plot_surface(x, y, z, rstride=1, cstride=1, linewidth=0,
+    ...                     alpha=0.2)
+    ...     ax.scatter(samples[:, 0], samples[:, 1], samples[:, 2], c='k', s=5)
+    ...     ax.scatter(mu[0], mu[1], mu[2], c='r', s=30)
+    ...     ax.set_aspect('equal')
+    ...     ax.view_init(azim=-130, elev=0)
+    ...     ax.axis('off')
+    ...     ax.set_title(rf"$\kappa={kappa}$")
+    >>> mu = np.array([-np.sqrt(0.5), -np.sqrt(0.5), 0])
+    >>> fig, axes = plt.subplots(nrows=1, ncols=3,
+    ...                          subplot_kw={"projection": "3d"},
+    ...                          figsize=(9, 4))
+    >>> left, middle, right = axes
+    >>> plot_vmf_samples(left, x, y, z, mu, 5)
+    >>> plot_vmf_samples(middle, x, y, z, mu, 20)
+    >>> plot_vmf_samples(right, x, y, z, mu, 100)
+    >>> plt.subplots_adjust(top=1, bottom=0.0, left=0.0,
+    ...                     right=1.0, wspace=0.)
+    >>> plt.show()
+
+    The plots show that with increasing concentration :math:`\kappa` the
+    resulting samples are centered more closely around the mean direction.
+
+    **Fitting the distribution parameters**
+
+    The distribution can be fitted to data using the ``fit`` method returning
+    the estimated parameters. As a toy example let's fit the distribution to
+    samples drawn from a known von Mises-Fisher distribution.
+
+    >>> mu, kappa = np.array([0, 0, 1]), 20
+    >>> samples = vonmises_fisher(mu, kappa).rvs(1000, random_state=rng)
+    >>> mu_fit, kappa_fit = vonmises_fisher.fit(samples)
+    >>> mu_fit, kappa_fit
+    (array([0.01126519, 0.01044501, 0.99988199]), 19.306398751730995)
+
+    We see that the estimated parameters `mu_fit` and `kappa_fit` are
+    very close to the ground truth parameters.
+    """
+    def __init__(self, seed=None):
+        super().__init__(seed)
+
+    def __call__(self, mu=None, kappa=1, seed=None):
+        """Create a frozen von Mises-Fisher distribution.
+
+        See `vonmises_fisher_frozen` for more information.
+        """
+        return vonmises_fisher_frozen(mu, kappa, seed=seed)
+
+    def _process_parameters(self, mu, kappa):
+        """
+        Infer dimensionality from mu and ensure that mu is a one-dimensional
+        unit vector and kappa positive.
+        """
+        mu = np.asarray(mu)
+        if mu.ndim > 1:
+            raise ValueError("'mu' must have one-dimensional shape.")
+        if not np.allclose(np.linalg.norm(mu), 1.):
+            raise ValueError("'mu' must be a unit vector of norm 1.")
+        if not mu.size > 1:
+            raise ValueError("'mu' must have at least two entries.")
+        kappa_error_msg = "'kappa' must be a positive scalar."
+        if not np.isscalar(kappa) or kappa < 0:
+            raise ValueError(kappa_error_msg)
+        if float(kappa) == 0.:
+            raise ValueError("For 'kappa=0' the von Mises-Fisher distribution "
+                             "becomes the uniform distribution on the sphere "
+                             "surface. Consider using "
+                             "'scipy.stats.uniform_direction' instead.")
+        dim = mu.size
+
+        return dim, mu, kappa
+
+    def _check_data_vs_dist(self, x, dim):
+        if x.shape[-1] != dim:
+            raise ValueError("The dimensionality of the last axis of 'x' must "
+                             "match the dimensionality of the "
+                             "von Mises Fisher distribution.")
+        if not np.allclose(np.linalg.norm(x, axis=-1), 1.):
+            msg = "'x' must be unit vectors of norm 1 along last dimension."
+            raise ValueError(msg)
+
+    def _log_norm_factor(self, dim, kappa):
+        # normalization factor is given by
+        # c = kappa**(dim/2-1)/((2*pi)**(dim/2)*I[dim/2-1](kappa))
+        #   = kappa**(dim/2-1)*exp(-kappa) /
+        #     ((2*pi)**(dim/2)*I[dim/2-1](kappa)*exp(-kappa)
+        #   = kappa**(dim/2-1)*exp(-kappa) /
+        #     ((2*pi)**(dim/2)*ive[dim/2-1](kappa)
+        # Then the log is given by
+        # log c = 1/2*(dim -1)*log(kappa) - kappa - -1/2*dim*ln(2*pi) -
+        #         ive[dim/2-1](kappa)
+        halfdim = 0.5 * dim
+        return (0.5 * (dim - 2)*np.log(kappa) - halfdim * _LOG_2PI -
+                np.log(ive(halfdim - 1, kappa)) - kappa)
+
+    def _logpdf(self, x, dim, mu, kappa):
+        """Log of the von Mises-Fisher probability density function.
+
+        As this function does no argument checking, it should not be
+        called directly; use 'logpdf' instead.
+
+        """
+        x = np.asarray(x)
+        self._check_data_vs_dist(x, dim)
+        dotproducts = np.einsum('i,...i->...', mu, x)
+        return self._log_norm_factor(dim, kappa) + kappa * dotproducts
+
+    def logpdf(self, x, mu=None, kappa=1):
+        """Log of the von Mises-Fisher probability density function.
+
+        Parameters
+        ----------
+        x : array_like
+            Points at which to evaluate the log of the probability
+            density function. The last axis of `x` must correspond
+            to unit vectors of the same dimensionality as the distribution.
+        mu : array_like, default: None
+            Mean direction of the distribution. Must be a one-dimensional unit
+            vector of norm 1.
+        kappa : float, default: 1
+            Concentration parameter. Must be positive.
+
+        Returns
+        -------
+        logpdf : ndarray or scalar
+            Log of the probability density function evaluated at `x`.
+
+        """
+        dim, mu, kappa = self._process_parameters(mu, kappa)
+        return self._logpdf(x, dim, mu, kappa)
+
+    def pdf(self, x, mu=None, kappa=1):
+        """Von Mises-Fisher probability density function.
+
+        Parameters
+        ----------
+        x : array_like
+            Points at which to evaluate the probability
+            density function. The last axis of `x` must correspond
+            to unit vectors of the same dimensionality as the distribution.
+        mu : array_like
+            Mean direction of the distribution. Must be a one-dimensional unit
+            vector of norm 1.
+        kappa : float
+            Concentration parameter. Must be positive.
+
+        Returns
+        -------
+        pdf : ndarray or scalar
+            Probability density function evaluated at `x`.
+
+        """
+        dim, mu, kappa = self._process_parameters(mu, kappa)
+        return np.exp(self._logpdf(x, dim, mu, kappa))
+
+    def _rvs_2d(self, mu, kappa, size, random_state):
+        """
+        In 2D, the von Mises-Fisher distribution reduces to the
+        von Mises distribution which can be efficiently sampled by numpy.
+        This method is much faster than the general rejection
+        sampling based algorithm.
+
+        """
+        mean_angle = np.arctan2(mu[1], mu[0])
+        angle_samples = random_state.vonmises(mean_angle, kappa, size=size)
+        samples = np.stack([np.cos(angle_samples), np.sin(angle_samples)],
+                           axis=-1)
+        return samples
+
+    def _rvs_3d(self, kappa, size, random_state):
+        """
+        Generate samples from a von Mises-Fisher distribution
+        with mu = [1, 0, 0] and kappa. Samples then have to be
+        rotated towards the desired mean direction mu.
+        This method is much faster than the general rejection
+        sampling based algorithm.
+        Reference: https://www.mitsuba-renderer.org/~wenzel/files/vmf.pdf
+
+        """
+        if size is None:
+            sample_size = 1
+        else:
+            sample_size = size
+
+        # compute x coordinate acc. to equation from section 3.1
+        x = random_state.random(sample_size)
+        x = 1. + np.log(x + (1. - x) * np.exp(-2 * kappa))/kappa
+
+        # (y, z) are random 2D vectors that only have to be
+        # normalized accordingly. Then (x, y z) follow a VMF distribution
+        temp = np.sqrt(1. - np.square(x))
+        uniformcircle = _sample_uniform_direction(2, sample_size, random_state)
+        samples = np.stack([x, temp * uniformcircle[..., 0],
+                            temp * uniformcircle[..., 1]],
+                           axis=-1)
+        if size is None:
+            samples = np.squeeze(samples)
+        return samples
+
+    def _rejection_sampling(self, dim, kappa, size, random_state):
+        """
+        Generate samples from an n-dimensional von Mises-Fisher distribution
+        with mu = [1, 0, ..., 0] and kappa via rejection sampling.
+        Samples then have to be rotated towards the desired mean direction mu.
+        Reference: :doi:`10.1080/03610919408813161`.
+        """
+        dim_minus_one = dim - 1
+        # calculate number of requested samples
+        if size is not None:
+            if not np.iterable(size):
+                size = (size, )
+            n_samples = math.prod(size)
+        else:
+            n_samples = 1
+        # calculate envelope for rejection sampler (eq. 4)
+        sqrt = np.sqrt(4 * kappa ** 2. + dim_minus_one ** 2)
+        envelop_param = (-2 * kappa + sqrt) / dim_minus_one
+        if envelop_param == 0:
+            # the regular formula suffers from loss of precision for high
+            # kappa. This can only be detected by checking for 0 here.
+            # Workaround: expansion for sqrt variable
+            # https://www.wolframalpha.com/input?i=sqrt%284*x%5E2%2Bd%5E2%29
+            # e = (-2 * k + sqrt(k**2 + d**2)) / d
+            #   ~ (-2 * k + 2 * k + d**2/(4 * k) - d**4/(64 * k**3)) / d
+            #   = d/(4 * k) - d**3/(64 * k**3)
+            envelop_param = (dim_minus_one/4 * kappa**-1.
+                             - dim_minus_one**3/64 * kappa**-3.)
+        # reference step 0
+        node = (1. - envelop_param) / (1. + envelop_param)
+        # t = ln(1 - ((1-x)/(1+x))**2)
+        #   = ln(4 * x / (1+x)**2)
+        #   = ln(4) + ln(x) - 2*log1p(x)
+        correction = (kappa * node + dim_minus_one
+                      * (np.log(4) + np.log(envelop_param)
+                      - 2 * np.log1p(envelop_param)))
+        n_accepted = 0
+        x = np.zeros((n_samples, ))
+        halfdim = 0.5 * dim_minus_one
+        # main loop
+        while n_accepted < n_samples:
+            # generate candidates acc. to reference step 1
+            sym_beta = random_state.beta(halfdim, halfdim,
+                                         size=n_samples - n_accepted)
+            coord_x = (1 - (1 + envelop_param) * sym_beta) / (
+                1 - (1 - envelop_param) * sym_beta)
+            # accept or reject: reference step 2
+            # reformulation for numerical stability:
+            # t = ln(1 - (1-x)/(1+x) * y)
+            #   = ln((1 + x - y +x*y)/(1 +x))
+            accept_tol = random_state.random(n_samples - n_accepted)
+            criterion = (
+                kappa * coord_x
+                + dim_minus_one * (np.log((1 + envelop_param - coord_x
+                + coord_x * envelop_param) / (1 + envelop_param)))
+                - correction) > np.log(accept_tol)
+            accepted_iter = np.sum(criterion)
+            x[n_accepted:n_accepted + accepted_iter] = coord_x[criterion]
+            n_accepted += accepted_iter
+        # concatenate x and remaining coordinates: step 3
+        coord_rest = _sample_uniform_direction(dim_minus_one, n_accepted,
+                                               random_state)
+        coord_rest = np.einsum(
+            '...,...i->...i', np.sqrt(1 - x ** 2), coord_rest)
+        samples = np.concatenate([x[..., None], coord_rest], axis=1)
+        # reshape output to (size, dim)
+        if size is not None:
+            samples = samples.reshape(size + (dim, ))
+        else:
+            samples = np.squeeze(samples)
+        return samples
+
+    def _rotate_samples(self, samples, mu, dim):
+        """A QR decomposition is used to find the rotation that maps the
+        north pole (1, 0,...,0) to the vector mu. This rotation is then
+        applied to all samples.
+
+        Parameters
+        ----------
+        samples: array_like, shape = [..., n]
+        mu : array-like, shape=[n, ]
+            Point to parametrise the rotation.
+
+        Returns
+        -------
+        samples : rotated samples
+
+        """
+        base_point = np.zeros((dim, ))
+        base_point[0] = 1.
+        embedded = np.concatenate([mu[None, :], np.zeros((dim - 1, dim))])
+        rotmatrix, _ = np.linalg.qr(np.transpose(embedded))
+        if np.allclose(np.matmul(rotmatrix, base_point[:, None])[:, 0], mu):
+            rotsign = 1
+        else:
+            rotsign = -1
+
+        # apply rotation
+        samples = np.einsum('ij,...j->...i', rotmatrix, samples) * rotsign
+        return samples
+
+    def _rvs(self, dim, mu, kappa, size, random_state):
+        if dim == 2:
+            samples = self._rvs_2d(mu, kappa, size, random_state)
+        elif dim == 3:
+            samples = self._rvs_3d(kappa, size, random_state)
+        else:
+            samples = self._rejection_sampling(dim, kappa, size,
+                                               random_state)
+
+        if dim != 2:
+            samples = self._rotate_samples(samples, mu, dim)
+        return samples
+
+    def rvs(self, mu=None, kappa=1, size=1, random_state=None):
+        """Draw random samples from a von Mises-Fisher distribution.
+
+        Parameters
+        ----------
+        mu : array_like
+            Mean direction of the distribution. Must be a one-dimensional unit
+            vector of norm 1.
+        kappa : float
+            Concentration parameter. Must be positive.
+        size : int or tuple of ints, optional
+            Given a shape of, for example, (m,n,k), m*n*k samples are
+            generated, and packed in an m-by-n-by-k arrangement.
+            Because each sample is N-dimensional, the output shape
+            is (m,n,k,N). If no shape is specified, a single (N-D)
+            sample is returned.
+        random_state : {None, int, np.random.RandomState, np.random.Generator},
+                        optional
+            Used for drawing random variates.
+            If `seed` is `None`, the `~np.random.RandomState` singleton is used.
+            If `seed` is an int, a new ``RandomState`` instance is used, seeded
+            with seed.
+            If `seed` is already a ``RandomState`` or ``Generator`` instance,
+            then that object is used.
+            Default is `None`.
+
+        Returns
+        -------
+        rvs : ndarray
+            Random variates of shape (`size`, `N`), where `N` is the
+            dimension of the distribution.
+
+        """
+        dim, mu, kappa = self._process_parameters(mu, kappa)
+        random_state = self._get_random_state(random_state)
+        samples = self._rvs(dim, mu, kappa, size, random_state)
+        return samples
+
+    def _entropy(self, dim, kappa):
+        halfdim = 0.5 * dim
+        return (-self._log_norm_factor(dim, kappa) - kappa *
+                ive(halfdim, kappa) / ive(halfdim - 1, kappa))
+
+    def entropy(self, mu=None, kappa=1):
+        """Compute the differential entropy of the von Mises-Fisher
+        distribution.
+
+        Parameters
+        ----------
+        mu : array_like, default: None
+            Mean direction of the distribution. Must be a one-dimensional unit
+            vector of norm 1.
+        kappa : float, default: 1
+            Concentration parameter. Must be positive.
+
+        Returns
+        -------
+        h : scalar
+            Entropy of the von Mises-Fisher distribution.
+
+        """
+        dim, _, kappa = self._process_parameters(mu, kappa)
+        return self._entropy(dim, kappa)
+
+    def fit(self, x):
+        """Fit the von Mises-Fisher distribution to data.
+
+        Parameters
+        ----------
+        x : array-like
+            Data the distribution is fitted to. Must be two dimensional.
+            The second axis of `x` must be unit vectors of norm 1 and
+            determine the dimensionality of the fitted
+            von Mises-Fisher distribution.
+
+        Returns
+        -------
+        mu : ndarray
+            Estimated mean direction.
+        kappa : float
+            Estimated concentration parameter.
+
+        """
+        # validate input data
+        x = np.asarray(x)
+        if x.ndim != 2:
+            raise ValueError("'x' must be two dimensional.")
+        if not np.allclose(np.linalg.norm(x, axis=-1), 1.):
+            msg = "'x' must be unit vectors of norm 1 along last dimension."
+            raise ValueError(msg)
+        dim = x.shape[-1]
+
+        # mu is simply the directional mean
+        dirstats = directional_stats(x)
+        mu = dirstats.mean_direction
+        r = dirstats.mean_resultant_length
+
+        # kappa is the solution to the equation:
+        # r = I[dim/2](kappa) / I[dim/2 -1](kappa)
+        #   = I[dim/2](kappa) * exp(-kappa) / I[dim/2 -1](kappa) * exp(-kappa)
+        #   = ive(dim/2, kappa) / ive(dim/2 -1, kappa)
+
+        halfdim = 0.5 * dim
+
+        def solve_for_kappa(kappa):
+            bessel_vals = ive([halfdim, halfdim - 1], kappa)
+            return bessel_vals[0]/bessel_vals[1] - r
+
+        root_res = root_scalar(solve_for_kappa, method="brentq",
+                               bracket=(1e-8, 1e9))
+        kappa = root_res.root
+        return mu, kappa
+
+
+vonmises_fisher = vonmises_fisher_gen()
+
+
+class vonmises_fisher_frozen(multi_rv_frozen):
+    def __init__(self, mu=None, kappa=1, seed=None):
+        """Create a frozen von Mises-Fisher distribution.
+
+        Parameters
+        ----------
+        mu : array_like, default: None
+            Mean direction of the distribution.
+        kappa : float, default: 1
+            Concentration parameter. Must be positive.
+        seed : {None, int, `numpy.random.Generator`,
+                `numpy.random.RandomState`}, optional
+            If `seed` is None (or `np.random`), the `numpy.random.RandomState`
+            singleton is used.
+            If `seed` is an int, a new ``RandomState`` instance is used,
+            seeded with `seed`.
+            If `seed` is already a ``Generator`` or ``RandomState`` instance
+            then that instance is used.
+
+        """
+        self._dist = vonmises_fisher_gen(seed)
+        self.dim, self.mu, self.kappa = (
+            self._dist._process_parameters(mu, kappa)
+        )
+
+    def logpdf(self, x):
+        """
+        Parameters
+        ----------
+        x : array_like
+            Points at which to evaluate the log of the probability
+            density function. The last axis of `x` must correspond
+            to unit vectors of the same dimensionality as the distribution.
+
+        Returns
+        -------
+        logpdf : ndarray or scalar
+            Log of probability density function evaluated at `x`.
+
+        """
+        return self._dist._logpdf(x, self.dim, self.mu, self.kappa)
+
+    def pdf(self, x):
+        """
+        Parameters
+        ----------
+        x : array_like
+            Points at which to evaluate the log of the probability
+            density function. The last axis of `x` must correspond
+            to unit vectors of the same dimensionality as the distribution.
+
+        Returns
+        -------
+        pdf : ndarray or scalar
+            Probability density function evaluated at `x`.
+
+        """
+        return np.exp(self.logpdf(x))
+
+    def rvs(self, size=1, random_state=None):
+        """Draw random variates from the Von Mises-Fisher distribution.
+
+        Parameters
+        ----------
+        size : int or tuple of ints, optional
+            Given a shape of, for example, (m,n,k), m*n*k samples are
+            generated, and packed in an m-by-n-by-k arrangement.
+            Because each sample is N-dimensional, the output shape
+            is (m,n,k,N). If no shape is specified, a single (N-D)
+            sample is returned.
+        random_state : {None, int, `numpy.random.Generator`,
+                        `numpy.random.RandomState`}, optional
+            If `seed` is None (or `np.random`), the `numpy.random.RandomState`
+            singleton is used.
+            If `seed` is an int, a new ``RandomState`` instance is used,
+            seeded with `seed`.
+            If `seed` is already a ``Generator`` or ``RandomState`` instance
+            then that instance is used.
+
+        Returns
+        -------
+        rvs : ndarray or scalar
+            Random variates of size (`size`, `N`), where `N` is the
+            dimension of the distribution.
+
+        """
+        random_state = self._dist._get_random_state(random_state)
+        return self._dist._rvs(self.dim, self.mu, self.kappa, size,
+                               random_state)
+
+    def entropy(self):
+        """
+        Calculate the differential entropy of the von Mises-Fisher
+        distribution.
+
+        Returns
+        -------
+        h: float
+            Entropy of the Von Mises-Fisher distribution.
+
+        """
+        return self._dist._entropy(self.dim, self.kappa)
+
+
+class normal_inverse_gamma_gen(multi_rv_generic):
+    r"""
+    Normal-inverse-gamma distribution.
+
+    The normal-inverse-gamma distribution is the conjugate prior of a normal
+    distribution with unknown mean and variance.
+
+    Parameters
+    ----------
+    mu, lmbda, a, b : array_like
+        Shape parameters of the distribution. See notes.
+    seed : {None, int, np.random.RandomState, np.random.Generator}, optional
+        Used for drawing random variates.
+        If `seed` is `None`, the `~np.random.RandomState` singleton is used.
+        If `seed` is an int, a new ``RandomState`` instance is used, seeded
+        with seed.
+        If `seed` is already a ``RandomState`` or ``Generator`` instance,
+        then that object is used.
+        Default is `None`.
+
+    Methods
+    -------
+    pdf(x, s2, mu=0, lmbda=1, a=1, b=1)
+        Probability density function.
+    logpdf(x, s2, mu=0, lmbda=1, a=1, b=1)
+        Log of the probability density function.
+    mean(mu=0, lmbda=1, a=1, b=1)
+        Distribution mean.
+    var(mu=0, lmbda=1, a=1, b=1)
+        Distribution variance.
+    rvs(mu=0, lmbda=1, a=1, b=1, size=None, random_state=None)
+        Draw random samples.
+
+    See Also
+    --------
+    norm
+    invgamma
+
+    Notes
+    -----
+
+    The probability density function of `normal_inverse_gamma` is:
+
+    .. math::
+
+        f(x, \sigma^2; \mu, \lambda, \alpha, \beta) =
+            \frac{\sqrt{\lambda}}{\sqrt{2 \pi \sigma^2}}
+            \frac{\beta^\alpha}{\Gamma(\alpha)}
+            \left( \frac{1}{\sigma^2} \right)^{\alpha + 1}
+            \exp \left(- \frac{2 \beta + \lambda (x - \mu)^2} {2 \sigma^2} \right)
+
+    where all parameters are real and finite, and :math:`\sigma^2 > 0`,
+    :math:`\lambda > 0`, :math:`\alpha > 0`, and :math:`\beta > 0`.
+
+    Methods ``normal_inverse_gamma.pdf`` and ``normal_inverse_gamma.logpdf``
+    accept `x` and `s2` for arguments :math:`x` and :math:`\sigma^2`.
+    All methods accept `mu`, `lmbda`, `a`, and `b` for shape parameters
+    :math:`\mu`, :math:`\lambda`, :math:`\alpha`, and :math:`\beta`,
+    respectively.
+
+    .. versionadded:: 1.15
+
+    References
+    ----------
+    .. [1] Normal-inverse-gamma distribution, Wikipedia,
+           https://en.wikipedia.org/wiki/Normal-inverse-gamma_distribution
+
+    Examples
+    --------
+    Suppose we wish to investigate the relationship between the
+    normal-inverse-gamma distribution and the inverse gamma distribution.
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> import matplotlib.pyplot as plt
+    >>> rng = np.random.default_rng(527484872345)
+    >>> mu, lmbda, a, b = 0, 1, 20, 20
+    >>> norm_inv_gamma = stats.normal_inverse_gamma(mu, lmbda, a, b)
+    >>> inv_gamma = stats.invgamma(a, scale=b)
+
+    One approach is to compare the distribution of the `s2` elements of
+    random variates against the PDF of an inverse gamma distribution.
+
+    >>> _, s2 = norm_inv_gamma.rvs(size=10000, random_state=rng)
+    >>> bins = np.linspace(s2.min(), s2.max(), 50)
+    >>> plt.hist(s2, bins=bins, density=True, label='Frequency density')
+    >>> s2 = np.linspace(s2.min(), s2.max(), 300)
+    >>> plt.plot(s2, inv_gamma.pdf(s2), label='PDF')
+    >>> plt.xlabel(r'$\sigma^2$')
+    >>> plt.ylabel('Frequency density / PMF')
+    >>> plt.show()
+
+    Similarly, we can compare the marginal distribution of `s2` against
+    an inverse gamma distribution.
+
+    >>> from scipy.integrate import quad_vec
+    >>> from scipy import integrate
+    >>> s2 = np.linspace(0.5, 3, 6)
+    >>> res = quad_vec(lambda x: norm_inv_gamma.pdf(x, s2), -np.inf, np.inf)[0]
+    >>> np.allclose(res, inv_gamma.pdf(s2))
+    True
+
+    The sample mean is comparable to the mean of the distribution.
+
+    >>> x, s2 = norm_inv_gamma.rvs(size=10000, random_state=rng)
+    >>> x.mean(), s2.mean()
+    (np.float64(-0.005254750127304425), np.float64(1.050438111436508))
+    >>> norm_inv_gamma.mean()
+    (np.float64(0.0), np.float64(1.0526315789473684))
+
+    Similarly, for the variance:
+
+    >>> x.var(ddof=1), s2.var(ddof=1)
+    (np.float64(1.0546150578185023), np.float64(0.061829865266330754))
+    >>> norm_inv_gamma.var()
+    (np.float64(1.0526315789473684), np.float64(0.061557402277623886))
+    """
+    def rvs(self, mu=0, lmbda=1, a=1, b=1, size=None, random_state=None):
+        """Draw random samples from the distribution.
+
+        Parameters
+        ----------
+        mu, lmbda, a, b : array_like, optional
+            Shape parameters. `lmbda`, `a`, and `b` must be greater
+            than zero.
+        size : int or tuple of ints, optional
+            Shape of samples to draw.
+        random_state : {None, int, np.random.RandomState, np.random.Generator}, optional
+            Used for drawing random variates.
+            If `random_state` is `None`, the `~np.random.RandomState` singleton is used.
+            If `random_state` is an int, a new ``RandomState`` instance is used, seeded
+            with `random_state`.
+            If `random_state` is already a ``RandomState`` or ``Generator`` instance,
+            then that object is used.
+            Default is `None`.
+
+        Returns
+        -------
+        x, s2 : ndarray
+            Random variates.
+
+        """
+        random_state = self._get_random_state(random_state)
+        s2 = invgamma(a, scale=b).rvs(size=size, random_state=random_state)
+        scale = (s2 / lmbda)**0.5
+        x = norm(loc=mu, scale=scale).rvs(size=size, random_state=random_state)
+        dtype = np.result_type(1.0, mu, lmbda, a, b)
+        return x.astype(dtype), s2.astype(dtype)
+
+    def _logpdf(self, x, s2, mu, lmbda, a, b):
+        t1 = 0.5 * (np.log(lmbda) - np.log(2 * np.pi * s2))
+        t2 = a*np.log(b) - special.gammaln(a).astype(a.dtype)
+        t3 = -(a + 1) * np.log(s2)
+        t4 = -(2*b + lmbda*(x - mu)**2) / (2*s2)
+        return t1 + t2 + t3 + t4
+
+    def logpdf(self, x, s2, mu=0, lmbda=1, a=1, b=1):
+        """Log of the probability density function.
+
+        Parameters
+        ----------
+        x, s2 : array_like
+            Arguments. `s2` must be greater than zero.
+        mu, lmbda, a, b : array_like, optional
+            Shape parameters. `lmbda`, `a`, and `b` must be greater
+            than zero.
+
+        Returns
+        -------
+        logpdf : ndarray or scalar
+            Log of the probability density function.
+
+        """
+        invalid, args = self._process_parameters_pdf(x, s2, mu, lmbda, a, b)
+        s2 = args[1]
+        # Keep it simple for now; lazyselect later, perhaps.
+        with np.errstate(all='ignore'):
+            logpdf = np.asarray(self._logpdf(*args))
+        logpdf[s2 <= 0] = -np.inf
+        logpdf[invalid] = np.nan
+        return logpdf[()]
+
+    def _pdf(self, x, s2, mu, lmbda, a, b):
+        t1 = np.sqrt(lmbda / (2 * np.pi * s2))
+        t2 = b**a / special.gamma(a).astype(a.dtype)
+        t3 = (1 / s2)**(a + 1)
+        t4 = np.exp(-(2*b + lmbda*(x - mu)**2) / (2*s2))
+        return t1 * t2 * t3 * t4
+
+    def pdf(self, x, s2, mu=0, lmbda=1, a=1, b=1):
+        """The probability density function.
+
+        Parameters
+        ----------
+        x, s2 : array_like
+            Arguments. `s2` must be greater than zero.
+        mu, lmbda, a, b : array_like, optional
+            Shape parameters. `lmbda`, `a`, and `b` must be greater
+            than zero.
+
+        Returns
+        -------
+        logpdf : ndarray or scalar
+            The probability density function.
+
+        """
+        invalid, args = self._process_parameters_pdf(x, s2, mu, lmbda, a, b)
+        s2 = args[1]
+        # Keep it simple for now; lazyselect later, perhaps.
+        with np.errstate(all='ignore'):
+            pdf = np.asarray(self._pdf(*args))
+        pdf[s2 <= 0] = 0
+        pdf[invalid] = np.nan
+        return pdf[()]
+
+    def mean(self, mu=0, lmbda=1, a=1, b=1):
+        """The mean of the distribution.
+
+        Parameters
+        ----------
+        mu, lmbda, a, b : array_like, optional
+            Shape parameters. `lmbda` and `b` must be greater
+            than zero, and `a` must be greater than one.
+
+        Returns
+        -------
+        x, s2 : ndarray
+            The mean of the distribution.
+
+        """
+        invalid, args = self._process_shapes(mu, lmbda, a, b)
+        mu, lmbda, a, b = args
+        invalid |= ~(a > 1)
+        mean_x = np.asarray(mu).copy()
+        mean_s2 = np.asarray(b / (a - 1))
+        mean_x[invalid] = np.nan
+        mean_s2[invalid] = np.nan
+        return mean_x[()], mean_s2[()]
+
+    def var(self, mu=0, lmbda=1, a=1, b=1):
+        """The variance of the distribution.
+
+        Parameters
+        ----------
+        mu, lmbda, a, b : array_like, optional
+            Shape parameters. `lmbda` and `b` must be greater
+            than zero, and `a` must be greater than two.
+
+        Returns
+        -------
+        x, s2 : ndarray
+            The variance of the distribution.
+
+        """
+        invalid, args = self._process_shapes(mu, lmbda, a, b)
+        mu, lmbda, a, b = args
+        invalid_x = invalid | ~(a > 1)
+        invalid_s2 = invalid | ~(a > 2)
+        var_x = b / ((a - 1) * lmbda)
+        var_s2 = b**2 / ((a - 1)**2 * (a - 2))
+        var_x, var_s2 = np.asarray(var_x), np.asarray(var_s2)
+        var_x[invalid_x] = np.nan
+        var_s2[invalid_s2] = np.nan
+        return var_x[()], var_s2[()]
+
+    def _process_parameters_pdf(self, x, s2, mu, lmbda, a, b):
+        args = np.broadcast_arrays(x, s2, mu, lmbda, a, b)
+        dtype = np.result_type(1.0, *(arg.dtype for arg in args))
+        args = [arg.astype(dtype, copy=False) for arg in args]
+        x, s2, mu, lmbda, a, b = args
+        invalid = ~((lmbda > 0) & (a > 0) & (b > 0))
+        return invalid, args
+
+    def _process_shapes(self, mu, lmbda, a, b):
+        args = np.broadcast_arrays(mu, lmbda, a, b)
+        dtype = np.result_type(1.0, *(arg.dtype for arg in args))
+        args = [arg.astype(dtype, copy=False) for arg in args]
+        mu, lmbda, a, b = args
+        invalid = ~((lmbda > 0) & (a > 0) & (b > 0))
+        return invalid, args
+
+    def __call__(self, mu=0, lmbda=1, a=1, b=1, seed=None):
+        return normal_inverse_gamma_frozen(mu, lmbda, a, b, seed=seed)
+
+
+normal_inverse_gamma = normal_inverse_gamma_gen()
+
+
+class normal_inverse_gamma_frozen(multi_rv_frozen):
+
+    def __init__(self, mu=0, lmbda=1, a=1, b=1, seed=None):
+        self._dist = normal_inverse_gamma_gen(seed)
+        self._shapes = mu, lmbda, a, b
+
+    def logpdf(self, x, s2):
+        return self._dist.logpdf(x, s2, *self._shapes)
+
+    def pdf(self, x, s2):
+        return self._dist.pdf(x, s2, *self._shapes)
+
+    def mean(self):
+        return self._dist.mean(*self._shapes)
+
+    def var(self):
+        return self._dist.var(*self._shapes)
+
+    def rvs(self, size=None, random_state=None):
+        return self._dist.rvs(*self._shapes, size=size, random_state=random_state)
+
+
+# Set frozen generator docstrings from corresponding docstrings in
+# normal_inverse_gamma_gen and fill in default strings in class docstrings
+for name in ['logpdf', 'pdf', 'mean', 'var', 'rvs']:
+    method = normal_inverse_gamma_gen.__dict__[name]
+    method_frozen = normal_inverse_gamma_frozen.__dict__[name]
+    method_frozen.__doc__ = doccer.docformat(method.__doc__,
+                                             mvn_docdict_noparams)
+    method.__doc__ = doccer.docformat(method.__doc__, mvn_docdict_params)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_new_distributions.py b/venv/lib/python3.12/site-packages/scipy/stats/_new_distributions.py
new file mode 100644
index 0000000000000000000000000000000000000000..8393e7718b7300cc4aed4f620f31c8d44c0848ce
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_new_distributions.py
@@ -0,0 +1,551 @@
+import sys
+
+import numpy as np
+from numpy import inf
+
+from scipy._external import array_api_extra as xpx
+from scipy import special
+from scipy.special import _ufuncs as scu
+from scipy.stats._distribution_infrastructure import (
+    ContinuousDistribution, DiscreteDistribution, _RealInterval, _IntegerInterval,
+    _RealParameter, _Parameterization, _combine_docs)
+
+__all__ = ['Normal', 'Logistic', 'Uniform', 'Binomial']
+
+
+class Normal(ContinuousDistribution):
+    r"""Normal distribution with prescribed mean and standard deviation.
+
+    The probability density function of the normal distribution is:
+
+    .. math::
+
+        f(x) = \frac{1}{\sigma \sqrt{2 \pi}} \exp {
+            \left( -\frac{1}{2}\left( \frac{x - \mu}{\sigma} \right)^2 \right)}
+
+    """
+    # `ShiftedScaledDistribution` allows this to be generated automatically from
+    # an instance of `StandardNormal`, but the normal distribution is so frequently
+    # used that it's worth a bit of code duplication to get better performance.
+    _mu_domain = _RealInterval(endpoints=(-inf, inf))
+    _sigma_domain = _RealInterval(endpoints=(0, inf))
+    _x_support = _RealInterval(endpoints=(-inf, inf))
+
+    _mu_param = _RealParameter('mu',  symbol=r'\mu', domain=_mu_domain,
+                               typical=(-1, 1))
+    _sigma_param = _RealParameter('sigma', symbol=r'\sigma', domain=_sigma_domain,
+                                  typical=(0.5, 1.5))
+    _x_param = _RealParameter('x', domain=_x_support, typical=(-1, 1))
+
+    _parameterizations = [_Parameterization(_mu_param, _sigma_param)]
+
+    _variable = _x_param
+    _normalization = 1/np.sqrt(2*np.pi)
+    _log_normalization = np.log(2*np.pi)/2
+
+    def __new__(cls, mu=None, sigma=None, **kwargs):
+        if mu is None and sigma is None:
+            return super().__new__(StandardNormal)
+        return super().__new__(cls)
+
+    def __init__(self, *, mu=0., sigma=1., **kwargs):
+        super().__init__(mu=mu, sigma=sigma, **kwargs)
+
+    def _logpdf_formula(self, x, *, mu, sigma, **kwargs):
+        return StandardNormal._logpdf_formula(self, (x - mu)/sigma) - np.log(sigma)
+
+    def _pdf_formula(self, x, *, mu, sigma, **kwargs):
+        return StandardNormal._pdf_formula(self, (x - mu)/sigma) / sigma
+
+    def _logcdf_formula(self, x, *, mu, sigma, **kwargs):
+        return StandardNormal._logcdf_formula(self, (x - mu)/sigma)
+
+    def _cdf_formula(self, x, *, mu, sigma, **kwargs):
+        return StandardNormal._cdf_formula(self, (x - mu)/sigma)
+
+    def _logccdf_formula(self, x, *, mu, sigma, **kwargs):
+        return StandardNormal._logccdf_formula(self, (x - mu)/sigma)
+
+    def _ccdf_formula(self, x, *, mu, sigma, **kwargs):
+        return StandardNormal._ccdf_formula(self, (x - mu)/sigma)
+
+    def _icdf_formula(self, x, *, mu, sigma, **kwargs):
+        return StandardNormal._icdf_formula(self, x) * sigma + mu
+
+    def _ilogcdf_formula(self, x, *, mu, sigma, **kwargs):
+        return StandardNormal._ilogcdf_formula(self, x) * sigma + mu
+
+    def _iccdf_formula(self, x, *, mu, sigma, **kwargs):
+        return StandardNormal._iccdf_formula(self, x) * sigma + mu
+
+    def _ilogccdf_formula(self, x, *, mu, sigma, **kwargs):
+        return StandardNormal._ilogccdf_formula(self, x) * sigma + mu
+
+    def _entropy_formula(self, *, mu, sigma, **kwargs):
+        return StandardNormal._entropy_formula(self) + np.log(abs(sigma))
+
+    def _logentropy_formula(self, *, mu, sigma, **kwargs):
+        lH0 = StandardNormal._logentropy_formula(self)
+        with np.errstate(divide='ignore'):
+            # sigma = 1 -> log(sigma) = 0 -> log(log(sigma)) = -inf
+            # Silence the unnecessary runtime warning
+            lls = np.log(np.log(abs(sigma))+0j)
+        return special.logsumexp(np.broadcast_arrays(lH0, lls), axis=0)
+
+    def _median_formula(self, *, mu, sigma, **kwargs):
+        return mu
+
+    def _mode_formula(self, *, mu, sigma, **kwargs):
+        return mu
+
+    def _moment_raw_formula(self, order, *, mu, sigma, **kwargs):
+        if order == 0:
+            return np.ones_like(mu)
+        elif order == 1:
+            return mu
+        else:
+            return None
+    _moment_raw_formula.orders = [0, 1]  # type: ignore[attr-defined]
+
+    def _moment_central_formula(self, order, *, mu, sigma, **kwargs):
+        if order == 0:
+            return np.ones_like(mu)
+        elif order % 2:
+            return np.zeros_like(mu)
+        else:
+            # exact is faster (and obviously more accurate) for reasonable orders
+            return sigma**order * special.factorial2(int(order) - 1, exact=True)
+
+    def _lmoment_formula(self, order, *, mu, sigma, **kwargs):
+        lscale = sigma / np.sqrt(np.pi)
+        lkurtosis = 30*np.arctan(np.sqrt(2))/np.pi - 9
+        lmoments = {1: mu, 2: lscale, 3: 0, 4: lkurtosis * lscale}
+        return lmoments.get(order, None)
+
+    def _sample_formula(self, full_shape, rng, *, mu, sigma, **kwargs):
+        return rng.normal(loc=mu, scale=sigma, size=full_shape)[()]
+
+
+def _log_diff(log_p, log_q):
+    return special.logsumexp([log_p, log_q+np.pi*1j], axis=0)
+
+
+class StandardNormal(Normal):
+    r"""Standard normal distribution.
+
+    The probability density function of the standard normal distribution is:
+
+    .. math::
+
+        f(x) = \frac{1}{\sqrt{2 \pi}} \exp \left( -\frac{1}{2} x^2 \right)
+
+    """
+    _x_support = _RealInterval(endpoints=(-inf, inf))
+    _x_param = _RealParameter('x', domain=_x_support, typical=(-5, 5))
+    _variable = _x_param
+    _parameterizations = []
+    _normalization = 1/np.sqrt(2*np.pi)
+    _log_normalization = np.log(2*np.pi)/2
+    mu = np.float64(0.)
+    sigma = np.float64(1.)
+
+    def __init__(self, **kwargs):
+        ContinuousDistribution.__init__(self, **kwargs)
+
+    def _logpdf_formula(self, x, **kwargs):
+        return -(self._log_normalization + x**2/2)
+
+    def _pdf_formula(self, x, **kwargs):
+        return self._normalization * np.exp(-x**2/2)
+
+    def _logcdf_formula(self, x, **kwargs):
+        return special.log_ndtr(x)
+
+    def _cdf_formula(self, x, **kwargs):
+        return special.ndtr(x)
+
+    def _logccdf_formula(self, x, **kwargs):
+        return special.log_ndtr(-x)
+
+    def _ccdf_formula(self, x, **kwargs):
+        return special.ndtr(-x)
+
+    def _icdf_formula(self, x, **kwargs):
+        return special.ndtri(x)
+
+    def _ilogcdf_formula(self, x, **kwargs):
+        return special.ndtri_exp(x)
+
+    def _iccdf_formula(self, x, **kwargs):
+        return -special.ndtri(x)
+
+    def _ilogccdf_formula(self, x, **kwargs):
+        return -special.ndtri_exp(x)
+
+    def _entropy_formula(self, **kwargs):
+        return (1 + np.log(2*np.pi))/2
+
+    def _logentropy_formula(self, **kwargs):
+        return np.log1p(np.log(2*np.pi)) - np.log(2)
+
+    def _median_formula(self, **kwargs):
+        return 0
+
+    def _mode_formula(self, **kwargs):
+        return 0
+
+    def _moment_raw_formula(self, order, **kwargs):
+        raw_moments = {0: 1, 1: 0, 2: 1, 3: 0, 4: 3, 5: 0}
+        return raw_moments.get(order, None)
+
+    def _moment_central_formula(self, order, **kwargs):
+        return self._moment_raw_formula(order, **kwargs)
+
+    def _moment_standardized_formula(self, order, **kwargs):
+        return self._moment_raw_formula(order, **kwargs)
+
+    def _lmoment_formula(self, order, **kwargs):
+        return super()._lmoment_formula(order, mu=0., sigma=1., **kwargs)
+
+    def _sample_formula(self, full_shape, rng, **kwargs):
+        return rng.normal(size=full_shape)[()]
+
+
+class Logistic(ContinuousDistribution):
+    r"""Standard logistic distribution.
+
+    The probability density function of the standard logistic distribution is:
+
+    .. math::
+
+        f(x) = \frac{1}{\left( e^{x / 2} + e^{-x / 2} \right)^2}
+
+    """
+    _x_support = _RealInterval(endpoints=(-inf, inf))
+    _variable = _x_param = _RealParameter('x', domain=_x_support, typical=(-9, 9))
+    _parameterizations = ()   # type:ignore[assignment]
+
+    _scale = np.pi / np.sqrt(3)
+
+    def _logpdf_formula(self, x, **kwargs):
+        y = -np.abs(x)
+        return y - 2 * special.log1p(np.exp(y))
+
+    def _pdf_formula(self, x, **kwargs):
+        # f(x) = sech(x / 2)**2 / 4
+        return (.5 / np.cosh(x / 2))**2
+
+    def _logcdf_formula(self, x, **kwargs):
+        return special.log_expit(x)
+
+    def _cdf_formula(self, x, **kwargs):
+        return special.expit(x)
+
+    def _logccdf_formula(self, x, **kwargs):
+        return special.log_expit(-x)
+
+    def _ccdf_formula(self, x, **kwargs):
+        return special.expit(-x)
+
+    def _icdf_formula(self, x, **kwargs):
+        return special.logit(x)
+
+    def _iccdf_formula(self, x, **kwargs):
+        return -special.logit(x)
+
+    def _entropy_formula(self, **kwargs):
+        return 2.0
+
+    def _logentropy_formula(self, **kwargs):
+        return np.log(2)
+
+    def _median_formula(self, **kwargs):
+        return 0
+
+    def _mode_formula(self, **kwargs):
+        return 0
+
+    def _moment_raw_formula(self, order, **kwargs):
+        n = int(order)
+        if n % 2:
+            return 0.0
+        return np.pi**n * abs((2**n - 2) * float(special.bernoulli(n)[-1]))
+
+    def _moment_central_formula(self, order, **kwargs):
+        return self._moment_raw_formula(order, **kwargs)
+
+    def _moment_standardized_formula(self, order, **kwargs):
+        return self._moment_raw_formula(order, **kwargs) / self._scale**order
+
+    def _lmoment_formula(self, order, **kwargs):
+        lmoments = {1: 0, 2: 1, 3: 0, 4: 1/6}
+        return lmoments.get(order, None)
+
+    def _sample_formula(self, full_shape, rng, **kwargs):
+        return rng.logistic(size=full_shape)[()]
+
+
+# currently for testing only
+class _LogUniform(ContinuousDistribution):
+    r"""Log-uniform distribution.
+
+    The probability density function of the log-uniform distribution is:
+
+    .. math::
+
+        f(x; a, b) = \frac{1}
+                          {x (\log(b) - \log(a))}
+
+    If :math:`\log(X)` is a random variable that follows a uniform distribution
+    between :math:`\log(a)` and :math:`\log(b)`, then :math:`X` is log-uniformly
+    distributed with shape parameters :math:`a` and :math:`b`.
+
+    """
+
+    _a_domain = _RealInterval(endpoints=(0, inf))
+    _b_domain = _RealInterval(endpoints=('a', inf))
+    _log_a_domain = _RealInterval(endpoints=(-inf, inf))
+    _log_b_domain = _RealInterval(endpoints=('log_a', inf))
+    _x_support = _RealInterval(endpoints=('a', 'b'), inclusive=(True, True))
+
+    _a_param = _RealParameter('a', domain=_a_domain, typical=(1e-3, 0.9))
+    _b_param = _RealParameter('b', domain=_b_domain, typical=(1.1, 1e3))
+    _log_a_param = _RealParameter('log_a', symbol=r'\log(a)',
+                                  domain=_log_a_domain, typical=(-3, -0.1))
+    _log_b_param = _RealParameter('log_b', symbol=r'\log(b)',
+                                  domain=_log_b_domain, typical=(0.1, 3))
+    _x_param = _RealParameter('x', domain=_x_support, typical=('a', 'b'))
+
+    _b_domain.define_parameters(_a_param)
+    _log_b_domain.define_parameters(_log_a_param)
+    _x_support.define_parameters(_a_param, _b_param)
+
+    _parameterizations = [_Parameterization(_log_a_param, _log_b_param),
+                          _Parameterization(_a_param, _b_param)]
+    _variable = _x_param
+
+    def __init__(self, *, a=None, b=None, log_a=None, log_b=None, **kwargs):
+        super().__init__(a=a, b=b, log_a=log_a, log_b=log_b, **kwargs)
+
+    def _process_parameters(self, a=None, b=None, log_a=None, log_b=None, **kwargs):
+        a = np.exp(log_a) if a is None else a
+        b = np.exp(log_b) if b is None else b
+        log_a = np.log(a) if log_a is None else log_a
+        log_b = np.log(b) if log_b is None else log_b
+        kwargs.update(dict(a=a, b=b, log_a=log_a, log_b=log_b))
+        return kwargs
+
+    def _pdf_formula(self, x, *, log_a, log_b, **kwargs):
+        return ((log_b - log_a)*x)**-1
+
+    def _moment_raw_formula(self, order, log_a, log_b, **kwargs):
+        if order == 0:
+            return self._one
+        t1 = self._one / (log_b - log_a) / order
+        t2 = np.real(np.exp(_log_diff(order * log_b, order * log_a)))
+        return t1 * t2
+
+
+class Uniform(ContinuousDistribution):
+    r"""Uniform distribution.
+
+    The probability density function of the uniform distribution is:
+
+    .. math::
+
+        f(x; a, b) = \frac{1}
+                          {b - a}
+
+    """
+
+    _a_domain = _RealInterval(endpoints=(-inf, inf))
+    _b_domain = _RealInterval(endpoints=('a', inf))
+    _x_support = _RealInterval(endpoints=('a', 'b'), inclusive=(True, True))
+
+    _a_param = _RealParameter('a', domain=_a_domain, typical=(1e-3, 0.9))
+    _b_param = _RealParameter('b', domain=_b_domain, typical=(1.1, 1e3))
+    _x_param = _RealParameter('x', domain=_x_support, typical=('a', 'b'))
+
+    _b_domain.define_parameters(_a_param)
+    _x_support.define_parameters(_a_param, _b_param)
+
+    _parameterizations = [_Parameterization(_a_param, _b_param)]
+    _variable = _x_param
+
+    def __init__(self, *, a=None, b=None, **kwargs):
+        super().__init__(a=a, b=b, **kwargs)
+
+    def _process_parameters(self, a=None, b=None, ab=None, **kwargs):
+        ab = b - a
+        kwargs.update(dict(a=a, b=b, ab=ab))
+        return kwargs
+
+    def _logpdf_formula(self, x, *, ab, **kwargs):
+        return np.where(np.isnan(x), np.nan, -np.log(ab))
+
+    def _pdf_formula(self, x, *, ab, **kwargs):
+        return np.where(np.isnan(x), np.nan, 1/ab)
+
+    def _logcdf_formula(self, x, *, a, ab, **kwargs):
+        with np.errstate(divide='ignore'):
+            return np.log(x - a) - np.log(ab)
+
+    def _cdf_formula(self, x, *, a, ab, **kwargs):
+        return (x - a) / ab
+
+    def _logccdf_formula(self, x, *, b, ab, **kwargs):
+        with np.errstate(divide='ignore'):
+            return np.log(b - x) - np.log(ab)
+
+    def _ccdf_formula(self, x, *, b, ab, **kwargs):
+        return (b - x) / ab
+
+    def _icdf_formula(self, p, *, a, ab, **kwargs):
+        return a + ab*p
+
+    def _iccdf_formula(self, p, *, b, ab, **kwargs):
+        return b - ab*p
+
+    def _entropy_formula(self, *, ab, **kwargs):
+        return np.log(ab)
+
+    def _mode_formula(self, *, a, b, ab, **kwargs):
+        return a + 0.5*ab
+
+    def _median_formula(self, *, a, b, ab, **kwargs):
+        return a + 0.5*ab
+
+    def _moment_raw_formula(self, order, a, b, ab, **kwargs):
+        np1 = order + 1
+        return (b**np1 - a**np1) / (np1 * ab)
+
+    def _moment_central_formula(self, order, ab, **kwargs):
+        return ab**2/12 if order == 2 else None
+
+    _moment_central_formula.orders = [2]  # type: ignore[attr-defined]
+
+    def _lmoment_formula(self, order, *, a, b, ab, **kwargs):
+        lmoments = {1: 0.5*(a + b), 2: ab / 6}
+        return lmoments.get(order, np.zeros_like(ab))
+
+    def _sample_formula(self, full_shape, rng, a, b, ab, **kwargs):
+        try:
+            return rng.uniform(a, b, size=full_shape)[()]
+        except OverflowError:  # happens when there are NaNs
+            return rng.uniform(0, 1, size=full_shape)*ab + a
+
+
+class _Gamma(ContinuousDistribution):
+    # Gamma distribution for testing only
+    _a_domain = _RealInterval(endpoints=(0, inf))
+    _x_support = _RealInterval(endpoints=(0, inf), inclusive=(False, False))
+
+    _a_param = _RealParameter('a', domain=_a_domain, typical=(0.1, 10))
+    _x_param = _RealParameter('x', domain=_x_support, typical=(0.1, 10))
+
+    _parameterizations = [_Parameterization(_a_param)]
+    _variable = _x_param
+
+    def _pdf_formula(self, x, *, a, **kwargs):
+        return x ** (a - 1) * np.exp(-x) / special.gamma(a)
+
+
+class Binomial(DiscreteDistribution):
+    r"""Binomial distribution with prescribed success probability and number of trials
+
+    The probability density function of the binomial distribution is:
+
+    .. math::
+
+        f(x) = {n \choose x} p^x (1 - p)^{n-x}
+
+    """
+    _n_domain = _IntegerInterval(endpoints=(0, inf), inclusive=(False, False))
+    _p_domain = _RealInterval(endpoints=(0, 1), inclusive=(False, False))
+    _x_support = _IntegerInterval(endpoints=(0, 'n'), inclusive=(True, True))
+
+    _n_param = _RealParameter('n', domain=_n_domain, typical=(10, 20))
+    _p_param = _RealParameter('p', domain=_p_domain, typical=(0.25, 0.75))
+    _x_param = _RealParameter('x', domain=_x_support, typical=(0, 10))
+
+    _parameterizations = [_Parameterization(_n_param, _p_param)]
+    _variable = _x_param
+
+    def __init__(self, *, n, p, **kwargs):
+        super().__init__(n=n, p=p, **kwargs)
+
+    def _pmf_formula(self, x, *, n, p, **kwargs):
+        return scu._binom_pmf(x, n, p)
+
+    def _logpmf_formula(self, x, *, n, p, **kwargs):
+        # This implementation is from the ``scipy.stats.binom`` and could be improved
+        # by using a more numerically sound implementation of the absolute value of
+        # the binomial coefficient.
+        combiln = (
+            special.gammaln(n+1) - (special.gammaln(x+1) + special.gammaln(n-x+1))
+        )
+        return combiln + special.xlogy(x, p) + special.xlog1py(n-x, -p)
+
+    def _cdf_formula(self, x, *, n, p, **kwargs):
+        return scu._binom_cdf(x, n, p)
+
+    def _logcdf_formula(self, x, *, n, p, **kwargs):
+        # todo: add this strategy to infrastructure more generally, but allow dist
+        #   author to specify threshold other than median in case median is expensive
+        median = self._icdf_formula(0.5, n=n, p=p)
+        return xpx.apply_where(x < median, (x, n, p),
+            lambda *args: np.log(scu._binom_cdf(*args)),
+            lambda *args: np.log1p(-scu._binom_sf(*args))
+        )
+
+    def _ccdf_formula(self, x, *, n, p, **kwargs):
+        return scu._binom_sf(x, n, p)
+
+    def _logccdf_formula(self, x, *, n, p, **kwargs):
+        median = self._icdf_formula(0.5, n=n, p=p)
+        return xpx.apply_where(x < median, (x, n, p),
+            lambda *args: np.log1p(-scu._binom_cdf(*args)),
+            lambda *args: np.log(scu._binom_sf(*args))
+        )
+
+    def _icdf_formula(self, x, *, n, p, **kwargs):
+        return scu._binom_ppf(x, n, p)
+
+    def _iccdf_formula(self, x, *, n, p, **kwargs):
+        return scu._binom_isf(x, n, p)
+
+    def _mode_formula(self, *, n, p, **kwargs):
+        # https://en.wikipedia.org/wiki/Binomial_distribution#Mode
+        mode = np.floor((n+1)*p)
+        mode = np.where(p == 1, mode - 1, mode)
+        return mode[()]
+
+    def _moment_raw_formula(self, order, *, n, p, **kwargs):
+        # https://en.wikipedia.org/wiki/Binomial_distribution#Higher_moments
+        if order == 1:
+            return n*p
+        if order == 2:
+            return n*p*(1 - p + n*p)
+        return None
+    _moment_raw_formula.orders = [1, 2]  # type: ignore[attr-defined]
+
+    def _moment_central_formula(self, order, *, n, p, **kwargs):
+        # https://en.wikipedia.org/wiki/Binomial_distribution#Higher_moments
+        if order == 1:
+            return np.zeros_like(n)
+        if order == 2:
+            return n*p*(1 - p)
+        if order == 3:
+            return n*p*(1 - p)*(1 - 2*p)
+        if order == 4:
+            return n*p*(1 - p)*(1 + (3*n - 6)*p*(1 - p))
+        return None
+    _moment_central_formula.orders = [1, 2, 3, 4]  # type: ignore[attr-defined]
+
+
+# Distribution classes need only define the summary and beginning of the extended
+# summary portion of the class documentation. All other documentation, including
+# examples, is generated automatically.
+_module = sys.modules[__name__].__dict__
+for dist_name in __all__:
+    _module[dist_name].__doc__ = _combine_docs(_module[dist_name])
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_odds_ratio.py b/venv/lib/python3.12/site-packages/scipy/stats/_odds_ratio.py
new file mode 100644
index 0000000000000000000000000000000000000000..bc593f5adc9a700c618c721b6c37c801809d868b
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_odds_ratio.py
@@ -0,0 +1,466 @@
+import numpy as np
+
+from scipy.special import ndtri
+from scipy.optimize import brentq
+from ._discrete_distns import nchypergeom_fisher
+from ._common import ConfidenceInterval
+
+
+def _sample_odds_ratio(table):
+    """
+    Given a table [[a, b], [c, d]], compute a*d/(b*c).
+
+    Return nan if the numerator and denominator are 0.
+    Return inf if just the denominator is 0.
+    """
+    # table must be a 2x2 numpy array.
+    if table[1, 0] > 0 and table[0, 1] > 0:
+        oddsratio = table[0, 0] * table[1, 1] / (table[1, 0] * table[0, 1])
+    elif table[0, 0] == 0 or table[1, 1] == 0:
+        oddsratio = np.nan
+    else:
+        oddsratio = np.inf
+    return oddsratio
+
+
+def _solve(func):
+    """
+    Solve func(nc) = 0.  func must be an increasing function.
+    """
+    # We could just as well call the variable `x` instead of `nc`, but we
+    # always call this function with functions for which nc (the noncentrality
+    # parameter) is the variable for which we are solving.
+    nc = 1.0
+    value = func(nc)
+    if value == 0:
+        return nc
+
+    # Multiplicative factor by which to increase or decrease nc when
+    # searching for a bracketing interval.
+    factor = 2.0
+    # Find a bracketing interval.
+    if value > 0:
+        nc /= factor
+        while func(nc) > 0:
+            nc /= factor
+        lo = nc
+        hi = factor*nc
+    else:
+        nc *= factor
+        while func(nc) < 0:
+            nc *= factor
+        lo = nc/factor
+        hi = nc
+
+    # lo and hi bracket the solution for nc.
+    nc = brentq(func, lo, hi, xtol=1e-13)
+    return nc
+
+
+def _nc_hypergeom_mean_inverse(x, M, n, N):
+    """
+    For the given noncentral hypergeometric parameters x, M, n,and N
+    (table[0,0], total, row 0 sum and column 0 sum, resp., of a 2x2
+    contingency table), find the noncentrality parameter of Fisher's
+    noncentral hypergeometric distribution whose mean is x.
+    """
+    nc = _solve(lambda nc: nchypergeom_fisher.mean(M, n, N, nc) - x)
+    return nc
+
+
+def _hypergeom_params_from_table(table):
+    # The notation M, n and N is consistent with stats.hypergeom and
+    # stats.nchypergeom_fisher.
+    x = table[0, 0]
+    M = table.sum()
+    n = table[0].sum()
+    N = table[:, 0].sum()
+    return x, M, n, N
+
+
+def _ci_upper(table, alpha):
+    """
+    Compute the upper end of the confidence interval.
+    """
+    if _sample_odds_ratio(table) == np.inf:
+        return np.inf
+
+    x, M, n, N = _hypergeom_params_from_table(table)
+
+    # nchypergeom_fisher.cdf is a decreasing function of nc, so we negate
+    # it in the lambda expression.
+    nc = _solve(lambda nc: -nchypergeom_fisher.cdf(x, M, n, N, nc) + alpha)
+    return nc
+
+
+def _ci_lower(table, alpha):
+    """
+    Compute the lower end of the confidence interval.
+    """
+    if _sample_odds_ratio(table) == 0:
+        return 0
+
+    x, M, n, N = _hypergeom_params_from_table(table)
+
+    nc = _solve(lambda nc: nchypergeom_fisher.sf(x - 1, M, n, N, nc) - alpha)
+    return nc
+
+
+def _conditional_oddsratio(table):
+    """
+    Conditional MLE of the odds ratio for the 2x2 contingency table.
+    """
+    x, M, n, N = _hypergeom_params_from_table(table)
+    # Get the bounds of the support.  The support of the noncentral
+    # hypergeometric distribution with parameters M, n, and N is the same
+    # for all values of the noncentrality parameter, so we can use 1 here.
+    lo, hi = nchypergeom_fisher.support(M, n, N, 1)
+
+    # Check if x is at one of the extremes of the support.  If so, we know
+    # the odds ratio is either 0 or inf.
+    if x == lo:
+        # x is at the low end of the support.
+        return 0
+    if x == hi:
+        # x is at the high end of the support.
+        return np.inf
+
+    nc = _nc_hypergeom_mean_inverse(x, M, n, N)
+    return nc
+
+
+def _conditional_oddsratio_ci(table, confidence_level=0.95,
+                              alternative='two-sided'):
+    """
+    Conditional exact confidence interval for the odds ratio.
+    """
+    if alternative == 'two-sided':
+        alpha = 0.5*(1 - confidence_level)
+        lower = _ci_lower(table, alpha)
+        upper = _ci_upper(table, alpha)
+    elif alternative == 'less':
+        lower = 0.0
+        upper = _ci_upper(table, 1 - confidence_level)
+    else:
+        # alternative == 'greater'
+        lower = _ci_lower(table, 1 - confidence_level)
+        upper = np.inf
+
+    return lower, upper
+
+
+def _sample_odds_ratio_ci(table, confidence_level=0.95,
+                          alternative='two-sided'):
+    oddsratio = _sample_odds_ratio(table)
+    log_or = np.log(oddsratio)
+    se = np.sqrt((1/table).sum())
+    if alternative == 'less':
+        z = ndtri(confidence_level)
+        loglow = -np.inf
+        loghigh = log_or + z*se
+    elif alternative == 'greater':
+        z = ndtri(confidence_level)
+        loglow = log_or - z*se
+        loghigh = np.inf
+    else:
+        # alternative is 'two-sided'
+        z = ndtri(0.5*confidence_level + 0.5)
+        loglow = log_or - z*se
+        loghigh = log_or + z*se
+
+    return np.exp(loglow), np.exp(loghigh)
+
+
+class OddsRatioResult:
+    """
+    Result of `scipy.stats.contingency.odds_ratio`.  See the
+    docstring for `odds_ratio` for more details.
+
+    Attributes
+    ----------
+    statistic : float
+        The computed odds ratio.
+
+        * If `kind` is ``'sample'``, this is sample (or unconditional)
+          estimate, given by
+          ``table[0, 0]*table[1, 1]/(table[0, 1]*table[1, 0])``.
+        * If `kind` is ``'conditional'``, this is the conditional
+          maximum likelihood estimate for the odds ratio. It is
+          the noncentrality parameter of Fisher's noncentral
+          hypergeometric distribution with the same hypergeometric
+          parameters as `table` and whose mean is ``table[0, 0]``.
+
+    Methods
+    -------
+    confidence_interval :
+        Confidence interval for the odds ratio.
+    """
+
+    def __init__(self, _table, _kind, statistic):
+        # for now, no need to make _table and _kind public, since this sort of
+        # information is returned in very few `scipy.stats` results
+        self._table = _table
+        self._kind = _kind
+        self.statistic = statistic
+
+    def __repr__(self):
+        return f"OddsRatioResult(statistic={self.statistic})"
+
+    def confidence_interval(self, confidence_level=0.95,
+                            alternative='two-sided'):
+        """
+        Confidence interval for the odds ratio.
+
+        Parameters
+        ----------
+        confidence_level: float
+            Desired confidence level for the confidence interval.
+            The value must be given as a fraction between 0 and 1.
+            Default is 0.95 (meaning 95%).
+
+        alternative : {'two-sided', 'less', 'greater'}, optional
+            The alternative hypothesis of the hypothesis test to which the
+            confidence interval corresponds. That is, suppose the null
+            hypothesis is that the true odds ratio equals ``OR`` and the
+            confidence interval is ``(low, high)``. Then the following options
+            for `alternative` are available (default is 'two-sided'):
+
+            * 'two-sided': the true odds ratio is not equal to ``OR``. There
+              is evidence against the null hypothesis at the chosen
+              `confidence_level` if ``high < OR`` or ``low > OR``.
+            * 'less': the true odds ratio is less than ``OR``. The ``low`` end
+              of the confidence interval is 0, and there is evidence against
+              the null hypothesis at  the chosen `confidence_level` if
+              ``high < OR``.
+            * 'greater': the true odds ratio is greater than ``OR``.  The
+              ``high`` end of the confidence interval is ``np.inf``, and there
+              is evidence against the null hypothesis at the chosen
+              `confidence_level` if ``low > OR``.
+
+        Returns
+        -------
+        ci : ``ConfidenceInterval`` instance
+            The confidence interval, represented as an object with
+            attributes ``low`` and ``high``.
+
+        Notes
+        -----
+        When `kind` is ``'conditional'``, the limits of the confidence
+        interval are the conditional "exact confidence limits" as described
+        by Fisher [1]_. The conditional odds ratio and confidence interval are
+        also discussed in Section 4.1.2 of the text by Sahai and Khurshid [2]_.
+
+        When `kind` is ``'sample'``, the confidence interval is computed
+        under the assumption that the logarithm of the odds ratio is normally
+        distributed with standard error given by::
+
+            se = sqrt(1/a + 1/b + 1/c + 1/d)
+
+        where ``a``, ``b``, ``c`` and ``d`` are the elements of the
+        contingency table.  (See, for example, [2]_, section 3.1.3.2,
+        or [3]_, section 2.3.3).
+
+        References
+        ----------
+        .. [1] R. A. Fisher (1935), The logic of inductive inference,
+               Journal of the Royal Statistical Society, Vol. 98, No. 1,
+               pp. 39-82.
+        .. [2] H. Sahai and A. Khurshid (1996), Statistics in Epidemiology:
+               Methods, Techniques, and Applications, CRC Press LLC, Boca
+               Raton, Florida.
+        .. [3] Alan Agresti, An Introduction to Categorical Data Analysis
+               (second edition), Wiley, Hoboken, NJ, USA (2007).
+        """
+        if alternative not in ['two-sided', 'less', 'greater']:
+            raise ValueError("`alternative` must be 'two-sided', 'less' or "
+                             "'greater'.")
+
+        if confidence_level < 0 or confidence_level > 1:
+            raise ValueError('confidence_level must be between 0 and 1')
+
+        if self._kind == 'conditional':
+            ci = self._conditional_odds_ratio_ci(confidence_level, alternative)
+        else:
+            ci = self._sample_odds_ratio_ci(confidence_level, alternative)
+        return ci
+
+    def _conditional_odds_ratio_ci(self, confidence_level=0.95,
+                                   alternative='two-sided'):
+        """
+        Confidence interval for the conditional odds ratio.
+        """
+
+        table = self._table
+        if 0 in table.sum(axis=0) or 0 in table.sum(axis=1):
+            # If both values in a row or column are zero, the p-value is 1,
+            # the odds ratio is NaN and the confidence interval is (0, inf).
+            ci = (0, np.inf)
+        else:
+            ci = _conditional_oddsratio_ci(table,
+                                           confidence_level=confidence_level,
+                                           alternative=alternative)
+        return ConfidenceInterval(low=ci[0], high=ci[1])
+
+    def _sample_odds_ratio_ci(self, confidence_level=0.95,
+                              alternative='two-sided'):
+        """
+        Confidence interval for the sample odds ratio.
+        """
+        if confidence_level < 0 or confidence_level > 1:
+            raise ValueError('confidence_level must be between 0 and 1')
+
+        table = self._table
+        if 0 in table.sum(axis=0) or 0 in table.sum(axis=1):
+            # If both values in a row or column are zero, the p-value is 1,
+            # the odds ratio is NaN and the confidence interval is (0, inf).
+            ci = (0, np.inf)
+        else:
+            ci = _sample_odds_ratio_ci(table,
+                                       confidence_level=confidence_level,
+                                       alternative=alternative)
+        return ConfidenceInterval(low=ci[0], high=ci[1])
+
+
+def odds_ratio(table, *, kind='conditional'):
+    r"""
+    Compute the odds ratio for a 2x2 contingency table.
+
+    Parameters
+    ----------
+    table : array_like of ints
+        A 2x2 contingency table.  Elements must be non-negative integers.
+    kind : str, optional
+        Which kind of odds ratio to compute, either the sample
+        odds ratio (``kind='sample'``) or the conditional odds ratio
+        (``kind='conditional'``).  Default is ``'conditional'``.
+
+    Returns
+    -------
+    result : `~scipy.stats._result_classes.OddsRatioResult` instance
+        The returned object has two computed attributes:
+
+        statistic : float
+            * If `kind` is ``'sample'``, this is sample (or unconditional)
+              estimate, given by
+              ``table[0, 0]*table[1, 1]/(table[0, 1]*table[1, 0])``.
+            * If `kind` is ``'conditional'``, this is the conditional
+              maximum likelihood estimate for the odds ratio. It is
+              the noncentrality parameter of Fisher's noncentral
+              hypergeometric distribution with the same hypergeometric
+              parameters as `table` and whose mean is ``table[0, 0]``.
+
+        The object has the method `confidence_interval` that computes
+        the confidence interval of the odds ratio.
+
+    See Also
+    --------
+    scipy.stats.fisher_exact
+    relative_risk
+    :ref:`hypothesis_odds_ratio` : Extended example
+
+    Notes
+    -----
+    The conditional odds ratio was discussed by Fisher (see "Example 1"
+    of [1]_).  Texts that cover the odds ratio include [2]_ and [3]_.
+
+    .. versionadded:: 1.10.0
+
+    References
+    ----------
+    .. [1] R. A. Fisher (1935), The logic of inductive inference,
+           Journal of the Royal Statistical Society, Vol. 98, No. 1,
+           pp. 39-82.
+    .. [2] Breslow NE, Day NE (1980). Statistical methods in cancer research.
+           Volume I - The analysis of case-control studies. IARC Sci Publ.
+           (32):5-338. PMID: 7216345. (See section 4.2.)
+    .. [3] H. Sahai and A. Khurshid (1996), Statistics in Epidemiology:
+           Methods, Techniques, and Applications, CRC Press LLC, Boca
+           Raton, Florida.
+
+    Examples
+    --------
+    In epidemiology, individuals are classified as "exposed" or
+    "unexposed" to some factor or treatment. If the occurrence of some
+    illness is under study, those who have the illness are often
+    classified as "cases", and those without it are "noncases".  The
+    counts of the occurrences of these classes gives a contingency
+    table::
+
+                    exposed    unexposed
+        cases          a           b
+        noncases       c           d
+
+    The sample odds ratio may be written ``(a/c) / (b/d)``.  ``a/c`` can
+    be interpreted as the odds of a case occurring in the exposed group,
+    and ``b/d`` as the odds of a case occurring in the unexposed group.
+    The sample odds ratio is the ratio of these odds.  If the odds ratio
+    is greater than 1, it suggests that there is a positive association
+    between being exposed and being a case.
+
+    Interchanging the rows or columns of the contingency table inverts
+    the odds ratio, so it is important to understand the meaning of labels
+    given to the rows and columns of the table when interpreting the
+    odds ratio.
+
+    Consider a hypothetical example where it is hypothesized that exposure to a
+    certain chemical is associated with increased occurrence of a certain
+    disease. Suppose we have the following table for a collection of 410 people::
+
+                exposed unexposed
+        cases        7       15
+        noncases    58      472
+
+    The question we ask is "Is exposure to the chemical associated with
+    increased risk of the disease?"
+
+    Compute the odds ratio:
+
+    >>> from scipy.stats.contingency import odds_ratio
+    >>> res = odds_ratio([[7, 15], [58, 472]])
+    >>> res.statistic
+    3.7836687705553493
+
+    For this sample, the odds of getting the disease for those who have been
+    exposed to the chemical are almost 3.8 times that of those who have not been
+    exposed.
+
+    We can compute the 95% confidence interval for the odds ratio:
+
+    >>> res.confidence_interval(confidence_level=0.95)
+    ConfidenceInterval(low=1.2514829132266785, high=10.363493716701269)
+
+    The 95% confidence interval for the conditional odds ratio is approximately
+    (1.25, 10.4).
+
+    For a more detailed example, see :ref:`hypothesis_odds_ratio`.
+    """
+    if kind not in ['conditional', 'sample']:
+        raise ValueError("`kind` must be 'conditional' or 'sample'.")
+
+    c = np.asarray(table)
+
+    if c.shape != (2, 2):
+        raise ValueError(f"Invalid shape {c.shape}. The input `table` must be "
+                         "of shape (2, 2).")
+
+    if not np.issubdtype(c.dtype, np.integer):
+        raise ValueError("`table` must be an array of integers, but got "
+                         f"type {c.dtype}")
+    c = c.astype(np.int64)
+
+    if np.any(c < 0):
+        raise ValueError("All values in `table` must be nonnegative.")
+
+    if 0 in c.sum(axis=0) or 0 in c.sum(axis=1):
+        # If both values in a row or column are zero, the p-value is NaN and
+        # the odds ratio is NaN.
+        result = OddsRatioResult(_table=c, _kind=kind, statistic=np.nan)
+        return result
+
+    if kind == 'sample':
+        oddsratio = _sample_odds_ratio(c)
+    else:  # kind is 'conditional'
+        oddsratio = _conditional_oddsratio(c)
+
+    result = OddsRatioResult(_table=c, _kind=kind, statistic=oddsratio)
+    return result
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_page_trend_test.py b/venv/lib/python3.12/site-packages/scipy/stats/_page_trend_test.py
new file mode 100644
index 0000000000000000000000000000000000000000..27f8dda8c043eafb0c0380f0cd3269afd30046e9
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_page_trend_test.py
@@ -0,0 +1,488 @@
+from dataclasses import dataclass
+from itertools import permutations
+import math
+import threading
+
+import numpy as np
+
+from ._continuous_distns import norm
+from scipy._lib._array_api import xp_capabilities
+import scipy.stats
+
+
+@dataclass
+class PageTrendTestResult:
+    statistic: float
+    pvalue: float
+    method: str
+
+
+@xp_capabilities(np_only=True)
+def page_trend_test(data, ranked=False, predicted_ranks=None, method='auto'):
+    r"""
+    Perform Page's Test, a measure of trend in observations between treatments.
+
+    Page's Test (also known as Page's :math:`L` test) is useful when:
+
+    * there are :math:`n \geq 3` treatments,
+    * :math:`m \geq 2` subjects are observed for each treatment, and
+    * the observations are hypothesized to have a particular order.
+
+    Specifically, the test considers the null hypothesis that
+
+    .. math::
+
+        m_1 = m_2 = m_3 \cdots = m_n,
+
+    where :math:`m_j` is the mean of the observed quantity under treatment
+    :math:`j`, against the alternative hypothesis that
+
+    .. math::
+
+        m_1 \leq m_2 \leq m_3 \leq \cdots \leq m_n,
+
+    where at least one inequality is strict.
+
+    As noted by [4]_, Page's :math:`L` test has greater statistical power than
+    the Friedman test against the alternative that there is a difference in
+    trend, as Friedman's test only considers a difference in the means of the
+    observations without considering their order. Whereas Spearman :math:`\rho`
+    considers the correlation between the ranked observations of two variables
+    (e.g. the airspeed velocity of a swallow vs. the weight of the coconut it
+    carries), Page's :math:`L` is concerned with a trend in an observation
+    (e.g. the airspeed velocity of a swallow) across several distinct
+    treatments (e.g. carrying each of five coconuts of different weight) even
+    as the observation is repeated with multiple subjects (e.g. one European
+    swallow and one African swallow).
+
+    Parameters
+    ----------
+    data : array-like
+        A :math:`m \times n` array; the element in row :math:`i` and
+        column :math:`j` is the observation corresponding with subject
+        :math:`i` and treatment :math:`j`. By default, the columns are
+        assumed to be arranged in order of increasing predicted mean.
+
+    ranked : bool, optional
+        By default, `data` is assumed to be observations rather than ranks;
+        it will be ranked with `scipy.stats.rankdata` along ``axis=1``. If
+        `data` is provided in the form of ranks, pass argument ``True``.
+
+    predicted_ranks : array-like, optional
+        The predicted ranks of the column means. If not specified,
+        the columns are assumed to be arranged in order of increasing
+        predicted mean, so the default `predicted_ranks` are
+        :math:`[1, 2, \dots, n-1, n]`.
+
+    method : {'auto', 'asymptotic', 'exact'}, optional
+        Selects the method used to calculate the *p*-value. The following
+        options are available.
+
+        * 'auto': selects between 'exact' and 'asymptotic' to
+          achieve reasonably accurate results in reasonable time (default)
+        * 'asymptotic': compares the standardized test statistic against
+          the normal distribution
+        * 'exact': computes the exact *p*-value by comparing the observed
+          :math:`L` statistic against those realized by all possible
+          permutations of ranks (under the null hypothesis that each
+          permutation is equally likely)
+
+    Returns
+    -------
+    res : PageTrendTestResult
+        An object containing attributes:
+
+        statistic : float
+            Page's :math:`L` test statistic.
+        pvalue : float
+            The associated *p*-value
+        method : {'asymptotic', 'exact'}
+            The method used to compute the *p*-value
+
+    See Also
+    --------
+    rankdata, friedmanchisquare, spearmanr
+
+    Notes
+    -----
+    As noted in [1]_, "the :math:`n` 'treatments' could just as well represent
+    :math:`n` objects or events or performances or persons or trials ranked."
+    Similarly, the :math:`m` 'subjects' could equally stand for :math:`m`
+    "groupings by ability or some other control variable, or judges doing
+    the ranking, or random replications of some other sort."
+
+    The procedure for calculating the :math:`L` statistic, adapted from
+    [1]_, is:
+
+    1. "Predetermine with careful logic the appropriate hypotheses
+       concerning the predicted ordering of the experimental results.
+       If no reasonable basis for ordering any treatments is known, the
+       :math:`L` test is not appropriate."
+    2. "As in other experiments, determine at what level of confidence
+       you will reject the null hypothesis that there is no agreement of
+       experimental results with the monotonic hypothesis."
+    3. "Cast the experimental material into a two-way table of :math:`n`
+       columns (treatments, objects ranked, conditions) and :math:`m`
+       rows (subjects, replication groups, levels of control variables)."
+    4. "When experimental observations are recorded, rank them across each
+       row", e.g. ``ranks = scipy.stats.rankdata(data, axis=1)``.
+    5. "Add the ranks in each column", e.g.
+       ``colsums = np.sum(ranks, axis=0)``.
+    6. "Multiply each sum of ranks by the predicted rank for that same
+       column", e.g. ``products = predicted_ranks * colsums``.
+    7. "Sum all such products", e.g. ``L = products.sum()``.
+
+    [1]_ continues by suggesting use of the standardized statistic
+
+    .. math::
+
+        \chi_L^2 = \frac{\left[12L-3mn(n+1)^2\right]^2}{mn^2(n^2-1)(n+1)}
+
+    "which is distributed approximately as chi-square with 1 degree of
+    freedom. The ordinary use of :math:`\chi^2` tables would be
+    equivalent to a two-sided test of agreement. If a one-sided test
+    is desired, *as will almost always be the case*, the probability
+    discovered in the chi-square table should be *halved*."
+
+    However, this standardized statistic does not distinguish between the
+    observed values being well correlated with the predicted ranks and being
+    _anti_-correlated with the predicted ranks. Instead, we follow [2]_
+    and calculate the standardized statistic
+
+    .. math::
+
+        \Lambda = \frac{L - E_0}{\sqrt{V_0}},
+
+    where :math:`E_0 = \frac{1}{4} mn(n+1)^2` and
+    :math:`V_0 = \frac{1}{144} mn^2(n+1)(n^2-1)`, "which is asymptotically
+    normal under the null hypothesis".
+
+    The *p*-value for ``method='exact'`` is generated by comparing the observed
+    value of :math:`L` against the :math:`L` values generated for all
+    :math:`(n!)^m` possible permutations of ranks. The calculation is performed
+    using the recursive method of [5].
+
+    The *p*-values are not adjusted for the possibility of ties. When
+    ties are present, the reported  ``'exact'`` *p*-values may be somewhat
+    larger (i.e. more conservative) than the true *p*-value [2]_. The
+    ``'asymptotic'`` *p*-values, however, tend to be smaller (i.e. less
+    conservative) than the ``'exact'`` *p*-values.
+
+    References
+    ----------
+    .. [1] Ellis Batten Page, "Ordered hypotheses for multiple treatments:
+       a significant test for linear ranks", *Journal of the American
+       Statistical Association* 58(301), p. 216--230, 1963.
+
+    .. [2] Markus Neuhauser, *Nonparametric Statistical Test: A computational
+       approach*, CRC Press, p. 150--152, 2012.
+
+    .. [3] Statext LLC, "Page's L Trend Test - Easy Statistics", *Statext -
+       Statistics Study*, https://www.statext.com/practice/PageTrendTest03.php,
+       Accessed July 12, 2020.
+
+    .. [4] "Page's Trend Test", *Wikipedia*, WikimediaFoundation,
+       https://en.wikipedia.org/wiki/Page%27s_trend_test,
+       Accessed July 12, 2020.
+
+    .. [5] Robert E. Odeh, "The exact distribution of Page's L-statistic in
+       the two-way layout", *Communications in Statistics - Simulation and
+       Computation*,  6(1), p. 49--61, 1977.
+
+    Examples
+    --------
+    We use the example from [3]_: 10 students are asked to rate three
+    teaching methods - tutorial, lecture, and seminar - on a scale of 1-5,
+    with 1 being the lowest and 5 being the highest. We have decided that
+    a confidence level of 99% is required to reject the null hypothesis in
+    favor of our alternative: that the seminar will have the highest ratings
+    and the tutorial will have the lowest. Initially, the data have been
+    tabulated with each row representing an individual student's ratings of
+    the three methods in the following order: tutorial, lecture, seminar.
+
+    >>> table = [[3, 4, 3],
+    ...          [2, 2, 4],
+    ...          [3, 3, 5],
+    ...          [1, 3, 2],
+    ...          [2, 3, 2],
+    ...          [2, 4, 5],
+    ...          [1, 2, 4],
+    ...          [3, 4, 4],
+    ...          [2, 4, 5],
+    ...          [1, 3, 4]]
+
+    Because the tutorial is hypothesized to have the lowest ratings, the
+    column corresponding with tutorial rankings should be first; the seminar
+    is hypothesized to have the highest ratings, so its column should be last.
+    Since the columns are already arranged in this order of increasing
+    predicted mean, we can pass the table directly into `page_trend_test`.
+
+    >>> from scipy.stats import page_trend_test
+    >>> res = page_trend_test(table)
+    >>> res
+    PageTrendTestResult(statistic=133.5, pvalue=0.0018191161948127822,
+                        method='exact')
+
+    This *p*-value indicates that there is a 0.1819% chance that
+    the :math:`L` statistic would reach such an extreme value under the null
+    hypothesis. Because 0.1819% is less than 1%, we have evidence to reject
+    the null hypothesis in favor of our alternative at a 99% confidence level.
+
+    The value of the :math:`L` statistic is 133.5. To check this manually,
+    we rank the data such that high scores correspond with high ranks, settling
+    ties with an average rank:
+
+    >>> from scipy.stats import rankdata
+    >>> ranks = rankdata(table, axis=1)
+    >>> ranks
+    array([[1.5, 3. , 1.5],
+           [1.5, 1.5, 3. ],
+           [1.5, 1.5, 3. ],
+           [1. , 3. , 2. ],
+           [1.5, 3. , 1.5],
+           [1. , 2. , 3. ],
+           [1. , 2. , 3. ],
+           [1. , 2.5, 2.5],
+           [1. , 2. , 3. ],
+           [1. , 2. , 3. ]])
+
+    We add the ranks within each column, multiply the sums by the
+    predicted ranks, and sum the products.
+
+    >>> import numpy as np
+    >>> m, n = ranks.shape
+    >>> predicted_ranks = np.arange(1, n+1)
+    >>> L = (predicted_ranks * np.sum(ranks, axis=0)).sum()
+    >>> res.statistic == L
+    True
+
+    As presented in [3]_, the asymptotic approximation of the *p*-value is the
+    survival function of the normal distribution evaluated at the standardized
+    test statistic:
+
+    >>> from scipy.stats import norm
+    >>> E0 = (m*n*(n+1)**2)/4
+    >>> V0 = (m*n**2*(n+1)*(n**2-1))/144
+    >>> Lambda = (L-E0)/np.sqrt(V0)
+    >>> p = norm.sf(Lambda)
+    >>> p
+    0.0012693433690751756
+
+    This does not precisely match the *p*-value reported by `page_trend_test`
+    above. The asymptotic distribution is not very accurate, nor conservative,
+    for :math:`m \leq 12` and :math:`n \leq 8`, so `page_trend_test` chose to
+    use ``method='exact'`` based on the dimensions of the table and the
+    recommendations in Page's original paper [1]_. To override
+    `page_trend_test`'s choice, provide the `method` argument.
+
+    >>> res = page_trend_test(table, method="asymptotic")
+    >>> res
+    PageTrendTestResult(statistic=133.5, pvalue=0.0012693433690751756,
+                        method='asymptotic')
+
+    If the data are already ranked, we can pass in the ``ranks`` instead of
+    the ``table`` to save computation time.
+
+    >>> res = page_trend_test(ranks,             # ranks of data
+    ...                       ranked=True,       # data is already ranked
+    ...                       )
+    >>> res
+    PageTrendTestResult(statistic=133.5, pvalue=0.0018191161948127822,
+                        method='exact')
+
+    Suppose the raw data had been tabulated in an order different from the
+    order of predicted means, say lecture, seminar, tutorial.
+
+    >>> table = np.asarray(table)[:, [1, 2, 0]]
+
+    Since the arrangement of this table is not consistent with the assumed
+    ordering, we can either rearrange the table or provide the
+    `predicted_ranks`. Remembering that the lecture is predicted
+    to have the middle rank, the seminar the highest, and tutorial the lowest,
+    we pass:
+
+    >>> res = page_trend_test(table,             # data as originally tabulated
+    ...                       predicted_ranks=[2, 3, 1],  # our predicted order
+    ...                       )
+    >>> res
+    PageTrendTestResult(statistic=133.5, pvalue=0.0018191161948127822,
+                        method='exact')
+
+    """
+    if not hasattr(_pagel_state, 'state'):
+        _pagel_state.state = _PageL()
+
+    # Possible values of the method parameter and the corresponding function
+    # used to evaluate the p value
+    methods = {"asymptotic": _l_p_asymptotic,
+               "exact": _l_p_exact,
+               "auto": None}
+    if method not in methods:
+        raise ValueError(f"`method` must be in {set(methods)}")
+
+    ranks = np.asarray(data)
+    if ranks.ndim != 2:  # TODO: relax this to accept 3d arrays?
+        raise ValueError("`data` must be a 2d array.")
+
+    m, n = ranks.shape
+    if m < 2 or n < 3:
+        raise ValueError("Page's L is only appropriate for data with two "
+                         "or more rows and three or more columns.")
+
+    if np.any(np.isnan(data)):
+        raise ValueError("`data` contains NaNs, which cannot be ranked "
+                         "meaningfully")
+
+    # ensure NumPy array and rank the data if it's not already ranked
+    if ranked:
+        # Only a basic check on whether data is ranked. Checking that the data
+        # is properly ranked could take as much time as ranking it.
+        if not (ranks.min() >= 1 and ranks.max() <= ranks.shape[1]):
+            raise ValueError("`data` is not properly ranked. Rank the data or "
+                             "pass `ranked=False`.")
+    else:
+        ranks = scipy.stats.rankdata(data, axis=-1)
+
+    # generate predicted ranks if not provided, ensure valid NumPy array
+    if predicted_ranks is None:
+        predicted_ranks = np.arange(1, n+1)
+    else:
+        predicted_ranks = np.asarray(predicted_ranks)
+        if (predicted_ranks.ndim < 1 or
+                (set(predicted_ranks) != set(range(1, n+1)) or
+                 len(predicted_ranks) != n)):
+            raise ValueError(f"`predicted_ranks` must include each integer "
+                             f"from 1 to {n} (the number of columns in "
+                             f"`data`) exactly once.")
+
+    if not isinstance(ranked, bool):
+        raise TypeError("`ranked` must be boolean.")
+
+    # Calculate the L statistic
+    L = _l_vectorized(ranks, predicted_ranks)
+
+    # Calculate the p-value
+    if method == "auto":
+        method = _choose_method(ranks)
+    p_fun = methods[method]  # get the function corresponding with the method
+    p = p_fun(L, m, n)
+
+    page_result = PageTrendTestResult(statistic=L, pvalue=p, method=method)
+    return page_result
+
+
+def _choose_method(ranks):
+    '''Choose method for computing p-value automatically'''
+    m, n = ranks.shape
+    if n > 8 or (m > 12 and n > 3) or m > 20:  # as in [1], [4]
+        method = "asymptotic"
+    else:
+        method = "exact"
+    return method
+
+
+def _l_vectorized(ranks, predicted_ranks):
+    '''Calculate's Page's L statistic for each page of a 3d array'''
+    colsums = ranks.sum(axis=-2, keepdims=True)
+    products = predicted_ranks * colsums
+    Ls = products.sum(axis=-1)
+    Ls = Ls[0] if Ls.size == 1 else Ls.ravel()
+    return Ls
+
+
+def _l_p_asymptotic(L, m, n):
+    '''Calculate the p-value of Page's L from the asymptotic distribution'''
+    # Using [1] as a reference, the asymptotic p-value would be calculated as:
+    # chi_L = (12*L - 3*m*n*(n+1)**2)**2/(m*n**2*(n**2-1)*(n+1))
+    # p = chi2.sf(chi_L, df=1, loc=0, scale=1)/2
+    # but this is insensitive to the direction of the hypothesized ranking
+
+    # See [2] page 151
+    E0 = (m*n*(n+1)**2)/4
+    V0 = (m*n**2*(n+1)*(n**2-1))/144
+    Lambda = (L-E0)/np.sqrt(V0)
+    # This is a one-sided "greater" test - calculate the probability that the
+    # L statistic under H0 would be greater than the observed L statistic
+    p = norm.sf(Lambda)
+    return p
+
+
+def _l_p_exact(L, m, n):
+    '''Calculate the p-value of Page's L exactly'''
+    # [1] uses m, n; [5] uses n, k.
+    # Switch convention here because exact calculation code references [5].
+    L, n, k = int(L), int(m), int(n)
+    _pagel_state.state.set_k(k)
+    return _pagel_state.state.sf(L, n)
+
+
+class _PageL:
+    '''Maintains state between `page_trend_test` executions'''
+
+    def __init__(self):
+        '''Lightweight initialization'''
+        self.all_pmfs = {}
+
+    def set_k(self, k):
+        '''Calculate lower and upper limits of L for single row'''
+        self.k = k
+        # See [5] top of page 52
+        self.a, self.b = (k*(k+1)*(k+2))//6, (k*(k+1)*(2*k+1))//6
+
+    def sf(self, l, n):
+        '''Survival function of Page's L statistic'''
+        ps = [self.pmf(l, n) for l in range(l, n*self.b + 1)]
+        return np.sum(ps)
+
+    def p_l_k_1(self):
+        '''Relative frequency of each L value over all possible single rows'''
+
+        # See [5] Equation (6)
+        ranks = range(1, self.k+1)
+        # generate all possible rows of length k
+        rank_perms = np.array(list(permutations(ranks)))
+        # compute Page's L for all possible rows
+        Ls = (ranks*rank_perms).sum(axis=1)
+        # count occurrences of each L value
+        counts = np.histogram(Ls, np.arange(self.a-0.5, self.b+1.5))[0]
+        # factorial(k) is number of possible permutations
+        return counts/math.factorial(self.k)
+
+    def pmf(self, l, n):
+        '''Recursive function to evaluate p(l, k, n); see [5] Equation 1'''
+
+        if n not in self.all_pmfs:
+            self.all_pmfs[n] = {}
+        if self.k not in self.all_pmfs[n]:
+            self.all_pmfs[n][self.k] = {}
+
+        # Cache results to avoid repeating calculation. Initially this was
+        # written with lru_cache, but this seems faster? Also, we could add
+        # an option to save this for future lookup.
+        if l in self.all_pmfs[n][self.k]:
+            return self.all_pmfs[n][self.k][l]
+
+        if n == 1:
+            ps = self.p_l_k_1()  # [5] Equation 6
+            ls = range(self.a, self.b+1)
+            # not fast, but we'll only be here once
+            self.all_pmfs[n][self.k] = {l: p for l, p in zip(ls, ps)}
+            return self.all_pmfs[n][self.k][l]
+
+        p = 0
+        low = max(l-(n-1)*self.b, self.a)  # [5] Equation 2
+        high = min(l-(n-1)*self.a, self.b)
+
+        # [5] Equation 1
+        for t in range(low, high+1):
+            p1 = self.pmf(l-t, n-1)
+            p2 = self.pmf(t, 1)
+            p += p1*p2
+        self.all_pmfs[n][self.k][l] = p
+        return p
+
+
+# Maintain state for faster repeat calls to page_trend_test w/ method='exact'
+# _PageL() is calculated once per thread and stored as an attribute on
+# this thread-local variable inside page_trend_test().
+_pagel_state = threading.local()
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_probability_distribution.py b/venv/lib/python3.12/site-packages/scipy/stats/_probability_distribution.py
new file mode 100644
index 0000000000000000000000000000000000000000..71ed8f48920f3031a88cf1285fae25e4bb28eefa
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_probability_distribution.py
@@ -0,0 +1,2091 @@
+# Temporary file separated from _distribution_infrastructure.py
+# to simplify the diff during PR review.
+from abc import ABC, abstractmethod
+from types import GenericAlias
+
+class _ProbabilityDistribution(ABC):
+
+    # generic type compatibility with scipy-stubs
+    __class_getitem__: classmethod = classmethod(GenericAlias)
+
+    @abstractmethod
+    def support(self):
+        r"""Support of the random variable
+
+        The support of a random variable is set of all possible outcomes;
+        i.e., the subset of the domain of argument :math:`x` for which
+        the probability density function :math:`f(x)` is nonzero.
+
+        This function returns lower and upper bounds of the support.
+
+        Returns
+        -------
+        out : tuple of Array
+            The lower and upper bounds of the support.
+
+        See Also
+        --------
+        pdf
+
+        References
+        ----------
+        .. [1] Support (mathematics), *Wikipedia*,
+               https://en.wikipedia.org/wiki/Support_(mathematics)
+
+        Notes
+        -----
+        Suppose a continuous probability distribution has support ``(l, r)``.
+        The following table summarizes the value returned by several
+        methods when the argument is outside the support.
+
+        +----------------+---------------------+---------------------+
+        | Method         | Value for ``x < l`` | Value for ``x > r`` |
+        +================+=====================+=====================+
+        | ``pdf(x)``     | 0                   | 0                   |
+        +----------------+---------------------+---------------------+
+        | ``logpdf(x)``  | -inf                | -inf                |
+        +----------------+---------------------+---------------------+
+        | ``cdf(x)``     | 0                   | 1                   |
+        +----------------+---------------------+---------------------+
+        | ``logcdf(x)``  | -inf                | 0                   |
+        +----------------+---------------------+---------------------+
+        | ``ccdf(x)``    | 1                   | 0                   |
+        +----------------+---------------------+---------------------+
+        | ``logccdf(x)`` | 0                   | -inf                |
+        +----------------+---------------------+---------------------+
+
+        For discrete distributions, the same table is applicable with
+        ``pmf`` and ``logpmf`` substituted for ``pdf`` and ``logpdf``.
+
+        For the ``cdf`` and related methods of continuous distributions, the
+        inequality need not be strict; i.e. the tabulated value is returned
+        when the method is evaluated *at* the corresponding boundary.
+
+        The following table summarizes the value returned by the inverse
+        methods for arguments ``0`` and ``1``, whether the distribution
+        is continuous or discrete.
+
+        +-------------+-----------+-----------+
+        | Method      | ``x = 0`` | ``x = 1`` |
+        +=============+===========+===========+
+        | ``icdf(x)`` | ``l``     | ``r``     |
+        +-------------+-----------+-----------+
+        | ``icdf(x)`` | ``r``     | ``l``     |
+        +-------------+-----------+-----------+
+
+        For the inverse log-functions, the same values are returned
+        for ``x = log(0)`` and ``x = log(1)``. All inverse functions return
+        ``nan`` when evaluated at an argument outside the domain ``0`` to ``1``.
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> from scipy import stats
+        >>> X = stats.Uniform(a=-0.5, b=0.5)
+
+        Retrieve the support of the distribution:
+
+        >>> X.support()
+        (-0.5, 0.5)
+
+        For a distribution with infinite support,
+
+        >>> X = stats.Normal()
+        >>> X.support()
+        (-inf, inf)
+
+        Due to underflow, the numerical value returned by the PDF may be zero
+        even for arguments within the support, even if the true value is
+        nonzero. In such cases, the log-PDF may be useful.
+
+        >>> X.pdf([-100., 100.])
+        array([0., 0.])
+        >>> X.logpdf([-100., 100.])
+        array([-5000.91893853, -5000.91893853])
+
+        Use cases for the log-CDF and related methods are analogous.
+
+        """
+        raise NotImplementedError()
+
+    @abstractmethod
+    def sample(self, shape, *, method, rng):
+        r"""Random sample from the distribution.
+
+        Parameters
+        ----------
+        shape : tuple of ints, default: ()
+            The shape of the sample to draw. If the parameters of the distribution
+            underlying the random variable are arrays of shape ``param_shape``,
+            the output array will be of shape ``shape + param_shape``.
+        method : {None, 'formula', 'inverse_transform'}
+            The strategy used to produce the sample. By default (``None``),
+            the infrastructure chooses between the following options,
+            listed in order of precedence.
+
+            - ``'formula'``: an implementation specific to the distribution
+            - ``'inverse_transform'``: generate a uniformly distributed sample and
+              return the inverse CDF at these arguments.
+
+            Not all `method` options are available for all distributions.
+            If the selected `method` is not available, a `NotImplementedError``
+            will be raised.
+        rng : `numpy.random.Generator` or `scipy.stats.qmc.QMCEngine`, optional
+            Pseudo- or quasi-random number generator state. When `rng` is None,
+            a new `numpy.random.Generator` is created using entropy from the
+            operating system. Types other than `numpy.random.Generator` and
+            `scipy.stats.qmc.QMCEngine` are passed to `numpy.random.default_rng`
+            to instantiate a ``Generator``.
+
+            If `rng` is an instance of `scipy.stats.qmc.QMCEngine` configured to use
+            scrambling and `shape` is not empty, then each slice along the zeroth
+            axis of the result is a "quasi-independent", low-discrepancy sequence;
+            that is, they are distinct sequences that can be treated as statistically
+            independent for most practical purposes. Separate calls to `sample`
+            produce new quasi-independent, low-discrepancy sequences. The dimensionality
+            (``d``) of the provided ``QMCEngine`` is ignored; new instances of the same
+            class and configuration options (``scramble``, ``optimization``, and
+            ``bits``, where applicable) will be created with ``d=1``.
+
+        References
+        ----------
+        .. [1] Sampling (statistics), *Wikipedia*,
+               https://en.wikipedia.org/wiki/Sampling_(statistics)
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> import numpy as np
+        >>> from scipy import stats
+        >>> X = stats.Uniform(a=0., b=1.)
+
+        Generate a pseudorandom sample:
+
+        >>> x = X.sample((1000, 1))
+        >>> octiles = (np.arange(8) + 1) / 8
+        >>> np.count_nonzero(x <= octiles, axis=0)
+        array([ 148,  263,  387,  516,  636,  751,  865, 1000])  # may vary
+
+        >>> X = stats.Uniform(a=np.zeros((3, 1)), b=np.ones(2))
+        >>> X.a.shape,
+        (3, 2)
+        >>> x = X.sample(shape=(5, 4))
+        >>> x.shape
+        (5, 4, 3, 2)
+
+        """
+        raise NotImplementedError()
+
+    @abstractmethod
+    def moment(self, order, kind, *, method):
+        r"""Raw, central, or standard moment of positive integer order.
+
+        In terms of probability density function :math:`f(x)` and support
+        :math:`\chi`, the "raw" moment (about the origin) of order :math:`n` of
+        a continuous random variable :math:`X` is:
+
+        .. math::
+
+            \mu'_n(X) = \int_{\chi} x^n f(x) dx
+
+        The "central" moment is the raw moment taken about the mean,
+        :math:`\mu = \mu'_1`:
+
+        .. math::
+
+            \mu_n(X) = \int_{\chi} (x - \mu) ^n f(x) dx
+
+        The "standardized" moment is the central moment normalized by the
+        :math:`n^\text{th}` power of the standard deviation
+        :math:`\sigma = \sqrt{\mu_2}` to produce a scale invariant quantity:
+
+        .. math::
+
+            \tilde{\mu}_n(X) = \frac{\mu_n(X)}
+                                    {\sigma^n}
+
+        The definitions for discrete random variables are analogous, with
+        sums over the support replacing the integrals.
+
+        Parameters
+        ----------
+        order : int
+            The integer order of the moment; i.e. :math:`n` in the formulae above.
+        kind : {'raw', 'central', 'standardized'}
+            Whether to return the raw (default), central, or standardized moment
+            defined above.
+        method : {None, 'formula', 'general', 'transform', 'normalize', 'quadrature', 'cache'}
+            The strategy used to evaluate the moment. By default (``None``),
+            the infrastructure chooses between the following options,
+            listed in order of precedence.
+
+            - ``'cache'``: use the value of the moment most recently calculated
+              via another method
+            - ``'formula'``: use a formula for the moment itself
+            - ``'general'``: use a general result that is true for all distributions
+              with finite moments; for instance, the zeroth raw moment is
+              identically 1
+            - ``'transform'``: transform a raw moment to a central moment or
+              vice versa (see Notes)
+            - ``'normalize'``: normalize a central moment to get a standardized
+              or vice versa
+            - ``'quadrature'``: numerically integrate (or, in the discrete case, sum)
+              according to the definition
+
+            Not all `method` options are available for all orders, kinds, and
+            distributions. If the selected `method` is not available, a
+            ``NotImplementedError`` will be raised.
+
+        Returns
+        -------
+        out : array
+            The moment of the random variable of the specified order and kind.
+
+        See Also
+        --------
+        pdf
+        mean
+        variance
+        standard_deviation
+        skewness
+        kurtosis
+        lmoment
+
+        Notes
+        -----
+        Not all distributions have finite moments of all orders; moments of some
+        orders may be undefined or infinite. If a formula for the moment is not
+        specifically implemented for the chosen distribution, SciPy will attempt
+        to compute the moment via a generic method, which may yield a finite
+        result where none exists. This is not a critical bug, but an opportunity
+        for an enhancement.
+
+        The definition of a raw moment in the summary is specific to the raw moment
+        about the origin. The raw moment about any point :math:`a` is:
+
+        .. math::
+
+            E[(X-a)^n] = \int_{\chi} (x-a)^n f(x) dx
+
+        In this notation, a raw moment about the origin is :math:`\mu'_n = E[x^n]`,
+        and a central moment is :math:`\mu_n = E[(x-\mu)^n]`, where :math:`\mu`
+        is the first raw moment; i.e. the mean.
+
+        The ``'transform'`` method takes advantage of the following relationships
+        between moments taken about different points :math:`a` and :math:`b`.
+
+        .. math::
+
+            E[(X-b)^n] =  \sum_{i=0}^n E[(X-a)^i] {n \choose i} (a - b)^{n-i}
+
+        For instance, to transform the raw moment to the central moment, we let
+        :math:`b = \mu` and :math:`a = 0`.
+
+        The distribution infrastructure provides flexibility for distribution
+        authors to implement separate formulas for raw moments, central moments,
+        and standardized moments of any order. By default, the moment of the
+        desired order and kind is evaluated from the formula if such a formula
+        is available; if not, the infrastructure uses any formulas that are
+        available rather than resorting directly to numerical integration.
+        For instance, if formulas for the first three raw moments are
+        available and the third standardized moments is desired, the
+        infrastructure will evaluate the raw moments and perform the transforms
+        and standardization required. The decision tree is somewhat complex,
+        but the strategy for obtaining a moment of a given order and kind
+        (possibly as an intermediate step due to the recursive nature of the
+        transform formula above) roughly follows this order of priority:
+
+        #. Use cache (if order of same moment and kind has been calculated)
+        #. Use formula (if available)
+        #. Transform between raw and central moment and/or normalize to convert
+           between central and standardized moments (if efficient)
+        #. Use a generic result true for most distributions (if available)
+        #. Use quadrature
+
+        References
+        ----------
+        .. [1] Moment, *Wikipedia*,
+               https://en.wikipedia.org/wiki/Moment_(mathematics)
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> from scipy import stats
+        >>> X = stats.Normal(mu=1., sigma=2.)
+
+        Evaluate the first raw moment:
+
+        >>> X.moment(order=1, kind='raw')
+        1.0
+        >>> X.moment(order=1, kind='raw') == X.mean() == X.mu
+        True
+
+        Evaluate the second central moment:
+
+        >>> X.moment(order=2, kind='central')
+        4.0
+        >>> X.moment(order=2, kind='central') == X.variance() == X.sigma**2
+        True
+
+        Evaluate the fourth standardized moment:
+
+        >>> X.moment(order=4, kind='standardized')
+        3.0
+        >>> X.moment(order=4, kind='standardized') == X.kurtosis(convention='non-excess')
+        True
+
+        """  # noqa:E501
+        raise NotImplementedError()
+
+    @abstractmethod
+    def lmoment(self, order, *, standardize, method):
+        r"""L-moment or L-moment ratio of positive integer order.
+
+        The L-moment of order :math:`n` of a continuous random variable :math:`X` is:
+
+        .. math::
+
+            \lambda_n(X) = \frac{1}{n} \sum_{k=0}^{n-1} (-1)^{k} {{n-1}\choose k} E[X_{(n-k)}]
+
+        where :math:`X_{(1)}, \dots, X_{(r)}, \dots, X_{(n)}` are the order statistics
+        of an independent sample of size :math:`n`.
+
+        The L-moment can also be expressed in terms of the random variable's inverse
+        cumulative distribution function :math:`F^{-1}` and the shifted Legendre
+        polynomial :math:`\widetilde{P}_{n-1}`:
+
+        .. math::
+
+            \lambda_n(X) = \int_0^1 F^{-1}(p) \widetilde{P}_{n-1}(p) dp
+
+        For order :math:`n \geq 3`, the "standardized" L-moment, known as the L-moment
+        ratio, is the L-moment normalized by the L-moment of order 2, resulting in a
+        scale invariant quantity:
+
+        .. math::
+
+            \tau_n(X) = \frac{\lambda_n(X)}
+                             {\lambda_2(X)}
+
+        Parameters
+        ----------
+        order : int
+            The positive integer order of the L-moment; i.e. :math:`n` in the formulae
+            above.
+        standardize : bool, default: True
+            Whether to return L-moment ratios for orders 3 and higher. L-moment ratios
+            are analogous to standardized conventional moments: they are the
+            non-standardized L-moments divided by the L-moment of order 2.
+        method : {None, 'formula', 'general', 'order_statistics', 'quadrature_icdf', 'cache'}
+            The strategy used to evaluate the L-moment. By default (``None``),
+            the infrastructure chooses between the following options,
+            listed in order of precedence.
+
+            - ``'cache'``: use the value of the L-moment most recently calculated
+              via another method
+            - ``'formula'``: use a formula specific to the distribution.
+            - ``'general'``: use a general result that is true for all distributions
+              with finite L-moments; for instance, the first L-moment is identically
+              equal to the mean.
+            - ``'quadrature_icdf'``: numerically integrate according to the definition
+              in terms of the inverse cumulative distribution function.
+            - ``'order_statistics'``: compute according to the definition in terms of
+              order statistics.
+
+            Not all `method` options are available for all orders and distributions.
+            If the selected `method` is not available, a ``NotImplementedError`` will
+            be raised.
+
+        Returns
+        -------
+        out : array
+            The L-moment of the random variable of the specified order.
+
+        See Also
+        --------
+        moment
+        order_statistic
+
+        Notes
+        -----
+        L-moments are only defined for distributions with finite mean. If a formula for
+        the L-moment is not specifically implemented for the chosen distribution, SciPy
+        will attempt to compute the moment via a generic method, which may yield a
+        finite result where none exists. This is not a critical bug, but an opportunity
+        for an enhancement.
+
+        SciPy offers only basic capabilities for working with L-moments. For more advanced
+        features, consider the ``lmo`` package [2]_.
+
+        References
+        ----------
+        .. [1] L-moment, *Wikipedia*,
+               https://en.wikipedia.org/wiki/L-moment
+        .. [2] @jorenham, *Lmo*, https://github.com/jorenham/Lmo/
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> import numpy as np
+        >>> from scipy import stats
+        >>> X = stats.Normal(mu=1., sigma=2.)
+
+        Evaluate the first L-moment:
+
+        >>> X.lmoment(order=1)
+        1.0
+        >>> X.lmoment(order=1) == X.mean() == X.mu
+        True
+
+        Evaluate the second L-moment:
+
+        >>> X.lmoment(order=2)
+        np.float64(1.1283791670955123)
+        >>> np.allclose(X.lmoment(order=2), X.sigma / np.sqrt(np.pi))
+        True
+
+        Evaluate the fourth L-moment ratio, that is, the L-kurtosis:
+
+        >>> X.lmoment(order=4)
+        np.float64(0.12260171954089069)
+        >>> X.lmoment(order=4) == X.lmoment(order=4, standardize=False) / X.lmoment(order=2)
+        True
+
+        """  # noqa:E501
+        raise NotImplementedError()
+
+    @abstractmethod
+    def mean(self, *, method):
+        r"""Mean (raw first moment about the origin)
+
+        Parameters
+        ----------
+        method : {None, 'formula', 'transform', 'quadrature', 'cache'}
+            Method used to calculate the raw first moment. Not
+            all methods are available for all distributions. See
+            `moment` for details.
+
+        See Also
+        --------
+        moment
+        median
+        mode
+
+        References
+        ----------
+        .. [1] Mean, *Wikipedia*,
+               https://en.wikipedia.org/wiki/Mean#Mean_of_a_probability_distribution
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> from scipy import stats
+        >>> X = stats.Normal(mu=1., sigma=2.)
+
+        Evaluate the variance:
+
+        >>> X.mean()
+        1.0
+        >>> X.mean() == X.moment(order=1, kind='raw') == X.mu
+        True
+
+        """
+        raise NotImplementedError()
+
+    @abstractmethod
+    def median(self, *, method):
+        r"""Median (50th percentile)
+
+        If a continuous random variable :math:`X` has probability :math:`0.5` of
+        taking on a value less than :math:`m`, then :math:`m` is the median.
+
+        More generally, a median is a value :math:`m` for which:
+
+        .. math::
+
+            P(X ≤ m) ≤ 0.5 ≥ P(X ≥ m)
+
+        For discrete random variables, the median may not be unique, in which
+        case the smallest value satisfying the definition is reported.
+
+        Parameters
+        ----------
+        method : {None, 'formula', 'icdf'}
+            The strategy used to evaluate the median.
+            By default (``None``), the infrastructure chooses between the
+            following options, listed in order of precedence.
+
+            - ``'formula'``: use a formula for the median
+            - ``'icdf'``: evaluate the inverse CDF of 0.5
+
+            Not all `method` options are available for all distributions.
+            If the selected `method` is not available, a ``NotImplementedError``
+            will be raised.
+
+        Returns
+        -------
+        out : array
+            The median
+
+        See Also
+        --------
+        mean
+        mode
+        icdf
+
+        References
+        ----------
+        .. [1] Median, *Wikipedia*,
+               https://en.wikipedia.org/wiki/Median#Probability_distributions
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> from scipy import stats
+        >>> X = stats.Uniform(a=0., b=10.)
+
+        Compute the median:
+
+        >>> X.median()
+        np.float64(5.0)
+        >>> X.median() == X.icdf(0.5) == X.iccdf(0.5)
+        True
+
+        """
+        raise NotImplementedError()
+
+    @abstractmethod
+    def mode(self, *, method):
+        r"""Mode (most likely value)
+
+        Informally, the mode is a value that a random variable has the highest
+        probability (density) of assuming. That is, the mode is the element of
+        the support :math:`\chi` that maximizes the probability density (or mass,
+        for discrete random variables) function :math:`f(x)`:
+
+        .. math::
+
+            \text{mode} = \arg\max_{x \in \chi} f(x)
+
+        Parameters
+        ----------
+        method : {None, 'formula', 'optimization'}
+            The strategy used to evaluate the mode.
+            By default (``None``), the infrastructure chooses between the
+            following options, listed in order of precedence.
+
+            - ``'formula'``: use a formula for the median
+            - ``'optimization'``: numerically maximize the PDF/PMF
+
+            Not all `method` options are available for all distributions.
+            If the selected `method` is not available, a ``NotImplementedError``
+            will be raised.
+
+        Returns
+        -------
+        out : array
+            The mode
+
+        See Also
+        --------
+        mean
+        median
+        pdf
+
+        Notes
+        -----
+        For some distributions
+
+        #. the mode is not unique (e.g. the uniform distribution);
+        #. the PDF has one or more singularities, and it is debatable whether
+           a singularity is considered to be in the domain and called the mode
+           (e.g. the gamma distribution with shape parameter less than 1); and/or
+        #. the probability density function may have one or more local maxima
+           that are not a global maximum (e.g. mixture distributions).
+
+        In such cases, `mode` will
+
+        #. return a single value,
+        #. consider the mode to occur at a singularity, and/or
+        #. return a local maximum which may or may not be a global maximum.
+
+        If a formula for the mode is not specifically implemented for the
+        chosen distribution, SciPy will attempt to compute the mode
+        numerically, which may not meet the user's preferred definition of a
+        mode. In such cases, the user is encouraged to subclass the
+        distribution and override ``mode``.
+
+        References
+        ----------
+        .. [1] Mode (statistics), *Wikipedia*,
+               https://en.wikipedia.org/wiki/Mode_(statistics)
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> from scipy import stats
+        >>> X = stats.Normal(mu=1., sigma=2.)
+
+        Evaluate the mode:
+
+        >>> X.mode()
+        1.0
+
+        If the mode is not uniquely defined, ``mode`` nonetheless returns a
+        single value.
+
+        >>> X = stats.Uniform(a=0., b=1.)
+        >>> X.mode()
+        0.5
+
+        If this choice does not satisfy your requirements, subclass the
+        distribution and override ``mode``:
+
+        >>> class BetterUniform(stats.Uniform):
+        ...     def mode(self):
+        ...         return self.b
+        >>> X = BetterUniform(a=0., b=1.)
+        >>> X.mode()
+        1.0
+
+        """
+        raise NotImplementedError()
+
+    @abstractmethod
+    def variance(self, *, method):
+        r"""Variance (central second moment)
+
+        Parameters
+        ----------
+        method : {None, 'formula', 'transform', 'normalize', 'quadrature', 'cache'}
+            Method used to calculate the central second moment. Not
+            all methods are available for all distributions. See
+            `moment` for details.
+
+        See Also
+        --------
+        moment
+        standard_deviation
+        mean
+
+        References
+        ----------
+        .. [1] Variance, *Wikipedia*,
+               https://en.wikipedia.org/wiki/Variance#Absolutely_continuous_random_variable
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> from scipy import stats
+        >>> X = stats.Normal(mu=1., sigma=2.)
+
+        Evaluate the variance:
+
+        >>> X.variance()
+        4.0
+        >>> X.variance() == X.moment(order=2, kind='central') == X.sigma**2
+        True
+
+        """
+        raise NotImplementedError()
+
+    @abstractmethod
+    def standard_deviation(self, *, method):
+        r"""Standard deviation (square root of the second central moment)
+
+        Parameters
+        ----------
+        method : {None, 'formula', 'transform', 'normalize', 'quadrature', 'cache'}
+            Method used to calculate the central second moment. Not
+            all methods are available for all distributions. See
+            `moment` for details.
+
+        See Also
+        --------
+        variance
+        mean
+        moment
+
+        References
+        ----------
+        .. [1] Standard deviation, *Wikipedia*,
+               https://en.wikipedia.org/wiki/Standard_deviation#Definition_of_population_values
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> from scipy import stats
+        >>> X = stats.Normal(mu=1., sigma=2.)
+
+        Evaluate the standard deviation:
+
+        >>> X.standard_deviation()
+        2.0
+        >>> X.standard_deviation() == X.moment(order=2, kind='central')**0.5 == X.sigma
+        True
+
+        """
+        raise NotImplementedError()
+
+    @abstractmethod
+    def skewness(self, *, method):
+        r"""Skewness (standardized third moment)
+
+        Parameters
+        ----------
+        method : {None, 'formula', 'general', 'transform', 'normalize', 'cache'}
+            Method used to calculate the standardized third moment. Not
+            all methods are available for all distributions. See
+            `moment` for details.
+
+        See Also
+        --------
+        moment
+        mean
+        variance
+
+        References
+        ----------
+        .. [1] Skewness, *Wikipedia*,
+               https://en.wikipedia.org/wiki/Skewness
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> from scipy import stats
+        >>> X = stats.Normal(mu=1., sigma=2.)
+
+        Evaluate the skewness:
+
+        >>> X.skewness()
+        0.0
+        >>> X.skewness() == X.moment(order=3, kind='standardized')
+        True
+
+        """
+        raise NotImplementedError()
+
+    @abstractmethod
+    def kurtosis(self, *, method):
+        r"""Kurtosis (standardized fourth moment)
+
+        By default, this is the standardized fourth moment, also known as the
+        "non-excess" or "Pearson" kurtosis (e.g. the kurtosis of the normal
+        distribution is 3). The "excess" or "Fisher" kurtosis (the standardized
+        fourth moment minus 3) is available via the `convention` parameter.
+
+        Parameters
+        ----------
+        method : {None, 'formula', 'general', 'transform', 'normalize', 'cache'}
+            Method used to calculate the standardized fourth moment. Not
+            all methods are available for all distributions. See
+            `moment` for details.
+        convention : {'non-excess', 'excess'}
+            Two distinct conventions are available:
+
+            - ``'non-excess'``: the standardized fourth moment (Pearson's kurtosis)
+            - ``'excess'``: the standardized fourth moment minus 3 (Fisher's kurtosis)
+
+            The default is ``'non-excess'``.
+
+        See Also
+        --------
+        moment
+        mean
+        variance
+
+        References
+        ----------
+        .. [1] Kurtosis, *Wikipedia*,
+               https://en.wikipedia.org/wiki/Kurtosis
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> from scipy import stats
+        >>> X = stats.Normal(mu=1., sigma=2.)
+
+        Evaluate the kurtosis:
+
+        >>> X.kurtosis()
+        3.0
+        >>> (X.kurtosis()
+        ...  == X.kurtosis(convention='excess') + 3.
+        ...  == X.moment(order=4, kind='standardized'))
+        True
+
+        """
+        raise NotImplementedError()
+
+    @abstractmethod
+    def pdf(self, x, /, *, method):
+        r"""Probability density function
+
+        The probability density function ("PDF"), denoted :math:`f(x)`, is the
+        probability *per unit length* that the random variable will assume the
+        value :math:`x`. Mathematically, it can be defined as the derivative
+        of the cumulative distribution function :math:`F(x)`:
+
+        .. math::
+
+            f(x) = \frac{d}{dx} F(x)
+
+        `pdf` accepts `x` for :math:`x`.
+
+        Parameters
+        ----------
+        x : array_like
+            The argument of the PDF.
+        method : {None, 'formula', 'logexp'}
+            The strategy used to evaluate the PDF. By default (``None``), the
+            infrastructure chooses between the following options, listed in
+            order of precedence.
+
+            - ``'formula'``: use a formula for the PDF itself
+            - ``'logexp'``: evaluate the log-PDF and exponentiate
+
+            Not all `method` options are available for all distributions.
+            If the selected `method` is not available, a ``NotImplementedError``
+            will be raised.
+
+        Returns
+        -------
+        out : array
+            The PDF evaluated at the argument `x`.
+
+        See Also
+        --------
+        cdf
+        logpdf
+
+        Notes
+        -----
+        Suppose a continuous probability distribution has support :math:`[l, r]`.
+        By definition of the support, the PDF evaluates to its minimum value
+        of :math:`0` outside the support; i.e. for :math:`x < l` or
+        :math:`x > r`. The maximum of the PDF may be less than or greater than
+        :math:`1`; since the value is a probability *density*, only its integral
+        over the support must equal :math:`1`.
+
+        For discrete distributions, `pdf` returns ``inf`` at supported points
+        and ``0`` elsewhere.
+
+        References
+        ----------
+        .. [1] Probability density function, *Wikipedia*,
+               https://en.wikipedia.org/wiki/Probability_density_function
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> from scipy import stats
+        >>> X = stats.Uniform(a=-1., b=1.)
+
+        Evaluate the PDF at the desired argument:
+
+        >>> X.pdf(0.25)
+        0.5
+
+        """
+        raise NotImplementedError()
+
+    @abstractmethod
+    def logpdf(self, x, /, *, method):
+        r"""Log of the probability density function
+
+        The probability density function ("PDF"), denoted :math:`f(x)`, is the
+        probability *per unit length* that the random variable will assume the
+        value :math:`x`. Mathematically, it can be defined as the derivative
+        of the cumulative distribution function :math:`F(x)`:
+
+        .. math::
+
+            f(x) = \frac{d}{dx} F(x)
+
+        `logpdf` computes the logarithm of the probability density function
+        ("log-PDF"), :math:`\log(f(x))`, but it may be numerically favorable
+        compared to the naive implementation (computing :math:`f(x)` and
+        taking the logarithm).
+
+        `logpdf` accepts `x` for :math:`x`.
+
+        Parameters
+        ----------
+        x : array_like
+            The argument of the log-PDF.
+        method : {None, 'formula', 'logexp'}
+            The strategy used to evaluate the log-PDF. By default (``None``), the
+            infrastructure chooses between the following options, listed in order
+            of precedence.
+
+            - ``'formula'``: use a formula for the log-PDF itself
+            - ``'logexp'``: evaluate the PDF and takes its logarithm
+
+            Not all `method` options are available for all distributions.
+            If the selected `method` is not available, a ``NotImplementedError``
+            will be raised.
+
+        Returns
+        -------
+        out : array
+            The log-PDF evaluated at the argument `x`.
+
+        See Also
+        --------
+        pdf
+        logcdf
+
+        Notes
+        -----
+        Suppose a continuous probability distribution has support :math:`[l, r]`.
+        By definition of the support, the log-PDF evaluates to its minimum value
+        of :math:`-\infty` (i.e. :math:`\log(0)`) outside the support; i.e. for
+        :math:`x < l` or :math:`x > r`. The maximum of the log-PDF may be less
+        than or greater than :math:`\log(1) = 0` because the maximum of the PDF
+        can be any positive real.
+
+        For distributions with infinite support, it is common for `pdf` to return
+        a value of ``0`` when the argument is theoretically within the support;
+        this can occur because the true value of the PDF is too small to be
+        represented by the chosen dtype. The log-PDF, however, will often be finite
+        (not ``-inf``) over a much larger domain. Consequently, it may be preferred
+        to work with the logarithms of probabilities and probability densities to
+        avoid underflow.
+
+        For discrete distributions, `logpdf` returns ``inf`` at supported points and
+        ``-inf`` (``log(0)``) elsewhere.
+
+        References
+        ----------
+        .. [1] Probability density function, *Wikipedia*,
+               https://en.wikipedia.org/wiki/Probability_density_function
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> import numpy as np
+        >>> from scipy import stats
+        >>> X = stats.Uniform(a=-1.0, b=1.0)
+
+        Evaluate the log-PDF at the desired argument:
+
+        >>> X.logpdf(0.5)
+        -0.6931471805599453
+        >>> np.allclose(X.logpdf(0.5), np.log(X.pdf(0.5)))
+        True
+
+        """
+        raise NotImplementedError()
+
+    def pmf(self, x, /, *, method=None):
+        r"""Probability mass function
+
+        The probability mass function ("PMF"), denoted :math:`f(x)`, is the
+        probability that the random variable :math:`X` will assume the value :math:`x`.
+
+        .. math::
+
+            f(x) = P(X = x)
+
+        `pmf` accepts `x` for :math:`x`.
+
+        Parameters
+        ----------
+        x : array_like
+            The argument of the PMF.
+        method : {None, 'formula', 'logexp'}
+            The strategy used to evaluate the PMF. By default (``None``), the
+            infrastructure chooses between the following options, listed in
+            order of precedence.
+
+            - ``'formula'``: use a formula for the PMF itself
+            - ``'logexp'``: evaluate the log-PMF and exponentiate
+
+            Not all `method` options are available for all distributions.
+            If the selected `method` is not available, a ``NotImplementedError``
+            will be raised.
+
+        Returns
+        -------
+        out : array
+            The PMF evaluated at the argument `x`.
+
+        See Also
+        --------
+        cdf
+        logpmf
+
+        Notes
+        -----
+        Suppose a discrete probability distribution has support over the integers
+        :math:`{l, l+1, ..., r-1, r}`.
+        By definition of the support, the PMF evaluates to its minimum value
+        of :math:`0` for non-integral :math:`x` and for :math:`x` outside the support;
+        i.e. for :math:`x < l` or :math:`x > r`.
+
+        For continuous distributions, `pmf` returns ``0`` at all real arguments.
+
+        References
+        ----------
+        .. [1] Probability mass function, *Wikipedia*,
+               https://en.wikipedia.org/wiki/Probability_mass_function
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> from scipy import stats
+        >>> X = stats.Binomial(n=10, p=0.5)
+
+        Evaluate the PMF at the desired argument:
+
+        >>> X.pmf(5)
+        np.float64(0.24609375)
+
+        """
+        raise NotImplementedError()
+
+    def logpmf(self, x, /, *, method=None):
+        r"""Log of the probability mass function
+
+        The probability mass function ("PMF"), denoted :math:`f(x)`, is the
+        probability that the random variable :math:`X` will assume the value :math:`x`.
+
+        .. math::
+
+            f(x) = \frac{d}{dx} F(x)
+
+        `logpmf` computes the logarithm of the probability mass function
+        ("log-PMF"), :math:`\log(f(x))`, but it may be numerically favorable
+        compared to the naive implementation (computing :math:`f(x)` and
+        taking the logarithm).
+
+        `logpmf` accepts `x` for :math:`x`.
+
+        Parameters
+        ----------
+        x : array_like
+            The argument of the log-PMF.
+        method : {None, 'formula', 'logexp'}
+            The strategy used to evaluate the log-PMF. By default (``None``), the
+            infrastructure chooses between the following options, listed in order
+            of precedence.
+
+            - ``'formula'``: use a formula for the log-PMF itself
+            - ``'logexp'``: evaluate the PMF and takes its logarithm
+
+            Not all `method` options are available for all distributions.
+            If the selected `method` is not available, a ``NotImplementedError``
+            will be raised.
+
+        Returns
+        -------
+        out : array
+            The log-PMF evaluated at the argument `x`.
+
+        See Also
+        --------
+        pmf
+        logcdf
+
+        Notes
+        -----
+        Suppose a discrete probability distribution has support over the integers
+        :math:`{l, l+1, ..., r-1, r}`.
+        By definition of the support, the log-PMF evaluates to its minimum value
+        of :math:`-\infty` (i.e. :math:`\log(0)`) for non-integral :math:`x` and
+        for :math:`x` outside the support; i.e. for :math:`x < l` or :math:`x > r`.
+
+        For distributions with infinite support, it is common for `pmf` to return
+        a value of ``0`` when the argument is theoretically within the support;
+        this can occur because the true value of the PMF is too small to be
+        represented by the chosen dtype. The log-PMF, however, will often be finite
+        (not ``-inf``) over a much larger domain. Consequently, it may be preferred
+        to work with the logarithms of probabilities and probability densities to
+        avoid underflow.
+
+        References
+        ----------
+        .. [1] Probability density function, *Wikipedia*,
+               https://en.wikipedia.org/wiki/Probability_density_function
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> import numpy as np
+        >>> from scipy import stats
+        >>> X = stats.Binomial(n=10, p=0.5)
+
+        Evaluate the log-PMF at the desired argument:
+
+        >>> X.logpmf(5)
+        np.float64(-1.4020427180880297)
+        >>> np.allclose(X.logpmf(5), np.log(X.pmf(5)))
+        True
+
+        """
+        raise NotImplementedError()
+
+    @abstractmethod
+    def cdf(self, x, y, /, *, method):
+        r"""Cumulative distribution function
+
+        The cumulative distribution function ("CDF"), denoted :math:`F(x)`, is
+        the probability the random variable :math:`X` will assume a value
+        less than or equal to :math:`x`:
+
+        .. math::
+
+            F(x) = P(X ≤ x)
+
+        A two-argument variant of this function is also defined as the
+        probability the random variable :math:`X` will assume a value between
+        :math:`x` and :math:`y`.
+
+        .. math::
+
+            F(x, y) = P(x ≤ X ≤ y)
+
+        `cdf` accepts `x` for :math:`x` and `y` for :math:`y`.
+
+        Parameters
+        ----------
+        x, y : array_like
+            The arguments of the CDF. `x` is required; `y` is optional.
+        method : {None, 'formula', 'logexp', 'complement', 'quadrature', 'subtraction'}
+            The strategy used to evaluate the CDF.
+            By default (``None``), the one-argument form of the function
+            chooses between the following options, listed in order of precedence.
+
+            - ``'formula'``: use a formula for the CDF itself
+            - ``'logexp'``: evaluate the log-CDF and exponentiate
+            - ``'complement'``: evaluate the CCDF and take the complement
+            - ``'quadrature'``: numerically integrate the PDF (or, in the discrete
+              case, sum the PMF)
+
+            In place of ``'complement'``, the two-argument form accepts:
+
+            - ``'subtraction'``: compute the CDF at each argument and take
+              the difference.
+
+            Not all `method` options are available for all distributions.
+            If the selected `method` is not available, a ``NotImplementedError``
+            will be raised.
+
+        Returns
+        -------
+        out : array
+            The CDF evaluated at the provided argument(s).
+
+        See Also
+        --------
+        logcdf
+        ccdf
+
+        Notes
+        -----
+        Suppose a continuous probability distribution has support :math:`[l, r]`.
+        The CDF :math:`F(x)` is related to the probability density function
+        :math:`f(x)` by:
+
+        .. math::
+
+            F(x) = \int_l^x f(u) du
+
+        The two argument version is:
+
+        .. math::
+
+            F(x, y) = \int_x^y f(u) du = F(y) - F(x)
+
+        The CDF evaluates to its minimum value of :math:`0` for :math:`x ≤ l`
+        and its maximum value of :math:`1` for :math:`x ≥ r`.
+
+        Suppose a discrete probability distribution has support :math:`[l, r]`.
+        The CDF :math:`F(x)` is related to the probability mass function
+        :math:`f(x)` by:
+
+        .. math::
+
+            F(x) = \sum_{u=l}^{\lfloor x \rfloor} f(u)
+
+        The CDF evaluates to its minimum value of :math:`0` for :math:`x < l`
+        and its maximum value of :math:`1` for :math:`x ≥ r`.
+
+        The CDF is also known simply as the "distribution function".
+
+        References
+        ----------
+        .. [1] Cumulative distribution function, *Wikipedia*,
+               https://en.wikipedia.org/wiki/Cumulative_distribution_function
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> from scipy import stats
+        >>> X = stats.Uniform(a=-0.5, b=0.5)
+
+        Evaluate the CDF at the desired argument:
+
+        >>> X.cdf(0.25)
+        0.75
+
+        Evaluate the cumulative probability between two arguments:
+
+        >>> X.cdf(-0.25, 0.25) == X.cdf(0.25) - X.cdf(-0.25)
+        True
+
+        """  # noqa: E501
+        raise NotImplementedError()
+
+    @abstractmethod
+    def icdf(self, p, /, *, method):
+        r"""Inverse of the cumulative distribution function.
+
+        For monotonic continuous distributions, the inverse of the cumulative
+        distribution function ("inverse CDF"), denoted :math:`F^{-1}(p)`, is the
+        argument :math:`x` for which the cumulative distribution function
+        :math:`F(x)` evaluates to :math:`p`.
+
+        .. math::
+
+            F^{-1}(p) = x \quad \text{s.t.} \quad F(x) = p
+
+        When a strict "inverse" of the cumulative distribution function does not
+        exist (e.g. discrete random variables), the "inverse CDF" is defined by
+        convention as the smallest value within the support :math:`\chi` for which
+        :math:`F(x)` is at least :math:`p`.
+
+        .. math::
+
+            F^{-1}(p) = \min_\chi \quad \text{s.t.} \quad F(x) ≥ p
+
+        `icdf` accepts `p` for :math:`p \in [0, 1]`.
+
+        Parameters
+        ----------
+        p : array_like
+            The argument of the inverse CDF.
+        method : {None, 'formula', 'complement', 'inversion'}
+            The strategy used to evaluate the inverse CDF.
+            By default (``None``), the infrastructure chooses between the
+            following options, listed in order of precedence.
+
+            - ``'formula'``: use a formula for the inverse CDF itself
+            - ``'complement'``: evaluate the inverse CCDF at the
+              complement of `p`
+            - ``'inversion'``: solve numerically for the argument at which the
+              CDF is equal to `p`
+
+            Not all `method` options are available for all distributions.
+            If the selected `method` is not available, a ``NotImplementedError``
+            will be raised.
+
+        Returns
+        -------
+        out : array
+            The inverse CDF evaluated at the provided argument.
+
+        See Also
+        --------
+        cdf
+        ilogcdf
+
+        Notes
+        -----
+        Suppose a probability distribution has support :math:`[l, r]`. The
+        inverse CDF returns its minimum value of :math:`l` at :math:`p = 0`
+        and its maximum value of :math:`r` at :math:`p = 1`. Because the CDF
+        has range :math:`[0, 1]`, the inverse CDF is only defined on the
+        domain :math:`[0, 1]`; for :math:`p < 0` and :math:`p > 1`, `icdf`
+        returns ``nan``.
+
+        The inverse CDF is also known as the quantile function, percentile function,
+        and percent-point function.
+
+        References
+        ----------
+        .. [1] Quantile function, *Wikipedia*,
+               https://en.wikipedia.org/wiki/Quantile_function
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> import numpy as np
+        >>> from scipy import stats
+        >>> X = stats.Uniform(a=-0.5, b=0.5)
+
+        Evaluate the inverse CDF at the desired argument:
+
+        >>> X.icdf(0.25)
+        -0.25
+        >>> np.allclose(X.cdf(X.icdf(0.25)), 0.25)
+        True
+
+        This function returns NaN when the argument is outside the domain.
+
+        >>> X.icdf([-0.1, 0, 1, 1.1])
+        array([ nan, -0.5,  0.5,  nan])
+
+        """
+        raise NotImplementedError()
+
+    @abstractmethod
+    def ccdf(self, x, y, /, *, method):
+        r"""Complementary cumulative distribution function
+
+        The complementary cumulative distribution function ("CCDF"), denoted
+        :math:`G(x)`, is the complement of the cumulative distribution function
+        :math:`F(x)`; i.e., probability the random variable :math:`X` will
+        assume a value greater than :math:`x`:
+
+        .. math::
+
+            G(x) = 1 - F(x) = P(X > x)
+
+        A two-argument variant of this function is:
+
+        .. math::
+
+            G(x, y) = 1 - F(x, y) = P(X < x \text{ or } X > y)
+
+        `ccdf` accepts `x` for :math:`x` and `y` for :math:`y`.
+
+        Parameters
+        ----------
+        x, y : array_like
+            The arguments of the CCDF. `x` is required; `y` is optional.
+        method : {None, 'formula', 'logexp', 'complement', 'quadrature', 'addition'}
+            The strategy used to evaluate the CCDF.
+            By default (``None``), the infrastructure chooses between the
+            following options, listed in order of precedence.
+
+            - ``'formula'``: use a formula for the CCDF itself
+            - ``'logexp'``: evaluate the log-CCDF and exponentiate
+            - ``'complement'``: evaluate the CDF and take the complement
+            - ``'quadrature'``: numerically integrate the PDF (or, in the discrete
+              case, sum the PMF)
+
+            The two-argument form chooses between:
+
+            - ``'formula'``: use a formula for the CCDF itself
+            - ``'addition'``: compute the CDF at `x` and the CCDF at `y`, then add
+
+            Not all `method` options are available for all distributions.
+            If the selected `method` is not available, a ``NotImplementedError``
+            will be raised.
+
+        Returns
+        -------
+        out : array
+            The CCDF evaluated at the provided argument(s).
+
+        See Also
+        --------
+        cdf
+        logccdf
+
+        Notes
+        -----
+        Suppose a continuous probability distribution has support :math:`[l, r]`.
+        The CCDF :math:`G(x)` is related to the probability density function
+        :math:`f(x)` by:
+
+        .. math::
+
+            G(x) = \int_x^r f(u) du
+
+        The two argument version is:
+
+        .. math::
+
+            G(x, y) = \int_l^x f(u) du + \int_y^r f(u) du
+
+        The CCDF returns its minimum value of :math:`0` for :math:`x ≥ r`
+        and its maximum value of :math:`1` for :math:`x ≤ l`.
+
+        Suppose a discrete probability distribution has support :math:`[l, r]`.
+        The CCDF :math:`G(x)` is related to the probability mass function
+        :math:`f(x)` by:
+
+        .. math::
+
+            G(x) = \sum_{u=\lfloor x + 1 \rfloor}^{r} f(u)
+
+        The CCDF evaluates to its minimum value of :math:`0` for :math:`x ≥ r`
+        and its maximum value of :math:`1` for :math:`x < l`.
+
+        The CCDF is also known as the "survival function".
+
+        References
+        ----------
+        .. [1] Cumulative distribution function, *Wikipedia*,
+               https://en.wikipedia.org/wiki/Cumulative_distribution_function#Derived_functions
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> import numpy as np
+        >>> from scipy import stats
+        >>> X = stats.Uniform(a=-0.5, b=0.5)
+
+        Evaluate the CCDF at the desired argument:
+
+        >>> X.ccdf(0.25)
+        0.25
+        >>> np.allclose(X.ccdf(0.25), 1-X.cdf(0.25))
+        True
+
+        Evaluate the complement of the cumulative probability between two arguments:
+
+        >>> X.ccdf(-0.25, 0.25) == X.cdf(-0.25) + X.ccdf(0.25)
+        True
+
+        """  # noqa: E501
+        raise NotImplementedError()
+
+    @abstractmethod
+    def iccdf(self, p, /, *, method):
+        r"""Inverse complementary cumulative distribution function.
+
+        The inverse complementary cumulative distribution function ("inverse CCDF"),
+        denoted :math:`G^{-1}(p)`, is the argument :math:`x` for which the
+        complementary cumulative distribution function :math:`G(x)` evaluates to
+        :math:`p`.
+
+        .. math::
+
+            G^{-1}(p) = x \quad \text{s.t.} \quad G(x) = p
+
+        When a strict "inverse" of the complementary cumulative distribution function
+        does not exist (e.g. discrete random variables), the "inverse CCDF" is defined
+        by convention as the smallest value within the support :math:`\chi` for which
+        :math:`G(x)` is no greater than :math:`p`.
+
+        .. math::
+
+            G^{-1}(p) = \min_\chi \quad \text{s.t.} \quad G(x) ≤ p
+
+        `iccdf` accepts `p` for :math:`p \in [0, 1]`.
+
+        Parameters
+        ----------
+        p : array_like
+            The argument of the inverse CCDF.
+        method : {None, 'formula', 'complement', 'inversion'}
+            The strategy used to evaluate the inverse CCDF.
+            By default (``None``), the infrastructure chooses between the
+            following options, listed in order of precedence.
+
+            - ``'formula'``: use a formula for the inverse CCDF itself
+            - ``'complement'``: evaluate the inverse CDF at the
+              complement of `p`
+            - ``'inversion'``: solve numerically for the argument at which the
+              CCDF is equal to `p`
+
+            Not all `method` options are available for all distributions.
+            If the selected `method` is not available, a ``NotImplementedError``
+            will be raised.
+
+        Returns
+        -------
+        out : array
+            The inverse CCDF evaluated at the provided argument.
+
+        Notes
+        -----
+        Suppose a probability distribution has support :math:`[l, r]`. The
+        inverse CCDF returns its minimum value of :math:`l` at :math:`p = 1`
+        and its maximum value of :math:`r` at :math:`p = 0`. Because the CCDF
+        has range :math:`[0, 1]`, the inverse CCDF is only defined on the
+        domain :math:`[0, 1]`; for :math:`p < 0` and :math:`p > 1`, ``iccdf``
+        returns ``nan``.
+
+        See Also
+        --------
+        icdf
+        ilogccdf
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> import numpy as np
+        >>> from scipy import stats
+        >>> X = stats.Uniform(a=-0.5, b=0.5)
+
+        Evaluate the inverse CCDF at the desired argument:
+
+        >>> X.iccdf(0.25)
+        0.25
+        >>> np.allclose(X.iccdf(0.25), X.icdf(1-0.25))
+        True
+
+        This function returns NaN when the argument is outside the domain.
+
+        >>> X.iccdf([-0.1, 0, 1, 1.1])
+        array([ nan,  0.5, -0.5,  nan])
+
+        """
+        raise NotImplementedError()
+
+    @abstractmethod
+    def logcdf(self, x, y, /, *, method):
+        r"""Log of the cumulative distribution function
+
+        The cumulative distribution function ("CDF"), denoted :math:`F(x)`, is
+        the probability the random variable :math:`X` will assume a value
+        less than or equal to :math:`x`:
+
+        .. math::
+
+            F(x) = P(X ≤ x)
+
+        A two-argument variant of this function is also defined as the
+        probability the random variable :math:`X` will assume a value between
+        :math:`x` and :math:`y`.
+
+        .. math::
+
+            F(x, y) = P(x ≤ X ≤ y)
+
+        `logcdf` computes the logarithm of the cumulative distribution function
+        ("log-CDF"), :math:`\log(F(x))`/:math:`\log(F(x, y))`, but it may be
+        numerically favorable compared to the naive implementation (computing
+        the CDF and taking the logarithm).
+
+        `logcdf` accepts `x` for :math:`x` and `y` for :math:`y`.
+
+        Parameters
+        ----------
+        x, y : array_like
+            The arguments of the log-CDF. `x` is required; `y` is optional.
+        method : {None, 'formula', 'logexp', 'complement', 'quadrature', 'subtraction'}
+            The strategy used to evaluate the log-CDF.
+            By default (``None``), the one-argument form of the function
+            chooses between the following options, listed in order of precedence.
+
+            - ``'formula'``: use a formula for the log-CDF itself
+            - ``'logexp'``: evaluate the CDF and take the logarithm
+            - ``'complement'``: evaluate the log-CCDF and take the
+              logarithmic complement (see Notes)
+            - ``'quadrature'``: numerically log-integrate the log-PDF (or, in the
+              discrete case, log-sum the log-PMF)
+
+            In place of ``'complement'``, the two-argument form accepts:
+
+            - ``'subtraction'``: compute the log-CDF at each argument and take
+              the logarithmic difference (see Notes)
+
+            Not all `method` options are available for all distributions.
+            If the selected `method` is not available, a ``NotImplementedError``
+            will be raised.
+
+        Returns
+        -------
+        out : array
+            The log-CDF evaluated at the provided argument(s).
+
+        See Also
+        --------
+        cdf
+        logccdf
+
+        Notes
+        -----
+        Suppose a continuous probability distribution has support :math:`[l, r]`.
+        The log-CDF evaluates to its minimum value of :math:`\log(0) = -\infty`
+        for :math:`x ≤ l` and its maximum value of :math:`\log(1) = 0` for
+        :math:`x ≥ r`. An analogous statement can be made for discrete distributions,
+        but the inequality governing the minimum value is strict.
+
+        For distributions with infinite support, it is common for
+        `cdf` to return a value of ``0`` when the argument
+        is theoretically within the support; this can occur because the true value
+        of the CDF is too small to be represented by the chosen dtype. `logcdf`,
+        however, will often return a finite (not ``-inf``) result over a much larger
+        domain. Similarly, `logcdf` may provided a strictly negative result with
+        arguments for which `cdf` would return ``1.0``. Consequently, it may be
+        preferred to work with the logarithms of probabilities to avoid underflow
+        and related limitations of floating point numbers.
+
+        The "logarithmic complement" of a number :math:`z` is mathematically
+        equivalent to :math:`\log(1-\exp(z))`, but it is computed to avoid loss
+        of precision when :math:`\exp(z)` is nearly :math:`0` or :math:`1`.
+        Similarly, the term "logarithmic difference" of :math:`w` and :math:`z`
+        is used here to mean :math:`\log(\exp(w)-\exp(z))`.
+
+        If ``y < x``, the CDF is negative, and therefore the log-CCDF
+        is complex with imaginary part :math:`\pi`. For
+        consistency, the result of this function always has complex dtype
+        when `y` is provided, regardless of the value of the imaginary part.
+
+        References
+        ----------
+        .. [1] Cumulative distribution function, *Wikipedia*,
+               https://en.wikipedia.org/wiki/Cumulative_distribution_function
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> import numpy as np
+        >>> from scipy import stats
+        >>> X = stats.Uniform(a=-0.5, b=0.5)
+
+        Evaluate the log-CDF at the desired argument:
+
+        >>> X.logcdf(0.25)
+        -0.287682072451781
+        >>> np.allclose(X.logcdf(0.), np.log(X.cdf(0.)))
+        True
+
+        """  # noqa: E501
+        raise NotImplementedError()
+
+    @abstractmethod
+    def ilogcdf(self, logp, /, *, method):
+        r"""Inverse of the logarithm of the cumulative distribution function.
+
+        The inverse of the logarithm of the cumulative distribution function
+        ("inverse log-CDF") is the argument :math:`x` for which the logarithm
+        of the cumulative distribution function :math:`\log(F(x))` evaluates
+        to :math:`\log(p)`.
+
+        Mathematically, it is equivalent to :math:`F^{-1}(\exp(y))`, where
+        :math:`y = \log(p)`, but it may be numerically favorable compared to
+        the naive implementation (computing :math:`p = \exp(y)`, then
+        :math:`F^{-1}(p)`).
+
+        `ilogcdf` accepts `logp` for :math:`\log(p) ≤ 0`.
+
+        Parameters
+        ----------
+        logp : array_like
+            The argument of the inverse log-CDF.
+        method : {None, 'formula', 'complement', 'inversion'}
+            The strategy used to evaluate the inverse log-CDF.
+            By default (``None``), the infrastructure chooses between the
+            following options, listed in order of precedence.
+
+            - ``'formula'``: use a formula for the inverse log-CDF itself
+            - ``'complement'``: evaluate the inverse log-CCDF at the
+              logarithmic complement of `logp` (see Notes)
+            - ``'inversion'``: solve numerically for the argument at which the
+              log-CDF is equal to `logp`
+
+            Not all `method` options are available for all distributions.
+            If the selected `method` is not available, a ``NotImplementedError``
+            will be raised.
+
+        Returns
+        -------
+        out : array
+            The inverse log-CDF evaluated at the provided argument.
+
+        See Also
+        --------
+        icdf
+        logcdf
+
+        Notes
+        -----
+        Suppose a probability distribution has support :math:`[l, r]`.
+        The inverse log-CDF returns its minimum value of :math:`l` at
+        :math:`\log(p) = \log(0) = -\infty` and its maximum value of :math:`r` at
+        :math:`\log(p) = \log(1) = 0`. Because the log-CDF has range
+        :math:`[-\infty, 0]`, the inverse log-CDF is only defined on the
+        negative reals; for :math:`\log(p) > 0`, `ilogcdf` returns ``nan``.
+
+        Occasionally, it is needed to find the argument of the CDF for which
+        the resulting probability is very close to ``0`` or ``1`` - too close to
+        represent accurately with floating point arithmetic. In many cases,
+        however, the *logarithm* of this resulting probability may be
+        represented in floating point arithmetic, in which case this function
+        may be used to find the argument of the CDF for which the *logarithm*
+        of the resulting probability is :math:`y = \log(p)`.
+
+        The "logarithmic complement" of a number :math:`z` is mathematically
+        equivalent to :math:`\log(1-\exp(z))`, but it is computed to avoid loss
+        of precision when :math:`\exp(z)` is nearly :math:`0` or :math:`1`.
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> import numpy as np
+        >>> from scipy import stats
+        >>> X = stats.Uniform(a=-0.5, b=0.5)
+
+        Evaluate the inverse log-CDF at the desired argument:
+
+        >>> X.ilogcdf(-0.25)
+        0.2788007830714034
+        >>> np.allclose(X.ilogcdf(-0.25), X.icdf(np.exp(-0.25)))
+        True
+
+        """
+        raise NotImplementedError()
+
+    @abstractmethod
+    def logccdf(self, x, y, /, *, method):
+        r"""Log of the complementary cumulative distribution function
+
+        The complementary cumulative distribution function ("CCDF"), denoted
+        :math:`G(x)` is the complement of the cumulative distribution function
+        :math:`F(x)`; i.e., probability the random variable :math:`X` will
+        assume a value greater than :math:`x`:
+
+        .. math::
+
+            G(x) = 1 - F(x) = P(X > x)
+
+         A two-argument variant of this function is:
+
+        .. math::
+
+            G(x, y) = 1 - F(x, y) = P(X < x \quad \text{or} \quad X > y)
+
+        `logccdf` computes the logarithm of the complementary cumulative
+        distribution function ("log-CCDF"), :math:`\log(G(x))`/:math:`\log(G(x, y))`,
+        but it may be numerically favorable compared to the naive implementation
+        (computing the CDF and taking the logarithm).
+
+        `logccdf` accepts `x` for :math:`x` and `y` for :math:`y`.
+
+        Parameters
+        ----------
+        x, y : array_like
+            The arguments of the log-CCDF. `x` is required; `y` is optional.
+        method : {None, 'formula', 'logexp', 'complement', 'quadrature', 'addition'}
+            The strategy used to evaluate the log-CCDF.
+            By default (``None``), the one-argument form of the function
+            chooses between the following options, listed in order of precedence.
+
+            - ``'formula'``: use a formula for the log CCDF itself
+            - ``'logexp'``: evaluate the CCDF and take the logarithm
+            - ``'complement'``: evaluate the log-CDF and take the
+              logarithmic complement (see Notes)
+            - ``'quadrature'``: numerically log-integrate the log-PDF (or, in the
+              discrete case, log-sum the log-PMF)
+
+            The two-argument form chooses between:
+
+            - ``'formula'``: use a formula for the log CCDF itself
+            - ``'addition'``: compute the log-CDF at `x` and the log-CCDF at `y`,
+              then take the logarithmic sum (see Notes)
+
+            Not all `method` options are available for all distributions.
+            If the selected `method` is not available, a ``NotImplementedError``
+            will be raised.
+
+        Returns
+        -------
+        out : array
+            The log-CCDF evaluated at the provided argument(s).
+
+        See Also
+        --------
+        ccdf
+        logcdf
+
+        Notes
+        -----
+        Suppose a continuous probability distribution has support :math:`[l, r]`.
+        The log-CCDF returns its minimum value of :math:`\log(0)=-\infty` for
+        :math:`x ≥ r` and its maximum value of :math:`\log(1) = 0` for
+        :math:`x ≤ l`. An analogous statement can be made for discrete distributions,
+        but the inequality governing the maximum value is strict.
+
+        For distributions with infinite support, it is common for
+        `ccdf` to return a value of ``0`` when the argument
+        is theoretically within the support; this can occur because the true value
+        of the CCDF is too small to be represented by the chosen dtype. The log
+        of the CCDF, however, will often be finite (not ``-inf``) over a much larger
+        domain. Similarly, `logccdf` may provided a strictly negative result with
+        arguments for which `ccdf` would return ``1.0``. Consequently, it may be
+        preferred to work with the logarithms of probabilities to avoid underflow
+        and related limitations of floating point numbers.
+
+        The "logarithmic complement" of a number :math:`z` is mathematically
+        equivalent to :math:`\log(1-\exp(z))`, but it is computed to avoid loss
+        of precision when :math:`\exp(z)` is nearly :math:`0` or :math:`1`.
+        Similarly, the term "logarithmic sum" of :math:`w` and :math:`z`
+        is used here to mean the :math:`\log(\exp(w)+\exp(z))`, AKA
+        :math:`\text{LogSumExp}(w, z)`.
+
+        References
+        ----------
+        .. [1] Cumulative distribution function, *Wikipedia*,
+               https://en.wikipedia.org/wiki/Cumulative_distribution_function#Derived_functions
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> import numpy as np
+        >>> from scipy import stats
+        >>> X = stats.Uniform(a=-0.5, b=0.5)
+
+        Evaluate the log-CCDF at the desired argument:
+
+        >>> X.logccdf(0.25)
+        -1.3862943611198906
+        >>> np.allclose(X.logccdf(0.), np.log(X.ccdf(0.)))
+        True
+
+        """  # noqa: E501
+        raise NotImplementedError()
+
+    @abstractmethod
+    def ilogccdf(self, logp, /, *, method):
+        r"""Inverse of the log of the complementary cumulative distribution function.
+
+        The inverse of the logarithm of the complementary cumulative distribution
+        function ("inverse log-CCDF") is the argument :math:`x` for which the logarithm
+        of the complementary cumulative distribution function :math:`\log(G(x))`
+        evaluates to :math:`\log(p)`.
+
+        Mathematically, it is equivalent to :math:`G^{-1}(\exp(y))`, where
+        :math:`y = \log(p)`, but it may be numerically favorable compared to the naive
+        implementation (computing :math:`p = \exp(y)`, then :math:`G^{-1}(p)`).
+
+        `ilogccdf` accepts `logp` for :math:`\log(p) ≤ 0`.
+
+        Parameters
+        ----------
+        x : array_like
+            The argument of the inverse log-CCDF.
+        method : {None, 'formula', 'complement', 'inversion'}
+            The strategy used to evaluate the inverse log-CCDF.
+            By default (``None``), the infrastructure chooses between the
+            following options, listed in order of precedence.
+
+            - ``'formula'``: use a formula for the inverse log-CCDF itself
+            - ``'complement'``: evaluate the inverse log-CDF at the
+              logarithmic complement of `x` (see Notes)
+            - ``'inversion'``: solve numerically for the argument at which the
+              log-CCDF is equal to `x`
+
+            Not all `method` options are available for all distributions.
+            If the selected `method` is not available, a ``NotImplementedError``
+            will be raised.
+
+        Returns
+        -------
+        out : array
+            The inverse log-CCDF evaluated at the provided argument.
+
+        Notes
+        -----
+        Suppose a probability distribution has support :math:`[l, r]`. The
+        inverse log-CCDF returns its minimum value of :math:`l` at
+        :math:`\log(p) = \log(1) = 0` and its maximum value of :math:`r` at
+        :math:`\log(p) = \log(0) = -\infty`. Because the log-CCDF has range
+        :math:`[-\infty, 0]`, the inverse log-CDF is only defined on the
+        negative reals; for :math:`\log(p) > 0`, `ilogccdf` returns ``nan``.
+
+        Occasionally, it is needed to find the argument of the CCDF for which
+        the resulting probability is very close to ``0`` or ``1`` - too close to
+        represent accurately with floating point arithmetic. In many cases,
+        however, the *logarithm* of this resulting probability may be
+        represented in floating point arithmetic, in which case this function
+        may be used to find the argument of the CCDF for which the *logarithm*
+        of the resulting probability is :math:`y = \log(p)`.
+
+        The "logarithmic complement" of a number :math:`z` is mathematically
+        equivalent to :math:`\log(1-\exp(z))`, but it is computed to avoid loss
+        of precision when :math:`\exp(z)` is nearly :math:`0` or :math:`1`.
+
+        See Also
+        --------
+        iccdf
+        ilogccdf
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> import numpy as np
+        >>> from scipy import stats
+        >>> X = stats.Uniform(a=-0.5, b=0.5)
+
+        Evaluate the inverse log-CCDF at the desired argument:
+
+        >>> X.ilogccdf(-0.25)
+        -0.2788007830714034
+        >>> np.allclose(X.ilogccdf(-0.25), X.iccdf(np.exp(-0.25)))
+        True
+
+        """
+        raise NotImplementedError()
+
+    @abstractmethod
+    def logentropy(self, *, method):
+        r"""Logarithm of the differential entropy
+
+        In terms of probability density function :math:`f(x)` and support
+        :math:`\chi`, the differential entropy (or simply "entropy") of a
+        continuous random variable :math:`X` is:
+
+        .. math::
+
+            h(X) = - \int_{\chi} f(x) \log f(x) dx
+
+        The definition for a discrete random variable is analogous, with the PMF
+        replacing the PDF and a sum over the support replacing the integral.
+
+        `logentropy` computes the logarithm of the differential entropy
+        ("log-entropy"), :math:`\log(h(X))`, but it may be numerically favorable
+        compared to the naive implementation (computing :math:`h(X)` then
+        taking the logarithm).
+
+        Parameters
+        ----------
+        method : {None, 'formula', 'logexp', 'quadrature}
+            The strategy used to evaluate the log-entropy. By default
+            (``None``), the infrastructure chooses between the following options,
+            listed in order of precedence.
+
+            - ``'formula'``: use a formula for the log-entropy itself
+            - ``'logexp'``: evaluate the entropy and take the logarithm
+            - ``'quadrature'``: numerically log-integrate (or, in the discrete
+              case, log-sum) the logarithm of the entropy integrand (summand)
+
+            Not all `method` options are available for all distributions.
+            If the selected `method` is not available, a ``NotImplementedError``
+            will be raised.
+
+        Returns
+        -------
+        out : array
+            The log-entropy.
+
+        See Also
+        --------
+        entropy
+        logpdf
+
+        Notes
+        -----
+        The differential entropy of a continuous distribution can be negative.
+        In this case, the log-entropy is complex with imaginary part :math:`\pi`.
+        For consistency, the result of this function always has complex dtype,
+        regardless of the value of the imaginary part.
+
+        References
+        ----------
+        .. [1] Differential entropy, *Wikipedia*,
+               https://en.wikipedia.org/wiki/Differential_entropy
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> import numpy as np
+        >>> from scipy import stats
+        >>> X = stats.Uniform(a=-1., b=1.)
+
+        Evaluate the log-entropy:
+
+        >>> X.logentropy()
+        (-0.3665129205816642+0j)
+        >>> np.allclose(np.exp(X.logentropy()), X.entropy())
+        True
+
+        For a random variable with negative entropy, the log-entropy has an
+        imaginary part equal to `np.pi`.
+
+        >>> X = stats.Uniform(a=-.1, b=.1)
+        >>> X.entropy(), X.logentropy()
+        (-1.6094379124341007, (0.4758849953271105+3.141592653589793j))
+
+        """
+        raise NotImplementedError()
+
+    @abstractmethod
+    def entropy(self, *, method):
+        r"""Differential entropy
+
+        In terms of probability density function :math:`f(x)` and support
+        :math:`\chi`, the differential entropy (or simply "entropy") of a
+        continuous random variable :math:`X` is:
+
+        .. math::
+
+            h(X) = - \int_{\chi} f(x) \log f(x) dx
+
+        The definition for a discrete random variable is analogous, with the
+        PMF replacing the PDF and a sum over the support replacing the integral.
+
+        Parameters
+        ----------
+        method : {None, 'formula', 'logexp', 'quadrature'}
+            The strategy used to evaluate the entropy. By default (``None``),
+            the infrastructure chooses between the following options, listed
+            in order of precedence.
+
+            - ``'formula'``: use a formula for the entropy itself
+            - ``'logexp'``: evaluate the log-entropy and exponentiate
+            - ``'quadrature'``:  numerically integrate (or, in the discrete
+              case, sum) the entropy integrand (summand)
+
+
+            Not all `method` options are available for all distributions.
+            If the selected `method` is not available, a ``NotImplementedError``
+            will be raised.
+
+        Returns
+        -------
+        out : array
+            The entropy of the random variable.
+
+        See Also
+        --------
+        logentropy
+        pdf
+
+        Notes
+        -----
+        This function calculates the entropy using the natural logarithm; i.e.
+        the logarithm with base :math:`e`. Consequently, the value is expressed
+        in (dimensionless) "units" of nats. To convert the entropy to different
+        units (i.e. corresponding with a different base), divide the result by
+        the natural logarithm of the desired base.
+
+        References
+        ----------
+        .. [1] Differential entropy, *Wikipedia*,
+               https://en.wikipedia.org/wiki/Differential_entropy
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> from scipy import stats
+        >>> X = stats.Uniform(a=-1., b=1.)
+
+        Evaluate the entropy:
+
+        >>> X.entropy()
+        0.6931471805599454
+
+        """
+        raise NotImplementedError()
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_qmc.py b/venv/lib/python3.12/site-packages/scipy/stats/_qmc.py
new file mode 100644
index 0000000000000000000000000000000000000000..3358bc68222035ddc02a5f7977041bd313f3d0a9
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_qmc.py
@@ -0,0 +1,2951 @@
+"""Quasi-Monte Carlo engines and helpers."""
+import copy
+import math
+import numbers
+import os
+import warnings
+from abc import ABC, abstractmethod
+from functools import partial
+from typing import (
+    ClassVar,
+    Literal,
+    overload,
+    TYPE_CHECKING,
+)
+from collections.abc import Callable
+
+import numpy as np
+
+from scipy._lib._util import DecimalNumber, GeneratorType, IntNumber, SeedType
+
+if TYPE_CHECKING:
+    import numpy.typing as npt
+
+import scipy.stats as stats
+from scipy._lib._util import rng_integers, _rng_spawn, _transition_to_rng
+from scipy.sparse.csgraph import minimum_spanning_tree
+from scipy.spatial import distance, Voronoi
+from scipy.special import gammainc
+from ._sobol import (
+    _initialize_v, _cscramble, _fill_p_cumulative, _draw, _fast_forward,
+    _categorize, _MAXDIM
+)
+from ._qmc_cy import (
+    _cy_wrapper_centered_discrepancy,
+    _cy_wrapper_wrap_around_discrepancy,
+    _cy_wrapper_mixture_discrepancy,
+    _cy_wrapper_l2_star_discrepancy,
+    _cy_wrapper_update_discrepancy,
+    _cy_van_der_corput_scrambled,
+    _cy_van_der_corput,
+)
+
+
+__all__ = ['scale', 'discrepancy', 'geometric_discrepancy', 'update_discrepancy',
+           'QMCEngine', 'Sobol', 'Halton', 'LatinHypercube', 'PoissonDisk',
+           'MultinomialQMC', 'MultivariateNormalQMC']
+
+
+@overload
+def check_random_state(seed: IntNumber | None = ...) -> np.random.Generator:
+    ...
+
+
+@overload
+def check_random_state(seed: GeneratorType) -> GeneratorType:
+    ...
+
+
+# Based on scipy._lib._util.check_random_state
+# This is going to be removed at the end of the SPEC 7 transition,
+# so I'll just leave the argument name `seed` alone
+def check_random_state(seed=None):
+    """Turn `seed` into a `numpy.random.Generator` instance.
+
+    Parameters
+    ----------
+    seed : {None, int, `numpy.random.Generator`, `numpy.random.RandomState`}, optional
+        If `seed` is an int or None, a new `numpy.random.Generator` is
+        created using ``np.random.default_rng(seed)``.
+        If `seed` is already a ``Generator`` or ``RandomState`` instance, then
+        the provided instance is used.
+
+    Returns
+    -------
+    seed : {`numpy.random.Generator`, `numpy.random.RandomState`}
+        Random number generator.
+
+    """
+    if seed is None or isinstance(seed, numbers.Integral | np.integer):
+        return np.random.default_rng(seed)
+    elif isinstance(seed, np.random.RandomState | np.random.Generator):
+        return seed
+    else:
+        raise ValueError(f'{seed!r} cannot be used to seed a'
+                         ' numpy.random.Generator instance')
+
+
+def scale(
+    sample: "npt.ArrayLike",
+    l_bounds: "npt.ArrayLike",
+    u_bounds: "npt.ArrayLike",
+    *,
+    reverse: bool = False
+) -> np.ndarray:
+    r"""Sample scaling from unit hypercube to different bounds.
+
+    To convert a sample from :math:`[0, 1)` to :math:`[a, b), b>a`,
+    with :math:`a` the lower bounds and :math:`b` the upper bounds.
+    The following transformation is used:
+
+    .. math::
+
+        (b - a) \cdot \text{sample} + a
+
+    Parameters
+    ----------
+    sample : array_like (n, d)
+        Sample to scale.
+    l_bounds, u_bounds : array_like (d,)
+        Lower and upper bounds (resp. :math:`a`, :math:`b`) of transformed
+        data. If `reverse` is True, range of the original data to transform
+        to the unit hypercube.
+    reverse : bool, optional
+        Reverse the transformation from different bounds to the unit hypercube.
+        Default is False.
+
+    Returns
+    -------
+    sample : array_like (n, d)
+        Scaled sample.
+
+    Examples
+    --------
+    Transform 3 samples in the unit hypercube to bounds:
+
+    >>> from scipy.stats import qmc
+    >>> l_bounds = [-2, 0]
+    >>> u_bounds = [6, 5]
+    >>> sample = [[0.5 , 0.75],
+    ...           [0.5 , 0.5],
+    ...           [0.75, 0.25]]
+    >>> sample_scaled = qmc.scale(sample, l_bounds, u_bounds)
+    >>> sample_scaled
+    array([[2.  , 3.75],
+           [2.  , 2.5 ],
+           [4.  , 1.25]])
+
+    And convert back to the unit hypercube:
+
+    >>> sample_ = qmc.scale(sample_scaled, l_bounds, u_bounds, reverse=True)
+    >>> sample_
+    array([[0.5 , 0.75],
+           [0.5 , 0.5 ],
+           [0.75, 0.25]])
+
+    """
+    sample = np.asarray(sample)
+
+    # Checking bounds and sample
+    if not sample.ndim == 2:
+        raise ValueError('Sample is not a 2D array')
+
+    lower, upper = _validate_bounds(
+        l_bounds=l_bounds, u_bounds=u_bounds, d=sample.shape[1]
+    )
+
+    if not reverse:
+        # Checking that sample is within the hypercube
+        if (sample.max() > 1.) or (sample.min() < 0.):
+            raise ValueError('Sample is not in unit hypercube')
+
+        return sample * (upper - lower) + lower
+    else:
+        # Checking that sample is within the bounds
+        if not (np.all(sample >= lower) and np.all(sample <= upper)):
+            raise ValueError('Sample is out of bounds')
+
+        return (sample - lower) / (upper - lower)
+
+
+def _ensure_in_unit_hypercube(sample: "npt.ArrayLike") -> np.ndarray:
+    """Ensure that sample is a 2D array and is within a unit hypercube
+
+    Parameters
+    ----------
+    sample : array_like (n, d)
+        A 2D array of points.
+
+    Returns
+    -------
+    np.ndarray
+        The array interpretation of the input sample
+
+    Raises
+    ------
+    ValueError
+        If the input is not a 2D array or contains points outside of
+        a unit hypercube.
+    """
+    sample = np.asarray(sample, dtype=np.float64, order="C")
+
+    if not sample.ndim == 2:
+        raise ValueError("Sample is not a 2D array")
+
+    if (sample.max() > 1.) or (sample.min() < 0.):
+        raise ValueError("Sample is not in unit hypercube")
+
+    return sample
+
+
+def discrepancy(
+        sample: "npt.ArrayLike",
+        *,
+        iterative: bool = False,
+        method: Literal["CD", "WD", "MD", "L2-star"] = "CD",
+        workers: IntNumber = 1) -> float:
+    """Discrepancy of a given sample.
+
+    Parameters
+    ----------
+    sample : array_like (n, d)
+        The sample to compute the discrepancy from.
+    iterative : bool, optional
+        Must be False if not using it for updating the discrepancy.
+        Default is False. Refer to the notes for more details.
+    method : str, optional
+        Type of discrepancy, can be ``CD``, ``WD``, ``MD`` or ``L2-star``.
+        Refer to the notes for more details. Default is ``CD``.
+    workers : int, optional
+        Number of workers to use for parallel processing. If -1 is given all
+        CPU threads are used. Default is 1.
+
+    Returns
+    -------
+    discrepancy : float
+        Discrepancy.
+
+    See Also
+    --------
+    geometric_discrepancy
+
+    Notes
+    -----
+    The discrepancy is a uniformity criterion used to assess the space filling
+    of a number of samples in a hypercube. A discrepancy quantifies the
+    distance between the continuous uniform distribution on a hypercube and the
+    discrete uniform distribution on :math:`n` distinct sample points.
+
+    The lower the value is, the better the coverage of the parameter space is.
+
+    For a collection of subsets of the hypercube, the discrepancy is the
+    difference between the fraction of sample points in one of those
+    subsets and the volume of that subset. There are different definitions of
+    discrepancy corresponding to different collections of subsets. Some
+    versions take a root mean square difference over subsets instead of
+    a maximum.
+
+    A measure of uniformity is reasonable if it satisfies the following
+    criteria [1]_:
+
+    1. It is invariant under permuting factors and/or runs.
+    2. It is invariant under rotation of the coordinates.
+    3. It can measure not only uniformity of the sample over the hypercube,
+       but also the projection uniformity of the sample over non-empty
+       subset of lower dimension hypercubes.
+    4. There is some reasonable geometric meaning.
+    5. It is easy to compute.
+    6. It satisfies the Koksma-Hlawka-like inequality.
+    7. It is consistent with other criteria in experimental design.
+
+    Four methods are available:
+
+    * ``CD``: Centered Discrepancy - subspace involves a corner of the
+      hypercube
+    * ``WD``: Wrap-around Discrepancy - subspace can wrap around bounds
+    * ``MD``: Mixture Discrepancy - mix between CD/WD covering more criteria
+    * ``L2-star``: L2-star discrepancy - like CD BUT variant to rotation
+
+    Methods ``CD``, ``WD``, and ``MD`` implement the right hand side of equations
+    9, 10, and 18 of [2]_, respectively; the square root is not taken. On the
+    other hand, ``L2-star`` computes the quantity given by equation 10 of
+    [3]_ as implemented by subsequent equations; the square root is taken.
+
+    Lastly, using ``iterative=True``, it is possible to compute the
+    discrepancy as if we had :math:`n+1` samples. This is useful if we want
+    to add a point to a sampling and check the candidate which would give the
+    lowest discrepancy. Then you could just update the discrepancy with
+    each candidate using `update_discrepancy`. This method is faster than
+    computing the discrepancy for a large number of candidates.
+
+    References
+    ----------
+    .. [1] Fang et al. "Design and modeling for computer experiments".
+       Computer Science and Data Analysis Series, 2006.
+    .. [2] Zhou Y.-D. et al. "Mixture discrepancy for quasi-random point sets."
+       Journal of Complexity, 29 (3-4) , pp. 283-301, 2013.
+    .. [3] T. T. Warnock. "Computational investigations of low discrepancy
+       point sets." Applications of Number Theory to Numerical
+       Analysis, Academic Press, pp. 319-343, 1972.
+
+    Examples
+    --------
+    Calculate the quality of the sample using the discrepancy:
+
+    >>> import numpy as np
+    >>> from scipy.stats import qmc
+    >>> space = np.array([[1, 3], [2, 6], [3, 2], [4, 5], [5, 1], [6, 4]])
+    >>> l_bounds = [0.5, 0.5]
+    >>> u_bounds = [6.5, 6.5]
+    >>> space = qmc.scale(space, l_bounds, u_bounds, reverse=True)
+    >>> space
+    array([[0.08333333, 0.41666667],
+           [0.25      , 0.91666667],
+           [0.41666667, 0.25      ],
+           [0.58333333, 0.75      ],
+           [0.75      , 0.08333333],
+           [0.91666667, 0.58333333]])
+    >>> qmc.discrepancy(space)
+    0.008142039609053464
+
+    We can also compute iteratively the ``CD`` discrepancy by using
+    ``iterative=True``.
+
+    >>> disc_init = qmc.discrepancy(space[:-1], iterative=True)
+    >>> disc_init
+    0.04769081147119336
+    >>> qmc.update_discrepancy(space[-1], space[:-1], disc_init)
+    0.008142039609053513
+
+    """
+    sample = _ensure_in_unit_hypercube(sample)
+
+    workers = _validate_workers(workers)
+
+    methods = {
+        "CD": _cy_wrapper_centered_discrepancy,
+        "WD": _cy_wrapper_wrap_around_discrepancy,
+        "MD": _cy_wrapper_mixture_discrepancy,
+        "L2-star": _cy_wrapper_l2_star_discrepancy,
+    }
+
+    if method in methods:
+        return methods[method](sample, iterative, workers=workers)
+    else:
+        raise ValueError(f"{method!r} is not a valid method. It must be one of"
+                         f" {set(methods)!r}")
+
+
+def geometric_discrepancy(
+        sample: "npt.ArrayLike",
+        method: Literal["mindist", "mst"] = "mindist",
+        metric: str = "euclidean") -> float:
+    """Discrepancy of a given sample based on its geometric properties.
+
+    Parameters
+    ----------
+    sample : array_like (n, d)
+        The sample to compute the discrepancy from.
+    method : {"mindist", "mst"}, optional
+        The method to use. One of ``mindist`` for minimum distance (default)
+        or ``mst`` for minimum spanning tree.
+    metric : str or callable, optional
+        The distance metric to use. See the documentation
+        for `scipy.spatial.distance.pdist` for the available metrics and
+        the default.
+
+    Returns
+    -------
+    discrepancy : float
+        Discrepancy (higher values correspond to greater sample uniformity).
+
+    See Also
+    --------
+    discrepancy
+
+    Notes
+    -----
+    The discrepancy can serve as a simple measure of quality of a random sample.
+    This measure is based on the geometric properties of the distribution of points
+    in the sample, such as the minimum distance between any pair of points, or
+    the mean edge length in a minimum spanning tree.
+
+    The higher the value is, the better the coverage of the parameter space is.
+    Note that this is different from `scipy.stats.qmc.discrepancy`, where lower
+    values correspond to higher quality of the sample.
+
+    Also note that when comparing different sampling strategies using this function,
+    the sample size must be kept constant.
+
+    It is possible to calculate two metrics from the minimum spanning tree:
+    the mean edge length and the standard deviation of edges lengths. Using
+    both metrics offers a better picture of uniformity than either metric alone,
+    with higher mean and lower standard deviation being preferable (see [1]_
+    for a brief discussion). This function currently only calculates the mean
+    edge length.
+
+    References
+    ----------
+    .. [1] Franco J. et al. "Minimum Spanning Tree: A new approach to assess the quality
+       of the design of computer experiments." Chemometrics and Intelligent Laboratory
+       Systems, 97 (2), pp. 164-169, 2009.
+
+    Examples
+    --------
+    Calculate the quality of the sample using the minimum euclidean distance
+    (the defaults):
+
+    >>> import numpy as np
+    >>> from scipy.stats import qmc
+    >>> rng = np.random.default_rng(191468432622931918890291693003068437394)
+    >>> sample = qmc.LatinHypercube(d=2, rng=rng).random(50)
+    >>> qmc.geometric_discrepancy(sample)
+    0.03708161435687876
+
+    Calculate the quality using the mean edge length in the minimum
+    spanning tree:
+
+    >>> qmc.geometric_discrepancy(sample, method='mst')
+    0.1105149978798376
+
+    Display the minimum spanning tree and the points with
+    the smallest distance:
+
+    >>> import matplotlib.pyplot as plt
+    >>> from matplotlib.lines import Line2D
+    >>> from scipy.sparse.csgraph import minimum_spanning_tree
+    >>> from scipy.spatial.distance import pdist, squareform
+    >>> dist = pdist(sample)
+    >>> mst = minimum_spanning_tree(squareform(dist))
+    >>> edges = np.where(mst.toarray() > 0)
+    >>> edges = np.asarray(edges).T
+    >>> min_dist = np.min(dist)
+    >>> min_idx = np.argwhere(squareform(dist) == min_dist)[0]
+    >>> fig, ax = plt.subplots(figsize=(10, 5))
+    >>> _ = ax.set(aspect='equal', xlabel=r'$x_1$', ylabel=r'$x_2$',
+    ...            xlim=[0, 1], ylim=[0, 1])
+    >>> for edge in edges:
+    ...     ax.plot(sample[edge, 0], sample[edge, 1], c='k')
+    >>> ax.scatter(sample[:, 0], sample[:, 1])
+    >>> ax.add_patch(plt.Circle(sample[min_idx[0]], min_dist, color='red', fill=False))
+    >>> markers = [
+    ...     Line2D([0], [0], marker='o', lw=0, label='Sample points'),
+    ...     Line2D([0], [0], color='k', label='Minimum spanning tree'),
+    ...     Line2D([0], [0], marker='o', lw=0, markerfacecolor='w', markeredgecolor='r',
+    ...            label='Minimum point-to-point distance'),
+    ... ]
+    >>> ax.legend(handles=markers, loc='center left', bbox_to_anchor=(1, 0.5));
+    >>> plt.show()
+
+    """
+    sample = _ensure_in_unit_hypercube(sample)
+    if sample.shape[0] < 2:
+        raise ValueError("Sample must contain at least two points")
+
+    distances = distance.pdist(sample, metric=metric)  # type: ignore[call-overload]
+
+    if np.any(distances == 0.0):
+        warnings.warn("Sample contains duplicate points.", stacklevel=2)
+
+    if method == "mindist":
+        return np.min(distances[distances.nonzero()])
+    elif method == "mst":
+        fully_connected_graph = distance.squareform(distances)
+        mst = minimum_spanning_tree(fully_connected_graph)
+        distances = mst[mst.nonzero()]
+        # TODO consider returning both the mean and the standard deviation
+        # see [1] for a discussion
+        return np.mean(distances)
+    else:
+        raise ValueError(f"{method!r} is not a valid method. "
+                         f"It must be one of {{'mindist', 'mst'}}")
+
+
+def update_discrepancy(
+        x_new: "npt.ArrayLike",
+        sample: "npt.ArrayLike",
+        initial_disc: DecimalNumber) -> float:
+    """Update the centered discrepancy with a new sample.
+
+    Parameters
+    ----------
+    x_new : array_like (1, d)
+        The new sample to add in `sample`.
+    sample : array_like (n, d)
+        The initial sample.
+    initial_disc : float
+        Centered discrepancy of the `sample`.
+
+    Returns
+    -------
+    discrepancy : float
+        Centered discrepancy of the sample composed of `x_new` and `sample`.
+
+    Examples
+    --------
+    We can also compute iteratively the discrepancy by using
+    ``iterative=True``.
+
+    >>> import numpy as np
+    >>> from scipy.stats import qmc
+    >>> space = np.array([[1, 3], [2, 6], [3, 2], [4, 5], [5, 1], [6, 4]])
+    >>> l_bounds = [0.5, 0.5]
+    >>> u_bounds = [6.5, 6.5]
+    >>> space = qmc.scale(space, l_bounds, u_bounds, reverse=True)
+    >>> disc_init = qmc.discrepancy(space[:-1], iterative=True)
+    >>> disc_init
+    0.04769081147119336
+    >>> qmc.update_discrepancy(space[-1], space[:-1], disc_init)
+    0.008142039609053513
+
+    """
+    sample = np.asarray(sample, dtype=np.float64, order="C")
+    x_new = np.asarray(x_new, dtype=np.float64, order="C")
+
+    # Checking that sample is within the hypercube and 2D
+    if not sample.ndim == 2:
+        raise ValueError('Sample is not a 2D array')
+
+    if (sample.max() > 1.) or (sample.min() < 0.):
+        raise ValueError('Sample is not in unit hypercube')
+
+    # Checking that x_new is within the hypercube and 1D
+    if not x_new.ndim == 1:
+        raise ValueError('x_new is not a 1D array')
+
+    if not (np.all(x_new >= 0) and np.all(x_new <= 1)):
+        raise ValueError('x_new is not in unit hypercube')
+
+    if x_new.shape[0] != sample.shape[1]:
+        raise ValueError("x_new and sample must be broadcastable")
+
+    return _cy_wrapper_update_discrepancy(x_new, sample, initial_disc)
+
+
+def _perturb_discrepancy(sample: np.ndarray, i1: int, i2: int, k: int,
+                         disc: float):
+    """Centered discrepancy after an elementary perturbation of a LHS.
+
+    An elementary perturbation consists of an exchange of coordinates between
+    two points: ``sample[i1, k] <-> sample[i2, k]``. By construction,
+    this operation conserves the LHS properties.
+
+    Parameters
+    ----------
+    sample : array_like (n, d)
+        The sample (before permutation) to compute the discrepancy from.
+    i1 : int
+        The first line of the elementary permutation.
+    i2 : int
+        The second line of the elementary permutation.
+    k : int
+        The column of the elementary permutation.
+    disc : float
+        Centered discrepancy of the design before permutation.
+
+    Returns
+    -------
+    discrepancy : float
+        Centered discrepancy of the design after permutation.
+
+    References
+    ----------
+    .. [1] Jin et al. "An efficient algorithm for constructing optimal design
+       of computer experiments", Journal of Statistical Planning and
+       Inference, 2005.
+
+    """
+    n = sample.shape[0]
+
+    z_ij = sample - 0.5
+
+    # Eq (19)
+    c_i1j = (1. / n ** 2.
+             * np.prod(0.5 * (2. + abs(z_ij[i1, :])
+                              + abs(z_ij) - abs(z_ij[i1, :] - z_ij)), axis=1))
+    c_i2j = (1. / n ** 2.
+             * np.prod(0.5 * (2. + abs(z_ij[i2, :])
+                              + abs(z_ij) - abs(z_ij[i2, :] - z_ij)), axis=1))
+
+    # Eq (20)
+    c_i1i1 = (1. / n ** 2 * np.prod(1 + abs(z_ij[i1, :]))
+              - 2. / n * np.prod(1. + 0.5 * abs(z_ij[i1, :])
+                                 - 0.5 * z_ij[i1, :] ** 2))
+    c_i2i2 = (1. / n ** 2 * np.prod(1 + abs(z_ij[i2, :]))
+              - 2. / n * np.prod(1. + 0.5 * abs(z_ij[i2, :])
+                                 - 0.5 * z_ij[i2, :] ** 2))
+
+    # Eq (22), typo in the article in the denominator i2 -> i1
+    num = (2 + abs(z_ij[i2, k]) + abs(z_ij[:, k])
+           - abs(z_ij[i2, k] - z_ij[:, k]))
+    denum = (2 + abs(z_ij[i1, k]) + abs(z_ij[:, k])
+             - abs(z_ij[i1, k] - z_ij[:, k]))
+    gamma = num / denum
+
+    # Eq (23)
+    c_p_i1j = gamma * c_i1j
+    # Eq (24)
+    c_p_i2j = c_i2j / gamma
+
+    alpha = (1 + abs(z_ij[i2, k])) / (1 + abs(z_ij[i1, k]))
+    beta = (2 - abs(z_ij[i2, k])) / (2 - abs(z_ij[i1, k]))
+
+    g_i1 = np.prod(1. + abs(z_ij[i1, :]))
+    g_i2 = np.prod(1. + abs(z_ij[i2, :]))
+    h_i1 = np.prod(1. + 0.5 * abs(z_ij[i1, :]) - 0.5 * (z_ij[i1, :] ** 2))
+    h_i2 = np.prod(1. + 0.5 * abs(z_ij[i2, :]) - 0.5 * (z_ij[i2, :] ** 2))
+
+    # Eq (25), typo in the article g is missing
+    c_p_i1i1 = ((g_i1 * alpha) / (n ** 2) - 2. * alpha * beta * h_i1 / n)
+    # Eq (26), typo in the article n ** 2
+    c_p_i2i2 = ((g_i2 / ((n ** 2) * alpha)) - (2. * h_i2 / (n * alpha * beta)))
+
+    # Eq (26)
+    sum_ = c_p_i1j - c_i1j + c_p_i2j - c_i2j
+
+    mask = np.ones(n, dtype=bool)
+    mask[[i1, i2]] = False
+    sum_ = sum(sum_[mask])
+
+    disc_ep = (disc + c_p_i1i1 - c_i1i1 + c_p_i2i2 - c_i2i2 + 2 * sum_)
+
+    return disc_ep
+
+
+def primes_from_2_to(n: int) -> np.ndarray:
+    """Prime numbers from 2 to *n*.
+
+    Parameters
+    ----------
+    n : int
+        Sup bound with ``n >= 6``.
+
+    Returns
+    -------
+    primes : list(int)
+        Primes in ``2 <= p < n``.
+
+    Notes
+    -----
+    Taken from [1]_ by P.T. Roy, written consent given on 23.04.2021
+    by the original author, Bruno Astrolino, for free use in SciPy under
+    the 3-clause BSD.
+
+    References
+    ----------
+    .. [1] `StackOverflow <https://stackoverflow.com/questions/2068372>`_.
+
+    """
+    sieve = np.ones(n // 3 + (n % 6 == 2), dtype=bool)
+    for i in range(1, int(n ** 0.5) // 3 + 1):
+        k = 3 * i + 1 | 1
+        sieve[k * k // 3::2 * k] = False
+        sieve[k * (k - 2 * (i & 1) + 4) // 3::2 * k] = False
+    return np.r_[2, 3, ((3 * np.nonzero(sieve)[0][1:] + 1) | 1)]
+
+
+def n_primes(n: IntNumber) -> list[int] | np.ndarray:
+    """List of the n-first prime numbers.
+
+    Parameters
+    ----------
+    n : int
+        Number of prime numbers wanted.
+
+    Returns
+    -------
+    primes : list(int)
+        List of primes.
+
+    """
+    primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59,
+              61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127,
+              131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193,
+              197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269,
+              271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349,
+              353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431,
+              433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503,
+              509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599,
+              601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673,
+              677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761,
+              769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857,
+              859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947,
+              953, 967, 971, 977, 983, 991, 997][:n]
+
+    if len(primes) < n:
+        big_number = 2000
+        while 'Not enough primes':
+            primes = primes_from_2_to(big_number)[:n]  # type: ignore
+            if len(primes) == n:
+                break
+            big_number += 1000
+
+    return primes
+
+
+def _van_der_corput_permutations(
+    base: IntNumber, *, rng: SeedType = None
+) -> np.ndarray:
+    """Permutations for scrambling a Van der Corput sequence.
+
+    Parameters
+    ----------
+    base : int
+        Base of the sequence.
+    rng : `numpy.random.Generator`, optional
+        Pseudorandom number generator state. When `rng` is None, a new
+        `numpy.random.Generator` is created using entropy from the
+        operating system. Types other than `numpy.random.Generator` are
+        passed to `numpy.random.default_rng` to instantiate a ``Generator``.
+
+        .. versionchanged:: 1.15.0
+
+            As part of the `SPEC-007 <https://scientific-python.org/specs/spec-0007/>`_
+            transition from use of `numpy.random.RandomState` to
+            `numpy.random.Generator`, this keyword was changed from `seed` to
+            `rng`. During the transition, the behavior documented above is not
+            accurate; see `check_random_state` for actual behavior. After the
+            transition, this admonition can be removed.
+
+    Returns
+    -------
+    permutations : array_like
+        Permutation indices.
+
+    Notes
+    -----
+    In Algorithm 1 of Owen 2017, a permutation of `np.arange(base)` is
+    created for each positive integer `k` such that ``1 - base**-k < 1``
+    using floating-point arithmetic. For double precision floats, the
+    condition ``1 - base**-k < 1`` can also be written as ``base**-k >
+    2**-54``, which makes it more apparent how many permutations we need
+    to create.
+    """
+    rng = check_random_state(rng)
+    count = math.ceil(54 / math.log2(base)) - 1
+    permutations = np.repeat(np.arange(base)[None], count, axis=0)
+    for perm in permutations:
+        rng.shuffle(perm)
+
+    return permutations
+
+
+def van_der_corput(
+        n: IntNumber,
+        base: IntNumber = 2,
+        *,
+        start_index: IntNumber = 0,
+        scramble: bool = False,
+        permutations: "npt.ArrayLike | None" = None,
+        rng: SeedType = None,
+        workers: IntNumber = 1) -> np.ndarray:
+    """Van der Corput sequence.
+
+    Pseudo-random number generator based on a b-adic expansion.
+
+    Scrambling uses permutations of the remainders (see [1]_). Multiple
+    permutations are applied to construct a point. The sequence of
+    permutations has to be the same for all points of the sequence.
+
+    Parameters
+    ----------
+    n : int
+        Number of element of the sequence.
+    base : int, optional
+        Base of the sequence. Default is 2.
+    start_index : int, optional
+        Index to start the sequence from. Default is 0.
+    scramble : bool, optional
+        If True, use Owen scrambling. Otherwise no scrambling is done.
+        Default is True.
+    permutations : array_like, optional
+        Permutations used for scrambling.
+    rng : `numpy.random.Generator`, optional
+        Pseudorandom number generator state. When `rng` is None, a new
+        `numpy.random.Generator` is created using entropy from the
+        operating system. Types other than `numpy.random.Generator` are
+        passed to `numpy.random.default_rng` to instantiate a ``Generator``.
+    workers : int, optional
+        Number of workers to use for parallel processing. If -1 is
+        given all CPU threads are used. Default is 1.
+
+    Returns
+    -------
+    sequence : list (n,)
+        Sequence of Van der Corput.
+
+    References
+    ----------
+    .. [1] A. B. Owen. "A randomized Halton algorithm in R",
+       :arxiv:`1706.02808`, 2017.
+
+    """
+    if base < 2:
+        raise ValueError("'base' must be at least 2")
+
+    if scramble:
+        if permutations is None:
+            permutations = _van_der_corput_permutations(
+                base=base, rng=rng
+            )
+        else:
+            permutations = np.asarray(permutations)
+
+        permutations = permutations.astype(np.int64)
+        return _cy_van_der_corput_scrambled(n, base, start_index,
+                                            permutations, workers)
+
+    else:
+        return _cy_van_der_corput(n, base, start_index, workers)
+
+
+class QMCEngine(ABC):
+    """A generic Quasi-Monte Carlo sampler class meant for subclassing.
+
+    QMCEngine is a base class to construct a specific Quasi-Monte Carlo
+    sampler. It cannot be used directly as a sampler.
+
+    Parameters
+    ----------
+    d : int
+        Dimension of the parameter space.
+    optimization : {None, "random-cd", "lloyd"}, optional
+        Whether to use an optimization scheme to improve the quality after
+        sampling. Note that this is a post-processing step that does not
+        guarantee that all properties of the sample will be conserved.
+        Default is None.
+
+        * ``random-cd``: random permutations of coordinates to lower the
+          centered discrepancy. The best sample based on the centered
+          discrepancy is constantly updated. Centered discrepancy-based
+          sampling shows better space-filling robustness toward 2D and 3D
+          subprojections compared to using other discrepancy measures.
+        * ``lloyd``: Perturb samples using a modified Lloyd-Max algorithm.
+          The process converges to equally spaced samples.
+
+        .. versionadded:: 1.10.0
+
+    rng : `numpy.random.Generator`, optional
+        Pseudorandom number generator state. When `rng` is None, a new
+        `numpy.random.Generator` is created using entropy from the
+        operating system. Types other than `numpy.random.Generator` are
+        passed to `numpy.random.default_rng` to instantiate a ``Generator``.
+
+        .. versionchanged:: 1.15.0
+
+            As part of the `SPEC-007 <https://scientific-python.org/specs/spec-0007/>`_
+            transition from use of `numpy.random.RandomState` to
+            `numpy.random.Generator`, this keyword was changed from `seed` to
+            `rng`. For an interim period, both keywords will continue to work, although
+            only one may be specified at a time. After the interim period, function
+            calls using the `seed` keyword will emit warnings. Following a
+            deprecation period, the `seed` keyword will be removed.
+
+    Notes
+    -----
+    By convention samples are distributed over the half-open interval
+    ``[0, 1)``. Instances of the class can access the attributes: ``d`` for
+    the dimension; and ``rng`` for the random number generator.
+
+    **Subclassing**
+
+    When subclassing `QMCEngine` to create a new sampler,  ``__init__`` and
+    ``random`` must be redefined.
+
+    * ``__init__(d, rng=None)``: at least fix the dimension. If the sampler
+      does not take advantage of a ``rng`` (deterministic methods like
+      Halton), this parameter can be omitted.
+    * ``_random(n, *, workers=1)``: draw ``n`` from the engine. ``workers``
+      is used for parallelism. See `Halton` for example.
+
+    Optionally, two other methods can be overwritten by subclasses:
+
+    * ``reset``: Reset the engine to its original state.
+    * ``fast_forward``: If the sequence is deterministic (like Halton
+      sequence), then ``fast_forward(n)`` is skipping the ``n`` first draw.
+
+    Examples
+    --------
+    To create a random sampler based on ``np.random.random``, we would do the
+    following:
+
+    >>> from scipy.stats import qmc
+    >>> class RandomEngine(qmc.QMCEngine):
+    ...     def __init__(self, d, rng=None):
+    ...         super().__init__(d=d, rng=rng)
+    ...
+    ...
+    ...     def _random(self, n=1, *, workers=1):
+    ...         return self.rng.random((n, self.d))
+    ...
+    ...
+    ...     def reset(self):
+    ...         super().__init__(d=self.d, rng=self.rng_seed)
+    ...         return self
+    ...
+    ...
+    ...     def fast_forward(self, n):
+    ...         self.random(n)
+    ...         return self
+
+    After subclassing `QMCEngine` to define the sampling strategy we want to
+    use, we can create an instance to sample from.
+
+    >>> engine = RandomEngine(2)
+    >>> engine.random(5)
+    array([[0.22733602, 0.31675834],  # random
+           [0.79736546, 0.67625467],
+           [0.39110955, 0.33281393],
+           [0.59830875, 0.18673419],
+           [0.67275604, 0.94180287]])
+
+    We can also reset the state of the generator and resample again.
+
+    >>> _ = engine.reset()
+    >>> engine.random(5)
+    array([[0.22733602, 0.31675834],  # random
+           [0.79736546, 0.67625467],
+           [0.39110955, 0.33281393],
+           [0.59830875, 0.18673419],
+           [0.67275604, 0.94180287]])
+
+    """
+
+    @abstractmethod
+    @_transition_to_rng('seed', replace_doc=False)
+    def __init__(
+        self,
+        d: IntNumber,
+        *,
+        optimization: Literal["random-cd", "lloyd"] | None = None,
+        rng: SeedType = None
+    ) -> None:
+        self._initialize(d, optimization=optimization, rng=rng)
+
+    # During SPEC 7 transition:
+    # `__init__` has to be wrapped with @_transition_to_rng decorator
+    # because it is public. Subclasses previously called `__init__`
+    # directly, but this was problematic because arguments passed to
+    # subclass `__init__` as `seed` would get passed to superclass
+    # `__init__` as `rng`, rejecting `RandomState` arguments.
+    def _initialize(
+        self,
+        d: IntNumber,
+        *,
+        optimization: Literal["random-cd", "lloyd"] | None = None,
+        rng: SeedType = None
+    ) -> None:
+        if not np.issubdtype(type(d), np.integer) or d < 0:
+            raise ValueError('d must be a non-negative integer value')
+
+        self.d = d
+
+        if isinstance(rng, np.random.Generator):
+            # Spawn a Generator that we can own and reset.
+            self.rng = _rng_spawn(rng, 1)[0]
+        else:
+            # Create our instance of Generator, does not need spawning
+            # Also catch RandomState which cannot be spawned
+            self.rng = check_random_state(rng)
+        self.rng_seed = copy.deepcopy(self.rng)
+
+        self.num_generated = 0
+
+        config = {
+            # random-cd
+            "n_nochange": 100,
+            "n_iters": 10_000,
+            "rng": self.rng,
+
+            # lloyd
+            "tol": 1e-5,
+            "maxiter": 10,
+            "qhull_options": None,
+        }
+        self._optimization = optimization
+        self.optimization_method = _select_optimizer(optimization, config)
+
+    @abstractmethod
+    def _random(
+        self, n: IntNumber = 1, *, workers: IntNumber = 1
+    ) -> np.ndarray:
+        ...
+
+    def random(
+        self, n: IntNumber = 1, *, workers: IntNumber = 1
+    ) -> np.ndarray:
+        """Draw `n` in the half-open interval ``[0, 1)``.
+
+        Parameters
+        ----------
+        n : int, optional
+            Number of samples to generate in the parameter space.
+            Default is 1.
+        workers : int, optional
+            Only supported with `Halton`.
+            Number of workers to use for parallel processing. If -1 is
+            given all CPU threads are used. Default is 1. It becomes faster
+            than one worker for `n` greater than :math:`10^3`.
+
+        Returns
+        -------
+        sample : array_like (n, d)
+            QMC sample.
+
+        """
+        sample = self._random(n, workers=workers)
+        if self.optimization_method is not None:
+            sample = self.optimization_method(sample)
+
+        self.num_generated += n
+        return sample
+
+    def integers(
+        self,
+        l_bounds: "npt.ArrayLike",
+        *,
+        u_bounds: "npt.ArrayLike | None" = None,
+        n: IntNumber = 1,
+        endpoint: bool = False,
+        workers: IntNumber = 1
+    ) -> np.ndarray:
+        r"""
+        Draw `n` integers from `l_bounds` (inclusive) to `u_bounds`
+        (exclusive), or if endpoint=True, `l_bounds` (inclusive) to
+        `u_bounds` (inclusive).
+
+        Parameters
+        ----------
+        l_bounds : int or array-like of ints
+            Lowest (signed) integers to be drawn (unless ``u_bounds=None``,
+            in which case this parameter is 0 and this value is used for
+            `u_bounds`).
+        u_bounds : int or array-like of ints, optional
+            If provided, one above the largest (signed) integer to be drawn
+            (see above for behavior if ``u_bounds=None``).
+            If array-like, must contain integer values.
+        n : int, optional
+            Number of samples to generate in the parameter space.
+            Default is 1.
+        endpoint : bool, optional
+            If true, sample from the interval ``[l_bounds, u_bounds]`` instead
+            of the default ``[l_bounds, u_bounds)``. Defaults is False.
+        workers : int, optional
+            Number of workers to use for parallel processing. If -1 is
+            given all CPU threads are used. Only supported when using `Halton`
+            Default is 1.
+
+        Returns
+        -------
+        sample : array_like (n, d)
+            QMC sample.
+
+        Notes
+        -----
+        It is safe to just use the same ``[0, 1)`` to integer mapping
+        with QMC that you would use with MC. You still get unbiasedness,
+        a strong law of large numbers, an asymptotically infinite variance
+        reduction and a finite sample variance bound.
+
+        To convert a sample from :math:`[0, 1)` to :math:`[a, b), b>a`,
+        with :math:`a` the lower bounds and :math:`b` the upper bounds,
+        the following transformation is used:
+
+        .. math::
+
+            \text{floor}((b - a) \cdot \text{sample} + a)
+
+        """
+        if u_bounds is None:
+            u_bounds = l_bounds
+            l_bounds = 0
+
+        u_bounds = np.atleast_1d(u_bounds)
+        l_bounds = np.atleast_1d(l_bounds)
+
+        if endpoint:
+            u_bounds = u_bounds + 1
+
+        if (not np.issubdtype(l_bounds.dtype, np.integer) or
+                not np.issubdtype(u_bounds.dtype, np.integer)):
+            message = ("'u_bounds' and 'l_bounds' must be integers or"
+                       " array-like of integers")
+            raise ValueError(message)
+
+        if isinstance(self, Halton):
+            sample = self.random(n=n, workers=workers)
+        else:
+            sample = self.random(n=n)
+
+        sample = scale(sample, l_bounds=l_bounds, u_bounds=u_bounds)
+        sample = np.floor(sample).astype(np.int64)
+
+        return sample
+
+    def reset(self) -> "QMCEngine":
+        """Reset the engine to base state.
+
+        Returns
+        -------
+        engine : QMCEngine
+            Engine reset to its base state.
+
+        """
+        rng = copy.deepcopy(self.rng_seed)
+        self.rng = check_random_state(rng)
+        self.num_generated = 0
+        return self
+
+    def fast_forward(self, n: IntNumber) -> "QMCEngine":
+        """Fast-forward the sequence by `n` positions.
+
+        Parameters
+        ----------
+        n : int
+            Number of points to skip in the sequence.
+
+        Returns
+        -------
+        engine : QMCEngine
+            Engine reset to its base state.
+
+        """
+        self.random(n=n)
+        return self
+
+
+class Halton(QMCEngine):
+    """Halton sequence.
+
+    Pseudo-random number generator that generalize the Van der Corput sequence
+    for multiple dimensions. The Halton sequence uses the base-two Van der
+    Corput sequence for the first dimension, base-three for its second and
+    base-:math:`p` for its :math:`n`-dimension, with :math:`p` the
+    :math:`n`'th prime.
+
+    Parameters
+    ----------
+    d : int
+        Dimension of the parameter space.
+    scramble : bool, optional
+        If True, use random scrambling from [2]_. Otherwise no scrambling
+        is done.
+        Default is True.
+    optimization : {None, "random-cd", "lloyd"}, optional
+        Whether to use an optimization scheme to improve the quality after
+        sampling. Note that this is a post-processing step that does not
+        guarantee that all properties of the sample will be conserved.
+        Default is None.
+
+        * ``random-cd``: random permutations of coordinates to lower the
+          centered discrepancy. The best sample based on the centered
+          discrepancy is constantly updated. Centered discrepancy-based
+          sampling shows better space-filling robustness toward 2D and 3D
+          subprojections compared to using other discrepancy measures.
+        * ``lloyd``: Perturb samples using a modified Lloyd-Max algorithm.
+          The process converges to equally spaced samples.
+
+        .. versionadded:: 1.10.0
+
+    rng : `numpy.random.Generator`, optional
+        Pseudorandom number generator state. When `rng` is None, a new
+        `numpy.random.Generator` is created using entropy from the
+        operating system. Types other than `numpy.random.Generator` are
+        passed to `numpy.random.default_rng` to instantiate a ``Generator``.
+
+        .. versionchanged:: 1.15.0
+
+            As part of the `SPEC-007 <https://scientific-python.org/specs/spec-0007/>`_
+            transition from use of `numpy.random.RandomState` to
+            `numpy.random.Generator`, this keyword was changed from `seed` to
+            `rng`. For an interim period, both keywords will continue to work, although
+            only one may be specified at a time. After the interim period, function
+            calls using the `seed` keyword will emit warnings. Following a
+            deprecation period, the `seed` keyword will be removed.
+
+    Notes
+    -----
+    The Halton sequence has severe striping artifacts for even modestly
+    large dimensions. These can be ameliorated by scrambling. Scrambling
+    also supports replication-based error estimates and extends
+    applicability to unbounded integrands.
+
+    References
+    ----------
+    .. [1] Halton, "On the efficiency of certain quasi-random sequences of
+       points in evaluating multi-dimensional integrals", Numerische
+       Mathematik, 1960.
+    .. [2] A. B. Owen. "A randomized Halton algorithm in R",
+       :arxiv:`1706.02808`, 2017.
+
+    Examples
+    --------
+    Generate samples from a low discrepancy sequence of Halton.
+
+    >>> from scipy.stats import qmc
+    >>> sampler = qmc.Halton(d=2, scramble=False)
+    >>> sample = sampler.random(n=5)
+    >>> sample
+    array([[0.        , 0.        ],
+           [0.5       , 0.33333333],
+           [0.25      , 0.66666667],
+           [0.75      , 0.11111111],
+           [0.125     , 0.44444444]])
+
+    Compute the quality of the sample using the discrepancy criterion.
+
+    >>> qmc.discrepancy(sample)
+    0.088893711419753
+
+    If some wants to continue an existing design, extra points can be obtained
+    by calling again `random`. Alternatively, you can skip some points like:
+
+    >>> _ = sampler.fast_forward(5)
+    >>> sample_continued = sampler.random(n=5)
+    >>> sample_continued
+    array([[0.3125    , 0.37037037],
+           [0.8125    , 0.7037037 ],
+           [0.1875    , 0.14814815],
+           [0.6875    , 0.48148148],
+           [0.4375    , 0.81481481]])
+
+    Finally, samples can be scaled to bounds.
+
+    >>> l_bounds = [0, 2]
+    >>> u_bounds = [10, 5]
+    >>> qmc.scale(sample_continued, l_bounds, u_bounds)
+    array([[3.125     , 3.11111111],
+           [8.125     , 4.11111111],
+           [1.875     , 2.44444444],
+           [6.875     , 3.44444444],
+           [4.375     , 4.44444444]])
+
+    """
+    @_transition_to_rng('seed', replace_doc=False)
+    def __init__(
+        self, d: IntNumber, *, scramble: bool = True,
+        optimization: Literal["random-cd", "lloyd"] | None = None,
+        rng: SeedType = None
+    ) -> None:
+        # Used in `scipy.integrate.qmc_quad`
+        self._init_quad = {'d': d, 'scramble': True,
+                           'optimization': optimization}
+        super()._initialize(d=d, optimization=optimization, rng=rng)
+
+        # important to have ``type(bdim) == int`` for performance reason
+        self.base = [int(bdim) for bdim in n_primes(d)]
+        self.scramble = scramble
+
+        self._initialize_permutations()
+
+    def _initialize_permutations(self) -> None:
+        """Initialize permutations for all Van der Corput sequences.
+
+        Permutations are only needed for scrambling.
+        """
+        self._permutations: list = [None] * len(self.base)
+        if self.scramble:
+            for i, bdim in enumerate(self.base):
+                permutations = _van_der_corput_permutations(
+                    base=bdim, rng=self.rng
+                )
+
+                self._permutations[i] = permutations
+
+    def _random(
+        self, n: IntNumber = 1, *, workers: IntNumber = 1
+    ) -> np.ndarray:
+        """Draw `n` in the half-open interval ``[0, 1)``.
+
+        Parameters
+        ----------
+        n : int, optional
+            Number of samples to generate in the parameter space. Default is 1.
+        workers : int, optional
+            Number of workers to use for parallel processing. If -1 is
+            given all CPU threads are used. Default is 1. It becomes faster
+            than one worker for `n` greater than :math:`10^3`.
+
+        Returns
+        -------
+        sample : array_like (n, d)
+            QMC sample.
+
+        """
+        workers = _validate_workers(workers)
+        # Generate a sample using a Van der Corput sequence per dimension.
+        sample = [van_der_corput(n, bdim, start_index=self.num_generated,
+                                 scramble=self.scramble,
+                                 permutations=self._permutations[i],
+                                 workers=workers)
+                  for i, bdim in enumerate(self.base)]
+
+        return np.array(sample).T.reshape(n, self.d)
+
+
+class LatinHypercube(QMCEngine):
+    r"""Latin hypercube sampling (LHS).
+
+    A Latin hypercube sample [1]_ generates :math:`n` points in
+    :math:`[0,1)^{d}`. Each univariate marginal distribution is stratified,
+    placing exactly one point in :math:`[j/n, (j+1)/n)` for
+    :math:`j=0,1,...,n-1`. They are still applicable when :math:`n << d`.
+
+    Parameters
+    ----------
+    d : int
+        Dimension of the parameter space.
+    scramble : bool, optional
+        When False, center samples within cells of a multi-dimensional grid.
+        Otherwise, samples are randomly placed within cells of the grid.
+
+        .. note::
+            Setting ``scramble=False`` does not ensure deterministic output.
+            For that, use the `rng` parameter.
+
+        Default is True.
+
+        .. versionadded:: 1.10.0
+
+    optimization : {None, "random-cd", "lloyd"}, optional
+        Whether to use an optimization scheme to improve the quality after
+        sampling. Note that this is a post-processing step that does not
+        guarantee that all properties of the sample will be conserved.
+        Default is None.
+
+        * ``random-cd``: random permutations of coordinates to lower the
+          centered discrepancy. The best sample based on the centered
+          discrepancy is constantly updated. Centered discrepancy-based
+          sampling shows better space-filling robustness toward 2D and 3D
+          subprojections compared to using other discrepancy measures.
+        * ``lloyd``: Perturb samples using a modified Lloyd-Max algorithm.
+          The process converges to equally spaced samples.
+
+        .. versionadded:: 1.8.0
+        .. versionchanged:: 1.10.0
+            Add ``lloyd``.
+
+    strength : {1, 2}, optional
+        Strength of the LHS. ``strength=1`` produces a plain LHS while
+        ``strength=2`` produces an orthogonal array based LHS of strength 2
+        [7]_, [8]_. In that case, only ``n=p**2`` points can be sampled,
+        with ``p`` a prime number. It also constrains ``d <= p + 1``.
+        Default is 1.
+
+        .. versionadded:: 1.8.0
+
+    rng : `numpy.random.Generator`, optional
+        Pseudorandom number generator state. When `rng` is None, a new
+        `numpy.random.Generator` is created using entropy from the
+        operating system. Types other than `numpy.random.Generator` are
+        passed to `numpy.random.default_rng` to instantiate a ``Generator``.
+
+        .. versionchanged:: 1.15.0
+
+            As part of the `SPEC-007 <https://scientific-python.org/specs/spec-0007/>`_
+            transition from use of `numpy.random.RandomState` to
+            `numpy.random.Generator`, this keyword was changed from `seed` to
+            `rng`. For an interim period, both keywords will continue to work, although
+            only one may be specified at a time. After the interim period, function
+            calls using the `seed` keyword will emit warnings. Following a
+            deprecation period, the `seed` keyword will be removed.
+
+    See Also
+    --------
+    :ref:`quasi-monte-carlo`
+
+    Notes
+    -----
+
+    When LHS is used for integrating a function :math:`f` over :math:`n`,
+    LHS is extremely effective on integrands that are nearly additive [2]_.
+    With a LHS of :math:`n` points, the variance of the integral is always
+    lower than plain MC on :math:`n-1` points [3]_. There is a central limit
+    theorem for LHS on the mean and variance of the integral [4]_, but not
+    necessarily for optimized LHS due to the randomization.
+
+    :math:`A` is called an orthogonal array of strength :math:`t` if in each
+    n-row-by-t-column submatrix of :math:`A`: all :math:`p^t` possible
+    distinct rows occur the same number of times. The elements of :math:`A`
+    are in the set :math:`\{0, 1, ..., p-1\}`, also called symbols.
+    The constraint that :math:`p` must be a prime number is to allow modular
+    arithmetic. Increasing strength adds some symmetry to the sub-projections
+    of a sample. With strength 2, samples are symmetric along the diagonals of
+    2D sub-projections. This may be undesirable, but on the other hand, the
+    sample dispersion is improved.
+
+    Strength 1 (plain LHS) brings an advantage over strength 0 (MC) and
+    strength 2 is a useful increment over strength 1. Going to strength 3 is
+    a smaller increment and scrambled QMC like Sobol', Halton are more
+    performant [7]_.
+
+    To create a LHS of strength 2, the orthogonal array :math:`A` is
+    randomized by applying a random, bijective map of the set of symbols onto
+    itself. For example, in column 0, all 0s might become 2; in column 1,
+    all 0s might become 1, etc.
+    Then, for each column :math:`i` and symbol :math:`j`, we add a plain,
+    one-dimensional LHS of size :math:`p` to the subarray where
+    :math:`A^i = j`. The resulting matrix is finally divided by :math:`p`.
+
+    References
+    ----------
+    .. [1] Mckay et al., "A Comparison of Three Methods for Selecting Values
+       of Input Variables in the Analysis of Output from a Computer Code."
+       Technometrics, 1979.
+    .. [2] M. Stein, "Large sample properties of simulations using Latin
+       hypercube sampling." Technometrics 29, no. 2: 143-151, 1987.
+    .. [3] A. B. Owen, "Monte Carlo variance of scrambled net quadrature."
+       SIAM Journal on Numerical Analysis 34, no. 5: 1884-1910, 1997
+    .. [4]  Loh, W.-L. "On Latin hypercube sampling." The annals of statistics
+       24, no. 5: 2058-2080, 1996.
+    .. [5] Fang et al. "Design and modeling for computer experiments".
+       Computer Science and Data Analysis Series, 2006.
+    .. [6] Damblin et al., "Numerical studies of space filling designs:
+       optimization of Latin Hypercube Samples and subprojection properties."
+       Journal of Simulation, 2013.
+    .. [7] A. B. Owen , "Orthogonal arrays for computer experiments,
+       integration and visualization." Statistica Sinica, 1992.
+    .. [8] B. Tang, "Orthogonal Array-Based Latin Hypercubes."
+       Journal of the American Statistical Association, 1993.
+    .. [9] Seaholm, Susan K. et al. (1988). Latin hypercube sampling and the
+       sensitivity analysis of a Monte Carlo epidemic model. Int J Biomed
+       Comput, 23(1-2), 97-112. :doi:`10.1016/0020-7101(88)90067-0`
+
+    Examples
+    --------
+    Generate samples from a Latin hypercube generator.
+
+    >>> from scipy.stats import qmc
+    >>> sampler = qmc.LatinHypercube(d=2)
+    >>> sample = sampler.random(n=5)
+    >>> sample
+    array([[0.1545328 , 0.53664833], # random
+            [0.84052691, 0.06474907],
+            [0.52177809, 0.93343721],
+            [0.68033825, 0.36265316],
+            [0.26544879, 0.61163943]])
+
+    Compute the quality of the sample using the discrepancy criterion.
+
+    >>> qmc.discrepancy(sample)
+    0.0196... # random
+
+    Samples can be scaled to bounds.
+
+    >>> l_bounds = [0, 2]
+    >>> u_bounds = [10, 5]
+    >>> qmc.scale(sample, l_bounds, u_bounds)
+    array([[1.54532796, 3.609945 ], # random
+            [8.40526909, 2.1942472 ],
+            [5.2177809 , 4.80031164],
+            [6.80338249, 3.08795949],
+            [2.65448791, 3.83491828]])
+
+    Below are other examples showing alternative ways to construct LHS with
+    even better coverage of the space.
+
+    Using a base LHS as a baseline.
+
+    >>> sampler = qmc.LatinHypercube(d=2)
+    >>> sample = sampler.random(n=5)
+    >>> qmc.discrepancy(sample)
+    0.0196...  # random
+
+    Use the `optimization` keyword argument to produce a LHS with
+    lower discrepancy at higher computational cost.
+
+    >>> sampler = qmc.LatinHypercube(d=2, optimization="random-cd")
+    >>> sample = sampler.random(n=5)
+    >>> qmc.discrepancy(sample)
+    0.0176...  # random
+
+    Use the `strength` keyword argument to produce an orthogonal array based
+    LHS of strength 2. In this case, the number of sample points must be the
+    square of a prime number.
+
+    >>> sampler = qmc.LatinHypercube(d=2, strength=2)
+    >>> sample = sampler.random(n=9)
+    >>> qmc.discrepancy(sample)
+    0.00526...  # random
+
+    Options could be combined to produce an optimized centered
+    orthogonal array based LHS. After optimization, the result would not
+    be guaranteed to be of strength 2.
+
+    **Real-world example**
+
+    In [9]_, a Latin Hypercube sampling (LHS) strategy was used to sample a
+    parameter space to study the importance of each parameter of an epidemic
+    model. Such analysis is also called a sensitivity analysis.
+
+    Since the dimensionality of the problem is high (6), it is computationally
+    expensive to cover the space. When numerical experiments are costly, QMC
+    enables analysis that may not be possible if using a grid.
+
+    The six parameters of the model represented the probability of illness,
+    the probability of withdrawal, and four contact probabilities. The
+    authors assumed uniform distributions for all parameters and generated
+    50 samples.
+
+    Using `scipy.stats.qmc.LatinHypercube` to replicate the protocol,
+    the first step is to create a sample in the unit hypercube:
+
+    >>> from scipy.stats import qmc
+    >>> sampler = qmc.LatinHypercube(d=6)
+    >>> sample = sampler.random(n=50)
+
+    Then the sample can be scaled to the appropriate bounds:
+
+    >>> l_bounds = [0.000125, 0.01, 0.0025, 0.05, 0.47, 0.7]
+    >>> u_bounds = [0.000375, 0.03, 0.0075, 0.15, 0.87, 0.9]
+    >>> sample_scaled = qmc.scale(sample, l_bounds, u_bounds)
+
+    Such a sample was used to run the model 50 times, and a polynomial
+    response surface was constructed. This allowed the authors to study the
+    relative importance of each parameter across the range of possibilities
+    of every other parameter.
+
+    In this computer experiment, they showed a 14-fold reduction in the
+    number of samples required to maintain an error below 2% on their
+    response surface when compared to a grid sampling.
+
+    """
+
+    @_transition_to_rng('seed', replace_doc=False)
+    def __init__(
+        self, d: IntNumber, *,
+        scramble: bool = True,
+        strength: int = 1,
+        optimization: Literal["random-cd", "lloyd"] | None = None,
+        rng: SeedType = None
+    ) -> None:
+        # Used in `scipy.integrate.qmc_quad`
+        self._init_quad = {'d': d, 'scramble': True, 'strength': strength,
+                           'optimization': optimization}
+        super()._initialize(d=d, rng=rng, optimization=optimization)
+        self.scramble = scramble
+
+        lhs_method_strength = {
+            1: self._random_lhs,
+            2: self._random_oa_lhs
+        }
+
+        try:
+            self.lhs_method: Callable = lhs_method_strength[strength]
+        except KeyError as exc:
+            message = (f"{strength!r} is not a valid strength. It must be one"
+                       f" of {set(lhs_method_strength)!r}")
+            raise ValueError(message) from exc
+
+    def _random(
+        self, n: IntNumber = 1, *, workers: IntNumber = 1
+    ) -> np.ndarray:
+        lhs = self.lhs_method(n)
+        return lhs
+
+    def _random_lhs(self, n: IntNumber = 1) -> np.ndarray:
+        """Base LHS algorithm."""
+        if not self.scramble:
+            samples: np.ndarray | float = 0.5
+        else:
+            samples = self.rng.uniform(size=(n, self.d))
+
+        perms = np.tile(np.arange(1, n + 1), (int(self.d), 1))
+        for i in range(self.d):
+            self.rng.shuffle(perms[i, :])
+        perms = perms.T
+
+        samples = (perms - samples) / n
+        return samples
+
+    def _random_oa_lhs(self, n: IntNumber = 4) -> np.ndarray:
+        """Orthogonal array based LHS of strength 2."""
+        p = np.sqrt(n).astype(int)
+        n_row = p**2
+        n_col = p + 1
+
+        primes = primes_from_2_to(p + 1)
+        if p not in primes or n != n_row:
+            raise ValueError(
+                "n is not the square of a prime number. Close"
+                f" values are {primes[-2:]**2}"
+            )
+        if self.d > p + 1:
+            raise ValueError("n is too small for d. Must be n > (d-1)**2")
+
+        oa_sample = np.zeros(shape=(n_row, n_col), dtype=int)
+
+        # OA of strength 2
+        arrays = np.tile(np.arange(p), (2, 1))
+        oa_sample[:, :2] = np.stack(np.meshgrid(*arrays),
+                                    axis=-1).reshape(-1, 2)
+        for p_ in range(1, p):
+            oa_sample[:, 2+p_-1] = np.mod(oa_sample[:, 0]
+                                          + p_*oa_sample[:, 1], p)
+
+        # scramble the OA
+        oa_sample_ = np.empty(shape=(n_row, n_col), dtype=int)
+        for j in range(n_col):
+            perms = self.rng.permutation(p)
+            oa_sample_[:, j] = perms[oa_sample[:, j]]
+
+        oa_sample = oa_sample_
+        # following is making a scrambled OA into an OA-LHS
+        oa_lhs_sample = np.zeros(shape=(n_row, n_col))
+        lhs_engine = LatinHypercube(d=1, scramble=self.scramble, strength=1,
+                                    rng=self.rng)  # type: QMCEngine
+        for j in range(n_col):
+            for k in range(p):
+                idx = oa_sample[:, j] == k
+                lhs = lhs_engine.random(p).flatten()
+                oa_lhs_sample[:, j][idx] = lhs + oa_sample[:, j][idx]
+
+        oa_lhs_sample /= p
+
+        return oa_lhs_sample[:, :self.d]
+
+
+class Sobol(QMCEngine):
+    """Engine for generating (scrambled) Sobol' sequences.
+
+    Sobol' sequences are low-discrepancy, quasi-random numbers. Points
+    can be drawn using two methods:
+
+    * `random_base2`: safely draw :math:`n=2^m` points. This method
+      guarantees the balance properties of the sequence.
+    * `random`: draw an arbitrary number of points from the
+      sequence. See warning below.
+
+    Parameters
+    ----------
+    d : int
+        Dimensionality of the sequence. Max dimensionality is 21201.
+    scramble : bool, optional
+        If True, use LMS+shift scrambling. Otherwise, no scrambling is done.
+        Default is True.
+    bits : int, optional
+        Number of bits of the generator. Control the maximum number of points
+        that can be generated, which is ``2**bits``. Maximal value is 64.
+        It does not correspond to the return type, which is always
+        ``np.float64`` to prevent points from repeating themselves.
+        Default is None, which for backward compatibility, corresponds to 30.
+
+        .. versionadded:: 1.9.0
+    optimization : {None, "random-cd", "lloyd"}, optional
+        Whether to use an optimization scheme to improve the quality after
+        sampling. Note that this is a post-processing step that does not
+        guarantee that all properties of the sample will be conserved.
+        Default is None.
+
+        * ``random-cd``: random permutations of coordinates to lower the
+          centered discrepancy. The best sample based on the centered
+          discrepancy is constantly updated. Centered discrepancy-based
+          sampling shows better space-filling robustness toward 2D and 3D
+          subprojections compared to using other discrepancy measures.
+        * ``lloyd``: Perturb samples using a modified Lloyd-Max algorithm.
+          The process converges to equally spaced samples.
+
+        .. versionadded:: 1.10.0
+
+    rng : `numpy.random.Generator`, optional
+        Pseudorandom number generator state. When `rng` is None, a new
+        `numpy.random.Generator` is created using entropy from the
+        operating system. Types other than `numpy.random.Generator` are
+        passed to `numpy.random.default_rng` to instantiate a ``Generator``.
+
+        .. versionchanged:: 1.15.0
+
+            As part of the `SPEC-007 <https://scientific-python.org/specs/spec-0007/>`_
+            transition from use of `numpy.random.RandomState` to
+            `numpy.random.Generator`, this keyword was changed from `seed` to
+            `rng`. For an interim period, both keywords will continue to work, although
+            only one may be specified at a time. After the interim period, function
+            calls using the `seed` keyword will emit warnings. Following a
+            deprecation period, the `seed` keyword will be removed.
+
+    Notes
+    -----
+    Sobol' sequences [1]_ provide :math:`n=2^m` low discrepancy points in
+    :math:`[0,1)^{d}`. Scrambling them [3]_ makes them suitable for singular
+    integrands, provides a means of error estimation, and can improve their
+    rate of convergence. The scrambling strategy which is implemented is a
+    (left) linear matrix scramble (LMS) followed by a digital random shift
+    (LMS+shift) [2]_.
+
+    There are many versions of Sobol' sequences depending on their
+    'direction numbers'. This code uses direction numbers from [4]_. Hence,
+    the maximum number of dimension is 21201. The direction numbers have been
+    precomputed with search criterion 6 and can be retrieved at
+    https://web.maths.unsw.edu.au/~fkuo/sobol/.
+
+    .. warning::
+
+       Sobol' sequences are a quadrature rule and they lose their balance
+       properties if one uses a sample size that is not a power of 2, or skips
+       the first point, or thins the sequence [5]_.
+
+       If :math:`n=2^m` points are not enough then one should take :math:`2^M`
+       points for :math:`M>m`. When scrambling, the number R of independent
+       replicates does not have to be a power of 2.
+
+       Sobol' sequences are generated to some number :math:`B` of bits.
+       After :math:`2^B` points have been generated, the sequence would
+       repeat. Hence, an error is raised.
+       The number of bits can be controlled with the parameter `bits`.
+
+    References
+    ----------
+    .. [1] I. M. Sobol', "The distribution of points in a cube and the accurate
+       evaluation of integrals." Zh. Vychisl. Mat. i Mat. Phys., 7:784-802,
+       1967.
+    .. [2] J. Matousek, "On the L2-discrepancy for anchored boxes."
+       J. of Complexity 14, 527-556, 1998.
+    .. [3] Art B. Owen, "Scrambling Sobol and Niederreiter-Xing points."
+       Journal of Complexity, 14(4):466-489, December 1998.
+    .. [4] S. Joe and F. Y. Kuo, "Constructing sobol sequences with better
+       two-dimensional projections." SIAM Journal on Scientific Computing,
+       30(5):2635-2654, 2008.
+    .. [5] Art B. Owen, "On dropping the first Sobol' point."
+       :arxiv:`2008.08051`, 2020.
+
+    Examples
+    --------
+    Generate samples from a low discrepancy sequence of Sobol'.
+
+    >>> from scipy.stats import qmc
+    >>> sampler = qmc.Sobol(d=2, scramble=False)
+    >>> sample = sampler.random_base2(m=3)
+    >>> sample
+    array([[0.   , 0.   ],
+           [0.5  , 0.5  ],
+           [0.75 , 0.25 ],
+           [0.25 , 0.75 ],
+           [0.375, 0.375],
+           [0.875, 0.875],
+           [0.625, 0.125],
+           [0.125, 0.625]])
+
+    Compute the quality of the sample using the discrepancy criterion.
+
+    >>> qmc.discrepancy(sample)
+    0.013882107204860938
+
+    To continue an existing design, extra points can be obtained
+    by calling again `random_base2`. Alternatively, you can skip some
+    points like:
+
+    >>> _ = sampler.reset()
+    >>> _ = sampler.fast_forward(4)
+    >>> sample_continued = sampler.random_base2(m=2)
+    >>> sample_continued
+    array([[0.375, 0.375],
+           [0.875, 0.875],
+           [0.625, 0.125],
+           [0.125, 0.625]])
+
+    Finally, samples can be scaled to bounds.
+
+    >>> l_bounds = [0, 2]
+    >>> u_bounds = [10, 5]
+    >>> qmc.scale(sample_continued, l_bounds, u_bounds)
+    array([[3.75 , 3.125],
+           [8.75 , 4.625],
+           [6.25 , 2.375],
+           [1.25 , 3.875]])
+
+    """
+
+    MAXDIM: ClassVar[int] = _MAXDIM
+
+    @_transition_to_rng('seed', replace_doc=False)
+    def __init__(
+        self, d: IntNumber, *, scramble: bool = True,
+        bits: IntNumber | None = None, rng: SeedType = None,
+        optimization: Literal["random-cd", "lloyd"] | None = None
+    ) -> None:
+        # Used in `scipy.integrate.qmc_quad`
+        self._init_quad = {'d': d, 'scramble': True, 'bits': bits,
+                           'optimization': optimization}
+
+        super()._initialize(d=d, optimization=optimization, rng=rng)
+        if d > self.MAXDIM:
+            raise ValueError(
+                f"Maximum supported dimensionality is {self.MAXDIM}."
+            )
+
+        self.bits = bits
+        self.dtype_i: type
+        self.scramble = scramble
+
+        if self.bits is None:
+            self.bits = 30
+
+        if self.bits <= 32:
+            self.dtype_i = np.uint32
+        elif 32 < self.bits <= 64:
+            self.dtype_i = np.uint64
+        else:
+            raise ValueError("Maximum supported 'bits' is 64")
+
+        self.maxn = 2**self.bits
+
+        # v is d x maxbit matrix
+        self._sv: np.ndarray = np.zeros((d, self.bits), dtype=self.dtype_i)
+        _initialize_v(self._sv, dim=d, bits=self.bits)
+
+        if not scramble:
+            self._shift: np.ndarray = np.zeros(d, dtype=self.dtype_i)
+        else:
+            # scramble self._shift and self._sv
+            self._scramble()
+
+        self._quasi = self._shift.copy()
+
+        # normalization constant with the largest possible number
+        # calculate in Python to not overflow int with 2**64
+        self._scale = 1.0 / 2 ** self.bits
+
+        self._first_point = (self._quasi * self._scale).reshape(1, -1)
+        # explicit casting to float64
+        self._first_point = self._first_point.astype(np.float64)
+
+    def _scramble(self) -> None:
+        """Scramble the sequence using LMS+shift."""
+        # Generate shift vector
+        self._shift = np.dot(
+            rng_integers(self.rng, 2, size=(self.d, self.bits),
+                         dtype=self.dtype_i),
+            # pyrefly:ignore[no-matching-overload]
+            2 ** np.arange(self.bits, dtype=self.dtype_i),
+        )
+        # Generate lower triangular matrices (stacked across dimensions)
+        ltm = np.tril(rng_integers(self.rng, 2,
+                                   size=(self.d, self.bits, self.bits),
+                                   dtype=self.dtype_i))
+        _cscramble(
+            dim=self.d, bits=self.bits,  # type: ignore[arg-type]
+            ltm=ltm, sv=self._sv
+        )
+
+    def _random(
+        self, n: IntNumber = 1, *, workers: IntNumber = 1
+    ) -> np.ndarray:
+        """Draw next point(s) in the Sobol' sequence.
+
+        Parameters
+        ----------
+        n : int, optional
+            Number of samples to generate in the parameter space. Default is 1.
+
+        Returns
+        -------
+        sample : array_like (n, d)
+            Sobol' sample.
+
+        """
+        sample: np.ndarray = np.empty((n, self.d), dtype=np.float64)
+
+        if n == 0:
+            return sample
+
+        total_n = self.num_generated + n
+        if total_n > self.maxn:
+            msg = (
+                f"At most 2**{self.bits}={self.maxn} distinct points can be "
+                f"generated. {self.num_generated} points have been previously "
+                f"generated, then: n={self.num_generated}+{n}={total_n}. "
+            )
+            if self.bits != 64:
+                msg += "Consider increasing `bits`."
+            raise ValueError(msg)
+
+        if self.num_generated == 0:
+            # verify n is 2**n
+            if not (n & (n - 1) == 0):
+                warnings.warn("The balance properties of Sobol' points require"
+                              " n to be a power of 2.", stacklevel=3)
+
+            if n == 1:
+                sample = self._first_point
+            else:
+                _draw(
+                    n=n - 1, num_gen=self.num_generated, dim=self.d,
+                    scale=self._scale, sv=self._sv, quasi=self._quasi,
+                    sample=sample
+                )
+                sample = np.concatenate(
+                    [self._first_point, sample]
+                )[:n]
+        else:
+            _draw(
+                n=n, num_gen=self.num_generated - 1, dim=self.d,
+                scale=self._scale, sv=self._sv, quasi=self._quasi,
+                sample=sample
+            )
+
+        return sample
+
+    def random_base2(self, m: IntNumber) -> np.ndarray:
+        """Draw point(s) from the Sobol' sequence.
+
+        This function draws :math:`n=2^m` points in the parameter space
+        ensuring the balance properties of the sequence.
+
+        Parameters
+        ----------
+        m : int
+            Logarithm in base 2 of the number of samples; i.e., n = 2^m.
+
+        Returns
+        -------
+        sample : array_like (n, d)
+            Sobol' sample.
+
+        """
+        n = 2 ** m
+
+        total_n = self.num_generated + n
+        if not (total_n & (total_n - 1) == 0):
+            raise ValueError('The balance properties of Sobol\' points require '
+                             f'n to be a power of 2. {self.num_generated} points '
+                             'have been previously generated, then: '
+                             f'n={self.num_generated}+2**{m}={total_n}. '
+                             'If you still want to do this, the function '
+                             '\'Sobol.random()\' can be used.'
+                             )
+
+        return self.random(n)
+
+    def reset(self) -> "Sobol":
+        """Reset the engine to base state.
+
+        Returns
+        -------
+        engine : Sobol
+            Engine reset to its base state.
+
+        """
+        super().reset()
+        self._quasi = self._shift.copy()
+        return self
+
+    def fast_forward(self, n: IntNumber) -> "Sobol":
+        """Fast-forward the sequence by `n` positions.
+
+        Parameters
+        ----------
+        n : int
+            Number of points to skip in the sequence.
+
+        Returns
+        -------
+        engine : Sobol
+            The fast-forwarded engine.
+
+        """
+        if self.num_generated == 0:
+            _fast_forward(
+                n=n - 1, num_gen=self.num_generated, dim=self.d,
+                sv=self._sv, quasi=self._quasi
+            )
+        else:
+            _fast_forward(
+                n=n, num_gen=self.num_generated - 1, dim=self.d,
+                sv=self._sv, quasi=self._quasi
+            )
+        self.num_generated += n
+        return self
+
+
+class PoissonDisk(QMCEngine):
+    """Poisson disk sampling.
+
+    Parameters
+    ----------
+    d : int
+        Dimension of the parameter space.
+    radius : float
+        Minimal distance to keep between points when sampling new candidates.
+    hypersphere : {"volume", "surface"}, optional
+        Sampling strategy to generate potential candidates to be added in the
+        final sample. Default is "volume".
+
+        * ``volume``: original Bridson algorithm as described in [1]_.
+          New candidates are sampled *within* the hypersphere.
+        * ``surface``: only sample the surface of the hypersphere.
+    ncandidates : int
+        Number of candidates to sample per iteration. More candidates result
+        in a denser sampling as more candidates can be accepted per iteration.
+    optimization : {None, "random-cd", "lloyd"}, optional
+        Whether to use an optimization scheme to improve the quality after
+        sampling. Note that this is a post-processing step that does not
+        guarantee that all properties of the sample will be conserved.
+        Default is None.
+
+        * ``random-cd``: random permutations of coordinates to lower the
+          centered discrepancy. The best sample based on the centered
+          discrepancy is constantly updated. Centered discrepancy-based
+          sampling shows better space-filling robustness toward 2D and 3D
+          subprojections compared to using other discrepancy measures.
+        * ``lloyd``: Perturb samples using a modified Lloyd-Max algorithm.
+          The process converges to equally spaced samples.
+
+        .. versionadded:: 1.10.0
+
+    rng : `numpy.random.Generator`, optional
+        Pseudorandom number generator state. When `rng` is None, a new
+        `numpy.random.Generator` is created using entropy from the
+        operating system. Types other than `numpy.random.Generator` are
+        passed to `numpy.random.default_rng` to instantiate a ``Generator``.
+
+        .. versionchanged:: 1.15.0
+
+            As part of the `SPEC-007 <https://scientific-python.org/specs/spec-0007/>`_
+            transition from use of `numpy.random.RandomState` to
+            `numpy.random.Generator`, this keyword was changed from `seed` to
+            `rng`. For an interim period, both keywords will continue to work, although
+            only one may be specified at a time. After the interim period, function
+            calls using the `seed` keyword will emit warnings. Following a
+            deprecation period, the `seed` keyword will be removed.
+
+    l_bounds, u_bounds : array_like (d,)
+        Lower and upper bounds of target sample data.
+
+    Notes
+    -----
+    Poisson disk sampling is an iterative sampling strategy. Starting from
+    a seed sample, `ncandidates` are sampled in the hypersphere
+    surrounding the seed. Candidates below a certain `radius` or outside the
+    domain are rejected. New samples are added in a pool of sample seed. The
+    process stops when the pool is empty or when the number of required
+    samples is reached.
+
+    The maximum number of point that a sample can contain is directly linked
+    to the `radius`. As the dimension of the space increases, a higher radius
+    spreads the points further and help overcome the curse of dimensionality.
+    See the :ref:`quasi monte carlo tutorial <quasi-monte-carlo>` for more
+    details.
+
+    .. warning::
+
+       The algorithm is more suitable for low dimensions and sampling size
+       due to its iterative nature and memory requirements.
+       Selecting a small radius with a high dimension would
+       mean that the space could contain more samples than using lower
+       dimension or a bigger radius.
+
+    Some code taken from [2]_, written consent given on 31.03.2021
+    by the original author, Shamis, for free use in SciPy under
+    the 3-clause BSD.
+
+    References
+    ----------
+    .. [1] Robert Bridson, "Fast Poisson Disk Sampling in Arbitrary
+       Dimensions." SIGGRAPH, 2007.
+    .. [2] `StackOverflow <https://stackoverflow.com/questions/66047540>`__.
+
+    Examples
+    --------
+    Generate a 2D sample using a `radius` of 0.2.
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from matplotlib.collections import PatchCollection
+    >>> from scipy.stats import qmc
+    >>>
+    >>> rng = np.random.default_rng()
+    >>> radius = 0.2
+    >>> engine = qmc.PoissonDisk(d=2, radius=radius, rng=rng)
+    >>> sample = engine.random(20)
+
+    Visualizing the 2D sample and showing that no points are closer than
+    `radius`. ``radius/2`` is used to visualize non-intersecting circles.
+    If two samples are exactly at `radius` from each other, then their circle
+    of radius ``radius/2`` will touch.
+
+    >>> fig, ax = plt.subplots()
+    >>> _ = ax.scatter(sample[:, 0], sample[:, 1])
+    >>> circles = [plt.Circle((xi, yi), radius=radius/2, fill=False)
+    ...            for xi, yi in sample]
+    >>> collection = PatchCollection(circles, match_original=True)
+    >>> ax.add_collection(collection)
+    >>> _ = ax.set(aspect='equal', xlabel=r'$x_1$', ylabel=r'$x_2$',
+    ...            xlim=[0, 1], ylim=[0, 1])
+    >>> plt.show()
+
+    Such visualization can be seen as circle packing: how many circle can
+    we put in the space. It is an np-hard problem. The method `fill_space`
+    can be used to add samples until no more samples can be added. This is
+    a hard problem and parameters may need to be adjusted manually. Beware of
+    the dimension: as the dimensionality increases, the number of samples
+    required to fill the space increases exponentially
+    (curse-of-dimensionality).
+
+    """
+
+    @_transition_to_rng('seed', replace_doc=False)
+    def __init__(
+        self,
+        d: IntNumber,
+        *,
+        radius: DecimalNumber = 0.05,
+        hypersphere: Literal["volume", "surface"] = "volume",
+        ncandidates: IntNumber = 30,
+        optimization: Literal["random-cd", "lloyd"] | None = None,
+        rng: SeedType = None,
+        l_bounds: "npt.ArrayLike | None" = None,
+        u_bounds: "npt.ArrayLike | None" = None,
+    ) -> None:
+        # Used in `scipy.integrate.qmc_quad`
+        self._init_quad = {'d': d, 'radius': radius,
+                           'hypersphere': hypersphere,
+                           'ncandidates': ncandidates,
+                           'optimization': optimization}
+        super()._initialize(d=d, optimization=optimization, rng=rng)
+
+        hypersphere_sample = {
+            "volume": self._hypersphere_volume_sample,
+            "surface": self._hypersphere_surface_sample
+        }
+
+        try:
+            self.hypersphere_method = hypersphere_sample[hypersphere]
+        except KeyError as exc:
+            message = (
+                f"{hypersphere!r} is not a valid hypersphere sampling"
+                f" method. It must be one of {set(hypersphere_sample)!r}")
+            raise ValueError(message) from exc
+
+        # size of the sphere from which the samples are drawn relative to the
+        # size of a disk (radius)
+        # for the surface sampler, all new points are almost exactly 1 radius
+        # away from at least one existing sample +eps to avoid rejection
+        self.radius_factor = 2 if hypersphere == "volume" else 1.001
+        self.radius = radius
+        self.radius_squared = self.radius**2
+
+        # sample to generate per iteration in the hypersphere around center
+        self.ncandidates = ncandidates
+
+        if u_bounds is None:
+            u_bounds = np.ones(d)
+        if l_bounds is None:
+            l_bounds = np.zeros(d)
+        self.l_bounds, self.u_bounds = _validate_bounds(
+            l_bounds=l_bounds, u_bounds=u_bounds, d=int(d)
+        )
+
+        with np.errstate(divide='ignore'):
+            self.cell_size = self.radius / np.sqrt(self.d)
+            self.grid_size = (
+                np.ceil((self.u_bounds - self.l_bounds) / self.cell_size)
+            ).astype(int)
+
+        self._initialize_grid_pool()
+
+    def _initialize_grid_pool(self):
+        """Sampling pool and sample grid."""
+        self.sample_pool = []
+        # Positions of cells
+        # n-dim value for each grid cell
+        self.sample_grid = np.empty(
+            np.append(self.grid_size, self.d),
+            dtype=np.float32
+        )
+        # Initialise empty cells with NaNs
+        self.sample_grid.fill(np.nan)
+
+    def _random(
+        self, n: IntNumber = 1, *, workers: IntNumber = 1
+    ) -> np.ndarray:
+        """Draw `n` in the interval ``[l_bounds, u_bounds]``.
+
+        Note that it can return fewer samples if the space is full.
+        See the note section of the class.
+
+        Parameters
+        ----------
+        n : int, optional
+            Number of samples to generate in the parameter space. Default is 1.
+
+        Returns
+        -------
+        sample : array_like (n, d)
+            QMC sample.
+
+        """
+        if n == 0 or self.d == 0:
+            return np.empty((n, self.d))
+
+        def in_limits(sample: np.ndarray) -> bool:
+            for i in range(self.d):
+                if (sample[i] > self.u_bounds[i] or sample[i] < self.l_bounds[i]):
+                    return False
+            return True
+
+        def in_neighborhood(candidate: np.ndarray, n: int = 2) -> bool:
+            """
+            Check if there are samples closer than ``radius_squared`` to the
+            `candidate` sample.
+            """
+            indices = ((candidate - self.l_bounds) / self.cell_size).astype(int)
+            ind_min = np.maximum(indices - n, 0)
+            ind_max = np.minimum(indices + n + 1, self.grid_size)
+
+            # Check if the center cell is empty
+            if not np.isnan(self.sample_grid[tuple(indices)][0]):
+                return True
+
+            a = [slice(ind_min[i], ind_max[i]) for i in range(self.d)]
+
+            # guards against: invalid value encountered in less as we are
+            # comparing with nan and returns False. Which is wanted.
+            with np.errstate(invalid='ignore'):
+                if np.any(
+                    np.sum(
+                        np.square(candidate - self.sample_grid[tuple(a)]),
+                        axis=self.d
+                    ) < self.radius_squared
+                ):
+                    return True
+
+            return False
+
+        def add_sample(candidate: np.ndarray) -> None:
+            self.sample_pool.append(candidate)
+            indices = ((candidate - self.l_bounds) / self.cell_size).astype(int)
+            self.sample_grid[tuple(indices)] = candidate
+            curr_sample.append(candidate)
+
+        curr_sample: list[np.ndarray] = []
+
+        if len(self.sample_pool) == 0:
+            # the pool is being initialized with a single random sample
+            add_sample(self.rng.uniform(self.l_bounds, self.u_bounds))
+            num_drawn = 1
+        else:
+            num_drawn = 0
+
+        # exhaust sample pool to have up to n sample
+        while len(self.sample_pool) and num_drawn < n:
+            # select a sample from the available pool
+            idx_center = rng_integers(self.rng, len(self.sample_pool))
+            center = self.sample_pool[idx_center]
+            del self.sample_pool[idx_center]
+
+            # generate candidates around the center sample
+            candidates = self.hypersphere_method(
+                center, self.radius * self.radius_factor, self.ncandidates
+            )
+
+            # keep candidates that satisfy some conditions
+            for candidate in candidates:
+                if in_limits(candidate) and not in_neighborhood(candidate):
+                    add_sample(candidate)
+
+                    num_drawn += 1
+                    if num_drawn >= n:
+                        break
+
+        self.num_generated += num_drawn
+        return np.array(curr_sample)
+
+    def fill_space(self) -> np.ndarray:
+        """Draw ``n`` samples in the interval ``[l_bounds, u_bounds]``.
+
+        Unlike `random`, this method will try to add points until
+        the space is full. Depending on ``candidates`` (and to a lesser extent
+        other parameters), some empty areas can still be present in the sample.
+
+        .. warning::
+
+           This can be extremely slow in high dimensions or if the
+           ``radius`` is very small-with respect to the dimensionality.
+
+        Returns
+        -------
+        sample : array_like (n, d)
+            QMC sample.
+
+        """
+        return self.random(np.inf)  # type: ignore[arg-type]
+
+    def reset(self) -> "PoissonDisk":
+        """Reset the engine to base state.
+
+        Returns
+        -------
+        engine : PoissonDisk
+            Engine reset to its base state.
+
+        """
+        super().reset()
+        self._initialize_grid_pool()
+        return self
+
+    def _hypersphere_volume_sample(
+        self, center: np.ndarray, radius: DecimalNumber,
+        candidates: IntNumber = 1
+    ) -> np.ndarray:
+        """Uniform sampling within hypersphere."""
+        # should remove samples within r/2
+        x = self.rng.standard_normal(size=(candidates, self.d))
+        ssq = np.sum(x**2, axis=1)
+        fr = radius * gammainc(self.d/2, ssq/2)**(1/self.d) / np.sqrt(ssq)
+        fr_tiled = np.tile(fr.reshape(-1, 1), (1, int(self.d)))
+        p = center + np.multiply(x, fr_tiled)
+        return p
+
+    def _hypersphere_surface_sample(
+        self, center: np.ndarray, radius: DecimalNumber,
+        candidates: IntNumber = 1
+    ) -> np.ndarray:
+        """Uniform sampling on the hypersphere's surface."""
+        vec = self.rng.standard_normal(size=(candidates, self.d))
+        vec /= np.linalg.norm(vec, axis=1)[:, None]
+        p = center + np.multiply(vec, radius)
+        return p
+
+
+class MultivariateNormalQMC:
+    r"""QMC sampling from a multivariate Normal :math:`N(\mu, \Sigma)`.
+
+    Parameters
+    ----------
+    mean : array_like (d,)
+        The mean vector. Where ``d`` is the dimension.
+    cov : array_like (d, d), optional
+        The covariance matrix. If omitted, use `cov_root` instead.
+        If both `cov` and `cov_root` are omitted, use the identity matrix.
+    cov_root : array_like (d, d'), optional
+        A root decomposition of the covariance matrix, where ``d'`` may be less
+        than ``d`` if the covariance is not full rank. If omitted, use `cov`.
+    inv_transform : bool, optional
+        If True, use inverse transform instead of Box-Muller. Default is True.
+    engine : QMCEngine, optional
+        Quasi-Monte Carlo engine sampler. If None, `Sobol` is used.
+    rng : `numpy.random.Generator`, optional
+        Pseudorandom number generator state. When `rng` is None, a new
+        `numpy.random.Generator` is created using entropy from the
+        operating system. Types other than `numpy.random.Generator` are
+        passed to `numpy.random.default_rng` to instantiate a ``Generator``.
+
+        .. versionchanged:: 1.15.0
+
+            As part of the `SPEC-007 <https://scientific-python.org/specs/spec-0007/>`_
+            transition from use of `numpy.random.RandomState` to
+            `numpy.random.Generator`, this keyword was changed from `seed` to
+            `rng`. For an interim period, both keywords will continue to work, although
+            only one may be specified at a time. After the interim period, function
+            calls using the `seed` keyword will emit warnings. Following a
+            deprecation period, the `seed` keyword will be removed.
+
+    Examples
+    --------
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.stats import qmc
+    >>> dist = qmc.MultivariateNormalQMC(mean=[0, 5], cov=[[1, 0], [0, 1]])
+    >>> sample = dist.random(512)
+    >>> _ = plt.scatter(sample[:, 0], sample[:, 1])
+    >>> plt.show()
+
+    """
+
+    @_transition_to_rng('seed', replace_doc=False)
+    def __init__(
+            self,
+            mean: "npt.ArrayLike",
+            cov: "npt.ArrayLike | None" = None,
+            *,
+            cov_root: "npt.ArrayLike | None" = None,
+            inv_transform: bool = True,
+            engine: QMCEngine | None = None,
+            rng: SeedType = None,
+    ) -> None:
+        mean = np.asarray(np.atleast_1d(mean))
+        d = mean.shape[0]
+        if cov is not None:
+            # covariance matrix provided
+            cov = np.asarray(np.atleast_2d(cov))
+            # check for square/symmetric cov matrix and mean vector has the
+            # same d
+            if not mean.shape[0] == cov.shape[0]:
+                raise ValueError("Dimension mismatch between mean and "
+                                 "covariance.")
+            if not np.allclose(cov, cov.transpose()):
+                raise ValueError("Covariance matrix is not symmetric.")
+            # compute Cholesky decomp; if it fails, do the eigen decomposition
+            try:
+                cov_root = np.linalg.cholesky(cov).transpose()
+            except np.linalg.LinAlgError:
+                eigval, eigvec = np.linalg.eigh(cov)
+                if not np.all(eigval >= -1.0e-8):
+                    raise ValueError("Covariance matrix not PSD.")
+                eigval = np.clip(eigval, 0.0, None)
+                cov_root = (eigvec * np.sqrt(eigval)).transpose()
+        elif cov_root is not None:
+            # root decomposition provided
+            cov_root = np.atleast_2d(cov_root)
+            if not mean.shape[0] == cov_root.shape[0]:
+                raise ValueError("Dimension mismatch between mean and "
+                                 "covariance.")
+        else:
+            # corresponds to identity covariance matrix
+            cov_root = None
+
+        self._inv_transform = inv_transform
+
+        if not inv_transform:
+            # to apply Box-Muller, we need an even number of dimensions
+            engine_dim = 2 * math.ceil(d / 2)
+        else:
+            engine_dim = d
+        if engine is None:
+            # Need this during SPEC 7 transition to prevent `RandomState`
+            # from being passed via `rng`.
+            kwarg = "seed" if isinstance(rng, np.random.RandomState) else "rng"
+            kwargs = {kwarg: rng}
+            self.engine: QMCEngine = Sobol(
+                d=engine_dim, scramble=True, bits=30, **kwargs
+            )
+        elif isinstance(engine, QMCEngine):
+            if engine.d != engine_dim:
+                raise ValueError("Dimension of `engine` must be consistent"
+                                 " with dimensions of mean and covariance."
+                                 " If `inv_transform` is False, it must be"
+                                 " an even number.")
+            self.engine = engine
+        else:
+            raise ValueError("`engine` must be an instance of "
+                             "`scipy.stats.qmc.QMCEngine` or `None`.")
+
+        self._mean = mean
+        self._corr_matrix = cov_root
+
+        self._d = d
+
+    def random(self, n: IntNumber = 1) -> np.ndarray:
+        """Draw `n` QMC samples from the multivariate Normal.
+
+        Parameters
+        ----------
+        n : int, optional
+            Number of samples to generate in the parameter space. Default is 1.
+
+        Returns
+        -------
+        sample : array_like (n, d)
+            Sample.
+
+        """
+        base_samples = self._standard_normal_samples(n)
+        return self._correlate(base_samples)
+
+    def _correlate(self, base_samples: np.ndarray) -> np.ndarray:
+        if self._corr_matrix is not None:
+            return base_samples @ self._corr_matrix + self._mean
+        else:
+            # avoid multiplying with identity here
+            return base_samples + self._mean
+
+    def _standard_normal_samples(self, n: IntNumber = 1) -> np.ndarray:
+        """Draw `n` QMC samples from the standard Normal :math:`N(0, I_d)`.
+
+        Parameters
+        ----------
+        n : int, optional
+            Number of samples to generate in the parameter space. Default is 1.
+
+        Returns
+        -------
+        sample : array_like (n, d)
+            Sample.
+
+        """
+        # get base samples
+        samples = self.engine.random(n)
+        if self._inv_transform:
+            # apply inverse transform
+            # (values to close to 0/1 result in inf values)
+            return stats.norm.ppf(0.5 + (1 - 1e-10) * (samples - 0.5))  # type: ignore[attr-defined]  # noqa: E501
+        else:
+            # apply Box-Muller transform (note: indexes starting from 1)
+            even = np.arange(0, samples.shape[-1], 2)
+            Rs = np.sqrt(-2 * np.log(samples[:, even]))
+            thetas = 2 * math.pi * samples[:, 1 + even]
+            cos = np.cos(thetas)
+            sin = np.sin(thetas)
+            transf_samples = np.stack([Rs * cos, Rs * sin],
+                                      -1).reshape(n, -1)
+            # make sure we only return the number of dimension requested
+            return transf_samples[:, : self._d]
+
+
+class MultinomialQMC:
+    r"""QMC sampling from a multinomial distribution.
+
+    Parameters
+    ----------
+    pvals : array_like (k,)
+        Vector of probabilities of size ``k``, where ``k`` is the number
+        of categories. Elements must be non-negative and sum to 1.
+    n_trials : int
+        Number of trials.
+    engine : QMCEngine, optional
+        Quasi-Monte Carlo engine sampler. If None, `Sobol` is used.
+    rng : `numpy.random.Generator`, optional
+        Pseudorandom number generator state. When `rng` is None, a new
+        `numpy.random.Generator` is created using entropy from the
+        operating system. Types other than `numpy.random.Generator` are
+        passed to `numpy.random.default_rng` to instantiate a ``Generator``.
+
+        .. versionchanged:: 1.15.0
+
+            As part of the `SPEC-007 <https://scientific-python.org/specs/spec-0007/>`_
+            transition from use of `numpy.random.RandomState` to
+            `numpy.random.Generator`, this keyword was changed from `seed` to
+            `rng`. For an interim period, both keywords will continue to work, although
+            only one may be specified at a time. After the interim period, function
+            calls using the `seed` keyword will emit warnings. Following a
+            deprecation period, the `seed` keyword will be removed.
+
+    Examples
+    --------
+    Let's define 3 categories and for a given sample, the sum of the trials
+    of each category is 8. The number of trials per category is determined
+    by the `pvals` associated to each category.
+    Then, we sample this distribution 64 times.
+
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.stats import qmc
+    >>> dist = qmc.MultinomialQMC(
+    ...     pvals=[0.2, 0.4, 0.4], n_trials=10, engine=qmc.Halton(d=1)
+    ... )
+    >>> sample = dist.random(64)
+
+    We can plot the sample and verify that the median of number of trials
+    for each category is following the `pvals`. That would be
+    ``pvals * n_trials = [2, 4, 4]``.
+
+    >>> fig, ax = plt.subplots()
+    >>> ax.yaxis.get_major_locator().set_params(integer=True)
+    >>> _ = ax.boxplot(sample)
+    >>> ax.set(xlabel="Categories", ylabel="Trials")
+    >>> plt.show()
+
+    """
+
+    @_transition_to_rng('seed', replace_doc=False)
+    def __init__(
+        self,
+        pvals: "npt.ArrayLike",
+        n_trials: IntNumber,
+        *,
+        engine: QMCEngine | None = None,
+        rng: SeedType = None,
+    ) -> None:
+        self.pvals = np.atleast_1d(np.asarray(pvals))
+        if np.min(pvals) < 0:
+            raise ValueError('Elements of pvals must be non-negative.')
+        if not np.isclose(np.sum(pvals), 1):
+            raise ValueError('Elements of pvals must sum to 1.')
+        self.n_trials = n_trials
+        if engine is None:
+            # Need this during SPEC 7 transition to prevent `RandomState`
+            # from being passed via `rng`.
+            kwarg = "seed" if isinstance(rng, np.random.RandomState) else "rng"
+            kwargs = {kwarg: rng}
+            self.engine: QMCEngine = Sobol(d=1, scramble=True, bits=30, **kwargs)
+        elif isinstance(engine, QMCEngine):
+            if engine.d != 1:
+                raise ValueError("Dimension of `engine` must be 1.")
+            self.engine = engine
+        else:
+            raise ValueError("`engine` must be an instance of "
+                             "`scipy.stats.qmc.QMCEngine` or `None`.")
+
+    def random(self, n: IntNumber = 1) -> np.ndarray:
+        """Draw `n` QMC samples from the multinomial distribution.
+
+        Parameters
+        ----------
+        n : int, optional
+            Number of samples to generate in the parameter space. Default is 1.
+
+        Returns
+        -------
+        samples : array_like (n, pvals)
+            Sample.
+
+        """
+        sample = np.empty((n, len(self.pvals)))
+        for i in range(n):
+            base_draws = self.engine.random(self.n_trials).ravel()
+            p_cumulative = np.empty_like(self.pvals, dtype=float)
+            _fill_p_cumulative(np.array(self.pvals, dtype=float), p_cumulative)
+            sample_ = np.zeros_like(self.pvals, dtype=np.intp)
+            _categorize(base_draws, p_cumulative, sample_)
+            sample[i] = sample_
+        return sample
+
+
+def _select_optimizer(
+    optimization: Literal["random-cd", "lloyd"] | None, config: dict
+) -> Callable | None:
+    """A factory for optimization methods."""
+    optimization_method: dict[str, Callable] = {
+        "random-cd": _random_cd,
+        "lloyd": _lloyd_centroidal_voronoi_tessellation
+    }
+
+    optimizer: partial | None
+    if optimization is not None:
+        try:
+            optimizer_ = optimization_method[optimization.lower()]
+        except KeyError as exc:
+            message = (f"{optimization!r} is not a valid optimization"
+                       f" method. It must be one of"
+                       f" {set(optimization_method)!r}")
+            raise ValueError(message) from exc
+
+        # config
+        optimizer = partial(optimizer_, **config)
+    else:
+        optimizer = None
+
+    return optimizer
+
+
+def _random_cd(
+    best_sample: np.ndarray, n_iters: int, n_nochange: int, rng: GeneratorType,
+    **kwargs: dict
+) -> np.ndarray:
+    """Optimal LHS on CD.
+
+    Create a base LHS and do random permutations of coordinates to
+    lower the centered discrepancy.
+    Because it starts with a normal LHS, it also works with the
+    `scramble` keyword argument.
+
+    Two stopping criterion are used to stop the algorithm: at most,
+    `n_iters` iterations are performed; or if there is no improvement
+    for `n_nochange` consecutive iterations.
+    """
+    del kwargs  # only use keywords which are defined, needed by factory
+
+    n, d = best_sample.shape
+
+    if d == 0 or n == 0:
+        return np.empty((n, d))
+
+    if d == 1 or n == 1:
+        # discrepancy measures are invariant under permuting factors and runs
+        return best_sample
+
+    best_disc = discrepancy(best_sample)
+
+    bounds = ([0, d - 1],
+              [0, n - 1],
+              [0, n - 1])
+
+    n_nochange_ = 0
+    n_iters_ = 0
+    while n_nochange_ < n_nochange and n_iters_ < n_iters:
+        n_iters_ += 1
+
+        col = rng_integers(rng, *bounds[0], endpoint=True)  # type: ignore[misc]
+        row_1 = rng_integers(rng, *bounds[1], endpoint=True)  # type: ignore[misc]
+        row_2 = rng_integers(rng, *bounds[2], endpoint=True)  # type: ignore[misc]
+        disc = _perturb_discrepancy(best_sample,
+                                    row_1, row_2, col,
+                                    best_disc)
+        if disc < best_disc:
+            best_sample[row_1, col], best_sample[row_2, col] = (
+                best_sample[row_2, col], best_sample[row_1, col])
+
+            best_disc = disc
+            n_nochange_ = 0
+        else:
+            n_nochange_ += 1
+
+    return best_sample
+
+
+def _l1_norm(sample: np.ndarray) -> float:
+    return distance.pdist(sample, 'cityblock').min()
+
+
+def _lloyd_iteration(
+    sample: np.ndarray,
+    decay: float,
+    qhull_options: str
+) -> np.ndarray:
+    """Lloyd-Max algorithm iteration.
+
+    Based on the implementation of Stéfan van der Walt:
+
+    https://github.com/stefanv/lloyd
+
+    which is:
+
+        Copyright (c) 2021-04-21 Stéfan van der Walt
+        https://github.com/stefanv/lloyd
+        MIT License
+
+    Parameters
+    ----------
+    sample : array_like (n, d)
+        The sample to iterate on.
+    decay : float
+        Relaxation decay. A positive value would move the samples toward
+        their centroid, and negative value would move them away.
+        1 would move the samples to their centroid.
+    qhull_options : str
+        Additional options to pass to Qhull. See Qhull manual
+        for details. (Default: "Qbb Qc Qz Qj Qx" for ndim > 4 and
+        "Qbb Qc Qz Qj" otherwise.)
+
+    Returns
+    -------
+    sample : array_like (n, d)
+        The sample after an iteration of Lloyd's algorithm.
+
+    """
+    new_sample = np.empty_like(sample)
+
+    voronoi = Voronoi(sample, qhull_options=qhull_options)
+
+    for ii, idx in enumerate(voronoi.point_region):
+        # the region is a series of indices into self.voronoi.vertices
+        # remove samples at infinity, designated by index -1
+        region = [i for i in voronoi.regions[idx] if i != -1]
+
+        # get the vertices for this region
+        verts = voronoi.vertices[region]
+
+        # clipping would be wrong, we need to intersect
+        # verts = np.clip(verts, 0, 1)
+
+        # move samples towards centroids:
+        # Centroid in n-D is the mean for uniformly distributed nodes
+        # of a geometry.
+        centroid = np.mean(verts, axis=0)
+        new_sample[ii] = sample[ii] + (centroid - sample[ii]) * decay
+
+    # only update sample to centroid within the region
+    is_valid = np.all(np.logical_and(new_sample >= 0, new_sample <= 1), axis=1)
+    sample[is_valid] = new_sample[is_valid]
+
+    return sample
+
+
+def _lloyd_centroidal_voronoi_tessellation(
+    sample: "npt.ArrayLike",
+    *,
+    tol: DecimalNumber = 1e-5,
+    maxiter: IntNumber = 10,
+    qhull_options: str | None = None,
+    **kwargs: dict
+) -> np.ndarray:
+    """Approximate Centroidal Voronoi Tessellation.
+
+    Perturb samples in N-dimensions using Lloyd-Max algorithm.
+
+    Parameters
+    ----------
+    sample : array_like (n, d)
+        The sample to iterate on. With ``n`` the number of samples and ``d``
+        the dimension. Samples must be in :math:`[0, 1]^d`, with ``d>=2``.
+    tol : float, optional
+        Tolerance for termination. If the min of the L1-norm over the samples
+        changes less than `tol`, it stops the algorithm. Default is 1e-5.
+    maxiter : int, optional
+        Maximum number of iterations. It will stop the algorithm even if
+        `tol` is above the threshold.
+        Too many iterations tend to cluster the samples as a hypersphere.
+        Default is 10.
+    qhull_options : str, optional
+        Additional options to pass to Qhull. See Qhull manual
+        for details. (Default: "Qbb Qc Qz Qj Qx" for ndim > 4 and
+        "Qbb Qc Qz Qj" otherwise.)
+
+    Returns
+    -------
+    sample : array_like (n, d)
+        The sample after being processed by Lloyd-Max algorithm.
+
+    Notes
+    -----
+    Lloyd-Max algorithm is an iterative process with the purpose of improving
+    the dispersion of samples. For given sample: (i) compute a Voronoi
+    Tessellation; (ii) find the centroid of each Voronoi cell; (iii) move the
+    samples toward the centroid of their respective cell. See [1]_, [2]_.
+
+    A relaxation factor is used to control how fast samples can move at each
+    iteration. This factor is starting at 2 and ending at 1 after `maxiter`
+    following an exponential decay.
+
+    The process converges to equally spaced samples. It implies that measures
+    like the discrepancy could suffer from too many iterations. On the other
+    hand, L1 and L2 distances should improve. This is especially true with
+    QMC methods which tend to favor the discrepancy over other criteria.
+
+    .. note::
+
+        The current implementation does not intersect the Voronoi Tessellation
+        with the boundaries. This implies that for a low number of samples,
+        empirically below 20, no Voronoi cell is touching the boundaries.
+        Hence, samples cannot be moved close to the boundaries.
+
+        Further improvements could consider the samples at infinity so that
+        all boundaries are segments of some Voronoi cells. This would fix
+        the computation of the centroid position.
+
+    .. warning::
+
+       The Voronoi Tessellation step is expensive and quickly becomes
+       intractable with dimensions as low as 10 even for a sample
+       of size as low as 1000.
+
+    .. versionadded:: 1.9.0
+
+    References
+    ----------
+    .. [1] Lloyd. "Least Squares Quantization in PCM".
+       IEEE Transactions on Information Theory, 1982.
+    .. [2] Max J. "Quantizing for minimum distortion".
+       IEEE Transactions on Information Theory, 1960.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.spatial import distance
+    >>> from scipy.stats._qmc import _lloyd_centroidal_voronoi_tessellation
+    >>> rng = np.random.default_rng()
+    >>> sample = rng.random((128, 2))
+
+    .. note::
+
+        The samples need to be in :math:`[0, 1]^d`. `scipy.stats.qmc.scale`
+        can be used to scale the samples from their
+        original bounds to :math:`[0, 1]^d`. And back to their original bounds.
+
+    Compute the quality of the sample using the L1 criterion.
+
+    >>> def l1_norm(sample):
+    ...    return distance.pdist(sample, 'cityblock').min()
+
+    >>> l1_norm(sample)
+    0.00161...  # random
+
+    Now process the sample using Lloyd's algorithm and check the improvement
+    on the L1. The value should increase.
+
+    >>> sample = _lloyd_centroidal_voronoi_tessellation(sample)
+    >>> l1_norm(sample)
+    0.0278...  # random
+
+    """
+    del kwargs  # only use keywords which are defined, needed by factory
+
+    sample = np.asarray(sample).copy()
+
+    if not sample.ndim == 2:
+        raise ValueError('`sample` is not a 2D array')
+
+    if not sample.shape[1] >= 2:
+        raise ValueError('`sample` dimension is not >= 2')
+
+    # Checking that sample is within the hypercube
+    if (sample.max() > 1.) or (sample.min() < 0.):
+        raise ValueError('`sample` is not in unit hypercube')
+
+    if qhull_options is None:
+        qhull_options = 'Qbb Qc Qz QJ'
+
+        if sample.shape[1] >= 5:
+            qhull_options += ' Qx'
+
+    # Fit an exponential to be 2 at 0 and 1 at `maxiter`.
+    # The decay is used for relaxation.
+    # analytical solution for y=exp(-maxiter/x) - 0.1
+    root = -maxiter / np.log(0.1)
+    decay = [np.exp(-x / root)+0.9 for x in range(maxiter)]
+
+    l1_old = _l1_norm(sample=sample)
+    for i in range(maxiter):
+        sample = _lloyd_iteration(
+                sample=sample, decay=decay[i],
+                qhull_options=qhull_options,
+        )
+
+        l1_new = _l1_norm(sample=sample)
+
+        if abs(l1_new - l1_old) < tol:
+            break
+        else:
+            l1_old = l1_new
+
+    return sample
+
+
+def _validate_workers(workers: IntNumber = 1) -> IntNumber:
+    """Validate `workers` based on platform and value.
+
+    Parameters
+    ----------
+    workers : int, optional
+        Number of workers to use for parallel processing. If -1 is
+        given all CPU threads are used. Default is 1.
+
+    Returns
+    -------
+    Workers : int
+        Number of CPU used by the algorithm
+
+    """
+    workers = int(workers)
+    if workers == -1:
+        workers = os.cpu_count()  # type: ignore[assignment]
+        if workers is None:
+            raise NotImplementedError(
+                "Cannot determine the number of cpus using os.cpu_count(), "
+                "cannot use -1 for the number of workers"
+            )
+    elif workers <= 0:
+        raise ValueError(f"Invalid number of workers: {workers}, must be -1 "
+                         "or > 0")
+
+    return workers
+
+
+def _validate_bounds(
+    l_bounds: "npt.ArrayLike", u_bounds: "npt.ArrayLike", d: int
+) -> tuple[np.ndarray, np.ndarray]:
+    """Bounds input validation.
+
+    Parameters
+    ----------
+    l_bounds, u_bounds : array_like (d,)
+        Lower and upper bounds.
+    d : int
+        Dimension to use for broadcasting.
+
+    Returns
+    -------
+    l_bounds, u_bounds : array_like (d,)
+        Lower and upper bounds.
+
+    """
+    try:
+        lower = np.broadcast_to(l_bounds, d)
+        upper = np.broadcast_to(u_bounds, d)
+    except ValueError as exc:
+        msg = ("'l_bounds' and 'u_bounds' must be broadcastable and respect"
+               " the sample dimension")
+        raise ValueError(msg) from exc
+
+    if not np.all(lower < upper):
+        raise ValueError("Bounds are not consistent 'l_bounds' < 'u_bounds'")
+
+    return lower, upper
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_qmc_cy.cpython-312-x86_64-linux-gnu.so b/venv/lib/python3.12/site-packages/scipy/stats/_qmc_cy.cpython-312-x86_64-linux-gnu.so
new file mode 100644
index 0000000000000000000000000000000000000000..668ea797d154ea1c664febcd147cc1daafbbe31f
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_qmc_cy.cpython-312-x86_64-linux-gnu.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:13d71387da10a610c119621119f26a981474737dc105153d24248ba566285fda
+size 130088
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_qmc_cy.pyi b/venv/lib/python3.12/site-packages/scipy/stats/_qmc_cy.pyi
new file mode 100644
index 0000000000000000000000000000000000000000..1006385a43179478a9a4a32ae5f825aa5b8b35c4
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_qmc_cy.pyi
@@ -0,0 +1,54 @@
+import numpy as np
+from scipy._lib._util import DecimalNumber, IntNumber
+
+
+def _cy_wrapper_centered_discrepancy(
+        sample: np.ndarray, 
+        iterative: bool, 
+        workers: IntNumber,
+) -> float: ...
+
+
+def _cy_wrapper_wrap_around_discrepancy(
+        sample: np.ndarray,
+        iterative: bool, 
+        workers: IntNumber,
+) -> float: ...
+
+
+def _cy_wrapper_mixture_discrepancy(
+        sample: np.ndarray,
+        iterative: bool, 
+        workers: IntNumber,
+) -> float: ...
+
+
+def _cy_wrapper_l2_star_discrepancy(
+        sample: np.ndarray,
+        iterative: bool,
+        workers: IntNumber,
+) -> float: ...
+
+
+def _cy_wrapper_update_discrepancy(
+        x_new_view: np.ndarray,
+        sample_view: np.ndarray,
+        initial_disc: DecimalNumber,
+) -> float: ...
+
+
+def _cy_van_der_corput(
+        n: IntNumber,
+        base: IntNumber,
+        start_index: IntNumber,
+        workers: IntNumber,
+) -> np.ndarray: ...
+
+
+def _cy_van_der_corput_scrambled(
+        n: IntNumber,
+        base: IntNumber,
+        start_index: IntNumber,
+        permutations: np.ndarray,
+        workers: IntNumber,
+) -> np.ndarray: ...
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_qmvnt.py b/venv/lib/python3.12/site-packages/scipy/stats/_qmvnt.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f942da89e0a03c456b4ee0011b711ba217b4024
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_qmvnt.py
@@ -0,0 +1,475 @@
+# Integration of multivariate normal and t distributions.
+
+# Adapted from the MATLAB original implementations by Dr. Alan Genz.
+
+#     http://www.math.wsu.edu/faculty/genz/software/software.html
+
+# Copyright (C) 2013, Alan Genz,  All rights reserved.
+# Python implementation is copyright (C) 2022, Robert Kern,  All rights
+# reserved.
+
+# Redistribution and use in source and binary forms, with or without
+# modification, are permitted provided the following conditions are met:
+#   1. Redistributions of source code must retain the above copyright
+#      notice, this list of conditions and the following disclaimer.
+#   2. Redistributions in binary form must reproduce the above copyright
+#      notice, this list of conditions and the following disclaimer in
+#      the documentation and/or other materials provided with the
+#      distribution.
+#   3. The contributor name(s) may not be used to endorse or promote
+#      products derived from this software without specific prior
+#      written permission.
+# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+# "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+# LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+# FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+# COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+# INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+# BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
+# OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
+# ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR
+# TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF USE
+# OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+
+import math
+import numpy as np
+
+from scipy.fft import fft, ifft
+from scipy.special import ndtr as phi, ndtri as phinv
+from scipy.special._ufuncs import _bivariate_normal_cdf as _bvnu
+from scipy.stats._qmc import primes_from_2_to
+
+from ._qmvnt_cy import _qmvn_inner, _qmvt_inner
+
+
+def _factorize_int(n):
+    """Return a sorted list of the unique prime factors of a positive integer.
+    """
+    # NOTE: There are lots faster ways to do this, but this isn't terrible.
+    factors = set()
+    for p in primes_from_2_to(int(np.sqrt(n)) + 1):
+        while not (n % p):
+            factors.add(p)
+            n //= p
+        if n == 1:
+            break
+    if n != 1:
+        factors.add(n)
+    return sorted(factors)
+
+
+def _primitive_root(p):
+    """Compute a primitive root of the prime number `p`.
+
+    Used in the CBC lattice construction.
+
+    References
+    ----------
+    .. [1] https://en.wikipedia.org/wiki/Primitive_root_modulo_n
+    """
+    # p is prime
+    pm = p - 1
+    factors = _factorize_int(pm)
+    n = len(factors)
+    r = 2
+    k = 0
+    while k < n:
+        d = pm // factors[k]
+        # pow() doesn't like numpy scalar types.
+        rd = pow(int(r), int(d), int(p))
+        if rd == 1:
+            r += 1
+            k = 0
+        else:
+            k += 1
+    return r
+
+
+def _cbc_lattice(n_dim, n_qmc_samples):
+    """Compute a QMC lattice generator using a Fast CBC construction.
+
+    Parameters
+    ----------
+    n_dim : int > 0
+        The number of dimensions for the lattice.
+    n_qmc_samples : int > 0
+        The desired number of QMC samples. This will be rounded down to the
+        nearest prime to enable the CBC construction.
+
+    Returns
+    -------
+    q : float array : shape=(n_dim,)
+        The lattice generator vector. All values are in the open interval
+        ``(0, 1)``.
+    actual_n_qmc_samples : int
+        The prime number of QMC samples that must be used with this lattice,
+        no more, no less.
+
+    References
+    ----------
+    .. [1] Nuyens, D. and Cools, R. "Fast Component-by-Component Construction,
+           a Reprise for Different Kernels", In H. Niederreiter and D. Talay,
+           editors, Monte-Carlo and Quasi-Monte Carlo Methods 2004,
+           Springer-Verlag, 2006, 371-385.
+    """
+    # Round down to the nearest prime number.
+    primes = primes_from_2_to(n_qmc_samples + 1)
+    n_qmc_samples = primes[-1]
+
+    bt = np.ones(n_dim)
+    gm = np.hstack([1.0, 0.8 ** np.arange(n_dim - 1)])
+    q = 1
+    w = 0
+    z = np.arange(1, n_dim + 1)
+    m = (n_qmc_samples - 1) // 2
+    g = _primitive_root(n_qmc_samples)
+    # Slightly faster way to compute perm[j] = pow(g, j, n_qmc_samples)
+    # Shame that we don't have modulo pow() implemented as a ufunc.
+    perm = np.ones(m, dtype=int)
+    for j in range(m - 1):
+        perm[j + 1] = (g * perm[j]) % n_qmc_samples
+    perm = np.minimum(n_qmc_samples - perm, perm)
+    pn = perm / n_qmc_samples
+    c = pn * pn - pn + 1.0 / 6
+    fc = fft(c)
+    for s in range(1, n_dim):
+        reordered = np.hstack([
+            c[:w+1][::-1],
+            c[w+1:m][::-1],
+        ])
+        q = q * (bt[s-1] + gm[s-1] * reordered)
+        w = ifft(fc * fft(q)).real.argmin()
+        z[s] = perm[w]
+    q = z / n_qmc_samples
+    return q, n_qmc_samples
+
+
+def _qauto(func, covar, low, high, rng, error=1e-3, limit=10_000, **kwds):
+    """Automatically rerun the integration to get the required error bound.
+
+    Parameters
+    ----------
+    func : callable
+        Either :func:`_qmvn` or :func:`_qmvt`.
+    covar, low, high : array
+        As specified in :func:`_qmvn` and :func:`_qmvt`.
+    rng : Generator, optional
+        default_rng(), yada, yada
+    error : float > 0
+        The desired error bound.
+    limit : int > 0:
+        The rough limit of the number of integration points to consider. The
+        integration will stop looping once this limit has been *exceeded*.
+    **kwds :
+        Other keyword arguments to pass to `func`. When using :func:`_qmvt`, be
+        sure to include ``nu=`` as one of these.
+
+    Returns
+    -------
+    prob : float
+        The estimated probability mass within the bounds.
+    est_error : float
+        3 times the standard error of the batch estimates.
+    n_samples : int
+        The number of integration points actually used.
+    """
+    n = len(covar)
+    n_samples = 0
+    if n == 1:
+        prob = phi(high / covar**0.5) - phi(low / covar**0.5)
+        # More or less
+        est_error = 1e-15
+    elif n == 2:
+        prob = _bvn(low, high, covar)
+        est_error = 1e-15
+    else:
+        mi = min(limit, n * 1000)
+        prob = 0.0
+        est_error = 1.0
+        ei = 0.0
+        while est_error > error and n_samples < limit:
+            mi = round(np.sqrt(2) * mi)
+            pi, ei, ni = func(mi, covar, low, high, rng=rng, **kwds)
+            n_samples += ni
+            wt = 1.0 / (1 + (ei / est_error)**2)
+            prob += wt * (pi - prob)
+            est_error = np.sqrt(wt) * ei
+    return prob, est_error, n_samples
+
+
+def _qmvn(m, covar, low, high, rng, lattice='cbc', n_batches=10):
+    """Multivariate normal integration over box bounds.
+
+    Parameters
+    ----------
+    m : int > n_batches
+        The number of points to sample. This number will be divided into
+        `n_batches` batches that apply random offsets of the sampling lattice
+        for each batch in order to estimate the error.
+    covar : (n, n) float array
+        Possibly singular, positive semidefinite symmetric covariance matrix.
+    low, high : (n,) float array
+        The low and high integration bounds.
+    rng : Generator, optional
+        default_rng(), yada, yada
+    lattice : 'cbc' or callable
+        The type of lattice rule to use to construct the integration points.
+    n_batches : int > 0, optional
+        The number of QMC batches to apply.
+
+    Returns
+    -------
+    prob : float
+        The estimated probability mass within the bounds.
+    est_error : float
+        3 times the standard error of the batch estimates.
+    """
+    cho, lo, hi = _permuted_cholesky(covar, low, high)
+    if not cho.flags.c_contiguous:
+        # qmvn_inner expects contiguous buffers
+        cho = cho.copy()
+
+    n = cho.shape[0]
+    q, n_qmc_samples = _cbc_lattice(n - 1, max(m // n_batches, 1))
+    rndm = rng.random(size=(n_batches, n))
+
+    prob, est_error, n_samples = _qmvn_inner(
+        q, rndm, int(n_qmc_samples), int(n_batches), cho, lo, hi
+    )
+    return prob, est_error, n_samples
+
+
+# Note: this function is not currently used or tested by any SciPy code. It is
+# included in this file to facilitate the resolution of gh-8367, gh-16142, and
+# possibly gh-14286, but must be reviewed and tested before use.
+def _mvn_qmc_integrand(covar, low, high, use_tent=False):
+    """Transform the multivariate normal integration into a QMC integrand over
+    a unit hypercube.
+
+    The dimensionality of the resulting hypercube integration domain is one
+    less than the dimensionality of the original integrand. Note that this
+    transformation subsumes the integration bounds in order to account for
+    infinite bounds. The QMC integration one does with the returned integrand
+    should be on the unit hypercube.
+
+    Parameters
+    ----------
+    covar : (n, n) float array
+        Possibly singular, positive semidefinite symmetric covariance matrix.
+    low, high : (n,) float array
+        The low and high integration bounds.
+    use_tent : bool, optional
+        If True, then use tent periodization. Only helpful for lattice rules.
+
+    Returns
+    -------
+    integrand : Callable[[NDArray], NDArray]
+        The QMC-integrable integrand. It takes an
+        ``(n_qmc_samples, ndim_integrand)`` array of QMC samples in the unit
+        hypercube and returns the ``(n_qmc_samples,)`` evaluations of at these
+        QMC points.
+    ndim_integrand : int
+        The dimensionality of the integrand. Equal to ``n-1``.
+    """
+    cho, lo, hi = _permuted_cholesky(covar, low, high)
+    n = cho.shape[0]
+    ndim_integrand = n - 1
+    ct = cho[0, 0]
+    c = phi(lo[0] / ct)
+    d = phi(hi[0] / ct)
+    ci = c
+    dci = d - ci
+
+    def integrand(*zs):
+        ndim_qmc = len(zs)
+        n_qmc_samples = len(np.atleast_1d(zs[0]))
+        assert ndim_qmc == ndim_integrand
+        y = np.zeros((ndim_qmc, n_qmc_samples))
+        c = np.full(n_qmc_samples, ci)
+        dc = np.full(n_qmc_samples, dci)
+        pv = dc.copy()
+        for i in range(1, n):
+            if use_tent:
+                # Tent periodization transform.
+                x = abs(2 * zs[i-1] - 1)
+            else:
+                x = zs[i-1]
+            y[i - 1, :] = phinv(c + x * dc)
+            s = cho[i, :i] @ y[:i, :]
+            ct = cho[i, i]
+            c = phi((lo[i] - s) / ct)
+            d = phi((hi[i] - s) / ct)
+            dc = d - c
+            pv = pv * dc
+        return pv
+
+    return integrand, ndim_integrand
+
+
+def _qmvt(m, nu, covar, low, high, rng, lattice='cbc', n_batches=10):
+    """Multivariate t integration over box bounds.
+
+    Parameters
+    ----------
+    m : int > n_batches
+        The number of points to sample. This number will be divided into
+        `n_batches` batches that apply random offsets of the sampling lattice
+        for each batch in order to estimate the error.
+    nu : float >= 0
+        The shape parameter of the multivariate t distribution.
+    covar : (n, n) float array
+        Possibly singular, positive semidefinite symmetric covariance matrix.
+    low, high : (n,) float array
+        The low and high integration bounds.
+    rng : Generator, optional
+        default_rng(), yada, yada
+    lattice : 'cbc' or callable
+        The type of lattice rule to use to construct the integration points.
+    n_batches : int > 0, optional
+        The number of QMC batches to apply.
+
+    Returns
+    -------
+    prob : float
+        The estimated probability mass within the bounds.
+    est_error : float
+        3 times the standard error of the batch estimates.
+    n_samples : int
+        The number of samples actually used.
+    """
+    sn = max(1.0, np.sqrt(nu))
+    low = np.asarray(low, dtype=np.float64)
+    high = np.asarray(high, dtype=np.float64)
+    cho, lo, hi = _permuted_cholesky(covar, low / sn, high / sn)
+    n = cho.shape[0]
+    q, n_qmc_samples = _cbc_lattice(n, max(m // n_batches, 1))
+    rndm = rng.random(size=(n_batches, n))
+    prob, est_error, n_samples = _qmvt_inner(
+        q, rndm, int(n_qmc_samples), int(n_batches), cho, lo, hi, float(nu)
+    )
+    return prob, est_error, n_samples
+
+
+def _permuted_cholesky(covar, low, high, tol=1e-10):
+    """Compute a scaled, permuted Cholesky factor, with integration bounds.
+
+    The scaling and permuting of the dimensions accomplishes part of the
+    transformation of the original integration problem into a more numerically
+    tractable form. The lower-triangular Cholesky factor will then be used in
+    the subsequent integration. The integration bounds will be scaled and
+    permuted as well.
+
+    Parameters
+    ----------
+    covar : (n, n) float array
+        Possibly singular, positive semidefinite symmetric covariance matrix.
+    low, high : (n,) float array
+        The low and high integration bounds.
+    tol : float, optional
+        The singularity tolerance.
+
+    Returns
+    -------
+    cho : (n, n) float array
+        Lower Cholesky factor, scaled and permuted.
+    new_low, new_high : (n,) float array
+        The scaled and permuted low and high integration bounds.
+    """
+    # Make copies for outputting.
+    cho = np.array(covar, dtype=np.float64)
+    new_lo = np.array(low, dtype=np.float64)
+    new_hi = np.array(high, dtype=np.float64)
+    n = cho.shape[0]
+    if cho.shape != (n, n):
+        raise ValueError("expected a square symmetric array")
+    if new_lo.shape != (n,) or new_hi.shape != (n,):
+        raise ValueError(
+            "expected integration boundaries the same dimensions "
+            "as the covariance matrix"
+        )
+    # Scale by the sqrt of the diagonal.
+    dc = np.sqrt(np.maximum(np.diag(cho), 0.0))
+    # But don't divide by 0.
+    dc[dc == 0.0] = 1.0
+    new_lo /= dc
+    new_hi /= dc
+    cho /= dc
+    cho /= dc[:, np.newaxis]
+
+    y = np.zeros(n)
+    sqtp = np.sqrt(2 * np.pi)
+    for k in range(n):
+        epk = (k + 1) * tol
+        im = k
+        ck = 0.0
+        dem = 1.0
+        s = 0.0
+        lo_m = 0.0
+        hi_m = 0.0
+        for i in range(k, n):
+            if cho[i, i] > tol:
+                ci = np.sqrt(cho[i, i])
+                if i > 0:
+                    s = cho[i, :k] @ y[:k]
+                lo_i = (new_lo[i] - s) / ci
+                hi_i = (new_hi[i] - s) / ci
+                de = phi(hi_i) - phi(lo_i)
+                if de <= dem:
+                    ck = ci
+                    dem = de
+                    lo_m = lo_i
+                    hi_m = hi_i
+                    im = i
+        if im > k:
+            # Swap im and k
+            cho[im, im] = cho[k, k]
+            _swap_slices(cho, np.s_[im, :k], np.s_[k, :k])
+            _swap_slices(cho, np.s_[im + 1:, im], np.s_[im + 1:, k])
+            _swap_slices(cho, np.s_[k + 1:im, k], np.s_[im, k + 1:im])
+            _swap_slices(new_lo, k, im)
+            _swap_slices(new_hi, k, im)
+        if ck > epk:
+            cho[k, k] = ck
+            cho[k, k + 1:] = 0.0
+            for i in range(k + 1, n):
+                cho[i, k] /= ck
+                cho[i, k + 1:i + 1] -= cho[i, k] * cho[k + 1:i + 1, k]
+            if abs(dem) > tol:
+                y[k] = ((np.exp(-lo_m * lo_m / 2) - np.exp(-hi_m * hi_m / 2)) /
+                        (sqtp * dem))
+            else:
+                y[k] = (lo_m + hi_m) / 2
+                if lo_m < -10:
+                    y[k] = hi_m
+                elif hi_m > 10:
+                    y[k] = lo_m
+            cho[k, :k + 1] /= ck
+            new_lo[k] /= ck
+            new_hi[k] /= ck
+        else:
+            cho[k:, k] = 0.0
+            y[k] = (new_lo[k] + new_hi[k]) / 2
+    return cho, new_lo, new_hi
+
+
+def _swap_slices(x, slc1, slc2):
+    t = x[slc1].copy()
+    x[slc1] = x[slc2].copy()
+    x[slc2] = t
+
+
+def _bvn(a, b, A):
+    # covariance matrix is written [[s1**2, rho*s1*s2], [rho*s1*s2, s2**2]]
+    # e.g. https://en.wikipedia.org/wiki/Multivariate_normal_distribution
+    # therefore, s12 = rho*s1*s2 -> rho = s12/(s1*s2)
+    s1 = math.sqrt(A[0, 0])
+    s2 = math.sqrt(A[1, 1])
+    s12 = A[0, 1]
+    r = s12 / (s1 * s2)
+    # the x and y coordinates seem to be normalized by the standard devs
+    xl, xu = a[0] / s1, b[0] / s1
+    yl, yu = a[1] / s2, b[1] / s2
+    p = _bvnu(xl, yl, r) - _bvnu(xu, yl, r) - _bvnu(xl, yu, r) + _bvnu(xu, yu, r)
+    p = max( 0., min( p, 1. ) )
+    return p
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_qmvnt_cy.cpython-312-x86_64-linux-gnu.so b/venv/lib/python3.12/site-packages/scipy/stats/_qmvnt_cy.cpython-312-x86_64-linux-gnu.so
new file mode 100644
index 0000000000000000000000000000000000000000..6750cbd6955d404fd94cd65107bbac35f06cedfc
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_qmvnt_cy.cpython-312-x86_64-linux-gnu.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f24c941ac05f683264bbc14ff0cc4da1468bb75a2d788f40b5fc68c484e7aec9
+size 126432
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_quantile.py b/venv/lib/python3.12/site-packages/scipy/stats/_quantile.py
new file mode 100644
index 0000000000000000000000000000000000000000..cd3756f23138ae04cfabb7b47dfaa24a47c4c10a
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_quantile.py
@@ -0,0 +1,816 @@
+import math
+import numpy as np
+from scipy.special import betainc
+from scipy._lib._array_api import (
+    xp_capabilities,
+    xp_ravel,
+    array_namespace,
+    xp_promote,
+    xp_device,
+    xp_size,
+    _count_nonmasked,
+    is_torch,
+    is_lazy_array,
+)
+import scipy._external.array_api_extra as xpx
+from scipy.stats._axis_nan_policy import _broadcast_arrays, _contains_nan
+
+
+def _quantile_iv(x, p, method, axis, nan_policy, keepdims, weights, fun='quantile'):
+    xp = array_namespace(x, p, weights)
+
+    if fun == "quantile":
+        methods = {'inverted_cdf', 'averaged_inverted_cdf', 'closest_observation',
+                   'hazen', 'interpolated_inverted_cdf', 'linear',
+                   'median_unbiased', 'normal_unbiased', 'weibull',
+                   'harrell-davis', '_lower', '_midpoint', '_higher', '_nearest',
+                   'round_outward', 'round_inward', 'round_nearest'}
+        allowed_types = 'real floating'
+        def mask_fun(p): return (p > 1) | (p < 0) | xp.isnan(p)
+        var2_name = 'p'
+        var2_type_msg = '`p` must have real floating dtype.'
+    else:
+        methods = set(_estimated_cdf_methods)
+        allowed_types = ('integral', 'real floating')
+        mask_fun = xp.isnan
+        var2_name = 'y'
+        var2_type_msg = '`y` must have real dtype.'
+
+    if not xp.isdtype(xp.asarray(x).dtype, ('integral', 'real floating')):
+        raise ValueError("`x` must have real dtype.")
+
+    if not xp.isdtype(xp.asarray(p).dtype, allowed_types):
+        raise ValueError(var2_type_msg)
+
+    if not (weights is None
+            or xp.isdtype(xp.asarray(weights).dtype, ('integral', 'real floating'))):
+        raise ValueError("`weights` must have real dtype.")
+
+    x, p, weights = xp_promote(x, p, weights, force_floating=True, xp=xp)
+    p = xp.asarray(p, device=xp_device(x))
+    dtype = x.dtype
+
+    axis_none = axis is None
+    ndim = max(x.ndim, p.ndim)
+    if axis_none:
+        x = xp_ravel(x)
+        p = xp_ravel(p)
+        axis = 0
+    elif np.iterable(axis) or int(axis) != axis:
+        message = "`axis` must be an integer or None."
+        raise ValueError(message)
+    elif (axis >= ndim) or (axis < -ndim):
+        message = "`axis` is not compatible with the shapes of the inputs."
+        raise ValueError(message)
+    axis = int(axis)
+
+    if method not in methods:
+        message = f"`method` must be one of {methods}"
+        raise ValueError(message)
+
+    no_weights = {'_lower', '_midpoint', '_higher', '_nearest', 'harrell-davis',
+                  'round_nearest', 'round_inward', 'round_outward'}
+    if weights is not None and method in no_weights:
+        message = f"`method='{method}'` does not support `weights`."
+        raise ValueError(message)
+
+    contains_nans = _contains_nan(x, nan_policy, xp_omit_okay=True, xp=xp)
+
+    if keepdims not in {None, True, False}:
+        message = "If specified, `keepdims` must be True or False."
+        raise ValueError(message)
+
+    # If data has length zero along `axis`, the result will be an array of NaNs just
+    # as if the data had length 1 along axis and were filled with NaNs. This is treated
+    # naturally below whether `nan_policy` is `'propagate'` or `'omit'`.
+    if x.shape[axis] == 0 and fun == 'quantile':
+        shape = list(x.shape)
+        shape[axis] = 1
+        x = xp.full(shape, xp.nan, dtype=dtype, device=xp_device(x))
+
+    if weights is None:
+        y = xp.sort(x, axis=axis, stable=False)
+        y, p = _broadcast_arrays((y, p), axis=axis)
+        n_zero_weight = None
+    else:
+        x, weights = xp.broadcast_arrays(x, weights)
+        i_zero_weight = (weights == 0)
+        n_zero_weight = xp.count_nonzero(i_zero_weight, axis=axis, keepdims=True)
+        x = xpx.at(x)[i_zero_weight].set(xp.inf, copy=True)
+        i_y = xp.argsort(x, axis=axis, stable=False)
+        y = xp.take_along_axis(x, i_y, axis=axis)
+        weights = xp.take_along_axis(weights, i_y, axis=axis)
+        y, p, weights, i_y, n_zero_weight = _broadcast_arrays(
+            (y, p, weights, i_y, n_zero_weight), axis=axis)
+
+    if (keepdims is False) and (p.shape[axis] != 1):
+        message = ("`keepdims` may be False only if the length of "
+                   f"`{var2_name}` along `axis` is 1.")
+        raise ValueError(message)
+    keepdims = (p.shape[axis] != 1) if keepdims is None else keepdims
+
+    y = xp.moveaxis(y, axis, -1)
+    p = xp.moveaxis(p, axis, -1)
+    weights = weights if weights is None else xp.moveaxis(weights, axis, -1)
+    n_zero_weight = (n_zero_weight if n_zero_weight is None
+                     else xp.moveaxis(n_zero_weight, axis, -1))
+
+    n = _count_nonmasked(y, -1, xp=xp, keepdims=True)
+    n = n if n_zero_weight is None else n - n_zero_weight
+
+    nan_out = None
+    if is_lazy_array(y) or contains_nans:
+        nans = xp.isnan(y)
+
+        # Note that if length along `axis` were 0 to begin with,
+        # it is now length 1 and filled with NaNs.
+        if nan_policy == 'propagate':
+            nan_out = xp.any(nans, axis=-1, keepdims=True)
+        else:  # 'omit'
+            n_int = n - xp.count_nonzero(nans, axis=-1, keepdims=True)
+            n = xp.astype(n_int, dtype)
+            # NaNs are produced only if slice is empty after removing NaNs
+            nan_out = n == 0
+            n = xpx.at(n, nan_out).set(y.shape[-1])  # avoids pytorch/pytorch#146211
+
+        if (is_lazy_array(nans) or xp.any(nans)) and (method == 'harrell-davis'):
+            y = xp.asarray(y, copy=True)  # ensure writable
+            y = xpx.at(y, nans).set(0)  # any non-nan will prevent NaN from propagating
+        if is_lazy_array(nan_out) or xp.any(nan_out):
+            y = xp.asarray(y, copy=True)  # ensure writable
+            y = xpx.at(y, xp.broadcast_to(nan_out, y.shape)).set(xp.nan)
+
+    n = xp.asarray(n, dtype=dtype, device=xp_device(y))
+
+    # apparently xpx.at is accepting nan_out as a mask even though it doesn't have the
+    # same number of dimensions as `y`, yet it still appears to work correctly?
+    # should refactor for clarity, and p_mask that gets returned here should probably
+    # get a different name - `nan_out` would be more appropriate!
+    p_mask = mask_fun(p) if nan_out is None else mask_fun(p) | nan_out
+    if is_lazy_array(p_mask) or xp.any(p_mask):
+        p = xp.where(p_mask, 0.5, p)  # these get NaN-ed out at the end
+
+    return (y, p, method, axis, nan_policy, keepdims,
+            n, axis_none, ndim, p_mask, weights, xp)
+
+
+@xp_capabilities(skip_backends=[("dask.array", "No take_along_axis yet.")],
+                 marray=True,
+                 extra_note=("Use of `weights` is incompatible with MArray. "
+                             "``method='harrell-davis'`` is CPU-only."))
+def quantile(x, p, *, method='linear', axis=0, nan_policy='propagate', keepdims=None,
+             weights=None):
+    """
+    Compute the p-th quantile of the data along the specified axis.
+
+    Parameters
+    ----------
+    x : array_like of real numbers
+        Data array.
+    p : array_like of float
+        Probability or sequence of probabilities of the quantiles to compute.
+        Values must be between 0 and 1 (inclusive).
+        While `numpy.quantile` can only compute quantiles according to the Cartesian
+        product of the first two arguments, this function enables calculation of
+        quantiles at different probabilities for each axis slice by following
+        broadcasting rules like those of `scipy.stats` reducing functions.
+        See `axis`, `keepdims`, and the examples.
+    method : str, default: 'linear'
+        The method to use for estimating the quantile.
+        The available options, numbered as they appear in [1]_, are:
+
+        1. 'inverted_cdf'
+        2. 'averaged_inverted_cdf'
+        3. 'closest_observation'
+        4. 'interpolated_inverted_cdf'
+        5. 'hazen'
+        6. 'weibull'
+        7. 'linear'  (default)
+        8. 'median_unbiased'
+        9. 'normal_unbiased'
+
+        'harrell-davis' is also available to compute the quantile estimate
+        according to [2]_.
+
+        'round_outward', 'round_inward', and 'round_nearest' are available for use
+        in trimming and winsorizing data.
+
+        See Notes for details.
+    axis : int or None, default: 0
+        Axis along which the quantiles are computed.
+        ``None`` ravels both `x` and `p` before performing the calculation,
+        without checking whether the original shapes were compatible.
+        As in other `scipy.stats` functions, a positive integer `axis` is resolved
+        after prepending 1s to the shape of `x` or `p` as needed until the two arrays
+        have the same dimensionality. When providing `x` and `p` with different
+        dimensionality, consider using negative `axis` integers for clarity.
+    nan_policy : str, default: 'propagate'
+        Defines how to handle NaNs in the input data `x`.
+
+        - ``propagate``: if a NaN is present in the axis slice (e.g. row) along
+          which the  statistic is computed, the corresponding slice of the output
+          will contain NaN(s).
+        - ``omit``: NaNs will be omitted when performing the calculation.
+          If insufficient data remains in the axis slice along which the
+          statistic is computed, the corresponding slice of the output will
+          contain NaN(s).
+        - ``raise``: if a NaN is present, a ``ValueError`` will be raised.
+
+        If NaNs are present in `p`, a ``ValueError`` will be raised.
+    keepdims : bool, optional
+        Consider the case in which `x` is 1-D and `p` is a scalar: the quantile
+        is a reducing statistic, and the default behavior is to return a scalar.
+        If `keepdims` is set to True, the axis will not be reduced away, and the
+        result will be a 1-D array with one element.
+
+        The general case is more subtle, since multiple quantiles may be
+        requested for each axis-slice of `x`. For instance, if both `x` and `p`
+        are 1-D and ``p.size > 1``, no axis can be reduced away; there must be an
+        axis to contain the number of quantiles given by ``p.size``. Therefore:
+
+        - By default, the axis will be reduced away if possible (i.e. if there is
+          exactly one element of `p` per axis-slice of `x`).
+        - If `keepdims` is set to True, the axis will not be reduced away.
+        - If `keepdims` is set to False, the axis will be reduced away
+          if possible, and an error will be raised otherwise.
+
+    weights : array_like of finite, non-negative real numbers
+        Frequency weights; e.g., for counting number weights,
+        ``quantile(x, p, weights=weights)`` is equivalent to
+        ``quantile(np.repeat(x, weights), p)``. Values other than finite counting
+        numbers are accepted, but may not have valid statistical interpretations.
+        Not compatible with ``method='harrell-davis'`` or those that begin with
+        ``'round_'``.
+
+    Returns
+    -------
+    quantile : scalar or ndarray
+        The resulting quantile(s). The dtype is the result dtype of `x` and `p`.
+
+    See Also
+    --------
+    numpy.quantile
+    estimated_cdf
+    :ref:`outliers`
+
+    Notes
+    -----
+    Given a sample `x` from an underlying distribution, `quantile` provides a
+    nonparametric estimate of the inverse cumulative distribution function.
+
+    By default, this is done by interpolating between adjacent elements in
+    ``y``, a sorted copy of `x`::
+
+        (1-g)*y[j] + g*y[j+1]
+
+    where the index ``j`` and coefficient ``g`` are the integral and
+    fractional components of ``p * (n-1)``, and ``n`` is the number of
+    elements in the sample.
+
+    This is a special case of Equation 1 of H&F [1]_. More generally,
+
+    - ``j = (p*n + m - 1) // 1``, and
+    - ``g = (p*n + m - 1) % 1``,
+
+    where ``m`` may be defined according to several different conventions.
+    The preferred convention may be selected using the ``method`` parameter:
+
+    =============================== =============== ===============
+    ``method``                      number in H&F   ``m``
+    =============================== =============== ===============
+    ``interpolated_inverted_cdf``   4               ``0``
+    ``hazen``                       5               ``1/2``
+    ``weibull``                     6               ``p``
+    ``linear`` (default)            7               ``1 - p``
+    ``median_unbiased``             8               ``p/3 + 1/3``
+    ``normal_unbiased``             9               ``p/4 + 3/8``
+    =============================== =============== ===============
+
+    Note that indices ``j`` and ``j + 1`` are clipped to the range ``0`` to
+    ``n - 1`` when the results of the formula would be outside the allowed
+    range of non-negative indices. When ``j`` is clipped to zero, ``g`` is
+    set to zero as well. The ``-1`` in the formulas for ``j`` and ``g``
+    accounts for Python's 0-based indexing.
+
+    The table above includes only the estimators from [1]_ that are continuous
+    functions of probability `p` (estimators 4-9). SciPy also provides the
+    three discontinuous estimators from [1]_ (estimators 1-3), where ``j`` is
+    defined as above, ``m`` is defined as follows, and ``g`` is ``0`` when
+    ``index = p*n + m - 1`` is less than ``0`` and otherwise is defined below.
+
+    1. ``inverted_cdf``: ``m = 0`` and ``g = int(index - j > 0)``
+    2. ``averaged_inverted_cdf``: ``m = 0`` and
+       ``g = (1 + int(index - j > 0)) / 2``
+    3. ``closest_observation``: ``m = -1/2`` and
+       ``g = 1 - int((index == j) & (j%2 == 1))``
+
+    Note that for methods ``inverted_cdf`` and ``averaged_inverted_cdf``, only the
+    relative proportions of tied observations (and relative weights) affect the
+    results; for all other methods, the total number of observations (and absolute
+    weights) matter.
+
+    A different strategy for computing quantiles from [2]_, ``method='harrell-davis'``,
+    uses a weighted combination of all elements. The weights are computed as:
+
+    .. math::
+
+        w_{n, i} = I_{i/n}(a, b) - I_{(i - 1)/n}(a, b)
+
+    where :math:`n` is the number of elements in the sample,
+    :math:`i` are the indices :math:`1, 2, ..., n-1, n` of the sorted elements,
+    :math:`a = p (n + 1)`, :math:`b = (1 - p)(n + 1)`,
+    :math:`p` is the probability of the quantile, and
+    :math:`I` is the regularized, lower incomplete beta function
+    (`scipy.special.betainc`).
+
+    ``method='round_nearest'`` is equivalent to indexing ``y[j]``, where::
+
+        j = int(np.round(p*n) if p < 0.5 else np.round(n*p - 1))
+
+    This is useful when winsorizing data: replacing ``p*n`` of the most extreme
+    observations with the next most extreme observation. ``method='round_outward'``
+    adjusts the direction of rounding to winsorize fewer elements::
+
+        j = int(np.floor(p*n) if p < 0.5 else np.ceil(n*p - 1))
+
+    and ``method='round_inward'`` rounds to winsorize more elements::
+
+        j = int(np.ceil(p*n) if p < 0.5 else np.floor(n*p - 1))
+
+    These methods are also useful for trimming data: removing ``p*n`` of the most
+    extreme observations. See :ref:`outliers` for example applications.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> x = np.asarray([[10, 8, 7, 5, 4],
+    ...                 [0, 1, 2, 3, 5]])
+
+    Take the median of each row.
+
+    >>> stats.quantile(x, 0.5, axis=-1)
+    array([7.,  2.])
+
+    Take a different quantile for each row.
+
+    >>> stats.quantile(x, [[0.25], [0.75]], axis=-1, keepdims=True)
+    array([[5.],
+           [3.]])
+
+    Take multiple quantiles for each row.
+
+    >>> stats.quantile(x, [0.25, 0.75], axis=-1)
+    array([[5., 8.],
+           [1., 3.]])
+
+    Take different quantiles for each row.
+
+    >>> p = np.asarray([[0.25, 0.75],
+    ...                 [0.5, 1.0]])
+    >>> stats.quantile(x, p, axis=-1)
+    array([[5., 8.],
+           [2., 5.]])
+
+    Take different quantiles for each column.
+
+    >>> stats.quantile(x.T, p.T, axis=0)
+    array([[5., 2.],
+           [8., 5.]])
+
+    References
+    ----------
+    .. [1] R. J. Hyndman and Y. Fan,
+       "Sample quantiles in statistical packages,"
+       The American Statistician, 50(4), pp. 361-365, 1996
+    .. [2] Harrell, Frank E., and C. E. Davis.
+       "A new distribution-free quantile estimator."
+       Biometrika 69.3 (1982): 635-640.
+
+    """
+    # Input validation / standardization
+
+    temp = _quantile_iv(x, p, method, axis, nan_policy, keepdims, weights)
+    (y, p, method, axis, nan_policy, keepdims,
+     n, axis_none, ndim, p_mask, weights, xp) = temp
+
+    if method in {'inverted_cdf', 'averaged_inverted_cdf', 'closest_observation',
+                  'hazen', 'interpolated_inverted_cdf', 'linear',
+                  'median_unbiased', 'normal_unbiased', 'weibull'}:
+        res = _quantile_hf(y, p, n, method, weights, xp)
+    elif method in {'harrell-davis'}:
+        res = _quantile_hd(y, p, n, xp)
+    elif method in {'_lower', '_midpoint', '_higher', '_nearest'}:
+        res = _quantile_bc(y, p, n, method, xp)
+    else:  # method.startswith('round'):
+        res = _quantile_winsor(y, p, n, method, xp)
+
+    return _post_quantile(res, p_mask, axis, axis_none, ndim, keepdims, xp)
+
+
+def _post_quantile(res, p_mask, axis, axis_none, ndim, keepdims, xp):
+    res = xpx.at(res, p_mask).set(xp.nan)
+
+    # Reshape per axis/keepdims
+    if axis_none and keepdims:
+        shape = (1,)*(ndim - 1) + res.shape
+        res = xp.reshape(res, shape)
+        axis = -1
+
+    res = xp.moveaxis(res, -1, axis)
+
+    if not keepdims:
+        res = xp.squeeze(res, axis=axis)
+
+    return res[()] if res.ndim == 0 else res
+
+
+def _quantile_hf(y, p, n, method, weights, xp):
+    ms = dict(inverted_cdf=0, averaged_inverted_cdf=0, closest_observation=-0.5,
+              interpolated_inverted_cdf=0, hazen=0.5, weibull=p, linear=1 - p,
+              median_unbiased=p/3 + 1/3, normal_unbiased=p/4 + 3/8)
+    m = ms[method]
+
+    if weights is None:
+        jg = p * n + m
+        jp1 = jg // 1
+        j = jp1 - 1
+    else:
+        cumulative_weights = xp.cumulative_sum(weights, axis=-1)
+        n_int = xp.asarray(n, dtype=xp.int64)
+        n_int = xp.broadcast_to(n_int, cumulative_weights.shape[:-1] + (1,))
+        total_weight = xp.take_along_axis(cumulative_weights, n_int-1, axis=-1)
+        jg = p * total_weight + m
+        jp1 = _xp_searchsorted(cumulative_weights, jg, side='right')
+        j = _xp_searchsorted(cumulative_weights, jg-1, side='right')
+        j, jp1 = xp.astype(j, y.dtype), xp.astype(jp1, y.dtype)
+
+    g = jg % 1
+    if method == 'inverted_cdf':
+        g = xp.astype((g > 0), jg.dtype)
+    elif method == 'averaged_inverted_cdf':
+        g = (1 + xp.astype((g > 0), jg.dtype)) / 2
+    elif method == 'closest_observation':
+        g = (1 - xp.astype((g == 0) & (j % 2 == 1), jg.dtype))
+    if method in {'inverted_cdf', 'averaged_inverted_cdf', 'closest_observation'}:
+        g = xp.asarray(g)
+        g = xpx.at(g, jg < 0).set(0)
+
+    g = xpx.at(g)[j < 0].set(0)
+    j = xp.clip(j, 0., n - 1)
+    jp1 = xp.clip(jp1, 0., n - 1)
+
+    return ((1 - g) * xp.take_along_axis(y, xp.astype(j, xp.int64), axis=-1)
+            + g * xp.take_along_axis(y, xp.astype(jp1, xp.int64), axis=-1))
+
+
+def _quantile_hd(y, p, n, xp):
+    # RE axis handling: We need to perform a reducing operation over rows of `y` for
+    # each element in the corresponding row of `p` (a la Cartesian product). Strategy:
+    # move rows of `p` to an axis at the front that is orthogonal to all the rest,
+    # perform the reducing operating over the last axis, then move the front axis back
+    # to the end.
+    p = xp.moveaxis(p, -1, 0)[..., xp.newaxis]
+    a = p * (n + 1)
+    b = (1 - p) * (n + 1)
+    i = xp.arange(y.shape[-1] + 1, dtype=y.dtype, device=xp_device(y))
+    w = betainc(a, b, i / n)
+    w = w[..., 1:] - w[..., :-1]
+    w = xpx.at(w, xp.isnan(w)).set(0)
+    res = xp.vecdot(w, y, axis=-1)
+    return xp.moveaxis(res, 0, -1)
+
+
+def _quantile_winsor(y, p, n, method, xp):
+    ops = dict(round_outward=(xp.floor, xp.ceil),
+               round_inward=(xp.ceil, xp.floor),
+               round_nearest=(xp.round, xp.round))
+    op_left, op_right = ops[method]
+    j = xp.where(p < 0.5, op_left(p*n), op_right(n*p - 1))
+    return xp.take_along_axis(y, xp.astype(j, xp.int64), axis=-1)
+
+
+def _quantile_bc(y, p, n, method, xp):
+    # Methods retained for backward compatibility. NumPy documentation is not
+    # quite right about what these methods do: if `p * (n - 1)` is integral,
+    # that is used as the index. See numpy/numpy#28910.
+    ij = p * (n - 1)
+    if method == '_midpoint':
+        return (xp.take_along_axis(y, xp.astype(xp.floor(ij), xp.int64), axis=-1)
+                + xp.take_along_axis(y, xp.astype(xp.ceil(ij), xp.int64), axis=-1)) / 2
+    elif method == '_lower':
+        k = xp.floor(ij)
+    elif method == '_higher':
+        k = xp.ceil(ij)
+    elif method == '_nearest':
+        k = xp.round(ij)
+    return xp.take_along_axis(y, xp.astype(k, xp.int64), axis=-1)
+
+
+@xp_capabilities(skip_backends=[("dask.array", "No take_along_axis yet.")])
+def _xp_searchsorted(x, y, *, side='left', xp=None):
+    # Vectorized xp.searchsorted. Search is performed along last axis. The shape of the
+    # output is that of `y`, broadcasting the batch dimensions with those of `x` if
+    # necessary.
+    xp = array_namespace(x, y) if xp is None else xp
+    xp_default_int = xp.asarray(1).dtype
+    y_0d = xp.asarray(y).ndim == 0
+    x, y = _broadcast_arrays((x, y), axis=-1, xp=xp)
+    x_1d = x.ndim <= 1
+
+    if x_1d or is_torch(xp):
+        y = xp.reshape(y, ()) if (y_0d and x_1d) else y
+        out = xp.searchsorted(x, y, side=side)
+        out = xp.astype(out, xp_default_int, copy=False)
+        return out
+
+    a = xp.full(y.shape, 0, device=xp_device(x))
+
+    if x.shape[-1] == 0:
+        return a
+
+    n = xp.count_nonzero(~xp.isnan(x), axis=-1, keepdims=True)
+    b = xp.broadcast_to(n, y.shape)
+
+    compare = xp.less_equal if side == 'left' else xp.less
+
+    # while xp.any(b - a > 1):
+    # refactored to for loop with ~log2(n) iterations for JAX JIT
+    for i in range(int(math.log2(x.shape[-1])) + 1):
+        c = (a + b) // 2
+        x0 = xp.take_along_axis(x, c, axis=-1)
+        j = compare(y, x0)
+        b = xp.where(j, c, b)
+        a = xp.where(j, a, c)
+
+    out = xp.where(compare(y, xp.min(x, axis=-1, keepdims=True)), 0, b)
+    out = xp.where(xp.isnan(y), x.shape[-1], out) if side == 'right' else out
+    out = xp.astype(out, xp_default_int, copy=False)
+    return out
+
+
+@xp_capabilities(skip_backends=[("dask.array", "No take_along_axis yet.")],
+                 marray=True)
+def estimated_cdf(x, y, *, method='linear',
+                  axis=0, nan_policy='propagate', keepdims=None):
+    """
+    Estimate the CDF of the distribution underlying a sample.
+
+    Parameters
+    ----------
+    x : array_like of real numbers
+        Data array.
+    y : array_like of real numbers
+        Points at which to evaluate the estimated cdf.
+        See `axis`, `keepdims`, and the examples for broadcasting behavior.
+    method : str, default: 'linear'
+        The method to use for estimating the cumulative distribution function.
+        The available options, numbered as they appear in [1]_, are:
+
+        1. 'inverted_cdf' (AKA *the* empirical cumulative distribution function)
+        2. 'averaged_inverted_cdf'
+        3. 'closest_observation'
+        4. 'interpolated_inverted_cdf'
+        5. 'hazen'
+        6. 'weibull'
+        7. 'linear'  (default)
+        8. 'median_unbiased'
+        9. 'normal_unbiased'
+
+        See Notes for details.
+    axis : int or None, default: 0
+        Axis along which samples in `x` are given in ND case.
+        ``None`` ravels both `x` and `y` before performing the calculation,
+        without checking whether the original shapes were compatible.
+        As in other `scipy.stats` functions, a positive integer `axis` is resolved
+        after prepending 1s to the shape of `x` or `y` as needed until the two arrays
+        have the same dimensionality. When providing `x` and `y` with different
+        dimensionality, consider using negative `axis` integers for clarity.
+    nan_policy : str, default: 'propagate'
+        Defines how to handle NaNs in the input data `x`.
+
+        - ``propagate``: if a NaN is present in the axis slice (e.g. row) along
+          which the  statistic is computed, the corresponding slice of the output
+          will contain NaN(s).
+        - ``omit``: NaNs will be omitted when performing the calculation.
+          If insufficient data remains in the axis slice along which the
+          statistic is computed, the corresponding slice of the output will
+          contain NaN(s).
+        - ``raise``: if a NaN is present, a ``ValueError`` will be raised.
+
+        If NaNs are present in `y`, the corresponding entries in the output will be NaN.
+    keepdims : bool, optional
+        Consider the case in which `x` is 1-D and `y` is a scalar: the estimated
+        cumulative distribution function at a point is a reducing statistic, and the
+        default behavior is to return a scalar.
+        If `keepdims` is set to True, the axis will not be reduced away, and the
+        result will be a 1-D array with one element.
+
+        The general case is more subtle, since multiple values of `y` may be
+        specified for each axis-slice of `x`. For instance, if both `x` and `y`
+        are 1-D and ``y.size > 1``, no axis can be reduced away; there must be an
+        axis to contain the number of values given by ``y.size``. Therefore:
+
+        - By default, the axis will be reduced away if possible (i.e. if there is
+          exactly one element of `y` per axis-slice of `x`).
+        - If `keepdims` is set to True, the axis will not be reduced away.
+        - If `keepdims` is set to False, the axis will be reduced away
+          if possible, and an error will be raised otherwise.
+
+    Returns
+    -------
+    probability : scalar or ndarray
+        The resulting probabilities(s). The dtype is the result dtype of `x`, `y`, and
+        the Python ``float`` type.
+
+    See Also
+    --------
+    quantile
+
+    Notes
+    -----
+    Given a sample `x` from an underlying distribution, `estimated_cdf` provides a
+    nonparametric estimate of the cumulative distribution function.
+
+    By default, this is done by computing the "fractional index" ``p`` at which ``y``
+    would appear within ``z``, a sorted copy of `x`::
+
+        p = 1 / (n - 1) * (j +  (     y - z[j])
+                              / (z[j+1] - z[j]))
+
+    where the index ``j`` is that of the largest element of ``z`` that does not exceed
+    ``y``, and ``n`` is the number of elements in the sample. Note that if ``y`` is an
+    element of ``z``, then ``j`` is the index such that ``y = z[j]``, and the formula
+    simplifies to the intuitive ``j / (n - 1)``. The full formula linearly interpolates
+    between ``j / (n - 1)`` and ``(j + 1) / (n - 1)``.
+
+    This is a special case of the more general::
+
+        p = (j + (y - z[j]) / (z[j+1] - z[j] + 1 - m) / n
+
+    where ``m`` may be defined according to several different conventions.
+    The preferred convention may be selected using the ``method`` parameter:
+
+    =============================== =============== ===============
+    ``method``                      number in H&F   ``m``
+    =============================== =============== ===============
+    ``interpolated_inverted_cdf``   4               ``0``
+    ``hazen``                       5               ``1/2``
+    ``weibull``                     6               ``p``
+    ``linear`` (default)            7               ``1 - p``
+    ``median_unbiased``             8               ``p/3 + 1/3``
+    ``normal_unbiased``             9               ``p/4 + 3/8``
+    =============================== =============== ===============
+
+    Note that indices ``j`` and ``j + 1`` are clipped to the range ``0`` to
+    ``n - 1`` when the results of the formula would be outside the allowed
+    range of non-negative indices, and resulting ``p`` is clipped to the range
+    ``0`` to ``1``.
+
+    The table above includes only the estimators from [1]_ that are continuous
+    functions of probability `p` (estimators 4-9). SciPy also provides the
+    three discontinuous estimators from [1]_ (estimators 1-3), where ``j`` is
+    defined as above, ``m`` is defined as follows, and ``g`` is ``0`` when
+    ``index = p*n + m - 1`` is less than ``0`` and otherwise is defined below.
+
+    1. ``inverted_cdf``: ``m = 0`` and ``g = int(index - j > 0)``
+    2. ``averaged_inverted_cdf``: ``m = 0`` and
+       ``g = (1 + int(index - j > 0)) / 2``
+    3. ``closest_observation``: ``m = -1/2`` and
+       ``g = 1 - int((index == j) & (j%2 == 1))``
+
+    When all the data in ``x`` are unique, `estimated_cdf` and `quantile` are are
+    inverses of one another within a certain domain.
+    Although `quantile` with ``method='linear'`` is invertible over the whole domain
+    of ``p`` from ``0`` to ``1``, this is not true of other methods.
+
+    References
+    ----------
+    .. [1] R. J. Hyndman and Y. Fan,
+           "Sample quantiles in statistical packages,"
+           The American Statistician, 50(4), pp. 361-365, 1996
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> x = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
+
+    Estimate the cumulative distribution function of one sample at a single point.
+
+    >>> stats.estimated_cdf(x, 5, axis=-1)
+    np.float64(0.5)
+
+    Estimate the cumulative distribution function of one sample at two points.
+
+    >>> stats.estimated_cdf(x, [2.5, 7.5], axis=-1)
+    array([0.25, 0.75])
+
+    Estimate the cumulative distribution function of two samples at different points.
+
+    >>> x = np.stack((np.arange(0, 11), np.arange(10, 21)))
+    >>> stats.estimated_cdf(x, [[2.5], [17.5]], axis=-1, keepdims=True)
+    array([[0.25],
+           [0.75]])
+
+    Estimate the cumulative distribution function at many points for each of two
+    samples.
+
+    >>> import matplotlib.pyplot as plt
+    >>> rng = np.random.default_rng(6110515095)
+    >>> x = stats.Normal(mu=[-1, 1]).sample(10000)
+    >>> y = np.linspace(-4, 4, 5000)[:, np.newaxis]
+    >>> p = stats.estimated_cdf(x, y, axis=0)
+    >>> plt.plot(y, p)
+    >>> plt.show()
+
+    Note that the `quantile` and `estimated_cdf` functions are inverses of one another
+    within a certain domain.
+
+    >>> p = np.linspace(0, 1, 300)
+    >>> x = rng.standard_normal(300)
+    >>> y = stats.quantile(x, p)
+    >>> p2 = stats.estimated_cdf(x, y)
+    >>> np.testing.assert_allclose(p2, p)
+    >>> y2 = stats.quantile(x, p2)
+    >>> np.testing.assert_allclose(y2, y)
+
+    However, the domain over which `quantile` can be inverted by `estimated_cdf` depends
+    on the `method` used. This is most noticeable when there are few observations in the
+    sample.
+
+    >>> x = np.asarray([0, 1])
+    >>> y_linear = stats.quantile(x, p, method='linear')
+    >>> y_weibull = stats.quantile(x, p, method='weibull')
+    >>> y_iicdf = stats.quantile(x, p, method='interpolated_inverted_cdf')
+    >>> plt.plot(p, y_linear, p, y_weibull, p, y_iicdf)
+    >>> plt.legend(['linear', 'weibull', 'iicdf'])
+    >>> plt.xlabel('p')
+    >>> plt.ylabel('y = quantile(x, p)')
+    >>> plt.show()
+
+    For example, in the case above, `quantile` is only invertible from
+    ``p = 0.5`` to ``p = 1.0`` with ``method = 'interpolated_inverted_cdf'``. This is a
+    fundamental characteristic of the methods, not a shortcoming of `estimated_cdf`.
+
+    """
+    temp = _quantile_iv(x, y, method, axis, nan_policy, keepdims, weights=None,
+                        fun='estimated_cdf')
+    x, y, method, axis, nan_policy, keepdims, n, axis_none, ndim, y_mask, _, xp = temp
+
+    if xp_size(x) == 0:
+        res = xp.full_like(y, xp.nan)
+    else:
+        res = _estimated_cdf_hf(x, y, n, method, xp)
+
+    return _post_quantile(res, y_mask, axis, axis_none, ndim, keepdims, xp)
+
+
+_estimated_cdf_discontinuous_methods = dict(
+    inverted_cdf=0.0,
+    averaged_inverted_cdf=0.0,
+    closest_observation=0.5,
+)
+
+
+_estimated_cdf_continuous_methods = dict(
+    interpolated_inverted_cdf=(0, 1),
+    hazen=(0.5, 0.5),
+    weibull=(0, 0),
+    linear=(1, 1),
+    median_unbiased=(1 / 3, 1 / 3),
+    normal_unbiased=(3 / 8, 3 / 8),
+)
+
+
+_estimated_cdf_methods = (set(_estimated_cdf_continuous_methods).union(
+                          set(_estimated_cdf_discontinuous_methods)))
+
+
+def _estimated_cdf_hf(x, y, n, method, xp):
+    n_int = xp.astype(n, xp.int64)
+    j_max = n_int - 1
+    j_min = xp.minimum(j_max, xp.asarray(1, dtype=j_max.dtype))
+    jp1 = _xp_searchsorted(x, y, side='right')
+
+    if method in _estimated_cdf_discontinuous_methods:
+        dp = _estimated_cdf_discontinuous_methods[method]
+        p = (xp.astype(jp1, x.dtype)+dp)/n
+
+    else:
+        jp1 = xp.clip(jp1, j_min, j_max)
+        j = xp.clip(jp1-1, 0)
+        xj = xp.take_along_axis(x, j, axis=-1)
+        xjp1 = xp.take_along_axis(x, jp1, axis=-1)
+        with np.errstate(divide='ignore', invalid='ignore'):  # refactor to apply_where?
+            delta = xp.where((xjp1 > xj) & xp.isfinite(xj), (y - xj) / (xjp1 - xj), 1.)
+
+        a, b = _estimated_cdf_continuous_methods[method]
+        p = (xp.astype(jp1, x.dtype) + delta - a) / (n + 1 - a - b)
+
+    xmin = x[..., :1]
+    xmax = (x[..., -1:] if n.shape == () else xp.take_along_axis(x, j_max))
+    p = xpx.at(p)[y < xmin].set(0.)
+    p = xpx.at(p)[y > xmax].set(1.)
+
+    return xp.clip(p, 0., 1.)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_rcont/__init__.py b/venv/lib/python3.12/site-packages/scipy/stats/_rcont/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..25728ead5f7ea277e6e94c359d5a5603b99eeb38
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_rcont/__init__.py
@@ -0,0 +1,4 @@
+#
+from .rcont import rvs_rcont1, rvs_rcont2
+
+__all__ = ["rvs_rcont1", "rvs_rcont2"]
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_rcont/__pycache__/__init__.cpython-312.pyc b/venv/lib/python3.12/site-packages/scipy/stats/_rcont/__pycache__/__init__.cpython-312.pyc
new file mode 100644
index 0000000000000000000000000000000000000000..5bb5b6821e3451099d908984fc89a5365c19520c
Binary files /dev/null and b/venv/lib/python3.12/site-packages/scipy/stats/_rcont/__pycache__/__init__.cpython-312.pyc differ
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_rcont/rcont.cpython-312-x86_64-linux-gnu.so b/venv/lib/python3.12/site-packages/scipy/stats/_rcont/rcont.cpython-312-x86_64-linux-gnu.so
new file mode 100644
index 0000000000000000000000000000000000000000..fa504763a219bb263466d5e5f6c79acbd9205322
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_rcont/rcont.cpython-312-x86_64-linux-gnu.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:cac8d420bff9e2bf24fd12b85bd3ab6d123a8fe13af3aa475cef7ce775205154
+size 107912
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_relative_risk.py b/venv/lib/python3.12/site-packages/scipy/stats/_relative_risk.py
new file mode 100644
index 0000000000000000000000000000000000000000..51525fd28adb37c72b12106450e4178c786091b2
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_relative_risk.py
@@ -0,0 +1,263 @@
+import operator
+from dataclasses import dataclass
+import numpy as np
+from scipy.special import ndtri
+from ._common import ConfidenceInterval
+
+
+def _validate_int(n, bound, name):
+    msg = f'{name} must be an integer not less than {bound}, but got {n!r}'
+    try:
+        n = operator.index(n)
+    except TypeError:
+        raise TypeError(msg) from None
+    if n < bound:
+        raise ValueError(msg)
+    return n
+
+
+@dataclass
+class RelativeRiskResult:
+    """
+    Result of `scipy.stats.contingency.relative_risk`.
+
+    Attributes
+    ----------
+    relative_risk : float
+        This is::
+
+            (exposed_cases/exposed_total) / (control_cases/control_total)
+
+    exposed_cases : int
+        The number of "cases" (i.e. occurrence of disease or other event
+        of interest) among the sample of "exposed" individuals.
+    exposed_total : int
+        The total number of "exposed" individuals in the sample.
+    control_cases : int
+        The number of "cases" among the sample of "control" or non-exposed
+        individuals.
+    control_total : int
+        The total number of "control" individuals in the sample.
+
+    Methods
+    -------
+    confidence_interval :
+        Compute the confidence interval for the relative risk estimate.
+    """
+
+    relative_risk: float
+    exposed_cases: int
+    exposed_total: int
+    control_cases: int
+    control_total: int
+
+    def confidence_interval(self, confidence_level=0.95):
+        """
+        Compute the confidence interval for the relative risk.
+
+        The confidence interval is computed using the Katz method
+        (i.e. "Method C" of [1]_; see also [2]_, section 3.1.2).
+
+        Parameters
+        ----------
+        confidence_level : float, optional
+            The confidence level to use for the confidence interval.
+            Default is 0.95.
+
+        Returns
+        -------
+        ci : ConfidenceInterval instance
+            The return value is an object with attributes ``low`` and
+            ``high`` that hold the confidence interval.
+
+        References
+        ----------
+        .. [1] D. Katz, J. Baptista, S. P. Azen and M. C. Pike, "Obtaining
+               confidence intervals for the risk ratio in cohort studies",
+               Biometrics, 34, 469-474 (1978).
+        .. [2] Hardeo Sahai and Anwer Khurshid, Statistics in Epidemiology,
+               CRC Press LLC, Boca Raton, FL, USA (1996).
+
+
+        Examples
+        --------
+        >>> from scipy.stats.contingency import relative_risk
+        >>> result = relative_risk(exposed_cases=10, exposed_total=75,
+        ...                        control_cases=12, control_total=225)
+        >>> result.relative_risk
+        2.5
+        >>> result.confidence_interval()
+        ConfidenceInterval(low=1.1261564003469628, high=5.549850800541033)
+        """
+        if not 0 <= confidence_level <= 1:
+            raise ValueError('confidence_level must be in the interval '
+                             '[0, 1].')
+
+        # Handle edge cases where either exposed_cases or control_cases
+        # is zero.  We follow the convention of the R function riskratio
+        # from the epitools library.
+        if self.exposed_cases == 0 and self.control_cases == 0:
+            # relative risk is nan.
+            return ConfidenceInterval(low=np.nan, high=np.nan)
+        elif self.exposed_cases == 0:
+            # relative risk is 0.
+            return ConfidenceInterval(low=0.0, high=np.nan)
+        elif self.control_cases == 0:
+            # relative risk is inf
+            return ConfidenceInterval(low=np.nan, high=np.inf)
+
+        alpha = 1 - confidence_level
+        z = ndtri(1 - alpha/2)
+        rr = self.relative_risk
+
+        # Estimate of the variance of log(rr) is
+        # var(log(rr)) = 1/exposed_cases - 1/exposed_total +
+        #                1/control_cases - 1/control_total
+        # and the standard error is the square root of that.
+        se = np.sqrt(1/self.exposed_cases - 1/self.exposed_total +
+                     1/self.control_cases - 1/self.control_total)
+        delta = z*se
+        katz_lo = rr*np.exp(-delta)
+        katz_hi = rr*np.exp(delta)
+        return ConfidenceInterval(low=katz_lo, high=katz_hi)
+
+
+def relative_risk(exposed_cases, exposed_total, control_cases, control_total):
+    """
+    Compute the relative risk (also known as the risk ratio).
+
+    This function computes the relative risk associated with a 2x2
+    contingency table ([1]_, section 2.2.3; [2]_, section 3.1.2). Instead
+    of accepting a table as an argument, the individual numbers that are
+    used to compute the relative risk are given as separate parameters.
+    This is to avoid the ambiguity of which row or column of the contingency
+    table corresponds to the "exposed" cases and which corresponds to the
+    "control" cases.  Unlike, say, the odds ratio, the relative risk is not
+    invariant under an interchange of the rows or columns.
+
+    Parameters
+    ----------
+    exposed_cases : nonnegative int
+        The number of "cases" (i.e. occurrence of disease or other event
+        of interest) among the sample of "exposed" individuals.
+    exposed_total : positive int
+        The total number of "exposed" individuals in the sample.
+    control_cases : nonnegative int
+        The number of "cases" among the sample of "control" or non-exposed
+        individuals.
+    control_total : positive int
+        The total number of "control" individuals in the sample.
+
+    Returns
+    -------
+    result : instance of `~scipy.stats._result_classes.RelativeRiskResult`
+        The object has the float attribute ``relative_risk``, which is::
+
+            rr = (exposed_cases/exposed_total) / (control_cases/control_total)
+
+        The object also has the method ``confidence_interval`` to compute
+        the confidence interval of the relative risk for a given confidence
+        level.
+
+    See Also
+    --------
+    odds_ratio
+
+    Notes
+    -----
+    The R package epitools has the function `riskratio`, which accepts
+    a table with the following layout::
+
+                        disease=0   disease=1
+        exposed=0 (ref)    n00         n01
+        exposed=1          n10         n11
+
+    With a 2x2 table in the above format, the estimate of the CI is
+    computed by `riskratio` when the argument method="wald" is given,
+    or with the function `riskratio.wald`.
+
+    For example, in a test of the incidence of lung cancer among a
+    sample of smokers and nonsmokers, the "exposed" category would
+    correspond to "is a smoker" and the "disease" category would
+    correspond to "has or had lung cancer".
+
+    To pass the same data to ``relative_risk``, use::
+
+        relative_risk(n11, n10 + n11, n01, n00 + n01)
+
+    .. versionadded:: 1.7.0
+
+    References
+    ----------
+    .. [1] Alan Agresti, An Introduction to Categorical Data Analysis
+           (second edition), Wiley, Hoboken, NJ, USA (2007).
+    .. [2] Hardeo Sahai and Anwer Khurshid, Statistics in Epidemiology,
+           CRC Press LLC, Boca Raton, FL, USA (1996).
+
+    Examples
+    --------
+    >>> from scipy.stats.contingency import relative_risk
+
+    This example is from Example 3.1 of [2]_.  The results of a heart
+    disease study are summarized in the following table::
+
+                 High CAT   Low CAT    Total
+                 --------   -------    -----
+        CHD         27         44        71
+        No CHD      95        443       538
+
+        Total      122        487       609
+
+    CHD is coronary heart disease, and CAT refers to the level of
+    circulating catecholamine.  CAT is the "exposure" variable, and
+    high CAT is the "exposed" category. So the data from the table
+    to be passed to ``relative_risk`` is::
+
+        exposed_cases = 27
+        exposed_total = 122
+        control_cases = 44
+        control_total = 487
+
+    >>> result = relative_risk(27, 122, 44, 487)
+    >>> result.relative_risk
+    2.4495156482861398
+
+    Find the confidence interval for the relative risk.
+
+    >>> result.confidence_interval(confidence_level=0.95)
+    ConfidenceInterval(low=1.5836990926700116, high=3.7886786315466354)
+
+    The interval does not contain 1, so the data supports the statement
+    that high CAT is associated with greater risk of CHD.
+    """
+    # Relative risk is a trivial calculation.  The nontrivial part is in the
+    # `confidence_interval` method of the RelativeRiskResult class.
+
+    exposed_cases = _validate_int(exposed_cases, 0, "exposed_cases")
+    exposed_total = _validate_int(exposed_total, 1, "exposed_total")
+    control_cases = _validate_int(control_cases, 0, "control_cases")
+    control_total = _validate_int(control_total, 1, "control_total")
+
+    if exposed_cases > exposed_total:
+        raise ValueError('exposed_cases must not exceed exposed_total.')
+    if control_cases > control_total:
+        raise ValueError('control_cases must not exceed control_total.')
+
+    if exposed_cases == 0 and control_cases == 0:
+        # relative risk is 0/0.
+        rr = np.nan
+    elif exposed_cases == 0:
+        # relative risk is 0/nonzero
+        rr = 0.0
+    elif control_cases == 0:
+        # relative risk is nonzero/0.
+        rr = np.inf
+    else:
+        p1 = exposed_cases / exposed_total
+        p2 = control_cases / control_total
+        rr = p1 / p2
+    return RelativeRiskResult(relative_risk=rr,
+                              exposed_cases=exposed_cases,
+                              exposed_total=exposed_total,
+                              control_cases=control_cases,
+                              control_total=control_total)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_resampling.py b/venv/lib/python3.12/site-packages/scipy/stats/_resampling.py
new file mode 100644
index 0000000000000000000000000000000000000000..3977e3718809ff6772dbee247c506f1257c9a624
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_resampling.py
@@ -0,0 +1,2425 @@
+import warnings
+import numpy as np
+from itertools import combinations, permutations, product, accumulate
+from collections.abc import Sequence
+from dataclasses import dataclass, field
+import inspect
+import math
+
+from scipy._lib._util import (check_random_state, _rename_parameter, rng_integers,
+                              _transition_to_rng)
+from scipy._lib._array_api import (
+    array_namespace,
+    is_numpy,
+    is_array_api_strict,
+    xp_capabilities,
+    xp_result_type,
+    xp_size,
+    xp_device,
+    xp_swapaxes,
+    is_lazy_array,
+)
+from scipy._external import array_api_extra as xpx
+from scipy.special import ndtr, ndtri
+from scipy import stats
+
+from ._common import ConfidenceInterval
+from ._axis_nan_policy import _broadcast_concatenate, _broadcast_arrays
+from ._warnings_errors import DegenerateDataWarning
+
+__all__ = ['bootstrap', 'monte_carlo_test', 'permutation_test']
+
+
+def _vectorize_statistic(statistic):
+    """Vectorize an n-sample statistic"""
+    # This is a little cleaner than np.nditer at the expense of some data
+    # copying: concatenate samples together, then use np.apply_along_axis
+    def stat_nd(*data, axis=0):
+        lengths = [sample.shape[axis] for sample in data]
+        split_indices = np.cumsum(lengths)[:-1]
+        z = _broadcast_concatenate(data, axis)
+
+        # move working axis to position 0 so that new dimensions in the output
+        # of `statistic` are _prepended_. ("This axis is removed, and replaced
+        # with new dimensions...")
+        z = np.moveaxis(z, axis, 0)
+
+        def stat_1d(z):
+            data = np.split(z, split_indices)
+            return statistic(*data)
+
+        return np.apply_along_axis(stat_1d, 0, z)[()]
+    return stat_nd
+
+
+def _jackknife_resample(sample, batch=None, *, xp):
+    """Jackknife resample the sample. Only one-sample stats for now."""
+    n = sample.shape[-1]
+    batch_nominal = batch or n
+
+    for k in range(0, n, batch_nominal):
+        # col_start:col_end are the observations to remove
+        batch_actual = min(batch_nominal, n-k)
+
+        # jackknife - each row leaves out one observation
+        j = np.ones((batch_actual, n), dtype=bool)
+        np.fill_diagonal(j[:, k:k+batch_actual], False)
+        i = np.arange(n)
+        i = np.broadcast_to(i, (batch_actual, n))
+        i = i[j].reshape((batch_actual, n-1))
+
+        i = xp.asarray(i, device=xp_device(sample))
+        yield _get_from_last_axis(sample, i, xp=xp)
+
+
+def _bootstrap_resample(sample, n_resamples=None, rng=None, *, xp):
+    """Bootstrap resample the sample."""
+    n = sample.shape[-1]
+
+    # bootstrap - each row is a random resample of original observations
+    i = rng_integers(rng, 0, n, (n_resamples, n))
+
+    i = xp.asarray(i, device=xp_device(sample))
+    return _get_from_last_axis(sample, i, xp=xp)
+
+
+def _get_from_last_axis(sample, i, xp):
+    if not is_array_api_strict(xp):
+        return sample[..., i]
+
+    # Equivalent to `sample[..., i]` as used in `bootstrap`. Assumes i.ndim <=2.
+    if i.ndim == 2:
+        sample = xp.expand_dims(sample, axis=-2)
+    sample, i = _broadcast_arrays((sample, i), axis=-1, xp=xp)
+    return xp.take_along_axis(sample, i, axis=-1)
+
+
+def _percentile_of_score(a, score, axis, xp):
+    """Vectorized, simplified `scipy.stats.percentileofscore`.
+    Uses logic of the 'mean' value of percentileofscore's kind parameter.
+
+    Unlike `stats.percentileofscore`, the percentile returned is a fraction
+    in [0, 1].
+    """
+    B = a.shape[axis]
+    nonzeros = (xp.count_nonzero(a < score, axis=axis)
+                + xp.count_nonzero(a <= score, axis=axis))
+    return xp.astype(nonzeros, score.dtype) / (2 * B)
+
+
+def _bca_interval(data, statistic, axis, alpha, theta_hat_b, batch, xp):
+    """Bias-corrected and accelerated interval."""
+    # closely follows [1] 14.3 and 15.4 (Eq. 15.36)
+
+    # calculate z0_hat
+    theta_hat = xp.expand_dims(statistic(*data, axis=axis), axis=-1)
+    percentile = _percentile_of_score(theta_hat_b, theta_hat, axis=-1, xp=xp)
+    percentile = xp.asarray(percentile, dtype=theta_hat.dtype,
+                            device=xp_device(theta_hat))
+    z0_hat = ndtri(percentile)
+
+    # calculate a_hat
+    theta_hat_ji = []  # j is for sample of data, i is for jackknife resample
+    for j, sample in enumerate(data):
+        # _jackknife_resample will add an axis prior to the last axis that
+        # corresponds with the different jackknife resamples. Do the same for
+        # each sample of the data to ensure broadcastability. We need to
+        # create a copy of the list containing the samples anyway, so do this
+        # in the loop to simplify the code. This is not the bottleneck...
+        samples = [xp.expand_dims(sample, axis=-2) for sample in data]
+        theta_hat_i = []
+        for jackknife_sample in _jackknife_resample(sample, batch, xp=xp):
+            samples[j] = jackknife_sample
+            broadcasted = _broadcast_arrays(samples, axis=-1, xp=xp)
+            theta_hat_i.append(statistic(*broadcasted, axis=-1))
+        theta_hat_ji.append(theta_hat_i)
+
+    theta_hat_ji = [xp.concat(theta_hat_i, axis=-1)
+                    for theta_hat_i in theta_hat_ji]
+
+    # CuPy array dtype is unstable in 1.13.6 when divided by large Python int:
+    # (cp.ones(1, dtype=cp.float32)/10000).dtype   # float32
+    # (cp.ones(1, dtype=cp.float32)/100000).dtype  # float64
+    # Solution for now is to make the divisor a Python float
+    # Looks like this will be fixed in 1.14.0
+    n_j = [float(theta_hat_i.shape[-1]) for theta_hat_i in theta_hat_ji]
+
+    theta_hat_j_dot = [xp.mean(theta_hat_i, axis=-1, keepdims=True)
+                       for theta_hat_i in theta_hat_ji]
+
+    U_ji = [(n - 1) * (theta_hat_dot - theta_hat_i)
+            for theta_hat_dot, theta_hat_i, n
+            in zip(theta_hat_j_dot, theta_hat_ji, n_j)]
+
+    nums = [xp.sum(U_i**3, axis=-1)/n**3 for U_i, n in zip(U_ji, n_j)]
+    dens = [xp.sum(U_i**2, axis=-1)/n**2 for U_i, n in zip(U_ji, n_j)]
+    a_hat = 1/6 * sum(nums) / sum(dens)**(3/2)
+
+    # calculate alpha_1, alpha_2
+    # `float` because dtype of ndtri output (float64) should not promote other vals
+    z_alpha = float(ndtri(alpha))
+    z_1alpha = -z_alpha
+    num1 = z0_hat + z_alpha
+    alpha_1 = ndtr(z0_hat + num1/(1 - a_hat*num1))
+    num2 = z0_hat + z_1alpha
+    alpha_2 = ndtr(z0_hat + num2/(1 - a_hat*num2))
+    return alpha_1, alpha_2, a_hat  # return a_hat for testing
+
+
+def _bootstrap_iv(data, statistic, vectorized, paired, axis, confidence_level,
+                  alternative, n_resamples, batch, method, bootstrap_result,
+                  rng):
+    """Input validation and standardization for `bootstrap`."""
+    xp = array_namespace(*data)
+
+    if vectorized not in {True, False, None}:
+        raise ValueError("`vectorized` must be `True`, `False`, or `None`.")
+
+    if vectorized is None:
+        vectorized = 'axis' in inspect.signature(statistic).parameters
+
+    if not vectorized:
+        if not is_numpy(xp):
+            message = (f"When using array library {xp.__name__}, `func` must be "
+                       "vectorized and accept argument `axis`.")
+            raise TypeError(message)
+
+        statistic = _vectorize_statistic(statistic)
+
+    axis_int = int(axis)
+    if axis != axis_int:
+        raise ValueError("`axis` must be an integer.")
+
+    n_samples = 0
+    try:
+        n_samples = len(data)
+    except TypeError:
+        raise ValueError("`data` must be a sequence of samples.")
+
+    if n_samples == 0:
+        raise ValueError("`data` must contain at least one sample.")
+
+    data = _broadcast_arrays(data, axis_int, xp=xp)
+
+    data_iv = []
+    for sample in data:
+        if sample.shape[axis_int] <= 1:
+            raise ValueError("each sample in `data` must contain two or more "
+                             "observations along `axis`.")
+        sample = xp.moveaxis(sample, axis_int, -1)
+        data_iv.append(sample)
+
+    if paired not in {True, False}:
+        raise ValueError("`paired` must be `True` or `False`.")
+
+    if paired:
+        n = data_iv[0].shape[-1]
+        for sample in data_iv[1:]:
+            if sample.shape[-1] != n:
+                message = ("When `paired is True`, all samples must have the "
+                           "same length along `axis`")
+                raise ValueError(message)
+
+        # to generate the bootstrap distribution for paired-sample statistics,
+        # resample the indices of the observations
+        def statistic(i, axis=-1, data=data_iv, unpaired_statistic=statistic):
+            # data = [sample[..., i] for sample in data]
+            data = [_get_from_last_axis(sample, i, xp=xp) for sample in data]
+            return unpaired_statistic(*data, axis=axis)
+
+        data_iv = [xp.arange(n)]
+
+    confidence_level_float = float(confidence_level)
+
+    alternative = alternative.lower()
+    alternatives = {'two-sided', 'less', 'greater'}
+    if alternative not in alternatives:
+        raise ValueError(f"`alternative` must be one of {alternatives}")
+
+    n_resamples_int = int(n_resamples)
+    if n_resamples != n_resamples_int or n_resamples_int < 0:
+        raise ValueError("`n_resamples` must be a non-negative integer.")
+
+    if batch is None:
+        batch_iv = batch
+    else:
+        batch_iv = int(batch)
+        if batch != batch_iv or batch_iv <= 0:
+            raise ValueError("`batch` must be a positive integer or None.")
+
+    methods = {'percentile', 'basic', 'bca'}
+    method = method.lower()
+    if method not in methods:
+        raise ValueError(f"`method` must be in {methods}")
+
+    message = "`bootstrap_result` must have attribute `bootstrap_distribution'"
+    if (bootstrap_result is not None
+            and not hasattr(bootstrap_result, "bootstrap_distribution")):
+        raise ValueError(message)
+
+    message = ("Either `bootstrap_result.bootstrap_distribution.size` or "
+               "`n_resamples` must be positive.")
+    if ((not bootstrap_result or
+         not xp_size(bootstrap_result.bootstrap_distribution))
+            and n_resamples_int == 0):
+        raise ValueError(message)
+
+    rng = check_random_state(rng)
+
+    return (data_iv, statistic, vectorized, paired, axis_int,
+            confidence_level_float, alternative, n_resamples_int, batch_iv,
+            method, bootstrap_result, rng, xp)
+
+
+@dataclass
+class BootstrapResult:
+    """Result object returned by `scipy.stats.bootstrap`.
+
+    Attributes
+    ----------
+    confidence_interval : ConfidenceInterval
+        The bootstrap confidence interval as an instance of
+        `collections.namedtuple` with attributes `low` and `high`.
+    bootstrap_distribution : ndarray
+        The bootstrap distribution, that is, the value of `statistic` for
+        each resample. The last dimension corresponds with the resamples
+        (e.g. ``res.bootstrap_distribution.shape[-1] == n_resamples``).
+    standard_error : float or ndarray
+        The bootstrap standard error, that is, the sample standard
+        deviation of the bootstrap distribution.
+
+    """
+    confidence_interval: ConfidenceInterval
+    bootstrap_distribution: np.ndarray
+    standard_error: float | np.ndarray
+
+
+@xp_capabilities(skip_backends=[("dask.array", "Dask doesn't have take_along_axis.")],
+                 jax_jit=False)  # a few failed assertions - not sure what's going on
+@_transition_to_rng('random_state')
+def bootstrap(data, statistic, *, n_resamples=9999, batch=None,
+              vectorized=None, paired=False, axis=0, confidence_level=0.95,
+              alternative='two-sided', method='BCa', bootstrap_result=None,
+              rng=None):
+    r"""
+    Compute a two-sided bootstrap confidence interval of a statistic.
+
+    When `method` is ``'percentile'`` and `alternative` is ``'two-sided'``,
+    a bootstrap confidence interval is computed according to the following
+    procedure.
+
+    1. Resample the data: for each sample in `data` and for each of
+       `n_resamples`, take a random sample of the original sample
+       (with replacement) of the same size as the original sample.
+
+    2. Compute the bootstrap distribution of the statistic: for each set of
+       resamples, compute the test statistic.
+
+    3. Determine the confidence interval: find the interval of the bootstrap
+       distribution that is
+
+       - symmetric about the median and
+       - contains `confidence_level` of the resampled statistic values.
+
+    While the ``'percentile'`` method is the most intuitive, it is rarely
+    used in practice. Two more common methods are available, ``'basic'``
+    ('reverse percentile') and ``'BCa'`` ('bias-corrected and accelerated');
+    they differ in how step 3 is performed.
+
+    If the samples in `data` are  taken at random from their respective
+    distributions :math:`n` times, the confidence interval returned by
+    `bootstrap` will contain the true value of the statistic for those
+    distributions approximately `confidence_level`:math:`\, \times \, n` times.
+
+    Parameters
+    ----------
+    data : sequence of array-like
+         Each element of `data` is a sample containing scalar observations from an
+         underlying distribution. Elements of `data` must be broadcastable to the
+         same shape (with the possible exception of the dimension specified by `axis`).
+    statistic : callable
+        Statistic for which the confidence interval is to be calculated.
+        `statistic` must be a callable that accepts ``len(data)`` samples
+        as separate arguments and returns the resulting statistic.
+        If `vectorized` is set ``True``,
+        `statistic` must also accept a keyword argument `axis` and be
+        vectorized to compute the statistic along the provided `axis`.
+    n_resamples : int, default: ``9999``
+        The number of resamples performed to form the bootstrap distribution
+        of the statistic.
+    batch : int, optional
+        The number of resamples to process in each vectorized call to
+        `statistic`. Memory usage is O( `batch` * ``n`` ), where ``n`` is the
+        sample size. Default is ``None``, in which case ``batch = n_resamples``
+        (or ``batch = max(n_resamples, n)`` for ``method='BCa'``).
+    vectorized : bool, optional
+        If `vectorized` is set ``False``, `statistic` will not be passed
+        keyword argument `axis` and is expected to calculate the statistic
+        only for 1D samples. If ``True``, `statistic` will be passed keyword
+        argument `axis` and is expected to calculate the statistic along `axis`
+        when passed an ND sample array. If ``None`` (default), `vectorized`
+        will be set ``True`` if ``axis`` is a parameter of `statistic`. Use of
+        a vectorized statistic typically reduces computation time.
+    paired : bool, default: ``False``
+        Whether the statistic treats corresponding elements of the samples
+        in `data` as paired. If True, `bootstrap` resamples an array of
+        *indices* and uses the same indices for all arrays in `data`; otherwise,
+        `bootstrap` independently resamples the elements of each array.
+    axis : int, default: ``0``
+        The axis of the samples in `data` along which the `statistic` is
+        calculated.
+    confidence_level : float, default: ``0.95``
+        The confidence level of the confidence interval.
+    alternative : {'two-sided', 'less', 'greater'}, default: ``'two-sided'``
+        Choose ``'two-sided'`` (default) for a two-sided confidence interval,
+        ``'less'`` for a one-sided confidence interval with the lower bound
+        at ``-np.inf``, and ``'greater'`` for a one-sided confidence interval
+        with the upper bound at ``np.inf``. The other bound of the one-sided
+        confidence intervals is the same as that of a two-sided confidence
+        interval with `confidence_level` twice as far from 1.0; e.g. the upper
+        bound of a 95% ``'less'``  confidence interval is the same as the upper
+        bound of a 90% ``'two-sided'`` confidence interval.
+    method : {'percentile', 'basic', 'bca'}, default: ``'BCa'``
+        Whether to return the 'percentile' bootstrap confidence interval
+        (``'percentile'``), the 'basic' (AKA 'reverse') bootstrap confidence
+        interval (``'basic'``), or the bias-corrected and accelerated bootstrap
+        confidence interval (``'BCa'``).
+    bootstrap_result : BootstrapResult, optional
+        Provide the result object returned by a previous call to `bootstrap`
+        to include the previous bootstrap distribution in the new bootstrap
+        distribution. This can be used, for example, to change
+        `confidence_level`, change `method`, or see the effect of performing
+        additional resampling without repeating computations.
+    rng : `numpy.random.Generator`, optional
+        Pseudorandom number generator state. When `rng` is None, a new
+        `numpy.random.Generator` is created using entropy from the
+        operating system. Types other than `numpy.random.Generator` are
+        passed to `numpy.random.default_rng` to instantiate a ``Generator``.
+
+    Returns
+    -------
+    res : BootstrapResult
+        An object with attributes:
+
+        confidence_interval : ConfidenceInterval
+            The bootstrap confidence interval as an instance of
+            `collections.namedtuple` with attributes `low` and `high`.
+        bootstrap_distribution : ndarray
+            The bootstrap distribution, that is, the value of `statistic` for
+            each resample. The last dimension corresponds with the resamples
+            (e.g. ``res.bootstrap_distribution.shape[-1] == n_resamples``).
+        standard_error : float or ndarray
+            The bootstrap standard error, that is, the sample standard
+            deviation of the bootstrap distribution.
+
+    Warns
+    -----
+    `~scipy.stats.DegenerateDataWarning`
+        Generated when ``method='BCa'`` and the bootstrap distribution is
+        degenerate (e.g. all elements are identical).
+
+    Notes
+    -----
+    Elements of the confidence interval may be NaN for ``method='BCa'`` if
+    the bootstrap distribution is degenerate (e.g. all elements are identical).
+    In this case, consider using another `method` or inspecting `data` for
+    indications that other analysis may be more appropriate (e.g. all
+    observations are identical).
+
+    References
+    ----------
+    .. [1] B. Efron and R. J. Tibshirani, An Introduction to the Bootstrap,
+       Chapman & Hall/CRC, Boca Raton, FL, USA (1993)
+    .. [2] Nathaniel E. Helwig, "Bootstrap Confidence Intervals",
+       http://users.stat.umn.edu/~helwig/notes/bootci-Notes.pdf
+    .. [3] Bootstrapping (statistics), Wikipedia,
+       https://en.wikipedia.org/wiki/Bootstrapping_%28statistics%29
+
+    Examples
+    --------
+    Suppose we have sampled data from an unknown distribution.
+
+    >>> import numpy as np
+    >>> rng = np.random.default_rng()
+    >>> from scipy.stats import norm
+    >>> dist = norm(loc=2, scale=4)  # our "unknown" distribution
+    >>> data = dist.rvs(size=100, random_state=rng)
+
+    We are interested in the standard deviation of the distribution.
+
+    >>> std_true = dist.std()      # the true value of the statistic
+    >>> print(std_true)
+    4.0
+    >>> std_sample = np.std(data)  # the sample statistic
+    >>> print(std_sample)
+    3.9460644295563863
+
+    The bootstrap is used to approximate the variability we would expect if we
+    were to repeatedly sample from the unknown distribution and calculate the
+    statistic of the sample each time. It does this by repeatedly resampling
+    values *from the original sample* with replacement and calculating the
+    statistic of each resample. This results in a "bootstrap distribution" of
+    the statistic.
+
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.stats import bootstrap
+    >>> data = (data,)  # samples must be in a sequence
+    >>> res = bootstrap(data, np.std, confidence_level=0.9, rng=rng)
+    >>> fig, ax = plt.subplots()
+    >>> ax.hist(res.bootstrap_distribution, bins=25)
+    >>> ax.set_title('Bootstrap Distribution')
+    >>> ax.set_xlabel('statistic value')
+    >>> ax.set_ylabel('frequency')
+    >>> plt.show()
+
+    The standard error quantifies this variability. It is calculated as the
+    standard deviation of the bootstrap distribution.
+
+    >>> res.standard_error
+    0.24427002125829136
+    >>> res.standard_error == np.std(res.bootstrap_distribution, ddof=1)
+    True
+
+    The bootstrap distribution of the statistic is often approximately normal
+    with scale equal to the standard error.
+
+    >>> x = np.linspace(3, 5)
+    >>> pdf = norm.pdf(x, loc=std_sample, scale=res.standard_error)
+    >>> fig, ax = plt.subplots()
+    >>> ax.hist(res.bootstrap_distribution, bins=25, density=True)
+    >>> ax.plot(x, pdf)
+    >>> ax.set_title('Normal Approximation of the Bootstrap Distribution')
+    >>> ax.set_xlabel('statistic value')
+    >>> ax.set_ylabel('pdf')
+    >>> plt.show()
+
+    This suggests that we could construct a 90% confidence interval on the
+    statistic based on quantiles of this normal distribution.
+
+    >>> norm.interval(0.9, loc=std_sample, scale=res.standard_error)
+    (3.5442759991341726, 4.3478528599786)
+
+    Due to central limit theorem, this normal approximation is accurate for a
+    variety of statistics and distributions underlying the samples; however,
+    the approximation is not reliable in all cases. Because `bootstrap` is
+    designed to work with arbitrary underlying distributions and statistics,
+    it uses more advanced techniques to generate an accurate confidence
+    interval.
+
+    >>> print(res.confidence_interval)
+    ConfidenceInterval(low=3.57655333533867, high=4.382043696342881)
+
+    If we sample from the original distribution 100 times and form a bootstrap
+    confidence interval for each sample, the confidence interval
+    contains the true value of the statistic approximately 90% of the time.
+
+    >>> n_trials = 100
+    >>> ci_contains_true_std = 0
+    >>> for i in range(n_trials):
+    ...    data = (dist.rvs(size=100, random_state=rng),)
+    ...    res = bootstrap(data, np.std, confidence_level=0.9,
+    ...                    n_resamples=999, rng=rng)
+    ...    ci = res.confidence_interval
+    ...    if ci[0] < std_true < ci[1]:
+    ...        ci_contains_true_std += 1
+    >>> print(ci_contains_true_std)
+    88
+
+    Rather than writing a loop, we can also determine the confidence intervals
+    for all 100 samples at once.
+
+    >>> data = (dist.rvs(size=(n_trials, 100), random_state=rng),)
+    >>> res = bootstrap(data, np.std, axis=-1, confidence_level=0.9,
+    ...                 n_resamples=999, rng=rng)
+    >>> ci_l, ci_u = res.confidence_interval
+
+    Here, `ci_l` and `ci_u` contain the confidence interval for each of the
+    ``n_trials = 100`` samples.
+
+    >>> print(ci_l[:5])
+    [3.86401283 3.33304394 3.52474647 3.54160981 3.80569252]
+    >>> print(ci_u[:5])
+    [4.80217409 4.18143252 4.39734707 4.37549713 4.72843584]
+
+    And again, approximately 90% contain the true value, ``std_true = 4``.
+
+    >>> print(np.sum((ci_l < std_true) & (std_true < ci_u)))
+    93
+
+    `bootstrap` can also be used to estimate confidence intervals of
+    multi-sample statistics. For example, to get a confidence interval
+    for the difference between means, we write a function that accepts
+    two sample arguments and returns only the statistic. The use of the
+    ``axis`` argument ensures that all mean calculations are perform in
+    a single vectorized call, which is faster than looping over pairs
+    of resamples in Python.
+
+    >>> def my_statistic(sample1, sample2, axis=-1):
+    ...     mean1 = np.mean(sample1, axis=axis)
+    ...     mean2 = np.mean(sample2, axis=axis)
+    ...     return mean1 - mean2
+
+    Here, we use the 'percentile' method with the default 95% confidence level.
+
+    >>> sample1 = norm.rvs(scale=1, size=100, random_state=rng)
+    >>> sample2 = norm.rvs(scale=2, size=100, random_state=rng)
+    >>> data = (sample1, sample2)
+    >>> res = bootstrap(data, my_statistic, method='basic', rng=rng)
+    >>> print(my_statistic(sample1, sample2))
+    0.16661030792089523
+    >>> print(res.confidence_interval)
+    ConfidenceInterval(low=-0.29087973240818693, high=0.6371338699912273)
+
+    The bootstrap estimate of the standard error is also available.
+
+    >>> print(res.standard_error)
+    0.238323948262459
+
+    Paired-sample statistics work, too. For example, consider the Pearson
+    correlation coefficient.
+
+    >>> from scipy.stats import pearsonr
+    >>> n = 100
+    >>> x = np.linspace(0, 10, n)
+    >>> y = x + rng.uniform(size=n)
+    >>> print(pearsonr(x, y)[0])  # element 0 is the statistic
+    0.9954306665125647
+
+    We wrap `pearsonr` so that it returns only the statistic, ensuring
+    that we use the `axis` argument because it is available.
+
+    >>> def my_statistic(x, y, axis=-1):
+    ...     return pearsonr(x, y, axis=axis)[0]
+
+    We call `bootstrap` using ``paired=True``.
+
+    >>> res = bootstrap((x, y), my_statistic, paired=True, rng=rng)
+    >>> print(res.confidence_interval)
+    ConfidenceInterval(low=0.9941504301315878, high=0.996377412215445)
+
+    The result object can be passed back into `bootstrap` to perform additional
+    resampling:
+
+    >>> len(res.bootstrap_distribution)
+    9999
+    >>> res = bootstrap((x, y), my_statistic, paired=True,
+    ...                 n_resamples=1000, rng=rng,
+    ...                 bootstrap_result=res)
+    >>> len(res.bootstrap_distribution)
+    10999
+
+    or to change the confidence interval options:
+
+    >>> res2 = bootstrap((x, y), my_statistic, paired=True,
+    ...                  n_resamples=0, rng=rng, bootstrap_result=res,
+    ...                  method='percentile', confidence_level=0.9)
+    >>> np.testing.assert_equal(res2.bootstrap_distribution,
+    ...                         res.bootstrap_distribution)
+    >>> res.confidence_interval
+    ConfidenceInterval(low=0.9941574828235082, high=0.9963781698210212)
+
+    without repeating computation of the original bootstrap distribution.
+
+    """
+    # Input validation
+    args = _bootstrap_iv(data, statistic, vectorized, paired, axis,
+                         confidence_level, alternative, n_resamples, batch,
+                         method, bootstrap_result, rng)
+    (data, statistic, vectorized, paired, axis, confidence_level,
+     alternative, n_resamples, batch, method, bootstrap_result,
+     rng, xp) = args
+
+    theta_hat_b = ([] if bootstrap_result is None
+                   else [bootstrap_result.bootstrap_distribution])
+
+    batch_nominal = batch or n_resamples or 1
+
+    for k in range(0, n_resamples, batch_nominal):
+        batch_actual = min(batch_nominal, n_resamples-k)
+        # Generate resamples
+        resampled_data = []
+        for sample in data:
+            resample = _bootstrap_resample(sample, n_resamples=batch_actual,
+                                           rng=rng, xp=xp)
+            resampled_data.append(resample)
+
+        # Compute bootstrap distribution of statistic
+        theta_hat_b.append(statistic(*resampled_data, axis=-1))
+    theta_hat_b = xp.concat(theta_hat_b, axis=-1)
+
+    # Calculate percentile interval
+    alpha = ((1 - confidence_level)/2 if alternative == 'two-sided'
+             else (1 - confidence_level))
+    if method == 'bca':
+        interval = _bca_interval(data, statistic, axis=-1, alpha=alpha,
+                                 theta_hat_b=theta_hat_b, batch=batch, xp=xp)[:2]
+    else:
+        alpha = xp.asarray(alpha, dtype=theta_hat_b.dtype,
+                           device=xp_device(theta_hat_b))
+        interval = alpha, 1 - alpha
+
+    # Calculate confidence interval of statistic
+    interval = xp.stack(interval, axis=-1)
+    ci = stats.quantile(theta_hat_b, interval, axis=-1)
+    if not is_lazy_array(ci) and xp.any(xp.isnan(ci)):
+        msg = (
+            "The BCa confidence interval cannot be calculated. "
+            "This problem is known to occur when the distribution "
+            "is degenerate or the statistic is np.min."
+        )
+        warnings.warn(DegenerateDataWarning(msg), stacklevel=2)
+
+    ci_l = ci[..., 0]
+    ci_u = ci[..., 1]
+
+    if method == 'basic':  # see [3]
+        theta_hat = statistic(*data, axis=-1)
+        ci_l, ci_u = 2*theta_hat - ci_u, 2*theta_hat - ci_l
+
+    if alternative == 'less':
+        ci_l = xp.full_like(ci_l, -xp.inf)
+    elif alternative == 'greater':
+        ci_u = xp.full_like(ci_u, xp.inf)
+
+    standard_error = xp.std(theta_hat_b, correction=1, axis=-1)
+
+    ci_l = ci_l[()] if ci_l.ndim == 0 else ci_l
+    ci_u = ci_u[()] if ci_u.ndim == 0 else ci_u
+    standard_error = standard_error[()] if standard_error.ndim == 0 else standard_error
+
+    return BootstrapResult(confidence_interval=ConfidenceInterval(ci_l, ci_u),
+                           bootstrap_distribution=theta_hat_b,
+                           standard_error=standard_error)
+
+
+def _monte_carlo_test_iv(data, rvs, statistic, vectorized, n_resamples,
+                         batch, alternative, axis):
+    """Input validation for `monte_carlo_test`."""
+    axis_int = int(axis)
+    if axis != axis_int:
+        raise ValueError("`axis` must be an integer.")
+
+    if vectorized not in {True, False, None}:
+        raise ValueError("`vectorized` must be `True`, `False`, or `None`.")
+
+    if not isinstance(rvs, Sequence):
+        rvs = (rvs,)
+        data = (data,)
+    for rvs_i in rvs:
+        if not callable(rvs_i):
+            raise TypeError("`rvs` must be callable or sequence of callables.")
+
+    # At this point, `data` should be a sequence
+    # If it isn't, the user passed a sequence for `rvs` but not `data`
+    message = "If `rvs` is a sequence, `len(rvs)` must equal `len(data)`."
+    try:
+        len(data)
+    except TypeError as e:
+        raise ValueError(message) from e
+    if not len(rvs) == len(data):
+        raise ValueError(message)
+
+    if not callable(statistic):
+        raise TypeError("`statistic` must be callable.")
+
+    if vectorized is None:
+        try:
+            signature = inspect.signature(statistic).parameters
+        except ValueError as e:
+            message = (f"Signature inspection of {statistic=} failed; "
+                       "pass `vectorize` explicitly.")
+            raise ValueError(message) from e
+        vectorized = 'axis' in signature
+
+    xp = array_namespace(*data)
+    dtype = xp_result_type(*data, force_floating=True, xp=xp)
+
+    if not vectorized:
+        if is_numpy(xp):
+            statistic_vectorized = _vectorize_statistic(statistic)
+        else:
+            message = ("`statistic` must be vectorized (i.e. support an `axis` "
+                       f"argument) when `data` contains {xp.__name__} arrays.")
+            raise ValueError(message)
+    else:
+        statistic_vectorized = statistic
+
+    data = _broadcast_arrays(data, axis, xp=xp)
+    data_iv = []
+    for sample in data:
+        sample = xp.broadcast_to(sample, (1,)) if sample.ndim == 0 else sample
+        sample = xp.moveaxis(sample, axis_int, -1)
+        data_iv.append(sample)
+
+    n_resamples_int = int(n_resamples)
+    if n_resamples != n_resamples_int or n_resamples_int <= 0:
+        raise ValueError("`n_resamples` must be a positive integer.")
+
+    if batch is None:
+        batch_iv = batch
+    else:
+        batch_iv = int(batch)
+        if batch != batch_iv or batch_iv <= 0:
+            raise ValueError("`batch` must be a positive integer or None.")
+
+    alternatives = {'two-sided', 'greater', 'less'}
+    alternative = alternative.lower()
+    if alternative not in alternatives:
+        raise ValueError(f"`alternative` must be in {alternatives}")
+
+    return (data_iv, rvs, statistic_vectorized, vectorized, n_resamples_int,
+            batch_iv, alternative, axis_int, dtype, xp)
+
+
+@dataclass
+class MonteCarloTestResult:
+    """Result object returned by `scipy.stats.monte_carlo_test`.
+
+    Attributes
+    ----------
+    statistic : float or ndarray
+        The observed test statistic of the sample.
+    pvalue : float or ndarray
+        The p-value for the given alternative.
+    null_distribution : ndarray
+        The values of the test statistic generated under the null
+        hypothesis.
+    """
+    statistic: float | np.ndarray
+    pvalue: float | np.ndarray
+    null_distribution: np.ndarray
+
+
+@xp_capabilities()
+@_rename_parameter('sample', 'data')
+def monte_carlo_test(data, rvs, statistic, *, vectorized=None,
+                     n_resamples=9999, batch=None, alternative="two-sided",
+                     axis=0):
+    r"""Perform a Monte Carlo hypothesis test.
+
+    `data` contains a sample or a sequence of one or more samples. `rvs`
+    specifies the distribution(s) of the sample(s) in `data` under the null
+    hypothesis. The value of `statistic` for the given `data` is compared
+    against a Monte Carlo null distribution: the value of the statistic for
+    each of `n_resamples` sets of samples generated using `rvs`. This gives
+    the p-value, the probability of observing such an extreme value of the
+    test statistic under the null hypothesis.
+
+    Parameters
+    ----------
+    data : array-like or sequence of array-like
+        An array or sequence of arrays of observations.
+    rvs : callable or tuple of callables
+        A callable or sequence of callables that generates random variates
+        under the null hypothesis. Each element of `rvs` must be a callable
+        that accepts keyword argument ``size`` (e.g. ``rvs(size=(m, n))``) and
+        returns an N-d array sample of that shape. If `rvs` is a sequence, the
+        number of callables in `rvs` must match the number of samples in
+        `data`, i.e. ``len(rvs) == len(data)``. If `rvs` is a single callable,
+        `data` is treated as a single sample.
+    statistic : callable
+        Statistic for which the p-value of the hypothesis test is to be
+        calculated. `statistic` must be a callable that accepts a sample
+        (e.g. ``statistic(sample)``) or ``len(rvs)`` separate samples (e.g.
+        ``statistic(samples1, sample2)`` if `rvs` contains two callables and
+        `data` contains two samples) and returns the resulting statistic.
+        If `vectorized` is set ``True``, `statistic` must also accept a keyword
+        argument `axis` and be vectorized to compute the statistic along the
+        provided `axis` of the samples in `data`.
+    vectorized : bool, optional
+        If `vectorized` is set ``False``, `statistic` will not be passed
+        keyword argument `axis` and is expected to calculate the statistic
+        only for 1D samples. If ``True``, `statistic` will be passed keyword
+        argument `axis` and is expected to calculate the statistic along `axis`
+        when passed ND sample arrays. If ``None`` (default), `vectorized`
+        will be set ``True`` if ``axis`` is a parameter of `statistic`. Use of
+        a vectorized statistic typically reduces computation time.
+    n_resamples : int, default: 9999
+        Number of samples drawn from each of the callables of `rvs`.
+        Equivalently, the number statistic values under the null hypothesis
+        used as the Monte Carlo null distribution.
+    batch : int, optional
+        The number of Monte Carlo samples to process in each call to
+        `statistic`. Memory usage is O( `batch` * ``sample.size[axis]`` ). Default
+        is ``None``, in which case `batch` equals `n_resamples`.
+    alternative : {'two-sided', 'less', 'greater'}
+        The alternative hypothesis for which the p-value is calculated.
+        For each alternative, the p-value is defined as follows.
+
+        - ``'greater'`` : the percentage of the null distribution that is
+          greater than or equal to the observed value of the test statistic.
+        - ``'less'`` : the percentage of the null distribution that is
+          less than or equal to the observed value of the test statistic.
+        - ``'two-sided'`` : twice the smaller of the p-values above.
+
+    axis : int, default: 0
+        The axis of `data` (or each sample within `data`) over which to
+        calculate the statistic.
+
+    Returns
+    -------
+    res : MonteCarloTestResult
+        An object with attributes:
+
+        statistic : float or ndarray
+            The test statistic of the observed `data`.
+        pvalue : float or ndarray
+            The p-value for the given alternative.
+        null_distribution : ndarray
+            The values of the test statistic generated under the null
+            hypothesis.
+
+    .. warning::
+        The p-value is calculated by counting the elements of the null
+        distribution that are as extreme or more extreme than the observed
+        value of the statistic. Due to the use of finite precision arithmetic,
+        some statistic functions return numerically distinct values when the
+        theoretical values would be exactly equal. In some cases, this could
+        lead to a large error in the calculated p-value. `monte_carlo_test`
+        guards against this by considering elements in the null distribution
+        that are "close" (within a relative tolerance of 100 times the
+        floating point epsilon of inexact dtypes) to the observed
+        value of the test statistic as equal to the observed value of the
+        test statistic. However, the user is advised to inspect the null
+        distribution to assess whether this method of comparison is
+        appropriate, and if not, calculate the p-value manually.
+
+    References
+    ----------
+
+    .. [1] B. Phipson and G. K. Smyth. "Permutation P-values Should Never Be
+       Zero: Calculating Exact P-values When Permutations Are Randomly Drawn."
+       Statistical Applications in Genetics and Molecular Biology 9.1 (2010).
+
+    Examples
+    --------
+
+    Suppose we wish to test whether a small sample has been drawn from a normal
+    distribution. We decide that we will use the skew of the sample as a
+    test statistic, and we will consider a p-value of 0.05 to be statistically
+    significant.
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> def statistic(x, axis):
+    ...     return stats.skew(x, axis)
+
+    After collecting our data, we calculate the observed value of the test
+    statistic.
+
+    >>> rng = np.random.default_rng()
+    >>> x = stats.skewnorm.rvs(a=1, size=50, random_state=rng)
+    >>> statistic(x, axis=0)
+    0.12457412450240658
+
+    To determine the probability of observing such an extreme value of the
+    skewness by chance if the sample were drawn from the normal distribution,
+    we can perform a Monte Carlo hypothesis test. The test will draw many
+    samples at random from their normal distribution, calculate the skewness
+    of each sample, and compare our original skewness against this
+    distribution to determine an approximate p-value.
+
+    >>> from scipy.stats import monte_carlo_test
+    >>> # because our statistic is vectorized, we pass `vectorized=True`
+    >>> rvs = lambda size: stats.norm.rvs(size=size, random_state=rng)
+    >>> res = monte_carlo_test(x, rvs, statistic, vectorized=True)
+    >>> print(res.statistic)
+    0.12457412450240658
+    >>> print(res.pvalue)
+    0.7012
+
+    The probability of obtaining a test statistic less than or equal to the
+    observed value under the null hypothesis is ~70%. This is greater than
+    our chosen threshold of 5%, so we cannot consider this to be significant
+    evidence against the null hypothesis.
+
+    Note that this p-value essentially matches that of
+    `scipy.stats.skewtest`, which relies on an asymptotic distribution of a
+    test statistic based on the sample skewness.
+
+    >>> stats.skewtest(x).pvalue
+    0.6892046027110614
+
+    This asymptotic approximation is not valid for small sample sizes, but
+    `monte_carlo_test` can be used with samples of any size.
+
+    >>> x = stats.skewnorm.rvs(a=1, size=7, random_state=rng)
+    >>> # stats.skewtest(x) would produce an error due to small sample
+    >>> res = monte_carlo_test(x, rvs, statistic, vectorized=True)
+
+    The Monte Carlo distribution of the test statistic is provided for
+    further investigation.
+
+    >>> import matplotlib.pyplot as plt
+    >>> fig, ax = plt.subplots()
+    >>> ax.hist(res.null_distribution, bins=50)
+    >>> ax.set_title("Monte Carlo distribution of test statistic")
+    >>> ax.set_xlabel("Value of Statistic")
+    >>> ax.set_ylabel("Frequency")
+    >>> plt.show()
+
+    """
+    args = _monte_carlo_test_iv(data, rvs, statistic, vectorized,
+                                n_resamples, batch, alternative, axis)
+    (data, rvs, statistic, vectorized, n_resamples,
+     batch, alternative, axis, dtype, xp) = args
+
+    # Some statistics return plain floats; ensure they're at least a NumPy float
+    observed = xp.asarray(statistic(*data, axis=-1))
+    observed = observed[()] if observed.ndim == 0 else observed
+
+    n_observations = [sample.shape[-1] for sample in data]
+    batch_nominal = batch or n_resamples
+    null_distribution = []
+    for k in range(0, n_resamples, batch_nominal):
+        batch_actual = min(batch_nominal, n_resamples - k)
+        resamples = [rvs_i(size=(batch_actual, n_observations_i))
+                     for rvs_i, n_observations_i in zip(rvs, n_observations)]
+        null_distribution.append(statistic(*resamples, axis=-1))
+    null_distribution = xp.concat(null_distribution)
+    null_distribution = xp.reshape(null_distribution, (-1,) + (1,)*observed.ndim)
+
+    # relative tolerance for detecting numerically distinct but
+    # theoretically equal values in the null distribution
+    eps =  (0 if not xp.isdtype(observed.dtype, ('real floating'))
+            else xp.finfo(observed.dtype).eps*100)
+    gamma = xp.abs(eps * observed)
+
+    def less(null_distribution, observed):
+        cmps = null_distribution <= observed + gamma
+        cmps = xp.asarray(cmps, dtype=dtype)
+        pvalues = (xp.sum(cmps, axis=0, dtype=dtype) + 1.) / (n_resamples + 1.)
+        return pvalues
+
+    def greater(null_distribution, observed):
+        cmps = null_distribution >= observed - gamma
+        cmps = xp.asarray(cmps, dtype=dtype)
+        pvalues = (xp.sum(cmps, axis=0, dtype=dtype) + 1.) / (n_resamples + 1.)
+        return pvalues
+
+    def two_sided(null_distribution, observed):
+        pvalues_less = less(null_distribution, observed)
+        pvalues_greater = greater(null_distribution, observed)
+        pvalues = xp.minimum(pvalues_less, pvalues_greater) * 2
+        return pvalues
+
+    compare = {"less": less,
+               "greater": greater,
+               "two-sided": two_sided}
+
+    pvalues = compare[alternative](null_distribution, observed)
+    pvalues = xp.clip(pvalues, 0., 1.)
+
+    return MonteCarloTestResult(observed, pvalues, null_distribution)
+
+
+@dataclass
+class PowerResult:
+    """Result object returned by `scipy.stats.power`.
+
+    Attributes
+    ----------
+    power : float or ndarray
+        The estimated power.
+    pvalues : float or ndarray
+        The simulated p-values.
+    """
+    power: float | np.ndarray
+    pvalues: float | np.ndarray
+
+
+def _wrap_kwargs(fun):
+    """Wrap callable to accept arbitrary kwargs and ignore unused ones"""
+
+    try:
+        keys = set(inspect.signature(fun).parameters.keys())
+    except ValueError:
+        # NumPy Generator methods can't be inspected
+        keys = {'size'}
+
+    # Set keys=keys/fun=fun to avoid late binding gotcha
+    def wrapped_rvs_i(*args, keys=keys, fun=fun, **all_kwargs):
+        kwargs = {key: val for key, val in all_kwargs.items()
+                  if key in keys}
+        return fun(*args, **kwargs)
+    return wrapped_rvs_i
+
+
+def _power_iv(rvs, test, n_observations, significance, vectorized,
+              n_resamples, batch, kwargs):
+    """Input validation for `monte_carlo_test`."""
+    if vectorized not in {True, False, None}:
+        raise ValueError("`vectorized` must be `True`, `False`, or `None`.")
+
+    if not isinstance(rvs, Sequence):
+        rvs = (rvs,)
+        n_observations = (n_observations,)
+    for rvs_i in rvs:
+        if not callable(rvs_i):
+            raise TypeError("`rvs` must be callable or sequence of callables.")
+
+    if not len(rvs) == len(n_observations):
+        message = ("If `rvs` is a sequence, `len(rvs)` "
+                   "must equal `len(n_observations)`.")
+        raise ValueError(message)
+
+    kwargs = dict() if kwargs is None else kwargs
+    if not isinstance(kwargs, dict):
+        raise TypeError("`kwargs` must be a dictionary that maps keywords to arrays.")
+
+    vals = kwargs.values()
+    keys = kwargs.keys()
+
+    xp = array_namespace(*n_observations, significance, *vals)
+
+    significance = xp.asarray(significance)
+    if not xp.isdtype(significance.dtype, "real floating"):
+        raise ValueError("`significance` must be of floating point dtype.")
+
+    if is_lazy_array(significance):
+        significance = xp.where((significance < 0.) | (significance > 1.),
+                                xp.nan, significance)
+    elif xp.min(significance) < 0. or xp.max(significance) > 1.:
+        raise ValueError("All elements of `significance` must be between 0. and 1.")
+
+    # Wrap callables to ignore unused keyword arguments
+    wrapped_rvs = [_wrap_kwargs(rvs_i) for rvs_i in rvs]
+
+    # Broadcast, then ravel nobs/kwarg combinations. In the end,
+    # `nobs` and `vals` have shape (# of combinations, number of variables)
+    # todo: find a better way to do this without combining arrays
+    tmp = xp.stack(xp.broadcast_arrays(*n_observations, *vals))
+    shape = tmp.shape
+    if tmp.ndim == 1:
+        tmp = xp.expand_dims(tmp, axis=0)
+    else:
+        tmp = xp.reshape(tmp, (shape[0], -1)).T
+    nobs, vals = tmp[:, :len(rvs)], tmp[:, len(rvs):]
+    integer_dtype = xp_result_type(*n_observations, xp=xp)
+    nobs = xp.astype(nobs, integer_dtype)
+
+    if not callable(test):
+        raise TypeError("`test` must be callable.")
+
+    if vectorized is None:
+        vectorized = 'axis' in inspect.signature(test).parameters
+
+    test_vectorized = test
+    if not vectorized:
+        if not is_numpy(xp):
+            message = (f"When using array library {xp.__name__}, `test` must be "
+                       "be vectorized and accept argument `axis`.")
+            raise TypeError(message)
+
+        test_vectorized = _vectorize_statistic(test)
+
+    # Wrap `test` function to ignore unused kwargs
+    test_vectorized = _wrap_kwargs(test_vectorized)
+
+    n_resamples_int = int(n_resamples)
+    if n_resamples != n_resamples_int or n_resamples_int <= 0:
+        raise ValueError("`n_resamples` must be a positive integer.")
+
+    if batch is None:
+        batch_iv = batch
+    else:
+        batch_iv = int(batch)
+        if batch != batch_iv or batch_iv <= 0:
+            raise ValueError("`batch` must be a positive integer or None.")
+
+    return (wrapped_rvs, test_vectorized, nobs, significance, vectorized,
+            n_resamples_int, batch_iv, vals, keys, shape[1:], xp)
+
+
+@xp_capabilities(skip_backends=[('dask.array', 'just because')],
+                 jax_jit=False)  # some problem with batch looping
+def power(test, rvs, n_observations, *, significance=0.01, vectorized=None,
+          n_resamples=10000, batch=None, kwargs=None):
+    r"""Simulate the power of a hypothesis test under an alternative hypothesis.
+
+    Parameters
+    ----------
+    test : callable
+        Hypothesis test for which the power is to be simulated.
+        `test` must be a callable that accepts a sample (e.g. ``test(sample)``)
+        or ``len(rvs)`` separate samples (e.g. ``test(samples1, sample2)`` if
+        `rvs` contains two callables and `n_observations` contains two values)
+        and returns the p-value of the test.
+        If `vectorized` is set to ``True``, `test` must also accept a keyword
+        argument `axis` and be vectorized to perform the test along the
+        provided `axis` of the samples.
+        Any callable from `scipy.stats` with an `axis` argument that returns an
+        object with a `pvalue` attribute is also acceptable.
+    rvs : callable or tuple of callables
+        A callable or sequence of callables that generate(s) random variates
+        under the alternative hypothesis. Each element of `rvs` must accept
+        keyword argument ``size`` (e.g. ``rvs(size=(m, n))``) and return an
+        N-d array of that shape. If `rvs` is a sequence, the number of callables
+        in `rvs` must match the number of elements of `n_observations`, i.e.
+        ``len(rvs) == len(n_observations)``. If `rvs` is a single callable,
+        `n_observations` is treated as a single element.
+    n_observations : tuple of ints or tuple of int arrays
+        If a sequence of ints, each is the sizes of a sample to be passed to `test`.
+        If a sequence of integer arrays, the power is simulated for each
+        set of corresponding sample sizes. See Examples.
+    significance : float or array_like of floats, default: 0.01
+        The threshold for significance; i.e., the p-value below which the
+        hypothesis test results will be considered as evidence against the null
+        hypothesis. Equivalently, the acceptable rate of Type I error under
+        the null hypothesis. If an array, the power is simulated for each
+        significance threshold.
+    vectorized : bool, optional
+        If `vectorized` is set to ``False``, `test` will not be passed keyword
+        argument `axis` and is expected to perform the test only for 1D samples.
+        If ``True``, `test` will be passed keyword argument `axis` and is
+        expected to perform the test along `axis` when passed N-D sample arrays.
+        If ``None`` (default), `vectorized` will be set ``True`` if ``axis`` is
+        a parameter of `test`. Use of a vectorized test typically reduces
+        computation time.
+    n_resamples : int, default: 10000
+        Number of samples drawn from each of the callables of `rvs`.
+        Equivalently, the number tests performed under the alternative
+        hypothesis to approximate the power.
+    batch : int, optional
+        The number of samples to process in each call to `test`. Memory usage is
+        proportional to the product of `batch` and the largest sample size. Default
+        is ``None``, in which case `batch` equals `n_resamples`.
+    kwargs : dict, optional
+        Keyword arguments to be passed to `rvs` and/or `test` callables.
+        Introspection is used to determine which keyword arguments may be
+        passed to each callable.
+        The value corresponding with each keyword must be an array.
+        Arrays must be broadcastable with one another and with each array in
+        `n_observations`. The power is simulated for each set of corresponding
+        sample sizes and arguments. See Examples.
+
+    Returns
+    -------
+    res : PowerResult
+        An object with attributes:
+
+        power : float or ndarray
+            The estimated power against the alternative.
+        pvalues : ndarray
+            The p-values observed under the alternative hypothesis.
+
+    Notes
+    -----
+    The power is simulated as follows:
+
+    - Draw many random samples (or sets of samples), each of the size(s)
+      specified by `n_observations`, under the alternative specified by
+      `rvs`.
+    - For each sample (or set of samples), compute the p-value according to
+      `test`. These p-values are recorded in the ``pvalues`` attribute of
+      the result object.
+    - Compute the proportion of p-values that are less than the `significance`
+      level. This is the power recorded in the ``power`` attribute of the
+      result object.
+
+    Suppose that `significance` is an array with shape ``shape1``, the elements
+    of `kwargs` and `n_observations` are mutually broadcastable to shape ``shape2``,
+    and `test` returns an array of p-values of shape ``shape3``. Then the result
+    object ``power`` attribute will be of shape ``shape1 + shape2 + shape3``, and
+    the ``pvalues`` attribute will be of shape ``shape2 + shape3 + (n_resamples,)``.
+
+    Examples
+    --------
+    Suppose we wish to simulate the power of the independent sample t-test
+    under the following conditions:
+
+    - The first sample has 10 observations drawn from a normal distribution
+      with mean 0.
+    - The second sample has 12 observations drawn from a normal distribution
+      with mean 1.0.
+    - The threshold on p-values for significance is 0.05.
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> rng = np.random.default_rng(2549598345528)
+    >>>
+    >>> test = stats.ttest_ind
+    >>> n_observations = (10, 12)
+    >>> rvs1 = rng.normal
+    >>> rvs2 = lambda size: rng.normal(loc=1, size=size)
+    >>> rvs = (rvs1, rvs2)
+    >>> res = stats.power(test, rvs, n_observations, significance=0.05)
+    >>> res.power
+    0.6116
+
+    With samples of size 10 and 12, respectively, the power of the t-test
+    with a significance threshold of 0.05 is approximately 60% under the chosen
+    alternative. We can investigate the effect of sample size on the power
+    by passing sample size arrays.
+
+    >>> import matplotlib.pyplot as plt
+    >>> nobs_x = np.arange(5, 21)
+    >>> nobs_y = nobs_x
+    >>> n_observations = (nobs_x, nobs_y)
+    >>> res = stats.power(test, rvs, n_observations, significance=0.05)
+    >>> ax = plt.subplot()
+    >>> ax.plot(nobs_x, res.power)
+    >>> ax.set_xlabel('Sample Size')
+    >>> ax.set_ylabel('Simulated Power')
+    >>> ax.set_title('Simulated Power of `ttest_ind` with Equal Sample Sizes')
+    >>> plt.show()
+
+    Alternatively, we can investigate the impact that effect size has on the power.
+    In this case, the effect size is the location of the distribution underlying
+    the second sample.
+
+    >>> n_observations = (10, 12)
+    >>> loc = np.linspace(0, 1, 20)
+    >>> rvs2 = lambda size, loc: rng.normal(loc=loc, size=size)
+    >>> rvs = (rvs1, rvs2)
+    >>> res = stats.power(test, rvs, n_observations, significance=0.05,
+    ...                   kwargs={'loc': loc})
+    >>> ax = plt.subplot()
+    >>> ax.plot(loc, res.power)
+    >>> ax.set_xlabel('Effect Size')
+    >>> ax.set_ylabel('Simulated Power')
+    >>> ax.set_title('Simulated Power of `ttest_ind`, Varying Effect Size')
+    >>> plt.show()
+
+    We can also use `power` to estimate the Type I error rate (also referred to by the
+    ambiguous term "size") of a test and assess whether it matches the nominal level.
+    For example, the null hypothesis of `jarque_bera` is that the sample was drawn from
+    a distribution with the same skewness and kurtosis as the normal distribution. To
+    estimate the Type I error rate, we can consider the null hypothesis to be a true
+    *alternative* hypothesis and calculate the power.
+
+    >>> test = stats.jarque_bera
+    >>> n_observations = 10
+    >>> rvs = rng.normal
+    >>> significance = np.linspace(0.0001, 0.1, 1000)
+    >>> res = stats.power(test, rvs, n_observations, significance=significance)
+    >>> size = res.power
+
+    As shown below, the Type I error rate of the test is far below the nominal level
+    for such a small sample, as mentioned in its documentation.
+
+    >>> ax = plt.subplot()
+    >>> ax.plot(significance, size)
+    >>> ax.plot([0, 0.1], [0, 0.1], '--')
+    >>> ax.set_xlabel('nominal significance level')
+    >>> ax.set_ylabel('estimated test size (Type I error rate)')
+    >>> ax.set_title('Estimated test size vs nominal significance level')
+    >>> ax.set_aspect('equal', 'box')
+    >>> ax.legend(('`ttest_1samp`', 'ideal test'))
+    >>> plt.show()
+
+    As one might expect from such a conservative test, the power is quite low with
+    respect to some alternatives. For example, the power of the test under the
+    alternative that the sample was drawn from the Laplace distribution may not
+    be much greater than the Type I error rate.
+
+    >>> rvs = rng.laplace
+    >>> significance = np.linspace(0.0001, 0.1, 1000)
+    >>> res = stats.power(test, rvs, n_observations, significance=0.05)
+    >>> print(res.power)
+    0.0587
+
+    This is not a mistake in SciPy's implementation; it is simply due to the fact
+    that the null distribution of the test statistic is derived under the assumption
+    that the sample size is large (i.e. approaches infinity), and this asymptotic
+    approximation is not accurate for small samples. In such cases, resampling
+    and Monte Carlo methods (e.g. `permutation_test`, `goodness_of_fit`,
+    `monte_carlo_test`) may be more appropriate.
+
+    """
+    tmp = _power_iv(rvs, test, n_observations, significance,
+                    vectorized, n_resamples, batch, kwargs)
+    (rvs, test, nobs, significance,
+     vectorized, n_resamples, batch, args, kwds, shape, xp) = tmp
+
+    batch_nominal = batch or n_resamples
+    pvalues = []  # results of various nobs/kwargs combinations
+    for i in range(nobs.shape[0]):
+        nobs_i, args_i = nobs[i, ...], args[i, ...]
+        kwargs_i = dict(zip(kwds, args_i))
+        pvalues_i = []  # results of batches; fixed nobs/kwargs combination
+        for k in range(0, n_resamples, batch_nominal):
+            batch_actual = min(batch_nominal, n_resamples - k)
+            resamples = [rvs_j(size=(batch_actual, int(nobs_ij)), **kwargs_i)
+                         for rvs_j, nobs_ij in zip(rvs, nobs_i)]
+            res = test(*resamples, **kwargs_i, axis=-1)
+            p = getattr(res, 'pvalue', res)
+            pvalues_i.append(p)
+        # Concatenate results from batches
+        pvalues_i = xp.concat(pvalues_i, axis=-1)
+        pvalues.append(pvalues_i)
+    # `test` can return result with array of p-values
+    shape += pvalues_i.shape[:-1]
+    # Concatenate results from various nobs/kwargs combinations
+    pvalues = xp.concat(pvalues, axis=0)
+    # nobs/kwargs arrays were raveled to single axis; unravel
+    pvalues = xp.reshape(pvalues, shape + (-1,))
+    if significance.ndim > 0:
+        newdims = tuple(range(significance.ndim, pvalues.ndim + significance.ndim))
+        significance = xpx.expand_dims(significance, axis=newdims)
+
+    float_dtype = xp_result_type(significance, pvalues, xp=xp)
+    powers = xp.mean(xp.astype(pvalues < significance, float_dtype), axis=-1)
+
+    return PowerResult(power=powers, pvalues=pvalues)
+
+
+@dataclass
+class PermutationTestResult:
+    """Result object returned by `scipy.stats.permutation_test`.
+
+    Attributes
+    ----------
+    statistic : float or ndarray
+        The observed test statistic of the data.
+    pvalue : float or ndarray
+        The p-value for the given alternative.
+    null_distribution : ndarray
+        The values of the test statistic generated under the null
+        hypothesis.
+    """
+    statistic: float | np.ndarray
+    pvalue: float | np.ndarray
+    null_distribution: np.ndarray
+
+
+def _all_partitions_concatenated(ns):
+    """
+    Generate all partitions of indices of groups of given sizes, concatenated
+
+    `ns` is an iterable of ints.
+    """
+    def all_partitions(z, n):
+        for c in combinations(z, n):
+            x0 = set(c)
+            x1 = z - x0
+            yield [x0, x1]
+
+    def all_partitions_n(z, ns):
+        if len(ns) == 0:
+            yield [z]
+            return
+        for c in all_partitions(z, ns[0]):
+            for d in all_partitions_n(c[1], ns[1:]):
+                yield c[0:1] + d
+
+    z = set(range(np.sum(ns)))
+    for partitioning in all_partitions_n(z, ns[:]):
+        x = np.concatenate([list(partition)
+                            for partition in partitioning]).astype(int)
+        yield x
+
+
+def _batch_generator(iterable, batch):
+    """A generator that yields batches of elements from an iterable"""
+    iterator = iter(iterable)
+    if batch <= 0:
+        raise ValueError("`batch` must be positive.")
+    z = [item for i, item in zip(range(batch), iterator)]
+    while z:  # we don't want StopIteration without yielding an empty list
+        yield z
+        z = [item for i, item in zip(range(batch), iterator)]
+
+
+def _pairings_permutations_gen(n_permutations, n_samples, n_obs_sample, batch,
+                               rng):
+    # Returns a generator that yields arrays of size
+    # `(batch, n_samples, n_obs_sample)`.
+    # Each row is an independent permutation of indices 0 to `n_obs_sample`.
+    batch = min(batch, n_permutations)
+
+    if hasattr(rng, 'permuted'):
+        def batched_perm_generator():
+            indices = np.arange(n_obs_sample)
+            indices = np.tile(indices, (batch, n_samples, 1))
+            for k in range(0, n_permutations, batch):
+                batch_actual = min(batch, n_permutations-k)
+                # Don't permute in place, otherwise results depend on `batch`
+                permuted_indices = rng.permuted(indices, axis=-1)
+                yield permuted_indices[:batch_actual]
+    else:  # RandomState and early Generators don't have `permuted`
+        def batched_perm_generator():
+            for k in range(0, n_permutations, batch):
+                batch_actual = min(batch, n_permutations-k)
+                size = (batch_actual, n_samples, n_obs_sample)
+                x = rng.random(size=size)
+                yield np.argsort(x, axis=-1)[:batch_actual]
+
+    return batched_perm_generator()
+
+
+def _calculate_null_both(data, statistic, n_permutations, batch,
+                         rng=None, *, xp):
+    """
+    Calculate null distribution for independent sample tests.
+    """
+    # compute number of permutations
+    # (distinct partitions of data into samples of these sizes)
+    n_obs_i = [sample.shape[-1] for sample in data]  # observations per sample
+    n_obs_ic = list(accumulate(n_obs_i, initial=0))
+    n_obs = n_obs_ic[-1]  # total number of observations
+    n_max = math.prod([math.comb(n, k) for n, k in zip(n_obs_ic[1:], n_obs_ic[:-1])])
+
+    # perm_generator is an iterator that produces permutations of indices
+    # from 0 to n_obs. We'll concatenate the samples, use these indices to
+    # permute the data, then split the samples apart again.
+    if n_permutations >= n_max:
+        exact_test = True
+        n_permutations = n_max
+        perm_generator = _all_partitions_concatenated(n_obs_i)
+    else:
+        exact_test = False
+        # Neither RandomState.permutation nor Generator.permutation
+        # can permute axis-slices independently. If this feature is
+        # added in the future, batches of the desired size should be
+        # generated in a single call.
+        perm_generator = (rng.permutation(n_obs)
+                          for i in range(n_permutations))
+
+    batch = batch or int(n_permutations)
+    null_distribution = []
+
+    # First, concatenate all the samples. In batches, permute samples with
+    # indices produced by the `perm_generator`, split them into new samples of
+    # the original sizes, compute the statistic for each batch, and add these
+    # statistic values to the null distribution.
+    data = xp.concat(data, axis=-1)
+    for indices in _batch_generator(perm_generator, batch=batch):
+        # Creating a tensor from a list of numpy.ndarrays is extremely slow...
+        indices = np.asarray(indices)
+        indices = xp.asarray(indices)
+
+        # `indices` is 2D: each row is a permutation of the indices.
+        # We use it to index `data` along its last axis, which corresponds
+        # with observations.
+        # After indexing, the second to last axis of `data_batch` corresponds
+        # with permutations, and the last axis corresponds with observations.
+        # data_batch = data[..., indices]
+        data_batch = _get_from_last_axis(data, indices, xp=xp)
+
+        # Move the permutation axis to the front: we'll concatenate a list
+        # of batched statistic values along this zeroth axis to form the
+        # null distribution.
+        data_batch = xp.moveaxis(data_batch, -2, 0)
+        # data_batch = np.split(data_batch, n_obs_ic[:-1], axis=-1)
+        data_batch = [data_batch[..., i:j] for i, j in zip(n_obs_ic[:-1], n_obs_ic[1:])]
+        null_distribution.append(statistic(*data_batch, axis=-1))
+    null_distribution = xp.concat(null_distribution, axis=0)
+
+    return null_distribution, n_permutations, exact_test
+
+
+def _calculate_null_pairings(data, statistic, n_permutations, batch,
+                             rng=None, *, xp):
+    """
+    Calculate null distribution for association tests.
+    """
+    n_samples = len(data)
+
+    # compute number of permutations (factorial(n) permutations of each sample)
+    n_obs_sample = data[0].shape[-1]  # observations per sample; same for each
+    n_max = math.factorial(n_obs_sample)**n_samples
+
+    # `perm_generator` is an iterator that produces a list of permutations of
+    # indices from 0 to n_obs_sample, one for each sample.
+    if n_permutations >= n_max:
+        exact_test = True
+        n_permutations = n_max
+        batch = batch or int(n_permutations)
+        # Cartesian product of the sets of all permutations of indices
+        perm_generator = product(*(permutations(range(n_obs_sample))
+                                   for i in range(n_samples)))
+        batched_perm_generator = _batch_generator(perm_generator, batch=batch)
+    else:
+        exact_test = False
+        batch = batch or int(n_permutations)
+        # Separate random permutations of indices for each sample.
+        # Again, it would be nice if RandomState/Generator.permutation
+        # could permute each axis-slice separately.
+        args = n_permutations, n_samples, n_obs_sample, batch, rng
+        batched_perm_generator = _pairings_permutations_gen(*args)
+
+    null_distribution = []
+
+    for indices in batched_perm_generator:
+        indices = xp.asarray(indices)
+
+        # `indices` is 3D: the zeroth axis is for permutations, the next is
+        # for samples, and the last is for observations. Swap the first two
+        # to make the zeroth axis correspond with samples, as it does for
+        # `data`.
+        indices = xp_swapaxes(indices, 0, 1, xp=xp)
+
+        # When we're done, `data_batch` will be a list of length `n_samples`.
+        # Each element will be a batch of random permutations of one sample.
+        # The zeroth axis of each batch will correspond with permutations,
+        # and the last will correspond with observations. (This makes it
+        # easy to pass into `statistic`.)
+        data_batch = [None]*n_samples
+        for i in range(n_samples):
+            # data_batch[i] = data[i][..., indices[i]]
+            data_batch[i] = _get_from_last_axis(data[i], indices[i, ...], xp=xp)
+            data_batch[i] = xp.moveaxis(data_batch[i], -2, 0)
+
+        null_distribution.append(statistic(*data_batch, axis=-1))
+    null_distribution = xp.concat(null_distribution, axis=0)
+
+    return null_distribution, n_permutations, exact_test
+
+
+def _calculate_null_samples(data, statistic, n_permutations, batch,
+                            rng=None, *, xp):
+    """
+    Calculate null distribution for paired-sample tests.
+    """
+    n_samples = len(data)
+
+    # By convention, the meaning of the "samples" permutations type for
+    # data with only one sample is to flip the sign of the observations.
+    # Achieve this by adding a second sample - the negative of the original.
+    if n_samples == 1:
+        data = [data[0], -data[0]]
+
+    # The "samples" permutation strategy is the same as the "pairings"
+    # strategy except the roles of samples and observations are flipped.
+    # So swap these axes, then we'll use the function for the "pairings"
+    # strategy to do all the work!
+    data = xp.stack(data, axis=0)
+    data = xp_swapaxes(data, 0, -1, xp=xp)
+
+    # (Of course, the user's statistic doesn't know what we've done here,
+    # so we need to pass it what it's expecting.)
+    def statistic_wrapped(*data, axis):
+        # can we do this without converting back and forth between
+        # array and list?
+        data = xp.stack(data, axis=0)
+        data = xp_swapaxes(data, 0, -1, xp=xp)
+        if n_samples == 1:
+            data = data[0:1, ...]
+        data = [data[i, ...] for i in range(data.shape[0])]
+        return statistic(*data, axis=axis)
+
+    data = [data[i, ...] for i in range(data.shape[0])]
+    return _calculate_null_pairings(data, statistic_wrapped, n_permutations,
+                                    batch, rng, xp=xp)
+
+
+def _permutation_test_iv(data, statistic, permutation_type, vectorized,
+                         n_resamples, batch, alternative, axis, rng):
+    """Input validation for `permutation_test`."""
+    axis_int = int(axis)
+    if axis != axis_int:
+        raise ValueError("`axis` must be an integer.")
+
+    permutation_types = {'samples', 'pairings', 'independent'}
+    permutation_type = permutation_type.lower()
+    if permutation_type not in permutation_types:
+        raise ValueError(f"`permutation_type` must be in {permutation_types}.")
+
+    if vectorized not in {True, False, None}:
+        raise ValueError("`vectorized` must be `True`, `False`, or `None`.")
+
+    if vectorized is None:
+        vectorized = 'axis' in inspect.signature(statistic).parameters
+
+    message = "`data` must be a tuple containing at least two samples"
+    try:
+        if len(data) < 2 and permutation_type == 'independent':
+            raise ValueError(message)
+    except TypeError:
+        raise TypeError(message)
+
+    xp = array_namespace(*data)
+
+    if not vectorized:
+        if not is_numpy(xp):
+            message = (f"When using array library {xp.__name__}, `func` must be "
+                       "vectorized and accept argument `axis`.")
+            raise TypeError(message)
+
+        statistic = _vectorize_statistic(statistic)
+
+    data = _broadcast_arrays(data, axis, xp=xp)
+    data_iv = []
+    for sample in data:
+        sample = xpx.atleast_nd(sample, ndim=1)
+        if sample.shape[axis] <= 1:
+            raise ValueError("each sample in `data` must contain two or more "
+                             "observations along `axis`.")
+        sample = xp.moveaxis(sample, axis_int, -1)
+        data_iv.append(sample)
+
+    n_resamples_int = (int(n_resamples) if not math.isinf(n_resamples)
+                       else xp.inf)
+    if n_resamples != n_resamples_int or n_resamples_int <= 0:
+        raise ValueError("`n_resamples` must be a positive integer.")
+
+    if batch is None:
+        batch_iv = batch
+    else:
+        batch_iv = int(batch)
+        if batch != batch_iv or batch_iv <= 0:
+            raise ValueError("`batch` must be a positive integer or None.")
+
+    alternatives = {'two-sided', 'greater', 'less'}
+    alternative = alternative.lower()
+    if alternative not in alternatives:
+        raise ValueError(f"`alternative` must be in {alternatives}")
+
+    rng = check_random_state(rng)
+
+    float_dtype = xp_result_type(*data_iv, force_floating=True, xp=xp)
+
+    return (data_iv, statistic, permutation_type, vectorized, n_resamples_int,
+            batch_iv, alternative, axis_int, rng, float_dtype, xp)
+
+
+@xp_capabilities(skip_backends=[('dask.array', "lacks required indexing capabilities")])
+@_transition_to_rng('random_state')
+def permutation_test(data, statistic, *, permutation_type='independent',
+                     vectorized=None, n_resamples=9999, batch=None,
+                     alternative="two-sided", axis=0, rng=None):
+    r"""
+    Performs a permutation test of a given statistic on provided data.
+
+    For independent sample statistics, the null hypothesis is that the data are
+    randomly sampled from the same distribution.
+    For paired sample statistics, two null hypothesis can be tested:
+    that the data are paired at random or that the data are assigned to samples
+    at random.
+
+    Parameters
+    ----------
+    data : iterable of array-like
+        Contains the samples, each of which is an array of observations.
+        Dimensions of sample arrays must be compatible for broadcasting except
+        along `axis`.
+    statistic : callable
+        Statistic for which the p-value of the hypothesis test is to be
+        calculated. `statistic` must be a callable that accepts samples
+        as separate arguments (e.g. ``statistic(*data)``) and returns the
+        resulting statistic.
+        If `vectorized` is set ``True``, `statistic` must also accept a keyword
+        argument `axis` and be vectorized to compute the statistic along the
+        provided `axis` of the sample arrays.
+    permutation_type : {'independent', 'samples', 'pairings'}, optional
+        The type of permutations to be performed, in accordance with the
+        null hypothesis. The first two permutation types are for paired sample
+        statistics, in which all samples contain the same number of
+        observations and observations with corresponding indices along `axis`
+        are considered to be paired; the third is for independent sample
+        statistics.
+
+        - ``'samples'`` : observations are assigned to different samples
+          but remain paired with the same observations from other samples.
+          This permutation type is appropriate for paired sample hypothesis
+          tests such as the Wilcoxon signed-rank test and the paired t-test.
+        - ``'pairings'`` : observations are paired with different observations,
+          but they remain within the same sample. This permutation type is
+          appropriate for association/correlation tests with statistics such
+          as Spearman's :math:`\rho`, Kendall's :math:`\tau`, and Pearson's
+          :math:`r`.
+        - ``'independent'`` (default) : observations are assigned to different
+          samples. Samples may contain different numbers of observations. This
+          permutation type is appropriate for independent sample hypothesis
+          tests such as the Mann-Whitney :math:`U` test and the independent
+          sample t-test.
+
+          Please see the Notes section below for more detailed descriptions
+          of the permutation types.
+
+    vectorized : bool, optional
+        If `vectorized` is set ``False``, `statistic` will not be passed
+        keyword argument `axis` and is expected to calculate the statistic
+        only for 1D samples. If ``True``, `statistic` will be passed keyword
+        argument `axis` and is expected to calculate the statistic along `axis`
+        when passed an ND sample array. If ``None`` (default), `vectorized`
+        will be set ``True`` if ``axis`` is a parameter of `statistic`. Use
+        of a vectorized statistic typically reduces computation time.
+    n_resamples : int or np.inf, default: 9999
+        Number of random permutations (resamples) used to approximate the null
+        distribution. If greater than or equal to the number of distinct
+        permutations, the exact null distribution will be computed.
+        Note that the number of distinct permutations grows very rapidly with
+        the sizes of samples, so exact tests are feasible only for very small
+        data sets.
+    batch : int, optional
+        The number of permutations to process in each call to `statistic`.
+        Memory usage is O( `batch` * ``n`` ), where ``n`` is the total size
+        of all samples, regardless of the value of `vectorized`. Default is
+        ``None``, in which case ``batch`` is the number of permutations.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        The alternative hypothesis for which the p-value is calculated.
+        For each alternative, the p-value is defined for exact tests as
+        follows.
+
+        - ``'greater'`` : the percentage of the null distribution that is
+          greater than or equal to the observed value of the test statistic.
+        - ``'less'`` : the percentage of the null distribution that is
+          less than or equal to the observed value of the test statistic.
+        - ``'two-sided'`` (default) : twice the smaller of the p-values above.
+
+        Note that p-values for randomized tests are calculated according to the
+        conservative (over-estimated) approximation suggested in [2]_ and [3]_
+        rather than the unbiased estimator suggested in [4]_. That is, when
+        calculating the proportion of the randomized null distribution that is
+        as extreme as the observed value of the test statistic, the values in
+        the numerator and denominator are both increased by one. An
+        interpretation of this adjustment is that the observed value of the
+        test statistic is always included as an element of the randomized
+        null distribution.
+        The convention used for two-sided p-values is not universal;
+        the observed test statistic and null distribution are returned in
+        case a different definition is preferred.
+
+    axis : int, default: 0
+        The axis of the (broadcasted) samples over which to calculate the
+        statistic. If samples have a different number of dimensions,
+        singleton dimensions are prepended to samples with fewer dimensions
+        before `axis` is considered.
+    rng : `numpy.random.Generator`, optional
+        Pseudorandom number generator state. When `rng` is None, a new
+        `numpy.random.Generator` is created using entropy from the
+        operating system. Types other than `numpy.random.Generator` are
+        passed to `numpy.random.default_rng` to instantiate a ``Generator``.
+
+    Returns
+    -------
+    res : PermutationTestResult
+        An object with attributes:
+
+        statistic : float or ndarray
+            The observed test statistic of the data.
+        pvalue : float or ndarray
+            The p-value for the given alternative.
+        null_distribution : ndarray
+            The values of the test statistic generated under the null
+            hypothesis.
+
+    Notes
+    -----
+
+    The three types of permutation tests supported by this function are
+    described below.
+
+    **Unpaired statistics** (``permutation_type='independent'``):
+
+    The null hypothesis associated with this permutation type is that all
+    observations are sampled from the same underlying distribution and that
+    they have been assigned to one of the samples at random.
+
+    Suppose ``data`` contains two samples; e.g. ``a, b = data``.
+    When ``1 < n_resamples < binom(n, k)``, where
+
+    * ``k`` is the number of observations in ``a``,
+    * ``n`` is the total number of observations in ``a`` and ``b``, and
+    * ``binom(n, k)`` is the binomial coefficient (``n`` choose ``k``),
+
+    the data are pooled (concatenated), randomly assigned to either the first
+    or second sample, and the statistic is calculated. This process is
+    performed repeatedly, `permutation` times, generating a distribution of the
+    statistic under the null hypothesis. The statistic of the original
+    data is compared to this distribution to determine the p-value.
+
+    When ``n_resamples >= binom(n, k)``, an exact test is performed: the data
+    are *partitioned* between the samples in each distinct way exactly once,
+    and the exact null distribution is formed.
+    Note that for a given partitioning of the data between the samples,
+    only one ordering/permutation of the data *within* each sample is
+    considered. For statistics that do not depend on the order of the data
+    within samples, this dramatically reduces computational cost without
+    affecting the shape of the null distribution (because the frequency/count
+    of each value is affected by the same factor).
+
+    For ``a = [a1, a2, a3, a4]`` and ``b = [b1, b2, b3]``, an example of this
+    permutation type is ``x = [b3, a1, a2, b2]`` and ``y = [a4, b1, a3]``.
+    Because only one ordering/permutation of the data *within* each sample
+    is considered in an exact test, a resampling like ``x = [b3, a1, b2, a2]``
+    and ``y = [a4, a3, b1]`` would *not* be considered distinct from the
+    example above.
+
+    ``permutation_type='independent'`` does not support one-sample statistics,
+    but it can be applied to statistics with more than two samples. In this
+    case, if ``n`` is an array of the number of observations within each
+    sample, the number of distinct partitions is::
+
+        np.prod([binom(sum(n[i:]), sum(n[i+1:])) for i in range(len(n)-1)])
+
+    **Paired statistics, permute pairings** (``permutation_type='pairings'``):
+
+    The null hypothesis associated with this permutation type is that
+    observations within each sample are drawn from the same underlying
+    distribution and that pairings with elements of other samples are
+    assigned at random.
+
+    Suppose ``data`` contains only one sample; e.g. ``a, = data``, and we
+    wish to consider all possible pairings of elements of ``a`` with elements
+    of a second sample, ``b``. Let ``n`` be the number of observations in
+    ``a``, which must also equal the number of observations in ``b``.
+
+    When ``1 < n_resamples < factorial(n)``, the elements of ``a`` are
+    randomly permuted. The user-supplied statistic accepts one data argument,
+    say ``a_perm``, and calculates the statistic considering ``a_perm`` and
+    ``b``. This process is performed repeatedly, `permutation` times,
+    generating a distribution of the statistic under the null hypothesis.
+    The statistic of the original data is compared to this distribution to
+    determine the p-value.
+
+    When ``n_resamples >= factorial(n)``, an exact test is performed:
+    ``a`` is permuted in each distinct way exactly once. Therefore, the
+    `statistic` is computed for each unique pairing of samples between ``a``
+    and ``b`` exactly once.
+
+    For ``a = [a1, a2, a3]`` and ``b = [b1, b2, b3]``, an example of this
+    permutation type is ``a_perm = [a3, a1, a2]`` while ``b`` is left
+    in its original order.
+
+    ``permutation_type='pairings'`` supports ``data`` containing any number
+    of samples, each of which must contain the same number of observations.
+    All samples provided in ``data`` are permuted *independently*. Therefore,
+    if ``m`` is the number of samples and ``n`` is the number of observations
+    within each sample, then the number of permutations in an exact test is::
+
+        factorial(n)**m
+
+    Note that if a two-sample statistic, for example, does not inherently
+    depend on the order in which observations are provided - only on the
+    *pairings* of observations - then only one of the two samples should be
+    provided in ``data``. This dramatically reduces computational cost without
+    affecting the shape of the null distribution (because the frequency/count
+    of each value is affected by the same factor).
+
+    **Paired statistics, permute samples** (``permutation_type='samples'``):
+
+    The null hypothesis associated with this permutation type is that
+    observations within each pair are drawn from the same underlying
+    distribution and that the sample to which they are assigned is random.
+
+    Suppose ``data`` contains two samples; e.g. ``a, b = data``.
+    Let ``n`` be the number of observations in ``a``, which must also equal
+    the number of observations in ``b``.
+
+    When ``1 < n_resamples < 2**n``, the elements of ``a`` are ``b`` are
+    randomly swapped between samples (maintaining their pairings) and the
+    statistic is calculated. This process is performed repeatedly,
+    `permutation` times,  generating a distribution of the statistic under the
+    null hypothesis. The statistic of the original data is compared to this
+    distribution to determine the p-value.
+
+    When ``n_resamples >= 2**n``, an exact test is performed: the observations
+    are assigned to the two samples in each distinct way (while maintaining
+    pairings) exactly once.
+
+    For ``a = [a1, a2, a3]`` and ``b = [b1, b2, b3]``, an example of this
+    permutation type is ``x = [b1, a2, b3]`` and ``y = [a1, b2, a3]``.
+
+    ``permutation_type='samples'`` supports ``data`` containing any number
+    of samples, each of which must contain the same number of observations.
+    If ``data`` contains more than one sample, paired observations within
+    ``data`` are exchanged between samples *independently*. Therefore, if ``m``
+    is the number of samples and ``n`` is the number of observations within
+    each sample, then the number of permutations in an exact test is::
+
+        factorial(m)**n
+
+    Several paired-sample statistical tests, such as the Wilcoxon signed rank
+    test and paired-sample t-test, can be performed considering only the
+    *difference* between two paired elements. Accordingly, if ``data`` contains
+    only one sample, then the null distribution is formed by independently
+    changing the *sign* of each observation.
+
+    .. warning::
+        The p-value is calculated by counting the elements of the null
+        distribution that are as extreme or more extreme than the observed
+        value of the statistic. Due to the use of finite precision arithmetic,
+        some statistic functions return numerically distinct values when the
+        theoretical values would be exactly equal. In some cases, this could
+        lead to a large error in the calculated p-value. `permutation_test`
+        guards against this by considering elements in the null distribution
+        that are "close" (within a relative tolerance of 100 times the
+        floating point epsilon of inexact dtypes) to the observed
+        value of the test statistic as equal to the observed value of the
+        test statistic. However, the user is advised to inspect the null
+        distribution to assess whether this method of comparison is
+        appropriate, and if not, calculate the p-value manually. See example
+        below.
+
+    References
+    ----------
+
+    .. [1] R. A. Fisher. The Design of Experiments, 6th Ed (1951).
+    .. [2] B. Phipson and G. K. Smyth. "Permutation P-values Should Never Be
+       Zero: Calculating Exact P-values When Permutations Are Randomly Drawn."
+       Statistical Applications in Genetics and Molecular Biology 9.1 (2010).
+    .. [3] M. D. Ernst. "Permutation Methods: A Basis for Exact Inference".
+       Statistical Science (2004).
+    .. [4] B. Efron and R. J. Tibshirani. An Introduction to the Bootstrap
+       (1993).
+
+    Examples
+    --------
+
+    Suppose we wish to test whether two samples are drawn from the same
+    distribution. Assume that the underlying distributions are unknown to us,
+    and that before observing the data, we hypothesized that the mean of the
+    first sample would be less than that of the second sample. We decide that
+    we will use the difference between the sample means as a test statistic,
+    and we will consider a p-value of 0.05 to be statistically significant.
+
+    For efficiency, we write the function defining the test statistic in a
+    vectorized fashion: the samples ``x`` and ``y`` can be ND arrays, and the
+    statistic will be calculated for each axis-slice along `axis`.
+
+    >>> import numpy as np
+    >>> def statistic(x, y, axis):
+    ...     return np.mean(x, axis=axis) - np.mean(y, axis=axis)
+
+    After collecting our data, we calculate the observed value of the test
+    statistic.
+
+    >>> from scipy.stats import norm
+    >>> rng = np.random.default_rng()
+    >>> x = norm.rvs(size=5, random_state=rng)
+    >>> y = norm.rvs(size=6, loc = 3, random_state=rng)
+    >>> statistic(x, y, 0)
+    -3.5411688580987266
+
+    Indeed, the test statistic is negative, suggesting that the true mean of
+    the distribution underlying ``x`` is less than that of the distribution
+    underlying ``y``. To determine the probability of this occurring by chance
+    if the two samples were drawn from the same distribution, we perform
+    a permutation test.
+
+    >>> from scipy.stats import permutation_test
+    >>> # because our statistic is vectorized, we pass `vectorized=True`
+    >>> # `n_resamples=np.inf` indicates that an exact test is to be performed
+    >>> res = permutation_test((x, y), statistic, vectorized=True,
+    ...                        n_resamples=np.inf, alternative='less')
+    >>> print(res.statistic)
+    -3.5411688580987266
+    >>> print(res.pvalue)
+    0.004329004329004329
+
+    The probability of obtaining a test statistic less than or equal to the
+    observed value under the null hypothesis is 0.4329%. This is less than our
+    chosen threshold of 5%, so we consider this to be significant evidence
+    against the null hypothesis in favor of the alternative.
+
+    Because the size of the samples above was small, `permutation_test` could
+    perform an exact test. For larger samples, we resort to a randomized
+    permutation test.
+
+    >>> x = norm.rvs(size=100, random_state=rng)
+    >>> y = norm.rvs(size=120, loc=0.2, random_state=rng)
+    >>> res = permutation_test((x, y), statistic, n_resamples=9999,
+    ...                        vectorized=True, alternative='less',
+    ...                        rng=rng)
+    >>> print(res.statistic)
+    -0.4230459671240913
+    >>> print(res.pvalue)
+    0.0015
+
+    The approximate probability of obtaining a test statistic less than or
+    equal to the observed value under the null hypothesis is 0.0225%. This is
+    again less than our chosen threshold of 5%, so again we have significant
+    evidence to reject the null hypothesis in favor of the alternative.
+
+    For large samples and number of permutations, the result is comparable to
+    that of the corresponding asymptotic test, the independent sample t-test.
+
+    >>> from scipy.stats import ttest_ind
+    >>> res_asymptotic = ttest_ind(x, y, alternative='less')
+    >>> print(res_asymptotic.pvalue)
+    0.0014669545224902675
+
+    The permutation distribution of the test statistic is provided for
+    further investigation.
+
+    >>> import matplotlib.pyplot as plt
+    >>> plt.hist(res.null_distribution, bins=50)
+    >>> plt.title("Permutation distribution of test statistic")
+    >>> plt.xlabel("Value of Statistic")
+    >>> plt.ylabel("Frequency")
+    >>> plt.show()
+
+    Inspection of the null distribution is essential if the statistic suffers
+    from inaccuracy due to limited machine precision. Consider the following
+    case:
+
+    >>> from scipy.stats import pearsonr
+    >>> x = [1, 2, 4, 3]
+    >>> y = [2, 4, 6, 8]
+    >>> def statistic(x, y, axis=-1):
+    ...     return pearsonr(x, y, axis=axis).statistic
+    >>> res = permutation_test((x, y), statistic, vectorized=True,
+    ...                        permutation_type='pairings',
+    ...                        alternative='greater')
+    >>> r, pvalue, null = res.statistic, res.pvalue, res.null_distribution
+
+    In this case, some elements of the null distribution differ from the
+    observed value of the correlation coefficient ``r`` due to numerical noise.
+    We manually inspect the elements of the null distribution that are nearly
+    the same as the observed value of the test statistic.
+
+    >>> r
+    0.7999999999999999
+    >>> unique = np.unique(null)
+    >>> unique
+    array([-1. , -1. , -0.8, -0.8, -0.8, -0.6, -0.4, -0.4, -0.2, -0.2, -0.2,
+        0. ,  0.2,  0.2,  0.2,  0.4,  0.4,  0.6,  0.8,  0.8,  0.8,  1. ,
+        1. ])  # may vary
+    >>> unique[np.isclose(r, unique)].tolist()
+    [0.7999999999999998, 0.7999999999999999, 0.8]  # may vary
+
+    If `permutation_test` were to perform the comparison naively, the
+    elements of the null distribution with value ``0.7999999999999998`` would
+    not be considered as extreme or more extreme as the observed value of the
+    statistic, so the calculated p-value would be too small.
+
+    >>> incorrect_pvalue = np.count_nonzero(null >= r) / len(null)
+    >>> incorrect_pvalue
+    0.14583333333333334  # may vary
+
+    Instead, `permutation_test` treats elements of the null distribution that
+    are within ``max(1e-14, abs(r)*1e-14)`` of the observed value of the
+    statistic ``r`` to be equal to ``r``.
+
+    >>> correct_pvalue = np.count_nonzero(null >= r - 1e-14) / len(null)
+    >>> correct_pvalue
+    0.16666666666666666
+    >>> res.pvalue == correct_pvalue
+    True
+
+    This method of comparison is expected to be accurate in most practical
+    situations, but the user is advised to assess this by inspecting the
+    elements of the null distribution that are close to the observed value
+    of the statistic. Also, consider the use of statistics that can be
+    calculated using exact arithmetic (e.g. integer statistics).
+
+    """
+    args = _permutation_test_iv(data, statistic, permutation_type, vectorized,
+                                n_resamples, batch, alternative, axis,
+                                rng)
+    (data, statistic, permutation_type, vectorized, n_resamples, batch,
+     alternative, axis, rng, float_dtype, xp) = args
+
+    observed = statistic(*data, axis=-1)
+
+    null_calculators = {"pairings": _calculate_null_pairings,
+                        "samples": _calculate_null_samples,
+                        "independent": _calculate_null_both}
+    null_calculator_args = (data, statistic, n_resamples,
+                            batch, rng)
+    calculate_null = null_calculators[permutation_type]
+    null_distribution, n_resamples, exact_test = (
+        calculate_null(*null_calculator_args, xp=xp))
+
+    # See References [2] and [3]
+    adjustment = 0 if exact_test else 1
+
+    # relative tolerance for detecting numerically distinct but
+    # theoretically equal values in the null distribution
+    eps =  (0 if not xp.isdtype(observed.dtype, 'real floating')
+            else xp.finfo(observed.dtype).eps*100)
+    gamma = xp.abs(eps * observed)
+
+    def less(null_distribution, observed):
+        cmps = null_distribution <= observed + gamma
+        count = xp.count_nonzero(cmps, axis=0) + adjustment
+        pvalues = xp.astype(count, float_dtype) / (n_resamples + adjustment)
+        return pvalues
+
+    def greater(null_distribution, observed):
+        cmps = null_distribution >= observed - gamma
+        count = xp.count_nonzero(cmps, axis=0) + adjustment
+        pvalues = xp.astype(count, float_dtype) / (n_resamples + adjustment)
+        return pvalues
+
+    def two_sided(null_distribution, observed):
+        pvalues_less = less(null_distribution, observed)
+        pvalues_greater = greater(null_distribution, observed)
+        pvalues = xp.minimum(pvalues_less, pvalues_greater) * 2
+        return pvalues
+
+    compare = {"less": less,
+               "greater": greater,
+               "two-sided": two_sided}
+
+    pvalues = compare[alternative](null_distribution, observed)
+    pvalues = xpx.at(pvalues)[xp.isnan(observed)].set(xp.nan)
+    pvalues = xp.clip(pvalues, 0., 1.)
+
+    return PermutationTestResult(observed, pvalues, null_distribution)
+
+
+@dataclass
+class ResamplingMethod:
+    """Configuration information for a statistical resampling method.
+
+    Instances of this class can be passed into the `method` parameter of some
+    hypothesis test functions to perform a resampling or Monte Carlo version
+    of the hypothesis test.
+
+    Attributes
+    ----------
+    n_resamples : int
+        The number of resamples to perform or Monte Carlo samples to draw.
+    batch : int, optional
+        The number of resamples to process in each vectorized call to
+        the statistic. Batch sizes >>1 tend to be faster when the statistic
+        is vectorized, but memory usage scales linearly with the batch size.
+        Default is ``None``, which processes all resamples in a single batch.
+
+    """
+    n_resamples: int = 9999
+    batch: int = None  # type: ignore[assignment]
+
+
+@dataclass
+class MonteCarloMethod(ResamplingMethod):
+    """Configuration information for a Monte Carlo hypothesis test.
+
+    Instances of this class can be passed into the `method` parameter of some
+    hypothesis test functions to perform a Monte Carlo version of the
+    hypothesis tests.
+
+    Parameters
+    ----------
+    n_resamples : int, optional
+        The number of Monte Carlo samples to draw. Default is 9999.
+    batch : int, optional
+        The number of Monte Carlo samples to process in each vectorized call to
+        the statistic. Batch sizes >>1 tend to be faster when the statistic
+        is vectorized, but memory usage scales linearly with the batch size.
+        Default is ``None``, which processes all samples in a single batch.
+    rvs : callable or tuple of callables, optional
+        A callable or sequence of callables that generates random variates
+        under the null hypothesis. Each element of `rvs` must be a callable
+        that accepts keyword argument ``size`` (e.g. ``rvs(size=(m, n))``) and
+        returns an N-d array sample of that shape. If `rvs` is a sequence, the
+        number of callables in `rvs` must match the number of samples passed
+        to the hypothesis test in which the `MonteCarloMethod` is used. Default
+        is ``None``, in which case the hypothesis test function chooses values
+        to match the standard version of the hypothesis test. For example,
+        the null hypothesis of `scipy.stats.pearsonr` is typically that the
+        samples are drawn from the standard normal distribution, so
+        ``rvs = (rng.normal, rng.normal)`` where
+        ``rng = np.random.default_rng()``.
+    rng : `numpy.random.Generator`, optional
+        Pseudorandom number generator state. When `rng` is None, a new
+        `numpy.random.Generator` is created using entropy from the
+        operating system. Types other than `numpy.random.Generator` are
+        passed to `numpy.random.default_rng` to instantiate a ``Generator``.
+
+    """
+    rvs: object = None
+    rng: object = None
+
+    def __init__(self, n_resamples=9999, batch=None, rvs=None, rng=None):
+        if (rvs is not None) and (rng is not None):
+            message = 'Use of `rvs` and `rng` are mutually exclusive.'
+            raise ValueError(message)
+
+        self.n_resamples = n_resamples
+        self.batch = batch
+        self.rvs = rvs
+        self.rng = rng
+
+    def _asdict(self):
+        # `dataclasses.asdict` deepcopies; we don't want that.
+        return dict(n_resamples=self.n_resamples, batch=self.batch,
+                    rvs=self.rvs, rng=self.rng)
+
+
+_rs_deprecation = ("Use of attribute `random_state` is deprecated and replaced by "
+                   "`rng`. Support for `random_state` will be removed in SciPy 1.19.0. "
+                   "To silence this warning and ensure consistent behavior in SciPy "
+                   "1.19.0, control the RNG using attribute `rng`. Values set using "
+                   "attribute `rng` will be validated by `np.random.default_rng`, so "
+                   "the behavior corresponding with a given value may change compared "
+                   "to use of `random_state`. For example, 1) `None` will result in "
+                   "unpredictable random numbers, 2) an integer will result in a "
+                   "different stream of random numbers, (with the same distribution), "
+                   "and 3) `np.random` or `RandomState` instances will result in an "
+                   "error. See the documentation of `default_rng` for more "
+                   "information.")
+
+
+@dataclass
+class PermutationMethod(ResamplingMethod):
+    """Configuration information for a permutation hypothesis test.
+
+    Instances of this class can be passed into the `method` parameter of some
+    hypothesis test functions to perform a permutation version of the
+    hypothesis tests.
+
+    Parameters
+    ----------
+    n_resamples : int, optional
+        The number of resamples to perform. Default is 9999.
+    batch : int, optional
+        The number of resamples to process in each vectorized call to
+        the statistic. Batch sizes >>1 tend to be faster when the statistic
+        is vectorized, but memory usage scales linearly with the batch size.
+        Default is ``None``, which processes all resamples in a single batch.
+    rng : `numpy.random.Generator`, optional
+        Pseudorandom number generator used to perform resampling.
+
+        If `rng` is passed by keyword to the initializer or the `rng` attribute is used
+        directly, types other than `numpy.random.Generator` are passed to
+        `numpy.random.default_rng` to instantiate a ``Generator`` before use.
+        If `rng` is already a ``Generator`` instance, then the provided instance is
+        used. Specify `rng` for repeatable behavior.
+
+        If this argument is passed by position, if `random_state` is passed by keyword
+        into the initializer, or if the `random_state` attribute is used directly,
+        legacy behavior for `random_state` applies:
+
+        - If `random_state` is None (or `numpy.random`), the `numpy.random.RandomState`
+          singleton is used.
+        - If `random_state` is an int, a new ``RandomState`` instance is used,
+          seeded with `random_state`.
+        - If `random_state` is already a ``Generator`` or ``RandomState`` instance then
+          that instance is used.
+
+        .. versionchanged:: 1.15.0
+
+            As part of the `SPEC-007 <https://scientific-python.org/specs/spec-0007/>`_
+            transition from use of `numpy.random.RandomState` to
+            `numpy.random.Generator`, this attribute name was changed from
+            `random_state` to `rng`. For an interim period, both names will continue to
+            work, although only one may be specified at a time. After the interim
+            period, uses of `random_state` will emit warnings. The behavior of both
+            `random_state` and `rng` are outlined above, but only `rng` should be used
+            in new code.
+
+    """
+    rng: object  # type: ignore[misc]
+    _rng: object = field(init=False, repr=False, default=None)  # type: ignore[assignment]
+
+    @property
+    def random_state(self):
+        # Uncomment in SciPy 1.17.0
+        # warnings.warn(_rs_deprecation, DeprecationWarning, stacklevel=2)
+        return self._random_state
+
+    @random_state.setter
+    def random_state(self, val):
+        # Uncomment in SciPy 1.17.0
+        # warnings.warn(_rs_deprecation, DeprecationWarning, stacklevel=2)
+        self._random_state = val
+
+    @property  # type: ignore[no-redef]
+    def rng(self):  # noqa: F811
+        return self._rng
+
+    def __init__(self, n_resamples=9999, batch=None, random_state=None, *, rng=None):
+        # Uncomment in SciPy 1.17.0
+        # warnings.warn(_rs_deprecation.replace('attribute', 'argument'),
+        #               DeprecationWarning, stacklevel=2)
+        self._rng = rng
+        self._random_state = random_state
+        super().__init__(n_resamples=n_resamples, batch=batch)
+
+    def _asdict(self):
+        # `dataclasses.asdict` deepcopies; we don't want that.
+        d = dict(n_resamples=self.n_resamples, batch=self.batch)
+        if self.rng is not None:
+            d['rng'] = self.rng
+        if self.random_state is not None:
+            d['random_state'] = self.random_state
+        return d
+
+
+@dataclass
+class BootstrapMethod(ResamplingMethod):
+    """Configuration information for a bootstrap confidence interval.
+
+    Instances of this class can be passed into the `method` parameter of some
+    confidence interval methods to generate a bootstrap confidence interval.
+
+    Parameters
+    ----------
+    n_resamples : int, optional
+        The number of resamples to perform. Default is 9999.
+    batch : int, optional
+        The number of resamples to process in each vectorized call to
+        the statistic. Batch sizes >>1 tend to be faster when the statistic
+        is vectorized, but memory usage scales linearly with the batch size.
+        Default is ``None``, which processes all resamples in a single batch.
+    rng : `numpy.random.Generator`, optional
+        Pseudorandom number generator used to perform resampling.
+
+        If `rng` is passed by keyword to the initializer or the `rng` attribute is used
+        directly, types other than `numpy.random.Generator` are passed to
+        `numpy.random.default_rng` to instantiate a ``Generator``  before use.
+        If `rng` is already a ``Generator`` instance, then the provided instance is
+        used. Specify `rng` for repeatable behavior.
+
+        If this argument is passed by position, if `random_state` is passed by keyword
+        into the initializer, or if the `random_state` attribute is used directly,
+        legacy behavior for `random_state` applies:
+
+        - If `random_state` is None (or `numpy.random`), the `numpy.random.RandomState`
+          singleton is used.
+        - If `random_state` is an int, a new ``RandomState`` instance is used,
+          seeded with `random_state`.
+        - If `random_state` is already a ``Generator`` or ``RandomState`` instance then
+          that instance is used.
+
+        .. versionchanged:: 1.15.0
+
+            As part of the `SPEC-007 <https://scientific-python.org/specs/spec-0007/>`_
+            transition from use of `numpy.random.RandomState` to
+            `numpy.random.Generator`, this attribute name was changed from
+            `random_state` to `rng`. For an interim period, both names will continue to
+            work, although only one may be specified at a time. After the interim
+            period, uses of `random_state` will emit warnings. The behavior of both
+            `random_state` and `rng` are outlined above, but only `rng` should be used
+            in new code.
+
+    method : {'BCa', 'percentile', 'basic'}
+        Whether to use the 'percentile' bootstrap ('percentile'), the 'basic'
+        (AKA 'reverse') bootstrap ('basic'), or the bias-corrected and
+        accelerated bootstrap ('BCa', default).
+
+    """
+    rng: object  # type: ignore[misc]
+    _rng: object = field(init=False, repr=False, default=None)  # type: ignore[assignment]
+    method: str = 'BCa'
+
+    @property
+    def random_state(self):
+        # Uncomment in SciPy 1.17.0
+        # warnings.warn(_rs_deprecation, DeprecationWarning, stacklevel=2)
+        return self._random_state
+
+    @random_state.setter
+    def random_state(self, val):
+        # Uncomment in SciPy 1.17.0
+        # warnings.warn(_rs_deprecation, DeprecationWarning, stacklevel=2)
+        self._random_state = val
+
+    @property  # type: ignore[no-redef]
+    def rng(self):  # noqa: F811
+        return self._rng
+
+    def __init__(self, n_resamples=9999, batch=None, random_state=None,
+                 method='BCa', *, rng=None):
+        # Uncomment in SciPy 1.17.0
+        # warnings.warn(_rs_deprecation.replace('attribute', 'argument'),
+        #               DeprecationWarning, stacklevel=2)
+        self._rng = rng  # don't validate with `default_rng`
+        self._random_state = random_state
+        self.method = method
+        super().__init__(n_resamples=n_resamples, batch=batch)
+
+    def _asdict(self):
+        # `dataclasses.asdict` deepcopies; we don't want that.
+        d = dict(n_resamples=self.n_resamples, batch=self.batch,
+                 method=self.method)
+        if self.rng is not None:
+            d['rng'] = self.rng
+        if self.random_state is not None:
+            d['random_state'] = self.random_state
+        return d
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_result_classes.py b/venv/lib/python3.12/site-packages/scipy/stats/_result_classes.py
new file mode 100644
index 0000000000000000000000000000000000000000..975af9310efb0c9a414439fd8d531fb95c988951
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_result_classes.py
@@ -0,0 +1,40 @@
+# This module exists only to allow Sphinx to generate docs
+# for the result objects returned by some functions in stats
+# _without_ adding them to the main stats documentation page.
+
+"""
+Result classes
+--------------
+
+.. currentmodule:: scipy.stats._result_classes
+
+.. autosummary::
+   :toctree: generated/
+
+   RelativeRiskResult
+   BinomTestResult
+   TukeyHSDResult
+   DunnettResult
+   PearsonRResult
+   FitResult
+   OddsRatioResult
+   TtestResult
+   ECDFResult
+   EmpiricalDistributionFunction
+
+"""
+
+__all__ = ['BinomTestResult', 'RelativeRiskResult', 'TukeyHSDResult',
+           'PearsonRResult', 'FitResult', 'OddsRatioResult',
+           'TtestResult', 'DunnettResult', 'ECDFResult',
+           'EmpiricalDistributionFunction']
+
+
+from ._binomtest import BinomTestResult
+from ._odds_ratio import OddsRatioResult
+from ._relative_risk import RelativeRiskResult
+from ._hypotests import TukeyHSDResult
+from ._multicomp import DunnettResult
+from ._stats_py import PearsonRResult, TtestResult
+from ._fit import FitResult
+from ._survival import ECDFResult, EmpiricalDistributionFunction
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_sampling.py b/venv/lib/python3.12/site-packages/scipy/stats/_sampling.py
new file mode 100644
index 0000000000000000000000000000000000000000..3c0abd14bb9e7f14bb3ae98cb13bcb2b6d8144c7
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_sampling.py
@@ -0,0 +1,1319 @@
+import math
+import numbers
+import numpy as np
+from scipy import stats
+from scipy import special as sc
+from ._qmc import (check_random_state as check_random_state_qmc,
+                   Halton, QMCEngine)
+from ._unuran.unuran_wrapper import NumericalInversePolynomial
+from scipy._lib._util import check_random_state
+
+
+__all__ = ['FastGeneratorInversion', 'RatioUniforms']
+
+
+# define pdfs and other helper functions to create the generators
+
+def argus_pdf(x, chi):
+    # approach follows Baumgarten/Hoermann: Generating ARGUS random variates
+    # for chi > 5, use relationship of the ARGUS distribution to Gamma(1.5)
+    if chi <= 5:
+        y = 1 - x * x
+        return x * math.sqrt(y) * math.exp(-0.5 * chi**2 * y)
+    return math.sqrt(x) * math.exp(-x)
+
+
+def argus_gamma_trf(x, chi):
+    if chi <= 5:
+        return x
+    return np.sqrt(1.0 - 2 * x / chi**2)
+
+
+def argus_gamma_inv_trf(x, chi):
+    if chi <= 5:
+        return x
+    return 0.5 * chi**2 * (1 - x**2)
+
+
+def betaprime_pdf(x, a, b):
+    if x > 0:
+        logf = (a - 1) * math.log(x) - (a + b) * math.log1p(x) - sc.betaln(a, b)
+        return math.exp(logf)
+    else:
+        # return pdf at x == 0 separately to avoid runtime warnings
+        if a > 1:
+            return 0
+        elif a < 1:
+            return np.inf
+        else:
+            return 1 / sc.beta(a, b)
+
+
+def beta_valid_params(a, b):
+    return (min(a, b) >= 0.1) and (max(a, b) <= 700)
+
+
+def gamma_pdf(x, a):
+    if x > 0:
+        return math.exp(-math.lgamma(a) + (a - 1.0) * math.log(x) - x)
+    else:
+        return 0 if a >= 1 else np.inf
+
+
+def invgamma_pdf(x, a):
+    if x > 0:
+        return math.exp(-(a + 1.0) * math.log(x) - math.lgamma(a) - 1 / x)
+    else:
+        return 0 if a >= 1 else np.inf
+
+
+def burr_pdf(x, cc, dd):
+    # note: we use np.exp instead of math.exp, otherwise an overflow
+    # error can occur in the setup, e.g., for parameters
+    # 1.89128135, 0.30195177, see test test_burr_overflow
+    if x > 0:
+        lx = math.log(x)
+        return np.exp(-(cc + 1) * lx - (dd + 1) * math.log1p(np.exp(-cc * lx)))
+    else:
+        return 0
+
+
+def burr12_pdf(x, cc, dd):
+    if x > 0:
+        lx = math.log(x)
+        logterm = math.log1p(math.exp(cc * lx))
+        return math.exp((cc - 1) * lx - (dd + 1) * logterm + math.log(cc * dd))
+    else:
+        return 0
+
+
+def chi_pdf(x, a):
+    if x > 0:
+        return math.exp(
+            (a - 1) * math.log(x)
+            - 0.5 * (x * x)
+            - (a / 2 - 1) * math.log(2)
+            - math.lgamma(0.5 * a)
+        )
+    else:
+        return 0 if a >= 1 else np.inf
+
+
+def chi2_pdf(x, df):
+    if x > 0:
+        return math.exp(
+            (df / 2 - 1) * math.log(x)
+            - 0.5 * x
+            - (df / 2) * math.log(2)
+            - math.lgamma(0.5 * df)
+        )
+    else:
+        return 0 if df >= 1 else np.inf
+
+
+def alpha_pdf(x, a):
+    if x > 0:
+        return math.exp(-2.0 * math.log(x) - 0.5 * (a - 1.0 / x) ** 2)
+    return 0.0
+
+
+def bradford_pdf(x, c):
+    if 0 <= x <= 1:
+        return 1.0 / (1.0 + c * x)
+    return 0.0
+
+
+def crystalball_pdf(x, b, m):
+    if x > -b:
+        return math.exp(-0.5 * x * x)
+    return math.exp(m * math.log(m / b) - 0.5 * b * b - m * math.log(m / b - b - x))
+
+
+def weibull_min_pdf(x, c):
+    if x > 0:
+        return c * math.exp((c - 1) * math.log(x) - x**c)
+    return 0.0
+
+
+def weibull_max_pdf(x, c):
+    if x < 0:
+        return c * math.exp((c - 1) * math.log(-x) - ((-x) ** c))
+    return 0.0
+
+
+def invweibull_pdf(x, c):
+    if x > 0:
+        return c * math.exp(-(c + 1) * math.log(x) - x ** (-c))
+    return 0.0
+
+
+def wald_pdf(x):
+    if x > 0:
+        return math.exp(-((x - 1) ** 2) / (2 * x)) / math.sqrt(x**3)
+    return 0.0
+
+
+def geninvgauss_mode(p, b):
+    if p > 1:  # equivalent mode formulas numerical more stable versions
+        return (math.sqrt((1 - p) ** 2 + b**2) - (1 - p)) / b
+    return b / (math.sqrt((1 - p) ** 2 + b**2) + (1 - p))
+
+
+def geninvgauss_pdf(x, p, b):
+    m = geninvgauss_mode(p, b)
+    lfm = (p - 1) * math.log(m) - 0.5 * b * (m + 1 / m)
+    if x > 0:
+        return math.exp((p - 1) * math.log(x) - 0.5 * b * (x + 1 / x) - lfm)
+    return 0.0
+
+
+def invgauss_mode(mu):
+    return 1.0 / (math.sqrt(1.5 * 1.5 + 1 / (mu * mu)) + 1.5)
+
+
+def invgauss_pdf(x, mu):
+    m = invgauss_mode(mu)
+    lfm = -1.5 * math.log(m) - (m - mu) ** 2 / (2 * m * mu**2)
+    if x > 0:
+        return math.exp(-1.5 * math.log(x) - (x - mu) ** 2 / (2 * x * mu**2) - lfm)
+    return 0.0
+
+
+def powerlaw_pdf(x, a):
+    if x > 0:
+        return x ** (a - 1)
+    return 0.0
+
+
+# Define a dictionary: for a given distribution (keys), another dictionary
+# (values) specifies the parameters for NumericalInversePolynomial (PINV).
+# The keys of the latter dictionary are:
+# - pdf: the pdf of the distribution (callable). The signature of the pdf
+#   is float -> float (i.e., the function does not have to be vectorized).
+#   If possible, functions like log or exp from the module math should be
+#   preferred over functions from numpy since the PINV setup will be faster
+#   in that case.
+# - check_pinv_params: callable f that returns true if the shape parameters
+#   (args) are recommended parameters for PINV (i.e., the u-error does
+#   not exceed the default tolerance)
+# - center: scalar if the center does not depend on args, otherwise
+#   callable that returns the center as a function of the shape parameters
+# - rvs_transform: a callable that can be used to transform the rvs that
+#   are distributed according to the pdf to the target distribution
+#   (as an example, see the entry for the beta distribution)
+# - rvs_transform_inv: the inverse of rvs_transform (it is required
+#   for the transformed ppf)
+# - mirror_uniform: bool or a callable that returns true or false
+#   depending on the shape parameters. If True, the ppf is applied
+#   to 1-u instead of u to generate rvs, where u is a uniform rv.
+#   While both u and 1-u are uniform, it can be required to use 1-u
+#   to compute the u-error correctly. This is only relevant for the argus
+#   distribution.
+# The only required keys are "pdf" and "check_pinv_params".
+# All other keys are optional.
+
+PINV_CONFIG = {
+    "alpha": {
+        "pdf": alpha_pdf,
+        "check_pinv_params": lambda a: 1.0e-11 <= a < 2.1e5,
+        "center": lambda a: 0.25 * (math.sqrt(a * a + 8.0) - a),
+    },
+    "anglit": {
+        "pdf": lambda x: math.cos(2 * x) + 1.0e-13,
+        # +1.e-13 is necessary, otherwise PINV has strange problems as
+        # f(upper border) is very close to 0
+        "center": 0,
+    },
+    "argus": {
+        "pdf": argus_pdf,
+        "center": lambda chi: 0.7 if chi <= 5 else 0.5,
+        "check_pinv_params": lambda chi: 1e-20 < chi < 901,
+        "rvs_transform": argus_gamma_trf,
+        "rvs_transform_inv": argus_gamma_inv_trf,
+        "mirror_uniform": lambda chi: chi > 5,
+    },
+    "beta": {
+        "pdf": betaprime_pdf,
+        "center": lambda a, b: max(0.1, (a - 1) / (b + 1)),
+        "check_pinv_params": beta_valid_params,
+        "rvs_transform": lambda x, *args: x / (1 + x),
+        "rvs_transform_inv": lambda x, *args: x / (1 - x) if x < 1 else np.inf,
+    },
+    "betaprime": {
+        "pdf": betaprime_pdf,
+        "center": lambda a, b: max(0.1, (a - 1) / (b + 1)),
+        "check_pinv_params": beta_valid_params,
+    },
+    "bradford": {
+        "pdf": bradford_pdf,
+        "check_pinv_params": lambda a: 1.0e-6 <= a <= 1e9,
+        "center": 0.5,
+    },
+    "burr": {
+        "pdf": burr_pdf,
+        "center": lambda a, b: (2 ** (1 / b) - 1) ** (-1 / a),
+        "check_pinv_params": lambda a, b: (min(a, b) >= 0.3) and (max(a, b) <= 50),
+    },
+    "burr12": {
+        "pdf": burr12_pdf,
+        "center": lambda a, b: (2 ** (1 / b) - 1) ** (1 / a),
+        "check_pinv_params": lambda a, b: (min(a, b) >= 0.2) and (max(a, b) <= 50),
+    },
+    "cauchy": {
+        "pdf": lambda x: 1 / (1 + (x * x)),
+        "center": 0,
+    },
+    "chi": {
+        "pdf": chi_pdf,
+        "check_pinv_params": lambda df: 0.05 <= df <= 1.0e6,
+        "center": lambda a: math.sqrt(a),
+    },
+    "chi2": {
+        "pdf": chi2_pdf,
+        "check_pinv_params": lambda df: 0.07 <= df <= 1e6,
+        "center": lambda a: a,
+    },
+    "cosine": {
+        "pdf": lambda x: 1 + math.cos(x),
+        "center": 0,
+    },
+    "crystalball": {
+        "pdf": crystalball_pdf,
+        "check_pinv_params": lambda b, m: (0.01 <= b <= 5.5)
+        and (1.1 <= m <= 75.1),
+        "center": 0.0,
+    },
+    "expon": {
+        "pdf": lambda x: math.exp(-x),
+        "center": 1.0,
+    },
+    "gamma": {
+        "pdf": gamma_pdf,
+        "check_pinv_params": lambda a: 0.04 <= a <= 1e6,
+        "center": lambda a: a,
+    },
+    "gennorm": {
+        "pdf": lambda x, b: math.exp(-abs(x) ** b),
+        "check_pinv_params": lambda b: 0.081 <= b <= 45.0,
+        "center": 0.0,
+    },
+    "geninvgauss": {
+        "pdf": geninvgauss_pdf,
+        "check_pinv_params": lambda p, b: (abs(p) <= 1200.0)
+        and (1.0e-10 <= b <= 1200.0),
+        "center": geninvgauss_mode,
+    },
+    "gumbel_l": {
+        "pdf": lambda x: math.exp(x - math.exp(x)),
+        "center": -0.6,
+    },
+    "gumbel_r": {
+        "pdf": lambda x: math.exp(-x - math.exp(-x)),
+        "center": 0.6,
+    },
+    "hypsecant": {
+        "pdf": lambda x: 1.0 / (math.exp(x) + math.exp(-x)),
+        "center": 0.0,
+    },
+    "invgamma": {
+        "pdf": invgamma_pdf,
+        "check_pinv_params": lambda a: 0.04 <= a <= 1e6,
+        "center": lambda a: 1 / a,
+    },
+    "invgauss": {
+        "pdf": invgauss_pdf,
+        "check_pinv_params": lambda mu: 1.0e-10 <= mu <= 1.0e9,
+        "center": invgauss_mode,
+    },
+    "invweibull": {
+        "pdf": invweibull_pdf,
+        "check_pinv_params": lambda a: 0.12 <= a <= 512,
+        "center": 1.0,
+    },
+    "laplace": {
+        "pdf": lambda x: math.exp(-abs(x)),
+        "center": 0.0,
+    },
+    "logistic": {
+        "pdf": lambda x: math.exp(-x) / (1 + math.exp(-x)) ** 2,
+        "center": 0.0,
+    },
+    "maxwell": {
+        "pdf": lambda x: x * x * math.exp(-0.5 * x * x),
+        "center": 1.41421,
+    },
+    "moyal": {
+        "pdf": lambda x: math.exp(-(x + math.exp(-x)) / 2),
+        "center": 1.2,
+    },
+    "norm": {
+        "pdf": lambda x: math.exp(-x * x / 2),
+        "center": 0.0,
+    },
+    "pareto": {
+        "pdf": lambda x, b: x ** -(b + 1),
+        "center": lambda b: b / (b - 1) if b > 2 else 1.5,
+        "check_pinv_params": lambda b: 0.08 <= b <= 400000,
+    },
+    "powerlaw": {
+        "pdf": powerlaw_pdf,
+        "center": 1.0,
+        "check_pinv_params": lambda a: 0.06 <= a <= 1.0e5,
+    },
+    "t": {
+        "pdf": lambda x, df: (1 + x * x / df) ** (-0.5 * (df + 1)),
+        "check_pinv_params": lambda a: 0.07 <= a <= 1e6,
+        "center": 0.0,
+    },
+    "rayleigh": {
+        "pdf": lambda x: x * math.exp(-0.5 * (x * x)),
+        "center": 1.0,
+    },
+    "semicircular": {
+        "pdf": lambda x: math.sqrt(1.0 - (x * x)),
+        "center": 0,
+    },
+    "wald": {
+        "pdf": wald_pdf,
+        "center": 1.0,
+    },
+    "weibull_max": {
+        "pdf": weibull_max_pdf,
+        "check_pinv_params": lambda a: 0.25 <= a <= 512,
+        "center": -1.0,
+    },
+    "weibull_min": {
+        "pdf": weibull_min_pdf,
+        "check_pinv_params": lambda a: 0.25 <= a <= 512,
+        "center": 1.0,
+    },
+}
+
+
+def _validate_qmc_input(qmc_engine, d, seed):
+    # Input validation for `qmc_engine` and `d`
+    # Error messages for invalid `d` are raised by QMCEngine
+    # we could probably use a stats.qmc.check_qrandom_state
+    if isinstance(qmc_engine, QMCEngine):
+        if d is not None and qmc_engine.d != d:
+            message = "`d` must be consistent with dimension of `qmc_engine`."
+            raise ValueError(message)
+        d = qmc_engine.d if d is None else d
+    elif qmc_engine is None:
+        d = 1 if d is None else d
+        qmc_engine = Halton(d, seed=seed)
+    else:
+        message = (
+            "`qmc_engine` must be an instance of "
+            "`scipy.stats.qmc.QMCEngine` or `None`."
+        )
+        raise ValueError(message)
+
+    return qmc_engine, d
+
+
+class CustomDistPINV:
+    def __init__(self, pdf, args):
+        self._pdf = lambda x: pdf(x, *args)
+
+    def pdf(self, x):
+        return self._pdf(x)
+
+
+class FastGeneratorInversion:
+    """
+    Fast sampling by numerical inversion of the CDF for a large class of
+    continuous distributions in `scipy.stats`.
+
+    Parameters
+    ----------
+    dist : rv_frozen object
+        Frozen distribution object from `scipy.stats`. The list of supported
+        distributions can be found in the Notes section. The shape parameters,
+        `loc` and `scale` used to create the distributions must be scalars.
+        For example, for the Gamma distribution with shape parameter `p`,
+        `p` has to be a float, and for the beta distribution with shape
+        parameters (a, b), both a and b have to be floats.
+    domain : tuple of floats, optional
+        If one wishes to sample from a truncated/conditional distribution,
+        the domain has to be specified.
+        The default is None. In that case, the random variates are not
+        truncated, and the domain is inferred from the support of the
+        distribution.
+    ignore_shape_range : bool, optional
+        If False, shape parameters that are outside of the valid range
+        of values to ensure that the numerical accuracy (see Notes) is
+        high, raise a ValueError. If True, any shape parameters that are valid
+        for the distribution are accepted. This can be useful for testing.
+        The default is False.
+    random_state : {None, int, `numpy.random.Generator`,
+                        `numpy.random.RandomState`}, optional
+
+            A NumPy random number generator or seed for the underlying NumPy
+            random number generator used to generate the stream of uniform
+            random numbers.
+            If `random_state` is None, it uses ``self.random_state``.
+            If `random_state` is an int,
+            ``np.random.default_rng(random_state)`` is used.
+            If `random_state` is already a ``Generator`` or ``RandomState``
+            instance then that instance is used.
+
+    Attributes
+    ----------
+    loc : float
+        The location parameter.
+    random_state : {`numpy.random.Generator`, `numpy.random.RandomState`}
+        The random state used in relevant methods like `rvs` (unless
+        another `random_state` is passed as an argument to these methods).
+    scale : float
+        The scale parameter.
+
+    Methods
+    -------
+    cdf
+    evaluate_error
+    ppf
+    qrvs
+    rvs
+    support
+
+    Notes
+    -----
+    The class creates an object for continuous distributions specified
+    by `dist`. The method `rvs` uses a generator from
+    `scipy.stats.sampling` that is created when the object is instantiated.
+    In addition, the methods `qrvs` and `ppf` are added.
+    `qrvs` generate samples based on quasi-random numbers from
+    `scipy.stats.qmc`. `ppf` is the PPF based on the
+    numerical inversion method in [1]_ (`NumericalInversePolynomial`) that is
+    used to generate random variates.
+
+    Supported distributions (`distname`) are:
+    ``alpha``, ``anglit``, ``argus``, ``beta``, ``betaprime``, ``bradford``,
+    ``burr``, ``burr12``, ``cauchy``, ``chi``, ``chi2``, ``cosine``,
+    ``crystalball``, ``expon``, ``gamma``, ``gennorm``, ``geninvgauss``,
+    ``gumbel_l``, ``gumbel_r``, ``hypsecant``, ``invgamma``, ``invgauss``,
+    ``invweibull``, ``laplace``, ``logistic``, ``maxwell``, ``moyal``,
+    ``norm``, ``pareto``, ``powerlaw``, ``t``, ``rayleigh``, ``semicircular``,
+    ``wald``, ``weibull_max``, ``weibull_min``.
+
+    `rvs` relies on the accuracy of the numerical inversion. If very extreme
+    shape parameters are used, the numerical inversion might not work. However,
+    for all implemented distributions, the admissible shape parameters have
+    been tested, and an error will be raised if the user supplies values
+    outside of the allowed range. The u-error should not exceed 1e-10 for all
+    valid parameters. Note that warnings might be raised even if parameters
+    are within the valid range when the object is instantiated.
+    To check numerical accuracy, the method `evaluate_error` can be used.
+
+    Note that all implemented distributions are also part of `scipy.stats`, and
+    the object created by `FastGeneratorInversion` relies on methods like
+    `ppf`, `cdf` and `pdf` from `rv_frozen`. The main benefit of using this
+    class can be summarized as follows: Once the generator to sample random
+    variates is created in the setup step, sampling and evaluation of
+    the PPF using `ppf` are very fast,
+    and performance is essentially independent of the distribution. Therefore,
+    a substantial speed-up can be achieved for many distributions if large
+    numbers of random variates are required. It is important to know that this
+    fast sampling is achieved by inversion of the CDF. Thus, one uniform
+    random variate is transformed into a non-uniform variate, which is an
+    advantage for several simulation methods, e.g., when
+    the variance reduction methods of common random variates or
+    antithetic variates are be used ([2]_).
+
+    In addition, inversion makes it possible to
+
+    - to use a QMC generator from `scipy.stats.qmc` (method `qrvs`),
+    - to generate random variates truncated to an interval. For example, if
+
+    one aims to sample standard normal random variates from
+    the interval (2, 4), this can be easily achieved by using the parameter
+    `domain`.
+
+    The location and scale that are initially defined by `dist`
+    can be reset without having to rerun the setup
+    step to create the generator that is used for sampling. The relation
+    of the distribution `Y` with `loc` and `scale` to the standard
+    distribution `X` (i.e., ``loc=0`` and ``scale=1``) is given by
+    ``Y = loc + scale * X``.
+
+    References
+    ----------
+    .. [1] Derflinger, Gerhard, Wolfgang Hörmann, and Josef Leydold.
+           "Random variate  generation by numerical inversion when only the
+           density is known." ACM Transactions on Modeling and Computer
+           Simulation (TOMACS) 20.4 (2010): 1-25.
+    .. [2] Hörmann, Wolfgang, Josef Leydold and Gerhard Derflinger.
+           "Automatic nonuniform random number generation."
+           Springer, 2004.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> from scipy.stats.sampling import FastGeneratorInversion
+
+    Let's start with a simple example to illustrate the main features:
+
+    >>> gamma_frozen = stats.gamma(1.5)
+    >>> gamma_dist = FastGeneratorInversion(gamma_frozen)
+    >>> r = gamma_dist.rvs(size=1000)
+
+    The mean should be approximately equal to the shape parameter 1.5:
+
+    >>> r.mean()
+    1.52423591130436  # may vary
+
+    Similarly, we can draw a sample based on quasi-random numbers:
+
+    >>> r = gamma_dist.qrvs(size=1000)
+    >>> r.mean()
+    1.4996639255942914  # may vary
+
+    Compare the PPF against approximation `ppf`.
+
+    >>> q = [0.001, 0.2, 0.5, 0.8, 0.999]
+    >>> np.max(np.abs(gamma_frozen.ppf(q) - gamma_dist.ppf(q)))
+    4.313394796895409e-08
+
+    To confirm that the numerical inversion is accurate, we evaluate the
+    approximation error (u-error), which should be below 1e-10 (for more
+    details, refer to the documentation of `evaluate_error`):
+
+    >>> gamma_dist.evaluate_error()
+    (7.446320551265581e-11, nan)  # may vary
+
+    Note that the location and scale can be changed without instantiating a
+    new generator:
+
+    >>> gamma_dist.loc = 2
+    >>> gamma_dist.scale = 3
+    >>> r = gamma_dist.rvs(size=1000)
+
+    The mean should be approximately 2 + 3*1.5 = 6.5.
+
+    >>> r.mean()
+    6.399549295242894  # may vary
+
+    Let us also illustrate how truncation can be applied:
+
+    >>> trunc_norm = FastGeneratorInversion(stats.norm(), domain=(3, 4))
+    >>> r = trunc_norm.rvs(size=1000)
+    >>> 3 < r.min() < r.max() < 4
+    True
+
+    Check the mean:
+
+    >>> r.mean()
+    3.250433367078603  # may vary
+
+    >>> stats.norm.expect(lb=3, ub=4, conditional=True)
+    3.260454285589997
+
+    In this particular, case, `scipy.stats.truncnorm` could also be used to
+    generate truncated normal random variates.
+
+    """
+
+    def __init__(
+        self,
+        dist,
+        *,
+        domain=None,
+        ignore_shape_range=False,
+        random_state=None,
+    ):
+
+        if isinstance(dist, stats.distributions.rv_frozen):
+            distname = dist.dist.name
+            if distname not in PINV_CONFIG.keys():
+                raise ValueError(
+                    f"Distribution '{distname}' is not supported."
+                    f"It must be one of {list(PINV_CONFIG.keys())}"
+                    )
+        else:
+            raise ValueError("`dist` must be a frozen distribution object")
+
+        loc = dist.kwds.get("loc", 0)
+        scale = dist.kwds.get("scale", 1)
+        args = dist.args
+        if not np.isscalar(loc):
+            raise ValueError("loc must be scalar.")
+        if not np.isscalar(scale):
+            raise ValueError("scale must be scalar.")
+
+        self._frozendist = getattr(stats, distname)(
+            *args,
+            loc=loc,
+            scale=scale,
+        )
+        self._distname = distname
+
+        nargs = np.broadcast_arrays(args)[0].size
+        nargs_expected = self._frozendist.dist.numargs
+        if nargs != nargs_expected:
+            raise ValueError(
+                f"Each of the {nargs_expected} shape parameters must be a "
+                f"scalar, but {nargs} values are provided."
+            )
+
+        self.random_state = random_state
+
+        if domain is None:
+            self._domain = self._frozendist.support()
+            self._p_lower = 0.0
+            self._p_domain = 1.0
+        else:
+            self._domain = domain
+            self._p_lower = self._frozendist.cdf(self._domain[0])
+            _p_domain = self._frozendist.cdf(self._domain[1]) - self._p_lower
+            self._p_domain = _p_domain
+        self._set_domain_adj()
+        self._ignore_shape_range = ignore_shape_range
+
+        # the domain to be passed to NumericalInversePolynomial
+        # define a separate variable since in case of a transformation,
+        # domain_pinv will not be the same as self._domain
+        self._domain_pinv = self._domain
+
+        # get information about the distribution from the config to set up
+        # the generator
+        dist = self._process_config(distname, args)
+
+        if self._rvs_transform_inv is not None:
+            d0 = self._rvs_transform_inv(self._domain[0], *args)
+            d1 = self._rvs_transform_inv(self._domain[1], *args)
+            if d0 > d1:
+                # swap values if transformation if decreasing
+                d0, d1 = d1, d0
+            # only update _domain_pinv and not _domain
+            # _domain refers to the original distribution, _domain_pinv
+            # to the transformed distribution
+            self._domain_pinv = d0, d1
+
+        # self._center has been set by the call self._process_config
+        # check if self._center is inside the transformed domain
+        # _domain_pinv, otherwise move it to the endpoint that is closer
+        if self._center is not None:
+            if self._center < self._domain_pinv[0]:
+                self._center = self._domain_pinv[0]
+            elif self._center > self._domain_pinv[1]:
+                self._center = self._domain_pinv[1]
+
+        self._rng = NumericalInversePolynomial(
+            dist,
+            random_state=self.random_state,
+            domain=self._domain_pinv,
+            center=self._center,
+            )
+
+    @property
+    def random_state(self):
+        return self._random_state
+
+    @random_state.setter
+    def random_state(self, random_state):
+        self._random_state = check_random_state_qmc(random_state)
+
+    @property
+    def loc(self):
+        return self._frozendist.kwds.get("loc", 0)
+
+    @loc.setter
+    def loc(self, loc):
+        if not np.isscalar(loc):
+            raise ValueError("loc must be scalar.")
+        self._frozendist.kwds["loc"] = loc
+        # update the adjusted domain that depends on loc and scale
+        self._set_domain_adj()
+
+    @property
+    def scale(self):
+        return self._frozendist.kwds.get("scale", 0)
+
+    @scale.setter
+    def scale(self, scale):
+        if not np.isscalar(scale):
+            raise ValueError("scale must be scalar.")
+        self._frozendist.kwds["scale"] = scale
+        # update the adjusted domain that depends on loc and scale
+        self._set_domain_adj()
+
+    def _set_domain_adj(self):
+        """ Adjust the domain based on loc and scale. """
+        loc = self.loc
+        scale = self.scale
+        lb = self._domain[0] * scale + loc
+        ub = self._domain[1] * scale + loc
+        self._domain_adj = (lb, ub)
+
+    def _process_config(self, distname, args):
+        cfg = PINV_CONFIG[distname]
+        if "check_pinv_params" in cfg:
+            if not self._ignore_shape_range:
+                if not cfg["check_pinv_params"](*args):
+                    msg = ("No generator is defined for the shape parameters "
+                           f"{args}. Use ignore_shape_range to proceed "
+                           "with the selected values.")
+                    raise ValueError(msg)
+
+        if "center" in cfg.keys():
+            if not np.isscalar(cfg["center"]):
+                self._center = cfg["center"](*args)
+            else:
+                self._center = cfg["center"]
+        else:
+            self._center = None
+        self._rvs_transform = cfg.get("rvs_transform", None)
+        self._rvs_transform_inv = cfg.get("rvs_transform_inv", None)
+        _mirror_uniform = cfg.get("mirror_uniform", None)
+        if _mirror_uniform is None:
+            self._mirror_uniform = False
+        else:
+            self._mirror_uniform = _mirror_uniform(*args)
+
+        return CustomDistPINV(cfg["pdf"], args)
+
+    def rvs(self, size=None):
+        """
+        Sample from the distribution by inversion.
+
+        Parameters
+        ----------
+        size : int or tuple, optional
+            The shape of samples. Default is ``None`` in which case a scalar
+            sample is returned.
+
+        Returns
+        -------
+        rvs : array_like
+            A NumPy array of random variates.
+
+        Notes
+        -----
+        Random variates are generated by numerical inversion of the CDF, i.e.,
+        `ppf` computed by `NumericalInversePolynomial` when the class
+        is instantiated. Note that the
+        default ``rvs`` method of the rv_continuous class is
+        overwritten. Hence, a different stream of random numbers is generated
+        even if the same seed is used.
+        """
+        # note: we cannot use self._rng.rvs directly in case
+        # self._mirror_uniform is true
+        u = self.random_state.uniform(size=size)
+        if self._mirror_uniform:
+            u = 1 - u
+        r = self._rng.ppf(u)
+        if self._rvs_transform is not None:
+            r = self._rvs_transform(r, *self._frozendist.args)
+        return self.loc + self.scale * r
+
+    def ppf(self, q):
+        """
+        Very fast PPF (inverse CDF) of the distribution which
+        is a very close approximation of the exact PPF values.
+
+        Parameters
+        ----------
+        q : array_like
+            Array with probabilities.
+
+        Returns
+        -------
+        ppf : array_like
+            Quantiles corresponding to the values in `q`.
+
+        Notes
+        -----
+        The evaluation of the PPF is very fast but it may have a large
+        relative error in the far tails. The numerical precision of the PPF
+        is controlled by the q-error, that is,
+        ``max |q - CDF(PPF(q))|`` where the max is taken over points in
+        the interval [0,1], see `evaluate_error`.
+
+        Note that this PPF is designed to generate random samples.
+        """
+        q = np.asarray(q)
+        if self._mirror_uniform:
+            x = self._rng.ppf(1 - q)
+        else:
+            x = self._rng.ppf(q)
+        if self._rvs_transform is not None:
+            x = self._rvs_transform(x, *self._frozendist.args)
+        return self.scale * x + self.loc
+
+    def qrvs(self, size=None, d=None, qmc_engine=None):
+        """
+        Quasi-random variates of the given distribution.
+
+        The `qmc_engine` is used to draw uniform quasi-random variates, and
+        these are converted to quasi-random variates of the given distribution
+        using inverse transform sampling.
+
+        Parameters
+        ----------
+        size : int, tuple of ints, or None; optional
+            Defines shape of random variates array. Default is ``None``.
+        d : int or None, optional
+            Defines dimension of uniform quasi-random variates to be
+            transformed. Default is ``None``.
+        qmc_engine : scipy.stats.qmc.QMCEngine(d=1), optional
+            Defines the object to use for drawing
+            quasi-random variates. Default is ``None``, which uses
+            `scipy.stats.qmc.Halton(1)`.
+
+        Returns
+        -------
+        rvs : ndarray or scalar
+            Quasi-random variates. See Notes for shape information.
+
+        Notes
+        -----
+        The shape of the output array depends on `size`, `d`, and `qmc_engine`.
+        The intent is for the interface to be natural, but the detailed rules
+        to achieve this are complicated.
+
+        - If `qmc_engine` is ``None``, a `scipy.stats.qmc.Halton` instance is
+          created with dimension `d`. If `d` is not provided, ``d=1``.
+        - If `qmc_engine` is not ``None`` and `d` is ``None``, `d` is
+          determined from the dimension of the `qmc_engine`.
+        - If `qmc_engine` is not ``None`` and `d` is not ``None`` but the
+          dimensions are inconsistent, a ``ValueError`` is raised.
+        - After `d` is determined according to the rules above, the output
+          shape is ``tuple_shape + d_shape``, where:
+
+              - ``tuple_shape = tuple()`` if `size` is ``None``,
+              - ``tuple_shape = (size,)`` if `size` is an ``int``,
+              - ``tuple_shape = size`` if `size` is a sequence,
+              - ``d_shape = tuple()`` if `d` is ``None`` or `d` is 1, and
+              - ``d_shape = (d,)`` if `d` is greater than 1.
+
+        The elements of the returned array are part of a low-discrepancy
+        sequence. If `d` is 1, this means that none of the samples are truly
+        independent. If `d` > 1, each slice ``rvs[..., i]`` will be of a
+        quasi-independent sequence; see `scipy.stats.qmc.QMCEngine` for
+        details. Note that when `d` > 1, the samples returned are still those
+        of the provided univariate distribution, not a multivariate
+        generalization of that distribution.
+
+        """
+        qmc_engine, d = _validate_qmc_input(qmc_engine, d, self.random_state)
+        # mainly copied from unuran_wrapper.pyx.templ
+        # `rvs` is flexible about whether `size` is an int or tuple, so this
+        # should be, too.
+        try:
+            if size is None:
+                tuple_size = (1,)
+            else:
+                tuple_size = tuple(size)
+        except TypeError:
+            tuple_size = (size,)
+        # we do not use rng.qrvs directly since we need to be
+        # able to apply the ppf to 1 - u
+        N = 1 if size is None else np.prod(size)
+        u = qmc_engine.random(N)
+        if self._mirror_uniform:
+            u = 1 - u
+        qrvs = self._ppf(u)
+        if self._rvs_transform is not None:
+            qrvs = self._rvs_transform(qrvs, *self._frozendist.args)
+        if size is None:
+            qrvs = qrvs.squeeze()[()]
+        else:
+            if d == 1:
+                qrvs = qrvs.reshape(tuple_size)
+            else:
+                qrvs = qrvs.reshape(tuple_size + (d,))
+        return self.loc + self.scale * qrvs
+
+    def evaluate_error(self, size=100000, random_state=None, x_error=False):
+        """
+        Evaluate the numerical accuracy of the inversion (u- and x-error).
+
+        Parameters
+        ----------
+        size : int, optional
+            The number of random points over which the error is estimated.
+            Default is ``100000``.
+        random_state : {None, int, `numpy.random.Generator`,
+                        `numpy.random.RandomState`}, optional
+
+            A NumPy random number generator or seed for the underlying NumPy
+            random number generator used to generate the stream of uniform
+            random numbers.
+            If `random_state` is None, use ``self.random_state``.
+            If `random_state` is an int,
+            ``np.random.default_rng(random_state)`` is used.
+            If `random_state` is already a ``Generator`` or ``RandomState``
+            instance then that instance is used.
+        x_error : bool
+            If ``True``, return the x-error, as per the notes section. If ``False``,
+            returns ``NaN``.
+
+        Returns
+        -------
+        u_error, x_error : tuple of floats
+            A NumPy array of random variates.
+
+        Notes
+        -----
+        The numerical precision of the inverse CDF `ppf` is controlled by
+        the u-error. It is computed as follows:
+        ``max |u - CDF(PPF(u))|`` where the max is taken `size` random
+        points in the interval [0,1]. `random_state` determines the random
+        sample. Note that if `ppf` was exact, the u-error would be zero.
+
+        The x-error measures the direct distance between the exact PPF
+        and `ppf`. If ``x_error`` is set to ``True`, it is
+        computed as the maximum of the minimum of the relative and absolute
+        x-error:
+        ``max(min(x_error_abs[i], x_error_rel[i]))`` where
+        ``x_error_abs[i] = |PPF(u[i]) - PPF_fast(u[i])|``,
+        ``x_error_rel[i] = max |(PPF(u[i]) - PPF_fast(u[i])) / PPF(u[i])|``.
+        Note that it is important to consider the relative x-error in the case
+        that ``PPF(u)`` is close to zero or very large.
+
+        By default, only the u-error is evaluated and the x-error is set to
+        ``np.nan``. Note that the evaluation of the x-error will be very slow
+        if the implementation of the PPF is slow.
+
+        Further information about these error measures can be found in [1]_.
+
+        References
+        ----------
+        .. [1] Derflinger, Gerhard, Wolfgang Hörmann, and Josef Leydold.
+               "Random variate  generation by numerical inversion when only the
+               density is known." ACM Transactions on Modeling and Computer
+               Simulation (TOMACS) 20.4 (2010): 1-25.
+
+        Examples
+        --------
+
+        >>> import numpy as np
+        >>> from scipy import stats
+        >>> from scipy.stats.sampling import FastGeneratorInversion
+
+        Create an object for the normal distribution:
+
+        >>> d_norm_frozen = stats.norm()
+        >>> d_norm = FastGeneratorInversion(d_norm_frozen)
+
+        To confirm that the numerical inversion is accurate, we evaluate the
+        approximation error (u-error and x-error).
+
+        >>> u_error, x_error = d_norm.evaluate_error(x_error=True)
+
+        The u-error should be below 1e-10:
+
+        >>> u_error
+        8.785783212061915e-11  # may vary
+
+        Compare the PPF against approximation `ppf`:
+
+        >>> q = [0.001, 0.2, 0.4, 0.6, 0.8, 0.999]
+        >>> diff = np.abs(d_norm_frozen.ppf(q) - d_norm.ppf(q))
+        >>> x_error_abs = np.max(diff)
+        >>> x_error_abs
+        1.2937954707581412e-08
+
+        This is the absolute x-error evaluated at the points q. The relative
+        error is given by
+
+        >>> x_error_rel = np.max(diff / np.abs(d_norm_frozen.ppf(q)))
+        >>> x_error_rel
+        4.186725600453555e-09
+
+        The x_error computed above is derived in a very similar way over a
+        much larger set of random values q. At each value q[i], the minimum
+        of the relative and absolute error is taken. The final value is then
+        derived as the maximum of these values. In our example, we get the
+        following value:
+
+        >>> x_error
+        4.507068014335139e-07  # may vary
+
+        """
+        if not isinstance(size, numbers.Integral | np.integer):
+            raise ValueError("size must be an integer.")
+        # urng will be used to draw the samples for testing the error
+        # it must not interfere with self.random_state. therefore, do not
+        # call self.rvs, but draw uniform random numbers and apply
+        # self.ppf (note: like in rvs, consider self._mirror_uniform)
+        urng = check_random_state_qmc(random_state)
+        u = urng.uniform(size=size)
+        if self._mirror_uniform:
+            u = 1 - u
+        x = self.ppf(u)
+        uerr = np.max(np.abs(self._cdf(x) - u))
+        if not x_error:
+            return uerr, np.nan
+        ppf_u = self._ppf(u)
+        x_error_abs = np.abs(self.ppf(u)-ppf_u)
+        x_error_rel = x_error_abs / np.abs(ppf_u)
+        x_error_combined = np.array([x_error_abs, x_error_rel]).min(axis=0)
+        return uerr, np.max(x_error_combined)
+
+    def support(self):
+        """Support of the distribution.
+
+        Returns
+        -------
+        a, b : float
+            end-points of the distribution's support.
+
+        Notes
+        -----
+
+        Note that the support of the distribution depends on `loc`,
+        `scale` and `domain`.
+
+        Examples
+        --------
+
+        >>> from scipy import stats
+        >>> from scipy.stats.sampling import FastGeneratorInversion
+
+        Define a truncated normal distribution:
+
+        >>> d_norm = FastGeneratorInversion(stats.norm(), domain=(0, 1))
+        >>> d_norm.support()
+        (0, 1)
+
+        Shift the distribution:
+
+        >>> d_norm.loc = 2.5
+        >>> d_norm.support()
+        (2.5, 3.5)
+
+        """
+        return self._domain_adj
+
+    def _cdf(self, x):
+        """Cumulative distribution function (CDF)
+
+        Parameters
+        ----------
+        x : array_like
+            The values where the CDF is evaluated
+
+        Returns
+        -------
+        y : ndarray
+            CDF evaluated at x
+
+        """
+        y = self._frozendist.cdf(x)
+        if self._p_domain == 1.0:
+            return y
+        return np.clip((y - self._p_lower) / self._p_domain, 0, 1)
+
+    def _ppf(self, q):
+        """Percent point function (inverse of `cdf`)
+
+        Parameters
+        ----------
+        q : array_like
+            lower tail probability
+
+        Returns
+        -------
+        x : array_like
+            quantile corresponding to the lower tail probability q.
+
+        """
+        if self._p_domain == 1.0:
+            return self._frozendist.ppf(q)
+        x = self._frozendist.ppf(self._p_domain * np.array(q) + self._p_lower)
+        return np.clip(x, self._domain_adj[0], self._domain_adj[1])
+
+
+class RatioUniforms:
+    """
+    Generate random samples from a probability density function using the
+    ratio-of-uniforms method.
+
+    Parameters
+    ----------
+    pdf : callable
+        A function with signature `pdf(x)` that is proportional to the
+        probability density function of the distribution.
+    umax : float
+        The upper bound of the bounding rectangle in the u-direction.
+    vmin : float
+        The lower bound of the bounding rectangle in the v-direction.
+    vmax : float
+        The upper bound of the bounding rectangle in the v-direction.
+    c : float, optional
+        Shift parameter of ratio-of-uniforms method, see Notes. Default is 0.
+    random_state : {None, int, `numpy.random.Generator`,
+                    `numpy.random.RandomState`}, optional
+
+        If `seed` is None (or `np.random`), the `numpy.random.RandomState`
+        singleton is used.
+        If `seed` is an int, a new ``RandomState`` instance is used,
+        seeded with `seed`.
+        If `seed` is already a ``Generator`` or ``RandomState`` instance then
+        that instance is used.
+
+    Methods
+    -------
+    rvs
+
+    Notes
+    -----
+    Given a univariate probability density function `pdf` and a constant `c`,
+    define the set ``A = {(u, v) : 0 < u <= sqrt(pdf(v/u + c))}``.
+    If ``(U, V)`` is a random vector uniformly distributed over ``A``,
+    then ``V/U + c`` follows a distribution according to `pdf`.
+
+    The above result (see [1]_, [2]_) can be used to sample random variables
+    using only the PDF, i.e. no inversion of the CDF is required. Typical
+    choices of `c` are zero or the mode of `pdf`. The set ``A`` is a subset of
+    the rectangle ``R = [0, umax] x [vmin, vmax]`` where
+
+    - ``umax = sup sqrt(pdf(x))``
+    - ``vmin = inf (x - c) sqrt(pdf(x))``
+    - ``vmax = sup (x - c) sqrt(pdf(x))``
+
+    In particular, these values are finite if `pdf` is bounded and
+    ``x**2 * pdf(x)`` is bounded (i.e. subquadratic tails).
+    One can generate ``(U, V)`` uniformly on ``R`` and return
+    ``V/U + c`` if ``(U, V)`` are also in ``A`` which can be directly
+    verified.
+
+    The algorithm is not changed if one replaces `pdf` by k * `pdf` for any
+    constant k > 0. Thus, it is often convenient to work with a function
+    that is proportional to the probability density function by dropping
+    unnecessary normalization factors.
+
+    Intuitively, the method works well if ``A`` fills up most of the
+    enclosing rectangle such that the probability is high that ``(U, V)``
+    lies in ``A`` whenever it lies in ``R`` as the number of required
+    iterations becomes too large otherwise. To be more precise, note that
+    the expected number of iterations to draw ``(U, V)`` uniformly
+    distributed on ``R`` such that ``(U, V)`` is also in ``A`` is given by
+    the ratio ``area(R) / area(A) = 2 * umax * (vmax - vmin) / area(pdf)``,
+    where `area(pdf)` is the integral of `pdf` (which is equal to one if the
+    probability density function is used but can take on other values if a
+    function proportional to the density is used). The equality holds since
+    the area of ``A`` is equal to ``0.5 * area(pdf)`` (Theorem 7.1 in [1]_).
+    If the sampling fails to generate a single random variate after 50000
+    iterations (i.e. not a single draw is in ``A``), an exception is raised.
+
+    If the bounding rectangle is not correctly specified (i.e. if it does not
+    contain ``A``), the algorithm samples from a distribution different from
+    the one given by `pdf`. It is therefore recommended to perform a
+    test such as `~scipy.stats.kstest` as a check.
+
+    References
+    ----------
+    .. [1] L. Devroye, "Non-Uniform Random Variate Generation",
+       Springer-Verlag, 1986.
+
+    .. [2] W. Hoermann and J. Leydold, "Generating generalized inverse Gaussian
+       random variates", Statistics and Computing, 24(4), p. 547--557, 2014.
+
+    .. [3] A.J. Kinderman and J.F. Monahan, "Computer Generation of Random
+       Variables Using the Ratio of Uniform Deviates",
+       ACM Transactions on Mathematical Software, 3(3), p. 257--260, 1977.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+
+    >>> from scipy.stats.sampling import RatioUniforms
+    >>> rng = np.random.default_rng()
+
+    Simulate normally distributed random variables. It is easy to compute the
+    bounding rectangle explicitly in that case. For simplicity, we drop the
+    normalization factor of the density.
+
+    >>> f = lambda x: np.exp(-x**2 / 2)
+    >>> v = np.sqrt(f(np.sqrt(2))) * np.sqrt(2)
+    >>> umax = np.sqrt(f(0))
+    >>> gen = RatioUniforms(f, umax=umax, vmin=-v, vmax=v, random_state=rng)
+    >>> r = gen.rvs(size=2500)
+
+    The K-S test confirms that the random variates are indeed normally
+    distributed (normality is not rejected at 5% significance level):
+
+    >>> stats.kstest(r, 'norm')[1]
+    0.250634764150542
+
+    The exponential distribution provides another example where the bounding
+    rectangle can be determined explicitly.
+
+    >>> gen = RatioUniforms(lambda x: np.exp(-x), umax=1, vmin=0,
+    ...                     vmax=2*np.exp(-1), random_state=rng)
+    >>> r = gen.rvs(1000)
+    >>> stats.kstest(r, 'expon')[1]
+    0.21121052054580314
+
+    """
+
+    def __init__(self, pdf, *, umax, vmin, vmax, c=0, random_state=None):
+        if vmin >= vmax:
+            raise ValueError("vmin must be smaller than vmax.")
+
+        if umax <= 0:
+            raise ValueError("umax must be positive.")
+
+        self._pdf = pdf
+        self._umax = umax
+        self._vmin = vmin
+        self._vmax = vmax
+        self._c = c
+        self._rng = check_random_state(random_state)
+
+    def rvs(self, size=1):
+        """Sampling of random variates.
+
+        Parameters
+        ----------
+        size : int or tuple of ints, optional
+            Number of random variates to be generated (default is 1).
+
+        Returns
+        -------
+        rvs : ndarray
+            The random variates distributed according to the probability
+            distribution defined by the pdf.
+
+        """
+        size1d = tuple(np.atleast_1d(size))
+        N = np.prod(size1d)  # number of rvs needed, reshape upon return
+
+        # start sampling using ratio of uniforms method
+        x = np.zeros(N)
+        simulated, i = 0, 1
+
+        # loop until N rvs have been generated: expected runtime is finite.
+        # to avoid infinite loop, raise exception if not a single rv has been
+        # generated after 50000 tries. even if the expected number of iterations
+        # is 1000, the probability of this event is (1-1/1000)**50000
+        # which is of order 10e-22
+        while simulated < N:
+            k = N - simulated
+            # simulate uniform rvs on [0, umax] and [vmin, vmax]
+            u1 = self._umax * self._rng.uniform(size=k)
+            v1 = self._rng.uniform(self._vmin, self._vmax, size=k)
+            # apply rejection method
+            rvs = v1 / u1 + self._c
+            accept = (u1**2 <= self._pdf(rvs))
+            num_accept = np.sum(accept)
+            if num_accept > 0:
+                x[simulated:(simulated + num_accept)] = rvs[accept]
+                simulated += num_accept
+
+            if (simulated == 0) and (i*N >= 50000):
+                msg = (
+                    f"Not a single random variate could be generated in {i*N} "
+                    "attempts. The ratio of uniforms method does not appear "
+                    "to work for the provided parameters. Please check the "
+                    "pdf and the bounds."
+                )
+                raise RuntimeError(msg)
+            i += 1
+
+        return np.reshape(x, size1d)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_sensitivity_analysis.py b/venv/lib/python3.12/site-packages/scipy/stats/_sensitivity_analysis.py
new file mode 100644
index 0000000000000000000000000000000000000000..529c1e6120a63ff65313928ee87b4ee1e881a73c
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_sensitivity_analysis.py
@@ -0,0 +1,718 @@
+import inspect
+from dataclasses import dataclass
+from typing import TYPE_CHECKING, Any
+from collections.abc import Callable
+
+import numpy as np
+
+from scipy.stats._common import ConfidenceInterval
+from scipy.stats._qmc import check_random_state
+from scipy.stats._resampling import BootstrapResult
+from scipy.stats import qmc, bootstrap
+from scipy._lib._array_api import xp_capabilities
+from scipy._lib._util import _transition_to_rng
+
+
+if TYPE_CHECKING:
+    import numpy.typing as npt
+    from scipy._lib._util import DecimalNumber, IntNumber
+
+
+__all__ = [
+    'sobol_indices'
+]
+
+
+def f_ishigami(x: "npt.ArrayLike") -> "npt.NDArray[np.inexact[Any]]":
+    r"""Ishigami function.
+
+    .. math::
+
+        Y(\mathbf{x}) = \sin x_1 + 7 \sin^2 x_2 + 0.1 x_3^4 \sin x_1
+
+    with :math:`\mathbf{x} \in [-\pi, \pi]^3`.
+
+    Parameters
+    ----------
+    x : array_like ([x1, x2, x3], n)
+
+    Returns
+    -------
+    f : array_like (n,)
+        Function evaluation.
+
+    References
+    ----------
+    .. [1] Ishigami, T. and T. Homma. "An importance quantification technique
+       in uncertainty analysis for computer models." IEEE,
+       :doi:`10.1109/ISUMA.1990.151285`, 1990.
+    """
+    x = np.atleast_2d(x)
+    f_eval = (
+        np.sin(x[0])
+        + 7 * np.sin(x[1])**2
+        + 0.1 * (x[2]**4) * np.sin(x[0])
+    )
+    return f_eval
+
+
+def sample_A_B(
+    n,
+    dists,
+    rng=None
+):
+    """Sample two matrices A and B.
+
+    Uses a Sobol' sequence with 2`d` columns to have 2 uncorrelated matrices.
+    This is more efficient than using 2 random draw of Sobol'.
+    See sec. 5 from [1]_.
+
+    Output shape is (d, n).
+
+    References
+    ----------
+    .. [1] Saltelli, A., P. Annoni, I. Azzini, F. Campolongo, M. Ratto, and
+       S. Tarantola. "Variance based sensitivity analysis of model
+       output. Design and estimator for the total sensitivity index."
+       Computer Physics Communications, 181(2):259-270,
+       :doi:`10.1016/j.cpc.2009.09.018`, 2010.
+    """
+    d = len(dists)
+    A_B = qmc.Sobol(d=2*d, seed=rng, bits=64).random(n).T
+    A_B = A_B.reshape(2, d, -1)
+    try:
+        for d_, dist in enumerate(dists):
+            A_B[:, d_] = dist.ppf(A_B[:, d_])
+    except AttributeError as exc:
+        message = "Each distribution in `dists` must have method `ppf`."
+        raise ValueError(message) from exc
+    return A_B
+
+
+def sample_AB(A: np.ndarray, B: np.ndarray) -> np.ndarray:
+    """AB matrix.
+
+    AB: rows of B into A. Shape (d, d, n).
+
+    - Copy A into d "pages"
+    - In the first page, replace 1st rows of A with 1st row of B.
+    ...
+    - In the dth page, replace dth row of A with dth row of B.
+    - return the stack of pages
+
+    """
+    d, n = A.shape
+    AB = np.tile(A, (d, 1, 1))
+    i = np.arange(d)
+    AB[i, i] = B[i]
+    return AB
+
+
+def saltelli_2010(
+    f_A: np.ndarray, f_B: np.ndarray, f_AB: np.ndarray
+) -> tuple[np.ndarray, np.ndarray]:
+    r"""Saltelli2010 formulation.
+
+    .. math::
+
+        S_i = \frac{1}{N} \sum_{j=1}^N
+        f(\mathbf{B})_j (f(\mathbf{AB}^{(i)})_j - f(\mathbf{A})_j)
+
+    .. math::
+
+        S_{T_i} = \frac{1}{N} \sum_{j=1}^N
+        (f(\mathbf{A})_j - f(\mathbf{AB}^{(i)})_j)^2
+
+    Parameters
+    ----------
+    f_A, f_B : array_like (s, n)
+        Function values at A and B, respectively
+    f_AB : array_like (d, s, n)
+        Function values at each of the AB pages
+
+    Returns
+    -------
+    s, st : array_like (s, d)
+        First order and total order Sobol' indices.
+
+    References
+    ----------
+    .. [1] Saltelli, A., P. Annoni, I. Azzini, F. Campolongo, M. Ratto, and
+       S. Tarantola. "Variance based sensitivity analysis of model
+       output. Design and estimator for the total sensitivity index."
+       Computer Physics Communications, 181(2):259-270,
+       :doi:`10.1016/j.cpc.2009.09.018`, 2010.
+    """
+    # Empirical variance calculated using output from A and B which are
+    # independent. Output of AB is not independent and cannot be used
+    var = np.var([f_A, f_B], axis=(0, -1))
+
+    # We divide by the variance to have a ratio of variance
+    # this leads to eq. 2
+    s = np.mean(f_B * (f_AB - f_A), axis=-1) / var  # Table 2 (b)
+    st = 0.5 * np.mean((f_A - f_AB) ** 2, axis=-1) / var  # Table 2 (f)
+
+    return s.T, st.T
+
+
+@dataclass
+class BootstrapSobolResult:
+    first_order: BootstrapResult
+    total_order: BootstrapResult
+
+
+@dataclass
+class SobolResult:
+    first_order: np.ndarray
+    total_order: np.ndarray
+    _indices_method: Callable
+    _f_A: np.ndarray
+    _f_B: np.ndarray
+    _f_AB: np.ndarray
+    _A: np.ndarray | None = None
+    _B: np.ndarray | None = None
+    _AB: np.ndarray | None = None
+    _bootstrap_result: BootstrapResult | None = None
+
+    def bootstrap(
+        self,
+        confidence_level: "DecimalNumber" = 0.95,
+        n_resamples: "IntNumber" = 999
+    ) -> BootstrapSobolResult:
+        """Bootstrap Sobol' indices to provide confidence intervals.
+
+        Parameters
+        ----------
+        confidence_level : float, default: ``0.95``
+            The confidence level of the confidence intervals.
+        n_resamples : int, default: ``999``
+            The number of resamples performed to form the bootstrap
+            distribution of the indices.
+
+        Returns
+        -------
+        res : BootstrapSobolResult
+            Bootstrap result containing the confidence intervals and the
+            bootstrap distribution of the indices.
+
+            An object with attributes:
+
+            first_order : BootstrapResult
+                Bootstrap result of the first order indices.
+            total_order : BootstrapResult
+                Bootstrap result of the total order indices.
+            See `BootstrapResult` for more details.
+
+        """
+        def statistic(idx):
+            f_A_ = self._f_A[:, idx]
+            f_B_ = self._f_B[:, idx]
+            f_AB_ = self._f_AB[..., idx]
+            return self._indices_method(f_A_, f_B_, f_AB_)
+
+        n = self._f_A.shape[1]
+
+        res = bootstrap(
+            [np.arange(n)], statistic=statistic, method="BCa",
+            n_resamples=n_resamples,
+            confidence_level=confidence_level,
+            bootstrap_result=self._bootstrap_result
+        )
+        self._bootstrap_result = res
+
+        first_order = BootstrapResult(
+            confidence_interval=ConfidenceInterval(
+                res.confidence_interval.low[0], res.confidence_interval.high[0]
+            ),
+            bootstrap_distribution=res.bootstrap_distribution[0],
+            standard_error=res.standard_error[0],
+        )
+        total_order = BootstrapResult(
+            confidence_interval=ConfidenceInterval(
+                res.confidence_interval.low[1], res.confidence_interval.high[1]
+            ),
+            bootstrap_distribution=res.bootstrap_distribution[1],
+            standard_error=res.standard_error[1],
+        )
+
+        return BootstrapSobolResult(
+            first_order=first_order, total_order=total_order
+        )
+
+
+@xp_capabilities(np_only=True)
+@_transition_to_rng('random_state', replace_doc=False)
+def sobol_indices(
+    *,
+    func,
+    n,
+    dists=None,
+    method='saltelli_2010',
+    rng=None
+):
+    r"""Global sensitivity indices of Sobol'.
+
+    Parameters
+    ----------
+    func : callable or dict(str, array_like)
+        If `func` is a callable, function to compute the Sobol' indices from.
+        Its signature must be::
+
+            func(x: ArrayLike) -> ArrayLike
+
+        with ``x`` of shape ``(d, n)`` and output of shape ``(s, n)`` where:
+
+        - ``d`` is the input dimensionality of `func`
+          (number of input variables),
+        - ``s`` is the output dimensionality of `func`
+          (number of output variables), and
+        - ``n`` is the number of samples (see `n` below).
+
+        Function evaluation values must be finite.
+
+        If `func` is a dictionary, contains the function evaluations from three
+        different arrays. Keys must be: ``f_A``, ``f_B`` and ``f_AB``.
+        ``f_A`` and ``f_B`` should have a shape ``(s, n)`` and ``f_AB``
+        should have a shape ``(d, s, n)``.
+        This is an advanced feature and misuse can lead to wrong analysis.
+    n : int
+        Number of samples used to generate the matrices ``A`` and ``B``.
+        Must be a power of 2. The total number of points at which `func` is
+        evaluated will be ``n*(d+2)``.
+    dists : list(distributions), optional
+        List of each parameter's distribution. The distribution of parameters
+        depends on the application and should be carefully chosen.
+        Parameters are assumed to be independently distributed, meaning there
+        is no constraint nor relationship between their values.
+
+        Distributions must be an instance of a class with a ``ppf``
+        method.
+
+        Must be specified if `func` is a callable, and ignored otherwise.
+    method : Callable or str, default: 'saltelli_2010'
+        Method used to compute the first and total Sobol' indices.
+
+        If a callable, its signature must be::
+
+            func(f_A: np.ndarray, f_B: np.ndarray, f_AB: np.ndarray)
+            -> tuple[np.ndarray, np.ndarray]
+
+        with ``f_A, f_B`` of shape ``(s, n)`` and ``f_AB`` of shape
+        ``(d, s, n)``.
+        These arrays contain the function evaluations from three different sets
+        of samples.
+        The output is a tuple of the first and total indices with
+        shape ``(s, d)``.
+        This is an advanced feature and misuse can lead to wrong analysis.
+    rng : `numpy.random.Generator`, optional
+        Pseudorandom number generator state. When `rng` is None, a new
+        `numpy.random.Generator` is created using entropy from the
+        operating system. Types other than `numpy.random.Generator` are
+        passed to `numpy.random.default_rng` to instantiate a ``Generator``.
+
+        .. versionchanged:: 1.15.0
+
+            As part of the `SPEC-007 <https://scientific-python.org/specs/spec-0007/>`_
+            transition from use of `numpy.random.RandomState` to
+            `numpy.random.Generator`, this keyword was changed from `random_state` to
+            `rng`. For an interim period, both keywords will continue to work, although
+            only one may be specified at a time. After the interim period, function
+            calls using the `random_state` keyword will emit warnings. Following a
+            deprecation period, the `random_state` keyword will be removed.
+
+    Returns
+    -------
+    res : SobolResult
+        An object with attributes:
+
+        first_order : ndarray of shape (s, d)
+            First order Sobol' indices.
+        total_order : ndarray of shape (s, d)
+            Total order Sobol' indices.
+
+        And method:
+
+        bootstrap(confidence_level: float, n_resamples: int)
+        -> BootstrapSobolResult
+
+            A method providing confidence intervals on the indices.
+            See `scipy.stats.bootstrap` for more details.
+
+            The bootstrapping is done on both first and total order indices,
+            and they are available in `BootstrapSobolResult` as attributes
+            ``first_order`` and ``total_order``.
+
+    Notes
+    -----
+    The Sobol' method [1]_, [2]_ is a variance-based Sensitivity Analysis which
+    obtains the contribution of each parameter to the variance of the
+    quantities of interest (QoIs; i.e., the outputs of `func`).
+    Respective contributions can be used to rank the parameters and
+    also gauge the complexity of the model by computing the
+    model's effective (or mean) dimension.
+
+    .. note::
+
+        Parameters are assumed to be independently distributed. Each
+        parameter can still follow any distribution. In fact, the distribution
+        is very important and should match the real distribution of the
+        parameters.
+
+    It uses a functional decomposition of the variance of the function to
+    explore
+
+    .. math::
+
+        \mathbb{V}(Y) = \sum_{i}^{d} \mathbb{V}_i (Y) + \sum_{i<j}^{d}
+        \mathbb{V}_{ij}(Y) + ... + \mathbb{V}_{1,2,...,d}(Y),
+
+    introducing conditional variances:
+
+    .. math::
+
+        \mathbb{V}_i(Y) = \mathbb{\mathbb{V}}[\mathbb{E}(Y|x_i)]
+        \qquad
+        \mathbb{V}_{ij}(Y) = \mathbb{\mathbb{V}}[\mathbb{E}(Y|x_i x_j)]
+        - \mathbb{V}_i(Y) - \mathbb{V}_j(Y),
+
+    Sobol' indices are expressed as
+
+    .. math::
+
+        S_i = \frac{\mathbb{V}_i(Y)}{\mathbb{V}[Y]}
+        \qquad
+        S_{ij} =\frac{\mathbb{V}_{ij}(Y)}{\mathbb{V}[Y]}.
+
+    :math:`S_{i}` corresponds to the first-order term which apprises the
+    contribution of the i-th parameter, while :math:`S_{ij}` corresponds to the
+    second-order term which informs about the contribution of interactions
+    between the i-th and the j-th parameters. These equations can be
+    generalized to compute higher order terms; however, they are expensive to
+    compute and their interpretation is complex.
+    This is why only first order indices are provided.
+
+    Total order indices represent the global contribution of the parameters
+    to the variance of the QoI and are defined as:
+
+    .. math::
+
+        S_{T_i} = S_i + \sum_j S_{ij} + \sum_{j,k} S_{ijk} + ...
+        = 1 - \frac{\mathbb{V}[\mathbb{E}(Y|x_{\sim i})]}{\mathbb{V}[Y]}.
+
+    First order indices sum to at most 1, while total order indices sum to at
+    least 1. If there are no interactions, then first and total order indices
+    are equal, and both first and total order indices sum to 1.
+
+    .. warning::
+
+        Negative Sobol' values are due to numerical errors. Increasing the
+        number of points `n` should help.
+
+        The number of sample required to have a good analysis increases with
+        the dimensionality of the problem. e.g. for a 3 dimension problem,
+        consider at minima ``n >= 2**12``. The more complex the model is,
+        the more samples will be needed.
+
+        Even for a purely additive model, the indices may not sum to 1 due
+        to numerical noise.
+
+    References
+    ----------
+    .. [1] Sobol, I. M.. "Sensitivity analysis for nonlinear mathematical
+       models." Mathematical Modeling and Computational Experiment, 1:407-414,
+       1993.
+    .. [2] Sobol, I. M. (2001). "Global sensitivity indices for nonlinear
+       mathematical models and their Monte Carlo estimates." Mathematics
+       and Computers in Simulation, 55(1-3):271-280,
+       :doi:`10.1016/S0378-4754(00)00270-6`, 2001.
+    .. [3] Saltelli, A. "Making best use of model evaluations to
+       compute sensitivity indices."  Computer Physics Communications,
+       145(2):280-297, :doi:`10.1016/S0010-4655(02)00280-1`, 2002.
+    .. [4] Saltelli, A., M. Ratto, T. Andres, F. Campolongo, J. Cariboni,
+       D. Gatelli, M. Saisana, and S. Tarantola. "Global Sensitivity Analysis.
+       The Primer." 2007.
+    .. [5] Saltelli, A., P. Annoni, I. Azzini, F. Campolongo, M. Ratto, and
+       S. Tarantola. "Variance based sensitivity analysis of model
+       output. Design and estimator for the total sensitivity index."
+       Computer Physics Communications, 181(2):259-270,
+       :doi:`10.1016/j.cpc.2009.09.018`, 2010.
+    .. [6] Ishigami, T. and T. Homma. "An importance quantification technique
+       in uncertainty analysis for computer models." IEEE,
+       :doi:`10.1109/ISUMA.1990.151285`, 1990.
+
+    Examples
+    --------
+    The following is an example with the Ishigami function [6]_
+
+    .. math::
+
+        Y(\mathbf{x}) = \sin x_1 + 7 \sin^2 x_2 + 0.1 x_3^4 \sin x_1,
+
+    with :math:`\mathbf{x} \in [-\pi, \pi]^3`. This function exhibits strong
+    non-linearity and non-monotonicity.
+
+    Remember, Sobol' indices assumes that samples are independently
+    distributed. In this case we use a uniform distribution on each marginals.
+
+    >>> import numpy as np
+    >>> from scipy.stats import sobol_indices, uniform
+    >>> rng = np.random.default_rng()
+    >>> def f_ishigami(x):
+    ...     f_eval = (
+    ...         np.sin(x[0])
+    ...         + 7 * np.sin(x[1])**2
+    ...         + 0.1 * (x[2]**4) * np.sin(x[0])
+    ...     )
+    ...     return f_eval
+    >>> indices = sobol_indices(
+    ...     func=f_ishigami, n=1024,
+    ...     dists=[
+    ...         uniform(loc=-np.pi, scale=2*np.pi),
+    ...         uniform(loc=-np.pi, scale=2*np.pi),
+    ...         uniform(loc=-np.pi, scale=2*np.pi)
+    ...     ],
+    ...     rng=rng
+    ... )
+    >>> indices.first_order
+    array([0.31637954, 0.43781162, 0.00318825])
+    >>> indices.total_order
+    array([0.56122127, 0.44287857, 0.24229595])
+
+    Confidence interval can be obtained using bootstrapping.
+
+    >>> boot = indices.bootstrap()
+
+    Then, this information can be easily visualized.
+
+    >>> import matplotlib.pyplot as plt
+    >>> fig, axs = plt.subplots(1, 2, figsize=(9, 4))
+    >>> _ = axs[0].errorbar(
+    ...     [1, 2, 3], indices.first_order, fmt='o',
+    ...     yerr=[
+    ...         indices.first_order - boot.first_order.confidence_interval.low,
+    ...         boot.first_order.confidence_interval.high - indices.first_order
+    ...     ],
+    ... )
+    >>> axs[0].set_ylabel("First order Sobol' indices")
+    >>> axs[0].set_xlabel('Input parameters')
+    >>> axs[0].set_xticks([1, 2, 3])
+    >>> _ = axs[1].errorbar(
+    ...     [1, 2, 3], indices.total_order, fmt='o',
+    ...     yerr=[
+    ...         indices.total_order - boot.total_order.confidence_interval.low,
+    ...         boot.total_order.confidence_interval.high - indices.total_order
+    ...     ],
+    ... )
+    >>> axs[1].set_ylabel("Total order Sobol' indices")
+    >>> axs[1].set_xlabel('Input parameters')
+    >>> axs[1].set_xticks([1, 2, 3])
+    >>> plt.tight_layout()
+    >>> plt.show()
+
+    .. note::
+
+        By default, `scipy.stats.uniform` has support ``[0, 1]``.
+        Using the parameters ``loc`` and ``scale``, one obtains the uniform
+        distribution on ``[loc, loc + scale]``.
+
+    This result is particularly interesting because the first order index
+    :math:`S_{x_3} = 0` whereas its total order is :math:`S_{T_{x_3}} = 0.244`.
+    This means that higher order interactions with :math:`x_3` are responsible
+    for the difference. Almost 25% of the observed variance
+    on the QoI is due to the correlations between :math:`x_3` and :math:`x_1`,
+    although :math:`x_3` by itself has no impact on the QoI.
+
+    The following gives a visual explanation of Sobol' indices on this
+    function. Let's generate 1024 samples in :math:`[-\pi, \pi]^3` and
+    calculate the value of the output.
+
+    >>> from scipy.stats import qmc
+    >>> n_dim = 3
+    >>> p_labels = ['$x_1$', '$x_2$', '$x_3$']
+    >>> sample = qmc.Sobol(d=n_dim, seed=rng).random(1024)
+    >>> sample = qmc.scale(
+    ...     sample=sample,
+    ...     l_bounds=[-np.pi, -np.pi, -np.pi],
+    ...     u_bounds=[np.pi, np.pi, np.pi]
+    ... )
+    >>> output = f_ishigami(sample.T)
+
+    Now we can do scatter plots of the output with respect to each parameter.
+    This gives a visual way to understand how each parameter impacts the
+    output of the function.
+
+    >>> fig, ax = plt.subplots(1, n_dim, figsize=(12, 4))
+    >>> for i in range(n_dim):
+    ...     xi = sample[:, i]
+    ...     ax[i].scatter(xi, output, marker='+')
+    ...     ax[i].set_xlabel(p_labels[i])
+    >>> ax[0].set_ylabel('Y')
+    >>> plt.tight_layout()
+    >>> plt.show()
+
+    Now Sobol' goes a step further:
+    by conditioning the output value by given values of the parameter
+    (black lines), the conditional output mean is computed. It corresponds to
+    the term :math:`\mathbb{E}(Y|x_i)`. Taking the variance of this term gives
+    the numerator of the Sobol' indices.
+
+    >>> mini = np.min(output)
+    >>> maxi = np.max(output)
+    >>> n_bins = 10
+    >>> bins = np.linspace(-np.pi, np.pi, num=n_bins, endpoint=False)
+    >>> dx = bins[1] - bins[0]
+    >>> fig, ax = plt.subplots(1, n_dim, figsize=(12, 4))
+    >>> for i in range(n_dim):
+    ...     xi = sample[:, i]
+    ...     ax[i].scatter(xi, output, marker='+')
+    ...     ax[i].set_xlabel(p_labels[i])
+    ...     for bin_ in bins:
+    ...         idx = np.where((bin_ <= xi) & (xi <= bin_ + dx))
+    ...         xi_ = xi[idx]
+    ...         y_ = output[idx]
+    ...         ave_y_ = np.mean(y_)
+    ...         ax[i].plot([bin_ + dx/2] * 2, [mini, maxi], c='k')
+    ...         ax[i].scatter(bin_ + dx/2, ave_y_, c='r')
+    >>> ax[0].set_ylabel('Y')
+    >>> plt.tight_layout()
+    >>> plt.show()
+
+    Looking at :math:`x_3`, the variance
+    of the mean is zero leading to :math:`S_{x_3} = 0`. But we can further
+    observe that the variance of the output is not constant along the parameter
+    values of :math:`x_3`. This heteroscedasticity is explained by higher order
+    interactions. Moreover, a heteroscedasticity is also noticeable on
+    :math:`x_1` leading to an interaction between :math:`x_3` and :math:`x_1`.
+    On :math:`x_2`, the variance seems to be constant and thus null interaction
+    with this parameter can be supposed.
+
+    This case is fairly simple to analyse visually---although it is only a
+    qualitative analysis. Nevertheless, when the number of input parameters
+    increases such analysis becomes unrealistic as it would be difficult to
+    conclude on high-order terms. Hence the benefit of using Sobol' indices.
+
+    """
+    rng = check_random_state(rng)
+
+    n_ = int(n)
+    if not (n_ & (n_ - 1) == 0) or n != n_:
+        raise ValueError(
+            "The balance properties of Sobol' points require 'n' "
+            "to be a power of 2."
+        )
+    n = n_
+
+    if not callable(method):
+        indices_methods = {
+            "saltelli_2010": saltelli_2010,
+        }
+        try:
+            method = method.lower()  # type: ignore[assignment]
+            indices_method_ = indices_methods[method]
+        except KeyError as exc:
+            message = (
+                f"{method!r} is not a valid 'method'. It must be one of"
+                f" {set(indices_methods)!r} or a callable."
+            )
+            raise ValueError(message) from exc
+    else:
+        indices_method_ = method
+        sig = inspect.signature(indices_method_)
+
+        if set(sig.parameters) != {'f_A', 'f_B', 'f_AB'}:
+            message = (
+                "If 'method' is a callable, it must have the following"
+                f" signature: {inspect.signature(saltelli_2010)}"
+            )
+            raise ValueError(message)
+
+    def indices_method(f_A, f_B, f_AB):
+        """Wrap indices method to ensure proper output dimension.
+
+        1D when single output, 2D otherwise.
+        """
+        return np.squeeze(indices_method_(f_A=f_A, f_B=f_B, f_AB=f_AB))
+
+    if callable(func):
+        if dists is None:
+            raise ValueError(
+                "'dists' must be defined when 'func' is a callable."
+            )
+
+        def wrapped_func(x):
+            return np.atleast_2d(func(x))
+
+        A, B = sample_A_B(n=n, dists=dists, rng=rng)
+        AB = sample_AB(A=A, B=B)
+
+        f_A = wrapped_func(A)
+
+        if f_A.shape[1] != n:
+            raise ValueError(
+                "'func' output should have a shape ``(s, -1)`` with ``s`` "
+                "the number of output."
+            )
+
+        def funcAB(AB):
+            d, d, n = AB.shape
+            AB = np.moveaxis(AB, 0, -1).reshape(d, n*d)
+            f_AB = wrapped_func(AB)
+            return np.moveaxis(f_AB.reshape((-1, n, d)), -1, 0)
+
+        f_B = wrapped_func(B)
+        f_AB = funcAB(AB)
+    else:
+        message = (
+            "When 'func' is a dictionary, it must contain the following "
+            "keys: 'f_A', 'f_B' and 'f_AB'."
+            "'f_A' and 'f_B' should have a shape ``(s, n)`` and 'f_AB' "
+            "should have a shape ``(d, s, n)``."
+        )
+        try:
+            f_A, f_B, f_AB = map(lambda arr: arr.copy(), np.atleast_2d(
+                func['f_A'], func['f_B'], func['f_AB']
+            ))
+        except KeyError as exc:
+            raise ValueError(message) from exc
+
+        if f_A.shape[1] != n or f_A.shape != f_B.shape or \
+                f_AB.shape == f_A.shape or f_AB.shape[-1] % n != 0:
+            raise ValueError(message)
+
+    # Normalization by mean
+    # Sobol', I. and Levitan, Y. L. (1999). On the use of variance reducing
+    # multipliers in monte carlo computations of a global sensitivity index.
+    # Computer Physics Communications, 117(1) :52-61.
+    mean = np.mean([f_A, f_B], axis=(0, -1)).reshape(-1, 1)
+    f_A -= mean
+    f_B -= mean
+    f_AB -= mean
+
+    # Compute indices
+    # Filter warnings for constant output as var = 0
+    with np.errstate(divide='ignore', invalid='ignore'):
+        first_order, total_order = indices_method(f_A=f_A, f_B=f_B, f_AB=f_AB)
+
+    # null variance means null indices
+    first_order[~np.isfinite(first_order)] = 0
+    total_order[~np.isfinite(total_order)] = 0
+
+    res = dict(
+        first_order=first_order,
+        total_order=total_order,
+        _indices_method=indices_method,
+        _f_A=f_A,
+        _f_B=f_B,
+        _f_AB=f_AB
+    )
+
+    if callable(func):
+        res.update(
+            dict(
+                _A=A,
+                _B=B,
+                _AB=AB,
+            )
+        )
+
+    return SobolResult(**res)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_sobol.cpython-312-x86_64-linux-gnu.so b/venv/lib/python3.12/site-packages/scipy/stats/_sobol.cpython-312-x86_64-linux-gnu.so
new file mode 100644
index 0000000000000000000000000000000000000000..5f7bf1850e616490ad4d74a43210a6e02b302299
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_sobol.cpython-312-x86_64-linux-gnu.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f26c7d98b4befa24ddfdf90406b3d7b33cff94f60b473d33a0af82ee329c9a77
+size 184960
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_sobol.pyi b/venv/lib/python3.12/site-packages/scipy/stats/_sobol.pyi
new file mode 100644
index 0000000000000000000000000000000000000000..7ca5e3a9c1a142b25ac26401e9ab1cb6726c877f
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_sobol.pyi
@@ -0,0 +1,54 @@
+import numpy as np
+from scipy._lib._util import IntNumber
+from typing import Literal
+
+def _initialize_v(
+    v : np.ndarray, 
+    dim : IntNumber,
+    bits: IntNumber
+) -> None: ...
+
+def _cscramble (
+    dim : IntNumber,
+    bits: IntNumber,
+    ltm : np.ndarray,
+    sv: np.ndarray
+) -> None: ...
+
+def _fill_p_cumulative(
+    p: np.ndarray,
+    p_cumulative: np.ndarray
+) -> None: ...
+
+def _draw(
+    n : IntNumber,
+    num_gen: IntNumber,
+    dim: IntNumber,
+    scale: float,
+    sv: np.ndarray,
+    quasi: np.ndarray,
+    sample: np.ndarray
+    ) -> None: ...
+
+def _fast_forward(
+    n: IntNumber,
+    num_gen: IntNumber,
+    dim: IntNumber,
+    sv: np.ndarray,
+    quasi: np.ndarray
+    ) -> None: ...
+
+def _categorize(
+    draws: np.ndarray,
+    p_cumulative: np.ndarray,
+    result: np.ndarray
+    ) -> None: ...
+
+_MAXDIM: Literal[21201]
+_MAXDEG: Literal[18]
+
+def _test_find_index(
+    p_cumulative: np.ndarray, 
+    size: int, 
+    value: float
+    ) -> int: ...
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_sobol_direction_numbers.npz b/venv/lib/python3.12/site-packages/scipy/stats/_sobol_direction_numbers.npz
new file mode 100644
index 0000000000000000000000000000000000000000..44f1f1e9ebd1eb188289ca9adb8027855c1a23b6
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_sobol_direction_numbers.npz
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4859931147d42ce465b8605cb277f957d98b839d03194fdf06579357906d193b
+size 589334
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_stats.cpython-312-x86_64-linux-gnu.so b/venv/lib/python3.12/site-packages/scipy/stats/_stats.cpython-312-x86_64-linux-gnu.so
new file mode 100644
index 0000000000000000000000000000000000000000..0d99a2a0098d2912fd938b0417230804463c47b8
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_stats.cpython-312-x86_64-linux-gnu.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ae458e9e7341aa4b88d2bb2225def5108b5fecc6092a9dee86634f8504d89d3a
+size 497368
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_stats.pxd b/venv/lib/python3.12/site-packages/scipy/stats/_stats.pxd
new file mode 100644
index 0000000000000000000000000000000000000000..e01565f75fe232446e4b8b0b50fdf645c8506108
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_stats.pxd
@@ -0,0 +1,10 @@
+# destined to be used in a LowLevelCallable
+
+cdef double _geninvgauss_pdf(double x, void *user_data) noexcept nogil
+cdef double _studentized_range_cdf(int n, double[2] x, void *user_data) noexcept nogil
+cdef double _studentized_range_cdf_asymptotic(double z, void *user_data) noexcept nogil
+cdef double _studentized_range_pdf(int n, double[2] x, void *user_data) noexcept nogil
+cdef double _studentized_range_pdf_asymptotic(double z, void *user_data) noexcept nogil
+cdef double _studentized_range_moment(int n, double[3] x_arg, void *user_data) noexcept nogil
+cdef double _genhyperbolic_pdf(double x, void *user_data) noexcept nogil
+cdef double _genhyperbolic_logpdf(double x, void *user_data) noexcept nogil
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_stats_mstats_common.py b/venv/lib/python3.12/site-packages/scipy/stats/_stats_mstats_common.py
new file mode 100644
index 0000000000000000000000000000000000000000..c272fcc1a31a6f296cb54c28859ea51b3ca03362
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_stats_mstats_common.py
@@ -0,0 +1,34 @@
+import numpy as np
+from .._lib._bunch import _make_tuple_bunch
+
+__all__ = ['_find_repeats']
+
+# This is not a namedtuple for backwards compatibility. See PR #12983
+TheilslopesResult = _make_tuple_bunch('TheilslopesResult',
+                                      ['slope', 'intercept',
+                                       'low_slope', 'high_slope'])
+SiegelslopesResult = _make_tuple_bunch('SiegelslopesResult',
+                                       ['slope', 'intercept'])
+
+
+def _n_samples_optional_x(kwargs):
+    return 2 if kwargs.get('x', None) is not None else 1
+
+
+def _find_repeats(arr):
+    # This function assumes it may clobber its input.
+    if len(arr) == 0:
+        return np.array(0, np.float64), np.array(0, np.intp)
+
+    # XXX This cast was previously needed for the Fortran implementation,
+    # should we ditch it?
+    arr = np.asarray(arr, np.float64).ravel()
+    arr.sort()
+
+    # Taken from NumPy 1.9's np.unique.
+    change = np.concatenate(([True], arr[1:] != arr[:-1]))
+    unique = arr[change]
+    change_idx = np.concatenate(np.nonzero(change) + ([arr.size],))
+    freq = np.diff(change_idx)
+    atleast2 = freq > 1
+    return unique[atleast2], freq[atleast2]
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_stats_py.py b/venv/lib/python3.12/site-packages/scipy/stats/_stats_py.py
new file mode 100644
index 0000000000000000000000000000000000000000..bf10af5738d8c2fa4ec7ea33cf0deca9e9bc2a19
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_stats_py.py
@@ -0,0 +1,11250 @@
+# Copyright 2002 Gary Strangman.  All rights reserved
+# Copyright 2002-2016 The SciPy Developers
+#
+# The original code from Gary Strangman was heavily adapted for
+# use in SciPy by Travis Oliphant.  The original code came with the
+# following disclaimer:
+#
+# This software is provided "as-is".  There are no expressed or implied
+# warranties of any kind, including, but not limited to, the warranties
+# of merchantability and fitness for a given application.  In no event
+# shall Gary Strangman be liable for any direct, indirect, incidental,
+# special, exemplary or consequential damages (including, but not limited
+# to, loss of use, data or profits, or business interruption) however
+# caused and on any theory of liability, whether in contract, strict
+# liability or tort (including negligence or otherwise) arising in any way
+# out of the use of this software, even if advised of the possibility of
+# such damage.
+
+"""
+A collection of basic statistical functions for Python.
+
+References
+----------
+.. [CRCProbStat2000] Zwillinger, D. and Kokoska, S. (2000). CRC Standard
+   Probability and Statistics Tables and Formulae. Chapman & Hall: New
+   York. 2000.
+
+"""
+import math
+import itertools
+import operator
+import warnings
+from collections import namedtuple
+from collections.abc import Sequence
+
+import numpy as np
+from numpy import array, asarray, ma
+
+from scipy import sparse
+from scipy.spatial.distance import cdist
+
+from scipy.optimize import milp, LinearConstraint
+from scipy.optimize.elementwise import find_root
+from scipy._lib._util import _get_nan, _rename_parameter, _contains_nan
+
+import scipy.special as special
+# Import unused here but needs to stay until end of deprecation periode
+# See https://github.com/scipy/scipy/issues/15765#issuecomment-1875564522
+from scipy import linalg  # noqa: F401
+from . import distributions
+from . import _mstats_basic as mstats_basic
+
+from ._stats import _kendall_dis, _toint64, _weightedrankedtau
+
+from dataclasses import dataclass, field
+from ._stats_pythran import _compute_outer_prob_inside_method
+from ._resampling import (MonteCarloMethod, PermutationMethod, BootstrapMethod,
+                          monte_carlo_test, permutation_test, bootstrap,)
+from ._axis_nan_policy import (_axis_nan_policy_factory, _broadcast_shapes,
+                               _broadcast_arrays,
+                               _broadcast_array_shapes_remove_axis, SmallSampleWarning,
+                               too_small_1d_not_omit, too_small_1d_omit,
+                               too_small_nd_not_omit, too_small_nd_omit)
+from ._binomtest import _binary_search_for_binom_tst as _binary_search, _SimpleBinomial
+from scipy._lib._bunch import _make_tuple_bunch
+from scipy import stats
+from scipy._lib._array_api import (
+    _asarray,
+    array_namespace,
+    is_lazy_array,
+    is_dask,
+    is_numpy,
+    is_cupy,
+    is_jax,
+    is_marray,
+    xp_size,
+    xp_vector_norm,
+    xp_promote,
+    xp_result_type,
+    xp_capabilities,
+    xp_ravel,
+    _count_nonmasked,
+    _share_masks,
+    _masked_apply,
+    xp_swapaxes,
+    xp_device,
+)
+import scipy._external.array_api_extra as xpx
+from scipy.stats._quantile import _xp_searchsorted
+
+
+# Functions/classes in other files should be added in `__init__.py`, not here
+__all__ = ['gmean', 'hmean', 'pmean', 'mode', 'tmean', 'tvar',
+           'tmin', 'tmax', 'tstd', 'tsem', 'moment',
+           'skew', 'kurtosis', 'describe', 'skewtest', 'kurtosistest',
+           'normaltest', 'jarque_bera',
+           'scoreatpercentile', 'percentileofscore',
+           'cumfreq', 'relfreq', 'obrientransform',
+           'sem', 'zmap', 'zscore', 'gzscore', 'iqr', 'gstd',
+           'median_abs_deviation',
+           'sigmaclip', 'trimboth', 'trim1', 'trim_mean',
+           'f_oneway', 'pearsonr', 'fisher_exact',
+           'spearmanr', 'pointbiserialr',
+           'kendalltau', 'weightedtau',
+           'linregress', 'ttest_1samp',
+           'ttest_ind', 'ttest_ind_from_stats', 'ttest_rel',
+           'kstest', 'ks_1samp', 'ks_2samp',
+           'chisquare', 'power_divergence',
+           'tiecorrect', 'ranksums', 'kruskal', 'friedmanchisquare',
+           'rankdata', 'combine_pvalues', 'quantile_test',
+           'wasserstein_distance', 'wasserstein_distance_nd', 'energy_distance',
+           'brunnermunzel', 'alexandergovern',
+           'expectile', 'lmoment']
+
+
+def _chk_asarray(a, axis, *, xp=None):
+    if xp is None:
+        xp = array_namespace(a)
+
+    if axis is None:
+        a = xp.reshape(a, (-1,))
+        outaxis = 0
+    else:
+        a = xp.asarray(a)
+        outaxis = axis
+
+    if a.ndim == 0:
+        a = xp.reshape(a, (-1,))
+
+    return a, outaxis
+
+
+SignificanceResult = _make_tuple_bunch('SignificanceResult',
+                                       ['statistic', 'pvalue'], [])
+# Let's call a SignificanceResult with legacy :correlation" attribute a
+# "CorrelationResult". Don't add to `extra_field_names`- shouldn't be in repr.
+
+
+def _pack_CorrelationResult(statistic, pvalue, correlation):
+    res = SignificanceResult(statistic, pvalue)
+    res.correlation = correlation
+    return res
+
+
+def _unpack_CorrelationResult(res, _):
+    return res.statistic, res.pvalue, res.correlation
+
+
+# note that `weights` are paired with `x`
+@xp_capabilities(marray=True)
+@_axis_nan_policy_factory(
+        lambda x: x, n_samples=1, n_outputs=1, too_small=0, paired=True,
+        result_to_tuple=lambda x, _: (x,), kwd_samples=['weights'])
+def gmean(a, axis=0, dtype=None, weights=None):
+    r"""Compute the weighted geometric mean along the specified axis.
+
+    The weighted geometric mean of the array :math:`a_i` associated to weights
+    :math:`w_i` is:
+
+    .. math::
+
+        \exp \left( \frac{ \sum_{i=1}^n w_i \ln a_i }{ \sum_{i=1}^n w_i }
+                   \right) \, ,
+
+    and, with equal weights, it gives:
+
+    .. math::
+
+        \sqrt[n]{ \prod_{i=1}^n a_i } \, .
+
+    Parameters
+    ----------
+    a : array_like
+        Input array or object that can be converted to an array.
+    axis : int or None, optional
+        Axis along which the geometric mean is computed. Default is 0.
+        If None, compute over the whole array `a`.
+    dtype : dtype, optional
+        (Floating point) dtype to which numerical arguments are cast before performing
+        the calculation. If `dtype` is not specified, it defaults to the floating point
+        result dtype of the numerical arguments.
+    weights : array_like, optional
+        The `weights` array must be broadcastable to the same shape as `a`.
+        Default is None, which gives each value a weight of 1.0.
+
+    Returns
+    -------
+    gmean : ndarray
+        See `dtype` parameter above.
+
+    See Also
+    --------
+    numpy.mean : Arithmetic average
+    numpy.average : Weighted average
+    hmean : Harmonic mean
+
+    Notes
+    -----
+    The sample geometric mean is the exponential of the mean of the natural
+    logarithms of the observations.
+    Negative observations will produce NaNs in the output because the *natural*
+    logarithm (as opposed to the *complex* logarithm) is defined only for
+    non-negative reals.
+
+    References
+    ----------
+    .. [1] "Weighted Geometric Mean", *Wikipedia*,
+           https://en.wikipedia.org/wiki/Weighted_geometric_mean.
+    .. [2] Grossman, J., Grossman, M., Katz, R., "Averages: A New Approach",
+           Archimedes Foundation, 1983
+
+    Examples
+    --------
+    >>> from scipy.stats import gmean
+    >>> gmean([1, 4])
+    2.0
+    >>> gmean([1, 2, 3, 4, 5, 6, 7])
+    3.3800151591412964
+    >>> gmean([1, 4, 7], weights=[3, 1, 3])
+    2.80668351922014
+
+    """
+    xp = array_namespace(a, weights)
+    dtype = (xp_result_type(a, weights, force_floating=True, xp=xp)
+             if dtype is None else dtype)
+    a = xp.asarray(a, dtype=dtype)
+
+    if weights is not None:
+        weights = xp.asarray(weights, dtype=dtype)
+
+    with np.errstate(divide='ignore'):
+        log_a = xp.log(a)
+
+    return xp.exp(_xp_mean(log_a, axis=axis, weights=weights))
+
+
+@xp_capabilities(marray=True)
+@_axis_nan_policy_factory(
+        lambda x: x, n_samples=1, n_outputs=1, too_small=0, paired=True,
+        result_to_tuple=lambda x, _: (x,), kwd_samples=['weights'])
+def hmean(a, axis=0, dtype=None, *, weights=None):
+    r"""Calculate the weighted harmonic mean along the specified axis.
+
+    The weighted harmonic mean of the array :math:`a_i` associated to weights
+    :math:`w_i` is:
+
+    .. math::
+
+        \frac{ \sum_{i=1}^n w_i }{ \sum_{i=1}^n \frac{w_i}{a_i} } \, ,
+
+    and, with equal weights, it gives:
+
+    .. math::
+
+        \frac{ n }{ \sum_{i=1}^n \frac{1}{a_i} } \, .
+
+    Parameters
+    ----------
+    a : array_like
+        Input array, masked array or object that can be converted to an array.
+    axis : int or None, optional
+        Axis along which the harmonic mean is computed. Default is 0.
+        If None, compute over the whole array `a`.
+    dtype : dtype, optional
+        (Floating point) dtype to which numerical arguments are cast before performing
+        the calculation. If `dtype` is not specified, it defaults to the floating point
+        result dtype of the numerical arguments.
+    weights : array_like, optional
+        The weights array can either be 1-D (in which case its length must be
+        the size of `a` along the given `axis`) or of the same shape as `a`.
+        Default is None, which gives each value a weight of 1.0.
+
+        .. versionadded:: 1.9
+
+    Returns
+    -------
+    hmean : ndarray
+        See `dtype` parameter above.
+
+    See Also
+    --------
+    numpy.mean : Arithmetic average
+    numpy.average : Weighted average
+    gmean : Geometric mean
+
+    Notes
+    -----
+    The sample harmonic mean is the reciprocal of the mean of the reciprocals
+    of the observations.
+
+    The harmonic mean is computed over a single dimension of the input
+    array, axis=0 by default, or all values in the array if axis=None.
+    float64 intermediate and return values are used for integer inputs.
+
+    The harmonic mean is only defined if all observations are non-negative;
+    otherwise, the result is NaN.
+
+    References
+    ----------
+    .. [1] "Weighted Harmonic Mean", *Wikipedia*,
+           https://en.wikipedia.org/wiki/Harmonic_mean#Weighted_harmonic_mean
+    .. [2] Ferger, F., "The nature and use of the harmonic mean", Journal of
+           the American Statistical Association, vol. 26, pp. 36-40, 1931
+
+    Examples
+    --------
+    >>> from scipy.stats import hmean
+    >>> hmean([1, 4])
+    1.6000000000000001
+    >>> hmean([1, 2, 3, 4, 5, 6, 7])
+    2.6997245179063363
+    >>> hmean([1, 4, 7], weights=[3, 1, 3])
+    1.9029126213592233
+
+    """
+    xp = array_namespace(a, weights)
+    dtype = (xp_result_type(a, weights, force_floating=True, xp=xp)
+             if dtype is None else dtype)
+    a = xp.asarray(a, dtype=dtype)
+
+    if weights is not None:
+        weights = xp.asarray(weights, dtype=dtype)
+
+    negative_mask = a < 0
+    a = xp.where(negative_mask, xp.nan, a)
+
+    if not is_lazy_array(negative_mask) and xp.any(negative_mask):
+        message = ("The harmonic mean is only defined if all elements are "
+                   "non-negative; otherwise, the result is NaN.")
+        warnings.warn(message, RuntimeWarning, stacklevel=2)
+
+    with np.errstate(divide='ignore'):
+        return 1.0 / _xp_mean(1.0 / a, axis=axis, weights=weights)
+
+
+@xp_capabilities(marray=True)
+@_axis_nan_policy_factory(
+        lambda x: x, n_samples=1, n_outputs=1, too_small=0, paired=True,
+        result_to_tuple=lambda x, _: (x,), kwd_samples=['weights'])
+def pmean(a, p, *, axis=0, dtype=None, weights=None):
+    r"""Calculate the weighted power mean along the specified axis.
+
+    The weighted power mean of the array :math:`a_i` associated to weights
+    :math:`w_i` is:
+
+    .. math::
+
+        \left( \frac{ \sum_{i=1}^n w_i a_i^p }{ \sum_{i=1}^n w_i }
+              \right)^{ 1 / p } \, ,
+
+    and, with equal weights, it gives:
+
+    .. math::
+
+        \left( \frac{ 1 }{ n } \sum_{i=1}^n a_i^p \right)^{ 1 / p }  \, .
+
+    When ``p=0``, it returns the geometric mean.
+
+    This mean is also called generalized mean or Hölder mean, and must not be
+    confused with the Kolmogorov generalized mean, also called
+    quasi-arithmetic mean or generalized f-mean [3]_.
+
+    Parameters
+    ----------
+    a : array_like
+        Input array, masked array or object that can be converted to an array.
+    p : int or float
+        Exponent. Must be finite.
+    axis : int or None, optional
+        Axis along which the power mean is computed. Default is 0.
+        If None, compute over the whole array `a`.
+    dtype : dtype, optional
+        (Floating point) dtype to which numerical arguments are cast before performing
+        the calculation. If `dtype` is not specified, it defaults to the floating point
+        result dtype of the numerical arguments.
+    weights : array_like, optional
+        The weights array can either be 1-D (in which case its length must be
+        the size of `a` along the given `axis`) or of the same shape as `a`.
+        Default is None, which gives each value a weight of 1.0.
+
+    Returns
+    -------
+    pmean : ndarray, see `dtype` parameter above.
+        Output array containing the power mean values.
+
+    See Also
+    --------
+    numpy.average : Weighted average
+    gmean : Geometric mean
+    hmean : Harmonic mean
+
+    Notes
+    -----
+    The power mean is computed over a single dimension of the input
+    array, ``axis=0`` by default, or all values in the array if ``axis=None``.
+    float64 intermediate and return values are used for integer inputs.
+
+    The power mean is only defined if all observations are non-negative;
+    otherwise, the result is NaN.
+
+    .. versionadded:: 1.9
+
+    References
+    ----------
+    .. [1] "Generalized Mean", *Wikipedia*,
+           https://en.wikipedia.org/wiki/Generalized_mean
+    .. [2] Norris, N., "Convexity properties of generalized mean value
+           functions", The Annals of Mathematical Statistics, vol. 8,
+           pp. 118-120, 1937
+    .. [3] Bullen, P.S., Handbook of Means and Their Inequalities, 2003
+
+    Examples
+    --------
+    >>> from scipy.stats import pmean, hmean, gmean
+    >>> pmean([1, 4], 1.3)
+    2.639372938300652
+    >>> pmean([1, 2, 3, 4, 5, 6, 7], 1.3)
+    4.157111214492084
+    >>> pmean([1, 4, 7], -2, weights=[3, 1, 3])
+    1.4969684896631954
+
+    For p=-1, power mean is equal to harmonic mean:
+
+    >>> pmean([1, 4, 7], -1, weights=[3, 1, 3])
+    1.9029126213592233
+    >>> hmean([1, 4, 7], weights=[3, 1, 3])
+    1.9029126213592233
+
+    For p=0, power mean is defined as the geometric mean:
+
+    >>> pmean([1, 4, 7], 0, weights=[3, 1, 3])
+    2.80668351922014
+    >>> gmean([1, 4, 7], weights=[3, 1, 3])
+    2.80668351922014
+
+    """
+    if not isinstance(p, int | float):
+        raise ValueError("Power mean only defined for exponent of type int or "
+                         "float.")
+    if p == 0:
+        return gmean(a, axis=axis, dtype=dtype, weights=weights)
+    elif math.isinf(p):
+        message = "Power mean only implemented for finite `p`"
+        raise NotImplementedError(message)
+
+    xp = array_namespace(a, weights)
+    dtype = (xp_result_type(a, p, weights, force_floating=True, xp=xp)
+             if dtype is None else dtype)
+    a = xp.asarray(a, dtype=dtype)
+
+    if weights is not None:
+        weights = xp.asarray(weights, dtype=dtype)
+
+    negative_mask = a < 0
+    a = xp.where(negative_mask, np.nan, a)
+
+    if not is_lazy_array(negative_mask) and xp.any(negative_mask):
+        message = ("The power mean is only defined if all elements are "
+                   "non-negative; otherwise, the result is NaN.")
+        warnings.warn(message, RuntimeWarning, stacklevel=2)
+
+    # Linearized approximation for small p to avoid numerical issues; see gh-23407
+    p_threshold = 2e-6
+    if abs(p) <= p_threshold:
+        return _linearized_pmean(a, p, axis=axis, weights=weights, xp=xp)
+
+    with np.errstate(divide='ignore', invalid='ignore'):
+        return _xp_mean(a**float(p), axis=axis, weights=weights)**(1/p)
+
+
+ModeResult = namedtuple('ModeResult', ('mode', 'count'))
+
+
+def _mode_result(mode, count):
+    # When a slice is empty, `_axis_nan_policy` automatically produces
+    # NaN for `mode` and `count`. This is a reasonable convention for `mode`,
+    # but `count` should not be NaN; it should be zero.
+    xp = array_namespace(mode, count)
+    i = xp.isnan(count)
+    if i.shape == ():
+        count = xp.asarray(0, dtype=count.dtype)[()] if i else count
+    else:
+        count = xpx.at(count)[i].set(0)
+    if is_numpy(xp) and mode.ndim > 0:
+        # When a) xp is NumPy, b) array is multidimensional, c) NaNs are present,
+        # and d) nan_policy='omit', `_axis_nan_policy` decorator uses
+        # `np.apply_along_axis` to compute mode/count along each axis-slice separately.
+        # The result is a single array with the result dtype of `mode` and `count`.
+        # We need to change `count` back to an integer.
+        count = xp.astype(count, xp.asarray(0).dtype)
+    return ModeResult(mode, count)
+
+
+@xp_capabilities(skip_backends=[('dask.array', "can't compute chunk size"),
+                                ('cupy', "data-apis/array-api-compat#312")],
+                 jax_jit=False,  # would delegate, but jax-ml/jax#34486
+                 marray=True,
+                 extra_note=("Values in MArray input must be real numbers "
+                             "that cast safely to floating point."))
+@_axis_nan_policy_factory(_mode_result, override={'nan_propagation': False})
+def mode(a, axis=0, nan_policy='propagate', keepdims=False):
+    r"""Return an array of the modal (most common) value in the passed array.
+
+    If there is more than one such value, only one is returned.
+    The bin-count for the modal bins is also returned.
+
+    Parameters
+    ----------
+    a : array_like
+        Numeric, n-dimensional array of which to find mode(s).
+    axis : int or None, optional
+        Axis along which to operate. Default is 0. If None, compute over
+        the whole array `a`.
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains nan.
+        The following options are available (default is 'propagate'):
+
+        * 'propagate': treats nan as it would treat any other value
+        * 'raise': throws an error
+        * 'omit': performs the calculations ignoring nan values
+
+    keepdims : bool, optional
+        If set to ``False``, the `axis` over which the statistic is taken
+        is consumed (eliminated from the output array). If set to ``True``,
+        the `axis` is retained with size one, and the result will broadcast
+        correctly against the input array.
+
+    Returns
+    -------
+    mode : ndarray
+        Array of modal values.
+    count : ndarray
+        Array of counts for each mode.
+
+    Notes
+    -----
+    The mode  is calculated using `numpy.unique`.
+    In NumPy versions 1.21 and after, all NaNs - even those with different
+    binary representations - are treated as equivalent and counted as separate
+    instances of the same value.
+
+    By convention, the mode of an empty array is NaN, and the associated count
+    is zero.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.array([[3, 0, 3, 7],
+    ...               [3, 2, 6, 2],
+    ...               [1, 7, 2, 8],
+    ...               [3, 0, 6, 1],
+    ...               [3, 2, 5, 5]])
+    >>> from scipy import stats
+    >>> stats.mode(a, keepdims=True)
+    ModeResult(mode=array([[3, 0, 6, 1]]), count=array([[4, 2, 2, 1]]))
+
+    To get mode of whole array, specify ``axis=None``:
+
+    >>> stats.mode(a, axis=None, keepdims=True)
+    ModeResult(mode=[[3]], count=[[5]])
+    >>> stats.mode(a, axis=None, keepdims=False)
+    ModeResult(mode=3, count=5)
+
+    """
+    xp = array_namespace(a)
+
+    # `axis`, `nan_policy`, and `keepdims` are handled by `_axis_nan_policy`
+    if not xp.isdtype(a.dtype, 'numeric'):
+        message = ("Argument `a` is not recognized as numeric. "
+                   "Support for input that cannot be coerced to a numeric "
+                   "array was deprecated in SciPy 1.9.0 and removed in SciPy "
+                   "1.11.0. Please consider `np.unique`.")
+        raise TypeError(message)
+
+    if xp_size(a) == 0:
+        NaN = _get_nan(a, xp=xp)
+        return ModeResult(*xp.asarray([NaN, 0], dtype=NaN.dtype))
+
+    if a.ndim == 1 and not is_marray(xp):
+        vals, cnts = xp.unique_counts(a)
+        # in contrast with np.unique, `unique_counts` treats all NaNs as distinct,
+        # but we have always grouped them. Replace `cnts` corresponding with NaNs
+        # with the number of NaNs.
+        mask = xp.isnan(vals)
+        cnts = xpx.at(cnts)[mask].set(xp.count_nonzero(mask))
+        modes, counts = vals[xp.argmax(cnts)], xp.max(cnts)
+        default_int = xp.asarray(1).dtype  # fail slow CI job failed - incorrect dtype
+        counts = xp.astype(counts, default_int, copy=False)
+        modes = modes[()] if modes.ndim == 0 else modes
+        counts = counts[()] if counts.ndim == 0 else counts
+        return ModeResult(modes, counts)
+
+    # `axis` is always -1 after the `_axis_nan_policy` decorator
+    y = xp.sort(a, axis=-1)
+
+    # Get boolean array of elements that are different from the previous element
+    if is_marray(xp):
+        # Treat masked elements as NaNs and *don't* count NaNs as equal. Two downsides:
+        # - integer arrays are converted to floating point, so some very large distinct
+        #   integers will no longer be distinct.
+        # - NaNs in the original data *will* be treated as distinct.
+        y_data = xp_promote(y.data, force_floating=True, xp=y._xp)
+        y_data = y._xp.where(y.mask, y._xp.nan, y_data)
+        i = xp.concat([xp.ones(y.shape[:-1] + (1,), dtype=xp.bool),
+                      (y_data[..., :-1] != y_data[..., 1:])], axis=-1)
+    else:
+        i = xp.concat([xp.ones(y.shape[:-1] + (1,), dtype=xp.bool),
+                      (y[..., :-1] != y[..., 1:]) & ~xp.isnan(y[..., :-1])], axis=-1)
+    # Get linear integer indices of these elements in a raveled array
+    indices = xp.arange(xp_size(y), device=xp_device(y))[xp_ravel(i)]
+    # The difference between integer indices is the number of repeats
+    append = xp.full(indices.shape[:-1] + (1,), xp_size(y), dtype=indices.dtype)
+    counts = xp.diff(indices, append=append)
+    # Now we form an array of `counts` corresponding with each element of `y`...
+    counts = xp.reshape(xp.repeat(counts, counts), y.shape)
+    # ... so we can get the argmax of *each slice* separately.
+    k = xp.argmax(counts, axis=-1, keepdims=True)
+    # Extract the corresponding element/count, and eliminate the reduced dimension
+    modes = xp.take_along_axis(y, k, axis=-1)[..., 0]
+    counts = xp.take_along_axis(counts, k, axis=-1)[..., 0]
+    modes = modes[()] if modes.ndim == 0 else modes
+    counts = counts[()] if counts.ndim == 0 else counts
+    return ModeResult(modes, counts)
+
+
+def _put_val_to_limits(a, limits, inclusive, val=np.nan, xp=None):
+    """Replace elements outside limits with a value.
+
+    This is primarily a utility function.
+
+    Parameters
+    ----------
+    a : array
+    limits : (float or None, float or None)
+        A tuple consisting of the (lower limit, upper limit).  Elements in the
+        input array less than the lower limit or greater than the upper limit
+        will be replaced with `val`. None implies no limit.
+    inclusive : (bool, bool)
+        A tuple consisting of the (lower flag, upper flag).  These flags
+        determine whether values exactly equal to lower or upper are allowed.
+    val : float, default: NaN
+        The value with which extreme elements of the array are replaced.
+
+    """
+    xp = array_namespace(a) if xp is None else xp
+    mask = xp.zeros_like(a, dtype=xp.bool)
+    if limits is None:
+        return a, mask
+    lower_limit, upper_limit = limits
+    lower_include, upper_include = inclusive
+    if lower_limit is not None:
+        mask = mask | ((a < lower_limit) if lower_include else a <= lower_limit)
+    if upper_limit is not None:
+        mask = mask | ((a > upper_limit) if upper_include else a >= upper_limit)
+    lazy = is_lazy_array(mask)
+    if not lazy and xp.all(mask):
+        raise ValueError("No array values within given limits")
+    if lazy or xp.any(mask):
+        a = xp.where(mask, val, a)
+    return a, mask
+
+
+@xp_capabilities(marray=True)
+@_axis_nan_policy_factory(
+    lambda x: x, n_outputs=1, default_axis=None,
+    result_to_tuple=lambda x, _: (x,)
+)
+def tmean(a, limits=None, inclusive=(True, True), axis=None):
+    """Compute the trimmed mean.
+
+    This function finds the arithmetic mean of given values, ignoring values
+    outside the given `limits`.
+
+    Parameters
+    ----------
+    a : array_like
+        Array of values.
+    limits : None or (lower limit, upper limit), optional
+        Values in the input array less than the lower limit or greater than the
+        upper limit will be ignored.  When limits is None (default), then all
+        values are used.  Either of the limit values in the tuple can also be
+        None representing a half-open interval.
+    inclusive : (bool, bool), optional
+        A tuple consisting of the (lower flag, upper flag).  These flags
+        determine whether values exactly equal to the lower or upper limits
+        are included.  The default value is (True, True).
+    axis : int or None, optional
+        Axis along which to compute test. Default is None.
+
+    Returns
+    -------
+    tmean : ndarray
+        Trimmed mean.
+
+    See Also
+    --------
+    trim_mean : Returns mean after trimming a proportion from both tails.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> x = np.arange(20)
+    >>> stats.tmean(x)
+    9.5
+    >>> stats.tmean(x, (3,17))
+    10.0
+
+    """
+    xp = array_namespace(a)
+    a, mask = _put_val_to_limits(a, limits, inclusive, val=0., xp=xp)
+    # explicit dtype specification required due to data-apis/array-api-compat#152
+    sum = xp.sum(a, axis=axis, dtype=a.dtype)
+    n = xp.sum(xp.asarray(~mask, dtype=a.dtype, device=xp_device(a)), axis=axis,
+               dtype=a.dtype)
+    mean = xpx.apply_where(n != 0, (sum, n), operator.truediv, fill_value=xp.nan)
+    return mean[()] if mean.ndim == 0 else mean
+
+
+@xp_capabilities(marray=True)
+@_axis_nan_policy_factory(
+    lambda x: x, n_outputs=1, result_to_tuple=lambda x, _: (x,)
+)
+def tvar(a, limits=None, inclusive=(True, True), axis=0, ddof=1):
+    """Compute the trimmed variance.
+
+    This function computes the sample variance of an array of values,
+    while ignoring values which are outside of given `limits`.
+
+    Parameters
+    ----------
+    a : array_like
+        Array of values.
+    limits : None or (lower limit, upper limit), optional
+        Values in the input array less than the lower limit or greater than the
+        upper limit will be ignored. When limits is None, then all values are
+        used. Either of the limit values in the tuple can also be None
+        representing a half-open interval.  The default value is None.
+    inclusive : (bool, bool), optional
+        A tuple consisting of the (lower flag, upper flag).  These flags
+        determine whether values exactly equal to the lower or upper limits
+        are included.  The default value is (True, True).
+    axis : int or None, optional
+        Axis along which to operate. Default is 0. If None, compute over the
+        whole array `a`.
+    ddof : int, optional
+        Delta degrees of freedom.  Default is 1.
+
+    Returns
+    -------
+    tvar : float
+        Trimmed variance.
+
+    Notes
+    -----
+    `tvar` computes the unbiased sample variance, i.e. it uses a correction
+    factor ``n / (n - 1)``.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> x = np.arange(20)
+    >>> stats.tvar(x)
+    35.0
+    >>> stats.tvar(x, (3,17))
+    20.0
+
+    """
+    xp = array_namespace(a)
+    a, _ = _put_val_to_limits(a, limits, inclusive, xp=xp)
+    with warnings.catch_warnings():
+        warnings.simplefilter("ignore", SmallSampleWarning)
+        # Currently, this behaves like nan_policy='omit' for alternative array
+        # backends, but nan_policy='propagate' will be handled for other backends
+        # by the axis_nan_policy decorator shortly.
+        return _xp_var(a, correction=ddof, axis=axis, nan_policy='omit', xp=xp)
+
+
+@xp_capabilities(marray=True)
+@_axis_nan_policy_factory(
+    lambda x: x, n_outputs=1, result_to_tuple=lambda x, _: (x,)
+)
+def tmin(a, lowerlimit=None, axis=0, inclusive=True, nan_policy='propagate'):
+    """Compute the trimmed minimum.
+
+    This function finds the minimum value of an array `a` along the
+    specified axis, but only considering values greater than a specified
+    lower limit.
+
+    Parameters
+    ----------
+    a : array_like
+        Array of values.
+    lowerlimit : None or float, optional
+        Values in the input array less than the given limit will be ignored.
+        When lowerlimit is None, then all values are used. The default value
+        is None.
+    axis : int or None, optional
+        Axis along which to operate. Default is 0. If None, compute over the
+        whole array `a`.
+    inclusive : {True, False}, optional
+        This flag determines whether values exactly equal to the lower limit
+        are included.  The default value is True.
+
+    Returns
+    -------
+    tmin : float, int or ndarray
+        Trimmed minimum.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> x = np.arange(20)
+    >>> stats.tmin(x)
+    0
+
+    >>> stats.tmin(x, 13)
+    13
+
+    >>> stats.tmin(x, 13, inclusive=False)
+    14
+
+    """
+    xp = array_namespace(a)
+
+    max_ = xp.iinfo(a.dtype).max if xp.isdtype(a.dtype, 'integral') else xp.inf
+    a, mask = _put_val_to_limits(a, (lowerlimit, None), (inclusive, None),
+                                 val=max_, xp=xp)
+
+    res = xp.min(a, axis=axis)
+    invalid = xp.all(mask, axis=axis)  # All elements are below lowerlimit
+
+    # For eager backends, output dtype is data-dependent
+    if is_lazy_array(invalid) or xp.any(invalid):
+        # Possible loss of precision for int types
+        res = xp_promote(res, force_floating=True, xp=xp)
+        res = xp.where(invalid, xp.nan, res)
+
+    return res[()] if res.ndim == 0 else res
+
+
+@xp_capabilities(marray=True)
+@_axis_nan_policy_factory(
+    lambda x: x, n_outputs=1, result_to_tuple=lambda x, _: (x,)
+)
+def tmax(a, upperlimit=None, axis=0, inclusive=True, nan_policy='propagate'):
+    """Compute the trimmed maximum.
+
+    This function computes the maximum value of an array along a given axis,
+    while ignoring values larger than a specified upper limit.
+
+    Parameters
+    ----------
+    a : array_like
+        Array of values.
+    upperlimit : None or float, optional
+        Values in the input array greater than the given limit will be ignored.
+        When upperlimit is None, then all values are used. The default value
+        is None.
+    axis : int or None, optional
+        Axis along which to operate. Default is 0. If None, compute over the
+        whole array `a`.
+    inclusive : {True, False}, optional
+        This flag determines whether values exactly equal to the upper limit
+        are included.  The default value is True.
+
+    Returns
+    -------
+    tmax : float, int or ndarray
+        Trimmed maximum.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> x = np.arange(20)
+    >>> stats.tmax(x)
+    19
+
+    >>> stats.tmax(x, 13)
+    13
+
+    >>> stats.tmax(x, 13, inclusive=False)
+    12
+
+    """
+    xp = array_namespace(a)
+
+    min_ = xp.iinfo(a.dtype).min if xp.isdtype(a.dtype, 'integral') else -xp.inf
+    a, mask = _put_val_to_limits(a, (None, upperlimit), (None, inclusive),
+                                 val=min_, xp=xp)
+
+    res = xp.max(a, axis=axis)
+    invalid = xp.all(mask, axis=axis)  # All elements are above upperlimit
+
+    # For eager backends, output dtype is data-dependent
+    if is_lazy_array(invalid) or xp.any(invalid):
+        # Possible loss of precision for int types
+        res = xp_promote(res, force_floating=True, xp=xp)
+        res = xp.where(invalid, xp.nan, res)
+
+    return res[()] if res.ndim == 0 else res
+
+
+@xp_capabilities(marray=True)
+@_axis_nan_policy_factory(
+    lambda x: x, n_outputs=1, result_to_tuple=lambda x, _: (x,)
+)
+def tstd(a, limits=None, inclusive=(True, True), axis=0, ddof=1):
+    """Compute the trimmed sample standard deviation.
+
+    This function finds the sample standard deviation of given values,
+    ignoring values outside the given `limits`.
+
+    Parameters
+    ----------
+    a : array_like
+        Array of values.
+    limits : None or (lower limit, upper limit), optional
+        Values in the input array less than the lower limit or greater than the
+        upper limit will be ignored. When limits is None, then all values are
+        used. Either of the limit values in the tuple can also be None
+        representing a half-open interval.  The default value is None.
+    inclusive : (bool, bool), optional
+        A tuple consisting of the (lower flag, upper flag).  These flags
+        determine whether values exactly equal to the lower or upper limits
+        are included.  The default value is (True, True).
+    axis : int or None, optional
+        Axis along which to operate. Default is 0. If None, compute over the
+        whole array `a`.
+    ddof : int, optional
+        Delta degrees of freedom.  Default is 1.
+
+    Returns
+    -------
+    tstd : float
+        Trimmed sample standard deviation.
+
+    Notes
+    -----
+    `tstd` computes the unbiased sample standard deviation, i.e. it uses a
+    correction factor ``n / (n - 1)``.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> x = np.arange(20)
+    >>> stats.tstd(x)
+    5.9160797830996161
+    >>> stats.tstd(x, (3,17))
+    4.4721359549995796
+
+    """
+    return tvar(a, limits, inclusive, axis, ddof, _no_deco=True)**0.5
+
+
+@xp_capabilities(marray=True)
+@_axis_nan_policy_factory(
+    lambda x: x, n_outputs=1, result_to_tuple=lambda x, _: (x,)
+)
+def tsem(a, limits=None, inclusive=(True, True), axis=0, ddof=1):
+    """Compute the trimmed standard error of the mean.
+
+    This function finds the standard error of the mean for given
+    values, ignoring values outside the given `limits`.
+
+    Parameters
+    ----------
+    a : array_like
+        Array of values.
+    limits : None or (lower limit, upper limit), optional
+        Values in the input array less than the lower limit or greater than the
+        upper limit will be ignored. When limits is None, then all values are
+        used. Either of the limit values in the tuple can also be None
+        representing a half-open interval.  The default value is None.
+    inclusive : (bool, bool), optional
+        A tuple consisting of the (lower flag, upper flag).  These flags
+        determine whether values exactly equal to the lower or upper limits
+        are included.  The default value is (True, True).
+    axis : int or None, optional
+        Axis along which to operate. Default is 0. If None, compute over the
+        whole array `a`.
+    ddof : int, optional
+        Delta degrees of freedom.  Default is 1.
+
+    Returns
+    -------
+    tsem : float
+        Trimmed standard error of the mean.
+
+    Notes
+    -----
+    `tsem` uses unbiased sample standard deviation, i.e. it uses a
+    correction factor ``n / (n - 1)``.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> x = np.arange(20)
+    >>> stats.tsem(x)
+    1.3228756555322954
+    >>> stats.tsem(x, (3,17))
+    1.1547005383792515
+
+    """
+    xp = array_namespace(a)
+    a, _ = _put_val_to_limits(a, limits, inclusive, xp=xp)
+
+    with warnings.catch_warnings():
+        warnings.simplefilter("ignore", SmallSampleWarning)
+        # Currently, this behaves like nan_policy='omit' for alternative array
+        # backends, but nan_policy='propagate' will be handled for other backends
+        # by the axis_nan_policy decorator shortly.
+        sd = _xp_var(a, correction=ddof, axis=axis, nan_policy='omit', xp=xp)**0.5
+
+    not_nan = xp.astype(~xp.isnan(a), a.dtype)
+    n_obs = xp.sum(not_nan, axis=axis, dtype=sd.dtype)
+    return sd / n_obs**0.5
+
+
+#####################################
+#              MOMENTS              #
+#####################################
+
+
+def _moment_outputs(kwds, default_order=1):
+    order = np.atleast_1d(kwds.get('order', default_order))
+    message = "`order` must be a scalar or a non-empty 1D array."
+    if order.size == 0 or order.ndim > 1:
+        raise ValueError(message)
+    return len(order)
+
+
+def _moment_result_object(*args):
+    if len(args) == 1:
+        return args[0]
+    xp = array_namespace(*args)
+    return xp.stack(args)
+
+
+# When `order` is array-like with size > 1, moment produces an *array*
+# rather than a tuple, but the zeroth dimension is to be treated like
+# separate outputs. It is important to make the distinction between
+# separate outputs when adding the reduced axes back (`keepdims=True`).
+def _moment_tuple(x, n_out):
+    return tuple(x[i, ...] for i in range(x.shape[0])) if n_out > 1 else (x,)
+
+
+# `moment` fits into the `_axis_nan_policy` pattern, but it is a bit unusual
+# because the number of outputs is variable. Specifically,
+# `result_to_tuple=lambda x: (x,)` may be surprising for a function that
+# can produce more than one output, but it is intended here.
+# When `moment is called to produce the output:
+# - `result_to_tuple` packs the returned array into a single-element tuple,
+# - `_moment_result_object` extracts and returns that single element.
+# However, when the input array is empty, `moment` is never called. Instead,
+# - `_check_empty_inputs` is used to produce an empty array with the
+#   appropriate dimensions.
+# - A list comprehension creates the appropriate number of copies of this
+#   array, depending on `n_outputs`.
+# - This list - which may have multiple elements - is passed into
+#   `_moment_result_object`.
+# - If there is a single output, `_moment_result_object` extracts and returns
+#   the single output from the list.
+# - If there are multiple outputs, and therefore multiple elements in the list,
+#   `_moment_result_object` converts the list of arrays to a single array and
+#   returns it.
+# Currently, this leads to a slight inconsistency: when the input array is
+# empty, there is no distinction between the `moment` function being called
+# with parameter `order=1` and `order=[1]`; the latter *should* produce
+# the same as the former but with a singleton zeroth dimension.
+@xp_capabilities(skip_backends=[('dask.array', 'needs axis_nan_policy decorator')],
+                 marray=True)
+@_rename_parameter('moment', 'order')
+@_axis_nan_policy_factory(  # noqa: E302
+    _moment_result_object, n_samples=1, result_to_tuple=_moment_tuple,
+    n_outputs=_moment_outputs
+)
+def moment(a, order=1, axis=0, nan_policy='propagate', *, center=None):
+    r"""Calculate the nth moment about the mean for a sample.
+
+    A moment is a specific quantitative measure of the shape of a set of
+    points. It is often used to calculate coefficients of skewness and kurtosis
+    due to its close relationship with them.
+
+    Parameters
+    ----------
+    a : array_like
+       Input array.
+    order : int or 1-D array_like of ints, optional
+       Order of central moment that is returned. Default is 1.
+    axis : int or None, optional
+       Axis along which the central moment is computed. Default is 0.
+       If None, compute over the whole array `a`.
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains nan.
+        The following options are available (default is 'propagate'):
+
+        * 'propagate': returns nan
+        * 'raise': throws an error
+        * 'omit': performs the calculations ignoring nan values
+
+    center : float or None, optional
+       The point about which moments are taken. This can be the sample mean,
+       the origin, or any other be point. If `None` (default) compute the
+       center as the sample mean.
+
+    Returns
+    -------
+    n-th moment about the `center` : ndarray or float
+       The appropriate moment along the given axis or over all values if axis
+       is None. The denominator for the moment calculation is the number of
+       observations, no degrees of freedom correction is done.
+
+    See Also
+    --------
+    kurtosis, skew, describe
+
+    Notes
+    -----
+    The k-th moment of a data sample is:
+
+    .. math::
+
+        m_k = \frac{1}{n} \sum_{i = 1}^n (x_i - c)^k
+
+    Where `n` is the number of samples, and `c` is the center around which the
+    moment is calculated. This function uses exponentiation by squares [1]_ for
+    efficiency.
+
+    Note that, if `a` is an empty array (``a.size == 0``), array `moment` with
+    one element (`moment.size == 1`) is treated the same as scalar `moment`
+    (``np.isscalar(moment)``). This might produce arrays of unexpected shape.
+
+    References
+    ----------
+    .. [1] https://eli.thegreenplace.net/2009/03/21/efficient-integer-exponentiation-algorithms
+
+    Examples
+    --------
+    >>> from scipy.stats import moment
+    >>> moment([1, 2, 3, 4, 5], order=1)
+    0.0
+    >>> moment([1, 2, 3, 4, 5], order=2)
+    2.0
+
+    """
+    xp = array_namespace(a)
+    a, center, order = xp_promote(a, center, order, force_floating=True, xp=xp)
+
+    if not is_lazy_array(order) and xp.any(order != xp.round(order)):
+        raise ValueError("All elements of `order` must be integral.")
+
+    # _axis_nan_policy decorator ensures that axis=-1
+    if order.ndim > 0:
+        order = xp.reshape(order, (-1,) + (1,)*a.ndim)
+        return _moment(a, order, axis=-1, center=center)
+    else:
+        res = _moment(a, order, axis=-1, center=center)
+        return res[()] if res.ndim == 0 else res
+
+
+def _demean(a, mean, axis, *, xp, precision_warning=True):
+    # subtracts `mean` from `a` and returns the result,
+    # warning if there is catastrophic cancellation. `mean`
+    # must be the mean of `a` along axis with `keepdims=True`.
+    # Used in e.g. `_moment`, `_zscore`, `_xp_var`. See gh-15905.
+    a_zero_mean = a - mean
+
+    if (xp_size(a_zero_mean) == 0 or not precision_warning
+        or is_lazy_array(a_zero_mean)):
+        return a_zero_mean
+
+    eps = xp.finfo(mean.dtype).eps * 10
+
+    with np.errstate(divide='ignore', invalid='ignore'):
+        rel_diff = xp.max(xp.abs(a_zero_mean), axis=axis,
+                          keepdims=True) / xp.abs(mean)
+
+    n = _count_nonmasked(a, axis, xp=xp)
+    with np.errstate(invalid='ignore'):
+        device = {'device': xp_device(a)}
+        precision_loss = xp.any(xp.asarray(rel_diff < eps, **device)
+                                & xp.asarray(n > 1, **device))
+
+    if precision_loss:
+        message = ("Precision loss occurred in moment calculation due to "
+                   "catastrophic cancellation. This occurs when the data "
+                   "are nearly identical. Results may be unreliable.")
+        warnings.warn(message, RuntimeWarning, stacklevel=5)
+    return a_zero_mean
+
+
+def _moment(a, order, axis, *, center=None, xp=None):
+    """Vectorized calculation of raw moment about specified center
+
+    When `center` is None, the mean is computed and used as the center;
+    otherwise, the provided value is used as the center.
+    """
+    xp = array_namespace(a) if xp is None else xp
+
+    order = xp.asarray(order, dtype=a.dtype, device=xp_device(a))
+    order_0 = order == 0
+    order_1 = (order == 1) & (center is None)
+    center = xp.mean(a, axis=axis, keepdims=True) if center is None else center
+    a_zero_mean = _demean(a, center, axis, xp=xp)
+    res = xp.mean(a_zero_mean**order, axis=axis, keepdims=True)
+    if a.shape[-1] > 0 and (is_lazy_array(res)
+                                or xp.any(order_0) or xp.any(order_1)):
+        res = xp.where(order_0, xp.ones_like(res), res)
+        res = xp.where(order_1, xp.zeros_like(res), res)
+
+    return xp.squeeze(res, axis=axis)
+
+
+def _var(x, axis=0, ddof=0, mean=None, xp=None):
+    # Calculate variance of sample, warning if precision is lost
+    xp = array_namespace(x) if xp is None else xp
+    var = _moment(x, 2, axis, center=mean, xp=xp)
+    if ddof != 0:
+        n = _count_nonmasked(x, axis, xp=xp)
+        n = xp.asarray(n, dtype=x.dtype, device=xp_device(x))
+        var *= (n / (n-ddof))  # to avoid error on division by zero
+    return var
+
+
+@xp_capabilities(marray=True)
+@_axis_nan_policy_factory(
+    lambda x: x, result_to_tuple=lambda x, _: (x,), n_outputs=1
+)
+# nan_policy handled by `_axis_nan_policy`, but needs to be left
+# in signature to preserve use as a positional argument
+def skew(a, axis=0, bias=True, nan_policy='propagate'):
+    r"""Compute the sample skewness of a data set.
+
+    For normally distributed data, the skewness should be about zero. For
+    unimodal continuous distributions, a skewness value greater than zero means
+    that there is more weight in the right tail of the distribution. The
+    function `skewtest` can be used to determine if the skewness value
+    is close enough to zero, statistically speaking.
+
+    Parameters
+    ----------
+    a : ndarray
+        Input array.
+    axis : int or None, optional
+        Axis along which skewness is calculated. Default is 0.
+        If None, compute over the whole array `a`.
+    bias : bool, optional
+        If False, then the calculations are corrected for statistical bias.
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains nan.
+        The following options are available (default is 'propagate'):
+
+        * 'propagate': returns nan
+        * 'raise': throws an error
+        * 'omit': performs the calculations ignoring nan values
+
+    Returns
+    -------
+    skewness : ndarray
+        The skewness of values along an axis, returning NaN where all values
+        are equal.
+
+    Notes
+    -----
+    The sample skewness is computed as the Fisher-Pearson coefficient
+    of skewness, i.e.
+
+    .. math::
+
+        g_1=\frac{m_3}{m_2^{3/2}}
+
+    where
+
+    .. math::
+
+        m_i=\frac{1}{N}\sum_{n=1}^N(x[n]-\bar{x})^i
+
+    is the biased sample :math:`i\texttt{th}` central moment, and
+    :math:`\bar{x}` is
+    the sample mean.  If ``bias`` is False, the calculations are
+    corrected for bias and the value computed is the adjusted
+    Fisher-Pearson standardized moment coefficient, i.e.
+
+    .. math::
+
+        G_1=\frac{k_3}{k_2^{3/2}}=
+            \frac{\sqrt{N(N-1)}}{N-2}\frac{m_3}{m_2^{3/2}}.
+
+    References
+    ----------
+    .. [1] Zwillinger, D. and Kokoska, S. (2000). CRC Standard
+       Probability and Statistics Tables and Formulae. Chapman & Hall: New
+       York. 2000.
+       Section 2.2.24.1
+
+    Examples
+    --------
+    >>> from scipy.stats import skew
+    >>> skew([1, 2, 3, 4, 5])
+    0.0
+    >>> skew([2, 8, 0, 4, 1, 9, 9, 0])
+    0.2650554122698573
+
+    """
+    xp = array_namespace(a)
+    a, axis = _chk_asarray(a, axis, xp=xp)
+    n = _count_nonmasked(a, axis, xp=xp)
+
+    mean = xp.mean(a, axis=axis, keepdims=True)
+    mean_reduced = xp.squeeze(mean, axis=axis)  # needed later
+    m2 = _moment(a, 2, axis, center=mean, xp=xp)
+    m3 = _moment(a, 3, axis, center=mean, xp=xp)
+    with np.errstate(all='ignore'):
+        eps = xp.finfo(m2.dtype).eps
+        zero = m2 <= (eps * mean_reduced)**2
+        vals = xp.where(zero, xp.nan, m3 / m2**1.5)
+    if not bias:
+        can_correct = ~zero & (n > 2)
+        if is_lazy_array(can_correct) or xp.any(can_correct):
+            nval = ((n - 1.0) * n)**0.5 / (n - 2.0) * m3 / m2**1.5
+            vals = xp.where(can_correct, nval, vals)
+
+    return vals[()] if vals.ndim == 0 else vals
+
+
+@xp_capabilities(marray=True)
+@_axis_nan_policy_factory(
+    lambda x: x, result_to_tuple=lambda x, _: (x,), n_outputs=1
+)
+# nan_policy handled by `_axis_nan_policy`, but needs to be left
+# in signature to preserve use as a positional argument
+def kurtosis(a, axis=0, fisher=True, bias=True, nan_policy='propagate'):
+    """Compute the kurtosis (Fisher or Pearson) of a dataset.
+
+    Kurtosis is the fourth central moment divided by the square of the
+    variance. If Fisher's definition is used, then 3.0 is subtracted from
+    the result to give 0.0 for a normal distribution.
+
+    If bias is False then the kurtosis is calculated using k statistics to
+    eliminate bias coming from biased moment estimators
+
+    Use `kurtosistest` to see if result is close enough to normal.
+
+    Parameters
+    ----------
+    a : array
+        Data for which the kurtosis is calculated.
+    axis : int or None, optional
+        Axis along which the kurtosis is calculated. Default is 0.
+        If None, compute over the whole array `a`.
+    fisher : bool, optional
+        If True, Fisher's definition is used (normal ==> 0.0). If False,
+        Pearson's definition is used (normal ==> 3.0).
+    bias : bool, optional
+        If False, then the calculations are corrected for statistical bias.
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains nan. 'propagate' returns nan,
+        'raise' throws an error, 'omit' performs the calculations ignoring nan
+        values. Default is 'propagate'.
+
+    Returns
+    -------
+    kurtosis : array
+        The kurtosis of values along an axis, returning NaN where all values
+        are equal.
+
+    References
+    ----------
+    .. [1] Zwillinger, D. and Kokoska, S. (2000). CRC Standard
+       Probability and Statistics Tables and Formulae. Chapman & Hall: New
+       York. 2000.
+
+    Examples
+    --------
+    In Fisher's definition, the kurtosis of the normal distribution is zero.
+    In the following example, the kurtosis is close to zero, because it was
+    calculated from the dataset, not from the continuous distribution.
+
+    >>> import numpy as np
+    >>> from scipy.stats import norm, kurtosis
+    >>> data = norm.rvs(size=1000, random_state=3)
+    >>> kurtosis(data)
+    -0.06928694200380558
+
+    The distribution with a higher kurtosis has a heavier tail.
+    The zero valued kurtosis of the normal distribution in Fisher's definition
+    can serve as a reference point.
+
+    >>> import matplotlib.pyplot as plt
+    >>> import scipy.stats as stats
+    >>> from scipy.stats import kurtosis
+
+    >>> x = np.linspace(-5, 5, 100)
+    >>> ax = plt.subplot()
+    >>> distnames = ['laplace', 'norm', 'uniform']
+
+    >>> for distname in distnames:
+    ...     if distname == 'uniform':
+    ...         dist = getattr(stats, distname)(loc=-2, scale=4)
+    ...     else:
+    ...         dist = getattr(stats, distname)
+    ...     data = dist.rvs(size=1000)
+    ...     kur = kurtosis(data, fisher=True)
+    ...     y = dist.pdf(x)
+    ...     ax.plot(x, y, label="{}, {}".format(distname, round(kur, 3)))
+    ...     ax.legend()
+
+    The Laplace distribution has a heavier tail than the normal distribution.
+    The uniform distribution (which has negative kurtosis) has the thinnest
+    tail.
+
+    """
+    xp = array_namespace(a)
+    a, axis = _chk_asarray(a, axis, xp=xp)
+
+    n = _count_nonmasked(a, axis, xp=xp)
+    mean = xp.mean(a, axis=axis, keepdims=True)
+    mean_reduced = xp.squeeze(mean, axis=axis)  # needed later
+    m2 = _moment(a, 2, axis, center=mean, xp=xp)
+    m4 = _moment(a, 4, axis, center=mean, xp=xp)
+    with np.errstate(all='ignore'):
+        zero = m2 <= (xp.finfo(m2.dtype).eps * mean_reduced)**2
+        vals = xp.where(zero, xp.nan, m4 / m2**2.0)
+
+    if not bias:
+        can_correct = ~zero & (n > 3)
+        if is_lazy_array(can_correct) or xp.any(can_correct):
+            nval = 1.0/(n-2)/(n-3) * ((n**2-1.0)*m4/m2**2.0 - 3*(n-1)**2.0)
+            vals = xp.where(can_correct, nval + 3.0, vals)
+
+    vals = vals - 3 if fisher else vals
+    return vals[()] if vals.ndim == 0 else vals
+
+
+DescribeResult = namedtuple('DescribeResult',
+                            ('nobs', 'minmax', 'mean', 'variance', 'skewness',
+                             'kurtosis'))
+
+
+@xp_capabilities(marray=True)
+def describe(a, axis=0, ddof=1, bias=True, nan_policy='propagate'):
+    """Compute several descriptive statistics of the passed array.
+
+    Parameters
+    ----------
+    a : array_like
+        Input data.
+    axis : int or None, optional
+        Axis along which statistics are calculated. Default is 0.
+        If None, compute over the whole array `a`.
+    ddof : int, optional
+        Delta degrees of freedom (only for variance).  Default is 1.
+    bias : bool, optional
+        If False, then the skewness and kurtosis calculations are corrected
+        for statistical bias.
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains nan.
+        The following options are available (default is 'propagate'):
+
+        * 'propagate': returns nan
+        * 'raise': throws an error
+        * 'omit': performs the calculations ignoring nan values
+
+    Returns
+    -------
+    nobs : int or ndarray of ints
+        Number of observations (length of data along `axis`).
+        When 'omit' is chosen as nan_policy, the length along each axis
+        slice is counted separately.
+    minmax: tuple of ndarrays or floats
+        Minimum and maximum value of `a` along the given axis.
+    mean : ndarray or float
+        Arithmetic mean of `a` along the given axis.
+    variance : ndarray or float
+        Unbiased variance of `a` along the given axis; denominator is number
+        of observations minus one.
+    skewness : ndarray or float
+        Skewness of `a` along the given axis, based on moment calculations
+        with denominator equal to the number of observations, i.e. no degrees
+        of freedom correction.
+    kurtosis : ndarray or float
+        Kurtosis (Fisher) of `a` along the given axis.  The kurtosis is
+        normalized so that it is zero for the normal distribution.  No
+        degrees of freedom are used.
+
+    Raises
+    ------
+    ValueError
+        If size of `a` is 0.
+
+    See Also
+    --------
+    skew, kurtosis
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> a = np.arange(10)
+    >>> stats.describe(a)
+    DescribeResult(nobs=10, minmax=(0, 9), mean=4.5,
+                   variance=9.166666666666666, skewness=0.0,
+                   kurtosis=-1.2242424242424244)
+    >>> b = [[1, 2], [3, 4]]
+    >>> stats.describe(b)
+    DescribeResult(nobs=2, minmax=(array([1, 2]), array([3, 4])),
+                   mean=array([2., 3.]), variance=array([2., 2.]),
+                   skewness=array([0., 0.]), kurtosis=array([-2., -2.]))
+
+    """
+    xp = array_namespace(a)
+    a, axis = _chk_asarray(a, axis, xp=xp)
+
+    contains_nan = _contains_nan(a, nan_policy)
+
+    # Test nan_policy before the implicit call to bool(contains_nan)
+    # to avoid raising on lazy xps on the default nan_policy='propagate'
+    if nan_policy == 'omit' and contains_nan:
+        # only NumPy gets here; `_contains_nan` raises error for the rest
+        a = ma.masked_invalid(a)
+        return mstats_basic.describe(a, axis, ddof, bias)
+
+    if xp_size(a) == 0:
+        raise ValueError("The input must not be empty.")
+
+    # use xp.astype when data-apis/array-api-compat#226 is resolved
+    n = xp.asarray(_count_nonmasked(a, axis, xp=xp), dtype=xp.int64,
+                   device=xp_device(a))
+    n = n[()] if n.ndim == 0 else n
+    mm = (xp.min(a, axis=axis), xp.max(a, axis=axis))
+    a = xp_promote(a, force_floating=True, xp=xp)
+    m = xp.mean(a, axis=axis)
+    v = _var(a, axis=axis, ddof=ddof, xp=xp)
+    v = v[()] if v.ndim == 0 else v
+    sk = skew(a, axis, bias=bias)
+    kurt = kurtosis(a, axis, bias=bias)
+
+    return DescribeResult(n, mm, m, v, sk, kurt)
+
+#####################################
+#         NORMALITY TESTS           #
+#####################################
+
+
+def _get_pvalue(statistic, distribution, alternative, symmetric=True, xp=None):
+    """Get p-value given the statistic, (continuous) distribution, and alternative"""
+    xp = array_namespace(statistic) if xp is None else xp
+
+    if alternative == 'less':
+        pvalue = distribution.cdf(statistic)
+    elif alternative == 'greater':
+        pvalue = distribution.sf(statistic)
+    elif alternative == 'two-sided':
+        pvalue = 2 * (distribution.sf(xp.abs(statistic)) if symmetric
+                      else xp.minimum(distribution.cdf(statistic),
+                                      distribution.sf(statistic)))
+    else:
+        message = "`alternative` must be 'less', 'greater', or 'two-sided'."
+        raise ValueError(message)
+
+    return pvalue
+
+
+SkewtestResult = namedtuple('SkewtestResult', ('statistic', 'pvalue'))
+
+
+@xp_capabilities(marray=True)
+@_axis_nan_policy_factory(SkewtestResult, n_samples=1, too_small=7)
+# nan_policy handled by `_axis_nan_policy`, but needs to be left
+# in signature to preserve use as a positional argument
+def skewtest(a, axis=0, nan_policy='propagate', alternative='two-sided'):
+    r"""Test whether the skew is different from the normal distribution.
+
+    This function tests the null hypothesis that the skewness of
+    the population that the sample was drawn from is the same
+    as that of a corresponding normal distribution.
+
+    Parameters
+    ----------
+    a : array
+        The data to be tested. Must contain at least eight observations.
+    axis : int or None, optional
+       Axis along which statistics are calculated. Default is 0.
+       If None, compute over the whole array `a`.
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains nan.
+        The following options are available (default is 'propagate'):
+
+        * 'propagate': returns nan
+        * 'raise': throws an error
+        * 'omit': performs the calculations ignoring nan values
+
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis. Default is 'two-sided'.
+        The following options are available:
+
+        * 'two-sided': the skewness of the distribution underlying the sample
+          is different from that of the normal distribution (i.e. 0)
+        * 'less': the skewness of the distribution underlying the sample
+          is less than that of the normal distribution
+        * 'greater': the skewness of the distribution underlying the sample
+          is greater than that of the normal distribution
+
+        .. versionadded:: 1.7.0
+
+    Returns
+    -------
+    statistic : float
+        The computed z-score for this test.
+    pvalue : float
+        The p-value for the hypothesis test.
+
+    See Also
+    --------
+    :ref:`hypothesis_skewtest` : Extended example
+
+    Notes
+    -----
+    The sample size must be at least 8.
+
+    References
+    ----------
+    .. [1] R. B. D'Agostino, A. J. Belanger and R. B. D'Agostino Jr.,
+            "A suggestion for using powerful and informative tests of
+            normality", American Statistician 44, pp. 316-321, 1990.
+
+    Examples
+    --------
+
+    >>> from scipy.stats import skewtest
+    >>> skewtest([1, 2, 3, 4, 5, 6, 7, 8])
+    SkewtestResult(statistic=1.0108048609177787, pvalue=0.3121098361421897)
+    >>> skewtest([2, 8, 0, 4, 1, 9, 9, 0])
+    SkewtestResult(statistic=0.44626385374196975, pvalue=0.6554066631275459)
+    >>> skewtest([1, 2, 3, 4, 5, 6, 7, 8000])
+    SkewtestResult(statistic=3.571773510360407, pvalue=0.0003545719905823133)
+    >>> skewtest([100, 100, 100, 100, 100, 100, 100, 101])
+    SkewtestResult(statistic=3.5717766638478072, pvalue=0.000354567720281634)
+    >>> skewtest([1, 2, 3, 4, 5, 6, 7, 8], alternative='less')
+    SkewtestResult(statistic=1.0108048609177787, pvalue=0.8439450819289052)
+    >>> skewtest([1, 2, 3, 4, 5, 6, 7, 8], alternative='greater')
+    SkewtestResult(statistic=1.0108048609177787, pvalue=0.15605491807109484)
+
+    For a more detailed example, see :ref:`hypothesis_skewtest`.
+    """
+    xp = array_namespace(a)
+    a, axis = _chk_asarray(a, axis, xp=xp)
+
+    b2 = skew(a, axis, _no_deco=True)
+
+    n = xp.asarray(_count_nonmasked(a, axis), dtype=b2.dtype, device=xp_device(a))
+    n = xpx.at(n, n < 8).set(xp.nan)
+
+    with np.errstate(divide='ignore', invalid='ignore'):
+        y = b2 * xp.sqrt(((n + 1) * (n + 3)) / (6.0 * (n - 2)))
+        beta2 = (3.0 * (n**2 + 27*n - 70) * (n+1) * (n+3) /
+                 ((n-2.0) * (n+5) * (n+7) * (n+9)))
+        W2 = -1 + xp.sqrt(2 * (beta2 - 1))
+        delta = 1 / xp.sqrt(0.5 * xp.log(W2))
+        alpha = xp.sqrt(2.0 / (W2 - 1))
+        y = xp.where(y == 0, 1., y)
+        Z = delta * xp.log(y / alpha + xp.sqrt((y / alpha)**2 + 1))
+        pvalue = _get_pvalue(Z, _SimpleNormal(), alternative, xp=xp)
+
+    Z = Z[()] if Z.ndim == 0 else Z
+    pvalue = pvalue[()] if pvalue.ndim == 0 else pvalue
+    return SkewtestResult(Z, pvalue)
+
+
+KurtosistestResult = namedtuple('KurtosistestResult', ('statistic', 'pvalue'))
+
+
+@xp_capabilities(marray=True)
+@_axis_nan_policy_factory(KurtosistestResult, n_samples=1, too_small=4)
+def kurtosistest(a, axis=0, nan_policy='propagate', alternative='two-sided'):
+    r"""Test whether a dataset has normal kurtosis.
+
+    This function tests the null hypothesis that the kurtosis
+    of the population from which the sample was drawn is that
+    of the normal distribution.
+
+    Parameters
+    ----------
+    a : array
+        Array of the sample data. Must contain at least five observations.
+    axis : int or None, optional
+       Axis along which to compute test. Default is 0. If None,
+       compute over the whole array `a`.
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains nan.
+        The following options are available (default is 'propagate'):
+
+        * 'propagate': returns nan
+        * 'raise': throws an error
+        * 'omit': performs the calculations ignoring nan values
+
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis.
+        The following options are available (default is 'two-sided'):
+
+        * 'two-sided': the kurtosis of the distribution underlying the sample
+          is different from that of the normal distribution
+        * 'less': the kurtosis of the distribution underlying the sample
+          is less than that of the normal distribution
+        * 'greater': the kurtosis of the distribution underlying the sample
+          is greater than that of the normal distribution
+
+        .. versionadded:: 1.7.0
+
+    Returns
+    -------
+    statistic : float
+        The computed z-score for this test.
+    pvalue : float
+        The p-value for the hypothesis test.
+
+    See Also
+    --------
+    :ref:`hypothesis_kurtosistest` : Extended example
+
+    Notes
+    -----
+    Valid only for n>20. This function uses the method described in [1]_.
+
+    References
+    ----------
+    .. [1] F. J. Anscombe, W. J. Glynn, "Distribution of the kurtosis
+       statistic b2 for normal samples", Biometrika, vol. 70, pp. 227-234, 1983.
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> from scipy.stats import kurtosistest
+    >>> kurtosistest(list(range(20)))
+    KurtosistestResult(statistic=-1.7058104152122062, pvalue=0.08804338332528348)
+    >>> kurtosistest(list(range(20)), alternative='less')
+    KurtosistestResult(statistic=-1.7058104152122062, pvalue=0.04402169166264174)
+    >>> kurtosistest(list(range(20)), alternative='greater')
+    KurtosistestResult(statistic=-1.7058104152122062, pvalue=0.9559783083373583)
+    >>> rng = np.random.default_rng()
+    >>> s = rng.normal(0, 1, 1000)
+    >>> kurtosistest(s)
+    KurtosistestResult(statistic=-1.475047944490622, pvalue=0.14019965402996987)
+
+    For a more detailed example, see :ref:`hypothesis_kurtosistest`.
+    """
+    xp = array_namespace(a)
+    a, axis = _chk_asarray(a, axis, xp=xp)
+
+    b2 = kurtosis(a, axis, fisher=False, _no_deco=True)
+
+    n = xp.asarray(_count_nonmasked(a, axis), dtype=b2.dtype, device=xp_device(a))
+    n = xpx.at(n, n < 5).set(xp.nan)
+
+    E = 3.0*(n-1) / (n+1)
+    varb2 = 24.0*n*(n-2)*(n-3) / ((n+1)*(n+1.)*(n+3)*(n+5))  # [1]_ Eq. 1
+    x = (b2-E) / varb2**0.5  # [1]_ Eq. 4
+    # [1]_ Eq. 2:
+    sqrtbeta1 = 6.0*(n*n-5*n+2)/((n+7)*(n+9)) * ((6.0*(n+3)*(n+5))
+                                                 / (n*(n-2)*(n-3)))**0.5
+    # [1]_ Eq. 3:
+    A = 6.0 + 8.0/sqrtbeta1 * (2.0/sqrtbeta1 + (1+4.0/(sqrtbeta1**2))**0.5)
+    term1 = 1 - 2/(9.0*A)
+    denom = 1 + x * (2/(A-4.0))**0.5
+    term2 = xp.sign(denom) * xp.where(denom == 0.0, xp.nan,
+                                      ((1-2.0/A)/xp.abs(denom))**(1/3))
+    if not is_lazy_array(denom) and xp.any(denom == 0):
+        msg = ("Test statistic not defined in some cases due to division by "
+               "zero. Return nan in that case...")
+        warnings.warn(msg, RuntimeWarning, stacklevel=2)
+
+    Z = (term1 - term2) / (2/(9.0*A))**0.5  # [1]_ Eq. 5
+    pvalue = _get_pvalue(Z, _SimpleNormal(), alternative, xp=xp)
+
+    Z = Z[()] if Z.ndim == 0 else Z
+    pvalue = pvalue[()] if pvalue.ndim == 0 else pvalue
+    return KurtosistestResult(Z, pvalue)
+
+
+NormaltestResult = namedtuple('NormaltestResult', ('statistic', 'pvalue'))
+
+
+@xp_capabilities(marray=True)
+@_axis_nan_policy_factory(NormaltestResult, n_samples=1, too_small=7)
+def normaltest(a, axis=0, nan_policy='propagate'):
+    r"""Test whether a sample differs from a normal distribution.
+
+    This function tests the null hypothesis that a sample comes
+    from a normal distribution.  It is based on D'Agostino and
+    Pearson's [1]_, [2]_ test that combines skew and kurtosis to
+    produce an omnibus test of normality.
+
+    Parameters
+    ----------
+    a : array_like
+        The array containing the sample to be tested. Must contain
+        at least eight observations.
+    axis : int or None, optional
+        Axis along which to compute test. Default is 0. If None,
+        compute over the whole array `a`.
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains nan.
+        The following options are available (default is 'propagate'):
+
+        * 'propagate': returns nan
+        * 'raise': throws an error
+        * 'omit': performs the calculations ignoring nan values
+
+    Returns
+    -------
+    statistic : float or array
+        ``s^2 + k^2``, where ``s`` is the z-score returned by `skewtest` and
+        ``k`` is the z-score returned by `kurtosistest`.
+    pvalue : float or array
+        A 2-sided chi squared probability for the hypothesis test.
+
+    See Also
+    --------
+    :ref:`hypothesis_normaltest` : Extended example
+
+    References
+    ----------
+    .. [1] D'Agostino, R. B. (1971), "An omnibus test of normality for
+            moderate and large sample size", Biometrika, 58, 341-348
+    .. [2] D'Agostino, R. and Pearson, E. S. (1973), "Tests for departure from
+            normality", Biometrika, 60, 613-622
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> rng = np.random.default_rng()
+    >>> pts = 1000
+    >>> a = rng.normal(0, 1, size=pts)
+    >>> b = rng.normal(2, 1, size=pts)
+    >>> x = np.concatenate((a, b))
+    >>> res = stats.normaltest(x)
+    >>> res.statistic
+    53.619...  # random
+    >>> res.pvalue
+    2.273917413209226e-12  # random
+
+    For a more detailed example, see :ref:`hypothesis_normaltest`.
+    """
+    xp = array_namespace(a)
+
+    s, _ = skewtest(a, axis, _no_deco=True)
+    k, _ = kurtosistest(a, axis, _no_deco=True)
+    statistic = s*s + k*k
+
+    chi2 = _SimpleChi2(xp.asarray(2., dtype=statistic.dtype, device=xp_device(a)))
+    pvalue = _get_pvalue(statistic, chi2, alternative='greater', symmetric=False, xp=xp)
+
+    statistic = statistic[()] if statistic.ndim == 0 else statistic
+    pvalue = pvalue[()] if pvalue.ndim == 0 else pvalue
+
+    return NormaltestResult(statistic, pvalue)
+
+
+@xp_capabilities(marray=True)
+@_axis_nan_policy_factory(SignificanceResult, default_axis=None)
+def jarque_bera(x, *, axis=None):
+    r"""Perform the Jarque-Bera goodness of fit test on sample data.
+
+    The Jarque-Bera test tests whether the sample data has the skewness and
+    kurtosis matching a normal distribution.
+
+    Note that this test only works for a large enough number of data samples
+    (>2000) as the test statistic asymptotically has a Chi-squared distribution
+    with 2 degrees of freedom.
+
+    Parameters
+    ----------
+    x : array_like
+        Observations of a random variable.
+    axis : int or None, default: 0
+        If an int, the axis of the input along which to compute the statistic.
+        The statistic of each axis-slice (e.g. row) of the input will appear in
+        a corresponding element of the output.
+        If ``None``, the input will be raveled before computing the statistic.
+
+    Returns
+    -------
+    result : SignificanceResult
+        An object with the following attributes:
+
+        statistic : float
+            The test statistic.
+        pvalue : float
+            The p-value for the hypothesis test.
+
+    See Also
+    --------
+    :ref:`hypothesis_jarque_bera` : Extended example
+
+    References
+    ----------
+    .. [1] Jarque, C. and Bera, A. (1980) "Efficient tests for normality,
+           homoscedasticity and serial independence of regression residuals",
+           6 Econometric Letters 255-259.
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> rng = np.random.default_rng()
+    >>> x = rng.normal(0, 1, 100000)
+    >>> jarque_bera_test = stats.jarque_bera(x)
+    >>> jarque_bera_test
+    Jarque_beraResult(statistic=3.3415184718131554, pvalue=0.18810419594996775)
+    >>> jarque_bera_test.statistic
+    3.3415184718131554
+    >>> jarque_bera_test.pvalue
+    0.18810419594996775
+
+    For a more detailed example, see :ref:`hypothesis_jarque_bera`.
+    """
+    xp = array_namespace(x)
+    x, axis = _chk_asarray(x, axis, xp=xp)
+
+    mu = _xp_mean(x, axis=axis, keepdims=True)
+    diffx = x - mu
+    s = skew(diffx, axis=axis, _no_deco=True)
+    k = kurtosis(diffx, axis=axis, _no_deco=True)
+
+    n = xp.asarray(_count_nonmasked(x, axis), dtype=mu.dtype, device=xp_device(x))
+    statistic = n / 6 * (s**2 + k**2 / 4)
+
+    chi2 = _SimpleChi2(xp.asarray(2., dtype=mu.dtype, device=xp_device(x)))
+    pvalue = _get_pvalue(statistic, chi2, alternative='greater', symmetric=False, xp=xp)
+
+    statistic = statistic[()] if statistic.ndim == 0 else statistic
+    pvalue = pvalue[()] if pvalue.ndim == 0 else pvalue
+
+    return SignificanceResult(statistic, pvalue)
+
+
+#####################################
+#        FREQUENCY FUNCTIONS        #
+#####################################
+
+
+@xp_capabilities(np_only=True)
+def scoreatpercentile(a, per, limit=(), interpolation_method='fraction',
+                      axis=None):
+    """Calculate the score at a given percentile of the input sequence.
+
+    For example, the score at ``per=50`` is the median. If the desired quantile
+    lies between two data points, we interpolate between them, according to
+    the value of `interpolation`. If the parameter `limit` is provided, it
+    should be a tuple (lower, upper) of two values.
+
+    Parameters
+    ----------
+    a : array_like
+        A 1-D array of values from which to extract score.
+    per : array_like
+        Percentile(s) at which to extract score.  Values should be in range
+        [0,100].
+    limit : tuple, optional
+        Tuple of two scalars, the lower and upper limits within which to
+        compute the percentile. Values of `a` outside
+        this (closed) interval will be ignored.
+    interpolation_method : {'fraction', 'lower', 'higher'}, optional
+        Specifies the interpolation method to use,
+        when the desired quantile lies between two data points `i` and `j`
+        The following options are available (default is 'fraction'):
+
+        * 'fraction': ``i + (j - i) * fraction`` where ``fraction`` is the
+            fractional part of the index surrounded by ``i`` and ``j``
+        * 'lower': ``i``
+        * 'higher': ``j``
+
+    axis : int, optional
+        Axis along which the percentiles are computed. Default is None. If
+        None, compute over the whole array `a`.
+
+    Returns
+    -------
+    score : float or ndarray
+        Score at percentile(s).
+
+    See Also
+    --------
+    percentileofscore, numpy.percentile
+
+    Notes
+    -----
+    This function will become obsolete in the future.
+    For NumPy 1.9 and higher, `numpy.percentile` provides all the functionality
+    that `scoreatpercentile` provides.  And it's significantly faster.
+    Therefore it's recommended to use `numpy.percentile` for users that have
+    numpy >= 1.9.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> a = np.arange(100)
+    >>> stats.scoreatpercentile(a, 50)
+    49.5
+
+    """
+    # adapted from NumPy's percentile function.  When we require numpy >= 1.8,
+    # the implementation of this function can be replaced by np.percentile.
+    a = np.asarray(a)
+    if a.size == 0:
+        # empty array, return nan(s) with shape matching `per`
+        if np.isscalar(per):
+            return np.nan
+        else:
+            return np.full(np.asarray(per).shape, np.nan, dtype=np.float64)
+
+    if limit:
+        a = a[(limit[0] <= a) & (a <= limit[1])]
+
+    sorted_ = np.sort(a, axis=axis)
+    if axis is None:
+        axis = 0
+
+    return _compute_qth_percentile(sorted_, per, interpolation_method, axis)
+
+
+# handle sequence of per's without calling sort multiple times
+def _compute_qth_percentile(sorted_, per, interpolation_method, axis):
+    if not np.isscalar(per):
+        score = [_compute_qth_percentile(sorted_, i,
+                                         interpolation_method, axis)
+                 for i in per]
+        return np.array(score)
+
+    if not (0 <= per <= 100):
+        raise ValueError("percentile must be in the range [0, 100]")
+
+    indexer = [slice(None)] * sorted_.ndim
+    idx = per / 100. * (sorted_.shape[axis] - 1)
+
+    if int(idx) != idx:
+        # round fractional indices according to interpolation method
+        if interpolation_method == 'lower':
+            idx = int(np.floor(idx))
+        elif interpolation_method == 'higher':
+            idx = int(np.ceil(idx))
+        elif interpolation_method == 'fraction':
+            pass  # keep idx as fraction and interpolate
+        else:
+            raise ValueError("interpolation_method can only be 'fraction', "
+                             "'lower' or 'higher'")
+
+    i = int(idx)
+    if i == idx:
+        indexer[axis] = slice(i, i + 1)
+        weights = array(1)
+        sumval = 1.0
+    else:
+        indexer[axis] = slice(i, i + 2)
+        j = i + 1
+        weights = array([(j - idx), (idx - i)], float)
+        wshape = [1] * sorted_.ndim
+        wshape[axis] = 2
+        weights = weights.reshape(wshape)
+        sumval = weights.sum()
+
+    # Use np.add.reduce (== np.sum but a little faster) to coerce data type
+    return np.add.reduce(sorted_[tuple(indexer)] * weights, axis=axis) / sumval
+
+
+@xp_capabilities(np_only=True)
+def percentileofscore(a, score, kind='rank', nan_policy='propagate'):
+    """Compute the percentile rank of a score relative to a list of scores.
+
+    A `percentileofscore` of, for example, 80% means that 80% of the
+    scores in `a` are below the given score. In the case of gaps or
+    ties, the exact definition depends on the optional keyword, `kind`.
+
+    Parameters
+    ----------
+    a : array_like
+        A 1-D array to which `score` is compared.
+    score : float or array_like
+        A float score or array of scores for which to compute the percentile(s).
+    kind : {'rank', 'weak', 'strict', 'mean'}, optional
+        Specifies the interpretation of the resulting score.
+        The following options are available (default is 'rank'):
+
+        * 'rank': Average percentage ranking of score.  In case of multiple
+          matches, average the percentage rankings of all matching scores.
+        * 'weak': This kind corresponds to the definition of a cumulative
+          distribution function.  A percentileofscore of 80% means that 80%
+          of values are less than or equal to the provided score.
+        * 'strict': Similar to "weak", except that only values that are
+          strictly less than the given score are counted.
+        * 'mean': The average of the "weak" and "strict" scores, often used
+          in testing.  See https://en.wikipedia.org/wiki/Percentile_rank
+
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Specifies how to treat `nan` values in `a`.
+        The following options are available (default is 'propagate'):
+
+        * 'propagate': returns nan (for each value in `score`).
+        * 'raise': throws an error
+        * 'omit': performs the calculations ignoring nan values
+
+    Returns
+    -------
+    pcos : float or array-like
+        Percentile-position(s) of `score` (0-100) relative to `a`.
+
+    See Also
+    --------
+    numpy.percentile
+    scipy.stats.scoreatpercentile, scipy.stats.rankdata
+
+    Examples
+    --------
+    Three-quarters of the given values lie below a given score:
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> stats.percentileofscore([1, 2, 3, 4], 3)
+    75.0
+
+    With multiple matches, note how the scores of the two matches, 0.6
+    and 0.8 respectively, are averaged:
+
+    >>> stats.percentileofscore([1, 2, 3, 3, 4], 3)
+    70.0
+
+    Only 2/5 values are strictly less than 3:
+
+    >>> stats.percentileofscore([1, 2, 3, 3, 4], 3, kind='strict')
+    40.0
+
+    But 4/5 values are less than or equal to 3:
+
+    >>> stats.percentileofscore([1, 2, 3, 3, 4], 3, kind='weak')
+    80.0
+
+    The average between the weak and the strict scores is:
+
+    >>> stats.percentileofscore([1, 2, 3, 3, 4], 3, kind='mean')
+    60.0
+
+    Score arrays (of any dimensionality) are supported:
+
+    >>> stats.percentileofscore([1, 2, 3, 3, 4], [2, 3])
+    array([40., 70.])
+
+    The inputs can be infinite:
+
+    >>> stats.percentileofscore([-np.inf, 0, 1, np.inf], [1, 2, np.inf])
+    array([75., 75., 100.])
+
+    If `a` is empty, then the resulting percentiles are all `nan`:
+
+    >>> stats.percentileofscore([], [1, 2])
+    array([nan, nan])
+    """
+
+    a = np.asarray(a)
+    score = np.asarray(score)
+
+    if a.ndim != 1:
+        raise ValueError("`a` must be 1-dimensional.")
+
+    n = len(a)
+
+    # Nan treatment
+    cna = _contains_nan(a, nan_policy)
+    cns = _contains_nan(score, nan_policy)
+
+    if cns:
+        # If a score is nan, then the output should be nan
+        # (also if nan_policy is "omit", because it only applies to `a`)
+        score = ma.masked_where(np.isnan(score), score)
+
+    if cna:
+        if nan_policy == "omit":
+            # Don't count nans
+            a = ma.masked_where(np.isnan(a), a)
+            n = a.count()
+
+        if nan_policy == "propagate":
+            # All outputs should be nans
+            n = 0
+
+    # Cannot compare to empty list ==> nan
+    if n == 0:
+        perct = np.full_like(score, np.nan, dtype=np.float64)
+
+    else:
+        # Prepare broadcasting
+        score = score[..., None]
+
+        def count(x):
+            return np.count_nonzero(x, -1)
+
+        # Main computations/logic
+        if kind == 'rank':
+            left = count(a < score)
+            right = count(a <= score)
+            plus1 = left < right
+            perct = (left + right + plus1) * (50.0 / n)
+        elif kind == 'strict':
+            perct = count(a < score) * (100.0 / n)
+        elif kind == 'weak':
+            perct = count(a <= score) * (100.0 / n)
+        elif kind == 'mean':
+            left = count(a < score)
+            right = count(a <= score)
+            perct = (left + right) * (50.0 / n)
+        else:
+            raise ValueError(
+                "kind can only be 'rank', 'strict', 'weak' or 'mean'")
+
+    # Re-insert nan values
+    perct = ma.filled(perct, np.nan)
+
+    if perct.ndim == 0:
+        return perct[()]
+    return perct
+
+
+HistogramResult = namedtuple('HistogramResult',
+                             ('count', 'lowerlimit', 'binsize', 'extrapoints'))
+
+
+def _histogram(a, numbins=10, defaultlimits=None, weights=None, *,
+               density=False, cumulative=False):
+    """Create a histogram.
+
+    Separate the range into several bins and return the number of instances
+    in each bin.
+
+    Parameters
+    ----------
+    a : array_like
+        Array of scores which will be put into bins.
+    numbins : int, optional
+        The number of bins to use for the histogram. Default is 10.
+    defaultlimits : tuple (lower, upper), optional
+        The lower and upper values for the range of the histogram.
+        If no value is given, a range slightly larger than the range of the
+        values in a is used. Specifically ``(a.min() - s, a.max() + s)``,
+        where ``s = (1/2)(a.max() - a.min()) / (numbins - 1)``.
+    weights : array_like, optional
+        The weights for each value in `a`. Default is None, which gives each
+        value a weight of 1.0
+
+    Returns
+    -------
+    count : ndarray
+        Number of points (or sum of weights) in each bin.
+    lowerlimit : float
+        Lowest value of histogram, the lower limit of the first bin.
+    binsize : float
+        The size of the bins (all bins have the same size).
+    extrapoints : int
+        The number of points outside the range of the histogram.
+
+    See Also
+    --------
+    numpy.histogram
+
+    Notes
+    -----
+    This histogram is based on numpy's histogram but has a larger range by
+    default if default limits is not set.
+
+    """
+    xp = array_namespace(a)
+    a = xp_ravel(a)
+    a, weights = xp_promote(a, weights, force_floating=True, xp=xp)
+
+    if defaultlimits is None:
+        if xp_size(a) == 0:
+            # handle empty arrays. Undetermined range, so use 0-1.
+            defaultlimits = xp.asarray(0., dtype=a.dtype), xp.asarray(1., dtype=a.dtype)
+        else:
+            # no range given, so use values in `a`
+            data_min = xp.min(a)
+            data_max = xp.max(a)
+            # Have bins extend past min and max values slightly
+            s = (data_max - data_min) / (2. * (numbins - 1.))
+            defaultlimits = (data_min - s, data_max + s)
+    else:
+        if not (np.iterable(defaultlimits) and len(defaultlimits)==2
+                and defaultlimits[0] < defaultlimits[1]):
+            message = ('If specified, `defaultreallimits` must be given as an iterable '
+                       'in the order (lower limit, upper limit).')
+            raise ValueError(message)
+        if not (xp.isdtype(a.dtype, 'real floating')
+                and (weights is None or xp.isdtype(weights.dtype, 'real floating'))):
+            message = '`a` and (if specified) `weights` must have real dtype.'
+            raise ValueError(message)
+        if weights is not None and not is_lazy_array(weights) and xp.any(weights < 0):
+            message = 'All `weights` must be non-negative.'
+            raise ValueError(message)
+
+    bin_edges = xp.linspace(*defaultlimits, numbins+1, dtype=a.dtype)
+    if weights is None:
+        indices = xp.searchsorted(xp.sort(a), bin_edges, side='left')
+        hist = xp.diff(indices)
+        n_right_limit = xp.count_nonzero(a == bin_edges[-1])
+        hist = xpx.at(hist)[-1].add(xp.astype(n_right_limit, hist.dtype))
+    else:
+        i = xp.argsort(a)
+        weights, a = weights[i], a[i]
+        cumulative_weights = xp.cumulative_sum(weights, include_initial=True)
+        indices = xp.searchsorted(a, bin_edges, side='left')
+        hist = xp.diff(xp.take_along_axis(cumulative_weights, indices, axis=-1))
+        hist = xpx.at(hist)[-1].add(xp.sum(xp.where(a == bin_edges[-1], weights, 0.)))
+
+    # fixed width for bins is assumed, as numpy's histogram gives
+    # fixed width bins for int values for 'bins'
+    binsize = bin_edges[1] - bin_edges[0]
+    # calculate number of extra points
+    binnedpoints = (xp.sum(hist) if weights is None
+                    else xp.count_nonzero((bin_edges[0] <= a) & (a <= bin_edges[-1])))
+    extrapoints = a.shape[0] - binnedpoints
+
+    lowerlimit = xp.asarray(defaultlimits[0], dtype=a.dtype)[()]
+
+    hist = xp.asarray(hist, dtype=a.dtype)
+    if density:
+        hist = hist / (a.shape[0] if weights is None else cumulative_weights[-1])
+    if cumulative:
+        hist = xp.cumulative_sum(hist, axis=0)
+
+    return HistogramResult(hist, lowerlimit, binsize, extrapoints)
+
+
+CumfreqResult = namedtuple('CumfreqResult',
+                           ('cumcount', 'lowerlimit', 'binsize',
+                            'extrapoints'))
+
+
+@xp_capabilities(skip_backends=[('dask.array', 'fails tests')])
+def cumfreq(a, numbins=10, defaultreallimits=None, weights=None):
+    """Return a cumulative frequency histogram, using the histogram function.
+
+    A cumulative histogram is a mapping that counts the cumulative number of
+    observations in all of the bins up to the specified bin.
+
+    Parameters
+    ----------
+    a : array_like
+        Input array.
+    numbins : int, optional
+        The number of bins to use for the histogram. Default is 10.
+    defaultreallimits : tuple (lower, upper), optional
+        The lower and upper values for the range of the histogram.
+        If no value is given, a range slightly larger than the range of the
+        values in `a` is used. Specifically ``(a.min() - s, a.max() + s)``,
+        where ``s = (1/2)(a.max() - a.min()) / (numbins - 1)``.
+    weights : array_like, optional
+        The weights for each value in `a`. Default is None, which gives each
+        value a weight of 1.0
+
+    Returns
+    -------
+    cumcount : ndarray
+        Binned values of cumulative frequency.
+    lowerlimit : float
+        Lower real limit
+    binsize : float
+        Width of each bin.
+    extrapoints : int
+        Extra points.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy import stats
+    >>> rng = np.random.default_rng()
+    >>> x = [1, 4, 2, 1, 3, 1]
+    >>> res = stats.cumfreq(x, numbins=4, defaultreallimits=(1.5, 5))
+    >>> res.cumcount
+    array([ 1.,  2.,  3.,  3.])
+    >>> res.extrapoints
+    3
+
+    Create a normal distribution with 1000 random values
+
+    >>> samples = stats.norm.rvs(size=1000, random_state=rng)
+
+    Calculate cumulative frequencies
+
+    >>> res = stats.cumfreq(samples, numbins=25)
+
+    Calculate space of values for x
+
+    >>> x = res.lowerlimit + np.linspace(0, res.binsize*res.cumcount.size,
+    ...                                  res.cumcount.size + 1)
+
+    Plot histogram and cumulative histogram
+
+    >>> fig = plt.figure(figsize=(10, 4))
+    >>> ax1 = fig.add_subplot(1, 2, 1)
+    >>> ax2 = fig.add_subplot(1, 2, 2)
+    >>> ax1.hist(samples, bins=25)
+    >>> ax1.set_title('Histogram')
+    >>> ax2.bar(x[:-1], res.cumcount, width=res.binsize, align='edge')
+    >>> ax2.set_title('Cumulative histogram')
+    >>> ax2.set_xlim([x.min(), x.max()])
+
+    >>> plt.show()
+
+    """
+    h, l, b, e = _histogram(a, numbins, defaultreallimits, weights=weights,
+                            cumulative=True)
+    return CumfreqResult(h, l, b, e)
+
+
+RelfreqResult = namedtuple('RelfreqResult',
+                           ('frequency', 'lowerlimit', 'binsize',
+                            'extrapoints'))
+
+
+@xp_capabilities(skip_backends=[('dask.array', 'fails tests')])
+def relfreq(a, numbins=10, defaultreallimits=None, weights=None):
+    """Return a relative frequency histogram, using the histogram function.
+
+    A relative frequency  histogram is a mapping of the number of
+    observations in each of the bins relative to the total of observations.
+
+    Parameters
+    ----------
+    a : array_like
+        Input array.
+    numbins : int, optional
+        The number of bins to use for the histogram. Default is 10.
+    defaultreallimits : tuple (lower, upper), optional
+        The lower and upper values for the range of the histogram.
+        If no value is given, a range slightly larger than the range of the
+        values in a is used. Specifically ``(a.min() - s, a.max() + s)``,
+        where ``s = (1/2)(a.max() - a.min()) / (numbins - 1)``.
+    weights : array_like, optional
+        The weights for each value in `a`. Default is None, which gives each
+        value a weight of 1.0
+
+    Returns
+    -------
+    frequency : ndarray
+        Binned values of relative frequency.
+    lowerlimit : float
+        Lower real limit.
+    binsize : float
+        Width of each bin.
+    extrapoints : int
+        Extra points.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy import stats
+    >>> rng = np.random.default_rng()
+    >>> a = np.array([2, 4, 1, 2, 3, 2])
+    >>> res = stats.relfreq(a, numbins=4)
+    >>> res.frequency
+    array([ 0.16666667, 0.5       , 0.16666667,  0.16666667])
+    >>> np.sum(res.frequency)  # relative frequencies should add up to 1
+    1.0
+
+    Create a normal distribution with 1000 random values
+
+    >>> samples = stats.norm.rvs(size=1000, random_state=rng)
+
+    Calculate relative frequencies
+
+    >>> res = stats.relfreq(samples, numbins=25)
+
+    Calculate space of values for x
+
+    >>> x = res.lowerlimit + np.linspace(0, res.binsize*res.frequency.size,
+    ...                                  res.frequency.size)
+
+    Plot relative frequency histogram
+
+    >>> fig = plt.figure(figsize=(5, 4))
+    >>> ax = fig.add_subplot(1, 1, 1)
+    >>> ax.bar(x, res.frequency, width=res.binsize)
+    >>> ax.set_title('Relative frequency histogram')
+    >>> ax.set_xlim([x.min(), x.max()])
+
+    >>> plt.show()
+
+    """
+    h, l, b, e = _histogram(a, numbins, defaultreallimits, weights=weights,
+                            density=True)
+    return RelfreqResult(h, l, b, e)
+
+
+#####################################
+#        VARIABILITY FUNCTIONS      #
+#####################################
+
+@xp_capabilities()
+def obrientransform(*samples, nan_policy='propagate'):
+    """Compute the O'Brien transform on input data (any number of arrays).
+
+    Used to test for homogeneity of variance prior to running one-way stats.
+    Each array in ``*samples`` is one level of a factor.
+    Significant results of `f_oneway` on the transformed data suggest that the
+    variances of the underlying distributions are unequal.
+    See Maxwell and Delaney [1]_, p.112.
+
+    Parameters
+    ----------
+    *samples : array_like
+        Any number of arrays.
+    nan_policy : {'propagate', 'omit', 'raise'}
+        Defines how to handle input NaNs.
+
+        - ``propagate``: if a NaN is present in a sample, all elements of the
+          transformed sample will be NaN.
+        - ``omit``: NaNs will be omitted when computing reducing statistics for the
+          transform, but NaNs in the sample will remain NaNs in the transformed sample.
+        - ``raise``: if a NaN is present, a ``ValueError`` will be raised.
+
+    Returns
+    -------
+    obrientransform : tuple of arrays
+        Transformed arrays for use in ANOVA.
+
+    Raises
+    ------
+    ValueError
+        If the mean of the transformed data is not equal to the original
+        variance, indicating a lack of convergence in the O'Brien transform.
+
+    References
+    ----------
+    .. [1] S. E. Maxwell and H. D. Delaney, "Designing Experiments and
+           Analyzing Data: A Model Comparison Perspective", Wadsworth, 1990.
+
+    Examples
+    --------
+    We'll test the following data sets for differences in their variance.
+
+    >>> x = [10, 11, 13, 9, 7, 12, 12, 9, 10]
+    >>> y = [13, 21, 5, 10, 8, 14, 10, 12, 7, 15]
+
+    Apply the O'Brien transform to the data.
+
+    >>> from scipy.stats import obrientransform
+    >>> tx, ty = obrientransform(x, y)
+
+    Use `scipy.stats.f_oneway` to apply a one-way ANOVA test to the
+    transformed data.
+
+    >>> from scipy.stats import f_oneway
+    >>> F, p = f_oneway(tx, ty)
+    >>> p
+    0.1314139477040335
+
+    If we require that ``p < 0.05`` for significance, we cannot conclude
+    that the variances are different.
+
+    """
+    xp = array_namespace(*samples)
+    n_samples = len(samples)
+    samples = xp_promote(*samples, force_floating=True, xp=xp)
+    samples = (samples,) if n_samples == 1 else samples
+    return tuple(_xp_obrientransform_one_sample(sample, xp=xp, nan_policy=nan_policy)
+                 for sample in samples)
+
+
+def _xp_obrientransform_one_sample(a, *, xp, nan_policy):
+    _contains_nan(a, nan_policy, xp_omit_okay=True)  # handle `nan_policy='raise'`
+    n = xp.asarray(xp.count_nonzero(~xp.isnan(a)), dtype=a.dtype)
+    mu = _xp_mean(a, nan_policy=nan_policy)
+    sq = (a - mu)**2
+    sumsq = _xp_mean(sq, nan_policy=nan_policy) * n
+    return ((n - 1.5) * n * sq - 0.5 * sumsq) / ((n - 1) * (n - 2))
+
+
+@xp_capabilities(marray=True)
+@_axis_nan_policy_factory(
+    lambda x: x, result_to_tuple=lambda x, _: (x,), n_outputs=1, too_small=1
+)
+def sem(a, axis=0, ddof=1, nan_policy='propagate'):
+    """Compute standard error of the mean.
+
+    Calculate the standard error of the mean (or standard error of
+    measurement) of the values in the input array.
+
+    Parameters
+    ----------
+    a : array_like
+        An array containing the values for which the standard error is
+        returned. Must contain at least two observations.
+    axis : int or None, optional
+        Axis along which to operate. Default is 0. If None, compute over
+        the whole array `a`.
+    ddof : int, optional
+        Delta degrees-of-freedom. How many degrees of freedom to adjust
+        for bias in limited samples relative to the population estimate
+        of variance. Defaults to 1.
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains nan.
+        The following options are available (default is 'propagate'):
+
+        * 'propagate': returns nan
+        * 'raise': throws an error
+        * 'omit': performs the calculations ignoring nan values
+
+    Returns
+    -------
+    s : ndarray or float
+        The standard error of the mean in the sample(s), along the input axis.
+
+    Notes
+    -----
+    The default value for `ddof` is different to the default (0) used by other
+    ddof containing routines, such as np.std and np.nanstd.
+
+    Examples
+    --------
+    Find standard error along the first axis:
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> a = np.arange(20).reshape(5,4)
+    >>> stats.sem(a)
+    array([ 2.8284,  2.8284,  2.8284,  2.8284])
+
+    Find standard error across the whole array, using n degrees of freedom:
+
+    >>> stats.sem(a, axis=None, ddof=0)
+    1.2893796958227628
+
+    """
+    xp = array_namespace(a)
+    if axis is None:
+        a = xp.reshape(a, (-1,))
+        axis = 0
+    a = xpx.atleast_nd(xp.asarray(a), ndim=1, xp=xp)
+    n = _count_nonmasked(a, axis, xp=xp)
+    s = xp.std(a, axis=axis, correction=ddof) / n**0.5
+    return s
+
+
+def _isconst(x):
+    """
+    Check if all values in x are the same.  nans are ignored.
+
+    x must be a 1d array.
+
+    The return value is a 1d array with length 1, so it can be used
+    in np.apply_along_axis.
+    """
+    y = x[~np.isnan(x)]
+    if y.size == 0:
+        return np.array([True])
+    else:
+        return (y[0] == y).all(keepdims=True)
+
+
+@xp_capabilities(marray=True)
+def zscore(a, axis=0, ddof=0, nan_policy='propagate'):
+    """
+    Compute the z score.
+
+    Compute the z score of each value in the sample, relative to the
+    sample mean and standard deviation.
+
+    Parameters
+    ----------
+    a : array_like
+        An array like object containing the sample data.
+    axis : int or None, optional
+        Axis along which to operate. Default is 0. If None, compute over
+        the whole array `a`.
+    ddof : int, optional
+        Degrees of freedom correction in the calculation of the
+        standard deviation. Default is 0.
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains nan. 'propagate' returns nan,
+        'raise' throws an error, 'omit' performs the calculations ignoring nan
+        values. Default is 'propagate'.  Note that when the value is 'omit',
+        nans in the input also propagate to the output, but they do not affect
+        the z-scores computed for the non-nan values.
+
+    Returns
+    -------
+    zscore : array_like
+        The z-scores, standardized by mean and standard deviation of
+        input array `a`.
+
+    See Also
+    --------
+    numpy.mean : Arithmetic average
+    numpy.std : Arithmetic standard deviation
+    scipy.stats.gzscore : Geometric standard score
+
+    Notes
+    -----
+    This function preserves ndarray subclasses, and works also with
+    matrices and masked arrays (it uses `asanyarray` instead of
+    `asarray` for parameters).
+
+    References
+    ----------
+    .. [1] "Standard score", *Wikipedia*,
+           https://en.wikipedia.org/wiki/Standard_score.
+    .. [2] Huck, S. W., Cross, T. L., Clark, S. B, "Overcoming misconceptions
+           about Z-scores", Teaching Statistics, vol. 8, pp. 38-40, 1986
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.array([ 0.7972,  0.0767,  0.4383,  0.7866,  0.8091,
+    ...                0.1954,  0.6307,  0.6599,  0.1065,  0.0508])
+    >>> from scipy import stats
+    >>> stats.zscore(a)
+    array([ 1.1273, -1.247 , -0.0552,  1.0923,  1.1664, -0.8559,  0.5786,
+            0.6748, -1.1488, -1.3324])
+
+    Computing along a specified axis, using n-1 degrees of freedom
+    (``ddof=1``) to calculate the standard deviation:
+
+    >>> b = np.array([[ 0.3148,  0.0478,  0.6243,  0.4608],
+    ...               [ 0.7149,  0.0775,  0.6072,  0.9656],
+    ...               [ 0.6341,  0.1403,  0.9759,  0.4064],
+    ...               [ 0.5918,  0.6948,  0.904 ,  0.3721],
+    ...               [ 0.0921,  0.2481,  0.1188,  0.1366]])
+    >>> stats.zscore(b, axis=1, ddof=1)
+    array([[-0.19264823, -1.28415119,  1.07259584,  0.40420358],
+           [ 0.33048416, -1.37380874,  0.04251374,  1.00081084],
+           [ 0.26796377, -1.12598418,  1.23283094, -0.37481053],
+           [-0.22095197,  0.24468594,  1.19042819, -1.21416216],
+           [-0.82780366,  1.4457416 , -0.43867764, -0.1792603 ]])
+
+    An example with ``nan_policy='omit'``:
+
+    >>> x = np.array([[25.11, 30.10, np.nan, 32.02, 43.15],
+    ...               [14.95, 16.06, 121.25, 94.35, 29.81]])
+    >>> stats.zscore(x, axis=1, nan_policy='omit')
+    array([[-1.13490897, -0.37830299,         nan, -0.08718406,  1.60039602],
+           [-0.91611681, -0.89090508,  1.4983032 ,  0.88731639, -0.5785977 ]])
+    """
+    return zmap(a, a, axis=axis, ddof=ddof, nan_policy=nan_policy)
+
+
+@xp_capabilities(marray=True)
+def gzscore(a, *, axis=0, ddof=0, nan_policy='propagate'):
+    """
+    Compute the geometric standard score.
+
+    Compute the geometric z score of each strictly positive value in the
+    sample, relative to the geometric mean and standard deviation.
+    Mathematically the geometric z score can be evaluated as::
+
+        gzscore = log(a/gmu) / log(gsigma)
+
+    where ``gmu`` (resp. ``gsigma``) is the geometric mean (resp. standard
+    deviation).
+
+    Parameters
+    ----------
+    a : array_like
+        Sample data.
+    axis : int or None, optional
+        Axis along which to operate. Default is 0. If None, compute over
+        the whole array `a`.
+    ddof : int, optional
+        Degrees of freedom correction in the calculation of the
+        standard deviation. Default is 0.
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains nan. 'propagate' returns nan,
+        'raise' throws an error, 'omit' performs the calculations ignoring nan
+        values. Default is 'propagate'.  Note that when the value is 'omit',
+        nans in the input also propagate to the output, but they do not affect
+        the geometric z scores computed for the non-nan values.
+
+    Returns
+    -------
+    gzscore : array_like
+        The geometric z scores, standardized by geometric mean and geometric
+        standard deviation of input array `a`.
+
+    See Also
+    --------
+    gmean : Geometric mean
+    gstd : Geometric standard deviation
+    zscore : Standard score
+
+    Notes
+    -----
+    This function preserves ndarray subclasses, and works also with
+    matrices and masked arrays (it uses ``asanyarray`` instead of
+    ``asarray`` for parameters).
+
+    .. versionadded:: 1.8
+
+    References
+    ----------
+    .. [1] "Geometric standard score", *Wikipedia*,
+           https://en.wikipedia.org/wiki/Geometric_standard_deviation#Geometric_standard_score.
+
+    Examples
+    --------
+    Draw samples from a log-normal distribution:
+
+    >>> import numpy as np
+    >>> from scipy.stats import zscore, gzscore
+    >>> import matplotlib.pyplot as plt
+
+    >>> rng = np.random.default_rng()
+    >>> mu, sigma = 3., 1.  # mean and standard deviation
+    >>> x = rng.lognormal(mu, sigma, size=500)
+
+    Display the histogram of the samples:
+
+    >>> fig, ax = plt.subplots()
+    >>> ax.hist(x, 50)
+    >>> plt.show()
+
+    Display the histogram of the samples standardized by the classical zscore.
+    Distribution is rescaled but its shape is unchanged.
+
+    >>> fig, ax = plt.subplots()
+    >>> ax.hist(zscore(x), 50)
+    >>> plt.show()
+
+    Demonstrate that the distribution of geometric zscores is rescaled and
+    quasinormal:
+
+    >>> fig, ax = plt.subplots()
+    >>> ax.hist(gzscore(x), 50)
+    >>> plt.show()
+
+    """
+    xp = array_namespace(a)
+    a = xp_promote(a, force_floating=True, xp=xp)
+    log = ma.log if isinstance(a, ma.MaskedArray) else xp.log
+    return zscore(log(a), axis=axis, ddof=ddof, nan_policy=nan_policy)
+
+
+@xp_capabilities(marray=True)
+def zmap(scores, compare, axis=0, ddof=0, nan_policy='propagate'):
+    """
+    Calculate the relative z-scores.
+
+    Return an array of z-scores, i.e., scores that are standardized to
+    zero mean and unit variance, where mean and variance are calculated
+    from the comparison array.
+
+    Parameters
+    ----------
+    scores : array_like
+        The input for which z-scores are calculated.
+    compare : array_like
+        The input from which the mean and standard deviation of the
+        normalization are taken; assumed to have the same dimension as
+        `scores`.
+    axis : int or None, optional
+        Axis over which mean and variance of `compare` are calculated.
+        Default is 0. If None, compute over the whole array `scores`.
+    ddof : int, optional
+        Degrees of freedom correction in the calculation of the
+        standard deviation. Default is 0.
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle the occurrence of nans in `compare`.
+        'propagate' returns nan, 'raise' raises an exception, 'omit'
+        performs the calculations ignoring nan values. Default is
+        'propagate'. Note that when the value is 'omit', nans in `scores`
+        also propagate to the output, but they do not affect the z-scores
+        computed for the non-nan values.
+
+    Returns
+    -------
+    zscore : array_like
+        Z-scores, in the same shape as `scores`.
+
+    Notes
+    -----
+    This function preserves ndarray subclasses, and works also with
+    matrices and masked arrays (it uses `asanyarray` instead of
+    `asarray` for parameters).
+
+    Examples
+    --------
+    >>> from scipy.stats import zmap
+    >>> a = [0.5, 2.0, 2.5, 3]
+    >>> b = [0, 1, 2, 3, 4]
+    >>> zmap(a, b)
+    array([-1.06066017,  0.        ,  0.35355339,  0.70710678])
+
+    """
+    # The docstring explicitly states that it preserves subclasses.
+    # Let's table deprecating that and just get the array API version
+    # working.
+
+    like_zscore = (scores is compare)
+    xp = array_namespace(scores, compare)
+    scores, compare = xp_promote(scores, compare, force_floating=True, xp=xp)
+
+    with warnings.catch_warnings():
+        if like_zscore:  # zscore should not emit SmallSampleWarning
+            warnings.simplefilter('ignore', SmallSampleWarning)
+
+        mn = _xp_mean(compare, axis=axis, keepdims=True, nan_policy=nan_policy)
+        std = _xp_var(compare, axis=axis, correction=ddof,
+                      keepdims=True, nan_policy=nan_policy)**0.5
+
+    with np.errstate(invalid='ignore', divide='ignore'):
+        z = _demean(scores, mn, axis, xp=xp, precision_warning=False) / std
+
+    # If we know that scores and compare are identical, we can infer that
+    # some slices should have NaNs.
+    if like_zscore:
+        eps = xp.finfo(z.dtype).eps
+        zero = std <= xp.abs(eps * mn)
+        zero = xp.broadcast_to(zero, z.shape)
+        z = xpx.at(z, zero).set(xp.nan)
+
+    return z
+
+
+@xp_capabilities(marray=True)
+def gstd(a, axis=0, ddof=1, *, keepdims=False, nan_policy='propagate'):
+    r"""
+    Calculate the geometric standard deviation of an array.
+
+    The geometric standard deviation describes the spread of a set of numbers
+    where the geometric mean is preferred. It is a multiplicative factor, and
+    so a dimensionless quantity.
+
+    It is defined as the exponential of the standard deviation of the
+    natural logarithms of the observations.
+
+    Parameters
+    ----------
+    a : array_like
+        An array containing finite, strictly positive, real numbers.
+    axis : int, tuple or None, optional
+        Axis along which to operate. Default is 0. If None, compute over
+        the whole array `a`.
+    ddof : int, optional
+        Degree of freedom correction in the calculation of the
+        geometric standard deviation. Default is 1.
+    keepdims : bool, optional
+        If this is set to ``True``, the axes which are reduced are left
+        in the result as dimensions with length one. With this option,
+        the result will broadcast correctly against the input array.
+    nan_policy : {'propagate', 'omit', 'raise'}, default: 'propagate'
+        Defines how to handle input NaNs.
+
+        - ``propagate``: if a NaN is present in the axis slice (e.g. row) along
+          which the statistic is computed, the corresponding entry of the output
+          will be NaN.
+        - ``omit``: NaNs will be omitted when performing the calculation.
+          If insufficient data remains in the axis slice along which the
+          statistic is computed, the corresponding entry of the output will be
+          NaN.
+        - ``raise``: if a NaN is present, a ``ValueError`` will be raised.
+
+    Returns
+    -------
+    gstd : ndarray or float
+        An array of the geometric standard deviation. If `axis` is None or `a`
+        is a 1d array a float is returned.
+
+    See Also
+    --------
+    gmean : Geometric mean
+    numpy.std : Standard deviation
+    gzscore : Geometric standard score
+
+    Notes
+    -----
+    Mathematically, the sample geometric standard deviation :math:`s_G` can be
+    defined in terms of the natural logarithms of the observations
+    :math:`y_i = \log(x_i)`:
+
+    .. math::
+
+        s_G = \exp(s), \quad s = \sqrt{\frac{1}{n - d} \sum_{i=1}^n (y_i - \bar y)^2}
+
+    where :math:`n` is the number of observations, :math:`d` is the adjustment `ddof`
+    to the degrees of freedom, and :math:`\bar y` denotes the mean of the natural
+    logarithms of the observations. Note that the default ``ddof=1`` is different from
+    the default value used by similar functions, such as `numpy.std` and `numpy.var`.
+
+    When an observation is infinite, the geometric standard deviation is
+    NaN (undefined). Non-positive observations will also produce NaNs in the
+    output because the *natural* logarithm (as opposed to the *complex*
+    logarithm) is defined and finite only for positive reals.
+    The geometric standard deviation is sometimes confused with the exponential
+    of the standard deviation, ``exp(std(a))``. Instead, the geometric standard
+    deviation is ``exp(std(log(a)))``.
+
+    References
+    ----------
+    .. [1] "Geometric standard deviation", *Wikipedia*,
+           https://en.wikipedia.org/wiki/Geometric_standard_deviation.
+    .. [2] Kirkwood, T. B., "Geometric means and measures of dispersion",
+           Biometrics, vol. 35, pp. 908-909, 1979
+
+    Examples
+    --------
+    Find the geometric standard deviation of a log-normally distributed sample.
+    Note that the standard deviation of the distribution is one; on a
+    log scale this evaluates to approximately ``exp(1)``.
+
+    >>> import numpy as np
+    >>> from scipy.stats import gstd
+    >>> rng = np.random.default_rng()
+    >>> sample = rng.lognormal(mean=0, sigma=1, size=1000)
+    >>> gstd(sample)
+    2.810010162475324
+
+    Compute the geometric standard deviation of a multidimensional array and
+    of a given axis.
+
+    >>> a = np.arange(1, 25).reshape(2, 3, 4)
+    >>> gstd(a, axis=None)
+    2.2944076136018947
+    >>> gstd(a, axis=2)
+    array([[1.82424757, 1.22436866, 1.13183117],
+           [1.09348306, 1.07244798, 1.05914985]])
+    >>> gstd(a, axis=(1,2))
+    array([2.12939215, 1.22120169])
+
+    """
+    xp = array_namespace(a)
+    a = xp_promote(a, force_floating=True, xp=xp)
+
+    kwargs = dict(axis=axis, correction=ddof, keepdims=keepdims, nan_policy=nan_policy)
+    with np.errstate(invalid='ignore', divide='ignore'):
+        res = xp.exp(_xp_var(xp.log(a), **kwargs)**0.5)
+
+    if not is_lazy_array(a) and xp.any(a <= 0):
+        message = ("The geometric standard deviation is only defined if all elements "
+                   "are greater than or equal to zero; otherwise, the result is NaN.")
+        warnings.warn(message, RuntimeWarning, stacklevel=2)
+
+    return res
+
+# Private dictionary initialized only once at module level
+# See https://en.wikipedia.org/wiki/Robust_measures_of_scale
+_scale_conversions = {'normal': float(special.erfinv(0.5) * 2.0 * math.sqrt(2.0))}
+
+
+@xp_capabilities(skip_backends=[('dask.array', 'no quantile (take_along_axis)')],
+                 marray=True)
+@_axis_nan_policy_factory(
+    lambda x: x, result_to_tuple=lambda x, _: (x,), n_outputs=1,
+    default_axis=None, override={'nan_propagation': False}
+)
+def iqr(x, axis=None, rng=(25, 75), scale=1.0, nan_policy='propagate',
+        interpolation='linear', keepdims=False):
+    r"""
+    Compute the interquartile range of the data along the specified axis.
+
+    The interquartile range (IQR) is the difference between the 75th and
+    25th percentile of the data. It is a measure of the dispersion
+    similar to standard deviation or variance, but is much more robust
+    against outliers [2]_.
+
+    The ``rng`` parameter allows this function to compute other
+    percentile ranges than the actual IQR. For example, setting
+    ``rng=(0, 100)`` is equivalent to `numpy.ptp`.
+
+    The IQR of an empty array is `np.nan`.
+
+    .. versionadded:: 0.18.0
+
+    Parameters
+    ----------
+    x : array_like
+        Input array or object that can be converted to an array.
+    axis : int or sequence of int, optional
+        Axis along which the range is computed. The default is to
+        compute the IQR for the entire array.
+    rng : Two-element sequence containing floats in range of [0,100] optional
+        Percentiles over which to compute the range. Each must be
+        between 0 and 100, inclusive. The default is the true IQR:
+        ``(25, 75)``. The order of the elements is not important.
+    scale : scalar or str or array_like of reals, optional
+        The numerical value of scale will be divided out of the final
+        result. The following string value is also recognized:
+
+        * 'normal' : Scale by
+          :math:`2 \sqrt{2} erf^{-1}(\frac{1}{2}) \approx 1.349`.
+
+        The default is 1.0.
+        Array-like `scale` of real dtype is also allowed, as long
+        as it broadcasts correctly to the output such that
+        ``out / scale`` is a valid operation. The output dimensions
+        depend on the input array, `x`, the `axis` argument, and the
+        `keepdims` flag.
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains nan.
+        The following options are available (default is 'propagate'):
+
+        * 'propagate': returns nan
+        * 'raise': throws an error
+        * 'omit': performs the calculations ignoring nan values
+
+    interpolation : str, optional
+
+        Specifies the interpolation method to use when the percentile
+        boundaries lie between two data points ``i`` and ``j``.
+        The following options are available (default is 'linear'):
+
+        * 'linear': ``i + (j - i)*fraction``, where ``fraction`` is the
+          fractional part of the index surrounded by ``i`` and ``j``.
+        * 'lower': ``i``.
+        * 'higher': ``j``.
+        * 'nearest': ``i`` or ``j`` whichever is nearest.
+        * 'midpoint': ``(i + j)/2``.
+
+        For NumPy >= 1.22.0, the additional options provided by the ``method``
+        keyword of `numpy.percentile` are also valid.
+
+    keepdims : bool, optional
+        If this is set to True, the reduced axes are left in the
+        result as dimensions with size one. With this option, the result
+        will broadcast correctly against the original array `x`.
+
+    Returns
+    -------
+    iqr : scalar or ndarray
+        If ``axis=None``, a scalar is returned. If the input contains
+        integers or floats of smaller precision than ``np.float64``, then the
+        output data-type is ``np.float64``. Otherwise, the output data-type is
+        the same as that of the input.
+
+    See Also
+    --------
+    numpy.std, numpy.var
+
+    References
+    ----------
+    .. [1] "Interquartile range" https://en.wikipedia.org/wiki/Interquartile_range
+    .. [2] "Robust measures of scale" https://en.wikipedia.org/wiki/Robust_measures_of_scale
+    .. [3] "Quantile" https://en.wikipedia.org/wiki/Quantile
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import iqr
+    >>> x = np.array([[10, 7, 4], [3, 2, 1]])
+    >>> x
+    array([[10,  7,  4],
+           [ 3,  2,  1]])
+    >>> iqr(x)
+    4.0
+    >>> iqr(x, axis=0)
+    array([ 3.5,  2.5,  1.5])
+    >>> iqr(x, axis=1)
+    array([ 3.,  1.])
+    >>> iqr(x, axis=1, keepdims=True)
+    array([[ 3.],
+           [ 1.]])
+
+    """
+    xp = array_namespace(x)
+
+    # An error may be raised here, so fail-fast, before doing lengthy
+    # computations, even though `scale` is not used until later
+    if isinstance(scale, str):
+        scale_key = scale.lower()
+        if scale_key not in _scale_conversions:
+            raise ValueError(f"{scale} not a valid scale for `iqr`")
+        scale = _scale_conversions[scale_key]
+
+    if len(rng) != 2:
+        raise TypeError("`rng` must be a two element sequence.")
+
+    if np.isnan(rng).any():  # OK to use NumPy; this shouldn't be an array
+        raise ValueError("`rng` must not contain NaNs.")
+
+    rng = (rng[0]/100, rng[1]/100) if rng[0] < rng[1] else (rng[1]/100, rng[0]/100)
+
+    if rng[0] < 0 or rng[1] > 1:
+        raise ValueError("Elements of `rng` must be in the range [0, 100].")
+
+    if interpolation in {'lower', 'midpoint', 'higher', 'nearest'}:
+        interpolation = '_' + interpolation
+
+    rng = xp.asarray(rng, dtype=xp_result_type(x, force_floating=True, xp=xp))
+    pct = stats.quantile(x, rng, axis=-1, method=interpolation, keepdims=True)
+    out = pct[..., 1:2] - pct[..., 0:1]
+
+    if scale != 1.0:
+        out /= scale
+
+    out = out if keepdims else xp.squeeze(out, axis=-1)
+    return out[()] if out.ndim == 0 else out
+
+
+def _mad_1d(x, center, nan_policy):
+    # Median absolute deviation for 1-d array x.
+    # This is a helper function for `median_abs_deviation`; it assumes its
+    # arguments have been validated already.  In particular,  x must be a
+    # 1-d numpy array, center must be callable, and if nan_policy is not
+    # 'propagate', it is assumed to be 'omit', because 'raise' is handled
+    # in `median_abs_deviation`.
+    # No warning is generated if x is empty or all nan.
+    isnan = np.isnan(x)
+    if isnan.any():
+        if nan_policy == 'propagate':
+            return np.nan
+        x = x[~isnan]
+    if x.size == 0:
+        # MAD of an empty array is nan.
+        return np.nan
+    # Edge cases have been handled, so do the basic MAD calculation.
+    med = center(x)
+    mad = np.median(np.abs(x - med))
+    return mad
+
+
+@xp_capabilities(skip_backends=[('dask.array', 'not supported by `quantile`')],
+                 marray=True)
+@_axis_nan_policy_factory(
+    lambda x: x, result_to_tuple=lambda x, _: (x,), n_outputs=1, default_axis=0
+)
+def median_abs_deviation(x, axis=0, center=None, scale=1.0,
+                         nan_policy='propagate'):
+    r"""
+    Compute the median absolute deviation of the data along the given axis.
+
+    The median absolute deviation (MAD, [1]_) computes the median over the
+    absolute deviations from the median. It is a measure of dispersion
+    similar to the standard deviation but more robust to outliers [2]_.
+
+    The MAD of an empty array is ``np.nan``.
+
+    .. versionadded:: 1.5.0
+
+    Parameters
+    ----------
+    x : array_like
+        Input array or object that can be converted to an array.
+    axis : int or None, optional
+        Axis along which the range is computed. Default is 0. If None, compute
+        the MAD over the entire array.
+    center : callable, optional
+        A function that will return the central value. The default is to use
+        np.median. Any user defined function used will need to have the
+        function signature ``func(arr, axis)``.
+    scale : scalar or str, optional
+        The numerical value of scale will be divided out of the final
+        result. The default is 1.0. The string "normal" is also accepted,
+        and results in `scale` being the inverse of the standard normal
+        quantile function at 0.75, which is approximately 0.67449.
+        Array-like scale is also allowed, as long as it broadcasts correctly
+        to the output such that ``out / scale`` is a valid operation. The
+        output dimensions depend on the input array, `x`, and the `axis`
+        argument.
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains nan.
+        The following options are available (default is 'propagate'):
+
+        * 'propagate': returns nan
+        * 'raise': throws an error
+        * 'omit': performs the calculations ignoring nan values
+
+    Returns
+    -------
+    mad : scalar or ndarray
+        If ``axis=None``, a scalar is returned. If the input contains
+        integers or floats of smaller precision than ``np.float64``, then the
+        output data-type is ``np.float64``. Otherwise, the output data-type is
+        the same as that of the input.
+
+    See Also
+    --------
+    numpy.std, numpy.var, numpy.median, scipy.stats.iqr, scipy.stats.tmean,
+    scipy.stats.tstd, scipy.stats.tvar
+
+    Notes
+    -----
+    The `center` argument only affects the calculation of the central value
+    around which the MAD is calculated. That is, passing in ``center=np.mean``
+    will calculate the MAD around the mean - it will not calculate the *mean*
+    absolute deviation.
+
+    The input array may contain `inf`, but if `center` returns `inf`, the
+    corresponding MAD for that data will be `nan`.
+
+    References
+    ----------
+    .. [1] "Median absolute deviation",
+           https://en.wikipedia.org/wiki/Median_absolute_deviation
+    .. [2] "Robust measures of scale",
+           https://en.wikipedia.org/wiki/Robust_measures_of_scale
+
+    Examples
+    --------
+    When comparing the behavior of `median_abs_deviation` with ``np.std``,
+    the latter is affected when we change a single value of an array to have an
+    outlier value while the MAD hardly changes:
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> x = stats.norm.rvs(size=100, scale=1, random_state=123456)
+    >>> x.std()
+    0.9973906394005013
+    >>> stats.median_abs_deviation(x)
+    0.82832610097857
+    >>> x[0] = 345.6
+    >>> x.std()
+    34.42304872314415
+    >>> stats.median_abs_deviation(x)
+    0.8323442311590675
+
+    Axis handling example:
+
+    >>> x = np.array([[10, 7, 4], [3, 2, 1]])
+    >>> x
+    array([[10,  7,  4],
+           [ 3,  2,  1]])
+    >>> stats.median_abs_deviation(x)
+    array([3.5, 2.5, 1.5])
+    >>> stats.median_abs_deviation(x, axis=None)
+    2.0
+
+    Scale normal example:
+
+    >>> x = stats.norm.rvs(size=1000000, scale=2, random_state=123456)
+    >>> stats.median_abs_deviation(x)
+    1.3487398527041636
+    >>> stats.median_abs_deviation(x, scale='normal')
+    1.9996446978061115
+
+    """
+    xp = array_namespace(x)
+    xp_median = (xp.median if is_numpy(xp)
+                 else lambda x, axis: stats.quantile(x, 0.5, axis=axis))
+    center = (xp_median if center is None else center)
+
+    if not callable(center):
+        raise TypeError("The argument 'center' must be callable. The given "
+                        f"value {repr(center)} is not callable.")
+
+    # An error may be raised here, so fail-fast, before doing lengthy
+    # computations, even though `scale` is not used until later
+    if isinstance(scale, str):
+        if scale.lower() == 'normal':
+            scale = 0.6744897501960817  # special.ndtri(0.75)
+        else:
+            raise ValueError(f"{scale} is not a valid scale value.")
+
+    # Wrap the call to center() in expand_dims() so it acts like
+    # keepdims=True was used.
+    med = xp.expand_dims(center(x, axis=axis), axis=axis)
+    mad = xp_median(xp.abs(x - med), axis=axis)
+
+    return mad / scale
+
+
+#####################################
+#         TRIMMING FUNCTIONS        #
+#####################################
+
+
+SigmaclipResult = namedtuple('SigmaclipResult', ('clipped', 'lower', 'upper'))
+
+
+@xp_capabilities(skip_backends=[('dask.array', "doesn't know array size")],
+                 jax_jit=False)
+def sigmaclip(a, low=4., high=4., *, nan_policy='propagate'):
+    """Perform iterative sigma-clipping of array elements.
+
+    Starting from the full sample, all elements outside the critical range are
+    removed, i.e. all elements of the input array `c` that satisfy either of
+    the following conditions::
+
+        c < mean(c) - std(c)*low
+        c > mean(c) + std(c)*high
+
+    The iteration continues with the updated sample until no
+    elements are outside the (updated) range.
+
+    Parameters
+    ----------
+    a : array_like
+        Data array, will be raveled if not 1-D.
+    low : float, optional
+        Lower bound factor of sigma clipping. Default is 4.
+    high : float, optional
+        Upper bound factor of sigma clipping. Default is 4.
+    nan_policy : {'propagate', 'omit', 'raise'}
+        Defines how to handle input NaNs.
+
+        - ``propagate``: if a NaN is present in the input, the clipped array will be
+          empty, and the upper and lower thresholds will be NaN.
+        - ``omit``: NaNs will be omitted when performing the calculation.
+        - ``raise``: if a NaN is present, a ``ValueError`` will be raised.
+
+    Returns
+    -------
+    clipped : ndarray
+        Input array with clipped elements removed.
+    lower : float
+        Lower threshold value use for clipping.
+    upper : float
+        Upper threshold value use for clipping.
+
+    Notes
+    -----
+    This function iteratively *removes* observations. Once observations are
+    removed, they are not re-added in subsequent iterations. Consequently,
+    although it is often the case that ``clipped`` is identical to
+    ``a[(a >= lower) & (a <= upper)]``, this property is not guaranteed to be
+    satisfied; ``clipped`` may have fewer elements.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import sigmaclip
+    >>> a = np.concatenate((np.linspace(9.5, 10.5, 31),
+    ...                     np.linspace(0, 20, 5)))
+    >>> fact = 1.5
+    >>> c, low, upp = sigmaclip(a, fact, fact)
+    >>> c
+    array([  9.96666667,  10.        ,  10.03333333,  10.        ])
+    >>> c.var(), c.std()
+    (0.00055555555555555165, 0.023570226039551501)
+    >>> low, c.mean() - fact*c.std(), c.min()
+    (9.9646446609406727, 9.9646446609406727, 9.9666666666666668)
+    >>> upp, c.mean() + fact*c.std(), c.max()
+    (10.035355339059327, 10.035355339059327, 10.033333333333333)
+
+    >>> a = np.concatenate((np.linspace(9.5, 10.5, 11),
+    ...                     np.linspace(-100, -50, 3)))
+    >>> c, low, upp = sigmaclip(a, 1.8, 1.8)
+    >>> (c == np.linspace(9.5, 10.5, 11)).all()
+    True
+
+    """
+    xp = array_namespace(a)
+    c = xp_ravel(xp.asarray(a))
+    contains_nan = _contains_nan(c, nan_policy, xp_omit_okay=True)
+    if contains_nan:
+        if nan_policy == 'propagate':
+            NaN = _get_nan(c, xp=xp)
+            clipped = xp.empty_like(c[0:0])
+            return SigmaclipResult(clipped, NaN, NaN)
+        elif nan_policy == 'omit':
+            c = c[~xp.isnan(c)]
+
+    delta = 1
+    while delta:
+        c_std = xp.std(c)
+        c_mean = xp.mean(c)
+        size = xp_size(c)
+        critlower = c_mean - c_std * low
+        critupper = c_mean + c_std * high
+        c = c[(c >= critlower) & (c <= critupper)]
+        delta = size - xp_size(c)
+
+    return SigmaclipResult(c, critlower, critupper)
+
+
+@xp_capabilities(np_only=True)
+def trimboth(a, proportiontocut, axis=0):
+    """Slice off a proportion of items from both ends of an array.
+
+    Slice off the passed proportion of items from both ends of the passed
+    array (i.e., with `proportiontocut` = 0.1, slices leftmost 10% **and**
+    rightmost 10% of scores). The trimmed values are the lowest and
+    highest ones.
+    Slice off less if proportion results in a non-integer slice index (i.e.
+    conservatively slices off `proportiontocut`).
+
+    Parameters
+    ----------
+    a : array_like
+        Data to trim.
+    proportiontocut : float
+        Proportion (in range 0-1) of total data set to trim of each end.
+    axis : int or None, optional
+        Axis along which to trim data. Default is 0. If None, compute over
+        the whole array `a`.
+
+    Returns
+    -------
+    out : ndarray
+        Trimmed version of array `a`. The order of the trimmed content
+        is undefined.
+
+    See Also
+    --------
+    trim_mean
+
+    Examples
+    --------
+    Create an array of 10 values and trim 10% of those values from each end:
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> a = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
+    >>> stats.trimboth(a, 0.1)
+    array([1, 3, 2, 4, 5, 6, 7, 8])
+
+    Note that the elements of the input array are trimmed by value, but the
+    output array is not necessarily sorted.
+
+    The proportion to trim is rounded down to the nearest integer. For
+    instance, trimming 25% of the values from each end of an array of 10
+    values will return an array of 6 values:
+
+    >>> b = np.arange(10)
+    >>> stats.trimboth(b, 1/4).shape
+    (6,)
+
+    Multidimensional arrays can be trimmed along any axis or across the entire
+    array:
+
+    >>> c = [2, 4, 6, 8, 0, 1, 3, 5, 7, 9]
+    >>> d = np.array([a, b, c])
+    >>> stats.trimboth(d, 0.4, axis=0).shape
+    (1, 10)
+    >>> stats.trimboth(d, 0.4, axis=1).shape
+    (3, 2)
+    >>> stats.trimboth(d, 0.4, axis=None).shape
+    (6,)
+
+    """
+    a = np.asarray(a)
+
+    if a.size == 0:
+        return a
+
+    if axis is None:
+        a = a.ravel()
+        axis = 0
+
+    nobs = a.shape[axis]
+    lowercut = int(proportiontocut * nobs)
+    uppercut = nobs - lowercut
+    if (lowercut >= uppercut):
+        raise ValueError("Proportion too big.")
+
+    atmp = np.partition(a, (lowercut, uppercut - 1), axis)
+
+    sl = [slice(None)] * atmp.ndim
+    sl[axis] = slice(lowercut, uppercut)
+    return atmp[tuple(sl)]
+
+
+@xp_capabilities(np_only=True)
+def trim1(a, proportiontocut, tail='right', axis=0):
+    """Slice off a proportion from ONE end of the passed array distribution.
+
+    If `proportiontocut` = 0.1, slices off 'leftmost' or 'rightmost'
+    10% of scores. The lowest or highest values are trimmed (depending on
+    the tail).
+    Slice off less if proportion results in a non-integer slice index
+    (i.e. conservatively slices off `proportiontocut` ).
+
+    Parameters
+    ----------
+    a : array_like
+        Input array.
+    proportiontocut : float
+        Fraction to cut off of 'left' or 'right' of distribution.
+    tail : {'left', 'right'}, optional
+        Defaults to 'right'.
+    axis : int or None, optional
+        Axis along which to trim data. Default is 0. If None, compute over
+        the whole array `a`.
+
+    Returns
+    -------
+    trim1 : ndarray
+        Trimmed version of array `a`. The order of the trimmed content is
+        undefined.
+
+    Examples
+    --------
+    Create an array of 10 values and trim 20% of its lowest values:
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> a = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
+    >>> stats.trim1(a, 0.2, 'left')
+    array([2, 4, 3, 5, 6, 7, 8, 9])
+
+    Note that the elements of the input array are trimmed by value, but the
+    output array is not necessarily sorted.
+
+    The proportion to trim is rounded down to the nearest integer. For
+    instance, trimming 25% of the values from an array of 10 values will
+    return an array of 8 values:
+
+    >>> b = np.arange(10)
+    >>> stats.trim1(b, 1/4).shape
+    (8,)
+
+    Multidimensional arrays can be trimmed along any axis or across the entire
+    array:
+
+    >>> c = [2, 4, 6, 8, 0, 1, 3, 5, 7, 9]
+    >>> d = np.array([a, b, c])
+    >>> stats.trim1(d, 0.8, axis=0).shape
+    (1, 10)
+    >>> stats.trim1(d, 0.8, axis=1).shape
+    (3, 2)
+    >>> stats.trim1(d, 0.8, axis=None).shape
+    (6,)
+
+    """
+    a = np.asarray(a)
+    if axis is None:
+        a = a.ravel()
+        axis = 0
+
+    nobs = a.shape[axis]
+
+    # avoid possible corner case
+    if proportiontocut >= 1:
+        return []
+
+    if tail.lower() == 'right':
+        lowercut = 0
+        uppercut = nobs - int(proportiontocut * nobs)
+
+    elif tail.lower() == 'left':
+        lowercut = int(proportiontocut * nobs)
+        uppercut = nobs
+
+    atmp = np.partition(a, (lowercut, uppercut - 1), axis)
+
+    sl = [slice(None)] * atmp.ndim
+    sl[axis] = slice(lowercut, uppercut)
+    return atmp[tuple(sl)]
+
+
+@xp_capabilities(marray=True)
+@_axis_nan_policy_factory(lambda x: x, result_to_tuple=lambda x, _: (x,), n_outputs=1)
+def trim_mean(a, proportiontocut, axis=0):
+    """Return mean of array after trimming a specified fraction of extreme values.
+
+    Removes the specified proportion of elements from *each* end of the
+    sorted array, then computes the mean of the remaining elements.
+
+    Parameters
+    ----------
+    a : array_like
+        Input array.
+    proportiontocut : float
+        Fraction of the most positive and most negative elements to remove.
+        When the specified proportion does not result in an integer number of
+        elements, the number of elements to trim is rounded down.
+    axis : int or None, default: 0
+        Axis along which the trimmed means are computed.
+        If None, compute over the raveled array.
+
+    Returns
+    -------
+    trim_mean : ndarray
+        Mean of trimmed array.
+
+    See Also
+    --------
+    trimboth : Remove a proportion of elements from each end of an array.
+    tmean : Compute the mean after trimming values outside specified limits.
+
+    Notes
+    -----
+    For 1-D array `a`, `trim_mean` is approximately equivalent to the following
+    calculation::
+
+        import numpy as np
+        a = np.sort(a)
+        m = int(proportiontocut * len(a))
+        np.mean(a[m: len(a) - m])
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> x = [1, 2, 3, 5]
+    >>> stats.trim_mean(x, 0.25)
+    2.5
+
+    When the specified proportion does not result in an integer number of
+    elements, the number of elements to trim is rounded down.
+
+    >>> stats.trim_mean(x, 0.24999) == np.mean(x)
+    True
+
+    Use `axis` to specify the axis along which the calculation is performed.
+
+    >>> x2 = [[1, 2, 3, 5],
+    ...       [10, 20, 30, 50]]
+    >>> stats.trim_mean(x2, 0.25)
+    array([ 5.5, 11. , 16.5, 27.5])
+    >>> stats.trim_mean(x2, 0.25, axis=1)
+    array([ 2.5, 25. ])
+
+    """
+    xp = array_namespace(a)
+
+    a = xp.asarray(a)
+
+    if xp_size(a) == 0:
+        return _get_nan(a, xp=xp)
+
+    if axis is None:
+        a = xp_ravel(a)
+        axis = 0
+
+    nobs = _count_nonmasked(a, axis=axis, keepdims=True, xp=xp)
+    lowercut = proportiontocut * nobs
+    nobs, lowercut = ((nobs, int(lowercut)) if not is_marray(xp)
+                      else (xp.astype(nobs, xp.int64), xp.astype(lowercut, xp.int64)))
+    uppercut = nobs - lowercut
+    if not is_marray(xp) and (lowercut > uppercut):
+        raise ValueError("Proportion too big.")
+
+    atmp = (np.partition(a, (lowercut, uppercut - 1), axis) if is_numpy(xp)
+            else xp.sort(a, axis=axis))
+
+    if is_marray(xp):
+        indices = xp.arange(a.shape[-1])  # axis_nan_policy decorator -> axis=-1
+        mask = (indices < lowercut) | (indices >= (nobs - lowercut)) | atmp.mask
+        trimmed = xp.asarray(atmp.data, mask=mask.data)
+    else:
+        sl = [slice(None)] * atmp.ndim
+        sl[axis] = slice(lowercut, uppercut)
+        trimmed = atmp[tuple(sl)]
+
+    trimmed = xp_promote(trimmed, force_floating=True, xp=xp)
+    return xp.mean(trimmed, axis=axis)
+
+
+F_onewayResult = namedtuple('F_onewayResult', ('statistic', 'pvalue'))
+
+
+def _f_oneway_is_too_small(samples, kwargs=None, axis=-1):
+    message = f"At least two samples are required; got {len(samples)}."
+    if len(samples) < 2:
+        raise TypeError(message)
+
+    # Check this after forming alldata, so shape errors are detected
+    # and reported before checking for 0 length inputs.
+    if any(sample.shape[axis] == 0 for sample in samples):
+        return True
+
+    # Must have at least one group with length greater than 1.
+    if all(sample.shape[axis] == 1 for sample in samples):
+        msg = ('all input arrays have length 1.  f_oneway requires that at '
+               'least one input has length greater than 1.')
+        warnings.warn(SmallSampleWarning(msg), stacklevel=2)
+        return True
+
+    return False
+
+
+# Torch GPU need fdtrc
+@xp_capabilities(cpu_only=True, exceptions=['cupy'], marray=True)
+@_axis_nan_policy_factory(
+    F_onewayResult, n_samples=None, too_small=_f_oneway_is_too_small)
+def f_oneway(*samples, axis=0, equal_var=True):
+    """Perform one-way ANOVA.
+
+    The one-way ANOVA tests the null hypothesis that two or more groups have
+    the same population mean.  The test is applied to samples from two or
+    more groups, possibly with differing sizes.
+
+    Parameters
+    ----------
+    *samples : array_like
+        The sample measurements for each group.  There must be at least
+        two arguments.  If the arrays are multidimensional, then all the
+        dimensions of the array must be the same except for `axis`.
+    axis : int, optional
+        Axis of the input arrays along which the test is applied.
+        Default is 0.
+    equal_var : bool, optional
+        If True (default), perform a standard one-way ANOVA test that
+        assumes equal population variances [2]_.
+        If False, perform Welch's ANOVA test, which does not assume
+        equal population variances [4]_.
+
+        .. versionadded:: 1.16.0
+
+    Returns
+    -------
+    statistic : float
+        The computed F statistic of the test.
+    pvalue : float
+        The associated p-value from the F distribution.
+
+    Warns
+    -----
+    `~scipy.stats.ConstantInputWarning`
+        Emitted if all values within each of the input arrays are identical.
+        In this case the F statistic is either infinite or isn't defined,
+        so ``np.inf`` or ``np.nan`` is returned.
+
+    RuntimeWarning
+        Emitted if the length of any input array is 0, or if all the input
+        arrays have length 1.  ``np.nan`` is returned for the F statistic
+        and the p-value in these cases.
+
+    Notes
+    -----
+    The ANOVA test has important assumptions that must be satisfied in order
+    for the associated p-value to be valid.
+
+    1. The samples are independent.
+    2. Each sample is from a normally distributed population.
+    3. The population standard deviations of the groups are all equal.  This
+       property is known as homoscedasticity.
+
+    If these assumptions are not true for a given set of data, it may still
+    be possible to use the Kruskal-Wallis H-test (`scipy.stats.kruskal`) or
+    the Alexander-Govern test (`scipy.stats.alexandergovern`) although with
+    some loss of power.
+
+    The length of each group must be at least one, and there must be at
+    least one group with length greater than one.  If these conditions
+    are not satisfied, a warning is generated and (``np.nan``, ``np.nan``)
+    is returned.
+
+    If all values in each group are identical, and there exist at least two
+    groups with different values, the function generates a warning and
+    returns (``np.inf``, 0).
+
+    If all values in all groups are the same, function generates a warning
+    and returns (``np.nan``, ``np.nan``).
+
+    The algorithm is from Heiman [2]_, pp.394-7.
+
+    References
+    ----------
+    .. [1] R. Lowry, "Concepts and Applications of Inferential Statistics",
+           Chapter 14, 2014, http://vassarstats.net/textbook/
+
+    .. [2] G.W. Heiman, "Understanding research methods and statistics: An
+           integrated introduction for psychology", Houghton, Mifflin and
+           Company, 2001.
+
+    .. [3] J.H. McDonald, "Handbook of Biological Statistics",
+           One-way ANOVA, 2014.
+           http://www.biostathandbook.com/onewayanova.html
+
+    .. [4] B. L. Welch, "On the Comparison of Several Mean Values:
+           An Alternative Approach", Biometrika, vol. 38, no. 3/4,
+           pp. 330-336, 1951. :doi:`10.2307/2332579`.
+
+    .. [5] J.H. McDonald, R. Seed and R.K. Koehn, "Allozymes and
+           morphometric characters of three species of Mytilus in
+           the Northern and Southern Hemispheres",
+           Marine Biology, vol. 111, pp. 323-333, 1991.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import f_oneway
+
+    Here are some data [3]_ on a shell measurement (the length of the anterior
+    adductor muscle scar, standardized by dividing by length) in the mussel
+    Mytilus trossulus from five locations: Tillamook, Oregon; Newport, Oregon;
+    Petersburg, Alaska; Magadan, Russia; and Tvarminne, Finland, taken from a
+    much larger data set used in [5]_.
+
+    >>> tillamook = [0.0571, 0.0813, 0.0831, 0.0976, 0.0817, 0.0859, 0.0735,
+    ...              0.0659, 0.0923, 0.0836]
+    >>> newport = [0.0873, 0.0662, 0.0672, 0.0819, 0.0749, 0.0649, 0.0835,
+    ...            0.0725]
+    >>> petersburg = [0.0974, 0.1352, 0.0817, 0.1016, 0.0968, 0.1064, 0.105]
+    >>> magadan = [0.1033, 0.0915, 0.0781, 0.0685, 0.0677, 0.0697, 0.0764,
+    ...            0.0689]
+    >>> tvarminne = [0.0703, 0.1026, 0.0956, 0.0973, 0.1039, 0.1045]
+    >>> f_oneway(tillamook, newport, petersburg, magadan, tvarminne)
+    F_onewayResult(statistic=7.121019471642447, pvalue=0.0002812242314534544)
+
+    `f_oneway` accepts multidimensional input arrays.  When the inputs
+    are multidimensional and `axis` is not given, the test is performed
+    along the first axis of the input arrays.  For the following data, the
+    test is performed three times, once for each column.
+
+    >>> a = np.array([[9.87, 9.03, 6.81],
+    ...               [7.18, 8.35, 7.00],
+    ...               [8.39, 7.58, 7.68],
+    ...               [7.45, 6.33, 9.35],
+    ...               [6.41, 7.10, 9.33],
+    ...               [8.00, 8.24, 8.44]])
+    >>> b = np.array([[6.35, 7.30, 7.16],
+    ...               [6.65, 6.68, 7.63],
+    ...               [5.72, 7.73, 6.72],
+    ...               [7.01, 9.19, 7.41],
+    ...               [7.75, 7.87, 8.30],
+    ...               [6.90, 7.97, 6.97]])
+    >>> c = np.array([[3.31, 8.77, 1.01],
+    ...               [8.25, 3.24, 3.62],
+    ...               [6.32, 8.81, 5.19],
+    ...               [7.48, 8.83, 8.91],
+    ...               [8.59, 6.01, 6.07],
+    ...               [3.07, 9.72, 7.48]])
+    >>> F = f_oneway(a, b, c)
+    >>> F.statistic
+    array([1.75676344, 0.03701228, 3.76439349])
+    >>> F.pvalue
+    array([0.20630784, 0.96375203, 0.04733157])
+
+    Welch ANOVA will be performed if `equal_var` is False.
+
+    """
+    xp = array_namespace(*samples)
+    samples = xp_promote(*samples, force_floating=True, xp=xp)
+
+    if len(samples) < 2:
+        raise TypeError('at least two inputs are required;'
+                        f' got {len(samples)}.')
+
+    # ANOVA on N groups, each in its own array
+    num_groups = len(samples)
+
+    # axis is guaranteed to be -1 by the _axis_nan_policy decorator
+    alldata = xp.concat(samples, axis=-1)
+    bign = _count_nonmasked(alldata, axis=-1, xp=xp)
+
+    # Check if the inputs are too small (for testing _axis_nan_policy decorator)
+    if _f_oneway_is_too_small(samples):
+        NaN = _get_nan(*samples, xp=xp)
+        return F_onewayResult(NaN, NaN)
+
+    # Check if all values within each group are identical, and if the common
+    # value in at least one group is different from that in another group.
+    # Based on https://github.com/scipy/scipy/issues/11669
+
+    # If axis=0, say, and the groups have shape (n0, ...), (n1, ...), ...,
+    # then is_const is a boolean array with shape (num_groups, ...).
+    # It is True if the values within the groups along the axis slice are
+    # identical. In the typical case where each input array is 1-d, is_const is
+    # a 1-d array with length num_groups.
+    is_const = xp.concat([xp.all(xp.diff(sample, axis=-1) == 0, axis=-1, keepdims=True)
+                          for sample in samples], axis=-1)
+
+    # all_const is a boolean array with shape (...) (see previous comment).
+    # It is True if the values within each group along the axis slice are
+    # the same (e.g. [[3, 3, 3], [5, 5, 5, 5], [4, 4, 4]]).
+    all_const = xp.all(is_const, axis=-1)
+
+    # all_same_const is True if all the values in the groups along the axis=0
+    # slice are the same (e.g. [[3, 3, 3], [3, 3, 3, 3], [3, 3, 3]]).
+    all_same_const = xp.all(xp.diff(alldata, axis=-1) == 0, axis=-1)
+
+    if not isinstance(equal_var, bool):
+        raise TypeError("Expected a boolean value for 'equal_var'")
+
+    if equal_var:
+        # Determine the mean of the data, and subtract that from all inputs to a
+        # variance (via sum_of_sq / sq_of_sum) calculation.  Variance is invariant
+        # to a shift in location, and centering all data around zero vastly
+        # improves numerical stability.
+        offset = xp.mean(alldata, axis=-1, keepdims=True)
+        alldata = alldata - offset
+
+        normalized_ss = xp.sum(alldata, axis=-1)**2. / bign
+
+        sstot = xp.vecdot(alldata, alldata, axis=-1) - normalized_ss
+
+        ssbn = 0
+        for sample in samples:
+            smo_ss = xp.sum(sample - offset, axis=-1)**2.
+            ssbn = ssbn + smo_ss / _count_nonmasked(sample, axis=-1, xp=xp)
+
+        # Naming: variables ending in bn/b are for "between treatments", wn/w are
+        # for "within treatments"
+        ssbn = ssbn - normalized_ss
+        sswn = sstot - ssbn
+        dfbn = num_groups - 1
+        dfwn = bign - num_groups
+        msb = ssbn / dfbn
+        msw = sswn / dfwn
+        with np.errstate(divide='ignore', invalid='ignore'):
+            f = msb / msw
+        dfn, dfd = dfbn, dfwn
+
+    else:
+        # calculate basic statistics for each sample
+        # Beginning of second paragraph [4] page 1:
+        # "As a particular case $y_t$ may be the means ... of samples
+        y_t = xp.stack([xp.mean(sample, axis=-1) for sample in samples])
+        # "... of $n_t$ observations..."
+        if is_marray(xp):
+            n_t = xp.stack([_count_nonmasked(sample, axis=-1, xp=xp)
+                            for sample in samples])
+            n_t = xp.asarray(n_t, dtype=n_t.dtype)
+        else:
+            n_t = xp.asarray([sample.shape[-1] for sample in samples], dtype=y_t.dtype)
+            n_t = xp.reshape(n_t, (-1,) + (1,) * (y_t.ndim - 1))
+        # "... from $k$ different normal populations..."
+        k = len(samples)
+        # "The separate samples provide estimates $s_t^2$ of the $\sigma_t^2$."
+        s_t2 = xp.stack([xp.var(sample, axis=-1, correction=1) for sample in samples])
+
+        # calculate weight by number of data and variance
+        # "we have $\lambda_t = 1 / n_t$ ... where w_t = 1 / {\lambda_t s_t^2}$"
+        w_t = n_t / s_t2
+        # sum of w_t
+        s_w_t = xp.sum(w_t, axis=0)
+
+        # calculate adjusted grand mean
+        # "... and $\hat{y} = \sum w_t y_t / \sum w_t$. When all..."
+        axis_zero = -w_t.ndim
+        y_hat = xp.vecdot(w_t, y_t, axis=axis_zero) / xp.sum(w_t, axis=0)
+
+        # adjust f statistic
+        # ref.[4] p.334 eq.29
+        numerator =  xp.vecdot(w_t, (y_t - y_hat)**2, axis=axis_zero) / (k - 1)
+        denominator = (
+                1 + 2 * (k - 2) / (k**2 - 1) *
+                xp.vecdot(1 / (n_t - 1), (1 - w_t / s_w_t)**2, axis=axis_zero)
+        )
+        f = numerator / denominator
+
+        # degree of freedom 1
+        # ref.[4] p.334 eq.30
+        hat_f1 = k - 1
+
+        # adjusted degree of freedom 2
+        # ref.[4] p.334 eq.30
+        hat_f2 = (
+                (k**2 - 1) /
+                (3 * xp.vecdot(1 / (n_t - 1), (1 - w_t / s_w_t)**2, axis=axis_zero))
+        )
+
+        dfn, dfd = hat_f1, hat_f2
+
+    # Fix any f values that should be inf or nan because the corresponding
+    # inputs were constant.
+    f = xpx.at(f)[all_const].set(xp.inf)
+    f = xpx.at(f)[all_same_const].set(xp.nan)
+
+    # calculate p value
+    # ref.[4] p.334 eq.28
+    prob = special.fdtrc(dfn, dfd, f)
+
+    f, prob = (f[()], prob[()]) if f.ndim == 0 else (f, prob)
+    return F_onewayResult(f, prob)
+
+
+@dataclass
+class AlexanderGovernResult:
+    statistic: float
+    pvalue: float
+
+
+@xp_capabilities(marray=True)
+@_axis_nan_policy_factory(
+    AlexanderGovernResult, n_samples=None,
+    result_to_tuple=lambda x, _: (x.statistic, x.pvalue),
+    too_small=1
+)
+def alexandergovern(*samples, nan_policy='propagate', axis=0):
+    """Performs the Alexander Govern test.
+
+    The Alexander-Govern approximation tests the equality of k independent
+    means in the face of heterogeneity of variance. The test is applied to
+    samples from two or more groups, possibly with differing sizes.
+
+    Parameters
+    ----------
+    *samples : array_like
+        The sample measurements for each group.  There must be at least
+        two samples, and each sample must contain at least two observations.
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains nan.
+        The following options are available (default is 'propagate'):
+
+        * 'propagate': returns nan
+        * 'raise': throws an error
+        * 'omit': performs the calculations ignoring nan values
+
+    Returns
+    -------
+    res : AlexanderGovernResult
+        An object with attributes:
+
+        statistic : float
+            The computed A statistic of the test.
+        pvalue : float
+            The associated p-value from the chi-squared distribution.
+
+    Warns
+    -----
+    `~scipy.stats.ConstantInputWarning`
+        Raised if an input is a constant array.  The statistic is not defined
+        in this case, so ``np.nan`` is returned.
+
+    See Also
+    --------
+    f_oneway : one-way ANOVA
+
+    Notes
+    -----
+    The use of this test relies on several assumptions.
+
+    1. The samples are independent.
+    2. Each sample is from a normally distributed population.
+    3. Unlike `f_oneway`, this test does not assume on homoscedasticity,
+       instead relaxing the assumption of equal variances.
+
+    Input samples must be finite, one dimensional, and with size greater than
+    one.
+
+    References
+    ----------
+    .. [1] Alexander, Ralph A., and Diane M. Govern. "A New and Simpler
+           Approximation for ANOVA under Variance Heterogeneity." Journal
+           of Educational Statistics, vol. 19, no. 2, 1994, pp. 91-101.
+           https://www.jstor.org/stable/1165140
+
+    Examples
+    --------
+    >>> from scipy.stats import alexandergovern
+
+    Here are some data on annual percentage rate of interest charged on
+    new car loans at nine of the largest banks in four American cities
+    taken from the National Institute of Standards and Technology's
+    ANOVA dataset.
+
+    We use `alexandergovern` to test the null hypothesis that all cities
+    have the same mean APR against the alternative that the cities do not
+    all have the same mean APR. We decide that a significance level of 5%
+    is required to reject the null hypothesis in favor of the alternative.
+
+    >>> atlanta = [13.75, 13.75, 13.5, 13.5, 13.0, 13.0, 13.0, 12.75, 12.5]
+    >>> chicago = [14.25, 13.0, 12.75, 12.5, 12.5, 12.4, 12.3, 11.9, 11.9]
+    >>> houston = [14.0, 14.0, 13.51, 13.5, 13.5, 13.25, 13.0, 12.5, 12.5]
+    >>> memphis = [15.0, 14.0, 13.75, 13.59, 13.25, 12.97, 12.5, 12.25,
+    ...           11.89]
+    >>> alexandergovern(atlanta, chicago, houston, memphis)
+    AlexanderGovernResult(statistic=4.65087071883494,
+                          pvalue=0.19922132490385214)
+
+    The p-value is 0.1992, indicating a nearly 20% chance of observing
+    such an extreme value of the test statistic under the null hypothesis.
+    This exceeds 5%, so we do not reject the null hypothesis in favor of
+    the alternative.
+
+    """
+    xp = array_namespace(*samples)
+    samples = _alexandergovern_input_validation(samples, nan_policy, axis, xp=xp)
+
+    # The following formula numbers reference the equation described on
+    # page 92 by Alexander, Govern. Formulas 5, 6, and 7 describe other
+    # tests that serve as the basis for equation (8) but are not needed
+    # to perform the test.
+
+    # precalculate mean and length of each sample
+    lengths = [_count_nonmasked(sample, axis=-1, xp=xp) for sample in samples]
+    means = xp.stack([_xp_mean(sample, axis=-1) for sample in samples])
+
+    # (1) determine standard error of the mean for each sample
+    se2 = [(_xp_var(sample, correction=1, axis=-1) / length)
+           for sample, length in zip(samples, lengths)]
+    standard_errors_squared = xp.stack(se2)
+    standard_errors = standard_errors_squared**0.5
+
+    # Special case: statistic is NaN when variance is zero
+    eps = xp.finfo(standard_errors.dtype).eps
+    zero = standard_errors <= xp.abs(eps * means)
+    NaN = xp.asarray(xp.nan, dtype=standard_errors.dtype)
+    standard_errors = xp.where(zero, NaN, standard_errors)
+
+    # (2) define a weight for each sample
+    inv_sq_se = 1 / standard_errors_squared
+    weights = inv_sq_se / xp.sum(inv_sq_se, axis=0, keepdims=True)
+
+    # (3) determine variance-weighted estimate of the common mean
+    # Consider replacing with vecdot when data-apis/array-api#910 is resolved
+    var_w = xp.sum(weights * means, axis=0, keepdims=True)
+
+    # (4) determine one-sample t statistic for each group
+    t_stats = _demean(means, var_w, axis=0, xp=xp) / standard_errors
+
+    # calculate parameters to be used in transformation
+    if is_marray(xp):
+        v = xp.stack(lengths) - 1
+    else:
+        v = xp.asarray(lengths, dtype=t_stats.dtype) - 1
+        # align along 0th axis, which corresponds with separate samples
+        v = xp.reshape(v, (-1,) + (1,)*(t_stats.ndim-1))
+    a = v - .5
+    b = 48 * a**2
+    c = (a * xp.log(1 + (t_stats ** 2)/v))**.5
+
+    # (8) perform a normalizing transformation on t statistic
+    z = (c + ((c**3 + 3*c)/b) -
+         ((4*c**7 + 33*c**5 + 240*c**3 + 855*c) /
+          (b**2*10 + 8*b*c**4 + 1000*b)))
+
+    # (9) calculate statistic
+    A = xp.vecdot(z, z, axis=-z.ndim)
+    A = A[()] if A.ndim == 0 else A  # data-apis/array-api-compat#355
+
+    # "[the p value is determined from] central chi-square random deviates
+    # with k - 1 degrees of freedom". Alexander, Govern (94)
+    df = xp.asarray(len(samples) - 1, dtype=A.dtype)
+    chi2 = _SimpleChi2(df)
+    p = _get_pvalue(A, chi2, alternative='greater', symmetric=False, xp=xp)
+    return AlexanderGovernResult(A, p)
+
+
+def _alexandergovern_input_validation(samples, nan_policy, axis, xp):
+    if len(samples) < 2:
+        raise TypeError(f"2 or more inputs required, got {len(samples)}")
+
+    for sample in samples:
+        if sample.shape[axis] <= 1:
+            raise ValueError("Input sample size must be greater than one.")
+
+    samples = [xp.moveaxis(sample, axis, -1) for sample in samples]
+
+    return samples
+
+
+def _pearsonr_fisher_ci(r, n, confidence_level, alternative):
+    """
+    Compute the confidence interval for Pearson's R.
+
+    Fisher's transformation is used to compute the confidence interval
+    (https://en.wikipedia.org/wiki/Fisher_transformation).
+    """
+    xp = array_namespace(r)
+
+    ones = xp.ones_like(r)
+    n = xp.asarray(n, dtype=r.dtype, device=xp_device(r))
+    confidence_level = xp.asarray(confidence_level, dtype=r.dtype, device=xp_device(r))
+
+    with np.errstate(divide='ignore', invalid='ignore'):
+        zr = xp.atanh(r)
+        se = xp.sqrt(1 / (n - 3))
+
+    if alternative == "two-sided":
+        h = special.ndtri(0.5 + confidence_level/2)
+        zlo = zr - h*se
+        zhi = zr + h*se
+        rlo = xp.tanh(zlo)
+        rhi = xp.tanh(zhi)
+    elif alternative == "less":
+        h = special.ndtri(confidence_level)
+        zhi = zr + h*se
+        rhi = xp.tanh(zhi)
+        rlo = -ones
+    else:
+        # alternative == "greater":
+        h = special.ndtri(confidence_level)
+        zlo = zr - h*se
+        rlo = xp.tanh(zlo)
+        rhi = ones
+
+    mask = (n <= 3)
+    if mask.ndim == 0:
+        # This is Array API legal, but Dask doesn't like it.
+        mask = xp.broadcast_to(mask, rlo.shape)
+
+    rlo = xpx.at(rlo)[mask].set(-1)
+    rhi = xpx.at(rhi)[mask].set(1)
+
+    rlo = rlo[()] if rlo.ndim == 0 else rlo
+    rhi = rhi[()] if rhi.ndim == 0 else rhi
+    return ConfidenceInterval(low=rlo, high=rhi)
+
+
+def _pearsonr_bootstrap_ci(confidence_level, method, x, y, alternative, axis):
+    """
+    Compute the confidence interval for Pearson's R using the bootstrap.
+    """
+    def statistic(x, y, axis):
+        statistic, _ = pearsonr(x, y, axis=axis)
+        return statistic
+
+    res = bootstrap((x, y), statistic, confidence_level=confidence_level, axis=axis,
+                    paired=True, alternative=alternative, **method._asdict())
+    # for one-sided confidence intervals, bootstrap gives +/- inf on one side
+    res.confidence_interval = np.clip(res.confidence_interval, -1, 1)
+
+    return ConfidenceInterval(*res.confidence_interval)
+
+
+ConfidenceInterval = namedtuple('ConfidenceInterval', ['low', 'high'])
+
+PearsonRResultBase = _make_tuple_bunch('PearsonRResultBase',
+                                       ['statistic', 'pvalue'], [])
+
+
+class PearsonRResult(PearsonRResultBase):
+    """
+    Result of `scipy.stats.pearsonr`
+
+    Attributes
+    ----------
+    statistic : float
+        Pearson product-moment correlation coefficient.
+    pvalue : float
+        The p-value associated with the chosen alternative.
+
+    Methods
+    -------
+    confidence_interval
+        Computes the confidence interval of the correlation
+        coefficient `statistic` for the given confidence level.
+
+    """
+    def __init__(self, statistic, pvalue, alternative, n, x, y, axis):
+        super().__init__(statistic, pvalue)
+        self._alternative = alternative
+        self._n = n
+        self._x = x
+        self._y = y
+        self._axis = axis
+
+        # add alias for consistency with other correlation functions
+        self.correlation = statistic
+
+    def confidence_interval(self, confidence_level=0.95, method=None):
+        """
+        The confidence interval for the correlation coefficient.
+
+        Compute the confidence interval for the correlation coefficient
+        ``statistic`` with the given confidence level.
+
+        If `method` is not provided,
+        The confidence interval is computed using the Fisher transformation
+        F(r) = arctanh(r) [1]_.  When the sample pairs are drawn from a
+        bivariate normal distribution, F(r) approximately follows a normal
+        distribution with standard error ``1/sqrt(n - 3)``, where ``n`` is the
+        length of the original samples along the calculation axis. When
+        ``n <= 3``, this approximation does not yield a finite, real standard
+        error, so we define the confidence interval to be -1 to 1.
+
+        If `method` is an instance of `BootstrapMethod`, the confidence
+        interval is computed using `scipy.stats.bootstrap` with the provided
+        configuration options and other appropriate settings. In some cases,
+        confidence limits may be NaN due to a degenerate resample, and this is
+        typical for very small samples (~6 observations).
+
+        Parameters
+        ----------
+        confidence_level : float
+            The confidence level for the calculation of the correlation
+            coefficient confidence interval. Default is 0.95.
+
+        method : BootstrapMethod, optional
+            Defines the method used to compute the confidence interval. See
+            method description for details.
+
+            .. versionadded:: 1.11.0
+
+        Returns
+        -------
+        ci : namedtuple
+            The confidence interval is returned in a ``namedtuple`` with
+            fields `low` and `high`.
+
+        References
+        ----------
+        .. [1] "Pearson correlation coefficient", Wikipedia,
+               https://en.wikipedia.org/wiki/Pearson_correlation_coefficient
+        """
+        if isinstance(method, BootstrapMethod):
+            xp = array_namespace(self._x)
+            message = ('`method` must be `None` if `pearsonr` '
+                       'arguments were not NumPy arrays.')
+            if not is_numpy(xp):
+                raise ValueError(message)
+
+            ci = _pearsonr_bootstrap_ci(confidence_level, method, self._x, self._y,
+                                        self._alternative, self._axis)
+        elif method is None:
+            ci = _pearsonr_fisher_ci(self.statistic, self._n, confidence_level,
+                                     self._alternative)
+        else:
+            message = ('`method` must be an instance of `BootstrapMethod` '
+                       'or None.')
+            raise ValueError(message)
+        return ci
+
+
+# Missing special.betainc on torch
+@xp_capabilities(cpu_only=True, exceptions=['cupy', 'jax.numpy'], marray=True,
+    extra_note='Only the default `method` is compatible with MArray input.')
+def pearsonr(x, y, *, alternative='two-sided', method=None, axis=0):
+    r"""
+    Pearson correlation coefficient and p-value for testing non-correlation.
+
+    The Pearson correlation coefficient [1]_ measures the linear relationship
+    between two datasets. Like other correlation
+    coefficients, this one varies between -1 and +1 with 0 implying no
+    correlation. Correlations of -1 or +1 imply an exact linear relationship.
+    Positive correlations imply that as x increases, so does y. Negative
+    correlations imply that as x increases, y decreases.
+
+    This function also performs a test of the null hypothesis that the
+    distributions underlying the samples are uncorrelated and normally
+    distributed. (See Kowalski [3]_
+    for a discussion of the effects of non-normality of the input on the
+    distribution of the correlation coefficient.)
+    The p-value roughly indicates the probability of an uncorrelated system
+    producing datasets that have a Pearson correlation at least as extreme
+    as the one computed from these datasets.
+
+    Parameters
+    ----------
+    x : array_like
+        Input array.
+    y : array_like
+        Input array.
+    alternative : {'two-sided', 'greater', 'less'}, optional
+        Defines the alternative hypothesis. Default is 'two-sided'.
+        The following options are available:
+
+        * 'two-sided': the correlation is nonzero
+        * 'less': the correlation is negative (less than zero)
+        * 'greater':  the correlation is positive (greater than zero)
+
+        .. versionadded:: 1.9.0
+    method : ResamplingMethod, optional
+        Defines the method used to compute the p-value. If `method` is an
+        instance of `PermutationMethod`/`MonteCarloMethod`, the p-value is
+        computed using
+        `scipy.stats.permutation_test`/`scipy.stats.monte_carlo_test` with the
+        provided configuration options and other appropriate settings.
+        Otherwise, the p-value is computed as documented in the notes.
+
+        .. versionadded:: 1.11.0
+    axis : int or None, default
+        Axis along which to perform the calculation. Default is 0.
+        If None, ravel both arrays before performing the calculation.
+
+        .. versionadded:: 1.14.0
+
+    Returns
+    -------
+    result : `~scipy.stats._result_classes.PearsonRResult`
+        An object with the following attributes:
+
+        statistic : float
+            Pearson product-moment correlation coefficient.
+        pvalue : float
+            The p-value associated with the chosen alternative.
+
+        The object has the following method:
+
+        confidence_interval(confidence_level, method)
+            This computes the confidence interval of the correlation
+            coefficient `statistic` for the given confidence level.
+            The confidence interval is returned in a ``namedtuple`` with
+            fields `low` and `high`. If `method` is not provided, the
+            confidence interval is computed using the Fisher transformation
+            [1]_. If `method` is an instance of `BootstrapMethod`, the
+            confidence interval is computed using `scipy.stats.bootstrap` with
+            the provided configuration options and other appropriate settings.
+            In some cases, confidence limits may be NaN due to a degenerate
+            resample, and this is typical for very small samples (~6
+            observations).
+
+    Raises
+    ------
+    ValueError
+        If `x` and `y` do not have length at least 2.
+
+    Warns
+    -----
+    `~scipy.stats.ConstantInputWarning`
+        Raised if an input is a constant array.  The correlation coefficient
+        is not defined in this case, so ``np.nan`` is returned.
+
+    `~scipy.stats.NearConstantInputWarning`
+        Raised if an input is "nearly" constant.  The array ``x`` is considered
+        nearly constant if ``norm(x - mean(x)) < 1e-13 * abs(mean(x))``.
+        Numerical errors in the calculation ``x - mean(x)`` in this case might
+        result in an inaccurate calculation of r.
+
+    See Also
+    --------
+    spearmanr : Spearman rank-order correlation coefficient.
+    kendalltau : Kendall's tau, a correlation measure for ordinal data.
+    :ref:`hypothesis_pearsonr` : Extended example
+
+    Notes
+    -----
+    The correlation coefficient is calculated as follows:
+
+    .. math::
+
+        r = \frac{\sum (x - m_x) (y - m_y)}
+                 {\sqrt{\sum (x - m_x)^2 \sum (y - m_y)^2}}
+
+    where :math:`m_x` is the mean of the vector x and :math:`m_y` is
+    the mean of the vector y.
+
+    Under the assumption that x and y are drawn from
+    independent normal distributions (so the population correlation coefficient
+    is 0), the probability density function of the sample correlation
+    coefficient r is ([1]_, [2]_):
+
+    .. math::
+        f(r) = \frac{{(1-r^2)}^{n/2-2}}{\mathrm{B}(\frac{1}{2},\frac{n}{2}-1)}
+
+    where n is the number of samples, and B is the beta function.  This
+    is sometimes referred to as the exact distribution of r.  This is
+    the distribution that is used in `pearsonr` to compute the p-value when
+    the `method` parameter is left at its default value (None).
+    The distribution is a beta distribution on the interval [-1, 1],
+    with equal shape parameters a = b = n/2 - 1.  In terms of SciPy's
+    implementation of the beta distribution, the distribution of r is::
+
+        dist = scipy.stats.beta(n/2 - 1, n/2 - 1, loc=-1, scale=2)
+
+    The default p-value returned by `pearsonr` is a two-sided p-value. For a
+    given sample with correlation coefficient r, the p-value is
+    the probability that abs(r') of a random sample x' and y' drawn from
+    the population with zero correlation would be greater than or equal
+    to abs(r). In terms of the object ``dist`` shown above, the p-value
+    for a given r and length n can be computed as::
+
+        p = 2*dist.cdf(-abs(r))
+
+    When n is 2, the above continuous distribution is not well-defined.
+    One can interpret the limit of the beta distribution as the shape
+    parameters a and b approach a = b = 0 as a discrete distribution with
+    equal probability masses at r = 1 and r = -1.  More directly, one
+    can observe that, given the data x = [x1, x2] and y = [y1, y2], and
+    assuming x1 != x2 and y1 != y2, the only possible values for r are 1
+    and -1.  Because abs(r') for any sample x' and y' with length 2 will
+    be 1, the two-sided p-value for a sample of length 2 is always 1.
+
+    For backwards compatibility, the object that is returned also behaves
+    like a tuple of length two that holds the statistic and the p-value.
+
+    References
+    ----------
+    .. [1] "Pearson correlation coefficient", Wikipedia,
+           https://en.wikipedia.org/wiki/Pearson_correlation_coefficient
+    .. [2] Student, "Probable error of a correlation coefficient",
+           Biometrika, Volume 6, Issue 2-3, 1 September 1908, pp. 302-310.
+    .. [3] C. J. Kowalski, "On the Effects of Non-Normality on the Distribution
+           of the Sample Product-Moment Correlation Coefficient"
+           Journal of the Royal Statistical Society. Series C (Applied
+           Statistics), Vol. 21, No. 1 (1972), pp. 1-12.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> x, y = [1, 2, 3, 4, 5, 6, 7], [10, 9, 2.5, 6, 4, 3, 2]
+    >>> res = stats.pearsonr(x, y)
+    >>> res
+    PearsonRResult(statistic=-0.828503883588428, pvalue=0.021280260007523286)
+
+    To perform an exact permutation version of the test:
+
+    >>> rng = np.random.default_rng(7796654889291491997)
+    >>> method = stats.PermutationMethod(n_resamples=np.inf, random_state=rng)
+    >>> stats.pearsonr(x, y, method=method)
+    PearsonRResult(statistic=-0.828503883588428, pvalue=0.028174603174603175)
+
+    To perform the test under the null hypothesis that the data were drawn from
+    *uniform* distributions:
+
+    >>> method = stats.MonteCarloMethod(rvs=(rng.uniform, rng.uniform))
+    >>> stats.pearsonr(x, y, method=method)
+    PearsonRResult(statistic=-0.828503883588428, pvalue=0.0188)
+
+    To produce an asymptotic 90% confidence interval:
+
+    >>> res.confidence_interval(confidence_level=0.9)
+    ConfidenceInterval(low=-0.9644331982722841, high=-0.3460237473272273)
+
+    And for a bootstrap confidence interval:
+
+    >>> method = stats.BootstrapMethod(method='BCa', rng=rng)
+    >>> res.confidence_interval(confidence_level=0.9, method=method)
+    ConfidenceInterval(low=-0.9983163756488651, high=-0.22771001702132443)  # may vary
+
+    If N-dimensional arrays are provided, multiple tests are performed in a
+    single call according to the same conventions as most `scipy.stats` functions:
+
+    >>> rng = np.random.default_rng(2348246935601934321)
+    >>> x = rng.standard_normal((8, 15))
+    >>> y = rng.standard_normal((8, 15))
+    >>> stats.pearsonr(x, y, axis=0).statistic.shape  # between corresponding columns
+    (15,)
+    >>> stats.pearsonr(x, y, axis=1).statistic.shape  # between corresponding rows
+    (8,)
+
+    To perform all pairwise comparisons between slices of the arrays,
+    use standard NumPy broadcasting techniques. For instance, to compute the
+    correlation between all pairs of rows:
+
+    >>> stats.pearsonr(x[:, np.newaxis, :], y, axis=-1).statistic.shape
+    (8, 8)
+
+    There is a linear dependence between x and y if y = a + b*x + e, where
+    a,b are constants and e is a random error term, assumed to be independent
+    of x. For simplicity, assume that x is standard normal, a=0, b=1 and let
+    e follow a normal distribution with mean zero and standard deviation s>0.
+
+    >>> rng = np.random.default_rng()
+    >>> s = 0.5
+    >>> x = stats.norm.rvs(size=500, random_state=rng)
+    >>> e = stats.norm.rvs(scale=s, size=500, random_state=rng)
+    >>> y = x + e
+    >>> stats.pearsonr(x, y).statistic
+    0.9001942438244763
+
+    This should be close to the exact value given by
+
+    >>> 1/np.sqrt(1 + s**2)
+    0.8944271909999159
+
+    For s=0.5, we observe a high level of correlation. In general, a large
+    variance of the noise reduces the correlation, while the correlation
+    approaches one as the variance of the error goes to zero.
+
+    It is important to keep in mind that no correlation does not imply
+    independence unless (x, y) is jointly normal. Correlation can even be zero
+    when there is a very simple dependence structure: if X follows a
+    standard normal distribution, let y = abs(x). Note that the correlation
+    between x and y is zero. Indeed, since the expectation of x is zero,
+    cov(x, y) = E[x*y]. By definition, this equals E[x*abs(x)] which is zero
+    by symmetry. The following lines of code illustrate this observation:
+
+    >>> y = np.abs(x)
+    >>> stats.pearsonr(x, y)
+    PearsonRResult(statistic=-0.05444919272687482, pvalue=0.22422294836207743)
+
+    A non-zero correlation coefficient can be misleading. For example, if X has
+    a standard normal distribution, define y = x if x < 0 and y = 0 otherwise.
+    A simple calculation shows that corr(x, y) = sqrt(2/Pi) = 0.797...,
+    implying a high level of correlation:
+
+    >>> y = np.where(x < 0, x, 0)
+    >>> stats.pearsonr(x, y)
+    PearsonRResult(statistic=0.861985781588, pvalue=4.813432002751103e-149)
+
+    This is unintuitive since there is no dependence of x and y if x is larger
+    than zero which happens in about half of the cases if we sample x and y.
+
+    For a more detailed example, see :ref:`hypothesis_pearsonr`.
+
+    """
+    xp = array_namespace(x, y)
+    x, y = xp_promote(x, y, force_floating=True, xp=xp)
+    dtype = x.dtype
+
+    if not is_numpy(xp) and method is not None:
+        method = 'invalid'
+
+    if axis is None:
+        x = xp.reshape(x, (-1,))
+        y = xp.reshape(y, (-1,))
+        axis = -1
+
+    axis_int = int(axis)
+    if axis_int != axis:
+        raise ValueError('`axis` must be an integer.')
+    axis = axis_int
+
+    try:
+        np.broadcast_shapes(x.shape, y.shape)
+        # For consistency with other `stats` functions, we need to
+        # match the dimensionalities before looking at `axis`.
+        # (Note: this is not the NEP 5 / gufunc order of operations;
+        #  see TestPearsonr::test_different_dimensionality for more information.)
+        ndim = max(x.ndim, y.ndim)
+        x = xp.reshape(x, (1,) * (ndim - x.ndim) + x.shape)
+        y = xp.reshape(y, (1,) * (ndim - y.ndim) + y.shape)
+
+    except (ValueError, RuntimeError) as e:
+        message = '`x` and `y` must be broadcastable.'
+        raise ValueError(message) from e
+
+    if x.shape[axis] != y.shape[axis]:
+        raise ValueError('`x` and `y` must have the same length along `axis`.')
+
+    if x.shape[axis] < 2:
+        raise ValueError('`x` and `y` must have length at least 2.')
+
+    x, y = _share_masks(x, y, xp=xp)
+    n = xp.asarray(_count_nonmasked(x, axis=axis), dtype=x.dtype)
+
+    x = xp.moveaxis(x, axis, -1)
+    y = xp.moveaxis(y, axis, -1)
+    axis = -1
+
+    if xp.isdtype(dtype, "complex floating"):
+        raise ValueError('This function does not support complex data')
+
+    x = xp.astype(x, dtype, copy=False)
+    y = xp.astype(y, dtype, copy=False)
+    threshold = xp.finfo(dtype).eps ** 0.75
+
+    # If an input is constant, the correlation coefficient is not defined.
+    if is_marray(xp):
+        # sort to ensure that we are comparing to a non-masked element
+        const_x = xp.all(x == xp.sort(x, axis=-1)[..., 0:1], axis=-1)
+        const_y = xp.all(y == xp.sort(y, axis=-1)[..., 0:1], axis=-1)
+    else:
+        const_x = xp.all(x == x[..., 0:1], axis=-1)
+        const_y = xp.all(y == y[..., 0:1], axis=-1)
+    const_xy = const_x | const_y
+
+    any_const_xy = xp.any(const_xy)
+    lazy = is_lazy_array(const_xy)
+    if not lazy and any_const_xy:
+        msg = ("An input array is constant; the correlation coefficient "
+               "is not defined.")
+        warnings.warn(stats.ConstantInputWarning(msg), stacklevel=2)
+    if lazy or any_const_xy:
+        x = xp.where(const_x[..., xp.newaxis], xp.nan, x)
+        y = xp.where(const_y[..., xp.newaxis], xp.nan, y)
+
+    if isinstance(method, PermutationMethod):
+        def statistic(y, axis):
+            statistic, _ = pearsonr(x, y, axis=axis, alternative=alternative)
+            return statistic
+
+        res = permutation_test((y,), statistic, permutation_type='pairings',
+                               axis=axis, alternative=alternative, **method._asdict())
+
+        return PearsonRResult(statistic=res.statistic, pvalue=res.pvalue, n=n,
+                              alternative=alternative, x=x, y=y, axis=axis)
+    elif isinstance(method, MonteCarloMethod):
+        def statistic(x, y, axis):
+            statistic, _ = pearsonr(x, y, axis=axis, alternative=alternative)
+            return statistic
+
+        # `monte_carlo_test` accepts an `rvs` tuple of callables, not an `rng`
+        # If the user specified an `rng`, replace it with the appropriate callables
+        method = method._asdict()
+        if (rng := method.pop('rng', None)) is not None:  # goo-goo g'joob
+            rng = np.random.default_rng(rng)
+            method['rvs'] = rng.normal, rng.normal
+
+        res = monte_carlo_test((x, y,), statistic=statistic, axis=axis,
+                               alternative=alternative, **method)
+
+        return PearsonRResult(statistic=res.statistic, pvalue=res.pvalue, n=n,
+                              alternative=alternative, x=x, y=y, axis=axis)
+    elif method == 'invalid':
+        message = '`method` must be `None` if arguments are not NumPy arrays.'
+        raise ValueError(message)
+    elif method is not None:
+        message = ('`method` must be an instance of `PermutationMethod`, '
+                   '`MonteCarloMethod`, or None.')
+        raise ValueError(message)
+
+    xmean = xp.mean(x, axis=axis, keepdims=True)
+    ymean = xp.mean(y, axis=axis, keepdims=True)
+    xm = x - xmean
+    ym = y - ymean
+
+    # scipy.linalg.norm(xm) avoids premature overflow when xm is e.g.
+    # [-5e210, 5e210, 3e200, -3e200]
+    # but not when `axis` is provided, so scale manually. scipy.linalg.norm
+    # also raises an error with NaN input rather than returning NaN, so
+    # use np.linalg.norm.
+    xmax = xp.max(xp.abs(xm), axis=axis, keepdims=True)
+    ymax = xp.max(xp.abs(ym), axis=axis, keepdims=True)
+    with np.errstate(invalid='ignore', divide='ignore'):
+        normxm = xmax * xp_vector_norm(xm/xmax, axis=axis, keepdims=True)
+        normym = ymax * xp_vector_norm(ym/ymax, axis=axis, keepdims=True)
+
+    if not lazy:
+        nconst_x = xp.any(normxm < threshold*xp.abs(xmean), axis=axis)
+        nconst_y = xp.any(normym < threshold*xp.abs(ymean), axis=axis)
+        nconst_xy = nconst_x | nconst_y
+        if xp.any(nconst_xy & (~const_xy)):
+            # If all the values in x (likewise y) are very close to the mean,
+            # the loss of precision that occurs in the subtraction xm = x - xmean
+            # might result in large errors in r.
+            msg = ("An input array is nearly constant; the computed "
+                "correlation coefficient may be inaccurate.")
+            warnings.warn(stats.NearConstantInputWarning(msg), stacklevel=2)
+
+    with np.errstate(invalid='ignore', divide='ignore'):
+        r = xp.vecdot(xm / normxm, ym / normym, axis=axis)
+
+    # Presumably, if abs(r) > 1, then it is only some small artifact of
+    # floating point arithmetic.
+    r = xp.clip(r, -1., 1.)
+    r = xpx.at(r, const_xy).set(xp.nan)
+
+    # As explained in the docstring, the distribution of `r` under the null
+    # hypothesis is the beta distribution on (-1, 1) with a = b = n/2 - 1.
+    ab = xp.asarray(n/2 - 1, dtype=dtype, device=xp_device(x))
+    dist = _SimpleBeta(ab, ab, loc=-1, scale=2)
+    pvalue = _get_pvalue(r, dist, alternative, xp=xp)
+
+    mask = (n == 2)   #  return exactly 1.0 or -1.0 values for n == 2 case as promised
+    # data-apis/array-api-extra#196
+    mxp = array_namespace(r._meta) if is_dask(xp) else xp
+    def special_case(r):
+        return mxp.where(mxp.isnan(r), mxp.nan, mxp.ones_like(r))
+    r = xpx.apply_where(mask, r, mxp.round, fill_value=r)
+    pvalue = xpx.apply_where(mask, (r,), special_case, fill_value=pvalue)
+
+    r = r[()] if r.ndim == 0 else r
+    pvalue = pvalue[()] if pvalue.ndim == 0 else pvalue
+    return PearsonRResult(statistic=r, pvalue=pvalue, n=n,
+                          alternative=alternative, x=x, y=y, axis=axis)
+
+
+@xp_capabilities(np_only=True)
+def fisher_exact(table, alternative=None, *, method=None):
+    """Perform a Fisher exact test on a contingency table.
+
+    For a 2x2 table,
+    the null hypothesis is that the true odds ratio of the populations
+    underlying the observations is one, and the observations were sampled
+    from these populations under a condition: the marginals of the
+    resulting table must equal those of the observed table.
+    The statistic is the unconditional maximum likelihood estimate of the odds
+    ratio, and the p-value is the probability under the null hypothesis of
+    obtaining a table at least as extreme as the one that was actually
+    observed.
+
+    For other table sizes, or if `method` is provided, the null hypothesis
+    is that the rows and columns of the tables have fixed sums and are
+    independent; i.e., the table was sampled from a `scipy.stats.random_table`
+    distribution with the observed marginals. The statistic is the
+    probability mass of this distribution evaluated at `table`, and the
+    p-value is the percentage of the population of tables with statistic at
+    least as extreme (small) as that of `table`. There is only one alternative
+    hypothesis available: the rows and columns are not independent.
+
+    There are other possible choices of statistic and two-sided
+    p-value definition associated with Fisher's exact test; please see the
+    Notes for more information.
+
+    Parameters
+    ----------
+    table : array_like of ints
+        A contingency table.  Elements must be non-negative integers.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis for 2x2 tables; unused for other
+        table sizes.
+        The following options are available (default is 'two-sided'):
+
+        * 'two-sided': the odds ratio of the underlying population is not one
+        * 'less': the odds ratio of the underlying population is less than one
+        * 'greater': the odds ratio of the underlying population is greater
+          than one
+
+        See the Notes for more details.
+
+    method : ResamplingMethod, optional
+        Defines the method used to compute the p-value.
+        If `method` is an instance of `PermutationMethod`/`MonteCarloMethod`,
+        the p-value is computed using
+        `scipy.stats.permutation_test`/`scipy.stats.monte_carlo_test` with the
+        provided configuration options and other appropriate settings.
+        Note that if `method` is an instance of `MonteCarloMethod`, the ``rvs``
+        attribute must be left unspecified; Monte Carlo samples are always drawn
+        using the ``rvs`` method of `scipy.stats.random_table`.
+        Otherwise, the p-value is computed as documented in the notes.
+
+        .. versionadded:: 1.15.0
+
+    Returns
+    -------
+    res : SignificanceResult
+        An object containing attributes:
+
+        statistic : float
+            For a 2x2 table with default `method`, this is the odds ratio - the
+            prior odds ratio not a posterior estimate. In all other cases, this
+            is the probability density of obtaining the observed table under the
+            null hypothesis of independence with marginals fixed.
+        pvalue : float
+            The probability under the null hypothesis of obtaining a
+            table at least as extreme as the one that was actually observed.
+
+    Raises
+    ------
+    ValueError
+        If `table` is not two-dimensional or has negative entries.
+
+    See Also
+    --------
+    chi2_contingency : Chi-square test of independence of variables in a
+        contingency table.  This can be used as an alternative to
+        `fisher_exact` when the numbers in the table are large.
+    contingency.odds_ratio : Compute the odds ratio (sample or conditional
+        MLE) for a 2x2 contingency table.
+    barnard_exact : Barnard's exact test, which is a more powerful alternative
+        than Fisher's exact test for 2x2 contingency tables.
+    boschloo_exact : Boschloo's exact test, which is a more powerful
+        alternative than Fisher's exact test for 2x2 contingency tables.
+    :ref:`hypothesis_fisher_exact` : Extended example
+
+    Notes
+    -----
+    *Null hypothesis and p-values*
+
+    The null hypothesis is that the true odds ratio of the populations
+    underlying the observations is one, and the observations were sampled at
+    random from these populations under a condition: the marginals of the
+    resulting table must equal those of the observed table. Equivalently,
+    the null hypothesis is that the input table is from the hypergeometric
+    distribution with parameters (as used in `hypergeom`)
+    ``M = a + b + c + d``, ``n = a + b`` and ``N = a + c``, where the
+    input table is ``[[a, b], [c, d]]``.  This distribution has support
+    ``max(0, N + n - M) <= x <= min(N, n)``, or, in terms of the values
+    in the input table, ``min(0, a - d) <= x <= a + min(b, c)``.  ``x``
+    can be interpreted as the upper-left element of a 2x2 table, so the
+    tables in the distribution have form::
+
+        [  x           n - x     ]
+        [N - x    M - (n + N) + x]
+
+    For example, if::
+
+        table = [6  2]
+                [1  4]
+
+    then the support is ``2 <= x <= 7``, and the tables in the distribution
+    are::
+
+        [2 6]   [3 5]   [4 4]   [5 3]   [6 2]  [7 1]
+        [5 0]   [4 1]   [3 2]   [2 3]   [1 4]  [0 5]
+
+    The probability of each table is given by the hypergeometric distribution
+    ``hypergeom.pmf(x, M, n, N)``.  For this example, these are (rounded to
+    three significant digits)::
+
+        x       2      3      4      5       6        7
+        p  0.0163  0.163  0.408  0.326  0.0816  0.00466
+
+    These can be computed with::
+
+        >>> import numpy as np
+        >>> from scipy.stats import hypergeom
+        >>> table = np.array([[6, 2], [1, 4]])
+        >>> M = table.sum()
+        >>> n = table[0].sum()
+        >>> N = table[:, 0].sum()
+        >>> start, end = hypergeom.support(M, n, N)
+        >>> hypergeom.pmf(np.arange(start, end+1), M, n, N)
+        array([0.01631702, 0.16317016, 0.40792541, 0.32634033, 0.08158508,
+               0.004662  ])
+
+    The two-sided p-value is the probability that, under the null hypothesis,
+    a random table would have a probability equal to or less than the
+    probability of the input table.  For our example, the probability of
+    the input table (where ``x = 6``) is 0.0816.  The x values where the
+    probability does not exceed this are 2, 6 and 7, so the two-sided p-value
+    is ``0.0163 + 0.0816 + 0.00466 ~= 0.10256``::
+
+        >>> from scipy.stats import fisher_exact
+        >>> res = fisher_exact(table, alternative='two-sided')
+        >>> res.pvalue
+        0.10256410256410257
+
+    The one-sided p-value for ``alternative='greater'`` is the probability
+    that a random table has ``x >= a``, which in our example is ``x >= 6``,
+    or ``0.0816 + 0.00466 ~= 0.08626``::
+
+        >>> res = fisher_exact(table, alternative='greater')
+        >>> res.pvalue
+        0.08624708624708627
+
+    This is equivalent to computing the survival function of the
+    distribution at ``x = 5`` (one less than ``x`` from the input table,
+    because we want to include the probability of ``x = 6`` in the sum)::
+
+        >>> hypergeom.sf(5, M, n, N)
+        0.08624708624708627
+
+    For ``alternative='less'``, the one-sided p-value is the probability
+    that a random table has ``x <= a``, (i.e. ``x <= 6`` in our example),
+    or ``0.0163 + 0.163 + 0.408 + 0.326 + 0.0816 ~= 0.9949``::
+
+        >>> res = fisher_exact(table, alternative='less')
+        >>> res.pvalue
+        0.9953379953379957
+
+    This is equivalent to computing the cumulative distribution function
+    of the distribution at ``x = 6``:
+
+        >>> hypergeom.cdf(6, M, n, N)
+        0.9953379953379957
+
+    *Odds ratio*
+
+    The calculated odds ratio is different from the value computed by the
+    R function ``fisher.test``.  This implementation returns the "sample"
+    or "unconditional" maximum likelihood estimate, while ``fisher.test``
+    in R uses the conditional maximum likelihood estimate.  To compute the
+    conditional maximum likelihood estimate of the odds ratio, use
+    `scipy.stats.contingency.odds_ratio`.
+
+    References
+    ----------
+    .. [1] Fisher, Sir Ronald A, "The Design of Experiments:
+           Mathematics of a Lady Tasting Tea." ISBN 978-0-486-41151-4, 1935.
+    .. [2] "Fisher's exact test",
+           https://en.wikipedia.org/wiki/Fisher's_exact_test
+
+    Examples
+    --------
+
+    >>> from scipy.stats import fisher_exact
+    >>> res = fisher_exact([[8, 2], [1, 5]])
+    >>> res.statistic
+    20.0
+    >>> res.pvalue
+    0.034965034965034975
+
+    For tables with shape other than ``(2, 2)``, provide an instance of
+    `scipy.stats.MonteCarloMethod` or `scipy.stats.PermutationMethod` for the
+    `method` parameter:
+
+    >>> import numpy as np
+    >>> from scipy.stats import MonteCarloMethod
+    >>> rng = np.random.default_rng(4507195762371367)
+    >>> method = MonteCarloMethod(rng=rng)
+    >>> fisher_exact([[8, 2, 3], [1, 5, 4]], method=method)
+    SignificanceResult(statistic=np.float64(0.005782), pvalue=np.float64(0.0603))
+
+    For a more detailed example, see :ref:`hypothesis_fisher_exact`.
+    """
+    hypergeom = distributions.hypergeom
+    # int32 is not enough for the algorithm
+    c = np.asarray(table, dtype=np.int64)
+    if not c.ndim == 2:
+        raise ValueError("The input `table` must have two dimensions.")
+
+    if np.any(c < 0):
+        raise ValueError("All values in `table` must be nonnegative.")
+
+    if not c.shape == (2, 2) or method is not None:
+        return _fisher_exact_rxc(c, alternative, method)
+    alternative = 'two-sided' if alternative is None else alternative
+
+    if 0 in c.sum(axis=0) or 0 in c.sum(axis=1):
+        # If both values in a row or column are zero, the p-value is 1 and
+        # the odds ratio is NaN.
+        return SignificanceResult(np.nan, 1.0)
+
+    if c[1, 0] > 0 and c[0, 1] > 0:
+        oddsratio = c[0, 0] * c[1, 1] / (c[1, 0] * c[0, 1])
+    else:
+        oddsratio = np.inf
+
+    n1 = c[0, 0] + c[0, 1]
+    n2 = c[1, 0] + c[1, 1]
+    n = c[0, 0] + c[1, 0]
+
+    def pmf(x):
+        return hypergeom.pmf(x, n1 + n2, n1, n)
+
+    if alternative == 'less':
+        pvalue = hypergeom.cdf(c[0, 0], n1 + n2, n1, n)
+    elif alternative == 'greater':
+        # Same formula as the 'less' case, but with the second column.
+        pvalue = hypergeom.cdf(c[0, 1], n1 + n2, n1, c[0, 1] + c[1, 1])
+    elif alternative == 'two-sided':
+        mode = int((n + 1) * (n1 + 1) / (n1 + n2 + 2))
+        pexact = hypergeom.pmf(c[0, 0], n1 + n2, n1, n)
+        pmode = hypergeom.pmf(mode, n1 + n2, n1, n)
+
+        epsilon = 1e-14
+        gamma = 1 + epsilon
+
+        if np.abs(pexact - pmode) / np.maximum(pexact, pmode) <= epsilon:
+            return SignificanceResult(oddsratio, 1.)
+
+        elif c[0, 0] < mode:
+            plower = hypergeom.cdf(c[0, 0], n1 + n2, n1, n)
+            if hypergeom.pmf(n, n1 + n2, n1, n) > pexact * gamma:
+                return SignificanceResult(oddsratio, plower)
+
+            guess = _binary_search(lambda x: -pmf(x), -pexact * gamma, mode, n, xp=np)
+            pvalue = plower + hypergeom.sf(guess, n1 + n2, n1, n)
+        else:
+            pupper = hypergeom.sf(c[0, 0] - 1, n1 + n2, n1, n)
+            if hypergeom.pmf(0, n1 + n2, n1, n) > pexact * gamma:
+                return SignificanceResult(oddsratio, pupper)
+
+            guess = _binary_search(pmf, pexact * gamma, 0, mode, xp=np)
+            pvalue = pupper + hypergeom.cdf(guess, n1 + n2, n1, n)
+    else:
+        msg = "`alternative` should be one of {'two-sided', 'less', 'greater'}"
+        raise ValueError(msg)
+
+    pvalue = min(pvalue, 1.0)
+
+    return SignificanceResult(oddsratio, pvalue)
+
+
+def _fisher_exact_rxc(table, alternative, method):
+    if alternative is not None:
+        message = ('`alternative` must be the default (None) unless '
+                  '`table` has shape `(2, 2)` and `method is None`.')
+        raise ValueError(message)
+
+    if table.size == 0:
+        raise ValueError("`table` must have at least one row and one column.")
+
+    if table.shape[0] == 1 or table.shape[1] == 1 or np.all(table == 0):
+        # Only one such table with those marginals
+        return SignificanceResult(1.0, 1.0)
+
+    if method is None:
+        method = stats.MonteCarloMethod()
+
+    if isinstance(method, stats.PermutationMethod):
+        res = _fisher_exact_permutation_method(table, method)
+    elif isinstance(method, stats.MonteCarloMethod):
+        res = _fisher_exact_monte_carlo_method(table, method)
+    else:
+        message = (f'`{method=}` not recognized; if provided, `method` must be an '
+                   'instance of `PermutationMethod` or `MonteCarloMethod`.')
+        raise ValueError(message)
+
+    return SignificanceResult(np.clip(res.statistic, None, 1.0), res.pvalue)
+
+
+def _fisher_exact_permutation_method(table, method):
+    x, y = _untabulate(table)
+    colsums = np.sum(table, axis=0)
+    rowsums = np.sum(table, axis=1)
+    X = stats.random_table(rowsums, colsums)
+
+    # `permutation_test` with `permutation_type='pairings' permutes the order of `x`,
+    # which pairs observations in `x` with different observations in `y`.
+    def statistic(x):
+        # crosstab the resample and compute the statistic
+        table = stats.contingency.crosstab(x, y)[1]
+        return X.pmf(table)
+
+    # tables with *smaller* probability mass are considered to be more extreme
+    return stats.permutation_test((x,), statistic, permutation_type='pairings',
+                                  alternative='less', **method._asdict())
+
+
+def _fisher_exact_monte_carlo_method(table, method):
+    method = method._asdict()
+
+    if method.pop('rvs', None) is not None:
+        message = ('If the `method` argument of `fisher_exact` is an '
+                   'instance of `MonteCarloMethod`, its `rvs` attribute '
+                   'must be unspecified. Use the `MonteCarloMethod` `rng` argument '
+                   'to control the random state.')
+        raise ValueError(message)
+    rng = np.random.default_rng(method.pop('rng', None))
+
+    # `random_table.rvs` produces random contingency tables with the given marginals
+    # under the null hypothesis of independence
+    shape = table.shape
+    colsums = np.sum(table, axis=0)
+    rowsums = np.sum(table, axis=1)
+    totsum = np.sum(table)
+    X = stats.random_table(rowsums, colsums, seed=rng)
+
+    def rvs(size):
+        n_resamples = size[0]
+        return X.rvs(size=n_resamples).reshape(size)
+
+    # axis signals to `monte_carlo_test` that statistic is vectorized, but we know
+    # how it will pass the table(s), so we don't need to use `axis` explicitly.
+    def statistic(table, axis):
+        shape_ = (-1,) + shape if table.size > totsum else shape
+        return X.pmf(table.reshape(shape_))
+
+    # tables with *smaller* probability mass are considered to be more extreme
+    return stats.monte_carlo_test(table.ravel(), rvs, statistic,
+                                  alternative='less', **method)
+
+
+def _untabulate(table):
+    # converts a contingency table to paired samples indicating the
+    # correspondence between row and column indices
+    r, c = table.shape
+    x, y = [], []
+    for i in range(r):
+        for j in range(c):
+            x.append([i] * table[i, j])
+            y.append([j] * table[i, j])
+    return np.concatenate(x), np.concatenate(y)
+
+
+@xp_capabilities(np_only=True)
+def spearmanr(a, b=None, axis=0, nan_policy='propagate',
+              alternative='two-sided'):
+    r"""Calculate a Spearman correlation coefficient with associated p-value.
+
+    The Spearman rank-order correlation coefficient is a nonparametric measure
+    of the monotonicity of the relationship between two datasets.
+    Like other correlation coefficients,
+    this one varies between -1 and +1 with 0 implying no correlation.
+    Correlations of -1 or +1 imply an exact monotonic relationship. Positive
+    correlations imply that as x increases, so does y. Negative correlations
+    imply that as x increases, y decreases.
+
+    The p-value roughly indicates the probability of an uncorrelated system
+    producing datasets that have a Spearman correlation at least as extreme
+    as the one computed from these datasets. Although calculation of the
+    p-value does not make strong assumptions about the distributions underlying
+    the samples, it is only accurate for very large samples (>500
+    observations). For smaller sample sizes, consider a permutation test (see
+    Examples section below).
+
+    Parameters
+    ----------
+    a, b : 1D or 2D array_like, b is optional
+        One or two 1-D or 2-D arrays containing multiple variables and
+        observations. When these are 1-D, each represents a vector of
+        observations of a single variable. For the behavior in the 2-D case,
+        see under ``axis``, below.
+        Both arrays need to have the same length in the ``axis`` dimension.
+    axis : int or None, optional
+        If axis=0 (default), then each column represents a variable, with
+        observations in the rows. If axis=1, the relationship is transposed:
+        each row represents a variable, while the columns contain observations.
+        If axis=None, then both arrays will be raveled.
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains nan.
+        The following options are available (default is 'propagate'):
+
+        * 'propagate': returns nan
+        * 'raise': throws an error
+        * 'omit': performs the calculations ignoring nan values
+
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis. Default is 'two-sided'.
+        The following options are available:
+
+        * 'two-sided': the correlation is nonzero
+        * 'less': the correlation is negative (less than zero)
+        * 'greater':  the correlation is positive (greater than zero)
+
+        .. versionadded:: 1.7.0
+
+    Returns
+    -------
+    res : SignificanceResult
+        An object containing attributes:
+
+        statistic : float or ndarray (2-D square)
+            Spearman correlation matrix or correlation coefficient (if only 2
+            variables are given as parameters). Correlation matrix is square
+            with length equal to total number of variables (columns or rows) in
+            ``a`` and ``b`` combined.
+        pvalue : float
+            The p-value for a hypothesis test whose null hypothesis
+            is that two samples have no ordinal correlation. See
+            `alternative` above for alternative hypotheses. `pvalue` has the
+            same shape as `statistic`.
+
+    Raises
+    ------
+    ValueError
+        If `axis` is not 0, 1 or None, or if the number of dimensions of `a`
+        is greater than 2, or if `b` is None and the number of dimensions of
+        `a` is less than 2.
+
+    Warns
+    -----
+    `~scipy.stats.ConstantInputWarning`
+        Raised if an input is a constant array.  The correlation coefficient
+        is not defined in this case, so ``np.nan`` is returned.
+
+    See Also
+    --------
+    :ref:`hypothesis_spearmanr` : Extended example
+
+    References
+    ----------
+    .. [1] Zwillinger, D. and Kokoska, S. (2000). CRC Standard
+       Probability and Statistics Tables and Formulae. Chapman & Hall: New
+       York. 2000.
+       Section  14.7
+    .. [2] Kendall, M. G. and Stuart, A. (1973).
+       The Advanced Theory of Statistics, Volume 2: Inference and Relationship.
+       Griffin. 1973.
+       Section 31.18
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> res = stats.spearmanr([1, 2, 3, 4, 5], [5, 6, 7, 8, 7])
+    >>> res.statistic
+    0.8207826816681233
+    >>> res.pvalue
+    0.08858700531354381
+
+    >>> rng = np.random.default_rng()
+    >>> x2n = rng.standard_normal((100, 2))
+    >>> y2n = rng.standard_normal((100, 2))
+    >>> res = stats.spearmanr(x2n)
+    >>> res.statistic, res.pvalue
+    (-0.07960396039603959, 0.4311168705769747)
+
+    >>> res = stats.spearmanr(x2n[:, 0], x2n[:, 1])
+    >>> res.statistic, res.pvalue
+    (-0.07960396039603959, 0.4311168705769747)
+
+    >>> res = stats.spearmanr(x2n, y2n)
+    >>> res.statistic
+    array([[ 1. , -0.07960396, -0.08314431, 0.09662166],
+           [-0.07960396, 1. , -0.14448245, 0.16738074],
+           [-0.08314431, -0.14448245, 1. , 0.03234323],
+           [ 0.09662166, 0.16738074, 0.03234323, 1. ]])
+    >>> res.pvalue
+    array([[0. , 0.43111687, 0.41084066, 0.33891628],
+           [0.43111687, 0. , 0.15151618, 0.09600687],
+           [0.41084066, 0.15151618, 0. , 0.74938561],
+           [0.33891628, 0.09600687, 0.74938561, 0. ]])
+
+    >>> res = stats.spearmanr(x2n.T, y2n.T, axis=1)
+    >>> res.statistic
+    array([[ 1. , -0.07960396, -0.08314431, 0.09662166],
+           [-0.07960396, 1. , -0.14448245, 0.16738074],
+           [-0.08314431, -0.14448245, 1. , 0.03234323],
+           [ 0.09662166, 0.16738074, 0.03234323, 1. ]])
+
+    >>> res = stats.spearmanr(x2n, y2n, axis=None)
+    >>> res.statistic, res.pvalue
+    (0.044981624540613524, 0.5270803651336189)
+
+    >>> res = stats.spearmanr(x2n.ravel(), y2n.ravel())
+    >>> res.statistic, res.pvalue
+    (0.044981624540613524, 0.5270803651336189)
+
+    >>> rng = np.random.default_rng()
+    >>> xint = rng.integers(10, size=(100, 2))
+    >>> res = stats.spearmanr(xint)
+    >>> res.statistic, res.pvalue
+    (0.09800224850707953, 0.3320271757932076)
+
+    For small samples, consider performing a permutation test instead of
+    relying on the asymptotic p-value. Note that to calculate the null
+    distribution of the statistic (for all possibly pairings between
+    observations in sample ``x`` and ``y``), only one of the two inputs needs
+    to be permuted.
+
+    >>> x = [1.76405235, 0.40015721, 0.97873798,
+    ... 2.2408932, 1.86755799, -0.97727788]
+    >>> y = [2.71414076, 0.2488, 0.87551913,
+    ... 2.6514917, 2.01160156, 0.47699563]
+
+    >>> def statistic(x): # permute only `x`
+    ...     return stats.spearmanr(x, y).statistic
+    >>> res_exact = stats.permutation_test((x,), statistic,
+    ...     permutation_type='pairings')
+    >>> res_asymptotic = stats.spearmanr(x, y)
+    >>> res_exact.pvalue, res_asymptotic.pvalue # asymptotic pvalue is too low
+    (0.10277777777777777, 0.07239650145772594)
+
+    For a more detailed example, see :ref:`hypothesis_spearmanr`.
+    """
+    if axis is not None and axis > 1:
+        raise ValueError("spearmanr only handles 1-D or 2-D arrays, "
+                         f"supplied axis argument {axis}, please use only "
+                         "values 0, 1 or None for axis")
+
+    a, axisout = _chk_asarray(a, axis)
+    if a.ndim > 2:
+        raise ValueError("spearmanr only handles 1-D or 2-D arrays")
+
+    if b is None:
+        if a.ndim < 2:
+            raise ValueError("`spearmanr` needs at least 2 "
+                             "variables to compare")
+    else:
+        # Concatenate a and b, so that we now only have to handle the case
+        # of a 2-D `a`.
+        b, _ = _chk_asarray(b, axis)
+        if axisout == 0:
+            a = np.column_stack((a, b))
+        else:
+            a = np.vstack((a, b))
+
+    n_vars = a.shape[1 - axisout]
+    n_obs = a.shape[axisout]
+    if n_obs <= 1:
+        # Handle empty arrays or single observations.
+        res = SignificanceResult(np.nan, np.nan)
+        res.correlation = np.nan
+        return res
+
+    warn_msg = ("An input array is constant; the correlation coefficient "
+                "is not defined.")
+
+    constant_axis = False
+    if axisout == 0:
+        constant_columns = np.all(a == a[0, :], axis=0)
+        constant_axis = np.any(constant_columns)
+        if constant_axis:
+            # If an input is constant, the correlation coefficient
+            # is not defined.
+            warnings.warn(stats.ConstantInputWarning(warn_msg), stacklevel=2)
+    else:  # case when axisout == 1 b/c a is 2 dim only
+        constant_rows = np.all(a.T == a.T[0, :], axis=0)
+        constant_axis = np.any(constant_rows)
+        if constant_axis:
+            # If an input is constant, the correlation coefficient
+            # is not defined.
+            warnings.warn(stats.ConstantInputWarning(warn_msg), stacklevel=2)
+
+    a_contains_nan = _contains_nan(a, nan_policy)
+    variable_has_nan = np.zeros(n_vars, dtype=bool)
+    if a_contains_nan:
+        if nan_policy == 'omit':
+            return mstats_basic.spearmanr(a, axis=axis, nan_policy=nan_policy,
+                                          alternative=alternative)
+        elif nan_policy == 'propagate':
+            if a.ndim == 1 or n_vars <= 2:
+                res = SignificanceResult(np.nan, np.nan)
+                res.correlation = np.nan
+                return res
+            else:
+                # Keep track of variables with NaNs, set the outputs to NaN
+                # only for those variables
+                variable_has_nan = np.isnan(a).any(axis=axisout)
+
+    a_ranked = np.apply_along_axis(rankdata, axisout, a)
+
+    if constant_axis:
+        with np.errstate(invalid='ignore'):
+            rs = np.corrcoef(a_ranked, rowvar=axisout)
+    else:
+        rs = np.corrcoef(a_ranked, rowvar=axisout)
+
+    dof = n_obs - 2  # degrees of freedom
+
+    # rs can have elements equal to 1, so avoid zero division warnings
+    with np.errstate(divide='ignore'):
+        # clip the small negative values possibly caused by rounding
+        # errors before taking the square root
+        t = rs * np.sqrt((dof/((rs+1.0)*(1.0-rs))).clip(0))
+
+    dist = _SimpleStudentT(dof)
+    prob = _get_pvalue(t, dist, alternative, xp=np)
+
+    # For backwards compatibility, return scalars when comparing 2 columns
+    if rs.shape == (2, 2):
+        res = SignificanceResult(rs[1, 0], prob[1, 0])
+        res.correlation = rs[1, 0]
+        return res
+    else:
+        rs[variable_has_nan, :] = np.nan
+        rs[:, variable_has_nan] = np.nan
+        res = SignificanceResult(rs[()], prob[()])
+        res.correlation = rs
+        return res
+
+
+@xp_capabilities(cpu_only=True, exceptions=['cupy', 'jax.numpy'], marray=True)
+@_axis_nan_policy_factory(_pack_CorrelationResult, n_samples=2,
+                          result_to_tuple=_unpack_CorrelationResult, paired=True,
+                          too_small=1, n_outputs=3)
+def pointbiserialr(x, y, *, axis=0):
+    r"""Calculate a point biserial correlation coefficient and its p-value.
+
+    The point biserial correlation is used to measure the relationship
+    between a binary variable, x, and a continuous variable, y. Like other
+    correlation coefficients, this one varies between -1 and +1 with 0
+    implying no correlation. Correlations of -1 or +1 imply a determinative
+    relationship.
+
+    This function may be computed using a shortcut formula but produces the
+    same result as `pearsonr`.
+
+    Parameters
+    ----------
+    x : array_like of bools
+        Input array.
+    y : array_like
+        Input array.
+    axis : int or None, default: 0
+        Axis along which to perform the calculation. Default is 0.
+        If None, ravel both arrays before performing the calculation.
+
+    Returns
+    -------
+    res: SignificanceResult
+        An object containing attributes:
+
+        statistic : float
+            The R value.
+        pvalue : float
+            The two-sided p-value.
+
+    Notes
+    -----
+    `pointbiserialr` uses a t-test with ``n-1`` degrees of freedom.
+    It is equivalent to `pearsonr`.
+
+    The value of the point-biserial correlation can be calculated from:
+
+    .. math::
+
+        r_{pb} = \frac{\overline{Y_1} - \overline{Y_0}}
+                      {s_y}
+                 \sqrt{\frac{N_0 N_1}
+                            {N (N - 1)}}
+
+    Where :math:`\overline{Y_{0}}` and :math:`\overline{Y_{1}}` are means
+    of the metric observations coded 0 and 1 respectively; :math:`N_{0}` and
+    :math:`N_{1}` are number of observations coded 0 and 1 respectively;
+    :math:`N` is the total number of observations and :math:`s_{y}` is the
+    standard deviation of all the metric observations.
+
+    A value of :math:`r_{pb}` that is significantly different from zero is
+    completely equivalent to a significant difference in means between the two
+    groups. Thus, an independent groups t Test with :math:`N-2` degrees of
+    freedom may be used to test whether :math:`r_{pb}` is nonzero. The
+    relation between the t-statistic for comparing two independent groups and
+    :math:`r_{pb}` is given by:
+
+    .. math::
+
+        t = \sqrt{N - 2}\frac{r_{pb}}{\sqrt{1 - r^{2}_{pb}}}
+
+    References
+    ----------
+    .. [1] J. Lev, "The Point Biserial Coefficient of Correlation", Ann. Math.
+           Statist., Vol. 20, no.1, pp. 125-126, 1949.
+
+    .. [2] R.F. Tate, "Correlation Between a Discrete and a Continuous
+           Variable. Point-Biserial Correlation.", Ann. Math. Statist., Vol. 25,
+           np. 3, pp. 603-607, 1954.
+
+    .. [3] D. Kornbrot "Point Biserial Correlation", In Wiley StatsRef:
+           Statistics Reference Online (eds N. Balakrishnan, et al.), 2014.
+           :doi:`10.1002/9781118445112.stat06227`
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> a = np.array([0, 0, 0, 1, 1, 1, 1])
+    >>> b = np.arange(7)
+    >>> stats.pointbiserialr(a, b)
+    (0.8660254037844386, 0.011724811003954652)
+    >>> stats.pearsonr(a, b)
+    (0.86602540378443871, 0.011724811003954626)
+    >>> np.corrcoef(a, b)
+    array([[ 1.       ,  0.8660254],
+           [ 0.8660254,  1.       ]])
+
+    """
+    rpb, prob = pearsonr(x, y, axis=axis)
+    # create result object with alias for backward compatibility
+    res = SignificanceResult(rpb, prob)
+    res.correlation = rpb
+    return res
+
+
+@xp_capabilities(cpu_only=True, jax_jit=False, allow_dask_compute=2,
+                 marray=True, extra_note=("`nan_policy='propagate'` is "
+                                          "incompatible with MArray input."))
+def kendalltau(x, y, *, nan_policy='propagate', method='auto', variant='b',
+               alternative='two-sided', axis=None, keepdims=False):
+    r"""Calculate Kendall's tau, a correlation measure for ordinal data.
+
+    Kendall's tau is a measure of the correspondence between two rankings.
+    Values close to 1 indicate strong agreement, and values close to -1
+    indicate strong disagreement. This implements two variants of Kendall's
+    tau: tau-b (the default) and tau-c (also known as Stuart's tau-c). These
+    differ only in how they are normalized to lie within the range -1 to 1;
+    the hypothesis tests (their p-values) are identical. Kendall's original
+    tau-a is not implemented separately because both tau-b and tau-c reduce
+    to tau-a in the absence of ties.
+
+    Although a naive implementation has O(n^2) complexity, this implementation
+    uses a Fenwick tree to do the computation in O(n log(n)) complexity.
+
+    Parameters
+    ----------
+    x, y : array_like
+        Arrays of rankings, of the same shape. If arrays are not 1-D, they
+        will be flattened to 1-D.
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains nan.
+        The following options are available (default is 'propagate'):
+
+        * 'propagate': returns nan
+        * 'raise': throws an error
+        * 'omit': performs the calculations ignoring nan values
+
+    method : {'auto', 'asymptotic', 'exact'}, optional
+        Defines which method is used to calculate the p-value [5]_.
+        The following options are available (default is 'auto'):
+
+        * 'auto': selects the appropriate method based on a trade-off
+          between speed and accuracy
+        * 'asymptotic': uses a normal approximation valid for large samples
+        * 'exact': computes the exact p-value, but can only be used if no ties
+          are present. As the sample size increases, the 'exact' computation
+          time may grow and the result may lose some precision.
+
+    variant : {'b', 'c'}, optional
+        Defines which variant of Kendall's tau is returned. Default is 'b'.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis. Default is 'two-sided'.
+        The following options are available:
+
+        * 'two-sided': the rank correlation is nonzero
+        * 'less': the rank correlation is negative (less than zero)
+        * 'greater': the rank correlation is positive (greater than zero)
+    axis : int or None, default: None
+        If an int, the axis of the input along which to compute the statistic.
+        The statistic of each axis-slice (e.g. row) of the input will appear in a
+        corresponding element of the output.
+        If ``None``, the input will be raveled before computing the statistic.
+    keepdims : bool, optional
+        If this is set to ``True``, the axes which are reduced are left
+        in the result as dimensions with length one. With this option,
+        the result will broadcast correctly against the input array.
+
+    Returns
+    -------
+    res : SignificanceResult
+        An object containing attributes:
+
+        statistic : float
+           The tau statistic.
+        pvalue : float
+           The p-value for a hypothesis test whose null hypothesis is
+           an absence of association, tau = 0.
+
+    Raises
+    ------
+    ValueError
+        If `nan_policy` is 'omit' and `variant` is not 'b' or
+        if `method` is 'exact' and there are ties between `x` and `y`.
+
+    See Also
+    --------
+    spearmanr : Calculates a Spearman rank-order correlation coefficient.
+    theilslopes : Computes the Theil-Sen estimator for a set of points (x, y).
+    weightedtau : Computes a weighted version of Kendall's tau.
+    :ref:`hypothesis_kendalltau` : Extended example
+
+    Notes
+    -----
+    The definition of Kendall's tau that is used is [2]_::
+
+      tau_b = (P - Q) / sqrt((P + Q + T) * (P + Q + U))
+
+      tau_c = 2 (P - Q) / (n**2 * (m - 1) / m)
+
+    where P is the number of concordant pairs, Q the number of discordant
+    pairs, T the number of tied pairs only in `x`, and U the number of tied pairs only
+    in `y`.  If a tie occurs for the same pair in both `x` and `y`, it is not
+    added to either T or U. n is the total number of samples, and m is the
+    number of unique values in either `x` or `y`, whichever is smaller.
+
+    References
+    ----------
+    .. [1] Maurice G. Kendall, "A New Measure of Rank Correlation", Biometrika
+           Vol. 30, No. 1/2, pp. 81-93, 1938.
+    .. [2] Maurice G. Kendall, "The treatment of ties in ranking problems",
+           Biometrika Vol. 33, No. 3, pp. 239-251. 1945.
+    .. [3] Gottfried E. Noether, "Elements of Nonparametric Statistics", John
+           Wiley & Sons, 1967.
+    .. [4] Peter M. Fenwick, "A new data structure for cumulative frequency
+           tables", Software: Practice and Experience, Vol. 24, No. 3,
+           pp. 327-336, 1994.
+    .. [5] Maurice G. Kendall, "Rank Correlation Methods" (4th Edition),
+           Charles Griffin & Co., 1970.
+
+    Examples
+    --------
+
+    >>> from scipy import stats
+    >>> x1 = [12, 2, 1, 12, 2]
+    >>> x2 = [1, 4, 7, 1, 0]
+    >>> res = stats.kendalltau(x1, x2)
+    >>> res.statistic
+    -0.47140452079103173
+    >>> res.pvalue
+    0.2827454599327748
+
+    For a more detailed example, see :ref:`hypothesis_kendalltau`.
+    """
+    xp = array_namespace(x, y)
+    x, y = xp_promote(x, y, force_floating=True, xp=xp)
+    dtype = x.dtype
+    if is_marray(xp):
+        mask_x, mask_y = np.asarray(x.mask), np.asarray(y.mask)
+        x, y = np.asarray(x.data).copy(), np.asarray(y.data).copy()
+        unmasked_nans = np.any(np.isnan(x[~mask_x])) | np.any(np.isnan(y[~mask_y]))
+        if unmasked_nans:
+            if nan_policy == 'propagate':
+                message = "`nan_policy='propagate'` is incompatible with MArray input."
+            elif nan_policy == 'raise':
+                message = "The input contains nan values."
+            raise ValueError(message)
+        nan_policy = 'omit'
+        x[mask_x], y[mask_y] = np.nan, np.nan
+    else:
+        x, y = _asarray(x, subok=True, xp=np), _asarray(y, subok=True, xp=np)
+    res = _kendalltau(x, y, nan_policy=nan_policy, method=method, variant=variant,
+                      alternative=alternative, axis=axis, keepdims=keepdims)
+    vals = res.statistic, res.pvalue, res.statistic
+    vals = (xp.asarray(val, dtype=dtype)[()] if val.ndim == 0
+            else xp.asarray(val, dtype=dtype) for val in vals)
+    return _pack_CorrelationResult(*vals)
+
+
+@_axis_nan_policy_factory(_pack_CorrelationResult, default_axis=None, n_samples=2,
+                          result_to_tuple=_unpack_CorrelationResult, paired=True,
+                          too_small=1, n_outputs=3)
+def _kendalltau(x, y, *, method='auto', variant='b', alternative='two-sided'):
+    x = np.asarray(x).ravel()
+    y = np.asarray(y).ravel()
+
+    if x.size != y.size:
+        raise ValueError("Array shapes are incompatible for broadcasting.")
+    elif not x.size or not y.size:
+        # Return NaN if arrays are empty
+        NaN = _get_nan(x, y)
+        res = SignificanceResult(NaN, NaN)
+        res.correlation = NaN
+        return res
+
+    def count_rank_tie(ranks):
+        cnt = np.bincount(ranks).astype('int64', copy=False)
+        cnt = cnt[cnt > 1]
+        # Python ints to avoid overflow down the line
+        return (int((cnt * (cnt - 1) // 2).sum()),
+                int((cnt * (cnt - 1.) * (cnt - 2)).sum()),
+                int((cnt * (cnt - 1.) * (2*cnt + 5)).sum()))
+
+    size = x.size
+    perm = np.argsort(y)  # sort on y and convert y to dense ranks
+    x, y = x[perm], y[perm]
+    y = np.r_[True, y[1:] != y[:-1]].cumsum(dtype=np.intp)
+
+    # stable sort on x and convert x to dense ranks
+    perm = np.argsort(x, kind='mergesort')
+    x, y = x[perm], y[perm]
+    x = np.r_[True, x[1:] != x[:-1]].cumsum(dtype=np.intp)
+
+    dis = _kendall_dis(x, y)  # discordant pairs
+
+    obs = np.r_[True, (x[1:] != x[:-1]) | (y[1:] != y[:-1]), True]
+    cnt = np.diff(np.nonzero(obs)[0]).astype('int64', copy=False)
+
+    ntie = int((cnt * (cnt - 1) // 2).sum())  # joint ties
+    xtie, x0, x1 = count_rank_tie(x)     # ties in x, stats
+    ytie, y0, y1 = count_rank_tie(y)     # ties in y, stats
+
+    tot = (size * (size - 1)) // 2
+
+    if xtie == tot or ytie == tot:
+        NaN = _get_nan(x, y)
+        res = SignificanceResult(NaN, NaN)
+        res.correlation = NaN
+        return res
+
+    # Note that tot = con + dis + (xtie - ntie) + (ytie - ntie) + ntie
+    #               = con + dis + xtie + ytie - ntie
+    con_minus_dis = tot - xtie - ytie + ntie - 2 * dis
+    if variant == 'b':
+        tau = con_minus_dis / np.sqrt(tot - xtie) / np.sqrt(tot - ytie)
+    elif variant == 'c':
+        minclasses = min(len(set(x)), len(set(y)))
+        tau = 2*con_minus_dis / (size**2 * (minclasses-1)/minclasses)
+    else:
+        raise ValueError(f"Unknown `variant` '{variant}' specified. "
+                         "`variant` must be 'b' or 'c'.")
+
+    # Limit range to fix computational errors
+    tau = np.minimum(1., max(-1., tau))
+
+    # The p-value calculation is the same for all variants since the p-value
+    # depends only on con_minus_dis.
+    if method == 'exact' and (xtie != 0 or ytie != 0):
+        raise ValueError("Ties found; exact method cannot be used.")
+
+    if method == 'auto':
+        if (xtie == 0 and ytie == 0) and (size <= 33 or
+                                          min(dis, tot-dis) <= 1):
+            method = 'exact'
+        else:
+            method = 'asymptotic'
+
+    if xtie == 0 and ytie == 0 and method == 'exact':
+        pvalue = mstats_basic._kendall_p_exact(size, tot-dis, alternative)
+    elif method == 'asymptotic':
+        # con_minus_dis is approx normally distributed with this variance [3]_
+        m = size * (size - 1.)
+        var = ((m * (2*size + 5) - x1 - y1) / 18 +
+               (2 * xtie * ytie) / m + x0 * y0 / (9 * m * (size - 2)))
+        z = con_minus_dis / np.sqrt(var)
+        pvalue = _get_pvalue(z, _SimpleNormal(), alternative, xp=np)
+    else:
+        raise ValueError(f"Unknown `method` '{method}' specified.  `method` must be"
+                         "'auto', 'exact' or 'asymptotic'.")
+
+    # create result object with alias for backward compatibility
+    res = SignificanceResult(tau[()], pvalue[()])
+    res.correlation = tau[()]
+    return res
+
+
+def _weightedtau_n_samples(kwargs):
+    rank = kwargs.get('rank', False)
+    return 2 if (isinstance(rank, bool) or rank is None) else 3
+
+
+@xp_capabilities(np_only=True)
+@_axis_nan_policy_factory(_pack_CorrelationResult, default_axis=None,
+                          n_samples=_weightedtau_n_samples,
+                          result_to_tuple=_unpack_CorrelationResult, paired=True,
+                          too_small=1, n_outputs=3, override={'nan_propagation': False})
+def weightedtau(x, y, rank=True, weigher=None, additive=True):
+    r"""Compute a weighted version of Kendall's :math:`\tau`.
+
+    The weighted :math:`\tau` is a weighted version of Kendall's
+    :math:`\tau` in which exchanges of high weight are more influential than
+    exchanges of low weight. The default parameters compute the additive
+    hyperbolic version of the index, :math:`\tau_\mathrm h`, which has
+    been shown to provide the best balance between important and
+    unimportant elements [1]_.
+
+    The weighting is defined by means of a rank array, which assigns a
+    nonnegative rank to each element (higher importance ranks being
+    associated with smaller values, e.g., 0 is the highest possible rank),
+    and a weigher function, which assigns a weight based on the rank to
+    each element. The weight of an exchange is then the sum or the product
+    of the weights of the ranks of the exchanged elements. The default
+    parameters compute :math:`\tau_\mathrm h`: an exchange between
+    elements with rank :math:`r` and :math:`s` (starting from zero) has
+    weight :math:`1/(r+1) + 1/(s+1)`.
+
+    Specifying a rank array is meaningful only if you have in mind an
+    external criterion of importance. If, as it usually happens, you do
+    not have in mind a specific rank, the weighted :math:`\tau` is
+    defined by averaging the values obtained using the decreasing
+    lexicographical rank by (`x`, `y`) and by (`y`, `x`). This is the
+    behavior with default parameters. Note that the convention used
+    here for ranking (lower values imply higher importance) is opposite
+    to that used by other SciPy statistical functions.
+
+    Parameters
+    ----------
+    x, y : array_like
+        Arrays of scores, of the same shape. If arrays are not 1-D, they will
+        be flattened to 1-D.
+    rank : array_like of ints or bool, optional
+        A nonnegative rank assigned to each element. If it is None, the
+        decreasing lexicographical rank by (`x`, `y`) will be used: elements of
+        higher rank will be those with larger `x`-values, using `y`-values to
+        break ties (in particular, swapping `x` and `y` will give a different
+        result). If it is False, the element indices will be used
+        directly as ranks. The default is True, in which case this
+        function returns the average of the values obtained using the
+        decreasing lexicographical rank by (`x`, `y`) and by (`y`, `x`).
+    weigher : callable, optional
+        The weigher function. Must map nonnegative integers (zero
+        representing the most important element) to a nonnegative weight.
+        The default, None, provides hyperbolic weighing, that is,
+        rank :math:`r` is mapped to weight :math:`1/(r+1)`.
+    additive : bool, optional
+        If True, the weight of an exchange is computed by adding the
+        weights of the ranks of the exchanged elements; otherwise, the weights
+        are multiplied. The default is True.
+
+    Returns
+    -------
+    res: SignificanceResult
+        An object containing attributes:
+
+        statistic : float
+           The weighted :math:`\tau` correlation index.
+        pvalue : float
+           Presently ``np.nan``, as the null distribution of the statistic is
+           unknown (even in the additive hyperbolic case).
+
+    See Also
+    --------
+    kendalltau : Calculates Kendall's tau.
+    spearmanr : Calculates a Spearman rank-order correlation coefficient.
+    theilslopes : Computes the Theil-Sen estimator for a set of points (x, y).
+
+    Notes
+    -----
+    This function uses an :math:`O(n \log n)`, mergesort-based algorithm
+    [1]_ that is a weighted extension of Knight's algorithm for Kendall's
+    :math:`\tau` [2]_. It can compute Shieh's weighted :math:`\tau` [3]_
+    between rankings without ties (i.e., permutations) by setting
+    `additive` and `rank` to False, as the definition given in [1]_ is a
+    generalization of Shieh's.
+
+    NaNs are considered the smallest possible score.
+
+    .. versionadded:: 0.19.0
+
+    References
+    ----------
+    .. [1] Sebastiano Vigna, "A weighted correlation index for rankings with
+           ties", Proceedings of the 24th international conference on World
+           Wide Web, pp. 1166-1176, ACM, 2015.
+    .. [2] W.R. Knight, "A Computer Method for Calculating Kendall's Tau with
+           Ungrouped Data", Journal of the American Statistical Association,
+           Vol. 61, No. 314, Part 1, pp. 436-439, 1966.
+    .. [3] Grace S. Shieh. "A weighted Kendall's tau statistic", Statistics &
+           Probability Letters, Vol. 39, No. 1, pp. 17-24, 1998.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> x = [12, 2, 1, 12, 2]
+    >>> y = [1, 4, 7, 1, 0]
+    >>> res = stats.weightedtau(x, y)
+    >>> res.statistic
+    -0.56694968153682723
+    >>> res.pvalue
+    nan
+    >>> res = stats.weightedtau(x, y, additive=False)
+    >>> res.statistic
+    -0.62205716951801038
+
+    NaNs are considered the smallest possible score:
+
+    >>> x = [12, 2, 1, 12, 2]
+    >>> y = [1, 4, 7, 1, np.nan]
+    >>> res = stats.weightedtau(x, y)
+    >>> res.statistic
+    -0.56694968153682723
+
+    This is exactly Kendall's tau:
+
+    >>> x = [12, 2, 1, 12, 2]
+    >>> y = [1, 4, 7, 1, 0]
+    >>> res = stats.weightedtau(x, y, weigher=lambda x: 1)
+    >>> res.statistic
+    -0.47140452079103173
+
+    >>> x = [12, 2, 1, 12, 2]
+    >>> y = [1, 4, 7, 1, 0]
+    >>> stats.weightedtau(x, y, rank=None)
+    SignificanceResult(statistic=-0.4157652301037516, pvalue=nan)
+    >>> stats.weightedtau(y, x, rank=None)
+    SignificanceResult(statistic=-0.7181341329699028, pvalue=nan)
+
+    """
+    x = np.asarray(x).ravel()
+    y = np.asarray(y).ravel()
+    NaN = _get_nan(x, y)
+
+    if x.size != y.size:
+        raise ValueError("Array shapes are incompatible for broadcasting.")
+    if not x.size:
+        # Return NaN if arrays are empty
+        res = SignificanceResult(NaN, NaN)
+        res.correlation = NaN
+        return res
+
+    # If there are NaNs we apply _toint64()
+    if np.isnan(np.sum(x)):
+        x = _toint64(x)
+    if np.isnan(np.sum(y)):
+        y = _toint64(y)
+
+    # Reduce to ranks unsupported types
+    if x.dtype != y.dtype:
+        if x.dtype != np.int64:
+            x = _toint64(x)
+        if y.dtype != np.int64:
+            y = _toint64(y)
+    else:
+        if x.dtype not in (np.int32, np.int64, np.float32, np.float64):
+            x = _toint64(x)
+            y = _toint64(y)
+
+    if rank is True:
+        tau = np.asarray(
+            _weightedrankedtau(x, y, None, weigher, additive) +
+            _weightedrankedtau(y, x, None, weigher, additive)
+        )[()] / 2
+        res = SignificanceResult(tau, NaN)
+        res.correlation = tau
+        return res
+
+    if rank is False:
+        rank = np.arange(x.size, dtype=np.intp)
+    elif rank is not None:
+        rank = np.asarray(rank).ravel()
+        rank = _toint64(rank).astype(np.intp)
+        if rank.size != x.size:
+            raise ValueError(
+                "All inputs to `weightedtau` must be of the same size, "
+                f"found x-size {x.size} and rank-size {rank.size}"
+            )
+
+    tau = np.asarray(_weightedrankedtau(x, y, rank, weigher, additive))[()]
+    res = SignificanceResult(tau, NaN)
+    res.correlation = tau
+    return res
+
+
+#####################################
+#       INFERENTIAL STATISTICS      #
+#####################################
+
+TtestResultBase = _make_tuple_bunch('TtestResultBase',
+                                    ['statistic', 'pvalue'], ['df'])
+
+
+class TtestResult(TtestResultBase):
+    """
+    Result of a t-test.
+
+    See the documentation of the particular t-test function for more
+    information about the definition of the statistic and meaning of
+    the confidence interval.
+
+    Attributes
+    ----------
+    statistic : float or array
+        The t-statistic of the sample.
+    pvalue : float or array
+        The p-value associated with the given alternative.
+    df : float or array
+        The number of degrees of freedom used in calculation of the
+        t-statistic; this is one less than the size of the sample
+        (``a.shape[axis]-1`` if there are no masked elements or omitted NaNs).
+
+    Methods
+    -------
+    confidence_interval
+        Computes a confidence interval around the population statistic
+        for the given confidence level.
+        The confidence interval is returned in a ``namedtuple`` with
+        fields `low` and `high`.
+
+    """
+
+    def __init__(self, statistic, pvalue, df,  # public
+                 alternative, standard_error, estimate,  # private
+                 statistic_np=None, xp=None):  # private
+        super().__init__(statistic, pvalue, df=df)
+        self._alternative = alternative
+        self._standard_error = standard_error  # denominator of t-statistic
+        self._estimate = estimate  # point estimate of sample mean
+        self._statistic_np = statistic if statistic_np is None else statistic_np
+        self._dtype = statistic.dtype
+        self._xp = array_namespace(statistic, pvalue) if xp is None else xp
+
+
+    def confidence_interval(self, confidence_level=0.95):
+        """
+        Parameters
+        ----------
+        confidence_level : float
+            The confidence level for the calculation of the population mean
+            confidence interval. Default is 0.95.
+
+        Returns
+        -------
+        ci : namedtuple
+            The confidence interval is returned in a ``namedtuple`` with
+            fields `low` and `high`.
+
+        """
+        low, high = _t_confidence_interval(self.df, self._statistic_np,
+                                           confidence_level, self._alternative,
+                                           self._dtype, self._xp)
+        low = low * self._standard_error + self._estimate
+        high = high * self._standard_error + self._estimate
+        return ConfidenceInterval(low=low, high=high)
+
+
+def pack_TtestResult(statistic, pvalue, df, alternative, standard_error,
+                     estimate):
+    xp = array_namespace(statistic, pvalue)
+    # Due to behavior of `_axis_nan_policy` decorator, `alternative` can be any number
+    # of dimensions, but there is at most one unique non-NaN value.
+    # `_xp_mean` with `nan_policy='omit'` is a JIT-compatible way to extract it.
+    alternative = xp.asarray(alternative)
+    alternative = (_xp_mean(alternative, axis=None, nan_policy='omit', warn=False)
+                   if xp_size(alternative) != 0 else xp.nan)
+    return TtestResult(statistic, pvalue, df=df, alternative=alternative,
+                       standard_error=standard_error, estimate=estimate)
+
+
+def unpack_TtestResult(res, _):
+    return (res.statistic, res.pvalue, res.df, res._alternative,
+            res._standard_error, res._estimate)
+
+
+@xp_capabilities(cpu_only=True, exceptions=["cupy", "jax.numpy"], marray=True,
+                 extra_note=("The ``confidence_interval`` method of the output object "
+                             "is incompatible with JAX JIT."))
+@_axis_nan_policy_factory(pack_TtestResult, default_axis=0, n_samples=2,
+                          result_to_tuple=unpack_TtestResult, n_outputs=6)
+# nan_policy handled by `_axis_nan_policy`, but needs to be left
+# in signature to preserve use as a positional argument
+def ttest_1samp(a, popmean, axis=0, nan_policy="propagate", alternative="two-sided"):
+    """Calculate the T-test for the mean of ONE group of scores.
+
+    This is a test for the null hypothesis that the expected value
+    (mean) of a sample of independent observations `a` is equal to the given
+    population mean, `popmean`.
+
+    Parameters
+    ----------
+    a : array_like
+        Sample observations.
+    popmean : float or array_like
+        Expected value in null hypothesis. If array_like, then its length along
+        `axis` must equal 1, and it must otherwise be broadcastable with `a`.
+    axis : int or None, optional
+        Axis along which to compute test; default is 0. If None, compute over
+        the whole array `a`.
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains nan.
+        The following options are available (default is 'propagate'):
+
+        * 'propagate': returns nan
+        * 'raise': throws an error
+        * 'omit': performs the calculations ignoring nan values
+
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis.
+        The following options are available (default is 'two-sided'):
+
+        * 'two-sided': the mean of the underlying distribution of the sample
+          is different than the given population mean (`popmean`)
+        * 'less': the mean of the underlying distribution of the sample is
+          less than the given population mean (`popmean`)
+        * 'greater': the mean of the underlying distribution of the sample is
+          greater than the given population mean (`popmean`)
+
+    Returns
+    -------
+    result : `~scipy.stats._result_classes.TtestResult`
+        An object with the following attributes:
+
+        statistic : float or array
+            The t-statistic.
+        pvalue : float or array
+            The p-value associated with the given alternative.
+        df : float or array
+            The number of degrees of freedom used in calculation of the
+            t-statistic; this is one less than the size of the sample
+            (``a.shape[axis]``).
+
+            .. versionadded:: 1.10.0
+
+        The object also has the following method:
+
+        confidence_interval(confidence_level=0.95)
+            Computes a confidence interval around the population
+            mean for the given confidence level.
+            The confidence interval is returned in a ``namedtuple`` with
+            fields `low` and `high`.
+
+            .. versionadded:: 1.10.0
+
+    Notes
+    -----
+    The statistic is calculated as ``(np.mean(a) - popmean)/se``, where
+    ``se`` is the standard error. Therefore, the statistic will be positive
+    when the sample mean is greater than the population mean and negative when
+    the sample mean is less than the population mean.
+
+    Examples
+    --------
+    Suppose we wish to test the null hypothesis that the mean of a population
+    is equal to 0.5. We choose a confidence level of 99%; that is, we will
+    reject the null hypothesis in favor of the alternative if the p-value is
+    less than 0.01.
+
+    When testing random variates from the standard uniform distribution, which
+    has a mean of 0.5, we expect the data to be consistent with the null
+    hypothesis most of the time.
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> rng = np.random.default_rng()
+    >>> rvs = stats.uniform.rvs(size=50, random_state=rng)
+    >>> stats.ttest_1samp(rvs, popmean=0.5)
+    TtestResult(statistic=2.456308468440, pvalue=0.017628209047638, df=49)
+
+    As expected, the p-value of 0.017 is not below our threshold of 0.01, so
+    we cannot reject the null hypothesis.
+
+    When testing data from the standard *normal* distribution, which has a mean
+    of 0, we would expect the null hypothesis to be rejected.
+
+    >>> rvs = stats.norm.rvs(size=50, random_state=rng)
+    >>> stats.ttest_1samp(rvs, popmean=0.5)
+    TtestResult(statistic=-7.433605518875, pvalue=1.416760157221e-09, df=49)
+
+    Indeed, the p-value is lower than our threshold of 0.01, so we reject the
+    null hypothesis in favor of the default "two-sided" alternative: the mean
+    of the population is *not* equal to 0.5.
+
+    However, suppose we were to test the null hypothesis against the
+    one-sided alternative that the mean of the population is *greater* than
+    0.5. Since the mean of the standard normal is less than 0.5, we would not
+    expect the null hypothesis to be rejected.
+
+    >>> stats.ttest_1samp(rvs, popmean=0.5, alternative='greater')
+    TtestResult(statistic=-7.433605518875, pvalue=0.99999999929, df=49)
+
+    Unsurprisingly, with a p-value greater than our threshold, we would not
+    reject the null hypothesis.
+
+    Note that when working with a confidence level of 99%, a true null
+    hypothesis will be rejected approximately 1% of the time.
+
+    >>> rvs = stats.uniform.rvs(size=(100, 50), random_state=rng)
+    >>> res = stats.ttest_1samp(rvs, popmean=0.5, axis=1)
+    >>> np.sum(res.pvalue < 0.01)
+    1
+
+    Indeed, even though all 100 samples above were drawn from the standard
+    uniform distribution, which *does* have a population mean of 0.5, we would
+    mistakenly reject the null hypothesis for one of them.
+
+    `ttest_1samp` can also compute a confidence interval around the population
+    mean.
+
+    >>> rvs = stats.norm.rvs(size=50, random_state=rng)
+    >>> res = stats.ttest_1samp(rvs, popmean=0)
+    >>> ci = res.confidence_interval(confidence_level=0.95)
+    >>> ci
+    ConfidenceInterval(low=-0.3193887540880017, high=0.2898583388980972)
+
+    The bounds of the 95% confidence interval are the
+    minimum and maximum values of the parameter `popmean` for which the
+    p-value of the test would be 0.05.
+
+    >>> res = stats.ttest_1samp(rvs, popmean=ci.low)
+    >>> np.testing.assert_allclose(res.pvalue, 0.05)
+    >>> res = stats.ttest_1samp(rvs, popmean=ci.high)
+    >>> np.testing.assert_allclose(res.pvalue, 0.05)
+
+    Under certain assumptions about the population from which a sample
+    is drawn, the confidence interval with confidence level 95% is expected
+    to contain the true population mean in 95% of sample replications.
+
+    >>> rvs = stats.norm.rvs(size=(50, 1000), loc=1, random_state=rng)
+    >>> res = stats.ttest_1samp(rvs, popmean=0)
+    >>> ci = res.confidence_interval()
+    >>> contains_pop_mean = (ci.low < 1) & (ci.high > 1)
+    >>> contains_pop_mean.sum()
+    953
+
+    """
+    xp = array_namespace(a)
+    a, popmean = xp_promote(a, popmean, force_floating=True, xp=xp)
+    a, axis = _chk_asarray(a, axis, xp=xp)
+
+    n = _count_nonmasked(a, axis)
+    df = n - 1
+
+    if a.shape[axis] == 0:
+        # This is really only needed for *testing* _axis_nan_policy decorator
+        # It won't happen when the decorator is used.
+        NaN = _get_nan(a)
+        return TtestResult(NaN, NaN, df=NaN, alternative=NaN,
+                           standard_error=NaN, estimate=NaN)
+
+    mean = xp.mean(a, axis=axis)
+    try:
+        popmean = xp.asarray(popmean)
+        popmean = xp.squeeze(popmean, axis=axis) if popmean.ndim > 0 else popmean
+    except ValueError as e:
+        raise ValueError("`popmean.shape[axis]` must equal 1.") from e
+    d = mean - popmean
+    v = _var(a, axis=axis, ddof=1)
+    denom = xp.sqrt(v / n)
+
+    with np.errstate(divide='ignore', invalid='ignore'):
+        t = xp.divide(d, denom)
+        t = t[()] if t.ndim == 0 else t
+
+    dist = _SimpleStudentT(xp.asarray(df, dtype=t.dtype, device=xp_device(a)))
+    prob = _get_pvalue(t, dist, alternative, xp=xp)
+    prob = prob[()] if prob.ndim == 0 else prob
+
+    # when nan_policy='omit', `df` can be different for different axis-slices
+    df = xp.broadcast_to(xp.asarray(df, device=xp_device(a)), t.shape)
+    df = df[()] if df.ndim == 0 else df
+    # _axis_nan_policy decorator doesn't play well with strings
+    alternative_num = {"less": -1, "two-sided": 0, "greater": 1}[alternative]
+    return TtestResult(t, prob, df=df, alternative=alternative_num,
+                       standard_error=denom, estimate=mean,
+                       statistic_np=xp.asarray(t), xp=xp)
+
+
+def _t_confidence_interval(df, t, confidence_level, alternative, dtype=None, xp=None):
+    # Input validation on `alternative` is already done
+    # We just need IV on confidence_level
+    dtype = t.dtype if dtype is None else dtype
+    xp = array_namespace(t) if xp is None else xp
+
+    if confidence_level < 0 or confidence_level > 1:
+        message = "`confidence_level` must be a number between 0 and 1."
+        raise ValueError(message)
+
+    confidence_level = xp.asarray(confidence_level, dtype=dtype, device=xp_device(t))
+    inf = xp.asarray(xp.inf, dtype=dtype)
+
+    if alternative < 0:  # 'less'
+        p = confidence_level
+        low, high = xp.broadcast_arrays(-inf, special.stdtrit(df, p))
+    elif alternative > 0:  # 'greater'
+        p = 1 - confidence_level
+        low, high = xp.broadcast_arrays(special.stdtrit(df, p), inf)
+    elif alternative == 0:  # 'two-sided'
+        tail_probability = (1 - confidence_level)/2
+        p = xp.stack((tail_probability, 1-tail_probability))
+        # axis of p must be the zeroth and orthogonal to all the rest
+        p = xp.reshape(p, tuple([2] + [1]*xp.asarray(df, device=xp_device(t)).ndim))
+        ci = special.stdtrit(df, p)
+        low, high = ci[0, ...], ci[1, ...]
+    else:  # alternative is NaN when input is empty (see _axis_nan_policy)
+        nan = xp.asarray(xp.nan, device=xp_device(t))
+        p, nans = xp.broadcast_arrays(t, nan)
+        low, high = nans, nans
+
+    low = xp.asarray(low, dtype=dtype)
+    low = low[()] if low.ndim == 0 else low
+    high = xp.asarray(high, dtype=dtype)
+    high = high[()] if high.ndim == 0 else high
+    return low, high
+
+
+def _ttest_ind_from_stats(mean1, mean2, denom, df, alternative, xp=None):
+    xp = array_namespace(mean1, mean2, denom) if xp is None else xp
+
+    d = mean1 - mean2
+    with np.errstate(divide='ignore', invalid='ignore'):
+        t = xp.divide(d, denom)
+
+    dist = _SimpleStudentT(xp.asarray(df, dtype=t.dtype, device=xp_device(t)))
+    prob = _get_pvalue(t, dist, alternative, xp=xp)
+    prob = prob[()] if prob.ndim == 0 else prob
+
+    t = t[()] if t.ndim == 0 else t
+    prob = prob[()] if prob.ndim == 0 else prob
+    return t, prob
+
+
+def _unequal_var_ttest_denom(v1, n1, v2, n2, xp=None):
+    xp = array_namespace(v1, v2) if xp is None else xp
+    vn1 = v1 / n1
+    vn2 = v2 / n2
+    with np.errstate(divide='ignore', invalid='ignore'):
+        df = (vn1 + vn2)**2 / (vn1**2 / (n1 - 1) + vn2**2 / (n2 - 1))
+
+    # If df is undefined, variances are zero (assumes n1 > 0 & n2 > 0).
+    # Hence it doesn't matter what df is as long as it's not NaN.
+    df = xp.where(xp.isnan(df), 1., df)
+    denom = xp.sqrt(vn1 + vn2)
+    return df, denom
+
+
+def _equal_var_ttest_denom(v1, n1, v2, n2, xp=None):
+    xp = array_namespace(v1, v2) if xp is None else xp
+
+    # If there is a single observation in one sample, this formula for pooled
+    # variance breaks down because the variance of that sample is undefined.
+    # The pooled variance is still defined, though, because the (n-1) in the
+    # numerator should cancel with the (n-1) in the denominator, leaving only
+    # the sum of squared differences from the mean: zero.
+    v1 = xp.where(xp.asarray(n1 == 1), 0., v1)
+    v2 = xp.where(xp.asarray(n2 == 1), 0., v2)
+
+    df = n1 + n2 - 2.0
+    svar = ((n1 - 1) * v1 + (n2 - 1) * v2) / df
+    denom = xp.sqrt(svar * (1.0 / n1 + 1.0 / n2))
+    df = xp.asarray(df, dtype=denom.dtype)
+    return df, denom
+
+
+Ttest_indResult = namedtuple('Ttest_indResult', ('statistic', 'pvalue'))
+
+
+@xp_capabilities(cpu_only=True, exceptions=["cupy", "jax.numpy"], marray=True)
+def ttest_ind_from_stats(mean1, std1, nobs1, mean2, std2, nobs2,
+                         equal_var=True, alternative="two-sided"):
+    r"""
+    T-test for means of two independent samples from descriptive statistics.
+
+    This is a test for the null hypothesis that two independent
+    samples have identical average (expected) values.
+
+    Parameters
+    ----------
+    mean1 : array_like
+        The mean(s) of sample 1.
+    std1 : array_like
+        The corrected sample standard deviation of sample 1 (i.e. ``ddof=1``).
+    nobs1 : array_like
+        The number(s) of observations of sample 1.
+    mean2 : array_like
+        The mean(s) of sample 2.
+    std2 : array_like
+        The corrected sample standard deviation of sample 2 (i.e. ``ddof=1``).
+    nobs2 : array_like
+        The number(s) of observations of sample 2.
+    equal_var : bool, optional
+        If True (default), perform a standard independent 2 sample test
+        that assumes equal population variances [1]_.
+        If False, perform Welch's t-test, which does not assume equal
+        population variance [2]_.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis.
+        The following options are available (default is 'two-sided'):
+
+        * 'two-sided': the means of the distributions are unequal.
+        * 'less': the mean of the first distribution is less than the
+          mean of the second distribution.
+        * 'greater': the mean of the first distribution is greater than the
+          mean of the second distribution.
+
+        .. versionadded:: 1.6.0
+
+    Returns
+    -------
+    statistic : float or array
+        The calculated t-statistics.
+    pvalue : float or array
+        The two-tailed p-value.
+
+    See Also
+    --------
+    scipy.stats.ttest_ind
+
+    Notes
+    -----
+    The statistic is calculated as ``(mean1 - mean2)/se``, where ``se`` is the
+    standard error. Therefore, the statistic will be positive when `mean1` is
+    greater than `mean2` and negative when `mean1` is less than `mean2`.
+
+    This method does not check whether any of the elements of `std1` or `std2`
+    are negative. If any elements of the `std1` or `std2` parameters are
+    negative in a call to this method, this method will return the same result
+    as if it were passed ``numpy.abs(std1)`` and ``numpy.abs(std2)``,
+    respectively, instead; no exceptions or warnings will be emitted.
+
+    References
+    ----------
+    .. [1] https://en.wikipedia.org/wiki/T-test#Independent_two-sample_t-test
+
+    .. [2] https://en.wikipedia.org/wiki/Welch%27s_t-test
+
+    Examples
+    --------
+    Suppose we have the summary data for two samples, as follows (with the
+    Sample Variance being the corrected sample variance)::
+
+                         Sample   Sample
+                   Size   Mean   Variance
+        Sample 1    13    15.0     87.5
+        Sample 2    11    12.0     39.0
+
+    Apply the t-test to this data (with the assumption that the population
+    variances are equal):
+
+    >>> import numpy as np
+    >>> from scipy.stats import ttest_ind_from_stats
+    >>> ttest_ind_from_stats(mean1=15.0, std1=np.sqrt(87.5), nobs1=13,
+    ...                      mean2=12.0, std2=np.sqrt(39.0), nobs2=11)
+    Ttest_indResult(statistic=0.9051358093310269, pvalue=0.3751996797581487)
+
+    For comparison, here is the data from which those summary statistics
+    were taken.  With this data, we can compute the same result using
+    `scipy.stats.ttest_ind`:
+
+    >>> a = np.array([1, 3, 4, 6, 11, 13, 15, 19, 22, 24, 25, 26, 26])
+    >>> b = np.array([2, 4, 6, 9, 11, 13, 14, 15, 18, 19, 21])
+    >>> from scipy.stats import ttest_ind
+    >>> ttest_ind(a, b)
+    TtestResult(statistic=0.905135809331027,
+                pvalue=0.3751996797581486,
+                df=22.0)
+
+    Suppose we instead have binary data and would like to apply a t-test to
+    compare the proportion of 1s in two independent groups::
+
+                          Number of    Sample     Sample
+                    Size    ones        Mean     Variance
+        Sample 1    150      30         0.2        0.161073
+        Sample 2    200      45         0.225      0.175251
+
+    The sample mean :math:`\hat{p}` is the proportion of ones in the sample
+    and the variance for a binary observation is estimated by
+    :math:`\hat{p}(1-\hat{p})`.
+
+    >>> ttest_ind_from_stats(mean1=0.2, std1=np.sqrt(0.161073), nobs1=150,
+    ...                      mean2=0.225, std2=np.sqrt(0.175251), nobs2=200)
+    Ttest_indResult(statistic=-0.5627187905196761, pvalue=0.5739887114209541)
+
+    For comparison, we could compute the t statistic and p-value using
+    arrays of 0s and 1s and `scipy.stat.ttest_ind`, as above.
+
+    >>> group1 = np.array([1]*30 + [0]*(150-30))
+    >>> group2 = np.array([1]*45 + [0]*(200-45))
+    >>> ttest_ind(group1, group2)
+    TtestResult(statistic=-0.5627179589855622,
+                pvalue=0.573989277115258,
+                df=348.0)
+
+    """
+    xp = array_namespace(mean1, std1, mean2, std2)
+
+    mean1, std1, nobs1, mean2, std2, nobs2 = xp_promote(
+        mean1, std1, nobs1, mean2, std2, nobs2, force_floating=True, xp=xp)
+
+    if equal_var:
+        df, denom = _equal_var_ttest_denom(std1**2, nobs1, std2**2, nobs2, xp=xp)
+    else:
+        df, denom = _unequal_var_ttest_denom(std1**2, nobs1, std2**2, nobs2, xp=xp)
+
+    res = _ttest_ind_from_stats(mean1, mean2, denom, df, alternative)
+    return Ttest_indResult(*res)
+
+
+@xp_capabilities(cpu_only=True, exceptions=["cupy", "jax.numpy"], marray=True,
+                 extra_note=("`trim` and `method` are incompatible with MArray input."
+                             "The ``confidence_interval`` method of the output object "
+                             "is incompatible with JAX JIT."))
+@_axis_nan_policy_factory(pack_TtestResult, default_axis=0, n_samples=2,
+                          result_to_tuple=unpack_TtestResult, n_outputs=6)
+def ttest_ind(a, b, *, axis=0, equal_var=True, nan_policy='propagate',
+              alternative="two-sided", trim=0, method=None):
+    """
+    Calculate the T-test for the means of *two independent* samples of scores.
+
+    This is a test for the null hypothesis that 2 independent samples
+    have identical average (expected) values. This test assumes that the
+    populations have identical variances by default.
+
+    Parameters
+    ----------
+    a, b : array_like
+        The arrays must have the same shape, except in the dimension
+        corresponding to `axis` (the first, by default).
+    axis : int or None, optional
+        Axis along which to compute test. If None, compute over the whole
+        arrays, `a`, and `b`.
+    equal_var : bool, optional
+        If True (default), perform a standard independent 2 sample test
+        that assumes equal population variances [1]_.
+        If False, perform Welch's t-test, which does not assume equal
+        population variance [2]_.
+
+        .. versionadded:: 0.11.0
+
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains nan.
+        The following options are available (default is 'propagate'):
+
+        * 'propagate': returns nan
+        * 'raise': throws an error
+        * 'omit': performs the calculations ignoring nan values
+
+        The 'omit' option is not currently available for one-sided asymptotic tests.
+
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis.
+        The following options are available (default is 'two-sided'):
+
+        * 'two-sided': the means of the distributions underlying the samples
+          are unequal.
+        * 'less': the mean of the distribution underlying the first sample
+          is less than the mean of the distribution underlying the second
+          sample.
+        * 'greater': the mean of the distribution underlying the first
+          sample is greater than the mean of the distribution underlying
+          the second sample.
+
+    trim : float, optional
+        If nonzero, performs a trimmed (Yuen's) t-test.
+        Defines the fraction of elements to be trimmed from each end of the
+        input samples. If 0 (default), no elements will be trimmed from either
+        side. The number of trimmed elements from each tail is the floor of the
+        trim times the number of elements. Valid range is [0, .5).
+    method : ResamplingMethod, optional
+        Defines the method used to compute the p-value. If `method` is an
+        instance of `PermutationMethod`/`MonteCarloMethod`, the p-value is
+        computed using
+        `scipy.stats.permutation_test`/`scipy.stats.monte_carlo_test` with the
+        provided configuration options and other appropriate settings.
+        Otherwise, the p-value is computed by comparing the test statistic
+        against a theoretical t-distribution.
+
+        .. versionadded:: 1.15.0
+
+    Returns
+    -------
+    result : `~scipy.stats._result_classes.TtestResult`
+        An object with the following attributes:
+
+        statistic : float or ndarray
+            The t-statistic.
+        pvalue : float or ndarray
+            The p-value associated with the given alternative.
+        df : float or ndarray
+            The number of degrees of freedom used in calculation of the
+            t-statistic.
+
+            .. versionadded:: 1.11.0
+
+        The object also has the following method:
+
+        confidence_interval(confidence_level=0.95)
+            Computes a confidence interval around the difference in
+            population means for the given confidence level.
+            The confidence interval is returned in a ``namedtuple`` with
+            fields ``low`` and ``high``.
+
+            .. versionadded:: 1.11.0
+
+    Notes
+    -----
+    Suppose we observe two independent samples, e.g. flower petal lengths, and
+    we are considering whether the two samples were drawn from the same
+    population (e.g. the same species of flower or two species with similar
+    petal characteristics) or two different populations.
+
+    The t-test quantifies the difference between the arithmetic means
+    of the two samples. The p-value quantifies the probability of observing
+    as or more extreme values assuming the null hypothesis, that the
+    samples are drawn from populations with the same population means, is true.
+    A p-value larger than a chosen threshold (e.g. 5% or 1%) indicates that
+    our observation is not so unlikely to have occurred by chance. Therefore,
+    we do not reject the null hypothesis of equal population means.
+    If the p-value is smaller than our threshold, then we have evidence
+    against the null hypothesis of equal population means.
+
+    By default, the p-value is determined by comparing the t-statistic of the
+    observed data against a theoretical t-distribution.
+
+    It is also possible to compute the test statistic using a permutation test by
+    passing ``method=scipy.stats.PermutationMethod(n_resamples=permutations)``,
+    where ``permutations`` is the desired number of "permutations" to use in
+    forming the null distribution. When ``1 < permutations < binom(n, k)``, where
+
+    * ``k`` is the number of observations in `a`,
+    * ``n`` is the total number of observations in `a` and `b`, and
+    * ``binom(n, k)`` is the binomial coefficient (``n`` choose ``k``),
+
+    the data are pooled (concatenated), randomly assigned to either group `a`
+    or `b`, and the t-statistic is calculated. This process is performed
+    repeatedly (``permutations`` times), generating a distribution of the
+    t-statistic under the null hypothesis, and the t-statistic of the observed
+    data is compared to this distribution to determine the p-value.
+    Specifically, the p-value reported is the "achieved significance level"
+    (ASL) as defined in 4.4 of [3]_. Note that there are other ways of
+    estimating p-values using randomized permutation tests; for other
+    options, see the more general `permutation_test`.
+
+    When ``permutations >= binom(n, k)``, an exact test is performed: the data
+    are partitioned between the groups in each distinct way exactly once.
+
+    The permutation test can be computationally expensive and not necessarily
+    more accurate than the analytical test, but it does not make strong
+    assumptions about the shape of the underlying distribution.
+
+    Use of trimming is commonly referred to as the trimmed t-test. At times
+    called Yuen's t-test, this is an extension of Welch's t-test, with the
+    difference being the use of winsorized means in calculation of the variance
+    and the trimmed sample size in calculation of the statistic. Trimming is
+    recommended if the underlying distribution is long-tailed or contaminated
+    with outliers [4]_.
+
+    The statistic is calculated as ``(np.mean(a) - np.mean(b))/se``, where
+    ``se`` is the standard error. Therefore, the statistic will be positive
+    when the sample mean of `a` is greater than the sample mean of `b` and
+    negative when the sample mean of `a` is less than the sample mean of
+    `b`.
+
+    References
+    ----------
+    .. [1] https://en.wikipedia.org/wiki/T-test#Independent_two-sample_t-test
+
+    .. [2] https://en.wikipedia.org/wiki/Welch%27s_t-test
+
+    .. [3] B. Efron and T. Hastie.
+           Computer Age Statistical Inference. (2016).
+
+    .. [4] Yuen, Karen K. "The Two-Sample Trimmed t for Unequal Population
+           Variances." Biometrika, vol. 61, no. 1, 1974, pp. 165-170.
+           https://www.jstor.org/stable/2334299
+
+    .. [5] Yuen, Karen K., and W. J. Dixon. "The Approximate Behaviour and
+           Performance of the Two-Sample Trimmed t." Biometrika, vol. 60,
+           no. 2, 1973, pp. 369-374.
+           https://www.jstor.org/stable/2334550
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> rng = np.random.default_rng()
+
+    Test with sample with identical means:
+
+    >>> rvs1 = stats.norm.rvs(loc=5, scale=10, size=500, random_state=rng)
+    >>> rvs2 = stats.norm.rvs(loc=5, scale=10, size=500, random_state=rng)
+    >>> stats.ttest_ind(rvs1, rvs2)
+    TtestResult(statistic=-0.4390847099199348,
+                pvalue=0.6606952038870015,
+                df=998.0)
+    >>> stats.ttest_ind(rvs1, rvs2, equal_var=False)
+    TtestResult(statistic=-0.4390847099199348,
+                pvalue=0.6606952553131064,
+                df=997.4602304121448)
+
+    `ttest_ind` underestimates p for unequal variances:
+
+    >>> rvs3 = stats.norm.rvs(loc=5, scale=20, size=500, random_state=rng)
+    >>> stats.ttest_ind(rvs1, rvs3)
+    TtestResult(statistic=-1.6370984482905417,
+                pvalue=0.1019251574705033,
+                df=998.0)
+    >>> stats.ttest_ind(rvs1, rvs3, equal_var=False)
+    TtestResult(statistic=-1.637098448290542,
+                pvalue=0.10202110497954867,
+                df=765.1098655246868)
+
+    When ``n1 != n2``, the equal variance t-statistic is no longer equal to the
+    unequal variance t-statistic:
+
+    >>> rvs4 = stats.norm.rvs(loc=5, scale=20, size=100, random_state=rng)
+    >>> stats.ttest_ind(rvs1, rvs4)
+    TtestResult(statistic=-1.9481646859513422,
+                pvalue=0.05186270935842703,
+                df=598.0)
+    >>> stats.ttest_ind(rvs1, rvs4, equal_var=False)
+    TtestResult(statistic=-1.3146566100751664,
+                pvalue=0.1913495266513811,
+                df=110.41349083985212)
+
+    T-test with different means, variance, and n:
+
+    >>> rvs5 = stats.norm.rvs(loc=8, scale=20, size=100, random_state=rng)
+    >>> stats.ttest_ind(rvs1, rvs5)
+    TtestResult(statistic=-2.8415950600298774,
+                pvalue=0.0046418707568707885,
+                df=598.0)
+    >>> stats.ttest_ind(rvs1, rvs5, equal_var=False)
+    TtestResult(statistic=-1.8686598649188084,
+                pvalue=0.06434714193919686,
+                df=109.32167496550137)
+
+    Take these two samples, one of which has an extreme tail.
+
+    >>> a = (56, 128.6, 12, 123.8, 64.34, 78, 763.3)
+    >>> b = (1.1, 2.9, 4.2)
+
+    Use the `trim` keyword to perform a trimmed (Yuen) t-test. For example,
+    using 20% trimming, ``trim=.2``, the test will reduce the impact of one
+    (``np.floor(trim*len(a))``) element from each tail of sample `a`. It will
+    have no effect on sample `b` because ``np.floor(trim*len(b))`` is 0.
+
+    >>> stats.ttest_ind(a, b, trim=.2)
+    TtestResult(statistic=3.4463884028073513,
+                pvalue=0.01369338726499547,
+                df=6.0)
+    """
+    xp = array_namespace(a, b)
+
+    a, b = xp_promote(a, b, force_floating=True, xp=xp)
+
+    if axis is None:
+        a, b, axis = xp_ravel(a), xp_ravel(b), 0
+
+    if not (0 <= trim < .5):
+        raise ValueError("Trimming percentage should be 0 <= `trim` < .5.")
+
+    if not isinstance(method, PermutationMethod | MonteCarloMethod | None):
+        message = ("`method` must be an instance of `PermutationMethod`, an instance "
+                   "of `MonteCarloMethod`, or None (default).")
+        raise ValueError(message)
+
+    result_shape = _broadcast_array_shapes_remove_axis((a, b), axis=axis)
+    NaN = _get_nan(a, b, shape=result_shape, xp=xp)
+    if xp_size(a) == 0 or xp_size(b) == 0:
+        return TtestResult(NaN, NaN, df=NaN, alternative=NaN,
+                           standard_error=NaN, estimate=NaN)
+
+    alternative_nums = {"less": -1, "two-sided": 0, "greater": 1}
+
+    n1 = _count_nonmasked(a, axis)
+    n2 = _count_nonmasked(b, axis)
+
+    if trim == 0:
+        with np.errstate(divide='ignore', invalid='ignore'):
+            v1 = _var(a, axis, ddof=1, xp=xp)
+            v2 = _var(b, axis, ddof=1, xp=xp)
+
+        m1 = xp.mean(a, axis=axis)
+        m2 = xp.mean(b, axis=axis)
+    else:
+        v1, m1, n1 = _ttest_trim_var_mean_len(a, trim, axis, xp=xp)
+        v2, m2, n2 = _ttest_trim_var_mean_len(b, trim, axis, xp=xp)
+
+    if equal_var:
+        df, denom = _equal_var_ttest_denom(v1, n1, v2, n2, xp=xp)
+    else:
+        df, denom = _unequal_var_ttest_denom(v1, n1, v2, n2, xp=xp)
+
+    if method is None:
+        t, prob = _ttest_ind_from_stats(m1, m2, denom, df, alternative)
+    else:
+        # nan_policy is taken care of by axis_nan_policy decorator
+        ttest_kwargs = dict(equal_var=equal_var, trim=trim)
+        t, prob = _ttest_resampling(a, b, axis, alternative,
+                                    ttest_kwargs, method, xp=xp)
+
+    # when nan_policy='omit', `df` can be different for different axis-slices
+    df = xp.broadcast_to(df, t.shape)
+    df = df[()] if df.ndim ==0 else df
+    estimate = m1 - m2
+
+    return TtestResult(t, prob, df=df, alternative=alternative_nums[alternative],
+                       standard_error=denom, estimate=estimate)
+
+
+def _ttest_resampling(x, y, axis, alternative, ttest_kwargs, method, *, xp):
+    def statistic(x, y, axis):
+        x, y = xp.asarray(x), xp.asarray(y)
+        return ttest_ind(x, y, axis=axis, **ttest_kwargs).statistic
+
+    test = (permutation_test if isinstance(method, PermutationMethod)
+            else monte_carlo_test)
+    method = method._asdict()
+
+    if test is monte_carlo_test:
+        # `monte_carlo_test` accepts an `rvs` tuple of callables, not an `rng`
+        # If the user specified an `rng`, replace it with the default callables
+        if (rng := method.pop('rng', None)) is not None:
+            rng = np.random.default_rng(rng)
+            method['rvs'] = rng.normal, rng.normal
+
+    res = test((x, y,), statistic=statistic, axis=axis,
+               alternative=alternative, **method)
+
+    return res.statistic, res.pvalue
+
+
+def _ttest_trim_var_mean_len(a, trim, axis, *, xp):
+    """Variance, mean, and length of winsorized input along specified axis"""
+    # for use with `ttest_ind` when trimming.
+    # further calculations in this test assume that the inputs are sorted.
+    # From [4] Section 1 "Let x_1, ..., x_n be n ordered observations..."
+    a = xp.sort(a, axis=axis)
+
+    # `g` is the number of elements to be replaced on each tail, converted
+    # from a percentage amount of trimming
+    n = a.shape[axis]
+    g = int(n * trim)
+
+    # Calculate the Winsorized variance of the input samples according to
+    # specified `g`
+    v = _calculate_winsorized_variance(a, g, axis, xp=xp)
+
+    # the total number of elements in the trimmed samples
+    n -= 2 * g
+
+    # calculate the g-times trimmed mean, as defined in [4] (1-1)
+    m = trim_mean(a, trim, axis=axis)
+    return v, m, n
+
+
+def _calculate_winsorized_variance(a, g, axis, *, xp):
+    """Calculates g-times winsorized variance along specified axis"""
+    # it is expected that the input `a` is sorted along the correct axis
+    if g == 0:
+        return _var(a, ddof=1, axis=axis, xp=xp)
+    # move the intended axis to the end that way it is easier to manipulate
+    a_win = xp.moveaxis(a, axis, -1)
+
+    # save where NaNs are for later use.
+    nans_indices = xp.any(xp.isnan(a_win), axis=-1)
+
+    # Winsorization and variance calculation are done in one step in [4]
+    # (1-3), but here winsorization is done first; replace the left and
+    # right sides with the repeating value. This can be see in effect in (
+    # 1-3) in [4], where the leftmost and rightmost tails are replaced with
+    # `(g + 1) * x_{g + 1}` on the left and `(g + 1) * x_{n - g}` on the
+    # right. Zero-indexing turns `g + 1` to `g`, and `n - g` to `- g - 1` in
+    # array indexing.
+    a_win = xpx.at(a_win)[..., :g].set(a_win[..., g:g+1])
+    a_win = xpx.at(a_win)[..., -g:].set(a_win[..., -g - 1:-g])
+
+    # Determine the variance. In [4], the degrees of freedom is expressed as
+    # `h - 1`, where `h = n - 2g` (unnumbered equations in Section 1, end of
+    # page 369, beginning of page 370). This is converted to NumPy's format,
+    # `n - ddof` for use with `np.var`. The result is converted to an
+    # array to accommodate indexing later.
+    var_win = xp.asarray(_var(a_win, ddof=(2 * g + 1), axis=-1, xp=xp))
+
+    # with `nan_policy='propagate'`, NaNs may be completely trimmed out
+    # because they were sorted into the tail of the array. In these cases,
+    # replace computed variances with `np.nan`.
+    var_win = xpx.at(var_win)[nans_indices].set(xp.nan)
+    return var_win
+
+
+@xp_capabilities(cpu_only=True, exceptions=["cupy", "jax.numpy"], marray=True,
+                 extra_note=("The ``confidence_interval`` method of the output object"
+                             "is incompatible with JAX JIT."))
+@_axis_nan_policy_factory(pack_TtestResult, default_axis=0, n_samples=2,
+                          result_to_tuple=unpack_TtestResult, n_outputs=6,
+                          paired=True)
+def ttest_rel(a, b, axis=0, nan_policy='propagate', alternative="two-sided"):
+    """Calculate the t-test on TWO RELATED samples of scores, a and b.
+
+    This is a test for the null hypothesis that two related or
+    repeated samples have identical average (expected) values.
+
+    Parameters
+    ----------
+    a, b : array_like
+        The arrays must have the same shape.
+    axis : int or None, optional
+        Axis along which to compute test. If None, compute over the whole
+        arrays, `a`, and `b`.
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains nan.
+        The following options are available (default is 'propagate'):
+
+        * 'propagate': returns nan
+        * 'raise': throws an error
+        * 'omit': performs the calculations ignoring nan values
+
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis.
+        The following options are available (default is 'two-sided'):
+
+        * 'two-sided': the means of the distributions underlying the samples
+          are unequal.
+        * 'less': the mean of the distribution underlying the first sample
+          is less than the mean of the distribution underlying the second
+          sample.
+        * 'greater': the mean of the distribution underlying the first
+          sample is greater than the mean of the distribution underlying
+          the second sample.
+
+        .. versionadded:: 1.6.0
+
+    Returns
+    -------
+    result : `~scipy.stats._result_classes.TtestResult`
+        An object with the following attributes:
+
+        statistic : float or array
+            The t-statistic.
+        pvalue : float or array
+            The p-value associated with the given alternative.
+        df : float or array
+            The number of degrees of freedom used in calculation of the
+            t-statistic; this is one less than the size of the sample
+            (``a.shape[axis]``).
+
+            .. versionadded:: 1.10.0
+
+        The object also has the following method:
+
+        confidence_interval(confidence_level=0.95)
+            Computes a confidence interval around the difference in
+            population means for the given confidence level.
+            The confidence interval is returned in a ``namedtuple`` with
+            fields `low` and `high`.
+
+            .. versionadded:: 1.10.0
+
+    Notes
+    -----
+    Examples for use are scores of the same set of student in
+    different exams, or repeated sampling from the same units. The
+    test measures whether the average score differs significantly
+    across samples (e.g. exams). If we observe a large p-value, for
+    example greater than 0.05 or 0.1 then we cannot reject the null
+    hypothesis of identical average scores. If the p-value is smaller
+    than the threshold, e.g. 1%, 5% or 10%, then we reject the null
+    hypothesis of equal averages. Small p-values are associated with
+    large t-statistics.
+
+    The t-statistic is calculated as ``np.mean(a - b)/se``, where ``se`` is the
+    standard error. Therefore, the t-statistic will be positive when the sample
+    mean of ``a - b`` is greater than zero and negative when the sample mean of
+    ``a - b`` is less than zero.
+
+    References
+    ----------
+    https://en.wikipedia.org/wiki/T-test#Dependent_t-test_for_paired_samples
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> rng = np.random.default_rng()
+
+    >>> rvs1 = stats.norm.rvs(loc=5, scale=10, size=500, random_state=rng)
+    >>> rvs2 = (stats.norm.rvs(loc=5, scale=10, size=500, random_state=rng)
+    ...         + stats.norm.rvs(scale=0.2, size=500, random_state=rng))
+    >>> stats.ttest_rel(rvs1, rvs2)
+    TtestResult(statistic=-0.4549717054410304, pvalue=0.6493274702088672, df=499)
+    >>> rvs3 = (stats.norm.rvs(loc=8, scale=10, size=500, random_state=rng)
+    ...         + stats.norm.rvs(scale=0.2, size=500, random_state=rng))
+    >>> stats.ttest_rel(rvs1, rvs3)
+    TtestResult(statistic=-5.879467544540889, pvalue=7.540777129099917e-09, df=499)
+
+    """
+    return ttest_1samp(a - b, popmean=0., axis=axis, alternative=alternative,
+                       _no_deco=True)
+
+
+# Map from names to lambda_ values used in power_divergence().
+_power_div_lambda_names = {
+    "pearson": 1,
+    "log-likelihood": 0,
+    "freeman-tukey": -0.5,
+    "mod-log-likelihood": -1,
+    "neyman": -2,
+    "cressie-read": 2/3,
+}
+
+
+Power_divergenceResult = namedtuple('Power_divergenceResult',
+                                    ('statistic', 'pvalue'))
+
+
+def _pd_nsamples(kwargs):
+    return 2 if kwargs.get('f_exp', None) is not None else 1
+
+
+@xp_capabilities(marray=True)
+@_axis_nan_policy_factory(Power_divergenceResult, paired=True, n_samples=_pd_nsamples,
+                          too_small=-1)
+def power_divergence(f_obs, f_exp=None, ddof=0, axis=0, lambda_=None):
+    """Cressie-Read power divergence statistic and goodness of fit test.
+
+    This function tests the null hypothesis that the categorical data
+    has the given frequencies, using the Cressie-Read power divergence
+    statistic.
+
+    Parameters
+    ----------
+    f_obs : array_like
+        Observed frequencies in each category.
+    f_exp : array_like, optional
+        Expected frequencies in each category.  By default the categories are
+        assumed to be equally likely.
+    ddof : int, optional
+        "Delta degrees of freedom": adjustment to the degrees of freedom
+        for the p-value.  The p-value is computed using a chi-squared
+        distribution with ``k - 1 - ddof`` degrees of freedom, where `k`
+        is the number of observed frequencies.  The default value of `ddof`
+        is 0.
+    axis : int or None, optional
+        The axis of the broadcast result of `f_obs` and `f_exp` along which to
+        apply the test.  If axis is None, all values in `f_obs` are treated
+        as a single data set.  Default is 0.
+    lambda_ : float or str, optional
+        The power in the Cressie-Read power divergence statistic.  The default
+        is 1.  For convenience, `lambda_` may be assigned one of the following
+        strings, in which case the corresponding numerical value is used:
+
+        * ``"pearson"`` (value 1)
+            Pearson's chi-squared statistic. In this case, the function is
+            equivalent to `chisquare`.
+        * ``"log-likelihood"`` (value 0)
+            Log-likelihood ratio. Also known as the G-test [3]_.
+        * ``"freeman-tukey"`` (value -1/2)
+            Freeman-Tukey statistic.
+        * ``"mod-log-likelihood"`` (value -1)
+            Modified log-likelihood ratio.
+        * ``"neyman"`` (value -2)
+            Neyman's statistic.
+        * ``"cressie-read"`` (value 2/3)
+            The power recommended in [5]_.
+
+    Returns
+    -------
+    res: Power_divergenceResult
+        An object containing attributes:
+
+        statistic : float or ndarray
+            The Cressie-Read power divergence test statistic.  The value is
+            a float if `axis` is None or if` `f_obs` and `f_exp` are 1-D.
+        pvalue : float or ndarray
+            The p-value of the test.  The value is a float if `ddof` and the
+            return value `stat` are scalars.
+
+    See Also
+    --------
+    chisquare
+
+    Notes
+    -----
+    This test is invalid when the observed or expected frequencies in each
+    category are too small.  A typical rule is that all of the observed
+    and expected frequencies should be at least 5.
+
+    Also, the sum of the observed and expected frequencies must be the same
+    for the test to be valid; `power_divergence` raises an error if the sums
+    do not agree within a relative tolerance of ``eps**0.5``, where ``eps``
+    is the precision of the input dtype.
+
+    When `lambda_` is less than zero, the formula for the statistic involves
+    dividing by `f_obs`, so a warning or error may be generated if any value
+    in `f_obs` is 0.
+
+    Similarly, a warning or error may be generated if any value in `f_exp` is
+    zero when `lambda_` >= 0.
+
+    The default degrees of freedom, k-1, are for the case when no parameters
+    of the distribution are estimated. If p parameters are estimated by
+    efficient maximum likelihood then the correct degrees of freedom are
+    k-1-p. If the parameters are estimated in a different way, then the
+    dof can be between k-1-p and k-1. However, it is also possible that
+    the asymptotic distribution is not a chisquare, in which case this
+    test is not appropriate.
+
+    References
+    ----------
+    .. [1] Lowry, Richard.  "Concepts and Applications of Inferential
+           Statistics". Chapter 8.
+           https://web.archive.org/web/20171015035606/http://faculty.vassar.edu/lowry/ch8pt1.html
+    .. [2] "Chi-squared test", https://en.wikipedia.org/wiki/Chi-squared_test
+    .. [3] "G-test", https://en.wikipedia.org/wiki/G-test
+    .. [4] Sokal, R. R. and Rohlf, F. J. "Biometry: the principles and
+           practice of statistics in biological research", New York: Freeman
+           (1981)
+    .. [5] Cressie, N. and Read, T. R. C., "Multinomial Goodness-of-Fit
+           Tests", J. Royal Stat. Soc. Series B, Vol. 46, No. 3 (1984),
+           pp. 440-464.
+
+    Examples
+    --------
+    (See `chisquare` for more examples.)
+
+    When just `f_obs` is given, it is assumed that the expected frequencies
+    are uniform and given by the mean of the observed frequencies.  Here we
+    perform a G-test (i.e. use the log-likelihood ratio statistic):
+
+    >>> import numpy as np
+    >>> from scipy.stats import power_divergence
+    >>> power_divergence([16, 18, 16, 14, 12, 12], lambda_='log-likelihood')
+    (2.006573162632538, 0.84823476779463769)
+
+    The expected frequencies can be given with the `f_exp` argument:
+
+    >>> power_divergence([16, 18, 16, 14, 12, 12],
+    ...                  f_exp=[16, 16, 16, 16, 16, 8],
+    ...                  lambda_='log-likelihood')
+    (3.3281031458963746, 0.6495419288047497)
+
+    When `f_obs` is 2-D, by default the test is applied to each column.
+
+    >>> obs = np.array([[16, 18, 16, 14, 12, 12], [32, 24, 16, 28, 20, 24]]).T
+    >>> obs.shape
+    (6, 2)
+    >>> power_divergence(obs, lambda_="log-likelihood")
+    (array([ 2.00657316,  6.77634498]), array([ 0.84823477,  0.23781225]))
+
+    By setting ``axis=None``, the test is applied to all data in the array,
+    which is equivalent to applying the test to the flattened array.
+
+    >>> power_divergence(obs, axis=None)
+    (23.31034482758621, 0.015975692534127565)
+    >>> power_divergence(obs.ravel())
+    (23.31034482758621, 0.015975692534127565)
+
+    `ddof` is the change to make to the default degrees of freedom.
+
+    >>> power_divergence([16, 18, 16, 14, 12, 12], ddof=1)
+    (2.0, 0.73575888234288467)
+
+    The calculation of the p-values is done by broadcasting the
+    test statistic with `ddof`.
+
+    >>> power_divergence([16, 18, 16, 14, 12, 12], ddof=[0,1,2])
+    (2.0, array([ 0.84914504,  0.73575888,  0.5724067 ]))
+
+    `f_obs` and `f_exp` are also broadcast.  In the following, `f_obs` has
+    shape (6,) and `f_exp` has shape (2, 6), so the result of broadcasting
+    `f_obs` and `f_exp` has shape (2, 6).  To compute the desired chi-squared
+    statistics, we must use ``axis=1``:
+
+    >>> power_divergence([16, 18, 16, 14, 12, 12],
+    ...                  f_exp=[[16, 16, 16, 16, 16, 8],
+    ...                         [8, 20, 20, 16, 12, 12]],
+    ...                  axis=1)
+    (array([ 3.5 ,  9.25]), array([ 0.62338763,  0.09949846]))
+
+    """
+    return _power_divergence(f_obs, f_exp=f_exp, ddof=ddof, axis=axis, lambda_=lambda_)
+
+
+def _power_divergence(f_obs, f_exp, ddof, axis, lambda_, sum_check=True):
+    xp = array_namespace(f_obs, f_exp, ddof)
+    f_obs, f_exp, ddof = xp_promote(f_obs, f_exp, ddof,
+                                    force_floating=True, xp=xp)
+
+    # Convert the input argument `lambda_` to a numerical value.
+    if isinstance(lambda_, str):
+        if lambda_ not in _power_div_lambda_names:
+            names = repr(list(_power_div_lambda_names.keys()))[1:-1]
+            raise ValueError(f"invalid string for lambda_: {lambda_!r}. "
+                             f"Valid strings are {names}")
+        lambda_ = _power_div_lambda_names[lambda_]
+    elif lambda_ is None:
+        lambda_ = 1
+
+    if f_exp is not None:
+        # not sure why we force to float64, but not going to touch it
+        f_obs_float = xp.asarray(f_obs, dtype=xp.float64)
+        bshape = _broadcast_shapes((f_obs_float.shape, f_exp.shape))
+        f_obs_float = xp.broadcast_to(f_obs_float, bshape)
+        f_exp = xp.broadcast_to(f_exp, bshape)
+        f_obs_float, f_exp = _share_masks(f_obs_float, f_exp, xp=xp)
+
+        if sum_check:
+            dtype_res = xp.result_type(f_obs.dtype, f_exp.dtype)
+            rtol = xp.finfo(dtype_res).eps**0.5  # to pass existing tests
+            with np.errstate(invalid='ignore'):
+                f_obs_sum = xp.sum(f_obs_float, axis=axis, keepdims=True)
+                f_exp_sum = xp.sum(f_exp, axis=axis, keepdims=True)
+                relative_diff = (xp.abs(f_obs_sum - f_exp_sum) /
+                                 xp.minimum(f_obs_sum, f_exp_sum))
+                diff_gt_tol = xp.any(relative_diff > rtol, axis=axis, keepdims=True)
+
+            if not is_lazy_array(diff_gt_tol) and xp.any(diff_gt_tol):
+                msg = (f"For each axis slice, the sum of the observed "
+                       f"frequencies must agree with the sum of the "
+                       f"expected frequencies to a relative tolerance "
+                       f"of {rtol}, but the percent differences are:\n"
+                       f"{relative_diff}")
+                raise ValueError(msg)
+            elif is_lazy_array(diff_gt_tol):
+                diff_gt_tol = xp.broadcast_to(diff_gt_tol, f_obs.shape)
+                f_obs = xpx.at(f_obs)[diff_gt_tol].set(xp.nan)
+
+    else:
+        # Avoid warnings with the edge case of a data set with length 0
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore")
+            f_exp = xp.mean(f_obs, axis=axis, keepdims=True)
+
+    # `terms` is the array of terms that are summed along `axis` to create
+    # the test statistic.  We use some specialized code for a few special
+    # cases of lambda_.
+    if lambda_ == 1:
+        # Pearson's chi-squared statistic
+        terms = (f_obs - f_exp)**2 / f_exp
+    elif lambda_ == 0:
+        # Log-likelihood ratio (i.e. G-test)
+        terms = 2.0 * special.xlogy(f_obs, f_obs / f_exp)
+    elif lambda_ == -1:
+        # Modified log-likelihood ratio
+        terms = 2.0 * special.xlogy(f_exp, f_exp / f_obs)
+    else:
+        # General Cressie-Read power divergence.
+        terms = f_obs * ((f_obs / f_exp)**lambda_ - 1)
+        terms /= 0.5 * lambda_ * (lambda_ + 1)
+
+    stat = xp.sum(terms, axis=axis)
+
+    num_obs = xp.asarray(_count_nonmasked(terms, axis), device=xp_device(terms),
+                         dtype=f_obs.dtype)
+
+    df = num_obs - 1 - ddof
+    chi2 = _SimpleChi2(df)
+    pvalue = _get_pvalue(stat, chi2 , alternative='greater', symmetric=False, xp=xp)
+
+    stat = stat[()] if stat.ndim == 0 else stat
+    pvalue = pvalue[()] if pvalue.ndim == 0 else pvalue
+
+    return Power_divergenceResult(stat, pvalue)
+
+
+
+@xp_capabilities(marray=True)
+@_axis_nan_policy_factory(Power_divergenceResult, paired=True, n_samples=_pd_nsamples,
+                          too_small=-1)
+def chisquare(f_obs, f_exp=None, ddof=0, axis=0, *, sum_check=True):
+    """Perform Pearson's chi-squared test.
+
+    Pearson's chi-squared test [1]_ is a goodness-of-fit test for a multinomial
+    distribution with given probabilities; that is, it assesses the null hypothesis
+    that the observed frequencies (counts) are obtained by independent
+    sampling of *N* observations from a categorical distribution with given
+    expected frequencies.
+
+    Parameters
+    ----------
+    f_obs : array_like
+        Observed frequencies in each category.
+    f_exp : array_like, optional
+        Expected frequencies in each category. By default, the categories are
+        assumed to be equally likely.
+    ddof : int, optional
+        "Delta degrees of freedom": adjustment to the degrees of freedom
+        for the p-value.  The p-value is computed using a chi-squared
+        distribution with ``k - 1 - ddof`` degrees of freedom, where ``k``
+        is the number of categories.  The default value of `ddof` is 0.
+    axis : int or None, optional
+        The axis of the broadcast result of `f_obs` and `f_exp` along which to
+        apply the test.  If axis is None, all values in `f_obs` are treated
+        as a single data set.  Default is 0.
+    sum_check : bool, optional
+        Whether to perform a check that ``sum(f_obs) - sum(f_exp) == 0``. If True,
+        (default) raise an error (or, for lazy backends, return NaN) when the relative
+        difference exceeds the square root of the precision of the data type.
+        See Notes for rationale and possible exceptions.
+
+    Returns
+    -------
+    res: Power_divergenceResult
+        An object containing attributes:
+
+        statistic : float or ndarray
+            The chi-squared test statistic.  The value is a float if `axis` is
+            None or `f_obs` and `f_exp` are 1-D.
+        pvalue : float or ndarray
+            The p-value of the test.  The value is a float if `ddof` and the
+            result attribute `statistic` are scalars.
+
+    See Also
+    --------
+    scipy.stats.power_divergence
+    scipy.stats.fisher_exact : Fisher exact test on a 2x2 contingency table.
+    scipy.stats.barnard_exact : An unconditional exact test. An alternative
+        to chi-squared test for small sample sizes.
+    :ref:`hypothesis_chisquare` : Extended example
+
+    Notes
+    -----
+    This test is invalid when the observed or expected frequencies in each
+    category are too small.  A typical rule is that all of the observed
+    and expected frequencies should be at least 5. According to [2]_, the
+    total number of observations is recommended to be greater than 13,
+    otherwise exact tests (such as Barnard's Exact test) should be used
+    because they do not overreject.
+
+    The default degrees of freedom, k-1, are for the case when no parameters
+    of the distribution are estimated. If p parameters are estimated by
+    efficient maximum likelihood then the correct degrees of freedom are
+    k-1-p. If the parameters are estimated in a different way, then the
+    dof can be between k-1-p and k-1. However, it is also possible that
+    the asymptotic distribution is not chi-square, in which case this test
+    is not appropriate.
+
+    For Pearson's chi-squared test, the total observed and expected counts must match
+    for the p-value to accurately reflect the probability of observing such an extreme
+    value of the statistic under the null hypothesis.
+    This function may be used to perform other statistical tests that do not require
+    the total counts to be equal. For instance, to test the null hypothesis that
+    ``f_obs[i]`` is Poisson-distributed with expectation ``f_exp[i]``, set ``ddof=-1``
+    and ``sum_check=False``. This test follows from the fact that a Poisson random
+    variable with mean and variance ``f_exp[i]`` is approximately normal with the
+    same mean and variance; the chi-squared statistic standardizes, squares, and sums
+    the observations; and the sum of ``n`` squared standard normal variables follows
+    the chi-squared distribution with ``n`` degrees of freedom.
+
+    References
+    ----------
+    .. [1] "Pearson's chi-squared test".
+           *Wikipedia*. https://en.wikipedia.org/wiki/Pearson%27s_chi-squared_test
+    .. [2] Pearson, Karl. "On the criterion that a given system of deviations from the probable
+           in the case of a correlated system of variables is such that it can be reasonably
+           supposed to have arisen from random sampling", Philosophical Magazine. Series 5. 50
+           (1900), pp. 157-175.
+
+    Examples
+    --------
+    When only the mandatory `f_obs` argument is given, it is assumed that the
+    expected frequencies are uniform and given by the mean of the observed
+    frequencies:
+
+    >>> import numpy as np
+    >>> from scipy.stats import chisquare
+    >>> chisquare([16, 18, 16, 14, 12, 12])
+    Power_divergenceResult(statistic=2.0, pvalue=0.84914503608460956)
+
+    The optional `f_exp` argument gives the expected frequencies.
+
+    >>> chisquare([16, 18, 16, 14, 12, 12], f_exp=[16, 16, 16, 16, 16, 8])
+    Power_divergenceResult(statistic=3.5, pvalue=0.62338762774958223)
+
+    When `f_obs` is 2-D, by default the test is applied to each column.
+
+    >>> obs = np.array([[16, 18, 16, 14, 12, 12], [32, 24, 16, 28, 20, 24]]).T
+    >>> obs.shape
+    (6, 2)
+    >>> chisquare(obs)
+    Power_divergenceResult(statistic=array([2.        , 6.66666667]), pvalue=array([0.84914504, 0.24663415]))
+
+    By setting ``axis=None``, the test is applied to all data in the array,
+    which is equivalent to applying the test to the flattened array.
+
+    >>> chisquare(obs, axis=None)
+    Power_divergenceResult(statistic=23.31034482758621, pvalue=0.015975692534127565)
+    >>> chisquare(obs.ravel())
+    Power_divergenceResult(statistic=23.310344827586206, pvalue=0.01597569253412758)
+
+    `ddof` is the change to make to the default degrees of freedom.
+
+    >>> chisquare([16, 18, 16, 14, 12, 12], ddof=1)
+    Power_divergenceResult(statistic=2.0, pvalue=0.7357588823428847)
+
+    The calculation of the p-values is done by broadcasting the
+    chi-squared statistic with `ddof`.
+
+    >>> chisquare([16, 18, 16, 14, 12, 12], ddof=[0, 1, 2])
+    Power_divergenceResult(statistic=2.0, pvalue=array([0.84914504, 0.73575888, 0.5724067 ]))
+
+    `f_obs` and `f_exp` are also broadcast.  In the following, `f_obs` has
+    shape (6,) and `f_exp` has shape (2, 6), so the result of broadcasting
+    `f_obs` and `f_exp` has shape (2, 6).  To compute the desired chi-squared
+    statistics, we use ``axis=1``:
+
+    >>> chisquare([16, 18, 16, 14, 12, 12],
+    ...           f_exp=[[16, 16, 16, 16, 16, 8], [8, 20, 20, 16, 12, 12]],
+    ...           axis=1)
+    Power_divergenceResult(statistic=array([3.5 , 9.25]), pvalue=array([0.62338763, 0.09949846]))
+
+    For a more detailed example, see :ref:`hypothesis_chisquare`.
+    """  # noqa: E501
+    return _power_divergence(f_obs, f_exp=f_exp, ddof=ddof, axis=axis,
+                             lambda_="pearson", sum_check=sum_check)
+
+
+KstestResult = _make_tuple_bunch('KstestResult', ['statistic', 'pvalue'],
+                                 ['statistic_location', 'statistic_sign'])
+
+
+def _compute_d(cdfvals, x, sign, xp=None):
+    """Computes D+/D- as used in the Kolmogorov-Smirnov test.
+
+    Vectorized along the last axis.
+
+    Parameters
+    ----------
+    cdfvals : array_like
+        Sorted array of CDF values between 0 and 1
+    x: array_like
+        Sorted array of the stochastic variable itself
+    sign: int
+        Indicates whether to compute D+ (+1) or D- (-1).
+
+    Returns
+    -------
+    D : float or array
+        The maximum distance of the CDF values below/above (D+/D-) Uniform(0, 1).
+    loc_max : float or array
+        The location at which the maximum is reached.
+    """
+    xp = array_namespace(cdfvals, x) if xp is None else xp
+    length = cdfvals.shape[-1]
+    n = _count_nonmasked(cdfvals, axis=-1, keepdims=True)
+    D = (xp.arange(1.0, length + 1, dtype=x.dtype) / n - cdfvals if sign == +1
+         else (cdfvals - xp.arange(0.0, length, dtype=x.dtype) / n))
+    amax = xp.argmax(D, axis=-1, keepdims=True)
+    loc_max = xp.squeeze(xp.take_along_axis(x, amax, axis=-1), axis=-1)
+    D = xp.squeeze(xp.take_along_axis(D, amax, axis=-1), axis=-1)
+    return D[()] if D.ndim == 0 else D, loc_max[()] if loc_max.ndim == 0 else loc_max
+
+
+def _tuple_to_KstestResult(statistic, pvalue,
+                           statistic_location, statistic_sign):
+    return KstestResult(statistic, pvalue,
+                        statistic_location=statistic_location,
+                        statistic_sign=statistic_sign)
+
+
+def _KstestResult_to_tuple(res, _):
+    return *res, res.statistic_location, res.statistic_sign
+
+
+# JAX JIT / Torch GPU / CuPy need null distribution
+@xp_capabilities(cpu_only=True, jax_jit=False, marray=True,
+                 skip_backends=[('dask.array', 'needs take_along_axis')])
+@_axis_nan_policy_factory(_tuple_to_KstestResult, n_samples=1, n_outputs=4,
+                          result_to_tuple=_KstestResult_to_tuple)
+@_rename_parameter("mode", "method")
+def ks_1samp(x, cdf, args=(), alternative='two-sided', method='auto', *, axis=0):
+    """
+    Performs the one-sample Kolmogorov-Smirnov test for goodness of fit.
+
+    This test compares the underlying distribution F(x) of a sample
+    against a given continuous distribution G(x). See Notes for a description
+    of the available null and alternative hypotheses.
+
+    Parameters
+    ----------
+    x : array_like
+        a 1-D array of observations of iid random variables.
+    cdf : callable
+        callable used to calculate the cdf.
+    args : tuple, sequence, optional
+        Distribution parameters, used with `cdf`.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the null and alternative hypotheses. Default is 'two-sided'.
+        Please see explanations in the Notes below.
+    method : {'auto', 'exact', 'approx', 'asymp'}, optional
+        Defines the distribution used for calculating the p-value.
+        The following options are available (default is 'auto'):
+
+        * 'auto' : selects one of the other options.
+        * 'exact' : uses the exact distribution of test statistic.
+        * 'approx' : approximates the two-sided probability with twice
+          the one-sided probability
+        * 'asymp': uses asymptotic distribution of test statistic
+
+    axis : int or tuple of ints, default: 0
+        If an int or tuple of ints, the axis or axes of the input along which
+        to compute the statistic. The statistic of each axis-slice (e.g. row)
+        of the input will appear in a corresponding element of the output.
+        If ``None``, the input will be raveled before computing the statistic.
+
+    Returns
+    -------
+    res: KstestResult
+        An object containing attributes:
+
+        statistic : float
+            KS test statistic, either D+, D-, or D (the maximum of the two)
+        pvalue : float
+            One-tailed or two-tailed p-value.
+        statistic_location : float
+            Value of `x` corresponding with the KS statistic; i.e., the
+            distance between the empirical distribution function and the
+            hypothesized cumulative distribution function is measured at this
+            observation.
+        statistic_sign : int
+            +1 if the KS statistic is the maximum positive difference between
+            the empirical distribution function and the hypothesized cumulative
+            distribution function (D+); -1 if the KS statistic is the maximum
+            negative difference (D-).
+
+
+    See Also
+    --------
+    ks_2samp, kstest
+
+    Notes
+    -----
+    There are three options for the null and corresponding alternative
+    hypothesis that can be selected using the `alternative` parameter.
+
+    - `two-sided`: The null hypothesis is that the two distributions are
+      identical, F(x)=G(x) for all x; the alternative is that they are not
+      identical.
+
+    - `less`: The null hypothesis is that F(x) >= G(x) for all x; the
+      alternative is that F(x) < G(x) for at least one x.
+
+    - `greater`: The null hypothesis is that F(x) <= G(x) for all x; the
+      alternative is that F(x) > G(x) for at least one x.
+
+    Note that the alternative hypotheses describe the *CDFs* of the
+    underlying distributions, not the observed values. For example,
+    suppose x1 ~ F and x2 ~ G. If F(x) > G(x) for all x, the values in
+    x1 tend to be less than those in x2.
+
+    Examples
+    --------
+    Suppose we wish to test the null hypothesis that a sample is distributed
+    according to the standard normal.
+    We choose a confidence level of 95%; that is, we will reject the null
+    hypothesis in favor of the alternative if the p-value is less than 0.05.
+
+    When testing uniformly distributed data, we would expect the
+    null hypothesis to be rejected.
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> rng = np.random.default_rng()
+    >>> stats.ks_1samp(stats.uniform.rvs(size=100, random_state=rng),
+    ...                stats.norm.cdf)
+    KstestResult(statistic=0.5001899973268688,
+                 pvalue=1.1616392184763533e-23,
+                 statistic_location=0.00047625268963724654,
+                 statistic_sign=-1)
+
+    Indeed, the p-value is lower than our threshold of 0.05, so we reject the
+    null hypothesis in favor of the default "two-sided" alternative: the data
+    are *not* distributed according to the standard normal.
+
+    When testing random variates from the standard normal distribution, we
+    expect the data to be consistent with the null hypothesis most of the time.
+
+    >>> x = stats.norm.rvs(size=100, random_state=rng)
+    >>> stats.ks_1samp(x, stats.norm.cdf)
+    KstestResult(statistic=0.05345882212970396,
+                 pvalue=0.9227159037744717,
+                 statistic_location=-1.2451343873745018,
+                 statistic_sign=1)
+
+    As expected, the p-value of 0.92 is not below our threshold of 0.05, so
+    we cannot reject the null hypothesis.
+
+    Suppose, however, that the random variates are distributed according to
+    a normal distribution that is shifted toward greater values. In this case,
+    the cumulative density function (CDF) of the underlying distribution tends
+    to be *less* than the CDF of the standard normal. Therefore, we would
+    expect the null hypothesis to be rejected with ``alternative='less'``:
+
+    >>> x = stats.norm.rvs(size=100, loc=0.5, random_state=rng)
+    >>> stats.ks_1samp(x, stats.norm.cdf, alternative='less')
+    KstestResult(statistic=0.17482387821055168,
+                 pvalue=0.001913921057766743,
+                 statistic_location=0.3713830565352756,
+                 statistic_sign=-1)
+
+    and indeed, with p-value smaller than our threshold, we reject the null
+    hypothesis in favor of the alternative.
+
+    """
+    # `_axis_nan_policy` decorator ensures `axis=-1`
+    xp = array_namespace(x)
+    mode = method
+    if mode not in ['auto', 'exact', 'approx', 'asymp']:
+        raise ValueError(
+            f"Invalid value for method: {mode!r}. "
+            f"Must be one of 'auto', 'exact', 'approx', 'asymp'."
+        )
+
+    alternative = {'t': 'two-sided', 'g': 'greater', 'l': 'less'}.get(
+        alternative.lower()[0], alternative)
+    if alternative not in ['two-sided', 'greater', 'less']:
+        raise ValueError(f"Unexpected value {alternative=}")
+
+    x = xp.sort(x, axis=-1)
+    x = xp_promote(x, force_floating=True, xp=xp)
+    N = _count_nonmasked(x, axis=-1, xp=xp)
+    cdfvals = _masked_apply(cdf, args=(x, *args), xp=xp)
+
+    ones = xp.ones(x.shape[:-1], dtype=xp.int8)
+    ones = ones[()] if ones.ndim == 0 else ones
+
+    if alternative == 'greater':
+        Dplus, d_location = _compute_d(cdfvals, x, +1)
+        pvalue = _masked_apply(distributions.ksone.sf, args=(Dplus, N), xp=xp)
+        pvalue = xp.asarray(pvalue, dtype=x.dtype)
+        pvalue = pvalue[()] if pvalue.ndim == 0 else pvalue
+        Dplus = xp.asarray(Dplus) if is_marray(xp) else Dplus
+        return KstestResult(Dplus, pvalue,
+                            statistic_location=d_location,
+                            statistic_sign=ones)
+
+    if alternative == 'less':
+        Dminus, d_location = _compute_d(cdfvals, x, -1)
+        pvalue = _masked_apply(distributions.ksone.sf, args=(Dminus, N), xp=xp)
+        pvalue = xp.asarray(pvalue, dtype=x.dtype)
+        pvalue = pvalue[()] if pvalue.ndim == 0 else pvalue
+        Dminus = xp.asarray(Dminus) if is_marray(xp) else Dminus
+        return KstestResult(Dminus, pvalue,
+                            statistic_location=d_location,
+                            statistic_sign=-ones)
+
+    # alternative == 'two-sided':
+    Dplus, dplus_location = _compute_d(cdfvals, x, +1)
+    Dminus, dminus_location = _compute_d(cdfvals, x, -1)
+    i_plus = Dplus > Dminus
+    D = xp.where(i_plus, Dplus, Dminus)
+    d_location = xp.where(i_plus, dplus_location, dminus_location)
+    d_sign = xp.where(i_plus, ones, -ones)
+    if D.ndim == 0:
+        D, d_location, d_sign = D[()], d_location[()], d_sign[()]
+
+    if mode == 'auto':  # Always select exact
+        mode = 'exact'
+    if mode == 'exact':
+        prob = _masked_apply(distributions.kstwo.sf, args=(D, N), xp=xp)
+    elif mode == 'asymp':
+        prob = _masked_apply(distributions.kstwobign.sf, args=(D * N**0.5,), xp=xp)
+    else:
+        # mode == 'approx'
+        prob = 2 * _masked_apply(distributions.ksone.sf, args=(D, N), xp=xp)
+    prob = xp.clip(xp.asarray(prob, dtype=x.dtype), 0., 1.)
+    return KstestResult(D, prob,
+                        statistic_location=d_location,
+                        statistic_sign=d_sign)
+
+
+Ks_2sampResult = KstestResult
+
+
+def _compute_prob_outside_square(n, h):
+    """
+    Compute the proportion of paths that pass outside the two diagonal lines.
+
+    Parameters
+    ----------
+    n : int
+        n > 0
+    h : int
+        0 <= h <= n
+
+    Returns
+    -------
+    p : float
+        The proportion of paths that pass outside the lines x-y = +/-h.
+
+    """
+    # Compute Pr(D_{n,n} >= h/n)
+    # Prob = 2 * ( binom(2n, n-h) - binom(2n, n-2a) + binom(2n, n-3a) - ... )
+    # / binom(2n, n)
+    # This formulation exhibits subtractive cancellation.
+    # Instead divide each term by binom(2n, n), then factor common terms
+    # and use a Horner-like algorithm
+    # P = 2 * A0 * (1 - A1*(1 - A2*(1 - A3*(1 - A4*(...)))))
+
+    P = 0.0
+    k = int(np.floor(n / h))
+    while k >= 0:
+        p1 = 1.0
+        # Each of the Ai terms has numerator and denominator with
+        # h simple terms.
+        for j in range(h):
+            p1 = (n - k * h - j) * p1 / (n + k * h + j + 1)
+        P = p1 * (1.0 - P)
+        k -= 1
+    return 2 * P
+
+
+def _count_paths_outside_method(m, n, g, h):
+    """Count the number of paths that pass outside the specified diagonal.
+
+    Parameters
+    ----------
+    m : int
+        m > 0
+    n : int
+        n > 0
+    g : int
+        g is greatest common divisor of m and n
+    h : int
+        0 <= h <= lcm(m,n)
+
+    Returns
+    -------
+    p : float
+        The number of paths that go low.
+        The calculation may overflow - check for a finite answer.
+
+    Notes
+    -----
+    Count the integer lattice paths from (0, 0) to (m, n), which at some
+    point (x, y) along the path, satisfy:
+      m*y <= n*x - h*g
+    The paths make steps of size +1 in either positive x or positive y
+    directions.
+
+    We generally follow Hodges' treatment of Drion/Gnedenko/Korolyuk.
+    Hodges, J.L. Jr.,
+    "The Significance Probability of the Smirnov Two-Sample Test,"
+    Arkiv fiur Matematik, 3, No. 43 (1958), 469-86.
+
+    """
+    # Compute #paths which stay lower than x/m-y/n = h/lcm(m,n)
+    # B(x, y) = #{paths from (0,0) to (x,y) without
+    #             previously crossing the boundary}
+    #         = binom(x, y) - #{paths which already reached the boundary}
+    # Multiply by the number of path extensions going from (x, y) to (m, n)
+    # Sum.
+
+    # Probability is symmetrical in m, n.  Computation below assumes m >= n.
+    if m < n:
+        m, n = n, m
+    mg = m // g
+    ng = n // g
+
+    # Not every x needs to be considered.
+    # xj holds the list of x values to be checked.
+    # Wherever n*x/m + ng*h crosses an integer
+    lxj = n + (mg-h)//mg
+    xj = [(h + mg * j + ng-1)//ng for j in range(lxj)]
+    # B is an array just holding a few values of B(x,y), the ones needed.
+    # B[j] == B(x_j, j)
+    if lxj == 0:
+        return special.binom(m + n, n)
+    B = np.zeros(lxj)
+    B[0] = 1
+    # Compute the B(x, y) terms
+    for j in range(1, lxj):
+        Bj = special.binom(xj[j] + j, j)
+        for i in range(j):
+            bin = special.binom(xj[j] - xj[i] + j - i, j-i)
+            Bj -= bin * B[i]
+        B[j] = Bj
+    # Compute the number of path extensions...
+    num_paths = 0
+    for j in range(lxj):
+        bin = special.binom((m-xj[j]) + (n - j), n-j)
+        term = B[j] * bin
+        num_paths += term
+    return num_paths
+
+
+def _attempt_exact_2kssamp(n1, n2, g, d, alternative):
+    """Attempts to compute the exact 2sample probability.
+
+    n1, n2 are the sample sizes
+    g is the gcd(n1, n2)
+    d is the computed max difference in ECDFs
+
+    Returns (success, d, probability)
+    """
+    lcm = (n1 // g) * n2
+    h = int(np.round(d * lcm))
+    d = h * 1.0 / lcm
+    if h == 0:
+        return True, d, 1.0
+    saw_fp_error, prob = False, np.nan
+    try:
+        with np.errstate(invalid="raise", over="raise"):
+            if alternative == 'two-sided':
+                if n1 == n2:
+                    prob = _compute_prob_outside_square(n1, h)
+                else:
+                    prob = _compute_outer_prob_inside_method(n1, n2, g, h)
+            else:
+                if n1 == n2:
+                    # prob = binom(2n, n-h) / binom(2n, n)
+                    # Evaluating in that form incurs roundoff errors
+                    # from special.binom. Instead calculate directly
+                    jrange = np.arange(h)
+                    prob = np.prod((n1 - jrange) / (n1 + jrange + 1.0))
+                else:
+                    with np.errstate(over='raise'):
+                        num_paths = _count_paths_outside_method(n1, n2, g, h)
+                    bin = special.binom(n1 + n2, n1)
+                    if num_paths > bin or np.isinf(bin):
+                        saw_fp_error = True
+                    else:
+                        prob = num_paths / bin
+
+    except (FloatingPointError, OverflowError):
+        saw_fp_error = True
+
+    if saw_fp_error:
+        return False, d, np.nan
+    if not (0 <= prob <= 1):
+        return False, d, prob
+    return True, d, prob
+
+
+@xp_capabilities(skip_backends=[('dask.array', 'no rankdata')],
+                 jax_jit=False, cpu_only=True,  # null distribution is NumPy-only
+                 marray=True)
+@_axis_nan_policy_factory(_tuple_to_KstestResult, n_samples=2, n_outputs=4,
+                          result_to_tuple=_KstestResult_to_tuple)
+@_rename_parameter("mode", "method")
+def ks_2samp(data1, data2, alternative='two-sided', method='auto', *, axis=0):
+    """
+    Performs the two-sample Kolmogorov-Smirnov test for goodness of fit.
+
+    This test compares the underlying continuous distributions F(x) and G(x)
+    of two independent samples.  See Notes for a description of the available
+    null and alternative hypotheses.
+
+    Parameters
+    ----------
+    data1, data2 : array_like, 1-Dimensional
+        Two arrays of sample observations assumed to be drawn from a continuous
+        distribution, sample sizes can be different.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the null and alternative hypotheses. Default is 'two-sided'.
+        Please see explanations in the Notes below.
+    method : {'auto', 'exact', 'asymp'}, optional
+        Defines the method used for calculating the p-value.
+        The following options are available (default is 'auto'):
+
+        * 'auto' : use 'exact' for small size arrays, 'asymp' for large
+        * 'exact' : use exact distribution of test statistic
+        * 'asymp' : use asymptotic distribution of test statistic
+
+    axis : int or tuple of ints, default: 0
+        If an int or tuple of ints, the axis or axes of the input along which
+        to compute the statistic. The statistic of each axis-slice (e.g. row)
+        of the input will appear in a corresponding element of the output.
+        If ``None``, the input will be raveled before computing the statistic.
+
+    Returns
+    -------
+    res: KstestResult
+        An object containing attributes:
+
+        statistic : float
+            KS test statistic.
+        pvalue : float
+            One-tailed or two-tailed p-value.
+        statistic_location : float
+            Value from `data1` or `data2` corresponding with the KS statistic;
+            i.e., the distance between the empirical distribution functions is
+            measured at this observation.
+        statistic_sign : int
+            +1 if the empirical distribution function of `data1` exceeds
+            the empirical distribution function of `data2` at
+            `statistic_location`, otherwise -1.
+
+    See Also
+    --------
+    kstest, ks_1samp, epps_singleton_2samp, anderson_ksamp
+
+    Notes
+    -----
+    There are three options for the null and corresponding alternative
+    hypothesis that can be selected using the `alternative` parameter.
+
+    - `less`: The null hypothesis is that F(x) >= G(x) for all x; the
+      alternative is that F(x) < G(x) for at least one x. The statistic
+      is the magnitude of the minimum (most negative) difference between the
+      empirical distribution functions of the samples.
+
+    - `greater`: The null hypothesis is that F(x) <= G(x) for all x; the
+      alternative is that F(x) > G(x) for at least one x. The statistic
+      is the maximum (most positive) difference between the empirical
+      distribution functions of the samples.
+
+    - `two-sided`: The null hypothesis is that the two distributions are
+      identical, F(x)=G(x) for all x; the alternative is that they are not
+      identical. The statistic is the maximum absolute difference between the
+      empirical distribution functions of the samples.
+
+    Note that the alternative hypotheses describe the *CDFs* of the
+    underlying distributions, not the observed values of the data. For example,
+    suppose x1 ~ F and x2 ~ G. If F(x) > G(x) for all x, the values in
+    x1 tend to be less than those in x2.
+
+    If the KS statistic is large, then the p-value will be small, and this may
+    be taken as evidence against the null hypothesis in favor of the
+    alternative.
+
+    If ``method='exact'``, `ks_2samp` attempts to compute an exact p-value,
+    that is, the probability under the null hypothesis of obtaining a test
+    statistic value as extreme as the value computed from the data.
+    If ``method='asymp'``, the asymptotic Kolmogorov-Smirnov distribution is
+    used to compute an approximate p-value.
+    If ``method='auto'``, an exact p-value computation is attempted if both
+    sample sizes are less than 10000; otherwise, the asymptotic method is used.
+    In any case, if an exact p-value calculation is attempted and fails, a
+    warning will be emitted, and the asymptotic p-value will be returned.
+
+    The 'two-sided' 'exact' computation computes the complementary probability
+    and then subtracts from 1.  As such, the minimum probability it can return
+    is about 1e-16.  While the algorithm itself is exact, numerical
+    errors may accumulate for large sample sizes.   It is most suited to
+    situations in which one of the sample sizes is only a few thousand.
+
+    We generally follow Hodges' treatment of Drion/Gnedenko/Korolyuk [1]_.
+
+    References
+    ----------
+    .. [1] Hodges, J.L. Jr.,  "The Significance Probability of the Smirnov
+           Two-Sample Test," Arkiv fiur Matematik, 3, No. 43 (1958), 469-486.
+
+    Examples
+    --------
+    Suppose we wish to test the null hypothesis that two samples were drawn
+    from the same distribution.
+    We choose a confidence level of 95%; that is, we will reject the null
+    hypothesis in favor of the alternative if the p-value is less than 0.05.
+
+    If the first sample were drawn from a uniform distribution and the second
+    were drawn from the standard normal, we would expect the null hypothesis
+    to be rejected.
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> rng = np.random.default_rng()
+    >>> sample1 = stats.uniform.rvs(size=100, random_state=rng)
+    >>> sample2 = stats.norm.rvs(size=110, random_state=rng)
+    >>> stats.ks_2samp(sample1, sample2)
+    KstestResult(statistic=0.5454545454545454,
+                 pvalue=7.37417839555191e-15,
+                 statistic_location=-0.014071496412861274,
+                 statistic_sign=-1)
+
+
+    Indeed, the p-value is lower than our threshold of 0.05, so we reject the
+    null hypothesis in favor of the default "two-sided" alternative: the data
+    were *not* drawn from the same distribution.
+
+    When both samples are drawn from the same distribution, we expect the data
+    to be consistent with the null hypothesis most of the time.
+
+    >>> sample1 = stats.norm.rvs(size=105, random_state=rng)
+    >>> sample2 = stats.norm.rvs(size=95, random_state=rng)
+    >>> stats.ks_2samp(sample1, sample2)
+    KstestResult(statistic=0.10927318295739348,
+                 pvalue=0.5438289009927495,
+                 statistic_location=-0.1670157701848795,
+                 statistic_sign=-1)
+
+    As expected, the p-value of 0.54 is not below our threshold of 0.05, so
+    we cannot reject the null hypothesis.
+
+    Suppose, however, that the first sample were drawn from
+    a normal distribution shifted toward greater values. In this case,
+    the cumulative density function (CDF) of the underlying distribution tends
+    to be *less* than the CDF underlying the second sample. Therefore, we would
+    expect the null hypothesis to be rejected with ``alternative='less'``:
+
+    >>> sample1 = stats.norm.rvs(size=105, loc=0.5, random_state=rng)
+    >>> stats.ks_2samp(sample1, sample2, alternative='less')
+    KstestResult(statistic=0.4055137844611529,
+                 pvalue=3.5474563068855554e-08,
+                 statistic_location=-0.13249370614972575,
+                 statistic_sign=-1)
+
+    and indeed, with p-value smaller than our threshold, we reject the null
+    hypothesis in favor of the alternative.
+
+    """
+    # because of the _axis_nan_policy decorator, we can assume the arrays
+    # are broadcasted and `axis=-1`
+    mode = method
+
+    if mode not in ['auto', 'exact', 'asymp']:
+        raise ValueError(f'Invalid value for mode: {mode}')
+    alternative = {'t': 'two-sided', 'g': 'greater', 'l': 'less'}.get(
+        alternative.lower()[0], alternative)
+    if alternative not in ['two-sided', 'less', 'greater']:
+        raise ValueError(f'Invalid value for alternative: {alternative}')
+    MAX_AUTO_N = 10000  # 'auto' will attempt to be exact if n1,n2 <= MAX_AUTO_N
+
+    xp = array_namespace(data1, data2)
+    data1 = xp.sort(data1, axis=-1)
+    data2 = xp.sort(data2, axis=-1)
+    n1 = data1.shape[-1]
+    n2 = data2.shape[-1]
+    if min(n1, n2) == 0:
+        raise ValueError('Data passed to ks_2samp must not be empty')
+
+    data_all = xp.concat((data1, data2), axis=-1)
+    batch_shape = data_all.shape[:-1]
+    dtype = xp_result_type(data1, data2, force_floating=True, xp=xp)
+
+    if is_marray(xp):
+        # Previously, we used this algorithm for all backends:
+        n1 = xp.astype(_count_nonmasked(data1, axis=-1), dtype)
+        n2 = xp.astype(_count_nonmasked(data2, axis=-1), dtype)
+        cdf1 = xp.astype(_xp_searchsorted(data1, data_all, side='right'), dtype)
+        cdf2 = xp.astype(_xp_searchsorted(data2, data_all, side='right'), dtype)
+        cddiffs = cdf1/n1[..., xp.newaxis] - cdf2/n2[..., xp.newaxis]
+        # but the switch from `xp.searchsorted` to `_xp_searchsorted` would come with a
+        # pretty steep performance hit, so the algorithm below is faster.
+        # When `xp.searchsorted` is vectorized, we can revert.
+    else:
+        n = n1 + n2
+
+        # We want the ECDF of each sample evaluated at *all* the points in the pooled
+        # sample. The values each ECDF can assume are given by:
+        cdf1_vals = xp.broadcast_to(xp.linspace(0, 1, n1 + 1, dtype=dtype),
+                                    batch_shape + (n1 + 1,))
+        cdf2_vals = xp.broadcast_to(xp.linspace(0, 1, n2 + 1, dtype=dtype),
+                                    batch_shape + (n2 + 1,))
+        # Now we "just" need to know how many times each of these values *will* be
+        # assumed when we evaluate the ECDFs at all points in the pooled sample.
+        # These counts are given by the differences between consecutive ("min" or "max")
+        # ranks corresponding with the observations in the (sorted) samples.
+        ranks, data_all, _ = _rankdata(data_all, method='min', return_sorted=True)
+        ranks = xp.astype(ranks, xp.asarray(1).dtype)  # default int type
+        one = xp.ones((*ranks.shape[:-1], 1), dtype=ranks.dtype,
+                      device=xp_device(ranks))
+        cdf1_counts = xp.diff(ranks[..., :n1], prepend=one, append=n + one, axis=-1)
+        cdf2_counts = xp.diff(ranks[..., -n2:], prepend=one, append=n + one, axis=-1)
+        # Repeat isn't vectorized - in general, this would produce a ragged array.
+        # However, in our case, the sum of repeats for each slice is the same, so we can
+        # do a vectorized repeat by raveling, repeating, then restoring the shape.
+        cdf1 = xp.repeat(xp_ravel(cdf1_vals), xp_ravel(cdf1_counts), axis=-1)
+        cdf2 = xp.repeat(xp_ravel(cdf2_vals), xp_ravel(cdf2_counts), axis=-1)
+        cddiffs = xp.reshape(cdf1 - cdf2, ranks.shape[:-1] + (-1,))
+
+    # Identify the location of the statistic
+    argminS = xp.argmin(cddiffs, axis=-1, keepdims=True)
+    argmaxS = xp.argmax(cddiffs, axis=-1, keepdims=True)
+    loc_minS = xp.squeeze(xp.take_along_axis(data_all, argminS, axis=-1), axis=-1)
+    loc_maxS = xp.squeeze(xp.take_along_axis(data_all, argmaxS, axis=-1), axis=-1)
+
+    # Ensure sign of minS is not negative.
+    minS = -xp.squeeze(xp.take_along_axis(cddiffs, argminS, axis=-1), axis=-1)
+    maxS = xp.squeeze(xp.take_along_axis(cddiffs, argmaxS, axis=-1), axis=-1)
+    minS = xp.clip(minS, 0., 1.)
+
+    if alternative == 'less':
+        selector = xp.ones(minS.shape, dtype=xp.bool)
+    elif alternative == 'two-sided':
+        selector = minS > maxS
+    else:
+        selector = xp.zeros(minS.shape, dtype=xp.bool)
+
+    d = xp.where(selector, minS, maxS)
+    d_location = xp.where(selector, loc_minS, loc_maxS)
+    one = xp.asarray(1, dtype=xp.int8)
+    d_sign = xp.where(selector, -one, one)
+
+    if is_marray(xp):
+        d = d.data  # converted to NumPy below
+        n1, n2 = np.asarray(n1.data, dtype=int), np.asarray(n2.data, dtype=int)
+    prob = _ks_2samp_prob(np.asarray(d), n1, n2, mode, MAX_AUTO_N, alternative)
+    dtype = xp_result_type(data1, data2, force_floating=True, xp=xp)
+    prob = xp.asarray(prob, dtype=dtype)
+    d = xp.asarray(d, dtype=dtype)
+    if d.ndim == 0:
+        d, prob, d_location, d_sign = d[()], prob[()], d_location[()], d_sign[()]
+    return KstestResult(d, prob, statistic_location=d_location, statistic_sign=d_sign)
+
+
+@np.vectorize(excluded={3, 4, 5}, otypes=[np.float64])
+def _ks_2samp_prob(d, n1, n2, mode, MAX_AUTO_N, alternative):
+    # math.gcd used to return an `int`, but now that these return arrays, NumPy can
+    # return an int32. Unless we want the pythranized functions to be compiled for
+    # int32, this needs to produce an int64.
+    g = np.gcd(n1, n2).astype(np.int64)
+    n1g = n1 // g
+    n2g = n2 // g
+    prob = -np.inf
+    if mode == 'auto':
+        mode = 'exact' if max(n1, n2) <= MAX_AUTO_N else 'asymp'
+    elif mode == 'exact':
+        # If lcm(n1, n2) is too big, switch from exact to asymp
+        if n1g >= np.iinfo(np.int32).max / n2g:
+            mode = 'asymp'
+            warnings.warn(
+                f"Exact ks_2samp calculation not possible with samples sizes "
+                f"{n1} and {n2}. Switching to 'asymp'.", RuntimeWarning,
+                stacklevel=3)
+
+    if mode == 'exact':
+        success, d, prob = _attempt_exact_2kssamp(n1, n2, g, d, alternative)
+        if not success:
+            mode = 'asymp'
+            warnings.warn(f"ks_2samp: Exact calculation unsuccessful. "
+                          f"Switching to method={mode}.", RuntimeWarning,
+                          stacklevel=3)
+
+    if mode == 'asymp':
+        # The product n1*n2 is large.  Use Smirnov's asymptotic formula.
+        # Ensure float to avoid overflow in multiplication
+        # sorted because the one-sided formula is not symmetric in n1, n2
+        m, n = sorted([float(n1), float(n2)], reverse=True)
+        en = m * n / (m + n)
+        if alternative == 'two-sided':
+            prob = distributions.kstwo.sf(d, np.round(en))
+        else:
+            z = np.sqrt(en) * d
+            # Use Hodges' suggested approximation Eqn 5.3
+            # Requires m to be the larger of (n1, n2)
+            expt = -2 * z**2 - 2 * z * (m + 2*n)/np.sqrt(m*n*(m+n))/3.0
+            prob = np.exp(expt)
+
+    prob = np.clip(prob, 0, 1)
+    return prob
+
+
+def _parse_kstest_args(data1, data2, args, N):
+    # kstest allows many different variations of arguments.
+    # Pull out the parsing into a separate function
+    # (xvals, yvals, )  # 2sample
+    # (xvals, cdf function,..)
+    # (xvals, name of distribution, ...)
+    # (name of distribution, name of distribution, ...)
+
+    # Returns xvals, yvals, cdf
+    # where cdf is a cdf function, or None
+    # and yvals is either an array_like of values, or None
+    # and xvals is array_like.
+    rvsfunc, cdf = None, None
+    if isinstance(data1, str):
+        rvsfunc = getattr(distributions, data1).rvs
+    elif callable(data1):
+        rvsfunc = data1
+
+    if isinstance(data2, str):
+        special_distributions = {'norm': special.ndtr}
+        cdf = special_distributions.get(data2, getattr(distributions, data2).cdf)
+        data2 = None
+    elif callable(data2):
+        cdf = data2
+        data2 = None
+
+    xp = array_namespace(data1, data2, *args)
+    data1 = xp.sort(rvsfunc(*args, size=N) if rvsfunc else data1)
+    return data1, data2, cdf
+
+
+def _kstest_n_samples(kwargs):
+    cdf = kwargs['cdf']
+    return 1 if (isinstance(cdf, str) or callable(cdf)) else 2
+
+
+@xp_capabilities(skip_backends=[('dask.array', 'no rankdata')],
+                 jax_jit=False, cpu_only=True,  # see ks_1samp/ks_2samp
+                 marray=True)
+@_axis_nan_policy_factory(_tuple_to_KstestResult, n_samples=_kstest_n_samples,
+                          n_outputs=4, result_to_tuple=_KstestResult_to_tuple)
+@_rename_parameter("mode", "method")
+def kstest(rvs, cdf, args=(), N=20, alternative='two-sided', method='auto', *,
+           axis=0):
+    """
+    Performs the (one-sample or two-sample) Kolmogorov-Smirnov test for
+    goodness of fit.
+
+    The one-sample test compares the underlying distribution F(x) of a sample
+    against a given distribution G(x). The two-sample test compares the
+    underlying distributions of two independent samples. Both tests are valid
+    only for continuous distributions.
+
+    Parameters
+    ----------
+    rvs : str, array_like, or callable
+        If an array, it should be a 1-D array of observations of random
+        variables.
+        If a callable, it should be a function to generate random variables;
+        it is required to have a keyword argument `size`.
+        If a string, it should be the name of a distribution in `scipy.stats`,
+        which will be used to generate random variables.
+    cdf : str, array_like or callable
+        If array_like, it should be a 1-D array of observations of random
+        variables, and the two-sample test is performed
+        (and rvs must be array_like).
+        If a callable, that callable is used to calculate the cdf.
+        If a string, it should be the name of a distribution in `scipy.stats`,
+        which will be used as the cdf function.
+    args : tuple, sequence, optional
+        Distribution parameters, used if `rvs` or `cdf` are strings or
+        callables.
+    N : int, optional
+        Sample size if `rvs` is string or callable.  Default is 20.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the null and alternative hypotheses. Default is 'two-sided'.
+        Please see explanations in the Notes below.
+    method : {'auto', 'exact', 'approx', 'asymp'}, optional
+        Defines the distribution used for calculating the p-value.
+        The following options are available (default is 'auto'):
+
+        * 'auto' : selects one of the other options.
+        * 'exact' : uses the exact distribution of test statistic.
+        * 'approx' : approximates the two-sided probability with twice the
+          one-sided probability
+        * 'asymp': uses asymptotic distribution of test statistic
+
+    Returns
+    -------
+    res: KstestResult
+        An object containing attributes:
+
+        statistic : float
+            KS test statistic, either D+, D-, or D (the maximum of the two)
+        pvalue : float
+            One-tailed or two-tailed p-value.
+        statistic_location : float
+            In a one-sample test, this is the value of `rvs`
+            corresponding with the KS statistic; i.e., the distance between
+            the empirical distribution function and the hypothesized cumulative
+            distribution function is measured at this observation.
+
+            In a two-sample test, this is the value from `rvs` or `cdf`
+            corresponding with the KS statistic; i.e., the distance between
+            the empirical distribution functions is measured at this
+            observation.
+        statistic_sign : int
+            In a one-sample test, this is +1 if the KS statistic is the
+            maximum positive difference between the empirical distribution
+            function and the hypothesized cumulative distribution function
+            (D+); it is -1 if the KS statistic is the maximum negative
+            difference (D-).
+
+            In a two-sample test, this is +1 if the empirical distribution
+            function of `rvs` exceeds the empirical distribution
+            function of `cdf` at `statistic_location`, otherwise -1.
+
+    See Also
+    --------
+    ks_1samp, ks_2samp
+
+    Notes
+    -----
+    There are three options for the null and corresponding alternative
+    hypothesis that can be selected using the `alternative` parameter.
+
+    - `two-sided`: The null hypothesis is that the two distributions are
+      identical, F(x)=G(x) for all x; the alternative is that they are not
+      identical.
+
+    - `less`: The null hypothesis is that F(x) >= G(x) for all x; the
+      alternative is that F(x) < G(x) for at least one x.
+
+    - `greater`: The null hypothesis is that F(x) <= G(x) for all x; the
+      alternative is that F(x) > G(x) for at least one x.
+
+    Note that the alternative hypotheses describe the *CDFs* of the
+    underlying distributions, not the observed values. For example,
+    suppose x1 ~ F and x2 ~ G. If F(x) > G(x) for all x, the values in
+    x1 tend to be less than those in x2.
+
+
+    Examples
+    --------
+    Suppose we wish to test the null hypothesis that a sample is distributed
+    according to the standard normal.
+    We choose a confidence level of 95%; that is, we will reject the null
+    hypothesis in favor of the alternative if the p-value is less than 0.05.
+
+    When testing uniformly distributed data, we would expect the
+    null hypothesis to be rejected.
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> rng = np.random.default_rng()
+    >>> stats.kstest(stats.uniform.rvs(size=100, random_state=rng),
+    ...              stats.norm.cdf)
+    KstestResult(statistic=0.5001899973268688,
+                 pvalue=1.1616392184763533e-23,
+                 statistic_location=0.00047625268963724654,
+                 statistic_sign=-1)
+
+    Indeed, the p-value is lower than our threshold of 0.05, so we reject the
+    null hypothesis in favor of the default "two-sided" alternative: the data
+    are *not* distributed according to the standard normal.
+
+    When testing random variates from the standard normal distribution, we
+    expect the data to be consistent with the null hypothesis most of the time.
+
+    >>> x = stats.norm.rvs(size=100, random_state=rng)
+    >>> stats.kstest(x, stats.norm.cdf)
+    KstestResult(statistic=0.05345882212970396,
+                 pvalue=0.9227159037744717,
+                 statistic_location=-1.2451343873745018,
+                 statistic_sign=1)
+
+
+    As expected, the p-value of 0.92 is not below our threshold of 0.05, so
+    we cannot reject the null hypothesis.
+
+    Suppose, however, that the random variates are distributed according to
+    a normal distribution that is shifted toward greater values. In this case,
+    the cumulative density function (CDF) of the underlying distribution tends
+    to be *less* than the CDF of the standard normal. Therefore, we would
+    expect the null hypothesis to be rejected with ``alternative='less'``:
+
+    >>> x = stats.norm.rvs(size=100, loc=0.5, random_state=rng)
+    >>> stats.kstest(x, stats.norm.cdf, alternative='less')
+    KstestResult(statistic=0.17482387821055168,
+                 pvalue=0.001913921057766743,
+                 statistic_location=0.3713830565352756,
+                 statistic_sign=-1)
+
+    and indeed, with p-value smaller than our threshold, we reject the null
+    hypothesis in favor of the alternative.
+
+    For convenience, the previous test can be performed using the name of the
+    distribution as the second argument.
+
+    >>> stats.kstest(x, "norm", alternative='less')
+    KstestResult(statistic=0.17482387821055168,
+                 pvalue=0.001913921057766743,
+                 statistic_location=0.3713830565352756,
+                 statistic_sign=-1)
+
+    The examples above have all been one-sample tests identical to those
+    performed by `ks_1samp`. Note that `kstest` can also perform two-sample
+    tests identical to those performed by `ks_2samp`. For example, when two
+    samples are drawn from the same distribution, we expect the data to be
+    consistent with the null hypothesis most of the time.
+
+    >>> sample1 = stats.laplace.rvs(size=105, random_state=rng)
+    >>> sample2 = stats.laplace.rvs(size=95, random_state=rng)
+    >>> stats.kstest(sample1, sample2)
+    KstestResult(statistic=0.11779448621553884,
+                 pvalue=0.4494256912629795,
+                 statistic_location=0.6138814275424155,
+                 statistic_sign=1)
+
+    As expected, the p-value of 0.45 is not below our threshold of 0.05, so
+    we cannot reject the null hypothesis.
+
+    """
+    # to not break compatibility with existing code
+    if alternative == 'two_sided':
+        alternative = 'two-sided'
+    if alternative not in ['two-sided', 'greater', 'less']:
+        raise ValueError(f"Unexpected alternative: {alternative}")
+    xvals, yvals, cdf = _parse_kstest_args(rvs, cdf, args, N)
+    if cdf:
+        return ks_1samp(xvals, cdf, args=args, alternative=alternative,
+                        method=method, axis=axis, _no_deco=True)
+    return ks_2samp(xvals, yvals, alternative=alternative, method=method,
+                    axis=axis, _no_deco=True)
+
+
+@xp_capabilities(np_only=True)
+def tiecorrect(rankvals):
+    """Tie correction factor for Mann-Whitney U and Kruskal-Wallis H tests.
+
+    Parameters
+    ----------
+    rankvals : array_like
+        A 1-D sequence of ranks.  Typically this will be the array
+        returned by `~scipy.stats.rankdata`.
+
+    Returns
+    -------
+    factor : float
+        Correction factor for U or H.
+
+    See Also
+    --------
+    rankdata : Assign ranks to the data
+    mannwhitneyu : Mann-Whitney rank test
+    kruskal : Kruskal-Wallis H test
+
+    References
+    ----------
+    .. [1] Siegel, S. (1956) Nonparametric Statistics for the Behavioral
+           Sciences.  New York: McGraw-Hill.
+
+    Examples
+    --------
+    >>> from scipy.stats import tiecorrect, rankdata
+    >>> tiecorrect([1, 2.5, 2.5, 4])
+    0.9
+    >>> ranks = rankdata([1, 3, 2, 4, 5, 7, 2, 8, 4])
+    >>> ranks
+    array([ 1. ,  4. ,  2.5,  5.5,  7. ,  8. ,  2.5,  9. ,  5.5])
+    >>> tiecorrect(ranks)
+    0.9833333333333333
+
+    """
+    arr = np.sort(rankvals)
+    idx = np.nonzero(np.r_[True, arr[1:] != arr[:-1], True])[0]
+    cnt = np.diff(idx).astype(np.float64)
+
+    size = np.float64(arr.size)
+    return 1.0 if size < 2 else 1.0 - (cnt**3 - cnt).sum() / (size**3 - size)
+
+
+RanksumsResult = namedtuple('RanksumsResult', ('statistic', 'pvalue'))
+
+
+@xp_capabilities(out_of_scope=True)  # legacy
+@_axis_nan_policy_factory(RanksumsResult, n_samples=2)
+def ranksums(x, y, alternative='two-sided'):
+    """Compute the Wilcoxon rank-sum statistic for two samples.
+
+    .. legacy:: function
+
+        This function includes a subset of the features of `mannwhitneyu`.
+        Its statistic and p-value can be reproduced using `mannwhitneyu` with
+        options ``use_continuity=False`` and ``method='asymptotic'``.
+        Prefer `mannwhitneyu` for use in new code.
+
+    The Wilcoxon rank-sum test tests the null hypothesis that two sets
+    of measurements are drawn from the same distribution.  The alternative
+    hypothesis is that values in one sample are more likely to be
+    larger than the values in the other sample.
+
+    This test should be used to compare two samples from continuous
+    distributions.  It does not handle ties between measurements
+    in x and y.  For tie-handling and an optional continuity correction
+    see `scipy.stats.mannwhitneyu`.
+
+    Parameters
+    ----------
+    x, y : array_like
+        The data from the two samples.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis. Default is 'two-sided'.
+        The following options are available:
+
+        * 'two-sided': one of the distributions (underlying `x` or `y`) is
+          stochastically greater than the other.
+        * 'less': the distribution underlying `x` is stochastically less
+          than the distribution underlying `y`.
+        * 'greater': the distribution underlying `x` is stochastically greater
+          than the distribution underlying `y`.
+
+        .. versionadded:: 1.7.0
+
+    Returns
+    -------
+    statistic : float
+        The test statistic under the large-sample approximation that the
+        rank sum statistic is normally distributed.
+    pvalue : float
+        The p-value of the test.
+
+    See Also
+    --------
+    scipy.stats.mannwhitneyu
+
+    References
+    ----------
+    .. [1] https://en.wikipedia.org/wiki/Wilcoxon_rank-sum_test
+
+    Examples
+    --------
+    We can test the hypothesis that two independent unequal-sized samples are
+    drawn from the same distribution with computing the Wilcoxon rank-sum
+    statistic.
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> rng = np.random.default_rng(6004253334)
+    >>> sample1 = rng.uniform(-1, 1, 200)
+    >>> sample2 = rng.uniform(-0.5, 1.5, 300) # a shifted distribution
+    >>> stats.ranksums(sample1, sample2)
+    RanksumsResult(statistic=np.float64(-7.576201867),
+                   pvalue=np.float64(3.5581802537469756e-14))
+    >>> stats.ranksums(sample1, sample2, alternative='less')
+    RanksumsResult(statistic=np.float64(-7.576201867066302),
+                   pvalue=np.float64(1.7790901268734878e-14))
+    >>> stats.ranksums(sample1, sample2, alternative='greater')
+    RanksumsResult(statistic=np.float64(-7.576201867066302),
+                   pvalue=np.float64(0.9999999999999822))
+
+    The p-value of less than ``0.05`` indicates that this test rejects the
+    hypothesis at the 5% significance level.
+
+    Note that identical hypothesis tests (and more accurate ones) can be performed
+    using `mannwhitneyu`. Prefer `mannwhitneyu` for use in new code.
+
+    >>> res = stats.mannwhitneyu(sample1, sample2, alternative='greater',
+    ...                          method='asymptotic', use_continuity = False)
+    >>> res.zstatistic
+    np.float64(-7.576201867066302)
+    >>> res.pvalue
+    np.float64(0.9999999999999822)
+    """
+    x, y = map(np.asarray, (x, y))
+    n1 = len(x)
+    n2 = len(y)
+    alldata = np.concatenate((x, y))
+    ranked = rankdata(alldata)
+    x = ranked[:n1]
+    s = np.sum(x, axis=0)
+    expected = n1 * (n1+n2+1) / 2.0
+    z = (s - expected) / np.sqrt(n1*n2*(n1+n2+1)/12.0)
+    pvalue = _get_pvalue(z, _SimpleNormal(), alternative, xp=np)
+
+    return RanksumsResult(z[()], pvalue[()])
+
+
+KruskalResult = namedtuple('KruskalResult', ('statistic', 'pvalue'))
+
+
+@xp_capabilities(skip_backends=[('dask.array', 'no rankdata')],
+                 marray=True)
+@_axis_nan_policy_factory(KruskalResult, n_samples=None)
+def kruskal(*samples, nan_policy='propagate', axis=0):
+    """Compute the Kruskal-Wallis H-test for independent samples.
+
+    The Kruskal-Wallis H-test tests the null hypothesis that the population
+    median of all of the groups are equal.  It is a non-parametric version of
+    ANOVA.  The test works on 2 or more independent samples, which may have
+    different sizes.  Note that rejecting the null hypothesis does not
+    indicate which of the groups differs.  Post hoc comparisons between
+    groups are required to determine which groups are different.
+
+    Parameters
+    ----------
+    *samples : array_like
+       Two or more arrays with the sample measurements can be given as
+       arguments. Samples must be one-dimensional.
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains nan.
+        The following options are available (default is 'propagate'):
+
+        * 'propagate': returns nan
+        * 'raise': throws an error
+        * 'omit': performs the calculations ignoring nan values
+
+    axis : int or tuple of ints, default: 0
+        If an int or tuple of ints, the axis or axes of the input along which
+        to compute the statistic. The statistic of each axis-slice (e.g. row)
+        of the input will appear in a corresponding element of the output.
+        If ``None``, the input will be raveled before computing the statistic.
+
+    Returns
+    -------
+    statistic : float
+       The Kruskal-Wallis H statistic, corrected for ties.
+    pvalue : float
+       The p-value for the test using the assumption that H has a chi
+       square distribution. The p-value returned is the survival function of
+       the chi square distribution evaluated at H.
+
+    See Also
+    --------
+    f_oneway : 1-way ANOVA.
+    mannwhitneyu : Mann-Whitney rank test on two samples.
+    friedmanchisquare : Friedman test for repeated measurements.
+
+    Notes
+    -----
+    Due to the assumption that H has a chi square distribution, the number
+    of samples in each group must not be too small.  A typical rule is
+    that each sample must have at least 5 measurements.
+
+    References
+    ----------
+    .. [1] W. H. Kruskal & W. W. Wallis, "Use of Ranks in
+       One-Criterion Variance Analysis", Journal of the American Statistical
+       Association, Vol. 47, Issue 260, pp. 583-621, 1952.
+    .. [2] https://en.wikipedia.org/wiki/Kruskal-Wallis_one-way_analysis_of_variance
+
+    Examples
+    --------
+    >>> from scipy import stats
+    >>> x = [1, 3, 5, 7, 9]
+    >>> y = [2, 4, 6, 8, 10]
+    >>> stats.kruskal(x, y)
+    KruskalResult(statistic=0.2727272727272734, pvalue=0.6015081344405895)
+
+    >>> x = [1, 1, 1]
+    >>> y = [2, 2, 2]
+    >>> z = [2, 2]
+    >>> stats.kruskal(x, y, z)
+    KruskalResult(statistic=7.0, pvalue=0.0301973834223185)
+
+    """
+    xp = array_namespace(*samples)
+    samples = xp_promote(*samples, force_floating=True, xp=xp)
+
+    num_groups = len(samples)
+    if num_groups < 2:
+        raise ValueError("Need at least two groups in stats.kruskal()")
+
+    lengths = [sample.shape[-1] for sample in samples]
+    if any(lengths) < 1:  # Only needed for `test_axis_nan_policy`
+        raise ValueError("Inputs must not be empty.")
+
+    alldata = xp.concat(samples, axis=-1)
+    ranked, _, t = _rankdata(alldata, method='average', return_ties=True)
+    counts = [xp.asarray(_count_nonmasked(sample, -1), dtype=t.dtype)
+              for sample in samples]
+    totaln = sum(counts)
+    ties = 1 - xp.sum(t**3 - t, axis=-1) / (totaln**3 - totaln)  # tiecorrect(ranked)
+
+    # Compute sum^2/count for each group and sum
+    j = list(itertools.accumulate(lengths, initial=0))
+    ssbn = sum(xp.sum(ranked[..., j[i]:j[i + 1]], axis=-1)**2 / counts[i]
+               for i in range(num_groups))
+
+    h = 12.0 / (totaln * (totaln + 1)) * ssbn - 3 * (totaln + 1)
+    df = xp.asarray(num_groups - 1, dtype=h.dtype)
+    h /= ties
+
+    chi2 = _SimpleChi2(df)
+    pvalue = _get_pvalue(h, chi2, alternative='greater', symmetric=False, xp=np)
+    return KruskalResult(h, pvalue)
+
+
+FriedmanchisquareResult = namedtuple('FriedmanchisquareResult',
+                                     ('statistic', 'pvalue'))
+
+
+@xp_capabilities(skip_backends=[("dask.array", "no rankdata")],
+                 marray=True)
+@_axis_nan_policy_factory(FriedmanchisquareResult, n_samples=None, paired=True)
+def friedmanchisquare(*samples, axis=0):
+    """Compute the Friedman test for repeated samples.
+
+    The Friedman test tests the null hypothesis that repeated samples of
+    the same individuals have the same distribution.  It is often used
+    to test for consistency among samples obtained in different ways.
+    For example, if two sampling techniques are used on the same set of
+    individuals, the Friedman test can be used to determine if the two
+    sampling techniques are consistent.
+
+    Parameters
+    ----------
+    *samples : array_like
+        Arrays of observations.  All of the arrays must have the same number
+        of elements.  At least three samples must be given.
+    axis : int or tuple of ints, default: 0
+        If an int or tuple of ints, the axis or axes of the input along which
+        to compute the statistic. The statistic of each axis-slice (e.g. row)
+        of the input will appear in a corresponding element of the output.
+        If ``None``, the input will be raveled before computing the statistic.
+
+    Returns
+    -------
+    statistic : float
+        The test statistic, correcting for ties.
+    pvalue : float
+        The associated p-value assuming that the test statistic has a chi
+        squared distribution.
+
+    See Also
+    --------
+    :ref:`hypothesis_friedmanchisquare` : Extended example
+
+    Notes
+    -----
+    Due to the assumption that the test statistic has a chi squared
+    distribution, the p-value is only reliable for n > 10 and more than
+    6 repeated samples.
+
+    References
+    ----------
+    .. [1] https://en.wikipedia.org/wiki/Friedman_test
+    .. [2] Demsar, J. (2006). Statistical comparisons of classifiers over
+           multiple data sets. Journal of Machine Learning Research, 7, 1-30.
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> rng = np.random.default_rng(seed=18)
+    >>> x = rng.random((6, 10))
+    >>> from scipy.stats import friedmanchisquare
+    >>> res = friedmanchisquare(x[0], x[1], x[2], x[3], x[4], x[5])
+    >>> res.statistic, res.pvalue
+    (11.428571428571416, 0.043514520866727614)
+
+    The p-value is less than 0.05; however, as noted above, the results may not
+    be reliable since we have a small number of repeated samples.
+
+    For a more detailed example, see :ref:`hypothesis_friedmanchisquare`.
+    """
+    k = len(samples)
+    if k < 3:
+        raise ValueError('At least 3 samples must be given '
+                         f'for Friedman test, got {k}.')
+
+    xp = array_namespace(*samples)
+    samples = xp_promote(*samples, force_floating=True, xp=xp)
+    dtype = samples[0].dtype
+    samples = _share_masks(*samples, xp=xp)  # paired-sample test
+
+    n = samples[0].shape[-1]
+    if n == 0:  # only for `test_axis_nan_policy`; user doesn't see this
+        raise ValueError("One or more sample arguments is too small.")
+
+    # Rank data
+    # axis-slices are aligned with axis -1 by decorator; stack puts samples along axis 0
+    # The transpose flips this so we can work with axis-slices along -1. This is a
+    # reducing statistic, so both axes 0 and -1 are consumed.
+    data = xp_swapaxes(xp.stack(samples), 0, -1)
+    data, _, t = _rankdata(data, method='average', return_ties=True)
+
+    # Handle ties
+    ties = xp.sum(t * (t*t - 1), axis=(0, -1))
+    count = xp.asarray(_count_nonmasked(samples[0], axis=-1), dtype=ties.dtype)
+    c = 1 - ties / (k*(k*k - 1)*count)
+
+    ssbn = xp.sum(xp.sum(data, axis=0)**2, axis=-1)
+    statistic = (12.0 / (k*count*(k+1)) * ssbn - 3*count*(k+1)) / c
+
+    chi2 = _SimpleChi2(xp.asarray(k - 1, dtype=dtype))
+    pvalue = _get_pvalue(statistic, chi2, alternative='greater', symmetric=False, xp=xp)
+    return FriedmanchisquareResult(statistic, pvalue)
+
+
+BrunnerMunzelResult = namedtuple('BrunnerMunzelResult',
+                                 ('statistic', 'pvalue'))
+
+
+@xp_capabilities(cpu_only=True, # torch GPU can't use `stdtr`
+                 marray=True,
+                 skip_backends=[('dask.array', 'needs rankdata')])
+@_axis_nan_policy_factory(BrunnerMunzelResult, n_samples=2)
+def brunnermunzel(x, y, alternative="two-sided", distribution="t",
+                  nan_policy='propagate', *, axis=0):
+    """Compute the Brunner-Munzel test on samples x and y.
+
+    The Brunner-Munzel test is a nonparametric test of the null hypothesis that
+    when values are taken one by one from each group, the probabilities of
+    getting large values in both groups are equal.
+    Unlike the Wilcoxon-Mann-Whitney's U test, this does not require the
+    assumption of equivariance of two groups. Note that this does not assume
+    the distributions are same. This test works on two independent samples,
+    which may have different sizes.
+
+    Parameters
+    ----------
+    x, y : array_like
+        Array of samples, should be one-dimensional.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis.
+        The following options are available (default is 'two-sided'):
+
+        * 'two-sided'
+        * 'less': one-sided
+        * 'greater': one-sided
+
+    distribution : {'t', 'normal'}, optional
+        Defines how to get the p-value.
+        The following options are available (default is 't'):
+
+        * 't': get the p-value by t-distribution
+        * 'normal': get the p-value by standard normal distribution.
+
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains nan.
+        The following options are available (default is 'propagate'):
+
+        * 'propagate': returns nan
+        * 'raise': throws an error
+        * 'omit': performs the calculations ignoring nan values
+
+    axis : int or None, default=0
+        If an int, the axis of the input along which to compute the statistic.
+        The statistic of each axis-slice (e.g. row) of the input will appear
+        in a corresponding element of the output. If None, the input will be
+        raveled before computing the statistic.
+
+    Returns
+    -------
+    statistic : float
+        The Brunner-Munzer W statistic.
+    pvalue : float
+        p-value assuming an t distribution. One-sided or
+        two-sided, depending on the choice of `alternative` and `distribution`.
+
+    See Also
+    --------
+    mannwhitneyu : Mann-Whitney rank test on two samples.
+
+    Notes
+    -----
+    Brunner and Munzel recommended to estimate the p-value by t-distribution
+    when the size of data is 50 or less. If the size is lower than 10, it would
+    be better to use permuted Brunner Munzel test (see [2]_).
+
+    References
+    ----------
+    .. [1] Brunner, E. and Munzel, U. "The nonparametric Benhrens-Fisher
+           problem: Asymptotic theory and a small-sample approximation".
+           Biometrical Journal. Vol. 42(2000): 17-25.
+    .. [2] Neubert, K. and Brunner, E. "A studentized permutation test for the
+           non-parametric Behrens-Fisher problem". Computational Statistics and
+           Data Analysis. Vol. 51(2007): 5192-5204.
+
+    Examples
+    --------
+    >>> from scipy import stats
+    >>> x1 = [1,2,1,1,1,1,1,1,1,1,2,4,1,1]
+    >>> x2 = [3,3,4,3,1,2,3,1,1,5,4]
+    >>> w, p_value = stats.brunnermunzel(x1, x2)
+    >>> w
+    3.1374674823029505
+    >>> p_value
+    0.0057862086661515377
+
+    """
+    # _axis_nan_policy decorator ensures we can work along the last axis
+    xp = array_namespace(x, y)
+    length_x = x.shape[-1]
+    nx = _count_nonmasked(x, axis=-1)
+    ny = _count_nonmasked(y, axis=-1)
+
+    rankc = rankdata(xp.concat((x, y), axis=axis), axis=-1)
+    rankcx = rankc[..., :length_x]
+    rankcy = rankc[..., length_x:]
+    rankcx_mean = xp.mean(rankcx, axis=-1, keepdims=True)
+    rankcy_mean = xp.mean(rankcy, axis=-1, keepdims=True)
+    rankx = rankdata(x, axis=-1)
+    ranky = rankdata(y, axis=-1)
+    rankx_mean = xp.mean(rankx, axis=-1, keepdims=True)
+    ranky_mean = xp.mean(ranky, axis=-1, keepdims=True)
+
+    temp_x = rankcx - rankx - rankcx_mean + rankx_mean
+    Sx = xp.vecdot(temp_x, temp_x, axis=-1)
+    Sx /= nx - 1
+    temp_y = rankcy - ranky - rankcy_mean + ranky_mean
+    Sy = xp.vecdot(temp_y, temp_y, axis=-1)
+    Sy /= ny - 1
+
+    rankcx_mean = xp.squeeze(rankcx_mean, axis=-1)
+    rankcy_mean = xp.squeeze(rankcy_mean, axis=-1)
+    wbfn = nx * ny * (rankcy_mean - rankcx_mean)
+    wbfn /= (nx + ny) * xp.sqrt(nx * Sx + ny * Sy)
+
+    if distribution == "t":
+        df_numer = xp.pow(nx * Sx + ny * Sy, 2.0)
+        df_denom = xp.pow(nx * Sx, 2.0) / (nx - 1)
+        df_denom += xp.pow(ny * Sy, 2.0) / (ny - 1)
+        df = df_numer / df_denom
+
+        if not is_lazy_array(df_numer) and not is_lazy_array(df_denom) and (
+                xp.any(df_numer == 0) and xp.any(df_denom == 0)):
+            message = ("p-value cannot be estimated with `distribution='t' "
+                       "because degrees of freedom parameter is undefined "
+                       "(0/0). Try using `distribution='normal'")
+            warnings.warn(message, RuntimeWarning, stacklevel=2)
+
+        distribution = _SimpleStudentT(df)
+    elif distribution == "normal":
+        distribution = _SimpleNormal()
+    else:
+        raise ValueError(
+            "distribution should be 't' or 'normal'")
+
+    p = _get_pvalue(-wbfn, distribution, alternative, xp=xp)
+
+    return BrunnerMunzelResult(wbfn, p)
+
+
+@xp_capabilities(cpu_only=True, exceptions=['cupy', 'jax.numpy'],
+    reason='Delegation for `special.stdtr` only implemented for CuPy and JAX.',
+    marray=True)
+@_axis_nan_policy_factory(SignificanceResult, kwd_samples=['weights'], paired=True)
+def combine_pvalues(pvalues, method='fisher', weights=None, *, axis=0):
+    """
+    Combine p-values from independent tests that bear upon the same hypothesis.
+
+    These methods are intended only for combining p-values from hypothesis
+    tests based upon continuous distributions.
+
+    Each method assumes that under the null hypothesis, the p-values are
+    sampled independently and uniformly from the interval [0, 1]. A test
+    statistic (different for each method) is computed and a combined
+    p-value is calculated based upon the distribution of this test statistic
+    under the null hypothesis.
+
+    Parameters
+    ----------
+    pvalues : array_like
+        Array of p-values assumed to come from independent tests based on
+        continuous distributions.
+    method : {'fisher', 'pearson', 'tippett', 'stouffer', 'mudholkar_george'}
+
+        Name of method to use to combine p-values.
+
+        The available methods are (see Notes for details):
+
+        * 'fisher': Fisher's method (Fisher's combined probability test)
+        * 'pearson': Pearson's method
+        * 'mudholkar_george': Mudholkar's and George's method
+        * 'tippett': Tippett's method
+        * 'stouffer': Stouffer's Z-score method
+
+    weights : array_like, optional
+        Optional array of weights used only for Stouffer's Z-score method.
+        Ignored by other methods.
+
+    Returns
+    -------
+    res : SignificanceResult
+        An object containing attributes:
+
+        statistic : float
+            The statistic calculated by the specified method.
+        pvalue : float
+            The combined p-value.
+
+    Examples
+    --------
+    Suppose we wish to combine p-values from four independent tests
+    of the same null hypothesis using Fisher's method (default).
+
+    >>> from scipy.stats import combine_pvalues
+    >>> pvalues = [0.1, 0.05, 0.02, 0.3]
+    >>> combine_pvalues(pvalues)
+    SignificanceResult(statistic=20.828626352604235, pvalue=0.007616871850449092)
+
+    When the individual p-values carry different weights, consider Stouffer's
+    method.
+
+    >>> weights = [1, 2, 3, 4]
+    >>> res = combine_pvalues(pvalues, method='stouffer', weights=weights)
+    >>> res.pvalue
+    0.009578891494533616
+
+    Notes
+    -----
+    If this function is applied to tests with a discrete statistics such as
+    any rank test or contingency-table test, it will yield systematically
+    wrong results, e.g. Fisher's method will systematically overestimate the
+    p-value [1]_. This problem becomes less severe for large sample sizes
+    when the discrete distributions become approximately continuous.
+
+    The differences between the methods can be best illustrated by their
+    statistics and what aspects of a combination of p-values they emphasise
+    when considering significance [2]_. For example, methods emphasising large
+    p-values are more sensitive to strong false and true negatives; conversely
+    methods focussing on small p-values are sensitive to positives.
+
+    * The statistics of Fisher's method (also known as Fisher's combined
+      probability test) [3]_ is :math:`-2\\sum_i \\log(p_i)`, which is
+      equivalent (as a test statistics) to the product of individual p-values:
+      :math:`\\prod_i p_i`. Under the null hypothesis, this statistics follows
+      a :math:`\\chi^2` distribution. This method emphasises small p-values.
+    * Pearson's method uses :math:`-2\\sum_i\\log(1-p_i)`, which is equivalent
+      to :math:`\\prod_i \\frac{1}{1-p_i}` [2]_.
+      It thus emphasises large p-values.
+    * Mudholkar and George compromise between Fisher's and Pearson's method by
+      averaging their statistics [4]_. Their method emphasises extreme
+      p-values, both close to 1 and 0.
+    * Stouffer's method [5]_ uses Z-scores and the statistic:
+      :math:`\\sum_i \\Phi^{-1} (p_i)`, where :math:`\\Phi` is the CDF of the
+      standard normal distribution. The advantage of this method is that it is
+      straightforward to introduce weights, which can make Stouffer's method
+      more powerful than Fisher's method when the p-values are from studies
+      of different size [6]_ [7]_.
+    * Tippett's method uses the smallest p-value as a statistic.
+      (Mind that this minimum is not the combined p-value.)
+
+    Fisher's method may be extended to combine p-values from dependent tests
+    [8]_. Extensions such as Brown's method and Kost's method are not currently
+    implemented.
+
+    .. versionadded:: 0.15.0
+
+    References
+    ----------
+    .. [1] Kincaid, W. M., "The Combination of Tests Based on Discrete
+           Distributions." Journal of the American Statistical Association 57,
+           no. 297 (1962), 10-19.
+    .. [2] Heard, N. and Rubin-Delanchey, P. "Choosing between methods of
+           combining p-values."  Biometrika 105.1 (2018): 239-246.
+    .. [3] https://en.wikipedia.org/wiki/Fisher%27s_method
+    .. [4] George, E. O., and G. S. Mudholkar. "On the convolution of logistic
+           random variables." Metrika 30.1 (1983): 1-13.
+    .. [5] https://en.wikipedia.org/wiki/Fisher%27s_method#Relation_to_Stouffer.27s_Z-score_method
+    .. [6] Whitlock, M. C. "Combining probability from independent tests: the
+           weighted Z-method is superior to Fisher's approach." Journal of
+           Evolutionary Biology 18, no. 5 (2005): 1368-1373.
+    .. [7] Zaykin, Dmitri V. "Optimally weighted Z-test is a powerful method
+           for combining probabilities in meta-analysis." Journal of
+           Evolutionary Biology 24, no. 8 (2011): 1836-1841.
+    .. [8] https://en.wikipedia.org/wiki/Extensions_of_Fisher%27s_method
+
+    """
+    xp = array_namespace(pvalues, weights)
+    pvalues, weights = xp_promote(pvalues, weights, broadcast=True,
+                                  force_floating=True, xp=xp)
+
+    if xp_size(pvalues) == 0:
+        # This is really only needed for *testing* _axis_nan_policy decorator
+        # It won't happen when the decorator is used.
+        NaN = _get_nan(pvalues)
+        return SignificanceResult(NaN, NaN)
+
+    n = _count_nonmasked(pvalues, axis)
+    n = xp.asarray(n, dtype=pvalues.dtype, device=xp_device(pvalues))
+
+    if method == 'fisher':
+        statistic = -2 * xp.sum(xp.log(pvalues), axis=axis)
+        chi2 = _SimpleChi2(2*n)
+        pval = _get_pvalue(statistic, chi2, alternative='greater',
+                           symmetric=False, xp=xp)
+    elif method == 'pearson':
+        statistic = 2 * xp.sum(xp.log1p(-pvalues), axis=axis)
+        chi2 = _SimpleChi2(2*n)
+        pval = _get_pvalue(-statistic, chi2, alternative='less', symmetric=False, xp=xp)
+    elif method == 'mudholkar_george':
+        normalizing_factor = xp.sqrt(3/n)/xp.pi
+        statistic = (-xp.sum(xp.log(pvalues), axis=axis)
+                     + xp.sum(xp.log1p(-pvalues), axis=axis))
+        nu = 5*n + 4
+        approx_factor = xp.sqrt(nu / (nu - 2))
+        t = _SimpleStudentT(nu)
+        pval = _get_pvalue(statistic * normalizing_factor * approx_factor, t,
+                           alternative="greater", xp=xp)
+    elif method == 'tippett':
+        statistic = xp.min(pvalues, axis=axis)
+        beta = _SimpleBeta(xp.ones_like(n), n)
+        pval = _get_pvalue(statistic, beta, alternative='less', symmetric=False, xp=xp)
+    elif method == 'stouffer':
+        if weights is None:
+            weights = xp.ones_like(pvalues, dtype=pvalues.dtype)
+        pvalues, weights = _share_masks(pvalues, weights, xp=xp)
+
+        norm = _SimpleNormal()
+        Zi = norm.isf(pvalues)
+        # Consider `vecdot` when data-apis/array-api#910 is resolved
+        statistic = (xp.sum(weights * Zi, axis=axis)
+                     / xp_vector_norm(weights, axis=axis))
+        pval = _get_pvalue(statistic, norm, alternative="greater", xp=xp)
+
+    else:
+        raise ValueError(
+            f"Invalid method {method!r}. Valid methods are 'fisher', "
+            "'pearson', 'mudholkar_george', 'tippett', and 'stouffer'"
+        )
+
+    return SignificanceResult(statistic, pval)
+
+
+@dataclass
+class QuantileTestResult:
+    r"""
+    Result of `scipy.stats.quantile_test`.
+
+    Attributes
+    ----------
+    statistic: float
+        The statistic used to calculate the p-value; either ``T1``, the
+        number of observations less than or equal to the hypothesized quantile,
+        or ``T2``, the number of observations strictly less than the
+        hypothesized quantile. Two test statistics are required to handle the
+        possibility the data was generated from a discrete or mixed
+        distribution.
+
+    statistic_type : int
+        ``1`` or ``2`` depending on which of ``T1`` or ``T2`` was used to
+        calculate the p-value respectively. ``T1`` corresponds to the
+        ``"greater"`` alternative hypothesis and ``T2`` to the ``"less"``.  For
+        the ``"two-sided"`` case, the statistic type that leads to smallest
+        p-value is used.  For significant tests, ``statistic_type = 1`` means
+        there is evidence that the population quantile is significantly greater
+        than the hypothesized value and ``statistic_type = 2`` means there is
+        evidence that it is significantly less than the hypothesized value.
+
+    pvalue : float
+        The p-value of the hypothesis test.
+    """
+    statistic: float
+    statistic_type: int
+    pvalue: float
+    _alternative: list[str] = field(repr=False)
+    _x : np.ndarray = field(repr=False)
+    _p : float = field(repr=False)
+    _statistic : float = field(repr=False)
+    _statistic_type : int = field(repr=False)
+    _pvalue : float = field(repr=False)
+    _axis : int = field(repr=False)
+    _axis_none : bool = field(repr=False)
+    _keepdims : bool = field(repr=False)
+    _ndim : int = field(repr=False)
+    _nan_out : bool = field(repr=False)
+    _xp : bool = field(repr=False)
+
+
+    def confidence_interval(self, confidence_level=0.95):
+        """
+        Compute the confidence interval of the quantile.
+
+        Parameters
+        ----------
+        confidence_level : float, default: 0.95
+            Confidence level for the computed confidence interval
+            of the quantile. Default is 0.95.
+
+        Returns
+        -------
+        ci : ``ConfidenceInterval`` object
+            The object has attributes ``low`` and ``high`` that hold the
+            lower and upper bounds of the confidence interval.
+
+        Examples
+        --------
+        >>> import numpy as np
+        >>> import scipy.stats as stats
+        >>> p = 0.75  # quantile of interest
+        >>> q = 0  # hypothesized value of the quantile
+        >>> x = np.exp(np.arange(0, 1.01, 0.01))
+        >>> res = stats.quantile_test(x, q=q, p=p, alternative='less')
+        >>> lb, ub = res.confidence_interval()
+        >>> lb, ub
+        (-inf, 2.293318740264183)
+        >>> res = stats.quantile_test(x, q=q, p=p, alternative='two-sided')
+        >>> lb, ub = res.confidence_interval(0.9)
+        >>> lb, ub
+        (1.9542373206359396, 2.293318740264183)
+        """
+
+        xp = self._xp
+        alternative = self._alternative
+        p = self._p
+        x = xp.sort(self._x, axis=-1)
+        n = x.shape[-1]
+        bd = _SimpleBinomial(n=n, p=p)
+        shape = p.shape
+
+        if confidence_level <= 0 or confidence_level >= 1:
+            message = "`confidence_level` must be a number between 0 and 1."
+            raise ValueError(message)
+
+        if n == 0:
+            zeros = xp.zeros(p.shape, dtype=x.dtype)
+            low, high = zeros, zeros
+        elif alternative == 'less':
+            p = 1 - confidence_level
+            low = xp.full(shape, -xp.inf)
+            high_index = xp.astype(bd.isf(p), xp.int64)
+            valid_index = high_index < n
+            high_index = xpx.at(high_index)[~valid_index].set(0)
+            x_high = xp.take_along_axis(x, high_index, axis=-1)
+            high = xp.where(valid_index, x_high, xp.nan)
+        elif alternative == 'greater':
+            p = 1 - confidence_level
+            low_index = xp.astype(bd.ppf(p), xp.int64) - 1
+            valid_index = low_index >= 0
+            low_index = xpx.at(low_index)[~valid_index].set(0)
+            x_low = xp.take_along_axis(x, low_index, axis=-1)
+            low = xp.where(valid_index, x_low, xp.nan)
+            high = xp.full(shape, xp.inf)
+        elif alternative == 'two-sided':
+            p = (1 - confidence_level) / 2
+            low_index = xp.astype(bd.ppf(p), xp.int64) - 1
+            valid_index = low_index >= 0
+            low_index = xpx.at(low_index)[~valid_index].set(0)
+            x_low = xp.take_along_axis(x, low_index, axis=-1)
+            low = xp.where(valid_index, x_low, xp.nan)
+            high_index = xp.astype(bd.isf(p), xp.int64)
+            valid_index = high_index < n
+            high_index = xpx.at(high_index)[~valid_index].set(0)
+            x_high = xp.take_along_axis(x, high_index, axis=-1)
+            high = xp.where(valid_index, x_high, xp.nan)
+
+        args = (self._axis, self._axis_none, self._keepdims,
+                self._ndim, self._nan_out, self._xp)
+        low = _quantile_test_postprocess(low, *args)
+        high = _quantile_test_postprocess(high, *args)
+        return ConfidenceInterval(low, high)
+
+
+def quantile_test_iv(x, q, p, alternative, axis, keepdims):
+    xp = array_namespace(x, q, p)
+    dtype = xp_result_type(x, q, p, force_floating=True, xp=xp)
+
+    x = xpx.atleast_nd(x, ndim=1, xp=xp)
+    message = '`x` must be an array of numbers.'
+    if not xp.isdtype(x.dtype, 'numeric'):
+        raise ValueError(message)
+
+    q = xp.asarray(q)
+    message = "`q` must be a scalar or array of numbers."
+    if not xp.isdtype(q.dtype, 'numeric'):
+        raise ValueError(message)
+
+    p = xp.asarray(p)
+    message = "`p` must be a scalar or array of floats."
+    if not xp.isdtype(p.dtype, 'real floating'):
+        raise ValueError(message)
+
+    axis_none = axis is None
+    ndim = max(x.ndim, p.ndim)
+    if axis_none:
+        x = xp_ravel(x)
+        q = xp_ravel(q)
+        p = xp_ravel(p)
+        axis = 0
+    elif np.iterable(axis) or int(axis) != axis:
+        message = "`axis` must be an integer or None."
+        raise ValueError(message)
+    elif (axis >= ndim) or (axis < -ndim):
+        message = "`axis` is not compatible with the shapes of the inputs."
+        raise ValueError(message)
+    axis = int(axis)
+
+    alternatives = {'two-sided', 'less', 'greater'}
+    message = f"`alternative` must be one of {alternatives}"
+    if alternative not in alternatives:
+        raise ValueError(message)
+
+    if keepdims not in {None, True, False}:
+        message = "If specified, `keepdims` must be True or False."
+        raise ValueError(message)
+
+    x = xp.sort(x, axis=axis)
+    q, p = xp.broadcast_arrays(q, p)  # length along axis matters for q and p
+    x, q, p = _broadcast_arrays((x, q, p), axis=axis, xp=xp)
+
+    if (keepdims is False) and (p.shape[axis] != 1):
+        message = ("`keepdims` may be False only if `p` and `q` are scalars or the "
+                   "length of `p` and `q` along `axis` is 1.")
+        raise ValueError(message)
+    keepdims = (p.shape[axis] != 1) if keepdims is None else keepdims
+
+    x = xp.moveaxis(x, axis, -1)
+    q = xp.moveaxis(q, axis, -1)
+    p = xp.moveaxis(p, axis, -1)
+
+    nan_out = ((p >= 1) | (p <= 0) | xp.isnan(p) | xp.isnan(q)
+               | xp.any(xp.isnan(x), axis=-1, keepdims=True))
+    if is_lazy_array(nan_out) or xp.any(nan_out):
+        # These get NaN-ed out at the end. In the meantime, we want them
+        # to pass through calculations without warnings or errors
+        q = xpx.at(q, nan_out).set(0.0, copy=True)
+        p = xpx.at(p, nan_out).set(0.5, copy=True)
+
+    return x, q, p, alternative, axis, keepdims, axis_none, ndim, nan_out, dtype, xp
+
+
+def _quantile_test_postprocess(res, axis, axis_none, keepdims, ndim, nan_out, xp):
+    # Reshape per axis/keepdims
+
+    res = xpx.at(res)[nan_out].set(xp.nan)
+
+    if axis_none and keepdims:
+        shape = (1,)*(ndim - 1) + res.shape
+        res = xp.reshape(res, shape)
+        axis = -1
+
+    res = xp.moveaxis(res, -1, axis)
+
+    if not keepdims:
+        res = xp.squeeze(res, axis=axis)
+    return res[()] if res.ndim == 0 else res
+
+
+@xp_capabilities(skip_backends=[("dask.array", "no `take_along_axis`")], cpu_only=True,
+                 reason="binomial distribution ufuncs only available for NumPy")
+def quantile_test(x, *, q=0.0, p=0.5, alternative='two-sided', axis=0, keepdims=None):
+    r"""
+    Perform a quantile test and compute a confidence interval of the quantile.
+
+    This function tests the null hypothesis that `q` is the value of the
+    quantile associated with probability `p` of the population underlying
+    sample `x`. For example, with default parameters, it tests that the
+    median of the population underlying `x` is zero. The function returns an
+    object including the test statistic, a p-value, and a method for computing
+    the confidence interval around the quantile.
+
+    Parameters
+    ----------
+    x : array_like
+        A one-dimensional sample.
+    q : float, default: 0
+        The hypothesized value of the quantile.
+    p : float, default: 0.5
+        The probability associated with the quantile; i.e. the proportion of
+        the population less than `q` is `p`. Must be strictly between 0 and 1.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis.
+        The following options are available (default is 'two-sided'):
+
+        * 'two-sided': the quantile associated with the probability `p`
+          is not `q`.
+        * 'less': the quantile associated with the probability `p` is less
+          than `q`.
+        * 'greater': the quantile associated with the probability `p` is
+          greater than `q`.
+    axis : int or None, default: 0
+        Axis of `x` along which the test is performed.
+        ``None`` ravels `x`, `q`, and `p` before performing the calculation,
+        without checking whether the original shapes were compatible.
+        As in other `scipy.stats` functions, a positive integer `axis` is resolved
+        after prepending 1s to the shape of `x`, `q`, and `p` as needed until the arrays
+        have the same dimensionality. When providing `x`, `q`, and `p` with different
+        dimensionality, consider using negative `axis` integers for clarity.
+    keepdims : bool, optional
+        Consider the case in which `x` is 1-D and `p` and `q` are scalars: the test
+        computes a reducing statistic, and the default behavior is to return a scalar.
+        If `keepdims` is set to True, the axis will not be reduced away, and the
+        result will be a 1-D array with one element.
+
+        The general case is more subtle, since multiple tests may be
+        requested for each axis-slice of `x`. For instance, if `x`, `q`, and `p`
+        are 1-D and ``p.size == q.size > 1``, no axis can be reduced away; there must be
+        an axis to contain the results. Therefore:
+
+        - By default, the axis will be reduced away if possible (i.e. if there is
+          exactly one element of `p` and `q` per axis-slice of `x`).
+        - If `keepdims` is set to True, the axis will not be reduced away.
+        - If `keepdims` is set to False, the axis will be reduced away
+          if possible, and an error will be raised otherwise.
+
+    Returns
+    -------
+    result : QuantileTestResult
+        An object with the following attributes:
+
+        statistic : float
+            One of two test statistics that may be used in the quantile test.
+            The first test statistic, ``T1``, is the number of observations in
+            `x` that are less than or equal to the hypothesized quantile
+            `q`. The second test statistic, ``T2``, is the number of
+            observations in `x` that are strictly less than the hypothesized
+            quantile `q`.
+
+            When ``alternative = 'greater'``, ``T1`` is used to calculate the
+            p-value and ``statistic`` is set to ``T1``.
+
+            When ``alternative = 'less'``, ``T2`` is used to calculate the
+            p-value and ``statistic`` is set to ``T2``.
+
+            When ``alternative = 'two-sided'``, both ``T1`` and ``T2`` are
+            considered, and the one that leads to the smallest p-value is used.
+
+        statistic_type : float
+            Either ``1.`` or ``2.`` depending on which of ``T1`` or ``T2`` was
+            used to calculate the p-value.
+
+        pvalue : float
+            The p-value associated with the given alternative.
+
+        The object also has the following method:
+
+        confidence_interval(confidence_level=0.95)
+            Computes a confidence interval around the the
+            population quantile associated with the probability `p`. The
+            confidence interval is returned in a ``namedtuple`` with
+            fields `low` and `high`.  Values are `nan` when there are
+            not enough observations to compute the confidence interval at
+            the desired confidence.
+
+    Notes
+    -----
+    This test and its method for computing confidence intervals are
+    non-parametric. They are valid if and only if the observations are i.i.d.
+
+    The implementation of the test follows Conover [1]_. Two test statistics
+    are considered.
+
+    ``T1``: The number of observations in `x` less than or equal to `q`.
+
+        ``T1 = (x <= q).sum()``
+
+    ``T2``: The number of observations in `x` strictly less than `q`.
+
+        ``T2 = (x < q).sum()``
+
+    The use of two test statistics is necessary to handle the possibility that
+    `x` was generated from a discrete or mixed distribution.
+
+    The null hypothesis for the test is:
+
+        H0: The :math:`p^{\mathrm{th}}` population quantile is `q`.
+
+    and the null distribution for each test statistic is
+    :math:`\mathrm{binom}\left(n, p\right)`. When ``alternative='less'``,
+    the alternative hypothesis is:
+
+        H1: The :math:`p^{\mathrm{th}}` population quantile is less than `q`.
+
+    and the p-value is the probability that the binomial random variable
+
+    .. math::
+        Y \sim \mathrm{binom}\left(n, p\right)
+
+    is greater than or equal to the observed value ``T2``.
+
+    When ``alternative='greater'``, the alternative hypothesis is:
+
+        H1: The :math:`p^{\mathrm{th}}` population quantile is greater than `q`
+
+    and the p-value is the probability that the binomial random variable Y
+    is less than or equal to the observed value ``T1``.
+
+    When ``alternative='two-sided'``, the alternative hypothesis is
+
+        H1: `q` is not the :math:`p^{\mathrm{th}}` population quantile.
+
+    and the p-value is twice the smaller of the p-values for the ``'less'``
+    and ``'greater'`` cases. Both of these p-values can exceed 0.5 for the same
+    data, so the value is clipped into the interval :math:`[0, 1]`.
+
+    The approach for confidence intervals is attributed to Thompson [2]_ and
+    later proven to be applicable to any i.i.d. sample [3]_. The
+    computation is based on the observation that the probability of a quantile
+    :math:`q` to be larger than any observations :math:`x_m (1\leq m \leq N)`
+    can be computed as
+
+    .. math::
+
+        \mathbb{P}(x_m \leq q) = 1 - \sum_{k=0}^{m-1} \binom{N}{k}
+        q^k(1-q)^{N-k}
+
+    By default, confidence intervals are computed for a 95% confidence level.
+    A common interpretation of a 95% confidence intervals is that if i.i.d.
+    samples are drawn repeatedly from the same population and confidence
+    intervals are formed each time, the confidence interval will contain the
+    true value of the specified quantile in approximately 95% of trials.
+
+    A similar function is available in the QuantileNPCI R package [4]_. The
+    foundation is the same, but it computes the confidence interval bounds by
+    doing interpolations between the sample values, whereas this function uses
+    only sample values as bounds. Thus, ``quantile_test.confidence_interval``
+    returns more conservative intervals (i.e., larger).
+
+    The same computation of confidence intervals for quantiles is included in
+    the confintr package [5]_.
+
+    Two-sided confidence intervals are not guaranteed to be optimal; i.e.,
+    there may exist a tighter interval that may contain the quantile of
+    interest with probability larger than the confidence level.
+    Without further assumption on the nature of the
+    underlying distribution, the one-sided intervals are optimally tight.
+
+    References
+    ----------
+    .. [1] W. J. Conover. Practical Nonparametric Statistics, 3rd Ed. 1999.
+    .. [2] W. R. Thompson, "On Confidence Ranges for the Median and Other
+           Expectation Distributions for Populations of Unknown Distribution
+           Form," The Annals of Mathematical Statistics, vol. 7, no. 3,
+           pp. 122-128, 1936, Accessed: Sep. 18, 2019. [Online]. Available:
+           https://www.jstor.org/stable/2957563.
+    .. [3] H. A. David and H. N. Nagaraja, "Order Statistics in Nonparametric
+           Inference" in Order Statistics, John Wiley & Sons, Ltd, 2005, pp.
+           159-170. :doi:`10.1002/0471722162.ch7`.
+    .. [4] N. Hutson, A. Hutson, L. Yan, "QuantileNPCI: Nonparametric
+           Confidence Intervals for Quantiles," R package,
+           https://cran.r-project.org/package=QuantileNPCI
+    .. [5] M. Mayer, "confintr: Confidence Intervals," R package,
+           https://cran.r-project.org/package=confintr
+
+
+    Examples
+    --------
+
+    Suppose we wish to test the null hypothesis that the median of a population
+    is equal to 0.5. We choose a confidence level of 99%; that is, we will
+    reject the null hypothesis in favor of the alternative if the p-value is
+    less than 0.01.
+
+    When testing random variates from the standard uniform distribution, which
+    has a median of 0.5, we expect the data to be consistent with the null
+    hypothesis most of the time.
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> rng = np.random.default_rng(6981396440634228121)
+    >>> rvs = stats.uniform.rvs(size=100, random_state=rng)
+    >>> stats.quantile_test(rvs, q=0.5, p=0.5)
+    QuantileTestResult(statistic=45, statistic_type=1, pvalue=0.36820161732669576)
+
+    As expected, the p-value is not below our threshold of 0.01, so
+    we cannot reject the null hypothesis.
+
+    When testing data from the standard *normal* distribution, which has a
+    median of 0, we would expect the null hypothesis to be rejected.
+
+    >>> rvs = stats.norm.rvs(size=100, random_state=rng)
+    >>> stats.quantile_test(rvs, q=0.5, p=0.5)
+    QuantileTestResult(statistic=67, statistic_type=2, pvalue=0.0008737198369123724)
+
+    Indeed, the p-value is lower than our threshold of 0.01, so we reject the
+    null hypothesis in favor of the default "two-sided" alternative: the median
+    of the population is *not* equal to 0.5.
+
+    However, suppose we were to test the null hypothesis against the
+    one-sided alternative that the median of the population is *greater* than
+    0.5. Since the median of the standard normal is less than 0.5, we would not
+    expect the null hypothesis to be rejected.
+
+    >>> stats.quantile_test(rvs, q=0.5, p=0.5, alternative='greater')
+    QuantileTestResult(statistic=67, statistic_type=1, pvalue=0.9997956114162866)
+
+    Unsurprisingly, with a p-value greater than our threshold, we would not
+    reject the null hypothesis in favor of the chosen alternative.
+
+    The quantile test can be used for any quantile, not only the median. For
+    example, we can test whether the third quartile of the distribution
+    underlying the sample is greater than 0.6.
+
+    >>> rvs = stats.uniform.rvs(size=100, random_state=rng)
+    >>> stats.quantile_test(rvs, q=0.6, p=0.75, alternative='greater')
+    QuantileTestResult(statistic=64, statistic_type=1, pvalue=0.00940696592998271)
+
+    The p-value is lower than the threshold. We reject the null hypothesis in
+    favor of the alternative: the third quartile of the distribution underlying
+    our sample is greater than 0.6.
+
+    `quantile_test` can also compute confidence intervals for any quantile.
+
+    >>> rvs = stats.norm.rvs(size=100, random_state=rng)
+    >>> res = stats.quantile_test(rvs, q=0.6, p=0.75)
+    >>> ci = res.confidence_interval(confidence_level=0.95)
+    >>> ci
+    ConfidenceInterval(low=0.284491604437432, high=0.8912531024914844)
+
+    When testing a one-sided alternative, the confidence interval contains
+    all observations such that if passed as `q`, the p-value of the
+    test would be greater than 0.05, and therefore the null hypothesis
+    would not be rejected. For example:
+
+    >>> rvs.sort()
+    >>> q, p, alpha = 0.6, 0.75, 0.95
+    >>> res = stats.quantile_test(rvs, q=q, p=p, alternative='less')
+    >>> ci = res.confidence_interval(confidence_level=alpha)
+    >>> for x in rvs[rvs <= ci.high]:
+    ...     res = stats.quantile_test(rvs, q=x, p=p, alternative='less')
+    ...     assert res.pvalue > 1-alpha
+    >>> for x in rvs[rvs > ci.high]:
+    ...     res = stats.quantile_test(rvs, q=x, p=p, alternative='less')
+    ...     assert res.pvalue < 1-alpha
+
+    Also, if a 95% confidence interval is repeatedly generated for random
+    samples, the confidence interval will contain the true quantile value in
+    approximately 95% of replications.
+
+    >>> dist = stats.rayleigh() # our "unknown" distribution
+    >>> p = 0.2
+    >>> true_stat = dist.ppf(p) # the true value of the statistic
+    >>> n_trials = 1000
+    >>> quantile_ci_contains_true_stat = 0
+    >>> for i in range(n_trials):
+    ...     data = dist.rvs(size=100, random_state=rng)
+    ...     res = stats.quantile_test(data, p=p)
+    ...     ci = res.confidence_interval(0.95)
+    ...     if ci[0] < true_stat < ci[1]:
+    ...         quantile_ci_contains_true_stat += 1
+    >>> quantile_ci_contains_true_stat >= 950
+    True
+
+    This works with any distribution and any quantile, as long as the observations
+    are i.i.d.
+    """
+    # Implementation carefully follows [1] 3.2
+    # "H0: the p*th quantile of X is x*"
+    # To facilitate comparison with [1], we'll use variable names that
+    # best match Conover's notation
+    X, x_star, p_star, H1, axis, keepdims, axis_none, ndim, nan_out, dtype, xp = (
+        quantile_test_iv(x, q, p, alternative, axis, keepdims))
+    # `axis` is the original `axis`; the working axis is -1.
+
+    # "We will use two test statistics in this test. Let T1 equal "
+    # "the number of observations less than or equal to x*, and "
+    # "let T2 equal the number of observations less than x*."
+    if X.shape[-1] > 0:
+        T1 = _xp_searchsorted(X, x_star, side='right', xp=xp)
+        T2 = _xp_searchsorted(X, x_star, side='left', xp=xp)
+        T1, T2 = xp.astype(T1, dtype), xp.astype(T2, dtype)
+    else:
+        nan_out = xp.ones_like(nan_out)
+        T = xp.zeros(x_star.shape, dtype=dtype)
+        T1, T2 = T, T
+
+    # "The null distribution of the test statistics T1 and T2 is "
+    # "the binomial distribution, with parameters n = sample size, and "
+    # "p = p* as given in the null hypothesis.... Y has the binomial "
+    # "distribution with parameters n and p*."
+    n = X.shape[-1]
+    Y = _SimpleBinomial(n=n, p=p_star)
+
+    # "H1: the p* population quantile is less than x*"
+    if H1 == 'less':
+        # "The p-value is the probability that a binomial random variable Y "
+        # "is greater than *or equal to* the observed value of T2...using p=p*"
+        pvalue = Y.sf(T2-1)  # Y.pmf(T2) + Y.sf(T2)
+        statistic = xp.broadcast_to(T2, pvalue.shape)
+        statistic_type = xp.full_like(statistic, 2.)
+    # "H1: the p* population quantile is greater than x*"
+    elif H1 == 'greater':
+        # "The p-value is the probability that a binomial random variable Y "
+        # "is less than or equal to the observed value of T1... using p = p*"
+        pvalue = Y.cdf(T1)
+        statistic = xp.broadcast_to(T1, pvalue.shape)
+        statistic_type = xp.full_like(statistic, 1.)
+    # "H1: x* is not the p*th population quantile"
+    elif H1 == 'two-sided':
+        # "The p-value is twice the smaller of the probabilities that a
+        # binomial random variable Y is less than or equal to the observed
+        # value of T1 or greater than or equal to the observed value of T2
+        # using p=p*."
+        # Note: both one-sided p-values can exceed 0.5 for the same data, so
+        # `clip`
+        p_min = xp.minimum(Y.cdf(T1), Y.sf(T2 - 1))
+        pvalue = xp.clip(2*p_min, 0., 1.)
+        i2 = Y.cdf(T1) > Y.sf(T2 - 1)
+        statistic = xp.where(i2, T2, T1)
+        statistic_type = xp.where(i2, xp.full_like(T2, 2.), xp.full_like(T1, 1.))
+
+    statistic = xp.astype(statistic, dtype)
+    statistic_type = xp.astype(statistic_type, dtype)
+    pvalue = xp.astype(pvalue, dtype)
+    X = xp.astype(X, dtype)
+
+    _statistic, _statistic_type, _pvalue = statistic, statistic_type, pvalue
+    args = axis, axis_none, keepdims, ndim, nan_out, xp
+    statistic = _quantile_test_postprocess(statistic, *args)
+    statistic_type = _quantile_test_postprocess(statistic_type, *args)
+    pvalue = _quantile_test_postprocess(pvalue, *args)
+
+    return QuantileTestResult(
+        statistic=statistic,
+        statistic_type=statistic_type,
+        pvalue=pvalue,
+        _alternative=H1,
+        _x=X,
+        _p=p_star,
+        _statistic=statistic,
+        _statistic_type=_statistic_type,
+        _pvalue=_pvalue,
+        _axis=axis,
+        _axis_none=axis_none,
+        _keepdims=keepdims,
+        _ndim=ndim,
+        _nan_out=nan_out,
+        _xp=xp,
+    )
+
+
+#####################################
+#       STATISTICAL DISTANCES       #
+#####################################
+
+
+@xp_capabilities(np_only=True)
+def wasserstein_distance_nd(u_values, v_values, u_weights=None, v_weights=None):
+    r"""
+    Compute the Wasserstein-1 distance between two N-D discrete distributions.
+
+    The Wasserstein distance, also called the Earth mover's distance or the
+    optimal transport distance, is a similarity metric between two probability
+    distributions [1]_. In the discrete case, the Wasserstein distance can be
+    understood as the cost of an optimal transport plan to convert one
+    distribution into the other. The cost is calculated as the product of the
+    amount of probability mass being moved and the distance it is being moved.
+    A brief and intuitive introduction can be found at [2]_.
+
+    .. versionadded:: 1.13.0
+
+    Parameters
+    ----------
+    u_values : 2d array_like
+        A sample from a probability distribution or the support (set of all
+        possible values) of a probability distribution. Each element along
+        axis 0 is an observation or possible value, and axis 1 represents the
+        dimensionality of the distribution; i.e., each row is a vector
+        observation or possible value.
+
+    v_values : 2d array_like
+        A sample from or the support of a second distribution.
+
+    u_weights, v_weights : 1d array_like, optional
+        Weights or counts corresponding with the sample or probability masses
+        corresponding with the support values. Sum of elements must be positive
+        and finite. If unspecified, each value is assigned the same weight.
+
+    Returns
+    -------
+    distance : float
+        The computed distance between the distributions.
+
+    Notes
+    -----
+    Given two probability mass functions, :math:`u`
+    and :math:`v`, the first Wasserstein distance between the distributions
+    using the Euclidean norm is:
+
+    .. math::
+
+        l_1 (u, v) = \inf_{\pi \in \Gamma (u, v)} \int \| x-y \|_2 \mathrm{d} \pi (x, y)
+
+    where :math:`\Gamma (u, v)` is the set of (probability) distributions on
+    :math:`\mathbb{R}^n \times \mathbb{R}^n` whose marginals are :math:`u` and
+    :math:`v` on the first and second factors respectively. For a given value
+    :math:`x`, :math:`u(x)` gives the probability of :math:`u` at position
+    :math:`x`, and the same for :math:`v(x)`.
+
+    This is also called the optimal transport problem or the Monge problem.
+    Let the finite point sets :math:`\{x_i\}` and :math:`\{y_j\}` denote
+    the support set of probability mass function :math:`u` and :math:`v`
+    respectively. The Monge problem can be expressed as follows,
+
+    Let :math:`\Gamma` denote the transport plan, :math:`D` denote the
+    distance matrix and,
+
+    .. math::
+
+        x = \text{vec}(\Gamma)          \\
+        c = \text{vec}(D)               \\
+        b = \begin{bmatrix}
+                u\\
+                v\\
+            \end{bmatrix}
+
+    The :math:`\text{vec}()` function denotes the Vectorization function
+    that transforms a matrix into a column vector by vertically stacking
+    the columns of the matrix.
+    The transport plan :math:`\Gamma` is a matrix :math:`[\gamma_{ij}]` in
+    which :math:`\gamma_{ij}` is a positive value representing the amount of
+    probability mass transported from :math:`u(x_i)` to :math:`v(y_i)`.
+    Summing over the rows of :math:`\Gamma` should give the source distribution
+    :math:`u` : :math:`\sum_j \gamma_{ij} = u(x_i)` holds for all :math:`i`
+    and summing over the columns of :math:`\Gamma` should give the target
+    distribution :math:`v`: :math:`\sum_i \gamma_{ij} = v(y_j)` holds for all
+    :math:`j`.
+    The distance matrix :math:`D` is a matrix :math:`[d_{ij}]`, in which
+    :math:`d_{ij} = d(x_i, y_j)`.
+
+    Given :math:`\Gamma`, :math:`D`, :math:`b`, the Monge problem can be
+    transformed into a linear programming problem by
+    taking :math:`A x = b` as constraints and :math:`z = c^T x` as minimization
+    target (sum of costs) , where matrix :math:`A` has the form
+
+    .. math::
+
+        \begin{array} {rrrr|rrrr|r|rrrr}
+            1 & 1 & \dots & 1 & 0 & 0 & \dots & 0 & \dots & 0 & 0 & \dots &
+                0 \cr
+            0 & 0 & \dots & 0 & 1 & 1 & \dots & 1 & \dots & 0 & 0 &\dots &
+                0 \cr
+            \vdots & \vdots & \ddots & \vdots & \vdots & \vdots & \ddots
+                & \vdots & \vdots & \vdots & \vdots & \ddots & \vdots  \cr
+            0 & 0 & \dots & 0 & 0 & 0 & \dots & 0 & \dots & 1 & 1 & \dots &
+                1 \cr \hline
+
+            1 & 0 & \dots & 0 & 1 & 0 & \dots & \dots & \dots & 1 & 0 & \dots &
+                0 \cr
+            0 & 1 & \dots & 0 & 0 & 1 & \dots & \dots & \dots & 0 & 1 & \dots &
+                0 \cr
+            \vdots & \vdots & \ddots & \vdots & \vdots & \vdots & \ddots &
+                \vdots & \vdots & \vdots & \vdots & \ddots & \vdots \cr
+            0 & 0 & \dots & 1 & 0 & 0 & \dots & 1 & \dots & 0 & 0 & \dots & 1
+        \end{array}
+
+    By solving the dual form of the above linear programming problem (with
+    solution :math:`y^*`), the Wasserstein distance :math:`l_1 (u, v)` can
+    be computed as :math:`b^T y^*`.
+
+    The above solution is inspired by Vincent Herrmann's blog [3]_ . For a
+    more thorough explanation, see [4]_ .
+
+    The input distributions can be empirical, therefore coming from samples
+    whose values are effectively inputs of the function, or they can be seen as
+    generalized functions, in which case they are weighted sums of Dirac delta
+    functions located at the specified values.
+
+    References
+    ----------
+    .. [1] "Wasserstein metric",
+           https://en.wikipedia.org/wiki/Wasserstein_metric
+    .. [2] Lili Weng, "What is Wasserstein distance?", Lil'log,
+           https://lilianweng.github.io/posts/2017-08-20-gan/#what-is-wasserstein-distance.
+    .. [3] Hermann, Vincent. "Wasserstein GAN and the Kantorovich-Rubinstein
+           Duality". https://vincentherrmann.github.io/blog/wasserstein/.
+    .. [4] Peyré, Gabriel, and Marco Cuturi. "Computational optimal
+           transport." Center for Research in Economics and Statistics
+           Working Papers 2017-86 (2017).
+
+    See Also
+    --------
+    wasserstein_distance: Compute the Wasserstein-1 distance between two
+        1D discrete distributions.
+
+    Examples
+    --------
+    Compute the Wasserstein distance between two three-dimensional samples,
+    each with two observations.
+
+    >>> from scipy.stats import wasserstein_distance_nd
+    >>> wasserstein_distance_nd([[0, 2, 3], [1, 2, 5]], [[3, 2, 3], [4, 2, 5]])
+    3.0
+
+    Compute the Wasserstein distance between two two-dimensional distributions
+    with three and two weighted observations, respectively.
+
+    >>> wasserstein_distance_nd([[0, 2.75], [2, 209.3], [0, 0]],
+    ...                      [[0.2, 0.322], [4.5, 25.1808]],
+    ...                      [0.4, 5.2, 0.114], [0.8, 1.5])
+    174.15840245217169
+    """
+    m, n = len(u_values), len(v_values)
+    u_values = asarray(u_values)
+    v_values = asarray(v_values)
+
+    if u_values.ndim > 2 or v_values.ndim > 2:
+        raise ValueError('Invalid input values. The inputs must have either '
+                         'one or two dimensions.')
+    # if dimensions are not equal throw error
+    if u_values.ndim != v_values.ndim:
+        raise ValueError('Invalid input values. Dimensions of inputs must be '
+                         'equal.')
+    # if data is 1D then call the cdf_distance function
+    if u_values.ndim == 1 and v_values.ndim == 1:
+        return _cdf_distance(1, u_values, v_values, u_weights, v_weights)
+
+    u_values, u_weights = _validate_distribution(u_values, u_weights)
+    v_values, v_weights = _validate_distribution(v_values, v_weights)
+    # if number of columns is not equal throw error
+    if u_values.shape[1] != v_values.shape[1]:
+        raise ValueError('Invalid input values. If two-dimensional, '
+                         '`u_values` and `v_values` must have the same '
+                         'number of columns.')
+
+    # if data contains np.inf then return inf or nan
+    if np.any(np.isinf(u_values)) ^ np.any(np.isinf(v_values)):
+        return np.inf
+    elif np.any(np.isinf(u_values)) and np.any(np.isinf(v_values)):
+        return np.nan
+
+    # create constraints
+    A_upper_part = sparse.block_diag((sparse.coo_array(np.ones((1, n))), ) * m)
+    A_lower_part = sparse.hstack((sparse.eye_array(n), ) * m)
+    # sparse constraint matrix of size (m + n)*(m * n)
+    A = sparse.vstack((A_upper_part, A_lower_part))
+
+    # get cost matrix
+    D = cdist(u_values, v_values)
+    cost = D.ravel()
+
+    # create the minimization target
+    p_u = np.full(m, 1/m) if u_weights is None else u_weights/np.sum(u_weights)
+    p_v = np.full(n, 1/n) if v_weights is None else v_weights/np.sum(v_weights)
+    b = np.concatenate((p_u, p_v), axis=0)
+
+    # solving LP
+    constraints = LinearConstraint(A=A.T, ub=cost)
+    opt_res = milp(c=-b, constraints=constraints, bounds=(-np.inf, np.inf))
+    return -opt_res.fun
+
+
+@xp_capabilities(np_only=True)
+def wasserstein_distance(u_values, v_values, u_weights=None, v_weights=None):
+    r"""
+    Compute the Wasserstein-1 distance between two 1D discrete distributions.
+
+    The Wasserstein distance, also called the Earth mover's distance or the
+    optimal transport distance, is a similarity metric between two probability
+    distributions [1]_. In the discrete case, the Wasserstein distance can be
+    understood as the cost of an optimal transport plan to convert one
+    distribution into the other. The cost is calculated as the product of the
+    amount of probability mass being moved and the distance it is being moved.
+    A brief and intuitive introduction can be found at [2]_.
+
+    .. versionadded:: 1.0.0
+
+    Parameters
+    ----------
+    u_values : 1d array_like
+        A sample from a probability distribution or the support (set of all
+        possible values) of a probability distribution. Each element is an
+        observation or possible value.
+
+    v_values : 1d array_like
+        A sample from or the support of a second distribution.
+
+    u_weights, v_weights : 1d array_like, optional
+        Weights or counts corresponding with the sample or probability masses
+        corresponding with the support values. Sum of elements must be positive
+        and finite. If unspecified, each value is assigned the same weight.
+
+    Returns
+    -------
+    distance : float
+        The computed distance between the distributions.
+
+    Notes
+    -----
+    Given two 1D probability mass functions, :math:`u` and :math:`v`, the first
+    Wasserstein distance between the distributions is:
+
+    .. math::
+
+        l_1 (u, v) = \inf_{\pi \in \Gamma (u, v)} \int_{\mathbb{R} \times
+        \mathbb{R}} |x-y| \mathrm{d} \pi (x, y)
+
+    where :math:`\Gamma (u, v)` is the set of (probability) distributions on
+    :math:`\mathbb{R} \times \mathbb{R}` whose marginals are :math:`u` and
+    :math:`v` on the first and second factors respectively. For a given value
+    :math:`x`, :math:`u(x)` gives the probability of :math:`u` at position
+    :math:`x`, and the same for :math:`v(x)`.
+
+    If :math:`U` and :math:`V` are the respective CDFs of :math:`u` and
+    :math:`v`, this distance also equals to:
+
+    .. math::
+
+        l_1(u, v) = \int_{-\infty}^{+\infty} |U-V|
+
+    See [3]_ for a proof of the equivalence of both definitions.
+
+    The input distributions can be empirical, therefore coming from samples
+    whose values are effectively inputs of the function, or they can be seen as
+    generalized functions, in which case they are weighted sums of Dirac delta
+    functions located at the specified values.
+
+    References
+    ----------
+    .. [1] "Wasserstein metric", https://en.wikipedia.org/wiki/Wasserstein_metric
+    .. [2] Lili Weng, "What is Wasserstein distance?", Lil'log,
+           https://lilianweng.github.io/posts/2017-08-20-gan/#what-is-wasserstein-distance.
+    .. [3] Ramdas, Garcia, Cuturi "On Wasserstein Two Sample Testing and Related
+           Families of Nonparametric Tests" (2015). :arXiv:`1509.02237`.
+
+    See Also
+    --------
+    wasserstein_distance_nd: Compute the Wasserstein-1 distance between two N-D
+        discrete distributions.
+
+    Examples
+    --------
+    >>> from scipy.stats import wasserstein_distance
+    >>> wasserstein_distance([0, 1, 3], [5, 6, 8])
+    5.0
+    >>> wasserstein_distance([0, 1], [0, 1], [3, 1], [2, 2])
+    0.25
+    >>> wasserstein_distance([3.4, 3.9, 7.5, 7.8], [4.5, 1.4],
+    ...                      [1.4, 0.9, 3.1, 7.2], [3.2, 3.5])
+    4.0781331438047861
+
+    """
+    return _cdf_distance(1, u_values, v_values, u_weights, v_weights)
+
+
+@xp_capabilities(np_only=True)
+def energy_distance(u_values, v_values, u_weights=None, v_weights=None):
+    r"""Compute the energy distance between two 1D distributions.
+
+    .. versionadded:: 1.0.0
+
+    Parameters
+    ----------
+    u_values, v_values : array_like
+        Values observed in the (empirical) distribution.
+    u_weights, v_weights : array_like, optional
+        Weight for each value. If unspecified, each value is assigned the same
+        weight.
+        `u_weights` (resp. `v_weights`) must have the same length as
+        `u_values` (resp. `v_values`). If the weight sum differs from 1, it
+        must still be positive and finite so that the weights can be normalized
+        to sum to 1.
+
+    Returns
+    -------
+    distance : float
+        The computed distance between the distributions.
+
+    Notes
+    -----
+    The energy distance between two distributions :math:`u` and :math:`v`, whose
+    respective CDFs are :math:`U` and :math:`V`, equals to:
+
+    .. math::
+
+        D(u, v) = \left( 2\mathbb E|X - Y| - \mathbb E|X - X'| -
+        \mathbb E|Y - Y'| \right)^{1/2}
+
+    where :math:`X` and :math:`X'` (resp. :math:`Y` and :math:`Y'`) are
+    independent random variables whose probability distribution is :math:`u`
+    (resp. :math:`v`).
+
+    Sometimes the square of this quantity is referred to as the "energy
+    distance" (e.g. in [2]_, [4]_), but as noted in [1]_ and [3]_, only the
+    definition above satisfies the axioms of a distance function (metric).
+
+    As shown in [2]_, for one-dimensional real-valued variables, the energy
+    distance is linked to the non-distribution-free version of the Cramér-von
+    Mises distance:
+
+    .. math::
+
+        D(u, v) = \sqrt{2} l_2(u, v) = \left( 2 \int_{-\infty}^{+\infty} (U-V)^2
+        \right)^{1/2}
+
+    Note that the common Cramér-von Mises criterion uses the distribution-free
+    version of the distance. See [2]_ (section 2), for more details about both
+    versions of the distance.
+
+    The input distributions can be empirical, therefore coming from samples
+    whose values are effectively inputs of the function, or they can be seen as
+    generalized functions, in which case they are weighted sums of Dirac delta
+    functions located at the specified values.
+
+    References
+    ----------
+    .. [1] Rizzo, Szekely "Energy distance." Wiley Interdisciplinary Reviews:
+           Computational Statistics, 8(1):27-38 (2015).
+    .. [2] Szekely "E-statistics: The energy of statistical samples." Bowling
+           Green State University, Department of Mathematics and Statistics,
+           Technical Report 02-16 (2002).
+    .. [3] "Energy distance", https://en.wikipedia.org/wiki/Energy_distance
+    .. [4] Bellemare, Danihelka, Dabney, Mohamed, Lakshminarayanan, Hoyer,
+           Munos "The Cramer Distance as a Solution to Biased Wasserstein
+           Gradients" (2017). :arXiv:`1705.10743`.
+
+    Examples
+    --------
+    >>> from scipy.stats import energy_distance
+    >>> energy_distance([0], [2])
+    2.0000000000000004
+    >>> energy_distance([0, 8], [0, 8], [3, 1], [2, 2])
+    1.0000000000000002
+    >>> energy_distance([0.7, 7.4, 2.4, 6.8], [1.4, 8. ],
+    ...                 [2.1, 4.2, 7.4, 8. ], [7.6, 8.8])
+    0.88003340976158217
+
+    """
+    return np.sqrt(2) * _cdf_distance(2, u_values, v_values,
+                                      u_weights, v_weights)
+
+
+def _cdf_distance(p, u_values, v_values, u_weights=None, v_weights=None):
+    r"""
+    Compute, between two one-dimensional distributions :math:`u` and
+    :math:`v`, whose respective CDFs are :math:`U` and :math:`V`, the
+    statistical distance that is defined as:
+
+    .. math::
+
+        l_p(u, v) = \left( \int_{-\infty}^{+\infty} |U-V|^p \right)^{1/p}
+
+    p is a positive parameter; p = 1 gives the Wasserstein distance, p = 2
+    gives the energy distance.
+
+    Parameters
+    ----------
+    u_values, v_values : array_like
+        Values observed in the (empirical) distribution.
+    u_weights, v_weights : array_like, optional
+        Weight for each value. If unspecified, each value is assigned the same
+        weight.
+        `u_weights` (resp. `v_weights`) must have the same length as
+        `u_values` (resp. `v_values`). If the weight sum differs from 1, it
+        must still be positive and finite so that the weights can be normalized
+        to sum to 1.
+
+    Returns
+    -------
+    distance : float
+        The computed distance between the distributions.
+
+    Notes
+    -----
+    The input distributions can be empirical, therefore coming from samples
+    whose values are effectively inputs of the function, or they can be seen as
+    generalized functions, in which case they are weighted sums of Dirac delta
+    functions located at the specified values.
+
+    References
+    ----------
+    .. [1] Bellemare, Danihelka, Dabney, Mohamed, Lakshminarayanan, Hoyer,
+           Munos "The Cramer Distance as a Solution to Biased Wasserstein
+           Gradients" (2017). :arXiv:`1705.10743`.
+
+    """
+    u_values, u_weights = _validate_distribution(u_values, u_weights)
+    v_values, v_weights = _validate_distribution(v_values, v_weights)
+
+    u_sorter = np.argsort(u_values)
+    v_sorter = np.argsort(v_values)
+
+    all_values = np.concatenate((u_values, v_values))
+    all_values.sort(kind='mergesort')
+
+    # Compute the differences between pairs of successive values of u and v.
+    deltas = np.diff(all_values)
+
+    # Get the respective positions of the values of u and v among the values of
+    # both distributions.
+    u_cdf_indices = u_values[u_sorter].searchsorted(all_values[:-1], 'right')
+    v_cdf_indices = v_values[v_sorter].searchsorted(all_values[:-1], 'right')
+
+    # Calculate the CDFs of u and v using their weights, if specified.
+    if u_weights is None:
+        u_cdf = u_cdf_indices / u_values.size
+    else:
+        u_sorted_cumweights = np.concatenate(([0],
+                                              np.cumsum(u_weights[u_sorter])))
+        u_cdf = u_sorted_cumweights[u_cdf_indices] / u_sorted_cumweights[-1]
+
+    if v_weights is None:
+        v_cdf = v_cdf_indices / v_values.size
+    else:
+        v_sorted_cumweights = np.concatenate(([0],
+                                              np.cumsum(v_weights[v_sorter])))
+        v_cdf = v_sorted_cumweights[v_cdf_indices] / v_sorted_cumweights[-1]
+
+    # Compute the value of the integral based on the CDFs.
+    # If p = 1 or p = 2, we avoid using np.power, which introduces an overhead
+    # of about 15%.
+    if p == 1:
+        return np.vecdot(np.abs(u_cdf - v_cdf), deltas)
+    if p == 2:
+        return np.sqrt(np.vecdot(np.square(u_cdf - v_cdf), deltas))
+    return np.power(np.vecdot(np.power(np.abs(u_cdf - v_cdf), p), deltas), 1/p)
+
+
+def _validate_distribution(values, weights):
+    """
+    Validate the values and weights from a distribution input of `cdf_distance`
+    and return them as ndarray objects.
+
+    Parameters
+    ----------
+    values : array_like
+        Values observed in the (empirical) distribution.
+    weights : array_like
+        Weight for each value.
+
+    Returns
+    -------
+    values : ndarray
+        Values as ndarray.
+    weights : ndarray
+        Weights as ndarray.
+
+    """
+    # Validate the value array.
+    values = np.asarray(values, dtype=float)
+    if len(values) == 0:
+        raise ValueError("Distribution can't be empty.")
+
+    # Validate the weight array, if specified.
+    if weights is not None:
+        weights = np.asarray(weights, dtype=float)
+        if len(weights) != len(values):
+            raise ValueError('Value and weight array-likes for the same '
+                             'empirical distribution must be of the same size.')
+        if np.any(weights < 0):
+            raise ValueError('All weights must be non-negative.')
+        if not 0 < np.sum(weights) < np.inf:
+            raise ValueError('Weight array-like sum must be positive and '
+                             'finite. Set as None for an equal distribution of '
+                             'weight.')
+
+        return values, weights
+
+    return values, None
+
+
+@xp_capabilities(skip_backends=[("dask.array", "no `take_along_axis`")],
+                 marray=True)
+def rankdata(a, method='average', *, axis=None, nan_policy='propagate'):
+    """Assign ranks to data, dealing with ties appropriately.
+
+    By default (``axis=None``), the data array is first flattened, and a flat
+    array of ranks is returned. Separately reshape the rank array to the
+    shape of the data array if desired (see Examples).
+
+    Ranks begin at 1.  The `method` argument controls how ranks are assigned
+    to equal values.  See [1]_ for further discussion of ranking methods.
+
+    Parameters
+    ----------
+    a : array_like
+        The array of values to be ranked.
+    method : {'average', 'min', 'max', 'dense', 'ordinal'}, optional
+        The method used to assign ranks to tied elements.
+        The following methods are available (default is 'average'):
+
+        * 'average': The average of the ranks that would have been assigned to
+          all the tied values is assigned to each value.
+        * 'min': The minimum of the ranks that would have been assigned to all
+          the tied values is assigned to each value.  (This is also
+          referred to as "competition" ranking.)
+        * 'max': The maximum of the ranks that would have been assigned to all
+          the tied values is assigned to each value.
+        * 'dense': Like 'min', but the rank of the next highest element is
+          assigned the rank immediately after those assigned to the tied
+          elements.
+        * 'ordinal': All values are given a distinct rank, corresponding to
+          the order that the values occur in `a`.
+
+    axis : {None, int}, optional
+        Axis along which to perform the ranking. If ``None``, the data array
+        is first flattened.
+    nan_policy : {'propagate', 'omit', 'raise'}, optional
+        Defines how to handle when input contains nan.
+        The following options are available (default is 'propagate'):
+
+        * 'propagate': propagates nans through the rank calculation
+        * 'omit': performs the calculations ignoring nan values
+        * 'raise': raises an error
+
+        .. note::
+
+            When `nan_policy` is 'propagate', the output is an array of *all*
+            nans because ranks relative to nans in the input are undefined.
+            When `nan_policy` is 'omit', nans in `a` are ignored when ranking
+            the other values, and the corresponding locations of the output
+            are nan.
+
+        .. versionadded:: 1.10
+
+    Returns
+    -------
+    ranks : ndarray
+         An array of size equal to the size of `a`, containing rank
+         scores. The dtype is the result dtype of `a` and a Python float.
+
+    References
+    ----------
+    .. [1] "Ranking", https://en.wikipedia.org/wiki/Ranking
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import rankdata
+    >>> rankdata([0, 2, 3, 2])
+    array([1. , 2.5, 4. , 2.5])
+    >>> rankdata([0, 2, 3, 2], method='min')
+    array([1., 2., 4., 2.])
+    >>> rankdata([0, 2, 3, 2], method='max')
+    array([1., 3., 4., 3.])
+    >>> rankdata([0, 2, 3, 2], method='dense')
+    array([1., 2., 3., 2.])
+    >>> rankdata([0, 2, 3, 2], method='ordinal')
+    array([1., 2., 4., 3.])
+    >>> rankdata([[0, 2], [3, 2]]).reshape(2, 2)
+    array([[1. , 2.5],
+           [4. , 2.5]])
+    >>> rankdata([[0, 2, 2], [3, 2, 5]], axis=1)
+    array([[1. , 2.5, 2.5],
+           [2. , 1. , 3. ]])
+    >>> rankdata([0, 2, 3, np.nan, -2, np.nan], nan_policy="propagate")
+    array([nan, nan, nan, nan, nan, nan])
+    >>> rankdata([0, 2, 3, np.nan, -2, np.nan], nan_policy="omit")
+    array([ 2.,  3.,  4., nan,  1., nan])
+
+    """
+    methods = ('average', 'min', 'max', 'dense', 'ordinal')
+    if method not in methods:
+        raise ValueError(f'unknown method "{method}"')
+
+    xp = array_namespace(a)
+    x = xp.asarray(a)
+
+    if axis is None:
+        x = xp_ravel(x)
+        axis = -1
+
+    if xp_size(x) == 0:
+        dtype = xp_result_type(x, force_floating=True, xp=xp)
+        return xp.empty_like(x, dtype=dtype)
+
+    contains_nan = _contains_nan(x, nan_policy)
+
+    x = xp_swapaxes(x, axis, -1, xp=xp)
+    ranks, _, _ = _rankdata(x, method, xp=xp)
+
+    # JIT won't allow use of `contains_nan` for control flow here, so we always have to
+    # run this with JIT.
+    if is_lazy_array(x) or contains_nan:
+        i_nan = (xp.isnan(x) if nan_policy == 'omit'
+                 else xp.any(xp.isnan(x), axis=-1, keepdims=True))
+        i_nan = xp.broadcast_to(i_nan, ranks.shape)
+        ranks = xpx.at(ranks)[i_nan].set(xp.nan)
+
+    ranks = xp_swapaxes(ranks, axis, -1, xp=xp)
+    return ranks
+
+
+def _order_ranks(ranks, j, *, xp):
+    # Reorder ascending order `ranks` according to `j`
+    xp = array_namespace(ranks) if xp is None else xp
+    if is_numpy(xp) or is_cupy(xp):
+        ordered_ranks = xp.empty(j.shape, dtype=ranks.dtype)
+        xp.put_along_axis(ordered_ranks, j, ranks, axis=-1)
+    else:
+        # `put_along_axis` not in array API (data-apis/array-api#177)
+        #  so argsort the argsort and take_along_axis...
+        j_inv = xp.argsort(j, axis=-1, stable=True)
+        ordered_ranks = xp.take_along_axis(ranks, j_inv, axis=-1)
+    return ordered_ranks
+
+
+def _rankdata(x, method, return_sorted=False, return_ties=False, xp=None):
+    # Rank data `x` by desired `method`. For methods other than 'ordinal':
+    # - `return_sorted=True` ensures that the second output is sorted `x`
+    # - `return_ties=True` ensures that the third output is tie data
+    # Otherwise, the second/third output will be None.
+    xp = array_namespace(x) if xp is None else xp
+    dtype = xp_result_type(x, force_floating=True, xp=xp)
+
+    if is_jax(xp):
+        import jax.scipy.stats as jax_stats
+        ranks = jax_stats.rankdata(x, method=method, axis=-1)
+        ranks = xp.astype(ranks, dtype, copy=False)
+        y = xp.sort(x, axis=-1) if (return_ties or return_sorted) else None
+        t = None
+        if return_ties:
+            max_ranks = jax_stats.rankdata(y, method='max', axis=-1)
+            t = xp.diff(max_ranks, axis=-1, prepend=0)
+            t = xp.astype(t, dtype, copy=False)
+        return ranks, y, t
+
+    if is_marray(xp):
+        data, mask = x.data, x.mask
+        uxp = array_namespace(data)
+        data = uxp.where(mask, uxp.nan, data)
+        ranks, sorted, ties = _rankdata(data, method, return_sorted, return_ties, uxp)
+        ranks = xp.asarray(ranks, mask=mask)
+        mask_sorted = uxp.isnan(sorted) if (return_sorted or return_ties) else None
+        sorted = xp.asarray(sorted, mask=mask_sorted) if return_sorted else None
+        ties = xp.asarray(ties, mask=mask_sorted) if return_ties else None
+        return ranks, sorted, ties
+
+    shape = x.shape
+
+    # Get sort order
+    j = xp.argsort(x, axis=-1, stable=True)
+    ordinal_ranks = xp.broadcast_to(xp.arange(1, shape[-1]+1, dtype=dtype), shape)
+
+    # Ordinal ranks is very easy because ties don't matter. We're done.
+    if method == 'ordinal':
+        ranks = _order_ranks(ordinal_ranks, j, xp=xp)
+        return (ranks, None, None)
+
+    # Sort array
+    y = xp.take_along_axis(x, j, axis=-1)
+    # Logical indices of unique elements
+    i = xp.concat([xp.ones(shape[:-1] + (1,), dtype=xp.bool),
+                   y[..., :-1] != y[..., 1:]], axis=-1)
+
+    # Integer indices of unique elements
+    indices = xp.arange(xp_size(y))[xp.reshape(i, (-1,))]  # i gets raveled
+    # Counts of unique elements
+    counts = xp.diff(indices, append=xp.asarray([xp_size(y)], dtype=indices.dtype))
+
+    # Compute `'min'`, `'max'`, and `'mid'` ranks of unique elements
+    if method == 'min':
+        ranks = ordinal_ranks[i]
+    elif method == 'max':
+        ranks = ordinal_ranks[i] + xp.astype(counts, dtype) - 1
+    elif method == 'average':
+        # array API doesn't promote integers to floats
+        ranks = ordinal_ranks[i] + (xp.astype(counts, dtype) - 1)/2
+    elif method == 'dense':
+        ranks = xp.cumulative_sum(xp.astype(i, dtype, copy=False), axis=-1)[i]
+
+    if not is_cupy(xp):
+        ranks = xp.reshape(xp.repeat(ranks, counts), shape)
+    else:
+        # workaround for cupy.repeat not accepting arrays for repeats
+        # (ref https://github.com/cupy/cupy/issues/3849).
+        # The cumulative sum over i will
+        # increment every time a new unique rank appears, giving the correct
+        # indices to replicate xp.repeats.
+        ranks = xp.reshape(
+            ranks[xp.cumulative_sum(xp.astype(xp.reshape(i, (-1,)), xp.int64)) - 1],
+            shape,
+        )
+    ranks = _order_ranks(ranks, j, xp=xp)
+
+    t = None
+    if return_ties:
+        # Tie information is returned in a format that is useful to functions that
+        # rely on this (private) function. Example:
+        # >>> x = np.asarray([3, 2, 1, 2, 2, 2, 1])
+        # >>> _, t = _rankdata(x, 'average', return_ties=True)
+        # >>> t  # array([2., 0., 4., 0., 0., 0., 1.])  # two 1s, four 2s, and one 3
+        # Unlike ranks, tie counts are *not* reordered to correspond with the order of
+        # the input; e.g. the number of appearances of the lowest rank element comes
+        # first. This is a useful format because:
+        # - The shape of the result is the shape of the input. Different slices can
+        #   have different numbers of tied elements but not result in a ragged array.
+        # - Functions that use `t` usually don't need to which each element of the
+        #   original array is associated with each tie count; they perform a reduction
+        #   over the tie counts onnly. The tie counts are naturally computed in a
+        #   sorted order, so this does not unnecessarily reorder them.
+        # - One exception is `wilcoxon`, which needs the number of zeros. Zeros always
+        #   have the lowest rank, so it is easy to find them at the zeroth index.
+        t = xp.zeros(shape, dtype=dtype)
+        t = xpx.at(t)[i].set(xp.astype(counts, dtype, copy=False))
+
+    return ranks, y, t
+
+
+@xp_capabilities(marray=True,
+    skip_backends=[('dask.array', 'uses `optimize.elementwise.find_root`'),
+                   ('array_api_strict', 'uses `optimize.elementwise.find_root`'),
+                   ('jax.numpy', 'uses `optimize.elementwise.find_root`')])
+@_axis_nan_policy_factory(
+    lambda x: x, n_outputs=1, result_to_tuple=lambda x, _: (x,),
+    kwd_samples=['weights'], paired=True
+)
+def expectile(a, alpha=0.5, *, weights=None, axis=None):
+    r"""Compute the expectile at the specified level.
+
+    Expectiles are a generalization of the expectation in the same way as
+    quantiles are a generalization of the median. The expectile at level
+    `alpha = 0.5` is the mean (average). See Notes for more details.
+
+    Parameters
+    ----------
+    a : array_like
+        Array containing numbers whose expectile is desired.
+    alpha : float, default: 0.5
+        The level of the expectile; e.g., ``alpha=0.5`` gives the mean.
+    weights : array_like, optional
+        An array of weights associated with the values in `a`.
+        The `weights` must be broadcastable to the same shape as `a`.
+        Default is None, which gives each value a weight of 1.0.
+        An integer valued weight element acts like repeating the corresponding
+        observation in `a` that many times. See Notes for more details.
+    axis : int or tuple of ints, default: None
+        If an int or tuple of ints, the axis or axes of the input along which
+        to compute the statistic. The statistic of each axis-slice (e.g. row)
+        of the input will appear in a corresponding element of the output.
+        If ``None``, the input will be raveled before computing the statistic.
+
+    Returns
+    -------
+    expectile : ndarray
+        The empirical expectile at level `alpha`.
+
+    See Also
+    --------
+    numpy.mean : Arithmetic average
+    numpy.quantile : Quantile
+
+    Notes
+    -----
+    In general, the expectile at level :math:`\alpha` of a random variable
+    :math:`X` with cumulative distribution function (CDF) :math:`F` is given
+    by the unique solution :math:`t` of:
+
+    .. math::
+
+        \alpha E((X - t)_+) = (1 - \alpha) E((t - X)_+) \,.
+
+    Here, :math:`(x)_+ = \max(0, x)` is the positive part of :math:`x`.
+    This equation can be equivalently written as:
+
+    .. math::
+
+        \alpha \int_t^\infty (x - t)\mathrm{d}F(x)
+        = (1 - \alpha) \int_{-\infty}^t (t - x)\mathrm{d}F(x) \,.
+
+    The empirical expectile at level :math:`\alpha` (`alpha`) of a sample
+    :math:`a_i` (the array `a`) is defined by plugging in the empirical CDF of
+    `a`. Given sample or case weights :math:`w` (the array `weights`), it
+    reads :math:`F_a(x) = \frac{1}{\sum_i w_i} \sum_i w_i 1_{a_i \leq x}`
+    with indicator function :math:`1_{A}`. This leads to the definition of the
+    empirical expectile at level `alpha` as the unique solution :math:`t` of:
+
+    .. math::
+
+        \alpha \sum_{i=1}^n w_i (a_i - t)_+ =
+            (1 - \alpha) \sum_{i=1}^n w_i (t - a_i)_+ \,.
+
+    For :math:`\alpha=0.5`, this simplifies to the weighted average.
+    Furthermore, the larger :math:`\alpha`, the larger the value of the
+    expectile.
+
+    As a final remark, the expectile at level :math:`\alpha` can also be
+    written as a minimization problem. One often used choice is
+
+    .. math::
+
+        \operatorname{argmin}_t
+        E(\lvert 1_{t\geq X} - \alpha\rvert(t - X)^2) \,.
+
+    References
+    ----------
+    .. [1] W. K. Newey and J. L. Powell (1987), "Asymmetric Least Squares
+           Estimation and Testing," Econometrica, 55, 819-847.
+    .. [2] T. Gneiting (2009). "Making and Evaluating Point Forecasts,"
+           Journal of the American Statistical Association, 106, 746 - 762.
+           :doi:`10.48550/arXiv.0912.0902`
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import expectile
+    >>> a = [1, 4, 2, -1]
+    >>> expectile(a, alpha=0.5) == np.mean(a)
+    True
+    >>> expectile(a, alpha=0.2)
+    0.42857142857142855
+    >>> expectile(a, alpha=0.8)
+    2.5714285714285716
+    >>> weights = [1, 3, 1, 1]
+    >>> expectile(a, alpha=0.8, weights=weights)
+    3.3333333333333335
+    """
+    xp = array_namespace(a, weights)
+    a, weights = xp_promote(a, weights, force_floating=True, xp=xp)
+
+    if alpha < 0 or alpha > 1:
+        raise ValueError(
+            "The expectile level alpha must be in the range [0, 1]."
+        )
+
+    if a.shape[-1] == 0:  #  Only for *testing* _axis_nan_policy decorator
+        return _get_nan(a, xp=xp)
+
+    # for simplicity, ensure that shape is (batch size, sample size) and at least 2d
+    shape = a.shape  # remember original shape, though, to ensure correct output shape
+    # `reshape` can't infer shape element -1 when array is size 0, so take `prod`
+    a = xp.reshape(a, (math.prod(shape[:-1]), shape[-1]))
+    weights = weights if weights is None else xp.reshape(weights, (-1, shape[-1]))
+
+    # This is the empirical equivalent of Eq. (13) with identification
+    # function from Table 9 (omitting a factor of 2) in [2] (their y is our
+    # data a, their x is our t)
+    def first_order(t, i):
+        ai = a[i, ...].T
+        wi = weights if weights is None else weights[i, ...].T
+        return _xp_mean(xp.abs(xp.astype(ai <= t, ai.dtype) - alpha) * (t - ai),
+                        weights=wi, axis=0)
+
+    # axis is -1 per the decorator. Use mean to produce NaNs of the correct shape/type.
+    x0 = xp.min(a, axis=-1)
+    x1 = xp.max(a, axis=-1)
+
+    # Note that the expectile is the unique solution, so no worries about
+    # finding a wrong root.
+    i = xp.arange(a.shape[0])
+    res = find_root(first_order, (x0, x1), args=(i,))
+    res = xp.reshape(res.x, shape[:-1])
+    return res[()] if res.ndim == 0 else res
+
+
+def _lmoment_iv(sample, order, axis, sorted, standardize, xp):
+    # input validation/standardization for `lmoment`
+    sample = xp_promote(sample, force_floating=True, xp=xp)
+
+    message = "`sample` must be an array of real numbers."
+    if not xp.isdtype(sample.dtype, "real floating"):
+        raise ValueError(message)
+
+    message = "`order` must be a scalar or a non-empty array of positive integers."
+    order = xp.arange(1, 5) if order is None else xp.asarray(order)
+    if (not xp.isdtype(order.dtype, "integral") or order.size == 0 or order.ndim > 1
+            or (not is_lazy_array(order) and xp.any(order <= 0))):
+        raise ValueError(message)
+
+    # input validation of non-array types can still be performed with NumPy
+    axis = np.asarray(axis)[()]
+    message = "`axis` must be an integer."
+    if not np.issubdtype(axis.dtype, np.integer) or axis.ndim != 0:
+        raise ValueError(message)
+    axis = int(axis)
+
+    sorted = np.asarray(sorted)[()]
+    message = "`sorted` must be True or False."
+    if not np.issubdtype(sorted.dtype, np.bool_) or sorted.ndim != 0:
+        raise ValueError(message)
+    sorted = bool(sorted)
+
+    standardize = np.asarray(standardize)[()]
+    message = "`standardize` must be True or False."
+    if not np.issubdtype(standardize.dtype, np.bool_) or standardize.ndim != 0:
+        raise ValueError(message)
+    standardize = bool(standardize)
+
+    sample = xp.moveaxis(sample, axis, -1)
+    sample = xp.sort(sample, axis=-1) if not sorted else sample
+
+    return sample, order, axis, sorted, standardize
+
+
+def _br(x, *, r=0, xp):
+    n = x.shape[-1]
+    x = xp.expand_dims(x, axis=-2)
+    x = xp.broadcast_to(x, x.shape[:-2] + (r.shape[0], n))
+    x = xp.triu(x)
+    j = xp.arange(n, dtype=x.dtype)
+    n = xp.asarray(n, dtype=x.dtype)[()]
+    binom_j_r = xpx.lazy_apply(special.binom, j, r[:, xp.newaxis])
+    binom_nm1_r = xpx.lazy_apply(special.binom, n-1, r)
+    return xp.vecdot(binom_j_r, x, axis=-1) / binom_nm1_r / n
+
+
+def _prk(r, k):
+    # Writen to match [1] Equation 27 closely to facilitate review.
+    # This does not protect against overflow, so improvements to
+    # robustness would be a welcome follow-up.
+    binom_r_k = xpx.lazy_apply(special.binom, r, k)
+    binom_rpk_k = xpx.lazy_apply(special.binom, r+k, k)
+    return (-1)**(r-k)*binom_r_k*binom_rpk_k
+
+
+@xp_capabilities(skip_backends=[('dask.array', "too many issues")],
+                 cpu_only=True,  # torch doesn't have `binom`
+                 exceptions=('cupy', 'jax.numpy'),
+                 extra_note="Lazy backends do not support `order` greater than 4.")
+@_axis_nan_policy_factory(  # noqa: E302
+    _moment_result_object, n_samples=1, result_to_tuple=_moment_tuple,
+    n_outputs=lambda kwds: _moment_outputs(kwds, [1, 2, 3, 4])
+)
+def lmoment(sample, order=None, *, axis=0, sorted=False, standardize=True):
+    r"""Compute L-moments of a sample from a continuous distribution.
+
+    The L-moments of a probability distribution are summary statistics with
+    uses similar to those of conventional moments, but they are defined in
+    terms of the expected values of order statistics.
+    Sample L-moments are defined analogously to population L-moments, and
+    they can serve as estimators of population L-moments. They tend to be less
+    sensitive to extreme observations than conventional moments.
+
+    Parameters
+    ----------
+    sample : array_like
+        The real-valued sample whose L-moments are desired.
+    order : array_like, optional
+        The (positive integer) orders of the desired L-moments.
+        Must be a scalar or non-empty 1D array. Default is [1, 2, 3, 4].
+    axis : int or None, default=0
+        If an int, the axis of the input along which to compute the statistic.
+        The statistic of each axis-slice (e.g. row) of the input will appear
+        in a corresponding element of the output. If None, the input will be
+        raveled before computing the statistic.
+    sorted : bool, default=False
+        Whether `sample` is already sorted in increasing order along `axis`.
+        If False (default), `sample` will be sorted.
+    standardize : bool, default=True
+        Whether to return L-moment ratios for orders 3 and higher.
+        L-moment ratios are analogous to standardized conventional
+        moments: they are the non-standardized L-moments divided
+        by the L-moment of order 2.
+
+    Returns
+    -------
+    lmoments : ndarray
+        The sample L-moments of order `order`.
+
+    See Also
+    --------
+    moment
+
+    Notes
+    -----
+    SciPy offers only basic capabilities for working with L-moments. For more advanced
+    features, consider the ``lmo`` package [4]_.
+
+    References
+    ----------
+    .. [1] D. Bilkova. "L-Moments and TL-Moments as an Alternative Tool of
+           Statistical Data Analysis". Journal of Applied Mathematics and
+           Physics. 2014. :doi:`10.4236/jamp.2014.210104`
+    .. [2] J. R. M. Hosking. "L-Moments: Analysis and Estimation of Distributions
+           Using Linear Combinations of Order Statistics". Journal of the Royal
+           Statistical Society. 1990. :doi:`10.1111/j.2517-6161.1990.tb01775.x`
+    .. [3] "L-moment". *Wikipedia*. https://en.wikipedia.org/wiki/L-moment.
+    .. [4] @jorenham, *Lmo*, https://github.com/jorenham/Lmo/
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> rng = np.random.default_rng(328458568356392)
+    >>> sample = rng.exponential(size=100000)
+    >>> stats.lmoment(sample)
+    array([1.00124272, 0.50111437, 0.3340092 , 0.16755338])
+
+    Note that the first four standardized population L-moments of the standard
+    exponential distribution are 1, 1/2, 1/3, and 1/6; the sample L-moments
+    provide reasonable estimates.
+
+    """
+    xp = array_namespace(sample)
+    args = _lmoment_iv(sample, order, axis, sorted, standardize, xp=xp)
+    sample, order, axis, sorted, standardize = args
+
+    n_moments = 4 if is_lazy_array(order) else int(xp.max(order))
+    k = xp.arange(n_moments, dtype=sample.dtype)
+    prk = _prk(xpx.expand_dims(k, axis=tuple(range(1, sample.ndim+1))), k)
+    bk = _br(sample, r=k, xp=xp)
+
+    n = sample.shape[-1]
+    if n < bk.shape[-1]:
+        bk = xpx.at(bk)[..., n:].set(0)  # remove NaNs due to n_moments > n
+
+    lmoms = xp.vecdot(prk, bk, axis=-1)
+    if standardize and n_moments > 2:
+        lmoms = xpx.at(lmoms)[2:, ...].divide(lmoms[1, ...])
+
+    if n < lmoms.shape[0]:
+        lmoms = xpx.at(lmoms)[n:, ...].set(xp.nan)  # add NaNs where appropriate
+    # return lmoms[order-1]  # strict can't handle fancy indexing plus ellipses
+    return xp.take(lmoms, order - 1, axis=0) if order.ndim == 1 else lmoms[order - 1]
+
+
+LinregressResult = _make_tuple_bunch('LinregressResult',
+                                     ['slope', 'intercept', 'rvalue',
+                                      'pvalue', 'stderr'],
+                                     extra_field_names=['intercept_stderr'])
+
+
+def _pack_LinregressResult(slope, intercept, rvalue, pvalue, stderr, intercept_stderr):
+    return LinregressResult(slope, intercept, rvalue, pvalue, stderr,
+                            intercept_stderr=intercept_stderr)
+
+
+def _unpack_LinregressResult(res, _):
+    return tuple(res) + (res.intercept_stderr,)
+
+
+@xp_capabilities(skip_backends=[('dask.array', '`dtype` inference failed....')],
+                 cpu_only=True, exceptions=['cupy', 'jax.numpy'],
+                 marray=True)
+@_axis_nan_policy_factory(_pack_LinregressResult, n_samples=2,
+                          result_to_tuple=_unpack_LinregressResult, paired=True,
+                          too_small=1, n_outputs=6)
+def linregress(x, y, alternative='two-sided', *, axis=0):
+    """
+    Calculate a linear least-squares regression for two sets of measurements.
+
+    Parameters
+    ----------
+    x, y : array_like
+        Two sets of measurements.  Both arrays should have the same length N.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis. Default is 'two-sided'.
+        The following options are available:
+
+        * 'two-sided': the slope of the regression line is nonzero
+        * 'less': the slope of the regression line is less than zero
+        * 'greater':  the slope of the regression line is greater than zero
+
+        .. versionadded:: 1.7.0
+    axis : int or None, default: 0
+        If an int, the axis of the input along which to compute the statistic.
+        The statistic of each axis-slice (e.g. row) of the input will appear in a
+        corresponding element of the output.
+        If ``None``, the input will be raveled before computing the statistic.
+
+    Returns
+    -------
+    result : ``LinregressResult`` instance
+        The return value is an object with the following attributes:
+
+        slope : float
+            Slope of the regression line.
+        intercept : float
+            Intercept of the regression line.
+        rvalue : float
+            The Pearson correlation coefficient. The square of ``rvalue``
+            is equal to the coefficient of determination.
+        pvalue : float
+            The p-value for a hypothesis test whose null hypothesis is
+            that the slope is zero, using Wald Test with t-distribution of
+            the test statistic. See `alternative` above for alternative
+            hypotheses.
+        stderr : float
+            Standard error of the estimated slope (gradient), under the
+            assumption of residual normality.
+        intercept_stderr : float
+            Standard error of the estimated intercept, under the assumption
+            of residual normality.
+
+    See Also
+    --------
+    scipy.optimize.curve_fit :
+        Use non-linear least squares to fit a function to data.
+    scipy.optimize.leastsq :
+        Minimize the sum of squares of a set of equations.
+
+    Notes
+    -----
+    For compatibility with older versions of SciPy, the return value acts
+    like a ``namedtuple`` of length 5, with fields ``slope``, ``intercept``,
+    ``rvalue``, ``pvalue`` and ``stderr``, so one can continue to write::
+
+        slope, intercept, r, p, se = linregress(x, y)
+
+    With that style, however, the standard error of the intercept is not
+    available.  To have access to all the computed values, including the
+    standard error of the intercept, use the return value as an object
+    with attributes, e.g.::
+
+        result = linregress(x, y)
+        print(result.intercept, result.intercept_stderr)
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy import stats
+    >>> rng = np.random.default_rng()
+
+    Generate some data:
+
+    >>> x = rng.random(10)
+    >>> y = 1.6*x + rng.random(10)
+
+    Perform the linear regression:
+
+    >>> res = stats.linregress(x, y)
+
+    Coefficient of determination (R-squared):
+
+    >>> print(f"R-squared: {res.rvalue**2:.6f}")
+    R-squared: 0.717533
+
+    Plot the data along with the fitted line:
+
+    >>> plt.plot(x, y, 'o', label='original data')
+    >>> plt.plot(x, res.intercept + res.slope*x, 'r', label='fitted line')
+    >>> plt.legend()
+    >>> plt.show()
+
+    Calculate 95% confidence interval on slope and intercept:
+
+    >>> # Two-sided inverse Students t-distribution
+    >>> # p - probability, df - degrees of freedom
+    >>> from scipy.stats import t
+    >>> tinv = lambda p, df: abs(t.ppf(p/2, df))
+
+    >>> ts = tinv(0.05, len(x)-2)
+    >>> print(f"slope (95%): {res.slope:.6f} +/- {ts*res.stderr:.6f}")
+    slope (95%): 1.453392 +/- 0.743465
+    >>> print(f"intercept (95%): {res.intercept:.6f}"
+    ...       f" +/- {ts*res.intercept_stderr:.6f}")
+    intercept (95%): 0.616950 +/- 0.544475
+
+    """
+    xp = array_namespace(x, y)
+    x, y = xp_promote(x, y, force_floating=True, xp=xp)
+
+    TINY = 1.0e-20
+
+    # _axis_nan_policy decorator ensures that `axis=-1`
+    x, y = _share_masks(x, y, xp=xp)
+    n = _count_nonmasked(x, axis=-1, keepdims=False, xp=xp)
+    xmean = xp.mean(x, axis=-1, keepdims=True)
+    ymean = xp.mean(y, axis=-1, keepdims=True)
+
+    # Average sums of square differences from the mean
+    #   ssxm = mean( (x-mean(x))^2 )
+    #   ssxym = mean( (x-mean(x)) * (y-mean(y)) )
+    x_ = _demean(x, xmean, axis=-1, xp=xp)
+    y_ = _demean(y, ymean, axis=-1, xp=xp, precision_warning=False)
+    xmean = xp.squeeze(xmean, axis=-1)
+    ymean = xp.squeeze(ymean, axis=-1)
+
+    ssxm = xp.vecdot(x_, x_, axis=-1) / n
+    ssym = xp.vecdot(y_, y_, axis=-1) / n
+    ssxym = xp.vecdot(x_, y_, axis=-1) / n
+
+    # R-value
+    #   r = ssxym / sqrt( ssxm * ssym )
+    degenerate = (ssxm == 0.0) | (ssym == 0.0)
+    NaN = xp.asarray(xp.nan, dtype=ssxym.dtype)
+    r = xpx.apply_where(
+        ~degenerate,
+        (ssxym, ssxm, ssym),
+        lambda ssxym, ssxm, ssym: xp.clip(ssxym / xp.sqrt(ssxm * ssym), -1.0, 1.0),
+        lambda ssxym, ssxm, ssym: xp.where(ssxym==0, NaN, 0.0)
+    )
+
+    slope = ssxym / ssxm
+    intercept = ymean - slope*xmean
+    with np.errstate(invalid='ignore', divide='ignore'):
+        df = n - 2  # Number of degrees of freedom
+        # n-2 degrees of freedom because 2 has been used up
+        # to estimate the mean and standard deviation
+        t = r * xp.sqrt(df / ((1.0 - r + TINY)*(1.0 + r + TINY)))
+
+        dist = _SimpleStudentT(xp.asarray(df, dtype=t.dtype))
+        prob = _get_pvalue(t, dist, alternative, xp=xp)
+        prob = prob[()] if prob.ndim == 0 else prob
+
+        slope_stderr = xp.sqrt((1 - r**2) * ssym / ssxm / df)
+
+        # Also calculate the standard error of the intercept
+        # The following relationship is used:
+        #   ssxm = mean( (x-mean(x))^2 )
+        #        = ssx - sx*sx
+        #        = mean( x^2 ) - mean(x)^2
+        intercept_stderr = slope_stderr * xp.sqrt(ssxm + xmean**2)
+
+    outputs = slope, intercept, r, prob, slope_stderr, intercept_stderr
+    outputs = (output[()] if output.ndim == 0 else output for output in outputs)
+    slope, intercept, r, prob, slope_stderr, intercept_stderr = outputs
+
+    return LinregressResult(slope=slope, intercept=intercept, rvalue=r,
+                            pvalue=prob, stderr=slope_stderr,
+                            intercept_stderr=intercept_stderr)
+
+def _linearized_pmean(a, p, *, axis=None, weights=None, xp=None):
+    # pmean linearized as a function of p about p = 0; see gh-23407
+    M0 = gmean(a, axis=axis, weights=weights)
+
+    loga = xp.log(a)
+
+    ln_avg = _xp_mean(loga, axis=axis, weights=weights)
+    ln2_avg = _xp_mean(loga * loga, axis=axis, weights=weights)
+
+    return M0 * (1 + 0.5 * p * (ln2_avg - ln_avg * ln_avg))
+
+
+@xp_capabilities()
+def _xp_mean(x, /, *, axis=None, weights=None, keepdims=False, nan_policy='propagate',
+             dtype=None, warn=True, xp=None):
+    r"""Compute the arithmetic mean along the specified axis.
+
+    Parameters
+    ----------
+    x : real array
+        Array containing real numbers whose mean is desired.
+    axis : int or tuple of ints, default: None
+        If an int or tuple of ints, the axis or axes of the input along which
+        to compute the statistic. The statistic of each axis-slice (e.g. row)
+        of the input will appear in a corresponding element of the output.
+        If ``None``, the input will be raveled before computing the statistic.
+    weights : real array, optional
+        If specified, an array of weights associated with the values in `x`;
+        otherwise ``1``. If `weights` and `x` do not have the same shape, the
+        arrays will be broadcasted before performing the calculation. See
+        Notes for details.
+    keepdims : bool, optional
+        If this is set to ``True``, the axes which are reduced are left
+        in the result as dimensions with length one. With this option,
+        the result will broadcast correctly against the input array.
+    nan_policy : {'propagate', 'omit', 'raise'}, default: 'propagate'
+        Defines how to handle input NaNs.
+
+        - ``propagate``: if a NaN is present in the axis slice (e.g. row) along
+          which the statistic is computed, the corresponding entry of the output
+          will be NaN.
+        - ``omit``: NaNs will be omitted when performing the calculation.
+          If insufficient data remains in the axis slice along which the
+          statistic is computed, the corresponding entry of the output will be
+          NaN.
+        - ``raise``: if a NaN is present, a ``ValueError`` will be raised.
+
+    dtype : dtype, optional
+        Type to use in computing the mean. For integer inputs, the default is
+        the default float type of the array library; for floating point inputs,
+        the dtype is that of the input.
+
+    Returns
+    -------
+    out : array
+        The mean of each slice
+
+    Notes
+    -----
+    Let :math:`x_i` represent element :math:`i` of data `x` and let :math:`w_i`
+    represent the corresponding element of `weights` after broadcasting. Then the
+    (weighted) mean :math:`\bar{x}_w` is given by:
+
+    .. math::
+
+        \bar{x}_w = \frac{ \sum_{i=0}^{n-1} w_i x_i }
+                         { \sum_{i=0}^{n-1} w_i }
+
+    where :math:`n` is the number of elements along a slice. Note that this simplifies
+    to the familiar :math:`(\sum_i x_i) / n` when the weights are all ``1`` (default).
+
+    The behavior of this function with respect to weights is somewhat different
+    from that of `np.average`. For instance,
+    `np.average` raises an error when `axis` is not specified and the shapes of `x`
+    and the `weights` array are not the same; `xp_mean` simply broadcasts the two.
+    Also, `np.average` raises an error when weights sum to zero along a slice;
+    `xp_mean` computes the appropriate result. The intent is for this function's
+    interface to be consistent with the rest of `scipy.stats`.
+
+    Note that according to the formula, including NaNs with zero weights is not
+    the same as *omitting* NaNs with ``nan_policy='omit'``; in the former case,
+    the NaNs will continue to propagate through the calculation whereas in the
+    latter case, the NaNs are excluded entirely.
+
+    """
+    # ensure that `x` and `weights` are array-API compatible arrays of identical shape
+    xp = array_namespace(x) if xp is None else xp
+    x = _asarray(x, dtype=dtype, subok=True)
+    weights = xp.asarray(weights, dtype=dtype) if weights is not None else weights
+
+    # to ensure that this matches the behavior of decorated functions when one of the
+    # arguments has size zero, it's easiest to call a similar decorated function.
+    if is_numpy(xp) and (xp_size(x) == 0
+                         or (weights is not None and xp_size(weights) == 0)):
+        return gmean(x, weights=weights, axis=axis, keepdims=keepdims)
+
+    x, weights = xp_promote(x, weights, broadcast=True, force_floating=True, xp=xp)
+    if weights is not None:
+        x, weights = _share_masks(x, weights, xp=xp)
+
+    # handle the special case of zero-sized arrays
+    message = (too_small_1d_not_omit if (x.ndim == 1 or axis is None)
+               else too_small_nd_not_omit)
+    if xp_size(x) == 0:
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore")
+            res = xp.mean(x, axis=axis, keepdims=keepdims)
+        if warn and xp_size(res) != 0:
+            warnings.warn(message, SmallSampleWarning, stacklevel=2)
+        return res
+
+    contains_nan = _contains_nan(x, nan_policy, xp_omit_okay=True, xp=xp)
+    if weights is not None:
+        contains_nan_w = _contains_nan(weights, nan_policy, xp_omit_okay=True, xp=xp)
+        contains_nan = contains_nan | contains_nan_w
+
+    # Handle `nan_policy='omit'` by giving zero weight to NaNs, whether they
+    # appear in `x` or `weights`. Emit warning if there is an all-NaN slice.
+    # Test nan_policy before the implicit call to bool(contains_nan)
+    # to avoid raising on lazy xps on the default nan_policy='propagate'
+    lazy = is_lazy_array(x)
+    if nan_policy == 'omit' and (lazy or contains_nan):
+        nan_mask = xp.isnan(x)
+        if weights is not None:
+            nan_mask |= xp.isnan(weights)
+        if warn and not lazy and xp.any(xp.all(nan_mask, axis=axis)):
+            message = (too_small_1d_omit if (x.ndim == 1 or axis is None)
+                       else too_small_nd_omit)
+            warnings.warn(message, SmallSampleWarning, stacklevel=2)
+        weights = xp.ones_like(x) if weights is None else weights
+        x = xp.where(nan_mask, 0., x)
+        weights = xp.where(nan_mask, 0., weights)
+
+    # Perform the mean calculation itself
+    if weights is None:
+        return xp.mean(x, axis=axis, keepdims=keepdims)
+
+    # consider using `vecdot` if `axis` tuple support is added (data-apis/array-api#910)
+    norm = xp.sum(weights, axis=axis)
+    wsum = xp.sum(x * weights, axis=axis)
+    with np.errstate(divide='ignore', invalid='ignore'):
+        res = wsum/norm
+
+    # Respect `keepdims` and convert NumPy 0-D arrays to scalars
+    if keepdims:
+
+        if axis is None:
+            final_shape = (1,) * len(x.shape)
+        else:
+            # axis can be a scalar or sequence
+            axes = (axis,) if not isinstance(axis, Sequence) else axis
+            final_shape = list(x.shape)
+            for i in axes:
+                final_shape[i] = 1
+
+        res = xp.reshape(res, tuple(final_shape))
+
+    return res[()] if res.ndim == 0 else res
+
+
+@xp_capabilities()
+def _xp_var(x, /, *, axis=None, correction=0, keepdims=False, nan_policy='propagate',
+            dtype=None, xp=None):
+    # an array-api compatible function for variance with scipy.stats interface
+    # and features (e.g. `nan_policy`).
+    xp = array_namespace(x) if xp is None else xp
+    x = _asarray(x, subok=True)
+
+    # use `_xp_mean` instead of `xp.var` for desired warning behavior
+    # it would be nice to combine this with `_var`, which uses `_moment`
+    # and therefore warns when precision is lost, but that does not support
+    # `axis` tuples or keepdims. Eventually, `_axis_nan_policy` will simplify
+    # `axis` tuples and implement `keepdims` for non-NumPy arrays; then it will
+    # be easy.
+    kwargs = dict(axis=axis, nan_policy=nan_policy, dtype=dtype, xp=xp)
+    mean = _xp_mean(x, keepdims=True, **kwargs)
+    x = _asarray(x, dtype=mean.dtype, subok=True)
+    x_mean = _demean(x, mean, axis, xp=xp)
+    x_mean_conj = (xp.conj(x_mean) if xp.isdtype(x_mean.dtype, 'complex floating')
+                   else x_mean)  # crossref data-apis/array-api#824
+    var = _xp_mean(x_mean * x_mean_conj, keepdims=keepdims, **kwargs)
+
+    if correction != 0:
+        n = _count_nonmasked(x, axis, xp=xp, keepdims=keepdims)
+        # Or two lines with ternaries : )
+        # axis = range(x.ndim) if axis is None else axis
+        # n = math.prod(x.shape[i] for i in axis) if iterable(axis) else x.shape[axis]
+
+        n = xp.asarray(n, dtype=var.dtype, device=xp_device(x))
+
+        if nan_policy == 'omit':
+            nan_mask = xp.astype(xp.isnan(x), var.dtype)
+            n = n - xp.sum(nan_mask, axis=axis, keepdims=keepdims)
+
+        # Produce NaNs silently when n - correction <= 0
+        nc = n - correction
+        factor = xpx.apply_where(nc > 0, (n, nc), operator.truediv, fill_value=xp.nan)
+        var *= factor
+
+    return var[()] if var.ndim == 0 else var
+
+
+class _SimpleNormal:
+    # A very simple, array-API compatible normal distribution for use in
+    # hypothesis tests. May be replaced by new infrastructure Normal
+    # distribution in due time.
+
+    def cdf(self, x):
+        return special.ndtr(x)
+
+    def sf(self, x):
+        return special.ndtr(-x)
+
+    def isf(self, x):
+        return -special.ndtri(x)
+
+
+class _SimpleChi2:
+    # A very simple, array-API compatible chi-squared distribution for use in
+    # hypothesis tests. May be replaced by new infrastructure chi-squared
+    # distribution in due time.
+    def __init__(self, df):
+        self.df = df
+
+    def cdf(self, x):
+        return special.chdtr(self.df, x)
+
+    def sf(self, x):
+        return special.chdtrc(self.df, x)
+
+
+class _SimpleBeta:
+    # A very simple, array-API compatible beta distribution for use in
+    # hypothesis tests. May be replaced by new infrastructure beta
+    # distribution in due time.
+    def __init__(self, a, b, *, loc=None, scale=None):
+        self.a = a
+        self.b = b
+        self.loc = loc
+        self.scale = scale
+
+    def cdf(self, x):
+        if self.loc is not None or self.scale is not None:
+            loc = 0 if self.loc is None else self.loc
+            scale = 1 if self.scale is None else self.scale
+            return special.betainc(self.a, self.b, (x - loc)/scale)
+        return special.betainc(self.a, self.b, x)
+
+    def sf(self, x):
+        if self.loc is not None or self.scale is not None:
+            loc = 0 if self.loc is None else self.loc
+            scale = 1 if self.scale is None else self.scale
+            return special.betaincc(self.a, self.b, (x - loc)/scale)
+        return special.betaincc(self.a, self.b, x)
+
+
+class _SimpleStudentT:
+    # A very simple, array-API compatible t distribution for use in
+    # hypothesis tests. May be replaced by new infrastructure t
+    # distribution in due time.
+    def __init__(self, df):
+        self.df = df
+
+    def cdf(self, t):
+        return special.stdtr(self.df, t)
+
+    def sf(self, t):
+        return special.stdtr(self.df, -t)
+
+
+class _SimpleF:
+    # A very simple, array-API compatible F distribution for use in
+    # hypothesis tests.
+    def __init__(self, dfn, dfd):
+        self.dfn = dfn
+        self.dfd = dfd
+
+    def cdf(self, x):
+        return special.fdtr(self.dfn, self.dfd, x)
+
+    def sf(self, x):
+        return special.fdtrc(self.dfn, self.dfd, x)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_stats_pythran.cpython-312-x86_64-linux-gnu.so b/venv/lib/python3.12/site-packages/scipy/stats/_stats_pythran.cpython-312-x86_64-linux-gnu.so
new file mode 100644
index 0000000000000000000000000000000000000000..46ab388331867a5e2dedb593a52a9ca5ef93d221
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_stats_pythran.cpython-312-x86_64-linux-gnu.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:14320c5a7e42ed3a39a3606acdeb108aae23f0038307e35ae28090808239c530
+size 136360
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_survival.py b/venv/lib/python3.12/site-packages/scipy/stats/_survival.py
new file mode 100644
index 0000000000000000000000000000000000000000..70a84806a95ae82b2968bb9cf5ee37f48808c59c
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_survival.py
@@ -0,0 +1,686 @@
+from dataclasses import dataclass, field
+from typing import TYPE_CHECKING, Literal
+import warnings
+
+import numpy as np
+from scipy import special, interpolate, stats
+from scipy._lib._array_api import xp_capabilities
+from scipy.stats._censored_data import CensoredData
+from scipy.stats._common import ConfidenceInterval
+
+if TYPE_CHECKING:
+    import numpy.typing as npt
+
+
+__all__ = ['ecdf', 'logrank']
+
+
+@dataclass
+class EmpiricalDistributionFunction:
+    """An empirical distribution function produced by `scipy.stats.ecdf`
+
+    Attributes
+    ----------
+    quantiles : ndarray
+        The unique values of the sample from which the
+        `EmpiricalDistributionFunction` was estimated.
+    probabilities : ndarray
+        The point estimates of the cumulative distribution function (CDF) or
+        its complement, the survival function (SF), corresponding with
+        `quantiles`.
+    """
+    quantiles: np.ndarray
+    probabilities: np.ndarray
+    # Exclude these from __str__
+    _n: np.ndarray = field(repr=False)  # number "at risk"
+    _d: np.ndarray = field(repr=False)  # number of "deaths"
+    _sf: np.ndarray = field(repr=False)  # survival function for var estimate
+    _kind: str = field(repr=False)  # type of function: "cdf" or "sf"
+
+    def __init__(self, q, p, n, d, kind):
+        self.probabilities = p
+        self.quantiles = q
+        self._n = n
+        self._d = d
+        self._sf = p if kind == 'sf' else 1 - p
+        self._kind = kind
+
+        f0 = 1 if kind == 'sf' else 0  # leftmost function value
+        f1 = 1 - f0
+        # fill_value can't handle edge cases at infinity
+        x = np.insert(q, [0, len(q)], [-np.inf, np.inf])
+        y = np.insert(p, [0, len(p)], [f0, f1])
+        # `or` conditions handle the case of empty x, points
+        self._f = interpolate.interp1d(x, y, kind='previous',
+                                       assume_sorted=True)
+
+    def evaluate(self, x):
+        """Evaluate the empirical CDF/SF function at the input.
+
+        Parameters
+        ----------
+        x : ndarray
+            Argument to the CDF/SF
+
+        Returns
+        -------
+        y : ndarray
+            The CDF/SF evaluated at the input
+        """
+        return self._f(x)
+
+    def plot(self, ax=None, **matplotlib_kwargs):
+        """Plot the empirical distribution function
+
+        Available only if ``matplotlib`` is installed.
+
+        Parameters
+        ----------
+        ax : matplotlib.axes.Axes
+            Axes object to draw the plot onto, otherwise uses the current Axes.
+
+        **matplotlib_kwargs : dict, optional
+            Keyword arguments passed directly to `matplotlib.axes.Axes.step`.
+            Unless overridden, ``where='post'``.
+
+        Returns
+        -------
+        lines : list of `matplotlib.lines.Line2D`
+            Objects representing the plotted data
+        """
+        try:
+            import matplotlib  # noqa: F401
+        except ModuleNotFoundError as exc:
+            message = "matplotlib must be installed to use method `plot`."
+            raise ModuleNotFoundError(message) from exc
+
+        if ax is None:
+            import matplotlib.pyplot as plt
+            ax = plt.gca()
+
+        kwargs = {'where': 'post'}
+        kwargs.update(matplotlib_kwargs)
+
+        delta = np.ptp(self.quantiles)*0.05  # how far past sample edge to plot
+        q = self.quantiles
+        q = [q[0] - delta] + list(q) + [q[-1] + delta]
+
+        return ax.step(q, self.evaluate(q), **kwargs)
+
+    def confidence_interval(self, confidence_level=0.95, *, method='linear'):
+        """Compute a confidence interval around the CDF/SF point estimate
+
+        Parameters
+        ----------
+        confidence_level : float, default: 0.95
+            Confidence level for the computed confidence interval
+
+        method : str, {"linear", "log-log"}
+            Method used to compute the confidence interval. Options are
+            "linear" for the conventional Greenwood confidence interval
+            (default)  and "log-log" for the "exponential Greenwood",
+            log-negative-log-transformed confidence interval.
+
+        Returns
+        -------
+        ci : ``ConfidenceInterval``
+            An object with attributes ``low`` and ``high``, instances of
+            `~scipy.stats._result_classes.EmpiricalDistributionFunction` that
+            represent the lower and upper bounds (respectively) of the
+            confidence interval.
+
+        Notes
+        -----
+        Confidence intervals are computed according to the Greenwood formula
+        (``method='linear'``) or the more recent "exponential Greenwood"
+        formula (``method='log-log'``) as described in [1]_. The conventional
+        Greenwood formula can result in lower confidence limits less than 0
+        and upper confidence limits greater than 1; these are clipped to the
+        unit interval. NaNs may be produced by either method; these are
+        features of the formulas.
+
+        References
+        ----------
+        .. [1] Sawyer, Stanley. "The Greenwood and Exponential Greenwood
+               Confidence Intervals in Survival Analysis."
+               https://www.math.wustl.edu/~sawyer/handouts/greenwood.pdf
+
+        """
+        message = ("Confidence interval bounds do not implement a "
+                   "`confidence_interval` method.")
+        if self._n is None:
+            raise NotImplementedError(message)
+
+        methods = {'linear': self._linear_ci,
+                   'log-log': self._loglog_ci}
+
+        message = f"`method` must be one of {set(methods)}."
+        if method.lower() not in methods:
+            raise ValueError(message)
+
+        message = "`confidence_level` must be a scalar between 0 and 1."
+        confidence_level = np.asarray(confidence_level)[()]
+        if confidence_level.shape or not (0 <= confidence_level <= 1):
+            raise ValueError(message)
+
+        method_fun = methods[method.lower()]
+        low, high = method_fun(confidence_level)
+
+        message = ("The confidence interval is undefined at some observations."
+                   " This is a feature of the mathematical formula used, not"
+                   " an error in its implementation.")
+        if np.any(np.isnan(low) | np.isnan(high)):
+            warnings.warn(message, RuntimeWarning, stacklevel=2)
+
+        low, high = np.clip(low, 0, 1), np.clip(high, 0, 1)
+        low = EmpiricalDistributionFunction(self.quantiles, low, None, None,
+                                            self._kind)
+        high = EmpiricalDistributionFunction(self.quantiles, high, None, None,
+                                             self._kind)
+        return ConfidenceInterval(low, high)
+
+    def _linear_ci(self, confidence_level):
+        sf, d, n = self._sf, self._d, self._n
+        # When n == d, Greenwood's formula divides by zero.
+        # When s != 0, this can be ignored: var == inf, and CI is [0, 1]
+        # When s == 0, this results in NaNs. Produce an informative warning.
+        with np.errstate(divide='ignore', invalid='ignore'):
+            var = sf ** 2 * np.cumsum(d / (n * (n - d)))
+
+        se = np.sqrt(var)
+        z = special.ndtri(1 / 2 + confidence_level / 2)
+
+        z_se = z * se
+        low = self.probabilities - z_se
+        high = self.probabilities + z_se
+
+        return low, high
+
+    def _loglog_ci(self, confidence_level):
+        sf, d, n = self._sf, self._d, self._n
+
+        with np.errstate(divide='ignore', invalid='ignore'):
+            var = 1 / np.log(sf) ** 2 * np.cumsum(d / (n * (n - d)))
+
+        se = np.sqrt(var)
+        z = special.ndtri(1 / 2 + confidence_level / 2)
+
+        with np.errstate(divide='ignore'):
+            lnl_points = np.log(-np.log(sf))
+
+        z_se = z * se
+        low = np.exp(-np.exp(lnl_points + z_se))
+        high = np.exp(-np.exp(lnl_points - z_se))
+        if self._kind == "cdf":
+            low, high = 1-high, 1-low
+
+        return low, high
+
+
+@dataclass
+class ECDFResult:
+    """ Result object returned by `scipy.stats.ecdf`
+
+    Attributes
+    ----------
+    cdf : `~scipy.stats._result_classes.EmpiricalDistributionFunction`
+        An object representing the empirical cumulative distribution function.
+    sf : `~scipy.stats._result_classes.EmpiricalDistributionFunction`
+        An object representing the complement of the empirical cumulative
+        distribution function.
+    """
+    cdf: EmpiricalDistributionFunction
+    sf: EmpiricalDistributionFunction
+
+    def __init__(self, q, cdf, sf, n, d):
+        self.cdf = EmpiricalDistributionFunction(q, cdf, n, d, "cdf")
+        self.sf = EmpiricalDistributionFunction(q, sf, n, d, "sf")
+
+
+def _iv_CensoredData(
+    sample: "npt.ArrayLike | CensoredData", param_name: str = "sample"
+) -> CensoredData:
+    """Attempt to convert `sample` to `CensoredData`."""
+    if not isinstance(sample, CensoredData):
+        try:  # takes care of input standardization/validation
+            sample = CensoredData(uncensored=sample)
+        except ValueError as e:
+            message = str(e).replace('uncensored', param_name)
+            raise type(e)(message) from e
+    return sample
+
+
+@xp_capabilities(np_only=True)
+def ecdf(sample: "npt.ArrayLike | CensoredData") -> ECDFResult:
+    """Empirical cumulative distribution function of a sample.
+
+    The empirical cumulative distribution function (ECDF) is a step function
+    estimate of the CDF of the distribution underlying a sample. This function
+    returns objects representing both the empirical distribution function and
+    its complement, the empirical survival function.
+
+    Parameters
+    ----------
+    sample : 1D array_like or `scipy.stats.CensoredData`
+        Besides array_like, instances of `scipy.stats.CensoredData` containing
+        uncensored and right-censored observations are supported. Currently,
+        other instances of `scipy.stats.CensoredData` will result in a
+        ``NotImplementedError``.
+
+    Returns
+    -------
+    res : `~scipy.stats._result_classes.ECDFResult`
+        An object with the following attributes.
+
+        cdf : `~scipy.stats._result_classes.EmpiricalDistributionFunction`
+            An object representing the empirical cumulative distribution
+            function.
+        sf : `~scipy.stats._result_classes.EmpiricalDistributionFunction`
+            An object representing the empirical survival function.
+
+        The `cdf` and `sf` attributes themselves have the following attributes.
+
+        quantiles : ndarray
+            The unique values in the sample that defines the empirical CDF/SF.
+        probabilities : ndarray
+            The point estimates of the probabilities corresponding with
+            `quantiles`.
+
+        And the following methods:
+
+        evaluate(x) :
+            Evaluate the CDF/SF at the argument.
+
+        plot(ax) :
+            Plot the CDF/SF on the provided axes.
+
+        confidence_interval(confidence_level=0.95) :
+            Compute the confidence interval around the CDF/SF at the values in
+            `quantiles`.
+
+    Notes
+    -----
+    When each observation of the sample is a precise measurement, the ECDF
+    steps up by ``1/len(sample)`` at each of the observations [1]_.
+
+    When observations are lower bounds, upper bounds, or both upper and lower
+    bounds, the data is said to be "censored", and `sample` may be provided as
+    an instance of `scipy.stats.CensoredData`.
+
+    For right-censored data, the ECDF is given by the Kaplan-Meier estimator
+    [2]_; other forms of censoring are not supported at this time.
+
+    Confidence intervals are computed according to the Greenwood formula or the
+    more recent "Exponential Greenwood" formula as described in [4]_.
+
+    References
+    ----------
+    .. [1] Conover, William Jay. Practical nonparametric statistics. Vol. 350.
+           John Wiley & Sons, 1999.
+
+    .. [2] Kaplan, Edward L., and Paul Meier. "Nonparametric estimation from
+           incomplete observations." Journal of the American statistical
+           association 53.282 (1958): 457-481.
+
+    .. [3] Goel, Manish Kumar, Pardeep Khanna, and Jugal Kishore.
+           "Understanding survival analysis: Kaplan-Meier estimate."
+           International journal of Ayurveda research 1.4 (2010): 274.
+
+    .. [4] Sawyer, Stanley. "The Greenwood and Exponential Greenwood Confidence
+           Intervals in Survival Analysis."
+           https://www.math.wustl.edu/~sawyer/handouts/greenwood.pdf
+
+    Examples
+    --------
+    **Uncensored Data**
+
+    As in the example from [1]_ page 79, five boys were selected at random from
+    those in a single high school. Their one-mile run times were recorded as
+    follows.
+
+    >>> sample = [6.23, 5.58, 7.06, 6.42, 5.20]  # one-mile run times (minutes)
+
+    The empirical distribution function, which approximates the distribution
+    function of one-mile run times of the population from which the boys were
+    sampled, is calculated as follows.
+
+    >>> from scipy import stats
+    >>> res = stats.ecdf(sample)
+    >>> res.cdf.quantiles
+    array([5.2 , 5.58, 6.23, 6.42, 7.06])
+    >>> res.cdf.probabilities
+    array([0.2, 0.4, 0.6, 0.8, 1. ])
+
+    To plot the result as a step function:
+
+    >>> import matplotlib.pyplot as plt
+    >>> ax = plt.subplot()
+    >>> res.cdf.plot(ax)
+    >>> ax.set_xlabel('One-Mile Run Time (minutes)')
+    >>> ax.set_ylabel('Empirical CDF')
+    >>> plt.show()
+
+    **Right-censored Data**
+
+    As in the example from [1]_ page 91, the lives of ten car fanbelts were
+    tested. Five tests concluded because the fanbelt being tested broke, but
+    the remaining tests concluded for other reasons (e.g. the study ran out of
+    funding, but the fanbelt was still functional). The mileage driven
+    with the fanbelts were recorded as follows.
+
+    >>> broken = [77, 47, 81, 56, 80]  # in thousands of miles driven
+    >>> unbroken = [62, 60, 43, 71, 37]
+
+    Precise survival times of the fanbelts that were still functional at the
+    end of the tests are unknown, but they are known to exceed the values
+    recorded in ``unbroken``. Therefore, these observations are said to be
+    "right-censored", and the data is represented using
+    `scipy.stats.CensoredData`.
+
+    >>> sample = stats.CensoredData(uncensored=broken, right=unbroken)
+
+    The empirical survival function is calculated as follows.
+
+    >>> res = stats.ecdf(sample)
+    >>> res.sf.quantiles
+    array([37., 43., 47., 56., 60., 62., 71., 77., 80., 81.])
+    >>> res.sf.probabilities
+    array([1.   , 1.   , 0.875, 0.75 , 0.75 , 0.75 , 0.75 , 0.5  , 0.25 , 0.   ])
+
+    To plot the result as a step function:
+
+    >>> ax = plt.subplot()
+    >>> res.sf.plot(ax)
+    >>> ax.set_xlabel('Fanbelt Survival Time (thousands of miles)')
+    >>> ax.set_ylabel('Empirical SF')
+    >>> plt.show()
+
+    """
+    sample = _iv_CensoredData(sample)
+
+    if sample.num_censored() == 0:
+        res = _ecdf_uncensored(sample._uncensor())
+    elif sample.num_censored() == sample._right.size:
+        res = _ecdf_right_censored(sample)
+    else:
+        # Support additional censoring options in follow-up PRs
+        message = ("Currently, only uncensored and right-censored data is "
+                   "supported.")
+        raise NotImplementedError(message)
+
+    t, cdf, sf, n, d = res
+    return ECDFResult(t, cdf, sf, n, d)
+
+
+def _ecdf_uncensored(sample):
+    sample = np.sort(sample)
+    x, counts = np.unique(sample, return_counts=True)
+
+    # [1].81 "the fraction of [observations] that are less than or equal to x
+    events = np.cumsum(counts)
+    n = sample.size
+    cdf = events / n
+
+    # [1].89 "the relative frequency of the sample that exceeds x in value"
+    sf = 1 - cdf
+
+    at_risk = np.concatenate(([n], n - events[:-1]))
+    return x, cdf, sf, at_risk, counts
+
+
+def _ecdf_right_censored(sample):
+    # It is conventional to discuss right-censored data in terms of
+    # "survival time", "death", and "loss" (e.g. [2]). We'll use that
+    # terminology here.
+    # This implementation was influenced by the references cited and also
+    # https://www.youtube.com/watch?v=lxoWsVco_iM
+    # https://en.wikipedia.org/wiki/Kaplan%E2%80%93Meier_estimator
+    # In retrospect it is probably most easily compared against [3].
+    # Ultimately, the data needs to be sorted, so this implementation is
+    # written to avoid a separate call to `unique` after sorting. In hope of
+    # better performance on large datasets, it also computes survival
+    # probabilities at unique times only rather than at each observation.
+    tod = sample._uncensored  # time of "death"
+    tol = sample._right  # time of "loss"
+    times = np.concatenate((tod, tol))
+    died = np.asarray([1]*tod.size + [0]*tol.size)
+
+    # sort by times
+    i = np.argsort(times)
+    times = times[i]
+    died = died[i]
+    at_risk = np.arange(times.size, 0, -1)
+
+    # logical indices of unique times
+    j = np.diff(times, prepend=-np.inf, append=np.inf) > 0
+    j_l = j[:-1]  # first instances of unique times
+    j_r = j[1:]  # last instances of unique times
+
+    # get number at risk and deaths at each unique time
+    t = times[j_l]  # unique times
+    n = at_risk[j_l]  # number at risk at each unique time
+    cd = np.cumsum(died)[j_r]  # cumulative deaths up to/including unique times
+    d = np.diff(cd, prepend=0)  # deaths at each unique time
+
+    # compute survival function
+    sf = np.cumprod((n - d) / n)
+    cdf = 1 - sf
+    return t, cdf, sf, n, d
+
+
+@dataclass
+class LogRankResult:
+    """Result object returned by `scipy.stats.logrank`.
+
+    Attributes
+    ----------
+    statistic : float ndarray
+        The computed statistic (defined below). Its magnitude is the
+        square root of the magnitude returned by most other logrank test
+        implementations.
+    pvalue : float ndarray
+        The computed p-value of the test.
+    """
+    statistic: np.ndarray
+    pvalue: np.ndarray
+
+
+@xp_capabilities(np_only=True)
+def logrank(
+    x: "npt.ArrayLike | CensoredData",
+    y: "npt.ArrayLike | CensoredData",
+    alternative: Literal['two-sided', 'less', 'greater'] = "two-sided"
+) -> LogRankResult:
+    r"""Compare the survival distributions of two samples via the logrank test.
+
+    Parameters
+    ----------
+    x, y : array_like or CensoredData
+        Samples to compare based on their empirical survival functions.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis.
+
+        The null hypothesis is that the survival distributions of the two
+        groups, say *X* and *Y*, are identical.
+
+        The following alternative hypotheses [4]_ are available (default is
+        'two-sided'):
+
+        * 'two-sided': the survival distributions of the two groups are not
+          identical.
+        * 'less': survival of group *X* is favored: the group *X* failure rate
+          function is less than the group *Y* failure rate function at some
+          times.
+        * 'greater': survival of group *Y* is favored: the group *X* failure
+          rate function is greater than the group *Y* failure rate function at
+          some times.
+
+    Returns
+    -------
+    res : `~scipy.stats._result_classes.LogRankResult`
+        An object containing attributes:
+
+        statistic : float ndarray
+            The computed statistic (defined below). Its magnitude is the
+            square root of the magnitude returned by most other logrank test
+            implementations.
+        pvalue : float ndarray
+            The computed p-value of the test.
+
+    See Also
+    --------
+    scipy.stats.ecdf
+
+    Notes
+    -----
+    The logrank test [1]_ compares the observed number of events to
+    the expected number of events under the null hypothesis that the two
+    samples were drawn from the same distribution. The statistic is
+
+    .. math::
+
+        Z_i = \frac{\sum_{j=1}^J(O_{i,j}-E_{i,j})}{\sqrt{\sum_{j=1}^J V_{i,j}}}
+        \rightarrow \mathcal{N}(0,1)
+
+    where
+
+    .. math::
+
+        E_{i,j} = O_j \frac{N_{i,j}}{N_j},
+        \qquad
+        V_{i,j} = E_{i,j} \left(\frac{N_j-O_j}{N_j}\right)
+        \left(\frac{N_j-N_{i,j}}{N_j-1}\right),
+
+    :math:`i` denotes the group (i.e. it may assume values :math:`x` or
+    :math:`y`, or it may be omitted to refer to the combined sample)
+    :math:`j` denotes the time (at which an event occurred),
+    :math:`N` is the number of subjects at risk just before an event occurred,
+    and :math:`O` is the observed number of events at that time.
+
+    The ``statistic`` :math:`Z_x` returned by `logrank` is the (signed) square
+    root of the statistic returned by many other implementations. Under the
+    null hypothesis, :math:`Z_x**2` is asymptotically distributed according to
+    the chi-squared distribution with one degree of freedom. Consequently,
+    :math:`Z_x` is asymptotically distributed according to the standard normal
+    distribution. The advantage of using :math:`Z_x` is that the sign
+    information (i.e. whether the observed number of events tends to be less
+    than or greater than the number expected under the null hypothesis) is
+    preserved, allowing `scipy.stats.logrank` to offer one-sided alternative
+    hypotheses.
+
+    References
+    ----------
+    .. [1] Mantel N. "Evaluation of survival data and two new rank order
+           statistics arising in its consideration."
+           Cancer Chemotherapy Reports, 50(3):163-170, PMID: 5910392, 1966
+    .. [2] Bland, Altman, "The logrank test", BMJ, 328:1073,
+           :doi:`10.1136/bmj.328.7447.1073`, 2004
+    .. [3] "Logrank test", Wikipedia,
+           https://en.wikipedia.org/wiki/Logrank_test
+    .. [4] Brown, Mark. "On the choice of variance for the log rank test."
+           Biometrika 71.1 (1984): 65-74.
+    .. [5] Klein, John P., and Melvin L. Moeschberger. Survival analysis:
+           techniques for censored and truncated data. Vol. 1230. New York:
+           Springer, 2003.
+
+    Examples
+    --------
+    Reference [2]_ compared the survival times of patients with two different
+    types of recurrent malignant gliomas. The samples below record the time
+    (number of weeks) for which each patient participated in the study. The
+    `scipy.stats.CensoredData` class is used because the data is
+    right-censored: the uncensored observations correspond with observed deaths
+    whereas the censored observations correspond with the patient leaving the
+    study for another reason.
+
+    >>> from scipy import stats
+    >>> x = stats.CensoredData(
+    ...     uncensored=[6, 13, 21, 30, 37, 38, 49, 50,
+    ...                 63, 79, 86, 98, 202, 219],
+    ...     right=[31, 47, 80, 82, 82, 149]
+    ... )
+    >>> y = stats.CensoredData(
+    ...     uncensored=[10, 10, 12, 13, 14, 15, 16, 17, 18, 20, 24, 24,
+    ...                 25, 28,30, 33, 35, 37, 40, 40, 46, 48, 76, 81,
+    ...                 82, 91, 112, 181],
+    ...     right=[34, 40, 70]
+    ... )
+
+    We can calculate and visualize the empirical survival functions
+    of both groups as follows.
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> ax = plt.subplot()
+    >>> ecdf_x = stats.ecdf(x)
+    >>> ecdf_x.sf.plot(ax, label='Astrocytoma')
+    >>> ecdf_y = stats.ecdf(y)
+    >>> ecdf_y.sf.plot(ax, label='Glioblastoma')
+    >>> ax.set_xlabel('Time to death (weeks)')
+    >>> ax.set_ylabel('Empirical SF')
+    >>> plt.legend()
+    >>> plt.show()
+
+    Visual inspection of the empirical survival functions suggests that the
+    survival times tend to be different between the two groups. To formally
+    assess whether the difference is significant at the 1% level, we use the
+    logrank test.
+
+    >>> res = stats.logrank(x=x, y=y)
+    >>> res.statistic
+    -2.73799
+    >>> res.pvalue
+    0.00618
+
+    The p-value is less than 1%, so we can consider the data to be evidence
+    against the null hypothesis in favor of the alternative that there is a
+    difference between the two survival functions.
+
+    """
+    # Input validation. `alternative` IV handled in `_get_pvalue` below.
+    x = _iv_CensoredData(sample=x, param_name='x')
+    y = _iv_CensoredData(sample=y, param_name='y')
+
+    # Combined sample. (Under H0, the two groups are identical.)
+    xy = CensoredData(
+        uncensored=np.concatenate((x._uncensored, y._uncensored)),
+        right=np.concatenate((x._right, y._right))
+    )
+
+    # Extract data from the combined sample
+    res = ecdf(xy)
+    idx = res.sf._d.astype(bool)  # indices of observed events
+    times_xy = res.sf.quantiles[idx]  # unique times of observed events
+    at_risk_xy = res.sf._n[idx]  # combined number of subjects at risk
+    deaths_xy = res.sf._d[idx]  # combined number of events
+
+    # Get the number at risk within each sample.
+    # First compute the number at risk in group X at each of the `times_xy`.
+    # Could use `interpolate_1d`, but this is more compact.
+    res_x = ecdf(x)
+    i = np.searchsorted(res_x.sf.quantiles, times_xy)
+    at_risk_x = np.append(res_x.sf._n, 0)[i]  # 0 at risk after last time
+    # Subtract from the combined number at risk to get number at risk in Y
+    at_risk_y = at_risk_xy - at_risk_x
+
+    # Compute the variance.
+    num = at_risk_x * at_risk_y * deaths_xy * (at_risk_xy - deaths_xy)
+    den = at_risk_xy**2 * (at_risk_xy - 1)
+    # Note: when `at_risk_xy == 1`, we would have `at_risk_xy - 1 == 0` in the
+    # numerator and denominator. Simplifying the fraction symbolically, we
+    # would always find the overall quotient to be zero, so don't compute it.
+    i = at_risk_xy > 1
+    sum_var = np.sum(num[i]/den[i])
+
+    # Get the observed and expected number of deaths in group X
+    n_died_x = x._uncensored.size
+    sum_exp_deaths_x = np.sum(at_risk_x * (deaths_xy/at_risk_xy))
+
+    # Compute the statistic. This is the square root of that in references.
+    statistic = (n_died_x - sum_exp_deaths_x)/np.sqrt(sum_var)
+
+    # Equivalent to chi2(df=1).sf(statistic**2) when alternative='two-sided'
+    norm = stats._stats_py._SimpleNormal()
+    pvalue = stats._stats_py._get_pvalue(statistic, norm, alternative, xp=np)
+
+    return LogRankResult(statistic=statistic[()], pvalue=pvalue[()])
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_tukeylambda_stats.py b/venv/lib/python3.12/site-packages/scipy/stats/_tukeylambda_stats.py
new file mode 100644
index 0000000000000000000000000000000000000000..d3cda54fa2801f7659419b3c9c68d15ed80fc13e
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_tukeylambda_stats.py
@@ -0,0 +1,199 @@
+import numpy as np
+from numpy import poly1d
+from scipy.special import beta
+
+
+# The following code was used to generate the Pade coefficients for the
+# Tukey Lambda variance function.  Version 0.17 of mpmath was used.
+#---------------------------------------------------------------------------
+# import mpmath as mp
+#
+# mp.mp.dps = 60
+#
+# one   = mp.mpf(1)
+# two   = mp.mpf(2)
+#
+# def mpvar(lam):
+#     if lam == 0:
+#         v = mp.pi**2 / three
+#     else:
+#         v = (two / lam**2) * (one / (one + two*lam) -
+#                               mp.beta(lam + one, lam + one))
+#     return v
+#
+# t = mp.taylor(mpvar, 0, 8)
+# p, q = mp.pade(t, 4, 4)
+# print("p =", [mp.fp.mpf(c) for c in p])
+# print("q =", [mp.fp.mpf(c) for c in q])
+#---------------------------------------------------------------------------
+
+# Pade coefficients for the Tukey Lambda variance function.
+_tukeylambda_var_pc = [3.289868133696453, 0.7306125098871127,
+                       -0.5370742306855439, 0.17292046290190008,
+                       -0.02371146284628187]
+_tukeylambda_var_qc = [1.0, 3.683605511659861, 4.184152498888124,
+                       1.7660926747377275, 0.2643989311168465]
+
+# numpy.poly1d instances for the numerator and denominator of the
+# Pade approximation to the Tukey Lambda variance.
+_tukeylambda_var_p = poly1d(_tukeylambda_var_pc[::-1])
+_tukeylambda_var_q = poly1d(_tukeylambda_var_qc[::-1])
+
+
+def tukeylambda_variance(lam):
+    """Variance of the Tukey Lambda distribution.
+
+    Parameters
+    ----------
+    lam : array_like
+        The lambda values at which to compute the variance.
+
+    Returns
+    -------
+    v : ndarray
+        The variance.  For lam < -0.5, the variance is not defined, so
+        np.nan is returned.  For lam = 0.5, np.inf is returned.
+
+    Notes
+    -----
+    In an interval around lambda=0, this function uses the [4,4] Pade
+    approximation to compute the variance.  Otherwise it uses the standard
+    formula (https://en.wikipedia.org/wiki/Tukey_lambda_distribution).  The
+    Pade approximation is used because the standard formula has a removable
+    discontinuity at lambda = 0, and does not produce accurate numerical
+    results near lambda = 0.
+    """
+    lam = np.asarray(lam)
+    shp = lam.shape
+    lam = np.atleast_1d(lam).astype(np.float64)
+
+    # For absolute values of lam less than threshold, use the Pade
+    # approximation.
+    threshold = 0.075
+
+    # Play games with masks to implement the conditional evaluation of
+    # the distribution.
+    # lambda < -0.5:  var = nan
+    low_mask = lam < -0.5
+    # lambda == -0.5: var = inf
+    neghalf_mask = lam == -0.5
+    # abs(lambda) < threshold:  use Pade approximation
+    small_mask = np.abs(lam) < threshold
+    # else the "regular" case:  use the explicit formula.
+    reg_mask = ~(low_mask | neghalf_mask | small_mask)
+
+    # Get the 'lam' values for the cases where they are needed.
+    small = lam[small_mask]
+    reg = lam[reg_mask]
+
+    # Compute the function for each case.
+    v = np.empty_like(lam)
+    v[low_mask] = np.nan
+    v[neghalf_mask] = np.inf
+    if small.size > 0:
+        # Use the Pade approximation near lambda = 0.
+        v[small_mask] = _tukeylambda_var_p(small) / _tukeylambda_var_q(small)
+    if reg.size > 0:
+        v[reg_mask] = (2.0 / reg**2) * (1.0 / (1.0 + 2 * reg) -
+                                        beta(reg + 1, reg + 1))
+    v = v.reshape(shp)
+    return v
+
+
+# The following code was used to generate the Pade coefficients for the
+# Tukey Lambda kurtosis function.  Version 0.17 of mpmath was used.
+#---------------------------------------------------------------------------
+# import mpmath as mp
+#
+# mp.mp.dps = 60
+#
+# one   = mp.mpf(1)
+# two   = mp.mpf(2)
+# three = mp.mpf(3)
+# four  = mp.mpf(4)
+#
+# def mpkurt(lam):
+#     if lam == 0:
+#         k = mp.mpf(6)/5
+#     else:
+#         numer = (one/(four*lam+one) - four*mp.beta(three*lam+one, lam+one) +
+#                  three*mp.beta(two*lam+one, two*lam+one))
+#         denom = two*(one/(two*lam+one) - mp.beta(lam+one,lam+one))**2
+#         k = numer / denom - three
+#     return k
+#
+# # There is a bug in mpmath 0.17: when we use the 'method' keyword of the
+# # taylor function and we request a degree 9 Taylor polynomial, we actually
+# # get degree 8.
+# t = mp.taylor(mpkurt, 0, 9, method='quad', radius=0.01)
+# t = [mp.chop(c, tol=1e-15) for c in t]
+# p, q = mp.pade(t, 4, 4)
+# print("p =", [mp.fp.mpf(c) for c in p])
+# print("q =", [mp.fp.mpf(c) for c in q])
+#---------------------------------------------------------------------------
+
+# Pade coefficients for the Tukey Lambda kurtosis function.
+_tukeylambda_kurt_pc = [1.2, -5.853465139719495, -22.653447381131077,
+                        0.20601184383406815, 4.59796302262789]
+_tukeylambda_kurt_qc = [1.0, 7.171149192233599, 12.96663094361842,
+                        0.43075235247853005, -2.789746758009912]
+
+# numpy.poly1d instances for the numerator and denominator of the
+# Pade approximation to the Tukey Lambda kurtosis.
+_tukeylambda_kurt_p = poly1d(_tukeylambda_kurt_pc[::-1])
+_tukeylambda_kurt_q = poly1d(_tukeylambda_kurt_qc[::-1])
+
+
+def tukeylambda_kurtosis(lam):
+    """Kurtosis of the Tukey Lambda distribution.
+
+    Parameters
+    ----------
+    lam : array_like
+        The lambda values at which to compute the variance.
+
+    Returns
+    -------
+    v : ndarray
+        The variance.  For lam < -0.25, the variance is not defined, so
+        np.nan is returned.  For lam = 0.25, np.inf is returned.
+
+    """
+    lam = np.asarray(lam)
+    shp = lam.shape
+    lam = np.atleast_1d(lam).astype(np.float64)
+
+    # For absolute values of lam less than threshold, use the Pade
+    # approximation.
+    threshold = 0.055
+
+    # Use masks to implement the conditional evaluation of the kurtosis.
+    # lambda < -0.25:  kurtosis = nan
+    low_mask = lam < -0.25
+    # lambda == -0.25: kurtosis = inf
+    negqrtr_mask = lam == -0.25
+    # lambda near 0:  use Pade approximation
+    small_mask = np.abs(lam) < threshold
+    # else the "regular" case:  use the explicit formula.
+    reg_mask = ~(low_mask | negqrtr_mask | small_mask)
+
+    # Get the 'lam' values for the cases where they are needed.
+    small = lam[small_mask]
+    reg = lam[reg_mask]
+
+    # Compute the function for each case.
+    k = np.empty_like(lam)
+    k[low_mask] = np.nan
+    k[negqrtr_mask] = np.inf
+    if small.size > 0:
+        k[small_mask] = _tukeylambda_kurt_p(small) / _tukeylambda_kurt_q(small)
+    if reg.size > 0:
+        numer = (1.0 / (4 * reg + 1) - 4 * beta(3 * reg + 1, reg + 1) +
+                 3 * beta(2 * reg + 1, 2 * reg + 1))
+        denom = 2 * (1.0/(2 * reg + 1) - beta(reg + 1, reg + 1))**2
+        k[reg_mask] = numer / denom - 3
+
+    # The return value will be a numpy array; resetting the shape ensures that
+    # if `lam` was a scalar, the return value is a 0-d array.
+    k = k.reshape(shp)
+    return k
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_unuran/__init__.py b/venv/lib/python3.12/site-packages/scipy/stats/_unuran/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_unuran/__pycache__/__init__.cpython-312.pyc b/venv/lib/python3.12/site-packages/scipy/stats/_unuran/__pycache__/__init__.cpython-312.pyc
new file mode 100644
index 0000000000000000000000000000000000000000..98207cc972e668589fb5848bc3052ccd27c4138f
Binary files /dev/null and b/venv/lib/python3.12/site-packages/scipy/stats/_unuran/__pycache__/__init__.cpython-312.pyc differ
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_unuran/unuran_wrapper.cpython-312-x86_64-linux-gnu.so b/venv/lib/python3.12/site-packages/scipy/stats/_unuran/unuran_wrapper.cpython-312-x86_64-linux-gnu.so
new file mode 100644
index 0000000000000000000000000000000000000000..9d27c1c06ffe4f4f1662f9128b5518478755c235
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_unuran/unuran_wrapper.cpython-312-x86_64-linux-gnu.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f6fc277c78c018ca5d7ef03d0ae46357e6af4aebc3137a3d0c005f9fe8c09f1b
+size 1335008
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_unuran/unuran_wrapper.pyi b/venv/lib/python3.12/site-packages/scipy/stats/_unuran/unuran_wrapper.pyi
new file mode 100644
index 0000000000000000000000000000000000000000..1ef1bd443b7dbf6a1d673fdc976c04536606c8d3
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_unuran/unuran_wrapper.pyi
@@ -0,0 +1,179 @@
+import numpy as np
+from typing import (overload, NamedTuple, Protocol)
+from collections.abc import Callable
+import numpy.typing as npt
+from scipy._lib._util import SeedType
+import scipy.stats as stats
+
+
+ArrayLike0D = bool | int | float | complex | str | bytes | np.generic
+
+
+__all__: list[str]
+
+
+class UNURANError(RuntimeError):
+    ...
+
+
+class Method:
+    @overload
+    def rvs(self, size: None = ...) -> float | int: ...  # type: ignore[overload-overlap]
+    @overload
+    def rvs(self, size: int | tuple[int, ...] = ...) -> np.ndarray: ...
+    def set_random_state(self, random_state: SeedType) -> None: ...
+
+
+class TDRDist(Protocol):
+    @property
+    def pdf(self) -> Callable[..., float]: ...
+    @property
+    def dpdf(self) -> Callable[..., float]: ...
+    @property
+    def support(self) -> tuple[float, float]: ...
+
+
+class TransformedDensityRejection(Method):
+    def __init__(self,
+                 dist: TDRDist,
+                 *,
+                 mode: None | float = ...,
+                 center: None | float = ...,
+                 domain: None | tuple[float, float] = ...,
+                 c: float = ...,
+                 construction_points: int | npt.ArrayLike = ...,
+                 use_dars: bool = ...,
+                 max_squeeze_hat_ratio: float = ...,
+                 random_state: SeedType = ...) -> None: ...
+    @property
+    def squeeze_hat_ratio(self) -> float: ...
+    @property
+    def squeeze_area(self) -> float: ...
+    @overload
+    def ppf_hat(self, u: ArrayLike0D) -> float: ...  # type: ignore[overload-overlap]
+    @overload
+    def ppf_hat(self, u: npt.ArrayLike) -> np.ndarray: ...
+
+
+class SROUDist(Protocol):
+    @property
+    def pdf(self) -> Callable[..., float]: ...
+    @property
+    def support(self) -> tuple[float, float]: ...
+
+
+class SimpleRatioUniforms(Method):
+    def __init__(self,
+                 dist: SROUDist,
+                 *,
+                 mode: None | float = ...,
+                 pdf_area: float = ...,
+                 domain: None | tuple[float, float] = ...,
+                 cdf_at_mode: float = ...,
+                 random_state: SeedType = ...) -> None: ...
+
+
+class UError(NamedTuple):
+    max_error: float
+    mean_absolute_error: float
+
+class PINVDist(Protocol):
+    @property
+    def pdf(self) -> Callable[..., float]: ...
+    @property
+    def cdf(self) -> Callable[..., float]: ...
+    @property
+    def logpdf(self) -> Callable[..., float]: ...
+
+
+class NumericalInversePolynomial(Method):
+    def __init__(self,
+                 dist: PINVDist,
+                 *,
+                 mode: None | float = ...,
+                 center: None | float = ...,
+                 domain: None | tuple[float, float] = ...,
+                 order: int = ...,
+                 u_resolution: float = ...,
+                 random_state: SeedType = ...) -> None: ...
+    @property
+    def intervals(self) -> int: ...
+    @overload
+    def ppf(self, u: ArrayLike0D) -> float: ...  # type: ignore[overload-overlap]
+    @overload
+    def ppf(self, u: npt.ArrayLike) -> np.ndarray: ...
+    @overload
+    def cdf(self, x: ArrayLike0D) -> float: ...  # type: ignore[overload-overlap]
+    @overload
+    def cdf(self, x: npt.ArrayLike) -> np.ndarray: ...
+    def u_error(self, sample_size: int = ...) -> UError: ...
+    def qrvs(self,
+             size: None | int | tuple[int, ...] = ...,
+             d: None | int = ...,
+             qmc_engine: None | stats.qmc.QMCEngine = ...) -> npt.ArrayLike: ...
+
+
+class HINVDist(Protocol):
+    @property
+    def pdf(self) -> Callable[..., float]: ...
+    @property
+    def cdf(self) -> Callable[..., float]: ...
+    @property
+    def support(self) -> tuple[float, float]: ...
+
+
+class NumericalInverseHermite(Method):
+    def __init__(self,
+                 dist: HINVDist,
+                 *,
+                 domain: None | tuple[float, float] = ...,
+                 order: int= ...,
+                 u_resolution: float = ...,
+                 construction_points: None | npt.ArrayLike = ...,
+                 max_intervals: int = ...,
+                 random_state: SeedType = ...) -> None: ...
+    @property
+    def intervals(self) -> int: ...
+    @overload
+    def ppf(self, u: ArrayLike0D) -> float: ...  # type: ignore[overload-overlap]
+    @overload
+    def ppf(self, u: npt.ArrayLike) -> np.ndarray: ...
+    def qrvs(self,
+             size: None | int | tuple[int, ...] = ...,
+             d: None | int = ...,
+             qmc_engine: None | stats.qmc.QMCEngine = ...) -> npt.ArrayLike: ...
+    def u_error(self, sample_size: int = ...) -> UError: ...
+
+
+class DAUDist(Protocol):
+    @property
+    def pmf(self) -> Callable[..., float]: ...
+    @property
+    def support(self) -> tuple[float, float]: ...
+
+class DiscreteAliasUrn(Method):
+    def __init__(self,
+                 dist: npt.ArrayLike | DAUDist,
+                 *,
+                 domain: None | tuple[float, float] = ...,
+                 urn_factor: float = ...,
+                 random_state: SeedType = ...) -> None: ...
+
+
+class DGTDist(Protocol):
+    @property
+    def pmf(self) -> Callable[..., float]: ...
+    @property
+    def support(self) -> tuple[float, float]: ...
+
+class DiscreteGuideTable(Method):
+    def __init__(self,
+                 dist: npt.ArrayLike | DGTDist,
+                 *,
+                 domain: None | tuple[float, float] = ...,
+                 guide_factor: float = ...,
+                 random_state: SeedType = ...) -> None: ...
+    @overload
+    def ppf(self, u: ArrayLike0D) -> float: ...  # type: ignore[overload-overlap]
+    @overload
+    def ppf(self, u: npt.ArrayLike) -> np.ndarray: ...
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_variation.py b/venv/lib/python3.12/site-packages/scipy/stats/_variation.py
new file mode 100644
index 0000000000000000000000000000000000000000..c991a70158a226a1b0fb6a1a0fce6f1ec4a67400
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_variation.py
@@ -0,0 +1,133 @@
+import warnings
+import numpy as np
+
+from scipy._lib._array_api import (
+    array_namespace,
+    xp_capabilities,
+    xp_device,
+    _count_nonmasked,
+    xp_promote,
+)
+import scipy._external.array_api_extra as xpx
+
+from ._axis_nan_policy import _axis_nan_policy_factory
+
+
+@xp_capabilities(marray=True)
+@_axis_nan_policy_factory(
+    lambda x: x, n_outputs=1, result_to_tuple=lambda x, _: (x,)
+)
+def variation(a, axis=0, nan_policy='propagate', ddof=0, *, keepdims=False):
+    """
+    Compute the coefficient of variation.
+
+    The coefficient of variation is the standard deviation divided by the
+    mean.  This function is equivalent to::
+
+        np.std(x, axis=axis, ddof=ddof) / np.mean(x)
+
+    The default for ``ddof`` is 0, but many definitions of the coefficient
+    of variation use the square root of the unbiased sample variance
+    for the sample standard deviation, which corresponds to ``ddof=1``.
+
+    The function does not take the absolute value of the mean of the data,
+    so the return value is negative if the mean is negative.
+
+    Parameters
+    ----------
+    a : array_like
+        Input array.
+    axis : int or None, optional
+        Axis along which to calculate the coefficient of variation.
+        Default is 0. If None, compute over the whole array `a`.
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains ``nan``.
+        The following options are available:
+
+        * 'propagate': return ``nan``
+        * 'raise': raise an exception
+        * 'omit': perform the calculation with ``nan`` values omitted
+
+        The default is 'propagate'.
+    ddof : int, optional
+        Gives the "Delta Degrees Of Freedom" used when computing the
+        standard deviation.  The divisor used in the calculation of the
+        standard deviation is ``N - ddof``, where ``N`` is the number of
+        elements.  `ddof` must be less than ``N``; if it isn't, the result
+        will be ``nan`` or ``inf``, depending on ``N`` and the values in
+        the array.  By default `ddof` is zero for backwards compatibility,
+        but it is recommended to use ``ddof=1`` to ensure that the sample
+        standard deviation is computed as the square root of the unbiased
+        sample variance.
+
+    Returns
+    -------
+    variation : ndarray
+        The calculated variation along the requested axis.
+
+    Notes
+    -----
+    There are several edge cases that are handled without generating a
+    warning:
+
+    * If both the mean and the standard deviation are zero, ``nan``
+      is returned.
+    * If the mean is zero and the standard deviation is nonzero, ``inf``
+      is returned.
+    * If the input has length zero (either because the array has zero
+      length, or all the input values are ``nan`` and ``nan_policy`` is
+      ``'omit'``), ``nan`` is returned.
+    * If the input contains ``inf``, ``nan`` is returned.
+
+    References
+    ----------
+    .. [1] Zwillinger, D. and Kokoska, S. (2000). CRC Standard
+       Probability and Statistics Tables and Formulae. Chapman & Hall: New
+       York. 2000.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import variation
+    >>> variation([1, 2, 3, 4, 5], ddof=1)
+    0.5270462766947299
+
+    Compute the variation along a given dimension of an array that contains
+    a few ``nan`` values:
+
+    >>> x = np.array([[  10.0, np.nan, 11.0, 19.0, 23.0, 29.0, 98.0],
+    ...               [  29.0,   30.0, 32.0, 33.0, 35.0, 56.0, 57.0],
+    ...               [np.nan, np.nan, 12.0, 13.0, 16.0, 16.0, 17.0]])
+    >>> variation(x, axis=1, ddof=1, nan_policy='omit')
+    array([1.05109361, 0.31428986, 0.146483  ])
+
+    """
+    xp = array_namespace(a)
+    a = xp_promote(a, force_floating=True, xp=xp)
+
+    # `nan_policy` and `keepdims` are handled by `_axis_nan_policy`
+    if axis is None:
+        a = xp.reshape(a, (-1,))
+        axis = 0
+
+    n = xp.asarray(_count_nonmasked(a, axis=axis), dtype=a.dtype, device=xp_device(a))
+
+    with (np.errstate(divide='ignore', invalid='ignore'), warnings.catch_warnings()):
+        warnings.simplefilter("ignore")
+        mean_a = xp.mean(a, axis=axis)
+        std_a = xp.std(a, axis=axis)
+        correction = (n / (n - ddof))**0.5  # we may need uncorrected std below
+        result = std_a * correction / mean_a
+
+    def special_case(std_a, mean_a):
+        # xref data-apis/array-api-extra#196
+        mxp = array_namespace(std_a, mean_a)
+        # `_xp_inf` is a workaround for torch.copysign not accepting a scalar yet,
+        # xref data-apis/array-api-compat#271
+        _xp_inf = mxp.asarray(mxp.inf, dtype=mean_a.dtype, device=xp_device(mean_a))
+        return mxp.where(std_a > 0, mxp.copysign(_xp_inf, mean_a), mxp.nan)
+
+    result = xpx.apply_where((ddof == n), (std_a, mean_a),
+                             special_case, fill_value=result)
+
+    return result[()] if result.ndim == 0 else result
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_warnings_errors.py b/venv/lib/python3.12/site-packages/scipy/stats/_warnings_errors.py
new file mode 100644
index 0000000000000000000000000000000000000000..57bc8fcabd7a0f382960046cd253bbc74d4b76e4
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_warnings_errors.py
@@ -0,0 +1,62 @@
+# Warnings
+
+
+class DegenerateDataWarning(RuntimeWarning):
+    """Warns when data is degenerate and results may not be reliable.
+
+    Parameters
+    ----------
+    msg : str, optional
+        Warning message.
+    """
+    def __init__(self, msg=None):
+        if msg is None:
+            msg = ("Degenerate data encountered; results may not be reliable.")
+        self.args = (msg,)
+
+
+class ConstantInputWarning(DegenerateDataWarning):
+    """Warns when all values in data are exactly equal.
+
+    Parameters
+    ----------
+    msg : str, optional
+        Warning message.
+    """
+    def __init__(self, msg=None):
+        if msg is None:
+            msg = ("All values in data are exactly equal; "
+                   "results may not be reliable.")
+        self.args = (msg,)
+
+
+class NearConstantInputWarning(DegenerateDataWarning):
+    """Warns when all values in data are nearly equal.
+
+    Parameters
+    ----------
+    msg : str, optional
+        Warning message.
+    """
+    def __init__(self, msg=None):
+        if msg is None:
+            msg = ("All values in data are nearly equal; "
+                   "results may not be reliable.")
+        self.args = (msg,)
+
+
+# Errors
+
+
+class FitError(RuntimeError):
+    """Represents an error condition when fitting a distribution to data.
+
+    Parameters
+    ----------
+    msg : str, optional
+        Error message.
+    """
+    def __init__(self, msg=None):
+        if msg is None:
+            msg = ("An error occurred when fitting a distribution to data.")
+        self.args = (msg,)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/_wilcoxon.py b/venv/lib/python3.12/site-packages/scipy/stats/_wilcoxon.py
new file mode 100644
index 0000000000000000000000000000000000000000..a4437ba01a80deb0a09d36b4f3fca54ae5da960e
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/_wilcoxon.py
@@ -0,0 +1,284 @@
+import numpy as np
+
+from scipy import stats
+from ._stats_py import _get_pvalue, _rankdata, _SimpleNormal
+from . import _morestats
+from ._axis_nan_policy import _broadcast_arrays
+from ._hypotests import _get_wilcoxon_distr
+from scipy._lib._util import _get_nan
+from scipy._lib._array_api import (array_namespace, xp_promote, xp_size, is_jax,
+                                   is_marray, _count_nonmasked)
+import scipy._external.array_api_extra as xpx
+
+
+class WilcoxonDistribution:
+
+    def __init__(self, n):
+        n = np.asarray(n).astype(int, copy=False)
+        self.n = n
+        self._dists = {ni: _get_wilcoxon_distr(ni) for ni in np.unique(n)}
+
+    def _cdf1(self, k, n):
+        pmfs = self._dists[n]
+        return pmfs[:k + 1].sum()
+
+    def _cdf(self, k, n):
+        return np.vectorize(self._cdf1, otypes=[float])(k, n)
+
+    def _sf1(self, k, n):
+        pmfs = self._dists[n]
+        return pmfs[k:].sum()
+
+    def _sf(self, k, n):
+        return np.vectorize(self._sf1, otypes=[float])(k, n)
+
+    def mean(self):
+        return self.n * (self.n + 1) / 4
+
+    def _prep(self, k):
+        k = np.asarray(k).astype(int, copy=False)
+        mn = self.mean()
+        out = np.empty(k.shape, dtype=np.float64)
+        return k, mn, out
+
+    def cdf(self, k):
+        k, mn, out = self._prep(k)
+        return xpx.apply_where(
+            k <= mn, (k, self.n),
+            self._cdf,
+            lambda k, n: 1 - self._sf(k+1, n))[()]
+
+    def sf(self, k):
+        k, mn, out = self._prep(k)
+        return xpx.apply_where(
+            k <= mn, (k, self.n),
+            self._sf,
+            lambda k, n: 1 - self._cdf(k-1, n))[()]
+
+
+def _wilcoxon_iv(x, y, zero_method, correction, alternative, method, axis):
+    xp = array_namespace(x, y)
+    x, y = xp_promote(x, y, force_floating=True, xp=xp)
+
+    axis = np.asarray(axis)[()]  # OK to use NumPy for input validation
+    message = "`axis` must be an integer."
+    if not np.issubdtype(axis.dtype, np.integer) or axis.ndim != 0:
+        raise ValueError(message)
+    axis = int(axis)
+
+    message = '`axis` must be compatible with the shape(s) of `x` (and `y`)'
+    AxisError = getattr(np, 'AxisError', None) or np.exceptions.AxisError
+    try:
+        if y is None:
+            d = x
+        else:
+            x, y = _broadcast_arrays((x, y), axis=axis, xp=xp)
+            d = x - y
+        d = xp.moveaxis(d, axis, -1)
+    except AxisError as e:
+        raise AxisError(message) from e
+
+    message = "`x` and `y` must have the same length along `axis`."
+    if y is not None and x.shape[axis] != y.shape[axis]:
+        raise ValueError(message)
+
+    message = "`x` (and `y`, if provided) must be an array of real numbers."
+    if not xp.isdtype(d.dtype, "real floating"):
+        raise ValueError(message)
+
+    zero_method = str(zero_method).lower()
+    zero_methods = {"wilcox", "pratt", "zsplit"}
+    message = f"`zero_method` must be one of {zero_methods}."
+    if zero_method not in zero_methods:
+        raise ValueError(message)
+
+    corrections = {True, False}
+    message = f"`correction` must be one of {corrections}."
+    if correction not in corrections:
+        raise ValueError(message)
+
+    alternative = str(alternative).lower()
+    alternatives = {"two-sided", "less", "greater"}
+    message = f"`alternative` must be one of {alternatives}."
+    if alternative not in alternatives:
+        raise ValueError(message)
+
+    if not isinstance(method, stats.PermutationMethod):
+        methods = {"auto", "asymptotic", "exact"}
+        message = (f"`method` must be one of {methods} or "
+                   "an instance of `stats.PermutationMethod`.")
+        if method not in methods:
+            raise ValueError(message)
+    output_z = True if method == 'asymptotic' else False
+
+    if is_jax(xp) and str(method) in {"auto", "exact"}:
+        message = ("When using `wilcoxon` with `jax.numpy` arrays, `method` must be "
+                   "either 'asymptotic' or an instance of `stats.PermutationMethod`.")
+        raise ValueError(message)
+
+    if is_marray(xp) and (method != "asymptotic" or zero_method != 'zsplit'):
+        message = ("Only `method='asymptotic'`/`zero_method='zsplit'` is compatible "
+                   "with MArrays.")
+        raise ValueError(message)
+
+    # For small samples, we decide later whether to perform an exact test or a
+    # permutation test. The reason is that the presence of ties is not
+    # known at the input validation stage.
+    n_zero = xp.count_nonzero(d == 0, axis=None)
+    if method == "auto" and d.shape[-1] > 50:
+        method = "asymptotic"
+
+    return d, zero_method, correction, alternative, method, axis, output_z, n_zero, xp
+
+
+def _wilcoxon_statistic(d, method, zero_method='wilcox', *, xp):
+    dtype = d.dtype
+    i_zeros = (d == 0)
+
+    if zero_method == 'wilcox':
+        # Wilcoxon's method for treating zeros was to remove them from
+        # the calculation. We do this by replacing 0s with NaNs, which
+        # are ignored anyway.
+        # Copy required for array-api-strict. See data-apis/array-api-extra#506.
+        d = xpx.at(d)[i_zeros].set(xp.nan, copy=True)
+
+    i_nan = xp.isnan(d)
+    n_nan = xp.astype(xp.count_nonzero(i_nan, axis=-1), dtype)
+    count = _count_nonmasked(d, axis=-1) - n_nan
+
+    r, _, t = _rankdata(xp.abs(d), 'average', return_ties=True, xp=xp)
+    r, t = xp.astype(r, dtype, copy=False), xp.astype(t, dtype, copy=False)
+
+    r_plus = xp.sum(xp.astype(d > 0, dtype) * r, axis=-1)
+    r_minus = xp.sum(xp.astype(d < 0, dtype) * r, axis=-1)
+
+    has_ties = xp.any(t == 0)
+
+    if zero_method == "zsplit":
+        # The "zero-split" method for treating zeros is to add half their contribution
+        # to r_plus and half to r_minus.
+        # See gh-2263 for the origin of this method.
+        r_zero_2 = xp.sum(xp.astype(i_zeros, dtype) * r, axis=-1) / 2
+        r_plus = xpx.at(r_plus)[...].add(r_zero_2)
+        r_minus = xpx.at(r_minus)[...].add(r_zero_2)
+
+    mn = count * (count + 1.) * 0.25
+    se = count * (count + 1.) * (2. * count + 1.)
+
+    if zero_method == "pratt":
+        # Pratt's method for treating zeros was just to modify the z-statistic.
+
+        # normal approximation needs to be adjusted, see Cureton (1967)
+        n_zero = xp.astype(xp.count_nonzero(i_zeros, axis=-1), dtype)
+        mn = xpx.at(mn)[...].subtract(n_zero * (n_zero + 1.) * 0.25)
+        se = xpx.at(se)[...].subtract(n_zero * (n_zero + 1.) * (2. * n_zero + 1.))
+
+        # zeros are not to be included in tie-correction.
+        # any tie counts corresponding with zeros are in the 0th column
+        # t[xp.any(i_zeros, axis=-1), 0] = 0
+        t_i_zeros = xp.zeros_like(i_zeros)
+        t_i_zeros = xpx.at(t_i_zeros)[..., 0].set(xp.any(i_zeros, axis=-1))
+        t = xpx.at(t)[t_i_zeros].set(0.)
+
+    tie_correct = xp.sum(t**3 - t, axis=-1)
+    se = xp.sqrt((se - tie_correct/2) / 24)
+
+    # se = 0 means that no non-zero values are left in d. we only need z
+    # if method is asymptotic. however, if method="auto", the switch to
+    # asymptotic might only happen after the statistic is calculated, so z
+    # needs to be computed. in all other cases, avoid division by zero warning
+    # (z is not needed anyways)
+    if method in ["asymptotic", "auto"]:
+        z = (r_plus - mn) / se
+    else:
+        z = xp.nan
+
+    return r_plus, r_minus, se, z, count, has_ties
+
+
+def _correction_sign(z, alternative, xp):
+    if alternative == 'greater':
+        return 1
+    elif alternative == 'less':
+        return -1
+    else:
+        return xp.sign(z)
+
+
+def _wilcoxon_nd(x, y=None, zero_method='wilcox', correction=True,
+                 alternative='two-sided', method='auto', axis=0):
+
+    temp = _wilcoxon_iv(x, y, zero_method, correction, alternative, method, axis)
+    d, zero_method, correction, alternative, method, axis, output_z, n_zero, xp = temp
+
+    if xp_size(d) == 0:
+        NaN = _get_nan(d, xp=xp)
+        res = _morestats.WilcoxonResult(statistic=NaN, pvalue=NaN)
+        if method == 'asymptotic':
+            res.zstatistic = NaN
+        return res
+
+    r_plus, r_minus, se, z, count, has_ties = _wilcoxon_statistic(
+        d, method, zero_method, xp=xp
+    )
+
+    # we only know if there are ties after computing the statistic and not
+    # at the input validation stage. if the original method was auto and
+    # the decision was to use an exact test, we override this to
+    # a permutation test now (since method='exact' is not exact in the
+    # presence of ties)
+    if method == "auto":
+        if not (has_ties or n_zero > 0):
+            method = "exact"
+        elif d.shape[-1] <= 13:
+            # the possible outcomes to be simulated by the permutation test
+            # are 2**n, where n is the sample size.
+            # if n <= 13, the p-value is deterministic since 2**13 is less
+            # than 9999, the default number of n_resamples
+            method = stats.PermutationMethod()
+        else:
+            # if there are ties and the sample size is too large to
+            # run a deterministic permutation test, fall back to asymptotic
+            method = "asymptotic"
+
+    if method == 'asymptotic':
+        if correction:
+            sign = _correction_sign(z, alternative, xp=xp)
+            z = xpx.at(z)[...].subtract(sign * 0.5 / se)
+        p = _get_pvalue(z, _SimpleNormal(), alternative, xp=xp)
+    elif method == 'exact':
+        dist = WilcoxonDistribution(count)
+        # The null distribution in `dist` is exact only if there are no ties
+        # or zeros. If there are ties or zeros, the statistic can be non-
+        # integral, but the null distribution is only defined for integral
+        # values of the statistic. Therefore, we're conservative: round
+        # non-integral statistic up before computing CDF and down before
+        # computing SF. This preserves symmetry w.r.t. alternatives and
+        # order of the input arguments. See gh-19872.
+        r_plus_np = np.asarray(r_plus)
+        if alternative == 'less':
+            p = dist.cdf(np.ceil(r_plus_np))
+        elif alternative == 'greater':
+            p = dist.sf(np.floor(r_plus_np))
+        else:
+            p = 2 * np.minimum(dist.sf(np.floor(r_plus_np)),
+                               dist.cdf(np.ceil(r_plus_np)))
+            p = np.clip(p, 0, 1)
+        p = xp.asarray(p, dtype=d.dtype)
+    else:  # `PermutationMethod` instance (already validated)
+        p = stats.permutation_test(
+            # permutation_test always uses `axis=-1` as `_wilcoxon_statistic` assumes
+            (d,), lambda d, axis: _wilcoxon_statistic(d, method, zero_method, xp=xp)[0],
+            permutation_type='samples', **method._asdict(),
+            alternative=alternative, axis=-1).pvalue
+
+    # for backward compatibility...
+    statistic = xp.minimum(r_plus, r_minus) if alternative=='two-sided' else r_plus
+    z = -xp.abs(z) if (alternative == 'two-sided' and method == 'asymptotic') else z
+
+    statistic = statistic[()] if statistic.ndim == 0 else statistic
+    p = p[()] if p.ndim == 0 else p
+    res = _morestats.WilcoxonResult(statistic=statistic, pvalue=p)
+    if output_z:
+        res.zstatistic = z[()] if z.ndim == 0 else z
+    return res
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/biasedurn.py b/venv/lib/python3.12/site-packages/scipy/stats/biasedurn.py
new file mode 100644
index 0000000000000000000000000000000000000000..2b1c9f1cf2b3b39acdcaeda97a90e8c11c589d89
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/biasedurn.py
@@ -0,0 +1,16 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+
+__all__: list[str] = []
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="stats", module="biasedurn",
+                                   private_modules=["_biasedurn"], all=__all__,
+                                   attribute=name)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/contingency.py b/venv/lib/python3.12/site-packages/scipy/stats/contingency.py
new file mode 100644
index 0000000000000000000000000000000000000000..c45112f3f1d7ae346681732d75943c75e6ef3fad
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/contingency.py
@@ -0,0 +1,526 @@
+"""
+Contingency table functions (:mod:`scipy.stats.contingency`)
+============================================================
+
+Functions for creating and analyzing contingency tables.
+
+.. currentmodule:: scipy.stats.contingency
+
+.. autosummary::
+   :toctree: generated/
+
+   chi2_contingency
+   relative_risk
+   odds_ratio
+   crosstab
+   association
+
+   expected_freq
+   margins
+
+"""
+
+
+from functools import reduce
+import math
+import numpy as np
+from ._stats_py import power_divergence, _untabulate
+from ._relative_risk import relative_risk
+from ._crosstab import crosstab
+from ._odds_ratio import odds_ratio
+from scipy._lib._array_api import xp_capabilities
+from scipy._lib._bunch import _make_tuple_bunch
+from scipy import stats
+
+
+__all__ = ['margins', 'expected_freq', 'chi2_contingency', 'crosstab',
+           'association', 'relative_risk', 'odds_ratio']
+
+
+@xp_capabilities(np_only=True)
+def margins(a):
+    """Return a list of the marginal sums of the array `a`.
+
+    Parameters
+    ----------
+    a : ndarray
+        The array for which to compute the marginal sums.
+
+    Returns
+    -------
+    margsums : list of ndarrays
+        A list of length `a.ndim`.  `margsums[k]` is the result
+        of summing `a` over all axes except `k`; it has the same
+        number of dimensions as `a`, but the length of each axis
+        except axis `k` will be 1.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats.contingency import margins
+
+    >>> a = np.arange(12).reshape(2, 6)
+    >>> a
+    array([[ 0,  1,  2,  3,  4,  5],
+           [ 6,  7,  8,  9, 10, 11]])
+    >>> m0, m1 = margins(a)
+    >>> m0
+    array([[15],
+           [51]])
+    >>> m1
+    array([[ 6,  8, 10, 12, 14, 16]])
+
+    >>> b = np.arange(24).reshape(2,3,4)
+    >>> m0, m1, m2 = margins(b)
+    >>> m0
+    array([[[ 66]],
+           [[210]]])
+    >>> m1
+    array([[[ 60],
+            [ 92],
+            [124]]])
+    >>> m2
+    array([[[60, 66, 72, 78]]])
+    """
+    margsums = []
+    ranged = list(range(a.ndim))
+    for k in ranged:
+        marg = np.apply_over_axes(np.sum, a, [j for j in ranged if j != k])
+        margsums.append(marg)
+    return margsums
+
+
+@xp_capabilities(np_only=True)
+def expected_freq(observed):
+    """
+    Compute the expected frequencies from a contingency table.
+
+    Given an n-dimensional contingency table of observed frequencies,
+    compute the expected frequencies for the table based on the marginal
+    sums under the assumption that the groups associated with each
+    dimension are independent.
+
+    Parameters
+    ----------
+    observed : array_like
+        The table of observed frequencies.  (While this function can handle
+        a 1-D array, that case is trivial.  Generally `observed` is at
+        least 2-D.)
+
+    Returns
+    -------
+    expected : ndarray of float64
+        The expected frequencies, based on the marginal sums of the table.
+        Same shape as `observed`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats.contingency import expected_freq
+    >>> observed = np.array([[10, 10, 20],[20, 20, 20]])
+    >>> expected_freq(observed)
+    array([[ 12.,  12.,  16.],
+           [ 18.,  18.,  24.]])
+
+    """
+    # Typically `observed` is an integer array. If `observed` has a large
+    # number of dimensions or holds large values, some of the following
+    # computations may overflow, so we first switch to floating point.
+    observed = np.asarray(observed, dtype=np.float64)
+
+    # Create a list of the marginal sums.
+    margsums = margins(observed)
+
+    # Create the array of expected frequencies.  The shapes of the
+    # marginal sums returned by apply_over_axes() are just what we
+    # need for broadcasting in the following product.
+    d = observed.ndim
+    expected = reduce(np.multiply, margsums) / observed.sum() ** (d - 1)
+    return expected
+
+
+Chi2ContingencyResult = _make_tuple_bunch(
+    'Chi2ContingencyResult',
+    ['statistic', 'pvalue', 'dof', 'expected_freq'], []
+)
+
+
+@xp_capabilities(np_only=True)
+def chi2_contingency(observed, correction=True, lambda_=None, *, method=None):
+    """Chi-square test of independence of variables in a contingency table.
+
+    This function computes the chi-square statistic and p-value for the
+    hypothesis test of independence of the observed frequencies in the
+    contingency table [1]_ `observed`.  The expected frequencies are computed
+    based on the marginal sums under the assumption of independence; see
+    `scipy.stats.contingency.expected_freq`.  The number of degrees of
+    freedom is (expressed using numpy functions and attributes)::
+
+        dof = observed.size - sum(observed.shape) + observed.ndim - 1
+
+
+    Parameters
+    ----------
+    observed : array_like
+        The contingency table. The table contains the observed frequencies
+        (i.e. number of occurrences) in each category.  In the two-dimensional
+        case, the table is often described as an "R x C table".
+    correction : bool, optional
+        If True, *and* the degrees of freedom is 1, apply Yates' correction
+        for continuity.  The effect of the correction is to adjust each
+        observed value by 0.5 towards the corresponding expected value.
+    lambda_ : float or str, optional
+        By default, the statistic computed in this test is Pearson's
+        chi-squared statistic [2]_.  `lambda_` allows a statistic from the
+        Cressie-Read power divergence family [3]_ to be used instead.  See
+        `scipy.stats.power_divergence` for details.
+    method : ResamplingMethod, optional
+        Defines the method used to compute the p-value. Compatible only with
+        ``correction=False``,  default `lambda_`, and two-way tables.
+        If `method` is an instance of `scipy.stats.PermutationMethod` or
+        `scipy.stats.MonteCarloMethod`, the p-value is computed using
+        `scipy.stats.permutation_test`/`scipy.stats.monte_carlo_test` with the
+        provided configuration options and other appropriate settings.
+        Otherwise, the p-value is computed as documented in the notes.
+        Note that if `method` is an instance of `scipy.stats.MonteCarloMethod`, the
+        ``rvs`` attribute must be left unspecified; Monte Carlo samples are always drawn
+        using the ``rvs`` method of `scipy.stats.random_table`.
+
+        .. versionadded:: 1.15.0
+
+
+    Returns
+    -------
+    res : Chi2ContingencyResult
+        An object containing attributes:
+
+        statistic : float
+            The test statistic.
+        pvalue : float
+            The p-value of the test.
+        dof : int
+            The degrees of freedom. NaN if `method` is not ``None``.
+        expected_freq : ndarray, same shape as `observed`
+            The expected frequencies, based on the marginal sums of the table.
+
+    See Also
+    --------
+    scipy.stats.contingency.expected_freq
+    scipy.stats.fisher_exact
+    scipy.stats.chisquare
+    scipy.stats.power_divergence
+    scipy.stats.barnard_exact
+    scipy.stats.boschloo_exact
+    :ref:`hypothesis_chi2_contingency` : Extended example
+
+    Notes
+    -----
+    An often quoted guideline for the validity of this calculation is that
+    the test should be used only if the observed and expected frequencies
+    in each cell are at least 5.
+
+    This is a test for the independence of different categories of a
+    population. The test is only meaningful when the dimension of
+    `observed` is two or more.  Applying the test to a one-dimensional
+    table will always result in `expected` equal to `observed` and a
+    chi-square statistic equal to 0.
+
+    This function does not handle masked arrays, because the calculation
+    does not make sense with missing values.
+
+    Like `scipy.stats.chisquare`, this function computes a chi-square
+    statistic; the convenience this function provides is to figure out the
+    expected frequencies and degrees of freedom from the given contingency
+    table. If these were already known, and if the Yates' correction was not
+    required, one could use `scipy.stats.chisquare`.  That is, if one calls::
+
+        res = chi2_contingency(obs, correction=False)
+
+    then the following is true::
+
+        (res.statistic, res.pvalue) == stats.chisquare(obs.ravel(),
+                                                       f_exp=ex.ravel(),
+                                                       ddof=obs.size - 1 - dof)
+
+    The `lambda_` argument was added in version 0.13.0 of scipy.
+
+    References
+    ----------
+    .. [1] "Contingency table",
+           https://en.wikipedia.org/wiki/Contingency_table
+    .. [2] "Pearson's chi-squared test",
+           https://en.wikipedia.org/wiki/Pearson%27s_chi-squared_test
+    .. [3] Cressie, N. and Read, T. R. C., "Multinomial Goodness-of-Fit
+           Tests", J. Royal Stat. Soc. Series B, Vol. 46, No. 3 (1984),
+           pp. 440-464.
+
+    Examples
+    --------
+    A two-way example (2 x 3):
+
+    >>> import numpy as np
+    >>> from scipy.stats import chi2_contingency
+    >>> obs = np.array([[10, 10, 20], [20, 20, 20]])
+    >>> res = chi2_contingency(obs)
+    >>> res.statistic
+    2.7777777777777777
+    >>> res.pvalue
+    0.24935220877729619
+    >>> res.dof
+    2
+    >>> res.expected_freq
+    array([[ 12.,  12.,  16.],
+           [ 18.,  18.,  24.]])
+
+    Perform the test using the log-likelihood ratio (i.e. the "G-test")
+    instead of Pearson's chi-squared statistic.
+
+    >>> res = chi2_contingency(obs, lambda_="log-likelihood")
+    >>> res.statistic
+    2.7688587616781319
+    >>> res.pvalue
+    0.25046668010954165
+
+    A four-way example (2 x 2 x 2 x 2):
+
+    >>> obs = np.array(
+    ...     [[[[12, 17],
+    ...        [11, 16]],
+    ...       [[11, 12],
+    ...        [15, 16]]],
+    ...      [[[23, 15],
+    ...        [30, 22]],
+    ...       [[14, 17],
+    ...        [15, 16]]]])
+    >>> res = chi2_contingency(obs)
+    >>> res.statistic
+    8.7584514426741897
+    >>> res.pvalue
+    0.64417725029295503
+
+    When the sum of the elements in a two-way table is small, the p-value
+    produced by the default asymptotic approximation may be inaccurate.
+    Consider passing a `PermutationMethod` or `MonteCarloMethod` as the
+    `method` parameter with `correction=False`.
+
+    >>> from scipy.stats import PermutationMethod
+    >>> obs = np.asarray([[12, 3],
+    ...                   [17, 16]])
+    >>> res = chi2_contingency(obs, correction=False)
+    >>> ref = chi2_contingency(obs, correction=False, method=PermutationMethod())
+    >>> res.pvalue, ref.pvalue
+    (0.0614122539870913, 0.1074)  # may vary
+
+    For a more detailed example, see :ref:`hypothesis_chi2_contingency`.
+
+    """
+    observed = np.asarray(observed)
+    if np.any(observed < 0):
+        raise ValueError("All values in `observed` must be nonnegative.")
+    if observed.size == 0:
+        raise ValueError("No data; `observed` has size 0.")
+
+    expected = expected_freq(observed)
+    if np.any(expected == 0):
+        # Include one of the positions where expected is zero in
+        # the exception message.
+        zeropos = list(zip(*np.nonzero(expected == 0)))[0]
+        raise ValueError("The internally computed table of expected "
+                         f"frequencies has a zero element at {zeropos}.")
+
+    if method is not None:
+        return _chi2_resampling_methods(observed, expected, correction, lambda_, method)
+
+    # The degrees of freedom
+    dof = expected.size - sum(expected.shape) + expected.ndim - 1
+
+    if dof == 0:
+        # Degenerate case; this occurs when `observed` is 1D (or, more
+        # generally, when it has only one nontrivial dimension).  In this
+        # case, we also have observed == expected, so chi2 is 0.
+        chi2 = 0.0
+        p = 1.0
+    else:
+        if dof == 1 and correction:
+            # Adjust `observed` according to Yates' correction for continuity.
+            # Magnitude of correction no bigger than difference; see gh-13875
+            diff = expected - observed
+            direction = np.sign(diff)
+            magnitude = np.minimum(0.5, np.abs(diff))
+            observed = observed + magnitude * direction
+
+        chi2, p = power_divergence(observed, expected,
+                                   ddof=observed.size - 1 - dof, axis=None,
+                                   lambda_=lambda_)
+
+    return Chi2ContingencyResult(chi2, p, dof, expected)
+
+
+def _chi2_resampling_methods(observed, expected, correction, lambda_, method):
+
+    if observed.ndim != 2:
+        message = 'Use of `method` is only compatible with two-way tables.'
+        raise ValueError(message)
+
+    if correction:
+        message = f'`{correction=}` is not compatible with `{method=}.`'
+        raise ValueError(message)
+
+    if lambda_ is not None:
+        message = f'`{lambda_=}` is not compatible with `{method=}.`'
+        raise ValueError(message)
+
+    if isinstance(method, stats.PermutationMethod):
+        res = _chi2_permutation_method(observed, expected, method)
+    elif isinstance(method, stats.MonteCarloMethod):
+        res = _chi2_monte_carlo_method(observed, expected, method)
+    else:
+        message = (f'`{method=}` not recognized; if provided, `method` must be an '
+                   'instance of `PermutationMethod` or `MonteCarloMethod`.')
+        raise ValueError(message)
+
+    return Chi2ContingencyResult(res.statistic, res.pvalue, np.nan, expected)
+
+
+def _chi2_permutation_method(observed, expected, method):
+    x, y = _untabulate(observed)
+    # `permutation_test` with `permutation_type='pairings' permutes the order of `x`,
+    # which pairs observations in `x` with different observations in `y`.
+    def statistic(x):
+        # crosstab the resample and compute the statistic
+        table = crosstab(x, y)[1]
+        return np.sum((table - expected)**2/expected)
+
+    return stats.permutation_test((x,), statistic, permutation_type='pairings',
+                                  alternative='greater', **method._asdict())
+
+
+def _chi2_monte_carlo_method(observed, expected, method):
+    method = method._asdict()
+
+    if method.pop('rvs', None) is not None:
+        message = ('If the `method` argument of `chi2_contingency` is an '
+                   'instance of `MonteCarloMethod`, its `rvs` attribute '
+                   'must be unspecified. Use the `MonteCarloMethod` `rng` argument '
+                   'to control the random state.')
+        raise ValueError(message)
+    rng = np.random.default_rng(method.pop('rng', None))
+
+    # `random_table.rvs` produces random contingency tables with the given marginals
+    # under the null hypothesis of independence
+    rowsums, colsums = stats.contingency.margins(observed)
+    X = stats.random_table(rowsums.ravel(), colsums.ravel(), seed=rng)
+    def rvs(size):
+        n_resamples = size[0]
+        return X.rvs(size=n_resamples).reshape(size)
+
+    expected = expected.ravel()
+    def statistic(table, axis):
+        return np.sum((table - expected)**2/expected, axis=axis)
+
+    return stats.monte_carlo_test(observed.ravel(), rvs, statistic,
+                                  alternative='greater', **method)
+
+
+@xp_capabilities(np_only=True)
+def association(observed, method="cramer", correction=False, lambda_=None):
+    """Calculates degree of association between two nominal variables.
+
+    The function provides the option for computing one of three measures of
+    association between two nominal variables from the data given in a 2d
+    contingency table: Tschuprow's T, Pearson's Contingency Coefficient
+    and Cramer's V.
+
+    Parameters
+    ----------
+    observed : array-like
+        The array of observed values
+    method : {"cramer", "tschuprow", "pearson"} (default = "cramer")
+        The association test statistic.
+    correction : bool, optional
+        Inherited from `scipy.stats.contingency.chi2_contingency()`
+    lambda_ : float or str, optional
+        Inherited from `scipy.stats.contingency.chi2_contingency()`
+
+    Returns
+    -------
+    statistic : float
+        Value of the test statistic
+
+    Notes
+    -----
+    Cramer's V, Tschuprow's T and Pearson's Contingency Coefficient, all
+    measure the degree to which two nominal or ordinal variables are related,
+    or the level of their association. This differs from correlation, although
+    many often mistakenly consider them equivalent. Correlation measures in
+    what way two variables are related, whereas, association measures how
+    related the variables are. As such, association does not subsume
+    independent variables, and is rather a test of independence. A value of
+    1.0 indicates perfect association, and 0.0 means the variables have no
+    association.
+
+    Both the Cramer's V and Tschuprow's T are extensions of the phi
+    coefficient.  Moreover, due to the close relationship between the
+    Cramer's V and Tschuprow's T the returned values can often be similar
+    or even equivalent.  They are likely to diverge more as the array shape
+    diverges from a 2x2.
+
+    References
+    ----------
+    .. [1] "Tschuprow's T",
+           https://en.wikipedia.org/wiki/Tschuprow's_T
+    .. [2] Tschuprow, A. A. (1939)
+           Principles of the Mathematical Theory of Correlation;
+           translated by M. Kantorowitsch. W. Hodge & Co.
+    .. [3] "Cramer's V", https://en.wikipedia.org/wiki/Cramer's_V
+    .. [4] "Nominal Association: Phi and Cramer's V",
+           http://www.people.vcu.edu/~pdattalo/702SuppRead/MeasAssoc/NominalAssoc.html
+    .. [5] Gingrich, Paul, "Association Between Variables",
+           http://uregina.ca/~gingrich/ch11a.pdf
+
+    Examples
+    --------
+    An example with a 4x2 contingency table:
+
+    >>> import numpy as np
+    >>> from scipy.stats.contingency import association
+    >>> obs4x2 = np.array([[100, 150], [203, 322], [420, 700], [320, 210]])
+
+    Pearson's contingency coefficient
+
+    >>> association(obs4x2, method="pearson")
+    0.18303298140595667
+
+    Cramer's V
+
+    >>> association(obs4x2, method="cramer")
+    0.18617813077483678
+
+    Tschuprow's T
+
+    >>> association(obs4x2, method="tschuprow")
+    0.14146478765062995
+    """
+    arr = np.asarray(observed)
+    if not np.issubdtype(arr.dtype, np.integer):
+        raise ValueError("`observed` must be an integer array.")
+
+    if len(arr.shape) != 2:
+        raise ValueError("method only accepts 2d arrays")
+
+    chi2_stat = chi2_contingency(arr, correction=correction,
+                                 lambda_=lambda_)
+
+    phi2 = chi2_stat.statistic / arr.sum()
+    n_rows, n_cols = arr.shape
+    if method == "cramer":
+        value = phi2 / min(n_cols - 1, n_rows - 1)
+    elif method == "tschuprow":
+        value = phi2 / math.sqrt((n_rows - 1) * (n_cols - 1))
+    elif method == 'pearson':
+        value = phi2 / (1 + phi2)
+    else:
+        raise ValueError("Invalid argument value: 'method' argument must "
+                         "be 'cramer', 'tschuprow', or 'pearson'")
+
+    return math.sqrt(value)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/distributions.py b/venv/lib/python3.12/site-packages/scipy/stats/distributions.py
new file mode 100644
index 0000000000000000000000000000000000000000..ac9c37aa98c9545b2616c8d32e8f676d8d49289e
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/distributions.py
@@ -0,0 +1,24 @@
+#
+# Author:  Travis Oliphant  2002-2011 with contributions from
+#          SciPy Developers 2004-2011
+#
+# NOTE: To look at history using `git blame`, use `git blame -M -C -C`
+#       instead of `git blame -Lxxx,+x`.
+#
+from ._distn_infrastructure import (rv_discrete, rv_continuous, rv_frozen)  # noqa: F401
+
+from . import _continuous_distns
+from . import _discrete_distns
+
+from ._continuous_distns import *  # noqa: F403
+from ._levy_stable import levy_stable
+from ._discrete_distns import *  # noqa: F403
+from ._entropy import entropy
+
+# For backwards compatibility e.g. pymc expects distributions.__all__.
+__all__ = ['rv_discrete', 'rv_continuous', 'rv_histogram', 'entropy']  # noqa: F405
+
+# Add only the distribution names, not the *_gen names.
+__all__ += _continuous_distns._distn_names
+__all__ += ['levy_stable']
+__all__ += _discrete_distns._distn_names
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/kde.py b/venv/lib/python3.12/site-packages/scipy/stats/kde.py
new file mode 100644
index 0000000000000000000000000000000000000000..4401da5a30f4452ab394232d3928493d0e3b77ec
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/kde.py
@@ -0,0 +1,18 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.stats` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+
+__all__ = ["gaussian_kde"]  # noqa: F822
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="stats", module="kde",
+                                   private_modules=["_kde"], all=__all__,
+                                   attribute=name)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/morestats.py b/venv/lib/python3.12/site-packages/scipy/stats/morestats.py
new file mode 100644
index 0000000000000000000000000000000000000000..76040ea0ca5251cabbdda7fb7936af4b281b3212
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/morestats.py
@@ -0,0 +1,27 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.stats` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+
+__all__ = [  # noqa: F822
+    'mvsdist',
+    'bayes_mvs', 'kstat', 'kstatvar', 'probplot', 'ppcc_max', 'ppcc_plot',
+    'boxcox_llf', 'boxcox', 'boxcox_normmax', 'boxcox_normplot',
+    'shapiro', 'anderson', 'ansari', 'bartlett', 'levene',
+    'fligner', 'mood', 'wilcoxon', 'median_test',
+    'circmean', 'circvar', 'circstd', 'anderson_ksamp',
+    'yeojohnson_llf', 'yeojohnson', 'yeojohnson_normmax',
+    'yeojohnson_normplot', 'chi2_contingency', 'distributions',
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="stats", module="morestats",
+                                   private_modules=["_morestats"], all=__all__,
+                                   attribute=name)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/mstats.py b/venv/lib/python3.12/site-packages/scipy/stats/mstats.py
new file mode 100644
index 0000000000000000000000000000000000000000..88016af71803dc5c4ebadba168f22cdcd8273dbb
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/mstats.py
@@ -0,0 +1,140 @@
+"""
+===================================================================
+Statistical functions for masked arrays (:mod:`scipy.stats.mstats`)
+===================================================================
+
+.. currentmodule:: scipy.stats.mstats
+
+This module contains a large number of statistical functions that can
+be used with masked arrays.
+
+Most of these functions are similar to those in `scipy.stats` but might
+have small differences in the API or in the algorithm used. Since this
+is a relatively new package, some API changes are still possible.
+
+Summary statistics
+==================
+
+.. autosummary::
+   :toctree: generated/
+
+   describe
+   gmean
+   hmean
+   kurtosis
+   mode
+   mquantiles
+   hdmedian
+   hdquantiles
+   hdquantiles_sd
+   idealfourths
+   plotting_positions
+   meppf
+   moment
+   skew
+   tmean
+   tvar
+   tmin
+   tmax
+   tsem
+   variation
+   find_repeats
+   sem
+   trimmed_mean
+   trimmed_mean_ci
+   trimmed_std
+   trimmed_var
+
+Frequency statistics
+====================
+
+.. autosummary::
+   :toctree: generated/
+
+   scoreatpercentile
+
+Correlation functions
+=====================
+
+.. autosummary::
+   :toctree: generated/
+
+   f_oneway
+   pearsonr
+   spearmanr
+   pointbiserialr
+   kendalltau
+   kendalltau_seasonal
+   linregress
+   siegelslopes
+   theilslopes
+   sen_seasonal_slopes
+
+Statistical tests
+=================
+
+.. autosummary::
+   :toctree: generated/
+
+   ttest_1samp
+   ttest_onesamp
+   ttest_ind
+   ttest_rel
+   chisquare
+   kstest
+   ks_2samp
+   ks_1samp
+   ks_twosamp
+   mannwhitneyu
+   rankdata
+   kruskal
+   kruskalwallis
+   friedmanchisquare
+   brunnermunzel
+   skewtest
+   kurtosistest
+   normaltest
+
+Transformations
+===============
+
+.. autosummary::
+   :toctree: generated/
+
+   obrientransform
+   trim
+   trima
+   trimmed_stde
+   trimr
+   trimtail
+   trimboth
+   winsorize
+   zmap
+   zscore
+
+Other
+=====
+
+.. autosummary::
+   :toctree: generated/
+
+   argstoarray
+   count_tied_groups
+   msign
+   compare_medians_ms
+   median_cihs
+   mjci
+   mquantiles_cimj
+   rsh
+
+"""
+from . import _mstats_basic
+from . import _mstats_extras
+from ._mstats_basic import *  # noqa: F403
+from ._mstats_extras import *  # noqa: F403
+# Functions that support masked array input in stats but need to be kept in the
+# mstats namespace for backwards compatibility:
+from scipy.stats import gmean, hmean, zmap, zscore, chisquare
+
+__all__ = _mstats_basic.__all__ + _mstats_extras.__all__
+__all__ += ['gmean', 'hmean', 'zmap', 'zscore', 'chisquare']
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/mstats_basic.py b/venv/lib/python3.12/site-packages/scipy/stats/mstats_basic.py
new file mode 100644
index 0000000000000000000000000000000000000000..19cc67a6acdfa054ffa2b29b6e774dd7aafda263
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/mstats_basic.py
@@ -0,0 +1,42 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.stats` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+
+__all__ = [  # noqa: F822
+    'argstoarray',
+    'count_tied_groups',
+    'describe',
+    'f_oneway', 'find_repeats','friedmanchisquare',
+    'kendalltau','kendalltau_seasonal','kruskal','kruskalwallis',
+    'ks_twosamp', 'ks_2samp', 'kurtosis', 'kurtosistest',
+    'ks_1samp', 'kstest',
+    'linregress',
+    'mannwhitneyu', 'meppf','mode','moment','mquantiles','msign',
+    'normaltest',
+    'obrientransform',
+    'pearsonr','plotting_positions','pointbiserialr',
+    'rankdata',
+    'scoreatpercentile','sem',
+    'sen_seasonal_slopes','skew','skewtest','spearmanr',
+    'siegelslopes', 'theilslopes',
+    'tmax','tmean','tmin','trim','trimboth',
+    'trimtail','trima','trimr','trimmed_mean','trimmed_std',
+    'trimmed_stde','trimmed_var','tsem','ttest_1samp','ttest_onesamp',
+    'ttest_ind','ttest_rel','tvar',
+    'variation',
+    'winsorize',
+    'brunnermunzel',
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="stats", module="mstats_basic",
+                                   private_modules=["_mstats_basic"], all=__all__,
+                                   attribute=name, correct_module="mstats")
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/mstats_extras.py b/venv/lib/python3.12/site-packages/scipy/stats/mstats_extras.py
new file mode 100644
index 0000000000000000000000000000000000000000..fec695329cf2c2d58a4918cc99e209c0650c3ea6
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/mstats_extras.py
@@ -0,0 +1,25 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.stats` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+
+__all__ = [  # noqa: F822
+    'compare_medians_ms',
+    'hdquantiles', 'hdmedian', 'hdquantiles_sd',
+    'idealfourths',
+    'median_cihs','mjci','mquantiles_cimj',
+    'rsh',
+    'trimmed_mean_ci',
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="stats", module="mstats_extras",
+                                   private_modules=["_mstats_extras"], all=__all__,
+                                   attribute=name, correct_module="mstats")
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/mvn.py b/venv/lib/python3.12/site-packages/scipy/stats/mvn.py
new file mode 100644
index 0000000000000000000000000000000000000000..65da9e20f6a4e6d24c1cb206c59821730fb6ab83
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/mvn.py
@@ -0,0 +1,17 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.stats` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+__all__: list[str] = []
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="stats", module="mvn",
+                                   private_modules=["_mvn"], all=__all__,
+                                   attribute=name)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/qmc.py b/venv/lib/python3.12/site-packages/scipy/stats/qmc.py
new file mode 100644
index 0000000000000000000000000000000000000000..a8a08343cf4c759938b31c29e32aaa644bf6e0fd
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/qmc.py
@@ -0,0 +1,236 @@
+r"""
+====================================================
+Quasi-Monte Carlo submodule (:mod:`scipy.stats.qmc`)
+====================================================
+
+.. currentmodule:: scipy.stats.qmc
+
+This module provides Quasi-Monte Carlo generators and associated helper
+functions.
+
+
+Quasi-Monte Carlo
+=================
+
+Engines
+-------
+
+.. autosummary::
+   :toctree: generated/
+
+   QMCEngine
+   Sobol
+   Halton
+   LatinHypercube
+   PoissonDisk
+   MultinomialQMC
+   MultivariateNormalQMC
+
+Helpers
+-------
+
+.. autosummary::
+   :toctree: generated/
+
+   discrepancy
+   geometric_discrepancy
+   update_discrepancy
+   scale
+
+
+Introduction to Quasi-Monte Carlo
+=================================
+
+Quasi-Monte Carlo (QMC) methods [1]_, [2]_, [3]_ provide an
+:math:`n \times d` array of numbers in :math:`[0,1]`. They can be used in
+place of :math:`n` points from the :math:`U[0,1]^{d}` distribution. Compared to
+random points, QMC points are designed to have fewer gaps and clumps. This is
+quantified by discrepancy measures [4]_. From the Koksma-Hlawka
+inequality [5]_ we know that low discrepancy reduces a bound on
+integration error. Averaging a function :math:`f` over :math:`n` QMC points
+can achieve an integration error close to :math:`O(n^{-1})` for well
+behaved functions [2]_.
+
+Most QMC constructions are designed for special values of :math:`n`
+such as powers of 2 or large primes. Changing the sample
+size by even one can degrade their performance, even their
+rate of convergence [6]_. For instance :math:`n=100` points may give less
+accuracy than :math:`n=64` if the method was designed for :math:`n=2^m`.
+
+Some QMC constructions are extensible in :math:`n`: we can find
+another special sample size :math:`n' > n` and often an infinite
+sequence of increasing special sample sizes. Some QMC
+constructions are extensible in :math:`d`: we can increase the dimension,
+possibly to some upper bound, and typically without requiring
+special values of :math:`d`. Some QMC methods are extensible in
+both :math:`n` and :math:`d`.
+
+QMC points are deterministic. That makes it hard to estimate the accuracy of
+integrals estimated by averages over QMC points. Randomized QMC (RQMC) [7]_
+points are constructed so that each point is individually :math:`U[0,1]^{d}`
+while collectively the :math:`n` points retain their low discrepancy.
+One can make :math:`R` independent replications of RQMC points to
+see how stable a computation is. From :math:`R` independent values,
+a t-test (or bootstrap t-test [8]_) then gives approximate confidence
+intervals on the mean value. Some RQMC methods produce a
+root mean squared error that is actually :math:`o(1/n)` and smaller than
+the rate seen in unrandomized QMC. An intuitive explanation is
+that the error is a sum of many small ones and random errors
+cancel in a way that deterministic ones do not. RQMC also
+has advantages on integrands that are singular or, for other
+reasons, fail to be Riemann integrable.
+
+(R)QMC cannot beat Bahkvalov's curse of dimension (see [9]_). For
+any random or deterministic method, there are worst case functions
+that will give it poor performance in high dimensions. A worst
+case function for QMC might be 0 at all n points but very
+large elsewhere. Worst case analyses get very pessimistic
+in high dimensions. (R)QMC can bring a great improvement over
+MC when the functions on which it is used are not worst case.
+For instance (R)QMC can be especially effective on integrands
+that are well approximated by sums of functions of
+some small number of their input variables at a time [10]_, [11]_.
+That property is often a surprising finding about those functions.
+
+Also, to see an improvement over IID MC, (R)QMC requires a bit of smoothness of
+the integrand, roughly the mixed first order derivative in each direction,
+:math:`\partial^d f/\partial x_1 \cdots \partial x_d`, must be integral.
+For instance, a function that is 1 inside the hypersphere and 0 outside of it
+has infinite variation in the sense of Hardy and Krause for any dimension
+:math:`d = 2`.
+
+Scrambled nets are a kind of RQMC that have some valuable robustness
+properties [12]_. If the integrand is square integrable, they give variance
+:math:`var_{SNET} = o(1/n)`. There is a finite upper bound on
+:math:`var_{SNET} / var_{MC}` that holds simultaneously for every square
+integrable integrand. Scrambled nets satisfy a strong law of large numbers
+for :math:`f` in :math:`L^p` when :math:`p>1`. In some
+special cases there is a central limit theorem [13]_. For smooth enough
+integrands they can achieve RMSE nearly :math:`O(n^{-3})`. See [12]_
+for references about these properties.
+
+The main kinds of QMC methods are lattice rules [14]_ and digital
+nets and sequences [2]_, [15]_. The theories meet up in polynomial
+lattice rules [16]_ which can produce digital nets. Lattice rules
+require some form of search for good constructions. For digital
+nets there are widely used default constructions.
+
+The most widely used QMC methods are Sobol' sequences [17]_.
+These are digital nets. They are extensible in both :math:`n` and :math:`d`.
+They can be scrambled. The special sample sizes are powers
+of 2. Another popular method are Halton sequences [18]_.
+The constructions resemble those of digital nets. The earlier
+dimensions have much better equidistribution properties than
+later ones. There are essentially no special sample sizes.
+They are not thought to be as accurate as Sobol' sequences.
+They can be scrambled. The nets of Faure [19]_ are also widely
+used. All dimensions are equally good, but the special sample
+sizes grow rapidly with dimension :math:`d`. They can be scrambled.
+The nets of Niederreiter and Xing [20]_ have the best asymptotic
+properties but have not shown good empirical performance [21]_.
+
+Higher order digital nets are formed by a digit interleaving process
+in the digits of the constructed points. They can achieve higher
+levels of asymptotic accuracy given higher smoothness conditions on :math:`f`
+and they can be scrambled [22]_. There is little or no empirical work
+showing the improved rate to be attained.
+
+Using QMC is like using the entire period of a small random
+number generator. The constructions are similar and so
+therefore are the computational costs [23]_.
+
+(R)QMC is sometimes improved by passing the points through
+a baker's transformation (tent function) prior to using them.
+That function has the form :math:`1-2|x-1/2|`. As :math:`x` goes from 0 to
+1, this function goes from 0 to 1 and then back. It is very
+useful to produce a periodic function for lattice rules [14]_,
+and sometimes it improves the convergence rate [24]_.
+
+It is not straightforward to apply QMC methods to Markov
+chain Monte Carlo (MCMC).  We can think of MCMC as using
+:math:`n=1` point in :math:`[0,1]^{d}` for very large :math:`d`, with
+ergodic results corresponding to :math:`d \to \infty`. One proposal is
+in [25]_ and under strong conditions an improved rate of convergence
+has been shown [26]_.
+
+Returning to Sobol' points: there are many versions depending
+on what are called direction numbers. Those are the result of
+searches and are tabulated. A very widely used set of direction
+numbers come from [27]_. It is extensible in dimension up to
+:math:`d=21201`.
+
+References
+----------
+.. [1] Owen, Art B. "Monte Carlo Book: the Quasi-Monte Carlo parts." 2019.
+.. [2] Niederreiter, Harald. "Random number generation and quasi-Monte Carlo
+   methods." Society for Industrial and Applied Mathematics, 1992.
+.. [3] Dick, Josef, Frances Y. Kuo, and Ian H. Sloan. "High-dimensional
+   integration: the quasi-Monte Carlo way." Acta Numerica no. 22: 133, 2013.
+.. [4] Aho, A. V., C. Aistleitner, T. Anderson, K. Appel, V. Arnol'd, N.
+   Aronszajn, D. Asotsky et al. "W. Chen et al.(eds.), "A Panorama of
+   Discrepancy Theory", Sringer International Publishing,
+   Switzerland: 679, 2014.
+.. [5] Hickernell, Fred J. "Koksma-Hlawka Inequality." Wiley StatsRef:
+   Statistics Reference Online, 2014.
+.. [6] Owen, Art B. "On dropping the first Sobol' point." :arxiv:`2008.08051`,
+   2020.
+.. [7] L'Ecuyer, Pierre, and Christiane Lemieux. "Recent advances in randomized
+   quasi-Monte Carlo methods." In Modeling uncertainty, pp. 419-474. Springer,
+   New York, NY, 2002.
+.. [8] DiCiccio, Thomas J., and Bradley Efron. "Bootstrap confidence
+   intervals." Statistical science: 189-212, 1996.
+.. [9] Dimov, Ivan T. "Monte Carlo methods for applied scientists." World
+   Scientific, 2008.
+.. [10] Caflisch, Russel E., William J. Morokoff, and Art B. Owen. "Valuation
+   of mortgage backed securities using Brownian bridges to reduce effective
+   dimension." Journal of Computational Finance: no. 1 27-46, 1997.
+.. [11] Sloan, Ian H., and Henryk Wozniakowski. "When are quasi-Monte Carlo
+   algorithms efficient for high dimensional integrals?." Journal of Complexity
+   14, no. 1 (1998): 1-33.
+.. [12] Owen, Art B., and Daniel Rudolf, "A strong law of large numbers for
+   scrambled net integration." SIAM Review, to appear.
+.. [13] Loh, Wei-Liem. "On the asymptotic distribution of scrambled net
+   quadrature." The Annals of Statistics 31, no. 4: 1282-1324, 2003.
+.. [14] Sloan, Ian H. and S. Joe. "Lattice methods for multiple integration."
+   Oxford University Press, 1994.
+.. [15] Dick, Josef, and Friedrich Pillichshammer. "Digital nets and sequences:
+   discrepancy theory and quasi-Monte Carlo integration." Cambridge University
+   Press, 2010.
+.. [16] Dick, Josef, F. Kuo, Friedrich Pillichshammer, and I. Sloan.
+   "Construction algorithms for polynomial lattice rules for multivariate
+   integration." Mathematics of computation 74, no. 252: 1895-1921, 2005.
+.. [17] Sobol', Il'ya Meerovich. "On the distribution of points in a cube and
+   the approximate evaluation of integrals." Zhurnal Vychislitel'noi Matematiki
+   i Matematicheskoi Fiziki 7, no. 4: 784-802, 1967.
+.. [18] Halton, John H. "On the efficiency of certain quasi-random sequences of
+   points in evaluating multi-dimensional integrals." Numerische Mathematik 2,
+   no. 1: 84-90, 1960.
+.. [19] Faure, Henri. "Discrepance de suites associees a un systeme de
+   numeration (en dimension s)." Acta arithmetica 41, no. 4: 337-351, 1982.
+.. [20] Niederreiter, Harold, and Chaoping Xing. "Low-discrepancy sequences and
+   global function fields with many rational places." Finite Fields and their
+   applications 2, no. 3: 241-273, 1996.
+.. [21] Hong, Hee Sun, and Fred J. Hickernell. "Algorithm 823: Implementing
+   scrambled digital sequences." ACM Transactions on Mathematical Software
+   (TOMS) 29, no. 2: 95-109, 2003.
+.. [22] Dick, Josef. "Higher order scrambled digital nets achieve the optimal
+   rate of the root mean square error for smooth integrands." The Annals of
+   Statistics 39, no. 3: 1372-1398, 2011.
+.. [23] Niederreiter, Harald. "Multidimensional numerical integration using
+   pseudorandom numbers." In Stochastic Programming 84 Part I, pp. 17-38.
+   Springer, Berlin, Heidelberg, 1986.
+.. [24] Hickernell, Fred J. "Obtaining O (N-2+e) Convergence for Lattice
+   Quadrature Rules." In Monte Carlo and Quasi-Monte Carlo Methods 2000,
+   pp. 274-289. Springer, Berlin, Heidelberg, 2002.
+.. [25] Owen, Art B., and Seth D. Tribble. "A quasi-Monte Carlo Metropolis
+   algorithm." Proceedings of the National Academy of Sciences 102,
+   no. 25: 8844-8849, 2005.
+.. [26] Chen, Su. "Consistency and convergence rate of Markov chain quasi Monte
+   Carlo with examples." PhD diss., Stanford University, 2011.
+.. [27] Joe, Stephen, and Frances Y. Kuo. "Constructing Sobol sequences with
+   better two-dimensional projections." SIAM Journal on Scientific Computing
+   30, no. 5: 2635-2654, 2008.
+
+"""
+from ._qmc import *  # noqa: F403
+from ._qmc import __all__  # noqa: F401
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/sampling.py b/venv/lib/python3.12/site-packages/scipy/stats/sampling.py
new file mode 100644
index 0000000000000000000000000000000000000000..12174d9dfb3cb93fa33811ed4b5d233817512e36
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/sampling.py
@@ -0,0 +1,73 @@
+"""
+======================================================
+Random Number Generators (:mod:`scipy.stats.sampling`)
+======================================================
+
+.. currentmodule:: scipy.stats.sampling
+
+This module contains a collection of random number generators to sample
+from univariate continuous and discrete distributions. It uses the
+implementation of a C library called "UNU.RAN". The only exception is
+RatioUniforms, which is a pure Python implementation of the
+Ratio-of-Uniforms method.
+
+Generators Wrapped
+==================
+
+For continuous distributions
+----------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   NumericalInverseHermite
+   NumericalInversePolynomial
+   TransformedDensityRejection
+   SimpleRatioUniforms
+   RatioUniforms
+
+For discrete distributions
+--------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   DiscreteAliasUrn
+   DiscreteGuideTable
+
+Warnings / Errors used in :mod:`scipy.stats.sampling`
+-----------------------------------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   UNURANError
+
+
+Generators for pre-defined distributions
+========================================
+
+To easily apply the above methods for some of the continuous distributions
+in :mod:`scipy.stats`, the following functionality can be used:
+
+.. autosummary::
+   :toctree: generated/
+
+   FastGeneratorInversion
+
+"""
+from ._sampling import FastGeneratorInversion, RatioUniforms  # noqa: F401
+from ._unuran.unuran_wrapper import (  # noqa: F401
+   TransformedDensityRejection,
+   DiscreteAliasUrn,
+   DiscreteGuideTable,
+   NumericalInversePolynomial,
+   NumericalInverseHermite,
+   SimpleRatioUniforms,
+   UNURANError
+)
+
+__all__ = ["NumericalInverseHermite", "NumericalInversePolynomial",
+           "TransformedDensityRejection", "SimpleRatioUniforms",
+           "RatioUniforms", "DiscreteAliasUrn", "DiscreteGuideTable",
+           "UNURANError", "FastGeneratorInversion"]
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/stats.py b/venv/lib/python3.12/site-packages/scipy/stats/stats.py
new file mode 100644
index 0000000000000000000000000000000000000000..d0589a9907d3cd181739135a3e6fd1d14d18dc50
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/stats.py
@@ -0,0 +1,43 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.stats` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+
+__all__ = [  # noqa: F822
+    'gmean', 'hmean', 'pmean', 'mode', 'tmean', 'tvar',
+    'tmin', 'tmax', 'tstd', 'tsem', 'moment',
+    'skew', 'kurtosis', 'describe', 'skewtest', 'kurtosistest',
+    'normaltest', 'jarque_bera',
+    'scoreatpercentile', 'percentileofscore',
+    'cumfreq', 'relfreq', 'obrientransform',
+    'sem', 'zmap', 'zscore', 'gzscore', 'iqr', 'gstd',
+    'median_abs_deviation',
+    'sigmaclip', 'trimboth', 'trim1', 'trim_mean',
+    'f_oneway',
+    'pearsonr', 'fisher_exact',
+    'spearmanr', 'pointbiserialr',
+    'kendalltau', 'weightedtau', 'multiscale_graphcorr',
+    'linregress', 'siegelslopes', 'theilslopes', 'ttest_1samp',
+    'ttest_ind', 'ttest_ind_from_stats', 'ttest_rel',
+    'kstest', 'ks_1samp', 'ks_2samp',
+    'chisquare', 'power_divergence',
+    'tiecorrect', 'ranksums', 'kruskal', 'friedmanchisquare',
+    'rankdata',
+    'combine_pvalues', 'wasserstein_distance', 'energy_distance',
+    'brunnermunzel', 'alexandergovern', 'distributions',
+    'mstats_basic',
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(
+        sub_package="stats", module="stats",
+        private_modules=["_stats_py", "_mgc", "_correlation"],
+        all=__all__,
+        attribute=name)
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--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/common_tests.py
@@ -0,0 +1,347 @@
+import pickle
+
+import numpy as np
+import numpy.testing as npt
+from numpy.testing import assert_allclose, assert_equal
+from pytest import raises as assert_raises
+
+import numpy.ma.testutils as ma_npt
+
+from scipy._lib._util import getfullargspec_no_self as _getfullargspec
+from scipy._lib._array_api_no_0d import xp_assert_equal
+from scipy import stats
+
+
+def check_named_results(res, attributes, ma=False, xp=None):
+    for i, attr in enumerate(attributes):
+        if ma:
+            ma_npt.assert_equal(res[i], getattr(res, attr))
+        elif xp is not None:
+            xp_assert_equal(res[i], getattr(res, attr))
+        else:
+            npt.assert_equal(res[i], getattr(res, attr))
+
+
+def check_normalization(distfn, args, distname):
+    norm_moment = distfn.moment(0, *args)
+    npt.assert_allclose(norm_moment, 1.0)
+
+    if distname == "rv_histogram_instance":
+        atol, rtol = 1e-5, 0
+    else:
+        atol, rtol = 1e-7, 1e-7
+
+    normalization_expect = distfn.expect(lambda x: 1, args=args)
+    npt.assert_allclose(normalization_expect, 1.0, atol=atol, rtol=rtol,
+                        err_msg=distname, verbose=True)
+
+    _a, _b = distfn.support(*args)
+    normalization_cdf = distfn.cdf(_b, *args)
+    npt.assert_allclose(normalization_cdf, 1.0)
+
+
+def check_moment(distfn, arg, m, v, msg):
+    m1 = distfn.moment(1, *arg)
+    m2 = distfn.moment(2, *arg)
+    if not np.isinf(m):
+        npt.assert_almost_equal(m1, m, decimal=10,
+                                err_msg=msg + ' - 1st moment')
+    else:                     # or np.isnan(m1),
+        npt.assert_(np.isinf(m1),
+                    msg + f' - 1st moment -infinite, m1={str(m1)}')
+
+    if not np.isinf(v):
+        npt.assert_almost_equal(m2 - m1 * m1, v, decimal=10,
+                                err_msg=msg + ' - 2ndt moment')
+    else:                     # or np.isnan(m2),
+        npt.assert_(np.isinf(m2), msg + f' - 2nd moment -infinite, {m2=}')
+
+
+def check_mean_expect(distfn, arg, m, msg):
+    if np.isfinite(m):
+        m1 = distfn.expect(lambda x: x, arg)
+        npt.assert_almost_equal(m1, m, decimal=5,
+                                err_msg=msg + ' - 1st moment (expect)')
+
+
+def check_var_expect(distfn, arg, m, v, msg):
+    dist_looser_tolerances = {"rv_histogram_instance" , "ksone"}
+    kwargs = {'rtol': 5e-6} if msg in dist_looser_tolerances else {}
+    if np.isfinite(v):
+        m2 = distfn.expect(lambda x: x*x, arg)
+        npt.assert_allclose(m2, v + m*m, **kwargs)
+
+
+def check_skew_expect(distfn, arg, m, v, s, msg):
+    if np.isfinite(s):
+        m3e = distfn.expect(lambda x: np.power(x-m, 3), arg)
+        npt.assert_almost_equal(m3e, s * np.power(v, 1.5),
+                                decimal=5, err_msg=msg + ' - skew')
+    else:
+        npt.assert_(np.isnan(s))
+
+
+def check_kurt_expect(distfn, arg, m, v, k, msg):
+    if np.isfinite(k):
+        m4e = distfn.expect(lambda x: np.power(x-m, 4), arg)
+        npt.assert_allclose(m4e, (k + 3.) * np.power(v, 2),
+                            atol=1e-5, rtol=1e-5,
+                            err_msg=msg + ' - kurtosis')
+    elif not np.isposinf(k):
+        npt.assert_(np.isnan(k))
+
+
+def check_munp_expect(dist, args, msg):
+    # If _munp is overridden, test a higher moment. (Before gh-18634, some
+    # distributions had issues with moments 5 and higher.)
+    if dist._munp.__func__ != stats.rv_continuous._munp:
+        res = dist.moment(5, *args)  # shouldn't raise an error
+        ref = dist.expect(lambda x: x ** 5, args, lb=-np.inf, ub=np.inf)
+        if not np.isfinite(res):  # could be valid; automated test can't know
+            return
+        # loose tolerance, mostly to see whether _munp returns *something*
+        assert_allclose(res, ref, atol=1e-10, rtol=1e-4,
+                        err_msg=msg + ' - higher moment / _munp')
+
+
+def check_entropy(distfn, arg, msg):
+    ent = distfn.entropy(*arg)
+    npt.assert_(not np.isnan(ent), msg + 'test Entropy is nan')
+
+
+def check_private_entropy(distfn, args, superclass):
+    # compare a generic _entropy with the distribution-specific implementation
+    npt.assert_allclose(distfn._entropy(*args),
+                        superclass._entropy(distfn, *args))
+
+
+def check_entropy_vect_scale(distfn, arg):
+    # check 2-d
+    sc = np.asarray([[1, 2], [3, 4]])
+    v_ent = distfn.entropy(*arg, scale=sc)
+    s_ent = [distfn.entropy(*arg, scale=s) for s in sc.ravel()]
+    s_ent = np.asarray(s_ent).reshape(v_ent.shape)
+    assert_allclose(v_ent, s_ent, atol=1e-14)
+
+    # check invalid value, check cast
+    sc = [1, 2, -3]
+    v_ent = distfn.entropy(*arg, scale=sc)
+    s_ent = [distfn.entropy(*arg, scale=s) for s in sc]
+    s_ent = np.asarray(s_ent).reshape(v_ent.shape)
+    assert_allclose(v_ent, s_ent, atol=1e-14)
+
+
+def check_edge_support(distfn, args):
+    # Make sure that x=self.a and self.b are handled correctly.
+    x = distfn.support(*args)
+    if isinstance(distfn, stats.rv_discrete):
+        x = x[0]-1, x[1]
+
+    npt.assert_equal(distfn.cdf(x, *args), [0.0, 1.0])
+    npt.assert_equal(distfn.sf(x, *args), [1.0, 0.0])
+
+    if distfn.name not in ('skellam', 'dlaplace'):
+        # with a = -inf, log(0) generates warnings
+        npt.assert_equal(distfn.logcdf(x, *args), [-np.inf, 0.0])
+        npt.assert_equal(distfn.logsf(x, *args), [0.0, -np.inf])
+
+    npt.assert_equal(distfn.ppf([0.0, 1.0], *args), x)
+    npt.assert_equal(distfn.isf([0.0, 1.0], *args), x[::-1])
+
+    # out-of-bounds for isf & ppf
+    npt.assert_(np.isnan(distfn.isf([-1, 2], *args)).all())
+    npt.assert_(np.isnan(distfn.ppf([-1, 2], *args)).all())
+
+
+def check_named_args(distfn, x, shape_args, defaults, meths):
+    ## Check calling w/ named arguments.
+
+    # check consistency of shapes, numargs and _parse signature
+    signature = _getfullargspec(distfn._parse_args)
+    npt.assert_(signature.varargs is None)
+    npt.assert_(signature.varkw is None)
+    npt.assert_(not signature.kwonlyargs)
+    npt.assert_(list(signature.defaults) == list(defaults))
+
+    shape_argnames = signature.args[:-len(defaults)]  # a, b, loc=0, scale=1
+    if distfn.shapes:
+        shapes_ = distfn.shapes.replace(',', ' ').split()
+    else:
+        shapes_ = ''
+    npt.assert_(len(shapes_) == distfn.numargs)
+    npt.assert_(len(shapes_) == len(shape_argnames))
+
+    # check calling w/ named arguments
+    shape_args = list(shape_args)
+
+    vals = [meth(x, *shape_args) for meth in meths]
+    npt.assert_(np.all(np.isfinite(vals)))
+
+    names, a, k = shape_argnames[:], shape_args[:], {}
+    while names:
+        k.update({names.pop(): a.pop()})
+        v = [meth(x, *a, **k) for meth in meths]
+        npt.assert_array_equal(vals, v)
+        if 'n' not in k.keys():
+            # `n` is first parameter of moment(), so can't be used as named arg
+            npt.assert_equal(distfn.moment(1, *a, **k),
+                             distfn.moment(1, *shape_args))
+
+    # unknown arguments should not go through:
+    k.update({'kaboom': 42})
+    assert_raises(TypeError, distfn.cdf, x, **k)
+
+
+def check_random_state_property(distfn, args):
+    # check the random_state attribute of a distribution *instance*
+
+    # baseline: this relies on the global state
+    np.random.seed(1234)  # valid use of np.random.seed
+    distfn.random_state = None
+    r0 = distfn.rvs(*args, size=8)
+
+    # use an explicit instance-level random_state
+    distfn.random_state = 1234
+    r1 = distfn.rvs(*args, size=8)
+    npt.assert_equal(r0, r1)
+
+    distfn.random_state = np.random.RandomState(1234)
+    r2 = distfn.rvs(*args, size=8)
+    npt.assert_equal(r0, r2)
+
+    # check that np.random.Generator can be used (numpy >= 1.17)
+    if hasattr(np.random, 'default_rng'):
+        # obtain a np.random.Generator object
+        rng = np.random.default_rng(1234)
+        distfn.rvs(*args, size=1, random_state=rng)
+
+    # can override the instance-level random_state for an individual .rvs call
+    distfn.random_state = 2
+    orig_state = distfn.random_state.get_state()
+
+    r3 = distfn.rvs(*args, size=8, random_state=np.random.RandomState(1234))
+    npt.assert_equal(r0, r3)
+
+    # ... and that does not alter the instance-level random_state!
+    npt.assert_equal(distfn.random_state.get_state(), orig_state)
+
+
+def check_meth_dtype(distfn, arg, meths):
+    q0 = [0.25, 0.5, 0.75]
+    x0 = distfn.ppf(q0, *arg)
+    x_cast = [x0.astype(tp) for tp in (np.long, np.float16, np.float32,
+                                       np.float64)]
+
+    for x in x_cast:
+        # casting may have clipped the values, exclude those
+        distfn._argcheck(*arg)
+        x = x[(distfn.a < x) & (x < distfn.b)]
+        for meth in meths:
+            val = meth(x, *arg)
+            npt.assert_(val.dtype == np.float64)
+
+
+def check_ppf_dtype(distfn, arg):
+    q0 = np.asarray([0.25, 0.5, 0.75])
+    q_cast = [q0.astype(tp) for tp in (np.float16, np.float32, np.float64)]
+    for q in q_cast:
+        for meth in [distfn.ppf, distfn.isf]:
+            val = meth(q, *arg)
+            npt.assert_(val.dtype == np.float64)
+
+
+def check_cmplx_deriv(distfn, arg):
+    # Distributions allow complex arguments.
+    def deriv(f, x, *arg):
+        x = np.asarray(x)
+        h = 1e-10
+        return (f(x + h*1j, *arg)/h).imag
+
+    x0 = distfn.ppf([0.25, 0.51, 0.75], *arg)
+    x_cast = [x0.astype(tp) for tp in (np.long, np.float16, np.float32,
+                                       np.float64)]
+
+    for x in x_cast:
+        # casting may have clipped the values, exclude those
+        distfn._argcheck(*arg)
+        x = x[(distfn.a < x) & (x < distfn.b)]
+
+        pdf, cdf, sf = distfn.pdf(x, *arg), distfn.cdf(x, *arg), distfn.sf(x, *arg)
+        assert_allclose(deriv(distfn.cdf, x, *arg), pdf, rtol=1e-5)
+        assert_allclose(deriv(distfn.logcdf, x, *arg), pdf/cdf, rtol=1e-5)
+
+        assert_allclose(deriv(distfn.sf, x, *arg), -pdf, rtol=1e-5)
+        assert_allclose(deriv(distfn.logsf, x, *arg), -pdf/sf, rtol=1e-5)
+
+        assert_allclose(deriv(distfn.logpdf, x, *arg),
+                        deriv(distfn.pdf, x, *arg) / distfn.pdf(x, *arg),
+                        rtol=1e-5)
+
+
+def check_pickling(distfn, args):
+    # check that a distribution instance pickles and unpickles
+    # pay special attention to the random_state property
+
+    # save the random_state (restore later)
+    rndm = distfn.random_state
+
+    # check unfrozen
+    distfn.random_state = 1234
+    distfn.rvs(*args, size=8)
+    s = pickle.dumps(distfn)
+    r0 = distfn.rvs(*args, size=8)
+
+    unpickled = pickle.loads(s)
+    r1 = unpickled.rvs(*args, size=8)
+    npt.assert_equal(r0, r1)
+
+    # also smoke test some methods
+    medians = [distfn.ppf(0.5, *args), unpickled.ppf(0.5, *args)]
+    npt.assert_equal(medians[0], medians[1])
+    npt.assert_equal(distfn.cdf(medians[0], *args),
+                     unpickled.cdf(medians[1], *args))
+
+    # check frozen pickling/unpickling with rvs
+    frozen_dist = distfn(*args)
+    pkl = pickle.dumps(frozen_dist)
+    unpickled = pickle.loads(pkl)
+
+    r0 = frozen_dist.rvs(size=8)
+    r1 = unpickled.rvs(size=8)
+    npt.assert_equal(r0, r1)
+
+    # check pickling/unpickling of .fit method
+    if hasattr(distfn, "fit"):
+        fit_function = distfn.fit
+        pickled_fit_function = pickle.dumps(fit_function)
+        unpickled_fit_function = pickle.loads(pickled_fit_function)
+        assert fit_function.__name__ == unpickled_fit_function.__name__ == "fit"
+
+    # restore the random_state
+    distfn.random_state = rndm
+
+
+def check_freezing(distfn, args):
+    # regression test for gh-11089: freezing a distribution fails
+    # if loc and/or scale are specified
+    if isinstance(distfn, stats.rv_continuous):
+        locscale = {'loc': 1, 'scale': 2}
+    else:
+        locscale = {'loc': 1}
+
+    rv = distfn(*args, **locscale)
+    assert rv.a == distfn(*args).a
+    assert rv.b == distfn(*args).b
+
+
+def check_rvs_broadcast(distfunc, distname, allargs, shape, shape_only, otype):
+    rng = np.random.RandomState(123)
+    sample = distfunc.rvs(*allargs, random_state=rng)
+    assert_equal(sample.shape, shape, f"{distname}: rvs failed to broadcast")
+    if not shape_only:
+        rvs = np.vectorize(
+            lambda *allargs: distfunc.rvs(*allargs, random_state=rng),
+            otypes=otype)
+        rng = np.random.RandomState(123)
+        expected = rvs(*allargs)
+        assert_allclose(sample, expected, rtol=1e-13)
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diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/data/_mvt.py b/venv/lib/python3.12/site-packages/scipy/stats/tests/data/_mvt.py
new file mode 100644
index 0000000000000000000000000000000000000000..c346d0daded4b6e734718742cc8950b84ed333f7
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/data/_mvt.py
@@ -0,0 +1,171 @@
+import math
+import numpy as np
+from scipy import special
+from scipy.stats._qmc import primes_from_2_to
+
+
+def _primes(n):
+    # Defined to facilitate comparison between translation and source
+    # In Matlab, primes(10.5) -> first four primes, primes(11.5) -> first five
+    return primes_from_2_to(math.ceil(n))
+
+
+def _gaminv(a, b):
+    # Defined to facilitate comparison between translation and source
+    # Matlab's `gaminv` is like `special.gammaincinv` but args are reversed
+    return special.gammaincinv(b, a)
+
+
+def _qsimvtv(m, nu, sigma, a, b, rng):
+    """Estimates the multivariate t CDF using randomized QMC
+
+    Parameters
+    ----------
+    m : int
+        The number of points
+    nu : float
+        Degrees of freedom
+    sigma : ndarray
+        A 2D positive semidefinite covariance matrix
+    a : ndarray
+        Lower integration limits
+    b : ndarray
+        Upper integration limits.
+    rng : Generator
+        Pseudorandom number generator
+
+    Returns
+    -------
+    p : float
+        The estimated CDF.
+    e : float
+        An absolute error estimate.
+
+    """
+    # _qsimvtv is a Python translation of the Matlab function qsimvtv,
+    # semicolons and all.
+    #
+    #   This function uses an algorithm given in the paper
+    #      "Comparison of Methods for the Numerical Computation of
+    #       Multivariate t Probabilities", in
+    #      J. of Computational and Graphical Stat., 11(2002), pp. 950-971, by
+    #          Alan Genz and Frank Bretz
+    #
+    #   The primary references for the numerical integration are
+    #    "On a Number-Theoretical Integration Method"
+    #    H. Niederreiter, Aequationes Mathematicae, 8(1972), pp. 304-11.
+    #    and
+    #    "Randomization of Number Theoretic Methods for Multiple Integration"
+    #     R. Cranley & T.N.L. Patterson, SIAM J Numer Anal, 13(1976), pp. 904-14.
+    #
+    #   Alan Genz is the author of this function and following Matlab functions.
+    #          Alan Genz, WSU Math, PO Box 643113, Pullman, WA 99164-3113
+    #          Email : alangenz@wsu.edu
+    #
+    # Copyright (C) 2013, Alan Genz,  All rights reserved.
+    #
+    # Redistribution and use in source and binary forms, with or without
+    # modification, are permitted provided the following conditions are met:
+    #   1. Redistributions of source code must retain the above copyright
+    #      notice, this list of conditions and the following disclaimer.
+    #   2. Redistributions in binary form must reproduce the above copyright
+    #      notice, this list of conditions and the following disclaimer in
+    #      the documentation and/or other materials provided with the
+    #      distribution.
+    #   3. The contributor name(s) may not be used to endorse or promote
+    #      products derived from this software without specific prior
+    #      written permission.
+    # THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+    # "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+    # LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+    # FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+    # COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+    # INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+    # BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
+    # OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
+    # ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR
+    # TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF USE
+    # OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+    # Initialization
+    sn = max(1, math.sqrt(nu)); ch, az, bz = _chlrps(sigma, a/sn, b/sn)
+    n = len(sigma); N = 10; P = math.ceil(m/N); on = np.ones(P); p = 0; e = 0
+    ps = np.sqrt(_primes(5*n*math.log(n+4)/4)); q = ps[:, np.newaxis]  # Richtmyer gens.
+
+    # Randomization loop for ns samples
+    c = None; dc = None
+    for S in range(N):
+        vp = on.copy(); s = np.zeros((n, P))
+        for i in range(n):
+            x = np.abs(2*np.mod(q[i]*np.arange(1, P+1) + rng.random(), 1)-1)  # periodizing transform
+            if i == 0:
+                r = on
+                if nu > 0:
+                    r = np.sqrt(2*_gaminv(x, nu/2))
+            else:
+                y = _Phinv(c + x*dc)
+                s[i:] += ch[i:, i-1:i] * y
+            si = s[i, :]; c = on.copy(); ai = az[i]*r - si; d = on.copy(); bi = bz[i]*r - si
+            c[ai <= -9] = 0; tl = abs(ai) < 9; c[tl] = _Phi(ai[tl])
+            d[bi <= -9] = 0; tl = abs(bi) < 9; d[tl] = _Phi(bi[tl])
+            dc = d - c; vp = vp * dc
+        d = (np.mean(vp) - p)/(S + 1); p = p + d; e = (S - 1)*e/(S + 1) + d**2
+    e = math.sqrt(e)  # error estimate is 3 times std error with N samples.
+    return p, e
+
+
+#  Standard statistical normal distribution functions
+def _Phi(z):
+    return special.ndtr(z)
+
+
+def _Phinv(p):
+    return special.ndtri(p)
+
+
+def _chlrps(R, a, b):
+    """
+    Computes permuted and scaled lower Cholesky factor c for R which may be
+    singular, also permuting and scaling integration limit vectors a and b.
+    """
+    ep = 1e-10  # singularity tolerance
+    eps = np.finfo(R.dtype).eps
+
+    n = len(R); c = R.copy(); ap = a.copy(); bp = b.copy(); d = np.sqrt(np.maximum(np.diag(c), 0))
+    for i in range(n):
+        if d[i] > 0:
+            c[:, i] /= d[i]; c[i, :] /= d[i]
+            ap[i] /= d[i]; bp[i] /= d[i]
+    y = np.zeros((n, 1)); sqtp = math.sqrt(2*math.pi)
+
+    for k in range(n):
+        im = k; ckk = 0; dem = 1; s = 0
+        for i in range(k, n):
+            if c[i, i] > eps:
+                cii = math.sqrt(max(c[i, i], 0))
+                if i > 0: s = c[i, :k] @ y[:k]
+                ai = (ap[i]-s)/cii; bi = (bp[i]-s)/cii; de = _Phi(bi)-_Phi(ai)
+                if de <= dem:
+                    ckk = cii; dem = de; am = ai; bm = bi; im = i
+        if im > k:
+            ap[[im, k]] = ap[[k, im]]; bp[[im, k]] = bp[[k, im]]; c[im, im] = c[k, k]
+            t = c[im, :k].copy(); c[im, :k] = c[k, :k]; c[k, :k] = t
+            t = c[im+1:, im].copy(); c[im+1:, im] = c[im+1:, k]; c[im+1:, k] = t
+            t = c[k+1:im, k].copy(); c[k+1:im, k] = c[im, k+1:im].T; c[im, k+1:im] = t.T
+        if ckk > ep*(k+1):
+            c[k, k] = ckk; c[k, k+1:] = 0
+            for i in range(k+1, n):
+                c[i, k] = c[i, k]/ckk; c[i, k+1:i+1] = c[i, k+1:i+1] - c[i, k]*c[k+1:i+1, k].T
+            if abs(dem) > ep:
+                y[k] = (np.exp(-am**2/2) - np.exp(-bm**2/2)) / (sqtp*dem)
+            else:
+                y[k] = (am + bm) / 2
+                if am < -10:
+                    y[k] = bm
+                elif bm > 10:
+                    y[k] = am
+            c[k, :k+1] /= ckk; ap[k] /= ckk; bp[k] /= ckk
+        else:
+            c[k:, k] = 0; y[k] = (ap[k] + bp[k])/2
+        pass
+    return c, ap, bp
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/data/fisher_exact_results_from_r.py b/venv/lib/python3.12/site-packages/scipy/stats/tests/data/fisher_exact_results_from_r.py
new file mode 100644
index 0000000000000000000000000000000000000000..b7dd8936018eae2f74cc6f5966235a86fa821793
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/data/fisher_exact_results_from_r.py
@@ -0,0 +1,607 @@
+# DO NOT EDIT THIS FILE!
+# This file was generated by the R script
+#     generate_fisher_exact_results_from_r.R
+# The script was run with R version 3.6.2 (2019-12-12) at 2020-11-09 06:16:09
+
+
+from collections import namedtuple
+import numpy as np
+
+
+Inf = np.inf
+
+Parameters = namedtuple('Parameters',
+                        ['table', 'confidence_level', 'alternative'])
+RResults = namedtuple('RResults',
+                      ['pvalue', 'conditional_odds_ratio',
+                       'conditional_odds_ratio_ci'])
+data = [
+    (Parameters(table=[[100, 2], [1000, 5]],
+                confidence_level=0.95,
+                alternative='two.sided'),
+     RResults(pvalue=0.1300759363430016,
+              conditional_odds_ratio=0.25055839934223,
+              conditional_odds_ratio_ci=(0.04035202926536294,
+                                         2.662846672960251))),
+    (Parameters(table=[[2, 7], [8, 2]],
+                confidence_level=0.95,
+                alternative='two.sided'),
+     RResults(pvalue=0.02301413756522116,
+              conditional_odds_ratio=0.0858623513573622,
+              conditional_odds_ratio_ci=(0.004668988338943325,
+                                         0.895792956493601))),
+    (Parameters(table=[[5, 1], [10, 10]],
+                confidence_level=0.95,
+                alternative='two.sided'),
+     RResults(pvalue=0.1973244147157191,
+              conditional_odds_ratio=4.725646047336587,
+              conditional_odds_ratio_ci=(0.4153910882532168,
+                                         259.2593661129417))),
+    (Parameters(table=[[5, 15], [20, 20]],
+                confidence_level=0.95,
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+              conditional_odds_ratio=0,
+              conditional_odds_ratio_ci=(0,
+                                         Inf))),
+    (Parameters(table=[[200, 7], [8, 300]],
+                confidence_level=0.99,
+                alternative='greater'),
+     RResults(pvalue=2.005657880388915e-122,
+              conditional_odds_ratio=977.7866978606228,
+              conditional_odds_ratio_ci=(297.9619252357688,
+                                         Inf))),
+    (Parameters(table=[[28, 21], [6, 1957]],
+                confidence_level=0.99,
+                alternative='greater'),
+     RResults(pvalue=5.728437460831983e-44,
+              conditional_odds_ratio=425.2403028434684,
+              conditional_odds_ratio_ci=(130.3213490295859,
+                                         Inf))),
+    (Parameters(table=[[190, 800], [200, 900]],
+                confidence_level=0.99,
+                alternative='greater'),
+     RResults(pvalue=0.2959825901308897,
+              conditional_odds_ratio=1.068697577856801,
+              conditional_odds_ratio_ci=(0.8176272148267533,
+                                         Inf))),
+]
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/data/jf_skew_t_gamlss_pdf_data.npy b/venv/lib/python3.12/site-packages/scipy/stats/tests/data/jf_skew_t_gamlss_pdf_data.npy
new file mode 100644
index 0000000000000000000000000000000000000000..721749bcd853fa5c5efe5a1f5ba6e105658395dc
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/data/jf_skew_t_gamlss_pdf_data.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:254d2dee4a4d547b9331c60243c6fcfcaffd26c8b104d08d4f6045a7645b3bba
+size 4064
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/data/levy_stable/stable-Z1-cdf-sample-data.npy b/venv/lib/python3.12/site-packages/scipy/stats/tests/data/levy_stable/stable-Z1-cdf-sample-data.npy
new file mode 100644
index 0000000000000000000000000000000000000000..adda664a7b5442fc0977ddbaa572c864ddd31f08
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/data/levy_stable/stable-Z1-cdf-sample-data.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:cf18c1f2d65a232bf2c7121282df31bf2a8be827afafc4ed810ed37457ee898a
+size 183728
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/data/levy_stable/stable-Z1-pdf-sample-data.npy b/venv/lib/python3.12/site-packages/scipy/stats/tests/data/levy_stable/stable-Z1-pdf-sample-data.npy
new file mode 100644
index 0000000000000000000000000000000000000000..6c41166721b891a801cdc6828804c6da7233d625
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/data/levy_stable/stable-Z1-pdf-sample-data.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:fee99512bab4ccc6569b47b924e4b034e1cdbab5624fafc7e120648bd5f7a128
+size 183688
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/data/levy_stable/stable-loc-scale-sample-data.npy b/venv/lib/python3.12/site-packages/scipy/stats/tests/data/levy_stable/stable-loc-scale-sample-data.npy
new file mode 100644
index 0000000000000000000000000000000000000000..0a1460e407521836a9b73a081609af4ccdb6deae
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/data/levy_stable/stable-loc-scale-sample-data.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f3c719edd5431fb9e7b9ecb6d19e3ca7a9095298bd19f226685b0fca40f0c073
+size 9328
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/AtmWtAg.dat b/venv/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/AtmWtAg.dat
new file mode 100644
index 0000000000000000000000000000000000000000..30537565fe8c47f74da0e63a39f4b46600f7768f
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/AtmWtAg.dat
@@ -0,0 +1,108 @@
+NIST/ITL StRD 
+Dataset Name:   AtmWtAg   (AtmWtAg.dat)
+
+
+File Format:    ASCII
+                Certified Values   (lines 41 to 47)
+                Data               (lines 61 to 108) 
+
+
+Procedure:      Analysis of Variance
+
+
+Reference:      Powell, L.J., Murphy, T.J. and Gramlich, J.W. (1982).
+                "The Absolute Isotopic Abundance & Atomic Weight
+                of a Reference Sample of Silver".
+                NBS Journal of Research, 87, pp. 9-19.
+
+
+Data:           1 Factor
+                2 Treatments
+                24 Replicates/Cell
+                48 Observations
+                7 Constant Leading Digits
+                Average Level of Difficulty
+                Observed Data
+
+
+Model:          3 Parameters (mu, tau_1, tau_2)
+                y_{ij} = mu + tau_i + epsilon_{ij}
+
+
+
+
+
+
+Certified Values:
+
+Source of                  Sums of               Mean               
+Variation          df      Squares              Squares             F Statistic
+
+
+Between Instrument  1 3.63834187500000E-09 3.63834187500000E-09 1.59467335677930E+01
+Within Instrument  46 1.04951729166667E-08 2.28155932971014E-10
+
+                   Certified R-Squared 2.57426544538321E-01
+
+                   Certified Residual
+                   Standard Deviation  1.51048314446410E-05
+
+
+
+
+
+
+
+
+
+
+
+Data:  Instrument           AgWt
+           1            107.8681568
+           1            107.8681465
+           1            107.8681572
+           1            107.8681785
+           1            107.8681446
+           1            107.8681903
+           1            107.8681526
+           1            107.8681494
+           1            107.8681616
+           1            107.8681587
+           1            107.8681519
+           1            107.8681486
+           1            107.8681419
+           1            107.8681569
+           1            107.8681508
+           1            107.8681672
+           1            107.8681385
+           1            107.8681518
+           1            107.8681662
+           1            107.8681424
+           1            107.8681360
+           1            107.8681333
+           1            107.8681610
+           1            107.8681477
+           2            107.8681079
+           2            107.8681344
+           2            107.8681513
+           2            107.8681197
+           2            107.8681604
+           2            107.8681385
+           2            107.8681642
+           2            107.8681365
+           2            107.8681151
+           2            107.8681082
+           2            107.8681517
+           2            107.8681448
+           2            107.8681198
+           2            107.8681482
+           2            107.8681334
+           2            107.8681609
+           2            107.8681101
+           2            107.8681512
+           2            107.8681469
+           2            107.8681360
+           2            107.8681254
+           2            107.8681261
+           2            107.8681450
+           2            107.8681368
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SiRstv.dat b/venv/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SiRstv.dat
new file mode 100644
index 0000000000000000000000000000000000000000..18ea8971fd7a4d67800dafe98ac5ea5acef53025
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SiRstv.dat
@@ -0,0 +1,85 @@
+NIST/ITL StRD 
+Dataset Name:   SiRstv     (SiRstv.dat)
+
+
+File Format:    ASCII
+                Certified Values   (lines 41 to 47)
+                Data               (lines 61 to 85) 
+
+
+Procedure:      Analysis of Variance
+
+
+Reference:      Ehrstein, James and Croarkin, M. Carroll.
+                Unpublished NIST dataset.
+
+
+Data:           1 Factor
+                5 Treatments
+                5  Replicates/Cell
+                25 Observations
+                3 Constant Leading Digits
+                Lower Level of Difficulty
+                Observed Data
+
+
+Model:          6 Parameters (mu,tau_1, ... , tau_5)
+                y_{ij} = mu + tau_i + epsilon_{ij}
+
+
+
+
+
+
+
+
+Certified Values:
+
+Source of                  Sums of               Mean               
+Variation          df      Squares              Squares             F Statistic
+
+Between Instrument  4 5.11462616000000E-02 1.27865654000000E-02 1.18046237440255E+00
+Within Instrument  20 2.16636560000000E-01 1.08318280000000E-02
+
+                   Certified R-Squared 1.90999039051129E-01
+
+                   Certified Residual
+                   Standard Deviation  1.04076068334656E-01
+
+
+
+
+
+
+
+
+
+
+
+
+Data:  Instrument   Resistance
+           1         196.3052
+           1         196.1240
+           1         196.1890
+           1         196.2569
+           1         196.3403
+           2         196.3042
+           2         196.3825
+           2         196.1669
+           2         196.3257
+           2         196.0422
+           3         196.1303
+           3         196.2005
+           3         196.2889
+           3         196.0343
+           3         196.1811
+           4         196.2795
+           4         196.1748
+           4         196.1494
+           4         196.1485
+           4         195.9885
+           5         196.2119
+           5         196.1051
+           5         196.1850
+           5         196.0052
+           5         196.2090
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs01.dat b/venv/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs01.dat
new file mode 100644
index 0000000000000000000000000000000000000000..945b24bf35422152a5faba73ed054ab78fda1bdf
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs01.dat
@@ -0,0 +1,249 @@
+NIST/ITL StRD 
+Dataset Name:   SmLs01   (SmLs01.dat)
+
+
+File Format:    ASCII
+                Certified Values   (lines 41 to 47)
+                Data               (lines 61 to 249) 
+
+
+Procedure:      Analysis of Variance
+
+
+Reference:      Simon, Stephen D. and Lesage, James P. (1989).
+                "Assessing the Accuracy of ANOVA Calculations in
+                Statistical Software".
+                Computational Statistics & Data Analysis, 8, pp. 325-332.
+
+
+Data:           1 Factor
+                9 Treatments
+                21 Replicates/Cell
+                189 Observations
+                1 Constant Leading Digit
+                Lower Level of Difficulty
+                Generated Data
+
+
+Model:          10 Parameters (mu,tau_1, ... , tau_9)
+                y_{ij} = mu + tau_i + epsilon_{ij}
+
+
+
+
+
+
+Certified Values:
+
+Source of                  Sums of               Mean               
+Variation          df      Squares              Squares            F Statistic
+
+Between Treatment   8 1.68000000000000E+00 2.10000000000000E-01 2.10000000000000E+01
+Within Treatment  180 1.80000000000000E+00 1.00000000000000E-02
+
+                  Certified R-Squared 4.82758620689655E-01
+
+                  Certified Residual
+                  Standard Deviation  1.00000000000000E-01
+
+
+
+
+
+
+
+
+
+
+
+
+Data:  Treatment   Response
+           1         1.4
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           2         1.3
+           2         1.2
+           2         1.4
+           2         1.2
+           2         1.4
+           2         1.2
+           2         1.4
+           2         1.2
+           2         1.4
+           2         1.2
+           2         1.4
+           2         1.2
+           2         1.4
+           2         1.2
+           2         1.4
+           2         1.2
+           2         1.4
+           2         1.2
+           2         1.4
+           2         1.2
+           2         1.4
+           3         1.5
+           3         1.4
+           3         1.6
+           3         1.4
+           3         1.6
+           3         1.4
+           3         1.6
+           3         1.4
+           3         1.6
+           3         1.4
+           3         1.6
+           3         1.4
+           3         1.6
+           3         1.4
+           3         1.6
+           3         1.4
+           3         1.6
+           3         1.4
+           3         1.6
+           3         1.4
+           3         1.6
+           4         1.3
+           4         1.2
+           4         1.4
+           4         1.2
+           4         1.4
+           4         1.2
+           4         1.4
+           4         1.2
+           4         1.4
+           4         1.2
+           4         1.4
+           4         1.2
+           4         1.4
+           4         1.2
+           4         1.4
+           4         1.2
+           4         1.4
+           4         1.2
+           4         1.4
+           4         1.2
+           4         1.4
+           5         1.5
+           5         1.4
+           5         1.6
+           5         1.4
+           5         1.6
+           5         1.4
+           5         1.6
+           5         1.4
+           5         1.6
+           5         1.4
+           5         1.6
+           5         1.4
+           5         1.6
+           5         1.4
+           5         1.6
+           5         1.4
+           5         1.6
+           5         1.4
+           5         1.6
+           5         1.4
+           5         1.6
+           6         1.3
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           7         1.5
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           8         1.3
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           9         1.5
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs02.dat b/venv/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs02.dat
new file mode 100644
index 0000000000000000000000000000000000000000..ee76633a660a48225064bbb86a25f6a2f36c6d9a
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs02.dat
@@ -0,0 +1,1869 @@
+NIST/ITL StRD 
+Dataset Name:   SmLs02   (SmLs02.dat)
+
+
+File Format:    ASCII
+                Certified Values   (lines 41 to 47)
+                Data               (lines 61 to 1869) 
+
+
+Procedure:      Analysis of Variance
+
+
+Reference:      Simon, Stephen D. and Lesage, James P. (1989).
+                "Assessing the Accuracy of ANOVA Calculations in
+                Statistical Software".
+                Computational Statistics & Data Analysis, 8, pp. 325-332.
+
+
+Data:           1 Factor
+                9 Treatments
+                201 Replicates/Cell
+                1809 Observations
+                1 Constant Leading Digit
+                Lower Level of Difficulty
+                Generated Data
+
+
+Model:          10 Parameters (mu,tau_1, ... , tau_9)
+                y_{ij} = mu + tau_i + epsilon_{ij}
+
+
+
+
+
+
+Certified Values:
+
+Source of                  Sums of               Mean               
+Variation          df      Squares              Squares             F Statistic
+
+Between Treatment    8 1.60800000000000E+01 2.01000000000000E+00 2.01000000000000E+02
+Within Treatment  1800 1.80000000000000E+01 1.00000000000000E-02
+
+                  Certified R-Squared 4.71830985915493E-01
+
+                  Certified Residual
+                  Standard Deviation  1.00000000000000E-01
+
+
+
+
+
+
+
+
+
+
+
+
+Data:  Treatment   Response
+           1         1.4
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
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+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           7         1.5
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           8         1.3
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           9         1.5
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs03.dat b/venv/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs03.dat
new file mode 100644
index 0000000000000000000000000000000000000000..55dfa2313ffb152709c58b47c0058567b710d903
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs03.dat
@@ -0,0 +1,18069 @@
+NIST/ITL StRD 
+Dataset Name:   SmLs03   (SmLs03.dat)
+
+
+File Format:    ASCII
+                Certified Values   (lines 41 to 47)
+                Data               (lines 61 to 18069) 
+
+
+Procedure:      Analysis of Variance
+
+
+Reference:      Simon, Stephen D. and Lesage, James P. (1989).
+                "Assessing the Accuracy of ANOVA Calculations in
+                Statistical Software".
+                Computational Statistics & Data Analysis, 8, pp. 325-332.
+
+
+Data:           1 Factor
+                9 Treatments
+                2001 Replicates/Cell
+                18009 Observations
+                1 Constant Leading Digit
+                Lower Level of Difficulty
+                Generated Data
+
+
+Model:          10 Parameters (mu,tau_1, ... , tau_9)
+                y_{ij} = mu + tau_i + epsilon_{ij}
+
+
+
+
+
+
+Certified Values:
+
+Source of                  Sums of               Mean               
+Variation          df      Squares              Squares             F Statistic
+
+Between Treatment     8 1.60080000000000E+02 2.00100000000000E+01 2.00100000000000E+03
+Within Treatment  18000 1.80000000000000E+02 1.00000000000000E-02
+
+                  Certified R-Squared 4.70712773465067E-01
+
+                  Certified Residual
+                  Standard Deviation  1.00000000000000E-01
+
+
+
+
+
+
+
+
+
+
+
+
+Data:  Treatment   Response
+           1         1.4
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
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diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs04.dat b/venv/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs04.dat
new file mode 100644
index 0000000000000000000000000000000000000000..6a2a9fc935a56989b166de9b23f3df3bc4f64879
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs04.dat
@@ -0,0 +1,249 @@
+NIST/ITL StRD 
+Dataset Name:   SmLs04   (SmLs04.dat)
+
+
+File Format:    ASCII
+                Certified Values   (lines 41 to 47)
+                Data               (lines 61 to 249) 
+
+
+Procedure:      Analysis of Variance
+
+
+Reference:      Simon, Stephen D. and Lesage, James P. (1989).
+                "Assessing the Accuracy of ANOVA Calculations in
+                Statistical Software".
+                Computational Statistics & Data Analysis, 8, pp. 325-332.
+
+
+Data:           1 Factor
+                9 Treatments
+                21 Replicates/Cell
+                189 Observations
+                7 Constant Leading Digits
+                Average Level of Difficulty
+                Generated Data
+
+
+Model:          10 Parameters (mu,tau_1, ... , tau_9)
+                y_{ij} = mu + tau_i + epsilon_{ij}
+
+
+
+
+
+
+Certified Values:
+
+Source of                  Sums of               Mean               
+Variation          df      Squares              Squares             F Statistic
+
+Between Treatment   8 1.68000000000000E+00 2.10000000000000E-01 2.10000000000000E+01
+Within Treatment  180 1.80000000000000E+00 1.00000000000000E-02
+
+                  Certified R-Squared 4.82758620689655E-01
+
+                  Certified Residual
+                  Standard Deviation  1.00000000000000E-01
+
+
+
+
+
+
+
+
+
+
+
+
+Data:  Treatment   Response
+           1       1000000.4
+           1       1000000.3
+           1       1000000.5
+           1       1000000.3
+           1       1000000.5
+           1       1000000.3
+           1       1000000.5
+           1       1000000.3
+           1       1000000.5
+           1       1000000.3
+           1       1000000.5
+           1       1000000.3
+           1       1000000.5
+           1       1000000.3
+           1       1000000.5
+           1       1000000.3
+           1       1000000.5
+           1       1000000.3
+           1       1000000.5
+           1       1000000.3
+           1       1000000.5
+           2       1000000.3
+           2       1000000.2
+           2       1000000.4
+           2       1000000.2
+           2       1000000.4
+           2       1000000.2
+           2       1000000.4
+           2       1000000.2
+           2       1000000.4
+           2       1000000.2
+           2       1000000.4
+           2       1000000.2
+           2       1000000.4
+           2       1000000.2
+           2       1000000.4
+           2       1000000.2
+           2       1000000.4
+           2       1000000.2
+           2       1000000.4
+           2       1000000.2
+           2       1000000.4
+           3       1000000.5
+           3       1000000.4
+           3       1000000.6
+           3       1000000.4
+           3       1000000.6
+           3       1000000.4
+           3       1000000.6
+           3       1000000.4
+           3       1000000.6
+           3       1000000.4
+           3       1000000.6
+           3       1000000.4
+           3       1000000.6
+           3       1000000.4
+           3       1000000.6
+           3       1000000.4
+           3       1000000.6
+           3       1000000.4
+           3       1000000.6
+           3       1000000.4
+           3       1000000.6
+           4       1000000.3
+           4       1000000.2
+           4       1000000.4
+           4       1000000.2
+           4       1000000.4
+           4       1000000.2
+           4       1000000.4
+           4       1000000.2
+           4       1000000.4
+           4       1000000.2
+           4       1000000.4
+           4       1000000.2
+           4       1000000.4
+           4       1000000.2
+           4       1000000.4
+           4       1000000.2
+           4       1000000.4
+           4       1000000.2
+           4       1000000.4
+           4       1000000.2
+           4       1000000.4
+           5       1000000.5
+           5       1000000.4
+           5       1000000.6
+           5       1000000.4
+           5       1000000.6
+           5       1000000.4
+           5       1000000.6
+           5       1000000.4
+           5       1000000.6
+           5       1000000.4
+           5       1000000.6
+           5       1000000.4
+           5       1000000.6
+           5       1000000.4
+           5       1000000.6
+           5       1000000.4
+           5       1000000.6
+           5       1000000.4
+           5       1000000.6
+           5       1000000.4
+           5       1000000.6
+           6       1000000.3
+           6       1000000.2
+           6       1000000.4
+           6       1000000.2
+           6       1000000.4
+           6       1000000.2
+           6       1000000.4
+           6       1000000.2
+           6       1000000.4
+           6       1000000.2
+           6       1000000.4
+           6       1000000.2
+           6       1000000.4
+           6       1000000.2
+           6       1000000.4
+           6       1000000.2
+           6       1000000.4
+           6       1000000.2
+           6       1000000.4
+           6       1000000.2
+           6       1000000.4
+           7       1000000.5
+           7       1000000.4
+           7       1000000.6
+           7       1000000.4
+           7       1000000.6
+           7       1000000.4
+           7       1000000.6
+           7       1000000.4
+           7       1000000.6
+           7       1000000.4
+           7       1000000.6
+           7       1000000.4
+           7       1000000.6
+           7       1000000.4
+           7       1000000.6
+           7       1000000.4
+           7       1000000.6
+           7       1000000.4
+           7       1000000.6
+           7       1000000.4
+           7       1000000.6
+           8       1000000.3
+           8       1000000.2
+           8       1000000.4
+           8       1000000.2
+           8       1000000.4
+           8       1000000.2
+           8       1000000.4
+           8       1000000.2
+           8       1000000.4
+           8       1000000.2
+           8       1000000.4
+           8       1000000.2
+           8       1000000.4
+           8       1000000.2
+           8       1000000.4
+           8       1000000.2
+           8       1000000.4
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diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs05.dat b/venv/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs05.dat
new file mode 100644
index 0000000000000000000000000000000000000000..fe11c40b5f51aefc81d4d1501a74e627f2b2d992
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs05.dat
@@ -0,0 +1,1869 @@
+NIST/ITL StRD 
+Dataset Name:   SmLs05   (SmLs05.dat)
+
+
+File Format:    ASCII
+                Certified Values   (lines 41 to 47)
+                Data               (lines 61 to 1869) 
+
+
+Procedure:      Analysis of Variance
+
+
+Reference:      Simon, Stephen D. and Lesage, James P. (1989).
+                "Assessing the Accuracy of ANOVA Calculations in
+                Statistical Software".
+                Computational Statistics & Data Analysis, 8, pp. 325-332.
+
+
+Data:           1 Factor
+                9 Treatments
+                201 Replicates/Cell
+                1809 Observations
+                7 Constant Leading Digits
+                Average Level of Difficulty
+                Generated Data
+
+
+Model:          10 Parameters (mu,tau_1, ... , tau_9)
+                y_{ij} = mu + tau_i + epsilon_{ij}
+
+
+
+
+
+
+Certified Values:
+
+Source of                  Sums of               Mean               
+Variation          df      Squares              Squares            F Statistic
+
+Between Treatment    8 1.60800000000000E+01 2.01000000000000E+00 2.01000000000000E+02
+Within Treatment  1800 1.80000000000000E+01 1.00000000000000E-02
+
+                  Certified R-Squared 4.71830985915493E-01
+
+                  Certified Residual
+                  Standard Deviation  1.00000000000000E-01
+
+
+
+
+
+
+
+
+
+
+
+
+Data:  Treatment   Response
+           1       1000000.4
+           1       1000000.3
+           1       1000000.5
+           1       1000000.3
+           1       1000000.5
+           1       1000000.3
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diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs06.dat b/venv/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs06.dat
new file mode 100644
index 0000000000000000000000000000000000000000..602e4fbdaa26bbb8d95ce78d1f48dbbfa883e7e9
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs06.dat
@@ -0,0 +1,18069 @@
+NIST/ITL StRD 
+Dataset Name:   SmLs06   (SmLs06.dat)
+
+
+File Format:    ASCII
+                Certified Values   (lines 41 to 47)
+                Data               (lines 61 to 18069) 
+
+
+Procedure:      Analysis of Variance
+
+
+Reference:      Simon, Stephen D. and Lesage, James P. (1989).
+                "Assessing the Accuracy of ANOVA Calculations in
+                Statistical Software".
+                Computational Statistics & Data Analysis, 8, pp. 325-332.
+
+
+Data:           1 Factor
+                9 Treatments
+                2001 Replicates/Cell
+                18009 Observations
+                7 Constant Leading Digits
+                Average Level of Difficulty
+                Generated Data
+
+
+Model:          10 Parameters (mu,tau_1, ... , tau_9)
+                y_{ij} = mu + tau_i + epsilon_{ij}
+
+
+
+
+
+
+Certified Values:
+
+Source of                  Sums of               Mean               
+Variation          df      Squares              Squares             F Statistic
+
+Between Treatment     8 1.60080000000000E+02 2.00100000000000E+01 2.00100000000000E+03
+Within Treatment  18000 1.80000000000000E+02 1.00000000000000E-02
+
+                  Certified R-Squared 4.70712773465067E-01
+
+                  Certified Residual
+                  Standard Deviation  1.00000000000000E-01
+
+
+
+
+
+
+
+
+
+
+
+
+Data:  Treatment   Response
+           1       1000000.4
+           1       1000000.3
+           1       1000000.5
+           1       1000000.3
+           1       1000000.5
+           1       1000000.3
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diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs07.dat b/venv/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs07.dat
new file mode 100644
index 0000000000000000000000000000000000000000..deeac955e65ffaf55838568baa54951efaf2662b
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs07.dat
@@ -0,0 +1,249 @@
+NIST/ITL StRD 
+Dataset Name:   SmLs07   (SmLs07.dat)
+
+
+File Format:    ASCII
+                Certified Values   (lines 41 to 47)
+                Data               (lines 61 to 249) 
+
+
+Procedure:      Analysis of Variance
+
+
+Reference:      Simon, Stephen D. and Lesage, James P. (1989).
+                "Assessing the Accuracy of ANOVA Calculations in
+                Statistical Software".
+                Computational Statistics & Data Analysis, 8, pp. 325-332.
+
+
+Data:           1 Factor
+                9 Treatments
+                21 Replicates/Cell
+                189 Observations
+                13 Constant Leading Digits
+                Higher Level of Difficulty
+                Generated Data
+
+
+Model:          10 Parameters (mu,tau_1, ... , tau_9)
+                y_{ij} = mu + tau_i + epsilon_{ij}
+
+
+
+
+
+
+Certified Values:
+
+Source of                  Sums of               Mean               
+Variation          df      Squares              Squares            F Statistic
+
+Between Treatment   8 1.68000000000000E+00 2.10000000000000E-01 2.10000000000000E+01
+Within Treatment  180 1.80000000000000E+00 1.00000000000000E-02
+
+                  Certified R-Squared 4.82758620689655E-01
+
+                  Certified Residual
+                  Standard Deviation  1.00000000000000E-01
+
+
+
+
+
+
+
+
+
+
+
+
+Data:  Treatment   Response
+           1    1000000000000.4
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           2    1000000000000.3
+           2    1000000000000.2
+           2    1000000000000.4
+           2    1000000000000.2
+           2    1000000000000.4
+           2    1000000000000.2
+           2    1000000000000.4
+           2    1000000000000.2
+           2    1000000000000.4
+           2    1000000000000.2
+           2    1000000000000.4
+           2    1000000000000.2
+           2    1000000000000.4
+           2    1000000000000.2
+           2    1000000000000.4
+           2    1000000000000.2
+           2    1000000000000.4
+           2    1000000000000.2
+           2    1000000000000.4
+           2    1000000000000.2
+           2    1000000000000.4
+           3    1000000000000.5
+           3    1000000000000.4
+           3    1000000000000.6
+           3    1000000000000.4
+           3    1000000000000.6
+           3    1000000000000.4
+           3    1000000000000.6
+           3    1000000000000.4
+           3    1000000000000.6
+           3    1000000000000.4
+           3    1000000000000.6
+           3    1000000000000.4
+           3    1000000000000.6
+           3    1000000000000.4
+           3    1000000000000.6
+           3    1000000000000.4
+           3    1000000000000.6
+           3    1000000000000.4
+           3    1000000000000.6
+           3    1000000000000.4
+           3    1000000000000.6
+           4    1000000000000.3
+           4    1000000000000.2
+           4    1000000000000.4
+           4    1000000000000.2
+           4    1000000000000.4
+           4    1000000000000.2
+           4    1000000000000.4
+           4    1000000000000.2
+           4    1000000000000.4
+           4    1000000000000.2
+           4    1000000000000.4
+           4    1000000000000.2
+           4    1000000000000.4
+           4    1000000000000.2
+           4    1000000000000.4
+           4    1000000000000.2
+           4    1000000000000.4
+           4    1000000000000.2
+           4    1000000000000.4
+           4    1000000000000.2
+           4    1000000000000.4
+           5    1000000000000.5
+           5    1000000000000.4
+           5    1000000000000.6
+           5    1000000000000.4
+           5    1000000000000.6
+           5    1000000000000.4
+           5    1000000000000.6
+           5    1000000000000.4
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+           5    1000000000000.4
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+           5    1000000000000.4
+           5    1000000000000.6
+           6    1000000000000.3
+           6    1000000000000.2
+           6    1000000000000.4
+           6    1000000000000.2
+           6    1000000000000.4
+           6    1000000000000.2
+           6    1000000000000.4
+           6    1000000000000.2
+           6    1000000000000.4
+           6    1000000000000.2
+           6    1000000000000.4
+           6    1000000000000.2
+           6    1000000000000.4
+           6    1000000000000.2
+           6    1000000000000.4
+           6    1000000000000.2
+           6    1000000000000.4
+           6    1000000000000.2
+           6    1000000000000.4
+           6    1000000000000.2
+           6    1000000000000.4
+           7    1000000000000.5
+           7    1000000000000.4
+           7    1000000000000.6
+           7    1000000000000.4
+           7    1000000000000.6
+           7    1000000000000.4
+           7    1000000000000.6
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+           7    1000000000000.4
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+           7    1000000000000.4
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+           7    1000000000000.4
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+           7    1000000000000.6
+           7    1000000000000.4
+           7    1000000000000.6
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+           7    1000000000000.6
+           8    1000000000000.3
+           8    1000000000000.2
+           8    1000000000000.4
+           8    1000000000000.2
+           8    1000000000000.4
+           8    1000000000000.2
+           8    1000000000000.4
+           8    1000000000000.2
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+           8    1000000000000.2
+           8    1000000000000.4
+           8    1000000000000.2
+           8    1000000000000.4
+           8    1000000000000.2
+           8    1000000000000.4
+           8    1000000000000.2
+           8    1000000000000.4
+           8    1000000000000.2
+           8    1000000000000.4
+           8    1000000000000.2
+           8    1000000000000.4
+           9    1000000000000.5
+           9    1000000000000.4
+           9    1000000000000.6
+           9    1000000000000.4
+           9    1000000000000.6
+           9    1000000000000.4
+           9    1000000000000.6
+           9    1000000000000.4
+           9    1000000000000.6
+           9    1000000000000.4
+           9    1000000000000.6
+           9    1000000000000.4
+           9    1000000000000.6
+           9    1000000000000.4
+           9    1000000000000.6
+           9    1000000000000.4
+           9    1000000000000.6
+           9    1000000000000.4
+           9    1000000000000.6
+           9    1000000000000.4
+           9    1000000000000.6
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs08.dat b/venv/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs08.dat
new file mode 100644
index 0000000000000000000000000000000000000000..c5ee643fb8c6ef849ab8e34352bc60f15c715a45
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs08.dat
@@ -0,0 +1,1869 @@
+NIST/ITL StRD 
+Dataset Name:   SmLs08   (SmLs08.dat)
+
+
+File Format:    ASCII
+                Certified Values   (lines 41 to 47)
+                Data               (lines 61 to 1869) 
+
+
+Procedure:      Analysis of Variance
+
+
+Reference:      Simon, Stephen D. and Lesage, James P. (1989).
+                "Assessing the Accuracy of ANOVA Calculations in
+                Statistical Software".
+                Computational Statistics & Data Analysis, 8, pp. 325-332.
+
+
+Data:           1 Factor
+                9 Treatments
+                201 Replicates/Cell
+                1809 Observations
+                13 Constant Leading Digits
+                Higher Level of Difficulty
+                Generated Data
+
+
+Model:          10 Parameters (mu,tau_1, ... , tau_9)
+                y_{ij} = mu + tau_i + epsilon_{ij}
+
+
+
+
+
+
+Certified Values:
+
+Source of                  Sums of               Mean               
+Variation          df      Squares              Squares              F Statistic
+
+Between Treatment    8 1.60800000000000E+01 2.01000000000000E+00 2.01000000000000E+02
+Within Treatment  1800 1.80000000000000E+01 1.00000000000000E-02
+
+                  Certified R-Squared 4.71830985915493E-01
+
+                  Certified Residual
+                  Standard Deviation  1.00000000000000E-01
+
+
+
+
+
+
+
+
+
+
+
+
+Data:  Treatment   Response
+           1    1000000000000.4
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
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+           1    1000000000000.3
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+           1    1000000000000.3
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+           1    1000000000000.3
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+           1    1000000000000.3
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+           1    1000000000000.3
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+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
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diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs09.dat b/venv/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs09.dat
new file mode 100644
index 0000000000000000000000000000000000000000..887905e355a2a13801f1b004187631f2301f7eef
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs09.dat
@@ -0,0 +1,18069 @@
+NIST/ITL StRD 
+Dataset Name:   SmLs09   (SmLs09.dat)
+
+
+File Format:    ASCII
+                Certified Values   (lines 41 to 47)
+                Data               (lines 61 to 18069) 
+
+
+Procedure:      Analysis of Variance
+
+
+Reference:      Simon, Stephen D. and Lesage, James P. (1989).
+                "Assessing the Accuracy of ANOVA Calculations in
+                Statistical Software".
+                Computational Statistics & Data Analysis, 8, pp. 325-332.
+
+
+Data:           1 Factor
+                9 Treatments
+                2001 Replicates/Cell
+                18009 Observations
+                13 Constant Leading Digits
+                Higher Level of Difficulty
+                Generated Data
+
+
+Model:          10 Parameters (mu,tau_1, ... , tau_9)
+                y_{ij} = mu + tau_i + epsilon_{ij}
+
+
+
+
+
+
+Certified Values:
+
+Source of                  Sums of               Mean               
+Variation          df      Squares              Squares              F Statistic
+
+Between Treatment     8 1.60080000000000E+02 2.00100000000000E+01 2.00100000000000E+03
+Within Treatment  18000 1.80000000000000E+02 1.00000000000000E-02
+
+                  Certified R-Squared 4.70712773465067E-01
+
+                  Certified Residual
+                  Standard Deviation  1.00000000000000E-01
+
+
+
+
+
+
+
+
+
+
+
+
+Data:  Treatment   Response
+           1    1000000000000.4
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
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diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/data/nist_linregress/Norris.dat b/venv/lib/python3.12/site-packages/scipy/stats/tests/data/nist_linregress/Norris.dat
new file mode 100644
index 0000000000000000000000000000000000000000..4bf8ed911cae75824b27e5f5d5e444e17fa8eae8
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/data/nist_linregress/Norris.dat
@@ -0,0 +1,97 @@
+NIST/ITL StRD
+Dataset Name:  Norris (Norris.dat)
+
+File Format:   ASCII
+               Certified Values  (lines 31 to 46)
+               Data              (lines 61 to 96)
+
+Procedure:     Linear Least Squares Regression
+
+Reference:     Norris, J., NIST.  
+               Calibration of Ozone Monitors.
+
+Data:          1 Response Variable (y)
+               1 Predictor Variable (x)
+               36 Observations
+               Lower Level of Difficulty
+               Observed Data
+
+Model:         Linear Class
+               2 Parameters (B0,B1)
+
+               y = B0 + B1*x + e
+
+
+
+               Certified Regression Statistics
+
+                                          Standard Deviation
+     Parameter          Estimate             of Estimate
+
+        B0        -0.262323073774029     0.232818234301152
+        B1         1.00211681802045      0.429796848199937E-03
+
+     Residual
+     Standard Deviation   0.884796396144373
+
+     R-Squared            0.999993745883712
+
+
+               Certified Analysis of Variance Table
+
+Source of Degrees of    Sums of             Mean  
+Variation  Freedom      Squares            Squares           F Statistic
+              
+Regression    1     4255954.13232369   4255954.13232369   5436385.54079785
+Residual     34     26.6173985294224   0.782864662630069
+
+                 
+                                          
+                                          
+                                                           
+
+                            
+                                   
+                                                       
+
+
+
+
+Data:       y          x
+           0.1        0.2
+         338.8      337.4
+         118.1      118.2
+         888.0      884.6
+           9.2       10.1
+         228.1      226.5
+         668.5      666.3
+         998.5      996.3
+         449.1      448.6
+         778.9      777.0
+         559.2      558.2
+           0.3        0.4
+           0.1        0.6
+         778.1      775.5
+         668.8      666.9
+         339.3      338.0
+         448.9      447.5
+          10.8       11.6
+         557.7      556.0
+         228.3      228.1
+         998.0      995.8
+         888.8      887.6
+         119.6      120.2
+           0.3        0.3
+           0.6        0.3
+         557.6      556.8
+         339.3      339.1
+         888.0      887.2
+         998.5      999.0
+         778.9      779.0
+          10.2       11.1
+         117.6      118.3
+         228.9      229.2
+         668.4      669.1
+         449.2      448.9
+           0.2        0.5
+                                   
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/data/rel_breitwigner_pdf_sample_data_ROOT.npy b/venv/lib/python3.12/site-packages/scipy/stats/tests/data/rel_breitwigner_pdf_sample_data_ROOT.npy
new file mode 100644
index 0000000000000000000000000000000000000000..80dde74dcda9a23dcdbf9a2f677eb9c98337b0a7
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/data/rel_breitwigner_pdf_sample_data_ROOT.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:eef4dc702dd8c6e31c18c74e1f81284c3e9ca2ab50282de39c9ad30b7bb8e76d
+size 38624
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/data/studentized_range_mpmath_ref.json b/venv/lib/python3.12/site-packages/scipy/stats/tests/data/studentized_range_mpmath_ref.json
new file mode 100644
index 0000000000000000000000000000000000000000..bb971286cf85b28738a80bacececfb90c2566782
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/data/studentized_range_mpmath_ref.json
@@ -0,0 +1,1499 @@
+{
+  "COMMENT": "!!!!!! THIS FILE WAS AUTOGENERATED BY RUNNING `python studentized_range_mpmath_ref.py` !!!!!!",
+  "moment_data": [
+    {
+      "src_case": {
+        "m": 0,
+        "k": 3,
+        "v": 10,
+        "expected_atol": 1e-09,
+        "expected_rtol": 1e-09
+      },
+      "mp_result": 1.0
+    },
+    {
+      "src_case": {
+        "m": 1,
+        "k": 3,
+        "v": 10,
+        "expected_atol": 1e-09,
+        "expected_rtol": 1e-09
+      },
+      "mp_result": 1.8342745127927962
+    },
+    {
+      "src_case": {
+        "m": 2,
+        "k": 3,
+        "v": 10,
+        "expected_atol": 1e-09,
+        "expected_rtol": 1e-09
+      },
+      "mp_result": 4.567483357831711
+    },
+    {
+      "src_case": {
+        "m": 3,
+        "k": 3,
+        "v": 10,
+        "expected_atol": 1e-09,
+        "expected_rtol": 1e-09
+      },
+      "mp_result": 14.412156886227011
+    },
+    {
+      "src_case": {
+        "m": 4,
+        "k": 3,
+        "v": 10,
+        "expected_atol": 1e-09,
+        "expected_rtol": 1e-09
+      },
+      "mp_result": 56.012250366720444
+    }
+  ],
+  "cdf_data": [
+    {
+      "src_case": {
+        "q": 0.1,
+        "k": 3,
+        "v": 3,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.0027502772229359594
+    },
+    {
+      "src_case": {
+        "q": 0.1,
+        "k": 10,
+        "v": 10,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 2.8544145010066327e-12
+    },
+    {
+      "src_case": {
+        "q": 0.1,
+        "k": 3,
+        "v": 10,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.0027520560662338336
+    },
+    {
+      "src_case": {
+        "q": 0.1,
+        "k": 10,
+        "v": 100,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 9.39089126131273e-13
+    },
+    {
+      "src_case": {
+        "q": 0.1,
+        "k": 3,
+        "v": 20,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.002752437649536182
+    },
+    {
+      "src_case": {
+        "q": 0.1,
+        "k": 10,
+        "v": 50,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 1.0862189999210748e-12
+    },
+    {
+      "src_case": {
+        "q": 0.1,
+        "k": 3,
+        "v": 120,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.002752755744313648
+    },
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+        "expected_rtol": 1e-11
+      },
+      "mp_result": 8.234556126446594e-11
+    },
+    {
+      "src_case": {
+        "q": 0.1,
+        "k": 20,
+        "v": 120,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 9.32929780487562e-26
+    },
+    {
+      "src_case": {
+        "q": 1,
+        "k": 3,
+        "v": 3,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.36083736990527154
+    },
+    {
+      "src_case": {
+        "q": 1,
+        "k": 3,
+        "v": 50,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.4137959132282269
+    },
+    {
+      "src_case": {
+        "q": 1,
+        "k": 3,
+        "v": 20,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.4080239698771056
+    },
+    {
+      "src_case": {
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+        "k": 3,
+        "v": 10,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.398772020275752
+    },
+    {
+      "src_case": {
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+        "v": 120,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.4160873922094346
+    },
+    {
+      "src_case": {
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+        "k": 3,
+        "v": 100,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.4157583991350054
+    },
+    {
+      "src_case": {
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+        "k": 10,
+        "v": 50,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
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+      "mp_result": 0.005210720148451848
+    },
+    {
+      "src_case": {
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+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
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+      "mp_result": 0.02575314059867804
+    },
+    {
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+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
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+      "mp_result": 0.009782573637596617
+    },
+    {
+      "src_case": {
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+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
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+      "mp_result": 0.006818708302379005
+    },
+    {
+      "src_case": {
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+        "v": 100,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.0047089182958790715
+    },
+    {
+      "src_case": {
+        "q": 1,
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+        "v": 120,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
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+      "mp_result": 0.004627085294166373
+    },
+    {
+      "src_case": {
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+        "k": 20,
+        "v": 3,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.0010886280311369462
+    },
+    {
+      "src_case": {
+        "q": 1,
+        "k": 20,
+        "v": 50,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 2.630674470916427e-06
+    },
+    {
+      "src_case": {
+        "q": 1,
+        "k": 20,
+        "v": 10,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 4.121713278199428e-05
+    },
+    {
+      "src_case": {
+        "q": 1,
+        "k": 20,
+        "v": 20,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 9.319506007252685e-06
+    },
+    {
+      "src_case": {
+        "q": 1,
+        "k": 20,
+        "v": 100,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 1.5585754418789747e-06
+    },
+    {
+      "src_case": {
+        "q": 1,
+        "k": 20,
+        "v": 120,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 1.4190335899441991e-06
+    },
+    {
+      "src_case": {
+        "q": 4,
+        "k": 3,
+        "v": 3,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.07185383302009114
+    },
+    {
+      "src_case": {
+        "q": 4,
+        "k": 3,
+        "v": 10,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.050268901219386576
+    },
+    {
+      "src_case": {
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+        "k": 3,
+        "v": 50,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
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+      "mp_result": 0.03321056847176124
+    },
+    {
+      "src_case": {
+        "q": 4,
+        "k": 3,
+        "v": 20,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.04044172384981084
+    },
+    {
+      "src_case": {
+        "q": 4,
+        "k": 3,
+        "v": 100,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.030571365659999617
+    },
+    {
+      "src_case": {
+        "q": 4,
+        "k": 3,
+        "v": 120,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.030120779149073032
+    },
+    {
+      "src_case": {
+        "q": 4,
+        "k": 10,
+        "v": 3,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.17501664247670937
+    },
+    {
+      "src_case": {
+        "q": 4,
+        "k": 10,
+        "v": 10,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.22374394725370736
+    },
+    {
+      "src_case": {
+        "q": 4,
+        "k": 10,
+        "v": 50,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.23246597521020534
+    },
+    {
+      "src_case": {
+        "q": 4,
+        "k": 10,
+        "v": 20,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.23239043677504484
+    },
+    {
+      "src_case": {
+        "q": 4,
+        "k": 10,
+        "v": 100,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.23057775622748988
+    },
+    {
+      "src_case": {
+        "q": 4,
+        "k": 10,
+        "v": 120,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.23012666145240815
+    },
+    {
+      "src_case": {
+        "q": 4,
+        "k": 20,
+        "v": 3,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.2073676639537027
+    },
+    {
+      "src_case": {
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+        "v": 10,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.3245990542431859
+    },
+    {
+      "src_case": {
+        "q": 10,
+        "k": 3,
+        "v": 3,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.0033733228559870584
+    },
+    {
+      "src_case": {
+        "q": 10,
+        "k": 3,
+        "v": 10,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 7.728665739003835e-05
+    },
+    {
+      "src_case": {
+        "q": 4,
+        "k": 20,
+        "v": 20,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.38244500549096866
+    },
+    {
+      "src_case": {
+        "q": 4,
+        "k": 20,
+        "v": 100,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.45434978340834464
+    },
+    {
+      "src_case": {
+        "q": 4,
+        "k": 20,
+        "v": 50,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.43334135870667473
+    },
+    {
+      "src_case": {
+        "q": 10,
+        "k": 3,
+        "v": 100,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 2.159522630228393e-09
+    },
+    {
+      "src_case": {
+        "q": 4,
+        "k": 20,
+        "v": 120,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.45807877248528855
+    },
+    {
+      "src_case": {
+        "q": 10,
+        "k": 3,
+        "v": 50,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 3.5303467191175695e-08
+    },
+    {
+      "src_case": {
+        "q": 10,
+        "k": 3,
+        "v": 20,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 3.121281850105421e-06
+    },
+    {
+      "src_case": {
+        "q": 10,
+        "k": 3,
+        "v": 120,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 1.1901591191700855e-09
+    },
+    {
+      "src_case": {
+        "q": 10,
+        "k": 10,
+        "v": 10,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.0006784051704217357
+    },
+    {
+      "src_case": {
+        "q": 10,
+        "k": 10,
+        "v": 3,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.011845582636101885
+    },
+    {
+      "src_case": {
+        "q": 10,
+        "k": 10,
+        "v": 20,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 3.844183552674918e-05
+    },
+    {
+      "src_case": {
+        "q": 10,
+        "k": 10,
+        "v": 100,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 3.215093171597309e-08
+    },
+    {
+      "src_case": {
+        "q": 10,
+        "k": 10,
+        "v": 50,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 5.125792577534542e-07
+    },
+    {
+      "src_case": {
+        "q": 10,
+        "k": 10,
+        "v": 120,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 1.7759015355532446e-08
+    },
+    {
+      "src_case": {
+        "q": 10,
+        "k": 20,
+        "v": 10,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.0017957646258393628
+    },
+    {
+      "src_case": {
+        "q": 10,
+        "k": 20,
+        "v": 3,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.018534407764819284
+    },
+    {
+      "src_case": {
+        "q": 10,
+        "k": 20,
+        "v": 20,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.00013316083413164858
+    },
+    {
+      "src_case": {
+        "q": 10,
+        "k": 20,
+        "v": 50,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 2.082489228991225e-06
+    },
+    {
+      "src_case": {
+        "q": 10,
+        "k": 20,
+        "v": 100,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 1.3444226792257012e-07
+    },
+    {
+      "src_case": {
+        "q": 10,
+        "k": 20,
+        "v": 120,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 7.446912854228521e-08
+    }
+  ]
+}
\ No newline at end of file
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/test_axis_nan_policy.py b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_axis_nan_policy.py
new file mode 100644
index 0000000000000000000000000000000000000000..2b7f1bccccbe41d1cd40dd7479159f31282be151
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_axis_nan_policy.py
@@ -0,0 +1,1495 @@
+# Many scipy.stats functions support `axis` and `nan_policy` parameters.
+# When the two are combined, it can be tricky to get all the behavior just
+# right. This file contains a suite of common tests for scipy.stats functions
+# that support `axis` and `nan_policy` and additional tests for some associated
+# functions in stats._util.
+
+from itertools import product, combinations_with_replacement, permutations
+import os
+import re
+import pickle
+import pytest
+import warnings
+
+import numpy as np
+from numpy.testing import assert_allclose, assert_equal
+from scipy import stats, special
+from scipy.stats._axis_nan_policy import (_masked_arrays_2_sentinel_arrays,
+                                          SmallSampleWarning,
+                                          too_small_nd_omit, too_small_nd_not_omit,
+                                          too_small_1d_omit, too_small_1d_not_omit)
+from scipy._lib._util import AxisError
+from scipy._lib._array_api import make_xp_test_case
+from scipy.conftest import skip_xp_invalid_arg
+
+
+SCIPY_XSLOW = int(os.environ.get('SCIPY_XSLOW', '0'))
+
+
+def _using_accelerate():
+    config = np.show_config('dicts')
+    return config['Build Dependencies']['blas']['name'].lower() == 'accelerate'
+
+
+RTOL = 1e-6 if _using_accelerate() else 1e-15
+
+
+tolerance_overrides = {stats.epps_singleton_2samp: 1e-10}
+
+
+def unpack_ttest_result(res):
+    low, high = res.confidence_interval()
+    return (res.statistic, res.pvalue, res.df, res._standard_error,
+            res._estimate, low, high)
+
+
+def _get_ttest_ci(ttest):
+    # get a function that returns the CI bounds of provided `ttest`
+    def ttest_ci(*args, **kwargs):
+        res = ttest(*args, **kwargs)
+        return res.confidence_interval()
+    return ttest_ci
+
+
+def xp_mean_1samp(*args, **kwargs):
+    kwargs.pop('_no_deco', None)
+    return stats._stats_py._xp_mean(*args, **kwargs)
+
+
+def xp_mean_2samp(*args, **kwargs):
+    kwargs.pop('_no_deco', None)
+    weights = args[1]
+    return stats._stats_py._xp_mean(args[0], *args[2:], weights=weights, **kwargs)
+
+
+def xp_var(*args, **kwargs):
+    kwargs.pop('_no_deco', None)
+    return stats._stats_py._xp_var(*args, **kwargs)
+
+
+def gstd(*args, **kwargs):
+    kwargs.pop('_no_deco', None)
+    return stats.gstd(*args, **kwargs)
+
+
+def combine_pvalues_weighted(*args, **kwargs):
+    return stats.combine_pvalues(args[0], *args[2:], weights=args[1],
+                                 method='stouffer', **kwargs)
+
+
+def weightedtau_weighted(x, y, rank, **kwargs):
+    axis = kwargs.get('axis', 0)
+    nan_policy = kwargs.get('nan_policy', 'propagate')
+    rank = stats.rankdata(rank, axis=axis, nan_policy=nan_policy)
+    return stats.weightedtau(x, y, rank, **kwargs)
+
+
+def boxcox_llf(data, lmb, axis=0, _no_deco=False, **kwargs):
+    if _no_deco:
+        return stats._morestats._boxcox_llf(data, lmb=lmb, axis=axis)
+    return stats.boxcox_llf(lmb, data, axis=axis, **kwargs)
+
+
+def yeojohnson_llf(data, lmb, axis=0, _no_deco=False, **kwargs):
+    if _no_deco:
+        return stats._morestats._yeojohnson_llf(data, lmb=lmb, axis=axis)
+    return stats.yeojohnson_llf(lmb, data, axis=axis, **kwargs)
+
+
+def kendalltau(*args, _no_deco=False, **kwargs):
+    if _no_deco:
+        return stats._stats_py._kendalltau(*args, _no_deco=_no_deco, **kwargs)
+    return stats.kendalltau(*args, **kwargs)
+
+
+axis_nan_policy_cases = [
+    # function, args, kwds, number of samples, number of outputs,
+    # ... paired, unpacker function
+    # args, kwds typically aren't needed; just showing that they work
+    (stats.kruskal, tuple(), dict(), 3, 2, False, None),  # 4 samples is slow
+    (stats.ranksums, ('less',), dict(), 2, 2, False, None),
+    (stats.mannwhitneyu, tuple(), {'method': 'asymptotic'}, 2, 3, False,
+     lambda res: (res.statistic, res.pvalue, res.zstatistic)),
+    (stats.mannwhitneyu, tuple(), {'method': 'auto'}, 2, 2, False, None),
+    (stats.wilcoxon, ('pratt',), {'mode': 'auto'}, 2, 2, True,
+     lambda res: (res.statistic, res.pvalue)),
+    (stats.wilcoxon, tuple(), dict(), 1, 2, True,
+     lambda res: (res.statistic, res.pvalue)),
+    (stats.wilcoxon, tuple(), {'method': 'asymptotic'}, 1, 3, True,
+     lambda res: (res.statistic, res.pvalue, res.zstatistic)),
+    (stats.gmean, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.hmean, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.pmean, (1.42,), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.trim_mean, (0.05,), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.sem, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.iqr, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.kurtosis, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.skew, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.kstat, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.kstatvar, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.moment, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.moment, tuple(), dict(order=[1, 2]), 1, 2, False, None),
+    (stats.jarque_bera, tuple(), dict(), 1, 2, False, None),
+    (stats.ttest_1samp, (np.array([0]),), dict(), 1, 7, False,
+     unpack_ttest_result),
+    (stats.ttest_rel, tuple(), dict(), 2, 7, True, unpack_ttest_result),
+    (stats.ttest_ind, tuple(), dict(), 2, 7, False, unpack_ttest_result),
+    (_get_ttest_ci(stats.ttest_1samp), (0,), dict(), 1, 2, False, None),
+    (_get_ttest_ci(stats.ttest_rel), tuple(), dict(), 2, 2, True, None),
+    (_get_ttest_ci(stats.ttest_ind), tuple(), dict(), 2, 2, False, None),
+    (stats.mode, tuple(), dict(), 1, 2, True, lambda x: (x.mode, x.count)),
+    (stats.differential_entropy, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.variation, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.friedmanchisquare, tuple(), dict(), 3, 2, True, None),
+    (stats.brunnermunzel, tuple(), dict(distribution='normal'), 2, 2, False, None),
+    (stats.mood, tuple(), {}, 2, 2, False, None),
+    (stats.shapiro, tuple(), {}, 1, 2, False, None),
+    (stats.ks_1samp, (special.ndtr,), dict(), 1, 4, False,
+     lambda res: (*res, res.statistic_location, res.statistic_sign)),
+    (stats.ks_1samp, (special.ndtr,), dict(alternative='greater'), 1, 4, False,
+     lambda res: (*res, res.statistic_location, res.statistic_sign)),
+    (stats.ks_1samp, (special.ndtr,), dict(alternative='less'), 1, 4, False,
+     lambda res: (*res, res.statistic_location, res.statistic_sign)),
+    (stats.ks_2samp, tuple(), dict(), 2, 4, False,
+     lambda res: (*res, res.statistic_location, res.statistic_sign)),
+    (stats.kstest, (special.ndtr,), dict(), 1, 4, False,
+     lambda res: (*res, res.statistic_location, res.statistic_sign)),
+    (stats.kstest, tuple(), dict(), 2, 4, False,
+     lambda res: (*res, res.statistic_location, res.statistic_sign)),
+    (stats.levene, tuple(), {}, 2, 2, False, None),
+    (stats.fligner, tuple(), {'center': 'trimmed', 'proportiontocut': 0.01},
+     2, 2, False, None),
+    (stats.ansari, tuple(), {}, 2, 2, False, None),
+    (stats.entropy, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.entropy, tuple(), dict(), 2, 1, True, lambda x: (x,)),
+    (stats.skewtest, tuple(), dict(), 1, 2, False, None),
+    (stats.kurtosistest, tuple(), dict(), 1, 2, False, None),
+    (stats.normaltest, tuple(), dict(), 1, 2, False, None),
+    (stats.cramervonmises, (special.ndtr,), dict(), 1, 2, False,
+     lambda res: (res.statistic, res.pvalue)),
+    (stats.cramervonmises_2samp, tuple(), dict(method='asymptotic'), 2, 2, False,
+     lambda res: (res.statistic, res.pvalue)),
+    (stats.epps_singleton_2samp, tuple(), dict(), 2, 2, False, None),
+    (stats.bartlett, tuple(), {}, 2, 2, False, None),
+    (stats.tmean, tuple(), {}, 1, 1, False, lambda x: (x,)),
+    (stats.tvar, tuple(), {}, 1, 1, False, lambda x: (x,)),
+    (stats.tmin, tuple(), {}, 1, 1, False, lambda x: (x,)),
+    (stats.tmax, tuple(), {}, 1, 1, False, lambda x: (x,)),
+    (stats.tstd, tuple(), {}, 1, 1, False, lambda x: (x,)),
+    (stats.tsem, tuple(), {}, 1, 1, False, lambda x: (x,)),
+    (stats.circmean, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.circvar, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.circstd, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.f_oneway, tuple(), {}, 2, 2, False, None),
+    (stats.f_oneway, tuple(), {'equal_var': False}, 2, 2, False, None),
+    (stats.alexandergovern, tuple(), {}, 2, 2, False,
+     lambda res: (res.statistic, res.pvalue)),
+    (stats.combine_pvalues, tuple(), {}, 1, 2, False, None),
+    (stats.lmoment, tuple(), dict(), 1, 4, False, lambda x: tuple(x)),
+    (combine_pvalues_weighted, tuple(), {}, 2, 2, True, None),
+    (xp_mean_1samp, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (xp_mean_2samp, tuple(), dict(), 2, 1, True, lambda x: (x,)),
+    (xp_var, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.chatterjeexi, tuple(), dict(), 2, 2, True,
+     lambda res: (res.statistic, res.pvalue)),
+    (stats.spearmanrho, tuple(), dict(), 2, 2, True,
+     lambda res: (res.statistic, res.pvalue)),
+    (stats.pointbiserialr, tuple(), dict(), 2, 3, True,
+     lambda res: (res.statistic, res.pvalue, res.correlation)),
+    (kendalltau, tuple(), dict(), 2, 3, True,
+     lambda res: (res.statistic, res.pvalue, res.correlation)),
+    (stats.weightedtau, tuple(), dict(), 2, 3, True,
+     lambda res: (res.statistic, res.pvalue, res.correlation)),
+    (weightedtau_weighted, tuple(), dict(), 3, 3, True,
+     lambda res: (res.statistic, res.pvalue, res.correlation)),
+    (stats.linregress, tuple(), dict(), 2, 6, True,
+     lambda res: tuple(res) + (res.intercept_stderr,)),
+    (stats.theilslopes, tuple(), dict(), 2, 4, True, tuple),
+    (stats.theilslopes, tuple(), dict(), 1, 4, True, tuple),
+    (stats.theilslopes, tuple(), dict(method='joint'), 2, 4, True, tuple),
+    (stats.siegelslopes, tuple(), dict(), 2, 2, True, tuple),
+    (stats.siegelslopes, tuple(), dict(), 1, 2, True, tuple),
+    (stats.siegelslopes, tuple(), dict(method='hierarchical'), 2, 2, True, tuple),
+    (gstd, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.power_divergence, tuple(), dict(), 1, 2, False, None),
+    (stats.chisquare, tuple(), dict(), 1, 2, False, None),
+    (stats.median_abs_deviation, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (boxcox_llf, tuple(), dict(lmb=1.5), 1, 1, False, lambda x: (x,)),
+    (yeojohnson_llf, tuple(), dict(lmb=1.5), 1, 1, False, lambda x: (x,)),
+    (stats.expectile, (0.4,), dict(), 1, 1, False, lambda x: (x,)),
+]
+
+# If the message is one of those expected, put nans in
+# appropriate places of `statistics` and `pvalues`
+too_small_messages = {"Degrees of freedom <= 0 for slice",
+                      "x and y should have at least 5 elements",
+                      "Data must be at least length 3",
+                      "The sample must contain at least two",
+                      "x and y must contain at least two",
+                      "division by zero",
+                      "Mean of empty slice",
+                      "Data passed to ks_2samp must not be empty",
+                      "Not enough test observations",
+                      "Not enough other observations",
+                      "Not enough observations.",
+                      "At least one observation is required",
+                      "zero-size array to reduction operation maximum",
+                      "`x` and `y` must be of nonzero size.",
+                      "The exact distribution of the Wilcoxon test",
+                      "Data input must not be empty",
+                      "Window length (0) must be positive and less",
+                      "Window length (1) must be positive and less",
+                      "Window length (2) must be positive and less",
+                      "`skewtest` requires at least",
+                      "`kurtosistest` requires at least",
+                      "attempt to get argmax of an empty sequence",
+                      "No array values within given limits",
+                      "Input sample size must be greater than one.",
+                      "At least one slice along `axis` has zero length",
+                      "One or more sample arguments is too small",
+                      "invalid value encountered",
+                      "divide by zero encountered",
+                      "`x` and `y` must have length at least 2.",
+                      "Inputs must not be empty.",
+                      "All `x` coordinates are identical.",
+}
+
+# If the message is one of these, results of the function may be inaccurate,
+# but NaNs are not to be placed
+inaccuracy_messages = {"Precision loss occurred in moment calculation",
+                       "Sample size too small for normal approximation."}
+
+# For some functions, nan_policy='propagate' should not just return NaNs
+override_propagate_funcs = {stats.mode, weightedtau_weighted, stats.weightedtau}
+
+# For some functions, empty arrays produce non-NaN results
+empty_special_case_funcs = {stats.entropy, stats.chisquare, stats.power_divergence}
+
+# Some functions don't follow the usual "too small" warning rules
+too_small_special_case_funcs = {stats.entropy, stats.chisquare, stats.power_divergence}
+
+def _mixed_data_generator(n_samples, n_repetitions, axis, rng,
+                          paired=False):
+    # generate random samples to check the response of hypothesis tests to
+    # samples with different (but broadcastable) shapes and various
+    # nan patterns (e.g. all nans, some nans, no nans) along axis-slices
+
+    data = []
+    for i in range(n_samples):
+        n_patterns = 6  # number of distinct nan patterns
+        n_obs = 20 if paired else 20 + i  # observations per axis-slice
+        x = np.ones((n_repetitions, n_patterns, n_obs)) * np.nan
+
+        for j in range(n_repetitions):
+            samples = x[j, :, :]
+
+            # case 0: axis-slice with all nans (0 reals)
+            # cases 1-3: axis-slice with 1-3 reals (the rest nans)
+            # case 4: axis-slice with mostly (all but two) reals
+            # case 5: axis slice with all reals
+            for k, n_reals in enumerate([0, 1, 2, 3, n_obs-2, n_obs]):
+                # for cases 1-3, need paired nansw  to be in the same place
+                indices = rng.permutation(n_obs)[:n_reals]
+                samples[k, indices] = rng.random(size=n_reals)
+
+            # permute the axis-slices just to show that order doesn't matter
+            samples[:] = rng.permutation(samples, axis=0)
+
+        # For multi-sample tests, we want to test broadcasting and check
+        # that nan policy works correctly for each nan pattern for each input.
+        # This takes care of both simultaneously.
+        new_shape = [n_repetitions] + [1]*n_samples + [n_obs]
+        new_shape[1 + i] = 6
+        x = x.reshape(new_shape)
+
+        x = np.moveaxis(x, -1, axis)
+        data.append(x)
+    return data
+
+
+def _homogeneous_data_generator(n_samples, n_repetitions, axis, rng,
+                                paired=False, all_nans=True):
+    # generate random samples to check the response of hypothesis tests to
+    # samples with different (but broadcastable) shapes and homogeneous
+    # data (all nans or all finite)
+    data = []
+    for i in range(n_samples):
+        n_obs = 20 if paired else 20 + i  # observations per axis-slice
+        shape = [n_repetitions] + [1]*n_samples + [n_obs]
+        shape[1 + i] = 2
+        x = np.ones(shape) * np.nan if all_nans else rng.random(shape)
+        x = np.moveaxis(x, -1, axis)
+        data.append(x)
+    return data
+
+
+def nan_policy_1d(hypotest, data1d, unpacker, *args, n_outputs=2,
+                  nan_policy='raise', paired=False, _no_deco=True, **kwds):
+    # Reference implementation for how `nan_policy` should work for 1d samples
+
+    if nan_policy == 'raise':
+        for sample in data1d:
+            if np.any(np.isnan(sample)):
+                raise ValueError("The input contains nan values")
+
+    elif (nan_policy == 'propagate'
+          and hypotest not in override_propagate_funcs):
+        # For all hypothesis tests tested, returning nans is the right thing.
+        # But many hypothesis tests don't propagate correctly (e.g. they treat
+        # np.nan the same as np.inf, which doesn't make sense when ranks are
+        # involved) so override that behavior here.
+        for sample in data1d:
+            if np.any(np.isnan(sample)):
+                return np.full(n_outputs, np.nan)
+
+    elif nan_policy == 'omit':
+        # manually omit nans (or pairs in which at least one element is nan)
+        if not paired:
+            data1d = [sample[~np.isnan(sample)] for sample in data1d]
+        else:
+            nan_mask = np.isnan(data1d[0])
+            for sample in data1d[1:]:
+                nan_mask = np.logical_or(nan_mask, np.isnan(sample))
+            data1d = [sample[~nan_mask] for sample in data1d]
+
+    return unpacker(hypotest(*data1d, *args, _no_deco=_no_deco, **kwds))
+
+
+# These three warnings are intentional
+# For `wilcoxon` when the sample size < 50
+@pytest.mark.filterwarnings('ignore:Sample size too small for normal:UserWarning')
+# `kurtosistest` and `normaltest` when sample size < 20
+@pytest.mark.filterwarnings('ignore:`kurtosistest` p-value may be:UserWarning')
+# `foneway`
+@pytest.mark.filterwarnings('ignore:all input arrays have length 1.:RuntimeWarning')
+
+# The rest of these may or may not be desirable. They need further investigation
+# to determine whether the function's decorator should define `too_small.
+# `bartlett`, `tvar`, `tstd`, `tsem`
+@pytest.mark.filterwarnings('ignore:Degrees of freedom <= 0 for slice:RuntimeWarning')
+# kstat, kstatvar, ttest_1samp, ttest_rel, ttest_ind, ttest_ci, brunnermunzel
+# mood, levene, fligner, bartlett
+@pytest.mark.filterwarnings('ignore:Invalid value encountered in:RuntimeWarning')
+# kstatvar, ttest_1samp, ttest_rel, ttest_ci, brunnermunzel, levene, bartlett
+@pytest.mark.filterwarnings('ignore:divide by zero encountered:RuntimeWarning')
+
+@pytest.mark.parametrize(("hypotest", "args", "kwds", "n_samples", "n_outputs",
+                          "paired", "unpacker"), axis_nan_policy_cases)
+@pytest.mark.parametrize(("nan_policy"), ("propagate", "omit", "raise"))
+@pytest.mark.parametrize(("axis"), (1,))
+@pytest.mark.parametrize(("data_generator"), ("mixed",))
+def test_axis_nan_policy_fast(hypotest, args, kwds, n_samples, n_outputs,
+                              paired, unpacker, nan_policy, axis,
+                              data_generator):
+    if hypotest in {stats.kruskal} and not SCIPY_XSLOW:
+        pytest.skip("Too slow.")
+    _axis_nan_policy_test(hypotest, args, kwds, n_samples, n_outputs, paired,
+                          unpacker, nan_policy, axis, data_generator)
+
+
+if SCIPY_XSLOW:
+    # Takes O(1 min) to run, and even skipping with the `xslow` decorator takes
+    # about 3 sec because this is >3,000 tests. So ensure pytest doesn't see
+    # them at all unless `SCIPY_XSLOW` is defined.
+
+    # These three warnings are intentional
+    # For `wilcoxon` when the sample size < 50
+    @pytest.mark.filterwarnings('ignore:Sample size too small for normal:UserWarning')
+    # `kurtosistest` and `normaltest` when sample size < 20
+    @pytest.mark.filterwarnings('ignore:`kurtosistest` p-value may be:UserWarning')
+    # `foneway`
+    @pytest.mark.filterwarnings('ignore:all input arrays have length 1.:RuntimeWarning')
+
+    # The rest of these may or may not be desirable. They need further investigation
+    # to determine whether the function's decorator should define `too_small.
+    # `bartlett`, `tvar`, `tstd`, `tsem`
+    @pytest.mark.filterwarnings('ignore:Degrees of freedom <= 0 for:RuntimeWarning')
+    # kstat, kstatvar, ttest_1samp, ttest_rel, ttest_ind, ttest_ci, brunnermunzel
+    # mood, levene, fligner, bartlett
+    @pytest.mark.filterwarnings('ignore:Invalid value encountered in:RuntimeWarning')
+    # kstatvar, ttest_1samp, ttest_rel, ttest_ci, brunnermunzel, levene, bartlett
+    @pytest.mark.filterwarnings('ignore:divide by zero encountered:RuntimeWarning')
+
+    @pytest.mark.parametrize(("hypotest", "args", "kwds", "n_samples", "n_outputs",
+                              "paired", "unpacker"), axis_nan_policy_cases)
+    @pytest.mark.parametrize(("nan_policy"), ("propagate", "omit", "raise"))
+    @pytest.mark.parametrize(("axis"), list(range(-3, 3)))
+    @pytest.mark.parametrize(("data_generator"),
+                             ("all_nans", "all_finite", "mixed"))
+    def test_axis_nan_policy_full(hypotest, args, kwds, n_samples, n_outputs,
+                                  paired, unpacker, nan_policy, axis,
+                                  data_generator):
+        _axis_nan_policy_test(hypotest, args, kwds, n_samples, n_outputs, paired,
+                              unpacker, nan_policy, axis, data_generator)
+
+
+def _axis_nan_policy_test(hypotest, args, kwds, n_samples, n_outputs, paired,
+                          unpacker, nan_policy, axis, data_generator):
+    # Tests the 1D and vectorized behavior of hypothesis tests against a
+    # reference implementation (nan_policy_1d with np.ndenumerate)
+
+    # Some hypothesis tests return a non-iterable that needs an `unpacker` to
+    # extract the statistic and p-value. For those that don't:
+    if not unpacker:
+        def unpacker(res):
+            return res
+
+    rng = np.random.default_rng(0)
+
+    # Generate multi-dimensional test data with all important combinations
+    # of patterns of nans along `axis`
+    n_repetitions = 3  # number of repetitions of each pattern
+    data_gen_kwds = {'n_samples': n_samples, 'n_repetitions': n_repetitions,
+                     'axis': axis, 'rng': rng, 'paired': paired}
+    if data_generator == 'mixed':
+        inherent_size = 6  # number of distinct types of patterns
+        data = _mixed_data_generator(**data_gen_kwds)
+    elif data_generator == 'all_nans':
+        inherent_size = 2  # hard-coded in _homogeneous_data_generator
+        data_gen_kwds['all_nans'] = True
+        data = _homogeneous_data_generator(**data_gen_kwds)
+    elif data_generator == 'all_finite':
+        inherent_size = 2  # hard-coded in _homogeneous_data_generator
+        data_gen_kwds['all_nans'] = False
+        data = _homogeneous_data_generator(**data_gen_kwds)
+
+    output_shape = [n_repetitions] + [inherent_size]*n_samples
+
+    # To generate reference behavior to compare against, loop over the axis-
+    # slices in data. Make indexing easier by moving `axis` to the end and
+    # broadcasting all samples to the same shape.
+    data_b = [np.moveaxis(sample, axis, -1) for sample in data]
+    data_b = [np.broadcast_to(sample, output_shape + [sample.shape[-1]])
+              for sample in data_b]
+    res_1d = np.zeros(output_shape + [n_outputs])
+
+    for i, _ in np.ndenumerate(np.zeros(output_shape)):
+        data1d = [sample[i] for sample in data_b]
+        contains_nan = any([np.isnan(sample).any() for sample in data1d])
+
+        # Take care of `nan_policy='raise'`.
+        # Afterward, the 1D part of the test is over
+        message = "The input contains nan values"
+        if nan_policy == 'raise' and contains_nan:
+            with pytest.raises(ValueError, match=message):
+                nan_policy_1d(hypotest, data1d, unpacker, *args,
+                              n_outputs=n_outputs,
+                              nan_policy=nan_policy,
+                              paired=paired, _no_deco=True, **kwds)
+
+            with pytest.raises(ValueError, match=message):
+                hypotest(*data1d, *args, nan_policy=nan_policy, **kwds)
+
+            continue
+
+        # Take care of `nan_policy='propagate'` and `nan_policy='omit'`
+
+        # Get results of simple reference implementation
+        try:
+            res_1da = nan_policy_1d(hypotest, data1d, unpacker, *args,
+                                    n_outputs=n_outputs,
+                                    nan_policy=nan_policy,
+                                    paired=paired, _no_deco=True, **kwds)
+        except (ValueError, RuntimeWarning, ZeroDivisionError, UserWarning) as ea:
+            ea_str = str(ea)
+            if any([str(ea_str).startswith(msg) for msg in too_small_messages]):
+                res_1da = np.full(n_outputs, np.nan)
+            else:
+                raise
+
+        # Get results of public function with 1D slices
+        # Should warn for all slices
+        if (nan_policy == 'omit' and data_generator == "all_nans"
+              and hypotest not in too_small_special_case_funcs):
+            with pytest.warns(SmallSampleWarning, match=too_small_1d_omit):
+                res = hypotest(*data1d, *args, nan_policy=nan_policy, **kwds)
+        # warning depends on slice
+        elif (nan_policy == 'omit' and data_generator == "mixed"
+              and hypotest not in too_small_special_case_funcs):
+            with warnings.catch_warnings():
+                warnings.filterwarnings("ignore", too_small_1d_omit, SmallSampleWarning)
+                res = hypotest(*data1d, *args, nan_policy=nan_policy, **kwds)
+        # shouldn't complain if there are no NaNs
+        else:
+            res = hypotest(*data1d, *args, nan_policy=nan_policy, **kwds)
+        res_1db = unpacker(res)
+
+        assert_allclose(res_1db, res_1da, rtol=RTOL)
+        res_1d[i] = res_1db
+
+    res_1d = np.moveaxis(res_1d, -1, 0)
+
+    # Perform a vectorized call to the hypothesis test.
+
+    # If `nan_policy == 'raise'`, check that it raises the appropriate error.
+    # Test is done, so return
+    if nan_policy == 'raise' and not data_generator == "all_finite":
+        message = 'The input contains nan values'
+        with pytest.raises(ValueError, match=message):
+            hypotest(*data, axis=axis, nan_policy=nan_policy, *args, **kwds)
+        return
+
+    # If `nan_policy == 'omit', we might be left with a small sample.
+    # Check for the appropriate warning.
+    if (nan_policy == 'omit' and data_generator in {"all_nans", "mixed"}
+          and hypotest not in too_small_special_case_funcs):
+        with pytest.warns(SmallSampleWarning, match=too_small_nd_omit):
+            res = hypotest(*data, axis=axis, nan_policy=nan_policy, *args, **kwds)
+    else:  # otherwise, there should be no warning
+        res = hypotest(*data, axis=axis, nan_policy=nan_policy, *args, **kwds)
+
+    # Compare against the output against looping over 1D slices
+    res_nd = unpacker(res)
+
+    rtol = max(tolerance_overrides.get(hypotest, RTOL), RTOL)
+    assert_allclose(res_nd, res_1d, rtol=rtol)
+
+# nan should not raise an exception in np.mean()
+# but does on some mips64el systems, triggering failure in some test cases
+# see https://github.com/scipy/scipy/issues/22360
+# and https://github.com/numpy/numpy/issues/23158
+def skip_nan_unexpected_exception():
+    try:
+        # should not raise an exception
+        with np.errstate(all='raise'):
+            x = np.asarray([1, 2, np.nan])
+            np.mean(x)
+    except Exception as e:
+        pytest.skip(f"nan raises unexpected {e.__class__.__name__} in numpy")
+
+@pytest.mark.parametrize(("hypotest", "args", "kwds", "n_samples", "n_outputs",
+                          "paired", "unpacker"), axis_nan_policy_cases)
+@pytest.mark.parametrize(("nan_policy"), ("propagate", "omit", "raise"))
+@pytest.mark.parametrize(("data_generator"),
+                         ("all_nans", "all_finite", "mixed", "empty"))
+def test_axis_nan_policy_axis_is_None(hypotest, args, kwds, n_samples,
+                                      n_outputs, paired, unpacker, nan_policy,
+                                      data_generator):
+    # check for correct behavior when `axis=None`
+    if not unpacker:
+        def unpacker(res):
+            return res
+
+    # skip if nan emits unexpected RuntimeWarning in np.mean()
+    # seen on mips64el, https://github.com/scipy/scipy/issues/22360
+    # Only affects nan_policy "mixed-propagate" for selected hypotests
+    if data_generator=="mixed" and nan_policy=="propagate":
+        # only skip affected hypotests
+        if hypotest.__name__ in ["iqr", "ttest_ci",
+                                 "xp_mean_1samp", "xp_mean_2samp", "xp_var",
+                                 "weightedtau", "weightedtau_weighted"]:
+            skip_nan_unexpected_exception()
+    # all_nans-propagate-ttest_ci is also affected, via scalar multiply
+    if (data_generator=="all_nans" and nan_policy=="propagate"
+        and hypotest.__name__=="ttest_ci"):
+        skip_nan_unexpected_exception()
+    # mixed-omit-xp_var is also affected, via subtract
+    if (data_generator=="mixed" and nan_policy=="omit"
+        and hypotest.__name__=="xp_var"):
+        skip_nan_unexpected_exception()
+
+    rng = np.random.default_rng(0)
+
+    if data_generator == "empty":
+        data = [rng.random((2, 0)) for i in range(n_samples)]
+    else:
+        data = [rng.random((2, 20)) for i in range(n_samples)]
+
+    if data_generator == "mixed":
+        masks = [rng.random((2, 20)) > 0.9 for i in range(n_samples)]
+        for sample, mask in zip(data, masks):
+            sample[mask] = np.nan
+    elif data_generator == "all_nans":
+        data = [sample * np.nan for sample in data]
+
+    data_raveled = [sample.ravel() for sample in data]
+
+    if nan_policy == 'raise' and data_generator not in {"all_finite", "empty"}:
+        message = 'The input contains nan values'
+
+        # check for correct behavior whether or not data is 1d to begin with
+        with pytest.raises(ValueError, match=message):
+            hypotest(*data, axis=None, nan_policy=nan_policy,
+                     *args, **kwds)
+        with pytest.raises(ValueError, match=message):
+            hypotest(*data_raveled, axis=None, nan_policy=nan_policy,
+                     *args, **kwds)
+
+        return
+
+    # behavior of reference implementation with 1d input, public function with 1d
+    # input, and public function with Nd input and `axis=None` should be consistent.
+    # This means:
+    # - If the reference version raises an error or emits a warning, it's because
+    #   the sample is too small, so check that the public function emits an
+    #   appropriate "too small" warning
+    # - Any results returned by the three versions should be the same.
+    with warnings.catch_warnings():  # treat warnings as errors
+        warnings.simplefilter("error")
+
+        ea_str, eb_str, ec_str = None, None, None
+        try:
+            res1da = nan_policy_1d(hypotest, data_raveled, unpacker, *args,
+                                   n_outputs=n_outputs, nan_policy=nan_policy,
+                                   paired=paired, _no_deco=True, **kwds)
+        except (RuntimeWarning, ValueError, ZeroDivisionError, UserWarning) as ea:
+            res1da = None
+            ea_str = str(ea)
+
+        try:
+            res1db = hypotest(*data_raveled, *args, nan_policy=nan_policy, **kwds)
+        except SmallSampleWarning as eb:
+            eb_str = str(eb)
+
+        try:
+            res1dc = hypotest(*data, *args, axis=None, nan_policy=nan_policy, **kwds)
+        except SmallSampleWarning as ec:
+            ec_str = str(ec)
+
+    if ea_str or eb_str or ec_str:  # *if* there is some sort of error or warning
+        # If the reference implemented generated an error or warning, make sure the
+        # message was one of the expected "too small" messages. Note that some
+        # functions don't complain at all without the decorator; that's OK, too.
+        ok_msg = any([str(ea_str).startswith(msg) for msg in too_small_messages])
+        assert (ea_str is None) or ok_msg
+
+        # make sure the wrapped function emits the *intended* warning
+        desired_warnings = {too_small_1d_omit, too_small_1d_not_omit}
+        assert str(eb_str) in desired_warnings
+        assert str(ec_str) in desired_warnings
+
+        with warnings.catch_warnings():  # ignore warnings to get return value
+            warnings.simplefilter("ignore")
+            res1db = hypotest(*data_raveled, *args, nan_policy=nan_policy, **kwds)
+            res1dc = hypotest(*data, *args, axis=None, nan_policy=nan_policy, **kwds)
+
+    # Make sure any results returned by reference/public function are identical
+    # and all attributes are *NumPy* scalars
+    res1db, res1dc = unpacker(res1db), unpacker(res1dc)
+    # changed from 1e-15 solely to appease macosx-x86_64+Accelerate
+    assert_allclose(res1dc, res1db, rtol=2e-14)
+    all_results = list(res1db) + list(res1dc)
+
+    if res1da is not None:
+        # changed from 1e-15 solely to appease macosx-x86_64+Accelerate
+        assert_allclose(res1db, res1da, rtol=2e-14)
+        all_results += list(res1da)
+
+    for item in all_results:
+        assert np.issubdtype(item.dtype, np.number)
+        assert np.isscalar(item)
+
+
+# Test keepdims for:
+#     - Axis negative, positive, None, and tuple
+#     - 1D with no NaNs
+#     - 1D with NaN propagation
+#     - Zero-sized output
+# We're working on making `stats` quieter, but that's not what this test
+# is about. For now, we expect all sorts of warnings here due to small samples.
+@pytest.mark.filterwarnings('ignore::UserWarning')
+@pytest.mark.filterwarnings('ignore::RuntimeWarning')
+@pytest.mark.parametrize("nan_policy", ("omit", "propagate"))
+@pytest.mark.parametrize(("hypotest", "args", "kwds", "n_samples", "n_outputs",
+                          "paired", "unpacker"), axis_nan_policy_cases)
+@pytest.mark.parametrize(
+    ("sample_shape", "axis_cases"),
+    (((2, 3, 3, 4), (None, 0, -1, (0, 2), (1, -1), (3, 1, 2, 0))),
+     ((10, ), (0, -1)),
+     ((20, 0), (0, 1)))
+)
+def test_keepdims(hypotest, args, kwds, n_samples, n_outputs, paired, unpacker,
+                  sample_shape, axis_cases, nan_policy):
+    small_sample_raises = {stats.skewtest, stats.kurtosistest, stats.normaltest,
+                           stats.differential_entropy, stats.epps_singleton_2samp,
+                           stats.shapiro}
+    if sample_shape == (2, 3, 3, 4) and hypotest in small_sample_raises:
+        pytest.skip("Sample too small; test raises error.")
+    if hypotest in {weightedtau_weighted}:
+        pytest.skip("`rankdata` used in testing doesn't support axis tuple.")
+    # test if keepdims parameter works correctly
+    if not unpacker:
+        def unpacker(res):
+            return res
+    rng = np.random.default_rng(0)
+    data = [rng.random(sample_shape) for _ in range(n_samples)]
+    nan_data = [sample.copy() for sample in data]
+    nan_mask = [rng.random(sample_shape) < 0.2 for _ in range(n_samples)]
+    for sample, mask in zip(nan_data, nan_mask):
+        sample[mask] = np.nan
+    for axis in axis_cases:
+        expected_shape = list(sample_shape)
+        if axis is None:
+            expected_shape = np.ones(len(sample_shape))
+        else:
+            if isinstance(axis, int):
+                expected_shape[axis] = 1
+            else:
+                for ax in axis:
+                    expected_shape[ax] = 1
+        expected_shape = tuple(expected_shape)
+        res = unpacker(hypotest(*data, *args, axis=axis, keepdims=True,
+                                **kwds))
+        res_base = unpacker(hypotest(*data, *args, axis=axis, keepdims=False,
+                                     **kwds))
+        nan_res = unpacker(hypotest(*nan_data, *args, axis=axis,
+                                    keepdims=True, nan_policy=nan_policy,
+                                    **kwds))
+        nan_res_base = unpacker(hypotest(*nan_data, *args, axis=axis,
+                                         keepdims=False,
+                                         nan_policy=nan_policy, **kwds))
+        for r, r_base, rn, rn_base in zip(res, res_base, nan_res,
+                                          nan_res_base):
+            assert r.shape == expected_shape
+            r = np.squeeze(r, axis=axis)
+            assert_allclose(r, r_base, atol=1e-16)
+            assert rn.shape == expected_shape
+            rn = np.squeeze(rn, axis=axis)
+            # ideally assert_equal, but `combine_pvalues` failed on 32-bit build
+            assert_allclose(rn, rn_base, atol=1e-16)
+
+
+@pytest.mark.parametrize(("fun", "nsamp"),
+                         [(stats.kstat, 1),
+                          (stats.kstatvar, 1)])
+def test_hypotest_back_compat_no_axis(fun, nsamp):
+    m, n = 8, 9
+
+    rng = np.random.default_rng(0)
+    x = rng.random((nsamp, m, n))
+    res = fun(*x)
+    res2 = fun(*x, _no_deco=True)
+    res3 = fun([xi.ravel() for xi in x])
+    assert_equal(res, res2)
+    assert_equal(res, res3)
+
+
+@pytest.mark.parametrize(("axis"), (0, 1, 2))
+def test_axis_nan_policy_decorated_positional_axis(axis):
+    # Test for correct behavior of function decorated with
+    # _axis_nan_policy_decorator whether `axis` is provided as positional or
+    # keyword argument
+
+    shape = (8, 9, 10)
+    rng = np.random.default_rng(0)
+    x = rng.random(shape)
+    y = rng.random(shape)
+    res1 = stats.mannwhitneyu(x, y, True, 'two-sided', axis)
+    res2 = stats.mannwhitneyu(x, y, True, 'two-sided', axis=axis)
+    assert_equal(res1, res2)
+
+    message = "mannwhitneyu() got multiple values for argument 'axis'"
+    with pytest.raises(TypeError, match=re.escape(message)):
+        stats.mannwhitneyu(x, y, True, 'two-sided', axis, axis=axis)
+
+
+def test_axis_nan_policy_decorated_positional_args():
+    # Test for correct behavior of function decorated with
+    # _axis_nan_policy_decorator when function accepts *args
+
+    shape = (3, 8, 9, 10)
+    rng = np.random.default_rng(0)
+    x = rng.random(shape)
+    x[0, 0, 0, 0] = np.nan
+    stats.kruskal(*x)
+
+    message = "kruskal() got an unexpected keyword argument 'samples'"
+    with pytest.raises(TypeError, match=re.escape(message)):
+        stats.kruskal(samples=x)
+
+    with pytest.raises(TypeError, match=re.escape(message)):
+        stats.kruskal(*x, samples=x)
+
+
+def test_axis_nan_policy_decorated_keyword_samples():
+    # Test for correct behavior of function decorated with
+    # _axis_nan_policy_decorator whether samples are provided as positional or
+    # keyword arguments
+
+    shape = (2, 8, 9, 10)
+    rng = np.random.default_rng(0)
+    x = rng.random(shape)
+    x[0, 0, 0, 0] = np.nan
+    res1 = stats.mannwhitneyu(*x)
+    res2 = stats.mannwhitneyu(x=x[0], y=x[1])
+    assert_equal(res1, res2)
+
+    message = "mannwhitneyu() got multiple values for argument"
+    with pytest.raises(TypeError, match=re.escape(message)):
+        stats.mannwhitneyu(*x, x=x[0], y=x[1])
+
+
+@pytest.mark.parametrize(("hypotest", "args", "kwds", "n_samples", "n_outputs",
+                          "paired", "unpacker"), axis_nan_policy_cases)
+def test_axis_nan_policy_decorated_pickled(hypotest, args, kwds, n_samples,
+                                           n_outputs, paired, unpacker):
+    if "ttest_ci" in hypotest.__name__:
+        pytest.skip("Can't pickle functions defined within functions.")
+
+    rng = np.random.default_rng(0)
+
+    # Some hypothesis tests return a non-iterable that needs an `unpacker` to
+    # extract the statistic and p-value. For those that don't:
+    if not unpacker:
+        def unpacker(res):
+            return res
+
+    data = rng.uniform(size=(n_samples, 2, 30))
+    pickled_hypotest = pickle.dumps(hypotest)
+    unpickled_hypotest = pickle.loads(pickled_hypotest)
+    res1 = unpacker(hypotest(*data, *args, axis=-1, **kwds))
+    res2 = unpacker(unpickled_hypotest(*data, *args, axis=-1, **kwds))
+    assert_allclose(res1, res2, rtol=1e-12)
+
+
+def test_check_empty_inputs():
+    # Test that _check_empty_inputs is doing its job, at least for single-
+    # sample inputs. (Multi-sample functionality is tested below.)
+    # If the input sample is not empty, it should return None.
+    # If the input sample is empty, it should return an array of NaNs or an
+    # empty array of appropriate shape. np.mean is used as a reference for the
+    # output because, like the statistics calculated by these functions,
+    # it works along and "consumes" `axis` but preserves the other axes.
+    for i in range(5):
+        for combo in combinations_with_replacement([0, 1, 2], i):
+            for axis in range(len(combo)):
+                samples = (np.zeros(combo),)
+                output = stats._axis_nan_policy._check_empty_inputs(samples,
+                                                                    axis)
+                if output is not None:
+                    with warnings.catch_warnings():
+                        warnings.filterwarnings(
+                            "ignore", "Mean of empty slice", RuntimeWarning)
+                        warnings.filterwarnings(
+                            "ignore", "invalid value encountered", RuntimeWarning)
+                        reference = samples[0].mean(axis=axis)
+                    np.testing.assert_equal(output, reference)
+
+
+def _check_arrays_broadcastable(arrays, axis):
+    # https://numpy.org/doc/stable/user/basics.broadcasting.html
+    # "When operating on two arrays, NumPy compares their shapes element-wise.
+    # It starts with the trailing (i.e. rightmost) dimensions and works its
+    # way left.
+    # Two dimensions are compatible when
+    # 1. they are equal, or
+    # 2. one of them is 1
+    # ...
+    # Arrays do not need to have the same number of dimensions."
+    # (Clarification: if the arrays are compatible according to the criteria
+    #  above and an array runs out of dimensions, it is still compatible.)
+    # Below, we follow the rules above except ignoring `axis`
+
+    n_dims = max([arr.ndim for arr in arrays])
+    if axis is not None:
+        # convert to negative axis
+        axis = (-n_dims + axis) if axis >= 0 else axis
+
+    for dim in range(1, n_dims+1):  # we'll index from -1 to -n_dims, inclusive
+        if -dim == axis:
+            continue  # ignore lengths along `axis`
+
+        dim_lengths = set()
+        for arr in arrays:
+            if dim <= arr.ndim and arr.shape[-dim] != 1:
+                dim_lengths.add(arr.shape[-dim])
+
+        if len(dim_lengths) > 1:
+            return False
+    return True
+
+
+@pytest.mark.slow
+@pytest.mark.parametrize(("hypotest", "args", "kwds", "n_samples", "n_outputs",
+                          "paired", "unpacker"), axis_nan_policy_cases)
+def test_empty(hypotest, args, kwds, n_samples, n_outputs, paired, unpacker):
+    # test for correct output shape when at least one input is empty
+    if hypotest in {stats.kruskal, stats.friedmanchisquare} and not SCIPY_XSLOW:
+        pytest.skip("Too slow.")
+
+    if hypotest in override_propagate_funcs:
+        reason = "Doesn't follow the usual pattern. Tested separately."
+        pytest.skip(reason=reason)
+
+    if unpacker is None:
+        unpacker = lambda res: (res[0], res[1])  # noqa: E731
+
+    def small_data_generator(n_samples, n_dims):
+
+        def small_sample_generator(n_dims):
+            # return all possible "small" arrays in up to n_dim dimensions
+            for i in n_dims:
+                # "small" means with size along dimension either 0 or 1
+                for combo in combinations_with_replacement([0, 1, 2], i):
+                    yield np.zeros(combo)
+
+        # yield all possible combinations of small samples
+        gens = [small_sample_generator(n_dims) for i in range(n_samples)]
+        yield from product(*gens)
+
+    n_dims = [1, 2, 3]
+    for samples in small_data_generator(n_samples, n_dims):
+
+        # this test is only for arrays of zero size
+        if not any(sample.size == 0 for sample in samples):
+            continue
+
+        max_axis = max(sample.ndim for sample in samples)
+
+        # need to test for all valid values of `axis` parameter, too
+        for axis in range(-max_axis, max_axis):
+
+            try:
+                # After broadcasting, all arrays are the same shape, so
+                # the shape of the output should be the same as a single-
+                # sample statistic. Use np.mean as a reference.
+                concat = stats._axis_nan_policy._broadcast_concatenate(samples, axis,
+                                                                       paired=paired)
+                with warnings.catch_warnings():
+                    warnings.filterwarnings(
+                        "ignore", "Mean of empty slice", RuntimeWarning)
+                    warnings.filterwarnings(
+                        "ignore", "invalid value encountered", RuntimeWarning)
+                    expected = np.mean(concat, axis=axis) * np.nan
+                    mask = np.isnan(expected)
+                    expected = [np.asarray(expected.copy()) for i in range(n_outputs)]
+
+                if hypotest in empty_special_case_funcs:
+                    empty_val = hypotest(*([[]]*len(samples)), *args, **kwds)
+                    empty_val = list(unpacker(empty_val))
+                    for i in range(n_outputs):
+                        expected[i][mask] = empty_val[i]
+
+                if expected[0].size and hypotest not in too_small_special_case_funcs:
+                    message = (too_small_1d_not_omit if max_axis == 1
+                               else too_small_nd_not_omit)
+                    with pytest.warns(SmallSampleWarning, match=message):
+                        res = hypotest(*samples, *args, axis=axis, **kwds)
+                else:
+                    with warnings.catch_warnings():
+                        # f_oneway special case
+                        msg = "all input arrays have length 1"
+                        warnings.filterwarnings("ignore", msg, SmallSampleWarning)
+                        res = hypotest(*samples, *args, axis=axis, **kwds)
+                res = unpacker(res)
+
+                for i in range(n_outputs):
+                    assert_equal(res[i], expected[i])
+
+            except ValueError:
+                # confirm that the arrays truly are not broadcastable
+                assert not _check_arrays_broadcastable(samples,
+                                                       None if paired else axis)
+
+                # confirm that _both_ `_broadcast_concatenate` and `hypotest`
+                # produce this information.
+                message = "Array shapes are incompatible for broadcasting."
+                with pytest.raises(ValueError, match=message):
+                    stats._axis_nan_policy._broadcast_concatenate(samples, axis, paired)
+                with pytest.raises(ValueError, match=message):
+                    hypotest(*samples, *args, axis=axis, **kwds)
+
+
+def paired_non_broadcastable_cases():
+    for case in axis_nan_policy_cases:
+        hypotest, args, kwds, n_samples, n_outputs, paired, unpacker = case
+        if n_samples == 1:  # broadcasting only needed with >1 sample
+            continue
+        yield case
+
+
+@pytest.mark.parametrize("axis", [0, 1])
+@pytest.mark.parametrize(("hypotest", "args", "kwds", "n_samples", "n_outputs",
+                          "paired", "unpacker"),
+                         list(paired_non_broadcastable_cases()))
+def test_non_broadcastable(hypotest, args, kwds, n_samples, n_outputs, paired,
+                           unpacker, axis):
+    # test for correct error message when shapes are not broadcastable
+    rng = np.random.default_rng(91359824598245)
+    get_samples = True
+    while get_samples:
+        samples = [rng.random(size=rng.integers(2, 100, size=2))
+                   for i in range(n_samples)]
+        # if samples are broadcastable, try again
+        get_samples = _check_arrays_broadcastable(samples, axis=axis)
+
+    message = "Array shapes are incompatible for broadcasting."
+    with pytest.raises(ValueError, match=message):
+        hypotest(*samples, *args, axis=axis, **kwds)
+
+    if not paired:  # there's another test for paired-sample statistics
+        return
+
+    # Previously, paired sample statistics did not raise an error
+    # message when the shapes were broadcastable except along `axis`
+    # https://github.com/scipy/scipy/pull/19578#pullrequestreview-1766857165
+    shape = rng.integers(2, 10, size=2)
+    most_samples = [rng.random(size=shape) for i in range(n_samples-1)]
+    shape = list(shape)
+    shape[axis] += 1
+    other_sample = rng.random(size=shape)
+    with pytest.raises(ValueError, match=message):
+        hypotest(other_sample, *most_samples, *args, axis=axis, **kwds)
+
+def test_masked_array_2_sentinel_array():
+    # prepare arrays
+    rng = np.random.default_rng(805715284)
+    A = rng.random((10, 11, 12))
+    B = rng.random(12)
+    mask = A < 0.5
+    A = np.ma.masked_array(A, mask)
+
+    # set arbitrary elements to special values
+    # (these values might have been considered for use as sentinel values)
+    max_float = np.finfo(np.float64).max
+    max_float2 = np.nextafter(max_float, -np.inf)
+    max_float3 = np.nextafter(max_float2, -np.inf)
+    A[3, 4, 1] = np.nan
+    A[4, 5, 2] = np.inf
+    A[5, 6, 3] = max_float
+    B[8] = np.nan
+    B[7] = np.inf
+    B[6] = max_float2
+
+    # convert masked A to array with sentinel value, don't modify B
+    out_arrays, sentinel = _masked_arrays_2_sentinel_arrays([A, B])
+    A_out, B_out = out_arrays
+
+    # check that good sentinel value was chosen (according to intended logic)
+    assert (sentinel != max_float) and (sentinel != max_float2)
+    assert sentinel == max_float3
+
+    # check that output arrays are as intended
+    A_reference = A.data
+    A_reference[A.mask] = sentinel
+    np.testing.assert_array_equal(A_out, A_reference)
+    assert B_out is B
+
+
+@skip_xp_invalid_arg
+def test_masked_dtype():
+    # When _masked_arrays_2_sentinel_arrays was first added, it always
+    # upcast the arrays to np.float64. After gh16662, check expected promotion
+    # and that the expected sentinel is found.
+
+    # these are important because the max of the promoted dtype is the first
+    # candidate to be the sentinel value
+    max16 = np.iinfo(np.int16).max
+    max128c = np.finfo(np.complex128).max
+
+    # a is a regular array, b has masked elements, and c has no masked elements
+    a = np.array([1, 2, max16], dtype=np.int16)
+    b = np.ma.array([1, 2, 1], dtype=np.int8, mask=[0, 1, 0])
+    c = np.ma.array([1, 2, 1], dtype=np.complex128, mask=[0, 0, 0])
+
+    # check integer masked -> sentinel conversion
+    out_arrays, sentinel = _masked_arrays_2_sentinel_arrays([a, b])
+    a_out, b_out = out_arrays
+    assert sentinel == max16-1  # not max16 because max16 was in the data
+    assert b_out.dtype == np.int16  # check expected promotion
+    assert_allclose(b_out, [b[0], sentinel, b[-1]])  # check sentinel placement
+    assert a_out is a  # not a masked array, so left untouched
+    assert not isinstance(b_out, np.ma.MaskedArray)  # b became regular array
+
+    # similarly with complex
+    out_arrays, sentinel = _masked_arrays_2_sentinel_arrays([b, c])
+    b_out, c_out = out_arrays
+    assert sentinel == max128c  # max128c was not in the data
+    assert b_out.dtype == np.complex128  # b got promoted
+    assert_allclose(b_out, [b[0], sentinel, b[-1]])  # check sentinel placement
+    assert not isinstance(b_out, np.ma.MaskedArray)  # b became regular array
+    assert not isinstance(c_out, np.ma.MaskedArray)  # c became regular array
+
+    # Also, check edge case when a sentinel value cannot be found in the data
+    min8, max8 = np.iinfo(np.int8).min, np.iinfo(np.int8).max
+    a = np.arange(min8, max8+1, dtype=np.int8)  # use all possible values
+    mask1 = np.zeros_like(a, dtype=bool)
+    mask0 = np.zeros_like(a, dtype=bool)
+
+    # a masked value can be used as the sentinel
+    mask1[1] = True
+    a1 = np.ma.array(a, mask=mask1)
+    out_arrays, sentinel = _masked_arrays_2_sentinel_arrays([a1])
+    assert sentinel == min8+1
+
+    # unless it's the smallest possible; skipped for simiplicity (see code)
+    mask0[0] = True
+    a0 = np.ma.array(a, mask=mask0)
+    message = "This function replaces masked elements with sentinel..."
+    with pytest.raises(ValueError, match=message):
+        _masked_arrays_2_sentinel_arrays([a0])
+
+    # test that dtype is preserved in functions
+    a = np.ma.array([1, 2, 3], mask=[0, 1, 0], dtype=np.float32)
+    assert stats.gmean(a).dtype == np.float32
+
+
+@skip_xp_invalid_arg
+def test_masked_stat_1d():
+    # basic test of _axis_nan_policy_factory with 1D masked sample
+    males = [19, 22, 16, 29, 24]
+    females = [20, 11, 17, 12]
+    res = stats.mannwhitneyu(males, females)
+
+    # same result when extra nan is omitted
+    females2 = [20, 11, 17, np.nan, 12]
+    res2 = stats.mannwhitneyu(males, females2, nan_policy='omit')
+    np.testing.assert_array_equal(res2, res)
+
+    # same result when extra element is masked
+    females3 = [20, 11, 17, 1000, 12]
+    mask3 = [False, False, False, True, False]
+    females3 = np.ma.masked_array(females3, mask=mask3)
+    res3 = stats.mannwhitneyu(males, females3)
+    np.testing.assert_array_equal(res3, res)
+
+    # same result when extra nan is omitted and additional element is masked
+    females4 = [20, 11, 17, np.nan, 1000, 12]
+    mask4 = [False, False, False, False, True, False]
+    females4 = np.ma.masked_array(females4, mask=mask4)
+    res4 = stats.mannwhitneyu(males, females4, nan_policy='omit')
+    np.testing.assert_array_equal(res4, res)
+
+    # same result when extra elements, including nan, are masked
+    females5 = [20, 11, 17, np.nan, 1000, 12]
+    mask5 = [False, False, False, True, True, False]
+    females5 = np.ma.masked_array(females5, mask=mask5)
+    res5 = stats.mannwhitneyu(males, females5, nan_policy='propagate')
+    res6 = stats.mannwhitneyu(males, females5, nan_policy='raise')
+    np.testing.assert_array_equal(res5, res)
+    np.testing.assert_array_equal(res6, res)
+
+
+@pytest.mark.filterwarnings('ignore:After omitting NaNs...')
+@pytest.mark.filterwarnings('ignore:One or more axis-slices of one...')
+@skip_xp_invalid_arg
+@pytest.mark.parametrize(("axis"), list(range(-3, 3)))
+def test_masked_stat_3d(axis):
+    # basic test of _axis_nan_policy_factory with 3D masked sample
+    rng = np.random.default_rng(3679428403)
+    a = rng.random((3, 4, 5))
+    b = rng.random((4, 5))
+    c = rng.random((4, 1))
+
+    mask_a = a < 0.1
+    mask_c = [False, False, False, True]
+    a_masked = np.ma.masked_array(a, mask=mask_a)
+    c_masked = np.ma.masked_array(c, mask=mask_c)
+
+    a_nans = a.copy()
+    a_nans[mask_a] = np.nan
+    c_nans = c.copy()
+    c_nans[mask_c] = np.nan
+
+    res = stats.kruskal(a_nans, b, c_nans, nan_policy='omit', axis=axis)
+    res2 = stats.kruskal(a_masked, b, c_masked, axis=axis)
+    np.testing.assert_array_equal(res, res2)
+
+
+@pytest.mark.filterwarnings('ignore:After omitting NaNs...')
+@pytest.mark.filterwarnings('ignore:One or more axis-slices of one...')
+@skip_xp_invalid_arg
+def test_mixed_mask_nan_1():
+    # targeted test of _axis_nan_policy_factory with 2D masked sample:
+    # omitting samples with masks and nan_policy='omit' are equivalent
+    # also checks paired-sample sentinel value removal
+    m, n = 3, 20
+    axis = -1
+
+    rng = np.random.RandomState(0)
+    a = rng.rand(m, n)
+    b = rng.rand(m, n)
+    mask_a1 = rng.rand(m, n) < 0.2
+    mask_a2 = rng.rand(m, n) < 0.1
+    mask_b1 = rng.rand(m, n) < 0.15
+    mask_b2 = rng.rand(m, n) < 0.15
+    mask_a1[2, :] = True
+
+    a_nans = a.copy()
+    b_nans = b.copy()
+    a_nans[mask_a1 | mask_a2] = np.nan
+    b_nans[mask_b1 | mask_b2] = np.nan
+
+    a_masked1 = np.ma.masked_array(a, mask=mask_a1)
+    b_masked1 = np.ma.masked_array(b, mask=mask_b1)
+    a_masked1[mask_a2] = np.nan
+    b_masked1[mask_b2] = np.nan
+
+    a_masked2 = np.ma.masked_array(a, mask=mask_a2)
+    b_masked2 = np.ma.masked_array(b, mask=mask_b2)
+    a_masked2[mask_a1] = np.nan
+    b_masked2[mask_b1] = np.nan
+
+    a_masked3 = np.ma.masked_array(a, mask=(mask_a1 | mask_a2))
+    b_masked3 = np.ma.masked_array(b, mask=(mask_b1 | mask_b2))
+
+    res = stats.wilcoxon(a_nans, b_nans, nan_policy='omit', axis=axis)
+    res1 = stats.wilcoxon(a_masked1, b_masked1, nan_policy='omit', axis=axis)
+    res2 = stats.wilcoxon(a_masked2, b_masked2, nan_policy='omit', axis=axis)
+    res3 = stats.wilcoxon(a_masked3, b_masked3, nan_policy='raise', axis=axis)
+    res4 = stats.wilcoxon(a_masked3, b_masked3,
+                          nan_policy='propagate', axis=axis)
+
+    np.testing.assert_array_equal(res1, res)
+    np.testing.assert_array_equal(res2, res)
+    np.testing.assert_array_equal(res3, res)
+    np.testing.assert_array_equal(res4, res)
+
+
+@pytest.mark.filterwarnings('ignore:After omitting NaNs...')
+@pytest.mark.filterwarnings('ignore:One or more axis-slices of one...')
+@skip_xp_invalid_arg
+def test_mixed_mask_nan_2():
+    # targeted test of _axis_nan_policy_factory with 2D masked sample:
+    # check for expected interaction between masks and nans
+
+    # Cases here are
+    # [mixed nan/mask, all nans, all masked,
+    # unmasked nan, masked nan, unmasked non-nan]
+    a = [[1, np.nan, 2], [np.nan, np.nan, np.nan], [1, 2, 3],
+         [1, np.nan, 3], [1, np.nan, 3], [1, 2, 3]]
+    mask = [[1, 0, 1], [0, 0, 0], [1, 1, 1],
+            [0, 0, 0], [0, 1, 0], [0, 0, 0]]
+    a_masked = np.ma.masked_array(a, mask=mask)
+    b = [[4, 5, 6]]
+    ref1 = stats.ranksums([1, 3], [4, 5, 6])
+    ref2 = stats.ranksums([1, 2, 3], [4, 5, 6])
+
+    # nan_policy = 'omit'
+    # all elements are removed from first three rows
+    # middle element is removed from fourth and fifth rows
+    # no elements removed from last row
+    res = stats.ranksums(a_masked, b, nan_policy='omit', axis=-1)
+    stat_ref = [np.nan, np.nan, np.nan,
+                ref1.statistic, ref1.statistic, ref2.statistic]
+    p_ref = [np.nan, np.nan, np.nan,
+             ref1.pvalue, ref1.pvalue, ref2.pvalue]
+    np.testing.assert_array_equal(res.statistic, stat_ref)
+    np.testing.assert_array_equal(res.pvalue, p_ref)
+
+    # nan_policy = 'propagate'
+    # nans propagate in first, second, and fourth row
+    # all elements are removed by mask from third row
+    # middle element is removed from fifth row
+    # no elements removed from last row
+    res = stats.ranksums(a_masked, b, nan_policy='propagate', axis=-1)
+    stat_ref = [np.nan, np.nan, np.nan,
+                np.nan, ref1.statistic, ref2.statistic]
+    p_ref = [np.nan, np.nan, np.nan,
+             np.nan, ref1.pvalue, ref2.pvalue]
+    np.testing.assert_array_equal(res.statistic, stat_ref)
+    np.testing.assert_array_equal(res.pvalue, p_ref)
+
+
+def test_axis_None_vs_tuple():
+    # `axis` `None` should be equivalent to tuple with all axes
+    shape = (3, 8, 9, 10)
+    rng = np.random.default_rng(0)
+    x = rng.random(shape)
+    res = stats.kruskal(*x, axis=None)
+    res2 = stats.kruskal(*x, axis=(0, 1, 2))
+    np.testing.assert_array_equal(res, res2)
+
+
+def test_axis_None_vs_tuple_with_broadcasting():
+    # `axis` `None` should be equivalent to tuple with all axes,
+    # which should be equivalent to raveling the arrays before passing them
+    rng = np.random.default_rng(0)
+    x = rng.random((5, 1))
+    y = rng.random((1, 5))
+    x2, y2 = np.broadcast_arrays(x, y)
+
+    res0 = stats.mannwhitneyu(x.ravel(), y.ravel())
+    res1 = stats.mannwhitneyu(x, y, axis=None)
+    res2 = stats.mannwhitneyu(x, y, axis=(0, 1))
+    res3 = stats.mannwhitneyu(x2.ravel(), y2.ravel())
+
+    assert res1 == res0
+    assert res2 == res0
+    assert res3 != res0
+
+
+@pytest.mark.parametrize(("axis"),
+                         list(permutations(range(-3, 3), 2)) + [(-4, 1)])
+def test_other_axis_tuples(axis):
+    # Check that _axis_nan_policy_factory treats all `axis` tuples as expected
+    rng = np.random.default_rng(0)
+    shape_x = (4, 5, 6)
+    shape_y = (1, 6)
+    x = rng.random(shape_x)
+    y = rng.random(shape_y)
+    axis_original = axis
+
+    # convert axis elements to positive
+    axis = tuple([(i if i >= 0 else 3 + i) for i in axis])
+    axis = sorted(axis)
+
+    if len(set(axis)) != len(axis):
+        message = "`axis` must contain only distinct elements"
+        with pytest.raises(AxisError, match=re.escape(message)):
+            stats.mannwhitneyu(x, y, axis=axis_original)
+        return
+
+    if axis[0] < 0 or axis[-1] > 2:
+        message = "`axis` is out of bounds for array of dimension 3"
+        with pytest.raises(AxisError, match=re.escape(message)):
+            stats.mannwhitneyu(x, y, axis=axis_original)
+        return
+
+    res = stats.mannwhitneyu(x, y, axis=axis_original)
+
+    # reference behavior
+    not_axis = {0, 1, 2} - set(axis)  # which axis is not part of `axis`
+    not_axis = next(iter(not_axis))  # take it out of the set
+
+    x2 = x
+    shape_y_broadcasted = [1, 1, 6]
+    shape_y_broadcasted[not_axis] = shape_x[not_axis]
+    y2 = np.broadcast_to(y, shape_y_broadcasted)
+
+    m = x2.shape[not_axis]
+    x2 = np.moveaxis(x2, axis, (1, 2))
+    y2 = np.moveaxis(y2, axis, (1, 2))
+    x2 = np.reshape(x2, (m, -1))
+    y2 = np.reshape(y2, (m, -1))
+    res2 = stats.mannwhitneyu(x2, y2, axis=1)
+
+    np.testing.assert_array_equal(res, res2)
+
+
+@pytest.mark.filterwarnings('ignore:After omitting NaNs...')
+@pytest.mark.filterwarnings('ignore:One or more axis-slices of one...')
+@skip_xp_invalid_arg
+@pytest.mark.parametrize(
+    ("weighted_fun_name, unpacker"),
+    [
+        ("gmean", lambda x: x),
+        ("hmean", lambda x: x),
+        ("pmean", lambda x: x),
+        ("combine_pvalues", lambda x: (x.pvalue, x.statistic)),
+    ],
+)
+def test_mean_mixed_mask_nan_weights(weighted_fun_name, unpacker):
+    # targeted test of _axis_nan_policy_factory with 2D masked sample:
+    # omitting samples with masks and nan_policy='omit' are equivalent
+    # also checks paired-sample sentinel value removal
+
+    if weighted_fun_name == 'pmean':
+        def weighted_fun(a, **kwargs):
+            return stats.pmean(a, p=0.42, **kwargs)
+    else:
+        weighted_fun = getattr(stats, weighted_fun_name)
+
+    def func(*args, **kwargs):
+        return unpacker(weighted_fun(*args, **kwargs))
+
+    m, n = 3, 20
+    axis = -1
+
+    rng = np.random.default_rng(6541968121)
+    a = rng.uniform(size=(m, n))
+    b = rng.uniform(size=(m, n))
+    mask_a1 = rng.uniform(size=(m, n)) < 0.2
+    mask_a2 = rng.uniform(size=(m, n)) < 0.1
+    mask_b1 = rng.uniform(size=(m, n)) < 0.15
+    mask_b2 = rng.uniform(size=(m, n)) < 0.15
+    mask_a1[2, :] = True
+
+    a_nans = a.copy()
+    b_nans = b.copy()
+    a_nans[mask_a1 | mask_a2] = np.nan
+    b_nans[mask_b1 | mask_b2] = np.nan
+
+    a_masked1 = np.ma.masked_array(a, mask=mask_a1)
+    b_masked1 = np.ma.masked_array(b, mask=mask_b1)
+    a_masked1[mask_a2] = np.nan
+    b_masked1[mask_b2] = np.nan
+
+    a_masked2 = np.ma.masked_array(a, mask=mask_a2)
+    b_masked2 = np.ma.masked_array(b, mask=mask_b2)
+    a_masked2[mask_a1] = np.nan
+    b_masked2[mask_b1] = np.nan
+
+    a_masked3 = np.ma.masked_array(a, mask=(mask_a1 | mask_a2))
+    b_masked3 = np.ma.masked_array(b, mask=(mask_b1 | mask_b2))
+
+    with warnings.catch_warnings():
+        message = 'invalid value encountered'
+        warnings.filterwarnings("ignore", message, RuntimeWarning)
+        res = func(a_nans, weights=b_nans, nan_policy="omit", axis=axis)
+        res1 = func(a_masked1, weights=b_masked1, nan_policy="omit", axis=axis)
+        res2 = func(a_masked2, weights=b_masked2, nan_policy="omit", axis=axis)
+        res3 = func(a_masked3, weights=b_masked3, nan_policy="raise", axis=axis)
+        res4 = func(a_masked3, weights=b_masked3, nan_policy="propagate", axis=axis)
+
+    np.testing.assert_array_equal(res1, res)
+    np.testing.assert_array_equal(res2, res)
+    np.testing.assert_array_equal(res3, res)
+    np.testing.assert_array_equal(res4, res)
+
+
+def test_raise_invalid_args_g17713():
+    # other cases are handled in:
+    # test_axis_nan_policy_decorated_positional_axis - multiple values for arg
+    # test_axis_nan_policy_decorated_positional_args - unexpected kwd arg
+    message = "got an unexpected keyword argument"
+    with pytest.raises(TypeError, match=message):
+        stats.gmean([1, 2, 3], invalid_arg=True)
+
+    message = " got multiple values for argument"
+    with pytest.raises(TypeError, match=message):
+        stats.gmean([1, 2, 3], a=True)
+
+    message = "missing 1 required positional argument"
+    with pytest.raises(TypeError, match=message):
+        stats.gmean()
+
+    message = "takes from 1 to 4 positional arguments but 5 were given"
+    with pytest.raises(TypeError, match=message):
+        stats.gmean([1, 2, 3], 0, float, [1, 1, 1], 10)
+
+
+@pytest.mark.parametrize('dtype', [np.int16, np.float32, np.complex128])
+def test_array_like_input(dtype):
+    # Check that `_axis_nan_policy`-decorated functions work with custom
+    # containers that are coercible to numeric arrays
+
+    class ArrLike:
+        def __init__(self, x, dtype):
+            self._x = x
+            self._dtype = dtype
+
+        def __array__(self, dtype=None, copy=None):
+            return np.asarray(x, dtype=self._dtype)
+
+        def __iter__(self):
+            # I don't know of a canonical way to determine whether an object should
+            # be coerced to a NumPy array or not. Currently, `xp_promote` checks
+            # whether they are iterable, and if so uses `_asarray` with whatever
+            # `xp` is. So for this to get coerced, it needs to be iterable.
+            return iter(self._x)
+
+    x = [1]*2 + [3, 4, 5]
+    res = stats.mode(ArrLike(x, dtype=dtype))
+    assert res.mode == 1
+    assert res.count == 2
+
+
+@make_xp_test_case(stats._axis_nan_policy._broadcast_concatenate)
+def test__broadcast_concatenate(xp):
+    # test that _broadcast_concatenate properly broadcasts arrays along all
+    # axes except `axis`, then concatenates along axis
+    rng = np.random.default_rng(7544340069)
+    a = rng.random((5, 4, 4, 3, 1, 6))
+    b = rng.random((4, 1, 8, 2, 6))
+    arrays = (xp.asarray(a), xp.asarray(b))
+    c = stats._axis_nan_policy._broadcast_concatenate(arrays, axis=-3, xp=xp)
+    # broadcast manually as an independent check
+    a = np.tile(a, (1, 1, 1, 1, 2, 1))
+    b = np.tile(b[None, ...], (5, 1, 4, 1, 1, 1))
+    for index in product(*(range(i) for i in c.shape)):
+        i, j, k, l, m, n = index
+        if l < a.shape[-3]:
+            assert a[i, j, k, l, m, n] == c[i, j, k, l, m, n]
+        else:
+            assert b[i, j, k, l - a.shape[-3], m, n] == c[i, j, k, l, m, n]
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/test_binned_statistic.py b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_binned_statistic.py
new file mode 100644
index 0000000000000000000000000000000000000000..a1fc499123f8f0eed07a767f2d9e361a84452bcb
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_binned_statistic.py
@@ -0,0 +1,602 @@
+import numpy as np
+from numpy.testing import assert_allclose
+import pytest
+from pytest import raises as assert_raises
+from scipy.stats import (binned_statistic, binned_statistic_2d,
+                         binned_statistic_dd)
+from scipy._lib._util import check_random_state
+
+from .common_tests import check_named_results
+
+
+class TestBinnedStatistic:
+
+    @classmethod
+    def setup_class(cls):
+        rng = check_random_state(9865)
+        cls.x = rng.uniform(size=100)
+        cls.y = rng.uniform(size=100)
+        cls.v = rng.uniform(size=100)
+        cls.X = rng.uniform(size=(100, 3))
+        cls.w = rng.uniform(size=100)
+        cls.u = rng.uniform(size=100) + 1e6
+
+    def test_1d_count(self):
+        x = self.x
+        v = self.v
+
+        count1, edges1, bc = binned_statistic(x, v, 'count', bins=10)
+        count2, edges2 = np.histogram(x, bins=10)
+
+        assert_allclose(count1, count2)
+        assert_allclose(edges1, edges2)
+
+    def test_gh5927(self):
+        # smoke test for gh5927 - binned_statistic was using `is` for string
+        # comparison
+        x = self.x
+        v = self.v
+        statistics = ['mean', 'median', 'count', 'sum']
+        for statistic in statistics:
+            binned_statistic(x, v, statistic, bins=10)
+
+    def test_big_number_std(self):
+        # tests for numerical stability of std calculation
+        # see issue gh-10126 for more
+        x = self.x
+        u = self.u
+        stat1, edges1, bc = binned_statistic(x, u, 'std', bins=10)
+        stat2, edges2, bc = binned_statistic(x, u, np.std, bins=10)
+
+        assert_allclose(stat1, stat2)
+
+    def test_empty_bins_std(self):
+        # tests that std returns gives nan for empty bins
+        x = self.x
+        u = self.u
+        print(binned_statistic(x, u, 'count', bins=1000))
+        stat1, edges1, bc = binned_statistic(x, u, 'std', bins=1000)
+        stat2, edges2, bc = binned_statistic(x, u, np.std, bins=1000)
+
+        assert_allclose(stat1, stat2)
+
+    def test_1d_result_attributes(self):
+        x = self.x
+        v = self.v
+
+        res = binned_statistic(x, v, 'count', bins=10)
+        attributes = ('statistic', 'bin_edges', 'binnumber')
+        check_named_results(res, attributes)
+
+    def test_1d_sum(self):
+        x = self.x
+        v = self.v
+
+        sum1, edges1, bc = binned_statistic(x, v, 'sum', bins=10)
+        sum2, edges2 = np.histogram(x, bins=10, weights=v)
+
+        assert_allclose(sum1, sum2)
+        assert_allclose(edges1, edges2)
+
+    def test_1d_mean(self):
+        x = self.x
+        v = self.v
+
+        stat1, edges1, bc = binned_statistic(x, v, 'mean', bins=10)
+        stat2, edges2, bc = binned_statistic(x, v, np.mean, bins=10)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(edges1, edges2)
+
+    def test_1d_std(self):
+        x = self.x
+        v = self.v
+
+        stat1, edges1, bc = binned_statistic(x, v, 'std', bins=10)
+        stat2, edges2, bc = binned_statistic(x, v, np.std, bins=10)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(edges1, edges2)
+
+    def test_1d_min(self):
+        x = self.x
+        v = self.v
+
+        stat1, edges1, bc = binned_statistic(x, v, 'min', bins=10)
+        stat2, edges2, bc = binned_statistic(x, v, np.min, bins=10)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(edges1, edges2)
+
+    def test_1d_max(self):
+        x = self.x
+        v = self.v
+
+        stat1, edges1, bc = binned_statistic(x, v, 'max', bins=10)
+        stat2, edges2, bc = binned_statistic(x, v, np.max, bins=10)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(edges1, edges2)
+
+    def test_1d_median(self):
+        x = self.x
+        v = self.v
+
+        stat1, edges1, bc = binned_statistic(x, v, 'median', bins=10)
+        stat2, edges2, bc = binned_statistic(x, v, np.median, bins=10)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(edges1, edges2)
+
+    def test_1d_bincode(self):
+        x = self.x[:20]
+        v = self.v[:20]
+
+        count1, edges1, bc = binned_statistic(x, v, 'count', bins=3)
+        bc2 = np.array([3, 2, 1, 3, 2, 3, 3, 3, 3, 1, 1, 3, 3, 1, 2, 3, 1,
+                        1, 2, 1])
+
+        bcount = [(bc == i).sum() for i in np.unique(bc)]
+
+        assert_allclose(bc, bc2)
+        assert_allclose(bcount, count1)
+
+    def test_1d_range_keyword(self):
+        # Regression test for gh-3063, range can be (min, max) or [(min, max)]
+        rng = np.random.default_rng(6823616729)
+        x = np.arange(30)
+        data = rng.random(30)
+
+        mean, bins, _ = binned_statistic(x[:15], data[:15])
+        mean_range, bins_range, _ = binned_statistic(x, data, range=[(0, 14)])
+        mean_range2, bins_range2, _ = binned_statistic(x, data, range=(0, 14))
+
+        assert_allclose(mean, mean_range)
+        assert_allclose(bins, bins_range)
+        assert_allclose(mean, mean_range2)
+        assert_allclose(bins, bins_range2)
+
+    def test_1d_multi_values(self):
+        x = self.x
+        v = self.v
+        w = self.w
+
+        stat1v, edges1v, bc1v = binned_statistic(x, v, 'mean', bins=10)
+        stat1w, edges1w, bc1w = binned_statistic(x, w, 'mean', bins=10)
+        stat2, edges2, bc2 = binned_statistic(x, [v, w], 'mean', bins=10)
+
+        assert_allclose(stat2[0], stat1v)
+        assert_allclose(stat2[1], stat1w)
+        assert_allclose(edges1v, edges2)
+        assert_allclose(bc1v, bc2)
+
+    def test_2d_count(self):
+        x = self.x
+        y = self.y
+        v = self.v
+
+        count1, binx1, biny1, bc = binned_statistic_2d(
+            x, y, v, 'count', bins=5)
+        count2, binx2, biny2 = np.histogram2d(x, y, bins=5)
+
+        assert_allclose(count1, count2)
+        assert_allclose(binx1, binx2)
+        assert_allclose(biny1, biny2)
+
+    def test_2d_result_attributes(self):
+        x = self.x
+        y = self.y
+        v = self.v
+
+        res = binned_statistic_2d(x, y, v, 'count', bins=5)
+        attributes = ('statistic', 'x_edge', 'y_edge', 'binnumber')
+        check_named_results(res, attributes)
+
+    def test_2d_sum(self):
+        x = self.x
+        y = self.y
+        v = self.v
+
+        sum1, binx1, biny1, bc = binned_statistic_2d(x, y, v, 'sum', bins=5)
+        sum2, binx2, biny2 = np.histogram2d(x, y, bins=5, weights=v)
+
+        assert_allclose(sum1, sum2)
+        assert_allclose(binx1, binx2)
+        assert_allclose(biny1, biny2)
+
+    def test_2d_mean(self):
+        x = self.x
+        y = self.y
+        v = self.v
+
+        stat1, binx1, biny1, bc = binned_statistic_2d(x, y, v, 'mean', bins=5)
+        stat2, binx2, biny2, bc = binned_statistic_2d(x, y, v, np.mean, bins=5)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(binx1, binx2)
+        assert_allclose(biny1, biny2)
+
+    def test_2d_mean_unicode(self):
+        x = self.x
+        y = self.y
+        v = self.v
+        stat1, binx1, biny1, bc = binned_statistic_2d(
+            x, y, v, 'mean', bins=5)
+        stat2, binx2, biny2, bc = binned_statistic_2d(x, y, v, np.mean, bins=5)
+        assert_allclose(stat1, stat2)
+        assert_allclose(binx1, binx2)
+        assert_allclose(biny1, biny2)
+
+    def test_2d_std(self):
+        x = self.x
+        y = self.y
+        v = self.v
+
+        stat1, binx1, biny1, bc = binned_statistic_2d(x, y, v, 'std', bins=5)
+        stat2, binx2, biny2, bc = binned_statistic_2d(x, y, v, np.std, bins=5)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(binx1, binx2)
+        assert_allclose(biny1, biny2)
+
+    def test_2d_min(self):
+        x = self.x
+        y = self.y
+        v = self.v
+
+        stat1, binx1, biny1, bc = binned_statistic_2d(x, y, v, 'min', bins=5)
+        stat2, binx2, biny2, bc = binned_statistic_2d(x, y, v, np.min, bins=5)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(binx1, binx2)
+        assert_allclose(biny1, biny2)
+
+    def test_2d_max(self):
+        x = self.x
+        y = self.y
+        v = self.v
+
+        stat1, binx1, biny1, bc = binned_statistic_2d(x, y, v, 'max', bins=5)
+        stat2, binx2, biny2, bc = binned_statistic_2d(x, y, v, np.max, bins=5)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(binx1, binx2)
+        assert_allclose(biny1, biny2)
+
+    def test_2d_median(self):
+        x = self.x
+        y = self.y
+        v = self.v
+
+        stat1, binx1, biny1, bc = binned_statistic_2d(
+            x, y, v, 'median', bins=5)
+        stat2, binx2, biny2, bc = binned_statistic_2d(
+            x, y, v, np.median, bins=5)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(binx1, binx2)
+        assert_allclose(biny1, biny2)
+
+    def test_2d_bincode(self):
+        x = self.x[:20]
+        y = self.y[:20]
+        v = self.v[:20]
+
+        count1, binx1, biny1, bc = binned_statistic_2d(
+            x, y, v, 'count', bins=3)
+        bc2 = np.array([17, 11, 6, 16, 11, 17, 18, 17, 17, 7, 6, 18, 16,
+                        6, 11, 16, 6, 6, 11, 8])
+
+        bcount = [(bc == i).sum() for i in np.unique(bc)]
+
+        assert_allclose(bc, bc2)
+        count1adj = count1[count1.nonzero()]
+        assert_allclose(bcount, count1adj)
+
+    def test_2d_multi_values(self):
+        x = self.x
+        y = self.y
+        v = self.v
+        w = self.w
+
+        stat1v, binx1v, biny1v, bc1v = binned_statistic_2d(
+            x, y, v, 'mean', bins=8)
+        stat1w, binx1w, biny1w, bc1w = binned_statistic_2d(
+            x, y, w, 'mean', bins=8)
+        stat2, binx2, biny2, bc2 = binned_statistic_2d(
+            x, y, [v, w], 'mean', bins=8)
+
+        assert_allclose(stat2[0], stat1v)
+        assert_allclose(stat2[1], stat1w)
+        assert_allclose(binx1v, binx2)
+        assert_allclose(biny1w, biny2)
+        assert_allclose(bc1v, bc2)
+
+    def test_2d_binnumbers_unraveled(self):
+        x = self.x
+        y = self.y
+        v = self.v
+
+        stat, edgesx, bcx = binned_statistic(x, v, 'mean', bins=20)
+        stat, edgesy, bcy = binned_statistic(y, v, 'mean', bins=10)
+
+        stat2, edgesx2, edgesy2, bc2 = binned_statistic_2d(
+            x, y, v, 'mean', bins=(20, 10), expand_binnumbers=True)
+
+        bcx3 = np.searchsorted(edgesx, x, side='right')
+        bcy3 = np.searchsorted(edgesy, y, side='right')
+
+        # `numpy.searchsorted` is non-inclusive on right-edge, compensate
+        bcx3[x == x.max()] -= 1
+        bcy3[y == y.max()] -= 1
+
+        assert_allclose(bcx, bc2[0])
+        assert_allclose(bcy, bc2[1])
+        assert_allclose(bcx3, bc2[0])
+        assert_allclose(bcy3, bc2[1])
+
+    def test_dd_count(self):
+        X = self.X
+        v = self.v
+
+        count1, edges1, bc = binned_statistic_dd(X, v, 'count', bins=3)
+        count2, edges2 = np.histogramdd(X, bins=3)
+
+        assert_allclose(count1, count2)
+        assert_allclose(edges1, edges2)
+
+    def test_dd_result_attributes(self):
+        X = self.X
+        v = self.v
+
+        res = binned_statistic_dd(X, v, 'count', bins=3)
+        attributes = ('statistic', 'bin_edges', 'binnumber')
+        check_named_results(res, attributes)
+
+    def test_dd_sum(self):
+        X = self.X
+        v = self.v
+
+        sum1, edges1, bc = binned_statistic_dd(X, v, 'sum', bins=3)
+        sum2, edges2 = np.histogramdd(X, bins=3, weights=v)
+        sum3, edges3, bc = binned_statistic_dd(X, v, np.sum, bins=3)
+
+        assert_allclose(sum1, sum2)
+        assert_allclose(edges1, edges2)
+        assert_allclose(sum1, sum3)
+        assert_allclose(edges1, edges3)
+
+    def test_dd_mean(self):
+        X = self.X
+        v = self.v
+
+        stat1, edges1, bc = binned_statistic_dd(X, v, 'mean', bins=3)
+        stat2, edges2, bc = binned_statistic_dd(X, v, np.mean, bins=3)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(edges1, edges2)
+
+    def test_dd_std(self):
+        X = self.X
+        v = self.v
+
+        stat1, edges1, bc = binned_statistic_dd(X, v, 'std', bins=3)
+        stat2, edges2, bc = binned_statistic_dd(X, v, np.std, bins=3)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(edges1, edges2)
+
+    def test_dd_min(self):
+        X = self.X
+        v = self.v
+
+        stat1, edges1, bc = binned_statistic_dd(X, v, 'min', bins=3)
+        stat2, edges2, bc = binned_statistic_dd(X, v, np.min, bins=3)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(edges1, edges2)
+
+    def test_dd_max(self):
+        X = self.X
+        v = self.v
+
+        stat1, edges1, bc = binned_statistic_dd(X, v, 'max', bins=3)
+        stat2, edges2, bc = binned_statistic_dd(X, v, np.max, bins=3)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(edges1, edges2)
+
+    def test_dd_median(self):
+        X = self.X
+        v = self.v
+
+        stat1, edges1, bc = binned_statistic_dd(X, v, 'median', bins=3)
+        stat2, edges2, bc = binned_statistic_dd(X, v, np.median, bins=3)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(edges1, edges2)
+
+    def test_dd_bincode(self):
+        X = self.X[:20]
+        v = self.v[:20]
+
+        count1, edges1, bc = binned_statistic_dd(X, v, 'count', bins=3)
+        bc2 = np.array([63, 33, 86, 83, 88, 67, 57, 33, 42, 41, 82, 83, 92,
+                        32, 36, 91, 43, 87, 81, 81])
+
+        bcount = [(bc == i).sum() for i in np.unique(bc)]
+
+        assert_allclose(bc, bc2)
+        count1adj = count1[count1.nonzero()]
+        assert_allclose(bcount, count1adj)
+
+    def test_dd_multi_values(self):
+        X = self.X
+        v = self.v
+        w = self.w
+
+        for stat in ["count", "sum", "mean", "std", "min", "max", "median",
+                     np.std]:
+            stat1v, edges1v, bc1v = binned_statistic_dd(X, v, stat, bins=8)
+            stat1w, edges1w, bc1w = binned_statistic_dd(X, w, stat, bins=8)
+            stat2, edges2, bc2 = binned_statistic_dd(X, [v, w], stat, bins=8)
+            assert_allclose(stat2[0], stat1v)
+            assert_allclose(stat2[1], stat1w)
+            assert_allclose(edges1v, edges2)
+            assert_allclose(edges1w, edges2)
+            assert_allclose(bc1v, bc2)
+
+    def test_dd_binnumbers_unraveled(self):
+        X = self.X
+        v = self.v
+
+        stat, edgesx, bcx = binned_statistic(X[:, 0], v, 'mean', bins=15)
+        stat, edgesy, bcy = binned_statistic(X[:, 1], v, 'mean', bins=20)
+        stat, edgesz, bcz = binned_statistic(X[:, 2], v, 'mean', bins=10)
+
+        stat2, edges2, bc2 = binned_statistic_dd(
+            X, v, 'mean', bins=(15, 20, 10), expand_binnumbers=True)
+
+        assert_allclose(bcx, bc2[0])
+        assert_allclose(bcy, bc2[1])
+        assert_allclose(bcz, bc2[2])
+
+    def test_dd_binned_statistic_result(self):
+        # NOTE: tests the reuse of bin_edges from previous call
+        rng = np.random.default_rng(8111360615)
+        x = rng.random((10000, 3))
+        v = rng.random(10000)
+        bins = np.linspace(0, 1, 10)
+        bins = (bins, bins, bins)
+
+        result = binned_statistic_dd(x, v, 'mean', bins=bins)
+        stat = result.statistic
+
+        result = binned_statistic_dd(x, v, 'mean',
+                                     binned_statistic_result=result)
+        stat2 = result.statistic
+
+        assert_allclose(stat, stat2)
+
+    def test_dd_zero_dedges(self):
+        rng = np.random.default_rng(1132724173)
+        x = rng.random((10000, 3))
+        v = rng.random(10000)
+        bins = np.linspace(0, 1, 10)
+        bins = np.append(bins, 1)
+        bins = (bins, bins, bins)
+        with assert_raises(ValueError, match='difference is numerically 0'):
+            binned_statistic_dd(x, v, 'mean', bins=bins)
+
+    def test_dd_range_errors(self):
+        # Test that descriptive exceptions are raised as appropriate for bad
+        # values of the `range` argument. (See gh-12996)
+        with assert_raises(ValueError,
+                           match='In range, start must be <= stop'):
+            binned_statistic_dd([self.y], self.v,
+                                range=[[1, 0]])
+        with assert_raises(
+                ValueError,
+                match='In dimension 1 of range, start must be <= stop'):
+            binned_statistic_dd([self.x, self.y], self.v,
+                                range=[[1, 0], [0, 1]])
+        with assert_raises(
+                ValueError,
+                match='In dimension 2 of range, start must be <= stop'):
+            binned_statistic_dd([self.x, self.y], self.v,
+                                range=[[0, 1], [1, 0]])
+        with assert_raises(
+                ValueError,
+                match='range given for 1 dimensions; 2 required'):
+            binned_statistic_dd([self.x, self.y], self.v,
+                                range=[[0, 1]])
+
+    def test_binned_statistic_float32(self):
+        X = np.array([0, 0.42358226], dtype=np.float32)
+        stat, _, _ = binned_statistic(X, None, 'count', bins=5)
+        assert_allclose(stat, np.array([1, 0, 0, 0, 1], dtype=np.float64))
+
+    def test_gh14332(self):
+        # Test the wrong output when the `sample` is close to bin edge
+        x = []
+        size = 20
+        for i in range(size):
+            x += [1-0.1**i]
+
+        bins = np.linspace(0,1,11)
+        sum1, edges1, bc = binned_statistic_dd(x, np.ones(len(x)),
+                                               bins=[bins], statistic='sum')
+        sum2, edges2 = np.histogram(x, bins=bins)
+
+        assert_allclose(sum1, sum2)
+        assert_allclose(edges1[0], edges2)
+
+    @pytest.mark.parametrize("dtype", [np.float64, np.complex128])
+    @pytest.mark.parametrize("statistic", [np.mean, np.median, np.sum, np.std,
+                                           np.min, np.max, 'count',
+                                           lambda x: (x**2).sum(),
+                                           lambda x: (x**2).sum() * 1j])
+    def test_dd_all(self, dtype, statistic):
+        def ref_statistic(x):
+            return len(x) if statistic == 'count' else statistic(x)
+
+        rng = np.random.default_rng(3704743126639371)
+        n = 10
+        x = rng.random(size=n)
+        i = x >= 0.5
+        v = rng.random(size=n)
+        if dtype is np.complex128:
+            v = v + rng.random(size=n)*1j
+
+        stat, _, _ = binned_statistic_dd(x, v, statistic, bins=2)
+        ref = np.array([ref_statistic(v[~i]), ref_statistic(v[i])])
+        assert_allclose(stat, ref)
+        assert stat.dtype == np.result_type(ref.dtype, np.float64)
+
+    @pytest.mark.parametrize('bins', [10, (10, 10, 10), [np.arange(10)]*3])
+    def test_nan_gh17154(self, bins):
+        # gh-17154 reported that `binned_statistic_dd` raised an error when `samples`
+        # contains NaNs and argued that this was an inappropriate default. gh-23751
+        # decided that it was indeed an appropriate choice, and went further, ensuring
+        # that the same error would be raised regardless of how `bins` is specified.
+
+        # Generate a samples (with NaNs) and values
+        rng = np.random.default_rng(529847529874529829)
+        samples = rng.standard_normal(size=(100, 3))
+        values = rng.standard_normal(100)
+        i = rng.random(samples.shape) < 0.05
+        samples[i] = np.nan
+
+        message = "The sample on which `values` is to be binned..."
+        with pytest.raises(ValueError, match=message):
+            binned_statistic_dd(samples, values)
+
+    def test_inf_gh17154(self):
+        # While addressing gh-17154, it seemed that `inf`s should not be ignored
+        # entirely; rather, values corresponding with `inf`s can always be in outlier
+        # bins.
+
+        # Generate a samples (with infs) and values
+        rng = np.random.default_rng(529847529874529829)
+        samples = rng.standard_normal(size=(100, 3))
+        values = rng.standard_normal(100)
+        i_pinf = rng.random(samples.shape) < 0.05
+        samples[i_pinf] = np.inf
+        i_ninf = rng.random(samples.shape) < 0.05
+        samples[i_ninf] = -np.inf
+
+        # Compute results
+        res = binned_statistic_dd(samples, values)
+
+        # Compute reference values (with bins computed ignoring infs)
+        i_inf = i_pinf | i_ninf
+        temp = samples.copy()
+        temp[i_inf] = 0
+        low = np.min(temp, axis=0)
+        high = np.max(temp, axis=0)
+        ref = binned_statistic_dd(samples, values, range=list(zip(low, high)))
+
+        # Compare results against reference values
+        np.testing.assert_allclose(res[0], ref[0])
+        np.testing.assert_allclose(res[1], ref[1])
+        np.testing.assert_allclose(res[2], ref[2])
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/test_censored_data.py b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_censored_data.py
new file mode 100644
index 0000000000000000000000000000000000000000..ae71dcfaccf899645051287f8944131ec48a1eee
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_censored_data.py
@@ -0,0 +1,152 @@
+# Tests for the CensoredData class.
+
+import pytest
+import numpy as np
+from numpy.testing import assert_equal, assert_array_equal
+from scipy.stats import CensoredData
+
+
+class TestCensoredData:
+
+    def test_basic(self):
+        uncensored = [1]
+        left = [0]
+        right = [2, 5]
+        interval = [[2, 3]]
+        data = CensoredData(uncensored, left=left, right=right,
+                            interval=interval)
+        assert_equal(data._uncensored, uncensored)
+        assert_equal(data._left, left)
+        assert_equal(data._right, right)
+        assert_equal(data._interval, interval)
+
+        udata = data._uncensor()
+        assert_equal(udata, np.concatenate((uncensored, left, right,
+                                            np.mean(interval, axis=1))))
+
+    def test_right_censored(self):
+        x = np.array([0, 3, 2.5])
+        is_censored = np.array([0, 1, 0], dtype=bool)
+        data = CensoredData.right_censored(x, is_censored)
+        assert_equal(data._uncensored, x[~is_censored])
+        assert_equal(data._right, x[is_censored])
+        assert_equal(data._left, [])
+        assert_equal(data._interval, np.empty((0, 2)))
+
+    def test_left_censored(self):
+        x = np.array([0, 3, 2.5])
+        is_censored = np.array([0, 1, 0], dtype=bool)
+        data = CensoredData.left_censored(x, is_censored)
+        assert_equal(data._uncensored, x[~is_censored])
+        assert_equal(data._left, x[is_censored])
+        assert_equal(data._right, [])
+        assert_equal(data._interval, np.empty((0, 2)))
+
+    def test_interval_censored_basic(self):
+        a = [0.5, 2.0, 3.0, 5.5]
+        b = [1.0, 2.5, 3.5, 7.0]
+        data = CensoredData.interval_censored(low=a, high=b)
+        assert_array_equal(data._interval, np.array(list(zip(a, b))))
+        assert data._uncensored.shape == (0,)
+        assert data._left.shape == (0,)
+        assert data._right.shape == (0,)
+
+    def test_interval_censored_mixed(self):
+        # This is actually a mix of uncensored, left-censored, right-censored
+        # and interval-censored data.  Check that when the `interval_censored`
+        # class method is used, the data is correctly separated into the
+        # appropriate arrays.
+        a = [0.5, -np.inf, -13.0, 2.0, 1.0, 10.0, -1.0]
+        b = [0.5, 2500.0, np.inf, 3.0, 1.0, 11.0, np.inf]
+        data = CensoredData.interval_censored(low=a, high=b)
+        assert_array_equal(data._interval, [[2.0, 3.0], [10.0, 11.0]])
+        assert_array_equal(data._uncensored, [0.5, 1.0])
+        assert_array_equal(data._left, [2500.0])
+        assert_array_equal(data._right, [-13.0, -1.0])
+
+    def test_interval_to_other_types(self):
+        # The interval parameter can represent uncensored and
+        # left- or right-censored data.  Test the conversion of such
+        # an example to the canonical form in which the different
+        # types have been split into the separate arrays.
+        interval = np.array([[0, 1],        # interval-censored
+                             [2, 2],        # not censored
+                             [3, 3],        # not censored
+                             [9, np.inf],   # right-censored
+                             [8, np.inf],   # right-censored
+                             [-np.inf, 0],  # left-censored
+                             [1, 2]])       # interval-censored
+        data = CensoredData(interval=interval)
+        assert_equal(data._uncensored, [2, 3])
+        assert_equal(data._left, [0])
+        assert_equal(data._right, [9, 8])
+        assert_equal(data._interval, [[0, 1], [1, 2]])
+
+    def test_empty_arrays(self):
+        data = CensoredData(uncensored=[], left=[], right=[], interval=[])
+        assert data._uncensored.shape == (0,)
+        assert data._left.shape == (0,)
+        assert data._right.shape == (0,)
+        assert data._interval.shape == (0, 2)
+        assert len(data) == 0
+
+    def test_invalid_constructor_args(self):
+        with pytest.raises(ValueError, match='must be a one-dimensional'):
+            CensoredData(uncensored=[[1, 2, 3]])
+        with pytest.raises(ValueError, match='must be a one-dimensional'):
+            CensoredData(left=[[1, 2, 3]])
+        with pytest.raises(ValueError, match='must be a one-dimensional'):
+            CensoredData(right=[[1, 2, 3]])
+        with pytest.raises(ValueError, match='must be a two-dimensional'):
+            CensoredData(interval=[[1, 2, 3]])
+
+        with pytest.raises(ValueError, match='must not contain nan'):
+            CensoredData(uncensored=[1, np.nan, 2])
+        with pytest.raises(ValueError, match='must not contain nan'):
+            CensoredData(left=[1, np.nan, 2])
+        with pytest.raises(ValueError, match='must not contain nan'):
+            CensoredData(right=[1, np.nan, 2])
+        with pytest.raises(ValueError, match='must not contain nan'):
+            CensoredData(interval=[[1, np.nan], [2, 3]])
+
+        with pytest.raises(ValueError,
+                           match='both values must not be infinite'):
+            CensoredData(interval=[[1, 3], [2, 9], [np.inf, np.inf]])
+
+        with pytest.raises(ValueError,
+                           match='left value must not exceed the right'):
+            CensoredData(interval=[[1, 0], [2, 2]])
+
+    @pytest.mark.parametrize('func', [CensoredData.left_censored,
+                                      CensoredData.right_censored])
+    def test_invalid_left_right_censored_args(self, func):
+        with pytest.raises(ValueError,
+                           match='`x` must be one-dimensional'):
+            func([[1, 2, 3]], [0, 1, 1])
+        with pytest.raises(ValueError,
+                           match='`censored` must be one-dimensional'):
+            func([1, 2, 3], [[0, 1, 1]])
+        with pytest.raises(ValueError, match='`x` must not contain'):
+            func([1, 2, np.nan], [0, 1, 1])
+        with pytest.raises(ValueError, match='must have the same length'):
+            func([1, 2, 3], [0, 0, 1, 1])
+
+    def test_invalid_censored_args(self):
+        with pytest.raises(ValueError,
+                           match='`low` must be a one-dimensional'):
+            CensoredData.interval_censored(low=[[3]], high=[4, 5])
+        with pytest.raises(ValueError,
+                           match='`high` must be a one-dimensional'):
+            CensoredData.interval_censored(low=[3], high=[[4, 5]])
+        with pytest.raises(ValueError, match='`low` must not contain'):
+            CensoredData.interval_censored([1, 2, np.nan], [0, 1, 1])
+        with pytest.raises(ValueError, match='must have the same length'):
+            CensoredData.interval_censored([1, 2, 3], [0, 0, 1, 1])
+
+    def test_count_censored(self):
+        x = [1, 2, 3]
+        # data1 has no censored data.
+        data1 = CensoredData(x)
+        assert data1.num_censored() == 0
+        data2 = CensoredData(uncensored=[2.5], left=[10], interval=[[0, 1]])
+        assert data2.num_censored() == 2
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/test_contingency.py b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_contingency.py
new file mode 100644
index 0000000000000000000000000000000000000000..aa83e05d7da6b3d21d5515a332344c2347f0d7eb
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_contingency.py
@@ -0,0 +1,294 @@
+import numpy as np
+from numpy.testing import (assert_equal, assert_array_equal,
+                           assert_array_almost_equal, assert_approx_equal,
+                           assert_allclose)
+import pytest
+from pytest import raises as assert_raises
+from scipy import stats
+from scipy.special import xlogy
+from scipy.stats.contingency import (margins, expected_freq,
+                                     chi2_contingency, association)
+
+
+def test_margins():
+    a = np.array([1])
+    m = margins(a)
+    assert_equal(len(m), 1)
+    m0 = m[0]
+    assert_array_equal(m0, np.array([1]))
+
+    a = np.array([[1]])
+    m0, m1 = margins(a)
+    expected0 = np.array([[1]])
+    expected1 = np.array([[1]])
+    assert_array_equal(m0, expected0)
+    assert_array_equal(m1, expected1)
+
+    a = np.arange(12).reshape(2, 6)
+    m0, m1 = margins(a)
+    expected0 = np.array([[15], [51]])
+    expected1 = np.array([[6, 8, 10, 12, 14, 16]])
+    assert_array_equal(m0, expected0)
+    assert_array_equal(m1, expected1)
+
+    a = np.arange(24).reshape(2, 3, 4)
+    m0, m1, m2 = margins(a)
+    expected0 = np.array([[[66]], [[210]]])
+    expected1 = np.array([[[60], [92], [124]]])
+    expected2 = np.array([[[60, 66, 72, 78]]])
+    assert_array_equal(m0, expected0)
+    assert_array_equal(m1, expected1)
+    assert_array_equal(m2, expected2)
+
+
+def test_expected_freq():
+    assert_array_equal(expected_freq([1]), np.array([1.0]))
+
+    observed = np.array([[[2, 0], [0, 2]], [[0, 2], [2, 0]], [[1, 1], [1, 1]]])
+    e = expected_freq(observed)
+    assert_array_equal(e, np.ones_like(observed))
+
+    observed = np.array([[10, 10, 20], [20, 20, 20]])
+    e = expected_freq(observed)
+    correct = np.array([[12., 12., 16.], [18., 18., 24.]])
+    assert_array_almost_equal(e, correct)
+
+
+class TestChi2Contingency:
+    def test_chi2_contingency_trivial(self):
+        # Some very simple tests for chi2_contingency.
+
+        # A trivial case
+        obs = np.array([[1, 2], [1, 2]])
+        chi2, p, dof, expected = chi2_contingency(obs, correction=False)
+        assert_equal(chi2, 0.0)
+        assert_equal(p, 1.0)
+        assert_equal(dof, 1)
+        assert_array_equal(obs, expected)
+
+        # A *really* trivial case: 1-D data.
+        obs = np.array([1, 2, 3])
+        chi2, p, dof, expected = chi2_contingency(obs, correction=False)
+        assert_equal(chi2, 0.0)
+        assert_equal(p, 1.0)
+        assert_equal(dof, 0)
+        assert_array_equal(obs, expected)
+
+    def test_chi2_contingency_R(self):
+        # Some test cases that were computed independently, using R.
+
+        # Rcode = \
+        # """
+        # # Data vector.
+        # data <- c(
+        #   12, 34, 23,     4,  47,  11,
+        #   35, 31, 11,    34,  10,  18,
+        #   12, 32,  9,    18,  13,  19,
+        #   12, 12, 14,     9,  33,  25
+        #   )
+        #
+        # # Create factor tags:r=rows, c=columns, t=tiers
+        # r <- factor(gl(4, 2*3, 2*3*4, labels=c("r1", "r2", "r3", "r4")))
+        # c <- factor(gl(3, 1,   2*3*4, labels=c("c1", "c2", "c3")))
+        # t <- factor(gl(2, 3,   2*3*4, labels=c("t1", "t2")))
+        #
+        # # 3-way Chi squared test of independence
+        # s = summary(xtabs(data~r+c+t))
+        # print(s)
+        # """
+        # Routput = \
+        # """
+        # Call: xtabs(formula = data ~ r + c + t)
+        # Number of cases in table: 478
+        # Number of factors: 3
+        # Test for independence of all factors:
+        #         Chisq = 102.17, df = 17, p-value = 3.514e-14
+        # """
+        obs = np.array(
+            [[[12, 34, 23],
+              [35, 31, 11],
+              [12, 32, 9],
+              [12, 12, 14]],
+             [[4, 47, 11],
+              [34, 10, 18],
+              [18, 13, 19],
+              [9, 33, 25]]])
+        chi2, p, dof, expected = chi2_contingency(obs)
+        assert_approx_equal(chi2, 102.17, significant=5)
+        assert_approx_equal(p, 3.514e-14, significant=4)
+        assert_equal(dof, 17)
+
+        # Rcode = \
+        # """
+        # # Data vector.
+        # data <- c(
+        #     #
+        #     12, 17,
+        #     11, 16,
+        #     #
+        #     11, 12,
+        #     15, 16,
+        #     #
+        #     23, 15,
+        #     30, 22,
+        #     #
+        #     14, 17,
+        #     15, 16
+        #     )
+        #
+        # # Create factor tags:r=rows, c=columns, d=depths(?), t=tiers
+        # r <- factor(gl(2, 2,  2*2*2*2, labels=c("r1", "r2")))
+        # c <- factor(gl(2, 1,  2*2*2*2, labels=c("c1", "c2")))
+        # d <- factor(gl(2, 4,  2*2*2*2, labels=c("d1", "d2")))
+        # t <- factor(gl(2, 8,  2*2*2*2, labels=c("t1", "t2")))
+        #
+        # # 4-way Chi squared test of independence
+        # s = summary(xtabs(data~r+c+d+t))
+        # print(s)
+        # """
+        # Routput = \
+        # """
+        # Call: xtabs(formula = data ~ r + c + d + t)
+        # Number of cases in table: 262
+        # Number of factors: 4
+        # Test for independence of all factors:
+        #         Chisq = 8.758, df = 11, p-value = 0.6442
+        # """
+        obs = np.array(
+            [[[[12, 17],
+               [11, 16]],
+              [[11, 12],
+               [15, 16]]],
+             [[[23, 15],
+               [30, 22]],
+              [[14, 17],
+               [15, 16]]]])
+        chi2, p, dof, expected = chi2_contingency(obs)
+        assert_approx_equal(chi2, 8.758, significant=4)
+        assert_approx_equal(p, 0.6442, significant=4)
+        assert_equal(dof, 11)
+
+    def test_chi2_contingency_g(self):
+        c = np.array([[15, 60], [15, 90]])
+        g, p, dof, e = chi2_contingency(c, lambda_='log-likelihood',
+                                        correction=False)
+        assert_allclose(g, 2*xlogy(c, c/e).sum())
+
+        g, p, dof, e = chi2_contingency(c, lambda_='log-likelihood',
+                                        correction=True)
+        c_corr = c + np.array([[-0.5, 0.5], [0.5, -0.5]])
+        assert_allclose(g, 2*xlogy(c_corr, c_corr/e).sum())
+
+        c = np.array([[10, 12, 10], [12, 10, 10]])
+        g, p, dof, e = chi2_contingency(c, lambda_='log-likelihood')
+        assert_allclose(g, 2*xlogy(c, c/e).sum())
+
+    def test_chi2_contingency_bad_args(self):
+        # Test that "bad" inputs raise a ValueError.
+
+        # Negative value in the array of observed frequencies.
+        obs = np.array([[-1, 10], [1, 2]])
+        assert_raises(ValueError, chi2_contingency, obs)
+
+        # The zeros in this will result in zeros in the array
+        # of expected frequencies.
+        obs = np.array([[0, 1], [0, 1]])
+        assert_raises(ValueError, chi2_contingency, obs)
+
+        # A degenerate case: `observed` has size 0.
+        obs = np.empty((0, 8))
+        assert_raises(ValueError, chi2_contingency, obs)
+
+    def test_chi2_contingency_yates_gh13875(self):
+        # Magnitude of Yates' continuity correction should not exceed difference
+        # between expected and observed value of the statistic; see gh-13875
+        observed = np.array([[1573, 3], [4, 0]])
+        p = chi2_contingency(observed)[1]
+        assert_allclose(p, 1, rtol=1e-12)
+
+    @pytest.mark.parametrize("correction", [False, True])
+    def test_result(self, correction):
+        obs = np.array([[1, 2], [1, 2]])
+        res = chi2_contingency(obs, correction=correction)
+        assert_equal((res.statistic, res.pvalue, res.dof, res.expected_freq), res)
+
+    @pytest.mark.slow
+    def test_exact_permutation(self):
+        table = np.arange(4).reshape(2, 2)
+        ref_statistic = chi2_contingency(table, correction=False).statistic
+        ref_pvalue = stats.fisher_exact(table).pvalue
+        method = stats.PermutationMethod(n_resamples=50000)
+        res = chi2_contingency(table, correction=False, method=method)
+        assert_equal(res.statistic, ref_statistic)
+        assert_allclose(res.pvalue, ref_pvalue, rtol=1e-15)
+
+    @pytest.mark.slow
+    @pytest.mark.parametrize('method', (stats.PermutationMethod,
+                                        stats.MonteCarloMethod))
+    def test_resampling_randomized(self, method):
+        rng = np.random.default_rng(2592340925)
+        # need to have big sum for asymptotic approximation to be good
+        rows = [300, 1000, 800]
+        cols = [200, 400, 800, 700]
+        table = stats.random_table(rows, cols, seed=rng).rvs()
+        res = chi2_contingency(table, correction=False, method=method(rng=rng))
+        ref = chi2_contingency(table, correction=False)
+        assert_equal(res.statistic, ref.statistic)
+        assert_allclose(res.pvalue, ref.pvalue, atol=5e-3)
+        assert_equal(res.dof, np.nan)
+        assert_equal(res.expected_freq, ref.expected_freq)
+
+    def test_resampling_invalid_args(self):
+        table = np.arange(8).reshape(2, 2, 2)
+
+        method = stats.PermutationMethod()
+        message = "Use of `method` is only compatible with two-way tables."
+        with pytest.raises(ValueError, match=message):
+            chi2_contingency(table, correction=False, method=method)
+
+        table = np.arange(4).reshape(2, 2)
+
+        method = stats.PermutationMethod()
+        message = "`correction=True` is not compatible with..."
+        with pytest.raises(ValueError, match=message):
+            chi2_contingency(table, method=method)
+
+        method = stats.MonteCarloMethod()
+        message = "`lambda_=2` is not compatible with..."
+        with pytest.raises(ValueError, match=message):
+            chi2_contingency(table, correction=False, lambda_=2, method=method)
+
+        method = 'herring'
+        message = "`method='herring'` not recognized; if provided, `method`..."
+        with pytest.raises(ValueError, match=message):
+            chi2_contingency(table, correction=False, method=method)
+
+        method = stats.MonteCarloMethod(rvs=stats.norm.rvs)
+        message = "If the `method` argument of `chi2_contingency` is..."
+        with pytest.raises(ValueError, match=message):
+            chi2_contingency(table, correction=False, method=method)
+
+
+def test_bad_association_args():
+    # Invalid Test Statistic
+    assert_raises(ValueError, association, [[1, 2], [3, 4]], "X")
+    # Invalid array shape
+    assert_raises(ValueError, association, [[[1, 2]], [[3, 4]]], "cramer")
+    # chi2_contingency exception
+    assert_raises(ValueError, association, [[-1, 10], [1, 2]], 'cramer')
+    # Invalid Array Item Data Type
+    assert_raises(ValueError, association,
+                  np.array([[1, 2], ["dd", 4]], dtype=object), 'cramer')
+
+
+@pytest.mark.parametrize('stat, expected',
+                         [('cramer', 0.09222412010290792),
+                          ('tschuprow', 0.0775509319944633),
+                          ('pearson', 0.12932925727138758)])
+def test_assoc(stat, expected):
+    # 2d Array
+    obs1 = np.array([[12, 13, 14, 15, 16],
+                     [17, 16, 18, 19, 11],
+                     [9, 15, 14, 12, 11]])
+    a = association(observed=obs1, method=stat)
+    assert_allclose(a, expected)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/test_continued_fraction.py b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_continued_fraction.py
new file mode 100644
index 0000000000000000000000000000000000000000..e6911aa4956cc66a95eeb1e87aedb04782e2440b
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_continued_fraction.py
@@ -0,0 +1,168 @@
+import math
+
+import pytest
+import numpy as np
+
+from scipy._lib._array_api import array_namespace
+from scipy._lib._array_api_no_0d import xp_assert_close, xp_assert_less, xp_assert_equal
+from scipy.stats._continued_fraction import _continued_fraction
+
+
+@pytest.mark.skip_xp_backends('array_api_strict', reason='No fancy indexing assignment')
+@pytest.mark.skip_xp_backends('jax.numpy', reason="Don't support mutation")
+# dask doesn't like lines like this
+# n = int(xp.real(xp_ravel(n))[0])
+# (at some point in here the shape becomes nan)
+@pytest.mark.skip_xp_backends('dask.array', reason="dask has issues with the shapes")
+@pytest.mark.uses_xp_capabilities(False, reason="private")
+class TestContinuedFraction:
+    rng = np.random.default_rng(5895448232066142650)
+    p = rng.uniform(1, 10, size=10)
+
+    def a1(self, n, x=1.5):
+        if n == 0:
+            y = 0*x
+        elif n == 1:
+            y = x
+        else:
+            y = -x**2
+        return y
+
+    def b1(self, n, x=1.5):
+        if n == 0:
+            y = 0*x
+        else:
+            one = x/x  # gets array of correct type, dtype, and shape
+            y = one * (2*n - 1)
+        return y
+
+    def log_a1(self, n, x):
+        xp = array_namespace(x)
+        if n == 0:
+            y = xp.full_like(x, -xp.asarray(math.inf, dtype=x.dtype))
+        elif n == 1:
+            y = xp.log(x)
+        else:
+            y = 2 * xp.log(x) + math.pi * 1j
+        return y
+
+    def log_b1(self, n, x):
+        xp = array_namespace(x)
+        if n == 0:
+            y = xp.full_like(x, -xp.asarray(math.inf, dtype=x.dtype))
+        else:
+            one = x - x  # gets array of correct type, dtype, and shape
+            y = one + math.log(2 * n - 1)
+        return y
+
+    def test_input_validation(self, xp):
+        a1 = self.a1
+        b1 = self.b1
+
+        message = '`a` and `b` must be callable.'
+        with pytest.raises(ValueError, match=message):
+            _continued_fraction(1, b1)
+        with pytest.raises(ValueError, match=message):
+            _continued_fraction(a1, 1)
+
+        message = r'`eps` and `tiny` must be \(or represent the logarithm of\)...'
+        with pytest.raises(ValueError, match=message):
+            _continued_fraction(a1, b1, tolerances={'eps': -10})
+        with pytest.raises(ValueError, match=message):
+            _continued_fraction(a1, b1, tolerances={'eps': np.nan})
+        with pytest.raises(ValueError, match=message):
+            _continued_fraction(a1, b1, tolerances={'eps': 1+1j}, log=True)
+        with pytest.raises(ValueError, match=message):
+            _continued_fraction(a1, b1, tolerances={'tiny': 0})
+        with pytest.raises(ValueError, match=message):
+            _continued_fraction(a1, b1, tolerances={'tiny': np.inf})
+        with pytest.raises(ValueError, match=message):
+            _continued_fraction(a1, b1, tolerances={'tiny': np.inf}, log=True)
+        # this should not raise
+        kwargs = dict(args=xp.asarray(1.5+0j), log=True, maxiter=0)
+        _continued_fraction(a1, b1, tolerances={'eps': -10}, **kwargs)
+        _continued_fraction(a1, b1, tolerances={'tiny': -10}, **kwargs)
+
+        message = '`maxiter` must be a non-negative integer.'
+        with pytest.raises(ValueError, match=message):
+            _continued_fraction(a1, b1, maxiter=-1)
+
+        message = '`log` must be boolean.'
+        with pytest.raises(ValueError, match=message):
+            _continued_fraction(a1, b1, log=2)
+
+    @pytest.mark.parametrize('dtype', ['float32', 'float64', 'complex64', 'complex128'])
+    @pytest.mark.parametrize('shape', [(), (1,), (3,), (3, 2)])
+    def test_basic(self, shape, dtype, xp):
+        np_dtype = getattr(np, dtype)
+        xp_dtype = getattr(xp, dtype)
+        rng = np.random.default_rng(2435908729190400)
+
+        x = rng.random(shape).astype(np_dtype)
+        x = x + rng.random(shape).astype(np_dtype)*1j if dtype.startswith('c') else x
+        x = xp.asarray(x, dtype=xp_dtype)
+
+        res = _continued_fraction(self.a1, self.b1, args=(x,))
+        ref = xp.tan(x)
+        xp_assert_close(res.f, ref)
+
+    @pytest.mark.skip_xp_backends('torch', reason='pytorch/pytorch#136063')
+    @pytest.mark.parametrize('dtype', ['float32', 'float64'])
+    @pytest.mark.parametrize('shape', [(), (1,), (3,), (3, 2)])
+    def test_log(self, shape, dtype, xp):
+        np_dtype = getattr(np, dtype)
+        rng = np.random.default_rng(2435908729190400)
+        x = rng.random(shape).astype(np_dtype)
+        x = xp.asarray(x)
+
+        res = _continued_fraction(self.log_a1, self.log_b1, args=(x + 0j,), log=True)
+        ref = xp.tan(x)
+        xp_assert_close(xp.exp(xp.real(res.f)), ref)
+
+    def test_maxiter(self, xp):
+        rng = np.random.default_rng(2435908729190400)
+        x = xp.asarray(rng.random(), dtype=xp.float64)
+        ref = xp.tan(x)
+
+        res1 = _continued_fraction(self.a1, self.b1, args=(x,), maxiter=3)
+        assert res1.nit == 3
+
+        res2 = _continued_fraction(self.a1, self.b1, args=(x,), maxiter=6)
+        assert res2.nit == 6
+
+        xp_assert_less(xp.abs(res2.f - ref), xp.abs(res1.f - ref))
+
+    def test_eps(self, xp):
+        x = xp.asarray(1.5, dtype=xp.float64)  # x = 1.5 is the default defined above
+        ref = xp.tan(x)
+        res1 = _continued_fraction(self.a1, self.b1, args=(x,),
+                                   tolerances={'eps': 1e-6})
+        res2 = _continued_fraction(self.a1, self.b1, args=(x,))
+        xp_assert_less(res1.nit, res2.nit)
+        xp_assert_less(xp.abs(res2.f - ref), xp.abs(res1.f - ref))
+
+    def test_feval(self, xp):
+        def a(n, x):
+            a.nfev += 1
+            return n * x
+
+        def b(n, x):
+            b.nfev += 1
+            return n * x
+
+        a.nfev, b.nfev = 0, 0
+
+        res = _continued_fraction(a, b, args=(xp.asarray(1.),))
+        assert res.nfev == a.nfev == b.nfev == res.nit + 1
+
+    def test_status(self, xp):
+        x = xp.asarray([1, 10, np.nan], dtype=xp.float64)
+        res = _continued_fraction(self.a1, self.b1, args=(x,), maxiter=15)
+        xp_assert_equal(res.success, xp.asarray([True, False, False]))
+        xp_assert_equal(res.status, xp.asarray([0, -2, -3], dtype=xp.int32))
+
+    def test_special_cases(self, xp):
+        one = xp.asarray(1)
+        res = _continued_fraction(lambda x: one, lambda x: one, maxiter=0)
+        xp_assert_close(res.f, xp.asarray(1.))
+        assert res.nit == res.nfev - 1 == 0
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/test_continuous.py b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_continuous.py
new file mode 100644
index 0000000000000000000000000000000000000000..898b7bcdf6b5ae4d72404fe98a3fd32ea8a90564
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_continuous.py
@@ -0,0 +1,2328 @@
+import itertools as it
+import os
+import pickle
+from copy import deepcopy
+
+import numpy as np
+from numpy import inf
+import pytest
+from numpy.testing import assert_allclose, assert_equal
+from hypothesis import strategies, given, reproduce_failure, settings  # noqa: F401
+import hypothesis.extra.numpy as npst
+
+from scipy import special
+from scipy import stats
+from scipy.stats._fit import _kolmogorov_smirnov
+from scipy.stats._ksstats import kolmogn
+from scipy.stats import qmc
+from scipy.stats._distr_params import distcont, distdiscrete
+from scipy.stats._distribution_infrastructure import (
+    _Domain, _RealInterval, _Parameter, _Parameterization, _RealParameter,
+    ContinuousDistribution, ShiftedScaledDistribution, _fiinfo,
+    _generate_domain_support, Mixture, _logexpxmexpy)
+from scipy.stats._new_distributions import StandardNormal, _LogUniform, _Gamma
+from scipy.stats._new_distributions import DiscreteDistribution
+from scipy.stats import Normal, Logistic, Uniform, Binomial
+
+
+class Test_RealInterval:
+    rng = np.random.default_rng(349849812549824)
+
+    def test_iv(self):
+        domain = _RealInterval(endpoints=('a', 'b'))
+        message = "The endpoints of the distribution are defined..."
+        with pytest.raises(TypeError, match=message):
+            domain.get_numerical_endpoints(dict)
+
+    @pytest.mark.parametrize('x', [rng.uniform(10, 10, size=(2, 3, 4)),
+                                   -np.inf, np.pi])
+    def test_contains_simple(self, x):
+        # Test `contains` when endpoints are defined by constants
+        a, b = -np.inf, np.pi
+        domain = _RealInterval(endpoints=(a, b), inclusive=(False, True))
+        assert_equal(domain.contains(x), (a < x) & (x <= b))
+
+    @pytest.mark.slow
+    @given(shapes=npst.mutually_broadcastable_shapes(num_shapes=3, min_side=0),
+           inclusive_a=strategies.booleans(),
+           inclusive_b=strategies.booleans(),
+           data=strategies.data())
+    def test_contains(self, shapes, inclusive_a, inclusive_b, data):
+        # Test `contains` when endpoints are defined by parameters
+        input_shapes, result_shape = shapes
+        shape_a, shape_b, shape_x = input_shapes
+
+        # Without defining min and max values, I spent forever trying to set
+        # up a valid test without overflows or similar just drawing arrays.
+        a_elements = dict(allow_nan=False, allow_infinity=False,
+                          min_value=-1e3, max_value=1)
+        b_elements = dict(allow_nan=False, allow_infinity=False,
+                          min_value=2, max_value=1e3)
+        a = data.draw(npst.arrays(npst.floating_dtypes(),
+                                  shape_a, elements=a_elements))
+        b = data.draw(npst.arrays(npst.floating_dtypes(),
+                                  shape_b, elements=b_elements))
+        # ensure some points are to the left, some to the right, and some
+        # are exactly on the boundary
+        d = b - a
+        x = np.concatenate([np.linspace(a-d, a, 10),
+                            np.linspace(a, b, 10),
+                            np.linspace(b, b+d, 10)])
+        # Domain is defined by two parameters, 'a' and 'b'
+        domain = _RealInterval(endpoints=('a', 'b'),
+                             inclusive=(inclusive_a, inclusive_b))
+        domain.define_parameters(_RealParameter('a', domain=_RealInterval()),
+                                 _RealParameter('b', domain=_RealInterval()))
+        # Check that domain and string evaluation give the same result
+        res = domain.contains(x, dict(a=a, b=b))
+
+        # Apparently, `np.float16([2]) < np.float32(2.0009766)` is False
+        # but `np.float16([2]) < np.float32([2.0009766])` is True
+        # dtype = np.result_type(a.dtype, b.dtype, x.dtype)
+        # a, b, x = a.astype(dtype), b.astype(dtype), x.astype(dtype)
+        # unclear whether we should be careful about this, since it will be
+        # fixed with NEP50. Just do what makes the test pass.
+        left_comparison = '<=' if inclusive_a else '<'
+        right_comparison = '<=' if inclusive_b else '<'
+        ref = eval(f'(a {left_comparison} x) & (x {right_comparison} b)')
+        assert_equal(res, ref)
+
+    @pytest.mark.parametrize("inclusive", list(it.product([True, False], repeat=2)))
+    @pytest.mark.parametrize("a,b", [(0, 1), (3, 1)])
+    def test_contains_function_endpoints(self, inclusive, a, b):
+        # Test `contains` when endpoints are defined by functions.
+        endpoints = (lambda a, b: (a - b) / 2, lambda a, b: (a + b) / 2)
+        domain = _RealInterval(endpoints=endpoints, inclusive=inclusive)
+        x = np.asarray([(a - 2*b)/2, (a - b)/2, a/2, (a + b)/2, (a + 2*b)/2])
+        res = domain.contains(x, dict(a=a, b=b))
+
+        numerical_endpoints = ((a - b) / 2, (a + b) / 2)
+        assert numerical_endpoints == domain.get_numerical_endpoints(dict(a=a, b=b))
+        alpha, beta = numerical_endpoints
+
+        above_left = alpha <= x if inclusive[0] else alpha < x
+        below_right = x <= beta if inclusive[1] else x < beta
+        ref = above_left & below_right
+        assert_equal(res, ref)
+
+
+    @pytest.mark.parametrize('case', [
+        (-np.inf, np.pi, False, True, r"(-\infty, \pi]"),
+        ('a', 5, True, False, "[a, 5)")
+    ])
+    def test_str(self, case):
+        domain = _RealInterval(endpoints=case[:2], inclusive=case[2:4])
+        assert str(domain) == case[4]
+
+    @pytest.mark.slow
+    @given(a=strategies.one_of(
+        strategies.decimals(allow_nan=False),
+        strategies.characters(whitelist_categories="L"),  # type: ignore[arg-type]
+        strategies.sampled_from(list(_Domain.symbols))),
+           b=strategies.one_of(
+        strategies.decimals(allow_nan=False),
+        strategies.characters(whitelist_categories="L"),  # type: ignore[arg-type]
+        strategies.sampled_from(list(_Domain.symbols))),
+           inclusive_a=strategies.booleans(),
+           inclusive_b=strategies.booleans(),
+           )
+    def test_str2(self, a, b, inclusive_a, inclusive_b):
+        # I wrote this independently from the implementation of __str__, but
+        # I imagine it looks pretty similar to __str__.
+        a = _Domain.symbols.get(a, a)
+        b = _Domain.symbols.get(b, b)
+        left_bracket = '[' if inclusive_a else '('
+        right_bracket = ']' if inclusive_b else ')'
+        domain = _RealInterval(endpoints=(a, b),
+                             inclusive=(inclusive_a, inclusive_b))
+        ref = f"{left_bracket}{a}, {b}{right_bracket}"
+        assert str(domain) == ref
+
+    def test_symbols_gh22137(self):
+        # `symbols` was accidentally shared between instances originally
+        # Check that this is no longer the case
+        domain1 = _RealInterval(endpoints=(0, 1))
+        domain2 = _RealInterval(endpoints=(0, 1))
+        assert domain1.symbols is not domain2.symbols
+
+
+def draw_distribution_from_family(family, data, rng, proportions, min_side=0):
+    # If the distribution has parameters, choose a parameterization and
+    # draw broadcastable shapes for the parameter arrays.
+    n_parameterizations = family._num_parameterizations()
+    if n_parameterizations > 0:
+        i = data.draw(strategies.integers(0, max_value=n_parameterizations-1))
+        n_parameters = family._num_parameters(i)
+        shapes, result_shape = data.draw(
+            npst.mutually_broadcastable_shapes(num_shapes=n_parameters,
+                                               min_side=min_side))
+        dist = family._draw(shapes, rng=rng, proportions=proportions,
+                            i_parameterization=i)
+    else:
+        dist = family._draw(rng=rng)
+        result_shape = tuple()
+
+    # Draw a broadcastable shape for the arguments, and draw values for the
+    # arguments.
+    x_shape = data.draw(npst.broadcastable_shapes(result_shape,
+                                                  min_side=min_side))
+    x = dist._variable.draw(x_shape, parameter_values=dist._parameters,
+                            proportions=proportions, rng=rng, region='typical')
+    x_result_shape = np.broadcast_shapes(x_shape, result_shape)
+    y_shape = data.draw(npst.broadcastable_shapes(x_result_shape,
+                                                  min_side=min_side))
+    y = dist._variable.draw(y_shape, parameter_values=dist._parameters,
+                            proportions=proportions, rng=rng, region='typical')
+    xy_result_shape = np.broadcast_shapes(y_shape, x_result_shape)
+    p_domain = _RealInterval((0, 1), (True, True))
+    p_var = _RealParameter('p', domain=p_domain)
+    p = p_var.draw(x_shape, proportions=proportions, rng=rng)
+    with np.errstate(divide='ignore', invalid='ignore'):
+        logp = np.log(p)
+
+    return dist, x, y, p, logp, result_shape, x_result_shape, xy_result_shape
+
+
+continuous_families = [
+    StandardNormal,
+    Normal,
+    Logistic,
+    Uniform,
+    _LogUniform
+]
+
+discrete_families = [
+    Binomial,
+]
+
+families = continuous_families + discrete_families
+
+
+class TestDistributions:
+    @pytest.mark.fail_slow(60)  # need to break up check_moment_funcs
+    @settings(max_examples=20)
+    @pytest.mark.parametrize('family', families)
+    @given(data=strategies.data(), seed=strategies.integers(min_value=0))
+    def test_support_moments_sample(self, family, data, seed):
+        rng = np.random.default_rng(seed)
+
+        # relative proportions of valid, endpoint, out of bounds, and NaN params
+        proportions = (0.7, 0.1, 0.1, 0.1)
+        tmp = draw_distribution_from_family(family, data, rng, proportions)
+        dist, x, y, p, logp, result_shape, x_result_shape, xy_result_shape = tmp
+        sample_shape = data.draw(npst.array_shapes(min_dims=0, min_side=0,
+                                                   max_side=20))
+
+        with np.errstate(invalid='ignore', divide='ignore'):
+            check_support(dist)
+            check_moment_funcs(dist, result_shape)  # this needs to get split up
+            check_lmoment_funcs(dist, result_shape)
+            check_sample_shape_NaNs(dist, 'sample', sample_shape, result_shape, rng)
+            qrng = qmc.Halton(d=1, seed=rng)
+            check_sample_shape_NaNs(dist, 'sample', sample_shape, result_shape, qrng)
+
+    @pytest.mark.fail_slow(10)
+    @pytest.mark.parametrize('family', families)
+    @pytest.mark.parametrize('func, methods, arg',
+                             [('entropy', {'log/exp', 'quadrature'}, None),
+                              ('logentropy', {'log/exp', 'quadrature'}, None),
+                              ('median', {'icdf'}, None),
+                              ('mode', {'optimization'}, None),
+                              ('mean', {'cache'}, None),
+                              ('variance', {'cache'}, None),
+                              ('skewness', {'cache'}, None),
+                              ('kurtosis', {'cache'}, None),
+                              ('pdf', {'log/exp'}, 'x'),
+                              ('logpdf', {'log/exp'}, 'x'),
+                              ('logcdf', {'log/exp', 'complement', 'quadrature'}, 'x'),
+                              ('cdf', {'log/exp', 'complement', 'quadrature'}, 'x'),
+                              ('logccdf', {'log/exp', 'complement', 'quadrature'}, 'x'),
+                              ('ccdf', {'log/exp', 'complement', 'quadrature'}, 'x'),
+                              ('ilogccdf', {'complement', 'inversion'}, 'logp'),
+                              ('iccdf', {'complement', 'inversion'}, 'p'),
+                              ])
+    @settings(max_examples=20)
+    @given(data=strategies.data(), seed=strategies.integers(min_value=0))
+    def test_funcs(self, family, data, seed, func, methods, arg):
+        if family == Uniform and func == 'mode':
+            pytest.skip("Mode is not unique; `method`s disagree.")
+
+        rng = np.random.default_rng(seed)
+
+        # relative proportions of valid, endpoint, out of bounds, and NaN params
+        proportions = (0.7, 0.1, 0.1, 0.1)
+        tmp = draw_distribution_from_family(family, data, rng, proportions)
+        dist, x, y, p, logp, result_shape, x_result_shape, xy_result_shape = tmp
+
+        args = {'x': x, 'p': p, 'logp': p}
+        with np.errstate(invalid='ignore', divide='ignore', over='ignore'):
+            if arg is None:
+                check_dist_func(dist, func, None, result_shape, methods)
+            elif arg in args:
+                check_dist_func(dist, func, args[arg], x_result_shape, methods)
+
+        if func == 'variance':
+            assert_allclose(dist.standard_deviation()**2, dist.variance())
+
+        # invalid and divide are to be expected; maybe look into over
+        with np.errstate(invalid='ignore', divide='ignore', over='ignore'):
+            if not isinstance(dist, ShiftedScaledDistribution):
+                if func == 'cdf':
+                    methods = {'quadrature'}
+                    check_cdf2(dist, False, x, y, xy_result_shape, methods)
+                    check_cdf2(dist, True, x, y, xy_result_shape, methods)
+                elif func == 'ccdf':
+                    methods = {'addition'}
+                    check_ccdf2(dist, False, x, y, xy_result_shape, methods)
+                    check_ccdf2(dist, True, x, y, xy_result_shape, methods)
+
+    def test_plot(self):
+        try:
+            import matplotlib.pyplot as plt
+        except ImportError:
+            return
+
+        X = Uniform(a=0., b=1.)
+        ax = X.plot()
+        assert ax == plt.gca()
+
+    @pytest.mark.parametrize('method_name', ['cdf', 'ccdf'])
+    def test_complement_safe(self, method_name):
+        X = stats.Normal(mu=1, sigma=2)
+        X.tol = 1e-12
+        p = np.asarray([1e-4, 1e-3])
+        func = getattr(X, method_name)
+        ifunc = getattr(X, 'i'+method_name)
+        x = ifunc(p, method='formula')
+        p1 = func(x, method='complement_safe')
+        p2 = func(x, method='complement')
+        assert_equal(p1[1], p2[1])
+        assert p1[0] != p2[0]
+        assert_allclose(p1[0], p[0], rtol=X.tol)
+
+    @pytest.mark.parametrize('method_name', ['cdf', 'ccdf'])
+    def test_icomplement_safe(self, method_name):
+        X = stats.Normal(mu=1, sigma=2)
+        X.tol = 1e-12
+        p = np.asarray([1e-4, 1e-3])
+        func = getattr(X, method_name)
+        ifunc = getattr(X, 'i'+method_name)
+        x1 = ifunc(p, method='complement_safe')
+        x2 = ifunc(p, method='complement')
+        assert_equal(x1[1], x2[1])
+        assert x1[0] != x2[0]
+        assert_allclose(func(x1[0]), p[0], rtol=X.tol)
+
+    def test_subtraction_safe(self):
+        X = stats.Normal()
+        X.tol = 1e-12
+
+        # Regular subtraction is fine in either tail (and of course, across tails)
+        x = [-11, -10, 10, 11]
+        y = [-10, -11, 11, 10]
+        p0 = X.cdf(x, y, method='quadrature')
+        p1 = X.cdf(x, y, method='subtraction_safe')
+        p2 = X.cdf(x, y, method='subtraction')
+        assert_equal(p2, p1)
+        assert_allclose(p1, p0, rtol=X.tol)
+
+        # Safe subtraction is needed in special cases
+        x = np.asarray([-1e-20, -1e-21, 1e-20, 1e-21, -1e-20])
+        y = np.asarray([-1e-21, -1e-20, 1e-21, 1e-20, 1e-20])
+
+
+        p0 = X.pdf(0)*(y-x)
+        p1 = X.cdf(x, y, method='subtraction_safe')
+        p2 = X.cdf(x, y, method='subtraction')
+        assert_equal(p2, 0)
+        assert_allclose(p1, p0, rtol=X.tol)
+
+    def test_logentropy_safe(self):
+        # simulate an `entropy` calculation over/underflowing with extreme parameters
+        class _Normal(stats.Normal):
+            def _entropy_formula(self, **params):
+                out = np.asarray(super()._entropy_formula(**params))
+                out[0] = 0
+                out[-1] = np.inf
+                return out
+
+        X = _Normal(sigma=[1, 2, 3])
+        with np.errstate(divide='ignore'):
+            res1 = X.logentropy(method='logexp_safe')
+            res2 = X.logentropy(method='logexp')
+        ref = X.logentropy(method='quadrature')
+        i_fl = [0, -1]  # first and last
+        assert np.isinf(res2[i_fl]).all()
+        assert res1[1] == res2[1]
+        # quadrature happens to be perfectly accurate on some platforms
+        # assert res1[1] != ref[1]
+        assert_equal(res1[i_fl], ref[i_fl])
+
+    def test_logcdf2_safe(self):
+        # test what happens when 2-arg `cdf` underflows
+        X = stats.Normal(sigma=[1, 2, 3])
+        x = [-301, 1, 300]
+        y = [-300, 2, 301]
+        with np.errstate(divide='ignore'):
+            res1 = X.logcdf(x, y, method='logexp_safe')
+            res2 = X.logcdf(x, y, method='logexp')
+        ref = X.logcdf(x, y, method='quadrature')
+        i_fl = [0, -1]  # first and last
+        assert np.isinf(res2[i_fl]).all()
+        assert res1[1] == res2[1]
+        # quadrature happens to be perfectly accurate on some platforms
+        # assert res1[1] != ref[1]
+        assert_equal(res1[i_fl], ref[i_fl])
+
+    @pytest.mark.parametrize('method_name', ['logcdf', 'logccdf'])
+    def test_logexp_safe(self, method_name):
+        # test what happens when `cdf`/`ccdf` underflows
+        X = stats.Normal(sigma=2)
+        x = [-301, 1] if method_name == 'logcdf' else [301, 1]
+        func = getattr(X, method_name)
+        with np.errstate(divide='ignore'):
+            res1 = func(x, method='logexp_safe')
+            res2 = func(x, method='logexp')
+        ref = func(x, method='quadrature')
+        assert res1[0] == ref[0]
+        assert res1[0] != res2[0]
+        assert res1[1] == res2[1]
+        assert res1[1] != ref[1]
+
+def check_sample_shape_NaNs(dist, fname, sample_shape, result_shape, rng):
+    full_shape = sample_shape + result_shape
+    if fname == 'sample':
+        sample_method = dist.sample
+
+    methods = {'inverse_transform'}
+    if dist._overrides(f'_{fname}_formula') and not isinstance(rng, qmc.QMCEngine):
+        methods.add('formula')
+
+    for method in methods:
+        res = sample_method(sample_shape, method=method, rng=rng)
+        valid_parameters = np.broadcast_to(get_valid_parameters(dist),
+                                           res.shape)
+        assert_equal(res.shape, full_shape)
+        np.testing.assert_equal(res.dtype, dist._dtype)
+
+        if full_shape == ():
+            # NumPy random makes a distinction between a 0d array and a scalar.
+            # In stats, we consistently turn 0d arrays into scalars, so
+            # maintain that behavior here. (With Array API arrays, this will
+            # change.)
+            assert np.isscalar(res)
+        assert np.all(np.isfinite(res[valid_parameters]))
+        assert_equal(res[~valid_parameters], np.nan)
+
+        sample1 = sample_method(sample_shape, method=method, rng=42)
+        sample2 = sample_method(sample_shape, method=method, rng=42)
+        if not isinstance(dist, DiscreteDistribution):
+            # The idea is that it's very unlikely that the random sample
+            # for a randomly chosen seed will match that for seed 42,
+            # but it is not so unlikely if `dist` is a discrete distribution.
+            assert not np.any(np.equal(res, sample1))
+        assert_equal(sample1, sample2)
+
+
+def check_support(dist):
+    a, b = dist.support()
+    check_nans_and_edges(dist, 'support', None, a)
+    check_nans_and_edges(dist, 'support', None, b)
+    assert a.shape == dist._shape
+    assert b.shape == dist._shape
+    assert a.dtype == dist._dtype
+    assert b.dtype == dist._dtype
+
+
+def check_dist_func(dist, fname, arg, result_shape, methods):
+    # Check that all computation methods of all distribution functions agree
+    # with one another, effectively testing the correctness of the generic
+    # computation methods and confirming the consistency of specific
+    # distributions with their pdf/logpdf.
+
+    args = tuple() if arg is None else (arg,)
+    methods = methods.copy()
+
+    if "cache" in methods:
+        # If "cache" is specified before the value has been evaluated, it
+        # raises an error. After the value is evaluated, it will succeed.
+        with pytest.raises(NotImplementedError):
+            getattr(dist, fname)(*args, method="cache")
+
+    ref = getattr(dist, fname)(*args)
+    check_nans_and_edges(dist, fname, arg, ref)
+
+    # Remove this after fixing `draw`
+    tol_override = {'atol': 1e-15}
+    # Mean can be 0, which makes logmean -inf.
+    if fname in {'logmean', 'mean', 'logskewness', 'skewness'}:
+        tol_override = {'atol': 1e-15}
+    elif fname in {'mode'}:
+        # can only expect about half of machine precision for optimization
+        # because math
+        tol_override = {'atol': 1e-6}
+    elif fname in {'logcdf'}:  # gh-22276
+        tol_override = {'rtol': 2e-7}
+
+    if dist._overrides(f'_{fname}_formula'):
+        methods.add('formula')
+
+    np.testing.assert_equal(ref.shape, result_shape)
+    # Until we convert to array API, let's do the familiar thing:
+    # 0d things are scalars, not arrays
+    if result_shape == tuple():
+        assert np.isscalar(ref)
+
+    for method in methods:
+        res = getattr(dist, fname)(*args, method=method)
+        if 'log' in fname:
+            np.testing.assert_allclose(np.exp(res), np.exp(ref),
+                                       **tol_override)
+        else:
+            np.testing.assert_allclose(res, ref, **tol_override)
+
+        # for now, make sure dtypes are consistent; later, we can check whether
+        # they are correct.
+        np.testing.assert_equal(res.dtype, ref.dtype)
+        np.testing.assert_equal(res.shape, result_shape)
+        if result_shape == tuple():
+            assert np.isscalar(res)
+
+def check_cdf2(dist, log, x, y, result_shape, methods):
+    # Specialized test for 2-arg cdf since the interface is a bit different
+    # from the other methods. Here, we'll use 1-arg cdf as a reference, and
+    # since we have already checked 1-arg cdf in `check_nans_and_edges`, this
+    # checks the equivalent of both `check_dist_func` and
+    # `check_nans_and_edges`.
+    methods = methods.copy()
+
+    if log:
+        if dist._overrides('_logcdf2_formula'):
+            methods.add('formula')
+        if dist._overrides('_logcdf_formula') or dist._overrides('_logccdf_formula'):
+            methods.add('subtraction')
+        if (dist._overrides('_cdf_formula')
+                or dist._overrides('_ccdf_formula')):
+            methods.add('log/exp')
+    else:
+        if dist._overrides('_cdf2_formula'):
+            methods.add('formula')
+        if dist._overrides('_cdf_formula') or dist._overrides('_ccdf_formula'):
+            methods.add('subtraction')
+        if (dist._overrides('_logcdf_formula')
+                or dist._overrides('_logccdf_formula')):
+            methods.add('log/exp')
+
+    ref = dist.cdf(y) - dist.cdf(x)
+    np.testing.assert_equal(ref.shape, result_shape)
+
+    if result_shape == tuple():
+        assert np.isscalar(ref)
+
+    for method in methods:
+        if isinstance(dist, DiscreteDistribution):
+            message = ("Two argument cdf functions are currently only supported for "
+                       "continuous distributions.")
+            with pytest.raises(NotImplementedError, match=message):
+                res = (np.exp(dist.logcdf(x, y, method=method)) if log
+                       else dist.cdf(x, y, method=method))
+            continue
+        res = (np.exp(dist.logcdf(x, y, method=method)) if log
+               else dist.cdf(x, y, method=method))
+        np.testing.assert_allclose(res, ref, atol=1e-14)
+        if log:
+            np.testing.assert_equal(res.dtype, (ref + 0j).dtype)
+        else:
+            np.testing.assert_equal(res.dtype, ref.dtype)
+        np.testing.assert_equal(res.shape, result_shape)
+        if result_shape == tuple():
+            assert np.isscalar(res)
+
+
+def check_ccdf2(dist, log, x, y, result_shape, methods):
+    # Specialized test for 2-arg ccdf since the interface is a bit different
+    # from the other methods. Could be combined with check_cdf2 above, but
+    # writing it separately is simpler.
+    methods = methods.copy()
+
+    if dist._overrides(f'_{"log" if log else ""}ccdf2_formula'):
+        methods.add('formula')
+
+    ref = dist.cdf(x) + dist.ccdf(y)
+    np.testing.assert_equal(ref.shape, result_shape)
+
+    if result_shape == tuple():
+        assert np.isscalar(ref)
+
+    for method in methods:
+        message = ("Two argument cdf functions are currently only supported for "
+                   "continuous distributions.")
+        if isinstance(dist, DiscreteDistribution):
+            with pytest.raises(NotImplementedError, match=message):
+                res = (np.exp(dist.logccdf(x, y, method=method)) if log
+                       else dist.ccdf(x, y, method=method))
+            continue
+        res = (np.exp(dist.logccdf(x, y, method=method)) if log
+               else dist.ccdf(x, y, method=method))
+        np.testing.assert_allclose(res, ref, atol=1e-14)
+        np.testing.assert_equal(res.dtype, ref.dtype)
+        np.testing.assert_equal(res.shape, result_shape)
+        if result_shape == tuple():
+            assert np.isscalar(res)
+
+
+def check_nans_and_edges(dist, fname, arg, res):
+
+    valid_parameters = get_valid_parameters(dist)
+    if fname in {'icdf', 'iccdf'}:
+        arg_domain = _RealInterval(endpoints=(0, 1), inclusive=(True, True))
+    elif fname in {'ilogcdf', 'ilogccdf'}:
+        arg_domain = _RealInterval(endpoints=(-inf, 0), inclusive=(True, True))
+    else:
+        arg_domain = dist._variable.domain
+
+    classified_args = classify_arg(dist, arg, arg_domain)
+    valid_parameters, *classified_args = np.broadcast_arrays(valid_parameters,
+                                                             *classified_args)
+    valid_arg, endpoint_arg, outside_arg, nan_arg = classified_args
+    all_valid = valid_arg & valid_parameters
+
+    # Check NaN pattern and edge cases
+    assert_equal(res[~valid_parameters], np.nan)
+    assert_equal(res[nan_arg], np.nan)
+
+    a, b = dist.support()
+    a = np.broadcast_to(a, res.shape)
+    b = np.broadcast_to(b, res.shape)
+
+    outside_arg_minus = (outside_arg == -1) & valid_parameters
+    outside_arg_plus = (outside_arg == 1) & valid_parameters
+    endpoint_arg_minus = (endpoint_arg == -1) & valid_parameters
+    endpoint_arg_plus = (endpoint_arg == 1) & valid_parameters
+
+    is_discrete = isinstance(dist, DiscreteDistribution)
+    # Writing this independently of how the are set in the distribution
+    # infrastructure. That is very compact; this is very verbose.
+    if fname in {'logpdf'}:
+        assert_equal(res[outside_arg_minus], -np.inf)
+        assert_equal(res[outside_arg_plus], -np.inf)
+        ref = -np.inf if not is_discrete else np.inf
+        assert_equal(res[endpoint_arg_minus & ~valid_arg], ref)
+        assert_equal(res[endpoint_arg_plus & ~valid_arg], ref)
+    elif fname in {'pdf'}:
+        assert_equal(res[outside_arg_minus], 0)
+        assert_equal(res[outside_arg_plus], 0)
+        ref = 0 if not is_discrete else np.inf
+        assert_equal(res[endpoint_arg_minus & ~valid_arg], ref)
+        assert_equal(res[endpoint_arg_plus & ~valid_arg], ref)
+    elif fname in {'logcdf'} and not is_discrete:
+        assert_equal(res[outside_arg_minus], -inf)
+        assert_equal(res[outside_arg_plus], 0)
+        assert_equal(res[endpoint_arg_minus], -inf)
+        assert_equal(res[endpoint_arg_plus], 0)
+    elif fname in {'cdf'} and not is_discrete:
+        assert_equal(res[outside_arg_minus], 0)
+        assert_equal(res[outside_arg_plus], 1)
+        assert_equal(res[endpoint_arg_minus], 0)
+        assert_equal(res[endpoint_arg_plus], 1)
+    elif fname in {'logccdf'} and not is_discrete:
+        assert_equal(res[outside_arg_minus], 0)
+        assert_equal(res[outside_arg_plus], -inf)
+        assert_equal(res[endpoint_arg_minus], 0)
+        assert_equal(res[endpoint_arg_plus], -inf)
+    elif fname in {'ccdf'} and not is_discrete:
+        assert_equal(res[outside_arg_minus], 1)
+        assert_equal(res[outside_arg_plus], 0)
+        assert_equal(res[endpoint_arg_minus], 1)
+        assert_equal(res[endpoint_arg_plus], 0)
+    elif fname in {'ilogcdf', 'icdf'} and not is_discrete:
+        assert_equal(res[outside_arg == -1], np.nan)
+        assert_equal(res[outside_arg == 1], np.nan)
+        assert_equal(res[endpoint_arg == -1], a[endpoint_arg == -1])
+        assert_equal(res[endpoint_arg == 1], b[endpoint_arg == 1])
+    elif fname in {'ilogccdf', 'iccdf'} and not is_discrete:
+        assert_equal(res[outside_arg == -1], np.nan)
+        assert_equal(res[outside_arg == 1], np.nan)
+        assert_equal(res[endpoint_arg == -1], b[endpoint_arg == -1])
+        assert_equal(res[endpoint_arg == 1], a[endpoint_arg == 1])
+
+    exclude = {'logmean', 'mean', 'logskewness', 'skewness', 'support'}
+    if isinstance(dist, DiscreteDistribution):
+        exclude.update({'pdf', 'logpdf'})
+
+    if fname not in exclude:
+        assert np.isfinite(res[all_valid & (endpoint_arg == 0)]).all()
+
+
+def check_moment_funcs(dist, result_shape):
+    # Check that all computation methods of all distribution functions agree
+    # with one another, effectively testing the correctness of the generic
+    # computation methods and confirming the consistency of specific
+    # distributions with their pdf/logpdf.
+
+    atol = 1e-9  # make this tighter (e.g. 1e-13) after fixing `draw`
+
+    def check(order, kind, method=None, ref=None, success=True):
+        if success:
+            res = dist.moment(order, kind, method=method)
+            assert_allclose(res, ref, atol=atol*10**order)
+            assert res.shape == ref.shape
+        else:
+            with pytest.raises(NotImplementedError):
+                dist.moment(order, kind, method=method)
+
+    def has_formula(order, kind):
+        formula_name = f'_moment_{kind}_formula'
+        overrides = dist._overrides(formula_name)
+        if not overrides:
+            return False
+        formula = getattr(dist, formula_name)
+        orders = getattr(formula, 'orders', set(range(6)))
+        return order in orders
+
+    dist.reset_cache()
+
+    ### Check Raw Moments ###
+    for i in range(6):
+        check(i, 'raw', 'cache', success=False)  # not cached yet
+        ref = dist.moment(i, 'raw', method='quadrature')
+        check_nans_and_edges(dist, 'moment', None, ref)
+        assert ref.shape == result_shape
+        check(i, 'raw','cache', ref, success=True)  # cached now
+        check(i, 'raw', 'formula', ref, success=has_formula(i, 'raw'))
+        check(i, 'raw', 'general', ref, success=(i == 0))
+        if dist.__class__ == stats.Normal:
+            check(i, 'raw', 'quadrature_icdf', ref, success=True)
+
+
+    # Clearing caches to better check their behavior
+    dist.reset_cache()
+
+    # If we have central or standard moment formulas, or if there are
+    # values in their cache, we can use method='transform'
+    dist.moment(0, 'central')  # build up the cache
+    dist.moment(1, 'central')
+    for i in range(2, 6):
+        ref = dist.moment(i, 'raw', method='quadrature')
+        check(i, 'raw', 'transform', ref,
+              success=has_formula(i, 'central') or has_formula(i, 'standardized'))
+        dist.moment(i, 'central')  # build up the cache
+        check(i, 'raw', 'transform', ref)
+
+    dist.reset_cache()
+
+    ### Check Central Moments ###
+
+    for i in range(6):
+        check(i, 'central', 'cache', success=False)
+        ref = dist.moment(i, 'central', method='quadrature')
+        assert ref.shape == result_shape
+        check(i, 'central', 'cache', ref, success=True)
+        check(i, 'central', 'formula', ref, success=has_formula(i, 'central'))
+        check(i, 'central', 'general', ref, success=i <= 1)
+        if dist.__class__ == stats.Normal:
+            check(i, 'central', 'quadrature_icdf', ref, success=True)
+        if not (dist.__class__ == stats.Uniform and i == 5):
+            # Quadrature is not super accurate for 5th central moment when the
+            # support is really big. Skip this one failing test. We need to come
+            # up with a better system of skipping individual failures w/ hypothesis.
+            check(i, 'central', 'transform', ref,
+                  success=has_formula(i, 'raw') or (i <= 1))
+        if not has_formula(i, 'raw'):
+            dist.moment(i, 'raw')
+            check(i, 'central', 'transform', ref)
+
+    variance = dist.variance()
+    dist.reset_cache()
+
+    # If we have standard moment formulas, or if there are
+    # values in their cache, we can use method='normalize'
+    dist.moment(0, 'standardized')  # build up the cache
+    dist.moment(1, 'standardized')
+    dist.moment(2, 'standardized')
+    for i in range(3, 6):
+        ref = dist.moment(i, 'central', method='quadrature')
+        check(i, 'central', 'normalize', ref,
+              success=has_formula(i, 'standardized') and not np.any(variance == 0))
+        dist.moment(i, 'standardized')  # build up the cache
+        check(i, 'central', 'normalize', ref, success=not np.any(variance == 0))
+
+    ### Check Standardized Moments ###
+
+    var = dist.moment(2, 'central', method='quadrature')
+    dist.reset_cache()
+
+    for i in range(6):
+        check(i, 'standardized', 'cache', success=False)
+        ref = dist.moment(i, 'central', method='quadrature') / var ** (i / 2)
+        assert ref.shape == result_shape
+        check(i, 'standardized', 'formula', ref,
+              success=has_formula(i, 'standardized'))
+        check(i, 'standardized', 'general', ref, success=i <= 2)
+        check(i, 'standardized', 'normalize', ref)
+
+    dist.reset_cache()
+
+
+def check_lmoment_funcs(dist, result_shape):
+    # Perform consistency check for L-moments similar to check_moment_funcs above
+
+    if not isinstance(dist, ContinuousDistribution):
+        message = "L-moments are currently available only for continuous..."
+        with pytest.raises(NotImplementedError, match=message):
+            dist.lmoment(1)
+        return
+
+    atol = 2e-9
+
+    def check(order, standardize=False, method=None, ref=None, success=True):
+        if success:
+            res = dist.lmoment(order, standardize=standardize, method=method)
+            assert_allclose(res, ref, atol=atol)
+            assert res.shape == ref.shape
+        else:
+            with pytest.raises(NotImplementedError):
+                dist.lmoment(order, standardize=standardize, method=method)
+
+    ### Check L-Moments ###
+
+    standardize = False
+    for i in range(1, 6):
+        check(i, standardize, 'cache', success=standardize)  # not cached yet
+        ref = dist.lmoment(i, standardize=standardize, method='order_statistics')
+        check_nans_and_edges(dist, 'lmoment', None, ref)
+        assert ref.shape == result_shape
+        check(i, standardize, 'cache', ref, success=True)  # cached now
+        check(i, standardize, 'formula', ref,
+              success=dist._overrides('_lmoment_formula')
+                      and (i < 5 or dist.__class__.__name__ == "Uniform"))
+        check(i, standardize, 'general', ref, success=(i == 1))
+        if dist._overrides('_icdf_formula'):
+            check(i, standardize, 'quadrature_icdf', ref, success=True)
+
+    standardize=True
+    for i in range(3, 6):
+        ref = dist.lmoment(i, standardize=standardize, method='order_statistics')
+        assert ref.shape == result_shape
+        check(i, standardize, 'formula', ref,
+              success=dist._overrides('_lmoment_formula')
+                      and (i < 5 or dist.__class__.__name__ == "Uniform"))
+        check(i, standardize, 'general', ref, success=False)
+        if dist._overrides('_icdf_formula'):
+            check(i, standardize, 'quadrature_icdf', ref, success=True)
+
+
+@pytest.mark.parametrize('family', (Normal,))
+@pytest.mark.parametrize('x_shape', [tuple(), (2, 3)])
+@pytest.mark.parametrize('dist_shape', [tuple(), (4, 1)])
+@pytest.mark.parametrize('fname', ['sample'])
+@pytest.mark.parametrize('rng_type', [np.random.Generator, qmc.Halton, qmc.Sobol])
+def test_sample_against_cdf(family, dist_shape, x_shape, fname, rng_type):
+    rng = np.random.default_rng(842582438235635)
+    num_parameters = family._num_parameters()
+
+    if dist_shape and num_parameters == 0:
+        pytest.skip("Distribution can't have a shape without parameters.")
+
+    dist = family._draw(dist_shape, rng)
+
+    n = 1024
+    sample_size = (n,) + x_shape
+    sample_array_shape = sample_size + dist_shape
+
+    if fname == 'sample':
+        sample_method = dist.sample
+
+    if rng_type != np.random.Generator:
+        rng = rng_type(d=1, seed=rng)
+    x = sample_method(sample_size, rng=rng)
+    assert x.shape == sample_array_shape
+
+    # probably should give `axis` argument to ks_1samp, review that separately
+    statistic = _kolmogorov_smirnov(dist, x, axis=0)
+    pvalue = kolmogn(x.shape[0], statistic, cdf=False)
+    p_threshold = 0.01
+    num_pvalues = pvalue.size
+    num_small_pvalues = np.sum(pvalue < p_threshold)
+    assert num_small_pvalues < p_threshold * num_pvalues
+
+
+def get_valid_parameters(dist):
+    # Given a distribution, return a logical array that is true where all
+    # distribution parameters are within their respective domains. The code
+    # here is probably quite similar to that used to form the `_invalid`
+    # attribute of the distribution, but this was written about a week later
+    # without referring to that code, so it is a somewhat independent check.
+
+    # Get all parameter values and `_Parameter` objects
+    parameter_values = dist._parameters
+    parameters = {}
+    for parameterization in dist._parameterizations:
+        parameters.update(parameterization.parameters)
+
+    all_valid = np.ones(dist._shape, dtype=bool)
+    for name, value in parameter_values.items():
+        if name not in parameters:  # cached value not part of parameterization
+            continue
+        parameter = parameters[name]
+
+        # Check that the numerical endpoints and inclusivity attribute
+        # agree with the `contains` method about which parameter values are
+        # within the domain.
+        a, b = parameter.domain.get_numerical_endpoints(
+            parameter_values=parameter_values)
+        a_included, b_included = parameter.domain.inclusive
+        valid = (a <= value) if a_included else a < value
+        valid &= (value <= b) if b_included else value < b
+        assert_equal(valid, parameter.domain.contains(
+            value, parameter_values=parameter_values))
+
+        # Form `all_valid` mask that is True where *all* parameters are valid
+        all_valid &= valid
+
+    # Check that the `all_valid` mask formed here is the complement of the
+    # `dist._invalid` mask stored by the infrastructure
+    assert_equal(~all_valid, dist._invalid)
+
+    return all_valid
+
+def classify_arg(dist, arg, arg_domain):
+    if arg is None:
+        valid_args = np.ones(dist._shape, dtype=bool)
+        endpoint_args = np.zeros(dist._shape, dtype=bool)
+        outside_args = np.zeros(dist._shape, dtype=bool)
+        nan_args = np.zeros(dist._shape, dtype=bool)
+        return valid_args, endpoint_args, outside_args, nan_args
+
+    a, b = arg_domain.get_numerical_endpoints(
+        parameter_values=dist._parameters)
+
+    a, b, arg = np.broadcast_arrays(a, b, arg)
+    a_included, b_included = arg_domain.inclusive
+
+    inside = (a <= arg) if a_included else a < arg
+    inside &= (arg <= b) if b_included else arg < b
+    # TODO: add `supported` method and check here
+    on = np.zeros(a.shape, dtype=int)
+    on[a == arg] = -1
+    on[b == arg] = 1
+    outside = np.zeros(a.shape, dtype=int)
+    outside[(arg < a) if a_included else arg <= a] = -1
+    outside[(b < arg) if b_included else b <= arg] = 1
+    nan = np.isnan(arg)
+
+    return inside, on, outside, nan
+
+
+def test_input_validation():
+    class Test(ContinuousDistribution):
+        _variable = _RealParameter('x', domain=_RealInterval())
+
+    message = ("The `Test` distribution family does not accept parameters, "
+               "but parameters `{'a'}` were provided.")
+    with pytest.raises(ValueError, match=message):
+        Test(a=1, )
+
+    message = "Attribute `tol` of `Test` must be a positive float, if specified."
+    with pytest.raises(ValueError, match=message):
+        Test(tol=np.asarray([]))
+    with pytest.raises(ValueError, match=message):
+        Test(tol=[1, 2, 3])
+    with pytest.raises(ValueError, match=message):
+        Test(tol=np.nan)
+    with pytest.raises(ValueError, match=message):
+        Test(tol=-1)
+
+    message = ("Argument `order` of `Test.moment` must be a "
+               "finite integer greater than or equal to 0.")
+    with pytest.raises(ValueError, match=message):
+        Test().moment(-1)
+    with pytest.raises(ValueError, match=message):
+        Test().moment(np.inf)
+
+    message = ("Argument `order` of `Test.lmoment` must be a "
+               "finite integer greater than or equal to 1.")
+    with pytest.raises(ValueError, match=message):
+        Test().lmoment(0)
+
+    message = "Argument `kind` of `Test.moment` must be one of..."
+    with pytest.raises(ValueError, match=message):
+        Test().moment(2, kind='coconut')
+
+    class Test2(ContinuousDistribution):
+        _p1 = _RealParameter('c', domain=_RealInterval())
+        _p2 = _RealParameter('d', domain=_RealInterval())
+        _parameterizations = [_Parameterization(_p1, _p2)]
+        _variable = _RealParameter('x', domain=_RealInterval())
+
+    message = ("The provided parameters `{a}` do not match a supported "
+               "parameterization of the `Test2` distribution family.")
+    with pytest.raises(ValueError, match=message):
+        Test2(a=1)
+
+    message = ("The `Test2` distribution family requires parameters, but none "
+               "were provided.")
+    with pytest.raises(ValueError, match=message):
+        Test2()
+
+    message = ("The parameters `{c, d}` provided to the `Test2` "
+               "distribution family cannot be broadcast to the same shape.")
+    with pytest.raises(ValueError, match=message):
+        Test2(c=[1, 2], d=[1, 2, 3])
+
+    message = ("The argument provided to `Test2.pdf` cannot be be broadcast to "
+              "the same shape as the distribution parameters.")
+    with pytest.raises(ValueError, match=message):
+        dist = Test2(c=[1, 2, 3], d=[1, 2, 3])
+        dist.pdf([1, 2])
+
+    message = "Parameter `c` must be of real dtype."
+    with pytest.raises(TypeError, match=message):
+        Test2(c=[1, object()], d=[1, 2])
+
+    message = "Parameter `convention` of `Test2.kurtosis` must be one of..."
+    with pytest.raises(ValueError, match=message):
+        dist = Test2(c=[1, 2, 3], d=[1, 2, 3])
+        dist.kurtosis(convention='coconut')
+
+
+def test_rng_deepcopy_pickle():
+    # test behavior of `rng` attribute and copy behavior
+    kwargs = dict(a=[-1, 2], b=10)
+    dist1 = Uniform(**kwargs)
+    dist2 = deepcopy(dist1)
+    dist3 = pickle.loads(pickle.dumps(dist1))
+
+    res1, res2, res3 = dist1.sample(), dist2.sample(), dist3.sample()
+    assert np.all(res2 != res1)
+    assert np.all(res3 != res1)
+
+    res1, res2, res3 = dist1.sample(rng=42), dist2.sample(rng=42), dist3.sample(rng=42)
+    assert np.all(res2 == res1)
+    assert np.all(res3 == res1)
+
+
+class TestAttributes:
+    def test_cache_policy(self):
+        dist = StandardNormal(cache_policy="no_cache")
+        # make error message more appropriate
+        message = "`StandardNormal` does not provide an accurate implementation of the "
+        with pytest.raises(NotImplementedError, match=message):
+            dist.mean(method='cache')
+        mean = dist.mean()
+        with pytest.raises(NotImplementedError, match=message):
+            dist.mean(method='cache')
+
+        # add to enum
+        dist.cache_policy = None
+        with pytest.raises(NotImplementedError, match=message):
+            dist.mean(method='cache')
+        mean = dist.mean()  # method is 'formula' by default
+        cached_mean = dist.mean(method='cache')
+        assert_equal(cached_mean, mean)
+
+        # cache is not cleared when used in a TransformedDistribution
+        dist2 = stats.exp(dist)
+        assert_equal(dist.mean(method='cache'), cached_mean)
+        dist2.reset_cache()
+        assert_equal(dist.mean(method='cache'), cached_mean)
+
+        # cache is overridden by latest evaluation
+        quadrature_mean = dist.mean(method='quadrature')
+        cached_mean = dist.mean(method='cache')
+        assert_equal(cached_mean, quadrature_mean)
+        assert not np.all(mean == quadrature_mean)
+
+        # We can turn the cache off, and it won't change, but the old cache is
+        # still available
+        dist.cache_policy = "no_cache"
+        mean = dist.mean(method='formula')
+        cached_mean = dist.mean(method='cache')
+        assert_equal(cached_mean, quadrature_mean)
+        assert not np.all(mean == quadrature_mean)
+
+        dist.reset_cache()
+        with pytest.raises(NotImplementedError, match=message):
+            dist.mean(method='cache')
+
+        message = "Attribute `cache_policy` of `StandardNormal`..."
+        with pytest.raises(ValueError, match=message):
+            dist.cache_policy = "invalid"
+
+    def test_tol(self):
+        x = 3.
+        X = stats.Normal()
+
+        message = "Attribute `tol` of `StandardNormal` must..."
+        with pytest.raises(ValueError, match=message):
+            X.tol = -1.
+        with pytest.raises(ValueError, match=message):
+            X.tol = (0.1,)
+        with pytest.raises(ValueError, match=message):
+            X.tol = np.nan
+
+        X1 = stats.Normal(tol=1e-1)
+        X2 = stats.Normal(tol=1e-12)
+        ref = X.cdf(x)
+        res1 = X1.cdf(x, method='quadrature')
+        res2 = X2.cdf(x, method='quadrature')
+        assert_allclose(res1, ref, rtol=X1.tol)
+        assert_allclose(res2, ref, rtol=X2.tol)
+        assert abs(res1 - ref) > abs(res2 - ref)
+
+        p = 0.99
+        X1.tol, X2.tol = X2.tol, X1.tol
+        ref = X.icdf(p)
+        res1 = X1.icdf(p, method='inversion')
+        res2 = X2.icdf(p, method='inversion')
+        assert_allclose(res1, ref, rtol=X1.tol)
+        assert_allclose(res2, ref, rtol=X2.tol)
+        assert abs(res2 - ref) > abs(res1 - ref)
+
+    def test_iv_policy(self):
+        X = Uniform(a=0, b=1)
+        assert X.pdf(2) == 0
+
+        X.validation_policy = 'skip_all'
+        assert X.pdf(np.asarray(2.)) == 1
+
+        # Tests _set_invalid_nan
+        a, b = np.asarray(1.), np.asarray(0.)  # invalid parameters
+        X = Uniform(a=a, b=b, validation_policy='skip_all')
+        assert X.pdf(np.asarray(2.)) == -1
+
+        # Tests _set_invalid_nan_property
+        class MyUniform(Uniform):
+            def _entropy_formula(self, *args, **kwargs):
+                return 'incorrect'
+
+            def _moment_raw_formula(self, order, **params):
+                return 'incorrect'
+
+        X = MyUniform(a=a, b=b, validation_policy='skip_all')
+        assert X.entropy() == 'incorrect'
+
+        # Tests _validate_order_kind
+        assert X.moment(kind='raw', order=-1) == 'incorrect'
+
+        # Test input validation
+        message = "Attribute `validation_policy` of `MyUniform`..."
+        with pytest.raises(ValueError, match=message):
+            X.validation_policy = "invalid"
+
+    def test_shapes(self):
+        X = stats.Normal(mu=1, sigma=2)
+        Y = stats.Normal(mu=[2], sigma=3)
+
+        # Check that attributes are available as expected
+        assert X.mu == 1
+        assert X.sigma == 2
+        assert Y.mu[0] == 2
+        assert Y.sigma[0] == 3
+
+        # Trying to set an attribute raises
+        # message depends on Python version
+        with pytest.raises(AttributeError):
+            X.mu = 2
+
+        # Trying to mutate an attribute really mutates a copy
+        Y.mu[0] = 10
+        assert Y.mu[0] == 2
+
+
+class TestMakeDistribution:
+    @pytest.mark.parametrize('i, distdata', list(enumerate(distcont + distdiscrete)))
+    def test_rv_generic(self, i, distdata):
+        distname = distdata[0]
+
+        slow = {'argus', 'exponpow', 'exponweib', 'genexpon', 'gompertz',
+                'johnsonsb', 'kappa4', 'ksone', 'kstwo', 'kstwobign', 'norminvgauss',
+                'powerlognorm', 'powernorm', 'recipinvgauss', 'studentized_range',
+                'vonmises_line'}  # continuous
+        if not int(os.environ.get('SCIPY_XSLOW', '0')) and distname in slow:
+            pytest.skip('Skipping as XSLOW')
+
+        if distname in {              # skip these distributions
+            'levy_stable',            # private methods seem to require >= 1d args
+            'vonmises',               # circular distribution; shouldn't work
+            'poisson_binom',          # vector shape parameter
+            'hypergeom',              # distribution functions need interpolation
+            'nchypergeom_fisher',     # distribution functions need interpolation
+            'nchypergeom_wallenius',  # distribution functions need interpolation
+        }:
+            return
+
+        # skip single test, mostly due to slight disagreement
+        custom_tolerances = {'ksone': 1e-5, 'kstwo': 1e-5}  # discontinuous PDF
+        skip_entropy = {'kstwobign', 'pearson3'}  # tolerance issue
+        skip_skewness = {'exponpow', 'ksone', 'nchypergeom_wallenius'}  # tolerance
+        skip_kurtosis = {'chi', 'exponpow', 'invgamma',  # tolerance
+                         'johnsonsb', 'ksone', 'kstwo',  # tolerance
+                         'nchypergeom_wallenius'}  # tolerance
+        skip_logccdf = {'arcsine', 'skewcauchy', 'trapezoid', 'triang',  # tolerance
+                        'dlaplace'}  # slight tolerance issue, but only for array shape
+        skip_raw = {2: {'alpha', 'foldcauchy', 'halfcauchy', 'levy', 'levy_l'},
+                    3: {'pareto'},  # stats.pareto is just wrong
+                    4: {'invgamma'}}  # tolerance issue
+        skip_standardized = {'exponpow', 'ksone'}  # tolerances
+
+        dist = getattr(stats, distname)
+        params = dict(zip(dist.shapes.split(', '), distdata[1])) if dist.shapes else {}
+        rng = np.random.default_rng(7548723590230982)
+        CustomDistribution = stats.make_distribution(dist)
+        params = {key: np.asarray([val, val]) for key, val in params.items()}
+        X = CustomDistribution(**params)
+        Y = dist(**params)
+        x = X.sample(shape=10, rng=rng)
+        p = X.cdf(x)
+        rtol = custom_tolerances.get(distname, 1e-7)
+        atol = 1e-12
+
+        with np.errstate(divide='ignore', invalid='ignore'):
+            m, v, s, k = Y.stats('mvsk')
+            assert_allclose(X.support(), Y.support())
+            if distname not in skip_entropy:
+                assert_allclose(X.entropy(), Y.entropy(), rtol=rtol)
+            if isinstance(Y, stats.rv_discrete):
+                # some continuous distributions have trouble with `logentropy` because
+                # it uses complex numbers
+                assert_allclose(np.exp(X.logentropy()), Y.entropy(), rtol=rtol)
+            assert_allclose(X.median(), Y.median(), rtol=rtol)
+            assert_allclose(X.mean(), m, rtol=rtol, atol=atol)
+            assert_allclose(X.variance(), v, rtol=rtol, atol=atol)
+            if distname not in skip_skewness:
+                assert_allclose(X.skewness(), s, rtol=rtol, atol=atol)
+            if distname not in skip_kurtosis:
+                assert_allclose(X.kurtosis(convention='excess'), k,
+                                rtol=rtol, atol=atol)
+            if isinstance(dist, stats.rv_continuous):
+                assert_allclose(X.logpdf(x), Y.logpdf(x), rtol=rtol)
+                assert_allclose(X.pdf(x), Y.pdf(x), rtol=rtol)
+            else:
+                assert_allclose(X.logpmf(x), Y.logpmf(x), rtol=rtol)
+                assert_allclose(X.pmf(x), Y.pmf(x), rtol=rtol)
+            assert_allclose(X.logcdf(x), Y.logcdf(x), rtol=rtol)
+            assert_allclose(X.cdf(x), Y.cdf(x), rtol=rtol)
+            if distname not in skip_logccdf:
+                assert_allclose(X.logccdf(x), Y.logsf(x), rtol=rtol)
+            assert_allclose(X.ccdf(x), Y.sf(x), rtol=rtol)
+
+            # old infrastructure convention for ppf(p=0) and isf(p=1) is different than
+            # new infrastructure. Adjust reference values accordingly.
+            a, _ = Y.support()
+            a, p = np.broadcast_arrays(a, p)
+            ref_ppf = Y.ppf(p)
+            ref_ppf[p == 0] = a[p == 0]
+            ref_isf = Y.isf(p)
+            ref_isf[p == 1] = a[p == 1]
+
+            assert_allclose(X.icdf(p), ref_ppf, rtol=rtol)
+            assert_allclose(X.iccdf(p), ref_isf, rtol=rtol)
+
+            for order in range(5):
+                if distname not in skip_raw.get(order, {}):
+                    assert_allclose(X.moment(order, kind='raw'),
+                                    Y.moment(order), rtol=rtol, atol=atol)
+            for order in range(3, 4):
+                if distname not in skip_standardized:
+                    assert_allclose(X.moment(order, kind='standardized'),
+                                    Y.stats('mvsk'[order-1]), rtol=rtol, atol=atol)
+            if isinstance(dist, stats.rv_continuous):
+                # For discrete distributions, these won't agree at the far left end
+                # of the support, and the new infrastructure is slow there (for now).
+                seed = 845298245687345
+                assert_allclose(X.sample(shape=10, rng=seed),
+                                Y.rvs(size=p.shape,
+                                      random_state=np.random.default_rng(seed)),
+                                rtol=rtol)
+
+    def test_custom(self):
+        rng = np.random.default_rng(7548723590230982)
+
+        class MyLogUniform:
+            @property
+            def __make_distribution_version__(self):
+                return "1.16.0"
+
+            @property
+            def parameters(self):
+                return {'a': {'endpoints': (0, np.inf), 'inclusive': (False, False)},
+                        'b': {'endpoints': ('a', np.inf), 'inclusive': (False, False)}}
+
+            @property
+            def support(self):
+                return {'endpoints': ('a', 'b')}
+
+            def pdf(self, x, a, b):
+                return 1 / (x * (np.log(b) - np.log(a)))
+
+            def sample(self, shape, *, a, b, rng=None):
+                p = rng.uniform(size=shape)
+                return np.exp(np.log(a) + p * (np.log(b) - np.log(a)))
+
+            def moment(self, order, kind='raw', *, a, b):
+                if order == 1 and kind == 'raw':
+                    # quadrature is perfectly accurate here; add 1e-10 error so we
+                    # can tell the difference between the two
+                    return (b - a) / np.log(b/a) + 1e-10
+
+            def lmoment(self, order, *, a, b):
+                s = np.log(b/a)
+                l1 = (b - a) / s
+                l2 = ((s - 2) * b + (s + 2) * a) / s**2
+                l3 = ((s**2 - 6*s + 12) * b - (s**2 + 6*s + 12) * a) / s ** 3
+                l4 = ((s**3 - 12*s**2 + 60*s - 120) * b
+                      + (s**3 + 12*s**2 + 60*s + 120) * a) / s ** 4
+                ls = {1: l1, 2: l2, 3: l3, 4: l4}
+                return ls.get(int(order), None)
+
+        LogUniform = stats.make_distribution(MyLogUniform())
+
+        X = LogUniform(a=1., b=np.e)
+        Y = stats.exp(Uniform(a=0., b=1.))
+
+        assert str(X) == f"MyLogUniform(a=1.0, b={np.e})"
+        assert repr(X) == f"MyLogUniform(a=np.float64(1.0), b=np.float64({np.e}))"
+
+        x = X.sample(shape=10, rng=rng)
+        p = X.cdf(x)
+
+        assert_allclose(X.support(), Y.support())
+        assert_allclose(X.entropy(), Y.entropy())
+        assert_allclose(X.median(), Y.median())
+        assert_allclose(X.logpdf(x), Y.logpdf(x))
+        assert_allclose(X.pdf(x), Y.pdf(x))
+        assert_allclose(X.logcdf(x), Y.logcdf(x))
+        assert_allclose(X.cdf(x), Y.cdf(x))
+        assert_allclose(X.logccdf(x), Y.logccdf(x))
+        assert_allclose(X.ccdf(x), Y.ccdf(x))
+        assert_allclose(X.icdf(p), Y.icdf(p))
+        assert_allclose(X.iccdf(p), Y.iccdf(p))
+        for kind in ['raw', 'central', 'standardized']:
+            for order in range(5):
+                assert_allclose(X.moment(order, kind=kind),
+                                Y.moment(order, kind=kind))
+        for standardize in [False, True]:
+            for order in range(1, 5):
+                if standardize and order < 3:
+                    continue
+                assert_allclose(X.lmoment(order, standardize=standardize),
+                                Y.lmoment(order, standardize=standardize))
+
+        # Confirm that the `sample` and `moment` methods are overriden as expected
+        sample_formula = X.sample(shape=10, rng=0, method='formula')
+        sample_inverse = X.sample(shape=10, rng=0, method='inverse_transform')
+        assert_allclose(sample_formula, sample_inverse)
+        assert not np.all(sample_formula == sample_inverse)
+
+        assert_allclose(X.mean(method='formula'), X.mean(method='quadrature'))
+        assert not X.mean(method='formula') == X.mean(method='quadrature')
+
+        assert_allclose(X.lmoment(method='formula'),
+                        X.lmoment(method='quadrature_icdf'))
+        assert not X.lmoment(method='formula') == X.lmoment(method='quadrature_icdf')
+
+    # pdf and cdf formulas below can warn on boundary of support in some cases.
+    # See https://github.com/scipy/scipy/pull/22560#discussion_r1962763840.
+    @pytest.mark.slow
+    @pytest.mark.filterwarnings("ignore::RuntimeWarning")
+    @pytest.mark.parametrize("c", [-1, 0, 1, np.asarray([-2.1, -1., 0., 1., 2.1])])
+    def test_custom_variable_support(self, c):
+        rng = np.random.default_rng(7548723590230982)
+
+        class MyGenExtreme:
+            @property
+            def __make_distribution_version__(self):
+                return "1.16.0"
+
+            @property
+            def parameters(self):
+                return {
+                    'c': {'endpoints': (-np.inf, np.inf), 'inclusive': (False, False)},
+                    'mu': {'endpoints': (-np.inf, np.inf), 'inclusive': (False, False)},
+                    'sigma': {'endpoints': (0, np.inf), 'inclusive': (False, False)}
+                }
+
+            @property
+            def support(self):
+                def left(*, c, mu, sigma):
+                    c, mu, sigma = np.broadcast_arrays(c, mu, sigma)
+                    result = np.empty_like(c)
+                    result[c >= 0] = -np.inf
+                    result[c < 0] = mu[c < 0] + sigma[c < 0] / c[c < 0]
+                    return result[()]
+
+                def right(*, c, mu, sigma):
+                    c, mu, sigma = np.broadcast_arrays(c, mu, sigma)
+                    result = np.empty_like(c)
+                    result[c <= 0] = np.inf
+                    result[c > 0] = mu[c > 0] + sigma[c > 0] / c[c > 0]
+                    return result[()]
+
+                return {"endpoints": (left, right), "inclusive": (False, False)}
+
+            def pdf(self, x, *, c, mu, sigma):
+                x, c, mu, sigma = np.broadcast_arrays(x, c, mu, sigma)
+                t = np.empty_like(x)
+                mask = (c == 0)
+                t[mask] = np.exp(-(x[mask] - mu[mask])/sigma[mask])
+                t[~mask] = (
+                    1  - c[~mask]*(x[~mask] - mu[~mask])/sigma[~mask]
+                )**(1/c[~mask])
+                result = 1/sigma * t**(1 - c)*np.exp(-t)
+                return result[()]
+
+            def cdf(self, x, *, c, mu, sigma):
+                x, c, mu, sigma = np.broadcast_arrays(x, c, mu, sigma)
+                t = np.empty_like(x)
+                mask = (c == 0)
+                t[mask] = np.exp(-(x[mask] - mu[mask])/sigma[mask])
+                t[~mask] = (
+                    1  - c[~mask]*(x[~mask] - mu[~mask])/sigma[~mask]
+                )**(1/c[~mask])
+                return np.exp(-t)[()]
+
+        GenExtreme1 = stats.make_distribution(MyGenExtreme())
+        GenExtreme2 = stats.make_distribution(stats.genextreme)
+
+        X1 = GenExtreme1(c=c, mu=0, sigma=1)
+        X2 = GenExtreme2(c=c)
+
+        x = X1.sample(shape=10, rng=rng)
+        p = X1.cdf(x)
+
+        assert_allclose(X1.support(), X2.support())
+        assert_allclose(X1.entropy(), X2.entropy(), rtol=5e-6)
+        assert_allclose(X1.median(), X2.median())
+        assert_allclose(X1.logpdf(x), X2.logpdf(x))
+        assert_allclose(X1.pdf(x), X2.pdf(x))
+        assert_allclose(X1.logcdf(x), X2.logcdf(x))
+        assert_allclose(X1.cdf(x), X2.cdf(x))
+        assert_allclose(X1.logccdf(x), X2.logccdf(x))
+        assert_allclose(X1.ccdf(x), X2.ccdf(x))
+        assert_allclose(X1.icdf(p), X2.icdf(p))
+        assert_allclose(X1.iccdf(p), X2.iccdf(p))
+
+    @pytest.mark.slow
+    @pytest.mark.parametrize("a", [0.5, np.asarray([0.5, 1.0, 2.0, 4.0, 8.0])])
+    @pytest.mark.parametrize("b", [0.5, np.asarray([0.5, 1.0, 2.0, 4.0, 8.0])])
+    def test_custom_multiple_parameterizations(self, a, b):
+        rng = np.random.default_rng(7548723590230982)
+        class MyBeta:
+            @property
+            def __make_distribution_version__(self):
+                return "1.16.0"
+
+            @property
+            def parameters(self):
+                return (
+                    {"a": (0, np.inf), "b": (0, np.inf)},
+                    {"mu": (0, 1), "nu": (0, np.inf)},
+                )
+
+            def process_parameters(self, a=None, b=None, mu=None, nu=None):
+                if a is not None and b is not None and mu is None and nu is None:
+                    nu = a + b
+                    mu = a / nu
+                else:
+                    a = mu * nu
+                    b = nu - a
+                return {"a": a, "b": b, "mu": mu, "nu": nu}
+
+            @property
+            def support(self):
+                return {'endpoints': (0, 1)}
+
+            def pdf(self, x, a, b, mu, nu):
+                return special._ufuncs._beta_pdf(x, a, b)
+
+            def cdf(self, x, a, b, mu, nu):
+                return special.betainc(a, b, x)
+
+        Beta = stats.make_distribution(stats.beta)
+        MyBeta = stats.make_distribution(MyBeta())
+
+        mu = a / (a + b)
+        nu = a + b
+
+        X = MyBeta(a=a, b=b)
+        Y = MyBeta(mu=mu, nu=nu)
+        Z = Beta(a=a, b=b)
+
+        x = Z.sample(shape=10, rng=rng)
+        p = Z.cdf(x)
+
+        assert_allclose(X.support(), Z.support())
+        assert_allclose(X.median(), Z.median())
+        assert_allclose(X.pdf(x), Z.pdf(x))
+        assert_allclose(X.cdf(x), Z.cdf(x))
+        assert_allclose(X.ccdf(x), Z.ccdf(x))
+        assert_allclose(X.icdf(p), Z.icdf(p))
+        assert_allclose(X.iccdf(p), Z.iccdf(p))
+
+        assert_allclose(Y.support(), Z.support())
+        assert_allclose(Y.median(), Z.median())
+        assert_allclose(Y.pdf(x), Z.pdf(x))
+        assert_allclose(Y.cdf(x), Z.cdf(x))
+        assert_allclose(Y.ccdf(x), Z.ccdf(x))
+        assert_allclose(Y.icdf(p), Z.icdf(p))
+        assert_allclose(Y.iccdf(p), Z.iccdf(p))
+
+    def test_input_validation(self):
+        message = '`levy_stable` is not supported.'
+        with pytest.raises(NotImplementedError, match=message):
+            stats.make_distribution(stats.levy_stable)
+
+        message = '`vonmises` is not supported.'
+        with pytest.raises(NotImplementedError, match=message):
+            stats.make_distribution(stats.vonmises)
+
+        message = "The argument must be an instance of..."
+        with pytest.raises(ValueError, match=message):
+            stats.make_distribution(object())
+
+    def test_repr_str_docs(self):
+        from scipy.stats._distribution_infrastructure import _distribution_names
+        for dist in _distribution_names.keys():
+            assert hasattr(stats, dist)
+
+        dist = stats.make_distribution(stats.gamma)
+        assert str(dist(a=2)) == "Gamma(a=2.0)"
+        assert repr(dist(a=2)) == "Gamma(a=np.float64(2.0))"
+        assert 'Gamma' in dist.__doc__
+
+        dist = stats.make_distribution(stats.halfgennorm)
+        assert str(dist(beta=2)) == "HalfGeneralizedNormal(beta=2.0)"
+        assert repr(dist(beta=2)) == "HalfGeneralizedNormal(beta=np.float64(2.0))"
+        assert 'HalfGeneralizedNormal' in dist.__doc__
+
+    @pytest.mark.slow  # just in case
+    @settings(max_examples=20)  # no need for more
+    @given(data=strategies.data())
+    def test_draw_distribution(self, data):
+        # `draw_distribution_from_family` is a private function right now, but we will
+        # want that functionality to be public someday. It was broken for custom
+        # distributions because the `typical` parameter of the support was ignored.
+        # Check that this is resolved.
+        rng = np.random.default_rng(8465652168548465121)
+        u_typical = tuple(np.sort(rng.standard_normal(2)))
+        s_typical = tuple(np.sort(rng.random(2)*2))
+        x_typical = tuple(np.sort(rng.standard_normal(2)))
+
+        class MyNormal:
+            __make_distribution_version__ = "1.16.0"
+            parameters = {'u': {'endpoints': (-np.inf, np.inf), 'typical': u_typical},
+                          's': {'endpoints': (0, np.inf), 'typical': s_typical}}
+            support = {'endpoints': (-np.inf, np.inf), 'typical': x_typical}
+
+            def pdf(self, x, u, s):
+                return 1 / np.sqrt(2*np.pi) / s * np.exp(-((x-u)/s)**2/2)
+
+        family = stats.make_distribution(MyNormal())
+        proportions = (1.0, 0., 0., 0.)
+        tmp = draw_distribution_from_family(family, data, rng, proportions, min_side=1)
+        dist, x, y, p, logp, result_shape, x_result_shape, xy_result_shape = tmp
+        assert u_typical[0] < np.min(dist.u) and np.max(dist.u) < u_typical[1]
+        assert s_typical[0] < np.min(dist.s) and np.max(dist.s) < s_typical[1]
+        assert x_typical[0] < np.min(x) and np.max(x) < x_typical[1]
+
+    @pytest.mark.parametrize('p', [None, ()])
+    def test_no_parameters(self, p):
+        # To create a distribution without parameters, it is natural to try an empty
+        # dictionary (since a dictionary with entries is valid if there is only
+        # one parameterization), but that didn't work; only an empty tuple (no
+        # parameterizations) worked originally. Check that this is resolved.
+        class MyStandardNormal:
+            __make_distribution_version__ = "1.16.0"
+            parameters = {} if p is None else p
+            support = {'endpoints': (-np.inf, np.inf)}
+
+            def pdf(self, x):
+                return 1 / np.sqrt(2*np.pi) * np.exp(-x**2/2)
+
+        StandardNormal = stats.make_distribution(MyStandardNormal())
+        X = StandardNormal()
+        assert X.support() == (-np.inf, np.inf)
+
+
+class TestTransforms:
+
+    def test_ContinuousDistribution_only(self):
+        X = stats.Binomial(n=10, p=0.5)
+        # This is applied at the top level TransformedDistribution,
+        # so testing one subclass is enough
+        message = "Transformations are currently only supported for continuous RVs."
+        with pytest.raises(NotImplementedError, match=message):
+            stats.exp(X)
+
+    def test_truncate(self):
+        rng = np.random.default_rng(81345982345826)
+        lb = rng.random((3, 1))
+        ub = rng.random((3, 1))
+        lb, ub = np.minimum(lb, ub), np.maximum(lb, ub)
+
+        Y = stats.truncate(Normal(), lb=lb, ub=ub)
+        Y0 = stats.truncnorm(lb, ub)
+
+        y = Y0.rvs((3, 10), random_state=rng)
+        p = Y0.cdf(y)
+
+        assert_allclose(Y.logentropy(), np.log(Y0.entropy() + 0j))
+        assert_allclose(Y.entropy(), Y0.entropy())
+        assert_allclose(Y.median(), Y0.ppf(0.5))
+        assert_allclose(Y.mean(), Y0.mean())
+        assert_allclose(Y.variance(), Y0.var())
+        assert_allclose(Y.standard_deviation(), np.sqrt(Y0.var()))
+        assert_allclose(Y.skewness(), Y0.stats('s'))
+        assert_allclose(Y.kurtosis(), Y0.stats('k') + 3)
+        assert_allclose(Y.support(), Y0.support())
+        assert_allclose(Y.pdf(y), Y0.pdf(y))
+        assert_allclose(Y.cdf(y), Y0.cdf(y))
+        assert_allclose(Y.ccdf(y), Y0.sf(y))
+        assert_allclose(Y.icdf(p), Y0.ppf(p))
+        assert_allclose(Y.iccdf(p), Y0.isf(p))
+        assert_allclose(Y.logpdf(y), Y0.logpdf(y))
+        assert_allclose(Y.logcdf(y), Y0.logcdf(y))
+        assert_allclose(Y.logccdf(y), Y0.logsf(y))
+        assert_allclose(Y.ilogcdf(np.log(p)), Y0.ppf(p))
+        assert_allclose(Y.ilogccdf(np.log(p)), Y0.isf(p))
+        sample = Y.sample(10)
+        assert np.all((sample > lb) & (sample < ub))
+
+    @pytest.mark.fail_slow(10)
+    @given(data=strategies.data(), seed=strategies.integers(min_value=0))
+    def test_loc_scale(self, data, seed):
+        # Need tests with negative scale
+        rng = np.random.default_rng(seed)
+
+        class TransformedNormal(ShiftedScaledDistribution):
+            def __init__(self, *args, **kwargs):
+                super().__init__(StandardNormal(), *args, **kwargs)
+
+        tmp = draw_distribution_from_family(
+            TransformedNormal, data, rng, proportions=(1, 0, 0, 0), min_side=1)
+        dist, x, y, p, logp, result_shape, x_result_shape, xy_result_shape = tmp
+
+        loc = dist.loc
+        scale = dist.scale
+        dist0 = StandardNormal()
+        dist_ref = stats.norm(loc=loc, scale=scale)
+        dist_ref_lmoment = Normal(mu=loc, sigma=scale)
+
+        x0 = (x - loc) / scale
+        y0 = (y - loc) / scale
+
+        a, b = dist.support()
+        a0, b0 = dist0.support()
+        assert_allclose(a, a0 + loc)
+        assert_allclose(b, b0 + loc)
+
+        with np.errstate(invalid='ignore', divide='ignore'):
+            assert_allclose(np.exp(dist.logentropy()), dist.entropy())
+            assert_allclose(dist.entropy(), dist_ref.entropy())
+            assert_allclose(dist.median(), dist0.median() + loc)
+            assert_allclose(dist.mode(), dist0.mode() + loc)
+            assert_allclose(dist.mean(), dist0.mean() + loc)
+            assert_allclose(dist.variance(), dist0.variance() * scale**2)
+            assert_allclose(dist.standard_deviation(), dist.variance()**0.5)
+            assert_allclose(dist.skewness(), dist0.skewness() * np.sign(scale))
+            assert_allclose(dist.kurtosis(), dist0.kurtosis())
+            assert_allclose(dist.logpdf(x), dist0.logpdf(x0) - np.log(scale))
+            assert_allclose(dist.pdf(x), dist0.pdf(x0) / scale)
+            assert_allclose(dist.logcdf(x), dist0.logcdf(x0))
+            assert_allclose(dist.cdf(x), dist0.cdf(x0))
+            assert_allclose(dist.logccdf(x), dist0.logccdf(x0))
+            assert_allclose(dist.ccdf(x), dist0.ccdf(x0))
+            assert_allclose(dist.logcdf(x, y), dist0.logcdf(x0, y0))
+            assert_allclose(dist.cdf(x, y), dist0.cdf(x0, y0))
+            assert_allclose(dist.logccdf(x, y), dist0.logccdf(x0, y0))
+            assert_allclose(dist.ccdf(x, y), dist0.ccdf(x0, y0))
+            assert_allclose(dist.ilogcdf(logp), dist0.ilogcdf(logp)*scale + loc)
+            assert_allclose(dist.icdf(p), dist0.icdf(p)*scale + loc)
+            assert_allclose(dist.ilogccdf(logp), dist0.ilogccdf(logp)*scale + loc)
+            assert_allclose(dist.iccdf(p), dist0.iccdf(p)*scale + loc)
+            for i in range(1, 5):
+                assert_allclose(dist.moment(i, 'raw'), dist_ref.moment(i))
+                assert_allclose(dist.moment(i, 'central'),
+                                dist0.moment(i, 'central') * scale**i)
+                assert_allclose(dist.moment(i, 'standardized'),
+                                dist0.moment(i, 'standardized') * np.sign(scale)**i)
+            for i in range(1, 5):
+                assert_allclose(dist.lmoment(i), dist_ref_lmoment.lmoment(i), atol=1e-8)
+                if i >= 3:
+                    assert_allclose(dist.lmoment(i, standardize=True),
+                                    dist_ref_lmoment.lmoment(i, standardize=True),
+                                    atol=1e-8)
+
+        # Transform back to the original distribution using all arithmetic
+        # operations; check that it behaves as expected.
+        dist = (dist - 2*loc) + loc
+        dist = dist/scale**2 * scale
+        z = np.zeros(dist._shape)  # compact broadcasting
+
+        a, b = dist.support()
+        a0, b0 = dist0.support()
+        assert_allclose(a, a0 + z)
+        assert_allclose(b, b0 + z)
+
+        with np.errstate(invalid='ignore', divide='ignore'):
+            assert_allclose(dist.logentropy(), dist0.logentropy() + z)
+            assert_allclose(dist.entropy(), dist0.entropy() + z)
+            assert_allclose(dist.median(), dist0.median() + z)
+            assert_allclose(dist.mode(), dist0.mode() + z)
+            assert_allclose(dist.mean(), dist0.mean() + z)
+            assert_allclose(dist.variance(), dist0.variance() + z)
+            assert_allclose(dist.standard_deviation(), dist0.standard_deviation() + z)
+            assert_allclose(dist.skewness(), dist0.skewness() + z)
+            assert_allclose(dist.kurtosis(), dist0.kurtosis() + z)
+            assert_allclose(dist.logpdf(x), dist0.logpdf(x)+z)
+            assert_allclose(dist.pdf(x), dist0.pdf(x) + z)
+            assert_allclose(dist.logcdf(x), dist0.logcdf(x) + z)
+            assert_allclose(dist.cdf(x), dist0.cdf(x) + z)
+            assert_allclose(dist.logccdf(x), dist0.logccdf(x) + z)
+            assert_allclose(dist.ccdf(x), dist0.ccdf(x) + z)
+            assert_allclose(dist.ilogcdf(logp), dist0.ilogcdf(logp) + z)
+            assert_allclose(dist.icdf(p), dist0.icdf(p) + z)
+            assert_allclose(dist.ilogccdf(logp), dist0.ilogccdf(logp) + z)
+            assert_allclose(dist.iccdf(p), dist0.iccdf(p) + z)
+            for i in range(1, 5):
+                assert_allclose(dist.moment(i, 'raw'), dist0.moment(i, 'raw'))
+                assert_allclose(dist.moment(i, 'central'), dist0.moment(i, 'central'))
+                assert_allclose(dist.moment(i, 'standardized'),
+                                dist0.moment(i, 'standardized'))
+            for i in range(1, 5):
+                assert_allclose(dist.lmoment(i), dist0.lmoment(i))
+                if i >= 3:
+                    assert_allclose(dist.lmoment(i, standardize=True),
+                                    dist0.lmoment(i, standardize=True))
+
+            # These are tough to compare because of the way the shape works
+            # rng = np.random.default_rng(seed)
+            # rng0 = np.random.default_rng(seed)
+            # assert_allclose(dist.sample(x_result_shape, rng=rng),
+            #                 dist0.sample(x_result_shape, rng=rng0) * scale + loc)
+            # Should also try to test fit, plot?
+
+    @pytest.mark.fail_slow(5)
+    @pytest.mark.parametrize('exp_pow', ['exp', 'pow'])
+    def test_exp_pow(self, exp_pow):
+        rng = np.random.default_rng(81345982345826)
+        mu = rng.random((3, 1))
+        sigma = rng.random((3, 1))
+
+        X = Normal()*sigma + mu
+        if exp_pow == 'exp':
+            Y = stats.exp(X)
+        else:
+            Y = np.e ** X
+        Y0 = stats.lognorm(sigma, scale=np.exp(mu))
+
+        y = Y0.rvs((3, 10), random_state=rng)
+        p = Y0.cdf(y)
+
+        assert_allclose(Y.logentropy(), np.log(Y0.entropy()))
+        assert_allclose(Y.entropy(), Y0.entropy())
+        assert_allclose(Y.median(), Y0.ppf(0.5))
+        assert_allclose(Y.mean(), Y0.mean())
+        assert_allclose(Y.variance(), Y0.var())
+        assert_allclose(Y.standard_deviation(), np.sqrt(Y0.var()))
+        assert_allclose(Y.skewness(), Y0.stats('s'))
+        assert_allclose(Y.kurtosis(), Y0.stats('k') + 3)
+        assert_allclose(Y.support(), Y0.support())
+        assert_allclose(Y.pdf(y), Y0.pdf(y))
+        assert_allclose(Y.cdf(y), Y0.cdf(y))
+        assert_allclose(Y.ccdf(y), Y0.sf(y))
+        assert_allclose(Y.icdf(p), Y0.ppf(p))
+        assert_allclose(Y.iccdf(p), Y0.isf(p))
+        assert_allclose(Y.logpdf(y), Y0.logpdf(y))
+        assert_allclose(Y.logcdf(y), Y0.logcdf(y))
+        assert_allclose(Y.logccdf(y), Y0.logsf(y))
+        assert_allclose(Y.ilogcdf(np.log(p)), Y0.ppf(p))
+        assert_allclose(Y.ilogccdf(np.log(p)), Y0.isf(p))
+        seed = 3984593485
+        assert_allclose(Y.sample(rng=seed), np.exp(X.sample(rng=seed)))
+
+
+    @pytest.mark.fail_slow(10)
+    @pytest.mark.parametrize('scale', [1, 2, -1])
+    @pytest.mark.xfail_on_32bit("`scale=-1` fails on 32-bit; needs investigation")
+    def test_reciprocal(self, scale):
+        rng = np.random.default_rng(81345982345826)
+        a = rng.random((3, 1))
+
+        # Separate sign from scale. It's easy to scale the resulting
+        # RV with negative scale; we want to test the ability to divide
+        # by a RV with negative support
+        sign, scale = np.sign(scale), abs(scale)
+
+        # Reference distribution
+        InvGamma = stats.make_distribution(stats.invgamma)
+        Y0 = sign * scale * InvGamma(a=a)
+
+        # Test distribution
+        X = _Gamma(a=a) if sign > 0 else -_Gamma(a=a)
+        Y = scale / X
+
+        y = Y0.sample(shape=(3, 10), rng=rng)
+        p = Y0.cdf(y)
+        logp = np.log(p)
+
+        assert_allclose(Y.logentropy(), np.log(Y0.entropy()))
+        assert_allclose(Y.entropy(), Y0.entropy())
+        assert_allclose(Y.median(), Y0.median())
+        # moments are not finite
+        assert_allclose(Y.support(), Y0.support())
+        assert_allclose(Y.pdf(y), Y0.pdf(y))
+        assert_allclose(Y.cdf(y), Y0.cdf(y))
+        assert_allclose(Y.ccdf(y), Y0.ccdf(y))
+        assert_allclose(Y.icdf(p), Y0.icdf(p))
+        assert_allclose(Y.iccdf(p), Y0.iccdf(p))
+        assert_allclose(Y.logpdf(y), Y0.logpdf(y))
+        assert_allclose(Y.logcdf(y), Y0.logcdf(y))
+        assert_allclose(Y.logccdf(y), Y0.logccdf(y))
+        with np.errstate(divide='ignore', invalid='ignore'):
+            assert_allclose(Y.ilogcdf(logp), Y0.ilogcdf(logp))
+            assert_allclose(Y.ilogccdf(logp), Y0.ilogccdf(logp))
+        seed = 3984593485
+        assert_allclose(Y.sample(rng=seed), scale/(X.sample(rng=seed)))
+
+    @pytest.mark.fail_slow(5)
+    def test_log(self):
+        rng = np.random.default_rng(81345982345826)
+        a = rng.random((3, 1))
+
+        X = _Gamma(a=a)
+        Y0 = stats.loggamma(a)
+        Y = stats.log(X)
+        y = Y0.rvs((3, 10), random_state=rng)
+        p = Y0.cdf(y)
+
+        assert_allclose(Y.logentropy(), np.log(Y0.entropy()))
+        assert_allclose(Y.entropy(), Y0.entropy())
+        assert_allclose(Y.median(), Y0.ppf(0.5))
+        assert_allclose(Y.mean(), Y0.mean())
+        assert_allclose(Y.variance(), Y0.var())
+        assert_allclose(Y.standard_deviation(), np.sqrt(Y0.var()))
+        assert_allclose(Y.skewness(), Y0.stats('s'))
+        assert_allclose(Y.kurtosis(), Y0.stats('k') + 3)
+        assert_allclose(Y.support(), Y0.support())
+        assert_allclose(Y.pdf(y), Y0.pdf(y))
+        assert_allclose(Y.cdf(y), Y0.cdf(y))
+        assert_allclose(Y.ccdf(y), Y0.sf(y))
+        assert_allclose(Y.icdf(p), Y0.ppf(p))
+        assert_allclose(Y.iccdf(p), Y0.isf(p))
+        assert_allclose(Y.logpdf(y), Y0.logpdf(y))
+        assert_allclose(Y.logcdf(y), Y0.logcdf(y))
+        assert_allclose(Y.logccdf(y), Y0.logsf(y))
+        with np.errstate(invalid='ignore'):
+            assert_allclose(Y.ilogcdf(np.log(p)), Y0.ppf(p))
+            assert_allclose(Y.ilogccdf(np.log(p)), Y0.isf(p))
+        seed = 3984593485
+        assert_allclose(Y.sample(rng=seed), np.log(X.sample(rng=seed)))
+
+    def test_monotonic_transforms(self):
+        # Some tests of monotonic transforms that are better to be grouped or
+        # don't fit well above
+
+        X = Uniform(a=1, b=2)
+        X_str = "Uniform(a=1.0, b=2.0)"
+
+        assert str(stats.log(X)) == f"log({X_str})"
+        assert str(1 / X) == f"1/({X_str})"
+        assert str(stats.exp(X)) == f"exp({X_str})"
+
+        X = Uniform(a=-1, b=2)
+        message = "Division by a random variable is only implemented when the..."
+        with pytest.raises(NotImplementedError, match=message):
+            1 / X
+        message = "The logarithm of a random variable is only implemented when the..."
+        with pytest.raises(NotImplementedError, match=message):
+            stats.log(X)
+        message = "Raising an argument to the power of a random variable is only..."
+        with pytest.raises(NotImplementedError, match=message):
+            (-2) ** X
+        with pytest.raises(NotImplementedError, match=message):
+            1 ** X
+        with pytest.raises(NotImplementedError, match=message):
+            [0.5, 1.5] ** X
+
+        message = "Raising a random variable to the power of an argument is only"
+        with pytest.raises(NotImplementedError, match=message):
+            X ** (-2)
+        with pytest.raises(NotImplementedError, match=message):
+            X ** 0
+        with pytest.raises(NotImplementedError, match=message):
+            X ** [0.5, 1.5]
+
+    def test_arithmetic_operators(self):
+        rng = np.random.default_rng(2348923495832349834)
+
+        a, b, loc, scale = 0.294, 1.34, 0.57, 1.16
+
+        x = rng.uniform(-3, 3, 100)
+        Y = _LogUniform(a=a, b=b)
+
+        X = scale*Y + loc
+        assert_allclose(X.cdf(x), Y.cdf((x - loc) / scale))
+        X = loc + Y*scale
+        assert_allclose(X.cdf(x), Y.cdf((x - loc) / scale))
+
+        X = Y/scale - loc
+        assert_allclose(X.cdf(x), Y.cdf((x + loc) * scale))
+        X = loc -_LogUniform(a=a, b=b)/scale
+        assert_allclose(X.cdf(x), Y.ccdf((-x + loc)*scale))
+
+    def test_abs(self):
+        rng = np.random.default_rng(81345982345826)
+        loc = rng.random((3, 1))
+
+        Y = stats.abs(Normal() + loc)
+        Y0 = stats.foldnorm(loc)
+
+        y = Y0.rvs((3, 10), random_state=rng)
+        p = Y0.cdf(y)
+
+        assert_allclose(Y.logentropy(), np.log(Y0.entropy() + 0j))
+        assert_allclose(Y.entropy(), Y0.entropy())
+        assert_allclose(Y.median(), Y0.ppf(0.5))
+        assert_allclose(Y.mean(), Y0.mean())
+        assert_allclose(Y.variance(), Y0.var())
+        assert_allclose(Y.standard_deviation(), np.sqrt(Y0.var()))
+        assert_allclose(Y.skewness(), Y0.stats('s'))
+        assert_allclose(Y.kurtosis(), Y0.stats('k') + 3)
+        assert_allclose(Y.support(), Y0.support())
+        assert_allclose(Y.pdf(y), Y0.pdf(y))
+        assert_allclose(Y.cdf(y), Y0.cdf(y))
+        assert_allclose(Y.ccdf(y), Y0.sf(y))
+        assert_allclose(Y.icdf(p), Y0.ppf(p))
+        assert_allclose(Y.iccdf(p), Y0.isf(p))
+        assert_allclose(Y.logpdf(y), Y0.logpdf(y))
+        assert_allclose(Y.logcdf(y), Y0.logcdf(y))
+        assert_allclose(Y.logccdf(y), Y0.logsf(y))
+        assert_allclose(Y.ilogcdf(np.log(p)), Y0.ppf(p))
+        assert_allclose(Y.ilogccdf(np.log(p)), Y0.isf(p))
+        sample = Y.sample(10)
+        assert np.all(sample > 0)
+
+    def test_abs_finite_support(self):
+        # The original implementation of `FoldedDistribution` might evaluate
+        # the private distribution methods outside the support. Check that this
+        # is resolved.
+        Weibull = stats.make_distribution(stats.weibull_min)
+        X = Weibull(c=2)
+        Y = abs(-X)
+        assert_equal(X.logpdf(1), Y.logpdf(1))
+        assert_equal(X.pdf(1), Y.pdf(1))
+        assert_equal(X.logcdf(1), Y.logcdf(1))
+        assert_equal(X.cdf(1), Y.cdf(1))
+        assert_equal(X.logccdf(1), Y.logccdf(1))
+        assert_equal(X.ccdf(1), Y.ccdf(1))
+
+    def test_pow(self):
+        rng = np.random.default_rng(81345982345826)
+
+        Y = Normal()**2
+        Y0 = stats.chi2(df=1)
+
+        y = Y0.rvs(10, random_state=rng)
+        p = Y0.cdf(y)
+
+        assert_allclose(Y.logentropy(), np.log(Y0.entropy() + 0j), rtol=1e-6)
+        assert_allclose(Y.entropy(), Y0.entropy(), rtol=1e-6)
+        assert_allclose(Y.median(), Y0.median())
+        assert_allclose(Y.mean(), Y0.mean())
+        assert_allclose(Y.variance(), Y0.var())
+        assert_allclose(Y.standard_deviation(), np.sqrt(Y0.var()))
+        assert_allclose(Y.skewness(), Y0.stats('s'))
+        assert_allclose(Y.kurtosis(), Y0.stats('k') + 3)
+        assert_allclose(Y.support(), Y0.support())
+        assert_allclose(Y.pdf(y), Y0.pdf(y))
+        assert_allclose(Y.cdf(y), Y0.cdf(y))
+        assert_allclose(Y.ccdf(y), Y0.sf(y))
+        assert_allclose(Y.icdf(p), Y0.ppf(p))
+        assert_allclose(Y.iccdf(p), Y0.isf(p))
+        assert_allclose(Y.logpdf(y), Y0.logpdf(y))
+        assert_allclose(Y.logcdf(y), Y0.logcdf(y))
+        assert_allclose(Y.logccdf(y), Y0.logsf(y))
+        assert_allclose(Y.ilogcdf(np.log(p)), Y0.ppf(p))
+        assert_allclose(Y.ilogccdf(np.log(p)), Y0.isf(p))
+        sample = Y.sample(10)
+        assert np.all(sample > 0)
+
+class TestOrderStatistic:
+    @pytest.mark.fail_slow(20)  # Moments require integration
+    def test_order_statistic(self):
+        rng = np.random.default_rng(7546349802439582)
+        X = Uniform(a=0, b=1)
+        n = 5
+        r = np.asarray([[1], [3], [5]])
+        Y = stats.order_statistic(X, n=n, r=r)
+        Y0 = stats.beta(r, n + 1 - r)
+
+        y = Y0.rvs((3, 10), random_state=rng)
+        p = Y0.cdf(y)
+
+        # log methods need some attention before merge
+        assert_allclose(np.exp(Y.logentropy()), Y0.entropy())
+        assert_allclose(Y.entropy(), Y0.entropy())
+        assert_allclose(Y.mean(), Y0.mean())
+        assert_allclose(Y.variance(), Y0.var())
+        assert_allclose(Y.skewness(), Y0.stats('s'), atol=1e-15)
+        assert_allclose(Y.kurtosis(), Y0.stats('k') + 3, atol=1e-15)
+        assert_allclose(Y.median(), Y0.ppf(0.5))
+        assert_allclose(Y.support(), Y0.support())
+        assert_allclose(Y.pdf(y), Y0.pdf(y))
+        assert_allclose(Y.cdf(y, method='formula'), Y.cdf(y, method='quadrature'))
+        assert_allclose(Y.ccdf(y, method='formula'), Y.ccdf(y, method='quadrature'))
+        assert_allclose(Y.icdf(p, method='formula'), Y.icdf(p, method='inversion'))
+        assert_allclose(Y.iccdf(p, method='formula'), Y.iccdf(p, method='inversion'))
+        assert_allclose(Y.logpdf(y), Y0.logpdf(y))
+        assert_allclose(Y.logcdf(y), Y0.logcdf(y))
+        assert_allclose(Y.logccdf(y), Y0.logsf(y))
+        with np.errstate(invalid='ignore', divide='ignore'):
+            assert_allclose(Y.ilogcdf(np.log(p),), Y0.ppf(p))
+            assert_allclose(Y.ilogccdf(np.log(p)), Y0.isf(p))
+
+        message = "`r` and `n` must contain only positive integers."
+        with pytest.raises(ValueError, match=message):
+            stats.order_statistic(X, n=n, r=-1)
+        with pytest.raises(ValueError, match=message):
+            stats.order_statistic(X, n=-1, r=r)
+        with pytest.raises(ValueError, match=message):
+            stats.order_statistic(X, n=n, r=1.5)
+        with pytest.raises(ValueError, match=message):
+            stats.order_statistic(X, n=1.5, r=r)
+
+    def test_support_gh22037(self):
+        # During review of gh-22037, it was noted that the `support` of
+        # an `OrderStatisticDistribution` returned incorrect results;
+        # this was resolved by overriding `_support`.
+        Uniform = stats.make_distribution(stats.uniform)
+        X = Uniform()
+        Y = X*5 + 2
+        Z = stats.order_statistic(Y, r=3, n=5)
+        assert_allclose(Z.support(), Y.support())
+
+    def test_composition_gh22037(self):
+        # During review of gh-22037, it was noted that an error was
+        # raised when creating an `OrderStatisticDistribution` from
+        # a `TruncatedDistribution`. This was resolved by overriding
+        # `_update_parameters`.
+        Normal = stats.make_distribution(stats.norm)
+        TruncatedNormal = stats.make_distribution(stats.truncnorm)
+        a, b = [-2, -1], 1
+        r, n = 3, [[4], [5]]
+        x = [[[-0.3]], [[0.1]]]
+        X1 = Normal()
+        Y1 = stats.truncate(X1, a, b)
+        Z1 = stats.order_statistic(Y1, r=r, n=n)
+        X2 = TruncatedNormal(a=a, b=b)
+        Z2 = stats.order_statistic(X2, r=r, n=n)
+        np.testing.assert_allclose(Z1.cdf(x), Z2.cdf(x))
+
+
+class TestFullCoverage:
+    # Adds tests just to get to 100% test coverage; this way it's more obvious
+    # if new lines are untested.
+    def test_Domain(self):
+        with pytest.raises(NotImplementedError):
+            _Domain.contains(None, 1.)
+        with pytest.raises(NotImplementedError):
+            _Domain.get_numerical_endpoints(None, 1.)
+        with pytest.raises(NotImplementedError):
+            _Domain.__str__(None)
+
+    def test_Parameter(self):
+        with pytest.raises(NotImplementedError):
+            _Parameter.validate(None, 1.)
+
+    @pytest.mark.parametrize(("dtype_in", "dtype_out"),
+                              [(np.float16, np.float16),
+                               (np.int16, np.float64)])
+    def test_RealParameter_uncommon_dtypes(self, dtype_in, dtype_out):
+        domain = _RealInterval((-1, 1))
+        parameter = _RealParameter('x', domain=domain)
+
+        x = np.asarray([0.5, 2.5], dtype=dtype_in)
+        arr, dtype, valid = parameter.validate(x, parameter_values={})
+        assert_equal(arr, x)
+        assert dtype == dtype_out
+        assert_equal(valid, [True, False])
+
+    def test_ContinuousDistribution_set_invalid_nan(self):
+        # Exercise code paths when formula returns wrong shape and dtype
+        # We could consider making this raise an error to force authors
+        # to return the right shape and dytpe, but this would need to be
+        # configurable.
+        class TestDist(ContinuousDistribution):
+            _variable = _RealParameter('x', domain=_RealInterval(endpoints=(0., 1.)))
+            def _logpdf_formula(self, x, *args, **kwargs):
+                return 0
+
+        X = TestDist()
+        dtype = np.float32
+        X._dtype = dtype
+        x = np.asarray([0.5], dtype=dtype)
+        assert X.logpdf(x).dtype == dtype
+
+    def test_fiinfo(self):
+        assert _fiinfo(np.float64(1.)).max == np.finfo(np.float64).max
+        assert _fiinfo(np.int64(1)).max == np.iinfo(np.int64).max
+
+    def test_generate_domain_support(self):
+        msg = _generate_domain_support(StandardNormal)
+        assert "accepts no distribution parameters" in msg
+
+        msg = _generate_domain_support(Normal)
+        assert "accepts one parameterization" in msg
+
+        msg = _generate_domain_support(_LogUniform)
+        assert "accepts two parameterizations" in msg
+
+    def test_ContinuousDistribution__repr__(self):
+        X = Uniform(a=0, b=1)
+        assert repr(X) == "Uniform(a=np.float64(0.0), b=np.float64(1.0))"
+        assert repr(X*3 + 2) == (
+            "np.float64(3.0)*Uniform(a=np.float64(0.0), b=np.float64(1.0))"
+            " + np.float64(2.0)"
+        )
+
+        X = Uniform(a=np.zeros(4), b=1)
+        assert repr(X) == "Uniform(a=array([0., 0., 0., 0.]), b=1)"
+
+        X = Uniform(a=np.zeros(4, dtype=np.float32), b=np.ones(4, dtype=np.float32))
+        assert repr(X) == (
+            "Uniform(a=array([0., 0., 0., 0.], dtype=float32),"
+            " b=array([1., 1., 1., 1.], dtype=float32))"
+        )
+
+
+class TestReprs:
+    U = Uniform(a=0, b=1)
+    V = Uniform(a=np.float32(0.0), b=np.float32(1.0))
+    X = Normal(mu=-1, sigma=1)
+    Y = Normal(mu=1, sigma=1)
+    Z = Normal(mu=np.zeros(1000), sigma=1)
+
+    @pytest.mark.parametrize(
+        "dist",
+        [
+            U,
+            U - np.array([1.0, 2.0]),
+            V,
+            np.ones(2, dtype=np.float32)*V + np.zeros(2, dtype=np.float64),
+            3*U + 2,
+            U**4,
+            (3*U + 2)**4,
+            (3*U + 2)**3,
+            2**U,
+            2**(3*U + 1),
+            1 / (1 + U),
+            stats.order_statistic(U, r=3, n=5),
+            stats.truncate(U, 0.2, 0.8),
+            stats.Mixture([X, Y], weights=[0.3, 0.7]),
+            abs(U),
+            stats.exp(U),
+            stats.log(1 + U),
+            np.array([1.0, 2.0])*U + np.array([2.0, 3.0]),
+        ]
+    )
+    def test_executable(self, dist):
+        # Test that reprs actually evaluate to proper distribution
+        # provided relevant imports are made.
+        from numpy import array  # noqa: F401
+        from numpy import float32  # noqa: F401
+        from scipy.stats import abs, exp, log, order_statistic, truncate # noqa: F401
+        from scipy.stats import Mixture, Normal # noqa: F401
+        from scipy.stats._new_distributions import Uniform # noqa: F401
+        new_dist = eval(repr(dist))
+        # A basic check that the distributions are the same
+        sample1 = dist.sample(shape=10, rng=1234)
+        sample2 = new_dist.sample(shape=10, rng=1234)
+        assert_equal(sample1, sample2)
+        assert sample1.dtype is sample2.dtype
+
+    @pytest.mark.parametrize(
+        "dist",
+        [
+            Z,
+            np.full(1000, 2.0) * X + 1.0,
+            2.0 * X + np.full(1000, 1.0),
+            np.full(1000, 2.0) * X + 1.0,
+            stats.truncate(Z, -1, 1),
+            stats.truncate(Z, -np.ones(1000), np.ones(1000)),
+            stats.order_statistic(X, r=np.arange(1, 1000), n=1000),
+            Z**2,
+            1.0 / (1 + stats.exp(Z)),
+            2**Z,
+        ]
+    )
+    def test_not_too_long(self, dist):
+        # Tests that array summarization is working to ensure reprs aren't too long.
+        # None of the reprs above will be executable.
+        assert len(repr(dist)) < 250
+
+
+class MixedDist(ContinuousDistribution):
+    _variable = _RealParameter('x', domain=_RealInterval(endpoints=(-np.inf, np.inf)))
+    def _pdf_formula(self, x, *args, **kwargs):
+        return (0.4 * 1/(1.1 * np.sqrt(2*np.pi)) * np.exp(-0.5*((x+0.25)/1.1)**2)
+                + 0.6 * 1/(0.9 * np.sqrt(2*np.pi)) * np.exp(-0.5*((x-0.5)/0.9)**2))
+
+
+class TestMixture:
+    def test_input_validation(self):
+        message = "`components` must contain at least one random variable."
+        with pytest.raises(ValueError, match=message):
+            Mixture([])
+
+        message = "Each element of `components` must be an instance..."
+        with pytest.raises(ValueError, match=message):
+            Mixture((1, 2, 3))
+
+        message = "All elements of `components` must have scalar shapes."
+        with pytest.raises(ValueError, match=message):
+            Mixture([Normal(mu=[1, 2]), Normal()])
+
+        message = "`components` and `weights` must have the same length."
+        with pytest.raises(ValueError, match=message):
+            Mixture([Normal()], weights=[0.5, 0.5])
+
+        message = "`weights` must have floating point dtype."
+        with pytest.raises(ValueError, match=message):
+            Mixture([Normal()], weights=[1])
+
+        message = "`weights` must have floating point dtype."
+        with pytest.raises(ValueError, match=message):
+            Mixture([Normal()], weights=[1])
+
+        message = "`weights` must sum to 1.0."
+        with pytest.raises(ValueError, match=message):
+            Mixture([Normal(), Normal()], weights=[0.5, 1.0])
+
+        message = "All `weights` must be non-negative."
+        with pytest.raises(ValueError, match=message):
+            Mixture([Normal(), Normal()], weights=[1.5, -0.5])
+
+    @pytest.mark.parametrize('shape', [(), (10,)])
+    def test_basic(self, shape):
+        rng = np.random.default_rng(582348972387243524)
+        X = Mixture((Normal(mu=-0.25, sigma=1.1), Normal(mu=0.5, sigma=0.9)),
+                    weights=(0.4, 0.6))
+        Y = MixedDist()
+        x = rng.random(shape)
+
+        def assert_allclose(res, ref, **kwargs):
+            if shape == ():
+                assert np.isscalar(res)
+            np.testing.assert_allclose(res, ref, **kwargs)
+
+        assert_allclose(X.logentropy(), Y.logentropy())
+        assert_allclose(X.entropy(), Y.entropy())
+        assert_allclose(X.mode(), Y.mode())
+        assert_allclose(X.median(), Y.median())
+        assert_allclose(X.mean(), Y.mean())
+        assert_allclose(X.variance(), Y.variance())
+        assert_allclose(X.standard_deviation(), Y.standard_deviation())
+        assert_allclose(X.skewness(), Y.skewness())
+        assert_allclose(X.kurtosis(), Y.kurtosis())
+        assert_allclose(X.logpdf(x), Y.logpdf(x))
+        assert_allclose(X.pdf(x), Y.pdf(x))
+        assert_allclose(X.logcdf(x), Y.logcdf(x))
+        assert_allclose(X.cdf(x), Y.cdf(x))
+        assert_allclose(X.logccdf(x), Y.logccdf(x))
+        assert_allclose(X.ccdf(x), Y.ccdf(x))
+        assert_allclose(X.ilogcdf(x), Y.ilogcdf(x))
+        assert_allclose(X.icdf(x), Y.icdf(x))
+        assert_allclose(X.ilogccdf(x), Y.ilogccdf(x))
+        assert_allclose(X.iccdf(x), Y.iccdf(x))
+        for kind in ['raw', 'central', 'standardized']:
+            for order in range(5):
+                assert_allclose(X.moment(order, kind=kind),
+                                Y.moment(order, kind=kind),
+                                atol=1e-15)
+        message = "L-moments are not currently available..."
+        with pytest.raises(NotImplementedError, match=message):
+            X.lmoment(1)
+
+        # weak test of `sample`
+        shape = (10, 20, 5)
+        y = X.sample(shape, rng=rng)
+        assert y.shape == shape
+        assert stats.ks_1samp(y.ravel(), X.cdf).pvalue > 0.05
+
+    def test_default_weights(self):
+        a = 1.1
+        Gamma = stats.make_distribution(stats.gamma)
+        X = Gamma(a=a)
+        Y = stats.Mixture((X, -X))
+        x = np.linspace(-4, 4, 300)
+        assert_allclose(Y.pdf(x), stats.dgamma(a=a).pdf(x))
+
+    def test_properties(self):
+        components = [Normal(mu=-0.25, sigma=1.1), Normal(mu=0.5, sigma=0.9)]
+        weights = (0.4, 0.6)
+        X = Mixture(components, weights=weights)
+
+        # Replacing properties doesn't work
+        # Different version of Python have different messages
+        with pytest.raises(AttributeError):
+            X.components = 10
+        with pytest.raises(AttributeError):
+            X.weights = 10
+
+        # Mutation doesn't work
+        X.components[0] = components[1]
+        assert X.components[0] == components[0]
+        X.weights[0] = weights[1]
+        assert X.weights[0] == weights[0]
+
+    def test_inverse(self):
+        # Originally, inverse relied on the mean to start the bracket search.
+        # This didn't work for distributions with non-finite mean. Check that
+        # this is resolved.
+        rng = np.random.default_rng(24358934657854237863456)
+        Cauchy = stats.make_distribution(stats.cauchy)
+        X0 = Cauchy()
+        X = stats.Mixture([X0, X0])
+        p = rng.random(size=10)
+        np.testing.assert_allclose(X.icdf(p), X0.icdf(p))
+        np.testing.assert_allclose(X.iccdf(p), X0.iccdf(p))
+        np.testing.assert_allclose(X.ilogcdf(p), X0.ilogcdf(p))
+        np.testing.assert_allclose(X.ilogccdf(p), X0.ilogccdf(p))
+
+
+def test_zipfian_distribution_wrapper():
+    # Regression test for gh-23678: calling the cdf method at the end
+    # point of the Zipfian distribution would generate a warning.
+    Zipfian = stats.make_distribution(stats.zipfian)
+    zdist = Zipfian(a=0.75, n=15)
+    # This should not generate any warnings.
+    assert_equal(zdist.cdf(15), 1.0)
+
+
+class Test_logexpxmexpy:
+    # Regression tests for some cases that the simplest version of `_logexpmexpy`
+    # did not originally handle correctly.
+
+    def test_x_equals_y(self):
+        # Test x - x == 0 in log-space
+        x = np.asarray(2.)
+        assert_equal(_logexpxmexpy(x, x), -np.inf)
+
+    def test_y_neg_inf(self):
+        # Test x - 0 == x in log-space
+        x, y = np.asarray(2.), np.asarray(-inf)
+        assert_equal(_logexpxmexpy(x, y), x)
+
+    def test_nan(self):
+        # operations involving NaNs should not produce warnings
+        x = np.asarray(np.nan)
+        assert_equal(_logexpxmexpy(x, x), x)
+
+
+def test_gh_25180():
+    lu = _LogUniform(log_a=np.float64(-0.28915434544814245),
+                     log_b=np.float64(0.3085224670197856))
+    actual = lu.mode(method='optimization')
+    assert np.isfinite(actual)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/test_continuous_basic.py b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_continuous_basic.py
new file mode 100644
index 0000000000000000000000000000000000000000..f2a8ee50c83d8149b8a551cfcd068683c2babe3f
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_continuous_basic.py
@@ -0,0 +1,1065 @@
+import sys
+import warnings
+import platform
+
+import numpy as np
+import numpy.testing as npt
+import pytest
+from pytest import raises as assert_raises
+from scipy.integrate import IntegrationWarning
+import itertools
+
+from scipy import stats
+from .common_tests import (check_normalization, check_moment,
+                           check_mean_expect,
+                           check_var_expect, check_skew_expect,
+                           check_kurt_expect, check_entropy,
+                           check_private_entropy, check_entropy_vect_scale,
+                           check_edge_support, check_named_args,
+                           check_random_state_property,
+                           check_meth_dtype, check_ppf_dtype,
+                           check_cmplx_deriv,
+                           check_pickling, check_rvs_broadcast,
+                           check_freezing, check_munp_expect,)
+from scipy.stats._distr_params import distcont
+from scipy.stats._distn_infrastructure import rv_continuous_frozen
+
+"""
+Test all continuous distributions.
+
+Parameters were chosen for those distributions that pass the
+Kolmogorov-Smirnov test.  This provides safe parameters for each
+distributions so that we can perform further testing of class methods.
+
+These tests currently check only/mostly for serious errors and exceptions,
+not for numerically exact results.
+"""
+
+# Note that you need to add new distributions you want tested
+# to _distr_params
+
+DECIMAL = 5  # specify the precision of the tests  # increased from 0 to 5
+_IS_32BIT = (sys.maxsize < 2**32)
+
+# Sets of tests to skip.
+# Entries sorted by speed (very slow to slow).
+# xslow took > 1s; slow took > 0.5s
+
+xslow_test_cont_basic = {'studentized_range', 'kstwo', 'ksone', 'vonmises', 'kappa4',
+                         'recipinvgauss', 'vonmises_line', 'gausshyper',
+                         'rel_breitwigner', 'norminvgauss'}
+slow_test_cont_basic = {'crystalball', 'powerlognorm', 'pearson3'}
+
+# test_moments is already marked slow
+xslow_test_moments = {'studentized_range', 'ksone', 'vonmises', 'vonmises_line',
+                      'recipinvgauss', 'kstwo', 'kappa4'}
+
+slow_fit_mle = {'exponweib', 'genexpon', 'genhyperbolic', 'johnsonsb',
+                'kappa4', 'powerlognorm', 'tukeylambda'}
+xslow_fit_mle = {'gausshyper', 'ncf', 'ncx2', 'recipinvgauss', 'vonmises_line'}
+xfail_fit_mle = {'ksone', 'kstwo', 'truncpareto', 'irwinhall'}
+skip_fit_mle = {'levy_stable', 'studentized_range'}  # far too slow (>10min)
+slow_fit_mm = {'chi2', 'expon', 'lognorm', 'loguniform', 'powerlaw', 'reciprocal'}
+xslow_fit_mm = {'argus', 'beta', 'exponpow', 'gausshyper', 'gengamma',
+                'genhalflogistic', 'geninvgauss', 'gompertz',
+                'johnsonsb', 'kstwobign', 'ncx2', 'norminvgauss', 'trapezoid',
+                'truncnorm', 'truncweibull_min', 'wrapcauchy'}
+xfail_fit_mm = {'alpha', 'betaprime', 'bradford', 'burr', 'burr12', 'cauchy',
+                'crystalball', 'dpareto_lognorm', 'exponweib', 'f', 'fisk',
+                'foldcauchy', 'genextreme', 'genpareto', 'halfcauchy', 'invgamma',
+                'irwinhall', 'jf_skew_t', 'johnsonsu', 'kappa3', 'kappa4', 'landau',
+                'levy', 'levy_l', 'loglaplace', 'lomax', 'mielke', 'ncf', 'nct',
+                'pareto', 'powerlognorm', 'powernorm', 'rel_breitwigner',
+                'skewcauchy', 't', 'truncexpon', 'truncpareto',
+                'tukeylambda', 'vonmises', 'vonmises_line'}
+skip_fit_mm = {'genexpon', 'genhyperbolic', 'ksone', 'kstwo', 'levy_stable',
+               'recipinvgauss', 'studentized_range'}  # far too slow (>10min)
+
+# These distributions fail the complex derivative test below.
+# Here 'fail' mean produce wrong results and/or raise exceptions, depending
+# on the implementation details of corresponding special functions.
+# cf https://github.com/scipy/scipy/pull/4979 for a discussion.
+fails_cmplx = {'argus', 'beta', 'betaprime', 'cauchy', 'chi', 'chi2', 'cosine',
+               'dgamma', 'dpareto_lognorm', 'dweibull', 'erlang', 'f', 'foldcauchy',
+               'gamma', 'gausshyper', 'gengamma', 'genhyperbolic',
+               'geninvgauss', 'gennorm', 'genpareto',
+               'halfcauchy', 'halfgennorm', 'invgamma', 'irwinhall', 'jf_skew_t',
+               'ksone', 'kstwo', 'kstwobign', 'landau', 'levy_l', 'loggamma',
+               'logistic', 'loguniform', 'maxwell', 'nakagami',
+               'ncf', 'nct', 'ncx2', 'norminvgauss', 'pearson3',
+               'powerlaw', 'rdist', 'reciprocal', 'rice',
+               'skewnorm', 't', 'truncpareto', 'truncweibull_min',
+               'tukeylambda', 'vonmises', 'vonmises_line',
+               'rv_histogram_instance', 'truncnorm', 'studentized_range',
+               'johnsonsb', 'halflogistic', 'rel_breitwigner'}
+
+# Slow test_method_with_lists
+slow_with_lists = {'studentized_range'}
+
+
+# rv_histogram instances, with uniform and non-uniform bins;
+# stored as (dist, arg) tuples for cases_test_cont_basic
+# and cases_test_moments.
+histogram_test_instances = []
+case1 = {'a': [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6,
+               6, 6, 6, 7, 7, 7, 8, 8, 9], 'bins': 8}  # equal width bins
+case2 = {'a': [1, 1], 'bins': [0, 1, 10]}  # unequal width bins
+for case, density in itertools.product([case1, case2], [True, False]):
+    _hist = np.histogram(**case, density=density)
+    _rv_hist = stats.rv_histogram(_hist, density=density)
+    histogram_test_instances.append((_rv_hist, tuple()))
+
+
+def cases_test_cont_basic():
+    for distname, arg in distcont[:] + histogram_test_instances:
+        if distname == 'levy_stable':  # fails; tested separately
+            continue
+        if distname in slow_test_cont_basic:
+            yield pytest.param(distname, arg, marks=pytest.mark.slow)
+        elif distname in xslow_test_cont_basic:
+            yield pytest.param(distname, arg, marks=pytest.mark.xslow)
+        else:
+            yield distname, arg
+
+
+@pytest.mark.parametrize('distname,arg', list(cases_test_cont_basic()))
+@pytest.mark.parametrize('sn', [500])
+def test_cont_basic(distname, arg, sn, num_parallel_threads):
+    try:
+        distfn = getattr(stats, distname)
+    except TypeError:
+        distfn = distname
+        distname = 'rv_histogram_instance'
+
+    rng = np.random.default_rng(7654565)
+    rvs = distfn.rvs(size=sn, *arg, random_state=rng)
+    m, v = distfn.stats(*arg)
+
+    if distname not in {'laplace_asymmetric'}:
+        # TODO: multiple checks in this function are not robust, tweaking the
+        # seed above will make different distributions fail.
+        check_sample_meanvar_(m, v, rvs, rng)
+    check_cdf_ppf(distfn, arg, distname)
+    check_sf_isf(distfn, arg, distname)
+    check_cdf_sf(distfn, arg, distname)
+    check_ppf_isf(distfn, arg, distname)
+    check_pdf(distfn, arg, distname)
+    check_pdf_logpdf(distfn, arg, distname)
+    check_pdf_logpdf_at_endpoints(distfn, arg, distname)
+    check_cdf_logcdf(distfn, arg, distname)
+    check_sf_logsf(distfn, arg, distname)
+    check_ppf_broadcast(distfn, arg, distname)
+
+    alpha = 0.01
+    if distname == 'rv_histogram_instance':
+        check_distribution_rvs(distfn.cdf, arg, alpha, rvs)
+    elif distname != 'geninvgauss':
+        # skip kstest for geninvgauss since cdf is too slow; see test for
+        # rv generation in TestGenInvGauss in test_distributions.py
+        check_distribution_rvs(distname, arg, alpha, rvs)
+
+    locscale_defaults = (0, 1)
+    meths = [distfn.pdf, distfn.logpdf, distfn.cdf, distfn.logcdf,
+             distfn.logsf]
+    # make sure arguments are within support
+    spec_x = {'weibull_max': -0.5, 'levy_l': -0.5,
+              'pareto': 1.5, 'truncpareto': 3.2, 'tukeylambda': 0.3,
+              'rv_histogram_instance': 5.0}
+    x = spec_x.get(distname, 0.5)
+    if distname == 'invweibull':
+        arg = (1,)
+    elif distname == 'ksone':
+        arg = (3,)
+
+    check_named_args(distfn, x, arg, locscale_defaults, meths)
+    if num_parallel_threads == 1:
+        check_random_state_property(distfn, arg)
+
+        if distname in ['rel_breitwigner'] and _IS_32BIT:
+            # gh18414
+            pytest.skip("fails on Linux 32-bit")
+        else:
+            check_pickling(distfn, arg)
+    check_freezing(distfn, arg)
+
+    # Entropy
+    if distname not in ['kstwobign', 'kstwo', 'ncf']:
+        check_entropy(distfn, arg, distname)
+
+    if distfn.numargs == 0:
+        check_vecentropy(distfn, arg)
+
+    if (distfn.__class__._entropy != stats.rv_continuous._entropy
+            and distname != 'vonmises'):
+        check_private_entropy(distfn, arg, stats.rv_continuous)
+
+    with warnings.catch_warnings():
+        warnings.filterwarnings(
+            "ignore", "The occurrence of roundoff error", IntegrationWarning)
+        warnings.filterwarnings("ignore", "Extremely bad integrand", IntegrationWarning)
+        warnings.filterwarnings("ignore", "invalid value", RuntimeWarning)
+        check_entropy_vect_scale(distfn, arg)
+
+    check_retrieving_support(distfn, arg)
+    check_edge_support(distfn, arg)
+
+    check_meth_dtype(distfn, arg, meths)
+    check_ppf_dtype(distfn, arg)
+
+    # complex special functions known to fail on sparc64 (gh-22577)
+    if distname not in fails_cmplx and platform.machine() != 'sparc64':
+        check_cmplx_deriv(distfn, arg)
+
+    if distname != 'truncnorm':
+        check_ppf_private(distfn, arg, distname)
+
+
+def cases_test_cont_basic_fit():
+    slow = pytest.mark.slow
+    xslow = pytest.mark.xslow
+    fail = pytest.mark.skip(reason="Test fails and may be slow.")
+    skip = pytest.mark.skip(reason="Test too slow to run to completion (>10m).")
+
+    for distname, arg in distcont[:] + histogram_test_instances:
+        for method in ["MLE", "MM"]:
+            for fix_args in [True, False]:
+                if method == 'MLE' and distname in slow_fit_mle:
+                    yield pytest.param(distname, arg, method, fix_args, marks=slow)
+                    continue
+                if method == 'MLE' and distname in xslow_fit_mle:
+                    yield pytest.param(distname, arg, method, fix_args, marks=xslow)
+                    continue
+                if method == 'MLE' and distname in xfail_fit_mle:
+                    yield pytest.param(distname, arg, method, fix_args, marks=fail)
+                    continue
+                if method == 'MLE' and distname in skip_fit_mle:
+                    yield pytest.param(distname, arg, method, fix_args, marks=skip)
+                    continue
+                if method == 'MM' and distname in slow_fit_mm:
+                    yield pytest.param(distname, arg, method, fix_args, marks=slow)
+                    continue
+                if method == 'MM' and distname in xslow_fit_mm:
+                    yield pytest.param(distname, arg, method, fix_args, marks=xslow)
+                    continue
+                if method == 'MM' and distname in xfail_fit_mm:
+                    yield pytest.param(distname, arg, method, fix_args, marks=fail)
+                    continue
+                if method == 'MM' and distname in skip_fit_mm:
+                    yield pytest.param(distname, arg, method, fix_args, marks=skip)
+                    continue
+
+                yield distname, arg, method, fix_args
+
+
+def test_cont_basic_fit_cases():
+    # Distribution names should not be in multiple MLE or MM sets
+    assert (len(xslow_fit_mle.union(xfail_fit_mle).union(skip_fit_mle)) ==
+            len(xslow_fit_mle) + len(xfail_fit_mle) + len(skip_fit_mle))
+    assert (len(xslow_fit_mm.union(xfail_fit_mm).union(skip_fit_mm)) ==
+            len(xslow_fit_mm) + len(xfail_fit_mm) + len(skip_fit_mm))
+
+
+@pytest.mark.parametrize('distname, arg, method, fix_args',
+                         list(cases_test_cont_basic_fit()))
+@pytest.mark.parametrize('n_fit_samples', [200])
+def test_cont_basic_fit(distname, arg, n_fit_samples, method, fix_args):
+    try:
+        distfn = getattr(stats, distname)
+    except TypeError:
+        distfn = distname
+
+    rng = np.random.RandomState(765456)
+    rvs = distfn.rvs(size=n_fit_samples, *arg, random_state=rng)
+    if fix_args:
+        check_fit_args_fix(distfn, arg, rvs, method)
+    else:
+        check_fit_args(distfn, arg, rvs, method)
+
+@pytest.mark.parametrize('distname,arg', list(cases_test_cont_basic()))
+def test_rvs_scalar(distname, arg):
+    # rvs should return a scalar when given scalar arguments (gh-12428)
+    try:
+        distfn = getattr(stats, distname)
+    except TypeError:
+        distfn = distname
+        distname = 'rv_histogram_instance'
+
+    assert np.isscalar(distfn.rvs(*arg))
+    assert np.isscalar(distfn.rvs(*arg, size=()))
+    assert np.isscalar(distfn.rvs(*arg, size=None))
+
+
+@pytest.mark.thread_unsafe(reason="global rng")
+def test_levy_stable_random_state_property():
+    # levy_stable only implements rvs(), so it is skipped in the
+    # main loop in test_cont_basic(). Here we apply just the test
+    # check_random_state_property to levy_stable.
+    check_random_state_property(stats.levy_stable, (0.5, 0.1))
+
+
+def cases_test_moments():
+    fail_normalization = set()
+    fail_higher = {'ncf'}
+    fail_moment = {'johnsonsu'}  # generic `munp` is inaccurate for johnsonsu
+
+    for distname, arg in distcont[:] + histogram_test_instances:
+        if distname == 'levy_stable':
+            continue
+
+        if distname in xslow_test_moments:
+            yield pytest.param(distname, arg, True, True, True, True,
+                               marks=pytest.mark.xslow(reason="too slow"))
+            continue
+
+        cond1 = distname not in fail_normalization
+        cond2 = distname not in fail_higher
+        cond3 = distname not in fail_moment
+
+        marks = list()
+        # Currently unused, `marks` can be used to add a timeout to a test of
+        # a specific distribution.  For example, this shows how a timeout could
+        # be added for the 'skewnorm' distribution:
+        #
+        #     marks = list()
+        #     if distname == 'skewnorm':
+        #         marks.append(pytest.mark.timeout(300))
+
+        yield pytest.param(distname, arg, cond1, cond2, cond3,
+                           False, marks=marks)
+
+        if not cond1 or not cond2 or not cond3:
+            # Run the distributions that have issues twice, once skipping the
+            # not_ok parts, once with the not_ok parts but marked as knownfail
+            yield pytest.param(distname, arg, True, True, True, True,
+                               marks=[pytest.mark.xfail] + marks)
+
+
+@pytest.mark.slow
+@pytest.mark.parametrize('distname,arg,normalization_ok,higher_ok,moment_ok,'
+                         'is_xfailing',
+                         list(cases_test_moments()))
+def test_moments(distname, arg, normalization_ok, higher_ok, moment_ok,
+                 is_xfailing):
+    try:
+        distfn = getattr(stats, distname)
+    except TypeError:
+        distfn = distname
+        distname = 'rv_histogram_instance'
+
+    with warnings.catch_warnings():
+        warnings.filterwarnings(
+            "ignore",
+            "The integral is probably divergent, or slowly convergent.",
+            IntegrationWarning,
+        )
+        warnings.filterwarnings(
+            "ignore",
+            "The maximum number of subdivisions.",
+            IntegrationWarning
+        )
+        warnings.filterwarnings(
+            "ignore",
+            "The algorithm does not converge.",
+            IntegrationWarning
+        )
+
+        if is_xfailing:
+            warnings.simplefilter("ignore", IntegrationWarning)
+
+        m, v, s, k = distfn.stats(*arg, moments='mvsk')
+
+        with np.errstate(all="ignore"):
+            if normalization_ok:
+                check_normalization(distfn, arg, distname)
+
+            if higher_ok:
+                check_mean_expect(distfn, arg, m, distname)
+                check_skew_expect(distfn, arg, m, v, s, distname)
+                check_var_expect(distfn, arg, m, v, distname)
+                check_kurt_expect(distfn, arg, m, v, k, distname)
+                check_munp_expect(distfn, arg, distname)
+
+        check_loc_scale(distfn, arg, m, v, distname)
+
+        if moment_ok:
+            check_moment(distfn, arg, m, v, distname)
+
+
+@pytest.mark.parametrize('dist,shape_args', distcont)
+def test_rvs_broadcast(dist, shape_args):
+    if dist in ['gausshyper', 'studentized_range']:
+        pytest.skip("too slow")
+
+    if dist in ['rel_breitwigner'] and _IS_32BIT:
+        # gh18414
+        pytest.skip("fails on Linux 32-bit")
+
+    # If shape_only is True, it means the _rvs method of the
+    # distribution uses more than one random number to generate a random
+    # variate.  That means the result of using rvs with broadcasting or
+    # with a nontrivial size will not necessarily be the same as using the
+    # numpy.vectorize'd version of rvs(), so we can only compare the shapes
+    # of the results, not the values.
+    # Whether or not a distribution is in the following list is an
+    # implementation detail of the distribution, not a requirement.  If
+    # the implementation the rvs() method of a distribution changes, this
+    # test might also have to be changed.
+    shape_only = dist in ['argus', 'betaprime', 'dgamma', 'dpareto_lognorm', 'dweibull',
+                          'exponnorm', 'genhyperbolic', 'geninvgauss', 'landau',
+                          'levy_stable', 'nct', 'norminvgauss', 'rice',
+                          'skewnorm', 'semicircular', 'gennorm', 'loggamma']
+
+    distfunc = getattr(stats, dist)
+    loc = np.zeros(2)
+    scale = np.ones((3, 1))
+    nargs = distfunc.numargs
+    allargs = []
+    bshape = [3, 2]
+    # Generate shape parameter arguments...
+    for k in range(nargs):
+        shp = (k + 4,) + (1,)*(k + 2)
+        allargs.append(shape_args[k]*np.ones(shp))
+        bshape.insert(0, k + 4)
+    allargs.extend([loc, scale])
+    # bshape holds the expected shape when loc, scale, and the shape
+    # parameters are all broadcast together.
+
+    check_rvs_broadcast(distfunc, dist, allargs, bshape, shape_only, 'd')
+
+
+# Expected values of the SF, CDF, PDF were computed using
+# mpmath with mpmath.mp.dps = 50 and output at 20:
+#
+# def ks(x, n):
+#     x = mpmath.mpf(x)
+#     logp = -mpmath.power(6.0*n*x+1.0, 2)/18.0/n
+#     sf, cdf = mpmath.exp(logp), -mpmath.expm1(logp)
+#     pdf = (6.0*n*x+1.0) * 2 * sf/3
+#     print(mpmath.nstr(sf, 20), mpmath.nstr(cdf, 20), mpmath.nstr(pdf, 20))
+#
+# Tests use 1/n < x < 1-1/n and n > 1e6 to use the asymptotic computation.
+# Larger x has a smaller sf.
+@pytest.mark.parametrize('x,n,sf,cdf,pdf,rtol',
+                         [(2.0e-5, 1000000000,
+                           0.44932297307934442379, 0.55067702692065557621,
+                           35946.137394996276407, 5e-15),
+                          (2.0e-9, 1000000000,
+                           0.99999999061111115519, 9.3888888448132728224e-9,
+                           8.6666665852962971765, 5e-14),
+                          (5.0e-4, 1000000000,
+                           7.1222019433090374624e-218, 1.0,
+                           1.4244408634752704094e-211, 5e-14)])
+def test_gh17775_regression(x, n, sf, cdf, pdf, rtol):
+    # Regression test for gh-17775. In scipy 1.9.3 and earlier,
+    # these test would fail.
+    #
+    # KS one asymptotic sf ~ e^(-(6nx+1)^2 / 18n)
+    # Given a large 32-bit integer n, 6n will overflow in the c implementation.
+    # Example of broken behaviour:
+    # ksone.sf(2.0e-5, 1000000000) == 0.9374359693473666
+    ks = stats.ksone
+    vals = np.array([ks.sf(x, n), ks.cdf(x, n), ks.pdf(x, n)])
+    expected = np.array([sf, cdf, pdf])
+    npt.assert_allclose(vals, expected, rtol=rtol)
+    # The sf+cdf must sum to 1.0.
+    npt.assert_equal(vals[0] + vals[1], 1.0)
+    # Check inverting the (potentially very small) sf (uses a lower tolerance)
+    npt.assert_allclose([ks.isf(sf, n)], [x], rtol=1e-8)
+
+
+def test_rvs_gh2069_regression():
+    # Regression tests for gh-2069.  In scipy 0.17 and earlier,
+    # these tests would fail.
+    #
+    # A typical example of the broken behavior:
+    # >>> norm.rvs(loc=np.zeros(5), scale=np.ones(5))
+    # array([-2.49613705, -2.49613705, -2.49613705, -2.49613705, -2.49613705])
+    rng = np.random.RandomState(123)
+    vals = stats.norm.rvs(loc=np.zeros(5), scale=1, random_state=rng)
+    d = np.diff(vals)
+    npt.assert_(np.all(d != 0), "All the values are equal, but they shouldn't be!")
+    vals = stats.norm.rvs(loc=0, scale=np.ones(5), random_state=rng)
+    d = np.diff(vals)
+    npt.assert_(np.all(d != 0), "All the values are equal, but they shouldn't be!")
+    vals = stats.norm.rvs(loc=np.zeros(5), scale=np.ones(5), random_state=rng)
+    d = np.diff(vals)
+    npt.assert_(np.all(d != 0), "All the values are equal, but they shouldn't be!")
+    vals = stats.norm.rvs(loc=np.array([[0], [0]]), scale=np.ones(5),
+                          random_state=rng)
+    d = np.diff(vals.ravel())
+    npt.assert_(np.all(d != 0), "All the values are equal, but they shouldn't be!")
+
+    assert_raises(ValueError, stats.norm.rvs, [[0, 0], [0, 0]],
+                  [[1, 1], [1, 1]], 1)
+    assert_raises(ValueError, stats.gamma.rvs, [2, 3, 4, 5], 0, 1, (2, 2))
+    assert_raises(ValueError, stats.gamma.rvs, [1, 1, 1, 1], [0, 0, 0, 0],
+                  [[1], [2]], (4,))
+
+
+def test_nomodify_gh9900_regression():
+    # Regression test for gh-9990
+    # Prior to gh-9990, calls to stats.truncnorm._cdf() use what ever was
+    # set inside the stats.truncnorm instance during stats.truncnorm.cdf().
+    # This could cause issues with multi-threaded code.
+    # Since then, the calls to cdf() are not permitted to modify the global
+    # stats.truncnorm instance.
+    tn = stats.truncnorm
+    # Use the right-half truncated normal
+    # Check that the cdf and _cdf return the same result.
+    npt.assert_almost_equal(tn.cdf(1, 0, np.inf),
+                            0.6826894921370859)
+    npt.assert_almost_equal(tn._cdf([1], [0], [np.inf]),
+                            0.6826894921370859)
+
+    # Now use the left-half truncated normal
+    npt.assert_almost_equal(tn.cdf(-1, -np.inf, 0),
+                            0.31731050786291415)
+    npt.assert_almost_equal(tn._cdf([-1], [-np.inf], [0]),
+                            0.31731050786291415)
+
+    # Check that the right-half truncated normal _cdf hasn't changed
+    npt.assert_almost_equal(tn._cdf([1], [0], [np.inf]),
+                            0.6826894921370859)  # Not 1.6826894921370859
+    npt.assert_almost_equal(tn.cdf(1, 0, np.inf),
+                            0.6826894921370859)
+
+    # Check that the left-half truncated normal _cdf hasn't changed
+    npt.assert_almost_equal(tn._cdf([-1], [-np.inf], [0]),
+                            0.31731050786291415)  # Not -0.6826894921370859
+    npt.assert_almost_equal(tn.cdf(1, -np.inf, 0),
+                            1)  # Not 1.6826894921370859
+    npt.assert_almost_equal(tn.cdf(-1, -np.inf, 0),
+                            0.31731050786291415)  # Not -0.6826894921370859
+
+
+def test_broadcast_gh9990_regression():
+    # Regression test for gh-9990
+    # The x-value 7 only lies within the support of 4 of the supplied
+    # distributions.  Prior to 9990, one array passed to
+    # stats.reciprocal._cdf would have 4 elements, but an array
+    # previously stored by stats.reciprocal_argcheck() would have 6, leading
+    # to a broadcast error.
+    a = np.array([1, 2, 3, 4, 5, 6])
+    b = np.array([8, 16, 1, 32, 1, 48])
+    ans = [stats.reciprocal.cdf(7, _a, _b) for _a, _b in zip(a,b)]
+    npt.assert_array_almost_equal(stats.reciprocal.cdf(7, a, b), ans)
+
+    ans = [stats.reciprocal.cdf(1, _a, _b) for _a, _b in zip(a,b)]
+    npt.assert_array_almost_equal(stats.reciprocal.cdf(1, a, b), ans)
+
+    ans = [stats.reciprocal.cdf(_a, _a, _b) for _a, _b in zip(a,b)]
+    npt.assert_array_almost_equal(stats.reciprocal.cdf(a, a, b), ans)
+
+    ans = [stats.reciprocal.cdf(_b, _a, _b) for _a, _b in zip(a,b)]
+    npt.assert_array_almost_equal(stats.reciprocal.cdf(b, a, b), ans)
+
+
+def test_broadcast_gh7933_regression():
+    # Check broadcast works
+    stats.truncnorm.logpdf(
+        np.array([3.0, 2.0, 1.0]),
+        a=(1.5 - np.array([6.0, 5.0, 4.0])) / 3.0,
+        b=np.inf,
+        loc=np.array([6.0, 5.0, 4.0]),
+        scale=3.0
+    )
+
+
+def test_gh2002_regression():
+    # Add a check that broadcast works in situations where only some
+    # x-values are compatible with some of the shape arguments.
+    x = np.r_[-2:2:101j]
+    a = np.r_[-np.ones(50), np.ones(51)]
+    expected = [stats.truncnorm.pdf(_x, _a, np.inf) for _x, _a in zip(x, a)]
+    ans = stats.truncnorm.pdf(x, a, np.inf)
+    npt.assert_array_almost_equal(ans, expected)
+
+
+def test_gh1320_regression():
+    # Check that the first example from gh-1320 now works.
+    c = 2.62
+    stats.genextreme.ppf(0.5, np.array([[c], [c + 0.5]]))
+    # The other examples in gh-1320 appear to have stopped working
+    # some time ago.
+    # ans = stats.genextreme.moment(2, np.array([c, c + 0.5]))
+    # expected = np.array([25.50105963, 115.11191437])
+    # stats.genextreme.moment(5, np.array([[c], [c + 0.5]]))
+    # stats.genextreme.moment(5, np.array([c, c + 0.5]))
+
+
+def test_method_of_moments():
+    # example from https://en.wikipedia.org/wiki/Method_of_moments_(statistics)
+    x = [0, 0, 0, 0, 1]
+    a = 1/5 - 2*np.sqrt(3)/5
+    b = 1/5 + 2*np.sqrt(3)/5
+    # force use of method of moments (uniform.fit is overridden)
+    loc, scale = super(type(stats.uniform), stats.uniform).fit(x, method="MM")
+    npt.assert_almost_equal(loc, a, decimal=4)
+    npt.assert_almost_equal(loc+scale, b, decimal=4)
+
+
+def check_sample_meanvar_(popmean, popvar, sample, rng):
+    if np.isfinite(popmean):
+        check_sample_mean(sample, popmean)
+    if np.isfinite(popvar):
+        check_sample_var(sample, popvar, rng)
+
+
+def check_sample_mean(sample, popmean):
+    # Checks for unlikely difference between sample mean and population mean
+    prob = stats.ttest_1samp(sample, popmean).pvalue
+    assert prob > 0.01
+
+
+def check_sample_var(sample, popvar, rng):
+    # check that population mean lies within the CI bootstrapped from the
+    # sample. This used to be a chi-squared test for variance, but there were
+    # too many false positives
+    res = stats.bootstrap(
+        (sample,),
+        lambda x, axis: x.var(ddof=1, axis=axis),
+        confidence_level=0.995,
+        rng=rng,
+    )
+    conf = res.confidence_interval
+    low, high = conf.low, conf.high
+    assert low <= popvar <= high
+
+
+def check_cdf_ppf(distfn, arg, msg):
+    values = [0.001, 0.5, 0.999]
+    npt.assert_almost_equal(distfn.cdf(distfn.ppf(values, *arg), *arg),
+                            values, decimal=DECIMAL, err_msg=msg +
+                            ' - cdf-ppf roundtrip')
+
+
+def check_sf_isf(distfn, arg, msg):
+    npt.assert_almost_equal(distfn.sf(distfn.isf([0.1, 0.5, 0.9], *arg), *arg),
+                            [0.1, 0.5, 0.9], decimal=DECIMAL, err_msg=msg +
+                            ' - sf-isf roundtrip')
+
+
+def check_cdf_sf(distfn, arg, msg):
+    npt.assert_almost_equal(distfn.cdf([0.1, 0.9], *arg),
+                            1.0 - distfn.sf([0.1, 0.9], *arg),
+                            decimal=DECIMAL, err_msg=msg +
+                            ' - cdf-sf relationship')
+
+
+def check_ppf_isf(distfn, arg, msg):
+    p = np.array([0.1, 0.9])
+    npt.assert_almost_equal(distfn.isf(p, *arg), distfn.ppf(1-p, *arg),
+                            decimal=DECIMAL, err_msg=msg +
+                            ' - ppf-isf relationship')
+
+
+def check_pdf(distfn, arg, msg):
+    # compares pdf at median with numerical derivative of cdf
+    median = distfn.ppf(0.5, *arg)
+    eps = 1e-6
+    pdfv = distfn.pdf(median, *arg)
+    if (pdfv < 1e-4) or (pdfv > 1e4):
+        # avoid checking a case where pdf is close to zero or
+        # huge (singularity)
+        median = median + 0.1
+        pdfv = distfn.pdf(median, *arg)
+    cdfdiff = (distfn.cdf(median + eps, *arg) -
+               distfn.cdf(median - eps, *arg))/eps/2.0
+    # replace with better diff and better test (more points),
+    # actually, this works pretty well
+    msg += ' - cdf-pdf relationship'
+    npt.assert_almost_equal(pdfv, cdfdiff, decimal=DECIMAL, err_msg=msg)
+
+
+def check_pdf_logpdf(distfn, args, msg):
+    # compares pdf at several points with the log of the pdf
+    points = np.array([0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8])
+    vals = distfn.ppf(points, *args)
+    vals = vals[np.isfinite(vals)]
+    pdf = distfn.pdf(vals, *args)
+    logpdf = distfn.logpdf(vals, *args)
+    pdf = pdf[(pdf != 0) & np.isfinite(pdf)]
+    logpdf = logpdf[np.isfinite(logpdf)]
+    msg += " - logpdf-log(pdf) relationship"
+    npt.assert_almost_equal(np.log(pdf), logpdf, decimal=7, err_msg=msg)
+
+
+def check_pdf_logpdf_at_endpoints(distfn, args, msg):
+    # compares pdf with the log of the pdf at the (finite) end points
+    points = np.array([0, 1])
+    vals = distfn.ppf(points, *args)
+    vals = vals[np.isfinite(vals)]
+    pdf = distfn.pdf(vals, *args)
+    logpdf = distfn.logpdf(vals, *args)
+    pdf = pdf[(pdf != 0) & np.isfinite(pdf)]
+    logpdf = logpdf[np.isfinite(logpdf)]
+    msg += " - logpdf-log(pdf) relationship"
+    npt.assert_almost_equal(np.log(pdf), logpdf, decimal=7, err_msg=msg)
+
+
+def check_sf_logsf(distfn, args, msg):
+    # compares sf at several points with the log of the sf
+    points = np.array([0.0, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 1.0])
+    vals = distfn.ppf(points, *args)
+    vals = vals[np.isfinite(vals)]
+    sf = distfn.sf(vals, *args)
+    logsf = distfn.logsf(vals, *args)
+    sf = sf[sf != 0]
+    logsf = logsf[np.isfinite(logsf)]
+    msg += " - logsf-log(sf) relationship"
+    npt.assert_almost_equal(np.log(sf), logsf, decimal=7, err_msg=msg)
+
+
+def check_cdf_logcdf(distfn, args, msg):
+    # compares cdf at several points with the log of the cdf
+    points = np.array([0, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 1.0])
+    vals = distfn.ppf(points, *args)
+    vals = vals[np.isfinite(vals)]
+    cdf = distfn.cdf(vals, *args)
+    logcdf = distfn.logcdf(vals, *args)
+    cdf = cdf[cdf != 0]
+    logcdf = logcdf[np.isfinite(logcdf)]
+    msg += " - logcdf-log(cdf) relationship"
+    npt.assert_almost_equal(np.log(cdf), logcdf, decimal=7, err_msg=msg)
+
+
+def check_ppf_broadcast(distfn, arg, msg):
+    # compares ppf for multiple argsets.
+    num_repeats = 5
+    args = [] * num_repeats
+    if arg:
+        args = [np.array([_] * num_repeats) for _ in arg]
+
+    median = distfn.ppf(0.5, *arg)
+    medians = distfn.ppf(0.5, *args)
+    msg += " - ppf multiple"
+    npt.assert_almost_equal(medians, [median] * num_repeats, decimal=7, err_msg=msg)
+
+
+def check_distribution_rvs(dist, args, alpha, rvs):
+    # dist is either a cdf function or name of a distribution in scipy.stats.
+    # args are the args for scipy.stats.dist(*args)
+    # alpha is a significance level, ~0.01
+    # rvs is array_like of random variables
+    # test from scipy.stats.tests
+    # this version reuses existing random variables
+    D, pval = stats.kstest(rvs, dist, args=args, N=1000)
+    if (pval < alpha):
+        # The rvs passed in failed the K-S test, which _could_ happen
+        # but is unlikely if alpha is small enough.
+        # Repeat the test with a new sample of rvs.
+        # Generate 1000 rvs, perform a K-S test that the new sample of rvs
+        # are distributed according to the distribution.
+        D, pval = stats.kstest(dist, dist, args=args, N=1000)
+        npt.assert_(pval > alpha, "D = " + str(D) + "; pval = " + str(pval) +
+                    "; alpha = " + str(alpha) + "\nargs = " + str(args))
+
+
+def check_vecentropy(distfn, args):
+    npt.assert_equal(distfn.vecentropy(*args), distfn._entropy(*args))
+
+
+def check_loc_scale(distfn, arg, m, v, msg):
+    # Make `loc` and `scale` arrays to catch bugs like gh-13580 where
+    # `loc` and `scale` arrays improperly broadcast with shapes.
+    loc, scale = np.array([10.0, 20.0]), np.array([10.0, 20.0])
+    mt, vt = distfn.stats(*arg, loc=loc, scale=scale)
+    npt.assert_allclose(m*scale + loc, mt)
+    npt.assert_allclose(v*scale*scale, vt)
+
+
+def check_ppf_private(distfn, arg, msg):
+    # fails by design for truncnorm self.nb not defined
+    ppfs = distfn._ppf(np.array([0.1, 0.5, 0.9]), *arg)
+    npt.assert_(not np.any(np.isnan(ppfs)), msg + 'ppf private is nan')
+
+
+def check_retrieving_support(distfn, args):
+    loc, scale = 1, 2
+    supp = distfn.support(*args)
+    supp_loc_scale = distfn.support(*args, loc=loc, scale=scale)
+    npt.assert_almost_equal(np.array(supp)*scale + loc,
+                            np.array(supp_loc_scale))
+
+
+def check_fit_args(distfn, arg, rvs, method):
+    with np.errstate(all='ignore'), warnings.catch_warnings():
+        warnings.filterwarnings("ignore", category=RuntimeWarning,
+                   message="The shape parameter of the erlang")
+        warnings.filterwarnings("ignore", category=RuntimeWarning,
+                   message="floating point number truncated")
+        vals = distfn.fit(rvs, method=method)
+        vals2 = distfn.fit(rvs, optimizer='powell', method=method)
+    # Only check the length of the return; accuracy tested in test_fit.py
+    npt.assert_(len(vals) == 2+len(arg))
+    npt.assert_(len(vals2) == 2+len(arg))
+
+
+def check_fit_args_fix(distfn, arg, rvs, method):
+    with np.errstate(all='ignore'), warnings.catch_warnings():
+        warnings.filterwarnings("ignore", category=RuntimeWarning,
+                   message="The shape parameter of the erlang")
+
+        vals = distfn.fit(rvs, floc=0, method=method)
+        vals2 = distfn.fit(rvs, fscale=1, method=method)
+        npt.assert_(len(vals) == 2+len(arg))
+        npt.assert_(vals[-2] == 0)
+        npt.assert_(vals2[-1] == 1)
+        npt.assert_(len(vals2) == 2+len(arg))
+        if len(arg) > 0:
+            vals3 = distfn.fit(rvs, f0=arg[0], method=method)
+            npt.assert_(len(vals3) == 2+len(arg))
+            npt.assert_(vals3[0] == arg[0])
+        if len(arg) > 1:
+            vals4 = distfn.fit(rvs, f1=arg[1], method=method)
+            npt.assert_(len(vals4) == 2+len(arg))
+            npt.assert_(vals4[1] == arg[1])
+        if len(arg) > 2:
+            vals5 = distfn.fit(rvs, f2=arg[2], method=method)
+            npt.assert_(len(vals5) == 2+len(arg))
+            npt.assert_(vals5[2] == arg[2])
+
+
+def cases_test_methods_with_lists():
+    for distname, arg in distcont:
+        if distname in slow_with_lists:
+            yield pytest.param(distname, arg, marks=pytest.mark.slow)
+        else:
+            yield distname, arg
+
+
+@pytest.mark.parametrize('method', ['pdf', 'logpdf', 'cdf', 'logcdf',
+                                    'sf', 'logsf', 'ppf', 'isf'])
+@pytest.mark.parametrize('distname, args', list(cases_test_methods_with_lists()))
+def test_methods_with_lists(method, distname, args):
+    # Test that the continuous distributions can accept Python lists
+    # as arguments.
+    dist = getattr(stats, distname)
+    f = getattr(dist, method)
+    if distname == 'invweibull' and method.startswith('log'):
+        x = [1.5, 2]
+    else:
+        x = [0.1, 0.2]
+
+    shape2 = [[a]*2 for a in args]
+    loc = [0, 0.1]
+    scale = [1, 1.01]
+    result = f(x, *shape2, loc=loc, scale=scale)
+    npt.assert_allclose(result,
+                        [f(*v) for v in zip(x, *shape2, loc, scale)],
+                        rtol=1e-14, atol=5e-14)
+
+
+def test_burr_fisk_moment_gh13234_regression():
+    vals0 = stats.burr.moment(1, 5, 4)
+    assert isinstance(vals0, float)
+
+    vals1 = stats.fisk.moment(1, 8)
+    assert isinstance(vals1, float)
+
+
+def test_moments_with_array_gh12192_regression():
+    # array loc and scalar scale
+    vals0 = stats.norm.moment(order=1, loc=np.array([1, 2, 3]), scale=1)
+    expected0 = np.array([1., 2., 3.])
+    npt.assert_equal(vals0, expected0)
+
+    # array loc and invalid scalar scale
+    vals1 = stats.norm.moment(order=1, loc=np.array([1, 2, 3]), scale=-1)
+    expected1 = np.array([np.nan, np.nan, np.nan])
+    npt.assert_equal(vals1, expected1)
+
+    # array loc and array scale with invalid entries
+    vals2 = stats.norm.moment(order=1, loc=np.array([1, 2, 3]),
+                              scale=[-3, 1, 0])
+    expected2 = np.array([np.nan, 2., np.nan])
+    npt.assert_equal(vals2, expected2)
+
+    # (loc == 0) & (scale < 0)
+    vals3 = stats.norm.moment(order=2, loc=0, scale=-4)
+    expected3 = np.nan
+    npt.assert_equal(vals3, expected3)
+    assert isinstance(vals3, expected3.__class__)
+
+    # array loc with 0 entries and scale with invalid entries
+    vals4 = stats.norm.moment(order=2, loc=[1, 0, 2], scale=[3, -4, -5])
+    expected4 = np.array([10., np.nan, np.nan])
+    npt.assert_equal(vals4, expected4)
+
+    # all(loc == 0) & (array scale with invalid entries)
+    vals5 = stats.norm.moment(order=2, loc=[0, 0, 0], scale=[5., -2, 100.])
+    expected5 = np.array([25., np.nan, 10000.])
+    npt.assert_equal(vals5, expected5)
+
+    # all( (loc == 0) & (scale < 0) )
+    vals6 = stats.norm.moment(order=2, loc=[0, 0, 0], scale=[-5., -2, -100.])
+    expected6 = np.array([np.nan, np.nan, np.nan])
+    npt.assert_equal(vals6, expected6)
+
+    # scalar args, loc, and scale
+    vals7 = stats.chi.moment(order=2, df=1, loc=0, scale=0)
+    expected7 = np.nan
+    npt.assert_equal(vals7, expected7)
+    assert isinstance(vals7, expected7.__class__)
+
+    # array args, scalar loc, and scalar scale
+    vals8 = stats.chi.moment(order=2, df=[1, 2, 3], loc=0, scale=0)
+    expected8 = np.array([np.nan, np.nan, np.nan])
+    npt.assert_equal(vals8, expected8)
+
+    # array args, array loc, and array scale
+    vals9 = stats.chi.moment(order=2, df=[1, 2, 3], loc=[1., 0., 2.],
+                             scale=[1., -3., 0.])
+    expected9 = np.array([3.59576912, np.nan, np.nan])
+    npt.assert_allclose(vals9, expected9, rtol=1e-8)
+
+    # (n > 4), all(loc != 0), and all(scale != 0)
+    vals10 = stats.norm.moment(5, [1., 2.], [1., 2.])
+    expected10 = np.array([26., 832.])
+    npt.assert_allclose(vals10, expected10, rtol=1e-13)
+
+    # test broadcasting and more
+    a = [-1.1, 0, 1, 2.2, np.pi]
+    b = [-1.1, 0, 1, 2.2, np.pi]
+    loc = [-1.1, 0, np.sqrt(2)]
+    scale = [-2.1, 0, 1, 2.2, np.pi]
+
+    a = np.array(a).reshape((-1, 1, 1, 1))
+    b = np.array(b).reshape((-1, 1, 1))
+    loc = np.array(loc).reshape((-1, 1))
+    scale = np.array(scale)
+
+    vals11 = stats.beta.moment(order=2, a=a, b=b, loc=loc, scale=scale)
+
+    a, b, loc, scale = np.broadcast_arrays(a, b, loc, scale)
+
+    for i in np.ndenumerate(a):
+        with np.errstate(invalid='ignore', divide='ignore'):
+            i = i[0]  # just get the index
+            # check against same function with scalar input
+            expected = stats.beta.moment(order=2, a=a[i], b=b[i],
+                                         loc=loc[i], scale=scale[i])
+            np.testing.assert_equal(vals11[i], expected)
+
+
+def test_broadcasting_in_moments_gh12192_regression():
+    vals0 = stats.norm.moment(order=1, loc=np.array([1, 2, 3]), scale=[[1]])
+    expected0 = np.array([[1., 2., 3.]])
+    npt.assert_equal(vals0, expected0)
+    assert vals0.shape == expected0.shape
+
+    vals1 = stats.norm.moment(order=1, loc=np.array([[1], [2], [3]]),
+                              scale=[1, 2, 3])
+    expected1 = np.array([[1., 1., 1.], [2., 2., 2.], [3., 3., 3.]])
+    npt.assert_equal(vals1, expected1)
+    assert vals1.shape == expected1.shape
+
+    vals2 = stats.chi.moment(order=1, df=[1., 2., 3.], loc=0., scale=1.)
+    expected2 = np.array([0.79788456, 1.25331414, 1.59576912])
+    npt.assert_allclose(vals2, expected2, rtol=1e-8)
+    assert vals2.shape == expected2.shape
+
+    vals3 = stats.chi.moment(order=1, df=[[1.], [2.], [3.]], loc=[0., 1., 2.],
+                             scale=[-1., 0., 3.])
+    expected3 = np.array([[np.nan, np.nan, 4.39365368],
+                          [np.nan, np.nan, 5.75994241],
+                          [np.nan, np.nan, 6.78730736]])
+    npt.assert_allclose(vals3, expected3, rtol=1e-8)
+    assert vals3.shape == expected3.shape
+
+
+@pytest.mark.slow
+def test_kappa3_array_gh13582():
+    # https://github.com/scipy/scipy/pull/15140#issuecomment-994958241
+    shapes = [0.5, 1.5, 2.5, 3.5, 4.5]
+    moments = 'mvsk'
+    res = np.array([[stats.kappa3.stats(shape, moments=moment)
+                   for shape in shapes] for moment in moments])
+    res2 = np.array(stats.kappa3.stats(shapes, moments=moments))
+    npt.assert_allclose(res, res2)
+
+
+@pytest.mark.xslow
+def test_kappa4_array_gh13582():
+    h = np.array([-0.5, 2.5, 3.5, 4.5, -3])
+    k = np.array([-0.5, 1, -1.5, 0, 3.5])
+    moments = 'mvsk'
+    res = np.array([[stats.kappa4.stats(h[i], k[i], moments=moment)
+                   for i in range(5)] for moment in moments])
+    res2 = np.array(stats.kappa4.stats(h, k, moments=moments))
+    npt.assert_allclose(res, res2)
+
+    # https://github.com/scipy/scipy/pull/15250#discussion_r775112913
+    h = np.array([-1, -1/4, -1/4, 1, -1, 0])
+    k = np.array([1, 1, 1/2, -1/3, -1, 0])
+    res = np.array([[stats.kappa4.stats(h[i], k[i], moments=moment)
+                   for i in range(6)] for moment in moments])
+    res2 = np.array(stats.kappa4.stats(h, k, moments=moments))
+    npt.assert_allclose(res, res2)
+
+    # https://github.com/scipy/scipy/pull/15250#discussion_r775115021
+    h = np.array([-1, -0.5, 1])
+    k = np.array([-1, -0.5, 0, 1])[:, None]
+    res2 = np.array(stats.kappa4.stats(h, k, moments=moments))
+    assert res2.shape == (4, 4, 3)
+
+
+def test_frozen_attributes(monkeypatch):
+    # gh-14827 reported that all frozen distributions had both pmf and pdf
+    # attributes; continuous should have pdf and discrete should have pmf.
+    message = "'rv_continuous_frozen' object has no attribute"
+    with pytest.raises(AttributeError, match=message):
+        stats.norm().pmf
+    with pytest.raises(AttributeError, match=message):
+        stats.norm().logpmf
+    monkeypatch.setattr(stats.norm, "pmf", "herring", raising=False)
+    frozen_norm = stats.norm()
+    assert isinstance(frozen_norm, rv_continuous_frozen)
+    assert not hasattr(frozen_norm, "pmf")
+
+
+def test_skewnorm_pdf_gh16038():
+    rng = np.random.default_rng(0)
+    x, a = -np.inf, 0
+    npt.assert_equal(stats.skewnorm.pdf(x, a), stats.norm.pdf(x))
+    x, a = rng.random(size=(3, 3)), rng.random(size=(3, 3))
+    mask = rng.random(size=(3, 3)) < 0.5
+    a[mask] = 0
+    x_norm = x[mask]
+    res = stats.skewnorm.pdf(x, a)
+    npt.assert_equal(res[mask], stats.norm.pdf(x_norm))
+    npt.assert_equal(res[~mask], stats.skewnorm.pdf(x[~mask], a[~mask]))
+
+
+# for scalar input, these functions should return scalar output
+scalar_out = [['rvs', []], ['pdf', [0]], ['logpdf', [0]], ['cdf', [0]],
+              ['logcdf', [0]], ['sf', [0]], ['logsf', [0]], ['ppf', [0]],
+              ['isf', [0]], ['moment', [1]], ['entropy', []], ['expect', []],
+              ['median', []], ['mean', []], ['std', []], ['var', []]]
+scalars_out = [['interval', [0.95]], ['support', []], ['stats', ['mv']]]
+
+
+@pytest.mark.parametrize('case', scalar_out + scalars_out)
+def test_scalar_for_scalar(case):
+    # Some rv_continuous functions returned 0d array instead of NumPy scalar
+    # Guard against regression
+    method_name, args = case
+    method = getattr(stats.norm(), method_name)
+    res = method(*args)
+    if case in scalar_out:
+        assert isinstance(res, np.number)
+    else:
+        assert isinstance(res[0], np.number)
+        assert isinstance(res[1], np.number)
+
+
+def test_scalar_for_scalar2():
+    # test methods that are not attributes of frozen distributions
+    res = stats.norm.fit([1, 2, 3])
+    assert isinstance(res[0], np.number)
+    assert isinstance(res[1], np.number)
+    res = stats.norm.fit_loc_scale([1, 2, 3])
+    assert isinstance(res[0], np.number)
+    assert isinstance(res[1], np.number)
+    res = stats.norm.nnlf((0, 1), [1, 2, 3])
+    assert isinstance(res, np.number)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/test_continuous_fit_censored.py b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_continuous_fit_censored.py
new file mode 100644
index 0000000000000000000000000000000000000000..4508b49712e5bc8975bf2f9b2681ccc6504b0ae0
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_continuous_fit_censored.py
@@ -0,0 +1,683 @@
+# Tests for fitting specific distributions to censored data.
+
+import numpy as np
+from numpy.testing import assert_allclose
+
+from scipy.optimize import fmin
+from scipy.stats import (CensoredData, beta, cauchy, chi2, expon, gamma,
+                         gumbel_l, gumbel_r, invgauss, invweibull, laplace,
+                         logistic, lognorm, nct, ncx2, norm, weibull_max,
+                         weibull_min)
+
+
+# In some tests, we'll use this optimizer for improved accuracy.
+def optimizer(func, x0, args=(), disp=0):
+    return fmin(func, x0, args=args, disp=disp, xtol=1e-12, ftol=1e-12)
+
+
+def test_beta():
+    """
+    Test fitting beta shape parameters to interval-censored data.
+
+    Calculation in R:
+
+    > library(fitdistrplus)
+    > data <- data.frame(left=c(0.10, 0.50, 0.75, 0.80),
+    +                    right=c(0.20, 0.55, 0.90, 0.95))
+    > result = fitdistcens(data, 'beta', control=list(reltol=1e-14))
+
+    > result
+    Fitting of the distribution ' beta ' on censored data by maximum likelihood
+    Parameters:
+           estimate
+    shape1 1.419941
+    shape2 1.027066
+    > result$sd
+       shape1    shape2
+    0.9914177 0.6866565
+    """
+    data = CensoredData(interval=[[0.10, 0.20],
+                                  [0.50, 0.55],
+                                  [0.75, 0.90],
+                                  [0.80, 0.95]])
+
+    # For this test, fit only the shape parameters; loc and scale are fixed.
+    a, b, loc, scale = beta.fit(data, floc=0, fscale=1, optimizer=optimizer)
+
+    assert_allclose(a, 1.419941, rtol=5e-6)
+    assert_allclose(b, 1.027066, rtol=5e-6)
+    assert loc == 0
+    assert scale == 1
+
+
+def test_cauchy_right_censored():
+    """
+    Test fitting the Cauchy distribution to right-censored data.
+
+    Calculation in R, with two values not censored [1, 10] and
+    one right-censored value [30].
+
+    > library(fitdistrplus)
+    > data <- data.frame(left=c(1, 10, 30), right=c(1, 10, NA))
+    > result = fitdistcens(data, 'cauchy', control=list(reltol=1e-14))
+    > result
+    Fitting of the distribution ' cauchy ' on censored data by maximum
+    likelihood
+    Parameters:
+             estimate
+    location 7.100001
+    scale    7.455866
+    """
+    data = CensoredData(uncensored=[1, 10], right=[30])
+    loc, scale = cauchy.fit(data, optimizer=optimizer)
+    assert_allclose(loc, 7.10001, rtol=5e-6)
+    assert_allclose(scale, 7.455866, rtol=5e-6)
+
+
+def test_cauchy_mixed():
+    """
+    Test fitting the Cauchy distribution to data with mixed censoring.
+
+    Calculation in R, with:
+    * two values not censored [1, 10],
+    * one left-censored [1],
+    * one right-censored [30], and
+    * one interval-censored [[4, 8]].
+
+    > library(fitdistrplus)
+    > data <- data.frame(left=c(NA, 1, 4, 10, 30), right=c(1, 1, 8, 10, NA))
+    > result = fitdistcens(data, 'cauchy', control=list(reltol=1e-14))
+    > result
+    Fitting of the distribution ' cauchy ' on censored data by maximum
+    likelihood
+    Parameters:
+             estimate
+    location 4.605150
+    scale    5.900852
+    """
+    data = CensoredData(uncensored=[1, 10], left=[1], right=[30],
+                        interval=[[4, 8]])
+    loc, scale = cauchy.fit(data, optimizer=optimizer)
+    assert_allclose(loc, 4.605150, rtol=5e-6)
+    assert_allclose(scale, 5.900852, rtol=5e-6)
+
+
+def test_chi2_mixed():
+    """
+    Test fitting just the shape parameter (df) of chi2 to mixed data.
+
+    Calculation in R, with:
+    * two values not censored [1, 10],
+    * one left-censored [1],
+    * one right-censored [30], and
+    * one interval-censored [[4, 8]].
+
+    > library(fitdistrplus)
+    > data <- data.frame(left=c(NA, 1, 4, 10, 30), right=c(1, 1, 8, 10, NA))
+    > result = fitdistcens(data, 'chisq', control=list(reltol=1e-14))
+    > result
+    Fitting of the distribution ' chisq ' on censored data by maximum
+    likelihood
+    Parameters:
+             estimate
+    df 5.060329
+    """
+    data = CensoredData(uncensored=[1, 10], left=[1], right=[30],
+                        interval=[[4, 8]])
+    df, loc, scale = chi2.fit(data, floc=0, fscale=1, optimizer=optimizer)
+    assert_allclose(df, 5.060329, rtol=5e-6)
+    assert loc == 0
+    assert scale == 1
+
+
+def test_expon_right_censored():
+    """
+    For the exponential distribution with loc=0, the exact solution for
+    fitting n uncensored points x[0]...x[n-1] and m right-censored points
+    x[n]..x[n+m-1] is
+
+        scale = sum(x)/n
+
+    That is, divide the sum of all the values (not censored and
+    right-censored) by the number of uncensored values.  (See, for example,
+    https://en.wikipedia.org/wiki/Censoring_(statistics)#Likelihood.)
+
+    The second derivative of the log-likelihood function is
+
+        n/scale**2 - 2*sum(x)/scale**3
+
+    from which the estimate of the standard error can be computed.
+
+    -----
+
+    Calculation in R, for reference only. The R results are not
+    used in the test.
+
+    > library(fitdistrplus)
+    > dexps <- function(x, scale) {
+    +     return(dexp(x, 1/scale))
+    + }
+    > pexps <- function(q, scale) {
+    +     return(pexp(q, 1/scale))
+    + }
+    > left <- c(1, 2.5, 3, 6, 7.5, 10, 12, 12, 14.5, 15,
+    +                                     16, 16, 20, 20, 21, 22)
+    > right <- c(1, 2.5, 3, 6, 7.5, 10, 12, 12, 14.5, 15,
+    +                                     NA, NA, NA, NA, NA, NA)
+    > result = fitdistcens(data, 'exps', start=list(scale=mean(data$left)),
+    +                      control=list(reltol=1e-14))
+    > result
+    Fitting of the distribution ' exps ' on censored data by maximum likelihood
+    Parameters:
+          estimate
+    scale    19.85
+    > result$sd
+       scale
+    6.277119
+    """
+    # This data has 10 uncensored values and 6 right-censored values.
+    obs = [1, 2.5, 3, 6, 7.5, 10, 12, 12, 14.5, 15, 16, 16, 20, 20, 21, 22]
+    cens = [False]*10 + [True]*6
+    data = CensoredData.right_censored(obs, cens)
+
+    loc, scale = expon.fit(data, floc=0, optimizer=optimizer)
+
+    assert loc == 0
+    # Use the analytical solution to compute the expected value.  This
+    # is the sum of the observed values divided by the number of uncensored
+    # values.
+    n = len(data) - data.num_censored()
+    total = data._uncensored.sum() + data._right.sum()
+    expected = total / n
+    assert_allclose(scale, expected, 1e-8)
+
+
+def test_gamma_right_censored():
+    """
+    Fit gamma shape and scale to data with one right-censored value.
+
+    Calculation in R:
+
+    > library(fitdistrplus)
+    > data <- data.frame(left=c(2.5, 2.9, 3.8, 9.1, 9.3, 12.0, 23.0, 25.0),
+    +                    right=c(2.5, 2.9, 3.8, 9.1, 9.3, 12.0, 23.0, NA))
+    > result = fitdistcens(data, 'gamma', start=list(shape=1, scale=10),
+    +                      control=list(reltol=1e-13))
+    > result
+    Fitting of the distribution ' gamma ' on censored data by maximum
+      likelihood
+    Parameters:
+          estimate
+    shape 1.447623
+    scale 8.360197
+    > result$sd
+        shape     scale
+    0.7053086 5.1016531
+    """
+    # The last value is right-censored.
+    x = CensoredData.right_censored([2.5, 2.9, 3.8, 9.1, 9.3, 12.0, 23.0,
+                                     25.0],
+                                    [0]*7 + [1])
+
+    a, loc, scale = gamma.fit(x, floc=0, optimizer=optimizer)
+
+    assert_allclose(a, 1.447623, rtol=5e-6)
+    assert loc == 0
+    assert_allclose(scale, 8.360197, rtol=5e-6)
+
+
+def test_gumbel():
+    """
+    Fit gumbel_l and gumbel_r to censored data.
+
+    This R calculation should match gumbel_r.
+
+    > library(evd)
+    > library(fitdistrplus)
+    > data = data.frame(left=c(0, 2, 3, 9, 10, 10),
+    +                   right=c(1, 2, 3, 9, NA, NA))
+    > result = fitdistcens(data, 'gumbel',
+    +                      control=list(reltol=1e-14),
+    +                      start=list(loc=4, scale=5))
+    > result
+    Fitting of the distribution ' gumbel ' on censored data by maximum
+    likelihood
+    Parameters:
+          estimate
+    loc   4.487853
+    scale 4.843640
+    """
+    # First value is interval-censored. Last two are right-censored.
+    uncensored = np.array([2, 3, 9])
+    right = np.array([10, 10])
+    interval = np.array([[0, 1]])
+    data = CensoredData(uncensored, right=right, interval=interval)
+    loc, scale = gumbel_r.fit(data, optimizer=optimizer)
+    assert_allclose(loc, 4.487853, rtol=5e-6)
+    assert_allclose(scale, 4.843640, rtol=5e-6)
+
+    # Negate the data and reverse the intervals, and test with gumbel_l.
+    data2 = CensoredData(-uncensored, left=-right,
+                         interval=-interval[:, ::-1])
+    # Fitting gumbel_l to data2 should give the same result as above, but
+    # with loc negated.
+    loc2, scale2 = gumbel_l.fit(data2, optimizer=optimizer)
+    assert_allclose(loc2, -4.487853, rtol=5e-6)
+    assert_allclose(scale2, 4.843640, rtol=5e-6)
+
+
+def test_invgauss():
+    """
+    Fit just the shape parameter of invgauss to data with one value
+    left-censored and one value right-censored.
+
+    Calculation in R; using a fixed dispersion parameter amounts to fixing
+    the scale to be 1.
+
+    > library(statmod)
+    > library(fitdistrplus)
+    > left <- c(NA, 0.4813096, 0.5571880, 0.5132463, 0.3801414, 0.5904386,
+    +           0.4822340, 0.3478597, 3, 0.7191797, 1.5810902, 0.4442299)
+    > right <- c(0.15, 0.4813096, 0.5571880, 0.5132463, 0.3801414, 0.5904386,
+    +            0.4822340, 0.3478597, NA, 0.7191797, 1.5810902, 0.4442299)
+    > data <- data.frame(left=left, right=right)
+    > result = fitdistcens(data, 'invgauss', control=list(reltol=1e-12),
+    +                      fix.arg=list(dispersion=1), start=list(mean=3))
+    > result
+    Fitting of the distribution ' invgauss ' on censored data by maximum
+      likelihood
+    Parameters:
+         estimate
+    mean 0.853469
+    Fixed parameters:
+               value
+    dispersion     1
+    > result$sd
+        mean
+    0.247636
+
+    Here's the R calculation with the dispersion as a free parameter to
+    be fit.
+
+    > result = fitdistcens(data, 'invgauss', control=list(reltol=1e-12),
+    +                      start=list(mean=3, dispersion=1))
+    > result
+    Fitting of the distribution ' invgauss ' on censored data by maximum
+    likelihood
+    Parameters:
+                estimate
+    mean       0.8699819
+    dispersion 1.2261362
+
+    The parametrization of the inverse Gaussian distribution in the
+    `statmod` package is not the same as in SciPy (see
+        https://arxiv.org/abs/1603.06687
+    for details).  The translation from R to SciPy is
+
+        scale = 1/dispersion
+        mu    = mean * dispersion
+
+    > 1/result$estimate['dispersion']  # 1/dispersion
+    dispersion
+     0.8155701
+    > result$estimate['mean'] * result$estimate['dispersion']
+        mean
+    1.066716
+
+    Those last two values are the SciPy scale and shape parameters.
+    """
+    # One point is left-censored, and one is right-censored.
+    x = [0.4813096, 0.5571880, 0.5132463, 0.3801414,
+         0.5904386, 0.4822340, 0.3478597, 0.7191797,
+         1.5810902, 0.4442299]
+    data = CensoredData(uncensored=x, left=[0.15], right=[3])
+
+    # Fit only the shape parameter.
+    mu, loc, scale = invgauss.fit(data, floc=0, fscale=1, optimizer=optimizer)
+
+    assert_allclose(mu, 0.853469, rtol=5e-5)
+    assert loc == 0
+    assert scale == 1
+
+    # Fit the shape and scale.
+    mu, loc, scale = invgauss.fit(data, floc=0, optimizer=optimizer)
+
+    assert_allclose(mu, 1.066716, rtol=5e-5)
+    assert loc == 0
+    assert_allclose(scale, 0.8155701, rtol=5e-5)
+
+
+def test_invweibull():
+    """
+    Fit invweibull to censored data.
+
+    Here is the calculation in R.  The 'frechet' distribution from the evd
+    package matches SciPy's invweibull distribution.  The `loc` parameter
+    is fixed at 0.
+
+    > library(evd)
+    > library(fitdistrplus)
+    > data = data.frame(left=c(0, 2, 3, 9, 10, 10),
+    +                   right=c(1, 2, 3, 9, NA, NA))
+    > result = fitdistcens(data, 'frechet',
+    +                      control=list(reltol=1e-14),
+    +                      start=list(loc=4, scale=5))
+    > result
+    Fitting of the distribution ' frechet ' on censored data by maximum
+    likelihood
+    Parameters:
+           estimate
+    scale 2.7902200
+    shape 0.6379845
+    Fixed parameters:
+        value
+    loc     0
+    """
+    # In the R data, the first value is interval-censored, and the last
+    # two are right-censored.  The rest are not censored.
+    data = CensoredData(uncensored=[2, 3, 9], right=[10, 10],
+                        interval=[[0, 1]])
+    c, loc, scale = invweibull.fit(data, floc=0, optimizer=optimizer)
+    assert_allclose(c, 0.6379845, rtol=5e-6)
+    assert loc == 0
+    assert_allclose(scale, 2.7902200, rtol=5e-6)
+
+
+def test_laplace():
+    """
+    Fir the Laplace distribution to left- and right-censored data.
+
+    Calculation in R:
+
+    > library(fitdistrplus)
+    > dlaplace <- function(x, location=0, scale=1) {
+    +     return(0.5*exp(-abs((x - location)/scale))/scale)
+    + }
+    > plaplace <- function(q, location=0, scale=1) {
+    +     z <- (q - location)/scale
+    +     s <- sign(z)
+    +     f <- -s*0.5*exp(-abs(z)) + (s+1)/2
+    +     return(f)
+    + }
+    > left <- c(NA, -41.564, 50.0, 15.7384, 50.0, 10.0452, -2.0684,
+    +           -19.5399, 50.0,   9.0005, 27.1227, 4.3113, -3.7372,
+    +           25.3111, 14.7987,  34.0887,  50.0, 42.8496, 18.5862,
+    +           32.8921, 9.0448, -27.4591, NA, 19.5083, -9.7199)
+    > right <- c(-50.0, -41.564,  NA, 15.7384, NA, 10.0452, -2.0684,
+    +            -19.5399, NA, 9.0005, 27.1227, 4.3113, -3.7372,
+    +            25.3111, 14.7987, 34.0887, NA,  42.8496, 18.5862,
+    +            32.8921, 9.0448, -27.4591, -50.0, 19.5083, -9.7199)
+    > data <- data.frame(left=left, right=right)
+    > result <- fitdistcens(data, 'laplace', start=list(location=10, scale=10),
+    +                       control=list(reltol=1e-13))
+    > result
+    Fitting of the distribution ' laplace ' on censored data by maximum
+      likelihood
+    Parameters:
+             estimate
+    location 14.79870
+    scale    30.93601
+    > result$sd
+         location     scale
+    0.1758864 7.0972125
+    """
+    # The value -50 is left-censored, and the value 50 is right-censored.
+    obs = np.array([-50.0, -41.564, 50.0, 15.7384, 50.0, 10.0452, -2.0684,
+                    -19.5399, 50.0, 9.0005, 27.1227, 4.3113, -3.7372,
+                    25.3111, 14.7987, 34.0887, 50.0, 42.8496, 18.5862,
+                    32.8921, 9.0448, -27.4591, -50.0, 19.5083, -9.7199])
+    x = obs[(obs != -50.0) & (obs != 50)]
+    left = obs[obs == -50.0]
+    right = obs[obs == 50.0]
+    data = CensoredData(uncensored=x, left=left, right=right)
+    loc, scale = laplace.fit(data, loc=10, scale=10, optimizer=optimizer)
+    assert_allclose(loc, 14.79870, rtol=5e-6)
+    assert_allclose(scale, 30.93601, rtol=5e-6)
+
+
+def test_logistic():
+    """
+    Fit the logistic distribution to left-censored data.
+
+    Calculation in R:
+    > library(fitdistrplus)
+    > left = c(13.5401, 37.4235, 11.906 , 13.998 ,  NA    ,  0.4023,  NA    ,
+    +          10.9044, 21.0629,  9.6985,  NA    , 12.9016, 39.164 , 34.6396,
+    +          NA    , 20.3665, 16.5889, 18.0952, 45.3818, 35.3306,  8.4949,
+    +          3.4041,  NA    ,  7.2828, 37.1265,  6.5969, 17.6868, 17.4977,
+    +          16.3391, 36.0541)
+    > right = c(13.5401, 37.4235, 11.906 , 13.998 ,  0.    ,  0.4023,  0.    ,
+    +           10.9044, 21.0629,  9.6985,  0.    , 12.9016, 39.164 , 34.6396,
+    +           0.    , 20.3665, 16.5889, 18.0952, 45.3818, 35.3306,  8.4949,
+    +           3.4041,  0.    ,  7.2828, 37.1265,  6.5969, 17.6868, 17.4977,
+    +           16.3391, 36.0541)
+    > data = data.frame(left=left, right=right)
+    > result = fitdistcens(data, 'logis', control=list(reltol=1e-14))
+    > result
+    Fitting of the distribution ' logis ' on censored data by maximum
+      likelihood
+    Parameters:
+              estimate
+    location 14.633459
+    scale     9.232736
+    > result$sd
+    location    scale
+    2.931505 1.546879
+    """
+    # Values that are zero are left-censored; the true values are less than 0.
+    x = np.array([13.5401, 37.4235, 11.906, 13.998, 0.0, 0.4023, 0.0, 10.9044,
+                  21.0629, 9.6985, 0.0, 12.9016, 39.164, 34.6396, 0.0, 20.3665,
+                  16.5889, 18.0952, 45.3818, 35.3306, 8.4949, 3.4041, 0.0,
+                  7.2828, 37.1265, 6.5969, 17.6868, 17.4977, 16.3391,
+                  36.0541])
+    data = CensoredData.left_censored(x, censored=(x == 0))
+    loc, scale = logistic.fit(data, optimizer=optimizer)
+    assert_allclose(loc, 14.633459, rtol=5e-7)
+    assert_allclose(scale, 9.232736, rtol=5e-6)
+
+
+def test_lognorm():
+    """
+    Ref: https://math.montana.edu/jobo/st528/documents/relc.pdf
+
+    The data is the locomotive control time to failure example that starts
+    on page 8.  That's the 8th page in the PDF; the page number shown in
+    the text is 270).
+    The document includes SAS output for the data.
+    """
+    # These are the uncensored measurements.  There are also 59 right-censored
+    # measurements where the lower bound is 135.
+    miles_to_fail = [22.5, 37.5, 46.0, 48.5, 51.5, 53.0, 54.5, 57.5, 66.5,
+                     68.0, 69.5, 76.5, 77.0, 78.5, 80.0, 81.5, 82.0, 83.0,
+                     84.0, 91.5, 93.5, 102.5, 107.0, 108.5, 112.5, 113.5,
+                     116.0, 117.0, 118.5, 119.0, 120.0, 122.5, 123.0, 127.5,
+                     131.0, 132.5, 134.0]
+
+    data = CensoredData.right_censored(miles_to_fail + [135]*59,
+                                       [0]*len(miles_to_fail) + [1]*59)
+    sigma, loc, scale = lognorm.fit(data, floc=0)
+
+    assert loc == 0
+    # Convert the lognorm parameters to the mu and sigma of the underlying
+    # normal distribution.
+    mu = np.log(scale)
+    # The expected results are from the 17th page of the PDF document
+    # (labeled page 279), in the SAS output on the right side of the page.
+    assert_allclose(mu, 5.1169, rtol=5e-4)
+    assert_allclose(sigma, 0.7055, rtol=5e-3)
+
+
+def test_nct():
+    """
+    Test fitting the noncentral t distribution to censored data.
+
+    Calculation in R:
+
+    > library(fitdistrplus)
+    > data <- data.frame(left=c(1, 2, 3, 5, 8, 10, 25, 25),
+    +                    right=c(1, 2, 3, 5, 8, 10, NA, NA))
+    > result = fitdistcens(data, 't', control=list(reltol=1e-14),
+    +                      start=list(df=1, ncp=2))
+    > result
+    Fitting of the distribution ' t ' on censored data by maximum likelihood
+    Parameters:
+         estimate
+    df  0.5432336
+    ncp 2.8893565
+
+    """
+    data = CensoredData.right_censored([1, 2, 3, 5, 8, 10, 25, 25],
+                                       [0, 0, 0, 0, 0, 0, 1, 1])
+    # Fit just the shape parameter df and nc; loc and scale are fixed.
+    with np.errstate(over='ignore'):  # remove context when gh-14901 is closed
+        df, nc, loc, scale = nct.fit(data, floc=0, fscale=1,
+                                     optimizer=optimizer)
+    assert_allclose(df, 0.5432336, rtol=5e-6)
+    assert_allclose(nc, 2.8893565, rtol=5e-6)
+    assert loc == 0
+    assert scale == 1
+
+
+def test_ncx2():
+    """
+    Test fitting the shape parameters (df, ncp) of ncx2 to mixed data.
+
+    Calculation in R, with
+    * 5 not censored values [2.7, 0.2, 6.5, 0.4, 0.1],
+    * 1 interval-censored value [[0.6, 1.0]], and
+    * 2 right-censored values [8, 8].
+
+    > library(fitdistrplus)
+    > data <- data.frame(left=c(2.7, 0.2, 6.5, 0.4, 0.1, 0.6, 8, 8),
+    +                    right=c(2.7, 0.2, 6.5, 0.4, 0.1, 1.0, NA, NA))
+    > result = fitdistcens(data, 'chisq', control=list(reltol=1e-14),
+    +                      start=list(df=1, ncp=2))
+    > result
+    Fitting of the distribution ' chisq ' on censored data by maximum
+    likelihood
+    Parameters:
+        estimate
+    df  1.052871
+    ncp 2.362934
+    """
+    data = CensoredData(uncensored=[2.7, 0.2, 6.5, 0.4, 0.1], right=[8, 8],
+                        interval=[[0.6, 1.0]])
+    with np.errstate(over='ignore'):  # remove context when gh-14901 is closed
+        df, ncp, loc, scale = ncx2.fit(data, floc=0, fscale=1,
+                                       optimizer=optimizer)
+    assert_allclose(df, 1.052871, rtol=5e-6)
+    assert_allclose(ncp, 2.362934, rtol=5e-6)
+    assert loc == 0
+    assert scale == 1
+
+
+def test_norm():
+    """
+    Test fitting the normal distribution to interval-censored data.
+
+    Calculation in R:
+
+    > library(fitdistrplus)
+    > data <- data.frame(left=c(0.10, 0.50, 0.75, 0.80),
+    +                    right=c(0.20, 0.55, 0.90, 0.95))
+    > result = fitdistcens(data, 'norm', control=list(reltol=1e-14))
+
+    > result
+    Fitting of the distribution ' norm ' on censored data by maximum likelihood
+    Parameters:
+          estimate
+    mean 0.5919990
+    sd   0.2868042
+    > result$sd
+         mean        sd
+    0.1444432 0.1029451
+    """
+    data = CensoredData(interval=[[0.10, 0.20],
+                                  [0.50, 0.55],
+                                  [0.75, 0.90],
+                                  [0.80, 0.95]])
+
+    loc, scale = norm.fit(data, optimizer=optimizer)
+
+    assert_allclose(loc, 0.5919990, rtol=5e-6)
+    assert_allclose(scale, 0.2868042, rtol=5e-6)
+
+
+def test_weibull_censored1():
+    # Ref: http://www.ams.sunysb.edu/~zhu/ams588/Lecture_3_likelihood.pdf
+
+    # Survival times; '*' indicates right-censored.
+    s = "3,5,6*,8,10*,11*,15,20*,22,23,27*,29,32,35,40,26,28,33*,21,24*"
+
+    times, cens = zip(*[(float(t[0]), len(t) == 2)
+                        for t in [w.split('*') for w in s.split(',')]])
+    data = CensoredData.right_censored(times, cens)
+
+    c, loc, scale = weibull_min.fit(data, floc=0)
+
+    # Expected values are from the reference.
+    assert_allclose(c, 2.149, rtol=1e-3)
+    assert loc == 0
+    assert_allclose(scale, 28.99, rtol=1e-3)
+
+    # Flip the sign of the data, and make the censored values
+    # left-censored. We should get the same parameters when we fit
+    # weibull_max to the flipped data.
+    data2 = CensoredData.left_censored(-np.array(times), cens)
+
+    c2, loc2, scale2 = weibull_max.fit(data2, floc=0)
+
+    assert_allclose(c2, 2.149, rtol=1e-3)
+    assert loc2 == 0
+    assert_allclose(scale2, 28.99, rtol=1e-3)
+
+
+def test_weibull_min_sas1():
+    # Data and SAS results from
+    #   https://support.sas.com/documentation/cdl/en/qcug/63922/HTML/default/
+    #         viewer.htm#qcug_reliability_sect004.htm
+
+    text = """
+           450 0    460 1   1150 0   1150 0   1560 1
+          1600 0   1660 1   1850 1   1850 1   1850 1
+          1850 1   1850 1   2030 1   2030 1   2030 1
+          2070 0   2070 0   2080 0   2200 1   3000 1
+          3000 1   3000 1   3000 1   3100 0   3200 1
+          3450 0   3750 1   3750 1   4150 1   4150 1
+          4150 1   4150 1   4300 1   4300 1   4300 1
+          4300 1   4600 0   4850 1   4850 1   4850 1
+          4850 1   5000 1   5000 1   5000 1   6100 1
+          6100 0   6100 1   6100 1   6300 1   6450 1
+          6450 1   6700 1   7450 1   7800 1   7800 1
+          8100 1   8100 1   8200 1   8500 1   8500 1
+          8500 1   8750 1   8750 0   8750 1   9400 1
+          9900 1  10100 1  10100 1  10100 1  11500 1
+    """
+
+    life, cens = np.array([int(w) for w in text.split()]).reshape(-1, 2).T
+    life = life/1000.0
+
+    data = CensoredData.right_censored(life, cens)
+
+    c, loc, scale = weibull_min.fit(data, floc=0, optimizer=optimizer)
+    assert_allclose(c, 1.0584, rtol=1e-4)
+    assert_allclose(scale, 26.2968, rtol=1e-5)
+    assert loc == 0
+
+
+def test_weibull_min_sas2():
+    # http://support.sas.com/documentation/cdl/en/ormpug/67517/HTML/default/
+    #      viewer.htm#ormpug_nlpsolver_examples06.htm
+
+    # The last two values are right-censored.
+    days = np.array([143, 164, 188, 188, 190, 192, 206, 209, 213, 216, 220,
+                     227, 230, 234, 246, 265, 304, 216, 244])
+
+    data = CensoredData.right_censored(days, [0]*(len(days) - 2) + [1]*2)
+
+    c, loc, scale = weibull_min.fit(data, 1, loc=100, scale=100,
+                                    optimizer=optimizer)
+
+    assert_allclose(c, 2.7112, rtol=5e-4)
+    assert_allclose(loc, 122.03, rtol=5e-4)
+    assert_allclose(scale, 108.37, rtol=5e-4)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/test_correlation.py b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_correlation.py
new file mode 100644
index 0000000000000000000000000000000000000000..fdc8abb068dd92b71aeb3081a895045c24faebe0
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_correlation.py
@@ -0,0 +1,423 @@
+import pytest
+import numpy as np
+from numpy.testing import assert_allclose
+
+from scipy.conftest import skip_xp_invalid_arg
+import scipy._external.array_api_extra as xpx
+from scipy._lib._array_api import (make_xp_test_case, xp_default_dtype, is_jax, is_cupy,
+                                   eager_warns, xp_result_type, is_array_api_strict)
+from scipy._lib._array_api_no_0d import xp_assert_close, xp_assert_equal
+from scipy import stats
+from scipy.stats._axis_nan_policy import SmallSampleWarning
+
+
+lazy_xp_modules = [stats]
+
+
+@make_xp_test_case(stats.chatterjeexi)
+class TestChatterjeeXi:
+    @pytest.mark.parametrize('case', [
+        dict(y_cont=True, statistic=-0.303030303030303, pvalue=0.9351329808526656),
+        dict(y_cont=False, statistic=0.07407407407407396, pvalue=0.3709859367123997)])
+    @pytest.mark.parametrize('dtype', ['float32', 'float64', None])
+    def test_against_R_XICOR(self, case, dtype, xp):
+        # Test against R package XICOR, e.g.
+        # library(XICOR)
+        # options(digits=16)
+        # x = c(0.11027287231363914, 0.8154770102474279, 0.7073943466920335,
+        #       0.6651317324378386, 0.6905752850115503, 0.06115250587536558,
+        #       0.5209906494474178, 0.3155763519785274, 0.18405731803625924,
+        #       0.8613557911541495)
+        # y = c(0.8402081904493103, 0.5946972833914318, 0.23481606164114155,
+        #       0.49754786197715384, 0.9146460831206026, 0.5848057749217579,
+        #       0.7620801065573549, 0.31410063302647495, 0.7935620302236199,
+        #       0.5423085761365468)
+        # xicor(x, y, ties=FALSE, pvalue=TRUE)
+        dtype = xp_default_dtype(xp) if dtype is None else getattr(xp, dtype)
+        rng = np.random.default_rng(25982435982346983)
+        x = rng.random(size=10)
+        y = (rng.random(size=10) if case['y_cont']
+             else rng.integers(0, 5, size=10))
+
+        x, y = xp.asarray(x, dtype=dtype), xp.asarray(y, dtype=dtype)
+        res = stats.chatterjeexi(x, y, y_continuous=case['y_cont'])
+
+        xp_assert_close(res.statistic, xp.asarray(case['statistic'], dtype=dtype))
+        xp_assert_close(res.pvalue, xp.asarray(case['pvalue'], dtype=dtype))
+
+    @pytest.mark.parametrize('y_continuous', (False, True))
+    def test_permutation_asymptotic(self, y_continuous):
+        # XICOR doesn't seem to perform the permutation test as advertised, so
+        # compare the result of a permutation test against an asymptotic test.
+        rng = np.random.default_rng(2524579827426)
+        n = np.floor(rng.uniform(100, 150)).astype(int)
+        shape = (2, n)
+        x = rng.random(size=shape)
+        y = (rng.random(size=shape) if y_continuous
+             else rng.integers(0, 10, size=shape))
+        method = stats.PermutationMethod(rng=rng)
+        res = stats.chatterjeexi(x, y, method=method,
+                                 y_continuous=y_continuous, axis=-1)
+        ref = stats.chatterjeexi(x, y, y_continuous=y_continuous, axis=-1)
+        np.testing.assert_allclose(res.statistic, ref.statistic, rtol=1e-15)
+        np.testing.assert_allclose(res.pvalue, ref.pvalue, rtol=2e-2)
+
+    def test_input_validation(self, xp):
+        rng = np.random.default_rng(25932435798274926)
+        x, y = rng.random(size=(2, 10))
+        x, y = xp.asarray(x), xp.asarray(y)
+
+        message = 'Array shapes are incompatible for broadcasting.|Incompatible shapes'
+        with pytest.raises((ValueError, TypeError), match=message):
+            stats.chatterjeexi(x, y[:-1])
+
+        if not (is_jax(xp) or is_cupy(xp)):
+            # jax misses out on some input validation from _axis_nan_policy decorator
+            # This also fails with cupy for reasons that need to be investigated.
+            message = '...axis 10 is out of bounds for array...|out of range'
+            with pytest.raises((ValueError, IndexError), match=message):
+                stats.chatterjeexi(x, y, axis=10)
+
+        message = '`y_continuous` must be boolean.'
+        with pytest.raises(ValueError, match=message):
+            stats.chatterjeexi(x, y, y_continuous='a herring')
+
+        message = "`method` must be 'asymptotic' or"
+        with pytest.raises(ValueError, match=message):
+            stats.chatterjeexi(x, y, method='ekki ekii')
+
+    def test_special_cases(self, xp):
+        message = 'One or more sample arguments is too small...'
+        with pytest.warns(SmallSampleWarning, match=message):
+            res = stats.chatterjeexi(xp.asarray([1]), xp.asarray([2]))
+
+        assert xp.isnan(res.statistic)
+        assert xp.isnan(res.pvalue)
+
+
+@make_xp_test_case(stats.spearmanrho)
+class TestSpearmanRho:
+    @pytest.mark.parametrize('alternative, statistic, pvalue', [
+        ('two-sided', -0.2727272727272727, 0.4458383415428),
+        ('greater', -0.2727272727272727, 0.7770808292286),
+        ('less', -0.2727272727272727, 0.2229191707714),
+    ])
+    @pytest.mark.parametrize('dtype', ['float32', 'float64', None])
+    def test_against_R_cor_test(self, alternative, statistic, pvalue, dtype, xp):
+        # Test against R cor.test, e.g.
+        # options(digits=16)
+        # x = c(0.11027287231363914, 0.8154770102474279, 0.7073943466920335,
+        #       0.6651317324378386, 0.6905752850115503, 0.06115250587536558,
+        #       0.5209906494474178, 0.3155763519785274, 0.18405731803625924,
+        #       0.8613557911541495)
+        # y = c(0.8402081904493103, 0.5946972833914318, 0.23481606164114155,
+        #       0.49754786197715384, 0.9146460831206026, 0.5848057749217579,
+        #       0.7620801065573549, 0.31410063302647495, 0.7935620302236199,
+        #       0.5423085761365468)
+        # cor.test(x, y, method='spearman', alternative='t', exact=FALSE)
+        dtype = xp_default_dtype(xp) if dtype is None else getattr(xp, dtype)
+        rng = np.random.default_rng(25982435982346983)
+        x = rng.random(size=10)
+        y = rng.random(size=10)
+
+        x, y = xp.asarray(x, dtype=dtype), xp.asarray(y, dtype=dtype)
+        res = stats.spearmanrho(x, y, alternative=alternative)
+
+        xp_assert_close(res.statistic, xp.asarray(statistic, dtype=dtype))
+        xp_assert_close(res.pvalue, xp.asarray(pvalue, dtype=dtype))
+
+
+    @pytest.mark.parametrize('alternative, statistic, pvalue', [
+        ('two-sided', -0.4857142857142857, 0.3555555555556),
+        ('greater', -0.4857142857142857, 0.8513888888889),
+        ('less', -0.4857142857142857, 0.1777777777778),
+    ])
+    def test_against_R_cor_test_exact(self, alternative, statistic, pvalue):
+        xp = np  # will test for multiple backends when gh-23772 merges
+        # Test against R cor.test exact=TRUE, e.g.
+        # options(digits=16)
+        # x = c(0.11027287231363914, 0.8154770102474279, 0.7073943466920335,
+        #       0.6651317324378386, 0.6905752850115503, 0.06115250587536558)
+        # y = c(0.5209906494474178, 0.3155763519785274, 0.18405731803625924,
+        #       0.8613557911541495, 0.8402081904493103, 0.5946972833914318)
+        # cor.test(x, y, method='spearman', alternative='t', exact=TRUE)
+        rng = np.random.default_rng(25982435982346983)
+        x = rng.random(size=6)
+        y = rng.random(size=6)
+        x, y = xp.asarray(x), xp.asarray(y)
+
+        method = stats.PermutationMethod()
+        res = stats.spearmanrho(x, y, method=method, alternative=alternative)
+
+        xp_assert_close(res.statistic, xp.asarray(statistic))
+        xp_assert_close(res.pvalue, xp.asarray(pvalue))
+
+
+    @pytest.mark.parametrize('alternative', ('two-sided', 'greater', 'less'))
+    @pytest.mark.parametrize('n', [9, 99, 999])
+    def test_against_scipy_spearmanr(self, alternative, n, xp):
+        rng = np.random.default_rng(5982435982346983)
+        x = rng.integers(n//2, size=n)
+        y = rng.integers(n//2, size=n)
+        dtype = xp_default_dtype(xp)
+
+        ref = stats.spearmanr(x, y, alternative=alternative)
+        ref_statistic = xp.asarray(ref.statistic, dtype=dtype)
+        ref_pvalue = xp.asarray(ref.pvalue, dtype=dtype)
+
+        x = xp.asarray(x, dtype=dtype)
+        y = xp.asarray(y, dtype=dtype)
+        res = stats.spearmanrho(x, y, alternative=alternative)
+
+        xp_assert_close(res.statistic, ref_statistic)
+        xp_assert_close(res.pvalue, ref_pvalue)
+
+
+    @pytest.mark.parametrize('axis', [-1, 0, 1])
+    def test_other_backends_nd(self, axis, xp):
+        # NumPy n-d behavior is tested by `test_axis_nan_policy`;
+        # check other backends against it.
+        rng = np.random.default_rng(8243598346983259)
+        shape = (8, 9, 10)
+        x = rng.standard_normal(size=shape)
+        y = rng.standard_normal(size=shape)
+        res = stats.spearmanrho(xp.asarray(x), xp.asarray(y), axis=axis)
+        ref = stats.spearmanrho(x, y, axis=axis)
+        xp_assert_close(res.statistic, xp.asarray(ref.statistic), atol=1e-16)
+        xp_assert_close(res.pvalue, xp.asarray(ref.pvalue), atol=1e-16)
+
+
+    def test_input_validation(self, xp):
+        rng = np.random.default_rng(25932435798274926)
+        x, y = rng.random(size=(2, 10))
+        x, y = xp.asarray(x), xp.asarray(y)
+
+        msg = 'incompatible for broadcasting|Incompatible shapes|must be broadcastable'
+        with pytest.raises((ValueError, TypeError), match=msg):
+            stats.spearmanrho(x, y[:-1])
+
+        if not is_jax(xp):
+            # jax misses out on some input validation from _axis_nan_policy decorator
+            message = '...axis 10 is out of bounds for array...|out of range'
+            with pytest.raises((ValueError, IndexError), match=message):
+                stats.spearmanrho(x, y, axis=10)
+
+        message = "`alternative` must be 'less', 'greater', or 'two-sided'."
+        with pytest.raises(ValueError, match=message):
+            stats.spearmanrho(x, y, alternative='alternative')
+
+        message = ("`method` must be...")
+        with pytest.raises(ValueError, match=message):
+            stats.spearmanrho(x, y, method='method')
+
+    def test_special_cases(self, xp):
+        def check_nan(res):
+            assert xp.isnan(res.statistic)
+            assert xp.isnan(res.pvalue)
+
+        message = 'One or more sample arguments is too small...'
+        with eager_warns(SmallSampleWarning, match=message, xp=xp):
+            res = stats.spearmanrho(xp.asarray([1]), xp.asarray([2]))
+            check_nan(res)
+
+        x = xp.asarray([1, 1, 1, 1, 1])
+        y = xp.asarray([1, 2, 3, 4, 5])
+        message = 'An input array is constant; the correlation coefficient...'
+        with eager_warns(stats.ConstantInputWarning, match=message, xp=xp):
+            res = stats.spearmanrho(x, y)
+            check_nan(res)
+        with eager_warns(stats.ConstantInputWarning, match=message, xp=xp):
+            res = stats.spearmanrho(y, x)
+            check_nan(res)
+
+
+class RobustSlopesTest:
+    #  'iv, mask, warnings, consistency, gh19678, mstats'
+    def test_input_validation(self, xp):
+        pfun = getattr(stats, self.pfun)
+        other_method = 'joint' if pfun == stats.theilslopes else 'hierarchical'
+        msg = (f"method must be either '{other_method}' or 'separate'. "
+               "'joint_separate' is invalid.")
+        with pytest.raises(ValueError, match=msg):
+            pfun(xp.asarray([0, 1, 1]), method='joint_separate')
+
+    @skip_xp_invalid_arg
+    @pytest.mark.parametrize("method", ['separate', 'other'])
+    def test_mask(self, method):
+        pfun = getattr(stats, self.pfun)
+        if method == 'other':
+            method = 'joint' if self.pfun =='theilslopes' else 'hierarchical'
+
+        # Test for correct masking.
+        mask = np.asarray([False, False, True, False])
+        y = np.ma.array([0, 1, 100, 1], mask=mask)
+        res = pfun(y, method=method)
+        ref = pfun(y[~mask], method=method)
+
+        assert_allclose(res.slope, ref.slope)
+        assert_allclose(res.intercept, ref.intercept)
+
+    def test_degenerate(self, xp):
+        # Test with degenerate input; see gh-15943
+        pfun = getattr(stats, self.pfun)
+        res = pfun(xp.asarray([0, 1]), xp.asarray([0, 0]))
+        assert xp.all(xp.isnan(xp.stack(res)))
+        res = pfun(xp.asarray([0, 0, 0]), xp.asarray([0, 1, 0]))
+        xp_assert_equal(res[0], xp.asarray(0.))
+        xp_assert_equal(res[1], xp.asarray(0.))
+        if pfun == stats.theilslopes:
+            xp_assert_equal(res[2], xp.asarray(xp.nan))
+            xp_assert_equal(res[3], xp.asarray(xp.nan))
+
+    def test_namedtuple_consistency(self, xp):
+        """
+        Simple test to ensure tuple backwards-compatibility of the returned object.
+        """
+        pfun = getattr(stats, self.pfun)
+
+        y = xp.asarray([1, 2, 4])
+        x = xp.asarray([4, 6, 8])
+
+        result = pfun(y, x)
+
+        # note both returned values are distinct here
+        xp_assert_equal(result[0], result.slope)
+        xp_assert_equal(result[1], result.intercept)
+        if pfun == stats.theilslopes:
+            xp_assert_equal(result[2], result.low_slope)
+            xp_assert_equal(result[3], result.high_slope)
+
+    def test_gh19678_uint8(self, xp):
+        # `theilslopes` returned unexpected results when `y` was an unsigned type.
+        # Check that this is resolved.
+        pfun = getattr(stats, self.pfun)
+        rng = np.random.default_rng(2549824598234528)
+        y = xp.asarray(rng.integers(0, 255, size=10, dtype=np.uint8))
+        res = pfun(y, y)
+        xp_assert_close(res.slope, xp.asarray(1.))
+
+    @pytest.mark.parametrize("method", ['separate', 'other'])
+    @pytest.mark.parametrize("case_number", [0, 1, 2, 3])
+    def test_against_mstats(self, method, case_number, xp):
+        pfun = getattr(stats, self.pfun)
+        if method == 'other':
+            method = 'joint' if self.pfun =='theilslopes' else 'hierarchical'
+
+        rng = np.random.default_rng(349824598234528554)
+        match case_number:
+            case 0:  # no x
+                x = None
+                y = rng.random(100)
+            case 1:  # no ties
+                x = rng.random(100)
+                y = rng.random(100)
+            case 2:  # no x ties
+                x = rng.random(100)
+                y = rng.integers(50, size=100)
+            case 3:  # ties in x and y
+                x = rng.integers(25, size=100)
+                y = rng.integers(50, size=100)
+
+        ref = pfun(y, x, method=method)
+
+        y, x = xp.asarray(y), x if x is None else xp.asarray(x)
+        if (is_array_api_strict(xp) and xp.isdtype(y.dtype, 'integral')
+                and xp.isdtype(x.dtype, 'real floating')):
+            # array API strict doesn't allow mixed type promotion, so promote for it
+            y = xp.astype(y, xp.float64)
+
+        dtype = xp_result_type(y, x, force_floating=True, xp=xp)
+
+        res = pfun(y, x, method=method, axis=-1)
+
+        assert res.slope != 0  # ensure randomly generated test case isn't trivial
+        xp_assert_close(res.slope, xp.asarray(ref.slope, dtype=dtype))
+        xp_assert_close(res.intercept, xp.asarray(ref.intercept, dtype=dtype))
+        if pfun == stats.theilslopes:
+            xp_assert_close(res.low_slope, xp.asarray(ref.low_slope, dtype=dtype))
+            xp_assert_close(res.high_slope, xp.asarray(ref.high_slope, dtype=dtype))
+
+
+@make_xp_test_case(stats.theilslopes)
+class TestTheilslopes(RobustSlopesTest):
+    pfun = 'theilslopes'
+    def test_theilslopes(self, xp):
+        # Test for basic slope and intercept.
+        y = xp.asarray([0, 1, 1])
+        slope, intercept, lower, upper = stats.theilslopes(y)
+        xp_assert_close(slope, xp.asarray(0.5))
+        xp_assert_close(intercept, xp.asarray(0.5))
+
+        slope, intercept, lower, upper = stats.theilslopes(y, method='joint')
+        xp_assert_close(slope, xp.asarray(0.5))
+        xp_assert_close(intercept, xp.asarray(0.0))
+
+        # Test of confidence intervals from example in Sen (1968).
+        x = xp.asarray([1, 2, 3, 4, 10, 12, 18])
+        y = xp.asarray([9, 15, 19, 20, 45, 55, 78])
+        slope, intercept, lower, upper = stats.theilslopes(y, x, 0.07)
+        xp_assert_close(slope, xp.asarray(4.0))
+        xp_assert_close(intercept, xp.asarray(4.0))
+        xp_assert_close(upper, xp.asarray(4.38), rtol=5e-3)
+        xp_assert_close(lower, xp.asarray(3.71), rtol=5e-3)
+
+        slope, intercept, lower, upper = stats.theilslopes(y, x, 0.07,
+                                                           method='joint')
+        xp_assert_close(slope, xp.asarray(4.0))
+        xp_assert_close(intercept, xp.asarray(6.0))
+        xp_assert_close(upper, xp.asarray(4.38), rtol=5e-3)
+        xp_assert_close(lower, xp.asarray(3.71), rtol=5e-3)
+
+
+@make_xp_test_case(stats.siegelslopes)
+class TestSiegelslopes(RobustSlopesTest):
+    pfun = 'siegelslopes'
+    def test_siegelslopes(self, xp):
+        # method should be exact for straight line
+        y = 2 * xp.arange(10.) + 0.5
+        slope, intercept = stats.siegelslopes(y)
+        xp_assert_close(slope, xp.asarray(2.0))
+        xp_assert_close(intercept, xp.asarray(0.5))
+        slope, intercept = stats.siegelslopes(y, method='separate')
+        xp_assert_close(slope, xp.asarray(2.0))
+        xp_assert_close(intercept, xp.asarray(0.5))
+
+        x = 2 * xp.arange(10.)
+        y = 5 * x - 3.0
+        slope, intercept = stats.siegelslopes(y, x)
+        xp_assert_close(slope, xp.asarray(5.0))
+        xp_assert_close(intercept, xp.asarray(-3.0))
+        slope, intercept = stats.siegelslopes(y, x, method='separate')
+        xp_assert_close(slope, xp.asarray(5.0))
+        xp_assert_close(intercept, xp.asarray(-3.0))
+
+        # method is robust to outliers: breakdown point of 50%
+        y = xpx.at(y)[:4].set(1000.)
+        xp_assert_close(slope, xp.asarray(5.0))
+        xp_assert_close(intercept, xp.asarray(-3.0))
+
+        # if there are no outliers, results should be comparable to linregress
+        x = np.arange(10.)
+        y = -2.3 + 0.3 * x + stats.norm.rvs(size=10, random_state=231)
+        slope_ols, intercept_ols, _, _, _ = stats.linregress(x, y)
+
+        y, x = xp.asarray(y), xp.asarray(x)
+        slope, intercept = stats.siegelslopes(y, x)
+        xp_assert_close(slope, xp.asarray(slope_ols), rtol=0.1)
+        xp_assert_close(intercept, xp.asarray(intercept_ols), rtol=0.1)
+
+        slope, intercept = stats.siegelslopes(y, x, method='separate')
+        xp_assert_close(slope, xp.asarray(slope_ols), rtol=0.1)
+        xp_assert_close(intercept, xp.asarray(intercept_ols), rtol=0.1)
+
+    def test_method(self, xp):
+        # Test that distinguishes between the methods. Reference values generated with
+        # SciPy 1.17 (results unchanged since at least 1.12, so assumed "correct") to
+        # detect *changes*.
+        y = xp.asarray([2, 1, 3, 0, 4])
+        slope, intercept = stats.siegelslopes(y, method='separate')
+        xp_assert_close(slope, xp.asarray(0.25))
+        xp_assert_close(intercept, xp.asarray(1.75))
+        slope, intercept = stats.siegelslopes(y, method='hierarchical')
+        xp_assert_close(slope, xp.asarray(0.25))  # always the same between the methods
+        xp_assert_close(intercept, xp.asarray(2.0))
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/test_crosstab.py b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_crosstab.py
new file mode 100644
index 0000000000000000000000000000000000000000..42dc525045b6e455c0bf498adcac5faabe2106ff
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_crosstab.py
@@ -0,0 +1,118 @@
+import pytest
+import numpy as np
+from numpy.testing import assert_array_equal, assert_equal
+from scipy.stats.contingency import crosstab
+
+
+@pytest.mark.parametrize('sparse', [False, True])
+def test_crosstab_basic(sparse):
+    a = [0, 0, 9, 9, 0, 0, 9]
+    b = [2, 1, 3, 1, 2, 3, 3]
+    expected_avals = [0, 9]
+    expected_bvals = [1, 2, 3]
+    expected_count = np.array([[1, 2, 1],
+                               [1, 0, 2]])
+    (avals, bvals), count = crosstab(a, b, sparse=sparse)
+    assert_array_equal(avals, expected_avals)
+    assert_array_equal(bvals, expected_bvals)
+    if sparse:
+        assert_array_equal(count.toarray(), expected_count)
+    else:
+        assert_array_equal(count, expected_count)
+
+
+@pytest.mark.parametrize('sparse', [False, True])
+def test_crosstab_basic_1d(sparse):
+    # Verify that a single input sequence works as expected.
+    x = [1, 2, 3, 1, 2, 3, 3]
+    expected_xvals = [1, 2, 3]
+    expected_count = np.array([2, 2, 3])
+    (xvals,), count = crosstab(x, sparse=sparse)
+    assert_array_equal(xvals, expected_xvals)
+    if sparse:
+        assert_array_equal(count.toarray(), expected_count)
+    else:
+        assert_array_equal(count, expected_count)
+
+
+@pytest.mark.parametrize('sparse', [False, True])
+def test_crosstab_basic_3d(sparse):
+    # Verify the function for three input sequences.
+    a = 'a'
+    b = 'b'
+    x = [0, 0, 9, 9, 0, 0, 9, 9]
+    y = [a, a, a, a, b, b, b, a]
+    z = [1, 2, 3, 1, 2, 3, 3, 1]
+    expected_xvals = [0, 9]
+    expected_yvals = [a, b]
+    expected_zvals = [1, 2, 3]
+    expected_count = np.array([[[1, 1, 0],
+                                [0, 1, 1]],
+                               [[2, 0, 1],
+                                [0, 0, 1]]])
+    (xvals, yvals, zvals), count = crosstab(x, y, z, sparse=sparse)
+    assert_array_equal(xvals, expected_xvals)
+    assert_array_equal(yvals, expected_yvals)
+    assert_array_equal(zvals, expected_zvals)
+    if sparse:
+        assert_array_equal(count.toarray(), expected_count)
+    else:
+        assert_array_equal(count, expected_count)
+
+
+@pytest.mark.parametrize('sparse', [False, True])
+def test_crosstab_levels(sparse):
+    a = [0, 0, 9, 9, 0, 0, 9]
+    b = [1, 2, 3, 1, 2, 3, 3]
+    expected_avals = [0, 9]
+    expected_bvals = [0, 1, 2, 3]
+    expected_count = np.array([[0, 1, 2, 1],
+                               [0, 1, 0, 2]])
+    (avals, bvals), count = crosstab(a, b, levels=[None, [0, 1, 2, 3]],
+                                     sparse=sparse)
+    assert_array_equal(avals, expected_avals)
+    assert_array_equal(bvals, expected_bvals)
+    if sparse:
+        assert_array_equal(count.toarray(), expected_count)
+    else:
+        assert_array_equal(count, expected_count)
+
+
+@pytest.mark.parametrize('sparse', [False, True])
+def test_crosstab_extra_levels(sparse):
+    # The pair of values (-1, 3) will be ignored, because we explicitly
+    # request the counted `a` values to be [0, 9].
+    a = [0, 0, 9, 9, 0, 0, 9, -1]
+    b = [1, 2, 3, 1, 2, 3, 3, 3]
+    expected_avals = [0, 9]
+    expected_bvals = [0, 1, 2, 3]
+    expected_count = np.array([[0, 1, 2, 1],
+                               [0, 1, 0, 2]])
+    (avals, bvals), count = crosstab(a, b, levels=[[0, 9], [0, 1, 2, 3]],
+                                     sparse=sparse)
+    assert_array_equal(avals, expected_avals)
+    assert_array_equal(bvals, expected_bvals)
+    if sparse:
+        assert_array_equal(count.toarray(), expected_count)
+    else:
+        assert_array_equal(count, expected_count)
+
+
+def test_validation_at_least_one():
+    with pytest.raises(TypeError, match='At least one'):
+        crosstab()
+
+
+def test_validation_same_lengths():
+    with pytest.raises(ValueError, match='must have the same length'):
+        crosstab([1, 2], [1, 2, 3, 4])
+
+
+def test_validation_len_levels_matches_args():
+    with pytest.raises(ValueError, match='number of input sequences'):
+        crosstab([0, 1, 1], [8, 8, 9], levels=([0, 1, 2, 3],))
+
+
+def test_result():
+    res = crosstab([0, 1], [1, 2])
+    assert_equal((res.elements, res.count), res)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/test_device_dtype.py b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_device_dtype.py
new file mode 100644
index 0000000000000000000000000000000000000000..c20bfc1104a7c3b0dcd2ee6484aed9169380eeef
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_device_dtype.py
@@ -0,0 +1,248 @@
+import pytest
+import numpy as np
+from scipy import stats
+
+from scipy._lib._array_api import xp_device, is_array_api_strict, is_torch
+from scipy.stats._stats_py import _xp_mean, _xp_var
+
+skip_xp_backends = pytest.mark.skip_xp_backends
+
+dtypes = ['float32', 'float64']
+
+
+def get_arrays(n_arrays, *, dtype=np.float64, xp=np, shape=(30,), device=None,
+               seed=84912165484321):
+    rng = np.random.default_rng(seed)
+
+    datas = []
+    for i in range(n_arrays):
+        data = 10*rng.random(size=shape)
+        if xp.isdtype(dtype, 'complex floating'):
+            data = data * 10j*rng.standard_normal(size=shape)
+        data = xp.asarray(data, dtype=dtype, device=device)
+        datas.append(data)
+
+    return datas
+
+
+@pytest.mark.parametrize('fun, kwargs', [(stats.gmean, {}),
+                                         (stats.hmean, {}),
+                                         (stats.pmean, {'p': 2}),
+                                         (_xp_mean, {}),
+                                         ])
+@pytest.mark.parametrize('dtype', dtypes)
+@pytest.mark.uses_xp_capabilities(False, reason="not used in this test yet")
+def test_xmean(fun, kwargs, dtype, xp, devices):
+    dtype = getattr(xp, dtype)
+    for device in devices:
+        x, weights = get_arrays(2, device=device, dtype=dtype, xp=xp)
+        res = fun(x, weights=weights, **kwargs)
+        assert xp_device(res) == xp_device(x)
+        assert x.dtype == dtype
+
+
+@skip_xp_backends('array_api_strict',
+                  reason="special functions don't work with 'device1'")
+@pytest.mark.parametrize('nargs', [1, 2])
+@pytest.mark.parametrize('dtype', dtypes)
+@pytest.mark.uses_xp_capabilities(False, reason="not used in this test yet")
+def test_entropy(nargs, dtype, xp, devices):
+    dtype = getattr(xp, dtype)
+    for device in devices:
+        args = get_arrays(nargs, device=device, dtype=dtype, xp=xp)
+        res = stats.entropy(*args)
+        assert xp_device(res) == xp_device(args[0])
+        assert res.dtype == dtype
+
+
+@pytest.mark.parametrize('dtype', dtypes)
+@pytest.mark.uses_xp_capabilities(False, reason="not used in this test yet")
+def test_directional_stats(dtype, xp, devices):
+    dtype = getattr(xp, dtype)
+    for device in devices:
+        x = get_arrays(1, shape=(30, 3), device=device, dtype=dtype, xp=xp)[0]
+        res = stats.directional_stats(x)
+        assert xp_device(res.mean_direction) == xp_device(x)
+        assert res.mean_direction.dtype == dtype
+        assert xp_device(res.mean_resultant_length) == xp_device(x)
+        assert res.mean_resultant_length.dtype == dtype
+
+
+@pytest.mark.parametrize('method', [
+    "vasicek",
+    "van es",
+    pytest.param(
+        "correa",
+        marks=[
+            skip_xp_backends("array_api_strict", reason="Invalid fancy indexing"),
+            skip_xp_backends("dask.array", reason="Invalid fancy indexing"),
+        ],
+    ),
+    "ebrahimi",
+    "auto",
+])
+@pytest.mark.parametrize('dtype', dtypes)
+@pytest.mark.uses_xp_capabilities(False, reason="not used in this test yet")
+def test_differential_entropy(method, dtype, xp, devices):
+    dtype = getattr(xp, dtype)
+    for device in devices:
+        values = get_arrays(1, device=device, dtype=dtype, xp=xp)[0]
+        res = stats.differential_entropy(values, method=method)
+        assert xp_device(res) == xp_device(values)
+        assert values.dtype == dtype
+
+
+@skip_xp_backends('dask.array', reason='no take_along_axis')
+@pytest.mark.parametrize('method', ['inverted_cdf', 'averaged_inverted_cdf',
+                                    'closest_observation', 'interpolated_inverted_cdf',
+                                    'hazen', 'weibull', 'linear', 'median_unbiased',
+                                    'normal_unbiased', 'harrell-davis'])
+@pytest.mark.parametrize('dtype', dtypes)
+@pytest.mark.uses_xp_capabilities(False, reason="not used in this test yet")
+def test_quantile(method, dtype, xp, devices):
+    if (is_array_api_strict(xp) or is_torch(xp)) and method == 'harrell-davis':
+        pytest.skip("'harrell-davis' not currently supported on GPU.")
+
+    dtype = getattr(xp, dtype)
+    for device in devices:
+        values = get_arrays(1, device=device, dtype=dtype, xp=xp)[0]
+        res = stats.quantile(values, 0.5, method=method)
+        assert xp_device(res) == xp_device(values)
+        assert values.dtype == dtype
+
+
+@pytest.mark.parametrize('dtype', dtypes)
+@pytest.mark.uses_xp_capabilities(False, reason="not used in this test yet")
+def test_boxcox_llf(dtype, xp, devices):
+    dtype = getattr(xp, dtype)
+    for device in devices:
+        data = get_arrays(1, device=device, dtype=dtype, xp=xp)[0]
+        res = stats.boxcox_llf(1, data)
+        assert xp_device(res) == xp_device(data)
+        assert data.dtype == dtype
+
+
+@pytest.mark.parametrize('fun, kwargs',
+    [(stats.moment, {'order': 2}),
+     (stats.skew, {}),
+     (stats.skew, {'bias': False}),
+     (stats.kurtosis, {}),
+     (stats.kurtosis, {'bias': False}),
+     (stats.sem, {}),
+     (stats.kstat, {'n': 1}),
+     (stats.kstat, {'n': 2}),
+     (stats.kstat, {'n': 3}),
+     (stats.kstat, {'n': 4}),
+     (stats.kstatvar, {'n': 1}),
+     (stats.kstatvar, {'n': 2}),
+     (stats.circmean, {}),
+     (stats.circvar, {}),
+     (stats.circstd, {}),
+     (_xp_var, {}),
+     (stats.gstd, {}),
+     (stats.variation, {}),
+     (stats.tmean, {'limits': (0.1, 0.9)}),
+     (stats.tvar, {'limits': (0.1, 0.9)}),
+     (stats.tmin, {'lowerlimit': 0.1}),
+     (stats.tmax, {'upperlimit': 0.9}),
+     (stats.tstd, {'limits': (0.1, 0.9)}),
+     (stats.tsem, {'limits': (0.1, 0.9)}),
+     ])
+@pytest.mark.parametrize('dtype', dtypes)
+@pytest.mark.uses_xp_capabilities(False, reason="not used in this test yet")
+def test_one_in_one_out(fun, kwargs, dtype, xp, devices):
+    dtype = getattr(xp, dtype)
+    for device in devices:
+        array = get_arrays(1, device=device, dtype=dtype, xp=xp)[0]
+        res = fun(array, **kwargs)
+        assert xp_device(res) == xp_device(array)
+        assert res.dtype == dtype
+
+
+@pytest.mark.parametrize('dtype', dtypes)
+@pytest.mark.uses_xp_capabilities(False, reason="not used in this test yet")
+def test_describe(dtype, xp, devices):
+    dtype = getattr(xp, dtype)
+    for device in devices:
+        array = get_arrays(1, shape=10, dtype=dtype, device=device, xp=xp)[0]
+        res = stats.describe(array, axis=-1)
+
+        assert xp_device(res.nobs) == xp_device(array)
+        assert xp_device(res.minmax[0]) == xp_device(array)
+        assert xp_device(res.minmax[1]) == xp_device(array)
+        assert xp_device(res.variance) == xp_device(array)
+        assert xp_device(res.skewness) == xp_device(array)
+        assert xp_device(res.kurtosis) == xp_device(array)
+
+        assert res.minmax[0].dtype == dtype
+        assert res.minmax[1].dtype == dtype
+        assert res.variance.dtype == dtype
+        assert res.skewness.dtype == dtype
+        assert res.kurtosis.dtype == dtype
+
+
+@pytest.mark.parametrize('fun', [stats.zscore, stats.gzscore, stats.zmap])
+@pytest.mark.parametrize('dtype', dtypes)
+@pytest.mark.uses_xp_capabilities(False, reason="not used in this test yet")
+def test_zscore(fun, dtype, xp, devices):
+    dtype = getattr(xp, dtype)
+    for device in devices:
+        n = 2 if (fun == stats.zmap) else 1
+        arrays = get_arrays(n, device=device, dtype=dtype, xp=xp)
+        res = fun(*arrays)
+        assert xp_device(res) == xp_device(arrays[0])
+        assert res.dtype == dtype
+
+
+@skip_xp_backends('array_api_strict', reason="special/_support_alternative_backends")
+@skip_xp_backends(cpu_only=True, exceptions=['cupy', 'jax.numpy'])
+@pytest.mark.parametrize('f_name', ['ttest_1samp', 'ttest_rel', 'ttest_ind', 'skewtest',
+                                    'kurtosistest', 'normaltest', 'jarque_bera',
+                                    'bartlett', 'pearsonr', 'chisquare',
+                                    'power_divergence'])
+@pytest.mark.parametrize('dtype', dtypes)
+@pytest.mark.uses_xp_capabilities(False, reason="not used in this test yet")
+def test_hypothesis_tests(f_name, dtype, xp, devices):
+    dtype = getattr(xp, dtype)
+    for device in devices:
+        f = getattr(stats, f_name)
+
+        n = 2 if f_name in {'ttest_1samp', 'ttest_rel', 'ttest_ind', 'bartlett',
+                            'pearsonr', 'chisquare'} else 1
+
+        arrays = get_arrays(n, xp=xp, dtype=dtype, device=device)
+        if f_name == 'ttest_1samp':
+            arrays[1] = xp.mean(arrays[1])
+        if f_name == 'chisquare':
+            arrays[1] = xp.sum(arrays[0]) * arrays[1] / xp.sum(arrays[1])
+
+        res = f(*arrays)
+        assert xp_device(res.statistic) == xp_device(arrays[0])
+        assert xp_device(res.pvalue) == xp_device(arrays[0])
+        assert res.statistic.dtype == dtype
+        assert res.pvalue.dtype == dtype
+
+        if f_name in {'ttest_1samp', 'ttest_rel', 'ttest_ind', 'pearsonr'}:
+            res_ci = res.confidence_interval()
+            assert xp_device(res_ci.low) == xp_device(arrays[0])
+            assert xp_device(res_ci.high) == xp_device(arrays[0])
+            assert res_ci.low.dtype == dtype
+            assert res_ci.high.dtype == dtype
+
+
+@skip_xp_backends('array_api_strict',
+                  reason="special functions don't work with 'device1'")
+@skip_xp_backends(cpu_only=True, exceptions=['cupy', 'jax.numpy'])
+@pytest.mark.parametrize('method', ['fisher', 'pearson', 'tippett', 'stouffer',
+                                    'mudholkar_george'])
+@pytest.mark.parametrize('dtype', dtypes)
+@pytest.mark.uses_xp_capabilities(False, reason="not used in this test yet")
+def test_combine_pvalues(method, dtype, xp, devices):
+    dtype = getattr(xp, dtype)
+    for device in devices:
+        pvalues = get_arrays(1, xp=xp, dtype=dtype, device=device)[0] / 10
+        res = stats.combine_pvalues(pvalues, method=method)
+        assert xp_device(res.statistic) == xp_device(pvalues)
+        assert xp_device(res.pvalue) == xp_device(pvalues)
+        assert res.statistic.dtype == dtype
+        assert res.pvalue.dtype == dtype
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/test_discrete_basic.py b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_discrete_basic.py
new file mode 100644
index 0000000000000000000000000000000000000000..8e67c60a21d193ee3f304b80f6660110fb95b177
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_discrete_basic.py
@@ -0,0 +1,625 @@
+import warnings
+
+import numpy.testing as npt
+from numpy.testing import assert_allclose
+
+import numpy as np
+import pytest
+
+from scipy import stats
+from scipy.special import _ufuncs
+from .common_tests import (check_normalization, check_moment,
+                           check_mean_expect,
+                           check_var_expect, check_skew_expect,
+                           check_kurt_expect, check_entropy,
+                           check_private_entropy, check_edge_support,
+                           check_named_args, check_random_state_property,
+                           check_pickling, check_rvs_broadcast,
+                           check_freezing,)
+from scipy.stats._distr_params import distdiscrete, invdistdiscrete
+from scipy.stats._distn_infrastructure import rv_discrete_frozen
+
+vals = ([1, 2, 3, 4], [0.1, 0.2, 0.3, 0.4])
+distdiscrete += [[stats.rv_discrete(values=vals), ()]]
+
+# For these distributions, test_discrete_basic only runs with test mode full
+distslow = {'nhypergeom'}
+
+# Override number of ULPs adjustment for `check_cdf_ppf`
+roundtrip_cdf_ppf_exceptions = {'nbinom': 30}
+
+def cases_test_discrete_basic():
+    seen = set()
+    for distname, arg in distdiscrete:
+        if distname in distslow:
+            yield pytest.param(distname, arg, distname, marks=pytest.mark.slow)
+        else:
+            yield distname, arg, distname not in seen
+        seen.add(distname)
+
+
+@pytest.mark.parametrize('distname,arg,first_case', list(cases_test_discrete_basic()))
+def test_discrete_basic(distname, arg, first_case, num_parallel_threads):
+    if (isinstance(distname, str) and distname.startswith('nchypergeom')
+            and num_parallel_threads > 1):
+        pytest.skip(reason='nchypergeom has a global random generator')
+
+    try:
+        distfn = getattr(stats, distname)
+    except TypeError:
+        distfn = distname
+        distname = 'sample distribution'
+    rng = np.random.RandomState(9765456)
+    rvs = distfn.rvs(*arg, size=2000, random_state=rng)
+    supp = np.unique(rvs)
+    m, v = distfn.stats(*arg)
+    check_cdf_ppf(distfn, arg, supp, distname + ' cdf_ppf')
+
+    check_pmf_cdf(distfn, arg, distname)
+    check_oth(distfn, arg, supp, distname + ' oth')
+    check_edge_support(distfn, arg)
+
+    alpha = 0.01
+    check_discrete_chisquare(distfn, arg, rvs, alpha,
+                             distname + ' chisquare')
+
+    if first_case:
+        locscale_defaults = (0,)
+        meths = [distfn.pmf, distfn.logpmf, distfn.cdf, distfn.logcdf,
+                 distfn.logsf]
+        # make sure arguments are within support
+        # for some distributions, this needs to be overridden
+        spec_k = {'randint': 11, 'hypergeom': 4, 'bernoulli': 0,
+                  'nchypergeom_wallenius': 6}
+        k = spec_k.get(distname, 1)
+        check_named_args(distfn, k, arg, locscale_defaults, meths)
+        if distname != 'sample distribution':
+            check_scale_docstring(distfn)
+        if num_parallel_threads == 1:
+            check_random_state_property(distfn, arg)
+            if distname not in {'poisson_binom'}:  # can't be pickled
+                check_pickling(distfn, arg)
+        check_freezing(distfn, arg)
+
+        # Entropy
+        check_entropy(distfn, arg, distname)
+        if distfn.__class__._entropy != stats.rv_discrete._entropy:
+            check_private_entropy(distfn, arg, stats.rv_discrete)
+
+
+@pytest.mark.parametrize('distname,arg', distdiscrete)
+def test_moments(distname, arg):
+    try:
+        distfn = getattr(stats, distname)
+    except TypeError:
+        distfn = distname
+        distname = 'sample distribution'
+    m, v, s, k = distfn.stats(*arg, moments='mvsk')
+    check_normalization(distfn, arg, distname)
+
+    # compare `stats` and `moment` methods
+    check_moment(distfn, arg, m, v, distname)
+    check_mean_expect(distfn, arg, m, distname)
+    check_var_expect(distfn, arg, m, v, distname)
+    check_skew_expect(distfn, arg, m, v, s, distname)
+    with warnings.catch_warnings():
+        if distname in ['zipf', 'betanbinom']:
+            warnings.simplefilter("ignore", RuntimeWarning)
+        check_kurt_expect(distfn, arg, m, v, k, distname)
+
+    # frozen distr moments
+    check_moment_frozen(distfn, arg, m, 1)
+    check_moment_frozen(distfn, arg, v+m*m, 2)
+
+
+@pytest.mark.parametrize('dist,shape_args', distdiscrete)
+def test_rvs_broadcast(dist, shape_args):
+    # If shape_only is True, it means the _rvs method of the
+    # distribution uses more than one random number to generate a random
+    # variate.  That means the result of using rvs with broadcasting or
+    # with a nontrivial size will not necessarily be the same as using the
+    # numpy.vectorize'd version of rvs(), so we can only compare the shapes
+    # of the results, not the values.
+    # Whether or not a distribution is in the following list is an
+    # implementation detail of the distribution, not a requirement.  If
+    # the implementation the rvs() method of a distribution changes, this
+    # test might also have to be changed.
+    shape_only = dist in ['betabinom', 'betanbinom', 'skellam', 'yulesimon',
+                          'dlaplace', 'nchypergeom_fisher',
+                          'nchypergeom_wallenius', 'poisson_binom']
+    try:
+        distfunc = getattr(stats, dist)
+    except TypeError:
+        distfunc = dist
+        dist = f'rv_discrete(values=({dist.xk!r}, {dist.pk!r}))'
+    loc = np.zeros(2)
+    nargs = distfunc.numargs
+    allargs = []
+    bshape = []
+
+    if dist == 'poisson_binom':
+        # normal rules apply except the last axis of `p` is ignored
+        p = np.full((3, 1, 10), 0.5)
+        allargs = (p, loc)
+        bshape = (3, 2)
+        check_rvs_broadcast(distfunc, dist, allargs,
+                            bshape, shape_only, [np.dtype(int)])
+        return
+
+    # Generate shape parameter arguments...
+    for k in range(nargs):
+        shp = (k + 3,) + (1,)*(k + 1)
+        param_val = shape_args[k]
+        allargs.append(np.full(shp, param_val))
+        bshape.insert(0, shp[0])
+    allargs.append(loc)
+    bshape.append(loc.size)
+    # bshape holds the expected shape when loc, scale, and the shape
+    # parameters are all broadcast together.
+    check_rvs_broadcast(
+        distfunc, dist, allargs, bshape, shape_only, [np.dtype(int)]
+    )
+
+
+@pytest.mark.parametrize('dist,args', distdiscrete)
+def test_ppf_with_loc(dist, args):
+    try:
+        distfn = getattr(stats, dist)
+    except TypeError:
+        distfn = dist
+    #check with a negative, no and positive relocation.
+    rng = np.random.default_rng(5108587887)
+
+    re_locs = [rng.integers(-10, -1), 0, rng.integers(1, 10)]
+    _a, _b = distfn.support(*args)
+    for loc in re_locs:
+        npt.assert_array_equal(
+            [_a-1+loc, _b+loc],
+            [distfn.ppf(0.0, *args, loc=loc), distfn.ppf(1.0, *args, loc=loc)]
+            )
+
+
+@pytest.mark.parametrize('dist, args', distdiscrete)
+def test_isf_with_loc(dist, args):
+    try:
+        distfn = getattr(stats, dist)
+    except TypeError:
+        distfn = dist
+    # check with a negative, no and positive relocation.
+    rng = np.random.default_rng(4030503535)
+    re_locs = [rng.integers(-10, -1), 0, rng.integers(1, 10)]
+    _a, _b = distfn.support(*args)
+    for loc in re_locs:
+        expected = _b + loc, _a - 1 + loc
+        res = distfn.isf(0., *args, loc=loc), distfn.isf(1., *args, loc=loc)
+        npt.assert_array_equal(expected, res)
+    # test broadcasting behaviour
+    re_locs = [rng.integers(-10, -1, size=(5, 3)),
+               np.zeros((5, 3)),
+               rng.integers(1, 10, size=(5, 3))]
+    _a, _b = distfn.support(*args)
+    for loc in re_locs:
+        expected = _b + loc, _a - 1 + loc
+        res = distfn.isf(0., *args, loc=loc), distfn.isf(1., *args, loc=loc)
+        npt.assert_array_equal(expected, res)
+
+
+def check_cdf_ppf(distfn, arg, supp, msg):
+    # supp is assumed to be an array of integers in the support of distfn
+    # (but not necessarily all the integers in the support).
+    # This test assumes that the PMF of any value in the support of the
+    # distribution is greater than 1e-8.
+
+    # cdf is a step function, and ppf(q) = min{k : cdf(k) >= q, k integer}
+    cdf_supp = distfn.cdf(supp, *arg)
+    # In very rare cases, the finite precision calculation of ppf(cdf(supp))
+    # can produce an array in which an element is off by one.  We nudge the
+    # CDF values down by a few ULPs help to avoid this.
+    n_ulps = roundtrip_cdf_ppf_exceptions.get(distfn.name, 15)
+    cdf_supp0 = cdf_supp - n_ulps*np.spacing(cdf_supp)
+    npt.assert_array_equal(distfn.ppf(cdf_supp0, *arg),
+                           supp, msg + '-roundtrip')
+    # Repeat the same calculation, but with the CDF values decreased by 1e-8.
+    npt.assert_array_equal(distfn.ppf(distfn.cdf(supp, *arg) - 1e-8, *arg),
+                           supp, msg + '-roundtrip')
+
+    if not hasattr(distfn, 'xk'):
+        _a, _b = distfn.support(*arg)
+        supp1 = supp[supp < _b]
+        npt.assert_array_equal(distfn.ppf(distfn.cdf(supp1, *arg) + 1e-8, *arg),
+                               supp1 + distfn.inc, msg + ' ppf-cdf-next')
+
+
+def check_pmf_cdf(distfn, arg, distname):
+    if hasattr(distfn, 'xk'):
+        index = distfn.xk
+    else:
+        startind = int(distfn.ppf(0.01, *arg) - 1)
+        index = list(range(startind, startind + 10))
+    cdfs = distfn.cdf(index, *arg)
+    pmfs_cum = distfn.pmf(index, *arg).cumsum()
+
+    atol, rtol = 1e-10, 1e-10
+    if distname == 'skellam':    # ncx2 accuracy
+        atol, rtol = 1e-5, 1e-5
+    npt.assert_allclose(cdfs - cdfs[0], pmfs_cum - pmfs_cum[0],
+                        atol=atol, rtol=rtol)
+
+    # also check that pmf at non-integral k is zero
+    k = np.asarray(index)
+    k_shifted = k[:-1] + np.diff(k)/2
+    npt.assert_equal(distfn.pmf(k_shifted, *arg), 0)
+
+    # better check frozen distributions, and also when loc != 0
+    loc = 0.5
+    dist = distfn(loc=loc, *arg)
+    npt.assert_allclose(dist.pmf(k[1:] + loc), np.diff(dist.cdf(k + loc)))
+    npt.assert_equal(dist.pmf(k_shifted + loc), 0)
+
+
+def check_moment_frozen(distfn, arg, m, k):
+    npt.assert_allclose(distfn(*arg).moment(k), m,
+                        atol=1e-10, rtol=1e-10)
+
+
+def check_oth(distfn, arg, supp, msg):
+    # checking other methods of distfn
+    npt.assert_allclose(distfn.sf(supp, *arg), 1. - distfn.cdf(supp, *arg),
+                        atol=1e-10, rtol=1e-10)
+
+    q = np.linspace(0.01, 0.99, 20)
+    npt.assert_allclose(distfn.isf(q, *arg), distfn.ppf(1. - q, *arg),
+                        atol=1e-10, rtol=1e-10)
+
+    median_sf = distfn.isf(0.5, *arg)
+    npt.assert_(distfn.sf(median_sf - 1, *arg) > 0.5)
+    npt.assert_(distfn.cdf(median_sf + 1, *arg) > 0.5)
+
+
+def check_discrete_chisquare(distfn, arg, rvs, alpha, msg):
+    """Perform chisquare test for random sample of a discrete distribution
+
+    Parameters
+    ----------
+    distname : str
+        name of distribution function
+    arg : sequence
+        parameters of distribution
+    alpha : float
+        significance level, threshold for p-value
+
+    Returns
+    -------
+    result : bool
+        0 if test passes, 1 if test fails
+
+    """
+    wsupp = 0.05
+
+    # construct intervals with minimum mass `wsupp`.
+    # intervals are left-half-open as in a cdf difference
+    _a, _b = distfn.support(*arg)
+    lo = int(max(_a, -1000))
+    high = int(min(_b, 1000)) + 1
+    distsupport = range(lo, high)
+    last = 0
+    distsupp = [lo]
+    distmass = []
+    for ii in distsupport:
+        current = distfn.cdf(ii, *arg)
+        if current - last >= wsupp - 1e-14:
+            distsupp.append(ii)
+            distmass.append(current - last)
+            last = current
+            if current > (1 - wsupp):
+                break
+    if distsupp[-1] < _b:
+        distsupp.append(_b)
+        distmass.append(1 - last)
+    distsupp = np.array(distsupp)
+    distmass = np.array(distmass)
+
+    # convert intervals to right-half-open as required by histogram
+    histsupp = distsupp + 1e-8
+    histsupp[0] = _a
+
+    # find sample frequencies and perform chisquare test
+    freq, hsupp = np.histogram(rvs, histsupp)
+    chis, pval = stats.chisquare(np.array(freq), len(rvs)*distmass)
+
+    npt.assert_(
+        pval > alpha,
+        f'chisquare - test for {msg} at arg = {str(arg)} with pval = {str(pval)}'
+    )
+
+
+def check_scale_docstring(distfn):
+    if distfn.__doc__ is not None:
+        # Docstrings can be stripped if interpreter is run with -OO
+        npt.assert_('scale' not in distfn.__doc__)
+
+
+@pytest.mark.parametrize('method', ['pmf', 'logpmf', 'cdf', 'logcdf',
+                                    'sf', 'logsf', 'ppf', 'isf'])
+@pytest.mark.parametrize('distname, args', distdiscrete)
+def test_methods_with_lists(method, distname, args):
+    # Test that the discrete distributions can accept Python lists
+    # as arguments.
+    try:
+        dist = getattr(stats, distname)
+    except TypeError:
+        return
+    dist_method = getattr(dist, method)
+    if method in ['ppf', 'isf']:
+        z = [0.1, 0.2]
+    else:
+        z = [0, 1]
+    p2 = [[p]*2 for p in args]
+    loc = [0, 1]
+    result = dist_method(z, *p2, loc=loc)
+    npt.assert_allclose(result,
+                        [dist_method(*v) for v in zip(z, *p2, loc)],
+                        rtol=1e-15, atol=1e-15)
+
+
+@pytest.mark.parametrize('distname, args', invdistdiscrete)
+def test_cdf_gh13280_regression(distname, args):
+    # Test for nan output when shape parameters are invalid
+    dist = getattr(stats, distname)
+    x = np.arange(-2, 15)
+    vals = dist.cdf(x, *args)
+    expected = np.nan
+    npt.assert_equal(vals, expected)
+
+
+def cases_test_discrete_integer_shapes():
+    # distributions parameters that are only allowed to be integral when
+    # fitting, but are allowed to be real as input to PDF, etc.
+    integrality_exceptions = {'nbinom': {'n'}, 'betanbinom': {'n'}}
+
+    seen = set()
+    for distname, shapes in distdiscrete:
+        if distname in seen:
+            continue
+        seen.add(distname)
+
+        try:
+            dist = getattr(stats, distname)
+        except TypeError:
+            continue
+
+        shape_info = dist._shape_info()
+
+        for i, shape in enumerate(shape_info):
+            if (shape.name in integrality_exceptions.get(distname, set()) or
+                    not shape.integrality):
+                continue
+
+            yield distname, shape.name, shapes
+
+
+@pytest.mark.parametrize('distname, shapename, shapes',
+                         list(cases_test_discrete_integer_shapes()))
+def test_integer_shapes(distname, shapename, shapes):
+    dist = getattr(stats, distname)
+    shape_info = dist._shape_info()
+    shape_names = [shape.name for shape in shape_info]
+    i = shape_names.index(shapename)  # this element of params must be integral
+
+    shapes_copy = list(shapes)
+
+    valid_shape = shapes[i]
+    invalid_shape = valid_shape - 0.5  # arbitrary non-integral value
+    new_valid_shape = valid_shape - 1
+    shapes_copy[i] = [[valid_shape], [invalid_shape], [new_valid_shape]]
+
+    a, b = dist.support(*shapes)
+    x = np.round(np.linspace(a, b, 5))
+
+    pmf = dist.pmf(x, *shapes_copy)
+    assert not np.any(np.isnan(pmf[0, :]))
+    assert np.all(np.isnan(pmf[1, :]))
+    assert not np.any(np.isnan(pmf[2, :]))
+
+
+def test_frozen_attributes(monkeypatch):
+    # gh-14827 reported that all frozen distributions had both pmf and pdf
+    # attributes; continuous should have pdf and discrete should have pmf.
+    message = "'rv_discrete_frozen' object has no attribute"
+    with pytest.raises(AttributeError, match=message):
+        stats.binom(10, 0.5).pdf
+    with pytest.raises(AttributeError, match=message):
+        stats.binom(10, 0.5).logpdf
+    monkeypatch.setattr(stats.binom, "pdf", "herring", raising=False)
+    frozen_binom = stats.binom(10, 0.5)
+    assert isinstance(frozen_binom, rv_discrete_frozen)
+    assert not hasattr(frozen_binom, "pdf")
+
+
+@pytest.mark.parametrize('distname, shapes', distdiscrete)
+def test_interval(distname, shapes):
+    # gh-11026 reported that `interval` returns incorrect values when
+    # `confidence=1`. The values were not incorrect, but it was not intuitive
+    # that the left end of the interval should extend beyond the support of the
+    # distribution. Confirm that this is the behavior for all distributions.
+    if isinstance(distname, str):
+        dist = getattr(stats, distname)
+    else:
+        dist = distname
+    a, b = dist.support(*shapes)
+    npt.assert_equal(dist.ppf([0, 1], *shapes), (a-1, b))
+    npt.assert_equal(dist.isf([1, 0], *shapes), (a-1, b))
+    npt.assert_equal(dist.interval(1, *shapes), (a-1, b))
+
+
+@pytest.mark.xfail_on_32bit("Sensible to machine precision")
+def test_rv_sample():
+    # Thoroughly test rv_sample and check that gh-3758 is resolved
+
+    # Generate a random discrete distribution
+    rng = np.random.default_rng(98430143469)
+    xk = np.sort(rng.random(10) * 10)
+    pk = rng.random(10)
+    pk /= np.sum(pk)
+    dist = stats.rv_discrete(values=(xk, pk))
+
+    # Generate points to the left and right of xk
+    xk_left = (np.array([0] + xk[:-1].tolist()) + xk)/2
+    xk_right = (np.array(xk[1:].tolist() + [xk[-1]+1]) + xk)/2
+
+    # Generate points to the left and right of cdf
+    cdf2 = np.cumsum(pk)
+    cdf2_left = (np.array([0] + cdf2[:-1].tolist()) + cdf2)/2
+    cdf2_right = (np.array(cdf2[1:].tolist() + [1]) + cdf2)/2
+
+    # support - leftmost and rightmost xk
+    a, b = dist.support()
+    assert_allclose(a, xk[0])
+    assert_allclose(b, xk[-1])
+
+    # pmf - supported only on the xk
+    assert_allclose(dist.pmf(xk), pk)
+    assert_allclose(dist.pmf(xk_right), 0)
+    assert_allclose(dist.pmf(xk_left), 0)
+
+    # logpmf is log of the pmf; log(0) = -np.inf
+    with np.errstate(divide='ignore'):
+        assert_allclose(dist.logpmf(xk), np.log(pk))
+        assert_allclose(dist.logpmf(xk_right), -np.inf)
+        assert_allclose(dist.logpmf(xk_left), -np.inf)
+
+    # cdf - the cumulative sum of the pmf
+    assert_allclose(dist.cdf(xk), cdf2)
+    assert_allclose(dist.cdf(xk_right), cdf2)
+    assert_allclose(dist.cdf(xk_left), [0]+cdf2[:-1].tolist())
+
+    with np.errstate(divide='ignore'):
+        assert_allclose(dist.logcdf(xk), np.log(dist.cdf(xk)),
+                        atol=1e-15)
+        assert_allclose(dist.logcdf(xk_right), np.log(dist.cdf(xk_right)),
+                        atol=1e-15)
+        assert_allclose(dist.logcdf(xk_left), np.log(dist.cdf(xk_left)),
+                        atol=1e-15)
+
+    # sf is 1-cdf
+    assert_allclose(dist.sf(xk), 1-dist.cdf(xk))
+    assert_allclose(dist.sf(xk_right), 1-dist.cdf(xk_right))
+    assert_allclose(dist.sf(xk_left), 1-dist.cdf(xk_left))
+
+    with np.errstate(divide='ignore'):
+        assert_allclose(dist.logsf(xk), np.log(dist.sf(xk)),
+                        atol=1e-15)
+        assert_allclose(dist.logsf(xk_right), np.log(dist.sf(xk_right)),
+                        atol=1e-15)
+        assert_allclose(dist.logsf(xk_left), np.log(dist.sf(xk_left)),
+                        atol=1e-15)
+
+    # ppf
+    assert_allclose(dist.ppf(cdf2), xk)
+    assert_allclose(dist.ppf(cdf2_left), xk)
+    assert_allclose(dist.ppf(cdf2_right)[:-1], xk[1:])
+    assert_allclose(dist.ppf(0), a - 1)
+    assert_allclose(dist.ppf(1), b)
+
+    # isf
+    sf2 = dist.sf(xk)
+    assert_allclose(dist.isf(sf2), xk)
+    assert_allclose(dist.isf(1-cdf2_left), dist.ppf(cdf2_left))
+    assert_allclose(dist.isf(1-cdf2_right), dist.ppf(cdf2_right))
+    assert_allclose(dist.isf(0), b)
+    assert_allclose(dist.isf(1), a - 1)
+
+    # interval is (ppf(alpha/2), isf(alpha/2))
+    ps = np.linspace(0.01, 0.99, 10)
+    int2 = dist.ppf(ps/2), dist.isf(ps/2)
+    assert_allclose(dist.interval(1-ps), int2)
+    assert_allclose(dist.interval(0), dist.median())
+    assert_allclose(dist.interval(1), (a-1, b))
+
+    # median is simply ppf(0.5)
+    med2 = dist.ppf(0.5)
+    assert_allclose(dist.median(), med2)
+
+    # all four stats (mean, var, skew, and kurtosis) from the definitions
+    mean2 = np.sum(xk*pk)
+    var2 = np.sum((xk - mean2)**2 * pk)
+    skew2 = np.sum((xk - mean2)**3 * pk) / var2**(3/2)
+    kurt2 = np.sum((xk - mean2)**4 * pk) / var2**2 - 3
+    assert_allclose(dist.mean(), mean2)
+    assert_allclose(dist.std(), np.sqrt(var2))
+    assert_allclose(dist.var(), var2)
+    assert_allclose(dist.stats(moments='mvsk'), (mean2, var2, skew2, kurt2))
+
+    # noncentral moment against definition
+    mom3 = np.sum((xk**3) * pk)
+    assert_allclose(dist.moment(3), mom3)
+
+    # expect - check against moments
+    assert_allclose(dist.expect(lambda x: 1), 1)
+    assert_allclose(dist.expect(), mean2)
+    assert_allclose(dist.expect(lambda x: x**3), mom3)
+
+    # entropy is the negative of the expected value of log(p)
+    with np.errstate(divide='ignore'):
+        assert_allclose(-dist.expect(lambda x: dist.logpmf(x)), dist.entropy())
+
+    # RVS is just ppf of uniform random variates
+    rng = np.random.default_rng(98430143469)
+    rvs = dist.rvs(size=100, random_state=rng)
+    rng = np.random.default_rng(98430143469)
+    rvs0 = dist.ppf(rng.random(size=100))
+    assert_allclose(rvs, rvs0)
+
+def test__pmf_float_input():
+    # gh-21272
+    # test that `rvs()` can be computed when `_pmf` requires float input
+
+    class rv_exponential(stats.rv_discrete):
+        def _pmf(self, i):
+            return (2/3)*3**(1 - i)
+
+    rv = rv_exponential(a=0.0, b=float('inf'))
+    rvs = rv.rvs(random_state=42)  # should not crash due to integer input to `_pmf`
+    assert_allclose(rvs, 0)
+
+
+def test_gh18919_ppf_array_args():
+    # gh-18919 reported incorrect results for ppf and isf of discrete distributions when
+    # arguments were arrays and first argument (`q`) had elements at the boundaries of
+    # the support.
+    q = [[0.5, 1.0, 0.5],
+         [1.0, 0.5, 1.0],
+         [0.5, 1.0, 0.5]]
+
+    n = [[45, 46, 47],
+         [48, 49, 50],
+         [51, 52, 53]]
+
+    p = 0.5
+
+    ref = _ufuncs._binom_ppf(q, n, p)
+    res = stats.binom.ppf(q, n, p)
+    np.testing.assert_allclose(res, ref)
+
+@pytest.mark.parametrize("dist", [stats.binom, stats.boltzmann])
+def test_gh18919_ppf_isf_array_args2(dist):
+    # a more general version of the test above. Requires that arguments are broadcasted
+    # by the infrastructure.
+    rng = np.random.default_rng(34873457824358729823)
+    q = rng.random(size=(30, 1, 1, 1))
+    n = rng.integers(10, 30, size=(10, 1, 1))
+    p = rng.random(size=(4, 1))
+    loc = rng.integers(5, size=(3,))
+
+    q[rng.random(size=30) > 0.7] = 0
+    q[rng.random(size=30) > 0.7] = 1
+
+    args = (q, n, p) if dist == stats.binom else (q, p, n)
+
+    res = dist.ppf(*args, loc=loc)
+    ref = np.vectorize(dist.ppf)(*args) + loc
+    np.testing.assert_allclose(res, ref)
+
+    res = dist.isf(*args, loc=loc)
+    ref = np.vectorize(dist.isf)(*args) + loc
+    np.testing.assert_allclose(res, ref)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/test_discrete_distns.py b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_discrete_distns.py
new file mode 100644
index 0000000000000000000000000000000000000000..8ba8da84e2dca928426a3b5283d85f5cf29be07d
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_discrete_distns.py
@@ -0,0 +1,747 @@
+import pytest
+import itertools
+import warnings
+
+from scipy import stats
+from scipy.stats import (betabinom, betanbinom, hypergeom, nhypergeom,
+                         bernoulli, boltzmann, skellam, zipf, zipfian, binom,
+                         nbinom, nchypergeom_fisher, nchypergeom_wallenius,
+                         randint, poisson_binom)
+
+import numpy as np
+from numpy.testing import (
+    assert_almost_equal, assert_equal, assert_allclose
+)
+from scipy.special import binom as special_binom
+from scipy.optimize import root_scalar
+from scipy.integrate import quad
+
+
+# The expected values were computed with Wolfram Alpha, using
+# the expression CDF[HypergeometricDistribution[N, n, M], k].
+@pytest.mark.parametrize('k, M, n, N, expected, rtol',
+                         [(3, 10, 4, 5,
+                           0.9761904761904762, 1e-15),
+                          (107, 10000, 3000, 215,
+                           0.9999999997226765, 1e-15),
+                          (10, 10000, 3000, 215,
+                           2.681682217692179e-21, 5e-11)])
+def test_hypergeom_cdf(k, M, n, N, expected, rtol):
+    p = hypergeom.cdf(k, M, n, N)
+    assert_allclose(p, expected, rtol=rtol)
+
+
+# The expected values were computed with Wolfram Alpha, using
+# the expression SurvivalFunction[HypergeometricDistribution[N, n, M], k].
+@pytest.mark.parametrize('k, M, n, N, expected, rtol',
+                         [(25, 10000, 3000, 215,
+                           0.9999999999052958, 1e-15),
+                          (125, 10000, 3000, 215,
+                           1.4416781705752128e-18, 5e-11)])
+def test_hypergeom_sf(k, M, n, N, expected, rtol):
+    p = hypergeom.sf(k, M, n, N)
+    assert_allclose(p, expected, rtol=rtol)
+
+
+def test_hypergeom_logpmf():
+    # symmetries test
+    # f(k,N,K,n) = f(n-k,N,N-K,n) = f(K-k,N,K,N-n) = f(k,N,n,K)
+    k = 5
+    N = 50
+    K = 10
+    n = 5
+    logpmf1 = hypergeom.logpmf(k, N, K, n)
+    logpmf2 = hypergeom.logpmf(n - k, N, N - K, n)
+    logpmf3 = hypergeom.logpmf(K - k, N, K, N - n)
+    logpmf4 = hypergeom.logpmf(k, N, n, K)
+    assert_almost_equal(logpmf1, logpmf2, decimal=12)
+    assert_almost_equal(logpmf1, logpmf3, decimal=12)
+    assert_almost_equal(logpmf1, logpmf4, decimal=12)
+
+    # test related distribution
+    # Bernoulli distribution if n = 1
+    k = 1
+    N = 10
+    K = 7
+    n = 1
+    hypergeom_logpmf = hypergeom.logpmf(k, N, K, n)
+    bernoulli_logpmf = bernoulli.logpmf(k, K/N)
+    assert_almost_equal(hypergeom_logpmf, bernoulli_logpmf, decimal=12)
+
+
+def test_nhypergeom_pmf():
+    # test with hypergeom
+    M, n, r = 45, 13, 8
+    k = 6
+    NHG = nhypergeom.pmf(k, M, n, r)
+    HG = hypergeom.pmf(k, M, n, k+r-1) * (M - n - (r-1)) / (M - (k+r-1))
+    assert_allclose(HG, NHG, rtol=1e-10)
+
+
+def test_nhypergeom_pmfcdf():
+    # test pmf and cdf with arbitrary values.
+    M = 8
+    n = 3
+    r = 4
+    support = np.arange(n+1)
+    pmf = nhypergeom.pmf(support, M, n, r)
+    cdf = nhypergeom.cdf(support, M, n, r)
+    assert_allclose(pmf, [1/14, 3/14, 5/14, 5/14], rtol=1e-13)
+    assert_allclose(cdf, [1/14, 4/14, 9/14, 1.0], rtol=1e-13)
+
+
+def test_nhypergeom_r0():
+    # test with `r = 0`.
+    M = 10
+    n = 3
+    r = 0
+    pmf = nhypergeom.pmf([[0, 1, 2, 0], [1, 2, 0, 3]], M, n, r)
+    assert_allclose(pmf, [[1, 0, 0, 1], [0, 0, 1, 0]], rtol=1e-13)
+
+
+def test_nhypergeom_rvs_shape():
+    # Check that when given a size with more dimensions than the
+    # dimensions of the broadcast parameters, rvs returns an array
+    # with the correct shape.
+    x = nhypergeom.rvs(22, [7, 8, 9], [[12], [13]], size=(5, 1, 2, 3))
+    assert x.shape == (5, 1, 2, 3)
+
+
+def test_nhypergeom_accuracy():
+    # Check that nhypergeom.rvs post-gh-13431 gives the same values as
+    # inverse transform sampling
+    rng = np.random.RandomState(0)
+    x = nhypergeom.rvs(22, 7, 11, size=100, random_state=rng)
+    rng = np.random.RandomState(0)
+    p = rng.uniform(size=100)
+    y = nhypergeom.ppf(p, 22, 7, 11)
+    assert_equal(x, y)
+
+
+def test_boltzmann_upper_bound():
+    k = np.arange(-3, 5)
+
+    N = 1
+    p = boltzmann.pmf(k, 0.123, N)
+    expected = k == 0
+    assert_equal(p, expected)
+
+    lam = np.log(2)
+    N = 3
+    p = boltzmann.pmf(k, lam, N)
+    expected = [0, 0, 0, 4/7, 2/7, 1/7, 0, 0]
+    assert_allclose(p, expected, rtol=1e-13)
+
+    c = boltzmann.cdf(k, lam, N)
+    expected = [0, 0, 0, 4/7, 6/7, 1, 1, 1]
+    assert_allclose(c, expected, rtol=1e-13)
+
+
+def test_betabinom_a_and_b_unity():
+    # test limiting case that betabinom(n, 1, 1) is a discrete uniform
+    # distribution from 0 to n
+    n = 20
+    k = np.arange(n + 1)
+    p = betabinom(n, 1, 1).pmf(k)
+    expected = np.repeat(1 / (n + 1), n + 1)
+    assert_almost_equal(p, expected)
+
+
+@pytest.mark.parametrize('dtypes', list(itertools.product(*[(int, float)]*3)))
+def test_betabinom_stats_a_and_b_integers_gh18026(dtypes):
+    # gh-18026 reported that `betabinom` kurtosis calculation fails when some
+    # parameters are integers. Check that this is resolved.
+    n_type, a_type, b_type = dtypes
+    n, a, b = n_type(10), a_type(2), b_type(3)
+    assert_allclose(betabinom.stats(n, a, b, moments='k'), -0.6904761904761907)
+
+
+def test_betabinom_bernoulli():
+    # test limiting case that betabinom(1, a, b) = bernoulli(a / (a + b))
+    a = 2.3
+    b = 0.63
+    k = np.arange(2)
+    p = betabinom(1, a, b).pmf(k)
+    expected = bernoulli(a / (a + b)).pmf(k)
+    assert_almost_equal(p, expected)
+
+
+def test_issue_10317():
+    alpha, n, p = 0.9, 10, 1
+    assert_equal(nbinom.interval(confidence=alpha, n=n, p=p), (0, 0))
+
+
+def test_issue_11134():
+    alpha, n, p = 0.95, 10, 0
+    assert_equal(binom.interval(confidence=alpha, n=n, p=p), (0, 0))
+
+
+def test_issue_7406():
+    rng = np.random.default_rng(4763112764)
+    assert_equal(binom.ppf(rng.random(10), 0, 0.5), 0)
+
+    # Also check that endpoints (q=0, q=1) are correct
+    assert_equal(binom.ppf(0, 0, 0.5), -1)
+    assert_equal(binom.ppf(1, 0, 0.5), 0)
+
+
+def test_issue_5122():
+    rng = np.random.default_rng(8312492117)
+    p = 0
+    n = rng.integers(100, size=10)
+
+    x = 0
+    ppf = binom.ppf(x, n, p)
+    assert_equal(ppf, -1)
+
+    x = np.linspace(0.01, 0.99, 10)
+    ppf = binom.ppf(x, n, p)
+    assert_equal(ppf, 0)
+
+    x = 1
+    ppf = binom.ppf(x, n, p)
+    assert_equal(ppf, n)
+
+
+def test_issue_1603():
+    assert_equal(binom(1000, np.logspace(-3, -100)).ppf(0.01), 0)
+
+
+def test_issue_5503():
+    p = 0.5
+    x = np.logspace(3, 14, 12)
+    assert_allclose(binom.cdf(x, 2*x, p), 0.5, atol=1e-2)
+
+
+@pytest.mark.parametrize('x, n, p, cdf_desired', [
+    (300, 1000, 3/10, 0.51559351981411995636),
+    (3000, 10000, 3/10, 0.50493298381929698016),
+    (30000, 100000, 3/10, 0.50156000591726422864),
+    (300000, 1000000, 3/10, 0.50049331906666960038),
+    (3000000, 10000000, 3/10, 0.50015600124585261196),
+    (30000000, 100000000, 3/10, 0.50004933192735230102),
+    (30010000, 100000000, 3/10, 0.98545384016570790717),
+    (29990000, 100000000, 3/10, 0.01455017177985268670),
+    (29950000, 100000000, 3/10, 5.02250963487432024943e-28),
+    (300_000_000, 1_000_000_000, 3/10, 0.50001560012523938),
+    (3_000_000_000, 10_000_000_000, 3/10, 0.50000493319275)
+])
+def test_issue_5503pt2(x, n, p, cdf_desired):
+    assert_allclose(binom.cdf(x, n, p), cdf_desired)
+
+
+def test_issue_5503pt3():
+    # From Wolfram Alpha: CDF[BinomialDistribution[1e12, 1e-12], 2]
+    assert_allclose(binom.cdf(2, 10**12, 10**-12), 0.91969860292869777384)
+
+
+def test_issue_6682():
+    # Reference value from R:
+    # options(digits=16)
+    # print(pnbinom(250, 50, 32/63, lower.tail=FALSE))
+    assert_allclose(nbinom.sf(250, 50, 32./63.), 1.460458510976452e-35)
+
+
+def test_issue_19747():
+    # test that negative k does not raise an error in nbinom.logcdf
+    result = nbinom.logcdf([5, -1, 1], 5, 0.5)
+    reference = [-0.47313352, -np.inf, -2.21297293]
+    assert_allclose(result, reference)
+
+
+def test_boost_divide_by_zero_issue_15101():
+    n = 1000
+    p = 0.01
+    k = 996
+    assert_allclose(binom.pmf(k, n, p), 0.0)
+
+
+def test_skellam_gh11474():
+    # test issue reported in gh-11474 caused by `cdfchn`
+    mu = [1, 10, 100, 1000, 5000, 5050, 5100, 5250, 6000]
+    cdf = skellam.cdf(0, mu, mu)
+    # generated in R
+    # library(skellam)
+    # options(digits = 16)
+    # mu = c(1, 10, 100, 1000, 5000, 5050, 5100, 5250, 6000)
+    # pskellam(0, mu, mu, TRUE)
+    cdf_expected = [0.6542541612768356, 0.5448901559424127, 0.5141135799745580,
+                    0.5044605891382528, 0.5019947363350450, 0.5019848365953181,
+                    0.5019750827993392, 0.5019466621805060, 0.5018209330219539]
+    assert_allclose(cdf, cdf_expected)
+
+
+class TestZipfian:
+    def test_zipfian_asymptotic(self):
+        # test limiting case that zipfian(a, n) -> zipf(a) as n-> oo
+        a = 6.5
+        N = 10000000
+        k = np.arange(1, 21)
+        assert_allclose(zipfian.pmf(k, a, N), zipf.pmf(k, a))
+        assert_allclose(zipfian.cdf(k, a, N), zipf.cdf(k, a))
+        assert_allclose(zipfian.sf(k, a, N), zipf.sf(k, a))
+        assert_allclose(zipfian.stats(a, N, moments='msvk'),
+                        zipf.stats(a, moments='msvk'))
+
+    def test_zipfian_continuity(self):
+        # test that zipfian(0.999999, n) ~ zipfian(1.000001, n)
+        # (a = 1 switches between methods of calculating harmonic sum)
+        alt1, agt1 = 0.99999999, 1.00000001
+        N = 30
+        k = np.arange(1, N + 1)
+        assert_allclose(zipfian.pmf(k, alt1, N), zipfian.pmf(k, agt1, N),
+                        rtol=5e-7)
+        assert_allclose(zipfian.cdf(k, alt1, N), zipfian.cdf(k, agt1, N),
+                        rtol=5e-7)
+        assert_allclose(zipfian.sf(k, alt1, N), zipfian.sf(k, agt1, N),
+                        rtol=5e-7)
+        assert_allclose(zipfian.stats(alt1, N, moments='msvk'),
+                        zipfian.stats(agt1, N, moments='msvk'), rtol=5e-7)
+
+    def test_zipfian_R(self):
+        # test against R VGAM package
+        # library(VGAM)
+        # k <- c(13, 16,  1,  4,  4,  8, 10, 19,  5,  7)
+        # a <- c(1.56712977, 3.72656295, 5.77665117, 9.12168729, 5.79977172,
+        #        4.92784796, 9.36078764, 4.3739616 , 7.48171872, 4.6824154)
+        # n <- c(70, 80, 48, 65, 83, 89, 50, 30, 20, 20)
+        # pmf <- dzipf(k, N = n, shape = a)
+        # cdf <- pzipf(k, N = n, shape = a)
+        # print(pmf)
+        # print(cdf)
+        rng = np.random.RandomState(0)
+        k = rng.randint(1, 20, size=10)
+        a = rng.rand(10)*10 + 1
+        n = rng.randint(1, 100, size=10)
+        pmf = [8.076972e-03, 2.950214e-05, 9.799333e-01, 3.216601e-06,
+               3.158895e-04, 3.412497e-05, 4.350472e-10, 2.405773e-06,
+               5.860662e-06, 1.053948e-04]
+        cdf = [0.8964133, 0.9998666, 0.9799333, 0.9999995, 0.9998584,
+               0.9999458, 1.0000000, 0.9999920, 0.9999977, 0.9998498]
+        # skip the first point; zipUC is not accurate for low a, n
+        assert_allclose(zipfian.pmf(k, a, n)[1:], pmf[1:], rtol=1e-6)
+        assert_allclose(zipfian.cdf(k, a, n)[1:], cdf[1:], rtol=5e-5)
+
+    rng = np.random.RandomState(0)
+    naive_tests = np.vstack((np.logspace(-2, 1, 10),
+                             rng.randint(2, 40, 10))).T
+
+    @pytest.mark.parametrize("a, n", list(naive_tests))
+    def test_zipfian_naive(self, a, n):
+        # test against bare-bones implementation
+
+        @np.vectorize
+        def Hns(n, s):
+            """Naive implementation of harmonic sum"""
+            return (1/np.arange(1, n+1)**s).sum()
+
+        @np.vectorize
+        def pzip(k, a, n):
+            """Naive implementation of zipfian pmf"""
+            if k < 1 or k > n:
+                return 0.
+            else:
+                return 1 / k**a / Hns(n, a)
+
+        k = np.arange(n+1)
+        pmf = pzip(k, a, n)
+        cdf = np.cumsum(pmf)
+        mean = np.average(k, weights=pmf)
+        var = np.average((k - mean)**2, weights=pmf)
+        std = var**0.5
+        skew = np.average(((k-mean)/std)**3, weights=pmf)
+        kurtosis = np.average(((k-mean)/std)**4, weights=pmf) - 3
+        assert_allclose(zipfian.pmf(k, a, n), pmf)
+        assert_allclose(zipfian.cdf(k, a, n), cdf)
+        assert_allclose(zipfian.stats(a, n, moments="mvsk"),
+                        [mean, var, skew, kurtosis])
+
+    def test_pmf_integer_k(self):
+        k = np.arange(0, 1000)
+        k_int32 = k.astype(np.int32)
+        dist = zipfian(111, 22)
+        pmf = dist.pmf(k)
+        pmf_k_int32 = dist.pmf(k_int32)
+        assert_equal(pmf, pmf_k_int32)
+
+    # Reference values were computed with mpmath.
+    @pytest.mark.parametrize(
+        'k, a, n, ref',
+        [(3, 1 + 1e-12, 10, 0.11380571738244807),
+         (995, 1 + 1e-9, 1000, 0.0001342634472310051)]
+    )
+    def test_pmf_against_mpmath(self, k, a, n, ref):
+        p = zipfian.pmf(k, a, n)
+        assert_allclose(p, ref, 5e-16)
+
+    # Reference values were computed with mpmath.
+    @pytest.mark.parametrize(
+        'k, a, n, ref',
+        [(4990, 1.25, 5000, 5.780138225335147e-05),
+         (9998, 3.5, 10000, 1.775352757966365e-14),
+         (50000, 3.5, 100000, 5.227803621367486e-13),
+         (10, 6.0, 100, 1.523108153557902e-06),
+         (95, 6.0, 100, 5.572438078308601e-12)]
+    )
+    def test_sf_against_mpmath(self, k, a, n, ref):
+        sf = zipfian.sf(k, a, n)
+        assert_allclose(sf, ref, rtol=8e-15)
+
+    # Reference values were computed with mpmath.
+    @pytest.mark.parametrize(
+        'a, n, ref',
+        [(1 + 1e-9, 100, 19.27756356649707),
+         (1 + 1e-7, 100000, 8271.194454731552),
+         (1.001, 3, 1.6360225521183804)]
+    )
+    def test_mean_against_mpmath(self, a, n, ref):
+        m = zipfian.mean(a, n)
+        assert_allclose(m, ref, rtol=8e-15)
+
+    def test_ridiculously_large_n(self):
+        # This should return nan with no errors or warnings.
+        a = 2.5
+        n = 1e100
+        p = zipfian.pmf(10, a, n)
+        assert_equal(p, np.nan)
+
+
+class TestNCH:
+    def setup_method(self):
+        rng = np.random.default_rng(7162434334)
+        shape = (2, 4, 3)
+        max_m = 100
+        m1 = rng.integers(1, max_m, size=shape)  # red balls
+        m2 = rng.integers(1, max_m, size=shape)  # white balls
+        N = m1 + m2  # total balls
+        n = randint.rvs(0, N, size=N.shape, random_state=rng)  # number of draws
+        xl = np.maximum(0, n-m2)  # lower bound of support
+        xu = np.minimum(n, m1)  # upper bound of support
+        x = randint.rvs(xl, xu, size=xl.shape, random_state=rng)
+        odds = rng.random(x.shape)*2
+        self.x, self.N, self.m1, self.n, self.odds = x, N, m1, n, odds
+
+    # test output is more readable when function names (strings) are passed
+    @pytest.mark.parametrize('dist_name',
+                             ['nchypergeom_fisher', 'nchypergeom_wallenius'])
+    def test_nch_hypergeom(self, dist_name):
+        # Both noncentral hypergeometric distributions reduce to the
+        # hypergeometric distribution when odds = 1
+        dists = {'nchypergeom_fisher': nchypergeom_fisher,
+                 'nchypergeom_wallenius': nchypergeom_wallenius}
+        dist = dists[dist_name]
+        x, N, m1, n = self.x, self.N, self.m1, self.n
+        assert_allclose(dist.pmf(x, N, m1, n, odds=1),
+                        hypergeom.pmf(x, N, m1, n))
+
+    def test_nchypergeom_fisher_naive(self):
+        # test against a very simple implementation
+        x, N, m1, n, odds = self.x, self.N, self.m1, self.n, self.odds
+
+        @np.vectorize
+        def pmf_mean_var(x, N, m1, n, w):
+            # simple implementation of nchypergeom_fisher pmf
+            m2 = N - m1
+            xl = np.maximum(0, n-m2)
+            xu = np.minimum(n, m1)
+
+            def f(x):
+                t1 = special_binom(m1, x)
+                t2 = special_binom(m2, n - x)
+                return t1 * t2 * w**x
+
+            def P(k):
+                return sum(f(y)*y**k for y in range(xl, xu + 1))
+
+            P0 = P(0)
+            P1 = P(1)
+            P2 = P(2)
+            pmf = f(x) / P0
+            mean = P1 / P0
+            var = P2 / P0 - (P1 / P0)**2
+            return pmf, mean, var
+
+        pmf, mean, var = pmf_mean_var(x, N, m1, n, odds)
+        assert_allclose(nchypergeom_fisher.pmf(x, N, m1, n, odds), pmf)
+        assert_allclose(nchypergeom_fisher.stats(N, m1, n, odds, moments='m'),
+                        mean)
+        assert_allclose(nchypergeom_fisher.stats(N, m1, n, odds, moments='v'),
+                        var)
+
+    def test_nchypergeom_wallenius_naive(self):
+        # test against a very simple implementation
+
+        rng = np.random.RandomState(2)
+        shape = (2, 4, 3)
+        max_m = 100
+        m1 = rng.randint(1, max_m, size=shape)
+        m2 = rng.randint(1, max_m, size=shape)
+        N = m1 + m2
+        n = randint.rvs(0, N, size=N.shape, random_state=rng)
+        xl = np.maximum(0, n-m2)
+        xu = np.minimum(n, m1)
+        x = randint.rvs(xl, xu, size=xl.shape, random_state=rng)
+        w = rng.rand(*x.shape)*2
+
+        def support(N, m1, n, w):
+            m2 = N - m1
+            xl = np.maximum(0, n-m2)
+            xu = np.minimum(n, m1)
+            return xl, xu
+
+        @np.vectorize
+        def mean(N, m1, n, w):
+            m2 = N - m1
+            xl, xu = support(N, m1, n, w)
+
+            def fun(u):
+                return u/m1 + (1 - (n-u)/m2)**w - 1
+
+            return root_scalar(fun, bracket=(xl, xu)).root
+
+        with warnings.catch_warnings():
+            warnings.filterwarnings("ignore", category=RuntimeWarning,
+                       message="invalid value encountered in mean")
+            assert_allclose(nchypergeom_wallenius.mean(N, m1, n, w),
+                            mean(N, m1, n, w), rtol=2e-2)
+
+        @np.vectorize
+        def variance(N, m1, n, w):
+            m2 = N - m1
+            u = mean(N, m1, n, w)
+            a = u * (m1 - u)
+            b = (n-u)*(u + m2 - n)
+            return N*a*b / ((N-1) * (m1*b + m2*a))
+
+        with warnings.catch_warnings():
+            warnings.filterwarnings("ignore", category=RuntimeWarning,
+                       message="invalid value encountered in mean")
+            assert_allclose(
+                nchypergeom_wallenius.stats(N, m1, n, w, moments='v'),
+                variance(N, m1, n, w),
+                rtol=5e-2
+            )
+
+        @np.vectorize
+        def pmf(x, N, m1, n, w):
+            m2 = N - m1
+            xl, xu = support(N, m1, n, w)
+
+            def integrand(t):
+                D = w*(m1 - x) + (m2 - (n-x))
+                res = (1-t**(w/D))**x * (1-t**(1/D))**(n-x)
+                return res
+
+            def f(x):
+                t1 = special_binom(m1, x)
+                t2 = special_binom(m2, n - x)
+                the_integral = quad(integrand, 0, 1,
+                                    epsrel=1e-16, epsabs=1e-16)
+                return t1 * t2 * the_integral[0]
+
+            return f(x)
+
+        pmf0 = pmf(x, N, m1, n, w)
+        pmf1 = nchypergeom_wallenius.pmf(x, N, m1, n, w)
+
+        atol, rtol = 1e-6, 1e-6
+        i = np.abs(pmf1 - pmf0) < atol + rtol*np.abs(pmf0)
+        assert i.sum() > np.prod(shape) / 2  # works at least half the time
+
+        # for those that fail, discredit the naive implementation
+        for N, m1, n, w in zip(N[~i], m1[~i], n[~i], w[~i]):
+            # get the support
+            m2 = N - m1
+            xl, xu = support(N, m1, n, w)
+            x = np.arange(xl, xu + 1)
+
+            # calculate sum of pmf over the support
+            # the naive implementation is very wrong in these cases
+            assert pmf(x, N, m1, n, w).sum() < .5
+            assert_allclose(nchypergeom_wallenius.pmf(x, N, m1, n, w).sum(), 1)
+
+    def test_wallenius_against_mpmath(self):
+        # precompute data with mpmath since naive implementation above
+        # is not reliable. See source code in gh-13330.
+        M = 50
+        n = 30
+        N = 20
+        odds = 2.25
+        # Expected results, computed with mpmath.
+        sup = np.arange(21)
+        pmf = np.array([3.699003068656875e-20,
+                        5.89398584245431e-17,
+                        2.1594437742911123e-14,
+                        3.221458044649955e-12,
+                        2.4658279241205077e-10,
+                        1.0965862603981212e-08,
+                        3.057890479665704e-07,
+                        5.622818831643761e-06,
+                        7.056482841531681e-05,
+                        0.000618899425358671,
+                        0.003854172932571669,
+                        0.01720592676256026,
+                        0.05528844897093792,
+                        0.12772363313574242,
+                        0.21065898367825722,
+                        0.24465958845359234,
+                        0.1955114898110033,
+                        0.10355390084949237,
+                        0.03414490375225675,
+                        0.006231989845775931,
+                        0.0004715577304677075])
+        mean = 14.808018384813426
+        var = 2.6085975877923717
+
+        # nchypergeom_wallenius.pmf returns 0 for pmf(0) and pmf(1), and pmf(2)
+        # has only three digits of accuracy (~ 2.1511e-14).
+        assert_allclose(nchypergeom_wallenius.pmf(sup, M, n, N, odds), pmf,
+                        rtol=1e-13, atol=1e-13)
+        assert_allclose(nchypergeom_wallenius.mean(M, n, N, odds),
+                        mean, rtol=1e-13)
+        assert_allclose(nchypergeom_wallenius.var(M, n, N, odds),
+                        var, rtol=1e-11)
+
+    @pytest.mark.parametrize('dist_name',
+                             ['nchypergeom_fisher', 'nchypergeom_wallenius'])
+    def test_rvs_shape(self, dist_name):
+        # Check that when given a size with more dimensions than the
+        # dimensions of the broadcast parameters, rvs returns an array
+        # with the correct shape.
+        dists = {'nchypergeom_fisher': nchypergeom_fisher,
+                 'nchypergeom_wallenius': nchypergeom_wallenius}
+        dist = dists[dist_name]
+        x = dist.rvs(50, 30, [[10], [20]], [0.5, 1.0, 2.0], size=(5, 1, 2, 3))
+        assert x.shape == (5, 1, 2, 3)
+
+
+@pytest.mark.parametrize("mu, q, expected",
+                         [[10, 120, -1.240089881791596e-38],
+                          [1500, 0, -86.61466680572661]])
+def test_nbinom_11465(mu, q, expected):
+    # test nbinom.logcdf at extreme tails
+    size = 20
+    n, p = size, size/(size+mu)
+    # In R:
+    # options(digits=16)
+    # pnbinom(mu=10, size=20, q=120, log.p=TRUE)
+    assert_allclose(nbinom.logcdf(q, n, p), expected)
+
+
+def test_gh_17146():
+    # Check that discrete distributions return PMF of zero at non-integral x.
+    # See gh-17146.
+    x = np.linspace(0, 1, 11)
+    p = 0.8
+    pmf = bernoulli(p).pmf(x)
+    i = (x % 1 == 0)
+    assert_allclose(pmf[-1], p)
+    assert_allclose(pmf[0], 1-p)
+    assert_equal(pmf[~i], 0)
+
+
+class TestBetaNBinom:
+    @pytest.mark.parametrize('x, n, a, b, ref',
+                            [[5, 5e6, 5, 20, 1.1520944824139114e-107],
+                            [100, 50, 5, 20, 0.002855762954310226],
+                            [10000, 1000, 5, 20, 1.9648515726019154e-05]])
+    def test_betanbinom_pmf(self, x, n, a, b, ref):
+        # test that PMF stays accurate in the distribution tails
+        # reference values computed with mpmath
+        # from mpmath import mp
+        # mp.dps = 500
+        # def betanbinom_pmf(k, n, a, b):
+        #     k = mp.mpf(k)
+        #     a = mp.mpf(a)
+        #     b = mp.mpf(b)
+        #     n = mp.mpf(n)
+        #     return float(mp.binomial(n + k - mp.one, k)
+        #                  * mp.beta(a + n, b + k) / mp.beta(a, b))
+        assert_allclose(betanbinom.pmf(x, n, a, b), ref, rtol=1e-10)
+
+
+    @pytest.mark.parametrize('n, a, b, ref',
+                            [[10000, 5000, 50, 0.12841520515722202],
+                            [10, 9, 9, 7.9224400871459695],
+                            [100, 1000, 10, 1.5849602176622748]])
+    def test_betanbinom_kurtosis(self, n, a, b, ref):
+        # reference values were computed via mpmath
+        # from mpmath import mp
+        # def kurtosis_betanegbinom(n, a, b):
+        #     n = mp.mpf(n)
+        #     a = mp.mpf(a)
+        #     b = mp.mpf(b)
+        #     four = mp.mpf(4.)
+        #     mean = n * b / (a - mp.one)
+        #     var = (n * b * (n + a - 1.) * (a + b - 1.)
+        #            / ((a - 2.) * (a - 1.)**2.))
+        #     def f(k):
+        #         return (mp.binomial(n + k - mp.one, k)
+        #                 * mp.beta(a + n, b + k) / mp.beta(a, b)
+        #                 * (k - mean)**four)
+        #      fourth_moment = mp.nsum(f, [0, mp.inf])
+        #      return float(fourth_moment/var**2 - 3.)
+        assert_allclose(betanbinom.stats(n, a, b, moments="k"),
+                        ref, rtol=3e-15)
+
+
+class TestZipf:
+    def test_gh20692(self):
+        # test that int32 data for k generates same output as double
+        k = np.arange(0, 1000)
+        k_int32 = k.astype(np.int32)
+        dist = zipf(9)
+        pmf = dist.pmf(k)
+        pmf_k_int32 = dist.pmf(k_int32)
+        assert_equal(pmf, pmf_k_int32)
+
+
+def test_gh20048():
+    # gh-20048 reported an infinite loop in _drv2_ppfsingle
+    # check that the one identified is resolved
+    class test_dist_gen(stats.rv_discrete):
+        def _cdf(self, k):
+            return min(k / 100, 0.99)
+
+    test_dist = test_dist_gen(b=np.inf)
+
+    message = "Arguments that bracket..."
+    with pytest.raises(RuntimeError, match=message):
+        test_dist.ppf(0.999)
+
+
+class TestPoissonBinomial:
+    def test_pmf(self):
+        # Test pmf against R `poisbinom` to confirm that this is indeed the Poisson
+        # binomial distribution. Consistency of other methods and all other behavior
+        # should be covered by generic tests. (If not, please add a generic test.)
+        # Like many other distributions, no special attempt is made to be more
+        # accurate than the usual formulas provide, so we use default tolerances.
+        #
+        # library(poisbinom)
+        # options(digits=16)
+        # k = c(0, 1, 2, 3, 4)
+        # p = c(0.9480654803913988, 0.052428488100509374,
+        #       0.25863527358887417, 0.057764076043633206)
+        # dpoisbinom(k, p)
+        rng = np.random.default_rng(259823598254)
+        n = rng.integers(10)  # 4
+        k = np.arange(n + 1)
+        p = rng.random(n)  #  [0.9480654803913988, 0.052428488100509374,
+                           #   0.25863527358887417, 0.057764076043633206]
+        res = poisson_binom.pmf(k, p)
+        ref = [0.0343763443678060318, 0.6435428452689714307, 0.2936345519235536994,
+               0.0277036647503902354, 0.0007425936892786034]
+        assert_allclose(res, ref)
+
+
+class TestRandInt:
+    def test_gh19759(self):
+        # test zero PMF values within the support reported by gh-19759
+        a = -354
+        max_range = abs(a)
+        all_b_1 = [a + 2 ** 31 + i for i in range(max_range)]
+        res = randint.pmf(325, a, all_b_1)
+        assert (res > 0).all()
+        ref = 1 / (np.asarray(all_b_1, dtype=np.float64) - a)
+        assert_allclose(res, ref)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/test_distributions.py b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_distributions.py
new file mode 100644
index 0000000000000000000000000000000000000000..a355a702807438358bd88c00de026008055dbc51
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_distributions.py
@@ -0,0 +1,10606 @@
+"""
+Test functions for stats module
+"""
+import warnings
+import re
+import sys
+import pickle
+import threading
+from pathlib import Path
+import os
+import json
+import platform
+
+from numpy.testing import (assert_equal, assert_array_equal,
+                           assert_almost_equal, assert_array_almost_equal,
+                           assert_allclose, assert_,
+                           assert_array_less, assert_array_max_ulp)
+import pytest
+from pytest import raises as assert_raises
+
+import numpy as np
+from numpy import typecodes, array
+from numpy.lib.recfunctions import rec_append_fields
+from scipy import special
+from scipy._lib._util import check_random_state
+from scipy.integrate import (IntegrationWarning, quad, trapezoid,
+                             cumulative_trapezoid)
+import scipy.stats as stats
+from scipy.stats._distn_infrastructure import argsreduce
+from scipy.stats._constants import _XMAX
+import scipy.stats.distributions
+
+from scipy.special import xlogy, polygamma, entr
+from scipy.stats._distr_params import distcont, invdistcont
+from .test_discrete_basic import distdiscrete, invdistdiscrete
+from scipy.stats._continuous_distns import FitDataError, _argus_phi
+from scipy.optimize import root, fmin, differential_evolution
+from itertools import product
+
+# python -OO strips docstrings
+DOCSTRINGS_STRIPPED = sys.flags.optimize > 1
+
+# Failing on macOS 11, Intel CPUs. See gh-14901
+MACOS_INTEL = (sys.platform == 'darwin') and (platform.machine() == 'x86_64')
+
+
+# distributions to skip while testing the fix for the support method
+# introduced in gh-13294. These distributions are skipped as they
+# always return a non-nan support for every parametrization.
+skip_test_support_gh13294_regression = ['tukeylambda', 'pearson3']
+
+
+def _assert_hasattr(a, b, msg=None):
+    if msg is None:
+        msg = f'{a} does not have attribute {b}'
+    assert_(hasattr(a, b), msg=msg)
+
+
+def test_api_regression():
+    # https://github.com/scipy/scipy/issues/3802
+    _assert_hasattr(scipy.stats.distributions, 'f_gen')
+
+
+def test_distributions_submodule():
+    actual = set(scipy.stats.distributions.__all__)
+    continuous = [dist[0] for dist in distcont]    # continuous dist names
+    discrete = [dist[0] for dist in distdiscrete]  # discrete dist names
+    other = ['rv_discrete', 'rv_continuous', 'rv_histogram',
+             'entropy']
+    expected = continuous + discrete + other
+
+    # need to remove, e.g.,
+    # <scipy.stats._continuous_distns.trapezoid_gen at 0x1df83bbc688>
+    expected = set(filter(lambda s: not str(s).startswith('<'), expected))
+
+    assert actual == expected
+
+
+class TestVonMises:
+    def setup_method(self):
+        self.rng = np.random.default_rng(6320571663)
+
+    @pytest.mark.parametrize('k', [0.1, 1, 101])
+    @pytest.mark.parametrize('x', [0, 1, np.pi, 10, 100])
+    def test_vonmises_periodic(self, k, x):
+        def check_vonmises_pdf_periodic(k, L, s, x):
+            vm = stats.vonmises(k, loc=L, scale=s)
+            assert_almost_equal(vm.pdf(x), vm.pdf(x % (2 * np.pi * s)))
+
+        def check_vonmises_cdf_periodic(k, L, s, x):
+            vm = stats.vonmises(k, loc=L, scale=s)
+            assert_almost_equal(vm.cdf(x) % 1,
+                                vm.cdf(x % (2 * np.pi * s)) % 1)
+
+        check_vonmises_pdf_periodic(k, 0, 1, x)
+        check_vonmises_pdf_periodic(k, 1, 1, x)
+        check_vonmises_pdf_periodic(k, 0, 10, x)
+
+        check_vonmises_cdf_periodic(k, 0, 1, x)
+        check_vonmises_cdf_periodic(k, 1, 1, x)
+        check_vonmises_cdf_periodic(k, 0, 10, x)
+
+    def test_vonmises_line_support(self):
+        assert_equal(stats.vonmises_line.a, -np.pi)
+        assert_equal(stats.vonmises_line.b, np.pi)
+
+    def test_vonmises_numerical(self):
+        vm = stats.vonmises(800)
+        assert_almost_equal(vm.cdf(0), 0.5)
+
+    # Expected values of the vonmises PDF were computed using
+    # mpmath with 50 digits of precision:
+    #
+    # def vmpdf_mp(x, kappa):
+    #     x = mpmath.mpf(x)
+    #     kappa = mpmath.mpf(kappa)
+    #     num = mpmath.exp(kappa*mpmath.cos(x))
+    #     den = 2 * mpmath.pi * mpmath.besseli(0, kappa)
+    #     return num/den
+
+    @pytest.mark.parametrize('x, kappa, expected_pdf',
+                             [(0.1, 0.01, 0.16074242744907072),
+                              (0.1, 25.0, 1.7515464099118245),
+                              (0.1, 800, 0.2073272544458798),
+                              (2.0, 0.01, 0.15849003875385817),
+                              (2.0, 25.0, 8.356882934278192e-16),
+                              (2.0, 800, 0.0)])
+    def test_vonmises_pdf(self, x, kappa, expected_pdf):
+        pdf = stats.vonmises.pdf(x, kappa)
+        assert_allclose(pdf, expected_pdf, rtol=1e-15)
+
+    # Expected values of the vonmises entropy were computed using
+    # mpmath with 50 digits of precision:
+    #
+    # def vonmises_entropy(kappa):
+    #     kappa = mpmath.mpf(kappa)
+    #     return (-kappa * mpmath.besseli(1, kappa) /
+    #             mpmath.besseli(0, kappa) + mpmath.log(2 * mpmath.pi *
+    #             mpmath.besseli(0, kappa)))
+    # >>> float(vonmises_entropy(kappa))
+
+    @pytest.mark.parametrize('kappa, expected_entropy',
+                             [(1, 1.6274014590199897),
+                              (5, 0.6756431570114528),
+                              (100, -0.8811275441649473),
+                              (1000, -2.03468891852547),
+                              (2000, -2.3813876496587847)])
+    def test_vonmises_entropy(self, kappa, expected_entropy):
+        entropy = stats.vonmises.entropy(kappa)
+        assert_allclose(entropy, expected_entropy, rtol=1e-13)
+
+    def test_vonmises_rvs_gh4598(self):
+        # check that random variates wrap around as discussed in gh-4598
+        seed = 30899520
+        rng1 = np.random.default_rng(seed)
+        rng2 = np.random.default_rng(seed)
+        rng3 = np.random.default_rng(seed)
+        rvs1 = stats.vonmises(1, loc=0, scale=1).rvs(random_state=rng1)
+        rvs2 = stats.vonmises(1, loc=2*np.pi, scale=1).rvs(random_state=rng2)
+        rvs3 = stats.vonmises(1, loc=0,
+                              scale=(2*np.pi/abs(rvs1)+1)).rvs(random_state=rng3)
+        assert_allclose(rvs1, rvs2, atol=1e-15)
+        assert_allclose(rvs1, rvs3, atol=1e-15)
+
+    # Expected values of the vonmises LOGPDF were computed
+    # using wolfram alpha:
+    # kappa * cos(x) - log(2*pi*I0(kappa))
+    @pytest.mark.parametrize('x, kappa, expected_logpdf',
+                             [(0.1, 0.01, -1.8279520246003170),
+                              (0.1, 25.0, 0.5604990605420549),
+                              (0.1, 800, -1.5734567947337514),
+                              (2.0, 0.01, -1.8420635346185686),
+                              (2.0, 25.0, -34.7182759850871489),
+                              (2.0, 800, -1130.4942582548682739)])
+    def test_vonmises_logpdf(self, x, kappa, expected_logpdf):
+        logpdf = stats.vonmises.logpdf(x, kappa)
+        assert_allclose(logpdf, expected_logpdf, rtol=1e-15)
+
+    def test_vonmises_expect(self):
+        """
+        Test that the vonmises expectation values are
+        computed correctly.  This test checks that the
+        numeric integration estimates the correct normalization
+        (1) and mean angle (loc).  These expectations are
+        independent of the chosen 2pi interval.
+        """
+        rng = np.random.default_rng(6762668991392531563)
+
+        loc, kappa, lb = rng.random(3) * 10
+        res = stats.vonmises(loc=loc, kappa=kappa).expect(lambda x: 1)
+        assert_allclose(res, 1)
+        assert np.issubdtype(res.dtype, np.floating)
+
+        bounds = lb, lb + 2 * np.pi
+        res = stats.vonmises(loc=loc, kappa=kappa).expect(lambda x: 1, *bounds)
+        assert_allclose(res, 1)
+        assert np.issubdtype(res.dtype, np.floating)
+
+        bounds = lb, lb + 2 * np.pi
+        res = stats.vonmises(loc=loc, kappa=kappa).expect(lambda x: np.exp(1j*x),
+                                                          *bounds, complex_func=1)
+        assert_allclose(np.angle(res), loc % (2*np.pi))
+        assert np.issubdtype(res.dtype, np.complexfloating)
+
+    @pytest.mark.xslow
+    @pytest.mark.parametrize("rvs_loc", [0, 2])
+    @pytest.mark.parametrize("rvs_shape", [1, 100, 1e8])
+    @pytest.mark.parametrize('fix_loc', [True, False])
+    @pytest.mark.parametrize('fix_shape', [True, False])
+    def test_fit_MLE_comp_optimizer(self, rvs_loc, rvs_shape,
+                                    fix_loc, fix_shape):
+        if fix_shape and fix_loc:
+            pytest.skip("Nothing to fit.")
+
+        rng = np.random.default_rng(6762668991392531563)
+        data = stats.vonmises.rvs(rvs_shape, size=1000, loc=rvs_loc,
+                                  random_state=rng)
+
+        kwds = {'fscale': 1}
+        if fix_loc:
+            kwds['floc'] = rvs_loc
+        if fix_shape:
+            kwds['f0'] = rvs_shape
+
+        _assert_less_or_close_loglike(stats.vonmises, data,
+                                      stats.vonmises.nnlf, **kwds)
+
+    @pytest.mark.slow
+    def test_vonmises_fit_bad_floc(self):
+        data = [-0.92923506, -0.32498224, 0.13054989, -0.97252014, 2.79658071,
+                -0.89110948, 1.22520295, 1.44398065, 2.49163859, 1.50315096,
+                3.05437696, -2.73126329, -3.06272048, 1.64647173, 1.94509247,
+                -1.14328023, 0.8499056, 2.36714682, -1.6823179, -0.88359996]
+        data = np.asarray(data)
+        loc = -0.5 * np.pi
+        kappa_fit, loc_fit, scale_fit = stats.vonmises.fit(data, floc=loc)
+        assert kappa_fit == np.finfo(float).tiny
+        _assert_less_or_close_loglike(stats.vonmises, data,
+                                      stats.vonmises.nnlf, fscale=1, floc=loc)
+
+    @pytest.mark.parametrize('sign', [-1, 1])
+    def test_vonmises_fit_unwrapped_data(self, sign):
+        rng = np.random.default_rng(6762668991392531563)
+        data = stats.vonmises(loc=sign*0.5*np.pi, kappa=10).rvs(100000,
+                                                                random_state=rng)
+        shifted_data = data + 4*np.pi
+        kappa_fit, loc_fit, scale_fit = stats.vonmises.fit(data)
+        kappa_fit_shifted, loc_fit_shifted, _ = stats.vonmises.fit(shifted_data)
+        assert_allclose(loc_fit, loc_fit_shifted)
+        assert_allclose(kappa_fit, kappa_fit_shifted)
+        assert scale_fit == 1
+        assert -np.pi < loc_fit < np.pi
+
+    def test_vonmises_kappa_0_gh18166(self):
+        # Check that kappa = 0 is supported.
+        dist = stats.vonmises(0)
+        assert_allclose(dist.pdf(0), 1 / (2 * np.pi), rtol=1e-15)
+        assert_allclose(dist.cdf(np.pi/2), 0.75, rtol=1e-15)
+        assert_allclose(dist.sf(-np.pi/2), 0.75, rtol=1e-15)
+        assert_allclose(dist.ppf(0.9), np.pi*0.8, rtol=1e-15)
+        assert_allclose(dist.mean(), 0, atol=1e-15)
+        assert_allclose(dist.expect(), 0, atol=1e-15)
+        assert np.all(np.abs(dist.rvs(size=10, random_state=self.rng)) <= np.pi)
+
+    def test_vonmises_fit_equal_data(self):
+        # When all data are equal, expect kappa = 1e16.
+        kappa, loc, scale = stats.vonmises.fit([0])
+        assert kappa == 1e16 and loc == 0 and scale == 1
+
+    def test_vonmises_fit_bounds(self):
+        # For certain input data, the root bracket is violated numerically.
+        # Test that this situation is handled.  The input data below are
+        # crafted to trigger the bound violation for the current choice of
+        # bounds and the specific way the bounds and the objective function
+        # are computed.
+
+        # Test that no exception is raised when the lower bound is violated.
+        scipy.stats.vonmises.fit([0, 3.7e-08], floc=0)
+
+        # Test that no exception is raised when the upper bound is violated.
+        scipy.stats.vonmises.fit([np.pi/2*(1-4.86e-9)], floc=0)
+
+
+def _assert_less_or_close_loglike(dist, data, func=None, maybe_identical=False,
+                                  **kwds):
+    """
+    This utility function checks that the negative log-likelihood function
+    (or `func`) of the result computed using dist.fit() is less than or equal
+    to the result computed using the generic fit method.  Because of
+    normal numerical imprecision, the "equality" check is made using
+    `np.allclose` with a relative tolerance of 1e-15.
+    """
+    if func is None:
+        func = dist.nnlf
+
+    mle_analytical = dist.fit(data, **kwds)
+    numerical_opt = super(type(dist), dist).fit(data, **kwds)
+
+    # Sanity check that the analytical MLE is actually executed.
+    # Due to floating point arithmetic, the generic MLE is unlikely
+    # to produce the exact same result as the analytical MLE.
+    if not maybe_identical:
+        assert np.any(mle_analytical != numerical_opt)
+
+    ll_mle_analytical = func(mle_analytical, data)
+    ll_numerical_opt = func(numerical_opt, data)
+    assert (ll_mle_analytical <= ll_numerical_opt or
+            np.allclose(ll_mle_analytical, ll_numerical_opt, rtol=1e-15))
+
+    # Ideally we'd check that shapes are correctly fixed, too, but that is
+    # complicated by the many ways of fixing them (e.g. f0, fix_a, fa).
+    if 'floc' in kwds:
+        assert mle_analytical[-2] == kwds['floc']
+    if 'fscale' in kwds:
+        assert mle_analytical[-1] == kwds['fscale']
+
+
+def assert_fit_warnings(dist):
+    param = ['floc', 'fscale']
+    if dist.shapes:
+        nshapes = len(dist.shapes.split(","))
+        param += ['f0', 'f1', 'f2'][:nshapes]
+    all_fixed = dict(zip(param, np.arange(len(param))))
+    data = [1, 2, 3]
+    with pytest.raises(RuntimeError,
+                       match="All parameters fixed. There is nothing "
+                       "to optimize."):
+        dist.fit(data, **all_fixed)
+    with pytest.raises(ValueError,
+                       match="The data contains non-finite values"):
+        dist.fit([np.nan])
+    with pytest.raises(ValueError,
+                       match="The data contains non-finite values"):
+        dist.fit([np.inf])
+    with pytest.raises(TypeError, match="Unknown keyword arguments:"):
+        dist.fit(data, extra_keyword=2)
+    with pytest.raises(TypeError, match="Too many positional arguments."):
+        dist.fit(data, *[1]*(len(param) - 1))
+
+
+@pytest.mark.parametrize('dist',
+                         ['alpha', 'betaprime',
+                          'fatiguelife', 'invgamma', 'invgauss', 'invweibull',
+                          'johnsonsb', 'levy', 'levy_l', 'lognorm', 'gibrat',
+                          'powerlognorm', 'rayleigh', 'wald'])
+def test_support(dist):
+    """gh-6235"""
+    dct = dict(distcont)
+    args = dct[dist]
+
+    dist = getattr(stats, dist)
+
+    assert_almost_equal(dist.pdf(dist.a, *args), 0)
+    assert_equal(dist.logpdf(dist.a, *args), -np.inf)
+    assert_almost_equal(dist.pdf(dist.b, *args), 0)
+    assert_equal(dist.logpdf(dist.b, *args), -np.inf)
+
+
+class TestRandInt:
+    def setup_method(self):
+        self.rng = np.random.default_rng(8826485737)
+
+    def test_rvs(self):
+        vals = stats.randint.rvs(5, 30, size=100, random_state=self.rng)
+        assert_(np.all(vals < 30) & np.all(vals >= 5))
+        assert_(len(vals) == 100)
+        vals = stats.randint.rvs(5, 30, size=(2, 50), random_state=self.rng)
+        assert_(np.shape(vals) == (2, 50))
+        assert_(vals.dtype.char in typecodes['AllInteger'])
+        val = stats.randint.rvs(15, 46, random_state=self.rng)
+        assert_((val >= 15) & (val < 46))
+        assert_(isinstance(val, np.ScalarType), msg=repr(type(val)))
+        val = stats.randint(15, 46).rvs(3, random_state=self.rng)
+        assert_(val.dtype.char in typecodes['AllInteger'])
+
+    def test_pdf(self):
+        k = np.r_[0:36]
+        out = np.where((k >= 5) & (k < 30), 1.0/(30-5), 0)
+        vals = stats.randint.pmf(k, 5, 30)
+        assert_array_almost_equal(vals, out)
+
+    def test_cdf(self):
+        x = np.linspace(0, 36, 100)
+        k = np.floor(x)
+        out = np.select([k >= 30, k >= 5], [1.0, (k-5.0+1)/(30-5.0)], 0)
+        vals = stats.randint.cdf(x, 5, 30)
+        assert_array_almost_equal(vals, out, decimal=12)
+
+
+class TestBinom:
+    def setup_method(self):
+        self.rng = np.random.default_rng(1778595878)
+
+    def test_rvs(self):
+        vals = stats.binom.rvs(10, 0.75, size=(2, 50), random_state=self.rng)
+        assert_(np.all(vals >= 0) & np.all(vals <= 10))
+        assert_(np.shape(vals) == (2, 50))
+        assert_(vals.dtype.char in typecodes['AllInteger'])
+        val = stats.binom.rvs(10, 0.75, random_state=self.rng)
+        assert_(isinstance(val, int))
+        val = stats.binom(10, 0.75).rvs(3, random_state=self.rng)
+        assert_(isinstance(val, np.ndarray))
+        assert_(val.dtype.char in typecodes['AllInteger'])
+
+    def test_pmf(self):
+        # regression test for Ticket #1842
+        vals1 = stats.binom.pmf(100, 100, 1)
+        vals2 = stats.binom.pmf(0, 100, 0)
+        assert_allclose(vals1, 1.0, rtol=1e-15, atol=0)
+        assert_allclose(vals2, 1.0, rtol=1e-15, atol=0)
+
+    def test_entropy(self):
+        # Basic entropy tests.
+        b = stats.binom(2, 0.5)
+        expected_p = np.array([0.25, 0.5, 0.25])
+        expected_h = -sum(xlogy(expected_p, expected_p))
+        h = b.entropy()
+        assert_allclose(h, expected_h)
+
+        b = stats.binom(2, 0.0)
+        h = b.entropy()
+        assert_equal(h, 0.0)
+
+        b = stats.binom(2, 1.0)
+        h = b.entropy()
+        assert_equal(h, 0.0)
+
+    def test_warns_p0(self):
+        # no spurious warnings are generated for p=0; gh-3817
+        with warnings.catch_warnings():
+            warnings.simplefilter("error", RuntimeWarning)
+            assert_equal(stats.binom(n=2, p=0).mean(), 0)
+            assert_equal(stats.binom(n=2, p=0).std(), 0)
+
+    def test_ppf_p1(self):
+        # Check that gh-17388 is resolved: PPF == n when p = 1
+        n = 4
+        assert stats.binom.ppf(q=0.3, n=n, p=1.0) == n
+
+    def test_pmf_poisson(self):
+        # Check that gh-17146 is resolved: binom -> poisson
+        n = 1541096362225563.0
+        p = 1.0477878413173978e-18
+        x = np.arange(3)
+        res = stats.binom.pmf(x, n=n, p=p)
+        ref = stats.poisson.pmf(x, n * p)
+        assert_allclose(res, ref, atol=1e-16)
+
+    def test_pmf_cdf(self):
+        # Check that gh-17809 is resolved: binom.pmf(0) ~ binom.cdf(0)
+        n = 25.0 * 10 ** 21
+        p = 1.0 * 10 ** -21
+        r = 0
+        res = stats.binom.pmf(r, n, p)
+        ref = stats.binom.cdf(r, n, p)
+        assert_allclose(res, ref, atol=1e-16)
+
+    def test_pmf_gh15101(self):
+        # Check that gh-15101 is resolved (no divide warnings when p~1, n~oo)
+        res = stats.binom.pmf(3, 2000, 0.999)
+        assert_allclose(res, 0, atol=1e-16)
+
+
+class TestArcsine:
+
+    def test_endpoints(self):
+        # Regression test for gh-13697.  The following calculation
+        # should not generate a warning.
+        p = stats.arcsine.pdf([0, 1])
+        assert_equal(p, [np.inf, np.inf])
+
+
+class TestBernoulli:
+    def setup_method(self):
+        self.rng = np.random.default_rng(7836792223)
+
+    def test_rvs(self):
+        vals = stats.bernoulli.rvs(0.75, size=(2, 50), random_state=self.rng)
+        assert_(np.all(vals >= 0) & np.all(vals <= 1))
+        assert_(np.shape(vals) == (2, 50))
+        assert_(vals.dtype.char in typecodes['AllInteger'])
+        val = stats.bernoulli.rvs(0.75, random_state=self.rng)
+        assert_(isinstance(val, int))
+        val = stats.bernoulli(0.75).rvs(3, random_state=self.rng)
+        assert_(isinstance(val, np.ndarray))
+        assert_(val.dtype.char in typecodes['AllInteger'])
+
+    def test_entropy(self):
+        # Simple tests of entropy.
+        b = stats.bernoulli(0.25)
+        expected_h = -0.25*np.log(0.25) - 0.75*np.log(0.75)
+        h = b.entropy()
+        assert_allclose(h, expected_h)
+
+        b = stats.bernoulli(0.0)
+        h = b.entropy()
+        assert_equal(h, 0.0)
+
+        b = stats.bernoulli(1.0)
+        h = b.entropy()
+        assert_equal(h, 0.0)
+
+
+class TestBradford:
+    # gh-6216
+    def test_cdf_ppf(self):
+        c = 0.1
+        x = np.logspace(-20, -4)
+        q = stats.bradford.cdf(x, c)
+        xx = stats.bradford.ppf(q, c)
+        assert_allclose(x, xx)
+
+
+class TestCauchy:
+
+    def test_pdf_no_overflow_warning(self):
+        # The argument is large enough that x**2 will overflow to
+        # infinity and 1/(1 + x**2) will be 0.  This should not
+        # trigger a warning.
+        p = stats.cauchy.pdf(1e200)
+        assert p == 0.0
+
+    # Reference values were computed with mpmath.
+    @pytest.mark.parametrize(
+        'x, ref',
+        [(0.0, -1.1447298858494002),
+         (5e-324, -1.1447298858494002),
+         (1e-34, -1.1447298858494002),
+         (2.2e-16, -1.1447298858494002),
+         (2e-8, -1.1447298858494006),
+         (5e-4, -1.144730135849369),
+         (0.1, -1.1546802167025683),
+         (1.5, -2.3233848821910463),
+         (2e18, -85.42408759475494),
+         (1e200, -922.1787670834676),
+         (_XMAX, -1420.7101556726175)])
+    def test_logpdf(self, x, ref):
+        logp = stats.cauchy.logpdf([x, -x])
+        assert_allclose(logp, [ref, ref], rtol=1e-15)
+
+    # Reference values were computed with mpmath.
+    @pytest.mark.parametrize(
+        'x, ref',
+        [(-5e15, 6.366197723675814e-17),
+         (-5, 0.06283295818900118),
+         (-1, 0.25),
+         (0, 0.5),
+         (1, 0.75),
+         (5, 0.9371670418109989),
+         (5e15, 0.9999999999999999)]
+    )
+    @pytest.mark.parametrize(
+        'method, sgn',
+        [(stats.cauchy.cdf, 1),
+         (stats.cauchy.sf, -1)]
+    )
+    def test_cdf_sf(self, x, ref, method, sgn):
+        p = method(sgn*x)
+        assert_allclose(p, ref, rtol=1e-15)
+
+    # Reference values were computed with mpmath.
+    @pytest.mark.parametrize('x, ref',
+                            [(4e250, -7.957747154594767e-252),
+                             (1e25, -3.1830988618379063e-26),
+                             (10.0, -0.03223967552667532),
+                             (0.0, -0.6931471805599453),
+                             (-10.0, -3.4506339556469654),
+                             (-7e45, -106.70696921963678),
+                             (-3e225, -520.3249880981778)])
+    def test_logcdf_logsf(self, x, ref):
+        logcdf = stats.cauchy.logcdf(x)
+        assert_allclose(logcdf, ref, rtol=5e-15)
+        logsf = stats.cauchy.logsf(-x)
+        assert_allclose(logsf, ref, rtol=5e-15)
+
+    # Reference values were computed with mpmath.
+    @pytest.mark.parametrize(
+        'p, ref',
+        [(1e-20, -3.1830988618379067e+19),
+         (1e-9, -318309886.1837906),
+         (0.25, -1.0),
+         (0.50, 0.0),
+         (0.75, 1.0),
+         (0.999999, 318309.88617359026),
+         (0.999999999999, 318316927901.77966)]
+    )
+    @pytest.mark.parametrize(
+        'method, sgn',
+        [(stats.cauchy.ppf, 1),
+         (stats.cauchy.isf, -1)])
+    def test_ppf_isf(self, p, ref, method, sgn):
+        x = sgn*method(p)
+        assert_allclose(x, ref, rtol=1e-15)
+
+
+class TestChi:
+
+    # "Exact" value of chi.sf(10, 4), as computed by Wolfram Alpha with
+    #     1 - CDF[ChiDistribution[4], 10]
+    CHI_SF_10_4 = 9.83662422461598e-21
+    # "Exact" value of chi.mean(df=1000) as computed by Wolfram Alpha with
+    #       Mean[ChiDistribution[1000]]
+    CHI_MEAN_1000 = 31.614871896980
+
+    def test_sf(self):
+        s = stats.chi.sf(10, 4)
+        assert_allclose(s, self.CHI_SF_10_4, rtol=1e-15)
+
+    def test_isf(self):
+        x = stats.chi.isf(self.CHI_SF_10_4, 4)
+        assert_allclose(x, 10, rtol=1e-15)
+
+    def test_logcdf(self):
+        x = 10.0
+        df = 15
+        logcdf = stats.chi.logcdf(x, df)
+        # Reference value computed with mpath.
+        assert_allclose(logcdf, -1.304704343625153e-14, rtol=5e-15)
+
+    def test_logsf(self):
+        x = 0.01
+        df = 15
+        logsf = stats.chi.logsf(x, df)
+        # Reference value computed with mpath.
+        assert_allclose(logsf, -3.936060782678026e-37, rtol=5e-15)
+
+    # reference value for 1e14 was computed via mpmath
+    # from mpmath import mp
+    # mp.dps = 500
+    # df = mp.mpf(1e14)
+    # float(mp.rf(mp.mpf(0.5) * df, mp.mpf(0.5)) * mp.sqrt(2.))
+
+    @pytest.mark.parametrize('df, ref',
+                             [(1e3, CHI_MEAN_1000),
+                              (1e14, 9999999.999999976)])
+    def test_mean(self, df, ref):
+        assert_allclose(stats.chi.mean(df), ref, rtol=1e-12)
+
+    # Entropy references values were computed with the following mpmath code
+    # from mpmath import mp
+    # mp.dps = 50
+    # def chi_entropy_mpmath(df):
+    #     df = mp.mpf(df)
+    #     half_df = 0.5 * df
+    #     entropy = mp.log(mp.gamma(half_df)) + 0.5 * \
+    #               (df - mp.log(2) - (df - mp.one) * mp.digamma(half_df))
+    #     return float(entropy)
+
+    @pytest.mark.parametrize('df, ref',
+                             [(1e-4, -9989.7316027504),
+                              (1, 0.7257913526447274),
+                              (1e3, 1.0721981095025448),
+                              (1e10, 1.0723649429080335),
+                              (1e100, 1.0723649429247002)])
+    def test_entropy(self, df, ref):
+        assert_allclose(stats.chi(df).entropy(), ref, rtol=1e-15)
+
+
+class TestCrystalBall:
+
+    def test_pdf(self):
+        """
+        All values are calculated using the independent implementation of the
+        ROOT framework (see https://root.cern.ch/).
+        Corresponding ROOT code is given in the comments.
+        """
+        X = np.linspace(-5.0, 5.0, 21)[:-1]
+
+        # for (double x = -5.0; x < 5.0; x += 0.5) {
+        #     cout << setprecision(16)
+        #          << ROOT::Math::crystalball_pdf(x, 1.0, 2.0, 1.0)
+        #          << ", ";
+        # }
+        calculated = stats.crystalball.pdf(X, beta=1.0, m=2.0)
+        expected = np.array([0.02028666423671257, 0.02414280702550917,
+                             0.02921279650086611, 0.03606518086526679,
+                             0.04564499453260328, 0.05961795204258388,
+                             0.08114665694685029, 0.1168511860034644,
+                             0.1825799781304131, 0.2656523006609301,
+                             0.3010234935475763, 0.2656523006609301,
+                             0.1825799781304131, 0.09772801991305094,
+                             0.0407390997601359, 0.01322604925508607,
+                             0.003344068947749631, 0.0006584862184997063,
+                             0.0001009821322058648, 1.206059579124873e-05])
+        assert_allclose(expected, calculated, rtol=1e-14)
+
+        # for (double x = -5.0; x < 5.0; x += 0.5) {
+        #     cout << setprecision(16)
+        #          << ROOT::Math::crystalball_pdf(x, 2.0, 3.0, 1.0)
+        #          << ", ";
+        # }
+        calculated = stats.crystalball.pdf(X, beta=2.0, m=3.0)
+        expected = np.array([0.00196480373120913, 0.0027975428126005,
+                             0.004175923965164595, 0.006631212592830816,
+                             0.01145873536041165, 0.022380342500804,
+                             0.05304970074264653, 0.1272596164638828,
+                             0.237752264003024, 0.3459275029304401,
+                             0.3919872148188981, 0.3459275029304401,
+                             0.237752264003024, 0.1272596164638828,
+                             0.05304970074264653, 0.01722271623872227,
+                             0.004354584612458383, 0.0008574685508575863,
+                             0.000131497061187334, 1.570508433595375e-05])
+        assert_allclose(expected, calculated, rtol=1e-14)
+
+        # for (double x = -5.0; x < 5.0; x += 0.5) {
+        #   cout << setprecision(16)
+        #        << ROOT::Math::crystalball_pdf(x, 2.0, 3.0, 2.0, 0.5)
+        #        << ", ";
+        # }
+        calculated = stats.crystalball.pdf(X, beta=2.0, m=3.0, loc=0.5, scale=2.0)
+        expected = np.array([0.007859214924836521, 0.011190171250402,
+                             0.01670369586065838, 0.02652485037132326,
+                             0.04238659020399594, 0.06362980823194138,
+                             0.08973241216601403, 0.118876132001512,
+                             0.1479437366093383, 0.17296375146522,
+                             0.1899635180461471, 0.1959936074094491,
+                             0.1899635180461471, 0.17296375146522,
+                             0.1479437366093383, 0.118876132001512,
+                             0.08973241216601403, 0.06362980823194138,
+                             0.04238659020399594, 0.02652485037132326])
+        assert_allclose(expected, calculated, rtol=1e-14)
+
+    def test_cdf(self):
+        """
+        All values are calculated using the independent implementation of the
+        ROOT framework (see https://root.cern.ch/).
+        Corresponding ROOT code is given in the comments.
+        """
+        X = np.linspace(-5.0, 5.0, 21)[:-1]
+
+        # for (double x = -5.0; x < 5.0; x += 0.5) {
+        #     cout << setprecision(16)
+        #          << ROOT::Math::crystalball_cdf(x, 1.0, 2.0, 1.0)
+        #          << ", ";
+        # }
+        calculated = stats.crystalball.cdf(X, beta=1.0, m=2.0)
+        expected = np.array([0.1217199854202754, 0.1327854386403005,
+                             0.1460639825043305, 0.1622933138937006,
+                             0.1825799781304132, 0.2086628321490436,
+                             0.2434399708405509, 0.292127965008661,
+                             0.3651599562608263, 0.4782542338198316,
+                             0.6227229998727213, 0.7671917659256111,
+                             0.8802860434846165, 0.9495903590367718,
+                             0.9828337969321823, 0.9953144721881936,
+                             0.9989814290402977, 0.9998244687978383,
+                             0.9999761023377818, 0.9999974362721522])
+        assert_allclose(expected, calculated, rtol=1e-13)
+
+        # for (double x = -5.0; x < 5.0; x += 0.5) {
+        #     cout << setprecision(16)
+        #          << ROOT::Math::crystalball_cdf(x, 2.0, 3.0, 1.0)
+        #          << ", ";
+        # }
+        calculated = stats.crystalball.cdf(X, beta=2.0, m=3.0)
+        expected = np.array([0.004420808395220632, 0.005595085625200946,
+                             0.007307866939038177, 0.009946818889246312,
+                             0.01432341920051472, 0.02238034250080412,
+                             0.03978727555698502, 0.08307626432678494,
+                             0.1733230597116304, 0.3205923321191123,
+                             0.508716882020547, 0.6968414319219818,
+                             0.8441107043294638, 0.934357499714309,
+                             0.9776464884841091, 0.9938985925142876,
+                             0.9986736357721329, 0.9997714265214375,
+                             0.9999688809071239, 0.9999966615611068])
+        assert_allclose(expected, calculated, rtol=1e-13)
+
+        # for (double x = -5.0; x < 5.0; x += 0.5) {
+        #     cout << setprecision(16)
+        #          << ROOT::Math::crystalball_cdf(x, 2.0, 3.0, 2.0, 0.5);
+        #          << ", ";
+        # }
+        calculated = stats.crystalball.cdf(X, beta=2.0, m=3.0, loc=0.5, scale=2.0)
+        expected = np.array([0.0176832335808822, 0.02238034250080412,
+                             0.02923146775615237, 0.03978727555698502,
+                             0.05679453901646225, 0.08307626432678494,
+                             0.1212416644828466, 0.1733230597116304,
+                             0.2401101486313661, 0.3205923321191123,
+                             0.4117313791289429, 0.508716882020547,
+                             0.6057023849121512, 0.6968414319219818,
+                             0.7773236154097279, 0.8441107043294638,
+                             0.8961920995582476, 0.934357499714309,
+                             0.9606392250246318, 0.9776464884841091])
+        assert_allclose(expected, calculated, rtol=1e-13)
+
+    # Reference value computed with ROOT, e.g.
+    #     cout << setprecision(16)
+    #          << ROOT::Math::crystalball_cdf_c(12.0, 1.0, 2.0, 1.0)
+    #          << endl;
+    @pytest.mark.parametrize(
+        'x, beta, m, rootref',
+        [(12.0, 1.0, 2.0, 1.340451684048897e-33),
+         (9.0, 4.0, 1.25, 1.12843537145273e-19),
+         (20, 0.1, 1.001, 6.929038716892384e-93),
+         (-4.5, 2.0, 3.0, 0.9944049143747991),
+         (-30.0, 0.5, 5.0, 0.9976994814571858),
+         (-1e50, 1.5, 1.1, 0.9999951099570382)]
+    )
+    def test_sf(self, x, beta, m, rootref):
+        sf = stats.crystalball.sf(x, beta=beta, m=m)
+        assert_allclose(sf, rootref, rtol=1e-13)
+
+    def test_moments(self):
+        """
+        All values are calculated using the pdf formula and the integrate function
+        of Mathematica
+        """
+        # The Last two (alpha, n) pairs test the special case n == alpha**2
+        beta = np.array([2.0, 1.0, 3.0, 2.0, 3.0])
+        m = np.array([3.0, 3.0, 2.0, 4.0, 9.0])
+
+        # The distribution should be correctly normalised
+        expected_0th_moment = np.array([1.0, 1.0, 1.0, 1.0, 1.0])
+        calculated_0th_moment = stats.crystalball._munp(0, beta, m)
+        assert_allclose(expected_0th_moment, calculated_0th_moment, rtol=0.001)
+
+        # calculated using wolframalpha.com
+        # e.g. for beta = 2 and m = 3 we calculate the norm like this:
+        #   integrate exp(-x^2/2) from -2 to infinity +
+        #   integrate (3/2)^3*exp(-2^2/2)*(3/2-2-x)^(-3) from -infinity to -2
+        norm = np.array([2.5511, 3.01873, 2.51065, 2.53983, 2.507410455])
+
+        a = np.array([-0.21992, -3.03265, np.inf, -0.135335, -0.003174])
+        expected_1th_moment = a / norm
+        calculated_1th_moment = stats.crystalball._munp(1, beta, m)
+        assert_allclose(expected_1th_moment, calculated_1th_moment, rtol=0.001)
+
+        a = np.array([np.inf, np.inf, np.inf, 3.2616, 2.519908])
+        expected_2th_moment = a / norm
+        calculated_2th_moment = stats.crystalball._munp(2, beta, m)
+        assert_allclose(expected_2th_moment, calculated_2th_moment, rtol=0.001)
+
+        a = np.array([np.inf, np.inf, np.inf, np.inf, -0.0577668])
+        expected_3th_moment = a / norm
+        calculated_3th_moment = stats.crystalball._munp(3, beta, m)
+        assert_allclose(expected_3th_moment, calculated_3th_moment, rtol=0.001)
+
+        a = np.array([np.inf, np.inf, np.inf, np.inf, 7.78468])
+        expected_4th_moment = a / norm
+        calculated_4th_moment = stats.crystalball._munp(4, beta, m)
+        assert_allclose(expected_4th_moment, calculated_4th_moment, rtol=0.001)
+
+        a = np.array([np.inf, np.inf, np.inf, np.inf, -1.31086])
+        expected_5th_moment = a / norm
+        calculated_5th_moment = stats.crystalball._munp(5, beta, m)
+        assert_allclose(expected_5th_moment, calculated_5th_moment, rtol=0.001)
+
+    def test_entropy(self):
+        # regression test for gh-13602
+        cb = stats.crystalball(2, 3)
+        res1 = cb.entropy()
+        # -20000 and 30 are negative and positive infinity, respectively
+        lo, hi, N = -20000, 30, 200000
+        x = np.linspace(lo, hi, N)
+        res2 = trapezoid(entr(cb.pdf(x)), x)
+        assert_allclose(res1, res2, rtol=1e-7)
+
+
+class TestNBinom:
+    def setup_method(self):
+        self.rng = np.random.default_rng(5861367021)
+
+    def test_rvs(self):
+        vals = stats.nbinom.rvs(10, 0.75, size=(2, 50), random_state=self.rng)
+        assert_(np.all(vals >= 0))
+        assert_(np.shape(vals) == (2, 50))
+        assert_(vals.dtype.char in typecodes['AllInteger'])
+        val = stats.nbinom.rvs(10, 0.75, random_state=self.rng)
+        assert_(isinstance(val, int))
+        val = stats.nbinom(10, 0.75).rvs(3, random_state=self.rng)
+        assert_(isinstance(val, np.ndarray))
+        assert_(val.dtype.char in typecodes['AllInteger'])
+
+    def test_pmf(self):
+        # regression test for ticket 1779
+        assert_allclose(np.exp(stats.nbinom.logpmf(700, 721, 0.52)),
+                        stats.nbinom.pmf(700, 721, 0.52))
+        # logpmf(0,1,1) shouldn't return nan (regression test for gh-4029)
+        val = scipy.stats.nbinom.logpmf(0, 1, 1)
+        assert_equal(val, 0)
+
+    def test_logcdf_gh16159(self):
+        # check that gh16159 is resolved.
+        vals = stats.nbinom.logcdf([0, 5, 0, 5], n=4.8, p=0.45)
+        ref = np.log(stats.nbinom.cdf([0, 5, 0, 5], n=4.8, p=0.45))
+        assert_allclose(vals, ref)
+
+
+class TestGenInvGauss:
+    def setup_method(self):
+        self.rng = np.random.default_rng(6473281180)
+
+    @pytest.mark.slow
+    def test_rvs_with_mode_shift(self):
+        # ratio_unif w/ mode shift
+        gig = stats.geninvgauss(2.3, 1.5)
+        _, p = stats.kstest(gig.rvs(size=1500, random_state=self.rng), gig.cdf)
+        assert_equal(p > 0.05, True)
+
+    @pytest.mark.slow
+    def test_rvs_without_mode_shift(self):
+        # ratio_unif w/o mode shift
+        gig = stats.geninvgauss(0.9, 0.75)
+        _, p = stats.kstest(gig.rvs(size=1500, random_state=self.rng), gig.cdf)
+        assert_equal(p > 0.05, True)
+
+    @pytest.mark.slow
+    def test_rvs_new_method(self):
+        # new algorithm of Hoermann / Leydold
+        gig = stats.geninvgauss(0.1, 0.2)
+        _, p = stats.kstest(gig.rvs(size=1500, random_state=self.rng), gig.cdf)
+        assert_equal(p > 0.05, True)
+
+    @pytest.mark.slow
+    def test_rvs_p_zero(self):
+        def my_ks_check(p, b):
+            gig = stats.geninvgauss(p, b)
+            rvs = gig.rvs(size=1500, random_state=self.rng)
+            return stats.kstest(rvs, gig.cdf)[1] > 0.05
+        # boundary cases when p = 0
+        assert_equal(my_ks_check(0, 0.2), True)  # new algo
+        assert_equal(my_ks_check(0, 0.9), True)  # ratio_unif w/o shift
+        assert_equal(my_ks_check(0, 1.5), True)  # ratio_unif with shift
+
+    def test_rvs_negative_p(self):
+        # if p negative, return inverse
+        assert_equal(
+                stats.geninvgauss(-1.5, 2).rvs(size=10, random_state=1234),
+                1 / stats.geninvgauss(1.5, 2).rvs(size=10, random_state=1234))
+
+    def test_invgauss(self):
+        # test that invgauss is special case
+        ig = stats.geninvgauss.rvs(size=1500, p=-0.5, b=1, random_state=1464878613)
+        assert_equal(stats.kstest(ig, 'invgauss', args=[1])[1] > 0.15, True)
+        # test pdf and cdf
+        mu, x = 100, np.linspace(0.01, 1, 10)
+        pdf_ig = stats.geninvgauss.pdf(x, p=-0.5, b=1 / mu, scale=mu)
+        assert_allclose(pdf_ig, stats.invgauss(mu).pdf(x))
+        cdf_ig = stats.geninvgauss.cdf(x, p=-0.5, b=1 / mu, scale=mu)
+        assert_allclose(cdf_ig, stats.invgauss(mu).cdf(x))
+
+    def test_pdf_R(self):
+        # test against R package GIGrvg
+        # x <- seq(0.01, 5, length.out = 10)
+        # GIGrvg::dgig(x, 0.5, 1, 1)
+        vals_R = np.array([2.081176820e-21, 4.488660034e-01, 3.747774338e-01,
+                           2.693297528e-01, 1.905637275e-01, 1.351476913e-01,
+                           9.636538981e-02, 6.909040154e-02, 4.978006801e-02,
+                           3.602084467e-02])
+        x = np.linspace(0.01, 5, 10)
+        assert_allclose(vals_R, stats.geninvgauss.pdf(x, 0.5, 1))
+
+    def test_pdf_zero(self):
+        # pdf at 0 is 0, needs special treatment to avoid 1/x in pdf
+        assert_equal(stats.geninvgauss.pdf(0, 0.5, 0.5), 0)
+        # if x is large and p is moderate, make sure that pdf does not
+        # overflow because of x**(p-1); exp(-b*x) forces pdf to zero
+        assert_equal(stats.geninvgauss.pdf(2e6, 50, 2), 0)
+
+
+class TestGenHyperbolic:
+
+    def test_pdf_r(self):
+        # test against R package GeneralizedHyperbolic
+        # x <- seq(-10, 10, length.out = 10)
+        # GeneralizedHyperbolic::dghyp(
+        #    x = x, lambda = 2, alpha = 2, beta = 1, delta = 1.5, mu = 0.5
+        # )
+        vals_R = np.array([
+            2.94895678275316e-13, 1.75746848647696e-10, 9.48149804073045e-08,
+            4.17862521692026e-05, 0.0103947630463822, 0.240864958986839,
+            0.162833527161649, 0.0374609592899472, 0.00634894847327781,
+            0.000941920705790324
+            ])
+
+        lmbda, alpha, beta = 2, 2, 1
+        mu, delta = 0.5, 1.5
+        args = (lmbda, alpha*delta, beta*delta)
+
+        gh = stats.genhyperbolic(*args, loc=mu, scale=delta)
+        x = np.linspace(-10, 10, 10)
+
+        assert_allclose(gh.pdf(x), vals_R, atol=0, rtol=1e-13)
+
+    def test_cdf_r(self):
+        # test against R package GeneralizedHyperbolic
+        # q <- seq(-10, 10, length.out = 10)
+        # GeneralizedHyperbolic::pghyp(
+        #   q = q, lambda = 2, alpha = 2, beta = 1, delta = 1.5, mu = 0.5
+        # )
+        vals_R = np.array([
+            1.01881590921421e-13, 6.13697274983578e-11, 3.37504977637992e-08,
+            1.55258698166181e-05, 0.00447005453832497, 0.228935323956347,
+            0.755759458895243, 0.953061062884484, 0.992598013917513,
+            0.998942646586662
+            ])
+
+        lmbda, alpha, beta = 2, 2, 1
+        mu, delta = 0.5, 1.5
+        args = (lmbda, alpha*delta, beta*delta)
+
+        gh = stats.genhyperbolic(*args, loc=mu, scale=delta)
+        x = np.linspace(-10, 10, 10)
+
+        assert_allclose(gh.cdf(x), vals_R, atol=0, rtol=1e-6)
+
+    # The reference values were computed by implementing the PDF with mpmath
+    # and integrating it with mp.quad.  The values were computed with
+    # mp.dps=250, and then again with mp.dps=400 to ensure the full 64 bit
+    # precision was computed.
+    @pytest.mark.parametrize(
+        'x, p, a, b, loc, scale, ref',
+        [(-15, 2, 3, 1.5, 0.5, 1.5, 4.770036428808252e-20),
+         (-15, 10, 1.5, 0.25, 1, 5, 0.03282964575089294),
+         (-15, 10, 1.5, 1.375, 0, 1, 3.3711159600215594e-23),
+         (-15, 0.125, 1.5, 1.49995, 0, 1, 4.729401428898605e-23),
+         (-1, 0.125, 1.5, 1.49995, 0, 1, 0.0003565725914786859),
+         (5, -0.125, 1.5, 1.49995, 0, 1, 0.2600651974023352),
+         (5, -0.125, 1000, 999, 0, 1, 5.923270556517253e-28),
+         (20, -0.125, 1000, 999, 0, 1, 0.23452293711665634),
+         (40, -0.125, 1000, 999, 0, 1, 0.9999648749561968),
+         (60, -0.125, 1000, 999, 0, 1, 0.9999999999975475)]
+    )
+    def test_cdf_mpmath(self, x, p, a, b, loc, scale, ref):
+        cdf = stats.genhyperbolic.cdf(x, p, a, b, loc=loc, scale=scale)
+        assert_allclose(cdf, ref, rtol=5e-12)
+
+    # The reference values were computed by implementing the PDF with mpmath
+    # and integrating it with mp.quad.  The values were computed with
+    # mp.dps=250, and then again with mp.dps=400 to ensure the full 64 bit
+    # precision was computed.
+    @pytest.mark.parametrize(
+        'x, p, a, b, loc, scale, ref',
+        [(0, 1e-6, 12, -1, 0, 1, 0.38520358671350524),
+         (-1, 3, 2.5, 2.375, 1, 3, 0.9999901774267577),
+         (-20, 3, 2.5, 2.375, 1, 3, 1.0),
+         (25, 2, 3, 1.5, 0.5, 1.5, 8.593419916523976e-10),
+         (300, 10, 1.5, 0.25, 1, 5, 6.137415609872158e-24),
+         (60, -0.125, 1000, 999, 0, 1, 2.4524915075944173e-12),
+         (75, -0.125, 1000, 999, 0, 1, 2.9435194886214633e-18)]
+    )
+    def test_sf_mpmath(self, x, p, a, b, loc, scale, ref):
+        sf = stats.genhyperbolic.sf(x, p, a, b, loc=loc, scale=scale)
+        assert_allclose(sf, ref, rtol=5e-12)
+
+    def test_moments_r(self):
+        # test against R package GeneralizedHyperbolic
+        # sapply(1:4,
+        #    function(x) GeneralizedHyperbolic::ghypMom(
+        #        order = x, lambda = 2, alpha = 2,
+        #        beta = 1, delta = 1.5, mu = 0.5,
+        #        momType = 'raw')
+        # )
+
+        vals_R = [2.36848366948115, 8.4739346779246,
+                  37.8870502710066, 205.76608511485]
+
+        lmbda, alpha, beta = 2, 2, 1
+        mu, delta = 0.5, 1.5
+        args = (lmbda, alpha*delta, beta*delta)
+
+        vals_us = [
+            stats.genhyperbolic(*args, loc=mu, scale=delta).moment(i)
+            for i in range(1, 5)
+            ]
+
+        assert_allclose(vals_us, vals_R, atol=0, rtol=1e-13)
+
+    def test_rvs(self):
+        # Kolmogorov-Smirnov test to ensure alignment
+        # of analytical and empirical cdfs
+
+        lmbda, alpha, beta = 2, 2, 1
+        mu, delta = 0.5, 1.5
+        args = (lmbda, alpha*delta, beta*delta)
+
+        gh = stats.genhyperbolic(*args, loc=mu, scale=delta)
+        _, p = stats.kstest(gh.rvs(size=1500, random_state=1234), gh.cdf)
+
+        assert_equal(p > 0.05, True)
+
+    def test_pdf_t(self):
+        # Test Against T-Student with 1 - 30 df
+        df = np.linspace(1, 30, 10)
+
+        # in principle alpha should be zero in practice for big lmbdas
+        # alpha cannot be too small else pdf does not integrate
+        alpha, beta = np.float_power(df, 2)*np.finfo(np.float32).eps, 0
+        mu, delta = 0, np.sqrt(df)
+        args = (-df/2, alpha, beta)
+
+        gh = stats.genhyperbolic(*args, loc=mu, scale=delta)
+        x = np.linspace(gh.ppf(0.01), gh.ppf(0.99), 50)[:, np.newaxis]
+
+        assert_allclose(
+            gh.pdf(x), stats.t.pdf(x, df),
+            atol=0, rtol=1e-6
+            )
+
+    def test_pdf_cauchy(self):
+        # Test Against Cauchy distribution
+
+        # in principle alpha should be zero in practice for big lmbdas
+        # alpha cannot be too small else pdf does not integrate
+        lmbda, alpha, beta = -0.5, np.finfo(np.float32).eps, 0
+        mu, delta = 0, 1
+        args = (lmbda, alpha, beta)
+
+        gh = stats.genhyperbolic(*args, loc=mu, scale=delta)
+        x = np.linspace(gh.ppf(0.01), gh.ppf(0.99), 50)[:, np.newaxis]
+
+        assert_allclose(
+            gh.pdf(x), stats.cauchy.pdf(x),
+            atol=0, rtol=1e-6
+            )
+
+    def test_pdf_laplace(self):
+        # Test Against Laplace with location param [-10, 10]
+        loc = np.linspace(-10, 10, 10)
+
+        # in principle delta should be zero in practice for big loc delta
+        # cannot be too small else pdf does not integrate
+        delta = np.finfo(np.float32).eps
+
+        lmbda, alpha, beta = 1, 1, 0
+        args = (lmbda, alpha*delta, beta*delta)
+
+        # ppf does not integrate for scale < 5e-4
+        # therefore using simple linspace to define the support
+        gh = stats.genhyperbolic(*args, loc=loc, scale=delta)
+        x = np.linspace(-20, 20, 50)[:, np.newaxis]
+
+        assert_allclose(
+            gh.pdf(x), stats.laplace.pdf(x, loc=loc, scale=1),
+            atol=0, rtol=1e-11
+            )
+
+    def test_pdf_norminvgauss(self):
+        # Test Against NIG with varying alpha/beta/delta/mu
+
+        alpha, beta, delta, mu = (
+                np.linspace(1, 20, 10),
+                np.linspace(0, 19, 10)*np.float_power(-1, range(10)),
+                np.linspace(1, 1, 10),
+                np.linspace(-100, 100, 10)
+                )
+
+        lmbda = - 0.5
+        args = (lmbda, alpha * delta, beta * delta)
+
+        gh = stats.genhyperbolic(*args, loc=mu, scale=delta)
+        x = np.linspace(gh.ppf(0.01), gh.ppf(0.99), 50)[:, np.newaxis]
+
+        assert_allclose(
+            gh.pdf(x), stats.norminvgauss.pdf(
+                x, a=alpha, b=beta, loc=mu, scale=delta),
+            atol=0, rtol=1e-13
+            )
+
+
+class TestHypSecant:
+
+    # Reference values were computed with the mpmath expression
+    #     float((2/mp.pi)*mp.atan(mp.exp(-x)))
+    # and mp.dps = 50.
+    @pytest.mark.parametrize('x, reference',
+                             [(30, 5.957247804324683e-14),
+                              (50, 1.2278802891647964e-22)])
+    def test_sf(self, x, reference):
+        sf = stats.hypsecant.sf(x)
+        assert_allclose(sf, reference, rtol=5e-15)
+
+    # Reference values were computed with the mpmath expression
+    #     float(-mp.log(mp.tan((mp.pi/2)*p)))
+    # and mp.dps = 50.
+    @pytest.mark.parametrize('p, reference',
+                             [(1e-6, 13.363927852673998),
+                              (1e-12, 27.179438410639094)])
+    def test_isf(self, p, reference):
+        x = stats.hypsecant.isf(p)
+        assert_allclose(x, reference, rtol=5e-15)
+
+    def test_logcdf_logsf(self):
+        x = 50.0
+        # Reference value was computed with mpmath.
+        ref = -1.2278802891647964e-22
+        logcdf = stats.hypsecant.logcdf(x)
+        assert_allclose(logcdf, ref, rtol=5e-15)
+        logsf = stats.hypsecant.logsf(-x)
+        assert_allclose(logsf, ref, rtol=5e-15)
+
+
+class TestNormInvGauss:
+    def test_cdf_R(self):
+        # test pdf and cdf vals against R
+        # require("GeneralizedHyperbolic")
+        # x_test <- c(-7, -5, 0, 8, 15)
+        # r_cdf <- GeneralizedHyperbolic::pnig(x_test, mu = 0, a = 1, b = 0.5)
+        # r_pdf <- GeneralizedHyperbolic::dnig(x_test, mu = 0, a = 1, b = 0.5)
+        r_cdf = np.array([8.034920282e-07, 2.512671945e-05, 3.186661051e-01,
+                          9.988650664e-01, 9.999848769e-01])
+        x_test = np.array([-7, -5, 0, 8, 15])
+        vals_cdf = stats.norminvgauss.cdf(x_test, a=1, b=0.5)
+        assert_allclose(vals_cdf, r_cdf, atol=1e-9)
+
+    def test_pdf_R(self):
+        # values from R as defined in test_cdf_R
+        r_pdf = np.array([1.359600783e-06, 4.413878805e-05, 4.555014266e-01,
+                          7.450485342e-04, 8.917889931e-06])
+        x_test = np.array([-7, -5, 0, 8, 15])
+        vals_pdf = stats.norminvgauss.pdf(x_test, a=1, b=0.5)
+        assert_allclose(vals_pdf, r_pdf, atol=1e-9)
+
+    @pytest.mark.parametrize('x, a, b, sf, rtol',
+                             [(-1, 1, 0, 0.8759652211005315, 1e-13),
+                              (25, 1, 0, 1.1318690184042579e-13, 1e-4),
+                              (1, 5, -1.5, 0.002066711134653577, 1e-12),
+                              (10, 5, -1.5, 2.308435233930669e-29, 1e-9)])
+    def test_sf_isf_mpmath(self, x, a, b, sf, rtol):
+        # Reference data generated with `reference_distributions.NormInvGauss`,
+        # e.g. `NormInvGauss(alpha=1, beta=0).sf(-1)` with mp.dps = 50
+        s = stats.norminvgauss.sf(x, a, b)
+        assert_allclose(s, sf, rtol=rtol)
+        i = stats.norminvgauss.isf(sf, a, b)
+        assert_allclose(i, x, rtol=rtol)
+
+    def test_sf_isf_mpmath_vectorized(self):
+        x = [-1, 25]
+        a = [1, 1]
+        b = 0
+        sf = [0.8759652211005315, 1.1318690184042579e-13]  # see previous test
+        s = stats.norminvgauss.sf(x, a, b)
+        assert_allclose(s, sf, rtol=1e-13, atol=1e-16)
+        i = stats.norminvgauss.isf(sf, a, b)
+        # Not perfect, but better than it was. See gh-13338.
+        assert_allclose(i, x, rtol=1e-6)
+
+    def test_gh8718(self):
+        # Add test that gh-13338 resolved gh-8718
+        dst = stats.norminvgauss(1, 0)
+        x = np.arange(0, 20, 2)
+        sf = dst.sf(x)
+        isf = dst.isf(sf)
+        assert_allclose(isf, x)
+
+    def test_stats(self):
+        a, b = 1, 0.5
+        gamma = np.sqrt(a**2 - b**2)
+        v_stats = (b / gamma, a**2 / gamma**3, 3.0 * b / (a * np.sqrt(gamma)),
+                   3.0 * (1 + 4 * b**2 / a**2) / gamma)
+        assert_equal(v_stats, stats.norminvgauss.stats(a, b, moments='mvsk'))
+
+    def test_ppf(self):
+        a, b = 1, 0.5
+        x_test = np.array([0.001, 0.5, 0.999])
+        vals = stats.norminvgauss.ppf(x_test, a, b)
+        assert_allclose(x_test, stats.norminvgauss.cdf(vals, a, b))
+
+    @pytest.mark.parametrize('a', [0.1, 1.0, 10.0])
+    @pytest.mark.parametrize('b_a', [-0.9, -0.5, -0.1, 0.1, 0.5, 0.9])
+    def test_gh23196_tails_cdf_sf(self, a, b_a):
+        # gh-23196 reported that the norminvgauss CDF would drop to zero in the far
+        # right tail. The SF had a similar problem, dropping to zero at the far left.
+        # Check that this is resolved by checking that values in the deep tails are
+        # close to 1.0.
+        b = b_a * a
+        res = stats.norminvgauss(a=a, b=b).cdf(300)
+        np.testing.assert_allclose(res, 1, atol=1e-2)
+        res = stats.norminvgauss(a=a, b=b).sf(-300)
+        np.testing.assert_allclose(res, 1, atol=1e-2)
+
+    @pytest.mark.parametrize("x, a, b, ref", [
+        (100, 1.0, 0.0, 1.0),  # originally reported in gh-23196
+        (1500, 0.1, 0.09, 0.9999999999418577),  # suggested in gh-24567
+    ])
+    def test_gh23196_tails_cdf_sf_accuracy(self, x, a, b, ref):
+        # Spot check the accuracy of the CDF/SF in the deep tails.
+        # library(GeneralizedHyperbolic)
+        # options(digits=16)
+        # pnig(1500, alpha=0.1, beta=0.09)
+        rtol = 1e-14
+        np.testing.assert_allclose(stats.norminvgauss(a=a, b=b).cdf(x), ref, rtol=rtol)
+        np.testing.assert_allclose(stats.norminvgauss(a=a, b=-b).sf(-x), ref, rtol=rtol)
+
+
+class TestGeom:
+    def setup_method(self):
+        self.rng = np.random.default_rng(7672986002)
+
+    def test_rvs(self):
+        vals = stats.geom.rvs(0.75, size=(2, 50), random_state=self.rng)
+        assert_(np.all(vals >= 0))
+        assert_(np.shape(vals) == (2, 50))
+        assert_(vals.dtype.char in typecodes['AllInteger'])
+        val = stats.geom.rvs(0.75, random_state=self.rng)
+        assert_(isinstance(val, int))
+        val = stats.geom(0.75).rvs(3, random_state=self.rng)
+        assert_(isinstance(val, np.ndarray))
+        assert_(val.dtype.char in typecodes['AllInteger'])
+
+    def test_rvs_9313(self):
+        # previously, RVS were converted to `np.int32` on some platforms,
+        # causing overflow for moderately large integer output (gh-9313).
+        # Check that this is resolved to the extent possible w/ `np.int64`.
+        rvs = stats.geom.rvs(np.exp(-35), size=5, random_state=self.rng)
+        assert rvs.dtype == np.int64
+        assert np.all(rvs > np.iinfo(np.int32).max)
+
+    def test_pmf(self):
+        vals = stats.geom.pmf([1, 2, 3], 0.5)
+        assert_array_almost_equal(vals, [0.5, 0.25, 0.125])
+
+    def test_logpmf(self):
+        # regression test for ticket 1793
+        vals1 = np.log(stats.geom.pmf([1, 2, 3], 0.5))
+        vals2 = stats.geom.logpmf([1, 2, 3], 0.5)
+        assert_allclose(vals1, vals2, rtol=1e-15, atol=0)
+
+        # regression test for gh-4028
+        val = stats.geom.logpmf(1, 1)
+        assert_equal(val, 0.0)
+
+    def test_cdf_sf(self):
+        vals = stats.geom.cdf([1, 2, 3], 0.5)
+        vals_sf = stats.geom.sf([1, 2, 3], 0.5)
+        expected = array([0.5, 0.75, 0.875])
+        assert_array_almost_equal(vals, expected)
+        assert_array_almost_equal(vals_sf, 1-expected)
+
+    def test_logcdf_logsf(self):
+        vals = stats.geom.logcdf([1, 2, 3], 0.5)
+        vals_sf = stats.geom.logsf([1, 2, 3], 0.5)
+        expected = array([0.5, 0.75, 0.875])
+        assert_array_almost_equal(vals, np.log(expected))
+        assert_array_almost_equal(vals_sf, np.log1p(-expected))
+
+    def test_ppf(self):
+        vals = stats.geom.ppf([0.5, 0.75, 0.875], 0.5)
+        expected = array([1.0, 2.0, 3.0])
+        assert_array_almost_equal(vals, expected)
+
+    def test_ppf_underflow(self):
+        # this should not underflow
+        assert_allclose(stats.geom.ppf(1e-20, 1e-20), 1.0, atol=1e-14)
+
+    def test_entropy_gh18226(self):
+        # gh-18226 reported that `geom.entropy` produced a warning and
+        # inaccurate output for small p. Check that this is resolved.
+        h = stats.geom(0.0146).entropy()
+        assert_allclose(h, 5.219397961962308, rtol=1e-15)
+
+    def test_rvs_gh18372(self):
+        # gh-18372 reported that `geom.rvs` could produce negative numbers,
+        # with `RandomState` PRNG, but the support is positive integers.
+        # Check that this is resolved.
+        random_state = np.random.RandomState(294582935)
+        assert (stats.geom.rvs(1e-30, size=10, random_state=random_state) > 0).all()
+
+
+class TestPlanck:
+
+    def test_sf(self):
+        vals = stats.planck.sf([1, 2, 3], 5.)
+        expected = array([4.5399929762484854e-05,
+                          3.0590232050182579e-07,
+                          2.0611536224385579e-09])
+        assert_array_almost_equal(vals, expected)
+
+    def test_logsf(self):
+        vals = stats.planck.logsf([1000., 2000., 3000.], 1000.)
+        expected = array([-1001000., -2001000., -3001000.])
+        assert_array_almost_equal(vals, expected)
+
+
+class TestGennorm:
+    def test_laplace(self):
+        # test against Laplace (special case for beta=1)
+        points = [1, 2, 3]
+        pdf1 = stats.gennorm.pdf(points, 1)
+        pdf2 = stats.laplace.pdf(points)
+        assert_almost_equal(pdf1, pdf2)
+
+    def test_norm(self):
+        # test against normal (special case for beta=2)
+        points = [1, 2, 3]
+        pdf1 = stats.gennorm.pdf(points, 2)
+        pdf2 = stats.norm.pdf(points, scale=2**-.5)
+        assert_almost_equal(pdf1, pdf2)
+
+    def test_rvs(self):
+        # 0 < beta < 1
+        dist = stats.gennorm(0.5)
+        rng = np.random.default_rng(2204049394)
+        rvs = dist.rvs(size=1000, random_state=rng)
+        assert stats.kstest(rvs, dist.cdf).pvalue > 0.1
+        # beta = 1
+        dist = stats.gennorm(1)
+        rvs = dist.rvs(size=1000, random_state=rng)
+        rvs_laplace = stats.laplace.rvs(size=1000, random_state=rng)
+        assert stats.ks_2samp(rvs, rvs_laplace).pvalue > 0.1
+        # beta = 2
+        dist = stats.gennorm(2)
+        dist.random_state = rng
+        rvs = dist.rvs(size=1000, random_state=rng)
+        rvs_norm = stats.norm.rvs(scale=1/2**0.5, size=1000, random_state=rng)
+        assert stats.ks_2samp(rvs, rvs_norm).pvalue > 0.1
+
+    def test_rvs_broadcasting(self):
+        dist = stats.gennorm([[0.5, 1.], [2., 5.]])
+        rng = np.random.default_rng(2204049394)
+        rvs = dist.rvs(size=[1000, 2, 2], random_state=rng)
+        assert stats.kstest(rvs[:, 0, 0], stats.gennorm(0.5).cdf)[1] > 0.1
+        assert stats.kstest(rvs[:, 0, 1], stats.gennorm(1.0).cdf)[1] > 0.1
+        assert stats.kstest(rvs[:, 1, 0], stats.gennorm(2.0).cdf)[1] > 0.1
+        assert stats.kstest(rvs[:, 1, 1], stats.gennorm(5.0).cdf)[1] > 0.1
+
+
+class TestGibrat:
+
+    # sfx is sf(x).  The values were computed with mpmath:
+    #
+    #   from mpmath import mp
+    #   mp.dps = 100
+    #   def gibrat_sf(x):
+    #       return 1 - mp.ncdf(mp.log(x))
+    #
+    # E.g.
+    #
+    #   >>> float(gibrat_sf(1.5))
+    #   0.3425678305148459
+    #
+    @pytest.mark.parametrize('x, sfx', [(1.5, 0.3425678305148459),
+                                        (5000, 8.173334352522493e-18)])
+    def test_sf_isf(self, x, sfx):
+        assert_allclose(stats.gibrat.sf(x), sfx, rtol=2e-14)
+        assert_allclose(stats.gibrat.isf(sfx), x, rtol=2e-14)
+
+
+class TestGompertz:
+
+    def test_gompertz_accuracy(self):
+        # Regression test for gh-4031
+        p = stats.gompertz.ppf(stats.gompertz.cdf(1e-100, 1), 1)
+        assert_allclose(p, 1e-100)
+
+    # sfx is sf(x).  The values were computed with mpmath:
+    #
+    #   from mpmath import mp
+    #   mp.dps = 100
+    #   def gompertz_sf(x, c):
+    #       return mp.exp(-c*mp.expm1(x))
+    #
+    # E.g.
+    #
+    #   >>> float(gompertz_sf(1, 2.5))
+    #   0.013626967146253437
+    #
+    @pytest.mark.parametrize('x, c, sfx', [(1, 2.5, 0.013626967146253437),
+                                           (3, 2.5, 1.8973243273704087e-21),
+                                           (0.05, 5, 0.7738668242570479),
+                                           (2.25, 5, 3.707795833465481e-19)])
+    def test_sf_isf(self, x, c, sfx):
+        assert_allclose(stats.gompertz.sf(x, c), sfx, rtol=1e-14)
+        assert_allclose(stats.gompertz.isf(sfx, c), x, rtol=1e-14)
+
+    def test_logcdf(self):
+        x = 8.0
+        c = 0.1
+        # Reference value computed with mpmath.
+        ref = -3.820049516821143e-130
+        logcdf = stats.gompertz.logcdf(x, c)
+        assert_allclose(logcdf, ref, rtol=5e-15)
+
+    def test_logsf(self):
+        x = 3e-80
+        c = 12
+        # Reference value computed with mpmath.
+        ref = -3.6e-79
+        logsf = stats.gompertz.logsf(x, c)
+        assert_allclose(logsf, ref, rtol=5e-15)
+
+    # reference values were computed with mpmath
+    # from mpmath import mp
+    # mp.dps = 100
+    # def gompertz_entropy(c):
+    #     c = mp.mpf(c)
+    #     return float(mp.one - mp.log(c) - mp.exp(c)*mp.e1(c))
+
+    @pytest.mark.parametrize('c, ref', [(1e-4, 1.5762523017634573),
+                                        (1, 0.4036526376768059),
+                                        (1000, -5.908754280976161),
+                                        (1e10, -22.025850930040455)])
+    def test_entropy(self, c, ref):
+        assert_allclose(stats.gompertz.entropy(c), ref, rtol=1e-14)
+
+
+class TestFoldNorm:
+
+    # reference values were computed with mpmath with 50 digits of precision
+    # from mpmath import mp
+    # mp.dps = 50
+    # mp.mpf(0.5) * (mp.erf((x - c)/mp.sqrt(2)) + mp.erf((x + c)/mp.sqrt(2)))
+
+    @pytest.mark.parametrize('x, c, ref', [(1e-4, 1e-8, 7.978845594730578e-05),
+                                           (1e-4, 1e-4, 7.97884555483635e-05)])
+    def test_cdf(self, x, c, ref):
+        assert_allclose(stats.foldnorm.cdf(x, c), ref, rtol=1e-15)
+
+
+class TestHalfNorm:
+
+    # sfx is sf(x).  The values were computed with mpmath:
+    #
+    #   from mpmath import mp
+    #   mp.dps = 100
+    #   def halfnorm_sf(x):
+    #       return 2*(1 - mp.ncdf(x))
+    #
+    # E.g.
+    #
+    #   >>> float(halfnorm_sf(1))
+    #   0.3173105078629141
+    #
+    @pytest.mark.parametrize('x, sfx', [(1, 0.3173105078629141),
+                                        (10, 1.523970604832105e-23)])
+    def test_sf_isf(self, x, sfx):
+        assert_allclose(stats.halfnorm.sf(x), sfx, rtol=1e-14)
+        assert_allclose(stats.halfnorm.isf(sfx), x, rtol=1e-14)
+
+    #   reference values were computed via mpmath
+    #   from mpmath import mp
+    #   mp.dps = 100
+    #   def halfnorm_cdf_mpmath(x):
+    #       x = mp.mpf(x)
+    #       return float(mp.erf(x/mp.sqrt(2.)))
+
+    @pytest.mark.parametrize('x, ref', [(1e-40, 7.978845608028653e-41),
+                                        (1e-18, 7.978845608028654e-19),
+                                        (8, 0.9999999999999988)])
+    def test_cdf(self, x, ref):
+        assert_allclose(stats.halfnorm.cdf(x), ref, rtol=1e-15)
+
+    @pytest.mark.parametrize("rvs_loc", [1e-5, 1e10])
+    @pytest.mark.parametrize("rvs_scale", [1e-2, 100, 1e8])
+    @pytest.mark.parametrize('fix_loc', [True, False])
+    @pytest.mark.parametrize('fix_scale', [True, False])
+    def test_fit_MLE_comp_optimizer(self, rvs_loc, rvs_scale,
+                                    fix_loc, fix_scale):
+
+        rng = np.random.default_rng(6762668991392531563)
+        data = stats.halfnorm.rvs(loc=rvs_loc, scale=rvs_scale, size=1000,
+                                  random_state=rng)
+
+        if fix_loc and fix_scale:
+            error_msg = ("All parameters fixed. There is nothing to "
+                         "optimize.")
+            with pytest.raises(RuntimeError, match=error_msg):
+                stats.halflogistic.fit(data, floc=rvs_loc, fscale=rvs_scale)
+            return
+
+        kwds = {}
+        if fix_loc:
+            kwds['floc'] = rvs_loc
+        if fix_scale:
+            kwds['fscale'] = rvs_scale
+
+        # Numerical result may equal analytical result if the initial guess
+        # computed from moment condition is already optimal.
+        _assert_less_or_close_loglike(stats.halfnorm, data, **kwds,
+                                      maybe_identical=True)
+
+    def test_fit_error(self):
+        # `floc` bigger than the minimal data point
+        with pytest.raises(FitDataError):
+            stats.halfnorm.fit([1, 2, 3], floc=2)
+
+
+class TestHalfCauchy:
+
+    @pytest.mark.parametrize("rvs_loc", [1e-5, 1e10])
+    @pytest.mark.parametrize("rvs_scale", [1e-2, 1e8])
+    @pytest.mark.parametrize('fix_loc', [True, False])
+    @pytest.mark.parametrize('fix_scale', [True, False])
+    def test_fit_MLE_comp_optimizer(self, rvs_loc, rvs_scale,
+                                    fix_loc, fix_scale):
+
+        rng = np.random.default_rng(6762668991392531563)
+        data = stats.halfnorm.rvs(loc=rvs_loc, scale=rvs_scale, size=1000,
+                                  random_state=rng)
+
+        if fix_loc and fix_scale:
+            error_msg = ("All parameters fixed. There is nothing to "
+                         "optimize.")
+            with pytest.raises(RuntimeError, match=error_msg):
+                stats.halfcauchy.fit(data, floc=rvs_loc, fscale=rvs_scale)
+            return
+
+        kwds = {}
+        if fix_loc:
+            kwds['floc'] = rvs_loc
+        if fix_scale:
+            kwds['fscale'] = rvs_scale
+
+        _assert_less_or_close_loglike(stats.halfcauchy, data, **kwds)
+
+    def test_fit_error(self):
+        # `floc` bigger than the minimal data point
+        with pytest.raises(FitDataError):
+            stats.halfcauchy.fit([1, 2, 3], floc=2)
+
+
+class TestHalfLogistic:
+    # survival function reference values were computed with mpmath
+    # from mpmath import mp
+    # mp.dps = 50
+    # def sf_mpmath(x):
+    #     x = mp.mpf(x)
+    #     return float(mp.mpf(2.)/(mp.exp(x) + mp.one))
+
+    @pytest.mark.parametrize('x, ref', [(100, 7.440151952041672e-44),
+                                        (200, 2.767793053473475e-87)])
+    def test_sf(self, x, ref):
+        assert_allclose(stats.halflogistic.sf(x), ref, rtol=1e-15)
+
+    # inverse survival function reference values were computed with mpmath
+    # from mpmath import mp
+    # mp.dps = 200
+    # def isf_mpmath(x):
+    #     halfx = mp.mpf(x)/2
+    #     return float(-mp.log(halfx/(mp.one - halfx)))
+
+    @pytest.mark.parametrize('q, ref', [(7.440151952041672e-44, 100),
+                                        (2.767793053473475e-87, 200),
+                                        (1-1e-9, 1.999999943436137e-09),
+                                        (1-1e-15, 1.9984014443252818e-15)])
+    def test_isf(self, q, ref):
+        assert_allclose(stats.halflogistic.isf(q), ref, rtol=1e-15)
+
+    def test_logcdf(self):
+        x = 30.0
+        # Reference value computed with mpmath.
+        ref = -1.871524593768035e-13
+        logcdf = stats.halflogistic.logcdf(x)
+        assert_allclose(logcdf, ref, rtol=5e-15)
+
+    def test_logsf(self):
+        x = 2e-14
+        # Reference value computed with mpmath.
+        ref = -1.000000000000005e-14
+        logsf = stats.halflogistic.logsf(x)
+        assert_allclose(logsf, ref, rtol=5e-15)
+
+    @pytest.mark.parametrize("rvs_loc", [1e-5, 1e10])
+    @pytest.mark.parametrize("rvs_scale", [1e-2, 100, 1e8])
+    @pytest.mark.parametrize('fix_loc', [True, False])
+    @pytest.mark.parametrize('fix_scale', [True, False])
+    def test_fit_MLE_comp_optimizer(self, rvs_loc, rvs_scale,
+                                    fix_loc, fix_scale):
+
+        rng = np.random.default_rng(6762668991392531563)
+        data = stats.halflogistic.rvs(loc=rvs_loc, scale=rvs_scale, size=1000,
+                                      random_state=rng)
+
+        kwds = {}
+        if fix_loc and fix_scale:
+            error_msg = ("All parameters fixed. There is nothing to "
+                         "optimize.")
+            with pytest.raises(RuntimeError, match=error_msg):
+                stats.halflogistic.fit(data, floc=rvs_loc, fscale=rvs_scale)
+            return
+
+        if fix_loc:
+            kwds['floc'] = rvs_loc
+        if fix_scale:
+            kwds['fscale'] = rvs_scale
+
+        # Numerical result may equal analytical result if the initial guess
+        # computed from moment condition is already optimal.
+        _assert_less_or_close_loglike(stats.halflogistic, data, **kwds,
+                                      maybe_identical=True)
+
+    def test_fit_bad_floc(self):
+        msg = r" Maximum likelihood estimation with 'halflogistic' requires"
+        with assert_raises(FitDataError, match=msg):
+            stats.halflogistic.fit([0, 2, 4], floc=1)
+
+
+class TestHalfgennorm:
+    def test_expon(self):
+        # test against exponential (special case for beta=1)
+        points = [1, 2, 3]
+        pdf1 = stats.halfgennorm.pdf(points, 1)
+        pdf2 = stats.expon.pdf(points)
+        assert_almost_equal(pdf1, pdf2)
+
+    def test_halfnorm(self):
+        # test against half normal (special case for beta=2)
+        points = [1, 2, 3]
+        pdf1 = stats.halfgennorm.pdf(points, 2)
+        pdf2 = stats.halfnorm.pdf(points, scale=2**-.5)
+        assert_almost_equal(pdf1, pdf2)
+
+    def test_gennorm(self):
+        # test against generalized normal
+        points = [1, 2, 3]
+        pdf1 = stats.halfgennorm.pdf(points, .497324)
+        pdf2 = stats.gennorm.pdf(points, .497324)
+        assert_almost_equal(pdf1, 2*pdf2)
+
+    # Reference values (e.g. for n=3, beta=1.25)
+    #    from mpmath import mp
+    #    mp.dps = 100
+    #    n = 3
+    #    beta = mp.mpf(1.25)
+    #    ref = float(mp.rf(1/beta, n/beta))
+    @pytest.mark.parametrize('n, beta, ref',
+                             [(0, 2.25, 1),
+                              (1, 0.5, 6.0),
+                              (2, 12.5, 0.3155489903298712),
+                              (3, 0.125, 1.631515605987683e+30)])
+    def test_munp(self, n, beta, ref):
+        munp = stats.halfgennorm._munp(n, beta)
+        assert_allclose(munp, ref, rtol=5e-15)
+
+    # Reference values (e.g. for beta=0.02)
+    #    from mpmath import mp
+    #    mp.dps = 100
+    #    beta = mp.mpf(0.02)
+    #    ref = float(mp.rf(1/beta, 1/beta))
+    @pytest.mark.parametrize('beta, ref',
+                             [(0.02, 1.5342593781274747e+93),
+                              (0.125, 259459200.0),
+                              (0.5, 6.0),
+                              (10.0, 0.48256057149575027),
+                              (125.0, 0.49777435261046765),
+                              (15000.0, 0.49998076533051666)])
+    def test_mean(self, beta, ref):
+        m = stats.halfgennorm.mean(beta)
+        assert_allclose(m, ref, rtol=1e-14)
+
+    # Reference values (e.g. for beta=0.02)
+    #    from mpmath import mp
+    #    mp.dps = 100
+    #    beta = mp.mpf(0.02)
+    #    mu = mp.rf(1/beta, 1/beta)
+    #    # var = E(X**2) - E(X)**2:
+    #    ref = float(mp.rf(1/beta, 2/beta) - mu**2)
+    @pytest.mark.parametrize('beta, ref',
+                             [(0.02, 6.261772482175519e+197),
+                              (0.125, 5.062049324107776e+18),
+                              (0.5, 84.0),
+                              (10.0, 0.08159018176717249),
+                              (125.0, 0.0826270885971827),
+                              (15000.0, 0.08332692433644018)])
+    def test_var(self, beta, ref):
+        v = stats.halfgennorm.var(beta)
+        assert_allclose(v, ref, rtol=1.5e-14)
+
+
+class TestLaplaceasymmetric:
+    def test_laplace(self):
+        # test against Laplace (special case for kappa=1)
+        points = np.array([1, 2, 3])
+        pdf1 = stats.laplace_asymmetric.pdf(points, 1)
+        pdf2 = stats.laplace.pdf(points)
+        assert_allclose(pdf1, pdf2)
+
+    def test_asymmetric_laplace_pdf(self):
+        # test asymmetric Laplace
+        points = np.array([1, 2, 3])
+        kappa = 2
+        kapinv = 1/kappa
+        pdf1 = stats.laplace_asymmetric.pdf(points, kappa)
+        pdf2 = stats.laplace_asymmetric.pdf(points*(kappa**2), kapinv)
+        assert_allclose(pdf1, pdf2)
+
+    def test_asymmetric_laplace_log_10_16(self):
+        # test asymmetric Laplace
+        points = np.array([-np.log(16), np.log(10)])
+        kappa = 2
+        pdf1 = stats.laplace_asymmetric.pdf(points, kappa)
+        cdf1 = stats.laplace_asymmetric.cdf(points, kappa)
+        sf1 = stats.laplace_asymmetric.sf(points, kappa)
+        pdf2 = np.array([1/10, 1/250])
+        cdf2 = np.array([1/5, 1 - 1/500])
+        sf2 = np.array([4/5, 1/500])
+        ppf1 = stats.laplace_asymmetric.ppf(cdf2, kappa)
+        ppf2 = points
+        isf1 = stats.laplace_asymmetric.isf(sf2, kappa)
+        isf2 = points
+        assert_allclose(np.concatenate((pdf1, cdf1, sf1, ppf1, isf1)),
+                        np.concatenate((pdf2, cdf2, sf2, ppf2, isf2)))
+
+
+class TestTruncnorm:
+    def setup_method(self):
+        self.rng = np.random.default_rng(3255963201)
+
+    @pytest.mark.parametrize("a, b, ref",
+                             [(0, 100, 0.7257913526447274),
+                             (0.6, 0.7, -2.3027610681852573),
+                             (1e-06, 2e-06, -13.815510557964274)])
+    def test_entropy(self, a, b, ref):
+        # All reference values were calculated with mpmath:
+        # import numpy as np
+        # from mpmath import mp
+        # mp.dps = 50
+        # def entropy_trun(a, b):
+        #     a, b = mp.mpf(a), mp.mpf(b)
+        #     Z = mp.ncdf(b) - mp.ncdf(a)
+        #
+        #     def pdf(x):
+        #         return mp.npdf(x) / Z
+        #
+        #     res = -mp.quad(lambda t: pdf(t) * mp.log(pdf(t)), [a, b])
+        #     return np.float64(res)
+        assert_allclose(stats.truncnorm.entropy(a, b), ref, rtol=1e-10)
+
+    @pytest.mark.parametrize("a, b, ref",
+                             [(1e-11, 10000000000.0, 0.725791352640738),
+                             (1e-100, 1e+100, 0.7257913526447274),
+                             (-1e-100, 1e+100, 0.7257913526447274),
+                             (-1e+100, 1e+100, 1.4189385332046727)])
+    def test_extreme_entropy(self, a, b, ref):
+        # The reference values were calculated with mpmath
+        # import numpy as np
+        # from mpmath import mp
+        # mp.dps = 50
+        # def trunc_norm_entropy(a, b):
+        #     a, b = mp.mpf(a), mp.mpf(b)
+        #     Z = mp.ncdf(b) - mp.ncdf(a)
+        #     A = mp.log(mp.sqrt(2 * mp.pi * mp.e) * Z)
+        #     B = (a * mp.npdf(a) - b * mp.npdf(b)) / (2 * Z)
+        #     return np.float64(A + B)
+        assert_allclose(stats.truncnorm.entropy(a, b), ref, rtol=1e-14)
+
+    def test_ppf_ticket1131(self):
+        vals = stats.truncnorm.ppf([-0.5, 0, 1e-4, 0.5, 1-1e-4, 1, 2], -1., 1.,
+                                   loc=[3]*7, scale=2)
+        expected = np.array([np.nan, 1, 1.00056419, 3, 4.99943581, 5, np.nan])
+        assert_array_almost_equal(vals, expected)
+
+    def test_isf_ticket1131(self):
+        vals = stats.truncnorm.isf([-0.5, 0, 1e-4, 0.5, 1-1e-4, 1, 2], -1., 1.,
+                                   loc=[3]*7, scale=2)
+        expected = np.array([np.nan, 5, 4.99943581, 3, 1.00056419, 1, np.nan])
+        assert_array_almost_equal(vals, expected)
+
+    def test_gh_2477_small_values(self):
+        # Check a case that worked in the original issue.
+        low, high = -11, -10
+        x = stats.truncnorm.rvs(low, high, 0, 1, size=10, random_state=self.rng)
+        assert_(low < x.min() < x.max() < high)
+        # Check a case that failed in the original issue.
+        low, high = 10, 11
+        x = stats.truncnorm.rvs(low, high, 0, 1, size=10, random_state=self.rng)
+        assert_(low < x.min() < x.max() < high)
+
+    def test_gh_2477_large_values(self):
+        # Check a case that used to fail because of extreme tailness.
+        low, high = 100, 101
+        x = stats.truncnorm.rvs(low, high, 0, 1, size=10, random_state=self.rng)
+        assert_(low <= x.min() <= x.max() <= high), str([low, high, x])
+
+        # Check some additional extreme tails
+        low, high = 1000, 1001
+        x = stats.truncnorm.rvs(low, high, 0, 1, size=10, random_state=self.rng)
+        assert_(low < x.min() < x.max() < high)
+
+        low, high = 10000, 10001
+        x = stats.truncnorm.rvs(low, high, 0, 1, size=10, random_state=self.rng)
+        assert_(low < x.min() < x.max() < high)
+
+        low, high = -10001, -10000
+        x = stats.truncnorm.rvs(low, high, 0, 1, size=10, random_state=self.rng)
+        assert_(low < x.min() < x.max() < high)
+
+    def test_gh_9403_nontail_values(self):
+        for low, high in [[3, 4], [-4, -3]]:
+            xvals = np.array([-np.inf, low, high, np.inf])
+            xmid = (high+low)/2.0
+            cdfs = stats.truncnorm.cdf(xvals, low, high)
+            sfs = stats.truncnorm.sf(xvals, low, high)
+            pdfs = stats.truncnorm.pdf(xvals, low, high)
+            expected_cdfs = np.array([0, 0, 1, 1])
+            expected_sfs = np.array([1.0, 1.0, 0.0, 0.0])
+            expected_pdfs = np.array([0, 3.3619772, 0.1015229, 0])
+            if low < 0:
+                expected_pdfs = np.array([0, 0.1015229, 3.3619772, 0])
+            assert_almost_equal(cdfs, expected_cdfs)
+            assert_almost_equal(sfs, expected_sfs)
+            assert_almost_equal(pdfs, expected_pdfs)
+            assert_almost_equal(np.log(expected_pdfs[1]/expected_pdfs[2]),
+                                low + 0.5)
+            pvals = np.array([0, 0.5, 1.0])
+            ppfs = stats.truncnorm.ppf(pvals, low, high)
+            expected_ppfs = np.array([low, np.sign(low)*3.1984741, high])
+            assert_almost_equal(ppfs, expected_ppfs)
+
+            if low < 0:
+                assert_almost_equal(stats.truncnorm.sf(xmid, low, high),
+                                    0.8475544278436675)
+                assert_almost_equal(stats.truncnorm.cdf(xmid, low, high),
+                                    0.1524455721563326)
+            else:
+                assert_almost_equal(stats.truncnorm.cdf(xmid, low, high),
+                                    0.8475544278436675)
+                assert_almost_equal(stats.truncnorm.sf(xmid, low, high),
+                                    0.1524455721563326)
+            pdf = stats.truncnorm.pdf(xmid, low, high)
+            assert_almost_equal(np.log(pdf/expected_pdfs[2]), (xmid+0.25)/2)
+
+    def test_gh_9403_medium_tail_values(self):
+        for low, high in [[39, 40], [-40, -39]]:
+            xvals = np.array([-np.inf, low, high, np.inf])
+            xmid = (high+low)/2.0
+            cdfs = stats.truncnorm.cdf(xvals, low, high)
+            sfs = stats.truncnorm.sf(xvals, low, high)
+            pdfs = stats.truncnorm.pdf(xvals, low, high)
+            expected_cdfs = np.array([0, 0, 1, 1])
+            expected_sfs = np.array([1.0, 1.0, 0.0, 0.0])
+            expected_pdfs = np.array([0, 3.90256074e+01, 2.73349092e-16, 0])
+            if low < 0:
+                expected_pdfs = np.array([0, 2.73349092e-16,
+                                          3.90256074e+01, 0])
+            assert_almost_equal(cdfs, expected_cdfs)
+            assert_almost_equal(sfs, expected_sfs)
+            assert_almost_equal(pdfs, expected_pdfs)
+            assert_almost_equal(np.log(expected_pdfs[1]/expected_pdfs[2]),
+                                low + 0.5)
+            pvals = np.array([0, 0.5, 1.0])
+            ppfs = stats.truncnorm.ppf(pvals, low, high)
+            expected_ppfs = np.array([low, np.sign(low)*39.01775731, high])
+            assert_almost_equal(ppfs, expected_ppfs)
+            cdfs = stats.truncnorm.cdf(ppfs, low, high)
+            assert_almost_equal(cdfs, pvals)
+
+            if low < 0:
+                assert_almost_equal(stats.truncnorm.sf(xmid, low, high),
+                                    0.9999999970389126)
+                assert_almost_equal(stats.truncnorm.cdf(xmid, low, high),
+                                    2.961048103554866e-09)
+            else:
+                assert_almost_equal(stats.truncnorm.cdf(xmid, low, high),
+                                    0.9999999970389126)
+                assert_almost_equal(stats.truncnorm.sf(xmid, low, high),
+                                    2.961048103554866e-09)
+            pdf = stats.truncnorm.pdf(xmid, low, high)
+            assert_almost_equal(np.log(pdf/expected_pdfs[2]), (xmid+0.25)/2)
+
+            xvals = np.linspace(low, high, 11)
+            xvals2 = -xvals[::-1]
+            assert_almost_equal(stats.truncnorm.cdf(xvals, low, high),
+                                stats.truncnorm.sf(xvals2, -high, -low)[::-1])
+            assert_almost_equal(stats.truncnorm.sf(xvals, low, high),
+                                stats.truncnorm.cdf(xvals2, -high, -low)[::-1])
+            assert_almost_equal(stats.truncnorm.pdf(xvals, low, high),
+                                stats.truncnorm.pdf(xvals2, -high, -low)[::-1])
+
+    def test_cdf_tail_15110_14753(self):
+        # Check accuracy issues reported in gh-14753 and gh-155110
+        # Ground truth values calculated using Wolfram Alpha, e.g.
+        # (CDF[NormalDistribution[0,1],83/10]-CDF[NormalDistribution[0,1],8])/
+        #     (1 - CDF[NormalDistribution[0,1],8])
+        assert_allclose(stats.truncnorm(13., 15.).cdf(14.),
+                        0.9999987259565643)
+        assert_allclose(stats.truncnorm(8, np.inf).cdf(8.3),
+                        0.9163220907327540)
+
+    # Test data for the truncnorm stats() method.
+    # The data in each row is:
+    #   a, b, mean, variance, skewness, excess kurtosis. Generated using
+    # https://gist.github.com/WarrenWeckesser/636b537ee889679227d53543d333a720
+    _truncnorm_stats_data = [
+        [-30, 30,
+         0.0, 1.0, 0.0, 0.0],
+        [-10, 10,
+         0.0, 1.0, 0.0, -1.4927521335810455e-19],
+        [-3, 3,
+         0.0, 0.9733369246625415, 0.0, -0.17111443639774404],
+        [-2, 2,
+         0.0, 0.7737413035499232, 0.0, -0.6344632828703505],
+        [0, np.inf,
+         0.7978845608028654,
+         0.3633802276324187,
+         0.995271746431156,
+         0.8691773036059741],
+        [-np.inf, 0,
+         -0.7978845608028654,
+         0.3633802276324187,
+         -0.995271746431156,
+         0.8691773036059741],
+        [-1, 3,
+         0.282786110727154,
+         0.6161417353578293,
+         0.5393018494027877,
+         -0.20582065135274694],
+        [-3, 1,
+         -0.282786110727154,
+         0.6161417353578293,
+         -0.5393018494027877,
+         -0.20582065135274694],
+        [-10, -9,
+         -9.108456288012409,
+         0.011448805821636248,
+         -1.8985607290949496,
+         5.0733461105025075],
+    ]
+    _truncnorm_stats_data = np.array(_truncnorm_stats_data)
+
+    @pytest.mark.parametrize("case", _truncnorm_stats_data)
+    def test_moments(self, case):
+        a, b, m0, v0, s0, k0 = case
+        m, v, s, k = stats.truncnorm.stats(a, b, moments='mvsk')
+        assert_allclose([m, v, s, k], [m0, v0, s0, k0], atol=1e-17)
+
+    def test_9902_moments(self):
+        m, v = stats.truncnorm.stats(0, np.inf, moments='mv')
+        assert_almost_equal(m, 0.79788456)
+        assert_almost_equal(v, 0.36338023)
+
+    def test_gh_1489_trac_962_rvs(self):
+        # Check the original example.
+        low, high = 10, 15
+        x = stats.truncnorm.rvs(low, high, 0, 1, size=10, random_state=self.rng)
+        assert_(low < x.min() < x.max() < high)
+
+    def test_gh_11299_rvs(self):
+        # Arose from investigating gh-11299
+        # Test multiple shape parameters simultaneously.
+        low = [-10, 10, -np.inf, -5, -np.inf, -np.inf, -45, -45, 40, -10, 40]
+        high = [-5, 11, 5, np.inf, 40, -40, 40, -40, 45, np.inf, np.inf]
+        x = stats.truncnorm.rvs(low, high, size=(5, len(low)), random_state=self.rng)
+        assert np.shape(x) == (5, len(low))
+        assert_(np.all(low <= x.min(axis=0)))
+        assert_(np.all(x.max(axis=0) <= high))
+
+    def test_rvs_Generator(self):
+        # check that rvs can use a Generator
+        if hasattr(np.random, "default_rng"):
+            stats.truncnorm.rvs(-10, -5, size=5, random_state=self.rng)
+
+    def test_logcdf_gh17064(self):
+        # regression test for gh-17064 - avoid roundoff error for logcdfs ~0
+        a = np.array([-np.inf, -np.inf, -8, -np.inf, 10])
+        b = np.array([np.inf, np.inf, 8, 10, np.inf])
+        x = np.array([10, 7.5, 7.5, 9, 20])
+        expected = [-7.619853024160525e-24, -3.190891672910947e-14,
+                    -3.128682067168231e-14, -1.1285122074235991e-19,
+                    -3.61374964828753e-66]
+        assert_allclose(stats.truncnorm(a, b).logcdf(x), expected)
+        assert_allclose(stats.truncnorm(-b, -a).logsf(-x), expected)
+
+    def test_moments_gh18634(self):
+        # gh-18634 reported that moments 5 and higher didn't work; check that
+        # this is resolved
+        res = stats.truncnorm(-2, 3).moment(5)
+        # From Mathematica:
+        # Moment[TruncatedDistribution[{-2, 3}, NormalDistribution[]], 5]
+        ref = 1.645309620208361
+        assert_allclose(res, ref)
+
+
+class TestGenLogistic:
+
+    # Expected values computed with mpmath with 50 digits of precision.
+    @pytest.mark.parametrize('x, expected', [(-1000, -1499.5945348918917),
+                                             (-125, -187.09453489189184),
+                                             (0, -1.3274028432916989),
+                                             (100, -99.59453489189184),
+                                             (1000, -999.5945348918918)])
+    def test_logpdf(self, x, expected):
+        c = 1.5
+        logp = stats.genlogistic.logpdf(x, c)
+        assert_allclose(logp, expected, rtol=1e-13)
+
+    # Expected values computed with mpmath with 50 digits of precision
+    # from mpmath import mp
+    # mp.dps = 50
+    # def entropy_mp(c):
+    #     c = mp.mpf(c)
+    #     return float(-mp.log(c)+mp.one+mp.digamma(c + mp.one) + mp.euler)
+
+    @pytest.mark.parametrize('c, ref', [(1e-100, 231.25850929940458),
+                                        (1e-4, 10.21050485336338),
+                                        (1e8, 1.577215669901533),
+                                        (1e100, 1.5772156649015328)])
+    def test_entropy(self, c, ref):
+        assert_allclose(stats.genlogistic.entropy(c), ref, rtol=5e-15)
+
+    # Expected values computed with mpmath with 50 digits of precision
+    # from mpmath import mp
+    # mp.dps = 1000
+    #
+    # def genlogistic_cdf_mp(x, c):
+    #     x = mp.mpf(x)
+    #     c = mp.mpf(c)
+    #     return (mp.one + mp.exp(-x)) ** (-c)
+    #
+    # def genlogistic_sf_mp(x, c):
+    #     return mp.one - genlogistic_cdf_mp(x, c)
+    #
+    # x, c, ref = 100, 0.02, -7.440151952041672e-466
+    # print(float(mp.log(genlogistic_cdf_mp(x, c))))
+    # ppf/isf reference values generated by passing in `ref` (`q` is produced)
+
+    @pytest.mark.parametrize('x, c, ref', [(200, 10, 1.3838965267367375e-86),
+                                           (500, 20, 1.424915281348257e-216)])
+    def test_sf(self, x, c, ref):
+        assert_allclose(stats.genlogistic.sf(x, c), ref, rtol=1e-14)
+
+    @pytest.mark.parametrize('q, c, ref', [(0.01, 200, 9.898441467379765),
+                                           (0.001, 2, 7.600152115573173)])
+    def test_isf(self, q, c, ref):
+        assert_allclose(stats.genlogistic.isf(q, c), ref, rtol=5e-16)
+
+    @pytest.mark.parametrize('q, c, ref', [(0.5, 200, 5.6630969187064615),
+                                           (0.99, 20, 7.595630231412436)])
+    def test_ppf(self, q, c, ref):
+        assert_allclose(stats.genlogistic.ppf(q, c), ref, rtol=5e-16)
+
+    @pytest.mark.parametrize('x, c, ref', [(100, 0.02, -7.440151952041672e-46),
+                                           (50, 20, -3.857499695927835e-21)])
+    def test_logcdf(self, x, c, ref):
+        assert_allclose(stats.genlogistic.logcdf(x, c), ref, rtol=1e-15)
+
+
+class TestHypergeom:
+    def setup_method(self):
+        self.rng = np.random.default_rng(1765545342)
+
+    def test_rvs(self):
+        vals = stats.hypergeom.rvs(20, 10, 3, size=(2, 50), random_state=self.rng)
+        assert np.all(vals >= 0) & np.all(vals <= 3)
+        assert np.shape(vals) == (2, 50)
+        assert vals.dtype.char in typecodes['AllInteger']
+        val = stats.hypergeom.rvs(20, 3, 10, random_state=self.rng)
+        assert isinstance(val, int)
+        val = stats.hypergeom(20, 3, 10).rvs(3, random_state=self.rng)
+        assert isinstance(val, np.ndarray)
+        assert val.dtype.char in typecodes['AllInteger']
+
+    def test_precision(self):
+        # comparison number from mpmath
+        M = 2500
+        n = 50
+        N = 500
+        tot = M
+        good = n
+        hgpmf = stats.hypergeom.pmf(2, tot, good, N)
+        assert_almost_equal(hgpmf, 0.0010114963068932233, 11)
+
+    def test_args(self):
+        # test correct output for corner cases of arguments
+        # see gh-2325
+        assert_almost_equal(stats.hypergeom.pmf(0, 2, 1, 0), 1.0, 11)
+        assert_almost_equal(stats.hypergeom.pmf(1, 2, 1, 0), 0.0, 11)
+
+        assert_almost_equal(stats.hypergeom.pmf(0, 2, 0, 2), 1.0, 11)
+        assert_almost_equal(stats.hypergeom.pmf(1, 2, 1, 0), 0.0, 11)
+
+    def test_cdf_above_one(self):
+        # for some values of parameters, hypergeom cdf was >1, see gh-2238
+        assert_(0 <= stats.hypergeom.cdf(30, 13397950, 4363, 12390) <= 1.0)
+
+    def test_precision2(self):
+        # Test hypergeom precision for large numbers.  See #1218.
+        # Results compared with those from R.
+        oranges = 9.9e4
+        pears = 1.1e5
+        fruits_eaten = np.array([3, 3.8, 3.9, 4, 4.1, 4.2, 5]) * 1e4
+        quantile = 2e4
+        res = [stats.hypergeom.sf(quantile, oranges + pears, oranges, eaten)
+               for eaten in fruits_eaten]
+        expected = np.array([0, 1.904153e-114, 2.752693e-66, 4.931217e-32,
+                             8.265601e-11, 0.1237904, 1])
+        assert_allclose(res, expected, atol=0, rtol=5e-7)
+
+        # Test with array_like first argument
+        quantiles = [1.9e4, 2e4, 2.1e4, 2.15e4]
+        res2 = stats.hypergeom.sf(quantiles, oranges + pears, oranges, 4.2e4)
+        expected2 = [1, 0.1237904, 6.511452e-34, 3.277667e-69]
+        assert_allclose(res2, expected2, atol=0, rtol=5e-7)
+
+    def test_entropy(self):
+        # Simple tests of entropy.
+        hg = stats.hypergeom(4, 1, 1)
+        h = hg.entropy()
+        expected_p = np.array([0.75, 0.25])
+        expected_h = -np.sum(xlogy(expected_p, expected_p))
+        assert_allclose(h, expected_h)
+
+        hg = stats.hypergeom(1, 1, 1)
+        h = hg.entropy()
+        assert_equal(h, 0.0)
+
+    def test_logsf(self):
+        # Test logsf for very large numbers. See issue #4982
+        # Results compare with those from R (v3.2.0):
+        # phyper(k, n, M-n, N, lower.tail=FALSE, log.p=TRUE)
+        # -2239.771
+
+        k = 1e4
+        M = 1e7
+        n = 1e6
+        N = 5e4
+
+        result = stats.hypergeom.logsf(k, M, n, N)
+        expected = -2239.771   # From R
+        assert_almost_equal(result, expected, decimal=3)
+
+        k = 1
+        M = 1600
+        n = 600
+        N = 300
+
+        result = stats.hypergeom.logsf(k, M, n, N)
+        expected = -2.566567e-68   # From R
+        assert_almost_equal(result, expected, decimal=15)
+
+    def test_logcdf(self):
+        # Test logcdf for very large numbers. See issue #8692
+        # Results compare with those from R (v3.3.2):
+        # phyper(k, n, M-n, N, lower.tail=TRUE, log.p=TRUE)
+        # -5273.335
+
+        k = 1
+        M = 1e7
+        n = 1e6
+        N = 5e4
+
+        result = stats.hypergeom.logcdf(k, M, n, N)
+        expected = -5273.335   # From R
+        assert_almost_equal(result, expected, decimal=3)
+
+        # Same example as in issue #8692
+        k = 40
+        M = 1600
+        n = 50
+        N = 300
+
+        result = stats.hypergeom.logcdf(k, M, n, N)
+        expected = -7.565148879229e-23    # From R
+        assert_almost_equal(result, expected, decimal=15)
+
+        k = 125
+        M = 1600
+        n = 250
+        N = 500
+
+        result = stats.hypergeom.logcdf(k, M, n, N)
+        expected = -4.242688e-12    # From R
+        assert_almost_equal(result, expected, decimal=15)
+
+        # test broadcasting robustness based on reviewer
+        # concerns in PR 9603; using an array version of
+        # the example from issue #8692
+        k = np.array([40, 40, 40])
+        M = 1600
+        n = 50
+        N = 300
+
+        result = stats.hypergeom.logcdf(k, M, n, N)
+        expected = np.full(3, -7.565148879229e-23)  # filled from R result
+        assert_almost_equal(result, expected, decimal=15)
+
+    def test_mean_gh18511(self):
+        # gh-18511 reported that the `mean` was incorrect for large arguments;
+        # check that this is resolved
+        M = 390_000
+        n = 370_000
+        N = 12_000
+
+        hm = stats.hypergeom.mean(M, n, N)
+        rm = n / M * N
+        assert_allclose(hm, rm)
+
+    @pytest.mark.xslow
+    def test_sf_gh18506(self):
+        # gh-18506 reported that `sf` was incorrect for large population;
+        # check that this is resolved
+        n = 10
+        N = 10**5
+        i = np.arange(5, 15)
+        population_size = 10.**i
+        p = stats.hypergeom.sf(n - 1, population_size, N, n)
+        assert np.all(p > 0)
+        assert np.all(np.diff(p) < 0)
+
+
+class TestLoggamma:
+    def setup_method(self):
+        self.rng = np.random.default_rng(8638464332)
+
+    # Expected cdf values were computed with mpmath. For given x and c,
+    #     x = mpmath.mpf(x)
+    #     c = mpmath.mpf(c)
+    #     cdf = mpmath.gammainc(c, 0, mpmath.exp(x),
+    #                           regularized=True)
+    @pytest.mark.parametrize('x, c, cdf',
+                             [(1, 2, 0.7546378854206702),
+                              (-1, 14, 6.768116452566383e-18),
+                              (-745.1, 0.001, 0.4749605142005238),
+                              (-800, 0.001, 0.44958802911019136),
+                              (-725, 0.1, 3.4301205868273265e-32),
+                              (-740, 0.75, 1.0074360436599631e-241)])
+    def test_cdf_ppf(self, x, c, cdf):
+        p = stats.loggamma.cdf(x, c)
+        assert_allclose(p, cdf, rtol=1e-13)
+        y = stats.loggamma.ppf(cdf, c)
+        assert_allclose(y, x, rtol=1e-13)
+
+    # Expected sf values were computed with mpmath. For given x and c,
+    #     x = mpmath.mpf(x)
+    #     c = mpmath.mpf(c)
+    #     sf = mpmath.gammainc(c, mpmath.exp(x), mpmath.inf,
+    #                          regularized=True)
+    @pytest.mark.parametrize('x, c, sf',
+                             [(4, 1.5, 1.6341528919488565e-23),
+                              (6, 100, 8.23836829202024e-74),
+                              (-800, 0.001, 0.5504119708898086),
+                              (-743, 0.0025, 0.8437131370024089)])
+    def test_sf_isf(self, x, c, sf):
+        s = stats.loggamma.sf(x, c)
+        assert_allclose(s, sf, rtol=1e-13)
+        y = stats.loggamma.isf(sf, c)
+        assert_allclose(y, x, rtol=1e-13)
+
+    def test_logpdf(self):
+        # Test logpdf with x=-500, c=2.  ln(gamma(2)) = 0, and
+        # exp(-500) ~= 7e-218, which is far smaller than the ULP
+        # of c*x=-1000, so logpdf(-500, 2) = c*x - exp(x) - ln(gamma(2))
+        # should give -1000.0.
+        lp = stats.loggamma.logpdf(-500, 2)
+        assert_allclose(lp, -1000.0, rtol=1e-14)
+
+    def test_logcdf(self):
+        x = 4.0
+        c = 4.5
+        logcdf = stats.loggamma.logcdf(x, c)
+        # Reference value computed with mpmath.
+        ref = -2.1429747073164531e-19
+        assert_allclose(logcdf, ref, rtol=5e-15)
+
+    def test_logsf(self):
+        x = -25.0
+        c = 3.5
+        logsf = stats.loggamma.logsf(x, c)
+        # Reference value computed with mpmath.
+        ref = -8.58200139319556e-40
+        assert_allclose(logsf, ref, rtol=5e-15)
+
+    def test_stats(self):
+        # The following precomputed values are from the table in section 2.2
+        # of "A Statistical Study of Log-Gamma Distribution", by Ping Shing
+        # Chan (thesis, McMaster University, 1993).
+        table = np.array([
+                # c,    mean,   var,    skew,    exc. kurt.
+                0.5, -1.9635, 4.9348, -1.5351, 4.0000,
+                1.0, -0.5772, 1.6449, -1.1395, 2.4000,
+                12.0, 2.4427, 0.0869, -0.2946, 0.1735,
+            ]).reshape(-1, 5)
+        for c, mean, var, skew, kurt in table:
+            computed = stats.loggamma.stats(c, moments='msvk')
+            assert_array_almost_equal(computed, [mean, var, skew, kurt],
+                                      decimal=4)
+
+    @pytest.mark.parametrize('c', [0.1, 0.001])
+    def test_rvs(self, c):
+        # Regression test for gh-11094.
+        x = stats.loggamma.rvs(c, size=100000, random_state=self.rng)
+        # Before gh-11094 was fixed, the case with c=0.001 would
+        # generate many -inf values.
+        assert np.isfinite(x).all()
+        # Crude statistical test.  About half the values should be
+        # less than the median and half greater than the median.
+        med = stats.loggamma.median(c)
+        btest = stats.binomtest(np.count_nonzero(x < med), len(x))
+        ci = btest.proportion_ci(confidence_level=0.999)
+        assert ci.low < 0.5 < ci.high
+
+    @pytest.mark.parametrize("c, ref",
+                             [(1e-8, 19.420680753952364),
+                              (1, 1.5772156649015328),
+                              (1e4, -3.186214986116763),
+                              (1e10, -10.093986931748889),
+                              (1e100, -113.71031611649761)])
+    def test_entropy(self, c, ref):
+
+        # Reference values were calculated with mpmath
+        # from mpmath import mp
+        # mp.dps = 500
+        # def loggamma_entropy_mpmath(c):
+        #     c = mp.mpf(c)
+        #     return float(mp.log(mp.gamma(c)) + c * (mp.one - mp.digamma(c)))
+
+        assert_allclose(stats.loggamma.entropy(c), ref, rtol=1e-14)
+
+
+class TestJohnsonsu:
+    # reference values were computed via mpmath
+    # from mpmath import mp
+    # mp.dps = 50
+    # def johnsonsu_sf(x, a, b):
+    #     x = mp.mpf(x)
+    #     a = mp.mpf(a)
+    #     b = mp.mpf(b)
+    #     return float(mp.ncdf(-(a + b * mp.log(x + mp.sqrt(x*x + 1)))))
+    # Order is x, a, b, sf, isf tol
+    # (Can't expect full precision when the ISF input is very nearly 1)
+    cases = [(-500, 1, 1, 0.9999999982660072, 1e-8),
+             (2000, 1, 1, 7.426351000595343e-21, 5e-14),
+             (100000, 1, 1, 4.046923979269977e-40, 5e-14)]
+
+    @pytest.mark.parametrize("case", cases)
+    def test_sf_isf(self, case):
+        x, a, b, sf, tol = case
+        assert_allclose(stats.johnsonsu.sf(x, a, b), sf, rtol=5e-14)
+        assert_allclose(stats.johnsonsu.isf(sf, a, b), x, rtol=tol)
+
+
+class TestJohnsonb:
+    # reference values were computed via mpmath
+    # from mpmath import mp
+    # mp.dps = 50
+    # def johnsonb_sf(x, a, b):
+    #     x = mp.mpf(x)
+    #     a = mp.mpf(a)
+    #     b = mp.mpf(b)
+    #     return float(mp.ncdf(-(a + b * mp.log(x/(mp.one - x)))))
+    # Order is x, a, b, sf, isf atol
+    # (Can't expect full precision when the ISF input is very nearly 1)
+    cases = [(1e-4, 1, 1, 0.9999999999999999, 1e-7),
+             (0.9999, 1, 1, 8.921114313932308e-25, 5e-14),
+             (0.999999, 1, 1, 5.815197487181902e-50, 5e-14)]
+
+    @pytest.mark.parametrize("case", cases)
+    def test_sf_isf(self, case):
+        x, a, b, sf, tol = case
+        assert_allclose(stats.johnsonsb.sf(x, a, b), sf, rtol=5e-14)
+        assert_allclose(stats.johnsonsb.isf(sf, a, b), x, atol=tol)
+
+
+class TestLogistic:
+    def setup_method(self):
+        self.rng = np.random.default_rng(2807014525)
+
+    # gh-6226
+    def test_cdf_ppf(self):
+        x = np.linspace(-20, 20)
+        y = stats.logistic.cdf(x)
+        xx = stats.logistic.ppf(y)
+        assert_allclose(x, xx)
+
+    def test_sf_isf(self):
+        x = np.linspace(-20, 20)
+        y = stats.logistic.sf(x)
+        xx = stats.logistic.isf(y)
+        assert_allclose(x, xx)
+
+    def test_extreme_values(self):
+        # p is chosen so that 1 - (1 - p) == p in double precision
+        p = 9.992007221626409e-16
+        desired = 34.53957599234088
+        assert_allclose(stats.logistic.ppf(1 - p), desired)
+        assert_allclose(stats.logistic.isf(p), desired)
+
+    def test_logpdf_basic(self):
+        logp = stats.logistic.logpdf([-15, 0, 10])
+        # Expected values computed with mpmath with 50 digits of precision.
+        expected = [-15.000000611804547,
+                    -1.3862943611198906,
+                    -10.000090797798434]
+        assert_allclose(logp, expected, rtol=1e-13)
+
+    def test_logpdf_extreme_values(self):
+        logp = stats.logistic.logpdf([800, -800])
+        # For such large arguments, logpdf(x) = -abs(x) when computed
+        # with 64 bit floating point.
+        assert_equal(logp, [-800, -800])
+
+    @pytest.mark.parametrize("loc_rvs,scale_rvs", [(0.4484955, 0.10216821),
+                                                   (0.62918191, 0.74367064)])
+    def test_fit(self, loc_rvs, scale_rvs):
+        data = stats.logistic.rvs(size=100, loc=loc_rvs, scale=scale_rvs,
+                                  random_state=self.rng)
+
+        # test that result of fit method is the same as optimization
+        def func(input, data):
+            a, b = input
+            n = len(data)
+            x1 = np.sum(np.exp((data - a) / b) /
+                        (1 + np.exp((data - a) / b))) - n / 2
+            x2 = np.sum(((data - a) / b) *
+                        ((np.exp((data - a) / b) - 1) /
+                         (np.exp((data - a) / b) + 1))) - n
+            return x1, x2
+
+        expected_solution = root(func, stats.logistic._fitstart(data), args=(
+            data,)).x
+        fit_method = stats.logistic.fit(data)
+
+        # other than computational variances, the fit method and the solution
+        # to this system of equations are equal
+        assert_allclose(fit_method, expected_solution, atol=1e-30)
+
+    def test_fit_comp_optimizer(self):
+        data = stats.logistic.rvs(size=100, loc=0.5, scale=2, random_state=self.rng)
+        _assert_less_or_close_loglike(stats.logistic, data)
+        _assert_less_or_close_loglike(stats.logistic, data, floc=1)
+        _assert_less_or_close_loglike(stats.logistic, data, fscale=1)
+
+    @pytest.mark.parametrize('testlogcdf', [True, False])
+    def test_logcdfsf_tails(self, testlogcdf):
+        # Test either logcdf or logsf.  By symmetry, we can use the same
+        # expected values for both by switching the sign of x for logsf.
+        x = np.array([-10000, -800, 17, 50, 500])
+        if testlogcdf:
+            y = stats.logistic.logcdf(x)
+        else:
+            y = stats.logistic.logsf(-x)
+        # The expected values were computed with mpmath.
+        expected = [-10000.0, -800.0, -4.139937633089748e-08,
+                    -1.9287498479639178e-22, -7.124576406741286e-218]
+        assert_allclose(y, expected, rtol=2e-15)
+
+    def test_fit_gh_18176(self):
+        # logistic.fit returned `scale < 0` for this data. Check that this has
+        # been fixed.
+        data = np.array([-459, 37, 43, 45, 45, 48, 54, 55, 58]
+                        + [59] * 3 + [61] * 9)
+        # If scale were negative, NLLF would be infinite, so this would fail
+        _assert_less_or_close_loglike(stats.logistic, data)
+
+
+class TestLogser:
+    def setup_method(self):
+        self.rng = np.random.default_rng(187505461)
+
+    def test_rvs(self):
+        vals = stats.logser.rvs(0.75, size=(2, 50), random_state=self.rng)
+        assert np.all(vals >= 1)
+        assert np.shape(vals) == (2, 50)
+        assert vals.dtype.char in typecodes['AllInteger']
+        val = stats.logser.rvs(0.75, random_state=self.rng)
+        assert isinstance(val, int)
+        val = stats.logser(0.75).rvs(3, random_state=self.rng)
+        assert isinstance(val, np.ndarray)
+        assert val.dtype.char in typecodes['AllInteger']
+
+    def test_pmf_small_p(self):
+        m = stats.logser.pmf(4, 1e-20)
+        # The expected value was computed using mpmath:
+        #   >>> import mpmath
+        #   >>> mpmath.mp.dps = 64
+        #   >>> k = 4
+        #   >>> p = mpmath.mpf('1e-20')
+        #   >>> float(-(p**k)/k/mpmath.log(1-p))
+        #   2.5e-61
+        # It is also clear from noticing that for very small p,
+        # log(1-p) is approximately -p, and the formula becomes
+        #    p**(k-1) / k
+        assert_allclose(m, 2.5e-61)
+
+    def test_mean_small_p(self):
+        m = stats.logser.mean(1e-8)
+        # The expected mean was computed using mpmath:
+        #   >>> import mpmath
+        #   >>> mpmath.dps = 60
+        #   >>> p = mpmath.mpf('1e-8')
+        #   >>> float(-p / ((1 - p)*mpmath.log(1 - p)))
+        #   1.000000005
+        assert_allclose(m, 1.000000005)
+
+    def test_sf(self):
+        p = [[0.5], [1e-5], [1 - 1e-5]]
+        k = [1, 10, 100, 1000]
+        # Reference values from Wolfram Alpha, e.g.
+        # SurvivalFunction[LogSeriesDistribution[99999/100000], 1000]
+        # 0.35068668662799737584735036958139157462633608106500173019897861351038286634
+        ref = [[0.2786524795555183, 0.00011876901682721189,
+                1.1159788564768581e-32, 1.3437300083506688e-304],
+               [5.000008333375e-06, 9.090946969973778e-52, 0, 0],
+               [0.9131419722083134, 0.745601735620566,
+                0.5495169511115096, 0.3506866866279974]]
+        res = stats.logser.sf(k, p)
+        np.testing.assert_allclose(res, ref, atol=1e-300)
+
+
+class TestGumbel_r_l:
+    @pytest.fixture(scope='function')
+    def rng(self):
+        return np.random.default_rng(1234)
+
+    @pytest.mark.parametrize("dist", [stats.gumbel_r, stats.gumbel_l])
+    @pytest.mark.parametrize("loc_rvs", [-1, 0, 1])
+    @pytest.mark.parametrize("scale_rvs", [.1, 1, 5])
+    @pytest.mark.parametrize('fix_loc, fix_scale',
+                             ([True, False], [False, True]))
+    def test_fit_comp_optimizer(self, dist, loc_rvs, scale_rvs,
+                                fix_loc, fix_scale, rng):
+        data = dist.rvs(size=100, loc=loc_rvs, scale=scale_rvs,
+                        random_state=rng)
+
+        kwds = dict()
+        # the fixed location and scales are arbitrarily modified to not be
+        # close to the true value.
+        if fix_loc:
+            kwds['floc'] = loc_rvs * 2
+        if fix_scale:
+            kwds['fscale'] = scale_rvs * 2
+
+        # test that the gumbel_* fit method is better than super method
+        _assert_less_or_close_loglike(dist, data, **kwds)
+
+    @pytest.mark.parametrize("dist, sgn", [(stats.gumbel_r, 1),
+                                           (stats.gumbel_l, -1)])
+    def test_fit(self, dist, sgn):
+        z = sgn*np.array([3, 3, 3, 3, 3, 3, 3, 3.00000001])
+        loc, scale = dist.fit(z)
+        # The expected values were computed with mpmath with 60 digits
+        # of precision.
+        assert_allclose(loc, sgn*3.0000000001667906)
+        assert_allclose(scale, 1.2495222465145514e-09, rtol=1e-6)
+
+
+class TestPareto:
+    def test_stats(self):
+        # Check the stats() method with some simple values. Also check
+        # that the calculations do not trigger RuntimeWarnings.
+        with warnings.catch_warnings():
+            warnings.simplefilter("error", RuntimeWarning)
+
+            m, v, s, k = stats.pareto.stats(0.5, moments='mvsk')
+            assert_equal(m, np.inf)
+            assert_equal(v, np.inf)
+            assert_equal(s, np.nan)
+            assert_equal(k, np.nan)
+
+            m, v, s, k = stats.pareto.stats(1.0, moments='mvsk')
+            assert_equal(m, np.inf)
+            assert_equal(v, np.inf)
+            assert_equal(s, np.nan)
+            assert_equal(k, np.nan)
+
+            m, v, s, k = stats.pareto.stats(1.5, moments='mvsk')
+            assert_equal(m, 3.0)
+            assert_equal(v, np.inf)
+            assert_equal(s, np.nan)
+            assert_equal(k, np.nan)
+
+            m, v, s, k = stats.pareto.stats(2.0, moments='mvsk')
+            assert_equal(m, 2.0)
+            assert_equal(v, np.inf)
+            assert_equal(s, np.nan)
+            assert_equal(k, np.nan)
+
+            m, v, s, k = stats.pareto.stats(2.5, moments='mvsk')
+            assert_allclose(m, 2.5 / 1.5)
+            assert_allclose(v, 2.5 / (1.5*1.5*0.5))
+            assert_equal(s, np.nan)
+            assert_equal(k, np.nan)
+
+            m, v, s, k = stats.pareto.stats(3.0, moments='mvsk')
+            assert_allclose(m, 1.5)
+            assert_allclose(v, 0.75)
+            assert_equal(s, np.nan)
+            assert_equal(k, np.nan)
+
+            m, v, s, k = stats.pareto.stats(3.5, moments='mvsk')
+            assert_allclose(m, 3.5 / 2.5)
+            assert_allclose(v, 3.5 / (2.5*2.5*1.5))
+            assert_allclose(s, (2*4.5/0.5)*np.sqrt(1.5/3.5))
+            assert_equal(k, np.nan)
+
+            m, v, s, k = stats.pareto.stats(4.0, moments='mvsk')
+            assert_allclose(m, 4.0 / 3.0)
+            assert_allclose(v, 4.0 / 18.0)
+            assert_allclose(s, 2*(1+4.0)/(4.0-3) * np.sqrt((4.0-2)/4.0))
+            assert_equal(k, np.nan)
+
+            m, v, s, k = stats.pareto.stats(4.5, moments='mvsk')
+            assert_allclose(m, 4.5 / 3.5)
+            assert_allclose(v, 4.5 / (3.5*3.5*2.5))
+            assert_allclose(s, (2*5.5/1.5) * np.sqrt(2.5/4.5))
+            assert_allclose(k, 6*(4.5**3 + 4.5**2 - 6*4.5 - 2)/(4.5*1.5*0.5))
+
+    def test_sf(self):
+        x = 1e9
+        b = 2
+        scale = 1.5
+        p = stats.pareto.sf(x, b, loc=0, scale=scale)
+        expected = (scale/x)**b   # 2.25e-18
+        assert_allclose(p, expected)
+
+    @pytest.mark.filterwarnings("ignore:invalid value encountered in "
+                                "double_scalars")
+    @pytest.mark.parametrize("rvs_shape", [1, 2])
+    @pytest.mark.parametrize("rvs_loc", [0, 2])
+    @pytest.mark.parametrize("rvs_scale", [1, 5])
+    def test_fit(self, rvs_shape, rvs_loc, rvs_scale):
+        rng = np.random.default_rng(1234)
+        data = stats.pareto.rvs(size=100, b=rvs_shape, scale=rvs_scale,
+                                loc=rvs_loc, random_state=rng)
+
+        # shape can still be fixed with multiple names
+        shape_mle_analytical1 = stats.pareto.fit(data, floc=0, f0=1.04)[0]
+        shape_mle_analytical2 = stats.pareto.fit(data, floc=0, fix_b=1.04)[0]
+        shape_mle_analytical3 = stats.pareto.fit(data, floc=0, fb=1.04)[0]
+        assert (shape_mle_analytical1 == shape_mle_analytical2 ==
+                shape_mle_analytical3 == 1.04)
+
+        # data can be shifted with changes to `loc`
+        data = stats.pareto.rvs(size=100, b=rvs_shape, scale=rvs_scale,
+                                loc=(rvs_loc + 2), random_state=rng)
+        shape_mle_a, loc_mle_a, scale_mle_a = stats.pareto.fit(data, floc=2)
+        assert_equal(scale_mle_a + 2, data.min())
+
+        data_shift = data - 2
+        ndata = data_shift.shape[0]
+        assert_equal(shape_mle_a,
+                     ndata / np.sum(np.log(data_shift/data_shift.min())))
+        assert_equal(loc_mle_a, 2)
+
+    @pytest.mark.parametrize("rvs_shape", [.1, 2])
+    @pytest.mark.parametrize("rvs_loc", [0, 2])
+    @pytest.mark.parametrize("rvs_scale", [1, 5])
+    @pytest.mark.parametrize('fix_shape, fix_loc, fix_scale',
+                             [p for p in product([True, False], repeat=3)
+                              if False in p])
+    @np.errstate(invalid="ignore")
+    def test_fit_MLE_comp_optimizer(self, rvs_shape, rvs_loc, rvs_scale,
+                                    fix_shape, fix_loc, fix_scale):
+        rng = np.random.default_rng(1234)
+        data = stats.pareto.rvs(size=100, b=rvs_shape, scale=rvs_scale,
+                                loc=rvs_loc, random_state=rng)
+
+        kwds = {}
+        if fix_shape:
+            kwds['f0'] = rvs_shape
+        if fix_loc:
+            kwds['floc'] = rvs_loc
+        if fix_scale:
+            kwds['fscale'] = rvs_scale
+
+        _assert_less_or_close_loglike(stats.pareto, data, **kwds)
+
+    @np.errstate(invalid="ignore")
+    def test_fit_known_bad_seed(self):
+        # Tests a known seed and set of parameters that would produce a result
+        # would violate the support of Pareto if the fit method did not check
+        # the constraint `fscale + floc < min(data)`.
+        shape, location, scale = 1, 0, 1
+        data = stats.pareto.rvs(shape, location, scale, size=100,
+                                random_state=np.random.default_rng(2535619))
+        _assert_less_or_close_loglike(stats.pareto, data)
+
+    def test_fit_warnings(self):
+        assert_fit_warnings(stats.pareto)
+        # `floc` that causes invalid negative data
+        assert_raises(FitDataError, stats.pareto.fit, [1, 2, 3], floc=2)
+        # `floc` and `fscale` combination causes invalid data
+        assert_raises(FitDataError, stats.pareto.fit, [5, 2, 3], floc=1,
+                      fscale=3)
+
+    def test_negative_data(self):
+        rng = np.random.default_rng(1234)
+        data = stats.pareto.rvs(loc=-130, b=1, size=100, random_state=rng)
+        assert_array_less(data, 0)
+        # The purpose of this test is to make sure that no runtime warnings are
+        # raised for all negative data, not the output of the fit method. Other
+        # methods test the output but have to silence warnings from the super
+        # method.
+        _ = stats.pareto.fit(data)
+
+
+class TestGenpareto:
+    def test_ab(self):
+        # c >= 0: a, b = [0, inf]
+        for c in [1., 0.]:
+            c = np.asarray(c)
+            a, b = stats.genpareto._get_support(c)
+            assert_equal(a, 0.)
+            assert_(np.isposinf(b))
+
+        # c < 0: a=0, b=1/|c|
+        c = np.asarray(-2.)
+        a, b = stats.genpareto._get_support(c)
+        assert_allclose([a, b], [0., 0.5])
+
+    def test_c0(self):
+        # with c=0, genpareto reduces to the exponential distribution
+        # rv = stats.genpareto(c=0.)
+        rv = stats.genpareto(c=0.)
+        x = np.linspace(0, 10., 30)
+        assert_allclose(rv.pdf(x), stats.expon.pdf(x))
+        assert_allclose(rv.cdf(x), stats.expon.cdf(x))
+        assert_allclose(rv.sf(x), stats.expon.sf(x))
+
+        q = np.linspace(0., 1., 10)
+        assert_allclose(rv.ppf(q), stats.expon.ppf(q))
+
+    def test_cm1(self):
+        # with c=-1, genpareto reduces to the uniform distr on [0, 1]
+        rv = stats.genpareto(c=-1.)
+        x = np.linspace(0, 10., 30)
+        assert_allclose(rv.pdf(x), stats.uniform.pdf(x))
+        assert_allclose(rv.cdf(x), stats.uniform.cdf(x))
+        assert_allclose(rv.sf(x), stats.uniform.sf(x))
+
+        q = np.linspace(0., 1., 10)
+        assert_allclose(rv.ppf(q), stats.uniform.ppf(q))
+
+        # logpdf(1., c=-1) should be zero
+        assert_allclose(rv.logpdf(1), 0)
+
+    def test_x_inf(self):
+        # make sure x=inf is handled gracefully
+        rv = stats.genpareto(c=0.1)
+        assert_allclose([rv.pdf(np.inf), rv.cdf(np.inf)], [0., 1.])
+        assert_(np.isneginf(rv.logpdf(np.inf)))
+
+        rv = stats.genpareto(c=0.)
+        assert_allclose([rv.pdf(np.inf), rv.cdf(np.inf)], [0., 1.])
+        assert_(np.isneginf(rv.logpdf(np.inf)))
+
+        rv = stats.genpareto(c=-1.)
+        assert_allclose([rv.pdf(np.inf), rv.cdf(np.inf)], [0., 1.])
+        assert_(np.isneginf(rv.logpdf(np.inf)))
+
+    def test_c_continuity(self):
+        # pdf is continuous at c=0, -1
+        x = np.linspace(0, 10, 30)
+        for c in [0, -1]:
+            pdf0 = stats.genpareto.pdf(x, c)
+            for dc in [1e-14, -1e-14]:
+                pdfc = stats.genpareto.pdf(x, c + dc)
+                assert_allclose(pdf0, pdfc, atol=1e-12)
+
+            cdf0 = stats.genpareto.cdf(x, c)
+            for dc in [1e-14, 1e-14]:
+                cdfc = stats.genpareto.cdf(x, c + dc)
+                assert_allclose(cdf0, cdfc, atol=1e-12)
+
+    def test_c_continuity_ppf(self):
+        q = np.r_[np.logspace(1e-12, 0.01, base=0.1),
+                  np.linspace(0.01, 1, 30, endpoint=False),
+                  1. - np.logspace(1e-12, 0.01, base=0.1)]
+        for c in [0., -1.]:
+            ppf0 = stats.genpareto.ppf(q, c)
+            for dc in [1e-14, -1e-14]:
+                ppfc = stats.genpareto.ppf(q, c + dc)
+                assert_allclose(ppf0, ppfc, atol=1e-12)
+
+    def test_c_continuity_isf(self):
+        q = np.r_[np.logspace(1e-12, 0.01, base=0.1),
+                  np.linspace(0.01, 1, 30, endpoint=False),
+                  1. - np.logspace(1e-12, 0.01, base=0.1)]
+        for c in [0., -1.]:
+            isf0 = stats.genpareto.isf(q, c)
+            for dc in [1e-14, -1e-14]:
+                isfc = stats.genpareto.isf(q, c + dc)
+                assert_allclose(isf0, isfc, atol=1e-12)
+
+    def test_cdf_ppf_roundtrip(self):
+        # this should pass with machine precision. hat tip @pbrod
+        q = np.r_[np.logspace(1e-12, 0.01, base=0.1),
+                  np.linspace(0.01, 1, 30, endpoint=False),
+                  1. - np.logspace(1e-12, 0.01, base=0.1)]
+        for c in [1e-8, -1e-18, 1e-15, -1e-15]:
+            assert_allclose(stats.genpareto.cdf(stats.genpareto.ppf(q, c), c),
+                            q, atol=1e-15)
+
+    def test_logsf(self):
+        logp = stats.genpareto.logsf(1e10, .01, 0, 1)
+        assert_allclose(logp, -1842.0680753952365)
+
+    # Values in 'expected_stats' are
+    # [mean, variance, skewness, excess kurtosis].
+    @pytest.mark.parametrize(
+        'c, expected_stats',
+        [(0, [1, 1, 2, 6]),
+         (1/4, [4/3, 32/9, 10/np.sqrt(2), np.nan]),
+         (1/9, [9/8, (81/64)*(9/7), (10/9)*np.sqrt(7), 754/45]),
+         (-1, [1/2, 1/12, 0, -6/5])])
+    def test_stats(self, c, expected_stats):
+        result = stats.genpareto.stats(c, moments='mvsk')
+        assert_allclose(result, expected_stats, rtol=1e-13, atol=1e-15)
+
+    def test_var(self):
+        # Regression test for gh-11168.
+        v = stats.genpareto.var(1e-8)
+        assert_allclose(v, 1.000000040000001, rtol=1e-13)
+
+
+class TestPearson3:
+    def setup_method(self):
+        self.rng = np.random.default_rng(2775995570)
+
+    def test_rvs(self):
+        vals = stats.pearson3.rvs(0.1, size=(2, 50), random_state=self.rng)
+        assert np.shape(vals) == (2, 50)
+        assert vals.dtype.char in typecodes['AllFloat']
+        val = stats.pearson3.rvs(0.5, random_state=self.rng)
+        assert isinstance(val, float)
+        val = stats.pearson3(0.5).rvs(3, random_state=self.rng)
+        assert isinstance(val, np.ndarray)
+        assert val.dtype.char in typecodes['AllFloat']
+        assert len(val) == 3
+
+    def test_pdf(self):
+        vals = stats.pearson3.pdf(2, [0.0, 0.1, 0.2])
+        assert_allclose(vals, np.array([0.05399097, 0.05555481, 0.05670246]),
+                        atol=1e-6)
+        vals = stats.pearson3.pdf(-3, 0.1)
+        assert_allclose(vals, np.array([0.00313791]), atol=1e-6)
+        vals = stats.pearson3.pdf([-3, -2, -1, 0, 1], 0.1)
+        assert_allclose(vals, np.array([0.00313791, 0.05192304, 0.25028092,
+                                        0.39885918, 0.23413173]), atol=1e-6)
+
+    def test_cdf(self):
+        vals = stats.pearson3.cdf(2, [0.0, 0.1, 0.2])
+        assert_allclose(vals, np.array([0.97724987, 0.97462004, 0.97213626]),
+                        atol=1e-6)
+        vals = stats.pearson3.cdf(-3, 0.1)
+        assert_allclose(vals, [0.00082256], atol=1e-6)
+        vals = stats.pearson3.cdf([-3, -2, -1, 0, 1], 0.1)
+        assert_allclose(vals, [8.22563821e-04, 1.99860448e-02, 1.58550710e-01,
+                               5.06649130e-01, 8.41442111e-01], atol=1e-6)
+
+    def test_negative_cdf_bug_11186(self):
+        # incorrect CDFs for negative skews in gh-11186; fixed in gh-12640
+        # Also check vectorization w/ negative, zero, and positive skews
+        skews = [-3, -1, 0, 0.5]
+        x_eval = 0.5
+        neg_inf = -30  # avoid RuntimeWarning caused by np.log(0)
+        cdfs = stats.pearson3.cdf(x_eval, skews)
+        int_pdfs = [quad(stats.pearson3(skew).pdf, neg_inf, x_eval)[0]
+                    for skew in skews]
+        assert_allclose(cdfs, int_pdfs)
+
+    def test_return_array_bug_11746(self):
+        # pearson3.moment was returning size 0 or 1 array instead of float
+        # The first moment is equal to the loc, which defaults to zero
+        moment = stats.pearson3.moment(1, 2)
+        assert_equal(moment, 0)
+        assert isinstance(moment, np.number)
+
+        moment = stats.pearson3.moment(1, 0.000001)
+        assert_equal(moment, 0)
+        assert isinstance(moment, np.number)
+
+    def test_ppf_bug_17050(self):
+        # incorrect PPF for negative skews were reported in gh-17050
+        # Check that this is fixed (even in the array case)
+        skews = [-3, -1, 0, 0.5]
+        x_eval = 0.5
+        res = stats.pearson3.ppf(stats.pearson3.cdf(x_eval, skews), skews)
+        assert_allclose(res, x_eval)
+
+        # Negation of the skew flips the distribution about the origin, so
+        # the following should hold
+        skew = np.array([[-0.5], [1.5]])
+        x = np.linspace(-2, 2)
+        assert_allclose(stats.pearson3.pdf(x, skew),
+                        stats.pearson3.pdf(-x, -skew))
+        assert_allclose(stats.pearson3.cdf(x, skew),
+                        stats.pearson3.sf(-x, -skew))
+        assert_allclose(stats.pearson3.ppf(x, skew),
+                        -stats.pearson3.isf(x, -skew))
+
+    def test_sf(self):
+        # reference values were computed via the reference distribution, e.g.
+        # mp.dps = 50; Pearson3(skew=skew).sf(x). Check positive, negative,
+        # and zero skew due to branching.
+        skew = [0.1, 0.5, 1.0, -0.1]
+        x = [5.0, 10.0, 50.0, 8.0]
+        ref = [1.64721926440872e-06, 8.271911573556123e-11,
+               1.3149506021756343e-40, 2.763057937820296e-21]
+        assert_allclose(stats.pearson3.sf(x, skew), ref, rtol=2e-14)
+        assert_allclose(stats.pearson3.sf(x, 0), stats.norm.sf(x), rtol=2e-14)
+
+
+class TestKappa4:
+    def test_cdf_genpareto(self):
+        # h = 1 and k != 0 is generalized Pareto
+        x = [0.0, 0.1, 0.2, 0.5]
+        h = 1.0
+        for k in [-1.9, -1.0, -0.5, -0.2, -0.1, 0.1, 0.2, 0.5, 1.0,
+                  1.9]:
+            vals = stats.kappa4.cdf(x, h, k)
+            # shape parameter is opposite what is expected
+            vals_comp = stats.genpareto.cdf(x, -k)
+            assert_allclose(vals, vals_comp)
+
+    def test_cdf_genextreme(self):
+        # h = 0 and k != 0 is generalized extreme value
+        x = np.linspace(-5, 5, 10)
+        h = 0.0
+        k = np.linspace(-3, 3, 10)
+        vals = stats.kappa4.cdf(x, h, k)
+        vals_comp = stats.genextreme.cdf(x, k)
+        assert_allclose(vals, vals_comp)
+
+    def test_cdf_expon(self):
+        # h = 1 and k = 0 is exponential
+        x = np.linspace(0, 10, 10)
+        h = 1.0
+        k = 0.0
+        vals = stats.kappa4.cdf(x, h, k)
+        vals_comp = stats.expon.cdf(x)
+        assert_allclose(vals, vals_comp)
+
+    def test_cdf_gumbel_r(self):
+        # h = 0 and k = 0 is gumbel_r
+        x = np.linspace(-5, 5, 10)
+        h = 0.0
+        k = 0.0
+        vals = stats.kappa4.cdf(x, h, k)
+        vals_comp = stats.gumbel_r.cdf(x)
+        assert_allclose(vals, vals_comp)
+
+    def test_cdf_logistic(self):
+        # h = -1 and k = 0 is logistic
+        x = np.linspace(-5, 5, 10)
+        h = -1.0
+        k = 0.0
+        vals = stats.kappa4.cdf(x, h, k)
+        vals_comp = stats.logistic.cdf(x)
+        assert_allclose(vals, vals_comp)
+
+    def test_cdf_uniform(self):
+        # h = 1 and k = 1 is uniform
+        x = np.linspace(-5, 5, 10)
+        h = 1.0
+        k = 1.0
+        vals = stats.kappa4.cdf(x, h, k)
+        vals_comp = stats.uniform.cdf(x)
+        assert_allclose(vals, vals_comp)
+
+    def test_integers_ctor(self):
+        # regression test for gh-7416: _argcheck fails for integer h and k
+        # in numpy 1.12
+        stats.kappa4(1, 2)
+
+
+class TestPoisson:
+    def setup_method(self):
+        self.rng = np.random.default_rng(9799340796)
+
+    def test_pmf_basic(self):
+        # Basic case
+        ln2 = np.log(2)
+        vals = stats.poisson.pmf([0, 1, 2], ln2)
+        expected = [0.5, ln2/2, ln2**2/4]
+        assert_allclose(vals, expected)
+
+    def test_mu0(self):
+        # Edge case: mu=0
+        vals = stats.poisson.pmf([0, 1, 2], 0)
+        expected = [1, 0, 0]
+        assert_array_equal(vals, expected)
+
+        interval = stats.poisson.interval(0.95, 0)
+        assert_equal(interval, (0, 0))
+
+    def test_rvs(self):
+        vals = stats.poisson.rvs(0.5, size=(2, 50), random_state=self.rng)
+        assert np.all(vals >= 0)
+        assert np.shape(vals) == (2, 50)
+        assert vals.dtype.char in typecodes['AllInteger']
+        val = stats.poisson.rvs(0.5, random_state=self.rng)
+        assert isinstance(val, int)
+        val = stats.poisson(0.5).rvs(3, random_state=self.rng)
+        assert isinstance(val, np.ndarray)
+        assert val.dtype.char in typecodes['AllInteger']
+
+    def test_stats(self):
+        mu = 16.0
+        result = stats.poisson.stats(mu, moments='mvsk')
+        assert_allclose(result, [mu, mu, np.sqrt(1.0/mu), 1.0/mu])
+
+        mu = np.array([0.0, 1.0, 2.0])
+        result = stats.poisson.stats(mu, moments='mvsk')
+        expected = (mu, mu, [np.inf, 1, 1/np.sqrt(2)], [np.inf, 1, 0.5])
+        assert_allclose(result, expected)
+
+
+class TestKSTwo:
+
+    def test_cdf(self):
+        for n in [1, 2, 3, 10, 100, 1000]:
+            # Test x-values:
+            #  0, 1/2n, where the cdf should be 0
+            #  1/n, where the cdf should be n!/n^n
+            #  0.5, where the cdf should match ksone.cdf
+            # 1-1/n, where cdf = 1-2/n^n
+            # 1, where cdf == 1
+            # (E.g. Exact values given by Eqn 1 in Simard / L'Ecuyer)
+            x = np.array([0, 0.5/n, 1/n, 0.5, 1-1.0/n, 1])
+            v1 = (1.0/n)**n
+            lg = scipy.special.gammaln(n+1)
+            elg = (np.exp(lg) if v1 != 0 else 0)
+            expected = np.array([0, 0, v1 * elg,
+                                 1 - 2*stats.ksone.sf(0.5, n),
+                                 max(1 - 2*v1, 0.0),
+                                 1.0])
+            vals_cdf = stats.kstwo.cdf(x, n)
+            assert_allclose(vals_cdf, expected)
+
+    def test_sf(self):
+        x = np.linspace(0, 1, 11)
+        for n in [1, 2, 3, 10, 100, 1000]:
+            # Same x values as in test_cdf, and use sf = 1 - cdf
+            x = np.array([0, 0.5/n, 1/n, 0.5, 1-1.0/n, 1])
+            v1 = (1.0/n)**n
+            lg = scipy.special.gammaln(n+1)
+            elg = (np.exp(lg) if v1 != 0 else 0)
+            expected = np.array([1.0, 1.0,
+                                 1 - v1 * elg,
+                                 2*stats.ksone.sf(0.5, n),
+                                 min(2*v1, 1.0), 0])
+            vals_sf = stats.kstwo.sf(x, n)
+            assert_allclose(vals_sf, expected)
+
+    def test_cdf_sqrtn(self):
+        # For fixed a, cdf(a/sqrt(n), n) -> kstwobign(a) as n->infinity
+        # cdf(a/sqrt(n), n) is an increasing function of n (and a)
+        # Check that the function is indeed increasing (allowing for some
+        # small floating point and algorithm differences.)
+        x = np.linspace(0, 2, 11)[1:]
+        ns = [50, 100, 200, 400, 1000, 2000]
+        for _x in x:
+            xn = _x / np.sqrt(ns)
+            probs = stats.kstwo.cdf(xn, ns)
+            diffs = np.diff(probs)
+            assert_array_less(diffs, 1e-8)
+
+    def test_cdf_sf(self):
+        x = np.linspace(0, 1, 11)
+        for n in [1, 2, 3, 10, 100, 1000]:
+            vals_cdf = stats.kstwo.cdf(x, n)
+            vals_sf = stats.kstwo.sf(x, n)
+            assert_array_almost_equal(vals_cdf, 1 - vals_sf)
+
+    def test_cdf_sf_sqrtn(self):
+        x = np.linspace(0, 1, 11)
+        for n in [1, 2, 3, 10, 100, 1000]:
+            xn = x / np.sqrt(n)
+            vals_cdf = stats.kstwo.cdf(xn, n)
+            vals_sf = stats.kstwo.sf(xn, n)
+            assert_array_almost_equal(vals_cdf, 1 - vals_sf)
+
+    def test_ppf_of_cdf(self):
+        x = np.linspace(0, 1, 11)
+        for n in [1, 2, 3, 10, 100, 1000]:
+            xn = x[x > 0.5/n]
+            vals_cdf = stats.kstwo.cdf(xn, n)
+            # CDFs close to 1 are better dealt with using the SF
+            cond = (0 < vals_cdf) & (vals_cdf < 0.99)
+            vals = stats.kstwo.ppf(vals_cdf, n)
+            assert_allclose(vals[cond], xn[cond], rtol=1e-4)
+
+    def test_isf_of_sf(self):
+        x = np.linspace(0, 1, 11)
+        for n in [1, 2, 3, 10, 100, 1000]:
+            xn = x[x > 0.5/n]
+            vals_isf = stats.kstwo.isf(xn, n)
+            cond = (0 < vals_isf) & (vals_isf < 1.0)
+            vals = stats.kstwo.sf(vals_isf, n)
+            assert_allclose(vals[cond], xn[cond], rtol=1e-4)
+
+    def test_ppf_of_cdf_sqrtn(self):
+        x = np.linspace(0, 1, 11)
+        for n in [1, 2, 3, 10, 100, 1000]:
+            xn = (x / np.sqrt(n))[x > 0.5/n]
+            vals_cdf = stats.kstwo.cdf(xn, n)
+            cond = (0 < vals_cdf) & (vals_cdf < 1.0)
+            vals = stats.kstwo.ppf(vals_cdf, n)
+            assert_allclose(vals[cond], xn[cond])
+
+    def test_isf_of_sf_sqrtn(self):
+        x = np.linspace(0, 1, 11)
+        for n in [1, 2, 3, 10, 100, 1000]:
+            xn = (x / np.sqrt(n))[x > 0.5/n]
+            vals_sf = stats.kstwo.sf(xn, n)
+            # SFs close to 1 are better dealt with using the CDF
+            cond = (0 < vals_sf) & (vals_sf < 0.95)
+            vals = stats.kstwo.isf(vals_sf, n)
+            assert_allclose(vals[cond], xn[cond])
+
+    def test_ppf(self):
+        probs = np.linspace(0, 1, 11)[1:]
+        for n in [1, 2, 3, 10, 100, 1000]:
+            xn = stats.kstwo.ppf(probs, n)
+            vals_cdf = stats.kstwo.cdf(xn, n)
+            assert_allclose(vals_cdf, probs)
+
+    def test_simard_lecuyer_table1(self):
+        # Compute the cdf for values near the mean of the distribution.
+        # The mean u ~ log(2)*sqrt(pi/(2n))
+        # Compute for x in [u/4, u/3, u/2, u, 2u, 3u]
+        # This is the computation of Table 1 of Simard, R., L'Ecuyer, P. (2011)
+        #  "Computing the Two-Sided Kolmogorov-Smirnov Distribution".
+        # Except that the values below are not from the published table, but
+        # were generated using an independent SageMath implementation of
+        # Durbin's algorithm (with the exponentiation and scaling of
+        # Marsaglia/Tsang/Wang's version) using 500 bit arithmetic.
+        # Some of the values in the published table have relative
+        # errors greater than 1e-4.
+        ns = [10, 50, 100, 200, 500, 1000]
+        ratios = np.array([1.0/4, 1.0/3, 1.0/2, 1, 2, 3])
+        expected = np.array([
+            [1.92155292e-08, 5.72933228e-05, 2.15233226e-02, 6.31566589e-01,
+             9.97685592e-01, 9.99999942e-01],
+            [2.28096224e-09, 1.99142563e-05, 1.42617934e-02, 5.95345542e-01,
+             9.96177701e-01, 9.99998662e-01],
+            [1.00201886e-09, 1.32673079e-05, 1.24608594e-02, 5.86163220e-01,
+             9.95866877e-01, 9.99998240e-01],
+            [4.93313022e-10, 9.52658029e-06, 1.12123138e-02, 5.79486872e-01,
+             9.95661824e-01, 9.99997964e-01],
+            [2.37049293e-10, 6.85002458e-06, 1.01309221e-02, 5.73427224e-01,
+             9.95491207e-01, 9.99997750e-01],
+            [1.56990874e-10, 5.71738276e-06, 9.59725430e-03, 5.70322692e-01,
+             9.95409545e-01, 9.99997657e-01]
+        ])
+        for idx, n in enumerate(ns):
+            x = ratios * np.log(2) * np.sqrt(np.pi/2/n)
+            vals_cdf = stats.kstwo.cdf(x, n)
+            assert_allclose(vals_cdf, expected[idx], rtol=1e-5)
+
+
+class TestZipf:
+    def setup_method(self):
+        self.rng = np.random.default_rng(2444103536)
+
+    def test_rvs(self):
+        vals = stats.zipf.rvs(1.5, size=(2, 50), random_state=self.rng)
+        assert np.all(vals >= 1)
+        assert np.shape(vals) == (2, 50)
+        assert vals.dtype.char in typecodes['AllInteger']
+        val = stats.zipf.rvs(1.5, random_state=self.rng)
+        assert isinstance(val, int)
+        val = stats.zipf(1.5).rvs(3, random_state=self.rng)
+        assert isinstance(val, np.ndarray)
+        assert val.dtype.char in typecodes['AllInteger']
+
+    def test_moments(self):
+        # n-th moment is finite iff a > n + 1
+        m, v = stats.zipf.stats(a=2.8)
+        assert_(np.isfinite(m))
+        assert_equal(v, np.inf)
+
+        s, k = stats.zipf.stats(a=4.8, moments='sk')
+        assert_(not np.isfinite([s, k]).all())
+
+
+class TestDLaplace:
+    def setup_method(self):
+        self.rng = np.random.default_rng(460403075)
+
+    def test_rvs(self):
+        vals = stats.dlaplace.rvs(1.5, size=(2, 50), random_state=self.rng)
+        assert np.shape(vals) == (2, 50)
+        assert vals.dtype.char in typecodes['AllInteger']
+        val = stats.dlaplace.rvs(1.5, random_state=self.rng)
+        assert isinstance(val, int)
+        val = stats.dlaplace(1.5).rvs(3, random_state=self.rng)
+        assert isinstance(val, np.ndarray)
+        assert val.dtype.char in typecodes['AllInteger']
+        assert stats.dlaplace.rvs(0.8, random_state=self.rng) is not None
+
+    def test_stats(self):
+        # compare the explicit formulas w/ direct summation using pmf
+        a = 1.
+        dl = stats.dlaplace(a)
+        m, v, s, k = dl.stats('mvsk')
+
+        N = 37
+        xx = np.arange(-N, N+1)
+        pp = dl.pmf(xx)
+        m2, m4 = np.sum(pp*xx**2), np.sum(pp*xx**4)
+        assert_equal((m, s), (0, 0))
+        assert_allclose((v, k), (m2, m4/m2**2 - 3.), atol=1e-14, rtol=1e-8)
+
+    def test_stats2(self):
+        a = np.log(2.)
+        dl = stats.dlaplace(a)
+        m, v, s, k = dl.stats('mvsk')
+        assert_equal((m, s), (0., 0.))
+        assert_allclose((v, k), (4., 3.25))
+
+
+class TestInvgauss:
+    def setup_method(self):
+        self.rng = np.random.default_rng(5422839947)
+
+    @pytest.mark.parametrize("rvs_mu,rvs_loc,rvs_scale",
+                             [(2, 0, 1), (4.635, 4.362, 6.303)])
+    def test_fit(self, rvs_mu, rvs_loc, rvs_scale):
+        data = stats.invgauss.rvs(size=100, mu=rvs_mu,
+                                  loc=rvs_loc, scale=rvs_scale, random_state=self.rng)
+        # Analytical MLEs are calculated with formula when `floc` is fixed
+        mu, loc, scale = stats.invgauss.fit(data, floc=rvs_loc)
+
+        data = data - rvs_loc
+        mu_temp = np.mean(data)
+        scale_mle = len(data) / (np.sum(data**(-1) - mu_temp**(-1)))
+        mu_mle = mu_temp/scale_mle
+
+        # `mu` and `scale` match analytical formula
+        assert_allclose(mu_mle, mu, atol=1e-15, rtol=1e-15)
+        assert_allclose(scale_mle, scale, atol=1e-15, rtol=1e-15)
+        assert_equal(loc, rvs_loc)
+        data = stats.invgauss.rvs(size=100, mu=rvs_mu,
+                                  loc=rvs_loc, scale=rvs_scale, random_state=self.rng)
+        # fixed parameters are returned
+        mu, loc, scale = stats.invgauss.fit(data, floc=rvs_loc - 1,
+                                            fscale=rvs_scale + 1)
+        assert_equal(rvs_scale + 1, scale)
+        assert_equal(rvs_loc - 1, loc)
+
+        # shape can still be fixed with multiple names
+        shape_mle1 = stats.invgauss.fit(data, fmu=1.04)[0]
+        shape_mle2 = stats.invgauss.fit(data, fix_mu=1.04)[0]
+        shape_mle3 = stats.invgauss.fit(data, f0=1.04)[0]
+        assert shape_mle1 == shape_mle2 == shape_mle3 == 1.04
+
+    @pytest.mark.parametrize("rvs_mu,rvs_loc,rvs_scale",
+                             [(2, 0, 1), (6.311, 3.225, 4.520)])
+    def test_fit_MLE_comp_optimizer(self, rvs_mu, rvs_loc, rvs_scale):
+        rng = np.random.RandomState(1234)
+        data = stats.invgauss.rvs(size=100, mu=rvs_mu,
+                                  loc=rvs_loc, scale=rvs_scale, random_state=rng)
+
+        super_fit = super(type(stats.invgauss), stats.invgauss).fit
+        # fitting without `floc` uses superclass fit method
+        super_fitted = super_fit(data)
+        invgauss_fit = stats.invgauss.fit(data)
+        assert_equal(super_fitted, invgauss_fit)
+
+        # fitting with `fmu` is uses superclass fit method
+        super_fitted = super_fit(data, floc=0, fmu=2)
+        invgauss_fit = stats.invgauss.fit(data, floc=0, fmu=2)
+        assert_equal(super_fitted, invgauss_fit)
+
+        # fixed `floc` uses analytical formula and provides better fit than
+        # super method
+        _assert_less_or_close_loglike(stats.invgauss, data, floc=rvs_loc)
+
+        # fixed `floc` not resulting in invalid data < 0 uses analytical
+        # formulas and provides a better fit than the super method
+        assert np.all((data - (rvs_loc - 1)) > 0)
+        _assert_less_or_close_loglike(stats.invgauss, data, floc=rvs_loc - 1)
+
+        # fixed `floc` to an arbitrary number, 0, still provides a better fit
+        # than the super method
+        _assert_less_or_close_loglike(stats.invgauss, data, floc=0)
+
+        # fixed `fscale` to an arbitrary number still provides a better fit
+        # than the super method
+        _assert_less_or_close_loglike(stats.invgauss, data, floc=rvs_loc,
+                                      fscale=self.rng.random(1)[0])
+
+    def test_fit_raise_errors(self):
+        assert_fit_warnings(stats.invgauss)
+        # FitDataError is raised when negative invalid data
+        with pytest.raises(FitDataError):
+            stats.invgauss.fit([1, 2, 3], floc=2)
+
+    def test_cdf_sf(self):
+        # Regression tests for gh-13614.
+        # Ground truth from R's statmod library (pinvgauss), e.g.
+        # library(statmod)
+        # options(digits=15)
+        # mu = c(4.17022005e-04, 7.20324493e-03, 1.14374817e-06,
+        #        3.02332573e-03, 1.46755891e-03)
+        # print(pinvgauss(5, mu, 1))
+
+        # make sure a finite value is returned when mu is very small. see
+        # GH-13614
+        mu = [4.17022005e-04, 7.20324493e-03, 1.14374817e-06,
+              3.02332573e-03, 1.46755891e-03]
+        expected = [1, 1, 1, 1, 1]
+        actual = stats.invgauss.cdf(0.4, mu=mu)
+        assert_equal(expected, actual)
+
+        # test if the function can distinguish small left/right tail
+        # probabilities from zero.
+        cdf_actual = stats.invgauss.cdf(0.001, mu=1.05)
+        assert_allclose(cdf_actual, 4.65246506892667e-219)
+        sf_actual = stats.invgauss.sf(110, mu=1.05)
+        assert_allclose(sf_actual, 4.12851625944048e-25)
+
+        # test if x does not cause numerical issues when mu is very small
+        # and x is close to mu in value.
+
+        # slightly smaller than mu
+        actual = stats.invgauss.cdf(0.00009, 0.0001)
+        assert_allclose(actual, 2.9458022894924e-26)
+
+        # slightly bigger than mu
+        actual = stats.invgauss.cdf(0.000102, 0.0001)
+        assert_allclose(actual, 0.976445540507925)
+
+    def test_logcdf_logsf(self):
+        # Regression tests for improvements made in gh-13616.
+        # Ground truth from R's statmod library (pinvgauss), e.g.
+        # library(statmod)
+        # options(digits=15)
+        # print(pinvgauss(0.001, 1.05, 1, log.p=TRUE, lower.tail=FALSE))
+
+        # test if logcdf and logsf can compute values too small to
+        # be represented on the unlogged scale. See: gh-13616
+        logcdf = stats.invgauss.logcdf(0.0001, mu=1.05)
+        assert_allclose(logcdf, -5003.87872590367)
+        logcdf = stats.invgauss.logcdf(110, 1.05)
+        assert_allclose(logcdf, -4.12851625944087e-25)
+        logsf = stats.invgauss.logsf(0.001, mu=1.05)
+        assert_allclose(logsf, -4.65246506892676e-219)
+        logsf = stats.invgauss.logsf(110, 1.05)
+        assert_allclose(logsf, -56.1467092416426)
+
+    # from mpmath import mp
+    # mp.dps = 100
+    # mu = mp.mpf(1e-2)
+    # ref = (1/2 * mp.log(2 * mp.pi * mp.e * mu**3)
+    #        - 3/2* mp.exp(2/mu) * mp.e1(2/mu))
+    @pytest.mark.parametrize("mu, ref", [(2e-8, -25.172361826883957),
+                                         (1e-3, -8.943444010642972),
+                                         (1e-2, -5.4962796152622335),
+                                         (1e8, 3.3244822568873476),
+                                         (1e100, 3.32448280139689)])
+    def test_entropy(self, mu, ref):
+        assert_allclose(stats.invgauss.entropy(mu), ref, rtol=5e-14)
+
+    def test_mu_inf_gh13666(self):
+        # invgauss methods should return correct result when mu=inf
+        # invgauss as mu -> oo is invgamma with shape and scale 0.5;
+        # see gh-13666 and gh-22496
+        dist = stats.invgauss(mu=np.inf)
+        dist0 = stats.invgamma(0.5, scale=0.5)
+        x, p = 1., 0.5
+        assert_allclose(dist.logpdf(x), dist0.logpdf(x))
+        assert_allclose(dist.pdf(x), dist0.pdf(x))
+        assert_allclose(dist.logcdf(x), dist0.logcdf(x))
+        assert_allclose(dist.cdf(x), dist0.cdf(x))
+        assert_allclose(dist.logsf(x), dist0.logsf(x))
+        assert_allclose(dist.sf(x), dist0.sf(x))
+        assert_allclose(dist.ppf(p), dist0.ppf(p))
+        assert_allclose(dist.isf(p), dist0.isf(p))
+
+
+class TestLandau:
+    @pytest.mark.parametrize('name', ['pdf', 'cdf', 'sf', 'ppf', 'isf'])
+    def test_landau_levy_agreement(self, name):
+        # Test PDF to confirm that this is the Landau distribution
+        # Test other methods with tighter tolerance than generic tests
+        # Levy entropy is slow and inaccurate, and RVS is tested generically
+        if name in {'ppf', 'isf'}:
+            x = np.linspace(0.1, 0.9, 5),
+        else:
+            x = np.linspace(-2, 5, 10),
+
+        landau_method = getattr(stats.landau, name)
+        levy_method = getattr(stats.levy_stable, name)
+        res = landau_method(*x)
+        ref = levy_method(*x, 1, 1)
+        assert_allclose(res, ref, rtol=1e-14)
+
+    def test_moments(self):
+        # I would test these against Levy above, but Levy says variance is infinite.
+        assert_equal(stats.landau.stats(moments='mvsk'), (np.nan,)*4)
+        assert_equal(stats.landau.moment(5), np.nan)
+
+
+class TestLaplace:
+    @pytest.mark.parametrize("rvs_loc", [-5, 0, 1, 2])
+    @pytest.mark.parametrize("rvs_scale", [1, 2, 3, 10])
+    def test_fit(self, rvs_loc, rvs_scale):
+        # tests that various inputs follow expected behavior
+        # for a variety of `loc` and `scale`.
+        rng = np.random.RandomState(1234)
+        data = stats.laplace.rvs(size=100, loc=rvs_loc, scale=rvs_scale,
+                                 random_state=rng)
+
+        # MLE estimates are given by
+        loc_mle = np.median(data)
+        scale_mle = np.sum(np.abs(data - loc_mle)) / len(data)
+
+        # standard outputs should match analytical MLE formulas
+        loc, scale = stats.laplace.fit(data)
+        assert_allclose(loc, loc_mle, atol=1e-15, rtol=1e-15)
+        assert_allclose(scale, scale_mle, atol=1e-15, rtol=1e-15)
+
+        # fixed parameter should use analytical formula for other
+        loc, scale = stats.laplace.fit(data, floc=loc_mle)
+        assert_allclose(scale, scale_mle, atol=1e-15, rtol=1e-15)
+        loc, scale = stats.laplace.fit(data, fscale=scale_mle)
+        assert_allclose(loc, loc_mle)
+
+        # test with non-mle fixed parameter
+        # create scale with non-median loc
+        loc = rvs_loc * 2
+        scale_mle = np.sum(np.abs(data - loc)) / len(data)
+
+        # fixed loc to non median, scale should match
+        # scale calculation with modified loc
+        loc, scale = stats.laplace.fit(data, floc=loc)
+        assert_equal(scale_mle, scale)
+
+        # fixed scale created with non median loc,
+        # loc output should still be the data median.
+        loc, scale = stats.laplace.fit(data, fscale=scale_mle)
+        assert_equal(loc_mle, loc)
+
+        # error raised when both `floc` and `fscale` are fixed
+        assert_raises(RuntimeError, stats.laplace.fit, data, floc=loc_mle,
+                      fscale=scale_mle)
+
+        # error is raised with non-finite values
+        assert_raises(ValueError, stats.laplace.fit, [np.nan])
+        assert_raises(ValueError, stats.laplace.fit, [np.inf])
+
+    @pytest.mark.parametrize("rvs_loc,rvs_scale", [(-5, 10),
+                                                   (10, 5),
+                                                   (0.5, 0.2)])
+    def test_fit_MLE_comp_optimizer(self, rvs_loc, rvs_scale):
+        rng = np.random.RandomState(1234)
+        data = stats.laplace.rvs(size=1000, loc=rvs_loc, scale=rvs_scale,
+                                 random_state=rng)
+
+        # the log-likelihood function for laplace is given by
+        def ll(loc, scale, data):
+            return -1 * (- (len(data)) * np.log(2*scale) -
+                         (1/scale)*np.sum(np.abs(data - loc)))
+
+        # test that the objective function result of the analytical MLEs is
+        # less than or equal to that of the numerically optimized estimate
+        loc, scale = stats.laplace.fit(data)
+        loc_opt, scale_opt = super(type(stats.laplace),
+                                   stats.laplace).fit(data)
+        ll_mle = ll(loc, scale, data)
+        ll_opt = ll(loc_opt, scale_opt, data)
+        assert ll_mle < ll_opt or np.allclose(ll_mle, ll_opt,
+                                              atol=1e-15, rtol=1e-15)
+
+    def test_fit_simple_non_random_data(self):
+        data = np.array([1.0, 1.0, 3.0, 5.0, 8.0, 14.0])
+        # with `floc` fixed to 6, scale should be 4.
+        loc, scale = stats.laplace.fit(data, floc=6)
+        assert_allclose(scale, 4, atol=1e-15, rtol=1e-15)
+        # with `fscale` fixed to 6, loc should be 4.
+        loc, scale = stats.laplace.fit(data, fscale=6)
+        assert_allclose(loc, 4, atol=1e-15, rtol=1e-15)
+
+    def test_sf_cdf_extremes(self):
+        # These calculations should not generate warnings.
+        x = 1000
+        p0 = stats.laplace.cdf(-x)
+        # The exact value is smaller than can be represented with
+        # 64 bit floating point, so the expected result is 0.
+        assert p0 == 0.0
+        # The closest 64 bit floating point representation of the
+        # exact value is 1.0.
+        p1 = stats.laplace.cdf(x)
+        assert p1 == 1.0
+
+        p0 = stats.laplace.sf(x)
+        # The exact value is smaller than can be represented with
+        # 64 bit floating point, so the expected result is 0.
+        assert p0 == 0.0
+        # The closest 64 bit floating point representation of the
+        # exact value is 1.0.
+        p1 = stats.laplace.sf(-x)
+        assert p1 == 1.0
+
+    def test_sf(self):
+        x = 200
+        p = stats.laplace.sf(x)
+        assert_allclose(p, np.exp(-x)/2, rtol=1e-13)
+
+    def test_isf(self):
+        p = 1e-25
+        x = stats.laplace.isf(p)
+        assert_allclose(x, -np.log(2*p), rtol=1e-13)
+
+    def test_logcdf_logsf(self):
+        x = 40
+        # Reference value computed with mpmath.
+        ref = -2.1241771276457944e-18
+        logcdf = stats.laplace.logcdf(x)
+        assert_allclose(logcdf, ref)
+        logsf = stats.laplace.logsf(-x)
+        assert_allclose(logsf, ref, rtol=5e-15)
+
+
+class TestLogLaplace:
+
+    def test_sf(self):
+        # reference values were computed via the reference distribution, e.g.
+        # mp.dps = 100; LogLaplace(c=c).sf(x).
+        c = np.array([2.0, 3.0, 5.0])
+        x = np.array([1e-5, 1e10, 1e15])
+        ref = [0.99999999995, 5e-31, 5e-76]
+        assert_allclose(stats.loglaplace.sf(x, c), ref, rtol=1e-15)
+
+    def test_isf(self):
+        # reference values were computed via the reference distribution, e.g.
+        # mp.dps = 100; LogLaplace(c=c).isf(q).
+        c = 3.25
+        q = [0.8, 0.1, 1e-10, 1e-20, 1e-40]
+        ref = [0.7543222539245642, 1.6408455124660906, 964.4916294395846,
+               1151387.578354072, 1640845512466.0906]
+        assert_allclose(stats.loglaplace.isf(q, c), ref, rtol=1e-14)
+
+    @pytest.mark.parametrize('r', [1, 2, 3, 4])
+    def test_moments_stats(self, r):
+        mom = 'mvsk'[r - 1]
+        c = np.arange(0.5, r + 0.5, 0.5)
+
+        # r-th non-central moment is infinite if |r| >= c.
+        assert_allclose(stats.loglaplace.moment(r, c), np.inf)
+
+        # r-th non-central moment is non-finite (inf or nan) if r >= c.
+        assert not np.any(np.isfinite(stats.loglaplace.stats(c, moments=mom)))
+
+    @pytest.mark.parametrize("c", [0.5, 1.0, 2.0])
+    @pytest.mark.parametrize("loc, scale", [(-1.2, 3.45)])
+    @pytest.mark.parametrize("fix_c", [True, False])
+    @pytest.mark.parametrize("fix_scale", [True, False])
+    def test_fit_analytic_mle(self, c, loc, scale, fix_c, fix_scale):
+        # Test that the analytical MLE produces no worse result than the
+        # generic (numerical) MLE.
+
+        rng = np.random.default_rng(6762668991392531563)
+        data = stats.loglaplace.rvs(c, loc=loc, scale=scale, size=100,
+                                    random_state=rng)
+
+        kwds = {'floc': loc}
+        if fix_c:
+            kwds['fc'] = c
+        if fix_scale:
+            kwds['fscale'] = scale
+        nfree = 3 - len(kwds)
+
+        if nfree == 0:
+            error_msg = "All parameters fixed. There is nothing to optimize."
+            with pytest.raises((RuntimeError, ValueError), match=error_msg):
+                stats.loglaplace.fit(data, **kwds)
+            return
+
+        _assert_less_or_close_loglike(stats.loglaplace, data, **kwds)
+
+
+class TestPowerlaw:
+
+    # In the following data, `sf` was computed with mpmath.
+    @pytest.mark.parametrize('x, a, sf',
+                             [(0.25, 2.0, 0.9375),
+                              (0.99609375, 1/256, 1.528855235208108e-05)])
+    def test_sf(self, x, a, sf):
+        assert_allclose(stats.powerlaw.sf(x, a), sf, rtol=1e-15)
+
+    @pytest.fixture(scope='function')
+    def rng(self):
+        return np.random.default_rng(1234)
+
+    @pytest.mark.parametrize("rvs_shape", [.1, .5, .75, 1, 2])
+    @pytest.mark.parametrize("rvs_loc", [-1, 0, 1])
+    @pytest.mark.parametrize("rvs_scale", [.1, 1, 5])
+    @pytest.mark.parametrize('fix_shape, fix_loc, fix_scale',
+                             [p for p in product([True, False], repeat=3)
+                              if False in p])
+    def test_fit_MLE_comp_optimizer(self, rvs_shape, rvs_loc, rvs_scale,
+                                    fix_shape, fix_loc, fix_scale, rng):
+        data = stats.powerlaw.rvs(size=250, a=rvs_shape, loc=rvs_loc,
+                                  scale=rvs_scale, random_state=rng)
+
+        kwds = dict()
+        if fix_shape:
+            kwds['f0'] = rvs_shape
+        if fix_loc:
+            kwds['floc'] = np.nextafter(data.min(), -np.inf)
+        if fix_scale:
+            kwds['fscale'] = rvs_scale
+
+        # Numerical result may equal analytical result if some code path
+        # of the analytical routine makes use of numerical optimization.
+        _assert_less_or_close_loglike(stats.powerlaw, data, **kwds,
+                                      maybe_identical=True)
+
+    def test_problem_case(self):
+        # An observed problem with the test method indicated that some fixed
+        # scale values could cause bad results, this is now corrected.
+        a = 2.50002862645130604506
+        location = 0.0
+        scale = 35.249023299873095
+
+        data = stats.powerlaw.rvs(a=a, loc=location, scale=scale, size=100,
+                                  random_state=np.random.default_rng(5))
+
+        kwds = {'fscale': np.ptp(data) * 2}
+
+        _assert_less_or_close_loglike(stats.powerlaw, data, **kwds)
+
+    def test_fit_warnings(self):
+        assert_fit_warnings(stats.powerlaw)
+        # test for error when `fscale + floc <= np.max(data)` is not satisfied
+        msg = r" Maximum likelihood estimation with 'powerlaw' requires"
+        with assert_raises(FitDataError, match=msg):
+            stats.powerlaw.fit([1, 2, 4], floc=0, fscale=3)
+
+        # test for error when `data - floc >= 0`  is not satisfied
+        msg = r" Maximum likelihood estimation with 'powerlaw' requires"
+        with assert_raises(FitDataError, match=msg):
+            stats.powerlaw.fit([1, 2, 4], floc=2)
+
+        # test for fixed location not less than `min(data)`.
+        msg = r" Maximum likelihood estimation with 'powerlaw' requires"
+        with assert_raises(FitDataError, match=msg):
+            stats.powerlaw.fit([1, 2, 4], floc=1)
+
+        # test for when fixed scale is less than or equal to range of data
+        msg = r"Negative or zero `fscale` is outside"
+        with assert_raises(ValueError, match=msg):
+            stats.powerlaw.fit([1, 2, 4], fscale=-3)
+
+        # test for when fixed scale is less than or equal to range of data
+        msg = r"`fscale` must be greater than the range of data."
+        with assert_raises(ValueError, match=msg):
+            stats.powerlaw.fit([1, 2, 4], fscale=3)
+
+    def test_minimum_data_zero_gh17801(self):
+        # gh-17801 reported an overflow error when the minimum value of the
+        # data is zero. Check that this problem is resolved.
+        data = [0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 5, 6]
+        dist = stats.powerlaw
+        with np.errstate(over='ignore'):
+            _assert_less_or_close_loglike(dist, data)
+
+
+class TestPowerLogNorm:
+
+    # reference values were computed via mpmath
+    # from mpmath import mp
+    # mp.dps = 80
+    # def powerlognorm_sf_mp(x, c, s):
+    #     x = mp.mpf(x)
+    #     c = mp.mpf(c)
+    #     s = mp.mpf(s)
+    #     return mp.ncdf(-mp.log(x) / s)**c
+    #
+    # def powerlognormal_cdf_mp(x, c, s):
+    #     return mp.one - powerlognorm_sf_mp(x, c, s)
+    #
+    # x, c, s = 100, 20, 1
+    # print(float(powerlognorm_sf_mp(x, c, s)))
+
+    @pytest.mark.parametrize("x, c, s, ref",
+                             [(100, 20, 1, 1.9057100820561928e-114),
+                              (1e-3, 20, 1, 0.9999999999507617),
+                              (1e-3, 0.02, 1, 0.9999999999999508),
+                              (1e22, 0.02, 1, 6.50744044621611e-12)])
+    def test_sf(self, x, c, s, ref):
+        assert_allclose(stats.powerlognorm.sf(x, c, s), ref, rtol=1e-13)
+
+    # reference values were computed via mpmath using the survival
+    # function above (passing in `ref` and getting `q`).
+    @pytest.mark.parametrize("q, c, s, ref",
+                             [(0.9999999587870905, 0.02, 1, 0.01),
+                              (6.690376686108851e-233, 20, 1, 1000)])
+    def test_isf(self, q, c, s, ref):
+        assert_allclose(stats.powerlognorm.isf(q, c, s), ref, rtol=5e-11)
+
+    @pytest.mark.parametrize("x, c, s, ref",
+                             [(1e25, 0.02, 1, 0.9999999999999963),
+                              (1e-6, 0.02, 1, 2.054921078040843e-45),
+                              (1e-6, 200, 1, 2.0549210780408428e-41),
+                              (0.3, 200, 1, 0.9999999999713368)])
+    def test_cdf(self, x, c, s, ref):
+        assert_allclose(stats.powerlognorm.cdf(x, c, s), ref, rtol=3e-14)
+
+    # reference values were computed via mpmath
+    # from mpmath import mp
+    # mp.dps = 50
+    # def powerlognorm_pdf_mpmath(x, c, s):
+    #     x = mp.mpf(x)
+    #     c = mp.mpf(c)
+    #     s = mp.mpf(s)
+    #     res = (c/(x * s) * mp.npdf(mp.log(x)/s) *
+    #            mp.ncdf(-mp.log(x)/s)**(c - mp.one))
+    #     return float(res)
+
+    @pytest.mark.parametrize("x, c, s, ref",
+                             [(1e22, 0.02, 1, 6.5954987852335016e-34),
+                              (1e20, 1e-3, 1, 1.588073750563988e-22),
+                              (1e40, 1e-3, 1, 1.3179391812506349e-43)])
+    def test_pdf(self, x, c, s, ref):
+        assert_allclose(stats.powerlognorm.pdf(x, c, s), ref, rtol=3e-12)
+
+
+class TestPowerNorm:
+
+    # survival function references were computed with mpmath via
+    # from mpmath import mp
+    # x = mp.mpf(x)
+    # c = mp.mpf(x)
+    # float(mp.ncdf(-x)**c)
+
+    @pytest.mark.parametrize("x, c, ref",
+                             [(9, 1, 1.1285884059538405e-19),
+                              (20, 2, 7.582445786569958e-178),
+                              (100, 0.02, 3.330957891903866e-44),
+                              (200, 0.01, 1.3004759092324774e-87)])
+    def test_sf(self, x, c, ref):
+        assert_allclose(stats.powernorm.sf(x, c), ref, rtol=1e-13)
+
+    # inverse survival function references were computed with mpmath via
+    # from mpmath import mp
+    # def isf_mp(q, c):
+    #     q = mp.mpf(q)
+    #     c = mp.mpf(c)
+    #     arg = q**(mp.one / c)
+    #     return float(-mp.sqrt(2) * mp.erfinv(mp.mpf(2.) * arg - mp.one))
+
+    @pytest.mark.parametrize("q, c, ref",
+                             [(1e-5, 20, -0.15690800666514138),
+                              (0.99999, 100, -5.19933666203545),
+                              (0.9999, 0.02, -2.576676052143387),
+                              (5e-2, 0.02, 17.089518110222244),
+                              (1e-18, 2, 5.9978070150076865),
+                              (1e-50, 5, 6.361340902404057)])
+    def test_isf(self, q, c, ref):
+        assert_allclose(stats.powernorm.isf(q, c), ref, rtol=5e-12)
+
+    # CDF reference values were computed with mpmath via
+    # from mpmath import mp
+    # def cdf_mp(x, c):
+    #     x = mp.mpf(x)
+    #     c = mp.mpf(c)
+    #     return float(mp.one - mp.ncdf(-x)**c)
+
+    @pytest.mark.parametrize("x, c, ref",
+                             [(-12, 9, 1.598833900869911e-32),
+                              (2, 9, 0.9999999999999983),
+                              (-20, 9, 2.4782617067456103e-88),
+                              (-5, 0.02, 5.733032242841443e-09),
+                              (-20, 0.02, 5.507248237212467e-91)])
+    def test_cdf(self, x, c, ref):
+        assert_allclose(stats.powernorm.cdf(x, c), ref, rtol=5e-14)
+
+
+class TestInvGamma:
+    def test_invgamma_inf_gh_1866(self):
+        # invgamma's moments are only finite for a>n
+        # specific numbers checked w/ boost 1.54
+        with warnings.catch_warnings():
+            warnings.simplefilter('error', RuntimeWarning)
+            mvsk = stats.invgamma.stats(a=19.31, moments='mvsk')
+            expected = [0.05461496450, 0.0001723162534, 1.020362676,
+                        2.055616582]
+            assert_allclose(mvsk, expected)
+
+            a = [1.1, 3.1, 5.6]
+            mvsk = stats.invgamma.stats(a=a, moments='mvsk')
+            expected = ([10., 0.476190476, 0.2173913043],       # mmm
+                        [np.inf, 0.2061430632, 0.01312749422],  # vvv
+                        [np.nan, 41.95235392, 2.919025532],     # sss
+                        [np.nan, np.nan, 24.51923076])          # kkk
+            for x, y in zip(mvsk, expected):
+                assert_almost_equal(x, y)
+
+    def test_cdf_ppf(self):
+        # gh-6245
+        x = np.logspace(-2.6, 0)
+        y = stats.invgamma.cdf(x, 1)
+        xx = stats.invgamma.ppf(y, 1)
+        assert_allclose(x, xx)
+
+    def test_sf_isf(self):
+        # gh-6245
+        if sys.maxsize > 2**32:
+            x = np.logspace(2, 100)
+        else:
+            # Invgamme roundtrip on 32-bit systems has relative accuracy
+            # ~1e-15 until x=1e+15, and becomes inf above x=1e+18
+            x = np.logspace(2, 18)
+
+        y = stats.invgamma.sf(x, 1)
+        xx = stats.invgamma.isf(y, 1)
+        assert_allclose(x, xx, rtol=1.0)
+
+    def test_logcdf(self):
+        x = 1e7
+        a = 2.25
+        # Reference value computed with mpmath.
+        ref = -6.97567687425534e-17
+        logcdf = stats.invgamma.logcdf(x, a)
+        assert_allclose(logcdf, ref, rtol=5e-15)
+
+    def test_logsf(self):
+        x = 0.01
+        a = 3.5
+        # Reference value computed with mpmath.
+        ref = -1.147781224014262e-39
+        logsf = stats.invgamma.logsf(x, a)
+        assert_allclose(logsf, ref, rtol=5e-15)
+
+    @pytest.mark.parametrize("a, ref",
+                             [(100000000.0, -26.21208257605721),
+                              (1e+100, -343.9688254159022)])
+    def test_large_entropy(self, a, ref):
+        # The reference values were calculated with mpmath:
+        # from mpmath import mp
+        # mp.dps = 500
+
+        # def invgamma_entropy(a):
+        #     a = mp.mpf(a)
+        #     h = a + mp.loggamma(a) - (mp.one + a) * mp.digamma(a)
+        #     return float(h)
+        assert_allclose(stats.invgamma.entropy(a), ref, rtol=1e-15)
+
+
+class TestF:
+    def test_endpoints(self):
+        # Compute the pdf at the left endpoint dst.a.
+        data = [[stats.f, (2, 1), 1.0]]
+        for _f, _args, _correct in data:
+            ans = _f.pdf(_f.a, *_args)
+
+        ans = [_f.pdf(_f.a, *_args) for _f, _args, _ in data]
+        correct = [_correct_ for _f, _args, _correct_ in data]
+        assert_array_almost_equal(ans, correct)
+
+    def test_f_moments(self):
+        # n-th moment of F distributions is only finite for n < dfd / 2
+        m, v, s, k = stats.f.stats(11, 6.5, moments='mvsk')
+        assert_(np.isfinite(m))
+        assert_(np.isfinite(v))
+        assert_(np.isfinite(s))
+        assert_(not np.isfinite(k))
+
+    def test_moments_warnings(self):
+        # no warnings should be generated for dfd = 2, 4, 6, 8 (div by zero)
+        with warnings.catch_warnings():
+            warnings.simplefilter('error', RuntimeWarning)
+            stats.f.stats(dfn=[11]*4, dfd=[2, 4, 6, 8], moments='mvsk')
+
+    def test_stats_broadcast(self):
+        dfn = np.array([[3], [11]])
+        dfd = np.array([11, 12])
+        m, v, s, k = stats.f.stats(dfn=dfn, dfd=dfd, moments='mvsk')
+        m2 = [dfd / (dfd - 2)]*2
+        assert_allclose(m, m2)
+        v2 = 2 * dfd**2 * (dfn + dfd - 2) / dfn / (dfd - 2)**2 / (dfd - 4)
+        assert_allclose(v, v2)
+        s2 = ((2*dfn + dfd - 2) * np.sqrt(8*(dfd - 4)) /
+              ((dfd - 6) * np.sqrt(dfn*(dfn + dfd - 2))))
+        assert_allclose(s, s2)
+        k2num = 12 * (dfn * (5*dfd - 22) * (dfn + dfd - 2) +
+                      (dfd - 4) * (dfd - 2)**2)
+        k2den = dfn * (dfd - 6) * (dfd - 8) * (dfn + dfd - 2)
+        k2 = k2num / k2den
+        assert_allclose(k, k2)
+
+
+class TestStudentT:
+    def test_rvgeneric_std(self):
+        # Regression test for #1191
+        assert_array_almost_equal(stats.t.std([5, 6]), [1.29099445, 1.22474487])
+
+    def test_moments_t(self):
+        # regression test for #8786
+        assert_equal(stats.t.stats(df=1, moments='mvsk'),
+                    (np.inf, np.nan, np.nan, np.nan))
+        assert_equal(stats.t.stats(df=1.01, moments='mvsk'),
+                    (0.0, np.inf, np.nan, np.nan))
+        assert_equal(stats.t.stats(df=2, moments='mvsk'),
+                    (0.0, np.inf, np.nan, np.nan))
+        assert_equal(stats.t.stats(df=2.01, moments='mvsk'),
+                    (0.0, 2.01/(2.01-2.0), np.nan, np.inf))
+        assert_equal(stats.t.stats(df=3, moments='sk'), (np.nan, np.inf))
+        assert_equal(stats.t.stats(df=3.01, moments='sk'), (0.0, np.inf))
+        assert_equal(stats.t.stats(df=4, moments='sk'), (0.0, np.inf))
+        assert_allclose(stats.t.stats(df=4.01, moments='sk'), (0.0, 6.0/(4.01 - 4.0)),
+                        rtol=1e-14)
+
+    def test_t_entropy(self):
+        df = [1, 2, 25, 100]
+        # Expected values were computed with mpmath.
+        expected = [2.5310242469692907, 1.9602792291600821,
+                    1.459327578078393, 1.4289633653182439]
+        assert_allclose(stats.t.entropy(df), expected, rtol=1e-13)
+
+    @pytest.mark.parametrize("v, ref",
+                            [(100, 1.4289633653182439),
+                            (1e+100, 1.4189385332046727)])
+    def test_t_extreme_entropy(self, v, ref):
+        # Reference values were calculated with mpmath:
+        # from mpmath import mp
+        # mp.dps = 500
+        #
+        # def t_entropy(v):
+        #   v = mp.mpf(v)
+        #   C = (v + mp.one) / 2
+        #   A = C * (mp.digamma(C) - mp.digamma(v / 2))
+        #   B = 0.5 * mp.log(v) + mp.log(mp.beta(v / 2, mp.one / 2))
+        #   h = A + B
+        #   return float(h)
+        assert_allclose(stats.t.entropy(v), ref, rtol=1e-14)
+
+    @pytest.mark.parametrize("methname", ["pdf", "logpdf", "cdf",
+                                        "ppf", "sf", "isf"])
+    @pytest.mark.parametrize("df_infmask", [[0, 0], [1, 1], [0, 1],
+                                            [[0, 1, 0], [1, 1, 1]],
+                                            [[1, 0], [0, 1]],
+                                            [[0], [1]]])
+    def test_t_inf_df(self, methname, df_infmask):
+        df_infmask = np.asarray(df_infmask, dtype=bool)
+        rng = np.random.default_rng(5442451539)
+        df = rng.uniform(0, 10, size=df_infmask.shape)
+        x = rng.standard_normal(df_infmask.shape)
+        df[df_infmask] = np.inf
+        t_dist = stats.t(df=df, loc=3, scale=1)
+        t_dist_ref = stats.t(df=df[~df_infmask], loc=3, scale=1)
+        norm_dist = stats.norm(loc=3, scale=1)
+        t_meth = getattr(t_dist, methname)
+        t_meth_ref = getattr(t_dist_ref, methname)
+        norm_meth = getattr(norm_dist, methname)
+        res = t_meth(x)
+        assert_allclose(res[df_infmask], norm_meth(x[df_infmask]), rtol=5e-15)
+        assert_equal(res[~df_infmask], t_meth_ref(x[~df_infmask]))
+
+    @pytest.mark.parametrize("df_infmask", [[0, 0], [1, 1], [0, 1],
+                                            [[0, 1, 0], [1, 1, 1]],
+                                            [[1, 0], [0, 1]],
+                                            [[0], [1]]])
+    def test_t_inf_df_stats_entropy(self, df_infmask):
+        df_infmask = np.asarray(df_infmask, dtype=bool)
+        rng = np.random.default_rng(5442451539)
+        df = rng.uniform(0, 10, size=df_infmask.shape)
+        df[df_infmask] = np.inf
+        res = stats.t.stats(df=df, loc=3, scale=1, moments='mvsk')
+        res_ex_inf = stats.norm.stats(loc=3, scale=1, moments='mvsk')
+        res_ex_noinf = stats.t.stats(df=df[~df_infmask], loc=3, scale=1,
+                                    moments='mvsk')
+        for i in range(4):
+            assert_equal(res[i][df_infmask], res_ex_inf[i])
+            assert_equal(res[i][~df_infmask], res_ex_noinf[i])
+
+        res = stats.t.entropy(df=df, loc=3, scale=1)
+        res_ex_inf = stats.norm.entropy(loc=3, scale=1)
+        res_ex_noinf = stats.t.entropy(df=df[~df_infmask], loc=3, scale=1)
+        assert_equal(res[df_infmask], res_ex_inf)
+        assert_equal(res[~df_infmask], res_ex_noinf)
+
+    def test_logpdf_pdf(self):
+        # reference values were computed via the reference distribution, e.g.
+        # mp.dps = 500; StudentT(df=df).logpdf(x), StudentT(df=df).pdf(x)
+        x = [1, 1e3, 10, 1]
+        df = [1e100, 1e50, 1e20, 1]
+        logpdf_ref = [-1.4189385332046727, -500000.9189385332,
+                      -50.918938533204674, -1.8378770664093456]
+        pdf_ref = [0.24197072451914334, 0,
+                   7.69459862670642e-23, 0.15915494309189535]
+        assert_allclose(stats.t.logpdf(x, df), logpdf_ref, rtol=1e-14)
+        assert_allclose(stats.t.pdf(x, df), pdf_ref, rtol=1e-14)
+
+    # Reference values were computed with mpmath, and double-checked with
+    # Wolfram Alpha.
+    @pytest.mark.parametrize('x, df, ref',
+                             [(-75.0, 15, -46.76036184546812),
+                              (0, 15, -0.6931471805599453),
+                              (75.0, 15, -4.9230344937641665e-21)])
+    def test_logcdf_logsf(self, x, df, ref):
+        logcdf = stats.t.logcdf(x, df)
+        assert_allclose(logcdf, ref, rtol=5e-15)
+        # The reference value is logcdf(x, df) == logsf(-x, df).
+        logsf = stats.t.logsf(-x, df)
+        assert_allclose(logsf, ref, rtol=5e-15)
+
+
+class TestRvDiscrete:
+    def setup_method(self):
+        self.rng = np.random.default_rng(333348228)
+
+    def test_rvs(self):
+        states = [-1, 0, 1, 2, 3, 4]
+        probability = [0.0, 0.3, 0.4, 0.0, 0.3, 0.0]
+        samples = 1000
+        r = stats.rv_discrete(name='sample', values=(states, probability))
+        x = r.rvs(size=samples, random_state=self.rng)
+        assert isinstance(x, np.ndarray)
+
+        for s, p in zip(states, probability):
+            assert abs(sum(x == s)/float(samples) - p) < 0.05
+
+        x = r.rvs(random_state=self.rng)
+        assert np.issubdtype(type(x), np.integer)
+
+    def test_entropy(self):
+        # Basic tests of entropy.
+        pvals = np.array([0.25, 0.45, 0.3])
+        p = stats.rv_discrete(values=([0, 1, 2], pvals))
+        expected_h = -sum(xlogy(pvals, pvals))
+        h = p.entropy()
+        assert_allclose(h, expected_h)
+
+        p = stats.rv_discrete(values=([0, 1, 2], [1.0, 0, 0]))
+        h = p.entropy()
+        assert_equal(h, 0.0)
+
+    def test_pmf(self):
+        xk = [1, 2, 4]
+        pk = [0.5, 0.3, 0.2]
+        rv = stats.rv_discrete(values=(xk, pk))
+
+        x = [[1., 4.],
+             [3., 2]]
+        assert_allclose(rv.pmf(x),
+                        [[0.5, 0.2],
+                         [0., 0.3]], atol=1e-14)
+
+    def test_cdf(self):
+        xk = [1, 2, 4]
+        pk = [0.5, 0.3, 0.2]
+        rv = stats.rv_discrete(values=(xk, pk))
+
+        x_values = [-2, 1., 1.1, 1.5, 2.0, 3.0, 4, 5]
+        expected = [0, 0.5, 0.5, 0.5, 0.8, 0.8, 1, 1]
+        assert_allclose(rv.cdf(x_values), expected, atol=1e-14)
+
+        # also check scalar arguments
+        assert_allclose([rv.cdf(xx) for xx in x_values],
+                        expected, atol=1e-14)
+
+    def test_ppf(self):
+        xk = [1, 2, 4]
+        pk = [0.5, 0.3, 0.2]
+        rv = stats.rv_discrete(values=(xk, pk))
+
+        q_values = [0.1, 0.5, 0.6, 0.8, 0.9, 1.]
+        expected = [1, 1, 2, 2, 4, 4]
+        assert_allclose(rv.ppf(q_values), expected, atol=1e-14)
+
+        # also check scalar arguments
+        assert_allclose([rv.ppf(q) for q in q_values],
+                        expected, atol=1e-14)
+
+    def test_cdf_ppf_next(self):
+        # copied and special cased from test_discrete_basic
+        vals = ([1, 2, 4, 7, 8], [0.1, 0.2, 0.3, 0.3, 0.1])
+        rv = stats.rv_discrete(values=vals)
+
+        assert_array_equal(rv.ppf(rv.cdf(rv.xk[:-1]) + 1e-8),
+                           rv.xk[1:])
+
+    def test_multidimension(self):
+        xk = np.arange(12).reshape((3, 4))
+        pk = np.array([[0.1, 0.1, 0.15, 0.05],
+                       [0.1, 0.1, 0.05, 0.05],
+                       [0.1, 0.1, 0.05, 0.05]])
+        rv = stats.rv_discrete(values=(xk, pk))
+
+        assert_allclose(rv.expect(), np.sum(rv.xk * rv.pk), atol=1e-14)
+
+    def test_bad_input(self):
+        xk = [1, 2, 3]
+        pk = [0.5, 0.5]
+        assert_raises(ValueError, stats.rv_discrete, **dict(values=(xk, pk)))
+
+        pk = [1, 2, 3]
+        assert_raises(ValueError, stats.rv_discrete, **dict(values=(xk, pk)))
+
+        xk = [1, 2, 3]
+        pk = [0.5, 1.2, -0.7]
+        assert_raises(ValueError, stats.rv_discrete, **dict(values=(xk, pk)))
+
+        xk = [1, 2, 3, 4, 5]
+        pk = [0.3, 0.3, 0.3, 0.3, -0.2]
+        assert_raises(ValueError, stats.rv_discrete, **dict(values=(xk, pk)))
+
+        xk = [1, 1]
+        pk = [0.5, 0.5]
+        assert_raises(ValueError, stats.rv_discrete, **dict(values=(xk, pk)))
+
+    def test_shape_rv_sample(self):
+        # tests added for gh-9565
+
+        # mismatch of 2d inputs
+        xk, pk = np.arange(4).reshape((2, 2)), np.full((2, 3), 1/6)
+        assert_raises(ValueError, stats.rv_discrete, **dict(values=(xk, pk)))
+
+        # same number of elements, but shapes not compatible
+        xk, pk = np.arange(6).reshape((3, 2)), np.full((2, 3), 1/6)
+        assert_raises(ValueError, stats.rv_discrete, **dict(values=(xk, pk)))
+
+        # same shapes => no error
+        xk, pk = np.arange(6).reshape((3, 2)), np.full((3, 2), 1/6)
+        assert_equal(stats.rv_discrete(values=(xk, pk)).pmf(0), 1/6)
+
+    def test_expect1(self):
+        xk = [1, 2, 4, 6, 7, 11]
+        pk = [0.1, 0.2, 0.2, 0.2, 0.2, 0.1]
+        rv = stats.rv_discrete(values=(xk, pk))
+
+        assert_allclose(rv.expect(), np.sum(rv.xk * rv.pk), atol=1e-14)
+
+    def test_expect2(self):
+        # rv_sample should override _expect. Bug report from
+        # https://stackoverflow.com/questions/63199792
+        y = [200.0, 300.0, 400.0, 500.0, 600.0, 700.0, 800.0, 900.0, 1000.0,
+             1100.0, 1200.0, 1300.0, 1400.0, 1500.0, 1600.0, 1700.0, 1800.0,
+             1900.0, 2000.0, 2100.0, 2200.0, 2300.0, 2400.0, 2500.0, 2600.0,
+             2700.0, 2800.0, 2900.0, 3000.0, 3100.0, 3200.0, 3300.0, 3400.0,
+             3500.0, 3600.0, 3700.0, 3800.0, 3900.0, 4000.0, 4100.0, 4200.0,
+             4300.0, 4400.0, 4500.0, 4600.0, 4700.0, 4800.0]
+
+        py = [0.0004, 0.0, 0.0033, 0.006500000000000001, 0.0, 0.0,
+              0.004399999999999999, 0.6862, 0.0, 0.0, 0.0,
+              0.00019999999999997797, 0.0006000000000000449,
+              0.024499999999999966, 0.006400000000000072,
+              0.0043999999999999595, 0.019499999999999962,
+              0.03770000000000007, 0.01759999999999995, 0.015199999999999991,
+              0.018100000000000005, 0.04500000000000004, 0.0025999999999999357,
+              0.0, 0.0041000000000001036, 0.005999999999999894,
+              0.0042000000000000925, 0.0050000000000000044,
+              0.0041999999999999815, 0.0004999999999999449,
+              0.009199999999999986, 0.008200000000000096,
+              0.0, 0.0, 0.0046999999999999265, 0.0019000000000000128,
+              0.0006000000000000449, 0.02510000000000001, 0.0,
+              0.007199999999999984, 0.0, 0.012699999999999934, 0.0, 0.0,
+              0.008199999999999985, 0.005600000000000049, 0.0]
+
+        rv = stats.rv_discrete(values=(y, py))
+
+        # check the mean
+        assert_allclose(rv.expect(), rv.mean(), atol=1e-14)
+        assert_allclose(rv.expect(),
+                        sum(v * w for v, w in zip(y, py)), atol=1e-14)
+
+        # also check the second moment
+        assert_allclose(rv.expect(lambda x: x**2),
+                        sum(v**2 * w for v, w in zip(y, py)), atol=1e-14)
+
+
+class TestSkewCauchy:
+    def test_cauchy(self):
+        x = np.linspace(-5, 5, 100)
+        assert_array_almost_equal(stats.skewcauchy.pdf(x, a=0),
+                                  stats.cauchy.pdf(x))
+        assert_array_almost_equal(stats.skewcauchy.cdf(x, a=0),
+                                  stats.cauchy.cdf(x))
+        assert_array_almost_equal(stats.skewcauchy.ppf(x, a=0),
+                                  stats.cauchy.ppf(x))
+
+    def test_skewcauchy_R(self):
+        # options(digits=16)
+        # library(sgt)
+        # # lmbda, x contain the values generated for a, x below
+        # lmbda <- c(0.0976270078546495, 0.430378732744839, 0.2055267521432877,
+        #            0.0897663659937937, -0.15269040132219, 0.2917882261333122,
+        #            -0.12482557747462, 0.7835460015641595, 0.9273255210020589,
+        #            -0.2331169623484446)
+        # x <- c(2.917250380826646, 0.2889491975290444, 0.6804456109393229,
+        #        4.25596638292661, -4.289639418021131, -4.1287070029845925,
+        #        -4.797816025596743, 3.32619845547938, 2.7815675094985046,
+        #        3.700121482468191)
+        # pdf = dsgt(x, mu=0, lambda=lambda, sigma=1, q=1/2, mean.cent=FALSE,
+        #            var.adj = sqrt(2))
+        # cdf = psgt(x, mu=0, lambda=lambda, sigma=1, q=1/2, mean.cent=FALSE,
+        #            var.adj = sqrt(2))
+        # qsgt(cdf, mu=0, lambda=lambda, sigma=1, q=1/2, mean.cent=FALSE,
+        #      var.adj = sqrt(2))
+
+        rng = np.random.RandomState(0)
+        a = rng.rand(10) * 2 - 1
+        x = rng.rand(10) * 10 - 5
+        pdf = [0.039473975217333909, 0.305829714049903223, 0.24140158118994162,
+               0.019585772402693054, 0.021436553695989482, 0.00909817103867518,
+               0.01658423410016873, 0.071083288030394126, 0.103250045941454524,
+               0.013110230778426242]
+        cdf = [0.87426677718213752, 0.37556468910780882, 0.59442096496538066,
+               0.91304659850890202, 0.09631964100300605, 0.03829624330921733,
+               0.08245240578402535, 0.72057062945510386, 0.62826415852515449,
+               0.95011308463898292]
+        assert_allclose(stats.skewcauchy.pdf(x, a), pdf)
+        assert_allclose(stats.skewcauchy.cdf(x, a), cdf)
+        assert_allclose(stats.skewcauchy.ppf(cdf, a), x)
+
+
+class TestJFSkewT:
+    def test_compare_t(self):
+        # Verify that jf_skew_t with a=b recovers the t distribution with 2a
+        # degrees of freedom
+        a = b = 5
+        df = a * 2
+        x = [-1.0, 0.0, 1.0, 2.0]
+        q = [0.0, 0.1, 0.25, 0.75, 0.90, 1.0]
+
+        jf = stats.jf_skew_t(a, b)
+        t = stats.t(df)
+
+        assert_allclose(jf.pdf(x), t.pdf(x))
+        assert_allclose(jf.cdf(x), t.cdf(x))
+        assert_allclose(jf.ppf(q), t.ppf(q))
+        assert_allclose(jf.stats('mvsk'), t.stats('mvsk'))
+
+    @pytest.fixture
+    def gamlss_pdf_data(self):
+        """Sample data points computed using the `ST5` distribution from the
+        GAMLSS package in R. The pdf has been calculated for (a,b)=(2,3),
+        (a,b)=(8,4), and (a,b)=(12,13) for x in `np.linspace(-10, 10, 41)`.
+
+        N.B. the `ST5` distribution in R uses an alternative parameterization
+        in terms of nu and tau, where:
+            - nu = (a - b) / (a * b * (a + b)) ** 0.5
+            - tau = 2 / (a + b)
+        """
+        data = np.load(
+            Path(__file__).parent / "data/jf_skew_t_gamlss_pdf_data.npy"
+        )
+        return np.rec.fromarrays(data, names="x,pdf,a,b")
+
+    @pytest.mark.parametrize("a,b", [(2, 3), (8, 4), (12, 13)])
+    def test_compare_with_gamlss_r(self, gamlss_pdf_data, a, b):
+        """Compare the pdf with a table of reference values. The table of
+        reference values was produced using R, where the Jones and Faddy skew
+        t distribution is available in the GAMLSS package as `ST5`.
+        """
+        data = gamlss_pdf_data[
+            (gamlss_pdf_data["a"] == a) & (gamlss_pdf_data["b"] == b)
+        ]
+        x, pdf = data["x"], data["pdf"]
+        assert_allclose(pdf, stats.jf_skew_t(a, b).pdf(x), rtol=1e-12)
+
+
+# Test data for TestSkewNorm.test_noncentral_moments()
+# The expected noncentral moments were computed by Wolfram Alpha.
+# In Wolfram Alpha, enter
+#    SkewNormalDistribution[0, 1, a] moment
+# with `a` replaced by the desired shape parameter.  In the results, there
+# should be a table of the first four moments. Click on "More" to get more
+# moments.  The expected moments start with the first moment (order = 1).
+_skewnorm_noncentral_moments = [
+    (2, [2*np.sqrt(2/(5*np.pi)),
+         1,
+         22/5*np.sqrt(2/(5*np.pi)),
+         3,
+         446/25*np.sqrt(2/(5*np.pi)),
+         15,
+         2682/25*np.sqrt(2/(5*np.pi)),
+         105,
+         107322/125*np.sqrt(2/(5*np.pi))]),
+    (0.1, [np.sqrt(2/(101*np.pi)),
+           1,
+           302/101*np.sqrt(2/(101*np.pi)),
+           3,
+           (152008*np.sqrt(2/(101*np.pi)))/10201,
+           15,
+           (107116848*np.sqrt(2/(101*np.pi)))/1030301,
+           105,
+           (97050413184*np.sqrt(2/(101*np.pi)))/104060401]),
+    (-3, [-3/np.sqrt(5*np.pi),
+          1,
+          -63/(10*np.sqrt(5*np.pi)),
+          3,
+          -2529/(100*np.sqrt(5*np.pi)),
+          15,
+          -30357/(200*np.sqrt(5*np.pi)),
+          105,
+          -2428623/(2000*np.sqrt(5*np.pi)),
+          945,
+          -242862867/(20000*np.sqrt(5*np.pi)),
+          10395,
+          -29143550277/(200000*np.sqrt(5*np.pi)),
+          135135]),
+]
+
+
+class TestSkewNorm:
+    def setup_method(self):
+        self.rng = check_random_state(1234)
+
+    def test_normal(self):
+        # When the skewness is 0 the distribution is normal
+        x = np.linspace(-5, 5, 100)
+        assert_array_almost_equal(stats.skewnorm.pdf(x, a=0),
+                                  stats.norm.pdf(x))
+
+    def test_rvs(self):
+        rng = check_random_state(1234)
+        shape = (3, 4, 5)
+        x = stats.skewnorm.rvs(a=0.75, size=shape, random_state=rng)
+        assert_equal(shape, x.shape)
+
+        x = stats.skewnorm.rvs(a=-3, size=shape, random_state=rng)
+        assert_equal(shape, x.shape)
+
+    def test_moments(self):
+        rng = check_random_state(1234)
+        X = stats.skewnorm.rvs(a=4, size=int(1e6), loc=5, scale=2,
+                               random_state=rng)
+        expected = [np.mean(X), np.var(X), stats.skew(X), stats.kurtosis(X)]
+        computed = stats.skewnorm.stats(a=4, loc=5, scale=2, moments='mvsk')
+        assert_array_almost_equal(computed, expected, decimal=2)
+
+        X = stats.skewnorm.rvs(a=-4, size=int(1e6), loc=5, scale=2,
+                               random_state=rng)
+        expected = [np.mean(X), np.var(X), stats.skew(X), stats.kurtosis(X)]
+        computed = stats.skewnorm.stats(a=-4, loc=5, scale=2, moments='mvsk')
+        assert_array_almost_equal(computed, expected, decimal=2)
+
+    def test_pdf_large_x(self):
+        # Triples are [x, a, logpdf(x, a)].  These values were computed
+        # using Log[PDF[SkewNormalDistribution[0, 1, a], x]] in Wolfram Alpha.
+        logpdfvals = [
+            [40, -1, -1604.834233366398515598970],
+            [40, -1/2, -1004.142946723741991369168],
+            [40, 0, -800.9189385332046727417803],
+            [40, 1/2, -800.2257913526447274323631],
+            [-40, -1/2, -800.2257913526447274323631],
+            [-2, 1e7, -2.000000000000199559727173e14],
+            [2, -1e7, -2.000000000000199559727173e14],
+        ]
+        for x, a, logpdfval in logpdfvals:
+            logp = stats.skewnorm.logpdf(x, a)
+            assert_allclose(logp, logpdfval, rtol=1e-8)
+
+    def test_cdf_large_x(self):
+        # Regression test for gh-7746.
+        # The x values are large enough that the closest 64 bit floating
+        # point representation of the exact CDF is 1.0.
+        p = stats.skewnorm.cdf([10, 20, 30], -1)
+        assert_allclose(p, np.ones(3), rtol=1e-14)
+        p = stats.skewnorm.cdf(25, 2.5)
+        assert_allclose(p, 1.0, rtol=1e-14)
+
+    def test_cdf_sf_small_values(self):
+        # Triples are [x, a, cdf(x, a)].  These values were computed
+        # using CDF[SkewNormalDistribution[0, 1, a], x] in Wolfram Alpha.
+        cdfvals = [
+            [-8, 1, 3.870035046664392611e-31],
+            [-4, 2, 8.1298399188811398e-21],
+            [-2, 5, 1.55326826787106273e-26],
+            [-9, -1, 2.257176811907681295e-19],
+            [-10, -4, 1.523970604832105213e-23],
+        ]
+        for x, a, cdfval in cdfvals:
+            p = stats.skewnorm.cdf(x, a)
+            assert_allclose(p, cdfval, rtol=1e-8)
+            # For the skew normal distribution, sf(-x, -a) = cdf(x, a).
+            p = stats.skewnorm.sf(-x, -a)
+            assert_allclose(p, cdfval, rtol=1e-8)
+
+    @pytest.mark.parametrize('a, moments', _skewnorm_noncentral_moments)
+    def test_noncentral_moments(self, a, moments):
+        for order, expected in enumerate(moments, start=1):
+            mom = stats.skewnorm.moment(order, a)
+            assert_allclose(mom, expected, rtol=1e-14)
+
+    def test_fit(self):
+        rng = np.random.default_rng(4609813989115202851)
+
+        a, loc, scale = -2, 3.5, 0.5  # arbitrary, valid parameters
+        dist = stats.skewnorm(a, loc, scale)
+        rvs = dist.rvs(size=100, random_state=rng)
+
+        # test that MLE still honors guesses and fixed parameters
+        a2, loc2, scale2 = stats.skewnorm.fit(rvs, -1.5, floc=3)
+        a3, loc3, scale3 = stats.skewnorm.fit(rvs, -1.6, floc=3)
+        assert loc2 == loc3 == 3  # fixed parameter is respected
+        assert a2 != a3  # different guess -> (slightly) different outcome
+        # quality of fit is tested elsewhere
+
+        # test that MoM honors fixed parameters, accepts (but ignores) guesses
+        a4, loc4, scale4 = stats.skewnorm.fit(rvs, 3, fscale=3, method='mm')
+        assert scale4 == 3
+        # because scale was fixed, only the mean and skewness will be matched
+        dist4 = stats.skewnorm(a4, loc4, scale4)
+        res = dist4.stats(moments='ms')
+        ref = np.mean(rvs), stats.skew(rvs)
+        assert_allclose(res, ref)
+
+        # Test behavior when skew of data is beyond maximum of skewnorm
+        rvs2 = stats.pareto.rvs(1, size=100, random_state=rng)
+
+        # MLE still works
+        res = stats.skewnorm.fit(rvs2)
+        assert np.all(np.isfinite(res))
+
+        # MoM fits variance and skewness
+        a5, loc5, scale5 = stats.skewnorm.fit(rvs2, method='mm')
+        assert np.isinf(a5)
+        # distribution infrastructure doesn't allow infinite shape parameters
+        # into _stats; it just bypasses it and produces NaNs. Calculate
+        # moments manually.
+        m, v = np.mean(rvs2), np.var(rvs2)
+        assert_allclose(m, loc5 + scale5 * np.sqrt(2/np.pi))
+        assert_allclose(v, scale5**2 * (1 - 2 / np.pi))
+
+        # test that MLE and MoM behave as expected under sign changes
+        a6p, loc6p, scale6p = stats.skewnorm.fit(rvs, method='mle')
+        a6m, loc6m, scale6m = stats.skewnorm.fit(-rvs, method='mle')
+        assert_allclose([a6m, loc6m, scale6m], [-a6p, -loc6p, scale6p])
+        a7p, loc7p, scale7p = stats.skewnorm.fit(rvs, method='mm')
+        a7m, loc7m, scale7m = stats.skewnorm.fit(-rvs, method='mm')
+        assert_allclose([a7m, loc7m, scale7m], [-a7p, -loc7p, scale7p])
+
+    def test_fit_gh19332(self):
+        # When the skewness of the data was high, `skewnorm.fit` fell back on
+        # generic `fit` behavior with a bad guess of the skewness parameter.
+        # Test that this is improved; `skewnorm.fit` is now better at finding
+        # the global optimum when the sample is highly skewed. See gh-19332.
+        x = np.array([-5, -1, 1 / 100_000] + 12 * [1] + [5])
+
+        params = stats.skewnorm.fit(x)
+        res = stats.skewnorm.nnlf(params, x)
+
+        # Compare overridden fit against generic fit.
+        # res should be about 32.01, and generic fit is worse at 32.64.
+        # In case the generic fit improves, remove this assertion (see gh-19333).
+        params_super = stats.skewnorm.fit(x, superfit=True)
+        ref = stats.skewnorm.nnlf(params_super, x)
+        assert res < ref - 0.5
+
+        # Compare overridden fit against stats.fit
+        rng = np.random.default_rng(9842356982345693637)
+        bounds = {'a': (-5, 5), 'loc': (-10, 10), 'scale': (1e-16, 10)}
+
+        def optimizer(fun, bounds):
+            return differential_evolution(fun, bounds, rng=rng)
+
+        fit_result = stats.fit(stats.skewnorm, x, bounds, optimizer=optimizer)
+        np.testing.assert_allclose(params, fit_result.params, rtol=1e-4)
+
+    def test_ppf(self):
+        # gh-20124 reported that Boost's ppf was wrong for high skewness
+        # Reference value was calculated using
+        # N[InverseCDF[SkewNormalDistribution[0, 1, 500], 1/100], 14] in Wolfram Alpha.
+        assert_allclose(stats.skewnorm.ppf(0.01, 500), 0.012533469508013, rtol=1e-13)
+
+
+class TestExpon:
+    def test_zero(self):
+        assert_equal(stats.expon.pdf(0), 1)
+
+    def test_tail(self):  # Regression test for ticket 807
+        assert_equal(stats.expon.cdf(1e-18), 1e-18)
+        assert_equal(stats.expon.isf(stats.expon.sf(40)), 40)
+
+    def test_nan_raises_error(self):
+        # see gh-issue 10300
+        x = np.array([1.6483, 2.7169, 2.4667, 1.1791, 3.5433, np.nan])
+        assert_raises(ValueError, stats.expon.fit, x)
+
+    def test_inf_raises_error(self):
+        # see gh-issue 10300
+        x = np.array([1.6483, 2.7169, 2.4667, 1.1791, 3.5433, np.inf])
+        assert_raises(ValueError, stats.expon.fit, x)
+
+
+class TestNorm:
+    def test_nan_raises_error(self):
+        # see gh-issue 10300
+        x = np.array([1.6483, 2.7169, 2.4667, 1.1791, 3.5433, np.nan])
+        assert_raises(ValueError, stats.norm.fit, x)
+
+    def test_inf_raises_error(self):
+        # see gh-issue 10300
+        x = np.array([1.6483, 2.7169, 2.4667, 1.1791, 3.5433, np.inf])
+        assert_raises(ValueError, stats.norm.fit, x)
+
+    def test_bad_keyword_arg(self):
+        x = [1, 2, 3]
+        assert_raises(TypeError, stats.norm.fit, x, plate="shrimp")
+
+    @pytest.mark.parametrize('loc', [0, 1])
+    def test_delta_cdf(self, loc):
+        # The expected value is computed with mpmath:
+        # >>> import mpmath
+        # >>> mpmath.mp.dps = 60
+        # >>> float(mpmath.ncdf(12) - mpmath.ncdf(11))
+        # 1.910641809677555e-28
+        expected = 1.910641809677555e-28
+        delta = stats.norm._delta_cdf(11+loc, 12+loc, loc=loc)
+        assert_allclose(delta, expected, rtol=1e-13)
+        delta = stats.norm._delta_cdf(-(12+loc), -(11+loc), loc=-loc)
+        assert_allclose(delta, expected, rtol=1e-13)
+
+
+class TestUniform:
+    """gh-10300"""
+    def test_nan_raises_error(self):
+        # see gh-issue 10300
+        x = np.array([1.6483, 2.7169, 2.4667, 1.1791, 3.5433, np.nan])
+        assert_raises(ValueError, stats.uniform.fit, x)
+
+    def test_inf_raises_error(self):
+        # see gh-issue 10300
+        x = np.array([1.6483, 2.7169, 2.4667, 1.1791, 3.5433, np.inf])
+        assert_raises(ValueError, stats.uniform.fit, x)
+
+
+class TestExponNorm:
+    def test_moments(self):
+        # Some moment test cases based on non-loc/scaled formula
+        def get_moms(lam, sig, mu):
+            # See wikipedia for these formulae
+            #  where it is listed as an exponentially modified gaussian
+            opK2 = 1.0 + 1 / (lam*sig)**2
+            exp_skew = 2 / (lam * sig)**3 * opK2**(-1.5)
+            exp_kurt = 6.0 * (1 + (lam * sig)**2)**(-2)
+            return [mu + 1/lam, sig*sig + 1.0/(lam*lam), exp_skew, exp_kurt]
+
+        mu, sig, lam = 0, 1, 1
+        K = 1.0 / (lam * sig)
+        sts = stats.exponnorm.stats(K, loc=mu, scale=sig, moments='mvsk')
+        assert_almost_equal(sts, get_moms(lam, sig, mu))
+        mu, sig, lam = -3, 2, 0.1
+        K = 1.0 / (lam * sig)
+        sts = stats.exponnorm.stats(K, loc=mu, scale=sig, moments='mvsk')
+        assert_almost_equal(sts, get_moms(lam, sig, mu))
+        mu, sig, lam = 0, 3, 1
+        K = 1.0 / (lam * sig)
+        sts = stats.exponnorm.stats(K, loc=mu, scale=sig, moments='mvsk')
+        assert_almost_equal(sts, get_moms(lam, sig, mu))
+        mu, sig, lam = -5, 11, 3.5
+        K = 1.0 / (lam * sig)
+        sts = stats.exponnorm.stats(K, loc=mu, scale=sig, moments='mvsk')
+        assert_almost_equal(sts, get_moms(lam, sig, mu))
+
+    def test_nan_raises_error(self):
+        # see gh-issue 10300
+        x = np.array([1.6483, 2.7169, 2.4667, 1.1791, 3.5433, np.nan])
+        assert_raises(ValueError, stats.exponnorm.fit, x, floc=0, fscale=1)
+
+    def test_inf_raises_error(self):
+        # see gh-issue 10300
+        x = np.array([1.6483, 2.7169, 2.4667, 1.1791, 3.5433, np.inf])
+        assert_raises(ValueError, stats.exponnorm.fit, x, floc=0, fscale=1)
+
+    def test_extremes_x(self):
+        # Test for extreme values against overflows
+        assert_almost_equal(stats.exponnorm.pdf(-900, 1), 0.0)
+        assert_almost_equal(stats.exponnorm.pdf(+900, 1), 0.0)
+        assert_almost_equal(stats.exponnorm.pdf(-900, 0.01), 0.0)
+        assert_almost_equal(stats.exponnorm.pdf(+900, 0.01), 0.0)
+
+    # Expected values for the PDF were computed with mpmath, with
+    # the following function, and with mpmath.mp.dps = 50.
+    #
+    #   def exponnorm_stdpdf(x, K):
+    #       x = mpmath.mpf(x)
+    #       K = mpmath.mpf(K)
+    #       t1 = mpmath.exp(1/(2*K**2) - x/K)
+    #       erfcarg = -(x - 1/K)/mpmath.sqrt(2)
+    #       t2 = mpmath.erfc(erfcarg)
+    #       return t1 * t2 / (2*K)
+    #
+    @pytest.mark.parametrize('x, K, expected',
+                             [(20, 0.01, 6.90010764753618e-88),
+                              (1, 0.01, 0.24438994313247364),
+                              (-1, 0.01, 0.23955149623472075),
+                              (-20, 0.01, 4.6004708690125477e-88),
+                              (10, 1, 7.48518298877006e-05),
+                              (10, 10000, 9.990005048283775e-05)])
+    def test_std_pdf(self, x, K, expected):
+        assert_allclose(stats.exponnorm.pdf(x, K), expected, rtol=5e-12)
+
+    # Expected values for the CDF were computed with mpmath using
+    # the following function and with mpmath.mp.dps = 60:
+    #
+    #   def mp_exponnorm_cdf(x, K, loc=0, scale=1):
+    #       x = mpmath.mpf(x)
+    #       K = mpmath.mpf(K)
+    #       loc = mpmath.mpf(loc)
+    #       scale = mpmath.mpf(scale)
+    #       z = (x - loc)/scale
+    #       return (mpmath.ncdf(z)
+    #               - mpmath.exp((1/(2*K) - z)/K)*mpmath.ncdf(z - 1/K))
+    #
+    @pytest.mark.parametrize('x, K, scale, expected',
+                             [[0, 0.01, 1, 0.4960109760186432],
+                              [-5, 0.005, 1, 2.7939945412195734e-07],
+                              [-1e4, 0.01, 100, 0.0],
+                              [-1e4, 0.01, 1000, 6.920401854427357e-24],
+                              [5, 0.001, 1, 0.9999997118542392]])
+    def test_cdf_small_K(self, x, K, scale, expected):
+        p = stats.exponnorm.cdf(x, K, scale=scale)
+        if expected == 0.0:
+            assert p == 0.0
+        else:
+            assert_allclose(p, expected, rtol=1e-13)
+
+    # Expected values for the SF were computed with mpmath using
+    # the following function and with mpmath.mp.dps = 60:
+    #
+    #   def mp_exponnorm_sf(x, K, loc=0, scale=1):
+    #       x = mpmath.mpf(x)
+    #       K = mpmath.mpf(K)
+    #       loc = mpmath.mpf(loc)
+    #       scale = mpmath.mpf(scale)
+    #       z = (x - loc)/scale
+    #       return (mpmath.ncdf(-z)
+    #               + mpmath.exp((1/(2*K) - z)/K)*mpmath.ncdf(z - 1/K))
+    #
+    @pytest.mark.parametrize('x, K, scale, expected',
+                             [[10, 0.01, 1, 8.474702916146657e-24],
+                              [2, 0.005, 1, 0.02302280664231312],
+                              [5, 0.005, 0.5, 8.024820681931086e-24],
+                              [10, 0.005, 0.5, 3.0603340062892486e-89],
+                              [20, 0.005, 0.5, 0.0],
+                              [-3, 0.001, 1, 0.9986545205566117]])
+    def test_sf_small_K(self, x, K, scale, expected):
+        p = stats.exponnorm.sf(x, K, scale=scale)
+        if expected == 0.0:
+            assert p == 0.0
+        else:
+            assert_allclose(p, expected, rtol=5e-13)
+
+    @pytest.mark.parametrize('K', [1e-9, 1e-12, 1e-15])
+    def test_extremely_small_K(self, K):
+        # see gh-issue 24551
+        # test whether distribution approaches standard normal for K -> 0
+        x = np.array([-10.5, -3.0, -1.0, 1.0, 3.0, 10.5])
+        dist = stats.exponnorm(K)
+        dist_norm = stats.norm()
+        assert_allclose(dist.logpdf(x), dist_norm.logpdf(x))
+        assert_allclose(dist.cdf(x), dist_norm.cdf(x))
+        assert_allclose(dist.sf(x), dist_norm.sf(x)) 
+
+class TestGenExpon:
+    def test_pdf_unity_area(self):
+        from scipy.integrate import simpson
+        # PDF should integrate to one
+        p = stats.genexpon.pdf(np.arange(0, 10, 0.01), 0.5, 0.5, 2.0)
+        assert_almost_equal(simpson(p, dx=0.01), 1, 1)
+
+    def test_cdf_bounds(self):
+        # CDF should always be positive
+        cdf = stats.genexpon.cdf(np.arange(0, 10, 0.01), 0.5, 0.5, 2.0)
+        assert np.all((0 <= cdf) & (cdf <= 1))
+
+    # The values of p in the following data were computed with mpmath.
+    # E.g. the script
+    #     from mpmath import mp
+    #     mp.dps = 80
+    #     x = mp.mpf('15.0')
+    #     a = mp.mpf('1.0')
+    #     b = mp.mpf('2.0')
+    #     c = mp.mpf('1.5')
+    #     print(float(mp.exp((-a-b)*x + (b/c)*-mp.expm1(-c*x))))
+    # prints
+    #     1.0859444834514553e-19
+    @pytest.mark.parametrize('x, p, a, b, c',
+                             [(15, 1.0859444834514553e-19, 1, 2, 1.5),
+                              (0.25, 0.7609068232534623, 0.5, 2, 3),
+                              (0.25, 0.09026661397565876, 9.5, 2, 0.5),
+                              (0.01, 0.9753038265071597, 2.5, 0.25, 0.5),
+                              (3.25, 0.0001962824553094492, 2.5, 0.25, 0.5),
+                              (0.125, 0.9508674287164001, 0.25, 5, 0.5)])
+    def test_sf_isf(self, x, p, a, b, c):
+        sf = stats.genexpon.sf(x, a, b, c)
+        assert_allclose(sf, p, rtol=2e-14)
+        isf = stats.genexpon.isf(p, a, b, c)
+        assert_allclose(isf, x, rtol=2e-14)
+
+    # The values of p in the following data were computed with mpmath.
+    @pytest.mark.parametrize('x, p, a, b, c',
+                             [(0.25, 0.2390931767465377, 0.5, 2, 3),
+                              (0.25, 0.9097333860243412, 9.5, 2, 0.5),
+                              (0.01, 0.0246961734928403, 2.5, 0.25, 0.5),
+                              (3.25, 0.9998037175446906, 2.5, 0.25, 0.5),
+                              (0.125, 0.04913257128359998, 0.25, 5, 0.5)])
+    def test_cdf_ppf(self, x, p, a, b, c):
+        cdf = stats.genexpon.cdf(x, a, b, c)
+        assert_allclose(cdf, p, rtol=2e-14)
+        ppf = stats.genexpon.ppf(p, a, b, c)
+        assert_allclose(ppf, x, rtol=2e-14)
+
+
+class TestTruncexpon:
+
+    def test_sf_isf(self):
+        # reference values were computed via the reference distribution, e.g.
+        # mp.dps = 50; TruncExpon(b=b).sf(x)
+        b = [20, 100]
+        x = [19.999999, 99.999999]
+        ref = [2.0611546593828472e-15, 3.7200778266671455e-50]
+        assert_allclose(stats.truncexpon.sf(x, b), ref, rtol=1.5e-10)
+        assert_allclose(stats.truncexpon.isf(ref, b), x, rtol=1e-12)
+
+
+class TestExponpow:
+    def test_tail(self):
+        assert_almost_equal(stats.exponpow.cdf(1e-10, 2.), 1e-20)
+        assert_almost_equal(stats.exponpow.isf(stats.exponpow.sf(5, .8), .8),
+                            5)
+
+
+class TestSkellam:
+    def test_pmf(self):
+        # comparison to R
+        k = np.arange(-10, 15)
+        mu1, mu2 = 10, 5
+        skpmfR = np.array(
+                   [4.2254582961926893e-005, 1.1404838449648488e-004,
+                    2.8979625801752660e-004, 6.9177078182101231e-004,
+                    1.5480716105844708e-003, 3.2412274963433889e-003,
+                    6.3373707175123292e-003, 1.1552351566696643e-002,
+                    1.9606152375042644e-002, 3.0947164083410337e-002,
+                    4.5401737566767360e-002, 6.1894328166820688e-002,
+                    7.8424609500170578e-002, 9.2418812533573133e-002,
+                    1.0139793148019728e-001, 1.0371927988298846e-001,
+                    9.9076583077406091e-002, 8.8546660073089561e-002,
+                    7.4187842052486810e-002, 5.8392772862200251e-002,
+                    4.3268692953013159e-002, 3.0248159818374226e-002,
+                    1.9991434305603021e-002, 1.2516877303301180e-002,
+                    7.4389876226229707e-003])
+
+        assert_almost_equal(stats.skellam.pmf(k, mu1, mu2), skpmfR, decimal=15)
+
+    def test_cdf(self):
+        # comparison to R, only 5 decimals
+        k = np.arange(-10, 15)
+        mu1, mu2 = 10, 5
+        skcdfR = np.array(
+                   [6.4061475386192104e-005, 1.7810985988267694e-004,
+                    4.6790611790020336e-004, 1.1596768997212152e-003,
+                    2.7077485103056847e-003, 5.9489760066490718e-003,
+                    1.2286346724161398e-002, 2.3838698290858034e-002,
+                    4.3444850665900668e-002, 7.4392014749310995e-002,
+                    1.1979375231607835e-001, 1.8168808048289900e-001,
+                    2.6011268998306952e-001, 3.5253150251664261e-001,
+                    4.5392943399683988e-001, 5.5764871387982828e-001,
+                    6.5672529695723436e-001, 7.4527195703032389e-001,
+                    8.1945979908281064e-001, 8.7785257194501087e-001,
+                    9.2112126489802404e-001, 9.5136942471639818e-001,
+                    9.7136085902200120e-001, 9.8387773632530240e-001,
+                    9.9131672394792536e-001])
+
+        assert_almost_equal(stats.skellam.cdf(k, mu1, mu2), skcdfR, decimal=5)
+
+    def test_extreme_mu2(self):
+        # check that crash reported by gh-17916 large mu2 is resolved
+        x, mu1, mu2 = 0, 1, 4820232647677555.0
+        assert_allclose(stats.skellam.pmf(x, mu1, mu2), 0, atol=1e-16)
+        assert_allclose(stats.skellam.cdf(x, mu1, mu2), 1, atol=1e-16)
+
+
+class TestLognorm:
+    def test_pdf(self):
+        # Regression test for Ticket #1471: avoid nan with 0/0 situation
+        # Also make sure there are no warnings at x=0, cf gh-5202
+        with warnings.catch_warnings():
+            warnings.simplefilter('error', RuntimeWarning)
+            pdf = stats.lognorm.pdf([0, 0.5, 1], 1)
+            assert_array_almost_equal(pdf, [0.0, 0.62749608, 0.39894228])
+
+    def test_logcdf(self):
+        # Regression test for gh-5940: sf et al would underflow too early
+        x2, mu, sigma = 201.68, 195, 0.149
+        assert_allclose(stats.lognorm.sf(x2-mu, s=sigma),
+                        stats.norm.sf(np.log(x2-mu)/sigma))
+        assert_allclose(stats.lognorm.logsf(x2-mu, s=sigma),
+                        stats.norm.logsf(np.log(x2-mu)/sigma))
+
+    @pytest.fixture(scope='function')
+    def rng(self):
+        return np.random.default_rng(1234)
+
+    @pytest.mark.parametrize("rvs_shape", [.1, 2])
+    @pytest.mark.parametrize("rvs_loc", [-2, 0, 2])
+    @pytest.mark.parametrize("rvs_scale", [.2, 1, 5])
+    @pytest.mark.parametrize('fix_shape, fix_loc, fix_scale',
+                             [e for e in product((False, True), repeat=3)
+                              if False in e])
+    @np.errstate(invalid="ignore")
+    def test_fit_MLE_comp_optimizer(self, rvs_shape, rvs_loc, rvs_scale,
+                                    fix_shape, fix_loc, fix_scale, rng):
+        data = stats.lognorm.rvs(size=100, s=rvs_shape, scale=rvs_scale,
+                                 loc=rvs_loc, random_state=rng)
+
+        kwds = {}
+        if fix_shape:
+            kwds['f0'] = rvs_shape
+        if fix_loc:
+            kwds['floc'] = rvs_loc
+        if fix_scale:
+            kwds['fscale'] = rvs_scale
+
+        # Numerical result may equal analytical result if some code path
+        # of the analytical routine makes use of numerical optimization.
+        _assert_less_or_close_loglike(stats.lognorm, data, **kwds,
+                                      maybe_identical=True)
+
+    def test_isf(self):
+        # reference values were computed via the reference distribution, e.g.
+        # mp.dps = 100;
+        # LogNormal(s=s).isf(q=0.1, guess=0)
+        # LogNormal(s=s).isf(q=2e-10, guess=100)
+        s = 0.954
+        q = [0.1, 2e-10, 5e-20, 6e-40]
+        ref = [3.3960065375794937, 390.07632793595974, 5830.5020828128445,
+               287872.84087457904]
+        assert_allclose(stats.lognorm.isf(q, s), ref, rtol=1e-14)
+
+
+class TestBeta:
+    def test_logpdf(self):
+        # Regression test for Ticket #1326: avoid nan with 0*log(0) situation
+        logpdf = stats.beta.logpdf(0, 1, 0.5)
+        assert_almost_equal(logpdf, -0.69314718056)
+        logpdf = stats.beta.logpdf(0, 0.5, 1)
+        assert_almost_equal(logpdf, np.inf)
+
+    def test_logpdf_ticket_1866(self):
+        alpha, beta = 267, 1472
+        x = np.array([0.2, 0.5, 0.6])
+        b = stats.beta(alpha, beta)
+        assert_allclose(b.logpdf(x).sum(), -1201.699061824062)
+        assert_allclose(b.pdf(x), np.exp(b.logpdf(x)))
+
+    def test_fit_bad_keyword_args(self):
+        x = [0.1, 0.5, 0.6]
+        assert_raises(TypeError, stats.beta.fit, x, floc=0, fscale=1,
+                      plate="shrimp")
+
+    def test_fit_duplicated_fixed_parameter(self):
+        # At most one of 'f0', 'fa' or 'fix_a' can be given to the fit method.
+        # More than one raises a ValueError.
+        x = [0.1, 0.5, 0.6]
+        assert_raises(ValueError, stats.beta.fit, x, fa=0.5, fix_a=0.5)
+
+    @pytest.mark.skipif(MACOS_INTEL, reason="Overflow, see gh-14901")
+    def test_issue_12635(self):
+        # Confirm that Boost's beta distribution resolves gh-12635.
+        # Check against R:
+        # options(digits=16)
+        # p = 0.9999999999997369
+        # a = 75.0
+        # b = 66334470.0
+        # print(qbeta(p, a, b))
+        p, a, b = 0.9999999999997369, 75.0, 66334470.0
+        assert_allclose(stats.beta.ppf(p, a, b), 2.343620802982393e-06)
+
+    @pytest.mark.skipif(MACOS_INTEL, reason="Overflow, see gh-14901")
+    def test_issue_12794(self):
+        # Confirm that Boost's beta distribution resolves gh-12794.
+        # Check against R.
+        # options(digits=16)
+        # p = 1e-11
+        # count_list = c(10,100,1000)
+        # print(qbeta(1-p, count_list + 1, 100000 - count_list))
+        inv_R = np.array([0.0004944464889611935,
+                          0.0018360586912635726,
+                          0.0122663919942518351])
+        count_list = np.array([10, 100, 1000])
+        p = 1e-11
+        inv = stats.beta.isf(p, count_list + 1, 100000 - count_list)
+        assert_allclose(inv, inv_R)
+        res = stats.beta.sf(inv, count_list + 1, 100000 - count_list)
+        assert_allclose(res, p)
+
+    @pytest.mark.skipif(MACOS_INTEL, reason="Overflow, see gh-14901")
+    def test_issue_12796(self):
+        # Confirm that Boost's beta distribution succeeds in the case
+        # of gh-12796
+        alpha_2 = 5e-6
+        count_ = np.arange(1, 20)
+        nobs = 100000
+        q, a, b = 1 - alpha_2, count_ + 1, nobs - count_
+        inv = stats.beta.ppf(q, a, b)
+        res = stats.beta.cdf(inv, a, b)
+        assert_allclose(res, 1 - alpha_2)
+
+    def test_endpoints(self):
+        # Confirm that boost's beta distribution returns inf at x=1
+        # when b<1
+        a, b = 1, 0.5
+        assert_equal(stats.beta.pdf(1, a, b), np.inf)
+
+        # Confirm that boost's beta distribution returns inf at x=0
+        # when a<1
+        a, b = 0.2, 3
+        assert_equal(stats.beta.pdf(0, a, b), np.inf)
+
+        # Confirm that boost's beta distribution returns 5 at x=0
+        # when a=1, b=5
+        a, b = 1, 5
+        assert_equal(stats.beta.pdf(0, a, b), 5)
+        assert_equal(stats.beta.pdf(1e-310, a, b), 5)
+
+        # Confirm that boost's beta distribution returns 5 at x=1
+        # when a=5, b=1
+        a, b = 5, 1
+        assert_equal(stats.beta.pdf(1, a, b), 5)
+        assert_equal(stats.beta.pdf(1-1e-310, a, b), 5)
+
+    def test_boost_eval_issue_14606(self):
+        q, a, b = 0.995, 1.0e11, 1.0e13
+        stats.beta.ppf(q, a, b)
+
+    @pytest.mark.parametrize('method', [stats.beta.ppf, stats.beta.isf])
+    @pytest.mark.parametrize('a, b', [(1e-310, 12.5), (12.5, 1e-310)])
+    def test_beta_ppf_with_subnormal_a_b(self, method, a, b):
+        # Regression test for gh-17444: beta.ppf(p, a, b) and beta.isf(p, a, b)
+        # would result in a segmentation fault if either a or b was subnormal.
+        p = 0.9
+        # Depending on the version of Boost that we have vendored and
+        # our setting of the Boost double promotion policy, the call
+        # `stats.beta.ppf(p, a, b)` might raise an OverflowError or
+        # return a value.  We'll accept either behavior (and not care about
+        # the value), because our goal here is to verify that the call does
+        # not trigger a segmentation fault.
+        try:
+            method(p, a, b)
+        except OverflowError:
+            # The OverflowError exception occurs with Boost 1.80 or earlier
+            # when Boost's double promotion policy is false; see
+            #   https://github.com/boostorg/math/issues/882
+            # and
+            #   https://github.com/boostorg/math/pull/883
+            # Once we have vendored the fixed version of Boost, we can drop
+            # this try-except wrapper and just call the function.
+            pass
+
+    # Reference values computed with mpmath.
+    @pytest.mark.parametrize('x, a, b, ref',
+                             [(0.999, 1.5, 2.5, -6.439838145196121e-08),
+                              (2e-9, 3.25, 2.5, -63.13030939685114)])
+    def test_logcdf(self, x, a, b, ref):
+        logcdf = stats.beta.logcdf(x, a, b)
+        assert_allclose(logcdf, ref, rtol=5e-15)
+
+    # Reference values computed with mpmath.
+    @pytest.mark.parametrize('x, a, b, ref',
+                             [(2e-9, 1.5, 2.5, -3.0368535131140806e-13),
+                              (0.998, 3.25, 2.5, -13.309796070871489)])
+    def test_logsf(self, x, a, b, ref):
+        logsf = stats.beta.logsf(x, a, b)
+        assert_allclose(logsf, ref, 5e-15)
+
+    # entropy accuracy was confirmed using the following mpmath function
+    # from mpmath import mp
+    # mp.dps = 50
+    # def beta_entropy_mpmath(a, b):
+    #     a = mp.mpf(a)
+    #     b = mp.mpf(b)
+    #     entropy = mp.log(mp.beta(a, b)) - (a - 1) * mp.digamma(a) -\
+    #              (b - 1) * mp.digamma(b) + (a + b -2) * mp.digamma(a + b)
+    #     return float(entropy)
+
+    @pytest.mark.parametrize('a, b, ref',
+                             [(0.5, 0.5, -0.24156447527049044),
+                              (0.001, 1, -992.0922447210179),
+                              (1, 10000, -8.210440371976183),
+                              (100000, 100000, -5.377247470132859)])
+    def test_entropy(self, a, b, ref):
+        assert_allclose(stats.beta(a, b).entropy(), ref)
+
+    @pytest.mark.parametrize(
+        "a, b, ref, tol",
+        [
+            (1, 10, -1.4025850929940458, 1e-14),
+            (10, 20, -1.0567887388936708, 1e-13),
+            (4e6, 4e6+20, -7.221686009678741, 1e-9),
+            (5e6, 5e6+10, -7.333257022834638, 1e-8),
+            (1e10, 1e10+20, -11.133707703130474, 1e-11),
+            (1e50, 1e50+20, -57.185409562486385, 1e-15),
+            (2, 1e10, -21.448635265288925, 1e-11),
+            (2, 1e20, -44.47448619497938, 1e-14),
+            (2, 1e50, -113.55203898480075, 1e-14),
+            (5, 1e10, -20.87226777401971, 1e-10),
+            (5, 1e20, -43.89811870326017, 1e-14),
+            (5, 1e50, -112.97567149308153, 1e-14),
+            (10, 1e10, -20.489796752909477, 1e-9),
+            (10, 1e20, -43.51564768139993, 1e-14),
+            (10, 1e50, -112.59320047122131, 1e-14),
+            (1e20, 2, -44.47448619497938, 1e-14),
+            (1e20, 5, -43.89811870326017, 1e-14),
+            (1e50, 10, -112.59320047122131, 1e-14),
+        ]
+    )
+    def test_extreme_entropy(self, a, b, ref, tol):
+        # Reference values were calculated with mpmath:
+        # from mpmath import mp
+        # mp.dps = 500
+        #
+        # def beta_entropy_mpmath(a, b):
+        #     a = mp.mpf(a)
+        #     b = mp.mpf(b)
+        #     entropy = (
+        #       mp.log(mp.beta(a, b)) - (a - 1) * mp.digamma(a)
+        #       - (b - 1) * mp.digamma(b) + (a + b - 2) * mp.digamma(a + b)
+        #     )
+        #     return float(entropy)
+        assert_allclose(stats.beta(a, b).entropy(), ref, rtol=tol)
+
+    def test_entropy_broadcasting(self):
+        # gh-23127 reported that the entropy method of the beta
+        # distribution did not broadcast correctly.
+        Beta = stats.make_distribution(stats.beta)
+        a = np.asarray([5e6, 100, 1e9, 10])
+        b = np.asarray([5e6, 1e9, 100, 20])
+        res = Beta(a=a, b=b).entropy()
+        ref = np.asarray([Beta(a=a[0], b=b[0]).entropy(),
+                          Beta(a=a[1], b=b[1]).entropy(),
+                          Beta(a=a[2], b=b[2]).entropy(),
+                          Beta(a=a[3], b=b[3]).entropy()])
+        assert_allclose(res, ref)
+
+
+class TestBetaPrime:
+    # the test values are used in test_cdf_gh_17631 / test_ppf_gh_17631
+    # They are computed with mpmath. Example:
+    # from mpmath import mp
+    # mp.dps = 50
+    # a, b = mp.mpf(0.05), mp.mpf(0.1)
+    # x = mp.mpf(1e22)
+    # float(mp.betainc(a, b, 0.0, x/(1+x), regularized=True))
+    # note: we use the values computed by the cdf to test whether
+    # ppf(cdf(x)) == x (up to a small tolerance)
+    # since the ppf can be very sensitive to small variations of the input,
+    # it can be required to generate the test case for the ppf separately,
+    # see self.test_ppf
+    cdf_vals = [
+        (1e22, 100.0, 0.05, 0.8973027435427167),
+        (1e10, 100.0, 0.05, 0.5911548582766262),
+        (1e8, 0.05, 0.1, 0.9467768090820048),
+        (1e8, 100.0, 0.05, 0.4852944858726726),
+        (1e-10, 0.05, 0.1, 0.21238845427095),
+        (1e-10, 1.5, 1.5, 1.697652726007973e-15),
+        (1e-10, 0.05, 100.0, 0.40884514172337383),
+        (1e-22, 0.05, 0.1, 0.053349567649287326),
+        (1e-22, 1.5, 1.5, 1.6976527263135503e-33),
+        (1e-22, 0.05, 100.0, 0.10269725645728331),
+        (1e-100, 0.05, 0.1, 6.7163126421919795e-06),
+        (1e-100, 1.5, 1.5, 1.6976527263135503e-150),
+        (1e-100, 0.05, 100.0, 1.2928818587561651e-05),
+    ]
+
+    def test_logpdf(self):
+        alpha, beta = 267, 1472
+        x = np.array([0.2, 0.5, 0.6])
+        b = stats.betaprime(alpha, beta)
+        assert_(np.isfinite(b.logpdf(x)).all())
+        assert_allclose(b.pdf(x), np.exp(b.logpdf(x)))
+
+    def test_cdf(self):
+        # regression test for gh-4030: Implementation of
+        # scipy.stats.betaprime.cdf()
+        x = stats.betaprime.cdf(0, 0.2, 0.3)
+        assert_equal(x, 0.0)
+
+        alpha, beta = 267, 1472
+        x = np.array([0.2, 0.5, 0.6])
+        cdfs = stats.betaprime.cdf(x, alpha, beta)
+        assert_(np.isfinite(cdfs).all())
+
+        # check the new cdf implementation vs generic one:
+        gen_cdf = stats.rv_continuous._cdf_single
+        cdfs_g = [gen_cdf(stats.betaprime, val, alpha, beta) for val in x]
+        assert_allclose(cdfs, cdfs_g, atol=0, rtol=2e-12)
+
+    # The expected values for test_ppf() were computed with mpmath, e.g.
+    #
+    #   from mpmath import mp
+    #   mp.dps = 125
+    #   p = 0.01
+    #   a, b = 1.25, 2.5
+    #   x = mp.findroot(lambda t: mp.betainc(a, b, x1=0, x2=t/(1+t),
+    #                                        regularized=True) - p,
+    #                   x0=(0.01, 0.011), method='secant')
+    #   print(float(x))
+    #
+    # prints
+    #
+    #   0.01080162700956614
+    #
+    @pytest.mark.parametrize(
+        'p, a, b, expected',
+        [(0.010, 1.25, 2.5, 0.01080162700956614),
+         (1e-12, 1.25, 2.5, 1.0610141996279122e-10),
+         (1e-18, 1.25, 2.5, 1.6815941817974941e-15),
+         (1e-17, 0.25, 7.0, 1.0179194531881782e-69),
+         (0.375, 0.25, 7.0, 0.002036820346115211),
+         (0.9978811466052919, 0.05, 0.1, 1.0000000000001218e22),]
+    )
+    def test_ppf(self, p, a, b, expected):
+        x = stats.betaprime.ppf(p, a, b)
+        assert_allclose(x, expected, rtol=1e-14)
+
+    @pytest.mark.parametrize('x, a, b, p', cdf_vals)
+    def test_ppf_gh_17631(self, x, a, b, p):
+        assert_allclose(stats.betaprime.ppf(p, a, b), x, rtol=2e-14)
+
+    def test__ppf(self):
+        # Verify that _ppf supports scalar arrays.
+        a = np.array(1.0)
+        b = np.array(1.0)
+        p = np.array(0.5)
+        assert_allclose(stats.betaprime._ppf(p, a, b), 1.0, rtol=5e-16)
+
+    @pytest.mark.parametrize(
+        'x, a, b, expected',
+        cdf_vals + [
+            (1e10, 1.5, 1.5, 0.9999999999999983),
+            (1e10, 0.05, 0.1, 0.9664184367890859),
+            (1e22, 0.05, 0.1, 0.9978811466052919),
+        ])
+    def test_cdf_gh_17631(self, x, a, b, expected):
+        assert_allclose(stats.betaprime.cdf(x, a, b), expected, rtol=1e-14)
+
+    @pytest.mark.parametrize(
+        'x, a, b, expected',
+        [(1e50, 0.05, 0.1, 0.9999966641709545),
+         (1e50, 100.0, 0.05, 0.995925162631006)])
+    def test_cdf_extreme_tails(self, x, a, b, expected):
+        # for even more extreme values, we only get a few correct digits
+        # results are still < 1
+        y = stats.betaprime.cdf(x, a, b)
+        assert y < 1.0
+        assert_allclose(y, expected, rtol=2e-5)
+
+    def test_sf(self):
+        # reference values were computed via the reference distribution,
+        # e.g.
+        # mp.dps = 50
+        # a, b = 5, 3
+        # x = 1e10
+        # BetaPrime(a=a, b=b).sf(x); returns 3.4999999979e-29
+        a = [5, 4, 2, 0.05, 0.05, 0.05, 0.05, 100.0, 100.0, 0.05, 0.05,
+             0.05, 1.5, 1.5]
+        b = [3, 2, 1, 0.1, 0.1, 0.1, 0.1, 0.05, 0.05, 100.0, 100.0,
+             100.0, 1.5, 1.5]
+        x = [1e10, 1e20, 1e30, 1e22, 1e-10, 1e-22, 1e-100, 1e22, 1e10,
+             1e-10, 1e-22, 1e-100, 1e10, 1e-10]
+        ref = [3.4999999979e-29, 9.999999999994357e-40, 1.9999999999999998e-30,
+               0.0021188533947081017, 0.78761154572905, 0.9466504323507127,
+               0.9999932836873578, 0.10269725645728331, 0.40884514172337383,
+               0.5911548582766262, 0.8973027435427167, 0.9999870711814124,
+               1.6976527260079727e-15, 0.9999999999999983]
+        sf_values = stats.betaprime.sf(x, a, b)
+        assert_allclose(sf_values, ref, rtol=1e-12)
+
+    def test_logcdf(self):
+        x = 800
+        a = 0.5
+        b = 5.0
+        ref = -7.467307556554531e-16
+        logcdf = stats.betaprime.logcdf(x, a, b)
+        assert_allclose(logcdf, ref, rtol=5e-15)
+
+    def test_logsf(self):
+        x = 1e-8
+        a = 4.5
+        b = 0.5
+        ref = -2.5868992866500915e-37
+        logsf = stats.betaprime.logsf(x, a, b)
+        assert_allclose(logsf, ref, rtol=5e-15)
+
+
+    def test_fit_stats_gh18274(self):
+        # gh-18274 reported spurious warning emitted when fitting `betaprime`
+        # to data. Some of these were emitted by stats, too. Check that the
+        # warnings are no longer emitted.
+        stats.betaprime.fit([0.1, 0.25, 0.3, 1.2, 1.6], floc=0, fscale=1)
+        stats.betaprime(a=1, b=1).stats('mvsk')
+
+    def test_moment_gh18634(self):
+        # Testing for gh-18634 revealed that `betaprime` raised a
+        # NotImplementedError for higher moments. Check that this is
+        # resolved. Parameters are arbitrary but lie on either side of the
+        # moment order (5) to test both branches of `xpx.apply_where`.
+        # Reference values produced with Mathematica, e.g.
+        # `Moment[BetaPrimeDistribution[2,7],5]`
+        ref = [np.inf, 0.867096912929055]
+        res = stats.betaprime(2, [4.2, 7.1]).moment(5)
+        assert_allclose(res, ref)
+
+
+class TestGamma:
+    def test_pdf(self):
+        # a few test cases to compare with R
+        pdf = stats.gamma.pdf(90, 394, scale=1./5)
+        assert_almost_equal(pdf, 0.002312341)
+
+        pdf = stats.gamma.pdf(3, 10, scale=1./5)
+        assert_almost_equal(pdf, 0.1620358)
+
+    def test_logpdf(self):
+        # Regression test for Ticket #1326: cornercase avoid nan with 0*log(0)
+        # situation
+        logpdf = stats.gamma.logpdf(0, 1)
+        assert_almost_equal(logpdf, 0)
+
+    def test_fit_bad_keyword_args(self):
+        x = [0.1, 0.5, 0.6]
+        assert_raises(TypeError, stats.gamma.fit, x, floc=0, plate="shrimp")
+
+    def test_isf(self):
+        # Test cases for when the probability is very small. See gh-13664.
+        # The expected values can be checked with mpmath.  With mpmath,
+        # the survival function sf(x, k) can be computed as
+        #
+        #     mpmath.gammainc(k, x, mpmath.inf, regularized=True)
+        #
+        # Here we have:
+        #
+        # >>> mpmath.mp.dps = 60
+        # >>> float(mpmath.gammainc(1, 39.14394658089878, mpmath.inf,
+        # ...                       regularized=True))
+        # 9.99999999999999e-18
+        # >>> float(mpmath.gammainc(100, 330.6557590436547, mpmath.inf,
+        #                           regularized=True))
+        # 1.000000000000028e-50
+        #
+        assert np.isclose(stats.gamma.isf(1e-17, 1),
+                          39.14394658089878, atol=1e-14)
+        assert np.isclose(stats.gamma.isf(1e-50, 100),
+                          330.6557590436547, atol=1e-13)
+
+    def test_logcdf(self):
+        x = 80
+        a = 7
+        ref = -7.096510270453943e-27
+        logcdf = stats.gamma.logcdf(x, a)
+        assert_allclose(logcdf, ref, rtol=5e-15)
+
+    def test_logsf(self):
+        x = 0.001
+        a = 3.0
+        ref = -1.6654171666664883e-10
+        logsf = stats.gamma.logsf(x, a)
+        assert_allclose(logsf, ref, rtol=5e-15)
+
+    @pytest.mark.parametrize('scale', [1.0, 5.0])
+    def test_delta_cdf(self, scale):
+        # Expected value computed with mpmath:
+        #
+        # >>> import mpmath
+        # >>> mpmath.mp.dps = 150
+        # >>> cdf1 = mpmath.gammainc(3, 0, 245, regularized=True)
+        # >>> cdf2 = mpmath.gammainc(3, 0, 250, regularized=True)
+        # >>> float(cdf2 - cdf1)
+        # 1.1902609356171962e-102
+        #
+        delta = stats.gamma._delta_cdf(scale*245, scale*250, 3, scale=scale)
+        assert_allclose(delta, 1.1902609356171962e-102, rtol=1e-13)
+
+    @pytest.mark.parametrize('a, ref, rtol',
+                             [(1e-4, -9990.366610819761, 1e-15),
+                              (2, 1.5772156649015328, 1e-15),
+                              (100, 3.7181819485047463, 1e-13),
+                              (1e4, 6.024075385026086, 1e-15),
+                              (1e18, 22.142204370151084, 1e-15),
+                              (1e100, 116.54819318290696, 1e-15)])
+    def test_entropy(self, a, ref, rtol):
+        # expected value computed with mpmath:
+        # from mpmath import mp
+        # mp.dps = 500
+        # def gamma_entropy_reference(x):
+        #     x = mp.mpf(x)
+        #     return float(mp.digamma(x) * (mp.one - x) + x + mp.loggamma(x))
+
+        assert_allclose(stats.gamma.entropy(a), ref, rtol=rtol)
+
+    @pytest.mark.parametrize("a", [1e-2, 1, 1e2])
+    @pytest.mark.parametrize("loc", [1e-2, 0, 1e2])
+    @pytest.mark.parametrize('scale', [1e-2, 1, 1e2])
+    @pytest.mark.parametrize('fix_a', [True, False])
+    @pytest.mark.parametrize('fix_loc', [True, False])
+    @pytest.mark.parametrize('fix_scale', [True, False])
+    def test_fit_mm(self, a, loc, scale, fix_a, fix_loc, fix_scale):
+        rng = np.random.default_rng(6762668991392531563)
+        data = stats.gamma.rvs(a, loc=loc, scale=scale, size=100,
+                               random_state=rng)
+
+        kwds = {}
+        if fix_a:
+            kwds['fa'] = a
+        if fix_loc:
+            kwds['floc'] = loc
+        if fix_scale:
+            kwds['fscale'] = scale
+        nfree = 3 - len(kwds)
+
+        if nfree == 0:
+            error_msg = "All parameters fixed. There is nothing to optimize."
+            with pytest.raises(ValueError, match=error_msg):
+                stats.gamma.fit(data, method='mm', **kwds)
+            return
+
+        theta = stats.gamma.fit(data, method='mm', **kwds)
+        dist = stats.gamma(*theta)
+        if nfree >= 1:
+            assert_allclose(dist.mean(), np.mean(data))
+        if nfree >= 2:
+            assert_allclose(dist.moment(2), np.mean(data**2))
+        if nfree >= 3:
+            assert_allclose(dist.moment(3), np.mean(data**3))
+
+
+def test_pdf_overflow_gh19616():
+    # Confirm that gh19616 (intermediate over/underflows in PDF) is resolved
+    # Reference value from R GeneralizedHyperbolic library
+    # library(GeneralizedHyperbolic)
+    # options(digits=16)
+    # jitter = 1e-3
+    # dnig(1, a=2**0.5 / jitter**2, b=1 / jitter**2)
+    jitter = 1e-3
+    Z = stats.norminvgauss(2**0.5 / jitter**2, 1 / jitter**2, loc=0, scale=1)
+    assert_allclose(Z.pdf(1.0), 282.0948446666433)
+
+
+class TestDgamma:
+    def test_pdf(self):
+        rng = np.random.default_rng(3791303244302340058)
+        size = 10  # number of points to check
+        x = rng.normal(scale=10, size=size)
+        a = rng.uniform(high=10, size=size)
+        res = stats.dgamma.pdf(x, a)
+        ref = stats.gamma.pdf(np.abs(x), a) / 2
+        assert_allclose(res, ref)
+
+        dist = stats.dgamma(a)
+        # There was an intermittent failure with assert_equal on Linux - 32 bit
+        assert_allclose(dist.pdf(x), res, rtol=5e-16)
+
+    # mpmath was used to compute the expected values.
+    # For x < 0, cdf(x, a) is mp.gammainc(a, -x, mp.inf, regularized=True)/2
+    # For x > 0, cdf(x, a) is (1 + mp.gammainc(a, 0, x, regularized=True))/2
+    # E.g.
+    #    from mpmath import mp
+    #    mp.dps = 50
+    #    print(float(mp.gammainc(1, 20, mp.inf, regularized=True)/2))
+    # prints
+    #    1.030576811219279e-09
+    @pytest.mark.parametrize('x, a, expected',
+                             [(-20, 1, 1.030576811219279e-09),
+                              (-40, 1, 2.1241771276457944e-18),
+                              (-50, 5, 2.7248509914602648e-17),
+                              (-25, 0.125, 5.333071920958156e-14),
+                              (5, 1, 0.9966310265004573)])
+    def test_cdf_ppf_sf_isf_tail(self, x, a, expected):
+        cdf = stats.dgamma.cdf(x, a)
+        assert_allclose(cdf, expected, rtol=5e-15)
+        ppf = stats.dgamma.ppf(expected, a)
+        assert_allclose(ppf, x, rtol=5e-15)
+        sf = stats.dgamma.sf(-x, a)
+        assert_allclose(sf, expected, rtol=5e-15)
+        isf = stats.dgamma.isf(expected, a)
+        assert_allclose(isf, -x, rtol=5e-15)
+
+    @pytest.mark.parametrize("a, ref",
+                             [(1.5, 2.0541199559354117),
+                             (1.3, 1.9357296377121247),
+                             (1.1, 1.7856502333412134)])
+    def test_entropy(self, a, ref):
+        # The reference values were calculated with mpmath:
+        # def entropy_dgamma(a):
+        #    def pdf(x):
+        #        A = mp.one / (mp.mpf(2.) * mp.gamma(a))
+        #        B = mp.fabs(x) ** (a - mp.one)
+        #        C = mp.exp(-mp.fabs(x))
+        #        h = A * B * C
+        #        return h
+        #
+        #    return -mp.quad(lambda t: pdf(t) * mp.log(pdf(t)),
+        #                    [-mp.inf, mp.inf])
+        assert_allclose(stats.dgamma.entropy(a), ref, rtol=1e-14)
+
+    @pytest.mark.parametrize("a, ref",
+                             [(1e-100, -1e+100),
+                             (1e-10, -9999999975.858217),
+                             (1e-5, -99987.37111657023),
+                             (1e4, 6.717222565586032),
+                             (1000000000000000.0, 19.38147391121996),
+                             (1e+100, 117.2413403634669)])
+    def test_entropy_entreme_values(self, a, ref):
+        # The reference values were calculated with mpmath:
+        # from mpmath import mp
+        # mp.dps = 500
+        # def second_dgamma(a):
+        #     a = mp.mpf(a)
+        #     x_1 = a + mp.log(2) + mp.loggamma(a)
+        #     x_2 = (mp.one - a) * mp.digamma(a)
+        #     h = x_1 + x_2
+        #     return h
+        assert_allclose(stats.dgamma.entropy(a), ref, rtol=1e-10)
+
+    def test_entropy_array_input(self):
+        x = np.array([1, 5, 1e20, 1e-5])
+        y = stats.dgamma.entropy(x)
+        for i in range(len(y)):
+            assert y[i] == stats.dgamma.entropy(x[i])
+
+
+class TestChi2:
+
+    # regression tests after precision improvements, ticket:1041, not verified
+    def test_precision(self):
+        assert_almost_equal(stats.chi2.pdf(1000, 1000), 8.919133934753128e-003,
+                            decimal=14)
+        assert_almost_equal(stats.chi2.pdf(100, 100), 0.028162503162596778,
+                            decimal=14)
+
+    # Reference values computed with mpmath.
+    @pytest.mark.parametrize(
+        'x, df, ref',
+        [(750.0, 3, -3.0172957781136564e-162),
+         (120.0, 15, -1.8924849646375648e-18),
+         (15.0, 13, -0.36723446372517876)]
+    )
+    def test_logcdf(self, x, df, ref):
+        logcdf = stats.chi2.logcdf(x, df)
+        assert_allclose(logcdf, ref, rtol=5e-15)
+
+    # Reference values computed with mpmath.
+    @pytest.mark.parametrize(
+        'x, df, ref',
+        [(1e-4, 15, -3.936060782678026e-37),
+         (1.5, 40, -6.384797888313517e-22),
+         (3.0, 10, -0.018750635779926784)]
+    )
+    def test_logsf(self, x, df, ref):
+        logsf = stats.chi2.logsf(x, df)
+        assert_allclose(logsf, ref, rtol=5e-15)
+
+    def test_ppf(self):
+        # Expected values computed with mpmath.
+        df = 4.8
+        x = stats.chi2.ppf(2e-47, df)
+        assert_allclose(x, 1.098472479575179840604902808e-19, rtol=1e-10)
+        x = stats.chi2.ppf(0.5, df)
+        assert_allclose(x, 4.15231407598589358660093156, rtol=1e-10)
+
+        df = 13
+        x = stats.chi2.ppf(2e-77, df)
+        assert_allclose(x, 1.0106330688195199050507943e-11, rtol=1e-10)
+        x = stats.chi2.ppf(0.1, df)
+        assert_allclose(x, 7.041504580095461859307179763, rtol=1e-10)
+
+    # Entropy references values were computed with the following mpmath code
+    # from mpmath import mp
+    # mp.dps = 50
+    # def chisq_entropy_mpmath(df):
+    #     df = mp.mpf(df)
+    #     half_df = 0.5 * df
+    #     entropy = (half_df + mp.log(2) + mp.log(mp.gamma(half_df)) +
+    #                (mp.one - half_df) * mp.digamma(half_df))
+    #     return float(entropy)
+
+    @pytest.mark.parametrize('df, ref',
+                             [(1e-4, -19988.980448690163),
+                              (1, 0.7837571104739337),
+                              (100, 4.061397128938114),
+                              (251, 4.525577254045129),
+                              (1e15, 19.034900320939986)])
+    def test_entropy(self, df, ref):
+        assert_allclose(stats.chi2(df).entropy(), ref, rtol=1e-13)
+
+    def test_regression_ticket_1326(self):
+        # adjust to avoid nan with 0*log(0)
+        assert_almost_equal(stats.chi2.pdf(0.0, 2), 0.5, 14)
+
+
+class TestGumbelL:
+    def setup_method(self):
+        self.rng = np.random.default_rng(3922444007)
+
+    # gh-6228
+    def test_cdf_ppf(self):
+        x = np.linspace(-100, -4)
+        y = stats.gumbel_l.cdf(x)
+        xx = stats.gumbel_l.ppf(y)
+        assert_allclose(x, xx)
+
+    def test_logcdf_logsf(self):
+        x = np.linspace(-100, -4)
+        y = stats.gumbel_l.logcdf(x)
+        z = stats.gumbel_l.logsf(x)
+        u = np.exp(y)
+        v = -special.expm1(z)
+        assert_allclose(u, v)
+
+    def test_sf_isf(self):
+        x = np.linspace(-20, 5)
+        y = stats.gumbel_l.sf(x)
+        xx = stats.gumbel_l.isf(y)
+        assert_allclose(x, xx)
+
+    @pytest.mark.parametrize('loc', [-1, 1])
+    def test_fit_fixed_param(self, loc):
+        # ensure fixed location is correctly reflected from `gumbel_r.fit`
+        # See comments at end of gh-12737.
+        data = stats.gumbel_l.rvs(size=100, loc=loc, random_state=self.rng)
+        fitted_loc, _ = stats.gumbel_l.fit(data, floc=loc)
+        assert_equal(fitted_loc, loc)
+
+
+class TestGumbelR:
+
+    def test_sf(self):
+        # Expected value computed with mpmath:
+        #   >>> import mpmath
+        #   >>> mpmath.mp.dps = 40
+        #   >>> float(mpmath.mp.one - mpmath.exp(-mpmath.exp(-50)))
+        #   1.9287498479639178e-22
+        assert_allclose(stats.gumbel_r.sf(50), 1.9287498479639178e-22,
+                        rtol=1e-14)
+
+    def test_isf(self):
+        # Expected value computed with mpmath:
+        #   >>> import mpmath
+        #   >>> mpmath.mp.dps = 40
+        #   >>> float(-mpmath.log(-mpmath.log(mpmath.mp.one - 1e-17)))
+        #   39.14394658089878
+        assert_allclose(stats.gumbel_r.isf(1e-17), 39.14394658089878,
+                        rtol=1e-14)
+
+
+class TestLevyStable:
+    def setup_method(self):
+        self.rng = np.random.default_rng(7195199371)
+
+    @pytest.fixture(autouse=True)
+    def reset_levy_stable_params(self):
+        """Setup default parameters for levy_stable generator"""
+        stats.levy_stable.parameterization = "S1"
+        stats.levy_stable.cdf_default_method = "piecewise"
+        stats.levy_stable.pdf_default_method = "piecewise"
+        stats.levy_stable.quad_eps = stats._levy_stable._QUAD_EPS
+
+    @pytest.fixture
+    def nolan_pdf_sample_data(self):
+        """Sample data points for pdf computed with Nolan's stablec
+
+        See - http://fs2.american.edu/jpnolan/www/stable/stable.html
+
+        There's a known limitation of Nolan's executable for alpha < 0.2.
+
+        The data table loaded below is generated from Nolan's stablec
+        with the following parameter space:
+
+            alpha = 0.1, 0.2, ..., 2.0
+            beta = -1.0, -0.9, ..., 1.0
+            p = 0.01, 0.05, 0.1, 0.25, 0.35, 0.5,
+        and the equivalent for the right tail
+
+        Typically inputs for stablec:
+
+            stablec.exe <<
+            1 # pdf
+            1 # Nolan S equivalent to S0 in scipy
+            .25,2,.25 # alpha
+            -1,-1,0 # beta
+            -10,10,1 # x
+            1,0 # gamma, delta
+            2 # output file
+        """
+        data = np.load(
+            Path(__file__).parent /
+            'data/levy_stable/stable-Z1-pdf-sample-data.npy'
+        )
+        data = np.rec.fromarrays(data.T, names='x,p,alpha,beta,pct')
+        return data
+
+    @pytest.fixture
+    def nolan_cdf_sample_data(self):
+        """Sample data points for cdf computed with Nolan's stablec
+
+        See - http://fs2.american.edu/jpnolan/www/stable/stable.html
+
+        There's a known limitation of Nolan's executable for alpha < 0.2.
+
+        The data table loaded below is generated from Nolan's stablec
+        with the following parameter space:
+
+            alpha = 0.1, 0.2, ..., 2.0
+            beta = -1.0, -0.9, ..., 1.0
+            p = 0.01, 0.05, 0.1, 0.25, 0.35, 0.5,
+
+        and the equivalent for the right tail
+
+        Ideally, Nolan's output for CDF values should match the percentile
+        from where they have been sampled from. Even more so as we extract
+        percentile x positions from stablec too. However, we note at places
+        Nolan's stablec will produce absolute errors in order of 1e-5. We
+        compare against his calculations here. In future, once we less
+        reliant on Nolan's paper we might switch to comparing directly at
+        percentiles (those x values being produced from some alternative
+        means).
+
+        Typically inputs for stablec:
+
+            stablec.exe <<
+            2 # cdf
+            1 # Nolan S equivalent to S0 in scipy
+            .25,2,.25 # alpha
+            -1,-1,0 # beta
+            -10,10,1 # x
+            1,0 # gamma, delta
+            2 # output file
+        """
+        data = np.load(
+            Path(__file__).parent /
+            'data/levy_stable/stable-Z1-cdf-sample-data.npy'
+        )
+        data = np.rec.fromarrays(data.T, names='x,p,alpha,beta,pct')
+        return data
+
+    @pytest.fixture
+    def nolan_loc_scale_sample_data(self):
+        """Sample data where loc, scale are different from 0, 1
+
+        Data extracted in similar way to pdf/cdf above using
+        Nolan's stablec but set to an arbitrary location scale of
+        (2, 3) for various important parameters alpha, beta and for
+        parameterisations S0 and S1.
+        """
+        data = np.load(
+            Path(__file__).parent /
+            'data/levy_stable/stable-loc-scale-sample-data.npy'
+        )
+        return data
+
+    @pytest.mark.slow
+    @pytest.mark.parametrize(
+        "sample_size", [
+            pytest.param(50), pytest.param(1500, marks=pytest.mark.slow)
+        ]
+    )
+    @pytest.mark.parametrize("parameterization", ["S0", "S1"])
+    @pytest.mark.parametrize(
+        "alpha,beta", [(1.0, 0), (1.0, -0.5), (1.5, 0), (1.9, 0.5)]
+    )
+    @pytest.mark.parametrize("gamma,delta", [(1, 0), (3, 2)])
+    def test_rvs(
+            self,
+            parameterization,
+            alpha,
+            beta,
+            gamma,
+            delta,
+            sample_size,
+    ):
+        stats.levy_stable.parameterization = parameterization
+        ls = stats.levy_stable(
+            alpha=alpha, beta=beta, scale=gamma, loc=delta
+        )
+        _, p = stats.kstest(
+            ls.rvs(size=sample_size, random_state=self.rng), ls.cdf
+        )
+        assert p > 0.05
+
+    @pytest.mark.xslow
+    @pytest.mark.parametrize('beta', [0.5, 1])
+    def test_rvs_alpha1(self, beta):
+        """Additional test cases for rvs for alpha equal to 1."""
+        alpha = 1.0
+        loc = 0.5
+        scale = 1.5
+        x = stats.levy_stable.rvs(alpha, beta, loc=loc, scale=scale,
+                                  size=5000, random_state=self.rng)
+        stat, p = stats.kstest(x, 'levy_stable',
+                               args=(alpha, beta, loc, scale))
+        assert p > 0.01
+
+    def test_fit(self):
+        # construct data to have percentiles that match
+        # example in McCulloch 1986.
+        x = [
+            -.05413, -.05413, 0., 0., 0., 0., .00533, .00533, .00533, .00533,
+            .00533, .03354, .03354, .03354, .03354, .03354, .05309, .05309,
+            .05309, .05309, .05309
+        ]
+        alpha1, beta1, loc1, scale1 = stats.levy_stable._fitstart(x)
+        assert_allclose(alpha1, 1.48, rtol=0, atol=0.01)
+        assert_almost_equal(beta1, -.22, 2)
+        assert_almost_equal(scale1, 0.01717, 4)
+        assert_almost_equal(
+            loc1, 0.00233, 2
+        )  # to 2 dps due to rounding error in McCulloch86
+
+        # cover alpha=2 scenario
+        x2 = x + [.05309, .05309, .05309, .05309, .05309]
+        alpha2, beta2, loc2, scale2 = stats.levy_stable._fitstart(x2)
+        assert_equal(alpha2, 2)
+        assert_equal(beta2, -1)
+        assert_almost_equal(scale2, .02503, 4)
+        assert_almost_equal(loc2, .03354, 4)
+
+    @pytest.mark.xfail(reason="Unknown problem with fitstart.")
+    @pytest.mark.parametrize(
+        "alpha,beta,delta,gamma",
+        [
+            (1.5, 0.4, 2, 3),
+            (1.0, 0.4, 2, 3),
+        ]
+    )
+    @pytest.mark.parametrize(
+        "parametrization", ["S0", "S1"]
+    )
+    def test_fit_rvs(self, alpha, beta, delta, gamma, parametrization):
+        """Test that fit agrees with rvs for each parametrization."""
+        stats.levy_stable.parametrization = parametrization
+        data = stats.levy_stable.rvs(
+            alpha, beta, loc=delta, scale=gamma, size=10000, random_state=self.rng
+        )
+        fit = stats.levy_stable._fitstart(data)
+        alpha_obs, beta_obs, delta_obs, gamma_obs = fit
+        assert_allclose(
+            [alpha, beta, delta, gamma],
+            [alpha_obs, beta_obs, delta_obs, gamma_obs],
+            rtol=0.01,
+        )
+
+    def test_fit_beta_flip(self):
+        # Confirm that sign of beta affects loc, not alpha or scale.
+        x = np.array([1, 1, 3, 3, 10, 10, 10, 30, 30, 100, 100])
+        alpha1, beta1, loc1, scale1 = stats.levy_stable._fitstart(x)
+        alpha2, beta2, loc2, scale2 = stats.levy_stable._fitstart(-x)
+        assert_equal(beta1, 1)
+        assert loc1 != 0
+        assert_almost_equal(alpha2, alpha1)
+        assert_almost_equal(beta2, -beta1)
+        assert_almost_equal(loc2, -loc1)
+        assert_almost_equal(scale2, scale1)
+
+    def test_fit_delta_shift(self):
+        # Confirm that loc slides up and down if data shifts.
+        SHIFT = 1
+        x = np.array([1, 1, 3, 3, 10, 10, 10, 30, 30, 100, 100])
+        alpha1, beta1, loc1, scale1 = stats.levy_stable._fitstart(-x)
+        alpha2, beta2, loc2, scale2 = stats.levy_stable._fitstart(-x + SHIFT)
+        assert_almost_equal(alpha2, alpha1)
+        assert_almost_equal(beta2, beta1)
+        assert_almost_equal(loc2, loc1 + SHIFT)
+        assert_almost_equal(scale2, scale1)
+
+    def test_fit_loc_extrap(self):
+        # Confirm that loc goes out of sample for alpha close to 1.
+        x = [1, 1, 3, 3, 10, 10, 10, 30, 30, 140, 140]
+        alpha1, beta1, loc1, scale1 = stats.levy_stable._fitstart(x)
+        assert alpha1 < 1, f"Expected alpha < 1, got {alpha1}"
+        assert loc1 < min(x), f"Expected loc < {min(x)}, got {loc1}"
+
+        x2 = [1, 1, 3, 3, 10, 10, 10, 30, 30, 130, 130]
+        alpha2, beta2, loc2, scale2 = stats.levy_stable._fitstart(x2)
+        assert alpha2 > 1, f"Expected alpha > 1, got {alpha2}"
+        assert loc2 > max(x2), f"Expected loc > {max(x2)}, got {loc2}"
+
+    @pytest.mark.slow
+    @pytest.mark.parametrize(
+        "pct_range,alpha_range,beta_range", [
+            pytest.param(
+                [.01, .5, .99],
+                [.1, 1, 2],
+                [-1, 0, .8],
+            ),
+            pytest.param(
+                [.01, .05, .5, .95, .99],
+                [.1, .5, 1, 1.5, 2],
+                [-.9, -.5, 0, .3, .6, 1],
+                marks=pytest.mark.slow
+            ),
+            pytest.param(
+                [.01, .05, .1, .25, .35, .5, .65, .75, .9, .95, .99],
+                np.linspace(0.1, 2, 20),
+                np.linspace(-1, 1, 21),
+                marks=pytest.mark.xslow,
+            ),
+        ]
+    )
+    def test_pdf_nolan_samples(
+            self, nolan_pdf_sample_data, pct_range, alpha_range, beta_range
+    ):
+        """Test pdf values against Nolan's stablec.exe output"""
+        data = nolan_pdf_sample_data
+
+        # some tests break on linux 32 bit
+        uname = platform.uname()
+        is_linux_32 = uname.system == 'Linux' and uname.machine == 'i686'
+        platform_desc = "/".join(
+            [uname.system, uname.machine, uname.processor])
+
+        # fmt: off
+        # There are a number of cases which fail on some but not all platforms.
+        # These are excluded by the filters below. TODO: Rewrite tests so that
+        # the now filtered out test cases are still run but marked in pytest as
+        # expected to fail.
+        tests = [
+            [
+                'dni', 1e-7, lambda r: (
+                    np.isin(r['pct'], pct_range) &
+                    np.isin(r['alpha'], alpha_range) &
+                    np.isin(r['beta'], beta_range) &
+                    ~(
+                        (
+                            (r['beta'] == 0) &
+                            (r['pct'] == 0.5)
+                        ) |
+                        (
+                            (r['beta'] >= 0.9) &
+                            (r['alpha'] >= 1.6) &
+                            (r['pct'] == 0.5)
+                        ) |
+                        (
+                            (r['alpha'] <= 0.4) &
+                            np.isin(r['pct'], [.01, .99])
+                        ) |
+                        (
+                            (r['alpha'] <= 0.3) &
+                            np.isin(r['pct'], [.05, .95])
+                        ) |
+                        (
+                            (r['alpha'] <= 0.2) &
+                            np.isin(r['pct'], [.1, .9])
+                        ) |
+                        (
+                            (r['alpha'] == 0.1) &
+                            np.isin(r['pct'], [.25, .75]) &
+                            np.isin(np.abs(r['beta']), [.5, .6, .7])
+                        ) |
+                        (
+                            (r['alpha'] == 0.1) &
+                            np.isin(r['pct'], [.5]) &
+                            np.isin(np.abs(r['beta']), [.1])
+                        ) |
+                        (
+                            (r['alpha'] == 0.1) &
+                            np.isin(r['pct'], [.35, .65]) &
+                            np.isin(np.abs(r['beta']), [-.4, -.3, .3, .4, .5])
+                        ) |
+                        (
+                            (r['alpha'] == 0.2) &
+                            (r['beta'] == 0.5) &
+                            (r['pct'] == 0.25)
+                        ) |
+                        (
+                            (r['alpha'] == 0.2) &
+                            (r['beta'] == -0.3) &
+                            (r['pct'] == 0.65)
+                        ) |
+                        (
+                            (r['alpha'] == 0.2) &
+                            (r['beta'] == 0.3) &
+                            (r['pct'] == 0.35)
+                        ) |
+                        (
+                            (r['alpha'] == 1.) &
+                            np.isin(r['pct'], [.5]) &
+                            np.isin(np.abs(r['beta']), [.1, .2, .3, .4])
+                        ) |
+                        (
+                            (r['alpha'] == 1.) &
+                            np.isin(r['pct'], [.35, .65]) &
+                            np.isin(np.abs(r['beta']), [.8, .9, 1.])
+                        ) |
+                        (
+                            (r['alpha'] == 1.) &
+                            np.isin(r['pct'], [.01, .99]) &
+                            np.isin(np.abs(r['beta']), [-.1, .1])
+                        ) |
+                        # various points ok but too sparse to list
+                        (r['alpha'] >= 1.1)
+                    )
+                )
+            ],
+            # piecewise generally good accuracy
+            [
+                'piecewise', 1e-11, lambda r: (
+                    np.isin(r['pct'], pct_range) &
+                    np.isin(r['alpha'], alpha_range) &
+                    np.isin(r['beta'], beta_range) &
+                    (r['alpha'] > 0.2) &
+                    (r['alpha'] != 1.)
+                )
+            ],
+            # for alpha = 1. for linux 32 bit optimize.bisect
+            # has some issues for .01 and .99 percentile
+            [
+                'piecewise', 1e-11, lambda r: (
+                    (r['alpha'] == 1.) &
+                    (not is_linux_32) &
+                    np.isin(r['pct'], pct_range) &
+                    (1. in alpha_range) &
+                    np.isin(r['beta'], beta_range)
+                )
+            ],
+            # for small alpha very slightly reduced accuracy
+            [
+                'piecewise', 2.5e-10, lambda r: (
+                    np.isin(r['pct'], pct_range) &
+                    np.isin(r['alpha'], alpha_range) &
+                    np.isin(r['beta'], beta_range) &
+                    (r['alpha'] <= 0.2)
+                )
+            ],
+            # fft accuracy reduces as alpha decreases
+            [
+                'fft-simpson', 1e-5, lambda r: (
+                    (r['alpha'] >= 1.9) &
+                    np.isin(r['pct'], pct_range) &
+                    np.isin(r['alpha'], alpha_range) &
+                    np.isin(r['beta'], beta_range)
+                ),
+            ],
+            [
+                'fft-simpson', 1e-6, lambda r: (
+                    np.isin(r['pct'], pct_range) &
+                    np.isin(r['alpha'], alpha_range) &
+                    np.isin(r['beta'], beta_range) &
+                    (r['alpha'] > 1) &
+                    (r['alpha'] < 1.9)
+                )
+            ],
+            # fft relative errors for alpha < 1, will raise if enabled
+            # ['fft-simpson', 1e-4, lambda r: r['alpha'] == 0.9],
+            # ['fft-simpson', 1e-3, lambda r: r['alpha'] == 0.8],
+            # ['fft-simpson', 1e-2, lambda r: r['alpha'] == 0.7],
+            # ['fft-simpson', 1e-1, lambda r: r['alpha'] == 0.6],
+        ]
+        # fmt: on
+        for ix, (default_method, rtol,
+                 filter_func) in enumerate(tests):
+            stats.levy_stable.pdf_default_method = default_method
+            subdata = data[filter_func(data)
+                           ] if filter_func is not None else data
+            msg = "Density calculations experimental for FFT method"
+            with warnings.catch_warnings():
+                warnings.filterwarnings("ignore", msg, RuntimeWarning)
+                # occurs in FFT methods only
+                p = stats.levy_stable.pdf(
+                    subdata['x'],
+                    subdata['alpha'],
+                    subdata['beta'],
+                    scale=1,
+                    loc=0
+                )
+                with np.errstate(over="ignore"):
+                    subdata2 = rec_append_fields(
+                        subdata,
+                        ['calc', 'abserr', 'relerr'],
+                        [
+                            p,
+                            np.abs(p - subdata['p']),
+                            np.abs(p - subdata['p']) / np.abs(subdata['p'])
+                        ]
+                    )
+                failures = subdata2[
+                  (subdata2['relerr'] >= rtol) |
+                  np.isnan(p)
+                ]
+                message = (
+                    f"pdf test {ix} failed with method '{default_method}' "
+                    f"[platform: {platform_desc}]\n{failures.dtype.names}\n{failures}"
+                )
+                assert_allclose(
+                    p,
+                    subdata['p'],
+                    rtol,
+                    err_msg=message,
+                    verbose=False
+                )
+
+    @pytest.mark.parametrize(
+        "pct_range,alpha_range,beta_range", [
+            pytest.param(
+                [.01, .5, .99],
+                [.1, 1, 2],
+                [-1, 0, .8],
+            ),
+            pytest.param(
+                [.01, .05, .5, .95, .99],
+                [.1, .5, 1, 1.5, 2],
+                [-.9, -.5, 0, .3, .6, 1],
+                marks=pytest.mark.slow
+            ),
+            pytest.param(
+                [.01, .05, .1, .25, .35, .5, .65, .75, .9, .95, .99],
+                np.linspace(0.1, 2, 20),
+                np.linspace(-1, 1, 21),
+                marks=pytest.mark.xslow,
+            ),
+        ]
+    )
+    def test_cdf_nolan_samples(
+            self, nolan_cdf_sample_data, pct_range, alpha_range, beta_range
+    ):
+        """ Test cdf values against Nolan's stablec.exe output."""
+        data = nolan_cdf_sample_data
+        tests = [
+            # piecewise generally good accuracy
+            [
+                'piecewise', 2e-12, lambda r: (
+                    np.isin(r['pct'], pct_range) &
+                    np.isin(r['alpha'], alpha_range) &
+                    np.isin(r['beta'], beta_range) &
+                    ~(
+                        (
+                            (r['alpha'] == 1.) &
+                            np.isin(r['beta'], [-0.3, -0.2, -0.1]) &
+                            (r['pct'] == 0.01)
+                        ) |
+                        (
+                            (r['alpha'] == 1.) &
+                            np.isin(r['beta'], [0.1, 0.2, 0.3]) &
+                            (r['pct'] == 0.99)
+                        )
+                    )
+                )
+            ],
+            # for some points with alpha=1, Nolan's STABLE clearly
+            # loses accuracy
+            [
+                'piecewise', 5e-2, lambda r: (
+                    np.isin(r['pct'], pct_range) &
+                    np.isin(r['alpha'], alpha_range) &
+                    np.isin(r['beta'], beta_range) &
+                    (
+                        (r['alpha'] == 1.) &
+                        np.isin(r['beta'], [-0.3, -0.2, -0.1]) &
+                        (r['pct'] == 0.01)
+                    ) |
+                    (
+                        (r['alpha'] == 1.) &
+                        np.isin(r['beta'], [0.1, 0.2, 0.3]) &
+                        (r['pct'] == 0.99)
+                    )
+                )
+            ],
+            # fft accuracy poor, very poor alpha < 1
+            [
+                'fft-simpson', 1e-5, lambda r: (
+                    np.isin(r['pct'], pct_range) &
+                    np.isin(r['alpha'], alpha_range) &
+                    np.isin(r['beta'], beta_range) &
+                    (r['alpha'] > 1.7)
+                )
+            ],
+            [
+                'fft-simpson', 1e-4, lambda r: (
+                    np.isin(r['pct'], pct_range) &
+                    np.isin(r['alpha'], alpha_range) &
+                    np.isin(r['beta'], beta_range) &
+                    (r['alpha'] > 1.5) &
+                    (r['alpha'] <= 1.7)
+                )
+            ],
+            [
+                'fft-simpson', 1e-3, lambda r: (
+                    np.isin(r['pct'], pct_range) &
+                    np.isin(r['alpha'], alpha_range) &
+                    np.isin(r['beta'], beta_range) &
+                    (r['alpha'] > 1.3) &
+                    (r['alpha'] <= 1.5)
+                )
+            ],
+            [
+                'fft-simpson', 1e-2, lambda r: (
+                    np.isin(r['pct'], pct_range) &
+                    np.isin(r['alpha'], alpha_range) &
+                    np.isin(r['beta'], beta_range) &
+                    (r['alpha'] > 1.0) &
+                    (r['alpha'] <= 1.3)
+                )
+            ],
+        ]
+        for ix, (default_method, rtol,
+                 filter_func) in enumerate(tests):
+            stats.levy_stable.cdf_default_method = default_method
+            subdata = data[filter_func(data)
+                           ] if filter_func is not None else data
+            with warnings.catch_warnings():
+                warnings.filterwarnings(
+                    'ignore',
+                    ('Cumulative density calculations experimental for FFT'
+                     ' method. Use piecewise method instead.'),
+                    RuntimeWarning)
+                p = stats.levy_stable.cdf(
+                    subdata['x'],
+                    subdata['alpha'],
+                    subdata['beta'],
+                    scale=1,
+                    loc=0
+                )
+                with np.errstate(over="ignore"):
+                    subdata2 = rec_append_fields(
+                        subdata,
+                        ['calc', 'abserr', 'relerr'],
+                        [
+                            p,
+                            np.abs(p - subdata['p']),
+                            np.abs(p - subdata['p']) / np.abs(subdata['p'])
+                        ]
+                    )
+                failures = subdata2[
+                  (subdata2['relerr'] >= rtol) |
+                  np.isnan(p)
+                ]
+                message = (f"cdf test {ix} failed with method '{default_method}'\n"
+                           f"{failures.dtype.names}\n{failures}")
+                assert_allclose(
+                    p,
+                    subdata['p'],
+                    rtol,
+                    err_msg=message,
+                    verbose=False
+                )
+
+    @pytest.mark.parametrize("param", [0, 1])
+    @pytest.mark.parametrize("case", ["pdf", "cdf"])
+    def test_location_scale(
+            self, nolan_loc_scale_sample_data, param, case
+    ):
+        """Tests for pdf and cdf where loc, scale are different from 0, 1
+        """
+
+        uname = platform.uname()
+        is_linux_32 = uname.system == 'Linux' and "32bit" in platform.architecture()[0]
+        # Test seems to be unstable (see gh-17839 for a bug report on Debian
+        # i386), so skip it.
+        if is_linux_32 and case == 'pdf':
+            pytest.skip("Test unstable on some platforms; see gh-17839, 17859")
+
+        data = nolan_loc_scale_sample_data
+        # We only test against piecewise as location/scale transforms
+        # are same for other methods.
+        stats.levy_stable.cdf_default_method = "piecewise"
+        stats.levy_stable.pdf_default_method = "piecewise"
+
+        subdata = data[data["param"] == param]
+        stats.levy_stable.parameterization = f"S{param}"
+
+        assert case in ["pdf", "cdf"]
+        function = (
+            stats.levy_stable.pdf if case == "pdf" else stats.levy_stable.cdf
+        )
+
+        v1 = function(
+            subdata['x'], subdata['alpha'], subdata['beta'], scale=2, loc=3
+        )
+        assert_allclose(v1, subdata[case], 1e-5)
+
+    @pytest.mark.parametrize(
+        "method,decimal_places",
+        [
+            ['dni', 4],
+            ['piecewise', 4],
+        ]
+    )
+    def test_pdf_alpha_equals_one_beta_non_zero(self, method, decimal_places):
+        """ sample points extracted from Tables and Graphs of Stable
+        Probability Density Functions - Donald R Holt - 1973 - p 187.
+        """
+        xs = np.array(
+            [0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4]
+        )
+        density = np.array(
+            [
+                .3183, .3096, .2925, .2622, .1591, .1587, .1599, .1635, .0637,
+                .0729, .0812, .0955, .0318, .0390, .0458, .0586, .0187, .0236,
+                .0285, .0384
+            ]
+        )
+        betas = np.array(
+            [
+                0, .25, .5, 1, 0, .25, .5, 1, 0, .25, .5, 1, 0, .25, .5, 1, 0,
+                .25, .5, 1
+            ]
+        )
+        with np.errstate(all='ignore'), warnings.catch_warnings():
+            warnings.filterwarnings("ignore",
+                category=RuntimeWarning,
+                message="Density calculation unstable.*"
+            )
+            stats.levy_stable.pdf_default_method = method
+            # stats.levy_stable.fft_grid_spacing = 0.0001
+            pdf = stats.levy_stable.pdf(xs, 1, betas, scale=1, loc=0)
+            assert_almost_equal(
+                pdf, density, decimal_places, method
+            )
+
+    @pytest.mark.parametrize(
+        "params,expected",
+        [
+            [(1.48, -.22, 0, 1), (0, np.inf, np.nan, np.nan)],
+            [(2, .9, 10, 1.5), (10, 4.5, 0, 0)]
+        ]
+    )
+    def test_stats(self, params, expected):
+        observed = stats.levy_stable.stats(
+            params[0], params[1], loc=params[2], scale=params[3],
+            moments='mvsk'
+        )
+        assert_almost_equal(observed, expected)
+
+    @pytest.mark.parametrize('alpha', [0.25, 0.5, 0.75])
+    @pytest.mark.parametrize(
+        'function,beta,points,expected',
+        [
+            (
+                stats.levy_stable.cdf,
+                1.0,
+                np.linspace(-25, 0, 10),
+                0.0,
+            ),
+            (
+                stats.levy_stable.pdf,
+                1.0,
+                np.linspace(-25, 0, 10),
+                0.0,
+            ),
+            (
+                stats.levy_stable.cdf,
+                -1.0,
+                np.linspace(0, 25, 10),
+                1.0,
+            ),
+            (
+                stats.levy_stable.pdf,
+                -1.0,
+                np.linspace(0, 25, 10),
+                0.0,
+            )
+        ]
+    )
+    def test_distribution_outside_support(
+            self, alpha, function, beta, points, expected
+    ):
+        """Ensure the pdf/cdf routines do not return nan outside support.
+
+        This distribution's support becomes truncated in a few special cases:
+            support is [mu, infty) if alpha < 1 and beta = 1
+            support is (-infty, mu] if alpha < 1 and beta = -1
+        Otherwise, the support is all reals. Here, mu is zero by default.
+        """
+        assert 0 < alpha < 1
+        assert_almost_equal(
+            function(points, alpha=alpha, beta=beta),
+            np.full(len(points), expected)
+        )
+
+    @pytest.mark.parametrize(
+        'x,alpha,beta,expected',
+        # Reference values from Matlab
+        # format long
+        # alphas = [1.7720732804618808, 1.9217001522410235, 1.5654806051633634,
+        #           1.7420803447784388, 1.5748002527689913];
+        # betas = [0.5059373136902996, -0.8779442746685926, -0.4016220341911392,
+        #          -0.38180029468259247, -0.25200194914153684];
+        # x0s = [0, 1e-4, -1e-4];
+        # for x0 = x0s
+        #     disp("x0 = " + x0)
+        #     for ii = 1:5
+        #         alpha = alphas(ii);
+        #         beta = betas(ii);
+        #         pd = makedist('Stable','alpha',alpha,'beta',beta,'gam',1,'delta',0);
+        #         % we need to adjust x. It is the same as x = 0 In scipy.
+        #         x = x0 - beta * tan(pi * alpha / 2);
+        #         disp(pd.pdf(x))
+        #     end
+        # end
+        [
+            (0, 1.7720732804618808, 0.5059373136902996, 0.278932636798268),
+            (0, 1.9217001522410235, -0.8779442746685926, 0.281054757202316),
+            (0, 1.5654806051633634, -0.4016220341911392, 0.271282133194204),
+            (0, 1.7420803447784388, -0.38180029468259247, 0.280202199244247),
+            (0, 1.5748002527689913, -0.25200194914153684, 0.280136576218665),
+        ]
+    )
+    def test_x_equal_zeta(
+            self, x, alpha, beta, expected
+    ):
+        """Test pdf for x equal to zeta.
+
+        With S1 parametrization: x0 = x + zeta if alpha != 1 So, for x = 0, x0
+        will be close to zeta.
+
+        When case "x equal zeta" is not handled properly and quad_eps is not
+        low enough: - pdf may be less than 0 - logpdf is nan
+
+        The points from the parametrize block are found randomly so that PDF is
+        less than 0.
+
+        Reference values taken from MATLAB
+        https://www.mathworks.com/help/stats/stable-distribution.html
+        """
+        stats.levy_stable.quad_eps = 1.2e-11
+
+        assert_almost_equal(
+            stats.levy_stable.pdf(x, alpha=alpha, beta=beta),
+            expected,
+        )
+
+    @pytest.mark.xfail
+    @pytest.mark.parametrize(
+        # See comment for test_x_equal_zeta for script for reference values
+        'x,alpha,beta,expected',
+        [
+            (1e-4, 1.7720732804618808, 0.5059373136902996, 0.278929165340670),
+            (1e-4, 1.9217001522410235, -0.8779442746685926, 0.281056564327953),
+            (1e-4, 1.5654806051633634, -0.4016220341911392, 0.271252432161167),
+            (1e-4, 1.7420803447784388, -0.38180029468259247, 0.280205311264134),
+            (1e-4, 1.5748002527689913, -0.25200194914153684, 0.280140965235426),
+            (-1e-4, 1.7720732804618808, 0.5059373136902996, 0.278936106741754),
+            (-1e-4, 1.9217001522410235, -0.8779442746685926, 0.281052948629429),
+            (-1e-4, 1.5654806051633634, -0.4016220341911392, 0.271275394392385),
+            (-1e-4, 1.7420803447784388, -0.38180029468259247, 0.280199085645099),
+            (-1e-4, 1.5748002527689913, -0.25200194914153684, 0.280132185432842),
+        ]
+    )
+    def test_x_near_zeta(
+            self, x, alpha, beta, expected
+    ):
+        """Test pdf for x near zeta.
+
+        With S1 parametrization: x0 = x + zeta if alpha != 1 So, for x = 0, x0
+        will be close to zeta.
+
+        When case "x near zeta" is not handled properly and quad_eps is not
+        low enough: - pdf may be less than 0 - logpdf is nan
+
+        The points from the parametrize block are found randomly so that PDF is
+        less than 0.
+
+        Reference values taken from MATLAB
+        https://www.mathworks.com/help/stats/stable-distribution.html
+        """
+        stats.levy_stable.quad_eps = 1.2e-11
+
+        assert_almost_equal(
+            stats.levy_stable.pdf(x, alpha=alpha, beta=beta),
+            expected,
+        )
+
+    @pytest.fixture
+    def levy_stable_lock(self):
+        return threading.Lock()
+
+    def test_frozen_parameterization_gh20821(self, levy_stable_lock):
+        # gh-20821 reported that frozen distributions ignore the parameterization.
+        # Check that this is resolved and that the frozen distribution's
+        # parameterization can be changed independently of stats.levy_stable
+        rng = np.random.default_rng
+        shapes = dict(alpha=1.9, beta=0.1, loc=0.0, scale=1.0)
+        unfrozen = stats.levy_stable
+        frozen = stats.levy_stable(**shapes)
+
+        with levy_stable_lock:
+            unfrozen.parameterization = "S0"
+            frozen.parameterization = "S1"
+            unfrozen_a = unfrozen.rvs(**shapes, size=10, random_state=rng(329823498))
+            frozen_a = frozen.rvs(size=10, random_state=rng(329823498))
+            assert not np.any(frozen_a == unfrozen_a)
+
+            unfrozen.parameterization = "S1"
+            frozen.parameterization = "S0"
+            unfrozen_b = unfrozen.rvs(**shapes, size=10, random_state=rng(329823498))
+            frozen_b = frozen.rvs(size=10, random_state=rng(329823498))
+            assert_equal(frozen_b, unfrozen_a)
+            assert_equal(unfrozen_b, frozen_a)
+
+    def test_frozen_parameterization_gh20821b(self, levy_stable_lock):
+        # Check that the parameterization of the frozen distribution is that of
+        # the unfrozen distribution at the time of freezing
+        rng = np.random.default_rng
+        shapes = dict(alpha=1.9, beta=0.1, loc=0.0, scale=1.0)
+        unfrozen = stats.levy_stable
+
+        with levy_stable_lock:
+            unfrozen.parameterization = "S0"
+            frozen = stats.levy_stable(**shapes)
+            unfrozen_a = unfrozen.rvs(**shapes, size=10, random_state=rng(329823498))
+            frozen_a = frozen.rvs(size=10, random_state=rng(329823498))
+            assert_equal(frozen_a, unfrozen_a)
+
+            unfrozen.parameterization = "S1"
+            frozen = stats.levy_stable(**shapes)
+            unfrozen_b = unfrozen.rvs(**shapes, size=10, random_state=rng(329823498))
+            frozen_b = frozen.rvs(size=10, random_state=rng(329823498))
+            assert_equal(frozen_b, unfrozen_b)
+
+    @pytest.mark.parametrize(
+        "param, alpha, beta, xs, expected",
+        [
+            (0, 1.6, 1, [-15, -14, -13], [-187.1444263, -157.1411663, -130.3526688]),
+            (1, 1.6, 1, [-15, -14, -13], [-165.0203129, -137.3671717, -112.8223545]),
+            (0, 1.4, -1, [13, 14, 15], [-367.1943293, -464.7049565, -579.4399286]),
+            (1, 1.4, -1, [13, 14, 15], [-258.1216497, -334.6139857, -426.0724094]),
+        ],
+    )
+    @pytest.mark.xfail_on_32bit("`bisect` fails to recognize valid bracket")
+    def test_logpdf_tail(self, param, alpha, beta, xs, expected):
+        # gh-20636
+        # Expected values computed from Mathematica. Mathematica command is:
+        # Log[PDF[StableDistribution[0, 1.6, 1, 0, 1], -15.0]] // InputForm
+        # Test levy_stable.logpdf accuracy in the tails when beta=1 or beta=-1
+        # for both S0/S1 parameterizations.
+        # Testing logpdf instead of pdf as more compact.
+        stats.levy_stable.parameterization = f"S{param}"
+        logpdfs = stats.levy_stable(alpha=alpha, beta=beta).logpdf(xs)
+        assert_allclose(logpdfs, expected, rtol=1e-5)
+
+class TestArrayArgument:  # test for ticket:992
+    def setup_method(self):
+        self.rng = np.random.default_rng(7556981556)
+
+    def test_noexception(self):
+        rvs = stats.norm.rvs(loc=(np.arange(5)), scale=np.ones(5),
+                             size=(10, 5), random_state=self.rng)
+        assert_equal(rvs.shape, (10, 5))
+
+
+class TestDocstring:
+    def test_docstrings(self):
+        # See ticket #761
+        if stats.rayleigh.__doc__ is not None:
+            assert_("rayleigh" in stats.rayleigh.__doc__.lower())
+        if stats.bernoulli.__doc__ is not None:
+            assert_("bernoulli" in stats.bernoulli.__doc__.lower())
+
+    def test_no_name_arg(self):
+        # If name is not given, construction shouldn't fail.  See #1508.
+        stats.rv_continuous()
+        stats.rv_discrete()
+
+
+def test_args_reduce():
+    a = array([1, 3, 2, 1, 2, 3, 3])
+    b, c = argsreduce(a > 1, a, 2)
+
+    assert_array_equal(b, [3, 2, 2, 3, 3])
+    assert_array_equal(c, [2])
+
+    b, c = argsreduce(2 > 1, a, 2)
+    assert_array_equal(b, a)
+    assert_array_equal(c, [2] * np.size(a))
+
+    b, c = argsreduce(a > 0, a, 2)
+    assert_array_equal(b, a)
+    assert_array_equal(c, [2] * np.size(a))
+
+
+class TestFitMethod:
+    # fitting assumes continuous parameters
+    skip = ['ncf', 'ksone', 'kstwo', 'irwinhall']
+
+    def setup_method(self):
+        self.rng = np.random.default_rng(4522425749)
+
+    # skip these b/c deprecated, or only loc and scale arguments
+    fitSkipNonFinite = ['expon', 'norm', 'uniform', 'irwinhall']
+
+    @pytest.mark.parametrize('dist,args', distcont)
+    def test_fit_w_non_finite_data_values(self, dist, args):
+        """gh-10300"""
+        if dist in self.fitSkipNonFinite:
+            pytest.skip(f"{dist} fit known to fail or deprecated")
+        x = np.array([1.6483, 2.7169, 2.4667, 1.1791, 3.5433, np.nan])
+        y = np.array([1.6483, 2.7169, 2.4667, 1.1791, 3.5433, np.inf])
+        distfunc = getattr(stats, dist)
+        assert_raises(ValueError, distfunc.fit, x, fscale=1)
+        assert_raises(ValueError, distfunc.fit, y, fscale=1)
+
+    def test_fix_fit_2args_lognorm(self):
+        # Regression test for #1551.
+        with np.errstate(all='ignore'):
+            x = stats.lognorm.rvs(0.25, 0., 20.0, size=20, random_state=self.rng)
+            expected_shape = np.sqrt(((np.log(x) - np.log(20))**2).mean())
+            assert_allclose(np.array(stats.lognorm.fit(x, floc=0, fscale=20)),
+                            [expected_shape, 0, 20], atol=1e-8)
+
+    def test_fix_fit_norm(self):
+        x = np.arange(1, 6)
+
+        loc, scale = stats.norm.fit(x)
+        assert_almost_equal(loc, 3)
+        assert_almost_equal(scale, np.sqrt(2))
+
+        loc, scale = stats.norm.fit(x, floc=2)
+        assert_equal(loc, 2)
+        assert_equal(scale, np.sqrt(3))
+
+        loc, scale = stats.norm.fit(x, fscale=2)
+        assert_almost_equal(loc, 3)
+        assert_equal(scale, 2)
+
+    def test_fix_fit_gamma(self):
+        x = np.arange(1, 6)
+        meanlog = np.log(x).mean()
+
+        # A basic test of gamma.fit with floc=0.
+        floc = 0
+        a, loc, scale = stats.gamma.fit(x, floc=floc)
+        s = np.log(x.mean()) - meanlog
+        assert_almost_equal(np.log(a) - special.digamma(a), s, decimal=5)
+        assert_equal(loc, floc)
+        assert_almost_equal(scale, x.mean()/a, decimal=8)
+
+        # Regression tests for gh-2514.
+        # The problem was that if `floc=0` was given, any other fixed
+        # parameters were ignored.
+        f0 = 1
+        floc = 0
+        a, loc, scale = stats.gamma.fit(x, f0=f0, floc=floc)
+        assert_equal(a, f0)
+        assert_equal(loc, floc)
+        assert_almost_equal(scale, x.mean()/a, decimal=8)
+
+        f0 = 2
+        floc = 0
+        a, loc, scale = stats.gamma.fit(x, f0=f0, floc=floc)
+        assert_equal(a, f0)
+        assert_equal(loc, floc)
+        assert_almost_equal(scale, x.mean()/a, decimal=8)
+
+        # loc and scale fixed.
+        floc = 0
+        fscale = 2
+        a, loc, scale = stats.gamma.fit(x, floc=floc, fscale=fscale)
+        assert_equal(loc, floc)
+        assert_equal(scale, fscale)
+        c = meanlog - np.log(fscale)
+        assert_almost_equal(special.digamma(a), c)
+
+    def test_fix_fit_beta(self):
+        # Test beta.fit when both floc and fscale are given.
+
+        def mlefunc(a, b, x):
+            # Zeros of this function are critical points of
+            # the maximum likelihood function.
+            n = len(x)
+            s1 = np.log(x).sum()
+            s2 = np.log(1-x).sum()
+            psiab = special.psi(a + b)
+            func = [s1 - n * (-psiab + special.psi(a)),
+                    s2 - n * (-psiab + special.psi(b))]
+            return func
+
+        # Basic test with floc and fscale given.
+        x = np.array([0.125, 0.25, 0.5])
+        a, b, loc, scale = stats.beta.fit(x, floc=0, fscale=1)
+        assert_equal(loc, 0)
+        assert_equal(scale, 1)
+        assert_allclose(mlefunc(a, b, x), [0, 0], atol=1e-6)
+
+        # Basic test with f0, floc and fscale given.
+        # This is also a regression test for gh-2514.
+        x = np.array([0.125, 0.25, 0.5])
+        a, b, loc, scale = stats.beta.fit(x, f0=2, floc=0, fscale=1)
+        assert_equal(a, 2)
+        assert_equal(loc, 0)
+        assert_equal(scale, 1)
+        da, db = mlefunc(a, b, x)
+        assert_allclose(db, 0, atol=1e-5)
+
+        # Same floc and fscale values as above, but reverse the data
+        # and fix b (f1).
+        x2 = 1 - x
+        a2, b2, loc2, scale2 = stats.beta.fit(x2, f1=2, floc=0, fscale=1)
+        assert_equal(b2, 2)
+        assert_equal(loc2, 0)
+        assert_equal(scale2, 1)
+        da, db = mlefunc(a2, b2, x2)
+        assert_allclose(da, 0, atol=1e-5)
+        # a2 of this test should equal b from above.
+        assert_almost_equal(a2, b)
+
+        # Check for detection of data out of bounds when floc and fscale
+        # are given.
+        assert_raises(ValueError, stats.beta.fit, x, floc=0.5, fscale=1)
+        y = np.array([0, .5, 1])
+        assert_raises(ValueError, stats.beta.fit, y, floc=0, fscale=1)
+        assert_raises(ValueError, stats.beta.fit, y, floc=0, fscale=1, f0=2)
+        assert_raises(ValueError, stats.beta.fit, y, floc=0, fscale=1, f1=2)
+
+        # Check that attempting to fix all the parameters raises a ValueError.
+        assert_raises(ValueError, stats.beta.fit, y, f0=0, f1=1,
+                      floc=2, fscale=3)
+
+    def test_expon_fit(self):
+        x = np.array([2, 2, 4, 4, 4, 4, 4, 8])
+
+        loc, scale = stats.expon.fit(x)
+        assert_equal(loc, 2)    # x.min()
+        assert_equal(scale, 2)  # x.mean() - x.min()
+
+        loc, scale = stats.expon.fit(x, fscale=3)
+        assert_equal(loc, 2)    # x.min()
+        assert_equal(scale, 3)  # fscale
+
+        loc, scale = stats.expon.fit(x, floc=0)
+        assert_equal(loc, 0)    # floc
+        assert_equal(scale, 4)  # x.mean() - loc
+
+    def test_lognorm_fit(self):
+        x = np.array([1.5, 3, 10, 15, 23, 59])
+        lnxm1 = np.log(x - 1)
+
+        shape, loc, scale = stats.lognorm.fit(x, floc=1)
+        assert_allclose(shape, lnxm1.std(), rtol=1e-12)
+        assert_equal(loc, 1)
+        assert_allclose(scale, np.exp(lnxm1.mean()), rtol=1e-12)
+
+        shape, loc, scale = stats.lognorm.fit(x, floc=1, fscale=6)
+        assert_allclose(shape, np.sqrt(((lnxm1 - np.log(6))**2).mean()),
+                        rtol=1e-12)
+        assert_equal(loc, 1)
+        assert_equal(scale, 6)
+
+        shape, loc, scale = stats.lognorm.fit(x, floc=1, fix_s=0.75)
+        assert_equal(shape, 0.75)
+        assert_equal(loc, 1)
+        assert_allclose(scale, np.exp(lnxm1.mean()), rtol=1e-12)
+
+    def test_uniform_fit(self):
+        x = np.array([1.0, 1.1, 1.2, 9.0])
+
+        loc, scale = stats.uniform.fit(x)
+        assert_equal(loc, x.min())
+        assert_equal(scale, np.ptp(x))
+
+        loc, scale = stats.uniform.fit(x, floc=0)
+        assert_equal(loc, 0)
+        assert_equal(scale, x.max())
+
+        loc, scale = stats.uniform.fit(x, fscale=10)
+        assert_equal(loc, 0)
+        assert_equal(scale, 10)
+
+        assert_raises(ValueError, stats.uniform.fit, x, floc=2.0)
+        assert_raises(ValueError, stats.uniform.fit, x, fscale=5.0)
+
+    @pytest.mark.xslow
+    @pytest.mark.parametrize("method", ["MLE", "MM"])
+    def test_fshapes(self, method):
+        # take a beta distribution, with shapes='a, b', and make sure that
+        # fa is equivalent to f0, and fb is equivalent to f1
+        a, b = 3., 4.
+        x = stats.beta.rvs(a, b, size=100, random_state=self.rng)
+        res_1 = stats.beta.fit(x, f0=3., method=method)
+        res_2 = stats.beta.fit(x, fa=3., method=method)
+        assert_allclose(res_1, res_2, atol=1e-12, rtol=1e-12)
+
+        res_2 = stats.beta.fit(x, fix_a=3., method=method)
+        assert_allclose(res_1, res_2, atol=1e-12, rtol=1e-12)
+
+        res_3 = stats.beta.fit(x, f1=4., method=method)
+        res_4 = stats.beta.fit(x, fb=4., method=method)
+        assert_allclose(res_3, res_4, atol=1e-12, rtol=1e-12)
+
+        res_4 = stats.beta.fit(x, fix_b=4., method=method)
+        assert_allclose(res_3, res_4, atol=1e-12, rtol=1e-12)
+
+        # cannot specify both positional and named args at the same time
+        assert_raises(ValueError, stats.beta.fit, x, fa=1, f0=2, method=method)
+
+        # check that attempting to fix all parameters raises a ValueError
+        assert_raises(ValueError, stats.beta.fit, x, fa=0, f1=1,
+                      floc=2, fscale=3, method=method)
+
+        # check that specifying floc, fscale and fshapes works for
+        # beta and gamma which override the generic fit method
+        res_5 = stats.beta.fit(x, fa=3., floc=0, fscale=1, method=method)
+        aa, bb, ll, ss = res_5
+        assert_equal([aa, ll, ss], [3., 0, 1])
+
+        # gamma distribution
+        a = 3.
+        data = stats.gamma.rvs(a, size=100, random_state=self.rng)
+        aa, ll, ss = stats.gamma.fit(data, fa=a, method=method)
+        assert_equal(aa, a)
+
+    @pytest.mark.parametrize("method", ["MLE", "MM"])
+    def test_extra_params(self, method):
+        # unknown parameters should raise rather than be silently ignored
+        dist = stats.exponnorm
+        data = dist.rvs(K=2, size=100, random_state=self.rng)
+        dct = dict(enikibeniki=-101)
+        assert_raises(TypeError, dist.fit, data, **dct, method=method)
+
+
+class TestFrozen:
+    # Test that a frozen distribution gives the same results as the original
+    # object.
+    #
+    # Only tested for the normal distribution (with loc and scale specified)
+    # and for the gamma distribution (with a shape parameter specified).
+    def test_norm(self):
+        dist = stats.norm
+        frozen = stats.norm(loc=10.0, scale=3.0)
+
+        result_f = frozen.pdf(20.0)
+        result = dist.pdf(20.0, loc=10.0, scale=3.0)
+        assert_equal(result_f, result)
+
+        result_f = frozen.cdf(20.0)
+        result = dist.cdf(20.0, loc=10.0, scale=3.0)
+        assert_equal(result_f, result)
+
+        result_f = frozen.ppf(0.25)
+        result = dist.ppf(0.25, loc=10.0, scale=3.0)
+        assert_equal(result_f, result)
+
+        result_f = frozen.isf(0.25)
+        result = dist.isf(0.25, loc=10.0, scale=3.0)
+        assert_equal(result_f, result)
+
+        result_f = frozen.sf(10.0)
+        result = dist.sf(10.0, loc=10.0, scale=3.0)
+        assert_equal(result_f, result)
+
+        result_f = frozen.median()
+        result = dist.median(loc=10.0, scale=3.0)
+        assert_equal(result_f, result)
+
+        result_f = frozen.mean()
+        result = dist.mean(loc=10.0, scale=3.0)
+        assert_equal(result_f, result)
+
+        result_f = frozen.var()
+        result = dist.var(loc=10.0, scale=3.0)
+        assert_equal(result_f, result)
+
+        result_f = frozen.std()
+        result = dist.std(loc=10.0, scale=3.0)
+        assert_equal(result_f, result)
+
+        result_f = frozen.entropy()
+        result = dist.entropy(loc=10.0, scale=3.0)
+        assert_equal(result_f, result)
+
+        result_f = frozen.moment(2)
+        result = dist.moment(2, loc=10.0, scale=3.0)
+        assert_equal(result_f, result)
+
+        assert_equal(frozen.a, dist.a)
+        assert_equal(frozen.b, dist.b)
+
+    def test_gamma(self):
+        a = 2.0
+        dist = stats.gamma
+        frozen = stats.gamma(a)
+
+        result_f = frozen.pdf(20.0)
+        result = dist.pdf(20.0, a)
+        assert_equal(result_f, result)
+
+        result_f = frozen.cdf(20.0)
+        result = dist.cdf(20.0, a)
+        assert_equal(result_f, result)
+
+        result_f = frozen.ppf(0.25)
+        result = dist.ppf(0.25, a)
+        assert_equal(result_f, result)
+
+        result_f = frozen.isf(0.25)
+        result = dist.isf(0.25, a)
+        assert_equal(result_f, result)
+
+        result_f = frozen.sf(10.0)
+        result = dist.sf(10.0, a)
+        assert_equal(result_f, result)
+
+        result_f = frozen.median()
+        result = dist.median(a)
+        assert_equal(result_f, result)
+
+        result_f = frozen.mean()
+        result = dist.mean(a)
+        assert_equal(result_f, result)
+
+        result_f = frozen.var()
+        result = dist.var(a)
+        assert_equal(result_f, result)
+
+        result_f = frozen.std()
+        result = dist.std(a)
+        assert_equal(result_f, result)
+
+        result_f = frozen.entropy()
+        result = dist.entropy(a)
+        assert_equal(result_f, result)
+
+        result_f = frozen.moment(2)
+        result = dist.moment(2, a)
+        assert_equal(result_f, result)
+
+        assert_equal(frozen.a, frozen.dist.a)
+        assert_equal(frozen.b, frozen.dist.b)
+
+    def test_regression_ticket_1293(self):
+        # Create a frozen distribution.
+        frozen = stats.lognorm(1)
+        # Call one of its methods that does not take any keyword arguments.
+        m1 = frozen.moment(2)
+        # Now call a method that takes a keyword argument.
+        frozen.stats(moments='mvsk')
+        # Call moment(2) again.
+        # After calling stats(), the following was raising an exception.
+        # So this test passes if the following does not raise an exception.
+        m2 = frozen.moment(2)
+        # The following should also be true, of course.  But it is not
+        # the focus of this test.
+        assert_equal(m1, m2)
+
+    def test_ab(self):
+        # test that the support of a frozen distribution
+        # (i) remains frozen even if it changes for the original one
+        # (ii) is actually correct if the shape parameters are such that
+        #      the values of [a, b] are not the default [0, inf]
+        # take a genpareto as an example where the support
+        # depends on the value of the shape parameter:
+        # for c > 0: a, b = 0, inf
+        # for c < 0: a, b = 0, -1/c
+
+        c = -0.1
+        rv = stats.genpareto(c=c)
+        a, b = rv.dist._get_support(c)
+        assert_equal([a, b], [0., 10.])
+
+        c = 0.1
+        stats.genpareto.pdf(0, c=c)
+        assert_equal(rv.dist._get_support(c), [0, np.inf])
+
+        c = -0.1
+        rv = stats.genpareto(c=c)
+        a, b = rv.dist._get_support(c)
+        assert_equal([a, b], [0., 10.])
+
+        c = 0.1
+        stats.genpareto.pdf(0, c)  # this should NOT change genpareto.b
+        assert_equal((rv.dist.a, rv.dist.b), stats.genpareto._get_support(c))
+
+        rv1 = stats.genpareto(c=0.1)
+        assert_(rv1.dist is not rv.dist)
+
+        # c >= 0: a, b = [0, inf]
+        for c in [1., 0.]:
+            c = np.asarray(c)
+            rv = stats.genpareto(c=c)
+            a, b = rv.a, rv.b
+            assert_equal(a, 0.)
+            assert_(np.isposinf(b))
+
+            # c < 0: a=0, b=1/|c|
+            c = np.asarray(-2.)
+            a, b = stats.genpareto._get_support(c)
+            assert_allclose([a, b], [0., 0.5])
+
+    def test_rv_frozen_in_namespace(self):
+        # Regression test for gh-3522
+        assert_(hasattr(stats.distributions, 'rv_frozen'))
+
+    def test_random_state(self):
+        # only check that the random_state attribute exists,
+        frozen = stats.norm()
+        assert_(hasattr(frozen, 'random_state'))
+
+        # ... that it can be set,
+        frozen.random_state = 42
+        assert_equal(frozen.random_state.get_state(),
+                     np.random.RandomState(42).get_state())
+
+        # ... and that .rvs method accepts it as an argument
+        rndm = np.random.RandomState(1234)
+        frozen.rvs(size=8, random_state=rndm)
+
+    def test_pickling(self):
+        # test that a frozen instance pickles and unpickles
+        # (this method is a clone of common_tests.check_pickling)
+        beta = stats.beta(2.3098496451481823, 0.62687954300963677)
+        poiss = stats.poisson(3.)
+        sample = stats.rv_discrete(values=([0, 1, 2, 3],
+                                           [0.1, 0.2, 0.3, 0.4]))
+
+        for distfn in [beta, poiss, sample]:
+            distfn.random_state = 1234
+            distfn.rvs(size=8)
+            s = pickle.dumps(distfn)
+            r0 = distfn.rvs(size=8)
+
+            unpickled = pickle.loads(s)
+            r1 = unpickled.rvs(size=8)
+            assert_equal(r0, r1)
+
+            # also smoke test some methods
+            medians = [distfn.ppf(0.5), unpickled.ppf(0.5)]
+            assert_equal(medians[0], medians[1])
+            assert_equal(distfn.cdf(medians[0]),
+                         unpickled.cdf(medians[1]))
+
+    def test_expect(self):
+        # smoke test the expect method of the frozen distribution
+        # only take a gamma w/loc and scale and poisson with loc specified
+        def func(x):
+            return x
+
+        gm = stats.gamma(a=2, loc=3, scale=4)
+        with np.errstate(invalid="ignore", divide="ignore"):
+            gm_val = gm.expect(func, lb=1, ub=2, conditional=True)
+            gamma_val = stats.gamma.expect(func, args=(2,), loc=3, scale=4,
+                                           lb=1, ub=2, conditional=True)
+        assert_allclose(gm_val, gamma_val)
+
+        p = stats.poisson(3, loc=4)
+        p_val = p.expect(func)
+        poisson_val = stats.poisson.expect(func, args=(3,), loc=4)
+        assert_allclose(p_val, poisson_val)
+
+
+class TestExpect:
+    # Test for expect method.
+    #
+    # Uses normal distribution and beta distribution for finite bounds, and
+    # hypergeom for discrete distribution with finite support
+    def test_norm(self):
+        v = stats.norm.expect(lambda x: (x-5)*(x-5), loc=5, scale=2)
+        assert_almost_equal(v, 4, decimal=14)
+
+        m = stats.norm.expect(lambda x: (x), loc=5, scale=2)
+        assert_almost_equal(m, 5, decimal=14)
+
+        lb = stats.norm.ppf(0.05, loc=5, scale=2)
+        ub = stats.norm.ppf(0.95, loc=5, scale=2)
+        prob90 = stats.norm.expect(lambda x: 1, loc=5, scale=2, lb=lb, ub=ub)
+        assert_almost_equal(prob90, 0.9, decimal=14)
+
+        prob90c = stats.norm.expect(lambda x: 1, loc=5, scale=2, lb=lb, ub=ub,
+                                    conditional=True)
+        assert_almost_equal(prob90c, 1., decimal=14)
+
+    def test_beta(self):
+        # case with finite support interval
+        v = stats.beta.expect(lambda x: (x-19/3.)*(x-19/3.), args=(10, 5),
+                              loc=5, scale=2)
+        assert_almost_equal(v, 1./18., decimal=13)
+
+        m = stats.beta.expect(lambda x: x, args=(10, 5), loc=5., scale=2.)
+        assert_almost_equal(m, 19/3., decimal=13)
+
+        ub = stats.beta.ppf(0.95, 10, 10, loc=5, scale=2)
+        lb = stats.beta.ppf(0.05, 10, 10, loc=5, scale=2)
+        prob90 = stats.beta.expect(lambda x: 1., args=(10, 10), loc=5.,
+                                   scale=2., lb=lb, ub=ub, conditional=False)
+        assert_almost_equal(prob90, 0.9, decimal=13)
+
+        prob90c = stats.beta.expect(lambda x: 1, args=(10, 10), loc=5,
+                                    scale=2, lb=lb, ub=ub, conditional=True)
+        assert_almost_equal(prob90c, 1., decimal=13)
+
+    def test_hypergeom(self):
+        # test case with finite bounds
+
+        # without specifying bounds
+        m_true, v_true = stats.hypergeom.stats(20, 10, 8, loc=5.)
+        m = stats.hypergeom.expect(lambda x: x, args=(20, 10, 8), loc=5.)
+        assert_almost_equal(m, m_true, decimal=13)
+
+        v = stats.hypergeom.expect(lambda x: (x-9.)**2, args=(20, 10, 8),
+                                   loc=5.)
+        assert_almost_equal(v, v_true, decimal=14)
+
+        # with bounds, bounds equal to shifted support
+        v_bounds = stats.hypergeom.expect(lambda x: (x-9.)**2,
+                                          args=(20, 10, 8),
+                                          loc=5., lb=5, ub=13)
+        assert_almost_equal(v_bounds, v_true, decimal=14)
+
+        # drop boundary points
+        prob_true = 1-stats.hypergeom.pmf([5, 13], 20, 10, 8, loc=5).sum()
+        prob_bounds = stats.hypergeom.expect(lambda x: 1, args=(20, 10, 8),
+                                             loc=5., lb=6, ub=12)
+        assert_almost_equal(prob_bounds, prob_true, decimal=13)
+
+        # conditional
+        prob_bc = stats.hypergeom.expect(lambda x: 1, args=(20, 10, 8), loc=5.,
+                                         lb=6, ub=12, conditional=True)
+        assert_almost_equal(prob_bc, 1, decimal=14)
+
+        # check simple integral
+        prob_b = stats.hypergeom.expect(lambda x: 1, args=(20, 10, 8),
+                                        lb=0, ub=8)
+        assert_almost_equal(prob_b, 1, decimal=13)
+
+    def test_poisson(self):
+        # poisson, use lower bound only
+        prob_bounds = stats.poisson.expect(lambda x: 1, args=(2,), lb=3,
+                                           conditional=False)
+        prob_b_true = 1-stats.poisson.cdf(2, 2)
+        assert_almost_equal(prob_bounds, prob_b_true, decimal=14)
+
+        prob_lb = stats.poisson.expect(lambda x: 1, args=(2,), lb=2,
+                                       conditional=True)
+        assert_almost_equal(prob_lb, 1, decimal=14)
+
+    def test_genhalflogistic(self):
+        # genhalflogistic, changes upper bound of support in _argcheck
+        # regression test for gh-2622
+        halflog = stats.genhalflogistic
+        # check consistency when calling expect twice with the same input
+        res1 = halflog.expect(args=(1.5,))
+        halflog.expect(args=(0.5,))
+        res2 = halflog.expect(args=(1.5,))
+        assert_almost_equal(res1, res2, decimal=14)
+
+    def test_rice_overflow(self):
+        # rice.pdf(999, 0.74) was inf since special.i0 silently overflows
+        # check that using i0e fixes it
+        assert_(np.isfinite(stats.rice.pdf(999, 0.74)))
+
+        assert_(np.isfinite(stats.rice.expect(lambda x: 1, args=(0.74,))))
+        assert_(np.isfinite(stats.rice.expect(lambda x: 2, args=(0.74,))))
+        assert_(np.isfinite(stats.rice.expect(lambda x: 3, args=(0.74,))))
+
+    def test_logser(self):
+        # test a discrete distribution with infinite support and loc
+        p, loc = 0.3, 3
+        res_0 = stats.logser.expect(lambda k: k, args=(p,))
+        # check against the correct answer (sum of a geom series)
+        assert_allclose(res_0,
+                        p / (p - 1.) / np.log(1. - p), atol=1e-15)
+
+        # now check it with `loc`
+        res_l = stats.logser.expect(lambda k: k, args=(p,), loc=loc)
+        assert_allclose(res_l, res_0 + loc, atol=1e-15)
+
+    def test_skellam(self):
+        # Use a discrete distribution w/ bi-infinite support. Compute two first
+        # moments and compare to known values (cf skellam.stats)
+        p1, p2 = 18, 22
+        m1 = stats.skellam.expect(lambda x: x, args=(p1, p2))
+        m2 = stats.skellam.expect(lambda x: x**2, args=(p1, p2))
+        assert_allclose(m1, p1 - p2, atol=1e-12)
+        assert_allclose(m2 - m1**2, p1 + p2, atol=1e-12)
+
+    def test_randint(self):
+        # Use a discrete distribution w/ parameter-dependent support, which
+        # is larger than the default chunksize
+        lo, hi = 0, 113
+        res = stats.randint.expect(lambda x: x, (lo, hi))
+        assert_allclose(res,
+                        sum(_ for _ in range(lo, hi)) / (hi - lo), atol=1e-15)
+
+    def test_zipf(self):
+        # Test that there is no infinite loop even if the sum diverges
+        with pytest.warns(RuntimeWarning):
+            stats.zipf.expect(lambda x: x**2, (2,))
+
+    def test_discrete_kwds(self):
+        # check that discrete expect accepts keywords to control the summation
+        n0 = stats.poisson.expect(lambda x: 1, args=(2,))
+        n1 = stats.poisson.expect(lambda x: 1, args=(2,),
+                                  maxcount=1001, chunksize=32, tolerance=1e-8)
+        assert_almost_equal(n0, n1, decimal=14)
+
+    def test_moment(self):
+        # test the .moment() method: compute a higher moment and compare to
+        # a known value
+        def poiss_moment5(mu):
+            return mu**5 + 10*mu**4 + 25*mu**3 + 15*mu**2 + mu
+
+        for mu in [5, 7]:
+            m5 = stats.poisson.moment(5, mu)
+            assert_allclose(m5, poiss_moment5(mu), rtol=1e-10)
+
+    def test_challenging_cases_gh8928(self):
+        # Several cases where `expect` failed to produce a correct result were
+        # reported in gh-8928. Check that these cases have been resolved.
+        assert_allclose(stats.norm.expect(loc=36, scale=1.0), 36)
+        assert_allclose(stats.norm.expect(loc=40, scale=1.0), 40)
+        assert_allclose(stats.norm.expect(loc=10, scale=0.1), 10)
+        assert_allclose(stats.gamma.expect(args=(148,)), 148)
+        assert_allclose(stats.logistic.expect(loc=85), 85)
+
+    def test_lb_ub_gh15855(self):
+        # Make sure changes to `expect` made in gh15855 treat lb/ub correctly
+        dist = stats.uniform
+        ref = dist.mean(loc=10, scale=5)  # 12.5
+        # moment over whole distribution
+        assert_allclose(dist.expect(loc=10, scale=5), ref)
+        # moment over whole distribution, lb and ub outside of support
+        assert_allclose(dist.expect(loc=10, scale=5, lb=9, ub=16), ref)
+        # moment over 60% of distribution, [lb, ub] centered within support
+        assert_allclose(dist.expect(loc=10, scale=5, lb=11, ub=14), ref*0.6)
+        # moment over truncated distribution, essentially
+        assert_allclose(dist.expect(loc=10, scale=5, lb=11, ub=14,
+                                    conditional=True), ref)
+        # moment over 40% of distribution, [lb, ub] not centered within support
+        assert_allclose(dist.expect(loc=10, scale=5, lb=11, ub=13), 12*0.4)
+        # moment with lb > ub
+        assert_allclose(dist.expect(loc=10, scale=5, lb=13, ub=11), -12*0.4)
+        # moment with lb > ub, conditional
+        assert_allclose(dist.expect(loc=10, scale=5, lb=13, ub=11,
+                                    conditional=True), 12)
+
+
+class TestNct:
+    def test_nc_parameter(self):
+        # Parameter values c<=0 were not enabled (gh-2402).
+        # For negative values c and for c=0 results of rv.cdf(0) below were nan
+        rv = stats.nct(5, 0)
+        assert_equal(rv.cdf(0), 0.5)
+        rv = stats.nct(5, -1)
+        assert_almost_equal(rv.cdf(0), 0.841344746069, decimal=10)
+
+    def test_broadcasting(self):
+        res = stats.nct.pdf(5, np.arange(4, 7)[:, None],
+                            np.linspace(0.1, 1, 4))
+        expected = array([[0.00321886, 0.00557466, 0.00918418, 0.01442997],
+                          [0.00217142, 0.00395366, 0.00683888, 0.01126276],
+                          [0.00153078, 0.00291093, 0.00525206, 0.00900815]])
+        assert_allclose(res, expected, rtol=1e-5)
+
+    def test_variance_gh_issue_2401(self):
+        # Computation of the variance of a non-central t-distribution resulted
+        # in a TypeError: ufunc 'isinf' not supported for the input types,
+        # and the inputs could not be safely coerced to any supported types
+        # according to the casting rule 'safe'
+        rv = stats.nct(4, 0)
+        assert_equal(rv.var(), 2.0)
+
+    def test_nct_inf_moments(self):
+        # n-th moment of nct only exists for df > n
+        m, v, s, k = stats.nct.stats(df=0.9, nc=0.3, moments='mvsk')
+        assert_equal([m, v, s, k], [np.nan, np.nan, np.nan, np.nan])
+
+        m, v, s, k = stats.nct.stats(df=1.9, nc=0.3, moments='mvsk')
+        assert_(np.isfinite(m))
+        assert_equal([v, s, k], [np.nan, np.nan, np.nan])
+
+        m, v, s, k = stats.nct.stats(df=3.1, nc=0.3, moments='mvsk')
+        assert_(np.isfinite([m, v, s]).all())
+        assert_equal(k, np.nan)
+
+    def test_nct_stats_large_df_values(self):
+        # previously gamma function was used which lost precision at df=345
+        # cf. https://github.com/scipy/scipy/issues/12919 for details
+        nct_mean_df_1000 = stats.nct.mean(1000, 2)
+        nct_stats_df_1000 = stats.nct.stats(1000, 2)
+        # These expected values were computed with mpmath. They were also
+        # verified with the Wolfram Alpha expressions:
+        #     Mean[NoncentralStudentTDistribution[1000, 2]]
+        #     Var[NoncentralStudentTDistribution[1000, 2]]
+        expected_stats_df_1000 = [2.0015015641422464, 1.0040115288163005]
+        assert_allclose(nct_mean_df_1000, expected_stats_df_1000[0],
+                        rtol=1e-10)
+        assert_allclose(nct_stats_df_1000, expected_stats_df_1000,
+                        rtol=1e-10)
+        # and a bigger df value
+        nct_mean = stats.nct.mean(100000, 2)
+        nct_stats = stats.nct.stats(100000, 2)
+        # These expected values were computed with mpmath.
+        expected_stats = [2.0000150001562518, 1.0000400011500288]
+        assert_allclose(nct_mean, expected_stats[0], rtol=1e-10)
+        assert_allclose(nct_stats, expected_stats, rtol=1e-9)
+
+    def test_cdf_large_nc(self):
+        # gh-17916 reported a crash with large `nc` values
+        assert_allclose(stats.nct.cdf(2, 2, float(2**16)), 0)
+
+    # PDF reference values were computed with mpmath
+    # with 100 digits of precision
+
+    # def nct_pdf(x, df, nc):
+    #     x = mp.mpf(x)
+    #     n = mp.mpf(df)
+    #     nc = mp.mpf(nc)
+
+    #     x2 = x*x
+    #     ncx2 = nc*nc*x2
+    #     fac1 = n + x2
+    #     trm1 = (n/2.*mp.log(n) + mp.loggamma(n + mp.one)
+    #             - (n * mp.log(2.) + nc*nc/2 + (n/2)*mp.log(fac1)
+    #                 + mp.loggamma(n/2)))
+    #     Px = mp.exp(trm1)
+    #     valF = ncx2 / (2*fac1)
+    #     trm1 = (mp.sqrt(2)*nc*x*mp.hyp1f1(n/2+1, 1.5, valF)
+    #             / (fac1*mp.gamma((n+1)/2)))
+    #     trm2 = (mp.hyp1f1((n+1)/2, 0.5, valF)
+    #             / (mp.sqrt(fac1)*mp.gamma(n/2 + mp.one)))
+    #     Px *= trm1+trm2
+    #     return float(Px)
+
+    @pytest.mark.parametrize("x, df, nc, expected", [
+        (10000, 10, 16, 3.394646922945872e-30),
+        (-10, 8, 16, 4.282769500264159e-70)
+        ])
+    def test_pdf_large_nc(self, x, df, nc, expected):
+        # gh-#20693 reported zero values for large `nc` values
+        assert_allclose(stats.nct.pdf(x, df, nc), expected, rtol=1e-12)
+
+
+class TestRecipInvGauss:
+
+    def test_pdf_endpoint(self):
+        p = stats.recipinvgauss.pdf(0, 0.6)
+        assert p == 0.0
+
+    def test_logpdf_endpoint(self):
+        logp = stats.recipinvgauss.logpdf(0, 0.6)
+        assert logp == -np.inf
+
+    def test_cdf_small_x(self):
+        # The expected value was computer with mpmath:
+        #
+        # import mpmath
+        #
+        # mpmath.mp.dps = 100
+        #
+        # def recipinvgauss_cdf_mp(x, mu):
+        #     x = mpmath.mpf(x)
+        #     mu = mpmath.mpf(mu)
+        #     trm1 = 1/mu - x
+        #     trm2 = 1/mu + x
+        #     isqx = 1/mpmath.sqrt(x)
+        #     return (mpmath.ncdf(-isqx*trm1)
+        #             - mpmath.exp(2/mu)*mpmath.ncdf(-isqx*trm2))
+        #
+        p = stats.recipinvgauss.cdf(0.05, 0.5)
+        expected = 6.590396159501331e-20
+        assert_allclose(p, expected, rtol=1e-14)
+
+    def test_sf_large_x(self):
+        # The expected value was computed with mpmath; see test_cdf_small.
+        p = stats.recipinvgauss.sf(80, 0.5)
+        expected = 2.699819200556787e-18
+        assert_allclose(p, expected, 5e-15)
+
+
+class TestRice:
+    def setup_method(self):
+        self.rng = np.random.default_rng(666822542)
+
+    def test_rice_zero_b(self):
+        # rice distribution should work with b=0, cf gh-2164
+        x = [0.2, 1., 5.]
+        assert_(np.isfinite(stats.rice.pdf(x, b=0.)).all())
+        assert_(np.isfinite(stats.rice.logpdf(x, b=0.)).all())
+        assert_(np.isfinite(stats.rice.cdf(x, b=0.)).all())
+        assert_(np.isfinite(stats.rice.logcdf(x, b=0.)).all())
+
+        q = [0.1, 0.1, 0.5, 0.9]
+        assert_(np.isfinite(stats.rice.ppf(q, b=0.)).all())
+
+        mvsk = stats.rice.stats(0, moments='mvsk')
+        assert_(np.isfinite(mvsk).all())
+
+        # furthermore, pdf is continuous as b\to 0
+        # rice.pdf(x, b\to 0) = x exp(-x^2/2) + O(b^2)
+        # see e.g. Abramovich & Stegun 9.6.7 & 9.6.10
+        b = 1e-8
+        assert_allclose(stats.rice.pdf(x, 0), stats.rice.pdf(x, b),
+                        atol=b, rtol=0)
+
+    def test_rice_rvs(self):
+        rvs = stats.rice.rvs
+        assert_equal(rvs(b=3., random_state=self.rng).size, 1)
+        assert_equal(rvs(b=3., size=(3, 5), random_state=self.rng).shape, (3, 5))
+
+    def test_rice_gh9836(self):
+        # test that gh-9836 is resolved; previously jumped to 1 at the end
+
+        cdf = stats.rice.cdf(np.arange(10, 160, 10), np.arange(10, 160, 10))
+        # Generated in R
+        # library(VGAM)
+        # options(digits=16)
+        # x = seq(10, 150, 10)
+        # print(price(x, sigma=1, vee=x))
+        cdf_exp = [0.4800278103504522, 0.4900233218590353, 0.4933500379379548,
+                   0.4950128317658719, 0.4960103776798502, 0.4966753655438764,
+                   0.4971503395812474, 0.4975065620443196, 0.4977836197921638,
+                   0.4980052636649550, 0.4981866072661382, 0.4983377260666599,
+                   0.4984655952615694, 0.4985751970541413, 0.4986701850071265]
+        assert_allclose(cdf, cdf_exp)
+
+        probabilities = np.arange(0.1, 1, 0.1)
+        ppf = stats.rice.ppf(probabilities, 500/4, scale=4)
+        # Generated in R
+        # library(VGAM)
+        # options(digits=16)
+        # p = seq(0.1, .9, by = .1)
+        # print(qrice(p, vee = 500, sigma = 4))
+        ppf_exp = [494.8898762347361, 496.6495690858350, 497.9184315188069,
+                   499.0026277378915, 500.0159999146250, 501.0293721352668,
+                   502.1135684981884, 503.3824312270405, 505.1421247157822]
+        assert_allclose(ppf, ppf_exp)
+
+        ppf = scipy.stats.rice.ppf(0.5, np.arange(10, 150, 10))
+        # Generated in R
+        # library(VGAM)
+        # options(digits=16)
+        # b <- seq(10, 140, 10)
+        # print(qrice(0.5, vee = b, sigma = 1))
+        ppf_exp = [10.04995862522287, 20.02499480078302, 30.01666512465732,
+                   40.01249934924363, 50.00999966676032, 60.00833314046875,
+                   70.00714273568241, 80.00624991862573, 90.00555549840364,
+                   100.00499995833597, 110.00454542324384, 120.00416664255323,
+                   130.00384613488120, 140.00357141338748]
+        assert_allclose(ppf, ppf_exp)
+
+
+class TestErlang:
+    def setup_method(self):
+        self.rng = np.random.default_rng(2792245532)
+
+    def test_erlang_runtimewarning(self):
+        # erlang should generate a RuntimeWarning if a non-integer
+        # shape parameter is used.
+        with warnings.catch_warnings():
+            warnings.simplefilter("error", RuntimeWarning)
+
+            # The non-integer shape parameter 1.3 should trigger a
+            # RuntimeWarning
+            assert_raises(RuntimeWarning, stats.erlang.rvs, 1.3, loc=0,
+                          scale=1, size=4, random_state=self.rng)
+
+            # Calling the fit method with `f0` set to an integer should
+            # *not* trigger a RuntimeWarning.  It should return the same
+            # values as gamma.fit(...).
+            data = [0.5, 1.0, 2.0, 4.0]
+            result_erlang = stats.erlang.fit(data, f0=1)
+            result_gamma = stats.gamma.fit(data, f0=1)
+            assert_allclose(result_erlang, result_gamma, rtol=1e-3)
+
+    def test_gh_pr_10949_argcheck(self):
+        assert_equal(stats.erlang.pdf(0.5, a=[1, -1]),
+                     stats.gamma.pdf(0.5, a=[1, -1]))
+
+
+class TestRayleigh:
+    def setup_method(self):
+        self.rng = np.random.default_rng(7186715712)
+
+    # gh-6227
+    def test_logpdf(self):
+        y = stats.rayleigh.logpdf(50)
+        assert_allclose(y, -1246.0879769945718)
+
+    def test_logsf(self):
+        y = stats.rayleigh.logsf(50)
+        assert_allclose(y, -1250)
+
+    @pytest.mark.parametrize("rvs_loc,rvs_scale", [(0.85373171, 0.86932204),
+                                                   (0.20558821, 0.61621008)])
+    def test_fit(self, rvs_loc, rvs_scale):
+        data = stats.rayleigh.rvs(size=250, loc=rvs_loc,
+                                  scale=rvs_scale, random_state=self.rng)
+
+        def scale_mle(data, floc):
+            return (np.sum((data - floc) ** 2) / (2 * len(data))) ** .5
+
+        # when `floc` is provided, `scale` is found with an analytical formula
+        scale_expect = scale_mle(data, rvs_loc)
+        loc, scale = stats.rayleigh.fit(data, floc=rvs_loc)
+        assert_equal(loc, rvs_loc)
+        assert_equal(scale, scale_expect)
+
+        # when `fscale` is fixed, superclass fit is used to determine `loc`.
+        loc, scale = stats.rayleigh.fit(data, fscale=.6)
+        assert_equal(scale, .6)
+
+        # with both parameters free, one dimensional optimization is done
+        # over a new function that takes into account the dependent relation
+        # of `scale` to `loc`.
+        loc, scale = stats.rayleigh.fit(data)
+        # test that `scale` is defined by its relation to `loc`
+        assert_equal(scale, scale_mle(data, loc))
+
+    @pytest.mark.parametrize("rvs_loc,rvs_scale", [[0.74, 0.01],
+                                                   [0.08464463, 0.12069025]])
+    def test_fit_comparison_super_method(self, rvs_loc, rvs_scale):
+        # test that the objective function result of the analytical MLEs is
+        # less than or equal to that of the numerically optimized estimate
+        data = stats.rayleigh.rvs(size=250, loc=rvs_loc,
+                                  scale=rvs_scale, random_state=self.rng)
+        _assert_less_or_close_loglike(stats.rayleigh, data)
+
+    def test_fit_warnings(self):
+        assert_fit_warnings(stats.rayleigh)
+
+    def test_fit_gh17088(self):
+        # `rayleigh.fit` could return a location that was inconsistent with
+        # the data. See gh-17088.
+        rng = np.random.default_rng(456)
+        loc, scale, size = 50, 600, 500
+        rvs = stats.rayleigh.rvs(loc, scale, size=size, random_state=rng)
+        loc_fit, _ = stats.rayleigh.fit(rvs)
+        assert loc_fit < np.min(rvs)
+        loc_fit, scale_fit = stats.rayleigh.fit(rvs, fscale=scale)
+        assert loc_fit < np.min(rvs)
+        assert scale_fit == scale
+
+
+class TestExponWeib:
+
+    def test_pdf_logpdf(self):
+        # Regression test for gh-3508.
+        x = 0.1
+        a = 1.0
+        c = 100.0
+        p = stats.exponweib.pdf(x, a, c)
+        logp = stats.exponweib.logpdf(x, a, c)
+        # Expected values were computed with mpmath.
+        assert_allclose([p, logp],
+                        [1.0000000000000054e-97, -223.35075402042244])
+
+    def test_a_is_1(self):
+        # For issue gh-3508.
+        # Check that when a=1, the pdf and logpdf methods of exponweib are the
+        # same as those of weibull_min.
+        x = np.logspace(-4, -1, 4)
+        a = 1
+        c = 100
+
+        p = stats.exponweib.pdf(x, a, c)
+        expected = stats.weibull_min.pdf(x, c)
+        assert_allclose(p, expected)
+
+        logp = stats.exponweib.logpdf(x, a, c)
+        expected = stats.weibull_min.logpdf(x, c)
+        assert_allclose(logp, expected)
+
+    def test_a_is_1_c_is_1(self):
+        # When a = 1 and c = 1, the distribution is exponential.
+        x = np.logspace(-8, 1, 10)
+        a = 1
+        c = 1
+
+        p = stats.exponweib.pdf(x, a, c)
+        expected = stats.expon.pdf(x)
+        assert_allclose(p, expected)
+
+        logp = stats.exponweib.logpdf(x, a, c)
+        expected = stats.expon.logpdf(x)
+        assert_allclose(logp, expected)
+
+    # Reference values were computed with mpmath, e.g:
+    #
+    #     from mpmath import mp
+    #
+    #     def mp_sf(x, a, c):
+    #         x = mp.mpf(x)
+    #         a = mp.mpf(a)
+    #         c = mp.mpf(c)
+    #         return -mp.powm1(-mp.expm1(-x**c)), a)
+    #
+    #     mp.dps = 100
+    #     print(float(mp_sf(1, 2.5, 0.75)))
+    #
+    # prints
+    #
+    #     0.6823127476985246
+    #
+    @pytest.mark.parametrize(
+        'x, a, c, ref',
+        [(1, 2.5, 0.75, 0.6823127476985246),
+         (50, 2.5, 0.75, 1.7056666054719663e-08),
+         (125, 2.5, 0.75, 1.4534393150714602e-16),
+         (250, 2.5, 0.75, 1.2391389689773512e-27),
+         (250, 0.03125, 0.75, 1.548923711221689e-29),
+         (3, 0.03125, 3.0,  5.873527551689983e-14),
+         (2e80, 10.0, 0.02, 2.9449084156902135e-17)]
+    )
+    def test_sf(self, x, a, c, ref):
+        sf = stats.exponweib.sf(x, a, c)
+        assert_allclose(sf, ref, rtol=1e-14)
+
+    # Reference values were computed with mpmath, e.g.
+    #
+    #     from mpmath import mp
+    #
+    #     def mp_isf(p, a, c):
+    #         p = mp.mpf(p)
+    #         a = mp.mpf(a)
+    #         c = mp.mpf(c)
+    #         return (-mp.log(-mp.expm1(mp.log1p(-p)/a)))**(1/c)
+    #
+    #     mp.dps = 100
+    #     print(float(mp_isf(0.25, 2.5, 0.75)))
+    #
+    # prints
+    #
+    #     2.8946008178158924
+    #
+    @pytest.mark.parametrize(
+        'p, a, c, ref',
+        [(0.25, 2.5, 0.75, 2.8946008178158924),
+         (3e-16, 2.5, 0.75, 121.77966713102938),
+         (1e-12, 1, 2, 5.256521769756932),
+         (2e-13, 0.03125, 3, 2.953915059484589),
+         (5e-14, 10.0, 0.02, 7.57094886384687e+75)]
+    )
+    def test_isf(self, p, a, c, ref):
+        isf = stats.exponweib.isf(p, a, c)
+        assert_allclose(isf, ref, rtol=5e-14)
+
+    # Reference values computed with mpmath.
+    @pytest.mark.parametrize('x, a, c, ref',
+                             [(2, 3, 8, -1.9848783170128456e-111),
+                              (1000, 0.5, 0.75, -2.946296827524972e-78)])
+    def test_logcdf(self, x, a, c, ref):
+        logcdf = stats.exponweib.logcdf(x, a, c)
+        assert_allclose(logcdf, ref, rtol=5e-15)
+
+    # Reference values computed with mpmath.
+    @pytest.mark.parametrize('x, a, c, ref',
+                             [(1e-65, 1.5, 1.25, -1.333521432163324e-122),
+                              (2e-10, 2, 10, -1.0485760000000007e-194)])
+    def test_logsf(self, x, a, c, ref):
+        logsf = stats.exponweib.logsf(x, a, c)
+        assert_allclose(logsf, ref, rtol=5e-15)
+
+
+class TestFatigueLife:
+
+    def test_sf_tail(self):
+        # Expected value computed with mpmath:
+        #     import mpmath
+        #     mpmath.mp.dps = 80
+        #     x = mpmath.mpf(800.0)
+        #     c = mpmath.mpf(2.5)
+        #     s = float(1 - mpmath.ncdf(1/c * (mpmath.sqrt(x)
+        #                                      - 1/mpmath.sqrt(x))))
+        #     print(s)
+        # Output:
+        #     6.593376447038406e-30
+        s = stats.fatiguelife.sf(800.0, 2.5)
+        assert_allclose(s, 6.593376447038406e-30, rtol=1e-13)
+
+    def test_isf_tail(self):
+        # See test_sf_tail for the mpmath code.
+        p = 6.593376447038406e-30
+        q = stats.fatiguelife.isf(p, 2.5)
+        assert_allclose(q, 800.0, rtol=1e-13)
+
+
+class TestWeibull:
+
+    def test_logpdf(self):
+        # gh-6217
+        y = stats.weibull_min.logpdf(0, 1)
+        assert_equal(y, 0)
+
+    def test_with_maxima_distrib(self):
+        # Tests for weibull_min and weibull_max.
+        # The expected values were computed using the symbolic algebra
+        # program 'maxima' with the package 'distrib', which has
+        # 'pdf_weibull' and 'cdf_weibull'.  The mapping between the
+        # scipy and maxima functions is as follows:
+        # -----------------------------------------------------------------
+        # scipy                              maxima
+        # ---------------------------------  ------------------------------
+        # weibull_min.pdf(x, a, scale=b)     pdf_weibull(x, a, b)
+        # weibull_min.logpdf(x, a, scale=b)  log(pdf_weibull(x, a, b))
+        # weibull_min.cdf(x, a, scale=b)     cdf_weibull(x, a, b)
+        # weibull_min.logcdf(x, a, scale=b)  log(cdf_weibull(x, a, b))
+        # weibull_min.sf(x, a, scale=b)      1 - cdf_weibull(x, a, b)
+        # weibull_min.logsf(x, a, scale=b)   log(1 - cdf_weibull(x, a, b))
+        #
+        # weibull_max.pdf(x, a, scale=b)     pdf_weibull(-x, a, b)
+        # weibull_max.logpdf(x, a, scale=b)  log(pdf_weibull(-x, a, b))
+        # weibull_max.cdf(x, a, scale=b)     1 - cdf_weibull(-x, a, b)
+        # weibull_max.logcdf(x, a, scale=b)  log(1 - cdf_weibull(-x, a, b))
+        # weibull_max.sf(x, a, scale=b)      cdf_weibull(-x, a, b)
+        # weibull_max.logsf(x, a, scale=b)   log(cdf_weibull(-x, a, b))
+        # -----------------------------------------------------------------
+        x = 1.5
+        a = 2.0
+        b = 3.0
+
+        # weibull_min
+
+        p = stats.weibull_min.pdf(x, a, scale=b)
+        assert_allclose(p, np.exp(-0.25)/3)
+
+        lp = stats.weibull_min.logpdf(x, a, scale=b)
+        assert_allclose(lp, -0.25 - np.log(3))
+
+        c = stats.weibull_min.cdf(x, a, scale=b)
+        assert_allclose(c, -special.expm1(-0.25))
+
+        lc = stats.weibull_min.logcdf(x, a, scale=b)
+        assert_allclose(lc, np.log(-special.expm1(-0.25)))
+
+        s = stats.weibull_min.sf(x, a, scale=b)
+        assert_allclose(s, np.exp(-0.25))
+
+        ls = stats.weibull_min.logsf(x, a, scale=b)
+        assert_allclose(ls, -0.25)
+
+        # Also test using a large value x, for which computing the survival
+        # function using the CDF would result in 0.
+        s = stats.weibull_min.sf(30, 2, scale=3)
+        assert_allclose(s, np.exp(-100))
+
+        ls = stats.weibull_min.logsf(30, 2, scale=3)
+        assert_allclose(ls, -100)
+
+        # weibull_max
+        x = -1.5
+
+        p = stats.weibull_max.pdf(x, a, scale=b)
+        assert_allclose(p, np.exp(-0.25)/3)
+
+        lp = stats.weibull_max.logpdf(x, a, scale=b)
+        assert_allclose(lp, -0.25 - np.log(3))
+
+        c = stats.weibull_max.cdf(x, a, scale=b)
+        assert_allclose(c, np.exp(-0.25))
+
+        lc = stats.weibull_max.logcdf(x, a, scale=b)
+        assert_allclose(lc, -0.25)
+
+        s = stats.weibull_max.sf(x, a, scale=b)
+        assert_allclose(s, -special.expm1(-0.25))
+
+        ls = stats.weibull_max.logsf(x, a, scale=b)
+        assert_allclose(ls, np.log(-special.expm1(-0.25)))
+
+        # Also test using a value of x close to 0, for which computing the
+        # survival function using the CDF would result in 0.
+        s = stats.weibull_max.sf(-1e-9, 2, scale=3)
+        assert_allclose(s, -special.expm1(-1/9000000000000000000))
+
+        ls = stats.weibull_max.logsf(-1e-9, 2, scale=3)
+        assert_allclose(ls, np.log(-special.expm1(-1/9000000000000000000)))
+
+    @pytest.mark.parametrize('scale', [1.0, 0.1])
+    def test_delta_cdf(self, scale):
+        # Expected value computed with mpmath:
+        #
+        # def weibull_min_sf(x, k, scale):
+        #     x = mpmath.mpf(x)
+        #     k = mpmath.mpf(k)
+        #     scale =mpmath.mpf(scale)
+        #     return mpmath.exp(-(x/scale)**k)
+        #
+        # >>> import mpmath
+        # >>> mpmath.mp.dps = 60
+        # >>> sf1 = weibull_min_sf(7.5, 3, 1)
+        # >>> sf2 = weibull_min_sf(8.0, 3, 1)
+        # >>> float(sf1 - sf2)
+        # 6.053624060118734e-184
+        #
+        delta = stats.weibull_min._delta_cdf(scale*7.5, scale*8, 3,
+                                             scale=scale)
+        assert_allclose(delta, 6.053624060118734e-184)
+
+    def test_fit_min(self):
+        rng = np.random.default_rng(5985959307161735394)
+
+        c, loc, scale = 2, 3.5, 0.5  # arbitrary, valid parameters
+        dist = stats.weibull_min(c, loc, scale)
+        rvs = dist.rvs(size=100, random_state=rng)
+
+        # test that MLE still honors guesses and fixed parameters
+        c2, loc2, scale2 = stats.weibull_min.fit(rvs, 1.5, floc=3)
+        c3, loc3, scale3 = stats.weibull_min.fit(rvs, 1.6, floc=3)
+        assert loc2 == loc3 == 3  # fixed parameter is respected
+        assert c2 != c3  # different guess -> (slightly) different outcome
+        # quality of fit is tested elsewhere
+
+        # test that MoM honors fixed parameters, accepts (but ignores) guesses
+        c4, loc4, scale4 = stats.weibull_min.fit(rvs, 3, fscale=3, method='mm')
+        assert scale4 == 3
+        # because scale was fixed, only the mean and skewness will be matched
+        dist4 = stats.weibull_min(c4, loc4, scale4)
+        res = dist4.stats(moments='ms')
+        ref = np.mean(rvs), stats.skew(rvs)
+        assert_allclose(res, ref)
+
+    # reference values were computed via mpmath
+    # from mpmath import mp
+    # def weibull_sf_mpmath(x, c):
+    #     x = mp.mpf(x)
+    #     c = mp.mpf(c)
+    #     return float(mp.exp(-x**c))
+
+    @pytest.mark.parametrize('x, c, ref', [(50, 1, 1.9287498479639178e-22),
+                                           (1000, 0.8,
+                                            8.131269637872743e-110)])
+    def test_sf_isf(self, x, c, ref):
+        assert_allclose(stats.weibull_min.sf(x, c), ref, rtol=5e-14)
+        assert_allclose(stats.weibull_min.isf(ref, c), x, rtol=5e-14)
+
+
+class TestDweibull:
+    def test_entropy(self):
+        # Test that dweibull entropy follows that of weibull_min.
+        # (Generic tests check that the dweibull entropy is consistent
+        #  with its PDF. As for accuracy, dweibull entropy should be just
+        #  as accurate as weibull_min entropy. Checks of accuracy against
+        #  a reference need only be applied to the fundamental distribution -
+        #  weibull_min.)
+        rng = np.random.default_rng(8486259129157041777)
+        c = 10**rng.normal(scale=100, size=10)
+        res = stats.dweibull.entropy(c)
+        ref = stats.weibull_min.entropy(c) - np.log(0.5)
+        assert_allclose(res, ref, rtol=1e-15)
+
+    def test_sf(self):
+        # test that for positive values the dweibull survival function is half
+        # the weibull_min survival function
+        rng = np.random.default_rng(8486259129157041777)
+        c = 10**rng.normal(scale=1, size=10)
+        x = 10 * rng.uniform()
+        res = stats.dweibull.sf(x, c)
+        ref = 0.5 * stats.weibull_min.sf(x, c)
+        assert_allclose(res, ref, rtol=1e-15)
+
+
+class TestTruncWeibull:
+
+    def test_pdf_bounds(self):
+        # test bounds
+        y = stats.truncweibull_min.pdf([0.1, 2.0], 2.0, 0.11, 1.99)
+        assert_equal(y, [0.0, 0.0])
+
+    def test_logpdf(self):
+        y = stats.truncweibull_min.logpdf(2.0, 1.0, 2.0, np.inf)
+        assert_equal(y, 0.0)
+
+        # hand calculation
+        y = stats.truncweibull_min.logpdf(2.0, 1.0, 2.0, 4.0)
+        assert_allclose(y, 0.14541345786885884)
+
+    def test_ppf_bounds(self):
+        # test bounds
+        y = stats.truncweibull_min.ppf([0.0, 1.0], 2.0, 0.1, 2.0)
+        assert_equal(y, [0.1, 2.0])
+
+    def test_cdf_to_ppf(self):
+        q = [0., 0.1, .25, 0.50, 0.75, 0.90, 1.]
+        x = stats.truncweibull_min.ppf(q, 2., 0., 3.)
+        q_out = stats.truncweibull_min.cdf(x, 2., 0., 3.)
+        assert_allclose(q, q_out)
+
+    def test_sf_to_isf(self):
+        q = [0., 0.1, .25, 0.50, 0.75, 0.90, 1.]
+        x = stats.truncweibull_min.isf(q, 2., 0., 3.)
+        q_out = stats.truncweibull_min.sf(x, 2., 0., 3.)
+        assert_allclose(q, q_out)
+
+    def test_munp(self):
+        c = 2.
+        a = 1.
+        b = 3.
+
+        def xnpdf(x, n):
+            return x**n*stats.truncweibull_min.pdf(x, c, a, b)
+
+        m0 = stats.truncweibull_min.moment(0, c, a, b)
+        assert_equal(m0, 1.)
+
+        m1 = stats.truncweibull_min.moment(1, c, a, b)
+        m1_expected, _ = quad(lambda x: xnpdf(x, 1), a, b)
+        assert_allclose(m1, m1_expected)
+
+        m2 = stats.truncweibull_min.moment(2, c, a, b)
+        m2_expected, _ = quad(lambda x: xnpdf(x, 2), a, b)
+        assert_allclose(m2, m2_expected)
+
+        m3 = stats.truncweibull_min.moment(3, c, a, b)
+        m3_expected, _ = quad(lambda x: xnpdf(x, 3), a, b)
+        assert_allclose(m3, m3_expected)
+
+        m4 = stats.truncweibull_min.moment(4, c, a, b)
+        m4_expected, _ = quad(lambda x: xnpdf(x, 4), a, b)
+        assert_allclose(m4, m4_expected)
+
+    def test_reference_values(self):
+        a = 1.
+        b = 3.
+        c = 2.
+        x_med = np.sqrt(1 - np.log(0.5 + np.exp(-(8. + np.log(2.)))))
+
+        cdf = stats.truncweibull_min.cdf(x_med, c, a, b)
+        assert_allclose(cdf, 0.5)
+
+        lc = stats.truncweibull_min.logcdf(x_med, c, a, b)
+        assert_allclose(lc, -np.log(2.))
+
+        ppf = stats.truncweibull_min.ppf(0.5, c, a, b)
+        assert_allclose(ppf, x_med)
+
+        sf = stats.truncweibull_min.sf(x_med, c, a, b)
+        assert_allclose(sf, 0.5)
+
+        ls = stats.truncweibull_min.logsf(x_med, c, a, b)
+        assert_allclose(ls, -np.log(2.))
+
+        isf = stats.truncweibull_min.isf(0.5, c, a, b)
+        assert_allclose(isf, x_med)
+
+    def test_compare_weibull_min(self):
+        # Verify that the truncweibull_min distribution gives the same results
+        # as the original weibull_min
+        x = 1.5
+        c = 2.0
+        a = 0.0
+        b = np.inf
+        scale = 3.0
+
+        p = stats.weibull_min.pdf(x, c, scale=scale)
+        p_trunc = stats.truncweibull_min.pdf(x, c, a, b, scale=scale)
+        assert_allclose(p, p_trunc)
+
+        lp = stats.weibull_min.logpdf(x, c, scale=scale)
+        lp_trunc = stats.truncweibull_min.logpdf(x, c, a, b, scale=scale)
+        assert_allclose(lp, lp_trunc)
+
+        cdf = stats.weibull_min.cdf(x, c, scale=scale)
+        cdf_trunc = stats.truncweibull_min.cdf(x, c, a, b, scale=scale)
+        assert_allclose(cdf, cdf_trunc)
+
+        lc = stats.weibull_min.logcdf(x, c, scale=scale)
+        lc_trunc = stats.truncweibull_min.logcdf(x, c, a, b, scale=scale)
+        assert_allclose(lc, lc_trunc)
+
+        s = stats.weibull_min.sf(x, c, scale=scale)
+        s_trunc = stats.truncweibull_min.sf(x, c, a, b, scale=scale)
+        assert_allclose(s, s_trunc)
+
+        ls = stats.weibull_min.logsf(x, c, scale=scale)
+        ls_trunc = stats.truncweibull_min.logsf(x, c, a, b, scale=scale)
+        assert_allclose(ls, ls_trunc)
+
+        # # Also test using a large value x, for which computing the survival
+        # # function using the CDF would result in 0.
+        s = stats.truncweibull_min.sf(30, 2, a, b, scale=3)
+        assert_allclose(s, np.exp(-100))
+
+        ls = stats.truncweibull_min.logsf(30, 2, a, b, scale=3)
+        assert_allclose(ls, -100)
+
+    def test_compare_weibull_min2(self):
+        # Verify that the truncweibull_min distribution PDF and CDF results
+        # are the same as those calculated from truncating weibull_min
+        c, a, b = 2.5, 0.25, 1.25
+        x = np.linspace(a, b, 100)
+
+        pdf1 = stats.truncweibull_min.pdf(x, c, a, b)
+        cdf1 = stats.truncweibull_min.cdf(x, c, a, b)
+
+        norm = stats.weibull_min.cdf(b, c) - stats.weibull_min.cdf(a, c)
+        pdf2 = stats.weibull_min.pdf(x, c) / norm
+        cdf2 = (stats.weibull_min.cdf(x, c) - stats.weibull_min.cdf(a, c))/norm
+
+        np.testing.assert_allclose(pdf1, pdf2)
+        np.testing.assert_allclose(cdf1, cdf2)
+
+
+class TestRdist:
+    def test_rdist_cdf_gh1285(self):
+        # check workaround in rdist._cdf for issue gh-1285.
+        distfn = stats.rdist
+        values = [0.001, 0.5, 0.999]
+        assert_almost_equal(distfn.cdf(distfn.ppf(values, 541.0), 541.0),
+                            values, decimal=5)
+
+    def test_rdist_beta(self):
+        # rdist is a special case of stats.beta
+        x = np.linspace(-0.99, 0.99, 10)
+        c = 2.7
+        assert_almost_equal(0.5*stats.beta(c/2, c/2).pdf((x + 1)/2),
+                            stats.rdist(c).pdf(x))
+
+    # reference values were computed via mpmath
+    # from mpmath import mp
+    # mp.dps = 200
+    # def rdist_sf_mpmath(x, c):
+    #     x = mp.mpf(x)
+    #     c = mp.mpf(c)
+    #     return float(mp.betainc(c/2, c/2, (x+1)/2, mp.one, regularized=True))
+    @pytest.mark.parametrize(
+        "x, c, ref",
+        [
+            (0.0001, 541, 0.49907251345565845),
+            (0.1, 241, 0.06000788166249205),
+            (0.5, 441, 1.0655898106047832e-29),
+            (0.8, 341, 6.025478373732215e-78),
+        ]
+    )
+    def test_rdist_sf(self, x, c, ref):
+        assert_allclose(stats.rdist.sf(x, c), ref, rtol=5e-14)
+
+
+class TestTrapezoid:
+    def test_reduces_to_triang(self):
+        modes = [0, 0.3, 0.5, 1]
+        for mode in modes:
+            x = [0, mode, 1]
+            assert_almost_equal(stats.trapezoid.pdf(x, mode, mode),
+                                stats.triang.pdf(x, mode))
+            assert_almost_equal(stats.trapezoid.cdf(x, mode, mode),
+                                stats.triang.cdf(x, mode))
+
+    def test_reduces_to_uniform(self):
+        x = np.linspace(0, 1, 10)
+        assert_almost_equal(stats.trapezoid.pdf(x, 0, 1), stats.uniform.pdf(x))
+        assert_almost_equal(stats.trapezoid.cdf(x, 0, 1), stats.uniform.cdf(x))
+
+    def test_cases(self):
+        # edge cases
+        assert_almost_equal(stats.trapezoid.pdf(0, 0, 0), 2)
+        assert_almost_equal(stats.trapezoid.pdf(1, 1, 1), 2)
+        assert_almost_equal(stats.trapezoid.pdf(0.5, 0, 0.8),
+                            1.11111111111111111)
+        assert_almost_equal(stats.trapezoid.pdf(0.5, 0.2, 1.0),
+                            1.11111111111111111)
+
+        # straightforward case
+        assert_almost_equal(stats.trapezoid.pdf(0.1, 0.2, 0.8), 0.625)
+        assert_almost_equal(stats.trapezoid.pdf(0.5, 0.2, 0.8), 1.25)
+        assert_almost_equal(stats.trapezoid.pdf(0.9, 0.2, 0.8), 0.625)
+
+        assert_almost_equal(stats.trapezoid.cdf(0.1, 0.2, 0.8), 0.03125)
+        assert_almost_equal(stats.trapezoid.cdf(0.2, 0.2, 0.8), 0.125)
+        assert_almost_equal(stats.trapezoid.cdf(0.5, 0.2, 0.8), 0.5)
+        assert_almost_equal(stats.trapezoid.cdf(0.9, 0.2, 0.8), 0.96875)
+        assert_almost_equal(stats.trapezoid.cdf(1.0, 0.2, 0.8), 1.0)
+
+    def test_moments_and_entropy(self):
+        # issue #11795: improve precision of trapezoid stats
+        # Apply formulas from Wikipedia for the following parameters:
+        a, b, c, d = -3, -1, 2, 3  # => 1/3, 5/6, -3, 6
+        p1, p2, loc, scale = (b-a) / (d-a), (c-a) / (d-a), a, d-a
+        h = 2 / (d+c-b-a)
+
+        def moment(n):
+            return (h * ((d**(n+2) - c**(n+2)) / (d-c)
+                         - (b**(n+2) - a**(n+2)) / (b-a)) /
+                    (n+1) / (n+2))
+
+        mean = moment(1)
+        var = moment(2) - mean**2
+        entropy = 0.5 * (d-c+b-a) / (d+c-b-a) + np.log(0.5 * (d+c-b-a))
+        assert_almost_equal(stats.trapezoid.mean(p1, p2, loc, scale),
+                            mean, decimal=13)
+        assert_almost_equal(stats.trapezoid.var(p1, p2, loc, scale),
+                            var, decimal=13)
+        assert_almost_equal(stats.trapezoid.entropy(p1, p2, loc, scale),
+                            entropy, decimal=13)
+
+        # Check boundary cases where scipy d=0 or d=1.
+        assert_almost_equal(stats.trapezoid.mean(0, 0, -3, 6), -1, decimal=13)
+        assert_almost_equal(stats.trapezoid.mean(0, 1, -3, 6), 0, decimal=13)
+        assert_almost_equal(stats.trapezoid.var(0, 1, -3, 6), 3, decimal=13)
+
+    def test_trapezoid_vect(self):
+        # test that array-valued shapes and arguments are handled
+        c = np.array([0.1, 0.2, 0.3])
+        d = np.array([0.5, 0.6])[:, None]
+        x = np.array([0.15, 0.25, 0.9])
+        v = stats.trapezoid.pdf(x, c, d)
+
+        cc, dd, xx = np.broadcast_arrays(c, d, x)
+
+        res = np.empty(xx.size, dtype=xx.dtype)
+        ind = np.arange(xx.size)
+        for i, x1, c1, d1 in zip(ind, xx.ravel(), cc.ravel(), dd.ravel()):
+            res[i] = stats.trapezoid.pdf(x1, c1, d1)
+
+        assert_allclose(v, res.reshape(v.shape), atol=1e-15)
+
+        # Check that the stats() method supports vector arguments.
+        v = np.asarray(stats.trapezoid.stats(c, d, moments="mvsk"))
+        cc, dd = np.broadcast_arrays(c, d)
+        res = np.empty((cc.size, 4))  # 4 stats returned per value
+        ind = np.arange(cc.size)
+        for i, c1, d1 in zip(ind, cc.ravel(), dd.ravel()):
+            res[i] = stats.trapezoid.stats(c1, d1, moments="mvsk")
+
+        assert_allclose(v, res.T.reshape(v.shape), atol=1e-15)
+
+    def test_trapezoid_fit_convergence_gh23503(self):
+        # gh-23503 reported that trapezoid.fit would consistently converge to a
+        # triangular distribution unless starting values were provided. Check that this
+        # is resolved.
+
+        # Generate test data from a trapezoidal distribution
+        rng = np.random.default_rng(23842359234598263956)
+        true_args = 0.3, 0.7, -1, 2
+        true_dist = stats.trapezoid(*true_args)
+        x = true_dist.rvs(1000, random_state=rng)
+
+        # fit to data
+        fitted_args = stats.trapezoid.fit(x)
+
+        # Should not converge to triangular distribution (c=d=1)
+        fitted_c, fitted_d = fitted_args[:2]
+        assert not np.allclose(fitted_c, 1, atol=0.1)
+        assert not np.allclose(fitted_d, 1, atol=0.1)
+
+        # objective function is better than with true values of parameters
+        true_llf = stats.trapezoid.nnlf(true_args, x)
+        fitted_llf = stats.trapezoid.nnlf(fitted_args, x)
+        assert fitted_llf < true_llf
+
+
+class TestTriang:
+    def test_edge_cases(self):
+        with np.errstate(all='raise'):
+            assert_equal(stats.triang.pdf(0, 0), 2.)
+            assert_equal(stats.triang.pdf(0.5, 0), 1.)
+            assert_equal(stats.triang.pdf(1, 0), 0.)
+
+            assert_equal(stats.triang.pdf(0, 1), 0)
+            assert_equal(stats.triang.pdf(0.5, 1), 1.)
+            assert_equal(stats.triang.pdf(1, 1), 2)
+
+            assert_equal(stats.triang.cdf(0., 0.), 0.)
+            assert_equal(stats.triang.cdf(0.5, 0.), 0.75)
+            assert_equal(stats.triang.cdf(1.0, 0.), 1.0)
+
+            assert_equal(stats.triang.cdf(0., 1.), 0.)
+            assert_equal(stats.triang.cdf(0.5, 1.), 0.25)
+            assert_equal(stats.triang.cdf(1., 1.), 1)
+
+
+class TestMaxwell:
+
+    # reference values were computed with wolfram alpha
+    # erfc(x/sqrt(2)) + sqrt(2/pi) * x * e^(-x^2/2)
+
+    @pytest.mark.parametrize("x, ref",
+                             [(20, 2.2138865931011177e-86),
+                              (0.01, 0.999999734046458435)])
+    def test_sf(self, x, ref):
+        assert_allclose(stats.maxwell.sf(x), ref, rtol=1e-14)
+
+    # reference values were computed with wolfram alpha
+    # sqrt(2) * sqrt(Q^(-1)(3/2, q))
+
+    @pytest.mark.parametrize("q, ref",
+                             [(0.001, 4.033142223656157022),
+                              (0.9999847412109375, 0.0385743284050381),
+                              (2**-55, 8.95564974719481)])
+    def test_isf(self, q, ref):
+        assert_allclose(stats.maxwell.isf(q), ref, rtol=1e-15)
+
+    def test_logcdf(self):
+        # Reference value computed with mpmath.
+        ref = -1.8729310110194814e-17
+        logcdf = stats.maxwell.logcdf(9)
+        assert_allclose(logcdf, ref, rtol=5e-15)
+
+    def test_logsf(self):
+        # Reference value computed with mpmath.
+        ref = -2.6596152026762177e-25
+        logsf = stats.maxwell.logsf(1e-8)
+        assert_allclose(logsf, ref, rtol=5e-15)
+
+
+class TestMielke:
+    def test_moments(self):
+        k, s = 4.642, 0.597
+        # n-th moment exists only if n < s
+        assert_equal(stats.mielke(k, s).moment(1), np.inf)
+        assert_equal(stats.mielke(k, 1.0).moment(1), np.inf)
+        assert_(np.isfinite(stats.mielke(k, 1.01).moment(1)))
+
+    def test_burr_equivalence(self):
+        x = np.linspace(0.01, 100, 50)
+        k, s = 2.45, 5.32
+        assert_allclose(stats.burr.pdf(x, s, k/s), stats.mielke.pdf(x, k, s))
+
+
+class TestBurr:
+    def test_endpoints_7491(self):
+        # gh-7491
+        # Compute the pdf at the left endpoint dst.a.
+        data = [
+            [stats.fisk, (1,), 1],
+            [stats.burr, (0.5, 2), 1],
+            [stats.burr, (1, 1), 1],
+            [stats.burr, (2, 0.5), 1],
+            [stats.burr12, (1, 0.5), 0.5],
+            [stats.burr12, (1, 1), 1.0],
+            [stats.burr12, (1, 2), 2.0]]
+
+        ans = [_f.pdf(_f.a, *_args) for _f, _args, _ in data]
+        correct = [_correct_ for _f, _args, _correct_ in data]
+        assert_array_almost_equal(ans, correct)
+
+        ans = [_f.logpdf(_f.a, *_args) for _f, _args, _ in data]
+        correct = [np.log(_correct_) for _f, _args, _correct_ in data]
+        assert_array_almost_equal(ans, correct)
+
+    def test_burr_stats_9544(self):
+        # gh-9544.  Test from gh-9978
+        c, d = 5.0, 3
+        mean, variance = stats.burr(c, d).stats()
+        # mean = sc.beta(3 + 1/5, 1. - 1/5) * 3  = 1.4110263...
+        # var =  sc.beta(3 + 2 / 5, 1. - 2 / 5) * 3 -
+        #        (sc.beta(3 + 1 / 5, 1. - 1 / 5) * 3) ** 2
+        mean_hc, variance_hc = 1.4110263183925857, 0.22879948026191643
+        assert_allclose(mean, mean_hc)
+        assert_allclose(variance, variance_hc)
+
+    def test_burr_nan_mean_var_9544(self):
+        # gh-9544.  Test from gh-9978
+        c, d = 0.5, 3
+        mean, variance = stats.burr(c, d).stats()
+        assert_(np.isnan(mean))
+        assert_(np.isnan(variance))
+        c, d = 1.5, 3
+        mean, variance = stats.burr(c, d).stats()
+        assert_(np.isfinite(mean))
+        assert_(np.isnan(variance))
+
+        c, d = 0.5, 3
+        e1, e2, e3, e4 = stats.burr._munp(np.array([1, 2, 3, 4]), c, d)
+        assert_(np.isnan(e1))
+        assert_(np.isnan(e2))
+        assert_(np.isnan(e3))
+        assert_(np.isnan(e4))
+        c, d = 1.5, 3
+        e1, e2, e3, e4 = stats.burr._munp([1, 2, 3, 4], c, d)
+        assert_(np.isfinite(e1))
+        assert_(np.isnan(e2))
+        assert_(np.isnan(e3))
+        assert_(np.isnan(e4))
+        c, d = 2.5, 3
+        e1, e2, e3, e4 = stats.burr._munp([1, 2, 3, 4], c, d)
+        assert_(np.isfinite(e1))
+        assert_(np.isfinite(e2))
+        assert_(np.isnan(e3))
+        assert_(np.isnan(e4))
+        c, d = 3.5, 3
+        e1, e2, e3, e4 = stats.burr._munp([1, 2, 3, 4], c, d)
+        assert_(np.isfinite(e1))
+        assert_(np.isfinite(e2))
+        assert_(np.isfinite(e3))
+        assert_(np.isnan(e4))
+        c, d = 4.5, 3
+        e1, e2, e3, e4 = stats.burr._munp([1, 2, 3, 4], c, d)
+        assert_(np.isfinite(e1))
+        assert_(np.isfinite(e2))
+        assert_(np.isfinite(e3))
+        assert_(np.isfinite(e4))
+
+    def test_burr_isf(self):
+        # reference values were computed via the reference distribution, e.g.
+        # mp.dps = 100
+        # Burr(c=5, d=3).isf([0.1, 1e-10, 1e-20, 1e-40])
+        c, d = 5.0, 3.0
+        q = [0.1, 1e-10, 1e-20, 1e-40]
+        ref = [1.9469686558286508, 124.57309395989076, 12457.309396155173,
+               124573093.96155174]
+        assert_allclose(stats.burr.isf(q, c, d), ref, rtol=1e-14)
+
+
+class TestBurr12:
+
+    @pytest.mark.parametrize('scale, expected',
+                             [(1.0, 2.3283064359965952e-170),
+                              (3.5, 5.987114417447875e-153)])
+    def test_delta_cdf(self, scale, expected):
+        # Expected value computed with mpmath:
+        #
+        # def burr12sf(x, c, d, scale):
+        #     x = mpmath.mpf(x)
+        #     c = mpmath.mpf(c)
+        #     d = mpmath.mpf(d)
+        #     scale = mpmath.mpf(scale)
+        #     return (mpmath.mp.one + (x/scale)**c)**(-d)
+        #
+        # >>> import mpmath
+        # >>> mpmath.mp.dps = 60
+        # >>> float(burr12sf(2e5, 4, 8, 1) - burr12sf(4e5, 4, 8, 1))
+        # 2.3283064359965952e-170
+        # >>> float(burr12sf(2e5, 4, 8, 3.5) - burr12sf(4e5, 4, 8, 3.5))
+        # 5.987114417447875e-153
+        #
+        delta = stats.burr12._delta_cdf(2e5, 4e5, 4, 8, scale=scale)
+        assert_allclose(delta, expected, rtol=1e-13)
+
+    def test_moments_edge(self):
+        # gh-18838 reported that burr12 moments could be invalid; see above.
+        # Check that this is resolved in an edge case where c*d == n, and
+        # compare the results against those produced by Mathematica, e.g.
+        # `SinghMaddalaDistribution[2, 2, 1]` at Wolfram Alpha.
+        c, d = 2, 2
+        mean = np.pi/4
+        var = 1 - np.pi**2/16
+        skew = np.pi**3/(32*var**1.5)
+        kurtosis = np.nan
+        ref = [mean, var, skew, kurtosis]
+        res = stats.burr12(c, d).stats('mvsk')
+        assert_allclose(res, ref, rtol=1e-14)
+
+    # Reference values were computed with mpmath using mp.dps = 80
+    # and then cast to float.
+    @pytest.mark.parametrize(
+        'p, c, d, ref',
+        [(1e-12, 20, 0.5, 15.848931924611135),
+         (1e-19, 20, 0.5, 79.43282347242815),
+         (1e-12, 0.25, 35, 2.0888618213462466),
+         (1e-80, 0.25, 35, 1360930951.7972188)]
+    )
+    def test_isf_near_zero(self, p, c, d, ref):
+        x = stats.burr12.isf(p, c, d)
+        assert_allclose(x, ref, rtol=1e-14)
+
+
+class TestStudentizedRange:
+    # For alpha = .05, .01, and .001, and for each value of
+    # v = [1, 3, 10, 20, 120, inf], a Q was picked from each table for
+    # k = [2, 8, 14, 20].
+
+    # these arrays are written with `k` as column, and `v` as rows.
+    # Q values are taken from table 3:
+    # https://www.jstor.org/stable/2237810
+    q05 = [17.97, 45.40, 54.33, 59.56,
+           4.501, 8.853, 10.35, 11.24,
+           3.151, 5.305, 6.028, 6.467,
+           2.950, 4.768, 5.357, 5.714,
+           2.800, 4.363, 4.842, 5.126,
+           2.772, 4.286, 4.743, 5.012]
+    q01 = [90.03, 227.2, 271.8, 298.0,
+           8.261, 15.64, 18.22, 19.77,
+           4.482, 6.875, 7.712, 8.226,
+           4.024, 5.839, 6.450, 6.823,
+           3.702, 5.118, 5.562, 5.827,
+           3.643, 4.987, 5.400, 5.645]
+    q001 = [900.3, 2272, 2718, 2980,
+            18.28, 34.12, 39.69, 43.05,
+            6.487, 9.352, 10.39, 11.03,
+            5.444, 7.313, 7.966, 8.370,
+            4.772, 6.039, 6.448, 6.695,
+            4.654, 5.823, 6.191, 6.411]
+    qs = np.concatenate((q05, q01, q001))
+    ps = [.95, .99, .999]
+    vs = [1, 3, 10, 20, 120, np.inf]
+    ks = [2, 8, 14, 20]
+
+    data = list(zip(product(ps, vs, ks), qs))
+
+    # A small selection of large-v cases generated with R's `ptukey`
+    # Each case is in the format (q, k, v, r_result)
+    r_data = [
+        (0.1, 3, 9001, 0.002752818526842),
+        (1, 10, 1000, 0.000526142388912),
+        (1, 3, np.inf, 0.240712641229283),
+        (4, 3, np.inf, 0.987012338626815),
+        (1, 10, np.inf, 0.000519869467083),
+    ]
+
+    @pytest.mark.slow
+    def test_cdf_against_tables(self):
+        for pvk, q in self.data:
+            p_expected, v, k = pvk
+            res_p = stats.studentized_range.cdf(q, k, v)
+            assert_allclose(res_p, p_expected, rtol=1e-4)
+
+    @pytest.mark.xslow
+    def test_ppf_against_tables(self):
+        for pvk, q_expected in self.data:
+            p, v, k = pvk
+            res_q = stats.studentized_range.ppf(p, k, v)
+            assert_allclose(res_q, q_expected, rtol=5e-4)
+
+    path_prefix = os.path.dirname(__file__)
+    relative_path = "data/studentized_range_mpmath_ref.json"
+    with open(os.path.join(path_prefix, relative_path)) as file:
+        pregenerated_data = json.load(file)
+
+    @pytest.mark.parametrize("case_result", pregenerated_data["cdf_data"])
+    def test_cdf_against_mp(self, case_result):
+        src_case = case_result["src_case"]
+        mp_result = case_result["mp_result"]
+        qkv = src_case["q"], src_case["k"], src_case["v"]
+        res = stats.studentized_range.cdf(*qkv)
+
+        assert_allclose(res, mp_result,
+                        atol=src_case["expected_atol"],
+                        rtol=src_case["expected_rtol"])
+
+    @pytest.mark.parametrize("case_result", pregenerated_data["pdf_data"])
+    def test_pdf_against_mp(self, case_result):
+        src_case = case_result["src_case"]
+        mp_result = case_result["mp_result"]
+        qkv = src_case["q"], src_case["k"], src_case["v"]
+        res = stats.studentized_range.pdf(*qkv)
+
+        assert_allclose(res, mp_result,
+                        atol=src_case["expected_atol"],
+                        rtol=src_case["expected_rtol"])
+
+    @pytest.mark.xslow
+    @pytest.mark.xfail_on_32bit("intermittent RuntimeWarning: invalid value.")
+    @pytest.mark.parametrize("case_result", pregenerated_data["moment_data"])
+    def test_moment_against_mp(self, case_result):
+        src_case = case_result["src_case"]
+        mp_result = case_result["mp_result"]
+        mkv = src_case["m"], src_case["k"], src_case["v"]
+
+        # Silence invalid value encountered warnings. Actual problems will be
+        # caught by the result comparison.
+        with np.errstate(invalid='ignore'):
+            res = stats.studentized_range.moment(*mkv)
+
+        assert_allclose(res, mp_result,
+                        atol=src_case["expected_atol"],
+                        rtol=src_case["expected_rtol"])
+
+    @pytest.mark.slow
+    def test_pdf_integration(self):
+        k, v = 3, 10
+        # Test whether PDF integration is 1 like it should be.
+        res = quad(stats.studentized_range.pdf, 0, np.inf, args=(k, v))
+        assert_allclose(res[0], 1)
+
+    @pytest.mark.xslow
+    def test_pdf_against_cdf(self):
+        k, v = 3, 10
+
+        # Test whether the integrated PDF matches the CDF using cumulative
+        # integration. Use a small step size to reduce error due to the
+        # summation. This is slow, but tests the results well.
+        x = np.arange(0, 10, step=0.01)
+
+        y_cdf = stats.studentized_range.cdf(x, k, v)[1:]
+        y_pdf_raw = stats.studentized_range.pdf(x, k, v)
+        y_pdf_cumulative = cumulative_trapezoid(y_pdf_raw, x)
+
+        # Because of error caused by the summation, use a relatively large rtol
+        assert_allclose(y_pdf_cumulative, y_cdf, rtol=1e-4)
+
+    @pytest.mark.parametrize("r_case_result", r_data)
+    def test_cdf_against_r(self, r_case_result):
+        # Test large `v` values using R
+        q, k, v, r_res = r_case_result
+        with np.errstate(invalid='ignore'):
+            res = stats.studentized_range.cdf(q, k, v)
+        assert_allclose(res, r_res)
+
+    @pytest.mark.xslow
+    @pytest.mark.xfail_on_32bit("intermittent RuntimeWarning: invalid value.")
+    def test_moment_vectorization(self):
+        # Test moment broadcasting. Calls `_munp` directly because
+        # `rv_continuous.moment` is broken at time of writing. See gh-12192
+
+        # Silence invalid value encountered warnings. Actual problems will be
+        # caught by the result comparison.
+        with np.errstate(invalid='ignore'):
+            m = stats.studentized_range._munp([1, 2], [4, 5], [10, 11])
+
+        assert_allclose(m.shape, (2,))
+
+        with pytest.raises(ValueError, match="...could not be broadcast..."):
+            stats.studentized_range._munp(1, [4, 5], [10, 11, 12])
+
+    @pytest.mark.xslow
+    def test_fitstart_valid(self):
+        with warnings.catch_warnings(), np.errstate(invalid="ignore"):
+            # the integration warning message may differ
+            warnings.simplefilter("ignore", IntegrationWarning)
+            k, df, _, _ = stats.studentized_range._fitstart([1, 2, 3])
+        assert_(stats.studentized_range._argcheck(k, df))
+
+    def test_infinite_df(self):
+        # Check that the CDF and PDF infinite and normal integrators
+        # roughly match for a high df case
+        res = stats.studentized_range.pdf(3, 10, np.inf)
+        res_finite = stats.studentized_range.pdf(3, 10, 99999)
+        assert_allclose(res, res_finite, atol=1e-4, rtol=1e-4)
+
+        res = stats.studentized_range.cdf(3, 10, np.inf)
+        res_finite = stats.studentized_range.cdf(3, 10, 99999)
+        assert_allclose(res, res_finite, atol=1e-4, rtol=1e-4)
+
+    def test_df_cutoff(self):
+        # Test that the CDF and PDF properly switch integrators at df=100,000.
+        # The infinite integrator should be different enough that it fails
+        # an allclose assertion. Also sanity check that using the same
+        # integrator does pass the allclose with a 1-df difference, which
+        # should be tiny.
+
+        res = stats.studentized_range.pdf(3, 10, 100000)
+        res_finite = stats.studentized_range.pdf(3, 10, 99999)
+        res_sanity = stats.studentized_range.pdf(3, 10, 99998)
+        assert_raises(AssertionError, assert_allclose, res, res_finite,
+                      atol=1e-6, rtol=1e-6)
+        assert_allclose(res_finite, res_sanity, atol=1e-6, rtol=1e-6)
+
+        res = stats.studentized_range.cdf(3, 10, 100000)
+        res_finite = stats.studentized_range.cdf(3, 10, 99999)
+        res_sanity = stats.studentized_range.cdf(3, 10, 99998)
+        assert_raises(AssertionError, assert_allclose, res, res_finite,
+                      atol=1e-6, rtol=1e-6)
+        assert_allclose(res_finite, res_sanity, atol=1e-6, rtol=1e-6)
+
+    def test_clipping(self):
+        # The result of this computation was -9.9253938401489e-14 on some
+        # systems. The correct result is very nearly zero, but should not be
+        # negative.
+        q, k, v = 34.6413996195345746, 3, 339
+        p = stats.studentized_range.sf(q, k, v)
+        assert_allclose(p, 0, atol=1e-10)
+        assert p >= 0
+
+
+class TestTukeyLambda:
+
+    @pytest.mark.parametrize(
+        'lam',
+        [0.0, -1.0, -2.0, np.array([[-1.0], [0.0], [-2.0]])]
+    )
+    def test_pdf_nonpositive_lambda(self, lam):
+        # Make sure that Tukey-Lambda distribution correctly handles
+        # non-positive lambdas.
+        # This is a crude test--it just checks that all the PDF values
+        # are finite and greater than 0.
+        x = np.linspace(-5.0, 5.0, 101)
+        p = stats.tukeylambda.pdf(x, lam)
+        assert np.isfinite(p).all()
+        assert (p > 0.0).all()
+
+    def test_pdf_mixed_lambda(self):
+        # Another crude test of the behavior of the PDF method.
+        x = np.linspace(-5.0, 5.0, 101)
+        lam = np.array([[-1.0], [0.0], [2.0]])
+        p = stats.tukeylambda.pdf(x, lam)
+        assert np.isfinite(p).all()
+        # For p[0] and p[1], where lam <= 0, the support is (-inf, inf),
+        # so the PDF should be nonzero everywhere (assuming we aren't so
+        # far in the tails that we get underflow).
+        assert (p[:2] > 0.0).all()
+        # For p[2], where lam=2.0, the support is [-0.5, 0.5], so in pdf(x),
+        # some values should be positive and some should be 0.
+        assert (p[2] > 0.0).any()
+        assert (p[2] == 0.0).any()
+
+    def test_support(self):
+        lam = np.array([-1.75, -0.5, 0.0, 0.25, 0.5, 2.0])
+        a, b = stats.tukeylambda.support(lam)
+        expected_b = np.array([np.inf, np.inf, np.inf, 4, 2, 0.5])
+        assert_equal(b, expected_b)
+        assert_equal(a, -expected_b)
+
+    def test_pdf_support_boundary(self):
+        # Verify that tukeylambda.pdf() doesn't generate a
+        # warning when evaluated at the bounds of the support.
+        # For lam=0.5, the support is (-2, 2).
+        p = stats.tukeylambda.pdf([-2.0, 2.0], 0.5)
+        assert_equal(p, [0.0, 0.0])
+
+    def test_tukeylambda_stats_ticket_1545(self):
+        # Some test for the variance and kurtosis of the Tukey Lambda distr.
+        # See test_tukeylamdba_stats.py for more tests.
+
+        mv = stats.tukeylambda.stats(0, moments='mvsk')
+        # Known exact values:
+        expected = [0, np.pi**2/3, 0, 1.2]
+        assert_almost_equal(mv, expected, decimal=10)
+
+        mv = stats.tukeylambda.stats(3.13, moments='mvsk')
+        # 'expected' computed with mpmath.
+        expected = [0, 0.0269220858861465102, 0, -0.898062386219224104]
+        assert_almost_equal(mv, expected, decimal=10)
+
+        mv = stats.tukeylambda.stats(0.14, moments='mvsk')
+        # 'expected' computed with mpmath.
+        expected = [0, 2.11029702221450250, 0, -0.02708377353223019456]
+        assert_almost_equal(mv, expected, decimal=10)
+
+    @pytest.mark.xfail(reason="Precision in tail hasn't been fixed in xsf")
+    def test_large_argument_ticket_21370(self):
+        # Check that survival function goes to 0 as x gets large
+        x = [1e4, 1e6, 1e8, 1e10, 1e12, 1e24]
+        lam = -0.5
+        sf = stats.tukeylambda.sf(x, lam)
+        # Check that the sf is 0 for large x
+        assert sf[-1] == 0.0
+        # Check that the sf is always decreasing except when it is 0
+        assert_array_less(np.diff(sf[sf > 0]), 0)
+
+        cdf = stats.tukeylambda.cdf(x, lam)
+        assert cdf[-1] == 1.0
+        # Check that the cdf is always increasing except when it saturates 
+        # to 1.0
+        assert np.all(np.diff(cdf[cdf < 1]) > 0)
+        
+class TestLevy:
+
+    def test_levy_cdf_ppf(self):
+        # Test levy.cdf, including small arguments.
+        x = np.array([1000, 1.0, 0.5, 0.1, 0.01, 0.001])
+
+        # Expected values were calculated separately with mpmath.
+        # E.g.
+        # >>> mpmath.mp.dps = 100
+        # >>> x = mpmath.mp.mpf('0.01')
+        # >>> cdf = mpmath.erfc(mpmath.sqrt(1/(2*x)))
+        expected = np.array([0.9747728793699604,
+                             0.3173105078629141,
+                             0.1572992070502851,
+                             0.0015654022580025495,
+                             1.523970604832105e-23,
+                             1.795832784800726e-219])
+
+        y = stats.levy.cdf(x)
+        assert_allclose(y, expected, rtol=1e-10)
+
+        # ppf(expected) should get us back to x.
+        xx = stats.levy.ppf(expected)
+        assert_allclose(xx, x, rtol=1e-13)
+
+    def test_levy_sf(self):
+        # Large values, far into the tail of the distribution.
+        x = np.array([1e15, 1e25, 1e35, 1e50])
+        # Expected values were calculated with mpmath.
+        expected = np.array([2.5231325220201597e-08,
+                             2.52313252202016e-13,
+                             2.52313252202016e-18,
+                             7.978845608028653e-26])
+        y = stats.levy.sf(x)
+        assert_allclose(y, expected, rtol=1e-14)
+
+    # The expected values for levy.isf(p) were calculated with mpmath.
+    # For loc=0 and scale=1, the inverse SF can be computed with
+    #
+    #     import mpmath
+    #
+    #     def levy_invsf(p):
+    #         return 1/(2*mpmath.erfinv(p)**2)
+    #
+    # For example, with mpmath.mp.dps set to 60, float(levy_invsf(1e-20))
+    # returns 6.366197723675814e+39.
+    #
+    @pytest.mark.parametrize('p, expected_isf',
+                             [(1e-20, 6.366197723675814e+39),
+                              (1e-8, 6366197723675813.0),
+                              (0.375, 4.185810119346273),
+                              (0.875, 0.42489442055310134),
+                              (0.999, 0.09235685880262713),
+                              (0.9999999962747097, 0.028766845244146945)])
+    def test_levy_isf(self, p, expected_isf):
+        x = stats.levy.isf(p)
+        assert_allclose(x, expected_isf, atol=5e-15)
+
+    def test_levy_logcdf(self):
+        x = 1e50
+        ref = -7.978845608028653e-26
+        logcdf = stats.levy.logcdf(x)
+        assert_allclose(logcdf, ref, rtol=5e-15)
+
+    def test_levy_logsf(self):
+        x = 5e-3
+        ref = -2.0884875837625492e-45
+        logsf = stats.levy.logsf(x)
+        assert_allclose(logsf, ref, rtol=5e-15)
+
+
+def test_540_567():
+    # test for nan returned in tickets 540, 567
+    assert_almost_equal(stats.norm.cdf(-1.7624320982), 0.03899815971089126,
+                        decimal=10, err_msg='test_540_567')
+    assert_almost_equal(stats.norm.cdf(-1.7624320983), 0.038998159702449846,
+                        decimal=10, err_msg='test_540_567')
+    assert_almost_equal(stats.norm.cdf(1.38629436112, loc=0.950273420309,
+                                       scale=0.204423758009),
+                        0.98353464004309321,
+                        decimal=10, err_msg='test_540_567')
+
+
+@pytest.mark.skipif(DOCSTRINGS_STRIPPED, reason="docstrings stripped")
+def test_regression_ticket_1421():
+    assert_('pdf(x, mu, loc=0, scale=1)' not in stats.poisson.__doc__)
+    assert_('pmf(x,' in stats.poisson.__doc__)
+
+
+def test_nan_arguments_gh_issue_1362():
+    with np.errstate(invalid='ignore'):
+        assert_(np.isnan(stats.t.logcdf(1, np.nan)))
+        assert_(np.isnan(stats.t.cdf(1, np.nan)))
+        assert_(np.isnan(stats.t.logsf(1, np.nan)))
+        assert_(np.isnan(stats.t.sf(1, np.nan)))
+        assert_(np.isnan(stats.t.pdf(1, np.nan)))
+        assert_(np.isnan(stats.t.logpdf(1, np.nan)))
+        assert_(np.isnan(stats.t.ppf(1, np.nan)))
+        assert_(np.isnan(stats.t.isf(1, np.nan)))
+
+        assert_(np.isnan(stats.bernoulli.logcdf(np.nan, 0.5)))
+        assert_(np.isnan(stats.bernoulli.cdf(np.nan, 0.5)))
+        assert_(np.isnan(stats.bernoulli.logsf(np.nan, 0.5)))
+        assert_(np.isnan(stats.bernoulli.sf(np.nan, 0.5)))
+        assert_(np.isnan(stats.bernoulli.pmf(np.nan, 0.5)))
+        assert_(np.isnan(stats.bernoulli.logpmf(np.nan, 0.5)))
+        assert_(np.isnan(stats.bernoulli.ppf(np.nan, 0.5)))
+        assert_(np.isnan(stats.bernoulli.isf(np.nan, 0.5)))
+
+
+def test_frozen_fit_ticket_1536():
+    rng = np.random.default_rng(5678)
+    true = np.array([0.25, 0., 0.5])
+    x = stats.lognorm.rvs(true[0], true[1], true[2], size=100, random_state=rng)
+
+    with np.errstate(divide='ignore'):
+        params = np.array(stats.lognorm.fit(x, floc=0.))
+
+    assert_almost_equal(params, true, decimal=2)
+
+    params = np.array(stats.lognorm.fit(x, fscale=0.5, loc=0))
+    assert_almost_equal(params, true, decimal=2)
+
+    params = np.array(stats.lognorm.fit(x, f0=0.25, loc=0))
+    assert_almost_equal(params, true, decimal=2)
+
+    params = np.array(stats.lognorm.fit(x, f0=0.25, floc=0))
+    assert_almost_equal(params, true, decimal=2)
+
+    rng = np.random.default_rng(5678)
+    loc = 1
+    floc = 0.9
+    x = stats.norm.rvs(loc, 2., size=100, random_state=rng)
+    params = np.array(stats.norm.fit(x, floc=floc))
+    expected = np.array([floc, np.sqrt(((x-floc)**2).mean())])
+    assert_almost_equal(params, expected, decimal=4)
+
+
+def test_regression_ticket_1530():
+    # Check the starting value works for Cauchy distribution fit.
+    rng = np.random.default_rng(654321)
+    rvs = stats.cauchy.rvs(size=100, random_state=rng)
+    params = stats.cauchy.fit(rvs)
+    expected = (0.045, 1.142)
+    assert_almost_equal(params, expected, decimal=1)
+
+
+def test_gh_pr_4806():
+    # Check starting values for Cauchy distribution fit.
+    rng = np.random.RandomState(1234)
+    x = rng.randn(42)
+    for offset in 10000.0, 1222333444.0:
+        loc, scale = stats.cauchy.fit(x + offset)
+        assert_allclose(loc, offset, atol=1.0)
+        assert_allclose(scale, 0.6, atol=1.0)
+
+
+def test_poisson_logpmf_ticket_1436():
+    assert_(np.isfinite(stats.poisson.logpmf(1500, 200)))
+
+
+def test_powerlaw_stats():
+    """Test the powerlaw stats function.
+
+    This unit test is also a regression test for ticket 1548.
+
+    The exact values are:
+    mean:
+        mu = a / (a + 1)
+    variance:
+        sigma**2 = a / ((a + 2) * (a + 1) ** 2)
+    skewness:
+        One formula (see https://en.wikipedia.org/wiki/Skewness) is
+            gamma_1 = (E[X**3] - 3*mu*E[X**2] + 2*mu**3) / sigma**3
+        A short calculation shows that E[X**k] is a / (a + k), so gamma_1
+        can be implemented as
+            n = a/(a+3) - 3*(a/(a+1))*a/(a+2) + 2*(a/(a+1))**3
+            d = sqrt(a/((a+2)*(a+1)**2)) ** 3
+            gamma_1 = n/d
+        Either by simplifying, or by a direct calculation of mu_3 / sigma**3,
+        one gets the more concise formula:
+            gamma_1 = -2.0 * ((a - 1) / (a + 3)) * sqrt((a + 2) / a)
+    kurtosis: (See https://en.wikipedia.org/wiki/Kurtosis)
+        The excess kurtosis is
+            gamma_2 = mu_4 / sigma**4 - 3
+        A bit of calculus and algebra (sympy helps) shows that
+            mu_4 = 3*a*(3*a**2 - a + 2) / ((a+1)**4 * (a+2) * (a+3) * (a+4))
+        so
+            gamma_2 = 3*(3*a**2 - a + 2) * (a+2) / (a*(a+3)*(a+4)) - 3
+        which can be rearranged to
+            gamma_2 = 6 * (a**3 - a**2 - 6*a + 2) / (a*(a+3)*(a+4))
+    """
+    cases = [(1.0, (0.5, 1./12, 0.0, -1.2)),
+             (2.0, (2./3, 2./36, -0.56568542494924734, -0.6))]
+    for a, exact_mvsk in cases:
+        mvsk = stats.powerlaw.stats(a, moments="mvsk")
+        assert_array_almost_equal(mvsk, exact_mvsk)
+
+
+def test_powerlaw_edge():
+    # Regression test for gh-3986.
+    p = stats.powerlaw.logpdf(0, 1)
+    assert_equal(p, 0.0)
+
+
+def test_exponpow_edge():
+    # Regression test for gh-3982.
+    p = stats.exponpow.logpdf(0, 1)
+    assert_equal(p, 0.0)
+
+    # Check pdf and logpdf at x = 0 for other values of b.
+    p = stats.exponpow.pdf(0, [0.25, 1.0, 1.5])
+    assert_equal(p, [np.inf, 1.0, 0.0])
+    p = stats.exponpow.logpdf(0, [0.25, 1.0, 1.5])
+    assert_equal(p, [np.inf, 0.0, -np.inf])
+
+
+class TestGenGamma:
+    def test_gengamma_edge(self):
+        # Regression test for gh-3985.
+        p = stats.gengamma.pdf(0, 1, 1)
+        assert_equal(p, 1.0)
+
+    @pytest.mark.parametrize("a, c, ref, tol",
+                             [(1500000.0, 1, 8.529426144018633, 1e-15),
+                              (1e+30, 1, 35.95771492811536, 1e-15),
+                              (1e+100, 1, 116.54819318290696, 1e-15),
+                              (3e3, 1, 5.422011196659015, 1e-13),
+                              (3e6, -1e100, -236.29663213396054, 1e-15),
+                              (3e60, 1e-100, 1.3925371786831085e+102, 1e-15)])
+    def test_gengamma_extreme_entropy(self, a, c, ref, tol):
+        # The reference values were calculated with mpmath:
+        # from mpmath import mp
+        # mp.dps = 500
+        #
+        # def gen_entropy(a, c):
+        #     a, c = mp.mpf(a), mp.mpf(c)
+        #     val = mp.digamma(a)
+        #     h = (a * (mp.one - val) + val/c + mp.loggamma(a) - mp.log(abs(c)))
+        #     return float(h)
+        assert_allclose(stats.gengamma.entropy(a, c), ref, rtol=tol)
+
+    def test_gengamma_endpoint_with_neg_c(self):
+        p = stats.gengamma.pdf(0, 1, -1)
+        assert p == 0.0
+        logp = stats.gengamma.logpdf(0, 1, -1)
+        assert logp == -np.inf
+
+    def test_gengamma_munp(self):
+        # Regression tests for gh-4724.
+        p = stats.gengamma._munp(-2, 200, 1.)
+        assert_almost_equal(p, 1./199/198)
+
+        p = stats.gengamma._munp(-2, 10, 1.)
+        assert_almost_equal(p, 1./9/8)
+
+    def test_gengamma_logpdf_broadcasting_gh24574(self):
+        # gh-24574 reported a broadcasting error when `x` included 0s.
+        assert_allclose(stats.gengamma.logpdf([0, 1, 1], 1, -1), [-np.inf, -1, -1])
+
+
+def test_ksone_fit_freeze():
+    # Regression test for ticket #1638.
+    d = np.array(
+        [-0.18879233, 0.15734249, 0.18695107, 0.27908787, -0.248649,
+         -0.2171497, 0.12233512, 0.15126419, 0.03119282, 0.4365294,
+         0.08930393, -0.23509903, 0.28231224, -0.09974875, -0.25196048,
+         0.11102028, 0.1427649, 0.10176452, 0.18754054, 0.25826724,
+         0.05988819, 0.0531668, 0.21906056, 0.32106729, 0.2117662,
+         0.10886442, 0.09375789, 0.24583286, -0.22968366, -0.07842391,
+         -0.31195432, -0.21271196, 0.1114243, -0.13293002, 0.01331725,
+         -0.04330977, -0.09485776, -0.28434547, 0.22245721, -0.18518199,
+         -0.10943985, -0.35243174, 0.06897665, -0.03553363, -0.0701746,
+         -0.06037974, 0.37670779, -0.21684405])
+
+    with np.errstate(invalid='ignore'):
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore",
+                "The maximum number of subdivisions .50. has been achieved.",
+                IntegrationWarning,
+            )
+            warnings.filterwarnings(
+                "ignore",
+                "floating point number truncated to an integer",
+                RuntimeWarning,
+            )
+            stats.ksone.fit(d)
+
+
+@pytest.mark.xfail(platform.machine() == "sparc64",
+    reason="complex special functions known to fail on sparc64 (gh-22577)")
+def test_norm_logcdf():
+    # Test precision of the logcdf of the normal distribution.
+    # This precision was enhanced in ticket 1614.
+    x = -np.asarray(list(range(0, 120, 4)))
+    # Values from R
+    expected = [-0.69314718, -10.36010149, -35.01343716, -75.41067300,
+                -131.69539607, -203.91715537, -292.09872100, -396.25241451,
+                -516.38564863, -652.50322759, -804.60844201, -972.70364403,
+                -1156.79057310, -1356.87055173, -1572.94460885, -1805.01356068,
+                -2053.07806561, -2317.13866238, -2597.19579746, -2893.24984493,
+                -3205.30112136, -3533.34989701, -3877.39640444, -4237.44084522,
+                -4613.48339520, -5005.52420869, -5413.56342187, -5837.60115548,
+                -6277.63751711, -6733.67260303]
+
+    assert_allclose(stats.norm().logcdf(x), expected, atol=1e-8)
+
+    # also test the complex-valued code path
+    assert_allclose(stats.norm().logcdf(x + 1e-14j).real, expected, atol=1e-8)
+
+    # test the accuracy: d(logcdf)/dx = pdf / cdf \equiv exp(logpdf - logcdf)
+    deriv = (stats.norm.logcdf(x + 1e-10j)/1e-10).imag
+    deriv_expected = np.exp(stats.norm.logpdf(x) - stats.norm.logcdf(x))
+    assert_allclose(deriv, deriv_expected, atol=1e-10)
+
+
+def test_levy_l_sf():
+    # Test levy_l.sf for small arguments.
+    x = np.array([-0.016, -0.01, -0.005, -0.0015])
+    # Expected values were calculated with mpmath.
+    expected = np.array([2.6644463892359302e-15,
+                         1.523970604832107e-23,
+                         2.0884875837625492e-45,
+                         5.302850374626878e-147])
+    y = stats.levy_l.sf(x)
+    assert_allclose(y, expected, rtol=1e-13)
+
+
+def test_levy_l_isf():
+    # Test roundtrip sf(isf(p)), including a small input value.
+    p = np.array([3.0e-15, 0.25, 0.99])
+    x = stats.levy_l.isf(p)
+    q = stats.levy_l.sf(x)
+    assert_allclose(q, p, rtol=5e-14)
+
+
+def test_hypergeom_interval_1802():
+    # these two had endless loops
+    assert_equal(stats.hypergeom.interval(.95, 187601, 43192, 757),
+                 (152.0, 197.0))
+    assert_equal(stats.hypergeom.interval(.945, 187601, 43192, 757),
+                 (152.0, 197.0))
+    # this was working also before
+    assert_equal(stats.hypergeom.interval(.94, 187601, 43192, 757),
+                 (153.0, 196.0))
+
+    # degenerate case .a == .b
+    assert_equal(stats.hypergeom.ppf(0.02, 100, 100, 8), 8)
+    assert_equal(stats.hypergeom.ppf(1, 100, 100, 8), 8)
+
+
+def test_distribution_too_many_args():
+    rng = np.random.default_rng(5976604568)
+    # Check that a TypeError is raised when too many args are given to a method
+    # Regression test for ticket 1815.
+    x = np.linspace(0.1, 0.7, num=5)
+    assert_raises(TypeError, stats.gamma.pdf, x, 2, 3, loc=1.0)
+    assert_raises(TypeError, stats.gamma.pdf, x, 2, 3, 4, loc=1.0)
+    assert_raises(TypeError, stats.gamma.pdf, x, 2, 3, 4, 5)
+    assert_raises(TypeError, stats.gamma.pdf, x, 2, 3, loc=1.0, scale=0.5)
+    assert_raises(TypeError, stats.gamma.rvs, 2., 3, loc=1.0, scale=0.5,
+                  random_state=rng)
+    assert_raises(TypeError, stats.gamma.cdf, x, 2., 3, loc=1.0, scale=0.5)
+    assert_raises(TypeError, stats.gamma.ppf, x, 2., 3, loc=1.0, scale=0.5)
+    assert_raises(TypeError, stats.gamma.stats, 2., 3, loc=1.0, scale=0.5)
+    assert_raises(TypeError, stats.gamma.entropy, 2., 3, loc=1.0, scale=0.5)
+    assert_raises(TypeError, stats.gamma.fit, x, 2., 3, loc=1.0, scale=0.5)
+
+    # These should not give errors
+    stats.gamma.pdf(x, 2, 3)  # loc=3
+    stats.gamma.pdf(x, 2, 3, 4)  # loc=3, scale=4
+    stats.gamma.stats(2., 3)
+    stats.gamma.stats(2., 3, 4)
+    stats.gamma.stats(2., 3, 4, 'mv')
+    stats.gamma.rvs(2., 3, 4, 5, random_state=rng)
+    stats.gamma.fit(stats.gamma.rvs(2., size=7, random_state=rng), 2.)
+
+    # Also for a discrete distribution
+    stats.geom.pmf(x, 2, loc=3)  # no error, loc=3
+    assert_raises(TypeError, stats.geom.pmf, x, 2, 3, 4)
+    assert_raises(TypeError, stats.geom.pmf, x, 2, 3, loc=4)
+
+    # And for distributions with 0, 2 and 3 args respectively
+    assert_raises(TypeError, stats.expon.pdf, x, 3, loc=1.0)
+    assert_raises(TypeError, stats.exponweib.pdf, x, 3, 4, 5, loc=1.0)
+    assert_raises(TypeError, stats.exponweib.pdf, x, 3, 4, 5, 0.1, 0.1)
+    assert_raises(TypeError, stats.ncf.pdf, x, 3, 4, 5, 6, loc=1.0)
+    assert_raises(TypeError, stats.ncf.pdf, x, 3, 4, 5, 6, 1.0, scale=0.5)
+    stats.ncf.pdf(x, 3, 4, 5, 6, 1.0)  # 3 args, plus loc/scale
+
+
+def test_ncx2_tails_ticket_955():
+    # Trac #955 -- check that the cdf computed by special functions
+    # matches the integrated pdf
+    a = stats.ncx2.cdf(np.arange(20, 25, 0.2), 2, 1.07458615e+02)
+    b = stats.ncx2._cdfvec(np.arange(20, 25, 0.2), 2, 1.07458615e+02)
+    assert_allclose(a, b, rtol=1e-3, atol=0)
+
+
+def test_ncx2_tails_pdf():
+    # ncx2.pdf does not return nans in extreme tails(example from gh-1577)
+    # NB: this is to check that nan_to_num is not needed in ncx2.pdf
+    with warnings.catch_warnings():
+        warnings.simplefilter('error', RuntimeWarning)
+        assert_equal(stats.ncx2.pdf(1, np.arange(340, 350), 2), 0)
+        logval = stats.ncx2.logpdf(1, np.arange(340, 350), 2)
+
+    assert_(np.isneginf(logval).all())
+
+    # Verify logpdf has extended precision when pdf underflows to 0
+    with warnings.catch_warnings():
+        warnings.simplefilter('error', RuntimeWarning)
+        assert_equal(stats.ncx2.pdf(10000, 3, 12), 0)
+        assert_allclose(stats.ncx2.logpdf(10000, 3, 12), -4662.444377524883)
+
+
+@pytest.mark.parametrize('method, expected', [
+    ('cdf', np.array([2.497951336e-09, 3.437288941e-10])),
+    ('pdf', np.array([1.238579980e-07, 1.710041145e-08])),
+    ('logpdf', np.array([-15.90413011, -17.88416331])),
+    ('ppf', np.array([4.865182052, 7.017182271]))
+])
+def test_ncx2_zero_nc(method, expected):
+    # gh-5441
+    # ncx2 with nc=0 is identical to chi2
+    # Comparison to R (v3.5.1)
+    # > options(digits=10)
+    # > pchisq(0.1, df=10, ncp=c(0,4))
+    # > dchisq(0.1, df=10, ncp=c(0,4))
+    # > dchisq(0.1, df=10, ncp=c(0,4), log=TRUE)
+    # > qchisq(0.1, df=10, ncp=c(0,4))
+
+    result = getattr(stats.ncx2, method)(0.1, nc=[0, 4], df=10)
+    assert_allclose(result, expected, atol=1e-15)
+
+
+def test_ncx2_zero_nc_rvs():
+    # gh-5441
+    # ncx2 with nc=0 is identical to chi2
+    result = stats.ncx2.rvs(df=10, nc=0, random_state=1)
+    expected = stats.chi2.rvs(df=10, random_state=1)
+    assert_allclose(result, expected, atol=1e-15)
+
+
+def test_ncx2_gh12731():
+    # test that gh-12731 is resolved; previously these were all 0.5
+    nc = 10**np.arange(5, 10)
+    assert_equal(stats.ncx2.cdf(1e4, df=1, nc=nc), 0)
+
+
+def test_ncx2_gh8665():
+    # test that gh-8665 is resolved; previously this tended to nonzero value
+    x = np.array([4.99515382e+00, 1.07617327e+01, 2.31854502e+01,
+                  4.99515382e+01, 1.07617327e+02, 2.31854502e+02,
+                  4.99515382e+02, 1.07617327e+03, 2.31854502e+03,
+                  4.99515382e+03, 1.07617327e+04, 2.31854502e+04,
+                  4.99515382e+04])
+    nu, lam = 20, 499.51538166556196
+
+    sf = stats.ncx2.sf(x, df=nu, nc=lam)
+    # computed in R. Couldn't find a survival function implementation
+    # options(digits=16)
+    # x <- c(4.99515382e+00, 1.07617327e+01, 2.31854502e+01, 4.99515382e+01,
+    #        1.07617327e+02, 2.31854502e+02, 4.99515382e+02, 1.07617327e+03,
+    #        2.31854502e+03, 4.99515382e+03, 1.07617327e+04, 2.31854502e+04,
+    #        4.99515382e+04)
+    # nu <- 20
+    # lam <- 499.51538166556196
+    # 1 - pchisq(x, df = nu, ncp = lam)
+    sf_expected = [1.0000000000000000, 1.0000000000000000, 1.0000000000000000,
+                   1.0000000000000000, 1.0000000000000000, 0.9999999999999888,
+                   0.6646525582135460, 0.0000000000000000, 0.0000000000000000,
+                   0.0000000000000000, 0.0000000000000000, 0.0000000000000000,
+                   0.0000000000000000]
+    assert_allclose(sf, sf_expected, atol=1e-12)
+
+
+def test_ncx2_gh11777():
+    # regression test for gh-11777:
+    # At high values of degrees of freedom df, ensure the pdf of ncx2 does
+    # not get clipped to zero when the non-centrality parameter is
+    # sufficiently less than df
+    df = 6700
+    nc = 5300
+    x = np.linspace(stats.ncx2.ppf(0.001, df, nc),
+                    stats.ncx2.ppf(0.999, df, nc), num=10000)
+    ncx2_pdf = stats.ncx2.pdf(x, df, nc)
+    gauss_approx = stats.norm.pdf(x, df + nc, np.sqrt(2 * df + 4 * nc))
+    # use huge tolerance as we're only looking for obvious discrepancy
+    assert_allclose(ncx2_pdf, gauss_approx, atol=1e-4)
+
+
+# Expected values for foldnorm.sf were computed with mpmath:
+#
+#    from mpmath import mp
+#    mp.dps = 60
+#    def foldcauchy_sf(x, c):
+#        x = mp.mpf(x)
+#        c = mp.mpf(c)
+#        return mp.one - (mp.atan(x - c) + mp.atan(x + c))/mp.pi
+#
+# E.g.
+#
+#    >>> float(foldcauchy_sf(2, 1))
+#    0.35241638234956674
+#
+@pytest.mark.parametrize('x, c, expected',
+                         [(2, 1, 0.35241638234956674),
+                          (2, 2, 0.5779791303773694),
+                          (1e13, 1, 6.366197723675813e-14),
+                          (2e16, 1, 3.183098861837907e-17),
+                          (1e13, 2e11, 6.368745221764519e-14),
+                          (0.125, 200, 0.999998010612169)])
+def test_foldcauchy_sf(x, c, expected):
+    sf = stats.foldcauchy.sf(x, c)
+    assert_allclose(sf, expected, 2e-15)
+
+
+# The same mpmath code shown in the comments above test_foldcauchy_sf()
+# is used to create these expected values.
+@pytest.mark.parametrize('x, expected',
+                         [(2, 0.2951672353008665),
+                          (1e13, 6.366197723675813e-14),
+                          (2e16, 3.183098861837907e-17),
+                          (5e80, 1.2732395447351629e-81)])
+def test_halfcauchy_sf(x, expected):
+    sf = stats.halfcauchy.sf(x)
+    assert_allclose(sf, expected, 2e-15)
+
+
+# Expected value computed with mpmath:
+#     expected = mp.cot(mp.pi*p/2)
+@pytest.mark.parametrize('p, expected',
+                         [(0.9999995, 7.853981633329977e-07),
+                          (0.975, 0.039290107007669675),
+                          (0.5, 1.0),
+                          (0.01, 63.65674116287158),
+                          (1e-14, 63661977236758.13),
+                          (5e-80, 1.2732395447351627e+79)])
+def test_halfcauchy_isf(p, expected):
+    x = stats.halfcauchy.isf(p)
+    assert_allclose(x, expected)
+
+
+def test_foldnorm_zero():
+    # Parameter value c=0 was not enabled, see gh-2399.
+    rv = stats.foldnorm(0, scale=1)
+    assert_equal(rv.cdf(0), 0)  # rv.cdf(0) previously resulted in: nan
+
+
+# Expected values for foldnorm.sf were computed with mpmath:
+#
+#    from mpmath import mp
+#    mp.dps = 60
+#    def foldnorm_sf(x, c):
+#        x = mp.mpf(x)
+#        c = mp.mpf(c)
+#        return mp.ncdf(-x+c) + mp.ncdf(-x-c)
+#
+# E.g.
+#
+#    >>> float(foldnorm_sf(2, 1))
+#    0.16000515196308715
+#
+@pytest.mark.parametrize('x, c, expected',
+                         [(2, 1, 0.16000515196308715),
+                          (20, 1, 8.527223952630977e-81),
+                          (10, 15, 0.9999997133484281),
+                          (25, 15, 7.619853024160525e-24)])
+def test_foldnorm_sf(x, c, expected):
+    sf = stats.foldnorm.sf(x, c)
+    assert_allclose(sf, expected, 1e-14)
+
+
+def test_stats_shapes_argcheck():
+    # stats method was failing for vector shapes if some of the values
+    # were outside of the allowed range, see gh-2678
+    mv3 = stats.invgamma.stats([0.0, 0.5, 1.0], 1, 0.5)  # 0 is not a legal `a`
+    mv2 = stats.invgamma.stats([0.5, 1.0], 1, 0.5)
+    mv2_augmented = tuple(np.r_[np.nan, _] for _ in mv2)
+    assert_equal(mv2_augmented, mv3)
+
+    # -1 is not a legal shape parameter
+    mv3 = stats.lognorm.stats([2, 2.4, -1])
+    mv2 = stats.lognorm.stats([2, 2.4])
+    mv2_augmented = tuple(np.r_[_, np.nan] for _ in mv2)
+    assert_equal(mv2_augmented, mv3)
+
+    # FIXME: this is only a quick-and-dirty test of a quick-and-dirty bugfix.
+    # stats method with multiple shape parameters is not properly vectorized
+    # anyway, so some distributions may or may not fail.
+
+
+# Test subclassing distributions w/ explicit shapes
+
+class _distr_gen(stats.rv_continuous):
+    def _pdf(self, x, a):
+        return 42
+
+
+class _distr2_gen(stats.rv_continuous):
+    def _cdf(self, x, a):
+        return 42 * a + x
+
+
+class _distr3_gen(stats.rv_continuous):
+    def _pdf(self, x, a, b):
+        return a + b
+
+    def _cdf(self, x, a):
+        # Different # of shape params from _pdf, to be able to check that
+        # inspection catches the inconsistency.
+        return 42 * a + x
+
+
+class _distr6_gen(stats.rv_continuous):
+    # Two shape parameters (both _pdf and _cdf defined, consistent shapes.)
+    def _pdf(self, x, a, b):
+        return a*x + b
+
+    def _cdf(self, x, a, b):
+        return 42 * a + x
+
+
+class TestSubclassingExplicitShapes:
+    # Construct a distribution w/ explicit shapes parameter and test it.
+
+    def test_correct_shapes(self):
+        dummy_distr = _distr_gen(name='dummy', shapes='a')
+        assert_equal(dummy_distr.pdf(1, a=1), 42)
+
+    def test_wrong_shapes_1(self):
+        dummy_distr = _distr_gen(name='dummy', shapes='A')
+        assert_raises(TypeError, dummy_distr.pdf, 1, **dict(a=1))
+
+    def test_wrong_shapes_2(self):
+        dummy_distr = _distr_gen(name='dummy', shapes='a, b, c')
+        dct = dict(a=1, b=2, c=3)
+        assert_raises(TypeError, dummy_distr.pdf, 1, **dct)
+
+    def test_shapes_string(self):
+        # shapes must be a string
+        dct = dict(name='dummy', shapes=42)
+        assert_raises(TypeError, _distr_gen, **dct)
+
+    def test_shapes_identifiers_1(self):
+        # shapes must be a comma-separated list of valid python identifiers
+        dct = dict(name='dummy', shapes='(!)')
+        assert_raises(SyntaxError, _distr_gen, **dct)
+
+    def test_shapes_identifiers_2(self):
+        dct = dict(name='dummy', shapes='4chan')
+        assert_raises(SyntaxError, _distr_gen, **dct)
+
+    def test_shapes_identifiers_3(self):
+        dct = dict(name='dummy', shapes='m(fti)')
+        assert_raises(SyntaxError, _distr_gen, **dct)
+
+    def test_shapes_identifiers_nodefaults(self):
+        dct = dict(name='dummy', shapes='a=2')
+        assert_raises(SyntaxError, _distr_gen, **dct)
+
+    def test_shapes_args(self):
+        dct = dict(name='dummy', shapes='*args')
+        assert_raises(SyntaxError, _distr_gen, **dct)
+
+    def test_shapes_kwargs(self):
+        dct = dict(name='dummy', shapes='**kwargs')
+        assert_raises(SyntaxError, _distr_gen, **dct)
+
+    def test_shapes_keywords(self):
+        # python keywords cannot be used for shape parameters
+        dct = dict(name='dummy', shapes='a, b, c, lambda')
+        assert_raises(SyntaxError, _distr_gen, **dct)
+
+    def test_shapes_signature(self):
+        # test explicit shapes which agree w/ the signature of _pdf
+        class _dist_gen(stats.rv_continuous):
+            def _pdf(self, x, a):
+                return stats.norm._pdf(x) * a
+
+        dist = _dist_gen(shapes='a')
+        assert_equal(dist.pdf(0.5, a=2), stats.norm.pdf(0.5)*2)
+
+    def test_shapes_signature_inconsistent(self):
+        # test explicit shapes which do not agree w/ the signature of _pdf
+        class _dist_gen(stats.rv_continuous):
+            def _pdf(self, x, a):
+                return stats.norm._pdf(x) * a
+
+        dist = _dist_gen(shapes='a, b')
+        assert_raises(TypeError, dist.pdf, 0.5, **dict(a=1, b=2))
+
+    def test_star_args(self):
+        # test _pdf with only starargs
+        # NB: **kwargs of pdf will never reach _pdf
+        class _dist_gen(stats.rv_continuous):
+            def _pdf(self, x, *args):
+                extra_kwarg = args[0]
+                return stats.norm._pdf(x) * extra_kwarg
+
+        dist = _dist_gen(shapes='extra_kwarg')
+        assert_equal(dist.pdf(0.5, extra_kwarg=33), stats.norm.pdf(0.5)*33)
+        assert_equal(dist.pdf(0.5, 33), stats.norm.pdf(0.5)*33)
+        assert_raises(TypeError, dist.pdf, 0.5, **dict(xxx=33))
+
+    def test_star_args_2(self):
+        # test _pdf with named & starargs
+        # NB: **kwargs of pdf will never reach _pdf
+        class _dist_gen(stats.rv_continuous):
+            def _pdf(self, x, offset, *args):
+                extra_kwarg = args[0]
+                return stats.norm._pdf(x) * extra_kwarg + offset
+
+        dist = _dist_gen(shapes='offset, extra_kwarg')
+        assert_equal(dist.pdf(0.5, offset=111, extra_kwarg=33),
+                     stats.norm.pdf(0.5)*33 + 111)
+        assert_equal(dist.pdf(0.5, 111, 33),
+                     stats.norm.pdf(0.5)*33 + 111)
+
+    def test_extra_kwarg(self):
+        # **kwargs to _pdf are ignored.
+        # this is a limitation of the framework (_pdf(x, *goodargs))
+        class _distr_gen(stats.rv_continuous):
+            def _pdf(self, x, *args, **kwargs):
+                # _pdf should handle *args, **kwargs itself.  Here "handling"
+                # is ignoring *args and looking for ``extra_kwarg`` and using
+                # that.
+                extra_kwarg = kwargs.pop('extra_kwarg', 1)
+                return stats.norm._pdf(x) * extra_kwarg
+
+        dist = _distr_gen(shapes='extra_kwarg')
+        assert_equal(dist.pdf(1, extra_kwarg=3), stats.norm.pdf(1))
+
+    def test_shapes_empty_string(self):
+        # shapes='' is equivalent to shapes=None
+        class _dist_gen(stats.rv_continuous):
+            def _pdf(self, x):
+                return stats.norm.pdf(x)
+
+        dist = _dist_gen(shapes='')
+        assert_equal(dist.pdf(0.5), stats.norm.pdf(0.5))
+
+
+class TestSubclassingNoShapes:
+    # Construct a distribution w/o explicit shapes parameter and test it.
+
+    def test_only__pdf(self):
+        dummy_distr = _distr_gen(name='dummy')
+        assert_equal(dummy_distr.pdf(1, a=1), 42)
+
+    def test_only__cdf(self):
+        # _pdf is determined from _cdf by taking numerical derivative
+        dummy_distr = _distr2_gen(name='dummy')
+        assert_almost_equal(dummy_distr.pdf(1, a=1), 1)
+
+    @pytest.mark.skipif(DOCSTRINGS_STRIPPED, reason="docstring stripped")
+    def test_signature_inspection(self):
+        # check that _pdf signature inspection works correctly, and is used in
+        # the class docstring
+        dummy_distr = _distr_gen(name='dummy')
+        assert_equal(dummy_distr.numargs, 1)
+        assert_equal(dummy_distr.shapes, 'a')
+        res = re.findall(r'logpdf\(x, a, loc=0, scale=1\)',
+                         dummy_distr.__doc__)
+        assert_(len(res) == 1)
+
+    @pytest.mark.skipif(DOCSTRINGS_STRIPPED, reason="docstring stripped")
+    def test_signature_inspection_2args(self):
+        # same for 2 shape params and both _pdf and _cdf defined
+        dummy_distr = _distr6_gen(name='dummy')
+        assert_equal(dummy_distr.numargs, 2)
+        assert_equal(dummy_distr.shapes, 'a, b')
+        res = re.findall(r'logpdf\(x, a, b, loc=0, scale=1\)',
+                         dummy_distr.__doc__)
+        assert_(len(res) == 1)
+
+    def test_signature_inspection_2args_incorrect_shapes(self):
+        # both _pdf and _cdf defined, but shapes are inconsistent: raises
+        assert_raises(TypeError, _distr3_gen, name='dummy')
+
+    def test_defaults_raise(self):
+        # default arguments should raise
+        class _dist_gen(stats.rv_continuous):
+            def _pdf(self, x, a=42):
+                return 42
+        assert_raises(TypeError, _dist_gen, **dict(name='dummy'))
+
+    def test_starargs_raise(self):
+        # without explicit shapes, *args are not allowed
+        class _dist_gen(stats.rv_continuous):
+            def _pdf(self, x, a, *args):
+                return 42
+        assert_raises(TypeError, _dist_gen, **dict(name='dummy'))
+
+    def test_kwargs_raise(self):
+        # without explicit shapes, **kwargs are not allowed
+        class _dist_gen(stats.rv_continuous):
+            def _pdf(self, x, a, **kwargs):
+                return 42
+        assert_raises(TypeError, _dist_gen, **dict(name='dummy'))
+
+
+@pytest.mark.skipif(DOCSTRINGS_STRIPPED, reason="docstring stripped")
+def test_docstrings():
+    badones = [r',\s*,', r'\(\s*,', r'^\s*:']
+    for distname in stats.__all__:
+        dist = getattr(stats, distname)
+        if isinstance(dist, (stats.rv_discrete | stats.rv_continuous)):
+            for regex in badones:
+                assert_(re.search(regex, dist.__doc__) is None)
+
+
+def test_infinite_input():
+    assert_almost_equal(stats.skellam.sf(np.inf, 10, 11), 0)
+    assert_almost_equal(stats.ncx2._cdf(np.inf, 8, 0.1), 1)
+
+
+def test_lomax_accuracy():
+    # regression test for gh-4033
+    p = stats.lomax.ppf(stats.lomax.cdf(1e-100, 1), 1)
+    assert_allclose(p, 1e-100)
+
+
+def test_truncexpon_accuracy():
+    # regression test for gh-4035
+    p = stats.truncexpon.ppf(stats.truncexpon.cdf(1e-100, 1), 1)
+    assert_allclose(p, 1e-100)
+
+
+def test_rayleigh_accuracy():
+    # regression test for gh-4034
+    p = stats.rayleigh.isf(stats.rayleigh.sf(9, 1), 1)
+    assert_almost_equal(p, 9.0, decimal=15)
+
+
+def test_genextreme_give_no_warnings():
+    """regression test for gh-6219"""
+
+    with warnings.catch_warnings(record=True) as w:
+        warnings.simplefilter("always")
+
+        stats.genextreme.cdf(.5, 0)
+        stats.genextreme.pdf(.5, 0)
+        stats.genextreme.ppf(.5, 0)
+        stats.genextreme.logpdf(-np.inf, 0.0)
+        number_of_warnings_thrown = len(w)
+        assert_equal(number_of_warnings_thrown, 0)
+
+
+def test_moments_gh22400():
+    # Regression test for gh-22400
+    # Check for correct results at c=0 with no warnings. While we're at it,
+    # check that NaN and sufficiently negative input produce NaNs, and output
+    # with `c=1` also agrees with reference values.
+    res = np.asarray(stats.genextreme.stats([0.0, np.nan, 1, -1.5], moments='mvsk'))
+
+    # Reference values for c=0 (Wikipedia)
+    mean = np.euler_gamma
+    var = np.pi**2 / 6
+    skew = 12 * np.sqrt(6) * special.zeta(3) / np.pi**3
+    kurt = 12 / 5
+    ref_0 = [mean, var, skew, kurt]
+    ref_1 = ref_3 = [np.nan]*4
+    ref_2 = [0, 1, -2, 6]  # Wolfram Alpha, MaxStableDistribution[0, 1, -1]
+
+    assert_allclose(res[:, 0], ref_0, rtol=1e-14)
+    assert_equal(res[:, 1], ref_1)
+    assert_allclose(res[:, 2], ref_2, rtol=1e-14)
+    assert_equal(res[:, 3], ref_3)
+
+
+def test_genextreme_entropy():
+    # regression test for gh-5181
+    euler_gamma = 0.5772156649015329
+
+    h = stats.genextreme.entropy(-1.0)
+    assert_allclose(h, 2*euler_gamma + 1, rtol=1e-14)
+
+    h = stats.genextreme.entropy(0)
+    assert_allclose(h, euler_gamma + 1, rtol=1e-14)
+
+    h = stats.genextreme.entropy(1.0)
+    assert_equal(h, 1)
+
+    h = stats.genextreme.entropy(-2.0, scale=10)
+    assert_allclose(h, euler_gamma*3 + np.log(10) + 1, rtol=1e-14)
+
+    h = stats.genextreme.entropy(10)
+    assert_allclose(h, -9*euler_gamma + 1, rtol=1e-14)
+
+    h = stats.genextreme.entropy(-10)
+    assert_allclose(h, 11*euler_gamma + 1, rtol=1e-14)
+
+
+def test_genextreme_sf_isf():
+    # Expected values were computed using mpmath:
+    #
+    #    import mpmath
+    #
+    #    def mp_genextreme_sf(x, xi, mu=0, sigma=1):
+    #        # Formula from wikipedia, which has a sign convention for xi that
+    #        # is the opposite of scipy's shape parameter.
+    #        if xi != 0:
+    #            t = mpmath.power(1 + ((x - mu)/sigma)*xi, -1/xi)
+    #        else:
+    #            t = mpmath.exp(-(x - mu)/sigma)
+    #        return 1 - mpmath.exp(-t)
+    #
+    # >>> mpmath.mp.dps = 1000
+    # >>> s = mp_genextreme_sf(mpmath.mp.mpf("1e8"), mpmath.mp.mpf("0.125"))
+    # >>> float(s)
+    # 1.6777205262585625e-57
+    # >>> s = mp_genextreme_sf(mpmath.mp.mpf("7.98"), mpmath.mp.mpf("-0.125"))
+    # >>> float(s)
+    # 1.52587890625e-21
+    # >>> s = mp_genextreme_sf(mpmath.mp.mpf("7.98"), mpmath.mp.mpf("0"))
+    # >>> float(s)
+    # 0.00034218086528426593
+
+    x = 1e8
+    s = stats.genextreme.sf(x, -0.125)
+    assert_allclose(s, 1.6777205262585625e-57)
+    x2 = stats.genextreme.isf(s, -0.125)
+    assert_allclose(x2, x)
+
+    x = 7.98
+    s = stats.genextreme.sf(x, 0.125)
+    assert_allclose(s, 1.52587890625e-21)
+    x2 = stats.genextreme.isf(s, 0.125)
+    assert_allclose(x2, x)
+
+    x = 7.98
+    s = stats.genextreme.sf(x, 0)
+    assert_allclose(s, 0.00034218086528426593)
+    x2 = stats.genextreme.isf(s, 0)
+    assert_allclose(x2, x)
+
+
+def test_burr12_ppf_small_arg():
+    prob = 1e-16
+    quantile = stats.burr12.ppf(prob, 2, 3)
+    # The expected quantile was computed using mpmath:
+    #   >>> import mpmath
+    #   >>> mpmath.mp.dps = 100
+    #   >>> prob = mpmath.mpf('1e-16')
+    #   >>> c = mpmath.mpf(2)
+    #   >>> d = mpmath.mpf(3)
+    #   >>> float(((1-prob)**(-1/d) - 1)**(1/c))
+    #   5.7735026918962575e-09
+    assert_allclose(quantile, 5.7735026918962575e-09)
+
+
+def test_invweibull_fit():
+    """
+    Test fitting invweibull to data.
+
+    Here is a the same calculation in R:
+
+    > library(evd)
+    > library(fitdistrplus)
+    > x = c(1, 1.25, 2, 2.5, 2.8,  3, 3.8, 4, 5, 8, 10, 12, 64, 99)
+    > result = fitdist(x, 'frechet', control=list(reltol=1e-13),
+    +                  fix.arg=list(loc=0), start=list(shape=2, scale=3))
+    > result
+    Fitting of the distribution ' frechet ' by maximum likelihood
+    Parameters:
+          estimate Std. Error
+    shape 1.048482  0.2261815
+    scale 3.099456  0.8292887
+    Fixed parameters:
+        value
+    loc     0
+
+    """
+
+    def optimizer(func, x0, args=(), disp=0):
+        return fmin(func, x0, args=args, disp=disp, xtol=1e-12, ftol=1e-12)
+
+    x = np.array([1, 1.25, 2, 2.5, 2.8, 3, 3.8, 4, 5, 8, 10, 12, 64, 99])
+    c, loc, scale = stats.invweibull.fit(x, floc=0, optimizer=optimizer)
+    assert_allclose(c, 1.048482, rtol=5e-6)
+    assert loc == 0
+    assert_allclose(scale, 3.099456, rtol=5e-6)
+
+
+# Expected values were computed with mpmath.
+@pytest.mark.parametrize('x, c, expected',
+                         [(3, 1.5, 0.175064510070713299327),
+                          (2000, 1.5, 1.11802773877318715787e-5),
+                          (2000, 9.25, 2.92060308832269637092e-31),
+                          (1e15, 1.5, 3.16227766016837933199884e-23)])
+def test_invweibull_sf(x, c, expected):
+    computed = stats.invweibull.sf(x, c)
+    assert_allclose(computed, expected, rtol=1e-15)
+
+
+# Expected values were computed with mpmath.
+@pytest.mark.parametrize('p, c, expected',
+                         [(0.5, 2.5, 1.15789669836468183976),
+                          (3e-18, 5, 3195.77171838060906447)])
+def test_invweibull_isf(p, c, expected):
+    computed = stats.invweibull.isf(p, c)
+    assert_allclose(computed, expected, rtol=1e-15)
+
+
+@pytest.mark.parametrize(
+    'df1,df2,x',
+    [(2, 2, [-0.5, 0.2, 1.0, 2.3]),
+     (4, 11, [-0.5, 0.2, 1.0, 2.3]),
+     (7, 17, [1, 2, 3, 4, 5])]
+)
+def test_ncf_edge_case(df1, df2, x):
+    # Test for edge case described in gh-11660.
+    # Non-central Fisher distribution when nc = 0
+    # should be the same as Fisher distribution.
+    nc = 0
+    expected_cdf = stats.f.cdf(x, df1, df2)
+    calculated_cdf = stats.ncf.cdf(x, df1, df2, nc)
+    assert_allclose(expected_cdf, calculated_cdf, rtol=1e-14)
+
+    # when ncf_gen._skip_pdf will be used instead of generic pdf,
+    # this additional test will be useful.
+    expected_pdf = stats.f.pdf(x, df1, df2)
+    calculated_pdf = stats.ncf.pdf(x, df1, df2, nc)
+    assert_allclose(expected_pdf, calculated_pdf, rtol=1e-6)
+
+
+def test_ncf_variance():
+    # Regression test for gh-10658 (incorrect variance formula for ncf).
+    # The correct value of ncf.var(2, 6, 4), 42.75, can be verified with, for
+    # example, Wolfram Alpha with the expression
+    #     Variance[NoncentralFRatioDistribution[2, 6, 4]]
+    # or with the implementation of the noncentral F distribution in the C++
+    # library Boost.
+    v = stats.ncf.var(2, 6, 4)
+    assert_allclose(v, 42.75, rtol=1e-14)
+
+
+def test_ncf_cdf_spotcheck():
+    # Regression test for gh-15582 testing against values from R/MATLAB
+    # Generate check_val from R or MATLAB as follows:
+    #          R: pf(20, df1 = 6, df2 = 33, ncp = 30.4) = 0.998921
+    #     MATLAB: ncfcdf(20, 6, 33, 30.4) = 0.998921
+    scipy_val = stats.ncf.cdf(20, 6, 33, 30.4)
+    check_val = 0.998921
+    assert_allclose(check_val, np.round(scipy_val, decimals=6))
+
+
+def test_ncf_ppf_issue_17026():
+    # Regression test for gh-17026
+    x = np.linspace(0, 1, 600)
+    x[0] = 1e-16
+    par = (0.1, 2, 5, 0, 1)
+    q = stats.ncf.ppf(x, *par)
+    q0 = [stats.ncf.ppf(xi, *par) for xi in x]
+    assert_allclose(q, q0)
+
+
+class TestHistogram:
+    def setup_method(self):
+        self.rng = np.random.default_rng(6561174822)
+
+        # We have 8 bins
+        # [1,2), [2,3), [3,4), [4,5), [5,6), [6,7), [7,8), [8,9)
+        # But actually np.histogram will put the last 9 also in the [8,9) bin!
+        # Therefore there is a slight difference below for the last bin, from
+        # what you might have expected.
+        histogram = np.histogram([1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5,
+                                  6, 6, 6, 6, 7, 7, 7, 8, 8, 9], bins=8)
+        self.template = stats.rv_histogram(histogram)
+
+        data = stats.norm.rvs(loc=1.0, scale=2.5, size=10000, random_state=self.rng)
+        norm_histogram = np.histogram(data, bins=50)
+        self.norm_template = stats.rv_histogram(norm_histogram)
+
+    def test_pdf(self):
+        values = np.array([0.0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5,
+                           5.0, 5.5, 6.0, 6.5, 7.0, 7.5, 8.0, 8.5, 9.0, 9.5])
+        pdf_values = np.asarray([0.0/25.0, 0.0/25.0, 1.0/25.0, 1.0/25.0,
+                                 2.0/25.0, 2.0/25.0, 3.0/25.0, 3.0/25.0,
+                                 4.0/25.0, 4.0/25.0, 5.0/25.0, 5.0/25.0,
+                                 4.0/25.0, 4.0/25.0, 3.0/25.0, 3.0/25.0,
+                                 3.0/25.0, 3.0/25.0, 0.0/25.0, 0.0/25.0])
+        assert_allclose(self.template.pdf(values), pdf_values)
+
+        # Test explicitly the corner cases:
+        # As stated above the pdf in the bin [8,9) is greater than
+        # one would naively expect because np.histogram putted the 9
+        # into the [8,9) bin.
+        assert_almost_equal(self.template.pdf(8.0), 3.0/25.0)
+        assert_almost_equal(self.template.pdf(8.5), 3.0/25.0)
+        # 9 is outside our defined bins [8,9) hence the pdf is already 0
+        # for a continuous distribution this is fine, because a single value
+        # does not have a finite probability!
+        assert_almost_equal(self.template.pdf(9.0), 0.0/25.0)
+        assert_almost_equal(self.template.pdf(10.0), 0.0/25.0)
+
+        x = np.linspace(-2, 2, 10)
+        assert_allclose(self.norm_template.pdf(x),
+                        stats.norm.pdf(x, loc=1.0, scale=2.5), rtol=0.1)
+
+    def test_cdf_ppf(self):
+        values = np.array([0.0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5,
+                           5.0, 5.5, 6.0, 6.5, 7.0, 7.5, 8.0, 8.5, 9.0, 9.5])
+        cdf_values = np.asarray([0.0/25.0, 0.0/25.0, 0.0/25.0, 0.5/25.0,
+                                 1.0/25.0, 2.0/25.0, 3.0/25.0, 4.5/25.0,
+                                 6.0/25.0, 8.0/25.0, 10.0/25.0, 12.5/25.0,
+                                 15.0/25.0, 17.0/25.0, 19.0/25.0, 20.5/25.0,
+                                 22.0/25.0, 23.5/25.0, 25.0/25.0, 25.0/25.0])
+        assert_allclose(self.template.cdf(values), cdf_values)
+        # First three and last two values in cdf_value are not unique
+        assert_allclose(self.template.ppf(cdf_values[2:-1]), values[2:-1])
+
+        # Test of cdf and ppf are inverse functions
+        x = np.linspace(1.0, 9.0, 100)
+        assert_allclose(self.template.ppf(self.template.cdf(x)), x)
+        x = np.linspace(0.0, 1.0, 100)
+        assert_allclose(self.template.cdf(self.template.ppf(x)), x)
+
+        x = np.linspace(-2, 2, 10)
+        assert_allclose(self.norm_template.cdf(x),
+                        stats.norm.cdf(x, loc=1.0, scale=2.5), rtol=0.1)
+
+    def test_rvs(self):
+        N = 10000
+        sample = self.template.rvs(size=N, random_state=self.rng)
+        assert_equal(np.sum(sample < 1.0), 0.0)
+        assert_allclose(np.sum(sample <= 2.0), 1.0/25.0 * N, rtol=0.2)
+        assert_allclose(np.sum(sample <= 2.5), 2.0/25.0 * N, rtol=0.2)
+        assert_allclose(np.sum(sample <= 3.0), 3.0/25.0 * N, rtol=0.1)
+        assert_allclose(np.sum(sample <= 3.5), 4.5/25.0 * N, rtol=0.1)
+        assert_allclose(np.sum(sample <= 4.0), 6.0/25.0 * N, rtol=0.1)
+        assert_allclose(np.sum(sample <= 4.5), 8.0/25.0 * N, rtol=0.1)
+        assert_allclose(np.sum(sample <= 5.0), 10.0/25.0 * N, rtol=0.05)
+        assert_allclose(np.sum(sample <= 5.5), 12.5/25.0 * N, rtol=0.05)
+        assert_allclose(np.sum(sample <= 6.0), 15.0/25.0 * N, rtol=0.05)
+        assert_allclose(np.sum(sample <= 6.5), 17.0/25.0 * N, rtol=0.05)
+        assert_allclose(np.sum(sample <= 7.0), 19.0/25.0 * N, rtol=0.05)
+        assert_allclose(np.sum(sample <= 7.5), 20.5/25.0 * N, rtol=0.05)
+        assert_allclose(np.sum(sample <= 8.0), 22.0/25.0 * N, rtol=0.05)
+        assert_allclose(np.sum(sample <= 8.5), 23.5/25.0 * N, rtol=0.05)
+        assert_allclose(np.sum(sample <= 9.0), 25.0/25.0 * N, rtol=0.05)
+        assert_allclose(np.sum(sample <= 9.0), 25.0/25.0 * N, rtol=0.05)
+        assert_equal(np.sum(sample > 9.0), 0.0)
+
+    def test_munp(self):
+        for n in range(4):
+            assert_allclose(self.norm_template._munp(n),
+                            stats.norm(1.0, 2.5).moment(n), rtol=0.05)
+
+    def test_entropy(self):
+        assert_allclose(self.norm_template.entropy(),
+                        stats.norm.entropy(loc=1.0, scale=2.5), rtol=0.05)
+
+
+def test_histogram_non_uniform():
+    # Tests rv_histogram works even for non-uniform bin widths
+    counts, bins = ([1, 1], [0, 1, 1001])
+
+    dist = stats.rv_histogram((counts, bins), density=False)
+    np.testing.assert_allclose(dist.pdf([0.5, 200]), [0.5, 0.0005])
+    assert dist.median() == 1
+
+    dist = stats.rv_histogram((counts, bins), density=True)
+    np.testing.assert_allclose(dist.pdf([0.5, 200]), 1/1001)
+    assert dist.median() == 1001/2
+
+    # Omitting density produces a warning for non-uniform bins...
+    message = "Bin widths are not constant. Assuming..."
+    with pytest.warns(RuntimeWarning, match=message):
+        dist = stats.rv_histogram((counts, bins))
+        assert dist.median() == 1001/2  # default is like `density=True`
+
+    # ... but not for uniform bins
+    dist = stats.rv_histogram((counts, [0, 1, 2]))
+    assert dist.median() == 1
+
+
+class TestLogUniform:
+    def test_alias(self):
+        # This test makes sure that "reciprocal" and "loguniform" are
+        # aliases of the same distribution and that both are log-uniform
+        rng = np.random.default_rng(98643218961)
+        rv = stats.loguniform(10 ** -3, 10 ** 0)
+        rvs = rv.rvs(size=10000, random_state=rng)
+
+        rng = np.random.default_rng(98643218961)
+        rv2 = stats.reciprocal(10 ** -3, 10 ** 0)
+        rvs2 = rv2.rvs(size=10000, random_state=rng)
+
+        assert_allclose(rvs2, rvs)
+
+        vals, _ = np.histogram(np.log10(rvs), bins=10)
+        assert 900 <= vals.min() <= vals.max() <= 1100
+        assert np.abs(np.median(vals) - 1000) <= 10
+
+    @pytest.mark.parametrize("method", ['mle', 'mm'])
+    def test_fit_override(self, method):
+        # loguniform is overparameterized, so check that fit override enforces
+        # scale=1 unless fscale is provided by the user
+        rng = np.random.default_rng(98643218961)
+        rvs = stats.loguniform.rvs(0.1, 1, size=1000, random_state=rng)
+
+        a, b, loc, scale = stats.loguniform.fit(rvs, method=method)
+        assert scale == 1
+
+        a, b, loc, scale = stats.loguniform.fit(rvs, fscale=2, method=method)
+        assert scale == 2
+
+    def test_overflow(self):
+        # original formulation had overflow issues; check that this is resolved
+        # Extensive accuracy tests elsewhere, no need to test all methods
+        rng = np.random.default_rng(7136519550773909093)
+        a, b = 1e-200, 1e200
+        dist = stats.loguniform(a, b)
+
+        # test roundtrip error
+        cdf = rng.uniform(0, 1, size=1000)
+        assert_allclose(dist.cdf(dist.ppf(cdf)), cdf)
+        rvs = dist.rvs(size=1000, random_state=rng)
+        assert_allclose(dist.ppf(dist.cdf(rvs)), rvs)
+
+        # test a property of the pdf (and that there is no overflow)
+        x = 10.**np.arange(-200, 200)
+        pdf = dist.pdf(x)  # no overflow
+        assert_allclose(pdf[:-1]/pdf[1:], 10)
+
+        # check munp against wikipedia reference
+        mean = (b - a)/(np.log(b) - np.log(a))
+        assert_allclose(dist.mean(), mean)
+
+
+class TestArgus:
+    def test_argus_rvs_large_chi(self):
+        # test that the algorithm can handle large values of chi
+        x = stats.argus.rvs(50, size=500, random_state=325)
+        assert_almost_equal(stats.argus(50).mean(), x.mean(), decimal=4)
+
+    @pytest.mark.parametrize('chi, random_state', [
+            [0.1, 325],   # chi <= 0.5: rejection method case 1
+            [1.3, 155],   # 0.5 < chi <= 1.8: rejection method case 2
+            [3.5, 135]    # chi > 1.8: transform conditional Gamma distribution
+        ])
+    def test_rvs(self, chi, random_state):
+        x = stats.argus.rvs(chi, size=500, random_state=random_state)
+        _, p = stats.kstest(x, "argus", (chi, ))
+        assert_(p > 0.05)
+
+    @pytest.mark.parametrize('chi', [1e-9, 1e-6])
+    def test_rvs_small_chi(self, chi):
+        # test for gh-11699 => rejection method case 1 can even handle chi=0
+        # the CDF of the distribution for chi=0 is 1 - (1 - x**2)**(3/2)
+        # test rvs against distribution of limit chi=0
+        r = stats.argus.rvs(chi, size=500, random_state=890981)
+        _, p = stats.kstest(r, lambda x: 1 - (1 - x**2)**(3/2))
+        assert_(p > 0.05)
+
+    # Expected values were computed with mpmath.
+    @pytest.mark.parametrize('chi, expected_mean',
+                             [(1, 0.6187026683551835),
+                              (10, 0.984805536783744),
+                              (40, 0.9990617659702923),
+                              (60, 0.9995831885165300),
+                              (99, 0.9998469348663028)])
+    def test_mean(self, chi, expected_mean):
+        m = stats.argus.mean(chi, scale=1)
+        assert_allclose(m, expected_mean, rtol=1e-13)
+
+    # Expected values were computed with mpmath.
+    @pytest.mark.parametrize('chi, expected_var, rtol',
+                             [(1, 0.05215651254197807, 1e-13),
+                              (10, 0.00015805472008165595, 1e-11),
+                              (40, 5.877763210262901e-07, 1e-8),
+                              (60, 1.1590179389611416e-07, 1e-8),
+                              (99, 1.5623277006064666e-08, 1e-8)])
+    def test_var(self, chi, expected_var, rtol):
+        v = stats.argus.var(chi, scale=1)
+        assert_allclose(v, expected_var, rtol=rtol)
+
+    # Expected values were computed with mpmath (code: see gh-13370).
+    @pytest.mark.parametrize('chi, expected, rtol',
+                             [(0.9, 0.07646314974436118, 1e-14),
+                              (0.5, 0.015429797891863365, 1e-14),
+                              (0.1, 0.0001325825293278049, 1e-14),
+                              (0.01, 1.3297677078224565e-07, 1e-15),
+                              (1e-3, 1.3298072023958999e-10, 1e-14),
+                              (1e-4, 1.3298075973486862e-13, 1e-14),
+                              (1e-6, 1.32980760133771e-19, 1e-14),
+                              (1e-9, 1.329807601338109e-28, 1e-15)])
+    def test_argus_phi_small_chi(self, chi, expected, rtol):
+        assert_allclose(_argus_phi(chi), expected, rtol=rtol)
+
+    # Expected values were computed with mpmath (code: see gh-13370).
+    @pytest.mark.parametrize(
+        'chi, expected',
+        [(0.5, (0.28414073302940573, 1.2742227939992954, 1.2381254688255896)),
+         (0.2, (0.296172952995264, 1.2951290588110516, 1.1865767100877576)),
+         (0.1, (0.29791447523536274, 1.29806307956989, 1.1793168289857412)),
+         (0.01, (0.2984904104866452, 1.2990283628160553, 1.1769268414080531)),
+         (1e-3, (0.298496172925224, 1.2990380082487925, 1.176902956021053)),
+         (1e-4, (0.29849623054991836, 1.2990381047023793, 1.1769027171686324)),
+         (1e-6, (0.2984962311319278, 1.2990381056765605, 1.1769027147562232)),
+         (1e-9, (0.298496231131986, 1.299038105676658, 1.1769027147559818))])
+    def test_pdf_small_chi(self, chi, expected):
+        x = np.array([0.1, 0.5, 0.9])
+        assert_allclose(stats.argus.pdf(x, chi), expected, rtol=1e-13)
+
+    # Expected values were computed with mpmath (code: see gh-13370).
+    @pytest.mark.parametrize(
+        'chi, expected',
+        [(0.5, (0.9857660526895221, 0.6616565930168475, 0.08796070398429937)),
+         (0.2, (0.9851555052359501, 0.6514666238985464, 0.08362690023746594)),
+         (0.1, (0.9850670974995661, 0.6500061310508574, 0.08302050640683846)),
+         (0.01, (0.9850378582451867, 0.6495239242251358, 0.08282109244852445)),
+         (1e-3, (0.9850375656906663, 0.6495191015522573, 0.08281910005231098)),
+         (1e-4, (0.9850375627651049, 0.6495190533254682, 0.08281908012852317)),
+         (1e-6, (0.9850375627355568, 0.6495190528383777, 0.08281907992729293)),
+         (1e-9, (0.9850375627355538, 0.649519052838329, 0.0828190799272728))])
+    def test_sf_small_chi(self, chi, expected):
+        x = np.array([0.1, 0.5, 0.9])
+        assert_allclose(stats.argus.sf(x, chi), expected, rtol=1e-14)
+
+    # Expected values were computed with mpmath.
+    @pytest.mark.parametrize(
+        'x, chi, expected',
+        [(0.9999999, 0.25, 9.113252974162428e-11),
+         (0.9999999, 3.0, 6.616650419714568e-10),
+         (0.999999999, 2.5, 4.130195911418939e-13),
+         (0.999999999, 10.0, 2.3788319094393724e-11)])
+    def test_sf_near_1(self, x, chi, expected):
+        sf = stats.argus.sf(x, chi)
+        assert_allclose(sf, expected, rtol=5e-15)
+
+    # Expected values were computed with mpmath (code: see gh-13370).
+    @pytest.mark.parametrize(
+        'chi, expected',
+        [(0.5, (0.0142339473104779, 0.3383434069831524, 0.9120392960157007)),
+         (0.2, (0.014844494764049919, 0.34853337610145363, 0.916373099762534)),
+         (0.1, (0.014932902500433911, 0.34999386894914264, 0.9169794935931616)),
+         (0.01, (0.014962141754813293, 0.35047607577486417, 0.9171789075514756)),
+         (1e-3, (0.01496243430933372, 0.35048089844774266, 0.917180899947689)),
+         (1e-4, (0.014962437234895118, 0.3504809466745317, 0.9171809198714769)),
+         (1e-6, (0.01496243726444329, 0.3504809471616223, 0.9171809200727071)),
+         (1e-9, (0.014962437264446245, 0.350480947161671, 0.9171809200727272))])
+    def test_cdf_small_chi(self, chi, expected):
+        x = np.array([0.1, 0.5, 0.9])
+        assert_allclose(stats.argus.cdf(x, chi), expected, rtol=1e-12)
+
+    # Expected values were computed with mpmath (code: see gh-13370).
+    @pytest.mark.parametrize(
+        'chi, expected, rtol',
+        [(0.5, (0.5964284712757741, 0.052890651988588604), 1e-12),
+         (0.101, (0.5893490968089076, 0.053017469847275685), 1e-11),
+         (0.1, (0.5893431757009437, 0.05301755449499372), 1e-13),
+         (0.01, (0.5890515677940915, 0.05302167905837031), 1e-13),
+         (1e-3, (0.5890486520005177, 0.053021719862088104), 1e-13),
+         (1e-4, (0.5890486228426105, 0.0530217202700811), 1e-13),
+         (1e-6, (0.5890486225481156, 0.05302172027420182), 1e-13),
+         (1e-9, (0.5890486225480862, 0.05302172027420224), 1e-13)])
+    def test_stats_small_chi(self, chi, expected, rtol):
+        val = stats.argus.stats(chi, moments='mv')
+        assert_allclose(val, expected, rtol=rtol)
+
+
+class TestNakagami:
+    def setup_method(self):
+        self.rng = np.random.default_rng(9626839526)
+
+    def test_logpdf(self):
+        # Test nakagami logpdf for an input where the PDF is smaller
+        # than can be represented with 64 bit floating point.
+        # The expected value of logpdf was computed with mpmath:
+        #
+        #   def logpdf(x, nu):
+        #       x = mpmath.mpf(x)
+        #       nu = mpmath.mpf(nu)
+        #       return (mpmath.log(2) + nu*mpmath.log(nu) -
+        #               mpmath.loggamma(nu) + (2*nu - 1)*mpmath.log(x) -
+        #               nu*x**2)
+        #
+        nu = 2.5
+        x = 25
+        logp = stats.nakagami.logpdf(x, nu)
+        assert_allclose(logp, -1546.9253055607549)
+
+    def test_sf_isf(self):
+        # Test nakagami sf and isf when the survival function
+        # value is very small.
+        # The expected value of the survival function was computed
+        # with mpmath:
+        #
+        #   def sf(x, nu):
+        #       x = mpmath.mpf(x)
+        #       nu = mpmath.mpf(nu)
+        #       return mpmath.gammainc(nu, nu*x*x, regularized=True)
+        #
+        nu = 2.5
+        x0 = 5.0
+        sf = stats.nakagami.sf(x0, nu)
+        assert_allclose(sf, 2.736273158588307e-25, rtol=1e-13)
+        # Check round trip back to x0.
+        x1 = stats.nakagami.isf(sf, nu)
+        assert_allclose(x1, x0, rtol=1e-13)
+
+    def test_logcdf(self):
+        x = 8
+        nu = 0.5
+        # Reference value computed with mpmath.
+        ref = -1.2441921148543576e-15
+        logcdf = stats.nakagami.logcdf(x, nu)
+        assert_allclose(logcdf, ref, rtol=5e-15)
+
+    def test_logsf(self):
+        x = 0.05
+        nu = 12
+        # Reference value computed with mpmath.
+        ref = -1.0791764722337046e-27
+        logsf = stats.nakagami.logsf(x, nu)
+        assert_allclose(logsf, ref, rtol=5e-15)
+
+    @pytest.mark.parametrize("m, ref",
+        [(5, -0.097341814372152),
+         (0.5, 0.7257913526447274),
+         (10, -0.43426184310934907)])
+    def test_entropy(self, m, ref):
+        # from sympy import *
+        # from mpmath import mp
+        # import numpy as np
+        # v, x = symbols('v, x', real=True, positive=True)
+        # pdf = 2 * v ** v / gamma(v) * x ** (2 * v - 1) * exp(-v * x ** 2)
+        # h = simplify(simplify(integrate(-pdf * log(pdf), (x, 0, oo))))
+        # entropy = lambdify(v, h, 'mpmath')
+        # mp.dps = 200
+        # nu = 5
+        # ref = np.float64(entropy(mp.mpf(nu)))
+        # print(ref)
+        assert_allclose(stats.nakagami.entropy(m), ref, rtol=1.1e-14)
+
+    @pytest.mark.parametrize("m, ref",
+        [(1e-100, -5.0e+99), (1e-10, -4999999965.442979),
+         (9.999e6, -7.333206478668433), (1.001e7, -7.3337562313259825),
+         (1e10, -10.787134112333835), (1e100, -114.40346329705756)])
+    def test_extreme_nu(self, m, ref):
+        assert_allclose(stats.nakagami.entropy(m), ref)
+
+    def test_entropy_overflow(self):
+        assert np.isfinite(stats.nakagami._entropy(1e100))
+        assert np.isfinite(stats.nakagami._entropy(1e-100))
+
+    @pytest.mark.parametrize("nu, ref",
+                             [(1e10, 0.9999999999875),
+                              (1e3, 0.9998750078173821),
+                              (1e-10, 1.772453850659802e-05)])
+    def test_mean(self, nu, ref):
+        # reference values were computed with mpmath
+        # from mpmath import mp
+        # mp.dps = 500
+        # nu = mp.mpf(1e10)
+        # float(mp.rf(nu, mp.mpf(0.5))/mp.sqrt(nu))
+        assert_allclose(stats.nakagami.mean(nu), ref, rtol=1e-12)
+
+    @pytest.mark.xfail(reason="Fit of nakagami not reliable, see gh-10908.")
+    @pytest.mark.parametrize('nu', [1.6, 2.5, 3.9])
+    @pytest.mark.parametrize('loc', [25.0, 10, 35])
+    @pytest.mark.parametrize('scale', [13, 5, 20])
+    def test_fit(self, nu, loc, scale):
+        # Regression test for gh-13396 (21/27 cases failed previously)
+        # The first tuple of the parameters' values is discussed in gh-10908
+        N = 100
+        samples = stats.nakagami.rvs(size=N, nu=nu, loc=loc,
+                                     scale=scale, random_state=self.rng)
+        nu_est, loc_est, scale_est = stats.nakagami.fit(samples)
+        assert_allclose(nu_est, nu, rtol=0.2)
+        assert_allclose(loc_est, loc, rtol=0.2)
+        assert_allclose(scale_est, scale, rtol=0.2)
+
+        def dlogl_dnu(nu, loc, scale):
+            return ((-2*nu + 1) * np.sum(1/(samples - loc))
+                    + 2*nu/scale**2 * np.sum(samples - loc))
+
+        def dlogl_dloc(nu, loc, scale):
+            return (N * (1 + np.log(nu) - polygamma(0, nu)) +
+                    2 * np.sum(np.log((samples - loc) / scale))
+                    - np.sum(((samples - loc) / scale)**2))
+
+        def dlogl_dscale(nu, loc, scale):
+            return (- 2 * N * nu / scale
+                    + 2 * nu / scale ** 3 * np.sum((samples - loc) ** 2))
+
+        assert_allclose(dlogl_dnu(nu_est, loc_est, scale_est), 0, atol=1e-3)
+        assert_allclose(dlogl_dloc(nu_est, loc_est, scale_est), 0, atol=1e-3)
+        assert_allclose(dlogl_dscale(nu_est, loc_est, scale_est), 0, atol=1e-3)
+
+    @pytest.mark.parametrize('loc', [25.0, 10, 35])
+    @pytest.mark.parametrize('scale', [13, 5, 20])
+    def test_fit_nu(self, loc, scale):
+        # For nu = 0.5, we have analytical values for
+        # the MLE of the loc and the scale
+        nu = 0.5
+        n = 100
+        samples = stats.nakagami.rvs(size=n, nu=nu, loc=loc,
+                                     scale=scale, random_state=self.rng)
+        nu_est, loc_est, scale_est = stats.nakagami.fit(samples, f0=nu)
+
+        # Analytical values
+        loc_theo = np.min(samples)
+        scale_theo = np.sqrt(np.mean((samples - loc_est) ** 2))
+
+        assert_allclose(nu_est, nu, rtol=1e-7)
+        assert_allclose(loc_est, loc_theo, rtol=1e-7)
+        assert_allclose(scale_est, scale_theo, rtol=1e-7)
+
+
+class TestWrapCauchy:
+    def setup_method(self):
+        self.rng = np.random.default_rng(2439107123)
+
+    def test_cdf_shape_broadcasting(self):
+        # Regression test for gh-13791.
+        # Check that wrapcauchy.cdf broadcasts the shape parameter
+        # correctly.
+        c = np.array([[0.03, 0.25], [0.5, 0.75]])
+        x = np.array([[1.0], [4.0]])
+        p = stats.wrapcauchy.cdf(x, c)
+        assert p.shape == (2, 2)
+        scalar_values = [stats.wrapcauchy.cdf(x1, c1)
+                         for (x1, c1) in np.nditer((x, c))]
+        assert_allclose(p.ravel(), scalar_values, rtol=1e-13)
+
+    def test_cdf_center(self):
+        p = stats.wrapcauchy.cdf(np.pi, 0.03)
+        assert_allclose(p, 0.5, rtol=1e-14)
+
+    def test_cdf(self):
+        x1 = 1.0  # less than pi
+        x2 = 4.0  # greater than pi
+        c = 0.75
+        p = stats.wrapcauchy.cdf([x1, x2], c)
+        cr = (1 + c)/(1 - c)
+        assert_allclose(p[0], np.arctan(cr*np.tan(x1/2))/np.pi)
+        assert_allclose(p[1], 1 - np.arctan(cr*np.tan(np.pi - x2/2))/np.pi)
+
+    @pytest.mark.parametrize('c', [1e-10, 1e-1])
+    @pytest.mark.parametrize('loc', [-100, -2*np.pi, -np.pi, 0, np.pi, 2*np.pi, 100])
+    @pytest.mark.parametrize('scale', [1e-10, 1, 1e10])
+    def test_rvs_lie_on_circle(self, c, loc, scale):
+        # Check that the random variates lie in range [0, 2*pi]
+        x = stats.wrapcauchy.rvs(c=c, loc=loc, scale=scale,
+                                 size=1000, random_state=self.rng)
+        assert np.all(x >= 0)
+        assert np.all(x <= 2 * np.pi)
+
+
+def test_rvs_no_size_error():
+    # _rvs methods must have parameter `size`; see gh-11394
+    class rvs_no_size_gen(stats.rv_continuous):
+        def _rvs(self):
+            return 1
+
+    rvs_no_size = rvs_no_size_gen(name='rvs_no_size')
+    rng = np.random.default_rng(1334886239)
+    with assert_raises(TypeError, match=r"_rvs\(\) got (an|\d) unexpected"):
+        rvs_no_size.rvs(random_state=rng)
+
+
+@pytest.mark.parametrize('distname, args', invdistdiscrete + invdistcont)
+def test_support_gh13294_regression(distname, args):
+    if distname in skip_test_support_gh13294_regression:
+        pytest.skip(f"skipping test for the support method for "
+                    f"distribution {distname}.")
+    dist = getattr(stats, distname)
+    # test support method with invalid arguments
+    if isinstance(dist, stats.rv_continuous):
+        # test with valid scale
+        if len(args) != 0:
+            a0, b0 = dist.support(*args)
+            assert_equal(a0, np.nan)
+            assert_equal(b0, np.nan)
+        # test with invalid scale
+        # For some distributions, that take no parameters,
+        # the case of only invalid scale occurs and hence,
+        # it is implicitly tested in this test case.
+        loc1, scale1 = 0, -1
+        a1, b1 = dist.support(*args, loc1, scale1)
+        assert_equal(a1, np.nan)
+        assert_equal(b1, np.nan)
+    else:
+        a, b = dist.support(*args)
+        assert_equal(a, np.nan)
+        assert_equal(b, np.nan)
+
+
+def test_support_broadcasting_gh13294_regression():
+    a0, b0 = stats.norm.support([0, 0, 0, 1], [1, 1, 1, -1])
+    ex_a0 = np.array([-np.inf, -np.inf, -np.inf, np.nan])
+    ex_b0 = np.array([np.inf, np.inf, np.inf, np.nan])
+    assert_equal(a0, ex_a0)
+    assert_equal(b0, ex_b0)
+    assert a0.shape == ex_a0.shape
+    assert b0.shape == ex_b0.shape
+
+    a1, b1 = stats.norm.support([], [])
+    ex_a1, ex_b1 = np.array([]), np.array([])
+    assert_equal(a1, ex_a1)
+    assert_equal(b1, ex_b1)
+    assert a1.shape == ex_a1.shape
+    assert b1.shape == ex_b1.shape
+
+    a2, b2 = stats.norm.support([0, 0, 0, 1], [-1])
+    ex_a2 = np.array(4*[np.nan])
+    ex_b2 = np.array(4*[np.nan])
+    assert_equal(a2, ex_a2)
+    assert_equal(b2, ex_b2)
+    assert a2.shape == ex_a2.shape
+    assert b2.shape == ex_b2.shape
+
+
+def test_stats_broadcasting_gh14953_regression():
+    # test case in gh14953
+    loc = [0., 0.]
+    scale = [[1.], [2.], [3.]]
+    assert_equal(stats.norm.var(loc, scale), [[1., 1.], [4., 4.], [9., 9.]])
+    # test some edge cases
+    loc = np.empty((0, ))
+    scale = np.empty((1, 0))
+    assert stats.norm.var(loc, scale).shape == (1, 0)
+
+
+# Check a few values of the cosine distribution's cdf, sf, ppf and
+# isf methods.  Expected values were computed with mpmath.
+
+@pytest.mark.parametrize('x, expected',
+                         [(-3.14159, 4.956444476505336e-19),
+                          (3.14, 0.9999999998928399)])
+def test_cosine_cdf_sf(x, expected):
+    assert_allclose(stats.cosine.cdf(x), expected)
+    assert_allclose(stats.cosine.sf(-x), expected)
+
+
+@pytest.mark.parametrize('p, expected',
+                         [(1e-6, -3.1080612413765905),
+                          (1e-17, -3.141585429601399),
+                          (0.975, 2.1447547020964923)])
+def test_cosine_ppf_isf(p, expected):
+    assert_allclose(stats.cosine.ppf(p), expected)
+    assert_allclose(stats.cosine.isf(p), -expected)
+
+
+def test_cosine_logpdf_endpoints():
+    logp = stats.cosine.logpdf([-np.pi, np.pi])
+    # reference value calculated using mpmath assuming `np.cos(-1)` is four
+    # floating point numbers too high. See gh-18382.
+    assert_array_less(logp, -37.18838327496655)
+
+
+def test_distr_params_lists():
+    # distribution objects are extra distributions added in
+    # test_discrete_basic. All other distributions are strings (names)
+    # and so we only choose those to compare whether both lists match.
+    discrete_distnames = {name for name, _ in distdiscrete
+                          if isinstance(name, str)}
+    invdiscrete_distnames = {name for name, _ in invdistdiscrete}
+    assert discrete_distnames == invdiscrete_distnames
+
+    cont_distnames = {name for name, _ in distcont}
+    invcont_distnames = {name for name, _ in invdistcont}
+    assert cont_distnames == invcont_distnames
+
+
+def test_moment_order_4():
+    # gh-13655 reported that if a distribution has a `_stats` method that
+    # accepts the `moments` parameter, then if the distribution's `moment`
+    # method is called with `order=4`, the faster/more accurate`_stats` gets
+    # called, but the results aren't used, and the generic `_munp` method is
+    # called to calculate the moment anyway. This tests that the issue has
+    # been fixed.
+    # stats.skewnorm._stats accepts the `moments` keyword
+    stats.skewnorm._stats(a=0, moments='k')  # no failure = has `moments`
+    # When `moment` is called, `_stats` is used, so the moment is very accurate
+    # (exactly equal to Pearson's kurtosis of the normal distribution, 3)
+    assert stats.skewnorm.moment(order=4, a=0) == 3.0
+    # At the time of gh-13655, skewnorm._munp() used the generic method
+    # to compute its result, which was inefficient and not very accurate.
+    # At that time, the following assertion would fail.  skewnorm._munp()
+    # has since been made more accurate and efficient, so now this test
+    # is expected to pass.
+    assert stats.skewnorm._munp(4, 0) == 3.0
+
+
+class TestRelativisticBW:
+    @pytest.fixture
+    def ROOT_pdf_sample_data(self):
+        """Sample data points for pdf computed with CERN's ROOT
+
+        See - https://root.cern/
+
+        Uses ROOT.TMath.BreitWignerRelativistic, available in ROOT
+        versions 6.27+
+
+        pdf calculated for Z0 Boson, W Boson, and Higgs Boson for
+        x in `np.linspace(0, 200, 401)`.
+        """
+        data = np.load(
+            Path(__file__).parent /
+            'data/rel_breitwigner_pdf_sample_data_ROOT.npy'
+        )
+        data = np.rec.fromarrays(data.T, names='x,pdf,rho,gamma')
+        return data
+
+    @pytest.mark.parametrize(
+        "rho,gamma,rtol", [
+            (36.545206797050334, 2.4952, 5e-14),  # Z0 Boson
+            (38.55107913669065, 2.085, 1e-14),  # W Boson
+            (96292.3076923077, 0.0013, 5e-13),  # Higgs Boson
+        ]
+    )
+    def test_pdf_against_ROOT(self, ROOT_pdf_sample_data, rho, gamma, rtol):
+        data = ROOT_pdf_sample_data[
+            (ROOT_pdf_sample_data['rho'] == rho)
+            & (ROOT_pdf_sample_data['gamma'] == gamma)
+        ]
+        x, pdf = data['x'], data['pdf']
+        assert_allclose(
+            pdf, stats.rel_breitwigner.pdf(x, rho, scale=gamma), rtol=rtol
+        )
+
+    @pytest.mark.parametrize("rho, Gamma, rtol", [
+              (36.545206797050334, 2.4952, 5e-13),  # Z0 Boson
+              (38.55107913669065, 2.085, 5e-13),  # W Boson
+              (96292.3076923077, 0.0013, 5e-10),  # Higgs Boson
+          ]
+      )
+    def test_pdf_against_simple_implementation(self, rho, Gamma, rtol):
+        # reference implementation straight from formulas on Wikipedia [1]
+        def pdf(E, M, Gamma):
+            gamma = np.sqrt(M**2 * (M**2 + Gamma**2))
+            k = (2 * np.sqrt(2) * M * Gamma * gamma
+                 / (np.pi * np.sqrt(M**2 + gamma)))
+            return k / ((E**2 - M**2)**2 + M**2*Gamma**2)
+        # get reasonable values at which to evaluate the CDF
+        p = np.linspace(0.05, 0.95, 10)
+        x = stats.rel_breitwigner.ppf(p, rho, scale=Gamma)
+        res = stats.rel_breitwigner.pdf(x, rho, scale=Gamma)
+        ref = pdf(x, rho*Gamma, Gamma)
+        assert_allclose(res, ref, rtol=rtol)
+
+    @pytest.mark.xslow
+    @pytest.mark.parametrize(
+        "rho,gamma", [
+            pytest.param(
+                36.545206797050334, 2.4952, marks=pytest.mark.slow
+            ),  # Z0 Boson
+            pytest.param(
+                38.55107913669065, 2.085, marks=pytest.mark.xslow
+            ),  # W Boson
+            pytest.param(
+                96292.3076923077, 0.0013, marks=pytest.mark.xslow
+            ),  # Higgs Boson
+        ]
+    )
+    def test_fit_floc(self, rho, gamma):
+        """Tests fit for cases where floc is set.
+
+        `rel_breitwigner` has special handling for these cases.
+        """
+        seed = 6936804688480013683
+        rng = np.random.default_rng(seed)
+        data = stats.rel_breitwigner.rvs(
+            rho, scale=gamma, size=1000, random_state=rng
+        )
+        fit = stats.rel_breitwigner.fit(data, floc=0)
+        assert_allclose((fit[0], fit[2]), (rho, gamma), rtol=2e-1)
+        assert fit[1] == 0
+        # Check again with fscale set.
+        fit = stats.rel_breitwigner.fit(data, floc=0, fscale=gamma)
+        assert_allclose(fit[0], rho, rtol=1e-2)
+        assert (fit[1], fit[2]) == (0, gamma)
+
+
+class TestJohnsonSU:
+    @pytest.mark.parametrize("case", [  # a, b, loc, scale, m1, m2, g1, g2
+            (-0.01, 1.1, 0.02, 0.0001, 0.02000137427557091,
+             2.1112742956578063e-08, 0.05989781342460999, 20.36324408592951-3),
+            (2.554395574161155, 2.2482281679651965, 0, 1, -1.54215386737391,
+             0.7629882028469993, -1.256656139406788, 6.303058419339775-3)])
+    def test_moment_gh18071(self, case):
+        # gh-18071 reported an IntegrationWarning emitted by johnsonsu.stats
+        # Check that the warning is no longer emitted and that the values
+        # are accurate compared against results from Mathematica.
+        # Reference values from Mathematica, e.g.
+        # Mean[JohnsonDistribution["SU",-0.01, 1.1, 0.02, 0.0001]]
+        res = stats.johnsonsu.stats(*case[:4], moments='mvsk')
+        assert_allclose(res, case[4:], rtol=1e-14)
+
+
+class TestTruncPareto:
+    def test_pdf(self):
+        # PDF is that of the truncated pareto distribution
+        b, c = 1.8, 5.3
+        x = np.linspace(1.8, 5.3)
+        res = stats.truncpareto(b, c).pdf(x)
+        ref = stats.pareto(b).pdf(x) / stats.pareto(b).cdf(c)
+        assert_allclose(res, ref)
+
+    def test_pdf_negative(self):
+        # truncpareto is equivalent to more general powerlaw from gh-23648
+        # exponent of truncpareto is negative in this case
+        a, xmin, xmax = 4, 3, 5
+        x = np.linspace(xmin, xmax)
+
+        # compute reference using PDF from gh-23648
+        C = a / (xmax ** a - xmin ** a)
+        ref = C * x ** (a - 1)
+
+        # compute using `truncpareto` with negative exponent
+        b = -a
+        c = xmax / xmin
+        scale = xmin
+        loc = 0
+        X = stats.truncpareto(b, c, loc, scale)
+
+        assert_allclose(X.pdf(x), ref)
+        assert_allclose(X.logpdf(x), np.log(X.pdf(x)))
+        # indexing avoids RuntimeWarning with `np.log(0)`
+        assert_allclose(X.logcdf(x[1:]), np.log(X.cdf(x[1:])))
+        assert_allclose(X.logsf(x[:-1]), np.log(X.sf(x[:-1])))
+
+    @pytest.mark.parametrize('fix_loc', [True, False])
+    @pytest.mark.parametrize('fix_scale', [True, False])
+    @pytest.mark.parametrize('fix_b', [True, False])
+    @pytest.mark.parametrize('fix_c', [True, False])
+    def test_fit(self, fix_loc, fix_scale, fix_b, fix_c):
+
+        rng = np.random.default_rng(6747363148258237171)
+        b, c, loc, scale = 1.8, 5.3, 1, 2.5
+        dist = stats.truncpareto(b, c, loc=loc, scale=scale)
+        data = dist.rvs(size=500, random_state=rng)
+
+        kwds = {}
+        if fix_loc:
+            kwds['floc'] = loc
+        if fix_scale:
+            kwds['fscale'] = scale
+        if fix_b:
+            kwds['f0'] = b
+        if fix_c:
+            kwds['f1'] = c
+
+        if fix_loc and fix_scale and fix_b and fix_c:
+            message = "All parameters fixed. There is nothing to optimize."
+            with pytest.raises(RuntimeError, match=message):
+                stats.truncpareto.fit(data, **kwds)
+        else:
+            _assert_less_or_close_loglike(stats.truncpareto, data, **kwds)
+
+
+class TestKappa3:
+    def test_sf(self):
+        # During development of gh-18822, we found that the override of
+        # kappa3.sf could experience overflow where the version in main did
+        # not. Check that this does not happen in final implementation.
+        sf0 = 1 - stats.kappa3.cdf(0.5, 1e5)
+        sf1 = stats.kappa3.sf(0.5, 1e5)
+        assert_allclose(sf1, sf0)
+
+
+class TestIrwinHall:
+    unif = stats.uniform(0, 1)
+    ih1 = stats.irwinhall(1)
+    ih10 = stats.irwinhall(10)
+
+    def test_stats_ih10(self):
+        # from Wolfram Alpha "mean variance skew kurtosis UniformSumDistribution[10]"
+        # W|A uses Pearson's definition of kurtosis so subtract 3
+        # should be exact integer division converted to fp64, without any further ops
+        assert_array_max_ulp(self.ih10.stats('mvsk'), (5, 10/12, 0, -3/25))
+
+    def test_moments_ih10(self):
+        # from Wolfram Alpha "values moments UniformSumDistribution[10]"
+        # algo should use integer division converted to fp64, without any further ops
+        # so these should be precise to the ulpm if not exact
+        vals = [5, 155 / 6, 275 / 2, 752, 12650 / 3,
+                677465 / 28, 567325 / 4,
+                15266213 / 18, 10333565 / 2]
+        moments = [self.ih10.moment(n+1) for n in range(len(vals))]
+        assert_array_max_ulp(moments, vals)
+        # also from Wolfram Alpha "50th moment UniformSumDistribution[10]"
+        m50 = self.ih10.moment(50)
+        m50_exact = 17453002755350010529309685557285098151740985685/4862
+        assert_array_max_ulp(m50, m50_exact)
+
+    def test_pdf_ih1_unif(self):
+        # IH(1) PDF is by definition U(0,1)
+        # we should be too, but differences in floating point eval order happen
+        # it's unclear if we can get down to the single ulp for doubles unless
+        # quads are used we're within 6-10 ulps otherwise (across sf/cdf/pdf)
+        # which is pretty good
+
+        pts = np.linspace(0, 1, 100)
+        pdf_unif = self.unif.pdf(pts)
+        pdf_ih1 = self.ih1.pdf(pts)
+        assert_array_max_ulp(pdf_ih1, pdf_unif, maxulp=10)
+
+    def test_pdf_ih2_triangle(self):
+        # IH(2) PDF is a triangle
+        ih2 = stats.irwinhall(2)
+        npts = 101
+        pts = np.linspace(0, 2, npts)
+        expected = np.linspace(0, 2, npts)
+        expected[(npts + 1) // 2:] = 2 - expected[(npts + 1) // 2:]
+        pdf_ih2 = ih2.pdf(pts)
+        assert_array_max_ulp(pdf_ih2, expected, maxulp=10)
+
+    def test_cdf_ih1_unif(self):
+        # CDF of IH(1) should be identical to uniform
+        pts = np.linspace(0, 1, 100)
+        cdf_unif = self.unif.cdf(pts)
+        cdf_ih1 = self.ih1.cdf(pts)
+
+        assert_array_max_ulp(cdf_ih1, cdf_unif, maxulp=10)
+
+    def test_cdf(self):
+        # CDF of IH is symmetric so CDF should be 0.5 at n/2
+        n = np.arange(1, 10)
+        ih = stats.irwinhall(n)
+        ih_cdf = ih.cdf(n / 2)
+        exact = np.repeat(1/2, len(n))
+        # should be identically 1/2 but fp order of eval differences happen
+        assert_array_max_ulp(ih_cdf, exact, maxulp=10)
+
+    def test_cdf_ih10_exact(self):
+        # from Wolfram Alpha "values CDF[UniformSumDistribution[10], x] x=0 to x=10"
+        # symmetric about n/2, i.e., cdf[n-x] = 1-cdf[x] = sf[x]
+        vals = [0, 1 / 3628800, 169 / 604800, 24427 / 1814400,
+                  252023 / 1814400, 1 / 2, 1562377 / 1814400,
+                  1789973 / 1814400, 604631 / 604800,
+                  3628799 / 3628800, 1]
+
+        # essentially a test of bspline evaluation
+        # this and the other ones are mostly to detect regressions
+        assert_array_max_ulp(self.ih10.cdf(np.arange(11)), vals, maxulp=10)
+
+        assert_array_max_ulp(self.ih10.cdf(1/10), 1/36288000000000000, maxulp=10)
+        ref = 36287999999999999/36288000000000000
+        assert_array_max_ulp(self.ih10.cdf(99/10), ref, maxulp=10)
+
+    def test_pdf_ih10_exact(self):
+        # from Wolfram Alpha "values PDF[UniformSumDistribution[10], x] x=0 to x=10"
+        # symmetric about n/2 = 5
+        vals = [0, 1 / 362880, 251 / 181440, 913 / 22680, 44117 / 181440]
+        vals += [15619 / 36288] + vals[::-1]
+        assert_array_max_ulp(self.ih10.pdf(np.arange(11)), vals, maxulp=10)
+
+    def test_sf_ih10_exact(self):
+        assert_allclose(self.ih10.sf(np.arange(11)), 1 - self.ih10.cdf(np.arange(11)))
+        # from Wolfram Alpha "SurvivalFunction[UniformSumDistribution[10],x] at x=1/10"
+        # and symmetry about n/2 = 5
+        # W|A returns 1 for CDF @ x=9.9
+        ref = 36287999999999999/36288000000000000
+        assert_array_max_ulp(self.ih10.sf(1/10), ref, maxulp=10)
+
+
+class TestDParetoLognorm:
+    def test_against_R(self):
+        # Test against R implementation in `distributionsrd`
+        # library(distributionsrd)
+        # options(digits=16)
+        # x = 1.1
+        # b = 2
+        # a = 1.5
+        # m = 3
+        # s = 1.2
+        # ddoubleparetolognormal(x, b, a, m, s)
+        # pdoubleparetolognormal(x, b, a, m, s)
+        x, m, s, a, b = 1.1, 3, 1.2, 1.5, 2
+        dist = stats.dpareto_lognorm(m, s, a, b)
+        np.testing.assert_allclose(dist.pdf(x), 0.02490187219085912)
+        np.testing.assert_allclose(dist.cdf(x), 0.01664024173822796)
+
+
+# Cases are (distribution name, log10 of smallest probability mass to test,
+# log10 of the complement of the largest probability mass to test, atol,
+# rtol). None uses default values.
+@pytest.mark.parametrize("case", [("kappa3", None, None, None, None),
+                                  ("loglaplace", None, None, None, None),
+                                  ("lognorm", None, None, None, None),
+                                  ("lomax", None, None, None, None),
+                                  ("pareto", None, None, None, None),])
+def test_sf_isf_overrides(case):
+    # Test that SF is the inverse of ISF. Supplements
+    # `test_continuous_basic.check_sf_isf` for distributions with overridden
+    # `sf` and `isf` methods.
+    distname, lp1, lp2, atol, rtol = case
+
+    lpm = np.log10(0.5)  # log10 of the probability mass at the median
+    lp1 = lp1 or -290
+    lp2 = lp2 or -14
+    atol = atol or 0
+    rtol = rtol or 1e-12
+    dist = getattr(stats, distname)
+    params = dict(distcont)[distname]
+    dist_frozen = dist(*params)
+
+    # Test (very deep) right tail to median. We can benchmark with random
+    # (loguniform) points, but strictly logspaced points are fine for tests.
+    ref = np.logspace(lp1, lpm)
+    res = dist_frozen.sf(dist_frozen.isf(ref))
+    assert_allclose(res, ref, atol=atol, rtol=rtol)
+
+    # test median to left tail
+    ref = 1 - np.logspace(lp2, lpm, 20)
+    res = dist_frozen.sf(dist_frozen.isf(ref))
+    assert_allclose(res, ref, atol=atol, rtol=rtol)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/test_entropy.py b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_entropy.py
new file mode 100644
index 0000000000000000000000000000000000000000..1302d21a8eedf9804176df9d9096a86b325d3558
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_entropy.py
@@ -0,0 +1,317 @@
+import math
+import pytest
+from pytest import raises as assert_raises
+
+import numpy as np
+
+from scipy import stats
+from scipy.stats import norm, expon  # type: ignore[attr-defined]
+from scipy._lib._array_api import make_xp_test_case
+from scipy._lib._array_api_no_0d import (xp_assert_close, xp_assert_equal,
+                                         xp_assert_less)
+
+lazy_xp_modules = [stats]
+skip_xp_backends = pytest.mark.skip_xp_backends
+
+@make_xp_test_case(stats.entropy)
+class TestEntropy:
+    def test_entropy_positive(self, xp):
+        # See ticket #497
+        pk = xp.asarray([0.5, 0.2, 0.3])
+        qk = xp.asarray([0.1, 0.25, 0.65])
+        eself = stats.entropy(pk, pk)
+        edouble = stats.entropy(pk, qk)
+        xp_assert_close(eself, xp.asarray(0.), atol=1e-16)
+        xp_assert_less(-edouble, xp.asarray(0.))
+
+    def test_entropy_base(self, xp):
+        pk = xp.ones(16)
+        S = stats.entropy(pk, base=2.)
+        xp_assert_less(xp.abs(S - 4.), xp.asarray(1.e-5))
+
+        qk = xp.ones(16)
+        qk = xp.where(xp.arange(16) < 8, 2., qk)
+        S = stats.entropy(pk, qk)
+        S2 = stats.entropy(pk, qk, base=2.)
+        xp_assert_less(xp.abs(S/S2 - math.log(2.)), xp.asarray(1.e-5))
+
+    def test_entropy_zero(self, xp):
+        # Test for PR-479
+        x = xp.asarray([0., 1., 2.])
+        xp_assert_close(stats.entropy(x),
+                        xp.asarray(0.63651416829481278))
+
+    def test_entropy_2d(self, xp):
+        pk = xp.asarray([[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]])
+        qk = xp.asarray([[0.2, 0.1], [0.3, 0.6], [0.5, 0.3]])
+        xp_assert_close(stats.entropy(pk, qk),
+                        xp.asarray([0.1933259, 0.18609809]))
+
+    def test_entropy_2d_zero(self, xp):
+        pk = xp.asarray([[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]])
+        qk = xp.asarray([[0.0, 0.1], [0.3, 0.6], [0.5, 0.3]])
+        xp_assert_close(stats.entropy(pk, qk),
+                        xp.asarray([xp.inf, 0.18609809]))
+
+        pk = xp.asarray([[0.0, 0.2], [0.6, 0.3], [0.3, 0.5]])
+        xp_assert_close(stats.entropy(pk, qk),
+                        xp.asarray([0.17403988, 0.18609809]))
+
+    def test_entropy_base_2d_nondefault_axis(self, xp):
+        pk = xp.asarray([[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]])
+        xp_assert_close(stats.entropy(pk, axis=1),
+                        xp.asarray([0.63651417, 0.63651417, 0.66156324]))
+
+    def test_entropy_2d_nondefault_axis(self, xp):
+        pk = xp.asarray([[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]])
+        qk = xp.asarray([[0.2, 0.1], [0.3, 0.6], [0.5, 0.3]])
+        xp_assert_close(stats.entropy(pk, qk, axis=1),
+                        xp.asarray([0.23104906, 0.23104906, 0.12770641]))
+
+    def test_entropy_raises_value_error(self, xp):
+        pk = xp.asarray([[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]])
+        qk = xp.asarray([[0.1, 0.2], [0.6, 0.3]])
+        message = "Array shapes are incompatible for broadcasting."
+        with pytest.raises(ValueError, match=message):
+            stats.entropy(pk, qk)
+
+    def test_base_entropy_with_axis_0_is_equal_to_default(self, xp):
+        pk = xp.asarray([[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]])
+        xp_assert_close(stats.entropy(pk, axis=0),
+                        stats.entropy(pk))
+
+    def test_entropy_with_axis_0_is_equal_to_default(self, xp):
+        pk = xp.asarray([[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]])
+        qk = xp.asarray([[0.2, 0.1], [0.3, 0.6], [0.5, 0.3]])
+        xp_assert_close(stats.entropy(pk, qk, axis=0),
+                        stats.entropy(pk, qk))
+
+    def test_base_entropy_transposed(self, xp):
+        pk = xp.asarray([[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]])
+        xp_assert_close(stats.entropy(pk.T),
+                        stats.entropy(pk, axis=1))
+
+    def test_entropy_transposed(self, xp):
+        pk = xp.asarray([[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]])
+        qk = xp.asarray([[0.2, 0.1], [0.3, 0.6], [0.5, 0.3]])
+        xp_assert_close(stats.entropy(pk.T, qk.T),
+                        stats.entropy(pk, qk, axis=1))
+
+    def test_entropy_broadcasting(self, xp):
+        rng = np.random.default_rng(74187315492831452)
+        x = xp.asarray(rng.random(3))
+        y = xp.asarray(rng.random((2, 1)))
+        res = stats.entropy(x, y, axis=-1)
+        xp_assert_close(res[0], stats.entropy(x, y[0, ...]))
+        xp_assert_close(res[1], stats.entropy(x, y[1, ...]))
+
+    def test_entropy_shape_mismatch(self, xp):
+        x = xp.ones((10, 1, 12))
+        y = xp.ones((11, 2))
+        message = "Array shapes are incompatible for broadcasting."
+        with pytest.raises(ValueError, match=message):
+            stats.entropy(x, y)
+
+    def test_input_validation(self, xp):
+        x = xp.ones(10)
+        message = "`base` must be a positive number."
+        with pytest.raises(ValueError, match=message):
+            stats.entropy(x, base=-2)
+
+
+@make_xp_test_case(stats.differential_entropy)
+class TestDifferentialEntropy:
+    """
+    Vasicek results are compared with the R package vsgoftest.
+
+    # library(vsgoftest)
+    #
+    # samp <- c(<values>)
+    # entropy.estimate(x = samp, window = <window_length>)
+
+    """
+    methods = pytest.mark.parametrize('method', [
+        "vasicek",
+        "van es",
+        pytest.param(
+            "correa",
+            marks=[
+                skip_xp_backends("array_api_strict", reason="Invalid fancy indexing"),
+                skip_xp_backends("dask.array", reason="Invalid fancy indexing"),
+            ],
+        ),
+        "ebrahimi",
+    ])
+
+    def test_differential_entropy_vasicek(self, xp):
+
+        random_state = np.random.RandomState(0)
+        values = random_state.standard_normal(100)
+        values = xp.asarray(values.tolist())
+
+        entropy = stats.differential_entropy(values, method='vasicek')
+        xp_assert_close(entropy, xp.asarray(1.342551187000946))
+
+        entropy = stats.differential_entropy(values, window_length=1,
+                                             method='vasicek')
+        xp_assert_close(entropy, xp.asarray(1.122044177725947))
+
+        entropy = stats.differential_entropy(values, window_length=8,
+                                             method='vasicek')
+        xp_assert_close(entropy, xp.asarray(1.349401487550325))
+
+    def test_differential_entropy_vasicek_2d_nondefault_axis(self, xp):
+        random_state = np.random.RandomState(0)
+        values = random_state.standard_normal((3, 100))
+        values = xp.asarray(values.tolist())
+
+        entropy = stats.differential_entropy(values, axis=1, method='vasicek')
+        ref = xp.asarray([1.342551187000946, 1.341825903922332, 1.293774601883585])
+        xp_assert_close(entropy, ref)
+
+        entropy = stats.differential_entropy(values, axis=1, window_length=1,
+                                             method='vasicek')
+        ref = xp.asarray([1.122044177725947, 1.10294413850758, 1.129615790292772])
+        xp_assert_close(entropy, ref)
+
+        entropy = stats.differential_entropy(values, axis=1, window_length=8,
+                                             method='vasicek')
+        ref = xp.asarray([1.349401487550325, 1.338514126301301, 1.292331889365405])
+        xp_assert_close(entropy, ref)
+
+
+    def test_differential_entropy_raises_value_error(self, xp):
+        random_state = np.random.RandomState(0)
+        values = random_state.standard_normal((3, 100))
+        values = xp.asarray(values.tolist())
+
+        error_str = (
+            r"Window length \({window_length}\) must be positive and less "
+            r"than half the sample size \({sample_size}\)."
+        )
+
+        sample_size = values.shape[1]
+
+        for window_length in {-1, 0, sample_size//2, sample_size}:
+
+            formatted_error_str = error_str.format(
+                window_length=window_length,
+                sample_size=sample_size,
+            )
+
+            with assert_raises(ValueError, match=formatted_error_str):
+                stats.differential_entropy(
+                    values,
+                    window_length=window_length,
+                    axis=1,
+                )
+
+    def test_base_differential_entropy_with_axis_0_is_equal_to_default(self, xp):
+        random_state = np.random.RandomState(0)
+        values = random_state.standard_normal((100, 3))
+        values = xp.asarray(values.tolist())
+
+        entropy = stats.differential_entropy(values, axis=0)
+        default_entropy = stats.differential_entropy(values)
+        xp_assert_close(entropy, default_entropy)
+
+    def test_base_differential_entropy_transposed(self, xp):
+        random_state = np.random.RandomState(0)
+        values = random_state.standard_normal((3, 100))
+        values = xp.asarray(values.tolist())
+
+        xp_assert_close(
+            stats.differential_entropy(values.T),
+            stats.differential_entropy(values, axis=1),
+        )
+
+    def test_input_validation(self, xp):
+        x = np.ones(10)
+        x = xp.asarray(x.tolist())
+
+        message = "`base` must be a positive number or `None`."
+        with pytest.raises(ValueError, match=message):
+            stats.differential_entropy(x, base=-2)
+
+        message = "`method` must be one of..."
+        with pytest.raises(ValueError, match=message):
+            stats.differential_entropy(x, method='ekki-ekki')
+
+    def test_window_length_is_none(self, xp):
+        rng = np.random.default_rng(358923459826738562)
+        x = xp.asarray(rng.random(size=10))
+        ref = stats.differential_entropy(x)
+        res = stats.differential_entropy(x, window_length=None)
+        xp_assert_close(res, ref, rtol=0.005)
+
+    @methods
+    def test_consistency(self, method, xp):
+        # test that method is a consistent estimator
+        n = 10000 if method == 'correa' else 1000000
+        rvs = stats.norm.rvs(size=n, random_state=0)
+        rvs = xp.asarray(rvs.tolist())
+        expected = xp.asarray(float(stats.norm.entropy()))
+        res = stats.differential_entropy(rvs, method=method)
+        xp_assert_close(res, expected, rtol=0.005)
+
+    # values from differential_entropy reference [6], table 1, n=50, m=7
+    norm_rmse_std_cases = {  # method: (RMSE, STD)
+                           'vasicek': (0.198, 0.109),
+                           'van es': (0.212, 0.110),
+                           'correa': (0.135, 0.112),
+                           'ebrahimi': (0.128, 0.109)
+                           }
+
+    # values from differential_entropy reference [6], table 2, n=50, m=7
+    expon_rmse_std_cases = {  # method: (RMSE, STD)
+                            'vasicek': (0.194, 0.148),
+                            'van es': (0.179, 0.149),
+                            'correa': (0.155, 0.152),
+                            'ebrahimi': (0.151, 0.148)
+                            }
+
+    rmse_std_cases = {norm: norm_rmse_std_cases,
+                      expon: expon_rmse_std_cases}
+
+    @methods
+    @pytest.mark.parametrize('dist', [norm, expon])
+    def test_rmse_std(self, method, dist, xp):
+        # test that RMSE and standard deviation of estimators matches values
+        # given in differential_entropy reference [6]. Incidentally, also
+        # tests vectorization.
+        reps, n, m = 10000, 50, 7
+        expected = self.rmse_std_cases[dist][method]
+        rmse_expected, std_expected = xp.asarray(expected[0]), xp.asarray(expected[1])
+        rvs = dist.rvs(size=(reps, n), random_state=0)
+        rvs = xp.asarray(rvs.tolist())
+        true_entropy = xp.asarray(float(dist.entropy()))
+        res = stats.differential_entropy(rvs, window_length=m,
+                                         method=method, axis=-1)
+        xp_assert_close(xp.sqrt(xp.mean((res - true_entropy)**2)),
+                        rmse_expected, atol=0.005)
+        xp_assert_close(xp.std(res, correction=0), std_expected, atol=0.002)
+
+    @pytest.mark.parametrize('n, method', [
+        (8, 'van es'),
+        (12, 'ebrahimi'),
+        (1001, 'vasicek')
+    ])
+    def test_method_auto(self, n, method, xp):
+        rvs = stats.norm.rvs(size=(n,), random_state=0)
+        rvs = xp.asarray(rvs.tolist())
+        res1 = stats.differential_entropy(rvs)
+        res2 = stats.differential_entropy(rvs, method=method)
+        xp_assert_equal(res1, res2)
+
+    @methods
+    @pytest.mark.parametrize('dtype', [None, 'float32', 'float64'])
+    def test_dtypes_gh21192(self, method, dtype, xp):
+        # gh-21192 noted a change in the output of method='ebrahimi'
+        # with integer input. Check that the output is consistent regardless
+        # of input dtype.
+        x = [1, 1, 2, 3, 3, 4, 5, 5, 6, 7, 8, 9, 10, 11]
+        dtype_in = getattr(xp, str(dtype), None)
+        dtype_out = getattr(xp, str(dtype), xp.asarray(1.).dtype)
+        res = stats.differential_entropy(xp.asarray(x, dtype=dtype_in), method=method)
+        ref = stats.differential_entropy(xp.asarray(x, dtype=xp.float64), method=method)
+        xp_assert_close(res, xp.asarray(ref, dtype=dtype_out)[()])
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/test_fast_gen_inversion.py b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_fast_gen_inversion.py
new file mode 100644
index 0000000000000000000000000000000000000000..dc57dd17d4562909f0a21b23a6ff2768c7373e3a
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_fast_gen_inversion.py
@@ -0,0 +1,434 @@
+import pytest
+import warnings
+import numpy as np
+from numpy.testing import assert_array_equal, assert_allclose
+from copy import deepcopy
+from scipy.stats.sampling import FastGeneratorInversion
+from scipy import stats
+from scipy._lib._testutils import IS_MUSL
+
+
+def test_bad_args():
+    # loc and scale must be scalar
+    with pytest.raises(ValueError, match="loc must be scalar"):
+        FastGeneratorInversion(stats.norm(loc=(1.2, 1.3)))
+    with pytest.raises(ValueError, match="scale must be scalar"):
+        FastGeneratorInversion(stats.norm(scale=[1.5, 5.7]))
+
+    with pytest.raises(ValueError, match="'test' cannot be used to seed"):
+        FastGeneratorInversion(stats.norm(), random_state="test")
+
+    msg = "Each of the 1 shape parameters must be a scalar"
+    with pytest.raises(ValueError, match=msg):
+        FastGeneratorInversion(stats.gamma([1.3, 2.5]))
+
+    with pytest.raises(ValueError, match="`dist` must be a frozen"):
+        FastGeneratorInversion("xy")
+
+    with pytest.raises(ValueError, match="Distribution 'truncnorm' is not"):
+        FastGeneratorInversion(stats.truncnorm(1.3, 4.5))
+
+
+def test_random_state():
+    # fixed seed
+    gen = FastGeneratorInversion(stats.norm(), random_state=68734509)
+    x1 = gen.rvs(size=10)
+    gen.random_state = 68734509
+    x2 = gen.rvs(size=10)
+    assert_array_equal(x1, x2)
+
+    # Generator
+    urng = np.random.default_rng(20375857)
+    gen = FastGeneratorInversion(stats.norm(), random_state=urng)
+    x1 = gen.rvs(size=10)
+    gen.random_state = np.random.default_rng(20375857)
+    x2 = gen.rvs(size=10)
+    assert_array_equal(x1, x2)
+
+    # RandomState
+    urng = np.random.RandomState(2364)
+    gen = FastGeneratorInversion(stats.norm(), random_state=urng)
+    x1 = gen.rvs(size=10)
+    gen.random_state = np.random.RandomState(2364)
+    x2 = gen.rvs(size=10)
+    assert_array_equal(x1, x2)
+
+    # if evaluate_error is called, it must not interfere with the random_state
+    # used by rvs
+    gen = FastGeneratorInversion(stats.norm(), random_state=68734509)
+    x1 = gen.rvs(size=10)
+    _ = gen.evaluate_error(size=5)  # this will generate 5 uniform rvs
+    x2 = gen.rvs(size=10)
+    gen.random_state = 68734509
+    x3 = gen.rvs(size=20)
+    assert_array_equal(x2, x3[10:])
+
+
+dists_with_params = [
+    ("alpha", (3.5,)),
+    ("anglit", ()),
+    ("argus", (3.5,)),
+    ("argus", (5.1,)),
+    ("beta", (1.5, 0.9)),
+    ("cosine", ()),
+    ("betaprime", (2.5, 3.3)),
+    ("bradford", (1.2,)),
+    ("burr", (1.3, 2.4)),
+    ("burr12", (0.7, 1.2)),
+    ("cauchy", ()),
+    ("chi2", (3.5,)),
+    ("chi", (4.5,)),
+    ("crystalball", (0.7, 1.2)),
+    ("expon", ()),
+    ("gamma", (1.5,)),
+    ("gennorm", (2.7,)),
+    ("gumbel_l", ()),
+    ("gumbel_r", ()),
+    ("hypsecant", ()),
+    ("invgauss", (3.1,)),
+    ("invweibull", (1.5,)),
+    ("laplace", ()),
+    ("logistic", ()),
+    ("maxwell", ()),
+    ("moyal", ()),
+    ("norm", ()),
+    ("pareto", (1.3,)),
+    ("powerlaw", (7.6,)),
+    ("rayleigh", ()),
+    ("semicircular", ()),
+    ("t", (5.7,)),
+    ("wald", ()),
+    ("weibull_max", (2.4,)),
+    ("weibull_min", (1.2,)),
+]
+
+
+@pytest.mark.parametrize(("distname, args"), dists_with_params)
+def test_rvs_and_ppf(distname, args):
+    # check sample against rvs generated by rv_continuous
+    urng = np.random.default_rng(9807324628097097)
+    rng1 = getattr(stats, distname)(*args)
+    rvs1 = rng1.rvs(size=500, random_state=urng)
+    rng2 = FastGeneratorInversion(rng1, random_state=urng)
+    rvs2 = rng2.rvs(size=500)
+    assert stats.cramervonmises_2samp(rvs1, rvs2).pvalue > 0.01
+
+    # check ppf
+    q = [0.001, 0.1, 0.5, 0.9, 0.999]
+    assert_allclose(rng1.ppf(q), rng2.ppf(q), atol=1e-10)
+
+
+@pytest.mark.parametrize(("distname, args"), dists_with_params)
+def test_u_error(distname, args):
+    # check sample against rvs generated by rv_continuous
+    dist = getattr(stats, distname)(*args)
+    with warnings.catch_warnings():
+        # filter the warnings thrown by UNU.RAN
+        warnings.simplefilter("ignore", RuntimeWarning)
+        rng = FastGeneratorInversion(dist)
+    u_error, x_error = rng.evaluate_error(
+        size=10_000, random_state=9807324628097097, x_error=False
+    )
+    assert u_error <= 1e-10
+
+
+@pytest.mark.xslow
+@pytest.mark.xfail(reason="geninvgauss CDF is not accurate")
+def test_geninvgauss_uerror():
+    dist = stats.geninvgauss(3.2, 1.5)
+    rng = FastGeneratorInversion(dist)
+    err = rng.evaluate_error(size=10_000, random_state=67982)
+    assert err[0] < 1e-10
+
+
+# TODO: add more distributions
+@pytest.mark.skipif(IS_MUSL, reason="Hits RecursionError, see gh-23172")
+@pytest.mark.fail_slow(5)
+@pytest.mark.parametrize(("distname, args"), [("beta", (0.11, 0.11))])
+def test_error_extreme_params(distname, args):
+    # take extreme parameters where u-error might not be below the tolerance
+    # due to limitations of floating point arithmetic
+    with warnings.catch_warnings():
+        # filter the warnings thrown by UNU.RAN for such extreme parameters
+        warnings.simplefilter("ignore", RuntimeWarning)
+        dist = getattr(stats, distname)(*args)
+        rng = FastGeneratorInversion(dist)
+    u_error, x_error = rng.evaluate_error(
+        size=10_000, random_state=980732462809709732623, x_error=True
+    )
+    if u_error >= 2.5 * 1e-10:
+        assert x_error < 1e-9
+
+
+def test_evaluate_error_inputs():
+    gen = FastGeneratorInversion(stats.norm())
+    with pytest.raises(ValueError, match="size must be an integer"):
+        gen.evaluate_error(size=3.5)
+    with pytest.raises(ValueError, match="size must be an integer"):
+        gen.evaluate_error(size=(3, 3))
+
+
+def test_rvs_ppf_loc_scale():
+    loc, scale = 3.5, 2.3
+    dist = stats.norm(loc=loc, scale=scale)
+    rng = FastGeneratorInversion(dist, random_state=1234)
+    r = rng.rvs(size=1000)
+    r_rescaled = (r - loc) / scale
+    assert stats.cramervonmises(r_rescaled, "norm").pvalue > 0.01
+    q = [0.001, 0.1, 0.5, 0.9, 0.999]
+    assert_allclose(rng._ppf(q), rng.ppf(q), atol=1e-10)
+
+
+def test_domain():
+    # only a basic check that the domain argument is passed to the
+    # UNU.RAN generators
+    rng = FastGeneratorInversion(stats.norm(), domain=(-1, 1))
+    r = rng.rvs(size=100)
+    assert -1 <= r.min() < r.max() <= 1
+
+    # if loc and scale are used, new domain is loc + scale*domain
+    loc, scale = 3.5, 1.3
+    dist = stats.norm(loc=loc, scale=scale)
+    rng = FastGeneratorInversion(dist, domain=(-1.5, 2))
+    r = rng.rvs(size=100)
+    lb, ub = loc - scale * 1.5, loc + scale * 2
+    assert lb <= r.min() < r.max() <= ub
+
+
+@pytest.mark.parametrize(("distname, args, expected"),
+                         [("beta", (3.5, 2.5), (0, 1)),
+                          ("norm", (), (-np.inf, np.inf))])
+def test_support(distname, args, expected):
+    # test that the support is updated if truncation and loc/scale are applied
+    # use beta distribution since it is a transformed betaprime distribution,
+    # so it is important that the correct support is considered
+    # (i.e., the support of beta is (0,1), while betaprime is (0, inf))
+    dist = getattr(stats, distname)(*args)
+    rng = FastGeneratorInversion(dist)
+    assert_array_equal(rng.support(), expected)
+    rng.loc = 1
+    rng.scale = 2
+    assert_array_equal(rng.support(), 1 + 2*np.array(expected))
+
+
+@pytest.mark.parametrize(("distname, args"),
+                         [("beta", (3.5, 2.5)), ("norm", ())])
+def test_support_truncation(distname, args):
+    # similar test for truncation
+    dist = getattr(stats, distname)(*args)
+    rng = FastGeneratorInversion(dist, domain=(0.5, 0.7))
+    assert_array_equal(rng.support(), (0.5, 0.7))
+    rng.loc = 1
+    rng.scale = 2
+    assert_array_equal(rng.support(), (1 + 2 * 0.5, 1 + 2 * 0.7))
+
+
+def test_domain_shift_truncation():
+    # center of norm is zero, it should be shifted to the left endpoint of
+    # domain. if this was not the case, PINV in UNURAN would raise a warning
+    # as the center is not inside the domain
+    with warnings.catch_warnings():
+        warnings.simplefilter("error")
+        rng = FastGeneratorInversion(stats.norm(), domain=(1, 2))
+    r = rng.rvs(size=100)
+    assert 1 <= r.min() < r.max() <= 2
+
+
+def test_non_rvs_methods_with_domain():
+    # as a first step, compare truncated normal against stats.truncnorm
+    rng = FastGeneratorInversion(stats.norm(), domain=(2.3, 3.2))
+    trunc_norm = stats.truncnorm(2.3, 3.2)
+    # take values that are inside and outside the domain
+    x = (2.0, 2.4, 3.0, 3.4)
+    p = (0.01, 0.5, 0.99)
+    assert_allclose(rng._cdf(x), trunc_norm.cdf(x))
+    assert_allclose(rng._ppf(p), trunc_norm.ppf(p))
+    loc, scale = 2, 3
+    rng.loc = 2
+    rng.scale = 3
+    trunc_norm = stats.truncnorm(2.3, 3.2, loc=loc, scale=scale)
+    x = np.array(x) * scale + loc
+    assert_allclose(rng._cdf(x), trunc_norm.cdf(x))
+    assert_allclose(rng._ppf(p), trunc_norm.ppf(p))
+
+    # do another sanity check with beta distribution
+    # in that case, it is important to use the correct domain since beta
+    # is a transformation of betaprime which has a different support
+    rng = FastGeneratorInversion(stats.beta(2.5, 3.5), domain=(0.3, 0.7))
+    rng.loc = 2
+    rng.scale = 2.5
+    # the support is 2.75, , 3.75 (2 + 2.5 * 0.3, 2 + 2.5 * 0.7)
+    assert_array_equal(rng.support(), (2.75, 3.75))
+    x = np.array([2.74, 2.76, 3.74, 3.76])
+    # the cdf needs to be zero outside of the domain
+    y_cdf = rng._cdf(x)
+    assert_array_equal((y_cdf[0], y_cdf[3]), (0, 1))
+    assert np.min(y_cdf[1:3]) > 0
+    # ppf needs to map 0 and 1 to the boundaries
+    assert_allclose(rng._ppf(y_cdf), (2.75, 2.76, 3.74, 3.75))
+
+
+def test_non_rvs_methods_without_domain():
+    norm_dist = stats.norm()
+    rng = FastGeneratorInversion(norm_dist)
+    x = np.linspace(-3, 3, num=10)
+    p = (0.01, 0.5, 0.99)
+    assert_allclose(rng._cdf(x), norm_dist.cdf(x))
+    assert_allclose(rng._ppf(p), norm_dist.ppf(p))
+    loc, scale = 0.5, 1.3
+    rng.loc = loc
+    rng.scale = scale
+    norm_dist = stats.norm(loc=loc, scale=scale)
+    assert_allclose(rng._cdf(x), norm_dist.cdf(x))
+    assert_allclose(rng._ppf(p), norm_dist.ppf(p))
+
+@pytest.mark.parametrize(("domain, x"),
+                         [(None, 0.5),
+                         ((0, 1), 0.5),
+                         ((0, 1), 1.5)])
+def test_scalar_inputs(domain, x):
+    """ pdf, cdf etc should map scalar values to scalars. check with and
+    w/o domain since domain impacts pdf, cdf etc
+    Take x inside and outside of domain """
+    rng = FastGeneratorInversion(stats.norm(), domain=domain)
+    assert np.isscalar(rng._cdf(x))
+    assert np.isscalar(rng._ppf(0.5))
+
+
+def test_domain_argus_large_chi():
+    # for large chi, the Gamma distribution is used and the domain has to be
+    # transformed. this is a test to ensure that the transformation works
+    chi, lb, ub = 5.5, 0.25, 0.75
+    rng = FastGeneratorInversion(stats.argus(chi), domain=(lb, ub))
+    rng.random_state = 4574
+    r = rng.rvs(size=500)
+    assert lb <= r.min() < r.max() <= ub
+    # perform goodness of fit test with conditional cdf
+    cdf = stats.argus(chi).cdf
+    prob = cdf(ub) - cdf(lb)
+    assert stats.cramervonmises(r, lambda x: cdf(x) / prob).pvalue > 0.05
+
+
+def test_setting_loc_scale():
+    rng = FastGeneratorInversion(stats.norm(), random_state=765765864)
+    r1 = rng.rvs(size=1000)
+    rng.loc = 3.0
+    rng.scale = 2.5
+    r2 = rng.rvs(1000)
+    # rescaled r2 should be again standard normal
+    assert stats.cramervonmises_2samp(r1, (r2 - 3) / 2.5).pvalue > 0.05
+    # reset values to default loc=0, scale=1
+    rng.loc = 0
+    rng.scale = 1
+    r2 = rng.rvs(1000)
+    assert stats.cramervonmises_2samp(r1, r2).pvalue > 0.05
+
+
+def test_ignore_shape_range():
+    msg = "No generator is defined for the shape parameters"
+    with pytest.raises(ValueError, match=msg):
+        rng = FastGeneratorInversion(stats.t(0.03))
+    rng = FastGeneratorInversion(stats.t(0.03), ignore_shape_range=True)
+    # we can ignore the recommended range of shape parameters
+    # but u-error can be expected to be too large in that case
+    u_err, _ = rng.evaluate_error(size=1000, random_state=234)
+    assert u_err >= 1e-6
+
+@pytest.mark.xfail_on_32bit(
+    "NumericalInversePolynomial.qrvs fails for Win 32-bit"
+)
+class TestQRVS:
+    def test_input_validation(self):
+        gen = FastGeneratorInversion(stats.norm())
+
+        match = "`qmc_engine` must be an instance of..."
+        with pytest.raises(ValueError, match=match):
+            gen.qrvs(qmc_engine=0)
+
+        match = "`d` must be consistent with dimension of `qmc_engine`."
+        with pytest.raises(ValueError, match=match):
+            gen.qrvs(d=3, qmc_engine=stats.qmc.Halton(2))
+
+    qrngs = [None, stats.qmc.Sobol(1, seed=0), stats.qmc.Halton(3, seed=0)]
+    # `size=None` should not add anything to the shape, `size=1` should
+    sizes = [
+        (None, tuple()),
+        (1, (1,)),
+        (4, (4,)),
+        ((4,), (4,)),
+        ((2, 4), (2, 4)),
+    ]
+    # Neither `d=None` nor `d=1` should add anything to the shape
+    ds = [(None, tuple()), (1, tuple()), (3, (3,))]
+
+    @pytest.mark.parametrize("qrng", qrngs)
+    @pytest.mark.parametrize("size_in, size_out", sizes)
+    @pytest.mark.parametrize("d_in, d_out", ds)
+    def test_QRVS_shape_consistency(self, qrng, size_in, size_out,
+                                    d_in, d_out):
+        gen = FastGeneratorInversion(stats.norm())
+
+        # If d and qrng.d are inconsistent, an error is raised
+        if d_in is not None and qrng is not None and qrng.d != d_in:
+            match = "`d` must be consistent with dimension of `qmc_engine`."
+            with pytest.raises(ValueError, match=match):
+                gen.qrvs(size_in, d=d_in, qmc_engine=qrng)
+            return
+
+        # Sometimes d is really determined by qrng
+        if d_in is None and qrng is not None and qrng.d != 1:
+            d_out = (qrng.d,)
+
+        shape_expected = size_out + d_out
+
+        qrng2 = deepcopy(qrng)
+        qrvs = gen.qrvs(size=size_in, d=d_in, qmc_engine=qrng)
+        if size_in is not None:
+            assert qrvs.shape == shape_expected
+
+        if qrng2 is not None:
+            uniform = qrng2.random(np.prod(size_in) or 1)
+            qrvs2 = stats.norm.ppf(uniform).reshape(shape_expected)
+            assert_allclose(qrvs, qrvs2, atol=1e-12)
+
+    def test_QRVS_size_tuple(self):
+        # QMCEngine samples are always of shape (n, d). When `size` is a tuple,
+        # we set `n = prod(size)` in the call to qmc_engine.random, transform
+        # the sample, and reshape it to the final dimensions. When we reshape,
+        # we need to be careful, because the _columns_ of the sample returned
+        # by a QMCEngine are "independent"-ish, but the elements within the
+        # columns are not. We need to make sure that this doesn't get mixed up
+        # by reshaping: qrvs[..., i] should remain "independent"-ish of
+        # qrvs[..., i+1], but the elements within qrvs[..., i] should be
+        # transformed from the same low-discrepancy sequence.
+
+        gen = FastGeneratorInversion(stats.norm())
+
+        size = (3, 4)
+        d = 5
+        qrng = stats.qmc.Halton(d, seed=0)
+        qrng2 = stats.qmc.Halton(d, seed=0)
+
+        uniform = qrng2.random(np.prod(size))
+
+        qrvs = gen.qrvs(size=size, d=d, qmc_engine=qrng)
+        qrvs2 = stats.norm.ppf(uniform)
+
+        for i in range(d):
+            sample = qrvs[..., i]
+            sample2 = qrvs2[:, i].reshape(size)
+            assert_allclose(sample, sample2, atol=1e-12)
+
+
+def test_burr_overflow():
+    # this case leads to an overflow error if math.exp is used
+    # in the definition of the burr pdf instead of np.exp
+    # a direct implementation of the PDF as x**(-c-1) / (1+x**(-c))**(d+1)
+    # also leads to an overflow error in the setup
+    args = (1.89128135, 0.30195177)
+    with warnings.catch_warnings():
+        # filter potential overflow warning
+        warnings.simplefilter("ignore", RuntimeWarning)
+        gen = FastGeneratorInversion(stats.burr(*args))
+    u_error, _ = gen.evaluate_error(random_state=4326)
+    assert u_error <= 1e-10
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/test_fit.py b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_fit.py
new file mode 100644
index 0000000000000000000000000000000000000000..e77cb931308948fb48b080ba180e20b7b9e9aefb
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_fit.py
@@ -0,0 +1,1092 @@
+import os
+import warnings
+
+import numpy as np
+from numpy.testing import assert_allclose, assert_equal
+import pytest
+from scipy import stats
+from scipy.optimize import differential_evolution
+
+from .test_continuous_basic import distcont
+from scipy.stats._distn_infrastructure import FitError
+from scipy.stats._distr_params import distdiscrete
+from scipy.stats import goodness_of_fit
+
+
+# this is not a proper statistical test for convergence, but only
+# verifies that the estimate and true values don't differ by too much
+
+fit_sizes = [1000, 5000, 10000]  # sample sizes to try
+
+thresh_percent = 0.25  # percent of true parameters for fail cut-off
+thresh_min = 0.75  # minimum difference estimate - true to fail test
+
+mle_failing_fits = [
+        'dpareto_lognorm',
+        'gausshyper',
+        'genexpon',
+        'gengamma',
+        'irwinhall',
+        'kappa4',
+        'ksone',
+        'kstwo',
+        'ncf',
+        'ncx2',
+        'truncexpon',
+        'tukeylambda',
+        'vonmises',
+        'levy_stable',
+        'truncpareto',
+        'truncweibull_min',
+        'studentized_range',
+]
+
+# these pass but are XSLOW (>1s)
+mle_Xslow_fits = ['betaprime', 'crystalball', 'exponweib', 'f', 'geninvgauss',
+                  'jf_skew_t', 'nct', 'recipinvgauss', 'rel_breitwigner',
+                  'vonmises_line']
+
+# The MLE fit method of these distributions doesn't perform well when all
+# parameters are fit, so test them with the location fixed at 0.
+mle_use_floc0 = [
+    'burr',
+    'chi',
+    'chi2',
+    'mielke',
+    'pearson3',
+    'genhalflogistic',
+    'rdist',
+    'pareto',
+    'powerlaw',  # distfn.nnlf(est2, rvs) > distfn.nnlf(est1, rvs) otherwise
+    'powerlognorm',
+    'wrapcauchy',
+    'rel_breitwigner',
+]
+
+mm_failing_fits = ['alpha', 'betaprime', 'burr', 'burr12', 'cauchy', 'chi',
+                   'chi2', 'crystalball', 'dgamma', 'dpareto_lognorm', 'dweibull',
+                   'f', 'fatiguelife', 'fisk', 'foldcauchy', 'genextreme',
+                   'gengamma', 'genhyperbolic', 'gennorm', 'genpareto',
+                   'halfcauchy', 'invgamma', 'invweibull', 'irwinhall', 'jf_skew_t',
+                   'johnsonsu', 'kappa3', 'ksone', 'kstwo', 'landau', 'levy', 'levy_l',
+                   'levy_stable', 'loglaplace', 'lomax', 'mielke', 'nakagami',
+                   'ncf', 'nct', 'ncx2', 'pareto', 'powerlognorm', 'powernorm',
+                   'rel_breitwigner', 'skewcauchy', 't', 'triang',
+                   'truncpareto', 'truncweibull_min', 'tukeylambda',
+                   'studentized_range']
+
+# not sure if these fail, but they caused my patience to fail
+mm_XXslow_fits = ['argus', 'exponpow', 'exponweib', 'gausshyper', 'genexpon',
+                  'genhalflogistic', 'gompertz', 'johnsonsb',
+                  'kappa4', 'kstwobign', 'recipinvgauss',
+                  'truncexpon', 'vonmises', 'vonmises_line']
+
+# these pass but are XSLOW (>1s)
+mm_Xslow_fits = ['wrapcauchy']
+
+failing_fits = {"MM": mm_failing_fits + mm_XXslow_fits, "MLE": mle_failing_fits}
+xslow_fits = {"MM": mm_Xslow_fits, "MLE": mle_Xslow_fits}
+fail_interval_censored = {"truncpareto"}
+
+# Don't run the fit test on these:
+skip_fit = [
+    'erlang',  # Subclass of gamma, generates a warning.
+    'genhyperbolic', 'norminvgauss',  # too slow
+]
+
+
+def cases_test_cont_fit():
+    # this tests the closeness of the estimated parameters to the true
+    # parameters with fit method of continuous distributions
+    # Note: is slow, some distributions don't converge with sample
+    # size <= 10000
+    for distname, arg in distcont:
+        if distname not in skip_fit:
+            yield distname, arg
+
+
+@pytest.mark.slow
+@pytest.mark.parametrize('distname,arg', list(cases_test_cont_fit()))
+@pytest.mark.parametrize('method', ["MLE", "MM"])
+def test_cont_fit(distname, arg, method):
+    run_xfail = int(os.getenv('SCIPY_XFAIL', default=False))
+    run_xslow = int(os.getenv('SCIPY_XSLOW', default=False))
+
+    if distname in failing_fits[method] and not run_xfail:
+        # The generic `fit` method can't be expected to work perfectly for all
+        # distributions, data, and guesses. Some failures are expected.
+        msg = "Failure expected; set environment variable SCIPY_XFAIL=1 to run."
+        pytest.xfail(msg)
+
+    if distname in xslow_fits[method] and not run_xslow:
+        msg = "Very slow; set environment variable SCIPY_XSLOW=1 to run."
+        pytest.skip(msg)
+
+    distfn = getattr(stats, distname)
+
+    truearg = np.hstack([arg, [0.0, 1.0]])
+    diffthreshold = np.max(np.vstack([truearg*thresh_percent,
+                                      np.full(distfn.numargs+2, thresh_min)]),
+                           0)
+
+    for fit_size in fit_sizes:
+        # Note that if a fit succeeds, the other fit_sizes are skipped
+        rng = np.random.default_rng(1234)
+
+        with np.errstate(all='ignore'):
+            rvs = distfn.rvs(size=fit_size, *arg, random_state=rng)
+            if method == 'MLE' and distfn.name in mle_use_floc0:
+                kwds = {'floc': 0}
+            else:
+                kwds = {}
+            # start with default values
+            est = distfn.fit(rvs, method=method, **kwds)
+            if method == 'MLE':
+                # Trivial test of the use of CensoredData.  The fit() method
+                # will check that data contains no actual censored data, and
+                # do a regular uncensored fit.
+                data1 = stats.CensoredData(rvs)
+                est1 = distfn.fit(data1, **kwds)
+                msg = ('Different results fitting uncensored data wrapped as'
+                       f' CensoredData: {distfn.name}: est={est} est1={est1}')
+                assert_allclose(est1, est, rtol=1e-10, err_msg=msg)
+            if method == 'MLE' and distname not in fail_interval_censored:
+                # Convert the first `nic` values in rvs to interval-censored
+                # values. The interval is small, so est2 should be close to
+                # est.
+                nic = 15
+                interval = np.column_stack((rvs, rvs))
+                interval[:nic, 0] *= 0.99
+                interval[:nic, 1] *= 1.01
+                interval.sort(axis=1)
+                data2 = stats.CensoredData(interval=interval)
+                est2 = distfn.fit(data2, **kwds)
+                msg = ('Different results fitting interval-censored'
+                       f' data: {distfn.name}: est={est} est2={est2}')
+                assert_allclose(est2, est, rtol=0.05, err_msg=msg)
+
+        diff = est - truearg
+
+        # threshold for location
+        diffthreshold[-2] = np.max([np.abs(rvs.mean())*thresh_percent,
+                                    thresh_min])
+
+        if np.any(np.isnan(est)):
+            raise AssertionError('nan returned in fit')
+        else:
+            if np.all(np.abs(diff) <= diffthreshold):
+                break
+    else:
+        txt = f'parameter: {str(truearg)}\n'
+        txt += f'estimated: {str(est)}\n'
+        txt += f'diff     : {str(diff)}\n'
+        raise AssertionError(f'fit not very good in {distfn.name}\n' + txt)
+
+
+def _check_loc_scale_mle_fit(name, data, desired, atol=None):
+    d = getattr(stats, name)
+    actual = d.fit(data)[-2:]
+    assert_allclose(actual, desired, atol=atol,
+                    err_msg=f'poor mle fit of (loc, scale) in {name}')
+
+
+def test_non_default_loc_scale_mle_fit():
+    data = np.array([1.01, 1.78, 1.78, 1.78, 1.88, 1.88, 1.88, 2.00])
+    _check_loc_scale_mle_fit('uniform', data, [1.01, 0.99], 1e-3)
+    _check_loc_scale_mle_fit('expon', data, [1.01, 0.73875], 1e-3)
+
+
+def test_expon_fit():
+    """gh-6167"""
+    data = [0, 0, 0, 0, 2, 2, 2, 2]
+    phat = stats.expon.fit(data, floc=0)
+    assert_allclose(phat, [0, 1.0], atol=1e-3)
+
+
+def test_fit_error():
+    data = np.concatenate([np.zeros(29), np.ones(21)])
+    message = "Optimization converged to parameters that are..."
+    with pytest.raises(FitError, match=message), \
+            pytest.warns(RuntimeWarning):
+        stats.beta.fit(data)
+
+
+@pytest.mark.parametrize("dist, params",
+                         [(stats.norm, (0.5, 2.5)),  # type: ignore[attr-defined]
+                          (stats.binom, (10, 0.3, 2))])  # type: ignore[attr-defined]
+def test_nnlf_and_related_methods(dist, params):
+    rng = np.random.default_rng(983459824)
+
+    if hasattr(dist, 'pdf'):
+        logpxf = dist.logpdf
+    else:
+        logpxf = dist.logpmf
+
+    x = dist.rvs(*params, size=100, random_state=rng)
+    ref = -logpxf(x, *params).sum()
+    res1 = dist.nnlf(params, x)
+    res2 = dist._penalized_nnlf(params, x)
+    assert_allclose(res1, ref)
+    assert_allclose(res2, ref)
+
+
+def cases_test_fit_mle():
+    # These fail default test or hang
+    skip_basic_fit = {'argus', 'irwinhall', 'foldnorm', 'truncpareto',
+                      'truncweibull_min', 'ksone', 'levy_stable',
+                      'studentized_range', 'kstwo',
+                      'beta', 'nakagami', 'truncnorm', # don't meet tolerance
+                      'poisson_binom'}  # vector-valued shape parameter
+
+    # Please keep this list in alphabetical order...
+    slow_basic_fit = {'alpha', 'arcsine', 'betaprime', 'binom', 'bradford', 'burr12',
+                      'chi', 'crystalball', 'dweibull', 'erlang', 'exponnorm',
+                      'exponpow', 'f', 'fatiguelife', 'fisk', 'foldcauchy', 'gamma',
+                      'genexpon', 'genextreme', 'gennorm', 'genpareto',
+                      'gompertz', 'invgamma', 'invgauss', 'invweibull',
+                      'jf_skew_t', 'johnsonsb', 'johnsonsu', 'kappa3',
+                      'kstwobign', 'loglaplace', 'lognorm', 'lomax', 'mielke',
+                      'nbinom', 'norminvgauss',
+                      'pareto', 'pearson3', 'powerlaw', 'powernorm',
+                      'randint', 'rdist', 'recipinvgauss', 'rice', 'skewnorm',
+                      't', 'uniform', 'weibull_max', 'weibull_min', 'wrapcauchy',
+                      'zipfian'}
+
+    # Please keep this list in alphabetical order...
+    xslow_basic_fit = {'betabinom', 'betanbinom', 'burr', 'dpareto_lognorm',
+                       'exponweib', 'gausshyper', 'gengamma', 'genhalflogistic',
+                       'genhyperbolic', 'geninvgauss',
+                       'hypergeom', 'kappa4', 'loguniform',
+                       'ncf', 'nchypergeom_fisher', 'nchypergeom_wallenius',
+                       'nct', 'ncx2', 'nhypergeom',
+                       'powerlognorm', 'reciprocal', 'rel_breitwigner',
+                       'skellam', 'trapezoid', 'triang',
+                       'tukeylambda', 'vonmises'}
+
+    for dist in dict(distdiscrete + distcont):
+        if dist in skip_basic_fit or not isinstance(dist, str):
+            reason = "tested separately"
+            yield pytest.param(dist, marks=pytest.mark.skip(reason=reason))
+        elif dist in slow_basic_fit:
+            reason = "too slow (>= 0.25s)"
+            yield pytest.param(dist, marks=pytest.mark.slow(reason=reason))
+        elif dist in xslow_basic_fit:
+            reason = "too slow (>= 1.0s)"
+            yield pytest.param(dist, marks=pytest.mark.xslow(reason=reason))
+        else:
+            yield dist
+
+
+def cases_test_fit_mse():
+    # the first four are so slow that I'm not sure whether they would pass
+    skip_basic_fit = {'levy_stable', 'studentized_range', 'ksone', 'skewnorm',
+                      'irwinhall', # hangs
+                      'norminvgauss',  # super slow (~1 hr) but passes
+                      'kstwo',  # very slow (~25 min) but passes
+                      'geninvgauss',  # quite slow (~4 minutes) but passes
+                      'gausshyper', 'genhyperbolic',  # integration warnings
+                      'tukeylambda',  # close, but doesn't meet tolerance
+                      'vonmises',  # can have negative CDF; doesn't play nice
+                      'arcsine', 'argus', 'powerlaw', 'rdist', # don't meet tolerance
+                      'poisson_binom',  # vector-valued shape parameter
+                      }
+
+    # Please keep this list in alphabetical order...
+    slow_basic_fit = {'alpha', 'anglit', 'betabinom', 'bradford',
+                      'chi', 'chi2', 'crystalball', 'dweibull',
+                      'erlang', 'exponnorm', 'exponpow', 'exponweib',
+                      'fatiguelife', 'fisk', 'foldcauchy', 'foldnorm',
+                      'gamma', 'genexpon', 'genextreme', 'genhalflogistic',
+                      'genlogistic', 'genpareto', 'gompertz',
+                      'hypergeom', 'invweibull',
+                      'johnsonsu', 'kappa3', 'kstwobign',
+                      'laplace_asymmetric', 'loggamma', 'loglaplace',
+                      'lognorm', 'lomax',
+                      'maxwell', 'nhypergeom',
+                      'pareto', 'powernorm', 'randint', 'recipinvgauss',
+                      'semicircular',
+                      't', 'triang', 'truncexpon', 'truncpareto',
+                      'uniform',
+                      'wald', 'weibull_max', 'weibull_min', 'wrapcauchy',
+                      'zipfian'}
+
+    # Please keep this list in alphabetical order...
+    xslow_basic_fit = {'argus', 'beta', 'betaprime', 'burr', 'burr12',
+                       'dgamma', 'dpareto_lognorm', 'f', 'gengamma', 'gennorm',
+                       'invgamma', 'invgauss', 'jf_skew_t',
+                       'johnsonsb', 'kappa4', 'loguniform', 'mielke',
+                       'nakagami', 'ncf', 'nchypergeom_fisher',
+                       'nchypergeom_wallenius', 'nct', 'ncx2',
+                       'pearson3', 'powerlognorm',
+                       'reciprocal', 'rel_breitwigner', 'rice',
+                       'trapezoid', 'truncnorm', 'truncweibull_min',
+                       'vonmises_line'}
+
+    warns_basic_fit = {'skellam'}  # can remove mark after gh-14901 is resolved
+
+    for dist in dict(distdiscrete + distcont):
+        if dist in skip_basic_fit or not isinstance(dist, str):
+            reason = "Fails. Oh well."
+            yield pytest.param(dist, marks=pytest.mark.skip(reason=reason))
+        elif dist in slow_basic_fit:
+            reason = "too slow (>= 0.25s)"
+            yield pytest.param(dist, marks=pytest.mark.slow(reason=reason))
+        elif dist in xslow_basic_fit:
+            reason = "too slow (>= 1.0s)"
+            yield pytest.param(dist, marks=pytest.mark.xslow(reason=reason))
+        elif dist in warns_basic_fit:
+            mark = pytest.mark.filterwarnings('ignore::RuntimeWarning')
+            yield pytest.param(dist, marks=mark)
+        else:
+            yield dist
+
+
+def cases_test_fitstart():
+    for distname, shapes in dict(distcont).items():
+        if (not isinstance(distname, str) or
+                distname in {'studentized_range', 'recipinvgauss'}):  # slow
+            continue
+        yield distname, shapes
+
+
+@pytest.mark.parametrize('distname, shapes', list(cases_test_fitstart()))
+def test_fitstart(distname, shapes):
+    dist = getattr(stats, distname)
+    rng = np.random.default_rng(216342614)
+    data = rng.random(10)
+
+    with np.errstate(invalid='ignore', divide='ignore'):  # irrelevant to test
+        guess = dist._fitstart(data)
+
+    assert dist._argcheck(*guess[:-2])
+
+
+def assert_nlff_less_or_close(dist, data, params1, params0, rtol=1e-7, atol=0,
+                              nlff_name='nnlf'):
+    nlff = getattr(dist, nlff_name)
+    nlff1 = nlff(params1, data)
+    nlff0 = nlff(params0, data)
+    if not (nlff1 < nlff0):
+        np.testing.assert_allclose(nlff1, nlff0, rtol=rtol, atol=atol)
+
+
+class TestFit:
+    dist = stats.binom  # type: ignore[attr-defined]
+    seed = 654634816187
+    rng = np.random.default_rng(seed)
+    data = stats.binom.rvs(5, 0.5, size=100, random_state=rng)  # type: ignore[attr-defined]  # noqa: E501
+    shape_bounds_a = [(1, 10), (0, 1)]
+    shape_bounds_d = {'n': (1, 10), 'p': (0, 1)}
+    atol = 5e-2
+    rtol = 1e-2
+    tols = {'atol': atol, 'rtol': rtol}
+
+    def opt(self, *args, rng=1, **kwds):
+        return differential_evolution(*args, rng=rng, **kwds)
+
+    def test_dist_iv(self):
+        message = "`dist` must be an instance of..."
+        with pytest.raises(ValueError, match=message):
+            stats.fit(10, self.data, self.shape_bounds_a)
+
+    def test_data_iv(self):
+        message = "`data` must be exactly one-dimensional."
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, [[1, 2, 3]], self.shape_bounds_a)
+
+        message = "All elements of `data` must be finite numbers."
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, [1, 2, 3, np.nan], self.shape_bounds_a)
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, [1, 2, 3, np.inf], self.shape_bounds_a)
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, ['1', '2', '3'], self.shape_bounds_a)
+
+    def test_bounds_iv(self):
+        message = "Bounds provided for the following unrecognized..."
+        shape_bounds = {'n': (1, 10), 'p': (0, 1), '1': (0, 10)}
+        with pytest.warns(RuntimeWarning, match=message):
+            stats.fit(self.dist, self.data, shape_bounds)
+
+        message = "Each element of a `bounds` sequence must be a tuple..."
+        shape_bounds = [(1, 10, 3), (0, 1)]
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, self.data, shape_bounds)
+
+        message = "Each element of `bounds` must be a tuple specifying..."
+        shape_bounds = [(1, 10, 3), (0, 1, 0.5)]
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, self.data, shape_bounds)
+        shape_bounds = [1, 0]
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, self.data, shape_bounds)
+
+        message = "A `bounds` sequence must contain at least 2 elements..."
+        shape_bounds = [(1, 10)]
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, self.data, shape_bounds)
+
+        message = "A `bounds` sequence may not contain more than 3 elements..."
+        bounds = [(1, 10), (1, 10), (1, 10), (1, 10)]
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, self.data, bounds)
+
+        message = "There are no values for `p` on the interval..."
+        shape_bounds = {'n': (1, 10), 'p': (1, 0)}
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, self.data, shape_bounds)
+
+        message = "There are no values for `n` on the interval..."
+        shape_bounds = [(10, 1), (0, 1)]
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, self.data, shape_bounds)
+
+        message = "There are no integer values for `n` on the interval..."
+        shape_bounds = [(1.4, 1.6), (0, 1)]
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, self.data, shape_bounds)
+
+        message = "The intersection of user-provided bounds for `n`"
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, self.data)
+        shape_bounds = [(-np.inf, np.inf), (0, 1)]
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, self.data, shape_bounds)
+
+    def test_guess_iv(self):
+        message = "Guesses provided for the following unrecognized..."
+        guess = {'n': 1, 'p': 0.5, '1': 255}
+        with pytest.warns(RuntimeWarning, match=message):
+            stats.fit(self.dist, self.data, self.shape_bounds_d, guess=guess)
+
+        message = "Each element of `guess` must be a scalar..."
+        guess = {'n': 1, 'p': 'hi'}
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, self.data, self.shape_bounds_d, guess=guess)
+        guess = [1, 'f']
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, self.data, self.shape_bounds_d, guess=guess)
+        guess = [[1, 2]]
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, self.data, self.shape_bounds_d, guess=guess)
+
+        message = "A `guess` sequence must contain at least 2..."
+        guess = [1]
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, self.data, self.shape_bounds_d, guess=guess)
+
+        message = "A `guess` sequence may not contain more than 3..."
+        guess = [1, 2, 3, 4]
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, self.data, self.shape_bounds_d, guess=guess)
+
+        message = "Guess for parameter `n` rounded.*|Guess for parameter `p` clipped.*"
+        guess = {'n': 4.5, 'p': -0.5}
+        with pytest.warns(RuntimeWarning, match=message):
+            stats.fit(self.dist, self.data, self.shape_bounds_d, guess=guess)
+
+        message = "Guess for parameter `loc` rounded..."
+        guess = [5, 0.5, 0.5]
+        with pytest.warns(RuntimeWarning, match=message):
+            stats.fit(self.dist, self.data, self.shape_bounds_d, guess=guess)
+
+        message = "Guess for parameter `p` clipped..."
+        guess = {'n': 5, 'p': -0.5}
+        with pytest.warns(RuntimeWarning, match=message):
+            stats.fit(self.dist, self.data, self.shape_bounds_d, guess=guess)
+
+        message = "Guess for parameter `loc` clipped..."
+        guess = [5, 0.5, 1]
+        with pytest.warns(RuntimeWarning, match=message):
+            stats.fit(self.dist, self.data, self.shape_bounds_d, guess=guess)
+
+    def basic_fit_test(self, dist_name, method, rng=1):
+
+        N = 5000
+        dist_data = dict(distcont + distdiscrete)
+        rng = np.random.default_rng(self.seed)
+        dist = getattr(stats, dist_name)
+        shapes = np.array(dist_data[dist_name])
+        bounds = np.empty((len(shapes) + 2, 2), dtype=np.float64)
+        bounds[:-2, 0] = shapes/10.**np.sign(shapes)
+        bounds[:-2, 1] = shapes*10.**np.sign(shapes)
+        bounds[-2] = (0, 10)
+        bounds[-1] = (1e-16, 10)
+        loc = rng.uniform(*bounds[-2])
+        scale = rng.uniform(*bounds[-1])
+        ref = list(dist_data[dist_name]) + [loc, scale]
+
+        if getattr(dist, 'pmf', False):
+            ref = ref[:-1]
+            ref[-1] = np.floor(loc)
+            data = dist.rvs(*ref, size=N, random_state=rng)
+            bounds = bounds[:-1]
+        if getattr(dist, 'pdf', False):
+            data = dist.rvs(*ref, size=N, random_state=rng)
+
+        with warnings.catch_warnings():
+            warnings.filterwarnings("ignore", "overflow encountered", RuntimeWarning)
+            res = stats.fit(dist, data, bounds, method=method,
+                            optimizer=self.opt)
+
+        nlff_names = {'mle': 'nnlf', 'mse': '_penalized_nlpsf'}
+        nlff_name = nlff_names[method]
+        assert_nlff_less_or_close(dist, data, res.params, ref, **self.tols,
+                                  nlff_name=nlff_name)
+
+    @pytest.mark.parametrize("dist_name", list(cases_test_fit_mle()))
+    def test_basic_fit_mle(self, dist_name):
+        self.basic_fit_test(dist_name, "mle", rng=5)
+
+    @pytest.mark.parametrize("dist_name", list(cases_test_fit_mse()))
+    def test_basic_fit_mse(self, dist_name):
+        self.basic_fit_test(dist_name, "mse", rng=2)
+
+    @pytest.mark.slow
+    def test_arcsine(self):
+        # Can't guarantee that all distributions will fit all data with
+        # arbitrary bounds. This distribution just happens to fail above.
+        # Try something slightly different.
+        N = 1000
+        rng = np.random.default_rng(self.seed)
+        dist = stats.arcsine
+        shapes = (1., 2.)
+        data = dist.rvs(*shapes, size=N, random_state=rng)
+        shape_bounds = {'loc': (0.1, 10), 'scale': (0.1, 10)}
+        res = stats.fit(dist, data, shape_bounds, method='mse', optimizer=self.opt)
+        assert_nlff_less_or_close(dist, data, res.params, shapes,
+                                  nlff_name='_penalized_nlpsf', **self.tols)
+
+    @pytest.mark.parametrize("method", ('mle', 'mse'))
+    def test_argus(self, method):
+        # Can't guarantee that all distributions will fit all data with
+        # arbitrary bounds. This distribution just happens to fail above.
+        # Try something slightly different.
+        N = 1000
+        rng = np.random.default_rng(self.seed)
+        dist = stats.argus
+        shapes = (1., 2., 3.)
+        data = dist.rvs(*shapes, size=N, random_state=rng)
+        shape_bounds = {'chi': (0.1, 10), 'loc': (0.1, 10), 'scale': (0.1, 10)}
+        res = stats.fit(dist, data, shape_bounds, optimizer=self.opt, method=method)
+        nlff_name = {'mle': 'nnlf', 'mse': '_penalized_nlpsf'}[method]
+        assert_nlff_less_or_close(dist, data, res.params, shapes, **self.tols,
+                                  nlff_name=nlff_name)
+
+    @pytest.mark.xslow
+    def test_beta(self):
+        # Can't guarantee that all distributions will fit all data with
+        # arbitrary bounds. This distribution just happens to fail above.
+        # Try something slightly different.
+        N = 1000
+        rng = np.random.default_rng(self.seed)
+        dist = stats.beta
+        shapes = (2.3098496451481823, 0.62687954300963677, 1., 2.)
+        data = dist.rvs(*shapes, size=N, random_state=rng)
+        shape_bounds = {'a': (0.1, 10), 'b':(0.1, 10),
+                        'loc': (0.1, 10), 'scale': (0.1, 10)}
+        res = stats.fit(dist, data, shape_bounds, method='mle', optimizer=self.opt)
+        assert_nlff_less_or_close(dist, data, res.params, shapes,
+                                  nlff_name='nnlf', **self.tols)
+
+    def test_foldnorm(self):
+        # Can't guarantee that all distributions will fit all data with
+        # arbitrary bounds. This distribution just happens to fail above.
+        # Try something slightly different.
+        N = 1000
+        rng = np.random.default_rng(self.seed)
+        dist = stats.foldnorm
+        shapes = (1.952125337355587, 2., 3.)
+        data = dist.rvs(*shapes, size=N, random_state=rng)
+        shape_bounds = {'c': (0.1, 10), 'loc': (0.1, 10), 'scale': (0.1, 10)}
+        res = stats.fit(dist, data, shape_bounds, optimizer=self.opt)
+
+        assert_nlff_less_or_close(dist, data, res.params, shapes, **self.tols)
+
+    def test_nakagami(self):
+        # Can't guarantee that all distributions will fit all data with
+        # arbitrary bounds. This distribution just happens to fail above.
+        # Try something slightly different.
+        N = 1000
+        rng = np.random.default_rng(self.seed)
+        dist = stats.nakagami
+        shapes = (4.9673794866666237, 1., 2.)
+        data = dist.rvs(*shapes, size=N, random_state=rng)
+        shape_bounds = {'nu':(0.1, 10), 'loc': (0.1, 10), 'scale': (0.1, 10)}
+        res = stats.fit(dist, data, shape_bounds, method='mle', optimizer=self.opt)
+        assert_nlff_less_or_close(dist, data, res.params, shapes,
+                                  nlff_name='nnlf', **self.tols)
+
+    @pytest.mark.slow
+    def test_powerlaw(self):
+        # Can't guarantee that all distributions will fit all data with
+        # arbitrary bounds. This distribution just happens to fail above.
+        # Try something slightly different.
+        N = 1000
+        rng = np.random.default_rng(self.seed)
+        dist = stats.powerlaw
+        shapes = (1.6591133289905851, 1., 2.)
+        data = dist.rvs(*shapes, size=N, random_state=rng)
+        shape_bounds = {'a': (0.1, 10), 'loc': (0.1, 10), 'scale': (0.1, 10)}
+        res = stats.fit(dist, data, shape_bounds, method='mse', optimizer=self.opt)
+        assert_nlff_less_or_close(dist, data, res.params, shapes,
+                                  nlff_name='_penalized_nlpsf', **self.tols)
+
+    def test_truncpareto(self):
+        # Can't guarantee that all distributions will fit all data with
+        # arbitrary bounds. This distribution just happens to fail above.
+        # Try something slightly different.
+        N = 1000
+        rng = np.random.default_rng(self.seed)
+        dist = stats.truncpareto
+        shapes = (1.8, 5.3, 2.3, 4.1)
+        data = dist.rvs(*shapes, size=N, random_state=rng)
+        shape_bounds = [(0.1, 10)]*4
+        res = stats.fit(dist, data, shape_bounds, optimizer=self.opt)
+
+        assert_nlff_less_or_close(dist, data, res.params, shapes, **self.tols)
+
+    @pytest.mark.slow
+    def test_truncweibull_min(self):
+        # Can't guarantee that all distributions will fit all data with
+        # arbitrary bounds. This distribution just happens to fail above.
+        # Try something slightly different.
+        N = 1000
+        rng = np.random.default_rng(self.seed)
+        dist = stats.truncweibull_min
+        shapes = (2.5, 0.25, 1.75, 2., 3.)
+        data = dist.rvs(*shapes, size=N, random_state=rng)
+        shape_bounds = [(0.1, 10)]*5
+        res = stats.fit(dist, data, shape_bounds, optimizer=self.opt)
+
+        assert_nlff_less_or_close(dist, data, res.params, shapes, **self.tols)
+
+    def test_missing_shape_bounds(self):
+        # some distributions have a small domain w.r.t. a parameter, e.g.
+        # $p \in [0, 1]$ for binomial distribution
+        # User does not need to provide these because the intersection of the
+        # user's bounds (none) and the distribution's domain is finite
+        N = 1000
+        rng = np.random.default_rng(self.seed)
+
+        dist = stats.binom
+        n, p, loc = 10, 0.65, 0
+        data = dist.rvs(n, p, loc=loc, size=N, random_state=rng)
+        shape_bounds = {'n': np.array([0, 20])}  # check arrays are OK, too
+        res = stats.fit(dist, data, shape_bounds, optimizer=self.opt)
+        assert_allclose(res.params, (n, p, loc), **self.tols)
+
+        dist = stats.bernoulli
+        p, loc = 0.314159, 0
+        data = dist.rvs(p, loc=loc, size=N, random_state=rng)
+        res = stats.fit(dist, data, optimizer=self.opt)
+        assert_allclose(res.params, (p, loc), **self.tols)
+
+    def test_fit_only_loc_scale(self):
+        # fit only loc
+        N = 5000
+        rng = np.random.default_rng(self.seed)
+
+        dist = stats.norm
+        loc, scale = 1.5, 1
+        data = dist.rvs(loc=loc, size=N, random_state=rng)
+        loc_bounds = (0, 5)
+        bounds = {'loc': loc_bounds}
+        res = stats.fit(dist, data, bounds, optimizer=self.opt)
+        assert_allclose(res.params, (loc, scale), **self.tols)
+
+        # fit only scale
+        loc, scale = 0, 2.5
+        data = dist.rvs(scale=scale, size=N, random_state=rng)
+        scale_bounds = (0.01, 5)
+        bounds = {'scale': scale_bounds}
+        res = stats.fit(dist, data, bounds, optimizer=self.opt)
+        assert_allclose(res.params, (loc, scale), **self.tols)
+
+        # fit only loc and scale
+        dist = stats.norm
+        loc, scale = 1.5, 2.5
+        data = dist.rvs(loc=loc, scale=scale, size=N, random_state=rng)
+        bounds = {'loc': loc_bounds, 'scale': scale_bounds}
+        res = stats.fit(dist, data, bounds, optimizer=self.opt)
+        assert_allclose(res.params, (loc, scale), **self.tols)
+
+    def test_everything_fixed(self):
+        N = 5000
+        rng = np.random.default_rng(self.seed)
+
+        dist = stats.norm
+        loc, scale = 1.5, 2.5
+        data = dist.rvs(loc=loc, scale=scale, size=N, random_state=rng)
+
+        # loc, scale fixed to 0, 1 by default
+        res = stats.fit(dist, data)
+        assert_allclose(res.params, (0, 1), **self.tols)
+
+        # loc, scale explicitly fixed
+        bounds = {'loc': (loc, loc), 'scale': (scale, scale)}
+        res = stats.fit(dist, data, bounds)
+        assert_allclose(res.params, (loc, scale), **self.tols)
+
+        # `n` gets fixed during polishing
+        dist = stats.binom
+        n, p, loc = 10, 0.65, 0
+        data = dist.rvs(n, p, loc=loc, size=N, random_state=rng)
+        shape_bounds = {'n': (0, 20), 'p': (0.65, 0.65)}
+        res = stats.fit(dist, data, shape_bounds, optimizer=self.opt)
+        assert_allclose(res.params, (n, p, loc), **self.tols)
+
+    def test_failure(self):
+        N = 5000
+        rng = np.random.default_rng(self.seed)
+
+        dist = stats.nbinom
+        shapes = (5, 0.5)
+        data = dist.rvs(*shapes, size=N, random_state=rng)
+
+        assert data.min() == 0
+        # With lower bounds on location at 0.5, likelihood is zero
+        bounds = [(0, 30), (0, 1), (0.5, 10)]
+        res = stats.fit(dist, data, bounds)
+        message = "Optimization converged to parameter values that are"
+        assert res.message.startswith(message)
+        assert res.success is False
+
+    @pytest.mark.xslow
+    def test_guess(self):
+        # Test that guess helps DE find the desired solution
+        N = 2000
+        # With some seeds, `fit` doesn't need a guess
+        rng = np.random.default_rng(196390444561)
+        dist = stats.nhypergeom
+        params = (20, 7, 12, 0)
+        bounds = [(2, 200), (0.7, 70), (1.2, 120), (0, 10)]
+
+        data = dist.rvs(*params, size=N, random_state=rng)
+
+        res = stats.fit(dist, data, bounds, optimizer=self.opt)
+        assert not np.allclose(res.params, params, **self.tols)
+
+        res = stats.fit(dist, data, bounds, guess=params, optimizer=self.opt)
+        assert_allclose(res.params, params, **self.tols)
+
+    def test_mse_accuracy_1(self):
+        # Test maximum spacing estimation against example from Wikipedia
+        # https://en.wikipedia.org/wiki/Maximum_spacing_estimation#Examples
+        data = [2, 4]
+        dist = stats.expon
+        bounds = {'loc': (0, 0), 'scale': (1e-8, 10)}
+        res_mle = stats.fit(dist, data, bounds=bounds, method='mle')
+        assert_allclose(res_mle.params.scale, 3, atol=1e-3)
+        res_mse = stats.fit(dist, data, bounds=bounds, method='mse')
+        assert_allclose(res_mse.params.scale, 3.915, atol=1e-3)
+
+    def test_mse_accuracy_2(self):
+        # Test maximum spacing estimation against example from Wikipedia
+        # https://en.wikipedia.org/wiki/Maximum_spacing_estimation#Examples
+        rng = np.random.default_rng(9843212616816518964)
+
+        dist = stats.uniform
+        n = 10
+        data = dist(3, 6).rvs(size=n, random_state=rng)
+        bounds = {'loc': (0, 10), 'scale': (1e-8, 10)}
+        res = stats.fit(dist, data, bounds=bounds, method='mse')
+        # (loc=3.608118420015416, scale=5.509323262055043)
+
+        x = np.sort(data)
+        a = (n*x[0] - x[-1])/(n - 1)
+        b = (n*x[-1] - x[0])/(n - 1)
+        ref = a, b-a  # (3.6081133632151503, 5.509328130317254)
+        assert_allclose(res.params, ref, rtol=1e-4)
+
+
+# Data from Matlab: https://www.mathworks.com/help/stats/lillietest.html
+examgrades = [65, 61, 81, 88, 69, 89, 55, 84, 86, 84, 71, 81, 84, 81, 78, 67,
+              96, 66, 73, 75, 59, 71, 69, 63, 79, 76, 63, 85, 87, 88, 80, 71,
+              65, 84, 71, 75, 81, 79, 64, 65, 84, 77, 70, 75, 84, 75, 73, 92,
+              90, 79, 80, 71, 73, 71, 58, 79, 73, 64, 77, 82, 81, 59, 54, 82,
+              57, 79, 79, 73, 74, 82, 63, 64, 73, 69, 87, 68, 81, 73, 83, 73,
+              80, 73, 73, 71, 66, 78, 64, 74, 68, 67, 75, 75, 80, 85, 74, 76,
+              80, 77, 93, 70, 86, 80, 81, 83, 68, 60, 85, 64, 74, 82, 81, 77,
+              66, 85, 75, 81, 69, 60, 83, 72]
+
+
+class TestGoodnessOfFit:
+
+    def test_gof_iv(self):
+        dist = stats.norm
+        x = [1, 2, 3]
+
+        message = r"`dist` must be a \(non-frozen\) instance of..."
+        with pytest.raises(TypeError, match=message):
+            goodness_of_fit(stats.norm(), x)
+
+        message = "`data` must be a one-dimensional array of numbers."
+        with pytest.raises(ValueError, match=message):
+            goodness_of_fit(dist, [[1, 2, 3]])
+
+        message = "`statistic` must be one of..."
+        with pytest.raises(ValueError, match=message):
+            goodness_of_fit(dist, x, statistic='mm')
+
+        message = "`n_mc_samples` must be an integer."
+        with pytest.raises(TypeError, match=message):
+            goodness_of_fit(dist, x, n_mc_samples=1000.5)
+
+        message = "SeedSequence expects int or sequence"
+        with pytest.raises(TypeError, match=message):
+            goodness_of_fit(dist, x, rng='herring')
+
+    def test_against_ks(self):
+        rng = np.random.default_rng(8517426291317196949)
+        x = examgrades
+        known_params = {'loc': np.mean(x), 'scale': np.std(x, ddof=1)}
+        res = goodness_of_fit(stats.norm, x, known_params=known_params,
+                              statistic='ks', rng=rng)
+        ref = stats.kstest(x, stats.norm(**known_params).cdf, method='exact')
+        assert_allclose(res.statistic, ref.statistic)  # ~0.0848
+        assert_allclose(res.pvalue, ref.pvalue, atol=5e-3)  # ~0.335
+
+    def test_against_lilliefors(self):
+        rng = np.random.default_rng(2291803665717442724)
+        x = examgrades
+        # preserve use of old random_state during SPEC 7 transition
+        res = goodness_of_fit(stats.norm, x, statistic='ks', random_state=rng)
+        known_params = {'loc': np.mean(x), 'scale': np.std(x, ddof=1)}
+        ref = stats.kstest(x, stats.norm(**known_params).cdf, method='exact')
+        assert_allclose(res.statistic, ref.statistic)  # ~0.0848
+        assert_allclose(res.pvalue, 0.0348, atol=5e-3)
+
+    def test_against_cvm(self):
+        rng = np.random.default_rng(8674330857509546614)
+        x = examgrades
+        known_params = {'loc': np.mean(x), 'scale': np.std(x, ddof=1)}
+        res = goodness_of_fit(stats.norm, x, known_params=known_params,
+                              statistic='cvm', rng=rng)
+        ref = stats.cramervonmises(x, stats.norm(**known_params).cdf)
+        assert_allclose(res.statistic, ref.statistic)  # ~0.090
+        assert_allclose(res.pvalue, ref.pvalue, atol=5e-3)  # ~0.636
+
+    def test_against_anderson_case_0(self):
+        # "Case 0" is where loc and scale are known [1]
+        rng = np.random.default_rng(7384539336846690410)
+        x = np.arange(1, 101)
+        # loc that produced critical value of statistic found w/ root_scalar
+        known_params = {'loc': 45.01575354024957, 'scale': 30}
+        res = goodness_of_fit(stats.norm, x, known_params=known_params,
+                              statistic='ad', rng=rng)
+        assert_allclose(res.statistic, 2.492)  # See [1] Table 1A 1.0
+        assert_allclose(res.pvalue, 0.05, atol=5e-3)
+
+    def test_against_anderson_case_1(self):
+        # "Case 1" is where scale is known and loc is fit [1]
+        rng = np.random.default_rng(5040212485680146248)
+        x = np.arange(1, 101)
+        # scale that produced critical value of statistic found w/ root_scalar
+        known_params = {'scale': 29.957112639101933}
+        res = goodness_of_fit(stats.norm, x, known_params=known_params,
+                              statistic='ad', rng=rng)
+        assert_allclose(res.statistic, 0.908)  # See [1] Table 1B 1.1
+        assert_allclose(res.pvalue, 0.1, atol=5e-3)
+
+    def test_against_anderson_case_2(self):
+        # "Case 2" is where loc is known and scale is fit [1]
+        rng = np.random.default_rng(726693985720914083)
+        x = np.arange(1, 101)
+        # loc that produced critical value of statistic found w/ root_scalar
+        known_params = {'loc': 44.5680212261933}
+        res = goodness_of_fit(stats.norm, x, known_params=known_params,
+                              statistic='ad', rng=rng)
+        assert_allclose(res.statistic, 2.904)  # See [1] Table 1B 1.2
+        assert_allclose(res.pvalue, 0.025, atol=5e-3)
+
+    def test_against_anderson_case_3(self):
+        # "Case 3" is where both loc and scale are fit [1]
+        rng = np.random.default_rng(6763691329830218206)
+        # c that produced critical value of statistic found w/ root_scalar
+        x = stats.skewnorm.rvs(1.4477847789132101, loc=1, scale=2, size=100,
+                               random_state=rng)
+        res = goodness_of_fit(stats.norm, x, statistic='ad', rng=rng)
+        assert_allclose(res.statistic, 0.559)  # See [1] Table 1B 1.2
+        assert_allclose(res.pvalue, 0.15, atol=5e-3)
+
+    @pytest.mark.xslow
+    def test_against_anderson_gumbel_r(self):
+        rng = np.random.default_rng(7302761058217743)
+        # c that produced critical value of statistic found w/ root_scalar
+        x = stats.genextreme(0.051896837188595134, loc=0.5,
+                             scale=1.5).rvs(size=1000, random_state=rng)
+        res = goodness_of_fit(stats.gumbel_r, x, statistic='ad', rng=rng)
+        ref = stats.anderson(x, dist='gumbel_r', method='interpolate')
+        assert_allclose(res.statistic, ref.statistic)
+        assert_allclose(res.pvalue, ref.pvalue, atol=5e-3)
+
+    def test_against_filliben_norm(self):
+        # Test against `stats.fit` ref. [7] Section 8 "Example"
+        rng = np.random.default_rng(8024266430745011915)
+        y = [6, 1, -4, 8, -2, 5, 0]
+        known_params = {'loc': 0, 'scale': 1}
+        res = stats.goodness_of_fit(stats.norm, y, known_params=known_params,
+                                    statistic="filliben", rng=rng)
+        # Slight discrepancy presumably due to roundoff in Filliben's
+        # calculation. Using exact order statistic medians instead of
+        # Filliben's approximation doesn't account for it.
+        assert_allclose(res.statistic, 0.98538, atol=1e-4)
+        assert 0.75 < res.pvalue < 0.9
+
+        # Using R's ppcc library:
+        # library(ppcc)
+        # options(digits=16)
+        # x < - c(6, 1, -4, 8, -2, 5, 0)
+        # set.seed(100)
+        # ppccTest(x, "qnorm", ppos="Filliben")
+        # Discrepancy with
+        assert_allclose(res.statistic, 0.98540957187084, rtol=2e-5)
+        assert_allclose(res.pvalue, 0.8875, rtol=2e-3)
+
+    def test_filliben_property(self):
+        # Filliben's statistic should be independent of data location and scale
+        rng = np.random.default_rng(8535677809395478813)
+        x = rng.normal(loc=10, scale=0.5, size=100)
+        res = stats.goodness_of_fit(stats.norm, x,
+                                    statistic="filliben", rng=rng)
+        known_params = {'loc': 0, 'scale': 1}
+        ref = stats.goodness_of_fit(stats.norm, x, known_params=known_params,
+                                    statistic="filliben", rng=rng)
+        assert_allclose(res.statistic, ref.statistic, rtol=1e-15)
+
+    @pytest.mark.parametrize('case', [(25, [.928, .937, .950, .958, .966]),
+                                      (50, [.959, .965, .972, .977, .981]),
+                                      (95, [.977, .979, .983, .986, .989])])
+    def test_against_filliben_norm_table(self, case):
+        # Test against `stats.fit` ref. [7] Table 1
+        rng = np.random.default_rng(504569995557928957)
+        n, ref = case
+        x = rng.random(n)
+        known_params = {'loc': 0, 'scale': 1}
+        res = stats.goodness_of_fit(stats.norm, x, known_params=known_params,
+                                    statistic="filliben", rng=rng)
+        percentiles = np.array([0.005, 0.01, 0.025, 0.05, 0.1])
+        res = stats.scoreatpercentile(res.null_distribution, percentiles*100)
+        assert_allclose(res, ref, atol=2e-3)
+
+    @pytest.mark.xslow
+    @pytest.mark.parametrize('case', [(5, 0.95772790260469, 0.4755),
+                                      (6, 0.95398832257958, 0.3848),
+                                      (7, 0.9432692889277, 0.2328)])
+    def test_against_ppcc(self, case):
+        # Test against R ppcc, e.g.
+        # library(ppcc)
+        # options(digits=16)
+        # x < - c(0.52325412, 1.06907699, -0.36084066, 0.15305959, 0.99093194)
+        # set.seed(100)
+        # ppccTest(x, "qrayleigh", ppos="Filliben")
+        n, ref_statistic, ref_pvalue = case
+        rng = np.random.default_rng(7777775561439803116)
+        x = rng.normal(size=n)
+        res = stats.goodness_of_fit(stats.rayleigh, x, statistic="filliben",
+                                    rng=rng)
+        assert_allclose(res.statistic, ref_statistic, rtol=1e-4)
+        assert_allclose(res.pvalue, ref_pvalue, atol=1.5e-2)
+
+    def test_params_effects(self):
+        # Ensure that `guessed_params`, `fit_params`, and `known_params` have
+        # the intended effects.
+        rng = np.random.default_rng(9121950977643805391)
+        x = stats.skewnorm.rvs(-5.044559778383153, loc=1, scale=2, size=50,
+                               random_state=rng)
+
+        # Show that `guessed_params` don't fit to the guess,
+        # but `fit_params` and `known_params` respect the provided fit
+        guessed_params = {'c': 13.4}
+        fit_params = {'scale': 13.73}
+        known_params = {'loc': -13.85}
+        rng = np.random.default_rng(9121950977643805391)
+        res1 = goodness_of_fit(stats.weibull_min, x, n_mc_samples=2,
+                               guessed_params=guessed_params,
+                               fit_params=fit_params,
+                               known_params=known_params, rng=rng)
+        assert not np.allclose(res1.fit_result.params.c, 13.4)
+        assert_equal(res1.fit_result.params.scale, 13.73)
+        assert_equal(res1.fit_result.params.loc, -13.85)
+
+        # Show that changing the guess changes the parameter that gets fit,
+        # and it changes the null distribution
+        guessed_params = {'c': 2}
+        rng = np.random.default_rng(9121950977643805391)
+        res2 = goodness_of_fit(stats.weibull_min, x, n_mc_samples=2,
+                               guessed_params=guessed_params,
+                               fit_params=fit_params,
+                               known_params=known_params, rng=rng)
+        assert not np.allclose(res2.fit_result.params.c,
+                               res1.fit_result.params.c, rtol=1e-8)
+        assert not np.allclose(res2.null_distribution,
+                               res1.null_distribution, rtol=1e-8)
+        assert_equal(res2.fit_result.params.scale, 13.73)
+        assert_equal(res2.fit_result.params.loc, -13.85)
+
+        # If we set all parameters as fit_params and known_params,
+        # they're all fixed to those values, but the null distribution
+        # varies.
+        fit_params = {'c': 13.4, 'scale': 13.73}
+        rng = np.random.default_rng(9121950977643805391)
+        res3 = goodness_of_fit(stats.weibull_min, x, n_mc_samples=2,
+                               guessed_params=guessed_params,
+                               fit_params=fit_params,
+                               known_params=known_params, rng=rng)
+        assert_equal(res3.fit_result.params.c, 13.4)
+        assert_equal(res3.fit_result.params.scale, 13.73)
+        assert_equal(res3.fit_result.params.loc, -13.85)
+        assert not np.allclose(res3.null_distribution, res1.null_distribution)
+
+    def test_custom_statistic(self):
+        # Test support for custom statistic function.
+
+        # References:
+        # [1] Pyke, R. (1965).  "Spacings".  Journal of the Royal Statistical
+        #     Society: Series B (Methodological), 27(3): 395-436.
+        # [2] Burrows, P. M. (1979).  "Selected Percentage Points of
+        #     Greenwood's Statistics".  Journal of the Royal Statistical
+        #     Society. Series A (General), 142(2): 256-258.
+
+        # Use the Greenwood statistic for illustration; see [1, p.402].
+        def greenwood(dist, data, *, axis):
+            x = np.sort(data, axis=axis)
+            y = dist.cdf(x)
+            d = np.diff(y, axis=axis, prepend=0, append=1)
+            return np.sum(d ** 2, axis=axis)
+
+        # Run the Monte Carlo test with sample size = 5 on a fully specified
+        # null distribution, and compare the simulated quantiles to the exact
+        # ones given in [2, Table 1, column (n = 5)].
+        rng = np.random.default_rng(9121950977643805391)
+        data = stats.expon.rvs(size=5, random_state=rng)
+        result = goodness_of_fit(stats.expon, data,
+                                 known_params={'loc': 0, 'scale': 1},
+                                 statistic=greenwood, rng=rng)
+        p = [.01, .05, .1, .2, .3, .4, .5, .6, .7, .8, .9, .95, .99]
+        exact_quantiles = [
+            .183863, .199403, .210088, .226040, .239947, .253677, .268422,
+            .285293, .306002, .334447, .382972, .432049, .547468]
+        simulated_quantiles = np.quantile(result.null_distribution, p)
+        assert_allclose(simulated_quantiles, exact_quantiles, atol=0.005)
+
+class TestFitResult:
+    def test_plot_iv(self):
+        rng = np.random.default_rng(1769658657308472721)
+        data = stats.norm.rvs(0, 1, size=100, random_state=rng)
+
+        def optimizer(*args, **kwargs):
+            return differential_evolution(*args, **kwargs, rng=rng)
+
+        bounds = [(0, 30), (0, 1)]
+        res = stats.fit(stats.norm, data, bounds, optimizer=optimizer)
+        try:
+            import matplotlib  # noqa: F401
+            message = r"`plot_type` must be one of \{'..."
+            with pytest.raises(ValueError, match=message):
+                res.plot(plot_type='llama')
+        except (ModuleNotFoundError, ImportError):
+            message = r"matplotlib must be installed to use method `plot`."
+            with pytest.raises(ModuleNotFoundError, match=message):
+                res.plot(plot_type='llama')
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diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/test_generation/generate_fisher_exact_results_from_r.R b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_generation/generate_fisher_exact_results_from_r.R
new file mode 100644
index 0000000000000000000000000000000000000000..f49f9fb7ab10701233ebc411dfe2a362f87719a2
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_generation/generate_fisher_exact_results_from_r.R
@@ -0,0 +1,84 @@
+# This R script generates the Python file fisher_exact_results_from_r.py.
+# To run this script, use
+# $ Rscript generate_fisher_exact_results_from_r.R
+
+sink("fisher_exact_results_from_r.py")
+
+options(digits=15)
+
+# Note that when converted to a matrix, `byrow=TRUE` is used, so
+# the first two values of each data set become the first row of
+# the contingency  table.  E.g.
+# > matrix(c(100, 2, 1000, 5), nrow=2, ncol=2, byrow=TRUE)
+#      [,1] [,2]
+# [1,]  100    2
+# [2,] 1000    5
+# 
+table_data = list(
+    c(100, 2, 1000, 5),
+    c(2, 7, 8, 2),
+    c(5, 1, 10, 10),
+    c(5, 15, 20, 20),
+    c(5, 16, 16, 25),
+    c(10, 5, 10, 1),
+    c(10, 5, 10, 0),
+    c(5, 0, 1, 4),
+    c(0, 5, 1, 4),
+    c(5, 1, 0, 4),
+    c(0, 1, 3, 2),
+    c(200, 7, 8, 300),
+    c(28, 21, 6, 1957),
+    c(190, 800, 200, 900)
+)
+confidence.levels = c(0.95, 0.99)
+alternatives = c("two.sided", "less", "greater")
+
+cat("# DO NOT EDIT THIS FILE!", fill=TRUE)
+cat("# This file was generated by the R script", fill=TRUE)
+cat("#     generate_fisher_exact_results_from_r.R", fill=TRUE)
+cat("# The script was run with", R.version.string, "at ")
+s = sprintf("%s", Sys.time())
+cat(s, fill=TRUE)
+cat("", fill=TRUE)
+cat("", fill=TRUE)
+cat("from collections import namedtuple", fill=TRUE)
+cat("import numpy as np", fill=TRUE)
+cat("", fill=TRUE)
+cat("", fill=TRUE)
+cat("Inf = np.inf", fill=TRUE)
+cat("", fill=TRUE)
+cat("Parameters = namedtuple('Parameters',", fill=TRUE)
+cat("                        ['table', 'confidence_level', 'alternative'])", fill=TRUE)
+cat("RResults = namedtuple('RResults',", fill=TRUE)
+cat("                      ['pvalue', 'conditional_odds_ratio',", fill=TRUE)
+cat("                       'conditional_odds_ratio_ci'])", fill=TRUE)
+cat("data = [", fill=TRUE)
+for (alternative in alternatives) {
+    for (conf.level in confidence.levels) {
+        for (data in table_data) {
+            table = matrix(data, nrow=2, ncol=2, byrow=TRUE)
+            #result = fisher.test(table, alternative=alternative, conf.level=conf.level)
+            result = fisher.test(table, alternative=alternative, conf.level=conf.level)
+            cat("    (")
+            cat("Parameters(table=")
+            s = sprintf("[[%.16g, %.16g], [%.16g, %.16g]],", table[1, 1], table[1, 2], table[2, 1], table[2, 2])
+            cat(s, fill=TRUE)
+            s = sprintf("                confidence_level=%.16g,", conf.level)
+            cat(s, fill=TRUE)
+            s = sprintf("                alternative='%s'),", alternative)
+            cat(s, fill=TRUE)
+            cat("     RResults(")
+            s = sprintf("pvalue=%.16g,", result$p.value)
+            cat(s, fill=TRUE)
+            s = sprintf("              conditional_odds_ratio=%.16g,", result$estimate)
+            cat(s, fill=TRUE)
+            s = sprintf("              conditional_odds_ratio_ci=(%.16g,", result$conf.int[1])
+            cat(s, fill=TRUE)
+            s = sprintf("                                         %.16g))),", result$conf.int[2])
+            cat(s, fill=TRUE)
+        }
+    }
+}
+cat("]", fill=TRUE)
+
+sink()
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/test_generation/reference_distribution_infrastructure_tests.py b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_generation/reference_distribution_infrastructure_tests.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f44d24da8804b8bf9c84685f6892dd11723d933
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_generation/reference_distribution_infrastructure_tests.py
@@ -0,0 +1,90 @@
+# Note: this file is to be run locally, not on CI. It is only for tests of the
+# reference distribution *infrastructure*; unit tests of SciPy distributions
+# do not go here.
+
+import numpy as np
+import pytest
+
+from scipy import stats
+from numpy.testing import assert_allclose
+import scipy.stats.tests.test_generation.reference_distributions as rd
+import mpmath
+from mpmath import mp
+
+def test_basic():
+
+    message = "`mpmath.mp.dps <= 15`. Set a higher precision..."
+    with pytest.raises(RuntimeError, match=message):
+        rd.Normal()
+
+    mpmath.dps = 20
+    message = "`mpmath.dps` has been assigned. This is not intended usage..."
+    with pytest.raises(RuntimeError, match=message):
+        rd.Normal()
+    del mpmath.dps
+
+    mp.dps = 20  # high enough to pass, not unreasonably slow
+
+    # Basic tests of the mpmath distribution infrastructure using a SciPy
+    # distribution as a reference. The intent is just to make sure that the
+    # implementations do not have *mistakes* and that broadcasting is working
+    # as expected. The accuracy is what it is.
+
+    rng = np.random.default_rng(6716188855217730280)
+
+    x = rng.random(size=3)
+    a = rng.random(size=(2, 1))
+    rtol = 1e-15
+
+    dist = rd.SkewNormal(a=a)
+    dist_ref = stats.skewnorm(a)
+
+    assert_allclose(dist.pdf(x), dist_ref.pdf(x), rtol=rtol)
+    assert_allclose(dist.cdf(x), dist_ref.cdf(x), rtol=rtol)
+    assert_allclose(dist.sf(x), dist_ref.sf(x), rtol=rtol)
+    assert_allclose(dist.ppf(x), dist_ref.ppf(x), rtol=rtol)
+    assert_allclose(dist.isf(x), dist_ref.isf(x), rtol=rtol)
+    assert_allclose(dist.logpdf(x), dist_ref.logpdf(x), rtol=rtol)
+    assert_allclose(dist.logcdf(x), dist_ref.logcdf(x), rtol=rtol)
+    assert_allclose(dist.logsf(x), dist_ref.logsf(x), rtol=rtol)
+    assert_allclose(dist.support(), dist_ref.support(), rtol=rtol)
+    assert_allclose(dist.entropy(), dist_ref.entropy(), rtol=rtol)
+    assert_allclose(dist.mean(), dist_ref.mean(), rtol=rtol)
+    assert_allclose(dist.var(), dist_ref.var(), rtol=rtol)
+    assert_allclose(dist.skew(), dist_ref.stats('s'), rtol=rtol)
+    assert_allclose(dist.kurtosis(), dist_ref.stats('k'), rtol=rtol)
+
+
+def test_complementary_method_use():
+    # Show that complementary methods are used as expected.
+    # E.g., use 1 - CDF to compute SF if CDF is overridden but SF is not
+
+    mp.dps = 50
+    x = np.linspace(0, 1, 10)
+    class MyDist(rd.ReferenceDistribution):
+        def _cdf(self, x):
+            return x
+
+    dist = MyDist()
+    assert_allclose(dist.sf(x), 1 - dist.cdf(x))
+
+    class MyDist(rd.ReferenceDistribution):
+        def _sf(self, x):
+            return 1-x
+
+    dist = MyDist()
+    assert_allclose(dist.cdf(x), 1 - dist.sf(x))
+
+    class MyDist(rd.ReferenceDistribution):
+        def _ppf(self, x, guess):
+            return x
+
+    dist = MyDist()
+    assert_allclose(dist.isf(x), dist.ppf(1-x))
+
+    class MyDist(rd.ReferenceDistribution):
+        def _isf(self, x, guess):
+            return 1-x
+
+    dist = MyDist()
+    assert_allclose(dist.ppf(x), dist.isf(1-x))
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/test_generation/reference_distributions.py b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_generation/reference_distributions.py
new file mode 100644
index 0000000000000000000000000000000000000000..037b16a2d0c88ddf75416fa1324d010d35e0b363
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_generation/reference_distributions.py
@@ -0,0 +1,430 @@
+import numpy as np
+import mpmath
+from mpmath import mp
+
+
+class ReferenceDistribution:
+    """Minimalist distribution infrastructure for generating reference data.
+
+    The purpose is to generate reference values for unit tests of SciPy
+    distribution accuracy and robustness.
+
+    Handles array input with standard broadcasting rules, and method
+    implementations are easily compared against their mathematical definitions.
+    No attempt is made to handle edge cases or be fast, and arbitrary precision
+    arithmetic is trusted for accuracy rather than making the method
+    implementations "smart".
+
+    Notes
+    -----
+
+    In this infrastructure, distributions families are classes, and
+    fully-specified distributions (i.e. with definite values of all family
+    parameters) are instances of these classes. Typically, the public methods
+    accept as input only the argument at which the at which the function is to
+    be evaluated. Unlike SciPy distributions, they never accept values of
+    distribution family shape, location, or scale parameters. A few
+    other parameters are noteworthy:
+
+    - All methods accept `dtype` to control the output data type. The default
+      is `np.float64`, but `object` or `mp.mpf` may be
+      specified to output the full `mpf`.
+    - `ppf`/`isf` accept a `guess` because they use a scalar rootfinder
+      to invert the `cdf`/`sf`. This is passed directly into the `x0` method
+      of `mpmath.findroot`; see its documentation for details.
+    - moment accepts `order`, an integer that specifies the order of the (raw)
+      moment, and `center`, which is the value about which the moment is
+      taken. The default is to calculate the mean and use it to calculate
+      central moments; passing ``0`` results in a noncentral moment. For
+      efficiency, the mean can be passed explicitly if it is already known.
+
+    Follow the example of SkewNormal to generate new reference distributions,
+    overriding only `__init__` and `_pdf`*. Use the reference distributions to
+    generate reference values for unit tests of SciPy distribution method
+    precision and robustness (e.g. for extreme arguments). If the a SciPy
+    methods implementation is independent and yet the output matches reference
+    values generated with this infrastructure, it is unlikely that the SciPy
+    and reference values are both inaccurate.
+
+    * If the SciPy output *doesn't* match and the cause appears to be
+    inaccuracy of the reference values (e.g. due to numerical issues that
+    mpmath's arbitrary precision arithmetic doesn't handle), then it may be
+    appropriate to override a method of the reference distribution rather than
+    relying on the generic implementation. Otherwise, hesitate to override
+    methods: the generic implementations are mathematically correct and easy
+    to verify, whereas an override introduces many possibilities of mistakes,
+    requires more time to write, and requires more time to review.
+
+    In general, do not create custom unit tests to ensure that
+    SciPy distribution methods are *correct* (in the sense of being consistent
+    with the rest of the distribution methods); generic tests take care of
+    that.
+    """
+
+    def __init__(self, **kwargs):
+        try:
+            if mpmath.dps is not None:
+                message = ("`mpmath.dps` has been assigned. This is not "
+                           "intended usage; instead, assign the desired "
+                           "precision to `mpmath.mp.dps` (e.g. `from mpmath "
+                           "as mp; mp.dps = 50.")
+                raise RuntimeError(message)
+        except AttributeError:
+            mpmath.dps = None
+
+        if mp.dps <= 15:
+            message = ("`mpmath.mp.dps <= 15`. Set a higher precision (e.g."
+                       "`50`) to use this distribution.")
+            raise RuntimeError(message)
+
+        self._params = {key:self._make_mpf_array(val)
+                        for key, val in kwargs.items()}
+
+    def _make_mpf_array(self, x):
+        shape = np.shape(x)
+        x = np.asarray(x, dtype=np.float64).ravel()
+        return np.asarray([mp.mpf(xi) for xi in x]).reshape(shape)[()]
+
+    def _pdf(self, x):
+        raise NotImplementedError("_pdf must be overridden.")
+
+    def _cdf(self, x, **kwargs):
+        if ((self._cdf.__func__ is ReferenceDistribution._cdf)
+                and (self._sf.__func__ is not ReferenceDistribution._sf)):
+            return mp.one - self._sf(x, **kwargs)
+
+        a, b = self._support(**kwargs)
+        res = mp.quad(lambda x: self._pdf(x, **kwargs), (a, x))
+        res = res if res < 0.5 else mp.one - self._sf(x, **kwargs)
+        return res
+
+    def _sf(self, x, **kwargs):
+        if ((self._sf.__func__ is ReferenceDistribution._sf)
+                and (self._cdf.__func__ is not ReferenceDistribution._cdf)):
+            return mp.one - self._cdf(x, **kwargs)
+
+        a, b = self._support(**kwargs)
+        res = mp.quad(lambda x: self._pdf(x, **kwargs), (x, b))
+        res = res if res < 0.5 else mp.one - self._cdf(x, **kwargs)
+        return res
+
+    def _ppf(self, p, guess=0, **kwargs):
+        if ((self._ppf.__func__ is ReferenceDistribution._ppf)
+                and (self._isf.__func__ is not ReferenceDistribution._isf)):
+            return self._isf(mp.one - p, guess, **kwargs)
+        def f(x):
+            return self._cdf(x, **kwargs) - p
+        return mp.findroot(f, guess)
+
+    def _isf(self, p, guess=0, **kwargs):
+        if ((self._isf.__func__ is ReferenceDistribution._isf)
+                and (self._ppf.__func__ is not ReferenceDistribution._ppf)):
+            return self._ppf(mp.one - p, guess, **kwargs)
+        def f(x):
+            return self._sf(x, **kwargs) - p
+        return mp.findroot(f, guess)
+
+    def _logpdf(self, x, **kwargs):
+        return mp.log(self._pdf(x, **kwargs))
+
+    def _logcdf(self, x, **kwargs):
+        return mp.log(self._cdf(x, **kwargs))
+
+    def _logsf(self, x, **kwargs):
+        return mp.log(self._sf(x, **kwargs))
+
+    def _support(self, **kwargs):
+        return -mp.inf, mp.inf
+
+    def _entropy(self, **kwargs):
+        def integrand(x):
+            logpdf = self._logpdf(x, **kwargs)
+            pdf = mp.exp(logpdf)
+            return  -pdf*logpdf
+
+        a, b = self._support(**kwargs)
+        return mp.quad(integrand, (a, b))
+
+    def _mean(self, **kwargs):
+        return self._moment(order=1, center=0, **kwargs)
+
+    def _var(self, **kwargs):
+        mu = self._mean(**kwargs)
+        return self._moment(order=2, center=mu, **kwargs)
+
+    def _skew(self, **kwargs):
+        mu = self._mean(**kwargs)
+        u2 = self._moment(order=2, center=mu, **kwargs)
+        sigma = mp.sqrt(u2)
+        u3 = self._moment(order=3, center=mu, **kwargs)
+        return u3 / sigma**3
+
+    def _kurtosis(self, **kwargs):
+        mu = self._mean(**kwargs)
+        u2 = self._moment(order=2, center=mu, **kwargs)
+        u4 = self._moment(order=4, center=mu, **kwargs)
+        return u4 / u2**2 - 3
+
+    def _moment(self, order, center, **kwargs):
+        def integrand(x):
+            return self._pdf(x, **kwargs)*(x - center)**order
+
+        if center is None:
+            center = self._mean(**kwargs)
+
+        a, b = self._support(**kwargs)
+        return mp.quad(integrand, (a, b))
+
+    def pdf(self, x, dtype=np.float64):
+        fun = np.vectorize(self._pdf)
+        x = self._make_mpf_array(x)
+        res = fun(x, **self._params)
+        return np.asarray(res, dtype=dtype)[()]
+
+    def cdf(self, x, dtype=np.float64):
+        fun = np.vectorize(self._cdf)
+        x = self._make_mpf_array(x)
+        res = fun(x, **self._params)
+        return np.asarray(res, dtype=dtype)[()]
+
+    def sf(self, x, dtype=np.float64):
+        fun = np.vectorize(self._sf)
+        x = self._make_mpf_array(x)
+        res = fun(x, **self._params)
+        return np.asarray(res, dtype=dtype)[()]
+
+    def ppf(self, x, guess=0, dtype=np.float64):
+        fun = np.vectorize(self._ppf, excluded={1})  # don't vectorize guess
+        x = self._make_mpf_array(x)
+        res = fun(x, guess, **self._params)
+        return np.asarray(res, dtype=dtype)[()]
+
+    def isf(self, x, guess=0, dtype=np.float64):
+        fun = np.vectorize(self._isf, excluded={1})  # don't vectorize guess
+        x = self._make_mpf_array(x)
+        res = fun(x, guess, **self._params)
+        return np.asarray(res, dtype=dtype)[()]
+
+    def logpdf(self, x, dtype=np.float64):
+        fun = np.vectorize(self._logpdf)
+        x = self._make_mpf_array(x)
+        res = fun(x, **self._params)
+        return np.asarray(res, dtype=dtype)[()]
+
+    def logcdf(self, x, dtype=np.float64):
+        fun = np.vectorize(self._logcdf)
+        x = self._make_mpf_array(x)
+        res = fun(x, **self._params)
+        return np.asarray(res, dtype=dtype)[()]
+
+    def logsf(self, x, dtype=np.float64):
+        fun = np.vectorize(self._logsf)
+        x = self._make_mpf_array(x)
+        res = fun(x, **self._params)
+        return np.asarray(res, dtype=dtype)[()]
+
+    def support(self, dtype=np.float64):
+        fun = np.vectorize(self._support)
+        res = fun(**self._params)
+        return np.asarray(res, dtype=dtype)[()]
+
+    def entropy(self, dtype=np.float64):
+        fun = np.vectorize(self._entropy)
+        res = fun(**self._params)
+        return np.asarray(res, dtype=dtype)[()]
+
+    def mean(self, dtype=np.float64):
+        fun = np.vectorize(self._mean)
+        res = fun(**self._params)
+        return np.asarray(res, dtype=dtype)[()]
+
+    def var(self, dtype=np.float64):
+        fun = np.vectorize(self._var)
+        res = fun(**self._params)
+        return np.asarray(res, dtype=dtype)[()]
+
+    def skew(self, dtype=np.float64):
+        fun = np.vectorize(self._skew)
+        res = fun(**self._params)
+        return np.asarray(res, dtype=dtype)[()]
+
+    def kurtosis(self, dtype=np.float64):
+        fun = np.vectorize(self._kurtosis)
+        res = fun(**self._params)
+        return np.asarray(res, dtype=dtype)[()]
+
+    def moment(self, order, center=None, dtype=np.float64):
+        fun = np.vectorize(self._moment)
+        order = self._make_mpf_array(order)
+        res = fun(order, **self._params)
+        return np.asarray(res, dtype=dtype)[()]
+
+
+class SkewNormal(ReferenceDistribution):
+    """Reference implementation of the SkewNormal distribution.
+
+    Follow the example here to generate new reference distributions.
+    Use the reference distributions to generate reference values of
+    distributions functions. For now, copy-paste the output into unit
+    tests. Full code to generate reference values does not need to be
+    included as a comment in the test; just refer to the reference
+    distribution used and the settings (e.g. mp.dps=50).
+    """
+
+    def __init__(self, *, a):
+        # Overriding __init__ is not necessary, but it allows IDEs to hint at
+        # shape parameters. All parameters are keyword only to avoid the
+        # ambiguity inherent in positional arguments. The infrastructure does
+        # not take care of location and scale; nonetheless, assume standard
+        # location and scale. Typically, there is no need to test the SciPy
+        # distribution infrastructure's treatment of location and scale
+        # separately for a specific distribution.
+        super().__init__(a=a)
+
+    def _support(self, a):
+        # Override _support if the support of the distribution is a subset of
+        # the real line
+        return -mp.inf, mp.inf
+
+    def _pdf(self, x, a):
+        # Write PDFs following a scholarly reference as closely as possible.
+        # Trust mpmath for the accuracy, and don't worry about speed. What's
+        # important is the ease of verifying the PDF against the reference. If
+        # the result is inaccurate, it will not match SciPy's output (whether
+        # SciPy is accurate or not). If this occurs, try increasing dps before
+        # implementing a numerically favorable (but presumably more complex)
+        # implementation.
+        return 2 * mp.npdf(x) * mp.ncdf(a * x)
+
+    # Avoid overriding other methods unless the generic implementation is
+    # believed to be inaccurate (e.g. due to numerical difficulties) or it is
+    # too slow. Why? Less code to write, less code to review, and a guarantee
+    # that there is no *mistake* in the implementation (e.g. wrong formula).
+
+
+class BetaPrime(ReferenceDistribution):
+
+    def __init__(self, *, a, b):
+        super().__init__(a=a, b=b)
+
+    def _support(self, **kwargs):
+        return mp.zero, mp.inf
+
+    def _logpdf(self, x, a, b):
+        return (a - mp.one)*mp.log(x) - (a + b)*mp.log1p(x) - mp.log(mp.beta(a, b))
+
+    def _pdf(self, x, a, b):
+        return mp.exp(self._logpdf(x=x, a=a, b=b))
+
+    def _sf(self, x, a, b):
+        return 1.0 - mp.betainc(a, b, 0, x/(1+x), regularized=True)
+
+
+class Burr(ReferenceDistribution):
+
+    def __init__(self, *, c, d):
+        super().__init__(c=c, d=d)
+
+    def _support(self, c, d):
+        return 0, mp.inf
+
+    def _pdf(self, x, c, d):
+        return c * d * x ** (-c - 1) * (1 + x ** (-c)) ** (-d - 1)
+
+    def _ppf(self, p, guess, c, d):
+        return (p**(-1.0/d) - 1)**(-1.0/c)
+
+
+class LogLaplace(ReferenceDistribution):
+
+    def __init__(self, *, c):
+        super().__init__(c=c)
+
+    def _support(self, c):
+        return 0, mp.inf
+
+    def _pdf(self, x, c):
+        if x < mp.one:
+            return c / 2 * x**(c - mp.one)
+        else:
+            return c / 2 * x**(-c - mp.one)
+
+    def _ppf(self, q, guess, c):
+        if q < 0.5:
+            return (2.0 * q)**(mp.one / c)
+        else:
+            return (2 * (mp.one - q))**(-mp.one / c)
+
+
+class LogNormal(ReferenceDistribution):
+
+    def __init__(self, *, s):
+        super().__init__(s=s)
+
+    def _support(self, s):
+        return 0, mp.inf
+
+    def _pdf(self, x, s):
+        return (
+            mp.one / (s * x * mp.sqrt(2 * mp.pi))
+            * mp.exp(-mp.one / 2 * (mp.log(x) / s)**2)
+        )
+
+    def _cdf(self, x, s):
+        return mp.ncdf(mp.log(x) / s)
+
+
+class Normal(ReferenceDistribution):
+
+    def _pdf(self, x):
+        return mp.npdf(x)
+
+
+class NormInvGauss(ReferenceDistribution):
+
+    def __init__(self, *, alpha, beta):
+        super().__init__(alpha=alpha, beta=beta)
+
+    def _pdf(self, x, alpha, beta):
+        # Implemented as described in https://www.jstor.org/stable/4616433
+        # Equations 2.1 - 2.3
+        q = mp.sqrt(1 + x**2)
+        a = mp.pi**-1 * alpha * mp.exp(mp.sqrt(alpha**2 - beta**2))
+        return a * q**-1 * mp.besselk(1, alpha*q) * mp.exp(beta*x)
+
+
+class Pearson3(ReferenceDistribution):
+    def __init__(self, *, skew):
+        super().__init__(skew=skew)
+
+    def _pdf(self, x, skew):
+        b = 2 / skew
+        a = b**2
+        c = -b
+        res = abs(b)/mp.gamma(a) * (b*(x-c))**(a-1) * mp.exp(-b*(x-c))
+        return res if abs(res.real) == res else 0
+
+
+class StudentT(ReferenceDistribution):
+
+    def __init(self, *, df):
+        super().__init__(df=df)
+
+    def _pdf(self, x, df):
+        return (mp.gamma((df + mp.one)/2)/(mp.sqrt(df * mp.pi) * mp.gamma(df/2))
+                * (mp.one + x*x/df)**(-(df + mp.one)/2))
+
+
+class TruncExpon(ReferenceDistribution):
+
+    def __init__(self, *, b):
+        super().__init__(b=b)
+
+    def _support(self, b):
+        return 0, b
+
+    def _pdf(self, x, b):
+        return -mp.exp(-x)/mp.expm1(-b)
+
+    def _sf(self, x, b):
+        return (mp.exp(-b) - mp.exp(-x))/mp.expm1(-b)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/test_generation/studentized_range_mpmath_ref.py b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_generation/studentized_range_mpmath_ref.py
new file mode 100644
index 0000000000000000000000000000000000000000..2f67a3453e08561cfab7f2d85b34a58d7e345992
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_generation/studentized_range_mpmath_ref.py
@@ -0,0 +1,252 @@
+# To run this script, run
+# `python studentized_range_mpmath_ref.py`
+# in the "scipy/stats/tests/" directory
+
+# This script generates a JSON file "./data/studentized_range_mpmath_ref.json"
+# that is used to compare the accuracy of `studentized_range` functions against
+# precise (20 DOP) results generated using `mpmath`.
+
+# Equations in this file have been taken from
+# https://en.wikipedia.org/wiki/Studentized_range_distribution
+# and have been checked against the following reference:
+# Lund, R. E., and J. R. Lund. "Algorithm AS 190: Probabilities and
+# Upper Quantiles for the Studentized Range." Journal of the Royal
+# Statistical Society. Series C (Applied Statistics), vol. 32, no. 2,
+# 1983, pp. 204-210. JSTOR, www.jstor.org/stable/2347300. Accessed 18
+# Feb. 2021.
+
+# Note: I would have preferred to use pickle rather than JSON, but -
+# due to security concerns - decided against it.
+import itertools
+from collections import namedtuple
+import json
+import time
+
+import os
+from multiprocessing import Pool, cpu_count
+
+from mpmath import gamma, pi, sqrt, quad, inf, mpf, mp
+from mpmath import npdf as phi
+from mpmath import ncdf as Phi
+
+results_filepath = "data/studentized_range_mpmath_ref.json"
+num_pools = max(cpu_count() - 1, 1)
+
+MPResult = namedtuple("MPResult", ["src_case", "mp_result"])
+
+CdfCase = namedtuple("CdfCase",
+                     ["q", "k", "v", "expected_atol", "expected_rtol"])
+
+MomentCase = namedtuple("MomentCase",
+                        ["m", "k", "v", "expected_atol", "expected_rtol"])
+
+# Load previously generated JSON results, or init a new dict if none exist
+if os.path.isfile(results_filepath):
+    res_dict = json.load(open(results_filepath))
+else:
+    res_dict = dict()
+
+# Frame out data structure. Store data with the function type as a top level
+# key to allow future expansion
+res_dict["COMMENT"] = ("!!!!!! THIS FILE WAS AUTOGENERATED BY RUNNING "
+                       "`python studentized_range_mpmath_ref.py` !!!!!!")
+res_dict.setdefault("cdf_data", [])
+res_dict.setdefault("pdf_data", [])
+res_dict.setdefault("moment_data", [])
+
+general_atol, general_rtol = 1e-11, 1e-11
+
+mp.dps = 24
+
+cp_q = [0.1, 1, 4, 10]
+cp_k = [3, 10, 20]
+cp_nu = [3, 10, 20, 50, 100, 120]
+
+cdf_pdf_cases = [
+    CdfCase(*case,
+            general_atol,
+            general_rtol)
+    for case in
+    itertools.product(cp_q, cp_k, cp_nu)
+]
+
+mom_atol, mom_rtol = 1e-9, 1e-9
+# These are EXTREMELY slow - Multiple days each in worst case.
+moment_cases = [
+    MomentCase(i, 3, 10, mom_atol, mom_rtol)
+    for i in range(5)
+]
+
+
+def write_data():
+    """Writes the current res_dict to the target JSON file"""
+    with open(results_filepath, mode="w") as f:
+        json.dump(res_dict, f, indent=2)
+
+
+def to_dict(named_tuple):
+    """Converts a namedtuple to a dict"""
+    return dict(named_tuple._asdict())
+
+
+def mp_res_to_dict(mp_result):
+    """Formats an MPResult namedtuple into a dict for JSON dumping"""
+    return {
+        "src_case": to_dict(mp_result.src_case),
+
+        # np assert can't handle mpf, so take the accuracy hit here.
+        "mp_result": float(mp_result.mp_result)
+    }
+
+
+def cdf_mp(q, k, nu):
+    """Straightforward implementation of studentized range CDF"""
+    q, k, nu = mpf(q), mpf(k), mpf(nu)
+
+    def inner(s, z):
+        return phi(z) * (Phi(z + q * s) - Phi(z)) ** (k - 1)
+
+    def outer(s, z):
+        return s ** (nu - 1) * phi(sqrt(nu) * s) * inner(s, z)
+
+    def whole(s, z):
+        return (sqrt(2 * pi) * k * nu ** (nu / 2)
+                / (gamma(nu / 2) * 2 ** (nu / 2 - 1)) * outer(s, z))
+
+    res = quad(whole, [0, inf], [-inf, inf],
+               method="gauss-legendre", maxdegree=10)
+    return res
+
+
+def pdf_mp(q, k, nu):
+    """Straightforward implementation of studentized range PDF"""
+    q, k, nu = mpf(q), mpf(k), mpf(nu)
+
+    def inner(s, z):
+        return phi(z + q * s) * phi(z) * (Phi(z + q * s) - Phi(z)) ** (k - 2)
+
+    def outer(s, z):
+        return s ** nu * phi(sqrt(nu) * s) * inner(s, z)
+
+    def whole(s, z):
+        return (sqrt(2 * pi) * k * (k - 1) * nu ** (nu / 2)
+                / (gamma(nu / 2) * 2 ** (nu / 2 - 1)) * outer(s, z))
+
+    res = quad(whole, [0, inf], [-inf, inf],
+               method="gauss-legendre", maxdegree=10)
+    return res
+
+
+def moment_mp(m, k, nu):
+    """Implementation of the studentized range moment"""
+    m, k, nu = mpf(m), mpf(k), mpf(nu)
+
+    def inner(q, s, z):
+        return phi(z + q * s) * phi(z) * (Phi(z + q * s) - Phi(z)) ** (k - 2)
+
+    def outer(q, s, z):
+        return s ** nu * phi(sqrt(nu) * s) * inner(q, s, z)
+
+    def pdf(q, s, z):
+        return (sqrt(2 * pi) * k * (k - 1) * nu ** (nu / 2)
+                / (gamma(nu / 2) * 2 ** (nu / 2 - 1)) * outer(q, s, z))
+
+    def whole(q, s, z):
+        return q ** m * pdf(q, s, z)
+
+    res = quad(whole, [0, inf], [0, inf], [-inf, inf],
+               method="gauss-legendre", maxdegree=10)
+    return res
+
+
+def result_exists(set_key, case):
+    """Searches the results dict for a result in the set that matches a case.
+    Returns True if such a case exists."""
+    if set_key not in res_dict:
+        raise ValueError(f"{set_key} not present in data structure!")
+
+    case_dict = to_dict(case)
+    existing_res = list(filter(
+        lambda res: res["src_case"] == case_dict,  # dict comparison
+        res_dict[set_key]))
+
+    return len(existing_res) > 0
+
+
+def run(case, run_lambda, set_key, index=0, total_cases=0):
+    """Runs the single passed case, returning an mp dictionary and index"""
+    t_start = time.perf_counter()
+
+    res = run_lambda(case)
+
+    print(f"Finished {index + 1}/{total_cases} in batch. "
+          f"(Took {time.perf_counter() - t_start}s)")
+
+    return index, set_key, mp_res_to_dict(MPResult(case, res))
+
+
+def write_result(res):
+    """A callback for completed jobs. Inserts and writes a calculated result
+     to file."""
+    index, set_key, result_dict = res
+    res_dict[set_key].insert(index, result_dict)
+    write_data()
+
+
+def run_cases(cases, run_lambda, set_key):
+    """Runs an array of cases and writes to file"""
+    # Generate jobs to run from cases that do not have a result in
+    # the previously loaded JSON.
+    job_arg = [(case, run_lambda, set_key, index, len(cases))
+               for index, case in enumerate(cases)
+               if not result_exists(set_key, case)]
+
+    print(f"{len(cases) - len(job_arg)}/{len(cases)} cases won't be "
+          f"calculated because their results already exist.")
+
+    jobs = []
+    pool = Pool(num_pools)
+
+    # Run all using multiprocess
+    for case in job_arg:
+        jobs.append(pool.apply_async(run, args=case, callback=write_result))
+
+    pool.close()
+    pool.join()
+
+
+def run_pdf(case):
+    return pdf_mp(case.q, case.k, case.v)
+
+
+def run_cdf(case):
+    return cdf_mp(case.q, case.k, case.v)
+
+
+def run_moment(case):
+    return moment_mp(case.m, case.k, case.v)
+
+
+def main():
+    t_start = time.perf_counter()
+
+    total_cases = 2 * len(cdf_pdf_cases) + len(moment_cases)
+    print(f"Processing {total_cases} test cases")
+
+    print(f"Running 1st batch ({len(cdf_pdf_cases)} PDF cases). "
+          f"These take about 30s each.")
+    run_cases(cdf_pdf_cases, run_pdf, "pdf_data")
+
+    print(f"Running 2nd batch ({len(cdf_pdf_cases)} CDF cases). "
+          f"These take about 30s each.")
+    run_cases(cdf_pdf_cases, run_cdf, "cdf_data")
+
+    print(f"Running 3rd batch ({len(moment_cases)} moment cases). "
+          f"These take about anywhere from a few hours to days each.")
+    run_cases(moment_cases, run_moment, "moment_data")
+
+    print(f"Test data generated in {time.perf_counter() - t_start}s")
+
+
+if __name__ == "__main__":
+    main()
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/test_hypotests.py b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_hypotests.py
new file mode 100644
index 0000000000000000000000000000000000000000..a5762185f7b8b4363e469c3974b20106fad7cb0b
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_hypotests.py
@@ -0,0 +1,2248 @@
+from itertools import product
+
+import numpy as np
+import functools
+import pytest
+from numpy.testing import assert_, assert_equal, assert_allclose
+from pytest import raises as assert_raises
+
+from scipy import stats, special
+from scipy.stats import distributions
+from scipy.stats._hypotests import (epps_singleton_2samp, cramervonmises,
+                                    _cdf_cvm, cramervonmises_2samp,
+                                    _pval_cvm_2samp_exact, barnard_exact,
+                                    boschloo_exact)
+from scipy.stats._mannwhitneyu import mannwhitneyu, _mwu_state, _MWU
+from scipy._lib._testutils import _TestPythranFunc
+from scipy._external import array_api_extra as xpx
+from scipy._lib._array_api import (make_xp_test_case, xp_default_dtype, is_numpy,
+                                   eager_warns, xp_ravel, is_jax)
+from scipy._lib._array_api_no_0d import xp_assert_equal, xp_assert_close
+from scipy.stats._axis_nan_policy import SmallSampleWarning, too_small_1d_not_omit
+
+lazy_xp_modules = [stats]
+skip_xp_backends = pytest.mark.skip_xp_backends
+
+
+@make_xp_test_case(epps_singleton_2samp)
+class TestEppsSingleton:
+    def test_epps_singleton_iv(self, xp):
+        # partial input validation test relevant to the addition of JIT support
+        # TODO: complete input validation tests
+        x = xp.asarray([-0.35, 2.55, 1.73, 0.73, 0.35])
+        y = xp.asarray([-1.15, -0.15, 2.48, 3.25, 3.71])
+        t = xp.asarray([0.4, -0.4])
+        if is_jax(xp):
+            w, p = epps_singleton_2samp(x, y, t=t)
+            xp_assert_equal(w, xp.asarray(xp.nan))
+            xp_assert_equal(p, xp.asarray(xp.nan))
+        else:
+            message = "t must contain positive elements only."
+            with pytest.raises(ValueError, match=message):
+                epps_singleton_2samp(x, y, t=t)
+
+    @pytest.mark.parametrize('dtype', [None, 'float32', 'float64'])
+    def test_statistic_1(self, dtype, xp):
+        # first example in Goerg & Kaiser, also in original paper of
+        # Epps & Singleton. Note: values do not match exactly, the
+        # value of the interquartile range varies depending on how
+        # quantiles are computed
+        dtype = xp_default_dtype(xp) if dtype is None else getattr(xp, dtype)
+        x = xp.asarray([-0.35, 2.55, 1.73, 0.73, 0.35,
+                        2.69, 0.46, -0.94, -0.37, 12.07], dtype=dtype)
+        y = xp.asarray([-1.15, -0.15, 2.48, 3.25, 3.71,
+                     4.29, 5.00, 7.74, 8.38, 8.60], dtype=dtype)
+        w, p = epps_singleton_2samp(x, y)
+        xp_assert_close(w, xp.asarray(15.14, dtype=dtype), atol=0.03)
+        xp_assert_close(p, xp.asarray(0.00442, dtype=dtype), atol=0.0001)
+
+    def test_statistic_2(self, xp):
+        # second example in Goerg & Kaiser, again not a perfect match
+        x = xp.asarray([0, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4,
+                        5, 5, 5, 5, 6, 10, 10, 10, 10])
+        y = xp.asarray([10, 4, 0, 5, 10, 10, 0, 5, 6, 7,
+                        10, 3, 1, 7, 0, 8, 1, 5, 8, 10])
+        w, p = epps_singleton_2samp(x, y)
+        xp_assert_close(w, xp.asarray(8.900), atol=1e-3)
+        xp_assert_close(p, xp.asarray(0.06364), atol=5e-5)
+
+    def test_epps_singleton_array_like(self):  # only relevant for NumPy
+        x, y = np.arange(30), np.arange(28)
+
+        w1, p1 = epps_singleton_2samp(list(x), list(y))
+        w2, p2 = epps_singleton_2samp(tuple(x), tuple(y))
+        w3, p3 = epps_singleton_2samp(x, y)
+
+        assert_(w1 == w2 == w3)
+        assert_(p1 == p2 == p3)
+
+    def test_epps_singleton_size(self, xp):
+        # warns if sample contains fewer than 5 elements
+        x, y = xp.asarray([1, 2, 3, 4]), xp.arange(10)
+        with eager_warns(SmallSampleWarning, match=too_small_1d_not_omit, xp=xp):
+            res = epps_singleton_2samp(x, y)
+            xp_assert_equal(res.statistic, xp.asarray(xp.nan))
+            xp_assert_equal(res.pvalue, xp.asarray(xp.nan))
+
+    def test_epps_singleton_nonfinite(self, xp):
+        rng = np.random.default_rng(83249872384543)
+        x = rng.random(size=(10, 11))
+        y = rng.random(size=(10, 12))
+        i = np.asarray([1, 4, 9])  # arbitrary rows
+
+        w_ref, p_ref = epps_singleton_2samp(x, y, axis=-1)
+        w_ref[i] = np.nan
+        p_ref[i] = np.nan
+
+        x[i[0], 0] = np.nan
+        x[i[1], 1] = np.inf
+        y[i[2], 2] = -np.inf
+
+        x, y = xp.asarray(x), xp.asarray(y)
+        w_res, p_res = epps_singleton_2samp(x, y, axis=-1)
+        xp_assert_close(w_res, xp.asarray(w_ref))
+        xp_assert_close(p_res, xp.asarray(p_ref))
+
+
+@make_xp_test_case(stats.cramervonmises)
+class TestCvm:
+    # the expected values of the cdfs are taken from Table 1 in
+    # Csorgo / Faraway: The Exact and Asymptotic Distribution of
+    # Cramér-von Mises Statistics, 1996.
+    @pytest.mark.parametrize('n, x, ref', [
+        (4, [0.02983, 0.04111, 0.12331, 0.94251], [0.01, 0.05, 0.5, 0.999]),
+        (10, [0.02657, 0.03830, 0.12068, 0.56643], [0.01, 0.05, 0.5, 0.975]),
+        (1000, [0.02481, 0.03658, 0.11889, 1.16120], [0.01, 0.05, 0.5, 0.999]),
+        (None, [0.02480, 0.03656, 0.11888, 1.16204], [0.01, 0.05, 0.5, 0.999]),
+    ])
+    def test_cdf_ref(self, n, x, ref, xp):
+        xp_assert_close(_cdf_cvm(xp.asarray(x), n), xp.asarray(ref), atol=1e-4)
+
+    def test_cdf_support(self, xp):
+        # cdf has support on [1/(12*n), n/3]
+        xp_assert_equal(_cdf_cvm(xp.asarray([1/(12*533), 533/3]), 533),
+                        xp.asarray([0., 1.]))
+        xp_assert_equal(_cdf_cvm(xp.asarray([1/(12*(27 + 1)), (27 + 1)/3]), 27),
+                        xp.asarray([0., 1.]))
+
+    def test_cdf_large_n(self, xp):
+        # test that asymptotic cdf and cdf for large samples are close
+        x = xp.asarray([0.02480, 0.03656, 0.11888, 1.16204, 100])
+        xp_assert_close(_cdf_cvm(x, 10000), _cdf_cvm(x), atol=1e-4)
+
+    def test_large_x(self, xp):
+        # for large values of x and n, the series used to compute the cdf
+        # converges slowly.
+        # this leads to bug in R package goftest and MAPLE code that is
+        # the basis of the implementation in scipy
+        # note: cdf = 1 for x >= 1000/3 and n = 1000
+        x = xp.asarray(333.3, dtype=xp.float64)
+        assert (0.99999 < _cdf_cvm(x, 1000) < 1.0)
+        assert (0.99999 < _cdf_cvm(x) < 1.0)
+
+    def test_low_p(self, xp):
+        # _cdf_cvm can return values larger than 1. In that case, we just
+        # return a p-value of zero.
+        n = 12
+        res = cramervonmises(xp.ones(n)*0.8, special.ndtr)
+        assert _cdf_cvm(res.statistic, n, xp=xp) > 1.0
+        xp_assert_equal(res.pvalue, xp.asarray(0.))
+
+    @pytest.mark.parametrize('x', [(), [1.5]])
+    def test_invalid_input(self, x, xp):
+        with pytest.warns(SmallSampleWarning, match=too_small_1d_not_omit):
+            res = cramervonmises(xp.asarray(x), special.ndtr)
+            xp_assert_equal(res.statistic, xp.asarray(xp.nan))
+            xp_assert_equal(res.pvalue, xp.asarray(xp.nan))
+
+    @pytest.mark.parametrize('dtype', [None, 'float32', 'float64'])
+    def test_values_R(self, dtype, xp):
+        dtype = xp_default_dtype(xp) if dtype is None else getattr(xp, dtype)
+        # compared against R package goftest, version 1.1.1
+        # library(goftest)
+        # options(digits=16)
+        # cvm.test(c(-1.7, 2, 0, 1.3, 4, 0.1, 0.6), "pnorm")
+        res = cramervonmises(xp.asarray([-1.7, 2, 0, 1.3, 4, 0.1, 0.6], dtype=dtype),
+                             special.ndtr)
+        xp_assert_close(res.statistic, xp.asarray(0.28815604599198, dtype=dtype))
+        xp_assert_close(res.pvalue, xp.asarray( 0.1453465252039, dtype=dtype))
+
+        # cvm.test(c(-1.7, 2, 0, 1.3, 4, 0.1, 0.6), "pnorm", mean = 3, sd = 1.5)
+        res = cramervonmises(xp.asarray([-1.7, 2, 0, 1.3, 4, 0.1, 0.6], dtype=dtype),
+                             lambda x: special.ndtr((x - 3)/1.5))
+        xp_assert_close(res.statistic, xp.asarray(0.94266847977072, dtype=dtype))
+        xp_assert_close(res.pvalue, xp.asarray(0.002026416728467, dtype=dtype))
+
+        # cvm.test(c(1, 2, 5, 1.4, 0.14, 11, 13, 0.9, 7.5), "pexp")
+        res = cramervonmises(
+            xp.asarray([1, 2, 5, 1.4, 0.14, 11, 13, 0.9, 7.5], dtype=dtype),
+            lambda x: -xp.expm1(-x))
+        xp_assert_close(res.statistic, xp.asarray(0.84218540922393, dtype=dtype))
+        xp_assert_close(res.pvalue, xp.asarray(0.004433406063014, dtype=dtype))
+
+    def test_str_cdf(self, xp):
+        if not is_numpy(xp):
+            message = "`cdf` must be a callable if `rvs` is a non-NumPy array."
+            with pytest.raises(ValueError, match=message):
+                cramervonmises(xp.asarray([1, 2, 3]), "beta")
+            return
+
+        x, args = np.arange(5), (1.4, 0.7)
+        ref = cramervonmises(x, distributions.expon.cdf)
+        res = cramervonmises(x, "expon")
+        assert_equal((res.statistic, res.pvalue), (ref.statistic, ref.pvalue))
+
+        ref = cramervonmises(x, distributions.beta.cdf, args)
+        res = cramervonmises(x, "beta", args)
+        assert_equal((res.statistic, res.pvalue), (ref.statistic, ref.pvalue))
+
+
+@make_xp_test_case(stats.mannwhitneyu)
+class TestMannWhitneyU:
+
+    # All magic numbers are from R wilcox.test unless otherwise specified
+    # https://rdrr.io/r/stats/wilcox.test.html
+
+    # --- Test Input Validation ---
+
+    def get_zstatistic_from_pvalue(self, p, U, n1, n2, alternative):
+        if alternative == 'less':
+            z = special.ndtri(p)
+        elif alternative == 'greater':
+            z = -special.ndtri(p)
+        else:
+            z = special.ndtri(p/2) if U < n1*n2/2 else -special.ndtri(p/2)
+        return z
+
+    def test_empty(self, xp):
+        x = xp.asarray([1, 2])  # generic, valid inputs
+        y = xp.asarray([3, 4])
+        empty = xp.asarray([], dtype=x.dtype)
+        nan = xp.asarray(xp.nan)
+
+        with pytest.warns(SmallSampleWarning, match=too_small_1d_not_omit):
+            res = mannwhitneyu(x, empty)
+            xp_assert_close(res.statistic, nan)
+            xp_assert_close(res.pvalue, nan)
+
+        with pytest.warns(SmallSampleWarning, match=too_small_1d_not_omit):
+            res = mannwhitneyu(empty, y)
+            xp_assert_close(res.statistic, nan)
+            xp_assert_close(res.pvalue, nan)
+
+        with pytest.warns(SmallSampleWarning, match=too_small_1d_not_omit):
+            res = mannwhitneyu(empty, empty)
+            xp_assert_close(res.statistic, nan)
+            xp_assert_close(res.pvalue, nan)
+
+    def test_input_validation(self, xp):
+        x = xp.asarray([1, 2])  # generic, valid inputs
+        y = xp.asarray([3, 4])
+        with assert_raises(ValueError, match="`use_continuity` must be one"):
+            mannwhitneyu(x, y, use_continuity='ekki')
+        with assert_raises(ValueError, match="`alternative` must be one of"):
+            mannwhitneyu(x, y, alternative='ekki')
+        with assert_raises(ValueError, match="`axis` must be an integer"):
+            mannwhitneyu(x, y, axis=1.5)
+        with assert_raises(ValueError, match="`method` must be one of"):
+            mannwhitneyu(x, y, method='ekki')
+
+    def test_auto(self, xp):
+        # Test that default method ('auto') chooses intended method
+        if is_jax(xp):
+            message = "`method='auto'` is incompatible with JAX arrays."
+            with pytest.raises(ValueError, match=message):
+                mannwhitneyu(xp.arange(10), xp.arange(10))
+            return
+
+        rng = np.random.default_rng(923823782530925934)
+        n = 8  # threshold to switch from exact to asymptotic
+
+        # both inputs are smaller than threshold; should use exact
+        x = xp.asarray(rng.random(n-1))
+        y = xp.asarray(rng.random(n-1))
+        auto = mannwhitneyu(x, y)
+        asymptotic = mannwhitneyu(x, y, method='asymptotic')
+        exact = mannwhitneyu(x, y, method='exact')
+        assert auto.pvalue == exact.pvalue
+        assert auto.pvalue != asymptotic.pvalue
+
+        # one input is smaller than threshold; should use exact
+        x = xp.asarray(rng.random(n-1))
+        y = xp.asarray(rng.random(n+1))
+        auto = mannwhitneyu(x, y)
+        asymptotic = mannwhitneyu(x, y, method='asymptotic')
+        exact = mannwhitneyu(x, y, method='exact')
+        assert auto.pvalue == exact.pvalue
+        assert auto.pvalue != asymptotic.pvalue
+
+        # other input is smaller than threshold; should use exact
+        auto = mannwhitneyu(y, x)
+        asymptotic = mannwhitneyu(x, y, method='asymptotic')
+        exact = mannwhitneyu(x, y, method='exact')
+        assert auto.pvalue == exact.pvalue
+        assert auto.pvalue != asymptotic.pvalue
+
+        # both inputs are larger than threshold; should use asymptotic
+        x = xp.asarray(rng.random(n+1))
+        y = xp.asarray(rng.random(n+1))
+        auto = mannwhitneyu(x, y)
+        asymptotic = mannwhitneyu(x, y, method='asymptotic')
+        exact = mannwhitneyu(x, y, method='exact')
+        assert auto.pvalue != exact.pvalue
+        assert auto.pvalue == asymptotic.pvalue
+
+        # both inputs are smaller than threshold, but there is a tie
+        # should use asymptotic
+        x = xp.asarray(rng.random(n-1))
+        y = xp.asarray(rng.random(n-1))
+        y = xpx.at(y)[3].set(x[3])
+        auto = mannwhitneyu(x, y)
+        asymptotic = mannwhitneyu(x, y, method='asymptotic')
+        exact = mannwhitneyu(x, y, method='exact')
+        assert auto.pvalue != exact.pvalue
+        assert auto.pvalue == asymptotic.pvalue
+
+    # --- Test Basic Functionality ---
+
+    x = [210.052110, 110.190630, 307.918612]
+    y = [436.08811482466416, 416.37397329768191, 179.96975939463582,
+         197.8118754228619, 34.038757281225756, 138.54220550921517,
+         128.7769351470246, 265.92721427951852, 275.6617533155341,
+         592.34083395416258, 448.73177590617018, 300.61495185038905,
+         187.97508449019588]
+
+    # This test was written for mann_whitney_u in gh-4933.
+    # Originally, the p-values for alternatives were swapped;
+    # this has been corrected and the tests have been refactored for
+    # compactness, but otherwise the tests are unchanged.
+    # R code for comparison, e.g.:
+    # options(digits = 16)
+    # x = c(210.052110, 110.190630, 307.918612)
+    # y = c(436.08811482466416, 416.37397329768191, 179.96975939463582,
+    #       197.8118754228619, 34.038757281225756, 138.54220550921517,
+    #       128.7769351470246, 265.92721427951852, 275.6617533155341,
+    #       592.34083395416258, 448.73177590617018, 300.61495185038905,
+    #       187.97508449019588)
+    # wilcox.test(x, y, alternative="g", exact=TRUE)
+    cases_basic = [[{"alternative": 'two-sided', "method": "asymptotic"},
+                    (16., 0.6865041817876)],
+                   [{"alternative": 'less', "method": "asymptotic"},
+                    (16., 0.3432520908938)],
+                   [{"alternative": 'greater', "method": "asymptotic"},
+                    (16., 0.7047591913255)],
+                   [{"alternative": 'two-sided', "method": "exact"},
+                    (16., 0.7035714285714)],
+                   [{"alternative": 'less', "method": "exact"},
+                    (16., 0.3517857142857)],
+                   [{"alternative": 'greater', "method": "exact"},
+                    (16., 0.6946428571429)]]
+
+    @pytest.mark.parametrize(("kwds", "expected"), cases_basic)
+    @pytest.mark.parametrize("dtype", [None, 'float32', 'float64'])
+    def test_basic(self, kwds, expected, dtype, xp):
+        dtype = xp_default_dtype(xp) if dtype is None else getattr(xp, dtype)
+        x, y = xp.asarray(self.x, dtype=dtype), xp.asarray(self.y, dtype=dtype)
+        res = mannwhitneyu(x, y, **kwds)
+        xp_assert_close(res.statistic, xp.asarray(expected[0], dtype=dtype))
+        xp_assert_close(res.pvalue, xp.asarray(expected[1], dtype=dtype))
+        if kwds['method'] == 'asymptotic':
+            z = self.get_zstatistic_from_pvalue(res.pvalue, res.statistic,
+                                                x.shape[0], y.shape[0],
+                                                alternative=kwds['alternative'])
+            xp_assert_close(res.zstatistic, xp.asarray(z, dtype=dtype))
+
+    cases_continuity = [[{"alternative": 'two-sided', "use_continuity": True},
+                         (23., 0.6865041817876)],
+                        [{"alternative": 'less', "use_continuity": True},
+                         (23., 0.7047591913255)],
+                        [{"alternative": 'greater', "use_continuity": True},
+                         (23., 0.3432520908938)],
+                        [{"alternative": 'two-sided', "use_continuity": False},
+                         (23., 0.6377328900502)],
+                        [{"alternative": 'less', "use_continuity": False},
+                         (23., 0.6811335549749)],
+                        [{"alternative": 'greater', "use_continuity": False},
+                         (23., 0.3188664450251)]]
+
+    @pytest.mark.parametrize(("kwds", "expected"), cases_continuity)
+    def test_continuity(self, kwds, expected, xp):
+        # When x and y are interchanged, less and greater p-values should
+        # swap (compare to above). This wouldn't happen if the continuity
+        # correction were applied in the wrong direction. Note that less and
+        # greater p-values do not sum to 1 when continuity correction is on,
+        # which is what we'd expect. Also check that results match R when
+        # continuity correction is turned off.
+        # Note that method='asymptotic' -> exact=FALSE
+        # and use_continuity=False -> correct=FALSE, e.g.:
+        # wilcox.test(x, y, alternative="t", exact=FALSE, correct=FALSE)
+        x, y = xp.asarray(self.x), xp.asarray(self.y)
+        res = mannwhitneyu(y, x, method='asymptotic', **kwds)
+        xp_assert_close(res.statistic, xp.asarray(expected[0]))
+        xp_assert_close(res.pvalue, xp.asarray(expected[1]))
+        z = self.get_zstatistic_from_pvalue(res.pvalue, res.statistic,
+                                            x.shape[0], y.shape[0],
+                                            alternative=kwds['alternative'])
+        xp_assert_close(res.zstatistic, xp.asarray(z))
+
+    def test_tie_correct(self, xp):
+        # Test tie correction against R's wilcox.test
+        # options(digits = 16)
+        # x = c(1, 2, 3, 4)
+        # y = c(1, 2, 3, 4, 5)
+        # wilcox.test(x, y, exact=FALSE)
+        x = xp.asarray([1., 2., 3., 4.])
+        y0 = xp.asarray([1., 2., 3., 4., 5.])
+        dy = xp.asarray([0., 1., 0., 1., 0.])*0.01
+        dy2 = xp.asarray([0., 0., 1., 0., 0.])*0.01
+        y = xp.stack([y0-0.01, y0-dy, y0-dy2, y0, y0+dy2, y0+dy, y0+0.01])
+        res = mannwhitneyu(x, y, axis=-1, method="asymptotic")
+        U_expected = [10, 9, 8.5, 8, 7.5, 7, 6]
+        p_expected = [1, 0.9017048037317, 0.804080657472, 0.7086240584439,
+                      0.6197963884941, 0.5368784563079, 0.3912672792826]
+        xp_assert_equal(res.statistic, xp.asarray(U_expected))
+        xp_assert_close(res.pvalue, xp.asarray(p_expected))
+
+    # --- Test Exact Distribution of U ---
+
+    # These are tabulated values of the CDF of the exact distribution of
+    # the test statistic from pg 52 of reference [1] (Mann-Whitney Original)
+    pn3 = {1: [0.25, 0.5, 0.75], 2: [0.1, 0.2, 0.4, 0.6],
+           3: [0.05, .1, 0.2, 0.35, 0.5, 0.65]}
+    pn4 = {1: [0.2, 0.4, 0.6], 2: [0.067, 0.133, 0.267, 0.4, 0.6],
+           3: [0.028, 0.057, 0.114, 0.2, .314, 0.429, 0.571],
+           4: [0.014, 0.029, 0.057, 0.1, 0.171, 0.243, 0.343, 0.443, 0.557]}
+    pm5 = {1: [0.167, 0.333, 0.5, 0.667],
+           2: [0.047, 0.095, 0.19, 0.286, 0.429, 0.571],
+           3: [0.018, 0.036, 0.071, 0.125, 0.196, 0.286, 0.393, 0.5, 0.607],
+           4: [0.008, 0.016, 0.032, 0.056, 0.095, 0.143,
+               0.206, 0.278, 0.365, 0.452, 0.548],
+           5: [0.004, 0.008, 0.016, 0.028, 0.048, 0.075, 0.111,
+               0.155, 0.21, 0.274, 0.345, .421, 0.5, 0.579]}
+    pm6 = {1: [0.143, 0.286, 0.428, 0.571],
+           2: [0.036, 0.071, 0.143, 0.214, 0.321, 0.429, 0.571],
+           3: [0.012, 0.024, 0.048, 0.083, 0.131,
+               0.19, 0.274, 0.357, 0.452, 0.548],
+           4: [0.005, 0.01, 0.019, 0.033, 0.057, 0.086, 0.129,
+               0.176, 0.238, 0.305, 0.381, 0.457, 0.543],  # the last element
+           # of the previous list, 0.543, has been modified from 0.545;
+           # I assume it was a typo
+           5: [0.002, 0.004, 0.009, 0.015, 0.026, 0.041, 0.063, 0.089,
+               0.123, 0.165, 0.214, 0.268, 0.331, 0.396, 0.465, 0.535],
+           6: [0.001, 0.002, 0.004, 0.008, 0.013, 0.021, 0.032, 0.047,
+               0.066, 0.09, 0.12, 0.155, 0.197, 0.242, 0.294, 0.350,
+               0.409, 0.469, 0.531]}
+
+    def test_exact_distribution(self):
+        # I considered parametrize. I decided against it.
+        setattr(_mwu_state, 's', _MWU(0, 0))
+
+        p_tables = {3: self.pn3, 4: self.pn4, 5: self.pm5, 6: self.pm6}
+        for n, table in p_tables.items():
+            for m, p in table.items():
+                # check p-value against table
+                u = np.arange(0, len(p))
+                _mwu_state.s.set_shapes(m, n)
+                assert_allclose(_mwu_state.s.cdf(k=u), p, atol=1e-3)
+
+                # check identity CDF + SF - PMF = 1
+                # ( In this implementation, SF(U) includes PMF(U) )
+                u2 = np.arange(0, m*n+1)
+                assert_allclose(_mwu_state.s.cdf(k=u2)
+                                + _mwu_state.s.sf(k=u2)
+                                - _mwu_state.s.pmf(k=u2), 1)
+
+                # check symmetry about mean of U, i.e. pmf(U) = pmf(m*n-U)
+                pmf = _mwu_state.s.pmf(k=u2)
+                assert_allclose(pmf, pmf[::-1])
+
+                # check symmetry w.r.t. interchange of m, n
+                _mwu_state.s.set_shapes(n, m)
+                pmf2 = _mwu_state.s.pmf(k=u2)
+                assert_allclose(pmf, pmf2)
+
+    def test_asymptotic_behavior(self, xp):
+        rng = np.random.default_rng(12543)
+
+        # for small samples, the asymptotic test is not very accurate
+        x = xp.asarray(rng.random(5))
+        y = xp.asarray(rng.random(5))
+        res1 = mannwhitneyu(x, y, method="exact")
+        res2 = mannwhitneyu(x, y, method="asymptotic")
+        assert res1.statistic == res2.statistic
+        assert xp.abs(res1.pvalue - res2.pvalue) > 1e-2
+
+        # for large samples, they agree reasonably well
+        x = xp.asarray(rng.random(40))
+        y = xp.asarray(rng.random(40))
+        res1 = mannwhitneyu(x, y, method="exact")
+        res2 = mannwhitneyu(x, y, method="asymptotic")
+        assert res1.statistic == res2.statistic
+        assert xp.abs(res1.pvalue - res2.pvalue) < 1e-3
+
+    # --- Test Corner Cases ---
+
+    def test_exact_U_equals_mean(self, xp):
+        # Test U == m*n/2 with exact method
+        # Without special treatment, two-sided p-value > 1 because both
+        # one-sided p-values are > 0.5
+        x, y = xp.asarray([1., 2., 3.]), xp.asarray([1.5, 2.5])
+        res_l = mannwhitneyu(x, y, alternative="less", method="exact")
+        res_g = mannwhitneyu(x, y, alternative="greater", method="exact")
+        xp_assert_equal(res_l.pvalue, res_g.pvalue)
+        assert res_l.pvalue > 0.5
+
+        res = mannwhitneyu(x, y, alternative="two-sided", method="exact")
+        xp_assert_equal(res.statistic, xp.asarray(3.))
+        xp_assert_equal(res.pvalue, xp.asarray(1.))
+        # U == m*n/2 for asymptotic case tested in test_gh_2118
+        # The reason it's tricky for the asymptotic test has to do with
+        # continuity correction.
+
+    cases_scalar = [[{"alternative": 'two-sided', "method": "asymptotic"},
+                     (0., 1.)],
+                    [{"alternative": 'less', "method": "asymptotic"},
+                     (0., 0.5)],
+                    [{"alternative": 'greater', "method": "asymptotic"},
+                     (0., 0.977249868052)],
+                    [{"alternative": 'two-sided', "method": "exact"}, (0., 1)],
+                    [{"alternative": 'less', "method": "exact"}, (0., 0.5)],
+                    [{"alternative": 'greater', "method": "exact"}, (0., 1)]]
+
+    @pytest.mark.parametrize(("kwds", "result"), cases_scalar)
+    def test_scalar_data(self, kwds, result):  # not important to preserve w/ array API
+        # just making sure scalars work
+        assert_allclose(mannwhitneyu(1, 2, **kwds), result)
+
+    def test_equal_scalar_data(self):  # not important to preserve w/ array API
+        # when two scalars are equal, there is an -0.5/0 in the asymptotic
+        # approximation. R gives pvalue=1.0 for alternatives 'less' and
+        # 'greater' but NA for 'two-sided'.
+        assert_equal(mannwhitneyu(1, 1, method="exact"), (0.5, 1))
+        assert_equal(mannwhitneyu(1, 1, method="asymptotic", alternative='less'),
+                     (0.5, 1))
+        assert_equal(mannwhitneyu(1, 1, method="asymptotic", alternative='greater'),
+                     (0.5, 1))
+        assert_equal(mannwhitneyu(1, 1, method="asymptotic"),
+                     (0.5, np.nan))
+
+        # without continuity correction, this definitely becomes 0/0, which really
+        # is undefined
+        assert_equal(mannwhitneyu(1, 1, method="asymptotic", alternative='less',
+                                  use_continuity=False), (0.5, np.nan))
+        assert_equal(mannwhitneyu(1, 1, method="asymptotic", alternative='greater',
+                                  use_continuity=False), (0.5, np.nan))
+        assert_equal(mannwhitneyu(1, 1, method="asymptotic",
+                                  use_continuity=False), (0.5, np.nan))
+
+    # --- Test Enhancements / Bug Reports ---
+
+    @pytest.mark.parametrize("method", ["asymptotic", "exact"])
+    def test_gh_12837_11113(self, method, xp):
+        # Test that behavior for broadcastable nd arrays is appropriate:
+        # output shape is correct and all values are equal to when the test
+        # is performed on one pair of samples at a time.
+        # Tests that gh-12837 and gh-11113 (requests for n-d input)
+        # are resolved
+        rng = np.random.default_rng(6083743794)
+
+        # arrays are broadcastable except for axis = -3
+        axis = -3
+        m, n = 7, 10  # sample sizes
+        x = rng.random((m, 3, 8))
+        y = rng.random((6, n, 1, 8)) + 0.1
+        res = mannwhitneyu(xp.asarray(x), xp.asarray(y), method=method, axis=axis)
+
+        shape = (6, 3, 8)  # appropriate shape of outputs, given inputs
+        assert res.pvalue.shape == shape
+        assert res.statistic.shape == shape
+
+        # move axis of test to end for simplicity
+        x, y = np.moveaxis(x, axis, -1), np.moveaxis(y, axis, -1)
+
+        x = x[None, ...]  # give x a zeroth dimension
+        assert x.ndim == y.ndim
+
+        x = np.broadcast_to(x, shape + (m,))
+        y = np.broadcast_to(y, shape + (n,))
+        assert x.shape[:-1] == shape
+        assert y.shape[:-1] == shape
+
+        # loop over pairs of samples
+        statistics = np.zeros(shape)
+        pvalues = np.zeros(shape)
+        for indices in product(*[range(i) for i in shape]):
+            xi = x[indices]
+            yi = y[indices]
+            temp = mannwhitneyu(xi, yi, method=method)
+            statistics[indices] = temp.statistic
+            pvalues[indices] = temp.pvalue
+
+        xp_assert_close(res.pvalue, xp.asarray(pvalues), atol=1e-16)
+        xp_assert_close(res.statistic, xp.asarray(statistics), atol=1e-16)
+
+    def test_gh_11355(self, xp):
+        # Test for correct behavior with NaN/Inf in input
+        x = [1, 2, 3, 4]
+        y = [3, 6, 7, 8, 9, 3, 2, 1, 4, 4, 5]
+        res1 = mannwhitneyu(xp.asarray(x), xp.asarray(y), method='asymptotic')
+
+        # Inf is not a problem. This is a rank test, and it's the largest value
+        x[0] = 1.  # ensure floating point
+        y[4] = np.inf
+        res2 = mannwhitneyu(xp.asarray(x), xp.asarray(y), method='asymptotic')
+
+        xp_assert_equal(res1.statistic, res2.statistic)
+        xp_assert_equal(res1.pvalue, res2.pvalue)
+
+    @skip_xp_backends("jax.numpy", reason="needs jax-ml/jax#34490")
+    def test_gh11355_nan(self, xp):
+        # NaNs should propagate by default.
+        x = [1., 2., 3., 4.]
+        y = [3, 6, 7, np.nan, 9, 3, 2, 1, 4, 4, 5]
+        res3 = mannwhitneyu(xp.asarray(x), xp.asarray(y))
+        xp_assert_equal(res3.statistic, xp.asarray(xp.nan))
+        xp_assert_equal(res3.pvalue, xp.asarray(xp.nan))
+
+    cases_11355 = [([1., 2, 3, 4],
+                    [3, 6, 7, 8, np.inf, 3, 2, 1, 4, 4, 5],
+                    10., 0.1297704873477),
+                   ([1., 2, 3, 4],
+                    [3, 6, 7, 8, np.inf, np.inf, 2, 1, 4, 4, 5],
+                    8.5, 0.08735617507695),
+                   ([1, 2, np.inf, 4],
+                    [3, 6, 7, 8, np.inf, 3, 2, 1, 4, 4, 5],
+                    17.5, 0.5988856695752),
+                   ([1, 2, np.inf, 4],
+                    [3, 6, 7, 8, np.inf, np.inf, 2, 1, 4, 4, 5],
+                    16., 0.4687165824462),
+                   ([1, np.inf, np.inf, 4],
+                    [3, 6, 7, 8, np.inf, np.inf, 2, 1, 4, 4, 5],
+                    24.5, 0.7912517950119)]
+
+    @pytest.mark.parametrize(("x", "y", "statistic", "pvalue"), cases_11355)
+    def test_gh_11355b(self, x, y, statistic, pvalue, xp):
+        # Test for correct behavior with NaN/Inf in input
+        res = mannwhitneyu(xp.asarray(x), xp.asarray(y), method='asymptotic')
+        xp_assert_close(res.statistic, xp.asarray(statistic), atol=1e-12)
+        xp_assert_close(res.pvalue, xp.asarray(pvalue), atol=1e-12)
+
+    cases_9184 = [[True, "less", "asymptotic", 0.900775348204],
+                  [True, "greater", "asymptotic", 0.1223118025635],
+                  [True, "two-sided", "asymptotic", 0.244623605127],
+                  [False, "less", "asymptotic", 0.8896643190401],
+                  [False, "greater", "asymptotic", 0.1103356809599],
+                  [False, "two-sided", "asymptotic", 0.2206713619198],
+                  [True, "less", "exact", 0.8967698967699],
+                  [True, "greater", "exact", 0.1272061272061],
+                  [True, "two-sided", "exact", 0.2544122544123]]
+
+    @pytest.mark.parametrize(("use_continuity", "alternative",
+                              "method", "pvalue_exp"), cases_9184)
+    def test_gh_9184(self, use_continuity, alternative, method, pvalue_exp, xp):
+        # gh-9184 might be considered a doc-only bug. Please see the
+        # documentation to confirm that mannwhitneyu correctly notes
+        # that the output statistic is that of the first sample (x). In any
+        # case, check the case provided there against output from R.
+        # R code:
+        # options(digits=16)
+        # x <- c(0.80, 0.83, 1.89, 1.04, 1.45, 1.38, 1.91, 1.64, 0.73, 1.46)
+        # y <- c(1.15, 0.88, 0.90, 0.74, 1.21)
+        # wilcox.test(x, y, alternative = "less", exact = FALSE)
+        # wilcox.test(x, y, alternative = "greater", exact = FALSE)
+        # wilcox.test(x, y, alternative = "two.sided", exact = FALSE)
+        # wilcox.test(x, y, alternative = "less", exact = FALSE,
+        #             correct=FALSE)
+        # wilcox.test(x, y, alternative = "greater", exact = FALSE,
+        #             correct=FALSE)
+        # wilcox.test(x, y, alternative = "two.sided", exact = FALSE,
+        #             correct=FALSE)
+        # wilcox.test(x, y, alternative = "less", exact = TRUE)
+        # wilcox.test(x, y, alternative = "greater", exact = TRUE)
+        # wilcox.test(x, y, alternative = "two.sided", exact = TRUE)
+        statistic_exp = 35.
+        x = xp.asarray([0.80, 0.83, 1.89, 1.04, 1.45, 1.38, 1.91, 1.64, 0.73, 1.46])
+        y = xp.asarray([1.15, 0.88, 0.90, 0.74, 1.21])
+        res = mannwhitneyu(x, y, use_continuity=use_continuity,
+                           alternative=alternative, method=method)
+        xp_assert_equal(res.statistic, xp.asarray(statistic_exp))
+        xp_assert_close(res.pvalue, xp.asarray(pvalue_exp))
+
+    @skip_xp_backends("jax.numpy", reason="needs jax-ml/jax#34490")
+    def test_gh_4067(self, xp):
+        # Test for correct behavior with all NaN input - default is propagate
+        nan = xp.asarray(xp.nan)
+        a = xp.stack([nan, nan, nan, nan, nan])
+        b = xp.stack([nan, nan, nan, nan, nan])
+        res = mannwhitneyu(a, b)
+        xp_assert_equal(res.statistic, xp.asarray(nan))
+        xp_assert_equal(res.pvalue, nan)
+
+    # All cases checked against R wilcox.test, e.g.
+    # options(digits=16)
+    # x = c(1, 2, 3)
+    # y = c(1.5, 2.5)
+    # wilcox.test(x, y, exact=FALSE, alternative='less')
+
+    cases_2118 = [[[1., 2., 3.], [1.5, 2.5], "greater", (3., 0.6135850036578)],
+                  [[1., 2., 3.], [1.5, 2.5], "less", (3., 0.6135850036578)],
+                  [[1., 2., 3.], [1.5, 2.5], "two-sided", (3., 1.0)],
+                  [[1, 2, 3], [2], "greater", (1.5, 0.681324055883)],
+                  [[1, 2, 3], [2], "less", (1.5, 0.681324055883)],
+                  [[1, 2, 3], [2], "two-sided", (1.5, 1.)],
+                  [[1, 2], [1, 2], "greater", (2., 0.667497228949)],
+                  [[1, 2], [1, 2], "less", (2., 0.667497228949)],
+                  [[1, 2], [1, 2], "two-sided", (2., 1.)]]
+
+    @pytest.mark.parametrize(["x", "y", "alternative", "expected"], cases_2118)
+    def test_gh_2118(self, x, y, alternative, expected, xp):
+        # test cases in which U == m*n/2 when method is asymptotic
+        # applying continuity correction could result in p-value > 1
+        res = mannwhitneyu(xp.asarray(x), xp.asarray(y), use_continuity=True,
+                           alternative=alternative, method="asymptotic")
+        rtol = 1e-6 if xp_default_dtype(xp) == xp.float32 else 1e-12
+        xp_assert_close(res.statistic, xp.asarray(expected[0]), rtol=rtol)
+        xp_assert_close(res.pvalue, xp.asarray(expected[1]), rtol=rtol)
+
+    def test_gh19692_smaller_table(self, xp):
+        # In gh-19692, we noted that the shape of the cache used in calculating
+        # p-values was dependent on the order of the inputs because the sample
+        # sizes n1 and n2 changed. This was indicative of unnecessary cache
+        # growth and redundant calculation. Check that this is resolved.
+        rng = np.random.default_rng(7600451795963068007)
+        m, n = 5, 11
+        x = xp.asarray(rng.random(size=m).tolist())
+        y = xp.asarray(rng.random(size=n).tolist())
+
+        setattr(_mwu_state, 's', _MWU(0, 0))
+        _mwu_state.s.reset()  # reset cache
+
+        res = stats.mannwhitneyu(x, y, method='exact')
+        shape = _mwu_state.s.configurations.shape
+        assert shape[-1] == min(res.statistic, m*n - res.statistic) + 1
+        stats.mannwhitneyu(y, x, method='exact')
+        assert shape == _mwu_state.s.configurations.shape  # same with reversed sizes
+
+        # Also, we weren't exploiting the symmetry of the null distribution
+        # to its full potential. Ensure that the null distribution is not
+        # evaluated explicitly for `k > m*n/2`.
+        _mwu_state.s.reset()  # reset cache
+        stats.mannwhitneyu(x, 0*y, method='exact', alternative='greater')
+        shape = _mwu_state.s.configurations.shape
+        assert shape[-1] == 1  # k is smallest possible
+        stats.mannwhitneyu(0*x, y, method='exact', alternative='greater')
+        assert shape == _mwu_state.s.configurations.shape
+
+    @pytest.mark.parametrize('alternative', ['less', 'greater', 'two-sided'])
+    def test_permutation_method(self, alternative, xp):
+        rng = np.random.default_rng(7600451795963068007)
+        x = xp.asarray(rng.random(size=(2, 5)))
+        y = xp.asarray(rng.random(size=(2, 6)))
+        res = stats.mannwhitneyu(x, y, method=stats.PermutationMethod(),
+                                 alternative=alternative, axis=1)
+        res2 = stats.mannwhitneyu(x, y, method='exact',
+                                  alternative=alternative, axis=1)
+        xp_assert_close(res.statistic, res2.statistic, rtol=1e-15)
+        xp_assert_close(res.pvalue, res2.pvalue, rtol=1e-15)
+
+    # Old tests moved from test_stats. Source of magic numbers unknown.
+    X = [19.8958398126694, 19.5452691647182, 19.0577309166425, 21.716543054589,
+         20.3269502208702, 20.0009273294025, 19.3440043632957, 20.4216806548105,
+         19.0649894736528, 18.7808043120398, 19.3680942943298, 19.4848044069953,
+         20.7514611265663, 19.0894948874598, 19.4975522356628, 18.9971170734274,
+         20.3239606288208, 20.6921298083835, 19.0724259532507, 18.9825187935021,
+         19.5144462609601, 19.8256857844223, 20.5174677102032, 21.1122407995892,
+         17.9490854922535, 18.2847521114727, 20.1072217648826, 18.6439891962179,
+         20.4970638083542, 19.5567594734914]
+
+    Y = [19.2790668029091, 16.993808441865, 18.5416338448258, 17.2634018833575,
+         19.1577183624616, 18.5119655377495, 18.6068455037221, 18.8358343362655,
+         19.0366413269742, 18.1135025515417, 19.2201873866958, 17.8344909022841,
+         18.2894380745856, 18.6661374133922, 19.9688601693252, 16.0672254617636,
+         19.00596360572, 19.201561539032, 19.0487501090183, 19.0847908674356]
+
+    rtol = 1e-14
+
+    def test_mannwhitneyu_one_sided(self, xp):
+        X, Y = xp.asarray(self.X), xp.asarray(self.Y)
+        kwargs = dict(method='asymptotic')
+        u1, p1 = stats.mannwhitneyu(X, Y, alternative='less', **kwargs)
+        u2, p2 = stats.mannwhitneyu(Y, X, alternative='greater', **kwargs)
+        u3, p3 = stats.mannwhitneyu(X, Y, alternative='greater', **kwargs)
+        u4, p4 = stats.mannwhitneyu(Y, X, alternative='less', **kwargs)
+
+        xp_assert_equal(p1, p2)
+        xp_assert_equal(p3, p4)
+        assert p1 != p3
+        xp_assert_equal(u1, xp.asarray(498.))
+        xp_assert_equal(u2, xp.asarray(102.))
+        xp_assert_equal(u3, xp.asarray(498.))
+        xp_assert_equal(u4, xp.asarray(102.))
+        assert_allclose(p1, xp.asarray(0.999957683256589), rtol=self.rtol)
+        rtol = self.rtol if X.dtype == xp.float64 else 5e-4
+        assert_allclose(p3, xp.asarray(4.5941632666275e-05), rtol=rtol, atol=1e-16)
+
+    def test_mannwhitneyu_two_sided(self, xp):
+        X, Y = xp.asarray(self.X), xp.asarray(self.Y)
+        kwargs = dict(alternative='two-sided', method='asymptotic')
+        u1, p1 = stats.mannwhitneyu(X, Y, **kwargs)
+        u2, p2 = stats.mannwhitneyu(Y, X, **kwargs)
+
+        xp_assert_equal(p1, p2)
+        xp_assert_equal(u1, xp.asarray(498.))
+        xp_assert_equal(u2, xp.asarray(102.))
+        rtol = self.rtol if X.dtype == xp.float64 else 5e-4
+        xp_assert_close(p1, xp.asarray(9.188326533255e-05), rtol=rtol, atol=1e-16)
+
+    def test_mannwhitneyu_no_correct_one_sided(self, xp):
+        X, Y = xp.asarray(self.X), xp.asarray(self.Y)
+        kwargs = dict(use_continuity=False, method='asymptotic')
+        u1, p1 = stats.mannwhitneyu(X, Y, alternative='less', **kwargs)
+        u2, p2 = stats.mannwhitneyu(Y, X, alternative='greater', **kwargs)
+        u3, p3 = stats.mannwhitneyu(X, Y, alternative='greater', **kwargs)
+        u4, p4 = stats.mannwhitneyu(Y, X, alternative='less', **kwargs)
+
+        xp_assert_equal(p1, p2)
+        xp_assert_equal(p3, p4)
+        assert p1 != p3
+        xp_assert_equal(u1, xp.asarray(498.))
+        xp_assert_equal(u2, xp.asarray(102.))
+        xp_assert_equal(u3, xp.asarray(498.))
+        xp_assert_equal(u4, xp.asarray(102.))
+        rtol = self.rtol if X.dtype == xp.float64 else 5e-4
+        xp_assert_close(p1, xp.asarray(0.999955905990004), rtol=rtol, atol=1e-16)
+        xp_assert_close(p3, xp.asarray(4.40940099958089e-05), rtol=rtol, atol=1e-16)
+
+    def test_mannwhitneyu_no_correct_two_sided(self, xp):
+        X, Y = xp.asarray(self.X), xp.asarray(self.Y)
+        kwargs = dict(use_continuity=False, method='asymptotic')
+        u1, p1 = stats.mannwhitneyu(X, Y, **kwargs)
+        u2, p2 = stats.mannwhitneyu(Y, X, **kwargs)
+
+        xp_assert_equal(p1, p2)
+        xp_assert_equal(u1, xp.asarray(498.))
+        xp_assert_equal(u2, xp.asarray(102.))
+        rtol = self.rtol if X.dtype == xp.float64 else 5e-4
+        xp_assert_close(p1, xp.asarray(8.81880199916178e-05), rtol=rtol, atol=1e-16)
+
+    def test_mannwhitneyu_ones(self, xp):
+        # test for gh-1428
+        x = xp.asarray([1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                        1., 1., 1., 1., 1., 1., 1., 2., 1., 1., 1., 1., 1., 1.,
+                        1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                        1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                        1., 1., 1., 1., 1., 1., 1., 2., 1., 1., 1., 1., 1., 1.,
+                        1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                        1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 2.,
+                        1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                        1., 1., 2., 1., 1., 1., 1., 2., 1., 1., 2., 1., 1., 2.,
+                        1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                        1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 2., 1.,
+                        1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                        1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                        1., 1., 1., 1., 1., 1., 1., 2., 1., 1., 1., 1., 1., 1.,
+                        1., 1., 1., 2., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                        1., 1., 1., 1., 1., 1., 1., 1., 3., 1., 1., 1., 1., 1.,
+                        1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                        1., 1., 1., 1., 1., 1.])
+
+        y = xp.asarray([1., 1., 1., 1., 1., 1., 1., 2., 1., 2., 1., 1., 1., 1.,
+                        2., 1., 1., 1., 2., 1., 1., 1., 1., 1., 2., 1., 1., 3.,
+                        1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 2., 1., 2., 1.,
+                        1., 1., 1., 1., 1., 2., 1., 1., 1., 1., 1., 1., 1., 1.,
+                        1., 1., 1., 1., 1., 1., 1., 2., 1., 1., 1., 1., 1., 2.,
+                        2., 1., 1., 2., 1., 1., 2., 1., 2., 1., 1., 1., 1., 2.,
+                        2., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                        1., 2., 1., 1., 1., 1., 1., 2., 2., 2., 1., 1., 1., 1.,
+                        1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                        2., 1., 1., 2., 1., 1., 1., 1., 2., 1., 1., 1., 1., 1.,
+                        1., 1., 1., 1., 1., 1., 1., 2., 1., 1., 1., 2., 1., 1.,
+                        1., 1., 1., 1.])
+
+        # p-value from R, e.g. wilcox.test(x, y, alternative="g")
+        kwargs = dict(method='asymptotic')
+        res = stats.mannwhitneyu(x, y, alternative='less', **kwargs)
+        xp_assert_close(res.statistic, xp.asarray(16980.5))
+        xp_assert_close(res.pvalue, xp.asarray(2.8214327656317373e-5))
+        res = stats.mannwhitneyu(x, y, alternative='greater', **kwargs)
+        xp_assert_close(res.statistic, xp.asarray(16980.5))
+        xp_assert_close(res.pvalue, xp.asarray(0.9999719954296))
+        res = stats.mannwhitneyu(x, y, alternative='two-sided', **kwargs)
+        xp_assert_close(res.statistic, xp.asarray(16980.5))
+        xp_assert_close(res.pvalue, xp.asarray(5.642865531266e-5))
+
+
+class TestSomersD(_TestPythranFunc):
+    def setup_method(self):
+        self.dtypes = self.ALL_INTEGER + self.ALL_FLOAT
+        self.arguments = {0: (np.arange(10),
+                              self.ALL_INTEGER + self.ALL_FLOAT),
+                          1: (np.arange(10),
+                              self.ALL_INTEGER + self.ALL_FLOAT)}
+        input_array = [self.arguments[idx][0] for idx in self.arguments]
+        # In this case, self.partialfunc can simply be stats.somersd,
+        # since `alternative` is an optional argument. If it is required,
+        # we can use functools.partial to freeze the value, because
+        # we only mainly test various array inputs, not str, etc.
+        self.partialfunc = functools.partial(stats.somersd,
+                                             alternative='two-sided')
+        self.expected = self.partialfunc(*input_array)
+
+    def pythranfunc(self, *args):
+        res = self.partialfunc(*args)
+        assert_allclose(res.statistic, self.expected.statistic, atol=1e-15)
+        assert_allclose(res.pvalue, self.expected.pvalue, atol=1e-15)
+
+    def test_pythranfunc_keywords(self):
+        # Not specifying the optional keyword args
+        table = [[27, 25, 14, 7, 0], [7, 14, 18, 35, 12], [1, 3, 2, 7, 17]]
+        res1 = stats.somersd(table)
+        # Specifying the optional keyword args with default value
+        optional_args = self.get_optional_args(stats.somersd)
+        res2 = stats.somersd(table, **optional_args)
+        # Check if the results are the same in two cases
+        assert_allclose(res1.statistic, res2.statistic, atol=1e-15)
+        assert_allclose(res1.pvalue, res2.pvalue, atol=1e-15)
+
+    def test_like_kendalltau(self):
+        # All tests correspond with one in test_stats.py `test_kendalltau`
+
+        # case without ties, con-dis equal zero
+        x = [5, 2, 1, 3, 6, 4, 7, 8]
+        y = [5, 2, 6, 3, 1, 8, 7, 4]
+        # Cross-check with result from SAS FREQ:
+        expected = (0.000000000000000, 1.000000000000000)
+        res = stats.somersd(x, y)
+        assert_allclose(res.statistic, expected[0], atol=1e-15)
+        assert_allclose(res.pvalue, expected[1], atol=1e-15)
+
+        # case without ties, con-dis equal zero
+        x = [0, 5, 2, 1, 3, 6, 4, 7, 8]
+        y = [5, 2, 0, 6, 3, 1, 8, 7, 4]
+        # Cross-check with result from SAS FREQ:
+        expected = (0.000000000000000, 1.000000000000000)
+        res = stats.somersd(x, y)
+        assert_allclose(res.statistic, expected[0], atol=1e-15)
+        assert_allclose(res.pvalue, expected[1], atol=1e-15)
+
+        # case without ties, con-dis close to zero
+        x = [5, 2, 1, 3, 6, 4, 7]
+        y = [5, 2, 6, 3, 1, 7, 4]
+        # Cross-check with result from SAS FREQ:
+        expected = (-0.142857142857140, 0.630326953157670)
+        res = stats.somersd(x, y)
+        assert_allclose(res.statistic, expected[0], atol=1e-15)
+        assert_allclose(res.pvalue, expected[1], atol=1e-15)
+
+        # simple case without ties
+        x = np.arange(10)
+        y = np.arange(10)
+        # Cross-check with result from SAS FREQ:
+        # SAS p value is not provided.
+        expected = (1.000000000000000, 0)
+        res = stats.somersd(x, y)
+        assert_allclose(res.statistic, expected[0], atol=1e-15)
+        assert_allclose(res.pvalue, expected[1], atol=1e-15)
+
+        # swap a couple values and a couple more
+        x = np.arange(10)
+        y = np.array([0, 2, 1, 3, 4, 6, 5, 7, 8, 9])
+        # Cross-check with result from SAS FREQ:
+        expected = (0.911111111111110, 0.000000000000000)
+        res = stats.somersd(x, y)
+        assert_allclose(res.statistic, expected[0], atol=1e-15)
+        assert_allclose(res.pvalue, expected[1], atol=1e-15)
+
+        # same in opposite direction
+        x = np.arange(10)
+        y = np.arange(10)[::-1]
+        # Cross-check with result from SAS FREQ:
+        # SAS p value is not provided.
+        expected = (-1.000000000000000, 0)
+        res = stats.somersd(x, y)
+        assert_allclose(res.statistic, expected[0], atol=1e-15)
+        assert_allclose(res.pvalue, expected[1], atol=1e-15)
+
+        # swap a couple values and a couple more
+        x = np.arange(10)
+        y = np.array([9, 7, 8, 6, 5, 3, 4, 2, 1, 0])
+        # Cross-check with result from SAS FREQ:
+        expected = (-0.9111111111111111, 0.000000000000000)
+        res = stats.somersd(x, y)
+        assert_allclose(res.statistic, expected[0], atol=1e-15)
+        assert_allclose(res.pvalue, expected[1], atol=1e-15)
+
+        # with some ties
+        x1 = [12, 2, 1, 12, 2]
+        x2 = [1, 4, 7, 1, 0]
+        # Cross-check with result from SAS FREQ:
+        expected = (-0.500000000000000, 0.304901788178780)
+        res = stats.somersd(x1, x2)
+        assert_allclose(res.statistic, expected[0], atol=1e-15)
+        assert_allclose(res.pvalue, expected[1], atol=1e-15)
+
+        # with only ties in one or both inputs
+        # SAS will not produce an output for these:
+        # NOTE: No statistics are computed for x * y because x has fewer
+        # than 2 nonmissing levels.
+        # WARNING: No OUTPUT data set is produced for this table because a
+        # row or column variable has fewer than 2 nonmissing levels and no
+        # statistics are computed.
+
+        res = stats.somersd([2, 2, 2], [2, 2, 2])
+        assert_allclose(res.statistic, np.nan)
+        assert_allclose(res.pvalue, np.nan)
+
+        res = stats.somersd([2, 0, 2], [2, 2, 2])
+        assert_allclose(res.statistic, np.nan)
+        assert_allclose(res.pvalue, np.nan)
+
+        res = stats.somersd([2, 2, 2], [2, 0, 2])
+        assert_allclose(res.statistic, np.nan)
+        assert_allclose(res.pvalue, np.nan)
+
+        res = stats.somersd([0], [0])
+        assert_allclose(res.statistic, np.nan)
+        assert_allclose(res.pvalue, np.nan)
+
+        # empty arrays provided as input
+        res = stats.somersd([], [])
+        assert_allclose(res.statistic, np.nan)
+        assert_allclose(res.pvalue, np.nan)
+
+        # test unequal length inputs
+        x = np.arange(10.)
+        y = np.arange(20.)
+        assert_raises(ValueError, stats.somersd, x, y)
+
+    def test_asymmetry(self):
+        # test that somersd is asymmetric w.r.t. input order and that
+        # convention is as described: first input is row variable & independent
+        # data is from Wikipedia:
+        # https://en.wikipedia.org/wiki/Somers%27_D
+        # but currently that example contradicts itself - it says X is
+        # independent yet take D_XY
+
+        x = [1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 1, 2,
+             2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3]
+        y = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2,
+             2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]
+        # Cross-check with result from SAS FREQ:
+        d_cr = 0.272727272727270
+        d_rc = 0.342857142857140
+        p = 0.092891940883700  # same p-value for either direction
+        res = stats.somersd(x, y)
+        assert_allclose(res.statistic, d_cr, atol=1e-15)
+        assert_allclose(res.pvalue, p, atol=1e-4)
+        assert_equal(res.table.shape, (3, 2))
+        res = stats.somersd(y, x)
+        assert_allclose(res.statistic, d_rc, atol=1e-15)
+        assert_allclose(res.pvalue, p, atol=1e-15)
+        assert_equal(res.table.shape, (2, 3))
+
+    def test_somers_original(self):
+        # test against Somers' original paper [1]
+
+        # Table 5A
+        # Somers' convention was column IV
+        table = np.array([[8, 2], [6, 5], [3, 4], [1, 3], [2, 3]])
+        # Our convention (and that of SAS FREQ) is row IV
+        table = table.T
+        dyx = 129/340
+        assert_allclose(stats.somersd(table).statistic, dyx)
+
+        # table 7A - d_yx = 1
+        table = np.array([[25, 0], [85, 0], [0, 30]])
+        dxy, dyx = 3300/5425, 3300/3300
+        assert_allclose(stats.somersd(table).statistic, dxy)
+        assert_allclose(stats.somersd(table.T).statistic, dyx)
+
+        # table 7B - d_yx < 0
+        table = np.array([[25, 0], [0, 30], [85, 0]])
+        dyx = -1800/3300
+        assert_allclose(stats.somersd(table.T).statistic, dyx)
+
+    def test_contingency_table_with_zero_rows_cols(self):
+        # test that zero rows/cols in contingency table don't affect result
+
+        N = 100
+        shape = 4, 6
+        size = np.prod(shape)
+
+        rng = np.random.RandomState(0)
+        s = stats.multinomial.rvs(N, p=np.ones(size)/size,
+                                  random_state=rng).reshape(shape)
+        res = stats.somersd(s)
+
+        s2 = np.insert(s, 2, np.zeros(shape[1]), axis=0)
+        res2 = stats.somersd(s2)
+
+        s3 = np.insert(s, 2, np.zeros(shape[0]), axis=1)
+        res3 = stats.somersd(s3)
+
+        s4 = np.insert(s2, 2, np.zeros(shape[0]+1), axis=1)
+        res4 = stats.somersd(s4)
+
+        # Cross-check with result from SAS FREQ:
+        assert_allclose(res.statistic, -0.116981132075470, atol=1e-15)
+        assert_allclose(res.statistic, res2.statistic)
+        assert_allclose(res.statistic, res3.statistic)
+        assert_allclose(res.statistic, res4.statistic)
+
+        assert_allclose(res.pvalue, 0.156376448188150, atol=1e-15)
+        assert_allclose(res.pvalue, res2.pvalue)
+        assert_allclose(res.pvalue, res3.pvalue)
+        assert_allclose(res.pvalue, res4.pvalue)
+
+    def test_invalid_contingency_tables(self):
+        N = 100
+        shape = 4, 6
+        size = np.prod(shape)
+
+        rng = np.random.default_rng(0)
+        # start with a valid contingency table
+        s = stats.multinomial.rvs(N, p=np.ones(size)/size,
+                                  random_state=rng).reshape(shape)
+
+        s5 = s - 2
+        message = "All elements of the contingency table must be non-negative"
+        with assert_raises(ValueError, match=message):
+            stats.somersd(s5)
+
+        s6 = s + 0.01
+        message = "All elements of the contingency table must be integer"
+        with assert_raises(ValueError, match=message):
+            stats.somersd(s6)
+
+        message = ("At least two elements of the contingency "
+                   "table must be nonzero.")
+        with assert_raises(ValueError, match=message):
+            stats.somersd([[]])
+
+        with assert_raises(ValueError, match=message):
+            stats.somersd([[1]])
+
+        s7 = np.zeros((3, 3))
+        with assert_raises(ValueError, match=message):
+            stats.somersd(s7)
+
+        s7[0, 1] = 1
+        with assert_raises(ValueError, match=message):
+            stats.somersd(s7)
+
+    def test_only_ranks_matter(self):
+        # only ranks of input data should matter
+        x = [1, 2, 3]
+        x2 = [-1, 2.1, np.inf]
+        y = [3, 2, 1]
+        y2 = [0, -0.5, -np.inf]
+        res = stats.somersd(x, y)
+        res2 = stats.somersd(x2, y2)
+        assert_equal(res.statistic, res2.statistic)
+        assert_equal(res.pvalue, res2.pvalue)
+
+    def test_contingency_table_return(self):
+        # check that contingency table is returned
+        x = np.arange(10)
+        y = np.arange(10)
+        res = stats.somersd(x, y)
+        assert_equal(res.table, np.eye(10))
+
+    def test_somersd_alternative(self):
+        # Test alternative parameter, asymptotic method (due to tie)
+
+        # Based on scipy.stats.test_stats.TestCorrSpearman2::test_alternative
+        x1 = [1, 2, 3, 4, 5]
+        x2 = [5, 6, 7, 8, 7]
+
+        # strong positive correlation
+        expected = stats.somersd(x1, x2, alternative="two-sided")
+        assert expected.statistic > 0
+
+        # rank correlation > 0 -> large "less" p-value
+        res = stats.somersd(x1, x2, alternative="less")
+        assert_equal(res.statistic, expected.statistic)
+        assert_allclose(res.pvalue, 1 - (expected.pvalue / 2))
+
+        # rank correlation > 0 -> small "greater" p-value
+        res = stats.somersd(x1, x2, alternative="greater")
+        assert_equal(res.statistic, expected.statistic)
+        assert_allclose(res.pvalue, expected.pvalue / 2)
+
+        # reverse the direction of rank correlation
+        x2.reverse()
+
+        # strong negative correlation
+        expected = stats.somersd(x1, x2, alternative="two-sided")
+        assert expected.statistic < 0
+
+        # rank correlation < 0 -> large "greater" p-value
+        res = stats.somersd(x1, x2, alternative="greater")
+        assert_equal(res.statistic, expected.statistic)
+        assert_allclose(res.pvalue, 1 - (expected.pvalue / 2))
+
+        # rank correlation < 0 -> small "less" p-value
+        res = stats.somersd(x1, x2, alternative="less")
+        assert_equal(res.statistic, expected.statistic)
+        assert_allclose(res.pvalue, expected.pvalue / 2)
+
+        with pytest.raises(ValueError, match="`alternative` must be..."):
+            stats.somersd(x1, x2, alternative="ekki-ekki")
+
+    @pytest.mark.parametrize("positive_correlation", (False, True))
+    def test_somersd_perfect_correlation(self, positive_correlation):
+        # Before the addition of `alternative`, perfect correlation was
+        # treated as a special case. Now it is treated like any other case, but
+        # make sure there are no divide by zero warnings or associated errors
+
+        x1 = np.arange(10)
+        x2 = x1 if positive_correlation else np.flip(x1)
+        expected_statistic = 1 if positive_correlation else -1
+
+        # perfect correlation -> small "two-sided" p-value (0)
+        res = stats.somersd(x1, x2, alternative="two-sided")
+        assert res.statistic == expected_statistic
+        assert res.pvalue == 0
+
+        # rank correlation > 0 -> large "less" p-value (1)
+        res = stats.somersd(x1, x2, alternative="less")
+        assert res.statistic == expected_statistic
+        assert res.pvalue == (1 if positive_correlation else 0)
+
+        # rank correlation > 0 -> small "greater" p-value (0)
+        res = stats.somersd(x1, x2, alternative="greater")
+        assert res.statistic == expected_statistic
+        assert res.pvalue == (0 if positive_correlation else 1)
+
+    def test_somersd_large_inputs_gh18132(self):
+        # Test that large inputs where potential overflows could occur give
+        # the expected output. This is tested in the case of binary inputs.
+        # See gh-18126.
+
+        # generate lists of random classes 1-2 (binary)
+        classes = [1, 2]
+        n_samples = 10 ** 6
+        rng = np.random.default_rng(6889320191)
+        x = rng.choice(classes, n_samples)
+        y = rng.choice(classes, n_samples)
+
+        # get value to compare with: sklearn output
+        # from sklearn import metrics
+        # val_auc_sklearn = metrics.roc_auc_score(x, y)
+        # # convert to the Gini coefficient (Gini = (AUC*2)-1)
+        # val_sklearn = 2 * val_auc_sklearn - 1
+        val_sklearn = 0.000624401938730923
+
+        # calculate the Somers' D statistic, which should be equal to the
+        # result of val_sklearn until approximately machine precision
+        val_scipy = stats.somersd(x, y).statistic
+        assert_allclose(val_sklearn, val_scipy, atol=1e-15)
+
+
+class TestBarnardExact:
+    """Some tests to show that barnard_exact() works correctly."""
+
+    @pytest.mark.parametrize(
+        "input_sample,expected",
+        [
+            ([[43, 40], [10, 39]], (3.555406779643, 0.000362832367)),
+            ([[100, 2], [1000, 5]], (-1.776382925679, 0.135126970878)),
+            ([[2, 7], [8, 2]], (-2.518474945157, 0.019210815430)),
+            ([[5, 1], [10, 10]], (1.449486150679, 0.156277546306)),
+            ([[5, 15], [20, 20]], (-1.851640199545, 0.066363501421)),
+            ([[5, 16], [20, 25]], (-1.609639949352, 0.116984852192)),
+            ([[10, 5], [10, 1]], (-1.449486150679, 0.177536588915)),
+            ([[5, 0], [1, 4]], (2.581988897472, 0.013671875000)),
+            ([[0, 1], [3, 2]], (-1.095445115010, 0.509667991877)),
+            ([[0, 2], [6, 4]], (-1.549193338483, 0.197019618792)),
+            ([[2, 7], [8, 2]], (-2.518474945157, 0.019210815430)),
+        ],
+    )
+    def test_precise(self, input_sample, expected):
+        """The expected values have been generated by R, using a resolution
+        for the nuisance parameter of 1e-6 :
+        ```R
+        library(Barnard)
+        options(digits=10)
+        barnard.test(43, 40, 10, 39, dp=1e-6, pooled=TRUE)
+        ```
+        """
+        res = barnard_exact(input_sample)
+        statistic, pvalue = res.statistic, res.pvalue
+        assert_allclose([statistic, pvalue], expected)
+
+    @pytest.mark.parametrize(
+        "input_sample,expected",
+        [
+            ([[43, 40], [10, 39]], (3.920362887717, 0.000289470662)),
+            ([[100, 2], [1000, 5]], (-1.139432816087, 0.950272080594)),
+            ([[2, 7], [8, 2]], (-3.079373904042, 0.020172119141)),
+            ([[5, 1], [10, 10]], (1.622375939458, 0.150599922226)),
+            ([[5, 15], [20, 20]], (-1.974771239528, 0.063038448651)),
+            ([[5, 16], [20, 25]], (-1.722122973346, 0.133329494287)),
+            ([[10, 5], [10, 1]], (-1.765469659009, 0.250566655215)),
+            ([[5, 0], [1, 4]], (5.477225575052, 0.007812500000)),
+            ([[0, 1], [3, 2]], (-1.224744871392, 0.509667991877)),
+            ([[0, 2], [6, 4]], (-1.732050807569, 0.197019618792)),
+            ([[2, 7], [8, 2]], (-3.079373904042, 0.020172119141)),
+        ],
+    )
+    def test_pooled_param(self, input_sample, expected):
+        """The expected values have been generated by R, using a resolution
+        for the nuisance parameter of 1e-6 :
+        ```R
+        library(Barnard)
+        options(digits=10)
+        barnard.test(43, 40, 10, 39, dp=1e-6, pooled=FALSE)
+        ```
+        """
+        res = barnard_exact(input_sample, pooled=False)
+        statistic, pvalue = res.statistic, res.pvalue
+        assert_allclose([statistic, pvalue], expected)
+
+    def test_raises(self):
+        # test we raise an error for wrong input number of nuisances.
+        error_msg = (
+            "Number of points `n` must be strictly positive, found 0"
+        )
+        with assert_raises(ValueError, match=error_msg):
+            barnard_exact([[1, 2], [3, 4]], n=0)
+
+        # test we raise an error for wrong shape of input.
+        error_msg = "The input `table` must be of shape \\(2, 2\\)."
+        with assert_raises(ValueError, match=error_msg):
+            barnard_exact(np.arange(6).reshape(2, 3))
+
+        # Test all values must be positives
+        error_msg = "All values in `table` must be nonnegative."
+        with assert_raises(ValueError, match=error_msg):
+            barnard_exact([[-1, 2], [3, 4]])
+
+        # Test value error on wrong alternative param
+        error_msg = (
+            "`alternative` should be one of {'two-sided', 'less', 'greater'},"
+            " found .*"
+        )
+        with assert_raises(ValueError, match=error_msg):
+            barnard_exact([[1, 2], [3, 4]], "not-correct")
+
+    @pytest.mark.parametrize(
+        "input_sample,expected",
+        [
+            ([[0, 0], [4, 3]], (1.0, 0)),
+        ],
+    )
+    def test_edge_cases(self, input_sample, expected):
+        res = barnard_exact(input_sample)
+        statistic, pvalue = res.statistic, res.pvalue
+        assert_equal(pvalue, expected[0])
+        assert_equal(statistic, expected[1])
+
+    @pytest.mark.parametrize(
+        "input_sample,expected",
+        [
+            ([[0, 5], [0, 10]], (1.0, np.nan)),
+            ([[5, 0], [10, 0]], (1.0, np.nan)),
+        ],
+    )
+    def test_row_or_col_zero(self, input_sample, expected):
+        res = barnard_exact(input_sample)
+        statistic, pvalue = res.statistic, res.pvalue
+        assert_equal(pvalue, expected[0])
+        assert_equal(statistic, expected[1])
+
+    @pytest.mark.parametrize(
+        "input_sample,expected",
+        [
+            ([[2, 7], [8, 2]], (-2.518474945157, 0.009886140845)),
+            ([[7, 200], [300, 8]], (-21.320036698460, 0.0)),
+            ([[21, 28], [1957, 6]], (-30.489638143953, 0.0)),
+        ],
+    )
+    @pytest.mark.parametrize("alternative", ["greater", "less"])
+    def test_less_greater(self, input_sample, expected, alternative):
+        """
+        "The expected values have been generated by R, using a resolution
+        for the nuisance parameter of 1e-6 :
+        ```R
+        library(Barnard)
+        options(digits=10)
+        a = barnard.test(2, 7, 8, 2, dp=1e-6, pooled=TRUE)
+        a$p.value[1]
+        ```
+        In this test, we are using the "one-sided" return value `a$p.value[1]`
+        to test our pvalue.
+        """
+        expected_stat, less_pvalue_expect = expected
+
+        if alternative == "greater":
+            input_sample = np.array(input_sample)[:, ::-1]
+            expected_stat = -expected_stat
+
+        res = barnard_exact(input_sample, alternative=alternative)
+        statistic, pvalue = res.statistic, res.pvalue
+        assert_allclose(
+            [statistic, pvalue], [expected_stat, less_pvalue_expect], atol=1e-7
+        )
+
+
+class TestBoschlooExact:
+    """Some tests to show that boschloo_exact() works correctly."""
+
+    ATOL = 1e-7
+
+    @pytest.mark.parametrize(
+        "input_sample,expected",
+        [
+            ([[2, 7], [8, 2]], (0.01852173, 0.009886142)),
+            ([[5, 1], [10, 10]], (0.9782609, 0.9450994)),
+            ([[5, 16], [20, 25]], (0.08913823, 0.05827348)),
+            ([[10, 5], [10, 1]], (0.1652174, 0.08565611)),
+            ([[5, 0], [1, 4]], (1, 1)),
+            ([[0, 1], [3, 2]], (0.5, 0.34375)),
+            ([[2, 7], [8, 2]], (0.01852173, 0.009886142)),
+            ([[7, 12], [8, 3]], (0.06406797, 0.03410916)),
+            ([[10, 24], [25, 37]], (0.2009359, 0.1512882)),
+        ],
+    )
+    def test_less(self, input_sample, expected):
+        """The expected values have been generated by R, using a resolution
+        for the nuisance parameter of 1e-8 :
+        ```R
+        library(Exact)
+        options(digits=10)
+        data <- matrix(c(43, 10, 40, 39), 2, 2, byrow=TRUE)
+        a = exact.test(data, method="Boschloo", alternative="less",
+                       tsmethod="central", np.interval=TRUE, beta=1e-8)
+        ```
+        """
+        res = boschloo_exact(input_sample, alternative="less")
+        statistic, pvalue = res.statistic, res.pvalue
+        assert_allclose([statistic, pvalue], expected, atol=self.ATOL)
+
+    @pytest.mark.parametrize(
+        "input_sample,expected",
+        [
+            ([[43, 40], [10, 39]], (0.0002875544, 0.0001615562)),
+            ([[2, 7], [8, 2]], (0.9990149, 0.9918327)),
+            ([[5, 1], [10, 10]], (0.1652174, 0.09008534)),
+            ([[5, 15], [20, 20]], (0.9849087, 0.9706997)),
+            ([[5, 16], [20, 25]], (0.972349, 0.9524124)),
+            ([[5, 0], [1, 4]], (0.02380952, 0.006865367)),
+            ([[0, 1], [3, 2]], (1, 1)),
+            ([[0, 2], [6, 4]], (1, 1)),
+            ([[2, 7], [8, 2]], (0.9990149, 0.9918327)),
+            ([[7, 12], [8, 3]], (0.9895302, 0.9771215)),
+            ([[10, 24], [25, 37]], (0.9012936, 0.8633275)),
+        ],
+    )
+    def test_greater(self, input_sample, expected):
+        """The expected values have been generated by R, using a resolution
+        for the nuisance parameter of 1e-8 :
+        ```R
+        library(Exact)
+        options(digits=10)
+        data <- matrix(c(43, 10, 40, 39), 2, 2, byrow=TRUE)
+        a = exact.test(data, method="Boschloo", alternative="greater",
+                       tsmethod="central", np.interval=TRUE, beta=1e-8)
+        ```
+        """
+        res = boschloo_exact(input_sample, alternative="greater")
+        statistic, pvalue = res.statistic, res.pvalue
+        assert_allclose([statistic, pvalue], expected, atol=self.ATOL)
+
+    @pytest.mark.parametrize(
+        "input_sample,expected",
+        [
+            ([[43, 40], [10, 39]], (0.0002875544, 0.0003231115)),
+            ([[2, 7], [8, 2]], (0.01852173, 0.01977228)),
+            ([[5, 1], [10, 10]], (0.1652174, 0.1801707)),
+            ([[5, 16], [20, 25]], (0.08913823, 0.116547)),
+            ([[5, 0], [1, 4]], (0.02380952, 0.01373073)),
+            ([[0, 1], [3, 2]], (0.5, 0.6875)),
+            ([[2, 7], [8, 2]], (0.01852173, 0.01977228)),
+            ([[7, 12], [8, 3]], (0.06406797, 0.06821831)),
+        ],
+    )
+    def test_two_sided(self, input_sample, expected):
+        """The expected values have been generated by R, using a resolution
+        for the nuisance parameter of 1e-8 :
+        ```R
+        library(Exact)
+        options(digits=10)
+        data <- matrix(c(43, 10, 40, 39), 2, 2, byrow=TRUE)
+        a = exact.test(data, method="Boschloo", alternative="two.sided",
+                       tsmethod="central", np.interval=TRUE, beta=1e-8)
+        ```
+        """
+        res = boschloo_exact(input_sample, alternative="two-sided", n=64)
+        # Need n = 64 for python 32-bit
+        statistic, pvalue = res.statistic, res.pvalue
+        assert_allclose([statistic, pvalue], expected, atol=self.ATOL)
+
+    def test_raises(self):
+        # test we raise an error for wrong input number of nuisances.
+        error_msg = (
+            "Number of points `n` must be strictly positive, found 0"
+        )
+        with assert_raises(ValueError, match=error_msg):
+            boschloo_exact([[1, 2], [3, 4]], n=0)
+
+        # test we raise an error for wrong shape of input.
+        error_msg = "The input `table` must be of shape \\(2, 2\\)."
+        with assert_raises(ValueError, match=error_msg):
+            boschloo_exact(np.arange(6).reshape(2, 3))
+
+        # Test all values must be positives
+        error_msg = "All values in `table` must be nonnegative."
+        with assert_raises(ValueError, match=error_msg):
+            boschloo_exact([[-1, 2], [3, 4]])
+
+        # Test value error on wrong alternative param
+        error_msg = (
+            r"`alternative` should be one of \('two-sided', 'less', "
+            r"'greater'\), found .*"
+        )
+        with assert_raises(ValueError, match=error_msg):
+            boschloo_exact([[1, 2], [3, 4]], "not-correct")
+
+    @pytest.mark.parametrize(
+        "input_sample,expected",
+        [
+            ([[0, 5], [0, 10]], (np.nan, np.nan)),
+            ([[5, 0], [10, 0]], (np.nan, np.nan)),
+        ],
+    )
+    def test_row_or_col_zero(self, input_sample, expected):
+        res = boschloo_exact(input_sample)
+        statistic, pvalue = res.statistic, res.pvalue
+        assert_equal(pvalue, expected[0])
+        assert_equal(statistic, expected[1])
+
+    def test_two_sided_gt_1(self):
+        # Check that returned p-value does not exceed 1 even when twice
+        # the minimum of the one-sided p-values does. See gh-15345.
+        tbl = [[1, 1], [13, 12]]
+        pl = boschloo_exact(tbl, alternative='less').pvalue
+        pg = boschloo_exact(tbl, alternative='greater').pvalue
+        assert 2*min(pl, pg) > 1
+        pt = boschloo_exact(tbl, alternative='two-sided').pvalue
+        assert pt == 1.0
+
+    @pytest.mark.parametrize("alternative", ("less", "greater"))
+    def test_against_fisher_exact(self, alternative):
+        # Check that the statistic of `boschloo_exact` is the same as the
+        # p-value of `fisher_exact` (for one-sided tests). See gh-15345.
+        tbl = [[2, 7], [8, 2]]
+        boschloo_stat = boschloo_exact(tbl, alternative=alternative).statistic
+        fisher_p = stats.fisher_exact(tbl, alternative=alternative)[1]
+        assert_allclose(boschloo_stat, fisher_p)
+
+
+@make_xp_test_case(cramervonmises_2samp)
+class TestCvm_2samp:
+    @pytest.mark.parametrize('args', [([], np.arange(5)),
+                                      (np.arange(5), [1])])
+    def test_too_small_input(self, args, xp):
+        args = (xp.asarray(arg, dtype=xp_default_dtype(xp)) for arg in args)
+        with eager_warns(SmallSampleWarning, match=too_small_1d_not_omit, xp=xp):
+            res = cramervonmises_2samp(*args)
+            xp_assert_equal(res.statistic, xp.asarray(xp.nan))
+            xp_assert_equal(res.pvalue, xp.asarray(xp.nan))
+
+    def test_invalid_input(self, xp):
+        y = xp.arange(5)
+        msg = 'method must be either auto, exact or asymptotic'
+        with pytest.raises(ValueError, match=msg):
+            cramervonmises_2samp(y, y, 'xyz')
+
+    def test_list_input(self):  # list input only relevant for NumPy
+        x = [2, 3, 4, 7, 6]
+        y = [0.2, 0.7, 12, 18]
+        r1 = cramervonmises_2samp(x, y)
+        r2 = cramervonmises_2samp(np.array(x), np.array(y))
+        assert_equal((r1.statistic, r1.pvalue), (r2.statistic, r2.pvalue))
+
+    @pytest.mark.parametrize('dtype', [None, 'float32', 'float64'])
+    def test_example_conover(self, dtype, xp):
+        # Example 2 in Section 6.2 of W.J. Conover: Practical Nonparametric
+        # Statistics, 1971.
+        dtype = xp_default_dtype(xp) if dtype is None else getattr(xp, dtype)
+        x = xp.asarray([7.6, 8.4, 8.6, 8.7, 9.3, 9.9, 10.1, 10.6, 11.2], dtype=dtype)
+        y = xp.asarray([5.2, 5.7, 5.9, 6.5, 6.8, 8.2, 9.1, 9.8,
+                        10.8, 11.3, 11.5, 12.3, 12.5, 13.4, 14.6], dtype=dtype)
+        r = cramervonmises_2samp(x, y)
+        xp_assert_close(r.statistic, xp.asarray(0.262, dtype=dtype), atol=1e-3)
+        xp_assert_close(r.pvalue, xp.asarray(.18, dtype=dtype), atol=1e-2)
+
+    @pytest.mark.parametrize('statistic, m, n, pval',
+                             [(710, 5, 6, 48./462),
+                              (1897, 7, 7, 117./1716),
+                              (576, 4, 6, 2./210),
+                              (1764, 6, 7, 2./1716)])
+    def test_exact_pvalue(self, statistic, m, n, pval):  # only implemented w/ NumPy
+        # the exact values are taken from Anderson: On the distribution of the
+        # two-sample Cramer-von-Mises criterion, 1962.
+        # The values are taken from Table 2, 3, 4 and 5
+        assert_equal(_pval_cvm_2samp_exact(statistic, m, n), pval)
+
+    @pytest.mark.xslow
+    def test_large_sample(self, xp):
+        # for large samples, the statistic U gets very large
+        # do a sanity check that p-value is not 0, 1 or nan
+        rng = np.random.default_rng(4367)
+        x = distributions.norm.rvs(size=1000000, random_state=rng)
+        y = distributions.norm.rvs(size=900000, random_state=rng)
+        x, y = xp.asarray(x), xp.asarray(y)
+        r = cramervonmises_2samp(x, y)
+        assert 0 < r.pvalue < 1
+        r = cramervonmises_2samp(x, y+0.1)
+        assert 0 < r.pvalue < 1
+
+    def test_exact_vs_asymptotic(self, xp):
+        rng = np.random.RandomState(0)
+        x = xp.asarray(rng.random(7))
+        y = xp.asarray(rng.random(8))
+        r1 = cramervonmises_2samp(x, y, method='exact')
+        r2 = cramervonmises_2samp(x, y, method='asymptotic')
+        xp_assert_equal(r1.statistic, r2.statistic)
+        xp_assert_close(r1.pvalue, r2.pvalue, atol=1e-2)
+
+    def test_method_auto(self, xp):
+        x = xp.arange(20.)
+        y = xp.asarray([0.5, 4.7, 13.1])
+        r1 = cramervonmises_2samp(x, y, method='exact')
+        r2 = cramervonmises_2samp(x, y, method='auto')
+        xp_assert_equal(r1.pvalue, r2.pvalue)
+        # switch to asymptotic if one sample has more than 20 observations
+        x = xp.arange(21.)
+        r1 = cramervonmises_2samp(x, y, method='asymptotic')
+        r2 = cramervonmises_2samp(x, y, method='auto')
+        xp_assert_equal(r1.pvalue, r2.pvalue)
+
+    def test_same_input(self, xp):
+        # make sure trivial edge case can be handled
+        # note that _cdf_cvm_inf(0) = nan. implementation avoids nan by
+        # returning pvalue=1 for very small values of the statistic
+        x = xp.arange(15)
+        res = cramervonmises_2samp(x, x)
+        xp_assert_equal(res.statistic, xp.asarray(0.))
+        xp_assert_equal(res.pvalue, xp.asarray(1.))
+        # check exact p-value
+        res = cramervonmises_2samp(x[:4], x[:4])
+        xp_assert_equal(res.statistic, xp.asarray(0.))
+        xp_assert_equal(res.pvalue, xp.asarray(1.))
+
+
+class TestTukeyHSD:
+
+    data_same_size = ([24.5, 23.5, 26.4, 27.1, 29.9],
+                      [28.4, 34.2, 29.5, 32.2, 30.1],
+                      [26.1, 28.3, 24.3, 26.2, 27.8])
+    data_diff_size = ([24.5, 23.5, 26.28, 26.4, 27.1, 29.9, 30.1, 30.1],
+                      [28.4, 34.2, 29.5, 32.2, 30.1],
+                      [26.1, 28.3, 24.3, 26.2, 27.8])
+    extreme_size = ([24.5, 23.5, 26.4],
+                    [28.4, 34.2, 29.5, 32.2, 30.1, 28.4, 34.2, 29.5, 32.2,
+                     30.1],
+                    [26.1, 28.3, 24.3, 26.2, 27.8])
+
+    sas_same_size = """
+    Comparison LowerCL Difference UpperCL Significance
+    2 - 3	0.6908830568	4.34	7.989116943	    1
+    2 - 1	0.9508830568	4.6 	8.249116943 	1
+    3 - 2	-7.989116943	-4.34	-0.6908830568	1
+    3 - 1	-3.389116943	0.26	3.909116943	    0
+    1 - 2	-8.249116943	-4.6	-0.9508830568	1
+    1 - 3	-3.909116943	-0.26	3.389116943	    0
+    """
+
+    sas_diff_size = """
+    Comparison LowerCL Difference UpperCL Significance
+    2 - 1	0.2679292645	3.645	7.022070736	    1
+    2 - 3	0.5934764007	4.34	8.086523599	    1
+    1 - 2	-7.022070736	-3.645	-0.2679292645	1
+    1 - 3	-2.682070736	0.695	4.072070736	    0
+    3 - 2	-8.086523599	-4.34	-0.5934764007	1
+    3 - 1	-4.072070736	-0.695	2.682070736	    0
+    """
+
+    sas_extreme = """
+    Comparison LowerCL Difference UpperCL Significance
+    2 - 3	1.561605075	    4.34	7.118394925	    1
+    2 - 1	2.740784879	    6.08	9.419215121	    1
+    3 - 2	-7.118394925	-4.34	-1.561605075	1
+    3 - 1	-1.964526566	1.74	5.444526566	    0
+    1 - 2	-9.419215121	-6.08	-2.740784879	1
+    1 - 3	-5.444526566	-1.74	1.964526566	    0
+    """
+
+    @pytest.mark.parametrize("data,res_expect_str,atol",
+                             ((data_same_size, sas_same_size, 1e-4),
+                              (data_diff_size, sas_diff_size, 1e-4),
+                              (extreme_size, sas_extreme, 1e-10),
+                              ),
+                             ids=["equal size sample",
+                                  "unequal sample size",
+                                  "extreme sample size differences"])
+    def test_compare_sas(self, data, res_expect_str, atol):
+        '''
+        SAS code used to generate results for each sample:
+        DATA ACHE;
+        INPUT BRAND RELIEF;
+        CARDS;
+        1 24.5
+        ...
+        3 27.8
+        ;
+        ods graphics on;   ODS RTF;ODS LISTING CLOSE;
+           PROC ANOVA DATA=ACHE;
+           CLASS BRAND;
+           MODEL RELIEF=BRAND;
+           MEANS BRAND/TUKEY CLDIFF;
+           TITLE 'COMPARE RELIEF ACROSS MEDICINES  - ANOVA EXAMPLE';
+           ods output  CLDiffs =tc;
+        proc print data=tc;
+            format LowerCL 17.16 UpperCL 17.16 Difference 17.16;
+            title "Output with many digits";
+        RUN;
+        QUIT;
+        ODS RTF close;
+        ODS LISTING;
+        '''
+        res_expect = np.asarray(res_expect_str.replace(" - ", " ").split()[5:],
+                                dtype=float).reshape((6, 6))
+        res_tukey = stats.tukey_hsd(*data)
+        conf = res_tukey.confidence_interval()
+        # loop over the comparisons
+        for i, j, l, s, h, sig in res_expect:
+            i, j = int(i) - 1, int(j) - 1
+            assert_allclose(conf.low[i, j], l, atol=atol)
+            assert_allclose(res_tukey.statistic[i, j], s, atol=atol)
+            assert_allclose(conf.high[i, j], h, atol=atol)
+            assert_allclose((res_tukey.pvalue[i, j] <= .05), sig == 1)
+
+    matlab_sm_siz = """
+        1	2	-8.2491590248597	-4.6	-0.9508409751403	0.0144483269098
+        1	3	-3.9091590248597	-0.26	3.3891590248597	0.9803107240900
+        2	3	0.6908409751403	4.34	7.9891590248597	0.0203311368795
+        """
+
+    matlab_diff_sz = """
+        1	2	-7.02207069748501	-3.645	-0.26792930251500 0.03371498443080
+        1	3	-2.68207069748500	0.695	4.07207069748500 0.85572267328807
+        2	3	0.59347644287720	4.34	8.08652355712281 0.02259047020620
+        """
+
+    @pytest.mark.parametrize("data,res_expect_str,atol",
+                             ((data_same_size, matlab_sm_siz, 1e-12),
+                              (data_diff_size, matlab_diff_sz, 1e-7)),
+                             ids=["equal size sample",
+                                  "unequal size sample"])
+    def test_compare_matlab(self, data, res_expect_str, atol):
+        """
+        vals = [24.5, 23.5,  26.4, 27.1, 29.9, 28.4, 34.2, 29.5, 32.2, 30.1,
+         26.1, 28.3, 24.3, 26.2, 27.8]
+        names = {'zero', 'zero', 'zero', 'zero', 'zero', 'one', 'one', 'one',
+         'one', 'one', 'two', 'two', 'two', 'two', 'two'}
+        [p,t,stats] = anova1(vals,names,"off");
+        [c,m,h,nms] = multcompare(stats, "CType","hsd");
+        """
+        res_expect = np.asarray(res_expect_str.split(),
+                                dtype=float).reshape((3, 6))
+        res_tukey = stats.tukey_hsd(*data)
+        conf = res_tukey.confidence_interval()
+        # loop over the comparisons
+        for i, j, l, s, h, p in res_expect:
+            i, j = int(i) - 1, int(j) - 1
+            assert_allclose(conf.low[i, j], l, atol=atol)
+            assert_allclose(res_tukey.statistic[i, j], s, atol=atol)
+            assert_allclose(conf.high[i, j], h, atol=atol)
+            assert_allclose(res_tukey.pvalue[i, j], p, atol=atol)
+
+    def test_compare_r(self):
+        """
+        Testing against results and p-values from R:
+        from: https://www.rdocumentation.org/packages/stats/versions/3.6.2/
+        topics/TukeyHSD
+        > require(graphics)
+        > summary(fm1 <- aov(breaks ~ tension, data = warpbreaks))
+        > TukeyHSD(fm1, "tension", ordered = TRUE)
+        > plot(TukeyHSD(fm1, "tension"))
+        Tukey multiple comparisons of means
+        95% family-wise confidence level
+        factor levels have been ordered
+        Fit: aov(formula = breaks ~ tension, data = warpbreaks)
+        $tension
+        """
+        str_res = """
+                diff        lwr      upr     p adj
+        2 - 3  4.722222 -4.8376022 14.28205 0.4630831
+        1 - 3 14.722222  5.1623978 24.28205 0.0014315
+        1 - 2 10.000000  0.4401756 19.55982 0.0384598
+        """
+        res_expect = np.asarray(str_res.replace(" - ", " ").split()[5:],
+                                dtype=float).reshape((3, 6))
+        data = ([26, 30, 54, 25, 70, 52, 51, 26, 67,
+                 27, 14, 29, 19, 29, 31, 41, 20, 44],
+                [18, 21, 29, 17, 12, 18, 35, 30, 36,
+                 42, 26, 19, 16, 39, 28, 21, 39, 29],
+                [36, 21, 24, 18, 10, 43, 28, 15, 26,
+                 20, 21, 24, 17, 13, 15, 15, 16, 28])
+
+        res_tukey = stats.tukey_hsd(*data)
+        conf = res_tukey.confidence_interval()
+        # loop over the comparisons
+        for i, j, s, l, h, p in res_expect:
+            i, j = int(i) - 1, int(j) - 1
+            # atols are set to the number of digits present in the r result.
+            assert_allclose(conf.low[i, j], l, atol=1e-7)
+            assert_allclose(res_tukey.statistic[i, j], s, atol=1e-6)
+            assert_allclose(conf.high[i, j], h, atol=1e-5)
+            assert_allclose(res_tukey.pvalue[i, j], p, atol=1e-7)
+
+    def test_engineering_stat_handbook(self):
+        '''
+        Example sourced from:
+        https://www.itl.nist.gov/div898/handbook/prc/section4/prc471.htm
+        '''
+        group1 = [6.9, 5.4, 5.8, 4.6, 4.0]
+        group2 = [8.3, 6.8, 7.8, 9.2, 6.5]
+        group3 = [8.0, 10.5, 8.1, 6.9, 9.3]
+        group4 = [5.8, 3.8, 6.1, 5.6, 6.2]
+        res = stats.tukey_hsd(group1, group2, group3, group4)
+        conf = res.confidence_interval()
+        lower = np.asarray([
+            [0, 0, 0, -2.25],
+            [.29, 0, -2.93, .13],
+            [1.13, 0, 0, .97],
+            [0, 0, 0, 0]])
+        upper = np.asarray([
+            [0, 0, 0, 1.93],
+            [4.47, 0, 1.25, 4.31],
+            [5.31, 0, 0, 5.15],
+            [0, 0, 0, 0]])
+
+        for (i, j) in [(1, 0), (2, 0), (0, 3), (1, 2), (2, 3)]:
+            assert_allclose(conf.low[i, j], lower[i, j], atol=1e-2)
+            assert_allclose(conf.high[i, j], upper[i, j], atol=1e-2)
+
+    def test_rand_symm(self):
+        # test some expected identities of the results
+        rng = np.random.default_rng(2699550179)
+        data = rng.random((3, 100))
+        res = stats.tukey_hsd(*data)
+        conf = res.confidence_interval()
+        # the confidence intervals should be negated symmetric of each other
+        assert_equal(conf.low, -conf.high.T)
+        # the `high` and `low` center diagonals should be the same since the
+        # mean difference in a self comparison is 0.
+        assert_equal(np.diagonal(conf.high), conf.high[0, 0])
+        assert_equal(np.diagonal(conf.low), conf.low[0, 0])
+        # statistic array should be antisymmetric with zeros on the diagonal
+        assert_equal(res.statistic, -res.statistic.T)
+        assert_equal(np.diagonal(res.statistic), 0)
+        # p-values should be symmetric and 1 when compared to itself
+        assert_equal(res.pvalue, res.pvalue.T)
+        assert_equal(np.diagonal(res.pvalue), 1)
+
+    def test_no_inf(self):
+        with assert_raises(ValueError, match="...must be finite."):
+            stats.tukey_hsd([1, 2, 3], [2, np.inf], [6, 7, 3])
+
+    def test_is_1d(self):
+        with assert_raises(ValueError, match="...must be one-dimensional"):
+            stats.tukey_hsd([[1, 2], [2, 3]], [2, 5], [5, 23, 6])
+
+    def test_no_empty(self):
+        with assert_raises(ValueError, match="...must be greater than one"):
+            stats.tukey_hsd([], [2, 5], [4, 5, 6])
+
+    def test_equal_var_input_validation(self):
+        msg = "Expected a boolean value for 'equal_var'"
+        with assert_raises(TypeError, match=msg):
+            stats.tukey_hsd([1, 2, 3], [2, 5], [6, 7], equal_var="False")
+
+    @pytest.mark.parametrize("nargs", (0, 1))
+    def test_not_enough_treatments(self, nargs):
+        with assert_raises(ValueError, match="...more than 1 treatment."):
+            stats.tukey_hsd(*([[23, 7, 3]] * nargs))
+
+    @pytest.mark.parametrize("cl", [-.5, 0, 1, 2])
+    def test_conf_level_invalid(self, cl):
+        with assert_raises(ValueError, match="must be between 0 and 1"):
+            r = stats.tukey_hsd([23, 7, 3], [3, 4], [9, 4])
+            r.confidence_interval(cl)
+
+    def test_2_args_ttest(self):
+        # that with 2 treatments the `pvalue` is equal to that of `ttest_ind`
+        res_tukey = stats.tukey_hsd(*self.data_diff_size[:2])
+        res_ttest = stats.ttest_ind(*self.data_diff_size[:2])
+        assert_allclose(res_ttest.pvalue, res_tukey.pvalue[0, 1])
+        assert_allclose(res_ttest.pvalue, res_tukey.pvalue[1, 0])
+
+
+class TestGamesHowell:
+    # data with unequal variances
+    data_same_size = ([24., 23., 31., 51.],
+                      [34., 18., 18., 26.],
+                      [17., 68., 59.,  7.])
+
+    data_diff_size = ([30., 23., 51.],
+                      [-81., 71., -27., 63.],
+                      [42., 11., 29., 19., 50.],
+                      [23., 22., 20., 18., 9.])
+
+    spss_same_size = """
+            Mean Diff      Lower Bound         Upper Bound         Sig
+    0 - 1   8.25000000    -16.5492749527311    33.0492749527311    0.558733632413559
+    0 - 2  -5.50000000    -63.6702454316458    52.6702454316458    0.941147750599221
+    1 - 2  -13.7500000    -74.3174374251372    46.8174374251372    0.682983914946841
+    """
+
+    spss_diff_size = """
+             Mean Diff       Lower Bound        Upper Bound         Sig
+    0 - 1	 28.16666667    -141.985416377670   198.318749711003	0.8727542747886180
+    0 - 2	 4.466666667	-37.2830676783904   46.2164010117237	0.9752628408671710
+    0 - 3	 16.26666667	-35.0933112382470   67.6266445715803	0.4262506151302880
+    1 - 2	-23.70000000	-195.315617201249   147.915617201249	0.9148950609000590
+    1 - 3	-11.90000000	-188.105478728519   164.305478728519	0.9861432250093960
+    2 - 3	 11.80000000	-16.2894857524254	39.8894857524254    0.4755344436335670
+    """
+
+    @pytest.mark.xslow
+    @pytest.mark.parametrize("data, res_expect_str",
+                            ((data_same_size, spss_same_size),
+                            (data_diff_size, spss_diff_size)),
+                            ids=["equal size sample",
+                                 "unequal sample size"])
+    def test_compare_spss(self, data, res_expect_str):
+        """
+        DATA LIST LIST /Group (F1.0) Value (F8.2).
+        BEGIN DATA
+        0 24
+        0 23
+        0 31
+        0 51
+        1 34
+        1 18
+        1 18
+        1 26
+        2 17
+        2 68
+        2 59
+        2 7
+        END DATA.
+
+        ONEWAY Value BY Group
+            /MISSING ANALYSIS
+            /POSTHOC=GH ALPHA(0.05).
+        """
+        res_expect = np.asarray(
+            res_expect_str.replace(" - ", " ").split()[7:],
+            dtype=float).reshape(-1, 6)
+        res_games = stats.tukey_hsd(*data, equal_var=False)
+        conf = res_games.confidence_interval()
+        # loop over the comparisons
+        for i, j, s, l, h, p in res_expect:
+            i, j = int(i), int(j)
+            assert_allclose(res_games.statistic[i, j], s, atol=1e-8)
+            assert_allclose(res_games.pvalue[i, j], p, atol=1e-8)
+            assert_allclose(conf.low[i, j], l, atol=1e-6)
+            assert_allclose(conf.high[i, j], h, atol=1e-5)
+
+    r_same_size = """
+                  q value             Pr(>|q|)
+    1 - 0 == 0   -1.5467805948856344  0.55873362851759
+    2 - 0 == 0    0.4726721776628535  0.94114775035993
+    2 - 1 == 0    1.246837541297872   0.68298393799782
+    """
+
+    r_diff_size = """
+                 q value             Pr(>|q|)
+    1 - 0 == 0  -1.0589317485313876  0.87275427357438
+    2 - 0 == 0  -0.5716222106144833  0.97526284087419
+    3 - 0 == 0  -2.6209678382077000  0.42625067714691
+    2 - 1 == 0   0.8971899898179028  0.91489506061850
+    3 - 1 == 0   0.4579447210555352  0.98614322544695
+    3 - 2 == 0  -2.198800177874794   0.47553444364614
+    """
+
+    @pytest.mark.parametrize("data, res_expect_str",
+                            ((data_same_size, r_same_size),
+                            (data_diff_size, r_diff_size)),
+                            ids=["equal size sample",
+                                 "unequal sample size"])
+    def test_compare_r(self, data, res_expect_str):
+        """
+        games-howell is provided by PMCMRplus package
+        https://search.r-project.org/CRAN/refmans/PMCMRplus/html/gamesHowellTest.html
+        > library("PMCMRplus")
+        > options(digits=16)
+        > table = data.frame(
+            values = c(24., 23., 31., 51., 34., 18., 18., 26., 17., 68., 59.,  7.),
+            groups = c("0", "0", "0", "0", "1", "1", "1", "1", "2", "2", "2", "2")
+          )
+        > table$groups = as.factor(table$groups)
+        > fit <-aov(values ~ groups, table)
+        > res = gamesHowellTest(fit)
+        > summary(res)
+        """
+        res_expect = np.asarray(
+            res_expect_str.replace(" - ", " ")
+            .replace(" == ", " ").split()[3:],
+            dtype=float).reshape(-1, 5)
+        res_games = stats.tukey_hsd(*data, equal_var=False)
+        # loop over the comparisons
+        # note confidence intervals are not provided by PMCMRplus
+        for j, i, _, _, p in res_expect:
+            i, j = int(i), int(j)
+            assert_allclose(res_games.pvalue[i, j], p, atol=1e-7)
+
+    # Data validation test has been covered by TestTukeyHSD
+    # like empty, 1d, inf, and lack of tretments
+    # because games_howell leverage _tukey_hsd_iv()
+
+class TestPoissonMeansTest:
+    @pytest.mark.parametrize("c1, n1, c2, n2, p_expect", (
+        # example from [1], 6. Illustrative examples: Example 1
+        [0, 100, 3, 100, 0.0884],
+        [2, 100, 6, 100, 0.1749]
+    ))
+    def test_paper_examples(self, c1, n1, c2, n2, p_expect):
+        res = stats.poisson_means_test(c1, n1, c2, n2)
+        assert_allclose(res.pvalue, p_expect, atol=1e-4)
+
+    @pytest.mark.parametrize("c1, n1, c2, n2, p_expect, alt, d", (
+        # These test cases are produced by the wrapped fortran code from the
+        # original authors. Using a slightly modified version of this fortran,
+        # found here, https://github.com/nolanbconaway/poisson-etest,
+        # additional tests were created.
+        [20, 10, 20, 10, 0.9999997568929630, 'two-sided', 0],
+        [10, 10, 10, 10, 0.9999998403241203, 'two-sided', 0],
+        [50, 15, 1, 1, 0.09920321053409643, 'two-sided', .05],
+        [3, 100, 20, 300, 0.12202725450896404, 'two-sided', 0],
+        [3, 12, 4, 20, 0.40416087318539173, 'greater', 0],
+        [4, 20, 3, 100, 0.008053640402974236, 'greater', 0],
+        # publishing paper does not include a `less` alternative,
+        # so it was calculated with switched argument order and
+        # alternative="greater"
+        [4, 20, 3, 10, 0.3083216325432898, 'less', 0],
+        [1, 1, 50, 15, 0.09322998607245102, 'less', 0]
+    ))
+    def test_fortran_authors(self, c1, n1, c2, n2, p_expect, alt, d):
+        res = stats.poisson_means_test(c1, n1, c2, n2, alternative=alt, diff=d)
+        assert_allclose(res.pvalue, p_expect, atol=2e-6, rtol=1e-16)
+
+    def test_different_results(self):
+        # The implementation in Fortran is known to break down at higher
+        # counts and observations, so we expect different results. By
+        # inspection we can infer the p-value to be near one.
+        count1, count2 = 10000, 10000
+        nobs1, nobs2 = 10000, 10000
+        res = stats.poisson_means_test(count1, nobs1, count2, nobs2)
+        assert_allclose(res.pvalue, 1)
+
+    def test_less_than_zero_lambda_hat2(self):
+        # demonstrates behavior that fixes a known fault from original Fortran.
+        # p-value should clearly be near one.
+        count1, count2 = 0, 0
+        nobs1, nobs2 = 1, 1
+        res = stats.poisson_means_test(count1, nobs1, count2, nobs2)
+        assert_allclose(res.pvalue, 1)
+
+    def test_input_validation(self):
+        count1, count2 = 0, 0
+        nobs1, nobs2 = 1, 1
+
+        # test non-integral events
+        message = '`k1` and `k2` must be integers.'
+        with assert_raises(TypeError, match=message):
+            stats.poisson_means_test(.7, nobs1, count2, nobs2)
+        with assert_raises(TypeError, match=message):
+            stats.poisson_means_test(count1, nobs1, .7, nobs2)
+
+        # test negative events
+        message = '`k1` and `k2` must be greater than or equal to 0.'
+        with assert_raises(ValueError, match=message):
+            stats.poisson_means_test(-1, nobs1, count2, nobs2)
+        with assert_raises(ValueError, match=message):
+            stats.poisson_means_test(count1, nobs1, -1, nobs2)
+
+        # test negative sample size
+        message = '`n1` and `n2` must be greater than 0.'
+        with assert_raises(ValueError, match=message):
+            stats.poisson_means_test(count1, -1, count2, nobs2)
+        with assert_raises(ValueError, match=message):
+            stats.poisson_means_test(count1, nobs1, count2, -1)
+
+        # test negative difference
+        message = 'diff must be greater than or equal to 0.'
+        with assert_raises(ValueError, match=message):
+            stats.poisson_means_test(count1, nobs1, count2, nobs2, diff=-1)
+
+        # test invalid alternative
+        message = 'Alternative must be one of ...'
+        with assert_raises(ValueError, match=message):
+            stats.poisson_means_test(1, 2, 1, 2, alternative='error')
+
+
+@make_xp_test_case(stats.bws_test)
+class TestBWSTest:
+
+    def test_bws_input_validation(self, xp):
+        rng = np.random.default_rng(4571775098104213308)
+
+        x, y = rng.random(size=(2, 7))
+        x, y = xp.asarray(x), xp.asarray(y)
+
+        message = '`axis` must be an integer or None.'
+        with pytest.raises(ValueError, match=message):
+            stats.bws_test(x, y, axis=1.5)
+
+        message = '`axis` is not compatible with the shapes of the inputs.'
+        with pytest.raises(ValueError, match=message):
+            stats.bws_test(x, y, axis=3)
+
+        message = '`x` and `y` must contain...'
+        with pytest.raises(ValueError, match=message):
+            stats.bws_test(x, xp.asarray([], dtype=x.dtype))
+
+        message = 'alternative` must be one of...'
+        with pytest.raises(ValueError, match=message):
+            stats.bws_test(x, y, alternative='ekki-ekki')
+
+        message = 'method` must be an instance of...'
+        with pytest.raises(ValueError, match=message):
+            stats.bws_test(x, y, method=42)
+
+    @pytest.mark.parametrize('dtype', [None, 'float32', 'float64'])
+    def test_against_published_reference(self, dtype, xp):
+        # Test against Example 2 in bws_test Reference [1], pg 9
+        # https://link.springer.com/content/pdf/10.1007/BF02762032.pdf
+        dtype = xp_default_dtype(xp) if dtype is None else getattr(xp, dtype)
+        x = xp.asarray([1, 2, 3, 4, 6, 7, 8], dtype=dtype)
+        y = xp.asarray([5, 9, 10, 11, 12, 13, 14], dtype=dtype)
+        res = stats.bws_test(x, y, alternative='two-sided')
+        xp_assert_close(res.statistic, xp.asarray(5.132, dtype=dtype), atol=1e-3)
+        xp_assert_close(res.pvalue, xp.asarray(10/3432, dtype=dtype))
+
+    @pytest.mark.parametrize(('alternative', 'statistic', 'pvalue'),
+                             [('two-sided', 1.7510204081633, 0.1264422777777),
+                              ('less', -1.7510204081633, 0.05754662004662),
+                              ('greater', -1.7510204081633, 0.9424533799534)])
+    def test_against_R(self, alternative, statistic, pvalue, xp):
+        # Test against R library BWStest function bws_test
+        # library(BWStest)
+        # options(digits=16)
+        # x = c(...)
+        # y = c(...)
+        # bws_test(x, y, alternative='two.sided')
+        rng = np.random.default_rng(4571775098104213308)
+        x, y = rng.random(size=(2, 7))
+        x, y = xp.asarray(x, dtype=xp.float64), xp.asarray(y, dtype=xp.float64)
+        res = stats.bws_test(x, y, alternative=alternative)
+        statistic = xp.asarray(statistic, dtype=xp.float64)
+        pvalue = xp.asarray(pvalue, dtype=xp.float64)
+        xp_assert_close(res.statistic, statistic, rtol=1e-13)
+        xp_assert_close(res.pvalue, pvalue, atol=1e-2, rtol=1e-1)
+
+    @pytest.mark.parametrize(('alternative', 'statistic', 'pvalue'),
+                             [('two-sided', 1.142629265891, 0.2903950180801),
+                              ('less', 0.99629665877411, 0.8545660222131),
+                              ('greater', 0.99629665877411, 0.1454339777869)])
+    def test_against_R_imbalanced(self, alternative, statistic, pvalue, xp):
+        # Test against R library BWStest function bws_test
+        # library(BWStest)
+        # options(digits=16)
+        # x = c(...)
+        # y = c(...)
+        # bws_test(x, y, alternative='two.sided')
+        rng = np.random.default_rng(5429015622386364034)
+        x = rng.random(size=9)
+        y = rng.random(size=8)
+        x, y = xp.asarray(x), xp.asarray(y)
+        res = stats.bws_test(x, y, alternative=alternative)
+        x, y = xp.asarray(x, dtype=xp.float64), xp.asarray(y, dtype=xp.float64)
+        res = stats.bws_test(x, y, alternative=alternative)
+        statistic = xp.asarray(statistic, dtype=xp.float64)
+        pvalue = xp.asarray(pvalue, dtype=xp.float64)
+        xp_assert_close(res.statistic, statistic, rtol=1e-13)
+        xp_assert_close(res.pvalue, pvalue, atol=1e-2, rtol=1e-1)
+
+    def test_method(self, xp):
+        # Test that `method` parameter has the desired effect
+        rng = np.random.default_rng(1520514347193347862)
+        x, y = rng.random(size=(2, 10))
+        x, y = xp.asarray(x), xp.asarray(y)
+
+        rng = np.random.default_rng(1520514347193347862)
+        method = stats.PermutationMethod(n_resamples=10, rng=rng)
+        res1 = stats.bws_test(x, y, method=method)
+
+        assert res1.null_distribution.shape[0] == 10
+
+        rng = np.random.default_rng(1520514347193347862)
+        method = stats.PermutationMethod(n_resamples=10, rng=rng)
+        res2 = stats.bws_test(x, y, method=method)
+
+        xp_assert_close(res1.null_distribution, res2.null_distribution)
+
+        rng = np.random.default_rng(5205143471933478621)
+        method = stats.PermutationMethod(n_resamples=10, rng=rng)
+        res3 = stats.bws_test(x, y, method=method)
+
+        assert xp.all(xp.abs(res3.null_distribution - res1.null_distribution) > 0.1)
+
+    def test_directions(self, xp):
+        # Sanity check of the sign of the one-sided statistic
+        rng = np.random.default_rng(1520514347193347862)
+        x = xp.asarray(rng.random(size=5))
+        y = x - 1.
+
+        pmin = xp.asarray(1 / 252, dtype=xp.float64)
+        pmax = xp.asarray(1, dtype=xp.float64)
+
+        res = stats.bws_test(x, y, alternative='greater')
+        assert res.statistic > 0
+        xp_assert_equal(res.pvalue, pmin)
+
+        res = stats.bws_test(x, y, alternative='less')
+        assert res.statistic > 0
+        xp_assert_equal(res.pvalue, pmax)
+
+        res = stats.bws_test(y, x, alternative='less')
+        assert res.statistic < 0
+        xp_assert_equal(res.pvalue, pmin)
+
+        res = stats.bws_test(y, x, alternative='greater')
+        assert res.statistic < 0
+        xp_assert_equal(res.pvalue, pmax)
+
+    @pytest.mark.parametrize('axis', [0, 1])
+    def test_nd(self, axis, xp):
+        rng = np.random.default_rng(1520514347193347862)
+        z = rng.random(size=(2, 3, 5))
+
+        x, y = z
+        res = stats.bws_test(xp.asarray(x), xp.asarray(y), axis=axis)
+
+        x, y = np.moveaxis(z, axis+1, -1)
+        ref_statistic, ref_pvalue = [], []
+        for x_, y_ in zip(x, y):
+            ref = stats.bws_test(xp.asarray(x_), xp.asarray(y_))
+            ref_statistic.append(ref.statistic)
+            ref_pvalue.append(ref.pvalue)
+        ref_statistic, ref_pvalue = xp.stack(ref_statistic), xp.stack(ref_pvalue)
+
+        xp_assert_close(res.statistic, ref_statistic)
+        xp_assert_close(res.pvalue, ref_pvalue)
+
+    def test_axis_None(self, xp):
+        rng = np.random.default_rng(5205143471933478621)
+        x, y = rng.random(size=(2, 2, 3))
+        x, y = xp.asarray(x), xp.asarray(y)
+        res = stats.bws_test(x, y, axis=None)
+        ref = stats.bws_test(xp_ravel(x), xp_ravel(y))
+        xp_assert_close(res.statistic, ref.statistic)
+        xp_assert_close(res.pvalue, ref.pvalue)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/test_kdeoth.py b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_kdeoth.py
new file mode 100644
index 0000000000000000000000000000000000000000..a4ceed5e477d7ae23d5f17324371bd6753fd7334
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_kdeoth.py
@@ -0,0 +1,678 @@
+from scipy import stats, linalg, integrate
+import numpy as np
+from numpy.testing import (assert_almost_equal, assert_, assert_equal,
+                           assert_array_almost_equal,
+                           assert_array_almost_equal_nulp, assert_allclose)
+import pytest
+from pytest import raises as assert_raises
+
+
+def test_kde_1d():
+    #some basic tests comparing to normal distribution
+    rng = np.random.default_rng(8765678)
+    n_basesample = 500
+    xn = rng.normal(0, 1, n_basesample)
+    xnmean = xn.mean()
+    xnstd = xn.std(ddof=1)
+
+    # get kde for original sample
+    gkde = stats.gaussian_kde(xn)
+
+    # evaluate the density function for the kde for some points
+    xx = np.asarray([0.1, 0.5, 0.9])
+    loc, scale = gkde.dataset, np.sqrt(gkde.covariance)
+    assert_allclose(
+        gkde(xx), 
+        stats.norm.pdf(xx[:, None], loc=loc, scale=scale).sum(axis=-1) / gkde.n,
+        rtol=5e-14
+    )
+
+    xs = np.linspace(-7, 7, 501)
+    kdepdf = gkde.evaluate(xs)
+    normpdf = stats.norm.pdf(xs, loc=xnmean, scale=xnstd)
+    intervall = xs[1] - xs[0]
+
+    assert_(np.sum((kdepdf - normpdf)**2)*intervall < 0.01)
+    prob1 = gkde.integrate_box_1d(xnmean, np.inf)
+    prob2 = gkde.integrate_box_1d(-np.inf, xnmean)
+    assert_almost_equal(prob1, 0.5, decimal=1)
+    assert_almost_equal(prob2, 0.5, decimal=1)
+    assert_almost_equal(gkde.integrate_box(xnmean, np.inf), prob1, decimal=13)
+    assert_almost_equal(gkde.integrate_box(-np.inf, xnmean), prob2, decimal=13)
+
+    assert_almost_equal(gkde.integrate_kde(gkde),
+                        (kdepdf**2).sum()*intervall, decimal=2)
+    assert_almost_equal(gkde.integrate_gaussian(xnmean, xnstd**2),
+                        (kdepdf*normpdf).sum()*intervall, decimal=2)
+
+
+def test_kde_1d_weighted():
+    #some basic tests comparing to normal distribution
+    rng = np.random.default_rng(8765678)
+    n_basesample = 500
+    xn = rng.normal(0, 1, n_basesample)
+    wn = rng.random(n_basesample)
+    xnmean = np.average(xn, weights=wn)
+    xnstd = np.sqrt(np.average((xn-xnmean)**2, weights=wn))
+
+    # get kde for original sample
+    gkde = stats.gaussian_kde(xn, weights=wn)
+
+    # evaluate the density function for the kde for some points
+    # evaluate the density function for the kde for some points
+    xx = np.asarray([0.1, 0.5, 0.9])
+    loc, scale = gkde.dataset, np.sqrt(gkde.covariance)
+
+    pdf = stats.norm.pdf
+    assert_allclose(
+        gkde(xx), 
+        np.sum(pdf(xx[:, None], loc=loc, scale=scale) * gkde.weights, axis=-1),
+        rtol=5e-14
+    )
+
+    xs = np.linspace(-7, 7, 501)
+    kdepdf = gkde.evaluate(xs)
+    normpdf = stats.norm.pdf(xs, loc=xnmean, scale=xnstd)
+    intervall = xs[1] - xs[0]
+
+    assert_(np.sum((kdepdf - normpdf)**2)*intervall < 0.01)
+    prob1 = gkde.integrate_box_1d(xnmean, np.inf)
+    prob2 = gkde.integrate_box_1d(-np.inf, xnmean)
+    assert_almost_equal(prob1, 0.5, decimal=1)
+    assert_almost_equal(prob2, 0.5, decimal=1)
+    assert_almost_equal(gkde.integrate_box(xnmean, np.inf), prob1, decimal=13)
+    assert_almost_equal(gkde.integrate_box(-np.inf, xnmean), prob2, decimal=13)
+
+    assert_almost_equal(gkde.integrate_kde(gkde),
+                        (kdepdf**2).sum()*intervall, decimal=2)
+    assert_almost_equal(gkde.integrate_gaussian(xnmean, xnstd**2),
+                        (kdepdf*normpdf).sum()*intervall, decimal=2)
+
+
+@pytest.mark.parametrize("n_basesample",
+                         [
+                            20,
+                            pytest.param(500, marks=[pytest.mark.xslow])
+                         ]
+)
+def test_kde_2d(n_basesample):
+    #some basic tests comparing to normal distribution
+    rng = np.random.default_rng(8765678)
+
+    mean = np.array([1.0, 3.0])
+    covariance = np.array([[1.0, 2.0], [2.0, 6.0]])
+
+    # Need transpose (shape (2, 500)) for kde
+    xn = rng.multivariate_normal(mean, covariance, size=n_basesample).T
+
+    # get kde for original sample
+    gkde = stats.gaussian_kde(xn)
+
+    # evaluate vs multivariate normal, using the KDE definition
+    xx = np.asarray([[1, 2], [3, 4], [5, 6]])
+    arg = xx[:, None, :] - gkde.dataset.T
+    pdf = stats.multivariate_normal.pdf
+    assert_allclose(
+        gkde(xx.T),
+        pdf(arg, cov=gkde.covariance).sum(axis=-1) / gkde.n,
+        rtol=5e-14
+    )
+
+    # ... and cdf
+    cdf = stats.multivariate_normal.cdf
+    lo, hi = [-1, -2], [0, 0]
+    lo_, hi_ = lo - gkde.dataset.T, hi - gkde.dataset.T
+    assert_allclose(
+        gkde.integrate_box(lo, hi, rng=rng),
+        cdf(hi_, lower_limit=lo_, cov=gkde.covariance, rng=rng).sum(axis=-1) / gkde.n,
+        rtol=5e-7
+    )
+
+    # evaluate the density function for the kde for some points
+    x, y = np.mgrid[-7:7:500j, -7:7:500j]
+    grid_coords = np.vstack([x.ravel(), y.ravel()])
+    kdepdf = gkde.evaluate(grid_coords)
+    kdepdf = kdepdf.reshape(500, 500)
+
+    normpdf = stats.multivariate_normal.pdf(np.dstack([x, y]),
+                                            mean=mean, cov=covariance)
+    intervall = y.ravel()[1] - y.ravel()[0]
+
+    assert_(np.sum((kdepdf - normpdf)**2) * (intervall**2) < 0.01)
+
+    small = -1e100
+    large = 1e100
+    prob1 = gkde.integrate_box([small, mean[1]], [large, large], rng=rng)
+    prob2 = gkde.integrate_box([small, small], [large, mean[1]], rng=rng)
+
+    assert_almost_equal(prob1, 0.5, decimal=1)
+    assert_almost_equal(prob2, 0.5, decimal=1)
+    assert_almost_equal(gkde.integrate_kde(gkde),
+                        (kdepdf**2).sum()*(intervall**2), decimal=2)
+    assert_almost_equal(gkde.integrate_gaussian(mean, covariance),
+                        (kdepdf*normpdf).sum()*(intervall**2), decimal=2)
+
+
+@pytest.mark.parametrize("n_basesample",
+                         [
+                            20,
+                            pytest.param(500, marks=[pytest.mark.xslow])
+                         ]
+)
+def test_kde_2d_weighted(n_basesample):
+    #some basic tests comparing to normal distribution
+    rng = np.random.RandomState(8765678)
+
+    mean = np.array([1.0, 3.0])
+    covariance = np.array([[1.0, 2.0], [2.0, 6.0]])
+
+    # Need transpose (shape (2, 500)) for kde
+    xn = rng.multivariate_normal(mean, covariance, size=n_basesample).T
+    wn = rng.rand(n_basesample)
+
+    # get kde for original sample
+    gkde = stats.gaussian_kde(xn, weights=wn)
+
+
+    # evaluate vs multivariate normal, using the kde definition
+    xx = np.asarray([[1, 2], [3, 4], [5, 6]])
+    arg = xx[:, None, :] - gkde.dataset.T
+    pdf = stats.multivariate_normal.pdf
+    assert_allclose(
+        gkde(xx.T),
+        np.sum(pdf(arg, cov=gkde.covariance) * gkde.weights, axis=-1),
+        rtol=5e-14
+    )
+
+    # ... and cdf
+    cdf = stats.multivariate_normal.cdf
+    lo, hi = [-1, -2], [0, 0]
+    lo_, hi_ = lo - gkde.dataset.T, hi - gkde.dataset.T
+    assert_allclose(
+        gkde.integrate_box(lo, hi, rng=rng),
+        np.sum(cdf(hi_, lower_limit=lo_, cov=gkde.covariance, rng=rng) *
+               gkde.weights, axis=-1),
+        rtol=5e-6
+    )
+
+    # evaluate the density function for the kde for some points
+    x, y = np.mgrid[-7:7:500j, -7:7:500j]
+    grid_coords = np.vstack([x.ravel(), y.ravel()])
+    kdepdf = gkde.evaluate(grid_coords)
+    kdepdf = kdepdf.reshape(500, 500)
+
+    normpdf = stats.multivariate_normal.pdf(np.dstack([x, y]),
+                                            mean=mean, cov=covariance)
+    intervall = y.ravel()[1] - y.ravel()[0]
+
+    assert_(np.sum((kdepdf - normpdf)**2) * (intervall**2) < 0.01)
+
+    small = -1e100
+    large = 1e100
+    prob1 = gkde.integrate_box([small, mean[1]], [large, large], rng=rng)
+    prob2 = gkde.integrate_box([small, small], [large, mean[1]], rng=rng)
+
+    assert_almost_equal(prob1, 0.5, decimal=1)
+    assert_almost_equal(prob2, 0.5, decimal=1)
+    assert_almost_equal(gkde.integrate_kde(gkde),
+                        (kdepdf**2).sum()*(intervall**2), decimal=2)
+    assert_almost_equal(gkde.integrate_gaussian(mean, covariance),
+                        (kdepdf*normpdf).sum()*(intervall**2), decimal=2)
+
+
+def test_kde_bandwidth_method():
+    def scotts_factor(kde_obj):
+        """Same as default, just check that it works."""
+        return np.power(kde_obj.n, -1./(kde_obj.d+4))
+
+    rng = np.random.default_rng(8765678)
+    n_basesample = 50
+    xn = rng.normal(0, 1, n_basesample)
+
+    # Default
+    gkde = stats.gaussian_kde(xn)
+    # Supply a callable
+    gkde2 = stats.gaussian_kde(xn, bw_method=scotts_factor)
+    # Supply a scalar
+    gkde3 = stats.gaussian_kde(xn, bw_method=gkde.factor)
+
+    xs = np.linspace(-7,7,51)
+    kdepdf = gkde.evaluate(xs)
+    kdepdf2 = gkde2.evaluate(xs)
+    assert_almost_equal(kdepdf, kdepdf2)
+    kdepdf3 = gkde3.evaluate(xs)
+    assert_almost_equal(kdepdf, kdepdf3)
+
+    assert_raises(ValueError, stats.gaussian_kde, xn, bw_method='wrongstring')
+
+
+def test_kde_bandwidth_method_weighted():
+    def scotts_factor(kde_obj):
+        """Same as default, just check that it works."""
+        return np.power(kde_obj.neff, -1./(kde_obj.d+4))
+
+    rng = np.random.default_rng(8765678)
+    n_basesample = 50
+    xn = rng.normal(0, 1, n_basesample)
+
+    # Default
+    gkde = stats.gaussian_kde(xn)
+    # Supply a callable
+    gkde2 = stats.gaussian_kde(xn, bw_method=scotts_factor)
+    # Supply a scalar
+    gkde3 = stats.gaussian_kde(xn, bw_method=gkde.factor)
+
+    xs = np.linspace(-7,7,51)
+    kdepdf = gkde.evaluate(xs)
+    kdepdf2 = gkde2.evaluate(xs)
+    assert_almost_equal(kdepdf, kdepdf2)
+    kdepdf3 = gkde3.evaluate(xs)
+    assert_almost_equal(kdepdf, kdepdf3)
+
+    assert_raises(ValueError, stats.gaussian_kde, xn, bw_method='wrongstring')
+
+
+# Subclasses that should stay working (extracted from various sources).
+# Unfortunately the earlier design of gaussian_kde made it necessary for users
+# to create these kinds of subclasses, or call _compute_covariance() directly.
+
+class _kde_subclass1(stats.gaussian_kde):
+    def __init__(self, dataset):
+        self.dataset = np.atleast_2d(dataset)
+        self.d, self.n = self.dataset.shape
+        self.covariance_factor = self.scotts_factor
+        self._compute_covariance()
+
+
+class _kde_subclass2(stats.gaussian_kde):
+    def __init__(self, dataset):
+        self.covariance_factor = self.scotts_factor
+        super().__init__(dataset)
+
+
+class _kde_subclass4(stats.gaussian_kde):
+    def covariance_factor(self):
+        return 0.5 * self.silverman_factor()
+
+
+def test_gaussian_kde_subclassing():
+    x1 = np.array([-7, -5, 1, 4, 5], dtype=float)
+    xs = np.linspace(-10, 10, num=50)
+
+    # gaussian_kde itself
+    kde = stats.gaussian_kde(x1)
+    ys = kde(xs)
+
+    # subclass 1
+    kde1 = _kde_subclass1(x1)
+    y1 = kde1(xs)
+    assert_array_almost_equal_nulp(ys, y1, nulp=10)
+
+    # subclass 2
+    kde2 = _kde_subclass2(x1)
+    y2 = kde2(xs)
+    assert_array_almost_equal_nulp(ys, y2, nulp=10)
+
+    # subclass 3 was removed because we have no obligation to maintain support
+    # for user invocation of private methods
+
+    # subclass 4
+    kde4 = _kde_subclass4(x1)
+    y4 = kde4(x1)
+    y_expected = [0.06292987, 0.06346938, 0.05860291, 0.08657652, 0.07904017]
+
+    assert_array_almost_equal(y_expected, y4, decimal=6)
+
+    # Not a subclass, but check for use of _compute_covariance()
+    kde5 = kde
+    kde5.covariance_factor = lambda: kde.factor
+    kde5._compute_covariance()
+    y5 = kde5(xs)
+    assert_array_almost_equal_nulp(ys, y5, nulp=10)
+
+
+def test_gaussian_kde_covariance_caching():
+    x1 = np.array([-7, -5, 1, 4, 5], dtype=float)
+    xs = np.linspace(-10, 10, num=5)
+    # These expected values are from scipy 0.10, before some changes to
+    # gaussian_kde.  They were not compared with any external reference.
+    y_expected = [0.02463386, 0.04689208, 0.05395444, 0.05337754, 0.01664475]
+
+    # Set the bandwidth, then reset it to the default.
+    kde = stats.gaussian_kde(x1)
+    kde.set_bandwidth(bw_method=0.5)
+    kde.set_bandwidth(bw_method='scott')
+    y2 = kde(xs)
+
+    assert_array_almost_equal(y_expected, y2, decimal=7)
+
+
+def test_gaussian_kde_monkeypatch():
+    """Ugly, but people may rely on this.  See scipy pull request 123,
+    specifically the linked ML thread "Width of the Gaussian in stats.kde".
+    If it is necessary to break this later on, that is to be discussed on ML.
+    """
+    x1 = np.array([-7, -5, 1, 4, 5], dtype=float)
+    xs = np.linspace(-10, 10, num=50)
+
+    # The old monkeypatched version to get at Silverman's Rule.
+    kde = stats.gaussian_kde(x1)
+    kde.covariance_factor = kde.silverman_factor
+    kde._compute_covariance()
+    y1 = kde(xs)
+
+    # The new saner version.
+    kde2 = stats.gaussian_kde(x1, bw_method='silverman')
+    y2 = kde2(xs)
+
+    assert_array_almost_equal_nulp(y1, y2, nulp=10)
+
+
+def test_kde_integer_input():
+    """Regression test for #1181."""
+    x1 = np.arange(5)
+    kde = stats.gaussian_kde(x1)
+    y_expected = [0.13480721, 0.18222869, 0.19514935, 0.18222869, 0.13480721]
+    assert_array_almost_equal(kde(x1), y_expected, decimal=6)
+
+
+_ftypes = ['float32', 'float64', 'float96', 'float128', 'int32', 'int64']
+
+
+@pytest.mark.filterwarnings("ignore::DeprecationWarning")
+@pytest.mark.parametrize("bw_type", _ftypes + ["scott", "silverman"])
+@pytest.mark.parametrize("dtype", _ftypes)
+def test_kde_output_dtype(dtype, bw_type):
+    # Check whether the datatypes are available
+    dtype = getattr(np, dtype, None)
+
+    if bw_type in ["scott", "silverman"]:
+        bw = bw_type
+    else:
+        bw_type = getattr(np, bw_type, None)
+        bw = bw_type(3) if bw_type else None
+
+    if any(dt is None for dt in [dtype, bw]):
+        pytest.skip()
+
+    weights = np.arange(5, dtype=dtype)
+    dataset = np.arange(5, dtype=dtype)
+    k = stats.gaussian_kde(dataset, bw_method=bw, weights=weights)
+    points = np.arange(5, dtype=dtype)
+    result = k(points)
+    # weights are always cast to float64
+    assert result.dtype == np.result_type(dataset, points, np.float64(weights),
+                                          k.factor)
+
+
+def test_pdf_logpdf_validation():
+    rng = np.random.default_rng(64202298293133848336925499069837723291)
+    xn = rng.standard_normal((2, 10))
+    gkde = stats.gaussian_kde(xn)
+    xs = rng.standard_normal((3, 10))
+
+    msg = "points have dimension 3, dataset has dimension 2"
+    with pytest.raises(ValueError, match=msg):
+        gkde.logpdf(xs)
+
+
+def test_pdf_logpdf():
+    rng = np.random.default_rng(1)
+    n_basesample = 50
+    xn = rng.normal(0, 1, n_basesample)
+
+    # Default
+    gkde = stats.gaussian_kde(xn)
+
+    xs = np.linspace(-15, 12, 25)
+    pdf = gkde.evaluate(xs)
+    pdf2 = gkde.pdf(xs)
+    assert_almost_equal(pdf, pdf2, decimal=12)
+
+    logpdf = np.log(pdf)
+    logpdf2 = gkde.logpdf(xs)
+    assert_almost_equal(logpdf, logpdf2, decimal=12)
+
+    # There are more points than data
+    gkde = stats.gaussian_kde(xs)
+    pdf = np.log(gkde.evaluate(xn))
+    pdf2 = gkde.logpdf(xn)
+    assert_almost_equal(pdf, pdf2, decimal=12)
+
+
+def test_pdf_logpdf_weighted():
+    rng = np.random.default_rng(1)
+    n_basesample = 50
+    xn = rng.normal(0, 1, n_basesample)
+    wn = rng.random(n_basesample)
+
+    # Default
+    gkde = stats.gaussian_kde(xn, weights=wn)
+
+    xs = np.linspace(-15, 12, 25)
+    pdf = gkde.evaluate(xs)
+    pdf2 = gkde.pdf(xs)
+    assert_almost_equal(pdf, pdf2, decimal=12)
+
+    logpdf = np.log(pdf)
+    logpdf2 = gkde.logpdf(xs)
+    assert_almost_equal(logpdf, logpdf2, decimal=12)
+
+    # There are more points than data
+    rng = np.random.default_rng(4531935345)
+    gkde = stats.gaussian_kde(xs, weights=rng.random(len(xs)))
+    pdf = np.log(gkde.evaluate(xn))
+    pdf2 = gkde.logpdf(xn)
+    assert_almost_equal(pdf, pdf2, decimal=12)
+
+
+def test_marginal_1_axis():
+    rng = np.random.default_rng(6111799263660870475)
+    n_data = 50
+    n_dim = 10
+    dataset = rng.normal(size=(n_dim, n_data))
+    points = rng.normal(size=(n_dim, 3))
+
+    dimensions = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9])  # dimensions to keep
+
+    kde = stats.gaussian_kde(dataset)
+    marginal = kde.marginal(dimensions)
+    pdf = marginal.pdf(points[dimensions])
+
+    def marginal_pdf_single(point):
+        def f(x):
+            x = np.concatenate(([x], point[dimensions]))
+            return kde.pdf(x)[0]
+        return integrate.quad(f, -np.inf, np.inf)[0]
+
+    def marginal_pdf(points):
+        return np.apply_along_axis(marginal_pdf_single, axis=0, arr=points)
+
+    ref = marginal_pdf(points)
+
+    assert_allclose(pdf, ref, rtol=1e-6)
+
+
+@pytest.mark.xslow
+def test_marginal_2_axis():
+    rng = np.random.default_rng(6111799263660870475)
+    n_data = 30
+    n_dim = 4
+    dataset = rng.normal(size=(n_dim, n_data))
+    points = rng.normal(size=(n_dim, 3))
+
+    dimensions = np.array([1, 3])  # dimensions to keep
+
+    kde = stats.gaussian_kde(dataset)
+    marginal = kde.marginal(dimensions)
+    pdf = marginal.pdf(points[dimensions])
+
+    def marginal_pdf(points):
+        def marginal_pdf_single(point):
+            def f(y, x):
+                w, z = point[dimensions]
+                x = np.array([x, w, y, z])
+                return kde.pdf(x)[0]
+            return integrate.dblquad(f, -np.inf, np.inf, -np.inf, np.inf)[0]
+
+        return np.apply_along_axis(marginal_pdf_single, axis=0, arr=points)
+
+    ref = marginal_pdf(points)
+
+    assert_allclose(pdf, ref, rtol=1e-6)
+
+
+def test_marginal_iv():
+    # test input validation
+    rng = np.random.default_rng(6111799263660870475)
+    n_data = 30
+    n_dim = 4
+    dataset = rng.normal(size=(n_dim, n_data))
+    points = rng.normal(size=(n_dim, 3))
+
+    kde = stats.gaussian_kde(dataset)
+
+    # check that positive and negative indices are equivalent
+    dimensions1 = [-1, 1]
+    marginal1 = kde.marginal(dimensions1)
+    pdf1 = marginal1.pdf(points[dimensions1])
+
+    dimensions2 = [3, -3]
+    marginal2 = kde.marginal(dimensions2)
+    pdf2 = marginal2.pdf(points[dimensions2])
+
+    assert_equal(pdf1, pdf2)
+
+    # IV for non-integer dimensions
+    message = "Elements of `dimensions` must be integers..."
+    with pytest.raises(ValueError, match=message):
+        kde.marginal([1, 2.5])
+
+    # IV for uniqueness
+    message = "All elements of `dimensions` must be unique."
+    with pytest.raises(ValueError, match=message):
+        kde.marginal([1, 2, 2])
+
+    # IV for non-integer dimensions
+    message = (r"Dimensions \[-5  6\] are invalid for a distribution in 4...")
+    with pytest.raises(ValueError, match=message):
+        kde.marginal([1, -5, 6])
+
+
+@pytest.mark.xslow
+def test_logpdf_overflow():
+    # regression test for gh-12988; testing against linalg instability for
+    # very high dimensionality kde
+    rng = np.random.default_rng(1)
+    n_dimensions = 2500
+    n_samples = 5000
+    xn = np.array([rng.normal(0, 1, n_samples) + (n) for n in range(
+        0, n_dimensions)])
+
+    # Default
+    gkde = stats.gaussian_kde(xn)
+
+    logpdf = gkde.logpdf(np.arange(0, n_dimensions))
+    np.testing.assert_equal(np.isneginf(logpdf[0]), False)
+    np.testing.assert_equal(np.isnan(logpdf[0]), False)
+
+
+def test_weights_intact():
+    # regression test for gh-9709: weights are not modified
+    rng = np.random.default_rng(12345)
+    vals = rng.lognormal(size=100)
+    weights = rng.choice([1.0, 10.0, 100], size=vals.size)
+    orig_weights = weights.copy()
+
+    stats.gaussian_kde(np.log10(vals), weights=weights)
+    assert_allclose(weights, orig_weights, atol=1e-14, rtol=1e-14)
+
+
+def test_weights_integer():
+    # integer weights are OK, cf gh-9709 (comment)
+    values = [0.2, 13.5, 21.0, 75.0, 99.0]
+    weights = [1, 2, 4, 8, 16]  # a list of integers
+    pdf_i = stats.gaussian_kde(values, weights=weights)
+    pdf_f = stats.gaussian_kde(values, weights=np.float64(weights))
+
+    xn = [0.3, 11, 88]
+    assert_allclose(pdf_i.evaluate(xn),
+                    pdf_f.evaluate(xn), atol=1e-14, rtol=1e-14)
+
+
+def test_seed():
+    # Test the seed option of the resample method
+    def test_seed_sub(gkde_trail):
+        n_sample = 200
+        # The results should be different without using seed
+        samp1 = gkde_trail.resample(n_sample)
+        samp2 = gkde_trail.resample(n_sample)
+        assert_raises(
+            AssertionError, assert_allclose, samp1, samp2, atol=1e-13
+        )
+        # Use integer seed
+        seed = 831
+        samp1 = gkde_trail.resample(n_sample, seed=seed)
+        samp2 = gkde_trail.resample(n_sample, seed=seed)
+        assert_allclose(samp1, samp2, atol=1e-13)
+        # Use RandomState
+        rstate1 = np.random.RandomState(seed=138)
+        samp1 = gkde_trail.resample(n_sample, seed=rstate1)
+        rstate2 = np.random.RandomState(seed=138)
+        samp2 = gkde_trail.resample(n_sample, seed=rstate2)
+        assert_allclose(samp1, samp2, atol=1e-13)
+
+        # check that np.random.Generator can be used (numpy >= 1.17)
+        if hasattr(np.random, 'default_rng'):
+            # obtain a np.random.Generator object
+            rng = np.random.default_rng(1234)
+            gkde_trail.resample(n_sample, seed=rng)
+
+    rng = np.random.default_rng(8765678)
+    n_basesample = 500
+    wn = rng.random(n_basesample)
+    # Test 1D case
+    xn_1d = rng.normal(0, 1, n_basesample)
+
+    gkde_1d = stats.gaussian_kde(xn_1d)
+    test_seed_sub(gkde_1d)
+    gkde_1d_weighted = stats.gaussian_kde(xn_1d, weights=wn)
+    test_seed_sub(gkde_1d_weighted)
+
+    # Test 2D case
+    mean = np.array([1.0, 3.0])
+    covariance = np.array([[1.0, 2.0], [2.0, 6.0]])
+    xn_2d = rng.multivariate_normal(mean, covariance, size=n_basesample).T
+
+    gkde_2d = stats.gaussian_kde(xn_2d)
+    test_seed_sub(gkde_2d)
+    gkde_2d_weighted = stats.gaussian_kde(xn_2d, weights=wn)
+    test_seed_sub(gkde_2d_weighted)
+
+
+def test_singular_data_covariance_gh10205():
+    # When the data lie in a lower-dimensional subspace and this causes
+    # and exception, check that the error message is informative.
+    rng = np.random.default_rng(2321583144339784787)
+    mu = np.array([1, 10, 20])
+    sigma = np.array([[4, 10, 0], [10, 25, 0], [0, 0, 100]])
+    data = rng.multivariate_normal(mu, sigma, 1000)
+    try:  # doesn't raise any error on some platforms, and that's OK
+        stats.gaussian_kde(data.T)
+    except linalg.LinAlgError:
+        msg = "The data appears to lie in a lower-dimensional subspace..."
+        with assert_raises(linalg.LinAlgError, match=msg):
+            stats.gaussian_kde(data.T)
+
+
+def test_fewer_points_than_dimensions_gh17436():
+    # When the number of points is fewer than the number of dimensions, the
+    # the covariance matrix would be singular, and the exception tested in
+    # test_singular_data_covariance_gh10205 would occur. However, sometimes
+    # this occurs when the user passes in the transpose of what `gaussian_kde`
+    # expects. This can result in a huge covariance matrix, so bail early.
+    rng = np.random.default_rng(2046127537594925772)
+    rvs = rng.multivariate_normal(np.zeros(3), np.eye(3), size=5)
+    message = "Number of dimensions is greater than number of samples..."
+    with pytest.raises(ValueError, match=message):
+        stats.gaussian_kde(rvs)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/test_marray.py b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_marray.py
new file mode 100644
index 0000000000000000000000000000000000000000..cbae7321f6acdf1222655ebac391dc874821a66f
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_marray.py
@@ -0,0 +1,613 @@
+import numpy as np
+import pytest
+from scipy import stats
+
+from scipy._lib._array_api import xp_assert_close, xp_assert_equal, _count_nonmasked
+from scipy._lib._array_api import make_xp_pytest_param, make_xp_test_case
+from scipy._lib._array_api import SCIPY_ARRAY_API, is_torch
+from scipy.stats._stats_py import _xp_mean, _xp_var
+
+
+marray = pytest.importorskip('marray')
+pytestmark = [
+    pytest.mark.skipif(
+        not SCIPY_ARRAY_API,
+        reason=(
+            "special function dispatch to marray required for these tests"
+            " is hidden behind SCIPY_ARRAY_API flag."
+        ),
+    ),
+]
+
+skip_backend = pytest.mark.skip_xp_backends
+
+def get_arrays(n_arrays, *, dtype='float64', xp=np, shape=(7, 8), all_unique=True,
+               seed=84912165484321):
+    mxp = marray._get_namespace(xp)
+    rng = np.random.default_rng(seed)
+
+    datas, masks = [], []
+    for i in range(n_arrays):
+        data = (rng.random(size=shape) if all_unique
+                else rng.integers(np.min(shape) // 2, size=shape))
+        if dtype.startswith('complex'):
+            data = 10*data * 10j*rng.standard_normal(size=shape)
+        data = data.astype(dtype)
+        datas.append(data)
+        mask = rng.random(size=shape) > 0.75
+        masks.append(mask)
+
+    marrays = []
+    nan_arrays = []
+    for array, mask in zip(datas, masks):
+        marrays.append(mxp.asarray(array, mask=mask))
+        nan_array = array.copy()
+        nan_array[mask] = xp.nan
+        nan_arrays.append(nan_array)
+
+    return mxp, marrays, nan_arrays
+
+
+@skip_backend('jax.numpy', reason="JAX doesn't allow item assignment.")
+@pytest.mark.parametrize('fun, kwargs', [
+    make_xp_pytest_param(stats.gmean, {}),
+    make_xp_pytest_param(stats.hmean, {}),
+    make_xp_pytest_param(stats.pmean, {'p': 2}),
+    make_xp_pytest_param(stats.expectile, {'alpha': 0.4}),
+    make_xp_pytest_param(_xp_mean, {}),
+])
+@pytest.mark.parametrize('weighted', [False, True])
+@pytest.mark.parametrize('axis', [0, 1, None])
+def test_one_sample_weighted_reducing(fun, kwargs, weighted, axis, xp):
+    mxp, marrays, narrays = get_arrays(2, xp=xp)
+    mweights = marrays[1] if weighted else None
+    nweights = narrays[1] if weighted else None
+    res = fun(marrays[0], weights=mweights, axis=axis, **kwargs)
+    ref = fun(narrays[0], weights=nweights, nan_policy='omit', axis=axis, **kwargs)
+    xp_assert_close(res.data, xp.asarray(ref))
+
+
+@skip_backend('dask.array', reason='Arrays need `device` attribute: dask/dask#11711')
+@skip_backend('jax.numpy', reason="JAX doesn't allow item assignment.")
+@pytest.mark.parametrize('fun, kwargs',
+    [make_xp_pytest_param(stats.moment, {'order': 2}),
+     make_xp_pytest_param(stats.moment, {'center': 0.5}),
+     make_xp_pytest_param(stats.skew, {}),
+     make_xp_pytest_param(stats.skew, {'bias': False}),
+     make_xp_pytest_param(stats.kurtosis, {}),
+     make_xp_pytest_param(stats.kurtosis, {'fisher': False, 'bias': False}),
+     make_xp_pytest_param(stats.sem, {}),
+     make_xp_pytest_param(stats.sem, {'ddof': 2}),
+     make_xp_pytest_param(stats.kstat, {'n': 1}),
+     make_xp_pytest_param(stats.kstat, {'n': 2}),
+     make_xp_pytest_param(stats.kstat, {'n': 3}),
+     make_xp_pytest_param(stats.kstat, {'n': 4}),
+     make_xp_pytest_param(stats.kstatvar, {'n': 1}),
+     make_xp_pytest_param(stats.kstatvar, {'n': 2}),
+     make_xp_pytest_param(stats.circmean, {}),
+     make_xp_pytest_param(stats.circmean, {'low': 0, 'high': 1}),
+     make_xp_pytest_param(stats.circvar, {}),
+     make_xp_pytest_param(stats.circvar, {'low': 0, 'high': 1}),
+     make_xp_pytest_param(stats.circstd, {}),
+     make_xp_pytest_param(stats.circstd, {'low': 0, 'high': 1, 'normalize':True}),
+     make_xp_pytest_param(stats.gstd, {}),
+     make_xp_pytest_param(stats.gstd, {'ddof': 2}),
+     make_xp_pytest_param(_xp_var, {}),
+     make_xp_pytest_param(_xp_var, {'correction': 1, 'keepdims': True}),
+     make_xp_pytest_param(stats.variation, {}),
+     make_xp_pytest_param(stats.variation, {'ddof': 1}),
+     make_xp_pytest_param(stats.tmean, dict(limits=(0.1, 0.9))),
+     make_xp_pytest_param(stats.tvar, dict(limits=(0.1, 0.9), inclusive=(False, True))),
+     make_xp_pytest_param(stats.tstd, dict(limits=(0.1, 0.9), inclusive=(True, False))),
+     make_xp_pytest_param(stats.tsem, dict(limits=(0.1, 0.9), inclusive=(False,)*2)),
+     make_xp_pytest_param(stats.tmin, dict(lowerlimit=0.5, inclusive=True)),
+     make_xp_pytest_param(stats.tmax, dict(upperlimit=0.5, inclusive=False)),
+     make_xp_pytest_param(stats.iqr, {'interpolation': 'nearest'}),
+     make_xp_pytest_param(stats.iqr, {'rng': (10, 90), 'scale': 'normal'}),
+     make_xp_pytest_param(stats.median_abs_deviation, {}),
+     make_xp_pytest_param(stats.median_abs_deviation, {'scale': 'normal'}),
+     make_xp_pytest_param(stats.trim_mean, {'proportiontocut': 0.1}),
+     ])
+@pytest.mark.parametrize('axis', [0, 1, None])
+def test_one_sample_reducing(fun, kwargs, axis, xp):
+    mxp, marrays, narrays = get_arrays(1, xp=xp)
+    kwargs = dict(axis=axis) | kwargs
+    res = fun(marrays[0], **kwargs)
+    ref = fun(narrays[0], nan_policy='omit', **kwargs)
+    xp_assert_close(res.data, xp.asarray(ref))
+
+
+@make_xp_test_case(stats.mode)
+@pytest.mark.parametrize('dtype', ['int32', 'float64'])
+@pytest.mark.parametrize('shape', [10, (7, 8)])
+@pytest.mark.parametrize('axis', [0, 1, None])
+def test_mode(dtype, shape, axis, xp):
+    mxp, marrays, narrays = get_arrays(1, shape=shape, all_unique=False, xp=xp)
+    res = stats.mode(mxp.astype(marrays[0], getattr(mxp, dtype)))
+    ref = stats.mode(*narrays, nan_policy='omit')
+    xp_assert_close(res.mode.data, xp.asarray(ref.mode.astype(dtype)))
+    xp_assert_close(res.count.data, xp.asarray(ref.count))
+
+
+@make_xp_test_case(stats.describe)
+@skip_backend('dask.array', reason='Arrays need `device` attribute: dask/dask#11711')
+@skip_backend('jax.numpy', reason="JAX doesn't allow item assignment.")
+@pytest.mark.parametrize('axis', [0, 1, None])
+@pytest.mark.parametrize('kwargs', [{}, {'bias': False}])
+def test_describe(axis, kwargs, xp):
+    mxp, marrays, narrays = get_arrays(1, xp=xp)
+    kwargs = dict(axis=axis) | kwargs
+    res = stats.describe(marrays[0], **kwargs)
+    ref = stats.describe(narrays[0], nan_policy='omit', **kwargs)
+    xp_assert_close(res.nobs.data, xp.asarray(ref.nobs))
+    xp_assert_close(res.minmax[0].data, xp.asarray(ref.minmax[0].data))
+    xp_assert_close(res.minmax[1].data, xp.asarray(ref.minmax[1].data))
+    # copy reference arrays due to torch complaint about non-writeable buffer
+    xp_assert_close(res.variance.data,
+                    xp.asarray(np.asarray(ref.variance.data, copy=True)))
+    xp_assert_close(res.skewness.data,
+                    xp.asarray(np.asarray(ref.skewness.data, copy=True)))
+    xp_assert_close(res.kurtosis.data,
+                    xp.asarray(np.asarray(ref.kurtosis.data, copy=True)))
+
+
+@skip_backend('dask.array', reason='shape (nan,) in _xp_var when ddof=1')
+@skip_backend('jax.numpy', reason="JAX doesn't allow item assignment.")
+@pytest.mark.parametrize('fun', [make_xp_pytest_param(stats.zscore),
+                                 make_xp_pytest_param(stats.gzscore),
+                                 make_xp_pytest_param(stats.zmap)])
+@pytest.mark.parametrize('ddof', [0, 1])
+@pytest.mark.parametrize('axis', [0, 1, None])
+def test_one_sample_non_reducing(fun, ddof, axis, xp):
+    mxp, marrays, narrays = (get_arrays(2, xp=xp) if fun == stats.zmap
+                             else get_arrays(1, xp=xp))
+    res = fun(*marrays, ddof=ddof, axis=axis)
+    ref = xp.asarray(fun(*narrays, ddof=ddof, nan_policy='omit', axis=axis))
+    xp_assert_close(res.data[~res.mask], ref[~xp.isnan(ref)])
+    xp_assert_equal(res.mask, marrays[0].mask)
+
+
+@skip_backend('dask.array', reason='Arrays need `device` attribute: dask/dask#11711')
+@skip_backend('jax.numpy', reason="JAX doesn't allow item assignment.")
+@pytest.mark.parametrize('f', [make_xp_pytest_param(stats.ttest_1samp),
+                               make_xp_pytest_param(stats.ttest_rel),
+                               make_xp_pytest_param(stats.ttest_ind)])
+@pytest.mark.parametrize('alternative', ['less', 'greater', 'two-sided'])
+@pytest.mark.parametrize('axis', [0, 1, None])
+def test_ttests(f, alternative, axis, xp):
+    f_name = f.__name__
+    mxp, marrays, narrays = get_arrays(2, xp=xp)
+    if f_name == 'ttest_1samp':
+        marrays[1] = mxp.mean(marrays[1], axis=axis, keepdims=axis is not None)
+        narrays[1] = np.nanmean(narrays[1], axis=axis, keepdims=axis is not None)
+    res = f(*marrays, alternative=alternative, axis=axis)
+    ref = f(*narrays, alternative=alternative, nan_policy='omit', axis=axis)
+    xp_assert_close(res.statistic.data, xp.asarray(ref.statistic))
+    xp_assert_close(res.pvalue.data, xp.asarray(ref.pvalue))
+    res_ci = res.confidence_interval()
+    ref_ci = ref.confidence_interval()
+    xp_assert_close(res_ci.low.data, xp.asarray(ref_ci.low))
+    xp_assert_close(res_ci.high.data, xp.asarray(ref_ci.high))
+
+
+@skip_backend('dask.array', reason='Arrays need `device` attribute: dask/dask#11711')
+@skip_backend('jax.numpy', reason="JAX doesn't allow item assignment.")
+@pytest.mark.filterwarnings("ignore::scipy.stats._axis_nan_policy.SmallSampleWarning")
+@pytest.mark.parametrize('f, args', [
+     make_xp_pytest_param(stats.skewtest, tuple()),
+     make_xp_pytest_param(stats.kurtosistest, tuple()),
+     make_xp_pytest_param(stats.normaltest, tuple()),
+     make_xp_pytest_param(stats.jarque_bera, tuple()),
+     make_xp_pytest_param(stats.cramervonmises, (stats.norm.cdf,)),  # type:ignore[attr-defined]
+])
+@pytest.mark.parametrize('alternative', ['less', 'greater', 'two-sided'])
+@pytest.mark.parametrize('axis', [0, 1, None])
+def test_goodness_of_fit(f, args, alternative, axis, xp):
+    mxp, marrays, narrays = get_arrays(1, xp=xp, shape=(10, 11))
+
+    if f in {stats.skewtest, stats.kurtosistest}:
+        kwds = {'alternative': alternative}
+    else:
+        if alternative != 'greater':
+            pytest.skip(f'str({f.__name__} does not support multiple alternatives.')
+        kwds = {}
+
+    res = f(*marrays, *args, **kwds, axis=axis)
+    ref = f(*narrays, *args, **kwds, nan_policy='omit', axis=axis)
+
+    xp_assert_close(res.statistic.data, xp.asarray(ref.statistic))
+    xp_assert_close(res.pvalue.data, xp.asarray(ref.pvalue), atol=1e-15)
+
+
+@skip_backend('dask.array', reason='Arrays need `device` attribute: dask/dask#11711')
+@skip_backend('jax.numpy', reason="JAX doesn't allow item assignment.")
+@pytest.mark.parametrize('f, lambda_', [
+    make_xp_pytest_param(stats.chisquare, {}),
+    make_xp_pytest_param(stats.power_divergence, {'lambda_': 'pearson'}),
+    make_xp_pytest_param(stats.power_divergence, {'lambda_': 'log-likelihood'}),
+    make_xp_pytest_param(stats.power_divergence, {'lambda_': 'freeman-tukey'}),
+    make_xp_pytest_param(stats.power_divergence,
+                         {'lambda_': 'mod-log-likelihood'}),
+    make_xp_pytest_param(stats.power_divergence, {'lambda_': 'neyman'}),
+    make_xp_pytest_param(stats.power_divergence, {'lambda_': 'cressie-read'}),
+])
+@pytest.mark.parametrize('ddof', [0, 1])
+@pytest.mark.parametrize('axis', [0, 1, None])
+def test_power_divergence_chisquare(f, lambda_, ddof, axis, xp):
+    mxp, marrays, narrays = get_arrays(2, xp=xp, shape=(5, 6))
+
+    kwargs = dict(axis=axis, ddof=ddof)
+
+    # test 1-arg
+    res = f(marrays[0], **lambda_, **kwargs)
+    ref = stats.power_divergence(narrays[0], nan_policy='omit', **lambda_, **kwargs)
+
+    xp_assert_close(res.statistic.data, xp.asarray(ref[0]))
+    xp_assert_close(res.pvalue.data, xp.asarray(ref[1]))
+
+    # test 2-arg
+    common_mask = np.isnan(narrays[0]) | np.isnan(narrays[1])
+    normalize = (np.nansum(narrays[1] * ~common_mask, axis=axis, keepdims=True)
+                 / np.nansum(narrays[0] * ~common_mask, axis=axis, keepdims=True))
+    marrays[0] *= xp.asarray(normalize)
+    narrays[0] *= normalize
+
+    res = f(*marrays, **lambda_, **kwargs)
+    ref = stats.power_divergence(*narrays, nan_policy='omit', **lambda_, **kwargs)
+
+    xp_assert_close(res.statistic.data, xp.asarray(ref[0]))
+    xp_assert_close(res.pvalue.data, xp.asarray(ref[1]))
+
+
+@make_xp_test_case(stats.combine_pvalues)
+@skip_backend('jax.numpy', reason="JAX doesn't allow item assignment.")
+@pytest.mark.parametrize('method', ['fisher', 'pearson', 'mudholkar_george',
+                                    'tippett', 'stouffer'])
+@pytest.mark.parametrize('axis', [0, 1, None])
+def test_combine_pvalues(method, axis, xp):
+    mxp, marrays, narrays = get_arrays(2, xp=xp, shape=(10, 11))
+
+    kwargs = dict(method=method, axis=axis)
+    res = stats.combine_pvalues(marrays[0], **kwargs)
+    ref = stats.combine_pvalues(narrays[0], nan_policy='omit', **kwargs)
+
+    xp_assert_close(res.statistic.data, xp.asarray(ref.statistic))
+    xp_assert_close(res.pvalue.data, xp.asarray(ref.pvalue))
+
+    if method != 'stouffer':
+        return
+
+    # test method='stouffer' with weights
+    res = stats.combine_pvalues(marrays[0], weights=marrays[1], **kwargs)
+    ref = stats.combine_pvalues(narrays[0], weights=narrays[1],
+                                nan_policy='omit', **kwargs)
+
+    xp_assert_close(res.statistic.data, xp.asarray(ref.statistic))
+    xp_assert_close(res.pvalue.data, xp.asarray(ref.pvalue))
+
+
+@make_xp_test_case(stats.ttest_ind_from_stats)
+@skip_backend('jax.numpy', reason="JAX doesn't allow item assignment.")
+@pytest.mark.parametrize("alternative", ['less', 'greater', 'two-sided'])
+@pytest.mark.parametrize("equal_var", [False, True])
+def test_ttest_ind_from_stats(alternative, equal_var, xp):
+    shape = (10, 11)
+    mxp, marrays, narrays = get_arrays(6, xp=xp, shape=shape)
+    mask = np.sum(np.stack([np.isnan(arg) for arg in narrays]), axis=0).astype(bool)
+    narrays = [arg[~mask] for arg in narrays]
+    marrays[2], marrays[5] = marrays[2] * 100, marrays[5] * 100
+    narrays[2], narrays[5] = narrays[2] * 100, narrays[5] * 100
+
+    kwargs = dict(alternative=alternative, equal_var=equal_var)
+    res = stats.ttest_ind_from_stats(*marrays, **kwargs)
+    ref = stats.ttest_ind_from_stats(*narrays, **kwargs)
+
+    mask = xp.asarray(mask)
+    assert xp.any(mask) and xp.any(~mask)
+    xp_assert_close(res.statistic.data[~mask], xp.asarray(ref.statistic))
+    xp_assert_close(res.pvalue.data[~mask], xp.asarray(ref.pvalue))
+    xp_assert_close(res.statistic.mask, mask)
+    xp_assert_close(res.pvalue.mask, mask)
+    assert res.statistic.shape == shape
+    assert res.pvalue.shape == shape
+
+
+def test_length_nonmasked_marray_iterable_axis_raises():
+    xp = marray._get_namespace(np)
+
+    data = [[1.0, 2.0], [3.0, 4.0]]
+    mask = [[False, False], [True, False]]
+    marr = xp.asarray(data, mask=mask)
+
+    # Axis tuples are not currently supported for MArray input.
+    # This test can be removed after support is added.
+    with pytest.raises(NotImplementedError,
+        match="`axis` must be an integer or None for use with `MArray`"):
+        _count_nonmasked(marr, axis=(0, 1), xp=xp)
+
+
+@make_xp_test_case(stats.directional_stats)
+@skip_backend('jax.numpy', reason="JAX doesn't allow item assignment.")
+@pytest.mark.filterwarnings("ignore::RuntimeWarning")  # mdhaber/marray#120
+@pytest.mark.parametrize('normalize', [False, True])
+@pytest.mark.parametrize('axis', [0, 1])
+def test_directional_stats(normalize, axis, xp):
+    mxp, marrays, narrays = get_arrays(1, shape=(19, 20, 3), xp=xp)
+    res = stats.directional_stats(*marrays, normalize=normalize, axis=axis)
+
+    x, = narrays
+    if axis == 0:
+        x = np.swapaxes(x, 0, 1)
+
+    for i in range(x.shape[0]):
+        xi = x[i]
+        xi = xi[~np.any(np.isnan(xi), axis=-1), :]
+        ref = stats.directional_stats(xi, normalize=normalize)
+        xp_assert_close(res.mean_direction.data[i, ...],
+                        xp.asarray(ref.mean_direction))
+        xp_assert_close(res.mean_resultant_length.data[i],
+                        xp.asarray(ref.mean_resultant_length)[()])
+    assert not xp.any(res.mean_direction.mask)
+    assert not xp.any(res.mean_resultant_length.mask)
+
+
+@make_xp_test_case(stats.wilcoxon)
+@skip_backend('jax.numpy', reason="JAX doesn't allow item assignment.")
+@pytest.mark.parametrize('n_samples', [1, 2])
+@pytest.mark.parametrize('zero_method', ['zsplit'])  # TODO: add 'wilcox', 'pratt'
+@pytest.mark.parametrize('correction', [False, True])
+@pytest.mark.parametrize('alternative', ['less', 'greater', 'two-sided'])
+@pytest.mark.parametrize('method', ['asymptotic'])  # TODO: add 'exact', 'auto'
+@pytest.mark.parametrize('axis', [0, 1, None])
+def test_wilcoxon(n_samples, zero_method, correction, alternative, method, axis, xp):
+    mxp, marrays, narrays = get_arrays(n_samples, xp=xp, seed=84912165484322)
+    kwargs = dict(zero_method=zero_method, correction=correction,
+                  alternative=alternative, method=method)
+    res = stats.wilcoxon(*marrays, axis=axis, **kwargs)
+    ref = stats.wilcoxon(*narrays, nan_policy='omit', axis=axis, **kwargs)
+    xp_assert_close(res.statistic.data, xp.asarray(ref.statistic))
+    xp_assert_close(res.pvalue.data, xp.asarray(ref.pvalue))
+
+
+@make_xp_test_case(stats.mannwhitneyu)
+@skip_backend('jax.numpy', reason="JAX doesn't allow item assignment.")
+@pytest.mark.parametrize('use_continuity', [False, True])
+@pytest.mark.parametrize('alternative', ['less', 'greater', 'two-sided'])
+@pytest.mark.parametrize('method', ['asymptotic'])  # TODO: add 'exact', 'auto'
+@pytest.mark.parametrize('axis', [0, 1, None])
+def test_mannwhitneyu(use_continuity, alternative, method, axis, xp):
+    mxp, marrays, narrays = get_arrays(2, xp=xp, seed=84912165484322)
+    kwargs = dict(use_continuity=use_continuity, alternative=alternative, method=method)
+    res = stats.mannwhitneyu(*marrays, axis=axis, **kwargs)
+    ref = stats.mannwhitneyu(*narrays, nan_policy='omit', axis=axis, **kwargs)
+    xp_assert_close(res.statistic.data, xp.asarray(ref.statistic))
+    xp_assert_close(res.pvalue.data, xp.asarray(ref.pvalue))
+
+
+@skip_backend('jax.numpy', reason="JAX doesn't allow item assignment.")
+@pytest.mark.parametrize('fun', [make_xp_pytest_param(stats.ks_1samp),
+                                 make_xp_pytest_param(stats.kstest)])
+@pytest.mark.parametrize('method', ['exact', 'approx', 'asymp'])  # auto == exact
+@pytest.mark.parametrize('alternative', ['less', 'greater', 'two-sided'])
+@pytest.mark.parametrize('axis', [0, 1, None])
+def test_ks_1samp(fun, method, alternative, axis, xp):
+    mxp, marrays, narrays = get_arrays(1, xp=xp, seed=84912165484322)
+    kwargs = dict(method=method, alternative=alternative, axis=axis)
+    res = fun(*marrays, stats.norm.cdf, **kwargs)
+    ref = stats.ks_1samp(*narrays, stats.norm.cdf, nan_policy='omit', **kwargs)
+    xp_assert_close(res.statistic.data, xp.asarray(ref.statistic))
+    xp_assert_close(res.pvalue.data, xp.asarray(ref.pvalue))
+    xp_assert_equal(res.statistic_location.data, xp.asarray(ref.statistic_location))
+    xp_assert_equal(res.statistic_sign.data,
+                    xp.asarray(ref.statistic_sign, dtype=xp.int8))
+
+
+@skip_backend('jax.numpy', reason="JAX doesn't allow item assignment.")
+@pytest.mark.parametrize('fun, kwargs', [
+    make_xp_pytest_param(stats.brunnermunzel, {}),
+    make_xp_pytest_param(stats.brunnermunzel, {'distribution': 'normal'}),
+    make_xp_pytest_param(stats.cramervonmises_2samp, {'method': 'exact'}),
+    # make_xp_pytest_param(stats.cramervonmises_2samp, {}),  # TODO: add methods
+])
+@pytest.mark.parametrize('axis', [0, 1, None])
+def test_two_sample_tests(fun, kwargs, axis, xp):
+    if fun == stats.cramervonmises_2samp and axis is None:
+        pytest.skip("Sample too large for exact method.")
+    mxp, marrays, narrays = get_arrays(2, xp=xp, seed=84912165484322)
+    res = fun(*marrays, axis=axis, **kwargs)
+    ref = fun(*narrays, nan_policy='omit', axis=axis, **kwargs)
+    xp_assert_close(res.statistic.data, xp.asarray(ref.statistic))
+    xp_assert_close(res.pvalue.data, xp.asarray(ref.pvalue))
+
+
+@make_xp_test_case(stats.ks_2samp)
+@skip_backend('jax.numpy', reason="JAX doesn't allow item assignment.")
+@pytest.mark.parametrize('fun', [make_xp_pytest_param(stats.ks_2samp),
+                                 make_xp_pytest_param(stats.kstest)])
+@pytest.mark.parametrize('method', ['exact', 'asymp', 'auto'])  # auto == exact
+@pytest.mark.parametrize('alternative', ['less', 'greater', 'two-sided'])
+@pytest.mark.parametrize('axis', [0, 1, None])
+def test_ks_2samp(fun, method, alternative, axis, xp):
+    mxp, marrays, narrays = get_arrays(2, xp=xp, seed=84912165484322)
+    kwargs = dict(method=method, alternative=alternative, axis=axis)
+    res = fun(*marrays, **kwargs)
+    ref = stats.ks_2samp(*narrays, nan_policy='omit', **kwargs)
+    xp_assert_close(res.statistic.data, xp.asarray(ref.statistic))
+    xp_assert_close(res.pvalue.data, xp.asarray(ref.pvalue))
+    # with this random data, there often multiple locations where the statistic assumes
+    # the most extreme value, so we can't expect these to always match
+    # xp_assert_equal(res.statistic_location.data, xp.asarray(ref.statistic_location))
+    xp_assert_equal(res.statistic_sign.data,
+                    xp.asarray(ref.statistic_sign, dtype=xp.int8))
+
+
+@make_xp_test_case(stats.kendalltau)
+class TestKendallTau:
+    @pytest.mark.parametrize('method', ['asymptotic', 'exact'])
+    @pytest.mark.parametrize('variant', ['b', 'c'])
+    @pytest.mark.parametrize('alternative', ['less', 'greater', 'two-sided'])
+    @pytest.mark.parametrize('axis', [0, 1, None])
+    def test_omit_masked_elements(self, method, variant, alternative, axis, xp):
+        mxp, marrays, narrays = get_arrays(2, shape=(17, 18),
+                                           xp=xp, seed=84912165484322)
+        kwargs = dict(method=method, variant=variant, alternative=alternative)
+        res = stats.kendalltau(*marrays, **kwargs, axis=axis)
+        ref = stats.kendalltau(*narrays, **kwargs, nan_policy='omit', axis=axis)
+        xp_assert_close(res.statistic.data, xp.asarray(ref.statistic))
+        xp_assert_close(res.pvalue.data, xp.asarray(ref.pvalue))
+
+    @pytest.mark.parametrize('nan_policy, message', [
+        ('propagate', "`nan_policy='propagate'` is incompatible with MArray input."),
+        ('raise', 'The input contains nan values.')
+    ])
+    def test_input_validation(self, nan_policy, message, xp):
+        mxp = marray._get_namespace(xp)
+        x = mxp.asarray([1, 2, 3, xp.nan])
+        with pytest.raises(ValueError, match=message):
+            stats.kendalltau(x, x, nan_policy=nan_policy)
+
+
+@skip_backend('dask.array', reason='Arrays need `device` attribute: dask/dask#11711')
+@skip_backend('jax.numpy', reason="JAX doesn't allow item assignment.")
+@pytest.mark.parametrize('fun, kwargs', [
+    make_xp_pytest_param(stats.bartlett, {}),
+    make_xp_pytest_param(stats.alexandergovern, {}),
+    make_xp_pytest_param(stats.levene, {'center': 'median'}),
+    make_xp_pytest_param(stats.levene, {'center': 'mean'}),
+    make_xp_pytest_param(stats.levene, {'center': 'trimmed'}),
+    make_xp_pytest_param(stats.f_oneway, {'equal_var': True}),
+    make_xp_pytest_param(stats.f_oneway, {'equal_var': False}),
+    make_xp_pytest_param(stats.kruskal, {}),
+    make_xp_pytest_param(stats.fligner, {'center': 'median'}),
+    make_xp_pytest_param(stats.fligner, {'center': 'mean'}),
+    make_xp_pytest_param(stats.fligner, {'center': 'trimmed'}),
+])
+@pytest.mark.parametrize('axis', [0, 1, None])
+def test_k_sample_tests(fun, kwargs, axis, xp):
+    mxp, marrays, narrays = get_arrays(3, xp=xp)
+    res = fun(*marrays, axis=axis, **kwargs)
+    ref = fun(*narrays, nan_policy='omit', axis=axis, **kwargs)
+    xp_assert_close(res.statistic.data, xp.asarray(ref.statistic))
+    xp_assert_close(res.pvalue.data, xp.asarray(ref.pvalue))
+
+
+@skip_backend('jax.numpy', reason="JAX currently incompatible with marray")
+@pytest.mark.parametrize('fun, kwargs', [
+    make_xp_pytest_param(stats.friedmanchisquare, {}),
+])
+@pytest.mark.parametrize('axis', [0, 1, None])
+def test_k_sample_paired_tests(fun, kwargs, axis, xp):
+    mxp, marrays, narrays = get_arrays(3, shape=(8, 9), xp=xp)
+    res = fun(*marrays, axis=axis, **kwargs)
+    ref = fun(*narrays, nan_policy='omit', axis=axis, **kwargs)
+    xp_assert_close(res.statistic.data, xp.asarray(ref.statistic))
+    xp_assert_close(res.pvalue.data, xp.asarray(ref.pvalue))
+
+
+@skip_backend('dask.array', reason='Arrays need `device` attribute: dask/dask#11711')
+@skip_backend('jax.numpy', reason="JAX doesn't allow item assignment.")
+@pytest.mark.parametrize('f', [
+    make_xp_pytest_param(stats.pearsonr),
+    make_xp_pytest_param(stats.pointbiserialr),
+    make_xp_pytest_param(stats.spearmanrho),
+])
+@pytest.mark.parametrize('alternative', ['less', 'greater', 'two-sided'])
+@pytest.mark.parametrize('axis', [0, 1, None])
+def test_correlation(f, alternative, axis, xp):
+    mxp, marrays, narrays = get_arrays(2, xp=xp)
+
+    kwargs = {} if f == stats.pointbiserialr else {'alternative': alternative}
+    res = f(*marrays, **kwargs, axis=axis)
+
+    # `pearsonr` does not have `axis_nan_policy`, so do this manually
+    x, y = narrays
+    if axis == 0:
+        x, y = x.T, y.T
+    elif axis is None:
+        x, y = x.ravel()[np.newaxis, :], y.ravel()[np.newaxis, :]
+
+    for i in range(x.shape[0]):
+        xi, yi = x[i, ...], y[i, ...]
+        i = () if axis is None else i
+
+        mask = np.isnan(xi) | np.isnan(yi)
+        ref = f(xi[~mask], yi[~mask], **kwargs)
+
+        atol = 1e-7 if (is_torch(xp) and f == stats.spearmanrho) else 0.
+        xp_assert_close(res.statistic.data[i], xp.asarray(ref.statistic)[()], atol=atol)
+        xp_assert_close(res.pvalue.data[i], xp.asarray(ref.pvalue)[()], atol=atol)
+
+        if f == stats.pearsonr:
+            res_ci_low, res_ci_high = res.confidence_interval()
+            ref_ci_low, ref_ci_high = ref.confidence_interval()
+            xp_assert_close(res_ci_low.data[i], xp.asarray(ref_ci_low)[()])
+            xp_assert_close(res_ci_high.data[i], xp.asarray(ref_ci_high)[()])
+
+
+@skip_backend('jax.numpy', reason="JAX doesn't allow item assignment.")
+@skip_backend('array_api_strict', reason="issue with clip.")
+@pytest.mark.parametrize('f, method', [
+    make_xp_pytest_param(stats.siegelslopes, {'method':'hierarchical'}),
+    make_xp_pytest_param(stats.siegelslopes, {'method':'separate'}),
+    make_xp_pytest_param(stats.theilslopes, {'method': 'joint'}),
+    make_xp_pytest_param(stats.theilslopes, {'method': 'separate'}),
+    make_xp_pytest_param(stats.linregress, {'alternative': 'less'}),
+    make_xp_pytest_param(stats.linregress, {'alternative': 'greater'}),
+    make_xp_pytest_param(stats.linregress, {'alternative': 'two-sided'}),
+])
+@pytest.mark.parametrize('axis', [0, 1, None])
+def test_slopes_intercepts(f, method, axis, xp):
+    mxp, marrays, narrays = get_arrays(2, shape=(19, 20), seed=84912165484320, xp=xp)
+    res = f(*marrays, axis=axis, **method)
+    ref = f(*narrays, nan_policy='omit', axis=axis, **method)
+
+    xp_assert_close(res.slope.data, xp.asarray(ref.slope))
+    xp_assert_close(res.intercept.data, xp.asarray(ref.intercept))
+
+    if f == stats.theilslopes:
+        xp_assert_close(res.low_slope.data, xp.asarray(ref.low_slope))
+        xp_assert_close(res.high_slope.data, xp.asarray(ref.high_slope))
+    elif f == stats.linregress:
+        xp_assert_close(res.rvalue.data, xp.asarray(ref.rvalue))
+        xp_assert_close(res.pvalue.data, xp.asarray(ref.pvalue))
+        xp_assert_close(res.stderr.data, xp.asarray(ref.stderr))
+        xp_assert_close(res.intercept_stderr.data, xp.asarray(ref.intercept_stderr))
+
+
+@make_xp_test_case(stats.entropy)
+@skip_backend('dask.array', reason="Dask doesn't like the /= when base is not None.")
+@skip_backend('jax.numpy', reason="JAX doesn't allow item assignment.")
+@pytest.mark.parametrize('qk', [False, True])
+@pytest.mark.parametrize('base', [None, 2])
+@pytest.mark.parametrize('axis', [0, 1, None])
+def test_entropy(qk, base, axis, xp):
+    mxp, marrays, narrays = get_arrays(2 if qk else 1, xp=xp)
+    res = stats.entropy(*marrays, base=base, axis=axis)
+    ref = stats.entropy(*narrays, base=base, nan_policy='omit', axis=axis)
+    xp_assert_close(res.data, xp.asarray(ref))
+
+
+@make_xp_test_case(stats.rankdata)
+@skip_backend('jax.numpy', reason="JAX currently incompatible with marray")
+@pytest.mark.parametrize('method', ['average', 'min', 'max', 'dense', 'ordinal'])
+@pytest.mark.parametrize('axis', [0, 1, None])
+def test_rankdata(method, axis, xp):
+    mxp, marrays, narrays = get_arrays(1, xp=xp)
+    res = stats.rankdata(*marrays, method=method, axis=axis)
+    ref = stats.rankdata(*narrays, method=method, nan_policy='omit', axis=axis)
+    xp_assert_close(res.data[~res.mask], xp.asarray(ref[~np.isnan(ref)]))
+    xp_assert_close(res.mask, xp.asarray(np.isnan(ref)))
+
+
+@make_xp_test_case(stats.obrientransform)
+@skip_backend('jax.numpy', reason="JAX currently incompatible with marray")
+@pytest.mark.parametrize('dtype', ['float32', 'float64'])
+@pytest.mark.parametrize('n_arrays', [1, 3])
+def test_obrientransform(dtype, n_arrays, xp):
+    # obrientransform is not yet vectorized
+    mxp, marrays, narrays = get_arrays(n_arrays, dtype=dtype, shape=(25,), xp=xp)
+    res = stats.obrientransform(*marrays)
+    ref = stats.obrientransform(*narrays, nan_policy='omit')
+    for res_i, ref_i in zip(res, ref):
+        xp_assert_close(res_i.data[~res_i.mask],
+                        xp.asarray(ref_i[~np.isnan(ref_i)], dtype=getattr(xp, dtype)))
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/test_mgc.py b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_mgc.py
new file mode 100644
index 0000000000000000000000000000000000000000..fd4d27d7c1647b0ab72cd668ccd0509f02b4684a
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_mgc.py
@@ -0,0 +1,233 @@
+import pytest
+from pytest import raises as assert_raises, warns as assert_warns
+
+import numpy as np
+from numpy.testing import assert_approx_equal, assert_allclose, assert_equal
+
+from scipy.spatial.distance import cdist
+from scipy import stats
+
+class TestMGCErrorWarnings:
+    """ Tests errors and warnings derived from MGC.
+    """
+    def test_error_notndarray(self):
+        # raises error if x or y is not an ndarray
+        x = np.arange(20)
+        y = [5] * 20
+        assert_raises(ValueError, stats.multiscale_graphcorr, x, y)
+        assert_raises(ValueError, stats.multiscale_graphcorr, y, x)
+
+    def test_error_shape(self):
+        # raises error if number of samples different (n)
+        x = np.arange(100).reshape(25, 4)
+        y = x.reshape(10, 10)
+        assert_raises(ValueError, stats.multiscale_graphcorr, x, y)
+
+    def test_error_lowsamples(self):
+        # raises error if samples are low (< 3)
+        x = np.arange(3)
+        y = np.arange(3)
+        assert_raises(ValueError, stats.multiscale_graphcorr, x, y)
+
+    def test_error_nans(self):
+        # raises error if inputs contain NaNs
+        x = np.arange(20, dtype=float)
+        x[0] = np.nan
+        assert_raises(ValueError, stats.multiscale_graphcorr, x, x)
+
+        y = np.arange(20)
+        assert_raises(ValueError, stats.multiscale_graphcorr, x, y)
+
+    def test_error_wrongdisttype(self):
+        # raises error if metric is not a function
+        x = np.arange(20)
+        compute_distance = 0
+        assert_raises(ValueError, stats.multiscale_graphcorr, x, x,
+                      compute_distance=compute_distance)
+
+    @pytest.mark.parametrize("reps", [
+        -1,    # reps is negative
+        '1',   # reps is not integer
+    ])
+    def test_error_reps(self, reps):
+        # raises error if reps is negative
+        x = np.arange(20)
+        assert_raises(ValueError, stats.multiscale_graphcorr, x, x, reps=reps)
+
+    def test_warns_reps(self):
+        # raises warning when reps is less than 1000
+        x = np.arange(20)
+        reps = 100
+        assert_warns(RuntimeWarning, stats.multiscale_graphcorr, x, x, reps=reps)
+
+    def test_error_infty(self):
+        # raises error if input contains infinities
+        x = np.arange(20)
+        y = np.ones(20) * np.inf
+        assert_raises(ValueError, stats.multiscale_graphcorr, x, y)
+
+
+class TestMGCStat:
+    """ Test validity of MGC test statistic
+    """
+    def setup_method(self):
+        self.rng = np.random.default_rng(1266219746)
+
+    def _simulations(self, samps=100, dims=1, sim_type="", rng=None):
+        rng = rng or self.rng
+        # linear simulation
+        if sim_type == "linear":
+            x = rng.uniform(-1, 1, size=(samps, 1))
+            y = x + 0.3 * rng.random(size=(x.size, 1))
+
+        # spiral simulation
+        elif sim_type == "nonlinear":
+            unif = np.array(self.rng.uniform(0, 5, size=(samps, 1)))
+            x = unif * np.cos(np.pi * unif)
+            y = (unif * np.sin(np.pi * unif) +
+                 0.4*self.rng.random(size=(x.size, 1)))
+
+        # independence (tests type I simulation)
+        elif sim_type == "independence":
+            u = self.rng.standard_normal(size=(samps, 1))
+            v = self.rng.standard_normal(size=(samps, 1))
+            u_2 = self.rng.binomial(1, p=0.5, size=(samps, 1))
+            v_2 = self.rng.binomial(1, p=0.5, size=(samps, 1))
+            x = u/3 + 2*u_2 - 1
+            y = v/3 + 2*v_2 - 1
+
+        # raises error if not approved sim_type
+        else:
+            raise ValueError("sim_type must be linear, nonlinear, or "
+                             "independence")
+
+        # add dimensions of noise for higher dimensions
+        if dims > 1:
+            dims_noise = self.rng.standard_normal(size=(samps, dims-1))
+            x = np.concatenate((x, dims_noise), axis=1)
+
+        return x, y
+
+    @pytest.mark.xslow
+    @pytest.mark.parametrize("sim_type, obs_stat, obs_pvalue", [
+        # Reference values produced by `multiscale_graphcorr` ->
+        # this only guards against unintended changes
+        ("linear", 0.970137188683, 0.000999000999),      # test linear simulation
+        ("nonlinear", 0.149843048137, 0.000999000999),   # test spiral simulation
+        ("independence", -0.003965353120, 0.4675324675)  # test independence simulation
+    ])
+    def test_oned(self, sim_type, obs_stat, obs_pvalue):
+        # generate x and y
+        rng = np.random.default_rng(8157117705)
+        x, y = self._simulations(samps=100, dims=1, sim_type=sim_type, rng=rng)
+
+        # test stat and pvalue
+        stat, pvalue, _ = stats.multiscale_graphcorr(x, y, random_state=rng)
+        assert_allclose(stat, obs_stat)
+        assert_allclose(pvalue, obs_pvalue)
+
+    @pytest.mark.xslow
+    @pytest.mark.parametrize("sim_type, obs_stat, obs_pvalue", [
+        # Reference values produced by `multiscale_graphcorr` ->
+        # this only guards against unintended changes
+        ("linear", 0.193063672972, 0.000999000999),     # test linear simulation
+        ("nonlinear", 0.010042844939, 0.216783216783),  # test spiral simulation
+    ])
+    def test_fived(self, sim_type, obs_stat, obs_pvalue):
+        # generate x and y
+        rng = np.random.default_rng(8157117705)
+        x, y = self._simulations(samps=100, dims=5, sim_type=sim_type, rng=rng)
+
+        # test stat and pvalue
+        stat, pvalue, _ = stats.multiscale_graphcorr(x, y, random_state=rng)
+        assert_allclose(stat, obs_stat)
+        assert_allclose(pvalue, obs_pvalue)
+
+    @pytest.mark.xslow
+    def test_twosamp(self):
+        # generate x and y
+        x = self.rng.binomial(100, 0.5, size=(100, 5))
+        y = self.rng.standard_normal(size=(80, 5))
+
+        # test stat and pvalue
+        stat, pvalue, _ = stats.multiscale_graphcorr(x, y, random_state=self.rng)
+        assert_approx_equal(stat, 1.0, significant=1)
+        assert_approx_equal(pvalue, 0.001, significant=1)
+
+        # generate x and y
+        y = self.rng.standard_normal(size=(100, 5))
+
+        # test stat and pvalue
+        stat, pvalue, _ = stats.multiscale_graphcorr(x, y, is_twosamp=True,
+                                                     random_state=self.rng)
+        assert_approx_equal(stat, 1.0, significant=1)
+        assert_approx_equal(pvalue, 0.001, significant=1)
+
+    @pytest.mark.xslow
+    def test_workers(self):
+        # generate x and y
+        x, y = self._simulations(samps=100, dims=1, sim_type="linear")
+
+        # test stat and pvalue
+        stat, pvalue, _ = stats.multiscale_graphcorr(x, y, workers=2,
+                                                     random_state=self.rng)
+        assert_approx_equal(stat, 0.97, significant=1)
+        assert_approx_equal(pvalue, 0.001, significant=1)
+
+    @pytest.mark.xslow
+    def test_random_state(self):
+        # generate x and y
+        x, y = self._simulations(samps=100, dims=1, sim_type="linear")
+
+        # test stat and pvalue
+        stat, pvalue, _ = stats.multiscale_graphcorr(x, y, random_state=1)
+        assert_approx_equal(stat, 0.97, significant=1)
+        assert_approx_equal(pvalue, 0.001, significant=1)
+
+    @pytest.mark.xslow
+    def test_dist_perm(self):
+        # generate x and y
+        x, y = self._simulations(samps=100, dims=1, sim_type="nonlinear")
+        distx = cdist(x, x, metric="euclidean")
+        disty = cdist(y, y, metric="euclidean")
+
+        stat_dist, pvalue_dist, _ = stats.multiscale_graphcorr(distx, disty,
+                                                               compute_distance=None,
+                                                               random_state=1)
+        assert_approx_equal(stat_dist, 0.163, significant=1)
+        assert_approx_equal(pvalue_dist, 0.001, significant=1)
+
+    @pytest.mark.fail_slow(20)  # all other tests are XSLOW; we need at least one to run
+    @pytest.mark.slow
+    def test_pvalue_literature(self):
+        # generate x and y
+        x, y = self._simulations(samps=100, dims=1, sim_type="linear")
+
+        # test stat and pvalue
+        _, pvalue, _ = stats.multiscale_graphcorr(x, y, random_state=1)
+        assert_allclose(pvalue, 1/1001)
+
+    def test_zero_distance_matrix_index_error(self):
+        # regression test for zero distance
+        # matrix IndexError issue; see gh-19769
+        n = 6
+        x = np.arange(n).reshape(-1, 1)
+
+        # valid distance matrix
+        distx = cdist(x, x)
+
+        # degenerate all-zero distance matrix
+        disty = np.zeros((n, n))
+
+        # test stat and pvalue
+        res = stats.multiscale_graphcorr(distx, disty, compute_distance=None)
+        assert_allclose(res.statistic, 0.0)
+        assert_allclose(res.pvalue, 1.0)
+    
+    @pytest.mark.xslow
+    def test_alias(self):
+        # generate x and y
+        x, y = self._simulations(samps=100, dims=1, sim_type="linear")
+
+        res = stats.multiscale_graphcorr(x, y, random_state=1)
+        assert_equal(res.stat, res.statistic)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/test_morestats.py b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_morestats.py
new file mode 100644
index 0000000000000000000000000000000000000000..e76b24c30556ec287ca173ab0aa2b7db991446c0
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_morestats.py
@@ -0,0 +1,3906 @@
+# Author:  Travis Oliphant, 2002
+#
+# Further enhancements and tests added by numerous SciPy developers.
+#
+import math
+import re
+import sys
+import warnings
+from functools import partial
+
+import numpy as np
+from numpy.random import RandomState
+from numpy.testing import (assert_array_equal, assert_almost_equal,
+                           assert_array_less, assert_array_almost_equal,
+                           assert_, assert_allclose, assert_equal)
+import pytest
+from pytest import raises as assert_raises
+
+from scipy import optimize, stats, special
+from scipy.stats._morestats import (_abw_state, _get_As_weibull, _Avals_weibull,
+                                    _yeojohnson_transform)
+from .common_tests import check_named_results
+from .._hypotests import _get_wilcoxon_distr, _get_wilcoxon_distr2
+from scipy.stats._ansari_swilk_statistics import swilk
+from scipy.stats._binomtest import _binary_search_for_binom_tst
+from scipy.stats._distr_params import distcont
+from scipy.stats._axis_nan_policy import (SmallSampleWarning, too_small_nd_omit,
+                                          too_small_1d_omit, too_small_1d_not_omit)
+
+import scipy._external.array_api_extra as xpx
+from scipy._lib._array_api import (is_torch, make_xp_test_case, eager_warns, xp_ravel,
+                                   is_numpy, xp_default_dtype, is_array_api_strict,
+                                   is_jax, is_lazy_array)
+from scipy._lib._array_api_no_0d import (
+    xp_assert_close,
+    xp_assert_equal,
+    xp_assert_less,
+)
+
+lazy_xp_modules = [stats]
+skip_xp_backends = pytest.mark.skip_xp_backends
+
+distcont = dict(distcont)  # type: ignore
+
+# Matplotlib is not a scipy dependency but is optionally used in probplot, so
+# check if it's available
+try:
+    import matplotlib
+    matplotlib.rcParams['backend'] = 'Agg'
+    import matplotlib.pyplot as plt
+    have_matplotlib = True
+except Exception:
+    have_matplotlib = False
+
+
+# test data gear.dat from NIST for Levene and Bartlett test
+# https://www.itl.nist.gov/div898/handbook/eda/section3/eda3581.htm
+g1 = [1.006, 0.996, 0.998, 1.000, 0.992, 0.993, 1.002, 0.999, 0.994, 1.000]
+g2 = [0.998, 1.006, 1.000, 1.002, 0.997, 0.998, 0.996, 1.000, 1.006, 0.988]
+g3 = [0.991, 0.987, 0.997, 0.999, 0.995, 0.994, 1.000, 0.999, 0.996, 0.996]
+g4 = [1.005, 1.002, 0.994, 1.000, 0.995, 0.994, 0.998, 0.996, 1.002, 0.996]
+g5 = [0.998, 0.998, 0.982, 0.990, 1.002, 0.984, 0.996, 0.993, 0.980, 0.996]
+g6 = [1.009, 1.013, 1.009, 0.997, 0.988, 1.002, 0.995, 0.998, 0.981, 0.996]
+g7 = [0.990, 1.004, 0.996, 1.001, 0.998, 1.000, 1.018, 1.010, 0.996, 1.002]
+g8 = [0.998, 1.000, 1.006, 1.000, 1.002, 0.996, 0.998, 0.996, 1.002, 1.006]
+g9 = [1.002, 0.998, 0.996, 0.995, 0.996, 1.004, 1.004, 0.998, 0.999, 0.991]
+g10 = [0.991, 0.995, 0.984, 0.994, 0.997, 0.997, 0.991, 0.998, 1.004, 0.997]
+
+
+# The loggamma RVS stream is changing due to gh-13349; this version
+# preserves the old stream so that tests don't change.
+def _old_loggamma_rvs(*args, **kwargs):
+    return np.log(stats.gamma.rvs(*args, **kwargs))
+
+
+class TestBayes_mvs:
+    def test_basic(self):
+        # Expected values in this test simply taken from the function.  For
+        # some checks regarding correctness of implementation, see review in
+        # gh-674
+        data = [6, 9, 12, 7, 8, 8, 13]
+        mean, var, std = stats.bayes_mvs(data)
+        assert_almost_equal(mean.statistic, 9.0)
+        assert_allclose(mean.minmax, (7.103650222492964, 10.896349777507034),
+                        rtol=1e-6)
+
+        assert_almost_equal(var.statistic, 10.0)
+        assert_allclose(var.minmax, (3.1767242068607087, 24.45910381334018),
+                        rtol=1e-09)
+
+        assert_almost_equal(std.statistic, 2.9724954732045084, decimal=14)
+        assert_allclose(std.minmax, (1.7823367265645145, 4.9456146050146312),
+                        rtol=1e-14)
+
+    def test_empty_input(self):
+        assert_raises(ValueError, stats.bayes_mvs, [])
+
+    def test_result_attributes(self):
+        x = np.arange(15)
+        attributes = ('statistic', 'minmax')
+        res = stats.bayes_mvs(x)
+
+        for i in res:
+            check_named_results(i, attributes)
+
+
+class TestMvsdist:
+    def test_basic(self):
+        data = [6, 9, 12, 7, 8, 8, 13]
+        mean, var, std = stats.mvsdist(data)
+        assert_almost_equal(mean.mean(), 9.0)
+        assert_allclose(mean.interval(0.9), (7.103650222492964,
+                                             10.896349777507034), rtol=1e-14)
+
+        assert_almost_equal(var.mean(), 10.0)
+        assert_allclose(var.interval(0.9), (3.1767242068607087,
+                                            24.45910381334018), rtol=1e-09)
+
+        assert_almost_equal(std.mean(), 2.9724954732045084, decimal=14)
+        assert_allclose(std.interval(0.9), (1.7823367265645145,
+                                            4.9456146050146312), rtol=1e-14)
+
+    def test_empty_input(self):
+        assert_raises(ValueError, stats.mvsdist, [])
+
+    def test_bad_arg(self):
+        # Raise ValueError if fewer than two data points are given.
+        data = [1]
+        assert_raises(ValueError, stats.mvsdist, data)
+
+    def test_warns(self):
+        # regression test for gh-5270
+        # make sure there are no spurious divide-by-zero warnings
+        with warnings.catch_warnings():
+            warnings.simplefilter('error', RuntimeWarning)
+            [x.mean() for x in stats.mvsdist([1, 2, 3])]
+            [x.mean() for x in stats.mvsdist([1, 2, 3, 4, 5])]
+
+
+@make_xp_test_case(stats.shapiro)
+class TestShapiro:
+    def test_basic(self, xp):
+        # reference values generated using R shapiro.test, e.g.
+        # options(digits=16)
+        # x = c(0.11, 7.87, 4.61, 10.14, 7.95, 3.14, 0.46,
+        #       4.43, 0.21, 4.75, 0.71, 1.52, 3.24,
+        #       0.93, 0.42, 4.97, 9.53, 4.55, 0.47, 6.66)
+        # shapiro.test(x)
+        x1 = [0.11, 7.87, 4.61, 10.14, 7.95, 3.14, 0.46,
+              4.43, 0.21, 4.75, 0.71, 1.52, 3.24,
+              0.93, 0.42, 4.97, 9.53, 4.55, 0.47, 6.66]
+        shapiro_test = stats.shapiro(xp.asarray(x1))
+        w, pw = shapiro_test
+        xp_assert_close(w, xp.asarray(0.90047287931756))
+        xp_assert_close(shapiro_test.statistic, xp.asarray(0.90047287931756))
+        xp_assert_close(pw, xp.asarray(0.04208957522226))
+        xp_assert_close(shapiro_test.pvalue, xp.asarray(0.04208957522226))
+
+        x2 = [1.36, 1.14, 2.92, 2.55, 1.46, 1.06, 5.27, -1.11,
+              3.48, 1.10, 0.88, -0.51, 1.46, 0.52, 6.20, 1.69,
+              0.08, 3.67, 2.81, 3.49]
+        shapiro_test = stats.shapiro(xp.asarray(x2))
+        xp_assert_close(shapiro_test.statistic, xp.asarray(0.95902694603234))
+        xp_assert_close(shapiro_test.pvalue, xp.asarray(0.5245979304707))
+
+        x3 = stats.norm.rvs(loc=5, scale=3, size=100, random_state=12345678)
+        shapiro_test = stats.shapiro(xp.asarray(x3.tolist()))
+        xp_assert_close(shapiro_test.statistic, xp.asarray(0.97728027037175))
+        xp_assert_close(shapiro_test.pvalue, xp.asarray(0.08143656270016))
+
+    @pytest.mark.parametrize('dtype', [None, 'float32', 'float64'])
+    def test_basic2(self, dtype, xp):
+        # # Data from original paper; additional precision from R shapiro.test
+        x4 = [0.139, 0.157, 0.175, 0.256, 0.344, 0.413, 0.503, 0.577, 0.614,
+              0.655, 0.954, 1.392, 1.557, 1.648, 1.690, 1.994, 2.174, 2.206,
+              3.245, 3.510, 3.571, 4.354, 4.980, 6.084, 8.351]
+        dtype = {'dtype': dtype if dtype is None else getattr(xp, dtype)}
+        W_expected = xp.asarray(0.83466627531817, **dtype)
+        p_expected = xp.asarray(0.000913490481813, **dtype)
+        shapiro_test = stats.shapiro(xp.asarray(x4, **dtype))
+        xp_assert_close(shapiro_test.statistic, xp.asarray(W_expected, **dtype))
+        xp_assert_close(shapiro_test.pvalue, xp.asarray(p_expected, **dtype))
+
+    @skip_xp_backends('jax.numpy', reason='lazy backend -> limited input validation')
+    @skip_xp_backends('dask.array', reason='lazy backend -> limited input validation')
+    @pytest.mark.parametrize('x', ([], [1], [1, 2]))
+    def test_not_enough_values(self, x, xp):
+        with eager_warns(SmallSampleWarning, match=too_small_1d_not_omit, xp=xp):
+            res = stats.shapiro(xp.asarray(x))
+            xp_assert_equal(res.statistic, xp.asarray(xp.nan))
+            xp_assert_equal(res.pvalue, xp.asarray(xp.nan))
+
+    def test_nan_input(self, xp):
+        x = xp.arange(10.)
+        x = xpx.at(x)[9].set(xp.nan)
+
+        shapiro_test = stats.shapiro(xp.asarray(x))
+        xp_assert_equal(shapiro_test.statistic, xp.asarray(xp.nan))
+        xp_assert_equal(shapiro_test.pvalue, xp.asarray(xp.nan))
+
+    def test_gh14462(self, xp):
+        # shapiro is theoretically location-invariant, but when the magnitude
+        # of the values is much greater than the variance, there can be
+        # numerical issues. Fixed by subtracting median from the data.
+        # See gh-14462.
+        trans_val, maxlog = stats.boxcox([122500, 474400, 110400])
+        dtype = xp.float64  # we need some precision to work with
+        res = stats.shapiro(xp.asarray(trans_val, dtype=dtype))
+
+        # Reference from R:
+        # options(digits=16)
+        # x = c(0.00000000e+00, 3.39996924e-08, -6.35166875e-09)
+        # shapiro.test(x)
+        ref_statistic = xp.asarray(0.86468431705371, dtype=dtype)
+        ref_pvalue = xp.asarray(0.2805581751566, dtype=dtype)
+
+        xp_assert_close(res.statistic, ref_statistic, rtol=5e-7)
+        xp_assert_close(res.pvalue, ref_pvalue, rtol=5e-7)
+
+    def test_length_3_gh18322(self, xp):
+        # gh-18322 reported that the p-value could be negative for input of
+        # length 3. Check that this is resolved.
+        res = stats.shapiro(xp.asarray([0.6931471805599453, 0.0, 0.0]))
+        assert res.pvalue >= 0
+
+        # R `shapiro.test` doesn't produce an accurate p-value in the case
+        # above. Check that the formula used in `stats.shapiro` is not wrong.
+        # options(digits=16)
+        # x = c(-0.7746653110021126, -0.4344432067942129, 1.8157053280290931)
+        # shapiro.test(x)
+        x = [-0.7746653110021126, -0.4344432067942129, 1.8157053280290931]
+        res = stats.shapiro(xp.asarray(x))
+        xp_assert_close(res.statistic, xp.asarray(0.84658770645509))
+        xp_assert_close(res.pvalue, xp.asarray(0.2313666489882))
+
+    @pytest.mark.parametrize('n', [3, 4, 5, 8, 11, 20, 100, 200, 500, 1000, 2000, 5000])
+    def test_against_as181(self, n, xp):
+        rng = np.random.default_rng(n)
+        x = rng.standard_normal(n)
+
+        a = np.zeros(n // 2, dtype=np.float64)
+        y = np.sort(x) - x[n // 2]
+        ref_statistic, ref_pvalue, _ = swilk(y, a, 0)
+
+        x = xp.asarray(x)
+        res = stats.shapiro(x)
+        ref_statistic = xp.asarray(ref_statistic, dtype=x.dtype)
+        ref_pvalue = xp.asarray(ref_pvalue, dtype=x.dtype)
+
+        xp_assert_close(res.statistic, ref_statistic, rtol=5e-7)
+        xp_assert_close(res.pvalue, ref_pvalue, rtol=5e-7)
+
+
+@pytest.mark.filterwarnings("ignore: As of SciPy 1.17: FutureWarning")
+class TestAnderson:
+    def test_normal(self):
+        rs = RandomState(1234567890)
+        x1 = rs.standard_exponential(size=50)
+        x2 = rs.standard_normal(size=50)
+        A, crit, sig = stats.anderson(x1)
+        assert_array_less(crit[:-1], A)
+        A, crit, sig = stats.anderson(x2)
+        assert_array_less(A, crit[-2:])
+
+        v = np.ones(10)
+        v[0] = 0
+        A, crit, sig = stats.anderson(v)
+        # The expected statistic 3.208057 was computed independently of scipy.
+        # For example, in R:
+        #   > library(nortest)
+        #   > v <- rep(1, 10)
+        #   > v[1] <- 0
+        #   > result <- ad.test(v)
+        #   > result$statistic
+        #          A
+        #   3.208057
+        assert_allclose(A, 3.208057)
+
+    def test_expon(self):
+        rs = RandomState(1234567890)
+        x1 = rs.standard_exponential(size=50)
+        x2 = rs.standard_normal(size=50)
+        A, crit, sig = stats.anderson(x1, 'expon')
+        assert_array_less(A, crit[-2:])
+        with np.errstate(all='ignore'):
+            A, crit, sig = stats.anderson(x2, 'expon')
+        assert_(A > crit[-1])
+
+    def test_gumbel(self):
+        # Regression test for gh-6306.  Before that issue was fixed,
+        # this case would return a2=inf.
+        v = np.ones(100)
+        v[0] = 0.0
+        a2, crit, sig = stats.anderson(v, 'gumbel')
+        # A brief reimplementation of the calculation of the statistic.
+        n = len(v)
+        xbar, s = stats.gumbel_l.fit(v)
+        logcdf = stats.gumbel_l.logcdf(v, xbar, s)
+        logsf = stats.gumbel_l.logsf(v, xbar, s)
+        i = np.arange(1, n+1)
+        expected_a2 = -n - np.mean((2*i - 1) * (logcdf + logsf[::-1]))
+
+        assert_allclose(a2, expected_a2)
+
+    def test_bad_arg(self):
+        assert_raises(ValueError, stats.anderson, [1], dist='plate_of_shrimp')
+
+    def test_result_attributes(self):
+        rs = RandomState(1234567890)
+        x = rs.standard_exponential(size=50)
+        res = stats.anderson(x)
+        attributes = ('statistic', 'critical_values', 'significance_level')
+        check_named_results(res, attributes)
+
+    def test_gumbel_l(self):
+        # gh-2592, gh-6337
+        # Adds support to 'gumbel_r' and 'gumbel_l' as valid inputs for dist.
+        rs = RandomState(1234567890)
+        x = rs.gumbel(size=100)
+        A1, crit1, sig1 = stats.anderson(x, 'gumbel')
+        A2, crit2, sig2 = stats.anderson(x, 'gumbel_l')
+
+        assert_allclose(A2, A1)
+
+    def test_gumbel_r(self):
+        # gh-2592, gh-6337
+        # Adds support to 'gumbel_r' and 'gumbel_l' as valid inputs for dist.
+        rs = RandomState(1234567890)
+        x1 = rs.gumbel(size=100)
+        x2 = np.ones(100)
+        # A constant array is a degenerate case and breaks gumbel_r.fit, so
+        # change one value in x2.
+        x2[0] = 0.996
+        A1, crit1, sig1 = stats.anderson(x1, 'gumbel_r')
+        A2, crit2, sig2 = stats.anderson(x2, 'gumbel_r')
+
+        assert_array_less(A1, crit1[-2:])
+        assert_(A2 > crit2[-1])
+
+    def test_weibull_min_case_A(self):
+        # data and reference values from `anderson` reference [7]
+        x = np.array([225, 171, 198, 189, 189, 135, 162, 135, 117, 162])
+        res = stats.anderson(x, 'weibull_min')
+        m, loc, scale = res.fit_result.params
+        assert_allclose((m, loc, scale), (2.38, 99.02, 78.23), rtol=2e-3)
+        assert_allclose(res.statistic, 0.260, rtol=1e-3)
+        assert res.statistic < res.critical_values[0]
+
+        c = 1 / m  # ~0.42
+        assert_allclose(c, 1/2.38, rtol=2e-3)
+        # interpolate between rows for c=0.4 and c=0.45, indices -3 and -2
+        As40 = _Avals_weibull[-3]
+        As45 = _Avals_weibull[-2]
+        As_ref = As40 + (c - 0.4)/(0.45 - 0.4) * (As45 - As40)
+        # atol=1e-3 because results are rounded up to the next third decimal
+        assert np.all(res.critical_values > As_ref)
+        assert_allclose(res.critical_values, As_ref, atol=1e-3)
+
+    def test_weibull_min_case_B(self):
+        # From `anderson` reference [7]
+        x = np.array([74, 57, 48, 29, 502, 12, 70, 21,
+                      29, 386, 59, 27, 153, 26, 326])
+        message = "Maximum likelihood estimation has converged to "
+        with pytest.raises(ValueError, match=message):
+            stats.anderson(x, 'weibull_min')
+
+    def test_weibull_warning_error(self):
+        # Check for warning message when there are too few observations
+        # This is also an example in which an error occurs during fitting
+        x = -np.array([225, 75, 57, 168, 107, 12, 61, 43, 29])
+        wmessage = "Critical values of the test statistic are given for the..."
+        emessage = "An error occurred while fitting the Weibull distribution..."
+        wcontext = pytest.warns(UserWarning, match=wmessage)
+        econtext = pytest.raises(ValueError, match=emessage)
+        with wcontext, econtext:
+            stats.anderson(x, 'weibull_min')
+
+    @pytest.mark.parametrize('distname',
+                             ['norm', 'expon', 'gumbel_l', 'extreme1',
+                              'gumbel', 'gumbel_r', 'logistic', 'weibull_min'])
+    def test_anderson_fit_params(self, distname):
+        # check that anderson now returns a FitResult
+        rng = np.random.default_rng(330691555377792039)
+        real_distname = ('gumbel_l' if distname in {'extreme1', 'gumbel'}
+                         else distname)
+        dist = getattr(stats, real_distname)
+        params = distcont[real_distname]
+        x = dist.rvs(*params, size=1000, random_state=rng)
+        res = stats.anderson(x, distname)
+        assert res.fit_result.success
+
+    def test_anderson_weibull_As(self):
+        m = 1  # "when mi < 2, so that c > 0.5, the last line...should be used"
+        assert_equal(_get_As_weibull(1/m), _Avals_weibull[-1])
+        m = np.inf
+        assert_equal(_get_As_weibull(1/m), _Avals_weibull[0])
+
+
+class TestAndersonMethod:
+    def test_warning(self):
+        message = "As of SciPy 1.17, users..."
+        with pytest.warns(FutureWarning, match=message):
+            stats.anderson([1, 2, 3], 'norm')
+
+    def test_method_input_validation(self):
+        message = "`method` must be either..."
+        with pytest.raises(ValueError, match=message):
+            stats.anderson([1, 2, 3], 'norm', method='ekki-ekki')
+
+    def test_monte_carlo_method(self):
+        rng = np.random.default_rng(94982389149239)
+
+        message = "The `rvs` attribute..."
+        with pytest.warns(UserWarning, match=message):
+            method = stats.MonteCarloMethod(rvs=rng.random)
+            stats.anderson([1, 2, 3], 'norm', method=method)
+
+        message = "The `batch` attribute..."
+        with pytest.warns(UserWarning, match=message):
+            method = stats.MonteCarloMethod(batch=10)
+            stats.anderson([1, 2, 3], 'norm', method=method)
+
+        method = stats.MonteCarloMethod(n_resamples=9, rng=rng)
+        res = stats.anderson([1, 2, 3], 'norm', method=method)
+        ten_p = res.pvalue * 10
+        # p-value will always be divisible by n_resamples + 1
+        assert np.round(ten_p) == ten_p
+
+        method = stats.MonteCarloMethod(rng=np.random.default_rng(23495984827))
+        ref = stats.anderson([1, 2, 3, 4, 5], 'norm', method=method)
+        method = stats.MonteCarloMethod(rng=np.random.default_rng(23495984827))
+        res = stats.anderson([1, 2, 3, 4, 5], 'norm', method=method)
+        assert res.pvalue == ref.pvalue  # same random state -> same p-value
+        method = stats.MonteCarloMethod(rng=np.random.default_rng(23495984828))
+        res = stats.anderson([1, 2, 3, 4, 5], 'norm', method=method)
+        assert res.pvalue != ref.pvalue  # different random state -> different p-value
+
+    @pytest.mark.parametrize('dist_name, seed',
+        [('norm', 4202165767275),
+         ('expon', 9094400417269),
+         pytest.param('logistic', 3776634590070, marks=pytest.mark.xslow),
+         pytest.param('gumbel_l', 7966588969335, marks=pytest.mark.xslow),
+         pytest.param('gumbel_r', 1886450383828, marks=pytest.mark.xslow)])
+    def test_method_consistency(self, dist_name, seed):
+        dist = getattr(stats, dist_name)
+        rng = np.random.default_rng(seed)
+        x = dist.rvs(size=50, random_state=rng)
+        ref = stats.anderson(x, dist_name, method='interpolate')
+        res = stats.anderson(x, dist_name, method=stats.MonteCarloMethod(rng=rng))
+        np.testing.assert_allclose(res.statistic, ref.statistic)
+        np.testing.assert_allclose(res.pvalue, ref.pvalue, atol=0.005)
+
+    @pytest.mark.parametrize('dist_name',
+        ['norm', 'expon', 'logistic', 'gumbel_l', 'gumbel_r', 'weibull_min'])
+    def test_interpolate_saturation(self, dist_name):
+        dist = getattr(stats, dist_name)
+        rng = np.random.default_rng(4202165767276)
+        args = (3.5,) if dist_name == 'weibull_min' else tuple()
+        x = dist.rvs(*args, size=50, random_state=rng)
+
+        with pytest.warns(FutureWarning):
+            res = stats.anderson(x, dist_name)
+        pvalues = (1 - np.asarray(res.significance_level) if dist_name == 'weibull_min'
+                   else np.asarray(res.significance_level) / 100)
+        pvalue_min = np.min(pvalues)
+        pvalue_max = np.max(pvalues)
+        statistic_min = np.min(res.critical_values)
+        statistic_max = np.max(res.critical_values)
+
+        # data drawn from distribution -> low statistic / high p-value
+        res = stats.anderson(x, dist_name, method='interpolate')
+        assert res.statistic < statistic_min
+        assert res.pvalue == pvalue_max
+
+        # data not from distribution -> high statistic / low p-value
+        res = stats.anderson(rng.random(size=50), dist_name, method='interpolate')
+        assert res.statistic > statistic_max
+        assert res.pvalue == pvalue_min
+
+
+@pytest.mark.filterwarnings("ignore:Parameter `variant`...:UserWarning")
+class TestAndersonKSamp:
+    def test_example1a(self):
+        # Example data from Scholz & Stephens (1987), originally
+        # published in Lehmann (1995, Nonparametrics, Statistical
+        # Methods Based on Ranks, p. 309)
+        # Pass a mixture of lists and arrays
+        t1 = [38.7, 41.5, 43.8, 44.5, 45.5, 46.0, 47.7, 58.0]
+        t2 = np.array([39.2, 39.3, 39.7, 41.4, 41.8, 42.9, 43.3, 45.8])
+        t3 = np.array([34.0, 35.0, 39.0, 40.0, 43.0, 43.0, 44.0, 45.0])
+        t4 = np.array([34.0, 34.8, 34.8, 35.4, 37.2, 37.8, 41.2, 42.8])
+
+        Tk, tm, p = stats.anderson_ksamp((t1, t2, t3, t4), midrank=False)
+
+        assert_almost_equal(Tk, 4.449, 3)
+        assert_array_almost_equal([0.4985, 1.3237, 1.9158, 2.4930, 3.2459],
+                                  tm[0:5], 4)
+        assert_allclose(p, 0.0021, atol=0.00025)
+
+    def test_example1b(self):
+        # Example data from Scholz & Stephens (1987), originally
+        # published in Lehmann (1995, Nonparametrics, Statistical
+        # Methods Based on Ranks, p. 309)
+        # Pass arrays
+        t1 = np.array([38.7, 41.5, 43.8, 44.5, 45.5, 46.0, 47.7, 58.0])
+        t2 = np.array([39.2, 39.3, 39.7, 41.4, 41.8, 42.9, 43.3, 45.8])
+        t3 = np.array([34.0, 35.0, 39.0, 40.0, 43.0, 43.0, 44.0, 45.0])
+        t4 = np.array([34.0, 34.8, 34.8, 35.4, 37.2, 37.8, 41.2, 42.8])
+        Tk, tm, p = stats.anderson_ksamp((t1, t2, t3, t4), midrank=True)
+
+        assert_almost_equal(Tk, 4.480, 3)
+        assert_array_almost_equal([0.4985, 1.3237, 1.9158, 2.4930, 3.2459],
+                                  tm[0:5], 4)
+        assert_allclose(p, 0.0020, atol=0.00025)
+
+    @pytest.mark.xslow
+    def test_example2a(self):
+        # Example data taken from an earlier technical report of
+        # Scholz and Stephens
+        # Pass lists instead of arrays
+        t1 = [194, 15, 41, 29, 33, 181]
+        t2 = [413, 14, 58, 37, 100, 65, 9, 169, 447, 184, 36, 201, 118]
+        t3 = [34, 31, 18, 18, 67, 57, 62, 7, 22, 34]
+        t4 = [90, 10, 60, 186, 61, 49, 14, 24, 56, 20, 79, 84, 44, 59, 29,
+              118, 25, 156, 310, 76, 26, 44, 23, 62]
+        t5 = [130, 208, 70, 101, 208]
+        t6 = [74, 57, 48, 29, 502, 12, 70, 21, 29, 386, 59, 27]
+        t7 = [55, 320, 56, 104, 220, 239, 47, 246, 176, 182, 33]
+        t8 = [23, 261, 87, 7, 120, 14, 62, 47, 225, 71, 246, 21, 42, 20, 5,
+              12, 120, 11, 3, 14, 71, 11, 14, 11, 16, 90, 1, 16, 52, 95]
+        t9 = [97, 51, 11, 4, 141, 18, 142, 68, 77, 80, 1, 16, 106, 206, 82,
+              54, 31, 216, 46, 111, 39, 63, 18, 191, 18, 163, 24]
+        t10 = [50, 44, 102, 72, 22, 39, 3, 15, 197, 188, 79, 88, 46, 5, 5, 36,
+               22, 139, 210, 97, 30, 23, 13, 14]
+        t11 = [359, 9, 12, 270, 603, 3, 104, 2, 438]
+        t12 = [50, 254, 5, 283, 35, 12]
+        t13 = [487, 18, 100, 7, 98, 5, 85, 91, 43, 230, 3, 130]
+        t14 = [102, 209, 14, 57, 54, 32, 67, 59, 134, 152, 27, 14, 230, 66,
+               61, 34]
+
+        samples = (t1, t2, t3, t4, t5, t6, t7, t8, t9, t10, t11, t12, t13, t14)
+        Tk, tm, p = stats.anderson_ksamp(samples, midrank=False)
+        assert_almost_equal(Tk, 3.288, 3)
+        assert_array_almost_equal([0.5990, 1.3269, 1.8052, 2.2486, 2.8009],
+                                  tm[0:5], 4)
+        assert_allclose(p, 0.0041, atol=0.00025)
+
+        rng = np.random.default_rng(6989860141921615054)
+        method = stats.PermutationMethod(n_resamples=9999, rng=rng)
+        res = stats.anderson_ksamp(samples, midrank=False, method=method)
+        assert_array_equal(res.statistic, Tk)
+        assert_array_equal(res.critical_values, tm)
+        assert_allclose(res.pvalue, p, atol=6e-4)
+
+    def test_example2b(self):
+        # Example data taken from an earlier technical report of
+        # Scholz and Stephens
+        t1 = [194, 15, 41, 29, 33, 181]
+        t2 = [413, 14, 58, 37, 100, 65, 9, 169, 447, 184, 36, 201, 118]
+        t3 = [34, 31, 18, 18, 67, 57, 62, 7, 22, 34]
+        t4 = [90, 10, 60, 186, 61, 49, 14, 24, 56, 20, 79, 84, 44, 59, 29,
+              118, 25, 156, 310, 76, 26, 44, 23, 62]
+        t5 = [130, 208, 70, 101, 208]
+        t6 = [74, 57, 48, 29, 502, 12, 70, 21, 29, 386, 59, 27]
+        t7 = [55, 320, 56, 104, 220, 239, 47, 246, 176, 182, 33]
+        t8 = [23, 261, 87, 7, 120, 14, 62, 47, 225, 71, 246, 21, 42, 20, 5,
+              12, 120, 11, 3, 14, 71, 11, 14, 11, 16, 90, 1, 16, 52, 95]
+        t9 = [97, 51, 11, 4, 141, 18, 142, 68, 77, 80, 1, 16, 106, 206, 82,
+              54, 31, 216, 46, 111, 39, 63, 18, 191, 18, 163, 24]
+        t10 = [50, 44, 102, 72, 22, 39, 3, 15, 197, 188, 79, 88, 46, 5, 5, 36,
+               22, 139, 210, 97, 30, 23, 13, 14]
+        t11 = [359, 9, 12, 270, 603, 3, 104, 2, 438]
+        t12 = [50, 254, 5, 283, 35, 12]
+        t13 = [487, 18, 100, 7, 98, 5, 85, 91, 43, 230, 3, 130]
+        t14 = [102, 209, 14, 57, 54, 32, 67, 59, 134, 152, 27, 14, 230, 66,
+               61, 34]
+
+        Tk, tm, p = stats.anderson_ksamp((t1, t2, t3, t4, t5, t6, t7, t8,
+                                          t9, t10, t11, t12, t13, t14),
+                                         midrank=True)
+
+        assert_almost_equal(Tk, 3.294, 3)
+        assert_array_almost_equal([0.5990, 1.3269, 1.8052, 2.2486, 2.8009],
+                                  tm[0:5], 4)
+        assert_allclose(p, 0.0041, atol=0.00025)
+
+    def test_R_kSamples(self):
+        # test values generates with R package kSamples
+        # package version 1.2-6 (2017-06-14)
+        # r1 = 1:100
+        # continuous case (no ties) --> version  1
+        # res <- kSamples::ad.test(r1, r1 + 40.5)
+        # res$ad[1, "T.AD"] #  41.105
+        # res$ad[1, " asympt. P-value"] #  5.8399e-18
+        #
+        # discrete case (ties allowed) --> version  2 (here: midrank=True)
+        # res$ad[2, "T.AD"] #  41.235
+        #
+        # res <- kSamples::ad.test(r1, r1 + .5)
+        # res$ad[1, "T.AD"] #  -1.2824
+        # res$ad[1, " asympt. P-value"] #  1
+        # res$ad[2, "T.AD"] #  -1.2944
+        #
+        # res <- kSamples::ad.test(r1, r1 + 7.5)
+        # res$ad[1, "T.AD"] # 1.4923
+        # res$ad[1, " asympt. P-value"] # 0.077501
+        #
+        # res <- kSamples::ad.test(r1, r1 + 6)
+        # res$ad[2, "T.AD"] # 0.63892
+        # res$ad[2, " asympt. P-value"] # 0.17981
+        #
+        # res <- kSamples::ad.test(r1, r1 + 11.5)
+        # res$ad[1, "T.AD"] # 4.5042
+        # res$ad[1, " asympt. P-value"] # 0.00545
+        #
+        # res <- kSamples::ad.test(r1, r1 + 13.5)
+        # res$ad[1, "T.AD"] # 6.2982
+        # res$ad[1, " asympt. P-value"] # 0.00118
+
+        x1 = np.linspace(1, 100, 100)
+        # test case: different distributions;p-value floored at 0.001
+        # test case for issue #5493 / #8536
+        with warnings.catch_warnings():
+            warnings.filterwarnings("ignore", 'p-value floored', UserWarning)
+            s, _, p = stats.anderson_ksamp([x1, x1 + 40.5], midrank=False)
+        assert_almost_equal(s, 41.105, 3)
+        assert_equal(p, 0.001)
+
+        with warnings.catch_warnings():
+            warnings.filterwarnings("ignore", 'p-value floored', UserWarning)
+            s, _, p = stats.anderson_ksamp([x1, x1 + 40.5])
+        assert_almost_equal(s, 41.235, 3)
+        assert_equal(p, 0.001)
+
+        # test case: similar distributions --> p-value capped at 0.25
+        with warnings.catch_warnings():
+            warnings.filterwarnings("ignore", 'p-value capped', UserWarning)
+            s, _, p = stats.anderson_ksamp([x1, x1 + .5], midrank=False)
+        assert_almost_equal(s, -1.2824, 4)
+        assert_equal(p, 0.25)
+
+        with warnings.catch_warnings():
+            warnings.filterwarnings("ignore", 'p-value capped', UserWarning)
+            s, _, p = stats.anderson_ksamp([x1, x1 + .5])
+        assert_almost_equal(s, -1.2944, 4)
+        assert_equal(p, 0.25)
+
+        # test case: check interpolated p-value in [0.01, 0.25] (no ties)
+        s, _, p = stats.anderson_ksamp([x1, x1 + 7.5], midrank=False)
+        assert_almost_equal(s, 1.4923, 4)
+        assert_allclose(p, 0.0775, atol=0.005, rtol=0)
+
+        # test case: check interpolated p-value in [0.01, 0.25] (w/ ties)
+        s, _, p = stats.anderson_ksamp([x1, x1 + 6])
+        assert_almost_equal(s, 0.6389, 4)
+        assert_allclose(p, 0.1798, atol=0.005, rtol=0)
+
+        # test extended critical values for p=0.001 and p=0.005
+        s, _, p = stats.anderson_ksamp([x1, x1 + 11.5], midrank=False)
+        assert_almost_equal(s, 4.5042, 4)
+        assert_allclose(p, 0.00545, atol=0.0005, rtol=0)
+
+        s, _, p = stats.anderson_ksamp([x1, x1 + 13.5], midrank=False)
+        assert_almost_equal(s, 6.2982, 4)
+        assert_allclose(p, 0.00118, atol=0.0001, rtol=0)
+
+    def test_not_enough_samples(self):
+        assert_raises(ValueError, stats.anderson_ksamp, np.ones(5))
+
+    def test_no_distinct_observations(self):
+        assert_raises(ValueError, stats.anderson_ksamp,
+                      (np.ones(5), np.ones(5)))
+
+    def test_empty_sample(self):
+        assert_raises(ValueError, stats.anderson_ksamp, (np.ones(5), []))
+
+    def test_result_attributes(self):
+        # Pass a mixture of lists and arrays
+        t1 = [38.7, 41.5, 43.8, 44.5, 45.5, 46.0, 47.7, 58.0]
+        t2 = np.array([39.2, 39.3, 39.7, 41.4, 41.8, 42.9, 43.3, 45.8])
+        res = stats.anderson_ksamp((t1, t2), midrank=False)
+
+        attributes = ('statistic', 'critical_values', 'significance_level')
+        check_named_results(res, attributes)
+
+        assert_equal(res.significance_level, res.pvalue)
+
+
+class TestAndersonKSampVariant:
+    def test_variant_values(self):
+        x = [1, 2, 2, 3, 4, 5]
+        y = [1, 2, 3, 4, 4, 5, 6, 6, 6, 7]
+        message = "Parameter `variant` has been introduced..."
+        with pytest.warns(UserWarning, match=message):
+            ref = stats.anderson_ksamp((x, y))
+        assert len(ref) == 3 and hasattr(ref, 'critical_values')
+
+        with pytest.warns(UserWarning, match=message):
+            res = stats.anderson_ksamp((x, y), midrank=True)
+        assert_equal(res.statistic, ref.statistic)
+        assert_equal(res.pvalue, ref.pvalue)
+        assert len(res) == 3 and hasattr(res, 'critical_values')
+
+        with pytest.warns(UserWarning, match=message):
+            res = stats.anderson_ksamp((x, y), midrank=False, variant='midrank')
+        assert_equal(res.statistic, ref.statistic)
+        assert_equal(res.pvalue, ref.pvalue)
+        assert not hasattr(res, 'critical_values')
+
+        res = stats.anderson_ksamp((x, y), variant='midrank')
+        assert_equal(res.statistic, ref.statistic)
+        assert_equal(res.pvalue, ref.pvalue)
+        assert not hasattr(res, 'critical_values')
+
+        with pytest.warns(UserWarning, match=message):
+            ref = stats.anderson_ksamp((x, y), midrank=False)
+        assert len(ref) == 3 and hasattr(ref, 'critical_values')
+
+        with pytest.warns(UserWarning, match=message):
+            res = stats.anderson_ksamp((x, y), midrank=True, variant='right')
+        assert_equal(res.statistic, ref.statistic)
+        assert_equal(res.pvalue, ref.pvalue)
+        assert not hasattr(res, 'critical_values')
+
+        res = stats.anderson_ksamp((x, y), variant='right')
+        assert_equal(res.statistic, ref.statistic)
+        assert_equal(res.pvalue, ref.pvalue)
+        assert not hasattr(res, 'critical_values')
+
+    def test_variant_input_validation(self):
+        x = np.arange(10)
+        message = "`variant` must be one of 'midrank', 'right', or 'continuous'."
+        with pytest.raises(ValueError, match=message):
+            stats.anderson_ksamp((x, x), variant='Camelot')
+
+    @pytest.mark.parametrize('n_samples', [2, 3])
+    def test_variant_continuous(self, n_samples):
+        rng = np.random.default_rng(20182053007)
+        samples = rng.random((n_samples, 15)) + 0.1*np.arange(n_samples)[:, np.newaxis]
+        ref = stats.anderson_ksamp(samples, variant='right')
+        res = stats.anderson_ksamp(samples, variant='continuous')
+        assert_allclose(res.statistic, ref.statistic)
+        assert_allclose(res.pvalue, ref.pvalue)
+
+
+@make_xp_test_case(stats.ansari)
+class TestAnsari:
+
+    def test_small(self, xp):
+        x = xp.asarray([1, 2, 3, 3, 4])
+        y = xp.asarray([3, 2, 6, 1, 6, 1, 4, 1])
+        W, pval = stats.ansari(x, y, method='asymptotic')
+        xp_assert_close(W, xp.asarray(23.5))
+        xp_assert_close(pval, xp.asarray(0.13499256881897437))
+
+    def test_approx(self, xp):
+        ramsay = xp.asarray([111, 107, 100, 99, 102, 106, 109, 108, 104, 99,
+                             101, 96, 97, 102, 107, 113, 116, 113, 110, 98])
+        parekh = xp.asarray([107, 108, 106, 98, 105, 103, 110, 105, 104,
+                             100, 96, 108, 103, 104, 114, 114, 113, 108,
+                             106, 99])
+
+        W, pval = stats.ansari(ramsay, parekh, method='asymptotic')
+        xp_assert_close(W, xp.asarray(185.5))
+        xp_assert_close(pval, xp.asarray(0.18145819972867083))
+
+    def test_exact(self, xp):
+        x, y = xp.asarray([1, 2, 3, 4]), xp.asarray([15, 5, 20, 8, 10, 12])
+        W, pval = stats.ansari(x, y, method='exact')
+        xp_assert_close(W, xp.asarray(10.0))
+        xp_assert_close(pval, xp.asarray(0.533333333333333333))
+
+    @pytest.mark.parametrize('args', [([], [1.]), ([1.], [])])
+    def test_bad_arg(self, args, xp):
+        args = [xp.asarray(arg) for arg in args]
+        with pytest.warns(SmallSampleWarning, match=too_small_1d_not_omit):
+            res = stats.ansari(*args)
+            xp_assert_equal(res.statistic, xp.asarray(xp.nan))
+            xp_assert_equal(res.pvalue, xp.asarray(xp.nan))
+
+    def test_bad_alternative(self, xp):
+        # invalid value for alternative must raise a ValueError
+        x1 = xp.asarray([1, 2, 3, 4])
+        x2 = xp.asarray([5, 6, 7, 8])
+        match = "'alternative' must be 'two-sided'"
+        with assert_raises(ValueError, match=match):
+            stats.ansari(x1, x2, alternative='foo')
+
+    def test_alternative_exact(self, xp):
+        x1 = xp.asarray([-5, 1, 5, 10, 15, 20, 25.])  # high scale, loc=10
+        x2 = xp.asarray([7.5, 8.5, 9.5, 10.5, 11.5, 12.5])  # low scale, loc=10
+        # ratio of scales is greater than 1. So, the
+        # p-value must be high when `alternative='less'`
+        # and low when `alternative='greater'`.
+        statistic, pval = stats.ansari(x1, x2, method='exact')
+        pval_l = stats.ansari(x1, x2, alternative='less', method='exact').pvalue
+        pval_g = stats.ansari(x1, x2, alternative='greater', method='exact').pvalue
+        assert pval_l > 0.95
+        assert pval_g < 0.05  # level of significance.
+        # also check if the p-values sum up to 1 plus the probability
+        # mass under the calculated statistic.
+        prob = _abw_state.a.pmf(float(statistic), x1.shape[0], x2.shape[0])
+        prob = xp.asarray(float(prob))
+        xp_assert_close(pval_g + pval_l, 1 + prob, atol=1e-12)
+        # also check if one of the one-sided p-value equals half the
+        # two-sided p-value and the other one-sided p-value is its
+        # compliment.
+        xp_assert_close(pval_g, pval/2, atol=1e-12)
+        xp_assert_close(pval_l, 1+prob-pval/2, atol=1e-12)
+        # sanity check. The result should flip if
+        # we exchange x and y.
+        pval_l_reverse = stats.ansari(x2, x1, alternative='less',
+                                      method='exact').pvalue
+        pval_g_reverse = stats.ansari(x2, x1, alternative='greater',
+                                      method='exact').pvalue
+        assert pval_l_reverse < 0.05
+        assert pval_g_reverse > 0.95
+
+    @pytest.mark.parametrize(
+        'x, y, alternative, expected',
+        # the tests are designed in such a way that the
+        # if else statement in ansari test for exact
+        # mode is covered.
+        [([1, 2, 3, 4], [5, 6, 7, 8], 'less', 0.6285714285714),
+         ([1, 2, 3, 4], [5, 6, 7, 8], 'greater', 0.6285714285714),
+         ([1, 2, 3], [4, 5, 6, 7, 8], 'less', 0.8928571428571),
+         ([1, 2, 3], [4, 5, 6, 7, 8], 'greater', 0.2857142857143),
+         ([1, 2, 3, 4, 5], [6, 7, 8], 'less', 0.2857142857143),
+         ([1, 2, 3, 4, 5], [6, 7, 8], 'greater', 0.8928571428571)]
+    )
+    def test_alternative_exact_with_R(self, x, y, alternative, expected, xp):
+        # testing with R on arbitrary data
+        # Sample R code used for the third test case above:
+        # ```R
+        # > options(digits=16)
+        # > x <- c(1,2,3)
+        # > y <- c(4,5,6,7,8)
+        # > ansari.test(x, y, alternative='less', exact=TRUE)
+        #
+        #     Ansari-Bradley test
+        #
+        # data:  x and y
+        # AB = 6, p-value = 0.8928571428571
+        # alternative hypothesis: true ratio of scales is less than 1
+        #
+        # ```
+        x, y = xp.asarray(x), xp.asarray(y)
+        pval = stats.ansari(x, y, alternative=alternative, method='exact').pvalue
+        xp_assert_close(pval, xp.asarray(expected), atol=1e-12)
+
+    def test_alternative_approx(self, xp):
+        # intuitive tests for approximation
+        x1 = xp.asarray(stats.norm.rvs(0, 5, size=100, random_state=123))
+        x2 = xp.asarray(stats.norm.rvs(0, 2, size=100, random_state=123))
+        # for m > 55 or n > 55, the test should automatically
+        # switch to approximation.
+        pval_l = stats.ansari(x1, x2, alternative='less', method='asymptotic').pvalue
+        pval_g = stats.ansari(x1, x2, alternative='greater', method='asymptotic').pvalue
+        xp_assert_close(pval_l, xp.asarray(1.0, dtype=xp.float64), atol=1e-12)
+        xp_assert_close(pval_g, xp.asarray(0.0, dtype=xp.float64), atol=1e-12)
+        # also check if one of the one-sided p-value equals half the
+        # two-sided p-value and the other one-sided p-value is its
+        # compliment.
+        x1 = xp.asarray(stats.norm.rvs(0, 2, size=60, random_state=123))
+        x2 = xp.asarray(stats.norm.rvs(0, 1.5, size=60, random_state=123))
+        pval = stats.ansari(x1, x2, method='asymptotic').pvalue
+        pval_l = stats.ansari(x1, x2, alternative='less', method='asymptotic').pvalue
+        pval_g = stats.ansari(x1, x2, alternative='greater', method='asymptotic').pvalue
+        xp_assert_close(pval_g, pval/2, atol=1e-12)
+        xp_assert_close(pval_l, 1-pval/2, atol=1e-12)
+
+    @pytest.mark.parametrize('dtype', [None, 'float32', 'float64'])
+    @pytest.mark.parametrize('n', [10, 100])  # affects code path
+    @pytest.mark.parametrize('ties', [False, True])  # affects code path
+    def test_dtypes(self, dtype, n, ties, xp):
+        if is_jax(xp) and dtype != 'float64':
+            pytest.xfail("p-value calculation works natively with 'float64 only")
+        dtype = xp_default_dtype(xp) if dtype is None else getattr(xp, dtype)
+        rng = np.random.default_rng(78587342806484)
+        x, y = rng.integers(6, size=(2, n)) if ties else rng.random(size=(2, n))
+        method = {'method': 'exact' if ((n <= 55) and not ties) else 'asymptotic'}
+        ref = stats.ansari(x, y, **method)
+        res = stats.ansari(xp.asarray(x, dtype=dtype), xp.asarray(y, dtype=dtype),
+                           **method)
+        xp_assert_close(res.statistic, xp.asarray(ref.statistic, dtype=dtype))
+        xp_assert_close(res.pvalue, xp.asarray(ref.pvalue, dtype=dtype))
+
+    @pytest.mark.parametrize('alternative', ['less', 'greater', 'two-sided'])
+    def test_permutation_method(self, alternative, xp):
+        # test that permutation test can reproduce results of method='exact',
+        # but can also be configured to perform randomized test
+        rng = np.random.default_rng(6123643029)
+        x = xp.asarray(rng.random(7).tolist())
+        y = xp.asarray(rng.random(6).tolist())
+        res = stats.ansari(x, y, alternative=alternative,
+                           method=stats.PermutationMethod(rng=rng))
+        ref = stats.ansari(x, y, alternative=alternative, method='exact')
+        xp_assert_close(res.statistic, xp.asarray(ref.statistic))
+        xp_assert_close(res.pvalue, xp.asarray(ref.pvalue))
+
+        if not is_lazy_array(x):  # randomized permutation test has side-effects
+            res = stats.ansari(x, y, alternative=alternative,
+                               method=stats.PermutationMethod(rng=rng, n_resamples=99))
+            xp_assert_close(res.statistic, xp.asarray(ref.statistic))
+            assert res.pvalue != ref.pvalue
+            assert res.pvalue == xp.round(res.pvalue*100)/100  # 99+1 in denominator
+
+    def test_method(self, xp):
+        # test that `method` selection works and 'auto' behaves as expected
+        # expected p-values computed with `ansari.test` (R)
+        # e.g. `ansari.test(x, y, exact=False)`
+        rng = np.random.default_rng(6123643029)
+
+        if is_jax(xp):
+            message = "`method` must be 'exact', 'asymptotic', or an instance..."
+            with pytest.raises(ValueError, match=message):
+                stats.ansari(xp.zeros(4), xp.ones(5))
+            return
+
+        # default is exact, but asymptotic can be selected
+        x = xp.asarray(rng.random(54).tolist())
+        y = xp.asarray(rng.random(54).tolist())
+        res1 = stats.ansari(x, y)
+        res2 = stats.ansari(x, y, method='exact')
+        res3 = stats.ansari(x, y, method='asymptotic')
+        xp_assert_close(res1.pvalue, res2.pvalue)
+        xp_assert_close(res3.pvalue, xp.asarray(0.01259674075933))
+
+        # default is asymptotic, but exact can be selected
+        x = xp.asarray(rng.random(55).tolist())
+        y = xp.asarray(rng.random(55).tolist())
+        res1 = stats.ansari(x, y)
+        res2 = stats.ansari(x, y, method='asymptotic')
+        res3 = stats.ansari(x, y, method='exact')
+        xp_assert_close(res1.pvalue, res2.pvalue)
+        xp_assert_close(res3.pvalue, xp.asarray(0.7613489076855))
+
+        # default is asymptotic because of ties
+        x = xp.asarray(rng.integers(10, size=20).tolist())
+        y = xp.asarray(rng.integers(10, size=20).tolist())
+        res1 = stats.ansari(x, y)
+        res2 = stats.ansari(x, y, method='asymptotic')
+        xp_assert_close(res1.pvalue, res2.pvalue)
+
+
+@make_xp_test_case(stats.bartlett)
+class TestBartlett:
+    def test_data(self, xp):
+        # https://www.itl.nist.gov/div898/handbook/eda/section3/eda357.htm
+        args = [g1, g2, g3, g4, g5, g6, g7, g8, g9, g10]
+        args = [xp.asarray(arg) for arg in args]
+        T, pval = stats.bartlett(*args)
+        xp_assert_close(T, xp.asarray(20.78587342806484))
+        xp_assert_close(pval, xp.asarray(0.0136358632781))
+
+    def test_too_few_args(self, xp):
+        message = "Must enter at least two input sample vectors."
+        with pytest.raises(ValueError, match=message):
+            stats.bartlett(xp.asarray([1.]))
+
+    def test_result_attributes(self, xp):
+        args = [g1, g2, g3, g4, g5, g6, g7, g8, g9, g10]
+        args = [xp.asarray(arg) for arg in args]
+        res = stats.bartlett(*args)
+        attributes = ('statistic', 'pvalue')
+        check_named_results(res, attributes, xp=xp)
+
+    @pytest.mark.filterwarnings("ignore:invalid value encountered")  # Dask
+    def test_empty_arg(self, xp):
+        args = (g1, g2, g3, g4, g5, g6, g7, g8, g9, g10, [])
+        args = [xp.asarray(arg) for arg in args]
+
+        with eager_warns(SmallSampleWarning, match=too_small_1d_not_omit, xp=xp):
+            res = stats.bartlett(*args)
+
+        NaN = xp.asarray(xp.nan)
+        xp_assert_equal(res.statistic, NaN)
+        xp_assert_equal(res.pvalue, NaN)
+
+    def test_negative_pvalue_gh21152(self, xp):
+        a = xp.asarray([10.1, 10.2, 10.3, 10.4], dtype=xp.float32)
+        b = xp.asarray([10.15, 10.25, 10.35, 10.45], dtype=xp.float32)
+        c = xp.asarray([10.05, 10.15, 10.25, 10.35], dtype=xp.float32)
+        res = stats.bartlett(a, b, c)
+        assert xp.all(res.statistic >= 0)
+
+
+@make_xp_test_case(stats.levene)
+class TestLevene:
+
+    def test_data(self, xp):
+        # https://www.itl.nist.gov/div898/handbook/eda/section3/eda35a.htm
+        args = [g1, g2, g3, g4, g5, g6, g7, g8, g9, g10]
+        args = [xp.asarray(arg) for arg in args]
+        W, pval = stats.levene(*args)
+        xp_assert_close(W, xp.asarray(1.7059176930008939))
+        xp_assert_close(pval, xp.asarray(0.0990829755522))
+
+    def test_mean(self, xp):
+        # numbers from R: leveneTest in package car
+        args = [g1, g2, g3, g4, g5, g6, g7, g8, g9, g10]
+        args = [xp.asarray(arg) for arg in args]
+        W, pval = stats.levene(*args, center="mean")
+        xp_assert_close(W, xp.asarray(2.15945985647285))
+        xp_assert_close(pval, xp.asarray(0.032236826559783))
+
+    def test_trimmed1(self, xp):
+        # Test that center='trimmed' gives the same result as center='mean'
+        # when proportiontocut=0.
+        args = (xp.asarray(g1), xp.asarray(g2), xp.asarray(g3))
+        W1, pval1 = stats.levene(*args, center='mean')
+        W2, pval2 = stats.levene(*args, center='trimmed', proportiontocut=0.0)
+        xp_assert_close(W1, W2)
+        xp_assert_close(pval1, pval2)
+
+    def test_trimmed2(self, xp):
+        # numbers from R: leveneTest in package car
+        args = [g1, g2, g3, g4, g5, g6, g7, g8, g9, g10]
+        args = [xp.asarray(arg) for arg in args]
+        W, pval = stats.levene(*args, center="trimmed", proportiontocut=0.25)
+        xp_assert_close(W, xp.asarray(2.07712845686874))
+        xp_assert_close(pval, xp.asarray(0.0397269688035377))
+
+    def test_equal_mean_median(self, xp):
+        x = np.linspace(-1, 1, 21)
+        rng = np.random.default_rng(4058827756)
+        x2 = rng.permutation(x)
+        y = x**3
+        x, x2, y = xp.asarray(x), xp.asarray(x2), xp.asarray(y)
+        W1, pval1 = stats.levene(x, y, center='mean')
+        W2, pval2 = stats.levene(x2, y, center='median')
+        xp_assert_close(W1, W2)
+        xp_assert_close(pval1, pval2)
+
+    def test_bad_center_value(self, xp):
+        x = xp.linspace(-1, 1, 21)
+        message = "center must be 'mean', 'median' or 'trimmed'."
+        with pytest.raises(ValueError, match=message):
+            stats.levene(x, x, center='trim')
+
+    def test_too_few_args(self, xp):
+        message = "Must provide at least two samples."
+        with pytest.raises(ValueError, match=message):
+            stats.levene(xp.asarray([1]))
+
+    def test_result_attributes(self, xp):
+        args = [g1, g2, g3, g4, g5, g6, g7, g8, g9, g10]
+        args = [xp.asarray(arg) for arg in args]
+        res = stats.levene(*args)
+        attributes = ('statistic', 'pvalue')
+        check_named_results(res, attributes, xp=xp)
+
+
+@make_xp_test_case(stats.binomtest)
+class TestBinomTest:
+    """Tests for stats.binomtest."""
+
+    # Expected results here are from R binom.test, e.g.
+    # options(digits=16)
+    # binom.test(484, 967, p=0.48)
+    @skip_xp_backends("jax.numpy", reason="'two-sided' is incompatible with JAX")
+    @pytest.mark.parametrize("k, n, p, ref, rtol",
+                             # aarch64 observed rtol: 1.5e-11
+                             [(10079999, 21000000, 0.48, 1.0, 1e-10),
+                              (10079990, 21000000, 0.48, 0.9966892187965, 1e-10),
+                              (10080009, 21000000, 0.48, 0.9970377203856, 1e-10),
+                              (10080017, 21000000, 0.48, 0.9940754817328, 1e-9)])
+    def test_two_sided_pvalues1(self, k, n, p, ref, rtol, xp):
+        # `tol` could be stricter on most architectures, but the value
+        # here is limited by accuracy of `binom.cdf` for large inputs on
+        # Linux_Python_37_32bit_full and aarch64
+        dtype = xp.float64  # because this tests precision
+        res = stats.binomtest(k, n, xp.asarray(p, dtype=dtype))
+        xp_assert_close(res.pvalue, xp.asarray(ref, dtype=dtype), rtol=rtol)
+
+    @skip_xp_backends("jax.numpy", reason="'two-sided' is incompatible with JAX")
+    @pytest.mark.parametrize("k, n, p, ref, rtol",
+                             # no aarch64 failure with 1e-15, preemptive bump
+                             [(9, 21, 0.48, 0.6689672431939, 1e-10),
+                              (4, 21, 0.48, 0.0081395634521, 1e-10),
+                              (11, 21, 0.48, 0.8278629664608, 1e-10),
+                              (7, 21, 0.48, 0.1966772901718, 1e-10),
+                              (3, 10, 0.5, 0.34375, 1e-10),
+                              (2, 2, 0.4, 0.16, 1e-10),
+                              (2, 4, 0.3, 0.5884, 1e-10)])
+    def test_two_sided_pvalues2(self, k, n, p, ref, rtol, xp):
+        dtype = xp.float64  # because this tests precision
+        res = stats.binomtest(k, n, xp.asarray(p, dtype=dtype))
+        xp_assert_close(res.pvalue, xp.asarray(ref, dtype=dtype), rtol=rtol)
+
+    @skip_xp_backends("jax.numpy", reason="'two-sided' is incompatible with JAX")
+    @pytest.mark.parametrize("k, n, p, ref, rtol",
+                             # no aarch64 failure with 1e-15, preemptive bump
+                             [(484, 967, 0.5, 1.0, 1e-10),
+                              (3, 47, 3/47, 1.0, 1e-10),
+                              (13, 46, 13/46, 1.0, 1e-10),
+                              (15, 44, 15/44, 1.0, 1e-10),
+                              (7, 13, 0.5, 1.0, 1e-10),
+                              (6, 11, 0.5, 1.0, 1e-10)])
+    def test_edge_cases(self, k, n, p, ref, rtol, xp):
+        dtype = xp.float64
+        res = stats.binomtest(k, n, xp.asarray(p, dtype=dtype))
+        xp_assert_close(res.pvalue, xp.asarray(ref, dtype=dtype), rtol=rtol)
+
+    # tests private function, so leave NumPy-only
+    def test_binary_srch_for_binom_tst(self):
+        # Test that old behavior of binomtest is maintained
+        # by the new binary search method in cases where d
+        # exactly equals the input on one side.
+        n = 10
+        p = 0.5
+        k = 3
+        # First test for the case where k > mode of PMF
+        i = np.arange(np.ceil(p * n), n+1)
+        d = stats.binom.pmf(k, n, p)
+        # Old way of calculating y, probably consistent with R.
+        y1 = np.sum(stats.binom.pmf(i, n, p) <= d, axis=0)
+        # New way with binary search.
+        ix = _binary_search_for_binom_tst(lambda x1:
+                                          -stats.binom.pmf(x1, n, p),
+                                          -d, np.ceil(p * n), n, xp=np)
+        y2 = n - ix + int(d == stats.binom.pmf(ix, n, p))
+        assert_allclose(y1, y2, rtol=1e-9)
+        # Now test for the other side.
+        k = 7
+        i = np.arange(np.floor(p * n) + 1)
+        d = stats.binom.pmf(k, n, p)
+        # Old way of calculating y.
+        y1 = np.sum(stats.binom.pmf(i, n, p) <= d, axis=0)
+        # New way with binary search.
+        ix = _binary_search_for_binom_tst(lambda x1:
+                                          stats.binom.pmf(x1, n, p),
+                                          d, 0, np.floor(p * n), xp=np)
+        y2 = ix + 1
+        assert_allclose(y1, y2, rtol=1e-9)
+
+    # Expected results here are from R 3.6.2 binom.test
+    @skip_xp_backends("array_api_strict", reason="needs find_root")
+    @skip_xp_backends("jax.numpy", reason="needs find_root")
+    @pytest.mark.parametrize('alternative, pval, ci_low, ci_high',
+                             [('less', 0.148831050443,
+                               0.0, 0.2772002496709138),
+                              ('greater', 0.9004695898947,
+                               0.1366613252458672, 1.0),
+                              ('two-sided', 0.2983720970096,
+                               0.1266555521019559, 0.2918426890886281)])
+    def test_confidence_intervals1(self, alternative, pval, ci_low, ci_high, xp):
+        dtype = xp.float64
+        res = stats.binomtest(20, n=100, p=xp.asarray(0.25, dtype=dtype),
+                              alternative=alternative)
+        xp_assert_close(res.pvalue, xp.asarray(pval, dtype=dtype), rtol=1e-12)
+        xp_assert_equal(res.statistic, xp.asarray(0.2, dtype=dtype))
+        ci = res.proportion_ci(confidence_level=0.95)
+        xp_assert_close(ci.low, xp.asarray(ci_low, dtype=dtype), rtol=1e-12)
+        xp_assert_close(ci.high, xp.asarray(ci_high, dtype=dtype), rtol=1e-12)
+
+    # Expected results here are from R 3.6.2 binom.test.
+    @skip_xp_backends("array_api_strict", reason="needs find_root")
+    @skip_xp_backends("jax.numpy", reason="needs find_root")
+    @pytest.mark.parametrize('alternative, pval, ci_low, ci_high',
+                             [('less',
+                               0.005656361, 0.0, 0.1872093),
+                              ('greater',
+                               0.9987146, 0.008860761, 1.0),
+                              ('two-sided',
+                               0.01191714, 0.006872485, 0.202706269)])
+    def test_confidence_intervals2(self, alternative, pval, ci_low, ci_high, xp):
+        dtype = xp.float64
+        res = stats.binomtest(3, n=50, p=xp.asarray(0.2, dtype=dtype),
+                              alternative=alternative)
+        xp_assert_close(res.pvalue, xp.asarray(pval, dtype=dtype), rtol=1e-6)
+        xp_assert_equal(res.statistic, xp.asarray(0.06, dtype=dtype))
+        ci = res.proportion_ci(confidence_level=0.99)
+        xp_assert_close(ci.low, xp.asarray(ci_low, dtype=dtype), rtol=1e-6)
+        xp_assert_close(ci.high, xp.asarray(ci_high, dtype=dtype), rtol=1e-6)
+
+    # Expected results here are from R 3.6.2 binom.test.
+    @skip_xp_backends("array_api_strict", reason="needs find_root")
+    @skip_xp_backends("jax.numpy", reason="needs find_root")
+    @pytest.mark.parametrize('alternative, pval, ci_high',
+                             [('less', 0.05631351, 0.2588656),
+                              ('greater', 1.0, 1.0),
+                              ('two-sided', 0.07604122, 0.3084971)])
+    def test_confidence_interval_exact_k0(self, alternative, pval, ci_high, xp):
+        # Test with k=0, n = 10.
+        dtype = xp.float64
+        res = stats.binomtest(0, n=10, p=xp.asarray(0.25, dtype=dtype),
+                              alternative=alternative)
+        xp_assert_close(res.pvalue, xp.asarray(pval, dtype=dtype), rtol=1e-6)
+        ci = res.proportion_ci(confidence_level=0.95)
+        xp_assert_equal(ci.low, xp.asarray(0.0, dtype=dtype))
+        xp_assert_close(ci.high, xp.asarray(ci_high, dtype=dtype), rtol=1e-6)
+
+    # Expected results here are from R 3.6.2 binom.test.
+    @skip_xp_backends("array_api_strict", reason="needs find_root")
+    @skip_xp_backends("jax.numpy", reason="needs find_root")
+    @pytest.mark.parametrize('alternative, pval, ci_low',
+                             [('less', 1.0, 0.0),
+                              ('greater', 9.536743e-07, 0.7411344),
+                              ('two-sided', 9.536743e-07, 0.6915029)])
+    def test_confidence_interval_exact_k_is_n(self, alternative, pval, ci_low, xp):
+        # Test with k = n = 10.
+        dtype = xp.float64
+        res = stats.binomtest(10, n=10, p=xp.asarray(0.25, dtype=dtype),
+                              alternative=alternative)
+        xp_assert_close(res.pvalue, xp.asarray(pval, dtype=dtype), rtol=1e-6)
+        ci = res.proportion_ci(confidence_level=0.95)
+        xp_assert_equal(ci.high, xp.asarray(1.0, dtype=dtype))
+        xp_assert_close(ci.low, xp.asarray(ci_low, dtype=dtype), rtol=1e-6)
+
+    # Expected results are from the prop.test function in R 3.6.2.
+    @skip_xp_backends("jax.numpy", reason="'two-sided' is incompatible with JAX")
+    @pytest.mark.parametrize(
+        'k, alternative, corr, conf, ci_low, ci_high',
+        [[3, 'two-sided', True, 0.95, 0.08094782, 0.64632928],
+         [3, 'two-sided', True, 0.99, 0.0586329, 0.7169416],
+         [3, 'two-sided', False, 0.95, 0.1077913, 0.6032219],
+         [3, 'two-sided', False, 0.99, 0.07956632, 0.6799753],
+         [3, 'less', True, 0.95, 0.0, 0.6043476],
+         [3, 'less', True, 0.99, 0.0, 0.6901811],
+         [3, 'less', False, 0.95, 0.0, 0.5583002],
+         [3, 'less', False, 0.99, 0.0, 0.6507187],
+         [3, 'greater', True, 0.95, 0.09644904, 1.0],
+         [3, 'greater', True, 0.99, 0.06659141, 1.0],
+         [3, 'greater', False, 0.95, 0.1268766, 1.0],
+         [3, 'greater', False, 0.99, 0.08974147, 1.0],
+
+         [0, 'two-sided', True, 0.95, 0.0, 0.3445372],
+         [0, 'two-sided', False, 0.95, 0.0, 0.2775328],
+         [0, 'less', True, 0.95, 0.0, 0.2847374],
+         [0, 'less', False, 0.95, 0.0, 0.212942],
+         [0, 'greater', True, 0.95, 0.0, 1.0],
+         [0, 'greater', False, 0.95, 0.0, 1.0],
+
+         [10, 'two-sided', True, 0.95, 0.6554628, 1.0],
+         [10, 'two-sided', False, 0.95, 0.7224672, 1.0],
+         [10, 'less', True, 0.95, 0.0, 1.0],
+         [10, 'less', False, 0.95, 0.0, 1.0],
+         [10, 'greater', True, 0.95, 0.7152626, 1.0],
+         [10, 'greater', False, 0.95, 0.787058, 1.0]]
+    )
+    def test_ci_wilson_method(self, k, alternative, corr, conf,
+                              ci_low, ci_high, xp):
+        dtype = xp.float64
+        res = stats.binomtest(k, n=10, p=xp.asarray(0.1, dtype=dtype),
+                              alternative=alternative)
+        if corr:
+            method = 'wilsoncc'
+        else:
+            method = 'wilson'
+        ci = res.proportion_ci(confidence_level=conf, method=method)
+        xp_assert_close(ci.low, xp.asarray(ci_low, dtype=dtype), rtol=1e-6)
+        xp_assert_close(ci.high, xp.asarray(ci_high, dtype=dtype), rtol=1e-6)
+
+    @skip_xp_backends("jax.numpy", reason="'two-sided' is incompatible with JAX")
+    def test_estimate_equals_hypothesized_prop(self, xp):
+        # Test the special case where the estimated proportion equals
+        # the hypothesized proportion.  When alternative is 'two-sided',
+        # the p-value is 1.
+        res = stats.binomtest(4, 16, xp.asarray(0.25))
+        xp_assert_equal(res.statistic, xp.asarray(0.25))
+        xp_assert_equal(res.pvalue, xp.asarray(1.0))
+
+    def test_invalid_confidence_level(self, xp):
+        res = stats.binomtest(3, n=10, p=xp.asarray(0.1), alternative='less')
+        message = r"confidence_level \(-1\) must be in the interval"
+        with pytest.raises(ValueError, match=message):
+            res.proportion_ci(confidence_level=-1)
+
+    def test_invalid_ci_method(self, xp):
+        res = stats.binomtest(3, n=10, p=xp.asarray(0.1), alternative='greater')
+        with pytest.raises(ValueError, match=r"method \('plate of shrimp'\) must be"):
+            res.proportion_ci(method="plate of shrimp")
+
+    def test_invalid_alternative(self, xp):
+        with pytest.raises(ValueError, match=r"alternative \('ekki'\) not..."):
+            stats.binomtest(3, n=10, p=xp.asarray(0.1), alternative='ekki')
+
+    def test_alias(self, xp):
+        res = stats.binomtest(3, n=10, p=xp.asarray(0.1), alternative='greater')
+        xp_assert_equal(res.proportion_estimate, res.statistic)
+
+    @pytest.mark.skipif(sys.maxsize <= 2**32, reason="32-bit does not overflow")
+    def test_boost_overflow_raises(self):  # NumPy-specific
+        # Boost.Math error policy should raise exceptions in Python
+        with pytest.raises(OverflowError, match='Error in function...'):
+            stats.binomtest(5, 6, p=sys.float_info.min)
+
+    @pytest.mark.parametrize("k, n, p",
+        [(-1, 10, 0.5), (11, 10, 0.5), (5.5, 10, 0.5), (np.nan, 10, 0.5),
+         (0, 0, 0.5), (5, 10.5, 0.5), (5, np.nan, 0.5),
+         (5, 10, -0.1), (5, 10, 1.1), (5, 10, np.nan)])
+    def test_invalid(self, k, n, p, xp):
+        res = stats.binomtest(k, n, xp.asarray(p), alternative='less')
+        xp_assert_equal(res.statistic, xp.asarray(np.nan))
+        xp_assert_equal(res.pvalue, xp.asarray(np.nan))
+
+    @pytest.mark.parametrize("alternative", ['less', 'greater', 'two-sided'])
+    @pytest.mark.parametrize("method", ['exact', 'wilson', 'wilsoncc'])
+    def test_scalar_0d_in_scalar_out(self, alternative, method):
+        # Tests that scalar / 0-D NumPy array input are equivalent and that both
+        # result in NumPy scalars (as confirmed by xp_assert_equal).
+        res = stats.binomtest(3, 11, 0.4, alternative=alternative)
+        ref = stats.binomtest(np.asarray(3), np.asarray(11), np.asarray(0.4),
+                              alternative=alternative)
+
+        xp_assert_equal(res.statistic, ref.statistic)
+        xp_assert_equal(res.pvalue, ref.pvalue)
+        xp_assert_equal(res.n, ref.n)
+        xp_assert_equal(res.k, ref.k)
+
+        res = res.proportion_ci(method=method)
+        ref = ref.proportion_ci(method=method)
+
+        xp_assert_equal(res.low, ref.low)
+        xp_assert_equal(res.high, ref.high)
+
+    @pytest.mark.parametrize("dtype", [None, 'float32', 'float64'])
+    @pytest.mark.parametrize("alternative", ['less', 'greater', 'two-sided'])
+    @pytest.mark.parametrize("method", ['exact', 'wilson', 'wilsoncc'])
+    def test_dtype(self, dtype, alternative, method, xp):
+        # Tests that output dtype is as expected
+        dtype = dtype if dtype is None else getattr(xp, dtype)
+        k = xp.asarray(3, dtype=dtype)
+        n = xp.asarray(11, dtype=dtype)
+        p = xp.asarray(0.4, dtype=dtype)
+        if is_jax(xp) and alternative=='two-sided':
+            message = "`alternative='two-sided'` is incompatible with JAX arrays."
+            with pytest.raises(ValueError, match=message):
+                stats.binomtest(k, n, p)
+            return
+
+        res = stats.binomtest(k, n, p, alternative=alternative)
+        ref = stats.binomtest(3, 11, 0.4, alternative=alternative)
+
+        xp_assert_close(res.statistic, xp.asarray(float(ref.statistic), dtype=dtype))
+        xp_assert_close(res.pvalue, xp.asarray(float(ref.pvalue), dtype=dtype))
+        xp_assert_close(res.n, xp.asarray(float(ref.n), dtype=dtype))
+        xp_assert_close(res.k, xp.asarray(float(ref.k), dtype=dtype))
+
+        if (is_array_api_strict(xp) or is_jax(xp)) and method == 'exact':
+            # array API strict and JAX don't support exact CI right now
+            return
+
+        res = res.proportion_ci(method=method)
+        ref = ref.proportion_ci(method=method)
+
+        xp_assert_close(res.low, xp.asarray(float(ref.low), dtype=dtype))
+        xp_assert_close(res.high, xp.asarray(float(ref.high), dtype=dtype))
+
+    @pytest.mark.parametrize("shape", [(), (7, 8, 9)])
+    @pytest.mark.parametrize("alternative", ["less", "greater", "two-sided"])
+    @pytest.mark.parametrize("method", ["exact", "wilson", "wilsoncc"])
+    def test_ndarray(self, shape, alternative, method, xp):
+        rng = np.random.default_rng(2150248640)
+        k = rng.integers(-1, 11, size=shape)
+        n = rng.integers(-1, 11, size=shape)
+        p = rng.uniform(-0.1, 1.1, size=shape)
+
+        if is_jax(xp) and alternative=='two-sided':
+            pytest.skip("`alternative='two-sided'` is incompatible with JAX arrays.")
+
+        res = stats.binomtest(xp.asarray(k), xp.asarray(n), xp.asarray(p),
+                              alternative=alternative)
+
+        @np.vectorize(excluded='alternative')
+        def binomtest_1d(k, n, p, alternative):
+            ref = stats.binomtest(k, n, p, alternative=alternative)
+            ci = ref.proportion_ci(method=method)
+            return ref.k, ref.n, ref.statistic, ref.pvalue, ci.low, ci.high
+
+        ref_k, ref_n, ref_statistic, ref_pvalue, ci_low, ci_high = binomtest_1d(
+            k, n, p, alternative)
+        xp_assert_close(res.k, xp.asarray(ref_k))
+        xp_assert_close(res.n, xp.asarray(ref_n))
+        xp_assert_close(res.statistic, xp.asarray(ref_statistic))
+        xp_assert_close(res.pvalue, xp.asarray(ref_pvalue))
+
+        if (is_array_api_strict(xp) or is_jax(xp)) and method == 'exact':
+            # array API strict and JAX don't support exact CI right now
+            return
+
+        ci = res.proportion_ci(method=method)
+        xp_assert_close(ci.low, xp.asarray(ci_low))
+        xp_assert_close(ci.high, xp.asarray(ci_high))
+
+    @skip_xp_backends('jax.numpy', reason="'two-sided' alternative needs root finder")
+    def test_binomtest(self, xp):
+        # precision tests compared to R for ticket:986
+        pp = xp.concat((xp.linspace(0.1, 0.2, 5),
+                        xp.linspace(0.45, 0.65, 5),
+                        xp.linspace(0.85, 0.95, 5)))
+        n = 501
+        x = 450
+        results = [0.0, 0.0, 1.0159969301994141e-304,
+                   2.9752418572150531e-275, 7.7668382922535275e-250,
+                   2.3381250925167094e-099, 7.8284591587323951e-081,
+                   9.9155947819961383e-065, 2.8729390725176308e-050,
+                   1.7175066298388421e-037, 0.0021070691951093692,
+                   0.12044570587262322, 0.88154763174802508, 0.027120993063129286,
+                   2.6102587134694721e-006]
+
+        xp_assert_close(stats.binomtest(x, n, pp).pvalue, xp.asarray(results))
+
+        xp_assert_close(stats.binomtest(50, 100, xp.asarray(0.1)).pvalue,
+                        xp.asarray(5.8320387857343647e-024))
+
+    @skip_xp_backends('jax.numpy', reason="'two-sided' alternative needs root finder")
+    def test_binomtest2(self, xp):
+        # test added for issue #2384
+        res2 = [
+            [1.0, 1.0],
+            [0.5, 1.0, 0.5],
+            [0.25, 1.00, 1.00, 0.25],
+            [0.125, 0.625, 1.000, 0.625, 0.125],
+            [0.0625, 0.3750, 1.0000, 1.0000, 0.3750, 0.0625],
+            [0.03125, 0.21875, 0.68750, 1.00000, 0.68750, 0.21875, 0.03125],
+            [0.015625, 0.125000, 0.453125, 1.000000, 1.000000, 0.453125, 0.125000,
+             0.015625],
+            [0.0078125, 0.0703125, 0.2890625, 0.7265625, 1.0000000, 0.7265625,
+             0.2890625, 0.0703125, 0.0078125],
+            [0.00390625, 0.03906250, 0.17968750, 0.50781250, 1.00000000,
+             1.00000000, 0.50781250, 0.17968750, 0.03906250, 0.00390625],
+            [0.001953125, 0.021484375, 0.109375000, 0.343750000, 0.753906250,
+             1.000000000, 0.753906250, 0.343750000, 0.109375000, 0.021484375,
+             0.001953125]
+        ]
+        for k in range(1, 11):
+            v = xp.arange(k+1, dtype=xp.float64)
+            res1 = stats.binomtest(v, k, 0.5).pvalue
+            xp_assert_close(res1, xp.asarray(res2[k-1], dtype=xp.float64))
+
+    @skip_xp_backends('jax.numpy', reason="'two-sided' alternative needs root finder")
+    def test_binomtest3(self, xp):
+        # test added for issue #2384
+        # test when x == n*p and neighbors
+        v = xp.arange(1., 11.)[:, xp.newaxis]
+        k = xp.arange(2., 11.)
+        shape = (v.shape[0], k.shape[0])
+
+        res3 = stats.binomtest(v, v*k, 1./k).pvalue
+        xp_assert_close(res3, xp.ones(shape))
+
+        # > bt=c()
+        # > for(i in as.single(1:10)) {
+        # +     for(k in as.single(2:10)) {
+        # +         bt = c(bt, binom.test(i-1, k*i,(1/k))$p.value);
+        # +         print(c(i+1, k*i,(1/k)))
+        # +     }
+        # + }
+        binom_testm1 = xp.asarray([
+             0.5, 0.5555555555555556, 0.578125, 0.5904000000000003,
+             0.5981224279835393, 0.603430543396034, 0.607304096221924,
+             0.610255656871054, 0.612579511000001, 0.625, 0.670781893004115,
+             0.68853759765625, 0.6980101120000006, 0.703906431368616,
+             0.70793209416498, 0.7108561134173507, 0.713076544331419,
+             0.714820192935702, 0.6875, 0.7268709038256367, 0.7418963909149174,
+             0.74986110468096, 0.7548015520398076, 0.7581671424768577,
+             0.760607984787832, 0.762459425024199, 0.7639120677676575, 0.7265625,
+             0.761553963657302, 0.774800934828818, 0.7818005980538996,
+             0.78613491480358, 0.789084353140195, 0.7912217659828884,
+             0.79284214559524, 0.794112956558801, 0.75390625, 0.7856929451142176,
+             0.7976688481430754, 0.8039848974727624, 0.807891868948366,
+             0.8105487660137676, 0.812473307174702, 0.8139318233591120,
+             0.815075399104785, 0.7744140625, 0.8037322594985427,
+             0.814742863657656, 0.8205425178645808, 0.8241275984172285,
+             0.8265645374416, 0.8283292196088257, 0.829666291102775,
+             0.8307144686362666, 0.7905273437499996, 0.8178712053954738,
+             0.828116983756619, 0.833508948940494, 0.8368403871552892,
+             0.839104213210105, 0.840743186196171, 0.84198481438049,
+             0.8429580531563676, 0.803619384765625, 0.829338573944648,
+             0.8389591907548646, 0.84401876783902, 0.84714369697889,
+             0.8492667010581667, 0.850803474598719, 0.851967542858308,
+             0.8528799045949524, 0.8145294189453126, 0.838881732845347,
+             0.847979024541911, 0.852760894015685, 0.8557134656773457,
+             0.8577190131799202, 0.85917058278431, 0.860270010472127,
+             0.861131648404582, 0.823802947998047, 0.846984756807511,
+             0.855635653643743, 0.860180994825685, 0.86298688573253,
+             0.864892525675245, 0.866271647085603, 0.867316125625004,
+             0.8681346531755114
+            ])
+
+        # > bt=c()
+        # > for(i in as.single(1:10)) {
+        # +     for(k in as.single(2:10)) {
+        # +         bt = c(bt, binom.test(i+1, k*i,(1/k))$p.value);
+        # +         print(c(i+1, k*i,(1/k)))
+        # +     }
+        # + }
+
+        binom_testp1 = xp.asarray([
+             0.5, 0.259259259259259, 0.26171875, 0.26272, 0.2632244513031551,
+             0.2635138663069203, 0.2636951804161073, 0.2638162407564354,
+             0.2639010709000002, 0.625, 0.4074074074074074, 0.42156982421875,
+             0.4295746560000003, 0.43473045988554, 0.4383309503172684,
+             0.4409884859402103, 0.4430309389962837, 0.444649849401104, 0.6875,
+             0.4927602499618962, 0.5096031427383425, 0.5189636628480,
+             0.5249280070771274, 0.5290623300865124, 0.5320974248125793,
+             0.5344204730474308, 0.536255847400756, 0.7265625, 0.5496019313526808,
+             0.5669248746708034, 0.576436455045805, 0.5824538812831795,
+             0.5866053321547824, 0.589642781414643, 0.5919618019300193,
+             0.593790427805202, 0.75390625, 0.590868349763505, 0.607983393277209,
+             0.617303847446822, 0.623172512167948, 0.627208862156123,
+             0.6301556891501057, 0.632401894928977, 0.6341708982290303,
+             0.7744140625, 0.622562037497196, 0.639236102912278, 0.648263335014579,
+             0.65392850011132, 0.657816519817211, 0.660650782947676,
+             0.662808780346311, 0.6645068560246006, 0.7905273437499996,
+             0.6478843304312477, 0.6640468318879372, 0.6727589686071775,
+             0.6782129857784873, 0.681950188903695, 0.684671508668418,
+             0.686741824999918, 0.688369886732168, 0.803619384765625,
+             0.668716055304315, 0.684360013879534, 0.6927642396829181,
+             0.6980155964704895, 0.701609591890657, 0.7042244320992127,
+             0.7062125081341817, 0.707775152962577, 0.8145294189453126,
+             0.686243374488305, 0.7013873696358975, 0.709501223328243,
+             0.714563595144314, 0.718024953392931, 0.7205416252126137,
+             0.722454130389843, 0.723956813292035, 0.823802947998047,
+             0.701255953767043, 0.715928221686075, 0.723772209289768,
+             0.7286603031173616, 0.7319999279787631, 0.7344267920995765,
+             0.736270323773157, 0.737718376096348
+            ])
+
+        k, v = xp.asarray(k, dtype=xp.float64), xp.asarray(v, dtype=xp.float64)
+        binom_testp1 = xp.reshape(xp.asarray(binom_testp1, dtype=xp.float64), shape)
+        binom_testm1 = xp.reshape(xp.asarray(binom_testm1, dtype=xp.float64), shape)
+
+        res4_p1 = stats.binomtest(v+1, v*k, 1./k).pvalue
+        res4_m1 = stats.binomtest(v-1, v*k, 1./k).pvalue
+
+        xp_assert_close(res4_p1, binom_testp1)
+        xp_assert_close(res4_m1, binom_testm1)
+
+
+@make_xp_test_case(stats.fligner)
+class TestFligner:
+
+    def _perturb(self, g, rng=124987234782812):
+        # g arrays have ties to which statistic is very sensitive; break them
+        rng = np.random.default_rng(rng)
+        return (np.asarray(g) + 1e-10 * rng.standard_normal(len(g))).tolist()
+
+    @pytest.mark.parametrize('dtype', [None, 'float32', 'float64'])
+    def test_data(self, dtype, xp):
+        # numbers from R: fligner.test in package stats
+        dtype = xp_default_dtype(xp) if dtype is None else getattr(xp, dtype)
+        x1 = xp.arange(5, dtype=dtype)
+        res = stats.fligner(x1, x1**2)
+        ref = (xp.asarray(3.2282229927203536, dtype=dtype),
+               xp.asarray(0.072379187848207877, dtype=dtype))
+        xp_assert_close(res[0], ref[0])
+        xp_assert_close(res[1], ref[1])
+
+    def test_trimmed1(self, xp):
+        # Perturb input to break ties in the transformed data
+        # See https://github.com/scipy/scipy/pull/8042 for more details
+        rng = np.random.default_rng(9952379681)
+        g1_ = xp.asarray(self._perturb(g1, rng=rng))
+        g2_ = xp.asarray(self._perturb(g2, rng=rng))
+        g3_ = xp.asarray(self._perturb(g3, rng=rng))
+        # Test that center='trimmed' gives the same result as center='mean'
+        # when proportiontocut=0.
+        Xsq1, pval1 = stats.fligner(g1_, g2_, g3_, center='mean')
+        Xsq2, pval2 = stats.fligner(g1_, g2_, g3_, center='trimmed',
+                                    proportiontocut=0.0)
+        xp_assert_close(Xsq1, Xsq2)
+        xp_assert_close(pval1, pval2)
+
+    @skip_xp_backends(np_only=True, reason="inconsistent tie-breaking across backends")
+    def test_trimmed_nonregression(self, xp):
+        # This is a non-regression test
+        # Expected results are *not* from an external gold standard,
+        # we're just making sure the results remain consistent
+        # in the future in case of changes
+        args = [g1, g2, g3, g4, g5, g6, g7, g8, g9, g10]
+        args = [xp.asarray(arg, dtype=xp.float64) for arg in args]
+        W, pval = stats.fligner(*args, center="trimmed", proportiontocut=0.25)
+        xp_assert_close(W, xp.asarray(15.953569890010614), rtol=5e-14)
+        xp_assert_close(pval, xp.asarray(0.06785752327432863), rtol=5e-14)
+
+    def test_trimmed_consistency(self, xp):
+        # Tests for consistency across multiple backends when ties are broken
+        rng = np.random.default_rng(4839206199)
+        args = [g1, g2, g3, g4, g5, g6, g7, g8, g9, g10]
+        args = [self._perturb(arg, rng=rng) for arg in args]
+        ref = stats.fligner(*args, center="trimmed", proportiontocut=0.25)
+        args = [xp.asarray(arg, dtype=xp.float64) for arg in args]
+        res = stats.fligner(*args, center="trimmed", proportiontocut=0.25)
+        xp_assert_close(res.statistic, xp.asarray(ref.statistic), rtol=5e-14)
+        xp_assert_close(res.pvalue, xp.asarray(ref.pvalue), rtol=5e-14)
+
+    def test_bad_center_value(self, xp):
+        x = xp.linspace(-1, 1, 21)
+        message = "center must be 'mean', 'median' or 'trimmed'."
+        with pytest.raises(ValueError, match=message):
+            stats.fligner(x, x, center='trim')
+
+    def test_bad_num_args(self, xp):
+        # Too few args raises ValueError.
+        message = "Must provide at least two samples."
+        with pytest.raises(ValueError, match=message):
+            stats.fligner(xp.asarray([1, 2]))
+
+    def test_empty_arg(self, xp):
+        x = xp.arange(5.)
+        with pytest.warns(SmallSampleWarning, match=too_small_1d_not_omit):
+            res = stats.fligner(x, x**2, xp.asarray([]))
+        xp_assert_equal(res.statistic, xp.asarray(xp.nan))
+        xp_assert_equal(res.pvalue, xp.asarray(xp.nan))
+
+
+def mood_cases_with_ties():
+    # Generate random `x` and `y` arrays with ties both between and within the
+    # samples. Expected results are (statistic, pvalue) from SAS.
+    expected_results = [(-1.76658511464992, .0386488678399305),
+                        (-.694031428192304, .2438312498647250),
+                        (-1.15093525352151, .1248794365836150)]
+    seeds = [23453254, 1298352315, 987234597]
+    for si, seed in enumerate(seeds):
+        rng = np.random.default_rng(seed)
+        xy = rng.random(100)
+        # Generate random indices to make ties
+        tie_ind = rng.integers(low=0, high=99, size=5)
+        # Generate a random number of ties for each index.
+        num_ties_per_ind = rng.integers(low=1, high=5, size=5)
+        # At each `tie_ind`, mark the next `n` indices equal to that value.
+        for i, n in zip(tie_ind, num_ties_per_ind):
+            for j in range(i + 1, i + n):
+                xy[j] = xy[i]
+        # scramble order of xy before splitting into `x, y`
+        rng.shuffle(xy)
+        x, y = np.split(xy, 2)
+        yield x, y, 'less', *expected_results[si]
+
+
+@make_xp_test_case(stats.mood)
+class TestMood:
+    @pytest.mark.parametrize("x,y,alternative,stat_expect,p_expect",
+                             list(mood_cases_with_ties()))
+    def test_against_SAS(self, x, y, alternative, stat_expect, p_expect, xp):
+        """
+        Example code used to generate SAS output:
+        DATA myData;
+        INPUT X Y;
+        CARDS;
+        1 0
+        1 1
+        1 2
+        1 3
+        1 4
+        2 0
+        2 1
+        2 4
+        2 9
+        2 16
+        ods graphics on;
+        proc npar1way mood data=myData ;
+           class X;
+            ods output  MoodTest=mt;
+        proc contents data=mt;
+        proc print data=mt;
+          format     Prob1 17.16 Prob2 17.16 Statistic 17.16 Z 17.16 ;
+            title "Mood Two-Sample Test";
+        proc print data=myData;
+            title "Data for above results";
+          run;
+        """
+        x, y = xp.asarray(x.tolist()), xp.asarray(y.tolist())
+        statistic, pvalue = stats.mood(x, y, alternative=alternative)
+        xp_assert_close(statistic, xp.asarray(stat_expect), atol=1e-16)
+        xp_assert_close(pvalue, xp.asarray(p_expect), atol=1e-16)
+
+    @pytest.mark.parametrize("dtype", [None, 'float32', 'float64'])
+    @pytest.mark.parametrize("alternative, expected",
+                             [('two-sided', (1.019938533549930,
+                                             .3077576129778760)),
+                              ('less', (1.019938533549930,
+                                        1 - .1538788064889380)),
+                              ('greater', (1.019938533549930,
+                                           .1538788064889380))])
+    def test_against_SAS_2(self, dtype, alternative, expected, xp):
+        # Code to run in SAS in above function
+        dtype = xp_default_dtype(xp) if dtype is None else getattr(xp, dtype)
+        x = [111, 107, 100, 99, 102, 106, 109, 108, 104, 99,
+             101, 96, 97, 102, 107, 113, 116, 113, 110, 98]
+        y = [107, 108, 106, 98, 105, 103, 110, 105, 104, 100,
+             96, 108, 103, 104, 114, 114, 113, 108, 106, 99]
+        x, y = xp.asarray(x, dtype=dtype), xp.asarray(y, dtype=dtype)
+        res = stats.mood(x, y, alternative=alternative)
+        xp_assert_close(res.statistic, xp.asarray(expected[0], dtype=dtype))
+        xp_assert_close(res.pvalue, xp.asarray(expected[1], dtype=dtype))
+
+    def test_mood_order_of_args(self, xp):
+        # z should change sign when the order of arguments changes, pvalue
+        # should not change
+        rng = np.random.default_rng(4058827756)
+        x1 = xp.asarray(rng.standard_normal((10, 1)))
+        x2 = xp.asarray(rng.standard_normal((15, 1)))
+        z1, p1 = stats.mood(x1, x2)
+        z2, p2 = stats.mood(x2, x1)
+        xp_assert_close(z2, -z1)
+        xp_assert_close(p2, p1)
+
+    def test_mood_with_axis_none(self, xp):
+        # Test with axis = None, compare with results from R
+        x1 = [-0.626453810742332, 0.183643324222082, -0.835628612410047,
+              1.59528080213779, 0.329507771815361, -0.820468384118015,
+              0.487429052428485, 0.738324705129217, 0.575781351653492,
+              -0.305388387156356, 1.51178116845085, 0.389843236411431,
+              -0.621240580541804, -2.2146998871775, 1.12493091814311,
+              -0.0449336090152309, -0.0161902630989461, 0.943836210685299,
+              0.821221195098089, 0.593901321217509]
+
+        x2 = [-0.896914546624981, 0.184849184646742, 1.58784533120882,
+              -1.13037567424629, -0.0802517565509893, 0.132420284381094,
+              0.707954729271733, -0.23969802417184, 1.98447393665293,
+              -0.138787012119665, 0.417650750792556, 0.981752777463662,
+              -0.392695355503813, -1.03966897694891, 1.78222896030858,
+              -2.31106908460517, 0.878604580921265, 0.035806718015226,
+              1.01282869212708, 0.432265154539617, 2.09081920524915,
+              -1.19992581964387, 1.58963820029007, 1.95465164222325,
+              0.00493777682814261, -2.45170638784613, 0.477237302613617,
+              -0.596558168631403, 0.792203270299649, 0.289636710177348]
+
+        x1 = xp.reshape(xp.asarray(x1), (10, 2))
+        x2 = xp.reshape(xp.asarray(x2), (15, 2))
+        res = stats.mood(x1, x2, axis=None)
+        xp_assert_close(res.statistic, xp.asarray(-1.31716607555))
+        xp_assert_close(res.pvalue, xp.asarray(0.18778296257))
+
+    @pytest.mark.parametrize('rng_method, args', [('standard_normal', tuple()),
+                                                  ('integers', (8,))])
+    def test_mood_2d(self, rng_method, args, xp):
+        # Test if the results of mood test in 2-D vectorized call are consistent
+        # with result when looping over the slices.
+        ny = 5
+        rng = np.random.default_rng(3602349075)
+        rng_method = getattr(rng, rng_method)
+        x1 = rng_method(*args, size=(10, ny))
+        x2 = rng_method(*args, size=(15, ny))
+        dtype = xp.float64
+        res = stats.mood(xp.asarray(x1, dtype=dtype), xp.asarray(x2, dtype=dtype))
+
+        for j in range(ny):
+            ref = stats.mood(x1[:, j], x2[:, j])
+            xp_assert_close(res.statistic[j], xp.asarray(ref.statistic))
+            xp_assert_close(res.pvalue[j], xp.asarray(ref.pvalue))
+
+        # inverse order of dimensions
+        x1 = x1.transpose()
+        x2 = x2.transpose()
+        res = stats.mood(xp.asarray(x1, dtype=dtype), xp.asarray(x2, dtype=dtype),
+                         axis=1)
+
+        for i in range(ny):
+            # check axis handling is self consistent
+            ref = stats.mood(x1[i, :], x2[i, :])
+            xp_assert_close(res.statistic[i], xp.asarray(ref.statistic), atol=1e-14)
+            xp_assert_close(res.pvalue[i], xp.asarray(ref.pvalue))
+
+    @pytest.mark.parametrize('rng_method, args', [('standard_normal', tuple()),
+                                                  ('integers', (8,))])
+    def test_mood_3d(self, rng_method, args, xp):
+        shape = (10, 5, 6)
+        rng = np.random.default_rng(3602349075)
+        rng_method = getattr(rng, rng_method)
+        x1 = xp.asarray(rng_method(*args, size=shape))
+        x2 = xp.asarray(rng_method(*args, size=shape))
+
+        for axis in range(3):
+            res = stats.mood(x1, x2, axis=axis)
+            # Tests that result for 3-D arrays is equal to that for the
+            # same calculation on a set of 1-D arrays taken from the
+            # 3-D array
+            axes_idx = ([1, 2], [0, 2], [0, 1])  # the two axes != axis
+            for i in range(shape[axes_idx[axis][0]]):
+                for j in range(shape[axes_idx[axis][1]]):
+                    if axis == 0:
+                        slice1 = x1[:, i, j]
+                        slice2 = x2[:, i, j]
+                    elif axis == 1:
+                        slice1 = x1[i, :, j]
+                        slice2 = x2[i, :, j]
+                    else:
+                        slice1 = x1[i, j, :]
+                        slice2 = x2[i, j, :]
+
+                    ref = stats.mood(slice1, slice2)
+                    xp_assert_close(res.statistic[i, j], ref.statistic, atol=1e-15)
+                    xp_assert_close(res.pvalue[i, j], ref.pvalue)
+
+    def test_mood_bad_arg(self, xp):
+        # Warns when the sum of the lengths of the args is less than 3
+        with eager_warns(SmallSampleWarning, match=too_small_1d_not_omit, xp=xp):
+            res = stats.mood(xp.asarray([1.]), xp.asarray([]))
+            xp_assert_equal(res.statistic, xp.asarray(np.nan))
+            xp_assert_equal(res.pvalue, xp.asarray(np.nan))
+
+    @pytest.mark.parametrize("dtype", [None, 'float32', 'float64'])
+    def test_mood_alternative(self, dtype, xp):
+        dtype = xp_default_dtype(xp) if dtype is None else getattr(xp, dtype)
+
+        rng = np.random.RandomState(0)
+        x = stats.norm.rvs(scale=0.75, size=100, random_state=rng)
+        y = stats.norm.rvs(scale=1.25, size=100, random_state=rng)
+        x, y = xp.asarray(x, dtype=dtype), xp.asarray(y, dtype=dtype)
+
+        stat1, p1 = stats.mood(x, y, alternative='two-sided')
+        stat2, p2 = stats.mood(x, y, alternative='less')
+        stat3, p3 = stats.mood(x, y, alternative='greater')
+
+        assert stat1 == stat2 == stat3
+        xp_assert_close(p1, xp.asarray(0., dtype=dtype), atol=1e-7)
+        xp_assert_close(p2, xp.asarray(p1/2, dtype=dtype))
+        xp_assert_close(p3, xp.asarray(1 - p1/2, dtype=dtype))
+
+        with pytest.raises(ValueError, match="`alternative` must be..."):
+            stats.mood(x, y, alternative='ekki-ekki')
+
+
+class TestProbplot:
+
+    def test_basic(self):
+        x = stats.norm.rvs(size=20, random_state=12345)
+        osm, osr = stats.probplot(x, fit=False)
+        osm_expected = [-1.8241636, -1.38768012, -1.11829229, -0.91222575,
+                        -0.73908135, -0.5857176, -0.44506467, -0.31273668,
+                        -0.18568928, -0.06158146, 0.06158146, 0.18568928,
+                        0.31273668, 0.44506467, 0.5857176, 0.73908135,
+                        0.91222575, 1.11829229, 1.38768012, 1.8241636]
+        assert_allclose(osr, np.sort(x))
+        assert_allclose(osm, osm_expected)
+
+        res, res_fit = stats.probplot(x, fit=True)
+        res_fit_expected = [1.05361841, 0.31297795, 0.98741609]
+        assert_allclose(res_fit, res_fit_expected)
+
+    def test_sparams_keyword(self):
+        x = stats.norm.rvs(size=100, random_state=123456)
+        # Check that None, () and 0 (loc=0, for normal distribution) all work
+        # and give the same results
+        osm1, osr1 = stats.probplot(x, sparams=None, fit=False)
+        osm2, osr2 = stats.probplot(x, sparams=0, fit=False)
+        osm3, osr3 = stats.probplot(x, sparams=(), fit=False)
+        assert_allclose(osm1, osm2)
+        assert_allclose(osm1, osm3)
+        assert_allclose(osr1, osr2)
+        assert_allclose(osr1, osr3)
+        # Check giving (loc, scale) params for normal distribution
+        osm, osr = stats.probplot(x, sparams=(), fit=False)
+
+    def test_dist_keyword(self):
+        x = stats.norm.rvs(size=20, random_state=12345)
+        osm1, osr1 = stats.probplot(x, fit=False, dist='t', sparams=(3,))
+        osm2, osr2 = stats.probplot(x, fit=False, dist=stats.t, sparams=(3,))
+        assert_allclose(osm1, osm2)
+        assert_allclose(osr1, osr2)
+
+        assert_raises(ValueError, stats.probplot, x, dist='wrong-dist-name')
+        assert_raises(AttributeError, stats.probplot, x, dist=[])
+
+        class custom_dist:
+            """Some class that looks just enough like a distribution."""
+            def ppf(self, q):
+                return stats.norm.ppf(q, loc=2)
+
+        osm1, osr1 = stats.probplot(x, sparams=(2,), fit=False)
+        osm2, osr2 = stats.probplot(x, dist=custom_dist(), fit=False)
+        assert_allclose(osm1, osm2)
+        assert_allclose(osr1, osr2)
+
+    @pytest.mark.skipif(not have_matplotlib, reason="no matplotlib")
+    def test_plot_kwarg(self):
+        fig = plt.figure()
+        fig.add_subplot(111)
+        x = stats.t.rvs(3, size=100, random_state=7654321)
+        res1, fitres1 = stats.probplot(x, plot=plt)
+        plt.close()
+        res2, fitres2 = stats.probplot(x, plot=None)
+        res3 = stats.probplot(x, fit=False, plot=plt)
+        plt.close()
+        res4 = stats.probplot(x, fit=False, plot=None)
+        # Check that results are consistent between combinations of `fit` and
+        # `plot` keywords.
+        assert_(len(res1) == len(res2) == len(res3) == len(res4) == 2)
+        assert_allclose(res1, res2)
+        assert_allclose(res1, res3)
+        assert_allclose(res1, res4)
+        assert_allclose(fitres1, fitres2)
+
+        # Check that a Matplotlib Axes object is accepted
+        fig = plt.figure()
+        ax = fig.add_subplot(111)
+        stats.probplot(x, fit=False, plot=ax)
+        plt.close()
+
+    def test_probplot_bad_args(self):
+        # Raise ValueError when given an invalid distribution.
+        assert_raises(ValueError, stats.probplot, [1], dist="plate_of_shrimp")
+
+    def test_empty(self):
+        assert_equal(stats.probplot([], fit=False),
+                     (np.array([]), np.array([])))
+        assert_equal(stats.probplot([], fit=True),
+                     ((np.array([]), np.array([])),
+                      (np.nan, np.nan, 0.0)))
+
+    def test_array_of_size_one(self):
+        message = "One or more sample arguments is too small..."
+        with (np.errstate(invalid='ignore'),
+              pytest.warns(SmallSampleWarning, match=message)):
+            assert_equal(stats.probplot([1], fit=True),
+                         ((np.array([0.]), np.array([1])),
+                          (np.nan, np.nan, np.nan)))
+
+
+@make_xp_test_case(stats.wilcoxon)
+class TestWilcoxon:
+    def test_wilcoxon_bad_arg(self, xp):
+        # Raise ValueError when two args of different lengths are given or
+        # zero_method is unknown.
+        x = xp.asarray([1, 2])
+        d = xp.asarray([1]*10)
+        message = "`zero_method` must be one of..."
+        with pytest.raises(ValueError, match=message):
+            stats.wilcoxon(x, x, "dummy...")
+        message = "`alternative` must be one of"
+        with pytest.raises(ValueError, match=message):
+            stats.wilcoxon(x, x, alternative="dummy")
+        message = "`method` must be one of..."
+        with pytest.raises(ValueError, match=message):
+            stats.wilcoxon(d, method="xyz")
+
+    def test_zero_diff(self, xp):
+        x = xp.arange(20)
+        # pratt and wilcox do not work if x - y == 0 and method == "asymptotic"
+        # => warning may be emitted and p-value is nan
+        with np.errstate(invalid="ignore"):
+            w, p = stats.wilcoxon(x, x, "wilcox", method="asymptotic")
+            xp_assert_equal(w, xp.asarray(0.0))
+            xp_assert_equal(p, xp.asarray(xp.nan))
+            w, p = stats.wilcoxon(x, x, "pratt", method="asymptotic")
+            xp_assert_equal(w, xp.asarray(0.0))
+            xp_assert_equal(p, xp.asarray(xp.nan))
+        # ranksum is n*(n+1)/2, split in half if zero_method == "zsplit"
+        w, p = stats.wilcoxon(x, x, "zsplit", method="asymptotic")
+        xp_assert_equal(w, xp.asarray(20*21/4))
+        xp_assert_equal(p, xp.asarray(1.0))
+
+    def test_pratt(self, xp):
+        # regression test for gh-6805: p-value matches value from R package
+        # coin (wilcoxsign_test) reported in the issue
+        x = xp.asarray([1, 2, 3, 4])
+        y = xp.asarray([1, 2, 3, 5])
+        res = stats.wilcoxon(x, y, zero_method="pratt", method="asymptotic",
+                             correction=False)
+        xp_assert_close(res.statistic, xp.asarray(0.0))
+        xp_assert_close(res.pvalue, xp.asarray(0.31731050786291415))
+
+    def test_wilcoxon_arg_type(self):
+        # Should be able to accept list as arguments.
+        # Address issue 6070.
+        arr = [1, 2, 3, 0, -1, 3, 1, 2, 1, 1, 2]
+
+        _ = stats.wilcoxon(arr, zero_method="pratt", method="asymptotic")
+        _ = stats.wilcoxon(arr, zero_method="zsplit", method="asymptotic")
+        _ = stats.wilcoxon(arr, zero_method="wilcox", method="asymptotic")
+
+    def test_accuracy_wilcoxon(self, xp):
+        freq = [1, 4, 16, 15, 8, 4, 5, 1, 2]
+        nums = range(-4, 5)
+        x = xp.asarray(np.concatenate([[u] * v for u, v in zip(nums, freq)]))
+        y = xp.zeros_like(x)
+
+        T, p = stats.wilcoxon(x, y, "pratt", method="asymptotic",
+                              correction=False)
+        xp_assert_close(T, xp.asarray(423.))
+        xp_assert_close(p, xp.asarray(0.0031724568006762576))
+
+        T, p = stats.wilcoxon(x, y, "zsplit", method="asymptotic",
+                              correction=False)
+        xp_assert_equal(T, xp.asarray(441.))
+        xp_assert_close(p, xp.asarray(0.0032145343172473055))
+
+        T, p = stats.wilcoxon(x, y, "wilcox", method="asymptotic",
+                              correction=False)
+        xp_assert_equal(T, xp.asarray(327.))
+        xp_assert_close(p, xp.asarray(0.00641346115861))
+
+        # Test the 'correction' option, using values computed in R with:
+        # > options(digits=16)
+        # > wilcox.test(x, y, paired=TRUE, exact=FALSE, correct={FALSE,TRUE})
+        x = xp.asarray([120, 114, 181, 188, 180, 146, 121, 191, 132, 113, 127, 112])
+        y = xp.asarray([133, 143, 119, 189, 112, 199, 198, 113, 115, 121, 142, 187])
+        T, p = stats.wilcoxon(x, y, correction=False, method="asymptotic")
+        xp_assert_equal(T, xp.asarray(34.))
+        xp_assert_close(p, xp.asarray(0.6948866023724735))
+        T, p = stats.wilcoxon(x, y, correction=True, method="asymptotic")
+        xp_assert_equal(T, xp.asarray(34.))
+        xp_assert_close(p, xp.asarray(0.7240816609153895))
+
+    @pytest.mark.parametrize("kwarg",
+        [{"method": "approx"}, {"mode": "approx"}, {"mode": "asymptotic"}])
+    def test_approx_mode(self, kwarg, xp):
+        # Check that `mode` is still an alias of keyword `method`,
+        # and `"approx"` is still an alias of argument `"asymptotic"`
+        x = xp.asarray([3, 5, 23, 7, 243, 58, 98, 2, 8, -3, 9, 11])
+        y = xp.asarray([2, -2, 1, 23, 0, 5, 12, 18, 99, 12, 17, 27])
+        res = stats.wilcoxon(x, y, "wilcox", **kwarg)
+        ref = stats.wilcoxon(x, y, "wilcox", method="asymptotic")
+        xp_assert_equal(res.statistic, ref.statistic)
+        xp_assert_equal(res.pvalue, ref.pvalue)
+
+    def test_wilcoxon_result_attributes(self, xp):
+        x = xp.asarray([120, 114, 181, 188, 180, 146, 121, 191, 132, 113, 127, 112])
+        y = xp.asarray([133, 143, 119, 189, 112, 199, 198, 113, 115, 121, 142, 187])
+        res = stats.wilcoxon(x, y, correction=False, method="asymptotic")
+        attributes = ('statistic', 'pvalue')
+        check_named_results(res, attributes, xp=xp)
+
+    def test_wilcoxon_has_zstatistic(self, xp):
+        rng = np.random.default_rng(89426135444)
+        x, y = rng.random(15), rng.random(15)
+        x, y = xp.asarray(x), xp.asarray(y)
+
+        res = stats.wilcoxon(x, y, method="asymptotic")
+        ref = special.ndtri(res.pvalue/2)
+        xp_assert_close(res.zstatistic, ref)
+
+        if is_jax(xp):
+            return
+
+        res = stats.wilcoxon(x, y, method="exact")
+        assert not hasattr(res, 'zstatistic')
+
+        res = stats.wilcoxon(x, y)
+        assert not hasattr(res, 'zstatistic')
+
+    def test_wilcoxon_tie(self, xp):
+        # Regression test for gh-2391.
+        # Corresponding R code is:
+        #   > result = wilcox.test(rep(0.1, 10), exact=FALSE, correct=FALSE)
+        #   > result$p.value
+        #   [1] 0.001565402258002551
+        #   > result = wilcox.test(rep(0.1, 10), exact=FALSE, correct=TRUE)
+        #   > result$p.value
+        #   [1] 0.00190419504300439
+        d = xp.asarray([0.1] * 10)
+        expected_stat = xp.asarray(0.0)
+
+        stat, p = stats.wilcoxon(d, method="asymptotic", correction=False)
+        expected_p = xp.asarray(0.001565402258002551)
+        xp_assert_equal(stat, expected_stat)
+        xp_assert_close(p, expected_p)
+
+        stat, p = stats.wilcoxon(d, method="asymptotic", correction=True)
+        expected_p = xp.asarray(0.00190419504300439)
+        xp_assert_equal(stat, expected_stat)
+        xp_assert_close(p, expected_p)
+
+    @pytest.mark.parametrize('dtype', [None, 'float32', 'float64'])
+    def test_onesided(self, dtype, xp):
+        # tested against "R version 4.0.3 (2020-10-10)"
+        #
+        # x <- c(125, 115, 130, 140, 140, 115, 140, 125, 140, 135)
+        # y <- c(110, 122, 125, 120, 140, 124, 123, 137, 135, 145)
+        # cfg <- list(x = x, y = y, paired = TRUE, exact = FALSE)
+        # do.call(wilcox.test, c(cfg, list(alternative = "less", correct = FALSE)))
+        # do.call(wilcox.test, c(cfg, list(alternative = "less", correct = TRUE)))
+        # do.call(wilcox.test, c(cfg, list(alternative = "greater", correct = FALSE)))
+        # do.call(wilcox.test, c(cfg, list(alternative = "greater", correct = TRUE)))
+
+        dtype = dtype if dtype is None else getattr(xp, dtype)
+        x = xp.asarray([125, 115, 130, 140, 140, 115, 140, 125, 140, 135], dtype=dtype)
+        y = xp.asarray([110, 122, 125, 120, 140, 124, 123, 137, 135, 145], dtype=dtype)
+
+        w_ref = xp.asarray(27.0, dtype=dtype)
+        w, p = stats.wilcoxon(x, y, alternative="less", method="asymptotic",
+                              correction=False)
+        xp_assert_equal(w, w_ref)
+        xp_assert_close(p, xp.asarray(0.7031847042787, dtype=dtype))
+
+        w, p = stats.wilcoxon(x, y, alternative="less", correction=True,
+                              method="asymptotic")
+        xp_assert_equal(w, w_ref)
+        xp_assert_close(p, xp.asarray(0.72336564289, dtype=dtype))
+
+        w, p = stats.wilcoxon(x, y, alternative="greater",
+                              method="asymptotic", correction=False)
+        xp_assert_equal(w, w_ref)
+        xp_assert_close(p, xp.asarray(0.2968152957213, dtype=dtype))
+
+        w, p = stats.wilcoxon(x, y, alternative="greater",
+                              correction=True, method="asymptotic")
+        xp_assert_equal(w, w_ref)
+        xp_assert_close(p, xp.asarray(0.3176446594176, dtype=dtype))
+
+    def test_exact_basic(self):  # exact distribution is NumPy-only
+        for n in range(1, 51):
+            pmf1 = _get_wilcoxon_distr(n)
+            pmf2 = _get_wilcoxon_distr2(n)
+            assert_equal(n*(n+1)/2 + 1, len(pmf1))
+            assert_equal(sum(pmf1), 1)
+            assert_array_almost_equal(pmf1, pmf2)
+
+    @skip_xp_backends("jax.numpy", reason="`method='exact'` is incompatible with JAX")
+    @pytest.mark.parametrize('dtype', [None, 'float32', 'float64'])
+    def test_exact_pval(self, dtype, xp):
+        # expected values computed with "R version 4.0.3 (2020-10-10)"
+        # options(digits=16)
+        # x < - c(1.81, 0.82, 1.56, -0.48, 0.81, 1.28, -1.04, 0.23, -0.75, 0.14)
+        # y < - c(0.71, 0.65, -0.2, 0.85, -1.1, -0.45, -0.84, -0.24, -0.68, -0.76)
+        # result = wilcox.test(x - y, exact=TRUE, alternative='l', correct=TRUE)
+        # result$p.value
+        dtype = dtype if dtype is None else getattr(xp, dtype)
+        x = xp.asarray([1.81, 0.82, 1.56, -0.48, 0.81, 1.28, -1.04, 0.23,
+                        -0.75, 0.14], dtype=dtype)
+        y = xp.asarray([0.71, 0.65, -0.2, 0.85, -1.1, -0.45, -0.84, -0.24,
+                        -0.68, -0.76], dtype=dtype)
+        _, p = stats.wilcoxon(x, y, alternative="two-sided", method="exact")
+        xp_assert_close(p, xp.asarray(0.10546875, dtype=dtype))
+        _, p = stats.wilcoxon(x, y, alternative="less", method="exact")
+        xp_assert_close(p, xp.asarray(0.95800781256, dtype=dtype))
+        _, p = stats.wilcoxon(x, y, alternative="greater", method="exact")
+        xp_assert_close(p, xp.asarray(0.052734375, dtype=dtype))
+
+        x = xp.arange(0., 20., dtype=dtype) + 0.5
+        y = xp.arange(20., 0., -1., dtype=dtype)
+        _, p = stats.wilcoxon(x, y, alternative="two-sided", method="exact")
+        xp_assert_close(p, xp.asarray(0.8694877624511719, dtype=dtype))
+        _, p = stats.wilcoxon(x, y, alternative="less", method="exact")
+        xp_assert_close(p, xp.asarray(0.4347438812255859, dtype=dtype))
+        _, p = stats.wilcoxon(x, y, alternative="greater", method="exact")
+        xp_assert_close(p, xp.asarray(0.5795888900756836, dtype=dtype))
+
+    # These inputs were chosen to give a W statistic that is either the
+    # center of the distribution (when the length of the support is odd), or
+    # the value to the left of the center (when the length of the support is
+    # even).  Also, the numbers are chosen so that the W statistic is the
+    # sum of the positive values.
+
+    @skip_xp_backends("jax.numpy", reason="`method='exact'` is incompatible with JAX")
+    @pytest.mark.parametrize('x', [[-1, -2, 3],
+                                   [-1, 2, -3, -4, 5],
+                                   [-1, -2, 3, -4, -5, -6, 7, 8]])
+    def test_exact_p_1(self, x, xp):
+        w, p = stats.wilcoxon(xp.asarray(x))
+        x = np.array(x)
+        wtrue = x[x > 0].sum()
+        xp_assert_equal(w, xp.asarray(float(wtrue)))
+        xp_assert_equal(p, xp.asarray(1.0))
+
+    def test_auto(self, xp):
+        # auto default to exact if there are no ties and n <= 50
+        x = xp.arange(0., 50.) + 0.5
+        y = xp.arange(50., 0., -1.)
+
+        if is_jax(xp):  #
+            message = "When using `wilcoxon` with `jax.numpy` arrays..."
+            with pytest.raises(ValueError, match=message):
+                stats.wilcoxon(x, y, method="auto")
+            with pytest.raises(ValueError, match=message):
+                stats.wilcoxon(x, y, method="exact")
+            return
+
+        xp_assert_equal(stats.wilcoxon(x, y).pvalue,
+                        stats.wilcoxon(x, y, method="exact").pvalue)
+
+        # n <= 50: if there are zeros in d = x-y, use PermutationMethod
+        pm = stats.PermutationMethod()
+        d = np.arange(-2, 5)
+        w, p = stats.wilcoxon(d)
+        # rerunning the test gives the same results since n_resamples
+        # is large enough to get deterministic results if n <= 13
+        # so we do not need to use a seed. to avoid longer runtimes of the
+        # test, use n=7 only. For n=13, see test_auto_permutation_edge_case
+        assert_equal((w, p), stats.wilcoxon(d, method=pm))
+
+        # for larger vectors (n > 13) with ties/zeros, use asymptotic test
+        d = xp.arange(-5, 9)  # zero
+        _, p = stats.wilcoxon(d)
+        xp_assert_equal(stats.wilcoxon(d, method="asymptotic").pvalue, xp.asarray(p))
+
+        d = xpx.at(d)[d == 0].set(1)  # tie
+        _, p = stats.wilcoxon(d)
+        xp_assert_equal(stats.wilcoxon(d, method="asymptotic").pvalue, xp.asarray(p))
+
+        # use approximation for samples > 50
+        d = xp.arange(1, 52)
+        _, p = stats.wilcoxon(d)
+        xp_assert_equal(stats.wilcoxon(d, method="asymptotic").pvalue, xp.asarray(p))
+
+    @pytest.mark.xslow
+    @skip_xp_backends("jax.numpy", reason="lazy -> limited `method` choices")
+    def test_auto_permutation_edge_case(self, xp):
+        # Check that `PermutationMethod()` is used and results are deterministic when
+        # `method='auto'`, there are zeros or ties in `d = x-y`, and `len(d) <= 13`.
+        d = np.arange(-5, 8)  # zero
+        res = stats.wilcoxon(xp.asarray(d))
+        # generated with stats.wilcoxon(d, method=PermutationMethod())
+        w, p = xp.asarray([27.5, 0.3955078125])
+        xp_assert_equal(res.statistic, w)
+        xp_assert_equal(res.pvalue, p)
+
+        d[d == 0] = 1  # tie
+        res = stats.wilcoxon(xp.asarray(d))
+        # generated with stats.wilcoxon(d, method=PermutationMethod())
+        w, p = xp.asarray([32, 0.3779296875])
+        xp_assert_equal(res.statistic, w)
+        xp_assert_equal(res.pvalue, p)
+
+    @pytest.mark.parametrize('size', [3, 5, 10])
+    def test_permutation_method(self, size, xp):
+        rng = np.random.default_rng(92348034828501345)
+        x = rng.random(size=size).tolist()
+        res = stats.wilcoxon(xp.asarray(x), method=stats.PermutationMethod())
+        ref = stats.wilcoxon(x, method='exact')  # all backends test against NumPy
+        dtype = xp_default_dtype(xp)
+        xp_assert_equal(res.statistic, xp.asarray(ref.statistic, dtype=dtype))
+        xp_assert_equal(res.pvalue, xp.asarray(ref.pvalue, dtype=dtype))
+
+        x = xp.asarray(rng.random(size=size*10))
+        rng = np.random.default_rng(59234803482850134)
+        pm = stats.PermutationMethod(n_resamples=99, rng=rng)
+        ref = stats.wilcoxon(x, method=pm)
+        # preserve use of old random_state during SPEC 7 transition
+        rng = np.random.default_rng(59234803482850134)
+        pm = stats.PermutationMethod(n_resamples=99, random_state=rng)
+        res = stats.wilcoxon(x, method=pm)
+
+        xp_assert_equal(xp.round(res.pvalue*100)/100, res.pvalue)  # n_resamples used
+        xp_assert_equal(res.pvalue, ref.pvalue)  # rng/random_state used
+
+    @skip_xp_backends("jax.numpy", reason="`method='auto'` is incompatible with JAX")
+    def test_method_auto_nan_propagate_ND_length_gt_50_gh20591(self, xp):
+        # When method!='asymptotic', nan_policy='propagate', and a slice of
+        # a >1 dimensional array input contained NaN, the result object of
+        # `wilcoxon` could (under yet other conditions) return `zstatistic`
+        # for some slices but not others. This resulted in an error because
+        # `apply_along_axis` would have to create a ragged array.
+        # Check that this is resolved.
+        rng = np.random.default_rng(235889269872456)
+        A = rng.normal(size=(51, 2))  # length along slice > exact threshold
+        A[5, 1] = np.nan
+        A = xp.asarray(A)
+        res = stats.wilcoxon(A)
+        ref = stats.wilcoxon(A, method='asymptotic')
+        xp_assert_close(res.statistic, ref.statistic)
+        xp_assert_close(res.pvalue, ref.pvalue)
+        assert hasattr(ref, 'zstatistic')
+        assert not hasattr(res, 'zstatistic')
+
+    @pytest.mark.parametrize('method', ['exact', 'asymptotic'])
+    def test_symmetry_gh19872_gh20752(self, method, xp):
+        if is_jax(xp) and method == 'exact':
+            pytest.skip("`method='exact'` is incompatible with JAX")
+        # Check that one-sided exact tests obey required symmetry. Bug reported
+        # in gh-19872 and again in gh-20752; example from gh-19872 is more concise:
+        var1 = xp.asarray([62, 66, 61, 68, 74, 62, 68, 62, 55, 59])
+        var2 = xp.asarray([71, 71, 69, 61, 75, 71, 77, 72, 62, 65])
+        ref = stats.wilcoxon(var1, var2, alternative='less', method=method)
+        res = stats.wilcoxon(var2, var1, alternative='greater', method=method)
+        max_statistic = var1.shape[0] * (var1.shape[0] + 1) / 2
+        assert int(res.statistic) != res.statistic
+        xp_assert_close(max_statistic - res.statistic, ref.statistic)
+        xp_assert_close(res.pvalue, ref.pvalue)
+
+    @pytest.mark.parametrize("method", ('exact', stats.PermutationMethod()))
+    def test_all_zeros_exact(self, method, xp):
+        if is_jax(xp) and method == 'exact':
+            pytest.skip("`method='exact'` is incompatible with JAX")
+        # previously, this raised a RuntimeWarning when calculating Z, even
+        # when the Z value was not needed. Confirm that this no longer
+        # occurs when `method` is 'exact' or a `PermutationMethod`.
+        res = stats.wilcoxon(xp.zeros(5), method=method)
+        xp_assert_close(res.statistic, xp.asarray(0.))
+        xp_assert_close(res.pvalue, xp.asarray(1.))
+
+    def test_wilcoxon_axis_broadcasting_errors_gh22051(self, xp):
+        # In previous versions of SciPy, `wilcoxon` gave an incorrect error
+        # message when `AxisError` was not found in the base NumPy namespace.
+        # Check that this is resolved with and without the ANP decorator.
+        x = xp.asarray([1, 2, 3])
+        y = xp.asarray([4, 5, 6])
+
+        message = "Array shapes are incompatible for broadcasting."
+        with pytest.raises(ValueError, match=message):
+            stats.wilcoxon(x, y[:-1])
+
+        if not is_numpy(xp):
+            return  # hard to generalize the rest
+
+        message = "operands could not be broadcast together with..."
+        with pytest.raises(ValueError, match=message):
+            stats.wilcoxon(x, y[:-1], _no_deco=True)
+
+        AxisError = getattr(np, 'AxisError', None) or np.exceptions.AxisError
+        message = "source: axis 3 is out of bounds for array of dimension 1"
+        with pytest.raises(AxisError, match=message):
+            stats.wilcoxon(x, y, axis=3)
+
+        message = "`axis` must be compatible with the shape..."
+        with pytest.raises(AxisError, match=message):
+            stats.wilcoxon(x, y, axis=3, _no_deco=True)
+
+
+# data for k-statistics tests from
+# https://cran.r-project.org/web/packages/kStatistics/kStatistics.pdf
+# see nKS "Examples"
+x_kstat = [16.34, 10.76, 11.84, 13.55, 15.85, 18.20, 7.51, 10.22, 12.52, 14.68,
+           16.08, 19.43, 8.12, 11.20, 12.95, 14.77, 16.83, 19.80, 8.55, 11.58,
+           12.10, 15.02, 16.83, 16.98, 19.92, 9.47, 11.68, 13.41, 15.35, 19.11]
+
+
+@make_xp_test_case(stats.kstat)
+class TestKstat:
+    def test_moments_normal_distribution(self, xp):
+        rng = np.random.RandomState(32149)
+        data = xp.asarray(rng.randn(12345), dtype=xp.float64)
+        moments = xp.stack([stats.kstat(data, n) for n in [1, 2, 3, 4]])
+
+        expected = xp.asarray([0.011315, 1.017931, 0.05811052, 0.0754134],
+                              dtype=data.dtype)
+        xp_assert_close(moments, expected, rtol=1e-4)
+
+        # test equivalence with `stats.moment`
+        m1 = stats.moment(data, order=1)
+        m2 = stats.moment(data, order=2)
+        m3 = stats.moment(data, order=3)
+        xp_assert_close(xp.stack((m1, m2, m3)), expected[:-1], atol=0.02, rtol=1e-2)
+
+    @pytest.mark.filterwarnings("ignore:invalid value encountered")  # Dask
+    def test_empty_input(self, xp):
+        with eager_warns(SmallSampleWarning, match=too_small_1d_not_omit, xp=xp):
+            res = stats.kstat(xp.asarray([]))
+        xp_assert_equal(res, xp.asarray(xp.nan))
+
+    def test_nan_input(self, xp):
+        data = xp.arange(10.)
+        data = xp.where(data == 6, xp.nan, data)
+
+        xp_assert_equal(stats.kstat(data), xp.asarray(xp.nan))
+
+    @pytest.mark.parametrize('n', [0, 4.001])
+    def test_kstat_bad_arg(self, n, xp):
+        # Raise ValueError if n > 4 or n < 1.
+        data = xp.arange(10)
+        message = 'k-statistics only supported for 1<=n<=4'
+        with pytest.raises(ValueError, match=message):
+            stats.kstat(data, n=n)
+
+    @pytest.mark.parametrize('case', [(1, 14.02166666666667),
+                                      (2, 12.65006954022974),
+                                      (3, -1.447059503280798),
+                                      (4, -141.6682291883626)])
+    def test_against_R(self, case, xp):
+        # Test against reference values computed with R kStatistics, e.g.
+        # options(digits=16)
+        # library(kStatistics)
+        # data <-c (16.34, 10.76, 11.84, 13.55, 15.85, 18.20, 7.51, 10.22,
+        #           12.52, 14.68, 16.08, 19.43, 8.12, 11.20, 12.95, 14.77,
+        #           16.83, 19.80, 8.55, 11.58, 12.10, 15.02, 16.83, 16.98,
+        #           19.92, 9.47, 11.68, 13.41, 15.35, 19.11)
+        # nKS(4, data)
+        n, ref = case
+        res = stats.kstat(xp.asarray(x_kstat), n)
+        xp_assert_close(res, xp.asarray(ref))
+
+
+@make_xp_test_case(stats.kstatvar)
+class TestKstatVar:
+    @pytest.mark.filterwarnings("ignore:invalid value encountered")  # Dask
+    def test_empty_input(self, xp):
+        x = xp.asarray([])
+        with eager_warns(SmallSampleWarning, match=too_small_1d_not_omit, xp=xp):
+            res = stats.kstatvar(x)
+        xp_assert_equal(res, xp.asarray(xp.nan))
+
+    def test_nan_input(self, xp):
+        data = xp.arange(10.)
+        data = xp.where(data == 6, xp.nan, data)
+
+        xp_assert_equal(stats.kstat(data), xp.asarray(xp.nan))
+
+    def test_bad_arg(self, xp):
+        # Raise ValueError is n is not 1 or 2.
+        data = xp.asarray([1])
+        n = 10
+        message = 'Only n=1 or n=2 supported.'
+        with pytest.raises(ValueError, match=message):
+            stats.kstatvar(data, n=n)
+
+    def test_against_R_mathworld(self, xp):
+        # Test against reference values computed using formulas exactly as
+        # they appear at https://mathworld.wolfram.com/k-Statistic.html
+        # This is *really* similar to how they appear in the implementation,
+        # but that could change, and this should not.
+        n = len(x_kstat)
+        k2 = 12.65006954022974  # see source code in TestKstat
+        k4 = -141.6682291883626
+
+        res = stats.kstatvar(xp.asarray(x_kstat), 1)
+        ref = k2 / n
+        xp_assert_close(res, xp.asarray(ref))
+
+        res = stats.kstatvar(xp.asarray(x_kstat), 2)
+        # *unbiased estimator* for var(k2)
+        ref = (2*k2**2*n + (n-1)*k4) / (n * (n+1))
+        xp_assert_close(res, xp.asarray(ref))
+
+
+class TestPpccPlot:
+    def setup_method(self):
+        self.x = _old_loggamma_rvs(5, size=500, random_state=7654321) + 5
+
+    def test_basic(self):
+        N = 5
+        svals, ppcc = stats.ppcc_plot(self.x, -10, 10, N=N)
+        ppcc_expected = [0.21139644, 0.21384059, 0.98766719, 0.97980182,
+                         0.93519298]
+        assert_allclose(svals, np.linspace(-10, 10, num=N))
+        assert_allclose(ppcc, ppcc_expected)
+
+    def test_dist(self):
+        # Test that we can specify distributions both by name and as objects.
+        svals1, ppcc1 = stats.ppcc_plot(self.x, -10, 10, dist='tukeylambda')
+        svals2, ppcc2 = stats.ppcc_plot(self.x, -10, 10,
+                                        dist=stats.tukeylambda)
+        assert_allclose(svals1, svals2, rtol=1e-20)
+        assert_allclose(ppcc1, ppcc2, rtol=1e-20)
+        # Test that 'tukeylambda' is the default dist
+        svals3, ppcc3 = stats.ppcc_plot(self.x, -10, 10)
+        assert_allclose(svals1, svals3, rtol=1e-20)
+        assert_allclose(ppcc1, ppcc3, rtol=1e-20)
+
+    @pytest.mark.skipif(not have_matplotlib, reason="no matplotlib")
+    def test_plot_kwarg(self):
+        # Check with the matplotlib.pyplot module
+        fig = plt.figure()
+        ax = fig.add_subplot(111)
+        stats.ppcc_plot(self.x, -20, 20, plot=plt)
+        fig.delaxes(ax)
+
+        # Check that a Matplotlib Axes object is accepted
+        ax = fig.add_subplot(111)
+        stats.ppcc_plot(self.x, -20, 20, plot=ax)
+        plt.close()
+
+    def test_invalid_inputs(self):
+        # `b` has to be larger than `a`
+        assert_raises(ValueError, stats.ppcc_plot, self.x, 1, 0)
+
+        # Raise ValueError when given an invalid distribution.
+        assert_raises(ValueError, stats.ppcc_plot, [1, 2, 3], 0, 1,
+                      dist="plate_of_shrimp")
+
+    def test_empty(self):
+        # For consistency with probplot return for one empty array,
+        # ppcc contains all zeros and svals is the same as for normal array
+        # input.
+        svals, ppcc = stats.ppcc_plot([], 0, 1)
+        assert_allclose(svals, np.linspace(0, 1, num=80))
+        assert_allclose(ppcc, np.zeros(80, dtype=float))
+
+
+class TestPpccMax:
+    def test_ppcc_max_bad_arg(self):
+        # Raise ValueError when given an invalid distribution.
+        data = [1]
+        assert_raises(ValueError, stats.ppcc_max, data, dist="plate_of_shrimp")
+
+    def test_ppcc_max_basic(self):
+        x = stats.tukeylambda.rvs(-0.7, loc=2, scale=0.5, size=10000,
+                                  random_state=1234567) + 1e4
+        assert_almost_equal(stats.ppcc_max(x), -0.71215366521264145, decimal=7)
+
+    def test_dist(self):
+        x = stats.tukeylambda.rvs(-0.7, loc=2, scale=0.5, size=10000,
+                                  random_state=1234567) + 1e4
+
+        # Test that we can specify distributions both by name and as objects.
+        max1 = stats.ppcc_max(x, dist='tukeylambda')
+        max2 = stats.ppcc_max(x, dist=stats.tukeylambda)
+        assert_almost_equal(max1, -0.71215366521264145, decimal=5)
+        assert_almost_equal(max2, -0.71215366521264145, decimal=5)
+
+        # Test that 'tukeylambda' is the default dist
+        max3 = stats.ppcc_max(x)
+        assert_almost_equal(max3, -0.71215366521264145, decimal=5)
+
+    def test_brack(self):
+        x = stats.tukeylambda.rvs(-0.7, loc=2, scale=0.5, size=10000,
+                                  random_state=1234567) + 1e4
+        assert_raises(ValueError, stats.ppcc_max, x, brack=(0.0, 1.0, 0.5))
+
+        assert_almost_equal(stats.ppcc_max(x, brack=(0, 1)),
+                            -0.71215366521264145, decimal=7)
+
+        assert_almost_equal(stats.ppcc_max(x, brack=(-2, 2)),
+                            -0.71215366521264145, decimal=7)
+
+
+@make_xp_test_case(stats.boxcox_llf)
+class TestBoxcox_llf:
+
+    @pytest.mark.parametrize("dtype", ["float32", "float64"])
+    def test_basic(self, dtype, xp):
+        dt = getattr(xp, dtype)
+        x = stats.norm.rvs(size=10000, loc=10, random_state=54321)
+        lmbda = 1
+        llf = stats.boxcox_llf(lmbda, xp.asarray(x, dtype=dt))
+        llf_expected = -x.size / 2. * np.log(np.sum(x.std()**2))
+        xp_assert_close(llf, xp.asarray(llf_expected, dtype=dt))
+
+    @skip_xp_backends(np_only=True,
+                      reason='array-likes only accepted for NumPy backend.')
+    def test_array_like(self, xp):
+        x = stats.norm.rvs(size=100, loc=10, random_state=54321)
+        lmbda = 1
+        llf = stats.boxcox_llf(lmbda, x)
+        llf2 = stats.boxcox_llf(lmbda, list(x))
+        xp_assert_close(llf, llf2, rtol=1e-12)
+
+    def test_2d_input(self, xp):
+        # Note: boxcox_llf() was already working with 2-D input (sort of), so
+        # keep it like that.  boxcox() doesn't work with 2-D input though, due
+        # to brent() returning a scalar.
+        x = stats.norm.rvs(size=100, loc=10, random_state=54321)
+        lmbda = 1
+        llf = stats.boxcox_llf(lmbda, x)
+        llf2 = stats.boxcox_llf(lmbda, np.vstack([x, x]).T)
+        xp_assert_close(xp.asarray([llf, llf]), xp.asarray(llf2), rtol=1e-12)
+
+    def test_empty(self, xp):
+        message = "One or more sample arguments is too small..."
+        with eager_warns(SmallSampleWarning, match=message, xp=xp):
+            assert xp.isnan(xp.asarray(stats.boxcox_llf(1, xp.asarray([]))))
+
+    def test_gh_6873(self, xp):
+        # Regression test for gh-6873.
+        # This example was taken from gh-7534, a duplicate of gh-6873.
+        data = xp.asarray([198.0, 233.0, 233.0, 392.0])
+        llf = stats.boxcox_llf(-8, data)
+        # The expected value was computed with mpmath.
+        xp_assert_close(llf, xp.asarray(-17.93934208579061))
+
+    def test_instability_gh20021(self, xp):
+        data = xp.asarray([2003, 1950, 1997, 2000, 2009], dtype=xp.float64)
+        llf = stats.boxcox_llf(1e-8, data)
+        # The expected value was computed with mpsci, set mpmath.mp.dps=100
+        # expect float64 output for integer input
+        xp_assert_close(llf, xp.asarray(-15.32401272869016598, dtype=xp.float64),
+                        rtol=5e-7)  # bumped tolerance from 1e-7 for Accelerate
+
+    def test_axis(self, xp):
+        data = xp.asarray([[100, 200], [300, 400]])
+        llf_axis_0 = stats.boxcox_llf(1, data, axis=0)
+        llf_0 = xp.stack([
+            stats.boxcox_llf(1, data[:, 0]),
+            stats.boxcox_llf(1, data[:, 1]),
+        ])
+        xp_assert_close(llf_axis_0, llf_0)
+        llf_axis_1 = stats.boxcox_llf(1, data, axis=1)
+        llf_1 = xp.stack([
+            stats.boxcox_llf(1, data[0, :]),
+            stats.boxcox_llf(1, data[1, :]),
+        ])
+        xp_assert_close(llf_axis_1, llf_1)
+
+
+# This is the data from GitHub user Qukaiyi, given as an example
+# of a data set that caused boxcox to fail.
+_boxcox_data = [
+    15957, 112079, 1039553, 711775, 173111, 307382, 183155, 53366, 760875,
+    207500, 160045, 473714, 40194, 440319, 133261, 265444, 155590, 36660,
+    904939, 55108, 138391, 339146, 458053, 63324, 1377727, 1342632, 41575,
+    68685, 172755, 63323, 368161, 199695, 538214, 167760, 388610, 398855,
+    1001873, 364591, 1320518, 194060, 194324, 2318551, 196114, 64225, 272000,
+    198668, 123585, 86420, 1925556, 695798, 88664, 46199, 759135, 28051,
+    345094, 1977752, 51778, 82746, 638126, 2560910, 45830, 140576, 1603787,
+    57371, 548730, 5343629, 2298913, 998813, 2156812, 423966, 68350, 145237,
+    131935, 1600305, 342359, 111398, 1409144, 281007, 60314, 242004, 113418,
+    246211, 61940, 95858, 957805, 40909, 307955, 174159, 124278, 241193,
+    872614, 304180, 146719, 64361, 87478, 509360, 167169, 933479, 620561,
+    483333, 97416, 143518, 286905, 597837, 2556043, 89065, 69944, 196858,
+    88883, 49379, 916265, 1527392, 626954, 54415, 89013, 2883386, 106096,
+    402697, 45578, 349852, 140379, 34648, 757343, 1305442, 2054757, 121232,
+    606048, 101492, 51426, 1820833, 83412, 136349, 1379924, 505977, 1303486,
+    95853, 146451, 285422, 2205423, 259020, 45864, 684547, 182014, 784334,
+    174793, 563068, 170745, 1195531, 63337, 71833, 199978, 2330904, 227335,
+    898280, 75294, 2011361, 116771, 157489, 807147, 1321443, 1148635, 2456524,
+    81839, 1228251, 97488, 1051892, 75397, 3009923, 2732230, 90923, 39735,
+    132433, 225033, 337555, 1204092, 686588, 1062402, 40362, 1361829, 1497217,
+    150074, 551459, 2019128, 39581, 45349, 1117187, 87845, 1877288, 164448,
+    10338362, 24942, 64737, 769946, 2469124, 2366997, 259124, 2667585, 29175,
+    56250, 74450, 96697, 5920978, 838375, 225914, 119494, 206004, 430907,
+    244083, 219495, 322239, 407426, 618748, 2087536, 2242124, 4736149, 124624,
+    406305, 240921, 2675273, 4425340, 821457, 578467, 28040, 348943, 48795,
+    145531, 52110, 1645730, 1768364, 348363, 85042, 2673847, 81935, 169075,
+    367733, 135474, 383327, 1207018, 93481, 5934183, 352190, 636533, 145870,
+    55659, 146215, 73191, 248681, 376907, 1606620, 169381, 81164, 246390,
+    236093, 885778, 335969, 49266, 381430, 307437, 350077, 34346, 49340,
+    84715, 527120, 40163, 46898, 4609439, 617038, 2239574, 159905, 118337,
+    120357, 430778, 3799158, 3516745, 54198, 2970796, 729239, 97848, 6317375,
+    887345, 58198, 88111, 867595, 210136, 1572103, 1420760, 574046, 845988,
+    509743, 397927, 1119016, 189955, 3883644, 291051, 126467, 1239907, 2556229,
+    411058, 657444, 2025234, 1211368, 93151, 577594, 4842264, 1531713, 305084,
+    479251, 20591, 1466166, 137417, 897756, 594767, 3606337, 32844, 82426,
+    1294831, 57174, 290167, 322066, 813146, 5671804, 4425684, 895607, 450598,
+    1048958, 232844, 56871, 46113, 70366, 701618, 97739, 157113, 865047,
+    194810, 1501615, 1765727, 38125, 2733376, 40642, 437590, 127337, 106310,
+    4167579, 665303, 809250, 1210317, 45750, 1853687, 348954, 156786, 90793,
+    1885504, 281501, 3902273, 359546, 797540, 623508, 3672775, 55330, 648221,
+    266831, 90030, 7118372, 735521, 1009925, 283901, 806005, 2434897, 94321,
+    309571, 4213597, 2213280, 120339, 64403, 8155209, 1686948, 4327743,
+    1868312, 135670, 3189615, 1569446, 706058, 58056, 2438625, 520619, 105201,
+    141961, 179990, 1351440, 3148662, 2804457, 2760144, 70775, 33807, 1926518,
+    2362142, 186761, 240941, 97860, 1040429, 1431035, 78892, 484039, 57845,
+    724126, 3166209, 175913, 159211, 1182095, 86734, 1921472, 513546, 326016,
+    1891609
+]
+
+
+class TransformTest:
+    def test_nan_policy(self):
+        transform = getattr(stats, self.transform)
+        normmax = getattr(stats, f"{self.transform}_normmax")
+        special_transform = getattr(special, self.transform, _yeojohnson_transform)
+
+        rng = np.random.default_rng(5908294582456923546)
+        x = rng.random(10)
+        x[3] = np.nan
+
+        # lmb provided
+        lmb = 1.0
+
+        with pytest.raises(ValueError, match="The input contains nan values"):
+            transform(x, lmb, nan_policy='raise')
+
+        res = transform(x, lmb, nan_policy='propagate')
+        np.testing.assert_allclose(res, special_transform(x, 1.))
+
+        res = transform(x, lmb, nan_policy='omit')
+        np.testing.assert_allclose(res, transform(x, lmb, nan_policy='propagate'))
+
+        # lmb not provided
+        with pytest.raises(ValueError, match="The input contains nan values"):
+            transform(x, nan_policy='raise')
+
+        res = transform(x, nan_policy='propagate')
+        np.testing.assert_equal(res[0], special_transform(x, np.nan))
+        np.testing.assert_equal(res[1], np.nan)
+
+        kwarg = {'method': 'mle'} if transform == stats.boxcox else {}
+        res = transform(x, nan_policy='omit')
+        lmb = normmax(x, nan_policy='omit', **kwarg)
+        ref = transform(x, lmb)
+        np.testing.assert_allclose(res[0], ref)
+        np.testing.assert_allclose(res[1], lmb)
+
+
+class TestBoxcox(TransformTest):
+    transform = 'boxcox'
+
+    def test_fixed_lmbda(self):
+        x = _old_loggamma_rvs(5, size=50, random_state=12345) + 5
+        xt = stats.boxcox(x, lmbda=1)
+        assert_allclose(xt, x - 1)
+        xt = stats.boxcox(x, lmbda=-1)
+        assert_allclose(xt, 1 - 1/x)
+
+        xt = stats.boxcox(x, lmbda=0)
+        assert_allclose(xt, np.log(x))
+
+        # Also test that array_like input works
+        xt = stats.boxcox(list(x), lmbda=0)
+        assert_allclose(xt, np.log(x))
+
+        # test that constant input is accepted; see gh-12225
+        xt = stats.boxcox(np.ones(10), 2)
+        assert_equal(xt, np.zeros(10))
+
+    def test_lmbda_None(self):
+        # Start from normal rv's, do inverse transform to check that
+        # optimization function gets close to the right answer.
+        lmbda = 2.5
+        x = stats.norm.rvs(loc=10, size=50000, random_state=1245)
+        x_inv = (x * lmbda + 1)**(-lmbda)
+        xt, maxlog = stats.boxcox(x_inv)
+
+        assert_almost_equal(maxlog, -1 / lmbda, decimal=2)
+
+    def test_alpha(self):
+        rng = np.random.RandomState(1234)
+        x = _old_loggamma_rvs(5, size=50, random_state=rng) + 5
+
+        # Some regular values for alpha, on a small sample size
+        _, _, interval = stats.boxcox(x, alpha=0.75)
+        assert_allclose(interval, [4.004485780226041, 5.138756355035744])
+        _, _, interval = stats.boxcox(x, alpha=0.05)
+        assert_allclose(interval, [1.2138178554857557, 8.209033272375663])
+
+        # Try some extreme values, see we don't hit the N=500 limit
+        x = _old_loggamma_rvs(7, size=500, random_state=rng) + 15
+        _, _, interval = stats.boxcox(x, alpha=0.001)
+        assert_allclose(interval, [0.3988867, 11.40553131])
+        _, _, interval = stats.boxcox(x, alpha=0.999)
+        assert_allclose(interval, [5.83316246, 5.83735292])
+
+    def test_boxcox_bad_arg(self):
+        # Raise ValueError if any data value is negative.
+        x = np.array([-1, 2])
+        assert_raises(ValueError, stats.boxcox, x)
+        # Raise ValueError if data is constant.
+        assert_raises(ValueError, stats.boxcox, np.array([1]))
+        # Raise ValueError if data is not 1-dimensional.
+        assert_raises(ValueError, stats.boxcox, np.array([[1], [2]]))
+
+    def test_empty(self):
+        assert_(stats.boxcox([]).shape == (0,))
+
+    def test_gh_6873(self):
+        # Regression test for gh-6873.
+        y, lam = stats.boxcox(_boxcox_data)
+        # The expected value of lam was computed with the function
+        # powerTransform in the R library 'car'.  I trust that value
+        # to only about five significant digits.
+        assert_allclose(lam, -0.051654, rtol=1e-5)
+
+    @pytest.mark.parametrize("bounds", [(-1, 1), (1.1, 2), (-2, -1.1)])
+    def test_bounded_optimizer_within_bounds(self, bounds):
+        # Define custom optimizer with bounds.
+        def optimizer(fun):
+            return optimize.minimize_scalar(fun, bounds=bounds,
+                                            method="bounded")
+
+        _, lmbda = stats.boxcox(_boxcox_data, lmbda=None, optimizer=optimizer)
+        assert bounds[0] < lmbda < bounds[1]
+
+    def test_bounded_optimizer_against_unbounded_optimizer(self):
+        # Test whether setting bounds on optimizer excludes solution from
+        # unbounded optimizer.
+
+        # Get unbounded solution.
+        _, lmbda = stats.boxcox(_boxcox_data, lmbda=None)
+
+        # Set tolerance and bounds around solution.
+        bounds = (lmbda + 0.1, lmbda + 1)
+        options = {'xatol': 1e-12}
+
+        def optimizer(fun):
+            return optimize.minimize_scalar(fun, bounds=bounds,
+                                            method="bounded", options=options)
+
+        # Check bounded solution. Lower bound should be active.
+        _, lmbda_bounded = stats.boxcox(_boxcox_data, lmbda=None,
+                                        optimizer=optimizer)
+        assert lmbda_bounded != lmbda
+        assert_allclose(lmbda_bounded, bounds[0])
+
+    @pytest.mark.parametrize("optimizer", ["str", (1, 2), 0.1])
+    def test_bad_optimizer_type_raises_error(self, optimizer):
+        # Check if error is raised if string, tuple or float is passed
+        with pytest.raises(ValueError, match="`optimizer` must be a callable"):
+            stats.boxcox(_boxcox_data, lmbda=None, optimizer=optimizer)
+
+    def test_bad_optimizer_value_raises_error(self):
+        # Check if error is raised if `optimizer` function does not return
+        # `OptimizeResult` object
+
+        # Define test function that always returns 1
+        def optimizer(fun):
+            return 1
+
+        message = "return an object containing the optimal `lmbda`"
+        with pytest.raises(ValueError, match=message):
+            stats.boxcox(_boxcox_data, lmbda=None, optimizer=optimizer)
+
+    @pytest.mark.parametrize(
+            "bad_x", [np.array([1, -42, 12345.6]), np.array([np.inf, 42, 1])]
+        )
+    def test_negative_x_value_raises_error(self, bad_x):
+        """Test boxcox_normmax raises ValueError if x contains non-positive values."""
+        message = "only positive, finite, real numbers"
+        with pytest.raises(ValueError, match=message):
+            stats.boxcox_normmax(bad_x)
+
+    @pytest.mark.parametrize('x', [
+        # Attempt to trigger overflow in power expressions.
+        np.array([2003.0, 1950.0, 1997.0, 2000.0, 2009.0,
+                  2009.0, 1980.0, 1999.0, 2007.0, 1991.0]),
+        # Attempt to trigger overflow with a large optimal lambda.
+        np.array([2003.0, 1950.0, 1997.0, 2000.0, 2009.0]),
+        # Attempt to trigger overflow with large data.
+        np.array([2003.0e200, 1950.0e200, 1997.0e200, 2000.0e200, 2009.0e200])
+    ])
+    def test_overflow(self, x):
+        with pytest.warns(UserWarning, match="The optimal lambda is"):
+            xt_bc, lam_bc = stats.boxcox(x)
+            assert np.all(np.isfinite(xt_bc))
+
+    def test_confidence_interval_nan_policy(self):
+        # other outputs with `nan_policy` tested in superclass
+        rng = np.random.default_rng(5908294582456923546)
+        x = rng.random(10)
+        x[3] = np.nan
+        alpha = 0.5
+
+        with pytest.raises(ValueError, match="The input contains nan values"):
+            stats.boxcox(x, alpha=alpha, nan_policy='raise')
+
+        res = stats.boxcox(x, alpha=alpha, nan_policy='propagate')[2]
+        np.testing.assert_equal(res, (np.nan, np.nan))
+
+        res = stats.boxcox(x, alpha=alpha, nan_policy='omit')[2]
+        ref = stats.boxcox(x[~np.isnan(x)], alpha=alpha)[2]
+        np.testing.assert_allclose(res, ref)
+
+
+class NormmaxTest:
+    def test_nan_policy(self):
+        transform_normmax = getattr(stats, self.transform_normmax)
+        rng = np.random.default_rng(5908294582456923546)
+        x = rng.random(10)
+        x[3] = np.nan
+
+        with pytest.raises(ValueError, match="The input contains nan values"):
+            transform_normmax(x, nan_policy='raise')
+
+        res = transform_normmax(x, nan_policy='propagate')
+        np.testing.assert_equal(res, np.nan)
+
+        res = transform_normmax(x, nan_policy='omit')
+        ref = transform_normmax(x[~np.isnan(x)])
+        np.testing.assert_allclose(res, ref)
+
+
+class TestBoxcoxNormmax(NormmaxTest):
+    transform_normmax = 'boxcox_normmax'
+
+    def setup_method(self):
+        self.x = _old_loggamma_rvs(5, size=50, random_state=12345) + 5
+
+    def test_pearsonr(self):
+        maxlog = stats.boxcox_normmax(self.x)
+        assert_allclose(maxlog, 1.804465, rtol=1e-6)
+
+    def test_mle(self):
+        maxlog = stats.boxcox_normmax(self.x, method='mle')
+        assert_allclose(maxlog, 1.758101, rtol=1e-6)
+
+        # Check that boxcox() uses 'mle'
+        _, maxlog_boxcox = stats.boxcox(self.x)
+        assert_allclose(maxlog_boxcox, maxlog)
+
+    def test_all(self):
+        maxlog_all = stats.boxcox_normmax(self.x, method='all')
+        assert_allclose(maxlog_all, [1.804465, 1.758101], rtol=1e-6)
+
+    @pytest.mark.parametrize("method", ["mle", "pearsonr", "all"])
+    @pytest.mark.parametrize("bounds", [(-1, 1), (1.1, 2), (-2, -1.1)])
+    def test_bounded_optimizer_within_bounds(self, method, bounds):
+
+        def optimizer(fun):
+            return optimize.minimize_scalar(fun, bounds=bounds,
+                                            method="bounded")
+
+        maxlog = stats.boxcox_normmax(self.x, method=method,
+                                      optimizer=optimizer)
+        assert np.all(bounds[0] < maxlog)
+        assert np.all(maxlog < bounds[1])
+
+    @pytest.mark.slow
+    def test_user_defined_optimizer(self):
+        # tests an optimizer that is not based on scipy.optimize.minimize
+        lmbda = stats.boxcox_normmax(self.x)
+        lmbda_rounded = np.round(lmbda, 5)
+        lmbda_range = np.linspace(lmbda_rounded-0.01, lmbda_rounded+0.01, 1001)
+
+        class MyResult:
+            pass
+
+        def optimizer(fun):
+            # brute force minimum over the range
+            objs = []
+            for lmbda in lmbda_range:
+                objs.append(fun(lmbda))
+            res = MyResult()
+            res.x = lmbda_range[np.argmin(objs)]
+            return res
+
+        lmbda2 = stats.boxcox_normmax(self.x, optimizer=optimizer)
+        assert lmbda2 != lmbda                 # not identical
+        assert_allclose(lmbda2, lmbda, 1e-5)   # but as close as it should be
+
+    def test_user_defined_optimizer_and_brack_raises_error(self):
+        optimizer = optimize.minimize_scalar
+
+        # Using default `brack=None` with user-defined `optimizer` works as
+        # expected.
+        stats.boxcox_normmax(self.x, brack=None, optimizer=optimizer)
+
+        # Using user-defined `brack` with user-defined `optimizer` is expected
+        # to throw an error. Instead, users should specify
+        # optimizer-specific parameters in the optimizer function itself.
+        with pytest.raises(ValueError, match="`brack` must be None if "
+                                             "`optimizer` is given"):
+
+            stats.boxcox_normmax(self.x, brack=(-2.0, 2.0),
+                                 optimizer=optimizer)
+
+    @pytest.mark.parametrize(
+        'x', ([2003.0, 1950.0, 1997.0, 2000.0, 2009.0],
+              [0.50000471, 0.50004979, 0.50005902, 0.50009312, 0.50001632]))
+    def test_overflow(self, x):
+        message = "The optimal lambda is..."
+        with pytest.warns(UserWarning, match=message):
+            lmbda = stats.boxcox_normmax(x, method='mle')
+        assert np.isfinite(special.boxcox(x, lmbda)).all()
+        # 10000 is safety factor used in boxcox_normmax
+        ymax = np.finfo(np.float64).max / 10000
+        x_treme = np.max(x) if lmbda > 0 else np.min(x)
+        y_extreme = special.boxcox(x_treme, lmbda)
+        assert_allclose(y_extreme, ymax * np.sign(lmbda))
+
+    def test_negative_ymax(self):
+        with pytest.raises(ValueError, match="`ymax` must be strictly positive"):
+            stats.boxcox_normmax(self.x, ymax=-1)
+
+    @pytest.mark.parametrize("x", [
+        # positive overflow in float64
+        np.array([2003.0, 1950.0, 1997.0, 2000.0, 2009.0],
+                 dtype=np.float64),
+        # negative overflow in float64
+        np.array([0.50000471, 0.50004979, 0.50005902, 0.50009312, 0.50001632],
+                 dtype=np.float64),
+        # positive overflow in float32
+        np.array([200.3, 195.0, 199.7, 200.0, 200.9],
+                 dtype=np.float32),
+        # negative overflow in float32
+        np.array([2e-30, 1e-30, 1e-30, 1e-30, 1e-30, 1e-30],
+                 dtype=np.float32),
+    ])
+    @pytest.mark.parametrize("ymax", [1e10, 1e30, None])
+    # TODO: add method "pearsonr" after fix overflow issue
+    @pytest.mark.parametrize("method", ["mle"])
+    def test_user_defined_ymax_input_float64_32(self, x, ymax, method):
+        # Test the maximum of the transformed data close to ymax
+        with pytest.warns(UserWarning, match="The optimal lambda is"):
+            kwarg = {'ymax': ymax} if ymax is not None else {}
+            lmb = stats.boxcox_normmax(x, method=method, **kwarg)
+            x_treme = [np.min(x), np.max(x)]
+            ymax_res = max(abs(stats.boxcox(x_treme, lmb)))
+            if ymax is None:
+                # 10000 is safety factor used in boxcox_normmax
+                ymax = np.finfo(x.dtype).max / 10000
+            assert_allclose(ymax, ymax_res, rtol=1e-5)
+
+    @pytest.mark.parametrize("x", [
+        # positive overflow in float32 but not float64
+        [200.3, 195.0, 199.7, 200.0, 200.9],
+        # negative overflow in float32 but not float64
+        [2e-30, 1e-30, 1e-30, 1e-30, 1e-30, 1e-30],
+    ])
+    # TODO: add method "pearsonr" after fix overflow issue
+    @pytest.mark.parametrize("method", ["mle"])
+    def test_user_defined_ymax_inf(self, x, method):
+        x_32 = np.asarray(x, dtype=np.float32)
+        x_64 = np.asarray(x, dtype=np.float64)
+
+        # assert overflow with float32 but not float64
+        with pytest.warns(UserWarning, match="The optimal lambda is"):
+            stats.boxcox_normmax(x_32, method=method)
+        stats.boxcox_normmax(x_64, method=method)
+
+        # compute the true optimal lambda then compare them
+        lmb_32 = stats.boxcox_normmax(x_32, ymax=np.inf, method=method)
+        lmb_64 = stats.boxcox_normmax(x_64, ymax=np.inf, method=method)
+        assert_allclose(lmb_32, lmb_64, rtol=1e-2)
+
+    def test_nan_policy_all(self):
+        # `nan_policy` with other `method`s tested in superclass
+        rng = np.random.default_rng(5908294582456923546)
+        x = rng.random(10)
+        x[3] = np.nan
+
+        with pytest.raises(ValueError, match="The input contains nan values"):
+            stats.boxcox_normmax(x, method='all', nan_policy='raise')
+
+        res = stats.boxcox_normmax(x, method='all', nan_policy='propagate')
+        np.testing.assert_equal(res, (np.nan, np.nan))
+
+        res = stats.boxcox_normmax(x, method='all', nan_policy='omit')
+        ref = stats.boxcox_normmax(x[~np.isnan(x)], method='all')
+        np.testing.assert_allclose(res, ref)
+
+
+class TestBoxcoxNormplot:
+    def setup_method(self):
+        self.x = _old_loggamma_rvs(5, size=500, random_state=7654321) + 5
+
+    def test_basic(self):
+        N = 5
+        lmbdas, ppcc = stats.boxcox_normplot(self.x, -10, 10, N=N)
+        ppcc_expected = [0.57783375, 0.83610988, 0.97524311, 0.99756057,
+                         0.95843297]
+        assert_allclose(lmbdas, np.linspace(-10, 10, num=N))
+        assert_allclose(ppcc, ppcc_expected)
+
+    @pytest.mark.skipif(not have_matplotlib, reason="no matplotlib")
+    def test_plot_kwarg(self):
+        # Check with the matplotlib.pyplot module
+        fig = plt.figure()
+        ax = fig.add_subplot(111)
+        stats.boxcox_normplot(self.x, -20, 20, plot=plt)
+        fig.delaxes(ax)
+
+        # Check that a Matplotlib Axes object is accepted
+        ax = fig.add_subplot(111)
+        stats.boxcox_normplot(self.x, -20, 20, plot=ax)
+        plt.close()
+
+    def test_invalid_inputs(self):
+        # `lb` has to be larger than `la`
+        assert_raises(ValueError, stats.boxcox_normplot, self.x, 1, 0)
+        # `x` can not contain negative values
+        assert_raises(ValueError, stats.boxcox_normplot, [-1, 1], 0, 1)
+
+    def test_empty(self):
+        assert_(stats.boxcox_normplot([], 0, 1).size == 0)
+
+
+@make_xp_test_case(stats.yeojohnson_llf)
+class TestYeojohnson_llf:
+
+    def test_array_like(self):
+        # array_like not applicable with SCIPY_ARRAY_API=1
+        x = stats.norm.rvs(size=100, loc=0, random_state=54321)
+        lmbda = 1
+        llf = stats.yeojohnson_llf(lmbda, x)
+        llf2 = stats.yeojohnson_llf(lmbda, list(x))
+        assert_allclose(llf, llf2, rtol=1e-12)
+
+    def test_2d_input(self, xp):
+        x = stats.norm.rvs(size=100, loc=10, random_state=54321)
+        x = xp.asarray(x)
+        lmbda = 1
+        ref = stats.yeojohnson_llf(lmbda, x)
+        res = stats.yeojohnson_llf(lmbda, xp.stack([x, x]).T)
+        xp_assert_close(res, xp.stack((ref, ref)), rtol=1e-12)
+
+    def test_empty(self, xp):
+        message = "One or more sample arguments is too small..."
+        with eager_warns(SmallSampleWarning, match=message, xp=xp):
+            assert xp.isnan(stats.yeojohnson_llf(1, xp.asarray([])))
+
+    @skip_xp_backends('jax.numpy', reason="JIT can't special-case for all >0 / <0")
+    def test_gh24172(self, xp):
+        # Test all negative and all positive data
+        data = xp.asarray([10, 10, 10, 9.9], dtype=xp.float64)
+        # The expected value was computed with mpsci, set mpmath.mp.dps=100
+        # 1. Test precision loss
+        xp_assert_close(stats.yeojohnson_llf(-14, data),
+                        xp.asarray(12.418595783381280, dtype=xp.float64), rtol=1e-7)
+        xp_assert_close(stats.yeojohnson_llf(16, -data),
+                        xp.asarray(12.418595783381280, dtype=xp.float64), rtol=1e-7)
+        # 2. Test overflow
+        xp_assert_close(stats.yeojohnson_llf(-20, data),
+                        xp.asarray(12.360966379200528, dtype=xp.float64), rtol=1e-7)
+        xp_assert_close(stats.yeojohnson_llf(20, -data),
+                        xp.asarray(12.380287243698629, dtype=xp.float64), rtol=1e-7)
+
+    @pytest.mark.parametrize("lmb, ref",
+                             [(-1.,  6.757930444097559),
+                              (0., 11.90755408530727),
+                              (1., 14.179952211901629),
+                              (2., 13.040657538043835)])
+    def test_against_reference(self, lmb, ref, xp):
+        # Reference values generated with mpsci, e.g.
+        # import numpy as np
+        # from mpmath import mp
+        # from mpsci.stats import yeojohnson_llf
+        # mp.dps = 100
+        # rng = np.random.default_rng(78435782834992002)
+        # x = rng.uniform(-1, 1, size=25)
+        # float(yeojohnson_llf(-1, x))  # 6.757930444097559
+        rng = np.random.default_rng(78435782834992002)
+        x = rng.uniform(-1, 1, size=25)
+        res = stats.yeojohnson_llf(lmb, xp.asarray(x.tolist()))
+        xp_assert_close(res, xp.asarray(ref))
+
+
+class TestYeojohnson(TransformTest):
+    transform = 'yeojohnson'
+
+    def test_fixed_lmbda(self):
+        rng = np.random.RandomState(12345)
+
+        # Test positive input
+        x = _old_loggamma_rvs(5, size=50, random_state=rng) + 5
+        assert np.all(x > 0)
+        xt = stats.yeojohnson(x, lmbda=1)
+        assert_allclose(xt, x)
+        xt = stats.yeojohnson(x, lmbda=-1)
+        assert_allclose(xt, 1 - 1 / (x + 1))
+        xt = stats.yeojohnson(x, lmbda=0)
+        assert_allclose(xt, np.log(x + 1))
+        xt = stats.yeojohnson(x, lmbda=1)
+        assert_allclose(xt, x)
+
+        # Test negative input
+        x = _old_loggamma_rvs(5, size=50, random_state=rng) - 5
+        assert np.all(x < 0)
+        xt = stats.yeojohnson(x, lmbda=2)
+        assert_allclose(xt, -np.log(-x + 1))
+        xt = stats.yeojohnson(x, lmbda=1)
+        assert_allclose(xt, x)
+        xt = stats.yeojohnson(x, lmbda=3)
+        assert_allclose(xt, 1 / (-x + 1) - 1)
+
+        # test both positive and negative input
+        x = _old_loggamma_rvs(5, size=50, random_state=rng) - 2
+        assert not np.all(x < 0)
+        assert not np.all(x >= 0)
+        pos = x >= 0
+        xt = stats.yeojohnson(x, lmbda=1)
+        assert_allclose(xt[pos], x[pos])
+        xt = stats.yeojohnson(x, lmbda=-1)
+        assert_allclose(xt[pos], 1 - 1 / (x[pos] + 1))
+        xt = stats.yeojohnson(x, lmbda=0)
+        assert_allclose(xt[pos], np.log(x[pos] + 1))
+        xt = stats.yeojohnson(x, lmbda=1)
+        assert_allclose(xt[pos], x[pos])
+
+        neg = ~pos
+        xt = stats.yeojohnson(x, lmbda=2)
+        assert_allclose(xt[neg], -np.log(-x[neg] + 1))
+        xt = stats.yeojohnson(x, lmbda=1)
+        assert_allclose(xt[neg], x[neg])
+        xt = stats.yeojohnson(x, lmbda=3)
+        assert_allclose(xt[neg], 1 / (-x[neg] + 1) - 1)
+
+    @pytest.mark.parametrize('lmbda', [0, .1, .5, 2])
+    def test_lmbda_None(self, lmbda):
+        # Start from normal rv's, do inverse transform to check that
+        # optimization function gets close to the right answer.
+
+        def _inverse_transform(x, lmbda):
+            x_inv = np.zeros(x.shape, dtype=x.dtype)
+            pos = x >= 0
+
+            # when x >= 0
+            if abs(lmbda) < np.spacing(1.):
+                x_inv[pos] = np.exp(x[pos]) - 1
+            else:  # lmbda != 0
+                x_inv[pos] = np.power(x[pos] * lmbda + 1, 1 / lmbda) - 1
+
+            # when x < 0
+            if abs(lmbda - 2) > np.spacing(1.):
+                x_inv[~pos] = 1 - np.power(-(2 - lmbda) * x[~pos] + 1,
+                                           1 / (2 - lmbda))
+            else:  # lmbda == 2
+                x_inv[~pos] = 1 - np.exp(-x[~pos])
+
+            return x_inv
+
+        n_samples = 20000
+        rng = np.random.RandomState(1234567)
+        x = rng.normal(loc=0, scale=1, size=(n_samples))
+
+        x_inv = _inverse_transform(x, lmbda)
+        xt, maxlog = stats.yeojohnson(x_inv)
+
+        assert_allclose(maxlog, lmbda, atol=1e-2)
+
+        assert_almost_equal(0, np.linalg.norm(x - xt) / n_samples, decimal=2)
+        assert_almost_equal(0, xt.mean(), decimal=1)
+        assert_almost_equal(1, xt.std(), decimal=1)
+
+    def test_empty(self):
+        assert_(stats.yeojohnson([]).shape == (0,))
+
+    def test_array_like(self):
+        x = stats.norm.rvs(size=100, loc=0, random_state=54321)
+        xt1, _ = stats.yeojohnson(x)
+        xt2, _ = stats.yeojohnson(list(x))
+        assert_allclose(xt1, xt2, rtol=1e-12)
+
+    @pytest.mark.parametrize('dtype', [np.complex64, np.complex128])
+    def test_input_dtype_complex(self, dtype):
+        x = np.arange(6, dtype=dtype)
+        err_msg = ('Yeo-Johnson transformation is not defined for complex '
+                   'numbers.')
+        with pytest.raises(ValueError, match=err_msg):
+            stats.yeojohnson(x)
+
+    @pytest.mark.parametrize('dtype', [np.int8, np.uint8, np.int16, np.int32])
+    def test_input_dtype_integer(self, dtype):
+        x_int = np.arange(8, dtype=dtype)
+        x_float = np.arange(8, dtype=np.float64)
+        xt_int, lmbda_int = stats.yeojohnson(x_int)
+        xt_float, lmbda_float = stats.yeojohnson(x_float)
+        assert_allclose(xt_int, xt_float, rtol=1e-7)
+        assert_allclose(lmbda_int, lmbda_float, rtol=1e-7)
+
+    def test_input_high_variance(self):
+        # non-regression test for gh-10821
+        x = np.array([3251637.22, 620695.44, 11642969.00, 2223468.22,
+                      85307500.00, 16494389.89, 917215.88, 11642969.00,
+                      2145773.87, 4962000.00, 620695.44, 651234.50,
+                      1907876.71, 4053297.88, 3251637.22, 3259103.08,
+                      9547969.00, 20631286.23, 12807072.08, 2383819.84,
+                      90114500.00, 17209575.46, 12852969.00, 2414609.99,
+                      2170368.23])
+        xt_yeo, lam_yeo = stats.yeojohnson(x)
+        xt_box, lam_box = stats.boxcox(x + 1)
+        assert_allclose(xt_yeo, xt_box, rtol=1e-6)
+        assert_allclose(lam_yeo, lam_box, rtol=1e-6)
+
+    @pytest.mark.parametrize('x', [
+        np.array([1.0, float("inf"), 2.0]),
+        np.array([1.0, -float("inf"), 2.0]),
+        np.array([-1.0, float("inf"), -float("inf"), 1.0])
+    ])
+    def test_nonfinite_input(self, x):
+        with pytest.raises(ValueError, match='Yeo-Johnson input must be finite'):
+            xt_yeo, lam_yeo = stats.yeojohnson(x)
+
+    @pytest.mark.parametrize('x', [
+        # Attempt to trigger overflow in power expressions.
+        np.array([2003.0, 1950.0, 1997.0, 2000.0, 2009.0,
+                  2009.0, 1980.0, 1999.0, 2007.0, 1991.0]),
+        # Attempt to trigger overflow with a large optimal lambda.
+        np.array([2003.0, 1950.0, 1997.0, 2000.0, 2009.0]),
+        # Attempt to trigger overflow with large data.
+        np.array([2003.0e200, 1950.0e200, 1997.0e200, 2000.0e200, 2009.0e200])
+    ])
+    def test_overflow(self, x):
+        # non-regression test for gh-18389
+
+        def optimizer(fun, lam_yeo):
+            out = optimize.fminbound(fun, -lam_yeo, lam_yeo, xtol=1.48e-08)
+            result = optimize.OptimizeResult()
+            result.x = out
+            return result
+
+        with np.errstate(all="raise"):
+            xt_yeo, lam_yeo = stats.yeojohnson(x)
+            xt_box, lam_box = stats.boxcox(
+                x + 1, optimizer=partial(optimizer, lam_yeo=lam_yeo))
+            assert np.isfinite(np.var(xt_yeo))
+            assert np.isfinite(np.var(xt_box))
+            assert_allclose(lam_yeo, lam_box, rtol=1e-6)
+            assert_allclose(xt_yeo, xt_box, rtol=1e-4)
+
+    @pytest.mark.parametrize('x', [
+        np.array([2003.0, 1950.0, 1997.0, 2000.0, 2009.0,
+                  2009.0, 1980.0, 1999.0, 2007.0, 1991.0]),
+        np.array([2003.0, 1950.0, 1997.0, 2000.0, 2009.0])
+    ])
+    @pytest.mark.parametrize('scale', [1, 1e-12, 1e-32, 1e-150, 1e32, 1e200])
+    @pytest.mark.parametrize('sign', [1, -1])
+    def test_overflow_underflow_signed_data(self, x, scale, sign):
+        # non-regression test for gh-18389
+        with np.errstate(all="raise"):
+            xt_yeo, lam_yeo = stats.yeojohnson(sign * x * scale)
+            assert np.all(np.sign(sign * x) == np.sign(xt_yeo))
+            assert np.isfinite(lam_yeo)
+            assert np.isfinite(np.var(xt_yeo))
+
+    @pytest.mark.parametrize('x', [
+        np.array([0, 1, 2, 3]),
+        np.array([0, -1, 2, -3]),
+        np.array([0, 0, 0])
+    ])
+    @pytest.mark.parametrize('sign', [1, -1])
+    @pytest.mark.parametrize('brack', [None, (-2, 2)])
+    def test_integer_signed_data(self, x, sign, brack):
+        with np.errstate(all="raise"):
+            x_int = sign * x
+            x_float = x_int.astype(np.float64)
+            lam_yeo_int = stats.yeojohnson_normmax(x_int, brack=brack)
+            xt_yeo_int = stats.yeojohnson(x_int, lmbda=lam_yeo_int)
+            lam_yeo_float = stats.yeojohnson_normmax(x_float, brack=brack)
+            xt_yeo_float = stats.yeojohnson(x_float, lmbda=lam_yeo_float)
+            assert np.all(np.sign(x_int) == np.sign(xt_yeo_int))
+            assert np.isfinite(lam_yeo_int)
+            assert np.isfinite(np.var(xt_yeo_int))
+            assert lam_yeo_int == lam_yeo_float
+            assert np.all(xt_yeo_int == xt_yeo_float)
+
+
+class TestYeojohnsonNormmax(NormmaxTest):
+    transform_normmax = 'yeojohnson_normmax'
+
+    def setup_method(self):
+        self.x = _old_loggamma_rvs(5, size=50, random_state=12345) + 5
+
+    def test_mle(self):
+        maxlog = stats.yeojohnson_normmax(self.x)
+        assert_allclose(maxlog, 1.876393, rtol=1e-6)
+
+    def test_darwin_example(self):
+        # test from original paper "A new family of power transformations to
+        # improve normality or symmetry" by Yeo and Johnson.
+        x = [6.1, -8.4, 1.0, 2.0, 0.7, 2.9, 3.5, 5.1, 1.8, 3.6, 7.0, 3.0, 9.3,
+             7.5, -6.0]
+        lmbda = stats.yeojohnson_normmax(x)
+        assert np.allclose(lmbda, 1.305, atol=1e-3)
+
+
+@make_xp_test_case(stats.circmean, stats.circvar, stats.circstd)
+class TestCircFuncs:
+    # In gh-5747, the R package `circular` was used to calculate reference
+    # values for the circular variance, e.g.:
+    # library(circular)
+    # options(digits=16)
+    # x = c(0, 2*pi/3, 5*pi/3)
+    # var.circular(x)
+    @pytest.mark.parametrize("test_func,expected",
+                             [(stats.circmean, 0.167690146),
+                              (stats.circvar, 0.006455174000787767),
+                              (stats.circstd, 6.520702116)])
+    def test_circfuncs(self, test_func, expected, xp):
+        x = xp.asarray([355., 5., 2., 359., 10., 350.])
+        xp_assert_close(test_func(x, high=360), xp.asarray(expected))
+
+    def test_circfuncs_small(self, xp):
+        # Default tolerances won't work here because the reference values
+        # are approximations. Ensure all array types work in float64 to
+        # avoid needing separate float32 and float64 tolerances.
+        x = xp.asarray([20, 21, 22, 18, 19, 20.5, 19.2], dtype=xp.float64)
+        M1 = xp.mean(x)
+        M2 = stats.circmean(x, high=360)
+        xp_assert_close(M2, M1, rtol=1e-5)
+
+        V1 = xp.var(x*xp.pi/180, correction=0)
+        # for small variations, circvar is approximately half the
+        # linear variance
+        V1 = V1 / 2.
+        V2 = stats.circvar(x, high=360)
+        xp_assert_close(V2, V1, rtol=1e-4)
+
+        S1 = xp.std(x, correction=0)
+        S2 = stats.circstd(x, high=360)
+        xp_assert_close(S2, S1, rtol=1e-4)
+
+    @pytest.mark.parametrize("test_func, numpy_func",
+                             [(stats.circmean, np.mean),
+                              (stats.circvar, np.var),
+                              (stats.circstd, np.std)])
+    def test_circfuncs_close(self, test_func, numpy_func, xp):
+        # circfuncs should handle very similar inputs (gh-12740)
+        x = np.asarray([0.12675364631578953] * 10 + [0.12675365920187928] * 100)
+        circstat = test_func(xp.asarray(x))
+        normal = xp.asarray(numpy_func(x))
+        xp_assert_close(circstat, normal, atol=2e-8)
+
+    @pytest.mark.parametrize('circfunc', [stats.circmean,
+                                          stats.circvar,
+                                          stats.circstd])
+    def test_circmean_axis(self, circfunc, xp):
+        x = xp.asarray([[355, 5, 2, 359, 10, 350],
+                        [351, 7, 4, 352, 9, 349],
+                        [357, 9, 8, 358, 4, 356.]])
+        res = circfunc(x, high=360)
+        ref = circfunc(xp.reshape(x, (-1,)), high=360)
+        xp_assert_close(res, xp.asarray(ref))
+
+        res = circfunc(x, high=360, axis=1)
+        ref = [circfunc(x[i, :], high=360) for i in range(x.shape[0])]
+        xp_assert_close(res, xp.stack(ref))
+
+        res = circfunc(x, high=360, axis=0)
+        ref = [circfunc(x[:, i], high=360) for i in range(x.shape[1])]
+        xp_assert_close(res, xp.stack(ref))
+
+    @pytest.mark.parametrize("test_func,expected",
+                             [(stats.circmean, 0.167690146),
+                              (stats.circvar, 0.006455174270186603),
+                              (stats.circstd, 6.520702116)])
+    def test_circfuncs_array_like(self, test_func, expected, xp):
+        x = xp.asarray([355, 5, 2, 359, 10, 350.])
+        xp_assert_close(test_func(x, high=360), xp.asarray(expected))
+
+    @pytest.mark.parametrize("test_func", [stats.circmean, stats.circvar,
+                                           stats.circstd])
+    def test_empty(self, test_func, xp):
+        dtype = xp.float64
+        x = xp.asarray([], dtype=dtype)
+        with eager_warns(SmallSampleWarning, match=too_small_1d_not_omit, xp=xp):
+            res = test_func(x)
+
+        xp_assert_equal(res, xp.asarray(xp.nan, dtype=dtype))
+
+    @pytest.mark.parametrize("test_func", [stats.circmean, stats.circvar,
+                                           stats.circstd])
+    def test_nan_propagate(self, test_func, xp):
+        x = xp.asarray([355, 5, 2, 359, 10, 350, np.nan])
+        xp_assert_equal(test_func(x, high=360), xp.asarray(xp.nan))
+
+    @pytest.mark.parametrize("test_func,expected",
+                             [(stats.circmean,
+                               {None: np.nan, 0: 355.66582264, 1: 0.28725053}),
+                              (stats.circvar,
+                               {None: np.nan,
+                                0: 0.002570671054089924,
+                                1: 0.005545914017677123}),
+                              (stats.circstd,
+                               {None: np.nan, 0: 4.11093193, 1: 6.04265394})])
+    def test_nan_propagate_array(self, test_func, expected, xp):
+        x = xp.asarray([[355, 5, 2, 359, 10, 350, 1],
+                        [351, 7, 4, 352, 9, 349, np.nan],
+                        [1, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan]])
+        for axis in expected.keys():
+            out = test_func(x, high=360, axis=axis)
+            if axis is None:
+                xp_assert_equal(out, xp.asarray(xp.nan))
+            else:
+                xp_assert_close(out[0], xp.asarray(expected[axis]))
+                xp_assert_equal(out[1:], xp.full_like(out[1:], xp.nan))
+
+    def test_circmean_scalar(self, xp):
+        x = xp.asarray(1.)[()]
+        M1 = x
+        M2 = stats.circmean(x)
+        xp_assert_close(M2, M1, rtol=1e-5)
+
+    def test_circmean_range(self, xp):
+        # regression test for gh-6420: circmean(..., high, low) must be
+        # between `high` and `low`
+        m = stats.circmean(xp.arange(0, 2, 0.1), xp.pi, -xp.pi)
+        xp_assert_less(m, xp.asarray(xp.pi))
+        xp_assert_less(-m, xp.asarray(xp.pi))
+
+    def test_circfuncs_uint8(self, xp):
+        # regression test for gh-7255: overflow when working with
+        # numpy uint8 data type
+        x = xp.asarray([150, 10], dtype=xp.uint8)
+        xp_assert_close(stats.circmean(x, high=180), xp.asarray(170.0))
+        xp_assert_close(stats.circvar(x, high=180), xp.asarray(0.2339555554617))
+        xp_assert_close(stats.circstd(x, high=180), xp.asarray(20.91551378))
+
+    def test_circstd_zero(self, xp):
+        # circstd() of a single number should return positive zero.
+        y = stats.circstd(xp.asarray([0]))
+        assert math.copysign(1.0, y) == 1.0
+
+    def test_circmean_accuracy_tiny_input(self, xp):
+        # For tiny x such that sin(x) == x and cos(x) == 1.0 numerically,
+        # circmean(x) should return x because atan2(sin(x), cos(x)) == x.
+        # This test verifies this.
+        #
+        # The purpose of this test is not to show that circmean() is
+        # accurate in the last digit for certain input, because this is
+        # neither guaranteed not particularly useful.  Rather, it is a
+        # "white-box" sanity check that no undue loss of precision is
+        # introduced by conversion between (high - low) and (2 * pi).
+
+        x = xp.linspace(1e-9, 6e-9, 50)
+        assert xp.all(xp.sin(x) == x) and xp.all(xp.cos(x) == 1.0)
+
+        m = (x * (2 * xp.pi) / (2 * xp.pi)) != x
+        assert xp.any(m)
+        x = x[m]
+
+        y = stats.circmean(x[:, None], axis=1)
+        assert xp.all(y == x)
+
+    def test_circmean_accuracy_huge_input(self, xp):
+        # White-box test that circmean() does not introduce undue loss of
+        # numerical accuracy by eagerly rotating the input.  This is detected
+        # by supplying a huge input x such that (x - low) == x numerically.
+        x = xp.asarray(1e17, dtype=xp.float64)
+        y = math.atan2(xp.sin(x), xp.cos(x))  # -2.6584887370946806
+        expected = xp.asarray(y, dtype=xp.float64)
+        actual = stats.circmean(x, high=xp.pi, low=-xp.pi)
+        xp_assert_close(actual, expected, rtol=1e-15, atol=0.0)
+
+
+class TestCircFuncsNanPolicy:
+    # `nan_policy` is implemented by the `_axis_nan_policy` decorator, which is
+    # not yet array-API compatible. When it is array-API compatible, the generic
+    # tests run on every function will be much stronger than these, so these
+    # will not be necessary. So I don't see a need to make these array-API compatible;
+    # when the time comes, they can just be removed.
+    @pytest.mark.parametrize("test_func,expected",
+                             [(stats.circmean,
+                               {None: 359.4178026893944,
+                                0: np.array([353.0, 6.0, 3.0, 355.5, 9.5,
+                                             349.5]),
+                                1: np.array([0.16769015, 358.66510252])}),
+                              (stats.circvar,
+                               {None: 0.008396678483192477,
+                                0: np.array([1.9997969, 0.4999873, 0.4999873,
+                                             6.1230956, 0.1249992, 0.1249992]
+                                            )*(np.pi/180)**2,
+                                1: np.array([0.006455174270186603,
+                                             0.01016767581393285])}),
+                              (stats.circstd,
+                               {None: 7.440570778057074,
+                                0: np.array([2.00020313, 1.00002539, 1.00002539,
+                                             3.50108929, 0.50000317,
+                                             0.50000317]),
+                                1: np.array([6.52070212, 8.19138093])})])
+    def test_nan_omit_array(self, test_func, expected):
+        x = np.array([[355, 5, 2, 359, 10, 350, np.nan],
+                      [351, 7, 4, 352, 9, 349, np.nan],
+                      [np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan]])
+        for axis in expected.keys():
+            if axis is None:
+                out = test_func(x, high=360, nan_policy='omit', axis=axis)
+                assert_allclose(out, expected[axis], rtol=1e-7)
+            else:
+                with pytest.warns(SmallSampleWarning, match=too_small_nd_omit):
+                    out = test_func(x, high=360, nan_policy='omit', axis=axis)
+                    assert_allclose(out[:-1], expected[axis], rtol=1e-7)
+                    assert_(np.isnan(out[-1]))
+
+    @pytest.mark.parametrize("test_func,expected",
+                             [(stats.circmean, 0.167690146),
+                              (stats.circvar, 0.006455174270186603),
+                              (stats.circstd, 6.520702116)])
+    def test_nan_omit(self, test_func, expected):
+        x = [355, 5, 2, 359, 10, 350, np.nan]
+        assert_allclose(test_func(x, high=360, nan_policy='omit'),
+                        expected, rtol=1e-7)
+
+    @pytest.mark.parametrize("test_func", [stats.circmean, stats.circvar,
+                                           stats.circstd])
+    def test_nan_omit_all(self, test_func):
+        x = [np.nan, np.nan, np.nan, np.nan, np.nan]
+        with pytest.warns(SmallSampleWarning, match=too_small_1d_omit):
+            assert_(np.isnan(test_func(x, nan_policy='omit')))
+
+    @pytest.mark.parametrize("test_func", [stats.circmean, stats.circvar,
+                                           stats.circstd])
+    def test_nan_omit_all_axis(self, test_func):
+        with pytest.warns(SmallSampleWarning, match=too_small_nd_omit):
+            x = np.array([[np.nan, np.nan, np.nan, np.nan, np.nan],
+                          [np.nan, np.nan, np.nan, np.nan, np.nan]])
+            out = test_func(x, nan_policy='omit', axis=1)
+            assert_(np.isnan(out).all())
+            assert_(len(out) == 2)
+
+    @pytest.mark.parametrize("x",
+                             [[355, 5, 2, 359, 10, 350, np.nan],
+                              np.array([[355, 5, 2, 359, 10, 350, np.nan],
+                                        [351, 7, 4, 352, np.nan, 9, 349]])])
+    @pytest.mark.parametrize("test_func", [stats.circmean, stats.circvar,
+                                           stats.circstd])
+    def test_nan_raise(self, test_func, x):
+        assert_raises(ValueError, test_func, x, high=360, nan_policy='raise')
+
+    @pytest.mark.parametrize("x",
+                             [[355, 5, 2, 359, 10, 350, np.nan],
+                              np.array([[355, 5, 2, 359, 10, 350, np.nan],
+                                        [351, 7, 4, 352, np.nan, 9, 349]])])
+    @pytest.mark.parametrize("test_func", [stats.circmean, stats.circvar,
+                                           stats.circstd])
+    def test_bad_nan_policy(self, test_func, x):
+        assert_raises(ValueError, test_func, x, high=360, nan_policy='foobar')
+
+
+class TestMedianTest:
+
+    def test_bad_n_samples(self):
+        # median_test requires at least two samples.
+        assert_raises(ValueError, stats.median_test, [1, 2, 3])
+
+    def test_empty_sample(self):
+        # Each sample must contain at least one value.
+        assert_raises(ValueError, stats.median_test, [], [1, 2, 3])
+
+    def test_empty_when_ties_ignored(self):
+        # The grand median is 1, and all values in the first argument are
+        # equal to the grand median.  With ties="ignore", those values are
+        # ignored, which results in the first sample being (in effect) empty.
+        # This should raise a ValueError.
+        assert_raises(ValueError, stats.median_test,
+                      [1, 1, 1, 1], [2, 0, 1], [2, 0], ties="ignore")
+
+    def test_empty_contingency_row(self):
+        # The grand median is 1, and with the default ties="below", all the
+        # values in the samples are counted as being below the grand median.
+        # This would result a row of zeros in the contingency table, which is
+        # an error.
+        assert_raises(ValueError, stats.median_test, [1, 1, 1], [1, 1, 1])
+
+        # With ties="above", all the values are counted as above the
+        # grand median.
+        assert_raises(ValueError, stats.median_test, [1, 1, 1], [1, 1, 1],
+                      ties="above")
+
+    def test_bad_ties(self):
+        assert_raises(ValueError, stats.median_test, [1, 2, 3], [4, 5],
+                      ties="foo")
+
+    def test_bad_nan_policy(self):
+        assert_raises(ValueError, stats.median_test, [1, 2, 3], [4, 5],
+                      nan_policy='foobar')
+
+    def test_bad_keyword(self):
+        assert_raises(TypeError, stats.median_test, [1, 2, 3], [4, 5],
+                      foo="foo")
+
+    def test_simple(self):
+        x = [1, 2, 3]
+        y = [1, 2, 3]
+        stat, p, med, tbl = stats.median_test(x, y)
+
+        # The median is floating point, but this equality test should be safe.
+        assert_equal(med, 2.0)
+
+        assert_array_equal(tbl, [[1, 1], [2, 2]])
+
+        # The expected values of the contingency table equal the contingency
+        # table, so the statistic should be 0 and the p-value should be 1.
+        assert_equal(stat, 0)
+        assert_equal(p, 1)
+
+    def test_ties_options(self):
+        # Test the contingency table calculation.
+        x = [1, 2, 3, 4]
+        y = [5, 6]
+        z = [7, 8, 9]
+        # grand median is 5.
+
+        # Default 'ties' option is "below".
+        stat, p, m, tbl = stats.median_test(x, y, z)
+        assert_equal(m, 5)
+        assert_equal(tbl, [[0, 1, 3], [4, 1, 0]])
+
+        stat, p, m, tbl = stats.median_test(x, y, z, ties="ignore")
+        assert_equal(m, 5)
+        assert_equal(tbl, [[0, 1, 3], [4, 0, 0]])
+
+        stat, p, m, tbl = stats.median_test(x, y, z, ties="above")
+        assert_equal(m, 5)
+        assert_equal(tbl, [[0, 2, 3], [4, 0, 0]])
+
+    def test_nan_policy_options(self):
+        x = [1, 2, np.nan]
+        y = [4, 5, 6]
+        mt1 = stats.median_test(x, y, nan_policy='propagate')
+        s, p, m, t = stats.median_test(x, y, nan_policy='omit')
+
+        assert_equal(mt1, (np.nan, np.nan, np.nan, None))
+        assert_allclose(s, 0.31250000000000006)
+        assert_allclose(p, 0.57615012203057869)
+        assert_equal(m, 4.0)
+        assert_equal(t, np.array([[0, 2], [2, 1]]))
+        assert_raises(ValueError, stats.median_test, x, y, nan_policy='raise')
+
+    def test_basic(self):
+        # median_test calls chi2_contingency to compute the test statistic
+        # and p-value.  Make sure it hasn't screwed up the call...
+
+        x = [1, 2, 3, 4, 5]
+        y = [2, 4, 6, 8]
+
+        stat, p, m, tbl = stats.median_test(x, y)
+        assert_equal(m, 4)
+        assert_equal(tbl, [[1, 2], [4, 2]])
+
+        exp_stat, exp_p, dof, e = stats.chi2_contingency(tbl)
+        assert_allclose(stat, exp_stat)
+        assert_allclose(p, exp_p)
+
+        stat, p, m, tbl = stats.median_test(x, y, lambda_=0)
+        assert_equal(m, 4)
+        assert_equal(tbl, [[1, 2], [4, 2]])
+
+        exp_stat, exp_p, dof, e = stats.chi2_contingency(tbl, lambda_=0)
+        assert_allclose(stat, exp_stat)
+        assert_allclose(p, exp_p)
+
+        stat, p, m, tbl = stats.median_test(x, y, correction=False)
+        assert_equal(m, 4)
+        assert_equal(tbl, [[1, 2], [4, 2]])
+
+        exp_stat, exp_p, dof, e = stats.chi2_contingency(tbl, correction=False)
+        assert_allclose(stat, exp_stat)
+        assert_allclose(p, exp_p)
+
+    @pytest.mark.parametrize("correction", [False, True])
+    def test_result(self, correction):
+        x = [1, 2, 3]
+        y = [1, 2, 3]
+
+        res = stats.median_test(x, y, correction=correction)
+        assert_equal((res.statistic, res.pvalue, res.median, res.table), res)
+
+
+@make_xp_test_case(stats.directional_stats)
+class TestDirectionalStats:
+    # Reference implementations are not available
+    def test_directional_stats_correctness(self, xp):
+        # Data from Fisher: Dispersion on a sphere, 1953 and
+        # Mardia and Jupp, Directional Statistics.
+        decl = -np.deg2rad(np.array([343.2, 62., 36.9, 27., 359.,
+                                     5.7, 50.4, 357.6, 44.]))
+        incl = -np.deg2rad(np.array([66.1, 68.7, 70.1, 82.1, 79.5,
+                                     73., 69.3, 58.8, 51.4]))
+        data = np.stack((np.cos(incl) * np.cos(decl),
+                         np.cos(incl) * np.sin(decl),
+                         np.sin(incl)),
+                        axis=1)
+
+        decl = xp.asarray(decl.tolist())
+        incl = xp.asarray(incl.tolist())
+        data = xp.asarray(data.tolist())
+
+        dirstats = stats.directional_stats(data)
+        directional_mean = dirstats.mean_direction
+
+        reference_mean = xp.asarray([0.2984, -0.1346, -0.9449])
+        xp_assert_close(directional_mean, reference_mean, atol=1e-4)
+
+    @pytest.mark.parametrize('angles, ref', [
+        ([-np.pi/2, np.pi/2], 1.),
+        ([0, 2 * np.pi], 0.)
+    ])
+    def test_directional_stats_2d_special_cases(self, angles, ref, xp):
+        angles = xp.asarray(angles)
+        ref = xp.asarray(ref)
+        data = xp.stack([xp.cos(angles), xp.sin(angles)], axis=1)
+        res = 1 - stats.directional_stats(data).mean_resultant_length
+        xp_assert_close(res, ref)
+
+    def test_directional_stats_2d(self, xp):
+        # Test that for circular data directional_stats
+        # yields the same result as circmean/circvar
+        rng = np.random.default_rng(0xec9a6899d5a2830e0d1af479dbe1fd0c)
+        testdata = xp.asarray(2 * xp.pi * rng.random((1000, )))
+        testdata_vector = xp.stack((xp.cos(testdata),
+                                    xp.sin(testdata)),
+                                   axis=1)
+        dirstats = stats.directional_stats(testdata_vector)
+        directional_mean = dirstats.mean_direction
+        directional_mean_angle = xp.atan2(directional_mean[1], directional_mean[0])
+        directional_mean_angle = directional_mean_angle % (2 * xp.pi)
+        circmean = stats.circmean(testdata)
+        xp_assert_close(directional_mean_angle, circmean)
+
+        directional_var = 1. - dirstats.mean_resultant_length
+        circular_var = stats.circvar(testdata)
+        xp_assert_close(directional_var, circular_var)
+
+    def test_directional_mean_higher_dim(self, xp):
+        # test that directional_stats works for higher dimensions
+        # here a 4D array is reduced over axis = 2
+        data = xp.asarray([[0.8660254, 0.5, 0.],
+                           [0.8660254, -0.5, 0.]])
+        full_array = xp.asarray(xp.tile(data, (2, 2, 2, 1)))
+        expected = xp.asarray([[[1., 0., 0.],
+                                [1., 0., 0.]],
+                               [[1., 0., 0.],
+                                [1., 0., 0.]]])
+        dirstats = stats.directional_stats(full_array, axis=2)
+        xp_assert_close(dirstats.mean_direction, expected)
+
+    @skip_xp_backends(np_only=True, reason='checking array-like input')
+    def test_directional_stats_list_ndarray_input(self, xp):
+        # test that list and numpy array inputs yield same results
+        data = [[0.8660254, 0.5, 0.], [0.8660254, -0.5, 0]]
+        data_array = xp.asarray(data, dtype=xp.float64)
+        ref = stats.directional_stats(data)
+        res = stats.directional_stats(data_array)
+        xp_assert_close(res.mean_direction,
+                        xp.asarray(ref.mean_direction))
+        xp_assert_close(res.mean_resultant_length,
+                        xp.asarray(res.mean_resultant_length))
+
+    def test_directional_stats_1d_error(self, xp):
+        # test that one-dimensional data raises ValueError
+        data = xp.ones((5, ))
+        message = (r"samples must at least be two-dimensional. "
+                   r"Instead samples has shape: (5,)")
+        with pytest.raises(ValueError, match=re.escape(message)):
+            stats.directional_stats(data)
+
+    @pytest.mark.parametrize("dtype", ["float32", "float64"])
+    def test_directional_stats_normalize(self, dtype, xp):
+        # test that directional stats calculations yield same results
+        # for unnormalized input with normalize=True and normalized
+        # input with normalize=False
+        data = np.array([[0.8660254, 0.5, 0.],
+                         [1.7320508, -1., 0.]], dtype=dtype)
+        res = stats.directional_stats(xp.asarray(data), normalize=True)
+        normalized_data = data / np.linalg.norm(data, axis=-1,
+                                                keepdims=True)
+        ref = stats.directional_stats(normalized_data, normalize=False)
+        xp_assert_close(res.mean_direction,
+                        xp.asarray(ref.mean_direction))
+        xp_assert_close(res.mean_resultant_length,
+                        xp.asarray(ref.mean_resultant_length))
+
+
+@make_xp_test_case(stats.false_discovery_control)
+class TestFDRControl:
+    @skip_xp_backends(eager_only=True)
+    def test_input_validation_ps(self, xp):
+        message = "All values in `ps` must lie between 0. and 1."
+        with pytest.raises(ValueError, match=message):
+            stats.false_discovery_control(xp.asarray([-1, 0.5, 0.7]))
+        with pytest.raises(ValueError, match=message):
+            stats.false_discovery_control(xp.asarray([0.5, 0.7, 2]))
+        with pytest.raises(ValueError, match=message):
+            stats.false_discovery_control(xp.asarray([0.5, 0.7, xp.nan]))
+
+    def test_input_validation(self, xp):
+        message = "`ps` must contain only real numbers."
+        with pytest.raises(ValueError, match=message):
+            stats.false_discovery_control(xp.asarray([1+1j, 2+2j]))
+
+        message = "Unrecognized `method` 'YAK'"
+        with pytest.raises(ValueError, match=message):
+            stats.false_discovery_control(xp.asarray([0.5, 0.7, 0.9]), method='YAK')
+
+        message = "`axis` must be an integer or `None`"
+        with pytest.raises(ValueError, match=message):
+            stats.false_discovery_control(xp.asarray([0.5, 0.7, 0.9]), axis=1.5)
+        with pytest.raises(ValueError, match=message):
+            stats.false_discovery_control(xp.asarray([0.5, 0.7, 0.9]), axis=(1, 2))
+
+    def test_against_TileStats(self, xp):
+        # See reference [3] of false_discovery_control
+        ps = xp.asarray([0.005, 0.009, 0.019, 0.022, 0.051, 0.101, 0.361, 0.387])
+        res = stats.false_discovery_control(ps)
+        ref = xp.asarray([0.036, 0.036, 0.044, 0.044, 0.082, 0.135, 0.387, 0.387])
+        xp_assert_close(res, ref, atol=1e-3)
+
+    @pytest.mark.parametrize("case",
+                             [([0.24617028, 0.01140030, 0.05652047, 0.06841983,
+                                0.07989886, 0.01841490, 0.17540784, 0.06841983,
+                                0.06841983, 0.25464082], 'bh'),
+                              ([0.72102493, 0.03339112, 0.16554665, 0.20039952,
+                                0.23402122, 0.05393666, 0.51376399, 0.20039952,
+                                0.20039952, 0.74583488], 'by')])
+    def test_against_R(self, case, xp):
+        # Test against p.adjust, e.g.
+        # p = c(0.22155325, 0.00114003,..., 0.0364813 , 0.25464082)
+        # p.adjust(p, "BY")
+        ref, method = case
+        rng = np.random.default_rng(6134137338861652935)
+        ps = stats.loguniform.rvs(1e-3, 0.5, size=10, random_state=rng).tolist()
+        ps[3] = ps[7]  # force a tie
+        res = stats.false_discovery_control(xp.asarray(ps), method=method)
+        xp_assert_close(res, xp.asarray(ref), atol=1e-6)
+
+    def test_axis_None(self, xp):
+        rng = np.random.default_rng(6134137338861652935)
+        ps = stats.loguniform.rvs(1e-3, 0.5, size=(3, 4, 5), random_state=rng)
+        ps = xp.asarray(ps)
+        res = stats.false_discovery_control(ps, axis=None)
+        ref = stats.false_discovery_control(xp_ravel(ps))
+        xp_assert_equal(res, ref)
+
+    @pytest.mark.parametrize("axis", [0, 1, -1])
+    def test_axis(self, axis, xp):
+        rng = np.random.default_rng(6134137338861652935)
+        ps = stats.loguniform.rvs(1e-3, 0.5, size=(3, 4, 5), random_state=rng)
+        res = stats.false_discovery_control(xp.asarray(ps), axis=axis)
+        ref = np.apply_along_axis(stats.false_discovery_control, axis, ps)
+        xp_assert_close(res, xp.asarray(ref))  # torch isn't *equal*
+
+    def test_edge_cases(self, xp):
+        ps = xp.asarray([0.25])
+        xp_assert_equal(stats.false_discovery_control(ps), ps)
+
+        ps = xp.asarray([])
+        xp_assert_equal(stats.false_discovery_control(ps), ps)
+
+        if is_numpy(xp):
+            xp_assert_equal(stats.false_discovery_control(0.25), 0.25)
+
+
+@pytest.mark.uses_xp_capabilities(False, reason="not used in this test yet")
+class TestCommonAxis:
+    # More thorough testing of `axis` in `test_axis_nan_policy`,
+    # but those tests aren't run with array API yet. This class
+    # is in `test_morestats` instead of `test_axis_nan_policy`
+    # because there is no reason to run `test_axis_nan_policy`
+    # with the array API CI job right now.
+
+    @pytest.mark.parametrize('case', [(stats.sem, {}),
+                                      (stats.kstat, {'n': 4}),
+                                      (stats.kstat, {'n': 2}),
+                                      (stats.variation, {})])
+    def test_axis(self, case, xp):
+        if is_torch(xp) and case[0] == stats.variation:
+            pytest.xfail(reason="copysign doesn't accept scalar array-api-compat#271")
+        fun, kwargs = case
+        rng = np.random.default_rng(24598245982345)
+        x = xp.asarray(rng.random((6, 7)))
+
+        res = fun(x, **kwargs, axis=0)
+        ref = xp.stack([fun(x[:, i], **kwargs) for i in range(x.shape[1])])
+        xp_assert_close(res, ref)
+
+        res = fun(x, **kwargs, axis=1)
+        ref = xp.stack([fun(x[i, :], **kwargs) for i in range(x.shape[0])])
+        xp_assert_close(res, ref)
+
+        res = fun(x, **kwargs, axis=None)
+        ref = fun(xp.reshape(x, (-1,)), **kwargs)
+        xp_assert_close(res, ref)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/test_mstats_basic.py b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_mstats_basic.py
new file mode 100644
index 0000000000000000000000000000000000000000..475ca50f7dd001d4d04326cc04a258ff739c3154
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_mstats_basic.py
@@ -0,0 +1,2146 @@
+"""
+Tests for the stats.mstats module (support for masked arrays)
+"""
+import warnings
+import platform
+
+import numpy as np
+from numpy import nan
+import numpy.ma as ma
+from numpy.ma import masked, nomask
+
+import scipy.stats.mstats as mstats
+from scipy import stats
+from .common_tests import check_named_results
+import pytest
+from pytest import raises as assert_raises
+from numpy.ma.testutils import (assert_equal, assert_almost_equal,
+                                assert_array_almost_equal,
+                                assert_array_almost_equal_nulp, assert_,
+                                assert_allclose, assert_array_equal)
+from scipy.stats import _mstats_basic, _stats_py
+from scipy.conftest import skip_xp_invalid_arg
+from scipy.stats._axis_nan_policy import SmallSampleWarning, too_small_1d_not_omit
+
+class TestMquantiles:
+    def test_mquantiles_limit_keyword(self):
+        # Regression test for Trac ticket #867
+        data = np.array([[6., 7., 1.],
+                         [47., 15., 2.],
+                         [49., 36., 3.],
+                         [15., 39., 4.],
+                         [42., 40., -999.],
+                         [41., 41., -999.],
+                         [7., -999., -999.],
+                         [39., -999., -999.],
+                         [43., -999., -999.],
+                         [40., -999., -999.],
+                         [36., -999., -999.]])
+        desired = [[19.2, 14.6, 1.45],
+                   [40.0, 37.5, 2.5],
+                   [42.8, 40.05, 3.55]]
+        quants = mstats.mquantiles(data, axis=0, limit=(0, 50))
+        assert_almost_equal(quants, desired)
+
+
+def check_equal_gmean(array_like, desired, axis=None, dtype=None, rtol=1e-7):
+    # Note this doesn't test when axis is not specified
+    x = mstats.gmean(array_like, axis=axis, dtype=dtype)
+    assert_allclose(x, desired, rtol=rtol)
+    assert_equal(x.dtype, dtype)
+
+
+def check_equal_hmean(array_like, desired, axis=None, dtype=None, rtol=1e-7):
+    x = stats.hmean(array_like, axis=axis, dtype=dtype)
+    assert_allclose(x, desired, rtol=rtol)
+    assert_equal(x.dtype, dtype)
+
+
+@skip_xp_invalid_arg
+class TestGeoMean:
+    def test_1d(self):
+        a = [1, 2, 3, 4]
+        desired = np.power(1*2*3*4, 1./4.)
+        check_equal_gmean(a, desired, rtol=1e-14)
+
+    def test_1d_ma(self):
+        #  Test a 1d masked array
+        a = ma.array([10, 20, 30, 40, 50, 60, 70, 80, 90, 100])
+        desired = 45.2872868812
+        check_equal_gmean(a, desired)
+
+        a = ma.array([1, 2, 3, 4], mask=[0, 0, 0, 1])
+        desired = np.power(1*2*3, 1./3.)
+        check_equal_gmean(a, desired, rtol=1e-14)
+
+    def test_1d_ma_value(self):
+        #  Test a 1d masked array with a masked value
+        a = np.ma.array([10, 20, 30, 40, 50, 60, 70, 80, 90, 100],
+                        mask=[0, 0, 0, 0, 0, 0, 0, 0, 0, 1])
+        desired = 41.4716627439
+        check_equal_gmean(a, desired)
+
+    def test_1d_ma0(self):
+        #  Test a 1d masked array with zero element
+        a = np.ma.array([10, 20, 30, 40, 50, 60, 70, 80, 90, 0])
+        desired = 0
+        check_equal_gmean(a, desired)
+
+    def test_1d_ma_inf(self):
+        #  Test a 1d masked array with negative element
+        a = np.ma.array([10, 20, 30, 40, 50, 60, 70, 80, 90, -1])
+        desired = np.nan
+        with np.errstate(invalid='ignore'):
+            check_equal_gmean(a, desired)
+
+    @pytest.mark.skipif(not hasattr(np, 'float96'),
+                        reason='cannot find float96 so skipping')
+    def test_1d_float96(self):
+        a = ma.array([1, 2, 3, 4], mask=[0, 0, 0, 1])
+        desired_dt = np.power(1*2*3, 1./3.).astype(np.float96)
+        check_equal_gmean(a, desired_dt, dtype=np.float96, rtol=1e-14)
+
+    def test_2d_ma(self):
+        a = ma.array([[1, 2, 3, 4], [1, 2, 3, 4], [1, 2, 3, 4]],
+                     mask=[[0, 0, 0, 0], [1, 0, 0, 1], [0, 1, 1, 0]])
+        desired = np.array([1, 2, 3, 4])
+        check_equal_gmean(a, desired, axis=0, rtol=1e-14)
+
+        desired = ma.array([np.power(1*2*3*4, 1./4.),
+                            np.power(2*3, 1./2.),
+                            np.power(1*4, 1./2.)])
+        check_equal_gmean(a, desired, axis=-1, rtol=1e-14)
+
+        #  Test a 2d masked array
+        a = [[10, 20, 30, 40], [50, 60, 70, 80], [90, 100, 110, 120]]
+        desired = 52.8885199
+        check_equal_gmean(np.ma.array(a), desired)
+
+
+@skip_xp_invalid_arg
+class TestHarMean:
+    def test_1d(self):
+        a = ma.array([1, 2, 3, 4], mask=[0, 0, 0, 1])
+        desired = 3. / (1./1 + 1./2 + 1./3)
+        check_equal_hmean(a, desired, rtol=1e-14)
+
+        a = np.ma.array([10, 20, 30, 40, 50, 60, 70, 80, 90, 100])
+        desired = 34.1417152147
+        check_equal_hmean(a, desired)
+
+        a = np.ma.array([10, 20, 30, 40, 50, 60, 70, 80, 90, 100],
+                        mask=[0, 0, 0, 0, 0, 0, 0, 0, 0, 1])
+        desired = 31.8137186141
+        check_equal_hmean(a, desired)
+
+    @pytest.mark.skipif(not hasattr(np, 'float96'),
+                        reason='cannot find float96 so skipping')
+    def test_1d_float96(self):
+        a = ma.array([1, 2, 3, 4], mask=[0, 0, 0, 1])
+        desired_dt = np.asarray(3. / (1./1 + 1./2 + 1./3), dtype=np.float96)
+        check_equal_hmean(a, desired_dt, dtype=np.float96)
+
+    def test_2d(self):
+        a = ma.array([[1, 2, 3, 4], [1, 2, 3, 4], [1, 2, 3, 4]],
+                     mask=[[0, 0, 0, 0], [1, 0, 0, 1], [0, 1, 1, 0]])
+        desired = ma.array([1, 2, 3, 4])
+        check_equal_hmean(a, desired, axis=0, rtol=1e-14)
+
+        desired = [4./(1/1.+1/2.+1/3.+1/4.), 2./(1/2.+1/3.), 2./(1/1.+1/4.)]
+        check_equal_hmean(a, desired, axis=-1, rtol=1e-14)
+
+        a = [[10, 20, 30, 40], [50, 60, 70, 80], [90, 100, 110, 120]]
+        desired = 38.6696271841
+        check_equal_hmean(np.ma.array(a), desired)
+
+
+class TestRanking:
+    def test_ranking(self):
+        x = ma.array([0,1,1,1,2,3,4,5,5,6,])
+        assert_almost_equal(mstats.rankdata(x),
+                            [1,3,3,3,5,6,7,8.5,8.5,10])
+        x[[3,4]] = masked
+        assert_almost_equal(mstats.rankdata(x),
+                            [1,2.5,2.5,0,0,4,5,6.5,6.5,8])
+        assert_almost_equal(mstats.rankdata(x, use_missing=True),
+                            [1,2.5,2.5,4.5,4.5,4,5,6.5,6.5,8])
+        x = ma.array([0,1,5,1,2,4,3,5,1,6,])
+        assert_almost_equal(mstats.rankdata(x),
+                            [1,3,8.5,3,5,7,6,8.5,3,10])
+        x = ma.array([[0,1,1,1,2], [3,4,5,5,6,]])
+        assert_almost_equal(mstats.rankdata(x),
+                            [[1,3,3,3,5], [6,7,8.5,8.5,10]])
+        assert_almost_equal(mstats.rankdata(x, axis=1),
+                            [[1,3,3,3,5], [1,2,3.5,3.5,5]])
+        assert_almost_equal(mstats.rankdata(x,axis=0),
+                            [[1,1,1,1,1], [2,2,2,2,2,]])
+
+
+class TestCorr:
+    def test_pearsonr(self):
+        # Tests some computations of Pearson's r
+        x = ma.arange(10)
+        with warnings.catch_warnings():
+            # The tests in this context are edge cases, with perfect
+            # correlation or anticorrelation, or totally masked data.
+            # None of these should trigger a RuntimeWarning.
+            warnings.simplefilter("error", RuntimeWarning)
+
+            assert_almost_equal(mstats.pearsonr(x, x)[0], 1.0)
+            assert_almost_equal(mstats.pearsonr(x, x[::-1])[0], -1.0)
+
+            x = ma.array(x, mask=True)
+            pr = mstats.pearsonr(x, x)
+            assert_(pr[0] is masked)
+            assert_(pr[1] is masked)
+
+        x1 = ma.array([-1.0, 0.0, 1.0])
+        y1 = ma.array([0, 0, 3])
+        r, p = mstats.pearsonr(x1, y1)
+        assert_almost_equal(r, np.sqrt(3)/2)
+        assert_almost_equal(p, 1.0/3)
+
+        # (x2, y2) have the same unmasked data as (x1, y1).
+        mask = [False, False, False, True]
+        x2 = ma.array([-1.0, 0.0, 1.0, 99.0], mask=mask)
+        y2 = ma.array([0, 0, 3, -1], mask=mask)
+        r, p = mstats.pearsonr(x2, y2)
+        assert_almost_equal(r, np.sqrt(3)/2)
+        assert_almost_equal(p, 1.0/3)
+
+    def test_pearsonr_misaligned_mask(self):
+        mx = np.ma.masked_array([1, 2, 3, 4, 5, 6], mask=[0, 1, 0, 0, 0, 0])
+        my = np.ma.masked_array([9, 8, 7, 6, 5, 9], mask=[0, 0, 1, 0, 0, 0])
+        x = np.array([1, 4, 5, 6])
+        y = np.array([9, 6, 5, 9])
+        mr, mp = mstats.pearsonr(mx, my)
+        r, p = stats.pearsonr(x, y)
+        assert_equal(mr, r)
+        assert_equal(mp, p)
+
+    def test_spearmanr(self):
+        # Tests some computations of Spearman's rho
+        (x, y) = ([5.05,6.75,3.21,2.66], [1.65,2.64,2.64,6.95])
+        assert_almost_equal(mstats.spearmanr(x,y)[0], -0.6324555)
+        (x, y) = ([5.05,6.75,3.21,2.66,np.nan],[1.65,2.64,2.64,6.95,np.nan])
+        (x, y) = (ma.fix_invalid(x), ma.fix_invalid(y))
+        assert_almost_equal(mstats.spearmanr(x,y)[0], -0.6324555)
+
+        x = [2.0, 47.4, 42.0, 10.8, 60.1, 1.7, 64.0, 63.1,
+             1.0, 1.4, 7.9, 0.3, 3.9, 0.3, 6.7]
+        y = [22.6, 8.3, 44.4, 11.9, 24.6, 0.6, 5.7, 41.6,
+             0.0, 0.6, 6.7, 3.8, 1.0, 1.2, 1.4]
+        assert_almost_equal(mstats.spearmanr(x,y)[0], 0.6887299)
+        x = [2.0, 47.4, 42.0, 10.8, 60.1, 1.7, 64.0, 63.1,
+             1.0, 1.4, 7.9, 0.3, 3.9, 0.3, 6.7, np.nan]
+        y = [22.6, 8.3, 44.4, 11.9, 24.6, 0.6, 5.7, 41.6,
+             0.0, 0.6, 6.7, 3.8, 1.0, 1.2, 1.4, np.nan]
+        (x, y) = (ma.fix_invalid(x), ma.fix_invalid(y))
+        assert_almost_equal(mstats.spearmanr(x,y)[0], 0.6887299)
+        # Next test is to make sure calculation uses sufficient precision.
+        # The denominator's value is ~n^3 and used to be represented as an
+        # int. 2000**3 > 2**32 so these arrays would cause overflow on
+        # some machines.
+        x = list(range(2000))
+        y = list(range(2000))
+        y[0], y[9] = y[9], y[0]
+        y[10], y[434] = y[434], y[10]
+        y[435], y[1509] = y[1509], y[435]
+        # rho = 1 - 6 * (2 * (9^2 + 424^2 + 1074^2))/(2000 * (2000^2 - 1))
+        #     = 1 - (1 / 500)
+        #     = 0.998
+        assert_almost_equal(mstats.spearmanr(x,y)[0], 0.998)
+
+        # test for namedtuple attributes
+        res = mstats.spearmanr(x, y)
+        attributes = ('correlation', 'pvalue')
+        check_named_results(res, attributes, ma=True)
+
+    def test_spearmanr_alternative(self):
+        # check against R
+        # options(digits=16)
+        # cor.test(c(2.0, 47.4, 42.0, 10.8, 60.1, 1.7, 64.0, 63.1,
+        #            1.0, 1.4, 7.9, 0.3, 3.9, 0.3, 6.7),
+        #          c(22.6, 8.3, 44.4, 11.9, 24.6, 0.6, 5.7, 41.6,
+        #            0.0, 0.6, 6.7, 3.8, 1.0, 1.2, 1.4),
+        #          alternative='two.sided', method='spearman')
+        x = [2.0, 47.4, 42.0, 10.8, 60.1, 1.7, 64.0, 63.1,
+             1.0, 1.4, 7.9, 0.3, 3.9, 0.3, 6.7]
+        y = [22.6, 8.3, 44.4, 11.9, 24.6, 0.6, 5.7, 41.6,
+             0.0, 0.6, 6.7, 3.8, 1.0, 1.2, 1.4]
+
+        r_exp = 0.6887298747763864  # from cor.test
+
+        r, p = mstats.spearmanr(x, y)
+        assert_allclose(r, r_exp)
+        assert_allclose(p, 0.004519192910756)
+
+        r, p = mstats.spearmanr(x, y, alternative='greater')
+        assert_allclose(r, r_exp)
+        assert_allclose(p, 0.002259596455378)
+
+        r, p = mstats.spearmanr(x, y, alternative='less')
+        assert_allclose(r, r_exp)
+        assert_allclose(p, 0.9977404035446)
+
+        # intuitive test (with obvious positive correlation)
+        rng = np.random.default_rng(9607138567)
+        n = 100
+        x = np.linspace(0, 5, n)
+        y = 0.1*x + rng.random(n)  # y is positively correlated w/ x
+
+        stat1, p1 = mstats.spearmanr(x, y)
+
+        stat2, p2 = mstats.spearmanr(x, y, alternative="greater")
+        assert_allclose(p2, p1 / 2)  # positive correlation -> small p
+
+        stat3, p3 = mstats.spearmanr(x, y, alternative="less")
+        assert_allclose(p3, 1 - p1 / 2)  # positive correlation -> large p
+
+        assert stat1 == stat2 == stat3
+
+        with pytest.raises(ValueError, match="alternative must be 'less'..."):
+            mstats.spearmanr(x, y, alternative="ekki-ekki")
+
+    @pytest.mark.skipif(platform.machine() == 'ppc64le',
+                        reason="fails/crashes on ppc64le")
+    def test_kendalltau(self):
+        # check case with maximum disorder and p=1
+        x = ma.array(np.array([9, 2, 5, 6]))
+        y = ma.array(np.array([4, 7, 9, 11]))
+        # Cross-check with exact result from R:
+        # cor.test(x,y,method="kendall",exact=1)
+        expected = [0.0, 1.0]
+        assert_almost_equal(np.asarray(mstats.kendalltau(x, y)), expected)
+
+        # simple case without ties
+        x = ma.array(np.arange(10))
+        y = ma.array(np.arange(10))
+        # Cross-check with exact result from R:
+        # cor.test(x,y,method="kendall",exact=1)
+        expected = [1.0, 5.511463844797e-07]
+        assert_almost_equal(np.asarray(mstats.kendalltau(x, y)), expected)
+
+        # check exception in case of invalid method keyword
+        assert_raises(ValueError, mstats.kendalltau, x, y, method='banana')
+
+        # swap a couple of values
+        b = y[1]
+        y[1] = y[2]
+        y[2] = b
+        # Cross-check with exact result from R:
+        # cor.test(x,y,method="kendall",exact=1)
+        expected = [0.9555555555555556, 5.511463844797e-06]
+        assert_almost_equal(np.asarray(mstats.kendalltau(x, y)), expected)
+
+        # swap a couple more
+        b = y[5]
+        y[5] = y[6]
+        y[6] = b
+        # Cross-check with exact result from R:
+        # cor.test(x,y,method="kendall",exact=1)
+        expected = [0.9111111111111111, 2.976190476190e-05]
+        assert_almost_equal(np.asarray(mstats.kendalltau(x, y)), expected)
+
+        # same in opposite direction
+        x = ma.array(np.arange(10))
+        y = ma.array(np.arange(10)[::-1])
+        # Cross-check with exact result from R:
+        # cor.test(x,y,method="kendall",exact=1)
+        expected = [-1.0, 5.511463844797e-07]
+        assert_almost_equal(np.asarray(mstats.kendalltau(x, y)), expected)
+
+        # swap a couple of values
+        b = y[1]
+        y[1] = y[2]
+        y[2] = b
+        # Cross-check with exact result from R:
+        # cor.test(x,y,method="kendall",exact=1)
+        expected = [-0.9555555555555556, 5.511463844797e-06]
+        assert_almost_equal(np.asarray(mstats.kendalltau(x, y)), expected)
+
+        # swap a couple more
+        b = y[5]
+        y[5] = y[6]
+        y[6] = b
+        # Cross-check with exact result from R:
+        # cor.test(x,y,method="kendall",exact=1)
+        expected = [-0.9111111111111111, 2.976190476190e-05]
+        assert_almost_equal(np.asarray(mstats.kendalltau(x, y)), expected)
+
+        # Tests some computations of Kendall's tau
+        x = ma.fix_invalid([5.05, 6.75, 3.21, 2.66, np.nan])
+        y = ma.fix_invalid([1.65, 26.5, -5.93, 7.96, np.nan])
+        z = ma.fix_invalid([1.65, 2.64, 2.64, 6.95, np.nan])
+        assert_almost_equal(np.asarray(mstats.kendalltau(x, y)),
+                            [+0.3333333, 0.75])
+        assert_almost_equal(np.asarray(mstats.kendalltau(x, y, method='asymptotic')),
+                            [+0.3333333, 0.4969059])
+        assert_almost_equal(np.asarray(mstats.kendalltau(x, z)),
+                            [-0.5477226, 0.2785987])
+        #
+        x = ma.fix_invalid([0, 0, 0, 0, 20, 20, 0, 60, 0, 20,
+                            10, 10, 0, 40, 0, 20, 0, 0, 0, 0, 0, np.nan])
+        y = ma.fix_invalid([0, 80, 80, 80, 10, 33, 60, 0, 67, 27,
+                            25, 80, 80, 80, 80, 80, 80, 0, 10, 45, np.nan, 0])
+        result = mstats.kendalltau(x, y)
+        assert_almost_equal(np.asarray(result), [-0.1585188, 0.4128009])
+
+        # test for namedtuple attributes
+        attributes = ('correlation', 'pvalue')
+        check_named_results(result, attributes, ma=True)
+
+    def test_overflow_gh6061(self):
+        # Regression test for GitHub issue #6061 - Overflow on Windows
+        x = np.arange(2000, dtype=float)
+        x = np.ma.masked_greater(x, 1995)
+        y = np.arange(2000, dtype=float)
+        y = np.concatenate((y[1000:], y[:1000]))
+        assert_(np.isfinite(stats.mstats.kendalltau(x,y)[1]))
+
+    def test_kendalltau_vs_mstats_basic(self):
+        rng = np.random.RandomState(42)
+        for s in range(3, 10):
+            a = []
+            # Generate rankings with ties
+            for i in range(s):
+                a += [i]*i
+            b = list(a)
+            rng.shuffle(a)
+            rng.shuffle(b)
+            expected = mstats.kendalltau(a, b)
+            actual = stats.kendalltau(a, b)
+            assert_almost_equal(actual[0], expected[0])
+            assert_almost_equal(actual[1], expected[1])
+
+    @pytest.mark.skipif(platform.machine() == 'ppc64le',
+                        reason="fails/crashes on ppc64le")
+    @pytest.mark.slow
+    def test_kendalltau_large(self):
+        # make sure internal variable use correct precision with
+        # larger arrays
+        x = np.arange(2000, dtype=float)
+        x = ma.masked_greater(x, 1995)
+        y = np.arange(2000, dtype=float)
+        y = np.concatenate((y[1000:], y[:1000]))
+        assert_(np.isfinite(mstats.kendalltau(x, y)[1]))
+
+    def test_kendalltau_seasonal(self):
+        # Tests the seasonal Kendall tau.
+        x = [[nan, nan, 4, 2, 16, 26, 5, 1, 5, 1, 2, 3, 1],
+             [4, 3, 5, 3, 2, 7, 3, 1, 1, 2, 3, 5, 3],
+             [3, 2, 5, 6, 18, 4, 9, 1, 1, nan, 1, 1, nan],
+             [nan, 6, 11, 4, 17, nan, 6, 1, 1, 2, 5, 1, 1]]
+        x = ma.fix_invalid(x).T
+        output = mstats.kendalltau_seasonal(x)
+        assert_almost_equal(output['global p-value (indep)'], 0.008, 3)
+        assert_almost_equal(output['seasonal p-value'].round(2),
+                            [0.18,0.53,0.20,0.04])
+
+    @pytest.mark.parametrize("method", ("exact", "asymptotic"))
+    @pytest.mark.parametrize("alternative", ("two-sided", "greater", "less"))
+    def test_kendalltau_mstats_vs_stats(self, method, alternative):
+        # Test that mstats.kendalltau and stats.kendalltau with
+        # nan_policy='omit' matches behavior of stats.kendalltau
+        # Accuracy of the alternatives is tested in stats/tests/test_stats.py
+
+        rng = np.random.default_rng(8755235945)
+        n = 50
+        x = rng.random(n)
+        y = rng.random(n)
+        mask = rng.random(n) > 0.5
+
+        x_masked = ma.array(x, mask=mask)
+        y_masked = ma.array(y, mask=mask)
+        res_masked = mstats.kendalltau(
+            x_masked, y_masked, method=method, alternative=alternative)
+
+        x_compressed = x_masked.compressed()
+        y_compressed = y_masked.compressed()
+        res_compressed = stats.kendalltau(
+            x_compressed, y_compressed, method=method, alternative=alternative)
+
+        x[mask] = np.nan
+        y[mask] = np.nan
+        res_nan = stats.kendalltau(
+            x, y, method=method, nan_policy='omit', alternative=alternative)
+
+        assert_allclose(res_masked, res_compressed)
+        assert_allclose(res_nan, res_compressed)
+
+    def test_kendall_p_exact_medium(self):
+        # Test for the exact method with medium samples (some n >= 171)
+        # expected values generated using SymPy
+        expectations = {(100, 2393): 0.62822615287956040664,
+                        (101, 2436): 0.60439525773513602669,
+                        (170, 0): 2.755801935583541e-307,
+                        (171, 0): 0.0,
+                        (171, 1): 2.755801935583541e-307,
+                        (172, 1): 0.0,
+                        (200, 9797): 0.74753983745929675209,
+                        (201, 9656): 0.40959218958120363618}
+        for nc, expected in expectations.items():
+            res = _mstats_basic._kendall_p_exact(nc[0], nc[1])
+            assert_almost_equal(res, expected)
+
+    @pytest.mark.xslow
+    def test_kendall_p_exact_large(self):
+        # Test for the exact method with large samples (n >= 171)
+        # expected values generated using SymPy
+        expectations = {(400, 38965): 0.48444283672113314099,
+                        (401, 39516): 0.66363159823474837662,
+                        (800, 156772): 0.42265448483120932055,
+                        (801, 157849): 0.53437553412194416236,
+                        (1600, 637472): 0.84200727400323538419,
+                        (1601, 630304): 0.34465255088058593946}
+
+        for nc, expected in expectations.items():
+            res = _mstats_basic._kendall_p_exact(nc[0], nc[1])
+            assert_almost_equal(res, expected)
+
+    @skip_xp_invalid_arg
+    # mstats.pointbiserialr returns a NumPy float for the statistic, but converts
+    # it to a masked array with no masked elements before calling `special.betainc`,
+    # which won't accept masked arrays when `SCIPY_ARRAY_API=1`.
+    def test_pointbiserial(self):
+        x = [1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0,
+             0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, -1]
+        y = [14.8, 13.8, 12.4, 10.1, 7.1, 6.1, 5.8, 4.6, 4.3, 3.5, 3.3, 3.2,
+             3.0, 2.8, 2.8, 2.5, 2.4, 2.3, 2.1, 1.7, 1.7, 1.5, 1.3, 1.3, 1.2,
+             1.2, 1.1, 0.8, 0.7, 0.6, 0.5, 0.2, 0.2, 0.1, np.nan]
+        assert_almost_equal(mstats.pointbiserialr(x, y)[0], 0.36149, 5)
+
+        # test for namedtuple attributes
+        res = mstats.pointbiserialr(x, y)
+        attributes = ('correlation', 'pvalue')
+        check_named_results(res, attributes, ma=True)
+
+
+@skip_xp_invalid_arg
+class TestTrimming:
+
+    def test_trim(self):
+        a = ma.arange(10)
+        assert_equal(mstats.trim(a), [0,1,2,3,4,5,6,7,8,9])
+        a = ma.arange(10)
+        assert_equal(mstats.trim(a,(2,8)), [None,None,2,3,4,5,6,7,8,None])
+        a = ma.arange(10)
+        assert_equal(mstats.trim(a,limits=(2,8),inclusive=(False,False)),
+                     [None,None,None,3,4,5,6,7,None,None])
+        a = ma.arange(10)
+        assert_equal(mstats.trim(a,limits=(0.1,0.2),relative=True),
+                     [None,1,2,3,4,5,6,7,None,None])
+
+        a = ma.arange(12)
+        a[[0,-1]] = a[5] = masked
+        assert_equal(mstats.trim(a, (2,8)),
+                     [None, None, 2, 3, 4, None, 6, 7, 8, None, None, None])
+
+        x = ma.arange(100).reshape(10, 10)
+        expected = [1]*10 + [0]*70 + [1]*20
+        trimx = mstats.trim(x, (0.1,0.2), relative=True, axis=None)
+        assert_equal(trimx._mask.ravel(), expected)
+        trimx = mstats.trim(x, (0.1,0.2), relative=True, axis=0)
+        assert_equal(trimx._mask.ravel(), expected)
+        trimx = mstats.trim(x, (0.1,0.2), relative=True, axis=-1)
+        assert_equal(trimx._mask.T.ravel(), expected)
+
+        # same as above, but with an extra masked row inserted
+        x = ma.arange(110).reshape(11, 10)
+        x[1] = masked
+        expected = [1]*20 + [0]*70 + [1]*20
+        trimx = mstats.trim(x, (0.1,0.2), relative=True, axis=None)
+        assert_equal(trimx._mask.ravel(), expected)
+        trimx = mstats.trim(x, (0.1,0.2), relative=True, axis=0)
+        assert_equal(trimx._mask.ravel(), expected)
+        trimx = mstats.trim(x.T, (0.1,0.2), relative=True, axis=-1)
+        assert_equal(trimx.T._mask.ravel(), expected)
+
+    def test_trim_old(self):
+        x = ma.arange(100)
+        assert_equal(mstats.trimboth(x).count(), 60)
+        assert_equal(mstats.trimtail(x,tail='r').count(), 80)
+        x[50:70] = masked
+        trimx = mstats.trimboth(x)
+        assert_equal(trimx.count(), 48)
+        assert_equal(trimx._mask, [1]*16 + [0]*34 + [1]*20 + [0]*14 + [1]*16)
+        x._mask = nomask
+        x = x.reshape((10,10))
+        assert_equal(mstats.trimboth(x).count(), 60)
+        assert_equal(mstats.trimtail(x).count(), 80)
+
+    def test_trimr(self):
+        x = ma.arange(10)
+        result = mstats.trimr(x, limits=(0.15, 0.14), inclusive=(False, False))
+        expected = ma.array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
+                            mask=[1, 1, 0, 0, 0, 0, 0, 0, 0, 1])
+        assert_equal(result, expected)
+        assert_equal(result.mask, expected.mask)
+
+    def test_trimmedmean(self):
+        data = ma.array([77, 87, 88,114,151,210,219,246,253,262,
+                         296,299,306,376,428,515,666,1310,2611])
+        assert_almost_equal(mstats.trimmed_mean(data,0.1), 343, 0)
+        assert_almost_equal(mstats.trimmed_mean(data,(0.1,0.1)), 343, 0)
+        assert_almost_equal(mstats.trimmed_mean(data,(0.2,0.2)), 283, 0)
+
+    def test_trimmedvar(self):
+        # Basic test. Additional tests of all arguments, edge cases,
+        # input validation, and proper treatment of masked arrays are needed.
+        rng = np.random.default_rng(3262323289434724460)
+        data_orig = rng.random(size=20)
+        data = np.sort(data_orig)
+        data = ma.array(data, mask=[1, 1, 0, 0, 0, 0, 0, 0, 0, 0,
+                                    0, 0, 0, 0, 0, 0, 0, 0, 1, 1])
+        assert_allclose(mstats.trimmed_var(data_orig, 0.1), data.var())
+
+    def test_trimmedstd(self):
+        # Basic test. Additional tests of all arguments, edge cases,
+        # input validation, and proper treatment of masked arrays are needed.
+        rng = np.random.default_rng(7121029245207162780)
+        data_orig = rng.random(size=20)
+        data = np.sort(data_orig)
+        data = ma.array(data, mask=[1, 1, 0, 0, 0, 0, 0, 0, 0, 0,
+                                    0, 0, 0, 0, 0, 0, 0, 0, 1, 1])
+        assert_allclose(mstats.trimmed_std(data_orig, 0.1), data.std())
+
+    def test_trimmed_stde(self):
+        data = ma.array([77, 87, 88,114,151,210,219,246,253,262,
+                         296,299,306,376,428,515,666,1310,2611])
+        assert_almost_equal(mstats.trimmed_stde(data,(0.2,0.2)), 56.13193, 5)
+        assert_almost_equal(mstats.trimmed_stde(data,0.2), 56.13193, 5)
+
+    def test_winsorization(self):
+        data = ma.array([77, 87, 88,114,151,210,219,246,253,262,
+                         296,299,306,376,428,515,666,1310,2611])
+        assert_almost_equal(mstats.winsorize(data,(0.2,0.2)).var(ddof=1),
+                            21551.4, 1)
+        assert_almost_equal(
+            mstats.winsorize(data, (0.2,0.2),(False,False)).var(ddof=1),
+            11887.3, 1)
+        data[5] = masked
+        winsorized = mstats.winsorize(data)
+        assert_equal(winsorized.mask, data.mask)
+
+    def test_winsorization_nan(self):
+        data = ma.array([np.nan, np.nan, 0, 1, 2])
+        assert_raises(ValueError, mstats.winsorize, data, (0.05, 0.05),
+                      nan_policy='raise')
+        # Testing propagate (default behavior)
+        assert_equal(mstats.winsorize(data, (0.4, 0.4)),
+                     ma.array([2, 2, 2, 2, 2]))
+        assert_equal(mstats.winsorize(data, (0.8, 0.8)),
+                     ma.array([np.nan, np.nan, np.nan, np.nan, np.nan]))
+        assert_equal(mstats.winsorize(data, (0.4, 0.4), nan_policy='omit'),
+                     ma.array([np.nan, np.nan, 2, 2, 2]))
+        assert_equal(mstats.winsorize(data, (0.8, 0.8), nan_policy='omit'),
+                     ma.array([np.nan, np.nan, 2, 2, 2]))
+
+
+@skip_xp_invalid_arg
+class TestMoments:
+    # Comparison numbers are found using R v.1.5.1
+    # note that length(testcase) = 4
+    # testmathworks comes from documentation for the
+    # Statistics Toolbox for Matlab and can be found at both
+    # https://www.mathworks.com/help/stats/kurtosis.html
+    # https://www.mathworks.com/help/stats/skewness.html
+    # Note that both test cases came from here.
+    testcase = [1,2,3,4]
+    testmathworks = ma.fix_invalid([1.165, 0.6268, 0.0751, 0.3516, -0.6965,
+                                    np.nan])
+    testcase_2d = ma.array(
+        np.array([[0.05245846, 0.50344235, 0.86589117, 0.36936353, 0.46961149],
+                  [0.11574073, 0.31299969, 0.45925772, 0.72618805, 0.75194407],
+                  [0.67696689, 0.91878127, 0.09769044, 0.04645137, 0.37615733],
+                  [0.05903624, 0.29908861, 0.34088298, 0.66216337, 0.83160998],
+                  [0.64619526, 0.94894632, 0.27855892, 0.0706151, 0.39962917]]),
+        mask=np.array([[True, False, False, True, False],
+                       [True, True, True, False, True],
+                       [False, False, False, False, False],
+                       [True, True, True, True, True],
+                       [False, False, True, False, False]], dtype=bool))
+
+    def _assert_equal(self, actual, expect, *, shape=None, dtype=None):
+        expect = np.asarray(expect)
+        if shape is not None:
+            expect = np.broadcast_to(expect, shape)
+        assert_array_equal(actual, expect)
+        if dtype is None:
+            dtype = expect.dtype
+        assert actual.dtype == dtype
+
+    def test_moment(self):
+        y = mstats.moment(self.testcase,1)
+        assert_almost_equal(y,0.0,10)
+        y = mstats.moment(self.testcase,2)
+        assert_almost_equal(y,1.25)
+        y = mstats.moment(self.testcase,3)
+        assert_almost_equal(y,0.0)
+        y = mstats.moment(self.testcase,4)
+        assert_almost_equal(y,2.5625)
+
+        # check array_like input for moment
+        y = mstats.moment(self.testcase, [1, 2, 3, 4])
+        assert_allclose(y, [0, 1.25, 0, 2.5625])
+
+        # check moment input consists only of integers
+        y = mstats.moment(self.testcase, 0.0)
+        assert_allclose(y, 1.0)
+        assert_raises(ValueError, mstats.moment, self.testcase, 1.2)
+        y = mstats.moment(self.testcase, [1.0, 2, 3, 4.0])
+        assert_allclose(y, [0, 1.25, 0, 2.5625])
+
+        # test empty input
+        y = mstats.moment([])
+        self._assert_equal(y, np.nan, dtype=np.float64)
+        y = mstats.moment(np.array([], dtype=np.float32))
+        self._assert_equal(y, np.nan, dtype=np.float32)
+        y = mstats.moment(np.zeros((1, 0)), axis=0)
+        self._assert_equal(y, [], shape=(0,), dtype=np.float64)
+        y = mstats.moment([[]], axis=1)
+        self._assert_equal(y, np.nan, shape=(1,), dtype=np.float64)
+        y = mstats.moment([[]], moment=[0, 1], axis=0)
+        self._assert_equal(y, [], shape=(2, 0))
+
+        x = np.arange(10.)
+        x[9] = np.nan
+        assert_equal(mstats.moment(x, 2), ma.masked)  # NaN value is ignored
+
+    def test_variation(self):
+        y = mstats.variation(self.testcase)
+        assert_almost_equal(y,0.44721359549996, 10)
+
+    def test_variation_ddof(self):
+        # test variation with delta degrees of freedom
+        # regression test for gh-13341
+        a = np.array([1, 2, 3, 4, 5])
+        y = mstats.variation(a, ddof=1)
+        assert_almost_equal(y, 0.5270462766947299)
+
+    def test_skewness(self):
+        y = mstats.skew(self.testmathworks)
+        assert_almost_equal(y,-0.29322304336607,10)
+        y = mstats.skew(self.testmathworks,bias=0)
+        assert_almost_equal(y,-0.437111105023940,10)
+        y = mstats.skew(self.testcase)
+        assert_almost_equal(y,0.0,10)
+
+        # test that skew works on multidimensional masked arrays
+        correct_2d = ma.array(
+            np.array([0.6882870394455785, 0, 0.2665647526856708,
+                      0, -0.05211472114254485]),
+            mask=np.array([False, False, False, True, False], dtype=bool)
+        )
+        assert_allclose(mstats.skew(self.testcase_2d, 1), correct_2d)
+        for i, row in enumerate(self.testcase_2d):
+            assert_almost_equal(mstats.skew(row), correct_2d[i])
+
+        correct_2d_bias_corrected = ma.array(
+            np.array([1.685952043212545, 0.0, 0.3973712716070531, 0,
+                      -0.09026534484117164]),
+            mask=np.array([False, False, False, True, False], dtype=bool)
+        )
+        assert_allclose(mstats.skew(self.testcase_2d, 1, bias=False),
+                        correct_2d_bias_corrected)
+        for i, row in enumerate(self.testcase_2d):
+            assert_almost_equal(mstats.skew(row, bias=False),
+                                correct_2d_bias_corrected[i])
+
+        # Check consistency between stats and mstats implementations
+        assert_allclose(mstats.skew(self.testcase_2d[2, :]),
+                        stats.skew(self.testcase_2d[2, :]))
+
+    def test_kurtosis(self):
+        # Set flags for axis = 0 and fisher=0 (Pearson's definition of kurtosis
+        # for compatibility with Matlab)
+        y = mstats.kurtosis(self.testmathworks, 0, fisher=0, bias=1)
+        assert_almost_equal(y, 2.1658856802973, 10)
+        # Note that MATLAB has confusing docs for the following case
+        #  kurtosis(x,0) gives an unbiased estimate of Pearson's skewness
+        #  kurtosis(x) gives a biased estimate of Fisher's skewness (Pearson-3)
+        #  The MATLAB docs imply that both should give Fisher's
+        y = mstats.kurtosis(self.testmathworks, fisher=0, bias=0)
+        assert_almost_equal(y, 3.663542721189047, 10)
+        y = mstats.kurtosis(self.testcase, 0, 0)
+        assert_almost_equal(y, 1.64)
+
+        # test that kurtosis works on multidimensional masked arrays
+        correct_2d = ma.array(np.array([-1.5, -3., -1.47247052385, 0.,
+                                        -1.26979517952]),
+                              mask=np.array([False, False, False, True,
+                                             False], dtype=bool))
+        assert_array_almost_equal(mstats.kurtosis(self.testcase_2d, 1),
+                                  correct_2d)
+        for i, row in enumerate(self.testcase_2d):
+            assert_almost_equal(mstats.kurtosis(row), correct_2d[i])
+
+        correct_2d_bias_corrected = ma.array(
+            np.array([-1.5, -3., -1.88988209538, 0., -0.5234638463918877]),
+            mask=np.array([False, False, False, True, False], dtype=bool))
+        assert_array_almost_equal(mstats.kurtosis(self.testcase_2d, 1,
+                                                  bias=False),
+                                  correct_2d_bias_corrected)
+        for i, row in enumerate(self.testcase_2d):
+            assert_almost_equal(mstats.kurtosis(row, bias=False),
+                                correct_2d_bias_corrected[i])
+
+        # Check consistency between stats and mstats implementations
+        assert_array_almost_equal_nulp(mstats.kurtosis(self.testcase_2d[2, :]),
+                                       stats.kurtosis(self.testcase_2d[2, :]),
+                                       nulp=4)
+
+
+class TestMode:
+    def test_mode(self):
+        a1 = [0,0,0,1,1,1,2,3,3,3,3,4,5,6,7]
+        a2 = np.reshape(a1, (3,5))
+        a3 = np.array([1,2,3,4,5,6])
+        a4 = np.reshape(a3, (3,2))
+        ma1 = ma.masked_where(ma.array(a1) > 2, a1)
+        ma2 = ma.masked_where(a2 > 2, a2)
+        ma3 = ma.masked_where(a3 < 2, a3)
+        ma4 = ma.masked_where(ma.array(a4) < 2, a4)
+        assert_equal(mstats.mode(a1, axis=None), (3,4))
+        assert_equal(mstats.mode(a1, axis=0), (3,4))
+        assert_equal(mstats.mode(ma1, axis=None), (0,3))
+        assert_equal(mstats.mode(a2, axis=None), (3,4))
+        assert_equal(mstats.mode(ma2, axis=None), (0,3))
+        assert_equal(mstats.mode(a3, axis=None), (1,1))
+        assert_equal(mstats.mode(ma3, axis=None), (2,1))
+        assert_equal(mstats.mode(a2, axis=0), ([[0,0,0,1,1]], [[1,1,1,1,1]]))
+        assert_equal(mstats.mode(ma2, axis=0), ([[0,0,0,1,1]], [[1,1,1,1,1]]))
+        assert_equal(mstats.mode(a2, axis=-1), ([[0],[3],[3]], [[3],[3],[1]]))
+        assert_equal(mstats.mode(ma2, axis=-1), ([[0],[1],[0]], [[3],[1],[0]]))
+        assert_equal(mstats.mode(ma4, axis=0), ([[3,2]], [[1,1]]))
+        assert_equal(mstats.mode(ma4, axis=-1), ([[2],[3],[5]], [[1],[1],[1]]))
+
+        a1_res = mstats.mode(a1, axis=None)
+
+        # test for namedtuple attributes
+        attributes = ('mode', 'count')
+        check_named_results(a1_res, attributes, ma=True)
+
+    def test_mode_modifies_input(self):
+        # regression test for gh-6428: mode(..., axis=None) may not modify
+        # the input array
+        im = np.zeros((100, 100))
+        im[:50, :] += 1
+        im[:, :50] += 1
+        cp = im.copy()
+        mstats.mode(im, None)
+        assert_equal(im, cp)
+
+
+class TestPercentile:
+    def setup_method(self):
+        self.a1 = [3, 4, 5, 10, -3, -5, 6]
+        self.a2 = [3, -6, -2, 8, 7, 4, 2, 1]
+        self.a3 = [3., 4, 5, 10, -3, -5, -6, 7.0]
+
+    def test_percentile(self):
+        x = np.arange(8) * 0.5
+        assert_equal(mstats.scoreatpercentile(x, 0), 0.)
+        assert_equal(mstats.scoreatpercentile(x, 100), 3.5)
+        assert_equal(mstats.scoreatpercentile(x, 50), 1.75)
+
+    def test_2D(self):
+        x = ma.array([[1, 1, 1],
+                      [1, 1, 1],
+                      [4, 4, 3],
+                      [1, 1, 1],
+                      [1, 1, 1]])
+        assert_equal(mstats.scoreatpercentile(x, 50), [1, 1, 1])
+
+
+@skip_xp_invalid_arg
+class TestVariability:
+    """  Comparison numbers are found using R v.1.5.1
+         note that length(testcase) = 4
+    """
+    testcase = ma.fix_invalid([1,2,3,4,np.nan])
+
+    def test_sem(self):
+        # This is not in R, so used: sqrt(var(testcase)*3/4) / sqrt(3)
+        y = mstats.sem(self.testcase)
+        assert_almost_equal(y, 0.6454972244)
+        n = self.testcase.count()
+        assert_allclose(mstats.sem(self.testcase, ddof=0) * np.sqrt(n/(n-2)),
+                        mstats.sem(self.testcase, ddof=2))
+
+    def test_zmap(self):
+        # This is not in R, so tested by using:
+        #    (testcase[i]-mean(testcase,axis=0)) / sqrt(var(testcase)*3/4)
+        y = mstats.zmap(self.testcase, self.testcase)
+        desired_unmaskedvals = ([-1.3416407864999, -0.44721359549996,
+                                 0.44721359549996, 1.3416407864999])
+        assert_array_almost_equal(desired_unmaskedvals,
+                                  y.data[y.mask == False], decimal=12)  # noqa: E712
+
+    def test_zscore(self):
+        # This is not in R, so tested by using:
+        #     (testcase[i]-mean(testcase,axis=0)) / sqrt(var(testcase)*3/4)
+        y = mstats.zscore(self.testcase)
+        desired = ma.fix_invalid([-1.3416407864999, -0.44721359549996,
+                                  0.44721359549996, 1.3416407864999, np.nan])
+        assert_almost_equal(desired, y, decimal=12)
+
+
+@skip_xp_invalid_arg
+class TestMisc:
+
+    def test_obrientransform(self):
+        args = [[5]*5+[6]*11+[7]*9+[8]*3+[9]*2+[10]*2,
+                [6]+[7]*2+[8]*4+[9]*9+[10]*16]
+        result = [5*[3.1828]+11*[0.5591]+9*[0.0344]+3*[1.6086]+2*[5.2817]+2*[11.0538],
+                  [10.4352]+2*[4.8599]+4*[1.3836]+9*[0.0061]+16*[0.7277]]
+        assert_almost_equal(np.round(mstats.obrientransform(*args).T, 4),
+                            result, 4)
+
+    def test_ks_2samp(self):
+        x = [[nan,nan, 4, 2, 16, 26, 5, 1, 5, 1, 2, 3, 1],
+             [4, 3, 5, 3, 2, 7, 3, 1, 1, 2, 3, 5, 3],
+             [3, 2, 5, 6, 18, 4, 9, 1, 1, nan, 1, 1, nan],
+             [nan, 6, 11, 4, 17, nan, 6, 1, 1, 2, 5, 1, 1]]
+        x = ma.fix_invalid(x).T
+        (winter, spring, summer, fall) = x.T
+
+        assert_almost_equal(np.round(mstats.ks_2samp(winter, spring), 4),
+                            (0.1818, 0.9628))
+        assert_almost_equal(np.round(mstats.ks_2samp(winter, spring, 'g'), 4),
+                            (0.1469, 0.6886))
+        assert_almost_equal(np.round(mstats.ks_2samp(winter, spring, 'l'), 4),
+                            (0.1818, 0.6011))
+
+    def test_friedmanchisq(self):
+        # No missing values
+        args = ([9.0,9.5,5.0,7.5,9.5,7.5,8.0,7.0,8.5,6.0],
+                [7.0,6.5,7.0,7.5,5.0,8.0,6.0,6.5,7.0,7.0],
+                [6.0,8.0,4.0,6.0,7.0,6.5,6.0,4.0,6.5,3.0])
+        result = mstats.friedmanchisquare(*args)
+        assert_almost_equal(result[0], 10.4737, 4)
+        assert_almost_equal(result[1], 0.005317, 6)
+        # Missing values
+        x = [[nan,nan, 4, 2, 16, 26, 5, 1, 5, 1, 2, 3, 1],
+             [4, 3, 5, 3, 2, 7, 3, 1, 1, 2, 3, 5, 3],
+             [3, 2, 5, 6, 18, 4, 9, 1, 1,nan, 1, 1,nan],
+             [nan, 6, 11, 4, 17,nan, 6, 1, 1, 2, 5, 1, 1]]
+        x = ma.fix_invalid(x)
+        result = mstats.friedmanchisquare(*x)
+        assert_almost_equal(result[0], 2.0156, 4)
+        assert_almost_equal(result[1], 0.5692, 4)
+
+        # test for namedtuple attributes
+        attributes = ('statistic', 'pvalue')
+        check_named_results(result, attributes, ma=True)
+
+        # copied from `test_stats.py`
+        array = np.ma.asarray
+        x1 = [array([0.763, 0.599, 0.954, 0.628, 0.882, 0.936, 0.661,
+                     0.583, 0.775, 1.0, 0.94, 0.619, 0.972, 0.957]),
+              array([0.768, 0.591, 0.971, 0.661, 0.888, 0.931, 0.668,
+                     0.583, 0.838, 1.0, 0.962, 0.666, 0.981, 0.978]),
+              array([0.771, 0.590, 0.968, 0.654, 0.886, 0.916, 0.609,
+                     0.563, 0.866, 1.0, 0.965, 0.614, 0.9751, 0.946]),
+              array([0.798, 0.569, 0.967, 0.657, 0.898, 0.931, 0.685,
+                     0.625, 0.875, 1.0, 0.962, 0.669, 0.975, 0.970])]
+
+        # From "Bioestadistica para las ciencias de la salud" Xf=18.95 p<0.001:
+        # x2 = [array([4, 3, 5, 3, 5, 3, 2, 5, 4, 4, 4, 3]),
+        #       array([2, 2, 1, 2, 3, 1, 2, 3, 2, 1, 1, 3]),
+        #       array([2, 4, 3, 3, 4, 3, 3, 4, 4, 1, 2, 1]),
+        #       array([3, 5, 4, 3, 4, 4, 3, 3, 3, 4, 4, 4])]
+
+        # From Jerrorl H. Zar, "Biostatistical Analysis"(example 12.6),
+        # Xf=10.68, 0.005 < p < 0.01:
+        # Probability from this example is inexact
+        # using Chisquare approximation of Friedman Chisquare.
+        x3 = [array([7.0, 9.9, 8.5, 5.1, 10.3]),
+              array([5.3, 5.7, 4.7, 3.5, 7.7]),
+              array([4.9, 7.6, 5.5, 2.8, 8.4]),
+              array([8.8, 8.9, 8.1, 3.3, 9.1])]
+
+        # test using mstats
+        assert_array_almost_equal(mstats.friedmanchisquare(*x1),
+                                  (10.2283464566929, 0.0167215803284414))
+
+        # the following fails
+        # assert_array_almost_equal(mstats.friedmanchisquare(*x2),
+        #                           (18.9428571428571, 0.000280938375189499))
+
+        assert_array_almost_equal(mstats.friedmanchisquare(*x3),
+                                  (10.68, 0.0135882729582176))
+        assert_raises(ValueError, mstats.friedmanchisquare, x3[0], x3[1])
+
+
+def test_regress_simple():
+    # Regress a line with sinusoidal noise. Test for #1273.
+    x = np.linspace(0, 100, 100)
+    y = 0.2 * np.linspace(0, 100, 100) + 10
+    y += np.sin(np.linspace(0, 20, 100))
+
+    result = mstats.linregress(x, y)
+
+    # Result is of a correct class and with correct fields
+    lr = _stats_py.LinregressResult
+    assert_(isinstance(result, lr))
+    attributes = ('slope', 'intercept', 'rvalue', 'pvalue', 'stderr')
+    check_named_results(result, attributes, ma=True)
+    assert 'intercept_stderr' in dir(result)
+
+    # Slope and intercept are estimated correctly
+    assert_almost_equal(result.slope, 0.19644990055858422)
+    assert_almost_equal(result.intercept, 10.211269918932341)
+    assert_almost_equal(result.stderr, 0.002395781449783862)
+    assert_almost_equal(result.intercept_stderr, 0.13866936078570702)
+
+
+def test_linregress_identical_x():
+    rng = np.random.default_rng(74578245698)
+    x = np.zeros(10)
+    y = rng.random(10)
+    msg = "Cannot calculate a linear regression if all x values are identical"
+    with assert_raises(ValueError, match=msg):
+        mstats.linregress(x, y)
+
+
+class TestTheilslopes:
+    def test_theilslopes(self):
+        # Test for basic slope and intercept.
+        slope, intercept, lower, upper = mstats.theilslopes([0, 1, 1])
+        assert_almost_equal(slope, 0.5)
+        assert_almost_equal(intercept, 0.5)
+
+        slope, intercept, lower, upper = mstats.theilslopes([0, 1, 1],
+                                                            method='joint')
+        assert_almost_equal(slope, 0.5)
+        assert_almost_equal(intercept, 0.0)
+
+        # Test for correct masking.
+        y = np.ma.array([0, 1, 100, 1], mask=[False, False, True, False])
+        slope, intercept, lower, upper = mstats.theilslopes(y)
+        # These reference values are incorrect. With 100 masked, the outputs
+        # should be the same as above.
+        assert_almost_equal(slope, 1./3)
+        assert_almost_equal(intercept, 2./3)
+
+        slope, intercept, lower, upper = mstats.theilslopes(y,
+                                                            method='joint')
+        assert_almost_equal(slope, 1./3)
+        assert_almost_equal(intercept, 0.0)
+
+        # Test of confidence intervals from example in Sen (1968).
+        x = [1, 2, 3, 4, 10, 12, 18]
+        y = [9, 15, 19, 20, 45, 55, 78]
+        slope, intercept, lower, upper = mstats.theilslopes(y, x, 0.07)
+        assert_almost_equal(slope, 4)
+        assert_almost_equal(intercept, 4.0)
+        assert_almost_equal(upper, 4.38, decimal=2)
+        assert_almost_equal(lower, 3.71, decimal=2)
+
+        slope, intercept, lower, upper = mstats.theilslopes(y, x, 0.07,
+                                                            method='joint')
+        assert_almost_equal(slope, 4)
+        assert_almost_equal(intercept, 6.0)
+        assert_almost_equal(upper, 4.38, decimal=2)
+        assert_almost_equal(lower, 3.71, decimal=2)
+
+
+    def test_theilslopes_warnings(self):
+        # Test `theilslopes` with degenerate input; see gh-15943
+        msg = "All `x` coordinates.*|Mean of empty slice|invalid value encountered.*"
+        with pytest.warns(RuntimeWarning, match=msg):
+            res = mstats.theilslopes([0, 1], [0, 0])
+            assert np.all(np.isnan(res))
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", "invalid value encountered...", RuntimeWarning)
+            res = mstats.theilslopes([0, 0, 0], [0, 1, 0])
+            assert_allclose(res, (0, 0, np.nan, np.nan))
+
+
+    def test_theilslopes_namedtuple_consistency(self):
+        """
+        Simple test to ensure tuple backwards-compatibility of the returned
+        TheilslopesResult object
+        """
+        y = [1, 2, 4]
+        x = [4, 6, 8]
+        slope, intercept, low_slope, high_slope = mstats.theilslopes(y, x)
+        result = mstats.theilslopes(y, x)
+
+        # note all four returned values are distinct here
+        assert_equal(slope, result.slope)
+        assert_equal(intercept, result.intercept)
+        assert_equal(low_slope, result.low_slope)
+        assert_equal(high_slope, result.high_slope)
+
+    def test_gh19678_uint8(self):
+        # `theilslopes` returned unexpected results when `y` was an unsigned type.
+        # Check that this is resolved.
+        rng = np.random.default_rng(2549824598234528)
+        y = rng.integers(0, 255, size=10, dtype=np.uint8)
+        res = stats.theilslopes(y, y)
+        np.testing.assert_allclose(res.slope, 1)
+
+
+def test_siegelslopes():
+    # method should be exact for straight line
+    y = 2 * np.arange(10) + 0.5
+    assert_equal(mstats.siegelslopes(y), (2.0, 0.5))
+    assert_equal(mstats.siegelslopes(y, method='separate'), (2.0, 0.5))
+
+    x = 2 * np.arange(10)
+    y = 5 * x - 3.0
+    assert_equal(mstats.siegelslopes(y, x), (5.0, -3.0))
+    assert_equal(mstats.siegelslopes(y, x, method='separate'), (5.0, -3.0))
+
+    # method is robust to outliers: brekdown point of 50%
+    y[:4] = 1000
+    assert_equal(mstats.siegelslopes(y, x), (5.0, -3.0))
+
+    # if there are no outliers, results should be comparable to linregress
+    x = np.arange(10)
+    y = -2.3 + 0.3*x + stats.norm.rvs(size=10, random_state=231)
+    slope_ols, intercept_ols, _, _, _ = stats.linregress(x, y)
+
+    slope, intercept = mstats.siegelslopes(y, x)
+    assert_allclose(slope, slope_ols, rtol=0.1)
+    assert_allclose(intercept, intercept_ols, rtol=0.1)
+
+    slope, intercept = mstats.siegelslopes(y, x, method='separate')
+    assert_allclose(slope, slope_ols, rtol=0.1)
+    assert_allclose(intercept, intercept_ols, rtol=0.1)
+
+
+def test_siegelslopes_namedtuple_consistency():
+    """
+    Simple test to ensure tuple backwards-compatibility of the returned
+    SiegelslopesResult object.
+    """
+    y = [1, 2, 4]
+    x = [4, 6, 8]
+    slope, intercept = mstats.siegelslopes(y, x)
+    result = mstats.siegelslopes(y, x)
+
+    # note both returned values are distinct here
+    assert_equal(slope, result.slope)
+    assert_equal(intercept, result.intercept)
+
+
+def test_sen_seasonal_slopes():
+    rng = np.random.default_rng(5765986256978575148)
+    x = rng.random(size=(100, 4))
+    intra_slope, inter_slope = mstats.sen_seasonal_slopes(x)
+
+    # reference implementation from the `sen_seasonal_slopes` documentation
+    def dijk(yi):
+        n = len(yi)
+        x = np.arange(n)
+        dy = yi - yi[:, np.newaxis]
+        dx = x - x[:, np.newaxis]
+        mask = np.triu(np.ones((n, n), dtype=bool), k=1)
+        return dy[mask]/dx[mask]
+
+    for i in range(4):
+        assert_allclose(np.median(dijk(x[:, i])), intra_slope[i])
+
+    all_slopes = np.concatenate([dijk(x[:, i]) for i in range(x.shape[1])])
+    assert_allclose(np.median(all_slopes), inter_slope)
+
+
+def test_plotting_positions():
+    # Regression test for #1256
+    pos = mstats.plotting_positions(np.arange(3), 0, 0)
+    assert_array_almost_equal(pos.data, np.array([0.25, 0.5, 0.75]))
+
+
+@skip_xp_invalid_arg
+class TestNormalitytests:
+
+    def test_vs_nonmasked(self):
+        x = np.array((-2, -1, 0, 1, 2, 3)*4)**2
+        assert_array_almost_equal(mstats.normaltest(x),
+                                  stats.normaltest(x))
+        assert_array_almost_equal(mstats.skewtest(x),
+                                  stats.skewtest(x))
+        assert_array_almost_equal(mstats.kurtosistest(x),
+                                  stats.kurtosistest(x))
+
+        funcs = [stats.normaltest, stats.skewtest, stats.kurtosistest]
+        mfuncs = [mstats.normaltest, mstats.skewtest, mstats.kurtosistest]
+        x = [1, 2, 3, 4]
+        for func, mfunc in zip(funcs, mfuncs):
+            with pytest.warns(SmallSampleWarning, match=too_small_1d_not_omit):
+                res = func(x)
+                assert np.isnan(res.statistic)
+                assert np.isnan(res.pvalue)
+            assert_raises(ValueError, mfunc, x)
+
+    def test_axis_None(self):
+        # Test axis=None (equal to axis=0 for 1-D input)
+        x = np.array((-2,-1,0,1,2,3)*4)**2
+        assert_allclose(mstats.normaltest(x, axis=None), mstats.normaltest(x))
+        assert_allclose(mstats.skewtest(x, axis=None), mstats.skewtest(x))
+        assert_allclose(mstats.kurtosistest(x, axis=None),
+                        mstats.kurtosistest(x))
+
+    def test_maskedarray_input(self):
+        # Add some masked values, test result doesn't change
+        x = np.array((-2, -1, 0, 1, 2, 3)*4)**2
+        xm = np.ma.array(np.r_[np.inf, x, 10],
+                         mask=np.r_[True, [False] * x.size, True])
+        assert_allclose(mstats.normaltest(xm), stats.normaltest(x))
+        assert_allclose(mstats.skewtest(xm), stats.skewtest(x))
+        assert_allclose(mstats.kurtosistest(xm), stats.kurtosistest(x))
+
+    def test_nd_input(self):
+        x = np.array((-2, -1, 0, 1, 2, 3)*4)**2
+        x_2d = np.vstack([x] * 2).T
+        for func in [mstats.normaltest, mstats.skewtest, mstats.kurtosistest]:
+            res_1d = func(x)
+            res_2d = func(x_2d)
+            assert_allclose(res_2d[0], [res_1d[0]] * 2)
+            assert_allclose(res_2d[1], [res_1d[1]] * 2)
+
+    def test_normaltest_result_attributes(self):
+        x = np.array((-2, -1, 0, 1, 2, 3)*4)**2
+        res = mstats.normaltest(x)
+        attributes = ('statistic', 'pvalue')
+        check_named_results(res, attributes, ma=True)
+
+    def test_kurtosistest_result_attributes(self):
+        x = np.array((-2, -1, 0, 1, 2, 3)*4)**2
+        res = mstats.kurtosistest(x)
+        attributes = ('statistic', 'pvalue')
+        check_named_results(res, attributes, ma=True)
+
+    def test_regression_9033(self):
+        # x clearly non-normal but power of negative denom needs
+        # to be handled correctly to reject normality
+        counts = [128, 0, 58, 7, 0, 41, 16, 0, 0, 167]
+        x = np.hstack([np.full(c, i) for i, c in enumerate(counts)])
+        assert_equal(mstats.kurtosistest(x)[1] < 0.01, True)
+
+    @pytest.mark.parametrize("test", ["skewtest", "kurtosistest"])
+    @pytest.mark.parametrize("alternative", ["less", "greater"])
+    def test_alternative(self, test, alternative):
+        x = stats.norm.rvs(loc=10, scale=2.5, size=30, random_state=123)
+
+        stats_test = getattr(stats, test)
+        mstats_test = getattr(mstats, test)
+
+        z_ex, p_ex = stats_test(x, alternative=alternative)
+        z, p = mstats_test(x, alternative=alternative)
+        assert_allclose(z, z_ex, atol=1e-12)
+        assert_allclose(p, p_ex, atol=1e-12)
+
+        # test with masked arrays
+        x[1:5] = np.nan
+        x = np.ma.masked_array(x, mask=np.isnan(x))
+        z_ex, p_ex = stats_test(x.compressed(), alternative=alternative)
+        z, p = mstats_test(x, alternative=alternative)
+        assert_allclose(z, z_ex, atol=1e-12)
+        assert_allclose(p, p_ex, atol=1e-12)
+
+    def test_bad_alternative(self):
+        x = stats.norm.rvs(size=20, random_state=123)
+        msg = r"`alternative` must be..."
+
+        with pytest.raises(ValueError, match=msg):
+            mstats.skewtest(x, alternative='error')
+
+        with pytest.raises(ValueError, match=msg):
+            mstats.kurtosistest(x, alternative='error')
+
+
+class TestFOneway:
+    def test_result_attributes(self):
+        a = np.array([655, 788], dtype=np.uint16)
+        b = np.array([789, 772], dtype=np.uint16)
+        res = mstats.f_oneway(a, b)
+        attributes = ('statistic', 'pvalue')
+        check_named_results(res, attributes, ma=True)
+
+
+class TestMannwhitneyu:
+    # data from gh-1428
+    x = np.array([1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                  1., 1., 1., 1., 1., 1., 1., 2., 1., 1., 1., 1., 1., 1.,
+                  1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                  1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                  1., 1., 1., 1., 1., 1., 1., 2., 1., 1., 1., 1., 1., 1.,
+                  1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                  1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 2.,
+                  1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                  1., 1., 2., 1., 1., 1., 1., 2., 1., 1., 2., 1., 1., 2.,
+                  1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                  1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 2., 1.,
+                  1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                  1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                  1., 1., 1., 1., 1., 1., 1., 2., 1., 1., 1., 1., 1., 1.,
+                  1., 1., 1., 2., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                  1., 1., 1., 1., 1., 1., 1., 1., 3., 1., 1., 1., 1., 1.,
+                  1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                  1., 1., 1., 1., 1., 1.])
+
+    y = np.array([1., 1., 1., 1., 1., 1., 1., 2., 1., 2., 1., 1., 1., 1.,
+                  2., 1., 1., 1., 2., 1., 1., 1., 1., 1., 2., 1., 1., 3.,
+                  1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 2., 1., 2., 1.,
+                  1., 1., 1., 1., 1., 2., 1., 1., 1., 1., 1., 1., 1., 1.,
+                  1., 1., 1., 1., 1., 1., 1., 2., 1., 1., 1., 1., 1., 2.,
+                  2., 1., 1., 2., 1., 1., 2., 1., 2., 1., 1., 1., 1., 2.,
+                  2., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                  1., 2., 1., 1., 1., 1., 1., 2., 2., 2., 1., 1., 1., 1.,
+                  1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                  2., 1., 1., 2., 1., 1., 1., 1., 2., 1., 1., 1., 1., 1.,
+                  1., 1., 1., 1., 1., 1., 1., 2., 1., 1., 1., 2., 1., 1.,
+                  1., 1., 1., 1.])
+
+    def test_result_attributes(self):
+        res = mstats.mannwhitneyu(self.x, self.y)
+        attributes = ('statistic', 'pvalue')
+        check_named_results(res, attributes, ma=True)
+
+    def test_against_stats(self):
+        # gh-4641 reported that stats.mannwhitneyu returned half the p-value
+        # of mstats.mannwhitneyu. Default alternative of stats.mannwhitneyu
+        # is now two-sided, so they match.
+        res1 = mstats.mannwhitneyu(self.x, self.y)
+        res2 = stats.mannwhitneyu(self.x, self.y)
+        assert res1.statistic == res2.statistic
+        assert_allclose(res1.pvalue, res2.pvalue)
+
+
+class TestKruskal:
+    def test_result_attributes(self):
+        x = [1, 3, 5, 7, 9]
+        y = [2, 4, 6, 8, 10]
+
+        res = mstats.kruskal(x, y)
+        attributes = ('statistic', 'pvalue')
+        check_named_results(res, attributes, ma=True)
+
+
+# TODO: for all ttest functions, add tests with masked array inputs
+class TestTtest_rel:
+    def setup_method(self):
+        self.rng = np.random.default_rng(9373599542)
+
+    def test_vs_nonmasked(self):
+        outcome = self.rng.standard_normal((20, 4)) + [0, 0, 1, 2]
+
+        # 1-D inputs
+        res1 = stats.ttest_rel(outcome[:, 0], outcome[:, 1])
+        res2 = mstats.ttest_rel(outcome[:, 0], outcome[:, 1])
+        assert_allclose(res1, res2)
+
+        # 2-D inputs
+        res1 = stats.ttest_rel(outcome[:, 0], outcome[:, 1], axis=None)
+        res2 = mstats.ttest_rel(outcome[:, 0], outcome[:, 1], axis=None)
+        assert_allclose(res1, res2)
+        res1 = stats.ttest_rel(outcome[:, :2], outcome[:, 2:], axis=0)
+        res2 = mstats.ttest_rel(outcome[:, :2], outcome[:, 2:], axis=0)
+        assert_allclose(res1, res2)
+
+        # Check default is axis=0
+        res3 = mstats.ttest_rel(outcome[:, :2], outcome[:, 2:])
+        assert_allclose(res2, res3)
+
+    def test_fully_masked(self):
+        outcome = ma.masked_array(self.rng.standard_normal((3, 2)),
+                                  mask=[[1, 1, 1], [0, 0, 0]])
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", "invalid value encountered in absolute", RuntimeWarning)
+            for pair in [(outcome[:, 0], outcome[:, 1]),
+                         ([np.nan, np.nan], [1.0, 2.0])]:
+                t, p = mstats.ttest_rel(*pair)
+                assert_array_equal(t, (np.nan, np.nan))
+                assert_array_equal(p, (np.nan, np.nan))
+
+    def test_result_attributes(self):
+        outcome = self.rng.standard_normal((20, 4)) + [0, 0, 1, 2]
+
+        res = mstats.ttest_rel(outcome[:, 0], outcome[:, 1])
+        attributes = ('statistic', 'pvalue')
+        check_named_results(res, attributes, ma=True)
+
+    def test_invalid_input_size(self):
+        assert_raises(ValueError, mstats.ttest_rel,
+                      np.arange(10), np.arange(11))
+        x = np.arange(24)
+        assert_raises(ValueError, mstats.ttest_rel,
+                      x.reshape(2, 3, 4), x.reshape(2, 4, 3), axis=1)
+        assert_raises(ValueError, mstats.ttest_rel,
+                      x.reshape(2, 3, 4), x.reshape(2, 4, 3), axis=2)
+
+    def test_empty(self):
+        res1 = mstats.ttest_rel([], [])
+        assert_(np.all(np.isnan(res1)))
+
+    def test_zero_division(self):
+        t, p = mstats.ttest_ind([0, 0, 0], [1, 1, 1])
+        assert_equal((np.abs(t), p), (np.inf, 0))
+
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", "invalid value encountered in absolute", RuntimeWarning)
+            t, p = mstats.ttest_ind([0, 0, 0], [0, 0, 0])
+            assert_array_equal(t, np.array([np.nan, np.nan]))
+            assert_array_equal(p, np.array([np.nan, np.nan]))
+
+    def test_bad_alternative(self):
+        msg = r"alternative must be 'less', 'greater' or 'two-sided'"
+        with pytest.raises(ValueError, match=msg):
+            mstats.ttest_ind([1, 2, 3], [4, 5, 6], alternative='foo')
+
+    @pytest.mark.parametrize("alternative", ["less", "greater"])
+    def test_alternative(self, alternative):
+        x = stats.norm.rvs(loc=10, scale=5, size=25, random_state=42)
+        y = stats.norm.rvs(loc=8, scale=2, size=25, random_state=42)
+
+        t_ex, p_ex = stats.ttest_rel(x, y, alternative=alternative)
+        t, p = mstats.ttest_rel(x, y, alternative=alternative)
+        assert_allclose(t, t_ex, rtol=1e-14)
+        assert_allclose(p, p_ex, rtol=1e-14)
+
+        # test with masked arrays
+        x[1:10] = np.nan
+        y[1:10] = np.nan
+        x = np.ma.masked_array(x, mask=np.isnan(x))
+        y = np.ma.masked_array(y, mask=np.isnan(y))
+        t, p = mstats.ttest_rel(x, y, alternative=alternative)
+        t_ex, p_ex = stats.ttest_rel(x.compressed(), y.compressed(),
+                                     alternative=alternative)
+        assert_allclose(t, t_ex, rtol=1e-14)
+        assert_allclose(p, p_ex, rtol=1e-14)
+
+
+class TestTtest_ind:
+    def setup_method(self):
+        self.rng = np.random.default_rng(4776115069)
+
+    def test_vs_nonmasked(self):
+        outcome = self.rng.standard_normal((20, 4)) + [0, 0, 1, 2]
+
+        # 1-D inputs
+        res1 = stats.ttest_ind(outcome[:, 0], outcome[:, 1])
+        res2 = mstats.ttest_ind(outcome[:, 0], outcome[:, 1])
+        assert_allclose(res1, res2)
+
+        # 2-D inputs
+        res1 = stats.ttest_ind(outcome[:, 0], outcome[:, 1], axis=None)
+        res2 = mstats.ttest_ind(outcome[:, 0], outcome[:, 1], axis=None)
+        assert_allclose(res1, res2)
+        res1 = stats.ttest_ind(outcome[:, :2], outcome[:, 2:], axis=0)
+        res2 = mstats.ttest_ind(outcome[:, :2], outcome[:, 2:], axis=0)
+        assert_allclose(res1, res2)
+
+        # Check default is axis=0
+        res3 = mstats.ttest_ind(outcome[:, :2], outcome[:, 2:])
+        assert_allclose(res2, res3)
+
+        # Check equal_var
+        res4 = stats.ttest_ind(outcome[:, 0], outcome[:, 1], equal_var=True)
+        res5 = mstats.ttest_ind(outcome[:, 0], outcome[:, 1], equal_var=True)
+        assert_allclose(res4, res5)
+        res4 = stats.ttest_ind(outcome[:, 0], outcome[:, 1], equal_var=False)
+        res5 = mstats.ttest_ind(outcome[:, 0], outcome[:, 1], equal_var=False)
+        assert_allclose(res4, res5)
+
+    def test_fully_masked(self):
+        outcome = ma.masked_array(self.rng.standard_normal((3, 2)),
+                                  mask=[[1, 1, 1], [0, 0, 0]])
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", "invalid value encountered in absolute", RuntimeWarning)
+            for pair in [(outcome[:, 0], outcome[:, 1]),
+                         ([np.nan, np.nan], [1.0, 2.0])]:
+                t, p = mstats.ttest_ind(*pair)
+                assert_array_equal(t, (np.nan, np.nan))
+                assert_array_equal(p, (np.nan, np.nan))
+
+    def test_result_attributes(self):
+        outcome = self.rng.standard_normal((20, 4)) + [0, 0, 1, 2]
+
+        res = mstats.ttest_ind(outcome[:, 0], outcome[:, 1])
+        attributes = ('statistic', 'pvalue')
+        check_named_results(res, attributes, ma=True)
+
+    def test_empty(self):
+        res1 = mstats.ttest_ind([], [])
+        assert_(np.all(np.isnan(res1)))
+
+    def test_zero_division(self):
+        t, p = mstats.ttest_ind([0, 0, 0], [1, 1, 1])
+        assert_equal((np.abs(t), p), (np.inf, 0))
+
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", "invalid value encountered in absolute", RuntimeWarning)
+            t, p = mstats.ttest_ind([0, 0, 0], [0, 0, 0])
+            assert_array_equal(t, (np.nan, np.nan))
+            assert_array_equal(p, (np.nan, np.nan))
+
+        t, p = mstats.ttest_ind([0, 0, 0], [1, 1, 1], equal_var=False)
+        assert_equal((np.abs(t), p), (np.inf, 0))
+        assert_array_equal(mstats.ttest_ind([0, 0, 0], [0, 0, 0],
+                                            equal_var=False), (np.nan, np.nan))
+
+    def test_bad_alternative(self):
+        msg = r"alternative must be 'less', 'greater' or 'two-sided'"
+        with pytest.raises(ValueError, match=msg):
+            mstats.ttest_ind([1, 2, 3], [4, 5, 6], alternative='foo')
+
+    @pytest.mark.parametrize("alternative", ["less", "greater"])
+    def test_alternative(self, alternative):
+        x = stats.norm.rvs(loc=10, scale=2, size=100, random_state=123)
+        y = stats.norm.rvs(loc=8, scale=2, size=100, random_state=123)
+
+        t_ex, p_ex = stats.ttest_ind(x, y, alternative=alternative)
+        t, p = mstats.ttest_ind(x, y, alternative=alternative)
+        assert_allclose(t, t_ex, rtol=1e-14)
+        assert_allclose(p, p_ex, rtol=1e-14)
+
+        # test with masked arrays
+        x[1:10] = np.nan
+        y[80:90] = np.nan
+        x = np.ma.masked_array(x, mask=np.isnan(x))
+        y = np.ma.masked_array(y, mask=np.isnan(y))
+        t_ex, p_ex = stats.ttest_ind(x.compressed(), y.compressed(),
+                                     alternative=alternative)
+        t, p = mstats.ttest_ind(x, y, alternative=alternative)
+        assert_allclose(t, t_ex, rtol=1e-14)
+        assert_allclose(p, p_ex, rtol=1e-14)
+
+
+class TestTtest_1samp:
+    def setup_method(self):
+        self.rng = np.random.default_rng(6043813830)
+
+    def test_vs_nonmasked(self):
+        outcome = self.rng.standard_normal((20, 4)) + [0, 0, 1, 2]
+
+        # 1-D inputs
+        res1 = stats.ttest_1samp(outcome[:, 0], 1)
+        res2 = mstats.ttest_1samp(outcome[:, 0], 1)
+        assert_allclose(res1, res2)
+
+    def test_fully_masked(self):
+        outcome = ma.masked_array(self.rng.standard_normal(3), mask=[1, 1, 1])
+        expected = (np.nan, np.nan)
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", "invalid value encountered in absolute", RuntimeWarning)
+            for pair in [((np.nan, np.nan), 0.0), (outcome, 0.0)]:
+                t, p = mstats.ttest_1samp(*pair)
+                assert_array_equal(p, expected)
+                assert_array_equal(t, expected)
+
+    def test_result_attributes(self):
+        outcome = self.rng.standard_normal((20, 4)) + [0, 0, 1, 2]
+
+        res = mstats.ttest_1samp(outcome[:, 0], 1)
+        attributes = ('statistic', 'pvalue')
+        check_named_results(res, attributes, ma=True)
+
+    def test_empty(self):
+        res1 = mstats.ttest_1samp([], 1)
+        assert_(np.all(np.isnan(res1)))
+
+    def test_zero_division(self):
+        t, p = mstats.ttest_1samp([0, 0, 0], 1)
+        assert_equal((np.abs(t), p), (np.inf, 0))
+
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", "invalid value encountered in absolute", RuntimeWarning)
+            t, p = mstats.ttest_1samp([0, 0, 0], 0)
+            assert_(np.isnan(t))
+            assert_array_equal(p, (np.nan, np.nan))
+
+    def test_bad_alternative(self):
+        msg = r"alternative must be 'less', 'greater' or 'two-sided'"
+        with pytest.raises(ValueError, match=msg):
+            mstats.ttest_1samp([1, 2, 3], 4, alternative='foo')
+
+    @pytest.mark.parametrize("alternative", ["less", "greater"])
+    def test_alternative(self, alternative):
+        x = stats.norm.rvs(loc=10, scale=2, size=100, random_state=123)
+
+        t_ex, p_ex = stats.ttest_1samp(x, 9, alternative=alternative)
+        t, p = mstats.ttest_1samp(x, 9, alternative=alternative)
+        assert_allclose(t, t_ex, rtol=1e-14)
+        assert_allclose(p, p_ex, rtol=1e-14)
+
+        # test with masked arrays
+        x[1:10] = np.nan
+        x = np.ma.masked_array(x, mask=np.isnan(x))
+        t_ex, p_ex = stats.ttest_1samp(x.compressed(), 9,
+                                       alternative=alternative)
+        t, p = mstats.ttest_1samp(x, 9, alternative=alternative)
+        assert_allclose(t, t_ex, rtol=1e-14)
+        assert_allclose(p, p_ex, rtol=1e-14)
+
+
+class TestDescribe:
+    """
+    Tests for mstats.describe.
+
+    Note that there are also tests for `mstats.describe` in the
+    class TestCompareWithStats.
+    """
+    def test_basic_with_axis(self):
+        # This is a basic test that is also a regression test for gh-7303.
+        a = np.ma.masked_array([[0, 1, 2, 3, 4, 9],
+                                [5, 5, 0, 9, 3, 3]],
+                               mask=[[0, 0, 0, 0, 0, 1],
+                                     [0, 0, 1, 1, 0, 0]])
+        result = mstats.describe(a, axis=1)
+        assert_equal(result.nobs, [5, 4])
+        amin, amax = result.minmax
+        assert_equal(amin, [0, 3])
+        assert_equal(amax, [4, 5])
+        assert_equal(result.mean, [2.0, 4.0])
+        assert_equal(result.variance, [2.0, 1.0])
+        assert_equal(result.skewness, [0.0, 0.0])
+        assert_allclose(result.kurtosis, [-1.3, -2.0])
+
+
+@skip_xp_invalid_arg
+class TestCompareWithStats:
+    """
+    Class to compare mstats results with stats results.
+
+    It is in general assumed that scipy.stats is at a more mature stage than
+    stats.mstats.  If a routine in mstats results in similar results like in
+    scipy.stats, this is considered also as a proper validation of scipy.mstats
+    routine.
+
+    Different sample sizes are used for testing, as some problems between stats
+    and mstats are dependent on sample size.
+
+    Author: Alexander Loew
+
+    NOTE that some tests fail. This might be caused by
+    a) actual differences or bugs between stats and mstats
+    b) numerical inaccuracies
+    c) different definitions of routine interfaces
+
+    These failures need to be checked. Current workaround is to have disabled these
+    tests, but issuing reports on scipy-dev
+
+    """
+    def get_n(self):
+        """ Returns list of sample sizes to be used for comparison. """
+        return [1000, 100, 10, 5]
+
+    def generate_xy_sample(self, n):
+        # This routine generates numpy arrays and corresponding masked arrays
+        # with the same data, but additional masked values
+        rng = np.random.RandomState(1234567)
+        x = rng.randn(n)
+        y = x + rng.randn(n)
+        xm = np.full(len(x) + 5, 1e16)
+        ym = np.full(len(y) + 5, 1e16)
+        xm[0:len(x)] = x
+        ym[0:len(y)] = y
+        mask = xm > 9e15
+        xm = np.ma.array(xm, mask=mask)
+        ym = np.ma.array(ym, mask=mask)
+        return x, y, xm, ym
+
+    def generate_xy_sample2D(self, n, nx):
+        x = np.full((n, nx), np.nan)
+        y = np.full((n, nx), np.nan)
+        xm = np.full((n+5, nx), np.nan)
+        ym = np.full((n+5, nx), np.nan)
+
+        for i in range(nx):
+            x[:, i], y[:, i], dx, dy = self.generate_xy_sample(n)
+
+        xm[0:n, :] = x[0:n]
+        ym[0:n, :] = y[0:n]
+        xm = np.ma.array(xm, mask=np.isnan(xm))
+        ym = np.ma.array(ym, mask=np.isnan(ym))
+        return x, y, xm, ym
+
+    def test_linregress(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            result1 = stats.linregress(x, y)
+            result2 = stats.mstats.linregress(xm, ym)
+            assert_allclose(np.asarray(result1), np.asarray(result2))
+
+    def test_pearsonr(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            r, p = stats.pearsonr(x, y)
+            rm, pm = stats.mstats.pearsonr(xm, ym)
+
+            assert_almost_equal(r, rm, decimal=14)
+            assert_almost_equal(p, pm, decimal=14)
+
+    def test_spearmanr(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            r, p = stats.spearmanr(x, y)
+            rm, pm = stats.mstats.spearmanr(xm, ym)
+            assert_almost_equal(r, rm, 14)
+            assert_almost_equal(p, pm, 14)
+
+    def test_spearmanr_backcompat_useties(self):
+        # A regression test to ensure we don't break backwards compat
+        # more than we have to (see gh-9204).
+        x = np.arange(6)
+        assert_raises(ValueError, mstats.spearmanr, x, x, False)
+
+    def test_gmean(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            r = stats.gmean(abs(x))
+            rm = stats.mstats.gmean(abs(xm))
+            assert_allclose(r, rm, rtol=1e-13)
+
+            r = stats.gmean(abs(y))
+            rm = stats.mstats.gmean(abs(ym))
+            assert_allclose(r, rm, rtol=1e-13)
+
+    def test_hmean(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+
+            r = stats.hmean(abs(x))
+            rm = stats.mstats.hmean(abs(xm))
+            assert_almost_equal(r, rm, 10)
+
+            r = stats.hmean(abs(y))
+            rm = stats.mstats.hmean(abs(ym))
+            assert_almost_equal(r, rm, 10)
+
+    def test_skew(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+
+            r = stats.skew(x)
+            rm = stats.mstats.skew(xm)
+            assert_almost_equal(r, rm, 10)
+
+            r = stats.skew(y)
+            rm = stats.mstats.skew(ym)
+            assert_almost_equal(r, rm, 10)
+
+    def test_moment(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+
+            r = stats.moment(x)
+            rm = stats.mstats.moment(xm)
+            assert_almost_equal(r, rm, 10)
+
+            r = stats.moment(y)
+            rm = stats.mstats.moment(ym)
+            assert_almost_equal(r, rm, 10)
+
+    def test_zscore(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+
+            # reference solution
+            zx = (x - x.mean()) / x.std()
+            zy = (y - y.mean()) / y.std()
+
+            # validate stats
+            assert_allclose(stats.zscore(x), zx, rtol=1e-10)
+            assert_allclose(stats.zscore(y), zy, rtol=1e-10)
+
+            # compare stats and mstats
+            assert_allclose(stats.zscore(x), stats.mstats.zscore(xm[0:len(x)]),
+                            rtol=1e-10)
+            assert_allclose(stats.zscore(y), stats.mstats.zscore(ym[0:len(y)]),
+                            rtol=1e-10)
+
+    def test_kurtosis(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            r = stats.kurtosis(x)
+            rm = stats.mstats.kurtosis(xm)
+            assert_almost_equal(r, rm, 10)
+
+            r = stats.kurtosis(y)
+            rm = stats.mstats.kurtosis(ym)
+            assert_almost_equal(r, rm, 10)
+
+    def test_sem(self):
+        # example from stats.sem doc
+        a = np.arange(20).reshape(5, 4)
+        am = np.ma.array(a)
+        r = stats.sem(a, ddof=1)
+        rm = stats.mstats.sem(am, ddof=1)
+
+        assert_allclose(r, 2.82842712, atol=1e-5)
+        assert_allclose(rm, 2.82842712, atol=1e-5)
+
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            assert_almost_equal(stats.mstats.sem(xm, axis=None, ddof=0),
+                                stats.sem(x, axis=None, ddof=0), decimal=13)
+            assert_almost_equal(stats.mstats.sem(ym, axis=None, ddof=0),
+                                stats.sem(y, axis=None, ddof=0), decimal=13)
+            assert_almost_equal(stats.mstats.sem(xm, axis=None, ddof=1),
+                                stats.sem(x, axis=None, ddof=1), decimal=13)
+            assert_almost_equal(stats.mstats.sem(ym, axis=None, ddof=1),
+                                stats.sem(y, axis=None, ddof=1), decimal=13)
+
+    def test_describe(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            r = stats.describe(x, ddof=1)
+            rm = stats.mstats.describe(xm, ddof=1)
+            for ii in range(6):
+                assert_almost_equal(np.asarray(r[ii]),
+                                    np.asarray(rm[ii]),
+                                    decimal=12)
+
+    def test_describe_result_attributes(self):
+        actual = mstats.describe(np.arange(5))
+        attributes = ('nobs', 'minmax', 'mean', 'variance', 'skewness',
+                      'kurtosis')
+        check_named_results(actual, attributes, ma=True)
+
+    def test_rankdata(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            r = stats.rankdata(x)
+            rm = stats.mstats.rankdata(x)
+            assert_allclose(r, rm)
+
+    def test_tmean(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            assert_almost_equal(stats.tmean(x),stats.mstats.tmean(xm), 14)
+            assert_almost_equal(stats.tmean(y),stats.mstats.tmean(ym), 14)
+
+    def test_tmax(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            assert_almost_equal(stats.tmax(x,2.),
+                                stats.mstats.tmax(xm,2.), 10)
+            assert_almost_equal(stats.tmax(y,2.),
+                                stats.mstats.tmax(ym,2.), 10)
+
+            assert_almost_equal(stats.tmax(x, upperlimit=3.),
+                                stats.mstats.tmax(xm, upperlimit=3.), 10)
+            assert_almost_equal(stats.tmax(y, upperlimit=3.),
+                                stats.mstats.tmax(ym, upperlimit=3.), 10)
+
+    def test_tmin(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            assert_equal(stats.tmin(x), stats.mstats.tmin(xm))
+            assert_equal(stats.tmin(y), stats.mstats.tmin(ym))
+
+            assert_almost_equal(stats.tmin(x, lowerlimit=-1.),
+                                stats.mstats.tmin(xm, lowerlimit=-1.), 10)
+            assert_almost_equal(stats.tmin(y, lowerlimit=-1.),
+                                stats.mstats.tmin(ym, lowerlimit=-1.), 10)
+
+    def test_zmap(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            z = stats.zmap(x, y)
+            zm = stats.mstats.zmap(xm, ym)
+            assert_allclose(z, zm[0:len(z)], atol=1e-10)
+
+    def test_variation(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            assert_almost_equal(stats.variation(x), stats.mstats.variation(xm),
+                                decimal=12)
+            assert_almost_equal(stats.variation(y), stats.mstats.variation(ym),
+                                decimal=12)
+
+    def test_tvar(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            assert_almost_equal(stats.tvar(x), stats.mstats.tvar(xm),
+                                decimal=12)
+            assert_almost_equal(stats.tvar(y), stats.mstats.tvar(ym),
+                                decimal=12)
+
+    def test_trimboth(self):
+        a = np.arange(20)
+        b = stats.trimboth(a, 0.1)
+        bm = stats.mstats.trimboth(a, 0.1)
+        assert_allclose(np.sort(b), bm.data[~bm.mask])
+
+    def test_tsem(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            assert_almost_equal(stats.tsem(x), stats.mstats.tsem(xm),
+                                decimal=14)
+            assert_almost_equal(stats.tsem(y), stats.mstats.tsem(ym),
+                                decimal=14)
+            assert_almost_equal(stats.tsem(x, limits=(-2., 2.)),
+                                stats.mstats.tsem(xm, limits=(-2., 2.)),
+                                decimal=14)
+
+    def test_skewtest(self):
+        # this test is for 1D data
+        for n in self.get_n():
+            if n > 8:
+                x, y, xm, ym = self.generate_xy_sample(n)
+                r = stats.skewtest(x)
+                rm = stats.mstats.skewtest(xm)
+                assert_allclose(r, rm)
+
+    def test_skewtest_result_attributes(self):
+        x = np.array((-2, -1, 0, 1, 2, 3)*4)**2
+        res = mstats.skewtest(x)
+        attributes = ('statistic', 'pvalue')
+        check_named_results(res, attributes, ma=True)
+
+    def test_skewtest_2D_notmasked(self):
+        # a normal ndarray is passed to the masked function
+        rng = np.random.default_rng(2790153686)
+        x = rng.random((20, 2)) * 20.
+        r = stats.skewtest(x)
+        rm = stats.mstats.skewtest(x)
+        assert_allclose(np.asarray(r), np.asarray(rm))
+
+    def test_skewtest_2D_WithMask(self):
+        nx = 2
+        for n in self.get_n():
+            if n > 8:
+                x, y, xm, ym = self.generate_xy_sample2D(n, nx)
+                r = stats.skewtest(x)
+                rm = stats.mstats.skewtest(xm)
+
+                assert_allclose(r[0][0], rm[0][0], rtol=1e-14)
+                assert_allclose(r[0][1], rm[0][1], rtol=1e-14)
+
+    def test_normaltest(self):
+        with np.errstate(over='raise'), warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", "`kurtosistest` p-value may be inaccurate", UserWarning)
+            warnings.filterwarnings(
+                "ignore", "kurtosistest only valid for n>=20", UserWarning)
+            for n in self.get_n():
+                if n > 8:
+                    x, y, xm, ym = self.generate_xy_sample(n)
+                    r = stats.normaltest(x)
+                    rm = stats.mstats.normaltest(xm)
+                    assert_allclose(np.asarray(r), np.asarray(rm))
+
+    def test_find_repeats(self):
+        x = np.asarray([1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 4]).astype('float')
+        tmp = np.asarray([1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5]).astype('float')
+        mask = (tmp == 5.)
+        xm = np.ma.array(tmp, mask=mask)
+        x_orig, xm_orig = x.copy(), xm.copy()
+
+        unique, unique_counts = np.unique(x, return_counts=True)
+        r = unique[unique_counts > 1], unique_counts[unique_counts > 1]
+        rm = stats.mstats.find_repeats(xm)
+
+        assert_equal(r, rm)
+        assert_equal(x, x_orig)
+        assert_equal(xm, xm_orig)
+
+        # This crazy behavior is expected by count_tied_groups, but is not
+        # in the docstring...
+        _, counts = stats.mstats.find_repeats([])
+        assert_equal(counts, np.array(0, dtype=np.intp))
+
+    def test_kendalltau(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            r = stats.kendalltau(x, y)
+            rm = stats.mstats.kendalltau(xm, ym)
+            assert_almost_equal(r[0], rm[0], decimal=10)
+            assert_almost_equal(r[1], rm[1], decimal=7)
+
+    def test_obrientransform(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            r = np.stack(stats.obrientransform(x))
+            rm = stats.mstats.obrientransform(xm)
+            assert_almost_equal(r.T, rm[0:len(x)])
+
+    def test_ks_1samp(self):
+        """Checks that mstats.ks_1samp and stats.ks_1samp agree on masked arrays."""
+        for mode in ['auto', 'exact', 'asymp']:
+            with warnings.catch_warnings():
+                for alternative in ['less', 'greater', 'two-sided']:
+                    for n in self.get_n():
+                        x, y, xm, ym = self.generate_xy_sample(n)
+                        res1 = stats.ks_1samp(x, stats.norm.cdf,
+                                              alternative=alternative, mode=mode)
+                        res2 = stats.mstats.ks_1samp(xm, stats.norm.cdf,
+                                                     alternative=alternative, mode=mode)
+                        assert_equal(np.asarray(res1), np.asarray(res2))
+                        res3 = stats.ks_1samp(xm, stats.norm.cdf,
+                                              alternative=alternative, mode=mode)
+                        assert_equal(np.asarray(res1), np.asarray(res3))
+
+    def test_kstest_1samp(self):
+        """
+        Checks that 1-sample mstats.kstest and stats.kstest agree on masked arrays.
+        """
+        for mode in ['auto', 'exact', 'asymp']:
+            with warnings.catch_warnings():
+                for alternative in ['less', 'greater', 'two-sided']:
+                    for n in self.get_n():
+                        x, y, xm, ym = self.generate_xy_sample(n)
+                        res1 = stats.kstest(x, 'norm',
+                                            alternative=alternative, mode=mode)
+                        res2 = stats.mstats.kstest(xm, 'norm',
+                                                   alternative=alternative, mode=mode)
+                        assert_equal(np.asarray(res1), np.asarray(res2))
+                        res3 = stats.kstest(xm, 'norm',
+                                            alternative=alternative, mode=mode)
+                        assert_equal(np.asarray(res1), np.asarray(res3))
+
+    def test_ks_2samp(self):
+        """Checks that mstats.ks_2samp and stats.ks_2samp agree on masked arrays.
+        gh-8431"""
+        for mode in ['auto', 'exact', 'asymp']:
+            with warnings.catch_warnings():
+                if mode in ['auto', 'exact']:
+                    message = "ks_2samp: Exact calculation unsuccessful."
+                    warnings.filterwarnings("ignore", message, RuntimeWarning)
+                for alternative in ['less', 'greater', 'two-sided']:
+                    for n in self.get_n():
+                        x, y, xm, ym = self.generate_xy_sample(n)
+                        res1 = stats.ks_2samp(x, y,
+                                              alternative=alternative, mode=mode)
+                        res2 = stats.mstats.ks_2samp(xm, ym,
+                                                     alternative=alternative, mode=mode)
+                        assert_equal(np.asarray(res1), np.asarray(res2))
+                        res3 = stats.ks_2samp(xm, y,
+                                              alternative=alternative, mode=mode)
+                        assert_equal(np.asarray(res1), np.asarray(res3))
+
+    def test_kstest_2samp(self):
+        """
+        Checks that 2-sample mstats.kstest and stats.kstest agree on masked arrays.
+        """
+        for mode in ['auto', 'exact', 'asymp']:
+            with warnings.catch_warnings():
+                if mode in ['auto', 'exact']:
+                    message = "ks_2samp: Exact calculation unsuccessful."
+                    warnings.filterwarnings("ignore", message, RuntimeWarning)
+                for alternative in ['less', 'greater', 'two-sided']:
+                    for n in self.get_n():
+                        x, y, xm, ym = self.generate_xy_sample(n)
+                        res1 = stats.kstest(x, y,
+                                            alternative=alternative, mode=mode)
+                        res2 = stats.mstats.kstest(xm, ym,
+                                                   alternative=alternative, mode=mode)
+                        assert_equal(np.asarray(res1), np.asarray(res2))
+                        res3 = stats.kstest(xm, y,
+                                            alternative=alternative, mode=mode)
+                        assert_equal(np.asarray(res1), np.asarray(res3))
+
+
+class TestBrunnerMunzel:
+    # Data from (Lumley, 1996)
+    X = np.ma.masked_invalid([1, 2, 1, 1, 1, np.nan, 1, 1,
+                              1, 1, 1, 2, 4, 1, 1, np.nan])
+    Y = np.ma.masked_invalid([3, 3, 4, 3, np.nan, 1, 2, 3, 1, 1, 5, 4])
+    significant = 14
+
+    def test_brunnermunzel_one_sided(self):
+        # Results are compared with R's lawstat package.
+        u1, p1 = mstats.brunnermunzel(self.X, self.Y, alternative='less')
+        u2, p2 = mstats.brunnermunzel(self.Y, self.X, alternative='greater')
+        u3, p3 = mstats.brunnermunzel(self.X, self.Y, alternative='greater')
+        u4, p4 = mstats.brunnermunzel(self.Y, self.X, alternative='less')
+
+        assert_almost_equal(p1, p2, decimal=self.significant)
+        assert_almost_equal(p3, p4, decimal=self.significant)
+        assert_(p1 != p3)
+        assert_almost_equal(u1, 3.1374674823029505,
+                            decimal=self.significant)
+        assert_almost_equal(u2, -3.1374674823029505,
+                            decimal=self.significant)
+        assert_almost_equal(u3, 3.1374674823029505,
+                            decimal=self.significant)
+        assert_almost_equal(u4, -3.1374674823029505,
+                            decimal=self.significant)
+        assert_almost_equal(p1, 0.0028931043330757342,
+                            decimal=self.significant)
+        assert_almost_equal(p3, 0.99710689566692423,
+                            decimal=self.significant)
+
+    def test_brunnermunzel_two_sided(self):
+        # Results are compared with R's lawstat package.
+        u1, p1 = mstats.brunnermunzel(self.X, self.Y, alternative='two-sided')
+        u2, p2 = mstats.brunnermunzel(self.Y, self.X, alternative='two-sided')
+
+        assert_almost_equal(p1, p2, decimal=self.significant)
+        assert_almost_equal(u1, 3.1374674823029505,
+                            decimal=self.significant)
+        assert_almost_equal(u2, -3.1374674823029505,
+                            decimal=self.significant)
+        assert_almost_equal(p1, 0.0057862086661515377,
+                            decimal=self.significant)
+
+    def test_brunnermunzel_default(self):
+        # The default value for alternative is two-sided
+        u1, p1 = mstats.brunnermunzel(self.X, self.Y)
+        u2, p2 = mstats.brunnermunzel(self.Y, self.X)
+
+        assert_almost_equal(p1, p2, decimal=self.significant)
+        assert_almost_equal(u1, 3.1374674823029505,
+                            decimal=self.significant)
+        assert_almost_equal(u2, -3.1374674823029505,
+                            decimal=self.significant)
+        assert_almost_equal(p1, 0.0057862086661515377,
+                            decimal=self.significant)
+
+    def test_brunnermunzel_alternative_error(self):
+        alternative = "error"
+        distribution = "t"
+        assert_(alternative not in ["two-sided", "greater", "less"])
+        assert_raises(ValueError,
+                      mstats.brunnermunzel,
+                      self.X,
+                      self.Y,
+                      alternative,
+                      distribution)
+
+    def test_brunnermunzel_distribution_norm(self):
+        u1, p1 = mstats.brunnermunzel(self.X, self.Y, distribution="normal")
+        u2, p2 = mstats.brunnermunzel(self.Y, self.X, distribution="normal")
+        assert_almost_equal(p1, p2, decimal=self.significant)
+        assert_almost_equal(u1, 3.1374674823029505,
+                            decimal=self.significant)
+        assert_almost_equal(u2, -3.1374674823029505,
+                            decimal=self.significant)
+        assert_almost_equal(p1, 0.0017041417600383024,
+                            decimal=self.significant)
+
+    def test_brunnermunzel_distribution_error(self):
+        alternative = "two-sided"
+        distribution = "error"
+        assert_(alternative not in ["t", "normal"])
+        assert_raises(ValueError,
+                      mstats.brunnermunzel,
+                      self.X,
+                      self.Y,
+                      alternative,
+                      distribution)
+
+    def test_brunnermunzel_empty_imput(self):
+        u1, p1 = mstats.brunnermunzel(self.X, [])
+        u2, p2 = mstats.brunnermunzel([], self.Y)
+        u3, p3 = mstats.brunnermunzel([], [])
+
+        assert_(np.isnan(u1))
+        assert_(np.isnan(p1))
+        assert_(np.isnan(u2))
+        assert_(np.isnan(p2))
+        assert_(np.isnan(u3))
+        assert_(np.isnan(p3))
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/test_mstats_extras.py b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_mstats_extras.py
new file mode 100644
index 0000000000000000000000000000000000000000..8b14455b417317a23abda8efe5297e8f4839ffd2
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_mstats_extras.py
@@ -0,0 +1,172 @@
+import numpy as np
+import numpy.ma as ma
+import scipy.stats.mstats as ms
+
+from numpy.testing import (assert_equal, assert_almost_equal, assert_,
+                           assert_allclose)
+
+
+def test_compare_medians_ms():
+    x = np.arange(7)
+    y = x + 10
+    assert_almost_equal(ms.compare_medians_ms(x, y), 0)
+
+    y2 = np.linspace(0, 1, num=10)
+    assert_almost_equal(ms.compare_medians_ms(x, y2), 0.017116406778)
+
+
+def test_hdmedian():
+    # 1-D array
+    x = ma.arange(11)
+    assert_allclose(ms.hdmedian(x), 5, rtol=1e-14)
+    x.mask = ma.make_mask(x)
+    x.mask[:7] = False
+    assert_allclose(ms.hdmedian(x), 3, rtol=1e-14)
+
+    # Check that `var` keyword returns a value.  TODO: check whether returned
+    # value is actually correct.
+    assert_(ms.hdmedian(x, var=True).size == 2)
+
+    # 2-D array
+    x2 = ma.arange(22).reshape((11, 2))
+    assert_allclose(ms.hdmedian(x2, axis=0), [10, 11])
+    x2.mask = ma.make_mask(x2)
+    x2.mask[:7, :] = False
+    assert_allclose(ms.hdmedian(x2, axis=0), [6, 7])
+
+
+def test_rsh():
+    rng = np.random.default_rng(806795795)
+    x = rng.standard_normal(100)
+    res = ms.rsh(x)
+    # Just a sanity check that the code runs and output shape is correct.
+    # TODO: check that implementation is correct.
+    assert_(res.shape == x.shape)
+
+    # Check points keyword
+    res = ms.rsh(x, points=[0, 1.])
+    assert_(res.size == 2)
+
+
+def test_mjci():
+    # Tests the Marits-Jarrett estimator
+    data = ma.array([77, 87, 88,114,151,210,219,246,253,262,
+                     296,299,306,376,428,515,666,1310,2611])
+    assert_almost_equal(ms.mjci(data),[55.76819,45.84028,198.87875],5)
+
+
+def test_trimmed_mean_ci():
+    # Tests the confidence intervals of the trimmed mean.
+    data = ma.array([545,555,558,572,575,576,578,580,
+                     594,605,635,651,653,661,666])
+    assert_almost_equal(ms.trimmed_mean(data,0.2), 596.2, 1)
+    assert_equal(np.round(ms.trimmed_mean_ci(data,(0.2,0.2)),1),
+                 [561.8, 630.6])
+
+
+def test_idealfourths():
+    # Tests ideal-fourths
+    test = np.arange(100)
+    assert_almost_equal(np.asarray(ms.idealfourths(test)),
+                        [24.416667,74.583333],6)
+    test_2D = test.repeat(3).reshape(-1,3)
+    assert_almost_equal(ms.idealfourths(test_2D, axis=0),
+                        [[24.416667,24.416667,24.416667],
+                         [74.583333,74.583333,74.583333]],6)
+    assert_almost_equal(ms.idealfourths(test_2D, axis=1),
+                        test.repeat(2).reshape(-1,2))
+    test = [0, 0]
+    _result = ms.idealfourths(test)
+    assert_(np.isnan(_result).all())
+
+
+class TestQuantiles:
+    data = [0.706560797,0.727229578,0.990399276,0.927065621,0.158953014,
+            0.887764025,0.239407086,0.349638551,0.972791145,0.149789972,
+            0.936947700,0.132359948,0.046041972,0.641675031,0.945530547,
+            0.224218684,0.771450991,0.820257774,0.336458052,0.589113496,
+            0.509736129,0.696838829,0.491323573,0.622767425,0.775189248,
+            0.641461450,0.118455200,0.773029450,0.319280007,0.752229111,
+            0.047841438,0.466295911,0.583850781,0.840581845,0.550086491,
+            0.466470062,0.504765074,0.226855960,0.362641207,0.891620942,
+            0.127898691,0.490094097,0.044882048,0.041441695,0.317976349,
+            0.504135618,0.567353033,0.434617473,0.636243375,0.231803616,
+            0.230154113,0.160011327,0.819464108,0.854706985,0.438809221,
+            0.487427267,0.786907310,0.408367937,0.405534192,0.250444460,
+            0.995309248,0.144389588,0.739947527,0.953543606,0.680051621,
+            0.388382017,0.863530727,0.006514031,0.118007779,0.924024803,
+            0.384236354,0.893687694,0.626534881,0.473051932,0.750134705,
+            0.241843555,0.432947602,0.689538104,0.136934797,0.150206859,
+            0.474335206,0.907775349,0.525869295,0.189184225,0.854284286,
+            0.831089744,0.251637345,0.587038213,0.254475554,0.237781276,
+            0.827928620,0.480283781,0.594514455,0.213641488,0.024194386,
+            0.536668589,0.699497811,0.892804071,0.093835427,0.731107772]
+
+    def test_hdquantiles(self):
+        data = self.data
+        assert_almost_equal(ms.hdquantiles(data,[0., 1.]),
+                            [0.006514031, 0.995309248])
+        hdq = ms.hdquantiles(data,[0.25, 0.5, 0.75])
+        assert_almost_equal(hdq, [0.253210762, 0.512847491, 0.762232442,])
+
+        data = np.array(data).reshape(10,10)
+        hdq = ms.hdquantiles(data,[0.25,0.5,0.75],axis=0)
+        assert_almost_equal(hdq[:,0], ms.hdquantiles(data[:,0],[0.25,0.5,0.75]))
+        assert_almost_equal(hdq[:,-1], ms.hdquantiles(data[:,-1],[0.25,0.5,0.75]))
+        hdq = ms.hdquantiles(data,[0.25,0.5,0.75],axis=0,var=True)
+        assert_almost_equal(hdq[...,0],
+                            ms.hdquantiles(data[:,0],[0.25,0.5,0.75],var=True))
+        assert_almost_equal(hdq[...,-1],
+                            ms.hdquantiles(data[:,-1],[0.25,0.5,0.75], var=True))
+
+    def test_hdquantiles_sd(self):
+        # Standard deviation is a jackknife estimator, so we can check if
+        # the efficient version (hdquantiles_sd) matches a rudimentary,
+        # but clear version here.
+
+        hd_std_errs = ms.hdquantiles_sd(self.data)
+
+        # jacknnife standard error, Introduction to the Bootstrap Eq. 11.5
+        n = len(self.data)
+        jdata = np.broadcast_to(self.data, (n, n))
+        jselector = np.logical_not(np.eye(n))  # leave out one sample each row
+        jdata = jdata[jselector].reshape(n, n-1)
+        jdist = ms.hdquantiles(jdata, axis=1)
+        jdist_mean = np.mean(jdist, axis=0)
+        jstd = ((n-1)/n * np.sum((jdist - jdist_mean)**2, axis=0))**.5
+
+        assert_almost_equal(hd_std_errs, jstd)
+        # Test actual values for good measure
+        assert_almost_equal(hd_std_errs, [0.0379258, 0.0380656, 0.0380013])
+
+        two_data_points = ms.hdquantiles_sd([1, 2])
+        assert_almost_equal(two_data_points, [0.5, 0.5, 0.5])
+
+    def test_mquantiles_cimj(self):
+        # Only test that code runs, implementation not checked for correctness
+        ci_lower, ci_upper = ms.mquantiles_cimj(self.data)
+        assert_(ci_lower.size == ci_upper.size == 3)
+
+
+def test_median_cihs():
+    # Basic test against R library EnvStats function `eqnpar`, e.g.
+    # library(EnvStats)
+    # options(digits=8)
+    # x = c(0.88612955, 0.35242375, 0.66240904, 0.94617974, 0.10929913,
+    #       0.76699506, 0.88550655, 0.62763754, 0.76818588, 0.68506508,
+    #       0.88043148, 0.03911248, 0.93805564, 0.95326961, 0.25291112,
+    #       0.16128487, 0.49784577, 0.24588924, 0.6597, 0.92239679)
+    # eqnpar(x, p=0.5,
+    #        ci.method = "interpolate", approx.conf.level = 0.95, ci = TRUE)
+    rng = np.random.default_rng(8824288259505800535)
+    x = rng.random(size=20)
+    assert_allclose(ms.median_cihs(x), (0.38663198, 0.88431272))
+
+    # SciPy's 90% CI upper limit doesn't match that of EnvStats eqnpar. SciPy
+    # doesn't look wrong, and it agrees with a different reference,
+    # `median_confint_hs` from `hoehleatsu/quantileCI`.
+    # In (e.g.) Colab with R runtime:
+    # devtools::install_github("hoehleatsu/quantileCI")
+    # library(quantileCI)
+    # median_confint_hs(x=x, conf.level=0.90, interpolate=TRUE)
+    assert_allclose(ms.median_cihs(x, 0.1), (0.48319773366, 0.88094268050))
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/test_multicomp.py b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_multicomp.py
new file mode 100644
index 0000000000000000000000000000000000000000..2860b142c38a339f96c50af92bd452c6de95e84d
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_multicomp.py
@@ -0,0 +1,405 @@
+import copy
+
+import numpy as np
+import pytest
+from numpy.testing import assert_allclose
+
+from scipy import stats
+from scipy.stats._multicomp import _pvalue_dunnett, DunnettResult
+
+
+class TestDunnett:
+    # For the following tests, p-values were computed using Matlab, e.g.
+    #     sample = [18.  15.  18.  16.  17.  15.  14.  14.  14.  15.  15....
+    #               14.  15.  14.  22.  18.  21.  21.  10.  10.  11.  9....
+    #               25.  26.  17.5 16.  15.5 14.5 22.  22.  24.  22.5 29....
+    #               24.5 20.  18.  18.5 17.5 26.5 13.  16.5 13.  13.  13....
+    #               28.  27.  34.  31.  29.  27.  24.  23.  38.  36.  25....
+    #               38. 26.  22.  36.  27.  27.  32.  28.  31....
+    #               24.  27.  33.  32.  28.  19. 37.  31.  36.  36....
+    #               34.  38.  32.  38.  32....
+    #               26.  24.  26.  25.  29. 29.5 16.5 36.  44....
+    #               25.  27.  19....
+    #               25.  20....
+    #               28.];
+    #     j = [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ...
+    #          0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ...
+    #          0 0 0 0...
+    #          1 1 1 1 1 1 1 1 1 1 1 1 1 1 1...
+    #          2 2 2 2 2 2 2 2 2...
+    #          3 3 3...
+    #          4 4...
+    #          5];
+    #     [~, ~, stats] = anova1(sample, j, "off");
+    #     [results, ~, ~, gnames] = multcompare(stats, ...
+    #     "CriticalValueType", "dunnett", ...
+    #     "Approximate", false);
+    #     tbl = array2table(results, "VariableNames", ...
+    #     ["Group", "Control Group", "Lower Limit", ...
+    #     "Difference", "Upper Limit", "P-value"]);
+    #     tbl.("Group") = gnames(tbl.("Group"));
+    #     tbl.("Control Group") = gnames(tbl.("Control Group"))
+
+    # Matlab doesn't report the statistic, so the statistics were
+    # computed using R multcomp `glht`, e.g.:
+    #     library(multcomp)
+    #     options(digits=16)
+    #     control < - c(18.0, 15.0, 18.0, 16.0, 17.0, 15.0, 14.0, 14.0, 14.0,
+    #                   15.0, 15.0, 14.0, 15.0, 14.0, 22.0, 18.0, 21.0, 21.0,
+    #                   10.0, 10.0, 11.0, 9.0, 25.0, 26.0, 17.5, 16.0, 15.5,
+    #                   14.5, 22.0, 22.0, 24.0, 22.5, 29.0, 24.5, 20.0, 18.0,
+    #                   18.5, 17.5, 26.5, 13.0, 16.5, 13.0, 13.0, 13.0, 28.0,
+    #                   27.0, 34.0, 31.0, 29.0, 27.0, 24.0, 23.0, 38.0, 36.0,
+    #                   25.0, 38.0, 26.0, 22.0, 36.0, 27.0, 27.0, 32.0, 28.0,
+    #                   31.0)
+    #     t < - c(24.0, 27.0, 33.0, 32.0, 28.0, 19.0, 37.0, 31.0, 36.0, 36.0,
+    #             34.0, 38.0, 32.0, 38.0, 32.0)
+    #     w < - c(26.0, 24.0, 26.0, 25.0, 29.0, 29.5, 16.5, 36.0, 44.0)
+    #     x < - c(25.0, 27.0, 19.0)
+    #     y < - c(25.0, 20.0)
+    #     z < - c(28.0)
+    #
+    #     groups = factor(rep(c("control", "t", "w", "x", "y", "z"),
+    #                         times=c(length(control), length(t), length(w),
+    #                                 length(x), length(y), length(z))))
+    #     df < - data.frame(response=c(control, t, w, x, y, z),
+    #                       group=groups)
+    #     model < - aov(response
+    #     ~group, data = df)
+    #     test < - glht(model=model,
+    #                   linfct=mcp(group="Dunnett"),
+    #                   alternative="g")
+    #     summary(test)
+    #     confint(test)
+    # p-values agreed with those produced by Matlab to at least atol=1e-3
+
+    # From Matlab's documentation on multcompare
+    samples_1 = [
+        [
+            24.0, 27.0, 33.0, 32.0, 28.0, 19.0, 37.0, 31.0, 36.0, 36.0,
+            34.0, 38.0, 32.0, 38.0, 32.0
+        ],
+        [26.0, 24.0, 26.0, 25.0, 29.0, 29.5, 16.5, 36.0, 44.0],
+        [25.0, 27.0, 19.0],
+        [25.0, 20.0],
+        [28.0]
+    ]
+    control_1 = [
+        18.0, 15.0, 18.0, 16.0, 17.0, 15.0, 14.0, 14.0, 14.0, 15.0, 15.0,
+        14.0, 15.0, 14.0, 22.0, 18.0, 21.0, 21.0, 10.0, 10.0, 11.0, 9.0,
+        25.0, 26.0, 17.5, 16.0, 15.5, 14.5, 22.0, 22.0, 24.0, 22.5, 29.0,
+        24.5, 20.0, 18.0, 18.5, 17.5, 26.5, 13.0, 16.5, 13.0, 13.0, 13.0,
+        28.0, 27.0, 34.0, 31.0, 29.0, 27.0, 24.0, 23.0, 38.0, 36.0, 25.0,
+        38.0, 26.0, 22.0, 36.0, 27.0, 27.0, 32.0, 28.0, 31.0
+    ]
+    pvalue_1 = [4.727e-06, 0.022346, 0.97912, 0.99953, 0.86579]  # Matlab
+    # Statistic, alternative p-values, and CIs computed with R multcomp `glht`
+    p_1_twosided = [1e-4, 0.02237, 0.97913, 0.99953, 0.86583]
+    p_1_greater = [1e-4, 0.011217, 0.768500, 0.896991, 0.577211]
+    p_1_less = [1, 1, 0.99660, 0.98398, .99953]
+    statistic_1 = [5.27356, 2.91270, 0.60831, 0.27002, 0.96637]
+    ci_1_twosided = [[5.3633917835622, 0.7296142201217, -8.3879817106607,
+                      -11.9090753452911, -11.7655021543469],
+                     [15.9709832164378, 13.8936496687672, 13.4556900439941,
+                      14.6434503452911, 25.4998771543469]]
+    ci_1_greater = [5.9036402398526, 1.4000632918725, -7.2754756323636,
+                    -10.5567456382391, -9.8675629499576]
+    ci_1_less = [15.4306165948619, 13.2230539537359, 12.3429406339544,
+                 13.2908248513211, 23.6015228251660]
+    pvalues_1 = dict(twosided=p_1_twosided, less=p_1_less, greater=p_1_greater)
+    cis_1 = dict(twosided=ci_1_twosided, less=ci_1_less, greater=ci_1_greater)
+    case_1 = dict(samples=samples_1, control=control_1, statistic=statistic_1,
+                  pvalues=pvalues_1, cis=cis_1)
+
+    # From Dunnett1955 comparing with R's DescTools: DunnettTest
+    samples_2 = [[9.76, 8.80, 7.68, 9.36], [12.80, 9.68, 12.16, 9.20, 10.55]]
+    control_2 = [7.40, 8.50, 7.20, 8.24, 9.84, 8.32]
+    pvalue_2 = [0.6201, 0.0058]
+    # Statistic, alternative p-values, and CIs computed with R multcomp `glht`
+    p_2_twosided = [0.6201020, 0.0058254]
+    p_2_greater = [0.3249776, 0.0029139]
+    p_2_less = [0.91676, 0.99984]
+    statistic_2 = [0.85703, 3.69375]
+    ci_2_twosided = [[-1.2564116462124, 0.8396273539789],
+                     [2.5564116462124, 4.4163726460211]]
+    ci_2_greater = [-0.9588591188156, 1.1187563667543]
+    ci_2_less = [2.2588591188156, 4.1372436332457]
+    pvalues_2 = dict(twosided=p_2_twosided, less=p_2_less, greater=p_2_greater)
+    cis_2 = dict(twosided=ci_2_twosided, less=ci_2_less, greater=ci_2_greater)
+    case_2 = dict(samples=samples_2, control=control_2, statistic=statistic_2,
+                  pvalues=pvalues_2, cis=cis_2)
+
+    samples_3 = [[55, 64, 64], [55, 49, 52], [50, 44, 41]]
+    control_3 = [55, 47, 48]
+    pvalue_3 = [0.0364, 0.8966, 0.4091]
+    # Statistic, alternative p-values, and CIs computed with R multcomp `glht`
+    p_3_twosided = [0.036407, 0.896539, 0.409295]
+    p_3_greater = [0.018277, 0.521109, 0.981892]
+    p_3_less = [0.99944, 0.90054, 0.20974]
+    statistic_3 = [3.09073, 0.56195, -1.40488]
+    ci_3_twosided = [[0.7529028025053, -8.2470971974947, -15.2470971974947],
+                     [21.2470971974947, 12.2470971974947, 5.2470971974947]]
+    ci_3_greater = [2.4023682323149, -6.5976317676851, -13.5976317676851]
+    ci_3_less = [19.5984402363662, 10.5984402363662, 3.5984402363662]
+    pvalues_3 = dict(twosided=p_3_twosided, less=p_3_less, greater=p_3_greater)
+    cis_3 = dict(twosided=ci_3_twosided, less=ci_3_less, greater=ci_3_greater)
+    case_3 = dict(samples=samples_3, control=control_3, statistic=statistic_3,
+                  pvalues=pvalues_3, cis=cis_3)
+
+    # From Thomson and Short,
+    # Mucociliary function in health, chronic obstructive airway disease,
+    # and asbestosis, Journal of Applied Physiology, 1969. Table 1
+    # Comparing with R's DescTools: DunnettTest
+    samples_4 = [[3.8, 2.7, 4.0, 2.4], [2.8, 3.4, 3.7, 2.2, 2.0]]
+    control_4 = [2.9, 3.0, 2.5, 2.6, 3.2]
+    pvalue_4 = [0.5832, 0.9982]
+    # Statistic, alternative p-values, and CIs computed with R multcomp `glht`
+    p_4_twosided = [0.58317, 0.99819]
+    p_4_greater = [0.30225, 0.69115]
+    p_4_less = [0.91929, 0.65212]
+    statistic_4 = [0.90875, -0.05007]
+    ci_4_twosided = [[-0.6898153448579, -1.0333456251632],
+                     [1.4598153448579, 0.9933456251632]]
+    ci_4_greater = [-0.5186459268412, -0.8719655502147 ]
+    ci_4_less = [1.2886459268412, 0.8319655502147]
+    pvalues_4 = dict(twosided=p_4_twosided, less=p_4_less, greater=p_4_greater)
+    cis_4 = dict(twosided=ci_4_twosided, less=ci_4_less, greater=ci_4_greater)
+    case_4 = dict(samples=samples_4, control=control_4, statistic=statistic_4,
+                  pvalues=pvalues_4, cis=cis_4)
+
+    @pytest.mark.parametrize(
+        'rho, n_groups, df, statistic, pvalue, alternative',
+        [
+            # From Dunnett1955
+            # Tables 1a and 1b pages 1117-1118
+            (0.5, 1, 10, 1.81, 0.05, "greater"),  # different than two-sided
+            (0.5, 3, 10, 2.34, 0.05, "greater"),
+            (0.5, 2, 30, 1.99, 0.05, "greater"),
+            (0.5, 5, 30, 2.33, 0.05, "greater"),
+            (0.5, 4, 12, 3.32, 0.01, "greater"),
+            (0.5, 7, 12, 3.56, 0.01, "greater"),
+            (0.5, 2, 60, 2.64, 0.01, "greater"),
+            (0.5, 4, 60, 2.87, 0.01, "greater"),
+            (0.5, 4, 60, [2.87, 2.21], [0.01, 0.05], "greater"),
+            # Tables 2a and 2b pages 1119-1120
+            (0.5, 1, 10, 2.23, 0.05, "two-sided"),  # two-sided
+            (0.5, 3, 10, 2.81, 0.05, "two-sided"),
+            (0.5, 2, 30, 2.32, 0.05, "two-sided"),
+            (0.5, 3, 20, 2.57, 0.05, "two-sided"),
+            (0.5, 4, 12, 3.76, 0.01, "two-sided"),
+            (0.5, 7, 12, 4.08, 0.01, "two-sided"),
+            (0.5, 2, 60, 2.90, 0.01, "two-sided"),
+            (0.5, 4, 60, 3.14, 0.01, "two-sided"),
+            (0.5, 4, 60, [3.14, 2.55], [0.01, 0.05], "two-sided"),
+        ],
+    )
+    def test_critical_values(
+        self, rho, n_groups, df, statistic, pvalue, alternative
+    ):
+        rng = np.random.default_rng(165250594791731684851746311027739134893)
+        rho = np.full((n_groups, n_groups), rho)
+        np.fill_diagonal(rho, 1)
+
+        statistic = np.array(statistic)
+        res = _pvalue_dunnett(
+            rho=rho, df=df, statistic=statistic,
+            alternative=alternative,
+            rng=rng
+        )
+        assert_allclose(res, pvalue, atol=5e-3)
+
+    @pytest.mark.parametrize(
+        'samples, control, pvalue, statistic',
+        [
+            (samples_1, control_1, pvalue_1, statistic_1),
+            (samples_2, control_2, pvalue_2, statistic_2),
+            (samples_3, control_3, pvalue_3, statistic_3),
+            (samples_4, control_4, pvalue_4, statistic_4),
+        ]
+    )
+    def test_basic(self, samples, control, pvalue, statistic):
+        rng = np.random.default_rng(11681140010308601919115036826969764808)
+
+        res = stats.dunnett(*samples, control=control, rng=rng)
+
+        assert isinstance(res, DunnettResult)
+        assert_allclose(res.statistic, statistic, rtol=5e-5)
+        assert_allclose(res.pvalue, pvalue, rtol=1e-2, atol=1e-4)
+
+    @pytest.mark.parametrize(
+        'alternative',
+        ['two-sided', 'less', 'greater']
+    )
+    def test_ttest_ind(self, alternative):
+        # check that `dunnett` agrees with `ttest_ind`
+        # when there are only two groups
+        rng = np.random.default_rng(114184017807316971636137493526995620351)
+
+        for _ in range(10):
+            sample = rng.integers(-100, 100, size=(10,))
+            control = rng.integers(-100, 100, size=(10,))
+
+            # preserve use of old random_state during SPEC 7 transition
+            res = stats.dunnett(
+                sample, control=control,
+                alternative=alternative, random_state=rng
+            )
+            ref = stats.ttest_ind(
+                sample, control,
+                alternative=alternative
+            )
+
+            assert_allclose(res.statistic, ref.statistic, rtol=1e-3, atol=1e-5)
+            assert_allclose(res.pvalue, ref.pvalue, rtol=1e-3, atol=1e-5)
+
+    @pytest.mark.parametrize(
+        'alternative, pvalue',
+        [
+            ('less', [0, 1]),
+            ('greater', [1, 0]),
+            ('two-sided', [0, 0]),
+        ]
+    )
+    def test_alternatives(self, alternative, pvalue):
+        rng = np.random.default_rng(114184017807316971636137493526995620351)
+
+        # width of 20 and min diff between samples/control is 60
+        # and maximal diff would be 100
+        sample_less = rng.integers(0, 20, size=(10,))
+        control = rng.integers(80, 100, size=(10,))
+        sample_greater = rng.integers(160, 180, size=(10,))
+
+        res = stats.dunnett(
+            sample_less, sample_greater, control=control,
+            alternative=alternative, rng=rng
+        )
+        assert_allclose(res.pvalue, pvalue, atol=1e-7)
+
+        ci = res.confidence_interval()
+        # two-sided is comparable for high/low
+        if alternative == 'less':
+            assert np.isneginf(ci.low).all()
+            assert -100 < ci.high[0] < -60
+            assert 60 < ci.high[1] < 100
+        elif alternative == 'greater':
+            assert -100 < ci.low[0] < -60
+            assert 60 < ci.low[1] < 100
+            assert np.isposinf(ci.high).all()
+        elif alternative == 'two-sided':
+            assert -100 < ci.low[0] < -60
+            assert 60 < ci.low[1] < 100
+            assert -100 < ci.high[0] < -60
+            assert 60 < ci.high[1] < 100
+
+    @pytest.mark.parametrize("case", [case_1, case_2, case_3, case_4])
+    @pytest.mark.parametrize("alternative", ['less', 'greater', 'two-sided'])
+    def test_against_R_multicomp_glht(self, case, alternative):
+        rng = np.random.default_rng(189117774084579816190295271136455278291)
+        samples = case['samples']
+        control = case['control']
+        alternatives = {'less': 'less', 'greater': 'greater',
+                        'two-sided': 'twosided'}
+        p_ref = case['pvalues'][alternative.replace('-', '')]
+
+        res = stats.dunnett(*samples, control=control, alternative=alternative,
+                            rng=rng)
+        # atol can't be tighter because R reports some pvalues as "< 1e-4"
+        assert_allclose(res.pvalue, p_ref, rtol=5e-3, atol=1e-4)
+
+        ci_ref = case['cis'][alternatives[alternative]]
+        if alternative == "greater":
+            ci_ref = [ci_ref, np.inf]
+        elif alternative == "less":
+            ci_ref = [-np.inf, ci_ref]
+        assert res._ci is None
+        assert res._ci_cl is None
+        ci = res.confidence_interval(confidence_level=0.95)
+        assert_allclose(ci.low, ci_ref[0], rtol=5e-3, atol=1e-5)
+        assert_allclose(ci.high, ci_ref[1], rtol=5e-3, atol=1e-5)
+
+        # re-run to use the cached value "is" to check id as same object
+        assert res._ci is ci
+        assert res._ci_cl == 0.95
+        ci_ = res.confidence_interval(confidence_level=0.95)
+        assert ci_ is ci
+
+    @pytest.mark.parametrize('alternative', ["two-sided", "less", "greater"])
+    def test_str(self, alternative):
+        rng = np.random.default_rng(189117774084579816190295271136455278291)
+
+        res = stats.dunnett(
+            *self.samples_3, control=self.control_3, alternative=alternative,
+            rng=rng
+        )
+
+        # check some str output
+        res_str = str(res)
+        assert '(Sample 2 - Control)' in res_str
+        assert '95.0%' in res_str
+
+        if alternative == 'less':
+            assert '-inf' in res_str
+            assert '19.' in res_str
+        elif alternative == 'greater':
+            assert 'inf' in res_str
+            assert '-13.' in res_str
+        else:
+            assert 'inf' not in res_str
+            assert '21.' in res_str
+
+    def test_warnings(self):
+        rng = np.random.default_rng(189117774084579816190295271136455278291)
+
+        res = stats.dunnett(
+            *self.samples_3, control=self.control_3, rng=rng
+        )
+        msg = r"Computation of the confidence interval did not converge"
+        with pytest.warns(UserWarning, match=msg):
+            res._allowance(tol=1e-5)
+
+    def test_raises(self):
+        samples, control = self.samples_3, self.control_3
+
+        # alternative
+        with pytest.raises(ValueError, match="alternative must be"):
+            stats.dunnett(*samples, control=control, alternative='bob')
+
+        # 2D for a sample
+        samples_ = copy.deepcopy(samples)
+        samples_[0] = [samples_[0]]
+        with pytest.raises(ValueError, match="must be 1D arrays"):
+            stats.dunnett(*samples_, control=control)
+
+        # 2D for control
+        control_ = copy.deepcopy(control)
+        control_ = [control_]
+        with pytest.raises(ValueError, match="must be 1D arrays"):
+            stats.dunnett(*samples, control=control_)
+
+        # No obs in a sample
+        samples_ = copy.deepcopy(samples)
+        samples_[1] = []
+        with pytest.raises(ValueError, match="at least 1 observation"):
+            stats.dunnett(*samples_, control=control)
+
+        # No obs in control
+        control_ = []
+        with pytest.raises(ValueError, match="at least 1 observation"):
+            stats.dunnett(*samples, control=control_)
+
+        res = stats.dunnett(*samples, control=control)
+        with pytest.raises(ValueError, match="Confidence level must"):
+            res.confidence_interval(confidence_level=3)
+
+    @pytest.mark.filterwarnings("ignore:Computation of the confidence")
+    @pytest.mark.parametrize('n_samples', [1, 2, 3])
+    def test_shapes(self, n_samples):
+        rng = np.random.default_rng(689448934110805334)
+        samples = rng.normal(size=(n_samples, 10))
+        control = rng.normal(size=10)
+        res = stats.dunnett(*samples, control=control, rng=rng)
+        assert res.statistic.shape == (n_samples,)
+        assert res.pvalue.shape == (n_samples,)
+        ci = res.confidence_interval()
+        assert ci.low.shape == (n_samples,)
+        assert ci.high.shape == (n_samples,)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/test_multivariate.py b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_multivariate.py
new file mode 100644
index 0000000000000000000000000000000000000000..46690b575a0c56c250d624bad87272f5a1fabd2e
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_multivariate.py
@@ -0,0 +1,5052 @@
+"""
+Test functions for multivariate normal, t, and related distributions.
+
+"""
+import pickle
+from dataclasses import dataclass
+
+from numpy.testing import (assert_allclose, assert_almost_equal,
+                           assert_array_almost_equal, assert_equal,
+                           assert_array_less, assert_)
+import pytest
+from pytest import raises as assert_raises
+
+from .test_continuous_basic import check_distribution_rvs
+
+import numpy as np
+
+import scipy.linalg
+
+from scipy.stats._multivariate import (_PSD,
+                                       _lnB,
+                                       multivariate_normal_frozen)
+from scipy.stats import (multivariate_normal, multivariate_hypergeom,
+                         matrix_normal, special_ortho_group, ortho_group,
+                         random_correlation, unitary_group, dirichlet,
+                         beta, wishart, multinomial, invwishart, chi2,
+                         invgamma, norm, uniform, ks_2samp, kstest, binom,
+                         hypergeom, multivariate_t, cauchy, normaltest,
+                         random_table, uniform_direction, vonmises_fisher,
+                         dirichlet_multinomial, vonmises, matrix_t)
+
+from scipy.stats import _covariance, Covariance
+from scipy.stats._continuous_distns import _norm_pdf as norm_pdf
+from scipy import stats
+
+from scipy.integrate import tanhsinh, cubature, quad
+from scipy.integrate import romb, qmc_quad, dblquad, tplquad
+from scipy.special import multigammaln
+import scipy.special as special
+
+from .common_tests import check_random_state_property
+from .data._mvt import _qsimvtv
+
+from unittest.mock import patch
+
+
+def assert_close(res, ref, *args, **kwargs):
+    res, ref = np.asarray(res), np.asarray(ref)
+    assert_allclose(res, ref, *args, **kwargs)
+    assert_equal(res.shape, ref.shape)
+
+
+class TestCovariance:
+
+    def test_input_validation(self):
+
+        message = "The input `precision` must be a square, two-dimensional..."
+        with pytest.raises(ValueError, match=message):
+            _covariance.CovViaPrecision(np.ones(2))
+
+        message = "`precision.shape` must equal `covariance.shape`."
+        with pytest.raises(ValueError, match=message):
+            _covariance.CovViaPrecision(np.eye(3), covariance=np.eye(2))
+
+        message = "The input `diagonal` must be a one-dimensional array..."
+        with pytest.raises(ValueError, match=message):
+            _covariance.CovViaDiagonal("alpaca")
+
+        message = "The input `cholesky` must be a square, two-dimensional..."
+        with pytest.raises(ValueError, match=message):
+            _covariance.CovViaCholesky(np.ones(2))
+
+        message = "The input `eigenvalues` must be a one-dimensional..."
+        with pytest.raises(ValueError, match=message):
+            _covariance.CovViaEigendecomposition(("alpaca", np.eye(2)))
+
+        message = "The input `eigenvectors` must be a square..."
+        with pytest.raises(ValueError, match=message):
+            _covariance.CovViaEigendecomposition((np.ones(2), "alpaca"))
+
+        message = "The shapes of `eigenvalues` and `eigenvectors` must be..."
+        with pytest.raises(ValueError, match=message):
+            _covariance.CovViaEigendecomposition(([1, 2, 3], np.eye(2)))
+
+    _covariance_preprocessing = {"Diagonal": np.diag,
+                                 "Precision": np.linalg.inv,
+                                 "Cholesky": np.linalg.cholesky,
+                                 "Eigendecomposition": np.linalg.eigh,
+                                 "PSD": lambda x:
+                                     _PSD(x, allow_singular=True)}
+    _all_covariance_types = np.array(list(_covariance_preprocessing))
+    _matrices = {"diagonal full rank": np.diag([1, 2, 3]),
+                 "general full rank": [[5, 1, 3], [1, 6, 4], [3, 4, 7]],
+                 "diagonal singular": np.diag([1, 0, 3]),
+                 "general singular": [[5, -1, 0], [-1, 5, 0], [0, 0, 0]]}
+    _cov_types = {"diagonal full rank": _all_covariance_types,
+                  "general full rank": _all_covariance_types[1:],
+                  "diagonal singular": _all_covariance_types[[0, -2, -1]],
+                  "general singular": _all_covariance_types[-2:]}
+
+    @pytest.mark.parametrize("cov_type_name", _all_covariance_types[:-1])
+    def test_factories(self, cov_type_name):
+        A = np.diag([1, 2, 3])
+        x = [-4, 2, 5]
+
+        cov_type = getattr(_covariance, f"CovVia{cov_type_name}")
+        preprocessing = self._covariance_preprocessing[cov_type_name]
+        factory = getattr(Covariance, f"from_{cov_type_name.lower()}")
+
+        res = factory(preprocessing(A))
+        ref = cov_type(preprocessing(A))
+        assert type(res) is type(ref)
+        assert_allclose(res.whiten(x), ref.whiten(x))
+
+    @pytest.mark.parametrize("matrix_type", list(_matrices))
+    @pytest.mark.parametrize("cov_type_name", _all_covariance_types)
+    def test_covariance(self, matrix_type, cov_type_name):
+        message = (f"CovVia{cov_type_name} does not support {matrix_type} "
+                   "matrices")
+        if cov_type_name not in self._cov_types[matrix_type]:
+            pytest.skip(message)
+
+        A = self._matrices[matrix_type]
+        cov_type = getattr(_covariance, f"CovVia{cov_type_name}")
+        preprocessing = self._covariance_preprocessing[cov_type_name]
+
+        psd = _PSD(A, allow_singular=True)
+
+        # test properties
+        cov_object = cov_type(preprocessing(A))
+        assert_close(cov_object.log_pdet, psd.log_pdet)
+        assert_equal(cov_object.rank, psd.rank)
+        assert_equal(cov_object.shape, np.asarray(A).shape)
+        assert_close(cov_object.covariance, np.asarray(A))
+
+        # test whitening/coloring 1D x
+        rng = np.random.default_rng(5292808890472453840)
+        x = rng.random(size=3)
+        res = cov_object.whiten(x)
+        ref = x @ psd.U
+        # res != ref in general; but res @ res == ref @ ref
+        assert_close(res @ res, ref @ ref)
+        if hasattr(cov_object, "_colorize") and "singular" not in matrix_type:
+            # CovViaPSD does not have _colorize
+            assert_close(cov_object.colorize(res), x)
+
+        # test whitening/coloring 3D x
+        x = rng.random(size=(2, 4, 3))
+        res = cov_object.whiten(x)
+        ref = x @ psd.U
+        assert_close((res**2).sum(axis=-1), (ref**2).sum(axis=-1))
+        if hasattr(cov_object, "_colorize") and "singular" not in matrix_type:
+            assert_close(cov_object.colorize(res), x)
+
+        # gh-19197 reported that multivariate normal `rvs` produced incorrect
+        # results when a singular Covariance object was produce using
+        # `from_eigenvalues`. This was due to an issue in `colorize` with
+        # singular covariance matrices. Check this edge case, which is skipped
+        # in the previous tests.
+        if hasattr(cov_object, "_colorize"):
+            res = cov_object.colorize(np.eye(len(A)))
+            assert_close(res.T @ res, A)
+
+    @pytest.mark.parametrize("size", [None, tuple(), 1, (2, 4, 3)])
+    @pytest.mark.parametrize("matrix_type", list(_matrices))
+    @pytest.mark.parametrize("cov_type_name", _all_covariance_types)
+    def test_mvn_with_covariance(self, size, matrix_type, cov_type_name):
+        message = (f"CovVia{cov_type_name} does not support {matrix_type} "
+                   "matrices")
+        if cov_type_name not in self._cov_types[matrix_type]:
+            pytest.skip(message)
+
+        A = self._matrices[matrix_type]
+        cov_type = getattr(_covariance, f"CovVia{cov_type_name}")
+        preprocessing = self._covariance_preprocessing[cov_type_name]
+
+        mean = [0.1, 0.2, 0.3]
+        cov_object = cov_type(preprocessing(A))
+        mvn = multivariate_normal
+        dist0 = multivariate_normal(mean, A, allow_singular=True)
+        dist1 = multivariate_normal(mean, cov_object, allow_singular=True)
+
+        rng = np.random.default_rng(5292808890472453840)
+        x = rng.multivariate_normal(mean, A, size=size)
+        rng = np.random.default_rng(5292808890472453840)
+        x1 = mvn.rvs(mean, cov_object, size=size, random_state=rng)
+        rng = np.random.default_rng(5292808890472453840)
+        x2 = mvn(mean, cov_object, seed=rng).rvs(size=size)
+        if isinstance(cov_object, _covariance.CovViaPSD):
+            assert_close(x1, np.squeeze(x))  # for backward compatibility
+            assert_close(x2, np.squeeze(x))
+        else:
+            assert_equal(x1.shape, x.shape)
+            assert_equal(x2.shape, x.shape)
+            assert_close(x2, x1)
+
+        assert_close(mvn.pdf(x, mean, cov_object), dist0.pdf(x))
+        assert_close(dist1.pdf(x), dist0.pdf(x))
+        assert_close(mvn.logpdf(x, mean, cov_object), dist0.logpdf(x))
+        assert_close(dist1.logpdf(x), dist0.logpdf(x))
+        assert_close(mvn.entropy(mean, cov_object), dist0.entropy())
+        assert_close(dist1.entropy(), dist0.entropy())
+
+    @pytest.mark.parametrize("size", [tuple(), (2, 4, 3)])
+    @pytest.mark.parametrize("cov_type_name", _all_covariance_types)
+    def test_mvn_with_covariance_cdf(self, size, cov_type_name):
+        # This is split from the test above because it's slow to be running
+        # with all matrix types, and there's no need because _mvn.mvnun
+        # does the calculation. All Covariance needs to do is pass is
+        # provide the `covariance` attribute.
+        matrix_type = "diagonal full rank"
+        A = self._matrices[matrix_type]
+        cov_type = getattr(_covariance, f"CovVia{cov_type_name}")
+        preprocessing = self._covariance_preprocessing[cov_type_name]
+
+        mean = [0.1, 0.2, 0.3]
+        cov_object = cov_type(preprocessing(A))
+        mvn = multivariate_normal
+        dist0 = multivariate_normal(mean, A, allow_singular=True)
+        dist1 = multivariate_normal(mean, cov_object, allow_singular=True)
+
+        rng = np.random.default_rng(5292808890472453840)
+        x = rng.multivariate_normal(mean, A, size=size)
+
+        assert_close(mvn.cdf(x, mean, cov_object), dist0.cdf(x))
+        assert_close(dist1.cdf(x), dist0.cdf(x))
+        assert_close(mvn.logcdf(x, mean, cov_object), dist0.logcdf(x))
+        assert_close(dist1.logcdf(x), dist0.logcdf(x))
+
+    def test_covariance_instantiation(self):
+        message = "The `Covariance` class cannot be instantiated directly."
+        with pytest.raises(NotImplementedError, match=message):
+            Covariance()
+
+    @pytest.mark.filterwarnings("ignore::RuntimeWarning")  # matrix not PSD
+    def test_gh9942(self):
+        # Originally there was a mistake in the `multivariate_normal_frozen`
+        # `rvs` method that caused all covariance objects to be processed as
+        # a `_CovViaPSD`. Ensure that this is resolved.
+        A = np.diag([1, 2, -1e-8])
+        n = A.shape[0]
+        mean = np.zeros(n)
+
+        # Error if the matrix is processed as a `_CovViaPSD`
+        with pytest.raises(ValueError, match="The input matrix must be..."):
+            multivariate_normal(mean, A).rvs()
+
+        # No error if it is provided as a `CovViaEigendecomposition`
+        seed = 3562050283508273023
+        rng1 = np.random.default_rng(seed)
+        rng2 = np.random.default_rng(seed)
+        cov = Covariance.from_eigendecomposition(np.linalg.eigh(A))
+        rv = multivariate_normal(mean, cov)
+        res = rv.rvs(random_state=rng1)
+        ref = multivariate_normal.rvs(mean, cov, random_state=rng2)
+        assert_equal(res, ref)
+
+    def test_gh19197(self):
+        # gh-19197 reported that multivariate normal `rvs` produced incorrect
+        # results when a singular Covariance object was produce using
+        # `from_eigenvalues`. Check that this specific issue is resolved;
+        # a more general test is included in `test_covariance`.
+        mean = np.ones(2)
+        cov = Covariance.from_eigendecomposition((np.zeros(2), np.eye(2)))
+        dist = scipy.stats.multivariate_normal(mean=mean, cov=cov)
+        rvs = dist.rvs(size=None)
+        assert_equal(rvs, mean)
+
+        cov = scipy.stats.Covariance.from_eigendecomposition(
+            (np.array([1., 0.]), np.array([[1., 0.], [0., 400.]])))
+        dist = scipy.stats.multivariate_normal(mean=mean, cov=cov)
+        rvs = dist.rvs(size=None)
+        assert rvs[0] != mean[0]
+        assert rvs[1] == mean[1]
+
+
+def _random_covariance(dim, evals, rng, singular=False):
+    # Generates random covariance matrix with dimensionality `dim` and
+    # eigenvalues `evals` using provided Generator `rng`. Randomly sets
+    # some evals to zero if `singular` is True.
+    A = rng.random((dim, dim))
+    A = A @ A.T
+    _, v = np.linalg.eigh(A)
+    if singular:
+        zero_eigs = rng.normal(size=dim) > 0
+        evals[zero_eigs] = 0
+    cov = v @ np.diag(evals) @ v.T
+    return cov
+
+
+def _sample_orthonormal_matrix(n):
+    rng = np.random.default_rng(9086764251)
+    M = rng.standard_normal((n, n))
+    u, s, v = scipy.linalg.svd(M)
+    return u
+
+def marginal_pdf(X, X_ndim, dimensions, x):
+    """Integrate marginalized dimensions of multivariate
+    probability distribution to calculate the marginalized
+    distribution.
+    """
+    # Sort input data based on order of dimensions
+    dimensions = np.asarray(dimensions)
+    dimensions[dimensions < 0] += X_ndim
+    dim_sort_idx = dimensions.argsort()
+    x = x[:, dim_sort_idx]
+
+    i_marginalize = np.ones(X_ndim, dtype=bool)
+    i_marginalize[dimensions] = False
+
+    def g(z):
+        y = np.empty((z.shape[0], x.shape[0], X_ndim))
+        y[..., i_marginalize] = z[:, np.newaxis, :]
+        y[..., ~i_marginalize] = x
+        return X.pdf(y)
+
+    inf = np.full(X_ndim - len(dimensions), np.inf)
+    return cubature(g, -inf, inf).estimate
+
+@dataclass
+class MVNProblem:
+    """Instantiate a multivariate normal integration problem with special structure.
+
+    When covariance matrix is a correlation matrix where the off-diagonal entries
+    ``covar[i, j] == lambdas[i]*lambdas[j]`` for ``i != j``, then the multidimensional
+    integral reduces to a simpler univariate integral that can be numerically integrated
+    easily.
+
+    The ``generate_*()`` classmethods provide a few options for creating variations
+    of this problem.
+
+    References
+    ----------
+    .. [1] Tong, Y.L. "The Multivariate Normal Distribution".
+           Springer-Verlag. p192. 1990.
+    """
+    ndim : int
+    low : np.ndarray
+    high : np.ndarray
+    lambdas : np.ndarray
+    covar : np.ndarray
+    target_val : float
+    target_err : float
+
+    #: The `generator_halves()` case has an analytically-known true value that we'll
+    #:  record here. It remain None for most cases, though.
+    true_val : float | None = None
+
+    def __init__(self, ndim, low, high, lambdas):
+        super().__init__()
+        self.ndim = ndim
+        self.low = low
+        self.high = high
+        self.lambdas = lambdas
+
+        self.covar = np.outer(self.lambdas, self.lambdas)
+        np.fill_diagonal(self.covar, 1.0)
+        self.find_target()
+
+    @classmethod
+    def generate_semigeneral(cls, ndim, rng=None):
+        """Random lambdas, random upper bounds, infinite lower bounds.
+        """
+        rng = np.random.default_rng(rng)
+        low = np.full(ndim, -np.inf)
+        high = rng.uniform(0.0, np.sqrt(ndim), size=ndim)
+        lambdas = rng.uniform(-1.0, 1.0, size=ndim)
+
+        self = cls(
+            ndim=ndim,
+            low=low,
+            high=high,
+            lambdas=lambdas,
+        )
+        return self
+
+    @classmethod
+    def generate_constant(cls, ndim, rng=None):
+        """Constant off-diagonal covariance, random upper bounds, infinite lower bounds.
+        """
+        rng = np.random.default_rng(rng)
+        low = np.full(ndim, -np.inf)
+        high = rng.uniform(0.0, np.sqrt(ndim), size=ndim)
+        sigma = np.sqrt(rng.uniform(0.0, 1.0))
+        lambdas = np.full(ndim, sigma)
+
+        self = cls(
+            ndim=ndim,
+            low=low,
+            high=high,
+            lambdas=lambdas,
+        )
+        return self
+
+    @classmethod
+    def generate_halves(cls, ndim, rng=None):
+        """Off-diagonal covariance of 0.5, negative orthant bounds.
+
+        True analytically-derived answer is 1/(ndim+1).
+        """
+        low = np.full(ndim, -np.inf)
+        high = np.zeros(ndim)
+        lambdas = np.sqrt(0.5)
+
+        self = cls(
+            ndim=ndim,
+            low=low,
+            high=high,
+            lambdas=lambdas,
+        )
+        self.true_val = 1 / (ndim+1)
+        return self
+
+    def find_target(self, **kwds):
+        """Perform the simplified integral and store the results.
+        """
+        d = dict(
+            a=-9.0,
+            b=+9.0,
+        )
+        d.update(kwds)
+        self.target_val, self.target_err = quad(self.univariate_func, **d)
+
+    def _univariate_term(self, t):
+        """The parameter-specific term of the univariate integrand,
+        for separate plotting.
+        """
+        denom = np.sqrt(1 - self.lambdas**2)
+        return np.prod(
+            special.ndtr((self.high + self.lambdas*t[:, np.newaxis]) / denom) -
+            special.ndtr((self.low + self.lambdas*t[:, np.newaxis]) / denom),
+            axis=1,
+        )
+
+    def univariate_func(self, t):
+        """Univariate integrand.
+        """
+        t = np.atleast_1d(t)
+        return np.squeeze(norm_pdf(t) * self._univariate_term(t))
+
+    def plot_integrand(self):
+        """Plot the univariate integrand and its component terms for understanding.
+        """
+        from matplotlib import pyplot as plt
+
+        t = np.linspace(-9.0, 9.0, 1001)
+        plt.plot(t, norm_pdf(t), label=r'$\phi(t)$')
+        plt.plot(t, self._univariate_term(t), label=r'$f(t)$')
+        plt.plot(t, self.univariate_func(t), label=r'$f(t)*phi(t)$')
+        plt.legend()
+
+
+@dataclass
+class SingularMVNProblem:
+    """Instantiate a multivariate normal integration problem with a special singular
+    covariance structure.
+
+    When covariance matrix is a correlation matrix where the off-diagonal entries
+    ``covar[i, j] == -lambdas[i]*lambdas[j]`` for ``i != j``, and
+    ``sum(lambdas**2 / (1+lambdas**2)) == 1``, then the matrix is singular, and
+    the multidimensional integral reduces to a simpler univariate integral that
+    can be numerically integrated fairly easily.
+
+    The lower bound must be infinite, though the upper bounds can be general.
+
+    References
+    ----------
+    .. [1] Kwong, K.-S. (1995). "Evaluation of the one-sided percentage points of the
+           singular multivariate normal distribution." Journal of Statistical
+           Computation and Simulation, 51(2-4), 121-135.
+           :doi:`10.1080/00949659508811627`.
+    """
+    ndim : int
+    low : np.ndarray
+    high : np.ndarray
+    lambdas : np.ndarray
+    covar : np.ndarray
+    target_val : float
+    target_err : float
+
+    def __init__(self, ndim, high, lambdas):
+        self.ndim = ndim
+        self.high = high
+        self.lambdas = lambdas
+
+        self.low = np.full(ndim, -np.inf)
+        self.covar = -np.outer(self.lambdas, self.lambdas)
+        np.fill_diagonal(self.covar, 1.0)
+        self.find_target()
+
+    @classmethod
+    def generate_semiinfinite(cls, ndim, rng=None):
+        """Singular lambdas, random upper bounds.
+        """
+        rng = np.random.default_rng(rng)
+        high = rng.uniform(0.0, np.sqrt(ndim), size=ndim)
+        p = rng.dirichlet(np.full(ndim, 1.0))
+        lambdas = np.sqrt(p / (1-p)) * rng.choice([-1.0, 1.0], size=ndim)
+
+        self = cls(
+            ndim=ndim,
+            high=high,
+            lambdas=lambdas,
+        )
+        return self
+
+    def find_target(self, **kwds):
+        d = dict(
+            a=-9.0,
+            b=+9.0,
+        )
+        d.update(kwds)
+        self.target_val, self.target_err = quad(self.univariate_func, **d)
+
+    def _univariate_term(self, t):
+        denom = np.sqrt(1 + self.lambdas**2)
+        i1 = np.prod(
+            special.ndtr((self.high - 1j*self.lambdas*t[:, np.newaxis]) / denom),
+            axis=1,
+        )
+        i2 = np.prod(
+            special.ndtr((-self.high + 1j*self.lambdas*t[:, np.newaxis]) / denom),
+            axis=1,
+        )
+        # The imaginary part is an odd function, so it can be ignored; it will integrate
+        # out to 0.
+        return (i1 - (-1)**self.ndim * i2).real
+
+    def univariate_func(self, t):
+        t = np.atleast_1d(t)
+        return (norm_pdf(t) * self._univariate_term(t)).squeeze()
+
+    def plot_integrand(self):
+        """Plot the univariate integrand and its component terms for understanding.
+        """
+        from matplotlib import pyplot as plt
+
+        t = np.linspace(-9.0, 9.0, 1001)
+        plt.plot(t, norm_pdf(t), label=r'$\phi(t)$')
+        plt.plot(t, self._univariate_term(t), label=r'$f(t)$')
+        plt.plot(t, self.univariate_func(t), label=r'$f(t)*phi(t)$')
+        plt.ylim(-0.1, 1.1)
+        plt.legend()
+
+
+class TestMultivariateNormal:
+    def test_input_shape(self):
+        mu = np.arange(3)
+        cov = np.identity(2)
+        assert_raises(ValueError, multivariate_normal.pdf, (0, 1), mu, cov)
+        assert_raises(ValueError, multivariate_normal.pdf, (0, 1, 2), mu, cov)
+        assert_raises(ValueError, multivariate_normal.cdf, (0, 1), mu, cov)
+        assert_raises(ValueError, multivariate_normal.cdf, (0, 1, 2), mu, cov)
+
+    def test_scalar_values(self):
+        rng = np.random.default_rng(1234)
+
+        # When evaluated on scalar data, the pdf should return a scalar
+        x, mean, cov = 1.5, 1.7, 2.5
+        pdf = multivariate_normal.pdf(x, mean, cov)
+        assert_equal(pdf.ndim, 0)
+
+        # When evaluated on a single vector, the pdf should return a scalar
+        x = rng.standard_normal(5)
+        mean = rng.standard_normal(5)
+        cov = np.abs(rng.standard_normal(5))  # Diagonal values for cov. matrix
+        pdf = multivariate_normal.pdf(x, mean, cov)
+        assert_equal(pdf.ndim, 0)
+
+        # When evaluated on scalar data, the cdf should return a scalar
+        x, mean, cov = 1.5, 1.7, 2.5
+        cdf = multivariate_normal.cdf(x, mean, cov)
+        assert_equal(cdf.ndim, 0)
+
+        # When evaluated on a single vector, the cdf should return a scalar
+        x = rng.standard_normal(5)
+        mean = rng.standard_normal(5)
+        cov = np.abs(rng.standard_normal(5))  # Diagonal values for cov. matrix
+        cdf = multivariate_normal.cdf(x, mean, cov)
+        assert_equal(cdf.ndim, 0)
+
+    def test_logpdf(self):
+        # Check that the log of the pdf is in fact the logpdf
+        rng = np.random.default_rng(1234)
+        x = rng.standard_normal(5)
+        mean = rng.standard_normal(5)
+        cov = np.abs(rng.standard_normal(5))
+        d1 = multivariate_normal.logpdf(x, mean, cov)
+        d2 = multivariate_normal.pdf(x, mean, cov)
+        assert_allclose(d1, np.log(d2))
+
+    def test_logpdf_default_values(self):
+        # Check that the log of the pdf is in fact the logpdf
+        # with default parameters Mean=None and cov = 1
+        rng = np.random.default_rng(1234)
+        x = rng.standard_normal(5)
+        d1 = multivariate_normal.logpdf(x)
+        d2 = multivariate_normal.pdf(x)
+        # check whether default values are being used
+        d3 = multivariate_normal.logpdf(x, None, 1)
+        d4 = multivariate_normal.pdf(x, None, 1)
+        assert_allclose(d1, np.log(d2))
+        assert_allclose(d3, np.log(d4))
+
+    def test_logcdf(self):
+        # Check that the log of the cdf is in fact the logcdf
+        rng = np.random.default_rng(1234)
+        x = rng.standard_normal(5)
+        mean = rng.standard_normal(5)
+        cov = np.abs(rng.standard_normal(5))
+        d1 = multivariate_normal.logcdf(x, mean, cov)
+        d2 = multivariate_normal.cdf(x, mean, cov)
+        assert_allclose(d1, np.log(d2))
+
+    def test_logcdf_default_values(self):
+        # Check that the log of the cdf is in fact the logcdf
+        # with default parameters Mean=None and cov = 1
+        rng = np.random.default_rng(1234)
+        x = rng.standard_normal(5)
+        d1 = multivariate_normal.logcdf(x)
+        d2 = multivariate_normal.cdf(x)
+        # check whether default values are being used
+        d3 = multivariate_normal.logcdf(x, None, 1)
+        d4 = multivariate_normal.cdf(x, None, 1)
+        assert_allclose(d1, np.log(d2))
+        assert_allclose(d3, np.log(d4))
+
+    def test_rank(self):
+        # Check that the rank is detected correctly.
+        rng = np.random.default_rng(1234)
+        n = 4
+        mean = rng.standard_normal(n)
+        for expected_rank in range(1, n + 1):
+            s = rng.standard_normal((n, expected_rank))
+            cov = np.dot(s, s.T)
+            distn = multivariate_normal(mean, cov, allow_singular=True)
+            assert_equal(distn.cov_object.rank, expected_rank)
+
+    def test_degenerate_distributions(self):
+        rng = np.random.default_rng(1234)
+        for n in range(1, 5):
+            z = rng.standard_normal(n)
+            for k in range(1, n):
+                # Sample a small covariance matrix.
+                s = rng.standard_normal((k, k))
+                cov_kk = np.dot(s, s.T)
+
+                # Embed the small covariance matrix into a larger singular one.
+                cov_nn = np.zeros((n, n))
+                cov_nn[:k, :k] = cov_kk
+
+                # Embed part of the vector in the same way
+                x = np.zeros(n)
+                x[:k] = z[:k]
+
+                # Define a rotation of the larger low rank matrix.
+                u = _sample_orthonormal_matrix(n)
+                cov_rr = np.dot(u, np.dot(cov_nn, u.T))
+                y = np.dot(u, x)
+
+                # Check some identities.
+                distn_kk = multivariate_normal(np.zeros(k), cov_kk,
+                                               allow_singular=True)
+                distn_nn = multivariate_normal(np.zeros(n), cov_nn,
+                                               allow_singular=True)
+                distn_rr = multivariate_normal(np.zeros(n), cov_rr,
+                                               allow_singular=True)
+                assert_equal(distn_kk.cov_object.rank, k)
+                assert_equal(distn_nn.cov_object.rank, k)
+                assert_equal(distn_rr.cov_object.rank, k)
+                pdf_kk = distn_kk.pdf(x[:k])
+                pdf_nn = distn_nn.pdf(x)
+                pdf_rr = distn_rr.pdf(y)
+                assert_allclose(pdf_kk, pdf_nn)
+                assert_allclose(pdf_kk, pdf_rr)
+                logpdf_kk = distn_kk.logpdf(x[:k])
+                logpdf_nn = distn_nn.logpdf(x)
+                logpdf_rr = distn_rr.logpdf(y)
+                assert_allclose(logpdf_kk, logpdf_nn)
+                assert_allclose(logpdf_kk, logpdf_rr)
+
+                # Add an orthogonal component and find the density
+                y_orth = y + u[:, -1]
+                pdf_rr_orth = distn_rr.pdf(y_orth)
+                logpdf_rr_orth = distn_rr.logpdf(y_orth)
+
+                # Ensure that this has zero probability
+                assert_equal(pdf_rr_orth, 0.0)
+                assert_equal(logpdf_rr_orth, -np.inf)
+
+    def test_degenerate_array(self):
+        # Test that we can generate arrays of random variate from a degenerate
+        # multivariate normal, and that the pdf for these samples is non-zero
+        # (i.e. samples from the distribution lie on the subspace)
+        k = 10
+        for n in range(2, 6):
+            for r in range(1, n):
+                mn = np.zeros(n)
+                u = _sample_orthonormal_matrix(n)[:, :r]
+                vr = np.dot(u, u.T)
+                X = multivariate_normal.rvs(mean=mn, cov=vr, size=k)
+
+                pdf = multivariate_normal.pdf(X, mean=mn, cov=vr,
+                                              allow_singular=True)
+                assert_equal(pdf.size, k)
+                assert np.all(pdf > 0.0)
+
+                logpdf = multivariate_normal.logpdf(X, mean=mn, cov=vr,
+                                                    allow_singular=True)
+                assert_equal(logpdf.size, k)
+                assert np.all(logpdf > -np.inf)
+
+    def test_large_pseudo_determinant(self):
+        # Check that large pseudo-determinants are handled appropriately.
+
+        # Construct a singular diagonal covariance matrix
+        # whose pseudo determinant overflows double precision.
+        large_total_log = 1000.0
+        npos = 100
+        nzero = 2
+        large_entry = np.exp(large_total_log / npos)
+        n = npos + nzero
+        cov = np.zeros((n, n), dtype=float)
+        np.fill_diagonal(cov, large_entry)
+        cov[-nzero:, -nzero:] = 0
+
+        # Check some determinants.
+        assert_equal(scipy.linalg.det(cov), 0)
+        assert_equal(scipy.linalg.det(cov[:npos, :npos]), np.inf)
+        assert_allclose(np.linalg.slogdet(cov[:npos, :npos]),
+                        (1, large_total_log))
+
+        # Check the pseudo-determinant.
+        psd = _PSD(cov)
+        assert_allclose(psd.log_pdet, large_total_log)
+
+    def test_broadcasting(self):
+        rng = np.random.RandomState(1234)
+        n = 4
+
+        # Construct a random covariance matrix.
+        data = rng.randn(n, n)
+        cov = np.dot(data, data.T)
+        mean = rng.randn(n)
+
+        # Construct an ndarray which can be interpreted as
+        # a 2x3 array whose elements are random data vectors.
+        X = rng.randn(2, 3, n)
+
+        # Check that multiple data points can be evaluated at once.
+        desired_pdf = multivariate_normal.pdf(X, mean, cov)
+        desired_cdf = multivariate_normal.cdf(X, mean, cov)
+        for i in range(2):
+            for j in range(3):
+                actual = multivariate_normal.pdf(X[i, j], mean, cov)
+                assert_allclose(actual, desired_pdf[i,j])
+                # Repeat for cdf
+                actual = multivariate_normal.cdf(X[i, j], mean, cov)
+                assert_allclose(actual, desired_cdf[i,j], rtol=1e-3)
+
+    def test_normal_1D(self):
+        # The probability density function for a 1D normal variable should
+        # agree with the standard normal distribution in scipy.stats.distributions
+        x = np.linspace(0, 2, 10)
+        mean, cov = 1.2, 0.9
+        scale = cov**0.5
+        d1 = norm.pdf(x, mean, scale)
+        d2 = multivariate_normal.pdf(x, mean, cov)
+        assert_allclose(d1, d2)
+        # The same should hold for the cumulative distribution function
+        d1 = norm.cdf(x, mean, scale)
+        d2 = multivariate_normal.cdf(x, mean, cov)
+        assert_allclose(d1, d2)
+
+    def test_marginalization(self):
+        # Integrating out one of the variables of a 2D Gaussian should
+        # yield a 1D Gaussian
+        mean = np.array([2.5, 3.5])
+        cov = np.array([[.5, 0.2], [0.2, .6]])
+        n = 2 ** 8 + 1  # Number of samples
+        delta = 6 / (n - 1)  # Grid spacing
+
+        v = np.linspace(0, 6, n)
+        xv, yv = np.meshgrid(v, v)
+        pos = np.empty((n, n, 2))
+        pos[:, :, 0] = xv
+        pos[:, :, 1] = yv
+        pdf = multivariate_normal.pdf(pos, mean, cov)
+
+        # Marginalize over x and y axis
+        margin_x = romb(pdf, delta, axis=0)
+        margin_y = romb(pdf, delta, axis=1)
+
+        # Compare with standard normal distribution
+        gauss_x = norm.pdf(v, loc=mean[0], scale=cov[0, 0] ** 0.5)
+        gauss_y = norm.pdf(v, loc=mean[1], scale=cov[1, 1] ** 0.5)
+        assert_allclose(margin_x, gauss_x, rtol=1e-2, atol=1e-2)
+        assert_allclose(margin_y, gauss_y, rtol=1e-2, atol=1e-2)
+
+    def test_frozen(self):
+        # The frozen distribution should agree with the regular one
+        rng = np.random.default_rng(1234)
+        x = rng.standard_normal(5)
+        mean = rng.standard_normal(5)
+        cov = np.abs(rng.standard_normal(5))
+        norm_frozen = multivariate_normal(mean, cov)
+        assert_allclose(norm_frozen.pdf(x), multivariate_normal.pdf(x, mean, cov))
+        assert_allclose(norm_frozen.logpdf(x),
+                        multivariate_normal.logpdf(x, mean, cov))
+        assert_allclose(norm_frozen.cdf(x), multivariate_normal.cdf(x, mean, cov))
+        assert_allclose(norm_frozen.logcdf(x),
+                        multivariate_normal.logcdf(x, mean, cov))
+
+    @pytest.mark.parametrize(
+        'covariance',
+        [
+            np.eye(2),
+            Covariance.from_diagonal([1, 1]),
+        ]
+    )
+    def test_frozen_multivariate_normal_exposes_attributes(self, covariance):
+        mean = np.ones((2,))
+        cov_should_be = np.eye(2)
+        norm_frozen = multivariate_normal(mean, covariance)
+        assert np.allclose(norm_frozen.mean, mean)
+        assert np.allclose(norm_frozen.cov, cov_should_be)
+
+    def test_pseudodet_pinv(self):
+        # Make sure that pseudo-inverse and pseudo-det agree on cutoff
+
+        # Assemble random covariance matrix with large and small eigenvalues
+        rng = np.random.default_rng(1234)
+        n = 7
+        x = rng.standard_normal((n, n))
+        cov = np.dot(x, x.T)
+        s, u = scipy.linalg.eigh(cov)
+        s = np.full(n, 0.5)
+        s[0] = 1.0
+        s[-1] = 1e-7
+        cov = np.dot(u, np.dot(np.diag(s), u.T))
+
+        # Set cond so that the lowest eigenvalue is below the cutoff
+        cond = 1e-5
+        psd = _PSD(cov, cond=cond)
+        psd_pinv = _PSD(psd.pinv, cond=cond)
+
+        # Check that the log pseudo-determinant agrees with the sum
+        # of the logs of all but the smallest eigenvalue
+        assert_allclose(psd.log_pdet, np.sum(np.log(s[:-1])))
+        # Check that the pseudo-determinant of the pseudo-inverse
+        # agrees with 1 / pseudo-determinant
+        assert_allclose(-psd.log_pdet, psd_pinv.log_pdet)
+
+    def test_exception_nonsquare_cov(self):
+        cov = [[1, 2, 3], [4, 5, 6]]
+        assert_raises(ValueError, _PSD, cov)
+
+    def test_exception_nonfinite_cov(self):
+        cov_nan = [[1, 0], [0, np.nan]]
+        assert_raises(ValueError, _PSD, cov_nan)
+        cov_inf = [[1, 0], [0, np.inf]]
+        assert_raises(ValueError, _PSD, cov_inf)
+
+    def test_exception_non_psd_cov(self):
+        cov = [[1, 0], [0, -1]]
+        assert_raises(ValueError, _PSD, cov)
+
+    def test_exception_singular_cov(self):
+        rng = np.random.default_rng(1234)
+        x = rng.standard_normal(5)
+        mean = rng.standard_normal(5)
+        cov = np.ones((5, 5))
+        e = np.linalg.LinAlgError
+        assert_raises(e, multivariate_normal, mean, cov)
+        assert_raises(e, multivariate_normal.pdf, x, mean, cov)
+        assert_raises(e, multivariate_normal.logpdf, x, mean, cov)
+        assert_raises(e, multivariate_normal.cdf, x, mean, cov)
+        assert_raises(e, multivariate_normal.logcdf, x, mean, cov)
+
+        # Message used to be "singular matrix", but this is more accurate.
+        # See gh-15508
+        cov = [[1., 0.], [1., 1.]]
+        msg = "When `allow_singular is False`, the input matrix"
+        with pytest.raises(np.linalg.LinAlgError, match=msg):
+            multivariate_normal(cov=cov)
+
+    def test_R_values(self):
+        # Compare the multivariate pdf with some values precomputed
+        # in R version 3.0.1 (2013-05-16) on Mac OS X 10.6.
+
+        # The values below were generated by the following R-script:
+        # > library(mnormt)
+        # > x <- seq(0, 2, length=5)
+        # > y <- 3*x - 2
+        # > z <- x + cos(y)
+        # > mu <- c(1, 3, 2)
+        # > Sigma <- matrix(c(1,2,0,2,5,0.5,0,0.5,3), 3, 3)
+        # > r_pdf <- dmnorm(cbind(x,y,z), mu, Sigma)
+        r_pdf = np.array([0.0002214706, 0.0013819953, 0.0049138692,
+                          0.0103803050, 0.0140250800])
+
+        x = np.linspace(0, 2, 5)
+        y = 3 * x - 2
+        z = x + np.cos(y)
+        r = np.array([x, y, z]).T
+
+        mean = np.array([1, 3, 2], 'd')
+        cov = np.array([[1, 2, 0], [2, 5, .5], [0, .5, 3]], 'd')
+
+        pdf = multivariate_normal.pdf(r, mean, cov)
+        assert_allclose(pdf, r_pdf, atol=1e-10)
+
+        # Compare the multivariate cdf with some values precomputed
+        # in R version 3.3.2 (2016-10-31) on Debian GNU/Linux.
+
+        # The values below were generated by the following R-script:
+        # > library(mnormt)
+        # > x <- seq(0, 2, length=5)
+        # > y <- 3*x - 2
+        # > z <- x + cos(y)
+        # > mu <- c(1, 3, 2)
+        # > Sigma <- matrix(c(1,2,0,2,5,0.5,0,0.5,3), 3, 3)
+        # > r_cdf <- pmnorm(cbind(x,y,z), mu, Sigma)
+        r_cdf = np.array([0.0017866215, 0.0267142892, 0.0857098761,
+                          0.1063242573, 0.2501068509])
+
+        cdf = multivariate_normal.cdf(r, mean, cov)
+        assert_allclose(cdf, r_cdf, atol=2e-5)
+
+        # Also test bivariate cdf with some values precomputed
+        # in R version 3.3.2 (2016-10-31) on Debian GNU/Linux.
+
+        # The values below were generated by the following R-script:
+        # > library(mnormt)
+        # > x <- seq(0, 2, length=5)
+        # > y <- 3*x - 2
+        # > mu <- c(1, 3)
+        # > Sigma <- matrix(c(1,2,2,5), 2, 2)
+        # > r_cdf2 <- pmnorm(cbind(x,y), mu, Sigma)
+        r_cdf2 = np.array([0.01262147, 0.05838989, 0.18389571,
+                           0.40696599, 0.66470577])
+
+        r2 = np.array([x, y]).T
+
+        mean2 = np.array([1, 3], 'd')
+        cov2 = np.array([[1, 2], [2, 5]], 'd')
+
+        cdf2 = multivariate_normal.cdf(r2, mean2, cov2)
+        assert_allclose(cdf2, r_cdf2, atol=1e-5)
+
+    def test_multivariate_normal_rvs_zero_covariance(self):
+        mean = np.zeros(2)
+        covariance = np.zeros((2, 2))
+        model = multivariate_normal(mean, covariance, allow_singular=True)
+        sample = model.rvs()
+        assert_equal(sample, [0, 0])
+
+    def test_rvs_shape(self):
+        # Check that rvs parses the mean and covariance correctly, and returns
+        # an array of the right shape
+        N = 300
+        d = 4
+        sample = multivariate_normal.rvs(mean=np.zeros(d), cov=1, size=N)
+        assert_equal(sample.shape, (N, d))
+
+        sample = multivariate_normal.rvs(mean=None,
+                                         cov=np.array([[2, .1], [.1, 1]]),
+                                         size=N)
+        assert_equal(sample.shape, (N, 2))
+
+        u = multivariate_normal(mean=0, cov=1)
+        sample = u.rvs(N)
+        assert_equal(sample.shape, (N, ))
+
+    def test_large_sample(self):
+        # Generate large sample and compare sample mean and sample covariance
+        # with mean and covariance matrix.
+
+        rng = np.random.RandomState(2846)
+
+        n = 3
+        mean = rng.randn(n)
+        M = rng.randn(n, n)
+        cov = np.dot(M, M.T)
+        size = 5000
+
+        sample = multivariate_normal.rvs(mean, cov, size, random_state=rng)
+
+        assert_allclose(np.cov(sample.T), cov, rtol=1e-1)
+        assert_allclose(sample.mean(0), mean, rtol=1e-1)
+
+    def test_entropy(self):
+        rng = np.random.RandomState(2846)
+
+        n = 3
+        mean = rng.randn(n)
+        M = rng.randn(n, n)
+        cov = np.dot(M, M.T)
+
+        rv = multivariate_normal(mean, cov)
+
+        # Check that frozen distribution agrees with entropy function
+        assert_almost_equal(rv.entropy(), multivariate_normal.entropy(mean, cov))
+        # Compare entropy with manually computed expression involving
+        # the sum of the logs of the eigenvalues of the covariance matrix
+        eigs = np.linalg.eig(cov)[0]
+        desired = 1 / 2 * (n * (np.log(2 * np.pi) + 1) + np.sum(np.log(eigs)))
+        assert_almost_equal(desired, rv.entropy())
+
+    def test_lnB(self):
+        alpha = np.array([1, 1, 1])
+        desired = .5  # e^lnB = 1/2 for [1, 1, 1]
+
+        assert_almost_equal(np.exp(_lnB(alpha)), desired)
+
+    def test_cdf_with_lower_limit_arrays(self):
+        # test CDF with lower limit in several dimensions
+        rng = np.random.default_rng(2408071309372769818)
+        mean = [0, 0]
+        cov = np.eye(2)
+        a = rng.random((4, 3, 2))*6 - 3
+        b = rng.random((4, 3, 2))*6 - 3
+
+        cdf1 = multivariate_normal.cdf(b, mean, cov, lower_limit=a)
+
+        cdf2a = multivariate_normal.cdf(b, mean, cov)
+        cdf2b = multivariate_normal.cdf(a, mean, cov)
+        ab1 = np.concatenate((a[..., 0:1], b[..., 1:2]), axis=-1)
+        ab2 = np.concatenate((a[..., 1:2], b[..., 0:1]), axis=-1)
+        cdf2ab1 = multivariate_normal.cdf(ab1, mean, cov)
+        cdf2ab2 = multivariate_normal.cdf(ab2, mean, cov)
+        cdf2 = cdf2a + cdf2b - cdf2ab1 - cdf2ab2
+
+        assert_allclose(cdf1, cdf2)
+
+    def test_cdf_with_lower_limit_consistency(self):
+        # check that multivariate normal CDF functions are consistent
+        rng = np.random.default_rng(2408071309372769818)
+        mean = rng.random(3)
+        cov = rng.random((3, 3))
+        cov = cov @ cov.T
+        a = rng.random((2, 3))*6 - 3
+        b = rng.random((2, 3))*6 - 3
+
+        cdf1 = multivariate_normal.cdf(b, mean, cov, lower_limit=a)
+        cdf2 = multivariate_normal(mean, cov).cdf(b, lower_limit=a)
+        cdf3 = np.exp(multivariate_normal.logcdf(b, mean, cov, lower_limit=a))
+        cdf4 = np.exp(multivariate_normal(mean, cov).logcdf(b, lower_limit=a))
+
+        assert_allclose(cdf2, cdf1, rtol=1e-4)
+        assert_allclose(cdf3, cdf1, rtol=1e-4)
+        assert_allclose(cdf4, cdf1, rtol=1e-4)
+
+    def test_cdf_signs(self):
+        # check that sign of output is correct when np.any(lower > x)
+        mean = np.zeros(3)
+        cov = np.eye(3)
+        b = [[1, 1, 1], [0, 0, 0], [1, 0, 1], [0, 1, 0]]
+        a = [[0, 0, 0], [1, 1, 1], [0, 1, 0], [1, 0, 1]]
+        # when odd number of elements of b < a, output is negative
+        expected_signs = np.array([1, -1, -1, 1])
+        cdf = multivariate_normal.cdf(b, mean, cov, lower_limit=a)
+        assert_allclose(cdf, cdf[0]*expected_signs)
+
+    @pytest.mark.slow
+    @pytest.mark.parametrize("ndim", [2, 3])
+    def test_cdf_vs_cubature(self, ndim):
+        rng = np.random.default_rng(123)
+        a = rng.uniform(size=(ndim, ndim))
+        cov = a.T @ a
+        m = rng.uniform(size=ndim)
+        dist = multivariate_normal(mean=m, cov=cov)
+        x = rng.uniform(low=-3, high=3, size=(ndim,))
+        cdf = dist.cdf(x)
+        dist_i = multivariate_normal(mean=[0]*ndim, cov=cov)
+        cdf_i = cubature(dist_i.pdf, [-np.inf]*ndim, x - m).estimate
+        assert_allclose(cdf, cdf_i, atol=5e-6)
+
+    def test_cdf_known(self):
+        # https://github.com/scipy/scipy/pull/17410#issuecomment-1312628547
+        for ndim in range(2, 12):
+            cov = np.full((ndim, ndim), 0.5)
+            np.fill_diagonal(cov, 1.)
+            dist = multivariate_normal([0]*ndim, cov=cov)
+            assert_allclose(
+                dist.cdf([0]*ndim),
+                1. / (1. + ndim),
+                atol=5e-5
+            )
+
+    @pytest.mark.parametrize("ndim", range(2, 10))
+    @pytest.mark.parametrize("seed", [0xdeadbeef, 0xdd24528764c9773579731c6b022b48e2])
+    def test_cdf_vs_univariate(self, seed, ndim):
+        rng = np.random.default_rng(seed)
+        case = MVNProblem.generate_semigeneral(ndim=ndim, rng=rng)
+        assert (case.low == -np.inf).all()
+
+        dist = multivariate_normal(mean=[0]*ndim, cov=case.covar)
+        cdf_val = dist.cdf(case.high, rng=rng)
+        assert_allclose(cdf_val, case.target_val, atol=5e-5)
+
+    @pytest.mark.parametrize("ndim", range(2, 11))
+    @pytest.mark.parametrize("seed", [0xdeadbeef, 0xdd24528764c9773579731c6b022b48e2])
+    def test_cdf_vs_univariate_2(self, seed, ndim):
+        rng = np.random.default_rng(seed)
+        case = MVNProblem.generate_constant(ndim=ndim, rng=rng)
+        assert (case.low == -np.inf).all()
+
+        dist = multivariate_normal(mean=[0]*ndim, cov=case.covar)
+        cdf_val = dist.cdf(case.high, rng=rng)
+        assert_allclose(cdf_val, case.target_val, atol=5e-5)
+
+    @pytest.mark.parametrize("ndim", range(4, 11))
+    @pytest.mark.parametrize("seed", [0xdeadbeef, 0xdd24528764c9773579731c6b022b48e4])
+    def test_cdf_vs_univariate_singular(self, seed, ndim):
+        # NB: ndim = 2, 3 has much poorer accuracy than ndim > 3 for many seeds.
+        # No idea why.
+        rng = np.random.default_rng(seed)
+        case = SingularMVNProblem.generate_semiinfinite(ndim=ndim, rng=rng)
+        assert (case.low == -np.inf).all()
+
+        dist = multivariate_normal(mean=[0]*ndim, cov=case.covar, allow_singular=True,
+                                   # default maxpts is too slow, limit it here
+                                   maxpts=10_000*case.covar.shape[0]
+        )
+        cdf_val = dist.cdf(case.high, rng=rng)
+        assert_allclose(cdf_val, case.target_val, atol=1e-3)
+
+    def test_mean_cov(self):
+        # test the interaction between a Covariance object and mean
+        P = np.diag(1 / np.array([1, 2, 3]))
+        cov_object = _covariance.CovViaPrecision(P)
+
+        message = "`cov` represents a covariance matrix in 3 dimensions..."
+        with pytest.raises(ValueError, match=message):
+            multivariate_normal.entropy([0, 0], cov_object)
+
+        with pytest.raises(ValueError, match=message):
+            multivariate_normal([0, 0], cov_object)
+
+        x = [0.5, 0.5, 0.5]
+        ref = multivariate_normal.pdf(x, [0, 0, 0], cov_object)
+        assert_equal(multivariate_normal.pdf(x, cov=cov_object), ref)
+
+        ref = multivariate_normal.pdf(x, [1, 1, 1], cov_object)
+        assert_equal(multivariate_normal.pdf(x, 1, cov=cov_object), ref)
+
+    def test_fit_wrong_fit_data_shape(self):
+        data = [1, 3]
+        error_msg = "`x` must be two-dimensional."
+        with pytest.raises(ValueError, match=error_msg):
+            multivariate_normal.fit(data)
+
+    @pytest.mark.parametrize('dim', (3, 5))
+    def test_fit_correctness(self, dim):
+        rng = np.random.default_rng(4385269356937404)
+        x = rng.random((100, dim))
+        mean_est, cov_est = multivariate_normal.fit(x)
+        mean_ref, cov_ref = np.mean(x, axis=0), np.cov(x.T, ddof=0)
+        assert_allclose(mean_est, mean_ref, atol=1e-15)
+        assert_allclose(cov_est, cov_ref, rtol=5e-15)
+
+    def test_fit_both_parameters_fixed(self):
+        data = np.full((2, 1), 3)
+        mean_fixed = 1.
+        cov_fixed = np.atleast_2d(1.)
+        mean, cov = multivariate_normal.fit(data, fix_mean=mean_fixed,
+                                            fix_cov=cov_fixed)
+        assert_equal(mean, mean_fixed)
+        assert_equal(cov, cov_fixed)
+
+    @pytest.mark.parametrize('fix_mean', [np.zeros((2, 2)),
+                                          np.zeros((3, ))])
+    def test_fit_fix_mean_input_validation(self, fix_mean):
+        msg = ("`fix_mean` must be a one-dimensional array the same "
+                "length as the dimensionality of the vectors `x`.")
+        with pytest.raises(ValueError, match=msg):
+            multivariate_normal.fit(np.eye(2), fix_mean=fix_mean)
+
+    @pytest.mark.parametrize('fix_cov', [np.zeros((2, )),
+                                         np.zeros((3, 2)),
+                                         np.zeros((4, 4))])
+    def test_fit_fix_cov_input_validation_dimension(self, fix_cov):
+        msg = ("`fix_cov` must be a two-dimensional square array "
+                "of same side length as the dimensionality of the "
+                "vectors `x`.")
+        with pytest.raises(ValueError, match=msg):
+            multivariate_normal.fit(np.eye(3), fix_cov=fix_cov)
+
+    def test_fit_fix_cov_not_positive_semidefinite(self):
+        error_msg = "`fix_cov` must be symmetric positive semidefinite."
+        with pytest.raises(ValueError, match=error_msg):
+            fix_cov = np.array([[1., 0.], [0., -1.]])
+            multivariate_normal.fit(np.eye(2), fix_cov=fix_cov)
+
+    def test_fit_fix_mean(self):
+        rng = np.random.default_rng(4385269356937404)
+        loc = rng.random(3)
+        A = rng.random((3, 3))
+        cov = np.dot(A, A.T)
+        samples = multivariate_normal.rvs(mean=loc, cov=cov, size=100,
+                                          random_state=rng)
+        mean_free, cov_free = multivariate_normal.fit(samples)
+        logp_free = multivariate_normal.logpdf(samples, mean=mean_free,
+                                               cov=cov_free).sum()
+        mean_fix, cov_fix = multivariate_normal.fit(samples, fix_mean=loc)
+        assert_equal(mean_fix, loc)
+        logp_fix = multivariate_normal.logpdf(samples, mean=mean_fix,
+                                              cov=cov_fix).sum()
+        # test that fixed parameters result in lower likelihood than free
+        # parameters
+        assert logp_fix < logp_free
+        # test that a small perturbation of the resulting parameters
+        # has lower likelihood than the estimated parameters
+        A = rng.random((3, 3))
+        m = 1e-8 * np.dot(A, A.T)
+        cov_perturbed = cov_fix + m
+        logp_perturbed = (multivariate_normal.logpdf(samples,
+                                                     mean=mean_fix,
+                                                     cov=cov_perturbed)
+                                                     ).sum()
+        assert logp_perturbed < logp_fix
+
+    def test_fit_fix_cov(self):
+        rng = np.random.default_rng(4385269356937404)
+        loc = rng.random(3)
+        A = rng.random((3, 3))
+        cov = np.dot(A, A.T)
+        samples = multivariate_normal.rvs(mean=loc, cov=cov,
+                                          size=100, random_state=rng)
+        mean_free, cov_free = multivariate_normal.fit(samples)
+        logp_free = multivariate_normal.logpdf(samples, mean=mean_free,
+                                               cov=cov_free).sum()
+        mean_fix, cov_fix = multivariate_normal.fit(samples, fix_cov=cov)
+        assert_equal(mean_fix, np.mean(samples, axis=0))
+        assert_equal(cov_fix, cov)
+        logp_fix = multivariate_normal.logpdf(samples, mean=mean_fix,
+                                              cov=cov_fix).sum()
+        # test that fixed parameters result in lower likelihood than free
+        # parameters
+        assert logp_fix < logp_free
+        # test that a small perturbation of the resulting parameters
+        # has lower likelihood than the estimated parameters
+        mean_perturbed = mean_fix + 1e-8 * rng.random(3)
+        logp_perturbed = (multivariate_normal.logpdf(samples,
+                                                     mean=mean_perturbed,
+                                                     cov=cov_fix)
+                                                     ).sum()
+        assert logp_perturbed < logp_fix
+
+
+class TestMarginal:
+    @pytest.mark.parametrize('dist,kwargs', [(multivariate_normal, {}),
+                                             (multivariate_t, {'df': 4})])
+    @pytest.mark.parametrize('X_ndim', [3])
+    @pytest.mark.parametrize('dimensions', [[1], [-1, 1]])
+    @pytest.mark.parametrize('frozen', [True, False])
+    @pytest.mark.parametrize('cov_object', [True, False])
+    def test_marginal_distribution(self, dist, X_ndim, dimensions, frozen,
+                                   cov_object, kwargs):
+        rng = np.random.default_rng(413911473)
+        loc = rng.standard_normal(X_ndim)
+        A = rng.standard_normal((X_ndim, X_ndim))
+        scale = A @ A.T
+
+        if cov_object and dist == multivariate_t:
+            pytest.skip('`multivariate_t` does not accept a `Covariance` object')
+        elif cov_object:
+            scale = _covariance.CovViaPrecision(scale)
+
+        # number of points at which to evaluate marginal PDF
+        x = np.random.standard_normal((4, len(dimensions)))
+        X = dist(loc, scale, **kwargs)
+
+        if frozen:
+            Y = X.marginal(dimensions)
+            res = Y.pdf(x)
+        else:
+            Y = dist.marginal(dimensions, loc, scale, **kwargs)
+            res = Y.pdf(x)
+
+        ref = marginal_pdf(X, X_ndim, dimensions, x)
+        assert_allclose(ref, res)
+
+    @pytest.mark.parametrize('dist', [multivariate_normal, multivariate_t])
+    def test_marginal_input_validation(self, dist):
+        rng = np.random.default_rng(413911473)
+        mean = rng.standard_normal(3)
+        A = rng.standard_normal((3, 3))
+        cov = A @ A.T
+
+        X = dist(mean, cov)
+
+        msg = r"Dimensions \[3\] are invalid .*"
+        with pytest.raises(ValueError, match=msg):
+            X.marginal(3)
+
+        with pytest.raises(ValueError, match=msg):
+            X.marginal([0, 1, 2, 3])
+
+        msg = r"All elements of `dimensions` must be unique."
+        with pytest.raises(ValueError, match=msg):
+            X.marginal([2, -1])
+
+        with pytest.raises(ValueError, match=msg):
+            X.marginal([[0, 1]])
+
+        msg = r"Elements of `dimensions` must be integers."
+        with pytest.raises(ValueError, match=msg):
+            X.marginal([1.1, 2.0])
+
+    @pytest.mark.parametrize('dist', [multivariate_normal, multivariate_t])
+    def test_marginal_special_cases(self, dist):
+        rng = np.random.default_rng(413911473)
+        loc = rng.standard_normal(3)
+        A = rng.standard_normal((3, 3))
+        scale = A @ A.T
+
+        X = dist(loc, scale)
+
+        msg = r"Cannot marginalize all dimensions."
+        with pytest.raises(ValueError, match=msg):
+            X.marginal([])
+
+
+class TestMatrixNormal:
+
+    def test_bad_input(self):
+        # Check that bad inputs raise errors
+        num_rows = 4
+        num_cols = 3
+        M = np.full((num_rows,num_cols), 0.3)
+        U = 0.5 * np.identity(num_rows) + np.full((num_rows, num_rows), 0.5)
+        V = 0.7 * np.identity(num_cols) + np.full((num_cols, num_cols), 0.3)
+
+        # Incorrect dimensions
+        assert_raises(ValueError, matrix_normal, np.zeros((5,4,3)))
+        assert_raises(ValueError, matrix_normal, M, np.zeros(10), V)
+        assert_raises(ValueError, matrix_normal, M, U, np.zeros(10))
+        assert_raises(ValueError, matrix_normal, M, U, U)
+        assert_raises(ValueError, matrix_normal, M, V, V)
+        assert_raises(ValueError, matrix_normal, M.T, U, V)
+
+        e = np.linalg.LinAlgError
+        # Singular covariance for the rvs method of a non-frozen instance
+        assert_raises(e, matrix_normal.rvs,
+                      M, U, np.ones((num_cols, num_cols)))
+        assert_raises(e, matrix_normal.rvs,
+                      M, np.ones((num_rows, num_rows)), V)
+        # Singular covariance for a frozen instance
+        assert_raises(e, matrix_normal, M, U, np.ones((num_cols, num_cols)))
+        assert_raises(e, matrix_normal, M, np.ones((num_rows, num_rows)), V)
+
+    def test_default_inputs(self):
+        # Check that default argument handling works
+        num_rows = 4
+        num_cols = 3
+        M = np.full((num_rows,num_cols), 0.3)
+        U = 0.5 * np.identity(num_rows) + np.full((num_rows, num_rows), 0.5)
+        V = 0.7 * np.identity(num_cols) + np.full((num_cols, num_cols), 0.3)
+        Z = np.zeros((num_rows, num_cols))
+        Zr = np.zeros((num_rows, 1))
+        Zc = np.zeros((1, num_cols))
+        Ir = np.identity(num_rows)
+        Ic = np.identity(num_cols)
+        I1 = np.identity(1)
+
+        assert_equal(matrix_normal.rvs(mean=M, rowcov=U, colcov=V).shape,
+                     (num_rows, num_cols))
+        assert_equal(matrix_normal.rvs(mean=M).shape,
+                     (num_rows, num_cols))
+        assert_equal(matrix_normal.rvs(rowcov=U).shape,
+                     (num_rows, 1))
+        assert_equal(matrix_normal.rvs(colcov=V).shape,
+                     (1, num_cols))
+        assert_equal(matrix_normal.rvs(mean=M, colcov=V).shape,
+                     (num_rows, num_cols))
+        assert_equal(matrix_normal.rvs(mean=M, rowcov=U).shape,
+                     (num_rows, num_cols))
+        assert_equal(matrix_normal.rvs(rowcov=U, colcov=V).shape,
+                     (num_rows, num_cols))
+
+        assert_equal(matrix_normal(mean=M).rowcov, Ir)
+        assert_equal(matrix_normal(mean=M).colcov, Ic)
+        assert_equal(matrix_normal(rowcov=U).mean, Zr)
+        assert_equal(matrix_normal(rowcov=U).colcov, I1)
+        assert_equal(matrix_normal(colcov=V).mean, Zc)
+        assert_equal(matrix_normal(colcov=V).rowcov, I1)
+        assert_equal(matrix_normal(mean=M, rowcov=U).colcov, Ic)
+        assert_equal(matrix_normal(mean=M, colcov=V).rowcov, Ir)
+        assert_equal(matrix_normal(rowcov=U, colcov=V).mean, Z)
+
+    def test_covariance_expansion(self):
+        # Check that covariance can be specified with scalar or vector
+        num_rows = 4
+        num_cols = 3
+        M = np.full((num_rows, num_cols), 0.3)
+        Uv = np.full(num_rows, 0.2)
+        Us = 0.2
+        Vv = np.full(num_cols, 0.1)
+        Vs = 0.1
+
+        Ir = np.identity(num_rows)
+        Ic = np.identity(num_cols)
+
+        assert_equal(matrix_normal(mean=M, rowcov=Uv, colcov=Vv).rowcov,
+                     0.2*Ir)
+        assert_equal(matrix_normal(mean=M, rowcov=Uv, colcov=Vv).colcov,
+                     0.1*Ic)
+        assert_equal(matrix_normal(mean=M, rowcov=Us, colcov=Vs).rowcov,
+                     0.2*Ir)
+        assert_equal(matrix_normal(mean=M, rowcov=Us, colcov=Vs).colcov,
+                     0.1*Ic)
+
+    def test_frozen_matrix_normal(self):
+        for i in range(1,5):
+            for j in range(1,5):
+                M = np.full((i,j), 0.3)
+                U = 0.5 * np.identity(i) + np.full((i,i), 0.5)
+                V = 0.7 * np.identity(j) + np.full((j,j), 0.3)
+
+                frozen = matrix_normal(mean=M, rowcov=U, colcov=V)
+
+                rvs1 = frozen.rvs(random_state=1234)
+                rvs2 = matrix_normal.rvs(mean=M, rowcov=U, colcov=V,
+                                         random_state=1234)
+                assert_equal(rvs1, rvs2)
+
+                X = frozen.rvs(random_state=1234)
+
+                pdf1 = frozen.pdf(X)
+                pdf2 = matrix_normal.pdf(X, mean=M, rowcov=U, colcov=V)
+                assert_equal(pdf1, pdf2)
+
+                logpdf1 = frozen.logpdf(X)
+                logpdf2 = matrix_normal.logpdf(X, mean=M, rowcov=U, colcov=V)
+                assert_equal(logpdf1, logpdf2)
+
+    def test_matches_multivariate(self):
+        # Check that the pdfs match those obtained by vectorising and
+        # treating as a multivariate normal.
+        for i in range(1,5):
+            for j in range(1,5):
+                M = np.full((i,j), 0.3)
+                U = 0.5 * np.identity(i) + np.full((i,i), 0.5)
+                V = 0.7 * np.identity(j) + np.full((j,j), 0.3)
+
+                frozen = matrix_normal(mean=M, rowcov=U, colcov=V)
+                X = frozen.rvs(random_state=1234)
+                pdf1 = frozen.pdf(X)
+                logpdf1 = frozen.logpdf(X)
+                entropy1 = frozen.entropy()
+
+                vecX = X.T.flatten()
+                vecM = M.T.flatten()
+                cov = np.kron(V,U)
+                pdf2 = multivariate_normal.pdf(vecX, mean=vecM, cov=cov)
+                logpdf2 = multivariate_normal.logpdf(vecX, mean=vecM, cov=cov)
+                entropy2 = multivariate_normal.entropy(mean=vecM, cov=cov)
+
+                assert_allclose(pdf1, pdf2, rtol=1E-10)
+                assert_allclose(logpdf1, logpdf2, rtol=1E-10)
+                assert_allclose(entropy1, entropy2)
+
+    def test_array_input(self):
+        # Check array of inputs has the same output as the separate entries.
+        num_rows = 4
+        num_cols = 3
+        M = np.full((num_rows,num_cols), 0.3)
+        U = 0.5 * np.identity(num_rows) + np.full((num_rows, num_rows), 0.5)
+        V = 0.7 * np.identity(num_cols) + np.full((num_cols, num_cols), 0.3)
+        N = 10
+
+        frozen = matrix_normal(mean=M, rowcov=U, colcov=V)
+        X1 = frozen.rvs(size=N, random_state=1234)
+        X2 = frozen.rvs(size=N, random_state=4321)
+        X = np.concatenate((X1[np.newaxis,:,:,:],X2[np.newaxis,:,:,:]), axis=0)
+        assert_equal(X.shape, (2, N, num_rows, num_cols))
+
+        array_logpdf = frozen.logpdf(X)
+        assert_equal(array_logpdf.shape, (2, N))
+        for i in range(2):
+            for j in range(N):
+                separate_logpdf = matrix_normal.logpdf(X[i,j], mean=M,
+                                                       rowcov=U, colcov=V)
+                assert_allclose(separate_logpdf, array_logpdf[i,j], 1E-10)
+
+    def test_moments(self):
+        # Check that the sample moments match the parameters
+        num_rows = 4
+        num_cols = 3
+        M = np.full((num_rows,num_cols), 0.3)
+        U = 0.5 * np.identity(num_rows) + np.full((num_rows, num_rows), 0.5)
+        V = 0.7 * np.identity(num_cols) + np.full((num_cols, num_cols), 0.3)
+        N = 1000
+
+        frozen = matrix_normal(mean=M, rowcov=U, colcov=V)
+        X = frozen.rvs(size=N, random_state=1234)
+
+        sample_mean = np.mean(X,axis=0)
+        assert_allclose(sample_mean, M, atol=0.1)
+
+        sample_colcov = np.cov(X.reshape(N*num_rows,num_cols).T)
+        assert_allclose(sample_colcov, V, atol=0.1)
+
+        sample_rowcov = np.cov(np.swapaxes(X,1,2).reshape(
+                                                        N*num_cols,num_rows).T)
+        assert_allclose(sample_rowcov, U, atol=0.1)
+
+    def test_samples(self):
+        # Regression test to ensure that we always generate the same stream of
+        # random variates.
+        actual = matrix_normal.rvs(
+            mean=np.array([[1, 2], [3, 4]]),
+            rowcov=np.array([[4, -1], [-1, 2]]),
+            colcov=np.array([[5, 1], [1, 10]]),
+            random_state=np.random.default_rng(0),
+            size=2
+        )
+        expected = np.array(
+            [[[1.56228264238181, -1.24136424071189],
+              [2.46865788392114, 6.22964440489445]],
+             [[3.86405716144353, 10.73714311429529],
+              [2.59428444080606, 5.79987854490876]]]
+        )
+        assert_allclose(actual, expected)
+
+
+class TestMatrixT:
+
+    def test_bad_input(self):
+        # Check that bad inputs raise errors
+        num_rows = 4
+        num_cols = 3
+        df = 5
+        M = np.full((num_rows, num_cols), 0.3)
+        U = 0.5 * np.identity(num_rows) + np.full((num_rows, num_rows), 0.5)
+        V = 0.7 * np.identity(num_cols) + np.full((num_cols, num_cols), 0.3)
+
+        # Nonpositive degrees of freedom
+        with pytest.raises(ValueError, match="Degrees of freedom must be positive."):
+            matrix_t(df=0)
+
+        # Incorrect dimensions
+        with pytest.raises(ValueError, match="Array `mean` must be 2D."):
+            matrix_t(mean=np.zeros((5, 4, 3)))
+
+        with pytest.raises(ValueError, match="Array `mean` has invalid shape."):
+            matrix_t(mean=np.zeros((4, 3, 0)))
+
+        with pytest.raises(ValueError, match="Array `row_spread` has invalid shape."):
+            matrix_t(row_spread=np.ones((1, 0)))
+
+        with pytest.raises(
+            ValueError, match="Array `row_spread` must be a scalar or a 2D array."
+        ):
+            matrix_t(row_spread=np.ones((1, 2, 3)))
+
+        with pytest.raises(ValueError, match="Array `row_spread` must be square."):
+            matrix_t(row_spread=np.ones((1, 2)))
+
+        with pytest.raises(ValueError, match="Array `col_spread` has invalid shape."):
+            matrix_t(col_spread=np.ones((1, 0)))
+
+        with pytest.raises(
+            ValueError, match="Array `col_spread` must be a scalar or a 2D array."
+        ):
+            matrix_t(col_spread=np.ones((1, 2, 3)))
+
+        with pytest.raises(ValueError, match="Array `col_spread` must be square."):
+            matrix_t(col_spread=np.ones((1, 2)))
+
+        with pytest.raises(
+            ValueError,
+            match="Arrays `mean` and `row_spread` must have the same number "
+            "of rows.",
+        ):
+            matrix_t(mean=M, row_spread=V)
+
+        with pytest.raises(
+            ValueError,
+            match="Arrays `mean` and `col_spread` must have the same number "
+            "of columns.",
+        ):
+            matrix_t(mean=M, col_spread=U)
+
+        # Incorrect dimension of input matrix
+        with pytest.raises(
+            ValueError,
+            match="The shape of array `X` is not conformal with "
+            "the distribution parameters.",
+        ):
+            matrix_t.pdf(X=np.zeros((num_rows, num_rows)), mean=M)
+
+        # Singular covariance for a non-frozen instance
+
+        with pytest.raises(
+            np.linalg.LinAlgError,
+            match="Internal potrf return info",
+        ):
+            matrix_t.rvs(M, U, np.ones((num_cols, num_cols)), df)
+
+        with pytest.raises(
+            np.linalg.LinAlgError,
+            match="Internal potrf return info",
+        ):
+            matrix_t.rvs(M, np.ones((num_rows, num_rows)), V, df)
+
+        # Singular covariance for a frozen instance
+
+        with pytest.raises(
+            np.linalg.LinAlgError,
+            match="When `allow_singular is False`, the input matrix must be "
+            "symmetric positive definite.",
+        ):
+            matrix_t(M, U, np.ones((num_cols, num_cols)), df)
+
+        with pytest.raises(
+            np.linalg.LinAlgError,
+            match="When `allow_singular is False`, the input matrix must be "
+            "symmetric positive definite.",
+        ):
+            matrix_t(M, np.ones((num_rows, num_rows)), V, df)
+
+    def test_default_inputs(self):
+        # Check that default argument handling works
+        num_rows = 4
+        num_cols = 3
+        df = 5
+        M = np.full((num_rows, num_cols), 0.3)
+        U = 0.5 * np.identity(num_rows) + np.full((num_rows, num_rows), 0.5)
+        V = 0.7 * np.identity(num_cols) + np.full((num_cols, num_cols), 0.3)
+        Z = np.zeros((num_rows, num_cols))
+        Zr = np.zeros((num_rows, 1))
+        Zc = np.zeros((1, num_cols))
+        Ir = np.identity(num_rows)
+        Ic = np.identity(num_cols)
+        I1 = np.identity(1)
+        dfdefault = 1
+
+        assert_equal(
+            matrix_t.rvs(mean=M, row_spread=U, col_spread=V, df=df).shape,
+            (num_rows, num_cols),
+        )
+        assert_equal(matrix_t.rvs(mean=M).shape, (num_rows, num_cols))
+        assert_equal(matrix_t.rvs(row_spread=U).shape, (num_rows, 1))
+        assert_equal(matrix_t.rvs(col_spread=V).shape, (1, num_cols))
+        assert_equal(matrix_t.rvs(mean=M, col_spread=V).shape, (num_rows, num_cols))
+        assert_equal(matrix_t.rvs(mean=M, row_spread=U).shape, (num_rows, num_cols))
+        assert_equal(
+            matrix_t.rvs(row_spread=U, col_spread=V).shape, (num_rows, num_cols)
+        )
+
+        assert_equal(matrix_t().df, dfdefault)
+        assert_equal(matrix_t(mean=M).row_spread, Ir)
+        assert_equal(matrix_t(mean=M).col_spread, Ic)
+        assert_equal(matrix_t(row_spread=U).mean, Zr)
+        assert_equal(matrix_t(row_spread=U).col_spread, I1)
+        assert_equal(matrix_t(col_spread=V).mean, Zc)
+        assert_equal(matrix_t(col_spread=V).row_spread, I1)
+        assert_equal(matrix_t(mean=M, row_spread=U).col_spread, Ic)
+        assert_equal(matrix_t(mean=M, col_spread=V).row_spread, Ir)
+        assert_equal(matrix_t(row_spread=U, col_spread=V, df=df).mean, Z)
+
+    def test_covariance_expansion(self):
+        # Check that covariance can be specified with scalar or vector
+        num_rows = 4
+        num_cols = 3
+        df = 1
+        M = np.full((num_rows, num_cols), 0.3)
+        Uv = np.full(num_rows, 0.2)
+        Us = 0.2
+        Vv = np.full(num_cols, 0.1)
+        Vs = 0.1
+
+        Ir = np.identity(num_rows)
+        Ic = np.identity(num_cols)
+
+        assert_equal(
+            matrix_t(mean=M, row_spread=Uv, col_spread=Vv, df=df).row_spread, 0.2 * Ir
+        )
+        assert_equal(
+            matrix_t(mean=M, row_spread=Uv, col_spread=Vv, df=df).col_spread, 0.1 * Ic
+        )
+        assert_equal(
+            matrix_t(mean=M, row_spread=Us, col_spread=Vs, df=df).row_spread, 0.2 * Ir
+        )
+        assert_equal(
+            matrix_t(mean=M, row_spread=Us, col_spread=Vs, df=df).col_spread, 0.1 * Ic
+        )
+
+    @pytest.mark.parametrize("i", range(1, 4))
+    @pytest.mark.parametrize("j", range(1, 4))
+    def test_frozen_matrix_t(self, i, j):
+
+        M = np.full((i, j), 0.3)
+        U = 0.5 * np.identity(i) + np.full((i, i), 0.5)
+        V = 0.7 * np.identity(j) + np.full((j, j), 0.3)
+        df = i + j
+
+        frozen = matrix_t(mean=M, row_spread=U, col_spread=V, df=df)
+
+        rvs1 = frozen.rvs(random_state=1234)
+        rvs2 = matrix_t.rvs(
+            mean=M, row_spread=U, col_spread=V, df=df, random_state=1234
+        )
+        assert_equal(rvs1, rvs2)
+
+        X = frozen.rvs(random_state=1234)
+
+        pdf1 = frozen.pdf(X)
+        pdf2 = matrix_t.pdf(X, mean=M, row_spread=U, col_spread=V, df=df)
+        assert_equal(pdf1, pdf2)
+
+        logpdf1 = frozen.logpdf(X)
+        logpdf2 = matrix_t.logpdf(X, mean=M, row_spread=U, col_spread=V, df=df)
+        assert_equal(logpdf1, logpdf2)
+
+    def test_array_input(self):
+        # Check array of inputs has the same output as the separate entries.
+        num_rows = 4
+        num_cols = 3
+        M = np.full((num_rows, num_cols), 0.3)
+        U = 0.5 * np.identity(num_rows) + np.full((num_rows, num_rows), 0.5)
+        V = 0.7 * np.identity(num_cols) + np.full((num_cols, num_cols), 0.3)
+        df = 1
+        N = 10
+
+        frozen = matrix_t(mean=M, row_spread=U, col_spread=V, df=df)
+        X1 = frozen.rvs(size=N, random_state=1234)
+        X2 = frozen.rvs(size=N, random_state=4321)
+        X = np.concatenate((X1[np.newaxis, :, :, :], X2[np.newaxis, :, :, :]), axis=0)
+        assert_equal(X.shape, (2, N, num_rows, num_cols))
+
+        array_logpdf = frozen.logpdf(X)
+        logpdf_shape = array_logpdf.shape
+        assert_equal(logpdf_shape, (2, N))
+        for i in range(2):
+            for j in range(N):
+                separate_logpdf = matrix_t.logpdf(
+                    X[i, j], mean=M, row_spread=U, col_spread=V, df=df
+                )
+                assert_allclose(separate_logpdf, array_logpdf[i, j], 1e-10)
+
+    @staticmethod
+    def relative_error(vec1: np.ndarray, vec2: np.ndarray):
+        numerator = np.linalg.norm(vec1 - vec2) ** 2
+        denominator = np.linalg.norm(vec1) ** 2 + np.linalg.norm(vec2) ** 2
+        return numerator / denominator
+
+    @staticmethod
+    def matrix_divergence(mat_true: np.ndarray, mat_est: np.ndarray) -> float:
+        mat_true_psd = _PSD(mat_true, allow_singular=False)
+        mat_est_psd = _PSD(mat_est, allow_singular=False)
+        if (np.exp(mat_est_psd.log_pdet) <= 0) or (np.exp(mat_true_psd.log_pdet) <= 0):
+            return np.inf
+        trace_term = np.trace(mat_est_psd.pinv @ mat_true)
+        log_detratio = mat_est_psd.log_pdet - mat_true_psd.log_pdet
+        return (trace_term + log_detratio - len(mat_true)) / 2
+
+    @staticmethod
+    def vec(a_mat: np.ndarray) -> np.ndarray:
+        """
+        For an (m,n) array `a_mat` the output `vec(a_mat)` is an (m*n, 1)
+        array formed by stacking the columns of `a_mat` in the order in
+        which they occur in `a_mat`.
+        """
+        assert a_mat.ndim == 2
+        return a_mat.T.reshape((a_mat.size,))
+
+    def test_moments(self):
+        r"""
+        Gupta and Nagar (2000) Theorem 4.3.1 (p.135)
+        --------------------------------------------
+        The covariance of the vectorized matrix variate t-distribution equals
+        $ (V \otimes U) / (\text{df} - 2)$, where $\otimes$
+        denotes the usual Kronecker product.
+        """
+
+        df = 5
+        num_rows = 4
+        num_cols = 3
+        M = np.full((num_rows, num_cols), 0.3)
+        U = 0.5 * np.identity(num_rows) + np.full((num_rows, num_rows), 0.5)
+        V = 0.7 * np.identity(num_cols) + np.full((num_cols, num_cols), 0.3)
+        N = 10**4
+        atol = 1e-1
+
+        frozen = matrix_t(mean=M, row_spread=U, col_spread=V, df=df)
+        X = frozen.rvs(size=N, random_state=42)
+
+        relerr = self.relative_error(M, X.mean(axis=0))
+        assert_close(relerr, 0, atol=atol)
+
+        cov_vec_true = np.kron(V, U) / (df - 2)
+        cov_vec_rvs = np.cov(np.array([self.vec(x) for x in X]), rowvar=False)
+        kl = self.matrix_divergence(cov_vec_true, cov_vec_rvs)
+        assert_close(kl, 0, atol=atol)
+
+    def test_pdf_against_julia(self):
+        """
+        Test values generated from Julia.
+
+        Dockerfile
+        ----------
+        FROM julia:1.11.5
+        RUN julia -e 'using Pkg; Pkg.add("Distributions"); Pkg.add("PDMats")'
+        WORKDIR /usr/src
+
+        Commands
+        --------
+        using DelimitedFiles
+        using Distributions
+        using PDMats
+        using Random
+        Random.seed!(42)
+        ν = 5
+        M = [1 2 3; 4 5 6]
+        Σ = PDMats.PDMat([1 0.5; 0.5 1])
+        Ω = PDMats.PDMat([1 0.3 0.2; 0.3 1 0.4; 0.2 0.4 1])
+        dist = MatrixTDist(ν, M, Σ, Ω)
+        samples = rand(dist, 10)
+        pdfs = [pdf(dist, s) for s in samples]
+        """
+
+        df = 5
+        M = np.array([[1, 2, 3], [4, 5, 6]])
+        U = np.array([[1, 0.5], [0.5, 1]])
+        V = np.array([[1, 0.3, 0.2], [0.3, 1, 0.4], [0.2, 0.4, 1]])
+
+        rtol = 1e-10
+
+        samples_j = np.array(
+            [
+                [
+                    [0.958884881003464, 2.328976673167312, 2.936195396714506],
+                    [3.656388568544394, 5.677549814962506, 6.292509556719057]
+                ],
+                [
+                    [0.830992685140180, 2.588946865508210, 3.310327469315906],
+                    [3.850637198786261, 5.106074165416971, 6.403143979925566]
+                ],
+                [
+                    [1.572053537500711, 1.760828063560249, 2.812123062636012],
+                    [4.156334686390513, 5.075942019982631, 5.827004350136873]
+                ],
+                [
+                    [1.683810860278459, 2.801203900480317, 4.054517744825265],
+                    [4.778239956376877, 5.070613721477604, 6.640349743267192]
+                ],
+                [
+                    [0.443183825511296, 2.072092271247398, 3.045385527559403],
+                    [4.374387994815022, 5.083432151729137, 5.958013783940404]
+                ],
+                [
+                    [0.311591337218329, 1.162836182564980, 2.562167762547456],
+                    [3.079154928756626, 4.202325496476140, 5.485839479663457]
+                ],
+                [
+                    [0.943713128785340, 1.923800464789872, 2.511941262351750],
+                    [4.124882619205123, 4.889406461458511, 5.689675454116582]
+                ],
+                [
+                    [1.487852512870631, 1.933859334657448, 2.681311906634522],
+                    [4.124418827930267, 5.335204598518954, 5.988120342017037]
+                ],
+                [
+                    [1.002470749319751, 1.386785511789551, 2.890832331097640],
+                    [4.372884362128993, 4.729718562700068, 6.732322315921552]
+                ],
+                [
+                    [1.421351511333299, 2.106946903600814, 2.654619331838720],
+                    [4.188693248790616, 5.336439611284261, 5.279121290355546]
+                ]
+            ]
+        )
+
+        pdfs_j = np.array(
+            [
+                0.082798951655369,
+                0.119993852401118,
+                0.151969434727803,
+                0.003620324481841,
+                0.072538716346179,
+                0.027002666410192,
+                0.485180162388507,
+                0.135740468069511,
+                0.013619162593841,
+                0.034813885519299
+            ]
+        )
+
+        pdfs_py = matrix_t.pdf(samples_j, mean=M, row_spread=U, col_spread=V, df=df)
+
+        assert_allclose(pdfs_j, pdfs_py, rtol=rtol)
+
+    def test_pdf_against_mathematica(self):
+        """
+        Test values generated from Mathematica 13.0.0 for Linux x86 (64-bit)
+        Release ID 13.0.0.0 (7522564, 2021120311723), Patch Level 0
+
+        mu={{1,2,3},{4,5,6}};
+        sigma={{1,0.5},{0.5,1}};
+        omega={{1,0.3,0.2},{0.3,1,0.4},{0.2,0.4,1}};
+        df=5;
+        sampleSize=10;
+        SeedRandom[42];
+        dist=MatrixTDistribution[mu,sigma,omega,df];
+        samples=SetPrecision[RandomVariate[dist,sampleSize],15];
+        pdfs=SetPrecision[PDF[dist,#]&/@samples,15];
+        """
+
+        df = 5
+        M = np.array([[1, 2, 3], [4, 5, 6]])
+        U = np.array([[1, 0.5], [0.5, 1]])
+        V = np.array([[1, 0.3, 0.2], [0.3, 1, 0.4], [0.2, 0.4, 1]])
+
+        rtol = 1e-10
+
+        samples_m = np.array(
+            [
+                [
+                    [0.639971699425374, 2.171718671534955, 2.575826093352771],
+                    [4.031082477912233, 5.021680958526638, 6.268126154787008],
+                ],
+                [
+                    [1.164842884206232, 2.526297099993045, 3.781375229865069],
+                    [3.912979114956833, 4.202714884504189, 5.661830748993523],
+                ],
+                [
+                    [1.00461853907369, 2.080028751298565, 3.406489485602410],
+                    [3.993327716320432, 5.655909265966448, 6.578059791357837],
+                ],
+                [
+                    [0.80625209501374, 2.529009560674907, 2.807513313302189],
+                    [3.722896768794995, 5.26987322525995, 5.801155613199776],
+                ],
+                [
+                    [0.445816208657817, 3.224059910964103, 2.954990980541423],
+                    [3.451520519442941, 7.064424621385415, 5.438834195890955],
+                ],
+                [
+                    [0.919232769636664, 2.374572300756703, 3.495118928313048],
+                    [3.924447237903237, 5.627654256287447, 5.806104608153957],
+                ],
+                [
+                    [2.014242004090113, 1.377018127709871, 3.114064311468686],
+                    [3.88881648137925, 4.603482820518904, 5.714205489738063],
+                ],
+                [
+                    [1.322000147426889, 2.602135838377777, 2.558921028724319],
+                    [4.50534702030683, 5.861137323151889, 5.181872548334852],
+                ],
+                [
+                    [1.448743656862261, 2.053847557652242, 3.637321543241769],
+                    [4.097711403906707, 4.506916241403669, 5.68010653497977],
+                ],
+                [
+                    [1.045187318995198, 1.645467189679729, 3.284396214544507],
+                    [3.648493466445393, 5.004212508553601, 6.301624351328048],
+                ],
+            ]
+        )
+
+        pdfs_m = np.array(
+            [
+                0.085671937131824,
+                0.004821273644067,
+                0.105978034029754,
+                0.174250448808208,
+                3.945711836053583e-05,
+                0.027158790350349,
+                0.00299095120309,
+                0.005594546018078,
+                0.025788366971310,
+                0.120210733598845,
+            ]
+        )
+
+        pdfs_py = matrix_t.pdf(samples_m, mean=M, row_spread=U, col_spread=V, df=df)
+
+        assert_allclose(pdfs_m, pdfs_py, rtol=rtol)
+
+    def test_samples(self):
+        df = 5
+        num_rows = 4
+        num_cols = 3
+        M = np.full((num_rows, num_cols), 0.3)
+        U = 0.5 * np.identity(num_rows) + np.full((num_rows, num_rows), 0.5)
+        V = 0.7 * np.identity(num_cols) + np.full((num_cols, num_cols), 0.3)
+        N = 10**4
+        rtol = 0.05
+
+        # `rvs` performs Cholesky-inverse-Wishart sampling on the smaller
+        # dimension of `mean`
+
+        frozen = matrix_t(mean=M, row_spread=U, col_spread=V, df=df)
+        X = frozen.rvs(size=N, random_state=42)  # column-wise rvs
+        m = X.mean(0)
+
+        frozenT = matrix_t(mean=M.T, row_spread=V, col_spread=U, df=df)
+        XT = frozenT.rvs(size=N, random_state=42)  # row-wise rvs
+        mT = XT.mean(0)
+
+        # Gupta and Nagar (2000) Theorem 4.3.3 (p.137)
+        # --------------------------------------------
+        # If T follows a matrix variate t-distribution with mean M and row_spread U
+        # and col_spread V and df degrees of freedom, then its transpose T.T follows
+        # a matrix variate t-distribution with mean M.T and row_spread V and
+        # col_spread U and df degrees of freedom.
+
+        assert_allclose(M, m, rtol=rtol)
+        assert_allclose(M.T, mT, rtol=rtol)
+        assert_allclose(m, mT.T, rtol=rtol)
+        assert_allclose(m.T, mT, rtol=rtol)
+
+    @pytest.mark.parametrize("shape_case", ["row", "col"])
+    def test_against_multivariate_t(self, shape_case):
+        r"""
+        Gupta and Nagar (2000) p.133f
+        When the number of rows or the number of columns equals 1 the
+        matrix t reduces to the multivariate t. But, the matrix t
+        is parameterized by raw 2nd moments whereas the multivariate t is
+        parameterized by a covariance (raw 2nd central moment normalized by df).
+        We can see the difference by comparing the author's notation
+            $t_p(n, \omega, \mathbf{\mu}, \Sigma)$
+        for a matrix t with a single column
+        to the formula (4.1.2) for the PDF of the multivariate t.
+        """
+        rtol = 1e-6
+        df = 5
+
+        if shape_case == "row":
+            num_rows = 1
+            num_cols = 3
+            row_spread = 1
+            col_spread = np.array([[1, 0.3, 0.2], [0.3, 1, 0.4], [0.2, 0.4, 1]])
+            shape = col_spread / df
+        else:  # shape_case == "col"
+            num_rows = 3
+            num_cols = 1
+            row_spread = np.array([[1, 0.3, 0.2], [0.3, 1, 0.4], [0.2, 0.4, 1]])
+            col_spread=1
+            shape = row_spread / df
+
+        M = np.full((num_rows, num_cols), 0.3)
+
+        t_mat = matrix_t(
+            mean=M, row_spread=row_spread, col_spread=col_spread, df=df
+        )
+        t_mvt = multivariate_t(loc=M.squeeze(), shape=shape, df=df)
+
+        X = t_mat.rvs(size=3, random_state=42)
+        t_mat_logpdf = t_mat.logpdf(X)
+        t_mvt_logpdf = t_mvt.logpdf(X.squeeze())
+        assert_allclose(t_mvt_logpdf, t_mat_logpdf, rtol=rtol)
+
+
+class TestDirichlet:
+
+    def test_frozen_dirichlet(self):
+        rng = np.random.default_rng(2846)
+
+        n = rng.integers(1, 32)
+        alpha = rng.uniform(10e-10, 100, n)
+
+        d = dirichlet(alpha)
+
+        assert_equal(d.var(), dirichlet.var(alpha))
+        assert_equal(d.mean(), dirichlet.mean(alpha))
+        assert_equal(d.entropy(), dirichlet.entropy(alpha))
+        num_tests = 10
+        for i in range(num_tests):
+            x = rng.uniform(10e-10, 100, n)
+            x /= np.sum(x)
+            assert_equal(d.pdf(x[:-1]), dirichlet.pdf(x[:-1], alpha))
+            assert_equal(d.logpdf(x[:-1]), dirichlet.logpdf(x[:-1], alpha))
+
+    def test_numpy_rvs_shape_compatibility(self):
+        rng = np.random.default_rng(2846)
+        alpha = np.array([1.0, 2.0, 3.0])
+        x = rng.dirichlet(alpha, size=7)
+        assert_equal(x.shape, (7, 3))
+        assert_raises(ValueError, dirichlet.pdf, x, alpha)
+        assert_raises(ValueError, dirichlet.logpdf, x, alpha)
+        dirichlet.pdf(x.T, alpha)
+        dirichlet.pdf(x.T[:-1], alpha)
+        dirichlet.logpdf(x.T, alpha)
+        dirichlet.logpdf(x.T[:-1], alpha)
+
+    def test_alpha_with_zeros(self):
+        rng = np.random.default_rng(2846)
+        alpha = [1.0, 0.0, 3.0]
+        # don't pass invalid alpha to np.random.dirichlet
+        x = rng.dirichlet(np.maximum(1e-9, alpha), size=7).T
+        assert_raises(ValueError, dirichlet.pdf, x, alpha)
+        assert_raises(ValueError, dirichlet.logpdf, x, alpha)
+
+    def test_alpha_with_negative_entries(self):
+        rng = np.random.default_rng(2846)
+        alpha = [1.0, -2.0, 3.0]
+        # don't pass invalid alpha to np.random.dirichlet
+        x = rng.dirichlet(np.maximum(1e-9, alpha), size=7).T
+        assert_raises(ValueError, dirichlet.pdf, x, alpha)
+        assert_raises(ValueError, dirichlet.logpdf, x, alpha)
+
+    def test_data_with_zeros(self):
+        alpha = np.array([1.0, 2.0, 3.0, 4.0])
+        x = np.array([0.1, 0.0, 0.2, 0.7])
+        dirichlet.pdf(x, alpha)
+        dirichlet.logpdf(x, alpha)
+        alpha = np.array([1.0, 1.0, 1.0, 1.0])
+        assert_almost_equal(dirichlet.pdf(x, alpha), 6)
+        assert_almost_equal(dirichlet.logpdf(x, alpha), np.log(6))
+
+    def test_data_with_zeros_and_small_alpha(self):
+        alpha = np.array([1.0, 0.5, 3.0, 4.0])
+        x = np.array([0.1, 0.0, 0.2, 0.7])
+        assert_raises(ValueError, dirichlet.pdf, x, alpha)
+        assert_raises(ValueError, dirichlet.logpdf, x, alpha)
+
+    def test_data_with_negative_entries(self):
+        alpha = np.array([1.0, 2.0, 3.0, 4.0])
+        x = np.array([0.1, -0.1, 0.3, 0.7])
+        assert_raises(ValueError, dirichlet.pdf, x, alpha)
+        assert_raises(ValueError, dirichlet.logpdf, x, alpha)
+
+    def test_data_with_too_large_entries(self):
+        alpha = np.array([1.0, 2.0, 3.0, 4.0])
+        x = np.array([0.1, 1.1, 0.3, 0.7])
+        assert_raises(ValueError, dirichlet.pdf, x, alpha)
+        assert_raises(ValueError, dirichlet.logpdf, x, alpha)
+
+    def test_data_too_deep_c(self):
+        alpha = np.array([1.0, 2.0, 3.0])
+        x = np.full((2, 7, 7), 1 / 14)
+        assert_raises(ValueError, dirichlet.pdf, x, alpha)
+        assert_raises(ValueError, dirichlet.logpdf, x, alpha)
+
+    def test_alpha_too_deep(self):
+        alpha = np.array([[1.0, 2.0], [3.0, 4.0]])
+        x = np.full((2, 2, 7), 1 / 4)
+        assert_raises(ValueError, dirichlet.pdf, x, alpha)
+        assert_raises(ValueError, dirichlet.logpdf, x, alpha)
+
+    def test_alpha_correct_depth(self):
+        alpha = np.array([1.0, 2.0, 3.0])
+        x = np.full((3, 7), 1 / 3)
+        dirichlet.pdf(x, alpha)
+        dirichlet.logpdf(x, alpha)
+
+    def test_non_simplex_data(self):
+        alpha = np.array([1.0, 2.0, 3.0])
+        x = np.full((3, 7), 1 / 2)
+        assert_raises(ValueError, dirichlet.pdf, x, alpha)
+        assert_raises(ValueError, dirichlet.logpdf, x, alpha)
+
+    def test_data_vector_too_short(self):
+        alpha = np.array([1.0, 2.0, 3.0, 4.0])
+        x = np.full((2, 7), 1 / 2)
+        assert_raises(ValueError, dirichlet.pdf, x, alpha)
+        assert_raises(ValueError, dirichlet.logpdf, x, alpha)
+
+    def test_data_vector_too_long(self):
+        alpha = np.array([1.0, 2.0, 3.0, 4.0])
+        x = np.full((5, 7), 1 / 5)
+        assert_raises(ValueError, dirichlet.pdf, x, alpha)
+        assert_raises(ValueError, dirichlet.logpdf, x, alpha)
+
+    def test_mean_var_cov(self):
+        # Reference values calculated by hand and confirmed with Mathematica, e.g.
+        # `Covariance[DirichletDistribution[{ 1, 0.8, 0.2, 10^-300}]]`
+        alpha = np.array([1., 0.8, 0.2])
+        d = dirichlet(alpha)
+
+        expected_mean = [0.5, 0.4, 0.1]
+        expected_var = [1. / 12., 0.08, 0.03]
+        expected_cov = [
+                [ 1. / 12, -1. / 15, -1. / 60],
+                [-1. / 15,  2. / 25, -1. / 75],
+                [-1. / 60, -1. / 75,  3. / 100],
+        ]
+
+        assert_array_almost_equal(d.mean(), expected_mean)
+        assert_array_almost_equal(d.var(), expected_var)
+        assert_array_almost_equal(d.cov(), expected_cov)
+
+    def test_scalar_values(self):
+        alpha = np.array([0.2])
+        d = dirichlet(alpha)
+
+        # For alpha of length 1, mean and var should be scalar instead of array
+        assert_equal(d.mean().ndim, 0)
+        assert_equal(d.var().ndim, 0)
+
+        assert_equal(d.pdf([1.]).ndim, 0)
+        assert_equal(d.logpdf([1.]).ndim, 0)
+
+    def test_K_and_K_minus_1_calls_equal(self):
+        # Test that calls with K and K-1 entries yield the same results.
+        rng = np.random.default_rng(2846)
+
+        n = rng.integers(1, 32)
+        alpha = rng.uniform(10e-10, 100, n)
+
+        d = dirichlet(alpha)
+        num_tests = 10
+        for i in range(num_tests):
+            x = rng.uniform(10e-10, 100, n)
+            x /= np.sum(x)
+            assert_almost_equal(d.pdf(x[:-1]), d.pdf(x))
+
+    def test_multiple_entry_calls(self):
+        # Test that calls with multiple x vectors as matrix work
+        rng = np.random.default_rng(2846)
+
+        n = rng.integers(1, 32)
+        alpha = rng.uniform(10e-10, 100, n)
+        d = dirichlet(alpha)
+
+        num_tests = 10
+        num_multiple = 5
+        xm = None
+        for i in range(num_tests):
+            for m in range(num_multiple):
+                x = rng.uniform(10e-10, 100, n)
+                x /= np.sum(x)
+                if xm is not None:
+                    xm = np.vstack((xm, x))
+                else:
+                    xm = x
+            rm = d.pdf(xm.T)
+            rs = None
+            for xs in xm:
+                r = d.pdf(xs)
+                if rs is not None:
+                    rs = np.append(rs, r)
+                else:
+                    rs = r
+            assert_array_almost_equal(rm, rs)
+
+    def test_2D_dirichlet_is_beta(self):
+        rng = np.random.default_rng(2846)
+
+        alpha = rng.uniform(10e-10, 100, 2)
+        d = dirichlet(alpha)
+        b = beta(alpha[0], alpha[1])
+
+        num_tests = 10
+        for i in range(num_tests):
+            x = rng.uniform(10e-10, 100, 2)
+            x /= np.sum(x)
+            assert_almost_equal(b.pdf(x), d.pdf([x]))
+
+        assert_almost_equal(b.mean(), d.mean()[0])
+        assert_almost_equal(b.var(), d.var()[0])
+
+
+def test_multivariate_normal_dimensions_mismatch():
+    # Regression test for GH #3493. Check that setting up a PDF with a mean of
+    # length M and a covariance matrix of size (N, N), where M != N, raises a
+    # ValueError with an informative error message.
+    mu = np.array([0.0, 0.0])
+    sigma = np.array([[1.0]])
+
+    assert_raises(ValueError, multivariate_normal, mu, sigma)
+
+    # A simple check that the right error message was passed along. Checking
+    # that the entire message is there, word for word, would be somewhat
+    # fragile, so we just check for the leading part.
+    try:
+        multivariate_normal(mu, sigma)
+    except ValueError as e:
+        msg = "Dimension mismatch"
+        assert_equal(str(e)[:len(msg)], msg)
+
+
+class TestWishart:
+    def test_scale_dimensions(self):
+        # Test that we can call the Wishart with various scale dimensions
+
+        # Test case: dim=1, scale=1
+        true_scale = np.array(1, ndmin=2)
+        scales = [
+            1,                    # scalar
+            [1],                  # iterable
+            np.array(1),          # 0-dim
+            np.r_[1],             # 1-dim
+            np.array(1, ndmin=2)  # 2-dim
+        ]
+        for scale in scales:
+            w = wishart(1, scale)
+            assert_equal(w.scale, true_scale)
+            assert_equal(w.scale.shape, true_scale.shape)
+
+        # Test case: dim=2, scale=[[1,0]
+        #                          [0,2]
+        true_scale = np.array([[1,0],
+                               [0,2]])
+        scales = [
+            [1,2],             # iterable
+            np.r_[1,2],        # 1-dim
+            np.array([[1,0],   # 2-dim
+                      [0,2]])
+        ]
+        for scale in scales:
+            w = wishart(2, scale)
+            assert_equal(w.scale, true_scale)
+            assert_equal(w.scale.shape, true_scale.shape)
+
+        # We cannot call with a df < dim - 1
+        assert_raises(ValueError, wishart, 1, np.eye(2))
+
+        # But we can call with dim - 1 < df < dim
+        wishart(1.1, np.eye(2))  # no error
+        # see gh-5562
+
+        # We cannot call with a 3-dimension array
+        scale = np.array(1, ndmin=3)
+        assert_raises(ValueError, wishart, 1, scale)
+
+    def test_quantile_dimensions(self):
+        # Test that we can call the Wishart rvs with various quantile dimensions
+
+        # If dim == 1, consider x.shape = [1,1,1]
+        X = [
+            1,                      # scalar
+            [1],                    # iterable
+            np.array(1),            # 0-dim
+            np.r_[1],               # 1-dim
+            np.array(1, ndmin=2),   # 2-dim
+            np.array([1], ndmin=3)  # 3-dim
+        ]
+
+        w = wishart(1,1)
+        density = w.pdf(np.array(1, ndmin=3))
+        for x in X:
+            assert_equal(w.pdf(x), density)
+
+        # If dim == 1, consider x.shape = [1,1,*]
+        X = [
+            [1,2,3],                     # iterable
+            np.r_[1,2,3],                # 1-dim
+            np.array([1,2,3], ndmin=3)   # 3-dim
+        ]
+
+        w = wishart(1,1)
+        density = w.pdf(np.array([1,2,3], ndmin=3))
+        for x in X:
+            assert_equal(w.pdf(x), density)
+
+        # If dim == 2, consider x.shape = [2,2,1]
+        # where x[:,:,*] = np.eye(1)*2
+        X = [
+            2,                    # scalar
+            [2,2],                # iterable
+            np.array(2),          # 0-dim
+            np.r_[2,2],           # 1-dim
+            np.array([[2,0],
+                      [0,2]]),    # 2-dim
+            np.array([[2,0],
+                      [0,2]])[:,:,np.newaxis]  # 3-dim
+        ]
+
+        w = wishart(2,np.eye(2))
+        density = w.pdf(np.array([[2,0],
+                                  [0,2]])[:,:,np.newaxis])
+        for x in X:
+            assert_equal(w.pdf(x), density)
+
+    def test_frozen(self):
+        # Test that the frozen and non-frozen Wishart gives the same answers
+
+        # Construct an arbitrary positive definite scale matrix
+        dim = 4
+        scale = np.diag(np.arange(dim)+1)
+        scale[np.tril_indices(dim, k=-1)] = np.arange(dim * (dim-1) // 2)
+        scale = np.dot(scale.T, scale)
+
+        # Construct a collection of positive definite matrices to test the PDF
+        X = []
+        for i in range(5):
+            x = np.diag(np.arange(dim)+(i+1)**2)
+            x[np.tril_indices(dim, k=-1)] = np.arange(dim * (dim-1) // 2)
+            x = np.dot(x.T, x)
+            X.append(x)
+        X = np.array(X).T
+
+        # Construct a 1D and 2D set of parameters
+        parameters = [
+            (10, 1, np.linspace(0.1, 10, 5)),  # 1D case
+            (10, scale, X)
+        ]
+
+        for (df, scale, x) in parameters:
+            w = wishart(df, scale)
+            assert_equal(w.var(), wishart.var(df, scale))
+            assert_equal(w.mean(), wishart.mean(df, scale))
+            assert_equal(w.mode(), wishart.mode(df, scale))
+            assert_equal(w.entropy(), wishart.entropy(df, scale))
+            assert_equal(w.pdf(x), wishart.pdf(x, df, scale))
+
+    def test_wishart_2D_rvs(self):
+        dim = 3
+        df = 10
+
+        # Construct a simple non-diagonal positive definite matrix
+        scale = np.eye(dim)
+        scale[0,1] = 0.5
+        scale[1,0] = 0.5
+
+        # Construct frozen Wishart random variables
+        w = wishart(df, scale)
+
+        # Get the generated random variables from a known seed
+        rng = np.random.RandomState(248042)
+        w_rvs = wishart.rvs(df, scale, random_state=rng)
+        rng = np.random.RandomState(248042)
+        frozen_w_rvs = w.rvs(random_state=rng)
+
+        # Manually calculate what it should be, based on the Bartlett (1933)
+        # decomposition of a Wishart into D A A' D', where D is the Cholesky
+        # factorization of the scale matrix and A is the lower triangular matrix
+        # with the square root of chi^2 variates on the diagonal and N(0,1)
+        # variates in the lower triangle.
+        rng = np.random.RandomState(248042)
+        covariances = rng.normal(size=3)
+        variances = np.r_[
+            rng.chisquare(df),
+            rng.chisquare(df-1),
+            rng.chisquare(df-2),
+        ]**0.5
+
+        # Construct the lower-triangular A matrix
+        A = np.diag(variances)
+        A[np.tril_indices(dim, k=-1)] = covariances
+
+        # Wishart random variate
+        D = np.linalg.cholesky(scale)
+        DA = D.dot(A)
+        manual_w_rvs = np.dot(DA, DA.T)
+
+        # Test for equality
+        assert_allclose(w_rvs, manual_w_rvs)
+        assert_allclose(frozen_w_rvs, manual_w_rvs)
+
+    def test_1D_is_chisquared(self):
+        # The 1-dimensional Wishart with an identity scale matrix is just a
+        # chi-squared distribution.
+        # Test variance, mean, entropy, pdf
+        # Kolgomorov-Smirnov test for rvs
+        rng = np.random.default_rng(482974)
+
+        sn = 500
+        dim = 1
+        scale = np.eye(dim)
+
+        df_range = np.arange(1, 10, 2, dtype=float)
+        X = np.linspace(0.1,10,num=10)
+        for df in df_range:
+            w = wishart(df, scale)
+            c = chi2(df)
+
+            # Statistics
+            assert_allclose(w.var(), c.var())
+            assert_allclose(w.mean(), c.mean())
+            assert_allclose(w.entropy(), c.entropy())
+
+            # PDF
+            assert_allclose(w.pdf(X), c.pdf(X))
+
+            # rvs
+            rvs = w.rvs(size=sn, random_state=rng)
+            args = (df,)
+            alpha = 0.01
+            check_distribution_rvs('chi2', args, alpha, rvs)
+
+    def test_is_scaled_chisquared(self):
+        # The 2-dimensional Wishart with an arbitrary scale matrix can be
+        # transformed to a scaled chi-squared distribution.
+        # For :math:`S \sim W_p(V,n)` and :math:`\lambda \in \mathbb{R}^p` we have
+        # :math:`\lambda' S \lambda \sim \lambda' V \lambda \times \chi^2(n)`
+        rng = np.random.default_rng(482974)
+
+        sn = 500
+        df = 10
+        dim = 4
+        # Construct an arbitrary positive definite matrix
+        scale = np.diag(np.arange(4)+1)
+        scale[np.tril_indices(4, k=-1)] = np.arange(6)
+        scale = np.dot(scale.T, scale)
+        # Use :math:`\lambda = [1, \dots, 1]'`
+        lamda = np.ones((dim,1))
+        sigma_lamda = lamda.T.dot(scale).dot(lamda).squeeze()
+        w = wishart(df, sigma_lamda)
+        c = chi2(df, scale=sigma_lamda)
+
+        # Statistics
+        assert_allclose(w.var(), c.var())
+        assert_allclose(w.mean(), c.mean())
+        assert_allclose(w.entropy(), c.entropy())
+
+        # PDF
+        X = np.linspace(0.1,10,num=10)
+        assert_allclose(w.pdf(X), c.pdf(X))
+
+        # rvs
+        rvs = w.rvs(size=sn, random_state=rng)
+        args = (df,0,sigma_lamda)
+        alpha = 0.01
+        check_distribution_rvs('chi2', args, alpha, rvs)
+
+class TestMultinomial:
+    def test_logpmf(self):
+        vals1 = multinomial.logpmf((3,4), 7, (0.3, 0.7))
+        assert_allclose(vals1, -1.483270127243324, rtol=1e-8)
+
+        vals2 = multinomial.logpmf([3, 4], 0, [.3, .7])
+        assert vals2 == -np.inf
+
+        vals3 = multinomial.logpmf([0, 0], 0, [.3, .7])
+        assert vals3 == 0
+
+        vals4 = multinomial.logpmf([3, 4], 0, [-2, 3])
+        assert_allclose(vals4, np.nan, rtol=1e-8)
+
+    def test_reduces_binomial(self):
+        # test that the multinomial pmf reduces to the binomial pmf in the 2d
+        # case
+        val1 = multinomial.logpmf((3, 4), 7, (0.3, 0.7))
+        val2 = binom.logpmf(3, 7, 0.3)
+        assert_allclose(val1, val2, rtol=1e-8)
+
+        val1 = multinomial.pmf((6, 8), 14, (0.1, 0.9))
+        val2 = binom.pmf(6, 14, 0.1)
+        assert_allclose(val1, val2, rtol=1e-8)
+
+    def test_R(self):
+        # test against the values produced by this R code
+        # (https://stat.ethz.ch/R-manual/R-devel/library/stats/html/Multinom.html)
+        # X <- t(as.matrix(expand.grid(0:3, 0:3))); X <- X[, colSums(X) <= 3]
+        # X <- rbind(X, 3:3 - colSums(X)); dimnames(X) <- list(letters[1:3], NULL)
+        # X
+        # apply(X, 2, function(x) dmultinom(x, prob = c(1,2,5)))
+
+        n, p = 3, [1./8, 2./8, 5./8]
+        r_vals = {(0, 0, 3): 0.244140625, (1, 0, 2): 0.146484375,
+                  (2, 0, 1): 0.029296875, (3, 0, 0): 0.001953125,
+                  (0, 1, 2): 0.292968750, (1, 1, 1): 0.117187500,
+                  (2, 1, 0): 0.011718750, (0, 2, 1): 0.117187500,
+                  (1, 2, 0): 0.023437500, (0, 3, 0): 0.015625000}
+        for x in r_vals:
+            assert_allclose(multinomial.pmf(x, n, p), r_vals[x], atol=1e-14)
+
+    @pytest.mark.parametrize("n", [0, 3])
+    def test_rvs_np(self, n):
+        # test that .rvs agrees w/numpy when `p` is valid
+        rndm = np.random.RandomState(123)
+        sc_rvs = multinomial.rvs(n, [1/3.]*3, size=7, random_state=123)
+        np_rvs = rndm.multinomial(n, [1/3.]*3, size=7)
+        assert_equal(sc_rvs, np_rvs)
+
+        rndm = np.random.RandomState(123)
+        sc_rvs = multinomial.rvs(n, [1/5.]*5, size=7, random_state=123)
+        np_rvs = rndm.multinomial(n, [1/5.]*5, size=7)
+        assert_equal(sc_rvs, np_rvs)
+
+    def test_pmf(self):
+        vals0 = multinomial.pmf((5,), 5, (1,))
+        assert_allclose(vals0, 1, rtol=1e-8)
+
+        vals1 = multinomial.pmf((3,4), 7, (.3, .7))
+        assert_allclose(vals1, .22689449999999994, rtol=1e-8)
+
+        vals2 = multinomial.pmf([[[3,5],[0,8]], [[-1, 9], [1, 1]]], 8,
+                                (.1, .9))
+        assert_allclose(vals2, [[.03306744, .43046721], [0, 0]], rtol=1e-8)
+
+        x = np.empty((0,2), dtype=np.float64)
+        vals3 = multinomial.pmf(x, 4, (.3, .7))
+        assert_equal(vals3, np.empty([], dtype=np.float64))
+
+        vals4 = multinomial.pmf([1,2], 4, (.3, .7))
+        assert_allclose(vals4, 0, rtol=1e-8)
+
+        vals5 = multinomial.pmf([3, 3, 0], 6, [2/3.0, 1/3.0, 0])
+        assert_allclose(vals5, 0.219478737997, rtol=1e-8)
+
+        vals5 = multinomial.pmf([0, 0, 0], 0, [2/3.0, 1/3.0, 0])
+        assert vals5 == 1
+
+        vals6 = multinomial.pmf([2, 1, 0], 0, [2/3.0, 1/3.0, 0])
+        assert vals6 == 0
+
+    def test_pmf_broadcasting(self):
+        vals0 = multinomial.pmf([1, 2], 3, [[.1, .9], [.2, .8]])
+        assert_allclose(vals0, [.243, .384], rtol=1e-8)
+
+        vals1 = multinomial.pmf([1, 2], [3, 4], [.1, .9])
+        assert_allclose(vals1, [.243, 0], rtol=1e-8)
+
+        vals2 = multinomial.pmf([[[1, 2], [1, 1]]], 3, [.1, .9])
+        assert_allclose(vals2, [[.243, 0]], rtol=1e-8)
+
+        vals3 = multinomial.pmf([1, 2], [[[3], [4]]], [.1, .9])
+        assert_allclose(vals3, [[[.243], [0]]], rtol=1e-8)
+
+        vals4 = multinomial.pmf([[1, 2], [1,1]], [[[[3]]]], [.1, .9])
+        assert_allclose(vals4, [[[[.243, 0]]]], rtol=1e-8)
+
+    @pytest.mark.parametrize("n", [0, 5])
+    def test_cov(self, n):
+        cov1 = multinomial.cov(n, (.2, .3, .5))
+        cov2 = [[n*.2*.8, -n*.2*.3, -n*.2*.5],
+                [-n*.3*.2, n*.3*.7, -n*.3*.5],
+                [-n*.5*.2, -n*.5*.3, n*.5*.5]]
+        assert_allclose(cov1, cov2, rtol=1e-8)
+
+    def test_cov_broadcasting(self):
+        cov1 = multinomial.cov(5, [[.1, .9], [.2, .8]])
+        cov2 = [[[.45, -.45],[-.45, .45]], [[.8, -.8], [-.8, .8]]]
+        assert_allclose(cov1, cov2, rtol=1e-8)
+
+        cov3 = multinomial.cov([4, 5], [.1, .9])
+        cov4 = [[[.36, -.36], [-.36, .36]], [[.45, -.45], [-.45, .45]]]
+        assert_allclose(cov3, cov4, rtol=1e-8)
+
+        cov5 = multinomial.cov([4, 5], [[.3, .7], [.4, .6]])
+        cov6 = [[[4*.3*.7, -4*.3*.7], [-4*.3*.7, 4*.3*.7]],
+                [[5*.4*.6, -5*.4*.6], [-5*.4*.6, 5*.4*.6]]]
+        assert_allclose(cov5, cov6, rtol=1e-8)
+
+    @pytest.mark.parametrize("n", [0, 2])
+    def test_entropy(self, n):
+        # this is equivalent to a binomial distribution with n=2, so the
+        # entropy .77899774929 is easily computed "by hand"
+        ent0 = multinomial.entropy(n, [.2, .8])
+        assert_allclose(ent0, binom.entropy(n, .2), rtol=1e-8)
+
+    def test_entropy_broadcasting(self):
+        ent0 = multinomial.entropy([2, 3], [.2, .8])
+        assert_allclose(ent0, [binom.entropy(2, .2), binom.entropy(3, .2)],
+                        rtol=1e-8)
+
+        ent1 = multinomial.entropy([7, 8], [[.3, .7], [.4, .6]])
+        assert_allclose(ent1, [binom.entropy(7, .3), binom.entropy(8, .4)],
+                        rtol=1e-8)
+
+        ent2 = multinomial.entropy([[7], [8]], [[.3, .7], [.4, .6]])
+        assert_allclose(ent2,
+                        [[binom.entropy(7, .3), binom.entropy(7, .4)],
+                         [binom.entropy(8, .3), binom.entropy(8, .4)]],
+                        rtol=1e-8)
+
+    @pytest.mark.parametrize("n", [0, 5])
+    def test_mean(self, n):
+        mean1 = multinomial.mean(n, [.2, .8])
+        assert_allclose(mean1, [n*.2, n*.8], rtol=1e-8)
+
+    def test_mean_broadcasting(self):
+        mean1 = multinomial.mean([5, 6], [.2, .8])
+        assert_allclose(mean1, [[5*.2, 5*.8], [6*.2, 6*.8]], rtol=1e-8)
+
+    def test_frozen(self):
+        # The frozen distribution should agree with the regular one
+        n = 12
+        pvals = (.1, .2, .3, .4)
+        x = [[0,0,0,12],[0,0,1,11],[0,1,1,10],[1,1,1,9],[1,1,2,8]]
+        x = np.asarray(x, dtype=np.float64)
+        mn_frozen = multinomial(n, pvals)
+        assert_allclose(mn_frozen.pmf(x), multinomial.pmf(x, n, pvals))
+        assert_allclose(mn_frozen.logpmf(x), multinomial.logpmf(x, n, pvals))
+        assert_allclose(mn_frozen.entropy(), multinomial.entropy(n, pvals))
+
+    def test_gh_11860(self):
+        # gh-11860 reported cases in which the adjustments made by multinomial
+        # to the last element of `p` can cause `nan`s even when the input is
+        # essentially valid. Check that a pathological case returns a finite,
+        # nonzero result. (This would fail in main before the PR.)
+        n = 88
+        rng = np.random.default_rng(8879715917488330089)
+        p = rng.random(n)
+        p[-1] = 1e-30
+        p /= np.sum(p)
+        x = np.ones(n)
+        logpmf = multinomial.logpmf(x, n, p)
+        assert np.isfinite(logpmf)
+
+    @pytest.mark.parametrize('dtype', [np.float32, np.float64])
+    def test_gh_22565(self, dtype):
+        # Same issue as gh-11860 above, essentially, but the original
+        # fix didn't completely solve the problem.
+        n = 19
+        p = np.asarray([0.2, 0.2, 0.2, 0.2, 0.2], dtype=dtype)
+        res1 = multinomial.pmf(x=[1, 2, 5, 7, 4], n=n, p=p)
+        res2 = multinomial.pmf(x=[1, 2, 4, 5, 7], n=n, p=p)
+        np.testing.assert_allclose(res1, res2, rtol=1e-15)
+
+    @pytest.mark.parametrize('psum', [0.75, 1.25])
+    def test_gh_22585(self, psum):
+        # gh-22585 warned that beginning in SciPy 1.18, rows of p that did not sum to
+        # 1.0 would produce NaNs. Check that this has been implemented.
+        rng = np.random.default_rng(8879715917488330089)
+        d, n = 5, 19  # arbitrary
+        p0 = rng.random(d)
+        p = p0 / np.sum(p0)
+        p_ = p * psum
+        x = multinomial.rvs(n=n, p=p)
+
+        assert np.all(np.isfinite(x))
+        with pytest.raises(ValueError, match="`multinomial.rvs` requires..."):
+            multinomial.rvs(n=n, p=p_)
+
+        assert np.isfinite(multinomial.pmf(x, n=n, p=p))
+        assert np.isnan(multinomial.pmf(x, n=n, p=p_))
+
+        assert np.isfinite(multinomial.pmf(x, n=n, p=p))
+        assert np.isnan(multinomial.pmf(x, n=n, p=p_))
+
+        assert np.isfinite(multinomial.entropy(n=n, p=p))
+        assert np.isnan(multinomial.entropy(n=n, p=p_))
+
+        assert np.all(np.isfinite(multinomial.cov(n=n, p=p)))
+        assert np.all(np.isnan(multinomial.cov(n=n, p=p_)))
+
+
+class TestInvwishart:
+    def test_frozen(self):
+        # Test that the frozen and non-frozen inverse Wishart gives the same
+        # answers
+
+        # Construct an arbitrary positive definite scale matrix
+        dim = 4
+        scale = np.diag(np.arange(dim)+1)
+        scale[np.tril_indices(dim, k=-1)] = np.arange(dim*(dim-1)/2)
+        scale = np.dot(scale.T, scale)
+
+        # Construct a collection of positive definite matrices to test the PDF
+        X = []
+        for i in range(5):
+            x = np.diag(np.arange(dim)+(i+1)**2)
+            x[np.tril_indices(dim, k=-1)] = np.arange(dim*(dim-1)/2)
+            x = np.dot(x.T, x)
+            X.append(x)
+        X = np.array(X).T
+
+        # Construct a 1D and 2D set of parameters
+        parameters = [
+            (10, 1, np.linspace(0.1, 10, 5)),  # 1D case
+            (10, scale, X)
+        ]
+
+        for (df, scale, x) in parameters:
+            iw = invwishart(df, scale)
+            assert_equal(iw.var(), invwishart.var(df, scale))
+            assert_equal(iw.mean(), invwishart.mean(df, scale))
+            assert_equal(iw.mode(), invwishart.mode(df, scale))
+            assert_allclose(iw.pdf(x), invwishart.pdf(x, df, scale))
+
+    def test_1D_is_invgamma(self):
+        # The 1-dimensional inverse Wishart with an identity scale matrix is
+        # just an inverse gamma distribution.
+        # Test variance, mean, pdf, entropy
+        # Kolgomorov-Smirnov test for rvs
+        rng = np.random.RandomState(482974)
+
+        sn = 500
+        dim = 1
+        scale = np.eye(dim)
+
+        df_range = np.arange(5, 20, 2, dtype=float)
+        X = np.linspace(0.1,10,num=10)
+        for df in df_range:
+            iw = invwishart(df, scale)
+            ig = invgamma(df/2, scale=1./2)
+
+            # Statistics
+            assert_allclose(iw.var(), ig.var())
+            assert_allclose(iw.mean(), ig.mean())
+
+            # PDF
+            assert_allclose(iw.pdf(X), ig.pdf(X))
+
+            # rvs
+            rvs = iw.rvs(size=sn, random_state=rng)
+            args = (df/2, 0, 1./2)
+            alpha = 0.01
+            check_distribution_rvs('invgamma', args, alpha, rvs)
+
+            # entropy
+            assert_allclose(iw.entropy(), ig.entropy())
+
+    def test_invwishart_2D_rvs(self):
+        dim = 3
+        df = 10
+
+        # Construct a simple non-diagonal positive definite matrix
+        scale = np.eye(dim)
+        scale[0,1] = 0.5
+        scale[1,0] = 0.5
+
+        # Construct frozen inverse-Wishart random variables
+        iw = invwishart(df, scale)
+
+        # Get the generated random variables from a known seed
+        rng = np.random.RandomState(608072)
+        iw_rvs = invwishart.rvs(df, scale, random_state=rng)
+        rng = np.random.RandomState(608072)
+        frozen_iw_rvs = iw.rvs(random_state=rng)
+
+        # Manually calculate what it should be, based on the decomposition in
+        # https://arxiv.org/abs/2310.15884 of an invers-Wishart into L L',
+        # where L A = D, D is the Cholesky factorization of the scale matrix,
+        # and A is the lower triangular matrix with the square root of chi^2
+        # variates on the diagonal and N(0,1) variates in the lower triangle.
+        # the diagonal chi^2 variates in this A are reversed compared to those
+        # in the Bartlett decomposition A for Wishart rvs.
+        rng = np.random.RandomState(608072)
+        covariances = rng.normal(size=3)
+        variances = np.r_[
+            rng.chisquare(df-2),
+            rng.chisquare(df-1),
+            rng.chisquare(df),
+        ]**0.5
+
+        # Construct the lower-triangular A matrix
+        A = np.diag(variances)
+        A[np.tril_indices(dim, k=-1)] = covariances
+
+        # inverse-Wishart random variate
+        D = np.linalg.cholesky(scale)
+        L = np.linalg.solve(A.T, D.T).T
+        manual_iw_rvs = np.dot(L, L.T)
+
+        # Test for equality
+        assert_allclose(iw_rvs, manual_iw_rvs)
+        assert_allclose(frozen_iw_rvs, manual_iw_rvs)
+
+    def test_sample_mean(self):
+        """Test that sample mean consistent with known mean."""
+        # Construct an arbitrary positive definite scale matrix
+        df = 10
+        sample_size = 20_000
+        for dim in [1, 5]:
+            scale = np.diag(np.arange(dim) + 1)
+            scale[np.tril_indices(dim, k=-1)] = np.arange(dim * (dim - 1) / 2)
+            scale = np.dot(scale.T, scale)
+
+            dist = invwishart(df, scale)
+            Xmean_exp = dist.mean()
+            Xvar_exp = dist.var()
+            Xmean_std = (Xvar_exp / sample_size)**0.5  # asymptotic SE of mean estimate
+
+            X = dist.rvs(size=sample_size, random_state=1234)
+            Xmean_est = X.mean(axis=0)
+
+            ntests = dim*(dim + 1)//2
+            fail_rate = 0.01 / ntests  # correct for multiple tests
+            max_diff = norm.ppf(1 - fail_rate / 2)
+            assert np.allclose(
+                (Xmean_est - Xmean_exp) / Xmean_std,
+                0,
+                atol=max_diff,
+            )
+
+    def test_logpdf_4x4(self):
+        """Regression test for gh-8844."""
+        X = np.array([[2, 1, 0, 0.5],
+                      [1, 2, 0.5, 0.5],
+                      [0, 0.5, 3, 1],
+                      [0.5, 0.5, 1, 2]])
+        Psi = np.array([[9, 7, 3, 1],
+                        [7, 9, 5, 1],
+                        [3, 5, 8, 2],
+                        [1, 1, 2, 9]])
+        nu = 6
+        prob = invwishart.logpdf(X, nu, Psi)
+        # Explicit calculation from the formula on wikipedia.
+        p = X.shape[0]
+        sig, logdetX = np.linalg.slogdet(X)
+        sig, logdetPsi = np.linalg.slogdet(Psi)
+        M = np.linalg.solve(X, Psi)
+        expected = ((nu/2)*logdetPsi
+                    - (nu*p/2)*np.log(2)
+                    - multigammaln(nu/2, p)
+                    - (nu + p + 1)/2*logdetX
+                    - 0.5*M.trace())
+        assert_allclose(prob, expected)
+
+
+class TestSpecialOrthoGroup:
+    def test_reproducibility(self):
+        x = special_ortho_group.rvs(3, random_state=np.random.default_rng(514))
+        expected = np.array([[-0.93200988, 0.01533561, -0.36210826],
+                             [0.35742128, 0.20446501, -0.91128705],
+                             [0.06006333, -0.97875374, -0.19604469]])
+        assert_array_almost_equal(x, expected)
+
+    def test_invalid_dim(self):
+        assert_raises(ValueError, special_ortho_group.rvs, None)
+        assert_raises(ValueError, special_ortho_group.rvs, (2, 2))
+        assert_raises(ValueError, special_ortho_group.rvs, -1)
+        assert_raises(ValueError, special_ortho_group.rvs, 2.5)
+
+    def test_frozen_matrix(self):
+        dim = 7
+        frozen = special_ortho_group(dim)
+
+        rvs1 = frozen.rvs(random_state=1234)
+        rvs2 = special_ortho_group.rvs(dim, random_state=1234)
+
+        assert_equal(rvs1, rvs2)
+
+    def test_det_and_ortho(self):
+        xs = [special_ortho_group.rvs(dim)
+              for dim in range(2,12)
+              for i in range(3)]
+
+        # Test that determinants are always +1
+        dets = [np.linalg.det(x) for x in xs]
+        assert_allclose(dets, [1.]*30, rtol=1e-13)
+
+        # Test that these are orthogonal matrices
+        for x in xs:
+            assert_array_almost_equal(np.dot(x, x.T),
+                                      np.eye(x.shape[0]))
+
+    def test_haar(self):
+        # Test that the distribution is constant under rotation
+        # Every column should have the same distribution
+        # Additionally, the distribution should be invariant under another rotation
+
+        # Generate samples
+        dim = 5
+        samples = 1000  # Not too many, or the test takes too long
+        ks_prob = .05
+        xs = special_ortho_group.rvs(
+            dim, size=samples, random_state=np.random.default_rng(513)
+        )
+
+        # Dot a few rows (0, 1, 2) with unit vectors (0, 2, 4, 3),
+        #   effectively picking off entries in the matrices of xs.
+        #   These projections should all have the same distribution,
+        #     establishing rotational invariance. We use the two-sided
+        #     KS test to confirm this.
+        #   We could instead test that angles between random vectors
+        #     are uniformly distributed, but the below is sufficient.
+        #   It is not feasible to consider all pairs, so pick a few.
+        els = ((0,0), (0,2), (1,4), (2,3))
+        #proj = {(er, ec): [x[er][ec] for x in xs] for er, ec in els}
+        proj = {(er, ec): sorted([x[er][ec] for x in xs]) for er, ec in els}
+        pairs = [(e0, e1) for e0 in els for e1 in els if e0 > e1]
+        ks_tests = [ks_2samp(proj[p0], proj[p1])[1] for (p0, p1) in pairs]
+        assert_array_less([ks_prob]*len(pairs), ks_tests)
+
+    def test_one_by_one(self):
+        # Test that the distribution is a delta function at the identity matrix
+        # when dim=1
+        assert_allclose(special_ortho_group.rvs(1, size=1000), 1, rtol=1e-13)
+
+    def test_zero_by_zero(self):
+        assert_equal(special_ortho_group.rvs(0, size=4).shape, (4, 0, 0))
+
+
+class TestOrthoGroup:
+    def test_reproducibility(self):
+        seed = 514
+        rng = np.random.RandomState(seed)
+        x = ortho_group.rvs(3, random_state=rng)
+        x2 = ortho_group.rvs(3, random_state=seed)
+        # Note this matrix has det -1, distinguishing O(N) from SO(N)
+        assert_almost_equal(np.linalg.det(x), -1)
+        expected = np.array([[0.381686, -0.090374, 0.919863],
+                             [0.905794, -0.161537, -0.391718],
+                             [-0.183993, -0.98272, -0.020204]])
+        assert_array_almost_equal(x, expected)
+        assert_array_almost_equal(x2, expected)
+
+    def test_invalid_dim(self):
+        assert_raises(ValueError, ortho_group.rvs, None)
+        assert_raises(ValueError, ortho_group.rvs, (2, 2))
+        assert_raises(ValueError, ortho_group.rvs, -1)
+        assert_raises(ValueError, ortho_group.rvs, 2.5)
+
+    def test_frozen_matrix(self):
+        dim = 7
+        frozen = ortho_group(dim)
+        frozen_seed = ortho_group(dim, seed=1234)
+
+        rvs1 = frozen.rvs(random_state=1234)
+        rvs2 = ortho_group.rvs(dim, random_state=1234)
+        rvs3 = frozen_seed.rvs(size=1)
+
+        assert_equal(rvs1, rvs2)
+        assert_equal(rvs1, rvs3)
+
+    def test_det_and_ortho(self):
+        xs = [[ortho_group.rvs(dim)
+               for i in range(10)]
+              for dim in range(2,12)]
+
+        # Test that abs determinants are always +1
+        dets = np.array([[np.linalg.det(x) for x in xx] for xx in xs])
+        assert_allclose(np.fabs(dets), np.ones(dets.shape), rtol=1e-13)
+
+        # Test that these are orthogonal matrices
+        for xx in xs:
+            for x in xx:
+                assert_array_almost_equal(np.dot(x, x.T),
+                                          np.eye(x.shape[0]))
+
+    @pytest.mark.parametrize("dim", [2, 5, 10, 20])
+    def test_det_distribution_gh18272(self, dim):
+        # Test that positive and negative determinants are equally likely.
+        rng = np.random.default_rng(6796248956179332344)
+        dist = ortho_group(dim=dim)
+        rvs = dist.rvs(size=5000, random_state=rng)
+        dets = scipy.linalg.det(rvs)
+        k = np.sum(dets > 0)
+        n = len(dets)
+        res = stats.binomtest(k, n)
+        low, high = res.proportion_ci(confidence_level=0.95)
+        assert low < 0.5 < high
+
+    def test_haar(self):
+        # Test that the distribution is constant under rotation
+        # Every column should have the same distribution
+        # Additionally, the distribution should be invariant under another rotation
+
+        # Generate samples
+        dim = 5
+        samples = 1000  # Not too many, or the test takes too long
+        ks_prob = .05
+        rng = np.random.RandomState(518)  # Note that the test is sensitive to seed too
+        xs = ortho_group.rvs(dim, size=samples, random_state=rng)
+
+        # Dot a few rows (0, 1, 2) with unit vectors (0, 2, 4, 3),
+        #   effectively picking off entries in the matrices of xs.
+        #   These projections should all have the same distribution,
+        #     establishing rotational invariance. We use the two-sided
+        #     KS test to confirm this.
+        #   We could instead test that angles between random vectors
+        #     are uniformly distributed, but the below is sufficient.
+        #   It is not feasible to consider all pairs, so pick a few.
+        els = ((0,0), (0,2), (1,4), (2,3))
+        #proj = {(er, ec): [x[er][ec] for x in xs] for er, ec in els}
+        proj = {(er, ec): sorted([x[er][ec] for x in xs]) for er, ec in els}
+        pairs = [(e0, e1) for e0 in els for e1 in els if e0 > e1]
+        ks_tests = [ks_2samp(proj[p0], proj[p1])[1] for (p0, p1) in pairs]
+        assert_array_less([ks_prob]*len(pairs), ks_tests)
+
+    def test_one_by_one(self):
+        # Test that the 1x1 distribution gives ±1 with equal probability.
+        dim = 1
+        xs = ortho_group.rvs(dim, size=5000, random_state=np.random.default_rng(514))
+        assert_allclose(np.abs(xs), 1, rtol=1e-13)
+        k = np.sum(xs > 0)
+        n = len(xs)
+        res = stats.binomtest(k, n)
+        low, high = res.proportion_ci(confidence_level=0.95)
+        assert low < 0.5 < high
+
+    def test_zero_by_zero(self):
+        assert_equal(special_ortho_group.rvs(0, size=4).shape, (4, 0, 0))
+
+    @pytest.mark.slow
+    def test_pairwise_distances(self):
+        # Test that the distribution of pairwise distances is close to correct.
+        rng = np.random.RandomState(514)
+
+        def random_ortho(dim, random_state):
+            u, _s, v = np.linalg.svd(random_state.normal(size=(dim, dim)))
+            return np.dot(u, v)
+
+        for dim in range(2, 6):
+            def generate_test_statistics(rvs, N=1000, eps=1e-10):
+                stats = np.array([
+                    np.sum((rvs(dim=dim, random_state=rng) -
+                            rvs(dim=dim, random_state=rng))**2)
+                    for _ in range(N)
+                ])
+                # Add a bit of noise to account for numeric accuracy.
+                stats += rng.uniform(-eps, eps, size=stats.shape)
+                return stats
+
+            expected = generate_test_statistics(random_ortho)
+            actual = generate_test_statistics(scipy.stats.ortho_group.rvs)
+
+            _D, p = scipy.stats.ks_2samp(expected, actual)
+
+            assert_array_less(.05, p)
+
+
+class TestRandomCorrelation:
+    def test_reproducibility(self):
+        rng = np.random.RandomState(514)
+        eigs = (.5, .8, 1.2, 1.5)
+        x = random_correlation.rvs(eigs, random_state=rng)
+        x2 = random_correlation.rvs(eigs, random_state=514)
+        expected = np.array([[1., -0.184851, 0.109017, -0.227494],
+                             [-0.184851, 1., 0.231236, 0.326669],
+                             [0.109017, 0.231236, 1., -0.178912],
+                             [-0.227494, 0.326669, -0.178912, 1.]])
+        assert_array_almost_equal(x, expected)
+        assert_array_almost_equal(x2, expected)
+
+    def test_invalid_eigs(self):
+        assert_raises(ValueError, random_correlation.rvs, None)
+        assert_raises(ValueError, random_correlation.rvs, 'test')
+        assert_raises(ValueError, random_correlation.rvs, 2.5)
+        assert_raises(ValueError, random_correlation.rvs, [2.5])
+        assert_raises(ValueError, random_correlation.rvs, [[1,2],[3,4]])
+        assert_raises(ValueError, random_correlation.rvs, [2.5, -.5])
+        assert_raises(ValueError, random_correlation.rvs, [1, 2, .1])
+
+    def test_frozen_matrix(self):
+        eigs = (.5, .8, 1.2, 1.5)
+        frozen = random_correlation(eigs)
+        frozen_seed = random_correlation(eigs, seed=514)
+
+        rvs1 = random_correlation.rvs(eigs, random_state=514)
+        rvs2 = frozen.rvs(random_state=514)
+        rvs3 = frozen_seed.rvs()
+
+        assert_equal(rvs1, rvs2)
+        assert_equal(rvs1, rvs3)
+
+    def test_definition(self):
+        # Test the definition of a correlation matrix in several dimensions:
+        #
+        # 1. Det is product of eigenvalues (and positive by construction
+        #    in examples)
+        # 2. 1's on diagonal
+        # 3. Matrix is symmetric
+
+        def norm(i, e):
+            return i*e/sum(e)
+
+        rng = np.random.RandomState(123)
+
+        eigs = [norm(i, rng.uniform(size=i)) for i in range(2, 6)]
+        eigs.append([4,0,0,0])
+
+        ones = [[1.]*len(e) for e in eigs]
+        xs = [random_correlation.rvs(e, random_state=rng) for e in eigs]
+
+        # Test that determinants are products of eigenvalues
+        #   These are positive by construction
+        # Could also test that the eigenvalues themselves are correct,
+        #   but this seems sufficient.
+        dets = [np.fabs(np.linalg.det(x)) for x in xs]
+        dets_known = [np.prod(e) for e in eigs]
+        assert_allclose(dets, dets_known, rtol=1e-13, atol=1e-13)
+
+        # Test for 1's on the diagonal
+        diags = [np.diag(x) for x in xs]
+        for a, b in zip(diags, ones):
+            assert_allclose(a, b, rtol=1e-13)
+
+        # Correlation matrices are symmetric
+        for x in xs:
+            assert_allclose(x, x.T, rtol=1e-13)
+
+    def test_to_corr(self):
+        # Check some corner cases in to_corr
+
+        # ajj == 1
+        m = np.array([[0.1, 0], [0, 1]], dtype=float)
+        m = random_correlation._to_corr(m)
+        assert_allclose(m, np.array([[1, 0], [0, 0.1]]))
+
+        # Floating point overflow; fails to compute the correct
+        # rotation, but should still produce some valid rotation
+        # rather than infs/nans
+        with np.errstate(over='ignore'):
+            g = np.array([[0, 1], [-1, 0]])
+
+            m0 = np.array([[1e300, 0], [0, np.nextafter(1, 0)]], dtype=float)
+            m = random_correlation._to_corr(m0.copy())
+            assert_allclose(m, g.T.dot(m0).dot(g))
+
+            m0 = np.array([[0.9, 1e300], [1e300, 1.1]], dtype=float)
+            m = random_correlation._to_corr(m0.copy())
+            assert_allclose(m, g.T.dot(m0).dot(g))
+
+        # Zero discriminant; should set the first diag entry to 1
+        m0 = np.array([[2, 1], [1, 2]], dtype=float)
+        m = random_correlation._to_corr(m0.copy())
+        assert_allclose(m[0,0], 1)
+
+        # Slightly negative discriminant; should be approx correct still
+        m0 = np.array([[2 + 1e-7, 1], [1, 2]], dtype=float)
+        m = random_correlation._to_corr(m0.copy())
+        assert_allclose(m[0,0], 1)
+
+
+class TestUniformDirection:
+    @pytest.mark.parametrize("dim", [1, 3])
+    @pytest.mark.parametrize("size", [None, 1, 5, (5, 4)])
+    def test_samples(self, dim, size):
+        # test that samples have correct shape and norm 1
+        rng = np.random.default_rng(2777937887058094419)
+        uniform_direction_dist = uniform_direction(dim, seed=rng)
+        samples = uniform_direction_dist.rvs(size)
+        mean, cov = np.zeros(dim), np.eye(dim)
+        expected_shape = rng.multivariate_normal(mean, cov, size=size).shape
+        assert samples.shape == expected_shape
+        norms = np.linalg.norm(samples, axis=-1)
+        assert_allclose(norms, 1.)
+
+    @pytest.mark.parametrize("dim", [None, 0, (2, 2), 2.5])
+    def test_invalid_dim(self, dim):
+        message = ("Dimension of vector must be specified, "
+                   "and must be an integer greater than 0.")
+        with pytest.raises(ValueError, match=message):
+            uniform_direction.rvs(dim)
+
+    def test_frozen_distribution(self):
+        dim = 5
+        frozen = uniform_direction(dim)
+        frozen_seed = uniform_direction(dim, seed=514)
+
+        rvs1 = frozen.rvs(random_state=514)
+        rvs2 = uniform_direction.rvs(dim, random_state=514)
+        rvs3 = frozen_seed.rvs()
+
+        assert_equal(rvs1, rvs2)
+        assert_equal(rvs1, rvs3)
+
+    @pytest.mark.parametrize("dim", [2, 5, 8])
+    def test_uniform(self, dim):
+        rng = np.random.default_rng(1036978481269651776)
+        spherical_dist = uniform_direction(dim, seed=rng)
+        # generate random, orthogonal vectors
+        v1, v2 = spherical_dist.rvs(size=2)
+        v2 -= v1 @ v2 * v1
+        v2 /= np.linalg.norm(v2)
+        assert_allclose(v1 @ v2, 0, atol=1e-14)  # orthogonal
+        # generate data and project onto orthogonal vectors
+        samples = spherical_dist.rvs(size=10000)
+        s1 = samples @ v1
+        s2 = samples @ v2
+        angles = np.arctan2(s1, s2)
+        # test that angles follow a uniform distribution
+        # normalize angles to range [0, 1]
+        angles += np.pi
+        angles /= 2*np.pi
+        # perform KS test
+        uniform_dist = uniform()
+        kstest_result = kstest(angles, uniform_dist.cdf)
+        assert kstest_result.pvalue > 0.05
+
+
+class TestUnitaryGroup:
+    def test_reproducibility(self):
+        rng = np.random.RandomState(514)
+        x = unitary_group.rvs(3, random_state=rng)
+        x2 = unitary_group.rvs(3, random_state=514)
+
+        expected = np.array(
+            [[0.308771+0.360312j, 0.044021+0.622082j, 0.160327+0.600173j],
+             [0.732757+0.297107j, 0.076692-0.4614j, -0.394349+0.022613j],
+             [-0.148844+0.357037j, -0.284602-0.557949j, 0.607051+0.299257j]]
+        )
+
+        assert_array_almost_equal(x, expected)
+        assert_array_almost_equal(x2, expected)
+
+    def test_invalid_dim(self):
+        assert_raises(ValueError, unitary_group.rvs, None)
+        assert_raises(ValueError, unitary_group.rvs, (2, 2))
+        assert_raises(ValueError, unitary_group.rvs, -1)
+        assert_raises(ValueError, unitary_group.rvs, 2.5)
+
+    def test_frozen_matrix(self):
+        dim = 7
+        frozen = unitary_group(dim)
+        frozen_seed = unitary_group(dim, seed=514)
+
+        rvs1 = frozen.rvs(random_state=514)
+        rvs2 = unitary_group.rvs(dim, random_state=514)
+        rvs3 = frozen_seed.rvs(size=1)
+
+        assert_equal(rvs1, rvs2)
+        assert_equal(rvs1, rvs3)
+
+    def test_unitarity(self):
+        xs = [unitary_group.rvs(dim)
+              for dim in range(2,12)
+              for i in range(3)]
+
+        # Test that these are unitary matrices
+        for x in xs:
+            assert_allclose(np.dot(x, x.conj().T), np.eye(x.shape[0]), atol=1e-15)
+
+    def test_haar(self):
+        # Test that the eigenvalues, which lie on the unit circle in
+        # the complex plane, are uncorrelated.
+
+        # Generate samples
+        for dim in (1, 5):
+            samples = 1000  # Not too many, or the test takes too long
+            # Note that the test is sensitive to seed too
+            xs = unitary_group.rvs(
+                dim, size=samples, random_state=np.random.default_rng(514)
+            )
+
+            # The angles "x" of the eigenvalues should be uniformly distributed
+            # Overall this seems to be a necessary but weak test of the distribution.
+            eigs = np.vstack([scipy.linalg.eigvals(x) for x in xs])
+            x = np.arctan2(eigs.imag, eigs.real)
+            res = kstest(x.ravel(), uniform(-np.pi, 2*np.pi).cdf)
+            assert_(res.pvalue > 0.05)
+
+    def test_zero_by_zero(self):
+        assert_equal(unitary_group.rvs(0, size=4).shape, (4, 0, 0))
+
+
+class TestMultivariateT:
+
+    # These tests were created by running vpa(mvtpdf(...)) in MATLAB. The
+    # function takes no `mu` parameter. The tests were run as
+    #
+    # >> ans = vpa(mvtpdf(x - mu, shape, df));
+    #
+    PDF_TESTS = [(
+        # x
+        [
+            [1, 2],
+            [4, 1],
+            [2, 1],
+            [2, 4],
+            [1, 4],
+            [4, 1],
+            [3, 2],
+            [3, 3],
+            [4, 4],
+            [5, 1],
+        ],
+        # loc
+        [0, 0],
+        # shape
+        [
+            [1, 0],
+            [0, 1]
+        ],
+        # df
+        4,
+        # ans
+        [
+            0.013972450422333741737457302178882,
+            0.0010998721906793330026219646100571,
+            0.013972450422333741737457302178882,
+            0.00073682844024025606101402363634634,
+            0.0010998721906793330026219646100571,
+            0.0010998721906793330026219646100571,
+            0.0020732579600816823488240725481546,
+            0.00095660371505271429414668515889275,
+            0.00021831953784896498569831346792114,
+            0.00037725616140301147447000396084604
+        ]
+
+    ), (
+        # x
+        [
+            [0.9718, 0.1298, 0.8134],
+            [0.4922, 0.5522, 0.7185],
+            [0.3010, 0.1491, 0.5008],
+            [0.5971, 0.2585, 0.8940],
+            [0.5434, 0.5287, 0.9507],
+        ],
+        # loc
+        [-1, 1, 50],
+        # shape
+        [
+            [1.0000, 0.5000, 0.2500],
+            [0.5000, 1.0000, -0.1000],
+            [0.2500, -0.1000, 1.0000],
+        ],
+        # df
+        8,
+        # ans
+        [
+            0.00000000000000069609279697467772867405511133763,
+            0.00000000000000073700739052207366474839369535934,
+            0.00000000000000069522909962669171512174435447027,
+            0.00000000000000074212293557998314091880208889767,
+            0.00000000000000077039675154022118593323030449058,
+        ]
+    )]
+
+    @pytest.mark.parametrize("x, loc, shape, df, ans", PDF_TESTS)
+    def test_pdf_correctness(self, x, loc, shape, df, ans):
+        dist = multivariate_t(loc, shape, df, seed=0)
+        val = dist.pdf(x)
+        assert_array_almost_equal(val, ans)
+
+    @pytest.mark.parametrize("x, loc, shape, df, ans", PDF_TESTS)
+    def test_logpdf_correct(self, x, loc, shape, df, ans):
+        dist = multivariate_t(loc, shape, df, seed=0)
+        val1 = dist.pdf(x)
+        val2 = dist.logpdf(x)
+        assert_array_almost_equal(np.log(val1), val2)
+
+    # https://github.com/scipy/scipy/issues/10042#issuecomment-576795195
+    def test_mvt_with_df_one_is_cauchy(self):
+        x = [9, 7, 4, 1, -3, 9, 0, -3, -1, 3]
+        val = multivariate_t.pdf(x, df=1)
+        ans = cauchy.pdf(x)
+        assert_array_almost_equal(val, ans)
+
+    def test_mvt_with_high_df_is_approx_normal(self):
+        # `normaltest` returns the chi-squared statistic and the associated
+        # p-value. The null hypothesis is that `x` came from a normal
+        # distribution, so a low p-value represents rejecting the null, i.e.
+        # that it is unlikely that `x` came a normal distribution.
+        P_VAL_MIN = 0.1
+
+        dist = multivariate_t(0, 1, df=100000, seed=1)
+        samples = dist.rvs(size=100000)
+        _, p = normaltest(samples)
+        assert (p > P_VAL_MIN)
+
+        dist = multivariate_t([-2, 3], [[10, -1], [-1, 10]], df=100000,
+                              seed=42)
+        samples = dist.rvs(size=100000)
+        _, p = normaltest(samples)
+        assert ((p > P_VAL_MIN).all())
+
+    @pytest.mark.thread_unsafe(reason="uses mocking")
+    @patch('scipy.stats.multivariate_normal._logpdf')
+    def test_mvt_with_inf_df_calls_normal(self, mock):
+        dist = multivariate_t(0, 1, df=np.inf, seed=7)
+        assert isinstance(dist, multivariate_normal_frozen)
+        multivariate_t.pdf(0, df=np.inf)
+        assert mock.call_count == 1
+        multivariate_t.logpdf(0, df=np.inf)
+        assert mock.call_count == 2
+
+    def test_shape_correctness(self):
+        # pdf and logpdf should return scalar when the
+        # number of samples in x is one.
+        dim = 4
+        loc = np.zeros(dim)
+        shape = np.eye(dim)
+        df = 4.5
+        x = np.zeros(dim)
+        res = multivariate_t(loc, shape, df).pdf(x)
+        assert np.isscalar(res)
+        res = multivariate_t(loc, shape, df).logpdf(x)
+        assert np.isscalar(res)
+
+        # pdf() and logpdf() should return probabilities of shape
+        # (n_samples,) when x has n_samples.
+        n_samples = 7
+        rng = np.random.default_rng(2767231913)
+        x = rng.random((n_samples, dim))
+        res = multivariate_t(loc, shape, df).pdf(x)
+        assert (res.shape == (n_samples,))
+        res = multivariate_t(loc, shape, df).logpdf(x)
+        assert (res.shape == (n_samples,))
+
+        # rvs() should return scalar unless a size argument is applied.
+        res = multivariate_t(np.zeros(1), np.eye(1), 1).rvs()
+        assert np.isscalar(res)
+
+        # rvs() should return vector of shape (size,) if size argument
+        # is applied.
+        size = 7
+        res = multivariate_t(np.zeros(1), np.eye(1), 1).rvs(size=size)
+        assert (res.shape == (size,))
+
+    def test_default_arguments(self):
+        dist = multivariate_t()
+        assert_equal(dist.loc, [0])
+        assert_equal(dist.shape, [[1]])
+        assert (dist.df == 1)
+
+    DEFAULT_ARGS_TESTS = [
+        (None, None, None, 0, 1, 1),
+        (None, None, 7, 0, 1, 7),
+        (None, [[7, 0], [0, 7]], None, [0, 0], [[7, 0], [0, 7]], 1),
+        (None, [[7, 0], [0, 7]], 7, [0, 0], [[7, 0], [0, 7]], 7),
+        ([7, 7], None, None, [7, 7], [[1, 0], [0, 1]], 1),
+        ([7, 7], None, 7, [7, 7], [[1, 0], [0, 1]], 7),
+        ([7, 7], [[7, 0], [0, 7]], None, [7, 7], [[7, 0], [0, 7]], 1),
+        ([7, 7], [[7, 0], [0, 7]], 7, [7, 7], [[7, 0], [0, 7]], 7)
+    ]
+
+    @pytest.mark.parametrize("loc, shape, df, loc_ans, shape_ans, df_ans",
+                             DEFAULT_ARGS_TESTS)
+    def test_default_args(self, loc, shape, df, loc_ans, shape_ans, df_ans):
+        dist = multivariate_t(loc=loc, shape=shape, df=df)
+        assert_equal(dist.loc, loc_ans)
+        assert_equal(dist.shape, shape_ans)
+        assert (dist.df == df_ans)
+
+    ARGS_SHAPES_TESTS = [
+        (-1, 2, 3, [-1], [[2]], 3),
+        ([-1], [2], 3, [-1], [[2]], 3),
+        (np.array([-1]), np.array([2]), 3, [-1], [[2]], 3)
+    ]
+
+    @pytest.mark.parametrize("loc, shape, df, loc_ans, shape_ans, df_ans",
+                             ARGS_SHAPES_TESTS)
+    def test_scalar_list_and_ndarray_arguments(self, loc, shape, df, loc_ans,
+                                               shape_ans, df_ans):
+        dist = multivariate_t(loc, shape, df)
+        assert_equal(dist.loc, loc_ans)
+        assert_equal(dist.shape, shape_ans)
+        assert_equal(dist.df, df_ans)
+
+    def test_argument_error_handling(self):
+        # `loc` should be a one-dimensional vector.
+        loc = [[1, 1]]
+        assert_raises(ValueError,
+                      multivariate_t,
+                      **dict(loc=loc))
+
+        # `shape` should be scalar or square matrix.
+        shape = [[1, 1], [2, 2], [3, 3]]
+        assert_raises(ValueError,
+                      multivariate_t,
+                      **dict(loc=loc, shape=shape))
+
+        # `df` should be greater than zero.
+        loc = np.zeros(2)
+        shape = np.eye(2)
+        df = -1
+        assert_raises(ValueError,
+                      multivariate_t,
+                      **dict(loc=loc, shape=shape, df=df))
+        df = 0
+        assert_raises(ValueError,
+                      multivariate_t,
+                      **dict(loc=loc, shape=shape, df=df))
+
+    def test_reproducibility(self):
+        rng = np.random.RandomState(4)
+        loc = rng.uniform(size=3)
+        shape = np.eye(3)
+        dist1 = multivariate_t(loc, shape, df=3, seed=2)
+        dist2 = multivariate_t(loc, shape, df=3, seed=2)
+        samples1 = dist1.rvs(size=10)
+        samples2 = dist2.rvs(size=10)
+        assert_equal(samples1, samples2)
+
+    def test_allow_singular(self):
+        # Make shape singular and verify error was raised.
+        args = dict(loc=[0,0], shape=[[0,0],[0,1]], df=1, allow_singular=False)
+        assert_raises(np.linalg.LinAlgError, multivariate_t, **args)
+
+    @pytest.mark.parametrize("size", [(10, 3), (5, 6, 4, 3)])
+    @pytest.mark.parametrize("dim", [2, 3, 4, 5])
+    @pytest.mark.parametrize("df", [1., 2., np.inf])
+    def test_rvs(self, size, dim, df):
+        dist = multivariate_t(np.zeros(dim), np.eye(dim), df)
+        rvs = dist.rvs(size=size)
+        assert rvs.shape == size + (dim, )
+
+    def test_cdf_signs(self):
+        # check that sign of output is correct when np.any(lower > x)
+        mean = np.zeros(3)
+        cov = np.eye(3)
+        df = 10
+        b = [[1, 1, 1], [0, 0, 0], [1, 0, 1], [0, 1, 0]]
+        a = [[0, 0, 0], [1, 1, 1], [0, 1, 0], [1, 0, 1]]
+        # when odd number of elements of b < a, output is negative
+        expected_signs = np.array([1, -1, -1, 1])
+        cdf = multivariate_normal.cdf(b, mean, cov, df, lower_limit=a)
+        assert_allclose(cdf, cdf[0]*expected_signs)
+
+    @pytest.mark.parametrize('dim', [1, 2, 5])
+    def test_cdf_against_multivariate_normal(self, dim):
+        # Check accuracy against MVN randomly-generated cases
+        self.cdf_against_mvn_test(dim)
+
+    @pytest.mark.parametrize('dim', [3, 6, 9])
+    def test_cdf_against_multivariate_normal_singular(self, dim):
+        # Check accuracy against MVN for randomly-generated singular cases
+        self.cdf_against_mvn_test(3, True)
+
+    def cdf_against_mvn_test(self, dim, singular=False):
+        # Check for accuracy in the limit that df -> oo and MVT -> MVN
+        rng = np.random.default_rng(413722918996573)
+        n = 3
+
+        w = 10**rng.uniform(-2, 1, size=dim)
+        cov = _random_covariance(dim, w, rng, singular)
+
+        mean = 10**rng.uniform(-1, 2, size=dim) * np.sign(rng.normal(size=dim))
+        a = -10**rng.uniform(-1, 2, size=(n, dim)) + mean
+        b = 10**rng.uniform(-1, 2, size=(n, dim)) + mean
+
+        res = stats.multivariate_t.cdf(b, mean, cov, df=10000, lower_limit=a,
+                                       allow_singular=True, random_state=rng)
+        ref = stats.multivariate_normal.cdf(b, mean, cov, allow_singular=True,
+                                            lower_limit=a)
+        assert_allclose(res, ref, atol=5e-4)
+
+    def test_cdf_against_univariate_t(self):
+        rng = np.random.default_rng(413722918996573)
+        cov = 2
+        mean = 0
+        x = rng.normal(size=10, scale=np.sqrt(cov))
+        df = 3
+
+        res = stats.multivariate_t.cdf(x, mean, cov, df, lower_limit=-np.inf,
+                                       random_state=rng)
+        ref = stats.t.cdf(x, df, mean, np.sqrt(cov))
+        incorrect = stats.norm.cdf(x, mean, np.sqrt(cov))
+
+        assert_allclose(res, ref, atol=5e-4)  # close to t
+        assert np.all(np.abs(res - incorrect) > 1e-3)  # not close to normal
+
+    @pytest.mark.parametrize("dim", [2, 3, 5, 10])
+    @pytest.mark.parametrize("seed", [3363958638, 7891119608, 3887698049,
+                                      5013150848, 1495033423, 6170824608])
+    @pytest.mark.parametrize("singular", [False, True])
+    def test_cdf_against_qsimvtv(self, dim, seed, singular):
+        if singular and seed != 3363958638:
+            pytest.skip('Agreement with qsimvtv is not great in singular case')
+        rng = np.random.default_rng(seed)
+        w = 10**rng.uniform(-2, 2, size=dim)
+        cov = _random_covariance(dim, w, rng, singular)
+        mean = rng.random(dim)
+        a = -rng.random(dim)
+        b = rng.random(dim)
+        df = rng.random() * 5
+
+        # no lower limit
+        res = stats.multivariate_t.cdf(b, mean, cov, df, random_state=rng,
+                                       allow_singular=True)
+        with np.errstate(invalid='ignore'):
+            ref = _qsimvtv(20000, df, cov, np.inf*a, b - mean, rng)[0]
+        assert_allclose(res, ref, atol=2e-4, rtol=1e-3)
+
+        # with lower limit
+        res = stats.multivariate_t.cdf(b, mean, cov, df, lower_limit=a,
+                                       random_state=rng, allow_singular=True)
+        with np.errstate(invalid='ignore'):
+            ref = _qsimvtv(20000, df, cov, a - mean, b - mean, rng)[0]
+        assert_allclose(res, ref, atol=1e-4, rtol=1e-3)
+
+    @pytest.mark.slow
+    def test_cdf_against_generic_integrators(self):
+        # Compare result against generic numerical integrators
+        dim = 3
+        rng = np.random.default_rng(41372291899657)
+        w = 10 ** rng.uniform(-1, 1, size=dim)
+        cov = _random_covariance(dim, w, rng, singular=True)
+        mean = rng.random(dim)
+        a = -rng.random(dim)
+        b = rng.random(dim)
+        df = rng.random() * 5
+
+        res = stats.multivariate_t.cdf(b, mean, cov, df, random_state=rng,
+                                       lower_limit=a)
+
+        def integrand(x):
+            return stats.multivariate_t.pdf(x.T, mean, cov, df)
+
+        ref = qmc_quad(integrand, a, b, qrng=stats.qmc.Halton(d=dim, seed=rng))
+        assert_allclose(res, ref.integral, rtol=1e-3)
+
+        def integrand(*zyx):
+            return stats.multivariate_t.pdf(zyx[::-1], mean, cov, df)
+
+        ref = tplquad(integrand, a[0], b[0], a[1], b[1], a[2], b[2])
+        assert_allclose(res, ref[0], rtol=1e-3)
+
+    def test_against_matlab(self):
+        # Test against matlab mvtcdf:
+        # C = [6.21786909  0.2333667 7.95506077;
+        #      0.2333667 29.67390923 16.53946426;
+        #      7.95506077 16.53946426 19.17725252]
+        # df = 1.9559939787727658
+        # mvtcdf([0, 0, 0], C, df)  % 0.2523
+        rng = np.random.default_rng(2967390923)
+        cov = np.array([[ 6.21786909,  0.2333667 ,  7.95506077],
+                        [ 0.2333667 , 29.67390923, 16.53946426],
+                        [ 7.95506077, 16.53946426, 19.17725252]])
+        df = 1.9559939787727658
+        dist = stats.multivariate_t(shape=cov, df=df)
+        res = dist.cdf([0, 0, 0], random_state=rng)
+        ref = 0.2523
+        assert_allclose(res, ref, rtol=1e-3)
+
+    def test_frozen(self):
+        seed = 4137229573
+        rng = np.random.default_rng(seed)
+        loc = rng.uniform(size=3)
+        x = rng.uniform(size=3) + loc
+        shape = np.eye(3)
+        df = rng.random()
+        args = (loc, shape, df)
+
+        rng_frozen = np.random.default_rng(seed)
+        rng_unfrozen = np.random.default_rng(seed)
+        dist = stats.multivariate_t(*args, seed=rng_frozen)
+        assert_equal(dist.cdf(x),
+                     multivariate_t.cdf(x, *args, random_state=rng_unfrozen))
+
+    def test_vectorized(self):
+        dim = 4
+        n = (2, 3)
+        rng = np.random.default_rng(413722918996573)
+        A = rng.random(size=(dim, dim))
+        cov = A @ A.T
+        mean = rng.random(dim)
+        x = rng.random(n + (dim,))
+        df = rng.random() * 5
+
+        res = stats.multivariate_t.cdf(x, mean, cov, df, random_state=rng)
+
+        def _cdf_1d(x):
+            return _qsimvtv(10000, df, cov, -np.inf*x, x-mean, rng)[0]
+
+        ref = np.apply_along_axis(_cdf_1d, -1, x)
+        assert_allclose(res, ref, atol=1e-4, rtol=1e-3)
+
+    @pytest.mark.parametrize("dim", (3, 7))
+    def test_against_analytical(self, dim):
+        rng = np.random.default_rng(413722918996573)
+        A = scipy.linalg.toeplitz(c=[1] + [0.5] * (dim - 1))
+        res = stats.multivariate_t(shape=A).cdf([0] * dim, random_state=rng)
+        ref = 1 / (dim + 1)
+        assert_allclose(res, ref, rtol=5e-5)
+
+    def test_entropy_inf_df(self):
+        cov = np.eye(3, 3)
+        df = np.inf
+        mvt_entropy = stats.multivariate_t.entropy(shape=cov, df=df)
+        mvn_entropy = stats.multivariate_normal.entropy(None, cov)
+        assert mvt_entropy == mvn_entropy
+
+    @pytest.mark.parametrize("df", [1, 10, 100])
+    def test_entropy_1d(self, df):
+        mvt_entropy = stats.multivariate_t.entropy(shape=1., df=df)
+        t_entropy = stats.t.entropy(df=df)
+        assert_allclose(mvt_entropy, t_entropy, rtol=1e-13)
+
+    # entropy reference values were computed via numerical integration
+    #
+    # def integrand(x, y, mvt):
+    #     vec = np.array([x, y])
+    #     return mvt.logpdf(vec) * mvt.pdf(vec)
+
+    # def multivariate_t_entropy_quad_2d(df, cov):
+    #     dim = cov.shape[0]
+    #     loc = np.zeros((dim, ))
+    #     mvt = stats.multivariate_t(loc, cov, df)
+    #     limit = 100
+    #     return -integrate.dblquad(integrand, -limit, limit, -limit, limit,
+    #                               args=(mvt, ))[0]
+
+    @pytest.mark.parametrize("df, cov, ref, tol",
+                             [(10, np.eye(2, 2), 3.0378770664093313, 1e-14),
+                              (100, np.array([[0.5, 1], [1, 10]]),
+                               3.55102424550609, 1e-8)])
+    def test_entropy_vs_numerical_integration(self, df, cov, ref, tol):
+        loc = np.zeros((2, ))
+        mvt = stats.multivariate_t(loc, cov, df)
+        assert_allclose(mvt.entropy(), ref, rtol=tol)
+
+    @pytest.mark.parametrize(
+        "df, dim, ref, tol",
+        [
+            (10, 1, 1.5212624929756808, 1e-15),
+            (100, 1, 1.4289633653182439, 1e-13),
+            (500, 1, 1.420939531869349, 1e-14),
+            (1e20, 1, 1.4189385332046727, 1e-15),
+            (1e100, 1, 1.4189385332046727, 1e-15),
+            (10, 10, 15.069150450832911, 1e-15),
+            (1000, 10, 14.19936546446673, 1e-13),
+            (1e20, 10, 14.189385332046728, 1e-15),
+            (1e100, 10, 14.189385332046728, 1e-15),
+            (10, 100, 148.28902883192654, 1e-15),
+            (1000, 100, 141.99155538003762, 1e-14),
+            (1e20, 100, 141.8938533204673, 1e-15),
+            (1e100, 100, 141.8938533204673, 1e-15),
+        ]
+    )
+    def test_extreme_entropy(self, df, dim, ref, tol):
+        # Reference values were calculated with mpmath:
+        # from mpmath import mp
+        # mp.dps = 500
+        #
+        # def mul_t_mpmath_entropy(dim, df=1):
+        #     dim = mp.mpf(dim)
+        #     df = mp.mpf(df)
+        #     halfsum = (dim + df)/2
+        #     half_df = df/2
+        #
+        #     return float(
+        #         -mp.loggamma(halfsum) + mp.loggamma(half_df)
+        #         + dim / 2 * mp.log(df * mp.pi)
+        #         + halfsum * (mp.digamma(halfsum) - mp.digamma(half_df))
+        #         + 0.0
+        #     )
+        mvt = stats.multivariate_t(shape=np.eye(dim), df=df)
+        assert_allclose(mvt.entropy(), ref, rtol=tol)
+
+    def test_entropy_with_covariance(self):
+        # Generated using np.randn(5, 5) and then rounding
+        # to two decimal places
+        _A = np.array([
+            [1.42, 0.09, -0.49, 0.17, 0.74],
+            [-1.13, -0.01,  0.71, 0.4, -0.56],
+            [1.07, 0.44, -0.28, -0.44, 0.29],
+            [-1.5, -0.94, -0.67, 0.73, -1.1],
+            [0.17, -0.08, 1.46, -0.32, 1.36]
+        ])
+        # Set cov to be a symmetric positive semi-definite matrix
+        cov = _A @ _A.T
+
+        # Test the asymptotic case. For large degrees of freedom
+        # the entropy approaches the multivariate normal entropy.
+        df = 1e20
+        mul_t_entropy = stats.multivariate_t.entropy(shape=cov, df=df)
+        mul_norm_entropy = multivariate_normal(None, cov=cov).entropy()
+        assert_allclose(mul_t_entropy, mul_norm_entropy, rtol=1e-15)
+
+        # Test the regular case. For a dim of 5 the threshold comes out
+        # to be approximately 766.45. So using slightly
+        # different dfs on each site of the threshold, the entropies
+        # are being compared.
+        df1 = 765
+        df2 = 768
+        _entropy1 = stats.multivariate_t.entropy(shape=cov, df=df1)
+        _entropy2 = stats.multivariate_t.entropy(shape=cov, df=df2)
+        assert_allclose(_entropy1, _entropy2, rtol=1e-5)
+
+    def test_logpdf_df_inf_gh19930(self):
+        # `multivariate_t._logpdf` (and `logpdf`/`pdf`) was not working with infinite
+        # `df` after an update to `multivariate_normal._logpdf`.
+
+        # Reproducible example from the issue
+        res = multivariate_t.logpdf(1, 1, 1, df=np.inf)
+        ref = multivariate_normal.logpdf(1, 1, 1)
+        assert_allclose(res, ref)
+
+        # More extensive test
+        # Generate a valid multivariate normal distribution and corresponding MVT
+        rng = np.random.default_rng(324893259825)
+        mean = rng.random(3)
+        cov = rng.random((3, 3)) + np.eye(3)*3
+        cov = cov.T + cov
+        X = multivariate_normal(mean=mean, cov=cov)
+        Y = multivariate_t(loc=mean, shape=cov, df=np.inf)
+
+        # compare the pdf and logpdf at 10 random points
+        x = X.rvs(10)
+        assert_allclose(Y.logpdf(x), X.logpdf(x))
+        assert_allclose(Y.pdf(x), X.pdf(x))
+
+
+class TestMultivariateHypergeom:
+    @pytest.mark.parametrize(
+        "x, m, n, expected",
+        [
+            # Ground truth value from R dmvhyper
+            ([3, 4], [5, 10], 7, -1.119814),
+            # test for `n=0`
+            ([3, 4], [5, 10], 0, -np.inf),
+            # test for `x < 0`
+            ([-3, 4], [5, 10], 7, -np.inf),
+            # test for `m < 0` (RuntimeWarning issue)
+            ([3, 4], [-5, 10], 7, np.nan),
+            # test for all `m < 0` and `x.sum() != n`
+            ([[1, 2], [3, 4]], [[-4, -6], [-5, -10]],
+             [3, 7], [np.nan, np.nan]),
+            # test for `x < 0` and `m < 0` (RuntimeWarning issue)
+            ([-3, 4], [-5, 10], 1, np.nan),
+            # test for `x > m`
+            ([1, 11], [10, 1], 12, np.nan),
+            # test for `m < 0` (RuntimeWarning issue)
+            ([1, 11], [10, -1], 12, np.nan),
+            # test for `n < 0`
+            ([3, 4], [5, 10], -7, np.nan),
+            # test for `x.sum() != n`
+            ([3, 3], [5, 10], 7, -np.inf)
+        ]
+    )
+    def test_logpmf(self, x, m, n, expected):
+        vals = multivariate_hypergeom.logpmf(x, m, n)
+        assert_allclose(vals, expected, rtol=1e-6)
+
+    def test_reduces_hypergeom(self):
+        # test that the multivariate_hypergeom pmf reduces to the
+        # hypergeom pmf in the 2d case.
+        val1 = multivariate_hypergeom.pmf(x=[3, 1], m=[10, 5], n=4)
+        val2 = hypergeom.pmf(k=3, M=15, n=4, N=10)
+        assert_allclose(val1, val2, rtol=1e-8)
+
+        val1 = multivariate_hypergeom.pmf(x=[7, 3], m=[15, 10], n=10)
+        val2 = hypergeom.pmf(k=7, M=25, n=10, N=15)
+        assert_allclose(val1, val2, rtol=1e-8)
+
+    def test_rvs(self):
+        # test if `rvs` is unbiased and large sample size converges
+        # to the true mean.
+        rv = multivariate_hypergeom(m=[3, 5], n=4)
+        rvs = rv.rvs(size=1000, random_state=123)
+        assert_allclose(rvs.mean(0), rv.mean(), rtol=1e-2)
+
+    def test_rvs_broadcasting(self):
+        rv = multivariate_hypergeom(m=[[3, 5], [5, 10]], n=[4, 9])
+        rvs = rv.rvs(size=(1000, 2), random_state=123)
+        assert_allclose(rvs.mean(0), rv.mean(), rtol=1e-2)
+
+    @pytest.mark.parametrize('m, n', (
+        ([0, 0, 20, 0, 0], 5), ([0, 0, 0, 0, 0], 0),
+        ([0, 0], 0), ([0], 0)
+    ))
+    def test_rvs_gh16171(self, m, n):
+        res = multivariate_hypergeom.rvs(m, n)
+        m = np.asarray(m)
+        res_ex = m.copy()
+        res_ex[m != 0] = n
+        assert_equal(res, res_ex)
+
+    @pytest.mark.parametrize(
+        "x, m, n, expected",
+        [
+            ([5], [5], 5, 1),
+            ([3, 4], [5, 10], 7, 0.3263403),
+            # Ground truth value from R dmvhyper
+            ([[[3, 5], [0, 8]], [[-1, 9], [1, 1]]],
+             [5, 10], [[8, 8], [8, 2]],
+             [[0.3916084, 0.006993007], [0, 0.4761905]]),
+            # test with empty arrays.
+            (np.array([], dtype=int), np.array([], dtype=int), 0, []),
+            ([1, 2], [4, 5], 5, 0),
+            # Ground truth value from R dmvhyper
+            ([3, 3, 0], [5, 6, 7], 6, 0.01077354)
+        ]
+    )
+    def test_pmf(self, x, m, n, expected):
+        vals = multivariate_hypergeom.pmf(x, m, n)
+        assert_allclose(vals, expected, rtol=1e-7)
+
+    @pytest.mark.parametrize(
+        "x, m, n, expected",
+        [
+            ([3, 4], [[5, 10], [10, 15]], 7, [0.3263403, 0.3407531]),
+            ([[1], [2]], [[3], [4]], [1, 3], [1., 0.]),
+            ([[[1], [2]]], [[3], [4]], [1, 3], [[1., 0.]]),
+            ([[1], [2]], [[[[3]]]], [1, 3], [[[1., 0.]]])
+        ]
+    )
+    def test_pmf_broadcasting(self, x, m, n, expected):
+        vals = multivariate_hypergeom.pmf(x, m, n)
+        assert_allclose(vals, expected, rtol=1e-7)
+
+    def test_cov(self):
+        cov1 = multivariate_hypergeom.cov(m=[3, 7, 10], n=12)
+        cov2 = [[0.64421053, -0.26526316, -0.37894737],
+                [-0.26526316, 1.14947368, -0.88421053],
+                [-0.37894737, -0.88421053, 1.26315789]]
+        assert_allclose(cov1, cov2, rtol=1e-8)
+
+    def test_cov_broadcasting(self):
+        cov1 = multivariate_hypergeom.cov(m=[[7, 9], [10, 15]], n=[8, 12])
+        cov2 = [[[1.05, -1.05], [-1.05, 1.05]],
+                [[1.56, -1.56], [-1.56, 1.56]]]
+        assert_allclose(cov1, cov2, rtol=1e-8)
+
+        cov3 = multivariate_hypergeom.cov(m=[[4], [5]], n=[4, 5])
+        cov4 = [[[0.]], [[0.]]]
+        assert_allclose(cov3, cov4, rtol=1e-8)
+
+        cov5 = multivariate_hypergeom.cov(m=[7, 9], n=[8, 12])
+        cov6 = [[[1.05, -1.05], [-1.05, 1.05]],
+                [[0.7875, -0.7875], [-0.7875, 0.7875]]]
+        assert_allclose(cov5, cov6, rtol=1e-8)
+
+    def test_var(self):
+        # test with hypergeom
+        var0 = multivariate_hypergeom.var(m=[10, 5], n=4)
+        var1 = hypergeom.var(M=15, n=4, N=10)
+        assert_allclose(var0, var1, rtol=1e-8)
+
+    def test_var_broadcasting(self):
+        var0 = multivariate_hypergeom.var(m=[10, 5], n=[4, 8])
+        var1 = multivariate_hypergeom.var(m=[10, 5], n=4)
+        var2 = multivariate_hypergeom.var(m=[10, 5], n=8)
+        assert_allclose(var0[0], var1, rtol=1e-8)
+        assert_allclose(var0[1], var2, rtol=1e-8)
+
+        var3 = multivariate_hypergeom.var(m=[[10, 5], [10, 14]], n=[4, 8])
+        var4 = [[0.6984127, 0.6984127], [1.352657, 1.352657]]
+        assert_allclose(var3, var4, rtol=1e-8)
+
+        var5 = multivariate_hypergeom.var(m=[[5], [10]], n=[5, 10])
+        var6 = [[0.], [0.]]
+        assert_allclose(var5, var6, rtol=1e-8)
+
+    def test_mean(self):
+        # test with hypergeom
+        mean0 = multivariate_hypergeom.mean(m=[10, 5], n=4)
+        mean1 = hypergeom.mean(M=15, n=4, N=10)
+        assert_allclose(mean0[0], mean1, rtol=1e-8)
+
+        mean2 = multivariate_hypergeom.mean(m=[12, 8], n=10)
+        mean3 = [12.*10./20., 8.*10./20.]
+        assert_allclose(mean2, mean3, rtol=1e-8)
+
+    def test_mean_broadcasting(self):
+        mean0 = multivariate_hypergeom.mean(m=[[3, 5], [10, 5]], n=[4, 8])
+        mean1 = [[3.*4./8., 5.*4./8.], [10.*8./15., 5.*8./15.]]
+        assert_allclose(mean0, mean1, rtol=1e-8)
+
+    def test_mean_edge_cases(self):
+        mean0 = multivariate_hypergeom.mean(m=[0, 0, 0], n=0)
+        assert_equal(mean0, [0., 0., 0.])
+
+        mean1 = multivariate_hypergeom.mean(m=[1, 0, 0], n=2)
+        assert_equal(mean1, [np.nan, np.nan, np.nan])
+
+        mean2 = multivariate_hypergeom.mean(m=[[1, 0, 0], [1, 0, 1]], n=2)
+        assert_allclose(mean2, [[np.nan, np.nan, np.nan], [1., 0., 1.]],
+                        rtol=1e-17)
+
+        mean3 = multivariate_hypergeom.mean(m=np.array([], dtype=int), n=0)
+        assert_equal(mean3, [])
+        assert_(mean3.shape == (0, ))
+
+    def test_var_edge_cases(self):
+        var0 = multivariate_hypergeom.var(m=[0, 0, 0], n=0)
+        assert_allclose(var0, [0., 0., 0.], rtol=1e-16)
+
+        var1 = multivariate_hypergeom.var(m=[1, 0, 0], n=2)
+        assert_equal(var1, [np.nan, np.nan, np.nan])
+
+        var2 = multivariate_hypergeom.var(m=[[1, 0, 0], [1, 0, 1]], n=2)
+        assert_allclose(var2, [[np.nan, np.nan, np.nan], [0., 0., 0.]],
+                        rtol=1e-17)
+
+        var3 = multivariate_hypergeom.var(m=np.array([], dtype=int), n=0)
+        assert_equal(var3, [])
+        assert_(var3.shape == (0, ))
+
+    def test_cov_edge_cases(self):
+        cov0 = multivariate_hypergeom.cov(m=[1, 0, 0], n=1)
+        cov1 = [[0., 0., 0.], [0., 0., 0.], [0., 0., 0.]]
+        assert_allclose(cov0, cov1, rtol=1e-17)
+
+        cov3 = multivariate_hypergeom.cov(m=[0, 0, 0], n=0)
+        cov4 = [[0., 0., 0.], [0., 0., 0.], [0., 0., 0.]]
+        assert_equal(cov3, cov4)
+
+        cov5 = multivariate_hypergeom.cov(m=np.array([], dtype=int), n=0)
+        cov6 = np.array([], dtype=np.float64).reshape(0, 0)
+        assert_allclose(cov5, cov6, rtol=1e-17)
+        assert_(cov5.shape == (0, 0))
+
+    def test_frozen(self):
+        # The frozen distribution should agree with the regular one
+        n = 12
+        m = [7, 9, 11, 13]
+        x = [[0, 0, 0, 12], [0, 0, 1, 11], [0, 1, 1, 10],
+             [1, 1, 1, 9], [1, 1, 2, 8]]
+        x = np.asarray(x, dtype=int)
+        mhg_frozen = multivariate_hypergeom(m, n)
+        assert_allclose(mhg_frozen.pmf(x),
+                        multivariate_hypergeom.pmf(x, m, n))
+        assert_allclose(mhg_frozen.logpmf(x),
+                        multivariate_hypergeom.logpmf(x, m, n))
+        assert_allclose(mhg_frozen.var(), multivariate_hypergeom.var(m, n))
+        assert_allclose(mhg_frozen.cov(), multivariate_hypergeom.cov(m, n))
+
+    def test_invalid_params(self):
+        assert_raises(ValueError, multivariate_hypergeom.pmf, 5, 10, 5)
+        assert_raises(ValueError, multivariate_hypergeom.pmf, 5, [10], 5)
+        assert_raises(ValueError, multivariate_hypergeom.pmf, [5, 4], [10], 5)
+        assert_raises(TypeError, multivariate_hypergeom.pmf, [5.5, 4.5],
+                      [10, 15], 5)
+        assert_raises(TypeError, multivariate_hypergeom.pmf, [5, 4],
+                      [10.5, 15.5], 5)
+        assert_raises(TypeError, multivariate_hypergeom.pmf, [5, 4],
+                      [10, 15], 5.5)
+
+
+class TestRandomTable:
+    def get_rng(self):
+        return np.random.default_rng(628174795866951638)
+
+    def test_process_parameters(self):
+        message = "`row` must be one-dimensional"
+        with pytest.raises(ValueError, match=message):
+            random_table([[1, 2]], [1, 2])
+
+        message = "`col` must be one-dimensional"
+        with pytest.raises(ValueError, match=message):
+            random_table([1, 2], [[1, 2]])
+
+        message = "each element of `row` must be non-negative"
+        with pytest.raises(ValueError, match=message):
+            random_table([1, -1], [1, 2])
+
+        message = "each element of `col` must be non-negative"
+        with pytest.raises(ValueError, match=message):
+            random_table([1, 2], [1, -2])
+
+        message = "sums over `row` and `col` must be equal"
+        with pytest.raises(ValueError, match=message):
+            random_table([1, 2], [1, 0])
+
+        message = "each element of `row` must be an integer"
+        with pytest.raises(ValueError, match=message):
+            random_table([2.1, 2.1], [1, 1, 2])
+
+        message = "each element of `col` must be an integer"
+        with pytest.raises(ValueError, match=message):
+            random_table([1, 2], [1.1, 1.1, 1])
+
+        row = [1, 3]
+        col = [2, 1, 1]
+        r, c, n = random_table._process_parameters([1, 3], [2, 1, 1])
+        assert_equal(row, r)
+        assert_equal(col, c)
+        assert n == np.sum(row)
+
+    @pytest.mark.parametrize("scale,method",
+                             ((1, "boyett"), (100, "patefield")))
+    def test_process_rvs_method_on_None(self, scale, method):
+        row = np.array([1, 3]) * scale
+        col = np.array([2, 1, 1]) * scale
+
+        ct = random_table
+        expected = ct.rvs(row, col, method=method, random_state=1)
+        got = ct.rvs(row, col, method=None, random_state=1)
+
+        assert_equal(expected, got)
+
+    def test_process_rvs_method_bad_argument(self):
+        row = [1, 3]
+        col = [2, 1, 1]
+
+        # order of items in set is random, so cannot check that
+        message = "'foo' not recognized, must be one of"
+        with pytest.raises(ValueError, match=message):
+            random_table.rvs(row, col, method="foo")
+
+    @pytest.mark.parametrize('frozen', (True, False))
+    @pytest.mark.parametrize('log', (True, False))
+    def test_pmf_logpmf(self, frozen, log):
+        # The pmf is tested through random sample generation
+        # with Boyett's algorithm, whose implementation is simple
+        # enough to verify manually for correctness.
+        rng = self.get_rng()
+        row = [2, 6]
+        col = [1, 3, 4]
+        rvs = random_table.rvs(row, col, size=1000,
+                               method="boyett", random_state=rng)
+
+        obj = random_table(row, col) if frozen else random_table
+        method = getattr(obj, "logpmf" if log else "pmf")
+        if not frozen:
+            original_method = method
+
+            def method(x):
+                return original_method(x, row, col)
+        pmf = (lambda x: np.exp(method(x))) if log else method
+
+        unique_rvs, counts = np.unique(rvs, axis=0, return_counts=True)
+
+        # rough accuracy check
+        p = pmf(unique_rvs)
+        assert_allclose(p * len(rvs), counts, rtol=0.1)
+
+        # accept any iterable
+        p2 = pmf(list(unique_rvs[0]))
+        assert_equal(p2, p[0])
+
+        # accept high-dimensional input and 2d input
+        rvs_nd = rvs.reshape((10, 100) + rvs.shape[1:])
+        p = pmf(rvs_nd)
+        assert p.shape == (10, 100)
+        for i in range(p.shape[0]):
+            for j in range(p.shape[1]):
+                pij = p[i, j]
+                rvij = rvs_nd[i, j]
+                qij = pmf(rvij)
+                assert_equal(pij, qij)
+
+        # probability is zero if column marginal does not match
+        x = [[0, 1, 1], [2, 1, 3]]
+        assert_equal(np.sum(x, axis=-1), row)
+        p = pmf(x)
+        assert p == 0
+
+        # probability is zero if row marginal does not match
+        x = [[0, 1, 2], [1, 2, 2]]
+        assert_equal(np.sum(x, axis=-2), col)
+        p = pmf(x)
+        assert p == 0
+
+        # response to invalid inputs
+        message = "`x` must be at least two-dimensional"
+        with pytest.raises(ValueError, match=message):
+            pmf([1])
+
+        message = "`x` must contain only integral values"
+        with pytest.raises(ValueError, match=message):
+            pmf([[1.1]])
+
+        message = "`x` must contain only integral values"
+        with pytest.raises(ValueError, match=message):
+            pmf([[np.nan]])
+
+        message = "`x` must contain only non-negative values"
+        with pytest.raises(ValueError, match=message):
+            pmf([[-1]])
+
+        message = "shape of `x` must agree with `row`"
+        with pytest.raises(ValueError, match=message):
+            pmf([[1, 2, 3]])
+
+        message = "shape of `x` must agree with `col`"
+        with pytest.raises(ValueError, match=message):
+            pmf([[1, 2],
+                 [3, 4]])
+
+    @pytest.mark.parametrize("method", ("boyett", "patefield"))
+    def test_rvs_mean(self, method):
+        # test if `rvs` is unbiased and large sample size converges
+        # to the true mean.
+        rng = self.get_rng()
+        row = [2, 6]
+        col = [1, 3, 4]
+        rvs = random_table.rvs(row, col, size=1000, method=method,
+                               random_state=rng)
+        mean = random_table.mean(row, col)
+        assert_equal(np.sum(mean), np.sum(row))
+        assert_allclose(rvs.mean(0), mean, atol=0.05)
+        assert_equal(rvs.sum(axis=-1), np.broadcast_to(row, (1000, 2)))
+        assert_equal(rvs.sum(axis=-2), np.broadcast_to(col, (1000, 3)))
+
+    def test_rvs_cov(self):
+        # test if `rvs` generated with patefield and boyett algorithms
+        # produce approximately the same covariance matrix
+        rng = self.get_rng()
+        row = [2, 6]
+        col = [1, 3, 4]
+        rvs1 = random_table.rvs(row, col, size=10000, method="boyett",
+                                random_state=rng)
+        rvs2 = random_table.rvs(row, col, size=10000, method="patefield",
+                                random_state=rng)
+        cov1 = np.var(rvs1, axis=0)
+        cov2 = np.var(rvs2, axis=0)
+        assert_allclose(cov1, cov2, atol=0.02)
+
+    @pytest.mark.parametrize("method", ("boyett", "patefield"))
+    def test_rvs_size(self, method):
+        row = [2, 6]
+        col = [1, 3, 4]
+
+        # test size `None`
+        rv = random_table.rvs(row, col, method=method,
+                              random_state=self.get_rng())
+        assert rv.shape == (2, 3)
+
+        # test size 1
+        rv2 = random_table.rvs(row, col, size=1, method=method,
+                               random_state=self.get_rng())
+        assert rv2.shape == (1, 2, 3)
+        assert_equal(rv, rv2[0])
+
+        # test size 0
+        rv3 = random_table.rvs(row, col, size=0, method=method,
+                               random_state=self.get_rng())
+        assert rv3.shape == (0, 2, 3)
+
+        # test other valid size
+        rv4 = random_table.rvs(row, col, size=20, method=method,
+                               random_state=self.get_rng())
+        assert rv4.shape == (20, 2, 3)
+
+        rv5 = random_table.rvs(row, col, size=(4, 5), method=method,
+                               random_state=self.get_rng())
+        assert rv5.shape == (4, 5, 2, 3)
+
+        assert_allclose(rv5.reshape(20, 2, 3), rv4, rtol=1e-15)
+
+        # test invalid size
+        message = "`size` must be a non-negative integer or `None`"
+        with pytest.raises(ValueError, match=message):
+            random_table.rvs(row, col, size=-1, method=method,
+                             random_state=self.get_rng())
+
+        with pytest.raises(ValueError, match=message):
+            random_table.rvs(row, col, size=np.nan, method=method,
+                             random_state=self.get_rng())
+
+    @pytest.mark.parametrize("method", ("boyett", "patefield"))
+    def test_rvs_method(self, method):
+        # This test assumes that pmf is correct and checks that random samples
+        # follow this probability distribution. This seems like a circular
+        # argument, since pmf is checked in test_pmf_logpmf with random samples
+        # generated with the rvs method. This test is not redundant, because
+        # test_pmf_logpmf intentionally uses rvs generation with Boyett only,
+        # but here we test both Boyett and Patefield.
+        row = [2, 6]
+        col = [1, 3, 4]
+
+        ct = random_table
+        rvs = ct.rvs(row, col, size=100000, method=method,
+                     random_state=self.get_rng())
+
+        unique_rvs, counts = np.unique(rvs, axis=0, return_counts=True)
+
+        # generated frequencies should match expected frequencies
+        p = ct.pmf(unique_rvs, row, col)
+        assert_allclose(p * len(rvs), counts, rtol=0.02)
+
+    @pytest.mark.parametrize("method", ("boyett", "patefield"))
+    def test_rvs_with_zeros_in_col_row(self, method):
+        row = [0, 1, 0]
+        col = [1, 0, 0, 0]
+        d = random_table(row, col)
+        rv = d.rvs(1000, method=method, random_state=self.get_rng())
+        expected = np.zeros((1000, len(row), len(col)))
+        expected[...] = [[0, 0, 0, 0],
+                         [1, 0, 0, 0],
+                         [0, 0, 0, 0]]
+        assert_equal(rv, expected)
+
+    @pytest.mark.parametrize("method", (None, "boyett", "patefield"))
+    @pytest.mark.parametrize("col", ([], [0]))
+    @pytest.mark.parametrize("row", ([], [0]))
+    def test_rvs_with_edge_cases(self, method, row, col):
+        d = random_table(row, col)
+        rv = d.rvs(10, method=method, random_state=self.get_rng())
+        expected = np.zeros((10, len(row), len(col)))
+        assert_equal(rv, expected)
+
+    @pytest.mark.parametrize('v', (1, 2))
+    def test_rvs_rcont(self, v):
+        # This test checks the internal low-level interface.
+        # It is implicitly also checked by the other test_rvs* calls.
+        import scipy.stats._rcont as _rcont
+
+        row = np.array([1, 3], dtype=np.int64)
+        col = np.array([2, 1, 1], dtype=np.int64)
+
+        rvs = getattr(_rcont, f"rvs_rcont{v}")
+
+        ntot = np.sum(row)
+        result = rvs(row, col, ntot, 1, self.get_rng())
+
+        assert result.shape == (1, len(row), len(col))
+        assert np.sum(result) == ntot
+
+    def test_frozen(self):
+        row = [2, 6]
+        col = [1, 3, 4]
+        d = random_table(row, col, seed=self.get_rng())
+
+        sample = d.rvs()
+
+        expected = random_table.mean(row, col)
+        assert_equal(expected, d.mean())
+
+        expected = random_table.pmf(sample, row, col)
+        assert_equal(expected, d.pmf(sample))
+
+        expected = random_table.logpmf(sample, row, col)
+        assert_equal(expected, d.logpmf(sample))
+
+    @pytest.mark.parametrize("method", ("boyett", "patefield"))
+    def test_rvs_frozen(self, method):
+        row = [2, 6]
+        col = [1, 3, 4]
+        d = random_table(row, col, seed=self.get_rng())
+
+        expected = random_table.rvs(row, col, size=10, method=method,
+                                    random_state=self.get_rng())
+        got = d.rvs(size=10, method=method)
+        assert_equal(expected, got)
+
+
+def check_pickling(distfn, args):
+    # check that a distribution instance pickles and unpickles
+    # pay special attention to the random_state property
+
+    # save the random_state (restore later)
+    rndm = distfn.random_state
+
+    distfn.random_state = 1234
+    distfn.rvs(*args, size=8)
+    s = pickle.dumps(distfn)
+    r0 = distfn.rvs(*args, size=8)
+
+    unpickled = pickle.loads(s)
+    r1 = unpickled.rvs(*args, size=8)
+    assert_equal(r0, r1)
+
+    # restore the random_state
+    distfn.random_state = rndm
+
+
+@pytest.mark.thread_unsafe(reason="uses numpy global random state and monkey-patching")
+def test_random_state_property():
+    scale = np.eye(3)
+    scale[0, 1] = 0.5
+    scale[1, 0] = 0.5
+    dists = [
+        [multivariate_normal, ()],
+        [dirichlet, (np.array([1.]), )],
+        [wishart, (10, scale)],
+        [invwishart, (10, scale)],
+        [multinomial, (5, [0.5, 0.4, 0.1])],
+        [ortho_group, (2,)],
+        [special_ortho_group, (2,)]
+    ]
+    for distfn, args in dists:
+        check_random_state_property(distfn, args)
+        check_pickling(distfn, args)
+
+
+class TestVonMises_Fisher:
+    @pytest.mark.parametrize("dim", [2, 3, 4, 6])
+    @pytest.mark.parametrize("size", [None, 1, 5, (5, 4)])
+    def test_samples(self, dim, size):
+        # test that samples have correct shape and norm 1
+        rng = np.random.default_rng(2777937887058094419)
+        mu = np.full((dim, ), 1/np.sqrt(dim))
+        vmf_dist = vonmises_fisher(mu, 1, seed=rng)
+        samples = vmf_dist.rvs(size)
+        mean, cov = np.zeros(dim), np.eye(dim)
+        expected_shape = rng.multivariate_normal(mean, cov, size=size).shape
+        assert samples.shape == expected_shape
+        norms = np.linalg.norm(samples, axis=-1)
+        assert_allclose(norms, 1.)
+
+    @pytest.mark.parametrize("dim", [5, 8])
+    @pytest.mark.parametrize("kappa", [1e15, 1e20, 1e30])
+    def test_sampling_high_concentration(self, dim, kappa):
+        # test that no warnings are encountered for high values
+        rng = np.random.default_rng(2777937887058094419)
+        mu = np.full((dim, ), 1/np.sqrt(dim))
+        vmf_dist = vonmises_fisher(mu, kappa, seed=rng)
+        vmf_dist.rvs(10)
+
+    def test_two_dimensional_mu(self):
+        mu = np.ones((2, 2))
+        msg = "'mu' must have one-dimensional shape."
+        with pytest.raises(ValueError, match=msg):
+            vonmises_fisher(mu, 1)
+
+    def test_wrong_norm_mu(self):
+        mu = np.ones((2, ))
+        msg = "'mu' must be a unit vector of norm 1."
+        with pytest.raises(ValueError, match=msg):
+            vonmises_fisher(mu, 1)
+
+    def test_one_entry_mu(self):
+        mu = np.ones((1, ))
+        msg = "'mu' must have at least two entries."
+        with pytest.raises(ValueError, match=msg):
+            vonmises_fisher(mu, 1)
+
+    @pytest.mark.parametrize("kappa", [-1, (5, 3)])
+    def test_kappa_validation(self, kappa):
+        msg = "'kappa' must be a positive scalar."
+        with pytest.raises(ValueError, match=msg):
+            vonmises_fisher([1, 0], kappa)
+
+    @pytest.mark.parametrize("kappa", [0, 0.])
+    def test_kappa_zero(self, kappa):
+        msg = ("For 'kappa=0' the von Mises-Fisher distribution "
+               "becomes the uniform distribution on the sphere "
+               "surface. Consider using 'scipy.stats.uniform_direction' "
+               "instead.")
+        with pytest.raises(ValueError, match=msg):
+            vonmises_fisher([1, 0], kappa)
+
+
+    @pytest.mark.parametrize("method", [vonmises_fisher.pdf,
+                                        vonmises_fisher.logpdf])
+    def test_invalid_shapes_pdf_logpdf(self, method):
+        x = np.array([1., 0., 0])
+        msg = ("The dimensionality of the last axis of 'x' must "
+               "match the dimensionality of the von Mises Fisher "
+               "distribution.")
+        with pytest.raises(ValueError, match=msg):
+            method(x, [1, 0], 1)
+
+    @pytest.mark.parametrize("method", [vonmises_fisher.pdf,
+                                        vonmises_fisher.logpdf])
+    def test_unnormalized_input(self, method):
+        x = np.array([0.5, 0.])
+        msg = "'x' must be unit vectors of norm 1 along last dimension."
+        with pytest.raises(ValueError, match=msg):
+            method(x, [1, 0], 1)
+
+    # Expected values of the vonmises-fisher logPDF were computed via mpmath
+    # from mpmath import mp
+    # import numpy as np
+    # mp.dps = 50
+    # def logpdf_mpmath(x, mu, kappa):
+    #     dim = mu.size
+    #     halfdim = mp.mpf(0.5 * dim)
+    #     kappa = mp.mpf(kappa)
+    #     const = (kappa**(halfdim - mp.one)/((2*mp.pi)**halfdim * \
+    #              mp.besseli(halfdim -mp.one, kappa)))
+    #     return float(const * mp.exp(kappa*mp.fdot(x, mu)))
+
+    @pytest.mark.parametrize('x, mu, kappa, reference',
+                             [(np.array([1., 0., 0.]), np.array([1., 0., 0.]),
+                               1e-4, 0.0795854295583605),
+                              (np.array([1., 0., 0]), np.array([0., 0., 1.]),
+                               1e-4, 0.07957747141331854),
+                              (np.array([1., 0., 0.]), np.array([1., 0., 0.]),
+                               100, 15.915494309189533),
+                              (np.array([1., 0., 0]), np.array([0., 0., 1.]),
+                               100, 5.920684802611232e-43),
+                              (np.array([1., 0., 0.]),
+                               np.array([np.sqrt(0.98), np.sqrt(0.02), 0.]),
+                               2000, 5.930499050746588e-07),
+                              (np.array([1., 0., 0]), np.array([1., 0., 0.]),
+                               2000, 318.3098861837907),
+                              (np.array([1., 0., 0., 0., 0.]),
+                               np.array([1., 0., 0., 0., 0.]),
+                               2000, 101371.86957712633),
+                              (np.array([1., 0., 0., 0., 0.]),
+                               np.array([np.sqrt(0.98), np.sqrt(0.02), 0.,
+                                         0, 0.]),
+                               2000, 0.00018886808182653578),
+                              (np.array([1., 0., 0., 0., 0.]),
+                               np.array([np.sqrt(0.8), np.sqrt(0.2), 0.,
+                                         0, 0.]),
+                               2000, 2.0255393314603194e-87)])
+    def test_pdf_accuracy(self, x, mu, kappa, reference):
+        pdf = vonmises_fisher(mu, kappa).pdf(x)
+        assert_allclose(pdf, reference, rtol=1e-13)
+
+    # Expected values of the vonmises-fisher logPDF were computed via mpmath
+    # from mpmath import mp
+    # import numpy as np
+    # mp.dps = 50
+    # def logpdf_mpmath(x, mu, kappa):
+    #     dim = mu.size
+    #     halfdim = mp.mpf(0.5 * dim)
+    #     kappa = mp.mpf(kappa)
+    #     two = mp.mpf(2.)
+    #     const = (kappa**(halfdim - mp.one)/((two*mp.pi)**halfdim * \
+    #              mp.besseli(halfdim - mp.one, kappa)))
+    #     return float(mp.log(const * mp.exp(kappa*mp.fdot(x, mu))))
+
+    @pytest.mark.parametrize('x, mu, kappa, reference',
+                             [(np.array([1., 0., 0.]), np.array([1., 0., 0.]),
+                               1e-4, -2.5309242486359573),
+                              (np.array([1., 0., 0]), np.array([0., 0., 1.]),
+                               1e-4, -2.5310242486359575),
+                              (np.array([1., 0., 0.]), np.array([1., 0., 0.]),
+                               100, 2.767293119578746),
+                              (np.array([1., 0., 0]), np.array([0., 0., 1.]),
+                               100, -97.23270688042125),
+                              (np.array([1., 0., 0.]),
+                               np.array([np.sqrt(0.98), np.sqrt(0.02), 0.]),
+                               2000, -14.337987284534103),
+                              (np.array([1., 0., 0]), np.array([1., 0., 0.]),
+                               2000, 5.763025393132737),
+                              (np.array([1., 0., 0., 0., 0.]),
+                               np.array([1., 0., 0., 0., 0.]),
+                               2000, 11.526550911307156),
+                              (np.array([1., 0., 0., 0., 0.]),
+                               np.array([np.sqrt(0.98), np.sqrt(0.02), 0.,
+                                         0, 0.]),
+                               2000, -8.574461766359684),
+                              (np.array([1., 0., 0., 0., 0.]),
+                               np.array([np.sqrt(0.8), np.sqrt(0.2), 0.,
+                                         0, 0.]),
+                               2000, -199.61906708886113)])
+    def test_logpdf_accuracy(self, x, mu, kappa, reference):
+        logpdf = vonmises_fisher(mu, kappa).logpdf(x)
+        assert_allclose(logpdf, reference, rtol=1e-14)
+
+    # Expected values of the vonmises-fisher entropy were computed via mpmath
+    # from mpmath import mp
+    # import numpy as np
+    # mp.dps = 50
+    # def entropy_mpmath(dim, kappa):
+    #     mu = np.full((dim, ), 1/np.sqrt(dim))
+    #     kappa = mp.mpf(kappa)
+    #     halfdim = mp.mpf(0.5 * dim)
+    #     logconstant = (mp.log(kappa**(halfdim - mp.one)
+    #                    /((2*mp.pi)**halfdim
+    #                    * mp.besseli(halfdim -mp.one, kappa)))
+    #     return float(-logconstant - kappa * mp.besseli(halfdim, kappa)/
+    #             mp.besseli(halfdim -1, kappa))
+
+    @pytest.mark.parametrize('dim, kappa, reference',
+                             [(3, 1e-4, 2.531024245302624),
+                              (3, 100, -1.7672931195787458),
+                              (5, 5000, -11.359032310024453),
+                              (8, 1, 3.4189526482545527)])
+    def test_entropy_accuracy(self, dim, kappa, reference):
+        mu = np.full((dim, ), 1/np.sqrt(dim))
+        entropy = vonmises_fisher(mu, kappa).entropy()
+        assert_allclose(entropy, reference, rtol=2e-14)
+
+    @pytest.mark.parametrize("method", [vonmises_fisher.pdf,
+                                        vonmises_fisher.logpdf])
+    def test_broadcasting(self, method):
+        # test that pdf and logpdf values are correctly broadcasted
+        testshape = (2, 2)
+        rng = np.random.default_rng(2777937887058094419)
+        x = uniform_direction(3).rvs(testshape, random_state=rng)
+        mu = np.full((3, ), 1/np.sqrt(3))
+        kappa = 5
+        result_all = method(x, mu, kappa)
+        assert result_all.shape == testshape
+        for i in range(testshape[0]):
+            for j in range(testshape[1]):
+                current_val = method(x[i, j, :], mu, kappa)
+                assert_allclose(current_val, result_all[i, j], rtol=1e-15)
+
+    def test_vs_vonmises_2d(self):
+        # test that in 2D, von Mises-Fisher yields the same results
+        # as the von Mises distribution
+        rng = np.random.default_rng(2777937887058094419)
+        mu = np.array([0, 1])
+        mu_angle = np.arctan2(mu[1], mu[0])
+        kappa = 20
+        vmf = vonmises_fisher(mu, kappa)
+        vonmises_dist = vonmises(loc=mu_angle, kappa=kappa)
+        vectors = uniform_direction(2).rvs(10, random_state=rng)
+        angles = np.arctan2(vectors[:, 1], vectors[:, 0])
+        assert_allclose(vonmises_dist.entropy(), vmf.entropy())
+        assert_allclose(vonmises_dist.pdf(angles), vmf.pdf(vectors))
+        assert_allclose(vonmises_dist.logpdf(angles), vmf.logpdf(vectors))
+
+    @pytest.mark.parametrize("dim", [2, 3, 6])
+    @pytest.mark.parametrize("kappa, mu_tol, kappa_tol",
+                             [(1, 5e-2, 5e-2),
+                              (10, 1e-2, 1e-2),
+                              (100, 5e-3, 2e-2),
+                              (1000, 1e-3, 2e-2)])
+    def test_fit_accuracy(self, dim, kappa, mu_tol, kappa_tol):
+        mu = np.full((dim, ), 1/np.sqrt(dim))
+        vmf_dist = vonmises_fisher(mu, kappa)
+        rng = np.random.default_rng(2777937887058094419)
+        n_samples = 10000
+        samples = vmf_dist.rvs(n_samples, random_state=rng)
+        mu_fit, kappa_fit = vonmises_fisher.fit(samples)
+        angular_error = np.arccos(mu.dot(mu_fit))
+        assert_allclose(angular_error, 0., atol=mu_tol, rtol=0)
+        assert_allclose(kappa, kappa_fit, rtol=kappa_tol)
+
+    def test_fit_error_one_dimensional_data(self):
+        x = np.zeros((3, ))
+        msg = "'x' must be two dimensional."
+        with pytest.raises(ValueError, match=msg):
+            vonmises_fisher.fit(x)
+
+    def test_fit_error_unnormalized_data(self):
+        x = np.ones((3, 3))
+        msg = "'x' must be unit vectors of norm 1 along last dimension."
+        with pytest.raises(ValueError, match=msg):
+            vonmises_fisher.fit(x)
+
+    def test_frozen_distribution(self):
+        mu = np.array([0, 0, 1])
+        kappa = 5
+        frozen = vonmises_fisher(mu, kappa)
+        frozen_seed = vonmises_fisher(mu, kappa, seed=514)
+
+        rvs1 = frozen.rvs(random_state=514)
+        rvs2 = vonmises_fisher.rvs(mu, kappa, random_state=514)
+        rvs3 = frozen_seed.rvs()
+
+        assert_equal(rvs1, rvs2)
+        assert_equal(rvs1, rvs3)
+
+
+class TestDirichletMultinomial:
+    @classmethod
+    def get_params(self, m):
+        rng = np.random.default_rng(28469824356873456)
+        alpha = rng.uniform(0, 100, size=2)
+        x = rng.integers(1, 20, size=(m, 2))
+        n = x.sum(axis=-1)
+        return rng, m, alpha, n, x
+
+    def test_frozen(self):
+        rng = np.random.default_rng(28469824356873456)
+
+        alpha = rng.uniform(0, 100, 10)
+        x = rng.integers(0, 10, 10)
+        n = np.sum(x, axis=-1)
+
+        d = dirichlet_multinomial(alpha, n)
+        assert_equal(d.logpmf(x), dirichlet_multinomial.logpmf(x, alpha, n))
+        assert_equal(d.pmf(x), dirichlet_multinomial.pmf(x, alpha, n))
+        assert_equal(d.mean(), dirichlet_multinomial.mean(alpha, n))
+        assert_equal(d.var(), dirichlet_multinomial.var(alpha, n))
+        assert_equal(d.cov(), dirichlet_multinomial.cov(alpha, n))
+
+    def test_pmf_logpmf_against_R(self):
+        # # Compare PMF against R's extraDistr ddirmnon
+        # # library(extraDistr)
+        # # options(digits=16)
+        # ddirmnom(c(1, 2, 3), 6, c(3, 4, 5))
+        x = np.array([1, 2, 3])
+        n = np.sum(x)
+        alpha = np.array([3, 4, 5])
+        res = dirichlet_multinomial.pmf(x, alpha, n)
+        logres = dirichlet_multinomial.logpmf(x, alpha, n)
+        ref = 0.08484162895927638
+        assert_allclose(res, ref)
+        assert_allclose(logres, np.log(ref))
+        assert res.shape == logres.shape == ()
+
+        # library(extraDistr)
+        # options(digits=16)
+        # ddirmnom(c(4, 3, 2, 0, 2, 3, 5, 7, 4, 7), 37,
+        #          c(45.01025314, 21.98739582, 15.14851365, 80.21588671,
+        #            52.84935481, 25.20905262, 53.85373737, 4.88568118,
+        #            89.06440654, 20.11359466))
+        rng = np.random.default_rng(28469824356873456)
+        alpha = rng.uniform(0, 100, 10)
+        x = rng.integers(0, 10, 10)
+        n = np.sum(x, axis=-1)
+        res = dirichlet_multinomial(alpha, n).pmf(x)
+        logres = dirichlet_multinomial.logpmf(x, alpha, n)
+        ref = 3.65409306285992e-16
+        assert_allclose(res, ref)
+        assert_allclose(logres, np.log(ref))
+
+    def test_pmf_logpmf_support(self):
+        # when the sum of the category counts does not equal the number of
+        # trials, the PMF is zero
+        rng, m, alpha, n, x = self.get_params(1)
+        n += 1
+        assert_equal(dirichlet_multinomial(alpha, n).pmf(x), 0)
+        assert_equal(dirichlet_multinomial(alpha, n).logpmf(x), -np.inf)
+
+        rng, m, alpha, n, x = self.get_params(10)
+        i = rng.random(size=10) > 0.5
+        x[i] = np.round(x[i] * 2)  # sum of these x does not equal n
+        assert_equal(dirichlet_multinomial(alpha, n).pmf(x)[i], 0)
+        assert_equal(dirichlet_multinomial(alpha, n).logpmf(x)[i], -np.inf)
+        assert np.all(dirichlet_multinomial(alpha, n).pmf(x)[~i] > 0)
+        assert np.all(dirichlet_multinomial(alpha, n).logpmf(x)[~i] > -np.inf)
+
+    def test_dimensionality_one(self):
+        # if the dimensionality is one, there is only one possible outcome
+        n = 6  # number of trials
+        alpha = [10]  # concentration parameters
+        x = np.asarray([n])  # counts
+        dist = dirichlet_multinomial(alpha, n)
+
+        assert_equal(dist.pmf(x), 1)
+        assert_equal(dist.pmf(x+1), 0)
+        assert_equal(dist.logpmf(x), 0)
+        assert_equal(dist.logpmf(x+1), -np.inf)
+        assert_equal(dist.mean(), n)
+        assert_equal(dist.var(), 0)
+        assert_equal(dist.cov(), 0)
+
+    def test_n_is_zero(self):
+        # similarly, only one possible outcome if n is zero
+        n = 0
+        alpha = np.asarray([1., 1.])
+        x = np.asarray([0, 0])
+        dist = dirichlet_multinomial(alpha, n)
+
+        assert_equal(dist.pmf(x), 1)
+        assert_equal(dist.pmf(x+1), 0)
+        assert_equal(dist.logpmf(x), 0)
+        assert_equal(dist.logpmf(x+1), -np.inf)
+        assert_equal(dist.mean(), [0, 0])
+        assert_equal(dist.var(), [0, 0])
+        assert_equal(dist.cov(), [[0, 0], [0, 0]])
+
+    @pytest.mark.parametrize('method_name', ['pmf', 'logpmf'])
+    def test_against_betabinom_pmf(self, method_name):
+        rng, m, alpha, n, x = self.get_params(100)
+
+        method = getattr(dirichlet_multinomial(alpha, n), method_name)
+        ref_method = getattr(stats.betabinom(n, *alpha.T), method_name)
+
+        res = method(x)
+        ref = ref_method(x.T[0])
+        assert_allclose(res, ref)
+
+    @pytest.mark.parametrize('method_name', ['mean', 'var'])
+    def test_against_betabinom_moments(self, method_name):
+        rng, m, alpha, n, x = self.get_params(100)
+
+        method = getattr(dirichlet_multinomial(alpha, n), method_name)
+        ref_method = getattr(stats.betabinom(n, *alpha.T), method_name)
+
+        res = method()[:, 0]
+        ref = ref_method()
+        assert_allclose(res, ref)
+
+    def test_moments(self):
+        rng = np.random.default_rng(28469824356873456)
+        dim = 5
+        n = rng.integers(1, 100)
+        alpha = rng.random(size=dim) * 10
+        dist = dirichlet_multinomial(alpha, n)
+
+        # Generate a random sample from the distribution using NumPy
+        m = 100000
+        p = rng.dirichlet(alpha, size=m)
+        x = rng.multinomial(n, p, size=m)
+
+        assert_allclose(dist.mean(), np.mean(x, axis=0), rtol=5e-3)
+        assert_allclose(dist.var(), np.var(x, axis=0), rtol=1e-2)
+        assert dist.mean().shape == dist.var().shape == (dim,)
+
+        cov = dist.cov()
+        assert cov.shape == (dim, dim)
+        assert_allclose(cov, np.cov(x.T), rtol=2e-2)
+        assert_equal(np.diag(cov), dist.var())
+        assert np.all(scipy.linalg.eigh(cov)[0] > 0)  # positive definite
+
+    def test_input_validation(self):
+        # valid inputs
+        x0 = np.array([1, 2, 3])
+        n0 = np.sum(x0)
+        alpha0 = np.array([3, 4, 5])
+
+        text = "`x` must contain only non-negative integers."
+        with assert_raises(ValueError, match=text):
+            dirichlet_multinomial.logpmf([1, -1, 3], alpha0, n0)
+        with assert_raises(ValueError, match=text):
+            dirichlet_multinomial.logpmf([1, 2.1, 3], alpha0, n0)
+
+        text = "`alpha` must contain only positive values."
+        with assert_raises(ValueError, match=text):
+            dirichlet_multinomial.logpmf(x0, [3, 0, 4], n0)
+        with assert_raises(ValueError, match=text):
+            dirichlet_multinomial.logpmf(x0, [3, -1, 4], n0)
+
+        text = "`n` must be a non-negative integer."
+        with assert_raises(ValueError, match=text):
+            dirichlet_multinomial.logpmf(x0, alpha0, 49.1)
+        with assert_raises(ValueError, match=text):
+            dirichlet_multinomial.logpmf(x0, alpha0, -1)
+
+        x = np.array([1, 2, 3, 4])
+        alpha = np.array([3, 4, 5])
+        text = "`x` and `alpha` must be broadcastable."
+        with assert_raises(ValueError, match=text):
+            dirichlet_multinomial.logpmf(x, alpha, x.sum())
+
+    @pytest.mark.parametrize('method', ['pmf', 'logpmf'])
+    def test_broadcasting_pmf(self, method):
+        alpha = np.array([[3, 4, 5], [4, 5, 6], [5, 5, 7], [8, 9, 10]])
+        n = np.array([[6], [7], [8]])
+        x = np.array([[1, 2, 3], [2, 2, 3]]).reshape((2, 1, 1, 3))
+        method = getattr(dirichlet_multinomial, method)
+        res = method(x, alpha, n)
+        assert res.shape == (2, 3, 4)
+        for i in range(len(x)):
+            for j in range(len(n)):
+                for k in range(len(alpha)):
+                    res_ijk = res[i, j, k]
+                    ref = method(x[i].squeeze(), alpha[k].squeeze(), n[j].squeeze())
+                    assert_allclose(res_ijk, ref)
+
+    @pytest.mark.parametrize('method_name', ['mean', 'var', 'cov'])
+    def test_broadcasting_moments(self, method_name):
+        alpha = np.array([[3, 4, 5], [4, 5, 6], [5, 5, 7], [8, 9, 10]])
+        n = np.array([[6], [7], [8]])
+        method = getattr(dirichlet_multinomial, method_name)
+        res = method(alpha, n)
+        assert res.shape == (3, 4, 3) if method_name != 'cov' else (3, 4, 3, 3)
+        for j in range(len(n)):
+            for k in range(len(alpha)):
+                res_ijk = res[j, k]
+                ref = method(alpha[k].squeeze(), n[j].squeeze())
+                assert_allclose(res_ijk, ref)
+
+
+class TestNormalInverseGamma:
+
+    def test_marginal_x(self):
+        # According to [1], sqrt(a * lmbda / b) * (x - u) should follow a t-distribution
+        # with 2*a degrees of freedom. Test that this is true of the PDF and random
+        # variates.
+        rng = np.random.default_rng(8925849245)
+        mu, lmbda, a, b = rng.random(4)
+
+        norm_inv_gamma = stats.normal_inverse_gamma(mu, lmbda, a, b)
+        t = stats.t(2*a, loc=mu, scale=1/np.sqrt(a * lmbda / b))
+
+        # Test PDF
+        x = np.linspace(-5, 5, 11)
+        res = tanhsinh(lambda s2, x: norm_inv_gamma.pdf(x, s2), 0, np.inf, args=(x,))
+        ref = t.pdf(x)
+        assert_allclose(res.integral, ref)
+
+        # Test RVS
+        res = norm_inv_gamma.rvs(size=10000, random_state=rng)
+        _, pvalue = stats.ks_1samp(res[0], t.cdf)
+        assert pvalue > 0.1
+
+    def test_marginal_s2(self):
+        # According to [1], s2 should follow an inverse gamma distribution with
+        # shapes a, b (where b is the scale in our parameterization). Test that
+        # this is true of the PDF and random variates.
+        rng = np.random.default_rng(8925849245)
+        mu, lmbda, a, b = rng.random(4)
+
+        norm_inv_gamma = stats.normal_inverse_gamma(mu, lmbda, a, b)
+        inv_gamma = stats.invgamma(a, scale=b)
+
+        # Test PDF
+        s2 = np.linspace(0.1, 10, 10)
+        res = tanhsinh(lambda x, s2: norm_inv_gamma.pdf(x, s2),
+                       -np.inf, np.inf, args=(s2,))
+        ref = inv_gamma.pdf(s2)
+        assert_allclose(res.integral, ref)
+
+        # Test RVS
+        res = norm_inv_gamma.rvs(size=10000, random_state=rng)
+        _, pvalue = stats.ks_1samp(res[1], inv_gamma.cdf)
+        assert pvalue > 0.1
+
+    def test_pdf_logpdf(self):
+        # Check that PDF and log-PDF are consistent
+        rng = np.random.default_rng(8925849245)
+        mu, lmbda, a, b = rng.random((4, 20)) - 0.25  # make some invalid
+        x, s2 = rng.random(size=(2, 20)) - 0.25
+        res = stats.normal_inverse_gamma(mu, lmbda, a, b).pdf(x, s2)
+        ref = stats.normal_inverse_gamma.logpdf(x, s2, mu, lmbda, a, b)
+        assert_allclose(res, np.exp(ref))
+
+    def test_invalid_and_special_cases(self):
+        # Test cases that are handled by input validation rather than the formulas
+        rng = np.random.default_rng(8925849245)
+        mu, lmbda, a, b = rng.random(4)
+        x, s2 = rng.random(2)
+
+        res = stats.normal_inverse_gamma(np.nan, lmbda, a, b).pdf(x, s2)
+        assert_equal(res, np.nan)
+
+        res = stats.normal_inverse_gamma(mu, -1, a, b).pdf(x, s2)
+        assert_equal(res, np.nan)
+
+        res = stats.normal_inverse_gamma(mu, lmbda, 0, b).pdf(x, s2)
+        assert_equal(res, np.nan)
+
+        res = stats.normal_inverse_gamma(mu, lmbda, a, -1).pdf(x, s2)
+        assert_equal(res, np.nan)
+
+        res = stats.normal_inverse_gamma(mu, lmbda, a, b).pdf(x, -1)
+        assert_equal(res, 0)
+
+        # PDF with out-of-support s2 is not zero if shape parameter is invalid
+        res = stats.normal_inverse_gamma(mu, [-1, np.nan], a, b).pdf(x, -1)
+        assert_equal(res, np.nan)
+
+        res = stats.normal_inverse_gamma(mu, -1, a, b).mean()
+        assert_equal(res, (np.nan, np.nan))
+
+        res = stats.normal_inverse_gamma(mu, lmbda, -1, b).var()
+        assert_equal(res, (np.nan, np.nan))
+
+        with pytest.raises(ValueError, match="Domain error in arguments..."):
+            stats.normal_inverse_gamma(mu, lmbda, a, -1).rvs()
+
+    def test_broadcasting(self):
+        # Test methods with broadcastable array parameters. Roughly speaking, the
+        # shapes should be the broadcasted shapes of all arguments, and the raveled
+        # outputs should be the same as the outputs with raveled inputs.
+        rng = np.random.default_rng(8925849245)
+        b = rng.random(2)
+        a = rng.random((3, 1)) + 2  # for defined moments
+        lmbda = rng.random((4, 1, 1))
+        mu = rng.random((5, 1, 1, 1))
+        s2 = rng.random((6, 1, 1, 1, 1))
+        x = rng.random((7, 1, 1, 1, 1, 1))
+        dist = stats.normal_inverse_gamma(mu, lmbda, a, b)
+
+        # Test PDF and log-PDF
+        broadcasted = np.broadcast_arrays(x, s2, mu, lmbda, a, b)
+        broadcasted_raveled = [np.ravel(arr) for arr in broadcasted]
+
+        res = dist.pdf(x, s2)
+        assert res.shape == broadcasted[0].shape
+        assert_allclose(res.ravel(),
+                        stats.normal_inverse_gamma.pdf(*broadcasted_raveled))
+
+        res = dist.logpdf(x, s2)
+        assert res.shape == broadcasted[0].shape
+        assert_allclose(res.ravel(),
+                        stats.normal_inverse_gamma.logpdf(*broadcasted_raveled))
+
+        # Test moments
+        broadcasted = np.broadcast_arrays(mu, lmbda, a, b)
+        broadcasted_raveled = [np.ravel(arr) for arr in broadcasted]
+
+        res = dist.mean()
+        assert res[0].shape == broadcasted[0].shape
+        assert_allclose((res[0].ravel(), res[1].ravel()),
+                        stats.normal_inverse_gamma.mean(*broadcasted_raveled))
+
+        res = dist.var()
+        assert res[0].shape == broadcasted[0].shape
+        assert_allclose((res[0].ravel(), res[1].ravel()),
+                        stats.normal_inverse_gamma.var(*broadcasted_raveled))
+
+        # Test RVS
+        size = (6, 5, 4, 3, 2)
+        rng = np.random.default_rng(2348923985324)
+        res = dist.rvs(size=size, random_state=rng)
+        rng = np.random.default_rng(2348923985324)
+        shape = 6, 5*4*3*2
+        ref = stats.normal_inverse_gamma.rvs(*broadcasted_raveled, size=shape,
+                                             random_state=rng)
+        assert_allclose((res[0].reshape(shape), res[1].reshape(shape)), ref)
+
+    @pytest.mark.slow
+    @pytest.mark.fail_slow(10)
+    def test_moments(self):
+        # Test moments against quadrature
+        rng = np.random.default_rng(8925849245)
+        mu, lmbda, a, b = rng.random(4)
+        a += 2  # ensure defined
+
+        dist = stats.normal_inverse_gamma(mu, lmbda, a, b)
+        res = dist.mean()
+
+        ref = dblquad(lambda s2, x: dist.pdf(x, s2) * x, -np.inf, np.inf, 0, np.inf)
+        assert_allclose(res[0], ref[0], rtol=1e-6)
+
+        ref = dblquad(lambda s2, x: dist.pdf(x, s2) * s2, -np.inf, np.inf, 0, np.inf)
+        assert_allclose(res[1], ref[0], rtol=1e-6)
+
+    @pytest.mark.parametrize('dtype', [np.int32, np.float16, np.float32, np.float64])
+    def test_dtype(self, dtype):
+        rng = np.random.default_rng(8925849245)
+        x, s2, mu, lmbda, a, b = rng.uniform(3, 10, size=6).astype(dtype)
+        dtype_out = np.result_type(1.0, dtype)
+        dist = stats.normal_inverse_gamma(mu, lmbda, a, b)
+        assert dist.rvs()[0].dtype == dtype_out
+        assert dist.rvs()[1].dtype == dtype_out
+        assert dist.mean()[0].dtype == dtype_out
+        assert dist.mean()[1].dtype == dtype_out
+        assert dist.var()[0].dtype == dtype_out
+        assert dist.var()[1].dtype == dtype_out
+        assert dist.logpdf(x, s2).dtype == dtype_out
+        assert dist.pdf(x, s2).dtype == dtype_out
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/test_new_distributions.py b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_new_distributions.py
new file mode 100644
index 0000000000000000000000000000000000000000..b266b07b858ee1571e988c59af23e6348a219e4d
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_new_distributions.py
@@ -0,0 +1,17 @@
+# file for distribution-specific tests with new infrastructure (UnivariateDistribution)
+import numpy as np
+from numpy.testing import assert_allclose
+from scipy import stats
+
+class TestBinomial:
+    def test_gh23708_binomial_logcdf_method_complement(self):
+        # gh-23708 found that `logcdf` method='complement' was inaccurate in the tails
+        x = np.asarray([0., 18.])
+        X = stats.Binomial(n=np.asarray([18.]), p=np.asarray(0.71022842))
+        assert_allclose(X.logcdf(x, method='complement'), X.logcdf(x), rtol=1e-15)
+        assert_allclose(X.logccdf(x, method='complement'), X.logccdf(x), rtol=1e-15)
+
+        # going even deeper into the tails
+        X = stats.Binomial(n=100, p=0.5)
+        assert_allclose(X.logcdf(0, method='complement'), X.logpmf(0), rtol=1e-15)
+        assert_allclose(X.logccdf(99, method='complement'), X.logpmf(100), rtol=1e-15)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/test_odds_ratio.py b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_odds_ratio.py
new file mode 100644
index 0000000000000000000000000000000000000000..14b5ca88d0fca9edb8c3c161c06e52054d594e62
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_odds_ratio.py
@@ -0,0 +1,148 @@
+import pytest
+import numpy as np
+from numpy.testing import assert_equal, assert_allclose
+from .._discrete_distns import nchypergeom_fisher, hypergeom
+from scipy.stats._odds_ratio import odds_ratio
+from .data.fisher_exact_results_from_r import data
+
+
+class TestOddsRatio:
+
+    @pytest.mark.parametrize('parameters, rresult', data)
+    def test_results_from_r(self, parameters, rresult):
+        alternative = parameters.alternative.replace('.', '-')
+        result = odds_ratio(parameters.table)
+        # The results computed by R are not very accurate.
+        if result.statistic < 400:
+            or_rtol = 5e-4
+            ci_rtol = 2e-2
+        else:
+            or_rtol = 5e-2
+            ci_rtol = 1e-1
+        assert_allclose(result.statistic,
+                        rresult.conditional_odds_ratio, rtol=or_rtol)
+        ci = result.confidence_interval(parameters.confidence_level,
+                                        alternative)
+        assert_allclose((ci.low, ci.high), rresult.conditional_odds_ratio_ci,
+                        rtol=ci_rtol)
+
+        # Also do a self-check for the conditional odds ratio.
+        # With the computed conditional odds ratio as the noncentrality
+        # parameter of the noncentral hypergeometric distribution with
+        # parameters table.sum(), table[0].sum(), and table[:,0].sum() as
+        # total, ngood and nsample, respectively, the mean of the distribution
+        # should equal table[0, 0].
+        cor = result.statistic
+        table = np.array(parameters.table)
+        total = table.sum()
+        ngood = table[0].sum()
+        nsample = table[:, 0].sum()
+        # nchypergeom_fisher does not allow the edge cases where the
+        # noncentrality parameter is 0 or inf, so handle those values
+        # separately here.
+        if cor == 0:
+            nchg_mean = hypergeom.support(total, ngood, nsample)[0]
+        elif cor == np.inf:
+            nchg_mean = hypergeom.support(total, ngood, nsample)[1]
+        else:
+            nchg_mean = nchypergeom_fisher.mean(total, ngood, nsample, cor)
+        assert_allclose(nchg_mean, table[0, 0], rtol=1e-13)
+
+        # Check that the confidence interval is correct.
+        alpha = 1 - parameters.confidence_level
+        if alternative == 'two-sided':
+            if ci.low > 0:
+                sf = nchypergeom_fisher.sf(table[0, 0] - 1,
+                                           total, ngood, nsample, ci.low)
+                assert_allclose(sf, alpha/2, rtol=1e-11)
+            if np.isfinite(ci.high):
+                cdf = nchypergeom_fisher.cdf(table[0, 0],
+                                             total, ngood, nsample, ci.high)
+                assert_allclose(cdf, alpha/2, rtol=1e-11)
+        elif alternative == 'less':
+            if np.isfinite(ci.high):
+                cdf = nchypergeom_fisher.cdf(table[0, 0],
+                                             total, ngood, nsample, ci.high)
+                assert_allclose(cdf, alpha, rtol=1e-11)
+        else:
+            # alternative == 'greater'
+            if ci.low > 0:
+                sf = nchypergeom_fisher.sf(table[0, 0] - 1,
+                                           total, ngood, nsample, ci.low)
+                assert_allclose(sf, alpha, rtol=1e-11)
+
+    @pytest.mark.parametrize('table', [
+        [[0, 0], [5, 10]],
+        [[5, 10], [0, 0]],
+        [[0, 5], [0, 10]],
+        [[5, 0], [10, 0]],
+    ])
+    def test_row_or_col_zero(self, table):
+        result = odds_ratio(table)
+        assert_equal(result.statistic, np.nan)
+        ci = result.confidence_interval()
+        assert_equal((ci.low, ci.high), (0, np.inf))
+
+    @pytest.mark.parametrize("case",
+                             [[0.95, 'two-sided', 0.4879913, 2.635883],
+                              [0.90, 'two-sided', 0.5588516, 2.301663]])
+    def test_sample_odds_ratio_ci(self, case):
+        # Compare the sample odds ratio confidence interval to the R function
+        # oddsratio.wald from the epitools package, e.g.
+        # > library(epitools)
+        # > table = matrix(c(10, 20, 41, 93), nrow=2, ncol=2, byrow=TRUE)
+        # > result = oddsratio.wald(table)
+        # > result$measure
+        #           odds ratio with 95% C.I.
+        # Predictor  estimate     lower    upper
+        #   Exposed1 1.000000        NA       NA
+        #   Exposed2 1.134146 0.4879913 2.635883
+
+        confidence_level, alternative, ref_low, ref_high = case
+        table = [[10, 20], [41, 93]]
+        result = odds_ratio(table, kind='sample')
+        assert_allclose(result.statistic, 1.134146, rtol=1e-6)
+        ci = result.confidence_interval(confidence_level, alternative)
+        assert_allclose([ci.low, ci.high], [ref_low, ref_high], rtol=1e-6)
+
+    @pytest.mark.slow
+    @pytest.mark.parametrize('alternative', ['less', 'greater', 'two-sided'])
+    def test_sample_odds_ratio_one_sided_ci(self, alternative):
+        # can't find a good reference for one-sided CI, so bump up the sample
+        # size and compare against the conditional odds ratio CI
+        table = [[1000, 2000], [4100, 9300]]
+        res = odds_ratio(table, kind='sample')
+        ref = odds_ratio(table, kind='conditional')
+        assert_allclose(res.statistic, ref.statistic, atol=1e-5)
+        assert_allclose(res.confidence_interval(alternative=alternative),
+                        ref.confidence_interval(alternative=alternative),
+                        atol=2e-3)
+
+    @pytest.mark.parametrize('kind', ['sample', 'conditional'])
+    @pytest.mark.parametrize('bad_table', [123, "foo", [10, 11, 12]])
+    def test_invalid_table_shape(self, kind, bad_table):
+        with pytest.raises(ValueError, match="Invalid shape"):
+            odds_ratio(bad_table, kind=kind)
+
+    def test_invalid_table_type(self):
+        with pytest.raises(ValueError, match='must be an array of integers'):
+            odds_ratio([[1.0, 3.4], [5.0, 9.9]])
+
+    def test_negative_table_values(self):
+        with pytest.raises(ValueError, match='must be nonnegative'):
+            odds_ratio([[1, 2], [3, -4]])
+
+    def test_invalid_kind(self):
+        with pytest.raises(ValueError, match='`kind` must be'):
+            odds_ratio([[10, 20], [30, 14]], kind='magnetoreluctance')
+
+    def test_invalid_alternative(self):
+        result = odds_ratio([[5, 10], [2, 32]])
+        with pytest.raises(ValueError, match='`alternative` must be'):
+            result.confidence_interval(alternative='depleneration')
+
+    @pytest.mark.parametrize('level', [-0.5, 1.5])
+    def test_invalid_confidence_level(self, level):
+        result = odds_ratio([[5, 10], [2, 32]])
+        with pytest.raises(ValueError, match='must be between 0 and 1'):
+            result.confidence_interval(confidence_level=level)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/test_qmc.py b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_qmc.py
new file mode 100644
index 0000000000000000000000000000000000000000..650a16e975c30e6df5b5a2b197d92d2a7f972ed3
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_qmc.py
@@ -0,0 +1,1535 @@
+import os
+from collections import Counter
+from itertools import combinations, product
+
+import pytest
+import numpy as np
+from numpy.testing import (assert_allclose, assert_equal, assert_array_equal,
+    assert_array_less)
+
+from scipy.spatial import distance
+from scipy.stats import shapiro
+from scipy.stats._sobol import _test_find_index, _test_low_0_bit
+from scipy.stats import qmc
+from scipy.stats._qmc import (
+    van_der_corput, n_primes, primes_from_2_to,
+    update_discrepancy, QMCEngine, _l1_norm,
+    _perturb_discrepancy, _lloyd_centroidal_voronoi_tessellation
+)
+
+
+class TestUtils:
+    def test_scale(self):
+        # 1d scalar
+        space = [[0], [1], [0.5]]
+        out = [[-2], [6], [2]]
+        scaled_space = qmc.scale(space, l_bounds=-2, u_bounds=6)
+
+        assert_allclose(scaled_space, out)
+
+        # 2d space
+        space = [[0, 0], [1, 1], [0.5, 0.5]]
+        bounds = np.array([[-2, 0], [6, 5]])
+        out = [[-2, 0], [6, 5], [2, 2.5]]
+
+        scaled_space = qmc.scale(space, l_bounds=bounds[0], u_bounds=bounds[1])
+
+        assert_allclose(scaled_space, out)
+
+        scaled_back_space = qmc.scale(scaled_space, l_bounds=bounds[0],
+                                      u_bounds=bounds[1], reverse=True)
+        assert_allclose(scaled_back_space, space)
+
+        # broadcast
+        space = [[0, 0, 0], [1, 1, 1], [0.5, 0.5, 0.5]]
+        l_bounds, u_bounds = 0, [6, 5, 3]
+        out = [[0, 0, 0], [6, 5, 3], [3, 2.5, 1.5]]
+
+        scaled_space = qmc.scale(space, l_bounds=l_bounds, u_bounds=u_bounds)
+
+        assert_allclose(scaled_space, out)
+
+    def test_scale_random(self):
+        rng = np.random.default_rng(317589836511269190194010915937762468165)
+        sample = rng.random((30, 10))
+        a = -rng.random(10) * 10
+        b = rng.random(10) * 10
+        scaled = qmc.scale(sample, a, b, reverse=False)
+        unscaled = qmc.scale(scaled, a, b, reverse=True)
+        assert_allclose(unscaled, sample)
+
+    def test_scale_errors(self):
+        with pytest.raises(ValueError, match=r"Sample is not a 2D array"):
+            space = [0, 1, 0.5]
+            qmc.scale(space, l_bounds=-2, u_bounds=6)
+
+        with pytest.raises(ValueError, match=r"Bounds are not consistent"):
+            space = [[0, 0], [1, 1], [0.5, 0.5]]
+            bounds = np.array([[-2, 6], [6, 5]])
+            qmc.scale(space, l_bounds=bounds[0], u_bounds=bounds[1])
+
+        with pytest.raises(ValueError, match=r"'l_bounds' and 'u_bounds'"
+                                             r" must be broadcastable"):
+            space = [[0, 0], [1, 1], [0.5, 0.5]]
+            l_bounds, u_bounds = [-2, 0, 2], [6, 5]
+            qmc.scale(space, l_bounds=l_bounds, u_bounds=u_bounds)
+
+        with pytest.raises(ValueError, match=r"'l_bounds' and 'u_bounds'"
+                                             r" must be broadcastable"):
+            space = [[0, 0], [1, 1], [0.5, 0.5]]
+            bounds = np.array([[-2, 0, 2], [6, 5, 5]])
+            qmc.scale(space, l_bounds=bounds[0], u_bounds=bounds[1])
+
+        with pytest.raises(ValueError, match=r"Sample is not in unit "
+                                             r"hypercube"):
+            space = [[0, 0], [1, 1.5], [0.5, 0.5]]
+            bounds = np.array([[-2, 0], [6, 5]])
+            qmc.scale(space, l_bounds=bounds[0], u_bounds=bounds[1])
+
+        with pytest.raises(ValueError, match=r"Sample is out of bounds"):
+            out = [[-2, 0], [6, 5], [8, 2.5]]
+            bounds = np.array([[-2, 0], [6, 5]])
+            qmc.scale(out, l_bounds=bounds[0], u_bounds=bounds[1],
+                      reverse=True)
+
+    def test_discrepancy(self):
+        space_1 = np.array([[1, 3], [2, 6], [3, 2], [4, 5], [5, 1], [6, 4]])
+        space_1 = (2.0 * space_1 - 1.0) / (2.0 * 6.0)
+        space_2 = np.array([[1, 5], [2, 4], [3, 3], [4, 2], [5, 1], [6, 6]])
+        space_2 = (2.0 * space_2 - 1.0) / (2.0 * 6.0)
+
+        # From Fang et al. Design and modeling for computer experiments, 2006
+        assert_allclose(qmc.discrepancy(space_1), 0.0081, atol=1e-4)
+        assert_allclose(qmc.discrepancy(space_2), 0.0105, atol=1e-4)
+
+        # From Zhou Y.-D. et al. Mixture discrepancy for quasi-random point
+        # sets. Journal of Complexity, 29 (3-4), pp. 283-301, 2013.
+        # Example 4 on Page 298
+        sample = np.array([[2, 1, 1, 2, 2, 2],
+                           [1, 2, 2, 2, 2, 2],
+                           [2, 1, 1, 1, 1, 1],
+                           [1, 1, 1, 1, 2, 2],
+                           [1, 2, 2, 2, 1, 1],
+                           [2, 2, 2, 2, 1, 1],
+                           [2, 2, 2, 1, 2, 2]])
+        sample = (2.0 * sample - 1.0) / (2.0 * 2.0)
+
+        assert_allclose(qmc.discrepancy(sample, method='MD'), 2.5000,
+                        atol=1e-4)
+        assert_allclose(qmc.discrepancy(sample, method='WD'), 1.3680,
+                        atol=1e-4)
+        assert_allclose(qmc.discrepancy(sample, method='CD'), 0.3172,
+                        atol=1e-4)
+
+        # From Tim P. et al. Minimizing the L2 and Linf star discrepancies
+        # of a single point in the unit hypercube. JCAM, 2005
+        # Table 1 on Page 283
+        for dim in [2, 4, 8, 16, 32, 64]:
+            ref = np.sqrt(3**(-dim))
+            assert_allclose(qmc.discrepancy(np.array([[1]*dim]),
+                                            method='L2-star'), ref)
+
+    def test_discrepancy_errors(self):
+        sample = np.array([[1, 3], [2, 6], [3, 2], [4, 5], [5, 1], [6, 4]])
+
+        with pytest.raises(
+            ValueError, match=r"Sample is not in unit hypercube"
+        ):
+            qmc.discrepancy(sample)
+
+        with pytest.raises(ValueError, match=r"Sample is not a 2D array"):
+            qmc.discrepancy([1, 3])
+
+        sample = [[0, 0], [1, 1], [0.5, 0.5]]
+        with pytest.raises(ValueError, match=r"'toto' is not a valid ..."):
+            qmc.discrepancy(sample, method="toto")
+
+    def test_discrepancy_parallel(self, monkeypatch):
+        sample = np.array([[2, 1, 1, 2, 2, 2],
+                           [1, 2, 2, 2, 2, 2],
+                           [2, 1, 1, 1, 1, 1],
+                           [1, 1, 1, 1, 2, 2],
+                           [1, 2, 2, 2, 1, 1],
+                           [2, 2, 2, 2, 1, 1],
+                           [2, 2, 2, 1, 2, 2]])
+        sample = (2.0 * sample - 1.0) / (2.0 * 2.0)
+
+        assert_allclose(qmc.discrepancy(sample, method='MD', workers=8),
+                        2.5000,
+                        atol=1e-4)
+        assert_allclose(qmc.discrepancy(sample, method='WD', workers=8),
+                        1.3680,
+                        atol=1e-4)
+        assert_allclose(qmc.discrepancy(sample, method='CD', workers=8),
+                        0.3172,
+                        atol=1e-4)
+
+        # From Tim P. et al. Minimizing the L2 and Linf star discrepancies
+        # of a single point in the unit hypercube. JCAM, 2005
+        # Table 1 on Page 283
+        for dim in [2, 4, 8, 16, 32, 64]:
+            ref = np.sqrt(3 ** (-dim))
+            assert_allclose(qmc.discrepancy(np.array([[1] * dim]),
+                                            method='L2-star', workers=-1), ref)
+
+        monkeypatch.setattr(os, 'cpu_count', lambda: None)
+        with pytest.raises(NotImplementedError, match="Cannot determine the"):
+            qmc.discrepancy(sample, workers=-1)
+
+        with pytest.raises(ValueError, match="Invalid number of workers..."):
+            qmc.discrepancy(sample, workers=-2)
+
+    def test_geometric_discrepancy_errors(self):
+        sample = np.array([[1, 3], [2, 6], [3, 2], [4, 5], [5, 1], [6, 4]])
+
+        with pytest.raises(ValueError, match=r"Sample is not in unit hypercube"):
+            qmc.geometric_discrepancy(sample)
+
+        with pytest.raises(ValueError, match=r"Sample is not a 2D array"):
+            qmc.geometric_discrepancy([1, 3])
+
+        sample = [[0, 0], [1, 1], [0.5, 0.5]]
+        with pytest.raises(ValueError, match=r"'toto' is not a valid ..."):
+            qmc.geometric_discrepancy(sample, method="toto")
+
+        sample = np.array([[0, 0], [0, 0], [0, 1]])
+        with pytest.warns(UserWarning, match="Sample contains duplicate points."):
+            qmc.geometric_discrepancy(sample)
+
+        sample = np.array([[0.5, 0.5]])
+        with pytest.raises(ValueError, match="Sample must contain at least two points"):
+            qmc.geometric_discrepancy(sample)
+
+    def test_geometric_discrepancy(self):
+        sample = np.array([[0, 0], [1, 1]])
+        assert_allclose(qmc.geometric_discrepancy(sample), np.sqrt(2))
+        assert_allclose(qmc.geometric_discrepancy(sample, method="mst"), np.sqrt(2))
+
+        sample = np.array([[0, 0], [0, 1], [0.5, 1]])
+        assert_allclose(qmc.geometric_discrepancy(sample), 0.5)
+        assert_allclose(qmc.geometric_discrepancy(sample, method="mst"), 0.75)
+
+        sample = np.array([[0, 0], [0.25, 0.25], [1, 1]])
+        assert_allclose(qmc.geometric_discrepancy(sample), np.sqrt(2) / 4)
+        assert_allclose(qmc.geometric_discrepancy(sample, method="mst"), np.sqrt(2) / 2)
+        assert_allclose(qmc.geometric_discrepancy(sample, metric="chebyshev"), 0.25)
+        assert_allclose(
+            qmc.geometric_discrepancy(sample, method="mst", metric="chebyshev"), 0.5
+        )
+
+        rng = np.random.default_rng(191468432622931918890291693003068437394)
+        sample = qmc.LatinHypercube(d=3, rng=rng).random(50)
+        assert_allclose(qmc.geometric_discrepancy(sample), 0.05106012076093356)
+        assert_allclose(
+            qmc.geometric_discrepancy(sample, method='mst'), 0.19704396643366182
+        )
+
+    @pytest.mark.xfail(
+            reason="minimum_spanning_tree ignores zero distances (#18892)",
+            strict=True,
+    )
+    @pytest.mark.thread_unsafe
+    def test_geometric_discrepancy_mst_with_zero_distances(self):
+        sample = np.array([[0, 0], [0, 0], [0, 1]])
+        assert_allclose(qmc.geometric_discrepancy(sample, method='mst'), 0.5)
+
+    def test_update_discrepancy(self):
+        # From Fang et al. Design and modeling for computer experiments, 2006
+        space_1 = np.array([[1, 3], [2, 6], [3, 2], [4, 5], [5, 1], [6, 4]])
+        space_1 = (2.0 * space_1 - 1.0) / (2.0 * 6.0)
+
+        disc_init = qmc.discrepancy(space_1[:-1], iterative=True)
+        disc_iter = update_discrepancy(space_1[-1], space_1[:-1], disc_init)
+
+        assert_allclose(disc_iter, 0.0081, atol=1e-4)
+
+        # n<d
+        rng = np.random.default_rng(241557431858162136881731220526394276199)
+        space_1 = rng.random((4, 10))
+
+        disc_ref = qmc.discrepancy(space_1)
+        disc_init = qmc.discrepancy(space_1[:-1], iterative=True)
+        disc_iter = update_discrepancy(space_1[-1], space_1[:-1], disc_init)
+
+        assert_allclose(disc_iter, disc_ref, atol=1e-4)
+
+        # errors
+        with pytest.raises(ValueError, match=r"Sample is not in unit "
+                                             r"hypercube"):
+            update_discrepancy(space_1[-1], space_1[:-1] + 1, disc_init)
+
+        with pytest.raises(ValueError, match=r"Sample is not a 2D array"):
+            update_discrepancy(space_1[-1], space_1[0], disc_init)
+
+        x_new = [1, 3]
+        with pytest.raises(ValueError, match=r"x_new is not in unit "
+                                             r"hypercube"):
+            update_discrepancy(x_new, space_1[:-1], disc_init)
+
+        x_new = [[0.5, 0.5]]
+        with pytest.raises(ValueError, match=r"x_new is not a 1D array"):
+            update_discrepancy(x_new, space_1[:-1], disc_init)
+
+        x_new = [0.3, 0.1, 0]
+        with pytest.raises(ValueError, match=r"x_new and sample must be "
+                                             r"broadcastable"):
+            update_discrepancy(x_new, space_1[:-1], disc_init)
+
+    def test_perm_discrepancy(self):
+        rng = np.random.default_rng(46449423132557934943847369749645759997)
+        qmc_gen = qmc.LatinHypercube(5, rng=rng)
+        sample = qmc_gen.random(10)
+        disc = qmc.discrepancy(sample)
+
+        for i in range(100):
+            row_1 = rng.integers(10)
+            row_2 = rng.integers(10)
+            col = rng.integers(5)
+
+            disc = _perturb_discrepancy(sample, row_1, row_2, col, disc)
+            sample[row_1, col], sample[row_2, col] = (
+                sample[row_2, col], sample[row_1, col])
+            disc_reference = qmc.discrepancy(sample)
+            assert_allclose(disc, disc_reference)
+
+    def test_discrepancy_alternative_implementation(self):
+        """Alternative definitions from Matt Haberland."""
+
+        def disc_c2(x):
+            n, s = x.shape
+            xij = x
+            disc1 = np.sum(np.prod((1
+                                    + 1/2*np.abs(xij-0.5)
+                                    - 1/2*np.abs(xij-0.5)**2), axis=1))
+            xij = x[None, :, :]
+            xkj = x[:, None, :]
+            disc2 = np.sum(np.sum(np.prod(1
+                                          + 1/2*np.abs(xij - 0.5)
+                                          + 1/2*np.abs(xkj - 0.5)
+                                          - 1/2*np.abs(xij - xkj), axis=2),
+                                  axis=0))
+            return (13/12)**s - 2/n * disc1 + 1/n**2*disc2
+
+        def disc_wd(x):
+            n, s = x.shape
+            xij = x[None, :, :]
+            xkj = x[:, None, :]
+            disc = np.sum(np.sum(np.prod(3/2
+                                         - np.abs(xij - xkj)
+                                         + np.abs(xij - xkj)**2, axis=2),
+                                 axis=0))
+            return -(4/3)**s + 1/n**2 * disc
+
+        def disc_md(x):
+            n, s = x.shape
+            xij = x
+            disc1 = np.sum(np.prod((5/3
+                                    - 1/4*np.abs(xij-0.5)
+                                    - 1/4*np.abs(xij-0.5)**2), axis=1))
+            xij = x[None, :, :]
+            xkj = x[:, None, :]
+            disc2 = np.sum(np.sum(np.prod(15/8
+                                          - 1/4*np.abs(xij - 0.5)
+                                          - 1/4*np.abs(xkj - 0.5)
+                                          - 3/4*np.abs(xij - xkj)
+                                          + 1/2*np.abs(xij - xkj)**2,
+                                          axis=2), axis=0))
+            return (19/12)**s - 2/n * disc1 + 1/n**2*disc2
+
+        def disc_star_l2(x):
+            n, s = x.shape
+            return np.sqrt(
+                3 ** (-s) - 2 ** (1 - s) / n
+                * np.sum(np.prod(1 - x ** 2, axis=1))
+                + np.sum([
+                    np.prod(1 - np.maximum(x[k, :], x[j, :]))
+                    for k in range(n) for j in range(n)
+                ]) / n ** 2
+            )
+
+        rng = np.random.default_rng(117065081482921065782761407107747179201)
+        sample = rng.random((30, 10))
+
+        disc_curr = qmc.discrepancy(sample, method='CD')
+        disc_alt = disc_c2(sample)
+        assert_allclose(disc_curr, disc_alt)
+
+        disc_curr = qmc.discrepancy(sample, method='WD')
+        disc_alt = disc_wd(sample)
+        assert_allclose(disc_curr, disc_alt)
+
+        disc_curr = qmc.discrepancy(sample, method='MD')
+        disc_alt = disc_md(sample)
+        assert_allclose(disc_curr, disc_alt)
+
+        disc_curr = qmc.discrepancy(sample, method='L2-star')
+        disc_alt = disc_star_l2(sample)
+        assert_allclose(disc_curr, disc_alt)
+
+    def test_n_primes(self):
+        primes = n_primes(10)
+        assert primes[-1] == 29
+
+        primes = n_primes(168)
+        assert primes[-1] == 997
+
+        primes = n_primes(350)
+        assert primes[-1] == 2357
+
+    def test_primes(self):
+        primes = primes_from_2_to(50)
+        out = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]
+        assert_allclose(primes, out)
+
+
+class TestVDC:
+    def test_van_der_corput(self):
+        sample = van_der_corput(10)
+        out = [0.0, 0.5, 0.25, 0.75, 0.125, 0.625,
+               0.375, 0.875, 0.0625, 0.5625]
+        assert_allclose(sample, out)
+
+        sample = van_der_corput(10, workers=4)
+        assert_allclose(sample, out)
+
+        sample = van_der_corput(10, workers=8)
+        assert_allclose(sample, out)
+
+        sample = van_der_corput(7, start_index=3)
+        assert_allclose(sample, out[3:])
+
+    def test_van_der_corput_scramble(self):
+        rng = 338213789010180879520345496831675783177
+        out = van_der_corput(10, scramble=True, rng=rng)
+
+        sample = van_der_corput(7, start_index=3, scramble=True, rng=rng)
+        assert_allclose(sample, out[3:])
+
+        sample = van_der_corput(
+            7, start_index=3, scramble=True, rng=rng, workers=4
+        )
+        assert_allclose(sample, out[3:])
+
+        sample = van_der_corput(
+            7, start_index=3, scramble=True, rng=rng, workers=8
+        )
+        assert_allclose(sample, out[3:])
+
+    def test_invalid_base_error(self):
+        with pytest.raises(ValueError, match=r"'base' must be at least 2"):
+            van_der_corput(10, base=1)
+
+
+class RandomEngine(qmc.QMCEngine):
+    def __init__(self, d, optimization=None, rng=None):
+        super().__init__(d=d, optimization=optimization, rng=rng)
+
+    def _random(self, n=1, *, workers=1):
+        sample = self.rng.random((n, self.d))
+        return sample
+
+
+def test_subclassing_QMCEngine():
+    engine = RandomEngine(2, rng=175180605424926556207367152557812293274)
+
+    sample_1 = engine.random(n=5)
+    sample_2 = engine.random(n=7)
+    assert engine.num_generated == 12
+
+    # reset and re-sample
+    engine.reset()
+    assert engine.num_generated == 0
+
+    sample_1_test = engine.random(n=5)
+    assert_equal(sample_1, sample_1_test)
+
+    # repeat reset and fast forward
+    engine.reset()
+    engine.fast_forward(n=5)
+    sample_2_test = engine.random(n=7)
+
+    assert_equal(sample_2, sample_2_test)
+    assert engine.num_generated == 12
+
+
+def test_raises():
+    # input validation
+    with pytest.raises(ValueError, match=r"d must be a non-negative integer"):
+        RandomEngine((2,))
+
+    with pytest.raises(ValueError, match=r"d must be a non-negative integer"):
+        RandomEngine(-1)
+
+    msg = r"'u_bounds' and 'l_bounds' must be integers"
+    with pytest.raises(ValueError, match=msg):
+        engine = RandomEngine(1)
+        engine.integers(l_bounds=1, u_bounds=1.1)
+
+
+def test_integers():
+    engine = RandomEngine(1, rng=231195739755290648063853336582377368684)
+
+    # basic tests
+    sample = engine.integers(1, n=10)
+    assert_equal(np.unique(sample), [0])
+
+    assert sample.dtype == np.dtype('int64')
+
+    sample = engine.integers(1, n=10, endpoint=True)
+    assert_equal(np.unique(sample), [0, 1])
+
+    low = -5
+    high = 7
+
+    # scaling logic
+    engine.reset()
+    ref_sample = engine.random(20)
+    ref_sample = ref_sample * (high - low) + low
+    ref_sample = np.floor(ref_sample).astype(np.int64)
+
+    engine.reset()
+    sample = engine.integers(low, u_bounds=high, n=20, endpoint=False)
+
+    assert_equal(sample, ref_sample)
+
+    # up to bounds, no less, no more
+    sample = engine.integers(low, u_bounds=high, n=100, endpoint=False)
+    assert_equal((sample.min(), sample.max()), (low, high-1))
+
+    sample = engine.integers(low, u_bounds=high, n=100, endpoint=True)
+    assert_equal((sample.min(), sample.max()), (low, high))
+
+
+def test_integers_nd():
+    d = 10
+    rng = np.random.default_rng(3716505122102428560615700415287450951)
+    low = rng.integers(low=-5, high=-1, size=d)
+    high = rng.integers(low=1, high=5, size=d, endpoint=True)
+    engine = RandomEngine(d, rng=rng)
+
+    sample = engine.integers(low, u_bounds=high, n=100, endpoint=False)
+    assert_equal(sample.min(axis=0), low)
+    assert_equal(sample.max(axis=0), high-1)
+
+    sample = engine.integers(low, u_bounds=high, n=100, endpoint=True)
+    assert_equal(sample.min(axis=0), low)
+    assert_equal(sample.max(axis=0), high)
+
+
+class QMCEngineTests:
+    """Generic tests for QMC engines."""
+    qmce = NotImplemented
+    can_scramble = NotImplemented
+    unscramble_nd = NotImplemented
+    scramble_nd = NotImplemented
+
+    scramble = [True, False]
+    ids = ["Scrambled", "Unscrambled"]
+
+    def engine(
+        self, scramble: bool,
+        rng=170382760648021597650530316304495310428,
+        **kwargs
+    ) -> QMCEngine:
+        # preserve use of `seed` during SPEC 7 transition because
+        # some tests rely on behavior with integer `seed` (which is
+        # different from behavior with integer `rng`)
+        if self.can_scramble:
+            return self.qmce(scramble=scramble, seed=rng, **kwargs)
+        else:
+            if scramble:
+                pytest.skip()
+            else:
+                return self.qmce(seed=rng, **kwargs)
+
+    def reference(self, scramble: bool) -> np.ndarray:
+        return self.scramble_nd if scramble else self.unscramble_nd
+
+    @pytest.mark.parametrize("scramble", scramble, ids=ids)
+    def test_0dim(self, scramble):
+        engine = self.engine(d=0, scramble=scramble)
+        sample = engine.random(4)
+        assert_array_equal(np.empty((4, 0)), sample)
+
+    @pytest.mark.parametrize("scramble", scramble, ids=ids)
+    def test_0sample(self, scramble):
+        engine = self.engine(d=2, scramble=scramble)
+        sample = engine.random(0)
+        assert_array_equal(np.empty((0, 2)), sample)
+
+    @pytest.mark.parametrize("scramble", scramble, ids=ids)
+    def test_1sample(self, scramble):
+        engine = self.engine(d=2, scramble=scramble)
+        sample = engine.random(1)
+        assert (1, 2) == sample.shape
+
+    @pytest.mark.parametrize("scramble", scramble, ids=ids)
+    def test_bounds(self, scramble):
+        engine = self.engine(d=100, scramble=scramble)
+        sample = engine.random(512)
+        assert np.all(sample >= 0)
+        assert np.all(sample <= 1)
+
+    @pytest.mark.parametrize("scramble", scramble, ids=ids)
+    def test_sample(self, scramble):
+        ref_sample = self.reference(scramble=scramble)
+        engine = self.engine(d=2, scramble=scramble)
+        sample = engine.random(n=len(ref_sample))
+
+        assert_allclose(sample, ref_sample, atol=1e-1)
+        assert engine.num_generated == len(ref_sample)
+
+    @pytest.mark.parametrize("scramble", scramble, ids=ids)
+    def test_continuing(self, scramble):
+        engine = self.engine(d=2, scramble=scramble)
+        ref_sample = engine.random(n=8)
+
+        engine = self.engine(d=2, scramble=scramble)
+
+        n_half = len(ref_sample) // 2
+
+        _ = engine.random(n=n_half)
+        sample = engine.random(n=n_half)
+        assert_allclose(sample, ref_sample[n_half:], atol=1e-1)
+
+    @pytest.mark.parametrize("scramble", scramble, ids=ids)
+    @pytest.mark.parametrize(
+        "rng",
+        (
+            170382760648021597650530316304495310428,
+            lambda: np.random.default_rng(170382760648021597650530316304495310428),
+            pytest.param(None, marks=pytest.mark.thread_unsafe),
+        ),
+    )
+    def test_reset(self, scramble, rng):
+        if callable(rng):
+            # Initialize local RNG here to make it thread-local in pytest-run-parallel
+            rng = rng()
+        engine = self.engine(d=2, scramble=scramble, rng=rng)
+        ref_sample = engine.random(n=8)
+
+        engine.reset()
+        assert engine.num_generated == 0
+
+        sample = engine.random(n=8)
+        assert_allclose(sample, ref_sample)
+
+    @pytest.mark.parametrize("scramble", scramble, ids=ids)
+    def test_fast_forward(self, scramble):
+        engine = self.engine(d=2, scramble=scramble)
+        ref_sample = engine.random(n=8)
+
+        engine = self.engine(d=2, scramble=scramble)
+
+        engine.fast_forward(4)
+        sample = engine.random(n=4)
+
+        assert_allclose(sample, ref_sample[4:], atol=1e-1)
+
+        # alternate fast forwarding with sampling
+        engine.reset()
+        even_draws = []
+        for i in range(8):
+            if i % 2 == 0:
+                even_draws.append(engine.random())
+            else:
+                engine.fast_forward(1)
+        assert_allclose(
+            ref_sample[[i for i in range(8) if i % 2 == 0]],
+            np.concatenate(even_draws),
+            atol=1e-5
+        )
+
+    @pytest.mark.parametrize("scramble", [True])
+    def test_distribution(self, scramble):
+        d = 50
+        engine = self.engine(d=d, scramble=scramble)
+        sample = engine.random(1024)
+        assert_allclose(
+            np.mean(sample, axis=0), np.repeat(0.5, d), atol=1e-2
+        )
+        assert_allclose(
+            np.percentile(sample, 25, axis=0), np.repeat(0.25, d), atol=1e-2
+        )
+        assert_allclose(
+            np.percentile(sample, 75, axis=0), np.repeat(0.75, d), atol=1e-2
+        )
+
+    def test_raises_optimizer(self):
+        message = r"'toto' is not a valid optimization method"
+        with pytest.raises(ValueError, match=message):
+            self.engine(d=1, scramble=False, optimization="toto")
+
+    @pytest.mark.parametrize(
+        "optimization,metric",
+        [
+            ("random-CD", qmc.discrepancy),
+            ("lloyd", lambda sample: -_l1_norm(sample))]
+    )
+    def test_optimizers(self, optimization, metric):
+        engine = self.engine(d=2, scramble=False)
+        sample_ref = engine.random(n=64)
+        metric_ref = metric(sample_ref)
+
+        optimal_ = self.engine(d=2, scramble=False, optimization=optimization)
+        sample_ = optimal_.random(n=64)
+        metric_ = metric(sample_)
+
+        assert metric_ < metric_ref
+
+    def test_consume_prng_state(self):
+        rng = np.random.default_rng(0xa29cabb11cfdf44ff6cac8bec254c2a0)
+        sample = []
+        for i in range(3):
+            engine = self.engine(d=2, scramble=True, rng=rng)
+            sample.append(engine.random(4))
+
+        with pytest.raises(AssertionError, match="Arrays are not equal"):
+            assert_equal(sample[0], sample[1])
+        with pytest.raises(AssertionError, match="Arrays are not equal"):
+            assert_equal(sample[0], sample[2])
+
+
+class TestHalton(QMCEngineTests):
+    qmce = qmc.Halton
+    can_scramble = True
+    # theoretical values known from Van der Corput
+    unscramble_nd = np.array([[0, 0], [1 / 2, 1 / 3],
+                              [1 / 4, 2 / 3], [3 / 4, 1 / 9],
+                              [1 / 8, 4 / 9], [5 / 8, 7 / 9],
+                              [3 / 8, 2 / 9], [7 / 8, 5 / 9]])
+    # theoretical values unknown: convergence properties checked
+    scramble_nd = np.array([[0.50246036, 0.93382481],
+                            [0.00246036, 0.26715815],
+                            [0.75246036, 0.60049148],
+                            [0.25246036, 0.8227137 ],
+                            [0.62746036, 0.15604704],
+                            [0.12746036, 0.48938037],
+                            [0.87746036, 0.71160259],
+                            [0.37746036, 0.04493592]])
+
+    def test_workers(self):
+        ref_sample = self.reference(scramble=True)
+        engine = self.engine(d=2, scramble=True)
+        sample = engine.random(n=len(ref_sample), workers=8)
+
+        assert_allclose(sample, ref_sample, atol=1e-3)
+
+        # worker + integers
+        engine.reset()
+        ref_sample = engine.integers(10)
+        engine.reset()
+        sample = engine.integers(10, workers=8)
+        assert_equal(sample, ref_sample)
+
+
+class TestLHS(QMCEngineTests):
+    qmce = qmc.LatinHypercube
+    can_scramble = True
+
+    def test_continuing(self, *args):
+        pytest.skip("Not applicable: not a sequence.")
+
+    def test_fast_forward(self, *args):
+        pytest.skip("Not applicable: not a sequence.")
+
+    def test_sample(self, *args):
+        pytest.skip("Not applicable: the value of reference sample is"
+                    " implementation dependent.")
+
+    @pytest.mark.parametrize("strength", [1, 2])
+    @pytest.mark.parametrize("scramble", [False, True])
+    @pytest.mark.parametrize("optimization", [None, "random-CD"])
+    def test_sample_stratified(self, optimization, scramble, strength):
+        rng = np.random.default_rng(37511836202578819870665127532742111260)
+        p = 5
+        n = p**2
+        d = 6
+
+        engine = qmc.LatinHypercube(d=d, scramble=scramble,
+                                    strength=strength,
+                                    optimization=optimization,
+                                    rng=rng)
+        sample = engine.random(n=n)
+        assert sample.shape == (n, d)
+        assert engine.num_generated == n
+
+        # centering stratifies samples in the middle of equal segments:
+        # * inter-sample distance is constant in 1D sub-projections
+        # * after ordering, columns are equal
+        expected1d = (np.arange(n) + 0.5) / n
+        expected = np.broadcast_to(expected1d, (d, n)).T
+        assert np.any(sample != expected)
+
+        sorted_sample = np.sort(sample, axis=0)
+        tol = 0.5 / n if scramble else 0
+
+        assert_allclose(sorted_sample, expected, atol=tol)
+        assert np.any(sample - expected > tol)
+
+        if strength == 2 and optimization is None:
+            unique_elements = np.arange(p)
+            desired = set(product(unique_elements, unique_elements))
+
+            for i, j in combinations(range(engine.d), 2):
+                samples_2d = sample[:, [i, j]]
+                res = (samples_2d * p).astype(int)
+                res_set = {tuple(row) for row in res}
+                assert_equal(res_set, desired)
+
+    def test_optimizer_1d(self):
+        # discrepancy measures are invariant under permuting factors and runs
+        engine = self.engine(d=1, scramble=False)
+        sample_ref = engine.random(n=64)
+
+        optimal_ = self.engine(d=1, scramble=False, optimization="random-CD")
+        sample_ = optimal_.random(n=64)
+
+        assert_array_equal(sample_ref, sample_)
+
+    def test_raises(self):
+        message = r"not a valid strength"
+        with pytest.raises(ValueError, match=message):
+            qmc.LatinHypercube(1, strength=3)
+
+        message = r"n is not the square of a prime number"
+        with pytest.raises(ValueError, match=message):
+            engine = qmc.LatinHypercube(d=2, strength=2)
+            engine.random(16)
+
+        message = r"n is not the square of a prime number"
+        with pytest.raises(ValueError, match=message):
+            engine = qmc.LatinHypercube(d=2, strength=2)
+            engine.random(5)  # because int(sqrt(5)) would result in 2
+
+        message = r"n is too small for d"
+        with pytest.raises(ValueError, match=message):
+            engine = qmc.LatinHypercube(d=5, strength=2)
+            engine.random(9)
+
+
+class TestSobol(QMCEngineTests):
+    qmce = qmc.Sobol
+    can_scramble = True
+    # theoretical values from Joe Kuo2010
+    unscramble_nd = np.array([[0., 0.],
+                              [0.5, 0.5],
+                              [0.75, 0.25],
+                              [0.25, 0.75],
+                              [0.375, 0.375],
+                              [0.875, 0.875],
+                              [0.625, 0.125],
+                              [0.125, 0.625]])
+
+    # theoretical values unknown: convergence properties checked
+    scramble_nd = np.array([[0.25331921, 0.41371179],
+                            [0.8654213, 0.9821167],
+                            [0.70097554, 0.03664616],
+                            [0.18027647, 0.60895735],
+                            [0.10521339, 0.21897069],
+                            [0.53019685, 0.66619033],
+                            [0.91122276, 0.34580743],
+                            [0.45337471, 0.78912079]])
+
+    def test_warning(self):
+        with pytest.warns(UserWarning, match=r"The balance properties of "
+                                             r"Sobol' points"):
+            engine = qmc.Sobol(1)
+            engine.random(10)
+
+    def test_random_base2(self):
+        engine = qmc.Sobol(2, scramble=False)
+        sample = engine.random_base2(2)
+        assert_array_equal(self.unscramble_nd[:4], sample)
+
+        # resampling still having N=2**n
+        sample = engine.random_base2(2)
+        assert_array_equal(self.unscramble_nd[4:8], sample)
+
+        # resampling again but leading to N!=2**n
+        with pytest.raises(ValueError, match=r"The balance properties of "
+                                             r"Sobol' points"):
+            engine.random_base2(2)
+
+    def test_raise(self):
+        with pytest.raises(ValueError, match=r"Maximum supported "
+                                             r"dimensionality"):
+            qmc.Sobol(qmc.Sobol.MAXDIM + 1)
+
+        with pytest.raises(ValueError, match=r"Maximum supported "
+                                             r"'bits' is 64"):
+            qmc.Sobol(1, bits=65)
+
+    def test_high_dim(self):
+        engine = qmc.Sobol(1111, scramble=False)
+        count1 = Counter(engine.random().flatten().tolist())
+        count2 = Counter(engine.random().flatten().tolist())
+        assert_equal(count1, Counter({0.0: 1111}))
+        assert_equal(count2, Counter({0.5: 1111}))
+
+    @pytest.mark.parametrize("bits", [2, 3])
+    def test_bits(self, bits):
+        engine = qmc.Sobol(2, scramble=False, bits=bits)
+        ns = 2**bits
+        sample = engine.random(ns)
+        assert_array_equal(self.unscramble_nd[:ns], sample)
+
+        with pytest.raises(ValueError, match="increasing `bits`"):
+            engine.random()
+
+    def test_64bits(self):
+        engine = qmc.Sobol(2, scramble=False, bits=64)
+        sample = engine.random(8)
+        assert_array_equal(self.unscramble_nd, sample)
+
+
+class TestLow0Bit:
+    def test_examples(self):
+        test_vector = [
+            # from low_0_bit's docstring
+            (0b0000, 1),
+            (0b0001, 2),
+            (0b0010, 1),
+            (0b0101, 2),
+            (0b0111, 4),
+            # gh-23409
+            (2 ** 32 - 1, 33),
+            (2 ** 32, 1),
+            (2 ** 33 - 1, 34),
+            (2 ** 64 - 1, 65),
+        ]
+        for in_, out in test_vector:
+            assert_equal(_test_low_0_bit(in_), out)
+
+
+class TestPoisson(QMCEngineTests):
+    qmce = qmc.PoissonDisk
+    can_scramble = False
+
+    def test_bounds(self, *args):
+        pytest.skip("Too costly in memory.")
+
+    def test_fast_forward(self, *args):
+        pytest.skip("Not applicable: recursive process.")
+
+    def test_sample(self, *args):
+        pytest.skip("Not applicable: the value of reference sample is"
+                    " implementation dependent.")
+
+    def test_continuing(self, *args):
+        # can continue a sampling, but will not preserve the same order
+        # because candidates are lost, so we will not select the same center
+        radius = 0.05
+        ns = 6
+        engine = self.engine(d=2, radius=radius, scramble=False)
+
+        sample_init = engine.random(n=ns)
+        assert len(sample_init) <= ns
+        assert l2_norm(sample_init) >= radius
+
+        sample_continued = engine.random(n=ns)
+        assert len(sample_continued) <= ns
+        assert l2_norm(sample_continued) >= radius
+
+        sample = np.concatenate([sample_init, sample_continued], axis=0)
+        assert len(sample) <= ns * 2
+        assert l2_norm(sample) >= radius
+
+    def test_mindist(self):
+        rng = np.random.default_rng(132074951149370773672162394161442690287)
+        ns = 50
+
+        low, high = 0.08, 0.2
+        radii = (high - low) * rng.random(5) + low
+
+        dimensions = [1, 3, 4]
+        hypersphere_methods = ["volume", "surface"]
+
+        gen = product(dimensions, radii, hypersphere_methods)
+
+        for d, radius, hypersphere in gen:
+            engine = self.qmce(
+                d=d, radius=radius, hypersphere=hypersphere, rng=rng
+            )
+            sample = engine.random(ns)
+
+            assert len(sample) <= ns
+            assert l2_norm(sample) >= radius
+
+    @pytest.mark.parametrize("l_bounds, u_bounds",  # add bounds to test gh-22819
+        [(None, None), ([-5, -5], [5, 5]),  ([1.1, 1.1], [5.1, 5.1])])
+    def test_fill_space(self, l_bounds, u_bounds):
+        radius = 0.2
+        engine = self.qmce(d=2, radius=radius, l_bounds=l_bounds, u_bounds=u_bounds)
+
+        sample = engine.fill_space()
+        # rtol to accommodate Accelerate; see gh-24486
+        rtol = 1e-6
+        assert l2_norm(sample) >= radius * (1 - rtol)
+
+    def test_bounds_shift_scale(self):
+        # test a reasonable property: as long as shape of region is a hypercube,
+        # bounds just shift and scale the sample.
+        radius = 0.2  # arbitrary parameters
+        shift = np.asarray([-2.1, 3.4])
+        scale = 2.6
+
+        rng = np.random.default_rng(8504196751)
+        engine = self.qmce(d=2, radius=radius*scale, rng=rng,
+                           l_bounds=shift, u_bounds=shift + scale)
+        res = engine.fill_space()
+
+        rng = np.random.default_rng(8504196751)
+        engine = self.qmce(d=2, radius=radius, rng=rng)
+        ref = engine.fill_space()
+
+        # circle packing problem is np complex
+        assert l2_norm(res) >= radius
+        assert_allclose(res, ref*scale + shift)
+
+    @pytest.mark.parametrize("l_bounds", [[-1, -2, -1], [1, 2, 1]])
+    def test_sample_inside_lower_bounds(self, l_bounds):
+        radius = 0.2
+        u_bounds=[3, 3, 2]
+        engine = self.qmce(
+            d=3, radius=radius, l_bounds=l_bounds, u_bounds=u_bounds
+        )
+        sample = engine.random(30)
+
+        for point in sample:
+            assert_array_less(point, u_bounds)
+            assert_array_less(l_bounds, point)
+
+    @pytest.mark.parametrize("u_bounds", [[-1, -2, -1], [1, 2, 1]])
+    def test_sample_inside_upper_bounds(self, u_bounds):
+        radius = 0.2
+        l_bounds=[-3, -3, -2]
+        engine = self.qmce(
+            d=3, radius=radius, l_bounds=l_bounds, u_bounds=u_bounds
+        )
+        sample = engine.random(30)
+
+        for point in sample:
+            assert_array_less(point, u_bounds)
+            assert_array_less(l_bounds, point)
+
+    def test_inconsistent_bound_value(self):
+        radius = 0.2
+        l_bounds=[3, 2, 1]
+        u_bounds=[-1, -2, -1]
+        with pytest.raises(
+            ValueError,
+            match="Bounds are not consistent 'l_bounds' < 'u_bounds'"):
+            self.qmce(d=3, radius=radius, l_bounds=l_bounds, u_bounds=u_bounds)
+
+    @pytest.mark.parametrize("u_bounds", [[-1, -2, -1], [-1, -2]])
+    @pytest.mark.parametrize("l_bounds", [[3, 2]])
+    def test_inconsistent_bounds(self, u_bounds, l_bounds):
+        radius = 0.2
+        with pytest.raises(
+            ValueError,
+            match="'l_bounds' and 'u_bounds' must be broadcastable and respect"
+            " the sample dimension"):
+            self.qmce(
+                d=3, radius=radius,
+                l_bounds=l_bounds, u_bounds=u_bounds
+            )
+
+    def test_raises(self):
+        message = r"'toto' is not a valid hypersphere sampling"
+        with pytest.raises(ValueError, match=message):
+            qmc.PoissonDisk(1, hypersphere="toto")
+
+
+class TestMultinomialQMC:
+    def test_validations(self):
+        # negative Ps
+        p = np.array([0.12, 0.26, -0.05, 0.35, 0.22])
+        with pytest.raises(ValueError, match=r"Elements of pvals must "
+                                             r"be non-negative."):
+            qmc.MultinomialQMC(p, n_trials=10)
+
+        # sum of P too large
+        p = np.array([0.12, 0.26, 0.1, 0.35, 0.22])
+        message = r"Elements of pvals must sum to 1."
+        with pytest.raises(ValueError, match=message):
+            qmc.MultinomialQMC(p, n_trials=10)
+
+        p = np.array([0.12, 0.26, 0.05, 0.35, 0.22])
+
+        message = r"Dimension of `engine` must be 1."
+        with pytest.raises(ValueError, match=message):
+            qmc.MultinomialQMC(p, n_trials=10, engine=qmc.Sobol(d=2))
+
+        message = r"`engine` must be an instance of..."
+        with pytest.raises(ValueError, match=message):
+            qmc.MultinomialQMC(p, n_trials=10, engine=np.random.default_rng())
+
+    @pytest.mark.filterwarnings('ignore::UserWarning')
+    def test_MultinomialBasicDraw(self):
+        rng = np.random.default_rng(6955663962957011631562466584467607969)
+        p = np.array([0.12, 0.26, 0.05, 0.35, 0.22])
+        n_trials = 100
+        expected = np.atleast_2d(n_trials * p).astype(int)
+        # preserve use of legacy keyword during SPEC 7 transition
+        engine = qmc.MultinomialQMC(p, n_trials=n_trials, seed=rng)
+        assert_allclose(engine.random(1), expected, atol=1)
+
+    def test_MultinomialDistribution(self):
+        rng = np.random.default_rng(77797854505813727292048130876699859000)
+        p = np.array([0.12, 0.26, 0.05, 0.35, 0.22])
+        engine = qmc.MultinomialQMC(p, n_trials=8192, rng=rng)
+        draws = engine.random(1)
+        assert_allclose(draws / np.sum(draws), np.atleast_2d(p), atol=1e-4)
+
+    def test_FindIndex(self):
+        p_cumulative = np.array([0.1, 0.4, 0.45, 0.6, 0.75, 0.9, 0.99, 1.0])
+        size = len(p_cumulative)
+        assert_equal(_test_find_index(p_cumulative, size, 0.0), 0)
+        assert_equal(_test_find_index(p_cumulative, size, 0.4), 2)
+        assert_equal(_test_find_index(p_cumulative, size, 0.44999), 2)
+        assert_equal(_test_find_index(p_cumulative, size, 0.45001), 3)
+        assert_equal(_test_find_index(p_cumulative, size, 1.0), size - 1)
+
+    @pytest.mark.filterwarnings('ignore::UserWarning')
+    def test_other_engine(self):
+        # same as test_MultinomialBasicDraw with different engine
+        rng = np.random.default_rng(283753519042773243071753037669078065412)
+        p = np.array([0.12, 0.26, 0.05, 0.35, 0.22])
+        n_trials = 100
+        expected = np.atleast_2d(n_trials * p).astype(int)
+        base_engine = qmc.Sobol(1, scramble=True, rng=rng)
+        engine = qmc.MultinomialQMC(p, n_trials=n_trials, engine=base_engine,
+                                    rng=rng)
+        assert_allclose(engine.random(1), expected, atol=1)
+
+
+class TestNormalQMC:
+    def test_NormalQMC(self):
+        # d = 1
+        engine = qmc.MultivariateNormalQMC(mean=np.zeros(1))
+        samples = engine.random()
+        assert_equal(samples.shape, (1, 1))
+        samples = engine.random(n=5)
+        assert_equal(samples.shape, (5, 1))
+        # d = 2
+        engine = qmc.MultivariateNormalQMC(mean=np.zeros(2))
+        samples = engine.random()
+        assert_equal(samples.shape, (1, 2))
+        samples = engine.random(n=5)
+        assert_equal(samples.shape, (5, 2))
+
+    def test_NormalQMCInvTransform(self):
+        # d = 1
+        engine = qmc.MultivariateNormalQMC(
+            mean=np.zeros(1), inv_transform=True)
+        samples = engine.random()
+        assert_equal(samples.shape, (1, 1))
+        samples = engine.random(n=5)
+        assert_equal(samples.shape, (5, 1))
+        # d = 2
+        engine = qmc.MultivariateNormalQMC(
+            mean=np.zeros(2), inv_transform=True)
+        samples = engine.random()
+        assert_equal(samples.shape, (1, 2))
+        samples = engine.random(n=5)
+        assert_equal(samples.shape, (5, 2))
+
+    def test_NormalQMCSeeded(self):
+        # test even dimension
+        rng = np.random.default_rng(274600237797326520096085022671371676017)
+        # preserve use of legacy keyword during SPEC 7 transition
+        engine = qmc.MultivariateNormalQMC(
+            mean=np.zeros(2), inv_transform=False, seed=rng)
+        samples = engine.random(n=2)
+        samples_expected = np.array([[-0.932001, -0.522923],
+                                     [-1.477655, 0.846851]])
+        assert_allclose(samples, samples_expected, atol=1e-4)
+
+        # test odd dimension
+        rng = np.random.default_rng(274600237797326520096085022671371676017)
+        engine = qmc.MultivariateNormalQMC(
+            mean=np.zeros(3), inv_transform=False, rng=rng)
+        samples = engine.random(n=2)
+        samples_expected = np.array([[-0.932001, -0.522923, 0.036578],
+                                     [-1.778011, 0.912428, -0.065421]])
+        assert_allclose(samples, samples_expected, atol=1e-4)
+
+        # same test with another engine
+        rng = np.random.default_rng(274600237797326520096085022671371676017)
+        base_engine = qmc.Sobol(4, scramble=True, rng=rng)
+        engine = qmc.MultivariateNormalQMC(
+            mean=np.zeros(3), inv_transform=False,
+            engine=base_engine, rng=rng
+        )
+        samples = engine.random(n=2)
+        samples_expected = np.array([[-0.932001, -0.522923, 0.036578],
+                                     [-1.778011, 0.912428, -0.065421]])
+        assert_allclose(samples, samples_expected, atol=1e-4)
+
+    def test_NormalQMCSeededInvTransform(self):
+        # test even dimension
+        rng = np.random.default_rng(288527772707286126646493545351112463929)
+        engine = qmc.MultivariateNormalQMC(
+            mean=np.zeros(2), rng=rng, inv_transform=True)
+        samples = engine.random(n=2)
+        samples_expected = np.array([[-0.913237, -0.964026],
+                                     [0.255904, 0.003068]])
+        assert_allclose(samples, samples_expected, atol=1e-4)
+
+        # test odd dimension
+        rng = np.random.default_rng(288527772707286126646493545351112463929)
+        engine = qmc.MultivariateNormalQMC(
+            mean=np.zeros(3), rng=rng, inv_transform=True)
+        samples = engine.random(n=2)
+        samples_expected = np.array([[-0.913237, -0.964026, 0.355501],
+                                     [0.699261, 2.90213 , -0.6418]])
+        assert_allclose(samples, samples_expected, atol=1e-4)
+
+    def test_other_engine(self):
+        for d in (0, 1, 2):
+            base_engine = qmc.Sobol(d=d, scramble=False)
+            engine = qmc.MultivariateNormalQMC(mean=np.zeros(d),
+                                               engine=base_engine,
+                                               inv_transform=True)
+            samples = engine.random()
+            assert_equal(samples.shape, (1, d))
+
+    def test_NormalQMCShapiro(self):
+        rng = np.random.default_rng(13242)
+        engine = qmc.MultivariateNormalQMC(mean=np.zeros(2), rng=rng)
+        samples = engine.random(n=256)
+        assert all(np.abs(samples.mean(axis=0)) < 1e-2)
+        assert all(np.abs(samples.std(axis=0) - 1) < 1e-2)
+        # perform Shapiro-Wilk test for normality
+        for i in (0, 1):
+            _, pval = shapiro(samples[:, i])
+            assert pval > 0.9
+        # make sure samples are uncorrelated
+        cov = np.cov(samples.transpose())
+        assert np.abs(cov[0, 1]) < 1e-2
+
+    def test_NormalQMCShapiroInvTransform(self):
+        rng = np.random.default_rng(32344554)
+        engine = qmc.MultivariateNormalQMC(
+            mean=np.zeros(2), inv_transform=True, rng=rng)
+        samples = engine.random(n=256)
+        assert all(np.abs(samples.mean(axis=0)) < 1e-2)
+        assert all(np.abs(samples.std(axis=0) - 1) < 1e-2)
+        # perform Shapiro-Wilk test for normality
+        for i in (0, 1):
+            _, pval = shapiro(samples[:, i])
+            assert pval > 0.9
+        # make sure samples are uncorrelated
+        cov = np.cov(samples.transpose())
+        assert np.abs(cov[0, 1]) < 1e-2
+
+
+class TestMultivariateNormalQMC:
+
+    def test_validations(self):
+
+        message = r"Dimension of `engine` must be consistent"
+        with pytest.raises(ValueError, match=message):
+            qmc.MultivariateNormalQMC([0], engine=qmc.Sobol(d=2))
+
+        message = r"Dimension of `engine` must be consistent"
+        with pytest.raises(ValueError, match=message):
+            qmc.MultivariateNormalQMC([0, 0, 0], engine=qmc.Sobol(d=4))
+
+        message = r"`engine` must be an instance of..."
+        with pytest.raises(ValueError, match=message):
+            qmc.MultivariateNormalQMC([0, 0], engine=np.random.default_rng())
+
+        message = r"Covariance matrix not PSD."
+        with pytest.raises(ValueError, match=message):
+            qmc.MultivariateNormalQMC([0, 0], [[1, 2], [2, 1]])
+
+        message = r"Covariance matrix is not symmetric."
+        with pytest.raises(ValueError, match=message):
+            qmc.MultivariateNormalQMC([0, 0], [[1, 0], [2, 1]])
+
+        message = r"Dimension mismatch between mean and covariance."
+        with pytest.raises(ValueError, match=message):
+            qmc.MultivariateNormalQMC([0], [[1, 0], [0, 1]])
+
+    def test_MultivariateNormalQMCNonPD(self):
+        # try with non-pd but psd cov; should work
+        engine = qmc.MultivariateNormalQMC(
+            [0, 0, 0], [[1, 0, 1], [0, 1, 1], [1, 1, 2]],
+        )
+        assert engine._corr_matrix is not None
+
+    def test_MultivariateNormalQMC(self):
+        # d = 1 scalar
+        engine = qmc.MultivariateNormalQMC(mean=0, cov=5)
+        samples = engine.random()
+        assert_equal(samples.shape, (1, 1))
+        samples = engine.random(n=5)
+        assert_equal(samples.shape, (5, 1))
+
+        # d = 2 list
+        engine = qmc.MultivariateNormalQMC(mean=[0, 1], cov=[[1, 0], [0, 1]])
+        samples = engine.random()
+        assert_equal(samples.shape, (1, 2))
+        samples = engine.random(n=5)
+        assert_equal(samples.shape, (5, 2))
+
+        # d = 3 np.array
+        mean = np.array([0, 1, 2])
+        cov = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
+        engine = qmc.MultivariateNormalQMC(mean, cov)
+        samples = engine.random()
+        assert_equal(samples.shape, (1, 3))
+        samples = engine.random(n=5)
+        assert_equal(samples.shape, (5, 3))
+
+    def test_MultivariateNormalQMCInvTransform(self):
+        # d = 1 scalar
+        engine = qmc.MultivariateNormalQMC(mean=0, cov=5, inv_transform=True)
+        samples = engine.random()
+        assert_equal(samples.shape, (1, 1))
+        samples = engine.random(n=5)
+        assert_equal(samples.shape, (5, 1))
+
+        # d = 2 list
+        engine = qmc.MultivariateNormalQMC(
+            mean=[0, 1], cov=[[1, 0], [0, 1]], inv_transform=True,
+        )
+        samples = engine.random()
+        assert_equal(samples.shape, (1, 2))
+        samples = engine.random(n=5)
+        assert_equal(samples.shape, (5, 2))
+
+        # d = 3 np.array
+        mean = np.array([0, 1, 2])
+        cov = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
+        engine = qmc.MultivariateNormalQMC(mean, cov, inv_transform=True)
+        samples = engine.random()
+        assert_equal(samples.shape, (1, 3))
+        samples = engine.random(n=5)
+        assert_equal(samples.shape, (5, 3))
+
+    def test_MultivariateNormalQMCSeeded(self):
+        # test even dimension
+        rng = np.random.default_rng(180182791534511062935571481899241825000)
+        a = rng.standard_normal((2, 2))
+        A = a @ a.transpose() + np.diag(rng.random(2))
+        engine = qmc.MultivariateNormalQMC(np.array([0, 0]), A,
+                                           inv_transform=False, rng=rng)
+        samples = engine.random(n=2)
+        samples_expected = np.array([[-0.64419, -0.882413],
+                                     [0.837199, 2.045301]])
+        assert_allclose(samples, samples_expected, atol=1e-4)
+
+        # test odd dimension
+        rng = np.random.default_rng(180182791534511062935571481899241825000)
+        a = rng.standard_normal((3, 3))
+        A = a @ a.transpose() + np.diag(rng.random(3))
+        engine = qmc.MultivariateNormalQMC(np.array([0, 0, 0]), A,
+                                           inv_transform=False, rng=rng)
+        samples = engine.random(n=2)
+        samples_expected = np.array([[-0.693853, -1.265338, -0.088024],
+                                     [1.620193, 2.679222, 0.457343]])
+        assert_allclose(samples, samples_expected, atol=1e-4)
+
+    def test_MultivariateNormalQMCSeededInvTransform(self):
+        # test even dimension
+        rng = np.random.default_rng(224125808928297329711992996940871155974)
+        a = rng.standard_normal((2, 2))
+        A = a @ a.transpose() + np.diag(rng.random(2))
+        engine = qmc.MultivariateNormalQMC(
+            np.array([0, 0]), A, rng=rng, inv_transform=True
+        )
+        samples = engine.random(n=2)
+        samples_expected = np.array([[0.682171, -3.114233],
+                                     [-0.098463, 0.668069]])
+        assert_allclose(samples, samples_expected, atol=1e-4)
+
+        # test odd dimension
+        rng = np.random.default_rng(224125808928297329711992996940871155974)
+        a = rng.standard_normal((3, 3))
+        A = a @ a.transpose() + np.diag(rng.random(3))
+        engine = qmc.MultivariateNormalQMC(
+            np.array([0, 0, 0]), A, rng=rng, inv_transform=True
+        )
+        samples = engine.random(n=2)
+        samples_expected = np.array([[0.988061, -1.644089, -0.877035],
+                                     [-1.771731, 1.096988, 2.024744]])
+        assert_allclose(samples, samples_expected, atol=1e-4)
+
+    def test_MultivariateNormalQMCShapiro(self):
+        # test the standard case
+        rng = np.random.default_rng(188960007281846377164494575845971640)
+        engine = qmc.MultivariateNormalQMC(
+            mean=[0, 0], cov=[[1, 0], [0, 1]], rng=rng
+        )
+        samples = engine.random(n=256)
+        assert all(np.abs(samples.mean(axis=0)) < 1e-2)
+        assert all(np.abs(samples.std(axis=0) - 1) < 1e-2)
+        # perform Shapiro-Wilk test for normality
+        for i in (0, 1):
+            _, pval = shapiro(samples[:, i])
+            assert pval > 0.9
+        # make sure samples are uncorrelated
+        cov = np.cov(samples.transpose())
+        assert np.abs(cov[0, 1]) < 1e-2
+
+        # test the correlated, non-zero mean case
+        engine = qmc.MultivariateNormalQMC(
+            mean=[1.0, 2.0], cov=[[1.5, 0.5], [0.5, 1.5]], rng=rng
+        )
+        samples = engine.random(n=256)
+        assert all(np.abs(samples.mean(axis=0) - [1, 2]) < 1e-2)
+        assert all(np.abs(samples.std(axis=0) - np.sqrt(1.5)) < 1e-2)
+        # perform Shapiro-Wilk test for normality
+        for i in (0, 1):
+            _, pval = shapiro(samples[:, i])
+            assert pval > 0.9
+        # check covariance
+        cov = np.cov(samples.transpose())
+        assert np.abs(cov[0, 1] - 0.5) < 1e-2
+
+    def test_MultivariateNormalQMCShapiroInvTransform(self):
+        # test the standard case
+        rng = np.random.default_rng(200089821034563288698994840831440331329)
+        engine = qmc.MultivariateNormalQMC(
+            mean=[0, 0], cov=[[1, 0], [0, 1]], rng=rng, inv_transform=True
+        )
+        samples = engine.random(n=256)
+        assert all(np.abs(samples.mean(axis=0)) < 1e-2)
+        assert all(np.abs(samples.std(axis=0) - 1) < 1e-2)
+        # perform Shapiro-Wilk test for normality
+        for i in (0, 1):
+            _, pval = shapiro(samples[:, i])
+            assert pval > 0.9
+        # make sure samples are uncorrelated
+        cov = np.cov(samples.transpose())
+        assert np.abs(cov[0, 1]) < 1e-2
+
+        # test the correlated, non-zero mean case
+        engine = qmc.MultivariateNormalQMC(
+            mean=[1.0, 2.0],
+            cov=[[1.5, 0.5], [0.5, 1.5]],
+            rng=rng,
+            inv_transform=True,
+        )
+        samples = engine.random(n=256)
+        assert all(np.abs(samples.mean(axis=0) - [1, 2]) < 1e-2)
+        assert all(np.abs(samples.std(axis=0) - np.sqrt(1.5)) < 1e-2)
+        # perform Shapiro-Wilk test for normality
+        for i in (0, 1):
+            _, pval = shapiro(samples[:, i])
+            assert pval > 0.9
+        # check covariance
+        cov = np.cov(samples.transpose())
+        assert np.abs(cov[0, 1] - 0.5) < 1e-2
+
+    def test_MultivariateNormalQMCDegenerate(self):
+        # X, Y iid standard Normal and Z = X + Y, random vector (X, Y, Z)
+        rng = np.random.default_rng(16320637417581448357869821654290448620)
+        engine = qmc.MultivariateNormalQMC(
+            mean=[0.0, 0.0, 0.0],
+            cov=[[1.0, 0.0, 1.0], [0.0, 1.0, 1.0], [1.0, 1.0, 2.0]],
+            rng=rng,
+        )
+        samples = engine.random(n=512)
+        assert all(np.abs(samples.mean(axis=0)) < 1e-2)
+        assert np.abs(np.std(samples[:, 0]) - 1) < 1e-2
+        assert np.abs(np.std(samples[:, 1]) - 1) < 1e-2
+        assert np.abs(np.std(samples[:, 2]) - np.sqrt(2)) < 1e-2
+        for i in (0, 1, 2):
+            _, pval = shapiro(samples[:, i])
+            assert pval > 0.8
+        cov = np.cov(samples.transpose())
+        assert np.abs(cov[0, 1]) < 1e-2
+        assert np.abs(cov[0, 2] - 1) < 1e-2
+        # check to see if X + Y = Z almost exactly
+        assert all(np.abs(samples[:, 0] + samples[:, 1] - samples[:, 2])
+                   < 1e-5)
+
+
+class TestLloyd:
+    def test_lloyd(self):
+        # quite sensible seed as it can go up before going further down
+        rng = np.random.RandomState(1809831)
+        sample = rng.uniform(0, 1, size=(128, 2))
+        base_l1 = _l1_norm(sample)
+        base_l2 = l2_norm(sample)
+
+        for _ in range(4):
+            sample_lloyd = _lloyd_centroidal_voronoi_tessellation(
+                    sample, maxiter=1,
+            )
+            curr_l1 = _l1_norm(sample_lloyd)
+            curr_l2 = l2_norm(sample_lloyd)
+
+            # higher is better for the distance measures
+            assert base_l1 < curr_l1
+            assert base_l2 < curr_l2
+
+            base_l1 = curr_l1
+            base_l2 = curr_l2
+
+            sample = sample_lloyd
+
+    def test_lloyd_non_mutating(self):
+        """
+        Verify that the input samples are not mutated in place and that they do
+        not share memory with the output.
+        """
+        sample_orig = np.array([[0.1, 0.1],
+                                [0.1, 0.2],
+                                [0.2, 0.1],
+                                [0.2, 0.2]])
+        sample_copy = sample_orig.copy()
+        new_sample = _lloyd_centroidal_voronoi_tessellation(
+            sample=sample_orig
+        )
+        assert_allclose(sample_orig, sample_copy)
+        assert not np.may_share_memory(sample_orig, new_sample)
+
+    def test_lloyd_errors(self):
+        with pytest.raises(ValueError, match=r"`sample` is not a 2D array"):
+            sample = [0, 1, 0.5]
+            _lloyd_centroidal_voronoi_tessellation(sample)
+
+        msg = r"`sample` dimension is not >= 2"
+        with pytest.raises(ValueError, match=msg):
+            sample = [[0], [0.4], [1]]
+            _lloyd_centroidal_voronoi_tessellation(sample)
+
+        msg = r"`sample` is not in unit hypercube"
+        with pytest.raises(ValueError, match=msg):
+            sample = [[-1.1, 0], [0.1, 0.4], [1, 2]]
+            _lloyd_centroidal_voronoi_tessellation(sample)
+
+
+# mindist
+def l2_norm(sample):
+    return distance.pdist(sample).min()
+
+
+@pytest.mark.parametrize('engine', [qmc.Halton, qmc.Sobol,
+                                    qmc.LatinHypercube, qmc.PoissonDisk])
+def test_deterministic(engine):
+    seed_number = 2359834584
+
+    rng = np.random.RandomState(seed_number)
+    res1 = engine(d=1, seed=rng).random(4)
+    rng = np.random.RandomState(seed_number)
+    res2 = engine(d=1, seed=rng).random(4)
+    assert_equal(res1, res2)
+
+    rng = np.random.default_rng(seed_number)
+    res1 = engine(d=1, seed=rng).random(4)
+    res2 = engine(d=1, rng=seed_number).random(4)
+    assert_equal(res1, res2)
+    rng = np.random.default_rng(seed_number)
+    res3 = engine(d=1, rng=rng).random(4)
+    assert_equal(res2, res1)
+    assert_equal(res3, res1)
+
+    message = "got multiple values for argument now known as `rng`"
+    with pytest.raises(TypeError, match=message):
+        engine(d=1, rng=seed_number, seed=seed_number)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/test_quantile.py b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_quantile.py
new file mode 100644
index 0000000000000000000000000000000000000000..4caa6341adb0123c783a60f324617d0fcaed7090
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_quantile.py
@@ -0,0 +1,774 @@
+import pytest
+import numpy as np
+
+from scipy import stats
+from scipy.stats._quantile import (_xp_searchsorted, _estimated_cdf_methods,
+    _estimated_cdf_discontinuous_methods, _estimated_cdf_continuous_methods)
+from scipy._lib._array_api import (
+    xp_default_dtype,
+    is_numpy,
+    is_torch,
+    is_jax,
+    is_cupy,
+    is_array_api_strict,
+    make_xp_test_case,
+    SCIPY_ARRAY_API,
+    xp_size,
+    xp_copy,
+)
+from scipy._lib._array_api_no_0d import xp_assert_close, xp_assert_equal
+from scipy._lib._util import _apply_over_batch
+import scipy._external.array_api_extra as xpx
+from scipy.stats._axis_nan_policy import _broadcast_arrays
+
+skip_xp_backends = pytest.mark.skip_xp_backends
+
+lazy_xp_modules = [stats]
+
+@_apply_over_batch(('x', 1), ('p', 1))
+def quantile_reference_last_axis(x, p, nan_policy, method):
+    if nan_policy == 'omit':
+        x = x[~np.isnan(x)]
+    p_mask = np.isnan(p)
+    p = p.copy()
+    p[p_mask] = 0.5
+    if method == 'harrell-davis':
+        # hdquantiles returns masked element if length along axis is 1 (bug)
+        res = (np.full_like(p, x[0]) if x.size == 1
+               else stats.mstats.hdquantiles(x, p).data)
+    elif method.startswith('round'):
+        res = winsor_reference_1d(np.sort(x), p, method)
+    else:
+        res = np.quantile(x, p, method=method)
+
+    res = np.asarray(res)
+    if nan_policy == 'propagate' and np.any(np.isnan(x)):
+        res[:] = np.nan
+
+    res[p_mask] = np.nan
+    return res
+
+
+@np.vectorize(excluded={0, 2})  # type: ignore[call-arg]
+def winsor_reference_1d(y, p, method):
+    # Adapted directly from the documentation
+    # Note: `y` is the sorted data array
+    n = len(y)
+    if method == 'round_nearest':
+        j = int(np.round(p * n) if p < 0.5 else np.round(n * p - 1))
+    elif method == 'round_outward':
+        j = int(np.floor(p * n) if p < 0.5 else np.ceil(n * p - 1))
+    elif method == 'round_inward':
+        j = int(np.ceil(p * n) if p < 0.5 else np.floor(n * p - 1))
+    return y[j]
+
+
+def quantile_reference(x, p, *, axis, nan_policy, keepdims, method):
+    x, p = np.moveaxis(x, axis, -1), np.moveaxis(np.atleast_1d(p), axis, -1)
+    res = quantile_reference_last_axis(x, p, nan_policy, method)
+    res = np.moveaxis(res, -1, axis)
+    if not keepdims:
+        res = np.squeeze(res, axis=axis)
+    return res
+
+
+@make_xp_test_case(stats.quantile)
+class TestQuantile:
+
+    def test_input_validation(self, xp):
+        x = xp.asarray([1, 2, 3])
+        p = xp.asarray(0.5)
+
+        message = "`x` must have real dtype."
+        with pytest.raises(ValueError, match=message):
+            stats.quantile(xp.asarray([True, False]), p)
+        with pytest.raises(ValueError):
+            stats.quantile(xp.asarray([1+1j, 2]), p)
+
+        message = "`p` must have real floating dtype."
+        with pytest.raises(ValueError, match=message):
+            stats.quantile(x, xp.asarray([0, 1]))
+
+        message = "`weights` must have real dtype."
+        with pytest.raises(ValueError, match=message):
+            stats.quantile(x, p, weights=xp.astype(x, xp.complex64))
+
+        message = "`axis` must be an integer or None."
+        with pytest.raises(ValueError, match=message):
+            stats.quantile(x, p, axis=0.5)
+        with pytest.raises(ValueError, match=message):
+            stats.quantile(x, p, axis=(0, -1))
+
+        message = "`axis` is not compatible with the shapes of the inputs."
+        with pytest.raises(ValueError, match=message):
+            stats.quantile(x, p, axis=2)
+
+        if not is_jax(xp):  # no data-dependent input validation for lazy arrays
+            message = "The input contains nan values"
+            with pytest.raises(ValueError, match=message):
+                stats.quantile(xp.asarray([xp.nan, 1, 2]), p, nan_policy='raise')
+
+        message = "`method` must be one of..."
+        with pytest.raises(ValueError, match=message):
+            stats.quantile(x, p, method='a duck')
+
+        message = "`method='harrell-davis'` does not support `weights`."
+        with pytest.raises(ValueError, match=message):
+            stats.quantile(x, p, weights=x, method='harrell-davis')
+
+        message = "`method='round_nearest'` does not support `weights`."
+        with pytest.raises(ValueError, match=message):
+            stats.quantile(x, p, weights=x, method='round_nearest')
+
+        message = "If specified, `keepdims` must be True or False."
+        with pytest.raises(ValueError, match=message):
+            stats.quantile(x, p, keepdims=42)
+
+        message = "`keepdims` may be False only if the length of `p` along `axis` is 1."
+        with pytest.raises(ValueError, match=message):
+            stats.quantile(x, xp.asarray([0.5, 0.6]), keepdims=False)
+
+
+    def _get_weights_x_rep(self, x, axis, rng):
+        x = np.swapaxes(x, axis, -1)
+        ndim = x.ndim
+        x = np.atleast_2d(x)
+        counts = rng.integers(10, size=x.shape[-1], dtype=np.int32)
+        x_rep = []
+        weights = []
+        for x_ in x:
+            counts_ = rng.permuted(counts)
+            x_rep.append(np.repeat(x_, counts_))
+            weights.append(counts_)
+        x_rep, weights = np.stack(x_rep), np.stack(weights)
+        if ndim < 2:
+            x_rep, weights = np.squeeze(x_rep, axis=0), np.squeeze(weights, axis=0)
+        x_rep, weights = np.swapaxes(x_rep, -1, axis), np.swapaxes(weights, -1, axis)
+        weights = np.asarray(weights, dtype=x.dtype)
+        return weights, x_rep
+
+
+    @skip_xp_backends(cpu_only=True, reason="PyTorch doesn't have `betainc`.",
+                      exceptions=['cupy'])
+    @pytest.mark.parametrize('method',
+         ['inverted_cdf', 'averaged_inverted_cdf', 'closest_observation',
+          'hazen', 'interpolated_inverted_cdf', 'linear',
+          'median_unbiased', 'normal_unbiased', 'weibull',
+          'harrell-davis', 'round_nearest', 'round_outward', 'round_inward',
+          '_lower', '_higher', '_midpoint', '_nearest'])
+    @pytest.mark.parametrize('shape_x, shape_p, axis',
+        [(10, None, -1), (10, 10, -1), (10, (2, 3), -1), ((10, 2), None, 0)])
+    @pytest.mark.parametrize('weights', [False, True])
+    def test_against_reference(self, method, shape_x, shape_p, axis, weights, xp):
+        # Test all methods with various data shapes
+        if weights and (method.startswith('_') or method.startswith('round')
+                        or method=='harrell-davis'):
+            pytest.skip('`weights` not supported by private (legacy) methods.')
+        dtype = xp_default_dtype(xp)
+        rng = np.random.default_rng(23458924568734956)
+        x = rng.random(size=shape_x)
+        p = rng.random(size=shape_p)
+
+        if weights:
+            weights, x_rep = self._get_weights_x_rep(x, axis, rng)
+        else:
+            weights, x_rep = None, x
+
+        ref = quantile_reference(
+            x_rep, p, method=method[1:] if method.startswith('_') else method,
+            axis=axis, nan_policy='propagate', keepdims=shape_p is not None)
+
+        x, p = xp.asarray(x, dtype=dtype), xp.asarray(p, dtype=dtype)
+        weights = weights if weights is None else xp.asarray(weights, dtype=dtype)
+        res = stats.quantile(x, p, method=method, weights=weights, axis=axis)
+
+        xp_assert_close(res, xp.asarray(ref, dtype=dtype))
+
+    @pytest.mark.filterwarnings("ignore:torch.searchsorted:UserWarning")
+    @skip_xp_backends(cpu_only=True, reason="PyTorch doesn't have `betainc`.",
+                      exceptions=['cupy', 'jax.numpy'])
+    @pytest.mark.parametrize('axis', [0, 1])
+    @pytest.mark.parametrize('keepdims', [False, True])
+    @pytest.mark.parametrize('nan_policy', ['omit', 'propagate', 'marray'])
+    @pytest.mark.parametrize('dtype', ['float32', 'float64'])
+    @pytest.mark.parametrize('method', ['linear', 'harrell-davis', 'round_nearest'])
+    @pytest.mark.parametrize('weights', [False, True])
+    def test_against_reference_2(self, axis, keepdims, nan_policy,
+                                 dtype, method, weights, xp):
+        # Test some methods with various combinations of arguments
+        if is_jax(xp) and nan_policy == 'marray':  # mdhaber/marray#146
+            pytest.skip("`marray` currently incompatible with JAX")
+        if weights and method in {'harrell-davis', 'round_nearest'}:
+            pytest.skip("These methods don't yet support weights")
+        rng = np.random.default_rng(23458924568734956)
+        shape = (5, 6)
+        x = rng.random(size=shape).astype(dtype)
+        p = rng.random(size=shape).astype(dtype)
+        mask = rng.random(size=shape) > 0.8
+        assert np.any(mask)
+        x[mask] = np.nan
+        if not keepdims:
+            p = np.mean(p, axis=axis, keepdims=True)
+
+        # inject p = 0 and p = 1 to test edge cases
+        # Currently would fail with CuPy/JAX (cupy/cupy#8934, jax-ml/jax#21900);
+        # remove the `if` when those are resolved.
+        if is_numpy(xp):
+            p0 = p.ravel()
+            p0[1] = 0.
+            p0[-2] = 1.
+
+        dtype = getattr(xp, dtype)
+
+        if weights:
+            weights, x_rep = self._get_weights_x_rep(x, axis, rng)
+            weights = weights if weights is None else xp.asarray(weights)
+        else:
+            weights, x_rep = None, x
+
+        if nan_policy == 'marray':
+            if not SCIPY_ARRAY_API:
+                pytest.skip("MArray is only available if SCIPY_ARRAY_API=1")
+            if weights is not None:
+                pytest.skip("MArray is not yet compatible with weights")
+            marray = pytest.importorskip('marray')
+            kwargs = dict(axis=axis, keepdims=keepdims, method=method)
+            mxp = marray._get_namespace(xp)
+            x_mp = mxp.asarray(x, mask=mask)
+            weights = weights if weights is None else mxp.asarray(weights)
+            res = stats.quantile(x_mp, mxp.asarray(p), weights=weights, **kwargs)
+            ref = quantile_reference(x_rep, p, nan_policy='omit', **kwargs)
+            xp_assert_close(res.data, xp.asarray(ref, dtype=dtype))
+            return
+
+        kwargs = dict(axis=axis, keepdims=keepdims,
+                      nan_policy=nan_policy, method=method)
+        res = stats.quantile(xp.asarray(x), xp.asarray(p), weights=weights, **kwargs)
+        ref = quantile_reference(x_rep, p, **kwargs)
+        xp_assert_close(res, xp.asarray(ref, dtype=dtype))
+
+    def test_integer_input_output_dtype(self, xp):
+        res = stats.quantile(xp.arange(10, dtype=xp.int64), 0.5)
+        assert res.dtype == xp_default_dtype(xp)
+
+    @pytest.mark.parametrize('x, p, ref, kwargs',
+        [([], 0.5, np.nan, {}),
+         ([1, 2, 3], [-1, 0, 1, 1.5, np.nan], [np.nan, 1, 3, np.nan, np.nan], {}),
+         ([1, 2, 3], [], [], {}),
+         ([[np.nan, 2]], 0.5, [np.nan, 2], {'nan_policy': 'omit'}),
+         ([[], []], 0.5, np.full(2, np.nan), {'axis': -1}),
+         ([[], []], 0.5, np.zeros((0,)), {'axis': 0, 'keepdims': False}),
+         ([[], []], 0.5, np.zeros((1, 0)), {'axis': 0, 'keepdims': True}),
+         ([], [0.5, 0.6], np.full(2, np.nan), {}),
+         (np.arange(1, 28).reshape((3, 3, 3)), 0.5, [[[14.]]],
+          {'axis': None, 'keepdims': True}),
+         ([[1, 2], [3, 4]], [0.25, 0.5, 0.75], [[1.75, 2.5, 3.25]],
+          {'axis': None, 'keepdims': True}),
+         # Known issue:
+         # ([1, 2, 3], 0.5, 2., {'weights': [0, 0, 0]})
+         # See https://github.com/scipy/scipy/pull/23941#issuecomment-3503554361
+         ])
+    def test_edge_cases(self, x, p, ref, kwargs, xp):
+        default_dtype = xp_default_dtype(xp)
+        x, p, ref = xp.asarray(x), xp.asarray(p), xp.asarray(ref, dtype=default_dtype)
+        res = stats.quantile(x, p, **kwargs)
+        xp_assert_equal(res, ref)
+
+    @pytest.mark.parametrize('axis', [0, 1, 2])
+    @pytest.mark.parametrize('keepdims', [False, True])
+    def test_size_0(self, axis, keepdims, xp):
+        shape = [3, 4, 0]
+        out_shape = shape.copy()
+        if keepdims:
+            out_shape[axis] = 1
+        else:
+            out_shape.pop(axis)
+        res = stats.quantile(xp.zeros(tuple(shape)), 0.5, axis=axis, keepdims=keepdims)
+        assert res.shape == tuple(out_shape)
+
+    @pytest.mark.parametrize('method',
+        ['inverted_cdf', 'averaged_inverted_cdf', 'closest_observation',
+         '_lower', '_higher', '_midpoint', '_nearest'])
+    def test_transition(self, method, xp):
+        # test that values of discontinuous estimators are correct when
+        # p*n + m - 1 is integral.
+        if method == 'closest_observation' and np.__version__ < '2.0.1':
+            pytest.skip('Bug in np.quantile (numpy/numpy#26656) fixed in 2.0.1')
+        x = np.arange(8., dtype=np.float64)
+        p = np.arange(0, 1.03125, 0.03125)
+        res = stats.quantile(xp.asarray(x), xp.asarray(p), method=method)
+        ref = np.quantile(x, p, method=method[1:] if method.startswith('_') else method)
+        xp_assert_equal(res, xp.asarray(ref, dtype=xp.float64))
+
+    @pytest.mark.parametrize('zero_weights', [False, True])
+    def test_weights_against_numpy(self, zero_weights, xp):
+        if is_numpy(xp) and xp.__version__ < "2.1.3" and zero_weights:
+            pytest.skip('`Bug in np.quantile (numpy/numpy#27563) fixed in 2.1.3')
+        dtype = xp_default_dtype(xp)
+        rng = np.random.default_rng(85468924398205602)
+        method = 'inverted_cdf'
+        x = rng.random(size=100)
+        weights = rng.random(size=100)
+        if zero_weights:
+            weights[weights < 0.5] = 0
+        p = np.linspace(0., 1., 300)
+        res = stats.quantile(xp.asarray(x, dtype=dtype), xp.asarray(p, dtype=dtype),
+                             method=method, weights=xp.asarray(weights, dtype=dtype))
+        ref = np.quantile(x, p, method=method, weights=weights)
+        xp_assert_close(res, xp.asarray(ref, dtype=dtype))
+
+    @pytest.mark.parametrize('method',
+        ['inverted_cdf', 'averaged_inverted_cdf', 'closest_observation', 'hazen',
+         'interpolated_inverted_cdf', 'linear','median_unbiased', 'normal_unbiased',
+         'weibull'])
+    def test_zero_weights(self, method, xp):
+        rng = np.random.default_rng(85468924398205602)
+
+        # test 1-D versus eliminating zero-weighted values
+        n = 100
+        x = xp.asarray(rng.random(size=n))
+        x0 = xp_copy(x)
+        p = xp.asarray(rng.random(size=n))
+        i_zero = xp.asarray(rng.random(size=n) < 0.1)
+        weights = xp.asarray(rng.random(size=n))
+        weights = xp.where(i_zero, 0., weights)
+        res = stats.quantile(x, p, weights=weights, method=method)
+        ref = stats.quantile(x[~i_zero], p, weights=weights[~i_zero], method=method)
+        xp_assert_close(res, ref)
+        xp_assert_equal(x, x0)  # no input mutation
+
+        # test multi-D versus `nan_policy='omit'`
+        shape = (5, 100)
+        x = xp.asarray(rng.random(size=shape))
+        x0 = xp_copy(x)
+        p = xp.asarray(rng.random(size=shape))
+        i_zero = xp.asarray(rng.random(size=shape) < 0.1)
+        weights = xp.asarray(rng.random(size=shape))
+        x_nanned = xp.where(i_zero, xp.nan, x)
+        weights_zeroed = xp.where(i_zero, 0., weights)
+        res = stats.quantile(x, p, weights=weights_zeroed, method=method, axis=-1)
+        ref = stats.quantile(x_nanned, p, weights=weights,
+                             nan_policy='omit', method=method, axis=-1)
+        xp_assert_close(res, ref)
+        xp_assert_equal(x, x0)  # no input mutation
+
+    @pytest.mark.filterwarnings("ignore:torch.searchsorted:UserWarning")
+    @pytest.mark.parametrize('method',
+        ['inverted_cdf', 'averaged_inverted_cdf', 'closest_observation', 'hazen',
+         'interpolated_inverted_cdf', 'linear','median_unbiased', 'normal_unbiased',
+         'weibull'])
+    @pytest.mark.parametrize('shape', [50, (50, 3)])
+    def test_unity_weights(self, method, shape, xp):
+        # Check that result is unchanged if all weights are `1.0`
+        rng = np.random.default_rng(28546892439820560)
+        x = xp.asarray(rng.random(size=shape))
+        p = xp.asarray(rng.random(size=shape))
+        weights = xp.ones_like(x)
+        res = stats.quantile(x, p, weights=weights, method=method)
+        ref = stats.quantile(x, p, method=method)
+        xp_assert_close(res, ref)
+
+    @skip_xp_backends(cpu_only=True, reason="PyTorch doesn't have `betainc`.",
+                      exceptions=['cupy', 'jax.numpy'])
+    def test_all_nan_harrell_davis_gh24707(self, xp):
+        # While working on gh-24707, there was a case in which if *all* elements of one
+        # slice were NaN, only some elements of another slice were NaN, and
+        # `nan_policy='omit'`, then the NaNs would not be ignored in the other slice.
+        # The same test case could fail with `nan_policy='propagate'` for a different
+        # reason, if the fix were not made carefully. Check that both these cases are
+        # resolved.
+        kwargs = dict(method='harrell-davis', axis=-1)
+        x = xp.asarray([[xp.nan, xp.nan, xp.nan], [xp.nan, 2, 3]])
+
+        res = stats.quantile(x, 0.5, **kwargs, nan_policy='omit')
+        xp_assert_close(res, xp.asarray([xp.nan, 2.5]))
+
+        res = stats.quantile(x, 0.5, **kwargs, nan_policy='propagate')
+        xp_assert_close(res, xp.asarray([xp.nan, xp.nan]))
+
+
+@_apply_over_batch(('a', 1), ('v', 1))
+def np_searchsorted(a, v, side):
+    return np.searchsorted(a, v, side=side)
+
+
+@make_xp_test_case(_xp_searchsorted)
+class Test_XPSearchsorted:
+    @pytest.mark.parametrize('side', ['left', 'right'])
+    @pytest.mark.parametrize('ties', [False, True])
+    @pytest.mark.parametrize('shape', [0, 1, 2, 10, 11, 1000, 10001,
+                                       (2, 0), (0, 2), (2, 10), (2, 3, 11)])
+    @pytest.mark.parametrize('nans_x', [False, True])
+    @pytest.mark.parametrize('infs_x', [False, True])
+    def test_nd(self, side, ties, shape, nans_x, infs_x, xp):
+        if nans_x and is_torch(xp):
+            pytest.skip('torch sorts NaNs differently')
+        rng = np.random.default_rng(945298725498274853)
+        if ties:
+            x = rng.integers(5, size=shape)
+        else:
+            x = rng.random(shape)
+        # float32 is to accommodate JAX - nextafter with `float64` is too small?
+        x = np.asarray(x, dtype=np.float32)
+        xr = np.nextafter(x, np.inf)
+        xl = np.nextafter(x, -np.inf)
+        x_ = np.asarray([-np.inf, np.inf, np.nan])
+        x_ = np.broadcast_to(x_, x.shape[:-1] + (3,))
+        y = rng.permuted(np.concatenate((xl, x, xr, x_), axis=-1), axis=-1)
+        if nans_x:
+            mask = rng.random(shape) < 0.1
+            x[mask] = np.nan
+        if infs_x:
+            mask = rng.random(shape) < 0.1
+            x[mask] = -np.inf
+            mask = rng.random(shape) > 0.9
+            x[mask] = np.inf
+        x = np.sort(x, axis=-1)
+        x, y = np.asarray(x, dtype=np.float64), np.asarray(y, dtype=np.float64)
+        xp_default_int = xp.asarray(1).dtype
+        if xp_size(x) == 0 and x.ndim > 0 and x.shape[-1] != 0:
+            ref = xp.empty(x.shape[:-1] + (y.shape[-1],), dtype=xp_default_int)
+        else:
+            ref = xp.asarray(np_searchsorted(x, y, side=side), dtype=xp_default_int)
+        x, y = xp.asarray(x), xp.asarray(y)
+        res = _xp_searchsorted(x, y, side=side)
+        xp_assert_equal(res, ref)
+
+
+@_apply_over_batch(('x', 1), ('y', 1))
+def estimated_cdf_reference_last_axis(x, y, nan_policy, method):
+    i_nan = np.isnan(x)
+    if nan_policy == 'propagate' and np.any(i_nan):
+        return np.full_like(y, np.nan)
+    elif nan_policy == 'omit':
+        x = x[~i_nan]
+    return stats.estimated_cdf(x, y, keepdims=True, method=method)
+
+
+def estimated_cdf_reference(x, y, *, axis=0, nan_policy='propagate',
+                        keepdims=None, method='linear'):
+    x, y = _broadcast_arrays((x, y), axis=axis)
+    x, y = np.moveaxis(x, axis, -1), np.moveaxis(y, axis, -1)
+    res = estimated_cdf_reference_last_axis(x, y, nan_policy, method)
+    res = np.moveaxis(res, -1, axis)
+    if not keepdims:
+        res = np.squeeze(res, axis=axis)
+    return res
+
+
+# avoid variable collection order issues
+_estimated_cdf_methods_list = sorted(list(_estimated_cdf_methods))
+
+
+@make_xp_test_case(stats.estimated_cdf)
+class TestEstimatedCDF:
+    def test_input_validation(self, xp):
+        x = xp.asarray([1, 2, 3])
+        y = xp.asarray(2)
+
+        message = "`x` must have real dtype."
+        with pytest.raises(ValueError, match=message):
+            stats.estimated_cdf(xp.asarray([True, False]), y)
+        with pytest.raises(ValueError):
+            stats.estimated_cdf(xp.asarray([1+1j, 2]), y)
+
+        message = "`y` must have real dtype."
+        with pytest.raises(ValueError, match=message):
+            stats.estimated_cdf(x, xp.asarray([0+1j, 1]))
+
+        message = "`axis` must be an integer or None."
+        with pytest.raises(ValueError, match=message):
+            stats.estimated_cdf(x, y, axis=0.5)
+        with pytest.raises(ValueError, match=message):
+            stats.estimated_cdf(x, y, axis=(0, -1))
+
+        message = "`axis` is not compatible with the shapes of the inputs."
+        with pytest.raises(ValueError, match=message):
+            stats.estimated_cdf(x, y, axis=2)
+
+        if not is_jax(xp):  # no data-dependent input validation for lazy arrays
+            message = "The input contains nan values"
+            with pytest.raises(ValueError, match=message):
+                stats.estimated_cdf(xp.asarray([xp.nan, 1, 2]), y, nan_policy='raise')
+
+        message = "method` must be one of..."
+        with pytest.raises(ValueError, match=message):
+            stats.estimated_cdf(x, y, method='a duck')
+
+        message = "If specified, `keepdims` must be True or False."
+        with pytest.raises(ValueError, match=message):
+            stats.estimated_cdf(x, y, keepdims=42)
+
+        message = "`keepdims` may be False only if the length of `y` along `axis` is 1."
+        with pytest.raises(ValueError, match=message):
+            stats.estimated_cdf(x, xp.asarray([0.5, 0.6]), keepdims=False)
+
+    @pytest.mark.parametrize('method', _estimated_cdf_methods_list)
+    @pytest.mark.parametrize('x_shape', [2, 10, 11, 100, 1001, (2, 10), (2, 3, 11)])
+    @pytest.mark.parametrize('y_shape', [None, 25])
+    @pytest.mark.parametrize('ties', [False, True])
+    def test_against_quantile(self, method, x_shape, y_shape, ties, xp):
+        discontinuous = method in _estimated_cdf_discontinuous_methods
+        dtype = xp_default_dtype(xp)  # removed parameterization to speed up tests
+        rng = np.random.default_rng(394529872549827485)
+        y_shape = x_shape if y_shape is None else y_shape
+
+        if ties:
+            x = xp.asarray(rng.integers(9, size=x_shape), dtype=dtype)
+        else:
+            x = xp.asarray(rng.standard_normal(size=x_shape), dtype=dtype)
+
+        p = xp.asarray(rng.random(size=y_shape), dtype=dtype)
+        y = stats.quantile(x, p, method=method, axis=-1)
+        res = stats.estimated_cdf(x, y, method=method, axis=-1)
+        ref = xp.broadcast_to(p, (*x.shape[:-1], y.shape[-1]))
+
+        # check that `quantile` is the inverse of `estimated_cdf`
+        # note that for discontinuous methods, res is right on the cusp of a transition,
+        # and there can be a tiny bit of error to the right or left. We shift it left
+        # to ensure we're on the correct side of the transition, producing the same `y2`
+        # as if the probability calculation were exact.
+        res = res - 1e-6 if discontinuous else res
+        y2 = stats.quantile(x, res, method=method, axis=-1)
+        atol = 1e-5 if dtype == xp.float32 else 1e-12
+        xp_assert_close(y2, y, atol=atol)
+
+        # if there are ties or method is discontinuous, `quantile` is not invertible
+        if ties or discontinuous:
+            return
+
+        # `quantile` is not invertible outside this domain
+        a, b = _estimated_cdf_continuous_methods[method]
+        n = x.shape[-1]
+        p_min = (1 - a) / (n + 1 - a - b)
+        p_max = (n - a) / (n + 1 - a - b)
+        i_very_low = y < xp.min(x, axis=-1, keepdims=True)
+        i_very_high = y > xp.max(x, axis=-1, keepdims=True)
+        i_low = (ref <= p_min) & ~i_very_low
+        i_high = (ref >= p_max) & ~i_very_high
+        i_ok = ~(i_low | i_high | i_very_low | i_very_high)
+
+        # check for correct inversion within the domain
+        xp_assert_close(res[i_ok], ref[i_ok])
+
+        # check that all other values get mapped to bottom or top of range
+        kwargs = dict(check_shape=False, check_dtype=False, check_0d=True)
+        xp_assert_close(res[i_low], xp.asarray(p_min), **kwargs)
+        xp_assert_close(res[i_high], xp.asarray(p_max), **kwargs)
+        xp_assert_close(res[i_very_low], xp.asarray(0.0), **kwargs)
+        xp_assert_close(res[i_very_high], xp.asarray(1.0), **kwargs)
+
+    @pytest.mark.filterwarnings("ignore:torch.searchsorted:UserWarning")
+    @pytest.mark.parametrize('axis', [0, 1])
+    @pytest.mark.parametrize('keepdims', [False, True])
+    @pytest.mark.parametrize('nan_policy', ['propagate', 'omit', 'marray'])
+    @pytest.mark.parametrize('dtype', ['float32', 'float64'])
+    @pytest.mark.parametrize('nans', [False, True])
+    @pytest.mark.parametrize('meth', ['linear', 'inverted_cdf'])
+    def test_against_reference(self, axis, keepdims, nan_policy, dtype, nans, meth, xp):
+        if is_jax(xp) and nan_policy == 'marray':  # mdhaber/marray#146
+            pytest.skip("`marray` currently incompatible with JAX")
+        rng = np.random.default_rng(23458924568734956)
+        shape = (5, 6)
+        x = rng.standard_normal(size=shape).astype(dtype)
+        y = rng.standard_normal(size=shape).astype(dtype)
+
+        mask = None
+        if nans:
+            mask = rng.random(size=shape) > 0.8
+            assert np.any(mask)
+            x[mask] = np.nan
+
+        if not keepdims:
+            y = np.mean(y, axis=axis, keepdims=True)
+
+        dtype = getattr(xp, dtype)
+
+        if nan_policy == 'marray':
+            if not SCIPY_ARRAY_API:
+                pytest.skip("MArray is only available if SCIPY_ARRAY_API=1")
+            marray = pytest.importorskip('marray')
+            kwargs = dict(axis=axis, keepdims=keepdims, method=meth)
+            mxp = marray._get_namespace(xp)
+            x_mp = mxp.asarray(x, mask=mask)
+            res = stats.estimated_cdf(x_mp, mxp.asarray(y), **kwargs)
+            ref = estimated_cdf_reference(x, y, nan_policy='omit', **kwargs)
+            xp_assert_close(res.data, xp.asarray(ref, dtype=dtype))
+            return
+
+        kwargs = dict(axis=axis, keepdims=keepdims,
+                      nan_policy=nan_policy, method=meth)
+        res = stats.estimated_cdf(xp.asarray(x), xp.asarray(y), **kwargs)
+        ref = estimated_cdf_reference(x, y, **kwargs)
+        xp_assert_close(res, xp.asarray(ref, dtype=dtype))
+
+    @pytest.mark.skip_xp_backends('torch', reason='issues with sorting NaNs')
+    @pytest.mark.parametrize('n', [50, 500])
+    @pytest.mark.parametrize('method, ab', _estimated_cdf_continuous_methods.items())
+    def test_plotting_positions(self, n, method, ab, xp):
+        a, b = ab
+        rng = np.random.default_rng(539452987254982748)
+        x = rng.standard_normal(n)
+
+        mask = rng.random(n) < 0.1
+        x[mask] = np.nan
+        mask = xp.asarray(mask)
+
+        x_masked = np.ma.masked_invalid(x)
+        ref = stats.mstats.plotting_positions(x_masked, a, b)
+        ref = xp.asarray(ref.data)
+
+        x = xp.asarray(x)
+        res = stats.estimated_cdf(x, x, nan_policy='omit', method=method)
+
+        xp_assert_close(res[~mask], ref[~mask])
+        assert xp.all(xp.isnan(res[mask]))
+
+    @pytest.mark.parametrize('ties', [False, True])
+    def test_against_ecdf_percentileofscore(self, ties, xp):
+        rng = np.random.default_rng(853945298725498274)
+        n = 50
+        dtype = xp_default_dtype(xp)
+        x = rng.integers(10, size=n) if ties else rng.standard_normal(size=n)
+        y = rng.integers(10, size=25) if ties else rng.standard_normal(size=25)
+        ref = stats.ecdf(x).cdf.evaluate(y)
+        ref2 = stats.percentileofscore(x, y, 'weak')
+        x, y = xp.asarray(x, dtype=dtype), xp.asarray(y, dtype=dtype)
+        res = stats.estimated_cdf(x, y, method='inverted_cdf')
+        ref, ref2 = xp.asarray(ref, dtype=dtype), xp.asarray(ref2, dtype=dtype)
+        xp_assert_close(res, ref)
+        xp_assert_close(res, ref2 / 100)
+
+    def test_integer_input_output_dtype(self, xp):
+        x = xp.arange(10, dtype=xp.int64)
+        res = stats.estimated_cdf(x, x)
+        assert res.dtype == xp_default_dtype(xp)
+
+    @pytest.mark.parametrize('nan_policy', ['propagate', 'omit', 'marray'])
+    @pytest.mark.parametrize('method', _estimated_cdf_methods_list)
+    def test_size_one_sample(self, nan_policy, method, xp):
+        discontinuous = method in _estimated_cdf_discontinuous_methods
+        x = xp.arange(10.)
+        y = xp.asarray([0., -1., 1.])
+        n = np.asarray(1.) if is_array_api_strict(xp) else xp.asarray(1.)
+        with np.errstate(divide='ignore', invalid='ignore'):  # for method = 'linear'
+            if discontinuous:
+                ref = xp.asarray([1., 0., 1.])
+            else:
+                a, b = _estimated_cdf_continuous_methods[method]
+                ref = xp.asarray([float((n - a) / (n + 1 - a - b)), 0., 1.])
+
+        if nan_policy == 'propagate':
+            x = x[:1]
+            kwargs = {'nan_policy': 'propagate'}
+        elif nan_policy == 'omit':
+            x = xpx.at(x)[1:].set(xp.nan)
+            kwargs = {'nan_policy': 'omit'}
+        elif nan_policy == 'marray':
+            if is_jax(xp):
+                pytest.skip("JAX currently incompatible with `marray`")
+            if not SCIPY_ARRAY_API:
+                pytest.skip("MArray is only available if SCIPY_ARRAY_API=1")
+            marray = pytest.importorskip('marray')
+            mxp = marray._get_namespace(xp)
+            mask = (x > 0.)
+            x = mxp.asarray(x, mask=mask)
+            y = mxp.asarray(y)
+            kwargs = {}
+
+        with np.errstate(divide='ignore', invalid='ignore'):  # for method = 'linear'
+            res = stats.estimated_cdf(x, y, method=method, **kwargs)
+        res = res.data if nan_policy == 'marray' else res
+        xp_assert_close(res, ref)
+
+    # skipping marray due to mdhaber/marray#24
+    @pytest.mark.parametrize('nan_policy', ['propagate', 'omit'])
+    @pytest.mark.parametrize('method', _estimated_cdf_methods_list)
+    def test_size_zero_sample(self, nan_policy, method, xp):
+        x = xp.arange(10.)
+        y = xp.asarray([0., -1., 1.])  # this should work
+        ref = xp.full_like(y, xp.nan)
+
+        if nan_policy == 'propagate':
+            x = x[0:0]
+            kwargs = {'nan_policy': 'propagate'}
+        elif nan_policy == 'omit':
+            x = xpx.at(x)[:].set(xp.nan)
+            kwargs = {'nan_policy': 'omit'}
+        elif nan_policy == 'marray':
+            if not SCIPY_ARRAY_API:
+                pytest.skip("MArray is only available if SCIPY_ARRAY_API=1")
+            if is_jax(xp):
+                pytest.skip("JAX currently incompatible with `marray`")
+            marray = pytest.importorskip('marray')
+            mxp = marray._get_namespace(xp)
+            mask = (x >= 0.)
+            x = mxp.asarray(x, mask=mask)
+            y = mxp.asarray(y)
+            kwargs = {}
+
+        with np.errstate(divide='ignore', invalid='ignore'):  # for method = 'linear'
+            res = stats.estimated_cdf(x, y, method=method, **kwargs)
+
+        if nan_policy == 'marray':
+            assert xp.all(res.mask)
+        else:
+            xp_assert_close(res, ref)
+
+    @pytest.mark.parametrize('x, y, ref, kwargs',
+        [
+         ([], 0.5, np.nan, {}),
+         ([1, 2, 3], [0.999, 3.001, np.nan], [0., 1., np.nan], {}),
+         ([1, 2, 3], [], [], {}),
+         ([[np.nan, 2]], 2, [np.nan, 0.5], {'nan_policy': 'omit', 'method': 'weibull'}),
+         ([[], []], 0.5, np.full(2, np.nan), {'axis': -1}),
+         ([[], []], 0.5, np.zeros((0,)), {'axis': 0, 'keepdims': False}),
+         ([[], []], 0.5, np.zeros((1, 0)), {'axis': 0, 'keepdims': True}),
+         ([], [0.5, 0.6], np.full(2, np.nan), {}),
+         (np.arange(1, 28).reshape((3, 3, 3)), 14., [[[0.5]]],
+          {'axis': None, 'keepdims': True}),
+         ([[1, 2], [3, 4]], [1.75, 2.5, 3.25], [[0.25, 0.5, 0.75]],
+          {'axis': None, 'keepdims': True}),
+         ([1, 2, 3], [-np.inf, np.inf], [0.0, 1.0], {}),
+         # It is our choice how much effort and computational overhead we want to put
+         # into adjusting for insane edge cases like when `x` contains infinite values,
+         # especially when `y` does, too.
+         # One practical argument would be that y = +/- inf should produce the same
+         # results as an extremely large finite number, in which case the 0th element
+         # of the 'linear' result should be `0`.
+         # Another argument would be for producing NaN below wherever y = +/- inf.
+         # Another would be that it's not appropriate to spend significant computation
+         # correcting these edge cases; we should just document what we do.
+         # In any case, this is the current status.
+         ([-np.inf, -1, 0, 1, np.inf], [-np.inf, -2, -1, 0, 1, 2, np.inf],
+          [0.25, 0.25, 0.25, 0.5 , 0.75, 0.75, np.nan], {'method':'linear'}),
+         ([-np.inf, -1, 0, 1, np.inf], [-np.inf, -2, -1, 0, 1, 2, np.inf],
+          [0.2, 0.2, 0.4, 0.6, 0.8, 0.8, 1.], {'method': 'inverted_cdf'}),
+        ])
+    def test_edge_cases(self, x, y, ref, kwargs, xp):
+        if kwargs.get('method', None) == 'weibull' and is_torch(xp):
+            pytest.skip('data-apis/array-api-compat#360')
+        if kwargs.get('axis', None) == -1 and is_cupy(xp):
+            pytest.skip('Fails; need to investigate.')
+        default_dtype = xp_default_dtype(xp)
+        x, y, ref = xp.asarray(x), xp.asarray(y), xp.asarray(ref, dtype=default_dtype)
+        res = stats.estimated_cdf(x, y, **kwargs)
+        xp_assert_close(res, ref, rtol=1e-15)
+
+    @pytest.mark.skip_xp_backends('jax.numpy', reason="-1e-45 is not less than 0?")
+    @pytest.mark.parametrize('method', _estimated_cdf_discontinuous_methods.keys())
+    def test_transition(self, method, xp):
+        # test that values of discontinuous estimators are as expected around
+        # transition point
+        x = np.arange(8., dtype=np.float64)
+        xl, xr = np.nextafter(x, -np.inf), np.nextafter(x, np.inf)
+        offset = 0.5 if method == 'closest_observation' else 0.0
+        ref_r = (x + 1 + offset) / 8
+        ref_r[-1] = 1.0  # value is greater than or equal to the maximum observation
+        ref_l = (x + offset) / 8
+        ref_l[0] = 0.0  # value is less than the minimum observation
+        x, xl, xr = xp.asarray(x), xp.asarray(xl), xp.asarray(xr)
+        ref_l, ref_r = xp.asarray(ref_l), xp.asarray(ref_r)
+        xp_assert_equal(stats.estimated_cdf(x, x, method=method), ref_r)
+        xp_assert_equal(stats.estimated_cdf(x, xr, method=method), ref_r)
+        xp_assert_equal(stats.estimated_cdf(x, xl, method=method), ref_l)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/test_rank.py b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_rank.py
new file mode 100644
index 0000000000000000000000000000000000000000..1d8e89cfea0315e30d1ab0c45e8bdab282360761
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_rank.py
@@ -0,0 +1,350 @@
+import numpy as np
+from numpy.testing import assert_equal, assert_array_equal
+import pytest
+
+from scipy import stats
+from scipy.conftest import skip_xp_invalid_arg
+from scipy.stats import rankdata, tiecorrect
+from scipy._lib._array_api import (xp_assert_equal, make_xp_test_case, xp_result_type,
+                                   xp_default_dtype)
+
+skip_xp_backends = pytest.mark.skip_xp_backends
+
+class TestTieCorrect:
+
+    def test_empty(self):
+        """An empty array requires no correction, should return 1.0."""
+        ranks = np.array([], dtype=np.float64)
+        c = tiecorrect(ranks)
+        assert_equal(c, 1.0)
+
+    def test_one(self):
+        """A single element requires no correction, should return 1.0."""
+        ranks = np.array([1.0], dtype=np.float64)
+        c = tiecorrect(ranks)
+        assert_equal(c, 1.0)
+
+    def test_no_correction(self):
+        """Arrays with no ties require no correction."""
+        ranks = np.arange(2.0)
+        c = tiecorrect(ranks)
+        assert_equal(c, 1.0)
+        ranks = np.arange(3.0)
+        c = tiecorrect(ranks)
+        assert_equal(c, 1.0)
+
+    def test_basic(self):
+        """Check a few basic examples of the tie correction factor."""
+        # One tie of two elements
+        ranks = np.array([1.0, 2.5, 2.5])
+        c = tiecorrect(ranks)
+        T = 2.0
+        N = ranks.size
+        expected = 1.0 - (T**3 - T) / (N**3 - N)
+        assert_equal(c, expected)
+
+        # One tie of two elements (same as above, but tie is not at the end)
+        ranks = np.array([1.5, 1.5, 3.0])
+        c = tiecorrect(ranks)
+        T = 2.0
+        N = ranks.size
+        expected = 1.0 - (T**3 - T) / (N**3 - N)
+        assert_equal(c, expected)
+
+        # One tie of three elements
+        ranks = np.array([1.0, 3.0, 3.0, 3.0])
+        c = tiecorrect(ranks)
+        T = 3.0
+        N = ranks.size
+        expected = 1.0 - (T**3 - T) / (N**3 - N)
+        assert_equal(c, expected)
+
+        # Two ties, lengths 2 and 3.
+        ranks = np.array([1.5, 1.5, 4.0, 4.0, 4.0])
+        c = tiecorrect(ranks)
+        T1 = 2.0
+        T2 = 3.0
+        N = ranks.size
+        expected = 1.0 - ((T1**3 - T1) + (T2**3 - T2)) / (N**3 - N)
+        assert_equal(c, expected)
+
+    def test_overflow(self):
+        ntie, k = 2000, 5
+        a = np.repeat(np.arange(k), ntie)
+        n = a.size  # ntie * k
+        out = tiecorrect(rankdata(a))
+        assert_equal(out, 1.0 - k * (ntie**3 - ntie) / float(n**3 - n))
+
+
+@make_xp_test_case(stats.rankdata)
+class TestRankData:
+
+    def desired_dtype(self, x, *, xp):
+        return xp_result_type(x, force_floating=True, xp=xp)
+
+    def test_empty(self, xp):
+        """stats.rankdata of empty array should return an empty array."""
+        a = xp.asarray([], dtype=xp.int64)
+        r = rankdata(a)
+        xp_assert_equal(r, xp.asarray([], dtype=self.desired_dtype(a, xp=xp)))
+
+    def test_list(self):
+        # test that NumPy still accepts lists
+        r = rankdata([])
+        assert_array_equal(r, np.array([]))
+
+        r = rankdata([40, 10, 30, 10, 50])
+        assert_equal(r, [4.0, 1.5, 3.0, 1.5, 5.0])
+
+    @pytest.mark.parametrize("shape", [(0, 1, 2)])
+    @pytest.mark.parametrize("axis", [None, *range(3)])
+    def test_empty_multidim(self, shape, axis, xp):
+        a = xp.empty(shape, dtype=xp.int64)
+        r = rankdata(a, axis=axis)
+        expected_shape = (0,) if axis is None else shape
+        xp_assert_equal(r, xp.empty(expected_shape, dtype=self.desired_dtype(a, xp=xp)))
+
+    def test_one(self, xp):
+        """Check stats.rankdata with an array of length 1."""
+        data = [100]
+        a = xp.asarray(data, dtype=xp.int64)
+        r = rankdata(a)
+        xp_assert_equal(r, xp.asarray([1.0], dtype=self.desired_dtype(a, xp=xp)))
+
+    def test_basic(self, xp):
+        """Basic tests of stats.rankdata."""
+        desired_dtype = xp_default_dtype(xp)
+
+        data = [100, 10, 50]
+        expected = xp.asarray([3.0, 1.0, 2.0], dtype=desired_dtype)
+        a = xp.asarray(data, dtype=xp.int64)
+        r = rankdata(a)
+        xp_assert_equal(r, expected)
+
+        data = [40, 10, 30, 10, 50]
+        expected = xp.asarray([4.0, 1.5, 3.0, 1.5, 5.0], dtype=desired_dtype)
+        a = xp.asarray(data, dtype=xp.int64)
+        r = rankdata(a)
+        xp_assert_equal(r, expected)
+
+        data = [20, 20, 20, 10, 10, 10]
+        expected = xp.asarray([5.0, 5.0, 5.0, 2.0, 2.0, 2.0], dtype=desired_dtype)
+        a = xp.asarray(data, dtype=xp.int64)
+        r = rankdata(a)
+        xp_assert_equal(r, expected)
+
+        # # The docstring states explicitly that the argument is flattened.
+        a2d = xp.reshape(a, (2, 3))
+        r = rankdata(a2d)
+        xp_assert_equal(r, expected)
+
+    @skip_xp_invalid_arg
+    def test_rankdata_object_string(self):
+
+        def min_rank(a):
+            return [1 + sum(i < j for i in a) for j in a]
+
+        def max_rank(a):
+            return [sum(i <= j for i in a) for j in a]
+
+        def ordinal_rank(a):
+            return min_rank([(x, i) for i, x in enumerate(a)])
+
+        def average_rank(a):
+            return [(i + j) / 2.0 for i, j in zip(min_rank(a), max_rank(a))]
+
+        def dense_rank(a):
+            b = np.unique(a)
+            return [1 + sum(i < j for i in b) for j in a]
+
+        rankf = dict(min=min_rank, max=max_rank, ordinal=ordinal_rank,
+                     average=average_rank, dense=dense_rank)
+
+        def check_ranks(a):
+            for method in 'min', 'max', 'dense', 'ordinal', 'average':
+                out = rankdata(a, method=method)
+                assert_array_equal(out, rankf[method](a))
+
+        val = ['foo', 'bar', 'qux', 'xyz', 'abc', 'efg', 'ace', 'qwe', 'qaz']
+        check_ranks(np.random.choice(val, 200))
+        check_ranks(np.random.choice(val, 200).astype('object'))
+
+        val = np.array([0, 1, 2, 2.718, 3, 3.141], dtype='object')
+        check_ranks(np.random.choice(val, 200).astype('object'))
+
+    @pytest.mark.skip_xp_backends("torch", reason="`take_along_axis` fails with uint64")
+    def test_large_uint(self, xp):
+        data = xp.asarray([2**60, 2**60+1], dtype=xp.uint64)
+        r = rankdata(data)
+        desired_dtype = self.desired_dtype(data, xp=xp)
+        xp_assert_equal(r, xp.asarray([1.0, 2.0], dtype=desired_dtype))
+
+    def test_large_int(self, xp):
+        data = xp.asarray([2**60, 2**60+1], dtype=xp.int64)
+        r = rankdata(data)
+        desired_dtype = self.desired_dtype(data, xp=xp)
+        xp_assert_equal(r, xp.asarray([1.0, 2.0], dtype=desired_dtype))
+
+        data = xp.asarray([2**60, -2**60+1], dtype=xp.int64)
+        r = rankdata(data)
+        xp_assert_equal(r, xp.asarray([2.0, 1.0], dtype=desired_dtype))
+
+    @pytest.mark.parametrize('n', [10000, 100000, 1000000])
+    def test_big_tie(self, n, xp):
+        data = xp.ones(n)
+        r = rankdata(data)
+        expected_rank = 0.5 * (n + 1)
+        ref = xp.asarray(expected_rank * data, dtype=self.desired_dtype(data, xp=xp))
+        xp_assert_equal(r, ref)
+
+    def test_axis(self, xp):
+        data = xp.asarray([[0, 2, 1], [4, 2, 2]])
+
+        expected0 = xp.asarray([[1., 1.5, 1.], [2., 1.5, 2.]])
+        r0 = rankdata(data, axis=0)
+        xp_assert_equal(r0, expected0)
+
+        expected1 = xp.asarray([[1., 3., 2.], [3., 1.5, 1.5]])
+        r1 = rankdata(data, axis=1)
+        xp_assert_equal(r1, expected1)
+
+    methods= ["average", "min", "max", "dense", "ordinal"]
+
+    @pytest.mark.parametrize("axis", [0, 1])
+    @pytest.mark.parametrize("method", methods)
+    def test_size_0_axis(self, axis, method, xp):
+        shape = (3, 0)
+        data = xp.zeros(shape)
+        desired_dtype = self.desired_dtype(data, xp=xp)
+        r = rankdata(data, method=method, axis=axis)
+        assert_equal(r.shape, shape)
+        assert_equal(r.dtype, desired_dtype)
+        xp_assert_equal(r, xp.empty(shape, dtype=desired_dtype))
+
+    @pytest.mark.parametrize('axis', range(3))
+    @pytest.mark.parametrize('method', methods)
+    def test_nan_policy_omit_3d(self, axis, method):
+        shape = (20, 21, 22)
+        rng = np.random.RandomState(23983242)
+
+        a = rng.random(size=shape)
+        i = rng.random(size=shape) < 0.4
+        j = rng.random(size=shape) < 0.1
+        k = rng.random(size=shape) < 0.1
+        a[i] = np.nan
+        a[j] = -np.inf
+        a[k] - np.inf
+
+        def rank_1d_omit(a, method):
+            out = np.zeros_like(a)
+            i = np.isnan(a)
+            a_compressed = a[~i]
+            res = rankdata(a_compressed, method)
+            out[~i] = res
+            out[i] = np.nan
+            return out
+
+        def rank_omit(a, method, axis):
+            return np.apply_along_axis(lambda a: rank_1d_omit(a, method),
+                                       axis, a)
+
+        res = rankdata(a, method, axis=axis, nan_policy='omit')
+        res0 = rank_omit(a, method, axis=axis)
+
+        assert_array_equal(res, res0)
+
+    def test_nan_policy_2d_axis_none(self):
+        # 2 2d-array test with axis=None
+        data = [[0, np.nan, 3],
+                [4, 2, np.nan],
+                [1, 2, 2]]
+        assert_array_equal(rankdata(data, axis=None, nan_policy='omit'),
+                           [1., np.nan, 6., 7., 4., np.nan, 2., 4., 4.])
+        assert_array_equal(rankdata(data, axis=None, nan_policy='propagate'),
+                           [np.nan, np.nan, np.nan, np.nan, np.nan, np.nan,
+                            np.nan, np.nan, np.nan])
+
+    def test_nan_policy_raise(self):
+        # 1 1d-array test
+        data = [0, 2, 3, -2, np.nan, np.nan]
+        with pytest.raises(ValueError, match="The input contains nan"):
+            rankdata(data, nan_policy='raise')
+
+        # 2 2d-array test
+        data = [[0, np.nan, 3],
+                [4, 2, np.nan],
+                [np.nan, 2, 2]]
+
+        with pytest.raises(ValueError, match="The input contains nan"):
+            rankdata(data, axis=0, nan_policy="raise")
+
+        with pytest.raises(ValueError, match="The input contains nan"):
+            rankdata(data, axis=1, nan_policy="raise")
+
+    def test_nan_policy_propagate(self):
+        # 1 1d-array test
+        data = [0, 2, 3, -2, np.nan, np.nan]
+        assert_array_equal(rankdata(data, nan_policy='propagate'),
+                           [np.nan, np.nan, np.nan, np.nan, np.nan, np.nan])
+
+        # 2 2d-array test
+        data = [[0, np.nan, 3],
+                [4, 2, np.nan],
+                [1, 2, 2]]
+        assert_array_equal(rankdata(data, axis=0, nan_policy='propagate'),
+                           [[1, np.nan, np.nan],
+                            [3, np.nan, np.nan],
+                            [2, np.nan, np.nan]])
+        assert_array_equal(rankdata(data, axis=1, nan_policy='propagate'),
+                           [[np.nan, np.nan, np.nan],
+                            [np.nan, np.nan, np.nan],
+                            [1, 2.5, 2.5]])
+
+    _rankdata_cases = (
+        # values, method, expected
+        ([], 'average', []),
+        ([], 'min', []),
+        ([], 'max', []),
+        ([], 'dense', []),
+        ([], 'ordinal', []),
+        #
+        ([100], 'average', [1.0]),
+        ([100], 'min', [1.0]),
+        ([100], 'max', [1.0]),
+        ([100], 'dense', [1.0]),
+        ([100], 'ordinal', [1.0]),
+        #
+        ([100, 100, 100], 'average', [2.0, 2.0, 2.0]),
+        ([100, 100, 100], 'min', [1.0, 1.0, 1.0]),
+        ([100, 100, 100], 'max', [3.0, 3.0, 3.0]),
+        ([100, 100, 100], 'dense', [1.0, 1.0, 1.0]),
+        ([100, 100, 100], 'ordinal', [1.0, 2.0, 3.0]),
+        #
+        ([100, 300, 200], 'average', [1.0, 3.0, 2.0]),
+        ([100, 300, 200], 'min', [1.0, 3.0, 2.0]),
+        ([100, 300, 200], 'max', [1.0, 3.0, 2.0]),
+        ([100, 300, 200], 'dense', [1.0, 3.0, 2.0]),
+        ([100, 300, 200], 'ordinal', [1.0, 3.0, 2.0]),
+        #
+        ([100, 200, 300, 200], 'average', [1.0, 2.5, 4.0, 2.5]),
+        ([100, 200, 300, 200], 'min', [1.0, 2.0, 4.0, 2.0]),
+        ([100, 200, 300, 200], 'max', [1.0, 3.0, 4.0, 3.0]),
+        ([100, 200, 300, 200], 'dense', [1.0, 2.0, 3.0, 2.0]),
+        ([100, 200, 300, 200], 'ordinal', [1.0, 2.0, 4.0, 3.0]),
+        #
+        ([100, 200, 300, 200, 100], 'average', [1.5, 3.5, 5.0, 3.5, 1.5]),
+        ([100, 200, 300, 200, 100], 'min', [1.0, 3.0, 5.0, 3.0, 1.0]),
+        ([100, 200, 300, 200, 100], 'max', [2.0, 4.0, 5.0, 4.0, 2.0]),
+        ([100, 200, 300, 200, 100], 'dense', [1.0, 2.0, 3.0, 2.0, 1.0]),
+        ([100, 200, 300, 200, 100], 'ordinal', [1.0, 3.0, 5.0, 4.0, 2.0]),
+        #
+        ([10] * 30, 'ordinal', np.arange(1.0, 31.0)),
+    )
+
+    @pytest.mark.parametrize('case', _rankdata_cases)
+    def test_cases(self, case, xp):
+        values, method, expected = case
+        values = xp.asarray(values)
+        r = rankdata(xp.asarray(values), method=method)
+        ref = xp.asarray(expected, dtype=self.desired_dtype(values, xp=xp))
+        xp_assert_equal(r, ref)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/test_relative_risk.py b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_relative_risk.py
new file mode 100644
index 0000000000000000000000000000000000000000..b75e64d929f319465b1f1d62af4fb2096c2ab2ac
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_relative_risk.py
@@ -0,0 +1,95 @@
+import pytest
+import numpy as np
+from numpy.testing import assert_allclose, assert_equal
+from scipy.stats.contingency import relative_risk
+
+
+# Test just the calculation of the relative risk, including edge
+# cases that result in a relative risk of 0, inf or nan.
+@pytest.mark.parametrize(
+    'exposed_cases, exposed_total, control_cases, control_total, expected_rr',
+    [(1, 4, 3, 8, 0.25 / 0.375),
+     (0, 10, 5, 20, 0),
+     (0, 10, 0, 20, np.nan),
+     (5, 15, 0, 20, np.inf)]
+)
+def test_relative_risk(exposed_cases, exposed_total,
+                       control_cases, control_total, expected_rr):
+    result = relative_risk(exposed_cases, exposed_total,
+                           control_cases, control_total)
+    assert_allclose(result.relative_risk, expected_rr, rtol=1e-13)
+
+
+def test_relative_risk_confidence_interval():
+    result = relative_risk(exposed_cases=16, exposed_total=128,
+                           control_cases=24, control_total=256)
+    rr = result.relative_risk
+    ci = result.confidence_interval(confidence_level=0.95)
+    # The corresponding calculation in R using the epitools package.
+    #
+    # > library(epitools)
+    # > c <- matrix(c(232, 112, 24, 16), nrow=2)
+    # > result <- riskratio(c)
+    # > result$measure
+    #               risk ratio with 95% C.I.
+    # Predictor  estimate     lower    upper
+    #   Exposed1 1.000000        NA       NA
+    #   Exposed2 1.333333 0.7347317 2.419628
+    #
+    # The last line is the result that we want.
+    assert_allclose(rr, 4/3)
+    assert_allclose((ci.low, ci.high), (0.7347317, 2.419628), rtol=5e-7)
+
+
+def test_relative_risk_ci_conflevel0():
+    result = relative_risk(exposed_cases=4, exposed_total=12,
+                           control_cases=5, control_total=30)
+    rr = result.relative_risk
+    assert_allclose(rr, 2.0, rtol=1e-14)
+    ci = result.confidence_interval(0)
+    assert_allclose((ci.low, ci.high), (2.0, 2.0), rtol=1e-12)
+
+
+def test_relative_risk_ci_conflevel1():
+    result = relative_risk(exposed_cases=4, exposed_total=12,
+                           control_cases=5, control_total=30)
+    ci = result.confidence_interval(1)
+    assert_equal((ci.low, ci.high), (0, np.inf))
+
+
+def test_relative_risk_ci_edge_cases_00():
+    result = relative_risk(exposed_cases=0, exposed_total=12,
+                           control_cases=0, control_total=30)
+    assert_equal(result.relative_risk, np.nan)
+    ci = result.confidence_interval()
+    assert_equal((ci.low, ci.high), (np.nan, np.nan))
+
+
+def test_relative_risk_ci_edge_cases_01():
+    result = relative_risk(exposed_cases=0, exposed_total=12,
+                           control_cases=1, control_total=30)
+    assert_equal(result.relative_risk, 0)
+    ci = result.confidence_interval()
+    assert_equal((ci.low, ci.high), (0.0, np.nan))
+
+
+def test_relative_risk_ci_edge_cases_10():
+    result = relative_risk(exposed_cases=1, exposed_total=12,
+                           control_cases=0, control_total=30)
+    assert_equal(result.relative_risk, np.inf)
+    ci = result.confidence_interval()
+    assert_equal((ci.low, ci.high), (np.nan, np.inf))
+
+
+@pytest.mark.parametrize('ec, et, cc, ct', [(0, 0, 10, 20),
+                                            (-1, 10, 1, 5),
+                                            (1, 10, 0, 0),
+                                            (1, 10, -1, 4)])
+def test_relative_risk_bad_value(ec, et, cc, ct):
+    with pytest.raises(ValueError, match="must be an integer not less than"):
+        relative_risk(ec, et, cc, ct)
+
+
+def test_relative_risk_bad_type():
+    with pytest.raises(TypeError, match="must be an integer"):
+        relative_risk(1, 10, 2.0, 40)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/test_resampling.py b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_resampling.py
new file mode 100644
index 0000000000000000000000000000000000000000..ec900da2d5a05570054596286f82c67f96fbdc0d
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_resampling.py
@@ -0,0 +1,2084 @@
+import warnings
+
+import pytest
+
+import numpy as np
+from numpy.testing import assert_allclose, assert_equal
+
+from scipy._lib._util import rng_integers
+from scipy._lib._array_api import (is_numpy, make_xp_test_case, xp_default_dtype,
+                                   xp_size, array_namespace, _xp_copy_to_numpy,
+                                   is_lazy_array, eager_warns)
+from scipy._lib._array_api_no_0d import xp_assert_close, xp_assert_equal
+from scipy._external import array_api_extra as xpx
+from scipy import stats, special
+from scipy.fft.tests.test_fftlog import skip_xp_backends
+from scipy.optimize import root
+
+from scipy.stats import bootstrap, monte_carlo_test, permutation_test, power
+import scipy.stats._resampling as _resampling
+
+
+lazy_xp_modules = [stats]
+
+
+@make_xp_test_case(bootstrap)
+class TestBootstrap:
+    @skip_xp_backends('numpy', reason='NumPy does not raise')
+    def test_bootstrap_iv_other(self, xp):
+        message = f"When using array library {xp.__name__}"
+        with pytest.raises(TypeError, match=message):
+            bootstrap((xp.asarray([1, 2, 3]),), lambda x: xp.mean(x))
+
+    def test_bootstrap_iv(self, xp):
+        sample = xp.asarray([1, 2, 3])
+
+        message = "`data` must contain at least one sample."
+        with pytest.raises(ValueError, match=message):
+            bootstrap(tuple(), xp.mean)
+
+        message = "each sample in `data` must contain two or more observations..."
+        with pytest.raises(ValueError, match=message):
+            bootstrap((sample, xp.asarray([1])), xp.mean)
+
+        message = ("When `paired is True`, all samples must have the same length ")
+        with pytest.raises(ValueError, match=message):
+            bootstrap((sample, xp.asarray([1, 2, 3, 4])), xp.mean, paired=True)
+
+        message = "`vectorized` must be `True`, `False`, or `None`."
+        with pytest.raises(ValueError, match=message):
+            bootstrap(sample, xp.mean, vectorized='ekki')
+
+        message = "`axis` must be an integer."
+        with pytest.raises(ValueError, match=message):
+            bootstrap((sample,), xp.mean, axis=1.5)
+
+        message = "could not convert string to float"
+        with pytest.raises(ValueError, match=message):
+            bootstrap((sample,), xp.mean, confidence_level='ni')
+
+        message = "`n_resamples` must be a non-negative integer."
+        with pytest.raises(ValueError, match=message):
+            bootstrap((sample,), xp.mean, n_resamples=-1000)
+
+        message = "`n_resamples` must be a non-negative integer."
+        with pytest.raises(ValueError, match=message):
+            bootstrap((sample,), xp.mean, n_resamples=1000.5)
+
+        message = "`batch` must be a positive integer or None."
+        with pytest.raises(ValueError, match=message):
+            bootstrap((sample,), xp.mean, batch=-1000)
+
+        message = "`batch` must be a positive integer or None."
+        with pytest.raises(ValueError, match=message):
+            bootstrap((sample,), xp.mean, batch=1000.5)
+
+        message = "`method` must be in"
+        with pytest.raises(ValueError, match=message):
+            bootstrap((sample,), xp.mean, method='ekki')
+
+        message = "`bootstrap_result` must have attribute `bootstrap_distribution'"
+        with pytest.raises(ValueError, match=message):
+            bootstrap((sample,), xp.mean, bootstrap_result=10)
+
+        message = "Either `bootstrap_result.bootstrap_distribution.size`"
+        with pytest.raises(ValueError, match=message):
+            bootstrap((sample,), xp.mean, n_resamples=0)
+
+        message = "SeedSequence expects int or sequence of ints"
+        with pytest.raises(TypeError, match=message):
+            bootstrap((sample,), xp.mean, rng='herring')
+
+    @pytest.mark.parametrize("method", ['basic', 'percentile', 'BCa'])
+    @pytest.mark.parametrize("axis", [0, 1, 2])
+    def test_bootstrap_batch(self, method, axis, xp):
+        # for one-sample statistics, batch size shouldn't affect the result
+        rng = np.random.RandomState(0)
+
+        x = rng.rand(10, 11, 12)
+        # SPEC-007 leave one call with random_state to ensure it still works
+        res1 = bootstrap((xp.asarray(x),), xp.mean, batch=None, method=method,
+                         random_state=0, axis=axis, n_resamples=100)
+        rng = np.random.RandomState(0)
+        res2 = bootstrap((xp.asarray(x),), xp.mean, batch=10, method=method,
+                         axis=axis, n_resamples=100, random_state=rng)
+
+        xp_assert_close(res2.confidence_interval.low, res1.confidence_interval.low)
+        xp_assert_close(res2.confidence_interval.high, res1.confidence_interval.high)
+        xp_assert_close(res2.standard_error, res1.standard_error)
+
+    @pytest.mark.parametrize("method", ['basic', 'percentile', 'BCa'])
+    def test_bootstrap_paired(self, method, xp):
+        # test that `paired` works as expected
+        rng = np.random.RandomState(0)
+        n = 100
+        x = xp.asarray(rng.rand(n))
+        y = xp.asarray(rng.rand(n))
+
+        def my_statistic(x, y, axis=-1):
+            return xp.mean((x-y)**2, axis=axis)
+
+        def my_paired_statistic(i, axis=-1):
+            a = x[i]
+            b = y[i]
+            res = my_statistic(a, b)
+            return res
+
+        i = xp.arange(x.shape[0])
+
+        res1 = bootstrap((i,), my_paired_statistic, rng=0)
+        res2 = bootstrap((x, y), my_statistic, paired=True, rng=0)
+
+        xp_assert_close(res1.confidence_interval.low, res2.confidence_interval.low)
+        xp_assert_close(res1.confidence_interval.high, res2.confidence_interval.high)
+        xp_assert_close(res1.standard_error, res2.standard_error)
+
+    @pytest.mark.parametrize("method", ['basic', 'percentile', 'BCa'])
+    @pytest.mark.parametrize("axis", [0, 1, 2])
+    @pytest.mark.parametrize("paired", [True, False])
+    def test_bootstrap_vectorized(self, method, axis, paired, xp):
+        # test that paired is vectorized as expected: when samples are tiled,
+        # CI and standard_error of each axis-slice is the same as those of the
+        # original 1d sample
+
+        rng = np.random.RandomState(0)
+
+        def my_statistic(x, y, z, axis=-1):
+            return xp.mean(x, axis=axis) + xp.mean(y, axis=axis) + xp.mean(z, axis=axis)
+
+        shape = 10, 11, 12
+        n_samples = shape[axis]
+
+        x = rng.rand(n_samples)
+        y = rng.rand(n_samples)
+        z = rng.rand(n_samples)
+        x, y, z = xp.asarray(x), xp.asarray(y), xp.asarray(z)
+
+        res1 = bootstrap((x, y, z), my_statistic, paired=paired, method=method,
+                         rng=0, axis=0, n_resamples=100)
+        assert (res1.bootstrap_distribution.shape
+                == res1.standard_error.shape + (100,))
+
+        reshape = [1, 1, 1]
+        reshape[axis] = n_samples
+        reshape = tuple(reshape)
+        x = xp.broadcast_to(xp.reshape(x, reshape), shape)
+        y = xp.broadcast_to(xp.reshape(y, reshape), shape)
+        z = xp.broadcast_to(xp.reshape(z, reshape), shape)
+        res2 = bootstrap((x, y, z), my_statistic, paired=paired, method=method,
+                         rng=0, axis=axis, n_resamples=100)
+
+        result_shape = list(shape)
+        result_shape.pop(axis)
+
+        ref_ci_low = xp.broadcast_to(res2.confidence_interval.low, result_shape)
+        ref_ci_high = xp.broadcast_to(res2.confidence_interval.high, result_shape)
+        ref_ci_standard_error = xp.broadcast_to(res2.standard_error, result_shape)
+
+        xp_assert_close(res2.confidence_interval.low, ref_ci_low)
+        xp_assert_close(res2.confidence_interval.high, ref_ci_high)
+        xp_assert_close(res2.standard_error, ref_ci_standard_error)
+
+    @pytest.mark.slow
+    @pytest.mark.xfail_on_32bit("MemoryError with BCa observed in CI")
+    @pytest.mark.parametrize("method", ['basic', 'percentile', 'BCa'])
+    def test_bootstrap_against_theory(self, method, xp):
+        # based on https://www.statology.org/confidence-intervals-python/
+        rng = np.random.default_rng(2442101192988600726)
+        data = stats.norm.rvs(loc=5, scale=2, size=5000, random_state=rng)
+        alpha = 0.95
+        dist = stats.t(df=len(data)-1, loc=np.mean(data), scale=stats.sem(data))
+        ref_low, ref_high = dist.interval(confidence=alpha)
+        ref_se = dist.std()
+
+        config = dict(data=(xp.asarray(data),), statistic=xp.mean, n_resamples=5000,
+                      method=method, rng=rng)
+        res = bootstrap(**config, confidence_level=alpha)
+
+        xp_assert_close(res.confidence_interval.low, xp.asarray(ref_low), rtol=5e-4)
+        xp_assert_close(res.confidence_interval.high, xp.asarray(ref_high), rtol=5e-4)
+        xp_assert_close(res.standard_error, xp.asarray(ref_se), atol=3e-4)
+
+        config.update(dict(n_resamples=0, bootstrap_result=res))
+        res = bootstrap(**config, confidence_level=alpha, alternative='less')
+        xp_assert_close(res.confidence_interval.high,
+                        xp.asarray(dist.ppf(alpha)), rtol=5e-4)
+
+        config.update(dict(n_resamples=0, bootstrap_result=res))
+        res = bootstrap(**config, confidence_level=alpha, alternative='greater')
+        xp_assert_close(res.confidence_interval.low,
+                        xp.asarray(dist.ppf(1-alpha)), rtol=5e-4)
+
+    tests_R = [("basic", 23.77, 79.12),
+               ("percentile", 28.86, 84.21),
+               ("BCa", 32.31, 91.43)]
+
+    @pytest.mark.parametrize("method, ref_low, ref_high", tests_R)
+    def test_bootstrap_against_R(self, method, ref_low, ref_high, xp):
+        # Compare against R's "boot" library
+        # library(boot)
+
+        # stat <- function (x, a) {
+        #     mean(x[a])
+        # }
+
+        # x <- c(10, 12, 12.5, 12.5, 13.9, 15, 21, 22,
+        #        23, 34, 50, 81, 89, 121, 134, 213)
+
+        # # Use a large value so we get a few significant digits for the CI.
+        # n = 1000000
+        # bootresult = boot(x, stat, n)
+        # result <- boot.ci(bootresult)
+        # print(result)
+        x = xp.asarray([10, 12, 12.5, 12.5, 13.9, 15, 21, 22,
+                        23, 34, 50, 81, 89, 121, 134, 213])
+        res = bootstrap((x,), xp.mean, n_resamples=1000000, method=method, rng=0)
+        xp_assert_close(res.confidence_interval.low, xp.asarray(ref_low), rtol=0.005)
+        xp_assert_close(res.confidence_interval.high, xp.asarray(ref_high), rtol=0.005)
+
+    def test_multisample_BCa_against_R(self, xp):
+        # Because bootstrap is stochastic, it's tricky to test against reference
+        # behavior. Here, we show that SciPy's BCa CI matches R wboot's BCa CI
+        # much more closely than the other SciPy CIs do.
+
+        # arbitrary skewed data
+        x = xp.asarray([0.75859206, 0.5910282, -0.4419409, -0.36654601,
+                        0.34955357, -1.38835871, 0.76735821])
+        y = xp.asarray([1.41186073, 0.49775975, 0.08275588, 0.24086388,
+                        0.03567057, 0.52024419, 0.31966611, 1.32067634])
+
+        # a multi-sample statistic for which the BCa CI tends to be different
+        # from the other CIs
+        def statistic(x, y, axis):
+            s1 = stats.skew(x, axis=axis)
+            s2 = stats.skew(y, axis=axis)
+            return s1 - s2
+
+        # compute confidence intervals using each method
+        rng = np.random.default_rng(468865032284792692)
+
+        res_basic = stats.bootstrap((x, y), statistic, method='basic',
+                                    batch=100, rng=rng)
+        res_percent = stats.bootstrap((x, y), statistic, method='percentile',
+                                      batch=100, rng=rng)
+        res_bca = stats.bootstrap((x, y), statistic, method='bca',
+                                  batch=100, rng=rng)
+
+        # compute midpoints so we can compare just one number for each
+        mid_basic = xp.mean(xp.stack(res_basic.confidence_interval))
+        mid_percent = xp.mean(xp.stack(res_percent.confidence_interval))
+        mid_bca = xp.mean(xp.stack(res_bca.confidence_interval))
+
+        # reference for BCA CI computed using R wboot package:
+        # library(wBoot)
+        # library(moments)
+
+        # x = c(0.75859206, 0.5910282, -0.4419409, -0.36654601,
+        #       0.34955357, -1.38835871,  0.76735821)
+        # y = c(1.41186073, 0.49775975, 0.08275588, 0.24086388,
+        #       0.03567057, 0.52024419, 0.31966611, 1.32067634)
+
+        # twoskew <- function(x1, y1) {skewness(x1) - skewness(y1)}
+        # boot.two.bca(x, y, skewness, conf.level = 0.95,
+        #              R = 9999, stacked = FALSE)
+        mid_wboot = -1.5519
+
+        # compute percent difference relative to wboot BCA method
+        diff_basic = (mid_basic - mid_wboot)/abs(mid_wboot)
+        diff_percent = (mid_percent - mid_wboot)/abs(mid_wboot)
+        diff_bca = (mid_bca - mid_wboot)/abs(mid_wboot)
+
+        # SciPy's BCa CI midpoint is much closer than that of the other methods
+        assert diff_basic < -0.15
+        assert diff_percent > 0.15
+        assert abs(diff_bca) < 0.03
+
+    def test_BCa_acceleration_against_reference(self, xp):
+        # Compare the (deterministic) acceleration parameter for a multi-sample
+        # problem against a reference value. The example is from [1], but Efron's
+        # value seems inaccurate. Straightforward code for computing the
+        # reference acceleration (0.011008228344026734) is available at:
+        # https://github.com/scipy/scipy/pull/16455#issuecomment-1193400981
+
+        y = xp.asarray([10., 27., 31., 40., 46., 50., 52., 104., 146.])
+        z = xp.asarray([16., 23., 38., 94., 99., 141., 197.])
+
+        def statistic(z, y, axis=0):
+            return xp.mean(z, axis=axis) - xp.mean(y, axis=axis)
+
+        data = [z, y]
+        res = stats.bootstrap(data, statistic)
+
+        axis = -1
+        alpha = 0.95
+        theta_hat_b = res.bootstrap_distribution
+        batch = 100
+        _, _, a_hat = _resampling._bca_interval(data, statistic, axis, alpha,
+                                                theta_hat_b, batch, xp)
+        xp_assert_close(a_hat, xp.asarray(0.011008228344026734))
+
+    tests_against_itself_1samp = {"basic": 1789,
+                                  "percentile": 1790,
+                                  "BCa": 1789}
+
+    @pytest.mark.slow
+    @pytest.mark.parametrize("method, expected",
+                             tests_against_itself_1samp.items())
+    def test_bootstrap_against_itself_1samp(self, method, expected, xp):
+        # The expected values in this test were generated using bootstrap
+        # to check for unintended changes in behavior. The test also makes sure
+        # that bootstrap works with multi-sample statistics and that the
+        # `axis` argument works as expected / function is vectorized.
+        rng = np.random.default_rng(9123847)
+
+        n = 100  # size of sample
+        n_resamples = 999  # number of bootstrap resamples used to form each CI
+        confidence_level = 0.9
+
+        # The true mean is 5
+        dist = stats.norm(loc=5, scale=1)
+        stat_true = float(dist.mean())
+
+        # Do the same thing 2000 times. (The code is fully vectorized.)
+        n_replications = 2000
+        data = dist.rvs(size=(n_replications, n), random_state=rng)
+        res = bootstrap((xp.asarray(data),),
+                        statistic=xp.mean,
+                        confidence_level=confidence_level,
+                        n_resamples=n_resamples,
+                        batch=50,
+                        method=method,
+                        axis=-1,
+                        rng=rng)
+        ci = res.confidence_interval
+
+        # ci contains vectors of lower and upper confidence interval bounds
+        ci_contains_true = xp.count_nonzero((ci[0] < stat_true) & (stat_true < ci[1]))
+        assert ci_contains_true == expected
+
+        # ci_contains_true is not inconsistent with confidence_level
+        pvalue = stats.binomtest(int(ci_contains_true), n_replications,
+                                 confidence_level).pvalue
+        assert pvalue > 0.1
+
+    tests_against_itself_2samp = {"basic": 892,
+                                  "percentile": 890}
+
+    @pytest.mark.slow
+    @pytest.mark.parametrize("method, expected",
+                             tests_against_itself_2samp.items())
+    def test_bootstrap_against_itself_2samp(self, method, expected, xp):
+        # The expected values in this test were generated using bootstrap
+        # to check for unintended changes in behavior. The test also makes sure
+        # that bootstrap works with multi-sample statistics and that the
+        # `axis` argument works as expected / function is vectorized.
+        rng = np.random.RandomState(0)
+
+        n1 = 100  # size of sample 1
+        n2 = 120  # size of sample 2
+        n_resamples = 999  # number of bootstrap resamples used to form each CI
+        confidence_level = 0.9
+
+        # The statistic we're interested in is the difference in means
+        def my_stat(data1, data2, axis=-1):
+            mean1 = xp.mean(data1, axis=axis)
+            mean2 = xp.mean(data2, axis=axis)
+            return mean1 - mean2
+
+        # The true difference in the means is -0.1
+        dist1 = stats.norm(loc=0, scale=1)
+        dist2 = stats.norm(loc=0.1, scale=1)
+        stat_true = float(dist1.mean() - dist2.mean())
+
+        # Do the same thing 1000 times. (The code is fully vectorized.)
+        n_replications = 1000
+        data1 = dist1.rvs(size=(n_replications, n1), random_state=rng)
+        data2 = dist2.rvs(size=(n_replications, n2), random_state=rng)
+        res = bootstrap((xp.asarray(data1), xp.asarray(data2)),
+                        statistic=my_stat,
+                        confidence_level=confidence_level,
+                        n_resamples=n_resamples,
+                        batch=50,
+                        method=method,
+                        axis=-1,
+                        random_state=rng)
+        ci = res.confidence_interval
+
+        # ci contains vectors of lower and upper confidence interval bounds
+        ci_contains_true = xp.count_nonzero((ci[0] < stat_true) & (stat_true < ci[1]))
+        assert ci_contains_true == expected
+
+        # ci_contains_true is not inconsistent with confidence_level
+        pvalue = stats.binomtest(int(ci_contains_true), n_replications,
+                                 confidence_level).pvalue
+        assert pvalue > 0.1
+
+    @pytest.mark.parametrize("method", ["basic", "percentile", "BCa"])
+    @pytest.mark.parametrize("axis", [0, 1])
+    @pytest.mark.parametrize("dtype", ['float32', 'float64'])
+    def test_bootstrap_vectorized_3samp(self, method, axis, dtype, xp):
+        def statistic(*data, axis=0):
+            # an arbitrary, vectorized statistic
+            return sum(xp.mean(sample, axis=axis) for sample in data)
+
+        def statistic_1d(*data):
+            # the same statistic, not vectorized
+            for sample in data:
+                assert sample.ndim == 1
+            return np.asarray(sum(sample.mean() for sample in data), dtype=dtype)
+
+        rng = np.random.RandomState(0)
+        x = rng.rand(4, 5).astype(dtype)
+        y = rng.rand(4, 5).astype(dtype)
+        z = rng.rand(4, 5).astype(dtype)
+        res1 = bootstrap((xp.asarray(x), xp.asarray(y), xp.asarray(z)),
+                         statistic, vectorized=True, axis=axis, n_resamples=100,
+                         method=method, rng=0)
+        res2 = bootstrap((x, y, z), statistic_1d, vectorized=False,
+                         axis=axis, n_resamples=100, method=method, rng=0)
+
+        rtol = 1e-6 if dtype == 'float32' else 1e-14
+        xp_assert_close(res1.confidence_interval.low,
+                        xp.asarray(res2.confidence_interval.low), rtol=rtol)
+        xp_assert_close(res1.confidence_interval.high,
+                        xp.asarray(res2.confidence_interval.high), rtol=rtol)
+        xp_assert_close(res1.standard_error, xp.asarray(res2.standard_error), rtol=rtol)
+
+    @pytest.mark.xfail_on_32bit("Failure is not concerning; see gh-14107")
+    @pytest.mark.parametrize("method", ["basic", "percentile", "BCa"])
+    @pytest.mark.parametrize("axis", [0, 1])
+    def test_bootstrap_vectorized_1samp(self, method, axis, xp):
+        def statistic(x, axis=0):
+            # an arbitrary, vectorized statistic
+            return xp.mean(x, axis=axis)
+
+        def statistic_1d(x):
+            # the same statistic, not vectorized
+            assert x.ndim == 1
+            return x.mean(axis=0)
+
+        rng = np.random.default_rng(7939952824)
+        x = rng.random((2, 3))
+        res1 = bootstrap((xp.asarray(x),), statistic, vectorized=True, axis=axis,
+                         n_resamples=100, batch=None, method=method, rng=0)
+        res2 = bootstrap((x,), statistic_1d, vectorized=False, axis=axis,
+                         n_resamples=100, batch=10, method=method, rng=0)
+        xp_assert_close(res1.confidence_interval.low,
+                        xp.asarray(res2.confidence_interval.low))
+        xp_assert_close(res1.confidence_interval.high,
+                        xp.asarray(res2.confidence_interval.high))
+        xp_assert_close(res1.standard_error, xp.asarray(res2.standard_error))
+
+    @pytest.mark.parametrize("method", ["basic", "percentile", "BCa"])
+    def test_bootstrap_degenerate(self, method, xp):
+        data = xp.full((35,), 10000.)
+        if method == "BCa":
+            with np.errstate(invalid='ignore'):
+                msg = "The BCa confidence interval cannot be calculated"
+                with eager_warns(stats.DegenerateDataWarning, match=msg, xp=xp):
+                    res = bootstrap([data, ], xp.mean, method=method)
+                    xp_assert_equal(res.confidence_interval.low, xp.asarray(xp.nan))
+                    xp_assert_equal(res.confidence_interval.high, xp.asarray(xp.nan))
+        else:
+            res = bootstrap([data, ], xp.mean, method=method)
+            xp_assert_equal(res.confidence_interval.low, xp.asarray(10000.))
+            xp_assert_equal(res.confidence_interval.high, xp.asarray(10000.))
+        xp_assert_close(res.standard_error, xp.asarray(0.), atol=1e-12)
+
+    @pytest.mark.parametrize("method", ["BCa", "basic", "percentile"])
+    def test_bootstrap_gh15678(self, method, xp):
+        # Check that gh-15678 is fixed: when statistic function returned a Python
+        # float, method="BCa" failed when trying to add a dimension to the float
+        rng = np.random.default_rng(354645618886684)
+        dist = stats.norm(loc=2, scale=4)
+        data = dist.rvs(size=100, random_state=rng)
+        res = bootstrap((xp.asarray(data),), stats.skew, method=method, n_resamples=100,
+                        rng=np.random.default_rng(9563))
+        # this always worked because np.apply_along_axis returns NumPy data type
+        ref = bootstrap((data,), stats.skew, method=method, n_resamples=100,
+                        rng=np.random.default_rng(9563), vectorized=False)
+        xp_assert_close(res.confidence_interval.low,
+                        xp.asarray(ref.confidence_interval.low))
+        xp_assert_close(res.confidence_interval.high,
+                        xp.asarray(ref.confidence_interval.high))
+        xp_assert_close(res.standard_error, xp.asarray(ref.standard_error))
+
+    def test_bootstrap_min(self, xp):
+        # Check that gh-15883 is fixed: percentileofscore should
+        # behave according to the 'mean' behavior and not trigger nan for BCa
+        rng = np.random.default_rng(1891289180021102)
+        dist = stats.norm(loc=2, scale=4)
+        data = dist.rvs(size=100, random_state=rng)
+        true_min = np.min(data)
+        data = xp.asarray(data)
+        res = bootstrap((data,), xp.min, method="BCa", n_resamples=100,
+                        rng=np.random.default_rng(3942))
+        xp_assert_equal(res.confidence_interval.low, xp.asarray(true_min))
+        res2 = bootstrap((-data,), xp.max, method="BCa", n_resamples=100,
+                         rng=np.random.default_rng(3942))
+        xp_assert_close(-res.confidence_interval.low, res2.confidence_interval.high)
+        xp_assert_close(-res.confidence_interval.high, res2.confidence_interval.low)
+
+    @pytest.mark.parametrize("additional_resamples", [0, 1000])
+    def test_re_bootstrap(self, additional_resamples, xp):
+        # Test behavior of parameter `bootstrap_result`
+        rng = np.random.default_rng(8958153316228384)
+        x = rng.random(size=100)
+
+        n1 = 1000
+        n2 = additional_resamples
+        n3 = n1 + additional_resamples
+
+        rng = np.random.default_rng(296689032789913033)
+        res = stats.bootstrap((xp.asarray(x),), xp.mean, n_resamples=n1, rng=rng,
+                              confidence_level=0.95, method='percentile')
+        res = stats.bootstrap((xp.asarray(x),), xp.mean, n_resamples=n2, rng=rng,
+                              confidence_level=0.90, method='BCa',
+                              bootstrap_result=res)
+
+        rng = np.random.default_rng(296689032789913033)
+        ref = stats.bootstrap((xp.asarray(x),), xp.mean, n_resamples=n3, rng=rng,
+                              confidence_level=0.90, method='BCa')
+
+        xp_assert_close(res.confidence_interval.low,
+                        xp.asarray(ref.confidence_interval.low),
+                        rtol=1e-14)
+        xp_assert_close(res.confidence_interval.high,
+                        xp.asarray(ref.confidence_interval.high),
+                        rtol=1e-14)
+        xp_assert_close(res.standard_error, xp.asarray(ref.standard_error), rtol=1e-14)
+
+    @pytest.mark.xfail_on_32bit("Sensitive to machine precision")
+    @pytest.mark.parametrize("method", ['basic', 'percentile', 'BCa'])
+    def test_bootstrap_alternative(self, method, xp):
+        rng = np.random.default_rng(5894822712842015040)
+        dist = stats.norm(loc=2, scale=4)
+        data = (xp.asarray(dist.rvs(size=(100), random_state=rng)),)
+
+        config = dict(data=data, statistic=xp.std, rng=rng, axis=-1)
+        t = stats.bootstrap(**config, confidence_level=0.9)
+
+        config.update(dict(n_resamples=0, bootstrap_result=t))
+        l = stats.bootstrap(**config, confidence_level=0.95, alternative='less')
+        g = stats.bootstrap(**config, confidence_level=0.95, alternative='greater')
+
+        xp_assert_close(l.confidence_interval.high, t.confidence_interval.high,
+                        rtol=1e-14)
+        xp_assert_close(g.confidence_interval.low, t.confidence_interval.low,
+                        rtol=1e-14)
+        assert xp.isinf(l.confidence_interval.low) and l.confidence_interval.low < 0
+        assert xp.isinf(g.confidence_interval.high) and g.confidence_interval.high > 0
+
+        with pytest.raises(ValueError, match='`alternative` must be one of'):
+            stats.bootstrap(**config, alternative='ekki-ekki')
+
+    def test_jackknife_resample(self, xp):
+        shape = 3, 4, 5, 6
+        rng = np.random.default_rng(5274950392)
+        x = rng.random(size=shape)
+        y = next(_resampling._jackknife_resample(xp.asarray(x), xp=xp))
+
+        for i in range(shape[-1]):
+            # each resample is indexed along second to last axis
+            # (last axis is the one the statistic will be taken over / consumed)
+            slc = y[..., i, :]
+            expected = np.delete(x, i, axis=-1)
+
+            xp_assert_equal(slc, xp.asarray(expected))
+
+        y2 = list(_resampling._jackknife_resample(xp.asarray(x), batch=2, xp=xp))
+        xp_assert_equal(xp.concat(y2, axis=-2), y)
+
+    @pytest.mark.skip_xp_backends("array_api_strict",
+                                  reason="Test uses ... + fancy indexing")
+    @pytest.mark.parametrize("rng_name", ["RandomState", "default_rng"])
+    def test_bootstrap_resample(self, rng_name, xp):
+        rng_gen = getattr(np.random, rng_name)
+        rng1 = rng_gen(3949441460)
+        rng2 = rng_gen(3949441460)
+
+        n_resamples = 10
+        shape = 3, 4, 5, 6
+
+        rng = np.random.default_rng(5274950392)
+        x = xp.asarray(rng.random(shape))
+        y = _resampling._bootstrap_resample(x, n_resamples, rng=rng1, xp=xp)
+
+        for i in range(n_resamples):
+            # each resample is indexed along second to last axis
+            # (last axis is the one the statistic will be taken over / consumed)
+            slc = y[..., i, :]
+
+            js = xp.asarray(rng_integers(rng2, 0, shape[-1], shape[-1]))
+            expected = x[..., js]
+
+            xp_assert_equal(slc, expected)
+
+    @pytest.mark.parametrize("score", [0, 0.5, 1])
+    @pytest.mark.parametrize("axis", [0, 1, 2])
+    def test_percentile_of_score(self, score, axis, xp):
+        shape = 10, 20, 30
+        rng = np.random.default_rng(5903363153)
+        x = rng.random(shape)
+        dtype = xp_default_dtype(xp)
+        p = _resampling._percentile_of_score(xp.asarray(x, dtype=dtype),
+                                             xp.asarray(score, dtype=dtype),
+                                             axis=-1, xp=xp)
+
+        def vectorized_pos(a, score, axis):
+            return np.apply_along_axis(stats.percentileofscore, axis, a, score)
+
+        p2 = vectorized_pos(x, score, axis=-1)/100
+
+        xp_assert_close(p, xp.asarray(p2, dtype=dtype), rtol=1e-15)
+
+    @pytest.mark.parametrize("axis", [0, 1, 2])
+    def test_vectorize_statistic(self, axis):
+        # test that _vectorize_statistic vectorizes a statistic along `axis`
+        # only used with NumPy arrays
+
+        def statistic(*data, axis):
+            # an arbitrary, vectorized statistic
+            return sum(sample.mean(axis) for sample in data)
+
+        def statistic_1d(*data):
+            # the same statistic, not vectorized
+            for sample in data:
+                assert sample.ndim == 1
+            return statistic(*data, axis=0)
+
+        # vectorize the non-vectorized statistic
+        statistic2 = _resampling._vectorize_statistic(statistic_1d)
+
+        rng = np.random.RandomState(0)
+        x = rng.rand(4, 5, 6)
+        y = rng.rand(4, 1, 6)
+        z = rng.rand(1, 5, 6)
+
+        res1 = statistic(x, y, z, axis=axis)
+        res2 = statistic2(x, y, z, axis=axis)
+        assert_allclose(res1, res2)
+
+    @pytest.mark.slow
+    @pytest.mark.parametrize("method", ["basic", "percentile", "BCa"])
+    def test_vector_valued_statistic(self, method, xp):
+        # Generate 95% confidence interval around MLE of normal distribution
+        # parameters. Repeat 100 times, each time on sample of size 100.
+        # Check that confidence interval contains true parameters ~95 times.
+        # Confidence intervals are estimated and stochastic; a test failure
+        # does not necessarily indicate that something is wrong. More important
+        # than values of `counts` below is that the shapes of the outputs are
+        # correct.
+
+        rng = np.random.default_rng(2196847219)
+        params = 1, 0.5
+        sample = xp.asarray(rng.normal(*params, size=(100, 100)))
+
+        def statistic(data, axis):
+            return xp.stack([xp.mean(data, axis=axis),
+                             xp.std(data, axis=axis, correction=1)])
+
+        res = bootstrap((sample,), statistic, method=method, axis=-1,
+                        n_resamples=9999, batch=200, random_state=rng)
+
+        params = xp.asarray([1, 0.5])
+        counts = xp.count_nonzero((res.confidence_interval.low.T < params)
+                                  & (res.confidence_interval.high.T > params),
+                                  axis=0)
+        assert xp.all(counts >= 90)
+        assert xp.all(counts <= 100)
+        assert res.confidence_interval.low.shape == (2, 100)
+        assert res.confidence_interval.high.shape == (2, 100)
+        assert res.standard_error.shape == (2, 100)
+        assert res.bootstrap_distribution.shape == (2, 100, 9999)
+
+    @pytest.mark.slow
+    @pytest.mark.filterwarnings('ignore::RuntimeWarning')
+    def test_vector_valued_statistic_gh17715(self):
+        # gh-17715 reported a mistake introduced in the extension of BCa to
+        # multi-sample statistics; a `len` should have been `.shape[-1]`. Check
+        # that this is resolved.
+        # If this is resolved for NumPy, it's resolved for the rest,
+        # let's only run this for NumPy.
+
+        rng = np.random.default_rng(141921000979291141)
+
+        def concordance(x, y, axis):
+            xm = x.mean(axis)
+            ym = y.mean(axis)
+            cov = ((x - xm[..., None]) * (y - ym[..., None])).mean(axis)
+            return (2 * cov) / (x.var(axis) + y.var(axis) + (xm - ym) ** 2)
+
+        def statistic(tp, tn, fp, fn, axis):
+            actual = tp + fp
+            expected = tp + fn
+            return np.nan_to_num(concordance(actual, expected, axis))
+
+        def statistic_extradim(*args, axis):
+            return statistic(*args, axis)[np.newaxis, ...]
+
+        data = [[4, 0, 0, 2],  # (tp, tn, fp, fn)
+                [2, 1, 2, 1],
+                [0, 6, 0, 0],
+                [0, 6, 3, 0],
+                [0, 8, 1, 0]]
+        data = np.array(data).T
+
+        res = bootstrap(data, statistic_extradim, rng=rng, paired=True)
+        ref = bootstrap(data, statistic, rng=rng, paired=True)
+        assert_allclose(res.confidence_interval.low[0],
+                        ref.confidence_interval.low, atol=1e-15)
+        assert_allclose(res.confidence_interval.high[0],
+                        ref.confidence_interval.high, atol=1e-15)
+
+    # torch doesn't have T distribution CDF and can't fall back to NumPy on GPU
+    @pytest.mark.skip_xp_backends(np_only=True, exceptions=['cupy'])
+    def test_gh_20850(self, xp):
+        rng = np.random.default_rng(2085020850)
+        x = xp.asarray(rng.random((10, 2)))
+        y = xp.asarray(rng.random((11, 2)))
+        def statistic(x, y, axis):
+            return stats.ttest_ind(x, y, axis=axis).statistic
+
+        # The shapes do *not* need to be the same along axis
+        stats.bootstrap((x, y), statistic)
+        stats.bootstrap((x.T, y.T), statistic, axis=1)
+        # But even when the shapes *are* the same along axis, the lengths
+        # along other dimensions have to be the same (or `bootstrap` warns).
+        message = "Array shapes are incompatible for broadcasting."
+        with pytest.raises(ValueError, match=message):
+            stats.bootstrap((x, y[:10, 0]), statistic)  # this won't work after 1.16
+        stats.bootstrap((x, y[:10, 0:1]), statistic)  # this will
+        stats.bootstrap((x.T, y.T[0:1, :10]), statistic, axis=1)  # this will
+
+# --- Test Monte Carlo Hypothesis Test --- #
+
+@make_xp_test_case(monte_carlo_test)
+class TestMonteCarloHypothesisTest:
+    atol = 2.5e-2  # for comparing p-value
+
+    def get_rvs(self, rvs_in, rs, dtype=None, xp=np):
+        return lambda *args, **kwds: xp.asarray(rvs_in(*args, random_state=rs, **kwds),
+                                                dtype=dtype)
+
+    def get_statistic(self, xp):
+        def statistic(x, axis):
+            m = xp.mean(x, axis=axis)
+            v = xp.var(x, axis=axis, correction=1)
+            n = x.shape[axis]
+            return m / (v/n)**0.5
+            # return stats.ttest_1samp(x, popmean=0., axis=axis).statistic)
+        return statistic
+
+    def test_input_validation(self, xp):
+        # test that the appropriate error messages are raised for invalid input
+
+        data = xp.asarray([1., 2., 3.])
+        def stat(x, axis=None):
+            return xp.mean(x, axis=axis)
+
+        message = "Array shapes are incompatible for broadcasting."
+        temp = (xp.zeros((2, 5)), xp.zeros((3, 5)))
+        rvs = (stats.norm.rvs, stats.norm.rvs)
+        with pytest.raises(ValueError, match=message):
+            monte_carlo_test(temp, rvs, lambda x, y, axis: 1, axis=-1)
+
+        message = "`axis` must be an integer."
+        with pytest.raises(ValueError, match=message):
+            monte_carlo_test(data, stats.norm.rvs, stat, axis=1.5)
+
+        message = "`vectorized` must be `True`, `False`, or `None`."
+        with pytest.raises(ValueError, match=message):
+            monte_carlo_test(data, stats.norm.rvs, stat, vectorized=1.5)
+
+        message = "`rvs` must be callable or sequence of callables."
+        with pytest.raises(TypeError, match=message):
+            monte_carlo_test(data, None, stat)
+        with pytest.raises(TypeError, match=message):
+            temp = xp.asarray([[1., 2.], [3., 4.]])
+            monte_carlo_test(temp, [lambda x: x, None], stat)
+
+        message = "If `rvs` is a sequence..."
+        with pytest.raises(ValueError, match=message):
+            temp = xp.asarray([[1., 2., 3.]])
+            monte_carlo_test(temp, [lambda x: x, lambda x: x], stat)
+
+        message = "`statistic` must be callable."
+        with pytest.raises(TypeError, match=message):
+            monte_carlo_test(data, stats.norm.rvs, None)
+
+        message = "`n_resamples` must be a positive integer."
+        with pytest.raises(ValueError, match=message):
+            monte_carlo_test(data, stats.norm.rvs, stat, n_resamples=-1000)
+
+        message = "`n_resamples` must be a positive integer."
+        with pytest.raises(ValueError, match=message):
+            monte_carlo_test(data, stats.norm.rvs, stat, n_resamples=1000.5)
+
+        message = "`batch` must be a positive integer or None."
+        with pytest.raises(ValueError, match=message):
+            monte_carlo_test(data, stats.norm.rvs, stat, batch=-1000)
+
+        message = "`batch` must be a positive integer or None."
+        with pytest.raises(ValueError, match=message):
+            monte_carlo_test(data, stats.norm.rvs, stat, batch=1000.5)
+
+        message = "`alternative` must be in..."
+        with pytest.raises(ValueError, match=message):
+            monte_carlo_test(data, stats.norm.rvs, stat, alternative='ekki')
+
+        # *If* this raises a value error, make sure it has the intended message
+        message = "Signature inspection of statistic"
+        def rvs(size):
+            return xp.asarray(stats.norm.rvs(size=size))
+        try:
+            monte_carlo_test(data, rvs, xp.mean)
+        except ValueError as e:
+            assert str(e).startswith(message)
+
+    def test_input_validation_xp(self, xp):
+        def non_vectorized_statistic(x):
+            return xp.mean(x)
+
+        message = "`statistic` must be vectorized..."
+        sample = xp.asarray([1., 2., 3.])
+        if is_numpy(xp):
+            monte_carlo_test(sample, stats.norm.rvs, non_vectorized_statistic)
+            return
+
+        with pytest.raises(ValueError, match=message):
+            monte_carlo_test(sample, stats.norm.rvs, non_vectorized_statistic)
+        with pytest.raises(ValueError, match=message):
+            monte_carlo_test(sample, stats.norm.rvs, xp.mean, vectorized=False)
+
+    @pytest.mark.xslow
+    def test_batch(self, xp):
+        # make sure that the `batch` parameter is respected by checking the
+        # maximum batch size provided in calls to `statistic`
+        rng = np.random.default_rng(23492340193)
+        x = xp.asarray(rng.standard_normal(size=10))
+
+        def statistic(x, axis):
+            batch_size = 1 if x.ndim == 1 else x.shape[0]
+            statistic.batch_size = max(batch_size, statistic.batch_size)
+            statistic.counter += 1
+            return self.get_statistic(xp)(x, axis=axis)
+        statistic.counter = 0
+        statistic.batch_size = 0
+
+        kwds = {'sample': x, 'statistic': statistic,
+                'n_resamples': 1000, 'vectorized': True}
+
+        kwds['rvs'] = self.get_rvs(stats.norm.rvs, np.random.default_rng(328423), xp=xp)
+        res1 = monte_carlo_test(batch=1, **kwds)
+        assert_equal(statistic.counter, 1001)
+        assert_equal(statistic.batch_size, 1)
+
+        kwds['rvs'] = self.get_rvs(stats.norm.rvs, np.random.default_rng(328423), xp=xp)
+        statistic.counter = 0
+        res2 = monte_carlo_test(batch=50, **kwds)
+        assert_equal(statistic.counter, 21)
+        assert_equal(statistic.batch_size, 50)
+
+        kwds['rvs'] = self.get_rvs(stats.norm.rvs, np.random.default_rng(328423), xp=xp)
+        statistic.counter = 0
+        res3 = monte_carlo_test(**kwds)
+        assert_equal(statistic.counter, 2)
+        assert_equal(statistic.batch_size, 1000)
+
+        xp_assert_equal(res1.pvalue, res3.pvalue)
+        xp_assert_equal(res2.pvalue, res3.pvalue)
+
+    @pytest.mark.parametrize('axis', range(-3, 3))
+    def test_axis_dtype(self, axis, xp):
+        # test that Nd-array samples are handled correctly for valid values
+        # of the `axis` parameter; also make sure non-default dtype is maintained
+        rng = np.random.default_rng(2389234)
+        size = [2, 3, 4]
+        size[axis] = 100
+
+        # Determine non-default dtype
+        dtype_default = xp.asarray(1.).dtype
+        dtype_str = 'float32'if ("64" in str(dtype_default)) else 'float64'
+        dtype_np = getattr(np, dtype_str)
+        dtype = getattr(xp, dtype_str)
+
+        # ttest_1samp is CPU array-API compatible, but it would be good to
+        # include CuPy in this test. We'll perform ttest_1samp with a
+        # NumPy array, but all the rest with be done with fully array-API
+        # compatible code.
+        x = rng.standard_normal(size=size, dtype=dtype_np)
+        expected = stats.ttest_1samp(x, popmean=0., axis=axis)
+
+        x = xp.asarray(x, dtype=dtype)
+        statistic = self.get_statistic(xp)
+        rvs = self.get_rvs(stats.norm.rvs, rng, dtype=dtype, xp=xp)
+
+        res = monte_carlo_test(x, rvs, statistic, vectorized=True,
+                               n_resamples=20000, axis=axis)
+
+        ref_statistic = xp.asarray(expected.statistic, dtype=dtype)
+        ref_pvalue = xp.asarray(expected.pvalue, dtype=dtype)
+        xp_assert_close(res.statistic, ref_statistic)
+        xp_assert_close(res.pvalue, ref_pvalue, atol=self.atol)
+
+    @pytest.mark.parametrize('alternative', ("two-sided", "less", "greater"))
+    def test_alternative(self, alternative, xp):
+        # test that `alternative` is working as expected
+        rng = np.random.default_rng(65723433)
+
+        x = rng.standard_normal(size=30)
+        ref = stats.ttest_1samp(x, 0., alternative=alternative)
+
+        x = xp.asarray(x)
+        statistic = self.get_statistic(xp)
+        rvs = self.get_rvs(stats.norm.rvs, rng, xp=xp)
+
+        res = monte_carlo_test(x, rvs, statistic, alternative=alternative)
+
+        xp_assert_close(res.statistic, xp.asarray(ref.statistic))
+        xp_assert_close(res.pvalue, xp.asarray(ref.pvalue), atol=self.atol)
+
+
+    # Tests below involve statistics that are not yet array-API compatible.
+    # They can be converted when the statistics are converted.
+    @pytest.mark.slow
+    @pytest.mark.parametrize('alternative', ("less", "greater"))
+    @pytest.mark.parametrize('a', np.linspace(-0.5, 0.5, 5))  # skewness
+    def test_against_ks_1samp(self, alternative, a):
+        # test that monte_carlo_test can reproduce pvalue of ks_1samp
+        rng = np.random.default_rng(65723433)
+
+        x = stats.skewnorm.rvs(a=a, size=30, random_state=rng)
+        expected = stats.ks_1samp(x, stats.norm.cdf, alternative=alternative)
+
+        def statistic1d(x):
+            return stats.ks_1samp(x, stats.norm.cdf, mode='asymp',
+                                  alternative=alternative).statistic
+
+        norm_rvs = self.get_rvs(stats.norm.rvs, rng)
+        res = monte_carlo_test(x, norm_rvs, statistic1d,
+                               n_resamples=1000, vectorized=False,
+                               alternative=alternative)
+
+        assert_allclose(res.statistic, expected.statistic)
+        if alternative == 'greater':
+            assert_allclose(res.pvalue, expected.pvalue, atol=self.atol)
+        elif alternative == 'less':
+            assert_allclose(1-res.pvalue, expected.pvalue, atol=self.atol)
+
+    @pytest.mark.parametrize('hypotest', (stats.skewtest, stats.kurtosistest))
+    @pytest.mark.parametrize('alternative', ("less", "greater", "two-sided"))
+    @pytest.mark.parametrize('a', np.linspace(-2, 2, 5))  # skewness
+    def test_against_normality_tests(self, hypotest, alternative, a):
+        # test that monte_carlo_test can reproduce pvalue of normality tests
+        rng = np.random.default_rng(85723405)
+
+        x = stats.skewnorm.rvs(a=a, size=150, random_state=rng)
+        expected = hypotest(x, alternative=alternative)
+
+        def statistic(x, axis):
+            return hypotest(x, axis=axis).statistic
+
+        norm_rvs = self.get_rvs(stats.norm.rvs, rng)
+        res = monte_carlo_test(x, norm_rvs, statistic, vectorized=True,
+                               alternative=alternative)
+
+        assert_allclose(res.statistic, expected.statistic)
+        assert_allclose(res.pvalue, expected.pvalue, atol=self.atol)
+
+    @pytest.mark.parametrize('a', np.arange(-2, 3))  # skewness parameter
+    def test_against_normaltest(self, a):
+        # test that monte_carlo_test can reproduce pvalue of normaltest
+        rng = np.random.default_rng(12340513)
+
+        x = stats.skewnorm.rvs(a=a, size=150, random_state=rng)
+        expected = stats.normaltest(x)
+
+        def statistic(x, axis):
+            return stats.normaltest(x, axis=axis).statistic
+
+        norm_rvs = self.get_rvs(stats.norm.rvs, rng)
+        res = monte_carlo_test(x, norm_rvs, statistic, vectorized=True,
+                               alternative='greater')
+
+        assert_allclose(res.statistic, expected.statistic)
+        assert_allclose(res.pvalue, expected.pvalue, atol=self.atol)
+
+    @pytest.mark.xslow
+    @pytest.mark.parametrize('a', np.linspace(-0.5, 0.5, 5))  # skewness
+    def test_against_cramervonmises(self, a):
+        # test that monte_carlo_test can reproduce pvalue of cramervonmises
+        rng = np.random.default_rng(234874135)
+
+        x = stats.skewnorm.rvs(a=a, size=30, random_state=rng)
+        expected = stats.cramervonmises(x, stats.norm.cdf)
+
+        def statistic1d(x):
+            return stats.cramervonmises(x, stats.norm.cdf).statistic
+
+        norm_rvs = self.get_rvs(stats.norm.rvs, rng)
+        res = monte_carlo_test(x, norm_rvs, statistic1d,
+                               n_resamples=1000, vectorized=False,
+                               alternative='greater')
+
+        assert_allclose(res.statistic, expected.statistic)
+        assert_allclose(res.pvalue, expected.pvalue, atol=self.atol)
+
+    @pytest.mark.slow
+    @pytest.mark.parametrize('dist_name', ['norm', 'logistic'])
+    @pytest.mark.parametrize('target_statistic', [0.6, 0.7, 0.8])
+    def test_against_anderson(self, dist_name, target_statistic):
+        # test that monte_carlo_test can reproduce results of `anderson`.
+
+        # find the skewness for which the sample statistic is within the range of
+        # values tubulated by `anderson`
+
+        def fun(a):
+            rng = np.random.default_rng(394295467)
+            x = stats.tukeylambda.rvs(a, size=100, random_state=rng)
+            expected = stats.anderson(x, dist_name, method='interpolate')
+            return expected.statistic - target_statistic
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", RuntimeWarning)
+            sol = root(fun, x0=0)
+        assert sol.success
+
+        # get the significance level (p-value) associated with that critical
+        # value
+        a = sol.x[0]
+        rng = np.random.default_rng(394295467)
+        x = stats.tukeylambda.rvs(a, size=100, random_state=rng)
+        expected = stats.anderson(x, dist_name, method='interpolate')
+        expected_stat = expected.statistic
+        expected_p = expected.pvalue
+
+        # perform equivalent Monte Carlo test and compare results
+        def statistic1d(x):
+            return stats.anderson(x, dist_name, method='interpolate').statistic
+
+        dist_rvs = self.get_rvs(getattr(stats, dist_name).rvs, rng)
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", RuntimeWarning)
+            res = monte_carlo_test(x, dist_rvs,
+                                   statistic1d, n_resamples=1000,
+                                   vectorized=False, alternative='greater')
+
+        assert_allclose(res.statistic, expected_stat)
+        assert_allclose(res.pvalue, expected_p, atol=2*self.atol)
+
+    def test_p_never_zero(self):
+        # Use biased estimate of p-value to ensure that p-value is never zero
+        # per monte_carlo_test reference [1]
+        rng = np.random.default_rng(2190176673029737545)
+        x = np.zeros(100)
+        res = monte_carlo_test(x, rng.random, np.mean,
+                               vectorized=True, alternative='less')
+        assert res.pvalue == 0.0001
+
+    def test_against_ttest_ind(self):
+        # test that `monte_carlo_test` can reproduce results of `ttest_ind`.
+        rng = np.random.default_rng(219017667302737545)
+        data = rng.random(size=(2, 5)), rng.random(size=7)  # broadcastable
+        rvs = rng.normal, rng.normal
+        def statistic(x, y, axis):
+            return stats.ttest_ind(x, y, axis=axis).statistic
+
+        res = stats.monte_carlo_test(data, rvs, statistic, axis=-1)
+        ref = stats.ttest_ind(data[0], [data[1]], axis=-1)
+        assert_allclose(res.statistic, ref.statistic)
+        assert_allclose(res.pvalue, ref.pvalue, rtol=2e-2)
+
+    def test_against_f_oneway(self):
+        # test that `monte_carlo_test` can reproduce results of `f_oneway`.
+        rng = np.random.default_rng(219017667302737545)
+        data = (rng.random(size=(2, 100)), rng.random(size=(2, 101)),
+                rng.random(size=(2, 102)), rng.random(size=(2, 103)))
+        rvs = rng.normal, rng.normal, rng.normal, rng.normal
+
+        def statistic(*args, axis):
+            return stats.f_oneway(*args, axis=axis).statistic
+
+        res = stats.monte_carlo_test(data, rvs, statistic, axis=-1,
+                                     alternative='greater')
+        ref = stats.f_oneway(*data, axis=-1)
+
+        assert_allclose(res.statistic, ref.statistic)
+        assert_allclose(res.pvalue, ref.pvalue, atol=1e-2)
+
+    @pytest.mark.fail_slow(2)
+    @pytest.mark.xfail_on_32bit("Statistic may not depend on sample order on 32-bit")
+    def test_finite_precision_statistic(self):
+        # Some statistics return numerically distinct values when the values
+        # should be equal in theory. Test that `monte_carlo_test` accounts
+        # for this in some way.
+        rng = np.random.default_rng(2549824598234528)
+        n_resamples = 9999
+        def rvs(size):
+            return 1. * stats.bernoulli(p=0.333).rvs(size=size, random_state=rng)
+
+        x = rvs(100)
+        res = stats.monte_carlo_test(x, rvs, np.var, alternative='less',
+                                     n_resamples=n_resamples)
+        # show that having a tolerance matters
+        c0 = np.sum(res.null_distribution <= res.statistic)
+        c1 = np.sum(res.null_distribution <= res.statistic*(1+1e-15))
+        assert c0 != c1
+        assert res.pvalue == (c1 + 1)/(n_resamples + 1)
+
+
+@make_xp_test_case(power)
+class TestPower:
+    def xp_normal(self, rng, *, xp, dtype=None):
+        dtype = xp_default_dtype(xp) if dtype is None else dtype
+        return lambda size: xp.asarray(rng.normal(size=size), dtype=dtype)
+
+    def test_input_validation(self, xp):
+        # test that the appropriate error messages are raised for invalid input
+        rng = np.random.default_rng(8519895914314711673)
+
+        test = stats.ttest_ind
+        rvs = (self.xp_normal(rng, xp=xp), self.xp_normal(rng, xp=xp))
+        n_observations = (xp.asarray(10), xp.asarray(12))
+
+        message = "`vectorized` must be `True`, `False`, or `None`."
+        with pytest.raises(ValueError, match=message):
+            power(test, rvs, n_observations, vectorized=1.5)
+
+        message = "`rvs` must be callable or sequence of callables."
+        with pytest.raises(TypeError, match=message):
+            power(test, None, n_observations)
+        with pytest.raises(TypeError, match=message):
+            power(test, (self.xp_normal(rng, xp=xp), 'ekki'), n_observations)
+
+        message = "If `rvs` is a sequence..."
+        with pytest.raises(ValueError, match=message):
+            power(test, (self.xp_normal(rng, xp=xp),), n_observations)
+        with pytest.raises(ValueError, match=message):
+            power(test, rvs, (10,))
+
+        message = "`significance` must be of floating point dtype."
+        with pytest.raises(ValueError, match=message):
+            power(test, rvs, n_observations, significance=xp.asarray(True))
+
+        significance = xp.asarray(2.)
+        if not is_lazy_array(significance):
+            message = "All elements of `significance` must be between 0. and 1."
+            with pytest.raises(ValueError, match=message):
+                power(test, rvs, n_observations, significance=significance)
+
+        message = "`kwargs` must be a dictionary"
+        with pytest.raises(TypeError, match=message):
+            power(test, rvs, n_observations, kwargs=(1, 2, 3))
+
+        message = (
+            "not be broadcast"
+            "|Chunks do not add"
+            "|Incompatible shapes"
+            "|Attempting to broadcast"
+        )
+        with pytest.raises((ValueError, RuntimeError), match=message):
+            power(test, rvs, (xp.asarray([10, 11]), xp.asarray([12, 13, 14])))
+        with pytest.raises((ValueError, RuntimeError), match=message):
+            power(test, rvs, (xp.asarray([10, 11]), xp.asarray([12, 13])),
+                  kwargs={'x': xp.asarray([1, 2, 3])})
+
+        message = "`test` must be callable"
+        with pytest.raises(TypeError, match=message):
+            power(None, rvs, n_observations)
+
+        message = "`n_resamples` must be a positive integer"
+        with pytest.raises(ValueError, match=message):
+            power(test, rvs, n_observations, n_resamples=-10)
+        with pytest.raises(ValueError, match=message):
+            power(test, rvs, n_observations, n_resamples=10.5)
+
+        message = "`batch` must be a positive integer"
+        with pytest.raises(ValueError, match=message):
+            power(test, rvs, n_observations, batch=-10)
+        with pytest.raises(ValueError, match=message):
+            power(test, rvs, n_observations, batch=10.5)
+
+    @pytest.mark.slow
+    def test_batch(self, xp):
+        # make sure that the `batch` parameter is respected by checking the
+        # maximum batch size provided in calls to `test`
+        rng = np.random.default_rng(23492340193)
+
+        def test(x, axis):
+            batch_size = 1 if x.ndim == 1 else x.shape[0]
+            test.batch_size = max(batch_size, test.batch_size)
+            test.counter += 1
+            return stats.ttest_1samp(x, xp.asarray(0.), axis=axis).pvalue
+        test.counter = 0
+        test.batch_size = 0
+
+        kwds = dict(test=test,
+                    n_observations=xp.asarray(10),
+                    n_resamples=1000)
+
+        rng = np.random.default_rng(23492340193)
+        res1 = power(**kwds, rvs=self.xp_normal(rng, xp=xp), batch=1)
+        assert test.counter == 1000
+        assert test.batch_size == 1
+
+        rng = np.random.default_rng(23492340193)
+        test.counter = 0
+        res2 = power(**kwds, rvs=self.xp_normal(rng, xp=xp), batch=50)
+        assert test.counter == 20
+        assert test.batch_size == 50
+
+        rng = np.random.default_rng(23492340193)
+        test.counter = 0
+        res3 = power(**kwds, rvs=self.xp_normal(rng, xp=xp), batch=1000)
+        assert test.counter == 1
+        assert test.batch_size == 1000
+
+        xp_assert_equal(res1.power, res3.power)
+        xp_assert_equal(res2.power, res3.power)
+
+    @pytest.mark.slow
+    def test_vectorization(self, xp):
+        # Test that `power` is vectorized as expected
+        rng = np.random.default_rng(25495254834552)
+        alternatives = {-1: 'less', 0:'two-sided', 1: 'greater'}
+
+        # Single vectorized call
+        popmeans = xp.asarray([0, 0.2])
+        def test(x, alternative, axis=-1):
+            # ensure that popmeans axis is zeroth and orthogonal to the rest
+            popmeans_expanded = xpx.expand_dims(popmeans,
+                                                axis=tuple(range(1, x.ndim + 1)))
+            alternative = alternatives[int(alternative)]
+            return stats.ttest_1samp(x, popmeans_expanded, alternative=alternative,
+                                     axis=axis)
+
+        # nx and kwargs broadcast against one another
+        nx = xp.asarray([10, 15, 20, 50, 100])[:, xp.newaxis]
+        kwargs = {'alternative': xp.asarray([-1, 0, 1])}
+
+        # This dimension is added to the beginning
+        significance = xp.asarray([0.01, 0.025, 0.05, 0.1])
+        res = stats.power(test, self.xp_normal(rng, xp=xp), nx,
+                          significance=significance, kwargs=kwargs)
+
+        # Looping over all combinations
+        ref = []
+        for significance_i in significance:
+            for i in range(nx.shape[0]):
+                nx_i = nx[i, ...]
+                for alternative_i in kwargs['alternative']:
+                    for j in range(popmeans.shape[0]):
+                        popmean_j = popmeans[j]
+                        def test2(x, axis=-1):
+                            return stats.ttest_1samp(x, popmean_j, axis=axis,
+                                alternative=alternatives[int(alternative_i)])
+
+                        tmp = stats.power(test2, self.xp_normal(rng, xp=xp), nx_i,
+                                          significance=significance_i)
+                        ref.append(tmp.power)
+        ref = xp.reshape(xp.stack(ref), res.power.shape)
+
+        # Show that results are similar
+        xp_assert_close(res.power, ref, rtol=2e-2, atol=1e-2)
+
+    @pytest.mark.skip_xp_backends(cpu_only=True,
+                                  exceptions=['cupy', 'jax.numpy', 'dask.array'])
+    def test_ttest_ind_null(self, xp):
+        # Check that the p-values of `ttest_ind` are uniformly distributed under
+        # the null hypothesis
+        rng = np.random.default_rng(254952548345528)
+
+        test = stats.ttest_ind
+        n_observations = (xp.asarray(rng.integers(10, 100, size=(10))),
+                          xp.asarray(rng.integers(10, 100, size=(10))))
+        rvs = self.xp_normal(rng, xp=xp), self.xp_normal(rng, xp=xp)
+        significance = xp.asarray([0.01, 0.05, 0.1])
+        res = stats.power(test, rvs, n_observations, significance=significance)
+        significance = xp.broadcast_to(significance[:, xp.newaxis], res.power.shape)
+        xp_assert_close(res.power, significance, atol=1e-2)
+
+    @pytest.mark.skip_xp_backends('array_api_strict',
+                                  reason='currently combines integer and float arrays')
+    @pytest.mark.skip_xp_backends(cpu_only=True,
+                                  exceptions=['cupy', 'jax.numpy', 'dask.array'])
+    def test_ttest_1samp_power(self, xp):
+        # Check simulated ttest_1samp power against reference
+        rng = np.random.default_rng(254952548345528)
+
+        # Reference values computed with statmodels
+        # import numpy as np
+        # from statsmodels.stats.power import tt_solve_power
+        # tt_solve_power = np.vectorize(tt_solve_power)
+        # tt_solve_power([0.1, 0.5, 0.9], [[10], [20]], [[[0.01]], [[0.05]]])
+        ref = [[[0.0126515 , 0.10269751, 0.40415802],
+                [0.01657775, 0.29734608, 0.86228288]],
+               [[0.0592903 , 0.29317561, 0.71718121],
+                [0.07094116, 0.56450441, 0.96815163]]]
+
+        kwargs = {'popmean': xp.asarray([0.1, 0.5, 0.9])}
+        n_observations = xp.asarray([[10], [20]])
+        significance = xp.asarray([0.01, 0.05])
+        res = stats.power(stats.ttest_1samp, self.xp_normal(rng, xp=xp), n_observations,
+                          significance=significance, kwargs=kwargs)
+        xp_assert_close(res.power, xp.asarray(ref), atol=1e-2)
+
+
+@make_xp_test_case(permutation_test)
+class TestPermutationTest:
+
+    rtol = 1e-14
+
+    def setup_method(self):
+        self.rng = np.random.default_rng(7170559330470561044)
+
+    # -- Input validation -- #
+    def test_permutation_test_iv(self, xp):
+
+        def stat(x, y, axis):
+            return stats.ttest_ind((x, y), axis).statistic
+
+        data = (xp.asarray([1, 2, 3]), xp.asarray([1, 2, 3]))
+
+        message = "each sample in `data` must contain two or more ..."
+        with pytest.raises(ValueError, match=message):
+            permutation_test((data[0], xp.asarray([0])), stat)
+
+        message = "`data` must be a tuple containing at least two samples"
+        with pytest.raises(ValueError, match=message):
+            permutation_test((1,), stat)
+        with pytest.raises(TypeError, match=message):
+            permutation_test(1, stat)
+
+        message = "`axis` must be an integer."
+        with pytest.raises(ValueError, match=message):
+            permutation_test(data, stat, axis=1.5)
+
+        message = "`permutation_type` must be in..."
+        with pytest.raises(ValueError, match=message):
+            permutation_test(data, stat,
+                             permutation_type="ekki")
+
+        message = "`vectorized` must be `True`, `False`, or `None`."
+        with pytest.raises(ValueError, match=message):
+            permutation_test(data, stat, vectorized=1.5)
+
+        message = "`n_resamples` must be a positive integer."
+        with pytest.raises(ValueError, match=message):
+            permutation_test(data, stat, n_resamples=-1000)
+
+        message = "`n_resamples` must be a positive integer."
+        with pytest.raises(ValueError, match=message):
+            permutation_test(data, stat, n_resamples=1000.5)
+
+        message = "`batch` must be a positive integer or None."
+        with pytest.raises(ValueError, match=message):
+            permutation_test(data, stat, batch=-1000)
+
+        message = "`batch` must be a positive integer or None."
+        with pytest.raises(ValueError, match=message):
+            permutation_test(data, stat, batch=1000.5)
+
+        message = "`alternative` must be in..."
+        with pytest.raises(ValueError, match=message):
+            permutation_test(data, stat, alternative='ekki')
+
+        message = "SeedSequence expects int or sequence of ints"
+        with pytest.raises(TypeError, match=message):
+            permutation_test(data, stat, rng='herring')
+
+    # -- Test Parameters -- #
+    # SPEC-007 leave one call with seed to check it still works
+    @pytest.mark.parametrize('random_state', [np.random.RandomState,
+                                              np.random.default_rng])
+    @pytest.mark.parametrize('permutation_type',
+                             ['pairings', 'samples', 'independent'])
+    def test_batch(self, permutation_type, random_state, xp):
+        # make sure that the `batch` parameter is respected by checking the
+        # maximum batch size provided in calls to `statistic`
+        x = xp.asarray(self.rng.random(10))
+        y = xp.asarray(self.rng.random(10))
+
+        def statistic(x, y, axis):
+            batch_size = 1 if x.ndim == 1 else x.shape[0]
+            statistic.batch_size = max(batch_size, statistic.batch_size)
+            statistic.counter += 1
+            return xp.mean(x, axis=axis) - xp.mean(y, axis=axis)
+        statistic.counter = 0
+        statistic.batch_size = 0
+
+        kwds = {'n_resamples': 100, 'permutation_type': permutation_type,
+                'vectorized': True}
+        res1 = stats.permutation_test((x, y), statistic, batch=1,
+                                      random_state=random_state(0), **kwds)
+        assert statistic.counter == 101
+        assert statistic.batch_size == 1
+
+        statistic.counter = 0
+        res2 = stats.permutation_test((x, y), statistic, batch=50,
+                                      random_state=random_state(0), **kwds)
+        assert statistic.counter == 3
+        assert statistic.batch_size == 50
+
+        statistic.counter = 0
+        res3 = stats.permutation_test((x, y), statistic, batch=100,
+                                      random_state=random_state(0), **kwds)
+        assert statistic.counter == 2
+        assert statistic.batch_size == 100
+
+        xp_assert_equal(res1.pvalue, res3.pvalue)
+        xp_assert_equal(res2.pvalue, res3.pvalue)
+
+    # SPEC-007 leave at least one call with seed to check it still works
+    @pytest.mark.parametrize('random_state', [np.random.RandomState,
+                                              np.random.default_rng])
+    @pytest.mark.parametrize('permutation_type, exact_size',
+                             [('pairings', special.factorial(3)**2),
+                              ('samples', 2**3),
+                              ('independent', special.binom(6, 3))])
+    def test_permutations(self, permutation_type, exact_size, random_state, xp):
+        # make sure that the `permutations` parameter is respected by checking
+        # the size of the null distribution
+        x = xp.asarray(self.rng.random(3))
+        y = xp.asarray(self.rng.random(3))
+
+        def statistic(x, y, axis):
+            return xp.mean(x, axis=axis) - xp.mean(y, axis=axis)
+
+        kwds = {'permutation_type': permutation_type,
+                'vectorized': True}
+        res = stats.permutation_test((x, y), statistic, n_resamples=3,
+                                     random_state=random_state(0), **kwds)
+        assert xp_size(res.null_distribution) == 3
+
+        res = stats.permutation_test((x, y), statistic, **kwds)
+        assert xp_size(res.null_distribution) == exact_size
+
+    # -- Randomized Permutation Tests -- #
+
+    # To get reasonable accuracy, these next three tests are somewhat slow.
+    # Originally, I had them passing for all combinations of permutation type,
+    # alternative, and RNG, but that takes too long for CI. Instead, split
+    # into three tests, each testing a particular combination of the three
+    # parameters.
+
+    def test_randomized_test_against_exact_both(self, xp):
+        # check that the randomized and exact tests agree to reasonable
+        # precision for permutation_type='both
+
+        alternative, rng = 'less', 0
+
+        nx, ny, permutations = 8, 9, 24000
+        assert special.binom(nx + ny, nx) > permutations
+
+        rng = np.random.default_rng(8235259808)
+        x = xp.asarray(rng.standard_normal(size=nx))
+        y = xp.asarray(rng.standard_normal(size=ny))
+        data = x, y
+
+        def statistic(x, y, axis):
+            return xp.mean(x, axis=axis) - xp.mean(y, axis=axis)
+
+        kwds = {'vectorized': True, 'permutation_type': 'independent',
+                'batch': 100, 'alternative': alternative, 'rng': rng}
+        res = permutation_test(data, statistic, n_resamples=permutations, **kwds)
+        res2 = permutation_test(data, statistic, n_resamples=xp.inf, **kwds)
+
+        assert res.statistic == res2.statistic
+        xp_assert_close(res.pvalue, res2.pvalue, atol=1e-2)
+
+    @pytest.mark.slow()
+    def test_randomized_test_against_exact_samples(self, xp):
+        # check that the randomized and exact tests agree to reasonable
+        # precision for permutation_type='samples'
+
+        alternative, rng = 'greater', None
+
+        nx, ny, permutations = 15, 15, 32000
+        assert 2**nx > permutations
+
+        rng = np.random.default_rng(8235259808)
+        x = xp.asarray(rng.standard_normal(size=nx))
+        y = xp.asarray(rng.standard_normal(size=ny))
+        data = x, y
+
+        def statistic(x, y, axis):
+            return xp.mean(x - y, axis=axis)
+
+        kwds = {'vectorized': True, 'permutation_type': 'samples',
+                'batch': 100, 'alternative': alternative, 'rng': rng}
+        res = permutation_test(data, statistic, n_resamples=permutations, **kwds)
+        res2 = permutation_test(data, statistic, n_resamples=xp.inf, **kwds)
+
+        assert res.statistic == res2.statistic
+        xp_assert_close(res.pvalue, res2.pvalue, atol=1e-2)
+
+    # I only need to skip torch on GPU because it doesn't have betaincc for pearsonr
+    @pytest.mark.skip_xp_backends(cpu_only=True, exceptions=['cupy', 'jax.numpy'])
+    def test_randomized_test_against_exact_pairings(self, xp):
+        # check that the randomized and exact tests agree to reasonable
+        # precision for permutation_type='pairings'
+
+        alternative, rng = 'two-sided', self.rng
+
+        nx, ny, permutations = 8, 8, 40000
+        assert special.factorial(nx) > permutations
+
+        rng = np.random.default_rng(8235259808)
+        x = xp.asarray(rng.standard_normal(size=nx))
+        y = xp.asarray(rng.standard_normal(size=ny))
+        data = [x]
+
+        def statistic(x, axis):
+            return stats.pearsonr(x, y, axis=axis).statistic
+
+        kwds = {'vectorized': True, 'permutation_type': 'samples',
+                'batch': 100, 'alternative': alternative, 'rng': rng}
+        res = permutation_test(data, statistic, n_resamples=permutations, **kwds)
+        res2 = permutation_test(data, statistic, n_resamples=xp.inf, **kwds)
+
+        assert res.statistic == res2.statistic
+        xp_assert_close(res.pvalue, res2.pvalue, atol=1e-2)
+
+    # -- Independent (Unpaired) Sample Tests -- #
+
+    @pytest.mark.skip_xp_backends(eager_only=True)  # TODO: change to jax_jit=False
+    @pytest.mark.parametrize('alternative', ("less", "greater", "two-sided"))
+    def test_against_ks_2samp(self, alternative, xp):
+        x = self.rng.normal(size=4, scale=1)
+        y = self.rng.normal(size=5, loc=3, scale=3)
+
+        expected = stats.ks_2samp(x, y, alternative=alternative, mode='exact')
+
+        def statistic(x, y, axis):
+            # todo: use `xp` as backend when `ks_2samp` supports more backends
+            x, y = _xp_copy_to_numpy(x), _xp_copy_to_numpy(y)
+            res = stats.ks_2samp(x, y, axis=axis, mode='asymp', alternative=alternative)
+            res = xp.asarray(res.statistic)
+            return res[()] if res.ndim == 0 else res
+
+        # ks_2samp is always a one-tailed 'greater' test
+        # it's the statistic that changes (D+ vs D- vs max(D+, D-))
+        x, y = xp.asarray(x), xp.asarray(y)
+        res = permutation_test((x, y), statistic, n_resamples=np.inf,
+                               alternative='greater', rng=self.rng)
+
+        xp_assert_close(res.statistic, xp.asarray(expected.statistic), rtol=self.rtol)
+        xp_assert_close(res.pvalue, xp.asarray(expected.pvalue), rtol=self.rtol)
+
+    @pytest.mark.skip_xp_backends(eager_only=True)  # TODO: change to jax_jit=False
+    @pytest.mark.parametrize('alternative', ("less", "greater", "two-sided"))
+    def test_against_ansari(self, alternative, xp):
+        x = self.rng.normal(size=4, scale=1)
+        y = self.rng.normal(size=5, scale=3)
+
+        # ansari has a different convention for 'alternative'
+        alternative_correspondence = {"less": "greater",
+                                      "greater": "less",
+                                      "two-sided": "two-sided"}
+        alternative_scipy = alternative_correspondence[alternative]
+        expected = stats.ansari(x, y, alternative=alternative_scipy)
+
+        def statistic(x, y, axis):
+            # todo: use `xp` as backend when `ansari` is translated to array API
+            x, y = _xp_copy_to_numpy(x), _xp_copy_to_numpy(y)
+            res = stats.ansari(x, y, axis=axis)
+            res = xp.asarray(res.statistic)
+            return res[()] if res.ndim == 0 else res
+
+        x, y = xp.asarray(x), xp.asarray(y)
+        res = permutation_test((x, y), statistic, n_resamples=np.inf,
+                               alternative=alternative, rng=self.rng)
+
+        xp_assert_close(res.statistic, xp.asarray(expected.statistic), rtol=self.rtol)
+        xp_assert_close(res.pvalue, xp.asarray(expected.pvalue), rtol=self.rtol)
+
+    @skip_xp_backends('cupy', reason='needs mannwhitneyu')
+    @skip_xp_backends(eager_only=True)  # mannwhitneyu does input validation
+    @pytest.mark.parametrize('alternative', ("less", "greater", "two-sided"))
+    def test_against_mannwhitneyu(self, alternative, xp):
+        x = stats.uniform.rvs(size=(3, 5, 2), loc=0, random_state=self.rng)
+        y = stats.uniform.rvs(size=(3, 5, 2), loc=0.05, random_state=self.rng)
+
+        expected = stats.mannwhitneyu(x, y, axis=1, alternative=alternative)
+
+        def statistic(x, y, axis):
+            return stats.mannwhitneyu(x, y, axis=axis, method='asymptotic').statistic
+
+        x, y = xp.asarray(x), xp.asarray(y)
+        res = permutation_test((x, y), statistic, vectorized=True,
+                               n_resamples=xp.inf, alternative=alternative,
+                               axis=1, rng=self.rng)
+
+        xp_assert_close(res.statistic, xp.asarray(expected.statistic), rtol=self.rtol)
+        xp_assert_close(res.pvalue, xp.asarray(expected.pvalue), rtol=self.rtol)
+
+    @skip_xp_backends('cupy', reason='needs cramervonmises_2samp')
+    @skip_xp_backends(eager_only=True)  # cramervonmises_2samp does input validation
+    @skip_xp_backends(cpu_only=True)  # torch doesn't have `kv`
+    def test_against_cvm(self, xp):
+        x = stats.norm.rvs(size=4, scale=1, random_state=self.rng)
+        y = stats.norm.rvs(size=5, loc=3, scale=3, random_state=self.rng)
+
+        expected = stats.cramervonmises_2samp(x, y, method='exact')
+
+        def statistic(x, y, axis):
+            res = stats.cramervonmises_2samp(x, y, axis=axis, method='asymptotic')
+            return res.statistic
+
+        # cramervonmises_2samp has only one alternative, greater
+        x, y = xp.asarray(x), xp.asarray(y)
+        res = permutation_test((x, y), statistic, n_resamples=np.inf,
+                               alternative='greater', rng=self.rng)
+
+        xp_assert_close(res.statistic, xp.asarray(expected.statistic), rtol=self.rtol)
+        xp_assert_close(res.pvalue, xp.asarray(expected.pvalue), rtol=self.rtol)
+
+    @skip_xp_backends(eager_only=True)  # kruskal does input validation
+    @pytest.mark.parametrize('axis', (-1, 2))
+    def test_vectorized_nsamp_ptype_both(self, axis, xp):
+        # statistic only available for NumPy
+
+        # Test that permutation_test with permutation_type='independent' works
+        # properly for a 3-sample statistic with nd array samples of different
+        # (but compatible) shapes and ndims. Show that exact permutation test
+        # and random permutation tests approximate SciPy's asymptotic pvalues
+        # and that exact and random permutation test results are even closer
+        # to one another (than they are to the asymptotic results).
+
+        # Three samples, different (but compatible) shapes with different ndims
+        rng = np.random.default_rng(6709265303529651545)
+        x = rng.random(size=(3))
+        y = rng.random(size=(1, 3, 2))
+        z = rng.random(size=(2, 1, 4))
+        data = (x, y, z)
+
+        expected = stats.kruskal(*data, axis=axis)
+
+        # Define the statistic (and pvalue for comparison)
+        def statistic(*data, axis):
+            return stats.kruskal(*data, axis=axis).statistic
+
+        # Calculate exact and randomized permutation results
+        kwds = {'axis': axis, 'alternative': 'greater',
+                'permutation_type': 'independent', 'rng': rng}
+        data = [xp.asarray(data_) for data_ in data]
+        res = permutation_test(data, statistic, n_resamples=xp.inf, **kwds)
+        res2 = permutation_test(data, statistic, n_resamples=1000, **kwds)
+
+        # Check results
+        xp_assert_close(res.statistic, xp.asarray(expected.statistic), rtol=self.rtol*5)
+        xp_assert_close(res.statistic, res2.statistic, rtol=self.rtol*5)
+        xp_assert_close(res.pvalue, xp.asarray(expected.pvalue), atol=6e-2)
+        xp_assert_close(res.pvalue, res2.pvalue, atol=3e-2)
+
+    # -- Paired-Sample Tests -- #
+
+    @pytest.mark.skip_xp_backends(eager_only=True)  # TODO: change to jax_jit=False
+    @pytest.mark.parametrize('alternative', ("less", "greater", "two-sided"))
+    def test_against_wilcoxon(self, alternative, xp):
+        x = stats.uniform.rvs(size=(3, 6, 2), loc=0, random_state=self.rng)
+        y = stats.uniform.rvs(size=(3, 6, 2), loc=0.05, random_state=self.rng)
+        expected = stats.wilcoxon(x, y, alternative=alternative, axis=1)
+
+        # We'll check both 1- and 2-sample versions of the same test;
+        # we expect identical results to wilcoxon in all cases.
+        def statistic_1samp_1d(z, axis):
+            # todo: use `xp` as backend when `wilcoxon` is translated to array API
+            # 'less' ensures we get the same of two statistics every time
+            z = _xp_copy_to_numpy(z)
+            res = stats.wilcoxon(z, alternative='less', axis=axis)
+            res = xp.asarray(res.statistic)
+            return res[()] if res.ndim == 0 else res
+
+        def statistic_2samp_1d(x, y, axis):
+            # todo: use `xp` as backend when `wilcoxon` is translated to array API
+            x, y = _xp_copy_to_numpy(x), _xp_copy_to_numpy(y)
+            res = stats.wilcoxon(x, y, alternative='less', axis=axis)
+            res = xp.asarray(res.statistic)
+            return res[()] if res.ndim == 0 else res
+
+        x, y = xp.asarray(x), xp.asarray(y)
+        kwds = {'axis': 1, 'alternative': alternative, 'permutation_type': 'samples',
+                'rng': self.rng, 'n_resamples': np.inf}
+        res1 = permutation_test((x-y,), statistic_1samp_1d, **kwds)
+        res2 = permutation_test((x, y), statistic_2samp_1d, **kwds)
+
+        # `wilcoxon` returns a different statistic with 'two-sided'
+        xp_assert_close(res1.statistic, res2.statistic, rtol=self.rtol)
+        if alternative != 'two-sided':
+            xp_assert_close(res2.statistic, xp.asarray(expected.statistic),
+                            rtol=self.rtol)
+
+        xp_assert_close(res2.pvalue, xp.asarray(expected.pvalue), rtol=self.rtol)
+        xp_assert_close(res1.pvalue, res2.pvalue, rtol=self.rtol)
+
+    @pytest.mark.parametrize('alternative', ("less", "greater", "two-sided"))
+    def test_against_binomtest(self, alternative, xp):
+
+        x = self.rng.integers(0, 2, size=10)
+        x[x == 0] = -1
+        # More naturally, the test would flip elements between 0 and one.
+        # However, permutation_test will flip the _signs_ of the elements.
+        # So we have to work with +1/-1 instead of 1/0.
+
+        def statistic(x, axis=0):
+            xp_ = array_namespace(x)
+            return xp_.count_nonzero(x > 0, axis=axis)
+
+        k, n, p = statistic(x), 10, 0.5
+        expected = stats.binomtest(k, n, p, alternative=alternative)
+
+        res = stats.permutation_test((xp.asarray(x, dtype=xp.float64),), statistic,
+                                     vectorized=True,
+                                     permutation_type='samples', n_resamples=xp.inf,
+                                     rng=self.rng, alternative=alternative)
+        xp_assert_close(res.pvalue, xp.asarray(expected.pvalue), rtol=self.rtol)
+
+    # -- Exact Association Tests -- #
+
+    @pytest.mark.skip_xp_backends(eager_only=True)  # TODO: change to jax_jit=False
+    def test_against_kendalltau(self, xp):
+        x = self.rng.normal(size=6)
+        y = x + self.rng.normal(size=6)
+
+        expected = stats.kendalltau(x, y, method='exact')
+
+        def statistic(x, axis):
+            # todo: use `xp` as backend when `kendalltau` is translated to array API
+            x = _xp_copy_to_numpy(x)
+            res = stats.kendalltau(x, y, method='asymptotic', axis=axis)
+            res = xp.asarray(res.statistic)
+            return res[()] if res.ndim == 0 else res
+
+        # kendalltau currently has only one alternative, two-sided
+        x = xp.asarray(x)
+        res = permutation_test((x,), statistic, permutation_type='pairings',
+                               n_resamples=np.inf, rng=self.rng)
+
+        xp_assert_close(res.statistic, xp.asarray(expected.statistic), rtol=self.rtol)
+        xp_assert_close(res.pvalue, xp.asarray(expected.pvalue), rtol=self.rtol)
+
+    @pytest.mark.parametrize('alternative', ('less', 'greater', 'two-sided'))
+    def test_against_fisher_exact(self, alternative, xp):
+        # x and y are binary random variables with some dependence
+        rng = np.random.default_rng(6235696159000529929)
+        x = (rng.random(7) > 0.6).astype(float)
+        y = (rng.random(7) + 0.25*x > 0.6).astype(float)
+        tab = stats.contingency.crosstab(x, y)[1]
+
+        x, y = xp.asarray(x), xp.asarray(y)
+        def statistic(x, axis):
+            return xp.count_nonzero((x == 1) & (y == 1), axis=axis)
+
+        res = permutation_test((x,), statistic, permutation_type='pairings',
+                               n_resamples=xp.inf, alternative=alternative,
+                               rng=rng)
+        res2 = stats.fisher_exact(tab, alternative=alternative)
+
+        xp_assert_close(res.pvalue, xp.asarray(res2.pvalue, dtype=x.dtype))
+
+    @pytest.mark.xslow()
+    @pytest.mark.parametrize('axis', (-2, 1))
+    def test_vectorized_nsamp_ptype_samples(self, axis):
+        # statistic only available for NumPy, and it's a pain to vectorize
+
+        # Test that permutation_test with permutation_type='samples' works
+        # properly for a 3-sample statistic with nd array samples of different
+        # (but compatible) shapes and ndims. Show that exact permutation test
+        # reproduces SciPy's exact pvalue and that random permutation test
+        # approximates it.
+
+        x = self.rng.random(size=(2, 4, 3))
+        y = self.rng.random(size=(1, 4, 3))
+        z = self.rng.random(size=(2, 4, 1))
+        x = stats.rankdata(x, axis=axis)
+        y = stats.rankdata(y, axis=axis)
+        z = stats.rankdata(z, axis=axis)
+        y = y[0]  # to check broadcast with different ndim
+        data = (x, y, z)
+
+        def statistic1d(*data):
+            return stats.page_trend_test(data, ranked=True,
+                                         method='asymptotic').statistic
+
+        def pvalue1d(*data):
+            return stats.page_trend_test(data, ranked=True,
+                                         method='exact').pvalue
+
+        statistic = _resampling._vectorize_statistic(statistic1d)
+        pvalue = _resampling._vectorize_statistic(pvalue1d)
+
+        expected_statistic = statistic(*np.broadcast_arrays(*data), axis=axis)
+        expected_pvalue = pvalue(*np.broadcast_arrays(*data), axis=axis)
+
+        # Let's forgive this use of an integer seed, please.
+        kwds = {'vectorized': False, 'axis': axis, 'alternative': 'greater',
+                'permutation_type': 'pairings', 'rng': 0}
+        res = permutation_test(data, statistic1d, n_resamples=np.inf, **kwds)
+        res2 = permutation_test(data, statistic1d, n_resamples=5000, **kwds)
+
+        assert_allclose(res.statistic, expected_statistic, rtol=self.rtol)
+        assert_allclose(res.statistic, res2.statistic, rtol=self.rtol)
+        assert_allclose(res.pvalue, expected_pvalue, rtol=self.rtol)
+        assert_allclose(res.pvalue, res2.pvalue, atol=3e-2)
+
+    # -- Test Against External References -- #
+
+    tie_case_1 = {'x': [1, 2, 3, 4], 'y': [1.5, 2, 2.5],
+                  'expected_less': 0.2000000000,
+                  'expected_2sided': 0.4,  # 2*expected_less
+                  'expected_Pr_gte_S_mean': 0.3428571429,  # see note below
+                  'expected_statistic': 7.5,
+                  'expected_avg': 9.142857, 'expected_std': 1.40698}
+    tie_case_2 = {'x': [111, 107, 100, 99, 102, 106, 109, 108],
+                  'y': [107, 108, 106, 98, 105, 103, 110, 105, 104],
+                  'expected_less': 0.1555738379,
+                  'expected_2sided': 0.3111476758,
+                  'expected_Pr_gte_S_mean': 0.2969971205,  # see note below
+                  'expected_statistic': 32.5,
+                  'expected_avg': 38.117647, 'expected_std': 5.172124}
+
+    @pytest.mark.skip_xp_backends(eager_only=True)  # TODO: change to jax_jit=False
+    @pytest.mark.xslow()  # only the second case is slow, really
+    @pytest.mark.parametrize('case', (tie_case_1, tie_case_2))
+    def test_with_ties(self, case, xp):
+        """
+        Results above from SAS PROC NPAR1WAY, e.g.
+
+        DATA myData;
+        INPUT X Y;
+        CARDS;
+        1 1
+        1 2
+        1 3
+        1 4
+        2 1.5
+        2 2
+        2 2.5
+        ods graphics on;
+        proc npar1way AB data=myData;
+            class X;
+            EXACT;
+        run;
+        ods graphics off;
+
+        Note: SAS provides Pr >= |S-Mean|, which is different from our
+        definition of a two-sided p-value.
+
+        """
+
+        x = case['x']
+        y = case['y']
+
+        expected_statistic = xp.asarray(case['expected_statistic'])
+        expected_less = xp.asarray(case['expected_less'])
+        expected_2sided = xp.asarray(case['expected_2sided'])
+        expected_Pr_gte_S_mean = xp.asarray(case['expected_Pr_gte_S_mean'])
+        expected_avg = xp.asarray(case['expected_avg'])
+        expected_std = xp.asarray(case['expected_std'])
+
+        def statistic(x, y, axis):
+            # todo: use `xp` as backend when `ansari` is translated to array API
+            x, y = _xp_copy_to_numpy(x), _xp_copy_to_numpy(y)
+            res = stats.ansari(x, y, axis=axis)
+            res = xp.asarray(res.statistic)
+            return res[()] if res.ndim == 0 else res
+
+        dtype = xp_default_dtype(xp)
+        x, y = xp.asarray(x, dtype=dtype), xp.asarray(y, dtype=dtype)
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", "Ties preclude use of exact statistic", UserWarning)
+            res = permutation_test((x, y), statistic, n_resamples=np.inf,
+                                   alternative='less')
+            res2 = permutation_test((x, y), statistic, n_resamples=np.inf,
+                                    alternative='two-sided')
+
+        xp_assert_close(res.statistic, expected_statistic, rtol=self.rtol)
+        xp_assert_close(res.pvalue, expected_less, atol=1e-10)
+        xp_assert_close(res2.pvalue, expected_2sided, atol=1e-10)
+        xp_assert_close(xp.mean(res2.null_distribution), expected_avg, rtol=1e-6)
+        xp_assert_close(xp.std(res2.null_distribution), expected_std, rtol=1e-6)
+
+        # SAS provides Pr >= |S-Mean|; might as well check against that, too
+        S = res.statistic
+        mean = xp.mean(res.null_distribution)
+        n = res.null_distribution.shape[0]
+        Pr_gte_S_mean = xp.astype(xp.count_nonzero(
+            xp.abs(res.null_distribution-mean) >= xp.abs(S-mean)), S.dtype) / n
+        xp_assert_close(Pr_gte_S_mean, expected_Pr_gte_S_mean)
+
+    @pytest.mark.slow
+    @pytest.mark.parametrize('alternative, expected_pvalue',
+                             (('less', 0.9708333333333),
+                              ('greater', 0.05138888888889),
+                              ('two-sided', 0.1027777777778)))
+    # I only need to skip torch on GPU because it doesn't have betaincc for pearsonr
+    @pytest.mark.skip_xp_backends(cpu_only=True, exceptions=['cupy', 'jax.numpy'])
+    @pytest.mark.skip_xp_backends(eager_only=True)  # TODO: change to jax_jit=False
+    def test_against_spearmanr_in_R(self, alternative, expected_pvalue, xp):
+        """
+        Results above from R cor.test, e.g.
+
+        options(digits=16)
+        x <- c(1.76405235, 0.40015721, 0.97873798,
+               2.2408932, 1.86755799, -0.97727788)
+        y <- c(2.71414076, 0.2488, 0.87551913,
+               2.6514917, 2.01160156, 0.47699563)
+        cor.test(x, y, method = "spearm", alternative = "t")
+        """
+        # data comes from
+        # np.random.seed(0)
+        # x = stats.norm.rvs(size=6)
+        # y = x + stats.norm.rvs(size=6)
+        x = xp.asarray([1.76405235, 0.40015721, 0.97873798,
+                        2.2408932, 1.86755799, -0.97727788])
+        y = xp.asarray([2.71414076, 0.2488, 0.87551913,
+                        2.6514917, 2.01160156, 0.47699563])
+        expected_statistic = 0.7714285714285715
+
+        y = xp.asarray(stats.rankdata(_xp_copy_to_numpy(y)))
+        def statistic(x, axis):
+            # `spearmanr` is not array api compatible, but `pearsonr` is. So for now
+            # use _xp_copy_to_numpy just for ranking so we can run this test w/ CuPy.
+            # TODO: use `xp` as backend when cupy works with `rankdata`
+            x = xp.asarray(stats.rankdata(_xp_copy_to_numpy(x), axis=axis))
+            return stats.pearsonr(x, y, axis=axis).statistic
+
+        res = permutation_test((x,), statistic, permutation_type='pairings',
+                               n_resamples=xp.inf, alternative=alternative)
+
+        xp_assert_close(res.statistic, xp.asarray(expected_statistic), rtol=self.rtol)
+        xp_assert_close(res.pvalue, xp.asarray(expected_pvalue), atol=1e-13)
+
+    @pytest.mark.parametrize("batch", (-1, 0))
+    def test_batch_generator_iv(self, batch):
+        with pytest.raises(ValueError, match="`batch` must be positive."):
+            list(_resampling._batch_generator([1, 2, 3], batch))
+
+    batch_generator_cases = [(range(0), 3, []),
+                             (range(6), 3, [[0, 1, 2], [3, 4, 5]]),
+                             (range(8), 3, [[0, 1, 2], [3, 4, 5], [6, 7]])]
+
+    @pytest.mark.parametrize("iterable, batch, expected",
+                             batch_generator_cases)
+    def test_batch_generator(self, iterable, batch, expected):
+        got = list(_resampling._batch_generator(iterable, batch))
+        assert got == expected
+
+    @pytest.mark.fail_slow(2)
+    # I only need to skip torch on GPU because it doesn't have betaincc for pearsonr
+    @pytest.mark.skip_xp_backends(cpu_only=True, exceptions=['cupy', 'jax.numpy'])
+    def test_finite_precision_statistic(self, xp):
+        # Some statistics return numerically distinct values when the values
+        # should be equal in theory. Test that `permutation_test` accounts
+        # for this in some way.
+        x = xp.asarray([1., 2., 4., 3.], dtype=xp.float64)
+        y = xp.asarray([2., 4., 6., 8.], dtype=xp.float64)
+
+        def statistic(x, y, axis):
+            return stats.pearsonr(x, y, axis=axis)[0]
+
+        res = stats.permutation_test((x, y), statistic,
+                                     permutation_type='pairings')
+        r, pvalue, null = res.statistic, res.pvalue, res.null_distribution
+
+        correct_p = 2 * float(xp.count_nonzero(null >= r - 1e-14)) / null.shape[0]
+        assert pvalue == correct_p == 1/3
+        # Compare against other exact correlation tests using R corr.test
+        # options(digits=16)
+        # x = c(1, 2, 4, 3)
+        # y = c(2, 4, 6, 8)
+        # cor.test(x, y, alternative = "t", method = "spearman")  # 0.333333333
+        # cor.test(x, y, alternative = "t", method = "kendall")  # 0.333333333
+
+    def test_nan_statistic(self, xp):
+        # Where the observed statistic is NaN, the p-value should be NaN
+        # (Whether a single NaN in the permutation distribution should make the p-value
+        #  NaN is debatable. Users can choose for themselves.)
+        rng = np.random.default_rng(8951482112)
+        dtype = xp_default_dtype(xp)
+        x = xp.asarray(rng.random(5), dtype=dtype)
+        x_nan = xp.asarray([0, 0, 0, xp.nan, 0])
+        y = xp.asarray(rng.random(6), dtype=dtype)
+
+        def statistic(x, y, axis):
+            return xp.mean(x, axis=axis) - xp.mean(y, axis=axis)
+
+        kwds = {'permutation_type': 'independent', 'rng': rng, 'axis': -1}
+
+        ref = permutation_test((x, y), statistic, **kwds)
+
+        data = (xp.stack([x, x + x_nan]), y)
+        res = permutation_test(data, statistic, **kwds)
+
+        NaN = xp.asarray(xp.nan, dtype=dtype)
+        xp_assert_equal(res.statistic[0], ref.statistic)
+        xp_assert_equal(res.pvalue[0], ref.pvalue)
+        xp_assert_equal(res.statistic[1], NaN)
+        xp_assert_equal(res.pvalue[1], NaN)
+
+
+def test_all_partitions_concatenated():
+    # make sure that _all_paritions_concatenated produces the correct number
+    # of partitions of the data into samples of the given sizes and that
+    # all are unique
+    n = np.array([3, 2, 4], dtype=int)
+    nc = np.cumsum(n)
+
+    all_partitions = set()
+    counter = 0
+    for partition_concatenated in _resampling._all_partitions_concatenated(n):
+        counter += 1
+        partitioning = np.split(partition_concatenated, nc[:-1])
+        all_partitions.add(tuple([frozenset(i) for i in partitioning]))
+
+    expected = np.prod([special.binom(sum(n[i:]), sum(n[i+1:]))
+                        for i in range(len(n)-1)])
+
+    assert_equal(counter, expected)
+    assert_equal(len(all_partitions), expected)
+
+
+@pytest.mark.parametrize('fun_name',
+                         ['bootstrap', 'permutation_test', 'monte_carlo_test'])
+def test_parameter_vectorized(fun_name):
+    # Check that parameter `vectorized` is working as desired for all
+    # resampling functions. Results don't matter; just don't fail asserts.
+    rng = np.random.default_rng(75245098234592)
+    sample = rng.random(size=10)
+
+    def rvs(size):  # needed by `monte_carlo_test`
+        return stats.norm.rvs(size=size, random_state=rng)
+
+    fun_options = {'bootstrap': {'data': (sample,), 'rng': rng,
+                                 'method': 'percentile'},
+                   'permutation_test': {'data': (sample,), 'rng': rng,
+                                        'permutation_type': 'samples'},
+                   'monte_carlo_test': {'sample': sample, 'rvs': rvs}}
+    common_options = {'n_resamples': 100}
+
+    fun = getattr(stats, fun_name)
+    options = fun_options[fun_name]
+    options.update(common_options)
+
+    def statistic(x, axis):
+        assert x.ndim > 1 or np.array_equal(x, sample)
+        return np.mean(x, axis=axis)
+    fun(statistic=statistic, vectorized=None, **options)
+    fun(statistic=statistic, vectorized=True, **options)
+
+    def statistic(x):
+        assert x.ndim == 1
+        return np.mean(x)
+    fun(statistic=statistic, vectorized=None, **options)
+    fun(statistic=statistic, vectorized=False, **options)
+
+
+class TestMonteCarloMethod:
+    def test_rvs_and_random_state(self):
+        message = "Use of `rvs` and `rng` are mutually exclusive."
+        rng = np.random.default_rng(34982345)
+        with pytest.raises(ValueError, match=message):
+            stats.MonteCarloMethod(rvs=rng.random, rng=rng)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/test_sampling.py b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_sampling.py
new file mode 100644
index 0000000000000000000000000000000000000000..6d50354d10e6713b6effeede7e92be226df01483
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_sampling.py
@@ -0,0 +1,1455 @@
+import threading
+import pickle
+import pytest
+from copy import deepcopy
+import platform
+import sys
+import math
+import warnings
+
+import numpy as np
+from numpy.testing import assert_allclose, assert_equal
+from scipy.stats.sampling import (
+    TransformedDensityRejection,
+    DiscreteAliasUrn,
+    DiscreteGuideTable,
+    NumericalInversePolynomial,
+    NumericalInverseHermite,
+    RatioUniforms,
+    SimpleRatioUniforms,
+    UNURANError
+)
+from pytest import raises as assert_raises
+from scipy import stats
+from scipy import special
+from scipy.stats import chisquare, cramervonmises
+from scipy.stats._distr_params import distdiscrete, distcont
+from scipy._lib._util import check_random_state
+from scipy._lib._gcutils import assert_deallocated
+
+
+# common test data: this data can be shared between all the tests.
+
+
+# Normal distribution shared between all the continuous methods
+class StandardNormal:
+    def pdf(self, x):
+        # normalization constant needed for NumericalInverseHermite
+        return 1./np.sqrt(2.*np.pi) * np.exp(-0.5 * x*x)
+
+    def dpdf(self, x):
+        return 1./np.sqrt(2.*np.pi) * -x * np.exp(-0.5 * x*x)
+
+    def cdf(self, x):
+        return special.ndtr(x)
+
+
+all_methods = [
+    ("TransformedDensityRejection", {"dist": StandardNormal()}),
+    ("DiscreteAliasUrn", {"dist": [0.02, 0.18, 0.8]}),
+    ("DiscreteGuideTable", {"dist": [0.02, 0.18, 0.8]}),
+    ("NumericalInversePolynomial", {"dist": StandardNormal()}),
+    ("NumericalInverseHermite", {"dist": StandardNormal()}),
+    ("SimpleRatioUniforms", {"dist": StandardNormal(), "mode": 0})
+]
+
+floaterr = r"must be real number, not list"
+# Make sure an internal error occurs in UNU.RAN when invalid callbacks are
+# passed. Moreover, different generators throw different error messages.
+# So, in case of an `UNURANError`, we do not validate the error message.
+bad_pdfs_common = [
+    # Negative PDF
+    (lambda x: -x, UNURANError, r"..."),
+    # Returning wrong type
+    (lambda x: [], TypeError, floaterr),
+    # Undefined name inside the function
+    (lambda x: foo, NameError, r"name 'foo' is not defined"),  # type: ignore[name-defined]  # noqa: F821, E501
+    # Infinite value returned => Overflow error.
+    (lambda x: np.inf, UNURANError, r"..."),
+    # NaN value => internal error in UNU.RAN
+    (lambda x: np.nan, UNURANError, r"..."),
+    # signature of PDF wrong
+    (lambda: 1.0, TypeError, r"takes 0 positional arguments but 1 was given")
+]
+
+
+# same approach for dpdf
+bad_dpdf_common = [
+    # Infinite value returned.
+    (lambda x: np.inf, UNURANError, r"..."),
+    # NaN value => internal error in UNU.RAN
+    (lambda x: np.nan, UNURANError, r"..."),
+    # Returning wrong type
+    (lambda x: [], TypeError, floaterr),
+    # Undefined name inside the function
+    (lambda x: foo, NameError, r"name 'foo' is not defined"),  # type: ignore[name-defined]  # noqa: F821, E501
+    # signature of dPDF wrong
+    (lambda: 1.0, TypeError, r"takes 0 positional arguments but 1 was given")
+]
+
+
+# same approach for logpdf
+bad_logpdfs_common = [
+    # Returning wrong type
+    (lambda x: [], TypeError, floaterr),
+    # Undefined name inside the function
+    (lambda x: foo, NameError, r"name 'foo' is not defined"),  # type: ignore[name-defined]  # noqa: F821, E501
+    # Infinite value returned => Overflow error.
+    (lambda x: np.inf, UNURANError, r"..."),
+    # NaN value => internal error in UNU.RAN
+    (lambda x: np.nan, UNURANError, r"..."),
+    # signature of logpdf wrong
+    (lambda: 1.0, TypeError, r"takes 0 positional arguments but 1 was given")
+]
+
+
+bad_pv_common = [
+    ([], r"must contain at least one element"),
+    ([[1.0, 0.0]], r"wrong number of dimensions \(expected 1, got 2\)"),
+    ([0.2, 0.4, np.nan, 0.8], r"must contain only finite / non-nan values"),
+    ([0.2, 0.4, np.inf, 0.8], r"must contain only finite / non-nan values"),
+    ([0.0, 0.0], r"must contain at least one non-zero value"),
+]
+
+
+# size of the domains is incorrect
+bad_sized_domains = [
+    # > 2 elements in the domain
+    ((1, 2, 3), ValueError, r"must be a length 2 tuple"),
+    # empty domain
+    ((), ValueError, r"must be a length 2 tuple")
+]
+
+# domain values are incorrect
+bad_domains = [
+    ((2, 1), UNURANError, r"left >= right"),
+    ((1, 1), UNURANError, r"left >= right"),
+]
+
+# infinite and nan values present in domain.
+inf_nan_domains = [
+    # left >= right
+    ((10, 10), UNURANError, r"left >= right"),
+    ((np.inf, np.inf), UNURANError, r"left >= right"),
+    ((-np.inf, -np.inf), UNURANError, r"left >= right"),
+    ((np.inf, -np.inf), UNURANError, r"left >= right"),
+    # Also include nans in some of the domains.
+    ((-np.inf, np.nan), ValueError, r"only non-nan values"),
+    ((np.nan, np.inf), ValueError, r"only non-nan values")
+]
+
+# `nan` values present in domain. Some distributions don't support
+# infinite tails, so don't mix the nan values with infinities.
+nan_domains = [
+    ((0, np.nan), ValueError, r"only non-nan values"),
+    ((np.nan, np.nan), ValueError, r"only non-nan values")
+]
+
+
+# all the methods should throw errors for nan, bad sized, and bad valued
+# domains.
+@pytest.mark.parametrize("domain, err, msg",
+                         bad_domains + bad_sized_domains +
+                         nan_domains)  # type: ignore[operator]
+@pytest.mark.parametrize("method, kwargs", all_methods)
+def test_bad_domain(domain, err, msg, method, kwargs):
+    Method = getattr(stats.sampling, method)
+    with pytest.raises(err, match=msg):
+        Method(**kwargs, domain=domain)
+
+
+@pytest.mark.parametrize("method, kwargs", all_methods)
+def test_random_state(method, kwargs):
+    Method = getattr(stats.sampling, method)
+
+    # simple seed that works for any version of NumPy
+    seed = 123
+    rng1 = Method(**kwargs, random_state=seed)
+    rng2 = Method(**kwargs, random_state=seed)
+    assert_equal(rng1.rvs(100), rng2.rvs(100))
+
+    # global seed
+    rng = np.random.RandomState(123)
+    rng1 = Method(**kwargs)
+    rvs1 = rng1.rvs(100, random_state=rng)
+    np.random.seed(None)  # valid use of np.random.seed
+    rng2 = Method(**kwargs, random_state=123)
+    rvs2 = rng2.rvs(100)
+    assert_equal(rvs1, rvs2)
+
+    # Generator seed for new NumPy
+    # when a RandomState is given, it should take the bitgen_t
+    # member of the class and create a Generator instance.
+    seed1 = np.random.RandomState(np.random.MT19937(123))
+    seed2 = np.random.Generator(np.random.MT19937(123))
+    rng1 = Method(**kwargs, random_state=seed1)
+    rng2 = Method(**kwargs, random_state=seed2)
+    assert_equal(rng1.rvs(100), rng2.rvs(100))
+
+
+def test_set_random_state():
+    rng1 = TransformedDensityRejection(StandardNormal(), random_state=123)
+    rng2 = TransformedDensityRejection(StandardNormal())
+    rng2.set_random_state(123)
+    assert_equal(rng1.rvs(100), rng2.rvs(100))
+    rng = TransformedDensityRejection(StandardNormal(), random_state=123)
+    rvs1 = rng.rvs(100)
+    rng.set_random_state(123)
+    rvs2 = rng.rvs(100)
+    assert_equal(rvs1, rvs2)
+
+
+def test_threading_behaviour():
+    # Test if the API is thread-safe.
+    # This verifies if the lock mechanism and the use of `PyErr_Occurred`
+    # is correct.
+    errors = {"err1": None, "err2": None}
+
+    class Distribution:
+        def __init__(self, pdf_msg):
+            self.pdf_msg = pdf_msg
+
+        def pdf(self, x):
+            if 49.9 < x < 50.0:
+                raise ValueError(self.pdf_msg)
+            return x
+
+        def dpdf(self, x):
+            return 1
+
+    def func1():
+        dist = Distribution('foo')
+        rng = TransformedDensityRejection(dist, domain=(10, 100),
+                                          random_state=12)
+        try:
+            rng.rvs(100000)
+        except ValueError as e:
+            errors['err1'] = e.args[0]
+
+    def func2():
+        dist = Distribution('bar')
+        rng = TransformedDensityRejection(dist, domain=(10, 100),
+                                          random_state=2)
+        try:
+            rng.rvs(100000)
+        except ValueError as e:
+            errors['err2'] = e.args[0]
+
+    t1 = threading.Thread(target=func1)
+    t2 = threading.Thread(target=func2)
+
+    t1.start()
+    t2.start()
+
+    t1.join()
+    t2.join()
+
+    assert errors['err1'] == 'foo'
+    assert errors['err2'] == 'bar'
+
+
+@pytest.mark.parametrize("method, kwargs", all_methods)
+def test_pickle(method, kwargs):
+    Method = getattr(stats.sampling, method)
+    rng1 = Method(**kwargs, random_state=123)
+    obj = pickle.dumps(rng1)
+    rng2 = pickle.loads(obj)
+    assert_equal(rng1.rvs(100), rng2.rvs(100))
+
+
+@pytest.mark.parametrize("size", [None, 0, (0, ), 1, (10, 3), (2, 3, 4, 5),
+                                  (0, 0), (0, 1)])
+def test_rvs_size(size):
+    # As the `rvs` method is present in the base class and shared between
+    # all the classes, we can just test with one of the methods.
+    rng = TransformedDensityRejection(StandardNormal())
+    if size is None:
+        assert np.isscalar(rng.rvs(size))
+    else:
+        if np.isscalar(size):
+            size = (size, )
+        assert rng.rvs(size).shape == size
+
+
+def test_with_scipy_distribution():
+    # test if the setup works with SciPy's rv_frozen distributions
+    dist = stats.norm()
+    urng = np.random.default_rng(0)
+    rng = NumericalInverseHermite(dist, random_state=urng)
+    u = np.linspace(0, 1, num=100)
+    check_cont_samples(rng, dist, dist.stats())
+    assert_allclose(dist.ppf(u), rng.ppf(u))
+    # test if it works with `loc` and `scale`
+    dist = stats.norm(loc=10., scale=5.)
+    rng = NumericalInverseHermite(dist, random_state=urng)
+    check_cont_samples(rng, dist, dist.stats())
+    assert_allclose(dist.ppf(u), rng.ppf(u))
+    # check for discrete distributions
+    dist = stats.binom(10, 0.2)
+    rng = DiscreteAliasUrn(dist, random_state=urng)
+    domain = dist.support()
+    pv = dist.pmf(np.arange(domain[0], domain[1]+1))
+    check_discr_samples(rng, pv, dist.stats())
+
+
+def test_NumericalInverseHermite_refcycle():
+    # test if NumericalInverseHermite contains a reference cycle
+    dist = stats.norm()
+    urng = np.random.default_rng(0)
+    with assert_deallocated(NumericalInverseHermite, dist, random_state=urng) as rng:
+        u = np.linspace(0, 1, num=100)
+        check_cont_samples(rng, dist, dist.stats())
+        assert_allclose(dist.ppf(u), rng.ppf(u))
+        del rng
+
+
+def check_cont_samples(rng, dist, mv_ex, rtol=1e-7, atol=1e-1):
+    rvs = rng.rvs(100000)
+    mv = rvs.mean(), rvs.var()
+    # test the moments only if the variance is finite
+    if np.isfinite(mv_ex[1]):
+        assert_allclose(mv, mv_ex, rtol=rtol, atol=atol)
+    # Cramer Von Mises test for goodness-of-fit
+    rvs = rng.rvs(500)
+    dist.cdf = np.vectorize(dist.cdf)
+    pval = cramervonmises(rvs, dist.cdf).pvalue
+    assert pval > 0.1
+
+
+def check_discr_samples(rng, pv, mv_ex, rtol=1e-3, atol=1e-1):
+    rvs = rng.rvs(100000)
+    # test if the first few moments match
+    mv = rvs.mean(), rvs.var()
+    assert_allclose(mv, mv_ex, rtol=rtol, atol=atol)
+    # normalize
+    pv = pv / pv.sum()
+    # chi-squared test for goodness-of-fit
+    obs_freqs = np.zeros_like(pv)
+    _, freqs = np.unique(rvs, return_counts=True)
+    freqs = freqs / freqs.sum()
+    obs_freqs[:freqs.size] = freqs
+    pval = chisquare(obs_freqs, pv).pvalue
+    assert pval > 0.1
+
+
+def test_warning_center_not_in_domain():
+    # UNURAN will warn if the center provided or the one computed w/o the
+    # domain is outside of the domain
+    msg = "102 : center moved into domain of distribution"
+    with pytest.warns(RuntimeWarning, match=msg):
+        NumericalInversePolynomial(StandardNormal(), center=0, domain=(3, 5))
+    with pytest.warns(RuntimeWarning, match=msg):
+        NumericalInversePolynomial(StandardNormal(), domain=(3, 5))
+
+
+@pytest.mark.parametrize('method', ["SimpleRatioUniforms",
+                                    "NumericalInversePolynomial",
+                                    "TransformedDensityRejection"])
+def test_error_mode_not_in_domain(method):
+    # UNURAN raises an error if the mode is not in the domain
+    # the behavior is different compared to the case that center is not in the
+    # domain. mode is supposed to be the exact value, center can be an
+    # approximate value
+    Method = getattr(stats.sampling, method)
+    msg = "17 : mode not in domain"
+    with pytest.raises(UNURANError, match=msg):
+        Method(StandardNormal(), mode=0, domain=(3, 5))
+
+
+@pytest.mark.parametrize('method', ["NumericalInverseHermite",
+                                    "NumericalInversePolynomial"])
+class TestQRVS:
+    def test_input_validation(self, method):
+        match = "`qmc_engine` must be an instance of..."
+        with pytest.raises(ValueError, match=match):
+            Method = getattr(stats.sampling, method)
+            gen = Method(StandardNormal())
+            gen.qrvs(qmc_engine=0)
+
+        # issues with QMCEngines and old NumPy
+        Method = getattr(stats.sampling, method)
+        gen = Method(StandardNormal())
+
+        match = "`d` must be consistent with dimension of `qmc_engine`."
+        with pytest.raises(ValueError, match=match):
+            gen.qrvs(d=3, qmc_engine=stats.qmc.Halton(2))
+
+    qrngs = [None, stats.qmc.Sobol(1, seed=0), stats.qmc.Halton(3, seed=0)]
+    # `size=None` should not add anything to the shape, `size=1` should
+    sizes = [(None, tuple()), (1, (1,)), (4, (4,)),
+             ((4,), (4,)), ((2, 4), (2, 4))]  # type: ignore
+    # Neither `d=None` nor `d=1` should add anything to the shape
+    ds = [(None, tuple()), (1, tuple()), (3, (3,))]
+
+    @pytest.mark.parametrize('qrng', qrngs)
+    @pytest.mark.parametrize('size_in, size_out', sizes)
+    @pytest.mark.parametrize('d_in, d_out', ds)
+    @pytest.mark.thread_unsafe(reason="fails in parallel")
+    def test_QRVS_shape_consistency(self, qrng, size_in, size_out,
+                                    d_in, d_out, method):
+        w32 = sys.platform == "win32" and platform.architecture()[0] == "32bit"
+        if w32 and method == "NumericalInversePolynomial":
+            pytest.xfail("NumericalInversePolynomial.qrvs fails for Win "
+                         "32-bit")
+
+        dist = StandardNormal()
+        Method = getattr(stats.sampling, method)
+        gen = Method(dist)
+
+        # If d and qrng.d are inconsistent, an error is raised
+        if d_in is not None and qrng is not None and qrng.d != d_in:
+            match = "`d` must be consistent with dimension of `qmc_engine`."
+            with pytest.raises(ValueError, match=match):
+                gen.qrvs(size_in, d=d_in, qmc_engine=qrng)
+            return
+
+        # Sometimes d is really determined by qrng
+        if d_in is None and qrng is not None and qrng.d != 1:
+            d_out = (qrng.d,)
+
+        shape_expected = size_out + d_out
+
+        qrng2 = deepcopy(qrng)
+        qrvs = gen.qrvs(size=size_in, d=d_in, qmc_engine=qrng)
+        if size_in is not None:
+            assert qrvs.shape == shape_expected
+
+        if qrng2 is not None:
+            uniform = qrng2.random(np.prod(size_in) or 1)
+            qrvs2 = stats.norm.ppf(uniform).reshape(shape_expected)
+            assert_allclose(qrvs, qrvs2, atol=1e-12)
+
+    def test_QRVS_size_tuple(self, method):
+        # QMCEngine samples are always of shape (n, d). When `size` is a tuple,
+        # we set `n = prod(size)` in the call to qmc_engine.random, transform
+        # the sample, and reshape it to the final dimensions. When we reshape,
+        # we need to be careful, because the _columns_ of the sample returned
+        # by a QMCEngine are "independent"-ish, but the elements within the
+        # columns are not. We need to make sure that this doesn't get mixed up
+        # by reshaping: qrvs[..., i] should remain "independent"-ish of
+        # qrvs[..., i+1], but the elements within qrvs[..., i] should be
+        # transformed from the same low-discrepancy sequence.
+
+        dist = StandardNormal()
+        Method = getattr(stats.sampling, method)
+        gen = Method(dist)
+
+        size = (3, 4)
+        d = 5
+        qrng = stats.qmc.Halton(d, seed=0)
+        qrng2 = stats.qmc.Halton(d, seed=0)
+
+        uniform = qrng2.random(np.prod(size))
+
+        qrvs = gen.qrvs(size=size, d=d, qmc_engine=qrng)
+        qrvs2 = stats.norm.ppf(uniform)
+
+        for i in range(d):
+            sample = qrvs[..., i]
+            sample2 = qrvs2[:, i].reshape(size)
+            assert_allclose(sample, sample2, atol=1e-12)
+
+
+class TestTransformedDensityRejection:
+    # Simple Custom Distribution
+    class dist0:
+        def pdf(self, x):
+            return 3/4 * (1-x*x)
+
+        def dpdf(self, x):
+            return 3/4 * (-2*x)
+
+        def cdf(self, x):
+            return 3/4 * (x - x**3/3 + 2/3)
+
+        def support(self):
+            return -1, 1
+
+    # Standard Normal Distribution
+    class dist1:
+        def pdf(self, x):
+            return stats.norm._pdf(x / 0.1)
+
+        def dpdf(self, x):
+            return -x / 0.01 * stats.norm._pdf(x / 0.1)
+
+        def cdf(self, x):
+            return stats.norm._cdf(x / 0.1)
+
+    # pdf with piecewise linear function as transformed density
+    # with T = -1/sqrt with shift. Taken from UNU.RAN test suite
+    # (from file t_tdr_ps.c)
+    class dist2:
+        def __init__(self, shift):
+            self.shift = shift
+
+        def pdf(self, x):
+            x -= self.shift
+            y = 1. / (abs(x) + 1.)
+            return 0.5 * y * y
+
+        def dpdf(self, x):
+            x -= self.shift
+            y = 1. / (abs(x) + 1.)
+            y = y * y * y
+            return y if (x < 0.) else -y
+
+        def cdf(self, x):
+            x -= self.shift
+            if x <= 0.:
+                return 0.5 / (1. - x)
+            else:
+                return 1. - 0.5 / (1. + x)
+
+    dists = [dist0(), dist1(), dist2(0.), dist2(10000.)]
+
+    # exact mean and variance of the distributions in the list dists
+    mv0 = [0., 4./15.]
+    mv1 = [0., 0.01]
+    mv2 = [0., np.inf]
+    mv3 = [10000., np.inf]
+    mvs = [mv0, mv1, mv2, mv3]
+
+    @pytest.mark.parametrize("dist, mv_ex",
+                             list(zip(dists, mvs)))
+    @pytest.mark.thread_unsafe(reason="deadlocks for unknown reasons")
+    def test_basic(self, dist, mv_ex):
+        with warnings.catch_warnings():
+            # filter the warnings thrown by UNU.RAN
+            warnings.simplefilter("ignore", RuntimeWarning)
+            rng = TransformedDensityRejection(dist, random_state=42)
+        check_cont_samples(rng, dist, mv_ex)
+
+    # PDF 0 everywhere => bad construction points
+    bad_pdfs = [(lambda x: 0, UNURANError, r"50 : bad construction points.")]
+    bad_pdfs += bad_pdfs_common  # type: ignore[arg-type]
+
+    @pytest.mark.parametrize("pdf, err, msg", bad_pdfs)
+    def test_bad_pdf(self, pdf, err, msg):
+        class dist:
+            pass
+        dist.pdf = pdf
+        dist.dpdf = lambda x: 1  # an arbitrary dPDF
+        with pytest.raises(err, match=msg):
+            TransformedDensityRejection(dist)
+
+    @pytest.mark.parametrize("dpdf, err, msg", bad_dpdf_common)
+    def test_bad_dpdf(self, dpdf, err, msg):
+        class dist:
+            pass
+        dist.pdf = lambda x: x
+        dist.dpdf = dpdf
+        with pytest.raises(err, match=msg):
+            TransformedDensityRejection(dist, domain=(1, 10))
+
+    # test domains with inf + nan in them. need to write a custom test for
+    # this because not all methods support infinite tails.
+    @pytest.mark.parametrize("domain, err, msg", inf_nan_domains)
+    def test_inf_nan_domains(self, domain, err, msg):
+        with pytest.raises(err, match=msg):
+            TransformedDensityRejection(StandardNormal(), domain=domain)
+
+    @pytest.mark.parametrize("construction_points", [-1, 0, 0.1])
+    def test_bad_construction_points_scalar(self, construction_points):
+        with pytest.raises(ValueError, match=r"`construction_points` must be "
+                                             r"a positive integer."):
+            TransformedDensityRejection(
+                StandardNormal(), construction_points=construction_points
+            )
+
+    def test_bad_construction_points_array(self):
+        # empty array
+        construction_points = []
+        with pytest.raises(ValueError, match=r"`construction_points` must "
+                                             r"either be a "
+                                             r"scalar or a non-empty array."):
+            TransformedDensityRejection(
+                StandardNormal(), construction_points=construction_points
+            )
+
+        # construction_points not monotonically increasing
+        construction_points = [1, 1, 1, 1, 1, 1]
+        with pytest.warns(RuntimeWarning, match=r"33 : starting points not "
+                                                r"strictly monotonically "
+                                                r"increasing"):
+            TransformedDensityRejection(
+                StandardNormal(), construction_points=construction_points
+            )
+
+        # construction_points containing nans
+        construction_points = [np.nan, np.nan, np.nan]
+        with pytest.raises(UNURANError, match=r"50 : bad construction "
+                                              r"points."):
+            TransformedDensityRejection(
+                StandardNormal(), construction_points=construction_points
+            )
+
+        # construction_points out of domain
+        construction_points = [-10, 10]
+        with pytest.warns(RuntimeWarning, match=r"50 : starting point out of "
+                                                r"domain"):
+            TransformedDensityRejection(
+                StandardNormal(), domain=(-3, 3),
+                construction_points=construction_points
+            )
+
+    @pytest.mark.parametrize("c", [-1., np.nan, np.inf, 0.1, 1.])
+    def test_bad_c(self, c):
+        msg = r"`c` must either be -0.5 or 0."
+        with pytest.raises(ValueError, match=msg):
+            TransformedDensityRejection(StandardNormal(), c=-1.)
+
+    u = [np.linspace(0, 1, num=1000), [], [[]], [np.nan],
+         [-np.inf, np.nan, np.inf], 0,
+         [[np.nan, 0.5, 0.1], [0.2, 0.4, np.inf], [-2, 3, 4]]]
+
+    @pytest.mark.parametrize("u", u)
+    def test_ppf_hat(self, u):
+        # Increase the `max_squeeze_hat_ratio` so the ppf_hat is more
+        # accurate.
+        rng = TransformedDensityRejection(StandardNormal(),
+                                          max_squeeze_hat_ratio=0.9999)
+        # Older versions of NumPy throw RuntimeWarnings for comparisons
+        # with nan.
+        with warnings.catch_warnings():
+            msg = "invalid value encountered in "
+            warnings.filterwarnings("ignore", msg + "greater", RuntimeWarning)
+            warnings.filterwarnings("ignore", msg + "greater_equal", RuntimeWarning)
+            warnings.filterwarnings("ignore", msg + "less", RuntimeWarning)
+            warnings.filterwarnings("ignore", msg + "less_equal", RuntimeWarning)
+            res = rng.ppf_hat(u)
+            expected = stats.norm.ppf(u)
+        assert_allclose(res, expected, rtol=1e-3, atol=1e-5)
+        assert res.shape == expected.shape
+
+    def test_bad_dist(self):
+        # Empty distribution
+        class dist:
+            ...
+
+        msg = r"`pdf` required but not found."
+        with pytest.raises(ValueError, match=msg):
+            TransformedDensityRejection(dist)
+
+        # dPDF not present in dist
+        class dist:
+            pdf = lambda x: 1-x*x  # noqa: E731
+
+        msg = r"`dpdf` required but not found."
+        with pytest.raises(ValueError, match=msg):
+            TransformedDensityRejection(dist)
+
+
+class TestDiscreteAliasUrn:
+    # DAU fails on these probably because of large domains and small
+    # computation errors in PMF. Mean/SD match but chi-squared test fails.
+    basic_fail_dists = {
+        'nchypergeom_fisher',  # numerical errors on tails
+        'nchypergeom_wallenius',  # numerical errors on tails
+        'randint'  # fails on 32-bit ubuntu
+    }
+
+    @pytest.mark.parametrize("distname, params", distdiscrete)
+    def test_basic(self, distname, params):
+        if distname in self.basic_fail_dists:
+            msg = ("DAU fails on these probably because of large domains "
+                   "and small computation errors in PMF.")
+            pytest.skip(msg)
+        if not isinstance(distname, str):
+            dist = distname
+        else:
+            dist = getattr(stats, distname)
+        dist = dist(*params)
+        domain = dist.support()
+        if not np.isfinite(domain[1] - domain[0]):
+            # DAU only works with finite domain. So, skip the distributions
+            # with infinite tails.
+            pytest.skip("DAU only works with a finite domain.")
+        k = np.arange(domain[0], domain[1]+1)
+        pv = dist.pmf(k)
+        mv_ex = dist.stats('mv')
+        rng = DiscreteAliasUrn(dist, random_state=42)
+        check_discr_samples(rng, pv, mv_ex)
+
+    # Can't use bad_pmf_common here as we evaluate PMF early on to avoid
+    # unhelpful errors from UNU.RAN.
+    bad_pmf = [
+        # inf returned
+        (lambda x: np.inf, ValueError,
+         r"must contain only finite / non-nan values"),
+        # nan returned
+        (lambda x: np.nan, ValueError,
+         r"must contain only finite / non-nan values"),
+        # all zeros
+        (lambda x: 0.0, ValueError,
+         r"must contain at least one non-zero value"),
+        # Undefined name inside the function
+        (lambda x: foo, NameError,  # type: ignore[name-defined]  # noqa: F821
+         r"name 'foo' is not defined"),
+        # Returning wrong type.
+        (lambda x: [], ValueError,
+         r"setting an array element with a sequence."),
+        # probabilities < 0
+        (lambda x: -x, UNURANError,
+         r"50 : probability < 0"),
+        # signature of PMF wrong
+        (lambda: 1.0, TypeError,
+         r"takes 0 positional arguments but 1 was given")
+    ]
+
+    @pytest.mark.parametrize("pmf, err, msg", bad_pmf)
+    def test_bad_pmf(self, pmf, err, msg):
+        class dist:
+            pass
+        dist.pmf = pmf
+        with pytest.raises(err, match=msg):
+            DiscreteAliasUrn(dist, domain=(1, 10))
+
+    @pytest.mark.parametrize("pv", [[0.18, 0.02, 0.8],
+                                    [1.0, 2.0, 3.0, 4.0, 5.0, 6.0]])
+    def test_sampling_with_pv(self, pv):
+        pv = np.asarray(pv, dtype=np.float64)
+        rng = DiscreteAliasUrn(pv, random_state=123)
+        rng.rvs(100_000)
+        pv = pv / pv.sum()
+        variates = np.arange(0, len(pv))
+        # test if the first few moments match
+        m_expected = np.average(variates, weights=pv)
+        v_expected = np.average((variates - m_expected) ** 2, weights=pv)
+        mv_expected = m_expected, v_expected
+        check_discr_samples(rng, pv, mv_expected)
+
+    @pytest.mark.parametrize("pv, msg", bad_pv_common)
+    def test_bad_pv(self, pv, msg):
+        with pytest.raises(ValueError, match=msg):
+            DiscreteAliasUrn(pv)
+
+    # DAU doesn't support infinite tails. So, it should throw an error when
+    # inf is present in the domain.
+    inf_domain = [(-np.inf, np.inf), (np.inf, np.inf), (-np.inf, -np.inf),
+                  (0, np.inf), (-np.inf, 0)]
+
+    @pytest.mark.parametrize("domain", inf_domain)
+    def test_inf_domain(self, domain):
+        with pytest.raises(ValueError, match=r"must be finite"):
+            DiscreteAliasUrn(stats.binom(10, 0.2), domain=domain)
+
+    def test_bad_urn_factor(self):
+        with pytest.warns(RuntimeWarning, match=r"relative urn size < 1."):
+            DiscreteAliasUrn([0.5, 0.5], urn_factor=-1)
+
+    def test_bad_args(self):
+        msg = (r"`domain` must be provided when the "
+               r"probability vector is not available.")
+
+        class dist:
+            def pmf(self, x):
+                return x
+
+        with pytest.raises(ValueError, match=msg):
+            DiscreteAliasUrn(dist)
+
+    def test_gh19359(self):
+        pv = special.softmax(np.ones((1533,)))
+        rng = DiscreteAliasUrn(pv, random_state=42)
+        # check the correctness
+        check_discr_samples(rng, pv, (1532 / 2, (1532**2 - 1) / 12),
+                            rtol=5e-3)
+
+
+class TestNumericalInversePolynomial:
+    # Simple Custom Distribution
+    class dist0:
+        def pdf(self, x):
+            return 3/4 * (1-x*x)
+
+        def cdf(self, x):
+            return 3/4 * (x - x**3/3 + 2/3)
+
+        def support(self):
+            return -1, 1
+
+    # Standard Normal Distribution
+    class dist1:
+        def pdf(self, x):
+            return stats.norm._pdf(x / 0.1)
+
+        def cdf(self, x):
+            return stats.norm._cdf(x / 0.1)
+
+    # Sin 2 distribution
+    #          /  0.05 + 0.45*(1 +sin(2 Pi x))  if |x| <= 1
+    #  f(x) = <
+    #          \  0        otherwise
+    # Taken from UNU.RAN test suite (from file t_pinv.c)
+    class dist2:
+        def pdf(self, x):
+            return 0.05 + 0.45 * (1 + np.sin(2*np.pi*x))
+
+        def cdf(self, x):
+            return (0.05*(x + 1) +
+                    0.9*(1. + 2.*np.pi*(1 + x) - np.cos(2.*np.pi*x)) /
+                    (4.*np.pi))
+
+        def support(self):
+            return -1, 1
+
+    # Sin 10 distribution
+    #          /  0.05 + 0.45*(1 +sin(2 Pi x))  if |x| <= 5
+    #  f(x) = <
+    #          \  0        otherwise
+    # Taken from UNU.RAN test suite (from file t_pinv.c)
+    class dist3:
+        def pdf(self, x):
+            return 0.2 * (0.05 + 0.45 * (1 + np.sin(2*np.pi*x)))
+
+        def cdf(self, x):
+            return x/10. + 0.5 + 0.09/(2*np.pi) * (np.cos(10*np.pi) -
+                                                   np.cos(2*np.pi*x))
+
+        def support(self):
+            return -5, 5
+
+    dists = [dist0(), dist1(), dist2(), dist3()]
+
+    # exact mean and variance of the distributions in the list dists
+    mv0 = [0., 4./15.]
+    mv1 = [0., 0.01]
+    mv2 = [-0.45/np.pi, 2/3*0.5 - 0.45**2/np.pi**2]
+    mv3 = [-0.45/np.pi, 0.2 * 250/3 * 0.5 - 0.45**2/np.pi**2]
+    mvs = [mv0, mv1, mv2, mv3]
+
+    @pytest.mark.thread_unsafe(reason="deadlocks for unknown reasons")
+    @pytest.mark.parametrize("dist, mv_ex",
+                             list(zip(dists, mvs)))
+    def test_basic(self, dist, mv_ex):
+        rng = NumericalInversePolynomial(dist, random_state=42)
+        check_cont_samples(rng, dist, mv_ex)
+
+    @pytest.mark.xslow
+    @pytest.mark.parametrize("distname, params", distcont)
+    def test_basic_all_scipy_dists(self, distname, params):
+
+        very_slow_dists = ['anglit', 'gausshyper', 'kappa4',
+                           'ksone', 'kstwo', 'levy_l',
+                           'levy_stable', 'studentized_range',
+                           'trapezoid', 'triang', 'vonmises']
+        # for these distributions, some assertions fail due to minor
+        # numerical differences. They can be avoided either by changing
+        # the seed or by increasing the u_resolution.
+        fail_dists = ['chi2', 'fatiguelife', 'gibrat',
+                      'halfgennorm', 'lognorm', 'ncf',
+                      'ncx2', 'pareto', 't']
+        # for these distributions, skip the check for agreement between sample
+        # moments and true moments. We cannot expect them to pass due to the
+        # high variance of sample moments.
+        skip_sample_moment_check = ['rel_breitwigner']
+
+        if distname in very_slow_dists:
+            pytest.skip(f"PINV too slow for {distname}")
+        if distname in fail_dists:
+            pytest.skip(f"PINV fails for {distname}")
+        dist = (getattr(stats, distname)
+                if isinstance(distname, str)
+                else distname)
+        dist = dist(*params)
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", RuntimeWarning)
+            rng = NumericalInversePolynomial(dist, random_state=42)
+        if distname in skip_sample_moment_check:
+            return
+        check_cont_samples(rng, dist, [dist.mean(), dist.var()])
+
+    @pytest.mark.parametrize("pdf, err, msg", bad_pdfs_common)
+    def test_bad_pdf(self, pdf, err, msg):
+        class dist:
+            pass
+        dist.pdf = pdf
+        with pytest.raises(err, match=msg):
+            NumericalInversePolynomial(dist, domain=[0, 5])
+
+    @pytest.mark.parametrize("logpdf, err, msg", bad_logpdfs_common)
+    def test_bad_logpdf(self, logpdf, err, msg):
+        class dist:
+            pass
+        dist.logpdf = logpdf
+        with pytest.raises(err, match=msg):
+            NumericalInversePolynomial(dist, domain=[0, 5])
+
+    # test domains with inf + nan in them. need to write a custom test for
+    # this because not all methods support infinite tails.
+    @pytest.mark.parametrize("domain, err, msg", inf_nan_domains)
+    def test_inf_nan_domains(self, domain, err, msg):
+        with pytest.raises(err, match=msg):
+            NumericalInversePolynomial(StandardNormal(), domain=domain)
+
+    u = [
+        # test if quantile 0 and 1 return -inf and inf respectively and check
+        # the correctness of the PPF for equidistant points between 0 and 1.
+        np.linspace(0, 1, num=10000),
+        # test the PPF method for empty arrays
+        [], [[]],
+        # test if nans and infs return nan result.
+        [np.nan], [-np.inf, np.nan, np.inf],
+        # test if a scalar is returned for a scalar input.
+        0,
+        # test for arrays with nans, values greater than 1 and less than 0,
+        # and some valid values.
+        [[np.nan, 0.5, 0.1], [0.2, 0.4, np.inf], [-2, 3, 4]]
+    ]
+
+    @pytest.mark.parametrize("u", u)
+    def test_ppf(self, u):
+        dist = StandardNormal()
+        rng = NumericalInversePolynomial(dist, u_resolution=1e-14)
+        # Older versions of NumPy throw RuntimeWarnings for comparisons
+        # with nan.
+        with warnings.catch_warnings():
+            msg = "invalid value encountered in "
+            warnings.filterwarnings("ignore", msg + "greater", RuntimeWarning)
+            warnings.filterwarnings("ignore", msg + "greater_equal", RuntimeWarning)
+            warnings.filterwarnings("ignore", msg + "less", RuntimeWarning)
+            warnings.filterwarnings("ignore", msg + "less_equal", RuntimeWarning)
+            res = rng.ppf(u)
+            expected = stats.norm.ppf(u)
+        assert_allclose(res, expected, rtol=1e-11, atol=1e-11)
+        assert res.shape == expected.shape
+
+    x = [np.linspace(-10, 10, num=10000), [], [[]], [np.nan],
+         [-np.inf, np.nan, np.inf], 0,
+         [[np.nan, 0.5, 0.1], [0.2, 0.4, np.inf], [-np.inf, 3, 4]]]
+
+    @pytest.mark.parametrize("x", x)
+    def test_cdf(self, x):
+        dist = StandardNormal()
+        rng = NumericalInversePolynomial(dist, u_resolution=1e-14)
+        # Older versions of NumPy throw RuntimeWarnings for comparisons
+        # with nan.
+        with warnings.catch_warnings():
+            msg = "invalid value encountered in "
+            warnings.filterwarnings("ignore", msg + "greater", RuntimeWarning)
+            warnings.filterwarnings("ignore", msg + "greater_equal", RuntimeWarning)
+            warnings.filterwarnings("ignore", msg + "less", RuntimeWarning)
+            warnings.filterwarnings("ignore", msg + "less_equal", RuntimeWarning)
+            res = rng.cdf(x)
+            expected = stats.norm.cdf(x)
+        assert_allclose(res, expected, rtol=1e-11, atol=1e-11)
+        assert res.shape == expected.shape
+
+    @pytest.mark.slow
+    def test_u_error(self):
+        dist = StandardNormal()
+        rng = NumericalInversePolynomial(dist, u_resolution=1e-10)
+        max_error, mae = rng.u_error()
+        assert max_error < 1e-10
+        assert mae <= max_error
+        rng = NumericalInversePolynomial(dist, u_resolution=1e-14)
+        max_error, mae = rng.u_error()
+        assert max_error < 1e-14
+        assert mae <= max_error
+
+    bad_orders = [1, 4.5, 20, np.inf, np.nan]
+    bad_u_resolution = [1e-20, 1e-1, np.inf, np.nan]
+
+    @pytest.mark.parametrize("order", bad_orders)
+    def test_bad_orders(self, order):
+        dist = StandardNormal()
+
+        msg = r"`order` must be an integer in the range \[3, 17\]."
+        with pytest.raises(ValueError, match=msg):
+            NumericalInversePolynomial(dist, order=order)
+
+    @pytest.mark.parametrize("u_resolution", bad_u_resolution)
+    def test_bad_u_resolution(self, u_resolution):
+        msg = r"`u_resolution` must be between 1e-15 and 1e-5."
+        with pytest.raises(ValueError, match=msg):
+            NumericalInversePolynomial(StandardNormal(),
+                                       u_resolution=u_resolution)
+
+    def test_bad_args(self):
+
+        class BadDist:
+            def cdf(self, x):
+                return stats.norm._cdf(x)
+
+        dist = BadDist()
+        msg = r"Either of the methods `pdf` or `logpdf` must be specified"
+        with pytest.raises(ValueError, match=msg):
+            rng = NumericalInversePolynomial(dist)
+
+        dist = StandardNormal()
+        rng = NumericalInversePolynomial(dist)
+        msg = r"`sample_size` must be greater than or equal to 1000."
+        with pytest.raises(ValueError, match=msg):
+            rng.u_error(10)
+
+        class Distribution:
+            def pdf(self, x):
+                return np.exp(-0.5 * x*x)
+
+        dist = Distribution()
+        rng = NumericalInversePolynomial(dist)
+        msg = r"Exact CDF required but not found."
+        with pytest.raises(ValueError, match=msg):
+            rng.u_error()
+
+    def test_logpdf_pdf_consistency(self):
+        # 1. check that PINV works with pdf and logpdf only
+        # 2. check that generated ppf is the same (up to a small tolerance)
+
+        class MyDist:
+            pass
+
+        # create generator from dist with only pdf
+        dist_pdf = MyDist()
+        dist_pdf.pdf = lambda x: math.exp(-x*x/2)
+        rng1 = NumericalInversePolynomial(dist_pdf)
+
+        # create dist with only logpdf
+        dist_logpdf = MyDist()
+        dist_logpdf.logpdf = lambda x: -x*x/2
+        rng2 = NumericalInversePolynomial(dist_logpdf)
+
+        q = np.linspace(1e-5, 1-1e-5, num=100)
+        assert_allclose(rng1.ppf(q), rng2.ppf(q))
+
+
+class TestNumericalInverseHermite:
+    #         /  (1 +sin(2 Pi x))/2  if |x| <= 1
+    # f(x) = <
+    #         \  0        otherwise
+    # Taken from UNU.RAN test suite (from file t_hinv.c)
+    class dist0:
+        def pdf(self, x):
+            return 0.5*(1. + np.sin(2.*np.pi*x))
+
+        def dpdf(self, x):
+            return np.pi*np.cos(2.*np.pi*x)
+
+        def cdf(self, x):
+            return (1. + 2.*np.pi*(1 + x) - np.cos(2.*np.pi*x)) / (4.*np.pi)
+
+        def support(self):
+            return -1, 1
+
+    #         /  Max(sin(2 Pi x)),0)Pi/2  if -1 < x <0.5
+    # f(x) = <
+    #         \  0        otherwise
+    # Taken from UNU.RAN test suite (from file t_hinv.c)
+    class dist1:
+        def pdf(self, x):
+            if (x <= -0.5):
+                return np.sin((2. * np.pi) * x) * 0.5 * np.pi
+            if (x < 0.):
+                return 0.
+            if (x <= 0.5):
+                return np.sin((2. * np.pi) * x) * 0.5 * np.pi
+
+        def dpdf(self, x):
+            if (x <= -0.5):
+                return np.cos((2. * np.pi) * x) * np.pi * np.pi
+            if (x < 0.):
+                return 0.
+            if (x <= 0.5):
+                return np.cos((2. * np.pi) * x) * np.pi * np.pi
+
+        def cdf(self, x):
+            if (x <= -0.5):
+                return 0.25 * (1 - np.cos((2. * np.pi) * x))
+            if (x < 0.):
+                return 0.5
+            if (x <= 0.5):
+                return 0.75 - 0.25 * np.cos((2. * np.pi) * x)
+
+        def support(self):
+            return -1, 0.5
+
+    dists = [dist0(), dist1()]
+
+    # exact mean and variance of the distributions in the list dists
+    mv0 = [-1/(2*np.pi), 1/3 - 1/(4*np.pi*np.pi)]
+    mv1 = [-1/4, 3/8-1/(2*np.pi*np.pi) - 1/16]
+    mvs = [mv0, mv1]
+
+    @pytest.mark.parametrize("dist, mv_ex",
+                             list(zip(dists, mvs)))
+    @pytest.mark.parametrize("order", [3, 5])
+    @pytest.mark.thread_unsafe
+    def test_basic(self, dist, mv_ex, order):
+        rng = NumericalInverseHermite(dist, order=order, random_state=42)
+        check_cont_samples(rng, dist, mv_ex)
+
+    # test domains with inf + nan in them. need to write a custom test for
+    # this because not all methods support infinite tails.
+    @pytest.mark.parametrize("domain, err, msg", inf_nan_domains)
+    def test_inf_nan_domains(self, domain, err, msg):
+        with pytest.raises(err, match=msg):
+            NumericalInverseHermite(StandardNormal(), domain=domain)
+
+    def basic_test_all_scipy_dists(self, distname, shapes):
+        slow_dists = {'ksone', 'kstwo', 'levy_stable', 'skewnorm'}
+        fail_dists = {'beta', 'gausshyper', 'geninvgauss', 'ncf', 'nct',
+                      'norminvgauss', 'genhyperbolic', 'studentized_range',
+                      'vonmises', 'kappa4', 'invgauss', 'wald'}
+
+        if distname in slow_dists:
+            pytest.skip("Distribution is too slow")
+        if distname in fail_dists:
+            # specific reasons documented in gh-13319
+            # https://github.com/scipy/scipy/pull/13319#discussion_r626188955
+            pytest.xfail("Fails - usually due to inaccurate CDF/PDF")
+
+        rng = np.random.default_rng(0)
+
+        dist = getattr(stats, distname)(*shapes)
+        fni = NumericalInverseHermite(dist)
+
+        x = rng.random(10)
+        p_tol = np.max(np.abs(dist.ppf(x)-fni.ppf(x))/np.abs(dist.ppf(x)))
+        u_tol = np.max(np.abs(dist.cdf(fni.ppf(x)) - x))
+
+        assert p_tol < 1e-8
+        assert u_tol < 1e-12
+
+    @pytest.mark.filterwarnings('ignore::RuntimeWarning')
+    @pytest.mark.xslow
+    @pytest.mark.parametrize(("distname", "shapes"), distcont)
+    def test_basic_all_scipy_dists(self, distname, shapes):
+        # if distname == "truncnorm":
+        #     pytest.skip("Tested separately")
+        self.basic_test_all_scipy_dists(distname, shapes)
+
+    @pytest.mark.fail_slow(5)
+    @pytest.mark.filterwarnings('ignore::RuntimeWarning')
+    @pytest.mark.parallel_threads_limit(4)  # Very slow
+    def test_basic_truncnorm_gh17155(self):
+        self.basic_test_all_scipy_dists("truncnorm", (0.1, 2))
+
+    def test_input_validation(self):
+        match = r"`order` must be either 1, 3, or 5."
+        with pytest.raises(ValueError, match=match):
+            NumericalInverseHermite(StandardNormal(), order=2)
+
+        match = "`cdf` required but not found"
+        with pytest.raises(ValueError, match=match):
+            NumericalInverseHermite("norm")
+
+        match = "could not convert string to float"
+        with pytest.raises(ValueError, match=match):
+            NumericalInverseHermite(StandardNormal(),
+                                    u_resolution='ekki')
+
+    rngs = [None, 0, np.random.RandomState(0)]
+    rngs.append(np.random.default_rng(0))  # type: ignore
+    sizes = [(None, tuple()), (8, (8,)), ((4, 5, 6), (4, 5, 6))]
+
+    @pytest.mark.parametrize('rng', rngs)
+    @pytest.mark.parametrize('size_in, size_out', sizes)
+    @pytest.mark.thread_unsafe
+    def test_RVS(self, rng, size_in, size_out):
+        dist = StandardNormal()
+        fni = NumericalInverseHermite(dist)
+
+        rng2 = deepcopy(rng)
+        rvs = fni.rvs(size=size_in, random_state=rng)
+        if size_in is not None:
+            assert rvs.shape == size_out
+
+        if rng2 is not None:
+            rng2 = check_random_state(rng2)
+            uniform = rng2.uniform(size=size_in)
+            rvs2 = stats.norm.ppf(uniform)
+            assert_allclose(rvs, rvs2)
+
+    def test_inaccurate_CDF(self):
+        # CDF function with inaccurate tail cannot be inverted; see gh-13319
+        # https://github.com/scipy/scipy/pull/13319#discussion_r626188955
+        shapes = (2.3098496451481823, 0.6268795430096368)
+        match = ("98 : one or more intervals very short; possibly due to "
+                 "numerical problems with a pole or very flat tail")
+
+        # fails with default tol
+        with pytest.warns(RuntimeWarning, match=match):
+            NumericalInverseHermite(stats.beta(*shapes))
+
+        # no error with coarser tol
+        NumericalInverseHermite(stats.beta(*shapes), u_resolution=1e-8)
+
+    def test_custom_distribution(self):
+        dist1 = StandardNormal()
+        fni1 = NumericalInverseHermite(dist1)
+
+        dist2 = stats.norm()
+        fni2 = NumericalInverseHermite(dist2)
+
+        assert_allclose(fni1.rvs(random_state=0), fni2.rvs(random_state=0))
+
+    u = [
+        # check the correctness of the PPF for equidistant points between
+        # 0.02 and 0.98.
+        np.linspace(0., 1., num=10000),
+        # test the PPF method for empty arrays
+        [], [[]],
+        # test if nans and infs return nan result.
+        [np.nan], [-np.inf, np.nan, np.inf],
+        # test if a scalar is returned for a scalar input.
+        0,
+        # test for arrays with nans, values greater than 1 and less than 0,
+        # and some valid values.
+        [[np.nan, 0.5, 0.1], [0.2, 0.4, np.inf], [-2, 3, 4]]
+    ]
+
+    @pytest.mark.parametrize("u", u)
+    def test_ppf(self, u):
+        dist = StandardNormal()
+        rng = NumericalInverseHermite(dist, u_resolution=1e-12)
+        # Older versions of NumPy throw RuntimeWarnings for comparisons
+        # with nan.
+        with warnings.catch_warnings():
+            msg = "invalid value encountered in "
+            warnings.filterwarnings("ignore", msg + "greater", RuntimeWarning)
+            warnings.filterwarnings("ignore", msg + "greater_equal", RuntimeWarning)
+            warnings.filterwarnings("ignore", msg + "less", RuntimeWarning)
+            warnings.filterwarnings("ignore", msg + "less_equal", RuntimeWarning)
+            res = rng.ppf(u)
+            expected = stats.norm.ppf(u)
+        assert_allclose(res, expected, rtol=1e-9, atol=3e-10)
+        assert res.shape == expected.shape
+
+    @pytest.mark.slow
+    def test_u_error(self):
+        dist = StandardNormal()
+        rng = NumericalInverseHermite(dist, u_resolution=1e-10)
+        max_error, mae = rng.u_error()
+        assert max_error < 1e-10
+        assert mae <= max_error
+        with warnings.catch_warnings():
+            # ignore warning about u-resolution being too small.
+            warnings.simplefilter("ignore", RuntimeWarning)
+            rng = NumericalInverseHermite(dist, u_resolution=1e-14)
+        max_error, mae = rng.u_error()
+        assert max_error < 1e-14
+        assert mae <= max_error
+
+
+class TestDiscreteGuideTable:
+    basic_fail_dists = {
+        'nchypergeom_fisher',  # numerical errors on tails
+        'nchypergeom_wallenius',  # numerical errors on tails
+        'randint'  # fails on 32-bit ubuntu
+    }
+
+    def test_guide_factor_gt3_raises_warning(self):
+        pv = [0.1, 0.3, 0.6]
+        urng = np.random.default_rng()
+        with pytest.warns(RuntimeWarning):
+            DiscreteGuideTable(pv, random_state=urng, guide_factor=7)
+
+    def test_guide_factor_zero_raises_warning(self):
+        pv = [0.1, 0.3, 0.6]
+        urng = np.random.default_rng()
+        with pytest.warns(RuntimeWarning):
+            DiscreteGuideTable(pv, random_state=urng, guide_factor=0)
+
+    def test_negative_guide_factor_raises_warning(self):
+        # This occurs from the UNU.RAN wrapper automatically.
+        # however it already gives a useful warning
+        # Here we just test that a warning is raised.
+        pv = [0.1, 0.3, 0.6]
+        urng = np.random.default_rng()
+        with pytest.warns(RuntimeWarning):
+            DiscreteGuideTable(pv, random_state=urng, guide_factor=-1)
+
+    @pytest.mark.parametrize("distname, params", distdiscrete)
+    def test_basic(self, distname, params):
+        if distname in self.basic_fail_dists:
+            msg = ("DGT fails on these probably because of large domains "
+                   "and small computation errors in PMF.")
+            pytest.skip(msg)
+
+        if not isinstance(distname, str):
+            dist = distname
+        else:
+            dist = getattr(stats, distname)
+
+        dist = dist(*params)
+        domain = dist.support()
+
+        if not np.isfinite(domain[1] - domain[0]):
+            # DGT only works with finite domain. So, skip the distributions
+            # with infinite tails.
+            pytest.skip("DGT only works with a finite domain.")
+
+        k = np.arange(domain[0], domain[1]+1)
+        pv = dist.pmf(k)
+        mv_ex = dist.stats('mv')
+        rng = DiscreteGuideTable(dist, random_state=42)
+        check_discr_samples(rng, pv, mv_ex)
+
+    u = [
+        # the correctness of the PPF for equidistant points between 0 and 1.
+        np.linspace(0, 1, num=10000),
+        # test the PPF method for empty arrays
+        [], [[]],
+        # test if nans and infs return nan result.
+        [np.nan], [-np.inf, np.nan, np.inf],
+        # test if a scalar is returned for a scalar input.
+        0,
+        # test for arrays with nans, values greater than 1 and less than 0,
+        # and some valid values.
+        [[np.nan, 0.5, 0.1], [0.2, 0.4, np.inf], [-2, 3, 4]]
+    ]
+
+    @pytest.mark.parametrize('u', u)
+    def test_ppf(self, u):
+        n, p = 4, 0.1
+        dist = stats.binom(n, p)
+        rng = DiscreteGuideTable(dist, random_state=42)
+
+        # Older versions of NumPy throw RuntimeWarnings for comparisons
+        # with nan.
+        with warnings.catch_warnings():
+            msg = "invalid value encountered in "
+            warnings.filterwarnings("ignore", msg + "greater", RuntimeWarning)
+            warnings.filterwarnings("ignore", msg + "greater_equal", RuntimeWarning)
+            warnings.filterwarnings("ignore", msg + "less", RuntimeWarning)
+            warnings.filterwarnings("ignore", msg + "less_equal", RuntimeWarning)
+            res = rng.ppf(u)
+            expected = stats.binom.ppf(u, n, p)
+        assert_equal(res.shape, expected.shape)
+        assert_equal(res, expected)
+
+    @pytest.mark.parametrize("pv, msg", bad_pv_common)
+    def test_bad_pv(self, pv, msg):
+        with pytest.raises(ValueError, match=msg):
+            DiscreteGuideTable(pv)
+
+    # DGT doesn't support infinite tails. So, it should throw an error when
+    # inf is present in the domain.
+    inf_domain = [(-np.inf, np.inf), (np.inf, np.inf), (-np.inf, -np.inf),
+                  (0, np.inf), (-np.inf, 0)]
+
+    @pytest.mark.parametrize("domain", inf_domain)
+    def test_inf_domain(self, domain):
+        with pytest.raises(ValueError, match=r"must be finite"):
+            DiscreteGuideTable(stats.binom(10, 0.2), domain=domain)
+
+
+class TestSimpleRatioUniforms:
+    # pdf with piecewise linear function as transformed density
+    # with T = -1/sqrt with shift. Taken from UNU.RAN test suite
+    # (from file t_srou.c)
+    class dist:
+        def __init__(self, shift):
+            self.shift = shift
+            self.mode = shift
+
+        def pdf(self, x):
+            x -= self.shift
+            y = 1. / (abs(x) + 1.)
+            return 0.5 * y * y
+
+        def cdf(self, x):
+            x -= self.shift
+            if x <= 0.:
+                return 0.5 / (1. - x)
+            else:
+                return 1. - 0.5 / (1. + x)
+
+    dists = [dist(0.), dist(10000.)]
+
+    # exact mean and variance of the distributions in the list dists
+    mv1 = [0., np.inf]
+    mv2 = [10000., np.inf]
+    mvs = [mv1, mv2]
+
+    @pytest.mark.parametrize("dist, mv_ex",
+                             list(zip(dists, mvs)))
+    @pytest.mark.thread_unsafe
+    def test_basic(self, dist, mv_ex):
+        rng = SimpleRatioUniforms(dist, mode=dist.mode, random_state=42)
+        check_cont_samples(rng, dist, mv_ex)
+        rng = SimpleRatioUniforms(dist, mode=dist.mode,
+                                  cdf_at_mode=dist.cdf(dist.mode),
+                                  random_state=42)
+        check_cont_samples(rng, dist, mv_ex)
+
+    # test domains with inf + nan in them. need to write a custom test for
+    # this because not all methods support infinite tails.
+    @pytest.mark.parametrize("domain, err, msg", inf_nan_domains)
+    def test_inf_nan_domains(self, domain, err, msg):
+        with pytest.raises(err, match=msg):
+            SimpleRatioUniforms(StandardNormal(), domain=domain)
+
+    def test_bad_args(self):
+        # pdf_area < 0
+        with pytest.raises(ValueError, match=r"`pdf_area` must be > 0"):
+            SimpleRatioUniforms(StandardNormal(), mode=0, pdf_area=-1)
+
+
+class TestRatioUniforms:
+    def test_rv_generation(self):
+        # use KS test to check distribution of rvs
+        # normal distribution
+        f = stats.norm.pdf
+        v = np.sqrt(f(np.sqrt(2))) * np.sqrt(2)
+        u = np.sqrt(f(0))
+        gen = RatioUniforms(f, umax=u, vmin=-v, vmax=v, random_state=12345)
+        assert_equal(stats.kstest(gen.rvs(2500), 'norm')[1] > 0.25, True)
+
+        # exponential distribution
+        gen = RatioUniforms(lambda x: np.exp(-x), umax=1,
+                            vmin=0, vmax=2*np.exp(-1), random_state=12345)
+        assert_equal(stats.kstest(gen.rvs(1000), 'expon')[1] > 0.25, True)
+
+    def test_shape(self):
+        # test shape of return value depending on size parameter
+        f = stats.norm.pdf
+        v = np.sqrt(f(np.sqrt(2))) * np.sqrt(2)
+        u = np.sqrt(f(0))
+
+        gen1 = RatioUniforms(f, umax=u, vmin=-v, vmax=v, random_state=1234)
+        gen2 = RatioUniforms(f, umax=u, vmin=-v, vmax=v, random_state=1234)
+        gen3 = RatioUniforms(f, umax=u, vmin=-v, vmax=v, random_state=1234)
+        r1, r2, r3 = gen1.rvs(3), gen2.rvs((3,)), gen3.rvs((3, 1))
+        assert_equal(r1, r2)
+        assert_equal(r2, r3.flatten())
+        assert_equal(r1.shape, (3,))
+        assert_equal(r3.shape, (3, 1))
+
+        gen4 = RatioUniforms(f, umax=u, vmin=-v, vmax=v, random_state=12)
+        gen5 = RatioUniforms(f, umax=u, vmin=-v, vmax=v, random_state=12)
+        r4, r5 = gen4.rvs(size=(3, 3, 3)), gen5.rvs(size=27)
+        assert_equal(r4.flatten(), r5)
+        assert_equal(r4.shape, (3, 3, 3))
+
+        gen6 = RatioUniforms(f, umax=u, vmin=-v, vmax=v, random_state=1234)
+        gen7 = RatioUniforms(f, umax=u, vmin=-v, vmax=v, random_state=1234)
+        gen8 = RatioUniforms(f, umax=u, vmin=-v, vmax=v, random_state=1234)
+        r6, r7, r8 = gen6.rvs(), gen7.rvs(1), gen8.rvs((1,))
+        assert_equal(r6, r7)
+        assert_equal(r7, r8)
+
+    def test_random_state(self):
+        f = stats.norm.pdf
+        v = np.sqrt(f(np.sqrt(2))) * np.sqrt(2)
+        umax = np.sqrt(f(0))
+        gen1 = RatioUniforms(f, umax=umax, vmin=-v, vmax=v, random_state=1234)
+        r1 = gen1.rvs(10)
+        rng = np.random.RandomState(1234)
+        gen2 = RatioUniforms(f, umax=umax, vmin=-v, vmax=v, random_state=rng)
+        r2 = gen2.rvs(10)
+        assert_equal(r1, r2)
+
+    def test_exceptions(self):
+        f = stats.norm.pdf
+        # need vmin < vmax
+        with assert_raises(ValueError, match="vmin must be smaller than vmax"):
+            RatioUniforms(pdf=f, umax=1, vmin=3, vmax=1)
+        with assert_raises(ValueError, match="vmin must be smaller than vmax"):
+            RatioUniforms(pdf=f, umax=1, vmin=1, vmax=1)
+        # need umax > 0
+        with assert_raises(ValueError, match="umax must be positive"):
+            RatioUniforms(pdf=f, umax=-1, vmin=1, vmax=3)
+        with assert_raises(ValueError, match="umax must be positive"):
+            RatioUniforms(pdf=f, umax=0, vmin=1, vmax=3)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/test_sensitivity_analysis.py b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_sensitivity_analysis.py
new file mode 100644
index 0000000000000000000000000000000000000000..9c8d53040380808c03358b905878cc4a8b9b9679
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_sensitivity_analysis.py
@@ -0,0 +1,310 @@
+import numpy as np
+from numpy.testing import assert_allclose, assert_array_less
+import pytest
+
+from scipy import stats
+from scipy.stats import sobol_indices
+from scipy.stats._resampling import BootstrapResult
+from scipy.stats._sensitivity_analysis import (
+    BootstrapSobolResult, f_ishigami, sample_AB, sample_A_B
+)
+
+
+@pytest.fixture(scope='session')
+def ishigami_ref_indices():
+    """Reference values for Ishigami from Saltelli2007.
+
+    Chapter 4, exercise 5 pages 179-182.
+    """
+    a = 7.
+    b = 0.1
+
+    var = 0.5 + a**2/8 + b*np.pi**4/5 + b**2*np.pi**8/18
+    v1 = 0.5 + b*np.pi**4/5 + b**2*np.pi**8/50
+    v2 = a**2/8
+    v3 = 0
+    v12 = 0
+    # v13: mistake in the book, see other derivations e.g. in 10.1002/nme.4856
+    v13 = b**2*np.pi**8*8/225
+    v23 = 0
+
+    s_first = np.array([v1, v2, v3])/var
+    s_second = np.array([
+        [0., 0., v13],
+        [v12, 0., v23],
+        [v13, v23, 0.]
+    ])/var
+    s_total = s_first + s_second.sum(axis=1)
+
+    return s_first, s_total
+
+
+def f_ishigami_vec(x):
+    """Output of shape (2, n)."""
+    res = f_ishigami(x)
+    return res, res
+
+
+class TestSobolIndices:
+
+    dists = [
+        stats.uniform(loc=-np.pi, scale=2*np.pi)  # type: ignore[attr-defined]
+    ] * 3
+
+    def test_sample_AB(self):
+        # (d, n)
+        A = np.array(
+            [[1, 4, 7, 10],
+             [2, 5, 8, 11],
+             [3, 6, 9, 12]]
+        )
+        B = A + 100
+        # (d, d, n)
+        ref = np.array(
+            [[[101, 104, 107, 110],
+              [2, 5, 8, 11],
+              [3, 6, 9, 12]],
+             [[1, 4, 7, 10],
+              [102, 105, 108, 111],
+              [3, 6, 9, 12]],
+             [[1, 4, 7, 10],
+              [2, 5, 8, 11],
+              [103, 106, 109, 112]]]
+        )
+        AB = sample_AB(A=A, B=B)
+        assert_allclose(AB, ref)
+
+    @pytest.mark.xslow
+    @pytest.mark.xfail_on_32bit("Can't create large array for test")
+    @pytest.mark.parametrize(
+        'func',
+        [f_ishigami, pytest.param(f_ishigami_vec, marks=pytest.mark.slow)],
+        ids=['scalar', 'vector']
+    )
+    def test_ishigami(self, ishigami_ref_indices, func):
+        rng = np.random.default_rng(28631265345463262246170309650372465332)
+        res = sobol_indices(
+            func=func, n=4096,
+            dists=self.dists,
+            rng=rng
+        )
+
+        if func.__name__ == 'f_ishigami_vec':
+            ishigami_ref_indices = [
+                    [ishigami_ref_indices[0], ishigami_ref_indices[0]],
+                    [ishigami_ref_indices[1], ishigami_ref_indices[1]]
+            ]
+
+        assert_allclose(res.first_order, ishigami_ref_indices[0], atol=1e-2)
+        assert_allclose(res.total_order, ishigami_ref_indices[1], atol=1e-2)
+
+        assert res._bootstrap_result is None
+        bootstrap_res = res.bootstrap(n_resamples=99)
+        assert isinstance(bootstrap_res, BootstrapSobolResult)
+        assert isinstance(res._bootstrap_result, BootstrapResult)
+
+        assert res._bootstrap_result.confidence_interval.low.shape[0] == 2
+        assert res._bootstrap_result.confidence_interval.low[1].shape \
+               == res.first_order.shape
+
+        assert bootstrap_res.first_order.confidence_interval.low.shape \
+               == res.first_order.shape
+        assert bootstrap_res.total_order.confidence_interval.low.shape \
+               == res.total_order.shape
+
+        assert_array_less(
+            bootstrap_res.first_order.confidence_interval.low, res.first_order
+        )
+        assert_array_less(
+            res.first_order, bootstrap_res.first_order.confidence_interval.high
+        )
+        assert_array_less(
+            bootstrap_res.total_order.confidence_interval.low, res.total_order
+        )
+        assert_array_less(
+            res.total_order, bootstrap_res.total_order.confidence_interval.high
+        )
+
+        # call again to use previous results and change a param
+        assert isinstance(
+            res.bootstrap(confidence_level=0.9, n_resamples=99),
+            BootstrapSobolResult
+        )
+        assert isinstance(res._bootstrap_result, BootstrapResult)
+
+    def test_func_dict(self, ishigami_ref_indices):
+        rng = np.random.default_rng(28631265345463262246170309650372465332)
+        n = 4096
+        dists = [
+            stats.uniform(loc=-np.pi, scale=2*np.pi),
+            stats.uniform(loc=-np.pi, scale=2*np.pi),
+            stats.uniform(loc=-np.pi, scale=2*np.pi)
+        ]
+
+        A, B = sample_A_B(n=n, dists=dists, rng=rng)
+        AB = sample_AB(A=A, B=B)
+
+        func = {
+            'f_A': f_ishigami(A).reshape(1, -1),
+            'f_B': f_ishigami(B).reshape(1, -1),
+            'f_AB': f_ishigami(AB).reshape((3, 1, -1))
+        }
+
+        # preserve use of old random_state during SPEC 7 transition
+        res = sobol_indices(
+            func=func, n=n,
+            dists=dists,
+            rng=rng
+        )
+        assert_allclose(res.first_order, ishigami_ref_indices[0], atol=1e-2)
+
+        res = sobol_indices(
+            func=func, n=n,
+            rng=rng
+        )
+        assert_allclose(res.first_order, ishigami_ref_indices[0], atol=1e-2)
+        # Ideally should be exactly equal but since f_ishigami
+        # uses floating point operations, so exact equality
+        # might not be possible (due to flakiness in computation).
+        # So, assert_allclose is used with default parameters
+        # Regression test for https://github.com/scipy/scipy/issues/21383
+        assert_allclose(f_ishigami(A).reshape(1, -1), func['f_A'])
+        assert_allclose(f_ishigami(B).reshape(1, -1), func['f_B'])
+        assert_allclose(f_ishigami(AB).reshape((3, 1, -1)), func['f_AB'])
+
+    def test_method(self, ishigami_ref_indices):
+        def jansen_sobol(f_A, f_B, f_AB):
+            """Jansen for S and Sobol' for St.
+
+            From Saltelli2010, table 2 formulations (c) and (e)."""
+            var = np.var([f_A, f_B], axis=(0, -1))
+
+            s = (var - 0.5*np.mean((f_B - f_AB)**2, axis=-1)) / var
+            st = np.mean(f_A*(f_A - f_AB), axis=-1) / var
+
+            return s.T, st.T
+
+        rng = np.random.default_rng(28631265345463262246170309650372465332)
+        res = sobol_indices(
+            func=f_ishigami, n=4096,
+            dists=self.dists,
+            method=jansen_sobol,
+            rng=rng
+        )
+
+        assert_allclose(res.first_order, ishigami_ref_indices[0], atol=1e-2)
+        assert_allclose(res.total_order, ishigami_ref_indices[1], atol=1e-2)
+
+        def jansen_sobol_typed(
+            f_A: np.ndarray, f_B: np.ndarray, f_AB: np.ndarray
+        ) -> tuple[np.ndarray, np.ndarray]:
+            return jansen_sobol(f_A, f_B, f_AB)
+
+        _ = sobol_indices(
+            func=f_ishigami, n=8,
+            dists=self.dists,
+            method=jansen_sobol_typed,
+            rng=rng
+        )
+
+    def test_normalization(self, ishigami_ref_indices):
+        rng = np.random.default_rng(28631265345463262246170309650372465332)
+        res = sobol_indices(
+            func=lambda x: f_ishigami(x) + 1000, n=4096,
+            dists=self.dists,
+            rng=rng
+        )
+
+        assert_allclose(res.first_order, ishigami_ref_indices[0], atol=1e-2)
+        assert_allclose(res.total_order, ishigami_ref_indices[1], atol=1e-2)
+
+    def test_constant_function(self, ishigami_ref_indices):
+
+        def f_ishigami_vec_const(x):
+            """Output of shape (3, n)."""
+            res = f_ishigami(x)
+            return res, res * 0 + 10, res
+
+        rng = np.random.default_rng(28631265345463262246170309650372465332)
+        res = sobol_indices(
+            func=f_ishigami_vec_const, n=4096,
+            dists=self.dists,
+            rng=rng
+        )
+
+        ishigami_vec_indices = [
+                [ishigami_ref_indices[0], [0, 0, 0], ishigami_ref_indices[0]],
+                [ishigami_ref_indices[1], [0, 0, 0], ishigami_ref_indices[1]]
+        ]
+
+        assert_allclose(res.first_order, ishigami_vec_indices[0], atol=1e-2)
+        assert_allclose(res.total_order, ishigami_vec_indices[1], atol=1e-2)
+
+    @pytest.mark.xfail_on_32bit("Can't create large array for test")
+    def test_more_converged(self, ishigami_ref_indices):
+        rng = np.random.default_rng(28631265345463262246170309650372465332)
+        res = sobol_indices(
+            func=f_ishigami, n=2**19,  # 524288
+            dists=self.dists,
+            rng=rng
+        )
+
+        assert_allclose(res.first_order, ishigami_ref_indices[0], atol=1e-4)
+        assert_allclose(res.total_order, ishigami_ref_indices[1], atol=1e-4)
+
+    def test_raises(self):
+
+        message = r"Each distribution in `dists` must have method `ppf`"
+        with pytest.raises(ValueError, match=message):
+            sobol_indices(n=0, func=f_ishigami, dists="uniform")
+
+        with pytest.raises(ValueError, match=message):
+            sobol_indices(n=0, func=f_ishigami, dists=[lambda x: x])
+
+        message = r"The balance properties of Sobol'"
+        with pytest.raises(ValueError, match=message):
+            sobol_indices(n=7, func=f_ishigami, dists=[stats.uniform()])
+
+        with pytest.raises(ValueError, match=message):
+            sobol_indices(n=4.1, func=f_ishigami, dists=[stats.uniform()])
+
+        message = r"'toto' is not a valid 'method'"
+        with pytest.raises(ValueError, match=message):
+            sobol_indices(n=0, func=f_ishigami, method='toto')
+
+        message = r"must have the following signature"
+        with pytest.raises(ValueError, match=message):
+            sobol_indices(n=0, func=f_ishigami, method=lambda x: x)
+
+        message = r"'dists' must be defined when 'func' is a callable"
+        with pytest.raises(ValueError, match=message):
+            sobol_indices(n=0, func=f_ishigami)
+
+        def func_wrong_shape_output(x):
+            return x.reshape(-1, 1)
+
+        message = r"'func' output should have a shape"
+        with pytest.raises(ValueError, match=message):
+            sobol_indices(
+                n=2, func=func_wrong_shape_output, dists=[stats.uniform()]
+            )
+
+        message = r"When 'func' is a dictionary"
+        with pytest.raises(ValueError, match=message):
+            sobol_indices(
+                n=2, func={'f_A': [], 'f_AB': []}, dists=[stats.uniform()]
+            )
+
+        with pytest.raises(ValueError, match=message):
+            # f_B malformed
+            sobol_indices(
+                n=2,
+                func={'f_A': [1, 2], 'f_B': [3], 'f_AB': [5, 6, 7, 8]},
+            )
+
+        with pytest.raises(ValueError, match=message):
+            # f_AB malformed
+            sobol_indices(
+                n=2,
+                func={'f_A': [1, 2], 'f_B': [3, 4], 'f_AB': [5, 6, 7]},
+            )
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/test_stats.py b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_stats.py
new file mode 100644
index 0000000000000000000000000000000000000000..0ac5db382f04d249b6c05d4f0e940fe75d26486a
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_stats.py
@@ -0,0 +1,9890 @@
+""" Test functions for stats module
+
+    WRITTEN BY LOUIS LUANGKESORN <lluang@yahoo.com> FOR THE STATS MODULE
+    BASED ON WILKINSON'S STATISTICS QUIZ
+    https://www.stanford.edu/~clint/bench/wilk.txt
+
+    Additional tests by a host of SciPy developers.
+"""
+import math
+import os
+import warnings
+from collections import namedtuple
+from itertools import product
+import hypothesis.extra.numpy as npst
+import hypothesis
+import contextlib
+
+from numpy.testing import (assert_, assert_equal,
+                           assert_almost_equal, assert_array_almost_equal,
+                           assert_array_equal, assert_approx_equal,
+                           assert_allclose)
+import pytest
+from pytest import raises as assert_raises
+from numpy import array, arange, power
+import numpy as np
+
+import scipy.stats as stats
+from scipy.stats._ksstats import kolmogn
+from scipy.special._testutils import FuncData
+from scipy import optimize, special
+from .common_tests import check_named_results
+from scipy.stats._axis_nan_policy import (SmallSampleWarning,
+                                          too_small_nd_omit, too_small_nd_not_omit,
+                                          too_small_1d_omit, too_small_1d_not_omit)
+from scipy.stats._stats_py import (_chk_asarray, _moment,
+                                   LinregressResult, _xp_mean, _xp_var, _SimpleChi2)
+from scipy._lib._util import AxisError
+from scipy.conftest import skip_xp_invalid_arg
+from scipy._lib._array_api import (array_namespace, eager_warns, is_lazy_array,
+                                   is_numpy, is_torch, xp_default_dtype, xp_size,
+                                   SCIPY_ARRAY_API, make_xp_test_case, xp_ravel,
+                                   xp_swapaxes, xp_result_type, is_jax, is_cupy,
+                                   xp_copy, xp_promote, make_xp_pytest_param)
+from scipy._lib._array_api_no_0d import xp_assert_close, xp_assert_equal, xp_assert_less
+import scipy._external.array_api_extra as xpx
+from scipy._lib._util import _apply_over_batch
+
+
+lazy_xp_modules = [stats]
+skip_xp_backends = pytest.mark.skip_xp_backends
+xfail_xp_backends = pytest.mark.xfail_xp_backends
+
+""" Numbers in docstrings beginning with 'W' refer to the section numbers
+    and headings found in the STATISTICS QUIZ of Leland Wilkinson.  These are
+    considered to be essential functionality.  True testing and
+    evaluation of a statistics package requires use of the
+    NIST Statistical test data.  See McCoullough(1999) Assessing The Reliability
+    of Statistical Software for a test methodology and its
+    implementation in testing SAS, SPSS, and S-Plus
+"""
+
+#  Datasets
+#  These data sets are from the nasty.dat sets used by Wilkinson
+#  For completeness, I should write the relevant tests and count them as failures
+#  Somewhat acceptable, since this is still beta software.  It would count as a
+#  good target for 1.0 status
+X = array([1,2,3,4,5,6,7,8,9], float)
+ZERO = array([0,0,0,0,0,0,0,0,0], float)
+BIG = array([99999991,99999992,99999993,99999994,99999995,99999996,99999997,
+             99999998,99999999], float)
+LITTLE = array([0.99999991,0.99999992,0.99999993,0.99999994,0.99999995,0.99999996,
+                0.99999997,0.99999998,0.99999999], float)
+HUGE = array([1e+12,2e+12,3e+12,4e+12,5e+12,6e+12,7e+12,8e+12,9e+12], float)
+TINY = array([1e-12,2e-12,3e-12,4e-12,5e-12,6e-12,7e-12,8e-12,9e-12], float)
+ROUND = array([0.5,1.5,2.5,3.5,4.5,5.5,6.5,7.5,8.5], float)
+
+
+class TestTrimmedStats:
+    # TODO: write these tests to handle missing values properly
+    dprec = np.finfo(np.float64).precision
+
+    @make_xp_test_case(stats.tmean)
+    def test_tmean(self, xp):
+        default_dtype = xp_default_dtype(xp)
+        x = xp.asarray(X, dtype=default_dtype)
+
+        y = stats.tmean(x, (2, 8), (True, True))
+        xp_assert_close(y, xp.asarray(5.0))
+
+        y1 = stats.tmean(x, limits=(2, 8), inclusive=(False, False))
+        y2 = stats.tmean(x, limits=None)
+        xp_assert_close(y1, y2)
+
+        x_2d = xp.reshape(xp.arange(63.), (9, 7))
+        y = stats.tmean(x_2d, axis=None)
+        xp_assert_close(y, xp.mean(x_2d))
+
+        y = stats.tmean(x_2d, axis=0)
+        xp_assert_close(y, xp.mean(x_2d, axis=0))
+
+        y = stats.tmean(x_2d, axis=1)
+        xp_assert_close(y, xp.mean(x_2d, axis=1))
+
+        y = stats.tmean(x_2d, limits=(2, 61), axis=None)
+        xp_assert_close(y, xp.asarray(31.5))
+
+        y = stats.tmean(x_2d, limits=(2, 21), axis=0)
+        y_true = [14, 11.5, 9, 10, 11, 12, 13]
+        xp_assert_close(y, xp.asarray(y_true))
+
+        y = stats.tmean(x_2d, limits=(2, 21), inclusive=(True, False), axis=0)
+        y_true = [10.5, 11.5, 9, 10, 11, 12, 13]
+        xp_assert_close(y, xp.asarray(y_true))
+
+        x_2d_with_nan = xpx.at(x_2d)[-1, -3:].set(xp.nan, copy=True)
+        y = stats.tmean(x_2d_with_nan, limits=(1, 13), axis=0)
+        y_true = [7, 4.5, 5.5, 6.5, xp.nan, xp.nan, xp.nan]
+        xp_assert_close(y, xp.asarray(y_true))
+
+        y = stats.tmean(x_2d, limits=(2, 21), axis=1)
+        y_true = [4, 10, 17, 21, xp.nan, xp.nan, xp.nan, xp.nan, xp.nan]
+        xp_assert_close(y, xp.asarray(y_true))
+
+        y = stats.tmean(x_2d, limits=(2, 21),
+                        inclusive=(False, True), axis=1)
+        y_true = [4.5, 10, 17, 21, xp.nan, xp.nan, xp.nan, xp.nan, xp.nan]
+        xp_assert_close(y, xp.asarray(y_true))
+
+    @make_xp_test_case(stats.tvar)
+    @pytest.mark.filterwarnings(
+        "ignore:invalid value encountered in divide:RuntimeWarning:dask"
+    )
+    def test_tvar(self, xp):
+        x = xp.asarray(X.tolist())  # use default dtype of xp
+
+        y = stats.tvar(x, limits=(2, 8), inclusive=(True, True))
+        xp_assert_close(y, xp.asarray(4.6666666666666661))
+
+        y = stats.tvar(x, limits=None)
+        xp_assert_close(y, xp.var(x, correction=1))
+
+        x_2d = xp.reshape(xp.arange(63.), (9, 7))
+        y = stats.tvar(x_2d, axis=None)
+        xp_assert_close(y, xp.var(x_2d, correction=1))
+
+        y = stats.tvar(x_2d, axis=0)
+        xp_assert_close(y, xp.full((7,), 367.5))
+
+        y = stats.tvar(x_2d, axis=1)
+        xp_assert_close(y, xp.full((9,), 4.66666667))
+
+        # Limiting some values along one axis
+        y = stats.tvar(x_2d, limits=(1, 5), axis=1, inclusive=(True, True))
+        xp_assert_close(y[0], xp.asarray(2.5))
+
+        # Limiting all values along one axis
+        y = stats.tvar(x_2d, limits=(0, 6), axis=1, inclusive=(True, True))
+        xp_assert_close(y[0], xp.asarray(4.666666666666667))
+        xp_assert_equal(y[1], xp.asarray(xp.nan))
+
+    @make_xp_test_case(stats.tstd)
+    def test_tstd(self, xp):
+        x = xp.asarray(X.tolist())  # use default dtype of xp
+
+        y = stats.tstd(x, (2, 8), (True, True))
+        xp_assert_close(y, xp.asarray(2.1602468994692865))
+
+        y = stats.tstd(x, limits=None)
+        xp_assert_close(y, xp.std(x, correction=1))
+
+    @make_xp_test_case(stats.tmin)
+    def test_tmin(self, xp):
+        x = xp.arange(10.)
+        xp_assert_equal(stats.tmin(x), xp.asarray(0.))
+        xp_assert_equal(stats.tmin(x, lowerlimit=0), xp.asarray(0.))
+        xp_assert_equal(stats.tmin(x, lowerlimit=0, inclusive=False), xp.asarray(1.))
+
+        x = xp.reshape(x, (5, 2))
+        xp_assert_equal(stats.tmin(x, lowerlimit=0, inclusive=False),
+                        xp.asarray([2., 1.]))
+        xp_assert_equal(stats.tmin(x, axis=1), xp.asarray([0., 2., 4., 6., 8.]))
+        xp_assert_equal(stats.tmin(x, axis=None), xp.asarray(0.))
+
+        x = xpx.at(xp.arange(10.), 9).set(xp.nan)
+        xp_assert_equal(stats.tmin(x), xp.asarray(xp.nan))
+
+        # check that if a full slice is masked, the output returns a
+        # nan instead of a garbage value.
+        x = xp.reshape(xp.arange(16), (4, 4))
+        res = stats.tmin(x, lowerlimit=4, axis=1)
+        xp_assert_equal(res, xp.asarray([np.nan, 4, 8, 12]))
+
+    @pytest.mark.parametrize('tfun', [stats.tmin, stats.tmax])
+    def test_tmin_tmax_scalar_input(self, tfun):  # scalar inputs are NumPy only
+        assert_equal(tfun(4), 4)
+
+    @skip_xp_backends(eager_only=True, reason="lazy -> reduced nan_policy capabilities")
+    @pytest.mark.parametrize('tfun, ref', [make_xp_pytest_param(stats.tmin, 0.),
+                                           make_xp_pytest_param(stats.tmax, 9.)])
+    def test_tmin_tmax_nanpolicy(self, tfun, ref, xp):
+        x = xp.arange(10.)
+        x[8] = xp.nan
+        xp_assert_equal(tfun(x, nan_policy='omit'), xp.asarray(ref))
+        msg = "The input contains nan values"
+        with assert_raises(ValueError, match=msg):
+            tfun(x, nan_policy='raise')
+        msg = "nan_policy must be one of..."
+        with assert_raises(ValueError, match=msg):
+            tfun(x, nan_policy='foobar')
+
+    @make_xp_test_case(stats.tmax)
+    def test_tmax(self, xp):
+        x = xp.arange(10.)
+        xp_assert_equal(stats.tmax(x), xp.asarray(9.))
+        xp_assert_equal(stats.tmax(x, upperlimit=9), xp.asarray(9.))
+        xp_assert_equal(stats.tmax(x, upperlimit=9, inclusive=False), xp.asarray(8.))
+
+        x = xp.reshape(x, (5, 2))
+        xp_assert_equal(stats.tmax(x, upperlimit=9, inclusive=False),
+                        xp.asarray([8., 7.]))
+        xp_assert_equal(stats.tmax(x, axis=1), xp.asarray([1., 3., 5., 7., 9.]))
+        xp_assert_equal(stats.tmax(x, axis=None), xp.asarray(9.))
+
+        x = xpx.at(xp.arange(10.), 9).set(xp.nan)
+        xp_assert_equal(stats.tmax(x), xp.asarray(xp.nan))
+
+        # check that if a full slice is masked, the output returns a
+        # nan instead of a garbage value.
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", "All-NaN slice encountered", RuntimeWarning)
+            x = xp.reshape(xp.arange(16), (4, 4))
+            res = stats.tmax(x, upperlimit=11, axis=1)
+            xp_assert_equal(res, xp.asarray([3, 7, 11, np.nan]))
+
+    @make_xp_test_case(stats.tmin, stats.tmax)
+    def test_tmin_tmax_int_dtype(self, xp):
+        x = xp.reshape(xp.arange(10, dtype=xp.int16), (2, 5)).T
+
+        # When tmin/tmax don't need to inject any NaNs,
+        # retain the input dtype. Dask/JAX can't inspect
+        # the data so they always return float.
+        expect_dtype = xp_default_dtype(xp) if is_lazy_array(x) else x.dtype
+        xp_assert_equal(stats.tmin(x), xp.asarray([0, 5], dtype=expect_dtype))
+        xp_assert_equal(stats.tmax(x), xp.asarray([4, 9], dtype=expect_dtype))
+
+        # When they do inject NaNs, all backends behave the same.
+        xp_assert_equal(stats.tmin(x, lowerlimit=6), xp.asarray([xp.nan, 6.]))
+        xp_assert_equal(stats.tmax(x, upperlimit=3), xp.asarray([3., xp.nan]))
+
+    @skip_xp_backends(eager_only=True, reason="Only with data-dependent output dtype")
+    @make_xp_test_case(stats.tmin, stats.tmax)
+    def test_gh_22626(self, xp):
+        # Test that `tmin`/`tmax` returns exact result with outrageously large integers
+        x = xp.arange(2**62, 2**62+10)
+        xp_assert_equal(stats.tmin(x[None, :]), x)
+        xp_assert_equal(stats.tmax(x[None, :]), x)
+
+    @make_xp_test_case(stats.tsem)
+    def test_tsem(self, xp):
+        x = xp.asarray(X.tolist())  # use default dtype of xp
+
+        y = stats.tsem(x, limits=(3, 8), inclusive=(False, True))
+        y_ref = xp.asarray([4., 5., 6., 7., 8.])
+        xp_assert_close(y, xp.std(y_ref, correction=1) / xp_size(y_ref)**0.5)
+        xp_assert_close(stats.tsem(x, limits=[-1, 10]), stats.tsem(x, limits=None))
+
+
+class TestPearsonrWilkinson:
+    """ W.II.D. Compute a correlation matrix on all the variables.
+
+        All the correlations, except for ZERO and MISS, should be exactly 1.
+        ZERO and MISS should have undefined or missing correlations with the
+        other variables.  The same should go for SPEARMAN correlations, if
+        your program has them.
+    """
+
+    def test_pXX(self):
+        y = stats.pearsonr(X,X)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_pXBIG(self):
+        y = stats.pearsonr(X,BIG)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_pXLITTLE(self):
+        y = stats.pearsonr(X,LITTLE)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_pXHUGE(self):
+        y = stats.pearsonr(X,HUGE)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_pXTINY(self):
+        y = stats.pearsonr(X,TINY)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_pXROUND(self):
+        y = stats.pearsonr(X,ROUND)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_pBIGBIG(self):
+        y = stats.pearsonr(BIG,BIG)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_pBIGLITTLE(self):
+        y = stats.pearsonr(BIG,LITTLE)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_pBIGHUGE(self):
+        y = stats.pearsonr(BIG,HUGE)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_pBIGTINY(self):
+        y = stats.pearsonr(BIG,TINY)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_pBIGROUND(self):
+        y = stats.pearsonr(BIG,ROUND)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_pLITTLELITTLE(self):
+        y = stats.pearsonr(LITTLE,LITTLE)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_pLITTLEHUGE(self):
+        y = stats.pearsonr(LITTLE,HUGE)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_pLITTLETINY(self):
+        y = stats.pearsonr(LITTLE,TINY)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_pLITTLEROUND(self):
+        y = stats.pearsonr(LITTLE,ROUND)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_pHUGEHUGE(self):
+        y = stats.pearsonr(HUGE,HUGE)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_pHUGETINY(self):
+        y = stats.pearsonr(HUGE,TINY)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_pHUGEROUND(self):
+        y = stats.pearsonr(HUGE,ROUND)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_pTINYTINY(self):
+        y = stats.pearsonr(TINY,TINY)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_pTINYROUND(self):
+        y = stats.pearsonr(TINY,ROUND)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_pROUNDROUND(self):
+        y = stats.pearsonr(ROUND,ROUND)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+
+@make_xp_test_case(stats.pearsonr)
+class TestPearsonr:
+    def test_pearsonr_result_attributes(self, xp):
+        res = stats.pearsonr(xp.asarray(X), xp.asarray(X))
+        attributes = ('correlation', 'pvalue')
+        check_named_results(res, attributes, xp=xp)
+        xp_assert_equal(res.correlation, res.statistic)
+
+    def test_r_almost_exactly_pos1(self, xp):
+        a = xp.arange(3.0)
+        r, prob = stats.pearsonr(a, a)
+
+        xp_assert_close(r, xp.asarray(1.0), atol=1e-15)
+        # With n = len(a) = 3, the error in prob grows like the
+        # square root of the error in r.
+        xp_assert_close(prob, xp.asarray(0.0), atol=np.sqrt(2*np.spacing(1.0)))
+
+    def test_r_almost_exactly_neg1(self, xp):
+        a = xp.arange(3.0)
+        r, prob = stats.pearsonr(a, -a)
+
+        xp_assert_close(r, xp.asarray(-1.0), atol=1e-15)
+        # With n = len(a) = 3, the error in prob grows like the
+        # square root of the error in r.
+        xp_assert_close(prob, xp.asarray(0.0), atol=np.sqrt(2*np.spacing(1.0)))
+
+    def test_basic(self, xp):
+        # A basic test, with a correlation coefficient
+        # that is not 1 or -1.
+        a = xp.asarray([-1, 0, 1])
+        b = xp.asarray([0, 0, 3])
+        r, prob = stats.pearsonr(a, b)
+        xp_assert_close(r, xp.asarray(3**0.5/2))
+        xp_assert_close(prob, xp.asarray(1/3))
+
+    def test_constant_input(self, xp):
+        # Zero variance input
+        # See https://github.com/scipy/scipy/issues/3728
+        x = xp.asarray([0.667, 0.667, 0.667])
+        y = xp.asarray([0.123, 0.456, 0.789])
+        msg = "An input array is constant"
+        with eager_warns(stats.ConstantInputWarning, match=msg, xp=xp):
+            r, p = stats.pearsonr(x, y)
+            xp_assert_close(r, xp.asarray(xp.nan))
+            xp_assert_close(p, xp.asarray(xp.nan))
+
+    @pytest.mark.parametrize('dtype', ['float32', 'float64'])
+    def test_near_constant_input(self, dtype, xp):
+        npdtype = getattr(np, dtype)
+        dtype = getattr(xp, dtype)
+        # Near constant input (but not constant):
+        x = xp.asarray([2, 2, 2 + np.spacing(2, dtype=npdtype)], dtype=dtype)
+        y = xp.asarray([3, 3, 3 + 6*np.spacing(3, dtype=npdtype)], dtype=dtype)
+        msg = "An input array is nearly constant; the computed"
+        with eager_warns(stats.NearConstantInputWarning, match=msg, xp=xp):
+            # r and p are garbage, so don't bother checking them in this case.
+            # (The exact value of r would be 1.)
+            stats.pearsonr(x, y)
+
+    def test_very_small_input_values(self, xp):
+        # Very small values in an input.  A naive implementation will
+        # suffer from underflow.
+        # See https://github.com/scipy/scipy/issues/9353
+        x = xp.asarray([0.004434375, 0.004756007, 0.003911996, 0.0038005, 0.003409971],
+                       dtype=xp.float64)
+        y = xp.asarray([2.48e-188, 7.41e-181, 4.09e-208, 2.08e-223, 2.66e-245],
+                       dtype=xp.float64)
+        r, p = stats.pearsonr(x, y)
+
+        # The expected values were computed using mpmath with 80 digits
+        # of precision.
+        xp_assert_close(r, xp.asarray(0.7272930540750450, dtype=xp.float64))
+        xp_assert_close(p, xp.asarray(0.1637805429533202, dtype=xp.float64))
+
+    def test_very_large_input_values(self, xp):
+        # Very large values in an input.  A naive implementation will
+        # suffer from overflow.
+        # See https://github.com/scipy/scipy/issues/8980
+        x = 1e90*xp.asarray([0, 0, 0, 1, 1, 1, 1], dtype=xp.float64)
+        y = 1e90*xp.arange(7, dtype=xp.float64)
+
+        r, p = stats.pearsonr(x, y)
+
+        # The expected values were computed using mpmath with 80 digits
+        # of precision.
+        xp_assert_close(r, xp.asarray(0.8660254037844386, dtype=xp.float64))
+        xp_assert_close(p, xp.asarray(0.011724811003954638, dtype=xp.float64))
+
+    def test_extremely_large_input_values(self, xp):
+        # Extremely large values in x and y.  These values would cause the
+        # product sigma_x * sigma_y to overflow if the two factors were
+        # computed independently.
+        x = xp.asarray([2.3e200, 4.5e200, 6.7e200, 8e200], dtype=xp.float64)
+        y = xp.asarray([1.2e199, 5.5e200, 3.3e201, 1.0e200], dtype=xp.float64)
+        r, p = stats.pearsonr(x, y)
+
+        # The expected values were computed using mpmath with 80 digits
+        # of precision.
+        xp_assert_close(r, xp.asarray(0.351312332103289, dtype=xp.float64))
+        xp_assert_close(p, xp.asarray(0.648687667896711, dtype=xp.float64))
+
+    @pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning:dask")
+    @pytest.mark.filterwarnings("ignore:divide by zero encountered:RuntimeWarning:dask")
+    def test_length_two_pos1(self, xp):
+        # Inputs with length 2.
+        # See https://github.com/scipy/scipy/issues/7730
+        x = xp.asarray([1., 2.])
+        y = xp.asarray([3., 5.])
+        res = stats.pearsonr(x, y)
+        r, p = res
+        one = xp.asarray(1.)
+        xp_assert_equal(r, one)
+        xp_assert_equal(p, one)
+        low, high = res.confidence_interval()
+        xp_assert_equal(low, -one)
+        xp_assert_equal(high, one)
+
+    @pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning:dask")
+    @pytest.mark.filterwarnings("ignore:divide by zero encountered:RuntimeWarning:dask")
+    def test_length_two_neg1(self, xp):
+        # Inputs with length 2.
+        # See https://github.com/scipy/scipy/issues/7730
+        x = xp.asarray([2., 1.])
+        y = xp.asarray([3., 5.])
+        res = stats.pearsonr(x, y)
+        r, p = res
+        one = xp.asarray(1.)
+        xp_assert_equal(r, -one)
+        xp_assert_equal(p, one)
+        low, high = res.confidence_interval()
+        xp_assert_equal(low, -one)
+        xp_assert_equal(high, one)
+
+    @pytest.mark.filterwarnings("ignore:invalid value encountered in divide")
+    def test_length_two_constant_input(self, xp):
+        # Zero variance input
+        # See https://github.com/scipy/scipy/issues/3728
+        # and https://github.com/scipy/scipy/issues/7730
+        x = xp.asarray([0.667, 0.667])
+        y = xp.asarray([0.123, 0.456])
+        msg = "An input array is constant"
+        with eager_warns(stats.ConstantInputWarning, match=msg, xp=xp):
+            r, p = stats.pearsonr(x, y)
+            xp_assert_close(r, xp.asarray(xp.nan))
+            xp_assert_close(p, xp.asarray(xp.nan))
+
+    # Expected values computed with R 3.6.2 cor.test, e.g.
+    # options(digits=16)
+    # x <- c(1, 2, 3, 4)
+    # y <- c(0, 1, 0.5, 1)
+    # cor.test(x, y, method = "pearson", alternative = "g")
+    # correlation coefficient and p-value for alternative='two-sided'
+    # calculated with mpmath agree to 16 digits.
+    @pytest.mark.parametrize('alternative, pval, rlow, rhigh, sign',
+            [('two-sided', 0.325800137536, -0.814938968841, 0.99230697523, 1),
+             ('less', 0.8370999312316, -1., 0.985600937290653, 1),
+             ('greater', 0.1629000687684, -0.6785654158217636, 1., 1),
+             ('two-sided', 0.325800137536, -0.992306975236, 0.81493896884, -1),
+             ('less', 0.1629000687684, -1.0, 0.6785654158217636, -1),
+             ('greater', 0.8370999312316, -0.985600937290653, 1.0, -1)])
+    def test_basic_example(self, alternative, pval, rlow, rhigh, sign, xp):
+        x = xp.asarray([1., 2., 3., 4.])
+        y = xp.asarray([0., 1., 0.5, 1.]) * sign
+        result = stats.pearsonr(x, y, alternative=alternative)
+        xp_assert_close(result.statistic, xp.asarray(0.6741998624632421*sign))
+        xp_assert_close(result.pvalue, xp.asarray(pval))
+        ci = result.confidence_interval()
+        xp_assert_close(ci.low, xp.asarray(rlow))
+        xp_assert_close(ci.high, xp.asarray(rhigh))
+
+    def test_negative_correlation_pvalue_gh17795(self, xp):
+        x = xp.arange(10.)
+        y = -x
+        test_greater = stats.pearsonr(x, y, alternative='greater')
+        test_less = stats.pearsonr(x, y, alternative='less')
+        xp_assert_close(test_greater.pvalue, xp.asarray(1.))
+        xp_assert_close(test_less.pvalue, xp.asarray(0.), atol=1e-20)
+
+    @pytest.mark.filterwarnings("ignore:divide by zero encountered:RuntimeWarning:dask")
+    def test_length3_r_exactly_negative_one(self, xp):
+        x = xp.asarray([1., 2., 3.])
+        y = xp.asarray([5., -4., -13.])
+        res = stats.pearsonr(x, y)
+
+        # The expected r and p are exact.
+        r, p = res
+        one = xp.asarray(1.0)
+        xp_assert_close(r, -one)
+        xp_assert_close(p, 0*one, atol=1e-7)
+        low, high = res.confidence_interval()
+        xp_assert_equal(low, -one)
+        xp_assert_equal(high, one)
+
+    def test_input_validation(self):
+        # Arraylike is np only
+        x = [1, 2, 3]
+        y = [4]
+        message = '`x` and `y` must have the same length along `axis`.'
+        with pytest.raises(ValueError, match=message):
+            stats.pearsonr(x, y)
+
+        x = [1, 2, 3]
+        y = [4, 5]
+        message = '`x` and `y` must be broadcastable.'
+        with pytest.raises(ValueError, match=message):
+            stats.pearsonr(x, y)
+
+        x = [1]
+        y = [2]
+        message = '`x` and `y` must have length at least 2.'
+        with pytest.raises(ValueError, match=message):
+            stats.pearsonr(x, y)
+
+        x = [-1j, -2j, -3.0j]
+        y = [-1j, -2j, -3.0j]
+        message = 'This function does not support complex data'
+        with pytest.raises(ValueError, match=message):
+            stats.pearsonr(x, y)
+
+        message = "`method` must be an instance of..."
+        with pytest.raises(ValueError, match=message):
+            stats.pearsonr([1, 2], [3, 4], method="asymptotic")
+
+        res = stats.pearsonr([1, 2], [3, 4])
+        with pytest.raises(ValueError, match=message):
+            res.confidence_interval(method="exact")
+
+    @pytest.mark.fail_slow(10)
+    @pytest.mark.xfail_on_32bit("Monte Carlo method needs > a few kB of memory")
+    @pytest.mark.parametrize('alternative', ('less', 'greater', 'two-sided'))
+    @pytest.mark.parametrize('method_name',
+                             ('permutation', 'monte_carlo', 'monte_carlo2'))
+    def test_resampling_pvalue(self, method_name, alternative):
+        rng = np.random.default_rng(24623935790378923)
+        size = (2, 100) if method_name == 'permutation' else (2, 1000)
+        x = rng.normal(size=size)
+        y = rng.normal(size=size)
+        methods = {'permutation': stats.PermutationMethod(rng=rng),
+                   'monte_carlo': stats.MonteCarloMethod(rvs=(rng.normal,)*2),
+                   'monte_carlo2': stats.MonteCarloMethod(rng=1294)}
+        method = methods[method_name]
+        res = stats.pearsonr(x, y, alternative=alternative, method=method, axis=-1)
+        ref = stats.pearsonr(x, y, alternative=alternative, axis=-1)
+        assert_allclose(res.statistic, ref.statistic, rtol=1e-15)
+        assert_allclose(res.pvalue, ref.pvalue, rtol=1e-2, atol=1e-3)
+
+        if method_name == 'monte_carlo2':
+            method = stats.MonteCarloMethod(rng=1294)
+            res2 = stats.pearsonr(x, y, alternative=alternative, method=method, axis=-1)
+            assert_equal(res2.statistic, res.statistic)
+            assert_equal(res2.pvalue, res.pvalue)
+
+    @pytest.mark.slow
+    @pytest.mark.parametrize('alternative', ('less', 'greater', 'two-sided'))
+    def test_bootstrap_ci(self, alternative):
+        rng = np.random.default_rng(2462935790378923)
+        x = rng.normal(size=(2, 100))
+        y = rng.normal(size=(2, 100))
+        res = stats.pearsonr(x, y, alternative=alternative, axis=-1)
+
+        # preserve use of old random_state during SPEC 7 transition
+        rng = np.random.default_rng(724358723498249852)
+        method = stats.BootstrapMethod(random_state=rng)
+        res_ci = res.confidence_interval(method=method)
+        ref_ci = res.confidence_interval()
+        assert_allclose(res_ci, ref_ci, atol=1.5e-2)
+
+        # `rng` is the new argument name`
+        rng = np.random.default_rng(724358723498249852)
+        method = stats.BootstrapMethod(rng=rng)
+        res_ci2 = res.confidence_interval(method=method)
+        assert_allclose(res_ci2, res_ci)
+
+    @pytest.mark.parametrize('axis', [0, 1])
+    def test_axis01(self, axis):
+        rng = np.random.default_rng(38572345825)
+        shape = (9, 10)
+        x, y = rng.normal(size=(2,) + shape)
+        res = stats.pearsonr(x, y, axis=axis)
+        ci = res.confidence_interval()
+        if axis == 0:
+            x, y = x.T, y.T
+        for i in range(x.shape[0]):
+            res_i = stats.pearsonr(x[i], y[i])
+            ci_i = res_i.confidence_interval()
+            assert_allclose(res.statistic[i], res_i.statistic)
+            assert_allclose(res.pvalue[i], res_i.pvalue)
+            assert_allclose(ci.low[i], ci_i.low)
+            assert_allclose(ci.high[i], ci_i.high)
+
+    def test_axis_None(self):
+        rng = np.random.default_rng(38572345825)
+        shape = (9, 10)
+        x, y = rng.normal(size=(2,) + shape)
+        res = stats.pearsonr(x, y, axis=None)
+        ci = res.confidence_interval()
+        ref = stats.pearsonr(x.ravel(), y.ravel())
+        ci_ref = ref.confidence_interval()
+        assert_allclose(res.statistic, ref.statistic)
+        assert_allclose(res.pvalue, ref.pvalue)
+        assert_allclose(ci, ci_ref)
+
+    def test_nd_input_validation(self, xp):
+        x = y = xp.ones((2, 5))
+        message = '`axis` must be an integer.'
+        with pytest.raises(ValueError, match=message):
+            stats.pearsonr(x, y, axis=1.5)
+
+        message = '`x` and `y` must have the same length along `axis`'
+        with pytest.raises(ValueError, match=message):
+            stats.pearsonr(x, xp.ones((2, 1)), axis=1)
+
+        message = '`x` and `y` must have length at least 2.'
+        with pytest.raises(ValueError, match=message):
+            stats.pearsonr(xp.ones((2, 1)), xp.ones((2, 1)), axis=1)
+
+        message = '`x` and `y` must be broadcastable.'
+        with pytest.raises(ValueError, match=message):
+            stats.pearsonr(x, xp.ones((3, 5)), axis=1)
+
+        message = '`method` must be `None` if arguments are not NumPy arrays.'
+        if not is_numpy(xp):
+            x = xp.arange(10)
+            with pytest.raises(ValueError, match=message):
+                stats.pearsonr(x, x, method=stats.PermutationMethod())
+
+    @pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning:dask")
+    @pytest.mark.filterwarnings("ignore:divide by zero encountered:RuntimeWarning:dask")
+    def test_nd_special_cases(self, xp):
+        rng = np.random.default_rng(34989235492245)
+
+        x0, y0 = rng.random((4, 5)), rng.random((4, 5))
+        x0[0, ...] = 1
+        y0[1, ...] = 2
+        x, y = xp.asarray(x0), xp.asarray(y0)
+        message = 'An input array is constant'
+        with eager_warns(stats.ConstantInputWarning, match=message, xp=xp):
+            res = stats.pearsonr(x, y, axis=1)
+            ci = res.confidence_interval()
+            nans = xp.asarray([xp.nan, xp.nan], dtype=xp.float64)
+            xp_assert_equal(res.statistic[0:2], nans)
+            xp_assert_equal(res.pvalue[0:2], nans)
+            xp_assert_equal(ci.low[0:2], nans)
+            xp_assert_equal(ci.high[0:2], nans)
+            assert xp.all(xp.isfinite(res.statistic[2:]))
+            assert xp.all(xp.isfinite(res.pvalue[2:]))
+            assert xp.all(xp.isfinite(ci.low[2:]))
+            assert xp.all(xp.isfinite(ci.high[2:]))
+
+        x0[0, 0], y0[1, 1] = 1 + 1e-15, 2 + 1e-15
+        x, y = xp.asarray(x0), xp.asarray(y0)
+        message = 'An input array is nearly constant'
+        with eager_warns(stats.NearConstantInputWarning, match=message, xp=xp):
+            stats.pearsonr(x, y, axis=1)
+
+        # length 2 along axis
+        x = xp.asarray([[1, 2], [1, 2], [2, 1], [2, 1.]])
+        y = xp.asarray([[1, 2], [2, 1], [1, 2], [2, 1.]])
+        ones = xp.ones(4)
+        res = stats.pearsonr(x, y, axis=-1)
+        ci = res.confidence_interval()
+        xp_assert_close(res.statistic, xp.asarray([1, -1, -1, 1.]))
+        xp_assert_close(res.pvalue, ones)
+        xp_assert_close(ci.low, -ones)
+        xp_assert_close(ci.high, ones)
+
+    def test_different_dimensionality(self, xp):
+        # For better or for worse, there is one difference between the broadcasting
+        # behavior of most stats functions and NumPy gufuncs / NEP 5: gufuncs `axis`
+        # refers to the core dimension *before* prepending `1`s to the array shapes
+        # to match dimensionality; SciPy's prepends `1`s first. For instance, in
+        # SciPy, `vecdot` would work just like `xp.sum(x * y, axis=axis)`, but this
+        # is NOT true of NumPy. The discrepancy only arises when there are multiple
+        # arguments with different dimensionality and positive indices are used,
+        # which is probably why it hasn't been a problem. There are pros and cons of
+        # each convention, and we might want to consider changing our behavior in
+        # SciPy 2.0. For now, preserve consistency / backward compatibility.
+        rng = np.random.default_rng(45834598265019344)
+        x = rng.random((3, 10))
+        y = rng.random(10)
+        res = stats.pearsonr(x, y, axis=1)
+        ref = stats.pearsonr(x, y, axis=-1)
+        assert_equal(res.statistic, ref.statistic)
+
+    @pytest.mark.parametrize('axis', [0, 1, None])
+    @pytest.mark.parametrize('alternative', ['less', 'greater', 'two-sided'])
+    def test_array_api(self, xp, axis, alternative):
+        rng = np.random.default_rng(2134418962)
+        x, y = rng.normal(size=(2, 10, 11))
+        res = stats.pearsonr(xp.asarray(x), xp.asarray(y),
+                             axis=axis, alternative=alternative)
+        ref = stats.pearsonr(x, y, axis=axis, alternative=alternative)
+        xp_assert_close(res.statistic, xp.asarray(ref.statistic))
+        xp_assert_close(res.pvalue, xp.asarray(ref.pvalue))
+
+        res_ci = res.confidence_interval()
+        ref_ci = ref.confidence_interval()
+        xp_assert_close(res_ci.low, xp.asarray(ref_ci.low))
+        xp_assert_close(res_ci.high, xp.asarray(ref_ci.high))
+
+
+class TestFisherExact:
+    """Some tests to show that fisher_exact() works correctly.
+
+    Note that in SciPy 0.9.0 this was not working well for large numbers due to
+    inaccuracy of the hypergeom distribution (see #1218). Fixed now.
+
+    Also note that R and SciPy have different argument formats for their
+    hypergeometric distribution functions.
+
+    R:
+    > phyper(18999, 99000, 110000, 39000, lower.tail = FALSE)
+    [1] 1.701815e-09
+    """
+
+    def test_basic(self):
+        fisher_exact = stats.fisher_exact
+
+        res = fisher_exact([[14500, 20000], [30000, 40000]])[1]
+        assert_approx_equal(res, 0.01106, significant=4)
+        res = fisher_exact([[100, 2], [1000, 5]])[1]
+        assert_approx_equal(res, 0.1301, significant=4)
+        res = fisher_exact([[2, 7], [8, 2]])[1]
+        assert_approx_equal(res, 0.0230141, significant=6)
+        res = fisher_exact([[5, 1], [10, 10]])[1]
+        assert_approx_equal(res, 0.1973244, significant=6)
+        res = fisher_exact([[5, 15], [20, 20]])[1]
+        assert_approx_equal(res, 0.0958044, significant=6)
+        res = fisher_exact([[5, 16], [20, 25]])[1]
+        assert_approx_equal(res, 0.1725862, significant=6)
+        res = fisher_exact([[10, 5], [10, 1]])[1]
+        assert_approx_equal(res, 0.1973244, significant=6)
+        res = fisher_exact([[5, 0], [1, 4]])[1]
+        assert_approx_equal(res, 0.04761904, significant=6)
+        res = fisher_exact([[0, 1], [3, 2]])[1]
+        assert_approx_equal(res, 1.0)
+        res = fisher_exact([[0, 2], [6, 4]])[1]
+        assert_approx_equal(res, 0.4545454545)
+        res = fisher_exact([[2, 7], [8, 2]])
+        assert_approx_equal(res[1], 0.0230141, significant=6)
+        assert_approx_equal(res[0], 4.0 / 56)
+
+    def test_precise(self):
+        # results from R
+        #
+        # R defines oddsratio differently (see Notes section of fisher_exact
+        # docstring), so those will not match.  We leave them in anyway, in
+        # case they will be useful later on. We test only the p-value.
+        tablist = [
+            ([[100, 2], [1000, 5]], (2.505583993422285e-001, 1.300759363430016e-001)),
+            ([[2, 7], [8, 2]], (8.586235135736206e-002, 2.301413756522114e-002)),
+            ([[5, 1], [10, 10]], (4.725646047336584e+000, 1.973244147157190e-001)),
+            ([[5, 15], [20, 20]], (3.394396617440852e-001, 9.580440012477637e-002)),
+            ([[5, 16], [20, 25]], (3.960558326183334e-001, 1.725864953812994e-001)),
+            ([[10, 5], [10, 1]], (2.116112781158483e-001, 1.973244147157190e-001)),
+            ([[10, 5], [10, 0]], (0.000000000000000e+000, 6.126482213438734e-002)),
+            ([[5, 0], [1, 4]], (np.inf, 4.761904761904762e-002)),
+            ([[0, 5], [1, 4]], (0.000000000000000e+000, 1.000000000000000e+000)),
+            ([[5, 1], [0, 4]], (np.inf, 4.761904761904758e-002)),
+            ([[0, 1], [3, 2]], (0.000000000000000e+000, 1.000000000000000e+000))
+            ]
+        for table, res_r in tablist:
+            res = stats.fisher_exact(np.asarray(table))
+            np.testing.assert_almost_equal(res[1], res_r[1], decimal=11,
+                                           verbose=True)
+
+    def test_gh4130(self):
+        # Previously, a fudge factor used to distinguish between theoretically
+        # and numerically different probability masses was 1e-4; it has been
+        # tightened to fix gh4130. Accuracy checked against R fisher.test.
+        # options(digits=16)
+        # table <- matrix(c(6, 108, 37, 200), nrow = 2)
+        # fisher.test(table, alternative = "t")
+        x = [[6, 37], [108, 200]]
+        res = stats.fisher_exact(x)
+        assert_allclose(res[1], 0.005092697748126)
+
+        # case from https://github.com/brentp/fishers_exact_test/issues/27
+        # That package has an (absolute?) fudge factor of 1e-6; too big
+        x = [[22, 0], [0, 102]]
+        res = stats.fisher_exact(x)
+        assert_allclose(res[1], 7.175066786244549e-25)
+
+        # case from https://github.com/brentp/fishers_exact_test/issues/1
+        x = [[94, 48], [3577, 16988]]
+        res = stats.fisher_exact(x)
+        assert_allclose(res[1], 2.069356340993818e-37)
+
+    def test_gh9231(self):
+        # Previously, fisher_exact was extremely slow for this table
+        # As reported in gh-9231, the p-value should be very nearly zero
+        x = [[5829225, 5692693], [5760959, 5760959]]
+        res = stats.fisher_exact(x)
+        assert_allclose(res[1], 0, atol=1e-170)
+
+    @pytest.mark.slow
+    def test_large_numbers(self):
+        # Test with some large numbers. Regression test for #1401
+        pvals = [5.56e-11, 2.666e-11, 1.363e-11]  # from R
+        for pval, num in zip(pvals, [75, 76, 77]):
+            res = stats.fisher_exact([[17704, 496], [1065, num]])[1]
+            assert_approx_equal(res, pval, significant=4)
+
+        res = stats.fisher_exact([[18000, 80000], [20000, 90000]])[1]
+        assert_approx_equal(res, 0.2751, significant=4)
+
+    def test_raises(self):
+        # test we raise an error for wrong number of dimensions.
+        message = "The input `table` must have two dimensions."
+        with pytest.raises(ValueError, match=message):
+            stats.fisher_exact(np.arange(6))
+
+    def test_row_or_col_zero(self):
+        tables = ([[0, 0], [5, 10]],
+                  [[5, 10], [0, 0]],
+                  [[0, 5], [0, 10]],
+                  [[5, 0], [10, 0]])
+        for table in tables:
+            oddsratio, pval = stats.fisher_exact(table)
+            assert_equal(pval, 1.0)
+            assert_equal(oddsratio, np.nan)
+
+    def test_less_greater(self):
+        tables = (
+            # Some tables to compare with R:
+            [[2, 7], [8, 2]],
+            [[200, 7], [8, 300]],
+            [[28, 21], [6, 1957]],
+            [[190, 800], [200, 900]],
+            # Some tables with simple exact values
+            # (includes regression test for ticket #1568):
+            [[0, 2], [3, 0]],
+            [[1, 1], [2, 1]],
+            [[2, 0], [1, 2]],
+            [[0, 1], [2, 3]],
+            [[1, 0], [1, 4]],
+            )
+        pvals = (
+            # from R:
+            [0.018521725952066501, 0.9990149169715733],
+            [1.0, 2.0056578803889148e-122],
+            [1.0, 5.7284374608319831e-44],
+            [0.7416227, 0.2959826],
+            # Exact:
+            [0.1, 1.0],
+            [0.7, 0.9],
+            [1.0, 0.3],
+            [2./3, 1.0],
+            [1.0, 1./3],
+            )
+        for table, pval in zip(tables, pvals):
+            res = []
+            res.append(stats.fisher_exact(table, alternative="less")[1])
+            res.append(stats.fisher_exact(table, alternative="greater")[1])
+            assert_allclose(res, pval, atol=0, rtol=1e-7)
+
+    def test_gh3014(self):
+        # check if issue #3014 has been fixed.
+        # before, this would have risen a ValueError
+        odds, pvalue = stats.fisher_exact([[1, 2], [9, 84419233]])
+
+    @pytest.mark.parametrize("alternative", ['two-sided', 'less', 'greater'])
+    def test_result(self, alternative):
+        table = np.array([[14500, 20000], [30000, 40000]])
+        res = stats.fisher_exact(table, alternative=alternative)
+        assert_equal((res.statistic, res.pvalue), res)
+
+    def test_input_validation_edge_cases_rxc(self):
+        rng = np.random.default_rng(2345783457834572345)
+        table = np.asarray([[2, 7], [8, 2]])
+
+        message = r"`alternative` must be the default \(None\) unless..."
+        with pytest.raises(ValueError, match=message):
+            method = stats.PermutationMethod(rng=rng)
+            stats.fisher_exact(table, method=method, alternative='less')
+
+        message = "...not recognized; if provided, `method` must be an..."
+        with pytest.raises(ValueError, match=message):
+            method = stats.BootstrapMethod(rng=rng)
+            stats.fisher_exact(table, method=method)
+
+        message = "If the `method` argument of `fisher_exact` is an..."
+        with pytest.raises(ValueError, match=message):
+            method = stats.MonteCarloMethod(rvs=stats.norm.rvs)
+            stats.fisher_exact(table, method=method)
+
+        message = "`table` must have at least one row and one column."
+        with pytest.raises(ValueError, match=message):
+            stats.fisher_exact(np.zeros((0, 1)))
+
+        # Specical case: when there is only one table with given marginals, the
+        # PMF of that case is 1.0, so the p-value is 1.0
+        np.testing.assert_equal(stats.fisher_exact([[1, 2, 3]]), (1, 1))
+        np.testing.assert_equal(stats.fisher_exact([[1], [2], [3]]), (1, 1))
+        np.testing.assert_equal(stats.fisher_exact(np.zeros((2, 3))), (1, 1))
+
+
+
+    @pytest.mark.fail_slow(10)
+    @pytest.mark.slow()
+    def test_resampling_2x2(self):
+        rng = np.random.default_rng(2345783457834572345)
+        table = np.asarray([[2, 7], [8, 2]])
+        ref = stats.fisher_exact(table)
+        ref_pvalue = ref.pvalue
+        ref_stat = stats.random_table(table.sum(axis=1), table.sum(axis=0)).pmf(table)
+
+        method = stats.MonteCarloMethod(rng=rng)
+        res = stats.fisher_exact(table, method=method)
+        assert_allclose(res.pvalue, ref_pvalue, atol=0.0025)
+        assert_equal(res.statistic, ref_stat)
+
+        method = stats.PermutationMethod(rng=rng)
+        res = stats.fisher_exact(table, method=method)
+        assert_allclose(res.pvalue, ref.pvalue, atol=0.0025)
+        assert_equal(res.statistic, ref_stat)
+
+    @pytest.mark.fail_slow(10)
+    @pytest.mark.slow()
+    def test_resampling_rxc(self):
+        # Compare against R fisher.exact
+        # options(digits=16)
+        # MP6 < - rbind(
+        #     c(1, 2, 2, 1, 1, 0, 1),
+        #     c(2, 0, 0, 2, 3, 0, 0),
+        #     c(0, 1, 1, 1, 2, 7, 3),
+        #     c(1, 1, 2, 0, 0, 0, 1),
+        #     c(0, 1, 1, 1, 1, 0, 0))
+        # fisher.test(MP6)
+
+        table = [[1, 2, 2, 1, 1, 0, 1],
+                 [2, 0, 0, 2, 3, 0, 0],
+                 [0, 1, 1, 1, 2, 7, 3],
+                 [1, 1, 2, 0, 0, 0, 1],
+                 [0, 1, 1, 1, 1, 0, 0]]
+        table = np.asarray(table)
+
+        ref_pvalue = 0.03928964365533
+        rng = np.random.default_rng(3928964365533)
+
+        method = stats.PermutationMethod(rng=rng)
+        res = stats.fisher_exact(table, method=method)
+        assert_allclose(res.pvalue, ref_pvalue, atol=5e-4)
+
+        method = stats.MonteCarloMethod(rng=rng, n_resamples=99999)
+        res = stats.fisher_exact(table, method=method)
+        assert_allclose(res.pvalue, ref_pvalue, atol=5e-4)
+
+    @pytest.mark.xslow()
+    def test_resampling_exact_2x2(self):
+        # Test that exact permutation p-value matches result of `fisher_exact`
+        rng = np.random.default_rng(2345783457834572345)
+        method = stats.PermutationMethod(rng=rng)
+
+        for a in range(1, 3):
+            for b in range(1, 3):
+                for c in range(1, 3):
+                    for d in range(1, 4):
+                        table = np.asarray([[a, b], [c, d]])
+                        ref = stats.fisher_exact(table)
+                        res = stats.fisher_exact(table, method=method)
+                        assert_allclose(res.pvalue, ref.pvalue, atol=1e-14)
+
+
+class TestCorrSpearmanr:
+    """ W.II.D. Compute a correlation matrix on all the variables.
+
+        All the correlations, except for ZERO and MISS, should be exactly 1.
+        ZERO and MISS should have undefined or missing correlations with the
+        other variables.  The same should go for SPEARMAN correlations, if
+        your program has them.
+    """
+
+    def setup_method(self):
+        self.rng = np.random.default_rng(228584263)
+
+    def test_scalar(self):
+        y = stats.spearmanr(4., 2.)
+        assert_(np.isnan(y).all())
+
+    def test_uneven_lengths(self):
+        assert_raises(ValueError, stats.spearmanr, [1, 2, 1], [8, 9])
+        assert_raises(ValueError, stats.spearmanr, [1, 2, 1], 8)
+
+    def test_uneven_2d_shapes(self):
+        # Different number of columns should work - those just get concatenated.
+        x = self.rng.standard_normal((4, 3))
+        y = self.rng.standard_normal((4, 2))
+        assert stats.spearmanr(x, y).statistic.shape == (5, 5)
+        assert stats.spearmanr(x.T, y.T, axis=1).pvalue.shape == (5, 5)
+
+        assert_raises(ValueError, stats.spearmanr, x, y, axis=1)
+        assert_raises(ValueError, stats.spearmanr, x.T, y.T)
+
+    def test_ndim_too_high(self):
+        x = self.rng.standard_normal((4, 3, 2))
+        assert_raises(ValueError, stats.spearmanr, x)
+        assert_raises(ValueError, stats.spearmanr, x, x)
+        assert_raises(ValueError, stats.spearmanr, x, None, None)
+        # But should work with axis=None (raveling axes) for two input arrays
+        assert_allclose(stats.spearmanr(x, x, axis=None),
+                        stats.spearmanr(x.flatten(), x.flatten(), axis=0))
+
+    def test_nan_policy(self):
+        x = np.arange(10.)
+        x[9] = np.nan
+        assert_array_equal(stats.spearmanr(x, x), (np.nan, np.nan))
+        assert_array_equal(stats.spearmanr(x, x, nan_policy='omit'),
+                           (1.0, 0.0))
+        assert_raises(ValueError, stats.spearmanr, x, x, nan_policy='raise')
+        assert_raises(ValueError, stats.spearmanr, x, x, nan_policy='foobar')
+
+    def test_nan_policy_bug_12458(self):
+        rng = np.random.default_rng(8119864466)
+        x = rng.random((5, 10))
+        k = 6
+        x[:, k] = np.nan
+        y = np.delete(x, k, axis=1)
+        corx, px = stats.spearmanr(x, nan_policy='omit')
+        cory, py = stats.spearmanr(y)
+        corx = np.delete(np.delete(corx, k, axis=1), k, axis=0)
+        px = np.delete(np.delete(px, k, axis=1), k, axis=0)
+        assert_allclose(corx, cory, atol=1e-14)
+        assert_allclose(px, py, atol=1e-14)
+
+    def test_nan_policy_bug_12411(self):
+        m = 5
+        n = 10
+        x = self.rng.standard_normal((m, n))
+        x[1, 0] = np.nan
+        x[3, -1] = np.nan
+        corr, pvalue = stats.spearmanr(x, axis=1, nan_policy="propagate")
+        res = [[stats.spearmanr(x[i, :], x[j, :]).statistic for i in range(m)]
+               for j in range(m)]
+        assert_allclose(corr, res)
+
+    @pytest.mark.parametrize("axis", [0, 1])
+    def test_constant_input_gh22816(self, axis):
+        X = np.zeros((10, 4))
+        X[:, 2] = np.arange(0, 10)
+        X[:, 3] = -np.arange(0, 10)
+
+        corr = np.array([[np.nan, np.nan, np.nan, np.nan],
+                         [np.nan, np.nan, np.nan, np.nan],
+                         [np.nan, np.nan, 1., -1.],
+                         [np.nan, np.nan, -1., 1.]])
+        if axis == 1:
+            X = X.T
+        with pytest.warns(stats._warnings_errors.ConstantInputWarning):
+            res = stats.spearmanr(X, axis=axis)
+        assert_allclose(res.statistic, corr)
+        assert_allclose(res.pvalue, 0*corr, atol=1e-50)
+
+    def test_sXX(self):
+        y = stats.spearmanr(X,X)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_sXBIG(self):
+        y = stats.spearmanr(X,BIG)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_sXLITTLE(self):
+        y = stats.spearmanr(X,LITTLE)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_sXHUGE(self):
+        y = stats.spearmanr(X,HUGE)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_sXTINY(self):
+        y = stats.spearmanr(X,TINY)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_sXROUND(self):
+        y = stats.spearmanr(X,ROUND)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_sBIGBIG(self):
+        y = stats.spearmanr(BIG,BIG)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_sBIGLITTLE(self):
+        y = stats.spearmanr(BIG,LITTLE)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_sBIGHUGE(self):
+        y = stats.spearmanr(BIG,HUGE)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_sBIGTINY(self):
+        y = stats.spearmanr(BIG,TINY)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_sBIGROUND(self):
+        y = stats.spearmanr(BIG,ROUND)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_sLITTLELITTLE(self):
+        y = stats.spearmanr(LITTLE,LITTLE)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_sLITTLEHUGE(self):
+        y = stats.spearmanr(LITTLE,HUGE)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_sLITTLETINY(self):
+        y = stats.spearmanr(LITTLE,TINY)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_sLITTLEROUND(self):
+        y = stats.spearmanr(LITTLE,ROUND)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_sHUGEHUGE(self):
+        y = stats.spearmanr(HUGE,HUGE)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_sHUGETINY(self):
+        y = stats.spearmanr(HUGE,TINY)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_sHUGEROUND(self):
+        y = stats.spearmanr(HUGE,ROUND)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_sTINYTINY(self):
+        y = stats.spearmanr(TINY,TINY)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_sTINYROUND(self):
+        y = stats.spearmanr(TINY,ROUND)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_sROUNDROUND(self):
+        y = stats.spearmanr(ROUND,ROUND)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_spearmanr_result_attributes(self):
+        res = stats.spearmanr(X, X)
+        attributes = ('correlation', 'pvalue')
+        check_named_results(res, attributes)
+        assert_equal(res.correlation, res.statistic)
+
+    def test_1d_vs_2d(self):
+        x1 = [1, 2, 3, 4, 5, 6]
+        x2 = [1, 2, 3, 4, 6, 5]
+        res1 = stats.spearmanr(x1, x2)
+        res2 = stats.spearmanr(np.asarray([x1, x2]).T)
+        assert_allclose(res1, res2)
+
+    def test_1d_vs_2d_nans(self):
+        # Now the same with NaNs present.  Regression test for gh-9103.
+        for nan_policy in ['propagate', 'omit']:
+            x1 = [1, np.nan, 3, 4, 5, 6]
+            x2 = [1, 2, 3, 4, 6, np.nan]
+            res1 = stats.spearmanr(x1, x2, nan_policy=nan_policy)
+            res2 = stats.spearmanr(np.asarray([x1, x2]).T, nan_policy=nan_policy)
+            assert_allclose(res1, res2)
+
+    def test_3cols(self):
+        x1 = np.arange(6)
+        x2 = -x1
+        x3 = np.array([0, 1, 2, 3, 5, 4])
+        x = np.asarray([x1, x2, x3]).T
+        actual = stats.spearmanr(x)
+        expected_corr = np.array([[1, -1, 0.94285714],
+                                  [-1, 1, -0.94285714],
+                                  [0.94285714, -0.94285714, 1]])
+        expected_pvalue = np.zeros((3, 3), dtype=float)
+        expected_pvalue[2, 0:2] = 0.00480466472
+        expected_pvalue[0:2, 2] = 0.00480466472
+
+        assert_allclose(actual.statistic, expected_corr)
+        assert_allclose(actual.pvalue, expected_pvalue)
+
+    def test_gh_9103(self):
+        # Regression test for gh-9103.
+        x = np.array([[np.nan, 3.0, 4.0, 5.0, 5.1, 6.0, 9.2],
+                      [5.0, np.nan, 4.1, 4.8, 4.9, 5.0, 4.1],
+                      [0.5, 4.0, 7.1, 3.8, 8.0, 5.1, 7.6]]).T
+        corr = np.array([[np.nan, np.nan, np.nan],
+                         [np.nan, np.nan, np.nan],
+                         [np.nan, np.nan, 1.]])
+        assert_allclose(stats.spearmanr(x, nan_policy='propagate').statistic,
+                        corr)
+
+        res = stats.spearmanr(x, nan_policy='omit').statistic
+        assert_allclose((res[0][1], res[0][2], res[1][2]),
+                        (0.2051957, 0.4857143, -0.4707919), rtol=1e-6)
+
+    def test_gh_8111(self):
+        # Regression test for gh-8111 (different result for float/int/bool).
+        n = 100
+        rng = np.random.RandomState(234568)
+        x = rng.rand(n)
+        m = rng.rand(n) > 0.7
+
+        # bool against float, no nans
+        a = (x > .5)
+        b = np.array(x)
+        res1 = stats.spearmanr(a, b, nan_policy='omit').statistic
+
+        # bool against float with NaNs
+        b[m] = np.nan
+        res2 = stats.spearmanr(a, b, nan_policy='omit').statistic
+
+        # int against float with NaNs
+        a = a.astype(np.int32)
+        res3 = stats.spearmanr(a, b, nan_policy='omit').statistic
+
+        expected = [0.865895477, 0.866100381, 0.866100381]
+        assert_allclose([res1, res2, res3], expected)
+
+
+class TestCorrSpearmanr2:
+    """Some further tests of the spearmanr function."""
+
+    def test_spearmanr_vs_r(self):
+        # Cross-check with R:
+        # cor.test(c(1,2,3,4,5),c(5,6,7,8,7),method="spearmanr")
+        x1 = [1, 2, 3, 4, 5]
+        x2 = [5, 6, 7, 8, 7]
+        expected = (0.82078268166812329, 0.088587005313543798)
+        res = stats.spearmanr(x1, x2)
+        assert_approx_equal(res[0], expected[0])
+        assert_approx_equal(res[1], expected[1])
+
+    def test_empty_arrays(self):
+        assert_equal(stats.spearmanr([], []), (np.nan, np.nan))
+
+    def test_normal_draws(self):
+        rng = np.random.RandomState(7546)
+        x = np.array([rng.normal(loc=1, scale=1, size=500),
+                      rng.normal(loc=1, scale=1, size=500)])
+        corr = [[1.0, 0.3],
+                [0.3, 1.0]]
+        x = np.dot(np.linalg.cholesky(corr), x)
+        expected = (0.28659685838743354, 6.579862219051161e-11)
+        res = stats.spearmanr(x[0], x[1])
+        assert_approx_equal(res[0], expected[0])
+        assert_approx_equal(res[1], expected[1])
+
+    def test_corr_1(self):
+        assert_approx_equal(stats.spearmanr([1, 1, 2], [1, 1, 2])[0], 1.0)
+
+    def test_nan_policies(self):
+        x = np.arange(10.)
+        x[9] = np.nan
+        assert_array_equal(stats.spearmanr(x, x), (np.nan, np.nan))
+        assert_allclose(stats.spearmanr(x, x, nan_policy='omit'),
+                        (1.0, 0))
+        assert_raises(ValueError, stats.spearmanr, x, x, nan_policy='raise')
+        assert_raises(ValueError, stats.spearmanr, x, x, nan_policy='foobar')
+
+    def test_unequal_lengths(self):
+        x = np.arange(10.)
+        y = np.arange(20.)
+        assert_raises(ValueError, stats.spearmanr, x, y)
+
+    def test_omit_paired_value(self):
+        x1 = [1, 2, 3, 4]
+        x2 = [8, 7, 6, np.nan]
+        res1 = stats.spearmanr(x1, x2, nan_policy='omit')
+        res2 = stats.spearmanr(x1[:3], x2[:3], nan_policy='omit')
+        assert_equal(res1, res2)
+
+    def test_gh_issue_6061_windows_overflow(self):
+        x = list(range(2000))
+        y = list(range(2000))
+        y[0], y[9] = y[9], y[0]
+        y[10], y[434] = y[434], y[10]
+        y[435], y[1509] = y[1509], y[435]
+        # rho = 1 - 6 * (2 * (9^2 + 424^2 + 1074^2))/(2000 * (2000^2 - 1))
+        #     = 1 - (1 / 500)
+        #     = 0.998
+        x.append(np.nan)
+        y.append(3.0)
+        assert_almost_equal(stats.spearmanr(x, y, nan_policy='omit')[0], 0.998)
+
+    def test_tie0(self):
+        # with only ties in one or both inputs
+        warn_msg = "An input array is constant"
+        with pytest.warns(stats.ConstantInputWarning, match=warn_msg):
+            r, p = stats.spearmanr([2, 2, 2], [2, 2, 2])
+            assert_equal(r, np.nan)
+            assert_equal(p, np.nan)
+            r, p = stats.spearmanr([2, 0, 2], [2, 2, 2])
+            assert_equal(r, np.nan)
+            assert_equal(p, np.nan)
+            r, p = stats.spearmanr([2, 2, 2], [2, 0, 2])
+            assert_equal(r, np.nan)
+            assert_equal(p, np.nan)
+
+    def test_tie1(self):
+        # Data
+        x = [1.0, 2.0, 3.0, 4.0]
+        y = [1.0, 2.0, 2.0, 3.0]
+        # Ranks of the data, with tie-handling.
+        xr = [1.0, 2.0, 3.0, 4.0]
+        yr = [1.0, 2.5, 2.5, 4.0]
+        # Result of spearmanr should be the same as applying
+        # pearsonr to the ranks.
+        sr = stats.spearmanr(x, y)
+        pr = stats.pearsonr(xr, yr)
+        assert_almost_equal(sr, pr)
+
+    def test_tie2(self):
+        # Test tie-handling if inputs contain nan's
+        # Data without nan's
+        x1 = [1, 2, 2.5, 2]
+        y1 = [1, 3, 2.5, 4]
+        # Same data with nan's
+        x2 = [1, 2, 2.5, 2, np.nan]
+        y2 = [1, 3, 2.5, 4, np.nan]
+
+        # Results for two data sets should be the same if nan's are ignored
+        sr1 = stats.spearmanr(x1, y1)
+        sr2 = stats.spearmanr(x2, y2, nan_policy='omit')
+        assert_almost_equal(sr1, sr2)
+
+    def test_ties_axis_1(self):
+        z1 = np.array([[1, 1, 1, 1], [1, 2, 3, 4]])
+        z2 = np.array([[1, 2, 3, 4], [1, 1, 1, 1]])
+        z3 = np.array([[1, 1, 1, 1], [1, 1, 1, 1]])
+        warn_msg = "An input array is constant"
+        with pytest.warns(stats.ConstantInputWarning, match=warn_msg):
+            r, p = stats.spearmanr(z1, axis=1)
+            assert_equal(r, np.nan)
+            assert_equal(p, np.nan)
+            r, p = stats.spearmanr(z2, axis=1)
+            assert_equal(r, np.nan)
+            assert_equal(p, np.nan)
+            r, p = stats.spearmanr(z3, axis=1)
+            assert_equal(r, np.nan)
+            assert_equal(p, np.nan)
+
+    def test_gh_11111(self):
+        x = np.array([1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0])
+        y = np.array([0, 0.009783728115345005, 0, 0, 0.0019759230121848587,
+                      0.0007535430349118562, 0.0002661781514710257, 0, 0,
+                      0.0007835762419683435])
+        warn_msg = "An input array is constant"
+        with pytest.warns(stats.ConstantInputWarning, match=warn_msg):
+            r, p = stats.spearmanr(x, y)
+            assert_equal(r, np.nan)
+            assert_equal(p, np.nan)
+
+    def test_index_error(self):
+        x = np.array([1.0, 7.0, 2.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0])
+        y = np.array([0, 0.009783728115345005, 0, 0, 0.0019759230121848587,
+                      0.0007535430349118562, 0.0002661781514710257, 0, 0,
+                      0.0007835762419683435])
+        assert_raises(ValueError, stats.spearmanr, x, y, axis=2)
+
+    def test_alternative(self):
+        # Test alternative parameter
+
+        # Simple test - Based on the above ``test_spearmanr_vs_r``
+        x1 = [1, 2, 3, 4, 5]
+        x2 = [5, 6, 7, 8, 7]
+
+        # strong positive correlation
+        expected = (0.82078268166812329, 0.088587005313543798)
+
+        # correlation > 0 -> large "less" p-value
+        res = stats.spearmanr(x1, x2, alternative="less")
+        assert_approx_equal(res[0], expected[0])
+        assert_approx_equal(res[1], 1 - (expected[1] / 2))
+
+        # correlation > 0 -> small "less" p-value
+        res = stats.spearmanr(x1, x2, alternative="greater")
+        assert_approx_equal(res[0], expected[0])
+        assert_approx_equal(res[1], expected[1] / 2)
+
+        with pytest.raises(ValueError, match="`alternative` must be 'less'..."):
+            stats.spearmanr(x1, x2, alternative="ekki-ekki")
+
+    @pytest.mark.parametrize("alternative", ('two-sided', 'less', 'greater'))
+    def test_alternative_nan_policy(self, alternative):
+        # Test nan policies
+        x1 = [1, 2, 3, 4, 5]
+        x2 = [5, 6, 7, 8, 7]
+        x1nan = x1 + [np.nan]
+        x2nan = x2 + [np.nan]
+
+        # test nan_policy="propagate"
+        assert_array_equal(stats.spearmanr(x1nan, x2nan), (np.nan, np.nan))
+
+        # test nan_policy="omit"
+        res_actual = stats.spearmanr(x1nan, x2nan, nan_policy='omit',
+                                     alternative=alternative)
+        res_expected = stats.spearmanr(x1, x2, alternative=alternative)
+        assert_allclose(res_actual, res_expected)
+
+        # test nan_policy="raise"
+        message = 'The input contains nan values'
+        with pytest.raises(ValueError, match=message):
+            stats.spearmanr(x1nan, x2nan, nan_policy='raise',
+                            alternative=alternative)
+
+        # test invalid nan_policy
+        message = "nan_policy must be one of..."
+        with pytest.raises(ValueError, match=message):
+            stats.spearmanr(x1nan, x2nan, nan_policy='ekki-ekki',
+                            alternative=alternative)
+
+
+@make_xp_test_case(stats.kendalltau)
+class TestKendallTau:
+    @pytest.mark.parametrize('x, y, statistic, pvalue', [
+        # For the cases without ties, both variants should give the same
+        # result. Reference values result from R:
+        # cor.test(x, y, method="kendall", exact=1)
+        ([5, 2, 1, 3, 6, 4, 7, 8], [5, 2, 6, 3, 1, 8, 7, 4], 0.0, 1.0),
+        ([0, 5, 2, 1, 3, 6, 4, 7, 8], [5, 2, 0, 6, 3, 1, 8, 7, 4], 0.0, 1.0),
+        ([5, 2, 1, 3, 6, 4, 7], [5, 2, 6, 3, 1, 7, 4], -0.14285714286, 0.77261904762),
+        ([2, 1, 3, 6, 4, 7, 8], [2, 6, 3, 1, 8, 7, 4], 0.047619047619, 1.0),
+        ([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
+         1.0, 5.511463844797e-07),
+        ([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 2, 1, 3, 4, 5, 6, 7, 8, 9],
+         0.9555555555555556, 5.511463844797e-06),
+        ([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 2, 1, 3, 4, 6, 5, 7, 8, 9],
+         0.9111111111111111, 2.976190476190e-05),
+        ([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [9, 8, 7, 6, 5, 4, 3, 2, 1, 0],
+         -1.0, 5.511463844797e-07),
+        ([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [9, 7, 8, 6, 5, 4, 3, 2, 1, 0],
+         -0.9555555555555556, 5.511463844797e-06),
+        ([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [9, 7, 8, 6, 5, 3, 4, 2, 1, 0],
+         -0.9111111111111111, 2.976190476190e-05),
+    ])
+    @pytest.mark.parametrize('variant', ['b', 'c'])
+    def test_kendalltau_no_ties(self, x, y, statistic, pvalue, variant, xp):
+        res = stats.kendalltau(xp.asarray(x), xp.asarray(y), variant=variant)
+        xp_assert_close(res[0], xp.asarray(statistic))
+        xp_assert_close(res[1], xp.asarray(pvalue))
+
+    def test_kendalltau_ties(self, xp):
+        # Check a case where variants are different
+        # Example values found from Kendall (1970).
+        # P-value is the same for the both variants
+        x = xp.asarray([1, 2, 2, 4, 4, 6, 6, 8, 9, 9])
+        y = xp.asarray([1, 2, 4, 4, 4, 4, 8, 8, 8, 10])
+        expected = 0.85895569
+        xp_assert_close(stats.kendalltau(x, y, variant='b')[0], xp.asarray(expected))
+        expected = 0.825
+        xp_assert_close(stats.kendalltau(x, y, variant='c')[0], xp.asarray(expected))
+
+        # tau-b with some ties
+        # Cross-check with R:
+        # cor.test(c(12, 2, 1, 12, 2), c(1, 4, 7, 1, 0), method="kendall", exact=FALSE)
+        x1 = xp.asarray([12, 2, 1, 12, 2])
+        x2 = xp.asarray([1, 4, 7, 1, 0])
+        expected = (-0.47140452079103173, 0.28274545993277478)
+        res = stats.kendalltau(x1, x2)
+        assert_approx_equal(res[0], xp.asarray(expected[0]))
+        assert_approx_equal(res[1], xp.asarray(expected[1]))
+
+        # this should result in 1 for tau-b but not tau-c
+        x = xp.asarray([1, 1, 2])
+        xp_assert_close(stats.kendalltau(x, x, variant='b')[0], xp.asarray(1.0))
+        xp_assert_close(stats.kendalltau(x, x, variant='c')[0], xp.asarray(0.88888888))
+
+    def test_input_validation_edge_cases(self, xp):
+        x = xp.asarray([1, 2, 2, 4, 4, 6, 6, 8, 9, 9])
+        y = xp.asarray([1, 2, 2, 4, 4, 4, 8, 8, 8, 10])
+
+        # check exception in case of ties and method='exact' requested
+        message = "Ties found; exact method cannot be used."
+        with pytest.raises(ValueError, match=message):
+            stats.kendalltau(x, y, method='exact')
+
+        # check exception in case of invalid method keyword
+        message = "Unknown `method` 'banana' specified."
+        with pytest.raises(ValueError, match=message):
+            stats.kendalltau(x, y, method='banana')
+
+        # check exception in case of invalid variant keyword
+        message = "Unknown `variant` 'rms' specified."
+        with pytest.raises(ValueError, match=message):
+            stats.kendalltau(x, y, variant='rms')
+
+        # empty arrays provided as input
+        with eager_warns(SmallSampleWarning, match="One or more sample...", xp=xp):
+            res = stats.kendalltau(xp.asarray([]), xp.asarray([]))
+        xp_assert_equal(res.statistic, xp.asarray(xp.nan))
+        xp_assert_equal(res.pvalue, xp.asarray(xp.nan))
+
+        # test too small
+        with pytest.warns(SmallSampleWarning, match="One or more sample..."):
+            tau, p_value = stats.kendalltau(xp.asarray([0]), xp.asarray([0]))
+        xp_assert_equal(tau, xp.asarray(np.nan))
+        xp_assert_equal(p_value, xp.asarray(np.nan))
+
+        # test unequal length inputs
+        x = np.arange(10.)
+        y = np.arange(20.)
+        message = "Array shapes are incompatible for broadcasting."
+        with pytest.raises(ValueError, match=message):
+            stats.kendalltau(x, y)
+
+    @pytest.mark.parametrize('variant', ['b', 'c'])
+    def test_attributes(self, variant, xp):
+        x1 = xp.asarray([1, 2, 2, 4, 4, 6, 6, 8, 9, 9])
+        x2 = xp.asarray([1, 2, 2, 4, 4, 4, 8, 8, 8, 10])
+        # test for namedtuple attribute results
+        attributes = ('correlation', 'pvalue')
+        res = stats.kendalltau(x1, x2, variant=variant)
+        check_named_results(res, attributes, xp=xp)
+        xp_assert_equal(res.correlation, res.statistic)
+
+    @pytest.mark.parametrize('x, y', [
+        ([2, 2, 2], [2, 2, 2]),
+        ([2, 0, 2], [2, 2, 2]),
+        ([2, 2, 2], [2, 0, 2]),
+    ])
+    @pytest.mark.parametrize('variant', ['b', 'c'])
+    def test_degenerate_input(self, x, y, variant, xp):
+        # with only ties in one or both inputs in tau-b or tau-c
+        x, y = xp.asarray(x), xp.asarray(y)
+        res = stats.kendalltau(x, y, variant=variant)
+        xp_assert_equal(res.statistic, xp.asarray(xp.nan))
+        xp_assert_equal(res.pvalue, xp.asarray(xp.nan))
+
+    @pytest.mark.parametrize('dtype', [None, 'float32', 'float64'])
+    def test_large_arrays(self, dtype, xp):
+        # check with larger arrays
+        dtype = xp_default_dtype(xp) if dtype is None else getattr(xp, dtype)
+        rng = np.random.RandomState(7546)
+        x = np.array([rng.normal(loc=1, scale=1, size=500),
+                      rng.normal(loc=1, scale=1, size=500)])
+        corr = [[1.0, 0.3],
+                [0.3, 1.0]]
+        x = np.dot(np.linalg.cholesky(corr), x)
+        x0 = xp.asarray(x[0], dtype=dtype)
+        x1 = xp.asarray(x[1], dtype=dtype)
+        expected = (0.19291382765531062, 1.1337095377742629e-10)
+        res = stats.kendalltau(x0, x1)
+        xp_assert_close(res[0], xp.asarray(expected[0], dtype=dtype))
+        xp_assert_close(res[1], xp.asarray(expected[1], dtype=dtype))
+
+    def test_nan_policy(self, xp):
+        # test nan_policy
+        x = np.arange(10.)
+        x[9] = np.nan
+        x = xp.asarray(x.tolist())
+
+        res = stats.kendalltau(x, x)
+        xp_assert_equal(res.statistic, xp.asarray(xp.nan))
+        xp_assert_equal(res.pvalue, xp.asarray(xp.nan))
+
+        res = stats.kendalltau(x, x, nan_policy='omit')
+        xp_assert_close(res.statistic, xp.asarray(1.0))
+        xp_assert_close(res.pvalue, xp.asarray(5.5114638e-6), rtol=1e-06)
+
+        res = stats.kendalltau(x, x, nan_policy='omit', method='asymptotic')
+        xp_assert_close(res.statistic, xp.asarray(1.0))
+        xp_assert_close(res.pvalue, xp.asarray(0.00017455009626808976), rtol=1e-06)
+
+        message = "The input contains nan values"
+        with pytest.raises(ValueError, match=message):
+            stats.kendalltau(x, x, nan_policy='raise')
+
+        message = "nan_policy must be one of..."
+        with pytest.raises(ValueError, match=message):
+            stats.kendalltau(x, x, nan_policy='foobar')
+
+    def test_kendalltau_nan_2nd_arg_gh6134(self, xp):
+        # regression test for gh-6134: nans in the second arg were not handled
+        x = xp.asarray([1., 2., 3., 4.])
+        y = xp.asarray([np.nan, 2.4, 3.4, 3.4])
+
+        r1 = stats.kendalltau(x, y, nan_policy='omit')
+        r2 = stats.kendalltau(x[1:], y[1:])
+        xp_assert_close(r1.statistic, r2.statistic, atol=1e-15)
+
+    @pytest.mark.thread_unsafe(reason="fails in parallel")
+    def test_kendalltau_gh18139_overflow(self, xp):
+        # gh-18139 reported an overflow in `kendalltau` that appeared after
+        # SciPy 0.15.1. Check that this particular overflow does not occur.
+        # (Test would fail if warning were emitted.)
+        import random
+        random.seed(6272161)
+        classes = [1, 2, 3, 4, 5, 6, 7]
+        n_samples = 2 * 10 ** 5
+        x = xp.asarray(random.choices(classes, k=n_samples))
+        y = xp.asarray(random.choices(classes, k=n_samples))
+        res = stats.kendalltau(x, y)
+        # Reference value from SciPy 0.15.1
+        xp_assert_close(res.statistic, xp.asarray(0.0011816493905730343))
+        # Reference p-value from `permutation_test` w/ n_resamples=9999 (default).
+        # Expected to be accurate to at least two digits.
+        xp_assert_close(res.pvalue, xp.asarray(0.4894), atol=2e-3)
+
+    def test_kendall_tau_large_nan_policy(self, xp):
+        n = 172
+        # Test omit policy
+        x = np.arange(n + 1).astype(float)
+        y = np.arange(n + 1).astype(float)
+        y[-1] = np.nan
+        x, y = xp.asarray(x.tolist()), xp.asarray(y.tolist())
+        _, pval = stats.kendalltau(x, y, method='exact', nan_policy='omit')
+        xp_assert_equal(pval, xp.asarray(0.0))
+
+
+@make_xp_test_case(stats.kendalltau)
+class TestKendallTauAlternative:
+    def test_kendalltau_alternative_asymptotic(self, xp):
+        # Test alternative parameter, asymptotic method (due to tie)
+
+        # Based on TestCorrSpearman2::test_alternative
+        x1 = [1, 2, 3, 4, 5]
+        x2 = [5, 6, 7, 8, 7]
+
+        # strong positive correlation
+        expected = stats.kendalltau(xp.asarray(x1), xp.asarray(x2),
+                                    alternative="two-sided")
+        assert expected[0] > 0
+
+        # rank correlation > 0 -> large "less" p-value
+        res = stats.kendalltau(xp.asarray(x1), xp.asarray(x2), alternative="less")
+        xp_assert_equal(res[0], xp.asarray(expected[0]))
+        xp_assert_close(res[1], xp.asarray(1 - (expected[1] / 2)))
+
+        # rank correlation > 0 -> small "greater" p-value
+        res = stats.kendalltau(xp.asarray(x1), xp.asarray(x2), alternative="greater")
+        xp_assert_equal(res[0], xp.asarray(expected[0]))
+        xp_assert_close(res[1], xp.asarray(expected[1] / 2))
+
+        # reverse the direction of rank correlation
+        x2.reverse()
+
+        # strong negative correlation
+        expected = stats.kendalltau(xp.asarray(x1), xp.asarray(x2),
+                                    alternative="two-sided")
+        assert expected[0] < 0
+
+        # rank correlation < 0 -> large "greater" p-value
+        res = stats.kendalltau(xp.asarray(x1), xp.asarray(x2), alternative="greater")
+        xp_assert_equal(res[0], xp.asarray(expected[0]))
+        xp_assert_close(res[1], xp.asarray(1 - (expected[1] / 2)))
+
+        # rank correlation < 0 -> small "less" p-value
+        res = stats.kendalltau(xp.asarray(x1), xp.asarray(x2), alternative="less")
+        xp_assert_equal(res[0], xp.asarray(expected[0]))
+        xp_assert_close(res[1], xp.asarray(expected[1] / 2))
+
+        with pytest.raises(ValueError, match="`alternative` must be 'less'..."):
+            stats.kendalltau(xp.asarray(x1), xp.asarray(x2), alternative="ekki-ekki")
+
+    # There are a lot of special cases considered in the calculation of the
+    # exact p-value, so we test each separately. We also need to test
+    # separately when the observed statistic is in the left tail vs the right
+    # tail because the code leverages symmetry of the null distribution; to
+    # do that we use the same test case but negate one of the samples.
+    # Reference values computed using R cor.test, e.g.
+    # options(digits=16)
+    # x <- c(44.4, 45.9, 41.9, 53.3, 44.7, 44.1, 50.7, 45.2, 60.1)
+    # y <- c( 2.6,  3.1,  2.5,  5.0,  3.6,  4.0,  5.2,  2.8,  3.8)
+    # cor.test(x, y, method = "kendall", alternative = "g")
+
+    alternatives = ('less', 'two-sided', 'greater')
+    p_n1 = [np.nan, np.nan, np.nan]
+    p_n2 = [1.0, 1.0, 0.5]
+    p_c0 = [1.0, 0.3333333333333, 0.1666666666667]
+    p_c1 = [0.9583333333333, 0.3333333333333, 0.1666666666667]
+    p_no_correlation = [0.5916666666667, 1.0, 0.5916666666667]
+    p_no_correlationb = [0.5475694444444, 1.0, 0.5475694444444]
+    p_n_lt_171 = [0.9624118165785, 0.1194389329806, 0.0597194664903]
+    p_n_lt_171b = [0.246236925303, 0.4924738506059, 0.755634083327]
+    p_n_lt_171c = [0.9847475308925, 0.03071385306533, 0.01535692653267]
+
+    def exact_test(self, x, y, alternative, rev, stat_expected, p_expected, xp):
+        x, y = xp.asarray(x), xp.asarray(y)
+        if rev:
+            y = -y
+            stat_expected *= -1
+        res = stats.kendalltau(x, y, method='exact', alternative=alternative)
+        xp_assert_close(res.statistic, xp.asarray(stat_expected))
+        xp_assert_close(res.pvalue, xp.asarray(p_expected))
+
+    case_R_n1 = (list(zip(alternatives, p_n1, [False]*3))
+                 + list(zip(alternatives, reversed(p_n1), [True]*3)))
+
+    @pytest.mark.parametrize("alternative, p_expected, rev", case_R_n1)
+    def test_against_R_n1(self, alternative, p_expected, rev, xp):
+        x, y = [1], [2]
+        stat_expected = np.nan
+        with pytest.warns(SmallSampleWarning, match="One or more sample..."):
+            self.exact_test(x, y, alternative, rev, stat_expected, p_expected, xp=xp)
+
+    case_R_n2 = (list(zip(alternatives, p_n2, [False]*3))
+                 + list(zip(alternatives, reversed(p_n2), [True]*3)))
+
+    @pytest.mark.parametrize("alternative, p_expected, rev", case_R_n2)
+    def test_against_R_n2(self, alternative, p_expected, rev, xp):
+        x, y = [1, 2], [3, 4]
+        stat_expected = 0.9999999999999998
+        self.exact_test(x, y, alternative, rev, stat_expected, p_expected, xp=xp)
+
+    case_R_c0 = (list(zip(alternatives, p_c0, [False]*3))
+                 + list(zip(alternatives, reversed(p_c0), [True]*3)))
+
+    @pytest.mark.parametrize("alternative, p_expected, rev", case_R_c0)
+    def test_against_R_c0(self, alternative, p_expected, rev, xp):
+        x, y = [1, 2, 3], [1, 2, 3]
+        stat_expected = 1.
+        self.exact_test(x, y, alternative, rev, stat_expected, p_expected, xp=xp)
+
+    case_R_c1 = (list(zip(alternatives, p_c1, [False]*3))
+                 + list(zip(alternatives, reversed(p_c1), [True]*3)))
+
+    @pytest.mark.parametrize("alternative, p_expected, rev", case_R_c1)
+    def test_against_R_c1(self, alternative, p_expected, rev, xp):
+        x, y = [1, 2, 3, 4], [1, 2, 4, 3]
+        stat_expected = 0.6666666666666667
+        self.exact_test(x, y, alternative, rev, stat_expected, p_expected, xp=xp)
+
+    case_R_no_corr = (list(zip(alternatives, p_no_correlation, [False]*3))
+                      + list(zip(alternatives, reversed(p_no_correlation),
+                                 [True]*3)))
+
+    @pytest.mark.parametrize("alternative, p_expected, rev", case_R_no_corr)
+    def test_against_R_no_correlation(self, alternative, p_expected, rev, xp):
+        x, y = [1, 2, 3, 4, 5], [1, 5, 4, 2, 3]
+        stat_expected = 0.
+        self.exact_test(x, y, alternative, rev, stat_expected, p_expected, xp=xp)
+
+    case_no_cor_b = (list(zip(alternatives, p_no_correlationb, [False]*3))
+                     + list(zip(alternatives, reversed(p_no_correlationb),
+                                [True]*3)))
+
+    @pytest.mark.parametrize("alternative, p_expected, rev", case_no_cor_b)
+    def test_against_R_no_correlationb(self, alternative, p_expected, rev, xp):
+        x, y = [1, 2, 3, 4, 5, 6, 7, 8], [8, 6, 1, 3, 2, 5, 4, 7]
+        stat_expected = 0.
+        self.exact_test(x, y, alternative, rev, stat_expected, p_expected, xp=xp)
+
+    case_R_lt_171 = (list(zip(alternatives, p_n_lt_171, [False]*3))
+                     + list(zip(alternatives, reversed(p_n_lt_171), [True]*3)))
+
+    @pytest.mark.parametrize("alternative, p_expected, rev", case_R_lt_171)
+    def test_against_R_lt_171(self, alternative, p_expected, rev, xp):
+        # Data from Hollander & Wolfe (1973), p. 187f.
+        # Used from https://rdrr.io/r/stats/cor.test.html
+        x = [44.4, 45.9, 41.9, 53.3, 44.7, 44.1, 50.7, 45.2, 60.1]
+        y = [2.6, 3.1, 2.5, 5.0, 3.6, 4.0, 5.2, 2.8, 3.8]
+        stat_expected = 0.4444444444444445
+        self.exact_test(x, y, alternative, rev, stat_expected, p_expected, xp=xp)
+
+    case_R_lt_171b = (list(zip(alternatives, p_n_lt_171b, [False]*3))
+                      + list(zip(alternatives, reversed(p_n_lt_171b),
+                                 [True]*3)))
+
+    @pytest.mark.parametrize("alternative, p_expected, rev", case_R_lt_171b)
+    def test_against_R_lt_171b(self, alternative, p_expected, rev, xp):
+        rng = np.random.RandomState(0)
+        x = rng.rand(100).tolist()
+        y = rng.rand(100).tolist()
+        stat_expected = -0.04686868686868687
+        self.exact_test(x, y, alternative, rev, stat_expected, p_expected, xp=xp)
+
+    case_R_lt_171c = (list(zip(alternatives, p_n_lt_171c, [False]*3))
+                      + list(zip(alternatives, reversed(p_n_lt_171c),
+                                 [True]*3)))
+
+    @pytest.mark.parametrize("alternative, p_expected, rev", case_R_lt_171c)
+    def test_against_R_lt_171c(self, alternative, p_expected, rev, xp):
+        rng = np.random.RandomState(0)
+        x = rng.rand(170).tolist()
+        y = rng.rand(170).tolist()
+        stat_expected = 0.1115906717716673
+        self.exact_test(x, y, alternative, rev, stat_expected, p_expected, xp=xp)
+
+    case_gt_171 = (list(zip(alternatives, [False]*3)) +
+                   list(zip(alternatives, [True]*3)))
+
+    @pytest.mark.parametrize("alternative, rev", case_gt_171)
+    def test_gt_171(self, alternative, rev, xp):
+        rng = np.random.RandomState(0)
+        x = xp.asarray(rng.rand(400).tolist())
+        y = xp.asarray(rng.rand(400).tolist())
+        res0 = stats.kendalltau(x, y, method='exact', alternative=alternative)
+        res1 = stats.kendalltau(x, y, method='asymptotic', alternative=alternative)
+        xp_assert_equal(res0[0], res1[0])
+        xp_assert_close(res0[1], res1[1], rtol=1e-3)
+
+    @pytest.mark.parametrize("method", ('exact', 'asymptotic'))
+    @pytest.mark.parametrize("alternative", ('two-sided', 'less', 'greater'))
+    def test_nan_policy(self, method, alternative, xp):
+        # Test nan policies
+        x1 = [1, 2, 3, 4, 5]
+        x2 = [5, 6, 7, 8, 9]
+        x1nan = x1 + [np.nan]
+        x2nan = x2 + [np.nan]
+        x1, x2 = xp.asarray(x1), xp.asarray(x2)
+        x1nan, x2nan = xp.asarray(x1nan), xp.asarray(x2nan)
+
+        # test nan_policy="propagate"
+        res_actual = stats.kendalltau(x1nan, x2nan,
+                                      method=method, alternative=alternative)
+        xp_assert_equal(res_actual.statistic, xp.asarray(xp.nan))
+        xp_assert_equal(res_actual.pvalue, xp.asarray(xp.nan))
+
+        # test nan_policy="omit"
+        res_actual = stats.kendalltau(x1nan, x2nan, nan_policy='omit',
+                                      method=method, alternative=alternative)
+        res_expected = stats.kendalltau(x1, x2, method=method,
+                                        alternative=alternative)
+        xp_assert_equal(res_actual.statistic, res_expected.statistic)
+        xp_assert_equal(res_actual.pvalue, res_expected.pvalue)
+
+        # test nan_policy="raise"
+        message = 'The input contains nan values'
+        with pytest.raises(ValueError, match=message):
+            stats.kendalltau(x1nan, x2nan, nan_policy='raise',
+                             method=method, alternative=alternative)
+
+        # test invalid nan_policy
+        message = "nan_policy must be one of..."
+        with pytest.raises(ValueError, match=message):
+            stats.kendalltau(x1nan, x2nan, nan_policy='ekki-ekki',
+                             method=method, alternative=alternative)
+
+
+class TestWeightedTau:
+    def test_weightedtau(self):
+        x = [12, 2, 1, 12, 2]
+        y = [1, 4, 7, 1, 0]
+        tau, p_value = stats.weightedtau(x, y)
+        assert_approx_equal(tau, -0.56694968153682723)
+        assert_equal(np.nan, p_value)
+        tau, p_value = stats.weightedtau(x, y, additive=False)
+        assert_approx_equal(tau, -0.62205716951801038)
+        assert_equal(np.nan, p_value)
+        # This must be exactly Kendall's tau
+        tau, p_value = stats.weightedtau(x, y, weigher=lambda x: 1)
+        assert_approx_equal(tau, -0.47140452079103173)
+        assert_equal(np.nan, p_value)
+
+        # test for namedtuple attribute results
+        res = stats.weightedtau(x, y)
+        attributes = ('correlation', 'pvalue')
+        check_named_results(res, attributes)
+        assert_equal(res.correlation, res.statistic)
+
+        # Asymmetric, ranked version
+        tau, p_value = stats.weightedtau(x, y, rank=None)
+        assert_approx_equal(tau, -0.4157652301037516)
+        assert_equal(np.nan, p_value)
+        tau, p_value = stats.weightedtau(y, x, rank=None)
+        assert_approx_equal(tau, -0.7181341329699029)
+        assert_equal(np.nan, p_value)
+        tau, p_value = stats.weightedtau(x, y, rank=None, additive=False)
+        assert_approx_equal(tau, -0.40644850966246893)
+        assert_equal(np.nan, p_value)
+        tau, p_value = stats.weightedtau(y, x, rank=None, additive=False)
+        assert_approx_equal(tau, -0.83766582937355172)
+        assert_equal(np.nan, p_value)
+        tau, p_value = stats.weightedtau(x, y, rank=False)
+        assert_approx_equal(tau, -0.51604397940261848)
+        assert_equal(np.nan, p_value)
+        # This must be exactly Kendall's tau
+        tau, p_value = stats.weightedtau(x, y, rank=True, weigher=lambda x: 1)
+        assert_approx_equal(tau, -0.47140452079103173)
+        assert_equal(np.nan, p_value)
+        tau, p_value = stats.weightedtau(y, x, rank=True, weigher=lambda x: 1)
+        assert_approx_equal(tau, -0.47140452079103173)
+        assert_equal(np.nan, p_value)
+        # Test argument conversion
+        tau, p_value = stats.weightedtau(np.asarray(x, dtype=np.float64), y)
+        assert_approx_equal(tau, -0.56694968153682723)
+        tau, p_value = stats.weightedtau(np.asarray(x, dtype=np.int16), y)
+        assert_approx_equal(tau, -0.56694968153682723)
+        tau, p_value = stats.weightedtau(np.asarray(x, dtype=np.float64),
+                                         np.asarray(y, dtype=np.float64))
+        assert_approx_equal(tau, -0.56694968153682723)
+        # All ties
+        with pytest.warns(SmallSampleWarning, match="One or more sample..."):
+            tau, p_value = stats.weightedtau([], [])
+        assert_equal(np.nan, tau)
+        assert_equal(np.nan, p_value)
+        with pytest.warns(SmallSampleWarning, match="One or more sample..."):
+            tau, p_value = stats.weightedtau([0], [0])
+        assert_equal(np.nan, tau)
+        assert_equal(np.nan, p_value)
+        # Size mismatches
+        assert_raises(ValueError, stats.weightedtau, [0, 1], [0, 1, 2])
+        assert_raises(ValueError, stats.weightedtau, [0, 1], [0, 1], [0, 1, 2])
+        # NaNs
+        x = [12, 2, 1, 12, 2]
+        y = [1, 4, 7, 1, np.nan]
+        tau, p_value = stats.weightedtau(x, y)
+        assert_approx_equal(tau, -0.56694968153682723)
+        x = [12, 2, np.nan, 12, 2]
+        tau, p_value = stats.weightedtau(x, y)
+        assert_approx_equal(tau, -0.56694968153682723)
+        # NaNs when the dtype of x and y are all np.float64
+        x = [12.0, 2.0, 1.0, 12.0, 2.0]
+        y = [1.0, 4.0, 7.0, 1.0, np.nan]
+        tau, p_value = stats.weightedtau(x, y)
+        assert_approx_equal(tau, -0.56694968153682723)
+        x = [12.0, 2.0, np.nan, 12.0, 2.0]
+        tau, p_value = stats.weightedtau(x, y)
+        assert_approx_equal(tau, -0.56694968153682723)
+        # NaNs when there are more than one NaN in x or y
+        x = [12.0, 2.0, 1.0, 12.0, 1.0]
+        y = [1.0, 4.0, 7.0, 1.0, 1.0]
+        tau, p_value = stats.weightedtau(x, y)
+        assert_approx_equal(tau, -0.6615242347139803)
+        x = [12.0, 2.0, np.nan, 12.0, np.nan]
+        tau, p_value = stats.weightedtau(x, y)
+        assert_approx_equal(tau, -0.6615242347139803)
+        y = [np.nan, 4.0, 7.0, np.nan, np.nan]
+        tau, p_value = stats.weightedtau(x, y)
+        assert_approx_equal(tau, -0.6615242347139803)
+
+
+    def test_segfault_issue_9710(self):
+        # https://github.com/scipy/scipy/issues/9710
+        # This test was created to check segfault
+        # In issue SEGFAULT only repros in optimized builds after calling
+        # the function twice
+        message = "One or more sample arguments is too small"
+        with pytest.warns(SmallSampleWarning, match=message):
+            stats.weightedtau([1], [1.0])
+            stats.weightedtau([1], [1.0])
+            # The code below also caused SEGFAULT
+            stats.weightedtau([np.nan], [52])
+
+
+    def test_weightedtau_vs_quadratic(self):
+        # Trivial quadratic implementation, all parameters mandatory
+        def wkq(x, y, rank, weigher, add):
+            tot = conc = disc = u = v = 0
+            for (i, j) in product(range(len(x)), range(len(x))):
+                w = weigher(rank[i]) + weigher(rank[j]) if add \
+                    else weigher(rank[i]) * weigher(rank[j])
+                tot += w
+                if x[i] == x[j]:
+                    u += w
+                if y[i] == y[j]:
+                    v += w
+                if x[i] < x[j] and y[i] < y[j] or x[i] > x[j] and y[i] > y[j]:
+                    conc += w
+                elif x[i] < x[j] and y[i] > y[j] or x[i] > x[j] and y[i] < y[j]:
+                    disc += w
+            return (conc - disc) / np.sqrt(tot - u) / np.sqrt(tot - v)
+
+        def weigher(x):
+            return 1. / (x + 1)
+
+        rng = np.random.default_rng(42)
+        for s in range(3,10):
+            a = []
+            # Generate rankings with ties
+            for i in range(s):
+                a += [i]*i
+            b = list(a)
+            rng.shuffle(a)
+            rng.shuffle(b)
+            # First pass: use element indices as ranks
+            rank = np.arange(len(a), dtype=np.intp)
+            for _ in range(2):
+                for add in [True, False]:
+                    expected = wkq(a, b, rank, weigher, add)
+                    actual = stats.weightedtau(a, b, rank, weigher, add).statistic
+                    assert_approx_equal(expected, actual)
+                # Second pass: use a random rank
+                rng.shuffle(rank)
+
+
+@make_xp_test_case(stats.linregress)
+class TestRegression:
+    def test_linregressBIGX(self, xp):
+        # W.II.F.  Regress BIG on X.
+        dtype = xp.float64  # needed for accurate results
+        result = stats.linregress(xp.asarray(X), xp.asarray(BIG))
+        xp_assert_close(result.intercept, xp.asarray(99999990., dtype=dtype))
+        xp_assert_close(result.rvalue, xp.asarray(1.0, dtype=dtype))
+        # The uncertainty ought to be almost zero
+        # since all points lie on a line
+        zero = xp.asarray(0.0, dtype=dtype)
+        xp_assert_close(result.stderr, zero, atol=1e-7)  # atol for JAX
+        xp_assert_close(result.intercept_stderr, zero, atol=1e-7)
+
+    def test_regressXX(self, xp):
+        # W.IV.B.  Regress X on X.
+        # The constant should be exactly 0 and the regression coefficient
+        # should be 1.  This is a perfectly valid regression and the
+        # program should not complain.
+        result = stats.linregress(xp.asarray(X.tolist()), xp.asarray(X.tolist()))
+        xp_assert_close(result.intercept, xp.asarray(0.0), atol=1e-15)
+        xp_assert_close(result.rvalue, xp.asarray(1.0))
+        # The uncertainly on regression through two points ought to be 0
+        xp_assert_close(result.stderr, xp.asarray(0.0), atol=1e-7)
+        xp_assert_close(result.intercept_stderr, xp.asarray(0.0), atol=1e-7)
+
+        # W.IV.C. Regress X on BIG and LITTLE (two predictors).  The program
+        # should tell you that this model is "singular" because BIG and
+        # LITTLE are linear combinations of each other.  Cryptic error
+        # messages are unacceptable here.  Singularity is the most
+        # fundamental regression error.
+        #
+        # Need to figure out how to handle multiple linear regression.
+        # This is not obvious
+
+    def test_regressZEROX(self, xp):
+        # W.IV.D. Regress ZERO on X.
+        # The program should inform you that ZERO has no variance or it should
+        # go ahead and compute the regression and report a correlation and
+        # total sum of squares of exactly 0.
+        result = stats.linregress(xp.asarray(X.tolist()), xp.asarray(ZERO.tolist()))
+        xp_assert_close(result.intercept, xp.asarray(0.0))
+        with eager_warns(stats.ConstantInputWarning, match="An input array...", xp=xp):
+            ref_rvalue = stats.pearsonr(xp.asarray(X.tolist()),
+                                        xp.asarray(ZERO.tolist())).statistic
+        xp_assert_close(result.rvalue, ref_rvalue)
+
+    def test_regress_simple(self, xp):
+        # Regress a line with sinusoidal noise.
+        x = xp.linspace(0, 100, 100)
+        y = 0.2 * xp.linspace(0, 100, 100) + 10
+        y = y + xp.sin(xp.linspace(0, 20, 100))
+
+        result = stats.linregress(x, y)
+        lr = LinregressResult
+        assert isinstance(result, lr)
+        xp_assert_close(result.stderr, xp.asarray(2.3957814497838803e-3))
+
+    def test_regress_alternative(self, xp):
+        # test alternative parameter
+        x = xp.linspace(0, 100, 100)
+        y = 0.2 * xp.linspace(0, 100, 100) + 10  # slope is greater than zero
+        y = y + xp.sin(xp.linspace(0, 20, 100))
+
+        with pytest.raises(ValueError, match="`alternative` must be 'less'..."):
+            stats.linregress(x, y, alternative="ekki-ekki")
+
+        res1 = stats.linregress(x, y, alternative="two-sided")
+
+        # slope is greater than zero, so "less" p-value should be large
+        res2 = stats.linregress(x, y, alternative="less")
+        xp_assert_close(res2.pvalue, 1 - (res1.pvalue / 2))
+
+        # slope is greater than zero, so "greater" p-value should be small
+        res3 = stats.linregress(x, y, alternative="greater")
+        xp_assert_close(res3.pvalue, res1.pvalue / 2)
+
+        assert res1.rvalue == res2.rvalue == res3.rvalue
+
+    @pytest.mark.parametrize("dtype", [None, 'float32', 'float64'])
+    def test_regress_against_R(self, dtype, xp):
+        # test against R `lm`
+        # options(digits=16)
+        # x <- c(151, 174, 138, 186, 128, 136, 179, 163, 152, 131)
+        # y <- c(63, 81, 56, 91, 47, 57, 76, 72, 62, 48)
+        # relation <- lm(y~x)
+        # print(summary(relation))
+        dtype = dtype if dtype is None else getattr(xp, dtype)
+        x = xp.asarray([151, 174, 138, 186, 128, 136, 179, 163, 152, 131], dtype=dtype)
+        y = xp.asarray([63, 81, 56, 91, 47, 57, 76, 72, 62, 48], dtype=dtype)
+        res = stats.linregress(x, y, alternative="two-sided")
+        # expected values from R's `lm` above
+        xp_assert_close(res.slope, xp.asarray(0.6746104491292, dtype=dtype))
+        xp_assert_close(res.intercept, xp.asarray(-38.4550870760770, dtype=dtype))
+        xp_assert_close(res.rvalue, xp.sqrt(xp.asarray(0.95478224775, dtype=dtype)))
+        xp_assert_close(res.pvalue, xp.asarray(1.16440531074e-06, dtype=dtype))
+        xp_assert_close(res.stderr, xp.asarray(0.0519051424731, dtype=dtype))
+        xp_assert_close(res.intercept_stderr, xp.asarray(8.0490133029927, dtype=dtype))
+
+    def test_linregress(self, xp):
+        # compared with multivariate ols with pinv
+        x = np.arange(11)
+        y = np.arange(5, 16)
+        y[[(1), (-2)]] -= 1
+        y[[(0), (-1)]] += 1
+
+        result = stats.linregress(xp.asarray(x), xp.asarray(y))
+
+        # This test used to use 'assert_array_almost_equal' but its
+        # formulation got confusing since LinregressResult became
+        # _lib._bunch._make_tuple_bunch instead of namedtuple
+        # (for backwards compatibility, see PR #12983)
+        def assert_ae(x, y):
+            return xp_assert_close(x, xp.asarray(y), atol=1e-14)
+        assert_ae(result.slope, 1.0)
+        assert_ae(result.intercept, 5.0)
+        assert_ae(result.rvalue, 0.98229948625750)
+        assert_ae(result.pvalue, 7.45259691e-008)
+        assert_ae(result.stderr, 0.063564172616372733)
+        assert_ae(result.intercept_stderr, 0.37605071654517686)
+
+    def test_regress_simple_negative_cor(self, xp):
+        # If the slope of the regression is negative the factor R tend
+        # to -1 not 1.  Sometimes rounding errors makes it < -1
+        # leading to stderr being NaN.
+        a, n = 1e-71, 100000
+        dtype = xp.float64
+        x = xp.linspace(a, 2 * a, n, dtype=dtype)  # doesn't pass with float32
+        y = xp.linspace(2 * a, a, n, dtype=dtype)
+        result = stats.linregress(x, y)
+
+        # Make sure propagated numerical errors
+        # did not bring rvalue below -1 (or were coerced)
+        assert result.rvalue >= -1
+        xp_assert_close(result.rvalue, xp.asarray(-1., dtype=dtype))
+
+        # slope and intercept stderror should stay numeric
+        assert not xp.isnan(result.stderr)
+        assert not xp.isnan(result.intercept_stderr)
+
+    def test_linregress_result_attributes(self, xp):
+        x = xp.linspace(0, 100, 100)
+        y = 0.2 * xp.linspace(0, 100, 100) + 10
+        y = y + xp.sin(xp.linspace(0, 20, 100))
+        result = stats.linregress(x, y)
+
+        # Result is of a correct class
+        lr = LinregressResult
+        assert isinstance(result, lr)
+
+        # LinregressResult elements have correct names
+        attributes = ('slope', 'intercept', 'rvalue', 'pvalue', 'stderr')
+        check_named_results(result, attributes, xp=xp)
+        # Also check that the extra attribute (intercept_stderr) is present
+        assert 'intercept_stderr' in dir(result)
+
+    def test_regress_two_inputs(self, xp):
+        # Regress a simple line formed by two points.
+        x = xp.arange(2)
+        y = xp.arange(3, 5)
+        result = stats.linregress(x, y)
+
+        xp_assert_close(result.slope, xp.asarray(1.0))
+        xp_assert_close(result.intercept, xp.asarray(3.0))
+        xp_assert_close(result.rvalue, xp.asarray(1.0))
+
+        NaN = xp.asarray(xp.nan)
+        xp_assert_equal(result.pvalue, NaN)
+        xp_assert_equal(result.stderr, NaN)
+        xp_assert_equal(result.intercept_stderr, NaN)
+
+    def test_regress_two_inputs_horizontal_line(self, xp):
+        # Regress a horizontal line formed by two points.
+        x = xp.arange(2.)
+        y = xp.ones(2)
+        result = stats.linregress(x, y)
+
+        # Horizontal line
+        xp_assert_close(result.slope, xp.asarray(0.0))
+        xp_assert_close(result.intercept, xp.asarray(1.0))
+
+        NaN = xp.asarray(xp.nan)
+        xp_assert_equal(result.rvalue, NaN)
+        xp_assert_equal(result.pvalue, NaN)
+        xp_assert_equal(result.stderr, NaN)
+        xp_assert_equal(result.intercept_stderr, NaN)
+
+    def test_nist_norris(self, xp):
+        # If this causes a lint failure in the future, please note the history of
+        # requests to allow extra whitespace in table formatting (e.g. gh-12367).
+        # Also see https://github.com/scipy/scipy/wiki/Why-do-we-not-use-an-auto%E2%80%90formatter%3F  # noqa: E501
+        x = [  0.2, 337.4, 118.2, 884.6, 10.1,  226.5,
+             666.3, 996.3, 448.6, 777.0, 558.2,   0.4,
+               0.6, 775.5, 666.9, 338.0, 447.5,  11.6,
+             556.0, 228.1, 995.8, 887.6, 120.2,   0.3,
+               0.3, 556.8, 339.1, 887.2, 999.0, 779.0,
+              11.1, 118.3, 229.2, 669.1, 448.9,   0.5]
+
+        y = [  0.1, 338.8, 118.1, 888.0, 9.2,   228.1,
+             668.5, 998.5, 449.1, 778.9, 559.2,   0.3,
+               0.1, 778.1, 668.8, 339.3, 448.9,  10.8,
+             557.7, 228.3, 998.0, 888.8, 119.6,   0.3,
+               0.6, 557.6, 339.3, 888.0, 998.5, 778.9,
+              10.2, 117.6, 228.9, 668.4, 449.2,   0.2]
+
+        result = stats.linregress(xp.asarray(x), xp.asarray(y))
+
+        xp_assert_close(result.slope, xp.asarray(1.00211681802045))
+        xp_assert_close(result.intercept, xp.asarray(-0.262323073774029))
+        xp_assert_close(result.rvalue**2, xp.asarray(0.999993745883712))
+        xp_assert_close(result.pvalue, xp.asarray(0.0), atol=1e-80)
+        if result.pvalue.dtype == xp.float64:  # these are inaccurate with float32
+            xp_assert_close(result.stderr, xp.asarray(0.00042979684820))
+            xp_assert_close(result.intercept_stderr, xp.asarray(0.23281823430153))
+
+    def test_compare_to_polyfit(self, xp):
+        x = np.linspace(0, 100, 100)
+        y = 0.2 * np.linspace(0, 100, 100) + 10
+        y += np.sin(np.linspace(0, 20, 100))
+        result = stats.linregress(xp.asarray(x), xp.asarray(y))
+        poly = np.polyfit(x, y, 1)  # Fit 1st degree polynomial
+
+        # Make sure linear regression slope and intercept
+        # match with results from numpy polyfit
+        xp_assert_close(result.slope, xp.asarray(poly[0]))
+        xp_assert_close(result.intercept, xp.asarray(poly[1]))
+
+    def test_linregress_two_points_nan_inference(self, xp):
+        # Test for gh-24684
+        x = xp.asarray([0., 1.])
+        y = xp.asarray([0., 1.])
+
+        res = stats.linregress(x, y)
+
+        NaN = xp.asarray(xp.nan)
+        xp_assert_equal(res.pvalue, NaN)
+        xp_assert_equal(res.stderr, NaN)
+        xp_assert_equal(res.intercept_stderr, NaN)
+
+        # Point estimates should still be correct
+        xp_assert_close(res.slope, xp.asarray(1.0))
+        xp_assert_close(res.intercept, xp.asarray(0.0))
+
+    def test_empty_input(self, xp):
+        with eager_warns(SmallSampleWarning, match="One or more sample...", xp=xp):
+            res = stats.linregress(xp.asarray([]), xp.asarray([]))
+            NaN = xp.asarray(xp.nan)
+            xp_assert_equal(res.slope, NaN)
+            xp_assert_equal(res.intercept, NaN)
+            xp_assert_equal(res.rvalue, NaN)
+            xp_assert_equal(res.pvalue, NaN)
+            xp_assert_equal(res.stderr, NaN)
+            xp_assert_equal(res.intercept_stderr, NaN)
+
+    def test_nan_input(self, xp):
+        x = np.arange(10.)
+        x[9] = np.nan
+        x = xp.asarray(x.tolist())
+
+        with np.errstate(invalid="ignore"):
+            result = stats.linregress(x, x)
+
+        # Make sure the result still comes back as `LinregressResult`
+        lr = LinregressResult
+        assert isinstance(result, lr)
+        NaN = xp.asarray(xp.nan)
+        xp_assert_equal(result.slope, NaN)
+        xp_assert_equal(result.intercept, NaN)
+        xp_assert_equal(result.rvalue, NaN)
+        xp_assert_equal(result.pvalue, NaN)
+        xp_assert_equal(result.stderr, NaN)
+        xp_assert_equal(result.intercept_stderr, NaN)
+
+    def test_identical_x(self, xp):
+        rng = np.random.default_rng(7872425088)
+        x = xp.zeros(10)
+        y = xp.asarray(rng.random(10).tolist())
+        with np.errstate(invalid='ignore'):
+            res = stats.linregress(x, y)
+        NaN = xp.asarray(xp.nan)
+        xp_assert_equal(res.slope, NaN)
+        xp_assert_equal(res.intercept, NaN)
+        xp_assert_equal(res.rvalue, NaN)
+        xp_assert_equal(res.pvalue, NaN)
+        xp_assert_equal(res.stderr, NaN)
+        xp_assert_equal(res.intercept_stderr, NaN)
+
+
+class HistFunctionsTest:
+    def test_input_validation(self, xp):
+        histfun = getattr(stats, self.histfun)
+        a = xp.arange(20)
+        numbins = 10
+        defaultreallimits = (0, 20)
+        weights = xp.ones(20)
+
+        message = "If specified, `defaultreallimits` must be..."
+        with pytest.raises(ValueError, match=message):
+            histfun(a, numbins, 10)
+        with pytest.raises(ValueError, match=message):
+            histfun(a, numbins, (1, 2, 3))
+        with pytest.raises(ValueError, match=message):
+            histfun(a, numbins, defaultreallimits[::-1])
+
+        message = r"`a` and \(if specified\) `weights` must have real dtype."
+        with pytest.raises(ValueError, match=message):
+            histfun(xp.astype(a, xp.complex128), numbins, defaultreallimits)
+        with pytest.raises(ValueError, match=message):
+            histfun(a, numbins, defaultreallimits, xp.astype(weights, xp.complex128))
+
+        if not is_lazy_array(weights):
+            message = "All `weights` must be non-negative."
+            with pytest.raises(ValueError, match=message):
+                histfun(a, numbins, defaultreallimits, -weights)
+
+    @pytest.mark.parametrize("dtype", [None, 'float32', 'float64'])
+    @pytest.mark.parametrize("edge_points", [False, True])
+    @pytest.mark.parametrize("specify_limits", [False, True])
+    @pytest.mark.parametrize("specify_weights", [False, True])
+    def test_against_reference(self, dtype, edge_points, specify_limits,
+                               specify_weights, xp):
+        rng = np.random.default_rng(5194553734)
+        nbins = int(rng.integers(10, 15))
+
+        if edge_points and not specify_limits:
+            pytest.skip("Limits must be specified to determine edge points.")
+        if edge_points and (is_jax(xp)
+                            or (dtype != 'float64' and is_torch(xp))
+                            or (dtype != 'float64' and is_cupy(xp))):
+            pytest.skip("Some backends are having trouble with edge point arithmetic.")
+
+        a = np.astype(rng.random(100), dtype)
+
+        if specify_limits:
+            limits = np.astype(np.sort(rng.random(2)), dtype)
+            range_ = limits
+        else:
+            # copy-pasted from documentation to generate reference values
+            s = (1 / 2)*(a.max() - a.min()) / (nbins - 1)
+            range_ = (a.min() - s, a.max() + s)
+            limits = None
+
+        if edge_points:
+            _, edges = np.histogram(a, bins=nbins, range=range_, density=False)
+            a2 = np.repeat(edges, rng.integers(5, size=edges.shape).tolist())
+            a = np.concat([a, a2], dtype=dtype)
+
+        weights = np.astype(rng.random(a.shape), dtype) if specify_weights else None
+
+        bin_counts, ref_bins = np.histogram(a, bins=nbins, range=range_, density=False)
+        ref_hist, _ = np.histogram(a, bins=nbins, range=range_,
+                                   weights=weights, density=False)
+
+        dtype = xp_default_dtype(xp) if dtype is None else getattr(xp, dtype)
+        histfun = getattr(stats, self.histfun)
+        weights = weights if weights is None else xp.asarray(weights, dtype=dtype)
+        res = histfun(xp.asarray(a, dtype=dtype), nbins, limits, weights)
+        ref_hist = xp.asarray(ref_hist, dtype=dtype)
+
+        rtol = 1e-12 if dtype == xp.float64 else 2e-5
+        if histfun == stats.cumfreq:
+            ref_cumcount = xp.cumulative_sum(ref_hist)
+            xp_assert_close(res.cumcount, ref_cumcount, rtol=rtol)
+        else:
+            den = a.shape[0] if weights is None else xp.sum(weights)
+            ref_frequency = xp.asarray(ref_hist/den, dtype=dtype)
+            xp_assert_close(res.frequency, ref_frequency, rtol=rtol)
+        xp_assert_close(res.lowerlimit, xp.asarray(ref_bins[0], dtype=dtype))
+        xp_assert_close(res.binsize, xp.asarray(ref_bins[1] - ref_bins[0], dtype=dtype))
+        xp_assert_close(res.extrapoints, xp.asarray(a.size - sum(bin_counts.tolist())))
+
+
+@make_xp_test_case(stats.cumfreq)
+class TestCumfreq(HistFunctionsTest):
+    histfun = 'cumfreq'
+
+    def test_cumfreq(self, xp):
+        x = xp.asarray([1, 4, 2, 1, 3, 1])
+        cumfreqs, lowlim, binsize, extrapoints = stats.cumfreq(x, numbins=4)
+        xp_assert_equal(cumfreqs, xp.asarray([3., 4., 5., 6.]))
+        cumfreqs, lowlim, binsize, extrapoints = stats.cumfreq(
+            x, numbins=4, defaultreallimits=(1.5, 5))
+        assert extrapoints == 3
+
+        # test for namedtuple attribute results
+        attributes = ('cumcount', 'lowerlimit', 'binsize', 'extrapoints')
+        res = stats.cumfreq(x, numbins=4, defaultreallimits=(1.5, 5))
+        check_named_results(res, attributes, xp=xp)
+
+
+@make_xp_test_case(stats.relfreq)
+class TestRelfreq(HistFunctionsTest):
+    histfun = 'relfreq'
+
+    def test_relfreq(self, xp):
+        a = xp.asarray([1, 4, 2, 1, 3, 1])
+        relfreqs, lowlim, binsize, extrapoints = stats.relfreq(a, numbins=4)
+        xp_assert_close(relfreqs, xp.asarray([0.5, 0.16666667, 0.16666667, 0.16666667]))
+
+        # test for namedtuple attribute results
+        attributes = ('frequency', 'lowerlimit', 'binsize', 'extrapoints')
+        res = stats.relfreq(a, numbins=4)
+        check_named_results(res, attributes, xp=xp)
+
+    def test_relfreq_array_like(self):  # array_like is np only
+        # check array_like input is accepted
+        a = [1, 4, 2, 1, 3, 1]
+        res, _, _, _ = stats.relfreq(a, numbins=4)
+        ref, _, _, _ = stats.relfreq(np.asarray(a), numbins=4)
+        xp_assert_equal(res, ref)
+
+
+class TestScoreatpercentile:
+    def setup_method(self):
+        self.a1 = [3, 4, 5, 10, -3, -5, 6]
+        self.a2 = [3, -6, -2, 8, 7, 4, 2, 1]
+        self.a3 = [3., 4, 5, 10, -3, -5, -6, 7.0]
+
+    def test_basic(self):
+        x = arange(8) * 0.5
+        assert_equal(stats.scoreatpercentile(x, 0), 0.)
+        assert_equal(stats.scoreatpercentile(x, 100), 3.5)
+        assert_equal(stats.scoreatpercentile(x, 50), 1.75)
+
+    def test_fraction(self):
+        scoreatperc = stats.scoreatpercentile
+
+        # Test defaults
+        assert_equal(scoreatperc(list(range(10)), 50), 4.5)
+        assert_equal(scoreatperc(list(range(10)), 50, (2,7)), 4.5)
+        assert_equal(scoreatperc(list(range(100)), 50, limit=(1, 8)), 4.5)
+        assert_equal(scoreatperc(np.array([1, 10,100]), 50, (10,100)), 55)
+        assert_equal(scoreatperc(np.array([1, 10,100]), 50, (1,10)), 5.5)
+
+        # explicitly specify interpolation_method 'fraction' (the default)
+        assert_equal(scoreatperc(list(range(10)), 50, interpolation_method='fraction'),
+                     4.5)
+        assert_equal(scoreatperc(list(range(10)), 50, limit=(2, 7),
+                                 interpolation_method='fraction'),
+                     4.5)
+        assert_equal(scoreatperc(list(range(100)), 50, limit=(1, 8),
+                                 interpolation_method='fraction'),
+                     4.5)
+        assert_equal(scoreatperc(np.array([1, 10,100]), 50, (10, 100),
+                                 interpolation_method='fraction'),
+                     55)
+        assert_equal(scoreatperc(np.array([1, 10,100]), 50, (1,10),
+                                 interpolation_method='fraction'),
+                     5.5)
+
+    def test_lower_higher(self):
+        scoreatperc = stats.scoreatpercentile
+
+        # interpolation_method 'lower'/'higher'
+        assert_equal(scoreatperc(list(range(10)), 50,
+                                 interpolation_method='lower'), 4)
+        assert_equal(scoreatperc(list(range(10)), 50,
+                                 interpolation_method='higher'), 5)
+        assert_equal(scoreatperc(list(range(10)), 50, (2,7),
+                                 interpolation_method='lower'), 4)
+        assert_equal(scoreatperc(list(range(10)), 50, limit=(2,7),
+                                 interpolation_method='higher'), 5)
+        assert_equal(scoreatperc(list(range(100)), 50, (1,8),
+                                 interpolation_method='lower'), 4)
+        assert_equal(scoreatperc(list(range(100)), 50, (1,8),
+                                 interpolation_method='higher'), 5)
+        assert_equal(scoreatperc(np.array([1, 10, 100]), 50, (10, 100),
+                                 interpolation_method='lower'), 10)
+        assert_equal(scoreatperc(np.array([1, 10, 100]), 50, limit=(10, 100),
+                                 interpolation_method='higher'), 100)
+        assert_equal(scoreatperc(np.array([1, 10, 100]), 50, (1, 10),
+                                 interpolation_method='lower'), 1)
+        assert_equal(scoreatperc(np.array([1, 10, 100]), 50, limit=(1, 10),
+                                 interpolation_method='higher'), 10)
+
+    def test_sequence_per(self):
+        x = arange(8) * 0.5
+        expected = np.array([0, 3.5, 1.75])
+        res = stats.scoreatpercentile(x, [0, 100, 50])
+        assert_allclose(res, expected)
+        assert_(isinstance(res, np.ndarray))
+        # Test with ndarray.  Regression test for gh-2861
+        assert_allclose(stats.scoreatpercentile(x, np.array([0, 100, 50])),
+                        expected)
+        # Also test combination of 2-D array, axis not None and array-like per
+        res2 = stats.scoreatpercentile(np.arange(12).reshape((3,4)),
+                                       np.array([0, 1, 100, 100]), axis=1)
+        expected2 = array([[0, 4, 8],
+                           [0.03, 4.03, 8.03],
+                           [3, 7, 11],
+                           [3, 7, 11]])
+        assert_allclose(res2, expected2)
+
+    def test_axis(self):
+        scoreatperc = stats.scoreatpercentile
+        x = arange(12).reshape(3, 4)
+
+        assert_equal(scoreatperc(x, (25, 50, 100)), [2.75, 5.5, 11.0])
+
+        r0 = [[2, 3, 4, 5], [4, 5, 6, 7], [8, 9, 10, 11]]
+        assert_equal(scoreatperc(x, (25, 50, 100), axis=0), r0)
+
+        r1 = [[0.75, 4.75, 8.75], [1.5, 5.5, 9.5], [3, 7, 11]]
+        assert_equal(scoreatperc(x, (25, 50, 100), axis=1), r1)
+
+        x = array([[1, 1, 1],
+                   [1, 1, 1],
+                   [4, 4, 3],
+                   [1, 1, 1],
+                   [1, 1, 1]])
+        score = stats.scoreatpercentile(x, 50)
+        assert_equal(score.shape, ())
+        assert_equal(score, 1.0)
+        score = stats.scoreatpercentile(x, 50, axis=0)
+        assert_equal(score.shape, (3,))
+        assert_equal(score, [1, 1, 1])
+
+    def test_exception(self):
+        assert_raises(ValueError, stats.scoreatpercentile, [1, 2], 56,
+                      interpolation_method='foobar')
+        assert_raises(ValueError, stats.scoreatpercentile, [1], 101)
+        assert_raises(ValueError, stats.scoreatpercentile, [1], -1)
+
+    def test_empty(self):
+        assert_equal(stats.scoreatpercentile([], 50), np.nan)
+        assert_equal(stats.scoreatpercentile(np.array([[], []]), 50), np.nan)
+        assert_equal(stats.scoreatpercentile([], [50, 99]), [np.nan, np.nan])
+
+
+@make_xp_test_case(stats.mode)
+class TestMode:
+
+    def test_empty(self, xp):
+        with eager_warns(SmallSampleWarning, match=too_small_1d_not_omit, xp=xp):
+            vals, counts = stats.mode(xp.asarray([]))
+        xp_assert_equal(vals, xp.asarray(xp.nan))
+        xp_assert_equal(counts, xp.asarray(0.))
+
+    def test_scalar(self):
+        vals, counts = stats.mode(4.)
+        assert_equal(vals, np.array([4.]))
+        assert_equal(counts, np.array([1]))
+
+    def test_basic(self, xp):
+        data1 = xp.asarray([3, 5, 1, 10, 23, 3, 2, 6, 8, 6, 10, 6])
+        vals = stats.mode(data1)
+        xp_assert_equal(vals[0], xp.asarray(6))
+        xp_assert_equal(vals[1], xp.asarray(3))
+
+    def test_axes_keepdims(self, xp):
+        data1 = [10, 10, 30, 40]
+        data2 = [10, 10, 10, 10]
+        data3 = [20, 10, 20, 20]
+        data4 = [30, 30, 30, 30]
+        data5 = [40, 30, 30, 30]
+        arr = xp.asarray([data1, data2, data3, data4, data5])
+
+        vals = stats.mode(arr, axis=None, keepdims=True)
+        xp_assert_equal(vals[0], xp.asarray([[30]]))
+        xp_assert_equal(vals[1], xp.asarray([[8]]))
+
+        vals = stats.mode(arr, axis=0, keepdims=True)
+        xp_assert_equal(vals[0], xp.asarray([[10, 10, 30, 30]]))
+        xp_assert_equal(vals[1], xp.asarray([[2, 3, 3, 2]]))
+
+        vals = stats.mode(arr, axis=1, keepdims=True)
+        xp_assert_equal(vals[0], xp.asarray([[10], [10], [20], [30], [30]]))
+        xp_assert_equal(vals[1], xp.asarray([[2], [4], [3], [4], [3]]))
+
+    def test_axes(self, xp):
+        data1 = [10, 10, 30, 40]
+        data2 = [10, 10, 10, 10]
+        data3 = [20, 10, 20, 20]
+        data4 = [30, 30, 30, 30]
+        data5 = [40, 30, 30, 30]
+        arr = xp.asarray([data1, data2, data3, data4, data5])
+
+        vals = stats.mode(arr, axis=None)
+        xp_assert_equal(vals[0], xp.asarray(30))
+        xp_assert_equal(vals[1], xp.asarray(8))
+
+        vals = stats.mode(arr, axis=0)
+        xp_assert_equal(vals[0], xp.asarray([10, 10, 30, 30]))
+        xp_assert_equal(vals[1], xp.asarray([2, 3, 3, 2]))
+
+        vals = stats.mode(arr, axis=1)
+        xp_assert_equal(vals[0], xp.asarray([10, 10, 20, 30, 30]))
+        xp_assert_equal(vals[1], xp.asarray([2, 4, 3, 4, 3]))
+
+    @pytest.mark.parametrize('axis', range(-4, 0))
+    def test_negative_axes_gh_15375(self, axis, xp):
+        rng = np.random.default_rng(7090348401)
+        a = xp.asarray(rng.random((10, 11, 12, 13)))
+        res0 = stats.mode(a, axis=a.ndim+axis)
+        res1 = stats.mode(a, axis=axis)
+        xp_assert_equal(res0.mode, res1.mode)
+        xp_assert_equal(res0.count, res1.count)
+
+    def test_mode_result_attributes(self, xp):
+        data1 = xp.asarray([3, 5, 1, 10, 23, 3, 2, 6, 8, 6, 10, 6])
+        data2 = xp.asarray([])
+        actual = stats.mode(data1)
+        attributes = ('mode', 'count')
+        check_named_results(actual, attributes, xp=xp)
+        with eager_warns(SmallSampleWarning, match=too_small_1d_not_omit, xp=xp):
+            actual2 = stats.mode(data2)
+        check_named_results(actual2, attributes, xp=xp)
+
+    def test_nan_propagate(self, xp):
+        data1 = xp.asarray([3, np.nan, 5, 1, 10, 23, 3, 2, 6, 8, 6, 10, 6])
+        actual = stats.mode(data1)
+        xp_assert_equal(actual[0], xp.asarray(6, dtype=data1.dtype))
+        xp_assert_equal(actual[1], xp.asarray(3))
+
+    @skip_xp_backends(eager_only=True, reason="lazy arrays don't do 'raise'.")
+    def test_nan_omit(self, xp):
+        data1 = xp.asarray([3, np.nan, 5, 1, 10, 23, 3, 2, 6, 8, 6, 10, 6])
+        res = stats.mode(data1, nan_policy='omit')
+        xp_assert_equal(res.mode, xp.asarray(6.))
+        xp_assert_equal(res.count, xp.asarray(3))
+        assert_raises(ValueError, stats.mode, data1, nan_policy='raise')
+        assert_raises(ValueError, stats.mode, data1, nan_policy='foobar')
+
+    @skip_xp_backends(eager_only=True, reason="lazy arrays don't do 'omit'.")
+    @pytest.mark.parametrize("data", [
+        [3, 5, 1, 1, 3.],
+        [3, np.nan, 5, 1, 1, 3],
+        [3, 5, 1.],
+        [3, np.nan, 5, 1],
+    ])
+    @pytest.mark.parametrize('keepdims', [False, True])
+    def test_smallest_equal(self, data, keepdims, xp):
+        result = stats.mode(xp.asarray(data), nan_policy='omit', keepdims=keepdims)
+        if keepdims:
+            xp_assert_equal(result[0][0], xp.asarray(1.))
+        else:
+            xp_assert_equal(result[0], xp.asarray(1.))
+
+    @pytest.mark.parametrize('axis', range(-3, 3))
+    def test_mode_shape_gh_9955(self, axis, xp):
+        rng = np.random.default_rng(984213899)
+        a = xp.asarray(rng.uniform(size=(3, 4, 5)))
+        res = stats.mode(a, axis=axis, keepdims=False)
+        reference_shape = list(a.shape)
+        reference_shape.pop(axis)
+        np.testing.assert_array_equal(res.mode.shape, reference_shape)
+        np.testing.assert_array_equal(res.count.shape, reference_shape)
+
+    def test_nan_policy_propagate_gh_9815(self, xp):
+        # mode should treat np.nan as it would any other object when
+        # nan_policy='propagate'
+        a = xp.asarray([2, np.nan, 1, np.nan])
+        res = stats.mode(a)
+        assert xp.isnan(res.mode) and res.count == 2
+
+    def test_keepdims_empty(self, xp):
+        # test empty arrays
+        a = xp.zeros((1, 2, 3, 0))
+
+        res = stats.mode(a, axis=1, keepdims=False)
+        assert res.mode.shape == res.count.shape == (1, 3, 0)
+
+        res = stats.mode(a, axis=1, keepdims=True)
+        assert res.mode.shape == res.count.shape == (1, 1, 3, 0)
+
+    def test_keepdims_nonempty(selfself, xp):
+        # test nan_policy='propagate'
+        a = xp.asarray([[1, 3, 3, np.nan], [1, 1, np.nan, 1]])
+
+        res = stats.mode(a, axis=1, keepdims=False)
+        xp_assert_equal(res.mode, xp.asarray([3., 1.]))
+        xp_assert_equal(res.count, xp.asarray([2, 3]))
+
+        res = stats.mode(a, axis=1, keepdims=True)
+        xp_assert_equal(res.mode, xp.asarray([[3.], [1.]]))
+        xp_assert_equal(res.count, xp.asarray([[2], [3]]))
+
+        a = xp.asarray(a)
+        res = stats.mode(a, axis=None, keepdims=False)
+        ref = stats.mode(xp_ravel(a), keepdims=False)
+        xp_assert_equal(res.mode, ref.mode)
+        xp_assert_equal(res.count, ref.count)
+        assert res.mode.shape == ref.mode.shape == ()
+
+        res = stats.mode(a, axis=None, keepdims=True)
+        ref = stats.mode(xp_ravel(a), keepdims=True)
+        xp_assert_equal(xp_ravel(res.mode), xp_ravel(ref.mode))
+        assert res.mode.shape == (1, 1)
+        xp_assert_equal(xp_ravel(res.count), xp_ravel(ref.count))
+        assert res.count.shape == (1, 1)
+
+    def test_keepdims_nan_omit(self):
+        # test nan_policy='omit'
+        a = [[1, np.nan, np.nan, np.nan, 1],
+             [np.nan, np.nan, np.nan, np.nan, 2],
+             [1, 2, np.nan, 5, 5]]
+
+        res = stats.mode(a, axis=1, keepdims=False, nan_policy='omit')
+        assert_array_equal(res.mode, [1, 2, 5])
+        assert_array_equal(res.count, [2, 1, 2])
+
+        res = stats.mode(a, axis=1, keepdims=True, nan_policy='omit')
+        assert_array_equal(res.mode, [[1], [2], [5]])
+        assert_array_equal(res.count, [[2], [1], [2]])
+
+        a = np.array(a)
+        res = stats.mode(a, axis=None, keepdims=False, nan_policy='omit')
+        ref = stats.mode(a.ravel(), keepdims=False, nan_policy='omit')
+        assert_array_equal(res, ref)
+        assert res.mode.shape == ref.mode.shape == ()
+
+        res = stats.mode(a, axis=None, keepdims=True, nan_policy='omit')
+        ref = stats.mode(a.ravel(), keepdims=True, nan_policy='omit')
+        assert_equal(res.mode.ravel(), ref.mode.ravel())
+        assert res.mode.shape == (1, 1)
+        assert_equal(res.count.ravel(), ref.count.ravel())
+        assert res.count.shape == (1, 1)
+
+    @pytest.mark.parametrize("nan_policy", ['propagate', 'omit'])
+    def test_gh16955(self, nan_policy):
+        # Check that bug reported in gh-16955 is resolved
+        shape = (4, 3)
+        data = np.ones(shape)
+        data[0, 0] = np.nan
+        res = stats.mode(a=data, axis=1, keepdims=False, nan_policy=nan_policy)
+        assert_array_equal(res.mode, [1, 1, 1, 1])
+        assert_array_equal(res.count, [2, 3, 3, 3])
+
+        # Test with input from gh-16595. Support for non-numeric input
+        # was deprecated, so check for the appropriate error.
+        my_dtype = np.dtype([('asdf', np.uint8), ('qwer', np.float64, (3,))])
+        test = np.zeros(10, dtype=my_dtype)
+        message = "Argument `a` is not....|An argument has dtype...|The DType..."
+        with pytest.raises(TypeError, match=message):
+            stats.mode(test, nan_policy=nan_policy)
+
+    def test_gh9955(self):
+        # The behavior of mode with empty slices (whether the input was empty
+        # or all elements were omitted) was inconsistent. Test that this is
+        # resolved: the mode of an empty slice is NaN and the count is zero.
+        with pytest.warns(SmallSampleWarning, match=too_small_1d_not_omit):
+            res = stats.mode([])
+        ref = (np.nan, 0)
+        assert_equal(res, ref)
+
+        with pytest.warns(SmallSampleWarning, match=too_small_1d_omit):
+            res = stats.mode([np.nan], nan_policy='omit')
+        assert_equal(res, ref)
+
+        a = [[10., 20., 20.], [np.nan, np.nan, np.nan]]
+        with pytest.warns(SmallSampleWarning, match=too_small_nd_omit):
+            res = stats.mode(a, axis=1, nan_policy='omit')
+        ref = ([20, np.nan], [2, 0])
+        assert_equal(res, ref)
+
+        res = stats.mode(a, axis=1, nan_policy='propagate')
+        ref = ([20, np.nan], [2, 3])
+        assert_equal(res, ref)
+
+        z = np.array([[], []])
+        with pytest.warns(SmallSampleWarning, match=too_small_nd_not_omit):
+            res = stats.mode(z, axis=1)
+        ref = ([np.nan, np.nan], [0, 0])
+        assert_equal(res, ref)
+
+    @pytest.mark.filterwarnings('ignore::RuntimeWarning')  # np.mean warns
+    @pytest.mark.parametrize('z', [np.empty((0, 1, 2)), np.empty((1, 1, 2))])
+    def test_gh17214(self, z, xp):
+        z = xp.asarray(z)
+        if z.size == 0:
+            with pytest.warns(SmallSampleWarning, match=too_small_1d_not_omit):
+                res = stats.mode(z, axis=None, keepdims=True)
+        else:
+            res = stats.mode(z, axis=None, keepdims=True)
+        ref = xp.mean(z, axis=None, keepdims=True)
+        assert res[0].shape == res[1].shape == ref.shape == (1, 1, 1)
+
+    def test_raise_non_numeric_gh18254(self):
+
+        class ArrLike:
+            def __init__(self, x):
+                self._x = x
+
+            def __array__(self, dtype=None, copy=None):
+                return self._x.astype(object)
+
+        message = ("...only boolean and numerical dtypes..." if SCIPY_ARRAY_API
+                   else "Cannot interpret...")
+
+        with pytest.raises(TypeError, match=message):
+            stats.mode(ArrLike(np.arange(3)))
+
+        message = ("...only boolean and numerical dtypes..." if SCIPY_ARRAY_API
+                   else "Argument `a` is not recognized as numeric.")
+        with pytest.raises(TypeError, match=message):
+            stats.mode(np.arange(3, dtype=object))
+
+
+@make_xp_test_case(stats.sem)
+class TestSEM:
+
+    testcase = [1., 2., 3., 4.]
+    scalar_testcase = 4.
+
+    @pytest.mark.filterwarnings("ignore:invalid value encountered in divide")
+    def test_sem_scalar(self, xp):
+        # This is not in R, so used:
+        #     sqrt(var(testcase)*3/4)/sqrt(3)
+
+        # y = stats.sem(self.shoes[0])
+        # assert_approx_equal(y,0.775177399)
+        scalar_testcase = xp.asarray(self.scalar_testcase)[()]
+        if is_numpy(xp):
+            with pytest.warns(SmallSampleWarning, match=too_small_1d_not_omit):
+                y = stats.sem(scalar_testcase)
+        else:
+            # Other array types can emit a variety of warnings.
+            with warnings.catch_warnings():
+                warnings.simplefilter("ignore", UserWarning)
+                warnings.simplefilter("ignore", RuntimeWarning)
+                y = stats.sem(scalar_testcase)
+        assert xp.isnan(y)
+
+    def test_sem(self, xp):
+        testcase = xp.asarray(self.testcase)
+        y = stats.sem(testcase)
+        xp_assert_close(y, xp.asarray(0.6454972244))
+        n = len(self.testcase)
+        xp_assert_close(stats.sem(testcase, ddof=0) * (n/(n-2))**0.5,
+                        stats.sem(testcase, ddof=2))
+
+        x = xp.arange(10.)
+        x = xp.where(x == 9, xp.nan, x)
+        xp_assert_equal(stats.sem(x), xp.asarray(xp.nan))
+
+    @skip_xp_backends(eager_only=True, reason='lazy -> reduced nan_policy capabilities')
+    def test_sem_nan_policy(self, xp):
+        x = xp.arange(10.)
+        x[9] = xp.nan
+        xp_assert_close(stats.sem(x, nan_policy='omit'), xp.asarray(0.9128709291752769))
+        message = "The input contains nan values"
+        with pytest.raises(ValueError, match=message):
+            stats.sem(x, nan_policy='raise')
+        message = "nan_policy must be one of..."
+        with pytest.raises(ValueError, match=message):
+            stats.sem(x, nan_policy='foobar')
+
+
+@make_xp_test_case(stats.zmap)
+class TestZmap:
+
+    @pytest.mark.parametrize(
+        'x, y',
+        [([1., 2., 3., 4.], [1., 2., 3., 4.]),
+         ([1., 2., 3.], [0., 1., 2., 3., 4.])]
+    )
+    def test_zmap(self, x, y, xp):
+        # For these simple cases, calculate the expected result directly
+        # by using the formula for the z-score.
+        x, y = xp.asarray(x), xp.asarray(y)
+        expected = (x - xp.mean(y)) / xp.std(y, correction=0)
+        z = stats.zmap(x, y)
+        xp_assert_close(z, expected)
+
+    def test_zmap_axis(self, xp):
+        # Test use of 'axis' keyword in zmap.
+        x = xp.asarray([[0.0, 0.0, 1.0, 1.0],
+                        [1.0, 1.0, 1.0, 2.0],
+                        [2.0, 0.0, 2.0, 0.0]])
+
+        t1 = 1.0/(2.0/3)**0.5
+        t2 = 3.**0.5/3
+        t3 = 2.**0.5
+
+        z0 = stats.zmap(x, x, axis=0)
+        z1 = stats.zmap(x, x, axis=1)
+
+        z0_expected = [[-t1, -t3/2, -t3/2, 0.0],
+                       [0.0, t3, -t3/2, t1],
+                       [t1, -t3/2, t3, -t1]]
+        z1_expected = [[-1.0, -1.0, 1.0, 1.0],
+                       [-t2, -t2, -t2, 3.**0.5],
+                       [1.0, -1.0, 1.0, -1.0]]
+        z0_expected = xp.asarray(z0_expected)
+        z1_expected = xp.asarray(z1_expected)
+
+        xp_assert_close(z0, z0_expected)
+        xp_assert_close(z1, z1_expected)
+
+    def test_zmap_ddof(self, xp):
+        # Test use of 'ddof' keyword in zmap.
+        x = xp.asarray([[0.0, 0.0, 1.0, 1.0],
+                        [0.0, 1.0, 2.0, 3.0]])
+
+        z = stats.zmap(x, x, axis=1, ddof=1)
+
+        z0_expected = xp.asarray([-0.5, -0.5, 0.5, 0.5])/(1.0/3**0.5)
+        z1_expected = xp.asarray([-1.5, -0.5, 0.5, 1.5])/(5./3)**0.5
+        xp_assert_close(z[0, :], z0_expected)
+        xp_assert_close(z[1, :], z1_expected)
+
+    @pytest.mark.parametrize('ddof', [0, 2])
+    def test_zmap_nan_policy_omit(self, ddof, xp):
+        # nans in `scores` are propagated, regardless of `nan_policy`.
+        # `nan_policy` only affects how nans in `compare` are handled.
+        scores = xp.asarray([-3, -1, 2, np.nan])
+        compare = xp.asarray([-8, -3, 2, 7, 12, np.nan])
+        z = stats.zmap(scores, compare, ddof=ddof, nan_policy='omit')
+        # exclude nans from compare, don't use isnan + mask since that messes up
+        # dask
+        ref = stats.zmap(scores, compare[:5], ddof=ddof)
+        xp_assert_close(z, ref)
+
+    @pytest.mark.parametrize('ddof', [0, 2])
+    def test_zmap_nan_policy_omit_with_axis(self, ddof, xp):
+        scores = xp.reshape(xp.arange(-5.0, 9.0), (2, -1))
+        compare = np.reshape(np.linspace(-8, 6, 24), (2, -1))
+        compare[0, 4] = np.nan
+        compare[0, 6] = np.nan
+        compare[1, 1] = np.nan
+        # convert from numpy since some libraries like dask
+        # can't handle the data-dependent shapes from the isnan masking
+        compare_0_notna = xp.asarray(compare[0, :][~np.isnan(compare[0, :])])
+        compare_1_notna = xp.asarray(compare[1, :][~np.isnan(compare[1, :])])
+        compare = xp.asarray(compare)
+
+        z = stats.zmap(scores, compare, nan_policy='omit', axis=1, ddof=ddof)
+        res0 = stats.zmap(scores[0, :], compare_0_notna,
+                          ddof=ddof)
+        res1 = stats.zmap(scores[1, :], compare_1_notna,
+                          ddof=ddof)
+        expected = xp.stack((res0, res1))
+        xp_assert_close(z, expected)
+
+    @skip_xp_backends(eager_only=True, reason="lazy arrays don't do 'raise'.")
+    def test_zmap_nan_policy_raise(self, xp):
+        scores = xp.asarray([1, 2, 3])
+        compare = xp.asarray([-8, -3, 2, 7, 12, xp.nan])
+        with pytest.raises(ValueError, match='input contains nan'):
+            stats.zmap(scores, compare, nan_policy='raise')
+
+    @pytest.mark.filterwarnings("ignore:divide by zero encountered:RuntimeWarning:dask")
+    @pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning:dask")
+    def test_degenerate_input(self, xp):
+        scores = xp.arange(3)
+        compare = xp.ones(3)
+        ref = xp.asarray([-xp.inf, xp.nan, xp.inf])
+        with eager_warns(RuntimeWarning, match="Precision loss occurred...", xp=xp):
+            res = stats.zmap(scores, compare)
+        xp_assert_equal(res, ref)
+
+    @pytest.mark.filterwarnings("ignore:divide by zero encountered:RuntimeWarning:dask")
+    def test_complex_gh22404(self, xp):
+        res = stats.zmap(xp.asarray([1, 2, 3, 4]), xp.asarray([1, 1j, -1, -1j]))
+        ref = xp.asarray([1.+0.j, 2.+0.j, 3.+0.j, 4.+0.j])
+        xp_assert_close(res, ref)
+
+
+@make_xp_test_case(stats.zscore)
+class TestZscore:
+    def test_zscore(self, xp):
+        # not in R, so tested by using:
+        #    (testcase[i] - mean(testcase, axis=0)) / sqrt(var(testcase) * 3/4)
+        y = stats.zscore(xp.asarray([1, 2, 3, 4]))
+        desired = [-1.3416407864999, -0.44721359549996,
+                   0.44721359549996, 1.3416407864999]
+        xp_assert_close(y, xp.asarray(desired))
+
+    def test_zscore_axis(self, xp):
+        # Test use of 'axis' keyword in zscore.
+        x = xp.asarray([[0.0, 0.0, 1.0, 1.0],
+                        [1.0, 1.0, 1.0, 2.0],
+                        [2.0, 0.0, 2.0, 0.0]])
+
+        t1 = 1.0/(2.0/3)**0.5
+        t2 = 3**0.5/3
+        t3 = 2**0.5
+
+        z0 = stats.zscore(x, axis=0)
+        z1 = stats.zscore(x, axis=1)
+
+        z0_expected = [[-t1, -t3/2, -t3/2, 0.0],
+                       [0.0, t3, -t3/2, t1],
+                       [t1, -t3/2, t3, -t1]]
+        z1_expected = [[-1.0, -1.0, 1.0, 1.0],
+                       [-t2, -t2, -t2, 3**0.5],
+                       [1.0, -1.0, 1.0, -1.0]]
+
+        xp_assert_close(z0, xp.asarray(z0_expected))
+        xp_assert_close(z1, xp.asarray(z1_expected))
+
+    def test_zscore_ddof(self, xp):
+        # Test use of 'ddof' keyword in zscore.
+        x = xp.asarray([[0.0, 0.0, 1.0, 1.0],
+                        [0.0, 1.0, 2.0, 3.0]])
+
+        z = stats.zscore(x, axis=1, ddof=1)
+
+        z0_expected = xp.asarray([-0.5, -0.5, 0.5, 0.5])/(1.0/3**0.5)
+        z1_expected = xp.asarray([-1.5, -0.5, 0.5, 1.5])/((5./3)**0.5)
+        xp_assert_close(z[0, :], z0_expected)
+        xp_assert_close(z[1, :], z1_expected)
+
+    def test_zscore_nan_propagate(self, xp):
+        x = xp.asarray([1, 2, np.nan, 4, 5])
+        z = stats.zscore(x, nan_policy='propagate')
+        xp_assert_equal(z, xp.full(x.shape, xp.nan))
+
+    def test_zscore_nan_omit(self, xp):
+        x = xp.asarray([1, 2, xp.nan, 4, 5])
+
+        z = stats.zscore(x, nan_policy='omit')
+
+        expected = xp.asarray([-1.2649110640673518,
+                               -0.6324555320336759,
+                               xp.nan,
+                               0.6324555320336759,
+                               1.2649110640673518
+                               ])
+        xp_assert_close(z, expected)
+
+    def test_zscore_nan_omit_with_ddof(self, xp):
+        x = xp.asarray([xp.nan, 1.0, 3.0, 5.0, 7.0, 9.0])
+        z = stats.zscore(x, ddof=1, nan_policy='omit')
+        expected = xp.concat([xp.asarray([xp.nan]), stats.zscore(x[1:], ddof=1)])
+        xp_assert_close(z, expected)
+
+    @skip_xp_backends(eager_only=True, reason="lazy arrays don't do 'raise'.")
+    def test_zscore_nan_raise(self, xp):
+        x = xp.asarray([1, 2, xp.nan, 4, 5])
+        with pytest.raises(ValueError, match="The input contains nan..."):
+            stats.zscore(x, nan_policy='raise')
+
+    def test_zscore_constant_input_1d(self, xp):
+        x = xp.asarray([-0.087] * 3)
+        with eager_warns(RuntimeWarning, match="Precision loss occurred...", xp=xp):
+            z = stats.zscore(x)
+        xp_assert_equal(z, xp.full(x.shape, xp.nan))
+
+    @pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning:dask")
+    def test_zscore_constant_input_2d(self, xp):
+        x = xp.asarray([[10.0, 10.0, 10.0, 10.0],
+                        [10.0, 11.0, 12.0, 13.0]])
+        with eager_warns(RuntimeWarning, match="Precision loss occurred...", xp=xp):
+            z0 = stats.zscore(x, axis=0)
+        xp_assert_close(z0, xp.asarray([[xp.nan, -1.0, -1.0, -1.0],
+                                        [xp.nan, 1.0, 1.0, 1.0]]))
+
+        with eager_warns(RuntimeWarning, match="Precision loss occurred...", xp=xp):
+            z1 = stats.zscore(x, axis=1)
+        xp_assert_equal(z1, xp.stack([xp.asarray([xp.nan, xp.nan, xp.nan, xp.nan]),
+                                      stats.zscore(x[1, :])]))
+
+        z = stats.zscore(x, axis=None)
+        xp_assert_equal(z, xp.reshape(stats.zscore(xp.reshape(x, (-1,))), x.shape))
+
+        y = xp.ones((3, 6))
+        with eager_warns(RuntimeWarning, match="Precision loss occurred...", xp=xp):
+            z = stats.zscore(y, axis=None)
+        xp_assert_equal(z, xp.full_like(y, xp.nan))
+
+    @pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning:dask")
+    def test_zscore_constant_input_2d_nan_policy_omit(self, xp):
+        x = xp.asarray([[10.0, 10.0, 10.0, 10.0],
+                        [10.0, 11.0, 12.0, xp.nan],
+                        [10.0, 12.0, xp.nan, 10.0]])
+        s = (3/2)**0.5
+        s2 = 2**0.5
+
+        with eager_warns(RuntimeWarning, match="Precision loss occurred...", xp=xp):
+            z0 = stats.zscore(x, nan_policy='omit', axis=0)
+        xp_assert_close(z0, xp.asarray([[xp.nan, -s, -1.0, xp.nan],
+                                        [xp.nan, 0, 1.0, xp.nan],
+                                        [xp.nan, s, xp.nan, xp.nan]]))
+
+        with eager_warns(RuntimeWarning, match="Precision loss occurred...", xp=xp):
+            z1 = stats.zscore(x, nan_policy='omit', axis=1)
+        xp_assert_close(z1, xp.asarray([[xp.nan, xp.nan, xp.nan, xp.nan],
+                                        [-s, 0, s, xp.nan],
+                                        [-s2/2, s2, xp.nan, -s2/2]]))
+
+    @pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning:dask")
+    def test_zscore_2d_all_nan_row(self, xp):
+        # A row is all nan, and we use axis=1.
+        x = xp.asarray([[np.nan, np.nan, np.nan, np.nan],
+                        [10.0, 10.0, 12.0, 12.0]])
+        z = stats.zscore(x, nan_policy='omit', axis=1)
+        xp_assert_close(z, xp.asarray([[np.nan, np.nan, np.nan, np.nan],
+                                       [-1.0, -1.0, 1.0, 1.0]]))
+
+    @pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning:dask")
+    def test_zscore_2d_all_nan(self, xp):
+        # The entire 2d array is nan, and we use axis=None.
+        y = xp.full((2, 3), xp.nan)
+        z = stats.zscore(y, nan_policy='omit', axis=None)
+        xp_assert_equal(z, y)
+
+    @pytest.mark.parametrize('x', [np.array([]), np.zeros((3, 0, 5))])
+    def test_zscore_empty_input(self, x, xp):
+        x = xp.asarray(x)
+        z = stats.zscore(x)
+        xp_assert_equal(z, x)
+
+    @skip_xp_invalid_arg
+    def test_zscore_masked_element_0_gh19039(self, xp):
+        # zscore returned all NaNs when 0th element was masked. See gh-19039.
+        rng = np.random.default_rng(8675309)
+        x = rng.standard_normal(10)
+        mask = np.zeros_like(x)
+        y = np.ma.masked_array(x, mask)
+        y.mask[0] = True
+
+        ref = stats.zscore(x[1:])  # compute reference from non-masked elements
+        assert not np.any(np.isnan(ref))
+        res = stats.zscore(y)
+        assert_allclose(res[1:], ref)
+        res = stats.zscore(y, axis=None)
+        assert_allclose(res[1:], ref)
+
+        y[1:] = y[1]  # when non-masked elements are identical, result is nan
+        with pytest.warns(RuntimeWarning, match="Precision loss occurred..."):
+            res = stats.zscore(y)
+        assert_equal(res[1:], np.nan)
+        with pytest.warns(RuntimeWarning, match="Precision loss occurred..."):
+            res = stats.zscore(y, axis=None)
+        assert_equal(res[1:], np.nan)
+
+
+@make_xp_test_case(stats.gzscore)
+class TestGZscore:
+    def test_gzscore_normal_array(self, xp):
+        x = np.asarray([1, 2, 3, 4])
+        z = stats.gzscore(xp.asarray(x))
+        desired = np.log(x / stats.gmean(x)) / np.log(stats.gstd(x, ddof=0))
+        xp_assert_close(z, xp.asarray(desired, dtype=xp.asarray(1.).dtype))
+
+    @skip_xp_invalid_arg
+    def test_gzscore_masked_array(self):
+        x = np.array([1, 2, -1, 3, 4])
+        mask = [0, 0, 1, 0, 0]
+        mx = np.ma.masked_array(x, mask=mask)
+        z = stats.gzscore(mx)
+        desired = ([-1.526072095151, -0.194700599824, np.inf, 0.584101799472,
+                    1.136670895503])
+        desired = np.ma.masked_array(desired, mask=mask)
+        assert_allclose(z.compressed(), desired.compressed())
+        assert_allclose(z.mask, desired.mask)
+        assert isinstance(z, np.ma.MaskedArray)
+
+
+@make_xp_test_case(stats.median_abs_deviation)
+class TestMedianAbsDeviation:
+    def setup_method(self):
+        self.dat_nan = [2.20, 2.20, 2.4, 2.4, 2.5, 2.7, 2.8, 2.9,
+                        3.03, 3.03, 3.10, 3.37, 3.4, 3.4, 3.4, 3.5,
+                        3.6, 3.7, 3.7, 3.7, 3.7, 3.77, 5.28, np.nan]
+        self.dat = [2.20, 2.20, 2.4, 2.4, 2.5, 2.7, 2.8, 2.9, 3.03,
+                    3.03, 3.10, 3.37, 3.4, 3.4, 3.4, 3.5, 3.6, 3.7,
+                    3.7, 3.7, 3.7, 3.77, 5.28, 28.95]
+
+    def test_median_abs_deviation(self, xp):
+        xp_assert_close(stats.median_abs_deviation(xp.asarray(self.dat), axis=None),
+                        xp.asarray(0.355))
+        dat = xp.reshape(xp.asarray(self.dat), (6, 4))
+        mad = stats.median_abs_deviation(dat, axis=0)
+        mad_expected = xp.asarray([0.435, 0.5, 0.45, 0.4])
+        xp_assert_close(mad, mad_expected)
+
+    @skip_xp_backends('jax.numpy', reason='lazy -> no nan_policy="omit"')
+    def test_mad_nan_omit(self, xp):
+        mad = stats.median_abs_deviation(xp.asarray(self.dat_nan), nan_policy='omit')
+        xp_assert_close(mad, xp.asarray(0.34))
+
+    def test_axis_and_nan(self, xp):
+        x = xp.asarray([[1.0, 2.0, 3.0, 4.0, np.nan],
+                        [1.0, 4.0, 5.0, 8.0, 9.0]])
+        mad = stats.median_abs_deviation(x, axis=1)
+        xp_assert_close(mad, xp.asarray([np.nan, 3.0]))
+
+    @skip_xp_backends('jax.numpy', reason='lazy -> no nan_policy="omit"')
+    def test_nan_policy_omit_with_inf(self, xp):
+        z = xp.asarray([1, 3, 4, 6, 99, np.nan, np.inf])
+        mad = stats.median_abs_deviation(z, nan_policy='omit')
+        xp_assert_close(mad, xp.asarray(3.0))
+
+    @pytest.mark.parametrize('axis', [0, 1, 2, None])
+    def test_size_zero_with_axis(self, axis, xp):
+        x = xp.zeros((3, 0, 4))
+        context = (eager_warns(SmallSampleWarning, match='too small', xp=np)
+                   if axis in {1, None} else contextlib.nullcontext())
+        with context:
+            mad = stats.median_abs_deviation(x, axis=axis)
+        xp_assert_close(mad, xp.full_like(xp.sum(x, axis=axis), fill_value=xp.nan))
+
+    @pytest.mark.parametrize('nan_policy, expected',
+                             [('omit', [np.nan, 1.5, 1.5]),
+                              ('propagate', [np.nan, np.nan, 1.5])])
+    def test_nan_policy_with_axis(self, nan_policy, expected, xp):
+        if nan_policy=='omit' and not is_numpy(xp):
+            pytest.skip("nan_policy='omit' with n-d input only supported by NumPy")
+
+        x = xp.asarray([[np.nan, np.nan, np.nan, np.nan, np.nan, np.nan],
+                        [1, 5, 3, 6, np.nan, np.nan],
+                        [5, 6, 7, 9, 9, 10]])
+
+        context = (eager_warns(SmallSampleWarning, match="too small", xp=np)
+                   if nan_policy == 'omit' else contextlib.nullcontext())
+        with context:
+            mad = stats.median_abs_deviation(x, nan_policy=nan_policy, axis=1)
+            xp_assert_close(mad, xp.asarray(expected))
+
+    @pytest.mark.parametrize('axis, expected',
+                             [(1, [2.5, 2.0, 12.0]), (None, 4.5)])
+    def test_center_mean_with_nan(self, axis, expected):
+        # nan_policy='omit' with multidimensional input only supported by NumPy
+        x = np.array([[1, 2, 4, 9, np.nan],
+                      [0, 1, 1, 1, 12],
+                      [-10, -10, -10, 20, 20]])
+        mad = stats.median_abs_deviation(x, center=np.mean, nan_policy='omit',
+                                         axis=axis)
+        xp_assert_close(mad, expected, rtol=1e-15, atol=1e-15)
+
+    def test_center_not_callable(self, xp):
+        with pytest.raises(TypeError, match='callable'):
+            stats.median_abs_deviation(xp.asarray([1, 2, 3, 5]), center=99)
+
+
+@make_xp_test_case(stats.iqr)
+class TestIQR:
+
+    @pytest.mark.parametrize('dtype', [None, 'float32', 'float64'])
+    def test_basic(self, dtype, xp):
+        x = np.arange(8) * 0.5
+        np.random.shuffle(x)
+        dtype = xp_default_dtype(xp) if dtype is None else getattr(xp, dtype)
+        xp_assert_equal(stats.iqr(xp.asarray(x, dtype=dtype)),
+                        xp.asarray(1.75, dtype=dtype))
+
+    def test_api(self, xp):
+        d = xp.ones((5, 5))
+        stats.iqr(d)
+        stats.iqr(d, None)
+        stats.iqr(d, 1)
+        stats.iqr(d, (0, 1))
+        stats.iqr(d, None, (10, 90))
+        stats.iqr(d, None, (30, 20), 1.0)
+        stats.iqr(d, None, (25, 75), 1.5, 'propagate')
+
+    @skip_xp_backends('jax.numpy', reason='lazy -> reduced nan_policy capabilities')
+    def test_api_eager(self, xp):
+        d = xp.ones((5, 5))
+        stats.iqr(d, None, (50, 50), 'normal', 'raise', 'linear')
+        stats.iqr(d, None, (25, 75), -0.4, 'omit', 'lower', True)
+
+    @pytest.mark.parametrize('x', [[], np.arange(0)])
+    def test_empty(self, x, xp):
+        with eager_warns(SmallSampleWarning, match=too_small_1d_not_omit, xp=xp):
+            xp_assert_equal(stats.iqr(xp.asarray(x)), xp.asarray(xp.nan))
+
+    def test_constant(self, xp):
+        # Constant array always gives 0
+        x = xp.ones((7, 4))
+        zero = xp.asarray(0.0)
+        xp_assert_equal(stats.iqr(x), zero)
+        xp_assert_equal(stats.iqr(x, axis=0), xp.zeros(4))
+        xp_assert_equal(stats.iqr(x, axis=1), xp.zeros(7))
+        xp_assert_equal(stats.iqr(x, interpolation='linear'), zero)
+        xp_assert_equal(stats.iqr(x, interpolation='midpoint'), zero)
+        xp_assert_equal(stats.iqr(x, interpolation='nearest'), zero)
+        xp_assert_equal(stats.iqr(x, interpolation='lower'), zero)
+        xp_assert_equal(stats.iqr(x, interpolation='higher'), zero)
+
+        # 0 only along constant dimensions
+        # This also tests much of `axis`
+        y = xp.ones((4, 5, 6)) * xp.arange(6.)
+        xp_assert_equal(stats.iqr(y, axis=0), xp.zeros((5, 6)))
+        xp_assert_equal(stats.iqr(y, axis=1), xp.zeros((4, 6)))
+        xp_assert_equal(stats.iqr(y, axis=2), xp.full((4, 5), 2.5))
+        xp_assert_equal(stats.iqr(y, axis=(0, 1)), xp.zeros(6))
+        xp_assert_equal(stats.iqr(y, axis=(0, 2)), xp.full(5, 3.))
+        xp_assert_equal(stats.iqr(y, axis=(1, 2)), xp.full(4, 3.))
+
+    def test_scalarlike(self, xp):
+        x = xp.arange(1.) + 7.0
+        xp_assert_equal(stats.iqr(x[0]), xp.asarray(0.0))
+        xp_assert_equal(stats.iqr(x), xp.asarray(0.0))
+        xp_assert_equal(stats.iqr(x, keepdims=True), xp.asarray([0.0]))
+
+    def test_2D(self, xp):
+        x = xp.reshape(xp.arange(15), (3, 5))
+        xp_assert_equal(stats.iqr(x), xp.asarray(7.0))
+        xp_assert_equal(stats.iqr(x, axis=0), xp.full(5, 5.))
+        xp_assert_equal(stats.iqr(x, axis=1), xp.full(3, 2.))
+        xp_assert_equal(stats.iqr(x, axis=(0, 1)), xp.asarray(7.0))
+        xp_assert_equal(stats.iqr(x, axis=(1, 0)), xp.asarray(7.0))
+
+    def test_axis(self, xp):
+        # The `axis` keyword is also put through its paces in `test_keepdims`.
+        o = np.random.normal(size=(71, 23))
+        x = np.dstack([o] * 10)                 # x.shape = (71, 23, 10)
+        o, x = xp.asarray(o), xp.asarray(x)
+        q = xp.broadcast_to(stats.iqr(o), (10,))
+
+        xp_assert_equal(stats.iqr(x, axis=(0, 1)), q)
+        x = xp.moveaxis(x, -1, 0)               # x.shape = (10, 71, 23)
+        xp_assert_equal(stats.iqr(x, axis=(2, 1)), q)
+        x = xp_swapaxes(x,0, 1, xp=xp)                    # x.shape = (71, 10, 23)
+        xp_assert_equal(stats.iqr(x, axis=(0, 2)), q)
+        x = xp_swapaxes(x,0, 1, xp=xp)                    # x.shape = (10, 71, 23)
+
+        xp_assert_equal(stats.iqr(x, axis=(0, 1, 2)),
+                        stats.iqr(x, axis=None))
+        xp_assert_equal(stats.iqr(x, axis=(0,)),
+                        stats.iqr(x, axis=0))
+
+        d = np.arange(3 * 5 * 7 * 11)
+        # Older versions of numpy only shuffle along axis=0.
+        # Not sure about newer, don't care.
+        np.random.shuffle(d)
+        d = d.reshape((3, 5, 7, 11))
+        d = xp.asarray(d)
+        xp_assert_equal(stats.iqr(d, axis=(0, 1, 2))[0],
+                        stats.iqr(xp_ravel(d[:,:,:, 0])))
+        xp_assert_equal(stats.iqr(d, axis=(0, 1, 3))[1],
+                        stats.iqr(xp_ravel(d[:,:, 1,:])))
+        xp_assert_equal(stats.iqr(d, axis=(3, 1, -4))[2],
+                        stats.iqr(xp_ravel(d[:,:, 2,:])))
+        xp_assert_equal(stats.iqr(d, axis=(3, 1, 2))[2],
+                        stats.iqr(xp_ravel(d[2,:,:,:])))
+        xp_assert_equal(stats.iqr(d, axis=(3, 2))[2, 1],
+                        stats.iqr(xp_ravel(d[2, 1,:,:])))
+        xp_assert_equal(stats.iqr(d, axis=(1, -2))[2, 1],
+                        stats.iqr(xp_ravel(d[2, :, :, 1])))
+        xp_assert_equal(stats.iqr(d, axis=(1, 3))[2, 2],
+                        stats.iqr(xp_ravel(d[2, :, 2,:])))
+
+        with pytest.raises(AxisError, match='`axis` is out of bounds...'):
+            stats.iqr(d, axis=4)
+        with pytest.raises(ValueError, match='`axis` must contain only...'):
+            stats.iqr(d, axis=(0, 0))
+
+    def test_rng(self, xp):
+        x = xp.arange(5)
+        xp_assert_close(stats.iqr(x), xp.asarray(2.))
+        xp_assert_close(stats.iqr(x, rng=(25, 87.5)), xp.asarray(2.5))
+        xp_assert_close(stats.iqr(x, rng=(12.5, 75)), xp.asarray(2.5))
+        xp_assert_close(stats.iqr(x, rng=(10, 50)), xp.asarray(1.6))  # 3-1.4
+
+        message = r"Elements of `rng` must be in the range \[0, 100\]."
+        with pytest.raises(ValueError, match=message):
+            stats.iqr(x, rng=(0, 101))
+
+        message = "`rng` must not contain NaNs."
+        with pytest.raises(ValueError, match=message):
+            stats.iqr(x, rng=(np.nan, 25))
+
+        message = "`rng` must be a two element sequence."
+        with pytest.raises(TypeError, match=message):
+            stats.iqr(x, rng=(0, 50, 60))
+
+    def test_interpolation(self, xp):
+        x = xp.arange(5)
+        y = xp.arange(4)
+        # Default
+        xp_assert_equal(stats.iqr(x), xp.asarray(2.))
+        xp_assert_equal(stats.iqr(y), xp.asarray(1.5))
+        # Linear
+        xp_assert_equal(stats.iqr(x, interpolation='linear'), xp.asarray(2.))
+        xp_assert_equal(stats.iqr(y, interpolation='linear'), xp.asarray(1.5))
+        # Higher
+        xp_assert_equal(stats.iqr(x, interpolation='higher'), xp.asarray(2.))
+        xp_assert_equal(stats.iqr(x, rng=(25, 80), interpolation='higher'),
+                        xp.asarray(3.))
+        xp_assert_equal(stats.iqr(y, interpolation='higher'), xp.asarray(2.))
+        # Lower (will generally, but not always be the same as higher)
+        xp_assert_equal(stats.iqr(x, interpolation='lower'), xp.asarray(2.))
+        xp_assert_equal(stats.iqr(x, rng=(25, 80), interpolation='lower'),
+                        xp.asarray(2.))
+        xp_assert_equal(stats.iqr(y, interpolation='lower'), xp.asarray(2.))
+        # Nearest
+        xp_assert_equal(stats.iqr(x, interpolation='nearest'), xp.asarray(2.))
+        xp_assert_equal(stats.iqr(y, interpolation='nearest'), xp.asarray(1.))
+        # Midpoint
+        xp_assert_equal(stats.iqr(x, interpolation='midpoint'), xp.asarray(2.))
+        xp_assert_equal(stats.iqr(x, rng=(25, 80), interpolation='midpoint'),
+                        xp.asarray(2.5))
+        xp_assert_equal(stats.iqr(y, interpolation='midpoint'), xp.asarray(2.))
+
+        # Check all method= values new in numpy 1.22.0 are accepted
+        for method in ('inverted_cdf', 'averaged_inverted_cdf',
+                       'closest_observation', 'interpolated_inverted_cdf',
+                       'hazen', 'weibull', 'median_unbiased',
+                       'normal_unbiased'):
+            stats.iqr(y, interpolation=method)
+
+        with pytest.raises(ValueError, match='`method` must be one of...'):
+            stats.iqr(x, interpolation='foobar')
+
+    def test_keepdims(self, xp):
+        # Also tests most of `axis`
+        x = xp.ones((3, 5, 7, 11))
+        assert_equal(stats.iqr(x, axis=None, keepdims=False).shape, ())
+        assert_equal(stats.iqr(x, axis=2, keepdims=False).shape, (3, 5, 11))
+        assert_equal(stats.iqr(x, axis=(0, 1), keepdims=False).shape, (7, 11))
+        assert_equal(stats.iqr(x, axis=(0, 3), keepdims=False).shape, (5, 7))
+        assert_equal(stats.iqr(x, axis=(1,), keepdims=False).shape, (3, 7, 11))
+        assert_equal(stats.iqr(x, (0, 1, 2, 3), keepdims=False).shape, ())
+        assert_equal(stats.iqr(x, axis=(0, 1, 3), keepdims=False).shape, (7,))
+
+        assert_equal(stats.iqr(x, axis=None, keepdims=True).shape, (1, 1, 1, 1))
+        assert_equal(stats.iqr(x, axis=2, keepdims=True).shape, (3, 5, 1, 11))
+        assert_equal(stats.iqr(x, axis=(0, 1), keepdims=True).shape, (1, 1, 7, 11))
+        assert_equal(stats.iqr(x, axis=(0, 3), keepdims=True).shape, (1, 5, 7, 1))
+        assert_equal(stats.iqr(x, axis=(1,), keepdims=True).shape, (3, 1, 7, 11))
+        assert_equal(stats.iqr(x, (0, 1, 2, 3), keepdims=True).shape, (1, 1, 1, 1))
+        assert_equal(stats.iqr(x, axis=(0, 1, 3), keepdims=True).shape, (1, 1, 7, 1))
+
+    @skip_xp_backends('jax.numpy', reason='lazy -> reduced nan_policy capabilitiesy')
+    def test_nanpolicy(self, xp):
+        x = xp.reshape(xp.arange(15.0), (3, 5))
+
+        # No NaNs
+        xp_assert_equal(stats.iqr(x, nan_policy='propagate'), xp.asarray(7.))
+        xp_assert_equal(stats.iqr(x, nan_policy='omit'), xp.asarray(7.))
+        xp_assert_equal(stats.iqr(x, nan_policy='raise'), xp.asarray(7.))
+
+        # Yes NaNs
+        x = xpx.at(x)[1, 2].set(xp.nan)
+        xp_assert_equal(stats.iqr(x, nan_policy='propagate'),
+                        xp.asarray(xp.nan))
+        xp_assert_equal(stats.iqr(x, axis=0, nan_policy='propagate'),
+                        xp.asarray([5, 5, xp.nan, 5, 5]))
+        xp_assert_equal(stats.iqr(x, axis=1, nan_policy='propagate'),
+                        xp.asarray([2, xp.nan, 2]))
+
+        xp_assert_equal(stats.iqr(x, nan_policy='omit'), xp.asarray(7.5))
+
+        message = "The input contains nan values"
+        with pytest.raises(ValueError, match=message):
+            stats.iqr(x, nan_policy='raise')
+
+        # Bad policy
+        message = "nan_policy must be one of..."
+        with pytest.raises(ValueError, match=message):
+            stats.iqr(x, nan_policy='barfood')
+
+    @skip_xp_backends(np_only=True,
+        reason="nan_policy w/ multidimensional arrays only available w/ NumPy")
+    def test_nanpolicy_nd(self, xp):
+        x = xp.reshape(xp.arange(15.0), (3, 5))
+        x[1, 2] = xp.nan
+        xp_assert_equal(stats.iqr(x, axis=0, nan_policy='omit'),
+                        xp.full(5, 5.))
+        xp_assert_equal(stats.iqr(x, axis=1, nan_policy='omit'),
+                        xp.asarray([2, 2.5, 2]))
+
+        message = "The input contains nan values"
+        with pytest.raises(ValueError, match=message):
+            stats.iqr(x, axis=0, nan_policy='raise')
+        with pytest.raises(ValueError, match=message):
+            stats.iqr(x, axis=1, nan_policy='raise')
+
+    def test_scale_no_nans(self, xp):
+        x = xp.reshape(xp.arange(15.0), (3, 5))
+        xp_assert_equal(stats.iqr(x, scale=1.0), xp.asarray(7.))
+        xp_assert_close(stats.iqr(x, scale='normal'), xp.asarray(7 / 1.3489795))
+        xp_assert_equal(stats.iqr(x, scale=2.0), xp.asarray(3.5))
+
+    def test_scale_with_nans(self, xp):
+        x = xp.reshape(xp.arange(15.0), (3, 5))
+        x = xpx.at(x)[1, 2].set(xp.nan)
+        nan = xp.asarray(xp.nan)
+        xp_assert_equal(stats.iqr(x, scale=1.0, nan_policy='propagate'), nan)
+        xp_assert_equal(stats.iqr(x, scale='normal', nan_policy='propagate'), nan)
+        xp_assert_equal(stats.iqr(x, scale=2.0, nan_policy='propagate'), nan)
+
+    def test_invalid_scale(self, xp):
+        x = xp.arange(15.0)
+        message = "foobar not a valid scale for `iqr`"
+        with pytest.raises(ValueError, match=message):
+            stats.iqr(x, scale='foobar')
+
+    @skip_xp_backends("jax.numpy", reason="lazy -> reduced nan_policy capabilities")
+    def test_scale_nan_policy_omit(self, xp):
+        x = xp.reshape(xp.arange(15.0), (3, 5))
+        x = xpx.at(x)[1, 2].set(xp.nan)
+        xp_assert_equal(stats.iqr(x, scale=1.0, nan_policy='omit'), xp.asarray(7.5))
+        xp_assert_close(stats.iqr(x, scale='normal', nan_policy='omit'),
+                        xp.asarray(7.5 / 1.3489795))
+        xp_assert_equal(stats.iqr(x, scale=2.0, nan_policy='omit'), xp.asarray(3.75))
+
+    def test_scale_nanpolicy_nd(self, xp):
+        # axis=1 chosen to show behavior with both nans and without
+        x = xp.reshape(xp.arange(15.0), (3, 5))
+        x = xpx.at(x)[1, 2].set(xp.nan)
+
+        xp_assert_equal(stats.iqr(x, axis=1, scale=1.0, nan_policy='propagate'),
+                        xp.asarray([2, np.nan, 2]))
+        xp_assert_close(stats.iqr(x, axis=1, scale='normal', nan_policy='propagate'),
+                        xp.asarray([2, np.nan, 2]) / 1.3489795)
+        xp_assert_equal(stats.iqr(x, axis=1, scale=2.0, nan_policy='propagate'),
+                        xp.asarray([1, np.nan, 1]))
+
+    def test_rng_order(self, xp):
+        # test that order of `rng` doesn't matter (as documented)
+        x = xp.arange(8.) * 0.5
+        res = stats.iqr(x, rng=(75, 25))
+        ref = stats.iqr(x)
+        xp_assert_equal(res, ref)
+
+
+@make_xp_test_case(stats.moment)
+class TestMoments:
+    """
+        Comparison numbers are found using R v.1.5.1
+        note that length(testcase) = 4
+        testmathworks comes from documentation for the
+        Statistics Toolbox for Matlab and can be found at both
+        https://www.mathworks.com/help/stats/kurtosis.html
+        https://www.mathworks.com/help/stats/skewness.html
+        Note that both test cases came from here.
+    """
+    testcase = [1., 2., 3., 4.]
+    scalar_testcase = 4.
+    rng = np.random.default_rng(2285049930)
+    testcase_moment_accuracy = rng.random(42)
+
+    @pytest.mark.parametrize('size', [10, (10, 2)])
+    @pytest.mark.parametrize('m, c', list(product((0, 1, 2, 3), (None, 0, 1))))
+    def test_moment_center_scalar_moment(self, size, m, c, xp):
+        rng = np.random.default_rng(6581432544381372042)
+        x = xp.asarray(rng.random(size=size))
+        res = stats.moment(x, m, center=c)
+        c = xp.mean(x, axis=0) if c is None else c
+        ref = xp.sum((x - c)**m, axis=0)/x.shape[0]
+        xp_assert_close(res, ref, atol=1e-16)
+
+    @pytest.mark.parametrize('size', [10, (10, 2)])
+    @pytest.mark.parametrize('c', (None, 0, 1))
+    def test_moment_center_array_moment(self, size, c, xp):
+        rng = np.random.default_rng(1706828300224046506)
+        x = xp.asarray(rng.random(size=size))
+        m = [0, 1, 2, 3]
+        res = stats.moment(x, m, center=c)
+        ref = xp.concat([stats.moment(x, i, center=c)[xp.newaxis, ...] for i in m])
+        xp_assert_close(res, ref)  # JAX JIT doesn't pass with equality
+
+    def test_moment(self, xp):
+        # mean((testcase-mean(testcase))**power,axis=0),axis=0))**power))
+        testcase = xp.asarray(self.testcase)
+
+        y = stats.moment(xp.asarray(self.scalar_testcase))
+        xp_assert_close(y, xp.asarray(0.0))
+
+        y = stats.moment(testcase, 0)
+        xp_assert_close(y, xp.asarray(1.0))
+        y = stats.moment(testcase, 1)
+        xp_assert_close(y, xp.asarray(0.0))
+        y = stats.moment(testcase, 2)
+        xp_assert_close(y, xp.asarray(1.25))
+        y = stats.moment(testcase, 3)
+        xp_assert_close(y, xp.asarray(0.0))
+        y = stats.moment(testcase, 4)
+        xp_assert_close(y, xp.asarray(2.5625))
+
+        # check array_like input for moment
+        y = stats.moment(testcase, [1, 2, 3, 4])
+        xp_assert_close(y, xp.asarray([0, 1.25, 0, 2.5625]))
+
+        # check floating point integer order
+        y = stats.moment(testcase, 0.0)
+        xp_assert_close(y, xp.asarray(1.0))
+
+        y = stats.moment(testcase, [1.0, 2, 3, 4.0])
+        xp_assert_close(y, xp.asarray([0, 1.25, 0, 2.5625]))
+
+    @skip_xp_backends("jax.numpy", reason="array value-dependent error")
+    def test_order_input_validation(self, xp):
+        testcase = xp.asarray(self.testcase)
+        message = 'All elements of `order` must be integral.'
+        with pytest.raises(ValueError, match=message):
+            stats.moment(testcase, 1.2)
+
+    def test_zero_size(self, xp):
+        message = "One or more sample arguments..."
+        with eager_warns(SmallSampleWarning, match=message, xp=xp):
+            y = stats.moment(xp.asarray([]))
+            xp_assert_equal(y, xp.asarray(xp.nan))
+        with eager_warns(SmallSampleWarning, match=message, xp=xp):
+            y = stats.moment(xp.asarray([], dtype=xp.float32))
+            xp_assert_equal(y, xp.asarray(xp.nan, dtype=xp.float32))
+
+        message = "All axis-slices of one or more"
+        with eager_warns(SmallSampleWarning, match=message, xp=xp):
+            y = stats.moment(xp.asarray([[]]), axis=1)
+            xp_assert_equal(y, xp.asarray([xp.nan]))
+
+        y = stats.moment(xp.zeros((1, 0)), axis=0)
+        xp_assert_equal(y, xp.empty((0,)))
+
+        y = stats.moment(xp.asarray([[]]), order=[0, 1], axis=0)
+        xp_assert_equal(y, xp.empty((2, 0)))
+
+    def test_nan_policy(self):
+        x = np.arange(10.)
+        x[9] = np.nan
+        assert_equal(stats.moment(x, 2), np.nan)
+        assert_almost_equal(stats.moment(x, nan_policy='omit'), 0.0)
+        assert_raises(ValueError, stats.moment, x, nan_policy='raise')
+        assert_raises(ValueError, stats.moment, x, nan_policy='foobar')
+
+    @pytest.mark.parametrize('dtype', ['float32', 'float64', 'complex128'])
+    @pytest.mark.parametrize('expect, order', [(0, 1), (1, 0)])
+    def test_constant_moments(self, dtype, expect, order, xp):
+        if dtype=='complex128' and is_torch(xp):
+            message = "torch can't round complex input; data-apis/array-api-compat#407"
+            pytest.skip(message)
+        dtype = getattr(xp, dtype)
+        rng = np.random.default_rng(3824693518)
+        x = xp.asarray(rng.random(5), dtype=dtype)
+        y = stats.moment(x, order=order)
+        xp_assert_equal(y, xp.asarray(expect, dtype=dtype))
+
+        message = "Precision loss occurred in moment calculation"
+        with eager_warns(RuntimeWarning, match=message, xp=xp):
+            y = stats.moment(xp.broadcast_to(x, (6, 5)), axis=0, order=order)
+            xp_assert_equal(y, xp.full((5,), expect, dtype=dtype))
+
+        with eager_warns(RuntimeWarning, match=message, xp=xp):
+            y = stats.moment(xp.broadcast_to(x, (1, 2, 3, 4, 5)), axis=2,
+                             order=order)
+            xp_assert_equal(y, xp.full((1, 2, 4, 5), expect, dtype=dtype))
+
+        y = stats.moment(xp.broadcast_to(x, (1, 2, 3, 4, 5)), axis=None,
+                         order=order)
+        xp_assert_equal(y, xp.full((), expect, dtype=dtype))
+
+    def test_moment_propagate_nan(self, xp):
+        # Check that the shape of the result is the same for inputs
+        # with and without nans, cf gh-5817
+        a = xp.reshape(xp.arange(8.), (2, -1))
+        a = xpx.at(a)[1, 0].set(xp.nan)
+
+        mm = stats.moment(xp.asarray(a), 2, axis=1)
+        xp_assert_close(mm, xp.asarray([1.25, xp.nan]), atol=1e-15)
+
+    def test_moment_empty_order(self, xp):
+        # tests moment with empty `order` list
+        with pytest.raises(ValueError, match=r"`order` must be a scalar or a"
+                                             r" non-empty 1D array."):
+            stats.moment(xp.asarray([1, 2, 3, 4]), order=[])
+
+    def test_rename_moment_order(self, xp):
+        # Parameter 'order' was formerly known as 'moment'. The old name
+        # has not been deprecated, so it must continue to work.
+        x = xp.arange(10)
+        res = stats.moment(x, moment=3)
+        ref = stats.moment(x, order=3)
+        xp_assert_equal(res, ref)
+
+    def test_moment_accuracy(self):
+        # 'moment' must have a small enough error compared to the slower
+        #  but very accurate numpy.power() implementation.
+        tc_no_mean = (self.testcase_moment_accuracy
+                      - np.mean(self.testcase_moment_accuracy))
+        assert_allclose(np.power(tc_no_mean, 42).mean(),
+                        stats.moment(self.testcase_moment_accuracy, 42))
+
+    @pytest.mark.parametrize('order', [0, 1, 2, 3])
+    @pytest.mark.parametrize('axis', [-1, 0, 1])
+    @pytest.mark.parametrize('center', [None, 0.])
+    def test_moment_array_api(self, xp, order, axis, center):
+        rng = np.random.default_rng(34823589259425)
+        x = rng.random(size=(5, 6, 7))
+        res = stats.moment(xp.asarray(x), order, axis=axis, center=center)
+        center = center if center is None else np.asarray(center)
+        ref = xp.asarray(_moment(x, order, axis, center=center)[()])
+        xp_assert_close(res, ref)
+
+
+class SkewKurtosisTest:
+    scalar_testcase = 4.
+    testcase = [1., 2., 3., 4.]
+    testmathworks = [1.165, 0.6268, 0.0751, 0.3516, -0.6965]
+
+    def test_empty_1d(self, xp):
+        x = xp.asarray([])
+        with eager_warns(SmallSampleWarning, match=too_small_1d_not_omit, xp=xp):
+            res = self.stat_fun(x)
+
+        xp_assert_equal(res, xp.asarray(xp.nan))
+
+
+@make_xp_test_case(stats.skew)
+class TestSkew(SkewKurtosisTest):
+    def stat_fun(self, x):
+        return stats.skew(x)
+
+    @pytest.mark.filterwarnings(
+        "ignore:invalid value encountered:RuntimeWarning:dask"
+    )
+    def test_skewness(self, xp):
+        # Scalar test case
+        y = stats.skew(xp.asarray(self.scalar_testcase))
+        xp_assert_close(y, xp.asarray(xp.nan))
+        # sum((testmathworks-mean(testmathworks,axis=0))**3,axis=0) /
+        #     ((sqrt(var(testmathworks)*4/5))**3)/5
+        y = stats.skew(xp.asarray(self.testmathworks))
+        xp_assert_close(y, xp.asarray(-0.29322304336607), atol=1e-10)
+        y = stats.skew(xp.asarray(self.testmathworks), bias=0)
+        xp_assert_close(y, xp.asarray(-0.437111105023940), atol=1e-10)
+        y = stats.skew(xp.asarray(self.testcase))
+        xp_assert_close(y, xp.asarray(0.0), atol=1e-10)
+
+    def test_nan_policy(self):
+        # initially, nan_policy is ignored with alternative backends
+        x = np.arange(10.)
+        x[9] = np.nan
+        with np.errstate(invalid='ignore'):
+            assert_equal(stats.skew(x), np.nan)
+        assert_equal(stats.skew(x, nan_policy='omit'), 0.)
+        assert_raises(ValueError, stats.skew, x, nan_policy='raise')
+        assert_raises(ValueError, stats.skew, x, nan_policy='foobar')
+
+    def test_skewness_scalar(self):
+        # `skew` must return a scalar for 1-dim input (only for NumPy arrays)
+        assert_equal(stats.skew(arange(10)), 0.0)
+
+    def test_skew_propagate_nan(self, xp):
+        # Check that the shape of the result is the same for inputs
+        # with and without nans, cf gh-5817
+        a = xp.arange(8.)
+        a = xp.reshape(a, (2, -1))
+        a = xpx.at(a)[1, 0].set(xp.nan)
+        with np.errstate(invalid='ignore'):
+            s = stats.skew(xp.asarray(a), axis=1)
+        xp_assert_equal(s, xp.asarray([0, xp.nan]))
+
+    def test_skew_constant_value(self, xp):
+        # Skewness of a constant input should be NaN (gh-16061)
+        a = xp.repeat(xp.asarray([-0.27829495]), 10)
+
+        with eager_warns(RuntimeWarning, match="Precision loss occurred", xp=xp):
+            xp_assert_equal(stats.skew(a), xp.asarray(xp.nan))
+            xp_assert_equal(stats.skew(a*2.**50), xp.asarray(xp.nan))
+            xp_assert_equal(stats.skew(a/2.**50), xp.asarray(xp.nan))
+            xp_assert_equal(stats.skew(a, bias=False), xp.asarray(xp.nan))
+
+            # # similarly, from gh-11086:
+            a = xp.asarray([14.3]*7)
+            xp_assert_equal(stats.skew(a), xp.asarray(xp.nan))
+            a = 1. + xp.arange(-3., 4)*1e-16
+            xp_assert_equal(stats.skew(a), xp.asarray(xp.nan))
+
+    def test_precision_loss_gh15554(self, xp):
+        # gh-15554 was one of several issues that have reported problems with
+        # constant or near-constant input. We can't always fix these, but
+        # make sure there's a warning.
+        with eager_warns(RuntimeWarning, match="Precision loss occurred", xp=xp):
+            rng = np.random.default_rng(34095309370)
+            a = rng.random(size=(100, 10))
+            a[:, 0] = 1.01
+            stats.skew(xp.asarray(a))
+
+    @pytest.mark.parametrize('axis', [-1, 0, 2, None])
+    @pytest.mark.parametrize('bias', [False, True])
+    def test_vectorization(self, xp, axis, bias):
+        # Behavior with array input is barely tested above. Compare
+        # against naive implementation.
+        rng = np.random.default_rng(1283413549926)
+        x = xp.asarray(rng.random((3, 4, 5)))
+
+        def skewness(a, axis, bias):
+            # Simple implementation of skewness
+            if axis is None:
+                a = xp.reshape(a, (-1,))
+                axis = 0
+            mean = xp.mean(a, axis=axis, keepdims=True)
+            mu3 = xp.mean((a - mean)**3, axis=axis)
+            std = xp.std(a, axis=axis)
+            res = mu3 / std ** 3
+            if not bias:
+                n = a.shape[axis]
+                res *= ((n - 1.0) * n) ** 0.5 / (n - 2.0)
+            return res
+
+        res = stats.skew(x, axis=axis, bias=bias)
+        ref = skewness(x, axis=axis, bias=bias)
+        xp_assert_close(res, ref)
+
+
+@make_xp_test_case(stats.kurtosis)
+class TestKurtosis(SkewKurtosisTest):
+    def stat_fun(self, x):
+        return stats.kurtosis(x)
+
+    @pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning:dask")
+    def test_kurtosis(self, xp):
+        # Scalar test case
+        y = stats.kurtosis(xp.asarray(self.scalar_testcase))
+        assert xp.isnan(y)
+
+        #   sum((testcase-mean(testcase,axis=0))**4,axis=0)
+        #   / ((sqrt(var(testcase)*3/4))**4)
+        #   / 4
+        #
+        #   sum((test2-mean(testmathworks,axis=0))**4,axis=0)
+        #   / ((sqrt(var(testmathworks)*4/5))**4)
+        #   / 5
+        #
+        #   Set flags for axis = 0 and
+        #   fisher=0 (Pearson's defn of kurtosis for compatibility with Matlab)
+        y = stats.kurtosis(xp.asarray(self.testmathworks), 0, fisher=0, bias=1)
+        xp_assert_close(y, xp.asarray(2.1658856802973))
+
+        # Note that MATLAB has confusing docs for the following case
+        #  kurtosis(x,0) gives an unbiased estimate of Pearson's skewness
+        #  kurtosis(x)  gives a biased estimate of Fisher's skewness (Pearson-3)
+        #  The MATLAB docs imply that both should give Fisher's
+        y = stats.kurtosis(xp.asarray(self.testmathworks), fisher=0, bias=0)
+        xp_assert_close(y, xp.asarray(3.663542721189047))
+        y = stats.kurtosis(xp.asarray(self.testcase), 0, 0)
+        xp_assert_close(y, xp.asarray(1.64))
+
+        x = xp.arange(10.)
+        x = xp.where(x == 8, xp.nan, x)
+        xp_assert_equal(stats.kurtosis(x), xp.asarray(xp.nan))
+
+    def test_kurtosis_nan_policy(self):
+        # nan_policy only for NumPy right now
+        x = np.arange(10.)
+        x[9] = np.nan
+        assert_almost_equal(stats.kurtosis(x, nan_policy='omit'), -1.230000)
+        assert_raises(ValueError, stats.kurtosis, x, nan_policy='raise')
+        assert_raises(ValueError, stats.kurtosis, x, nan_policy='foobar')
+
+    def test_kurtosis_array_scalar(self):
+        # "array scalars" do not exist in other backends
+        assert_equal(type(stats.kurtosis([1, 2, 3])), np.float64)
+
+    def test_kurtosis_propagate_nan(self):
+        # nan_policy only for NumPy right now
+        # Check that the shape of the result is the same for inputs
+        # with and without nans, cf gh-5817
+        a = np.arange(8).reshape(2, -1).astype(float)
+        a[1, 0] = np.nan
+        k = stats.kurtosis(a, axis=1, nan_policy="propagate")
+        np.testing.assert_allclose(k, [-1.36, np.nan], atol=1e-15)
+
+    def test_kurtosis_constant_value(self, xp):
+        # Kurtosis of a constant input should be NaN (gh-16061)
+        a = xp.asarray([-0.27829495]*10)
+        with eager_warns(RuntimeWarning, match="Precision loss occurred", xp=xp):
+            assert xp.isnan(stats.kurtosis(a, fisher=False))
+            assert xp.isnan(stats.kurtosis(a * float(2**50), fisher=False))
+            assert xp.isnan(stats.kurtosis(a / float(2**50), fisher=False))
+            assert xp.isnan(stats.kurtosis(a, fisher=False, bias=False))
+
+    @pytest.mark.parametrize('axis', [-1, 0, 2, None])
+    @pytest.mark.parametrize('bias', [False, True])
+    @pytest.mark.parametrize('fisher', [False, True])
+    def test_vectorization(self, xp, axis, bias, fisher):
+        # Behavior with array input is not tested above. Compare
+        # against naive implementation.
+        rng = np.random.default_rng(1283413549926)
+        x = xp.asarray(rng.random((4, 5, 6)))
+
+        def kurtosis(a, axis, bias, fisher):
+            # Simple implementation of kurtosis
+            if axis is None:
+                a = xp.reshape(a, (-1,))
+                axis = 0
+            mean = xp.mean(a, axis=axis, keepdims=True)
+            mu4 = xp.mean((a - mean)**4, axis=axis)
+            mu2 = xp.var(a, axis=axis, correction=0)
+            if bias:
+                res = mu4 / mu2**2 - 3
+            else:
+                n = a.shape[axis]
+                # https://en.wikipedia.org/wiki/Kurtosis#Standard_unbiased_estimator
+                res = (n-1) / ((n-2) * (n-3)) * ((n + 1) * mu4/mu2**2 - 3*(n-1))
+
+            # I know it looks strange to subtract then add 3,
+            # but it is simpler than the alternatives
+            return res if fisher else res + 3
+
+        res = stats.kurtosis(x, axis=axis, bias=bias, fisher=fisher)
+        ref = kurtosis(x, axis=axis, bias=bias, fisher=fisher)
+        xp_assert_close(res, ref)
+
+
+@hypothesis.strategies.composite
+def ttest_data_axis_strategy(draw):
+    # draw an array under shape and value constraints
+    elements = dict(allow_nan=False, allow_infinity=False)
+    shape = npst.array_shapes(min_dims=1, min_side=2)
+    # The test that uses this, `test_pvalue_ci`, uses `float64` to test
+    # extreme `alpha`. It could be adjusted to test a dtype-dependent
+    # range of `alpha` if this strategy is needed to generate other floats.
+    data = draw(npst.arrays(dtype=np.float64, elements=elements, shape=shape))
+
+    # determine axes over which nonzero variance can be computed accurately
+    ok_axes = []
+    # Locally, I don't need catch_warnings or simplefilter, and I can just
+    # suppress RuntimeWarning. I include all that in hope of getting the same
+    # behavior on CI.
+    with warnings.catch_warnings():
+        warnings.simplefilter("error")
+        for axis in range(len(data.shape)):
+            with contextlib.suppress(Exception):
+                var = stats.moment(data, order=2, axis=axis)
+                if np.all(var > 0) and np.all(np.isfinite(var)):
+                    ok_axes.append(axis)
+    # if there are no valid axes, tell hypothesis to try a different example
+    hypothesis.assume(ok_axes)
+
+    # draw one of the valid axes
+    axis = draw(hypothesis.strategies.sampled_from(ok_axes))
+
+    return data, axis
+
+
+@make_xp_test_case(stats.ttest_1samp)
+class TestTTest_1samp:
+    # Preserving original test cases.
+    # Recomputed statistics and p-values with R t.test, e.g.
+    # options(digits=16)
+    # t.test(c(-1., 0., 1.), mu=2)
+    X1 = [-1., 0., 1.]
+    X2 = [0., 1., 2.]
+    T1_0 = 0.
+    P1_0 = 1.
+    T1_1 = -1.7320508075689
+    P1_1 = 0.2254033307585
+    T1_2 = -3.4641016151378
+    P1_2 = 0.07417990022745
+    T2_0 = 1.7320508075689
+    P2_0 = 0.2254033307585
+    P1_1_l = P1_1 / 2
+    P1_1_g = 1 - (P1_1 / 2)
+
+    @pytest.mark.filterwarnings("ignore:divide by zero encountered:RuntimeWarning:dask")
+    @pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning:dask")
+    def test_onesample(self, xp):
+        with warnings.catch_warnings(), \
+                np.errstate(invalid="ignore", divide="ignore"):
+            warnings.filterwarnings(
+                "ignore", "Degrees of freedom <= 0 for slice", RuntimeWarning)
+            a = xp.asarray(4.) if not is_numpy(xp) else 4.
+            t, p = stats.ttest_1samp(a, 3.)
+        xp_assert_equal(t, xp.asarray(xp.nan))
+        xp_assert_equal(p, xp.asarray(xp.nan))
+
+        t, p = stats.ttest_1samp(xp.asarray(self.X1), 0.)
+        xp_assert_close(t, xp.asarray(self.T1_0))
+        xp_assert_close(p, xp.asarray(self.P1_0))
+
+        res = stats.ttest_1samp(xp.asarray(self.X1), 0.)
+        attributes = ('statistic', 'pvalue')
+        check_named_results(res, attributes, xp=xp)
+
+        t, p = stats.ttest_1samp(xp.asarray(self.X2), 0.)
+
+        xp_assert_close(t, xp.asarray(self.T2_0))
+        xp_assert_close(p, xp.asarray(self.P2_0))
+
+        t, p = stats.ttest_1samp(xp.asarray(self.X1), 1.)
+
+        xp_assert_close(t, xp.asarray(self.T1_1))
+        xp_assert_close(p, xp.asarray(self.P1_1))
+
+        t, p = stats.ttest_1samp(xp.asarray(self.X1), 2.)
+
+        xp_assert_close(t, xp.asarray(self.T1_2))
+        xp_assert_close(p, xp.asarray(self.P1_2))
+
+    def test_onesample_nan_policy_propagate(self, xp):
+        x = stats.norm.rvs(loc=5, scale=10, size=51, random_state=7654567)
+        x[50] = np.nan
+        x = xp.asarray(x, dtype=xp_default_dtype(xp))
+
+        res = stats.ttest_1samp(x, 5.0)
+        xp_assert_equal(res.statistic, xp.asarray(xp.nan))
+        xp_assert_equal(res.pvalue, xp.asarray(xp.nan))
+
+    @skip_xp_backends(eager_only=True, reason="lazy arrays don't do 'raise'.")
+    def test_onesample_nan_policy_omit_raise(self, xp):
+        x = stats.norm.rvs(loc=5, scale=10, size=51, random_state=7654567)
+        x[50] = np.nan
+        x = xp.asarray(x, dtype=xp_default_dtype(xp))
+
+        res = stats.ttest_1samp(x, 5.0, nan_policy='omit')
+        xp_assert_close(res.statistic, xp.asarray(-1.6412624074367159))
+        xp_assert_close(res.pvalue, xp.asarray(0.107147027334048005))
+
+        with pytest.raises(ValueError, match="The input contains nan values"):
+            stats.ttest_1samp(x, 5.0, nan_policy='raise')
+
+        with pytest.raises(ValueError, match="nan_policy must be one of"):
+            stats.ttest_1samp(x, 5.0, nan_policy='foobar')
+
+
+    @pytest.mark.filterwarnings("ignore:divide by zero encountered in divide")
+    def test_1samp_alternative(self, xp):
+        message = "`alternative` must be 'less', 'greater', or 'two-sided'."
+        with pytest.raises(ValueError, match=message):
+            stats.ttest_1samp(xp.asarray(self.X1), 0., alternative="error")
+
+        t, p = stats.ttest_1samp(xp.asarray(self.X1), 1., alternative="less")
+        xp_assert_close(p, xp.asarray(self.P1_1_l))
+        xp_assert_close(t, xp.asarray(self.T1_1))
+
+        t, p = stats.ttest_1samp(xp.asarray(self.X1), 1., alternative="greater")
+        xp_assert_close(p, xp.asarray(self.P1_1_g))
+        xp_assert_close(t, xp.asarray(self.T1_1))
+
+    @skip_xp_backends('jax.numpy', reason='Generic stdtrit mutates array.')
+    @pytest.mark.parametrize("alternative", ['two-sided', 'less', 'greater'])
+    def test_1samp_ci_1d(self, xp, alternative):
+        # test confidence interval method against reference values
+        rng = np.random.default_rng(8066178009154342972)
+        n = 10
+        x = rng.normal(size=n, loc=1.5, scale=2)
+        popmean = rng.normal()  # this shouldn't affect confidence interval
+        # Reference values generated with R t.test:
+        # options(digits=16)
+        # x = c(2.75532884,  0.93892217,  0.94835861,  1.49489446, -0.62396595,
+        #      -1.88019867, -1.55684465,  4.88777104,  5.15310979,  4.34656348)
+        # t.test(x, conf.level=0.85, alternative='l')
+        dtype = xp.asarray(1.0).dtype
+        x = xp.asarray(x, dtype=dtype)
+        popmean = xp.asarray(popmean, dtype=dtype)
+
+        ref = {'two-sided': [0.3594423211709136, 2.9333455028290860],
+               'greater': [0.7470806207371626, np.inf],
+               'less': [-np.inf, 2.545707203262837]}
+        res = stats.ttest_1samp(x, popmean=popmean, alternative=alternative)
+        ci = res.confidence_interval(confidence_level=0.85)
+        xp_assert_close(ci.low, xp.asarray(ref[alternative][0]))
+        xp_assert_close(ci.high, xp.asarray(ref[alternative][1]))
+        xp_assert_equal(res.df, xp.asarray(n-1))
+
+    def test_1samp_ci_iv(self, xp):
+        # test `confidence_interval` method input validation
+        res = stats.ttest_1samp(xp.arange(10.), 0.)
+        message = '`confidence_level` must be a number between 0 and 1.'
+        with pytest.raises(ValueError, match=message):
+            res.confidence_interval(confidence_level=10)
+
+    @skip_xp_backends(np_only=True, reason='Too slow.')
+    @pytest.mark.xslow
+    @hypothesis.given(alpha=hypothesis.strategies.floats(1e-15, 1-1e-15),
+                      data_axis=ttest_data_axis_strategy())
+    @pytest.mark.parametrize('alternative', ['less', 'greater'])
+    def test_pvalue_ci(self, alpha, data_axis, alternative, xp):
+        # test relationship between one-sided p-values and confidence intervals
+        data, axis = data_axis
+        data = xp.asarray(data)
+        res = stats.ttest_1samp(data, 0.,
+                                alternative=alternative, axis=axis)
+        l, u = res.confidence_interval(confidence_level=alpha)
+        popmean = l if alternative == 'greater' else u
+        popmean = xp.expand_dims(popmean, axis=axis)
+        res = stats.ttest_1samp(data, popmean, alternative=alternative, axis=axis)
+        shape = list(data.shape)
+        shape.pop(axis)
+        # `float64` is used to correspond with extreme range of `alpha`
+        ref = xp.broadcast_to(xp.asarray(1-alpha, dtype=xp.float64), shape)
+        xp_assert_close(res.pvalue, ref)
+
+
+class TestPercentileOfScore:
+
+    def f(self, *args, **kwargs):
+        return stats.percentileofscore(*args, **kwargs)
+
+    @pytest.mark.parametrize("kind, result", [("rank", 40),
+                                              ("mean", 35),
+                                              ("strict", 30),
+                                              ("weak", 40)])
+    def test_unique(self, kind, result):
+        a = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
+        assert_equal(self.f(a, 4, kind=kind), result)
+
+    @pytest.mark.parametrize("kind, result", [("rank", 45),
+                                              ("mean", 40),
+                                              ("strict", 30),
+                                              ("weak", 50)])
+    def test_multiple2(self, kind, result):
+        a = [1, 2, 3, 4, 4, 5, 6, 7, 8, 9]
+        assert_equal(self.f(a, 4, kind=kind), result)
+
+    @pytest.mark.parametrize("kind, result", [("rank", 50),
+                                              ("mean", 45),
+                                              ("strict", 30),
+                                              ("weak", 60)])
+    def test_multiple3(self, kind, result):
+        a = [1, 2, 3, 4, 4, 4, 5, 6, 7, 8]
+        assert_equal(self.f(a, 4, kind=kind), result)
+
+    @pytest.mark.parametrize("kind, result", [("rank", 30),
+                                              ("mean", 30),
+                                              ("strict", 30),
+                                              ("weak", 30)])
+    def test_missing(self, kind, result):
+        a = [1, 2, 3, 5, 6, 7, 8, 9, 10, 11]
+        assert_equal(self.f(a, 4, kind=kind), result)
+
+    @pytest.mark.parametrize("kind, result", [("rank", 40),
+                                              ("mean", 35),
+                                              ("strict", 30),
+                                              ("weak", 40)])
+    def test_large_numbers(self, kind, result):
+        a = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]
+        assert_equal(self.f(a, 40, kind=kind), result)
+
+    @pytest.mark.parametrize("kind, result", [("rank", 50),
+                                              ("mean", 45),
+                                              ("strict", 30),
+                                              ("weak", 60)])
+    def test_large_numbers_multiple3(self, kind, result):
+        a = [10, 20, 30, 40, 40, 40, 50, 60, 70, 80]
+        assert_equal(self.f(a, 40, kind=kind), result)
+
+    @pytest.mark.parametrize("kind, result", [("rank", 30),
+                                              ("mean", 30),
+                                              ("strict", 30),
+                                              ("weak", 30)])
+    def test_large_numbers_missing(self, kind, result):
+        a = [10, 20, 30, 50, 60, 70, 80, 90, 100, 110]
+        assert_equal(self.f(a, 40, kind=kind), result)
+
+    @pytest.mark.parametrize("kind, result", [("rank", [0, 10, 100, 100]),
+                                              ("mean", [0, 5, 95, 100]),
+                                              ("strict", [0, 0, 90, 100]),
+                                              ("weak", [0, 10, 100, 100])])
+    def test_boundaries(self, kind, result):
+        a = [10, 20, 30, 50, 60, 70, 80, 90, 100, 110]
+        assert_equal(self.f(a, [0, 10, 110, 200], kind=kind), result)
+
+    @pytest.mark.parametrize("kind, result", [("rank", [0, 10, 100]),
+                                              ("mean", [0, 5, 95]),
+                                              ("strict", [0, 0, 90]),
+                                              ("weak", [0, 10, 100])])
+    def test_inf(self, kind, result):
+        a = [1, 2, 3, 4, 5, 6, 7, 8, 9, +np.inf]
+        assert_equal(self.f(a, [-np.inf, 1, +np.inf], kind=kind), result)
+
+    cases = [("propagate", [], 1, np.nan),
+             ("propagate", [np.nan], 1, np.nan),
+             ("propagate", [np.nan], [0, 1, 2], [np.nan, np.nan, np.nan]),
+             ("propagate", [1, 2], [1, 2, np.nan], [50, 100, np.nan]),
+             ("omit", [1, 2, np.nan], [0, 1, 2], [0, 50, 100]),
+             ("omit", [1, 2], [0, 1, np.nan], [0, 50, np.nan]),
+             ("omit", [np.nan, np.nan], [0, 1, 2], [np.nan, np.nan, np.nan])]
+
+    @pytest.mark.parametrize("policy, a, score, result", cases)
+    def test_nans_ok(self, policy, a, score, result):
+        assert_equal(self.f(a, score, nan_policy=policy), result)
+
+    cases = [
+        ("raise", [1, 2, 3, np.nan], [1, 2, 3],
+         "The input contains nan values"),
+        ("raise", [1, 2, 3], [1, 2, 3, np.nan],
+         "The input contains nan values"),
+    ]
+
+    @pytest.mark.parametrize("policy, a, score, message", cases)
+    def test_nans_fail(self, policy, a, score, message):
+        with assert_raises(ValueError, match=message):
+            self.f(a, score, nan_policy=policy)
+
+    @pytest.mark.parametrize("shape", [
+        (6, ),
+        (2, 3),
+        (2, 1, 3),
+        (2, 1, 1, 3),
+    ])
+    def test_nd(self, shape):
+        a = np.array([0, 1, 2, 3, 4, 5])
+        scores = a.reshape(shape)
+        results = scores*10
+        a = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
+        assert_equal(self.f(a, scores, kind="rank"), results)
+
+    def test_multidimensional_error(self):
+        # gh-21563 reported that `percentileofscore` accepted multidimensional
+        # arrays but did not produce meaningful results.
+        message = "`a` must be 1-dimensional."
+        with pytest.raises(ValueError, match=message):
+            stats.percentileofscore(np.ones((3, 3)), 1)
+
+
+PowerDivCase = namedtuple('Case',  # type: ignore[name-match]
+                          ['f_obs', 'f_exp', 'ddof', 'axis',
+                           'chi2',     # Pearson's
+                           'log',      # G-test (log-likelihood)
+                           'mod_log',  # Modified log-likelihood
+                           'cr',       # Cressie-Read (lambda=2/3)
+                           ])
+
+# The details of the first two elements in power_div_1d_cases are used
+# in a test in TestPowerDivergence.  Check that code before making
+# any changes here.
+power_div_1d_cases = [
+    # Use the default f_exp.
+    PowerDivCase(f_obs=[4, 8, 12, 8], f_exp=None, ddof=0, axis=None,
+                 chi2=4,
+                 log=2*(4*np.log(4/8) + 12*np.log(12/8)),
+                 mod_log=2*(8*np.log(8/4) + 8*np.log(8/12)),
+                 cr=(4*((4/8)**(2/3) - 1) + 12*((12/8)**(2/3) - 1))/(5/9)),
+    # Give a non-uniform f_exp.
+    PowerDivCase(f_obs=[4, 8, 12, 8], f_exp=[2, 16, 12, 2], ddof=0, axis=None,
+                 chi2=24,
+                 log=2*(4*np.log(4/2) + 8*np.log(8/16) + 8*np.log(8/2)),
+                 mod_log=2*(2*np.log(2/4) + 16*np.log(16/8) + 2*np.log(2/8)),
+                 cr=(4*((4/2)**(2/3) - 1) + 8*((8/16)**(2/3) - 1) +
+                     8*((8/2)**(2/3) - 1))/(5/9)),
+    # f_exp is a scalar.
+    PowerDivCase(f_obs=[4, 8, 12, 8], f_exp=8, ddof=0, axis=None,
+                 chi2=4,
+                 log=2*(4*np.log(4/8) + 12*np.log(12/8)),
+                 mod_log=2*(8*np.log(8/4) + 8*np.log(8/12)),
+                 cr=(4*((4/8)**(2/3) - 1) + 12*((12/8)**(2/3) - 1))/(5/9)),
+    # f_exp equal to f_obs.
+    PowerDivCase(f_obs=[3, 5, 7, 9], f_exp=[3, 5, 7, 9], ddof=0, axis=0,
+                 chi2=0, log=0, mod_log=0, cr=0),
+]
+
+
+power_div_empty_cases = [
+    # Shape is (0,)--a data set with length 0.  The computed
+    # test statistic should be 0.
+    PowerDivCase(f_obs=[],
+                 f_exp=None, ddof=0, axis=0,
+                 chi2=0, log=0, mod_log=0, cr=0),
+    # Shape is (0, 3).  This is 3 data sets, but each data set has
+    # length 0, so the computed test statistic should be [0, 0, 0].
+    PowerDivCase(f_obs=np.array([[],[],[]]).T,
+                 f_exp=None, ddof=0, axis=0,
+                 chi2=[0, 0, 0],
+                 log=[0, 0, 0],
+                 mod_log=[0, 0, 0],
+                 cr=[0, 0, 0]),
+    # Shape is (3, 0).  This represents an empty collection of
+    # data sets in which each data set has length 3.  The test
+    # statistic should be an empty array.
+    PowerDivCase(f_obs=np.array([[],[],[]]),
+                 f_exp=None, ddof=0, axis=0,
+                 chi2=[],
+                 log=[],
+                 mod_log=[],
+                 cr=[]),
+]
+
+
+@make_xp_test_case(stats.power_divergence)
+class TestPowerDivergence:
+
+    def check_power_divergence(self, f_obs, f_exp, ddof, axis, lambda_,
+                               expected_stat, xp):
+        dtype = xp.asarray(1.).dtype
+
+        f_obs = xp.asarray(f_obs, dtype=dtype)
+        f_exp = xp.asarray(f_exp, dtype=dtype) if f_exp is not None else f_exp
+
+        if axis is None:
+            num_obs = xp_size(f_obs)
+        else:
+            arrays = (xp.broadcast_arrays(f_obs, f_exp) if f_exp is not None
+                      else (f_obs,))
+            num_obs = arrays[0].shape[axis]
+
+        with warnings.catch_warnings():
+            warnings.filterwarnings("ignore", "Mean of empty slice", RuntimeWarning)
+            stat, p = stats.power_divergence(
+                                f_obs, f_exp=f_exp, ddof=ddof,
+                                axis=axis, lambda_=lambda_)
+            xp_assert_close(stat, xp.asarray(expected_stat, dtype=dtype))
+
+            if lambda_ == 1 or lambda_ == "pearson":
+                # Also test stats.chisquare.
+                stat, p = stats.chisquare(f_obs, f_exp=f_exp, ddof=ddof,
+                                          axis=axis)
+                xp_assert_close(stat, xp.asarray(expected_stat, dtype=dtype))
+
+        ddof = np.asarray(ddof)
+        expected_p = stats.distributions.chi2.sf(expected_stat,
+                                                 num_obs - 1 - ddof)
+        xp_assert_close(p, xp.asarray(expected_p, dtype=dtype))
+
+    @pytest.mark.parametrize('case', power_div_1d_cases)
+    @pytest.mark.parametrize('lambda_stat',
+        [(None, 'chi2'), ('pearson', 'chi2'), (1, 'chi2'),
+         ('log-likelihood', 'log'), ('mod-log-likelihood', 'mod_log'),
+         ('cressie-read', 'cr'), (2/3, 'cr')])
+    def test_basic(self, case, lambda_stat, xp):
+        lambda_, attr = lambda_stat
+        expected_stat = getattr(case, attr)
+        self.check_power_divergence(case.f_obs, case.f_exp, case.ddof, case.axis,
+                                    lambda_, expected_stat, xp)
+
+    def test_axis(self, xp):
+        case0 = power_div_1d_cases[0]
+        case1 = power_div_1d_cases[1]
+        f_obs = np.vstack((case0.f_obs, case1.f_obs))
+        f_exp = np.vstack((np.ones_like(case0.f_obs)*np.mean(case0.f_obs),
+                           case1.f_exp))
+        # Check the four computational code paths in power_divergence
+        # using a 2D array with axis=1.
+        f_obs = xp.asarray(f_obs)
+        f_exp = xp.asarray(f_exp) if f_exp is not None else f_exp
+        self.check_power_divergence(
+               f_obs, f_exp, 0, 1,
+               "pearson", [case0.chi2, case1.chi2], xp=xp)
+        self.check_power_divergence(
+               f_obs, f_exp, 0, 1,
+               "log-likelihood", [case0.log, case1.log], xp=xp)
+        self.check_power_divergence(
+               f_obs, f_exp, 0, 1,
+               "mod-log-likelihood", [case0.mod_log, case1.mod_log], xp=xp)
+        self.check_power_divergence(
+               f_obs, f_exp, 0, 1,
+               "cressie-read", [case0.cr, case1.cr], xp=xp)
+        # Reshape case0.f_obs to shape (2,2), and use axis=None.
+        # The result should be the same.
+        f_obs_reshape = xp.reshape(xp.asarray(case0.f_obs), (2, 2))
+        self.check_power_divergence(
+               f_obs_reshape, None, 0, None,
+               "pearson", case0.chi2, xp=xp)
+
+    def test_ddof_broadcasting(self, xp):
+        # Test that ddof broadcasts correctly.
+        # ddof does not affect the test statistic.  It is broadcast
+        # with the computed test statistic for the computation of
+        # the p value.
+
+        case0 = power_div_1d_cases[0]
+        case1 = power_div_1d_cases[1]
+        # Create 4x2 arrays of observed and expected frequencies.
+        f_obs = np.vstack((case0.f_obs, case1.f_obs)).T
+        f_exp = np.vstack((np.ones_like(case0.f_obs)*np.mean(case0.f_obs),
+                           case1.f_exp)).T
+
+        expected_chi2 = [case0.chi2, case1.chi2]
+
+        dtype = xp.asarray(1.).dtype
+        f_obs = xp.asarray(f_obs, dtype=dtype)
+        f_exp = xp.asarray(f_exp, dtype=dtype)
+        expected_chi2 = xp.asarray(expected_chi2, dtype=dtype)
+
+        # ddof has shape (2, 1).  This is broadcast with the computed
+        # statistic, so p will have shape (2,2).
+        ddof = xp.asarray([[0], [1]])
+
+        stat, p = stats.power_divergence(f_obs, f_exp, ddof=ddof)
+        xp_assert_close(stat, expected_chi2)
+
+        # Compute the p values separately, passing in scalars for ddof.
+        _, p0 = stats.power_divergence(f_obs, f_exp, ddof=ddof[0, 0])
+        _, p1 = stats.power_divergence(f_obs, f_exp, ddof=ddof[1, 0])
+
+        expected_p = xp.concat((p0[xp.newaxis, :], p1[xp.newaxis, :]), axis=0)
+        xp_assert_close(p, expected_p)
+
+    @pytest.mark.parametrize('case', power_div_empty_cases)
+    @pytest.mark.parametrize('lambda_stat',
+        [('pearson', 'chi2'), ('log-likelihood', 'log'),
+         ('mod-log-likelihood', 'mod_log'),
+         ('cressie-read', 'cr'), (2/3, 'cr')])
+    def test_empty_cases(self, case, lambda_stat, xp):
+        lambda_, attr = lambda_stat
+        expected_stat = getattr(case, attr)
+        with warnings.catch_warnings():
+            self.check_power_divergence(
+                case.f_obs, case.f_exp, case.ddof, case.axis,
+                lambda_, expected_stat, xp)
+
+    def test_power_divergence_result_attributes(self, xp):
+        f_obs = power_div_1d_cases[0].f_obs
+        f_exp = power_div_1d_cases[0].f_exp
+        ddof = power_div_1d_cases[0].ddof
+        axis = power_div_1d_cases[0].axis
+        dtype = xp.asarray(1.).dtype
+        f_obs = xp.asarray(f_obs, dtype=dtype)
+        # f_exp is None
+
+        res = stats.power_divergence(f_obs, f_exp=f_exp, ddof=ddof,
+                                     axis=axis, lambda_="pearson")
+        attributes = ('statistic', 'pvalue')
+        check_named_results(res, attributes, xp=xp)
+
+    def test_power_divergence_gh_12282(self, xp):
+        # The sums of observed and expected frequencies must match
+        f_obs = xp.asarray([[10., 20.], [30., 20.]])
+        f_exp = xp.asarray([[5., 15.], [35., 25.]])
+        stat, pval = stats.power_divergence(f_obs, f_exp=f_exp)
+        xp_assert_close(stat, xp.asarray([5.71428571, 2.66666667]))
+        xp_assert_close(pval, xp.asarray([0.01682741, 0.10247043]))
+
+        if is_lazy_array(f_obs):
+            res = stats.power_divergence(f_obs, f_exp=xp.asarray([30., 60.]))
+            xp_assert_equal(res.statistic, xp.asarray([xp.nan, xp.nan]))
+            xp_assert_equal(res.pvalue, xp.asarray([xp.nan, xp.nan]))
+
+            res = stats.power_divergence(f_obs, f_exp=f_exp, axis=1)
+            xp_assert_equal(res.statistic, xp.asarray([xp.nan, xp.nan]))
+            xp_assert_equal(res.pvalue, xp.asarray([xp.nan, xp.nan]))
+
+            # only slices with unequal sums result in NaN
+            f_exp = xp.asarray([[5., 25.], [35., 25.]])
+            res = stats.power_divergence(f_obs, f_exp=f_exp)
+            xp_assert_close(res.statistic, xp.asarray([stat[0], xp.nan]))
+            xp_assert_close(res.pvalue, xp.asarray([pval[0], xp.nan]))
+        else:
+            message = 'For each axis slice...'
+            with pytest.raises(ValueError, match=message):
+                stats.power_divergence(f_obs, f_exp=xp.asarray([30., 60.]))
+            with pytest.raises(ValueError, match=message):
+                stats.power_divergence(f_obs, f_exp=f_exp, axis=1)
+
+    def test_power_divergence_against_cressie_read_data(self, xp):
+        # Test stats.power_divergence against tables 4 and 5 from
+        # Cressie and Read, "Multimonial Goodness-of-Fit Tests",
+        # J. R. Statist. Soc. B (1984), Vol 46, No. 3, pp. 440-464.
+        # This tests the calculation for several values of lambda.
+
+        # Table 4 data recalculated for greater precision according to:
+        # Shelby J. Haberman, Analysis of Qualitative Data: Volume 1
+        # Introductory Topics, Academic Press, New York, USA (1978).
+        obs = xp.asarray([15., 11., 14., 17., 5., 11., 10., 4., 8.,
+                          10., 7., 9., 11., 3., 6., 1., 1., 4.])
+        beta = -0.083769  # Haberman (1978), p. 15
+        i = xp.arange(1., obs.shape[0] + 1.)
+        alpha = xp.log(xp.sum(obs) / xp.sum(xp.exp(beta*i)))
+        expected_counts = xp.exp(alpha + beta*i)
+
+        # `table4` holds just the second and third columns from Table 4.
+        table4 = xp.concat((obs[xp.newaxis, :],
+                            expected_counts[xp.newaxis, :])).T
+
+        table5 = np.asarray([
+            # lambda, statistic
+            -10.0, 72.2e3,
+            -5.0, 28.9e1,
+            -3.0, 65.6,
+            -2.0, 40.6,
+            -1.5, 34.0,
+            -1.0, 29.5,
+            -0.5, 26.5,
+            0.0, 24.6,
+            0.5, 23.4,
+            0.67, 23.1,
+            1.0, 22.7,
+            1.5, 22.6,
+            2.0, 22.9,
+            3.0, 24.8,
+            5.0, 35.5,
+            10.0, 21.4e1,
+            ])
+        table5 = np.reshape(table5, (-1, 2))
+
+        for i in range(table5.shape[0]):
+            lambda_, expected_stat = float(table5[i, 0]), float(table5[i, 1])
+            stat, p = stats.power_divergence(table4[:, 0], table4[:, 1],
+                                             lambda_=lambda_)
+            xp_assert_close(stat, xp.asarray(expected_stat), rtol=5e-3)
+
+
+@make_xp_test_case(stats.chisquare)
+class TestChisquare:
+    def test_chisquare_12282a(self, xp):
+        # Currently `chisquare` is implemented via power_divergence
+        # in case that ever changes, perform a basic test like
+        # test_power_divergence_gh_12282
+        f_obs = xp.asarray([10., 20.])
+        f_exp = xp.asarray([30., 60.])
+        if is_lazy_array(f_obs):
+            res = stats.chisquare(f_obs, f_exp=f_exp)
+            xp_assert_equal(res.statistic, xp.asarray(xp.nan))
+            xp_assert_equal(res.pvalue, xp.asarray(xp.nan))
+        else:
+            with assert_raises(ValueError, match='For each axis slice...'):
+                stats.chisquare(f_obs, f_exp=f_exp)
+
+    def test_chisquare_12282b(self, xp):
+        # Check that users can now disable the sum check tested in
+        # test_chisquare_12282a. Also, confirm that statistic and p-value
+        # are as expected.
+        rng = np.random.default_rng(3843874358728234)
+        n = 10
+        lam = rng.uniform(1000, 2000, size=n)
+        x = rng.poisson(lam)
+        lam = xp.asarray(lam)
+        x = xp.asarray(x, dtype=lam.dtype)
+        res = stats.chisquare(x, f_exp=lam, ddof=-1, sum_check=False)
+        # Poisson is approximately normal with mean and variance lam
+        z = (x - lam) / xp.sqrt(lam)
+        statistic = xp.sum(z**2)
+        xp_assert_close(res.statistic, statistic)
+        # Sum of `n` squared standard normal variables follows chi2 with `n` DoF
+        X2 = _SimpleChi2(xp.asarray(n, dtype=statistic.dtype))
+        xp_assert_close(res.pvalue, X2.sf(statistic))
+
+    @pytest.mark.parametrize("n, dtype", [(200, 'uint8'), (1000000, 'int32')])
+    def test_chiquare_data_types_attributes(self, n, dtype, xp):
+        # Regression test for gh-10159 and gh-18368
+        dtype = getattr(xp, dtype)
+        obs = xp.asarray([n, 0], dtype=dtype)
+        exp = xp.asarray([n // 2, n // 2], dtype=dtype)
+        res = stats.chisquare(obs, exp)
+        stat, p = res
+        xp_assert_close(stat, xp.asarray(n, dtype=xp.asarray(1.).dtype), rtol=1e-13)
+        # check that attributes are identical to unpacked outputs - see gh-18368
+        xp_assert_equal(res.statistic, stat)
+        xp_assert_equal(res.pvalue, p)
+
+
+@make_xp_test_case(stats.friedmanchisquare)
+class TestFriedmanChiSquare:
+    # verified with matlab and R
+    # From Demsar "Statistical Comparisons of Classifiers over Multiple Data Sets"
+    # 2006, Xf=9.28 (no tie handling, tie corrected Xf >=9.28)
+    x1 = [[0.763, 0.599, 0.954, 0.628, 0.882, 0.936, 0.661,
+           0.583, 0.775, 1.0, 0.94, 0.619, 0.972, 0.957],
+          [0.768, 0.591, 0.971, 0.661, 0.888, 0.931, 0.668,
+           0.583, 0.838, 1.0, 0.962, 0.666, 0.981, 0.978],
+          [0.771, 0.590, 0.968, 0.654, 0.886, 0.916, 0.609,
+           0.563, 0.866, 1.0, 0.965, 0.614, 0.9751, 0.946],
+          [0.798, 0.569, 0.967, 0.657, 0.898, 0.931, 0.685,
+           0.625, 0.875, 1.0, 0.962, 0.669, 0.975, 0.970]]
+    ref1 = (10.2283464566929, 0.0167215803284414)
+
+    # From "Bioestadistica para las ciencias de la salud" Xf=18.95 p<0.001:
+    x2 = [[4, 3, 5, 3, 5, 3, 2, 5, 4, 4, 4, 3],
+          [2, 2, 1, 2, 3, 1, 2, 3, 2, 1, 1, 3],
+          [2, 4, 3, 3, 4, 3, 3, 4, 4, 1, 2, 1],
+          [3, 5, 4, 3, 4, 4, 3, 3, 3, 4, 4, 4]]
+    ref2 = (18.9428571428571, 0.000280938375189499)
+
+    # From Jerrorl H. Zar, "Biostatistical Analysis"(example 12.6),
+    # Xf=10.68, 0.005 < p < 0.01:
+    # Probability from this example is inexact
+    # using Chisquare approximation of Friedman Chisquare.
+    x3 = [[7.0, 9.9, 8.5, 5.1, 10.3],
+          [5.3, 5.7, 4.7, 3.5, 7.7],
+          [4.9, 7.6, 5.5, 2.8, 8.4],
+          [8.8, 8.9, 8.1, 3.3, 9.1]]
+    ref3 = (10.68, 0.0135882729582176)
+
+    @pytest.mark.parametrize("dtype", [None, "float32", "float64"])
+    @pytest.mark.parametrize("data, ref", [(x1, ref1), (x2, ref2), (x3, ref3)])
+    def test_against_references(self, dtype, data, ref, xp):
+        dtype = dtype if dtype is None else getattr(xp, dtype)
+        data = [xp.asarray(array, dtype=dtype) for array in data]
+        res = stats.friedmanchisquare(*data)
+        xp_assert_close(res.statistic, xp.asarray(ref[0], dtype=dtype))
+        xp_assert_close(res.pvalue, xp.asarray(ref[1], dtype=dtype))
+
+    def test_too_few_samples(self, xp):
+        message = "At least 3 samples must be given"
+        with pytest.raises(ValueError, match=message):
+            stats.friedmanchisquare(xp.asarray(self.x3[0]), xp.asarray(self.x3[1]))
+
+
+@make_xp_test_case(stats.kstest)
+class TestKSTest:
+    """Tests kstest and ks_1samp agree with K-S various sizes, alternatives, modes."""
+
+    def _test_kstest_and_ks1samp(self, x, alternative, mode='auto', decimal=14):
+        result = stats.kstest(x, 'norm', alternative=alternative, mode=mode)
+        result_1samp = stats.ks_1samp(x, special.ndtr,
+                                      alternative=alternative, mode=mode)
+        xp_assert_close(result.statistic, result_1samp.statistic)
+        xp_assert_close(result.pvalue, result_1samp.pvalue)
+        xp_assert_equal(result.statistic_location, result.statistic_location)
+        xp_assert_equal(result.statistic_sign, result.statistic_sign)
+
+    def test_namedtuple_attributes(self, xp):
+        x = xp.linspace(-1, 1, 9)
+        # test for namedtuple attribute results
+        attributes = ('statistic', 'pvalue')
+        res = stats.kstest(x, special.ndtr)
+        check_named_results(res, attributes, xp=xp)
+
+    def test_agree_with_ks_1samp(self, xp):
+        x = xp.linspace(-1, 1, 9)
+        self._test_kstest_and_ks1samp(x, 'two-sided')
+
+        x = xp.linspace(-15, 15, 9)
+        self._test_kstest_and_ks1samp(x, 'two-sided')
+
+        x = [-1.23, 0.06, -0.60, 0.17, 0.66, -0.17, -0.08, 0.27, -0.98, -0.99]
+        x = xp.asarray(x)
+        self._test_kstest_and_ks1samp(x, 'two-sided')
+        self._test_kstest_and_ks1samp(x, 'greater', mode='exact')
+        self._test_kstest_and_ks1samp(x, 'less', mode='exact')
+
+    # parametrize over function-specific options to make sure they're passed through;
+    # `test_axis_nan_policy` takes care of the rest.
+    @pytest.mark.parametrize("method", ["auto", "exact", "asymp"])
+    @pytest.mark.parametrize("alternative", ['two-sided', 'less', 'greater'])
+    def test_agree_with_ks_2samp(self, method, alternative, xp):
+        rng = np.random.default_rng(236114087)
+        x, y = rng.random((2, 9, 10))
+        x, y = xp.asarray(x), xp.asarray(y)
+        res = stats.kstest(x, y, alternative=alternative, method=method)
+        ref = stats.ks_2samp(x, y, alternative=alternative, method=method)
+        xp_assert_equal(res.statistic, ref.statistic)
+        xp_assert_equal(res.pvalue, ref.pvalue)
+        xp_assert_equal(res.statistic_location, ref.statistic_location)
+        xp_assert_equal(res.statistic_sign, ref.statistic_sign)
+
+    def test_pm_inf_gh20386(self, xp):
+        # Check that gh-20386 is resolved - `kstest` does not
+        # return NaNs when both -inf and inf are in sample.
+        vals = xp.asarray([-xp.inf, 0, 1, xp.inf])
+        def cdf(x):  # Cauchy CDF
+            return xp.atan2(xp.ones_like(x), -x) / xp.pi
+        res = stats.kstest(vals, cdf)
+        ref = stats.kstest(vals, cdf, _no_deco=True)
+        assert xp.isfinite(res.statistic)
+        assert xp.isfinite(res.pvalue)
+        assert xp.isfinite(res.statistic_location)
+        assert xp.isfinite(res.statistic_sign)
+        xp_assert_equal(res.statistic, ref.statistic)
+        xp_assert_equal(res.pvalue, ref.pvalue)
+        xp_assert_equal(res.statistic_location, ref.statistic_location)
+        xp_assert_equal(res.statistic_sign, ref.statistic_sign)
+
+    # missing: no test that uses *args
+
+
+@make_xp_test_case(stats.ks_1samp)
+class TestKSOneSample:
+    """
+    Tests kstest and ks_samp 1-samples with K-S various sizes, alternatives, modes.
+    """
+
+    def _testOne(self, x, alternative, expected_statistic, expected_prob, *,
+                 mode='auto', dtype, xp):
+        rtol = 5e-14 if dtype == xp.float64 else 1e-5
+        res = stats.ks_1samp(x, special.ndtr, alternative=alternative, mode=mode)
+        ref_statistic = xp.asarray(expected_statistic, dtype=dtype)
+        ref_pvalue = xp.asarray(expected_prob, dtype=dtype)
+        xp_assert_close(res.statistic, ref_statistic, rtol=rtol)
+        xp_assert_close(res.pvalue, ref_pvalue, rtol=rtol)
+
+    @pytest.mark.parametrize('dtype', [None, 'float32', 'float64'])
+    def test_agree_with_r(self, dtype, xp):
+        # comparing with some values from R
+        dtype = xp_default_dtype(xp) if dtype is None else getattr(xp, dtype)
+        x = xp.linspace(-1, 1, 9, dtype=dtype)
+        self._testOne(x, 'two-sided', 0.15865525393145705, 0.95164069201518386,
+                      dtype=dtype, xp=xp)
+
+        x = xp.linspace(-15, 15, 9, dtype=dtype)
+        self._testOne(x, 'two-sided', 0.44435602715924361, 0.038850140086788665,
+                      dtype=dtype, xp=xp)
+
+        x = [-1.23, 0.06, -0.60, 0.17, 0.66, -0.17, -0.08, 0.27, -0.98, -0.99]
+        x = xp.asarray(x, dtype=dtype)
+        self._testOne(x, 'two-sided', 0.293580126801961, 0.293408463684361,
+                      dtype=dtype, xp=xp)
+        self._testOne(x, 'greater', 0.293580126801961, 0.146988835042376, mode='exact',
+                      dtype=dtype, xp=xp)
+        self._testOne(x, 'less', 0.109348552425692, 0.732768892470675, mode='exact',
+                      dtype=dtype, xp=xp)
+
+    @pytest.mark.parametrize('dtype', [None, 'float32', 'float64'])
+    def test_known_examples(self, xp, dtype):
+        # the following tests rely on deterministically replicated rvs
+        dtype = xp_default_dtype(xp) if dtype is None else getattr(xp, dtype)
+        x = stats.norm.rvs(loc=0.2, size=100, random_state=987654321)
+        x = xp.asarray(x, dtype=dtype)
+        self._testOne(x, 'two-sided', 0.12464329735846891, 0.089444888711820769,
+                      mode='asymp', xp=xp, dtype=dtype)
+        self._testOne(x, 'less', 0.12464329735846891, 0.040989164077641749,
+                      xp=xp, dtype=dtype)
+        self._testOne(x, 'greater', 0.0072115233216310994, 0.98531158590396228,
+                      xp=xp, dtype=dtype)
+
+    # this is a test of the exact p-value calculation, available only with NumPy.
+    def test_ks1samp_allpaths(self):
+        # Check NaN input, output.
+        assert_(np.isnan(kolmogn(np.nan, 1, True)))
+        with assert_raises(ValueError, match='n is not integral: 1.5'):
+            kolmogn(1.5, 1, True)
+        assert_(np.isnan(kolmogn(-1, 1, True)))
+
+        dataset = np.asarray([
+            # Check x out of range
+            (101, 1, True, 1.0),
+            (101, 1.1, True, 1.0),
+            (101, 0, True, 0.0),
+            (101, -0.1, True, 0.0),
+
+            (32, 1.0 / 64, True, 0.0),  # Ruben-Gambino
+            (32, 1.0 / 64, False, 1.0),  # Ruben-Gambino
+
+            # Miller
+            (32, 0.5, True, 0.9999999363163307),
+            # Miller 2 * special.smirnov(32, 0.5)
+            (32, 0.5, False, 6.368366937916623e-08),
+
+            # Check some other paths
+            (32, 1.0 / 8, True, 0.34624229979775223),
+            (32, 1.0 / 4, True, 0.9699508336558085),
+            (1600, 0.49, False, 0.0),
+            # 2 * special.smirnov(1600, 1/16.0)
+            (1600, 1 / 16.0, False, 7.0837876229702195e-06),
+            # _kolmogn_DMTW
+            (1600, 14 / 1600, False, 0.99962357317602),
+            # _kolmogn_PelzGood
+            (1600, 1 / 32, False, 0.08603386296651416),
+        ])
+        FuncData(kolmogn, dataset, (0, 1, 2), 3).check(dtypes=[int, float, bool])
+
+    @pytest.mark.parametrize("ksfunc", [stats.kstest, stats.ks_1samp])
+    @pytest.mark.parametrize("alternative, x6val, ref_location, ref_sign",
+                             [('greater', 6., 6., +1),
+                              ('less', 7., 7., -1),
+                              ('two-sided', 6., 6., +1),
+                              ('two-sided', 7., 7., -1)])
+    def test_location_sign(self, ksfunc, alternative,
+                           x6val, ref_location, ref_sign, xp):
+        # Test that location and sign corresponding with statistic are as
+        # expected. (Test is designed to be easy to predict.)
+        x = xp.arange(10.) + 0.5
+        x = xpx.at(x)[6].set(x6val)
+        # cdf = stats.uniform(scale=10).cdf
+        def cdf(x): return x / 10.
+        res = ksfunc(xp.asarray(x), cdf, alternative=alternative)
+        rtol = 1e-15 if x.dtype == xp.float64 else 1e-6
+        xp_assert_close(res.statistic, xp.asarray(0.1), rtol=rtol)
+        xp_assert_equal(res.statistic_location, xp.asarray(ref_location))
+        xp_assert_equal(res.statistic_sign, xp.asarray(ref_sign, dtype=xp.int8))
+
+    def test_invalid_method_raises(self):
+        # gh-24737: unrecognized method strings must raise ValueError, not
+        # silently fall through to the 'approx' else-clause.
+        rng = np.random.default_rng(42)
+        x = rng.standard_normal(10)
+        with pytest.raises(ValueError, match="Invalid value for method"):
+            stats.ks_1samp(x, special.ndtr, method='any_other_string')
+        # must fire for one-sided alternatives too, not just two-sided
+        with pytest.raises(ValueError, match="Invalid value for method"):
+            stats.ks_1samp(x, special.ndtr, method='typo',
+                           alternative='greater')
+        with pytest.raises(ValueError, match="Invalid value for method"):
+            stats.ks_1samp(x, special.ndtr, method='typo',
+                           alternative='less')
+        # kstest wrapper must also raise
+        with pytest.raises(ValueError, match="Invalid value for method"):
+            stats.kstest(x, stats.norm.cdf, method='any_other_string')
+
+@make_xp_test_case(stats.ks_2samp)
+class TestKSTwoSamples:
+    """Tests 2-samples with K-S various sizes, alternatives, modes."""
+
+    def _check_warnings(self, warn_list, expected_type, expected_len):
+        """
+        Checks that all of the warnings from a list returned by
+        `warnings.catch_all(record=True)` are of the required type and that the list
+        contains expected number of warnings.
+        """
+        assert_equal(len(warn_list), expected_len, "number of warnings")
+        for warn_ in warn_list:
+            assert_(warn_.category is expected_type)
+
+    def _testOne(self, x1, x2, alternative, ref_statistic, ref_pvalue,
+                 mode='auto', *, xp):
+        x1, x2 = xp.asarray(x1), xp.asarray(x2)
+        dtype = xp_result_type(x1, x2, force_floating=True, xp=xp)
+        res_statistic, res_pvalue = stats.ks_2samp(x1, x2, alternative, mode=mode)
+        ref_statistic = xp.asarray(ref_statistic, dtype=dtype)
+        ref_pvalue = xp.asarray(ref_pvalue, dtype=dtype)
+        xp_assert_close(res_statistic, ref_statistic)
+        # The original tests used assert_array_almost_equal, which has an absolute
+        # tolerance by default. It would be good to test with only a relative tolerance,
+        # but that would require computing p-values with another reference. R would be
+        # the natural choice, but it clips tiny p-values.
+        xp_assert_close(res_pvalue, ref_pvalue, atol=1e-14)
+
+    def testSmall(self, xp):
+        self._testOne([0], [1], 'two-sided', 1.0/1, 1.0, xp=xp)
+        self._testOne([0], [1], 'greater', 1.0/1, 0.5, xp=xp)
+        self._testOne([0], [1], 'less', 0.0/1, 1.0, xp=xp)
+        self._testOne([1], [0], 'two-sided', 1.0/1, 1.0, xp=xp)
+        self._testOne([1], [0], 'greater', 0.0/1, 1.0, xp=xp)
+        self._testOne([1], [0], 'less', 1.0/1, 0.5, xp=xp)
+
+    def testTwoVsThree(self, xp):
+        data1 = xp.asarray([1.0, 2.0])
+        data1p = data1 + 0.01
+        data1m = data1 - 0.01
+        data2 = xp.asarray([1.0, 2.0, 3.0])
+        self._testOne(data1p, data2, 'two-sided', 1.0 / 3, 1.0, xp=xp)
+        self._testOne(data1p, data2, 'greater', 1.0 / 3, 0.7, xp=xp)
+        self._testOne(data1p, data2, 'less', 1.0 / 3, 0.7, xp=xp)
+        self._testOne(data1m, data2, 'two-sided', 2.0 / 3, 0.6, xp=xp)
+        self._testOne(data1m, data2, 'greater', 2.0 / 3, 0.3, xp=xp)
+        self._testOne(data1m, data2, 'less', 0, 1.0, xp=xp)
+
+    def testTwoVsFour(self, xp):
+        data1 = xp.asarray([1.0, 2.0])
+        data1p = data1 + 0.01
+        data1m = data1 - 0.01
+        data2 = xp.asarray([1.0, 2.0, 3.0, 4.0])
+        self._testOne(data1p, data2, 'two-sided', 2.0 / 4, 14.0/15, xp=xp)
+        self._testOne(data1p, data2, 'greater', 2.0 / 4, 8.0/15, xp=xp)
+        self._testOne(data1p, data2, 'less', 1.0 / 4, 12.0/15, xp=xp)
+
+        self._testOne(data1m, data2, 'two-sided', 3.0 / 4, 6.0/15, xp=xp)
+        self._testOne(data1m, data2, 'greater', 3.0 / 4, 3.0/15, xp=xp)
+        self._testOne(data1m, data2, 'less', 0, 1.0, xp=xp)
+
+    def test100_100(self, xp):
+        x100 = xp.linspace(1, 100, 100)
+        x100_2_p1 = x100 + 2 + 0.1
+        x100_2_m1 = x100 + 2 - 0.1
+        self._testOne(x100, x100_2_p1, 'two-sided', 3.0 / 100, 0.999999999996206, xp=xp)
+        self._testOne(x100, x100_2_p1, 'greater', 3.0 / 100, 0.9143290114276248, xp=xp)
+        self._testOne(x100, x100_2_p1, 'less', 0, 1.0, xp=xp)
+        self._testOne(x100, x100_2_m1, 'two-sided', 2.0 / 100, 1.0, xp=xp)
+        self._testOne(x100, x100_2_m1, 'greater', 2.0 / 100, 0.960978450786184, xp=xp)
+        self._testOne(x100, x100_2_m1, 'less', 0, 1.0, xp=xp)
+
+    def test100_110(self, xp):
+        x100 = xp.linspace(1, 100, 100)
+        x110 = xp.linspace(1, 100, 110)
+        x110_20_p1 = x110 + 20 + 0.1
+        x110_20_m1 = x110 + 20 - 0.1
+        # 100, 110
+        self._testOne(x100, x110_20_p1, 'two-sided',
+                      232.0 / 1100, 0.015739183865607353, xp=xp)
+        self._testOne(x100, x110_20_p1, 'greater',
+                      232.0 / 1100, 0.007869594319053203, xp=xp)
+        self._testOne(x100, x110_20_p1, 'less',
+                      0, 1, xp=xp)
+        self._testOne(x100, x110_20_m1, 'two-sided',
+                      229.0 / 1100, 0.017803803861026313, xp=xp)
+        self._testOne(x100, x110_20_m1, 'greater',
+                      229.0 / 1100, 0.008901905958245056, xp=xp)
+        self._testOne(x100, x110_20_m1, 'less',
+                      0.0, 1.0, xp=xp)
+
+    def testRepeatedValues(self, xp):
+        x2233 = xp.asarray([2] * 3 + [3] * 4 + [5] * 5 + [6] * 4)
+        x3344 = x2233 + 1
+        x2356 = xp.asarray([2] * 3 + [3] * 4 + [5] * 10 + [6] * 4)
+        x3467 = xp.asarray([3] * 10 + [4] * 2 + [6] * 10 + [7] * 4)
+        self._testOne(x2233, x3344, 'two-sided', 5.0/16, 0.4262934613454952, xp=xp)
+        self._testOne(x2233, x3344, 'greater', 5.0/16, 0.21465428276573786, xp=xp)
+        self._testOne(x2233, x3344, 'less', 0.0/16, 1.0, xp=xp)
+        self._testOne(x2356, x3467, 'two-sided', 190.0/21/26, 0.0919245790168125, xp=xp)
+        self._testOne(x2356, x3467, 'greater', 190.0/21/26, 0.0459633806858544, xp=xp)
+        self._testOne(x2356, x3467, 'less', 70.0/21/26, 0.6121593130022775, xp=xp)
+
+    def testEqualSizes(self, xp):
+        data2 = xp.asarray([1.0, 2.0, 3.0])
+        self._testOne(data2, data2+1, 'two-sided', 1.0/3, 1.0, xp=xp)
+        self._testOne(data2, data2+1, 'greater', 1.0/3, 0.75, xp=xp)
+        self._testOne(data2, data2+1, 'less', 0.0/3, 1., xp=xp)
+        self._testOne(data2, data2+0.5, 'two-sided', 1.0/3, 1.0, xp=xp)
+        self._testOne(data2, data2+0.5, 'greater', 1.0/3, 0.75, xp=xp)
+        self._testOne(data2, data2+0.5, 'less', 0.0/3, 1., xp=xp)
+        self._testOne(data2, data2-0.5, 'two-sided', 1.0/3, 1.0, xp=xp)
+        self._testOne(data2, data2-0.5, 'greater', 0.0/3, 1.0, xp=xp)
+        self._testOne(data2, data2-0.5, 'less', 1.0/3, 0.75, xp=xp)
+
+    @pytest.mark.slow
+    def testMiddlingBoth(self, xp):
+        # 500, 600
+        n1, n2 = 500, 600
+        delta = 1.0/n1/n2/2/2
+        x = xp.linspace(1., 200., n1) - delta
+        y = xp.linspace(2., 200., n2)
+        self._testOne(x, y, 'two-sided', 2000.0 / n1 / n2, 1.0,
+                      mode='auto', xp=xp)
+        self._testOne(x, y, 'two-sided', 2000.0 / n1 / n2, 1.0,
+                      mode='asymp', xp=xp)
+        self._testOne(x, y, 'greater', 2000.0 / n1 / n2, 0.9697596024683929,
+                      mode='asymp', xp=xp)
+        self._testOne(x, y, 'less', 500.0 / n1 / n2, 0.9968735843165021,
+                      mode='asymp', xp=xp)
+        with warnings.catch_warnings():
+            message = "ks_2samp: Exact calculation unsuccessful."
+            warnings.filterwarnings("ignore", message, RuntimeWarning)
+            self._testOne(x, y, 'greater', 2000.0 / n1 / n2, 0.9697596024683929,
+                          mode='exact', xp=xp)
+            self._testOne(x, y, 'less', 500.0 / n1 / n2, 0.9968735843165021,
+                          mode='exact', xp=xp)
+        with warnings.catch_warnings(record=True) as w:
+            warnings.simplefilter("always")
+            self._testOne(x, y, 'less', 500.0 / n1 / n2, 0.9968735843165021,
+                          mode='exact', xp=xp)
+            self._check_warnings(w, RuntimeWarning, 1)
+
+    @pytest.mark.slow
+    def testMediumBoth(self, xp):
+        # 1000, 1100
+        n1, n2 = 1000, 1100
+        delta = 1.0/n1/n2/2/2
+        x = xp.linspace(1., 200., n1) - delta
+        y = xp.linspace(2., 200., n2)
+        self._testOne(x, y, 'two-sided', 6600.0 / n1 / n2, 1.0,
+                      mode='asymp', xp=xp)
+        self._testOne(x, y, 'two-sided', 6600.0 / n1 / n2, 1.0,
+                      mode='auto', xp=xp)
+        self._testOne(x, y, 'greater', 6600.0 / n1 / n2, 0.9573185808092622,
+                      mode='asymp', xp=xp)
+        self._testOne(x, y, 'less', 1000.0 / n1 / n2, 0.9982410869433984,
+                      mode='asymp', xp=xp)
+
+        with warnings.catch_warnings():
+            message = "ks_2samp: Exact calculation unsuccessful."
+            warnings.filterwarnings("ignore", message, RuntimeWarning)
+            self._testOne(x, y, 'greater', 6600.0 / n1 / n2, 0.9573185808092622,
+                          mode='exact', xp=xp)
+            self._testOne(x, y, 'less', 1000.0 / n1 / n2, 0.9982410869433984,
+                          mode='exact', xp=xp)
+        with warnings.catch_warnings(record=True) as w:
+            warnings.simplefilter("always")
+            self._testOne(x, y, 'less', 1000.0 / n1 / n2, 0.9982410869433984,
+                          mode='exact', xp=xp)
+            self._check_warnings(w, RuntimeWarning, 1)
+
+    def testLarge(self, xp):
+        # 10000, 110
+        n1, n2 = 10000, 110
+        lcm = n1*11.0
+        delta = 1.0/n1/n2/2/2
+        x = xp.linspace(1., 200., n1) - delta
+        y = xp.linspace(2., 100., n2)
+        self._testOne(x, y, 'two-sided', 55275.0 / lcm, 4.2188474935755949e-15, xp=xp)
+        self._testOne(x, y, 'greater', 561.0 / lcm, 0.99115454582047591, xp=xp)
+        self._testOne(x, y, 'less', 55275.0 / lcm, 3.1317328311518713e-26, xp=xp)
+
+    def test_gh11184(self, xp):
+        # 3000, 3001, exact two-sided
+        rng = np.random.RandomState(123456)
+        x = rng.normal(size=3000).tolist()
+        y = rng.normal(size=3001, scale=1.5).tolist()
+        self._testOne(x, y, 'two-sided', 0.11292880151060758, 2.7755575615628914e-15,
+                      mode='asymp', xp=xp)
+        self._testOne(x, y, 'two-sided', 0.11292880151060758, 2.7755575615628914e-15,
+                      mode='exact', xp=xp)
+
+    @pytest.mark.xslow
+    def test_gh11184_bigger(self, xp):
+        # 10000, 10001, exact two-sided
+        rng = np.random.RandomState(123456)
+        x = rng.normal(size=10000).tolist()
+        y = rng.normal(size=10001, scale=1.5).tolist()
+        self._testOne(x, y, 'two-sided', 0.10597913208679133, 3.3149311398483503e-49,
+                      mode='asymp', xp=xp)
+        self._testOne(x, y, 'two-sided', 0.10597913208679133, 2.7755575615628914e-15,
+                      mode='exact', xp=xp)
+        self._testOne(x, y, 'greater', 0.10597913208679133, 2.7947433906389253e-41,
+                      mode='asymp', xp=xp)
+        self._testOne(x, y, 'less', 0.09658002199780022, 2.7947433906389253e-41,
+                      mode='asymp', xp=xp)
+
+    @pytest.mark.xslow
+    def test_gh12999(self, xp):
+        rng = np.random.RandomState(123456)
+        for x in range(1000, 12000, 1000):
+            vals1 = xp.asarray(rng.normal(size=(x)))
+            vals2 = xp.asarray(rng.normal(size=(x + 10), loc=0.5))
+            exact = stats.ks_2samp(vals1, vals2, mode='exact').pvalue
+            asymp = stats.ks_2samp(vals1, vals2, mode='asymp').pvalue
+            # these two p-values should be in line with each other
+            xp_assert_less(exact, 3 * asymp)
+            xp_assert_less(asymp, 3 * exact)
+
+    @pytest.mark.slow
+    def testLargeBoth(self, xp):
+        # 10000, 11000
+        n1, n2 = 10000, 11000
+        lcm = n1*11.0
+        delta = 1.0/n1/n2/2/2
+        x = xp.linspace(1, 200, n1) - delta
+        y = xp.linspace(2, 200, n2)
+        self._testOne(x, y, 'two-sided', 563.0 / lcm, 0.9990660108966576,
+                      mode='asymp', xp=xp)
+        self._testOne(x, y, 'two-sided', 563.0 / lcm, 0.9990456491488628,
+                      mode='exact', xp=xp)
+        self._testOne(x, y, 'two-sided', 563.0 / lcm, 0.9990660108966576,
+                      mode='auto', xp=xp)
+        self._testOne(x, y, 'greater', 563.0 / lcm, 0.7561851877420673, xp=xp)
+        self._testOne(x, y, 'less', 10.0 / lcm, 0.9998239693191724, xp=xp)
+        with warnings.catch_warnings():
+            message = "ks_2samp: Exact calculation unsuccessful."
+            warnings.filterwarnings("ignore", message, RuntimeWarning)
+            self._testOne(x, y, 'greater', 563.0 / lcm, 0.7561851877420673,
+                          mode='exact', xp=xp)
+            self._testOne(x, y, 'less', 10.0 / lcm, 0.9998239693191724,
+                          mode='exact', xp=xp)
+
+    def testNamedAttributes(self, xp):
+        # test for namedtuple attribute results
+        attributes = ('statistic', 'pvalue')
+        res = stats.ks_2samp(xp.asarray([1, 2]), xp.asarray([3]))
+        check_named_results(res, attributes, xp=xp)
+
+    @pytest.mark.slow
+    @skip_xp_backends(np_only=True)
+    def test_some_code_paths(self):
+        # Check that some code paths are executed
+        from scipy.stats._stats_py import (
+            _count_paths_outside_method,
+            _compute_outer_prob_inside_method
+        )
+
+        _compute_outer_prob_inside_method(1, 1, 1, 1)
+        _count_paths_outside_method(1000, 1, 1, 1001)
+
+        with np.errstate(invalid='raise'):
+            assert_raises(FloatingPointError, _count_paths_outside_method,
+                          1100, 1099, 1, 1)
+            assert_raises(FloatingPointError, _count_paths_outside_method,
+                          2000, 1000, 1, 1)
+
+    @pytest.mark.parametrize('case', (([], [1.]), ([1.], []), ([], [])))
+    def test_argument_checking(self, case, xp):
+        # Check that an empty array warns
+        with eager_warns(SmallSampleWarning, match=too_small_1d_not_omit, xp=xp):
+            res = stats.ks_2samp(xp.asarray(case[0]), xp.asarray(case[1]))
+            xp_assert_equal(res.statistic, xp.asarray(np.nan))
+            xp_assert_equal(res.pvalue, xp.asarray(np.nan))
+
+    @pytest.mark.xslow
+    def test_gh12218(self, xp):
+        """Ensure gh-12218 is fixed."""
+        # gh-1228 triggered a TypeError calculating sqrt(n1*n2*(n1+n2)).
+        # n1, n2 both large integers, the product exceeded 2^64
+        rng = np.random.default_rng(8751495592)
+        n1 = 2097152  # 2*^21
+        rvs1 = xp.asarray(stats.uniform.rvs(size=n1, random_state=rng).tolist())
+        rvs2 = rvs1 + 1  # Exact value of rvs2 doesn't matter.
+        stats.ks_2samp(rvs1, rvs2, alternative='greater', mode='asymp')
+        stats.ks_2samp(rvs1, rvs2, alternative='less', mode='asymp')
+        stats.ks_2samp(rvs1, rvs2, alternative='two-sided', mode='asymp')
+
+    @pytest.mark.parametrize("dtype", [None, 'float32', 'float64'])
+    def test_warnings_gh_14019(self, dtype, xp):
+        dtype = xp_default_dtype(xp) if dtype is None else getattr(xp, dtype)
+        # Check that RuntimeWarning is raised when method='auto' and exact
+        # p-value calculation fails. See gh-14019.
+        rng = np.random.RandomState(seed=23493549)
+        # random samples of the same size as in the issue
+        data1 = xp.asarray(rng.random(size=881) + 0.5, dtype=dtype)
+        data2 = xp.asarray(rng.random(size=369), dtype=dtype)
+        message = "ks_2samp: Exact calculation unsuccessful"
+        with eager_warns(RuntimeWarning, match=message, xp=xp):
+            res = stats.ks_2samp(data1, data2, alternative='less')
+            xp_assert_close(res.pvalue, xp.asarray(0., dtype=dtype), atol=1e-14)
+
+    @pytest.mark.parametrize("ksfunc", [stats.kstest, stats.ks_2samp])
+    @pytest.mark.parametrize("alternative, x6val, ref_location, ref_sign",
+                             [('greater', 5.9, 5.9, +1),
+                              ('less', 6.1, 6.0, -1),
+                              ('two-sided', 5.9, 5.9, +1),
+                              ('two-sided', 6.1, 6.0, -1)])
+    def test_location_sign(self, ksfunc, alternative,
+                           x6val, ref_location, ref_sign, xp):
+        # Test that location and sign corresponding with statistic are as
+        # expected. (Test is designed to be easy to predict.)
+        x = xp.arange(10., dtype=xp.float64)
+        y = xp_copy(x)
+        x = xpx.at(x)[6].set(x6val)
+        res = stats.ks_2samp(x, y, alternative=alternative)
+        xp_assert_close(res.statistic, xp.asarray(0.1, dtype=xp.float64), rtol=1e-15)
+        assert res.statistic_location == ref_location
+        assert res.statistic_sign == ref_sign
+
+
+@pytest.mark.filterwarnings('ignore:divide by zero:RuntimeWarning:dask')
+@pytest.mark.filterwarnings('ignore:invalid value:RuntimeWarning:dask')
+@make_xp_test_case(stats.ttest_rel)
+class TestTTestRel:
+    def test_ttest_rel_xp(self, xp):
+        # stats.ttest_rel had no tests using the xp fixture. As a temporary
+        # measure to get tools/check_xp_untested.py to pass, a portion of
+        # test_ttest_rel has been converted. It might seem unnecessary to
+        # require tests for a trivial wrapper of a well-tested function, but
+        # this seems simpler than having a way to carve out exceptions to
+        # check_xp_untested.
+        tr = xp.asarray(0.81248591389165692, dtype=xp.float64)
+        pr = xp.asarray(0.41846234511362157, dtype=xp.float64)
+
+        rvs1 = xp.linspace(1, 100, 100, dtype=xp.float64)
+        rvs2 = xp.linspace(1.01, 99.989, 100, dtype=xp.float64)
+        rvs1_2D = xp.stack(
+            [
+                xp.linspace(1,100, 100, dtype=xp.float64),
+                xp.linspace(1.01, 99.989, 100, dtype=xp.float64)
+            ]
+        )
+        rvs2_2D = xp.stack(
+            [
+                xp.linspace(1.01, 99.989, 100, dtype=xp.float64),
+                xp.linspace(1, 100, 100, dtype=xp.float64)
+            ]
+        )
+
+        t, p = stats.ttest_rel(rvs1, rvs2, axis=0)
+        xp_assert_close(t, tr)
+        xp_assert_close(p, pr)
+
+        t, p = stats.ttest_rel(rvs1_2D.T, rvs2_2D.T, axis=0)
+        xp_assert_close(t, xp.stack([tr, -tr]))
+        xp_assert_close(p, xp.stack([pr, pr]))
+
+        t, p = stats.ttest_rel(rvs1_2D, rvs2_2D, axis=1)
+        xp_assert_close(t, xp.stack([tr, -tr]))
+        xp_assert_close(p, xp.stack([pr, pr]))
+
+    def test_ttest_rel(self, xp):
+        dtype = xp.float64  # doesn't pass with default tolerances otherwise
+
+        # regression test
+        tr = xp.asarray(0.81248591389165692, dtype=dtype)
+        pr = xp.asarray(0.41846234511362157, dtype=dtype)
+        tpr = xp.stack([tr, -tr]), xp.stack([pr, pr])
+
+        rvs1 = xp.linspace(1, 100, 100, dtype=dtype)
+        rvs2 = xp.linspace(1.01, 99.989, 100, dtype=dtype)
+        rvs1_2D = xp.stack([xp.linspace(1, 100, 100, dtype=dtype),
+                            xp.linspace(1.01, 99.989, 100, dtype=dtype)])
+        rvs2_2D = xp.stack([xp.linspace(1.01, 99.989, 100, dtype=dtype),
+                            xp.linspace(1, 100, 100, dtype=dtype)])
+
+        t, p = stats.ttest_rel(rvs1, rvs2, axis=0)
+        xp_assert_close(t, tr)
+        xp_assert_close(p, pr)
+        t,p = stats.ttest_rel(rvs1_2D.T, rvs2_2D.T, axis=0)
+        xp_assert_close(t, tpr[0])
+        xp_assert_close(p, tpr[1])
+        t,p = stats.ttest_rel(rvs1_2D, rvs2_2D, axis=1)
+        xp_assert_close(t, tpr[0])
+        xp_assert_close(p, tpr[1])
+
+        # test scalars
+        with warnings.catch_warnings(), \
+                np.errstate(invalid="ignore", divide="ignore"):
+            warnings.filterwarnings(
+                "ignore", "Degrees of freedom <= 0 for slice", RuntimeWarning)
+            t, p = stats.ttest_rel(xp.asarray(4.), xp.asarray(3.))
+        assert xp.isnan(t)
+        assert xp.isnan(p)
+
+        # test for namedtuple attribute results
+        attributes = ('statistic', 'pvalue')
+        res = stats.ttest_rel(rvs1, rvs2, axis=0)
+        check_named_results(res, attributes, xp=xp)
+
+        # test on 3 dimensions
+        rvs1_3D = xp.stack([rvs1_2D, rvs1_2D, rvs1_2D])
+        rvs2_3D = xp.stack([rvs2_2D, rvs2_2D, rvs2_2D])
+        t, p = stats.ttest_rel(rvs1_3D, rvs2_3D, axis=-1)
+        xp_assert_close(t, xp.stack((tpr[0],)*3))
+        xp_assert_close(p, xp.stack((tpr[1],)*3))
+
+        t, p = stats.ttest_rel(xp.moveaxis(rvs1_3D, 2, 1),
+                               xp.moveaxis(rvs2_3D, 2, 1),
+                               axis=1)
+        xp_assert_close(t, xp.stack((tpr[0],)*3))
+        xp_assert_close(p, xp.stack((tpr[1],)*3))
+
+        # test alternative parameter
+        message = "`alternative` must be 'less', 'greater', or 'two-sided'."
+        with pytest.raises(ValueError, match=message):
+            stats.ttest_rel(rvs1, rvs2, alternative="error")
+
+        t, p = stats.ttest_rel(rvs1, rvs2, axis=0, alternative="less")
+        xp_assert_close(p, xp.asarray(1 - pr/2))
+        xp_assert_close(t, xp.asarray(tr))
+
+        t, p = stats.ttest_rel(rvs1, rvs2, axis=0, alternative="greater")
+        xp_assert_close(p, xp.asarray(pr/2))
+        xp_assert_close(t, xp.asarray(tr))
+
+    def test_nan_policy_propagate(self, xp):
+        # check nan policy
+        rng = np.random.RandomState(12345678)
+        x = stats.norm.rvs(loc=5, scale=10, size=501, random_state=rng)
+        x[500] = np.nan
+        y = (stats.norm.rvs(loc=5, scale=10, size=501, random_state=rng) +
+             stats.norm.rvs(scale=0.2, size=501, random_state=rng))
+        y[500] = np.nan
+        x, y = xp.asarray(x.tolist()), xp.asarray(y.tolist())
+
+        res = stats.ttest_rel(x, x)
+        xp_assert_equal(res.statistic, xp.asarray(xp.nan))
+        xp_assert_equal(res.pvalue, xp.asarray(xp.nan))
+
+    @skip_xp_backends(eager_only=True, reason='lazy->limited nan_policy support')
+    def test_nan_policy(self, xp):
+        # check nan policy
+        rng = np.random.RandomState(12345678)
+        x = stats.norm.rvs(loc=5, scale=10, size=501, random_state=rng)
+        x[500] = np.nan
+        y = (stats.norm.rvs(loc=5, scale=10, size=501, random_state=rng) +
+             stats.norm.rvs(scale=0.2, size=501, random_state=rng))
+        y[500] = np.nan
+        x, y = xp.asarray(x.tolist()), xp.asarray(y.tolist())
+
+        res = stats.ttest_rel(x, y, nan_policy='omit')
+        xp_assert_close(res.statistic, xp.asarray(0.25299925303978066))
+        xp_assert_close(res.pvalue, xp.asarray(0.8003729814201519))
+
+        message = "The input contains nan values"
+        with pytest.raises(ValueError, match=message):
+            stats.ttest_rel(x, y, nan_policy='raise')
+
+        message = "nan_policy must be one of"
+        with pytest.raises(ValueError, match=message):
+            stats.ttest_rel(x, y, nan_policy='foobar')
+
+    def test_edge_cases(self, xp):
+        # test zero division problem
+        with eager_warns(RuntimeWarning, match="Precision loss occurred", xp=xp):
+            t, p = stats.ttest_rel(xp.asarray([0, 0, 0]), xp.asarray([1, 1, 1]))
+
+        xp_assert_equal(xp.abs(t), xp.asarray(xp.inf))
+        xp_assert_equal(p, xp.asarray(0.0))
+
+        with np.errstate(invalid="ignore"):
+            res = stats.ttest_rel(xp.asarray([0, 0, 0]), xp.asarray([0, 0, 0]))
+        xp_assert_equal(res.statistic, xp.asarray(xp.nan))
+        xp_assert_equal(res.pvalue, xp.asarray(xp.nan))
+
+        anan = xp.asarray([[1., np.nan], [-1., 1.]])
+        res = stats.ttest_rel(anan, xp.zeros((2, 2)))
+        xp_assert_equal(res.statistic, xp.asarray([0, np.nan]))
+        xp_assert_equal(res.pvalue, xp.asarray([1, np.nan]))
+
+        # test incorrect input shape raise an error
+        x = xp.arange(24)
+        message = ("Array shapes are incompatible for broadcasting.|"
+                   "operands could not be broadcast together")
+        with pytest.raises(ValueError, match=message):
+            stats.ttest_rel(xp.reshape(x, (8, 3)), xp.reshape(x, (2, 3, 4)))
+
+    @skip_xp_backends(np_only=True, reason="multidimensional 'omit' is np-only")
+    def test_multidimensional_nan_policy_omit(self, xp):
+        rvs1_2D = np.stack([np.linspace(1, 100, 100),
+                            np.linspace(1.01, 99.989, 100)])
+        rvs2_2D = np.stack([np.linspace(1.01, 99.989, 100),
+                            np.linspace(1, 100, 100)])
+        rvs1_2D[:, 20:30] = np.nan
+        rvs2_2D[:, 15:25] = np.nan
+
+        # Convert from two-sided p-values to one sided using T result data.
+        @np.vectorize
+        def converter(t, p, alt):
+            if (t < 0 and alt == "less") or (t > 0 and alt == "greater"):
+                return p / 2
+            return 1 - (p / 2)
+
+        with pytest.warns(SmallSampleWarning, match=too_small_nd_omit):
+            tr, pr = stats.ttest_rel(rvs1_2D, rvs2_2D, 0, nan_policy='omit')
+
+        with pytest.warns(SmallSampleWarning, match=too_small_nd_omit):
+            t, p = stats.ttest_rel(rvs1_2D, rvs2_2D, 0,
+                                   nan_policy='omit', alternative='less')
+        assert_allclose(t, tr, rtol=1e-14)
+        with np.errstate(invalid='ignore'):
+            assert_allclose(p, converter(tr, pr, 'less'), rtol=1e-14)
+
+        with pytest.warns(SmallSampleWarning, match=too_small_nd_omit):
+            t, p = stats.ttest_rel(rvs1_2D, rvs2_2D, 0,
+                                   nan_policy='omit', alternative='greater')
+        assert_allclose(t, tr, rtol=1e-14)
+        with np.errstate(invalid='ignore'):
+            assert_allclose(p, converter(tr, pr, 'greater'), rtol=1e-14)
+
+    @skip_xp_backends(eager_only=True, reason="lazy -> limited nan_policy support")
+    def test_ttest_rel_nan_2nd_arg(self, xp):
+        # regression test for gh-6134: nans in the second arg were not handled
+        x = xp.asarray([xp.nan, 2.0, 3.0, 4.0])
+        y = xp.asarray([1.0, 2.0, 1.0, 2.0])
+
+        r1 = stats.ttest_rel(x, y, nan_policy='omit')
+        r2 = stats.ttest_rel(y, x, nan_policy='omit')
+        xp_assert_close(r2.statistic, -r1.statistic)
+        xp_assert_close(r2.pvalue, r1.pvalue)
+
+        # NB: arguments are paired when NaNs are dropped
+        r3 = stats.ttest_rel(y[1:], x[1:])
+        xp_assert_close(r2.statistic, r3.statistic)
+        xp_assert_close(r2.pvalue, r3.pvalue)
+
+        # .. and this is consistent with R. R code:
+        # x = c(NA, 2.0, 3.0, 4.0)
+        # y = c(1.0, 2.0, 1.0, 2.0)
+        # t.test(x, y, paired=TRUE)),
+        xp_assert_close(r2.statistic, xp.asarray(-2.), atol=1e-4)
+        xp_assert_close(r2.pvalue, xp.asarray(0.1835), atol=1e-4)
+
+    def test_ttest_rel_empty_1d_returns_nan(self, xp):
+        # Two empty inputs should return a TtestResult containing nan
+        # for both values.
+        with eager_warns(SmallSampleWarning, match=too_small_1d_not_omit, xp=xp):
+            result = stats.ttest_rel(xp.asarray([]), xp.asarray([]))
+        assert isinstance(result, stats._stats_py.TtestResult)
+        xp_assert_equal(result.statistic, xp.asarray(xp.nan))
+        xp_assert_equal(result.pvalue, xp.asarray(xp.nan))
+
+    @skip_xp_backends("dask.array", reason="dask fails this one")
+    @pytest.mark.parametrize('b, expected_shape',
+                             [(np.empty((1, 5, 0)), (3, 5)),
+                              (np.empty((1, 0, 0)), (3, 0))])
+    def test_ttest_rel_axis_size_zero(self, b, expected_shape, xp):
+        # In this test, the length of the axis dimension is zero.
+        # The results should be arrays containing nan with shape
+        # given by the broadcast nonaxis dimensions.
+        a = xp.empty((3, 1, 0))
+        b = xp.asarray(b, dtype=a.dtype)
+        with warnings.catch_warnings():
+            # first case should warn, second shouldn't?
+            warnings.filterwarnings("ignore", too_small_nd_not_omit, SmallSampleWarning)
+            result = stats.ttest_rel(a, b, axis=-1)
+        assert isinstance(result, stats._stats_py.TtestResult)
+        expected_value = xp.full(expected_shape, fill_value=xp.nan)
+        xp_assert_equal(result.statistic, expected_value)
+        xp_assert_equal(result.pvalue, expected_value)
+
+    def test_ttest_rel_nonaxis_size_zero(self, xp):
+        # In this test, the length of the axis dimension is nonzero,
+        # but one of the nonaxis dimensions has length 0.  Check that
+        # we still get the correctly broadcast shape, which is (5, 0)
+        # in this case.
+        a = xp.empty((1, 8, 0))
+        b = xp.empty((5, 8, 1))
+        result = stats.ttest_rel(a, b, axis=1)
+        assert isinstance(result, stats._stats_py.TtestResult)
+        assert result.statistic.shape == (5, 0)
+        assert result.pvalue.shape == (5, 0)
+
+    @skip_xp_backends("jax.numpy", reason="needs stdtrit; lazy->can't use root finder")
+    @pytest.mark.parametrize("alternative", ['two-sided', 'less', 'greater'])
+    def test_ttest_rel_ci_1d(self, alternative, xp):
+        # test confidence interval method against reference values
+        rng = np.random.default_rng(3749065329432213059)
+        n = 10
+        x = xp.asarray(rng.normal(size=n, loc=1.5, scale=2).tolist())
+        y = xp.asarray(rng.normal(size=n, loc=2, scale=2).tolist())
+        # Reference values generated with R t.test:
+        # options(digits=16)
+        # x = c(1.22825792,  1.63950485,  4.39025641,  0.68609437,  2.03813481,
+        #       -1.20040109,  1.81997937,  1.86854636,  2.94694282,  3.94291373)
+        # y = c(3.49961496, 1.53192536, 5.53620083, 2.91687718, 0.04858043,
+        #       3.78505943, 3.3077496 , 2.30468892, 3.42168074, 0.56797592)
+        # t.test(x, y, paired=TRUE, conf.level=0.85, alternative='l')
+
+        ref = {'two-sided': [-1.912194489914035, 0.400169725914035],
+               'greater': [-1.563944820311475, np.inf],
+               'less': [-np.inf, 0.05192005631147523]}
+        res = stats.ttest_rel(x, y, alternative=alternative)
+        ci = res.confidence_interval(confidence_level=0.85)
+        xp_assert_close(ci.low, xp.asarray(ref[alternative][0]))
+        xp_assert_close(ci.high, xp.asarray(ref[alternative][1]))
+        xp_assert_close(res.df, xp.asarray(n-1))
+
+
+@pytest.mark.parametrize("test_fun, args", [
+    make_xp_pytest_param(stats.ttest_1samp, (np.arange(10), 0)),
+    make_xp_pytest_param(stats.ttest_rel, (np.arange(10), np.arange(10)))])
+def test_ttest_ci_iv(test_fun, args, xp):
+    # test `confidence_interval` method input validation
+    res = test_fun(*(xp.asarray(arg) for arg in args))
+    message = '`confidence_level` must be a number between 0 and 1.'
+    with pytest.raises(ValueError, match=message):
+        res.confidence_interval(confidence_level=10)
+
+
+def _desc_stats(x1, x2, axis=0, *, xp=None):
+    xp = array_namespace(x1, x2) if xp is None else xp
+
+    def _stats(x, axis=0):
+        x = xp.asarray(x)
+        mu = xp.mean(x, axis=axis)
+        std = xp.std(x, axis=axis, correction=1)
+        nobs = x.shape[axis]
+        return mu, std, nobs
+
+    return _stats(x1, axis) + _stats(x2, axis)
+
+
+@make_xp_test_case(stats.ttest_ind, stats.ttest_ind_from_stats)
+class TestTTestInd:
+    def test_ttest_ind(self, xp):
+        # regression test
+        tr = xp.asarray(1.0912746897927283)
+        pr = xp.asarray(0.27647818616351882)
+        tr_2D = xp.stack([tr, -tr])
+        pr_2D = xp.stack([pr, pr])
+
+        rvs1 = xp.linspace(5, 105, 100)
+        rvs2 = xp.linspace(1, 100, 100)
+        rvs1_2D = xp.stack([rvs1, rvs2])
+        rvs2_2D = xp.stack([rvs2, rvs1])
+
+        res = stats.ttest_ind(rvs1, rvs2, axis=0)
+        t, p = res  # check that result object can be unpacked
+        xp_assert_close(t, tr)
+        xp_assert_close(p, pr)
+
+        res = stats.ttest_ind_from_stats(*_desc_stats(rvs1, rvs2))
+        t, p = res  # check that result object can be unpacked
+        xp_assert_close(t, tr)
+        xp_assert_close(p, pr)
+
+        res = stats.ttest_ind(rvs1_2D.T, rvs2_2D.T, axis=0)
+        xp_assert_close(res.statistic, tr_2D)
+        xp_assert_close(res.pvalue, pr_2D)
+
+        res = stats.ttest_ind_from_stats(*_desc_stats(rvs1_2D.T, rvs2_2D.T))
+        xp_assert_close(res.statistic, tr_2D)
+        xp_assert_close(res.pvalue, pr_2D)
+
+        res = stats.ttest_ind(rvs1_2D, rvs2_2D, axis=1)
+        xp_assert_close(res.statistic, tr_2D)
+        xp_assert_close(res.pvalue, pr_2D)
+
+        res = stats.ttest_ind_from_stats(*_desc_stats(rvs1_2D, rvs2_2D, axis=1))
+        xp_assert_close(res.statistic, tr_2D)
+        xp_assert_close(res.pvalue, pr_2D)
+
+        # test on 3 dimensions removed because generic tests in
+        # test_axis_nan_policy are much stronger
+
+        # test alternative parameter
+        message = "`alternative` must be 'less', 'greater', or 'two-sided'."
+        with pytest.raises(ValueError, match=message):
+            stats.ttest_ind(rvs1, rvs2, alternative = "error")
+
+        args = _desc_stats(rvs1_2D.T, rvs2_2D.T)
+        with pytest.raises(ValueError, match=message):
+            stats.ttest_ind_from_stats(*args, alternative = "error")
+
+        t, p = stats.ttest_ind(rvs1, rvs2, alternative="less")
+        xp_assert_close(p, 1 - (pr/2))
+        xp_assert_close(t, tr)
+
+        t, p = stats.ttest_ind(rvs1, rvs2, alternative="greater")
+        xp_assert_close(p, pr/2)
+        xp_assert_close(t, tr)
+
+        # Check that ttest_ind_from_stats agrees with ttest_ind
+        res1 = stats.ttest_ind(rvs1_2D.T, rvs2_2D.T, axis=0, alternative="less")
+        args = _desc_stats(rvs1_2D.T, rvs2_2D.T)
+        res2 = stats.ttest_ind_from_stats(*args, alternative="less")
+        xp_assert_close(res1.statistic, res2.statistic)
+        xp_assert_close(res1.pvalue, res2.pvalue)
+
+        res1 = stats.ttest_ind(rvs1_2D.T, rvs2_2D.T, axis=0, alternative="less")
+        args = _desc_stats(rvs1_2D.T, rvs2_2D.T)
+        res2 = stats.ttest_ind_from_stats(*args, alternative="less")
+        xp_assert_close(res1.statistic, res2.statistic)
+        xp_assert_close(res1.pvalue, res2.pvalue)
+
+        # test NaNs
+        NaN = xp.asarray(xp.nan)
+        rvs1 = xp.where(xp.arange(rvs1.shape[0]) == 0, NaN, rvs1)
+
+        res = stats.ttest_ind(rvs1, rvs2, axis=0)
+        xp_assert_equal(res.statistic, NaN)
+        xp_assert_equal(res.pvalue, NaN)
+
+        res = stats.ttest_ind_from_stats(*_desc_stats(rvs1, rvs2))
+        xp_assert_equal(res.statistic, NaN)
+        xp_assert_equal(res.pvalue, NaN)
+
+    @skip_xp_backends(eager_only=True, reason='lazy -> limited nan_policy support')
+    def test_special_cases(self, xp):
+        # check nan policy
+        rng = np.random.default_rng(22199381)
+        x = stats.norm.rvs(loc=5, scale=10, size=501, random_state=rng)
+        y = stats.norm.rvs(loc=5, scale=10, size=500, random_state=rng)
+        x[500] = np.nan
+        x, y = xp.asarray(x.tolist()), xp.asarray(y.tolist())
+
+        res = stats.ttest_ind(x, y)
+        xp_assert_equal(res.statistic, xp.asarray(xp.nan))
+        xp_assert_equal(res.pvalue, xp.asarray(xp.nan))
+
+        # test zero division problem
+        with eager_warns(RuntimeWarning, match="Precision loss occurred", xp=xp):
+            t, p = stats.ttest_ind(xp.asarray([0, 0, 0]), xp.asarray([1, 1, 1]))
+        xp_assert_equal(t, xp.asarray(-xp.inf))
+        xp_assert_equal(p, xp.asarray(0.))
+
+        x = xp.asarray([0, 0, 0])
+        res = stats.ttest_ind(x, x)
+        xp_assert_equal(res.statistic, xp.asarray(xp.nan))
+        xp_assert_equal(res.pvalue, xp.asarray(xp.nan))
+
+        # check that nan in input array result in nan output
+        anan = xp.asarray([[1, np.nan], [-1, 1]])
+        res = stats.ttest_ind(anan, xp.zeros((2, 2)))
+        xp_assert_equal(res.statistic, xp.asarray([0, xp.nan]))
+        xp_assert_equal(res.pvalue, xp.asarray([1, xp.nan]))
+
+    @skip_xp_backends(eager_only=True, reason='lazy -> limited nan_policy support')
+    def test_ttest_ind_nan_policy(self, xp):
+        rng = np.random.default_rng(61481957)
+        x = stats.norm.rvs(loc=5, scale=10, size=501, random_state=rng)
+        y = stats.norm.rvs(loc=5, scale=10, size=500, random_state=rng)
+        x[500] = np.nan
+        x, y = xp.asarray(x.tolist()), xp.asarray(y.tolist())
+
+        res = stats.ttest_ind(x, y, nan_policy='omit')
+        ref = stats.ttest_ind(x[~xp.isnan(x)], y, nan_policy='omit')
+        xp_assert_close(res.statistic, ref.statistic)
+        xp_assert_close(res.pvalue, ref.pvalue)
+
+        message = "The input contains nan values"
+        with pytest.raises(ValueError, match=message):
+            stats.ttest_ind(x, y, nan_policy='raise')
+
+        message = "nan_policy must be one of"
+        with pytest.raises(ValueError, match=message):
+            stats.ttest_ind(x, y, nan_policy='foobar')
+
+    def test_3D_nan_policy_omit(self):  # ND nan_policy='omit' is NumPy only
+        rvs1 = np.linspace(5, 105, 100)
+        rvs2 = np.linspace(1, 100, 100)
+        rvs1_2D = np.array([rvs1, rvs2])
+        rvs2_2D = np.array([rvs2, rvs1])
+        rvs1_3D = np.dstack([rvs1_2D, rvs1_2D, rvs1_2D])
+        rvs2_3D = np.dstack([rvs2_2D, rvs2_2D, rvs2_2D])
+
+        rvs1_3D[:, :, 10:15] = np.nan
+        rvs2_3D[:, :, 6:12] = np.nan
+
+        # Convert from two-sided p-values to one sided using T result data.
+        def convert(t, p, alt):
+            if (t < 0 and alt == "less") or (t > 0 and alt == "greater"):
+                return p / 2
+            return 1 - (p / 2)
+        converter = np.vectorize(convert)
+
+        tr, pr = stats.ttest_ind(rvs1_3D, rvs2_3D, axis=0, nan_policy='omit')
+
+        t, p = stats.ttest_ind(rvs1_3D, rvs2_3D, axis=0, nan_policy='omit',
+                               alternative='less')
+        assert_allclose(t, tr, rtol=1e-14)
+        assert_allclose(p, converter(tr, pr, 'less'), rtol=1e-14)
+
+        t, p = stats.ttest_ind(rvs1_3D, rvs2_3D, axis=0, nan_policy='omit',
+                               alternative='greater')
+        assert_allclose(t, tr, rtol=1e-14)
+        assert_allclose(p, converter(tr, pr, 'greater'), rtol=1e-14)
+
+
+    def test_ttest_ind_scalar(self):  # ttest_ind for scalar input is legacy/np-only
+        # test scalars
+        with warnings.catch_warnings(), np.errstate(invalid="ignore"):
+            warnings.filterwarnings(
+                "ignore", "Degrees of freedom <= 0 for slice", RuntimeWarning)
+            t, p = stats.ttest_ind(4., 3.)
+        assert np.isnan(t)
+        assert np.isnan(p)
+
+
+@make_xp_test_case(stats.ttest_ind)
+@skip_xp_backends('dask.array', reason="Dask doesn't support ResamplingMethods")
+@pytest.mark.filterwarnings("ignore:Arguments...:DeprecationWarning")
+class TestTTestIndResampling:
+    N = 20
+
+    # data for most tests
+    rng = np.random.default_rng(169708062)
+    a = np.vstack((np.arange(3*N//4), rng.random(3*N//4)))
+    b = np.vstack((np.arange(N//4) + 100, rng.random(N//4)))
+
+    # data for equal variance tests
+    a2 = np.arange(10)
+    b2 = np.arange(10) + 100
+
+    # data for exact test
+    a3 = [1, 2]
+    b3 = [3, 4]
+
+    # data for bigger test
+    rvs1 = stats.norm.rvs(loc=5, scale=10,  # type: ignore
+                          size=500, random_state=rng).reshape(100, 5).T
+    rvs2 = stats.norm.rvs(loc=8, scale=20, size=100, random_state=rng)  # type: ignore
+
+    p_d = [1/1001, (676+1)/1001]  # desired pvalues
+    p_d_gen = [1/1001, (672 + 1)/1001]  # desired pvalues for Generator seed
+    p_d_big = [(993+1)/1001, (685+1)/1001, (840+1)/1001,
+               (955+1)/1001, (255+1)/1001]
+
+    params = [
+        (a, b, {"axis": 1}, p_d),                     # basic test
+        (a.T, b.T, {'axis': 0}, p_d),                 # along axis 0
+        (a[0, :], b[0, :], {'axis': None}, p_d[0]),   # 1d data
+        (a[0, :].tolist(), b[0, :].tolist(), {'axis': None}, p_d[0]),
+        # different seeds
+        (a, b, {'random_state': 0, "axis": 1}, p_d),
+        (a, b, {'random_state': np.random.RandomState(0), "axis": 1}, p_d),
+        (a2, b2, {'equal_var': True}, 1/1001),  # equal variances
+        (rvs1, rvs2, {'axis': -1, 'random_state': 0}, p_d_big),  # bigger test
+        (a3, b3, {}, 1/3),  # exact test
+        (a, b, {'random_state': np.random.default_rng(0), "axis": 1}, p_d_gen),
+        ]
+
+    @pytest.mark.parametrize("alternative", ['less', 'greater', 'two-sided'])
+    @pytest.mark.parametrize("shape", [(12,), (2, 12)])
+    def test_permutation_method(self, alternative, shape, xp):
+        rng = np.random.default_rng(2348934579834565)
+        x = xp.asarray(rng.random(size=shape).tolist())
+        y = xp.asarray(rng.random(size=13).tolist())
+
+        kwargs = dict(n_resamples=999)
+
+        # Use ttest_ind with `method`
+        rng = np.random.default_rng(348934579834565)
+        method = stats.PermutationMethod(rng=rng, **kwargs)
+        res = stats.ttest_ind(x, y, axis=-1, alternative=alternative, method=method)
+
+        # Use `permutation_test` directly
+        def statistic(x, y, axis): return stats.ttest_ind(x, y, axis=axis).statistic
+        rng = np.random.default_rng(348934579834565)
+        ref = stats.permutation_test((x, y), statistic, axis=-1, rng=rng,
+                                     alternative=alternative, **kwargs)
+
+        xp_assert_close(res.statistic, ref.statistic)
+        xp_assert_close(res.pvalue, ref.pvalue)
+
+        # Sanity check against theoretical t-test
+        ref = stats.ttest_ind(x, y, axis=-1, alternative=alternative)
+        xp_assert_close(res.statistic, ref.statistic)
+        xp_assert_close(res.pvalue, ref.pvalue, rtol=3e-2)
+
+    @pytest.mark.parametrize("alternative", ['less', 'greater', 'two-sided'])
+    @pytest.mark.parametrize("shape", [(12,), (2, 12)])
+    def test_monte_carlo_method(self, alternative, shape, xp):
+        rng = np.random.default_rng(2348934579834565)
+        x = xp.asarray(rng.random(size=shape).tolist())
+        y = xp.asarray(rng.random(size=13).tolist())
+
+        kwargs = dict(n_resamples=999)
+
+        # Use `monte_carlo` directly
+        def statistic(x, y, axis):
+            x, y = xp.asarray(x), xp.asarray(y)
+            return stats.ttest_ind(x, y, axis=axis).statistic
+
+        rng = np.random.default_rng(348934579834565)
+        rvs = [rng.standard_normal, rng.standard_normal]
+        ref = stats.monte_carlo_test((x, y), rvs=rvs, statistic=statistic, axis=-1,
+                                     alternative=alternative, **kwargs)
+
+        # Use ttest_ind with `method`
+        rng = np.random.default_rng(348934579834565)
+        rvs = [rng.standard_normal, rng.standard_normal]
+        method = stats.MonteCarloMethod(rvs=rvs, **kwargs)
+        res = stats.ttest_ind(x, y, axis=-1, alternative=alternative, method=method)
+        xp_assert_close(res.statistic, ref.statistic)
+        xp_assert_close(res.pvalue, ref.pvalue)
+
+        # Passing `rng` instead of `rvs`
+        method = stats.MonteCarloMethod(rng=348934579834565, **kwargs)
+        res = stats.ttest_ind(x, y, axis=-1, alternative=alternative, method=method)
+        xp_assert_close(res.statistic, ref.statistic)
+        xp_assert_close(res.pvalue, ref.pvalue)
+
+        # Sanity check against theoretical t-test
+        ref = stats.ttest_ind(x, y, axis=-1, alternative=alternative)
+        xp_assert_close(res.statistic, ref.statistic)
+        xp_assert_close(res.pvalue, ref.pvalue, rtol=6e-2)
+
+    def test_resampling_input_validation(self, xp):
+        message = "`method` must be an instance of `PermutationMethod`, an instance..."
+        with pytest.raises(ValueError, match=message):
+            x, y = xp.asarray([1, 2, 3]), xp.asarray([4, 5, 6])
+            stats.ttest_ind(x, y, method='migratory')
+
+
+@make_xp_test_case(stats.ttest_ind)
+class TestTTestIndCommon:
+    # for tests that are performed on variations of the t-test (e.g. trimmed)
+    @pytest.mark.parametrize("kwds", [{'trim': .2}, {}],
+                             ids=["trim", "basic"])
+    @pytest.mark.parametrize('equal_var', [True, False],
+                             ids=['equal_var', 'unequal_var'])
+    def test_ttest_many_dims_fast(self, kwds, equal_var, xp):
+        # Test that ttest_ind works on many-dimensional arrays
+        rng = np.random.default_rng(3815288136)
+        a = xp.asarray(rng.random((5, 4, 4, 7, 1, 6)).tolist())
+        b = xp.asarray(rng.random((4, 1, 8, 2, 6)).tolist())
+        res = stats.ttest_ind(a, b, axis=-3, **kwds)
+
+        # compare fully-vectorized t-test against t-test on smaller slice
+        i, j, k = 2, 3, 1
+        a2 = a[i, :, j, :, 0, :]
+        b2 = b[:, 0, :, k, :]
+        res2 = stats.ttest_ind(a2, b2, axis=-2, **kwds)
+        xp_assert_close(res.statistic[i, :, j, k, :], res2.statistic)
+        xp_assert_close(res.pvalue[i, :, j, k, :], res2.pvalue)
+
+    @pytest.mark.xslow
+    @pytest.mark.parametrize("kwds", [{'trim': .2}, {}],
+                             ids=["trim", "basic"])
+    @pytest.mark.parametrize('equal_var', [True, False],
+                             ids=['equal_var', 'unequal_var'])
+    @skip_xp_backends('array_api_strict', reason="indexing in test is too fancy")
+    @skip_xp_backends('jax.numpy', reason="indexing in test is too fancy")
+    @skip_xp_backends('dask.array', reason="too slow")
+    def test_ttest_many_dims_full(self, kwds, equal_var, xp):
+        # compare against t-test on one axis-slice at a time
+        rng = np.random.default_rng(3815288136)
+        a = rng.random((5, 4, 4, 7, 1, 6)).tolist()
+        b = rng.random((4, 1, 8, 2, 6)).tolist()
+        res = stats.ttest_ind(xp.asarray(a), xp.asarray(b), axis=-3, **kwds)
+
+        # manually broadcast with tile; move axis to end to simplify
+        x = np.moveaxis(np.tile(a, (1, 1, 1, 1, 2, 1)), -3, -1)
+        y = np.moveaxis(np.tile(b, (5, 1, 4, 1, 1, 1)), -3, -1)
+        x, y = xp.asarray(x.tolist()), xp.asarray(y.tolist())
+
+        shape = x.shape[:-1]
+        statistics = xp.zeros(shape)
+        pvalues = xp.zeros(shape)
+        for indices in product(*(range(i) for i in shape)):
+            xi = x[indices]  # use tuple to index single axis slice
+            yi = y[indices]
+            res3 = stats.ttest_ind(xi, yi, axis=-1, **kwds)
+            statistics[indices] = res3.statistic
+            pvalues[indices] = res3.pvalue
+
+        xp_assert_close(res.statistic, statistics)
+        xp_assert_close(res.pvalue, pvalues)
+
+    @pytest.mark.parametrize("kwds", [{'trim': .2}, {}],
+                             ids=["trim", "basic"])
+    @pytest.mark.parametrize("axis", [-1, 0])
+    def test_nans_on_axis(self, kwds, axis, xp):
+        # confirm that with `nan_policy='propagate'`, NaN results are returned
+        # on the correct location
+        rng = np.random.default_rng(363836384995579937222)
+        a = rng.integers(10, size=(5, 3, 10)).astype('float')
+        b = rng.integers(10, size=(5, 3, 10)).astype('float')
+        # set some indices in `a` and `b` to be `np.nan`.
+        a[0][2][3] = np.nan
+        b[2][0][6] = np.nan
+        a, b = xp.asarray(a.tolist()), xp.asarray(b.tolist())
+
+        # arbitrarily use `np.sum` as a baseline for which indices should be NaNs
+        expected = xp.isnan(xp.sum(a + b, axis=axis))
+
+        # multidimensional inputs to `t.sf(np.abs(t), df)` with NaNs on some
+        # indices throws an warning. See issue gh-13844
+        with warnings.catch_warnings(), np.errstate(invalid="ignore"):
+            warnings.filterwarnings(
+                "ignore", "invalid value encountered in less_equal", RuntimeWarning)
+            warnings.filterwarnings("ignore", "Precision loss occurred", RuntimeWarning)
+            res = stats.ttest_ind(a, b, axis=axis, **kwds)
+
+        p_nans = xp.isnan(res.pvalue)
+        xp_assert_equal(p_nans, expected)
+        statistic_nans = xp.isnan(res.statistic)
+        xp_assert_equal(statistic_nans, expected)
+
+
+@make_xp_test_case(stats.ttest_ind)
+class TestTTestTrimmed:
+    params = [
+        [[1., 2., 3.], [1.1, 2.9, 4.2], 0.53619490753126731, -0.6864951273557258, .2],
+        [[56., 128.6, 12, 123.8, 64.34, 78, 763.3], [1.1, 2.9, 4.2],
+         0.00998909252078421, 4.591598691181999, .2],
+        [[56., 128.6, 12., 123.8, 64.34, 78., 763.3], [1.1, 2.9, 4.2],
+         0.10512380092302633, 2.832256715395378, .32],
+        [[2.7, 2.7, 1.1, 3.0, 1.9, 3.0, 3.8, 3.8, 0.3, 1.9, 1.9],
+         [6.5, 5.4, 8.1, 3.5, 0.5, 3.8, 6.8, 4.9, 9.5, 6.2, 4.1],
+         0.002878909511344, -4.2461168970325, .2],
+        [[-0.84504783, 0.13366078, 3.53601757, -0.62908581, 0.54119466,
+          -1.16511574, -0.08836614, 1.18495416, 2.48028757, -1.58925028,
+          -1.6706357, 0.3090472, -2.12258305, 0.3697304, -1.0415207,
+          -0.57783497, -0.90997008, 1.09850192, 0.41270579, -1.4927376],
+         [1.2725522, 1.1657899, 2.7509041, 1.2389013, -0.9490494, -1.0752459,
+          1.1038576, 2.9912821, 3.5349111, 0.4171922, 1.0168959, -0.7625041,
+          -0.4300008, 3.0431921, 1.6035947, 0.5285634, -0.7649405, 1.5575896,
+          1.3670797, 1.1726023], 0.005293305834235, -3.0983317739483, .2]]
+
+    @pytest.mark.parametrize("a, b, pr, tr, trim", params)
+    @pytest.mark.parametrize("dtype", [None, 'float32', 'float64'])
+    def test_ttest_compare_r(self, a, b, pr, tr, trim, dtype, xp):
+        '''
+        Using PairedData's yuen.t.test method. Something to note is that there
+        are at least 3 R packages that come with a trimmed t-test method, and
+        comparisons were made between them. It was found that PairedData's
+        method's results match this method, SAS, and one of the other R
+        methods. A notable discrepancy was the DescTools implementation of the
+        function, which only sometimes agreed with SAS, WRS2, PairedData and
+        this implementation. For this reason, most comparisons in R are made
+        against PairedData's method.
+
+        Rather than providing the input and output for all evaluations, here is
+        a representative example:
+        > library(PairedData)
+        > a <- c(1, 2, 3)
+        > b <- c(1.1, 2.9, 4.2)
+        > options(digits=16)
+        > yuen.t.test(a, b, tr=.2)
+
+            Two-sample Yuen test, trim=0.2
+
+        data:  x and y
+        t = -0.68649512735573, df = 3.4104431643464, p-value = 0.5361949075313
+        alternative hypothesis: true difference in trimmed means is not equal
+        to 0
+        95 percent confidence interval:
+         -3.912777195645217  2.446110528978550
+        sample estimates:
+        trimmed mean of x trimmed mean of y
+        2.000000000000000 2.73333333333333
+        '''
+        dtype = dtype if dtype is None else getattr(xp, dtype)
+        a, b = xp.asarray(a, dtype=dtype), xp.asarray(b, dtype=dtype)
+        statistic, pvalue = stats.ttest_ind(a, b, trim=trim, equal_var=False)
+        xp_assert_close(statistic, xp.asarray(tr, dtype=dtype))
+        xp_assert_close(pvalue, xp.asarray(pr, dtype=dtype))
+
+    def test_compare_SAS(self, xp):
+        # Source of the data used in this test:
+        # https://support.sas.com/resources/papers/proceedings14/1660-2014.pdf
+        a = [12, 14, 18, 25, 32, 44, 12, 14, 18, 25, 32, 44]
+        b = [17, 22, 14, 12, 30, 29, 19, 17, 22, 14, 12, 30, 29, 19]
+        a, b = xp.asarray(a), xp.asarray(b)
+        # In this paper, a trimming percentage of 5% is used. However,
+        # in their implementation, the number of values trimmed is rounded to
+        # the nearest whole number. However, consistent with
+        # `scipy.stats.trimmed_mean`, this test truncates to the lower
+        # whole number. In this example, the paper notes that 1 value is
+        # trimmed off of each side. 9% replicates this amount of trimming.
+        statistic, pvalue = stats.ttest_ind(a, b, trim=.09, equal_var=False)
+        xp_assert_close(pvalue, xp.asarray(0.514522), atol=1e-6)
+        xp_assert_close(statistic, xp.asarray(0.669169), atol=1e-6)
+
+    def test_equal_var(self, xp):
+        '''
+        The PairedData library only supports unequal variances. To compare
+        samples with equal variances, the multicon library is used.
+        > library(multicon)
+        > a <- c(2.7, 2.7, 1.1, 3.0, 1.9, 3.0, 3.8, 3.8, 0.3, 1.9, 1.9)
+        > b <- c(6.5, 5.4, 8.1, 3.5, 0.5, 3.8, 6.8, 4.9, 9.5, 6.2, 4.1)
+        > dv = c(a,b)
+        > iv = c(rep('a', length(a)), rep('b', length(b)))
+        > yuenContrast(dv~ iv, EQVAR = TRUE)
+        $Ms
+           N                 M wgt
+        a 11 2.442857142857143   1
+        b 11 5.385714285714286  -1
+
+        $test
+                              stat df              crit                   p
+        results -4.246116897032513 12 2.178812829667228 0.00113508833897713
+        '''
+        a = [2.7, 2.7, 1.1, 3.0, 1.9, 3.0, 3.8, 3.8, 0.3, 1.9, 1.9]
+        b = [6.5, 5.4, 8.1, 3.5, 0.5, 3.8, 6.8, 4.9, 9.5, 6.2, 4.1]
+        a, b = xp.asarray(a), xp.asarray(b)
+        # `equal_var=True` is default
+        statistic, pvalue = stats.ttest_ind(a, b, trim=.2)
+        xp_assert_close(pvalue, xp.asarray(0.00113508833897713))
+        xp_assert_close(statistic, xp.asarray(-4.246116897032513))
+
+    @pytest.mark.parametrize('alt,pr,tr',
+                             (('greater', 0.9985605452443, -4.2461168970325),
+                              ('less', 0.001439454755672, -4.2461168970325),),
+                             )
+    def test_alternatives(self, alt, pr, tr, xp):
+        '''
+        > library(PairedData)
+        > a <- c(2.7,2.7,1.1,3.0,1.9,3.0,3.8,3.8,0.3,1.9,1.9)
+        > b <- c(6.5,5.4,8.1,3.5,0.5,3.8,6.8,4.9,9.5,6.2,4.1)
+        > options(digits=16)
+        > yuen.t.test(a, b, alternative = 'greater')
+        '''
+        a = [2.7, 2.7, 1.1, 3.0, 1.9, 3.0, 3.8, 3.8, 0.3, 1.9, 1.9]
+        b = [6.5, 5.4, 8.1, 3.5, 0.5, 3.8, 6.8, 4.9, 9.5, 6.2, 4.1]
+        a, b = xp.asarray(a), xp.asarray(b)
+        statistic, pvalue = stats.ttest_ind(a, b, trim=.2, equal_var=False,
+                                            alternative=alt)
+        xp_assert_close(pvalue, xp.asarray(pr))
+        xp_assert_close(statistic, xp.asarray(tr))
+
+    @pytest.mark.parametrize("trim", [-.2, .5, 1])
+    def test_trim_bounds_error(self, trim, xp):
+        match = "Trimming percentage should be 0 <= `trim` < .5."
+        with assert_raises(ValueError, match=match):
+            stats.ttest_ind(xp.asarray([1, 2]), xp.asarray([2, 1]), trim=trim)
+
+
+@make_xp_test_case(stats.ttest_ind)
+class TestTTestCI:
+    # indices in order [alternative={two-sided, less, greater},
+    #                   equal_var={False, True}, trim={0, 0.2}]
+    # reference values in order `statistic, df, pvalue, low, high`
+    # equal_var=False reference values computed with R PairedData yuen.t.test:
+    #
+    # library(PairedData)
+    # options(digits=16)
+    # a < - c(0.88236329, 0.97318744, 0.4549262, 0.97893335, 0.0606677,
+    #         0.44013366, 0.55806018, 0.40151434, 0.14453315, 0.25860601,
+    #         0.20202162)
+    # b < - c(0.93455277, 0.42680603, 0.49751939, 0.14152846, 0.711435,
+    #         0.77669667, 0.20507578, 0.78702772, 0.94691855, 0.32464958,
+    #         0.3873582, 0.35187468, 0.21731811)
+    # yuen.t.test(a, b, tr=0, conf.level = 0.9, alternative = 'l')
+    #
+    # equal_var=True reference values computed with R multicon yuenContrast:
+    #
+    # library(multicon)
+    # options(digits=16)
+    # a < - c(0.88236329, 0.97318744, 0.4549262, 0.97893335, 0.0606677,
+    #         0.44013366, 0.55806018, 0.40151434, 0.14453315, 0.25860601,
+    #         0.20202162)
+    # b < - c(0.93455277, 0.42680603, 0.49751939, 0.14152846, 0.711435,
+    #         0.77669667, 0.20507578, 0.78702772, 0.94691855, 0.32464958,
+    #         0.3873582, 0.35187468, 0.21731811)
+    # dv = c(a, b)
+    # iv = c(rep('a', length(a)), rep('b', length(b)))
+    # yuenContrast(dv~iv, EQVAR = FALSE, alternative = 'unequal', tr = 0.2)
+    r = np.empty(shape=(3, 2, 2, 5))
+    r[0, 0, 0] = [-0.2314607, 19.894435, 0.8193209, -0.247220294, 0.188729943]
+    r[1, 0, 0] = [-0.2314607, 19.894435, 0.40966045, -np.inf, 0.1382426469]
+    r[2, 0, 0] = [-0.2314607, 19.894435, 0.5903395, -0.1967329982, np.inf]
+    r[0, 0, 1] = [-0.2452886, 11.427896, 0.8105823, -0.34057446, 0.25847383]
+    r[1, 0, 1] = [-0.2452886, 11.427896, 0.40529115, -np.inf, 0.1865829074]
+    r[2, 0, 1] = [-0.2452886, 11.427896, 0.5947089, -0.268683541, np.inf]
+    # confidence interval not available for equal_var=True
+    r[0, 1, 0] = [-0.2345625322555006, 22, 0.8167175905643815, np.nan, np.nan]
+    r[1, 1, 0] = [-0.2345625322555006, 22, 0.4083587952821908, np.nan, np.nan]
+    r[2, 1, 0] = [-0.2345625322555006, 22, 0.5916412047178092, np.nan, np.nan]
+    r[0, 1, 1] = [-0.2505369406507428, 14, 0.8058115135702835, np.nan, np.nan]
+    r[1, 1, 1] = [-0.2505369406507428, 14, 0.4029057567851417, np.nan, np.nan]
+    r[2, 1, 1] = [-0.2505369406507428, 14, 0.5970942432148583, np.nan, np.nan]
+    @pytest.mark.parametrize('alternative', ['two-sided', 'less', 'greater'])
+    @pytest.mark.parametrize('equal_var', [False, True])
+    @pytest.mark.parametrize('trim', [0, 0.2])
+    @skip_xp_backends('jax.numpy', reason='Generic stdtrit mutates array.')
+    def test_confidence_interval(self, alternative, equal_var, trim, xp):
+        if equal_var and trim:
+            pytest.xfail('Discrepancy in `main`; needs further investigation.')
+
+        if trim and not is_numpy(xp):
+            pytest.skip('`trim` is only compatible with NumPy input')
+
+        rng = np.random.default_rng(3810954496107292580)
+        x = xp.asarray(rng.random(11))
+        y = xp.asarray(rng.random(13))
+
+        res = stats.ttest_ind(x, y, alternative=alternative,
+                              equal_var=equal_var, trim=trim)
+
+        alternatives = {'two-sided': 0, 'less': 1, 'greater': 2}
+        ref = self.r[alternatives[alternative], int(equal_var), int(np.ceil(trim))]
+        statistic, df, pvalue, low, high = ref
+
+        rtol = 1e-7  # only 7 digits in reference
+        xp_assert_close(res.statistic, xp.asarray(statistic), rtol=rtol)
+        xp_assert_close(res.df, xp.asarray(df), rtol=rtol)
+        xp_assert_close(res.pvalue, xp.asarray(pvalue), rtol=rtol)
+
+        if not equal_var:  # CI not available when `equal_var is True`
+            ci = res.confidence_interval(0.9)
+            xp_assert_close(ci.low, xp.asarray(low), rtol=rtol)
+            xp_assert_close(ci.high, xp.asarray(high), rtol=rtol)
+
+
+@make_xp_test_case(stats.ttest_ind)
+class TestTTestIndMore:
+    @make_xp_test_case(stats.ttest_ind_from_stats)
+    def test_ttest_ind_with_uneq_var(self, xp):
+        # check vs. R `t.test`, e.g.
+        # options(digits=20)
+        # a = c(1., 2., 3.)
+        # b = c(1.1, 2.9, 4.2)
+        # t.test(a, b, equal.var=FALSE)
+
+        a = xp.asarray([1., 2., 3.])
+        b = xp.asarray([1.1, 2.9, 4.2])
+        pr = xp.asarray(0.53619490753126686)
+        tr = xp.asarray(-0.686495127355726265)
+
+        t, p = stats.ttest_ind(a, b, equal_var=False)
+        xp_assert_close(t, tr)
+        xp_assert_close(p, pr)
+
+        t, p = stats.ttest_ind_from_stats(*_desc_stats(a, b), equal_var=False)
+        xp_assert_close(t, tr)
+        xp_assert_close(p, pr)
+
+        a = xp.asarray([1., 2., 3., 4.])
+        pr = xp.asarray(0.84354139131608252)
+        tr = xp.asarray(-0.210866331595072315)
+
+        t, p = stats.ttest_ind(a, b, equal_var=False)
+        xp_assert_close(t, tr)
+        xp_assert_close(p, pr)
+
+        t, p = stats.ttest_ind_from_stats(*_desc_stats(a, b), equal_var=False)
+        xp_assert_close(t, tr)
+        xp_assert_close(p, pr)
+
+        # regression test
+        tr = xp.asarray(1.0912746897927283)
+        tr_uneq_n = xp.asarray(0.66745638708050492)
+        pr = xp.asarray(0.27647831993021388)
+        pr_uneq_n = xp.asarray(0.50873585065616544)
+        tr_2D = xp.stack([tr, -tr])
+        pr_2D = xp.stack([pr, pr])
+
+        rvs3 = xp.linspace(1, 100, 25)
+        rvs2 = xp.linspace(1, 100, 100)
+        rvs1 = xp.linspace(5, 105, 100)
+        rvs1_2D = xp.stack([rvs1, rvs2])
+        rvs2_2D = xp.stack([rvs2, rvs1])
+
+        t, p = stats.ttest_ind(rvs1, rvs2, axis=0, equal_var=False)
+        xp_assert_close(t, tr)
+        xp_assert_close(p, pr)
+
+        t, p = stats.ttest_ind_from_stats(*_desc_stats(rvs1, rvs2), equal_var=False)
+        xp_assert_close(t, tr)
+        xp_assert_close(p, pr)
+
+        t, p = stats.ttest_ind(rvs1, rvs3, axis=0, equal_var=False)
+        xp_assert_close(t, tr_uneq_n)
+        xp_assert_close(p, pr_uneq_n)
+
+        t, p = stats.ttest_ind_from_stats(*_desc_stats(rvs1, rvs3), equal_var=False)
+        xp_assert_close(t, tr_uneq_n)
+        xp_assert_close(p, pr_uneq_n)
+
+        res = stats.ttest_ind(rvs1_2D.T, rvs2_2D.T, axis=0, equal_var=False)
+        xp_assert_close(res.statistic, tr_2D)
+        xp_assert_close(res.pvalue, pr_2D)
+
+        args = _desc_stats(rvs1_2D.T, rvs2_2D.T)
+        res = stats.ttest_ind_from_stats(*args, equal_var=False)
+        xp_assert_close(res.statistic, tr_2D)
+        xp_assert_close(res.pvalue, pr_2D)
+
+        res = stats.ttest_ind(rvs1_2D, rvs2_2D, axis=1, equal_var=False)
+        xp_assert_close(res.statistic, tr_2D)
+        xp_assert_close(res.pvalue, pr_2D)
+
+        args = _desc_stats(rvs1_2D, rvs2_2D, axis=1)
+        res = stats.ttest_ind_from_stats(*args, equal_var=False)
+        xp_assert_close(res.statistic, tr_2D)
+        xp_assert_close(res.pvalue, pr_2D)
+
+    @pytest.mark.filterwarnings(
+        "ignore:divide by zero encountered:RuntimeWarning"
+    ) # for dask
+    @pytest.mark.filterwarnings(
+        "ignore:invalid value encountered:RuntimeWarning"
+    ) # for dask
+    def test_ttest_ind_zero_division(self, xp):
+        # test zero division problem
+        x = xp.zeros(3)
+        y = xp.ones(3)
+
+        with eager_warns(RuntimeWarning, match="Precision loss occurred", xp=xp):
+            t, p = stats.ttest_ind(x, y, equal_var=False)
+
+        xp_assert_equal(t, xp.asarray(-xp.inf))
+        xp_assert_equal(p, xp.asarray(0.))
+
+        with np.errstate(all='ignore'):
+            t, p = stats.ttest_ind(x, x, equal_var=False)
+            xp_assert_equal(t, xp.asarray(xp.nan))
+            xp_assert_equal(p, xp.asarray(xp.nan))
+
+            # check that nan in input array result in nan output
+            anan = xp.asarray([[1, xp.nan], [-1, 1]])
+            t, p = stats.ttest_ind(anan, xp.zeros((2, 2)), equal_var=False)
+            xp_assert_equal(t, xp.asarray([0., np.nan]))
+            xp_assert_equal(p, xp.asarray([1., np.nan]))
+
+    def test_ttest_ind_nan_2nd_arg(self):
+        # regression test for gh-6134: nans in the second arg were not handled
+        x = [np.nan, 2.0, 3.0, 4.0]
+        y = [1.0, 2.0, 1.0, 2.0]
+
+        r1 = stats.ttest_ind(x, y, nan_policy='omit')
+        r2 = stats.ttest_ind(y, x, nan_policy='omit')
+        assert_allclose(r2.statistic, -r1.statistic, atol=1e-15)
+        assert_allclose(r2.pvalue, r1.pvalue, atol=1e-15)
+
+        # NB: arguments are not paired when NaNs are dropped
+        r3 = stats.ttest_ind(y, x[1:])
+        assert_allclose(r2, r3, atol=1e-15)
+
+        # .. and this is consistent with R. R code:
+        # x = c(NA, 2.0, 3.0, 4.0)
+        # y = c(1.0, 2.0, 1.0, 2.0)
+        # t.test(x, y, var.equal=TRUE)
+        assert_allclose(r2, (-2.5354627641855498, 0.052181400457057901),
+                        atol=1e-15)
+
+    def test_ttest_ind_empty_1d_returns_nan(self, xp):
+        # Two empty inputs should return a TtestResult containing nan
+        # for both values.
+        with eager_warns(SmallSampleWarning, match=too_small_1d_not_omit, xp=xp):
+            res = stats.ttest_ind(xp.asarray([]), xp.asarray([]))
+        assert isinstance(res, stats._stats_py.TtestResult)
+        NaN = xp.asarray(xp.nan)[()]
+        xp_assert_equal(res.statistic, NaN)
+        xp_assert_equal(res.pvalue, NaN)
+
+    @pytest.mark.parametrize('b, expected_shape',
+                            [(np.empty((1, 5, 0)), (3, 5)),
+                            (np.empty((1, 0, 0)), (3, 0))])
+    def test_ttest_ind_axis_size_zero(self, b, expected_shape, xp):
+        # In this test, the length of the axis dimension is zero.
+        # The results should be arrays containing nan with shape
+        # given by the broadcast nonaxis dimensions.
+        a = xp.empty((3, 1, 0))
+        b = xp.asarray(b, dtype=a.dtype)
+        with warnings.catch_warnings():
+            # first case should warn, second shouldn't?
+            warnings.filterwarnings("ignore", too_small_nd_not_omit, SmallSampleWarning)
+            res = stats.ttest_ind(a, b, axis=-1)
+        assert isinstance(res, stats._stats_py.TtestResult)
+        expected_value = xp.full(expected_shape, fill_value=xp.nan)
+        xp_assert_equal(res.statistic, expected_value)
+        xp_assert_equal(res.pvalue, expected_value)
+
+    def test_ttest_ind_nonaxis_size_zero(self, xp):
+        # In this test, the length of the axis dimension is nonzero,
+        # but one of the nonaxis dimensions has length 0.  Check that
+        # we still get the correctly broadcast shape, which is (5, 0)
+        # in this case.
+        a = xp.empty((1, 8, 0))
+        b = xp.empty((5, 8, 1))
+        res = stats.ttest_ind(a, b, axis=1)
+        assert isinstance(res, stats._stats_py.TtestResult)
+        assert res.statistic.shape ==(5, 0)
+        assert res.pvalue.shape == (5, 0)
+
+    def test_ttest_ind_nonaxis_size_zero_different_lengths(self, xp):
+        # In this test, the length of the axis dimension is nonzero,
+        # and that size is different in the two inputs,
+        # and one of the nonaxis dimensions has length 0.  Check that
+        # we still get the correctly broadcast shape, which is (5, 0)
+        # in this case.
+        a = xp.empty((1, 7, 0))
+        b = xp.empty((5, 8, 1))
+        res = stats.ttest_ind(a, b, axis=1)
+        assert isinstance(res, stats._stats_py.TtestResult)
+        assert res.statistic.shape ==(5, 0)
+        assert res.pvalue.shape == (5, 0)
+
+    @pytest.mark.skip_xp_backends(cpu_only=True, reason='Test uses ks_1samp')
+    @pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning:dask")
+    @pytest.mark.filterwarnings("ignore:divide by zero encountered:RuntimeWarning:dask")
+    @pytest.mark.uses_xp_capabilities(False, reason="not used in this test yet")
+    def test_ttest_uniform_pvalues(self, xp):
+        # test that p-values are uniformly distributed under the null hypothesis
+        rng = np.random.default_rng(246834602926842)
+        x = xp.asarray(rng.normal(size=(10000, 2)))
+        y = xp.asarray(rng.normal(size=(10000, 1)))
+        q = rng.uniform(size=100)
+
+        res = stats.ttest_ind(x, y, equal_var=True, axis=-1)
+        pvalue = np.asarray(res.pvalue)
+        # TODO: isolate use of alt backend to ttest_ind
+        assert stats.ks_1samp(pvalue, stats.uniform().cdf).pvalue > 0.1
+        assert_allclose(np.quantile(pvalue, q), q, atol=1e-2)
+
+        res = stats.ttest_ind(y, x, equal_var=True, axis=-1)
+        pvalue = np.asarray(res.pvalue)
+        assert stats.ks_1samp(pvalue, stats.uniform().cdf).pvalue > 0.1
+        assert_allclose(np.quantile(pvalue, q), q, atol=1e-2)
+
+        # reference values from R:
+        # options(digits=16)
+        # t.test(c(2, 3, 5), c(1.5), var.equal=TRUE)
+        x, y = xp.asarray([2., 3., 5.]), xp.asarray([1.5])
+
+        res = stats.ttest_ind(x, y, equal_var=True)
+        xp_assert_close(res.statistic, xp.asarray(1.0394023007754))
+        xp_assert_close(res.pvalue, xp.asarray(0.407779907736))
+
+
+@make_xp_test_case(stats.ttest_ind_from_stats)
+class TestTTestIndFromStats:
+    def test_gh5686(self, xp):
+        mean1, mean2 = xp.asarray([1, 2]), xp.asarray([3, 4])
+        std1, std2 = xp.asarray([5, 3]), xp.asarray([4, 5])
+        nobs1, nobs2 = xp.asarray([130, 140]), xp.asarray([100, 150])
+        # This will raise a TypeError unless gh-5686 is fixed.
+        stats.ttest_ind_from_stats(mean1, std1, nobs1, mean2, std2, nobs2)
+
+    @pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning")
+    def test_ttest_ind_from_stats_inputs_zero(self, xp):
+        # Regression test for gh-6409.
+        zero = xp.asarray(0.)
+        six = xp.asarray(6.)
+        NaN = xp.asarray(xp.nan)
+        res = stats.ttest_ind_from_stats(zero, zero, six, zero, zero, six,
+                                         equal_var=False)
+        xp_assert_equal(res.statistic, NaN)
+        xp_assert_equal(res.pvalue, NaN)
+
+
+@make_xp_test_case(stats.ttest_1samp)
+class TestTTest1Samp:
+    def _convert_pvalue_alternative(self, t, p, alt, xp):
+        # test alternative parameter
+        # Convert from two-sided p-values to one sided using T result data.
+        less = xp.asarray(alt == "less")
+        greater = xp.asarray(alt == "greater")
+        i = ((t < 0) & less) | ((t > 0) & greater)
+        return xp.where(i, p/2, 1 - p/2)
+
+    @pytest.mark.slow
+    @pytest.mark.filterwarnings("ignore:divide by zero encountered:RuntimeWarning:dask")
+    @pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning:dask")
+    def test_ttest_1samp_new(self, xp):
+        rng = np.random.default_rng(88123290)
+        n1, n2, n3 = (10, 15, 20)
+        rvn1 = stats.norm.rvs(loc=5, scale=10, size=(n1, n2, n3), random_state=rng)
+        rvn1 = xp.asarray(rvn1)
+
+        # check multidimensional array and correct axis handling
+        # deterministic rvn1 and rvn2 would be better as in test_ttest_rel
+        popmean = xp.ones((1, n2, n3))
+        t1, p1 = stats.ttest_1samp(rvn1, popmean, axis=0)
+        t2, p2 = stats.ttest_1samp(rvn1, 1., axis=0)
+        t3, p3 = stats.ttest_1samp(rvn1[:, 0, 0], 1.)
+        xp_assert_close(t1, t2, rtol=1e-14)
+        xp_assert_close(t1[0, 0], t3, rtol=1e-14)
+        assert_equal(t1.shape, (n2, n3))
+
+        popmean = xp.ones((n1, 1, n3))
+        t1, p1 = stats.ttest_1samp(rvn1, popmean, axis=1)
+        t2, p2 = stats.ttest_1samp(rvn1, 1., axis=1)
+        t3, p3 = stats.ttest_1samp(rvn1[0, :, 0], 1.)
+        xp_assert_close(t1, t2, rtol=1e-14)
+        xp_assert_close(t1[0, 0], t3, rtol=1e-14)
+        assert_equal(t1.shape, (n1, n3))
+
+        popmean = xp.ones((n1, n2, 1))
+        t1, p1 = stats.ttest_1samp(rvn1, popmean, axis=2)
+        t2, p2 = stats.ttest_1samp(rvn1, 1., axis=2)
+        t3, p3 = stats.ttest_1samp(rvn1[0, 0, :], 1.)
+        xp_assert_close(t1, t2, rtol=1e-14)
+        xp_assert_close(t1[0, 0], t3, rtol=1e-14)
+        assert_equal(t1.shape, (n1, n2))
+
+        # test zero division problem
+        t, p = stats.ttest_1samp(xp.asarray([0., 0., 0.]), 1.)
+        xp_assert_equal(xp.abs(t), xp.asarray(xp.inf))
+        xp_assert_equal(p, xp.asarray(0.))
+
+        tr, pr = stats.ttest_1samp(rvn1[:, :, :], 1.)
+
+        t, p = stats.ttest_1samp(rvn1[:, :, :], 1., alternative="greater")
+        pc = self._convert_pvalue_alternative(tr, pr, "greater", xp)
+        xp_assert_close(p, pc)
+        xp_assert_close(t, tr)
+
+        t, p = stats.ttest_1samp(rvn1[:, :, :], 1., alternative="less")
+        pc = self._convert_pvalue_alternative(tr, pr, "less", xp)
+        xp_assert_close(p, pc)
+        xp_assert_close(t, tr)
+
+        with np.errstate(all='ignore'):
+            res = stats.ttest_1samp(xp.asarray([0., 0., 0.]), 0.)
+            xp_assert_equal(res.statistic, xp.asarray(xp.nan))
+            xp_assert_equal(res.pvalue, xp.asarray(xp.nan))
+
+            # check that nan in input array result in nan output
+            anan = xp.asarray([[1., np.nan], [-1., 1.]])
+            res = stats.ttest_1samp(anan, 0.)
+            xp_assert_equal(res.statistic, xp.asarray([0., xp.nan]))
+            xp_assert_equal(res.pvalue, xp.asarray([1., xp.nan]))
+
+    @skip_xp_backends(eager_only=True, reason="lazy -> reduced nan_policy capabilities")
+    def test_ttest_1samp_new_omit(self, xp):
+        rng = np.random.default_rng(4008400329)
+        n1, n2, n3 = (5, 10, 15)
+        rvn1 = stats.norm.rvs(loc=5, scale=10, size=(n1, n2, n3), random_state=rng)
+        rvn1 = xp.asarray(rvn1)
+
+        rvn1[0:2, 1:3, 4:8] = xp.nan
+
+        tr, pr = stats.ttest_1samp(rvn1[:, :, :], 1., nan_policy='omit')
+
+        t, p = stats.ttest_1samp(rvn1[:, :, :], 1., nan_policy='omit',
+                                 alternative="greater")
+        pc = self._convert_pvalue_alternative(tr, pr, "greater", xp)
+        xp_assert_close(p, pc)
+        xp_assert_close(t, tr)
+
+        t, p = stats.ttest_1samp(rvn1[:, :, :], 1., nan_policy='omit',
+                                 alternative="less")
+        pc = self._convert_pvalue_alternative(tr, pr, "less", xp)
+        xp_assert_close(p, pc)
+        xp_assert_close(t, tr)
+
+    @pytest.mark.skip_xp_backends('jax.numpy', reason='Generic stdtrit mutates array.')
+    def test_ttest_1samp_popmean_array(self, xp):
+        # when popmean.shape[axis] != 1, raise an error
+        # if the user wants to test multiple null hypotheses simultaneously,
+        # use standard broadcasting rules
+        rng = np.random.default_rng(2913300596553337193)
+        x = rng.random(size=(1, 15, 20))
+        x = xp.asarray(x)
+
+        message = r"`popmean.shape\[axis\]` must equal 1."
+        popmean = xp.asarray(rng.random(size=(5, 2, 20)))
+        with pytest.raises(ValueError, match=message):
+            stats.ttest_1samp(x, popmean=popmean, axis=-2)
+
+        popmean = xp.asarray(rng.random(size=(5, 1, 20)))
+        res = stats.ttest_1samp(x, popmean=popmean, axis=-2)
+        assert res.statistic.shape == (5, 20)
+
+        l, u = res.confidence_interval()
+        l = xp.expand_dims(l, axis=-2)
+        u = xp.expand_dims(u, axis=-2)
+
+        res = stats.ttest_1samp(x, popmean=l, axis=-2)
+        ref = xp.broadcast_to(xp.asarray(0.05, dtype=xp.float64), res.pvalue.shape)
+        xp_assert_close(res.pvalue, ref)
+
+        res = stats.ttest_1samp(x, popmean=u, axis=-2)
+        xp_assert_close(res.pvalue, ref)
+
+
+@make_xp_test_case(stats.describe)
+class TestDescribe:
+    @pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning:dask")
+    @pytest.mark.filterwarnings("ignore:divide by zero encountered:RuntimeWarning:dask")
+    def test_describe_scalar(self, xp):
+        with warnings.catch_warnings(), \
+              np.errstate(invalid="ignore", divide="ignore"):
+            warnings.filterwarnings(
+                "ignore", "Degrees of freedom <= 0 for slice", RuntimeWarning)
+            n, mm, m, v, sk, kurt = stats.describe(xp.asarray(4.)[()])
+        assert n == 1
+        xp_assert_equal(mm[0], xp.asarray(4.0))
+        xp_assert_equal(mm[1], xp.asarray(4.0))
+        xp_assert_equal(m, xp.asarray(4.0))
+        xp_assert_equal(v ,xp.asarray(xp.nan))
+        xp_assert_equal(sk, xp.asarray(xp.nan))
+        xp_assert_equal(kurt, xp.asarray(xp.nan))
+
+    def test_describe_numbers(self, xp):
+        x = xp.concat((xp.ones((3, 4)), xp.full((2, 4), 2.)))
+        nc = 5
+        mmc = (xp.asarray([1., 1., 1., 1.]), xp.asarray([2., 2., 2., 2.]))
+        mc = xp.asarray([1.4, 1.4, 1.4, 1.4])
+        vc = xp.asarray([0.3, 0.3, 0.3, 0.3])
+        skc = xp.asarray([0.40824829046386357] * 4)
+        kurtc = xp.asarray([-1.833333333333333] * 4)
+        n, mm, m, v, sk, kurt = stats.describe(x)
+        assert n == nc
+        xp_assert_equal(mm[0], mmc[0])
+        xp_assert_equal(mm[1], mmc[1])
+        xp_assert_close(m, mc, rtol=4 * xp.finfo(m.dtype).eps)
+        xp_assert_close(v, vc, rtol=4 * xp.finfo(m.dtype).eps)
+        xp_assert_close(sk, skc)
+        xp_assert_close(kurt, kurtc)
+
+        n, mm, m, v, sk, kurt = stats.describe(x.T, axis=1)
+        assert n == nc
+        xp_assert_equal(mm[0], mmc[0])
+        xp_assert_equal(mm[1], mmc[1])
+        xp_assert_close(m, mc, rtol=4 * xp.finfo(m.dtype).eps)
+        xp_assert_close(v, vc, rtol=4 * xp.finfo(m.dtype).eps)
+        xp_assert_close(sk, skc)
+        xp_assert_close(kurt, kurtc)
+
+    def describe_nan_policy_omit_test(self):
+        x = np.arange(10.)
+        x[9] = np.nan
+
+        nc, mmc = (9, (0.0, 8.0))
+        mc = 4.0
+        vc = 7.5
+        skc = 0.0
+        kurtc = -1.2300000000000002
+        n, mm, m, v, sk, kurt = stats.describe(x, nan_policy='omit')
+        assert_equal(n, nc)
+        assert_equal(mm, mmc)
+        assert_equal(m, mc)
+        assert_equal(v, vc)
+        assert_array_almost_equal(sk, skc)
+        assert_array_almost_equal(kurt, kurtc, decimal=13)
+
+    def test_describe_nan_policy_other(self, xp):
+        x = xp.arange(10.)
+        x = xp.where(x==9, xp.nan, x)
+
+        if is_lazy_array(x):
+            with pytest.raises(TypeError, match='not supported for lazy arrays'):
+                stats.describe(x, nan_policy='raise')
+        else:
+            with pytest.raises(ValueError, match='The input contains nan values'):
+                stats.describe(x, nan_policy='raise')
+
+        n, mm, m, v, sk, kurt = stats.describe(x, nan_policy='propagate')
+        ref = xp.asarray(xp.nan)[()]
+        assert n == 10
+        xp_assert_equal(mm[0], ref)
+        xp_assert_equal(mm[1], ref)
+        xp_assert_equal(m, ref)
+        xp_assert_equal(v, ref)
+        xp_assert_equal(sk, ref)
+        xp_assert_equal(kurt, ref)
+
+        if is_numpy(xp):
+            self.describe_nan_policy_omit_test()
+        elif is_lazy_array(x):
+            with pytest.raises(TypeError, match='not supported for lazy arrays'):
+                stats.describe(x, nan_policy='omit')
+
+        message = 'nan_policy must be one of...'
+        with pytest.raises(ValueError, match=message):
+            stats.describe(x, nan_policy='foobar')
+
+    def test_describe_result_attributes(self):
+        # some result attributes are tuples, which aren't meant to be compared
+        # with `xp_assert_close`
+        actual = stats.describe(np.arange(5.))
+        attributes = ('nobs', 'minmax', 'mean', 'variance', 'skewness', 'kurtosis')
+        check_named_results(actual, attributes)
+
+    def test_describe_ddof(self, xp):
+        x = xp.concat((xp.ones((3, 4)), xp.full((2, 4), 2.)))
+        nc = 5
+        mmc = (xp.asarray([1., 1., 1., 1.]), xp.asarray([2., 2., 2., 2.]))
+        mc = xp.asarray([1.4, 1.4, 1.4, 1.4])
+        vc = xp.asarray([0.24, 0.24, 0.24, 0.24])
+        skc = xp.asarray([0.40824829046386357] * 4)
+        kurtc = xp.asarray([-1.833333333333333] * 4)
+        n, mm, m, v, sk, kurt = stats.describe(x, ddof=0)
+        assert n == nc
+        xp_assert_equal(mm[0], mmc[0])
+        xp_assert_equal(mm[1], mmc[1])
+        xp_assert_close(m, mc)
+        xp_assert_close(v, vc)
+        xp_assert_close(sk, skc)
+        xp_assert_close(kurt, kurtc)
+
+    def test_describe_axis_none(self, xp):
+        x = xp.concat((xp.ones((3, 4)), xp.full((2, 4), 2.)))
+
+        # expected values
+        nc = 20
+        mmc = (xp.asarray(1.0), xp.asarray(2.0))
+        mc = xp.asarray(1.3999999999999999)
+        vc = xp.asarray(0.25263157894736848)
+        skc = xp.asarray(0.4082482904638634)
+        kurtc = xp.asarray(-1.8333333333333333)
+
+        # actual values
+        n, mm, m, v, sk, kurt = stats.describe(x, axis=None)
+
+        assert n == nc
+        xp_assert_equal(mm[0], mmc[0])
+        xp_assert_equal(mm[1], mmc[1])
+        xp_assert_close(m, mc)
+        xp_assert_close(v, vc)
+        xp_assert_close(sk, skc)
+        xp_assert_close(kurt, kurtc)
+
+    def test_describe_empty(self, xp):
+        message = "The input must not be empty."
+        with pytest.raises(ValueError, match=message):
+            stats.describe(xp.asarray([]))
+    
+    @skip_xp_backends("array_api_strict", reason="min/max don't accept boolean input")
+    def test_boolean_input_gh24847(self, xp):
+        # gh-24847 reported that `describe` failed with boolean input
+        rng = np.random.default_rng(3248923598734583)
+        n = 20
+        x = xp.asarray(rng.random(n) < 0.5)
+        res = stats.describe(x)
+        xp_assert_equal(res.nobs, xp.asarray(n, dtype=xp.int64))
+        xp_assert_equal(res.minmax[0], xp.min(x))
+        xp_assert_equal(res.minmax[1], xp.max(x))
+        x = xp_promote(x, force_floating=True, xp=xp)
+        xp_assert_close(res.mean, xp.mean(x))
+        xp_assert_close(res.variance, xp.var(x, correction=1))
+        xp_assert_close(res.skewness, stats.skew(x))
+        xp_assert_close(res.kurtosis, stats.kurtosis(x))
+
+
+class NormalityTests:
+
+    @pytest.mark.parametrize("alternative", ['two-sided', 'less', 'greater'])
+    def test_against_R(self, alternative, xp):
+        # testa against R `dagoTest` from package `fBasics`
+        # library(fBasics)
+        # options(digits=16)
+        # x = c(-2, -1, 0, 1, 2, 3)**2
+        # x = rep(x, times=4)
+        # test_result <- dagoTest(x)
+        # test_result@test$statistic
+        # test_result@test$p.value
+        test_name = self.test_name
+        test_fun = getattr(stats, test_name)
+        ref_statistic= xp.asarray(self.case_ref[0])
+        ref_pvalue = xp.asarray(self.case_ref[1])
+
+        kwargs = {}
+        if alternative in {'less', 'greater'}:
+            if test_name in {'skewtest', 'kurtosistest'}:
+                ref_pvalue = ref_pvalue/2 if alternative == "less" else 1-ref_pvalue/2
+                ref_pvalue = 1-ref_pvalue if test_name == 'skewtest' else ref_pvalue
+                kwargs['alternative'] = alternative
+            else:
+                pytest.skip('`alternative` not available for `normaltest`')
+
+        x = xp.asarray((-2, -1, 0, 1, 2, 3.)*4)**2
+        res = test_fun(x, **kwargs)
+        res_statistic, res_pvalue = res
+        xp_assert_close(res_statistic, ref_statistic)
+        xp_assert_close(res_pvalue, ref_pvalue)
+        check_named_results(res, ('statistic', 'pvalue'), xp=xp)
+
+    def test_nan(self, xp):
+        # nan in input -> nan output (default nan_policy='propagate')
+        test_fun = getattr(stats, self.test_name)
+        x = xp.arange(30.)
+        NaN = xp.asarray(xp.nan, dtype=x.dtype)
+        x = xp.where(x == 29, NaN, x)
+        with np.errstate(invalid="ignore"):
+            res = test_fun(x)
+            xp_assert_equal(res.statistic, NaN)
+            xp_assert_equal(res.pvalue, NaN)
+
+
+@make_xp_test_case(stats.skewtest)
+class TestSkewTest(NormalityTests):
+    test_name = 'skewtest'
+    case_ref = (1.98078826090875881, 0.04761502382843208)  # statistic, pvalue
+
+    def test_intuitive(self, xp):
+        # intuitive tests; see gh-13549. skewnorm with parameter 1 has skew > 0
+        a1 = stats.skewnorm.rvs(a=1, size=10000, random_state=123)
+        a1_xp = xp.asarray(a1)
+        pval = stats.skewtest(a1_xp, alternative='greater').pvalue
+        xp_assert_close(pval, xp.asarray(0.0, dtype=a1_xp.dtype), atol=9e-6)
+
+    def test_skewtest_too_few_observations(self, xp):
+        # Regression test for ticket #1492.
+        # skewtest requires at least 8 observations; 7 should warn and return NaN.
+        stats.skewtest(xp.arange(8.0))
+
+        x = xp.arange(7.0)
+
+        with eager_warns(SmallSampleWarning, match=too_small_1d_not_omit, xp=xp):
+            res = stats.skewtest(x)
+            NaN = xp.asarray(xp.nan)
+            xp_assert_equal(res.statistic, NaN)
+            xp_assert_equal(res.pvalue, NaN)
+
+
+@make_xp_test_case(stats.kurtosistest)
+class TestKurtosisTest(NormalityTests):
+    test_name = 'kurtosistest'
+    case_ref = (-0.01403734404759738, 0.98880018772590561)  # statistic, pvalue
+
+    def test_intuitive(self, xp):
+        # intuitive tests; see gh-13549. excess kurtosis of laplace is 3 > 0
+        a2 = stats.laplace.rvs(size=10000, random_state=123)
+        a2_xp = xp.asarray(a2)
+        pval = stats.kurtosistest(a2_xp, alternative='greater').pvalue
+        xp_assert_close(pval, xp.asarray(0.0, dtype=a2_xp.dtype), atol=1e-15)
+
+    def test_gh9033_regression(self, xp):
+        # regression test for issue gh-9033: x clearly non-normal but power of
+        # negative denom needs to be handled correctly to reject normality
+        counts = [128, 0, 58, 7, 0, 41, 16, 0, 0, 167]
+        x = np.hstack([np.full(c, i) for i, c in enumerate(counts)])
+        x = xp.asarray(x, dtype=xp.float64)
+        assert stats.kurtosistest(x)[1] < 0.01
+
+    def test_kurtosistest_too_few_observations(self, xp):
+        # kurtosistest requires at least 5 observations; 4 should warn and return NaN.
+        # Regression test for ticket #1425.
+        stats.kurtosistest(xp.arange(5.0))
+
+        with eager_warns(SmallSampleWarning, match=too_small_1d_not_omit, xp=xp):
+            res = stats.kurtosistest(xp.arange(4.))
+            NaN = xp.asarray(xp.nan)
+            xp_assert_equal(res.statistic, NaN)
+            xp_assert_equal(res.pvalue, NaN)
+
+
+@make_xp_test_case(stats.normaltest)
+class TestNormalTest(NormalityTests):
+    test_name = 'normaltest'
+    case_ref = (3.92371918158185551, 0.14059672529747502)  # statistic, pvalue
+
+    def test_too_few_observations(self, xp):
+        stats.normaltest(xp.arange(8.))
+
+        # 1D sample has too few observations -> warning / NaN output
+        with eager_warns(SmallSampleWarning, match=too_small_1d_not_omit, xp=xp):
+            res = stats.normaltest(xp.arange(7.))
+            NaN = xp.asarray(xp.nan)
+            xp_assert_equal(res.statistic, NaN)
+            xp_assert_equal(res.pvalue, NaN)
+
+
+class TestRankSums:
+
+    @pytest.mark.parametrize('alternative', ['less', 'greater', 'two-sided'])
+    def test_ranksums_is_mannwhitneyu(self, alternative):
+        rng = np.random.default_rng(3417115752)
+        x, y = rng.random((2, 10))
+
+        # ranksums pval = mannwhitneyu pval w/out continuity or tie correction
+        res1 = stats.ranksums(x, y, alternative=alternative)
+        res2 = stats.mannwhitneyu(x, y, use_continuity=False,
+                                  alternative=alternative, method='asymptotic')
+        assert_allclose(res1.pvalue, res2.pvalue)
+        assert_allclose(res1.statistic, res2.zstatistic)
+
+    def test_ranksums_named_results(self):
+        res = stats.ranksums(np.arange(10), np.arange(10))
+        check_named_results(res, ('statistic', 'pvalue'))
+
+    def test_input_validation(self):
+        with assert_raises(ValueError, match="`alternative` must be 'less'"):
+            stats.ranksums(np.arange(10), np.arange(10), alternative='foobar')
+
+
+@make_xp_test_case(stats.jarque_bera)
+class TestJarqueBera:
+    def test_jarque_bera_against_R(self, xp):
+        # library(tseries)
+        # options(digits=16)
+        # x < - rnorm(5)
+        # jarque.bera.test(x)
+        x = [-0.160104223201523288,  1.131262000934478040, -0.001235254523709458,
+             -0.776440091309490987, -2.072959999533182884]
+        x = xp.asarray(x)
+        ref = xp.asarray([0.17651605223752, 0.9155246169805])
+        res = stats.jarque_bera(x)
+        xp_assert_close(res.statistic, ref[0])
+        xp_assert_close(res.pvalue, ref[1])
+
+    @skip_xp_backends(np_only=True)
+    def test_jarque_bera_array_like(self, xp):
+        # array-like only relevant for NumPy
+        rng = np.random.default_rng(9294968266)
+        x = rng.standard_normal(size=100000)
+
+        jb_test1 = JB1, p1 = stats.jarque_bera(list(x))
+        jb_test2 = JB2, p2 = stats.jarque_bera(tuple(x))
+        jb_test3 = JB3, p3 = stats.jarque_bera(x.reshape(2, 50000))
+
+        assert JB1 == JB2 == JB3 == jb_test1.statistic == jb_test2.statistic == jb_test3.statistic  # noqa: E501
+        assert p1 == p2 == p3 == jb_test1.pvalue == jb_test2.pvalue == jb_test3.pvalue
+
+    def test_jarque_bera_too_few_observations(self, xp):
+        x = xp.asarray([])
+
+        with pytest.warns(SmallSampleWarning, match=too_small_1d_not_omit):
+            res = stats.jarque_bera(x)
+            NaN = xp.asarray(xp.nan)
+            xp_assert_equal(res.statistic, NaN)
+            xp_assert_equal(res.pvalue, NaN)
+
+    def test_axis(self, xp):
+        rng = np.random.RandomState(seed=122398129)
+        x = xp.asarray(rng.random(size=(2, 45)))
+
+        res = stats.jarque_bera(x, axis=None)
+        ref = stats.jarque_bera(xp.reshape(x, (-1,)))
+        xp_assert_equal(res.statistic, ref.statistic)
+        xp_assert_equal(res.pvalue, ref.pvalue)
+
+        res = stats.jarque_bera(x, axis=1)
+        s0, p0 = stats.jarque_bera(x[0, :])
+        s1, p1 = stats.jarque_bera(x[1, :])
+        xp_assert_close(res.statistic, xp.stack([s0, s1]))
+        xp_assert_close(res.pvalue, xp.stack([p0, p1]))
+
+        resT = stats.jarque_bera(x.T, axis=0)
+        xp_assert_close(res.statistic, resT.statistic)
+        xp_assert_close(res.pvalue, resT.pvalue)
+
+
+@make_xp_test_case(stats.pointbiserialr)
+class TestPointBiserialR:
+    def test_pointbiserial(self, xp):
+        # same as mstats test except for the nan
+        # Test data: https://web.archive.org/web/20060504220742/https://support.sas.com/ctx/samples/index.jsp?sid=490&tab=output
+        x = [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0,0,1,0,
+             0,0,0,0,1.]
+        y = [14.8,13.8,12.4,10.1,7.1,6.1,5.8,4.6,4.3,3.5,3.3,3.2,3.0,
+             2.8,2.8,2.5,2.4,2.3,2.1,1.7,1.7,1.5,1.3,1.3,1.2,1.2,1.1,
+             0.8,0.7,0.6,0.5,0.2,0.2,0.1]
+        res = stats.pointbiserialr(xp.asarray(x), xp.asarray(y))
+        xp_assert_close(res[0], xp.asarray(0.36149), atol=1e-5)
+
+        # test for namedtuple attribute results
+        attributes = ('correlation', 'pvalue')
+        check_named_results(res, attributes, xp=xp)
+        xp_assert_equal(res.correlation, res.statistic)
+
+
+@make_xp_test_case(stats.obrientransform)
+class TestObrientransform:
+    def test_basic(self, xp):
+        # A couple tests calculated by hand.
+        x1 = xp.asarray([0, 2, 4])
+        t1 = stats.obrientransform(x1)
+        expected = xp.asarray([7., -2., 7.])
+        xp_assert_close(t1[0][:], expected)
+
+        x2 = xp.asarray([0, 3, 6, 9])
+        t2 = stats.obrientransform(x2)
+        expected = xp.asarray([30., 0., 0., 30.])
+        xp_assert_close(t2[0][:], expected)
+
+        # Test two arguments.
+        a, b = stats.obrientransform(x1, x2)
+        xp_assert_close(a, t1[0][:])
+        xp_assert_close(b, t2[0][:])
+
+        # Test three arguments.
+        a, b, c = stats.obrientransform(x1, x2, x1)
+        xp_assert_close(a, t1[0][:])
+        xp_assert_close(b, t2[0][:])
+        xp_assert_close(c, t1[0][:])
+
+    def test_something(self, xp):
+        # This is a regression test to check np.var replacement.
+        # The author of this test didn't separately verify the numbers.
+        x1 = xp.arange(5)
+        ref = xp.asarray(
+          [[5.41666667, 1.04166667, -0.41666667, 1.04166667, 5.41666667],
+           [21.66666667, 4.16666667, -1.66666667, 4.16666667, 21.66666667]])
+        res = stats.obrientransform(x1, 2*x1)
+        xp_assert_close(res[0], ref[0, ...])
+        xp_assert_close(res[1], ref[1, ...])
+
+    def test_reference(self, xp):
+        # Example from "O'Brien Test for Homogeneity of Variance" by Herve Abdi.
+        values = np.arange(5, 11)
+        reps = [5, 11, 9, 3, 2, 2]
+        data = np.repeat(values, reps)
+        transformed_values = np.asarray([3.1828, 0.5591, 0.0344,
+                                         1.6086, 5.2817, 11.0538])
+        expected = np.repeat(transformed_values, reps)
+        result = stats.obrientransform(xp.asarray(data))
+        xp_assert_close(result[0][:], xp.asarray(expected.tolist()), rtol=1e-3)
+
+    def test_nan_policy(self, xp):
+        rng = np.random.default_rng(4284359689201882838835)
+        x = rng.random(10)
+        x[3] = np.nan
+        x = xp.asarray(x)
+
+        # nan_policy='raise'
+        if not is_lazy_array(x):
+            with pytest.raises(ValueError, match="The input contains nan values"):
+                stats.obrientransform(x, nan_policy='raise')
+        else:
+            with pytest.raises(TypeError, match="nan_policy='raise' is not supported"):
+                stats.obrientransform(x, nan_policy='raise')
+
+        # nan_policy='propagate'
+        res = stats.obrientransform(x, nan_policy='propagate')[0]
+        xp_assert_equal(res, xp.full_like(x, xp.nan))
+
+        # nan_policy='omit'
+        i = xp.isnan(x)
+        res = stats.obrientransform(x, nan_policy='omit')[0]
+        ref = stats.obrientransform(x[~i])[0]
+        xp_assert_equal(res[i], x[i])
+        xp_assert_close(res[~i], ref)
+
+
+def check_equal_xmean(*args, xp, mean_fun, axis=None, dtype=None,
+                      rtol=None, weights=None):
+    # Note this doesn't test when axis is not specified
+    dtype = dtype or xp.float64
+    if len(args) == 2:
+        array_like, desired = args
+    else:
+        array_like, p, desired = args
+    array_like = xp.asarray(array_like, dtype=dtype)
+    dtype_reference = (xp_result_type(array_like, force_floating=True, xp=xp)
+                       if xp != np.ma else None)
+    desired = xp.asarray(desired, dtype=dtype_reference)
+    weights = xp.asarray(weights, dtype=dtype) if weights is not None else weights
+    args = (array_like,) if len(args) == 2 else (array_like, p)
+    x = mean_fun(*args, axis=axis, weights=weights)
+    xp_assert_close(x, desired, rtol=rtol)
+
+
+def check_equal_gmean(*args, **kwargs):
+    return check_equal_xmean(*args, mean_fun=stats.gmean, **kwargs)
+
+
+def check_equal_hmean(*args, **kwargs):
+    return check_equal_xmean(*args, mean_fun=stats.hmean, **kwargs)
+
+
+def check_equal_pmean(*args, **kwargs):
+    return check_equal_xmean(*args, mean_fun=stats.pmean, **kwargs)
+
+
+@make_xp_test_case(stats.hmean)
+class TestHMean:
+    @pytest.mark.filterwarnings("ignore:divide by zero encountered:RuntimeWarning:dask")
+    def test_0(self, xp):
+        a = [1, 0, 2]
+        desired = 0
+        check_equal_hmean(a, desired, xp=xp)
+
+    @pytest.mark.parametrize('dtype', [None, 'int64', 'float32', 'float64'])
+    def test_1d(self, dtype, xp):
+        dtype = dtype if dtype is None else getattr(xp, dtype)
+
+        #  Test a 1d case
+        a = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]
+        desired = 34.1417152147
+        check_equal_hmean(a, desired, dtype=dtype, xp=xp)
+
+        a = [1, 2, 3, 4]
+        desired = 4. / (1. / 1 + 1. / 2 + 1. / 3 + 1. / 4)
+        check_equal_hmean(a, desired, dtype=dtype, xp=xp)
+
+    @pytest.mark.filterwarnings("ignore:divide by zero encountered:RuntimeWarning:dask")
+    @pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning:dask")
+    def test_1d_with_zero(self, xp):
+        a = np.array([1, 0])
+        desired = 0.0
+        check_equal_hmean(a, desired, xp=xp, rtol=0.0)
+
+    @pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning:dask")
+    @pytest.mark.filterwarnings("ignore:divide by zero encountered:RuntimeWarning:dask")
+    def test_1d_with_negative_value(self, xp):
+        a = np.array([1, 0, -1])
+        message = "The harmonic mean is only defined..."
+        with eager_warns(RuntimeWarning, match=message, xp=xp):
+            check_equal_hmean(a, xp.nan, xp=xp, rtol=0.0)
+
+    # Note the next tests use axis=None as default, not axis=0
+    def test_2d(self, xp):
+        #  Test a 2d case
+        a = [[10, 20, 30, 40], [50, 60, 70, 80], [90, 100, 110, 120]]
+        desired = 38.6696271841
+        check_equal_hmean(np.array(a), desired, xp=xp)
+
+    def test_2d_axis0(self, xp):
+        #  Test a 2d case with axis=0
+        a = [[10, 20, 30, 40], [50, 60, 70, 80], [90, 100, 110, 120]]
+        desired = np.array([22.88135593, 39.13043478, 52.90076336, 65.45454545])
+        check_equal_hmean(a, desired, axis=0, xp=xp)
+
+    @pytest.mark.filterwarnings("ignore:divide by zero encountered:RuntimeWarning:dask")
+    def test_2d_axis0_with_zero(self, xp):
+        a = [[10, 0, 30, 40], [50, 60, 70, 80], [90, 100, 110, 120]]
+        desired = np.array([22.88135593, 0.0, 52.90076336, 65.45454545])
+        check_equal_hmean(a, desired, axis=0, xp=xp)
+
+    def test_2d_axis1(self, xp):
+        #  Test a 2d case with axis=1
+        a = [[10, 20, 30, 40], [50, 60, 70, 80], [90, 100, 110, 120]]
+        desired = np.array([19.2, 63.03939962, 103.80078637])
+        check_equal_hmean(a, desired, axis=1, xp=xp)
+
+    @pytest.mark.filterwarnings("ignore:divide by zero encountered:RuntimeWarning:dask")
+    def test_2d_axis1_with_zero(self, xp):
+        a = [[10, 0, 30, 40], [50, 60, 70, 80], [90, 100, 110, 120]]
+        desired = np.array([0.0, 63.03939962, 103.80078637])
+        check_equal_hmean(a, desired, axis=1, xp=xp)
+
+    @skip_xp_backends(
+        np_only=True,
+        reason='array-likes only supported for NumPy backend',
+    )
+    def test_weights_1d_list(self, xp):
+        # Desired result from:
+        # https://www.hackmath.net/en/math-problem/35871
+        a = [2, 10, 6]
+        weights = [10, 5, 3]
+        desired = 3.
+        # all the other tests use `check_equal_hmean`, which now converts
+        # the input to an xp-array before calling `hmean`. This time, check
+        # that the function still accepts the lists of ints.
+        res = stats.hmean(a, weights=weights)
+        xp_assert_close(res, np.asarray(desired), rtol=1e-5)
+
+    def test_weights_1d(self, xp):
+        # Desired result from:
+        # https://www.hackmath.net/en/math-problem/35871
+        a = np.asarray([2, 10, 6])
+        weights = np.asarray([10, 5, 3])
+        desired = 3
+        check_equal_hmean(a, desired, weights=weights, rtol=1e-5, xp=xp)
+
+    def test_weights_2d_axis0(self, xp):
+        # Desired result from:
+        # https://www.hackmath.net/en/math-problem/35871
+        a = np.array([[2, 5], [10, 5], [6, 5]])
+        weights = np.array([[10, 1], [5, 1], [3, 1]])
+        desired = np.array([3, 5])
+        check_equal_hmean(a, desired, axis=0, weights=weights, rtol=1e-5, xp=xp)
+
+    def test_weights_2d_axis1(self, xp):
+        # Desired result from:
+        # https://www.hackmath.net/en/math-problem/35871
+        a = np.array([[2, 10, 6], [7, 7, 7]])
+        weights = np.array([[10, 5, 3], [1, 1, 1]])
+        desired = np.array([3, 7])
+        check_equal_hmean(a, desired, axis=1, weights=weights, rtol=1e-5, xp=xp)
+
+    @skip_xp_invalid_arg
+    def test_weights_masked_1d_array(self, xp):
+        # Desired result from:
+        # https://www.hackmath.net/en/math-problem/35871
+        a = np.array([2., 10., 6., 42.])
+        weights = np.ma.array([10., 5., 3., 42.], mask=[0, 0, 0, 1])
+        desired = 3.
+        xp = np.ma  # check_equal_hmean uses xp.asarray; this will preserve the mask
+        check_equal_hmean(a, desired, weights=weights, rtol=1e-5,
+                          dtype=np.float64, xp=xp)
+
+
+@make_xp_test_case(stats.gmean)
+class TestGMean:
+    @pytest.mark.filterwarnings(
+        "ignore:divide by zero encountered in log:RuntimeWarning:dask"
+    )
+    def test_0(self, xp):
+        a = [1, 0, 2]
+        desired = 0
+        check_equal_gmean(a, desired, xp=xp)
+
+    @pytest.mark.parametrize('dtype', [None, 'int64', 'float32', 'float64'])
+    def test_1d(self, dtype, xp):
+        dtype = dtype if dtype is None else getattr(xp, dtype)
+
+        #  Test a 1d case
+        a = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]
+        desired = 45.2872868812
+        check_equal_gmean(a, desired, dtype=dtype, xp=xp)
+
+        a = [1, 2, 3, 4]
+        desired = power(1 * 2 * 3 * 4, 1. / 4.)
+        check_equal_gmean(a, desired, dtype=dtype, rtol=1e-14, xp=xp)
+
+    # Note the next tests use axis=None as default, not axis=0
+    def test_2d(self, xp):
+        #  Test a 2d case
+        a = [[10, 20, 30, 40], [50, 60, 70, 80], [90, 100, 110, 120]]
+        desired = 52.8885199
+        check_equal_gmean(a, desired, xp=xp)
+
+    def test_2d_axis0(self, xp):
+        #  Test a 2d case with axis=0
+        a = [[10, 20, 30, 40], [50, 60, 70, 80], [90, 100, 110, 120]]
+        desired = np.array([35.56893304, 49.32424149, 61.3579244, 72.68482371])
+        check_equal_gmean(a, desired, axis=0, xp=xp)
+
+        a = array([[1, 2, 3, 4], [1, 2, 3, 4], [1, 2, 3, 4]])
+        desired = array([1, 2, 3, 4])
+        check_equal_gmean(a, desired, axis=0, rtol=1e-14, xp=xp)
+
+    def test_2d_axis1(self, xp):
+        #  Test a 2d case with axis=1
+        a = [[10, 20, 30, 40], [50, 60, 70, 80], [90, 100, 110, 120]]
+        desired = np.array([22.13363839, 64.02171746, 104.40086817])
+        check_equal_gmean(a, desired, axis=1, xp=xp)
+
+        a = array([[1, 2, 3, 4], [1, 2, 3, 4], [1, 2, 3, 4]])
+        v = power(1 * 2 * 3 * 4, 1. / 4.)
+        desired = array([v, v, v])
+        check_equal_gmean(a, desired, axis=1, rtol=1e-14, xp=xp)
+
+    def test_large_values(self, xp):
+        a = array([1e100, 1e200, 1e300])
+        desired = 1e200
+        check_equal_gmean(a, desired, rtol=1e-13, xp=xp)
+
+    @pytest.mark.filterwarnings(
+        "ignore:divide by zero encountered in log:RuntimeWarning:dask"
+    )
+    def test_1d_with_0(self, xp):
+        #  Test a 1d case with zero element
+        a = [10, 20, 30, 40, 50, 60, 70, 80, 90, 0]
+        desired = 0.0  # due to exp(-inf)=0
+        with np.errstate(all='ignore'):
+            check_equal_gmean(a, desired, xp=xp)
+
+    @pytest.mark.filterwarnings(
+        "ignore:invalid value encountered in log:RuntimeWarning:dask"
+    )
+    def test_1d_neg(self, xp):
+        #  Test a 1d case with negative element
+        a = [10, 20, 30, 40, 50, 60, 70, 80, 90, -1]
+        desired = np.nan  # due to log(-1) = nan
+        with np.errstate(invalid='ignore'):
+            check_equal_gmean(a, desired, xp=xp)
+
+    @skip_xp_backends(
+        np_only=True,
+        reason='array-likes only supported for NumPy backend',
+    )
+    def test_weights_1d_list(self, xp):
+        # Desired result from:
+        # https://www.dummies.com/education/math/business-statistics/how-to-find-the-weighted-geometric-mean-of-a-data-set/
+        a = [1, 2, 3, 4, 5]
+        weights = [2, 5, 6, 4, 3]
+        desired = 2.77748
+
+        # all the other tests use `check_equal_gmean`, which now converts
+        # the input to an xp-array before calling `gmean`. This time, check
+        # that the function still accepts the lists of ints.
+        res = stats.gmean(a, weights=weights)
+        xp_assert_close(res, np.asarray(desired), rtol=1e-5)
+
+    def test_weights_1d(self, xp):
+        # Desired result from:
+        # https://www.dummies.com/education/math/business-statistics/how-to-find-the-weighted-geometric-mean-of-a-data-set/
+        a = np.array([1, 2, 3, 4, 5])
+        weights = np.array([2, 5, 6, 4, 3])
+        desired = 2.77748
+        check_equal_gmean(a, desired, weights=weights, rtol=1e-5, xp=xp)
+
+    @skip_xp_invalid_arg
+    def test_weights_masked_1d_array(self, xp):
+        # Desired result from:
+        # https://www.dummies.com/education/math/business-statistics/how-to-find-the-weighted-geometric-mean-of-a-data-set/
+        a = np.array([1., 2., 3., 4., 5., 6.])
+        weights = np.ma.array([2., 5., 6., 4., 3., 5.], mask=[0, 0, 0, 0, 0, 1])
+        desired = 2.77748
+        xp = np.ma  # check_equal_gmean uses xp.asarray; this will preserve the mask
+        check_equal_gmean(a, desired, weights=weights, rtol=1e-5,
+                          dtype=np.float64, xp=xp)
+
+
+@make_xp_test_case(stats.pmean)
+class TestPMean:
+
+    def pmean_reference(a, p):
+        return (np.sum(a**p) / a.size)**(1/p)
+
+    def wpmean_reference(a, p, weights):
+        return (np.sum(weights * a**p) / np.sum(weights))**(1/p)
+
+    def test_bad_exponent(self, xp):
+        with pytest.raises(ValueError, match='Power mean only defined for'):
+            stats.pmean(xp.asarray([1, 2, 3]), xp.asarray([0]))
+
+    @pytest.mark.parametrize('dtype', [None, 'int64', 'float32', 'float64'])
+    def test_1d(self, dtype, xp):
+        dtype = dtype if dtype is None else getattr(xp, dtype)
+
+        a, p = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], 3.5
+        desired = TestPMean.pmean_reference(np.array(a), p)
+        check_equal_pmean(a, p, desired, dtype=dtype, xp=xp)
+
+        a, p = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], -2.5
+        desired = TestPMean.pmean_reference(np.array(a), p)
+        check_equal_pmean(a, p, desired, dtype=dtype, xp=xp)
+
+        a, p = [1, 2, 3, 4], 2
+        desired = np.sqrt((1**2 + 2**2 + 3**2 + 4**2) / 4)
+        check_equal_pmean(a, p, desired, dtype=dtype, xp=xp)
+
+    @pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning:dask")
+    @pytest.mark.filterwarnings("ignore:divide by zero encountered:RuntimeWarning:dask")
+    def test_1d_with_zero(self, xp):
+        a, p = np.array([1, 0]), -1
+        desired = 0.0
+        check_equal_pmean(a, p, desired, rtol=0.0, xp=xp)
+
+    def test_1d_with_negative_value(self, xp):
+        a, p = np.array([1, 0, -1]), 1.23
+        message = "The power mean is only defined..."
+        with eager_warns(RuntimeWarning, match=message, xp=xp):
+            check_equal_pmean(a, p, xp.nan, xp=xp)
+
+    @pytest.mark.parametrize(
+        ("a", "p"),
+        [([[10, 20], [50, 60], [90, 100]], -0.5),
+         (np.array([[10, 20], [50, 60], [90, 100]]), 0.5)]
+    )
+    def test_2d_axisnone(self, a, p, xp):
+        desired = TestPMean.pmean_reference(np.array(a), p)
+        check_equal_pmean(a, p, desired, xp=xp)
+
+    @pytest.mark.parametrize(
+        ("a", "p"),
+        [([[10, 20, 30, 40], [50, 60, 70, 80], [90, 100, 110, 120]], -0.5),
+         ([[10, 0, 30, 40], [50, 60, 70, 80], [90, 100, 110, 120]], 0.5)]
+    )
+    def test_2d_axis0(self, a, p, xp):
+        desired = [
+            TestPMean.pmean_reference(
+                np.array([a[i][j] for i in range(len(a))]), p
+            )
+            for j in range(len(a[0]))
+        ]
+        check_equal_pmean(a, p, desired, axis=0, xp=xp)
+
+    @pytest.mark.parametrize(
+        ("a", "p"),
+        [([[10, 20, 30, 40], [50, 60, 70, 80], [90, 100, 110, 120]], -0.5),
+         ([[10, 0, 30, 40], [50, 60, 70, 80], [90, 100, 110, 120]], 0.5)]
+    )
+    def test_2d_axis1(self, a, p, xp):
+        desired = [TestPMean.pmean_reference(np.array(a_), p) for a_ in a]
+        check_equal_pmean(a, p, desired, axis=1, xp=xp)
+
+    def test_weights_1d(self, xp):
+        a, p = [2, 10, 6], -1.23456789
+        weights = [10, 5, 3]
+        desired = TestPMean.wpmean_reference(np.array(a), p, weights)
+        check_equal_pmean(a, p, desired, weights=weights, rtol=1e-5, xp=xp)
+
+    @skip_xp_backends(
+        np_only=True,
+        reason='array-likes only supported for NumPy backend',
+    )
+    def test_weights_1d_list(self, xp):
+        a, p = [2, 10, 6], -1.23456789
+        weights = [10, 5, 3]
+        desired = TestPMean.wpmean_reference(np.array(a), p, weights)
+        # all the other tests use `check_equal_pmean`, which now converts
+        # the input to an xp-array before calling `pmean`. This time, check
+        # that the function still accepts the lists of ints.
+        res = stats.pmean(a, p, weights=weights)
+        xp_assert_close(res, np.asarray(desired), rtol=1e-5)
+
+    @skip_xp_invalid_arg
+    def test_weights_masked_1d_array(self, xp):
+        a, p = np.array([2., 10., 6., 42.]), 1
+        weights = np.ma.array([10., 5., 3., 42.], mask=[0, 0, 0, 1])
+        desired = np.average(a, weights=weights)
+        xp = np.ma  # check_equal_pmean uses xp.asarray; this will preserve the mask
+        check_equal_pmean(a, p, desired, weights=weights, rtol=1e-5,
+                          dtype=np.float64, xp=xp)
+
+    @pytest.mark.parametrize(
+        ("axis", "fun_name", "p"),
+        [(None, "wpmean_reference", 9.87654321),
+         (0, "gmean", 0),
+         (1, "hmean", -1)]
+    )
+    def test_weights_2d(self, axis, fun_name, p, xp):
+        if fun_name == 'wpmean_reference':
+            def fun(a, axis, weights):
+                return TestPMean.wpmean_reference(a, p, weights)
+        else:
+            fun = getattr(stats, fun_name)
+        a = np.array([[2, 5], [10, 5], [6, 5]])
+        weights = np.array([[10, 1], [5, 1], [3, 1]])
+        desired = fun(a, axis=axis, weights=weights)
+        check_equal_pmean(a, p, desired, axis=axis, weights=weights, rtol=1e-5, xp=xp)
+
+    def test_infinite_p_gh23111(self):
+        # gh-23111 reported that `pmean` didn't work properly with infinite `p`;
+        # check that this raises an appropriate error message
+        message = "Power mean only implemented for finite `p`"
+        with pytest.raises(NotImplementedError, match=message):
+            stats.pmean([2], np.inf)
+
+
+    @pytest.mark.parametrize(
+        "p, weights, ref",
+        [
+            # import numpy as np
+            # from mpmath import mp
+            # mp.dps = 1000
+            #
+            # x = [50., 100., 300., 70., 25., 100., 2.]
+            # w = [1., 2., 1., 1., 1., 2., 1.]
+            #
+            # x = np.asarray([mp.mpf(x_) for x_ in x])
+            # w = np.asarray([mp.mpf(w_) for w_ in w])
+            # p = mp.mpf(2e-16)
+            #
+            # res = np.average(x**p)**(1/p)
+            # float(res) # 47.23984586445856
+            #
+            (2e-16, None, 47.23984586445856),
+            #
+            # res = np.average(x**p, weights=w)**(1/p)
+            # float(res) # 55.80644618389137
+            #
+            (2e-16, [1., 2., 1., 1., 1., 2., 1.], 55.80644618389137),
+        ],
+    )
+    def test_small_p_gh23407(self, xp, p, weights, ref):
+        # gh-23407 reported that pmean had
+        # poor numerical behavior for very small nonzero p
+        x = xp.asarray(
+            [50., 100., 300., 70., 25., 100., 2.]
+        )
+        w = None if weights is None else xp.asarray(weights)
+
+        res = stats.pmean(x, p, weights=w)
+        xp_assert_close(res, xp.asarray(ref))
+
+
+@make_xp_test_case(stats.gstd)
+class TestGSTD:
+    # must add 1 as `gstd` is only defined for positive values
+    array_1d = (np.arange(2 * 3 * 4) + 1).tolist()
+    gstd_array_1d = 2.294407613602
+    array_3d = np.reshape(array_1d, (2, 3, 4)).tolist()
+
+    def test_1d_array(self, xp):
+        gstd_actual = stats.gstd(xp.asarray(self.array_1d))
+        xp_assert_close(gstd_actual, xp.asarray(self.gstd_array_1d))
+
+    @skip_xp_backends(np_only=True, reason="Only NumPy supports array-like input")
+    def test_1d_numeric_array_like_input(self, xp):
+        gstd_actual = stats.gstd(tuple(self.array_1d))
+        assert_allclose(gstd_actual, self.gstd_array_1d)
+
+    @skip_xp_invalid_arg
+    def test_raises_error_non_numeric_input(self, xp):
+        message = "could not convert string to float|The DType..."
+        with pytest.raises((ValueError, TypeError), match=message):
+            stats.gstd('You cannot take the logarithm of a string.')
+
+    @pytest.mark.filterwarnings("ignore:divide by zero encountered:RuntimeWarning:dask")
+    @pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning:dask")
+    @pytest.mark.parametrize('bad_value', (0, -1, np.inf, np.nan))
+    def test_returns_nan_invalid_value(self, bad_value, xp):
+        x = xp.asarray(self.array_1d + [bad_value])
+        if np.isfinite(bad_value) and not is_lazy_array(x):
+            message = "The geometric standard deviation is only defined..."
+            with pytest.warns(RuntimeWarning, match=message):
+                res = stats.gstd(x)
+        else:
+            res = stats.gstd(x)
+        xp_assert_equal(res, xp.asarray(np.nan))
+
+    def test_propagates_nan_values(self, xp):
+        a = xp.asarray([[1, 1, 1, 16], [xp.nan, 1, 2, 3]])
+        gstd_actual = stats.gstd(a, axis=1)
+        xp_assert_close(gstd_actual, xp.asarray([4, np.nan]))
+
+    def test_ddof_equal_to_number_of_observations(self, xp):
+        x = xp.asarray(self.array_1d)
+        res = stats.gstd(x, ddof=x.shape[0])
+        xp_assert_equal(res, xp.asarray(xp.nan))
+
+    def test_3d_array(self, xp):
+        x = xp.asarray(self.array_3d)
+        gstd_actual = stats.gstd(x, axis=None)
+        ref = xp.asarray(self.gstd_array_1d)
+        xp_assert_close(gstd_actual, ref)
+
+    def test_3d_array_axis_type_tuple(self, xp):
+        x = xp.asarray(self.array_3d)
+        gstd_actual = stats.gstd(x, axis=(1, 2))
+        ref = xp.asarray([2.12939215, 1.22120169])
+        xp_assert_close(gstd_actual, ref)
+
+    def test_3d_array_axis_0(self, xp):
+        x = xp.asarray(self.array_3d)
+        gstd_actual = stats.gstd(x, axis=0)
+        gstd_desired = xp.asarray([
+            [6.1330555493918, 3.958900210120, 3.1206598248344, 2.6651441426902],
+            [2.3758135028411, 2.174581428192, 2.0260062829505, 1.9115518327308],
+            [1.8205343606803, 1.746342404566, 1.6846557065742, 1.6325269194382]
+        ])
+        xp_assert_close(gstd_actual, gstd_desired)
+
+    def test_3d_array_axis_1(self, xp):
+        x = xp.asarray(self.array_3d)
+        gstd_actual = stats.gstd(x, axis=1)
+        gstd_desired = xp.asarray([
+            [3.118993630946, 2.275985934063, 1.933995977619, 1.742896469724],
+            [1.271693593916, 1.254158641801, 1.238774141609, 1.225164057869]
+        ])
+        xp_assert_close(gstd_actual, gstd_desired)
+
+    def test_3d_array_axis_2(self, xp):
+        x = xp.asarray(self.array_3d)
+        gstd_actual = stats.gstd(x, axis=2)
+        gstd_desired = xp.asarray([
+            [1.8242475707664, 1.2243686572447, 1.1318311657788],
+            [1.0934830582351, 1.0724479791887, 1.0591498540749]
+        ])
+        xp_assert_close(gstd_actual, gstd_desired)
+
+
+class TestTrim:
+    # test trim functions
+    def test_trim1(self):
+        a = np.arange(11)
+        assert_equal(np.sort(stats.trim1(a, 0.1)), np.arange(10))
+        assert_equal(np.sort(stats.trim1(a, 0.2)), np.arange(9))
+        assert_equal(np.sort(stats.trim1(a, 0.2, tail='left')),
+                     np.arange(2, 11))
+        assert_equal(np.sort(stats.trim1(a, 3/11., tail='left')),
+                     np.arange(3, 11))
+        assert_equal(stats.trim1(a, 1.0), [])
+        assert_equal(stats.trim1(a, 1.0, tail='left'), [])
+
+        # empty input
+        assert_equal(stats.trim1([], 0.1), [])
+        assert_equal(stats.trim1([], 3/11., tail='left'), [])
+        assert_equal(stats.trim1([], 4/6.), [])
+
+        # test axis
+        a = np.arange(24).reshape(6, 4)
+        ref = np.arange(4, 24).reshape(5, 4)  # first row trimmed
+
+        axis = 0
+        trimmed = stats.trim1(a, 0.2, tail='left', axis=axis)
+        assert_equal(np.sort(trimmed, axis=axis), ref)
+
+        axis = 1
+        trimmed = stats.trim1(a.T, 0.2, tail='left', axis=axis)
+        assert_equal(np.sort(trimmed, axis=axis), ref.T)
+
+    def test_trimboth(self):
+        a = np.arange(11)
+        assert_equal(np.sort(stats.trimboth(a, 3/11.)), np.arange(3, 8))
+        assert_equal(np.sort(stats.trimboth(a, 0.2)),
+                     np.array([2, 3, 4, 5, 6, 7, 8]))
+        assert_equal(np.sort(stats.trimboth(np.arange(24).reshape(6, 4), 0.2)),
+                     np.arange(4, 20).reshape(4, 4))
+        assert_equal(np.sort(stats.trimboth(np.arange(24).reshape(4, 6).T,
+                                            2/6.)),
+                     np.array([[2, 8, 14, 20], [3, 9, 15, 21]]))
+        assert_raises(ValueError, stats.trimboth,
+                      np.arange(24).reshape(4, 6).T, 4/6.)
+
+        # empty input
+        assert_equal(stats.trimboth([], 0.1), [])
+        assert_equal(stats.trimboth([], 3/11.), [])
+        assert_equal(stats.trimboth([], 4/6.), [])
+
+
+@make_xp_test_case(stats.trim_mean)
+class TestTrimMean:
+    def test_trim_mean(self, xp):
+        # don't use pre-sorted arrays
+        idx = np.array([3, 5, 0, 1, 2, 4])
+        a2 = np.arange(24).reshape(6, 4)[idx, :]
+        a3 = np.arange(24).reshape(6, 4, order='F')[idx, :]
+
+        xp_assert_equal(stats.trim_mean(xp.asarray(a3), 2/6.),
+                        xp.asarray([2.5, 8.5, 14.5, 20.5]))
+        xp_assert_equal(stats.trim_mean(xp.asarray(a2), 2/6.),
+                        xp.asarray([10., 11., 12., 13.]))
+
+        idx4 = np.array([1, 0, 3, 2])
+        a4 = np.arange(24).reshape(4, 6)[idx4, :]
+        xp_assert_equal(stats.trim_mean(xp.asarray(a4), 2/6.),
+                        xp.asarray([9., 10., 11., 12., 13., 14.]))
+
+        # shuffled arange(24) as array_like
+        a = [7, 11, 12, 21, 16, 6, 22, 1, 5, 0, 18, 10, 17, 9, 19, 15, 23,
+             20, 2, 14, 4, 13, 8, 3]
+        xp_assert_equal(stats.trim_mean(xp.asarray(a), 2/6.), xp.asarray(11.5))
+        xp_assert_equal(stats.trim_mean(xp.asarray([5, 4, 3, 1, 2, 0]), 2/6.),
+                        xp.asarray(2.5))
+
+        # check axis argument
+        rng = np.random.default_rng(3417115752)
+        a = rng.integers(20, size=(5, 6, 4, 7))
+        a = xp.asarray(a)
+        for axis in [0, 1, 2, 3, -1]:
+            res1 = stats.trim_mean(a, 2/6., axis=axis)
+            res2 = stats.trim_mean(xp.moveaxis(a, axis, 0), 2/6.)
+            xp_assert_equal(res1, res2)
+
+        res1 = stats.trim_mean(a, 2/6., axis=None)
+        res2 = stats.trim_mean(xp_ravel(a), 2/6.)
+        xp_assert_equal(res1, res2)
+
+        with pytest.raises(ValueError, match="Proportion too big."):
+            stats.trim_mean(a, 0.6)
+
+    @skip_xp_backends('dask.array', reason="lazy -> no _axis_nan_policy")
+    def test_empty_input(self, xp):
+        # empty input
+        with pytest.warns(SmallSampleWarning, match='too small'):
+            xp_assert_equal(stats.trim_mean(xp.asarray([]), 0.0), xp.asarray(xp.nan))
+        with pytest.warns(SmallSampleWarning, match='too small'):
+            xp_assert_equal(stats.trim_mean(xp.asarray([]), 0.6), xp.asarray(xp.nan))
+
+
+@make_xp_test_case(stats.sigmaclip)
+class TestSigmaClip:
+    def test_sigmaclip1(self, xp):
+        a = xp.concat((xp.linspace(9.5, 10.5, 31),
+                       xp.linspace(0., 20., 5)))
+        fact = 4  # default
+        c, low, upp = stats.sigmaclip(a)
+        assert xp.min(c) > low
+        assert xp.max(c) < upp
+        xp_assert_equal(low, xp.mean(c) - fact*xp.std(c))
+        xp_assert_equal(upp, xp.mean(c) + fact*xp.std(c))
+        assert c.shape == a.shape
+
+    def test_sigmaclip2(self, xp):
+        a = xp.concat((xp.linspace(9.5, 10.5, 31),
+                       xp.linspace(0., 20., 5)))
+        fact = 1.5
+        c, low, upp = stats.sigmaclip(a, fact, fact)
+        assert xp.min(c) > low
+        assert xp.max(c) < upp
+        xp_assert_equal(low, xp.mean(c) - fact*xp.std(c))
+        xp_assert_equal(upp, xp.mean(c) + fact*xp.std(c))
+        assert c.shape == (4,)
+        assert a.shape == (36,)
+
+    def test_sigmaclip3(self, xp):
+        a = xp.concat((xp.linspace(9.5, 10.5, 11),
+                       xp.linspace(-100., -50., 3)))
+        fact = 1.8
+        c, low, upp = stats.sigmaclip(a, fact, fact)
+        assert xp.min(c) > low
+        assert xp.max(c) < upp
+        xp_assert_equal(low, xp.mean(c) - fact*xp.std(c))
+        xp_assert_equal(upp, xp.mean(c) + fact*xp.std(c))
+        xp_assert_equal(c, xp.linspace(9.5, 10.5, 11))
+
+    def test_sigmaclip_result_attributes(self, xp):
+        a = xp.concat((xp.linspace(9.5, 10.5, 11),
+                       xp.linspace(-100., -50., 3)))
+        fact = 1.8
+        res = stats.sigmaclip(a, fact, fact)
+        attributes = ('clipped', 'lower', 'upper')
+        check_named_results(res, attributes, xp=xp)
+
+    def test_std_zero(self, xp):
+        # regression test #8632
+        x = xp.ones(10)
+        xp_assert_equal(stats.sigmaclip(x)[0], x)
+
+    @pytest.mark.parametrize("dtype", [None, 'float32', 'float64'])
+    def test_nan_policy(self, dtype, xp):
+        dtype = None if dtype is None else getattr(xp, dtype)
+        rng = np.random.default_rng(243587919486245906119)
+        x = rng.random(10)
+        x[3] = np.nan
+        x = xp.asarray(x.tolist(), dtype=dtype)
+
+        # nan_policy='raise'
+        if not is_lazy_array(x):
+            with pytest.raises(ValueError, match="The input contains nan values"):
+                stats.sigmaclip(x, nan_policy='raise')
+        else:
+            with pytest.raises(TypeError, match="nan_policy='raise' is not supported"):
+                stats.sigmaclip(x, nan_policy='raise')
+
+        # nan_policy='propagate'
+        res = stats.sigmaclip(x, nan_policy='propagate')
+        xp_assert_equal(res.clipped, xp.asarray([], dtype=dtype))
+        xp_assert_equal(res.lower, xp.asarray(xp.nan, dtype=dtype))
+        xp_assert_equal(res.upper, xp.asarray(xp.nan, dtype=dtype))
+
+        # nan_policy='omit'
+        res = stats.sigmaclip(x, nan_policy='omit')
+        ref = stats.sigmaclip(x[~xp.isnan(x)])
+        xp_assert_equal(res.clipped, ref.clipped)
+        xp_assert_equal(res.lower, ref.lower)
+        xp_assert_equal(res.upper, ref.upper)
+
+
+@make_xp_test_case(stats.alexandergovern)
+class TestAlexanderGovern:
+    def test_compare_dtypes(self):
+        # leave this NumPy only
+        args = [[13, 13, 13, 13, 13, 13, 13, 12, 12],
+                [14, 13, 12, 12, 12, 12, 12, 11, 11],
+                [14, 14, 13, 13, 13, 13, 13, 12, 12],
+                [15, 14, 13, 13, 13, 12, 12, 12, 11]]
+        args_int16 = [np.asarray(arg, dtype=np.int16) for arg in args]
+        args_int32 = [np.asarray(arg, dtype=np.int32) for arg in args]
+        args_uint8 = [np.asarray(arg, dtype=np.uint8) for arg in args]
+        args_float64 = [np.asarray(arg, dtype=np.float64) for arg in args]
+
+        res_int16 = stats.alexandergovern(*args_int16)
+        res_int32 = stats.alexandergovern(*args_int32)
+        res_uint8 = stats.alexandergovern(*args_uint8)
+        res_float64 = stats.alexandergovern(*args_float64)
+
+        assert (res_int16.pvalue == res_int32.pvalue ==
+                res_uint8.pvalue == res_float64.pvalue)
+        assert (res_int16.statistic == res_int32.statistic ==
+                res_uint8.statistic == res_float64.statistic)
+
+    @skip_xp_backends('dask.array', reason="Requires `_axis_nan_policy` decorator")
+    @pytest.mark.parametrize('case',[([1, 2], []), ([1, 2], 2), ([1, 2], [2])])
+    def test_too_small_inputs(self, case, xp):
+        # input array is of size zero or too small
+        dtype = xp_default_dtype(xp)
+        case = xp.asarray(case[0], dtype=dtype), xp.asarray(case[1], dtype=dtype)
+        with pytest.warns(SmallSampleWarning, match=too_small_1d_not_omit):
+            res = stats.alexandergovern(*case)
+        xp_assert_equal(res.statistic, xp.asarray(xp.nan))
+        xp_assert_equal(res.pvalue, xp.asarray(xp.nan))
+
+    @pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning")
+    def test_bad_inputs(self, xp):
+        # inputs are not finite (infinity)
+        samples = xp.asarray([1., 2.]), xp.asarray([xp.inf, xp.inf])
+        res = stats.alexandergovern(*samples)
+        xp_assert_equal(res.statistic, xp.asarray(xp.nan))
+        xp_assert_equal(res.pvalue, xp.asarray(xp.nan))
+
+    def test_compare_r(self, xp):
+        '''
+        Data generated in R with
+        > set.seed(1)
+        > library("onewaytests")
+        > library("tibble")
+        > y <- c(rnorm(40, sd=10),
+        +        rnorm(30, sd=15),
+        +        rnorm(20, sd=20))
+        > x <- c(rep("one", times=40),
+        +        rep("two", times=30),
+        +        rep("eight", times=20))
+        > x <- factor(x)
+        > ag.test(y ~ x, tibble(y,x))
+
+        Alexander-Govern Test (alpha = 0.05)
+        -------------------------------------------------------------
+        data : y and x
+
+        statistic  : 1.359941
+        parameter  : 2
+        p.value    : 0.5066321
+
+        Result     : Difference is not statistically significant.
+        -------------------------------------------------------------
+        Example adapted from:
+        https://eval-serv2.metpsy.uni-jena.de/wiki-metheval-hp/index.php/R_FUN_Alexander-Govern
+
+        '''
+        one = [-6.264538107423324, 1.8364332422208225, -8.356286124100471,
+               15.952808021377916, 3.295077718153605, -8.204683841180152,
+               4.874290524284853, 7.383247051292173, 5.757813516534923,
+               -3.0538838715635603, 15.11781168450848, 3.898432364114311,
+               -6.2124058054180376, -22.146998871774997, 11.249309181431082,
+               -0.4493360901523085, -0.16190263098946087, 9.438362106852992,
+               8.212211950980885, 5.939013212175088, 9.189773716082183,
+               7.821363007310671, 0.745649833651906, -19.89351695863373,
+               6.198257478947102, -0.5612873952900078, -1.557955067053293,
+               -14.707523838992744, -4.781500551086204, 4.179415601997024,
+               13.58679551529044, -1.0278772734299553, 3.876716115593691,
+               -0.5380504058290512, -13.770595568286065, -4.149945632996798,
+               -3.942899537103493, -0.5931339671118566, 11.000253719838831,
+               7.631757484575442]
+
+        two = [-2.4678539438038034, -3.8004252020476135, 10.454450631071062,
+               8.34994798010486, -10.331335418242798, -10.612427354431794,
+               5.468729432052455, 11.527993867731237, -1.6851931822534207,
+               13.216615896813222, 5.971588205506021, -9.180395898761569,
+               5.116795371366372, -16.94044644121189, 21.495355525515556,
+               29.7059984775879, -5.508322146997636, -15.662019394747961,
+               8.545794411636193, -2.0258190582123654, 36.024266407571645,
+               -0.5886000409975387, 10.346090436761651, 0.4200323817099909,
+               -11.14909813323608, 2.8318844927151434, -27.074379433365568,
+               21.98332292344329, 2.2988000731784655, 32.58917505543229]
+
+        eight = [9.510190577993251, -14.198928618436291, 12.214527069781099,
+                 -18.68195263288503, -25.07266800478204, 5.828924710349257,
+                 -8.86583746436866, 0.02210703263248262, 1.4868264830332811,
+                 -11.79041892376144, -11.37337465637004, -2.7035723024766414,
+                 23.56173993146409, -30.47133600859524, 11.878923752568431,
+                 6.659007424270365, 21.261996745527256, -6.083678472686013,
+                 7.400376198325763, 5.341975815444621]
+
+        one, two, eight = xp.asarray(one), xp.asarray(two), xp.asarray(eight)
+        soln = stats.alexandergovern(one, two, eight)
+        xp_assert_close(soln.statistic, xp.asarray(1.3599405447999450836))
+        xp_assert_close(soln.pvalue, xp.asarray(0.50663205309676440091))
+
+    def test_compare_scholar(self, xp):
+        '''
+        Data taken from 'The Modification and Evaluation of the
+        Alexander-Govern Test in Terms of Power' by Kingsley Ochuko, T.,
+        Abdullah, S., Binti Zain, Z., & Soaad Syed Yahaya, S. (2015).
+        '''
+        young = [482.43, 484.36, 488.84, 495.15, 495.24, 502.69, 504.62,
+                 518.29, 519.1, 524.1, 524.12, 531.18, 548.42, 572.1, 584.68,
+                 609.09, 609.53, 666.63, 676.4]
+        middle = [335.59, 338.43, 353.54, 404.27, 437.5, 469.01, 485.85,
+                  487.3, 493.08, 494.31, 499.1, 886.41]
+        old = [519.01, 528.5, 530.23, 536.03, 538.56, 538.83, 557.24, 558.61,
+               558.95, 565.43, 586.39, 594.69, 629.22, 645.69, 691.84]
+        young, middle, old = xp.asarray(young), xp.asarray(middle), xp.asarray(old)
+        soln = stats.alexandergovern(young, middle, old)
+        xp_assert_close(soln.statistic, xp.asarray(5.3237), atol=1e-3)
+        xp_assert_close(soln.pvalue, xp.asarray(0.06982), atol=1e-4)
+
+        # verify with ag.test in r
+        '''
+        > library("onewaytests")
+        > library("tibble")
+        > young <- c(482.43, 484.36, 488.84, 495.15, 495.24, 502.69, 504.62,
+        +                  518.29, 519.1, 524.1, 524.12, 531.18, 548.42, 572.1,
+        +                  584.68, 609.09, 609.53, 666.63, 676.4)
+        > middle <- c(335.59, 338.43, 353.54, 404.27, 437.5, 469.01, 485.85,
+        +                   487.3, 493.08, 494.31, 499.1, 886.41)
+        > old <- c(519.01, 528.5, 530.23, 536.03, 538.56, 538.83, 557.24,
+        +                   558.61, 558.95, 565.43, 586.39, 594.69, 629.22,
+        +                   645.69, 691.84)
+        > young_fct <- c(rep("young", times=19))
+        > middle_fct <-c(rep("middle", times=12))
+        > old_fct <- c(rep("old", times=15))
+        > ag.test(a ~ b, tibble(a=c(young, middle, old), b=factor(c(young_fct,
+        +                                              middle_fct, old_fct))))
+
+        Alexander-Govern Test (alpha = 0.05)
+        -------------------------------------------------------------
+        data : a and b
+
+        statistic  : 5.324629
+        parameter  : 2
+        p.value    : 0.06978651
+
+        Result     : Difference is not statistically significant.
+        -------------------------------------------------------------
+
+        '''
+        xp_assert_close(soln.statistic, xp.asarray(5.324629), rtol=2e-6)
+        xp_assert_close(soln.pvalue, xp.asarray(0.06978651), rtol=2e-6)
+
+    def test_compare_scholar3(self, xp):
+        '''
+        Data taken from 'Robustness And Comparative Power Of WelchAspin,
+        Alexander-Govern And Yuen Tests Under Non-Normality And Variance
+        Heteroscedasticity', by Ayed A. Almoied. 2017. Page 34-37.
+        https://digitalcommons.wayne.edu/cgi/viewcontent.cgi?article=2775&context=oa_dissertations
+        '''
+        x1 = [-1.77559, -1.4113, -0.69457, -0.54148, -0.18808, -0.07152,
+              0.04696, 0.051183, 0.148695, 0.168052, 0.422561, 0.458555,
+              0.616123, 0.709968, 0.839956, 0.857226, 0.929159, 0.981442,
+              0.999554, 1.642958]
+        x2 = [-1.47973, -1.2722, -0.91914, -0.80916, -0.75977, -0.72253,
+              -0.3601, -0.33273, -0.28859, -0.09637, -0.08969, -0.01824,
+              0.260131, 0.289278, 0.518254, 0.683003, 0.877618, 1.172475,
+              1.33964, 1.576766]
+        x1, x2 = xp.asarray(x1), xp.asarray(x2)
+        soln = stats.alexandergovern(x1, x2)
+        xp_assert_close(soln.statistic, xp.asarray(0.713526), atol=1e-5)
+        xp_assert_close(soln.pvalue, xp.asarray(0.398276), atol=1e-5)
+
+        '''
+        tested in ag.test in R:
+        > library("onewaytests")
+        > library("tibble")
+        > x1 <- c(-1.77559, -1.4113, -0.69457, -0.54148, -0.18808, -0.07152,
+        +          0.04696, 0.051183, 0.148695, 0.168052, 0.422561, 0.458555,
+        +          0.616123, 0.709968, 0.839956, 0.857226, 0.929159, 0.981442,
+        +          0.999554, 1.642958)
+        > x2 <- c(-1.47973, -1.2722, -0.91914, -0.80916, -0.75977, -0.72253,
+        +         -0.3601, -0.33273, -0.28859, -0.09637, -0.08969, -0.01824,
+        +         0.260131, 0.289278, 0.518254, 0.683003, 0.877618, 1.172475,
+        +         1.33964, 1.576766)
+        > x1_fact <- c(rep("x1", times=20))
+        > x2_fact <- c(rep("x2", times=20))
+        > a <- c(x1, x2)
+        > b <- factor(c(x1_fact, x2_fact))
+        > ag.test(a ~ b, tibble(a, b))
+        Alexander-Govern Test (alpha = 0.05)
+        -------------------------------------------------------------
+        data : a and b
+
+        statistic  : 0.7135182
+        parameter  : 1
+        p.value    : 0.3982783
+
+        Result     : Difference is not statistically significant.
+        -------------------------------------------------------------
+        '''
+        xp_assert_close(soln.statistic, xp.asarray(0.7135182), rtol=2e-6)
+        xp_assert_close(soln.pvalue, xp.asarray(0.3982783), rtol=2e-6)
+
+    def test_nan_policy_propagate(self, xp):
+        args = xp.asarray([1., 2., 3., 4.]), xp.asarray([1, xp.nan])
+        # default nan_policy is 'propagate'
+        res = stats.alexandergovern(*args)
+        xp_assert_equal(res.pvalue, xp.asarray(xp.nan))
+        xp_assert_equal(res.statistic, xp.asarray(xp.nan))
+
+    @skip_xp_backends(eager_only=True, reason="lazy -> reduced nan_policy capabilities")
+    def test_nan_policy_raise(self, xp):
+        args = xp.asarray([1., 2., 3., 4.]), xp.asarray([1., xp.nan])
+        with assert_raises(ValueError, match="The input contains nan values"):
+            stats.alexandergovern(*args, nan_policy='raise')
+
+    @skip_xp_backends(eager_only=True, reason="lazy -> reduced nan_policy capabilities")
+    def test_nan_policy_omit(self, xp):
+        args_nan = xp.asarray([1, 2, 3, xp.nan, 4]), xp.asarray([1, xp.nan, 19, 25])
+        args_no_nan = xp.asarray([1, 2, 3, 4]), xp.asarray([1, 19, 25])
+        res_nan = stats.alexandergovern(*args_nan, nan_policy='omit')
+        res_no_nan = stats.alexandergovern(*args_no_nan)
+        xp_assert_equal(res_nan.pvalue, res_no_nan.pvalue)
+        xp_assert_equal(res_nan.statistic, res_no_nan.statistic)
+
+    @skip_xp_backends(eager_only=True, reason="lazy -> no data-dependent warnings")
+    def test_constant_input(self, xp):
+        # Zero variance input, consistent with `stats.pearsonr`
+        x1 = xp.asarray([0.667, 0.667, 0.667])
+        x2 = xp.asarray([0.123, 0.456, 0.789])
+        with pytest.warns(RuntimeWarning, match="Precision loss occurred..."):
+            res = stats.alexandergovern(x1, x2)
+        xp_assert_equal(res.statistic, xp.asarray(xp.nan))
+        xp_assert_equal(res.pvalue, xp.asarray(xp.nan))
+
+    @skip_xp_backends('dask.array', reason="Requires `_axis_nan_policy` decorator")
+    @pytest.mark.parametrize('axis', [0, 1, None])
+    def test_2d_input(self, xp, axis):
+        # much more extensive testing for NumPy in `test_axis_nan_policy.py`
+        rng = np.random.default_rng(23498389754392854235)
+        shape = (11, 12)
+        samples = [rng.random(shape) for i in range(3)]
+        xp_samples = [xp.asarray(sample) for sample in samples]
+        ref = stats.alexandergovern(*samples, axis=axis)
+        res = stats.alexandergovern(*xp_samples, axis=axis)
+        xp_assert_close(res.statistic, xp.asarray(ref.statistic))
+        xp_assert_close(res.pvalue, xp.asarray(ref.pvalue))
+
+
+@make_xp_test_case(stats.f_oneway)
+class TestFOneWay:
+
+    def test_trivial(self, xp):
+        # A trivial test of stats.f_oneway, with F=0.
+        F, p = stats.f_oneway(xp.asarray([0, 2]), xp.asarray([0, 2]))
+        xp_assert_equal(F, xp.asarray(0.0))
+        xp_assert_equal(p, xp.asarray(1.0))
+
+    @pytest.mark.parametrize("dtype", [None, "float32", "float64"])
+    def test_basic(self, dtype, xp):
+        # Despite being a floating point calculation, this data should
+        # result in F being exactly 2.0.
+        dtype = None if dtype is None else getattr(xp, dtype)
+        F, p = stats.f_oneway(xp.asarray([0, 2], dtype=dtype),
+                              xp.asarray([2, 4], dtype=dtype))
+        xp_assert_equal(F, xp.asarray(2.0, dtype=dtype))
+        xp_assert_close(p, xp.asarray(1 - 0.5**0.5, dtype=dtype))
+
+    @pytest.mark.parametrize("dtype", [None, "float32", "float64"])
+    def test_unequal_var(self, dtype, xp):
+        # toy samples with unequal variances and different observations
+        dtype = None if dtype is None else getattr(xp, dtype)
+        samples = [xp.asarray([-50.42, 40.31, -18.09, 35.58, -6.8, 0.22], dtype=dtype),
+                   xp.asarray([23.44, 4.5, 15.1, 9.66], dtype=dtype),
+                   xp.asarray([11.94, 11.1 , 9.87, 9.09, 3.33], dtype=dtype)]
+
+        F, p = stats.f_oneway(*samples, equal_var=False)
+
+        # R language as benchmark
+        # group1 <- c(-50.42, 40.31, -18.09, 35.58, -6.8, 0.22)
+        # group2 <- c(23.44, 4.5, 15.1, 9.66)
+        # group3 <- c(11.94, 11.1 , 9.87, 9.09, 3.33)
+        #
+        # data <- data.frame(
+        #     value = c(group1, group2, group3),
+        #     group = factor(c(rep("G1", length(group1)),
+        #                      rep("G2", length(group2)),
+        #                      rep("G3", length(group3))))
+        # )
+        # welch_anova <- oneway.test(value ~ group, data = data, var.equal = FALSE)
+        # welch_anova$statistic
+        ## F: 0.609740409019517
+        # welch_anova$p.value
+        ## 0.574838941286302
+
+        xp_assert_close(F, xp.asarray(0.609740409019517, dtype=dtype))
+        xp_assert_close(p, xp.asarray(0.574838941286302, dtype=dtype))
+
+    def test_equal_var_input_validation(self, xp):
+        samples = [xp.asarray([-50.42, 40.31, -18.09, 35.58, -6.8, 0.22]),
+                   xp.asarray([23.44, 4.5, 15.1, 9.66]),
+                   xp.asarray([11.94, 11.1 , 9.87, 9.09, 3.33])]
+
+        message = "Expected a boolean value for 'equal_var'"
+        with pytest.raises(TypeError, match=message):
+            stats.f_oneway(*samples, equal_var="False")
+
+    def test_known_exact(self, xp):
+        # Another trivial dataset for which the exact F and p can be
+        # calculated on most platforms
+        F, p = stats.f_oneway(xp.asarray([2]), xp.asarray([2]),
+                              xp.asarray([2, 3, 4]))
+        xp_assert_close(F, xp.asarray(3/5))  # assert_equal fails on some CI platforms
+        xp_assert_close(p, xp.asarray(5/8))
+
+    def test_large_integer_array(self, xp):
+        a = xp.asarray([655, 788], dtype=xp.uint16)
+        b = xp.asarray([789, 772], dtype=xp.uint16)
+        F, p = stats.f_oneway(a, b)
+        # The expected value was verified by computing it with mpmath with
+        # 40 digits of precision.
+        xp_assert_close(F, xp.asarray(0.77450216931805540))
+
+    def test_result_attributes(self, xp):
+        a = xp.asarray([655, 788], dtype=xp.uint16)
+        b = xp.asarray([789, 772], dtype=xp.uint16)
+        res = stats.f_oneway(a, b)
+        attributes = ('statistic', 'pvalue')
+        check_named_results(res, attributes, xp=xp)
+
+    @pytest.mark.parametrize('test_case',
+        ['SiRstv', 'SmLs01', 'SmLs02', 'SmLs03', 'AtmWtAg', 'SmLs04', 'SmLs05',
+         'SmLs06', 'SmLs07', 'SmLs08', 'SmLs09'])
+    def test_nist(self, test_case, xp):
+        # These are the nist ANOVA files. They can be found at:
+        # https://www.itl.nist.gov/div898/strd/anova/anova.html
+        filename = test_case + ".dat"
+        rtol = 1e-7
+        fname = os.path.abspath(os.path.join(os.path.dirname(__file__),
+                                             'data/nist_anova', filename))
+        with open(fname) as f:
+            content = f.read().split('\n')
+        certified = [line.split() for line in content[40:48]
+                     if line.strip()]
+        dataf = np.loadtxt(fname, skiprows=60)
+        y, x = dataf.T
+        y = y.astype(int)
+        caty = np.unique(y)
+        f = float(certified[0][-1])
+
+        xlist = [xp.asarray(x[y == i]) for i in caty]
+        res = stats.f_oneway(*xlist)
+
+        # With the hard test cases we relax the tolerance a bit.
+        hard_tc = ('SmLs07', 'SmLs08', 'SmLs09')
+        if test_case in hard_tc:
+            rtol = 1e-4
+
+        xp_assert_close(res[0], xp.asarray(f, dtype=xp.float64), rtol=rtol)
+
+    @pytest.mark.filterwarnings('ignore')  # Dask emits NumPy warnings
+    @pytest.mark.parametrize("a, b, expected", [
+        (np.array([42, 42, 42]), np.array([7, 7, 7]), (np.inf, 0.)),
+        (np.array([42, 42, 42]), np.array([42, 42, 42]), (np.nan, np.nan))
+        ])
+    def test_constant_input(self, a, b, expected, xp):
+        # For more details, look on https://github.com/scipy/scipy/issues/11669
+        f, p = stats.f_oneway(xp.asarray(a), xp.asarray(b))
+        xp_assert_equal(f, xp.asarray(expected[0]))
+        xp_assert_equal(p, xp.asarray(expected[1]))
+
+    @skip_xp_backends('dask.array', reason='needs _axis_nan_policy')
+    @pytest.mark.parametrize('axis', [-2, -1, 0, 1])
+    def test_2d_inputs(self, axis, xp):
+        a = np.array([[1, 4, 3, 3],
+                      [2, 5, 3, 3],
+                      [3, 6, 3, 3],
+                      [2, 3, 3, 3],
+                      [1, 4, 3, 3]], dtype=np.float64)
+        b = np.array([[3, 1, 5, 3],
+                      [4, 6, 5, 3],
+                      [4, 3, 5, 3],
+                      [1, 5, 5, 3],
+                      [5, 5, 5, 3],
+                      [2, 3, 5, 3],
+                      [8, 2, 5, 3],
+                      [2, 2, 5, 3]], dtype=np.float64)
+        c = np.array([[4, 3, 4, 3],
+                      [4, 2, 4, 3],
+                      [5, 4, 4, 3],
+                      [5, 4, 4, 3]], dtype=np.float64)
+
+        if axis in [-1, 1]:
+            a = a.T
+            b = b.T
+            c = c.T
+            take_axis = 0
+        else:
+            take_axis = 1
+
+        f, p = stats.f_oneway(xp.asarray(a), xp.asarray(b), xp.asarray(c),
+                              axis=axis)
+
+        # Verify that the result computed with the 2d arrays matches
+        # the result of calling f_oneway individually on each slice.
+        for j in [0, 1]:
+            fj, pj = stats.f_oneway(np.take(a, j, take_axis),
+                                    np.take(b, j, take_axis),
+                                    np.take(c, j, take_axis))
+            xp_assert_close(f[j], xp.asarray(fj))
+            xp_assert_close(p[j], xp.asarray(pj))
+        for j in [2, 3]:
+            fj, pj = stats.f_oneway(np.take(a, j, take_axis),
+                                    np.take(b, j, take_axis),
+                                    np.take(c, j, take_axis))
+            xp_assert_close(f[j], xp.asarray(fj))
+            xp_assert_close(p[j], xp.asarray(pj))
+
+    @skip_xp_backends('dask.array', reason='needs _axis_nan_policy')
+    def test_3d_inputs(self, xp):
+        # Some 3-d arrays. (There is nothing special about the values.)
+        a = xp.reshape(1/xp.arange(1.0, 4*5*7 + 1., dtype=xp.float64), (4, 5, 7))
+        b = xp.reshape(2/xp.arange(1.0, 4*8*7 + 1., dtype=xp.float64), (4, 8, 7))
+        c = xp.reshape(1/xp.arange(1.0, 4*4*7 + 1., dtype=xp.float64), (4, 4, 7))
+        c = xp.cos(c)
+
+        f, p = stats.f_oneway(a, b, c, axis=1)
+
+        assert f.shape == (4, 7)
+        assert p.shape == (4, 7)
+
+        for i in range(a.shape[0]):
+            for j in range(a.shape[2]):
+                fij, pij = stats.f_oneway(a[i, :, j], b[i, :, j], c[i, :, j])
+                xp_assert_close(fij, f[i, j])
+                xp_assert_close(pij, p[i, j])
+
+    def test_length0_1d_error(self, xp):
+        # Require at least one value in each group.
+        with eager_warns(SmallSampleWarning, match=too_small_1d_not_omit, xp=xp):
+            result = stats.f_oneway(xp.asarray([1., 2., 3.]), xp.asarray([]),
+                                    xp.asarray([4., 5., 6., 7.]))
+            xp_assert_equal(result.statistic, xp.asarray(xp.nan))
+            xp_assert_equal(result.pvalue, xp.asarray(xp.nan))
+
+    @skip_xp_backends('dask.array', reason='needs _axis_nan_policy')
+    def test_length0_2d_error(self, xp):
+        with eager_warns(SmallSampleWarning, match=too_small_nd_not_omit, xp=xp):
+            ncols = 3
+            a = xp.ones((4, ncols))
+            b = xp.ones((0, ncols))
+            c = xp.ones((5, ncols))
+            f, p = stats.f_oneway(a, b, c)
+            nans = xp.full((ncols,), fill_value=xp.nan)
+            xp_assert_equal(f, nans)
+            xp_assert_equal(p, nans)
+
+    def test_all_length_one(self, xp):
+        samples = xp.asarray([10]), xp.asarray([11]), xp.asarray([12]), xp.asarray([13])
+        with eager_warns(SmallSampleWarning, xp=xp):
+            result = stats.f_oneway(*samples)
+            xp_assert_equal(result.statistic, xp.asarray(xp.nan))
+            xp_assert_equal(result.pvalue, xp.asarray(xp.nan))
+
+    @skip_xp_backends('dask.array', reason='lazy->reduced input validation')
+    @pytest.mark.parametrize('args', [(), ([1, 2, 3],)])
+    def test_too_few_inputs(self, args, xp):
+        args = [xp.asarray(arg) for arg in args]
+        message = "At least two samples are required..."
+        with pytest.raises(TypeError, match=message):
+            stats.f_oneway(*args)
+
+    @skip_xp_backends('dask.array', reason='lazy->reduced input validation')
+    def test_axis_error(self, xp):
+        a = xp.ones((3, 4))
+        b = xp.ones((5, 4))
+        with pytest.raises(AxisError):
+            stats.f_oneway(a, b, axis=2)
+
+    def test_bad_shapes(self, xp):
+        a = xp.ones((3, 4))
+        b = xp.ones((5, 4))
+        with pytest.raises(ValueError):
+            stats.f_oneway(a, b, axis=1)
+
+
+@make_xp_test_case(stats.kruskal)
+class TestKruskal:
+    def test_array_like(self):
+        h, p = stats.kruskal([1], [2])
+        assert_equal(h, 1.0)
+        assert_allclose(p, stats.chi2.sf(h, 1))
+
+    def test_simple(self, xp):
+        x = xp.asarray([1])
+        y = xp.asarray([2])
+        h, p = stats.kruskal(x, y)
+        xp_assert_close(h, xp.asarray(1.0))
+        dtype = xp_default_dtype(xp)
+        xp_assert_close(p, xp.asarray(stats.chi2.sf(1, 1), dtype=dtype))
+
+    @pytest.mark.parametrize("dtype", ['float32', 'float64', None])
+    def test_basic(self, xp, dtype):
+        dtype = xp_default_dtype(xp) if dtype is None else getattr(xp, dtype)
+        x = xp.asarray([1, 3, 5, 7, 9], dtype=dtype)
+        y = xp.asarray([2, 4, 6, 8, 10], dtype=dtype)
+        h, p = stats.kruskal(x, y)
+        xp_assert_close(h, xp.asarray(3/11, dtype=dtype))
+        xp_assert_close(p, xp.asarray(stats.chi2.sf(3/11, 1), dtype=dtype))
+
+    def test_simple_tie(self, xp):
+        x = [1]
+        y = [1, 2]
+        h, p = stats.kruskal(xp.asarray(x), xp.asarray(y))
+
+        h_uncorr = 1.5**2 + 2*2.25**2 - 12
+        corr = 0.75
+        expected = xp.asarray(h_uncorr / corr)   # 0.5
+
+        # Since the expression is simple and the exact answer is 0.5, it
+        # should be safe to use assert_equal().
+        xp_assert_equal(h, expected)
+        xp_assert_close(p, special.chdtrc(xp.asarray(1.), expected))
+
+    def test_another_tie(self, xp):
+        x = [1, 1, 1, 2]
+        y = [2, 2, 2, 2]
+        h, p = stats.kruskal(xp.asarray(x), xp.asarray(y))
+
+        h_uncorr = (12. / 8. / 9.) * 4 * (3**2 + 6**2) - 3 * 9
+        corr = 1 - float(3**3 - 3 + 5**3 - 5) / (8**3 - 8)
+        expected = xp.asarray(h_uncorr / corr)
+
+        xp_assert_close(h, expected)
+        xp_assert_close(p, special.chdtrc(xp.asarray(1.), expected))
+
+    def test_three_groups(self, xp):
+        # A test of stats.kruskal with three groups, with ties.
+        x = [1, 1, 1]
+        y = [2, 2, 2]
+        z = [2, 2]
+        h, p = stats.kruskal(xp.asarray(x), xp.asarray(y), xp.asarray(z))
+
+        h_uncorr = (12. / 8. / 9.) * (3*2**2 + 3*6**2 + 2*6**2) - 3 * 9  # 5.0
+        corr = 1 - float(3**3 - 3 + 5**3 - 5) / (8**3 - 8)
+        expected = xp.asarray(h_uncorr / corr)  # 7.0
+
+        xp_assert_close(h, expected)
+        xp_assert_close(p, special.chdtrc(xp.asarray(2.), expected))
+
+    def test_empty(self, xp):
+        # A test of stats.kruskal with three groups, with ties.
+        x = xp.asarray([1, 1, 1])
+        y = xp.asarray([2, 2, 2])
+        z = xp.asarray([], dtype=y.dtype)
+        with pytest.warns(SmallSampleWarning, match=too_small_1d_not_omit):
+            res = stats.kruskal(x, y, z)
+        xp_assert_equal(res.statistic, xp.asarray(xp.nan))
+        xp_assert_equal(res.pvalue, xp.asarray(xp.nan))
+
+    @skip_xp_backends('jax.numpy', reason='needs jax-ml/jax#34628')
+    def test_nan_policy_propagate(self, xp):
+        x = xp.arange(10.)
+        x = xpx.at(x)[9].set(xp.nan)
+
+        res = stats.kruskal(x, x)
+        xp_assert_equal(res.statistic, xp.asarray(xp.nan))
+        xp_assert_equal(res.pvalue, xp.asarray(xp.nan))
+
+    @skip_xp_backends('jax.numpy', reason='lazy -> reduced nan_policy capabilities')
+    @xfail_xp_backends('cupy', reason='cupy returns small but nonzero res.statistic')
+    def test_nan_policy_omit_raise(self, xp):
+        x = xp.arange(10.)
+        x = xpx.at(x)[9].set(xp.nan)
+
+        res = stats.kruskal(x, x, nan_policy='omit')
+        xp_assert_equal(res.statistic, xp.asarray(0.0))
+        xp_assert_equal(res.pvalue, xp.asarray(1.0))
+
+        with pytest.raises(ValueError, match='The input contains nan values'):
+            stats.kruskal(x, x, nan_policy='raise')
+
+        with pytest.raises(ValueError, match='nan_policy must be one of...'):
+            stats.kruskal(x, x, nan_policy='foobar')
+
+    def test_large_samples(self, xp):
+        # Test to see if large samples are handled correctly.
+        n = 50000
+        rng = np.random.default_rng(1808365978)
+        x = xp.asarray(rng.standard_normal(n))
+        y = xp.asarray(rng.standard_normal(n) + 50)
+        h, p = stats.kruskal(x, y)
+        xp_assert_close(p, xp.asarray(0., dtype=x.dtype))
+
+    def test_no_args_gh20661(self, xp):
+        message = r"Need at least two groups in stats.kruskal\(\)"
+        with pytest.raises(ValueError, match=message):
+            stats.kruskal()
+
+
+@make_xp_test_case(stats.combine_pvalues)
+class TestCombinePvalues:
+    # Reference values computed using the following R code:
+    # options(digits=16)
+    # library(metap)
+    # x = c(0.01, 0.2, 0.3)
+    # sumlog(x)  # fisher
+    # sumz(x)  # stouffer
+    # sumlog(1-x)  # pearson (negative statistic and complement of p-value)
+    # minimump(x)  # tippett
+    @pytest.mark.parametrize(
+        "method, expected_statistic, expected_pvalue",
+        [("fisher", 14.83716180549625 , 0.02156175132483465),
+         ("stouffer", 2.131790594240385, 0.01651203260896294),
+         ("pearson", -1.179737662212887, 1-0.9778736999143087),
+         ("tippett", 0.01, 0.02970100000000002),
+         # mudholkar_george: library(transite); p_combine(x, method="MG")
+         ("mudholkar_george", 6.828712071641684, 0.01654551838539527)])
+    def test_reference_values(self, xp, method, expected_statistic, expected_pvalue):
+        x = [.01, .2, .3]
+        res = stats.combine_pvalues(xp.asarray(x), method=method)
+        xp_assert_close(res.statistic, xp.asarray(expected_statistic))
+        xp_assert_close(res.pvalue, xp.asarray(expected_pvalue))
+
+    @pytest.mark.parametrize(
+        # Reference values computed using R `metap` `sumz`:
+        # options(digits=16)
+        # library(metap)
+        # x = c(0.01, 0.2, 0.3)
+        # sumz(x, weights=c(1., 1., 1.))
+        # sumz(x, weights=c(1., 4., 9.))
+        "weights, expected_statistic, expected_pvalue",
+        [([1., 1., 1.], 2.131790594240385, 0.01651203260896294),
+         ([1., 4., 9.], 1.051815015753598, 0.1464422142261314)])
+    def test_weighted_stouffer(self, xp, weights, expected_statistic, expected_pvalue):
+        x = xp.asarray([.01, .2, .3])
+        res = stats.combine_pvalues(x, method='stouffer', weights=xp.asarray(weights))
+        xp_assert_close(res.statistic, xp.asarray(expected_statistic))
+        xp_assert_close(res.pvalue, xp.asarray(expected_pvalue))
+
+    methods = ["fisher", "pearson", "tippett", "stouffer", "mudholkar_george"]
+
+    @pytest.mark.parametrize("variant", ["single", "all", "random"])
+    @pytest.mark.parametrize("method", methods)
+    def test_monotonicity(self, variant, method, xp):
+        # Test that result increases monotonically with respect to input.
+        m, n = 10, 7
+        rng = np.random.default_rng(278448169958891062669391462690811630763)
+
+        # `pvaluess` is an m × n array of p values. Each row corresponds to
+        # a set of p values to be combined with p values increasing
+        # monotonically down one column (single), simultaneously down each
+        # column (all), or independently down each column (random).
+        if variant == "single":
+            pvaluess = xp.broadcast_to(xp.asarray(rng.random(n)), (m, n))
+            pvaluess = xp.concat([xp.reshape(xp.linspace(0.1, 0.9, m), (-1, 1)),
+                                  pvaluess[:, 1:]], axis=1)
+        elif variant == "all":
+            pvaluess = xp.broadcast_to(xp.linspace(0.1, 0.9, m), (n, m)).T
+        elif variant == "random":
+            pvaluess = xp.sort(xp.asarray(rng.uniform(0, 1, size=(m, n))), axis=0)
+
+        combined_pvalues = xp.asarray([
+            float(stats.combine_pvalues(pvaluess[i, :], method=method)[1])
+            for i in range(pvaluess.shape[0])
+        ])
+        assert xp.all(combined_pvalues[1:] - combined_pvalues[:-1] >= 0)
+
+    @pytest.mark.parametrize("method", methods)
+    def test_result(self, method, xp):
+        res = stats.combine_pvalues(xp.asarray([.01, .2, .3]), method=method)
+        xp_assert_equal(res.statistic, res[0])
+        xp_assert_equal(res.pvalue, res[1])
+
+    @pytest.mark.parametrize("method", methods)
+    @pytest.mark.parametrize("axis", [0, 1, None])
+    def test_axis(self, method, axis, xp):
+        rng = np.random.default_rng(234892349810482)
+        x = xp.asarray(rng.random(size=(2, 10)))
+        x = x.T if (axis == 0) else x
+        res = stats.combine_pvalues(x, axis=axis, method=method)
+
+        if axis is None:
+            x = xp.reshape(x, (-1,))
+            ref = stats.combine_pvalues(x, method=method)
+            xp_assert_close(res.statistic, ref.statistic)
+            xp_assert_close(res.pvalue, ref.pvalue)
+            return
+
+        x = x.T if (axis == 0) else x
+        x0, x1 = x[0, :], x[1, :]
+        ref0 = stats.combine_pvalues(x0, method=method)
+        ref1 = stats.combine_pvalues(x1, method=method)
+
+        xp_assert_close(res.statistic[0], ref0.statistic)
+        xp_assert_close(res.statistic[1], ref1.statistic)
+        xp_assert_close(res.pvalue[0], ref0.pvalue)
+        xp_assert_close(res.pvalue[1], ref1.pvalue)
+
+
+class TestCdfDistanceValidation:
+    """
+    Test that _cdf_distance() (via wasserstein_distance()) raises ValueErrors
+    for bad inputs.
+    """
+
+    def test_distinct_value_and_weight_lengths(self):
+        # When the number of weights does not match the number of values,
+        # a ValueError should be raised.
+        assert_raises(ValueError, stats.wasserstein_distance,
+                      [1], [2], [4], [3, 1])
+        assert_raises(ValueError, stats.wasserstein_distance, [1], [2], [1, 0])
+
+    def test_zero_weight(self):
+        # When a distribution is given zero weight, a ValueError should be
+        # raised.
+        assert_raises(ValueError, stats.wasserstein_distance,
+                      [0, 1], [2], [0, 0])
+        assert_raises(ValueError, stats.wasserstein_distance,
+                      [0, 1], [2], [3, 1], [0])
+
+    def test_negative_weights(self):
+        # A ValueError should be raised if there are any negative weights.
+        assert_raises(ValueError, stats.wasserstein_distance,
+                      [0, 1], [2, 2], [1, 1], [3, -1])
+
+    def test_empty_distribution(self):
+        # A ValueError should be raised when trying to measure the distance
+        # between something and nothing.
+        assert_raises(ValueError, stats.wasserstein_distance, [], [2, 2])
+        assert_raises(ValueError, stats.wasserstein_distance, [1], [])
+
+    def test_inf_weight(self):
+        # An inf weight is not valid.
+        assert_raises(ValueError, stats.wasserstein_distance,
+                      [1, 2, 1], [1, 1], [1, np.inf, 1], [1, 1])
+
+
+class TestWassersteinDistanceND:
+    """ Tests for wasserstein_distance_nd() output values.
+    """
+
+    def test_published_values(self):
+        # Compare against published values and manually computed results.
+        # The values and computed result are posted at James D. McCaffrey's blog,
+        # https://jamesmccaffrey.wordpress.com/2018/03/05/earth-mover-distance
+        # -wasserstein-metric-example-calculation/
+        u = [(1,1), (1,1), (1,1), (1,1), (1,1), (1,1), (1,1), (1,1), (1,1), (1,1),
+             (4,2), (6,1), (6,1)]
+        v = [(2,1), (2,1), (3,2), (3,2), (3,2), (5,1), (5,1), (5,1), (5,1), (5,1),
+             (5,1), (5,1), (7,1)]
+
+        res = stats.wasserstein_distance_nd(u, v)
+        # In original post, the author kept two decimal places for ease of calculation.
+        # This test uses the more precise value of distance to get the precise results.
+        # For comparison, please see the table and figure in the original blog post.
+        flow = np.array([2., 3., 5., 1., 1., 1.])
+        dist = np.array([1.00, 5**0.5, 4.00, 2**0.5, 1.00, 1.00])
+        ref = np.sum(flow * dist)/np.sum(flow)
+        assert_allclose(res, ref)
+
+    @pytest.mark.parametrize('n_value', (4, 15, 35))
+    @pytest.mark.parametrize('ndim', (3, 4, 7))
+    @pytest.mark.parametrize('max_repeats', (5, 10))
+    def test_same_distribution_nD(self, ndim, n_value, max_repeats):
+        # Any distribution moved to itself should have a Wasserstein distance
+        # of zero.
+        rng = np.random.default_rng(363836384995579937222333)
+        repeats = rng.integers(1, max_repeats, size=n_value, dtype=int)
+
+        u_values = rng.random(size=(n_value, ndim))
+        v_values = np.repeat(u_values, repeats, axis=0)
+        v_weights = rng.random(np.sum(repeats))
+        range_repeat = np.repeat(np.arange(len(repeats)), repeats)
+        u_weights = np.bincount(range_repeat, weights=v_weights)
+        index = rng.permutation(len(v_weights))
+        v_values, v_weights = v_values[index], v_weights[index]
+
+        res = stats.wasserstein_distance_nd(u_values, v_values, u_weights, v_weights)
+        assert_allclose(res, 0, atol=1e-15)
+
+    @pytest.mark.parametrize('nu', (8, 9, 38))
+    @pytest.mark.parametrize('nv', (8, 12, 17))
+    @pytest.mark.parametrize('ndim', (3, 5, 23))
+    def test_collapse_nD(self, nu, nv, ndim):
+        # test collapse for n dimensional values
+        # Collapsing a n-D distribution to a point distribution at zero
+        # is equivalent to taking the average of the norm of data.
+        rng = np.random.default_rng(38573488467338826109)
+        u_values = rng.random(size=(nu, ndim))
+        v_values = np.zeros((nv, ndim))
+        u_weights = rng.random(size=nu)
+        v_weights = rng.random(size=nv)
+        ref = np.average(np.linalg.norm(u_values, axis=1), weights=u_weights)
+        res = stats.wasserstein_distance_nd(u_values, v_values, u_weights, v_weights)
+        assert_allclose(res, ref)
+
+    @pytest.mark.parametrize('nu', (8, 16, 32))
+    @pytest.mark.parametrize('nv', (8, 16, 32))
+    @pytest.mark.parametrize('ndim', (1, 2, 6))
+    def test_zero_weight_nD(self, nu, nv, ndim):
+        # Values with zero weight have no impact on the Wasserstein distance.
+        rng = np.random.default_rng(38573488467338826109)
+        u_values = rng.random(size=(nu, ndim))
+        v_values = rng.random(size=(nv, ndim))
+        u_weights = rng.random(size=nu)
+        v_weights = rng.random(size=nv)
+        ref = stats.wasserstein_distance_nd(u_values, v_values, u_weights, v_weights)
+
+        add_row, nrows = rng.integers(0, nu, size=2)
+        add_value = rng.random(size=(nrows, ndim))
+        u_values = np.insert(u_values, add_row, add_value, axis=0)
+        u_weights = np.insert(u_weights, add_row, np.zeros(nrows), axis=0)
+        res = stats.wasserstein_distance_nd(u_values, v_values, u_weights, v_weights)
+        assert_allclose(res, ref)
+
+    def test_inf_values(self):
+        # Inf values can lead to an inf distance or trigger a RuntimeWarning
+        # (and return NaN) if the distance is undefined.
+        uv, vv, uw = [[1, 1], [2, 1]], [[np.inf, -np.inf]], [1, 1]
+        distance = stats.wasserstein_distance_nd(uv, vv, uw)
+        assert_equal(distance, np.inf)
+        with np.errstate(invalid='ignore'):
+            uv, vv = [[np.inf, np.inf]], [[np.inf, -np.inf]]
+            distance = stats.wasserstein_distance_nd(uv, vv)
+            assert_equal(distance, np.nan)
+
+    @pytest.mark.parametrize('nu', (10, 15, 20))
+    @pytest.mark.parametrize('nv', (10, 15, 20))
+    @pytest.mark.parametrize('ndim', (1, 3, 5))
+    def test_multi_dim_nD(self, nu, nv, ndim):
+        # Adding dimension on distributions do not affect the result
+        rng = np.random.default_rng(2736495738494849509)
+        u_values = rng.random(size=(nu, ndim))
+        v_values = rng.random(size=(nv, ndim))
+        u_weights = rng.random(size=nu)
+        v_weights = rng.random(size=nv)
+        ref = stats.wasserstein_distance_nd(u_values, v_values, u_weights, v_weights)
+
+        add_dim = rng.integers(0, ndim)
+        add_value = rng.random()
+
+        u_values = np.insert(u_values, add_dim, add_value, axis=1)
+        v_values = np.insert(v_values, add_dim, add_value, axis=1)
+        res = stats.wasserstein_distance_nd(u_values, v_values, u_weights, v_weights)
+        assert_allclose(res, ref)
+
+    @pytest.mark.parametrize('nu', (7, 13, 19))
+    @pytest.mark.parametrize('nv', (7, 13, 19))
+    @pytest.mark.parametrize('ndim', (2, 4, 7))
+    def test_orthogonal_nD(self, nu, nv, ndim):
+        # orthogonal transformations do not affect the result of the
+        # wasserstein_distance
+        rng = np.random.default_rng(34746837464536)
+        u_values = rng.random(size=(nu, ndim))
+        v_values = rng.random(size=(nv, ndim))
+        u_weights = rng.random(size=nu)
+        v_weights = rng.random(size=nv)
+        ref = stats.wasserstein_distance_nd(u_values, v_values, u_weights, v_weights)
+
+        dist = stats.ortho_group(ndim)
+        transform = dist.rvs(random_state=rng)
+        shift = rng.random(size=ndim)
+        res = stats.wasserstein_distance_nd(u_values @ transform + shift,
+                                         v_values @ transform + shift,
+                                         u_weights, v_weights)
+        assert_allclose(res, ref)
+
+    def test_error_code(self):
+        rng = np.random.default_rng(52473644737485644836320101)
+        with pytest.raises(ValueError, match='Invalid input values. The inputs'):
+            u_values = rng.random(size=(4, 10, 15))
+            v_values = rng.random(size=(6, 2, 7))
+            _ = stats.wasserstein_distance_nd(u_values, v_values)
+        with pytest.raises(ValueError, match='Invalid input values. Dimensions'):
+            u_values = rng.random(size=(15,))
+            v_values = rng.random(size=(3, 15))
+            _ = stats.wasserstein_distance_nd(u_values, v_values)
+        with pytest.raises(ValueError,
+            match='Invalid input values. If two-dimensional'):
+            u_values = rng.random(size=(2, 10))
+            v_values = rng.random(size=(2, 2))
+            _ = stats.wasserstein_distance_nd(u_values, v_values)
+
+    @pytest.mark.parametrize('u_size', [1, 10, 50])
+    @pytest.mark.parametrize('v_size', [1, 10, 50])
+    def test_optimization_vs_analytical(self, u_size, v_size):
+        rng = np.random.default_rng(45634745675)
+        # Test when u_weights = None, v_weights = None
+        u_values = rng.random(size=(u_size, 1))
+        v_values = rng.random(size=(v_size, 1))
+        u_values_flat = u_values.ravel()
+        v_values_flat = v_values.ravel()
+        # These three calculations are done using different backends
+        # but they must be equal
+        d1 = stats.wasserstein_distance(u_values_flat, v_values_flat)
+        d2 = stats.wasserstein_distance_nd(u_values, v_values)
+        d3 = stats.wasserstein_distance_nd(u_values_flat, v_values_flat)
+        assert_allclose(d2, d1)
+        assert_allclose(d3, d1)
+        # Test with u_weights and v_weights specified.
+        u_weights = rng.random(size=u_size)
+        v_weights = rng.random(size=v_size)
+        d1 = stats.wasserstein_distance(u_values_flat, v_values_flat,
+                                        u_weights, v_weights)
+        d2 = stats.wasserstein_distance_nd(u_values, v_values,
+                                        u_weights, v_weights)
+        d3 = stats.wasserstein_distance_nd(u_values_flat, v_values_flat,
+                                        u_weights, v_weights)
+        assert_allclose(d2, d1)
+        assert_allclose(d3, d1)
+
+
+class TestWassersteinDistance:
+    """ Tests for wasserstein_distance() output values.
+    """
+
+    def test_simple(self):
+        # For basic distributions, the value of the Wasserstein distance is
+        # straightforward.
+        assert_allclose(
+            stats.wasserstein_distance([0, 1], [0], [1, 1], [1]),
+            .5)
+        assert_allclose(stats.wasserstein_distance(
+            [0, 1], [0], [3, 1], [1]),
+            .25)
+        assert_allclose(stats.wasserstein_distance(
+            [0, 2], [0], [1, 1], [1]),
+            1)
+        assert_allclose(stats.wasserstein_distance(
+            [0, 1, 2], [1, 2, 3]),
+            1)
+
+    def test_same_distribution(self):
+        # Any distribution moved to itself should have a Wasserstein distance
+        # of zero.
+        assert_equal(stats.wasserstein_distance([1, 2, 3], [2, 1, 3]), 0)
+        assert_equal(
+            stats.wasserstein_distance([1, 1, 1, 4], [4, 1],
+                                       [1, 1, 1, 1], [1, 3]),
+            0)
+
+    def test_shift(self):
+        # If the whole distribution is shifted by x, then the Wasserstein
+        # distance should be the norm of x.
+        assert_allclose(stats.wasserstein_distance([0], [1]), 1)
+        assert_allclose(stats.wasserstein_distance([-5], [5]), 10)
+        assert_allclose(
+            stats.wasserstein_distance([1, 2, 3, 4, 5], [11, 12, 13, 14, 15]),
+            10)
+        assert_allclose(
+            stats.wasserstein_distance([4.5, 6.7, 2.1], [4.6, 7, 9.2],
+                                       [3, 1, 1], [1, 3, 1]),
+            2.5)
+
+    def test_combine_weights(self):
+        # Assigning a weight w to a value is equivalent to including that value
+        # w times in the value array with weight of 1.
+        assert_allclose(
+            stats.wasserstein_distance(
+                [0, 0, 1, 1, 1, 1, 5], [0, 3, 3, 3, 3, 4, 4],
+                [1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1]),
+            stats.wasserstein_distance([5, 0, 1], [0, 4, 3],
+                                       [1, 2, 4], [1, 2, 4]))
+
+    def test_collapse(self):
+        # Collapsing a distribution to a point distribution at zero is
+        # equivalent to taking the average of the absolute values of the
+        # values.
+        u = np.arange(-10, 30, 0.3)
+        v = np.zeros_like(u)
+        assert_allclose(
+            stats.wasserstein_distance(u, v),
+            np.mean(np.abs(u)))
+
+        u_weights = np.arange(len(u))
+        v_weights = u_weights[::-1]
+        assert_allclose(
+            stats.wasserstein_distance(u, v, u_weights, v_weights),
+            np.average(np.abs(u), weights=u_weights))
+
+    def test_zero_weight(self):
+        # Values with zero weight have no impact on the Wasserstein distance.
+        assert_allclose(
+            stats.wasserstein_distance([1, 2, 100000], [1, 1],
+                                       [1, 1, 0], [1, 1]),
+            stats.wasserstein_distance([1, 2], [1, 1], [1, 1], [1, 1]))
+
+    def test_inf_values(self):
+        # Inf values can lead to an inf distance or trigger a RuntimeWarning
+        # (and return NaN) if the distance is undefined.
+        assert_equal(
+            stats.wasserstein_distance([1, 2, np.inf], [1, 1]),
+            np.inf)
+        assert_equal(
+            stats.wasserstein_distance([1, 2, np.inf], [-np.inf, 1]),
+            np.inf)
+        assert_equal(
+            stats.wasserstein_distance([1, -np.inf, np.inf], [1, 1]),
+            np.inf)
+        with pytest.warns(RuntimeWarning, match="invalid value"):
+            assert_equal(
+                stats.wasserstein_distance([1, 2, np.inf], [np.inf, 1]),
+                np.nan)
+
+
+class TestEnergyDistance:
+    """ Tests for energy_distance() output values.
+    """
+
+    def test_simple(self):
+        # For basic distributions, the value of the energy distance is
+        # straightforward.
+        assert_almost_equal(
+            stats.energy_distance([0, 1], [0], [1, 1], [1]),
+            np.sqrt(2) * .5)
+        assert_almost_equal(stats.energy_distance(
+            [0, 1], [0], [3, 1], [1]),
+            np.sqrt(2) * .25)
+        assert_almost_equal(stats.energy_distance(
+            [0, 2], [0], [1, 1], [1]),
+            2 * .5)
+        assert_almost_equal(
+            stats.energy_distance([0, 1, 2], [1, 2, 3]),
+            np.sqrt(2) * (3*(1./3**2))**.5)
+
+    def test_same_distribution(self):
+        # Any distribution moved to itself should have a energy distance of
+        # zero.
+        assert_equal(stats.energy_distance([1, 2, 3], [2, 1, 3]), 0)
+        assert_equal(
+            stats.energy_distance([1, 1, 1, 4], [4, 1], [1, 1, 1, 1], [1, 3]),
+            0)
+
+    def test_shift(self):
+        # If a single-point distribution is shifted by x, then the energy
+        # distance should be sqrt(2) * sqrt(x).
+        assert_almost_equal(stats.energy_distance([0], [1]), np.sqrt(2))
+        assert_almost_equal(
+            stats.energy_distance([-5], [5]),
+            np.sqrt(2) * 10**.5)
+
+    def test_combine_weights(self):
+        # Assigning a weight w to a value is equivalent to including that value
+        # w times in the value array with weight of 1.
+        assert_almost_equal(
+            stats.energy_distance([0, 0, 1, 1, 1, 1, 5], [0, 3, 3, 3, 3, 4, 4],
+                                  [1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1]),
+            stats.energy_distance([5, 0, 1], [0, 4, 3], [1, 2, 4], [1, 2, 4]))
+
+    def test_zero_weight(self):
+        # Values with zero weight have no impact on the energy distance.
+        assert_almost_equal(
+            stats.energy_distance([1, 2, 100000], [1, 1], [1, 1, 0], [1, 1]),
+            stats.energy_distance([1, 2], [1, 1], [1, 1], [1, 1]))
+
+    def test_inf_values(self):
+        # Inf values can lead to an inf distance or trigger a RuntimeWarning
+        # (and return NaN) if the distance is undefined.
+        assert_equal(stats.energy_distance([1, 2, np.inf], [1, 1]), np.inf)
+        assert_equal(
+            stats.energy_distance([1, 2, np.inf], [-np.inf, 1]),
+            np.inf)
+        assert_equal(
+            stats.energy_distance([1, -np.inf, np.inf], [1, 1]),
+            np.inf)
+        with pytest.warns(RuntimeWarning, match="invalid value"):
+            assert_equal(
+                stats.energy_distance([1, 2, np.inf], [np.inf, 1]),
+                np.nan)
+
+
+@make_xp_test_case(stats.brunnermunzel)
+class TestBrunnerMunzel:
+    # Data from (Lumley, 1996)
+    X = [1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 4, 1, 1]
+    Y = [3, 3, 4, 3, 1, 2, 3, 1, 1, 5, 4]
+
+    def test_brunnermunzel_one_sided(self, xp):
+        # Results are compared with R's lawstat package.
+        X, Y = xp.asarray(self.X), xp.asarray(self.Y)
+        u1, p1 = stats.brunnermunzel(X, Y, alternative='less')
+        u2, p2 = stats.brunnermunzel(Y, X, alternative='greater')
+        u3, p3 = stats.brunnermunzel(X, Y, alternative='greater')
+        u4, p4 = stats.brunnermunzel(Y, X, alternative='less')
+
+        xp_assert_close(p1, p2)
+        xp_assert_close(p3, p4)
+        assert p1 != p3
+        xp_assert_close(u1, xp.asarray(3.1374674823029505))
+        xp_assert_close(u2, xp.asarray(-3.1374674823029505))
+        xp_assert_close(u3, xp.asarray(3.1374674823029505))
+        xp_assert_close(u4, xp.asarray(-3.1374674823029505))
+
+        xp_assert_close(p1, xp.asarray(0.0028931043330757342))
+        xp_assert_close(p3, xp.asarray(0.99710689566692423))
+
+    def test_brunnermunzel_two_sided(self, xp):
+        # Results are compared with R's lawstat package.
+        X, Y = xp.asarray(self.X), xp.asarray(self.Y)
+        u1, p1 = stats.brunnermunzel(X, Y, alternative='two-sided')
+        u2, p2 = stats.brunnermunzel(Y, X, alternative='two-sided')
+
+        xp_assert_close(p1, xp.asarray(p2))
+        xp_assert_close(u1, xp.asarray(3.1374674823029505))
+        xp_assert_close(u2, xp.asarray(-3.1374674823029505))
+        xp_assert_close(p1, xp.asarray(0.0057862086661515377))
+
+    def test_brunnermunzel_default(self, xp):
+        # The default value for alternative is two-sided
+        X, Y = xp.asarray(self.X), xp.asarray(self.Y)
+        u1, p1 = stats.brunnermunzel(X, Y)
+        u2, p2 = stats.brunnermunzel(Y, X)
+
+        xp_assert_close(p1, p2)
+        xp_assert_close(u1, xp.asarray(3.1374674823029505))
+        xp_assert_close(u2, xp.asarray(-3.1374674823029505))
+        xp_assert_close(p1, xp.asarray(0.0057862086661515377))
+
+    def test_brunnermunzel_alternative_error(self, xp):
+        alternative = "error"
+        distribution = "t"
+        nan_policy = "propagate"
+        assert alternative not in ["two-sided", "greater", "less"]
+        message = "`alternative` must be 'less', 'greater', or 'two-sided'."
+        with pytest.raises(ValueError, match=message):
+            stats.brunnermunzel(xp.asarray(self.X), xp.asarray(self.Y),
+                                alternative, distribution, nan_policy)
+
+    def test_brunnermunzel_distribution_norm(self, xp):
+        X, Y = xp.asarray(self.X), xp.asarray(self.Y)
+        u1, p1 = stats.brunnermunzel(X, Y, distribution="normal")
+        u2, p2 = stats.brunnermunzel(Y, X, distribution="normal")
+        xp_assert_close(p1, xp.asarray(p2))
+        xp_assert_close(u1, xp.asarray(3.1374674823029505))
+        xp_assert_close(u2, xp.asarray(-3.1374674823029505))
+        xp_assert_close(p1, xp.asarray(0.0017041417600383024))
+
+    def test_brunnermunzel_distribution_error(self, xp):
+        alternative = "two-sided"
+        distribution = "error"
+        nan_policy = "propagate"
+        assert distribution not in ["t", "normal"]
+        message = "distribution should be 't' or 'normal'"
+        with pytest.raises(ValueError, match=message):
+            stats.brunnermunzel(xp.asarray(self.X), xp.asarray(self.Y),
+                                alternative, distribution, nan_policy)
+
+    @pytest.mark.parametrize("kwarg_update", [{'y': []}, {'x': []},
+                                              {'x': [], 'y': []}])
+    def test_brunnermunzel_empty_imput(self, kwarg_update, xp):
+        kwargs = {'x': self.X, 'y': self.Y}
+        kwargs.update(kwarg_update)
+        kwargs = {key:xp.asarray(val, dtype=xp_default_dtype(xp))
+                  for key, val in kwargs.items()}
+        with eager_warns(SmallSampleWarning, match=too_small_1d_not_omit, xp=xp):
+            statistic, pvalue = stats.brunnermunzel(**kwargs)
+        xp_assert_equal(statistic, xp.asarray(xp.nan))
+        xp_assert_equal(pvalue, xp.asarray(xp.nan))
+
+    @skip_xp_backends('jax.numpy', reason='needs jax-ml/jax#34628')
+    def test_brunnermunzel_nan_input_propagate(self, xp):
+        X = xp.asarray([1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 4, 1, 1, xp.nan])
+        Y = xp.asarray([3, 3, 4, 3, 1, 2, 3, 1, 1, 5, 4.])
+        u1, p1 = stats.brunnermunzel(X, Y, nan_policy="propagate")
+        u2, p2 = stats.brunnermunzel(Y, X, nan_policy="propagate")
+
+        xp_assert_equal(u1, xp.asarray(xp.nan))
+        xp_assert_equal(p1, xp.asarray(xp.nan))
+        xp_assert_equal(u2, xp.asarray(xp.nan))
+        xp_assert_equal(p2, xp.asarray(xp.nan))
+
+    @skip_xp_backends('jax.numpy', reason='lazy -> reduced nan_policy capabilities')
+    def test_brunnermunzel_nan_input_raise(self, xp):
+        X = xp.asarray([1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 4, 1, 1, xp.nan])
+        Y = xp.asarray([3, 3, 4, 3, 1, 2, 3, 1, 1, 5, 4.])
+        alternative = "two-sided"
+        distribution = "t"
+        nan_policy = "raise"
+
+        message = "The input contains nan values"
+        with pytest.raises(ValueError, match=message):
+            stats.brunnermunzel(X, Y, alternative, distribution, nan_policy)
+        with pytest.raises(ValueError, match=message):
+            stats.brunnermunzel(Y, X, alternative, distribution, nan_policy)
+
+    @skip_xp_backends('jax.numpy', reason='lazy -> reduced nan_policy capabilities')
+    def test_brunnermunzel_nan_input_omit(self, xp):
+        X = xp.asarray([1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 4, 1, 1, np.nan])
+        Y = xp.asarray([3, 3, 4, 3, 1, 2, 3, 1, 1, 5, 4.])
+        u1, p1 = stats.brunnermunzel(X, Y, nan_policy="omit")
+        u2, p2 = stats.brunnermunzel(Y, X, nan_policy="omit")
+
+        xp_assert_close(p1, p2)
+        xp_assert_close(u1, xp.asarray(3.1374674823029505))
+        xp_assert_close(u2, xp.asarray(-3.1374674823029505))
+        xp_assert_close(p1, xp.asarray(0.0057862086661515377))
+
+    @pytest.mark.parametrize("vectorized_call", [False, True])
+    def test_brunnermunzel_return_nan(self, vectorized_call, xp):
+        """ tests that a warning is emitted when p is nan
+        p-value with t-distributions can be nan (0/0) (see gh-15843)
+        """
+        x = xp.asarray([1., 2., 3.])
+        y = xp.asarray([5., 6., 7., 8., 9.])
+
+        if vectorized_call:
+            x = xp.stack((x, x)).T
+            y = xp.stack((y, y)).T
+
+        msg = "p-value cannot be estimated|divide by zero|invalid value encountered"
+        with eager_warns(RuntimeWarning, match=msg, xp=xp):
+            stats.brunnermunzel(x, y, distribution="t")
+
+    def test_brunnermunzel_normal_dist(self, xp):
+        """ tests that a p is 0 for datasets that cause p->nan
+        when t-distribution is used (see gh-15843)
+        """
+        x = xp.asarray([1., 2., 3.])
+        y = xp.asarray([5., 6., 7., 8., 9.])
+
+        with eager_warns(RuntimeWarning, match='divide by zero', xp=xp):
+            _, p = stats.brunnermunzel(x, y, distribution="normal")
+        xp_assert_equal(p, xp.asarray(0.))
+
+
+@_apply_over_batch(('x', 1), ('q', 1), ('p', 1))
+def quantile_test_reference(x, q, p, alternative):
+    res = stats.quantile_test(x, q=q, p=p, alternative=alternative)
+    return res.statistic, res.pvalue, *res.confidence_interval()
+
+
+@make_xp_test_case(stats.quantile_test)
+class TestQuantileTest:
+    r""" Test the non-parametric quantile test,
+    including the computation of confidence intervals
+    """
+
+    def test_quantile_test_iv(self, xp):
+        x = xp.asarray([1, 2, 3])
+
+        message = "`x` must be an array of numbers."
+        with pytest.raises(ValueError, match=message):
+            stats.quantile_test(xp.astype(x, xp.bool))
+
+        message = "`q` must be a scalar or array of numbers."
+        with pytest.raises(ValueError, match=message):
+            stats.quantile_test(x, q=False)
+
+        message = "`p` must be a scalar or array of floats."
+        with pytest.raises(ValueError, match=message):
+            stats.quantile_test(x, p=2)
+
+        # should p == 0. / p == 1. be valid?
+        p = xp.asarray([-1., 0., 1., 1.5, xp.nan])
+        res = stats.quantile_test(x, p=p)
+        xp_assert_equal(res.statistic, xp.full_like(p, xp.nan))
+        xp_assert_equal(res.statistic_type, xp.full_like(p, xp.nan))
+        xp_assert_equal(res.pvalue, xp.full_like(p, xp.nan))
+
+        message = "`axis` must be an integer or None."
+        with pytest.raises(ValueError, match=message):
+            stats.quantile_test(x, axis=2.5)
+
+        message = "`axis` is not compatible with the shapes of the inputs."
+        with pytest.raises(ValueError, match=message):
+            stats.quantile_test(x, axis=2)
+
+        message = "If specified, `keepdims` must be True or False."
+        with pytest.raises(ValueError, match=message):
+            stats.quantile_test(x, keepdims=10)
+
+        message = ("`keepdims` may be False only if...")
+        with pytest.raises(ValueError, match=message):
+            stats.quantile_test(x, p=xp.asarray([0.1, 0.2]), keepdims=False)
+
+        message = "`alternative` must be one of..."
+        with pytest.raises(ValueError, match=message):
+            stats.quantile_test(x, alternative='one-sided')
+
+        message = "`confidence_level` must be a number between 0 and 1."
+        with pytest.raises(ValueError, match=message):
+            stats.quantile_test(x).confidence_interval(1)
+
+    @pytest.mark.parametrize(
+        'p, alpha, lb, ub, alternative',
+        [[0.3, 0.95, 1.221402758160170, 1.476980793882643, 'two-sided'],
+         [0.5, 0.9, 1.506817785112854, 1.803988415397857, 'two-sided'],
+         [0.25, 0.95, -np.inf, 1.39096812846378, 'less'],
+         [0.8, 0.9, 2.117000016612675, np.inf, 'greater']]
+    )
+    def test_R_ci_quantile(self, p, alpha, lb, ub, alternative, xp):
+        # Test against R library `confintr` function `ci_quantile`, e.g.
+        # library(confintr)
+        # options(digits=16)
+        # x <- exp(seq(0, 1, by = 0.01))
+        # ci_quantile(x, q = 0.3)$interval
+        # ci_quantile(x, q = 0.5, probs = c(0.05, 0.95))$interval
+        # ci_quantile(x, q = 0.25, probs = c(0, 0.95))$interval
+        # ci_quantile(x, q = 0.8, probs = c(0.1, 1))$interval
+        x = xp.exp(xp.arange(0.0, 1.01, 0.01))
+        res = stats.quantile_test(x, p=p, alternative=alternative)
+        ci = res.confidence_interval(alpha)
+        xp_assert_close(ci.low, xp.asarray(lb))
+        xp_assert_close(ci.high, xp.asarray(ub))
+
+    @pytest.mark.parametrize(
+        'q, p, alternative, ref',
+        [[1.2, 0.3, 'two-sided', 0.01515567517648],
+         [1.8, 0.5, 'two-sided', 0.1109183496606]]
+    )
+    def test_R_pvalue(self, q, p, alternative, ref, xp):
+        # Test against R library `snpar` function `quant.test`, e.g.
+        # library(snpar)
+        # options(digits=16)
+        # x < - exp(seq(0, 1, by=0.01))
+        # quant.test(x, q=1.2, p=0.3, exact=TRUE, alternative='t')
+        x = xp.exp(xp.arange(0.0, 1.01, 0.01))
+        res = stats.quantile_test(x, q=q, p=p, alternative=alternative)
+        xp_assert_close(res.pvalue, xp.asarray(ref))
+
+    @pytest.mark.parametrize('case', ['continuous', 'discrete'])
+    @pytest.mark.parametrize('alternative', ['less', 'greater'])
+    @pytest.mark.parametrize('alpha', [0.9, 0.95])
+    def test_pval_ci_match(self, case, alternative, alpha, xp):
+        # Verify that the following statement holds:
+
+        # The 95% confidence interval corresponding with alternative='less'
+        # has -inf as its lower bound, and the upper bound `xu` is the greatest
+        # element from the sample `x` such that:
+        # `stats.quantile_test(x, q=xu, p=p, alternative='less').pvalue``
+        # will be greater than 5%.
+
+        # And the corresponding statement for the alternative='greater' case.
+
+        seed = int((7**len(case) + len(alternative))*alpha)
+        rng = np.random.default_rng(seed)
+        if case == 'continuous':
+            p, q = rng.random(size=2)
+            rvs = rng.random(size=100)
+        else:
+            rvs = rng.integers(1, 11, size=100)
+            p = rng.random()
+            q = rng.integers(1, 11)
+
+        rvs, p, q = xp.asarray(rvs.tolist()), float(p), float(q)
+        res = stats.quantile_test(rvs, q=q, p=p, alternative=alternative)
+        ci = res.confidence_interval(confidence_level=alpha)
+
+        # select elements inside the confidence interval based on alternative
+        if alternative == 'less':
+            i_inside = xp.astype(rvs, ci.high.dtype) <= ci.high
+        else:
+            i_inside = xp.astype(rvs, ci.low.dtype) >= ci.low
+
+        for x in rvs[i_inside]:
+            res = stats.quantile_test(rvs, q=x, p=p, alternative=alternative)
+            assert res.pvalue > 1 - alpha
+
+        for x in rvs[~i_inside]:
+            res = stats.quantile_test(rvs, q=x, p=p, alternative=alternative)
+            assert res.pvalue < 1 - alpha
+
+    @pytest.mark.parametrize('dtype', [None, 'float32', 'float64'])
+    def test_match_conover_examples(self, dtype, xp):
+        # Test against the examples in [1] (Conover Practical Nonparametric
+        # Statistics Third Edition) pg 139
+
+        # Example 1
+        # Data is [189, 233, 195, 160, 212, 176, 231, 185, 199, 213, 202, 193,
+        # 174, 166, 248]
+        # Two-sided test of whether the upper quartile (p=0.75) equals 193
+        # (q=193). Conover shows that 7 of the observations are less than or
+        # equal to 193, and "for the binomial random variable Y, P(Y<=7) =
+        # 0.0173", so the two-sided p-value is twice that, 0.0346.
+        dtype = xp_default_dtype(xp) if dtype is None else getattr(xp, dtype)
+        x = xp.asarray([189, 233, 195, 160, 212, 176, 231, 185,
+                        199, 213, 202, 193, 174, 166, 248], dtype=dtype)
+        pvalue_ref = 0.0346
+        res = stats.quantile_test(x, q=193, p=0.75, alternative='two-sided')
+        xp_assert_close(res.pvalue, xp.asarray(pvalue_ref, dtype=dtype), rtol=1e-5)
+
+        # Example 2
+        # Conover doesn't give explicit data, just that 8 out of 112
+        # observations are 60 or less. The test is whether the median time is
+        # equal to 60 against the alternative that the median is greater than
+        # 60. The p-value is calculated as P(Y<=8), where Y is again a binomial
+        # distributed random variable, now with p=0.5 and n=112. Conover uses a
+        # normal approximation, but we can easily calculate the CDF of the
+        # binomial distribution.
+        x = xp.asarray([59]*8 + [61]*(112-8), dtype=dtype)
+        pvalue_ref = float(stats.binom(p=0.5, n=112).pmf(k=8))
+        res = stats.quantile_test(x, q=60, p=0.5, alternative='greater')
+        xp_assert_close(res.pvalue, xp.asarray(pvalue_ref, dtype=dtype), atol=1e-10)
+
+    @skip_xp_backends('array_api_strict', reason='indexing in _apply_over_batch')
+    @pytest.mark.parametrize('alternative', ['less', 'greater', 'two-sided'])
+    @pytest.mark.parametrize('axis', [0, 1])
+    def test_multidimensional(self, alternative, axis, xp):
+        rng = np.random.default_rng(85468924398205602)
+        x = rng.random(size=(2, 20))
+        p = rng.random(size=(1, 3,))
+        q = p + rng.random(size=(2, 1))*0.01
+
+        x, p, q = (xp.asarray(arr.tolist()) for arr in (x, p, q))
+
+        ref = quantile_test_reference(x, q, p, alternative=alternative)
+        ref_statistic, ref_pvalue, ref_low, ref_high = ref
+
+        if axis == 0:
+            x, p, q = x.T, p.T, q.T
+        res = stats.quantile_test(x, q=q, p=p, alternative=alternative, axis=axis)
+        res_statistic, res_pvalue = res.statistic, res.pvalue
+        res_low, res_high = res.confidence_interval()
+        if axis == 0:
+            res_statistic, res_pvalue = res_statistic.T, res_pvalue.T
+            res_low, res_high = res_low.T, res_high.T
+
+        xp_assert_close(res_statistic, ref_statistic)
+        xp_assert_close(res_pvalue, ref_pvalue)
+        xp_assert_close(res_low, res_low)
+        xp_assert_close(res_low, ref_low)
+
+    def test_zero_size(self, xp):
+        rng = np.random.default_rng(883771738488451943)
+        x_shape = (2, 50)
+        qp_shape = (2, 10)
+        x = rng.random(x_shape)
+        q = rng.random(qp_shape)
+        p = q + rng.random(qp_shape) * 1e-2
+
+        x, p, q = (xp.asarray(arr.tolist()) for arr in (x, p, q))
+
+        # case 1: p/q is size zero.
+        qp_zero = xp.empty((0, *qp_shape))
+        out = qp_zero
+        res = stats.quantile_test(x, q=qp_zero, p=qp_zero, axis=-1)
+        ci = res.confidence_interval()
+        # different default int on different platforms
+        xp_assert_equal(res.statistic, xp.asarray(out))
+        xp_assert_equal(res.statistic_type, xp.asarray(out))
+        xp_assert_equal(res.pvalue, out)
+        xp_assert_equal(ci.low, out)
+        xp_assert_equal(ci.high, out)
+
+        # case 2: x is size zero with nonzero length along axis.
+        x_zero = xp.empty((0, *x_shape))
+        out = xp.empty((0, *qp_shape))
+        res = stats.quantile_test(x_zero, q=q, p=p, axis=-1)
+        ci = res.confidence_interval()
+        # different default int on different platforms
+        xp_assert_equal(res.statistic, xp.asarray(out))
+        xp_assert_equal(res.statistic_type, xp.asarray(out))
+        xp_assert_equal(res.pvalue, out)
+        xp_assert_equal(ci.low, out)
+        xp_assert_equal(ci.high, out)
+
+        # case 3: x has zero length along axis.
+        x_zero = xp.empty((x.shape[0], 0))
+        out = xp.full(qp_shape, xp.nan)
+        res = stats.quantile_test(x_zero, q=q, p=p, axis=-1)
+        ci = res.confidence_interval()
+        # different default int on different platforms
+        xp_assert_equal(res.statistic, out)
+        xp_assert_equal(res.statistic_type, out)
+        xp_assert_equal(res.pvalue, out)
+        xp_assert_equal(ci.low, out)
+        xp_assert_equal(ci.high, out)
+
+    def test_nans(self, xp):
+        rng = np.random.default_rng(2920028761208905)
+        x = rng.random((10, 50))
+        q = rng.random((10, 10))
+        p = q + rng.random((10, 10)) * 1e-2
+        x, p, q = (xp.asarray(arr.tolist()) for arr in (x, p, q))
+
+        ref = stats.quantile_test(x, q=q, p=p, axis=-1)
+        ref_low, ref_high = ref.confidence_interval()
+
+        x_ = xp_copy(x)
+        i_nan = xp.asarray(rng.random(x.shape) < 0.01)
+        x_ = xpx.at(x_)[i_nan].set(xp.nan)
+        i_nan_out = xp.any(i_nan, axis=-1)
+        assert not xp.all(i_nan_out)
+        res = stats.quantile_test(x_, q=q, p=p, axis=-1)
+        res_low, res_high = res.confidence_interval()
+
+        assert xp.all(xp.isnan(res.statistic[i_nan_out]))
+        assert xp.all(xp.isnan(res.statistic_type[i_nan_out]))
+        assert xp.all(xp.isnan(res.pvalue[i_nan_out]))
+        assert xp.all(xp.isnan(res_low[i_nan_out]))
+        assert xp.all(xp.isnan(res_high[i_nan_out]))
+        xp_assert_equal(res.statistic[~i_nan_out], ref.statistic[~i_nan_out])
+        xp_assert_equal(res.statistic_type[~i_nan_out], ref.statistic_type[~i_nan_out])
+        xp_assert_equal(res.pvalue[~i_nan_out], ref.pvalue[~i_nan_out])
+        xp_assert_equal(res_low[~i_nan_out], ref_low[~i_nan_out])
+        xp_assert_equal(res_high[~i_nan_out], ref_high[~i_nan_out])
+
+        i_nan_q = xp.asarray(rng.random(q.shape) < 0.01)
+        i_nan_p = xp.asarray(rng.random(p.shape) < 0.01)
+        assert xp.any(i_nan_q)
+        assert xp.any(i_nan_p)
+        q = xpx.at(q)[xp.broadcast_to(i_nan_q, q.shape)].set(xp.nan)
+        p = xpx.at(p)[xp.broadcast_to(i_nan_p, p.shape)].set(xp.nan)
+
+        i_nan_out = xp.asarray(i_nan_q | i_nan_p)
+        assert not xp.all(i_nan_out)
+
+        res = stats.quantile_test(x, q=q, p=p, axis=-1)
+        res_low, res_high = res.confidence_interval()
+        assert xp.all(xp.isnan(res.statistic[i_nan_out]))
+        assert xp.all(xp.isnan(res.statistic_type[i_nan_out]))
+        assert xp.all(xp.isnan(res.pvalue[i_nan_out]))
+        assert xp.all(xp.isnan(res_low[i_nan_out]))
+        assert xp.all(xp.isnan(res_high[i_nan_out]))
+        xp_assert_equal(res.statistic[~i_nan_out], ref.statistic[~i_nan_out])
+        xp_assert_equal(res.statistic_type[~i_nan_out], ref.statistic_type[~i_nan_out])
+        xp_assert_equal(res.pvalue[~i_nan_out], ref.pvalue[~i_nan_out])
+        xp_assert_equal(res_low[~i_nan_out], ref_low[~i_nan_out])
+        xp_assert_equal(res_high[~i_nan_out], ref_high[~i_nan_out])
+
+    def test_axis_none(self, xp):
+        rng = np.random.default_rng(883771738488451943)
+        x_shape = (2, 50)
+        qp_shape = (2, 10)
+        x = rng.random(x_shape)
+        q = rng.random(qp_shape)
+        p = q + rng.random(qp_shape) * 1e-2
+        x, p, q = (xp.asarray(arr.tolist()) for arr in (x, p, q))
+
+        res = stats.quantile_test(x, q=q, p=p, axis=None)
+        res_low, res_high = res.confidence_interval()
+        ref = stats.quantile_test(xp_ravel(x), q=xp_ravel(q), p=xp_ravel(p), axis=None)
+        ref_low, ref_high = ref.confidence_interval()
+        xp_assert_equal(res.statistic, ref.statistic[xp.newaxis, :])
+        xp_assert_equal(res.statistic_type, ref.statistic_type[xp.newaxis, :])
+        xp_assert_equal(res.pvalue, ref.pvalue[xp.newaxis, :])
+        xp_assert_equal(res_low, ref_low[xp.newaxis, :])
+        xp_assert_equal(res_high, ref_high[xp.newaxis, :])
+
+        res = stats.quantile_test(x, q=0.5, p=0.5, axis=None)
+        res_low, res_high = res.confidence_interval()
+        ref = stats.quantile_test(xp_ravel(x), q=0.5, p=0.5, axis=None)
+        ref_low, ref_high = ref.confidence_interval()
+        xp_assert_equal(res.statistic, ref.statistic)
+        xp_assert_equal(res.statistic_type, ref.statistic_type)
+        xp_assert_equal(res.pvalue, ref.pvalue)
+        xp_assert_equal(res_low, ref_low)
+        xp_assert_equal(res_high, ref_high)
+
+    @pytest.mark.filterwarnings("ignore:torch:UserWarning")
+    @pytest.mark.parametrize("x_shape, qp_shape, axis, keepdims, res_shape", [
+        ((1, 3), (1,), None, False, ()),
+        ((1, 3), (1,), None, True, (1, 1)),
+        ((1, 3), (2, 1), -1, False, (2,)),
+        ((1, 3), (2, 1), -1, True, (2, 1)),
+    ])
+    def test_keepdims(self, x_shape, qp_shape, axis, keepdims, res_shape, xp):
+        rng = np.random.default_rng(883771738488451943)
+        x, qp = xp.asarray(rng.random(x_shape)), xp.asarray(rng.random(qp_shape))
+        res = stats.quantile_test(x, q=qp, p=qp, axis=axis, keepdims=keepdims)
+        assert res.statistic.shape == res_shape
+
+
+class TestPageTrendTest:
+    def setup_method(self):
+        self.rng = np.random.default_rng(1808365978)
+
+    # expected statistic and p-values generated using R at
+    # https://rdrr.io/cran/cultevo/, e.g.
+    # library(cultevo)
+    # data = rbind(c(72, 47, 73, 35, 47, 96, 30, 59, 41, 36, 56, 49, 81, 43,
+    #                   70, 47, 28, 28, 62, 20, 61, 20, 80, 24, 50),
+    #              c(68, 52, 60, 34, 44, 20, 65, 88, 21, 81, 48, 31, 31, 67,
+    #                69, 94, 30, 24, 40, 87, 70, 43, 50, 96, 43),
+    #              c(81, 13, 85, 35, 79, 12, 92, 86, 21, 64, 16, 64, 68, 17,
+    #                16, 89, 71, 43, 43, 36, 54, 13, 66, 51, 55))
+    # result = page.test(data, verbose=FALSE)
+    # Most test cases generated to achieve common critical p-values so that
+    # results could be checked (to limited precision) against tables in
+    # scipy.stats.page_trend_test reference [1]
+
+    rng = np.random.default_rng(3113562111)
+    data_3_25 = rng.random((3, 25))
+    rng = np.random.default_rng(3113562111)
+    data_10_26 = rng.random((10, 26))
+
+    ts = [
+          (12949, 0.275539045444, False, 'asymptotic', data_3_25),
+          (47221, 0.5703651063709, False, 'asymptotic', data_10_26),
+          (12332, 0.7722477197436702, False, 'asymptotic',
+           [[72, 47, 73, 35, 47, 96, 30, 59, 41, 36, 56, 49, 81,
+             43, 70, 47, 28, 28, 62, 20, 61, 20, 80, 24, 50],
+            [68, 52, 60, 34, 44, 20, 65, 88, 21, 81, 48, 31, 31,
+             67, 69, 94, 30, 24, 40, 87, 70, 43, 50, 96, 43],
+            [81, 13, 85, 35, 79, 12, 92, 86, 21, 64, 16, 64, 68,
+             17, 16, 89, 71, 43, 43, 36, 54, 13, 66, 51, 55]]),
+          (266, 4.121656378600823e-05, False, 'exact',
+           [[1.5, 4., 8.3, 5, 19, 11],
+            [5, 4, 3.5, 10, 20, 21],
+            [8.4, 3.2, 10, 12, 14, 15]]),
+          (332, 0.9566400920502488, True, 'exact',
+           [[4, 3, 2, 1], [4, 3, 2, 1], [4, 3, 2, 1], [4, 3, 2, 1],
+            [4, 3, 2, 1], [4, 3, 2, 1], [4, 3, 2, 1], [4, 3, 2, 1],
+            [3, 4, 1, 2], [1, 2, 3, 4], [1, 2, 3, 4], [1, 2, 3, 4],
+            [1, 2, 3, 4], [1, 2, 3, 4]]),
+          (241, 0.9622210164861476, True, 'exact',
+           [[3, 2, 1], [3, 2, 1], [3, 2, 1], [3, 2, 1], [3, 2, 1], [3, 2, 1],
+            [3, 2, 1], [3, 2, 1], [3, 2, 1], [3, 2, 1], [3, 2, 1], [3, 2, 1],
+            [3, 2, 1], [2, 1, 3], [1, 2, 3], [1, 2, 3], [1, 2, 3], [1, 2, 3],
+            [1, 2, 3], [1, 2, 3], [1, 2, 3]]),
+          (197, 0.9619432897162209, True, 'exact',
+           [[6, 5, 4, 3, 2, 1], [6, 5, 4, 3, 2, 1], [1, 3, 4, 5, 2, 6]]),
+          (423, 0.9590458306880073, True, 'exact',
+           [[5, 4, 3, 2, 1], [5, 4, 3, 2, 1], [5, 4, 3, 2, 1],
+            [5, 4, 3, 2, 1], [5, 4, 3, 2, 1], [5, 4, 3, 2, 1],
+            [4, 1, 3, 2, 5], [1, 2, 3, 4, 5], [1, 2, 3, 4, 5],
+            [1, 2, 3, 4, 5]]),
+          (217, 0.9693058575034678, True, 'exact',
+           [[3, 2, 1], [3, 2, 1], [3, 2, 1], [3, 2, 1], [3, 2, 1], [3, 2, 1],
+            [3, 2, 1], [3, 2, 1], [3, 2, 1], [3, 2, 1], [3, 2, 1], [3, 2, 1],
+            [2, 1, 3], [1, 2, 3], [1, 2, 3], [1, 2, 3], [1, 2, 3], [1, 2, 3],
+            [1, 2, 3]]),
+          (395, 0.991530289351305, True, 'exact',
+           [[7, 6, 5, 4, 3, 2, 1], [7, 6, 5, 4, 3, 2, 1],
+            [6, 5, 7, 4, 3, 2, 1], [1, 2, 3, 4, 5, 6, 7]]),
+          (117, 0.9997817843373017, True, 'exact',
+           [[3, 2, 1], [3, 2, 1], [3, 2, 1], [3, 2, 1], [3, 2, 1], [3, 2, 1],
+            [3, 2, 1], [3, 2, 1], [3, 2, 1], [2, 1, 3], [1, 2, 3]]),
+         ]
+
+    @pytest.mark.parametrize("L, p, ranked, method, data", ts)
+    def test_accuracy(self, L, p, ranked, method, data):
+        res = stats.page_trend_test(data, ranked=ranked, method=method)
+        assert_equal(L, res.statistic)
+        assert_allclose(p, res.pvalue)
+        assert_equal(method, res.method)
+
+    ts2 = [
+           (542, 0.9481266260876332, True, 'exact',
+            [[10, 9, 8, 7, 6, 5, 4, 3, 2, 1],
+             [1, 8, 4, 7, 6, 5, 9, 3, 2, 10]]),
+           (1322, 0.9993113928199309, True, 'exact',
+            [[10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [10, 9, 8, 7, 6, 5, 4, 3, 2, 1],
+             [10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [9, 2, 8, 7, 6, 5, 4, 3, 10, 1],
+             [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]]),
+           (2286, 0.9908688345484833, True, 'exact',
+            [[8, 7, 6, 5, 4, 3, 2, 1], [8, 7, 6, 5, 4, 3, 2, 1],
+             [8, 7, 6, 5, 4, 3, 2, 1], [8, 7, 6, 5, 4, 3, 2, 1],
+             [8, 7, 6, 5, 4, 3, 2, 1], [8, 7, 6, 5, 4, 3, 2, 1],
+             [8, 7, 6, 5, 4, 3, 2, 1], [8, 7, 6, 5, 4, 3, 2, 1],
+             [8, 7, 6, 5, 4, 3, 2, 1], [1, 3, 5, 6, 4, 7, 2, 8],
+             [1, 2, 3, 4, 5, 6, 7, 8], [1, 2, 3, 4, 5, 6, 7, 8],
+             [1, 2, 3, 4, 5, 6, 7, 8], [1, 2, 3, 4, 5, 6, 7, 8],
+             [1, 2, 3, 4, 5, 6, 7, 8]]),
+          ]
+    # only the first of these appears slow because intermediate data are
+    # cached and used on the rest
+    @pytest.mark.parametrize("L, p, ranked, method, data", ts2)
+    @pytest.mark.slow()
+    def test_accuracy2(self, L, p, ranked, method, data):
+        res = stats.page_trend_test(data, ranked=ranked, method=method)
+        assert_equal(L, res.statistic)
+        assert_allclose(p, res.pvalue)
+        assert_equal(method, res.method)
+
+    def test_options(self):
+        rng = np.random.default_rng(183973867)
+        m, n = 10, 20
+        predicted_ranks = np.arange(1, n+1)
+        perm = rng.permutation(np.arange(n))
+        data = rng.random((m, n))
+        ranks = stats.rankdata(data, axis=1)
+        res1 = stats.page_trend_test(ranks)
+        res2 = stats.page_trend_test(ranks, ranked=True)
+        res3 = stats.page_trend_test(data, ranked=False)
+        res4 = stats.page_trend_test(ranks, predicted_ranks=predicted_ranks)
+        res5 = stats.page_trend_test(ranks[:, perm],
+                                     predicted_ranks=predicted_ranks[perm])
+        assert_equal(res1.statistic, res2.statistic)
+        assert_equal(res1.statistic, res3.statistic)
+        assert_equal(res1.statistic, res4.statistic)
+        assert_equal(res1.statistic, res5.statistic)
+
+    def test_Ames_assay(self):
+        # test from _page_trend_test.py [2] page 151; data on page 144
+        data = [[101, 117, 111], [91, 90, 107], [103, 133, 121],
+                [136, 140, 144], [190, 161, 201], [146, 120, 116]]
+        data = np.array(data).T
+        predicted_ranks = np.arange(1, 7)
+
+        res = stats.page_trend_test(data, ranked=False,
+                                    predicted_ranks=predicted_ranks,
+                                    method="asymptotic")
+        assert_equal(res.statistic, 257)
+        assert_almost_equal(res.pvalue, 0.0035, decimal=4)
+
+        res = stats.page_trend_test(data, ranked=False,
+                                    predicted_ranks=predicted_ranks,
+                                    method="exact")
+        assert_equal(res.statistic, 257)
+        assert_almost_equal(res.pvalue, 0.0023, decimal=4)
+
+    def test_input_validation(self):
+        # test data not a 2d array
+        with assert_raises(ValueError, match="`data` must be a 2d array."):
+            stats.page_trend_test(None)
+        with assert_raises(ValueError, match="`data` must be a 2d array."):
+            stats.page_trend_test([])
+        with assert_raises(ValueError, match="`data` must be a 2d array."):
+            stats.page_trend_test([1, 2])
+        with assert_raises(ValueError, match="`data` must be a 2d array."):
+            stats.page_trend_test([[[1]]])
+
+        # test invalid dimensions
+        rng = np.random.default_rng(2482566048)
+        with assert_raises(ValueError, match="Page's L is only appropriate"):
+            stats.page_trend_test(rng.random((1, 3)))
+        with assert_raises(ValueError, match="Page's L is only appropriate"):
+            stats.page_trend_test(rng.random((2, 2)))
+
+        # predicted ranks must include each integer [1, 2, 3] exactly once
+        message = "`predicted_ranks` must include each integer"
+        with assert_raises(ValueError, match=message):
+            stats.page_trend_test(data=[[1, 2, 3], [1, 2, 3]],
+                                  predicted_ranks=[0, 1, 2])
+        with assert_raises(ValueError, match=message):
+            stats.page_trend_test(data=[[1, 2, 3], [1, 2, 3]],
+                                  predicted_ranks=[1.1, 2, 3])
+        with assert_raises(ValueError, match=message):
+            stats.page_trend_test(data=[[1, 2, 3], [1, 2, 3]],
+                                  predicted_ranks=[1, 2, 3, 3])
+        with assert_raises(ValueError, match=message):
+            stats.page_trend_test(data=[[1, 2, 3], [1, 2, 3]],
+                                  predicted_ranks="invalid")
+
+        # test improperly ranked data
+        with assert_raises(ValueError, match="`data` is not properly ranked"):
+            stats.page_trend_test([[0, 2, 3], [1, 2, 3]], True)
+        with assert_raises(ValueError, match="`data` is not properly ranked"):
+            stats.page_trend_test([[1, 2, 3], [1, 2, 4]], True)
+
+        # various
+        with assert_raises(ValueError, match="`data` contains NaNs"):
+            stats.page_trend_test([[1, 2, 3], [1, 2, np.nan]],
+                                  ranked=False)
+        with assert_raises(ValueError, match="`method` must be in"):
+            stats.page_trend_test(data=[[1, 2, 3], [1, 2, 3]],
+                                  method="ekki")
+        with assert_raises(TypeError, match="`ranked` must be boolean."):
+            stats.page_trend_test(data=[[1, 2, 3], [1, 2, 3]],
+                                  ranked="ekki")
+
+
+@make_xp_test_case(stats.expectile)
+class TestExpectile:
+    @pytest.mark.parametrize('dtype', [None, 'float32', 'float64'])
+    def test_same_as_mean(self, dtype, xp):
+        dtype = dtype if dtype is None else getattr(xp, dtype)
+        rng = np.random.default_rng(42)
+
+        x = xp.asarray(rng.random(size=20).tolist(), dtype=dtype)
+        xp_assert_close(stats.expectile(x, 0.5), xp.mean(x))
+
+        w = xp.asarray(rng.random(size=20).tolist(), dtype=dtype)
+        xp_assert_close(stats.expectile(x, 0.5, weights=w), _xp_mean(x, weights=w))
+
+    def test_minimum(self, xp):
+        rng = np.random.default_rng(42)
+        x = xp.asarray(rng.random(size=20))
+        xp_assert_close(stats.expectile(x, alpha=0), xp.min(x))
+
+    def test_maximum(self, xp):
+        rng = np.random.default_rng(42)
+        x = xp.asarray(rng.random(size=20))
+        xp_assert_close(stats.expectile(x, alpha=1), xp.max(x))
+
+    def test_weights(self, xp):
+        # expectile should minimize `fun` defined below; see
+        # F. Sobotka and T. Kneib, "Geoadditive expectile regression",
+        # Computational Statistics and Data Analysis 56 (2012) 755-767
+        # https://doi.org/10.1016/j.csda.2010.11.015
+        rng = np.random.default_rng(1856392524598679138)
+
+        def fun(u, a, alpha, weights):
+            w = np.full_like(a, fill_value=alpha)
+            w[a <= u] = 1 - alpha
+            return np.sum(w * weights * (a - u)**2)
+
+        def expectile2(a, alpha, weights):
+            bracket = np.min(a), np.max(a)
+            return optimize.minimize_scalar(fun, bracket=bracket,
+                                            args=(a, alpha, weights)).x
+
+        n = 10
+        a = rng.random(n)
+        alpha = rng.random()
+        weights = rng.random(n)
+
+        res = stats.expectile(xp.asarray(a), alpha, weights=xp.asarray(weights))
+        ref = expectile2(a, alpha, weights)
+        xp_assert_close(res, xp.asarray(ref))
+
+    @pytest.mark.parametrize(
+        "alpha", [0.2, 0.5 - 1e-12, 0.5, 0.5 + 1e-12, 0.8]
+    )
+    @pytest.mark.parametrize("n", [20, 2000])
+    def test_expectile_properties(self, alpha, n, xp):
+        """
+        See Section 6 of
+        I. Steinwart, C. Pasin, R.C. Williamson & S. Zhang (2014).
+        "Elicitation and Identification of Properties". COLT.
+        http://proceedings.mlr.press/v35/steinwart14.html
+
+        and
+
+        Propositions 5, 6, 7 of
+        F. Bellini, B. Klar, and A. Müller and E. Rosazza Gianin (2013).
+        "Generalized Quantiles as Risk Measures"
+        http://doi.org/10.2139/ssrn.2225751
+        """
+        rng = np.random.default_rng(42)
+        x = xp.asarray(rng.normal(size=n))
+
+        # 0. definite / constancy
+        # Let T(X) denote the expectile of rv X ~ F.
+        # T(c) = c for constant c
+        for c in [-5., 0., 0.5]:
+            xp_assert_close(
+                stats.expectile(xp.full(shape=n, fill_value=c), alpha=alpha),
+                xp.asarray(c)
+            )
+
+        # 1. translation equivariance
+        # T(X + c) = T(X) + c
+        c = xp.asarray(rng.exponential())
+        xp_assert_close(
+            stats.expectile(x + c, alpha=alpha),
+            stats.expectile(x, alpha=alpha) + c,
+        )
+        xp_assert_close(
+            stats.expectile(x - c, alpha=alpha),
+            stats.expectile(x, alpha=alpha) - c,
+        )
+
+        # 2. positively homogeneity
+        # T(cX) = c * T(X) for c > 0
+        xp_assert_close(
+            stats.expectile(c * x, alpha=alpha),
+            c * stats.expectile(x, alpha=alpha),
+        )
+
+        # 3. subadditivity
+        # Note that subadditivity holds for alpha >= 0.5.
+        # T(X + Y) <= T(X) + T(Y)
+        # For alpha = 0.5, i.e. the mean, strict equality holds.
+        # For alpha < 0.5, one can use property 6. to show
+        # T(X + Y) >= T(X) + T(Y)
+        y = xp.asarray(rng.logistic(size=n, loc=10))  # different distribution than x
+        if alpha == 0.5:
+            def assert_op(a, b):
+                xp_assert_close(a, b)
+
+        elif alpha > 0.5:
+            def assert_op(a, b):
+                assert a < b
+
+        else:
+            def assert_op(a, b):
+                assert a > b
+
+        assert_op(
+            stats.expectile(x + y, alpha=alpha),
+            stats.expectile(x, alpha=alpha)
+            + stats.expectile(y, alpha=alpha)
+        )
+
+        # 4. monotonicity
+        # This holds for first order stochastic dominance X:
+        # X >= Y whenever P(X <= x) < P(Y <= x)
+        # T(X) <= T(Y) whenever X <= Y
+        y = xp.asarray(rng.normal(size=n, loc=5))
+        assert (
+            stats.expectile(x, alpha=alpha) <= stats.expectile(y, alpha=alpha)
+        )
+
+        # 5. convexity for alpha > 0.5, concavity for alpha < 0.5
+        # convexity is
+        # T((1 - c) X + c Y) <= (1 - c) T(X) + c T(Y) for 0 <= c <= 1
+        y = xp.asarray(rng.logistic(size=n, loc=10))
+        for c in [0.1, 0.5, 0.8]:
+            assert_op(
+                stats.expectile((1-c)*x + c*y, alpha=alpha),
+                (1-c) * stats.expectile(x, alpha=alpha) +
+                c * stats.expectile(y, alpha=alpha)
+            )
+
+        # 6. negative argument
+        # T_{alpha}(-X) = -T_{1-alpha}(X)
+        xp_assert_close(
+            stats.expectile(-x, alpha=alpha),
+            -stats.expectile(x, alpha=1-alpha),
+        )
+
+    @pytest.mark.parametrize("n", [20, 2000])
+    def test_monotonicity_in_alpha(self, n, xp):
+        rng = np.random.default_rng(42)
+        x = xp.asarray(rng.pareto(a=2, size=n))
+        e_list = []
+        alpha_seq = np.logspace(-15, np.log10(0.5), 100)
+        # sorted list of unique alpha values in interval (0, 1)
+        for alpha in np.r_[0, alpha_seq, 1 - alpha_seq[:-1:-1], 1]:
+            e_list.append(stats.expectile(x, alpha=float(alpha)))
+        assert xp.all(xp.diff(xp.asarray(e_list)) > 0)
+
+
+@make_xp_test_case(stats.lmoment)
+class TestLMoment:
+    # data from https://github.com/scipy/scipy/issues/19460
+    data = [0.87, 0.87, 1.29, 1.5, 1.7, 0.66, 1.5, 0.5, 1., 1.25, 2.3,
+            1.03, 2.85, 0.68, 1.74, 1.94, 0.63, 2.04, 1.2, 0.64, 2.05, 0.97,
+            2.81, 1.02, 2.76, 0.86, 1.36, 1.29, 1.68, 0.72, 1.67, 1.15, 3.26,
+            0.93, 0.83, 0.91, 0.92, 2.32, 1.12, 3.21, 1.23, 1.22, 1.29, 2.08,
+            0.64, 2.83, 2.68, 1.77, 0.69, 1.69, 0.7, 1.83, 2.25, 1.23, 1.17,
+            0.94, 1.22, 0.76, 0.69, 0.48, 1.04, 2.49, 1.38, 1.57, 1.79, 1.59,
+            1.3, 1.54, 1.07, 1.03, 0.76, 2.35, 2.05, 2.02, 2.36, 1.59, 0.97,
+            1.63, 1.66, 0.94, 1.45, 1.26, 1.25, 0.68, 2.96, 0.8, 1.16, 0.82,
+            0.64, 0.87, 1.33, 1.28, 1.26, 1.19, 1.24, 1.12, 1.45, 1.03, 1.37,
+            1.4, 1.35, 1.28, 1.04, 1.31, 0.87, 0.96, 2.55, 1.72, 1.05, 1.15,
+            1.73, 1.03, 1.53, 2.41, 1.36, 2.08, 0.92, 0.73, 1.56, 1.94, 0.78]
+
+    not_integers = [1.5, [1, 2, 3.5], math.nan, math.inf]
+
+    def test_dtype_iv(self, xp):
+        message = '`sample` must be an array of real numbers.'
+        with pytest.raises(ValueError, match=message):
+            stats.lmoment(xp.asarray(self.data, dtype=xp.complex128))
+
+    @skip_xp_invalid_arg
+    def test_dtype_iv_non_numeric(self):
+        message = '`sample` must be an array of real numbers.'
+        with pytest.raises(ValueError, match=message):
+            stats.lmoment(np.array(self.data, dtype=object))
+
+    @pytest.mark.parametrize('order', not_integers + [0, -1, [], [[1, 2, 3]]])
+    def test_order_iv(self, order, xp):
+        if is_jax(xp) and np.isscalar(order) and order < 1:
+            pytest.skip("Order is treated as an array; can't do value-based IV")
+        message = '`order` must be a scalar or a non-empty...'
+        with pytest.raises(ValueError, match=message):
+            stats.lmoment(xp.asarray(self.data), order=order)
+
+    @pytest.mark.parametrize('axis', not_integers)
+    def test_axis_iv(self, axis, xp):
+        message = '`axis` must be an integer'
+        with pytest.raises(ValueError, match=message):
+            stats.lmoment(xp.asarray(self.data), axis=axis)
+
+    @pytest.mark.parametrize('sorted', not_integers)
+    def test_sorted_iv(self, sorted, xp):
+        message = '`sorted` must be True or False.'
+        with pytest.raises(ValueError, match=message):
+            stats.lmoment(xp.asarray(self.data), sorted=sorted)
+
+    @pytest.mark.parametrize('standardize', not_integers)
+    def test_standardize_iv(self, standardize, xp):
+        message = '`standardize` must be True or False.'
+        with pytest.raises(ValueError, match=message):
+            stats.lmoment(xp.asarray(self.data), standardize=standardize)
+
+    @pytest.mark.parametrize('order', [1, 4, [1, 2, 3, 4]])
+    @pytest.mark.parametrize('standardize', [False, True])
+    @pytest.mark.parametrize('presorted', [False, True])
+    def test_lmoment(self, order, standardize, presorted, xp):
+        # Reference values from R package `lmom`
+        # options(digits=16)
+        # library(lmom)
+        # data= c(0.87, 0.87,..., 1.94, 0.78)
+        # samlmu(data)
+        ref = xp.asarray([1.4087603305785130, 0.3415936639118458,
+                          0.2189964482831403, 0.1328186463415905])
+
+        if not standardize:
+            ref = xpx.at(ref)[2:].multiply(ref[1])
+
+        data = sorted(self.data) if presorted else self.data
+        data = xp.asarray(data)
+
+        res = stats.lmoment(data, order, standardize=standardize, sorted=presorted)
+        xp_assert_close(res, ref[xp.asarray(order)-1])
+
+    def test_dtype(self, xp):
+        dtype = xp.float32
+        sample = xp.asarray(self.data)
+        res = stats.lmoment(xp.astype(sample, dtype))
+        ref = xp.astype(stats.lmoment(sample), dtype)
+        xp_assert_close(res, ref, rtol=1e-4)
+
+        dtype = xp.int64
+        sample = xp.asarray([1, 2, 3, 4, 5])
+        res = stats.lmoment(xp.astype(sample, dtype))
+        ref = stats.lmoment(xp.astype(sample, xp_default_dtype(xp)))
+        xp_assert_close(res, ref)
+
+    @pytest.mark.parametrize("axis", [0, 1])
+    def test_axis(self, axis, xp):
+        # nd input is tested extensively in `test_axis_nan_policy`, but only for NumPy
+        rng = np.random.default_rng(234923498149931248151)
+        x = rng.random(size=(10, 11))
+        res = stats.lmoment(xp.asarray(x), axis=axis)
+        ref = xp.asarray(stats.lmoment(x, axis=axis))
+        xp_assert_close(res, ref)
+
+
+@make_xp_test_case(_xp_mean)
+class TestXP_Mean:
+    @pytest.mark.parametrize('axis', [None, 1, -1, (-2, 2)])
+    @pytest.mark.parametrize('weights', [None, True])
+    @pytest.mark.parametrize('keepdims', [False, True])
+    def test_xp_mean_basic(self, xp, axis, weights, keepdims):
+        rng = np.random.default_rng(90359458245906)
+        x = rng.random((3, 4, 5))
+        x_xp = xp.asarray(x)
+        w = w_xp = None
+
+        if weights:
+            w = rng.random((1, 5))
+            w_xp = xp.asarray(w)
+            x, w = np.broadcast_arrays(x, w)
+
+        res = _xp_mean(x_xp, weights=w_xp, axis=axis, keepdims=keepdims)
+        ref = np.average(x, weights=w, axis=axis, keepdims=keepdims)
+
+        xp_assert_close(res, xp.asarray(ref))
+
+    def test_non_broadcastable(self, xp):
+        # non-broadcastable x and weights
+        x, w = xp.arange(10.), xp.zeros(5)
+        message = "Array shapes are incompatible for broadcasting."
+        with pytest.raises(ValueError, match=message):
+            _xp_mean(x, weights=w)
+
+    @pytest.mark.filterwarnings("ignore:divide by zero encountered:RuntimeWarning:dask")
+    @pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning:dask")
+    def test_special_cases(self, xp):
+        # weights sum to zero
+        weights = xp.asarray([-1., 0., 1.])
+
+        res = _xp_mean(xp.asarray([1., 1., 1.]), weights=weights)
+        xp_assert_close(res, xp.asarray(xp.nan))
+
+        res = _xp_mean(xp.asarray([2., 1., 1.]), weights=weights)
+        xp_assert_close(res, xp.asarray(-np.inf))
+
+        res = _xp_mean(xp.asarray([1., 1., 2.]), weights=weights)
+        xp_assert_close(res, xp.asarray(np.inf))
+
+    @pytest.mark.filterwarnings(
+        "ignore:invalid value encountered:RuntimeWarning"
+    ) # for dask
+    def test_nan_policy(self, xp):
+        x = xp.arange(10.)
+        mask = (x == 3)
+        x = xp.where(mask, xp.nan, x)
+
+        # nan_policy='raise' raises an error
+        if is_lazy_array(x):
+            with pytest.raises(TypeError, match='not supported for lazy arrays'):
+                _xp_mean(x, nan_policy='raise')
+        else:
+            with pytest.raises(ValueError, match='The input contains nan values'):
+                _xp_mean(x, nan_policy='raise')
+
+        # `nan_policy='propagate'` is the default, and the result is NaN
+        res1 = _xp_mean(x)
+        res2 = _xp_mean(x, nan_policy='propagate')
+        ref = xp.asarray(xp.nan)
+        xp_assert_equal(res1, ref)
+        xp_assert_equal(res2, ref)
+
+        # `nan_policy='omit'` omits NaNs in `x`
+        res = _xp_mean(x, nan_policy='omit')
+        ref = xp.mean(x[~mask])
+        xp_assert_close(res, ref)
+
+        # `nan_policy='omit'` omits NaNs in `weights`, too
+        weights = xp.ones(10)
+        weights = xp.where(mask, xp.nan, weights)
+        res = _xp_mean(xp.arange(10.), weights=weights, nan_policy='omit')
+        ref = xp.mean(x[~mask])
+        xp_assert_close(res, ref)
+
+    @pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning")
+    def test_nan_policy_warns(self, xp):
+        x = xp.arange(10.)
+        x = xp.where(x == 3, xp.nan, x)
+
+        # Check for warning if omitting NaNs causes empty slice
+        message = 'After omitting NaNs...'
+        with eager_warns(RuntimeWarning, match=message, xp=xp):
+            res = _xp_mean(x * np.nan, nan_policy='omit')
+            ref = xp.asarray(xp.nan)
+            xp_assert_equal(res, ref)
+
+    def test_empty(self, xp):
+        message = 'One or more sample arguments is too small...'
+        with pytest.warns(SmallSampleWarning, match=message):
+            res = _xp_mean(xp.asarray([]))
+            ref = xp.asarray(xp.nan)
+            xp_assert_equal(res, ref)
+
+        message = "All axis-slices of one or more sample arguments..."
+        with pytest.warns(SmallSampleWarning, match=message):
+            res = _xp_mean(xp.asarray([[]]), axis=1)
+            ref = xp.asarray([xp.nan])
+            xp_assert_equal(res, ref)
+
+        res = _xp_mean(xp.asarray([[]]), axis=0)
+        ref = xp.asarray([])
+        xp_assert_equal(res, ref)
+
+    @pytest.mark.filterwarnings(
+        "ignore:overflow encountered in reduce:RuntimeWarning"
+    ) # for dask
+    def test_dtype(self, xp):
+        max = xp.finfo(xp.float32).max
+        x_np = np.asarray([max, max], dtype=np.float32)
+        x_xp = xp.asarray(x_np)
+
+        # Overflow occurs for float32 input
+        with np.errstate(over='ignore'):
+            res = _xp_mean(x_xp)
+            ref = np.mean(x_np)
+            np.testing.assert_equal(ref, np.inf)
+            xp_assert_close(res, xp.asarray(ref))
+
+        # correct result is returned if `float64` is used
+        res = _xp_mean(x_xp, dtype=xp.float64)
+        ref = xp.asarray(np.mean(np.asarray(x_np, dtype=np.float64)))
+        xp_assert_close(res, ref)
+
+    def test_integer(self, xp):
+        # integer inputs are converted to the appropriate float
+        x = xp.arange(10)
+        y = xp.arange(10.)
+        xp_assert_equal(_xp_mean(x), _xp_mean(y))
+        xp_assert_equal(_xp_mean(y, weights=x), _xp_mean(y, weights=y))
+
+    def test_complex_gh22404(self, xp):
+        rng = np.random.default_rng(90359458245906)
+        x, y, wx, wy = rng.random((4, 20))
+        res = _xp_mean(xp.asarray(x + y*1j), weights=xp.asarray(wx + wy*1j))
+        ref = np.average(x + y*1j, weights=wx + wy*1j)
+        xp_assert_close(res, xp.asarray(ref))
+
+
+@make_xp_test_case(_xp_var)
+class TestXP_Var:
+    @pytest.mark.parametrize('axis', [None, 1, -1, (-2, 2)])
+    @pytest.mark.parametrize('keepdims', [False, True])
+    @pytest.mark.parametrize('correction', [0, 1])
+    @pytest.mark.parametrize('nan_policy', ['propagate', 'omit'])
+    def test_xp_var_basic(self, xp, axis, keepdims, correction, nan_policy):
+        rng = np.random.default_rng(90359458245906)
+        x = rng.random((3, 4, 5))
+        var_ref = np.var
+
+        if nan_policy == 'omit':
+            nan_mask = rng.random(size=x.shape) > 0.5
+            x[nan_mask] = np.nan
+            var_ref = np.nanvar
+
+        x_xp = xp.asarray(x)
+
+        res = _xp_var(x_xp, axis=axis, keepdims=keepdims, correction=correction,
+                      nan_policy=nan_policy)
+
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", "Degrees of freedom <= 0 for slice", RuntimeWarning)
+            ref = var_ref(x, axis=axis, keepdims=keepdims, ddof=correction)
+
+        xp_assert_close(res, xp.asarray(ref))
+
+    def test_special_cases(self, xp):
+        # correction too big
+        res = _xp_var(xp.asarray([1., 2.]), correction=3)
+        xp_assert_close(res, xp.asarray(xp.nan))
+
+    def test_nan_policy(self, xp):
+        x = xp.arange(10.)
+        mask = (x == 3)
+        x = xp.where(mask, xp.nan, x)
+
+        # `nan_policy='propagate'` is the default, and the result is NaN
+        res1 = _xp_var(x)
+        res2 = _xp_var(x, nan_policy='propagate')
+        ref = xp.asarray(xp.nan)
+        xp_assert_equal(res1, ref)
+        xp_assert_equal(res2, ref)
+
+        # `nan_policy='omit'` omits NaNs in `x`
+        res = _xp_var(x, nan_policy='omit')
+        ref = xp.var(x[~mask])
+        xp_assert_close(res, ref)
+
+    @pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning")
+    def test_nan_policy_warns(self, xp):
+        x = xp.arange(10.)
+        x = xp.where(x == 3, xp.nan, x)
+
+        # Check for warning if omitting NaNs causes empty slice
+        message = 'After omitting NaNs...'
+        with eager_warns(RuntimeWarning, match=message, xp=xp):
+            res = _xp_var(x * np.nan, nan_policy='omit')
+            ref = xp.asarray(xp.nan)
+            xp_assert_equal(res, ref)
+
+    @skip_xp_backends(eager_only=True)
+    def test_nan_policy_raise(self, xp):
+        # nan_policy='raise' raises an error when NaNs are present
+        message = 'The input contains nan values'
+        with pytest.raises(ValueError, match=message):
+            _xp_var(xp.asarray([1, 2, xp.nan]), nan_policy='raise')
+
+    def test_empty(self, xp):
+        message = 'One or more sample arguments is too small...'
+        with pytest.warns(SmallSampleWarning, match=message):
+            res = _xp_var(xp.asarray([]))
+            ref = xp.asarray(xp.nan)
+            xp_assert_equal(res, ref)
+
+        message = "All axis-slices of one or more sample arguments..."
+        with pytest.warns(SmallSampleWarning, match=message):
+            res = _xp_var(xp.asarray([[]]), axis=1)
+            ref = xp.asarray([xp.nan])
+            xp_assert_equal(res, ref)
+
+        res = _xp_var(xp.asarray([[]]), axis=0)
+        ref = xp.asarray([])
+        xp_assert_equal(res, ref)
+
+    @pytest.mark.filterwarnings(
+        "ignore:overflow encountered in reduce:RuntimeWarning"
+    ) # Overflow occurs for float32 input
+    def test_dtype(self, xp):
+        max = xp.finfo(xp.float32).max
+        x_np = np.asarray([max, max/2], dtype=np.float32)
+        x_xp = xp.asarray(x_np)
+
+        res = _xp_var(x_xp)
+        ref = np.var(x_np)
+        np.testing.assert_equal(ref, np.inf)
+        xp_assert_close(res, xp.asarray(ref))
+
+        # correct result is returned if `float64` is used
+        res = _xp_var(x_xp, dtype=xp.float64)
+        ref = xp.asarray(np.var(np.asarray(x_np, dtype=np.float64)))
+        xp_assert_close(res, ref)
+
+    def test_integer(self, xp):
+        # integer inputs are converted to the appropriate float
+        x = xp.arange(10)
+        y = xp.arange(10.)
+        xp_assert_equal(_xp_var(x), _xp_var(y))
+
+    def test_complex_gh22404(self, xp):
+        rng = np.random.default_rng(90359458245906)
+        x, y = rng.random((2, 20))
+        res = _xp_var(xp.asarray(x + y*1j))
+        ref = np.var(x + y*1j)
+        xp_assert_close(res, xp.asarray(ref), check_dtype=False)
+
+
+@pytest.mark.uses_xp_capabilities(False, reason="private")
+def test_chk_asarray(xp):
+    rng = np.random.default_rng(2348923425434)
+    x0 = rng.random(size=(2, 3, 4))
+    x = xp.asarray(x0)
+
+    axis = 1
+    x_out, axis_out = _chk_asarray(x, axis=axis, xp=xp)
+    xp_assert_equal(x_out, xp.asarray(x0))
+    assert_equal(axis_out, axis)
+
+    axis = None
+    x_out, axis_out = _chk_asarray(x, axis=axis, xp=xp)
+    xp_assert_equal(x_out, xp.asarray(x0.ravel()))
+    assert_equal(axis_out, 0)
+
+    axis = 2
+    x_out, axis_out = _chk_asarray(x[0, 0, 0], axis=axis, xp=xp)
+    xp_assert_equal(x_out, xp.asarray(np.atleast_1d(x0[0, 0, 0])))
+    assert_equal(axis_out, axis)
+
+
+@skip_xp_backends("jax.numpy", reason="JAX+wilcoxon+'exact' incompatible")
+@pytest.mark.parametrize("fun", [
+    make_xp_pytest_param(stats.wilcoxon),
+    make_xp_pytest_param(stats.ks_1samp),
+    make_xp_pytest_param(stats.ks_2samp),
+    make_xp_pytest_param(stats.kstest)
+])
+def test_rename_mode_method(fun, xp):
+    rng = np.random.default_rng(23498459284629827814)
+    x = xp.asarray(rng.random(10))
+    y = xp.asarray(rng.random(10))
+
+    if fun == stats.wilcoxon:
+        args = (x,)
+    elif fun == stats.ks_1samp:
+        args = (x, special.ndtr)
+    else:
+        args = (x, y)
+
+    res = fun(*args, method='exact')
+    res2 = fun(*args, mode='exact')
+    xp_assert_equal(res.statistic, res2.statistic)
+    xp_assert_equal(res.pvalue, res2.pvalue)
+
+    err = rf"{fun.__name__}\(\) got multiple values for argument"
+    with pytest.raises(TypeError, match=err):
+        fun(*args, method='exact', mode='exact')
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/test_survival.py b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_survival.py
new file mode 100644
index 0000000000000000000000000000000000000000..60a5fef27ae281c028ade8af523bdf1f62f8f664
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_survival.py
@@ -0,0 +1,466 @@
+import pytest
+import numpy as np
+from numpy.testing import assert_equal, assert_allclose
+from scipy import stats
+from scipy.stats import _survival
+
+
+def _kaplan_meier_reference(times, censored):
+    # This is a very straightforward implementation of the Kaplan-Meier
+    # estimator that does almost everything differently from the implementation
+    # in stats.ecdf.
+
+    # Begin by sorting the raw data. Note that the order of death and loss
+    # at a given time matters: death happens first. See [2] page 461:
+    # "These conventions may be paraphrased by saying that deaths recorded as
+    # of an age t are treated as if they occurred slightly before t, and losses
+    # recorded as of an age t are treated as occurring slightly after t."
+    # We implement this by sorting the data first by time, then by `censored`,
+    # (which is 0 when there is a death and 1 when there is only a loss).
+    dtype = [('time', float), ('censored', int)]
+    data = np.array([(t, d) for t, d in zip(times, censored)], dtype=dtype)
+    data = np.sort(data, order=('time', 'censored'))
+    times = data['time']
+    died = np.logical_not(data['censored'])
+
+    m = times.size
+    n = np.arange(m, 0, -1)  # number at risk
+    sf = np.cumprod((n - died) / n)
+
+    # Find the indices of the *last* occurrence of unique times. The
+    # corresponding entries of `times` and `sf` are what we want.
+    _, indices = np.unique(times[::-1], return_index=True)
+    ref_times = times[-indices - 1]
+    ref_sf = sf[-indices - 1]
+    return ref_times, ref_sf
+
+
+class TestSurvival:
+
+    @staticmethod
+    def get_random_sample(rng, n_unique):
+        # generate random sample
+        unique_times = rng.random(n_unique)
+        # convert to `np.int32` to resolve `np.repeat` failure in 32-bit CI
+        repeats = rng.integers(1, 4, n_unique).astype(np.int32)
+        times = rng.permuted(np.repeat(unique_times, repeats))
+        censored = rng.random(size=times.size) > rng.random()
+        sample = stats.CensoredData.right_censored(times, censored)
+        return sample, times, censored
+
+    def test_input_validation(self):
+        message = '`sample` must be a one-dimensional sequence.'
+        with pytest.raises(ValueError, match=message):
+            stats.ecdf([[1]])
+        with pytest.raises(ValueError, match=message):
+            stats.ecdf(1)
+
+        message = '`sample` must not contain nan'
+        with pytest.raises(ValueError, match=message):
+            stats.ecdf([np.nan])
+
+        message = 'Currently, only uncensored and right-censored data...'
+        with pytest.raises(NotImplementedError, match=message):
+            stats.ecdf(stats.CensoredData.left_censored([1], censored=[True]))
+
+        message = 'method` must be one of...'
+        res = stats.ecdf([1, 2, 3])
+        with pytest.raises(ValueError, match=message):
+            res.cdf.confidence_interval(method='ekki-ekki')
+        with pytest.raises(ValueError, match=message):
+            res.sf.confidence_interval(method='shrubbery')
+
+        message = 'confidence_level` must be a scalar between 0 and 1'
+        with pytest.raises(ValueError, match=message):
+            res.cdf.confidence_interval(-1)
+        with pytest.raises(ValueError, match=message):
+            res.sf.confidence_interval([0.5, 0.6])
+
+        message = 'The confidence interval is undefined at some observations.'
+        with pytest.warns(RuntimeWarning, match=message):
+            ci = res.cdf.confidence_interval()
+
+        message = 'Confidence interval bounds do not implement...'
+        with pytest.raises(NotImplementedError, match=message):
+            ci.low.confidence_interval()
+        with pytest.raises(NotImplementedError, match=message):
+            ci.high.confidence_interval()
+
+    def test_edge_cases(self):
+        res = stats.ecdf([])
+        assert_equal(res.cdf.quantiles, [])
+        assert_equal(res.cdf.probabilities, [])
+
+        res = stats.ecdf([1])
+        assert_equal(res.cdf.quantiles, [1])
+        assert_equal(res.cdf.probabilities, [1])
+
+    def test_unique(self):
+        # Example with unique observations; `stats.ecdf` ref. [1] page 80
+        sample = [6.23, 5.58, 7.06, 6.42, 5.20]
+        res = stats.ecdf(sample)
+        ref_x = np.sort(np.unique(sample))
+        ref_cdf = np.arange(1, 6) / 5
+        ref_sf = 1 - ref_cdf
+        assert_equal(res.cdf.quantiles, ref_x)
+        assert_equal(res.cdf.probabilities, ref_cdf)
+        assert_equal(res.sf.quantiles, ref_x)
+        assert_equal(res.sf.probabilities, ref_sf)
+
+    def test_nonunique(self):
+        # Example with non-unique observations; `stats.ecdf` ref. [1] page 82
+        sample = [0, 2, 1, 2, 3, 4]
+        res = stats.ecdf(sample)
+        ref_x = np.sort(np.unique(sample))
+        ref_cdf = np.array([1/6, 2/6, 4/6, 5/6, 1])
+        ref_sf = 1 - ref_cdf
+        assert_equal(res.cdf.quantiles, ref_x)
+        assert_equal(res.cdf.probabilities, ref_cdf)
+        assert_equal(res.sf.quantiles, ref_x)
+        assert_equal(res.sf.probabilities, ref_sf)
+
+    def test_evaluate_methods(self):
+        # Test CDF and SF `evaluate` methods
+        rng = np.random.default_rng(1162729143302572461)
+        sample, _, _ = self.get_random_sample(rng, 15)
+        res = stats.ecdf(sample)
+        x = res.cdf.quantiles
+        xr = x + np.diff(x, append=x[-1]+1)/2  # right shifted points
+
+        assert_equal(res.cdf.evaluate(x), res.cdf.probabilities)
+        assert_equal(res.cdf.evaluate(xr), res.cdf.probabilities)
+        assert_equal(res.cdf.evaluate(x[0]-1), 0)  # CDF starts at 0
+        assert_equal(res.cdf.evaluate([-np.inf, np.inf]), [0, 1])
+
+        assert_equal(res.sf.evaluate(x), res.sf.probabilities)
+        assert_equal(res.sf.evaluate(xr), res.sf.probabilities)
+        assert_equal(res.sf.evaluate(x[0]-1), 1)  # SF starts at 1
+        assert_equal(res.sf.evaluate([-np.inf, np.inf]), [1, 0])
+
+    # ref. [1] page 91
+    t1 = [37, 43, 47, 56, 60, 62, 71, 77, 80, 81]  # times
+    d1 = [0, 0, 1, 1, 0, 0, 0, 1, 1, 1]  # 1 means deaths (not censored)
+    r1 = [1, 1, 0.875, 0.75, 0.75, 0.75, 0.75, 0.5, 0.25, 0]  # reference SF
+
+    # https://sphweb.bumc.bu.edu/otlt/mph-modules/bs/bs704_survival/BS704_Survival5.html
+    t2 = [8, 12, 26, 14, 21, 27, 8, 32, 20, 40]
+    d2 = [1, 1, 1, 1, 1, 1, 0, 0, 0, 0]
+    r2 = [0.9, 0.788, 0.675, 0.675, 0.54, 0.405, 0.27, 0.27, 0.27]
+    t3 = [33, 28, 41, 48, 48, 25, 37, 48, 25, 43]
+    d3 = [1, 1, 1, 0, 0, 0, 0, 0, 0, 0]
+    r3 = [1, 0.875, 0.75, 0.75, 0.6, 0.6, 0.6]
+
+    # https://sphweb.bumc.bu.edu/otlt/mph-modules/bs/bs704_survival/bs704_survival4.html
+    t4 = [24, 3, 11, 19, 24, 13, 14, 2, 18, 17,
+          24, 21, 12, 1, 10, 23, 6, 5, 9, 17]
+    d4 = [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1]
+    r4 = [0.95, 0.95, 0.897, 0.844, 0.844, 0.844, 0.844, 0.844, 0.844,
+          0.844, 0.76, 0.676, 0.676, 0.676, 0.676, 0.507, 0.507]
+
+    # https://www.real-statistics.com/survival-analysis/kaplan-meier-procedure/confidence-interval-for-the-survival-function/
+    t5 = [3, 5, 8, 10, 5, 5, 8, 12, 15, 14, 2, 11, 10, 9, 12, 5, 8, 11]
+    d5 = [1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1]
+    r5 = [0.944, 0.889, 0.722, 0.542, 0.542, 0.542, 0.361, 0.181, 0.181, 0.181]
+
+    @pytest.mark.parametrize("case", [(t1, d1, r1), (t2, d2, r2), (t3, d3, r3),
+                                      (t4, d4, r4), (t5, d5, r5)])
+    def test_right_censored_against_examples(self, case):
+        # test `ecdf` against other implementations on example problems
+        times, died, ref = case
+        sample = stats.CensoredData.right_censored(times, np.logical_not(died))
+        res = stats.ecdf(sample)
+        assert_allclose(res.sf.probabilities, ref, atol=1e-3)
+        assert_equal(res.sf.quantiles, np.sort(np.unique(times)))
+
+        # test reference implementation against other implementations
+        res = _kaplan_meier_reference(times, np.logical_not(died))
+        assert_equal(res[0], np.sort(np.unique(times)))
+        assert_allclose(res[1], ref, atol=1e-3)
+
+    @pytest.mark.parametrize('seed', [182746786639392128, 737379171436494115,
+                                      576033618403180168, 308115465002673650])
+    def test_right_censored_against_reference_implementation(self, seed):
+        # test `ecdf` against reference implementation on random problems
+        rng = np.random.default_rng(seed)
+        n_unique = rng.integers(10, 100)
+        sample, times, censored = self.get_random_sample(rng, n_unique)
+        res = stats.ecdf(sample)
+        ref = _kaplan_meier_reference(times, censored)
+        assert_allclose(res.sf.quantiles, ref[0])
+        assert_allclose(res.sf.probabilities, ref[1])
+
+        # If all observations are uncensored, the KM estimate should match
+        # the usual estimate for uncensored data
+        sample = stats.CensoredData(uncensored=times)
+        res = _survival._ecdf_right_censored(sample)  # force Kaplan-Meier
+        ref = stats.ecdf(times)
+        assert_equal(res[0], ref.sf.quantiles)
+        assert_allclose(res[1], ref.cdf.probabilities, rtol=1e-14)
+        assert_allclose(res[2], ref.sf.probabilities, rtol=1e-14)
+
+    def test_right_censored_ci(self):
+        # test "greenwood" confidence interval against example 4 (URL above).
+        times, died = self.t4, self.d4
+        sample = stats.CensoredData.right_censored(times, np.logical_not(died))
+        res = stats.ecdf(sample)
+        ref_allowance = [0.096, 0.096, 0.135, 0.162, 0.162, 0.162, 0.162,
+                         0.162, 0.162, 0.162, 0.214, 0.246, 0.246, 0.246,
+                         0.246, 0.341, 0.341]
+
+        sf_ci = res.sf.confidence_interval()
+        cdf_ci = res.cdf.confidence_interval()
+        allowance = res.sf.probabilities - sf_ci.low.probabilities
+
+        assert_allclose(allowance, ref_allowance, atol=1e-3)
+        assert_allclose(sf_ci.low.probabilities,
+                        np.clip(res.sf.probabilities - allowance, 0, 1))
+        assert_allclose(sf_ci.high.probabilities,
+                        np.clip(res.sf.probabilities + allowance, 0, 1))
+        assert_allclose(cdf_ci.low.probabilities,
+                        np.clip(res.cdf.probabilities - allowance, 0, 1))
+        assert_allclose(cdf_ci.high.probabilities,
+                        np.clip(res.cdf.probabilities + allowance, 0, 1))
+
+        # test "log-log" confidence interval against Mathematica
+        # e = {24, 3, 11, 19, 24, 13, 14, 2, 18, 17, 24, 21, 12, 1, 10, 23, 6, 5,
+        #      9, 17}
+        # ci = {1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0}
+        # R = EventData[e, ci]
+        # S = SurvivalModelFit[R]
+        # S["PointwiseIntervals", ConfidenceLevel->0.95,
+        #   ConfidenceTransform->"LogLog"]
+
+        ref_low = [0.694743, 0.694743, 0.647529, 0.591142, 0.591142, 0.591142,
+                   0.591142, 0.591142, 0.591142, 0.591142, 0.464605, 0.370359,
+                   0.370359, 0.370359, 0.370359, 0.160489, 0.160489]
+        ref_high = [0.992802, 0.992802, 0.973299, 0.947073, 0.947073, 0.947073,
+                    0.947073, 0.947073, 0.947073, 0.947073, 0.906422, 0.856521,
+                    0.856521, 0.856521, 0.856521, 0.776724, 0.776724]
+        sf_ci = res.sf.confidence_interval(method='log-log')
+        assert_allclose(sf_ci.low.probabilities, ref_low, atol=1e-6)
+        assert_allclose(sf_ci.high.probabilities, ref_high, atol=1e-6)
+
+    def test_right_censored_ci_example_5(self):
+        # test "exponential greenwood" confidence interval against example 5
+        times, died = self.t5, self.d5
+        sample = stats.CensoredData.right_censored(times, np.logical_not(died))
+        res = stats.ecdf(sample)
+        lower = np.array([0.66639, 0.624174, 0.456179, 0.287822, 0.287822,
+                          0.287822, 0.128489, 0.030957, 0.030957, 0.030957])
+        upper = np.array([0.991983, 0.970995, 0.87378, 0.739467, 0.739467,
+                          0.739467, 0.603133, 0.430365, 0.430365, 0.430365])
+
+        sf_ci = res.sf.confidence_interval(method='log-log')
+        cdf_ci = res.cdf.confidence_interval(method='log-log')
+
+        assert_allclose(sf_ci.low.probabilities, lower, atol=1e-5)
+        assert_allclose(sf_ci.high.probabilities, upper, atol=1e-5)
+        assert_allclose(cdf_ci.low.probabilities, 1-upper, atol=1e-5)
+        assert_allclose(cdf_ci.high.probabilities, 1-lower, atol=1e-5)
+
+        # Test against R's `survival` library `survfit` function, 90%CI
+        # library(survival)
+        # options(digits=16)
+        # time = c(3, 5, 8, 10, 5, 5, 8, 12, 15, 14, 2, 11, 10, 9, 12, 5, 8, 11)
+        # status = c(1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1)
+        # res = survfit(Surv(time, status)
+        # ~1, conf.type = "log-log", conf.int = 0.90)
+        # res$time; res$lower; res$upper
+        low = [0.74366748406861172, 0.68582332289196246, 0.50596835651480121,
+               0.32913131413336727, 0.32913131413336727, 0.32913131413336727,
+               0.15986912028781664, 0.04499539918147757, 0.04499539918147757,
+               0.04499539918147757]
+        high = [0.9890291867238429, 0.9638835422144144, 0.8560366823086629,
+                0.7130167643978450, 0.7130167643978450, 0.7130167643978450,
+                0.5678602982997164, 0.3887616766886558, 0.3887616766886558,
+                0.3887616766886558]
+        sf_ci = res.sf.confidence_interval(method='log-log',
+                                           confidence_level=0.9)
+        assert_allclose(sf_ci.low.probabilities, low)
+        assert_allclose(sf_ci.high.probabilities, high)
+
+        # And with conf.type = "plain"
+        low = [0.8556383113628162, 0.7670478794850761, 0.5485720663578469,
+               0.3441515412527123, 0.3441515412527123, 0.3441515412527123,
+               0.1449184105424544, 0., 0., 0.]
+        high = [1., 1., 0.8958723780865975, 0.7391817920806210,
+                0.7391817920806210, 0.7391817920806210, 0.5773038116797676,
+                0.3642270254596720, 0.3642270254596720, 0.3642270254596720]
+        sf_ci = res.sf.confidence_interval(confidence_level=0.9)
+        assert_allclose(sf_ci.low.probabilities, low)
+        assert_allclose(sf_ci.high.probabilities, high)
+
+    def test_right_censored_ci_nans(self):
+        # test `ecdf` confidence interval on a problem that results in NaNs
+        times, died = self.t1, self.d1
+        sample = stats.CensoredData.right_censored(times, np.logical_not(died))
+        res = stats.ecdf(sample)
+
+        # Reference values generated with Matlab
+        # format long
+        # t = [37 43 47 56 60 62 71 77 80 81];
+        # d = [0 0 1 1 0 0 0 1 1 1];
+        # censored = ~d1;
+        # [f, x, flo, fup] = ecdf(t, 'Censoring', censored, 'Alpha', 0.05);
+        x = [37, 47, 56, 77, 80, 81]
+        flo = [np.nan, 0, 0, 0.052701464070711, 0.337611126231790, np.nan]
+        fup = [np.nan, 0.35417230377, 0.5500569798, 0.9472985359, 1.0, np.nan]
+        i = np.searchsorted(res.cdf.quantiles, x)
+
+        message = "The confidence interval is undefined at some observations"
+        with pytest.warns(RuntimeWarning, match=message):
+            ci = res.cdf.confidence_interval()
+
+        # Matlab gives NaN as the first element of the CIs. Mathematica agrees,
+        # but R's survfit does not. It makes some sense, but it's not what the
+        # formula gives, so skip that element.
+        assert_allclose(ci.low.probabilities[i][1:], flo[1:])
+        assert_allclose(ci.high.probabilities[i][1:], fup[1:])
+
+        # [f, x, flo, fup] = ecdf(t, 'Censoring', censored, 'Function',
+        #                        'survivor', 'Alpha', 0.05);
+        flo = [np.nan, 0.64582769623, 0.449943020228, 0.05270146407, 0, np.nan]
+        fup = [np.nan, 1.0, 1.0, 0.947298535929289, 0.662388873768210, np.nan]
+        i = np.searchsorted(res.cdf.quantiles, x)
+
+        with pytest.warns(RuntimeWarning, match=message):
+            ci = res.sf.confidence_interval()
+
+        assert_allclose(ci.low.probabilities[i][1:], flo[1:])
+        assert_allclose(ci.high.probabilities[i][1:], fup[1:])
+
+        # With the same data, R's `survival` library `survfit` function
+        # doesn't produce the leading NaN
+        # library(survival)
+        # options(digits=16)
+        # time = c(37, 43, 47, 56, 60, 62, 71, 77, 80, 81)
+        # status = c(0, 0, 1, 1, 0, 0, 0, 1, 1, 1)
+        # res = survfit(Surv(time, status)
+        # ~1, conf.type = "plain", conf.int = 0.95)
+        # res$time
+        # res$lower
+        # res$upper
+        low = [1., 1., 0.64582769623233816, 0.44994302022779326,
+               0.44994302022779326, 0.44994302022779326, 0.44994302022779326,
+               0.05270146407071086, 0., np.nan]
+        high = [1., 1., 1., 1., 1., 1., 1., 0.9472985359292891,
+                0.6623888737682101, np.nan]
+        assert_allclose(ci.low.probabilities, low)
+        assert_allclose(ci.high.probabilities, high)
+
+        # It does with conf.type="log-log", as do we
+        with pytest.warns(RuntimeWarning, match=message):
+            ci = res.sf.confidence_interval(method='log-log')
+        low = [np.nan, np.nan, 0.38700001403202522, 0.31480711370551911,
+               0.31480711370551911, 0.31480711370551911, 0.31480711370551911,
+               0.08048821148507734, 0.01049958986680601, np.nan]
+        high = [np.nan, np.nan, 0.9813929658789660, 0.9308983170906275,
+                0.9308983170906275, 0.9308983170906275, 0.9308983170906275,
+                0.8263946341076415, 0.6558775085110887, np.nan]
+        assert_allclose(ci.low.probabilities, low)
+        assert_allclose(ci.high.probabilities, high)
+
+    def test_right_censored_against_uncensored(self):
+        rng = np.random.default_rng(7463952748044886637)
+        sample = rng.integers(10, 100, size=1000)
+        censored = np.zeros_like(sample)
+        censored[np.argmax(sample)] = True
+        res = stats.ecdf(sample)
+        ref = stats.ecdf(stats.CensoredData.right_censored(sample, censored))
+        assert_equal(res.sf.quantiles, ref.sf.quantiles)
+        assert_equal(res.sf._n, ref.sf._n)
+        assert_equal(res.sf._d[:-1], ref.sf._d[:-1])  # difference @ [-1]
+        assert_allclose(res.sf._sf[:-1], ref.sf._sf[:-1], rtol=1e-14)
+
+    def test_plot_iv(self):
+        rng = np.random.default_rng(1769658657308472721)
+        n_unique = rng.integers(10, 100)
+        sample, _, _ = self.get_random_sample(rng, n_unique)
+        res = stats.ecdf(sample)
+
+        try:
+            import matplotlib.pyplot as plt  # noqa: F401
+            res.sf.plot()  # no other errors occur
+        except (ModuleNotFoundError, ImportError):
+            message = r"matplotlib must be installed to use method `plot`."
+            with pytest.raises(ModuleNotFoundError, match=message):
+                res.sf.plot()
+
+
+class TestLogRank:
+
+    @pytest.mark.parametrize(
+        "x, y, statistic, pvalue",
+        # Results validate with R
+        # library(survival)
+        # options(digits=16)
+        #
+        # futime_1 <- c(8, 12, 26, 14, 21, 27, 8, 32, 20, 40)
+        # fustat_1 <- c(1, 1, 1, 1, 1, 1, 0, 0, 0, 0)
+        # rx_1 <- c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
+        #
+        # futime_2 <- c(33, 28, 41, 48, 48, 25, 37, 48, 25, 43)
+        # fustat_2 <- c(1, 1, 1, 0, 0, 0, 0, 0, 0, 0)
+        # rx_2 <- c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1)
+        #
+        # futime <- c(futime_1, futime_2)
+        # fustat <- c(fustat_1, fustat_2)
+        # rx <- c(rx_1, rx_2)
+        #
+        # survdiff(formula = Surv(futime, fustat) ~ rx)
+        #
+        # Also check against another library which handle alternatives
+        # library(nph)
+        # logrank.test(futime, fustat, rx, alternative = "two.sided")
+        # res["test"]
+        [(
+              # https://sphweb.bumc.bu.edu/otlt/mph-modules/bs/bs704_survival/BS704_Survival5.html
+              # uncensored, censored
+              [[8, 12, 26, 14, 21, 27], [8, 32, 20, 40]],
+              [[33, 28, 41], [48, 48, 25, 37, 48, 25, 43]],
+              # chi2, ["two-sided", "less", "greater"]
+              6.91598157449,
+              [0.008542873404, 0.9957285632979385, 0.004271436702061537]
+         ),
+         (
+              # https://sphweb.bumc.bu.edu/otlt/mph-modules/bs/bs704_survival/BS704_Survival5.html
+              [[19, 6, 5, 4], [20, 19, 17, 14]],
+              [[16, 21, 7], [21, 15, 18, 18, 5]],
+              0.835004855038,
+              [0.3608293039, 0.8195853480676912, 0.1804146519323088]
+         ),
+         (
+              # Bland, Altman, "The logrank test", BMJ, 2004
+              # https://www.bmj.com/content/328/7447/1073.short
+              [[6, 13, 21, 30, 37, 38, 49, 50, 63, 79, 86, 98, 202, 219],
+               [31, 47, 80, 82, 82, 149]],
+              [[10, 10, 12, 13, 14, 15, 16, 17, 18, 20, 24, 24, 25, 28, 30,
+                33, 35, 37, 40, 40, 46, 48, 76, 81, 82, 91, 112, 181],
+               [34, 40, 70]],
+              7.49659416854,
+              [0.006181578637, 0.003090789318730882, 0.9969092106812691]
+         )]
+    )
+    def test_log_rank(self, x, y, statistic, pvalue):
+        x = stats.CensoredData(uncensored=x[0], right=x[1])
+        y = stats.CensoredData(uncensored=y[0], right=y[1])
+
+        for i, alternative in enumerate(["two-sided", "less", "greater"]):
+            res = stats.logrank(x=x, y=y, alternative=alternative)
+
+            # we return z and use the normal distribution while other framework
+            # return z**2. The p-value are directly comparable, but we have to
+            # square the statistic
+            assert_allclose(res.statistic**2, statistic, atol=1e-10)
+            assert_allclose(res.pvalue, pvalue[i], atol=1e-10)
+
+    def test_raises(self):
+        sample = stats.CensoredData([1, 2])
+
+        msg = r"`y` must be"
+        with pytest.raises(ValueError, match=msg):
+            stats.logrank(x=sample, y=[[1, 2]])
+
+        msg = r"`x` must be"
+        with pytest.raises(ValueError, match=msg):
+            stats.logrank(x=[[1, 2]], y=sample)
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/test_tukeylambda_stats.py b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_tukeylambda_stats.py
new file mode 100644
index 0000000000000000000000000000000000000000..8041658599a6ed5b2cd70def1a92bffe0d851792
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_tukeylambda_stats.py
@@ -0,0 +1,85 @@
+import numpy as np
+from numpy.testing import assert_allclose, assert_equal
+
+from scipy.stats._tukeylambda_stats import (tukeylambda_variance,
+                                            tukeylambda_kurtosis)
+
+
+def test_tukeylambda_stats_known_exact():
+    """Compare results with some known exact formulas."""
+    # Some exact values of the Tukey Lambda variance and kurtosis:
+    # lambda   var      kurtosis
+    #   0     pi**2/3     6/5     (logistic distribution)
+    #  0.5    4 - pi    (5/3 - pi/2)/(pi/4 - 1)**2 - 3
+    #   1      1/3       -6/5     (uniform distribution on (-1,1))
+    #   2      1/12      -6/5     (uniform distribution on (-1/2, 1/2))
+
+    # lambda = 0
+    var = tukeylambda_variance(0)
+    assert_allclose(var, np.pi**2 / 3, atol=1e-12)
+    kurt = tukeylambda_kurtosis(0)
+    assert_allclose(kurt, 1.2, atol=1e-10)
+
+    # lambda = 0.5
+    var = tukeylambda_variance(0.5)
+    assert_allclose(var, 4 - np.pi, atol=1e-12)
+    kurt = tukeylambda_kurtosis(0.5)
+    desired = (5./3 - np.pi/2) / (np.pi/4 - 1)**2 - 3
+    assert_allclose(kurt, desired, atol=1e-10)
+
+    # lambda = 1
+    var = tukeylambda_variance(1)
+    assert_allclose(var, 1.0 / 3, atol=1e-12)
+    kurt = tukeylambda_kurtosis(1)
+    assert_allclose(kurt, -1.2, atol=1e-10)
+
+    # lambda = 2
+    var = tukeylambda_variance(2)
+    assert_allclose(var, 1.0 / 12, atol=1e-12)
+    kurt = tukeylambda_kurtosis(2)
+    assert_allclose(kurt, -1.2, atol=1e-10)
+
+
+def test_tukeylambda_stats_mpmath():
+    """Compare results with some values that were computed using mpmath."""
+    a10 = dict(atol=1e-10, rtol=0)
+    a12 = dict(atol=1e-12, rtol=0)
+    data = [
+        # lambda        variance              kurtosis
+        [-0.1, 4.78050217874253547, 3.78559520346454510],
+        [-0.0649, 4.16428023599895777, 2.52019675947435718],
+        [-0.05, 3.93672267890775277, 2.13129793057777277],
+        [-0.001, 3.30128380390964882, 1.21452460083542988],
+        [0.001, 3.27850775649572176, 1.18560634779287585],
+        [0.03125, 2.95927803254615800, 0.804487555161819980],
+        [0.05, 2.78281053405464501, 0.611604043886644327],
+        [0.0649, 2.65282386754100551, 0.476834119532774540],
+        [1.2, 0.242153920578588346, -1.23428047169049726],
+        [10.0, 0.00095237579757703597, 2.37810697355144933],
+        [20.0, 0.00012195121951131043, 7.37654321002709531],
+    ]
+
+    for lam, var_expected, kurt_expected in data:
+        var = tukeylambda_variance(lam)
+        assert_allclose(var, var_expected, **a12)
+        kurt = tukeylambda_kurtosis(lam)
+        assert_allclose(kurt, kurt_expected, **a10)
+
+    # Test with vector arguments (most of the other tests are for single
+    # values).
+    lam, var_expected, kurt_expected = zip(*data)
+    var = tukeylambda_variance(lam)
+    assert_allclose(var, var_expected, **a12)
+    kurt = tukeylambda_kurtosis(lam)
+    assert_allclose(kurt, kurt_expected, **a10)
+
+
+def test_tukeylambda_stats_invalid():
+    """Test values of lambda outside the domains of the functions."""
+    lam = [-1.0, -0.5]
+    var = tukeylambda_variance(lam)
+    assert_equal(var, np.array([np.nan, np.inf]))
+
+    lam = [-1.0, -0.25]
+    kurt = tukeylambda_kurtosis(lam)
+    assert_equal(kurt, np.array([np.nan, np.inf]))
diff --git a/venv/lib/python3.12/site-packages/scipy/stats/tests/test_variation.py b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_variation.py
new file mode 100644
index 0000000000000000000000000000000000000000..2a07ac1bfcdf85e9be609ff7a5c1445f32e22cba
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/stats/tests/test_variation.py
@@ -0,0 +1,205 @@
+import math
+
+import numpy as np
+import pytest
+
+from scipy._lib._util import AxisError
+from scipy._lib._array_api import make_xp_test_case, eager_warns, is_numpy
+from scipy._lib._array_api_no_0d import xp_assert_equal, xp_assert_close
+from scipy._external import array_api_extra as xpx
+
+from scipy import stats
+from scipy.stats import variation
+from scipy.stats._axis_nan_policy import (too_small_nd_omit, too_small_nd_not_omit,
+                                          SmallSampleWarning)
+
+lazy_xp_modules = [stats]
+skip_xp_backends = pytest.mark.skip_xp_backends
+
+
+@make_xp_test_case(variation)
+class TestVariation:
+    """
+    Test class for scipy.stats.variation
+    """
+
+    def test_ddof(self, xp):
+        x = xp.arange(9.0)
+        xp_assert_close(variation(x, ddof=1), xp.asarray(math.sqrt(60/8)/4))
+
+    @pytest.mark.parametrize('sgn', [1, -1])
+    def test_sign(self, sgn, xp):
+        x = xp.asarray([1., 2., 3., 4., 5.])
+        v = variation(sgn*x)
+        expected = xp.asarray(sgn*math.sqrt(2)/3)
+        xp_assert_close(v, expected, rtol=1e-10)
+
+    @skip_xp_backends(np_only=True, reason="test plain python scalar input")
+    def test_scalar(self, xp):
+        # A scalar is treated like a 1-d sequence with length 1.
+        assert variation(4.0) == 0.0
+
+    @pytest.mark.parametrize('nan_policy, expected',
+                             [('propagate', np.nan),
+                              ('omit', math.sqrt(20/3)/4)])
+    @skip_xp_backends(eager_only=True, reason='lazy -> limited nan_policy support')
+    def test_variation_nan(self, nan_policy, expected, xp):
+        x = xp.arange(10.)
+        x[9] = xp.nan
+        xp_assert_close(variation(x, nan_policy=nan_policy), xp.asarray(expected))
+
+    @skip_xp_backends(eager_only=True, reason='lazy -> limited nan_policy support')
+    def test_nan_policy_raise(self, xp):
+        x = xp.asarray([1.0, 2.0, xp.nan, 3.0])
+        with pytest.raises(ValueError, match='input contains nan'):
+            variation(x, nan_policy='raise')
+
+    @skip_xp_backends("dask.array", reason='needs `_axis_nan_policy`')
+    def test_bad_nan_policy(self, xp):
+        with pytest.raises(ValueError, match='must be one of'):
+            variation(xp.asarray([1, 2, 3]), nan_policy='foobar')
+
+    @skip_xp_backends("dask.array", reason='needs `_axis_nan_policy`')
+    def test_keepdims(self, xp):
+        x = xp.reshape(xp.arange(10), (2, 5))
+        y = variation(x, axis=1, keepdims=True)
+        expected = 2**0.5 / xp.asarray([[2.], [7.]])
+        xp_assert_close(y, expected)
+
+    @skip_xp_backends("dask.array", reason='needs `_axis_nan_policy`')
+    @pytest.mark.parametrize('axis, expected',
+                             [(0, np.empty((1, 0)).tolist()),
+                              (1, np.full((5, 1), fill_value=np.nan).tolist())])
+    def test_keepdims_size0(self, axis, expected, xp):
+        x = xp.zeros((5, 0))
+        if axis == 1:
+            with pytest.warns(SmallSampleWarning, match=too_small_nd_not_omit):
+                y = variation(x, axis=axis, keepdims=True)
+        else:
+            y = variation(x, axis=axis, keepdims=True)
+        xp_assert_equal(y, xp.asarray(expected))
+
+    @skip_xp_backends("dask.array", reason='needs `_axis_nan_policy`')
+    @pytest.mark.parametrize('incr, expected_fill', [(0, np.inf), (1, np.nan)])
+    def test_keepdims_and_ddof_eq_len_plus_incr(self, incr, expected_fill, xp):
+        x = xp.asarray([[1, 1, 2, 2], [1, 2, 3, 3]])
+        y = variation(x, axis=1, ddof=x.shape[1] + incr, keepdims=True)
+        xp_assert_equal(y, xp.full((2, 1), fill_value=expected_fill))
+
+    @skip_xp_backends("dask.array", reason='needs `_axis_nan_policy`')
+    def test_propagate_nan(self, xp):
+        # Check that the shape of the result is the same for inputs
+        # with and without nans, cf gh-5817
+        a = xp.reshape(xp.arange(8.), (2, -1))
+        a = xpx.at(a)[1, 0].set(xp.nan)
+        v = variation(a, axis=1, nan_policy="propagate")
+        xp_assert_close(v, xp.asarray([math.sqrt(5/4)/1.5, xp.nan]))
+
+    def test_axis_none(self, xp):
+        # Check that `variation` computes the result on the flattened
+        # input when axis is None.
+        y = variation(xp.asarray([[0, 1], [2, 3]]), axis=None)
+        xp_assert_close(y, xp.asarray(math.sqrt(5/4)/1.5))
+
+    def test_bad_axis(self, xp):
+        # Check that an invalid axis raises np.exceptions.AxisError.
+        x = xp.asarray([[1, 2, 3], [4, 5, 6]])
+        with pytest.raises((AxisError, IndexError)):
+            variation(x, axis=10)
+
+    @pytest.mark.filterwarnings("ignore:divide by zero encountered:RuntimeWarning:dask")
+    def test_mean_zero(self, xp):
+        # Check that `variation` returns inf for a sequence that is not
+        # identically zero but whose mean is zero.
+        x = xp.asarray([10., -3., 1., -4., -4.])
+        y = variation(x)
+        xp_assert_equal(y, xp.asarray(xp.inf))
+
+        x2 = xp.stack([x, -10.*x])
+        y2 = variation(x2, axis=1)
+        xp_assert_equal(y2, xp.asarray([xp.inf, xp.inf]))
+
+    @pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning:dask")
+    @pytest.mark.parametrize('x', [[0.]*5, [1, 2, np.inf, 9]])
+    def test_return_nan(self, x, xp):
+        x = xp.asarray(x)
+        # Test some cases where `variation` returns nan.
+        y = variation(x)
+        xp_assert_equal(y, xp.asarray(xp.nan, dtype=x.dtype))
+
+    @pytest.mark.filterwarnings('ignore:Invalid value encountered:RuntimeWarning:dask')
+    @pytest.mark.parametrize('axis, expected',
+                             [(0, []), (1, [np.nan]*3), (None, np.nan)])
+    def test_2d_size_zero_with_axis(self, axis, expected, xp):
+        x = xp.empty((3, 0))
+        if axis != 0:
+            # specific message depends on `axis`, and `SmallSampleWarning`
+            # is specific enough.
+            with eager_warns(SmallSampleWarning, xp=xp):
+                y = variation(x, axis=axis)
+        else:
+            y = variation(x, axis=axis)
+        xp_assert_equal(y, xp.asarray(expected))
+
+    @pytest.mark.filterwarnings('ignore:divide by zero encountered:RuntimeWarning:dask')
+    def test_neg_inf(self, xp):
+        # Edge case that produces -inf: ddof equals the number of non-nan
+        # values, the values are not constant, and the mean is negative.
+        x1 = xp.asarray([-3., -5.])
+        xp_assert_equal(variation(x1, ddof=2), xp.asarray(-xp.inf))
+
+    @skip_xp_backends(np_only=True, reason='only NumPy supports ND nan_policy="omit"')
+    def test_neg_inf_nan(self, xp):
+        x2 = xp.asarray([[xp.nan, 1, -10, xp.nan],
+                         [-20, -3, xp.nan, xp.nan]])
+        xp_assert_equal(variation(x2, axis=1, ddof=2, nan_policy='omit'),
+                        xp.asarray([-xp.inf, -xp.inf]))
+
+    @pytest.mark.parametrize("nan_policy", ['propagate', 'omit'])
+    def test_combined_edge_cases(self, nan_policy, xp):
+        if not is_numpy(xp):
+            pytest.skip("Only NumPy supports ND nan_policy='omit'")
+        x = xp.asarray([[0, 10, xp.nan, 1],
+                        [0, -5, xp.nan, 2],
+                        [0, -5, xp.nan, 3]])
+        if nan_policy == 'omit':
+            with pytest.warns(SmallSampleWarning, match=too_small_nd_omit):
+                y = variation(x, axis=0, nan_policy=nan_policy)
+        else:
+            y = variation(x, axis=0, nan_policy=nan_policy)
+        xp_assert_close(y, xp.asarray([xp.nan, xp.inf, xp.nan, math.sqrt(2/3)/2]))
+
+    @skip_xp_backends(np_only=True, reason='only NumPy supports ND nan_policy="omit"')
+    @pytest.mark.parametrize(
+        'ddof, expected',
+        [(0, [np.sqrt(1/6), np.sqrt(5/8), np.inf, 0, np.nan, 0.0, np.nan]),
+         (1, [0.5, np.sqrt(5/6), np.inf, 0, np.nan, 0, np.nan]),
+         (2, [np.sqrt(0.5), np.sqrt(5/4), np.inf, np.nan, np.nan, 0, np.nan])]
+    )
+    def test_more_nan_policy_omit_tests(self, ddof, expected, xp):
+        # The slightly strange formatting in the follow array is my attempt to
+        # maintain a clean tabular arrangement of the data while satisfying
+        # the demands of pycodestyle.  Currently, E201 and E241 are not
+        # disabled by the `noqa` annotation.
+        nan = xp.nan
+        x = xp.asarray([[1.0, 2.0, nan, 3.0],
+                        [0.0, 4.0, 3.0, 1.0],
+                        [nan, -.5, 0.5, nan],
+                        [nan, 9.0, 9.0, nan],
+                        [nan, nan, nan, nan],
+                        [3.0, 3.0, 3.0, 3.0],
+                        [0.0, 0.0, 0.0, 0.0]])
+        with pytest.warns(SmallSampleWarning, match=too_small_nd_omit):
+            v = variation(x, axis=1, ddof=ddof, nan_policy='omit')
+        xp_assert_close(v, expected)
+
+    @skip_xp_backends(eager_only=True, reason='lazy -> limited nan_policy support')
+    def test_variation_ddof(self, xp):
+        # test variation with delta degrees of freedom
+        # regression test for gh-13341
+        a = xp.asarray([1., 2., 3., 4., 5.])
+        nan_a = xp.asarray([1, 2, 3, xp.nan, 4, 5, xp.nan])
+        y = variation(a, ddof=1)
+        nan_y = variation(nan_a, nan_policy="omit", ddof=1)
+        xp_assert_close(y, xp.asarray(math.sqrt(5/2)/3))
+        assert y == nan_y
diff --git a/venv/lib/python3.12/site-packages/scipy/version.py b/venv/lib/python3.12/site-packages/scipy/version.py
new file mode 100644
index 0000000000000000000000000000000000000000..7b5916676f0da28d5e9b581853314ec581917ab2
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/scipy/version.py
@@ -0,0 +1,12 @@
+
+"""
+Module to expose more detailed version info for the installed `scipy`
+"""
+version = "1.18.0"
+full_version = version
+short_version = version.split('.dev')[0]
+git_revision = "54ef5423f2e4376230ec3bfda6912a07a50958e3"
+release = 'dev' not in version and '+' not in version
+
+if not release:
+    version = full_version
diff --git a/venv/lib/python3.12/site-packages/setuptools/__init__.py b/venv/lib/python3.12/site-packages/setuptools/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..87ca47bbc9fd4d1e5083d4dedb7a6c86f43c73fc
--- /dev/null
+++ b/venv/lib/python3.12/site-packages/setuptools/__init__.py
@@ -0,0 +1,256 @@
+"""Extensions to the 'distutils' for large or complex distributions"""
+# mypy: disable_error_code=override
+# Command.reinitialize_command has an extra **kw param that distutils doesn't have
+# Can't disable on the exact line because distutils doesn't exists on Python 3.12
+# and mypy isn't aware of distutils_hack, causing distutils.core.Command to be Any,
+# and a [unused-ignore] to be raised on 3.12+
+
+from __future__ import annotations
+
+import functools
+import os
+import sys
+from abc import abstractmethod
+from collections.abc import Mapping
+from typing import TYPE_CHECKING, TypeVar, overload
+
+sys.path.extend(((vendor_path := os.path.join(os.path.dirname(os.path.dirname(__file__)), 'setuptools', '_vendor')) not in sys.path) * [vendor_path])  # fmt: skip
+# workaround for #4476
+sys.modules.pop('backports', None)
+
+import _distutils_hack.override  # noqa: F401
+
+from . import logging, monkey
+from .depends import Require
+from .discovery import PackageFinder, PEP420PackageFinder
+from .dist import Distribution
+from .extension import Extension
+from .version import __version__ as __version__
+from .warnings import SetuptoolsDeprecationWarning
+
+import distutils.core
+
+__all__ = [
+    'setup',
+    'Distribution',
+    'Command',
+    'Extension',
+    'Require',
+    'SetuptoolsDeprecationWarning',
+    'find_packages',
+    'find_namespace_packages',
+]
+
+_CommandT = TypeVar("_CommandT", bound="_Command")
+
+bootstrap_install_from = None
+
+find_packages = PackageFinder.find
+find_namespace_packages = PEP420PackageFinder.find
+
+
+def _install_setup_requires(attrs):
+    # Note: do not use `setuptools.Distribution` directly, as
+    # our PEP 517 backend patch `distutils.core.Distribution`.
+    class MinimalDistribution(distutils.core.Distribution):
+        """
+        A minimal version of a distribution for supporting the
+        fetch_build_eggs interface.
+        """
+
+        def __init__(self, attrs: Mapping[str, object]) -> None:
+            _incl = 'dependency_links', 'setup_requires'
+            filtered = {k: attrs[k] for k in set(_incl) & set(attrs)}
+            super().__init__(filtered)
+            # Prevent accidentally triggering discovery with incomplete set of attrs
+            self.set_defaults._disable()
+
+        def _get_project_config_files(self, filenames=None):
+            """Ignore ``pyproject.toml``, they are not related to setup_requires"""
+            try:
+                cfg, _toml = super()._split_standard_project_metadata(filenames)
+            except Exception:
+                return filenames, ()
+            return cfg, ()
+
+        def finalize_options(self):
+            """
+            Disable finalize_options to avoid building the working set.
+            Ref #2158.
+            """
+
+    dist = MinimalDistribution(attrs)
+
+    # Honor setup.cfg's options.
+    dist.parse_config_files(ignore_option_errors=True)
+    if dist.setup_requires:
+        _fetch_build_eggs(dist)
+
+
+def _fetch_build_eggs(dist: Distribution):
+    try:
+        dist.fetch_build_eggs(dist.setup_requires)
+    except Exception as ex:
+        msg = """
+        It is possible a package already installed in your system
+        contains an version that is invalid according to PEP 440.
+        You can try `pip install --use-pep517` as a workaround for this problem,
+        or rely on a new virtual environment.
+
+        If the problem refers to a package that is not installed yet,
+        please contact that package's maintainers or distributors.
+        """
+        if "InvalidVersion" in ex.__class__.__name__:
+            if hasattr(ex, "add_note"):
+                ex.add_note(msg)  # PEP 678
+            else:
+                dist.announce(f"\n{msg}\n")
+        raise
+
+
+def setup(**attrs) -> Distribution:
+    logging.configure()
+    # Make sure we have any requirements needed to interpret 'attrs'.
+    _install_setup_requires(attrs)
+    # Override return type of distutils.core.Distribution with setuptools.dist.Distribution
+    # (implicitly implemented via `setuptools.monkey.patch_all`).
+    return distutils.core.setup(**attrs)  # type: ignore[return-value]
+
+
+setup.__doc__ = distutils.core.setup.__doc__
+
+if TYPE_CHECKING:
+    # Work around a mypy issue where type[T] can't be used as a base: https://github.com/python/mypy/issues/10962
+    from distutils.core import Command as _Command
+else:
+    _Command = monkey.get_unpatched(distutils.core.Command)
+
+
+class Command(_Command):
+    """
+    Setuptools internal actions are organized using a *command design pattern*.
+    This means that each action (or group of closely related actions) executed during
+    the build should be implemented as a ``Command`` subclass.
+
+    These commands are abstractions and do not necessarily correspond to a command that
+    can (or should) be executed via a terminal, in a CLI fashion (although historically
+    they would).
+
+    When creating a new command from scratch, custom defined classes **SHOULD** inherit
+    from ``setuptools.Command`` and implement a few mandatory methods.
+    Between these mandatory methods, are listed:
+    :meth:`initialize_options`, :meth:`finalize_options` and :meth:`run`.
+
+    A useful analogy for command classes is to think of them as subroutines with local
+    variables called "options".  The options are "declared" in :meth:`initialize_options`
+    and "defined" (given their final values, aka "finalized") in :meth:`finalize_options`,
+    both of which must be defined by every command class. The "body" of the subroutine,
+    (where it does all the work) is the :meth:`run` method.
+    Between :meth:`initialize_options` and :meth:`finalize_options`, ``setuptools`` may set
+    the values for options/attributes based on user's input (or circumstance),
+    which means that the implementation should be careful to not overwrite values in
+    :meth:`finalize_options` unless necessary.
+
+    Please note that other commands (or other parts of setuptools) may also overwrite
+    the values of the command's options/attributes multiple times during the build
+    process.
+    Therefore it is important to consistently implement :meth:`initialize_options` and
+    :meth:`finalize_options`. For example, all derived attributes (or attributes that
+    depend on the value of other attributes) **SHOULD** be recomputed in
+    :meth:`finalize_options`.
+
+    When overwriting existing commands, custom defined classes **MUST** abide by the
+    same APIs implemented by the original class. They also **SHOULD** inherit from the
+    original class.
+    """
+
+    command_consumes_arguments = False
+    distribution: Distribution  # override distutils.dist.Distribution with setuptools.dist.Distribution
+
+    dry_run = False  # type: ignore[assignment] # pyright: ignore[reportAssignmentType] (until #4689; see #4872)
+    """
+    For compatibility with vendored bdist_wheel.
+    https://github.com/pypa/setuptools/pull/4872/files#r1986395142
+    """
+
+    def __init__(self, dist: Distribution, **kw) -> None:
+        """
+        Construct the command for dist, updating
+        vars(self) with any keyword parameters.
+        """
+        super().__init__(dist)
+        vars(self).update(kw)
+
+    @overload
+    def reinitialize_command(
+        self, command: str, reinit_subcommands: bool = False, **kw
+    ) -> Command: ...  # override distutils.cmd.Command with setuptools.Command
+    @overload
+    def reinitialize_command(
+        self, command: _CommandT, reinit_subcommands: bool = False, **kw
+    ) -> _CommandT: ...
+    def reinitialize_command(
+        self, command: str | _Command, reinit_subcommands: bool = False, **kw
+    ) -> Command | _Command:
+        cmd = _Command.reinitialize_command(self, command, reinit_subcommands)
+        vars(cmd).update(kw)
+        return cmd  # pyright: ignore[reportReturnType] # pypa/distutils#307
+
+    @abstractmethod
+    def initialize_options(self) -> None:
+        """
+        Set or (reset) all options/attributes/caches used by the command
+        to their default values. Note that these values may be overwritten during
+        the build.
+        """
+        raise NotImplementedError
+
+    @abstractmethod
+    def finalize_options(self) -> None:
+        """
+        Set final values for all options/attributes used by the command.
+        Most of the time, each option/attribute/cache should only be set if it does not
+        have any value yet (e.g. ``if self.attr is None: self.attr = val``).
+        """
+        raise NotImplementedError
+
+    @abstractmethod
+    def run(self) -> None:
+        """
+        Execute the actions intended by the command.
+        (Side effects **SHOULD** only take place when :meth:`run` is executed,
+        for example, creating new files or writing to the terminal output).
+        """
+        raise NotImplementedError
+
+
+def _find_all_simple(path):
+    """
+    Find all files under 'path'
+    """
+    results = (
+        os.path.join(base, file)
+        for base, dirs, files in os.walk(path, followlinks=True)
+        for file in files
+    )
+    return filter(os.path.isfile, results)
+
+
+def findall(dir=os.curdir):
+    """
+    Find all files under 'dir' and return the list of full filenames.
+    Unless dir is '.', return full filenames with dir prepended.
+    """
+    files = _find_all_simple(dir)
+    if dir == os.curdir:
+        make_rel = functools.partial(os.path.relpath, start=dir)
+        files = map(make_rel, files)
+    return list(files)
+
+
+class sic(str):
+    """Treat this string as-is (https://en.wikipedia.org/wiki/Sic)"""
+
+
+# Apply monkey patches
+monkey.patch_all()
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